LMFDB - Embedded newform 276.2.c.b.47.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.18
Character	$\chi$	$=$	276.47
Dual form			276.2.c.b.47.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15961 + 0.809507i) q^{2} +(1.20859 + 1.24069i) q^{3} +(0.689397 + 1.87743i) q^{4} -3.47795i q^{5} +(0.397138 + 2.41708i) q^{6} +0.968466i q^{7} +(-0.720358 + 2.73516i) q^{8} +(-0.0786444 + 2.99897i) q^{9} +O(q^{10})$	\(q+(1.15961 + 0.809507i) q^{2} +(1.20859 + 1.24069i) q^{3} +(0.689397 + 1.87743i) q^{4} -3.47795i q^{5} +(0.397138 + 2.41708i) q^{6} +0.968466i q^{7} +(-0.720358 + 2.73516i) q^{8} +(-0.0786444 + 2.99897i) q^{9} +(2.81542 - 4.03307i) q^{10} +2.17307 q^{11} +(-1.49612 + 3.12436i) q^{12} -3.21098 q^{13} +(-0.783980 + 1.12304i) q^{14} +(4.31507 - 4.20339i) q^{15} +(-3.04946 + 2.58858i) q^{16} -1.26490i q^{17} +(-2.51888 + 3.41398i) q^{18} -4.03623i q^{19} +(6.52959 - 2.39769i) q^{20} +(-1.20157 + 1.17047i) q^{21} +(2.51992 + 1.75912i) q^{22} -1.00000 q^{23} +(-4.26411 + 2.41193i) q^{24} -7.09612 q^{25} +(-3.72349 - 2.59931i) q^{26} +(-3.81585 + 3.52694i) q^{27} +(-1.81822 + 0.667657i) q^{28} -8.56092i q^{29} +(8.40648 - 1.38123i) q^{30} -1.32974i q^{31} +(-5.63167 + 0.533190i) q^{32} +(2.62634 + 2.69612i) q^{33} +(1.02395 - 1.46679i) q^{34} +3.36827 q^{35} +(-5.68456 + 1.91983i) q^{36} -10.0527 q^{37} +(3.26735 - 4.68045i) q^{38} +(-3.88075 - 3.98385i) q^{39} +(9.51273 + 2.50537i) q^{40} +7.60029i q^{41} +(-2.34086 + 0.384615i) q^{42} +1.64095i q^{43} +(1.49811 + 4.07978i) q^{44} +(10.4303 + 0.273521i) q^{45} +(-1.15961 - 0.809507i) q^{46} +12.6881 q^{47} +(-6.89718 - 0.654928i) q^{48} +6.06207 q^{49} +(-8.22874 - 5.74436i) q^{50} +(1.56936 - 1.52874i) q^{51} +(-2.21364 - 6.02839i) q^{52} -8.41184i q^{53} +(-7.27998 + 1.00092i) q^{54} -7.55782i q^{55} +(-2.64891 - 0.697642i) q^{56} +(5.00772 - 4.87812i) q^{57} +(6.93013 - 9.92734i) q^{58} +1.24592 q^{59} +(10.8664 + 5.20342i) q^{60} +5.28282 q^{61} +(1.07643 - 1.54198i) q^{62} +(-2.90440 - 0.0761644i) q^{63} +(-6.96217 - 3.94058i) q^{64} +11.1676i q^{65} +(0.863009 + 5.25249i) q^{66} +14.1014i q^{67} +(2.37476 - 0.872019i) q^{68} +(-1.20859 - 1.24069i) q^{69} +(3.90589 + 2.72664i) q^{70} -12.0576 q^{71} +(-8.14600 - 2.37544i) q^{72} +4.42105 q^{73} +(-11.6572 - 8.13772i) q^{74} +(-8.57626 - 8.80411i) q^{75} +(7.57772 - 2.78256i) q^{76} +2.10454i q^{77} +(-1.27520 - 7.76121i) q^{78} +7.01409i q^{79} +(9.00296 + 10.6059i) q^{80} +(-8.98763 - 0.471704i) q^{81} +(-6.15249 + 8.81338i) q^{82} -8.36193 q^{83} +(-3.02584 - 1.44894i) q^{84} -4.39926 q^{85} +(-1.32836 + 1.90287i) q^{86} +(10.6215 - 10.3466i) q^{87} +(-1.56539 + 5.94369i) q^{88} -3.00302i q^{89} +(11.8736 + 8.76054i) q^{90} -3.10973i q^{91} +(-0.689397 - 1.87743i) q^{92} +(1.64980 - 1.60710i) q^{93} +(14.7133 + 10.2711i) q^{94} -14.0378 q^{95} +(-7.46788 - 6.34278i) q^{96} -9.68965 q^{97} +(7.02965 + 4.90729i) q^{98} +(-0.170900 + 6.51697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q + 9 * q^8 - 2 * q^9	$ 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) $ 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.15961	+	0.809507i	0.819969	+	0.572408i
$2$	1.15961	+	0.809507i	0.819969	+	0.572408i
$3$	1.20859	+	1.24069i	0.697777	+	0.716315i
$3$	1.20859	+	1.24069i	0.697777	+	0.716315i
$4$	0.689397	+	1.87743i	0.344698	+	0.938713i
$5$		−	3.47795i		−	1.55539i	−0.628645	−	0.777693i	$-0.716390\pi$
$5$		−	3.47795i		−	1.55539i	0.628645	−	0.777693i	$-0.283610\pi$
$6$	0.397138	+	2.41708i	0.162131	+	0.986769i
$7$			0.968466i			0.366046i	0.983109	+	0.183023i	$0.0585882\pi$
$7$			0.968466i			0.366046i	−0.983109	+	0.183023i	$0.941412\pi$
$8$	−0.720358	+	2.73516i	−0.254685	+	0.967024i
$9$	−0.0786444	+	2.99897i	−0.0262148	+	0.999656i
$10$	2.81542	−	4.03307i	0.890315	−	1.27537i
$11$	2.17307			0.655205			0.327603	−	0.944816i	$-0.393759\pi$
$11$	2.17307			0.655205			0.327603	+	0.944816i	$0.393759\pi$
$12$	−1.49612	+	3.12436i	−0.431892	+	0.901925i
$13$	−3.21098			−0.890567			−0.445283	−	0.895390i	$-0.646897\pi$
$13$	−3.21098			−0.890567			−0.445283	+	0.895390i	$0.646897\pi$
$14$	−0.783980	+	1.12304i	−0.209527	+	0.300146i
$15$	4.31507	−	4.20339i	1.11415	−	1.08531i
$16$	−3.04946	+	2.58858i	−0.762366	+	0.647146i
$17$		−	1.26490i		−	0.306784i	−0.988165	−	0.153392i	$-0.950980\pi$
$17$		−	1.26490i		−	0.306784i	0.988165	−	0.153392i	$-0.0490197\pi$
$18$	−2.51888	+	3.41398i	−0.593706	+	0.804682i
$19$		−	4.03623i		−	0.925974i	−0.886365	−	0.462987i	$-0.846778\pi$
$19$		−	4.03623i		−	0.925974i	0.886365	−	0.462987i	$-0.153222\pi$
$20$	6.52959	−	2.39769i	1.46006	−	0.536139i
$21$	−1.20157	+	1.17047i	−0.262204	+	0.255418i
$22$	2.51992	+	1.75912i	0.537248	+	0.375045i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−4.26411	+	2.41193i	−0.870407	+	0.492332i
$25$	−7.09612			−1.41922
$26$	−3.72349	−	2.59931i	−0.730237	−	0.509767i
$27$	−3.81585	+	3.52694i	−0.734361	+	0.678759i
$28$	−1.81822	+	0.667657i	−0.343612	+	0.126175i
$29$		−	8.56092i		−	1.58972i	−0.606791	−	0.794862i	$-0.707543\pi$
$29$		−	8.56092i		−	1.58972i	0.606791	−	0.794862i	$-0.292457\pi$
$30$	8.40648	−	1.38123i	1.53481	−	0.252176i
$31$		−	1.32974i		−	0.238828i	−0.992845	−	0.119414i	$-0.961898\pi$
$31$		−	1.32974i		−	0.238828i	0.992845	−	0.119414i	$-0.0381015\pi$
$32$	−5.63167	+	0.533190i	−0.995548	+	0.0942555i
$33$	2.62634	+	2.69612i	0.457187	+	0.469334i
$34$	1.02395	−	1.46679i	0.175605	−	0.251553i
$35$	3.36827			0.569342
$36$	−5.68456	+	1.91983i	−0.947427	+	0.319972i
$37$	−10.0527			−1.65265			−0.826325	−	0.563193i	$-0.809573\pi$
$37$	−10.0527			−1.65265			−0.826325	+	0.563193i	$0.809573\pi$
$38$	3.26735	−	4.68045i	0.530035	−	0.759270i
$39$	−3.88075	−	3.98385i	−0.621417	−	0.637926i
$40$	9.51273	+	2.50537i	1.50409	+	0.396133i
$41$			7.60029i			1.18697i	0.804847	+	0.593483i	$0.202248\pi$
$41$			7.60029i			1.18697i	−0.804847	+	0.593483i	$0.797752\pi$
$42$	−2.34086	+	0.384615i	−0.361203	+	0.0593473i
$43$			1.64095i			0.250243i	0.992141	+	0.125122i	$0.0399321\pi$
$43$			1.64095i			0.250243i	−0.992141	+	0.125122i	$0.960068\pi$
$44$	1.49811	+	4.07978i	0.225848	+	0.615050i
$45$	10.4303	+	0.273521i	1.55485	+	0.0407741i
$46$	−1.15961	−	0.809507i	−0.170975	−	0.119355i
$47$	12.6881			1.85075			0.925375	−	0.379052i	$-0.123750\pi$
$47$	12.6881			1.85075			0.925375	+	0.379052i	$0.123750\pi$
$48$	−6.89718	−	0.654928i	−0.995522	−	0.0945307i
$49$	6.06207			0.866011
$50$	−8.22874	−	5.74436i	−1.16372	−	0.812375i
$51$	1.56936	−	1.52874i	0.219754	−	0.214067i
$52$	−2.21364	−	6.02839i	−0.306977	−	0.835987i
$53$		−	8.41184i		−	1.15545i	−0.816230	−	0.577727i	$-0.803940\pi$
$53$		−	8.41184i		−	1.15545i	0.816230	−	0.577727i	$-0.196060\pi$
$54$	−7.27998	+	1.00092i	−0.990680	+	0.136207i
$55$		−	7.55782i		−	1.01910i
$56$	−2.64891	−	0.697642i	−0.353975	−	0.0932263i
$57$	5.00772	−	4.87812i	0.663289	−	0.646123i
$58$	6.93013	−	9.92734i	0.909970	−	1.30352i
$59$	1.24592			0.162206			0.0811028	−	0.996706i	$-0.474156\pi$
$59$	1.24592			0.162206			0.0811028	+	0.996706i	$0.474156\pi$
$60$	10.8664	+	5.20342i	1.40284	+	0.671759i
$61$	5.28282			0.676396			0.338198	−	0.941075i	$-0.390183\pi$
$61$	5.28282			0.676396			0.338198	+	0.941075i	$0.390183\pi$
$62$	1.07643	−	1.54198i	0.136707	−	0.195831i
$63$	−2.90440	−	0.0761644i	−0.365920	−	0.00959581i
$64$	−6.96217	−	3.94058i	−0.870271	−	0.492573i
$65$			11.1676i			1.38517i
$66$	0.863009	+	5.25249i	0.106229	+	0.646536i
$67$			14.1014i			1.72276i	0.507964	+	0.861378i	$0.330398\pi$
$67$			14.1014i			1.72276i	−0.507964	+	0.861378i	$0.669602\pi$
$68$	2.37476	−	0.872019i	0.287982	−	0.105748i
$69$	−1.20859	−	1.24069i	−0.145497	−	0.149362i
$70$	3.90589	+	2.72664i	0.466843	+	0.325896i
$71$	−12.0576			−1.43098			−0.715488	−	0.698625i	$-0.753796\pi$
$71$	−12.0576			−1.43098			−0.715488	+	0.698625i	$0.753796\pi$
$72$	−8.14600	−	2.37544i	−0.960015	−	0.279948i
$73$	4.42105			0.517445			0.258722	−	0.965952i	$-0.416699\pi$
$73$	4.42105			0.517445			0.258722	+	0.965952i	$0.416699\pi$
$74$	−11.6572	−	8.13772i	−1.35512	−	0.945990i
$75$	−8.57626	−	8.80411i	−0.990301	−	1.01661i
$76$	7.57772	−	2.78256i	0.869224	−	0.319182i
$77$			2.10454i			0.239835i
$78$	−1.27520	−	7.76121i	−0.144388	−	0.878784i
$79$			7.01409i			0.789147i	0.918864	+	0.394574i	$0.129108\pi$
$79$			7.01409i			0.789147i	−0.918864	+	0.394574i	$0.870892\pi$
$80$	9.00296	+	10.6059i	1.00656	+	1.18577i
$81$	−8.98763	−	0.471704i	−0.998626	−	0.0524116i
$82$	−6.15249	+	8.81338i	−0.679429	+	0.973275i
$83$	−8.36193			−0.917841			−0.458920	−	0.888477i	$-0.651764\pi$
$83$	−8.36193			−0.917841			−0.458920	+	0.888477i	$0.651764\pi$
$84$	−3.02584	−	1.44894i	−0.330146	−	0.158092i
$85$	−4.39926			−0.477167
$86$	−1.32836	+	1.90287i	−0.143241	+	0.205192i
$87$	10.6215	−	10.3466i	1.13874	−	1.10927i
$88$	−1.56539	+	5.94369i	−0.166871	+	0.633599i
$89$		−	3.00302i		−	0.318319i	−0.987253	−	0.159160i	$-0.949122\pi$
$89$		−	3.00302i		−	0.318319i	0.987253	−	0.159160i	$-0.0508785\pi$
$90$	11.8736	+	8.76054i	1.25159	+	0.923442i
$91$		−	3.10973i		−	0.325988i
$92$	−0.689397	−	1.87743i	−0.0718746	−	0.195735i
$93$	1.64980	−	1.60710i	0.171076	−	0.166649i
$94$	14.7133	+	10.2711i	1.51756	+	1.05938i
$95$	−14.0378			−1.44025
$96$	−7.46788	−	6.34278i	−0.762187	−	0.647357i
$97$	−9.68965			−0.983835			−0.491918	−	0.870642i	$-0.663704\pi$
$97$	−9.68965			−0.983835			−0.491918	+	0.870642i	$0.663704\pi$
$98$	7.02965	+	4.90729i	0.710102	+	0.495711i
$99$	−0.170900	+	6.51697i	−0.0171761	+	0.654980i
$100$	−4.89204	−	13.3224i	−0.489204	−	1.33224i
$101$			9.71644i			0.966822i	0.875394	+	0.483411i	$0.160602\pi$
$101$			9.71644i			0.966822i	−0.875394	+	0.483411i	$0.839398\pi$
$102$	3.05737	−	0.502341i	0.302725	−	0.0497392i
$103$			10.8186i			1.06599i	0.846119	+	0.532994i	$0.178933\pi$
$103$			10.8186i			1.06599i	−0.846119	+	0.532994i	$0.821067\pi$
$104$	2.31306	−	8.78254i	0.226814	−	0.861199i
$105$	4.07084	+	4.17900i	0.397274	+	0.407828i
$106$	6.80944	−	9.75446i	0.661391	−	0.947437i
$107$	0.893799			0.0864068			0.0432034	−	0.999066i	$-0.486244\pi$
$107$	0.893799			0.0864068			0.0432034	+	0.999066i	$0.486244\pi$
$108$	−9.25220	−	4.73253i	−0.890293	−	0.455387i
$109$	16.3878			1.56967			0.784834	−	0.619706i	$-0.212748\pi$
$109$	16.3878			1.56967			0.784834	+	0.619706i	$0.212748\pi$
$110$	6.11811	−	8.76414i	0.583339	−	0.835628i
$111$	−12.1495	−	12.4723i	−1.15318	−	1.18382i
$112$	−2.50696	−	2.95330i	−0.236885	−	0.279061i
$113$		−	11.1150i		−	1.04561i	−0.852451	−	0.522807i	$-0.824885\pi$
$113$		−	11.1150i		−	1.04561i	0.852451	−	0.522807i	$-0.175115\pi$
$114$	9.75588	−	1.60294i	0.913722	−	0.150129i
$115$			3.47795i			0.324320i
$116$	16.0725	−	5.90187i	1.49229	−	0.547975i
$117$	0.252526	−	9.62964i	0.0233460	−	0.890260i
$118$	1.44479	+	1.00858i	0.133004	+	0.0928478i
$119$	1.22501			0.112297
$120$	8.38855	+	14.8303i	0.765767	+	1.35382i
$121$	−6.27777			−0.570706
$122$	6.12602	+	4.27648i	0.554624	+	0.387174i
$123$	−9.42964	+	9.18560i	−0.850242	+	0.828237i
$124$	2.49648	−	0.916717i	0.224191	−	0.0823236i
$125$			7.29018i			0.652054i
$126$	−3.30632	−	2.43945i	−0.294550	−	0.217324i
$127$			11.8811i			1.05428i	0.849779	+	0.527139i	$0.176735\pi$
$127$			11.8811i			1.05428i	−0.849779	+	0.527139i	$0.823265\pi$
$128$	−4.88348	−	10.2055i	−0.431643	−	0.902045i
$129$	−2.03592	+	1.98323i	−0.179253	+	0.174614i
$130$	−9.04027	+	12.9501i	−0.792885	+	1.13580i
$131$	19.7266			1.72352			0.861759	−	0.507319i	$-0.169363\pi$
$131$	19.7266			1.72352			0.861759	+	0.507319i	$0.169363\pi$
$132$	−3.25117	+	6.78946i	−0.282978	+	0.590946i
$133$	3.90895			0.338949
$134$	−11.4152	+	16.3521i	−0.986119	+	1.41261i
$135$	12.2665	+	13.2713i	1.05573	+	1.14221i
$136$	3.45971	+	0.911182i	0.296667	+	0.0781332i
$137$			5.08776i			0.434677i	0.976096	+	0.217339i	$0.0697376\pi$
$137$			5.08776i			0.434677i	−0.976096	+	0.217339i	$0.930262\pi$
$138$	−0.397138	−	2.41708i	−0.0338067	−	0.205756i
$139$			1.70015i			0.144205i	0.997397	+	0.0721023i	$0.0229708\pi$
$139$			1.70015i			0.144205i	−0.997397	+	0.0721023i	$0.977029\pi$
$140$	2.32208	+	6.32368i	0.196251	+	0.534449i
$141$	15.3347	+	15.7421i	1.29141	+	1.32572i
$142$	−13.9822	−	9.76073i	−1.17336	−	0.819102i
$143$	−6.97769			−0.583504
$144$	−7.52326	−	9.34883i	−0.626938	−	0.779069i
$145$	−29.7744			−2.47263
$146$	5.12670	+	3.57887i	0.424289	+	0.296189i
$147$	7.32653	+	7.52118i	0.604282	+	0.620337i
$148$	−6.93029	−	18.8732i	−0.569666	−	1.55137i
$149$		−	3.77498i		−	0.309258i	−0.987973	−	0.154629i	$-0.950582\pi$
$149$		−	3.77498i		−	0.309258i	0.987973	−	0.154629i	$-0.0494183\pi$
$150$	−2.81814	−	17.1519i	−0.230100	−	1.40045i
$151$			19.5955i			1.59466i	0.603545	+	0.797329i	$0.293755\pi$
$151$			19.5955i			1.59466i	−0.603545	+	0.797329i	$0.706245\pi$
$152$	11.0397	+	2.90753i	0.895439	+	0.235832i
$153$	3.79340	+	0.0994775i	0.306678	+	0.00804228i
$154$	−1.70364	+	2.44045i	−0.137283	+	0.196657i
$155$	−4.62475			−0.371469
$156$	4.80401	−	10.0323i	0.384629	−	0.803224i
$157$	10.3968			0.829758			0.414879	−	0.909877i	$-0.363824\pi$
$157$	10.3968			0.829758			0.414879	+	0.909877i	$0.363824\pi$
$158$	−5.67796	+	8.13362i	−0.451714	+	0.647076i
$159$	10.4365	−	10.1664i	0.827670	−	0.806250i
$160$	1.85441	+	19.5867i	0.146604	+	1.54846i
$161$		−	0.968466i		−	0.0763258i
$162$	−10.0403	−	7.82254i	−0.788841	−	0.614597i
$163$		−	5.65715i		−	0.443102i	−0.975149	−	0.221551i	$-0.928888\pi$
$163$		−	5.65715i		−	0.443102i	0.975149	−	0.221551i	$-0.0711119\pi$
$164$	−14.2690	+	5.23962i	−1.11422	+	0.409145i
$165$	9.37695	−	9.13427i	0.729994	−	0.711102i
$166$	−9.69659	−	6.76904i	−0.752601	−	0.525379i
$167$	−14.4620			−1.11910			−0.559550	−	0.828796i	$-0.689026\pi$
$167$	−14.4620			−1.11910			−0.559550	+	0.828796i	$0.689026\pi$
$168$	−2.33587	−	4.12964i	−0.180216	−	0.318609i
$169$	−2.68959			−0.206891
$170$	−5.10143	−	3.56123i	−0.391262	−	0.273134i
$171$	12.1045	+	0.317427i	0.925655	+	0.0242742i
$172$	−3.08077	+	1.13127i	−0.234907	+	0.0862584i
$173$		−	5.19603i		−	0.395047i	−0.980298	−	0.197523i	$-0.936710\pi$
$173$		−	5.19603i		−	0.395047i	0.980298	−	0.197523i	$-0.0632898\pi$
$174$	20.6924	−	3.39987i	1.56869	−	0.257743i
$175$		−	6.87234i		−	0.519500i
$176$	−6.62670	+	5.62518i	−0.499506	+	0.424014i
$177$	1.50581	+	1.54581i	0.113183	+	0.116190i
$178$	2.43097	−	3.48234i	0.182209	−	0.261012i
$179$	−1.56350			−0.116861			−0.0584307	−	0.998291i	$-0.518610\pi$
$179$	−1.56350			−0.116861			−0.0584307	+	0.998291i	$0.518610\pi$
$180$	6.67707	+	19.7706i	0.497679	+	1.47361i
$181$	7.64219			0.568040			0.284020	−	0.958818i	$-0.408332\pi$
$181$	7.64219			0.568040			0.284020	+	0.958818i	$0.408332\pi$
$182$	2.51735	−	3.60607i	0.186598	−	0.267300i
$183$	6.38474	+	6.55436i	0.471973	+	0.484513i
$184$	0.720358	−	2.73516i	0.0531055	−	0.201638i
$185$			34.9627i			2.57051i
$186$	3.21408	−	0.528089i	0.235668	−	0.0387214i
$187$		−	2.74872i		−	0.201006i
$188$	8.74714	+	23.8210i	0.637951	+	1.73732i
$189$	−3.41572	−	3.69552i	−0.248457	−	0.268810i
$190$	−16.2784	−	11.3637i	−1.18096	−	0.824408i
$191$	10.7297			0.776375			0.388187	−	0.921580i	$-0.373101\pi$
$191$	10.7297			0.776375			0.388187	+	0.921580i	$0.373101\pi$
$192$	−3.52531	−	13.4005i	−0.254418	−	0.967094i
$193$	−6.69309			−0.481779			−0.240890	−	0.970553i	$-0.577439\pi$
$193$	−6.69309			−0.481779			−0.240890	+	0.970553i	$0.577439\pi$
$194$	−11.2362	−	7.84384i	−0.806715	−	0.563155i
$195$	−13.8556	+	13.4970i	−0.992221	+	0.966542i
$196$	4.17918	+	11.3811i	0.298513	+	0.812936i
$197$			5.79072i			0.412572i	0.978492	+	0.206286i	$0.0661377\pi$
$197$			5.79072i			0.412572i	−0.978492	+	0.206286i	$0.933862\pi$
$198$	−5.47371	+	7.41881i	−0.389000	+	0.527232i
$199$		−	21.6024i		−	1.53135i	−0.643226	−	0.765676i	$-0.722405\pi$
$199$		−	21.6024i		−	1.53135i	0.643226	−	0.765676i	$-0.277595\pi$
$200$	5.11174	−	19.4090i	0.361455	−	1.37242i
$201$	−17.4955	+	17.0427i	−1.23404	+	1.20210i
$202$	−7.86553	+	11.2673i	−0.553416	+	0.792764i
$203$	8.29096			0.581911
$204$	3.95201	+	1.89244i	0.276696	+	0.132497i
$205$	26.4334			1.84619
$206$	−8.75773	+	12.5454i	−0.610180	+	0.874077i
$207$	0.0786444	−	2.99897i	0.00546616	−	0.208443i
$208$	9.79178	−	8.31190i	0.678938	−	0.576327i
$209$		−	8.77100i		−	0.606703i
$210$	1.33767	+	8.14139i	0.0923080	+	0.561809i
$211$			4.59546i			0.316365i	0.987410	+	0.158182i	$0.0505634\pi$
$211$			4.59546i			0.316365i	−0.987410	+	0.158182i	$0.949437\pi$
$212$	15.7926	−	5.79910i	1.08464	−	0.398283i
$213$	−14.5727	−	14.9598i	−0.998502	−	1.02503i
$214$	1.03646	+	0.723537i	0.0708509	+	0.0494600i
$215$	5.70715			0.389224
$216$	−6.89794	−	12.9776i	−0.469346	−	0.883015i
$217$	1.28780			0.0874219
$218$	19.0035	+	13.2661i	1.28708	+	0.898491i
$219$	5.34321	+	5.48517i	0.361061	+	0.370653i
$220$	14.1893	−	5.21034i	0.956640	−	0.351281i
$221$			4.06158i			0.273211i
$222$	−3.99231	−	24.2982i	−0.267946	−	1.63079i
$223$		−	19.0355i		−	1.27471i	−0.770568	−	0.637357i	$-0.780028\pi$
$223$		−	19.0355i		−	1.27471i	0.770568	−	0.637357i	$-0.219972\pi$
$224$	−0.516376	−	5.45408i	−0.0345018	−	0.364416i
$225$	0.558070	−	21.2810i	0.0372047	−	1.41874i
$226$	8.99770	−	12.8891i	0.598518	−	0.857371i
$227$	2.91162			0.193251			0.0966256	−	0.995321i	$-0.469195\pi$
$227$	2.91162			0.193251			0.0966256	+	0.995321i	$0.469195\pi$
$228$	12.6106	+	6.03867i	0.835159	+	0.399921i
$229$	−12.8792			−0.851082			−0.425541	−	0.904939i	$-0.639916\pi$
$229$	−12.8792			−0.851082			−0.425541	+	0.904939i	$0.639916\pi$
$230$	−2.81542	+	4.03307i	−0.185643	+	0.265933i
$231$	−2.61110	+	2.54352i	−0.171797	+	0.167351i
$232$	23.4155	+	6.16693i	1.53730	+	0.404879i
$233$			7.10818i			0.465672i	0.972516	+	0.232836i	$0.0748006\pi$
$233$			7.10818i			0.465672i	−0.972516	+	0.232836i	$0.925199\pi$
$234$	8.08809	−	10.9622i	0.528735	−	0.716623i
$235$		−	44.1286i		−	2.87863i
$236$	0.858937	+	2.33913i	0.0559120	+	0.152265i
$237$	−8.70234	+	8.47713i	−0.565278	+	0.550649i
$238$	1.42054	+	0.991657i	0.0920799	+	0.0642796i
$239$	−7.54379			−0.487967			−0.243984	−	0.969779i	$-0.578454\pi$
$239$	−7.54379			−0.487967			−0.243984	+	0.969779i	$0.578454\pi$
$240$	−2.27780	+	23.9880i	−0.147032	+	1.54842i
$241$	29.2219			1.88235			0.941174	−	0.337923i	$-0.109725\pi$
$241$	29.2219			1.88235			0.941174	+	0.337923i	$0.109725\pi$
$242$	−7.27977	−	5.08189i	−0.467961	−	0.326677i
$243$	−10.2771	−	11.7210i	−0.659275	−	0.751902i
$244$	3.64196	+	9.91811i	0.233153	+	0.634942i
$245$		−	21.0836i		−	1.34698i
$246$	−18.3705	+	3.01837i	−1.17126	+	0.192444i
$247$			12.9603i			0.824641i
$248$	3.63704	+	0.957886i	0.230952	+	0.0608258i
$249$	−10.1061	−	10.3746i	−0.640448	−	0.657463i
$250$	−5.90145	+	8.45378i	−0.373241	+	0.534664i
$251$	−8.74423			−0.551931			−0.275965	−	0.961168i	$-0.588998\pi$
$251$	−8.74423			−0.551931			−0.275965	+	0.961168i	$0.588998\pi$
$252$	−1.85929	−	5.50530i	−0.117124	−	0.346802i
$253$	−2.17307			−0.136620
$254$	−9.61783	+	13.7775i	−0.603477	+	0.864475i
$255$	−5.31688	−	5.45814i	−0.332956	−	0.341802i
$256$	2.59846	−	15.7876i	0.162404	−	0.986724i
$257$			4.42023i			0.275726i	0.990451	+	0.137863i	$0.0440234\pi$
$257$			4.42023i			0.275726i	−0.990451	+	0.137863i	$0.955977\pi$
$258$	−3.96632	+	0.651685i	−0.246932	+	0.0405722i
$259$		−	9.73568i		−	0.604946i
$260$	−20.9664	+	7.69893i	−1.30028	+	0.477467i
$261$	25.6739	+	0.673269i	1.58918	+	0.0416743i
$262$	22.8751	+	15.9688i	1.41323	+	0.986555i
$263$	−6.11158			−0.376856			−0.188428	−	0.982087i	$-0.560339\pi$
$263$	−6.11158			−0.376856			−0.188428	+	0.982087i	$0.560339\pi$
$264$	−9.26621	+	5.24129i	−0.570295	+	0.322579i
$265$	−29.2559			−1.79718
$266$	4.53286	+	3.16432i	0.277927	+	0.194017i
$267$	3.72583	−	3.62941i	0.228017	−	0.222116i
$268$	−26.4743	+	9.72144i	−1.61717	+	0.593831i
$269$		−	16.8382i		−	1.02664i	−0.858196	−	0.513322i	$-0.828415\pi$
$269$		−	16.8382i		−	1.02664i	0.858196	−	0.513322i	$-0.171585\pi$
$270$	3.48113	+	25.3194i	0.211855	+	1.54089i
$271$			19.5135i			1.18536i	0.805437	+	0.592682i	$0.201931\pi$
$271$			19.5135i			1.18536i	−0.805437	+	0.592682i	$0.798069\pi$
$272$	3.27431	+	3.85727i	0.198534	+	0.233882i
$273$	3.85822	−	3.75837i	0.233510	−	0.227467i
$274$	−4.11858	+	5.89983i	−0.248813	+	0.356422i
$275$	−15.4204			−0.929883
$276$	1.49612	−	3.12436i	0.0900557	−	0.188064i
$277$	−17.4006			−1.04550			−0.522751	−	0.852485i	$-0.675094\pi$
$277$	−17.4006			−1.04550			−0.522751	+	0.852485i	$0.675094\pi$
$278$	−1.37628	+	1.97151i	−0.0825438	+	0.118243i
$279$	3.98784	+	0.104576i	0.238746	+	0.00626082i
$280$	−2.42636	+	9.21275i	−0.145003	+	0.550567i
$281$		−	27.2670i		−	1.62661i	−0.581834	−	0.813307i	$-0.697665\pi$
$281$		−	27.2670i		−	1.62661i	0.581834	−	0.813307i	$-0.302335\pi$
$282$	5.03893	+	30.6682i	0.300064	+	1.82626i
$283$		−	18.6980i		−	1.11148i	−0.831356	−	0.555740i	$-0.812435\pi$
$283$		−	18.6980i		−	1.11148i	0.831356	−	0.555740i	$-0.187565\pi$
$284$	−8.31249	−	22.6373i	−0.493255	−	1.34328i
$285$	−16.9658	−	17.4166i	−1.00497	−	1.03167i
$286$	−8.09141	−	5.64849i	−0.478455	−	0.334002i
$287$	−7.36062			−0.434484
$288$	−1.15612	−	16.9311i	−0.0681250	−	0.997677i
$289$	15.4000			0.905884
$290$	−34.5268	−	24.1026i	−2.02748	−	1.41535i
$291$	−11.7108	−	12.0219i	−0.686498	−	0.704736i
$292$	3.04786	+	8.30020i	0.178362	+	0.485732i
$293$			23.4417i			1.36948i	0.728788	+	0.684739i	$0.240084\pi$
$293$			23.4417i			1.36948i	−0.728788	+	0.684739i	$0.759916\pi$
$294$	2.40748	+	14.6525i	0.140407	+	0.854553i
$295$		−	4.33326i		−	0.252292i
$296$	7.24153	−	27.4957i	0.420905	−	1.59815i
$297$	−8.29211	+	7.66428i	−0.481157	+	0.444727i
$298$	3.05587	−	4.37751i	0.177022	−	0.253582i
$299$	3.21098			0.185696
$300$	10.6166	−	22.1708i	0.612951	−	1.28003i
$301$	−1.58921			−0.0916004
$302$	−15.8627	+	22.7232i	−0.912795	+	1.30757i
$303$	−12.0551	+	11.7431i	−0.692549	+	0.674626i
$304$	10.4481	+	12.3083i	0.599240	+	0.705931i
$305$		−	18.3734i		−	1.05206i
$306$	4.31834	+	3.18614i	0.246863	+	0.182140i
$307$			6.00519i			0.342734i	0.985207	+	0.171367i	$0.0548184\pi$
$307$			6.00519i			0.342734i	−0.985207	+	0.171367i	$0.945182\pi$
$308$	−3.95113	+	1.45087i	−0.225136	+	0.0826708i
$309$	−13.4226	+	13.0752i	−0.763583	+	0.743822i
$310$	−5.36292	−	3.74377i	−0.304593	−	0.212632i
$311$	21.3726			1.21193			0.605965	−	0.795491i	$-0.292787\pi$
$311$	21.3726			1.21193			0.605965	+	0.795491i	$0.292787\pi$
$312$	13.6920	−	7.74466i	0.775156	−	0.438455i
$313$	16.5423			0.935026			0.467513	−	0.883986i	$-0.345150\pi$
$313$	16.5423			0.935026			0.467513	+	0.883986i	$0.345150\pi$
$314$	12.0563	+	8.41631i	0.680376	+	0.474960i
$315$	−0.264896	+	10.1013i	−0.0149252	+	0.569146i
$316$	−13.1684	+	4.83549i	−0.740783	+	0.272018i
$317$		−	11.2127i		−	0.629771i	−0.949130	−	0.314885i	$-0.898034\pi$
$317$		−	11.2127i		−	0.629771i	0.949130	−	0.314885i	$-0.101966\pi$
$318$	20.3321	−	3.34066i	1.14017	−	0.187335i
$319$		−	18.6035i		−	1.04160i
$320$	−13.7051	+	24.2141i	−0.766141	+	1.35361i
$321$	1.08023	+	1.10893i	0.0602927	+	0.0618945i
$322$	0.783980	−	1.12304i	0.0436895	−	0.0625848i
$323$	−5.10543			−0.284074
$324$	−5.31045	−	17.1988i	−0.295025	−	0.955489i
$325$	22.7855			1.26391
$326$	4.57950	−	6.56009i	0.253635	−	0.363330i
$327$	19.8061	+	20.3323i	1.09528	+	1.12438i
$328$	−20.7880	−	5.47493i	−1.14782	−	0.302302i
$329$			12.2880i			0.677459i
$330$	18.2679	−	3.00150i	1.00561	−	0.165227i
$331$		−	10.8174i		−	0.594576i	−0.954788	−	0.297288i	$-0.903918\pi$
$331$		−	10.8174i		−	0.594576i	0.954788	−	0.297288i	$-0.0960822\pi$
$332$	−5.76469	−	15.6989i	−0.316378	−	0.861589i
$333$	0.790587	−	30.1477i	0.0433239	−	1.65208i
$334$	−16.7703	−	11.7071i	−0.917628	−	0.640582i
$335$	49.0438			2.67955
$336$	0.634275	−	6.67968i	0.0346025	−	0.364406i
$337$	−23.7190			−1.29205			−0.646027	−	0.763315i	$-0.723571\pi$
$337$	−23.7190			−1.29205			−0.646027	+	0.763315i	$0.723571\pi$
$338$	−3.11887	−	2.17724i	−0.169644	−	0.118426i
$339$	13.7904	−	13.4335i	0.748989	−	0.729606i
$340$	−3.03284	−	8.25929i	−0.164479	−	0.447923i
$341$		−	2.88961i		−	0.156481i
$342$	13.7796	+	10.1668i	0.745114	+	0.549757i
$343$			12.6502i			0.683045i
$344$	−4.48827	−	1.18207i	−0.241991	−	0.0637331i
$345$	−4.31507	+	4.20339i	−0.232316	+	0.226303i
$346$	4.20622	−	6.02537i	0.226128	−	0.323926i
$347$	21.0417			1.12958			0.564789	−	0.825235i	$-0.308958\pi$
$347$	21.0417			1.12958			0.564789	+	0.825235i	$0.308958\pi$
$348$	26.7474	+	12.8082i	1.43381	+	0.686589i
$349$	5.31487			0.284499			0.142249	−	0.989831i	$-0.454567\pi$
$349$	5.31487			0.284499			0.142249	+	0.989831i	$0.454567\pi$
$350$	5.56321	−	7.96925i	0.297366	−	0.425974i
$351$	12.2526	−	11.3249i	0.653997	−	0.604480i
$352$	−12.2380	+	1.15866i	−0.652288	+	0.0617567i
$353$		−	4.77728i		−	0.254269i	−0.991885	−	0.127135i	$-0.959422\pi$
$353$		−	4.77728i		−	0.254269i	0.991885	−	0.127135i	$-0.0405780\pi$
$354$	0.494804	+	3.01150i	0.0262986	+	0.160059i
$355$			41.9358i			2.22572i
$356$	5.63795	−	2.07027i	0.298811	−	0.109724i
$357$	1.48053	+	1.51987i	0.0783581	+	0.0804399i
$358$	−1.81305	−	1.26566i	−0.0958228	−	0.0668924i
$359$	−2.32014			−0.122452			−0.0612261	−	0.998124i	$-0.519501\pi$
$359$	−2.32014			−0.122452			−0.0612261	+	0.998124i	$0.519501\pi$
$360$	−8.26164	+	28.3314i	−0.435427	+	1.49319i
$361$	2.70888			0.142573
$362$	8.86197	+	6.18641i	0.465775	+	0.325150i
$363$	−7.58721	−	7.78879i	−0.398225	−	0.408805i
$364$	5.83829	−	2.14384i	0.306009	−	0.112368i
$365$		−	15.3762i		−	0.804826i
$366$	2.09801	+	12.7690i	0.109665	+	0.667447i
$367$		−	5.02862i		−	0.262492i	−0.991350	−	0.131246i	$-0.958102\pi$
$367$		−	5.02862i		−	0.262492i	0.991350	−	0.131246i	$-0.0418977\pi$
$368$	3.04946	−	2.58858i	0.158964	−	0.134939i
$369$	−22.7930	−	0.597720i	−1.18656	−	0.0311161i
$370$	−28.3026	+	40.5431i	−1.47138	+	2.10774i
$371$	8.14658			0.422949
$372$	4.15458	+	1.98944i	0.215405	+	0.103148i
$373$	−2.47323			−0.128059			−0.0640296	−	0.997948i	$-0.520395\pi$
$373$	−2.47323			−0.128059			−0.0640296	+	0.997948i	$0.520395\pi$
$374$	2.22511	−	3.18745i	0.115058	−	0.164819i
$375$	−9.04488	+	8.81080i	−0.467076	+	0.454988i
$376$	−9.13998	+	34.7040i	−0.471358	+	1.78972i
$377$			27.4890i			1.41575i
$378$	−0.969352	−	7.05041i	−0.0498581	−	0.362634i
$379$		−	33.4612i		−	1.71879i	−0.511315	−	0.859393i	$-0.670842\pi$
$379$		−	33.4612i		−	1.71879i	0.511315	−	0.859393i	$-0.329158\pi$
$380$	−9.67760	−	26.3549i	−0.496450	−	1.35198i
$381$	−14.7408	+	14.3593i	−0.755195	+	0.735650i
$382$	12.4423	+	8.68578i	0.636603	+	0.444403i
$383$	−21.8474			−1.11635			−0.558176	−	0.829722i	$-0.688499\pi$
$383$	−21.8474			−1.11635			−0.558176	+	0.829722i	$0.688499\pi$
$384$	6.75977	−	18.3931i	0.344958	−	0.938618i
$385$	7.31949			0.373036
$386$	−7.76138	−	5.41810i	−0.395044	−	0.275774i
$387$	−4.92117	−	0.129052i	−0.250157	−	0.00656007i
$388$	−6.68002	−	18.1916i	−0.339127	−	0.923539i
$389$		−	6.25554i		−	0.317168i	−0.987345	−	0.158584i	$-0.949307\pi$
$389$		−	6.25554i		−	0.317168i	0.987345	−	0.158584i	$-0.0506929\pi$
$390$	−26.9931	+	4.43509i	−1.36685	+	0.224580i
$391$			1.26490i			0.0639688i
$392$	−4.36686	+	16.5807i	−0.220560	+	0.837453i
$393$	23.8412	+	24.4746i	1.20263	+	1.23458i
$394$	−4.68763	+	6.71499i	−0.236159	+	0.338296i
$395$	24.3946			1.22743
$396$	−12.3530	+	4.17193i	−0.620759	+	0.209647i
$397$	29.8282			1.49704			0.748518	−	0.663114i	$-0.230766\pi$
$397$	29.8282			1.49704			0.748518	+	0.663114i	$0.230766\pi$
$398$	17.4873	−	25.0504i	0.876558	−	1.25566i
$399$	4.72429	+	4.84981i	0.236510	+	0.242794i
$400$	21.6393	−	18.3689i	1.08197	−	0.918445i
$401$			17.6227i			0.880033i	0.897990	+	0.440017i	$0.145027\pi$
$401$			17.6227i			0.880033i	−0.897990	+	0.440017i	$0.854973\pi$
$402$	−34.0841	+	5.60019i	−1.69996	+	0.279312i
$403$			4.26976i			0.212692i
$404$	−18.2419	+	6.69848i	−0.907569	+	0.333262i
$405$	−1.64056	+	31.2585i	−0.0815202	+	1.55325i
$406$	9.61429	+	6.71159i	0.477149	+	0.333091i
$407$	−21.8452			−1.08283
$408$	3.05085	+	5.39368i	0.151040	+	0.267027i
$409$	−31.3375			−1.54954			−0.774769	−	0.632244i	$-0.782134\pi$
$409$	−31.3375			−1.54954			−0.774769	+	0.632244i	$0.782134\pi$
$410$	30.6525	+	21.3980i	1.51382	+	1.05677i
$411$	−6.31236	+	6.14900i	−0.311366	+	0.303308i
$412$	−20.3111	+	7.45831i	−1.00066	+	0.367444i
$413$			1.20664i			0.0593746i
$414$	2.51888	−	3.41398i	0.123796	−	0.167788i
$415$			29.0823i			1.42760i
$416$	18.0832	−	1.71206i	0.886602	−	0.0839408i
$417$	−2.10936	+	2.05477i	−0.103296	+	0.100623i
$418$	7.10019	−	10.1710i	0.347281	−	0.497478i
$419$	8.72402			0.426196			0.213098	−	0.977031i	$-0.431645\pi$
$419$	8.72402			0.426196			0.213098	+	0.977031i	$0.431645\pi$
$420$	−5.03933	+	10.5237i	−0.245894	+	0.513504i
$421$	7.78947			0.379636			0.189818	−	0.981819i	$-0.439210\pi$
$421$	7.78947			0.379636			0.189818	+	0.981819i	$0.439210\pi$
$422$	−3.72006	+	5.32895i	−0.181090	+	0.259409i
$423$	−0.997849	+	38.0512i	−0.0485171	+	1.85011i
$424$	23.0077	+	6.05953i	1.11735	+	0.294277i
$425$			8.97589i			0.435395i
$426$	−4.78854	−	29.1443i	−0.232006	−	1.41204i
$427$			5.11623i			0.247592i
$428$	0.616182	+	1.67804i	0.0297843	+	0.0811113i
$429$	−8.43313	−	8.65718i	−0.407156	−	0.417973i
$430$	6.61808	+	4.61998i	0.319152	+	0.222795i
$431$	−12.1743			−0.586416			−0.293208	−	0.956049i	$-0.594723\pi$
$431$	−12.1743			−0.586416			−0.293208	+	0.956049i	$0.594723\pi$
$432$	2.50653	−	20.6329i	0.120596	−	0.992702i
$433$	35.1939			1.69131			0.845656	−	0.533729i	$-0.179210\pi$
$433$	35.1939			1.69131			0.845656	+	0.533729i	$0.179210\pi$
$434$	1.49335	+	1.04249i	0.0716832	+	0.0500410i
$435$	−35.9849	−	36.9410i	−1.72535	−	1.77118i
$436$	11.2977	+	30.7669i	0.541062	+	1.47347i
$437$			4.03623i			0.193079i
$438$	1.75577	+	10.6860i	0.0838938	+	0.510598i
$439$		−	18.3988i		−	0.878127i	−0.898456	−	0.439063i	$-0.855310\pi$
$439$		−	18.3988i		−	0.878127i	0.898456	−	0.439063i	$-0.144690\pi$
$440$	20.6718	+	5.44434i	0.985491	+	0.259549i
$441$	−0.476748	+	18.1800i	−0.0227023	+	0.865713i
$442$	−3.28788	+	4.70985i	−0.156388	+	0.224025i
$443$	10.1139			0.480528			0.240264	−	0.970708i	$-0.422766\pi$
$443$	10.1139			0.480528			0.240264	+	0.970708i	$0.422766\pi$
$444$	15.0400	−	31.4082i	0.713767	−	1.49057i
$445$	−10.4443			−0.495109
$446$	15.4094	−	22.0738i	0.729657	−	1.04523i
$447$	4.68359	−	4.56238i	0.221526	−	0.215793i
$448$	3.81632	−	6.74262i	0.180304	−	0.318559i
$449$			7.51879i			0.354834i	0.984136	+	0.177417i	$0.0567741\pi$
$449$			7.51879i			0.354834i	−0.984136	+	0.177417i	$0.943226\pi$
$450$	17.8743	−	24.2260i	0.842602	−	1.14202i
$451$			16.5160i			0.777706i
$452$	20.8677	−	7.66267i	0.981532	−	0.360422i
$453$	−24.3120	+	23.6828i	−1.14228	+	1.11272i
$454$	3.37635	+	2.35698i	0.158460	+	0.110619i
$455$	−10.8155			−0.507037
$456$	9.73508	+	17.2109i	0.455887	+	0.805974i
$457$	−2.08553			−0.0975568			−0.0487784	−	0.998810i	$-0.515533\pi$
$457$	−2.08553			−0.0975568			−0.0487784	+	0.998810i	$0.515533\pi$
$458$	−14.9349	−	10.4258i	−0.697861	−	0.487166i
$459$	4.46123	+	4.82668i	0.208232	+	0.225290i
$460$	−6.52959	+	2.39769i	−0.304444	+	0.111793i
$461$		−	15.7777i		−	0.734843i	−0.930055	−	0.367421i	$-0.880241\pi$
$461$		−	15.7777i		−	0.734843i	0.930055	−	0.367421i	$-0.119759\pi$
$462$	−5.08685	+	0.835795i	−0.236662	+	0.0388847i
$463$		−	2.55088i		−	0.118550i	−0.998242	−	0.0592748i	$-0.981121\pi$
$463$		−	2.55088i		−	0.118550i	0.998242	−	0.0592748i	$-0.0188788\pi$
$464$	22.1607	+	26.1062i	1.02878	+	1.21195i
$465$	−5.58941	−	5.73791i	−0.259203	−	0.266089i
$466$	−5.75412	+	8.24272i	−0.266554	+	0.381837i
$467$	33.4176			1.54638			0.773191	−	0.634173i	$-0.218659\pi$
$467$	33.4176			1.54638			0.773191	+	0.634173i	$0.218659\pi$
$468$	18.2530	−	6.16454i	0.843747	−	0.284956i
$469$	−13.6567			−0.630607
$470$	35.7224	−	51.1720i	1.64775	−	2.36039i
$471$	12.5655	+	12.8993i	0.578986	+	0.594368i
$472$	−0.897512	+	3.40780i	−0.0413113	+	0.156857i
$473$			3.56591i			0.163961i
$474$	−16.9536	+	2.78556i	−0.778706	+	0.127945i
$475$			28.6415i			1.31416i
$476$	0.844521	+	2.29987i	0.0387085	+	0.105415i
$477$	25.2268	+	0.661544i	1.15506	+	0.0302900i
$478$	−8.74787	−	6.10675i	−0.400118	−	0.279316i
$479$	−39.1406			−1.78838			−0.894191	−	0.447686i	$-0.852248\pi$
$479$	−39.1406			−1.78838			−0.894191	+	0.447686i	$0.852248\pi$
$480$	−22.0598	+	25.9729i	−1.00689	+	1.18549i
$481$	32.2790			1.47180
$482$	33.8860	+	23.6553i	1.54347	+	1.07747i
$483$	1.20157	−	1.17047i	0.0546733	−	0.0532584i
$484$	−4.32787	−	11.7860i	−0.196721	−	0.535729i
$485$			33.7001i			1.53024i
$486$	−2.42918	−	21.9112i	−0.110190	−	0.993911i
$487$		−	21.4979i		−	0.974164i	−0.873356	−	0.487082i	$-0.838061\pi$
$487$		−	21.4979i		−	0.974164i	0.873356	−	0.487082i	$-0.161939\pi$
$488$	−3.80552	+	14.4493i	−0.172268	+	0.654091i
$489$	7.01879	−	6.83714i	0.317401	−	0.309186i
$490$	17.0673	−	24.4488i	0.771022	−	1.10448i
$491$	−12.9162			−0.582901			−0.291450	−	0.956586i	$-0.594138\pi$
$491$	−12.9162			−0.582901			−0.291450	+	0.956586i	$0.594138\pi$
$492$	−23.7460	−	11.3709i	−1.07055	−	0.512641i
$493$	−10.8287			−0.487701
$494$	−10.4914	+	15.0289i	−0.472031	+	0.676180i
$495$	22.6657	+	0.594381i	1.01875	+	0.0267154i
$496$	3.44214	+	4.05498i	0.154557	+	0.182074i
$497$		−	11.6774i		−	0.523803i
$498$	−3.32084	−	20.2115i	−0.148810	−	0.905697i
$499$			0.320130i			0.0143310i	0.999974	+	0.00716550i	$0.00228087\pi$
$499$			0.320130i			0.0143310i	−0.999974	+	0.00716550i	$0.997719\pi$
$500$	−13.6868	+	5.02583i	−0.612091	+	0.224762i
$501$	−17.4785	−	17.9429i	−0.780882	−	0.801629i
$502$	−10.1399	−	7.07852i	−0.452566	−	0.315930i
$503$	−43.6123			−1.94457			−0.972287	−	0.233788i	$-0.924888\pi$
$503$	−43.6123			−1.94457			−0.972287	+	0.233788i	$0.924888\pi$
$504$	2.30053	−	7.88912i	0.102474	−	0.351409i
$505$	33.7933			1.50378
$506$	−2.51992	−	1.75912i	−0.112024	−	0.0782022i
$507$	−3.25059	−	3.33695i	−0.144364	−	0.148199i
$508$	−22.3059	+	8.19079i	−0.989664	+	0.363408i
$509$		−	29.9888i		−	1.32923i	−0.747185	−	0.664616i	$-0.768595\pi$
$509$		−	29.9888i		−	1.32923i	0.747185	−	0.664616i	$-0.231405\pi$
$510$	−1.74712	−	10.6334i	−0.0773636	−	0.470854i
$511$			4.28163i			0.189408i
$512$	15.7934	−	16.2040i	0.697975	−	0.716122i
$513$	14.2355	+	15.4016i	0.628513	+	0.679999i
$514$	−3.57821	+	5.12575i	−0.157828	+	0.226087i
$515$	37.6265			1.65802
$516$	−5.12693	−	2.45506i	−0.225701	−	0.108078i
$517$	27.5721			1.21262
$518$	7.88110	−	11.2896i	0.346276	−	0.496037i
$519$	6.44668	−	6.27984i	0.282978	−	0.275654i
$520$	−30.5452	−	8.04469i	−1.33950	−	0.352783i
$521$		−	23.0966i		−	1.01188i	−0.862569	−	0.505940i	$-0.831146\pi$
$521$		−	23.0966i		−	1.01188i	0.862569	−	0.505940i	$-0.168854\pi$
$522$	29.2268	+	21.5640i	1.27922	+	0.943829i
$523$			0.00853164i			0.000373063i	1.00000		0.000186531i	$5.93747e-5\pi$
$523$			0.00853164i			0.000373063i	−1.00000		0.000186531i	$0.999941\pi$
$524$	13.5994	+	37.0352i	0.594094	+	1.61789i
$525$	8.52648	−	8.30581i	0.372126	−	0.362495i
$526$	−7.08706	−	4.94737i	−0.309011	−	0.215716i
$527$	−1.68199			−0.0732685
$528$	−14.9881	−	1.42320i	−0.652271	−	0.0619370i
$529$	1.00000			0.0434783
$530$	−33.9255	−	23.6829i	−1.47363	−	1.02872i
$531$	−0.0979850	+	3.73649i	−0.00425219	+	0.162150i
$532$	2.69481	+	7.33876i	0.116835	+	0.318176i
$533$		−	24.4044i		−	1.05707i
$534$	7.25854	−	1.19261i	0.314108	−	0.0516095i
$535$		−	3.10859i		−	0.134396i
$536$	−38.5695	−	10.1580i	−1.66595	−	0.438760i
$537$	−1.88962	−	1.93983i	−0.0815432	−	0.0837096i
$538$	13.6306	−	19.5258i	0.587659	−	0.841816i
$539$	13.1733			0.567415
$540$	−16.4595	+	32.1787i	−0.708303	+	1.38475i
$541$	−13.8833			−0.596889			−0.298444	−	0.954427i	$-0.596468\pi$
$541$	−13.8833			−0.596889			−0.298444	+	0.954427i	$0.596468\pi$
$542$	−15.7964	+	22.6281i	−0.678511	+	0.971961i
$543$	9.23624	+	9.48162i	0.396365	+	0.406895i
$544$	0.674433	+	7.12351i	0.0289161	+	0.305418i
$545$		−	56.9960i		−	2.44144i
$546$	7.51646	−	1.23499i	0.321675	−	0.0528528i
$547$			30.7960i			1.31674i	0.752694	+	0.658371i	$0.228754\pi$
$547$			30.7960i			1.31674i	−0.752694	+	0.658371i	$0.771246\pi$
$548$	−9.55191	+	3.50749i	−0.408037	+	0.149832i
$549$	−0.415464	+	15.8430i	−0.0177316	+	0.676163i
$550$	−17.8816	−	12.4829i	−0.762475	−	0.532272i
$551$	−34.5538			−1.47204
$552$	4.26411	−	2.41193i	0.181492	−	0.102658i
$553$	−6.79291			−0.288864
$554$	−20.1780	−	14.0859i	−0.857280	−	0.598454i
$555$	−43.3780	+	42.2554i	−1.84129	+	1.79364i
$556$	−3.19190	+	1.17208i	−0.135367	+	0.0497071i
$557$			1.22730i			0.0520025i	0.999662	+	0.0260013i	$0.00827739\pi$
$557$			1.22730i			0.0520025i	−0.999662	+	0.0260013i	$0.991723\pi$
$558$	4.53969	+	3.34945i	0.192180	+	0.141794i
$559$		−	5.26907i		−	0.222858i
$560$	−10.2714	+	8.71906i	−0.434047	+	0.368447i
$561$	3.41032	−	3.32206i	0.143984	−	0.140258i
$562$	22.0729	−	31.6192i	0.931087	−	1.33377i
$563$	−38.4789			−1.62169			−0.810845	−	0.585260i	$-0.800992\pi$
$563$	−38.4789			−1.62169			−0.810845	+	0.585260i	$0.800992\pi$
$564$	−18.9829	+	39.6422i	−0.799325	+	1.66924i
$565$	−38.6575			−1.62633
$566$	15.1361	−	21.6824i	0.636219	−	0.911378i
$567$	0.456829	−	8.70421i	0.0191850	−	0.365542i
$568$	8.68580	−	32.9795i	0.364448	−	1.38379i
$569$		−	20.2841i		−	0.850352i	−0.905111	−	0.425176i	$-0.860212\pi$
$569$		−	20.2841i		−	0.850352i	0.905111	−	0.425176i	$-0.139788\pi$
$570$	−5.57494	−	33.9304i	−0.233508	−	1.42119i
$571$			24.8535i			1.04009i	0.854140	+	0.520043i	$0.174084\pi$
$571$			24.8535i			1.04009i	−0.854140	+	0.520043i	$0.825916\pi$
$572$	−4.81040	−	13.1001i	−0.201133	−	0.547743i
$573$	12.9678	+	13.3123i	0.541736	+	0.556129i
$574$	−8.53546	−	5.95847i	−0.356263	−	0.248702i
$575$	7.09612			0.295928
$576$	12.3652	−	20.5694i	0.515218	−	0.857059i
$577$	−8.07340			−0.336100			−0.168050	−	0.985778i	$-0.553747\pi$
$577$	−8.07340			−0.336100			−0.168050	+	0.985778i	$0.553747\pi$
$578$	17.8580	+	12.4664i	0.742797	+	0.518535i
$579$	−8.08917	−	8.30408i	−0.336174	−	0.345106i
$580$	−20.5264	−	55.8993i	−0.852313	−	2.32109i
$581$		−	8.09824i		−	0.335972i
$582$	−3.84813	−	23.4207i	−0.159510	−	0.970818i
$583$		−	18.2795i		−	0.757060i
$584$	−3.18474	+	12.0923i	−0.131785	+	0.500381i
$585$	−33.4914	−	0.878272i	−1.38470	−	0.0363121i
$586$	−18.9762	+	27.1833i	−0.783900	+	1.12293i
$587$	−29.4596			−1.21593			−0.607963	−	0.793965i	$-0.708013\pi$
$587$	−29.4596			−1.21593			−0.607963	+	0.793965i	$0.708013\pi$
$588$	−9.06958	+	18.9401i	−0.374023	+	0.781077i
$589$	−5.36712			−0.221148
$590$	3.50780	−	5.02490i	0.144414	−	0.206872i
$591$	−7.18452	+	6.99858i	−0.295531	+	0.287883i
$592$	30.6553	−	26.0222i	1.25992	−	1.06951i
$593$			33.5340i			1.37708i	0.725201	+	0.688538i	$0.241747\pi$
$593$			33.5340i			1.37708i	−0.725201	+	0.688538i	$0.758253\pi$
$594$	−15.8199	+	2.17506i	−0.649099	+	0.0892438i
$595$		−	4.26053i		−	0.174665i
$596$	7.08724	−	2.60246i	0.290305	−	0.106601i
$597$	26.8019	−	26.1083i	1.09693	−	1.06854i
$598$	3.72349	+	2.59931i	0.152265	+	0.106294i
$599$	7.01737			0.286722			0.143361	−	0.989670i	$-0.454209\pi$
$599$	7.01737			0.286722			0.143361	+	0.989670i	$0.454209\pi$
$600$	30.2586	−	17.1153i	1.23530	−	0.698730i
$601$	−12.3163			−0.502394			−0.251197	−	0.967936i	$-0.580824\pi$
$601$	−12.3163			−0.502394			−0.251197	+	0.967936i	$0.580824\pi$
$602$	−1.84286	−	1.28647i	−0.0751095	−	0.0524328i
$603$	−42.2896	−	1.10899i	−1.72216	−	0.0451617i
$604$	−36.7891	+	13.5091i	−1.49693	+	0.549676i
$605$			21.8337i			0.887668i
$606$	−23.4854	+	3.85877i	−0.954030	+	0.156752i
$607$			5.90740i			0.239774i	0.992788	+	0.119887i	$0.0382532\pi$
$607$			5.90740i			0.239774i	−0.992788	+	0.119887i	$0.961747\pi$
$608$	2.15207	+	22.7307i	0.0872781	+	0.921851i
$609$	10.0203	+	10.2865i	0.406044	+	0.416832i
$610$	14.8734	−	21.3060i	0.602205	−	0.862653i
$611$	−40.7413			−1.64822
$612$	2.42840	+	7.19041i	0.0981622	+	0.290655i
$613$	22.8771			0.923998			0.461999	−	0.886880i	$-0.347132\pi$
$613$	22.8771			0.923998			0.461999	+	0.886880i	$0.347132\pi$
$614$	−4.86124	+	6.96369i	−0.196184	+	0.281031i
$615$	31.9470	+	32.7958i	1.28823	+	1.32245i
$616$	−5.75626	−	1.51602i	−0.231926	−	0.0610824i
$617$			21.9932i			0.885412i	0.896667	+	0.442706i	$0.145981\pi$
$617$			21.9932i			0.885412i	−0.896667	+	0.442706i	$0.854019\pi$
$618$	−26.1494	+	4.29648i	−1.05188	+	0.172830i
$619$		−	24.4284i		−	0.981860i	−0.871199	−	0.490930i	$-0.836657\pi$
$619$		−	24.4284i		−	0.981860i	0.871199	−	0.490930i	$-0.163343\pi$
$620$	−3.18829	−	8.68264i	−0.128045	−	0.348703i
$621$	3.81585	−	3.52694i	0.153125	−	0.141531i
$622$	24.7839	+	17.3013i	0.993745	+	0.693718i
$623$	2.90832			0.116519
$624$	22.1467	+	2.10296i	0.886579	+	0.0841858i
$625$	−10.1257			−0.405029
$626$	19.1826	+	13.3911i	0.766693	+	0.535217i
$627$	10.8821	−	10.6005i	0.434590	−	0.423343i
$628$	7.16755	+	19.5193i	0.286016	+	0.778905i
$629$			12.7157i			0.507007i
$630$	−8.48428	+	11.4992i	−0.338022	+	0.458139i
$631$		−	35.8355i		−	1.42659i	−0.700864	−	0.713295i	$-0.747202\pi$
$631$		−	35.8355i		−	1.42659i	0.700864	−	0.713295i	$-0.252798\pi$
$632$	−19.1846	−	5.05266i	−0.763124	−	0.200984i
$633$	−5.70156	+	5.55401i	−0.226617	+	0.220752i
$634$	9.07680	−	13.0024i	0.360486	−	0.516392i
$635$	41.3218			1.63981
$636$	26.2816	+	12.5851i	1.04213	+	0.499032i
$637$	−19.4652			−0.771240
$638$	15.0597	−	21.5728i	0.596217	−	0.854076i
$639$	0.948265	−	36.1604i	0.0375128	−	1.43048i
$640$	−35.4941	+	16.9845i	−1.40303	+	0.671371i
$641$		−	1.09239i		−	0.0431470i	−0.999767	−	0.0215735i	$-0.993132\pi$
$641$		−	1.09239i		−	0.0431470i	0.999767	−	0.0215735i	$-0.00686759\pi$
$642$	0.354962	+	2.16039i	0.0140092	+	0.0852636i
$643$		−	2.35877i		−	0.0930209i	−0.998918	−	0.0465104i	$-0.985190\pi$
$643$		−	2.35877i		−	0.0930209i	0.998918	−	0.0465104i	$-0.0148101\pi$
$644$	1.81822	−	0.667657i	0.0716480	−	0.0263094i
$645$	6.89758	+	7.08083i	0.271592	+	0.278807i
$646$	−5.92031	−	4.13288i	−0.232932	−	0.162606i
$647$	29.6773			1.16673			0.583367	−	0.812209i	$-0.301735\pi$
$647$	29.6773			1.16673			0.583367	+	0.812209i	$0.301735\pi$
$648$	7.76449	−	24.2428i	0.305018	−	0.952347i
$649$	2.70748			0.106278
$650$	26.4223	+	18.4450i	1.03637	+	0.723474i
$651$	1.55642	+	1.59777i	0.0610010	+	0.0626216i
$652$	10.6209	−	3.90002i	0.415946	−	0.152737i
$653$			24.5837i			0.962036i	0.876711	+	0.481018i	$0.159733\pi$
$653$			24.5837i			0.962036i	−0.876711	+	0.481018i	$0.840267\pi$
$654$	6.50823	+	39.6107i	0.254492	+	1.54890i
$655$		−	68.6079i		−	2.68073i
$656$	−19.6740	−	23.1768i	−0.768140	−	0.904902i
$657$	−0.347691	+	13.2586i	−0.0135647	+	0.517267i
$658$	−9.94722	+	14.2493i	−0.387783	+	0.555495i
$659$	−17.1318			−0.667360			−0.333680	−	0.942686i	$-0.608290\pi$
$659$	−17.1318			−0.667360			−0.333680	+	0.942686i	$0.608290\pi$
$660$	23.6134	+	11.3074i	0.919149	+	0.440140i
$661$	−14.2786			−0.555372			−0.277686	−	0.960672i	$-0.589568\pi$
$661$	−14.2786			−0.555372			−0.277686	+	0.960672i	$0.589568\pi$
$662$	8.75674	−	12.5439i	0.340340	−	0.487534i
$663$	−5.03918	+	4.90876i	−0.195705	+	0.190641i
$664$	6.02358	−	22.8712i	0.233760	−	0.887574i
$665$		−	13.5951i		−	0.527196i
$666$	25.3215	−	34.3196i	0.981190	−	1.32986i
$667$			8.56092i			0.331480i
$668$	−9.97003	−	27.1513i	−0.385752	−	1.05051i
$669$	23.6173	−	23.0061i	0.913097	−	0.889466i
$670$	56.8718	+	39.7013i	2.19715	+	1.53380i
$671$	11.4799			0.443178
$672$	6.14276	−	7.23238i	0.236962	−	0.278995i
$673$	49.5003			1.90809			0.954047	−	0.299656i	$-0.0968719\pi$
$673$	49.5003			1.90809			0.954047	+	0.299656i	$0.0968719\pi$
$674$	−27.5048	−	19.2007i	−1.05944	−	0.739582i
$675$	27.0777	−	25.0275i	1.04222	−	0.963311i
$676$	−1.85419	−	5.04950i	−0.0713151	−	0.194212i
$677$			27.9706i			1.07500i	0.843265	+	0.537499i	$0.180631\pi$
$677$			27.9706i			1.07500i	−0.843265	+	0.537499i	$0.819369\pi$
$678$	26.8659	−	4.41420i	1.03178	−	0.169527i
$679$		−	9.38410i		−	0.360129i
$680$	3.16904	−	12.0327i	0.121527	−	0.461432i
$681$	3.51894	+	3.61243i	0.134846	+	0.138429i
$682$	2.33916	−	3.35083i	0.0895711	−	0.128310i
$683$	−6.90440			−0.264190			−0.132095	−	0.991237i	$-0.542170\pi$
$683$	−6.90440			−0.264190			−0.132095	+	0.991237i	$0.542170\pi$
$684$	7.74887	+	22.9442i	0.296285	+	0.877292i
$685$	17.6950			0.676090
$686$	−10.2404	+	14.6693i	−0.390980	+	0.560076i
$687$	−15.5656	−	15.9792i	−0.593865	−	0.609643i
$688$	−4.24775	−	5.00403i	−0.161944	−	0.190777i
$689$			27.0103i			1.02901i
$690$	−8.40648	+	1.38123i	−0.320029	+	0.0525824i
$691$		−	22.9606i		−	0.873464i	−0.899592	−	0.436732i	$-0.856136\pi$
$691$		−	22.9606i		−	0.873464i	0.899592	−	0.436732i	$-0.143864\pi$
$692$	9.75516	−	3.58213i	0.370836	−	0.136172i
$693$	−6.31146	−	0.165511i	−0.239753	−	0.00628723i
$694$	24.4002	+	17.0334i	0.926219	+	0.646579i
$695$	5.91302			0.224294
$696$	20.6483	+	36.5047i	0.782672	+	1.38371i
$697$	9.61362			0.364142
$698$	6.16318	+	4.30242i	0.233280	+	0.162849i
$699$	−8.81908	+	8.59084i	−0.333568	+	0.324935i
$700$	12.9023	−	4.73777i	0.487662	−	0.179071i
$701$			5.56795i			0.210299i	0.994456	+	0.105149i	$0.0335321\pi$
$701$			5.56795i			0.210299i	−0.994456	+	0.105149i	$0.966468\pi$
$702$	23.3759	−	3.21392i	0.882267	−	0.121302i
$703$			40.5749i			1.53031i
$704$	−15.1293	−	8.56316i	−0.570206	−	0.322736i
$705$	54.7501	−	53.3331i	2.06201	−	2.00864i
$706$	3.86724	−	5.53979i	0.145546	−	0.208493i
$707$	−9.41004			−0.353901
$708$	−1.86405	+	3.89272i	−0.0700553	+	0.146297i
$709$	−20.8573			−0.783312			−0.391656	−	0.920112i	$-0.628098\pi$
$709$	−20.8573			−0.783312			−0.391656	+	0.920112i	$0.628098\pi$
$710$	−33.9473	+	48.6292i	−1.27402	+	1.82502i
$711$	−21.0350	−	0.551619i	−0.788876	−	0.0206873i
$712$	8.21373	+	2.16325i	0.307823	+	0.0810712i
$713$			1.32974i			0.0497990i
$714$	0.486500	+	2.96096i	0.0182068	+	0.110811i
$715$			24.2680i			0.907573i
$716$	−1.07787	−	2.93536i	−0.0402820	−	0.109699i
$717$	−9.11731	−	9.35954i	−0.340492	−	0.349538i
$718$	−2.69046	−	1.87817i	−0.100407	−	0.0700927i
$719$	7.25040			0.270394			0.135197	−	0.990819i	$-0.456833\pi$
$719$	7.25040			0.270394			0.135197	+	0.990819i	$0.456833\pi$
$720$	−32.5147	+	26.1655i	−1.21175	+	0.975131i
$721$	−10.4774			−0.390200
$722$	3.14125	+	2.19286i	0.116905	+	0.0816098i
$723$	35.3171	+	36.2554i	1.31346	+	1.34835i
$724$	5.26850	+	14.3477i	0.195802	+	0.533226i
$725$			60.7493i			2.25617i
$726$	−2.49314	−	15.1739i	−0.0925291	−	0.563155i
$727$			23.1133i			0.857226i	0.903488	+	0.428613i	$0.140998\pi$
$727$			23.1133i			0.857226i	−0.903488	+	0.428613i	$0.859002\pi$
$728$	8.50559	+	2.24012i	0.315238	+	0.0830242i
$729$	2.12145	−	26.9165i	0.0785723	−	0.996908i
$730$	12.4471	−	17.8304i	0.460689	−	0.659932i
$731$	2.07565			0.0767705
$732$	−7.90372	+	16.5054i	−0.292130	+	0.610058i
$733$	−16.3066			−0.602298			−0.301149	−	0.953577i	$-0.597370\pi$
$733$	−16.3066			−0.602298			−0.301149	+	0.953577i	$0.597370\pi$
$734$	4.07070	−	5.83124i	0.150252	−	0.215235i
$735$	26.1583	−	25.4813i	0.964862	−	0.939892i
$736$	5.63167	−	0.533190i	0.207586	−	0.0196536i
$737$			30.6433i			1.12876i
$738$	−25.9472	−	19.1442i	−0.955130	−	0.704709i
$739$			0.249325i			0.00917157i	0.999989	+	0.00458578i	$0.00145971\pi$
$739$			0.249325i			0.00917157i	−0.999989	+	0.00458578i	$0.998540\pi$
$740$	−65.6399	+	24.1032i	−2.41297	+	0.886050i
$741$	−16.0797	+	15.6636i	−0.590703	+	0.575416i
$742$	9.44686	+	6.59471i	0.346805	+	0.242099i
$743$	−5.26258			−0.193065			−0.0965327	−	0.995330i	$-0.530775\pi$
$743$	−5.26258			−0.193065			−0.0965327	+	0.995330i	$0.530775\pi$
$744$	3.20723	+	5.67014i	0.117583	+	0.207877i
$745$	−13.1292			−0.481016
$746$	−2.86799	−	2.00210i	−0.105005	−	0.0733021i
$747$	0.657619	−	25.0772i	0.0240610	−	0.917525i
$748$	5.16052	−	1.89496i	0.188687	−	0.0692866i
$749$			0.865614i			0.0316288i
$750$	−17.6210	+	2.89521i	−0.643426	+	0.105718i
$751$			39.6947i			1.44848i	0.689548	+	0.724240i	$0.257809\pi$
$751$			39.6947i			1.44848i	−0.689548	+	0.724240i	$0.742191\pi$
$752$	−38.6919	+	32.8442i	−1.41095	+	1.19771i
$753$	−10.5681	−	10.8489i	−0.385125	−	0.395357i
$754$	−22.2525	+	31.8765i	−0.810389	+	1.16087i
$755$	68.1521			2.48031
$756$	4.58329	−	8.96044i	0.166693	−	0.325888i
$757$	−33.3186			−1.21098			−0.605492	−	0.795851i	$-0.707024\pi$
$757$	−33.3186			−1.21098			−0.605492	+	0.795851i	$0.707024\pi$
$758$	27.0871	−	38.8020i	0.983847	−	1.40935i
$759$	−2.62634	−	2.69612i	−0.0953301	−	0.0978628i
$760$	10.1122	−	38.3955i	0.366809	−	1.39275i
$761$		−	32.9587i		−	1.19475i	−0.801961	−	0.597376i	$-0.796210\pi$
$761$		−	32.9587i		−	1.19475i	0.801961	−	0.597376i	$-0.203790\pi$
$762$	−28.7176	+	4.71844i	−1.04033	+	0.170931i
$763$			15.8710i			0.574570i
$764$	7.39703	+	20.1443i	0.267615	+	0.728794i
$765$	0.345977	−	13.1932i	0.0125088	−	0.477003i
$766$	−25.3345	−	17.6857i	−0.915374	−	0.639009i
$767$	−4.00064			−0.144455
$768$	22.7280	−	15.8568i	0.820127	−	0.572181i
$769$	−4.87232			−0.175700			−0.0878501	−	0.996134i	$-0.528000\pi$
$769$	−4.87232			−0.175700			−0.0878501	+	0.996134i	$0.528000\pi$
$770$	8.48777	+	5.92518i	0.305878	+	0.213529i
$771$	−5.48416	+	5.34223i	−0.197507	+	0.192396i
$772$	−4.61420	−	12.5658i	−0.166069	−	0.452253i
$773$			31.4066i			1.12962i	0.825222	+	0.564809i	$0.191050\pi$
$773$			31.4066i			1.12962i	−0.825222	+	0.564809i	$0.808950\pi$
$774$	−5.60218	−	4.13337i	−0.201366	−	0.148571i
$775$			9.43597i			0.338950i
$776$	6.98002	−	26.5027i	0.250568	−	0.951392i
$777$	12.0790	−	11.7664i	0.433332	−	0.422117i
$778$	5.06390	−	7.25399i	0.181550	−	0.260068i
$779$	30.6765			1.09910
$780$	−34.8917	−	16.7081i	−1.24932	−	0.598246i
$781$	−26.2021			−0.937584
$782$	−1.02395	+	1.46679i	−0.0366163	+	0.0524525i
$783$	30.1938	+	32.6672i	1.07904	+	1.16743i
$784$	−18.4861	+	15.6922i	−0.660217	+	0.560435i
$785$		−	36.1597i		−	1.29059i
$786$	7.83417	+	47.6807i	0.279436	+	1.70071i
$787$		−	2.31176i		−	0.0824055i	−0.999151	−	0.0412027i	$-0.986881\pi$
$787$		−	2.31176i		−	0.0824055i	0.999151	−	0.0412027i	$-0.0131189\pi$
$788$	−10.8717	+	3.99211i	−0.387287	+	0.142213i
$789$	−7.38637	−	7.58261i	−0.262962	−	0.269948i
$790$	28.2883	+	19.7476i	1.00645	+	0.702589i
$791$	10.7645			0.382743
$792$	−17.7018	−	5.16199i	−0.629007	−	0.183423i
$793$	−16.9630			−0.602375
$794$	34.5892	+	24.1462i	1.22752	+	0.856915i
$795$	−35.3583	−	36.2977i	−1.25403	−	1.28735i
$796$	40.5569	−	14.8926i	1.43750	−	0.527855i
$797$		−	31.0641i		−	1.10035i	−0.835050	−	0.550174i	$-0.814561\pi$
$797$		−	31.0641i		−	1.10035i	0.835050	−	0.550174i	$-0.185439\pi$
$798$	1.55239	+	9.44824i	0.0549541	+	0.334464i
$799$		−	16.0492i		−	0.567780i
$800$	39.9630	−	3.78358i	1.41290	−	0.133770i
$801$	9.00596	+	0.236171i	0.318210	+	0.00834468i
$802$	−14.2657	+	20.4354i	−0.503738	+	0.721600i
$803$	9.60725			0.339032
$804$	−44.0578	−	21.0973i	−1.55380	−	0.744045i
$805$	−3.36827			−0.118716
$806$	−3.45640	+	4.95127i	−0.121747	+	0.174401i
$807$	20.8911	−	20.3504i	0.735400	−	0.716368i
$808$	−26.5760	−	6.99931i	−0.934940	−	0.246235i
$809$			0.108932i			0.00382986i	0.999998	+	0.00191493i	$0.000609542\pi$
$809$			0.108932i			0.00382986i	−0.999998	+	0.00191493i	$0.999390\pi$
$810$	−27.2064	+	34.9197i	−0.955935	+	1.22695i
$811$			8.77168i			0.308015i	0.988070	+	0.154008i	$0.0492181\pi$
$811$			8.77168i			0.308015i	−0.988070	+	0.154008i	$0.950782\pi$
$812$	5.71576	+	15.5657i	0.200584	+	0.546248i
$813$	−24.2103	+	23.5838i	−0.849094	+	0.827119i
$814$	−25.3319	−	17.6838i	−0.887884	−	0.619818i
$815$	−19.6753			−0.689194
$816$	−0.828419	+	8.72425i	−0.0290005	+	0.305410i
$817$	6.62326			0.231718
$818$	−36.3393	−	25.3679i	−1.27057	−	0.886968i
$819$	9.32597	+	0.244563i	0.325876	+	0.00854571i
$820$	18.2231	+	49.6268i	0.636378	+	1.73304i
$821$			5.77012i			0.201379i	0.994918	+	0.100689i	$0.0321048\pi$
$821$			5.77012i			0.201379i	−0.994918	+	0.100689i	$0.967895\pi$
$822$	−12.2975	+	2.02055i	−0.428926	+	0.0704746i
$823$		−	15.1010i		−	0.526388i	−0.964743	−	0.263194i	$-0.915224\pi$
$823$		−	15.1010i		−	0.526388i	0.964743	−	0.263194i	$-0.0847760\pi$
$824$	−29.5906	−	7.79326i	−1.03084	−	0.271491i
$825$	−18.6368	−	19.1320i	−0.648851	−	0.666089i
$826$	−0.976780	+	1.39923i	−0.0339865	+	0.0486854i
$827$	18.2056			0.633070			0.316535	−	0.948581i	$-0.397481\pi$
$827$	18.2056			0.633070			0.316535	+	0.948581i	$0.397481\pi$
$828$	5.68456	−	1.91983i	0.197552	−	0.0667187i
$829$	−5.98714			−0.207942			−0.103971	−	0.994580i	$-0.533155\pi$
$829$	−5.98714			−0.207942			−0.103971	+	0.994580i	$0.533155\pi$
$830$	−23.5424	+	33.7242i	−0.817167	+	1.17058i
$831$	−21.0301	−	21.5889i	−0.729528	−	0.748909i
$832$	22.3554	+	12.6531i	0.775034	+	0.438669i
$833$		−	7.66793i		−	0.265678i
$834$	−4.10939	+	0.675193i	−0.142297	+	0.0233800i
$835$			50.2979i			1.74063i
$836$	16.4669	−	6.04670i	0.569520	−	0.209130i
$837$	4.68990	+	5.07408i	0.162107	+	0.175386i
$838$	10.1165	+	7.06215i	0.349468	+	0.243958i
$839$	15.7901			0.545135			0.272568	−	0.962137i	$-0.412127\pi$
$839$	15.7901			0.545135			0.272568	+	0.962137i	$0.412127\pi$
$840$	−14.3627	+	8.12402i	−0.495559	+	0.280305i
$841$	−44.2894			−1.52722
$842$	9.03276	+	6.30563i	0.311289	+	0.217306i
$843$	33.8300	−	32.9545i	1.16517	−	1.13501i
$844$	−8.62765	+	3.16810i	−0.296976	+	0.109050i
$845$			9.35424i			0.321796i
$846$	−31.9599	+	43.3169i	−1.09880	+	1.48927i
$847$		−	6.07980i		−	0.208904i
$848$	21.7748	+	25.6516i	0.747748	+	0.880879i
$849$	23.1985	−	22.5981i	0.796169	−	0.775564i
$850$	−7.26605	+	10.4085i	−0.249223	+	0.357010i
$851$	10.0527			0.344602
$852$	18.0396	−	37.6724i	0.618027	−	1.29063i
$853$	35.0159			1.19892			0.599460	−	0.800405i	$-0.295382\pi$
$853$	35.0159			1.19892			0.599460	+	0.800405i	$0.295382\pi$
$854$	−4.14162	+	5.93284i	−0.141723	+	0.203018i
$855$	1.10399	−	42.0989i	0.0377558	−	1.43975i
$856$	−0.643855	+	2.44468i	−0.0220065	+	0.0835575i
$857$			0.666549i			0.0227689i	0.999935	+	0.0113844i	$0.00362386\pi$
$857$			0.666549i			0.0227689i	−0.999935	+	0.0113844i	$0.996376\pi$
$858$	−2.77111	−	16.8656i	−0.0946041	−	0.575784i
$859$			49.7997i			1.69914i	0.527473	+	0.849572i	$0.323139\pi$
$859$			49.7997i			1.69914i	−0.527473	+	0.849572i	$0.676861\pi$
$860$	3.93449	+	10.7148i	0.134165	+	0.365370i
$861$	−8.89593	−	9.13228i	−0.303173	−	0.311227i
$862$	−14.1175	−	9.85519i	−0.480843	−	0.335669i
$863$	26.0464			0.886630			0.443315	−	0.896366i	$-0.353802\pi$
$863$	26.0464			0.886630			0.443315	+	0.896366i	$0.353802\pi$
$864$	19.6091	−	21.8971i	0.667115	−	0.744955i
$865$	−18.0715			−0.614450
$866$	40.8113	+	28.4897i	1.38682	+	0.968120i
$867$	18.6122	+	19.1067i	0.632105	+	0.648898i
$868$	0.887808	+	2.41776i	0.0301342	+	0.0820641i
$869$			15.2421i			0.517053i
$870$	−11.8246	−	71.9672i	−0.400890	−	2.43992i
$871$		−	45.2793i		−	1.53423i
$872$	−11.8051	+	44.8233i	−0.399771	+	1.51791i
$873$	0.762037	−	29.0590i	0.0257910	−	0.983497i
$874$	−3.26735	+	4.68045i	−0.110520	+	0.158319i
$875$	−7.06029			−0.238681
$876$	−6.61441	+	13.8130i	−0.223480	+	0.466696i
$877$	−32.8441			−1.10907			−0.554534	−	0.832161i	$-0.687103\pi$
$877$	−32.8441			−1.10907			−0.554534	+	0.832161i	$0.687103\pi$
$878$	14.8940	−	21.3354i	0.502647	−	0.720037i
$879$	−29.0840	+	28.3313i	−0.980978	+	0.955590i
$880$	19.5641	+	23.0473i	0.659505	+	0.776925i
$881$		−	32.7570i		−	1.10361i	−0.833973	−	0.551806i	$-0.813939\pi$
$881$		−	32.7570i		−	1.10361i	0.833973	−	0.551806i	$-0.186061\pi$
$882$	−15.2697	+	20.6958i	−0.514156	+	0.696863i
$883$		−	6.19776i		−	0.208571i	−0.994547	−	0.104286i	$-0.966744\pi$
$883$		−	6.19776i		−	0.208571i	0.994547	−	0.104286i	$-0.0332556\pi$
$884$	−7.62532	+	2.80004i	−0.256467	+	0.0941755i
$885$	5.37625	−	5.23711i	0.180721	−	0.176044i
$886$	11.7282	+	8.18730i	0.394018	+	0.275058i
$887$	−4.08365			−0.137116			−0.0685578	−	0.997647i	$-0.521840\pi$
$887$	−4.08365			−0.137116			−0.0685578	+	0.997647i	$0.521840\pi$
$888$	42.8657	−	24.2463i	1.43848	−	0.813654i
$889$	−11.5064			−0.385913
$890$	−12.1114	−	8.45477i	−0.405974	−	0.283405i
$891$	−19.5308	−	1.02505i	−0.654305	−	0.0343404i
$892$	35.7378	−	13.1230i	1.19659	−	0.439392i
$893$		−	51.2121i		−	1.71375i
$894$	9.12443	−	1.49919i	0.305166	−	0.0501403i
$895$			5.43777i			0.181765i
$896$	9.88365	−	4.72948i	0.330189	−	0.158001i
$897$	3.88075	+	3.98385i	0.129574	+	0.133017i
$898$	−6.08651	+	8.71887i	−0.203109	+	0.290952i
$899$	−11.3838			−0.379670
$900$	40.3383	−	13.6233i	1.34461	−	0.454111i
$901$	−10.6402			−0.354475
$902$	−13.3698	+	19.1521i	−0.445165	+	0.637695i
$903$	−1.92069	−	1.97172i	−0.0639166	−	0.0656147i
$904$	30.4014	+	8.00680i	1.01113	+	0.266302i
$905$		−	26.5791i		−	0.883520i
$906$	−47.3639	+	7.78212i	−1.57356	+	0.258544i
$907$			1.12490i			0.0373518i	0.999826	+	0.0186759i	$0.00594507\pi$
$907$			1.12490i			0.0373518i	−0.999826	+	0.0186759i	$0.994055\pi$
$908$	2.00726	+	5.46636i	0.0666134	+	0.181407i
$909$	−29.1393	−	0.764144i	−0.966490	−	0.0253450i
$910$	−12.5417	−	8.75520i	−0.415755	−	0.290232i
$911$	−34.1959			−1.13296			−0.566480	−	0.824076i	$-0.691695\pi$
$911$	−34.1959			−1.13296			−0.566480	+	0.824076i	$0.691695\pi$
$912$	−2.64344	+	27.8386i	−0.0875329	+	0.921827i
$913$	−18.1711			−0.601374
$914$	−2.41840	−	1.68825i	−0.0799936	−	0.0558423i
$915$	22.7957	−	22.2058i	0.753604	−	0.734100i
$916$	−8.87888	−	24.1798i	−0.293367	−	0.798922i
$917$			19.1045i			0.630886i
$918$	1.26606	+	9.20847i	0.0417862	+	0.303925i
$919$			23.3449i			0.770077i	0.922900	+	0.385039i	$0.125812\pi$
$919$			23.3449i			0.770077i	−0.922900	+	0.385039i	$0.874188\pi$
$920$	−9.51273	−	2.50537i	−0.313625	−	0.0825995i
$921$	−7.45060	+	7.25778i	−0.245506	+	0.239152i
$922$	12.7722	−	18.2961i	0.420630	−	0.602548i
$923$	38.7168			1.27438
$924$	−6.57535	−	3.14865i	−0.216313	−	0.103583i
$925$	71.3350			2.34548
$926$	2.06496	−	2.95803i	0.0678587	−	0.0972069i
$927$	−32.4446	−	0.850822i	−1.06562	−	0.0279447i
$928$	4.56460	+	48.2123i	0.149840	+	1.58265i
$929$			37.2985i			1.22372i	0.790964	+	0.611862i	$0.209579\pi$
$929$			37.2985i			1.22372i	−0.790964	+	0.611862i	$0.790421\pi$
$930$	−1.83667	−	11.1784i	−0.0602267	−	0.366554i
$931$		−	24.4679i		−	0.801903i
$932$	−13.3451	+	4.90036i	−0.437133	+	0.160517i
$933$	25.8306	+	26.5169i	0.845657	+	0.868124i
$934$	38.7514	+	27.0518i	1.26799	+	0.885162i
$935$	−9.55991			−0.312642
$936$	26.1567	+	7.62748i	0.854957	+	0.249312i
$937$	2.97285			0.0971187			0.0485594	−	0.998820i	$-0.484537\pi$
$937$	2.97285			0.0971187			0.0485594	+	0.998820i	$0.484537\pi$
$938$	−15.8365	−	11.0552i	−0.517078	−	0.360965i
$939$	19.9928	+	20.5239i	0.652440	+	0.669774i
$940$	82.8482	−	30.4221i	2.70221	−	0.992259i
$941$		−	11.8277i		−	0.385574i	−0.981241	−	0.192787i	$-0.938247\pi$
$941$		−	11.8277i		−	0.385574i	0.981241	−	0.192787i	$-0.0617526\pi$
$942$	4.12898	+	25.1300i	0.134530	+	0.818780i
$943$		−	7.60029i		−	0.247499i
$944$	−3.79940	+	3.22518i	−0.123660	+	0.104971i
$945$	−12.8528	+	11.8797i	−0.418103	+	0.386446i
$946$	−2.88663	+	4.13507i	−0.0938523	+	0.134443i
$947$	−57.2763			−1.86123			−0.930614	−	0.366001i	$-0.880727\pi$
$947$	−57.2763			−1.86123			−0.930614	+	0.366001i	$0.880727\pi$
$948$	−21.9146	−	10.4939i	−0.711752	−	0.340826i
$949$	−14.1959			−0.460819
$950$	−23.1855	+	33.2130i	−0.752237	+	1.07757i
$951$	13.9116	−	13.5516i	0.451114	−	0.439439i
$952$	−0.882448	+	3.35061i	−0.0286003	+	0.108594i
$953$		−	6.33817i		−	0.205313i	−0.994717	−	0.102657i	$-0.967266\pi$
$953$		−	6.33817i		−	0.205313i	0.994717	−	0.102657i	$-0.0327343\pi$
$954$	28.7178	+	21.1884i	0.929773	+	0.686001i
$955$		−	37.3174i		−	1.20756i
$956$	−5.20067	−	14.1629i	−0.168202	−	0.458062i
$957$	23.0812	−	22.4839i	0.746111	−	0.726801i
$958$	−45.3879	−	31.6846i	−1.46642	−	1.02368i
$959$	−4.92732			−0.159112
$960$	−46.6061	+	12.2609i	−1.50420	+	0.395717i
$961$	29.2318			0.942961
$962$	37.4311	+	26.1301i	1.20683	+	0.842467i
$963$	−0.0702923	+	2.68048i	−0.00226514	+	0.0863771i
$964$	20.1455	+	54.8620i	0.648842	+	1.76698i
$965$			23.2782i			0.749352i
$966$	2.34086	−	0.384615i	0.0753159	−	0.0123748i
$967$			33.4403i			1.07537i	0.843147	+	0.537683i	$0.180700\pi$
$967$			33.4403i			1.07537i	−0.843147	+	0.537683i	$0.819300\pi$
$968$	4.52224	−	17.1707i	0.145350	−	0.551886i
$969$	−6.17035	−	6.33428i	−0.198220	−	0.203486i
$970$	−27.2805	+	39.0790i	−0.875923	+	1.25475i
$971$	4.33228			0.139029			0.0695147	−	0.997581i	$-0.477855\pi$
$971$	4.33228			0.139029			0.0695147	+	0.997581i	$0.477855\pi$
$972$	14.9203	−	27.3749i	0.478570	−	0.878050i
$973$	−1.64653			−0.0527854
$974$	17.4027	−	24.9292i	0.557619	−	0.798785i
$975$	27.5382	+	28.2699i	0.881929	+	0.905360i
$976$	−16.1098	+	13.6750i	−0.515661	+	0.437727i
$977$		−	46.2330i		−	1.47913i	−0.673087	−	0.739563i	$-0.735032\pi$
$977$		−	46.2330i		−	1.47913i	0.673087	−	0.739563i	$-0.264968\pi$
$978$	13.6738	−	2.24667i	0.437239	−	0.0718406i
$979$		−	6.52577i		−	0.208565i
$980$	39.5829	−	14.5350i	1.26443	−	0.464302i
$981$	−1.28881	+	49.1466i	−0.0411486	+	1.56913i
$982$	−14.9778	−	10.4558i	−0.477961	−	0.333657i
$983$	−10.8968			−0.347553			−0.173777	−	0.984785i	$-0.555597\pi$
$983$	−10.8968			−0.347553			−0.173777	+	0.984785i	$0.555597\pi$
$984$	−18.3313	−	32.4084i	−0.584382	−	1.03314i
$985$	20.1398			0.641708
$986$	−12.5571	−	8.76593i	−0.399900	−	0.279164i
$987$	−15.2456	+	14.8511i	−0.485274	+	0.472715i
$988$	−24.3319	+	8.93476i	−0.774102	+	0.284253i
$989$		−	1.64095i		−	0.0521793i
$990$	25.8022	+	19.0373i	0.820048	+	0.605044i
$991$			50.1034i			1.59159i	0.605568	+	0.795794i	$0.292946\pi$
$991$			50.1034i			1.59159i	−0.605568	+	0.795794i	$0.707054\pi$
$992$	0.709002	+	7.48864i	0.0225108	+	0.237765i
$993$	13.4210	−	13.0737i	0.425904	−	0.414882i
$994$	9.45293	−	13.5412i	0.299829	−	0.429502i
$995$	−75.1319			−2.38184
$996$	12.5104	−	26.1257i	0.396408	−	0.827824i
$997$	−11.2113			−0.355066			−0.177533	−	0.984115i	$-0.556812\pi$
$997$	−11.2113			−0.355066			−0.177533	+	0.984115i	$0.556812\pi$
$998$	−0.259148	+	0.371227i	−0.00820318	+	0.0117510i
$999$	38.3596	−	35.4552i	1.21364	−	1.12175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.b.47.18	yes	22
3.2	odd	2		276.2.c.a.47.5	✓	22
4.3	odd	2		276.2.c.a.47.6	yes	22
12.11	even	2	inner	276.2.c.b.47.17	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.5	✓	22	3.2	odd	2
276.2.c.a.47.6	yes	22	4.3	odd	2
276.2.c.b.47.17	yes	22	12.11	even	2	inner
276.2.c.b.47.18	yes	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15961 + 0.809507i) q^{2} +(1.20859 + 1.24069i) q^{3} +(0.689397 + 1.87743i) q^{4} -3.47795i q^{5} +(0.397138 + 2.41708i) q^{6} +0.968466i q^{7} +(-0.720358 + 2.73516i) q^{8} +(-0.0786444 + 2.99897i) q^{9} +O(q^{10})\)	\(q+(1.15961 + 0.809507i) q^{2} +(1.20859 + 1.24069i) q^{3} +(0.689397 + 1.87743i) q^{4} -3.47795i q^{5} +(0.397138 + 2.41708i) q^{6} +0.968466i q^{7} +(-0.720358 + 2.73516i) q^{8} +(-0.0786444 + 2.99897i) q^{9} +(2.81542 - 4.03307i) q^{10} +2.17307 q^{11} +(-1.49612 + 3.12436i) q^{12} -3.21098 q^{13} +(-0.783980 + 1.12304i) q^{14} +(4.31507 - 4.20339i) q^{15} +(-3.04946 + 2.58858i) q^{16} -1.26490i q^{17} +(-2.51888 + 3.41398i) q^{18} -4.03623i q^{19} +(6.52959 - 2.39769i) q^{20} +(-1.20157 + 1.17047i) q^{21} +(2.51992 + 1.75912i) q^{22} -1.00000 q^{23} +(-4.26411 + 2.41193i) q^{24} -7.09612 q^{25} +(-3.72349 - 2.59931i) q^{26} +(-3.81585 + 3.52694i) q^{27} +(-1.81822 + 0.667657i) q^{28} -8.56092i q^{29} +(8.40648 - 1.38123i) q^{30} -1.32974i q^{31} +(-5.63167 + 0.533190i) q^{32} +(2.62634 + 2.69612i) q^{33} +(1.02395 - 1.46679i) q^{34} +3.36827 q^{35} +(-5.68456 + 1.91983i) q^{36} -10.0527 q^{37} +(3.26735 - 4.68045i) q^{38} +(-3.88075 - 3.98385i) q^{39} +(9.51273 + 2.50537i) q^{40} +7.60029i q^{41} +(-2.34086 + 0.384615i) q^{42} +1.64095i q^{43} +(1.49811 + 4.07978i) q^{44} +(10.4303 + 0.273521i) q^{45} +(-1.15961 - 0.809507i) q^{46} +12.6881 q^{47} +(-6.89718 - 0.654928i) q^{48} +6.06207 q^{49} +(-8.22874 - 5.74436i) q^{50} +(1.56936 - 1.52874i) q^{51} +(-2.21364 - 6.02839i) q^{52} -8.41184i q^{53} +(-7.27998 + 1.00092i) q^{54} -7.55782i q^{55} +(-2.64891 - 0.697642i) q^{56} +(5.00772 - 4.87812i) q^{57} +(6.93013 - 9.92734i) q^{58} +1.24592 q^{59} +(10.8664 + 5.20342i) q^{60} +5.28282 q^{61} +(1.07643 - 1.54198i) q^{62} +(-2.90440 - 0.0761644i) q^{63} +(-6.96217 - 3.94058i) q^{64} +11.1676i q^{65} +(0.863009 + 5.25249i) q^{66} +14.1014i q^{67} +(2.37476 - 0.872019i) q^{68} +(-1.20859 - 1.24069i) q^{69} +(3.90589 + 2.72664i) q^{70} -12.0576 q^{71} +(-8.14600 - 2.37544i) q^{72} +4.42105 q^{73} +(-11.6572 - 8.13772i) q^{74} +(-8.57626 - 8.80411i) q^{75} +(7.57772 - 2.78256i) q^{76} +2.10454i q^{77} +(-1.27520 - 7.76121i) q^{78} +7.01409i q^{79} +(9.00296 + 10.6059i) q^{80} +(-8.98763 - 0.471704i) q^{81} +(-6.15249 + 8.81338i) q^{82} -8.36193 q^{83} +(-3.02584 - 1.44894i) q^{84} -4.39926 q^{85} +(-1.32836 + 1.90287i) q^{86} +(10.6215 - 10.3466i) q^{87} +(-1.56539 + 5.94369i) q^{88} -3.00302i q^{89} +(11.8736 + 8.76054i) q^{90} -3.10973i q^{91} +(-0.689397 - 1.87743i) q^{92} +(1.64980 - 1.60710i) q^{93} +(14.7133 + 10.2711i) q^{94} -14.0378 q^{95} +(-7.46788 - 6.34278i) q^{96} -9.68965 q^{97} +(7.02965 + 4.90729i) q^{98} +(-0.170900 + 6.51697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q + 9 * q^8 - 2 * q^9	\( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more