LMFDB - Embedded newform 1110.2.u.e.191.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (of order $4$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.17
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.912132 + 1.47242i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.396182 + 1.68613i) q^{6} +0.363832 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33603 + 2.68608i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.912132 + 1.47242i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.396182 + 1.68613i) q^{6} +0.363832 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33603 + 2.68608i) q^{9} +1.00000 q^{10} -1.23669 q^{11} +(-1.47242 + 0.912132i) q^{12} +(2.54719 + 2.54719i) q^{13} +(0.257268 + 0.257268i) q^{14} +(1.68613 + 0.396182i) q^{15} -1.00000 q^{16} +(-2.79453 + 2.79453i) q^{17} +(-2.84406 + 0.954629i) q^{18} +(1.40229 + 1.40229i) q^{19} +(0.707107 + 0.707107i) q^{20} +(0.331863 + 0.535713i) q^{21} +(-0.874474 - 0.874474i) q^{22} +(-0.456993 + 0.456993i) q^{23} +(-1.68613 - 0.396182i) q^{24} -1.00000i q^{25} +3.60228i q^{26} +(-5.17367 + 0.482863i) q^{27} +0.363832i q^{28} +(1.61230 + 1.61230i) q^{29} +(0.912132 + 1.47242i) q^{30} +(0.163461 - 0.163461i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.12803 - 1.82093i) q^{33} -3.95206 q^{34} +(0.257268 - 0.257268i) q^{35} +(-2.68608 - 1.33603i) q^{36} +(5.07126 + 3.35892i) q^{37} +1.98313i q^{38} +(-1.42716 + 6.07391i) q^{39} +1.00000i q^{40} +0.545166 q^{41} +(-0.144144 + 0.613469i) q^{42} +(4.75447 + 4.75447i) q^{43} -1.23669i q^{44} +(0.954629 + 2.84406i) q^{45} -0.646286 q^{46} +1.60456i q^{47} +(-0.912132 - 1.47242i) q^{48} -6.86763 q^{49} +(0.707107 - 0.707107i) q^{50} +(-6.66370 - 1.56574i) q^{51} +(-2.54719 + 2.54719i) q^{52} -8.02046i q^{53} +(-3.99977 - 3.31690i) q^{54} +(-0.874474 + 0.874474i) q^{55} +(-0.257268 + 0.257268i) q^{56} +(-0.785681 + 3.34382i) q^{57} +2.28014i q^{58} +(6.45749 - 6.45749i) q^{59} +(-0.396182 + 1.68613i) q^{60} +(2.60993 - 2.60993i) q^{61} +0.231169 q^{62} +(-0.486091 + 0.977282i) q^{63} -1.00000i q^{64} +3.60228 q^{65} +(0.489956 - 2.08523i) q^{66} +4.94984i q^{67} +(-2.79453 - 2.79453i) q^{68} +(-1.08972 - 0.256047i) q^{69} +0.363832 q^{70} -14.8100i q^{71} +(-0.954629 - 2.84406i) q^{72} +1.60743i q^{73} +(1.21080 + 5.96104i) q^{74} +(1.47242 - 0.912132i) q^{75} +(-1.40229 + 1.40229i) q^{76} -0.449949 q^{77} +(-5.30406 + 3.28575i) q^{78} +(2.32156 + 2.32156i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-5.43004 - 7.17737i) q^{81} +(0.385490 + 0.385490i) q^{82} -8.43976i q^{83} +(-0.535713 + 0.331863i) q^{84} +3.95206i q^{85} +6.72384i q^{86} +(-0.903350 + 3.84461i) q^{87} +(0.874474 - 0.874474i) q^{88} +(0.550261 + 0.550261i) q^{89} +(-1.33603 + 2.68608i) q^{90} +(0.926751 + 0.926751i) q^{91} +(-0.456993 - 0.456993i) q^{92} +(0.389781 + 0.0915850i) q^{93} +(-1.13460 + 1.13460i) q^{94} +1.98313 q^{95} +(0.396182 - 1.68613i) q^{96} +(-0.870659 - 0.870659i) q^{97} +(-4.85614 - 4.85614i) q^{98} +(1.65226 - 3.32185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.912132	+	1.47242i	0.526620	+	0.850101i
$3$	0.912132	+	1.47242i	0.526620	+	0.850101i
$4$			1.00000i			0.500000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.396182	+	1.68613i	−0.161741	+	0.688360i
$7$	0.363832			0.137516			0.0687578	−	0.997633i	$-0.478096\pi$
$7$	0.363832			0.137516			0.0687578	+	0.997633i	$0.478096\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.33603	+	2.68608i	−0.445344	+	0.895360i
$10$	1.00000			0.316228
$11$	−1.23669			−0.372877			−0.186438	−	0.982467i	$-0.559694\pi$
$11$	−1.23669			−0.372877			−0.186438	+	0.982467i	$0.559694\pi$
$12$	−1.47242	+	0.912132i	−0.425051	+	0.263310i
$13$	2.54719	+	2.54719i	0.706464	+	0.706464i	0.965790	−	0.259326i	$-0.0835002\pi$
$13$	2.54719	+	2.54719i	0.706464	+	0.706464i	−0.259326	+	0.965790i	$0.583500\pi$
$14$	0.257268	+	0.257268i	0.0687578	+	0.0687578i
$15$	1.68613	+	0.396182i	0.435357	+	0.102294i
$16$	−1.00000			−0.250000
$17$	−2.79453	+	2.79453i	−0.677773	+	0.677773i	−0.959496	−	0.281723i	$-0.909094\pi$
$17$	−2.79453	+	2.79453i	−0.677773	+	0.677773i	0.281723	+	0.959496i	$0.409094\pi$
$18$	−2.84406	+	0.954629i	−0.670352	+	0.225008i
$19$	1.40229	+	1.40229i	0.321706	+	0.321706i	0.849421	−	0.527715i	$-0.176951\pi$
$19$	1.40229	+	1.40229i	0.321706	+	0.321706i	−0.527715	+	0.849421i	$0.676951\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	0.331863	+	0.535713i	0.0724184	+	0.116902i
$22$	−0.874474	−	0.874474i	−0.186438	−	0.186438i
$23$	−0.456993	+	0.456993i	−0.0952897	+	0.0952897i	−0.753145	−	0.657855i	$-0.771464\pi$
$23$	−0.456993	+	0.456993i	−0.0952897	+	0.0952897i	0.657855	+	0.753145i	$0.271464\pi$
$24$	−1.68613	−	0.396182i	−0.344180	−	0.0808704i
$25$		−	1.00000i		−	0.200000i
$26$			3.60228i			0.706464i
$27$	−5.17367	+	0.482863i	−0.995673	+	0.0929270i
$28$			0.363832i			0.0687578i
$29$	1.61230	+	1.61230i	0.299397	+	0.299397i	0.840778	−	0.541381i	$-0.182098\pi$
$29$	1.61230	+	1.61230i	0.299397	+	0.299397i	−0.541381	+	0.840778i	$0.682098\pi$
$30$	0.912132	+	1.47242i	0.166532	+	0.268826i
$31$	0.163461	−	0.163461i	0.0293585	−	0.0293585i	−0.692275	−	0.721634i	$-0.743392\pi$
$31$	0.163461	−	0.163461i	0.0293585	−	0.0293585i	0.721634	+	0.692275i	$0.243392\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.12803	−	1.82093i	−0.196364	−	0.316983i
$34$	−3.95206			−0.677773
$35$	0.257268	−	0.257268i	0.0434863	−	0.0434863i
$36$	−2.68608	−	1.33603i	−0.447680	−	0.222672i
$37$	5.07126	+	3.35892i	0.833709	+	0.552204i
$37$	5.07126	+	3.35892i	0.833709	+	0.552204i
$38$			1.98313i			0.321706i
$39$	−1.42716	+	6.07391i	−0.228528	+	0.972604i
$40$			1.00000i			0.158114i
$41$	0.545166			0.0851406			0.0425703	−	0.999093i	$-0.486445\pi$
$41$	0.545166			0.0851406			0.0425703	+	0.999093i	$0.486445\pi$
$42$	−0.144144	+	0.613469i	−0.0222419	+	0.0946603i
$43$	4.75447	+	4.75447i	0.725050	+	0.725050i	0.969629	−	0.244579i	$-0.0786498\pi$
$43$	4.75447	+	4.75447i	0.725050	+	0.725050i	−0.244579	+	0.969629i	$0.578650\pi$
$44$		−	1.23669i		−	0.186438i
$45$	0.954629	+	2.84406i	0.142308	+	0.423968i
$46$	−0.646286			−0.0952897
$47$			1.60456i			0.234049i	0.993129	+	0.117025i	$0.0373357\pi$
$47$			1.60456i			0.234049i	−0.993129	+	0.117025i	$0.962664\pi$
$48$	−0.912132	−	1.47242i	−0.131655	−	0.212525i
$49$	−6.86763			−0.981089
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	−6.66370	−	1.56574i	−0.933105	−	0.219247i
$52$	−2.54719	+	2.54719i	−0.353232	+	0.353232i
$53$		−	8.02046i		−	1.10169i	−0.834606	−	0.550847i	$-0.814305\pi$
$53$		−	8.02046i		−	1.10169i	0.834606	−	0.550847i	$-0.185695\pi$
$54$	−3.99977	−	3.31690i	−0.544300	−	0.451373i
$55$	−0.874474	+	0.874474i	−0.117914	+	0.117914i
$56$	−0.257268	+	0.257268i	−0.0343789	+	0.0343789i
$57$	−0.785681	+	3.34382i	−0.104066	+	0.442900i
$58$			2.28014i			0.299397i
$59$	6.45749	−	6.45749i	0.840694	−	0.840694i	−0.148255	−	0.988949i	$-0.547366\pi$
$59$	6.45749	−	6.45749i	0.840694	−	0.840694i	0.988949	+	0.148255i	$0.0473657\pi$
$60$	−0.396182	+	1.68613i	−0.0511469	+	0.217679i
$61$	2.60993	−	2.60993i	0.334167	−	0.334167i	−0.520000	−	0.854167i	$-0.674068\pi$
$61$	2.60993	−	2.60993i	0.334167	−	0.334167i	0.854167	+	0.520000i	$0.174068\pi$
$62$	0.231169			0.0293585
$63$	−0.486091	+	0.977282i	−0.0612417	+	0.123126i
$64$		−	1.00000i		−	0.125000i
$65$	3.60228			0.446807
$66$	0.489956	−	2.08523i	0.0603094	−	0.256674i
$67$			4.94984i			0.604719i	0.953194	+	0.302359i	$0.0977743\pi$
$67$			4.94984i			0.604719i	−0.953194	+	0.302359i	$0.902226\pi$
$68$	−2.79453	−	2.79453i	−0.338887	−	0.338887i
$69$	−1.08972	−	0.256047i	−0.131187	−	0.0308244i
$70$	0.363832			0.0434863
$71$		−	14.8100i		−	1.75762i	−0.477174	−	0.878809i	$-0.658339\pi$
$71$		−	14.8100i		−	1.75762i	0.477174	−	0.878809i	$-0.341661\pi$
$72$	−0.954629	−	2.84406i	−0.112504	−	0.335176i
$73$			1.60743i			0.188135i	0.995566	+	0.0940675i	$0.0299869\pi$
$73$			1.60743i			0.188135i	−0.995566	+	0.0940675i	$0.970013\pi$
$74$	1.21080	+	5.96104i	0.140753	+	0.692956i
$75$	1.47242	−	0.912132i	0.170020	−	0.105324i
$76$	−1.40229	+	1.40229i	−0.160853	+	0.160853i
$77$	−0.449949			−0.0512764
$78$	−5.30406	+	3.28575i	−0.600566	+	0.372038i
$79$	2.32156	+	2.32156i	0.261196	+	0.261196i	0.825540	−	0.564344i	$-0.190871\pi$
$79$	2.32156	+	2.32156i	0.261196	+	0.261196i	−0.564344	+	0.825540i	$0.690871\pi$
$80$	−0.707107	+	0.707107i	−0.0790569	+	0.0790569i
$81$	−5.43004	−	7.17737i	−0.603338	−	0.797485i
$82$	0.385490	+	0.385490i	0.0425703	+	0.0425703i
$83$		−	8.43976i		−	0.926384i	−0.886258	−	0.463192i	$-0.846704\pi$
$83$		−	8.43976i		−	0.926384i	0.886258	−	0.463192i	$-0.153296\pi$
$84$	−0.535713	+	0.331863i	−0.0584511	+	0.0362092i
$85$			3.95206i			0.428662i
$86$			6.72384i			0.725050i
$87$	−0.903350	+	3.84461i	−0.0968493	+	0.412186i
$88$	0.874474	−	0.874474i	0.0932192	−	0.0932192i
$89$	0.550261	+	0.550261i	0.0583276	+	0.0583276i	0.735669	−	0.677341i	$-0.236868\pi$
$89$	0.550261	+	0.550261i	0.0583276	+	0.0583276i	−0.677341	+	0.735669i	$0.736868\pi$
$90$	−1.33603	+	2.68608i	−0.140830	+	0.283138i
$91$	0.926751	+	0.926751i	0.0971499	+	0.0971499i
$92$	−0.456993	−	0.456993i	−0.0476448	−	0.0476448i
$93$	0.389781	+	0.0915850i	0.0404184	+	0.00949692i
$94$	−1.13460	+	1.13460i	−0.117025	+	0.117025i
$95$	1.98313			0.203465
$96$	0.396182	−	1.68613i	0.0404352	−	0.172090i
$97$	−0.870659	−	0.870659i	−0.0884021	−	0.0884021i	0.661523	−	0.749925i	$-0.269910\pi$
$97$	−0.870659	−	0.870659i	−0.0884021	−	0.0884021i	−0.749925	+	0.661523i	$0.769910\pi$
$98$	−4.85614	−	4.85614i	−0.490545	−	0.490545i
$99$	1.65226	−	3.32185i	0.166058	−	0.333859i
$100$	1.00000			0.100000
$101$	−0.868845			−0.0864533			−0.0432267	−	0.999065i	$-0.513764\pi$
$101$	−0.868845			−0.0864533			−0.0432267	+	0.999065i	$0.513764\pi$
$102$	−3.60480	−	5.81909i	−0.356929	−	0.576176i
$103$	7.68967	−	7.68967i	0.757686	−	0.757686i	−0.218215	−	0.975901i	$-0.570023\pi$
$103$	7.68967	−	7.68967i	0.757686	−	0.757686i	0.975901	+	0.218215i	$0.0700234\pi$
$104$	−3.60228			−0.353232
$105$	0.613469	+	0.144144i	0.0598684	+	0.0140670i
$106$	5.67132	−	5.67132i	0.550847	−	0.550847i
$107$		−	8.05854i		−	0.779048i	−0.921016	−	0.389524i	$-0.872639\pi$
$107$		−	8.05854i		−	0.779048i	0.921016	−	0.389524i	$-0.127361\pi$
$108$	−0.482863	−	5.17367i	−0.0464635	−	0.497836i
$109$	0.884855	+	0.884855i	0.0847537	+	0.0847537i	0.748213	−	0.663459i	$-0.230912\pi$
$109$	0.884855	+	0.884855i	0.0847537	+	0.0847537i	−0.663459	+	0.748213i	$0.730912\pi$
$110$	−1.23669			−0.117914
$111$	−0.320087	+	10.5308i	−0.0303813	+	0.999538i
$112$	−0.363832			−0.0343789
$113$	−7.40005	−	7.40005i	−0.696138	−	0.696138i	0.267437	−	0.963575i	$-0.413823\pi$
$113$	−7.40005	−	7.40005i	−0.696138	−	0.696138i	−0.963575	+	0.267437i	$0.913823\pi$
$114$	−2.92000	+	1.80888i	−0.273483	+	0.169417i
$115$			0.646286i			0.0602665i
$116$	−1.61230	+	1.61230i	−0.149698	+	0.149698i
$117$	−10.2451	+	3.43884i	−0.947159	+	0.317920i
$118$	9.13227			0.840694
$119$	−1.01674	+	1.01674i	−0.0932044	+	0.0932044i
$120$	−1.47242	+	0.912132i	−0.134413	+	0.0832659i
$121$	−9.47059			−0.860963
$122$	3.69100			0.334167
$123$	0.497263	+	0.802712i	0.0448367	+	0.0723781i
$124$	0.163461	+	0.163461i	0.0146792	+	0.0146792i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−1.03476	+	0.347325i	−0.0921839	+	0.0309421i
$127$	18.9130			1.67825			0.839127	−	0.543936i	$-0.183067\pi$
$127$	18.9130			1.67825			0.839127	+	0.543936i	$0.183067\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−2.66386	+	11.3373i	−0.234540	+	0.998191i
$130$	2.54719	+	2.54719i	0.223404	+	0.223404i
$131$	−1.74566	−	1.74566i	−0.152519	−	0.152519i	0.626723	−	0.779242i	$-0.284396\pi$
$131$	−1.74566	−	1.74566i	−0.152519	−	0.152519i	−0.779242	+	0.626723i	$0.784396\pi$
$132$	1.82093	−	1.12803i	0.158491	−	0.0981821i
$133$	0.510197	+	0.510197i	0.0442397	+	0.0442397i
$134$	−3.50006	+	3.50006i	−0.302359	+	0.302359i
$135$	−3.31690	+	3.99977i	−0.285473	+	0.344246i
$136$		−	3.95206i		−	0.338887i
$137$			8.31134i			0.710085i	0.934850	+	0.355043i	$0.115534\pi$
$137$			8.31134i			0.710085i	−0.934850	+	0.355043i	$0.884466\pi$
$138$	−0.589498	−	0.951603i	−0.0501814	−	0.0810058i
$139$			2.62959i			0.223039i	0.993762	+	0.111520i	$0.0355718\pi$
$139$			2.62959i			0.223039i	−0.993762	+	0.111520i	$0.964428\pi$
$140$	0.257268	+	0.257268i	0.0217431	+	0.0217431i
$141$	−2.36259	+	1.46357i	−0.198966	+	0.123255i
$142$	10.4722	−	10.4722i	0.878809	−	0.878809i
$143$	−3.15010	−	3.15010i	−0.263424	−	0.263424i
$144$	1.33603	−	2.68608i	0.111336	−	0.223840i
$145$	2.28014			0.189355
$146$	−1.13662	+	1.13662i	−0.0940675	+	0.0940675i
$147$	−6.26418	−	10.1120i	−0.516661	−	0.834025i
$148$	−3.35892	+	5.07126i	−0.276102	+	0.416855i
$149$			10.2673i			0.841131i	0.907262	+	0.420566i	$0.138168\pi$
$149$			10.2673i			0.841131i	−0.907262	+	0.420566i	$0.861832\pi$
$150$	1.68613	+	0.396182i	0.137672	+	0.0323481i
$151$		−	5.53248i		−	0.450226i	−0.974333	−	0.225113i	$-0.927725\pi$
$151$		−	5.53248i		−	0.450226i	0.974333	−	0.225113i	$-0.0722752\pi$
$152$	−1.98313			−0.160853
$153$	−3.77275	−	11.2399i	−0.305009	−	0.908693i
$154$	−0.318162	−	0.318162i	−0.0256382	−	0.0256382i
$155$		−	0.231169i		−	0.0185679i
$156$	−6.07391	−	1.42716i	−0.486302	−	0.114264i
$157$	7.35707			0.587158			0.293579	−	0.955935i	$-0.405154\pi$
$157$	7.35707			0.587158			0.293579	+	0.955935i	$0.405154\pi$
$158$			3.28319i			0.261196i
$159$	11.8095	−	7.31572i	0.936552	−	0.580174i
$160$	−1.00000			−0.0790569
$161$	−0.166269	+	0.166269i	−0.0131038	+	0.0131038i
$162$	1.23555	−	8.91479i	0.0970736	−	0.700412i
$163$	8.15725	−	8.15725i	0.638925	−	0.638925i	−0.311365	−	0.950290i	$-0.600786\pi$
$163$	8.15725	−	8.15725i	0.638925	−	0.638925i	0.950290	+	0.311365i	$0.100786\pi$
$164$			0.545166i			0.0425703i
$165$	−2.08523	−	0.489956i	−0.162335	−	0.0381430i
$166$	5.96781	−	5.96781i	0.463192	−	0.463192i
$167$	7.06777	−	7.06777i	0.546921	−	0.546921i	−0.378628	−	0.925549i	$-0.623604\pi$
$167$	7.06777	−	7.06777i	0.546921	−	0.546921i	0.925549	+	0.378628i	$0.123604\pi$
$168$	−0.613469	−	0.144144i	−0.0473302	−	0.0111209i
$169$		−	0.0236067i		−	0.00181590i
$170$	−2.79453	+	2.79453i	−0.214331	+	0.214331i
$171$	−5.64015	+	1.89315i	−0.431313	+	0.144773i
$172$	−4.75447	+	4.75447i	−0.362525	+	0.362525i
$173$	6.52900			0.496391			0.248195	−	0.968710i	$-0.420163\pi$
$173$	6.52900			0.496391			0.248195	+	0.968710i	$0.420163\pi$
$174$	−3.35732	+	2.07979i	−0.254517	+	0.157668i
$175$		−	0.363832i		−	0.0275031i
$176$	1.23669			0.0932192
$177$	15.3982	+	3.61804i	1.15740	+	0.271949i
$178$			0.778187i			0.0583276i
$179$	5.04499	+	5.04499i	0.377080	+	0.377080i	0.870048	−	0.492968i	$-0.164088\pi$
$179$	5.04499	+	5.04499i	0.377080	+	0.377080i	−0.492968	+	0.870048i	$0.664088\pi$
$180$	−2.84406	+	0.954629i	−0.211984	+	0.0711538i
$181$	1.67529			0.124523			0.0622617	−	0.998060i	$-0.480169\pi$
$181$	1.67529			0.124523			0.0622617	+	0.998060i	$0.480169\pi$
$182$			1.31062i			0.0971499i
$183$	6.22350	+	1.46231i	0.460055	+	0.108097i
$184$		−	0.646286i		−	0.0476448i
$185$	5.96104	−	1.21080i	0.438264	−	0.0890199i
$186$	0.210857	+	0.340377i	0.0154608	+	0.0249577i
$187$	3.45598	−	3.45598i	0.252726	−	0.252726i
$188$	−1.60456			−0.117025
$189$	−1.88235	+	0.175681i	−0.136921	+	0.0127789i
$190$	1.40229	+	1.40229i	0.101732	+	0.101732i
$191$	6.28026	−	6.28026i	0.454424	−	0.454424i	−0.442396	−	0.896820i	$-0.645871\pi$
$191$	6.28026	−	6.28026i	0.454424	−	0.454424i	0.896820	+	0.442396i	$0.145871\pi$
$192$	1.47242	−	0.912132i	0.106263	−	0.0658275i
$193$	4.14557	+	4.14557i	0.298405	+	0.298405i	0.840389	−	0.541984i	$-0.182327\pi$
$193$	4.14557	+	4.14557i	0.298405	+	0.298405i	−0.541984	+	0.840389i	$0.682327\pi$
$194$		−	1.23130i		−	0.0884021i
$195$	3.28575	+	5.30406i	0.235298	+	0.379831i
$196$		−	6.86763i		−	0.490545i
$197$			17.9073i			1.27584i	0.770102	+	0.637921i	$0.220205\pi$
$197$			17.9073i			1.27584i	−0.770102	+	0.637921i	$0.779795\pi$
$198$	3.51723	−	1.18058i	0.249959	−	0.0839003i
$199$	−16.9444	+	16.9444i	−1.20116	+	1.20116i	−0.227343	+	0.973815i	$0.573004\pi$
$199$	−16.9444	+	16.9444i	−1.20116	+	1.20116i	−0.973815	+	0.227343i	$0.926996\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	−7.28823	+	4.51490i	−0.514072	+	0.318457i
$202$	−0.614366	−	0.614366i	−0.0432267	−	0.0432267i
$203$	0.586607	+	0.586607i	0.0411717	+	0.0411717i
$204$	1.56574	−	6.66370i	0.109624	−	0.466552i
$205$	0.385490	−	0.385490i	0.0269238	−	0.0269238i
$206$	10.8748			0.757686
$207$	−0.616963	−	1.83808i	−0.0428819	−	0.127755i
$208$	−2.54719	−	2.54719i	−0.176616	−	0.176616i
$209$	−1.73420	−	1.73420i	−0.119957	−	0.119957i
$210$	0.331863	+	0.535713i	0.0229007	+	0.0369677i
$211$	21.7223			1.49543			0.747714	−	0.664021i	$-0.231152\pi$
$211$	21.7223			1.49543			0.747714	+	0.664021i	$0.231152\pi$
$212$	8.02046			0.550847
$213$	21.8064	−	13.5086i	1.49415	−	0.925596i
$214$	5.69825	−	5.69825i	0.389524	−	0.389524i
$215$	6.72384			0.458562
$216$	3.31690	−	3.99977i	0.225686	−	0.272150i
$217$	0.0594724	−	0.0594724i	0.00403725	−	0.00403725i
$218$			1.25137i			0.0847537i
$219$	−2.36680	+	1.46618i	−0.159934	+	0.0990755i
$220$	−0.874474	−	0.874474i	−0.0589570	−	0.0589570i
$221$	−14.2364			−0.957646
$222$	−7.67273	+	7.22006i	−0.514960	+	0.484579i
$223$	7.24611			0.485235			0.242618	−	0.970122i	$-0.421994\pi$
$223$	7.24611			0.485235			0.242618	+	0.970122i	$0.421994\pi$
$224$	−0.257268	−	0.257268i	−0.0171895	−	0.0171895i
$225$	2.68608	+	1.33603i	0.179072	+	0.0890687i
$226$		−	10.4652i		−	0.696138i
$227$	7.21839	−	7.21839i	0.479102	−	0.479102i	−0.425743	−	0.904844i	$-0.639987\pi$
$227$	7.21839	−	7.21839i	0.479102	−	0.479102i	0.904844	+	0.425743i	$0.139987\pi$
$228$	−3.34382	−	0.785681i	−0.221450	−	0.0520330i
$229$	−15.0972			−0.997648			−0.498824	−	0.866703i	$-0.666235\pi$
$229$	−15.0972			−0.997648			−0.498824	+	0.866703i	$0.666235\pi$
$230$	−0.456993	+	0.456993i	−0.0301332	+	0.0301332i
$231$	−0.410412	−	0.662512i	−0.0270032	−	0.0435901i
$232$	−2.28014			−0.149698
$233$	1.67396			0.109665			0.0548324	−	0.998496i	$-0.482538\pi$
$233$	1.67396			0.109665			0.0548324	+	0.998496i	$0.482538\pi$
$234$	−9.67600	−	4.81275i	−0.632540	−	0.314619i
$235$	1.13460	+	1.13460i	0.0740129	+	0.0740129i
$236$	6.45749	+	6.45749i	0.420347	+	0.420347i
$237$	−1.30074	+	5.53589i	−0.0844922	+	0.359595i
$238$	−1.43789			−0.0932044
$239$	−8.93980	+	8.93980i	−0.578268	+	0.578268i	−0.934426	−	0.356158i	$-0.884086\pi$
$239$	−8.93980	+	8.93980i	−0.578268	+	0.578268i	0.356158	+	0.934426i	$0.384086\pi$
$240$	−1.68613	−	0.396182i	−0.108839	−	0.0255735i
$241$	−1.90045	−	1.90045i	−0.122419	−	0.122419i	0.643243	−	0.765662i	$-0.277588\pi$
$241$	−1.90045	−	1.90045i	−0.122419	−	0.122419i	−0.765662	+	0.643243i	$0.777588\pi$
$242$	−6.69672	−	6.69672i	−0.430481	−	0.430481i
$243$	5.61517	−	14.5420i	0.360213	−	0.932870i
$244$	2.60993	+	2.60993i	0.167084	+	0.167084i
$245$	−4.85614	+	4.85614i	−0.310248	+	0.310248i
$246$	−0.215985	+	0.919221i	−0.0137707	+	0.0586074i
$247$			7.14379i			0.454548i
$248$			0.231169i			0.0146792i
$249$	12.4269	−	7.69817i	0.787520	−	0.487852i
$250$		−	1.00000i		−	0.0632456i
$251$	−7.01214	−	7.01214i	−0.442602	−	0.442602i	0.450283	−	0.892886i	$-0.351323\pi$
$251$	−7.01214	−	7.01214i	−0.442602	−	0.442602i	−0.892886	+	0.450283i	$0.851323\pi$
$252$	−0.977282	−	0.486091i	−0.0615630	−	0.0306209i
$253$	0.565160	−	0.565160i	0.0355313	−	0.0355313i
$254$	13.3735	+	13.3735i	0.839127	+	0.839127i
$255$	−5.81909	+	3.60480i	−0.364406	+	0.225742i
$256$	1.00000			0.0625000
$257$	14.2100	−	14.2100i	0.886395	−	0.886395i	−0.107779	−	0.994175i	$-0.534374\pi$
$257$	14.2100	−	14.2100i	0.886395	−	0.886395i	0.994175	+	0.107779i	$0.0343740\pi$
$258$	−9.90030	+	6.13303i	−0.616366	+	0.381826i
$259$	1.84509	+	1.22208i	0.114648	+	0.0759367i
$260$			3.60228i			0.223404i
$261$	−6.48485	+	2.17668i	−0.401402	+	0.134733i
$262$		−	2.46874i		−	0.152519i
$263$	−19.1855			−1.18303			−0.591514	−	0.806295i	$-0.701470\pi$
$263$	−19.1855			−1.18303			−0.591514	+	0.806295i	$0.701470\pi$
$264$	2.08523	+	0.489956i	0.128337	+	0.0301547i
$265$	−5.67132	−	5.67132i	−0.348386	−	0.348386i
$266$			0.721527i			0.0442397i
$267$	−0.308304	+	1.31213i	−0.0188679	+	0.0803008i
$268$	−4.94984			−0.302359
$269$			28.0625i			1.71100i	0.517804	+	0.855499i	$0.326750\pi$
$269$			28.0625i			1.71100i	−0.517804	+	0.855499i	$0.673250\pi$
$270$	−5.17367	+	0.482863i	−0.314859	+	0.0293861i
$271$	16.3324			0.992121			0.496060	−	0.868288i	$-0.334779\pi$
$271$	16.3324			0.992121			0.496060	+	0.868288i	$0.334779\pi$
$272$	2.79453	−	2.79453i	0.169443	−	0.169443i
$273$	−0.519246	+	2.20988i	−0.0314262	+	0.133748i
$274$	−5.87700	+	5.87700i	−0.355043	+	0.355043i
$275$			1.23669i			0.0745754i
$276$	0.256047	−	1.08972i	0.0154122	−	0.0655936i
$277$	−3.32318	+	3.32318i	−0.199670	+	0.199670i	−0.799859	−	0.600188i	$-0.795092\pi$
$277$	−3.32318	+	3.32318i	−0.199670	+	0.199670i	0.600188	+	0.799859i	$0.295092\pi$
$278$	−1.85940	+	1.85940i	−0.111520	+	0.111520i
$279$	0.220680	+	0.657458i	0.0132118	+	0.0393610i
$280$			0.363832i			0.0217431i
$281$	−2.25670	+	2.25670i	−0.134624	+	0.134624i	−0.771207	−	0.636584i	$-0.780347\pi$
$281$	−2.25670	+	2.25670i	−0.134624	+	0.134624i	0.636584	+	0.771207i	$0.280347\pi$
$282$	−2.70550	−	0.635699i	−0.161110	−	0.0378553i
$283$	13.9425	−	13.9425i	0.828796	−	0.828796i	−0.158554	−	0.987350i	$-0.550683\pi$
$283$	13.9425	−	13.9425i	0.828796	−	0.828796i	0.987350	+	0.158554i	$0.0506833\pi$
$284$	14.8100			0.878809
$285$	1.80888	+	2.92000i	0.107149	+	0.172966i
$286$		−	4.45491i		−	0.263424i
$287$	0.198349			0.0117082
$288$	2.84406	−	0.954629i	0.167588	−	0.0562520i
$289$			1.38119i			0.0812466i
$290$	1.61230	+	1.61230i	0.0946776	+	0.0946776i
$291$	0.487818	−	2.07613i	0.0285964	−	0.121705i
$292$	−1.60743			−0.0940675
$293$		−	17.4323i		−	1.01841i	−0.860646	−	0.509203i	$-0.829940\pi$
$293$		−	17.4323i		−	1.01841i	0.860646	−	0.509203i	$-0.170060\pi$
$294$	2.72083	−	11.5797i	0.158682	−	0.675343i
$295$		−	9.13227i		−	0.531702i
$296$	−5.96104	+	1.21080i	−0.346478	+	0.0703764i
$297$	6.39824	−	0.597153i	0.371263	−	0.0346503i
$298$	−7.26009	+	7.26009i	−0.420566	+	0.420566i
$299$	−2.32810			−0.134638
$300$	0.912132	+	1.47242i	0.0526620	+	0.0850101i
$301$	1.72983	+	1.72983i	0.0997057	+	0.0997057i
$302$	3.91205	−	3.91205i	0.225113	−	0.225113i
$303$	−0.792501	−	1.27930i	−0.0455280	−	0.0734941i
$304$	−1.40229	−	1.40229i	−0.0804266	−	0.0804266i
$305$		−	3.69100i		−	0.211346i
$306$	5.28008	−	10.6156i	0.301842	−	0.606851i
$307$			5.19902i			0.296724i	0.988933	+	0.148362i	$0.0474001\pi$
$307$			5.19902i			0.296724i	−0.988933	+	0.148362i	$0.952600\pi$
$308$		−	0.449949i		−	0.0256382i
$309$	18.3364	+	4.30842i	1.04312	+	0.245097i
$310$	0.163461	−	0.163461i	0.00928397	−	0.00928397i
$311$	−3.82476	−	3.82476i	−0.216882	−	0.216882i	0.590301	−	0.807183i	$-0.299009\pi$
$311$	−3.82476	−	3.82476i	−0.216882	−	0.216882i	−0.807183	+	0.590301i	$0.799009\pi$
$312$	−3.28575	−	5.30406i	−0.186019	−	0.300283i
$313$	−23.6109	−	23.6109i	−1.33457	−	1.33457i	−0.901235	−	0.433331i	$-0.857338\pi$
$313$	−23.6109	−	23.6109i	−1.33457	−	1.33457i	−0.433331	−	0.901235i	$-0.642662\pi$
$314$	5.20223	+	5.20223i	0.293579	+	0.293579i
$315$	0.347325	+	1.03476i	0.0195695	+	0.0583022i
$316$	−2.32156	+	2.32156i	−0.130598	+	0.130598i
$317$	14.6490			0.822767			0.411384	−	0.911462i	$-0.365046\pi$
$317$	14.6490			0.822767			0.411384	+	0.911462i	$0.365046\pi$
$318$	13.5235	+	3.17756i	0.758363	+	0.178189i
$319$	−1.99392	−	1.99392i	−0.111638	−	0.111638i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	11.8655	−	7.35045i	0.662270	−	0.410262i
$322$	−0.235140			−0.0131038
$323$	−7.83746			−0.436088
$324$	7.17737	−	5.43004i	0.398743	−	0.301669i
$325$	2.54719	−	2.54719i	0.141293	−	0.141293i
$326$	11.5361			0.638925
$327$	−0.495772	+	2.10998i	−0.0274163	+	0.116682i
$328$	−0.385490	+	0.385490i	−0.0212851	+	0.0212851i
$329$			0.583791i			0.0321855i
$330$	−1.12803	−	1.82093i	−0.0620958	−	0.100239i
$331$	−2.77763	−	2.77763i	−0.152672	−	0.152672i	0.626638	−	0.779310i	$-0.284430\pi$
$331$	−2.77763	−	2.77763i	−0.152672	−	0.152672i	−0.779310	+	0.626638i	$0.784430\pi$
$332$	8.43976			0.463192
$333$	−15.7977	+	9.13417i	−0.865708	+	0.500549i
$334$	9.99534			0.546921
$335$	3.50006	+	3.50006i	0.191229	+	0.191229i
$336$	−0.331863	−	0.535713i	−0.0181046	−	0.0292256i
$337$			11.7097i			0.637870i	0.947777	+	0.318935i	$0.103325\pi$
$337$			11.7097i			0.637870i	−0.947777	+	0.318935i	$0.896675\pi$
$338$	0.0166925	−	0.0166925i	0.000907951	−	0.000907951i
$339$	4.14614	−	17.6458i	0.225188	−	0.958387i
$340$	−3.95206			−0.214331
$341$	−0.202151	+	0.202151i	−0.0109471	+	0.0109471i
$342$	−5.32685	−	2.64952i	−0.288043	−	0.143270i
$343$	−5.04549			−0.272431
$344$	−6.72384			−0.362525
$345$	−0.951603	+	0.589498i	−0.0512326	+	0.0317375i
$346$	4.61670	+	4.61670i	0.248195	+	0.248195i
$347$	−19.9380	−	19.9380i	−1.07033	−	1.07033i	−0.997332	−	0.0729969i	$-0.976744\pi$
$347$	−19.9380	−	19.9380i	−1.07033	−	1.07033i	−0.0729969	−	0.997332i	$-0.523256\pi$
$348$	−3.84461	−	0.903350i	−0.206093	−	0.0484246i
$349$	−20.6832			−1.10715			−0.553574	−	0.832800i	$-0.686736\pi$
$349$	−20.6832			−1.10715			−0.553574	+	0.832800i	$0.686736\pi$
$350$	0.257268	−	0.257268i	0.0137516	−	0.0137516i
$351$	−14.4083	−	11.9484i	−0.769057	−	0.637758i
$352$	0.874474	+	0.874474i	0.0466096	+	0.0466096i
$353$	5.36743	+	5.36743i	0.285680	+	0.285680i	0.835369	−	0.549690i	$-0.185254\pi$
$353$	5.36743	+	5.36743i	0.285680	+	0.285680i	−0.549690	+	0.835369i	$0.685254\pi$
$354$	8.32984	+	13.4465i	0.442726	+	0.714675i
$355$	−10.4722	−	10.4722i	−0.555808	−	0.555808i
$356$	−0.550261	+	0.550261i	−0.0291638	+	0.0291638i
$357$	−2.42447	−	0.569666i	−0.128316	−	0.0301499i
$358$			7.13469i			0.377080i
$359$			15.5141i			0.818802i	0.912355	+	0.409401i	$0.134262\pi$
$359$			15.5141i			0.818802i	−0.912355	+	0.409401i	$0.865738\pi$
$360$	−2.68608	−	1.33603i	−0.141569	−	0.0704150i
$361$		−	15.0672i		−	0.793010i
$362$	1.18461	+	1.18461i	0.0622617	+	0.0622617i
$363$	−8.63843	−	13.9447i	−0.453400	−	0.731905i
$364$	−0.926751	+	0.926751i	−0.0485750	+	0.0485750i
$365$	1.13662	+	1.13662i	0.0594935	+	0.0594935i
$366$	3.36667	+	5.43469i	0.175979	+	0.284076i
$367$	−23.5145			−1.22745			−0.613724	−	0.789521i	$-0.710329\pi$
$367$	−23.5145			−1.22745			−0.613724	+	0.789521i	$0.710329\pi$
$368$	0.456993	−	0.456993i	0.0238224	−	0.0238224i
$369$	−0.728358	+	1.46436i	−0.0379168	+	0.0762315i
$370$	5.07126	+	3.35892i	0.263642	+	0.174622i
$371$		−	2.91810i		−	0.151500i
$372$	−0.0915850	+	0.389781i	−0.00474846	+	0.0202092i
$373$		−	37.4002i		−	1.93651i	−0.249963	−	0.968255i	$-0.580419\pi$
$373$		−	37.4002i		−	1.93651i	0.249963	−	0.968255i	$-0.419581\pi$
$374$	4.88749			0.252726
$375$	0.396182	−	1.68613i	0.0204588	−	0.0870715i
$376$	−1.13460	−	1.13460i	−0.0585124	−	0.0585124i
$377$			8.21369i			0.423026i
$378$	−1.45525	−	1.20680i	−0.0748498	−	0.0620709i
$379$	30.3654			1.55977			0.779883	−	0.625925i	$-0.215279\pi$
$379$	30.3654			1.55977			0.779883	+	0.625925i	$0.215279\pi$
$380$			1.98313i			0.101732i
$381$	17.2511	+	27.8478i	0.883801	+	1.42668i
$382$	8.88163			0.454424
$383$	3.46804	−	3.46804i	0.177209	−	0.177209i	−0.612929	−	0.790138i	$-0.710009\pi$
$383$	3.46804	−	3.46804i	0.177209	−	0.177209i	0.790138	+	0.612929i	$0.210009\pi$
$384$	1.68613	+	0.396182i	0.0860450	+	0.0202176i
$385$	−0.318162	+	0.318162i	−0.0162150	+	0.0162150i
$386$			5.86272i			0.298405i
$387$	−19.1230	+	6.41877i	−0.972077	+	0.326284i
$388$	0.870659	−	0.870659i	0.0442010	−	0.0442010i
$389$	−7.62835	+	7.62835i	−0.386772	+	0.386772i	−0.873535	−	0.486762i	$-0.838178\pi$
$389$	−7.62835	+	7.62835i	−0.386772	+	0.386772i	0.486762	+	0.873535i	$0.338178\pi$
$390$	−1.42716	+	6.07391i	−0.0722669	+	0.307564i
$391$		−	2.55416i		−	0.129170i
$392$	4.85614	−	4.85614i	0.245272	−	0.245272i
$393$	0.978070	−	4.16262i	0.0493371	−	0.209976i
$394$	−12.6624	+	12.6624i	−0.637921	+	0.637921i
$395$	3.28319			0.165195
$396$	3.32185	+	1.65226i	0.166929	+	0.0830291i
$397$			15.6581i			0.785860i	0.919568	+	0.392930i	$0.128539\pi$
$397$			15.6581i			0.785860i	−0.919568	+	0.392930i	$0.871461\pi$
$398$	−23.9630			−1.20116
$399$	−0.285856	+	1.21659i	−0.0143107	+	0.0609057i
$400$			1.00000i			0.0500000i
$401$	12.5130	+	12.5130i	0.624871	+	0.624871i	0.946773	−	0.321902i	$-0.104322\pi$
$401$	12.5130	+	12.5130i	0.624871	+	0.624871i	−0.321902	+	0.946773i	$0.604322\pi$
$402$	−8.34608	−	1.96104i	−0.416264	−	0.0978077i
$403$	0.832734			0.0414814
$404$		−	0.868845i		−	0.0432267i
$405$	−8.91479	−	1.23555i	−0.442979	−	0.0613947i
$406$			0.829588i			0.0411717i
$407$	−6.27158	−	4.15396i	−0.310871	−	0.205904i
$408$	5.81909	−	3.60480i	0.288088	−	0.178464i
$409$	−10.4273	+	10.4273i	−0.515599	+	0.515599i	−0.916236	−	0.400638i	$-0.868789\pi$
$409$	−10.4273	+	10.4273i	−0.515599	+	0.515599i	0.400638	+	0.916236i	$0.368789\pi$
$410$	0.545166			0.0269238
$411$	−12.2378	+	7.58103i	−0.603644	+	0.373945i
$412$	7.68967	+	7.68967i	0.378843	+	0.378843i
$413$	2.34944	−	2.34944i	0.115609	−	0.115609i
$414$	0.863458	−	1.73598i	0.0424366	−	0.0853185i
$415$	−5.96781	−	5.96781i	−0.292948	−	0.292948i
$416$		−	3.60228i		−	0.176616i
$417$	−3.87186	+	2.39854i	−0.189606	+	0.117457i
$418$		−	2.45252i		−	0.119957i
$419$			7.73667i			0.377961i	0.981981	+	0.188980i	$0.0605183\pi$
$419$			7.73667i			0.377961i	−0.981981	+	0.188980i	$0.939482\pi$
$420$	−0.144144	+	0.613469i	−0.00703350	+	0.0299342i
$421$	−7.36859	+	7.36859i	−0.359123	+	0.359123i	−0.863490	−	0.504366i	$-0.831726\pi$
$421$	−7.36859	+	7.36859i	−0.359123	+	0.359123i	0.504366	+	0.863490i	$0.331726\pi$
$422$	15.3600	+	15.3600i	0.747714	+	0.747714i
$423$	−4.30998	−	2.14374i	−0.209558	−	0.104232i
$424$	5.67132	+	5.67132i	0.275424	+	0.275424i
$425$	2.79453	+	2.79453i	0.135555	+	0.135555i
$426$	24.9715	+	5.86744i	1.20987	+	0.284278i
$427$	0.949576	−	0.949576i	0.0459532	−	0.0459532i
$428$	8.05854			0.389524
$429$	1.76496	−	7.51156i	0.0852128	−	0.362662i
$430$	4.75447	+	4.75447i	0.229281	+	0.229281i
$431$	−21.5577	−	21.5577i	−1.03840	−	1.03840i	−0.999233	−	0.0391638i	$-0.987531\pi$
$431$	−21.5577	−	21.5577i	−1.03840	−	1.03840i	−0.0391638	−	0.999233i	$-0.512469\pi$
$432$	5.17367	−	0.482863i	0.248918	−	0.0232317i
$433$	35.8755			1.72407			0.862034	−	0.506851i	$-0.169190\pi$
$433$	35.8755			1.72407			0.862034	+	0.506851i	$0.169190\pi$
$434$	0.0841067			0.00403725
$435$	2.07979	+	3.35732i	0.0997181	+	0.160971i
$436$	−0.884855	+	0.884855i	−0.0423769	+	0.0423769i
$437$	−1.28167			−0.0613106
$438$	−2.71033	−	0.636833i	−0.129505	−	0.0304291i
$439$	13.1830	−	13.1830i	0.629190	−	0.629190i	−0.318674	−	0.947864i	$-0.603238\pi$
$439$	13.1830	−	13.1830i	0.629190	−	0.629190i	0.947864	+	0.318674i	$0.103238\pi$
$440$		−	1.23669i		−	0.0589570i
$441$	9.17536	−	18.4470i	0.436922	−	0.878428i
$442$	−10.0667	−	10.0667i	−0.478823	−	0.478823i
$443$	−39.5691			−1.87999			−0.939993	−	0.341193i	$-0.889169\pi$
$443$	−39.5691			−1.87999			−0.939993	+	0.341193i	$0.889169\pi$
$444$	−10.5308	−	0.320087i	−0.499769	−	0.0151906i
$445$	0.778187			0.0368896
$446$	5.12377	+	5.12377i	0.242618	+	0.242618i
$447$	−15.1178	+	9.36514i	−0.715046	+	0.442956i
$448$		−	0.363832i		−	0.0171895i
$449$	−12.2930	+	12.2930i	−0.580144	+	0.580144i	−0.934943	−	0.354799i	$-0.884549\pi$
$449$	−12.2930	+	12.2930i	−0.580144	+	0.580144i	0.354799	+	0.934943i	$0.384549\pi$
$450$	0.954629	+	2.84406i	0.0450016	+	0.134070i
$451$	−0.674202			−0.0317470
$452$	7.40005	−	7.40005i	0.348069	−	0.348069i
$453$	8.14612	−	5.04635i	0.382738	−	0.237098i
$454$	10.2083			0.479102
$455$	1.31062			0.0614430
$456$	−1.80888	−	2.92000i	−0.0847084	−	0.136741i
$457$	16.2368	+	16.2368i	0.759525	+	0.759525i	0.976236	−	0.216711i	$-0.0695328\pi$
$457$	16.2368	+	16.2368i	0.759525	+	0.759525i	−0.216711	+	0.976236i	$0.569533\pi$
$458$	−10.6753	−	10.6753i	−0.498824	−	0.498824i
$459$	13.1086	−	15.8074i	0.611857	−	0.737824i
$460$	−0.646286			−0.0301332
$461$	−24.0001	+	24.0001i	−1.11780	+	1.11780i	−0.125733	+	0.992064i	$0.540128\pi$
$461$	−24.0001	+	24.0001i	−1.11780	+	1.11780i	−0.992064	+	0.125733i	$0.959872\pi$
$462$	0.178262	−	0.758672i	0.00829348	−	0.0352966i
$463$	−9.18675	−	9.18675i	−0.426945	−	0.426945i	0.460642	−	0.887586i	$-0.347619\pi$
$463$	−9.18675	−	9.18675i	−0.426945	−	0.426945i	−0.887586	+	0.460642i	$0.847619\pi$
$464$	−1.61230	−	1.61230i	−0.0748492	−	0.0748492i
$465$	0.340377	−	0.210857i	0.0157846	−	0.00977824i
$466$	1.18367	+	1.18367i	0.0548324	+	0.0548324i
$467$	19.8576	−	19.8576i	0.918901	−	0.918901i	−0.0780485	−	0.996950i	$-0.524869\pi$
$467$	19.8576	−	19.8576i	0.918901	−	0.918901i	0.996950	+	0.0780485i	$0.0248689\pi$
$468$	−3.43884	−	10.2451i	−0.158960	−	0.473580i
$469$			1.80091i			0.0831583i
$470$			1.60456i			0.0740129i
$471$	6.71061	+	10.8327i	0.309209	+	0.499143i
$472$			9.13227i			0.420347i
$473$	−5.87982	−	5.87982i	−0.270354	−	0.270354i
$474$	−4.83423	+	2.99470i	−0.222043	+	0.137551i
$475$	1.40229	−	1.40229i	0.0643413	−	0.0643413i
$476$	−1.01674	−	1.01674i	−0.0466022	−	0.0466022i
$477$	21.5436	+	10.7156i	0.986413	+	0.490633i
$478$	−12.6428			−0.578268
$479$	11.7978	−	11.7978i	0.539054	−	0.539054i	−0.384197	−	0.923251i	$-0.625522\pi$
$479$	11.7978	−	11.7978i	0.539054	−	0.539054i	0.923251	+	0.384197i	$0.125522\pi$
$480$	−0.912132	−	1.47242i	−0.0416329	−	0.0672064i
$481$	4.36164	+	21.4733i	0.198874	+	0.979098i
$482$		−	2.68764i		−	0.122419i
$483$	−0.396476	−	0.0931582i	−0.0180403	−	0.00423884i
$484$		−	9.47059i		−	0.430481i
$485$	−1.23130			−0.0559104
$486$	14.2533	−	6.31222i	0.646542	−	0.286328i
$487$	−25.1254	−	25.1254i	−1.13854	−	1.13854i	−0.988712	−	0.149830i	$-0.952127\pi$
$487$	−25.1254	−	25.1254i	−1.13854	−	1.13854i	−0.149830	−	0.988712i	$-0.547873\pi$
$488$			3.69100i			0.167084i
$489$	19.4514	+	4.57039i	0.879621	+	0.206680i
$490$	−6.86763			−0.310248
$491$			4.62838i			0.208876i	0.994531	+	0.104438i	$0.0333044\pi$
$491$			4.62838i			0.208876i	−0.994531	+	0.104438i	$0.966696\pi$
$492$	−0.802712	+	0.497263i	−0.0361891	+	0.0224184i
$493$	−9.01125			−0.405846
$494$	−5.05142	+	5.05142i	−0.227274	+	0.227274i
$495$	−1.18058	−	3.51723i	−0.0530632	−	0.158088i
$496$	−0.163461	+	0.163461i	−0.00733962	+	0.00733962i
$497$		−	5.38834i		−	0.241700i
$498$	14.2305	+	3.34368i	0.637686	+	0.149834i
$499$	−5.53591	+	5.53591i	−0.247822	+	0.247822i	−0.820076	−	0.572255i	$-0.806069\pi$
$499$	−5.53591	+	5.53591i	−0.247822	+	0.247822i	0.572255	+	0.820076i	$0.306069\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$	16.8535	+	3.95998i	0.752957	+	0.176919i
$502$		−	9.91666i		−	0.442602i
$503$	−17.6402	+	17.6402i	−0.786536	+	0.786536i	−0.980925	−	0.194388i	$-0.937728\pi$
$503$	−17.6402	+	17.6402i	−0.786536	+	0.786536i	0.194388	+	0.980925i	$0.437728\pi$
$504$	−0.347325	−	1.03476i	−0.0154711	−	0.0460919i
$505$	−0.614366	+	0.614366i	−0.0273389	+	0.0273389i
$506$	0.799257			0.0355313
$507$	0.0347590	−	0.0215324i	0.00154370	−	0.000956289i
$508$			18.9130i			0.839127i
$509$	−24.0229			−1.06480			−0.532398	−	0.846494i	$-0.678709\pi$
$509$	−24.0229			−1.06480			−0.532398	+	0.846494i	$0.678709\pi$
$510$	−6.66370	−	1.56574i	−0.295074	−	0.0693320i
$511$			0.584833i			0.0258715i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−7.93207	−	6.57785i	−0.350210	−	0.290419i
$514$	20.0960			0.886395
$515$		−	10.8748i		−	0.479203i
$516$	−11.3373	−	2.66386i	−0.499096	−	0.117270i
$517$		−	1.98435i		−	0.0872716i
$518$	0.440529	+	2.16882i	0.0193557	+	0.0952924i
$519$	5.95531	+	9.61342i	0.261409	+	0.421982i
$520$	−2.54719	+	2.54719i	−0.111702	+	0.111702i
$521$	−15.1389			−0.663247			−0.331623	−	0.943412i	$-0.607596\pi$
$521$	−15.1389			−0.663247			−0.331623	+	0.943412i	$0.607596\pi$
$522$	−6.12463	−	3.04633i	−0.268068	−	0.133334i
$523$	−1.01795	−	1.01795i	−0.0445119	−	0.0445119i	0.684500	−	0.729012i	$-0.260020\pi$
$523$	−1.01795	−	1.01795i	−0.0445119	−	0.0445119i	−0.729012	+	0.684500i	$0.760020\pi$
$524$	1.74566	−	1.74566i	0.0762596	−	0.0762596i
$525$	0.535713	−	0.331863i	0.0233804	−	0.0144837i
$526$	−13.5662	−	13.5662i	−0.591514	−	0.591514i
$527$			0.913594i			0.0397968i
$528$	1.12803	+	1.82093i	0.0490911	+	0.0792457i
$529$			22.5823i			0.981840i
$530$		−	8.02046i		−	0.348386i
$531$	8.71793	+	25.9727i	0.378326	+	1.12712i
$532$	−0.510197	+	0.510197i	−0.0221198	+	0.0221198i
$533$	1.38864	+	1.38864i	0.0601488	+	0.0601488i
$534$	−1.14582	+	0.709809i	−0.0495843	+	0.0307165i
$535$	−5.69825	−	5.69825i	−0.246357	−	0.246357i
$536$	−3.50006	−	3.50006i	−0.151180	−	0.151180i
$537$	−2.82664	+	12.0300i	−0.121978	+	0.519134i
$538$	−19.8432	+	19.8432i	−0.855499	+	0.855499i
$539$	8.49314			0.365825
$540$	−3.99977	−	3.31690i	−0.172123	−	0.142737i
$541$	8.31756	+	8.31756i	0.357600	+	0.357600i	0.862928	−	0.505328i	$-0.168628\pi$
$541$	8.31756	+	8.31756i	0.357600	+	0.357600i	−0.505328	+	0.862928i	$0.668628\pi$
$542$	11.5487	+	11.5487i	0.496060	+	0.496060i
$543$	1.52809	+	2.46673i	0.0655765	+	0.105857i
$544$	3.95206			0.169443
$545$	1.25137			0.0536030
$546$	−1.92979	+	1.19546i	−0.0825873	+	0.0511611i
$547$	−11.6801	+	11.6801i	−0.499403	+	0.499403i	−0.911252	−	0.411849i	$-0.864883\pi$
$547$	−11.6801	+	11.6801i	−0.499403	+	0.499403i	0.411849	+	0.911252i	$0.364883\pi$
$548$	−8.31134			−0.355043
$549$	3.52353	+	10.4974i	0.150381	+	0.448019i
$550$	−0.874474	+	0.874474i	−0.0372877	+	0.0372877i
$551$			4.52181i			0.192636i
$552$	0.951603	−	0.589498i	0.0405029	−	0.0250907i
$553$	0.844660	+	0.844660i	0.0359186	+	0.0359186i
$554$	−4.69968			−0.199670
$555$	7.22006	+	7.67273i	0.306474	+	0.325689i
$556$	−2.62959			−0.111520
$557$	−31.2058	−	31.2058i	−1.32223	−	1.32223i	−0.911964	−	0.410270i	$-0.865434\pi$
$557$	−31.2058	−	31.2058i	−1.32223	−	1.32223i	−0.410270	−	0.911964i	$-0.634566\pi$
$558$	−0.308849	+	0.620938i	−0.0130746	+	0.0262864i
$559$			24.2211i			1.02444i
$560$	−0.257268	+	0.257268i	−0.0108716	+	0.0108716i
$561$	8.24095	+	1.93634i	0.347933	+	0.0817522i
$562$	−3.19146			−0.134624
$563$	2.07352	−	2.07352i	0.0873885	−	0.0873885i	−0.662061	−	0.749450i	$-0.730318\pi$
$563$	2.07352	−	2.07352i	0.0873885	−	0.0873885i	0.749450	+	0.662061i	$0.230318\pi$
$564$	−1.46357	−	2.36259i	−0.0616275	−	0.0994828i
$565$	−10.4652			−0.440276
$566$	19.7177			0.828796
$567$	−1.97563	−	2.61136i	−0.0829685	−	0.109667i
$568$	10.4722	+	10.4722i	0.439404	+	0.439404i
$569$	−14.1395	−	14.1395i	−0.592758	−	0.592758i	0.345617	−	0.938376i	$-0.387670\pi$
$569$	−14.1395	−	14.1395i	−0.592758	−	0.592758i	−0.938376	+	0.345617i	$0.887670\pi$
$570$	−0.785681	+	3.34382i	−0.0329086	+	0.140057i
$571$	−17.4906			−0.731960			−0.365980	−	0.930623i	$-0.619266\pi$
$571$	−17.4906			−0.731960			−0.365980	+	0.930623i	$0.619266\pi$
$572$	3.15010	−	3.15010i	0.131712	−	0.131712i
$573$	14.9756	+	3.51874i	0.625615	+	0.146998i
$574$	0.140254	+	0.140254i	0.00585408	+	0.00585408i
$575$	0.456993	+	0.456993i	0.0190579	+	0.0190579i
$576$	2.68608	+	1.33603i	0.111920	+	0.0556679i
$577$	23.1142	+	23.1142i	0.962256	+	0.962256i	0.999313	−	0.0370574i	$-0.0117984\pi$
$577$	23.1142	+	23.1142i	0.962256	+	0.962256i	−0.0370574	+	0.999313i	$0.511798\pi$
$578$	−0.976650	+	0.976650i	−0.0406233	+	0.0406233i
$579$	−2.32271	+	9.88532i	−0.0965284	+	0.410820i
$580$			2.28014i			0.0946776i
$581$		−	3.07066i		−	0.127392i
$582$	1.81299	−	1.12311i	0.0751507	−	0.0465543i
$583$			9.91884i			0.410796i
$584$	−1.13662	−	1.13662i	−0.0470337	−	0.0470337i
$585$	−4.81275	+	9.67600i	−0.198983	+	0.400053i
$586$	12.3265	−	12.3265i	0.509203	−	0.509203i
$587$	−16.8989	−	16.8989i	−0.697491	−	0.697491i	0.266378	−	0.963869i	$-0.414173\pi$
$587$	−16.8989	−	16.8989i	−0.697491	−	0.697491i	−0.963869	+	0.266378i	$0.914173\pi$
$588$	10.1120	−	6.26418i	0.417013	−	0.258330i
$589$	0.458438			0.0188896
$590$	6.45749	−	6.45749i	0.265851	−	0.265851i
$591$	−26.3670	+	16.3338i	−1.08459	+	0.671883i
$592$	−5.07126	−	3.35892i	−0.208427	−	0.138051i
$593$			35.3242i			1.45059i	0.688438	+	0.725295i	$0.258297\pi$
$593$			35.3242i			1.45059i	−0.688438	+	0.725295i	$0.741703\pi$
$594$	4.94649	+	4.10199i	0.202957	+	0.168307i
$595$			1.43789i			0.0589477i
$596$	−10.2673			−0.420566
$597$	−40.4048	−	9.49372i	−1.65366	−	0.388552i
$598$	−1.64622	−	1.64622i	−0.0673188	−	0.0673188i
$599$			14.7052i			0.600838i	0.953807	+	0.300419i	$0.0971264\pi$
$599$			14.7052i			0.600838i	−0.953807	+	0.300419i	$0.902874\pi$
$600$	−0.396182	+	1.68613i	−0.0161741	+	0.0688360i
$601$	−5.81380			−0.237150			−0.118575	−	0.992945i	$-0.537833\pi$
$601$	−5.81380			−0.237150			−0.118575	+	0.992945i	$0.537833\pi$
$602$			2.44635i			0.0997057i
$603$	−13.2957	−	6.61313i	−0.541441	−	0.269308i
$604$	5.53248			0.225113
$605$	−6.69672	+	6.69672i	−0.272260	+	0.272260i
$606$	0.344221	−	1.46499i	0.0139830	−	0.0595110i
$607$	−4.11260	+	4.11260i	−0.166925	+	0.166925i	−0.785626	−	0.618701i	$-0.787659\pi$
$607$	−4.11260	+	4.11260i	−0.166925	+	0.166925i	0.618701	+	0.785626i	$0.287659\pi$
$608$		−	1.98313i		−	0.0804266i
$609$	−0.328668	+	1.39879i	−0.0133183	+	0.0566820i
$610$	2.60993	−	2.60993i	0.105673	−	0.105673i
$611$	−4.08713	+	4.08713i	−0.165348	+	0.165348i
$612$	11.2399	−	3.77275i	0.454346	−	0.152504i
$613$		−	9.41341i		−	0.380204i	−0.981764	−	0.190102i	$-0.939118\pi$
$613$		−	9.41341i		−	0.380204i	0.981764	−	0.190102i	$-0.0608819\pi$
$614$	−3.67626	+	3.67626i	−0.148362	+	0.148362i
$615$	0.919221	+	0.215985i	0.0370666	+	0.00870936i
$616$	0.318162	−	0.318162i	0.0128191	−	0.0128191i
$617$	24.1161			0.970877			0.485438	−	0.874271i	$-0.338660\pi$
$617$	24.1161			0.970877			0.485438	+	0.874271i	$0.338660\pi$
$618$	9.91928	+	16.0123i	0.399012	+	0.644109i
$619$		−	36.1762i		−	1.45404i	−0.686614	−	0.727022i	$-0.740904\pi$
$619$		−	36.1762i		−	1.45404i	0.686614	−	0.727022i	$-0.259096\pi$
$620$	0.231169			0.00928397
$621$	2.14367	−	2.58500i	0.0860224	−	0.103732i
$622$		−	5.40903i		−	0.216882i
$623$	0.200203	+	0.200203i	0.00802096	+	0.00802096i
$624$	1.42716	−	6.07391i	0.0571320	−	0.243151i
$625$	−1.00000			−0.0400000
$626$		−	33.3908i		−	1.33457i
$627$	0.971646	−	4.13528i	0.0388038	−	0.165147i
$628$			7.35707i			0.293579i
$629$	−23.5584	+	4.78516i	−0.939335	+	0.190797i
$630$	−0.486091	+	0.977282i	−0.0193663	+	0.0389359i
$631$	−21.7680	+	21.7680i	−0.866571	+	0.866571i	−0.992091	−	0.125520i	$-0.959940\pi$
$631$	−21.7680	+	21.7680i	−0.866571	+	0.866571i	0.125520	+	0.992091i	$0.459940\pi$
$632$	−3.28319			−0.130598
$633$	19.8136	+	31.9844i	0.787521	+	1.27126i
$634$	10.3584	+	10.3584i	0.411384	+	0.411384i
$635$	13.3735	−	13.3735i	0.530710	−	0.530710i
$636$	7.31572	+	11.8095i	0.290087	+	0.468276i
$637$	−17.4932	−	17.4932i	−0.693105	−	0.693105i
$638$		−	2.81983i		−	0.111638i
$639$	39.7807	+	19.7865i	1.57370	+	0.782744i
$640$		−	1.00000i		−	0.0395285i
$641$		−	4.70643i		−	0.185893i	−0.995671	−	0.0929463i	$-0.970371\pi$
$641$		−	4.70643i		−	0.185893i	0.995671	−	0.0929463i	$-0.0296285\pi$
$642$	13.5878	+	3.19265i	0.536266	+	0.126004i
$643$	−17.4164	+	17.4164i	−0.686836	+	0.686836i	−0.961531	−	0.274695i	$-0.911423\pi$
$643$	−17.4164	+	17.4164i	−0.686836	+	0.686836i	0.274695	+	0.961531i	$0.411423\pi$
$644$	−0.166269	−	0.166269i	−0.00655191	−	0.00655191i
$645$	6.13303	+	9.90030i	0.241488	+	0.389824i
$646$	−5.54192	−	5.54192i	−0.218044	−	0.218044i
$647$	−4.39908	−	4.39908i	−0.172946	−	0.172946i	0.615327	−	0.788272i	$-0.289024\pi$
$647$	−4.39908	−	4.39908i	−0.172946	−	0.172946i	−0.788272	+	0.615327i	$0.789024\pi$
$648$	8.91479	+	1.23555i	0.350206	+	0.0485368i
$649$	−7.98593	+	7.98593i	−0.313475	+	0.313475i
$650$	3.60228			0.141293
$651$	0.141815	+	0.0333216i	0.00555817	+	0.00130598i
$652$	8.15725	+	8.15725i	0.319463	+	0.319463i
$653$	29.2611	+	29.2611i	1.14507	+	1.14507i	0.987508	+	0.157567i	$0.0503649\pi$
$653$	29.2611	+	29.2611i	1.14507	+	1.14507i	0.157567	+	0.987508i	$0.449635\pi$
$654$	−1.84255	+	1.14142i	−0.0720492	+	0.0446330i
$655$	−2.46874			−0.0964616
$656$	−0.545166			−0.0212851
$657$	−4.31767	−	2.14757i	−0.168448	−	0.0837847i
$658$	−0.412803	+	0.412803i	−0.0160927	+	0.0160927i
$659$	1.26482			0.0492703			0.0246351	−	0.999697i	$-0.492158\pi$
$659$	1.26482			0.0492703			0.0246351	+	0.999697i	$0.492158\pi$
$660$	0.489956	−	2.08523i	0.0190715	−	0.0811673i
$661$	−14.4067	+	14.4067i	−0.560357	+	0.560357i	−0.929409	−	0.369052i	$-0.879682\pi$
$661$	−14.4067	+	14.4067i	−0.560357	+	0.560357i	0.369052	+	0.929409i	$0.379682\pi$
$662$		−	3.92816i		−	0.152672i
$663$	−12.9855	−	20.9620i	−0.504315	−	0.814096i
$664$	5.96781	+	5.96781i	0.231596	+	0.231596i
$665$	0.721527			0.0279796
$666$	−17.6295	−	4.71182i	−0.683129	−	0.182579i
$667$	−1.47362			−0.0570588
$668$	7.06777	+	7.06777i	0.273460	+	0.273460i
$669$	6.60940	+	10.6693i	0.255534	+	0.412499i
$670$			4.94984i			0.191229i
$671$	−3.22768	+	3.22768i	−0.124603	+	0.124603i
$672$	0.144144	−	0.613469i	0.00556047	−	0.0236651i
$673$	−4.92341			−0.189784			−0.0948918	−	0.995488i	$-0.530251\pi$
$673$	−4.92341			−0.189784			−0.0948918	+	0.995488i	$0.530251\pi$
$674$	−8.28004	+	8.28004i	−0.318935	+	0.318935i
$675$	0.482863	+	5.17367i	0.0185854	+	0.199135i
$676$	0.0236067			0.000907951
$677$	−27.8288			−1.06955			−0.534775	−	0.844995i	$-0.679604\pi$
$677$	−27.8288			−1.06955			−0.534775	+	0.844995i	$0.679604\pi$
$678$	15.4092	−	9.54569i	0.591788	−	0.366600i
$679$	−0.316774	−	0.316774i	−0.0121567	−	0.0121567i
$680$	−2.79453	−	2.79453i	−0.107165	−	0.107165i
$681$	17.2126	+	4.04437i	0.659589	+	0.154980i
$682$	−0.285885			−0.0109471
$683$	−0.306666	+	0.306666i	−0.0117343	+	0.0117343i	−0.712950	−	0.701215i	$-0.752641\pi$
$683$	−0.306666	+	0.306666i	−0.0117343	+	0.0117343i	0.701215	+	0.712950i	$0.252641\pi$
$684$	−1.89315	−	5.64015i	−0.0723865	−	0.215656i
$685$	5.87700	+	5.87700i	0.224549	+	0.224549i
$686$	−3.56770	−	3.56770i	−0.136215	−	0.136215i
$687$	−13.7706	−	22.2293i	−0.525381	−	0.848102i
$688$	−4.75447	−	4.75447i	−0.181263	−	0.181263i
$689$	20.4297	−	20.4297i	0.778308	−	0.778308i
$690$	−1.08972	−	0.256047i	−0.0414851	−	0.00974754i
$691$		−	6.54668i		−	0.249048i	−0.992217	−	0.124524i	$-0.960260\pi$
$691$		−	6.54668i		−	0.249048i	0.992217	−	0.124524i	$-0.0397403\pi$
$692$			6.52900i			0.248195i
$693$	0.601145	−	1.20860i	0.0228356	−	0.0459108i
$694$		−	28.1966i		−	1.07033i
$695$	1.85940	+	1.85940i	0.0705312	+	0.0705312i
$696$	−2.07979	−	3.35732i	−0.0788341	−	0.127259i
$697$	−1.52348	+	1.52348i	−0.0577060	+	0.0577060i
$698$	−14.6252	−	14.6252i	−0.553574	−	0.553574i
$699$	1.52687	+	2.46477i	0.0577517	+	0.0932262i
$700$	0.363832			0.0137516
$701$	15.0325	−	15.0325i	0.567769	−	0.567769i	−0.363734	−	0.931503i	$-0.618498\pi$
$701$	15.0325	−	15.0325i	0.567769	−	0.567769i	0.931503	+	0.363734i	$0.118498\pi$
$702$	−1.73940	−	18.6370i	−0.0656496	−	0.703408i
$703$	2.40118	+	11.8215i	0.0905621	+	0.445857i
$704$			1.23669i			0.0466096i
$705$	−0.635699	+	2.70550i	−0.0239418	+	0.101895i
$706$			7.59069i			0.285680i
$707$	−0.316114			−0.0118887
$708$	−3.61804	+	15.3982i	−0.135974	+	0.578700i
$709$	−36.1363	−	36.1363i	−1.35713	−	1.35713i	−0.877438	−	0.479690i	$-0.840749\pi$
$709$	−36.1363	−	36.1363i	−1.35713	−	1.35713i	−0.479690	−	0.877438i	$-0.659251\pi$
$710$		−	14.8100i		−	0.555808i
$711$	−9.33759	+	3.13422i	−0.350187	+	0.117543i
$712$	−0.778187			−0.0291638
$713$			0.149401i			0.00559512i
$714$	−1.31154	−	2.11717i	−0.0490833	−	0.0792332i
$715$	−4.45491			−0.166604
$716$	−5.04499	+	5.04499i	−0.188540	+	0.188540i
$717$	−21.3174	−	5.00885i	−0.796113	−	0.187059i
$718$	−10.9701	+	10.9701i	−0.409401	+	0.409401i
$719$			17.6902i			0.659734i	0.944027	+	0.329867i	$0.107004\pi$
$719$			17.6902i			0.659734i	−0.944027	+	0.329867i	$0.892996\pi$
$720$	−0.954629	−	2.84406i	−0.0355769	−	0.105992i
$721$	2.79775	−	2.79775i	0.104194	−	0.104194i
$722$	10.6541	−	10.6541i	0.396505	−	0.396505i
$723$	1.06480	−	4.53172i	0.0396002	−	0.168536i
$724$			1.67529i			0.0622617i
$725$	1.61230	−	1.61230i	0.0598793	−	0.0598793i
$726$	3.75208	−	15.9687i	0.139253	−	0.592653i
$727$	−28.1049	+	28.1049i	−1.04235	+	1.04235i	−0.0432905	+	0.999063i	$0.513784\pi$
$727$	−28.1049	+	28.1049i	−1.04235	+	1.04235i	−0.999063	+	0.0432905i	$0.986216\pi$
$728$	−1.31062			−0.0485750
$729$	26.5337	−	4.99634i	0.982729	−	0.185050i
$730$			1.60743i			0.0594935i
$731$	−26.5730			−0.982839
$732$	−1.46231	+	6.22350i	−0.0540484	+	0.230027i
$733$		−	13.3828i		−	0.494305i	−0.968977	−	0.247152i	$-0.920505\pi$
$733$		−	13.3828i		−	0.494305i	0.968977	−	0.247152i	$-0.0794948\pi$
$734$	−16.6273	−	16.6273i	−0.613724	−	0.613724i
$735$	−11.5797	−	2.72083i	−0.427124	−	0.100359i
$736$	0.646286			0.0238224
$737$		−	6.12143i		−	0.225486i
$738$	−1.55048	+	0.520431i	−0.0570741	+	0.0191573i
$739$		−	16.3486i		−	0.601394i	−0.953720	−	0.300697i	$-0.902781\pi$
$739$		−	16.3486i		−	0.601394i	0.953720	−	0.300697i	$-0.0972192\pi$
$740$	1.21080	+	5.96104i	0.0445099	+	0.219132i
$741$	−10.5186	+	6.51608i	−0.386412	+	0.239374i
$742$	2.06341	−	2.06341i	0.0757501	−	0.0757501i
$743$	30.1894			1.10754			0.553770	−	0.832670i	$-0.313189\pi$
$743$	30.1894			1.10754			0.553770	+	0.832670i	$0.313189\pi$
$744$	−0.340377	+	0.210857i	−0.0124788	+	0.00773038i
$745$	7.26009	+	7.26009i	0.265989	+	0.265989i
$746$	26.4460	−	26.4460i	0.968255	−	0.968255i
$747$	22.6699	+	11.2758i	0.829447	+	0.412559i
$748$	3.45598	+	3.45598i	0.126363	+	0.126363i
$749$		−	2.93196i		−	0.107131i
$750$	1.47242	−	0.912132i	0.0537651	−	0.0333063i
$751$		−	18.3159i		−	0.668356i	−0.942510	−	0.334178i	$-0.891541\pi$
$751$		−	18.3159i		−	0.668356i	0.942510	−	0.334178i	$-0.108459\pi$
$752$		−	1.60456i		−	0.0585124i
$753$	3.92880	−	16.7208i	0.143174	−	0.609340i
$754$	−5.80795	+	5.80795i	−0.211513	+	0.211513i
$755$	−3.91205	−	3.91205i	−0.142374	−	0.142374i
$756$	−0.175681	−	1.88235i	−0.00638946	−	0.0684603i
$757$	−24.8581	−	24.8581i	−0.903485	−	0.903485i	0.0922511	−	0.995736i	$-0.470594\pi$
$757$	−24.8581	−	24.8581i	−0.903485	−	0.903485i	−0.995736	+	0.0922511i	$0.970594\pi$
$758$	21.4716	+	21.4716i	0.779883	+	0.779883i
$759$	1.34765	+	0.316651i	0.0489167	+	0.0114937i
$760$	−1.40229	+	1.40229i	−0.0508662	+	0.0508662i
$761$	5.56719			0.201811			0.100905	−	0.994896i	$-0.467826\pi$
$761$	5.56719			0.201811			0.100905	+	0.994896i	$0.467826\pi$
$762$	−7.49298	+	31.8897i	−0.271442	+	1.15524i
$763$	0.321939	+	0.321939i	0.0116550	+	0.0116550i
$764$	6.28026	+	6.28026i	0.227212	+	0.227212i
$765$	−10.6156	−	5.28008i	−0.383806	−	0.190902i
$766$	4.90455			0.177209
$767$	32.8970			1.18784
$768$	0.912132	+	1.47242i	0.0329137	+	0.0531313i
$769$	−27.1725	+	27.1725i	−0.979867	+	0.979867i	−0.999801	−	0.0199341i	$-0.993654\pi$
$769$	−27.1725	+	27.1725i	−0.979867	+	0.979867i	0.0199341	+	0.999801i	$0.493654\pi$
$770$	−0.449949			−0.0162150
$771$	33.8845	+	7.96167i	1.22032	+	0.286732i
$772$	−4.14557	+	4.14557i	−0.149202	+	0.149202i
$773$			33.3633i			1.19999i	0.800002	+	0.599997i	$0.204832\pi$
$773$			33.3633i			1.19999i	−0.800002	+	0.599997i	$0.795168\pi$
$774$	−18.0608	−	8.98325i	−0.649181	−	0.322896i
$775$	−0.163461	−	0.163461i	−0.00587170	−	0.00587170i
$776$	1.23130			0.0442010
$777$	−0.116458	+	3.83144i	−0.00417790	+	0.137452i
$778$	−10.7881			−0.386772
$779$	0.764478	+	0.764478i	0.0273903	+	0.0273903i
$780$	−5.30406	+	3.28575i	−0.189916	+	0.117649i
$781$			18.3154i			0.655375i
$782$	1.80607	−	1.80607i	0.0645848	−	0.0645848i
$783$	−9.12003	−	7.56299i	−0.325923	−	0.270279i
$784$	6.86763			0.245272
$785$	5.20223	−	5.20223i	0.185676	−	0.185676i
$786$	3.63502	−	2.25182i	0.129657	−	0.0803196i
$787$	−33.9347			−1.20964			−0.604820	−	0.796362i	$-0.706755\pi$
$787$	−33.9347			−1.20964			−0.604820	+	0.796362i	$0.706755\pi$
$788$	−17.9073			−0.637921
$789$	−17.4997	−	28.2491i	−0.623006	−	1.00569i
$790$	2.32156	+	2.32156i	0.0825976	+	0.0825976i
$791$	−2.69238	−	2.69238i	−0.0957299	−	0.0957299i
$792$	1.18058	+	3.51723i	0.0419501	+	0.124979i
$793$	13.2960			0.472154
$794$	−11.0720	+	11.0720i	−0.392930	+	0.392930i
$795$	3.17756	−	13.5235i	0.112697	−	0.479631i
$796$	−16.9444	−	16.9444i	−0.600579	−	0.600579i
$797$	13.6606	+	13.6606i	0.483882	+	0.483882i	0.906369	−	0.422487i	$-0.138843\pi$
$797$	13.6606	+	13.6606i	0.483882	+	0.483882i	−0.422487	+	0.906369i	$0.638843\pi$
$798$	−1.06239	+	0.658128i	−0.0376082	+	0.0232975i
$799$	−4.48400	−	4.48400i	−0.158632	−	0.158632i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	−2.21321	+	0.742880i	−0.0782000	+	0.0262484i
$802$			17.6961i			0.624871i
$803$		−	1.98789i		−	0.0701511i
$804$	−4.51490	−	7.28823i	−0.159228	−	0.257036i
$805$			0.235140i			0.00828758i
$806$	0.588832	+	0.588832i	0.0207407	+	0.0207407i
$807$	−41.3197	+	25.5967i	−1.45452	+	0.901045i
$808$	0.614366	−	0.614366i	0.0216133	−	0.0216133i
$809$	−34.7920	−	34.7920i	−1.22322	−	1.22322i	−0.966481	−	0.256739i	$-0.917352\pi$
$809$	−34.7920	−	34.7920i	−1.22322	−	1.22322i	−0.256739	−	0.966481i	$-0.582648\pi$
$810$	−5.43004	−	7.17737i	−0.190792	−	0.252187i
$811$	26.1483			0.918190			0.459095	−	0.888387i	$-0.348174\pi$
$811$	26.1483			0.918190			0.459095	+	0.888387i	$0.348174\pi$
$812$	−0.586607	+	0.586607i	−0.0205859	+	0.0205859i
$813$	14.8973	+	24.0481i	0.522470	+	0.843403i
$814$	−1.49739	−	7.37197i	−0.0524834	−	0.258387i
$815$		−	11.5361i		−	0.404092i
$816$	6.66370	+	1.56574i	0.233276	+	0.0548118i
$817$			13.3343i			0.466506i
$818$	−14.7465			−0.515599
$819$	−3.72750	+	1.25116i	−0.130249	+	0.0437190i
$820$	0.385490	+	0.385490i	0.0134619	+	0.0134619i
$821$			47.8121i			1.66865i	0.551271	+	0.834326i	$0.314143\pi$
$821$			47.8121i			1.66865i	−0.551271	+	0.834326i	$0.685857\pi$
$822$	−14.0140	−	3.29280i	−0.488795	−	0.114850i
$823$	40.9071			1.42593			0.712967	−	0.701198i	$-0.247351\pi$
$823$	40.9071			1.42593			0.712967	+	0.701198i	$0.247351\pi$
$824$			10.8748i			0.378843i
$825$	−1.82093	+	1.12803i	−0.0633966	+	0.0392728i
$826$	3.32262			0.115609
$827$	5.09416	−	5.09416i	0.177141	−	0.177141i	−0.612967	−	0.790108i	$-0.710024\pi$
$827$	5.09416	−	5.09416i	0.177141	−	0.177141i	0.790108	+	0.612967i	$0.210024\pi$
$828$	1.83808	−	0.616963i	0.0638776	−	0.0214409i
$829$	0.526668	−	0.526668i	0.0182919	−	0.0182919i	−0.697902	−	0.716194i	$-0.745883\pi$
$829$	0.526668	−	0.526668i	0.0182919	−	0.0182919i	0.716194	+	0.697902i	$0.245883\pi$
$830$		−	8.43976i		−	0.292948i
$831$	−7.92428	−	1.86193i	−0.274890	−	0.0645897i
$832$	2.54719	−	2.54719i	0.0883081	−	0.0883081i
$833$	19.1918	−	19.1918i	0.664956	−	0.664956i
$834$	−4.43384	−	1.04180i	−0.153531	−	0.0360745i
$835$		−	9.99534i		−	0.345903i
$836$	1.73420	−	1.73420i	0.0599784	−	0.0599784i
$837$	−0.766764	+	0.924623i	−0.0265032	+	0.0319596i
$838$	−5.47065	+	5.47065i	−0.188980	+	0.188980i
$839$	−5.09230			−0.175806			−0.0879029	−	0.996129i	$-0.528017\pi$
$839$	−5.09230			−0.175806			−0.0879029	+	0.996129i	$0.528017\pi$
$840$	−0.535713	+	0.331863i	−0.0184839	+	0.0114504i
$841$		−	23.8010i		−	0.820723i
$842$	−10.4208			−0.359123
$843$	−5.38122	−	1.26440i	−0.185339	−	0.0435483i
$844$			21.7223i			0.747714i
$845$	−0.0166925	−	0.0166925i	−0.000574239	−	0.000574239i
$846$	−1.53176	−	4.56347i	−0.0526630	−	0.156895i
$847$	−3.44571			−0.118396
$848$			8.02046i			0.275424i
$849$	33.2466	+	7.81179i	1.14102	+	0.268100i
$850$			3.95206i			0.135555i
$851$	−3.85253	+	0.782524i	−0.132063	+	0.0268246i
$852$	13.5086	+	21.8064i	0.462798	+	0.747076i
$853$	−4.43543	+	4.43543i	−0.151866	+	0.151866i	−0.778951	−	0.627085i	$-0.784248\pi$
$853$	−4.43543	+	4.43543i	−0.151866	+	0.151866i	0.627085	+	0.778951i	$0.284248\pi$
$854$	1.34290			0.0459532
$855$	−2.64952	+	5.32685i	−0.0906118	+	0.182174i
$856$	5.69825	+	5.69825i	0.194762	+	0.194762i
$857$	26.3940	−	26.3940i	0.901603	−	0.901603i	−0.0939721	−	0.995575i	$-0.529956\pi$
$857$	26.3940	−	26.3940i	0.901603	−	0.901603i	0.995575	+	0.0939721i	$0.0299564\pi$
$858$	6.55949	−	4.06346i	0.223937	−	0.138724i
$859$	10.3149	+	10.3149i	0.351939	+	0.351939i	0.860831	−	0.508891i	$-0.169945\pi$
$859$	10.3149	+	10.3149i	0.351939	+	0.351939i	−0.508891	+	0.860831i	$0.669945\pi$
$860$			6.72384i			0.229281i
$861$	0.180920	+	0.292053i	0.00616575	+	0.00995312i
$862$		−	30.4872i		−	1.03840i
$863$			23.7580i			0.808733i	0.914597	+	0.404366i	$0.132508\pi$
$863$			23.7580i			0.808733i	−0.914597	+	0.404366i	$0.867492\pi$
$864$	3.99977	+	3.31690i	0.136075	+	0.112843i
$865$	4.61670	−	4.61670i	0.156973	−	0.156973i
$866$	25.3678	+	25.3678i	0.862034	+	0.862034i
$867$	−2.03369	+	1.25983i	−0.0690678	+	0.0427860i
$868$	0.0594724	+	0.0594724i	0.00201863	+	0.00201863i
$869$	−2.87106	−	2.87106i	−0.0973941	−	0.0973941i
$870$	−0.903350	+	3.84461i	−0.0306264	+	0.130345i
$871$	−12.6082	+	12.6082i	−0.427212	+	0.427212i
$872$	−1.25137			−0.0423769
$873$	3.50189	−	1.17543i	0.118521	−	0.0397824i
$874$	−0.906278	−	0.906278i	−0.0306553	−	0.0306553i
$875$	−0.257268	−	0.257268i	−0.00869725	−	0.00869725i
$876$	−1.46618	−	2.36680i	−0.0495378	−	0.0799668i
$877$	26.5447			0.896350			0.448175	−	0.893946i	$-0.352074\pi$
$877$	26.5447			0.896350			0.448175	+	0.893946i	$0.352074\pi$
$878$	18.6436			0.629190
$879$	25.6676	−	15.9006i	0.865748	−	0.536313i
$880$	0.874474	−	0.874474i	0.0294785	−	0.0294785i
$881$	42.4433			1.42995			0.714975	−	0.699150i	$-0.246438\pi$
$881$	42.4433			1.42995			0.714975	+	0.699150i	$0.246438\pi$
$882$	19.5319	−	6.55603i	0.657675	−	0.220753i
$883$	5.29583	−	5.29583i	0.178219	−	0.178219i	−0.612360	−	0.790579i	$-0.709780\pi$
$883$	5.29583	−	5.29583i	0.178219	−	0.178219i	0.790579	+	0.612360i	$0.209780\pi$
$884$		−	14.2364i		−	0.478823i
$885$	13.4465	−	8.32984i	0.452000	−	0.280004i
$886$	−27.9796	−	27.9796i	−0.939993	−	0.939993i
$887$	24.9714			0.838457			0.419228	−	0.907881i	$-0.362301\pi$
$887$	24.9714			0.838457			0.419228	+	0.907881i	$0.362301\pi$
$888$	−7.22006	−	7.67273i	−0.242289	−	0.257480i
$889$	6.88114			0.230786
$890$	0.550261	+	0.550261i	0.0184448	+	0.0184448i
$891$	6.71529	+	8.87620i	0.224971	+	0.297364i
$892$			7.24611i			0.242618i
$893$	−2.25005	+	2.25005i	−0.0752952	+	0.0752952i
$894$	−17.3120	−	4.06773i	−0.579001	−	0.136045i
$895$	7.13469			0.238486
$896$	0.257268	−	0.257268i	0.00859473	−	0.00859473i
$897$	−2.12353	−	3.42794i	−0.0709028	−	0.114456i
$898$	−17.3850			−0.580144
$899$	0.527097			0.0175797
$900$	−1.33603	+	2.68608i	−0.0445344	+	0.0895360i
$901$	22.4134	+	22.4134i	0.746699	+	0.746699i
$902$	−0.476733	−	0.476733i	−0.0158735	−	0.0158735i
$903$	−0.969200	+	4.12487i	−0.0322530	+	0.137267i
$904$	10.4652			0.348069
$905$	1.18461	−	1.18461i	0.0393778	−	0.0393778i
$906$	9.32848	+	2.19187i	0.309918	+	0.0728199i
$907$	−18.6705	−	18.6705i	−0.619943	−	0.619943i	0.325573	−	0.945517i	$-0.394443\pi$
$907$	−18.6705	−	18.6705i	−0.619943	−	0.619943i	−0.945517	+	0.325573i	$0.894443\pi$
$908$	7.21839	+	7.21839i	0.239551	+	0.239551i
$909$	1.16080	−	2.33379i	0.0385014	−	0.0774068i
$910$	0.926751	+	0.926751i	0.0307215	+	0.0307215i
$911$	27.8252	−	27.8252i	0.921888	−	0.921888i	−0.0752744	−	0.997163i	$-0.523983\pi$
$911$	27.8252	−	27.8252i	0.921888	−	0.921888i	0.997163	+	0.0752744i	$0.0239833\pi$
$912$	0.785681	−	3.34382i	0.0260165	−	0.110725i
$913$			10.4374i			0.345427i
$914$			22.9623i			0.759525i
$915$	5.43469	−	3.36667i	0.179665	−	0.111299i
$916$		−	15.0972i		−	0.498824i
$917$	−0.635128	−	0.635128i	−0.0209738	−	0.0209738i
$918$	20.4467	−	1.90830i	0.674841	−	0.0629834i
$919$	−3.11659	+	3.11659i	−0.102807	+	0.102807i	−0.756639	−	0.653833i	$-0.773160\pi$
$919$	−3.11659	+	3.11659i	−0.102807	+	0.102807i	0.653833	+	0.756639i	$0.273160\pi$
$920$	−0.456993	−	0.456993i	−0.0150666	−	0.0150666i
$921$	−7.65513	+	4.74219i	−0.252245	+	0.156261i
$922$	−33.9413			−1.11780
$923$	37.7238	−	37.7238i	1.24169	−	1.24169i
$924$	0.662512	−	0.410412i	0.0217951	−	0.0135016i
$925$	3.35892	−	5.07126i	0.110441	−	0.166742i
$926$		−	12.9920i		−	0.426945i
$927$	10.3814	+	30.9287i	0.340971	+	1.01583i
$928$		−	2.28014i		−	0.0748492i
$929$	−27.4680			−0.901196			−0.450598	−	0.892727i	$-0.648789\pi$
$929$	−27.4680			−0.901196			−0.450598	+	0.892727i	$0.648789\pi$
$930$	0.389781	+	0.0915850i	0.0127814	+	0.00300319i
$931$	−9.63037	−	9.63037i	−0.315623	−	0.315623i
$932$			1.67396i			0.0548324i
$933$	2.14296	−	9.12033i	0.0701574	−	0.298586i
$934$	28.0829			0.918901
$935$		−	4.88749i		−	0.159838i
$936$	4.81275	−	9.67600i	0.157310	−	0.316270i
$937$	3.88068			0.126776			0.0633881	−	0.997989i	$-0.479809\pi$
$937$	3.88068			0.126776			0.0633881	+	0.997989i	$0.479809\pi$
$938$	−1.27344	+	1.27344i	−0.0415792	+	0.0415792i
$939$	13.2289	−	56.3013i	0.431707	−	1.83732i
$940$	−1.13460	+	1.13460i	−0.0370065	+	0.0370065i
$941$			6.69963i			0.218402i	0.994020	+	0.109201i	$0.0348292\pi$
$941$			6.69963i			0.218402i	−0.994020	+	0.109201i	$0.965171\pi$
$942$	−2.91474	+	12.4050i	−0.0949673	+	0.404176i
$943$	−0.249137	+	0.249137i	−0.00811302	+	0.00811302i
$944$	−6.45749	+	6.45749i	−0.210174	+	0.210174i
$945$	−1.20680	+	1.45525i	−0.0392571	+	0.0473391i
$946$		−	8.31532i		−	0.270354i
$947$	36.9175	−	36.9175i	1.19966	−	1.19966i	0.225387	−	0.974269i	$-0.427635\pi$
$947$	36.9175	−	36.9175i	1.19966	−	1.19966i	0.974269	−	0.225387i	$-0.0723646\pi$
$948$	−5.53589	−	1.30074i	−0.179797	−	0.0422461i
$949$	−4.09442	+	4.09442i	−0.132911	+	0.132911i
$950$	1.98313			0.0643413
$951$	13.3618	+	21.5694i	0.433285	+	0.699435i
$952$		−	1.43789i		−	0.0466022i
$953$	39.3439			1.27447			0.637237	−	0.770668i	$-0.280077\pi$
$953$	39.3439			1.27447			0.637237	+	0.770668i	$0.280077\pi$
$954$	7.65656	+	22.8107i	0.247890	+	0.738523i
$955$		−	8.88163i		−	0.287403i
$956$	−8.93980	−	8.93980i	−0.289134	−	0.289134i
$957$	1.11717	−	4.75460i	0.0361129	−	0.153694i
$958$	16.6846			0.539054
$959$			3.02393i			0.0976478i
$960$	0.396182	−	1.68613i	0.0127867	−	0.0544197i
$961$			30.9466i			0.998276i
$962$	−12.0998	+	18.2681i	−0.390112	+	0.588986i
$963$	21.6459	+	10.7665i	0.697528	+	0.346944i
$964$	1.90045	−	1.90045i	0.0612094	−	0.0612094i
$965$	5.86272			0.188728
$966$	−0.214478	−	0.346224i	−0.00690073	−	0.0111396i
$967$	−37.0888	−	37.0888i	−1.19269	−	1.19269i	−0.976308	−	0.216386i	$-0.930573\pi$
$967$	−37.0888	−	37.0888i	−1.19269	−	1.19269i	−0.216386	−	0.976308i	$-0.569427\pi$
$968$	6.69672	−	6.69672i	0.215241	−	0.215241i
$969$	−7.14880	−	11.5400i	−0.229653	−	0.370719i
$970$	−0.870659	−	0.870659i	−0.0279552	−	0.0279552i
$971$			56.6923i			1.81934i	0.415328	+	0.909672i	$0.363667\pi$
$971$			56.6923i			1.81934i	−0.415328	+	0.909672i	$0.636333\pi$
$972$	14.5420	+	5.61517i	0.466435	+	0.180107i
$973$			0.956730i			0.0306714i
$974$		−	35.5327i		−	1.13854i
$975$	6.07391	+	1.42716i	0.194521	+	0.0457056i
$976$	−2.60993	+	2.60993i	−0.0835418	+	0.0835418i
$977$	3.60270	+	3.60270i	0.115261	+	0.115261i	0.762385	−	0.647124i	$-0.224028\pi$
$977$	3.60270	+	3.60270i	0.115261	+	0.115261i	−0.647124	+	0.762385i	$0.724028\pi$
$978$	10.5224	+	16.9860i	0.336470	+	0.543151i
$979$	−0.680504	−	0.680504i	−0.0217490	−	0.0217490i
$980$	−4.85614	−	4.85614i	−0.155124	−	0.155124i
$981$	−3.55898	+	1.19460i	−0.113630	+	0.0381405i
$982$	−3.27276	+	3.27276i	−0.104438	+	0.104438i
$983$	1.73393			0.0553037			0.0276518	−	0.999618i	$-0.491197\pi$
$983$	1.73393			0.0553037			0.0276518	+	0.999618i	$0.491197\pi$
$984$	−0.919221	−	0.215985i	−0.0293037	−	0.00688535i
$985$	12.6624	+	12.6624i	0.403457	+	0.403457i
$986$	−6.37192	−	6.37192i	−0.202923	−	0.202923i
$987$	−0.859585	+	0.532495i	−0.0273609	+	0.0169495i
$988$	−7.14379			−0.227274
$989$	−4.34552			−0.138180
$990$	1.65226	−	3.32185i	0.0525122	−	0.105575i
$991$	2.15717	−	2.15717i	0.0685249	−	0.0685249i	−0.672014	−	0.740539i	$-0.734570\pi$
$991$	2.15717	−	2.15717i	0.0685249	−	0.0685249i	0.740539	+	0.672014i	$0.234570\pi$
$992$	−0.231169			−0.00733962
$993$	1.55627	−	6.62340i	0.0493867	−	0.210187i
$994$	3.81013	−	3.81013i	0.120850	−	0.120850i
$995$			23.9630i			0.759679i
$996$	7.69817	+	12.4269i	0.243926	+	0.393760i
$997$	−22.8790	−	22.8790i	−0.724584	−	0.724584i	0.244951	−	0.969535i	$-0.421228\pi$
$997$	−22.8790	−	22.8790i	−0.724584	−	0.724584i	−0.969535	+	0.244951i	$0.921228\pi$
$998$	−7.82896			−0.247822
$999$	−27.8589	−	14.9292i	−0.881416	−	0.472340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.191.17	yes	40
3.2	odd	2	inner	1110.2.u.e.191.6	✓	40
37.31	odd	4	inner	1110.2.u.e.401.6	yes	40
111.68	even	4	inner	1110.2.u.e.401.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.6	✓	40	3.2	odd	2	inner
1110.2.u.e.191.17	yes	40	1.1	even	1	trivial
1110.2.u.e.401.6	yes	40	37.31	odd	4	inner
1110.2.u.e.401.17	yes	40	111.68	even	4	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.912132 + 1.47242i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.396182 + 1.68613i) q^{6} +0.363832 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33603 + 2.68608i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.912132 + 1.47242i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.396182 + 1.68613i) q^{6} +0.363832 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33603 + 2.68608i) q^{9} +1.00000 q^{10} -1.23669 q^{11} +(-1.47242 + 0.912132i) q^{12} +(2.54719 + 2.54719i) q^{13} +(0.257268 + 0.257268i) q^{14} +(1.68613 + 0.396182i) q^{15} -1.00000 q^{16} +(-2.79453 + 2.79453i) q^{17} +(-2.84406 + 0.954629i) q^{18} +(1.40229 + 1.40229i) q^{19} +(0.707107 + 0.707107i) q^{20} +(0.331863 + 0.535713i) q^{21} +(-0.874474 - 0.874474i) q^{22} +(-0.456993 + 0.456993i) q^{23} +(-1.68613 - 0.396182i) q^{24} -1.00000i q^{25} +3.60228i q^{26} +(-5.17367 + 0.482863i) q^{27} +0.363832i q^{28} +(1.61230 + 1.61230i) q^{29} +(0.912132 + 1.47242i) q^{30} +(0.163461 - 0.163461i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.12803 - 1.82093i) q^{33} -3.95206 q^{34} +(0.257268 - 0.257268i) q^{35} +(-2.68608 - 1.33603i) q^{36} +(5.07126 + 3.35892i) q^{37} +1.98313i q^{38} +(-1.42716 + 6.07391i) q^{39} +1.00000i q^{40} +0.545166 q^{41} +(-0.144144 + 0.613469i) q^{42} +(4.75447 + 4.75447i) q^{43} -1.23669i q^{44} +(0.954629 + 2.84406i) q^{45} -0.646286 q^{46} +1.60456i q^{47} +(-0.912132 - 1.47242i) q^{48} -6.86763 q^{49} +(0.707107 - 0.707107i) q^{50} +(-6.66370 - 1.56574i) q^{51} +(-2.54719 + 2.54719i) q^{52} -8.02046i q^{53} +(-3.99977 - 3.31690i) q^{54} +(-0.874474 + 0.874474i) q^{55} +(-0.257268 + 0.257268i) q^{56} +(-0.785681 + 3.34382i) q^{57} +2.28014i q^{58} +(6.45749 - 6.45749i) q^{59} +(-0.396182 + 1.68613i) q^{60} +(2.60993 - 2.60993i) q^{61} +0.231169 q^{62} +(-0.486091 + 0.977282i) q^{63} -1.00000i q^{64} +3.60228 q^{65} +(0.489956 - 2.08523i) q^{66} +4.94984i q^{67} +(-2.79453 - 2.79453i) q^{68} +(-1.08972 - 0.256047i) q^{69} +0.363832 q^{70} -14.8100i q^{71} +(-0.954629 - 2.84406i) q^{72} +1.60743i q^{73} +(1.21080 + 5.96104i) q^{74} +(1.47242 - 0.912132i) q^{75} +(-1.40229 + 1.40229i) q^{76} -0.449949 q^{77} +(-5.30406 + 3.28575i) q^{78} +(2.32156 + 2.32156i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-5.43004 - 7.17737i) q^{81} +(0.385490 + 0.385490i) q^{82} -8.43976i q^{83} +(-0.535713 + 0.331863i) q^{84} +3.95206i q^{85} +6.72384i q^{86} +(-0.903350 + 3.84461i) q^{87} +(0.874474 - 0.874474i) q^{88} +(0.550261 + 0.550261i) q^{89} +(-1.33603 + 2.68608i) q^{90} +(0.926751 + 0.926751i) q^{91} +(-0.456993 - 0.456993i) q^{92} +(0.389781 + 0.0915850i) q^{93} +(-1.13460 + 1.13460i) q^{94} +1.98313 q^{95} +(0.396182 - 1.68613i) q^{96} +(-0.870659 - 0.870659i) q^{97} +(-4.85614 - 4.85614i) q^{98} +(1.65226 - 3.32185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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