LMFDB - Embedded newform 231.2.w.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(13,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("231.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	231.13
Dual form			231.2.w.a.160.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36445 - 0.768257i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.38238 + 2.45745i) q^{4} +(-1.43953 + 0.467733i) q^{5} +(-0.768257 - 2.36445i) q^{6} +(-2.17258 + 1.50993i) q^{7} +(-3.18691 - 4.38641i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-2.36445 - 0.768257i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.38238 + 2.45745i) q^{4} +(-1.43953 + 0.467733i) q^{5} +(-0.768257 - 2.36445i) q^{6} +(-2.17258 + 1.50993i) q^{7} +(-3.18691 - 4.38641i) q^{8} +(-0.309017 + 0.951057i) q^{9} +3.76305 q^{10} +(-3.31648 + 0.0306870i) q^{11} +4.18086i q^{12} +(2.04482 - 6.29331i) q^{13} +(6.29698 - 1.90106i) q^{14} +(-1.22454 - 0.889681i) q^{15} +(1.58150 + 4.86735i) q^{16} +(-1.64748 - 5.07043i) q^{17} +(1.46131 - 2.01132i) q^{18} +(-5.70150 + 4.14238i) q^{19} +(-6.01849 - 1.95552i) q^{20} +(-2.49857 - 0.870141i) q^{21} +(7.86524 + 2.47535i) q^{22} +1.84535 q^{23} +(1.67546 - 5.15653i) q^{24} +(-2.19160 + 1.59229i) q^{25} +(-9.66976 + 13.3093i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-11.0591 - 0.231840i) q^{28} +(-2.36985 + 3.26181i) q^{29} +(2.21187 + 3.04437i) q^{30} +(-7.28836 - 2.36813i) q^{31} -1.87984i q^{32} +(-1.97421 - 2.66505i) q^{33} +13.2545i q^{34} +(2.42126 - 3.18978i) q^{35} +(-3.38238 + 2.45745i) q^{36} +(1.50020 + 1.08996i) q^{37} +(16.6633 - 5.41424i) q^{38} +(6.29331 - 2.04482i) q^{39} +(6.63933 + 4.82376i) q^{40} +(-0.563227 + 0.409208i) q^{41} +(5.23926 + 3.97695i) q^{42} -3.70678i q^{43} +(-11.2930 - 8.04628i) q^{44} -1.51362i q^{45} +(-4.36324 - 1.41770i) q^{46} +(1.27570 + 1.75584i) q^{47} +(-3.00819 + 4.14042i) q^{48} +(2.44022 - 6.56089i) q^{49} +(6.40522 - 2.08118i) q^{50} +(3.13370 - 4.31316i) q^{51} +(22.3818 - 16.2614i) q^{52} +(-1.71523 + 5.27894i) q^{53} +2.48613 q^{54} +(4.75984 - 1.59540i) q^{55} +(13.5470 + 4.71781i) q^{56} +(-6.70251 - 2.17778i) q^{57} +(8.10930 - 5.89175i) q^{58} +(0.189027 - 0.260174i) q^{59} +(-1.95552 - 6.01849i) q^{60} +(0.918719 + 2.82753i) q^{61} +(15.4136 + 11.1987i) q^{62} +(-0.764664 - 2.53284i) q^{63} +(1.71880 - 5.28992i) q^{64} +10.0159i q^{65} +(2.62047 + 7.81809i) q^{66} -1.21768 q^{67} +(6.88788 - 21.1987i) q^{68} +(1.08467 + 1.49292i) q^{69} +(-8.17554 + 5.68194i) q^{70} +(3.92242 + 12.0720i) q^{71} +(5.15653 - 1.67546i) q^{72} +(1.97075 + 1.43183i) q^{73} +(-2.70979 - 3.72971i) q^{74} +(-2.57638 - 0.837117i) q^{75} -29.4643 q^{76} +(7.15900 - 5.07433i) q^{77} -16.4512 q^{78} +(-2.72717 - 0.886112i) q^{79} +(-4.55325 - 6.26701i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.64610 - 0.534850i) q^{82} +(0.746175 + 2.29649i) q^{83} +(-6.31280 - 9.08325i) q^{84} +(4.74322 + 6.52848i) q^{85} +(-2.84776 + 8.76452i) q^{86} -4.03182 q^{87} +(10.7039 + 14.4496i) q^{88} -11.3795i q^{89} +(-1.16285 + 3.57887i) q^{90} +(5.05992 + 16.7603i) q^{91} +(6.24168 + 4.53485i) q^{92} +(-2.36813 - 7.28836i) q^{93} +(-1.66738 - 5.13167i) q^{94} +(6.26997 - 8.62988i) q^{95} +(1.52082 - 1.10494i) q^{96} +(-6.85422 - 2.22707i) q^{97} +(-10.8102 + 13.6382i) q^{98} +(0.995664 - 3.16365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−2.36445	−	0.768257i	−1.67192	−	0.543240i	−0.688603	−	0.725138i	$-0.741776\pi$
$2$	−2.36445	−	0.768257i	−1.67192	−	0.543240i	−0.983317	+	0.181899i	$0.941776\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	3.38238	+	2.45745i	1.69119	+	1.22872i
$5$	−1.43953	+	0.467733i	−0.643779	+	0.209177i	−0.612669	−	0.790339i	$-0.709904\pi$
$5$	−1.43953	+	0.467733i	−0.643779	+	0.209177i	−0.0311101	+	0.999516i	$0.509904\pi$
$6$	−0.768257	−	2.36445i	−0.313640	−	0.965284i
$7$	−2.17258	+	1.50993i	−0.821159	+	0.570700i
$7$	−2.17258	+	1.50993i	−0.821159	+	0.570700i
$8$	−3.18691	−	4.38641i	−1.12674	−	1.55083i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	3.76305			1.18998
$11$	−3.31648	+	0.0306870i	−0.999957	+	0.00925249i
$11$	−3.31648	+	0.0306870i	−0.999957	+	0.00925249i
$12$			4.18086i			1.20691i
$13$	2.04482	−	6.29331i	0.567131	−	1.74545i	−0.0944015	−	0.995534i	$-0.530094\pi$
$13$	2.04482	−	6.29331i	0.567131	−	1.74545i	0.661533	−	0.749916i	$-0.269906\pi$
$14$	6.29698	−	1.90106i	1.68294	−	0.508078i
$15$	−1.22454	−	0.889681i	−0.316175	−	0.229715i
$16$	1.58150	+	4.86735i	0.395375	+	1.21684i
$17$	−1.64748	−	5.07043i	−0.399573	−	1.22976i	−0.925342	−	0.379132i	$-0.876222\pi$
$17$	−1.64748	−	5.07043i	−0.399573	−	1.22976i	0.525769	−	0.850627i	$-0.323778\pi$
$18$	1.46131	−	2.01132i	0.344435	−	0.474073i
$19$	−5.70150	+	4.14238i	−1.30801	+	0.950327i	−0.999999	−	0.00105499i	$-0.999664\pi$
$19$	−5.70150	+	4.14238i	−1.30801	+	0.950327i	−0.308013	+	0.951382i	$0.599664\pi$
$20$	−6.01849	−	1.95552i	−1.34577	−	0.437269i
$21$	−2.49857	−	0.870141i	−0.545233	−	0.189880i
$22$	7.86524	+	2.47535i	1.67688	+	0.527747i
$23$	1.84535			0.384782			0.192391	−	0.981318i	$-0.438376\pi$
$23$	1.84535			0.384782			0.192391	+	0.981318i	$0.438376\pi$
$24$	1.67546	−	5.15653i	0.342001	−	1.05257i
$25$	−2.19160	+	1.59229i	−0.438320	+	0.318458i
$26$	−9.66976	+	13.3093i	−1.89640	+	2.61017i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−11.0591	−	0.231840i	−2.08997	−	0.0438137i
$29$	−2.36985	+	3.26181i	−0.440069	+	0.605703i	−0.970228	−	0.242195i	$-0.922133\pi$
$29$	−2.36985	+	3.26181i	−0.440069	+	0.605703i	0.530158	+	0.847899i	$0.322133\pi$
$30$	2.21187	+	3.04437i	0.403830	+	0.555824i
$31$	−7.28836	−	2.36813i	−1.30903	−	0.425329i	−0.430315	−	0.902679i	$-0.641597\pi$
$31$	−7.28836	−	2.36813i	−1.30903	−	0.425329i	−0.878713	+	0.477350i	$0.841597\pi$
$32$		−	1.87984i		−	0.332311i
$33$	−1.97421	−	2.66505i	−0.343665	−	0.463926i
$34$			13.2545i			2.27312i
$35$	2.42126	−	3.18978i	0.409268	−	0.539172i
$36$	−3.38238	+	2.45745i	−0.563730	+	0.409574i
$37$	1.50020	+	1.08996i	0.246632	+	0.179189i	0.704233	−	0.709969i	$-0.251291\pi$
$37$	1.50020	+	1.08996i	0.246632	+	0.179189i	−0.457601	+	0.889158i	$0.651291\pi$
$38$	16.6633	−	5.41424i	2.70315	−	0.878306i
$39$	6.29331	−	2.04482i	1.00774	−	0.327433i
$40$	6.63933	+	4.82376i	1.04977	+	0.762703i
$41$	−0.563227	+	0.409208i	−0.0879612	+	0.0639076i	−0.630897	−	0.775867i	$-0.717313\pi$
$41$	−0.563227	+	0.409208i	−0.0879612	+	0.0639076i	0.542935	+	0.839774i	$0.317313\pi$
$42$	5.23926	+	3.97695i	0.808435	+	0.613657i
$43$		−	3.70678i		−	0.565279i	−0.959226	−	0.282640i	$-0.908790\pi$
$43$		−	3.70678i		−	0.565279i	0.959226	−	0.282640i	$-0.0912101\pi$
$44$	−11.2930	−	8.04628i	−1.70249	−	1.21302i
$45$		−	1.51362i		−	0.225637i
$46$	−4.36324	−	1.41770i	−0.643325	−	0.209029i
$47$	1.27570	+	1.75584i	0.186079	+	0.256116i	0.891857	−	0.452317i	$-0.149402\pi$
$47$	1.27570	+	1.75584i	0.186079	+	0.256116i	−0.705778	+	0.708433i	$0.749402\pi$
$48$	−3.00819	+	4.14042i	−0.434195	+	0.597618i
$49$	2.44022	−	6.56089i	0.348604	−	0.937270i
$50$	6.40522	−	2.08118i	0.905835	−	0.294324i
$51$	3.13370	−	4.31316i	0.438805	−	0.603964i
$52$	22.3818	−	16.2614i	3.10380	−	2.25504i
$53$	−1.71523	+	5.27894i	−0.235605	+	0.725118i	0.761435	+	0.648241i	$0.224495\pi$
$53$	−1.71523	+	5.27894i	−0.235605	+	0.725118i	−0.997041	+	0.0768773i	$0.975505\pi$
$54$	2.48613			0.338320
$55$	4.75984	−	1.59540i	0.641816	−	0.215124i
$56$	13.5470	+	4.71781i	1.81029	+	0.630445i
$57$	−6.70251	−	2.17778i	−0.887769	−	0.288454i
$58$	8.10930	−	5.89175i	1.06480	−	0.773625i
$59$	0.189027	−	0.260174i	0.0246093	−	0.0338718i	−0.796535	−	0.604592i	$-0.793336\pi$
$59$	0.189027	−	0.260174i	0.0246093	−	0.0338718i	0.821144	+	0.570721i	$0.193336\pi$
$60$	−1.95552	−	6.01849i	−0.252457	−	0.776983i
$61$	0.918719	+	2.82753i	0.117630	+	0.362028i	0.992486	−	0.122355i	$-0.0390445\pi$
$61$	0.918719	+	2.82753i	0.117630	+	0.362028i	−0.874857	+	0.484382i	$0.839044\pi$
$62$	15.4136	+	11.1987i	1.95754	+	1.42223i
$63$	−0.764664	−	2.53284i	−0.0963386	−	0.319108i
$64$	1.71880	−	5.28992i	0.214850	−	0.661240i
$65$			10.0159i			1.24232i
$66$	2.62047	+	7.81809i	0.322558	+	0.962340i
$67$	−1.21768			−0.148763			−0.0743814	−	0.997230i	$-0.523698\pi$
$67$	−1.21768			−0.148763			−0.0743814	+	0.997230i	$0.523698\pi$
$68$	6.88788	−	21.1987i	0.835279	−	2.57072i
$69$	1.08467	+	1.49292i	0.130579	+	0.179726i
$70$	−8.17554	+	5.68194i	−0.977163	+	0.679122i
$71$	3.92242	+	12.0720i	0.465505	+	1.43268i	0.858346	+	0.513071i	$0.171492\pi$
$71$	3.92242	+	12.0720i	0.465505	+	1.43268i	−0.392841	+	0.919607i	$0.628508\pi$
$72$	5.15653	−	1.67546i	0.607703	−	0.197455i
$73$	1.97075	+	1.43183i	0.230658	+	0.167583i	0.697111	−	0.716963i	$-0.254468\pi$
$73$	1.97075	+	1.43183i	0.230658	+	0.167583i	−0.466453	+	0.884546i	$0.654468\pi$
$74$	−2.70979	−	3.72971i	−0.315007	−	0.433570i
$75$	−2.57638	−	0.837117i	−0.297495	−	0.0966619i
$76$	−29.4643			−3.37979
$77$	7.15900	−	5.07433i	0.815843	−	0.578273i
$78$	−16.4512			−1.86273
$79$	−2.72717	−	0.886112i	−0.306831	−	0.0996954i	0.151555	−	0.988449i	$-0.451572\pi$
$79$	−2.72717	−	0.886112i	−0.306831	−	0.0996954i	−0.458386	+	0.888753i	$0.651572\pi$
$80$	−4.55325	−	6.26701i	−0.509068	−	0.700673i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.64610	−	0.534850i	0.181781	−	0.0590643i
$83$	0.746175	+	2.29649i	0.0819034	+	0.252073i	0.983620	−	0.180255i	$-0.0576923\pi$
$83$	0.746175	+	2.29649i	0.0819034	+	0.252073i	−0.901717	+	0.432328i	$0.857692\pi$
$84$	−6.31280	−	9.08325i	−0.688783	−	0.991064i
$85$	4.74322	+	6.52848i	0.514474	+	0.708113i
$86$	−2.84776	+	8.76452i	−0.307082	+	0.945102i
$87$	−4.03182			−0.432257
$88$	10.7039	+	14.4496i	1.14104	+	1.54034i
$89$		−	11.3795i		−	1.20623i	−0.797656	−	0.603113i	$-0.793927\pi$
$89$		−	11.3795i		−	1.20623i	0.797656	−	0.603113i	$-0.206073\pi$
$90$	−1.16285	+	3.57887i	−0.122575	+	0.377246i
$91$	5.05992	+	16.7603i	0.530423	+	1.75695i
$92$	6.24168	+	4.53485i	0.650740	+	0.472790i
$93$	−2.36813	−	7.28836i	−0.245564	−	0.755768i
$94$	−1.66738	−	5.13167i	−0.171977	−	0.529292i
$95$	6.26997	−	8.62988i	0.643286	−	0.885407i
$96$	1.52082	−	1.10494i	0.155218	−	0.112773i
$97$	−6.85422	−	2.22707i	−0.695941	−	0.226125i	−0.0603796	−	0.998175i	$-0.519231\pi$
$97$	−6.85422	−	2.22707i	−0.695941	−	0.226125i	−0.635561	+	0.772051i	$0.719231\pi$
$98$	−10.8102	+	13.6382i	−1.09200	+	1.37767i
$99$	0.995664	−	3.16365i	0.100068	−	0.317958i
$100$	−11.3258			−1.13258
$101$	−2.95152	+	9.08384i	−0.293687	+	0.903876i	0.689972	+	0.723836i	$0.257623\pi$
$101$	−2.95152	+	9.08384i	−0.293687	+	0.903876i	−0.983659	+	0.180040i	$0.942377\pi$
$102$	−10.7231	+	7.79079i	−1.06174	+	0.771403i
$103$	−1.47774	+	2.03393i	−0.145606	+	0.200409i	−0.875590	−	0.483054i	$-0.839527\pi$
$103$	−1.47774	+	2.03393i	−0.145606	+	0.200409i	0.729984	+	0.683464i	$0.239527\pi$
$104$	−34.1217	+	11.0868i	−3.34591	+	1.08715i
$105$	4.00377	+	0.0839343i	0.390728	+	0.00819115i
$106$	8.11117	−	11.1641i	0.787826	−	1.08435i
$107$	−6.87484	−	9.46240i	−0.664616	−	0.914765i	0.335007	−	0.942215i	$-0.391261\pi$
$107$	−6.87484	−	9.46240i	−0.664616	−	0.914765i	−0.999623	+	0.0274504i	$0.991261\pi$
$108$	−3.97623	−	1.29196i	−0.382613	−	0.124318i
$109$			6.64292i			0.636276i	0.948044	+	0.318138i	$0.103058\pi$
$109$			6.64292i			0.636276i	−0.948044	+	0.318138i	$0.896942\pi$
$110$	−12.4801	+	0.115477i	−1.18993	+	0.0110103i
$111$			1.85435i			0.176008i
$112$	−10.7853	−	8.18677i	−1.01912	−	0.773577i
$113$	7.85072	−	5.70388i	0.738534	−	0.536576i	−0.153718	−	0.988115i	$-0.549125\pi$
$113$	7.85072	−	5.70388i	0.738534	−	0.536576i	0.892252	+	0.451539i	$0.149125\pi$
$114$	14.1747	+	10.2985i	1.32758	+	0.964543i
$115$	−2.65645	+	0.863131i	−0.247715	+	0.0804874i
$116$	−16.0315	+	5.20893i	−1.48848	+	0.483637i
$117$	5.35341	+	3.88948i	0.494923	+	0.359583i
$118$	−0.646827	+	0.469947i	−0.0595452	+	0.0432621i
$119$	11.2353	+	8.52834i	1.02994	+	0.781792i
$120$			8.20667i			0.749163i
$121$	10.9981	−	0.203546i	0.999829	−	0.0185042i
$122$		−	7.39136i		−	0.669182i
$123$	−0.662113	−	0.215133i	−0.0597007	−	0.0193979i
$124$	−18.8325	−	25.9207i	−1.69121	−	2.32774i
$125$	6.85852	−	9.43995i	0.613445	−	0.844334i
$126$	−0.137863	+	6.57624i	−0.0122818	+	0.585858i
$127$	−18.9521	+	6.15792i	−1.68173	+	0.546427i	−0.985246	−	0.171147i	$-0.945253\pi$
$127$	−18.9521	+	6.15792i	−1.68173	+	0.546427i	−0.696483	+	0.717574i	$0.745253\pi$
$128$	−10.3379	+	14.2289i	−0.913752	+	1.25767i
$129$	2.99885	−	2.17879i	0.264034	−	0.191832i
$130$	7.69476	−	23.6820i	0.674875	−	2.07705i
$131$	0.891344			0.0778771			0.0389386	−	0.999242i	$-0.487602\pi$
$131$	0.891344			0.0778771			0.0389386	+	0.999242i	$0.487602\pi$
$132$	−0.128298	−	13.8657i	−0.0111669	−	1.20686i
$133$	6.13227	−	17.6085i	0.531735	−	1.52685i
$134$	2.87914	+	0.935488i	0.248719	+	0.0808138i
$135$	1.22454	−	0.889681i	0.105392	−	0.0765716i
$136$	−16.9906	+	23.3855i	−1.45693	+	2.00529i
$137$	−2.68784	−	8.27232i	−0.229638	−	0.706752i	−0.997788	−	0.0664821i	$-0.978822\pi$
$137$	−2.68784	−	8.27232i	−0.229638	−	0.706752i	0.768150	−	0.640270i	$-0.221178\pi$
$138$	−1.41770	−	4.36324i	−0.120683	−	0.371424i
$139$	18.0182	+	13.0910i	1.52828	+	1.11036i	0.957184	+	0.289480i	$0.0934825\pi$
$139$	18.0182	+	13.0910i	1.52828	+	1.11036i	0.571098	+	0.820882i	$0.306518\pi$
$140$	16.0284	−	4.83895i	1.35464	−	0.408966i
$141$	−0.670673	+	2.06412i	−0.0564809	+	0.173830i
$142$		−	31.5570i		−	2.64820i
$143$	−6.58849	+	20.9344i	−0.550957	+	1.75062i
$144$	−5.11784			−0.426487
$145$	1.88582	−	5.80395i	0.156609	−	0.481992i
$146$	−3.55972	−	4.89953i	−0.294605	−	0.405488i
$147$	6.74220	−	1.88221i	0.556087	−	0.155242i
$148$	2.39574	+	7.37334i	0.196929	+	0.606085i
$149$	−9.26938	+	3.01181i	−0.759378	+	0.246737i	−0.663011	−	0.748609i	$-0.730722\pi$
$149$	−9.26938	+	3.01181i	−0.759378	+	0.246737i	−0.0963661	+	0.995346i	$0.530722\pi$
$150$	5.44861	+	3.95864i	0.444877	+	0.323222i
$151$	8.13209	+	11.1929i	0.661780	+	0.910862i	0.999539	−	0.0303708i	$-0.00966881\pi$
$151$	8.13209	+	11.1929i	0.661780	+	0.910862i	−0.337759	+	0.941233i	$0.609669\pi$
$152$	36.3403	+	11.8077i	2.94759	+	0.957730i
$153$	5.33136			0.431015
$154$	−20.8255	+	6.49805i	−1.67817	+	0.523628i
$155$	11.5995			0.931694
$156$	26.3114	+	8.54910i	2.10660	+	0.684476i
$157$	−1.31734	−	1.81316i	−0.105135	−	0.144706i	0.753208	−	0.657783i	$-0.228506\pi$
$157$	−1.31734	−	1.81316i	−0.105135	−	0.144706i	−0.858343	+	0.513077i	$0.828506\pi$
$158$	5.76751	+	4.19034i	0.458838	+	0.333366i
$159$	−5.27894	+	1.71523i	−0.418647	+	0.136027i
$160$	0.879262	+	2.70609i	0.0695118	+	0.213935i
$161$	−4.00917	+	2.78635i	−0.315967	+	0.219595i
$162$	1.46131	+	2.01132i	0.114812	+	0.158024i
$163$	−0.635344	+	1.95539i	−0.0497640	+	0.153158i	−0.972850	−	0.231435i	$-0.925658\pi$
$163$	−0.635344	+	1.95539i	−0.0497640	+	0.153158i	0.923086	+	0.384592i	$0.125658\pi$
$164$	−2.91065			−0.227284
$165$	4.08847	+	2.91304i	0.318287	+	0.226779i
$166$		−	6.00320i		−	0.465939i
$167$	−0.660136	+	2.03169i	−0.0510828	+	0.157217i	−0.973344	−	0.229351i	$-0.926340\pi$
$167$	−0.660136	+	2.03169i	−0.0510828	+	0.157217i	0.922261	+	0.386568i	$0.126340\pi$
$168$	4.14593	+	13.7328i	0.319865	+	1.05951i
$169$	−24.9073	−	18.0962i	−1.91594	−	1.39201i
$170$	−6.19956	−	19.0803i	−0.475484	−	1.46339i
$171$	−2.17778	−	6.70251i	−0.166539	−	0.512554i
$172$	9.10922	−	12.5378i	0.694571	−	0.955995i
$173$	−18.9169	+	13.7440i	−1.43823	+	1.04493i	−0.449819	+	0.893120i	$0.648511\pi$
$173$	−18.9169	+	13.7440i	−1.43823	+	1.04493i	−0.988409	+	0.151814i	$0.951489\pi$
$174$	9.53305	+	3.09748i	0.722699	+	0.234819i
$175$	2.35718	−	6.76854i	0.178186	−	0.511654i
$176$	−5.39438	−	16.0940i	−0.406617	−	1.21313i
$177$	0.321593			0.0241724
$178$	−8.74239	+	26.9063i	−0.655270	+	2.01671i
$179$	10.3393	−	7.51197i	0.772798	−	0.561471i	−0.130011	−	0.991513i	$-0.541501\pi$
$179$	10.3393	−	7.51197i	0.772798	−	0.561471i	0.902809	+	0.430042i	$0.141501\pi$
$180$	3.71963	−	5.11963i	0.277245	−	0.381595i
$181$	−12.0602	+	3.91860i	−0.896429	+	0.291267i	−0.720762	−	0.693182i	$-0.756208\pi$
$181$	−12.0602	+	3.91860i	−0.896429	+	0.291267i	−0.175666	+	0.984450i	$0.556208\pi$
$182$	0.912265	−	43.5162i	0.0676216	−	3.22563i
$183$	−1.74751	+	2.40524i	−0.129179	+	0.177800i
$184$	−5.88097	−	8.09445i	−0.433551	−	0.596731i
$185$	−2.66941	−	0.867343i	−0.196259	−	0.0637683i
$186$			19.0523i			1.39698i
$187$	5.61944	+	16.7654i	0.410934	+	1.22601i
$188$			9.07389i			0.661782i
$189$	1.59965	−	2.10739i	0.116358	−	0.153290i
$190$	−21.4550	+	15.5880i	−1.55651	+	1.13087i
$191$	−0.850289	−	0.617771i	−0.0615248	−	0.0447004i	0.556598	−	0.830782i	$-0.312106\pi$
$191$	−0.850289	−	0.617771i	−0.0615248	−	0.0447004i	−0.618123	+	0.786082i	$0.712106\pi$
$192$	5.28992	−	1.71880i	0.381767	−	0.124044i
$193$	11.8403	−	3.84713i	0.852280	−	0.276923i	0.149879	−	0.988704i	$-0.452112\pi$
$193$	11.8403	−	3.84713i	0.852280	−	0.276923i	0.702401	+	0.711782i	$0.252112\pi$
$194$	14.4955	+	10.5316i	1.04072	+	0.756125i
$195$	−8.10301	+	5.88718i	−0.580268	+	0.421590i
$196$	24.3768	−	16.1947i	1.74120	−	1.15677i
$197$		−	5.65161i		−	0.402660i	−0.979523	−	0.201330i	$-0.935474\pi$
$197$		−	5.65161i		−	0.402660i	0.979523	−	0.201330i	$-0.0645264\pi$
$198$	−4.78469	+	6.71536i	−0.340033	+	0.477240i
$199$		−	7.39805i		−	0.524434i	−0.965009	−	0.262217i	$-0.915546\pi$
$199$		−	7.39805i		−	0.524434i	0.965009	−	0.262217i	$-0.0844536\pi$
$200$	13.9689	+	4.53876i	0.987748	+	0.320939i
$201$	−0.715732	−	0.985120i	−0.0504838	−	0.0694850i
$202$	13.9574	−	19.2108i	0.982043	−	1.35167i
$203$	0.223576	−	10.6649i	0.0156920	−	0.748526i
$204$	21.1987	−	6.88788i	1.48421	−	0.482248i
$205$	0.619384	−	0.852509i	0.0432597	−	0.0595418i
$206$	5.05663	−	3.67386i	0.352312	−	0.255970i
$207$	−0.570245	+	1.75503i	−0.0396347	+	0.121983i
$208$	33.8657			2.34816
$209$	18.7818	−	13.9131i	1.29916	−	0.962389i
$210$	−9.40225	−	3.27439i	−0.648817	−	0.225954i
$211$	12.3248	+	4.00458i	0.848476	+	0.275687i	0.700808	−	0.713350i	$-0.252823\pi$
$211$	12.3248	+	4.00458i	0.848476	+	0.275687i	0.147669	+	0.989037i	$0.452823\pi$
$212$	−18.7743	+	13.6403i	−1.28942	+	0.936820i
$213$	−7.46088	+	10.2690i	−0.511211	+	0.703622i
$214$	8.98567	+	27.6550i	0.614248	+	1.89046i
$215$	1.73379	+	5.33604i	0.118243	+	0.363915i
$216$	4.38641	+	3.18691i	0.298457	+	0.216842i
$217$	19.4103	−	5.85995i	1.31766	−	0.397799i
$218$	5.10347	−	15.7069i	0.345651	−	1.06380i
$219$			2.43598i			0.164608i
$220$	20.0202	+	6.30077i	1.34976	+	0.424798i
$221$	−35.2786			−2.37310
$222$	1.42462	−	4.38453i	0.0956143	−	0.294271i
$223$	5.54639	+	7.63395i	0.371413	+	0.511207i	0.953284	−	0.302074i	$-0.0976791\pi$
$223$	5.54639	+	7.63395i	0.371413	+	0.511207i	−0.581871	+	0.813281i	$0.697679\pi$
$224$	2.83842	+	4.08410i	0.189650	+	0.272880i
$225$	−0.837117	−	2.57638i	−0.0558078	−	0.171759i
$226$	−22.9447	+	7.45519i	−1.52626	+	0.495912i
$227$	−13.7746	−	10.0078i	−0.914253	−	0.664244i	0.0278341	−	0.999613i	$-0.491139\pi$
$227$	−13.7746	−	10.0078i	−0.914253	−	0.664244i	−0.942087	+	0.335369i	$0.891139\pi$
$228$	−17.3187	−	23.8371i	−1.14696	−	1.57865i
$229$	2.10476	+	0.683879i	0.139087	+	0.0451920i	0.377733	−	0.925915i	$-0.376704\pi$
$229$	2.10476	+	0.683879i	0.139087	+	0.0451920i	−0.238646	+	0.971107i	$0.576704\pi$
$230$	6.94415			0.457883
$231$	8.31317	+	2.80914i	0.546966	+	0.184828i
$232$	21.8601			1.43519
$233$	−1.23903	−	0.402587i	−0.0811718	−	0.0263743i	0.268150	−	0.963377i	$-0.413588\pi$
$233$	−1.23903	−	0.402587i	−0.0811718	−	0.0263743i	−0.349321	+	0.937003i	$0.613588\pi$
$234$	−9.66976	−	13.3093i	−0.632132	−	0.870055i
$235$	−2.65767	−	1.93091i	−0.173368	−	0.125959i
$236$	1.27873	−	0.415483i	0.0832380	−	0.0270457i
$237$	−0.886112	−	2.72717i	−0.0575592	−	0.177149i
$238$	−20.0133	−	28.7964i	−1.29727	−	1.86660i
$239$	5.06819	+	6.97576i	0.327834	+	0.451224i	0.940839	−	0.338855i	$-0.110039\pi$
$239$	5.06819	+	6.97576i	0.327834	+	0.451224i	−0.613005	+	0.790079i	$0.710039\pi$
$240$	2.39378	−	7.36731i	0.154518	−	0.475558i
$241$	−20.4954			−1.32022			−0.660112	−	0.751167i	$-0.729491\pi$
$241$	−20.4954			−1.32022			−0.660112	+	0.751167i	$0.729491\pi$
$242$	−26.1609	−	7.96811i	−1.68169	−	0.512209i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.84103	+	11.8215i	−0.245897	+	0.756792i
$245$	−0.444041	+	10.5860i	−0.0283688	+	0.676315i
$246$	1.40026	+	1.01735i	0.0892771	+	0.0648636i
$247$	14.4107	+	44.3517i	0.916934	+	2.82203i
$248$	12.8398	+	39.5167i	0.815326	+	2.50931i
$249$	−1.41931	+	1.95351i	−0.0899451	+	0.123799i
$250$	−23.4690	+	17.0512i	−1.48431	+	1.07841i
$251$	−20.2317	−	6.57366i	−1.27701	−	0.414926i	−0.409484	−	0.912317i	$-0.634291\pi$
$251$	−20.2317	−	6.57366i	−1.27701	−	0.414926i	−0.867526	+	0.497391i	$0.834291\pi$
$252$	3.63793	−	10.4462i	0.229168	−	0.658046i
$253$	−6.12007	+	0.0566283i	−0.384766	+	0.00356019i
$254$	49.5422			3.10856
$255$	−2.49366	+	7.67468i	−0.156159	+	0.480607i
$256$	26.3753	−	19.1627i	1.64845	−	1.19767i
$257$	−1.08190	+	1.48910i	−0.0674869	+	0.0928878i	−0.841426	−	0.540372i	$-0.818284\pi$
$257$	−1.08190	+	1.48910i	−0.0674869	+	0.0928878i	0.773939	+	0.633260i	$0.218284\pi$
$258$	−8.76452	+	2.84776i	−0.545655	+	0.177294i
$259$	−4.90508	−	0.102829i	−0.304787	−	0.00638950i
$260$	−24.6134	+	33.8775i	−1.52646	+	2.10099i
$261$	−2.36985	−	3.26181i	−0.146690	−	0.201901i
$262$	−2.10754	−	0.684782i	−0.130204	−	0.0423060i
$263$		−	19.7863i		−	1.22007i	−0.792373	−	0.610037i	$-0.791155\pi$
$263$		−	19.7863i		−	1.22007i	0.792373	−	0.610037i	$-0.208845\pi$
$264$	−5.39839	+	17.1530i	−0.332248	+	1.05569i
$265$		−	8.40149i		−	0.516099i
$266$	−28.0273	+	36.9233i	−1.71847	+	2.26392i
$267$	9.20621	−	6.68871i	0.563411	−	0.409342i
$268$	−4.11864	−	2.99237i	−0.251586	−	0.182788i
$269$	−1.80640	+	0.586935i	−0.110138	+	0.0357860i	−0.363568	−	0.931568i	$-0.618441\pi$
$269$	−1.80640	+	0.586935i	−0.110138	+	0.0357860i	0.253429	+	0.967354i	$0.418441\pi$
$270$	−3.57887	+	1.16285i	−0.217803	+	0.0707686i
$271$	−12.0414	−	8.74856i	−0.731461	−	0.531437i	0.158564	−	0.987349i	$-0.449313\pi$
$271$	−12.0414	−	8.74856i	−0.731461	−	0.531437i	−0.890025	+	0.455911i	$0.849313\pi$
$272$	22.0741	−	16.0378i	1.33844	−	0.972432i
$273$	−10.5852	+	13.9450i	−0.640645	+	0.843990i
$274$			21.6245i			1.30638i
$275$	7.21954	−	5.34806i	0.435355	−	0.322500i
$276$			7.71514i			0.464397i
$277$	5.83386	+	1.89553i	0.350522	+	0.113892i	0.478986	−	0.877823i	$-0.341005\pi$
$277$	5.83386	+	1.89553i	0.350522	+	0.113892i	−0.128463	+	0.991714i	$0.541005\pi$
$278$	−32.5459	−	44.7956i	−1.95197	−	2.68666i
$279$	4.50445	−	6.19985i	0.269675	−	0.371175i
$280$	−21.7080	−	0.455083i	−1.29730	−	0.0271964i
$281$	18.3619	−	5.96614i	1.09538	−	0.355910i	0.295056	−	0.955480i	$-0.404662\pi$
$281$	18.3619	−	5.96614i	1.09538	−	0.355910i	0.800322	+	0.599570i	$0.204662\pi$
$282$	3.17155	−	4.36526i	0.188863	−	0.259948i
$283$	−16.8899	+	12.2712i	−1.00400	+	0.729447i	−0.962942	−	0.269710i	$-0.913072\pi$
$283$	−16.8899	+	12.2712i	−1.00400	+	0.729447i	−0.0410563	+	0.999157i	$0.513072\pi$
$284$	−16.3991	+	50.4711i	−0.973105	+	2.99491i
$285$	10.6671			0.631865
$286$	31.6612	−	44.4368i	1.87216	−	2.62760i
$287$	0.605781	−	1.73947i	0.0357581	−	0.102678i
$288$	1.78783	+	0.580902i	0.105349	+	0.0342300i
$289$	−9.24176	+	6.71453i	−0.543633	+	0.394973i
$290$	−8.91785	+	12.2744i	−0.523674	+	0.720776i
$291$	−2.22707	−	6.85422i	−0.130553	−	0.401801i
$292$	3.14717	+	9.68600i	0.184174	+	0.566830i
$293$	−12.8846	−	9.36124i	−0.752729	−	0.546889i	0.143943	−	0.989586i	$-0.454022\pi$
$293$	−12.8846	−	9.36124i	−0.752729	−	0.546889i	−0.896671	+	0.442697i	$0.854022\pi$
$294$	−17.3876	−	0.729343i	−1.01407	−	0.0425361i
$295$	−0.150420	+	0.462944i	−0.00875776	+	0.0269536i
$296$		−	10.0541i		−	0.584384i
$297$	3.14468	−	1.05403i	0.182473	−	0.0611613i
$298$	24.2309			1.40366
$299$	3.77341	−	11.6134i	0.218222	−	0.671618i
$300$	−6.65714	−	9.16276i	−0.384350	−	0.529012i
$301$	5.59698	+	8.05329i	0.322605	+	0.464184i
$302$	−10.6289	−	32.7125i	−0.611627	−	1.88239i
$303$	−9.08384	+	2.95152i	−0.521853	+	0.169560i
$304$	−29.1793	−	21.2000i	−1.67355	−	1.21591i
$305$	−2.64505	−	3.64061i	−0.151455	−	0.208460i
$306$	−12.6058	−	4.09586i	−0.720623	−	0.234145i
$307$	17.1537			0.979014			0.489507	−	0.871999i	$-0.337177\pi$
$307$	17.1537			0.979014			0.489507	+	0.871999i	$0.337177\pi$
$308$	36.6843	+	0.429524i	2.09028	+	0.0244744i
$309$	−2.51408			−0.143021
$310$	−27.4265	−	8.91140i	−1.55772	−	0.506133i
$311$	2.75596	+	3.79326i	0.156276	+	0.215096i	0.879975	−	0.475020i	$-0.157559\pi$
$311$	2.75596	+	3.79326i	0.156276	+	0.215096i	−0.723698	+	0.690116i	$0.757559\pi$
$312$	−29.0256	−	21.0884i	−1.64325	−	1.19389i
$313$	21.3080	−	6.92340i	1.20440	−	0.391334i	0.363023	−	0.931780i	$-0.381745\pi$
$313$	21.3080	−	6.92340i	1.20440	−	0.391334i	0.841378	+	0.540447i	$0.181745\pi$
$314$	1.72181	+	5.29919i	0.0971675	+	0.299051i
$315$	2.28545	+	3.28846i	0.128771	+	0.185283i
$316$	−7.04677	−	9.69905i	−0.396412	−	0.545614i
$317$	3.75630	−	11.5607i	0.210975	−	0.649313i	−0.788440	−	0.615111i	$-0.789111\pi$
$317$	3.75630	−	11.5607i	0.210975	−	0.649313i	0.999415	−	0.0342017i	$-0.0108889\pi$
$318$	13.7995			0.773840
$319$	7.75946	−	10.8905i	0.434446	−	0.609749i
$320$			8.41897i			0.470634i
$321$	3.61432	−	11.1237i	0.201731	−	0.620866i
$322$	11.6201	−	3.50811i	0.647565	−	0.195499i
$323$	30.3968	+	22.0845i	1.69132	+	1.22882i
$324$	−1.29196	−	3.97623i	−0.0717753	−	0.220902i
$325$	5.53935	+	17.0484i	0.307268	+	0.945673i
$326$	3.00448	−	4.13531i	0.166403	−	0.229034i
$327$	−5.37423	+	3.90461i	−0.297196	+	0.215925i
$328$	3.58991	+	1.16643i	0.198219	+	0.0644054i
$329$	−5.42276	−	1.88851i	−0.298966	−	0.104117i
$330$	−7.42904	−	10.0287i	−0.408955	−	0.552063i
$331$	−25.8290			−1.41969			−0.709846	−	0.704357i	$-0.751235\pi$
$331$	−25.8290			−1.41969			−0.709846	+	0.704357i	$0.751235\pi$
$332$	−3.11965	+	9.60130i	−0.171213	+	0.526940i
$333$	−1.50020	+	1.08996i	−0.0822107	+	0.0597296i
$334$	3.12172	−	4.29668i	0.170813	−	0.235104i
$335$	1.75289	−	0.569547i	0.0957704	−	0.0311177i
$336$	0.283799	−	13.5376i	0.0154825	−	0.738534i
$337$	−3.01959	+	4.15611i	−0.164487	+	0.226397i	−0.883302	−	0.468804i	$-0.844685\pi$
$337$	−3.01959	+	4.15611i	−0.164487	+	0.226397i	0.718815	+	0.695202i	$0.244685\pi$
$338$	44.9895	+	61.9227i	2.44711	+	3.36815i
$339$	9.22908	+	2.99871i	0.501255	+	0.162867i
$340$			33.7380i			1.82970i
$341$	24.2444	+	7.63021i	1.31291	+	0.413199i
$342$			17.5209i			0.947420i
$343$	4.60490	+	17.9386i	0.248641	+	0.968596i
$344$	−16.2595	+	11.8132i	−0.876651	+	0.636924i
$345$	−2.25971	−	1.64177i	−0.121659	−	0.0883901i
$346$	55.2871	−	17.9639i	2.97225	−	0.965743i
$347$	−22.9645	+	7.46163i	−1.23280	+	0.400561i	−0.851728	−	0.523984i	$-0.824445\pi$
$347$	−22.9645	+	7.46163i	−1.23280	+	0.400561i	−0.381073	+	0.924545i	$0.624445\pi$
$348$	−13.6372	−	9.90798i	−0.731029	−	0.531124i
$349$	−19.2722	+	14.0021i	−1.03162	+	0.749515i	−0.968632	−	0.248500i	$-0.920063\pi$
$349$	−19.2722	+	14.0021i	−1.03162	+	0.749515i	−0.0629865	+	0.998014i	$0.520063\pi$
$350$	−10.7734	+	14.1930i	−0.575864	+	0.758646i
$351$			6.61718i			0.353199i
$352$	0.0576866	+	6.23445i	0.00307471	+	0.332297i
$353$		−	34.2944i		−	1.82531i	−0.408732	−	0.912654i	$-0.634029\pi$
$353$		−	34.2944i		−	1.82531i	0.408732	−	0.912654i	$-0.365971\pi$
$354$	−0.760391	−	0.247066i	−0.0404143	−	0.0131314i
$355$	−11.2929	−	15.5434i	−0.599365	−	0.824956i
$356$	27.9645	−	38.4898i	1.48212	−	2.03996i
$357$	−0.295639	+	14.1024i	−0.0156469	+	0.746376i
$358$	−30.2180	+	9.81842i	−1.59707	+	0.518920i
$359$	19.9129	−	27.4077i	1.05096	−	1.44652i	0.162987	−	0.986628i	$-0.447887\pi$
$359$	19.9129	−	27.4077i	1.05096	−	1.44652i	0.887974	−	0.459895i	$-0.152113\pi$
$360$	−6.63933	+	4.82376i	−0.349924	+	0.254234i
$361$	9.47643	−	29.1654i	0.498759	−	1.53502i
$362$	31.5263			1.65699
$363$	6.62920	+	8.77802i	0.347943	+	0.460727i
$364$	−24.0729	+	69.1241i	−1.26176	+	3.62309i
$365$	−3.50667	−	1.13939i	−0.183548	−	0.0596382i
$366$	5.97974	−	4.34453i	0.312566	−	0.227092i
$367$	4.87645	−	6.71186i	0.254549	−	0.350356i	−0.662549	−	0.749018i	$-0.730525\pi$
$367$	4.87645	−	6.71186i	0.254549	−	0.350356i	0.917098	+	0.398662i	$0.130525\pi$
$368$	2.91842	+	8.98197i	0.152133	+	0.468218i
$369$	−0.215133	−	0.662113i	−0.0111994	−	0.0344682i
$370$	5.64534	+	4.10158i	0.293488	+	0.213231i
$371$	−4.24435	−	14.0588i	−0.220356	−	0.729897i
$372$	9.90082	−	30.4716i	0.513333	−	1.57988i
$373$		−	27.7613i		−	1.43743i	−0.695306	−	0.718713i	$-0.744731\pi$
$373$		−	27.7613i		−	1.43743i	0.695306	−	0.718713i	$-0.255269\pi$
$374$	−0.406741	−	43.9583i	−0.0210321	−	2.27303i
$375$	11.6684			0.602554
$376$	3.63632	−	11.1914i	0.187529	−	0.577154i
$377$	15.6817	+	21.5840i	0.807648	+	1.11163i
$378$	−5.40133	+	3.75389i	−0.277814	+	0.193079i
$379$	−8.09239	−	24.9058i	−0.415678	−	1.27933i	−0.911643	−	0.410983i	$-0.865185\pi$
$379$	−8.09239	−	24.9058i	−0.415678	−	1.27933i	0.495964	−	0.868343i	$-0.334815\pi$
$380$	42.4149	−	13.7814i	2.17584	−	0.706973i
$381$	−16.1216	−	11.7131i	−0.825936	−	0.600078i
$382$	1.53586	+	2.11393i	0.0785815	+	0.108158i
$383$	−9.14670	−	2.97194i	−0.467375	−	0.151859i	0.0658559	−	0.997829i	$-0.479022\pi$
$383$	−9.14670	−	2.97194i	−0.467375	−	0.151859i	−0.533231	+	0.845970i	$0.679022\pi$
$384$	−17.5879			−0.897530
$385$	−7.93219	+	10.6532i	−0.404262	+	0.542936i
$386$	−30.9513			−1.57538
$387$	3.52536	+	1.14546i	0.179204	+	0.0582270i
$388$	−17.7107	−	24.3767i	−0.899124	−	1.23754i
$389$	20.3789	+	14.8061i	1.03325	+	0.750701i	0.968957	−	0.247230i	$-0.0795204\pi$
$389$	20.3789	+	14.8061i	1.03325	+	0.750701i	0.0642941	+	0.997931i	$0.479520\pi$
$390$	23.6820	−	7.69476i	1.19919	−	0.389640i
$391$	−3.04018	−	9.35672i	−0.153749	−	0.473190i
$392$	−36.5555	+	10.2052i	−1.84633	+	0.515438i
$393$	0.523919	+	0.721113i	0.0264282	+	0.0363753i
$394$	−4.34189	+	13.3630i	−0.218741	+	0.673216i
$395$	4.34032			0.218385
$396$	11.1422	−	8.25387i	0.559917	−	0.414773i
$397$			3.19180i			0.160192i	0.996787	+	0.0800960i	$0.0255227\pi$
$397$			3.19180i			0.160192i	−0.996787	+	0.0800960i	$0.974477\pi$
$398$	−5.68360	+	17.4923i	−0.284893	+	0.876811i
$399$	17.8500	−	5.38892i	0.893620	−	0.269783i
$400$	−11.2163	−	8.14909i	−0.560813	−	0.407454i
$401$	−1.98533	−	6.11023i	−0.0991428	−	0.305130i	0.889168	−	0.457580i	$-0.151284\pi$
$401$	−1.98533	−	6.11023i	−0.0991428	−	0.305130i	−0.988311	+	0.152450i	$0.951284\pi$
$402$	0.935488	+	2.87914i	0.0466579	+	0.143598i
$403$	−29.8068	+	41.0255i	−1.48478	+	2.04363i
$404$	−32.3062	+	23.4718i	−1.60729	+	1.16777i
$405$	1.43953	+	0.467733i	0.0715310	+	0.0232418i
$406$	−8.72199	+	25.0448i	−0.432865	+	1.24295i
$407$	−5.00885	−	3.56880i	−0.248279	−	0.176899i
$408$	−28.9061			−1.43107
$409$	9.10803	−	28.0316i	0.450363	−	1.38607i	−0.426131	−	0.904661i	$-0.640124\pi$
$409$	9.10803	−	28.0316i	0.450363	−	1.38607i	0.876494	−	0.481413i	$-0.159876\pi$
$410$	−2.11945	+	1.53987i	−0.104672	+	0.0760488i
$411$	5.11258	−	7.03686i	0.252185	−	0.347103i
$412$	−9.99656	+	3.24808i	−0.492495	+	0.160021i
$413$	−0.0178332	+	0.850667i	−0.000877516	+	0.0418586i
$414$	2.69663	−	3.71160i	0.132532	−	0.182415i
$415$	−2.14829	−	2.95687i	−0.105455	−	0.145147i
$416$	−11.8304	−	3.84393i	−0.580033	−	0.188464i
$417$			22.2717i			1.09065i
$418$	−55.0975	+	18.4676i	−2.69491	+	0.903280i
$419$			34.0007i			1.66104i	0.556988	+	0.830521i	$0.311957\pi$
$419$			34.0007i			1.66104i	−0.556988	+	0.830521i	$0.688043\pi$
$420$	13.3360	+	10.1229i	0.650731	+	0.493949i
$421$	−1.05591	+	0.767163i	−0.0514619	+	0.0373892i	−0.613219	−	0.789913i	$-0.710126\pi$
$421$	−1.05591	+	0.767163i	−0.0514619	+	0.0373892i	0.561757	+	0.827302i	$0.310126\pi$
$422$	−26.0649	−	18.9373i	−1.26882	−	0.921852i
$423$	−2.06412	+	0.670673i	−0.100361	+	0.0326092i
$424$	28.6219	−	9.29981i	1.39000	−	0.451638i
$425$	11.6842	+	8.48908i	0.566768	+	0.411781i
$426$	25.5302	−	18.5487i	1.23694	−	0.898689i
$427$	−6.26536	−	4.75583i	−0.303202	−	0.230151i
$428$		−	48.9000i		−	2.36367i
$429$	−20.8089	+	6.97474i	−1.00466	+	0.336743i
$430$		−	13.9488i		−	0.672672i
$431$	−11.6649	−	3.79014i	−0.561876	−	0.182565i	0.0142889	−	0.999898i	$-0.495452\pi$
$431$	−11.6649	−	3.79014i	−0.561876	−	0.182565i	−0.576165	+	0.817333i	$0.695452\pi$
$432$	−3.00819	−	4.14042i	−0.144732	−	0.199206i
$433$	−7.23662	+	9.96036i	−0.347770	+	0.478664i	−0.946691	−	0.322144i	$-0.895596\pi$
$433$	−7.23662	+	9.96036i	−0.347770	+	0.478664i	0.598921	+	0.800808i	$0.295596\pi$
$434$	−50.3966	−	1.05651i	−2.41911	−	0.0507139i
$435$	5.80395	−	1.88582i	0.278278	−	0.0904180i
$436$	−16.3246	+	22.4689i	−0.781807	+	1.07606i
$437$	−10.5213	+	7.64414i	−0.503300	+	0.365669i
$438$	1.87146	−	5.75975i	0.0894216	−	0.275211i
$439$	29.9692			1.43035			0.715177	−	0.698943i	$-0.246346\pi$
$439$	29.9692			1.43035			0.715177	+	0.698943i	$0.246346\pi$
$440$	−22.1673	−	15.7942i	−1.05678	−	0.752958i
$441$	5.48571	+	4.34822i	0.261224	+	0.207058i
$442$	83.4146	+	27.1030i	3.96763	+	1.28916i
$443$	−14.9776	+	10.8818i	−0.711605	+	0.517011i	−0.883691	−	0.468071i	$-0.844949\pi$
$443$	−14.9776	+	10.8818i	−0.711605	+	0.517011i	0.172086	+	0.985082i	$0.444949\pi$
$444$	−4.55697	+	6.27214i	−0.216264	+	0.297662i
$445$	5.32257	+	16.3812i	0.252314	+	0.776543i
$446$	−7.24933	−	22.3112i	−0.343266	−	1.05646i
$447$	−7.88501	−	5.72879i	−0.372948	−	0.270963i
$448$	4.25318	+	14.0881i	0.200944	+	0.665598i
$449$	−9.72739	+	29.9378i	−0.459064	+	1.41285i	0.407233	+	0.913324i	$0.366494\pi$
$449$	−9.72739	+	29.9378i	−0.459064	+	1.41285i	−0.866297	+	0.499529i	$0.833506\pi$
$450$			6.73485i			0.317484i
$451$	1.85537	−	1.37442i	0.0873662	−	0.0647187i
$452$	40.5711			1.90831
$453$	−4.27529	+	13.1580i	−0.200871	+	0.618217i
$454$	24.8808	+	34.2455i	1.16771	+	1.60722i
$455$	−15.1233	−	21.7603i	−0.708989	−	1.02014i
$456$	11.8077	+	36.3403i	0.552945	+	1.70179i
$457$	10.4792	−	3.40489i	0.490196	−	0.159274i	−0.0534812	−	0.998569i	$-0.517032\pi$
$457$	10.4792	−	3.40489i	0.490196	−	0.159274i	0.543677	+	0.839295i	$0.317032\pi$
$458$	−4.45122	−	3.23400i	−0.207992	−	0.151115i
$459$	3.13370	+	4.31316i	0.146268	+	0.201321i
$460$	−11.1062	−	3.60863i	−0.517830	−	0.168253i
$461$	−37.0945			−1.72766			−0.863830	−	0.503783i	$-0.831941\pi$
$461$	−37.0945			−1.72766			−0.863830	+	0.503783i	$0.831941\pi$
$462$	−17.4980	−	13.0287i	−0.814078	−	0.606151i
$463$	3.14877			0.146336			0.0731679	−	0.997320i	$-0.476689\pi$
$463$	3.14877			0.146336			0.0731679	+	0.997320i	$0.476689\pi$
$464$	−19.6243	−	6.37633i	−0.911036	−	0.296013i
$465$	6.81801	+	9.38419i	0.316178	+	0.435181i
$466$	2.62035	+	1.90379i	0.121385	+	0.0881916i
$467$	−26.2072	+	8.51522i	−1.21272	+	0.394037i	−0.844427	−	0.535671i	$-0.820059\pi$
$467$	−26.2072	+	8.51522i	−1.21272	+	0.394037i	−0.368296	+	0.929709i	$0.620059\pi$
$468$	8.54910	+	26.3114i	0.395182	+	1.21625i
$469$	2.64550	−	1.83860i	0.122158	−	0.0848989i
$470$	4.80051	+	6.60733i	0.221431	+	0.304773i
$471$	0.692567	−	2.13150i	0.0319118	−	0.0982144i
$472$	−1.74364			−0.0802576
$473$	0.113750	+	12.2935i	0.00523024	+	0.565255i
$474$			7.12903i			0.327447i
$475$	5.89953	−	18.1569i	0.270689	−	0.833095i
$476$	17.0441	+	56.4562i	0.781215	+	2.58767i
$477$	−4.49053	−	3.26256i	−0.205607	−	0.149383i
$478$	−6.62431	−	20.3875i	−0.302989	−	0.932504i
$479$	0.786951	+	2.42199i	0.0359567	+	0.110663i	0.967424	−	0.253162i	$-0.0814705\pi$
$479$	0.786951	+	2.42199i	0.0359567	+	0.110663i	−0.931467	+	0.363825i	$0.881471\pi$
$480$	−1.67246	+	2.30194i	−0.0763368	+	0.105069i
$481$	9.92712	−	7.21248i	0.452638	−	0.328861i
$482$	48.4604	+	15.7457i	2.20731	+	0.717199i
$483$	−4.61074	−	1.60572i	−0.209796	−	0.0730626i
$484$	37.7000	+	26.3388i	1.71364	+	1.19722i
$485$	10.9086			0.495332
$486$	−0.768257	+	2.36445i	−0.0348489	+	0.107254i
$487$	17.9829	−	13.0653i	0.814881	−	0.592046i	−0.100360	−	0.994951i	$-0.532000\pi$
$487$	17.9829	−	13.0653i	0.814881	−	0.592046i	0.915242	+	0.402905i	$0.132000\pi$
$488$	9.47480	−	13.0409i	0.428904	−	0.590336i
$489$	−1.95539	+	0.635344i	−0.0884256	+	0.0287312i
$490$	9.18269	−	24.6890i	0.414832	−	1.11533i
$491$	12.3286	−	16.9689i	0.556382	−	0.765793i	−0.434479	−	0.900682i	$-0.643068\pi$
$491$	12.3286	−	16.9689i	0.556382	−	0.765793i	0.990861	+	0.134888i	$0.0430676\pi$
$492$	−1.71084	−	2.35477i	−0.0771306	−	0.106161i
$493$	20.4431	+	6.64236i	0.920710	+	0.299157i
$494$		−	115.939i		−	5.21633i
$495$	0.0464484	+	5.01988i	0.00208770	+	0.225627i
$496$		−	39.2202i		−	1.76104i
$497$	−26.7496	−	20.3047i	−1.19988	−	0.910792i
$498$	4.85669	−	3.52859i	0.217633	−	0.158120i
$499$	−0.321874	−	0.233855i	−0.0144091	−	0.0104688i	0.580557	−	0.814219i	$-0.302835\pi$
$499$	−0.321874	−	0.233855i	−0.0144091	−	0.0104688i	−0.594966	+	0.803751i	$0.702835\pi$
$500$	46.3963	−	15.0751i	2.07491	−	0.674178i
$501$	−2.03169	+	0.660136i	−0.0907692	+	0.0294927i
$502$	42.7865	+	31.0862i	1.90966	+	1.38745i
$503$	19.7145	−	14.3234i	0.879024	−	0.638649i	−0.0539688	−	0.998543i	$-0.517187\pi$
$503$	19.7145	−	14.3234i	0.879024	−	0.638649i	0.932993	+	0.359894i	$0.117187\pi$
$504$	−8.67316	+	11.4261i	−0.386333	+	0.508957i
$505$		−	14.4570i		−	0.643329i
$506$	14.5141	+	4.56789i	0.645232	+	0.203068i
$507$		−	30.7871i		−	1.36730i
$508$	−79.2360	−	25.7454i	−3.51553	−	1.14227i
$509$	5.45038	+	7.50181i	0.241584	+	0.332512i	0.912542	−	0.408984i	$-0.134117\pi$
$509$	5.45038	+	7.50181i	0.241584	+	0.332512i	−0.670958	+	0.741496i	$0.734117\pi$
$510$	11.7923	−	16.2307i	0.522170	−	0.718706i
$511$	−6.44357	−	0.135082i	−0.285047	−	0.00597567i
$512$	−43.6307	+	14.1765i	−1.92822	+	0.626518i
$513$	4.14238	−	5.70150i	0.182891	−	0.251727i
$514$	3.70211	−	2.68974i	0.163293	−	0.118639i
$515$	1.17592	−	3.61911i	0.0518172	−	0.159477i
$516$	15.4975			0.682241
$517$	−4.28470	−	5.78408i	−0.188441	−	0.254384i
$518$	11.5188	+	4.01150i	0.506109	+	0.176255i
$519$	−22.2382	−	7.22563i	−0.976148	−	0.317170i
$520$	43.9337	−	31.9197i	1.92662	−	1.39977i
$521$	3.47352	−	4.78088i	0.152178	−	0.209454i	−0.726121	−	0.687567i	$-0.758679\pi$
$521$	3.47352	−	4.78088i	0.152178	−	0.209454i	0.878299	+	0.478112i	$0.158679\pi$
$522$	3.09748	+	9.53305i	0.135573	+	0.417250i
$523$	−3.90501	−	12.0184i	−0.170754	−	0.525527i	0.828660	−	0.559752i	$-0.189104\pi$
$523$	−3.90501	−	12.0184i	−0.170754	−	0.525527i	−0.999414	+	0.0342251i	$0.989104\pi$
$524$	3.01487	+	2.19043i	0.131705	+	0.0956894i
$525$	6.86138	−	2.07145i	0.299455	−	0.0904054i
$526$	−15.2009	+	46.7837i	−0.662793	+	2.03987i
$527$			40.8566i			1.77974i
$528$	9.84956	−	13.8239i	0.428647	−	0.601610i
$529$	−19.5947			−0.851943
$530$	−6.45450	+	19.8649i	−0.280366	+	0.862877i
$531$	0.189027	+	0.260174i	0.00820309	+	0.0112906i
$532$	64.0136	−	44.4890i	2.77534	−	1.92884i
$533$	1.42358	+	4.38132i	0.0616619	+	0.189776i
$534$	−26.9063	+	8.74239i	−1.16435	+	0.378320i
$535$	14.3224	+	10.4059i	0.619213	+	0.449885i
$536$	3.88062	+	5.34122i	0.167617	+	0.230705i
$537$	12.1546	+	3.94928i	0.524511	+	0.170424i
$538$	4.72206			0.203583
$539$	−7.89163	+	21.8340i	−0.339917	+	0.940456i
$540$	6.32821			0.272323
$541$	42.1488	+	13.6950i	1.81212	+	0.588792i	0.999986	+	0.00531691i	$0.00169243\pi$
$541$	42.1488	+	13.6950i	1.81212	+	0.588792i	0.812131	+	0.583475i	$0.198308\pi$
$542$	21.7501	+	29.9364i	0.934246	+	1.28588i
$543$	−10.2590	−	7.45362i	−0.440257	−	0.319866i
$544$	−9.53158	+	3.09700i	−0.408663	+	0.132783i
$545$	−3.10711	−	9.56271i	−0.133094	−	0.409621i
$546$	35.7415	−	24.8401i	1.52960	−	1.06306i
$547$	−16.3362	−	22.4848i	−0.698484	−	0.961381i	−0.999969	−	0.00790963i	$-0.997482\pi$
$547$	−16.3362	−	22.4848i	−0.698484	−	0.961381i	0.301485	−	0.953471i	$-0.402518\pi$
$548$	11.2375	−	34.5854i	0.480041	−	1.47741i
$549$	−2.97304			−0.126886
$550$	−21.1789	+	7.09876i	−0.903073	+	0.302692i
$551$		−	28.4140i		−	1.21048i
$552$	3.09181	−	9.51560i	0.131596	−	0.405011i
$553$	7.26298	−	2.19269i	0.308853	−	0.0932426i
$554$	−12.3376	−	8.96380i	−0.524175	−	0.380835i
$555$	−0.867343	−	2.66941i	−0.0368167	−	0.113310i
$556$	28.7740	+	88.5574i	1.22029	+	3.75567i
$557$	7.27151	−	10.0084i	0.308104	−	0.424068i	−0.626685	−	0.779273i	$-0.715589\pi$
$557$	7.27151	−	10.0084i	0.308104	−	0.424068i	0.934789	+	0.355204i	$0.115589\pi$
$558$	−15.4136	+	11.1987i	−0.652512	+	0.474077i
$559$	−23.3279	−	7.57971i	−0.986667	−	0.320588i
$560$	19.3550	+	6.74050i	0.817900	+	0.284838i
$561$	−10.2605	+	14.4007i	−0.433198	+	0.607998i
$562$	−47.9993			−2.02473
$563$	0.964326	−	2.96789i	0.0406415	−	0.125082i	−0.928677	−	0.370889i	$-0.879053\pi$
$563$	0.964326	−	2.96789i	0.0406415	−	0.125082i	0.969319	+	0.245807i	$0.0790531\pi$
$564$	−7.34093	+	5.33350i	−0.309109	+	0.224581i
$565$	−8.63349	+	11.8830i	−0.363214	+	0.499921i
$566$	49.3627	−	16.0389i	2.07487	−	0.674166i
$567$	2.64517	+	0.0554529i	0.111087	+	0.00232880i
$568$	40.4521	−	55.6776i	1.69733	−	2.33618i
$569$	−3.95977	−	5.45015i	−0.166002	−	0.228482i	0.717909	−	0.696137i	$-0.245099\pi$
$569$	−3.95977	−	5.45015i	−0.166002	−	0.228482i	−0.883911	+	0.467654i	$0.845099\pi$
$570$	−25.2219	−	8.19509i	−1.05643	−	0.343254i
$571$			21.6416i			0.905671i	0.891594	+	0.452835i	$0.149587\pi$
$571$			21.6416i			0.905671i	−0.891594	+	0.452835i	$0.850413\pi$
$572$	−73.7300	+	54.6173i	−3.08280	+	2.28367i
$573$		−	1.05102i		−	0.0439068i
$574$	−2.76870	+	3.64750i	−0.115563	+	0.152244i
$575$	−4.04427	+	2.93833i	−0.168658	+	0.122537i
$576$	4.49988	+	3.26935i	0.187495	+	0.136223i
$577$	−32.2275	+	10.4714i	−1.34165	+	0.435928i	−0.889875	−	0.456204i	$-0.849209\pi$
$577$	−32.2275	+	10.4714i	−1.34165	+	0.435928i	−0.451774	+	0.892132i	$0.649209\pi$
$578$	27.0102	−	8.77615i	1.12348	−	0.365040i
$579$	10.0719	+	7.31768i	0.418575	+	0.304112i
$580$	20.6414	−	14.9969i	0.857089	−	0.622712i
$581$	−5.08867	−	3.86264i	−0.211113	−	0.160249i
$582$			17.9174i			0.742702i
$583$	5.52654	−	17.5601i	0.228886	−	0.727267i
$584$		−	13.2076i		−	0.546534i
$585$	−9.52566	−	3.09507i	−0.393837	−	0.127966i
$586$	23.2733	+	32.0329i	0.961410	+	1.32327i
$587$	−10.0378	+	13.8159i	−0.414305	+	0.570243i	−0.964262	−	0.264951i	$-0.914644\pi$
$587$	−10.0378	+	13.8159i	−0.414305	+	0.570243i	0.549956	+	0.835193i	$0.314644\pi$
$588$	27.4301	+	10.2022i	1.13120	+	0.420733i
$589$	51.3643	−	16.6893i	2.11643	−	0.687669i
$590$	0.711320	−	0.979048i	0.0292846	−	0.0403067i
$591$	4.57225	−	3.32193i	0.188077	−	0.136646i
$592$	−2.93266	+	9.02580i	−0.120532	+	0.370958i
$593$	39.2625			1.61232			0.806159	−	0.591699i	$-0.201543\pi$
$593$	39.2625			1.61232			0.806159	+	0.591699i	$0.201543\pi$
$594$	−8.24522	+	0.0762920i	−0.338305	+	0.00313030i
$595$	−20.1626	−	7.02173i	−0.826584	−	0.287863i
$596$	−38.7540	−	12.5919i	−1.58742	−	0.515785i
$597$	5.98515	−	4.34846i	0.244956	−	0.177971i
$598$	−17.8441	+	24.5603i	−0.729700	+	1.00435i
$599$	1.89391	+	5.82884i	0.0773829	+	0.238160i	0.982264	−	0.187505i	$-0.0600401\pi$
$599$	1.89391	+	5.82884i	0.0773829	+	0.238160i	−0.904881	+	0.425665i	$0.860040\pi$
$600$	4.53876	+	13.9689i	0.185294	+	0.570276i
$601$	−33.2495	−	24.1572i	−1.35628	−	0.985393i	−0.998672	−	0.0515194i	$-0.983594\pi$
$601$	−33.2495	−	24.1572i	−1.35628	−	0.985393i	−0.357605	−	0.933873i	$-0.616406\pi$
$602$	−7.04680	−	23.3416i	−0.287206	−	0.951331i
$603$	0.376282	−	1.15808i	0.0153234	−	0.0471606i
$604$			57.8427i			2.35359i
$605$	−15.7370	+	5.43719i	−0.639799	+	0.221053i
$606$	23.7458			0.964608
$607$	1.76020	−	5.41733i	0.0714441	−	0.219882i	−0.908959	−	0.416887i	$-0.863121\pi$
$607$	1.76020	−	5.41733i	0.0714441	−	0.219882i	0.980403	+	0.197004i	$0.0631212\pi$
$608$	7.78700	+	10.7179i	0.315805	+	0.434668i
$609$	8.75947	−	6.08777i	0.354951	−	0.246689i
$610$	3.45718	+	10.6401i	0.139977	+	0.430806i
$611$	13.6586	−	4.43796i	0.552570	−	0.179541i
$612$	18.0327	+	13.1015i	0.728929	+	0.529598i
$613$	4.16013	+	5.72592i	0.168026	+	0.231268i	0.884723	−	0.466116i	$-0.154347\pi$
$613$	4.16013	+	5.72592i	0.168026	+	0.231268i	−0.716698	+	0.697384i	$0.754347\pi$
$614$	−40.5591	−	13.1785i	−1.63683	−	0.531839i
$615$	1.05376			0.0424917
$616$	−45.0731	−	15.2308i	−1.81605	−	0.613668i
$617$	−28.9810			−1.16673			−0.583366	−	0.812209i	$-0.698265\pi$
$617$	−28.9810			−1.16673			−0.583366	+	0.812209i	$0.698265\pi$
$618$	5.94442	+	1.93146i	0.239120	+	0.0776947i
$619$	−3.19646	−	4.39955i	−0.128477	−	0.176833i	0.739933	−	0.672681i	$-0.234857\pi$
$619$	−3.19646	−	4.39955i	−0.128477	−	0.176833i	−0.868409	+	0.495848i	$0.834857\pi$
$620$	39.2339	+	28.5051i	1.57567	+	1.14479i
$621$	−1.75503	+	0.570245i	−0.0704270	+	0.0228831i
$622$	−3.60215	−	11.0863i	−0.144433	−	0.444519i
$623$	17.1823	+	24.7229i	0.688393	+	0.990503i
$624$	19.9057	+	27.3979i	0.796867	+	1.09679i
$625$	−1.27212	+	3.91519i	−0.0508849	+	0.156608i
$626$	−55.7008			−2.22625
$627$	22.2956	+	7.01688i	0.890400	+	0.280227i
$628$		−	9.37010i		−	0.373908i
$629$	3.05502	−	9.40237i	0.121811	−	0.374897i
$630$	−2.87747	−	9.53121i	−0.114641	−	0.379733i
$631$	−23.4207	−	17.0161i	−0.932364	−	0.677402i	0.0142068	−	0.999899i	$-0.495478\pi$
$631$	−23.4207	−	17.0161i	−0.932364	−	0.677402i	−0.946570	+	0.322497i	$0.895478\pi$
$632$	4.80441	+	14.7864i	0.191109	+	0.588173i
$633$	4.00458	+	12.3248i	0.159168	+	0.489868i
$634$	−17.7632	+	24.4489i	−0.705465	+	0.970990i
$635$	24.4020	−	17.7291i	0.968362	−	0.703556i
$636$	−22.0705	−	7.17113i	−0.875152	−	0.284354i
$637$	−36.2999	−	28.7729i	−1.43825	−	1.14003i
$638$	−26.7136	+	19.7887i	−1.05760	+	0.783444i
$639$	−12.6932			−0.502136
$640$	8.22646	−	25.3184i	0.325179	−	1.00080i
$641$	−7.88211	+	5.72668i	−0.311324	+	0.226190i	−0.732465	−	0.680805i	$-0.761630\pi$
$641$	−7.88211	+	5.72668i	−0.311324	+	0.226190i	0.421140	+	0.906996i	$0.361630\pi$
$642$	−17.0918	+	23.5248i	−0.674558	+	0.928449i
$643$	0.109336	−	0.0355256i	0.00431181	−	0.00140099i	−0.306860	−	0.951755i	$-0.599278\pi$
$643$	0.109336	−	0.0355256i	0.00431181	−	0.00140099i	0.311172	+	0.950354i	$0.399278\pi$
$644$	−20.4079	−	0.427827i	−0.804182	−	0.0168587i
$645$	−3.29786	+	4.53911i	−0.129853	+	0.178727i
$646$	−54.9051	−	75.5704i	−2.16021	−	2.97328i
$647$	−18.2874	−	5.94194i	−0.718952	−	0.233602i	−0.0733831	−	0.997304i	$-0.523380\pi$
$647$	−18.2874	−	5.94194i	−0.718952	−	0.233602i	−0.645569	+	0.763702i	$0.723380\pi$
$648$			5.42190i			0.212992i
$649$	−0.618922	+	0.868663i	−0.0242948	+	0.0340980i
$650$		−	44.5657i		−	1.74801i
$651$	16.1499	+	12.2588i	0.632963	+	0.480462i
$652$	−6.95423	+	5.05254i	−0.272349	+	0.197873i
$653$	23.5451	+	17.1065i	0.921392	+	0.669430i	0.943870	−	0.330317i	$-0.107156\pi$
$653$	23.5451	+	17.1065i	0.921392	+	0.669430i	−0.0224784	+	0.999747i	$0.507156\pi$
$654$	15.7069	−	5.10347i	0.614187	−	0.199561i
$655$	−1.28312	+	0.416911i	−0.0501357	+	0.0162901i
$656$	−2.88250	−	2.09426i	−0.112543	−	0.0817672i
$657$	−1.97075	+	1.43183i	−0.0768861	+	0.0558610i
$658$	11.3710	+	8.63135i	0.443287	+	0.336485i
$659$			41.7453i			1.62617i	0.582148	+	0.813083i	$0.302212\pi$
$659$			41.7453i			1.62617i	−0.582148	+	0.813083i	$0.697788\pi$
$660$	6.67015	+	19.9002i	0.259635	+	0.774614i
$661$			8.23382i			0.320258i	0.987096	+	0.160129i	$0.0511911\pi$
$661$			8.23382i			0.320258i	−0.987096	+	0.160129i	$0.948809\pi$
$662$	61.0715	+	19.8433i	2.37361	+	0.771233i
$663$	−20.7362	−	28.5410i	−0.805329	−	1.10844i
$664$	7.69535	−	10.5917i	0.298637	−	0.411039i
$665$	−0.591522	+	28.2163i	−0.0229382	+	1.09418i
$666$	4.38453	−	1.42462i	0.169897	−	0.0552030i
$667$	−4.37320	+	6.01919i	−0.169331	+	0.233064i
$668$	−7.22559	+	5.24970i	−0.279567	+	0.203117i
$669$	−2.91591	+	8.97424i	−0.112736	+	0.346964i
$670$	−4.58217			−0.177025
$671$	−3.13368	−	9.34925i	−0.120974	−	0.360924i
$672$	−1.63572	+	4.69691i	−0.0630994	+	0.181187i
$673$	−3.19105	−	1.03684i	−0.123006	−	0.0399671i	0.246867	−	0.969049i	$-0.420599\pi$
$673$	−3.19105	−	1.03684i	−0.123006	−	0.0399671i	−0.369873	+	0.929082i	$0.620599\pi$
$674$	10.3326	−	7.50709i	0.397998	−	0.289162i
$675$	1.59229	−	2.19160i	0.0612873	−	0.0843547i
$676$	−39.7755	−	122.416i	−1.52983	−	4.70832i
$677$	11.6251	+	35.7785i	0.446790	+	1.37508i	0.880509	+	0.474030i	$0.157201\pi$
$677$	11.6251	+	35.7785i	0.446790	+	1.37508i	−0.433719	+	0.901048i	$0.642799\pi$
$678$	−19.5179	−	14.1806i	−0.749582	−	0.544603i
$679$	18.2541	−	5.51090i	0.700527	−	0.211489i
$680$	13.5203	−	41.6113i	0.518481	−	1.59572i
$681$		−	17.0264i		−	0.652451i
$682$	−51.4627	−	36.6672i	−1.97061	−	1.40406i
$683$	22.7042			0.868754			0.434377	−	0.900731i	$-0.356969\pi$
$683$	22.7042			0.868754			0.434377	+	0.900731i	$0.356969\pi$
$684$	9.10497	−	28.0222i	0.348137	−	1.07146i
$685$	7.73848	+	10.6511i	0.295672	+	0.406958i
$686$	2.89343	−	45.9528i	0.110472	−	1.75449i
$687$	0.683879	+	2.10476i	0.0260916	+	0.0803018i
$688$	18.0422	−	5.86228i	0.687854	−	0.223497i
$689$	29.7147	+	21.5890i	1.13204	+	0.822474i
$690$	4.08167	+	5.61793i	0.155386	+	0.213871i
$691$	−31.3236	−	10.1777i	−1.19161	−	0.387177i	−0.354940	−	0.934889i	$-0.615499\pi$
$691$	−31.3236	−	10.1777i	−1.19161	−	0.387177i	−0.836667	+	0.547712i	$0.815499\pi$
$692$	−97.7593			−3.71625
$693$	2.61372	+	8.37666i	0.0992870	+	0.318203i
$694$	60.0310			2.27875
$695$	−32.0609	−	10.4172i	−1.21614	−	0.395147i
$696$	12.8491	+	17.6852i	0.487042	+	0.670356i
$697$	3.00277	+	2.18164i	0.113738	+	0.0826354i
$698$	56.3255	−	18.3013i	2.13195	−	0.692713i
$699$	−0.402587	−	1.23903i	−0.0152272	−	0.0468646i
$700$	24.6062	−	17.1012i	0.930028	−	0.646363i
$701$	25.5609	+	35.1815i	0.965420	+	1.32879i	0.944327	+	0.329009i	$0.106715\pi$
$701$	25.5609	+	35.1815i	0.965420	+	1.32879i	0.0210936	+	0.999778i	$0.493285\pi$
$702$	5.08370	−	15.6460i	0.191872	−	0.590520i
$703$	−13.0684			−0.492886
$704$	−5.53804	+	17.5967i	−0.208723	+	0.663200i
$705$		−	3.28507i		−	0.123723i
$706$	−26.3469	+	81.0876i	−0.991580	+	3.05177i
$707$	−7.30354	−	24.1920i	−0.274678	−	0.909833i
$708$	1.08775	+	0.790296i	0.0408801	+	0.0297012i
$709$	−5.89295	−	18.1366i	−0.221315	−	0.681136i	−0.998645	−	0.0520434i	$-0.983427\pi$
$709$	−5.89295	−	18.1366i	−0.221315	−	0.681136i	0.777330	−	0.629093i	$-0.216573\pi$
$710$	14.7603	+	45.4274i	0.553943	+	1.70486i
$711$	1.68549	−	2.31987i	0.0632107	−	0.0870020i
$712$	−49.9151	+	36.2655i	−1.87065	+	1.35911i
$713$	−13.4496	−	4.37003i	−0.503691	−	0.163659i
$714$	11.5333	−	33.1172i	0.431622	−	1.23938i
$715$	−0.307357	−	33.2175i	−0.0114945	−	1.24226i
$716$	53.4319			1.99684
$717$	−2.66450	+	8.20050i	−0.0995077	+	0.306253i
$718$	−68.1392	+	49.5060i	−2.54293	+	1.84755i
$719$	20.6768	−	28.4592i	0.771115	−	1.06135i	−0.225092	−	0.974338i	$-0.572268\pi$
$719$	20.6768	−	28.4592i	0.771115	−	1.06135i	0.996207	−	0.0870118i	$-0.0277318\pi$
$720$	7.36731	−	2.39378i	0.274563	−	0.0892110i
$721$	0.139413	−	6.65017i	0.00519201	−	0.247665i
$722$	−44.8131	+	61.6800i	−1.66777	+	2.29549i
$723$	−12.0469	−	16.5811i	−0.448029	−	0.616659i
$724$	−50.4220	−	16.3831i	−1.87392	−	0.608873i
$725$		−	10.9221i		−	0.405636i
$726$	−8.93066	−	25.8481i	−0.331448	−	0.959315i
$727$			39.2173i			1.45449i	0.686379	+	0.727244i	$0.259199\pi$
$727$			39.2173i			1.45449i	−0.686379	+	0.727244i	$0.740801\pi$
$728$	57.3918	−	75.6083i	2.12708	−	2.80223i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	7.41601	+	5.38805i	0.274479	+	0.199421i
$731$	−18.7950	+	6.10686i	−0.695158	+	0.225870i
$732$	−11.8215	+	3.84103i	−0.436934	+	0.141969i
$733$	−2.04282	−	1.48420i	−0.0754533	−	0.0548200i	0.549419	−	0.835547i	$-0.314849\pi$
$733$	−2.04282	−	1.48420i	−0.0754533	−	0.0548200i	−0.624872	+	0.780727i	$0.714849\pi$
$734$	−16.6866	+	12.1235i	−0.615912	+	0.447486i
$735$	−8.82526	+	5.86306i	−0.325525	+	0.216262i
$736$		−	3.46896i		−	0.127868i
$737$	4.03840	−	0.0373668i	0.148756	−	0.00137643i
$738$			1.73081i			0.0637121i
$739$	4.66793	+	1.51670i	0.171712	+	0.0557927i	0.393611	−	0.919277i	$-0.371226\pi$
$739$	4.66793	+	1.51670i	0.171712	+	0.0557927i	−0.221899	+	0.975070i	$0.571226\pi$
$740$	−6.89751	−	9.49361i	−0.253558	−	0.348992i
$741$	−27.4109	+	37.7278i	−1.00696	+	1.38597i
$742$	−0.765224	+	36.5021i	−0.0280923	+	1.34004i
$743$	−6.78320	+	2.20400i	−0.248852	+	0.0808568i	−0.430787	−	0.902454i	$-0.641764\pi$
$743$	−6.78320	+	2.20400i	−0.248852	+	0.0808568i	0.181935	+	0.983311i	$0.441764\pi$
$744$	−24.4227	+	33.6149i	−0.895379	+	1.23238i
$745$	11.9349	−	8.67120i	0.437260	−	0.317688i
$746$	−21.3278	+	65.6403i	−0.780868	+	2.40326i
$747$	−2.41467			−0.0883483
$748$	−22.1930	+	70.5166i	−0.811457	+	2.57834i
$749$	29.2237	+	10.1773i	1.06781	+	0.371871i
$750$	−27.5894	−	8.96434i	−1.00742	−	0.327332i
$751$	−21.3764	+	15.5308i	−0.780035	+	0.566729i	−0.904990	−	0.425434i	$-0.860122\pi$
$751$	−21.3764	+	15.5308i	−0.780035	+	0.566729i	0.124954	+	0.992162i	$0.460122\pi$
$752$	−6.52881	+	8.98613i	−0.238081	+	0.327690i
$753$	−6.57366	−	20.2317i	−0.239558	−	0.737282i
$754$	−20.4966	−	63.0819i	−0.746441	−	2.29731i
$755$	−16.9417	−	12.3089i	−0.616571	−	0.447965i
$756$	10.5894	−	3.19695i	0.385134	−	0.116272i
$757$	−2.44256	+	7.51743i	−0.0887764	+	0.273226i	−0.985582	−	0.169199i	$-0.945882\pi$
$757$	−2.44256	+	7.51743i	−0.0887764	+	0.273226i	0.896805	+	0.442425i	$0.145882\pi$
$758$			65.1057i			2.36474i
$759$	−3.64310	−	4.91796i	−0.132236	−	0.178511i
$760$	−57.8360			−2.09793
$761$	4.58841	−	14.1217i	0.166330	−	0.511910i	−0.832802	−	0.553571i	$-0.813265\pi$
$761$	4.58841	−	14.1217i	0.166330	−	0.511910i	0.999132	+	0.0416609i	$0.0132649\pi$
$762$	29.1202	+	40.0805i	1.05491	+	1.45196i
$763$	−10.0303	−	14.4323i	−0.363123	−	0.522484i
$764$	−1.35786	−	4.17908i	−0.0491258	−	0.151194i
$765$	−7.67468	+	2.49366i	−0.277479	+	0.0901583i
$766$	19.3437	+	14.0540i	0.698917	+	0.507793i
$767$	−1.25083	−	1.72162i	−0.0451648	−	0.0621640i
$768$	31.0060	+	10.0745i	1.11883	+	0.363530i
$769$	−2.69047			−0.0970209			−0.0485105	−	0.998823i	$-0.515447\pi$
$769$	−2.69047			−0.0970209			−0.0485105	+	0.998823i	$0.515447\pi$
$770$	26.9397	−	19.0949i	0.970838	−	0.688134i
$771$	−1.84063			−0.0662888
$772$	49.5024	+	16.0843i	1.78163	+	0.578887i
$773$	−13.8048	−	19.0006i	−0.496523	−	0.683405i	0.485052	−	0.874485i	$-0.338801\pi$
$773$	−13.8048	−	19.0006i	−0.496523	−	0.683405i	−0.981574	+	0.191081i	$0.938801\pi$
$774$	−7.45554	−	5.41677i	−0.267984	−	0.194702i
$775$	19.7439	−	6.41519i	0.709222	−	0.230440i
$776$	12.0749	+	37.1629i	0.433465	+	1.33407i
$777$	−2.79995	−	4.02874i	−0.100447	−	0.144530i
$778$	−36.8100	−	50.6646i	−1.31970	−	1.81641i
$779$	1.51614	−	4.66620i	0.0543213	−	0.167184i
$780$	−41.8749			−1.49936
$781$	−13.3791	−	39.9161i	−0.478741	−	1.42831i
$782$			24.4592i			0.874658i
$783$	1.24590	−	3.83449i	0.0445249	−	0.137034i
$784$	35.7934	+	1.50139i	1.27834	+	0.0536212i
$785$	2.74443	+	1.99395i	0.0979530	+	0.0711670i
$786$	−0.684782	−	2.10754i	−0.0244254	−	0.0751735i
$787$	0.475316	+	1.46287i	0.0169432	+	0.0521458i	0.959171	−	0.282828i	$-0.0912725\pi$
$787$	0.475316	+	1.46287i	0.0169432	+	0.0521458i	−0.942227	+	0.334974i	$0.891273\pi$
$788$	13.8885	−	19.1159i	0.494758	−	0.680976i
$789$	16.0074	−	11.6301i	0.569880	−	0.414042i
$790$	−10.2625	−	3.33449i	−0.365123	−	0.118636i
$791$	−8.44387	+	24.2462i	−0.300230	+	0.862095i
$792$	−17.0501	+	5.71487i	−0.605850	+	0.203069i
$793$	19.6731			0.698613
$794$	2.45213	−	7.54687i	0.0870227	−	0.267828i
$795$	6.79695	−	4.93827i	0.241063	−	0.175142i
$796$	18.1803	−	25.0230i	0.644384	−	0.886918i
$797$	−12.7928	+	4.15662i	−0.453143	+	0.147235i	−0.526691	−	0.850057i	$-0.676568\pi$
$797$	−12.7928	+	4.15662i	−0.453143	+	0.147235i	0.0735485	+	0.997292i	$0.476568\pi$
$798$	−46.3457	−	0.971582i	−1.64062	−	0.0343936i
$799$	6.80120	−	9.36105i	0.240609	−	0.331170i
$800$	2.99325	+	4.11985i	0.105827	+	0.145659i
$801$	10.8226	+	3.51646i	0.382396	+	0.124248i
$802$			15.9726i			0.564012i
$803$	−6.57988	−	4.68816i	−0.232199	−	0.165442i
$804$		−	5.09092i		−	0.179543i
$805$	4.46808	−	5.88627i	0.157479	−	0.207464i
$806$	101.995	−	74.1036i	3.59262	−	2.61019i
$807$	−1.53661	−	1.11642i	−0.0540914	−	0.0392997i
$808$	49.2516	−	16.0028i	1.73267	−	0.562977i
$809$	−49.6626	+	16.1363i	−1.74604	+	0.567324i	−0.995608	−	0.0936202i	$-0.970156\pi$
$809$	−49.6626	+	16.1363i	−1.74604	+	0.567324i	−0.750435	+	0.660944i	$0.770156\pi$
$810$	−3.04437	−	2.21187i	−0.106968	−	0.0777170i
$811$	26.2388	−	19.0636i	0.921370	−	0.669415i	−0.0224943	−	0.999747i	$-0.507161\pi$
$811$	26.2388	−	19.0636i	0.921370	−	0.669415i	0.943865	+	0.330332i	$0.107161\pi$
$812$	26.9645	−	35.5232i	0.946269	−	1.24662i
$813$		−	14.8839i		−	0.522003i
$814$	9.10143	+	12.2864i	0.319005	+	0.430636i
$815$		−	3.11202i		−	0.109009i
$816$	25.9496	+	8.43155i	0.908419	+	0.295163i
$817$	15.3549	+	21.1342i	0.537200	+	0.739393i
$818$	−43.0710	+	59.2821i	−1.50594	+	2.07275i
$819$	−17.5036	−	0.366941i	−0.611624	−	0.0128220i
$820$	4.18999	−	1.36141i	0.146321	−	0.0475425i
$821$	−17.0759	+	23.5030i	−0.595954	+	0.820261i	−0.995330	−	0.0965264i	$-0.969227\pi$
$821$	−17.0759	+	23.5030i	−0.595954	+	0.820261i	0.399376	+	0.916787i	$0.369227\pi$
$822$	−17.4946	+	12.7105i	−0.610193	+	0.443331i
$823$	−0.0510760	+	0.157196i	−0.00178040	+	0.00547950i	−0.951943	−	0.306276i	$-0.900917\pi$
$823$	−0.0510760	+	0.157196i	−0.00178040	+	0.00547950i	0.950162	+	0.311755i	$0.100917\pi$
$824$	13.6311			0.474861
$825$	8.57021	+	2.69722i	0.298376	+	0.0939052i
$826$	0.695697	−	1.99766i	0.0242064	−	0.0695075i
$827$	0.804112	+	0.261272i	0.0279617	+	0.00908532i	0.322964	−	0.946411i	$-0.395321\pi$
$827$	0.804112	+	0.261272i	0.0279617	+	0.00908532i	−0.295003	+	0.955496i	$0.595321\pi$
$828$	−6.24168	+	4.53485i	−0.216913	+	0.157597i
$829$	2.77523	−	3.81977i	0.0963877	−	0.132666i	−0.758099	−	0.652139i	$-0.773872\pi$
$829$	2.77523	−	3.81977i	0.0963877	−	0.132666i	0.854487	+	0.519473i	$0.173872\pi$
$830$	2.80789	+	8.64181i	0.0974634	+	0.299962i
$831$	1.89553	+	5.83386i	0.0657554	+	0.202374i
$832$	−29.7765	−	21.6339i	−1.03231	−	0.750020i
$833$	−37.2868	−	1.56403i	−1.29191	−	0.0541905i
$834$	17.1104	−	52.6604i	0.592484	−	1.82348i
$835$		−	3.23345i		−	0.111898i
$836$	97.7179	−	0.904172i	3.37964	−	0.0312714i
$837$	7.66343			0.264887
$838$	26.1213	−	80.3930i	0.902344	−	2.77713i
$839$	21.2769	+	29.2851i	0.734560	+	1.01104i	0.998913	+	0.0466091i	$0.0148415\pi$
$839$	21.2769	+	29.2851i	0.734560	+	1.01104i	−0.264353	+	0.964426i	$0.585158\pi$
$840$	−12.3915	−	17.8297i	−0.427547	−	0.615182i
$841$	3.93824	+	12.1206i	0.135801	+	0.417953i
$842$	3.08603	−	1.00271i	0.106351	−	0.0345557i
$843$	15.6195	+	11.3483i	0.537966	+	0.390855i
$844$	31.8463	+	43.8326i	1.09619	+	1.50878i
$845$	44.3190	+	14.4001i	1.52462	+	0.495379i
$846$	5.39576			0.185510
$847$	−23.5870	+	17.0486i	−0.810458	+	0.585797i
$848$	−28.4071			−0.975504
$849$	−19.8552	−	6.45135i	−0.681429	−	0.221410i
$850$	−21.1050	−	29.0485i	−0.723895	−	0.996356i
$851$	2.76840	+	2.01136i	0.0948996	+	0.0689486i
$852$	−50.4711	+	16.3991i	−1.72911	+	0.561823i
$853$	4.77497	+	14.6958i	0.163492	+	0.503176i	0.998922	−	0.0464206i	$-0.0147815\pi$
$853$	4.77497	+	14.6958i	0.163492	+	0.503176i	−0.835430	+	0.549597i	$0.814781\pi$
$854$	11.1604	+	16.0583i	0.381902	+	0.549505i
$855$	6.26997	+	8.62988i	0.214429	+	0.295136i
$856$	−19.5964	+	60.3117i	−0.669793	+	2.06141i
$857$	42.2531			1.44334			0.721670	−	0.692237i	$-0.243375\pi$
$857$	42.2531			1.44334			0.721670	+	0.692237i	$0.243375\pi$
$858$	54.5601	−	0.504838i	1.86265	−	0.0172349i
$859$			17.4829i			0.596510i	0.954486	+	0.298255i	$0.0964047\pi$
$859$			17.4829i			0.596510i	−0.954486	+	0.298255i	$0.903595\pi$
$860$	−7.24871	+	22.3092i	−0.247179	+	0.760738i
$861$	1.76333	−	0.532349i	0.0600941	−	0.0181424i
$862$	24.6692	+	17.9232i	0.840236	+	0.610467i
$863$	5.41047	+	16.6517i	0.184175	+	0.566831i	0.999933	−	0.0115614i	$-0.00368020\pi$
$863$	5.41047	+	16.6517i	0.184175	+	0.566831i	−0.815759	+	0.578393i	$0.803680\pi$
$864$	0.580902	+	1.78783i	0.0197627	+	0.0608233i
$865$	20.8031	−	28.6330i	0.707326	−	0.973550i
$866$	24.7628	−	17.9912i	0.841473	−	0.611366i
$867$	−10.8643	−	3.53004i	−0.368972	−	0.119886i
$868$	80.0535	+	27.8791i	2.71719	+	0.946277i
$869$	9.07182	+	2.85509i	0.307740	+	0.0968522i
$870$	−15.1720			−0.514377
$871$	−2.48993	+	7.66321i	−0.0843680	+	0.259658i
$872$	29.1385	−	21.1704i	0.986755	−	0.716920i
$873$	4.23614	−	5.83055i	0.143372	−	0.197334i
$874$	30.7497	−	9.99118i	1.04012	−	0.337957i
$875$	−0.647047	+	30.8649i	−0.0218742	+	1.04343i
$876$	−5.98627	+	8.23940i	−0.202257	+	0.278384i
$877$	25.3847	+	34.9391i	0.857181	+	1.17981i	0.982234	+	0.187659i	$0.0600899\pi$
$877$	25.3847	+	34.9391i	0.857181	+	1.17981i	−0.125053	+	0.992150i	$0.539910\pi$
$878$	−70.8609	−	23.0241i	−2.39144	−	0.777025i
$879$		−	15.9263i		−	0.537181i
$880$	15.2931	+	20.6447i	0.515530	+	0.695932i
$881$			43.9336i			1.48016i	0.672518	+	0.740081i	$0.265213\pi$
$881$			43.9336i			1.48016i	−0.672518	+	0.740081i	$0.734787\pi$
$882$	−9.63015	−	14.4956i	−0.324264	−	0.488092i
$883$	−42.1520	+	30.6252i	−1.41853	+	1.03062i	−0.426514	+	0.904481i	$0.640259\pi$
$883$	−42.1520	+	30.6252i	−1.41853	+	1.03062i	−0.992013	+	0.126139i	$0.959741\pi$
$884$	−119.326	−	86.6952i	−4.01336	−	2.91588i
$885$	−0.462944	+	0.150420i	−0.0155617	+	0.00505630i
$886$	43.7738	−	14.2230i	1.47061	−	0.477829i
$887$	−41.7087	−	30.3032i	−1.40044	−	1.01748i	−0.994627	−	0.103525i	$-0.966988\pi$
$887$	−41.7087	−	30.3032i	−1.40044	−	1.01748i	−0.405815	−	0.913955i	$-0.633012\pi$
$888$	8.13395	−	5.90966i	0.272958	−	0.198315i
$889$	31.8770	−	41.9949i	1.06912	−	1.40846i
$890$		−	42.8217i		−	1.43539i
$891$	2.70113	+	1.92455i	0.0904912	+	0.0644750i
$892$			39.4509i			1.32091i
$893$	−14.5467	−	4.72653i	−0.486788	−	0.158167i
$894$	14.2425	+	19.6032i	0.476342	+	0.655628i
$895$	−11.3702	+	15.6498i	−0.380065	+	0.523115i
$896$	0.975301	−	46.5231i	0.0325825	−	1.55423i
$897$	11.6134	−	3.77341i	0.387759	−	0.125991i
$898$	45.9999	−	63.3134i	1.53504	−	2.11280i
$899$	24.9967	−	18.1612i	0.833686	−	0.605709i
$900$	3.49986	−	10.7715i	0.116662	−	0.359049i
$901$	29.5923			0.985863
$902$	−5.44285	+	1.82434i	−0.181227	+	0.0607437i
$903$	−3.22543	+	9.26166i	−0.107335	+	0.308209i
$904$	−50.0391	−	16.2587i	−1.66428	−	0.540756i
$905$	15.5282	−	11.2819i	0.516176	−	0.375024i
$906$	20.2174	−	27.8269i	0.671680	−	0.924488i
$907$	3.56244	+	10.9641i	0.118289	+	0.364056i	0.992619	−	0.121276i	$-0.0386987\pi$
$907$	3.56244	+	10.9641i	0.118289	+	0.364056i	−0.874330	+	0.485332i	$0.838699\pi$
$908$	−21.9973	−	67.7007i	−0.730005	−	2.24673i
$909$	−7.72717	−	5.61412i	−0.256294	−	0.186209i
$910$	19.0407	+	63.0697i	0.631194	+	2.09074i
$911$	6.68282	−	20.5676i	0.221412	−	0.681435i	−0.777224	−	0.629224i	$-0.783373\pi$
$911$	6.68282	−	20.5676i	0.221412	−	0.681435i	0.998636	−	0.0522116i	$-0.0166270\pi$
$912$		−	36.0677i		−	1.19432i
$913$	−2.54515	−	7.59337i	−0.0842322	−	0.251304i
$914$	−27.3934			−0.906092
$915$	1.39059	−	4.27979i	0.0459714	−	0.141485i
$916$	5.43852	+	7.48549i	0.179694	+	0.247327i
$917$	−1.93652	+	1.34587i	−0.0639495	+	0.0444444i
$918$	−4.09586	−	12.6058i	−0.135184	−	0.416052i
$919$	28.0074	−	9.10016i	0.923880	−	0.300187i	0.191822	−	0.981430i	$-0.438560\pi$
$919$	28.0074	−	9.10016i	0.923880	−	0.300187i	0.732057	+	0.681243i	$0.238560\pi$
$920$	12.2519	+	8.90152i	0.403933	+	0.293475i
$921$	10.0827	+	13.8776i	0.332236	+	0.457284i
$922$	87.7081	+	28.4981i	2.88851	+	0.938534i
$923$	83.9932			2.76467
$924$	21.2150	+	29.9307i	0.697923	+	0.984649i
$925$	−5.02338			−0.165168
$926$	−7.44512	−	2.41906i	−0.244662	−	0.0794954i
$927$	−1.47774	−	2.03393i	−0.0485353	−	0.0668032i
$928$	6.13168	+	4.45493i	0.201282	+	0.146240i
$929$	19.6849	−	6.39603i	0.645842	−	0.209847i	0.0322622	−	0.999479i	$-0.489729\pi$
$929$	19.6849	−	6.39603i	0.645842	−	0.209847i	0.613580	+	0.789633i	$0.289729\pi$
$930$	−8.91140	−	27.4265i	−0.292216	−	0.899349i
$931$	13.2648	+	47.5152i	0.434735	+	1.55725i
$932$	−3.20155	−	4.40656i	−0.104870	−	0.144342i
$933$	−1.44890	+	4.45924i	−0.0474347	+	0.145989i
$934$	68.5074			2.24163
$935$	−15.9311	−	21.5060i	−0.521004	−	0.703322i
$936$		−	35.8777i		−	1.17270i
$937$	10.0922	−	31.0607i	0.329699	−	1.01471i	−0.639576	−	0.768728i	$-0.720890\pi$
$937$	10.0922	−	31.0607i	0.329699	−	1.01471i	0.969275	−	0.245981i	$-0.0791100\pi$
$938$	−7.66768	+	2.31487i	−0.250359	+	0.0755831i
$939$	18.1257	+	13.1691i	0.591510	+	0.429757i
$940$	−4.24416	−	13.0622i	−0.138429	−	0.426041i
$941$	14.4684	+	44.5291i	0.471656	+	1.45161i	0.850415	+	0.526112i	$0.176351\pi$
$941$	14.4684	+	44.5291i	0.471656	+	1.45161i	−0.378760	+	0.925495i	$0.623649\pi$
$942$	−3.27508	+	4.50776i	−0.106708	+	0.146871i
$943$	−1.03935	+	0.755132i	−0.0338459	+	0.0245905i
$944$	1.56531	+	0.508599i	0.0509464	+	0.0165535i
$945$	−1.31706	+	3.78188i	−0.0428440	+	0.123024i
$946$	9.17560	−	29.1548i	0.298325	−	0.947903i
$947$	33.7507			1.09675			0.548375	−	0.836233i	$-0.315247\pi$
$947$	33.7507			1.09675			0.548375	+	0.836233i	$0.315247\pi$
$948$	3.70471	−	11.4019i	0.120323	−	0.370317i
$949$	13.0408	−	9.47468i	0.423321	−	0.307561i
$950$	−27.8983	+	38.3987i	−0.905140	+	1.24582i
$951$	11.5607	−	3.75630i	0.374881	−	0.121806i
$952$	1.60293	−	76.4616i	0.0519511	−	2.47813i
$953$	7.98661	−	10.9926i	0.258712	−	0.356086i	−0.659827	−	0.751418i	$-0.729370\pi$
$953$	7.98661	−	10.9926i	0.258712	−	0.356086i	0.918538	+	0.395332i	$0.129370\pi$
$954$	8.11117	+	11.1641i	0.262609	+	0.361450i
$955$	1.51297	+	0.491595i	0.0489586	+	0.0159076i
$956$			36.0495i			1.16592i
$957$	13.3715	−	0.123725i	0.432238	−	0.00399945i
$958$		−	6.33125i		−	0.204553i
$959$	18.3302	+	13.9138i	0.591912	+	0.449302i
$960$	−6.81109	+	4.94854i	−0.219827	+	0.159714i
$961$	22.4326	+	16.2982i	0.723633	+	0.525750i
$962$	−29.0132	+	9.42697i	−0.935425	+	0.303938i
$963$	11.1237	−	3.61432i	0.358457	−	0.116470i
$964$	−69.3233	−	50.3663i	−2.23275	−	1.62219i
$965$	−15.2450	+	11.0762i	−0.490755	+	0.356554i
$966$	9.66827	+	7.33887i	0.311071	+	0.236124i
$967$		−	47.7893i		−	1.53680i	−0.639970	−	0.768400i	$-0.721053\pi$
$967$		−	47.7893i		−	1.53680i	0.639970	−	0.768400i	$-0.278947\pi$
$968$	−35.9428	−	47.5935i	−1.15525	−	1.52971i
$969$			37.5725i			1.20700i
$970$	−25.7928	−	8.38058i	−0.828156	−	0.269084i
$971$	−18.2970	−	25.1836i	−0.587177	−	0.808180i	0.407282	−	0.913302i	$-0.366477\pi$
$971$	−18.2970	−	25.1836i	−0.587177	−	0.808180i	−0.994459	+	0.105122i	$0.966477\pi$
$972$	2.45745	−	3.38238i	0.0788226	−	0.108490i
$973$	−58.9124	−	1.23503i	−1.88865	−	0.0395932i
$974$	−52.5572	+	17.0769i	−1.68404	+	0.547178i
$975$	−10.5365	+	14.5022i	−0.337437	+	0.464442i
$976$	−12.3096	+	8.94346i	−0.394021	+	0.286273i
$977$	3.79628	−	11.6838i	0.121454	−	0.373796i	−0.871785	−	0.489890i	$-0.837037\pi$
$977$	3.79628	−	11.6838i	0.121454	−	0.373796i	0.993238	+	0.116093i	$0.0370371\pi$
$978$	5.11153			0.163449
$979$	0.349203	+	37.7399i	0.0111606	+	1.20617i
$980$	−27.5164	+	34.7147i	−0.878980	+	1.10892i
$981$	−6.31779	−	2.05277i	−0.201712	−	0.0655400i
$982$	−42.1868	+	30.6505i	−1.34624	+	0.978097i
$983$	10.6431	−	14.6490i	0.339462	−	0.467229i	−0.604822	−	0.796361i	$-0.706756\pi$
$983$	10.6431	−	14.6490i	0.339462	−	0.467229i	0.944284	+	0.329131i	$0.106756\pi$
$984$	1.16643	+	3.58991i	0.0371845	+	0.114442i
$985$	2.64344	+	8.13568i	0.0842271	+	0.259224i
$986$	−43.2336	−	31.4111i	−1.37684	−	1.00033i
$987$	−1.65958	−	5.49714i	−0.0528251	−	0.174976i
$988$	−60.2492	+	185.428i	−1.91678	+	5.89925i
$989$		−	6.84031i		−	0.217509i
$990$	3.74674	−	11.9050i	0.119079	−	0.378364i
$991$	34.8856			1.10818			0.554089	−	0.832457i	$-0.313067\pi$
$991$	34.8856			1.10818			0.554089	+	0.832457i	$0.313067\pi$
$992$	−4.45170	+	13.7009i	−0.141342	+	0.435005i
$993$	−15.1819	−	20.8961i	−0.481784	−	0.663118i
$994$	47.6489	+	68.5602i	1.51133	+	2.17460i
$995$	3.46031	+	10.6497i	0.109699	+	0.337620i
$996$	−9.60130	+	3.11965i	−0.304229	+	0.0988499i
$997$	16.3959	+	11.9123i	0.519263	+	0.377267i	0.816326	−	0.577591i	$-0.196007\pi$
$997$	16.3959	+	11.9123i	0.519263	+	0.377267i	−0.297063	+	0.954858i	$0.596007\pi$
$998$	0.581395	+	0.800222i	0.0184037	+	0.0253306i
$999$	−1.76360	−	0.573027i	−0.0557977	−	0.0181298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.w.a.13.2	yes	64
3.2	odd	2		693.2.bu.f.244.16		64
7.6	odd	2	inner	231.2.w.a.13.1	✓	64
11.6	odd	10	inner	231.2.w.a.160.1	yes	64
21.20	even	2		693.2.bu.f.244.15		64
33.17	even	10		693.2.bu.f.622.15		64
77.6	even	10	inner	231.2.w.a.160.2	yes	64
231.83	odd	10		693.2.bu.f.622.16		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.w.a.13.1	✓	64	7.6	odd	2	inner
231.2.w.a.13.2	yes	64	1.1	even	1	trivial
231.2.w.a.160.1	yes	64	11.6	odd	10	inner
231.2.w.a.160.2	yes	64	77.6	even	10	inner
693.2.bu.f.244.15		64	21.20	even	2
693.2.bu.f.244.16		64	3.2	odd	2
693.2.bu.f.622.15		64	33.17	even	10
693.2.bu.f.622.16		64	231.83	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.36445 - 0.768257i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.38238 + 2.45745i) q^{4} +(-1.43953 + 0.467733i) q^{5} +(-0.768257 - 2.36445i) q^{6} +(-2.17258 + 1.50993i) q^{7} +(-3.18691 - 4.38641i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-2.36445 - 0.768257i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.38238 + 2.45745i) q^{4} +(-1.43953 + 0.467733i) q^{5} +(-0.768257 - 2.36445i) q^{6} +(-2.17258 + 1.50993i) q^{7} +(-3.18691 - 4.38641i) q^{8} +(-0.309017 + 0.951057i) q^{9} +3.76305 q^{10} +(-3.31648 + 0.0306870i) q^{11} +4.18086i q^{12} +(2.04482 - 6.29331i) q^{13} +(6.29698 - 1.90106i) q^{14} +(-1.22454 - 0.889681i) q^{15} +(1.58150 + 4.86735i) q^{16} +(-1.64748 - 5.07043i) q^{17} +(1.46131 - 2.01132i) q^{18} +(-5.70150 + 4.14238i) q^{19} +(-6.01849 - 1.95552i) q^{20} +(-2.49857 - 0.870141i) q^{21} +(7.86524 + 2.47535i) q^{22} +1.84535 q^{23} +(1.67546 - 5.15653i) q^{24} +(-2.19160 + 1.59229i) q^{25} +(-9.66976 + 13.3093i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-11.0591 - 0.231840i) q^{28} +(-2.36985 + 3.26181i) q^{29} +(2.21187 + 3.04437i) q^{30} +(-7.28836 - 2.36813i) q^{31} -1.87984i q^{32} +(-1.97421 - 2.66505i) q^{33} +13.2545i q^{34} +(2.42126 - 3.18978i) q^{35} +(-3.38238 + 2.45745i) q^{36} +(1.50020 + 1.08996i) q^{37} +(16.6633 - 5.41424i) q^{38} +(6.29331 - 2.04482i) q^{39} +(6.63933 + 4.82376i) q^{40} +(-0.563227 + 0.409208i) q^{41} +(5.23926 + 3.97695i) q^{42} -3.70678i q^{43} +(-11.2930 - 8.04628i) q^{44} -1.51362i q^{45} +(-4.36324 - 1.41770i) q^{46} +(1.27570 + 1.75584i) q^{47} +(-3.00819 + 4.14042i) q^{48} +(2.44022 - 6.56089i) q^{49} +(6.40522 - 2.08118i) q^{50} +(3.13370 - 4.31316i) q^{51} +(22.3818 - 16.2614i) q^{52} +(-1.71523 + 5.27894i) q^{53} +2.48613 q^{54} +(4.75984 - 1.59540i) q^{55} +(13.5470 + 4.71781i) q^{56} +(-6.70251 - 2.17778i) q^{57} +(8.10930 - 5.89175i) q^{58} +(0.189027 - 0.260174i) q^{59} +(-1.95552 - 6.01849i) q^{60} +(0.918719 + 2.82753i) q^{61} +(15.4136 + 11.1987i) q^{62} +(-0.764664 - 2.53284i) q^{63} +(1.71880 - 5.28992i) q^{64} +10.0159i q^{65} +(2.62047 + 7.81809i) q^{66} -1.21768 q^{67} +(6.88788 - 21.1987i) q^{68} +(1.08467 + 1.49292i) q^{69} +(-8.17554 + 5.68194i) q^{70} +(3.92242 + 12.0720i) q^{71} +(5.15653 - 1.67546i) q^{72} +(1.97075 + 1.43183i) q^{73} +(-2.70979 - 3.72971i) q^{74} +(-2.57638 - 0.837117i) q^{75} -29.4643 q^{76} +(7.15900 - 5.07433i) q^{77} -16.4512 q^{78} +(-2.72717 - 0.886112i) q^{79} +(-4.55325 - 6.26701i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.64610 - 0.534850i) q^{82} +(0.746175 + 2.29649i) q^{83} +(-6.31280 - 9.08325i) q^{84} +(4.74322 + 6.52848i) q^{85} +(-2.84776 + 8.76452i) q^{86} -4.03182 q^{87} +(10.7039 + 14.4496i) q^{88} -11.3795i q^{89} +(-1.16285 + 3.57887i) q^{90} +(5.05992 + 16.7603i) q^{91} +(6.24168 + 4.53485i) q^{92} +(-2.36813 - 7.28836i) q^{93} +(-1.66738 - 5.13167i) q^{94} +(6.26997 - 8.62988i) q^{95} +(1.52082 - 1.10494i) q^{96} +(-6.85422 - 2.22707i) q^{97} +(-10.8102 + 13.6382i) q^{98} +(0.995664 - 3.16365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

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