LMFDB - Embedded newform 231.2.w.a.13.1

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			13.1
Character	$\chi$	$=$	231.13
Dual form			231.2.w.a.160.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36445 - 0.768257i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.38238 + 2.45745i) q^{4} +(1.43953 - 0.467733i) q^{5} +(0.768257 + 2.36445i) q^{6} +(-0.764664 + 2.53284i) q^{7} +(-3.18691 - 4.38641i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(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} +(-0.764664 + 2.53284i) 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} +(3.75389 - 5.40133i) 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} +(-8.81071 + 6.68792i) 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} +(0.0839343 + 4.00377i) 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} +(-6.57624 + 0.137863i) 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} +(-5.83058 - 3.87355i) 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} +(-2.17258 - 1.50993i) 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} +(2.87747 - 9.53121i) 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} +(2.45827 - 8.42359i) 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} +(10.5894 + 3.19695i) 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} +(-14.3764 - 9.99148i) 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	0.0311101	−	0.999516i	$-0.490096\pi$
$5$	1.43953	−	0.467733i	0.643779	−	0.209177i	0.612669	+	0.790339i	$0.290096\pi$
$6$	0.768257	+	2.36445i	0.313640	+	0.965284i
$7$	−0.764664	+	2.53284i	−0.289016	+	0.957324i
$7$	−0.764664	+	2.53284i	−0.289016	+	0.957324i
$8$	−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	$0.469906\pi$
$13$	−2.04482	+	6.29331i	−0.567131	+	1.74545i	−0.661533	+	0.749916i	$0.730094\pi$
$14$	3.75389	−	5.40133i	1.00327	−	1.44357i
$15$	−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	$0.123778\pi$
$17$	1.64748	+	5.07043i	0.399573	+	1.22976i	−0.525769	+	0.850627i	$0.676222\pi$
$18$	1.46131	−	2.01132i	0.344435	−	0.474073i
$19$	5.70150	−	4.14238i	1.30801	−	0.950327i	0.308013	−	0.951382i	$-0.400336\pi$
$19$	5.70150	−	4.14238i	1.30801	−	0.950327i	0.999999	+	0.00105499i	$0.000335814\pi$
$20$	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
$28$	−8.81071	+	6.68792i	−1.66507	+	1.26390i
$29$	−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	0.878713	−	0.477350i	$-0.158403\pi$
$31$	7.28836	+	2.36813i	1.30903	+	0.425329i	0.430315	+	0.902679i	$0.358403\pi$
$32$		−	1.87984i		−	0.332311i
$33$	1.97421	+	2.66505i	0.343665	+	0.463926i
$34$		−	13.2545i		−	2.27312i
$35$	0.0839343	+	4.00377i	0.0141875	+	0.676761i
$36$	−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	−0.542935	−	0.839774i	$-0.682687\pi$
$41$	0.563227	−	0.409208i	0.0879612	−	0.0639076i	0.630897	+	0.775867i	$0.282687\pi$
$42$	−6.57624	+	0.137863i	−1.01474	+	0.0212727i
$43$		−	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	0.705778	−	0.708433i	$-0.250598\pi$
$47$	−1.27570	−	1.75584i	−0.186079	−	0.256116i	−0.891857	+	0.452317i	$0.850598\pi$
$48$	3.00819	−	4.14042i	0.434195	−	0.597618i
$49$	−5.83058	−	3.87355i	−0.832940	−	0.553364i
$50$	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	−0.821144	−	0.570721i	$-0.806664\pi$
$59$	−0.189027	+	0.260174i	−0.0246093	+	0.0338718i	0.796535	+	0.604592i	$0.206664\pi$
$60$	−1.95552	−	6.01849i	−0.252457	−	0.776983i
$61$	−0.918719	−	2.82753i	−0.117630	−	0.362028i	0.874857	−	0.484382i	$-0.160956\pi$
$61$	−0.918719	−	2.82753i	−0.117630	−	0.362028i	−0.992486	+	0.122355i	$0.960956\pi$
$62$	−15.4136	−	11.1987i	−1.95754	−	1.42223i
$63$	−2.17258	−	1.50993i	−0.273720	−	0.190233i
$64$	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
$70$	2.87747	−	9.53121i	0.343923	−	1.13920i
$71$	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	0.466453	−	0.884546i	$-0.345532\pi$
$73$	−1.97075	−	1.43183i	−0.230658	−	0.167583i	−0.697111	+	0.716963i	$0.745532\pi$
$74$	−2.70979	−	3.72971i	−0.315007	−	0.433570i
$75$	2.57638	+	0.837117i	0.297495	+	0.0966619i
$76$	29.4643			3.37979
$77$	2.45827	−	8.42359i	0.280146	−	0.959957i
$78$	−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	0.901717	−	0.432328i	$-0.142308\pi$
$83$	−0.746175	−	2.29649i	−0.0819034	−	0.252073i	−0.983620	+	0.180255i	$0.942308\pi$
$84$	10.5894	+	3.19695i	1.15540	+	0.348816i
$85$	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	$0.206073\pi$
$89$			11.3795i			1.20623i	−0.797656	+	0.603113i	$0.793927\pi$
$90$	1.16285	−	3.57887i	0.122575	−	0.377246i
$91$	−14.3764	−	9.99148i	−1.50705	−	1.04739i
$92$	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	0.635561	−	0.772051i	$-0.280769\pi$
$97$	6.85422	+	2.22707i	0.695941	+	0.226125i	0.0603796	+	0.998175i	$0.480769\pi$
$98$	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	$-0.742377\pi$
$101$	2.95152	−	9.08384i	0.293687	−	0.903876i	0.983659	−	0.180040i	$-0.0576227\pi$
$102$	−10.7231	+	7.79079i	−1.06174	+	0.771403i
$103$	1.47774	−	2.03393i	0.145606	−	0.200409i	−0.729984	−	0.683464i	$-0.760473\pi$
$103$	1.47774	−	2.03393i	0.145606	−	0.200409i	0.875590	+	0.483054i	$0.160473\pi$
$104$	34.1217	−	11.0868i	3.34591	−	1.08715i
$105$	3.18978	−	2.42126i	0.311291	−	0.236291i
$106$	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
$112$	−13.5376	+	0.283799i	−1.27918	+	0.0268165i
$113$	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
$119$	−14.1024	+	0.295639i	−1.29276	+	0.0271012i
$120$			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
$126$	3.97695	+	5.23926i	0.354295	+	0.466750i
$127$	−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	$-0.512398\pi$
$131$	−0.891344			−0.0778771			−0.0389386	+	0.999242i	$0.512398\pi$
$132$	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	$-0.906518\pi$
$139$	−18.0182	−	13.0910i	−1.52828	−	1.11036i	−0.571098	−	0.820882i	$-0.693482\pi$
$140$	−9.55515	+	13.7486i	−0.807558	+	1.16196i
$141$	−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
$147$	0.293364	+	6.99385i	0.0241963	+	0.576843i
$148$	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
$154$	−12.2839	+	18.0286i	−0.989869	+	1.45279i
$155$	11.5995			0.931694
$156$	26.3114	+	8.54910i	2.10660	+	0.684476i
$157$	1.31734	+	1.81316i	0.105135	+	0.144706i	0.858343	−	0.513077i	$-0.171494\pi$
$157$	1.31734	+	1.81316i	0.105135	+	0.144706i	−0.753208	+	0.657783i	$0.771494\pi$
$158$	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
$161$	−1.41107	+	4.67398i	−0.111208	+	0.368361i
$162$	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	−0.922261	−	0.386568i	$-0.873660\pi$
$167$	0.660136	−	2.03169i	0.0510828	−	0.157217i	0.973344	+	0.229351i	$0.0736604\pi$
$168$	−11.7795	−	8.18668i	−0.908809	−	0.631616i
$169$	−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	$-0.351489\pi$
$173$	18.9169	−	13.7440i	1.43823	−	1.04493i	0.988409	−	0.151814i	$-0.0485114\pi$
$174$	−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	0.175666	−	0.984450i	$-0.443792\pi$
$181$	12.0602	−	3.91860i	0.896429	−	0.291267i	0.720762	+	0.693182i	$0.243792\pi$
$182$	26.3162	+	34.6691i	1.95069	+	2.56985i
$183$	−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
$189$	0.0554529	+	2.64517i	0.00403360	+	0.192408i
$190$	−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
$196$	−10.2022	−	27.4301i	−0.728730	−	1.95930i
$197$		−	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	$0.0844536\pi$
$199$			7.39805i			0.524434i	−0.965009	+	0.262217i	$0.915546\pi$
$200$	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
$203$	−6.44952	−	8.49664i	−0.452668	−	0.596347i
$204$	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
$217$	−11.5712	+	16.6494i	−0.785507	+	1.13024i
$218$	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	0.581871	−	0.813281i	$-0.302321\pi$
$223$	−5.54639	−	7.63395i	−0.371413	−	0.511207i	−0.953284	+	0.302074i	$0.902321\pi$
$224$	4.76133	+	1.43744i	0.318130	+	0.0960432i
$225$	−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	0.942087	−	0.335369i	$-0.108861\pi$
$227$	13.7746	+	10.0078i	0.914253	+	0.664244i	−0.0278341	+	0.999613i	$0.508861\pi$
$228$	−17.3187	−	23.8371i	−1.14696	−	1.57865i
$229$	−2.10476	−	0.683879i	−0.139087	−	0.0451920i	0.238646	−	0.971107i	$-0.423296\pi$
$229$	−2.10476	−	0.683879i	−0.139087	−	0.0451920i	−0.377733	+	0.925915i	$0.623296\pi$
$230$	−6.94415			−0.457883
$231$	−8.25976	+	2.96248i	−0.543453	+	0.194917i
$232$	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
$238$	33.5715	+	10.1352i	2.17612	+	0.656969i
$239$	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	$-0.270509\pi$
$241$	20.4954			1.32022			0.660112	+	0.751167i	$0.270509\pi$
$242$	−26.1609	−	7.96811i	−1.68169	−	0.512209i
$243$			1.00000i			0.0641500i
$244$	3.84103	−	11.8215i	0.245897	−	0.756792i
$245$	−10.2051	−	2.84895i	−0.651980	−	0.182013i
$246$	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	0.867526	−	0.497391i	$-0.165709\pi$
$251$	20.2317	+	6.57366i	1.27701	+	0.414926i	0.409484	+	0.912317i	$0.365709\pi$
$252$	−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	−0.773939	−	0.633260i	$-0.781716\pi$
$257$	1.08190	−	1.48910i	0.0674869	−	0.0928878i	0.841426	+	0.540372i	$0.181716\pi$
$258$	8.76452	−	2.84776i	0.545655	−	0.177294i
$259$	−3.90785	+	2.96633i	−0.242822	+	0.184319i
$260$	−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
$266$	−0.971582	−	46.3457i	−0.0595715	−	2.84163i
$267$	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	−0.253429	−	0.967354i	$-0.581559\pi$
$269$	1.80640	−	0.586935i	0.110138	−	0.0357860i	0.363568	+	0.931568i	$0.381559\pi$
$270$	−3.57887	+	1.16285i	−0.217803	+	0.0707686i
$271$	12.0414	+	8.74856i	0.731461	+	0.531437i	0.890025	−	0.455911i	$-0.150687\pi$
$271$	12.0414	+	8.74856i	0.731461	+	0.531437i	−0.158564	+	0.987349i	$0.550687\pi$
$272$	−22.0741	+	16.0378i	−1.33844	+	0.972432i
$273$	0.366941	+	17.5036i	0.0222083	+	1.05936i
$274$			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
$280$	17.2947	−	13.1278i	1.03355	−	0.784538i
$281$	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	0.0410563	−	0.999157i	$-0.486928\pi$
$283$	16.8899	−	12.2712i	1.00400	−	0.729447i	0.962942	+	0.269710i	$0.0869277\pi$
$284$	−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	0.896671	−	0.442697i	$-0.145978\pi$
$293$	12.8846	+	9.36124i	0.752729	+	0.546889i	−0.143943	+	0.989586i	$0.545978\pi$
$294$	4.67943	−	16.7620i	0.272910	−	0.977580i
$295$	−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
$301$	9.38870	+	2.83444i	0.541156	+	0.163375i
$302$	−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	$-0.662823\pi$
$307$	−17.1537			−0.979014			−0.489507	+	0.871999i	$0.662823\pi$
$308$	29.0153	−	22.4508i	1.65330	−	1.27925i
$309$	−2.51408			−0.143021
$310$	−27.4265	−	8.91140i	−1.55772	−	0.506133i
$311$	−2.75596	−	3.79326i	−0.156276	−	0.215096i	0.723698	−	0.690116i	$-0.242441\pi$
$311$	−2.75596	−	3.79326i	−0.156276	−	0.215096i	−0.879975	+	0.475020i	$0.842441\pi$
$312$	−29.0256	−	21.0884i	−1.64325	−	1.19389i
$313$	−21.3080	+	6.92340i	−1.20440	+	0.391334i	−0.841378	−	0.540447i	$-0.818255\pi$
$313$	−21.3080	+	6.92340i	−1.20440	+	0.391334i	−0.363023	+	0.931780i	$0.618255\pi$
$314$	−1.72181	−	5.29919i	−0.0971675	−	0.299051i
$315$	−3.83375	−	1.15741i	−0.216007	−	0.0652125i
$316$	−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
$322$	6.92723	−	9.96734i	0.386040	−	0.555458i
$323$	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
$336$	8.18677	+	10.7853i	0.446625	+	0.588386i
$337$	−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
$343$	14.2695	−	11.8060i	0.770481	−	0.637463i
$344$	−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	0.0629865	−	0.998014i	$-0.479937\pi$
$349$	19.2722	−	14.0021i	1.03162	−	0.749515i	0.968632	+	0.248500i	$0.0799375\pi$
$350$	0.373467	+	17.8148i	0.0199626	+	0.952242i
$351$			6.61718i			0.353199i
$352$	0.0576866	+	6.23445i	0.00307471	+	0.332297i
$353$			34.2944i			1.82531i	0.408732	+	0.912654i	$0.365971\pi$
$353$			34.2944i			1.82531i	−0.408732	+	0.912654i	$0.634029\pi$
$354$	−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
$357$	8.52834	+	11.2353i	0.451368	+	0.594634i
$358$	−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	−0.917098	−	0.398662i	$-0.869475\pi$
$367$	−4.87645	+	6.71186i	−0.254549	+	0.350356i	0.662549	+	0.749018i	$0.269475\pi$
$368$	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
$371$	−12.0591	−	8.38102i	−0.626080	−	0.435121i
$372$	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
$378$	1.90106	−	6.29698i	0.0977797	−	0.323882i
$379$	−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	0.533231	−	0.845970i	$-0.320978\pi$
$383$	9.14670	+	2.97194i	0.467375	+	0.151859i	−0.0658559	+	0.997829i	$0.520978\pi$
$384$	17.5879			0.897530
$385$	−0.401231	−	13.2759i	−0.0204486	−	0.676601i
$386$	−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
$392$	1.59059	+	37.9199i	0.0803370	+	1.91525i
$393$	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	$-0.974477\pi$
$397$		−	3.19180i		−	0.160192i	0.996787	−	0.0800960i	$-0.0255227\pi$
$398$	5.68360	−	17.4923i	0.284893	−	0.876811i
$399$	10.6411	−	15.3111i	0.532723	−	0.766515i
$400$	−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	$0.359876\pi$
$409$	−9.10803	+	28.0316i	−0.450363	+	1.38607i	−0.876494	+	0.481413i	$0.840124\pi$
$410$	−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
$413$	−0.514437	−	0.677722i	−0.0253138	−	0.0333485i
$414$	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	$-0.688043\pi$
$419$		−	34.0007i		−	1.66104i	0.556988	−	0.830521i	$-0.311957\pi$
$420$	16.7392	−	0.350917i	0.816789	−	0.0171230i
$421$	−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
$427$	7.86419	−	0.164863i	0.380575	−	0.00797830i
$428$		−	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	−0.598921	−	0.800808i	$-0.704404\pi$
$433$	7.23662	−	9.96036i	0.347770	−	0.478664i	0.946691	+	0.322144i	$0.104404\pi$
$434$	40.1507	−	30.4771i	1.92730	−	1.46295i
$435$	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	$-0.753654\pi$
$439$	−29.9692			−1.43035			−0.715177	+	0.698943i	$0.753654\pi$
$440$	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
$448$	12.0842	+	8.39846i	0.570926	+	0.396790i
$449$	−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
$455$	−25.3686	−	7.65877i	−1.18930	−	0.359049i
$456$	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	$-0.168059\pi$
$461$	37.0945			1.72766			0.863830	+	0.503783i	$0.168059\pi$
$462$	21.8058	−	0.659026i	1.01450	−	0.0306607i
$463$	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	0.368296	−	0.929709i	$-0.379941\pi$
$467$	26.2072	−	8.51522i	1.21272	−	0.394037i	0.844427	+	0.535671i	$0.179941\pi$
$468$	−8.54910	−	26.3114i	−0.395182	−	1.21625i
$469$	0.931112	−	3.08418i	0.0429948	−	0.142414i
$470$	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
$476$	−48.4261	−	33.6558i	−2.21961	−	1.54261i
$477$	−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	0.931467	−	0.363825i	$-0.118529\pi$
$479$	−0.786951	−	2.42199i	−0.0359567	−	0.110663i	−0.967424	+	0.253162i	$0.918529\pi$
$480$	−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
$490$	21.9408	+	14.5763i	0.991183	+	0.658492i
$491$	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
$497$	−33.5757	+	0.703875i	−1.50608	+	0.0315731i
$498$	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	−0.932993	−	0.359894i	$-0.882813\pi$
$503$	−19.7145	+	14.3234i	−0.879024	+	0.638649i	0.0539688	+	0.998543i	$0.482813\pi$
$504$	0.300660	+	14.3418i	0.0133924	+	0.638836i
$505$		−	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	0.670958	−	0.741496i	$-0.265883\pi$
$509$	−5.45038	−	7.50181i	−0.241584	−	0.332512i	−0.912542	+	0.408984i	$0.865883\pi$
$510$	−11.7923	+	16.2307i	−0.522170	+	0.718706i
$511$	5.13356	−	3.89672i	0.227095	−	0.172381i
$512$	−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	−0.878299	−	0.478112i	$-0.841321\pi$
$521$	−3.47352	+	4.78088i	−0.152178	+	0.209454i	0.726121	+	0.687567i	$0.241321\pi$
$522$	3.09748	+	9.53305i	0.135573	+	0.417250i
$523$	3.90501	+	12.0184i	0.170754	+	0.525527i	0.999414	−	0.0342251i	$-0.0108963\pi$
$523$	3.90501	+	12.0184i	0.170754	+	0.525527i	−0.828660	+	0.559752i	$0.810896\pi$
$524$	−3.01487	−	2.19043i	−0.131705	−	0.0956894i
$525$	−4.09035	+	5.88545i	−0.178517	+	0.256862i
$526$	−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
$532$	−22.5303	+	74.6285i	−0.976812	+	3.23555i
$533$	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
$539$	19.4559	+	12.6676i	0.838024	+	0.545633i
$540$	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
$546$	12.5796	−	41.6683i	0.538358	−	1.78324i
$547$	−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
$553$	4.32975	−	6.22992i	0.184120	−	0.264923i
$554$	−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	−0.969319	−	0.245807i	$-0.920947\pi$
$563$	−0.964326	+	2.96789i	−0.0406415	+	0.125082i	0.928677	+	0.370889i	$0.120947\pi$
$564$	−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
$567$	2.10739	−	1.59965i	0.0885022	−	0.0671792i
$568$	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
$574$	−0.0959785	−	4.57829i	−0.00400606	−	0.191094i
$575$	−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	0.451774	−	0.892132i	$-0.350791\pi$
$577$	32.2275	−	10.4714i	1.34165	−	0.435928i	0.889875	+	0.456204i	$0.150791\pi$
$578$	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
$581$	6.38722	−	0.133901i	0.264987	−	0.00555513i
$582$			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	−0.549956	−	0.835193i	$-0.685356\pi$
$587$	10.0378	−	13.8159i	0.414305	−	0.570243i	0.964262	+	0.264951i	$0.0853557\pi$
$588$	−16.1947	+	24.3768i	−0.667859	+	1.00528i
$589$	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	$-0.798457\pi$
$593$	−39.2625			−1.61232			−0.806159	+	0.591699i	$0.798457\pi$
$594$	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	$0.0164064\pi$
$601$	33.2495	+	24.1572i	1.35628	+	0.985393i	0.357605	+	0.933873i	$0.383594\pi$
$602$	−20.0216	−	13.9148i	−0.816018	−	0.567127i
$603$	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	−0.980403	−	0.197004i	$-0.936879\pi$
$607$	−1.76020	+	5.41733i	−0.0714441	+	0.219882i	0.908959	+	0.416887i	$0.136879\pi$
$608$	−7.78700	−	10.7179i	−0.315805	−	0.434668i
$609$	−3.08299	+	10.2120i	−0.124929	+	0.413810i
$610$	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
$616$	−44.7836	+	16.0623i	−1.80438	+	0.647167i
$617$	−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	0.868409	−	0.495848i	$-0.165143\pi$
$619$	3.19646	+	4.39955i	0.128477	+	0.176833i	−0.739933	+	0.672681i	$0.765143\pi$
$620$	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
$623$	−28.8225	−	8.70150i	−1.15475	−	0.348618i
$624$	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
$630$	8.17554	+	5.68194i	0.325721	+	0.226374i
$631$	−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	−0.311172	−	0.950354i	$-0.600722\pi$
$643$	−0.109336	+	0.0355256i	−0.00431181	+	0.00140099i	0.306860	+	0.951755i	$0.400722\pi$
$644$	−16.2588	+	12.3416i	−0.640688	+	0.486326i
$645$	−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	0.645569	−	0.763702i	$-0.276620\pi$
$647$	18.2874	+	5.94194i	0.718952	+	0.233602i	0.0733831	+	0.997304i	$0.476620\pi$
$648$			5.42190i			0.212992i
$649$	0.618922	−	0.868663i	0.0242948	−	0.0340980i
$650$			44.5657i			1.74801i
$651$	20.2711	−	0.424959i	0.794487	−	0.0166555i
$652$	−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
$658$	−14.2727	+	0.299210i	−0.556408	+	0.0116644i
$659$			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	$-0.948809\pi$
$661$		−	8.23382i		−	0.320258i	0.987096	−	0.160129i	$-0.0511911\pi$
$662$	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
$665$	17.0637	+	22.4798i	0.661702	+	0.871729i
$666$	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	$-0.842799\pi$
$677$	−11.6251	−	35.7785i	−0.446790	−	1.37508i	0.433719	−	0.901048i	$-0.357201\pi$
$678$	19.5179	+	14.1806i	0.749582	+	0.544603i
$679$	−10.8820	+	15.6577i	−0.417613	+	0.600887i
$680$	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
$686$	−42.8096	+	16.9520i	−1.63448	+	0.647231i
$687$	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	0.836667	−	0.547712i	$-0.184501\pi$
$691$	31.3236	+	10.1777i	1.19161	+	0.387177i	0.354940	+	0.934889i	$0.384501\pi$
$692$	97.7593			3.71625
$693$	7.25167	+	4.94099i	0.275468	+	0.187693i
$694$	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
$700$	8.66042	−	28.6865i	0.327333	−	1.08425i
$701$	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
$707$	20.7510	+	14.4218i	0.780422	+	0.542388i
$708$	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	$0.427732\pi$
$719$	−20.6768	+	28.4592i	−0.771115	+	1.06135i	−0.996207	+	0.0870118i	$0.972268\pi$
$720$	−7.36731	+	2.39378i	−0.274563	+	0.0892110i
$721$	4.02166	+	5.29816i	0.149774	+	0.197314i
$722$	−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	$-0.740801\pi$
$727$		−	39.2173i		−	1.45449i	0.686379	−	0.727244i	$-0.259199\pi$
$728$	1.98952	+	94.9025i	0.0737364	+	3.51732i
$729$	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	0.624872	−	0.780727i	$-0.285151\pi$
$733$	2.04282	+	1.48420i	0.0754533	+	0.0548200i	−0.549419	+	0.835547i	$0.685151\pi$
$734$	16.6866	−	12.1235i	0.615912	−	0.447486i
$735$	3.69356	+	9.93067i	0.136239	+	0.366298i
$736$		−	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
$742$	22.0745	+	29.0811i	0.810380	+	1.06760i
$743$	−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
$756$	−6.31280	+	9.08325i	−0.229594	+	0.330355i
$757$	−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	−0.999132	−	0.0416609i	$-0.986735\pi$
$761$	−4.58841	+	14.1217i	−0.166330	+	0.511910i	0.832802	+	0.553571i	$0.186735\pi$
$762$	−29.1202	−	40.0805i	−1.05491	−	1.45196i
$763$	−16.8255	−	5.07960i	−0.609123	−	0.183894i
$764$	−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	$-0.484553\pi$
$769$	2.69047			0.0970209			0.0485105	+	0.998823i	$0.484553\pi$
$770$	−9.25059	+	31.6984i	−0.333368	+	1.14233i
$771$	−1.84063			−0.0662888
$772$	49.5024	+	16.0843i	1.78163	+	0.578887i
$773$	13.8048	+	19.0006i	0.496523	+	0.683405i	0.981574	−	0.191081i	$-0.0611992\pi$
$773$	13.8048	+	19.0006i	0.496523	+	0.683405i	−0.485052	+	0.874485i	$0.661199\pi$
$774$	−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
$777$	4.69679	+	1.41796i	0.168496	+	0.0508690i
$778$	−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
$784$	9.63286	−	34.5055i	0.344031	−	1.23234i
$785$	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	0.942227	−	0.334974i	$-0.108727\pi$
$787$	−0.475316	−	1.46287i	−0.0169432	−	0.0521458i	−0.959171	+	0.282828i	$0.908727\pi$
$788$	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	−0.0735485	−	0.997292i	$-0.523432\pi$
$797$	12.7928	−	4.15662i	0.453143	−	0.147235i	0.526691	+	0.850057i	$0.323432\pi$
$798$	−36.9233	+	28.0273i	−1.30707	+	0.992156i
$799$	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
$805$	0.154888	+	7.38836i	0.00545909	+	0.260406i
$806$	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	−0.943865	−	0.330332i	$-0.892839\pi$
$811$	−26.2388	+	19.0636i	−0.921370	+	0.669415i	0.0224943	+	0.999747i	$0.492839\pi$
$812$	−0.934739	−	44.5882i	−0.0328029	−	1.56474i
$813$		−	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
$819$	13.9450	−	10.5852i	0.487278	−	0.369877i
$820$	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	−0.854487	−	0.519473i	$-0.826128\pi$
$829$	−2.77523	+	3.81977i	−0.0963877	+	0.132666i	0.758099	+	0.652139i	$0.226128\pi$
$830$	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
$833$	10.0348	−	35.9451i	0.347684	−	1.24543i
$834$	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	$-0.985158\pi$
$839$	−21.2769	−	29.2851i	−0.734560	−	1.01104i	0.264353	−	0.964426i	$-0.414842\pi$
$840$	−20.7862	−	6.27534i	−0.717192	−	0.216520i
$841$	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
$847$	−7.89431	+	28.0121i	−0.271252	+	0.962508i
$848$	−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	0.835430	−	0.549597i	$-0.185219\pi$
$853$	−4.77497	−	14.6958i	−0.163492	−	0.503176i	−0.998922	+	0.0464206i	$0.985219\pi$
$854$	−18.7212	−	5.65191i	−0.640625	−	0.193404i
$855$	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	$-0.756625\pi$
$857$	−42.2531			−1.44334			−0.721670	+	0.692237i	$0.756625\pi$
$858$	54.5601	−	0.504838i	1.86265	−	0.0172349i
$859$		−	17.4829i		−	0.596510i	−0.954486	−	0.298255i	$-0.903595\pi$
$859$		−	17.4829i		−	0.596510i	0.954486	−	0.298255i	$-0.0964047\pi$
$860$	7.24871	−	22.3092i	0.247179	−	0.760738i
$861$	1.05119	−	1.51252i	0.0358245	−	0.0515466i
$862$	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
$875$	−18.6654	−	24.5899i	−0.631007	−	0.831292i
$876$	−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	$-0.734787\pi$
$881$		−	43.9336i		−	1.48016i	0.672518	−	0.740081i	$-0.265213\pi$
$882$	−16.3112	+	6.06672i	−0.549228	+	0.204277i
$883$	−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	$0.0330123\pi$
$887$	41.7087	+	30.3032i	1.40044	+	1.01748i	0.405815	+	0.913955i	$0.366988\pi$
$888$	−8.13395	+	5.90966i	−0.272958	+	0.198315i
$889$	−1.10503	−	52.7115i	−0.0370616	−	1.76789i
$890$		−	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
$896$	−28.1346	−	37.0647i	−0.939911	−	1.23824i
$897$	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
$910$	54.0990	+	37.5984i	1.79336	+	1.24638i
$911$	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
$917$	0.681579	−	2.25763i	0.0225077	−	0.0745537i
$918$	−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
$924$	−35.2178	−	10.2777i	−1.15858	−	0.338110i
$925$	−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	−0.613580	−	0.789633i	$-0.710271\pi$
$929$	−19.6849	+	6.39603i	−0.645842	+	0.209847i	−0.0322622	+	0.999479i	$0.510271\pi$
$930$	8.91140	+	27.4265i	0.292216	+	0.899349i
$931$	−49.2887	+	2.06747i	−1.61537	+	0.0677585i
$932$	−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	$0.279110\pi$
$937$	−10.0922	+	31.0607i	−0.329699	+	1.01471i	−0.969275	+	0.245981i	$0.920890\pi$
$938$	−4.57101	+	6.57706i	−0.149249	+	0.214749i
$939$	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	$-0.823649\pi$
$941$	−14.4684	−	44.5291i	−0.471656	−	1.45161i	0.378760	−	0.925495i	$-0.376351\pi$
$942$	−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
$952$	46.2398	+	60.9165i	1.49864	+	1.97432i
$953$	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
$959$	23.0078	−	0.482331i	0.742960	−	0.0155753i
$960$	−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
$966$	−12.1355	+	0.254406i	−0.390452	+	0.00818537i
$967$		−	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	0.994459	−	0.105122i	$-0.0335234\pi$
$971$	18.2970	+	25.1836i	0.587177	+	0.808180i	−0.407282	+	0.913302i	$0.633523\pi$
$972$	−2.45745	+	3.38238i	−0.0788226	+	0.108490i
$973$	46.9352	−	35.6270i	1.50467	−	1.14215i
$974$	−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	−0.944284	−	0.329131i	$-0.893244\pi$
$983$	−10.6431	+	14.6490i	−0.339462	+	0.467229i	0.604822	+	0.796361i	$0.293244\pi$
$984$	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
$987$	−4.71525	−	3.27707i	−0.150088	−	0.104310i
$988$	−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
$994$	79.9289	+	24.1305i	2.53519	+	0.765373i
$995$	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	0.297063	−	0.954858i	$-0.403993\pi$
$997$	−16.3959	−	11.9123i	−0.519263	−	0.377267i	−0.816326	+	0.577591i	$0.803993\pi$
$998$	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.13.1	✓	64
3.2	odd	2		693.2.bu.f.244.15		64
7.6	odd	2	inner	231.2.w.a.13.2	yes	64
11.6	odd	10	inner	231.2.w.a.160.2	yes	64
21.20	even	2		693.2.bu.f.244.16		64
33.17	even	10		693.2.bu.f.622.16		64
77.6	even	10	inner	231.2.w.a.160.1	yes	64
231.83	odd	10		693.2.bu.f.622.15		64

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.36445 - 0.768257i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.38238 + 2.45745i) q^{4} +(1.43953 - 0.467733i) q^{5} +(0.768257 + 2.36445i) q^{6} +(-0.764664 + 2.53284i) q^{7} +(-3.18691 - 4.38641i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(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} +(-0.764664 + 2.53284i) 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} +(3.75389 - 5.40133i) 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} +(-8.81071 + 6.68792i) 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} +(0.0839343 + 4.00377i) 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} +(-6.57624 + 0.137863i) 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} +(-5.83058 - 3.87355i) 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} +(-2.17258 - 1.50993i) 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} +(2.87747 - 9.53121i) 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} +(2.45827 - 8.42359i) 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} +(10.5894 + 3.19695i) 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} +(-14.3764 - 9.99148i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more