LMFDB - Embedded newform 950.2.h.d.191.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.11
Character	$\chi$	$=$	950.191
Dual form			950.2.h.d.761.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.863749 + 2.65835i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.38530 + 1.75527i) q^{5} +(-0.863749 + 2.65835i) q^{6} +3.39982 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-3.89370 + 2.82894i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.863749 + 2.65835i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.38530 + 1.75527i) q^{5} +(-0.863749 + 2.65835i) q^{6} +3.39982 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-3.89370 + 2.82894i) q^{9} +(-2.15245 + 0.605783i) q^{10} +(-1.25715 - 0.913371i) q^{11} +(-2.26133 + 1.64295i) q^{12} +(0.899528 - 0.653546i) q^{13} +(2.75052 + 1.99837i) q^{14} +(-5.86265 - 2.16649i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.607327 + 1.86916i) q^{17} -4.81287 q^{18} +(-0.309017 + 0.951057i) q^{19} +(-2.09744 - 0.775087i) q^{20} +(2.93660 + 9.03791i) q^{21} +(-0.480188 - 1.47787i) q^{22} +(3.41299 + 2.47968i) q^{23} -2.79515 q^{24} +(-1.16191 - 4.86312i) q^{25} +1.11188 q^{26} +(-4.09950 - 2.97846i) q^{27} +(1.05060 + 3.23342i) q^{28} +(-2.56370 - 7.89024i) q^{29} +(-3.46956 - 5.19871i) q^{30} +(-2.32636 + 7.15980i) q^{31} -1.00000 q^{32} +(1.34220 - 4.13086i) q^{33} +(-1.59000 + 1.15520i) q^{34} +(-4.70976 + 5.96759i) q^{35} +(-3.89370 - 2.82894i) q^{36} +(6.90672 - 5.01802i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(2.51432 + 1.82676i) q^{39} +(-1.24128 - 1.85990i) q^{40} +(4.20723 - 3.05673i) q^{41} +(-2.93660 + 9.03791i) q^{42} +2.61277 q^{43} +(0.480188 - 1.47787i) q^{44} +(0.428386 - 10.7534i) q^{45} +(1.30365 + 4.01221i) q^{46} +(-3.07530 - 9.46481i) q^{47} +(-2.26133 - 1.64295i) q^{48} +4.55880 q^{49} +(1.91846 - 4.61730i) q^{50} -5.49346 q^{51} +(0.899528 + 0.653546i) q^{52} +(-1.40732 - 4.33127i) q^{53} +(-1.56587 - 4.81925i) q^{54} +(3.34473 - 0.941339i) q^{55} +(-1.05060 + 3.23342i) q^{56} -2.79515 q^{57} +(2.56370 - 7.89024i) q^{58} +(-4.90084 + 3.56067i) q^{59} +(0.248792 - 6.24520i) q^{60} +(4.81340 + 3.49714i) q^{61} +(-6.09049 + 4.42500i) q^{62} +(-13.2379 + 9.61788i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.0989664 + 2.48426i) q^{65} +(3.51392 - 2.55301i) q^{66} +(2.54878 - 7.84433i) q^{67} -1.96535 q^{68} +(-3.64389 + 11.2147i) q^{69} +(-7.31794 + 2.05956i) q^{70} +(3.14148 + 9.66847i) q^{71} +(-1.48726 - 4.57731i) q^{72} +(4.00149 + 2.90725i) q^{73} +8.53717 q^{74} +(11.9243 - 7.28929i) q^{75} -1.00000 q^{76} +(-4.27408 - 3.10530i) q^{77} +(0.960384 + 2.95576i) q^{78} +(0.210916 + 0.649132i) q^{79} +(0.0890083 - 2.23430i) q^{80} +(-0.0849399 + 0.261418i) q^{81} +5.20042 q^{82} +(-3.81223 + 11.7328i) q^{83} +(-7.68811 + 5.58574i) q^{84} +(-2.43955 - 3.65536i) q^{85} +(2.11378 + 1.53575i) q^{86} +(18.7606 - 13.6304i) q^{87} +(1.25715 - 0.913371i) q^{88} +(-8.27484 - 6.01202i) q^{89} +(6.66725 - 8.44787i) q^{90} +(3.05824 - 2.22194i) q^{91} +(-1.30365 + 4.01221i) q^{92} -21.0426 q^{93} +(3.07530 - 9.46481i) q^{94} +(-1.24128 - 1.85990i) q^{95} +(-0.863749 - 2.65835i) q^{96} +(2.61643 + 8.05256i) q^{97} +(3.68815 + 2.67960i) q^{98} +7.47882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.863749	+	2.65835i	0.498686	+	1.53480i	0.811133	+	0.584862i	$0.198851\pi$
$3$	0.863749	+	2.65835i	0.498686	+	1.53480i	−0.312447	+	0.949935i	$0.601149\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.38530	+	1.75527i	−0.619523	+	0.784979i
$5$	−1.38530	+	1.75527i	−0.619523	+	0.784979i
$6$	−0.863749	+	2.65835i	−0.352624	+	1.08527i
$7$	3.39982			1.28501			0.642506	−	0.766280i	$-0.277895\pi$
$7$	3.39982			1.28501			0.642506	+	0.766280i	$0.277895\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−3.89370	+	2.82894i	−1.29790	+	0.942979i
$10$	−2.15245	+	0.605783i	−0.680663	+	0.191566i
$11$	−1.25715	−	0.913371i	−0.379044	−	0.275392i	0.381907	−	0.924201i	$-0.375267\pi$
$11$	−1.25715	−	0.913371i	−0.379044	−	0.275392i	−0.760951	+	0.648809i	$0.775267\pi$
$12$	−2.26133	+	1.64295i	−0.652788	+	0.474279i
$13$	0.899528	−	0.653546i	0.249484	−	0.181261i	−0.456014	−	0.889973i	$-0.650723\pi$
$13$	0.899528	−	0.653546i	0.249484	−	0.181261i	0.705498	+	0.708712i	$0.250723\pi$
$14$	2.75052	+	1.99837i	0.735106	+	0.534086i
$15$	−5.86265	−	2.16649i	−1.51373	−	0.559384i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.607327	+	1.86916i	−0.147298	+	0.453338i	−0.997299	−	0.0734431i	$-0.976601\pi$
$17$	−0.607327	+	1.86916i	−0.147298	+	0.453338i	0.850001	+	0.526781i	$0.176601\pi$
$18$	−4.81287			−1.13441
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$20$	−2.09744	−	0.775087i	−0.469001	−	0.173315i
$21$	2.93660	+	9.03791i	0.640818	+	1.97223i
$22$	−0.480188	−	1.47787i	−0.102376	−	0.315082i
$23$	3.41299	+	2.47968i	0.711657	+	0.517049i	0.883708	−	0.468039i	$-0.155039\pi$
$23$	3.41299	+	2.47968i	0.711657	+	0.517049i	−0.172050	+	0.985088i	$0.555039\pi$
$24$	−2.79515			−0.570558
$25$	−1.16191	−	4.86312i	−0.232383	−	0.972624i
$26$	1.11188			0.218057
$27$	−4.09950	−	2.97846i	−0.788948	−	0.573205i
$28$	1.05060	+	3.23342i	0.198545	+	0.611060i
$29$	−2.56370	−	7.89024i	−0.476066	−	1.46518i	−0.844514	−	0.535533i	$-0.820111\pi$
$29$	−2.56370	−	7.89024i	−0.476066	−	1.46518i	0.368448	−	0.929648i	$-0.379889\pi$
$30$	−3.46956	−	5.19871i	−0.633452	−	0.949149i
$31$	−2.32636	+	7.15980i	−0.417827	+	1.28594i	0.491871	+	0.870668i	$0.336313\pi$
$31$	−2.32636	+	7.15980i	−0.417827	+	1.28594i	−0.909698	+	0.415270i	$0.863687\pi$
$32$	−1.00000			−0.176777
$33$	1.34220	−	4.13086i	0.233647	−	0.719090i
$34$	−1.59000	+	1.15520i	−0.272683	+	0.198116i
$35$	−4.70976	+	5.96759i	−0.796095	+	1.00871i
$36$	−3.89370	−	2.82894i	−0.648949	−	0.471489i
$37$	6.90672	−	5.01802i	1.13546	−	0.824958i	0.148977	−	0.988841i	$-0.452402\pi$
$37$	6.90672	−	5.01802i	1.13546	−	0.824958i	0.986480	+	0.163883i	$0.0524018\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	2.51432	+	1.82676i	0.402613	+	0.292516i
$40$	−1.24128	−	1.85990i	−0.196263	−	0.294076i
$41$	4.20723	−	3.05673i	0.657059	−	0.477381i	−0.208609	−	0.977999i	$-0.566894\pi$
$41$	4.20723	−	3.05673i	0.657059	−	0.477381i	0.865668	+	0.500618i	$0.166894\pi$
$42$	−2.93660	+	9.03791i	−0.453127	+	1.39458i
$43$	2.61277			0.398444			0.199222	−	0.979954i	$-0.436158\pi$
$43$	2.61277			0.398444			0.199222	+	0.979954i	$0.436158\pi$
$44$	0.480188	−	1.47787i	0.0723910	−	0.222797i
$45$	0.428386	−	10.7534i	0.0638600	−	1.60302i
$46$	1.30365	+	4.01221i	0.192212	+	0.591568i
$47$	−3.07530	−	9.46481i	−0.448579	−	1.38058i	−0.878511	−	0.477723i	$-0.841462\pi$
$47$	−3.07530	−	9.46481i	−0.448579	−	1.38058i	0.429931	−	0.902862i	$-0.358538\pi$
$48$	−2.26133	−	1.64295i	−0.326394	−	0.237139i
$49$	4.55880			0.651257
$50$	1.91846	−	4.61730i	0.271312	−	0.652985i
$51$	−5.49346			−0.769238
$52$	0.899528	+	0.653546i	0.124742	+	0.0906305i
$53$	−1.40732	−	4.33127i	−0.193310	−	0.594946i	−0.999992	−	0.00396107i	$-0.998739\pi$
$53$	−1.40732	−	4.33127i	−0.193310	−	0.594946i	0.806682	−	0.590985i	$-0.201261\pi$
$54$	−1.56587	−	4.81925i	−0.213088	−	0.655816i
$55$	3.34473	−	0.941339i	0.451003	−	0.126930i
$56$	−1.05060	+	3.23342i	−0.140393	+	0.432085i
$57$	−2.79515			−0.370227
$58$	2.56370	−	7.89024i	0.336630	−	1.03604i
$59$	−4.90084	+	3.56067i	−0.638035	+	0.463560i	−0.859175	−	0.511682i	$-0.829022\pi$
$59$	−4.90084	+	3.56067i	−0.638035	+	0.463560i	0.221139	+	0.975242i	$0.429022\pi$
$60$	0.248792	−	6.24520i	0.0321189	−	0.806251i
$61$	4.81340	+	3.49714i	0.616292	+	0.447763i	0.851624	−	0.524152i	$-0.175618\pi$
$61$	4.81340	+	3.49714i	0.616292	+	0.447763i	−0.235332	+	0.971915i	$0.575618\pi$
$62$	−6.09049	+	4.42500i	−0.773493	+	0.561976i
$63$	−13.2379	+	9.61788i	−1.66782	+	1.21174i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.0989664	+	2.48426i	−0.0122753	+	0.308135i
$66$	3.51392	−	2.55301i	0.432533	−	0.314254i
$67$	2.54878	−	7.84433i	0.311383	−	0.958337i	−0.665835	−	0.746099i	$-0.731925\pi$
$67$	2.54878	−	7.84433i	0.311383	−	0.958337i	0.977218	−	0.212238i	$-0.0680753\pi$
$68$	−1.96535			−0.238334
$69$	−3.64389	+	11.2147i	−0.438673	+	1.35010i
$70$	−7.31794	+	2.05956i	−0.874661	+	0.246164i
$71$	3.14148	+	9.66847i	0.372825	+	1.14744i	0.944935	+	0.327259i	$0.106125\pi$
$71$	3.14148	+	9.66847i	0.372825	+	1.14744i	−0.572110	+	0.820177i	$0.693875\pi$
$72$	−1.48726	−	4.57731i	−0.175275	−	0.539442i
$73$	4.00149	+	2.90725i	0.468339	+	0.340268i	0.796794	−	0.604252i	$-0.206528\pi$
$73$	4.00149	+	2.90725i	0.468339	+	0.340268i	−0.328455	+	0.944520i	$0.606528\pi$
$74$	8.53717			0.992426
$75$	11.9243	−	7.28929i	1.37690	−	0.841695i
$76$	−1.00000			−0.114708
$77$	−4.27408	−	3.10530i	−0.487077	−	0.353882i
$78$	0.960384	+	2.95576i	0.108742	+	0.334674i
$79$	0.210916	+	0.649132i	0.0237299	+	0.0730330i	0.962220	−	0.272273i	$-0.0877753\pi$
$79$	0.210916	+	0.649132i	0.0237299	+	0.0730330i	−0.938490	+	0.345306i	$0.887775\pi$
$80$	0.0890083	−	2.23430i	0.00995143	−	0.249802i
$81$	−0.0849399	+	0.261418i	−0.00943777	+	0.0290465i
$82$	5.20042			0.574291
$83$	−3.81223	+	11.7328i	−0.418446	+	1.28785i	0.490686	+	0.871337i	$0.336746\pi$
$83$	−3.81223	+	11.7328i	−0.418446	+	1.28785i	−0.909132	+	0.416508i	$0.863254\pi$
$84$	−7.68811	+	5.58574i	−0.838841	+	0.609454i
$85$	−2.43955	−	3.65536i	−0.264606	−	0.396479i
$86$	2.11378	+	1.53575i	0.227935	+	0.165604i
$87$	18.7606	−	13.6304i	2.01135	−	1.46133i
$88$	1.25715	−	0.913371i	0.134012	−	0.0973657i
$89$	−8.27484	−	6.01202i	−0.877131	−	0.637273i	0.0553596	−	0.998466i	$-0.482369\pi$
$89$	−8.27484	−	6.01202i	−0.877131	−	0.637273i	−0.932491	+	0.361193i	$0.882369\pi$
$90$	6.66725	−	8.44787i	0.702790	−	0.890484i
$91$	3.05824	−	2.22194i	0.320590	−	0.232923i
$92$	−1.30365	+	4.01221i	−0.135914	+	0.418302i
$93$	−21.0426			−2.18202
$94$	3.07530	−	9.46481i	0.317193	−	0.976221i
$95$	−1.24128	−	1.85990i	−0.127352	−	0.190822i
$96$	−0.863749	−	2.65835i	−0.0881561	−	0.271316i
$97$	2.61643	+	8.05256i	0.265659	+	0.817613i	0.991541	+	0.129794i	$0.0414317\pi$
$97$	2.61643	+	8.05256i	0.265659	+	0.817613i	−0.725882	+	0.687819i	$0.758568\pi$
$98$	3.68815	+	2.67960i	0.372559	+	0.270680i
$99$	7.47882			0.751650
$100$	4.26605	−	2.60783i	0.426605	−	0.260783i
$101$	6.26877			0.623766			0.311883	−	0.950121i	$-0.399040\pi$
$101$	6.26877			0.623766			0.311883	+	0.950121i	$0.399040\pi$
$102$	−4.44430	−	3.22897i	−0.440051	−	0.319716i
$103$	−0.375763	−	1.15648i	−0.0370250	−	0.113951i	0.930836	−	0.365438i	$-0.119081\pi$
$103$	−0.375763	−	1.15648i	−0.0370250	−	0.113951i	−0.967861	+	0.251486i	$0.919081\pi$
$104$	0.343589	+	1.05746i	0.0336917	+	0.103692i
$105$	−19.9320	−	7.36567i	−1.94516	−	0.718816i
$106$	1.40732	−	4.33127i	0.136691	−	0.420691i
$107$	4.43916			0.429150			0.214575	−	0.976708i	$-0.431163\pi$
$107$	4.43916			0.429150			0.214575	+	0.976708i	$0.431163\pi$
$108$	1.56587	−	4.81925i	0.150676	−	0.463732i
$109$	10.5900	−	7.69406i	1.01434	−	0.736958i	0.0492213	−	0.998788i	$-0.484326\pi$
$109$	10.5900	−	7.69406i	1.01434	−	0.736958i	0.965114	+	0.261830i	$0.0843261\pi$
$110$	3.25925	+	1.20442i	0.310757	+	0.114837i
$111$	19.3053	+	14.0261i	1.83238	+	1.33130i
$112$	−2.75052	+	1.99837i	−0.259899	+	0.188828i
$113$	−9.91006	+	7.20008i	−0.932260	+	0.677327i	−0.946545	−	0.322571i	$-0.895453\pi$
$113$	−9.91006	+	7.20008i	−0.932260	+	0.677327i	0.0142848	+	0.999898i	$0.495453\pi$
$114$	−2.26133	−	1.64295i	−0.211793	−	0.153876i
$115$	−9.08050	+	2.55561i	−0.846761	+	0.238312i
$116$	6.71184	−	4.87644i	0.623179	−	0.452766i
$117$	−1.65365	+	5.08942i	−0.152880	+	0.470517i
$118$	−6.05777			−0.557663
$119$	−2.06481	+	6.35482i	−0.189280	+	0.582545i
$120$	3.87211	−	4.90623i	0.353474	−	0.447876i
$121$	−2.65301	−	8.16514i	−0.241183	−	0.742285i
$122$	1.83855	+	5.65849i	0.166455	+	0.512295i
$123$	11.7598	+	8.54403i	1.06035	+	0.770389i
$124$	−7.52826			−0.676058
$125$	10.1457	+	4.69739i	0.907456	+	0.420148i
$126$	−16.3629			−1.45772
$127$	7.17945	+	5.21617i	0.637073	+	0.462861i	0.858843	−	0.512238i	$-0.171184\pi$
$127$	7.17945	+	5.21617i	0.637073	+	0.462861i	−0.221770	+	0.975099i	$0.571184\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.25678	+	6.94566i	0.198699	+	0.611531i
$130$	−1.54028	+	1.95164i	−0.135091	+	0.171170i
$131$	2.02766	−	6.24050i	0.177158	−	0.545235i	−0.822568	−	0.568667i	$-0.807459\pi$
$131$	2.02766	−	6.24050i	0.177158	−	0.545235i	0.999725	+	0.0234319i	$0.00745929\pi$
$132$	4.34344			0.378048
$133$	−1.05060	+	3.23342i	−0.0910989	+	0.280373i
$134$	6.67278	−	4.84806i	0.576441	−	0.418809i
$135$	10.9070	−	3.06966i	0.938725	−	0.264194i
$136$	−1.59000	−	1.15520i	−0.136342	−	0.0990580i
$137$	−10.9067	+	7.92418i	−0.931823	+	0.677009i	−0.946438	−	0.322884i	$-0.895347\pi$
$137$	−10.9067	+	7.92418i	−0.931823	+	0.677009i	0.0146158	+	0.999893i	$0.495347\pi$
$138$	−9.53982	+	6.93109i	−0.812084	+	0.590013i
$139$	4.36486	+	3.17126i	0.370223	+	0.268983i	0.757303	−	0.653063i	$-0.226516\pi$
$139$	4.36486	+	3.17126i	0.370223	+	0.268983i	−0.387080	+	0.922046i	$0.626516\pi$
$140$	−7.13091	−	2.63516i	−0.602672	−	0.222712i
$141$	22.5045	−	16.3504i	1.89522	−	1.37696i
$142$	−3.14148	+	9.66847i	−0.263627	+	0.811360i
$143$	−1.72777			−0.144483
$144$	1.48726	−	4.57731i	0.123938	−	0.381443i
$145$	17.4009	+	6.43035i	1.44507	+	0.534012i
$146$	1.52843	+	4.70403i	0.126494	+	0.389308i
$147$	3.93766	+	12.1189i	0.324773	+	0.999548i
$148$	6.90672	+	5.01802i	0.567729	+	0.412479i
$149$	0.796120			0.0652207			0.0326103	−	0.999468i	$-0.489618\pi$
$149$	0.796120			0.0652207			0.0326103	+	0.999468i	$0.489618\pi$
$150$	13.9315	+	1.11175i	1.13750	+	0.0907739i
$151$	14.1686			1.15303			0.576513	−	0.817088i	$-0.304413\pi$
$151$	14.1686			1.15303			0.576513	+	0.817088i	$0.304413\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	−2.92299	−	8.99603i	−0.236310	−	0.727286i
$154$	−1.63255	−	5.02448i	−0.131555	−	0.404884i
$155$	−9.34466	−	14.0018i	−0.750581	−	1.12465i
$156$	−0.960384	+	2.95576i	−0.0768923	+	0.236650i
$157$	−18.3313			−1.46300			−0.731500	−	0.681841i	$-0.761180\pi$
$157$	−18.3313			−1.46300			−0.731500	+	0.681841i	$0.761180\pi$
$158$	−0.210916	+	0.649132i	−0.0167796	+	0.0516422i
$159$	10.2985	−	7.48227i	0.816721	−	0.593383i
$160$	1.38530	−	1.75527i	0.109517	−	0.138766i
$161$	11.6036	+	8.43048i	0.914489	+	0.664415i
$162$	−0.222376	+	0.161565i	−0.0174715	+	0.0126938i
$163$	19.3123	−	14.0312i	1.51265	−	1.09901i	0.547673	−	0.836693i	$-0.315514\pi$
$163$	19.3123	−	14.0312i	1.51265	−	1.09901i	0.964982	−	0.262316i	$-0.0844861\pi$
$164$	4.20723	+	3.05673i	0.328530	+	0.238691i
$165$	5.39141	+	8.07837i	0.419721	+	0.628900i
$166$	−9.98054	+	7.25129i	−0.774640	+	0.562809i
$167$	−5.59624	+	17.2234i	−0.433050	+	1.33279i	0.462022	+	0.886868i	$0.347124\pi$
$167$	−5.59624	+	17.2234i	−0.433050	+	1.33279i	−0.895072	+	0.445922i	$0.852876\pi$
$168$	−9.50302			−0.733174
$169$	−3.63519	+	11.1880i	−0.279630	+	0.860613i
$170$	0.174933	−	4.39118i	0.0134167	−	0.336788i
$171$	−1.48726	−	4.57731i	−0.113734	−	0.350036i
$172$	0.807391	+	2.48490i	0.0615630	+	0.189471i
$173$	−3.12083	−	2.26741i	−0.237272	−	0.172388i	0.462795	−	0.886465i	$-0.346847\pi$
$173$	−3.12083	−	2.26741i	−0.237272	−	0.172388i	−0.700067	+	0.714077i	$0.746847\pi$
$174$	23.1894			1.75798
$175$	−3.95030	−	16.5338i	−0.298615	−	1.24983i
$176$	1.55392			0.117131
$177$	−13.6986	−	9.95261i	−1.02965	−	0.748084i
$178$	−3.16071	−	9.72766i	−0.236905	−	0.729119i
$179$	−7.55268	−	23.2448i	−0.564514	−	1.73739i	−0.669392	−	0.742910i	$-0.733445\pi$
$179$	−7.55268	−	23.2448i	−0.564514	−	1.73739i	0.104878	−	0.994485i	$-0.466555\pi$
$180$	10.3595	−	2.91556i	0.772148	−	0.217313i
$181$	−7.81088	+	24.0394i	−0.580578	+	1.78684i	0.0357670	+	0.999360i	$0.488613\pi$
$181$	−7.81088	+	24.0394i	−0.580578	+	1.78684i	−0.616345	+	0.787476i	$0.711387\pi$
$182$	3.78019			0.280206
$183$	−5.13904	+	15.8163i	−0.379889	+	1.16918i
$184$	−3.41299	+	2.47968i	−0.251609	+	0.182805i
$185$	−0.759879	+	19.0746i	−0.0558674	+	1.40239i
$186$	−17.0238	−	12.3685i	−1.24825	−	0.906906i
$187$	2.47074	−	1.79510i	0.180678	−	0.131270i
$188$	8.05125	−	5.84957i	0.587198	−	0.426624i
$189$	−13.9376	−	10.1262i	−1.01381	−	0.736575i
$190$	0.0890083	−	2.23430i	0.00645734	−	0.162093i
$191$	−11.8020	+	8.57468i	−0.853966	+	0.620442i	−0.926237	−	0.376943i	$-0.876975\pi$
$191$	−11.8020	+	8.57468i	−0.853966	+	0.620442i	0.0722709	+	0.997385i	$0.476975\pi$
$192$	0.863749	−	2.65835i	0.0623357	−	0.191850i
$193$	−3.04978			−0.219528			−0.109764	−	0.993958i	$-0.535009\pi$
$193$	−3.04978			−0.219528			−0.109764	+	0.993958i	$0.535009\pi$
$194$	−2.61643	+	8.05256i	−0.187849	+	0.578140i
$195$	−6.68952	+	1.88270i	−0.479047	+	0.134823i
$196$	1.40875	+	4.33568i	0.100625	+	0.309691i
$197$	4.20486	+	12.9412i	0.299584	+	0.922025i	0.981643	+	0.190728i	$0.0610847\pi$
$197$	4.20486	+	12.9412i	0.299584	+	0.922025i	−0.682059	+	0.731297i	$0.738915\pi$
$198$	6.05049	+	4.39594i	0.429990	+	0.312406i
$199$	1.84681			0.130917			0.0654584	−	0.997855i	$-0.479149\pi$
$199$	1.84681			0.130917			0.0654584	+	0.997855i	$0.479149\pi$
$200$	4.98416	+	0.397742i	0.352433	+	0.0281246i
$201$	23.0544			1.62614
$202$	5.07154	+	3.68469i	0.356832	+	0.259254i
$203$	−8.71611	−	26.8254i	−0.611751	−	1.88278i
$204$	−1.69757	−	5.22459i	−0.118854	−	0.365794i
$205$	−0.462881	+	11.6193i	−0.0323290	+	0.811526i
$206$	0.375763	−	1.15648i	0.0261806	−	0.0805757i
$207$	−20.3040			−1.41123
$208$	−0.343589	+	1.05746i	−0.0238236	+	0.0733216i
$209$	1.25715	−	0.913371i	0.0869587	−	0.0631792i
$210$	−11.7959	−	17.6747i	−0.813993	−	1.21967i
$211$	−2.31870	−	1.68464i	−0.159626	−	0.115975i	0.505105	−	0.863058i	$-0.331454\pi$
$211$	−2.31870	−	1.68464i	−0.159626	−	0.115975i	−0.664731	+	0.747083i	$0.731454\pi$
$212$	3.68440	−	2.67687i	0.253046	−	0.183849i
$213$	−22.9887	+	16.7023i	−1.57516	+	1.14442i
$214$	3.59136	+	2.60927i	0.245500	+	0.178366i
$215$	−3.61946	+	4.58611i	−0.246845	+	0.312770i
$216$	4.09950	−	2.97846i	0.278935	−	0.202658i
$217$	−7.90922	+	24.3421i	−0.536913	+	1.65245i
$218$	13.0899			0.886561
$219$	−4.27220	+	13.1485i	−0.288689	+	0.888492i
$220$	1.92884	+	2.89014i	0.130043	+	0.194853i
$221$	0.675274	+	2.07828i	0.0454238	+	0.139800i
$222$	7.37398	+	22.6948i	0.494909	+	1.52317i
$223$	−4.18882	−	3.04336i	−0.280504	−	0.203798i	0.438633	−	0.898666i	$-0.355463\pi$
$223$	−4.18882	−	3.04336i	−0.280504	−	0.203798i	−0.719137	+	0.694868i	$0.755463\pi$
$224$	−3.39982			−0.227160
$225$	18.2816	+	15.6485i	1.21877	+	1.04324i
$226$	−12.2495			−0.814826
$227$	−3.46723	−	2.51909i	−0.230128	−	0.167198i	0.466746	−	0.884391i	$-0.345426\pi$
$227$	−3.46723	−	2.51909i	−0.230128	−	0.167198i	−0.696874	+	0.717194i	$0.745426\pi$
$228$	−0.863749	−	2.65835i	−0.0572032	−	0.176053i
$229$	−7.09086	−	21.8234i	−0.468577	−	1.44213i	−0.854428	−	0.519571i	$-0.826092\pi$
$229$	−7.09086	−	21.8234i	−0.468577	−	1.44213i	0.385850	−	0.922561i	$-0.373908\pi$
$230$	−8.84843	−	3.26985i	−0.583448	−	0.215608i
$231$	4.56323	−	14.0442i	0.300239	−	0.924040i
$232$	8.29629			0.544678
$233$	6.89161	−	21.2102i	0.451484	−	1.38953i	−0.423730	−	0.905789i	$-0.639279\pi$
$233$	6.89161	−	21.2102i	0.451484	−	1.38953i	0.875214	−	0.483737i	$-0.160721\pi$
$234$	−4.32932	+	3.14543i	−0.283016	+	0.205623i
$235$	20.8735	+	7.71358i	1.36163	+	0.503179i
$236$	−4.90084	−	3.56067i	−0.319018	−	0.231780i
$237$	−1.54344	+	1.12137i	−0.100257	+	0.0728411i
$238$	−5.40573	+	3.92749i	−0.350401	+	0.254582i
$239$	−1.72252	−	1.25148i	−0.111420	−	0.0809516i	0.530680	−	0.847572i	$-0.321937\pi$
$239$	−1.72252	−	1.25148i	−0.111420	−	0.0809516i	−0.642100	+	0.766621i	$0.721937\pi$
$240$	6.01641	−	1.69326i	0.388358	−	0.109299i
$241$	17.9813	−	13.0641i	1.15827	−	0.841536i	0.168716	−	0.985665i	$-0.446038\pi$
$241$	17.9813	−	13.0641i	1.15827	−	0.841536i	0.989559	+	0.144129i	$0.0460380\pi$
$242$	2.65301	−	8.16514i	0.170542	−	0.524875i
$243$	−15.9701			−1.02448
$244$	−1.83855	+	5.65849i	−0.117701	+	0.362247i
$245$	−6.31529	+	8.00191i	−0.403469	+	0.511223i
$246$	4.49186	+	13.8245i	0.286391	+	0.881420i
$247$	0.343589	+	1.05746i	0.0218621	+	0.0672845i
$248$	−6.09049	−	4.42500i	−0.386747	−	0.280988i
$249$	−34.4827			−2.18525
$250$	5.44696	+	9.76374i	0.344496	+	0.617513i
$251$	12.7427			0.804310			0.402155	−	0.915572i	$-0.368261\pi$
$251$	12.7427			0.804310			0.402155	+	0.915572i	$0.368261\pi$
$252$	−13.2379	−	9.61788i	−0.833908	−	0.605870i
$253$	−2.02576	−	6.23465i	−0.127359	−	0.391969i
$254$	2.74230	+	8.43995i	0.172068	+	0.529569i
$255$	7.61006	−	9.64247i	0.476560	−	0.603835i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	25.8265			1.61101			0.805506	−	0.592588i	$-0.201894\pi$
$257$	25.8265			1.61101			0.805506	+	0.592588i	$0.201894\pi$
$258$	−2.25678	+	6.94566i	−0.140501	+	0.432418i
$259$	23.4816	−	17.0604i	1.45908	−	1.06008i
$260$	−2.39326	+	0.673557i	−0.148424	+	0.0417723i
$261$	32.3032	+	23.4697i	1.99952	+	1.45274i
$262$	5.30849	−	3.85684i	0.327959	−	0.238277i
$263$	22.0513	−	16.0212i	1.35974	−	0.987911i	0.361281	−	0.932457i	$-0.382339\pi$
$263$	22.0513	−	16.0212i	1.35974	−	0.987911i	0.998461	−	0.0554537i	$-0.0176605\pi$
$264$	3.51392	+	2.55301i	0.216267	+	0.157127i
$265$	9.55208	+	3.52988i	0.586780	+	0.216839i
$266$	−2.75052	+	1.99837i	−0.168645	+	0.122528i
$267$	8.83466	−	27.1903i	0.540672	−	1.66402i
$268$	8.24801			0.503828
$269$	−4.28523	+	13.1886i	−0.261275	+	0.804121i	0.731253	+	0.682106i	$0.238936\pi$
$269$	−4.28523	+	13.1886i	−0.261275	+	0.804121i	−0.992528	+	0.122015i	$0.961064\pi$
$270$	10.6282	+	3.92757i	0.646814	+	0.239024i
$271$	−2.90929	−	8.95388i	−0.176727	−	0.543910i	0.822981	−	0.568069i	$-0.192309\pi$
$271$	−2.90929	−	8.95388i	−0.176727	−	0.543910i	−0.999708	+	0.0241590i	$0.992309\pi$
$272$	−0.607327	−	1.86916i	−0.0368246	−	0.113335i
$273$	8.54824	+	6.21066i	0.517363	+	0.375886i
$274$	−13.4814			−0.814443
$275$	−2.98114	+	7.17492i	−0.179769	+	0.432664i
$276$	−11.7919			−0.709787
$277$	−13.5562	−	9.84919i	−0.814516	−	0.591780i	0.100620	−	0.994925i	$-0.467917\pi$
$277$	−13.5562	−	9.84919i	−0.814516	−	0.591780i	−0.915136	+	0.403144i	$0.867917\pi$
$278$	1.66723	+	5.13120i	0.0999938	+	0.307749i
$279$	−11.1965	−	34.4592i	−0.670316	−	2.06302i
$280$	−4.22012	−	6.32334i	−0.252201	−	0.377892i
$281$	10.2627	−	31.5855i	0.612224	−	1.88423i	0.176006	−	0.984389i	$-0.443682\pi$
$281$	10.2627	−	31.5855i	0.612224	−	1.88423i	0.436217	−	0.899841i	$-0.356318\pi$
$282$	27.8170			1.65648
$283$	7.46107	−	22.9628i	0.443515	−	1.36500i	−0.440590	−	0.897708i	$-0.645231\pi$
$283$	7.46107	−	22.9628i	0.443515	−	1.36500i	0.884105	−	0.467289i	$-0.154769\pi$
$284$	−8.22449	+	5.97544i	−0.488034	+	0.354577i
$285$	3.87211	−	4.90623i	0.229364	−	0.290620i
$286$	−1.39779	−	1.01556i	−0.0826533	−	0.0600512i
$287$	14.3038	−	10.3923i	0.844329	−	0.613441i
$288$	3.89370	−	2.82894i	0.229438	−	0.166697i
$289$	10.6284	+	7.72197i	0.625198	+	0.454233i
$290$	10.2980	+	15.4303i	0.604719	+	0.906098i
$291$	−19.1465	+	13.9108i	−1.12239	+	0.815464i
$292$	−1.52843	+	4.70403i	−0.0894447	+	0.275283i
$293$	−10.0219			−0.585485			−0.292742	−	0.956191i	$-0.594568\pi$
$293$	−10.0219			−0.585485			−0.292742	+	0.956191i	$0.594568\pi$
$294$	−3.93766	+	12.1189i	−0.229649	+	0.706787i
$295$	0.539192	−	13.5349i	0.0313930	−	0.788030i
$296$	2.63813	+	8.11933i	0.153338	+	0.471927i
$297$	2.43323	+	7.48872i	0.141191	+	0.434540i
$298$	0.644075	+	0.467948i	0.0373102	+	0.0271075i
$299$	4.69067			0.271268
$300$	10.6173	+	9.08814i	0.612992	+	0.524704i
$301$	8.88297			0.512006
$302$	11.4627	+	8.32811i	0.659602	+	0.479229i
$303$	5.41464	+	16.6646i	0.311063	+	0.957354i
$304$	−0.309017	−	0.951057i	−0.0177233	−	0.0545468i
$305$	−12.8064	+	3.60422i	−0.733291	+	0.206377i
$306$	2.92299	−	8.99603i	0.167096	−	0.514269i
$307$	7.20860			0.411417			0.205708	−	0.978613i	$-0.434050\pi$
$307$	7.20860			0.411417			0.205708	+	0.978613i	$0.434050\pi$
$308$	1.63255	−	5.02448i	0.0930234	−	0.286296i
$309$	2.74976	−	1.99781i	0.156428	−	0.113652i
$310$	0.670078	−	16.8204i	0.0380579	−	0.955332i
$311$	−0.572300	−	0.415800i	−0.0324522	−	0.0235779i	0.571441	−	0.820643i	$-0.306385\pi$
$311$	−0.572300	−	0.415800i	−0.0324522	−	0.0235779i	−0.603893	+	0.797065i	$0.706385\pi$
$312$	−2.51432	+	1.82676i	−0.142345	+	0.103420i
$313$	−15.7211	+	11.4221i	−0.888610	+	0.645613i	−0.935515	−	0.353287i	$-0.885064\pi$
$313$	−15.7211	+	11.4221i	−0.888610	+	0.645613i	0.0469054	+	0.998899i	$0.485064\pi$
$314$	−14.8304	−	10.7749i	−0.836926	−	0.608063i
$315$	1.45644	−	36.5596i	0.0820609	−	2.05990i
$316$	−0.552185	+	0.401186i	−0.0310628	+	0.0225685i
$317$	−1.77991	+	5.47799i	−0.0999695	+	0.307674i	−0.988517	−	0.151110i	$-0.951715\pi$
$317$	−1.77991	+	5.47799i	−0.0999695	+	0.307674i	0.888547	+	0.458785i	$0.151715\pi$
$318$	12.7296			0.713841
$319$	−3.98378	+	12.2608i	−0.223049	+	0.686473i
$320$	2.15245	−	0.605783i	0.120325	−	0.0338643i
$321$	3.83432	+	11.8008i	0.214011	+	0.658658i
$322$	4.43217	+	13.6408i	0.246995	+	0.760172i
$323$	−1.59000	−	1.15520i	−0.0884701	−	0.0642773i
$324$	−0.274871			−0.0152706
$325$	−4.22345	−	3.61515i	−0.234275	−	0.200533i
$326$	23.8713			1.32211
$327$	29.6006	+	21.5061i	1.63692	+	1.18929i
$328$	1.60702	+	4.94590i	0.0887328	+	0.273091i
$329$	−10.4555	−	32.1787i	−0.576430	−	1.77407i
$330$	−0.386602	+	9.70453i	−0.0212818	+	0.534217i
$331$	3.30213	−	10.1629i	0.181501	−	0.558604i	−0.818369	−	0.574693i	$-0.805122\pi$
$331$	3.30213	−	10.1629i	0.181501	−	0.558604i	0.999871	+	0.0160891i	$0.00512156\pi$
$332$	−12.3366			−0.677060
$333$	−12.6970	+	39.0773i	−0.695791	+	2.14142i
$334$	−14.6511	+	10.6447i	−0.801675	+	0.582451i
$335$	10.2381	+	15.3405i	0.559365	+	0.838140i
$336$	−7.68811	−	5.58574i	−0.419421	−	0.304727i
$337$	−15.3165	+	11.1281i	−0.834342	+	0.606185i	−0.920785	−	0.390072i	$-0.872450\pi$
$337$	−15.3165	+	11.1281i	−0.834342	+	0.606185i	0.0864421	+	0.996257i	$0.472450\pi$
$338$	−9.51705	+	6.91455i	−0.517660	+	0.376102i
$339$	−27.7001	−	20.1253i	−1.50446	−	1.09306i
$340$	2.72259	−	3.44971i	0.147653	−	0.187087i
$341$	9.46413	−	6.87610i	0.512512	−	0.372361i
$342$	1.48726	−	4.57731i	0.0804218	−	0.247513i
$343$	−8.29965			−0.448139
$344$	−0.807391	+	2.48490i	−0.0435316	+	0.133977i
$345$	−14.6370	−	21.9317i	−0.788028	−	1.18076i
$346$	−1.19205	−	3.66875i	−0.0640850	−	0.197233i
$347$	−3.88085	−	11.9440i	−0.208335	−	0.641189i	−0.999560	−	0.0296637i	$-0.990556\pi$
$347$	−3.88085	−	11.9440i	−0.208335	−	0.641189i	0.791225	−	0.611525i	$-0.209444\pi$
$348$	18.7606	+	13.6304i	1.00567	+	0.730665i
$349$	−8.63527			−0.462236			−0.231118	−	0.972926i	$-0.574238\pi$
$349$	−8.63527			−0.462236			−0.231118	+	0.972926i	$0.574238\pi$
$350$	6.52244	−	15.6980i	0.348639	−	0.839094i
$351$	−5.63417			−0.300730
$352$	1.25715	+	0.913371i	0.0670062	+	0.0486828i
$353$	−2.66683	−	8.20766i	−0.141941	−	0.436850i	0.854664	−	0.519182i	$-0.173763\pi$
$353$	−2.66683	−	8.20766i	−0.141941	−	0.436850i	−0.996605	+	0.0823321i	$0.973763\pi$
$354$	−5.23240	−	16.1037i	−0.278099	−	0.855900i
$355$	−21.3226	−	7.87956i	−1.13169	−	0.418204i
$356$	3.16071	−	9.72766i	0.167517	−	0.515565i
$357$	−18.6768			−0.988480
$358$	7.55268	−	23.2448i	0.399172	−	1.22852i
$359$	0.366090	−	0.265980i	0.0193215	−	0.0140379i	−0.578083	−	0.815978i	$-0.696199\pi$
$359$	0.366090	−	0.265980i	0.0193215	−	0.0140379i	0.597404	+	0.801940i	$0.296199\pi$
$360$	10.0947	+	3.73040i	0.532037	+	0.196609i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−20.4492	+	14.8572i	−1.07478	+	0.780876i
$363$	19.4142	−	14.1053i	1.01898	−	0.740334i
$364$	3.05824	+	2.22194i	0.160295	+	0.116461i
$365$	−10.6462	+	2.99627i	−0.557250	+	0.156832i
$366$	−13.4542	+	9.77503i	−0.703261	+	0.510949i
$367$	2.02599	−	6.23537i	0.105756	−	0.325484i	−0.884151	−	0.467201i	$-0.845262\pi$
$367$	2.02599	−	6.23537i	0.105756	−	0.325484i	0.989907	+	0.141717i	$0.0452624\pi$
$368$	−4.21869			−0.219914
$369$	−7.73438	+	23.8040i	−0.402636	+	1.23919i
$370$	−11.8265	+	14.9850i	−0.614831	+	0.779033i
$371$	−4.78463	−	14.7256i	−0.248405	−	0.764513i
$372$	−6.50253	−	20.0127i	−0.337141	−	1.03761i
$373$	30.5687	+	22.2095i	1.58279	+	1.14996i	0.913408	+	0.407045i	$0.133441\pi$
$373$	30.5687	+	22.2095i	1.58279	+	1.14996i	0.669381	+	0.742919i	$0.266559\pi$
$374$	3.05400			0.157919
$375$	−3.72399	+	31.0281i	−0.192306	+	1.60228i
$376$	9.95189			0.513230
$377$	−7.46275	−	5.42201i	−0.384351	−	0.279248i
$378$	−5.32368	−	16.3846i	−0.273820	−	0.842732i
$379$	−3.58058	−	11.0199i	−0.183922	−	0.566053i	0.816006	−	0.578043i	$-0.196183\pi$
$379$	−3.58058	−	11.0199i	−0.183922	−	0.566053i	−0.999928	+	0.0119897i	$0.996183\pi$
$380$	1.38530	−	1.75527i	0.0710642	−	0.0900432i
$381$	−7.66516	+	23.5909i	−0.392698	+	1.20860i
$382$	−14.5881			−0.746393
$383$	2.57833	−	7.93529i	0.131747	−	0.405474i	−0.863323	−	0.504651i	$-0.831621\pi$
$383$	2.57833	−	7.93529i	0.131747	−	0.405474i	0.995070	+	0.0991771i	$0.0316210\pi$
$384$	2.26133	−	1.64295i	0.115398	−	0.0838414i
$385$	11.3715	−	3.20039i	0.579545	−	0.163107i
$386$	−2.46732	−	1.79262i	−0.125583	−	0.0912417i
$387$	−10.1733	+	7.39137i	−0.517140	+	0.375724i
$388$	−6.84991	+	4.97675i	−0.347752	+	0.252656i
$389$	−27.5030	−	19.9821i	−1.39446	−	1.01313i	−0.995360	−	0.0962256i	$-0.969323\pi$
$389$	−27.5030	−	19.9821i	−1.39446	−	1.01313i	−0.399099	−	0.916908i	$-0.630677\pi$
$390$	−6.51856	−	2.40887i	−0.330080	−	0.121978i
$391$	−6.70772	+	4.87345i	−0.339224	+	0.246461i
$392$	−1.40875	+	4.33568i	−0.0711525	+	0.218985i
$393$	18.3408			0.925172
$394$	−4.20486	+	12.9412i	−0.211838	+	0.651970i
$395$	−1.43158	−	0.529026i	−0.0720306	−	0.0266182i
$396$	2.31108	+	7.11278i	0.116136	+	0.357431i
$397$	−8.45120	−	26.0101i	−0.424153	−	1.30541i	−0.903803	−	0.427950i	$-0.859236\pi$
$397$	−8.45120	−	26.0101i	−0.424153	−	1.30541i	0.479649	−	0.877460i	$-0.340764\pi$
$398$	1.49410	+	1.08553i	0.0748925	+	0.0544126i
$399$	−9.50302			−0.475746
$400$	3.79848	+	3.25139i	0.189924	+	0.162570i
$401$	31.8197			1.58900			0.794500	−	0.607264i	$-0.207733\pi$
$401$	31.8197			1.58900			0.794500	+	0.607264i	$0.207733\pi$
$402$	18.6514	+	13.5511i	0.930249	+	0.675866i
$403$	2.58663	+	7.96083i	0.128849	+	0.396557i
$404$	1.93716	+	5.96195i	0.0963771	+	0.296618i
$405$	−0.341191	−	0.511233i	−0.0169539	−	0.0254034i
$406$	8.71611	−	26.8254i	0.432573	−	1.33132i
$407$	−13.2661			−0.657575
$408$	1.69757	−	5.22459i	0.0840423	−	0.258656i
$409$	−16.3219	+	11.8586i	−0.807066	+	0.586368i	−0.912979	−	0.408007i	$-0.866224\pi$
$409$	−16.3219	+	11.8586i	−0.807066	+	0.586368i	0.105912	+	0.994375i	$0.466224\pi$
$410$	−7.20412	+	9.12812i	−0.355786	+	0.450806i
$411$	−30.4859	−	22.1493i	−1.50376	−	1.09254i
$412$	0.983759	−	0.714743i	0.0484663	−	0.0352129i
$413$	−16.6620	+	12.1056i	−0.819883	+	0.595680i
$414$	−16.4263	−	11.9344i	−0.807308	−	0.586544i
$415$	−15.3132	−	22.9449i	−0.751694	−	1.12632i
$416$	−0.899528	+	0.653546i	−0.0441030	+	0.0320427i
$417$	−4.66016	+	14.3425i	−0.228209	+	0.702355i
$418$	1.55392			0.0760047
$419$	−4.62742	+	14.2417i	−0.226064	+	0.695755i	0.772117	+	0.635480i	$0.219198\pi$
$419$	−4.62742	+	14.2417i	−0.226064	+	0.695755i	−0.998182	+	0.0602748i	$0.980802\pi$
$420$	0.845848	−	21.2326i	0.0412732	−	1.03604i
$421$	−6.86717	−	21.1350i	−0.334685	−	1.03006i	−0.966877	−	0.255243i	$-0.917844\pi$
$421$	−6.86717	−	21.1350i	−0.334685	−	1.03006i	0.632191	−	0.774812i	$-0.282156\pi$
$422$	−0.885666	−	2.72580i	−0.0431135	−	0.132690i
$423$	38.7496	+	28.1533i	1.88407	+	1.36886i
$424$	4.55417			0.221170
$425$	9.79562	+	0.781702i	0.475157	+	0.0379181i
$426$	−28.4156			−1.37674
$427$	16.3647	+	11.8896i	0.791943	+	0.575380i
$428$	1.37178	+	4.22189i	0.0663073	+	0.204073i
$429$	−1.49236	−	4.59301i	−0.0720518	−	0.221753i
$430$	−5.62386	+	1.58277i	−0.271206	+	0.0763282i
$431$	2.66936	−	8.21545i	0.128579	−	0.395724i	−0.865957	−	0.500118i	$-0.833290\pi$
$431$	2.66936	−	8.21545i	0.128579	−	0.395724i	0.994536	+	0.104393i	$0.0332901\pi$
$432$	5.06726			0.243798
$433$	11.7995	−	36.3151i	0.567047	−	1.74519i	−0.0947420	−	0.995502i	$-0.530203\pi$
$433$	11.7995	−	36.3151i	0.567047	−	1.74519i	0.661789	−	0.749690i	$-0.269797\pi$
$434$	−20.7066	+	15.0442i	−0.993948	+	0.722146i
$435$	−2.06405	+	51.8120i	−0.0989636	+	2.48419i
$436$	10.5900	+	7.69406i	0.507168	+	0.368479i
$437$	−3.41299	+	2.47968i	−0.163265	+	0.118619i
$438$	−11.1848	+	8.12621i	−0.534429	+	0.388285i
$439$	−2.06354	−	1.49925i	−0.0984876	−	0.0715554i	0.537452	−	0.843295i	$-0.319387\pi$
$439$	−2.06354	−	1.49925i	−0.0984876	−	0.0715554i	−0.635939	+	0.771739i	$0.719387\pi$
$440$	−0.138312	+	3.47192i	−0.00659376	+	0.165517i
$441$	−17.7506	+	12.8966i	−0.845266	+	0.614122i
$442$	−0.675274	+	2.07828i	−0.0321195	+	0.0988537i
$443$	−30.8375			−1.46514			−0.732568	−	0.680694i	$-0.761678\pi$
$443$	−30.8375			−1.46514			−0.732568	+	0.680694i	$0.761678\pi$
$444$	−7.37398	+	22.6948i	−0.349953	+	1.07705i
$445$	22.0158	−	6.19611i	1.04365	−	0.293724i
$446$	−1.59999	−	4.92426i	−0.0757616	−	0.233170i
$447$	0.687648	+	2.11636i	0.0325246	+	0.100101i
$448$	−2.75052	−	1.99837i	−0.129950	−	0.0944139i
$449$	19.6110			0.925501			0.462751	−	0.886489i	$-0.346863\pi$
$449$	19.6110			0.925501			0.462751	+	0.886489i	$0.346863\pi$
$450$	5.59214	+	23.4056i	0.263616	+	1.10335i
$451$	−8.08104			−0.380521
$452$	−9.91006	−	7.20008i	−0.466130	−	0.338663i
$453$	12.2381	+	37.6651i	0.574998	+	1.76966i
$454$	−1.32436	−	4.07597i	−0.0621554	−	0.191295i
$455$	−0.336468	+	8.44606i	−0.0157739	+	0.395958i
$456$	0.863749	−	2.65835i	0.0404488	−	0.124489i
$457$	−38.1002			−1.78225			−0.891127	−	0.453755i	$-0.850084\pi$
$457$	−38.1002			−1.78225			−0.891127	+	0.453755i	$0.850084\pi$
$458$	7.09086	−	21.8234i	0.331334	−	1.01974i
$459$	8.05695	−	5.85372i	0.376066	−	0.273228i
$460$	−5.23656	−	7.84634i	−0.244156	−	0.365837i
$461$	−5.36671	−	3.89914i	−0.249953	−	0.181601i	0.455753	−	0.890106i	$-0.349370\pi$
$461$	−5.36671	−	3.89914i	−0.249953	−	0.181601i	−0.705706	+	0.708505i	$0.749370\pi$
$462$	11.9467	−	8.67979i	0.555811	−	0.403820i
$463$	−17.8087	+	12.9388i	−0.827642	+	0.601317i	−0.918891	−	0.394511i	$-0.870914\pi$
$463$	−17.8087	+	12.9388i	−0.827642	+	0.601317i	0.0912495	+	0.995828i	$0.470914\pi$
$464$	6.71184	+	4.87644i	0.311589	+	0.226383i
$465$	29.1503	−	36.9354i	1.35181	−	1.71284i
$466$	18.0425	−	13.1086i	0.835801	−	0.607245i
$467$	5.44404	−	16.7550i	0.251920	−	0.775330i	−0.742501	−	0.669845i	$-0.766360\pi$
$467$	5.44404	−	16.7550i	0.251920	−	0.775330i	0.994421	−	0.105485i	$-0.0336396\pi$
$468$	−5.35133			−0.247365
$469$	8.66539	−	26.6693i	0.400130	−	1.23147i
$470$	12.3531	+	18.5095i	0.569804	+	0.853781i
$471$	−15.8337	−	48.7311i	−0.729578	−	2.24541i
$472$	−1.87195	−	5.76128i	−0.0861637	−	0.265185i
$473$	−3.28464	−	2.38643i	−0.151028	−	0.109728i
$474$	−1.90780			−0.0876280
$475$	4.98416	+	0.397742i	0.228689	+	0.0182496i
$476$	−6.68185			−0.306262
$477$	17.7326	+	12.8835i	0.811918	+	0.589893i
$478$	−0.657943	−	2.02494i	−0.0300936	−	0.0926186i
$479$	11.7239	+	36.0826i	0.535681	+	1.64866i	0.742173	+	0.670208i	$0.233795\pi$
$479$	11.7239	+	36.0826i	0.535681	+	1.64866i	−0.206492	+	0.978448i	$0.566205\pi$
$480$	5.86265	+	2.16649i	0.267592	+	0.0988861i
$481$	2.93328	−	9.02771i	0.133746	−	0.411628i
$482$	22.2261			1.01237
$483$	−12.3886	+	38.1281i	−0.563700	+	1.73489i
$484$	6.94568	−	5.04633i	0.315713	−	0.229379i
$485$	−17.7589	−	6.56263i	−0.806390	−	0.297994i
$486$	−12.9201	−	9.38697i	−0.586066	−	0.425802i
$487$	−11.2563	+	8.17815i	−0.510070	+	0.370587i	−0.812850	−	0.582473i	$-0.802085\pi$
$487$	−11.2563	+	8.17815i	−0.510070	+	0.370587i	0.302780	+	0.953060i	$0.402085\pi$
$488$	−4.81340	+	3.49714i	−0.217892	+	0.158308i
$489$	53.9808	+	39.2193i	2.44109	+	1.77356i
$490$	−9.81258	+	2.76165i	−0.443287	+	0.124758i
$491$	−12.5380	+	9.10936i	−0.565830	+	0.411100i	−0.833588	−	0.552387i	$-0.813717\pi$
$491$	−12.5380	+	9.10936i	−0.565830	+	0.411100i	0.267758	+	0.963486i	$0.413717\pi$
$492$	−4.49186	+	13.8245i	−0.202509	+	0.623258i
$493$	16.3051			0.734346
$494$	−0.343589	+	1.05746i	−0.0154588	+	0.0475773i
$495$	−10.3604	+	13.1273i	−0.465664	+	0.590029i
$496$	−2.32636	−	7.15980i	−0.104457	−	0.321485i
$497$	10.6805	+	32.8711i	0.479084	+	1.47447i
$498$	−27.8971	−	20.2684i	−1.25010	−	0.908251i
$499$	2.55037			0.114170			0.0570850	−	0.998369i	$-0.481819\pi$
$499$	2.55037			0.114170			0.0570850	+	0.998369i	$0.481819\pi$
$500$	−1.33230	+	11.1007i	−0.0595824	+	0.496437i
$501$	−50.6196			−2.26152
$502$	10.3090	+	7.48995i	0.460115	+	0.334293i
$503$	9.81418	+	30.2050i	0.437593	+	1.34677i	0.890406	+	0.455167i	$0.150420\pi$
$503$	9.81418	+	30.2050i	0.437593	+	1.34677i	−0.452813	+	0.891605i	$0.649580\pi$
$504$	−5.05642	−	15.5621i	−0.225231	−	0.693189i
$505$	−8.68409	+	11.0034i	−0.386437	+	0.489643i
$506$	2.02576	−	6.23465i	0.0900561	−	0.277164i
$507$	−32.8814			−1.46031
$508$	−2.74230	+	8.43995i	−0.121670	+	0.374462i
$509$	13.1970	−	9.58818i	0.584947	−	0.424989i	−0.255557	−	0.966794i	$-0.582259\pi$
$509$	13.1970	−	9.58818i	0.584947	−	0.424989i	0.840504	+	0.541805i	$0.182259\pi$
$510$	11.8244	−	3.32784i	0.523592	−	0.147359i
$511$	13.6044	+	9.88414i	0.601821	+	0.437249i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	4.09950	−	2.97846i	0.180997	−	0.131502i
$514$	20.8941	+	15.1804i	0.921597	+	0.669580i
$515$	2.55047	+	0.942501i	0.112387	+	0.0415316i
$516$	−5.90833	+	4.29265i	−0.260100	+	0.188974i
$517$	−4.77877	+	14.7076i	−0.210170	+	0.646838i
$518$	29.0249			1.27528
$519$	3.33196	−	10.2547i	0.146257	−	0.450132i
$520$	−2.33209	−	0.861803i	−0.102269	−	0.0377925i
$521$	3.31306	+	10.1965i	0.145148	+	0.446719i	0.997030	−	0.0770147i	$-0.0245388\pi$
$521$	3.31306	+	10.1965i	0.145148	+	0.446719i	−0.851882	+	0.523733i	$0.824539\pi$
$522$	12.3387	+	37.9747i	0.540052	+	1.66211i
$523$	−6.87242	−	4.99310i	−0.300510	−	0.218333i	0.427304	−	0.904108i	$-0.359463\pi$
$523$	−6.87242	−	4.99310i	−0.300510	−	0.218333i	−0.727814	+	0.685775i	$0.759463\pi$
$524$	6.56165			0.286647
$525$	40.5404	−	24.7823i	1.76933	−	1.08159i
$526$	27.2569			1.18846
$527$	−11.9700	−	8.69668i	−0.521420	−	0.378833i
$528$	1.34220	+	4.13086i	0.0584116	+	0.179773i
$529$	−1.60772	−	4.94804i	−0.0699007	−	0.215132i
$530$	5.65299	+	8.47031i	0.245550	+	0.367927i
$531$	9.00948	−	27.7283i	0.390978	−	1.20331i
$532$	−3.39982			−0.147401
$533$	1.78681	−	5.49923i	0.0773953	−	0.238198i
$534$	23.1294	−	16.8045i	1.00091	−	0.727203i
$535$	−6.14955	+	7.79191i	−0.265868	+	0.336874i
$536$	6.67278	+	4.84806i	0.288220	+	0.209404i
$537$	55.2690	−	40.1553i	2.38503	−	1.73283i
$538$	−11.2189	+	8.15098i	−0.483680	+	0.351414i
$539$	−5.73109	−	4.16388i	−0.246855	−	0.179351i
$540$	6.28987	+	9.42459i	0.270673	+	0.405570i
$541$	−30.3381	+	22.0419i	−1.30434	+	0.947655i	−0.999988	−	0.00490554i	$-0.998439\pi$
$541$	−30.3381	+	22.0419i	−1.30434	+	0.947655i	−0.304348	+	0.952561i	$0.598439\pi$
$542$	2.90929	−	8.95388i	0.124965	−	0.384602i
$543$	−70.6518			−3.03196
$544$	0.607327	−	1.86916i	0.0260389	−	0.0801396i
$545$	−1.16511	+	29.2468i	−0.0499079	+	1.25279i
$546$	3.26514	+	10.0491i	0.139735	+	0.430060i
$547$	3.24146	+	9.97618i	0.138595	+	0.426550i	0.996132	−	0.0878715i	$-0.0280065\pi$
$547$	3.24146	+	9.97618i	0.138595	+	0.426550i	−0.857537	+	0.514422i	$0.828006\pi$
$548$	−10.9067	−	7.92418i	−0.465911	−	0.338504i
$549$	−28.6351			−1.22212
$550$	−6.62910	+	4.05236i	−0.282666	+	0.172793i
$551$	8.29629			0.353434
$552$	−9.53982	−	6.93109i	−0.406042	−	0.295007i
$553$	0.717076	+	2.20693i	0.0304932	+	0.0938484i
$554$	−5.17803	−	15.9363i	−0.219993	−	0.677069i
$555$	−51.3632	+	14.4556i	−2.18024	+	0.613607i
$556$	−1.66723	+	5.13120i	−0.0707063	+	0.217612i
$557$	−33.4974			−1.41933			−0.709665	−	0.704539i	$-0.751154\pi$
$557$	−33.4974			−1.41933			−0.709665	+	0.704539i	$0.751154\pi$
$558$	11.1965	−	34.4592i	0.473985	−	1.45877i
$559$	2.35026	−	1.70757i	0.0994056	−	0.0722224i
$560$	0.302613	−	7.59621i	0.0127877	−	0.320999i
$561$	6.90609	+	5.01756i	0.291575	+	0.211842i
$562$	26.8682	−	19.5209i	1.13337	−	0.823439i
$563$	22.7150	−	16.5034i	0.957323	−	0.695536i	0.00479526	−	0.999989i	$-0.498474\pi$
$563$	22.7150	−	16.5034i	0.957323	−	0.695536i	0.952527	+	0.304453i	$0.0984736\pi$
$564$	22.5045	+	16.3504i	0.947609	+	0.688478i
$565$	1.09031	−	27.3690i	0.0458696	−	1.15142i
$566$	19.5333	−	14.1918i	0.821047	−	0.596526i
$567$	−0.288781	+	0.888776i	−0.0121276	+	0.0373251i
$568$	−10.1660			−0.426557
$569$	−0.712106	+	2.19164i	−0.0298530	+	0.0918781i	−0.964873	−	0.262717i	$-0.915381\pi$
$569$	−0.712106	+	2.19164i	−0.0298530	+	0.0918781i	0.935020	+	0.354595i	$0.115381\pi$
$570$	6.01641	−	1.69326i	0.252000	−	0.0709227i
$571$	−4.01597	−	12.3599i	−0.168063	−	0.517245i	0.831186	−	0.555995i	$-0.187662\pi$
$571$	−4.01597	−	12.3599i	−0.168063	−	0.517245i	−0.999249	+	0.0387498i	$0.987662\pi$
$572$	−0.533910	−	1.64321i	−0.0223239	−	0.0687059i
$573$	−32.9885	−	23.9675i	−1.37811	−	1.00126i
$574$	17.6805			0.737971
$575$	8.09340	−	19.4790i	0.337518	−	0.812329i
$576$	4.81287			0.200536
$577$	23.7781	+	17.2758i	0.989894	+	0.719200i	0.959898	−	0.280350i	$-0.0904504\pi$
$577$	23.7781	+	17.2758i	0.989894	+	0.719200i	0.0299963	+	0.999550i	$0.490450\pi$
$578$	4.05968	+	12.4944i	0.168860	+	0.519699i
$579$	−2.63425	−	8.10737i	−0.109475	−	0.336931i
$580$	−0.738439	+	18.5364i	−0.0306620	+	0.769681i
$581$	−12.9609	+	39.8895i	−0.537709	+	1.65490i
$582$	−23.6664			−0.981005
$583$	−2.18686	+	6.73045i	−0.0905704	+	0.278747i
$584$	−4.00149	+	2.90725i	−0.165583	+	0.120303i
$585$	−6.64248	−	9.95294i	−0.274633	−	0.411504i
$586$	−8.10787	−	5.89072i	−0.334933	−	0.243343i
$587$	−3.74196	+	2.71869i	−0.154447	+	0.112213i	−0.662325	−	0.749217i	$-0.730430\pi$
$587$	−3.74196	+	2.71869i	−0.154447	+	0.112213i	0.507878	+	0.861429i	$0.330430\pi$
$588$	−10.3089	+	7.48988i	−0.425133	+	0.308877i
$589$	−6.09049	−	4.42500i	−0.250954	−	0.182329i
$590$	8.39180	−	10.6330i	0.345485	−	0.437754i
$591$	−30.7704	+	22.3560i	−1.26572	+	0.919602i
$592$	−2.63813	+	8.11933i	−0.108427	+	0.333703i
$593$	−29.7426			−1.22138			−0.610691	−	0.791869i	$-0.709108\pi$
$593$	−29.7426			−1.22138			−0.610691	+	0.791869i	$0.709108\pi$
$594$	−2.43323	+	7.48872i	−0.0998368	+	0.307266i
$595$	−8.29403	−	12.4276i	−0.340022	−	0.509481i
$596$	0.246015	+	0.757155i	0.0100772	+	0.0310143i
$597$	1.59518	+	4.90946i	0.0652864	+	0.200931i
$598$	3.79483	+	2.75710i	0.155182	+	0.112746i
$599$	−3.02018			−0.123401			−0.0617007	−	0.998095i	$-0.519652\pi$
$599$	−3.02018			−0.123401			−0.0617007	+	0.998095i	$0.519652\pi$
$600$	3.24773	+	13.5932i	0.132588	+	0.554939i
$601$	34.3796			1.40237			0.701186	−	0.712978i	$-0.252654\pi$
$601$	34.3796			1.40237			0.701186	+	0.712978i	$0.252654\pi$
$602$	7.18647	+	5.22128i	0.292899	+	0.212803i
$603$	12.2669	+	37.7537i	0.499548	+	1.53745i
$604$	4.37835	+	13.4752i	0.178152	+	0.548297i
$605$	18.0072	+	6.65438i	0.732096	+	0.270539i
$606$	−5.41464	+	16.6646i	−0.219955	+	0.676951i
$607$	15.4693			0.627881			0.313940	−	0.949443i	$-0.398351\pi$
$607$	15.4693			0.627881			0.313940	+	0.949443i	$0.398351\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	63.7828	−	46.3409i	2.58461	−	1.87783i
$610$	−12.4791	−	4.61153i	−0.505263	−	0.186715i
$611$	−8.95201	−	6.50401i	−0.362159	−	0.263124i
$612$	7.65248	−	5.55985i	0.309333	−	0.224744i
$613$	6.13996	−	4.46094i	0.247991	−	0.180176i	−0.456845	−	0.889546i	$-0.651021\pi$
$613$	6.13996	−	4.46094i	0.247991	−	0.180176i	0.704836	+	0.709370i	$0.251021\pi$
$614$	5.83188	+	4.23711i	0.235356	+	0.170996i
$615$	−31.2879	+	8.80565i	−1.26165	+	0.355078i
$616$	4.27408	−	3.10530i	0.172208	−	0.125116i
$617$	−9.29333	+	28.6019i	−0.374135	+	1.15147i	0.569925	+	0.821697i	$0.306972\pi$
$617$	−9.29333	+	28.6019i	−0.374135	+	1.15147i	−0.944060	+	0.329773i	$0.893028\pi$
$618$	3.39889			0.136723
$619$	7.90327	−	24.3238i	0.317659	−	0.977655i	−0.656987	−	0.753902i	$-0.728169\pi$
$619$	7.90327	−	24.3238i	0.317659	−	0.977655i	0.974646	−	0.223753i	$-0.0718308\pi$
$620$	10.4289	−	13.2141i	0.418833	−	0.530691i
$621$	−6.60591	−	20.3309i	−0.265086	−	0.815851i
$622$	−0.218599	−	0.672779i	−0.00876503	−	0.0269760i
$623$	−28.1330	−	20.4398i	−1.12712	−	0.818904i
$624$	−3.10787			−0.124414
$625$	−22.2999	+	11.3011i	−0.891997	+	0.452042i
$626$	−19.4324			−0.776673
$627$	3.51392	+	2.55301i	0.140332	+	0.101957i
$628$	−5.66470	−	17.4341i	−0.226046	−	0.695698i
$629$	5.18486	+	15.9573i	0.206734	+	0.636261i
$630$	22.6675	−	28.7213i	0.903094	−	1.14428i
$631$	12.0792	−	37.1759i	0.480864	−	1.47995i	−0.357018	−	0.934097i	$-0.616207\pi$
$631$	12.0792	−	37.1759i	0.480864	−	1.47995i	0.837883	−	0.545850i	$-0.183793\pi$
$632$	−0.682538			−0.0271499
$633$	2.47557	−	7.61902i	0.0983951	−	0.302829i
$634$	−4.65985	+	3.38558i	−0.185066	+	0.134459i
$635$	−19.1014	+	5.37589i	−0.758017	+	0.213336i
$636$	10.2985	+	7.48227i	0.408361	+	0.296691i
$637$	4.10077	−	2.97938i	0.162478	−	0.118048i
$638$	−10.4297	+	7.57760i	−0.412914	+	0.300000i
$639$	−39.5834	−	28.7590i	−1.56590	−	1.13769i
$640$	2.09744	+	0.775087i	0.0829085	+	0.0306380i
$641$	−27.2364	+	19.7884i	−1.07577	+	0.781595i	−0.976941	−	0.213510i	$-0.931511\pi$
$641$	−27.2364	+	19.7884i	−1.07577	+	0.781595i	−0.0988318	+	0.995104i	$0.531511\pi$
$642$	−3.83432	+	11.8008i	−0.151329	+	0.465742i
$643$	27.0749			1.06773			0.533865	−	0.845570i	$-0.320739\pi$
$643$	27.0749			1.06773			0.533865	+	0.845570i	$0.320739\pi$
$644$	−4.43217	+	13.6408i	−0.174652	+	0.537523i
$645$	−15.3178	−	5.66054i	−0.603137	−	0.222883i
$646$	−0.607327	−	1.86916i	−0.0238950	−	0.0735411i
$647$	−4.71544	−	14.5126i	−0.185383	−	0.570550i	0.814572	−	0.580063i	$-0.196972\pi$
$647$	−4.71544	−	14.5126i	−0.185383	−	0.570550i	−0.999955	+	0.00951251i	$0.996972\pi$
$648$	−0.222376	−	0.161565i	−0.00873574	−	0.00634688i
$649$	9.41329			0.369504
$650$	−1.29191	−	5.40720i	−0.0506727	−	0.212088i
$651$	−71.5412			−2.80392
$652$	19.3123	+	14.0312i	0.756327	+	0.549504i
$653$	−7.10735	−	21.8742i	−0.278132	−	0.856003i	−0.988374	−	0.152045i	$-0.951414\pi$
$653$	−7.10735	−	21.8742i	−0.278132	−	0.856003i	0.710241	−	0.703958i	$-0.248586\pi$
$654$	11.3064	+	34.7976i	0.442116	+	1.36069i
$655$	8.14483	+	12.2040i	0.318245	+	0.476851i
$656$	−1.60702	+	4.94590i	−0.0627436	+	0.193105i
$657$	−23.8050			−0.928722
$658$	10.4555	−	32.1787i	0.407597	−	1.25446i
$659$	9.66424	−	7.02148i	0.376465	−	0.273518i	−0.383421	−	0.923574i	$-0.625254\pi$
$659$	9.66424	−	7.02148i	0.376465	−	0.273518i	0.759887	+	0.650055i	$0.225254\pi$
$660$	−6.01695	+	7.62389i	−0.234209	+	0.296760i
$661$	−15.5939	−	11.3296i	−0.606531	−	0.440671i	0.241660	−	0.970361i	$-0.422308\pi$
$661$	−15.5939	−	11.3296i	−0.606531	−	0.440671i	−0.848191	+	0.529690i	$0.822308\pi$
$662$	8.64508	−	6.28102i	0.336001	−	0.244119i
$663$	−4.94152	+	3.59022i	−0.191913	+	0.139433i
$664$	−9.98054	−	7.25129i	−0.387320	−	0.281404i
$665$	−4.22012	−	6.32334i	−0.163649	−	0.245208i
$666$	−33.2412	+	24.1511i	−1.28807	+	0.935837i
$667$	10.8154	−	33.2865i	0.418775	−	1.28886i
$668$	−18.1098			−0.700689
$669$	4.47221	−	13.7640i	0.172906	−	0.532149i
$670$	−0.734142	+	18.4285i	−0.0283624	+	0.711955i
$671$	−2.85697	−	8.79283i	−0.110292	−	0.339444i
$672$	−2.93660	−	9.03791i	−0.113282	−	0.348645i
$673$	20.9600	+	15.2283i	0.807949	+	0.587009i	0.913235	−	0.407433i	$-0.133576\pi$
$673$	20.9600	+	15.2283i	0.807949	+	0.587009i	−0.105287	+	0.994442i	$0.533576\pi$
$674$	−18.9322			−0.729242
$675$	−9.72135	+	23.3971i	−0.374175	+	0.900553i
$676$	−11.7637			−0.452451
$677$	−39.2481	−	28.5154i	−1.50843	−	1.09594i	−0.966869	−	0.255274i	$-0.917834\pi$
$677$	−39.2481	−	28.5154i	−1.50843	−	1.09594i	−0.541559	−	0.840663i	$-0.682166\pi$
$678$	−10.5805	−	32.5635i	−0.406342	−	1.25059i
$679$	8.89541	+	27.3773i	0.341375	+	1.05064i
$680$	4.23031	−	1.19058i	0.162225	−	0.0456566i
$681$	3.70180	−	11.3930i	0.141853	−	0.436579i
$682$	11.6983			0.447952
$683$	7.41303	−	22.8150i	0.283652	−	0.872991i	−0.703148	−	0.711044i	$-0.748223\pi$
$683$	7.41303	−	22.8150i	0.283652	−	0.872991i	0.986799	−	0.161947i	$-0.0517773\pi$
$684$	3.89370	−	2.82894i	0.148879	−	0.108167i
$685$	1.19996	−	30.1215i	0.0458481	−	1.15088i
$686$	−6.71455	−	4.87841i	−0.256363	−	0.186259i
$687$	51.8895	−	37.6999i	1.97971	−	1.43834i
$688$	−2.11378	+	1.53575i	−0.0805870	+	0.0585499i
$689$	−4.09661	−	2.97636i	−0.156068	−	0.113390i
$690$	1.04957	−	26.3465i	0.0399566	−	1.00300i
$691$	−12.1976	+	8.86210i	−0.464020	+	0.337130i	−0.795106	−	0.606470i	$-0.792585\pi$
$691$	−12.1976	+	8.86210i	−0.464020	+	0.337130i	0.331086	+	0.943600i	$0.392585\pi$
$692$	1.19205	−	3.66875i	0.0453150	−	0.139465i
$693$	25.4267			0.965879
$694$	3.88085	−	11.9440i	0.147315	−	0.453389i
$695$	−11.6130	+	3.26836i	−0.440507	+	0.123976i
$696$	7.16592	+	22.0544i	0.271623	+	0.835971i
$697$	3.15836	+	9.72043i	0.119631	+	0.368187i
$698$	−6.98608	−	5.07569i	−0.264427	−	0.192118i
$699$	62.3367			2.35779
$700$	14.5038	−	8.86617i	0.548193	−	0.335110i
$701$	16.5326			0.624428			0.312214	−	0.950012i	$-0.398929\pi$
$701$	16.5326			0.624428			0.312214	+	0.950012i	$0.398929\pi$
$702$	−4.55814	−	3.31168i	−0.172036	−	0.124991i
$703$	2.63813	+	8.11933i	0.0994990	+	0.306226i
$704$	0.480188	+	1.47787i	0.0180978	+	0.0556992i
$705$	−2.47595	+	62.1515i	−0.0932496	+	2.34076i
$706$	2.66683	−	8.20766i	0.100367	−	0.308899i
$707$	21.3127			0.801547
$708$	5.23240	−	16.1037i	0.196646	−	0.605213i
$709$	−20.0028	+	14.5329i	−0.751220	+	0.545793i	−0.896205	−	0.443641i	$-0.853687\pi$
$709$	−20.0028	+	14.5329i	−0.751220	+	0.545793i	0.144985	+	0.989434i	$0.453687\pi$
$710$	−12.6189	−	18.9078i	−0.473577	−	0.709597i
$711$	−2.65759	−	1.93086i	−0.0996676	−	0.0724127i
$712$	8.27484	−	6.01202i	0.310113	−	0.225310i
$713$	−25.6939	+	18.6677i	−0.962243	+	0.699111i
$714$	−15.1098	−	10.9779i	−0.565471	−	0.410839i
$715$	2.39347	−	3.03269i	0.0895107	−	0.113416i
$716$	19.7732	−	14.3661i	0.738958	−	0.536885i
$717$	1.83905	−	5.66001i	0.0686806	−	0.211377i
$718$	0.452512			0.0168876
$719$	0.422509	−	1.30035i	0.0157569	−	0.0484948i	−0.942869	−	0.333164i	$-0.891884\pi$
$719$	0.422509	−	1.30035i	0.0157569	−	0.0484948i	0.958626	+	0.284669i	$0.0918837\pi$
$720$	5.97411	+	8.95147i	0.222642	+	0.333602i
$721$	−1.27753	−	3.93182i	−0.0475776	−	0.146429i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	50.2603	+	36.5163i	1.86920	+	1.35806i
$724$	−25.2765			−0.939395
$725$	−35.3924	+	21.6353i	−1.31444	+	0.803517i
$726$	23.9973			0.890624
$727$	−6.48272	−	4.70997i	−0.240431	−	0.174683i	0.461044	−	0.887377i	$-0.347475\pi$
$727$	−6.48272	−	4.70997i	−0.240431	−	0.174683i	−0.701475	+	0.712694i	$0.747475\pi$
$728$	1.16814	+	3.59517i	0.0432943	+	0.133246i
$729$	−13.5393	−	41.6697i	−0.501456	−	1.54332i
$730$	−10.3742	−	3.83367i	−0.383965	−	0.141890i
$731$	−1.58681	+	4.88369i	−0.0586902	+	0.180630i
$732$	−16.6303			−0.614673
$733$	−5.37492	+	16.5423i	−0.198527	+	0.611004i	0.801390	+	0.598142i	$0.204094\pi$
$733$	−5.37492	+	16.5423i	−0.198527	+	0.611004i	−0.999917	+	0.0128619i	$0.995906\pi$
$734$	5.30412	−	3.85367i	0.195779	−	0.142242i
$735$	−26.7267	−	9.87658i	−0.985828	−	0.364303i
$736$	−3.41299	−	2.47968i	−0.125804	−	0.0914023i
$737$	−10.3690	+	7.53350i	−0.381946	+	0.277500i
$738$	−20.2489	+	14.7117i	−0.745371	+	0.541544i
$739$	−9.29033	−	6.74982i	−0.341750	−	0.248296i	0.403650	−	0.914914i	$-0.367741\pi$
$739$	−9.29033	−	6.74982i	−0.341750	−	0.248296i	−0.745400	+	0.666617i	$0.767741\pi$
$740$	−18.3758	+	5.17168i	−0.675508	+	0.190115i
$741$	−2.51432	+	1.82676i	−0.0923658	+	0.0671077i
$742$	4.78463	−	14.7256i	0.175649	−	0.540593i
$743$	−45.7346			−1.67784			−0.838920	−	0.544254i	$-0.816813\pi$
$743$	−45.7346			−1.67784			−0.838920	+	0.544254i	$0.816813\pi$
$744$	6.50253	−	20.0127i	0.238394	−	0.733702i
$745$	−1.10286	+	1.39740i	−0.0404057	+	0.0511968i
$746$	11.6762	+	35.9357i	0.427497	+	1.31570i
$747$	−18.3478	−	56.4686i	−0.671310	−	2.06608i
$748$	2.47074	+	1.79510i	0.0903391	+	0.0656352i
$749$	15.0924			0.551463
$750$	−21.2506	+	22.9133i	−0.775963	+	0.836676i
$751$	44.6693			1.63000			0.815002	−	0.579458i	$-0.196736\pi$
$751$	44.6693			1.63000			0.815002	+	0.579458i	$0.196736\pi$
$752$	8.05125	+	5.84957i	0.293599	+	0.213312i
$753$	11.0065	+	33.8744i	0.401098	+	1.23445i
$754$	−2.85052	−	8.77299i	−0.103810	−	0.319493i
$755$	−19.6277	+	24.8697i	−0.714327	+	0.905101i
$756$	5.32368	−	16.3846i	0.193620	−	0.595902i
$757$	−7.20216			−0.261767			−0.130883	−	0.991398i	$-0.541781\pi$
$757$	−7.20216			−0.261767			−0.130883	+	0.991398i	$0.541781\pi$
$758$	3.58058	−	11.0199i	0.130052	−	0.400260i
$759$	14.8241	−	10.7704i	0.538081	−	0.390939i
$760$	2.15245	−	0.605783i	0.0780774	−	0.0219741i
$761$	10.5434	+	7.66024i	0.382199	+	0.277684i	0.762251	−	0.647281i	$-0.224094\pi$
$761$	10.5434	+	7.66024i	0.382199	+	0.277684i	−0.380053	+	0.924965i	$0.624094\pi$
$762$	−20.0676	+	14.5800i	−0.726974	+	0.528178i
$763$	36.0040	−	26.1585i	1.30343	−	0.947000i
$764$	−11.8020	−	8.57468i	−0.426983	−	0.310221i
$765$	19.8396	+	7.33154i	0.717303	+	0.265072i
$766$	6.75016	−	4.90428i	0.243893	−	0.177199i
$767$	−2.08139	+	6.40585i	−0.0751545	+	0.231302i
$768$	2.79515			0.100861
$769$	−1.23577	+	3.80331i	−0.0445630	+	0.137151i	−0.970863	−	0.239637i	$-0.922972\pi$
$769$	−1.23577	+	3.80331i	−0.0445630	+	0.137151i	0.926299	+	0.376788i	$0.122972\pi$
$770$	11.0809	+	4.09483i	0.399327	+	0.147567i
$771$	22.3076	+	68.6557i	0.803389	+	2.47258i
$772$	−0.942434	−	2.90051i	−0.0339189	−	0.104392i
$773$	4.25658	+	3.09259i	0.153099	+	0.111233i	0.661697	−	0.749771i	$-0.269836\pi$
$773$	4.25658	+	3.09259i	0.153099	+	0.111233i	−0.508599	+	0.861004i	$0.669836\pi$
$774$	−12.5749			−0.451997
$775$	37.5220	+	2.99430i	1.34783	+	0.107559i
$776$	−8.46696			−0.303946
$777$	65.6347	+	47.6864i	2.35463	+	1.71074i
$778$	−10.5052	−	32.3317i	−0.376630	−	1.15915i
$779$	1.60702	+	4.94590i	0.0575774	+	0.177205i
$780$	−3.85773	−	5.78033i	−0.138129	−	0.206969i
$781$	4.88160	−	15.0240i	0.174677	−	0.537602i
$782$	−8.29120			−0.296493
$783$	−12.9909	+	39.9819i	−0.464257	+	1.42884i
$784$	−3.68815	+	2.67960i	−0.131720	+	0.0956999i
$785$	25.3943	−	32.1764i	0.906363	−	1.14842i
$786$	14.8380	+	10.7805i	0.529255	+	0.384526i
$787$	23.8095	−	17.2986i	0.848718	−	0.616629i	−0.0760745	−	0.997102i	$-0.524239\pi$
$787$	23.8095	−	17.2986i	0.848718	−	0.616629i	0.924792	+	0.380473i	$0.124239\pi$
$788$	−11.0085	+	7.99812i	−0.392161	+	0.284921i
$789$	61.6368	+	44.7817i	2.19433	+	1.59427i
$790$	−0.847218	−	1.26945i	−0.0301427	−	0.0451651i
$791$	−33.6925	+	24.4790i	−1.19797	+	0.870374i
$792$	−2.31108	+	7.11278i	−0.0821207	+	0.252742i
$793$	6.61533			0.234917
$794$	8.45120	−	26.0101i	0.299922	−	0.923064i
$795$	−1.13304	+	28.4417i	−0.0401848	+	1.00872i
$796$	0.570696	+	1.75642i	0.0202278	+	0.0622547i
$797$	−4.66658	−	14.3623i	−0.165299	−	0.508738i	0.833759	−	0.552128i	$-0.186184\pi$
$797$	−4.66658	−	14.3623i	−0.165299	−	0.508738i	−0.999058	+	0.0433904i	$0.986184\pi$
$798$	−7.68811	−	5.58574i	−0.272156	−	0.197733i
$799$	19.5590			0.691946
$800$	1.16191	+	4.86312i	0.0410799	+	0.171937i
$801$	49.2273			1.73936
$802$	25.7427	+	18.7032i	0.909006	+	0.660431i
$803$	−2.37506	−	7.30969i	−0.0838141	−	0.257953i
$804$	7.12422	+	21.9261i	0.251252	+	0.773273i
$805$	−30.8721	+	8.68863i	−1.08810	+	0.306234i
$806$	−2.58663	+	7.96083i	−0.0911101	+	0.280408i
$807$	−38.7612			−1.36446
$808$	−1.93716	+	5.96195i	−0.0681489	+	0.209741i
$809$	1.96131	−	1.42498i	0.0689560	−	0.0500995i	−0.552773	−	0.833332i	$-0.686430\pi$
$809$	1.96131	−	1.42498i	0.0689560	−	0.0500995i	0.621729	+	0.783232i	$0.286430\pi$
$810$	0.0244658	−	0.614144i	0.000859642	−	0.0215788i
$811$	−35.7065	−	25.9423i	−1.25382	−	0.910957i	−0.255387	−	0.966839i	$-0.582203\pi$
$811$	−35.7065	−	25.9423i	−1.25382	−	0.910957i	−0.998437	+	0.0558823i	$0.982203\pi$
$812$	22.8191	−	16.5790i	0.800793	−	0.581810i
$813$	21.2896	−	15.4678i	0.746660	−	0.542480i
$814$	−10.7325	−	7.79761i	−0.376173	−	0.273306i
$815$	−2.12474	+	53.3355i	−0.0744265	+	1.86826i
$816$	4.44430	−	3.22897i	0.155582	−	0.113037i
$817$	−0.807391	+	2.48490i	−0.0282470	+	0.0869355i
$818$	−20.1750			−0.705402
$819$	−5.62212	+	17.3031i	−0.196453	+	0.604620i
$820$	−11.1936	+	3.15033i	−0.390899	+	0.110014i
$821$	16.7035	+	51.4082i	0.582958	+	1.79416i	0.607321	+	0.794457i	$0.292244\pi$
$821$	16.7035	+	51.4082i	0.582958	+	1.79416i	−0.0243632	+	0.999703i	$0.507756\pi$
$822$	−11.6446	−	35.8383i	−0.406151	−	1.25000i
$823$	−3.32225	−	2.41376i	−0.115806	−	0.0841382i	0.528375	−	0.849011i	$-0.322802\pi$
$823$	−3.32225	−	2.41376i	−0.115806	−	0.0841382i	−0.644181	+	0.764873i	$0.722802\pi$
$824$	1.21599			0.0423611
$825$	−21.6484	−	1.72757i	−0.753700	−	0.0601462i
$826$	−20.5954			−0.716604
$827$	1.64701	+	1.19662i	0.0572721	+	0.0416106i	0.616053	−	0.787705i	$-0.288731\pi$
$827$	1.64701	+	1.19662i	0.0572721	+	0.0416106i	−0.558781	+	0.829315i	$0.688731\pi$
$828$	−6.27428	−	19.3103i	−0.218046	−	0.671078i
$829$	6.76444	+	20.8188i	0.234939	+	0.723067i	0.997130	+	0.0757145i	$0.0241238\pi$
$829$	6.76444	+	20.8188i	0.234939	+	0.723067i	−0.762191	+	0.647352i	$0.775876\pi$
$830$	1.09806	−	27.5637i	0.0381143	−	0.956749i
$831$	14.4734	−	44.5444i	0.502076	−	1.54523i
$832$	−1.11188			−0.0385474
$833$	−2.76868	+	8.52113i	−0.0959292	+	0.295240i
$834$	−12.2005	+	8.86415i	−0.422467	+	0.306940i
$835$	−22.4793	−	33.6824i	−0.777927	−	1.16563i
$836$	1.25715	+	0.913371i	0.0434794	+	0.0315896i
$837$	30.8621	−	22.4226i	1.06675	−	0.775039i
$838$	−12.1148	+	8.80188i	−0.418497	+	0.304056i
$839$	31.8318	+	23.1271i	1.09895	+	0.798437i	0.980889	−	0.194568i	$-0.0623306\pi$
$839$	31.8318	+	23.1271i	1.09895	+	0.798437i	0.118066	+	0.993006i	$0.462331\pi$
$840$	13.1645	−	16.6803i	0.454218	−	0.575526i
$841$	−32.2219	+	23.4106i	−1.11110	+	0.807262i
$842$	6.86717	−	21.1350i	0.236658	−	0.728359i
$843$	92.8295			3.19722
$844$	0.885666	−	2.72580i	0.0304859	−	0.0938258i
$845$	−14.6020	−	21.8794i	−0.502326	−	0.752673i
$846$	14.8010	+	45.5529i	0.508870	+	1.56614i
$847$	−9.01978	−	27.7600i	−0.309923	−	0.953846i
$848$	3.68440	+	2.67687i	0.126523	+	0.0919243i
$849$	67.4876			2.31617
$850$	7.46535	+	6.39013i	0.256059	+	0.219180i
$851$	36.0157			1.23460
$852$	−22.9887	−	16.7023i	−0.787580	−	0.572210i
$853$	−14.8804	−	45.7972i	−0.509496	−	1.56807i	−0.793079	−	0.609119i	$-0.791523\pi$
$853$	−14.8804	−	45.7972i	−0.509496	−	1.56807i	0.283583	−	0.958948i	$-0.408477\pi$
$854$	6.25076	+	19.2379i	0.213897	+	0.658306i
$855$	10.0947	+	3.73040i	0.345231	+	0.127577i
$856$	−1.37178	+	4.22189i	−0.0468864	+	0.144301i
$857$	34.9172			1.19275			0.596375	−	0.802706i	$-0.296607\pi$
$857$	34.9172			1.19275			0.596375	+	0.802706i	$0.296607\pi$
$858$	1.49236	−	4.59301i	0.0509483	−	0.156803i
$859$	39.3694	−	28.6036i	1.34327	−	0.975941i	0.343951	−	0.938988i	$-0.388235\pi$
$859$	39.3694	−	28.6036i	1.34327	−	0.975941i	0.999317	−	0.0369537i	$-0.0117654\pi$
$860$	−5.48013	−	2.02513i	−0.186871	−	0.0690563i
$861$	39.9814	+	29.0482i	1.36256	+	0.989960i
$862$	6.98848	−	5.07743i	0.238029	−	0.172938i
$863$	10.8479	−	7.88145i	0.369266	−	0.268288i	−0.387640	−	0.921811i	$-0.626710\pi$
$863$	10.8479	−	7.88145i	0.369266	−	0.268288i	0.756907	+	0.653523i	$0.226710\pi$
$864$	4.09950	+	2.97846i	0.139468	+	0.101329i
$865$	8.30318	−	2.33684i	0.282317	−	0.0794551i
$866$	30.8915	−	22.4440i	1.04973	−	0.762677i
$867$	−11.3474	+	34.9238i	−0.385378	+	1.18607i
$868$	−25.5948			−0.868743
$869$	0.327746	−	1.00870i	0.0111180	−	0.0342178i
$870$	−32.1242	+	40.7036i	−1.08911	+	1.37998i
$871$	−2.83393	−	8.72194i	−0.0960240	−	0.295531i
$872$	4.04501	+	12.4493i	0.136981	+	0.421585i
$873$	−32.9678	−	23.9525i	−1.11579	−	0.810669i
$874$	−4.21869			−0.142699
$875$	34.4935	+	15.9703i	1.16609	+	0.539895i
$876$	−13.8251			−0.467108
$877$	−24.2514	−	17.6197i	−0.818911	−	0.594974i	0.0974895	−	0.995237i	$-0.468919\pi$
$877$	−24.2514	−	17.6197i	−0.818911	−	0.594974i	−0.916400	+	0.400263i	$0.868919\pi$
$878$	−0.788204	−	2.42584i	−0.0266006	−	0.0818682i
$879$	−8.65640	−	26.6416i	−0.291973	−	0.898601i
$880$	−2.15264	+	2.72754i	−0.0725654	+	0.0919454i
$881$	−8.43266	+	25.9531i	−0.284104	+	0.874381i	0.702562	+	0.711622i	$0.252039\pi$
$881$	−8.43266	+	25.9531i	−0.284104	+	0.874381i	−0.986666	+	0.162759i	$0.947961\pi$
$882$	−21.9409			−0.738790
$883$	11.1382	−	34.2800i	0.374832	−	1.15361i	−0.568760	−	0.822503i	$-0.692577\pi$
$883$	11.1382	−	34.2800i	0.374832	−	1.15361i	0.943592	−	0.331110i	$-0.107423\pi$
$884$	−1.76789	+	1.28445i	−0.0594606	+	0.0432006i
$885$	36.4461	−	10.2574i	1.22512	−	0.344798i
$886$	−24.9481	−	18.1258i	−0.838147	−	0.608950i
$887$	−3.20286	+	2.32701i	−0.107542	+	0.0781335i	−0.640256	−	0.768161i	$-0.721172\pi$
$887$	−3.20286	+	2.32701i	−0.107542	+	0.0781335i	0.532715	+	0.846295i	$0.321172\pi$
$888$	−19.3053	+	14.0261i	−0.647844	+	0.470686i
$889$	24.4089	+	17.7341i	0.818647	+	0.594782i
$890$	21.4531	+	7.92780i	0.719111	+	0.265740i
$891$	0.345554	−	0.251059i	0.0115765	−	0.00841081i
$892$	1.59999	−	4.92426i	0.0535716	−	0.164876i
$893$	9.95189			0.333027
$894$	−0.687648	+	2.11636i	−0.0229984	+	0.0707818i
$895$	51.2634	+	18.9439i	1.71355	+	0.633225i
$896$	−1.05060	−	3.23342i	−0.0350982	−	0.108021i
$897$	4.05156	+	12.4694i	0.135278	+	0.416342i
$898$	15.8656	+	11.5271i	0.529443	+	0.384663i
$899$	62.4567			2.08305
$900$	−9.23332	+	22.2225i	−0.307777	+	0.740750i
$901$	8.95055			0.298186
$902$	−6.53770	−	4.74992i	−0.217682	−	0.158155i
$903$	7.67266	+	23.6140i	0.255330	+	0.785825i
$904$	−3.78531	−	11.6500i	−0.125897	−	0.387473i
$905$	−31.3752	−	47.0119i	−1.04295	−	1.56273i
$906$	−12.2381	+	37.6651i	−0.406585	+	1.25134i
$907$	−33.5465			−1.11389			−0.556946	−	0.830549i	$-0.688027\pi$
$907$	−33.5465			−1.11389			−0.556946	+	0.830549i	$0.688027\pi$
$908$	1.32436	−	4.07597i	0.0439505	−	0.135266i
$909$	−24.4087	+	17.7339i	−0.809585	+	0.588198i
$910$	−5.23668	+	6.63524i	−0.173594	+	0.219956i
$911$	23.6116	+	17.1548i	0.782287	+	0.568365i	0.905664	−	0.423995i	$-0.139373\pi$
$911$	23.6116	+	17.1548i	0.782287	+	0.568365i	−0.123378	+	0.992360i	$0.539373\pi$
$912$	2.26133	−	1.64295i	0.0748800	−	0.0544035i
$913$	15.5090	−	11.2679i	0.513272	−	0.372914i
$914$	−30.8237	−	22.3947i	−1.01956	−	0.740752i
$915$	−20.6428	−	30.9307i	−0.682429	−	1.02254i
$916$	18.5641	−	13.4876i	0.613375	−	0.445643i
$917$	6.89369	−	21.2166i	0.227650	−	0.700634i
$918$	9.95894			0.328694
$919$	−8.99489	+	27.6834i	−0.296714	+	0.913192i	0.685926	+	0.727671i	$0.259397\pi$
$919$	−8.99489	+	27.6834i	−0.296714	+	0.913192i	−0.982640	+	0.185521i	$0.940603\pi$
$920$	0.375498	−	9.42579i	0.0123798	−	0.310759i
$921$	6.22643	+	19.1630i	0.205168	+	0.631441i
$922$	−2.04990	−	6.30894i	−0.0675099	−	0.207774i
$923$	9.14463	+	6.64396i	0.300999	+	0.218689i
$924$	14.7669			0.485797
$925$	−32.4283	−	27.7577i	−1.06623	−	0.912667i
$926$	−22.0128			−0.723385
$927$	4.73471	+	3.43997i	0.155508	+	0.112983i
$928$	2.56370	+	7.89024i	0.0841574	+	0.259010i
$929$	3.47997	+	10.7102i	0.114174	+	0.351391i	0.991774	−	0.128002i	$-0.0408565\pi$
$929$	3.47997	+	10.7102i	0.114174	+	0.351391i	−0.877600	+	0.479394i	$0.840857\pi$
$930$	45.2931	−	12.7473i	1.48522	−	0.418000i
$931$	−1.40875	+	4.33568i	−0.0461698	+	0.142096i
$932$	22.3017			0.730517
$933$	0.611018	−	1.88052i	0.0200038	−	0.0615655i
$934$	14.2527	−	10.3552i	0.466362	−	0.338832i
$935$	−0.271831	+	6.82354i	−0.00888983	+	0.223154i
$936$	−4.32932	−	3.14543i	−0.141508	−	0.102812i
$937$	−37.5315	+	27.2682i	−1.22610	+	0.890815i	−0.996592	−	0.0824918i	$-0.973712\pi$
$937$	−37.5315	+	27.2682i	−1.22610	+	0.890815i	−0.229509	+	0.973306i	$0.573712\pi$
$938$	22.6863	−	16.4825i	0.740733	−	0.538174i
$939$	−43.9429	−	31.9264i	−1.43402	−	1.04188i
$940$	−0.885801	+	22.2355i	−0.0288916	+	0.725241i
$941$	−22.1207	+	16.0716i	−0.721113	+	0.523919i	−0.886740	−	0.462269i	$-0.847035\pi$
$941$	−22.1207	+	16.0716i	−0.721113	+	0.523919i	0.165627	+	0.986189i	$0.447035\pi$
$942$	15.8337	−	48.7311i	0.515890	−	1.58774i
$943$	21.9390			0.714431
$944$	1.87195	−	5.76128i	0.0609269	−	0.187514i
$945$	37.0819	−	10.4363i	1.20627	−	0.339493i
$946$	−1.25462	−	3.86133i	−0.0407913	−	0.125543i
$947$	−15.4549	−	47.5654i	−0.502218	−	1.54567i	−0.805398	−	0.592735i	$-0.798048\pi$
$947$	−15.4549	−	47.5654i	−0.502218	−	1.54567i	0.303180	−	0.952933i	$-0.401952\pi$
$948$	−1.54344	−	1.12137i	−0.0501286	−	0.0364206i
$949$	5.49947			0.178520
$950$	3.79848	+	3.25139i	0.123239	+	0.105489i
$951$	−16.0998			−0.522071
$952$	−5.40573	−	3.92749i	−0.175201	−	0.127291i
$953$	−9.57328	−	29.4635i	−0.310109	−	0.954417i	−0.977721	−	0.209908i	$-0.932684\pi$
$953$	−9.57328	−	29.4635i	−0.310109	−	0.954417i	0.667612	−	0.744509i	$-0.267316\pi$
$954$	6.77324	+	20.8459i	0.219292	+	0.674910i
$955$	1.29846	−	32.5942i	0.0420173	−	1.05472i
$956$	0.657943	−	2.02494i	0.0212794	−	0.0654912i
$957$	−36.0345			−1.16483
$958$	−11.7239	+	36.0826i	−0.378784	+	1.16578i
$959$	−37.0809	+	26.9408i	−1.19740	+	0.869965i
$960$	3.46956	+	5.19871i	0.111979	+	0.167787i
$961$	−20.7713	−	15.0912i	−0.670041	−	0.486813i
$962$	7.67943	−	5.57943i	0.247595	−	0.179888i
$963$	−17.2847	+	12.5581i	−0.556993	+	0.404679i
$964$	17.9813	+	13.0641i	0.579137	+	0.420768i
$965$	4.22485	−	5.35317i	0.136003	−	0.172325i
$966$	−32.4337	+	23.5645i	−1.04354	+	0.758175i
$967$	−10.6400	+	32.7464i	−0.342158	+	1.05305i	0.620930	+	0.783866i	$0.286755\pi$
$967$	−10.6400	+	32.7464i	−0.342158	+	1.05305i	−0.963088	+	0.269187i	$0.913245\pi$
$968$	8.58533			0.275943
$969$	1.69757	−	5.22459i	0.0545338	−	0.167838i
$970$	−10.5098	−	15.7477i	−0.337451	−	0.505628i
$971$	9.31735	+	28.6759i	0.299008	+	0.920252i	0.981846	+	0.189682i	$0.0607457\pi$
$971$	9.31735	+	28.6759i	0.299008	+	0.920252i	−0.682838	+	0.730570i	$0.739254\pi$
$972$	−4.93502	−	15.1884i	−0.158291	−	0.487170i
$973$	14.8398	+	10.7817i	0.475741	+	0.345646i
$974$	−13.9135			−0.445817
$975$	5.96233	−	14.3500i	0.190947	−	0.459567i
$976$	−5.94968			−0.190445
$977$	−10.0121	−	7.27420i	−0.320315	−	0.232722i	0.415995	−	0.909367i	$-0.363433\pi$
$977$	−10.0121	−	7.27420i	−0.320315	−	0.232722i	−0.736310	+	0.676645i	$0.763433\pi$
$978$	20.6188	+	63.4582i	0.659317	+	2.02917i
$979$	4.91149	+	15.1160i	0.156972	+	0.483110i
$980$	−9.56180	−	3.53347i	−0.305440	−	0.112873i
$981$	−19.4681	+	59.9167i	−0.621569	+	1.91299i
$982$	−15.4978			−0.494554
$983$	0.275899	−	0.849129i	0.00879980	−	0.0270830i	−0.946560	−	0.322527i	$-0.895468\pi$
$983$	0.275899	−	0.849129i	0.00879980	−	0.0270830i	0.955360	+	0.295444i	$0.0954676\pi$
$984$	−11.7598	+	8.54403i	−0.374890	+	0.272374i
$985$	−28.5403	−	10.5468i	−0.909369	−	0.336048i
$986$	13.1911	+	9.58392i	0.420091	+	0.305214i
$987$	76.5112	−	55.5886i	2.43538	−	1.76941i
$988$	−0.899528	+	0.653546i	−0.0286178	+	0.0207921i
$989$	8.91737	+	6.47885i	0.283556	+	0.206015i
$990$	−16.0978	+	4.53054i	−0.511620	+	0.143990i
$991$	−16.5190	+	12.0018i	−0.524745	+	0.381249i	−0.818388	−	0.574666i	$-0.805132\pi$
$991$	−16.5190	+	12.0018i	−0.524745	+	0.381249i	0.293644	+	0.955915i	$0.405132\pi$
$992$	2.32636	−	7.15980i	0.0738620	−	0.227324i
$993$	29.8687			0.947856
$994$	−10.6805	+	32.8711i	−0.338764	+	1.04261i
$995$	−2.55838	+	3.24164i	−0.0811060	+	0.102767i
$996$	−10.6558	−	32.7950i	−0.337640	−	1.03915i
$997$	6.70580	+	20.6383i	0.212375	+	0.653622i	0.999330	+	0.0366116i	$0.0116564\pi$
$997$	6.70580	+	20.6383i	0.212375	+	0.653622i	−0.786955	+	0.617011i	$0.788344\pi$
$998$	2.06329	+	1.49907i	0.0653123	+	0.0474522i
$999$	−43.2600			−1.36869

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.d.191.11	✓	44
25.11	even	5	inner	950.2.h.d.761.11	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.d.191.11	✓	44	1.1	even	1	trivial
950.2.h.d.761.11	yes	44	25.11	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.863749 + 2.65835i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.38530 + 1.75527i) q^{5} +(-0.863749 + 2.65835i) q^{6} +3.39982 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-3.89370 + 2.82894i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.863749 + 2.65835i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.38530 + 1.75527i) q^{5} +(-0.863749 + 2.65835i) q^{6} +3.39982 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-3.89370 + 2.82894i) q^{9} +(-2.15245 + 0.605783i) q^{10} +(-1.25715 - 0.913371i) q^{11} +(-2.26133 + 1.64295i) q^{12} +(0.899528 - 0.653546i) q^{13} +(2.75052 + 1.99837i) q^{14} +(-5.86265 - 2.16649i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.607327 + 1.86916i) q^{17} -4.81287 q^{18} +(-0.309017 + 0.951057i) q^{19} +(-2.09744 - 0.775087i) q^{20} +(2.93660 + 9.03791i) q^{21} +(-0.480188 - 1.47787i) q^{22} +(3.41299 + 2.47968i) q^{23} -2.79515 q^{24} +(-1.16191 - 4.86312i) q^{25} +1.11188 q^{26} +(-4.09950 - 2.97846i) q^{27} +(1.05060 + 3.23342i) q^{28} +(-2.56370 - 7.89024i) q^{29} +(-3.46956 - 5.19871i) q^{30} +(-2.32636 + 7.15980i) q^{31} -1.00000 q^{32} +(1.34220 - 4.13086i) q^{33} +(-1.59000 + 1.15520i) q^{34} +(-4.70976 + 5.96759i) q^{35} +(-3.89370 - 2.82894i) q^{36} +(6.90672 - 5.01802i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(2.51432 + 1.82676i) q^{39} +(-1.24128 - 1.85990i) q^{40} +(4.20723 - 3.05673i) q^{41} +(-2.93660 + 9.03791i) q^{42} +2.61277 q^{43} +(0.480188 - 1.47787i) q^{44} +(0.428386 - 10.7534i) q^{45} +(1.30365 + 4.01221i) q^{46} +(-3.07530 - 9.46481i) q^{47} +(-2.26133 - 1.64295i) q^{48} +4.55880 q^{49} +(1.91846 - 4.61730i) q^{50} -5.49346 q^{51} +(0.899528 + 0.653546i) q^{52} +(-1.40732 - 4.33127i) q^{53} +(-1.56587 - 4.81925i) q^{54} +(3.34473 - 0.941339i) q^{55} +(-1.05060 + 3.23342i) q^{56} -2.79515 q^{57} +(2.56370 - 7.89024i) q^{58} +(-4.90084 + 3.56067i) q^{59} +(0.248792 - 6.24520i) q^{60} +(4.81340 + 3.49714i) q^{61} +(-6.09049 + 4.42500i) q^{62} +(-13.2379 + 9.61788i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.0989664 + 2.48426i) q^{65} +(3.51392 - 2.55301i) q^{66} +(2.54878 - 7.84433i) q^{67} -1.96535 q^{68} +(-3.64389 + 11.2147i) q^{69} +(-7.31794 + 2.05956i) q^{70} +(3.14148 + 9.66847i) q^{71} +(-1.48726 - 4.57731i) q^{72} +(4.00149 + 2.90725i) q^{73} +8.53717 q^{74} +(11.9243 - 7.28929i) q^{75} -1.00000 q^{76} +(-4.27408 - 3.10530i) q^{77} +(0.960384 + 2.95576i) q^{78} +(0.210916 + 0.649132i) q^{79} +(0.0890083 - 2.23430i) q^{80} +(-0.0849399 + 0.261418i) q^{81} +5.20042 q^{82} +(-3.81223 + 11.7328i) q^{83} +(-7.68811 + 5.58574i) q^{84} +(-2.43955 - 3.65536i) q^{85} +(2.11378 + 1.53575i) q^{86} +(18.7606 - 13.6304i) q^{87} +(1.25715 - 0.913371i) q^{88} +(-8.27484 - 6.01202i) q^{89} +(6.66725 - 8.44787i) q^{90} +(3.05824 - 2.22194i) q^{91} +(-1.30365 + 4.01221i) q^{92} -21.0426 q^{93} +(3.07530 - 9.46481i) q^{94} +(-1.24128 - 1.85990i) q^{95} +(-0.863749 - 2.65835i) q^{96} +(2.61643 + 8.05256i) q^{97} +(3.68815 + 2.67960i) q^{98} +7.47882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Introduction

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