LMFDB - Embedded newform 91.2.f.c.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			29.2
Root			$-0.115680 - 0.200364i$ of defining polynomial
Character	$\chi$	$=$	91.29
Dual form			91.2.f.c.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.115680 - 0.200364i) q^{2} +(1.66113 + 2.87716i) q^{3} +(0.973236 - 1.68569i) q^{4} -2.23136 q^{5} +(0.384320 - 0.665661i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.913059 q^{8} +(-4.01868 + 6.96056i) q^{9} +O(q^{10})$	\(q+(-0.115680 - 0.200364i) q^{2} +(1.66113 + 2.87716i) q^{3} +(0.973236 - 1.68569i) q^{4} -2.23136 q^{5} +(0.384320 - 0.665661i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.913059 q^{8} +(-4.01868 + 6.96056i) q^{9} +(0.258125 + 0.447085i) q^{10} +(-1.66113 - 2.87716i) q^{11} +6.46667 q^{12} +(3.40300 - 1.19146i) q^{13} -0.231361 q^{14} +(-3.70657 - 6.41997i) q^{15} +(-1.84085 - 3.18844i) q^{16} +(0.687890 - 1.19146i) q^{17} +1.85953 q^{18} +(-1.61766 + 2.80186i) q^{19} +(-2.17164 + 3.76139i) q^{20} +3.32225 q^{21} +(-0.384320 + 0.665661i) q^{22} +(-0.419251 - 0.726164i) q^{23} +(-1.51671 - 2.62701i) q^{24} -0.0210289 q^{25} +(-0.632387 - 0.544012i) q^{26} -16.7354 q^{27} +(-0.973236 - 1.68569i) q^{28} +(0.303571 + 0.525800i) q^{29} +(-0.857556 + 1.48533i) q^{30} +1.71511 q^{31} +(-1.33896 + 2.31915i) q^{32} +(5.51868 - 9.55864i) q^{33} -0.318302 q^{34} +(-1.11568 + 1.93242i) q^{35} +(7.82225 + 13.5485i) q^{36} +(-0.776807 - 1.34547i) q^{37} +0.748524 q^{38} +(9.08083 + 7.81180i) q^{39} +2.03736 q^{40} +(4.58892 + 7.94824i) q^{41} +(-0.384320 - 0.665661i) q^{42} +(-0.615680 + 1.06639i) q^{43} -6.46667 q^{44} +(8.96713 - 15.5315i) q^{45} +(-0.0969983 + 0.168006i) q^{46} -1.62817 q^{47} +(6.11577 - 10.5928i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.00243263 + 0.00421343i) q^{50} +4.57069 q^{51} +(1.30348 - 6.89599i) q^{52} +8.39607 q^{53} +(1.93596 + 3.35318i) q^{54} +(3.70657 + 6.41997i) q^{55} +(-0.456530 + 0.790732i) q^{56} -10.7485 q^{57} +(0.0702344 - 0.121650i) q^{58} +(-4.41117 + 7.64037i) q^{59} -14.4295 q^{60} +(-2.73334 + 4.73428i) q^{61} +(-0.198405 - 0.343647i) q^{62} +(4.01868 + 6.96056i) q^{63} -6.74383 q^{64} +(-7.59332 + 2.65858i) q^{65} -2.55361 q^{66} +(5.09287 + 8.82111i) q^{67} +(-1.33896 - 2.31915i) q^{68} +(1.39286 - 2.41250i) q^{69} +0.516249 q^{70} +(2.60714 - 4.51570i) q^{71} +(3.66929 - 6.35540i) q^{72} -3.96355 q^{73} +(-0.179723 + 0.311289i) q^{74} +(-0.0349316 - 0.0605033i) q^{75} +(3.14872 + 5.45375i) q^{76} -3.32225 q^{77} +(0.514731 - 2.72315i) q^{78} +6.45051 q^{79} +(4.10760 + 7.11457i) q^{80} +(-15.7436 - 27.2687i) q^{81} +(1.06170 - 1.83891i) q^{82} -4.64055 q^{83} +(3.23334 - 5.60030i) q^{84} +(-1.53493 + 2.65858i) q^{85} +0.284889 q^{86} +(-1.00854 + 1.74684i) q^{87} +(1.51671 + 2.62701i) q^{88} +(-4.56413 - 7.90530i) q^{89} -4.14929 q^{90} +(0.669665 - 3.54282i) q^{91} -1.63212 q^{92} +(2.84902 + 4.93464i) q^{93} +(0.188347 + 0.326227i) q^{94} +(3.60957 - 6.25197i) q^{95} -8.89672 q^{96} +(7.67944 - 13.3012i) q^{97} +(-0.115680 + 0.200364i) q^{98} +26.7022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 3 * q^15 - 19 * q^16 + 4 * q^17 - 6 * q^18 - q^19 + 2 * q^20 - 2 * q^21 - 5 * q^22 + 2 * q^23 + 3 * q^24 + 10 * q^25 + 12 * q^26 - 52 * q^27 + 5 * q^28 - q^29 + 4 * q^30 - 8 * q^31 + 33 * q^32 + 19 * q^33 + 6 * q^34 - 7 * q^35 + 34 * q^36 + 10 * q^37 - 46 * q^38 + 20 * q^39 - 34 * q^40 + 22 * q^41 - 5 * q^42 - 3 * q^43 - 24 * q^44 + 11 * q^45 - 24 * q^46 + 4 * q^47 - 11 * q^48 - 4 * q^49 - 43 * q^50 + 14 * q^51 + 65 * q^52 + 4 * q^53 - 5 * q^54 + 3 * q^55 - 6 * q^56 - 34 * q^57 + 11 * q^58 + 8 * q^59 - 22 * q^60 - 8 * q^61 + 5 * q^62 + 7 * q^63 + 28 * q^64 + 7 * q^65 + 12 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 22 * q^70 + 14 * q^71 - 5 * q^72 - 16 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 + 2 * q^77 - q^78 - 52 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 + 12 * q^84 - 5 * q^85 + 24 * q^86 - 13 * q^87 - 3 * q^88 + q^89 + 52 * q^90 - 4 * q^91 + 24 * q^92 + 7 * q^93 - 33 * q^94 - 21 * q^95 - 116 * q^96 - 3 * q^97 + q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.115680	−	0.200364i	−0.0817984	−	0.141679i	0.822224	−	0.569164i	$-0.192733\pi$
$2$	−0.115680	−	0.200364i	−0.0817984	−	0.141679i	−0.904022	+	0.427485i	$0.859400\pi$
$3$	1.66113	+	2.87716i	0.959052	+	1.66113i	0.724811	+	0.688948i	$0.241927\pi$
$3$	1.66113	+	2.87716i	0.959052	+	1.66113i	0.234241	+	0.972179i	$0.424740\pi$
$4$	0.973236	−	1.68569i	0.486618	−	0.842847i
$5$	−2.23136			−0.997895			−0.498947	−	0.866632i	$-0.666280\pi$
$5$	−2.23136			−0.997895			−0.498947	+	0.866632i	$0.666280\pi$
$6$	0.384320	−	0.665661i	0.156898	−	0.271755i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−0.913059			−0.322815
$9$	−4.01868	+	6.96056i	−1.33956	+	2.32019i
$10$	0.258125	+	0.447085i	0.0816262	+	0.141381i
$11$	−1.66113	−	2.87716i	−0.500848	−	0.867495i	−1.00000		0.000980003i	$-0.999688\pi$
$11$	−1.66113	−	2.87716i	−0.500848	−	0.867495i	0.499151	−	0.866515i	$-0.333645\pi$
$12$	6.46667			1.86677
$13$	3.40300	−	1.19146i	0.943823	−	0.330452i
$13$	3.40300	−	1.19146i	0.943823	−	0.330452i
$14$	−0.231361			−0.0618338
$15$	−3.70657	−	6.41997i	−0.957033	−	1.65763i
$16$	−1.84085	−	3.18844i	−0.460212	−	0.797111i
$17$	0.687890	−	1.19146i	0.166838	−	0.288972i	−0.770469	−	0.637478i	$-0.779978\pi$
$17$	0.687890	−	1.19146i	0.166838	−	0.288972i	0.937306	+	0.348506i	$0.113311\pi$
$18$	1.85953			0.438296
$19$	−1.61766	+	2.80186i	−0.371116	+	0.642791i	−0.989737	−	0.142898i	$-0.954358\pi$
$19$	−1.61766	+	2.80186i	−0.371116	+	0.642791i	0.618622	+	0.785689i	$0.287691\pi$
$20$	−2.17164	+	3.76139i	−0.485594	+	0.841073i
$21$	3.32225			0.724975
$22$	−0.384320	+	0.665661i	−0.0819372	+	0.141919i
$23$	−0.419251	−	0.726164i	−0.0874199	−	0.151416i	0.819000	−	0.573794i	$-0.194529\pi$
$23$	−0.419251	−	0.726164i	−0.0874199	−	0.151416i	−0.906420	+	0.422378i	$0.861196\pi$
$24$	−1.51671	−	2.62701i	−0.309596	−	0.536237i
$25$	−0.0210289			−0.00420577
$26$	−0.632387	−	0.544012i	−0.124021	−	0.106689i
$27$	−16.7354			−3.22073
$28$	−0.973236	−	1.68569i	−0.183924	−	0.318566i
$29$	0.303571	+	0.525800i	0.0563717	+	0.0976386i	0.892834	−	0.450386i	$-0.148713\pi$
$29$	0.303571	+	0.525800i	0.0563717	+	0.0976386i	−0.836462	+	0.548024i	$0.815380\pi$
$30$	−0.857556	+	1.48533i	−0.156568	+	0.271183i
$31$	1.71511			0.308043			0.154022	−	0.988067i	$-0.450777\pi$
$31$	1.71511			0.308043			0.154022	+	0.988067i	$0.450777\pi$
$32$	−1.33896	+	2.31915i	−0.236697	+	0.409971i
$33$	5.51868	−	9.55864i	0.960679	−	1.66395i
$34$	−0.318302			−0.0545883
$35$	−1.11568	+	1.93242i	−0.188584	+	0.326638i
$36$	7.82225	+	13.5485i	1.30371	+	2.25809i
$37$	−0.776807	−	1.34547i	−0.127706	−	0.221194i	0.795081	−	0.606503i	$-0.207428\pi$
$37$	−0.776807	−	1.34547i	−0.127706	−	0.221194i	−0.922788	+	0.385309i	$0.874095\pi$
$38$	0.748524			0.121427
$39$	9.08083	+	7.81180i	1.45410	+	1.25089i
$40$	2.03736			0.322136
$41$	4.58892	+	7.94824i	0.716668	+	1.24131i	0.962313	+	0.271946i	$0.0876672\pi$
$41$	4.58892	+	7.94824i	0.716668	+	1.24131i	−0.245644	+	0.969360i	$0.578999\pi$
$42$	−0.384320	−	0.665661i	−0.0593018	−	0.102714i
$43$	−0.615680	+	1.06639i	−0.0938904	+	0.162623i	−0.909145	−	0.416480i	$-0.863264\pi$
$43$	−0.615680	+	1.06639i	−0.0938904	+	0.162623i	0.815255	+	0.579103i	$0.196597\pi$
$44$	−6.46667			−0.974888
$45$	8.96713	−	15.5315i	1.33674	−	2.31530i
$46$	−0.0969983	+	0.168006i	−0.0143016	+	0.0247711i
$47$	−1.62817			−0.237493			−0.118747	−	0.992925i	$-0.537888\pi$
$47$	−1.62817			−0.237493			−0.118747	+	0.992925i	$0.537888\pi$
$48$	6.11577	−	10.5928i	0.882735	−	1.52894i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.00243263	+	0.00421343i	0.000344025	+	0.000595870i
$51$	4.57069			0.640025
$52$	1.30348	−	6.89599i	0.180761	−	0.956302i
$53$	8.39607			1.15329			0.576644	−	0.816995i	$-0.304362\pi$
$53$	8.39607			1.15329			0.576644	+	0.816995i	$0.304362\pi$
$54$	1.93596	+	3.35318i	0.263450	+	0.456310i
$55$	3.70657	+	6.41997i	0.499794	+	0.865669i
$56$	−0.456530	+	0.790732i	−0.0610063	+	0.105666i
$57$	−10.7485			−1.42368
$58$	0.0702344	−	0.121650i	0.00922223	−	0.0159734i
$59$	−4.41117	+	7.64037i	−0.574285	+	0.994691i	0.421834	+	0.906673i	$0.361387\pi$
$59$	−4.41117	+	7.64037i	−0.574285	+	0.994691i	−0.996119	+	0.0880181i	$0.971947\pi$
$60$	−14.4295			−1.86284
$61$	−2.73334	+	4.73428i	−0.349968	+	0.606162i	−0.986243	−	0.165300i	$-0.947141\pi$
$61$	−2.73334	+	4.73428i	−0.349968	+	0.606162i	0.636276	+	0.771462i	$0.280474\pi$
$62$	−0.198405	−	0.343647i	−0.0251974	−	0.0436432i
$63$	4.01868	+	6.96056i	0.506306	+	0.876948i
$64$	−6.74383			−0.842979
$65$	−7.59332	+	2.65858i	−0.941836	+	0.329756i
$66$	−2.55361			−0.314328
$67$	5.09287	+	8.82111i	0.622193	+	1.07767i	0.989077	+	0.147403i	$0.0470913\pi$
$67$	5.09287	+	8.82111i	0.622193	+	1.07767i	−0.366884	+	0.930267i	$0.619575\pi$
$68$	−1.33896	−	2.31915i	−0.162373	−	0.281238i
$69$	1.39286	−	2.41250i	0.167680	−	0.290431i
$70$	0.516249			0.0617036
$71$	2.60714	−	4.51570i	0.309411	−	0.535915i	−0.668823	−	0.743422i	$-0.733202\pi$
$71$	2.60714	−	4.51570i	0.309411	−	0.535915i	0.978234	+	0.207507i	$0.0665349\pi$
$72$	3.66929	−	6.35540i	0.432430	−	0.748992i
$73$	−3.96355			−0.463898			−0.231949	−	0.972728i	$-0.574510\pi$
$73$	−3.96355			−0.463898			−0.231949	+	0.972728i	$0.574510\pi$
$74$	−0.179723	+	0.311289i	−0.0208923	+	0.0361866i
$75$	−0.0349316	−	0.0605033i	−0.00403355	−	0.00698632i
$76$	3.14872	+	5.45375i	0.361183	+	0.625588i
$77$	−3.32225			−0.378606
$78$	0.514731	−	2.72315i	0.0582818	−	0.308336i
$79$	6.45051			0.725739			0.362869	−	0.931840i	$-0.381797\pi$
$79$	6.45051			0.725739			0.362869	+	0.931840i	$0.381797\pi$
$80$	4.10760	+	7.11457i	0.459243	+	0.795433i
$81$	−15.7436	−	27.2687i	−1.74929	−	3.02985i
$82$	1.06170	−	1.83891i	0.117245	−	0.203074i
$83$	−4.64055			−0.509367			−0.254684	−	0.967024i	$-0.581971\pi$
$83$	−4.64055			−0.509367			−0.254684	+	0.967024i	$0.581971\pi$
$84$	3.23334	−	5.60030i	0.352786	−	0.611043i
$85$	−1.53493	+	2.65858i	−0.166487	+	0.288363i
$86$	0.284889			0.0307203
$87$	−1.00854	+	1.74684i	−0.108127	+	0.187281i
$88$	1.51671	+	2.62701i	0.161681	+	0.280041i
$89$	−4.56413	−	7.90530i	−0.483797	−	0.837960i	0.516030	−	0.856570i	$-0.327409\pi$
$89$	−4.56413	−	7.90530i	−0.483797	−	0.837960i	−0.999827	+	0.0186101i	$0.994076\pi$
$90$	−4.14929			−0.437373
$91$	0.669665	−	3.54282i	0.0702000	−	0.371388i
$92$	−1.63212			−0.170160
$93$	2.84902	+	4.93464i	0.295429	+	0.511699i
$94$	0.188347	+	0.326227i	0.0194266	+	0.0336478i
$95$	3.60957	−	6.25197i	0.370334	−	0.641438i
$96$	−8.89672			−0.908018
$97$	7.67944	−	13.3012i	0.779729	−	1.35053i	−0.152369	−	0.988324i	$-0.548690\pi$
$97$	7.67944	−	13.3012i	0.779729	−	1.35053i	0.932098	−	0.362206i	$-0.117976\pi$
$98$	−0.115680	+	0.200364i	−0.0116855	+	0.0202399i
$99$	26.7022			2.68367
$100$	−0.0204660	+	0.0354482i	−0.00204660	+	0.00354482i
$101$	3.97521	+	6.88527i	0.395548	+	0.685110i	0.993171	−	0.116668i	$-0.0372212\pi$
$101$	3.97521	+	6.88527i	0.395548	+	0.685110i	−0.597623	+	0.801777i	$0.703888\pi$
$102$	−0.528739	−	0.915804i	−0.0523530	−	0.0906781i
$103$	0.694825			0.0684631			0.0342316	−	0.999414i	$-0.489102\pi$
$103$	0.694825			0.0684631			0.0342316	+	0.999414i	$0.489102\pi$
$104$	−3.10714	+	1.08787i	−0.304680	+	0.106675i
$105$	−7.41314			−0.723449
$106$	−0.971261	−	1.68227i	−0.0943372	−	0.163397i
$107$	−4.47324	−	7.74787i	−0.432444	−	0.749015i	0.564639	−	0.825338i	$-0.309015\pi$
$107$	−4.47324	−	7.74787i	−0.432444	−	0.749015i	−0.997083	+	0.0763228i	$0.975682\pi$
$108$	−16.2875	+	28.2108i	−1.56726	+	2.71458i
$109$	−2.27268			−0.217683			−0.108841	−	0.994059i	$-0.534714\pi$
$109$	−2.27268			−0.217683			−0.108841	+	0.994059i	$0.534714\pi$
$110$	0.857556	−	1.48533i	0.0817647	−	0.141621i
$111$	2.58075	−	4.46999i	0.244954	−	0.424272i
$112$	−3.68170			−0.347888
$113$	4.75239	−	8.23138i	0.447067	−	0.774343i	−0.551126	−	0.834422i	$-0.685802\pi$
$113$	4.75239	−	8.23138i	0.447067	−	0.774343i	0.998194	+	0.0600786i	$0.0191351\pi$
$114$	1.24339	+	2.15362i	0.116454	+	0.201705i
$115$	0.935501	+	1.62033i	0.0872359	+	0.151097i
$116$	1.18178			0.109726
$117$	−5.38234	+	28.4749i	−0.497598	+	2.63251i
$118$	2.04114			0.187902
$119$	−0.687890	−	1.19146i	−0.0630588	−	0.109221i
$120$	3.38432	+	5.86181i	0.308945	+	0.535108i
$121$	−0.0186821	+	0.0323584i	−0.00169837	+	0.00294167i
$122$	1.26477			0.114507
$123$	−15.2455	+	26.4061i	−1.37464	+	2.38095i
$124$	1.66921	−	2.89115i	0.149899	−	0.259633i
$125$	11.2037			1.00209
$126$	0.929766	−	1.61040i	0.0828301	−	0.143466i
$127$	−9.21672	−	15.9638i	−0.817851	−	1.41656i	−0.907262	−	0.420565i	$-0.861832\pi$
$127$	−9.21672	−	15.9638i	−0.817851	−	1.41656i	0.0894111	−	0.995995i	$-0.471502\pi$
$128$	3.45805	+	5.98951i	0.305651	+	0.529403i
$129$	−4.09089			−0.360183
$130$	1.41108	+	1.21389i	0.123760	+	0.106465i
$131$	−1.74835			−0.152754			−0.0763771	−	0.997079i	$-0.524335\pi$
$131$	−1.74835			−0.152754			−0.0763771	+	0.997079i	$0.524335\pi$
$132$	−10.7420	−	18.6056i	−0.934968	−	1.61941i
$133$	1.61766	+	2.80186i	0.140269	+	0.242952i
$134$	1.17829	−	2.04086i	0.101789	−	0.176303i
$135$	37.3427			3.21395
$136$	−0.628085	+	1.08787i	−0.0538578	+	0.0932845i
$137$	9.00160	−	15.5912i	0.769059	−	1.33205i	−0.169015	−	0.985614i	$-0.554059\pi$
$137$	9.00160	−	15.5912i	0.769059	−	1.33205i	0.938074	−	0.346436i	$-0.112608\pi$
$138$	−0.644506			−0.0548640
$139$	−6.95896	+	12.0533i	−0.590251	+	1.02235i	0.403947	+	0.914782i	$0.367638\pi$
$139$	−6.95896	+	12.0533i	−0.590251	+	1.02235i	−0.994198	+	0.107563i	$0.965695\pi$
$140$	2.17164	+	3.76139i	0.183537	+	0.317896i
$141$	−2.70460	−	4.68450i	−0.227768	−	0.394506i
$142$	−1.20638			−0.101237
$143$	−9.08083	−	7.81180i	−0.759378	−	0.653255i
$144$	29.5911			2.46593
$145$	−0.677376	−	1.17325i	−0.0562530	−	0.0974331i
$146$	0.458505	+	0.794154i	0.0379462	+	0.0657247i
$147$	1.66113	−	2.87716i	0.137007	−	0.237304i
$148$	−3.02407			−0.248577
$149$	7.96515	−	13.7961i	0.652531	−	1.13022i	−0.329976	−	0.943989i	$-0.607041\pi$
$149$	7.96515	−	13.7961i	0.652531	−	1.13022i	0.982507	−	0.186227i	$-0.0596261\pi$
$150$	−0.00808180	+	0.0139981i	−0.000659876	+	0.00114294i
$151$	−13.9497			−1.13521			−0.567604	−	0.823301i	$-0.692130\pi$
$151$	−13.9497			−1.13521			−0.567604	+	0.823301i	$0.692130\pi$
$152$	1.47702	−	2.55827i	0.119802	−	0.207503i
$153$	5.52883	+	9.57621i	0.446979	+	0.774190i
$154$	0.384320	+	0.665661i	0.0309694	+	0.0536405i
$155$	−3.82703			−0.307395
$156$	22.0061	−	7.70479i	1.76190	−	0.616877i
$157$	−12.9747			−1.03549			−0.517745	−	0.855535i	$-0.673229\pi$
$157$	−12.9747			−1.03549			−0.517745	+	0.855535i	$0.673229\pi$
$158$	−0.746198	−	1.29245i	−0.0593643	−	0.102822i
$159$	13.9469	+	24.1568i	1.10606	+	1.91576i
$160$	2.98770	−	5.17485i	0.236199	−	0.409108i
$161$	−0.838502			−0.0660832
$162$	−3.64244	+	6.30890i	−0.286177	+	0.495674i
$163$	−9.20423	+	15.9422i	−0.720931	+	1.24869i	0.239697	+	0.970848i	$0.422952\pi$
$163$	−9.20423	+	15.9422i	−0.720931	+	1.24869i	−0.960627	+	0.277841i	$0.910381\pi$
$164$	17.8644			1.39498
$165$	−12.3142	+	21.3288i	−0.958657	+	1.66044i
$166$	0.536821	+	0.929802i	0.0416654	+	0.0721666i
$167$	9.24967	+	16.0209i	0.715761	+	1.23973i	0.962665	+	0.270695i	$0.0872534\pi$
$167$	9.24967	+	16.0209i	0.715761	+	1.23973i	−0.246904	+	0.969040i	$0.579413\pi$
$168$	−3.03341			−0.234033
$169$	10.1608	−	8.10909i	0.781603	−	0.623776i
$170$	0.710246			0.0544734
$171$	−13.0017	−	22.5196i	−0.994264	−	1.72212i
$172$	1.19840	+	2.07570i	0.0913775	+	0.158270i
$173$	8.59906	−	14.8940i	0.653774	−	1.13237i	−0.328425	−	0.944530i	$-0.606518\pi$
$173$	8.59906	−	14.8940i	0.653774	−	1.13237i	0.982200	−	0.187840i	$-0.0601488\pi$
$174$	0.466673			0.0353784
$175$	−0.0105144	+	0.0182115i	−0.000794816	+	0.00137666i
$176$	−6.11577	+	10.5928i	−0.460993	+	0.798464i
$177$	−29.3100			−2.20308
$178$	−1.05596	+	1.82898i	−0.0791476	+	0.137088i
$179$	−7.24431	−	12.5475i	−0.541465	−	0.937845i	−0.998820	−	0.0485608i	$-0.984537\pi$
$179$	−7.24431	−	12.5475i	−0.541465	−	0.937845i	0.457355	−	0.889284i	$-0.348797\pi$
$180$	−17.4543	−	30.2317i	−1.30096	−	2.25334i
$181$	6.85484			0.509516			0.254758	−	0.967005i	$-0.418004\pi$
$181$	6.85484			0.509516			0.254758	+	0.967005i	$0.418004\pi$
$182$	−0.787321	+	0.275657i	−0.0583601	+	0.0204331i
$183$	−18.1617			−1.34255
$184$	0.382801	+	0.663031i	0.0282205	+	0.0488793i
$185$	1.73334	+	3.00223i	0.127437	+	0.220728i
$186$	0.659151	−	1.14168i	0.0483313	−	0.0837122i
$187$	−4.57069			−0.334242
$188$	−1.58459	+	2.74460i	−0.115568	+	0.200170i
$189$	−8.36770	+	14.4933i	−0.608661	+	1.05423i
$190$	−1.67023			−0.121171
$191$	1.42581	−	2.46958i	0.103168	−	0.178693i	−0.809820	−	0.586678i	$-0.800435\pi$
$191$	1.42581	−	2.46958i	0.103168	−	0.178693i	0.912988	+	0.407986i	$0.133769\pi$
$192$	−11.2024	−	19.4030i	−0.808460	−	1.40029i
$193$	5.02525	+	8.70398i	0.361725	+	0.626526i	0.988245	−	0.152879i	$-0.0488546\pi$
$193$	5.02525	+	8.70398i	0.361725	+	0.626526i	−0.626520	+	0.779406i	$0.715521\pi$
$194$	−3.55344			−0.255122
$195$	−20.2626	−	17.4309i	−1.45104	−	1.24826i
$196$	−1.94647			−0.139034
$197$	12.7085	+	22.0119i	0.905447	+	1.56828i	0.820317	+	0.571910i	$0.193797\pi$
$197$	12.7085	+	22.0119i	0.905447	+	1.56828i	0.0851299	+	0.996370i	$0.472869\pi$
$198$	−3.08892	−	5.35016i	−0.219520	−	0.380219i
$199$	6.22328	−	10.7790i	0.441157	−	0.764106i	−0.556619	−	0.830768i	$-0.687902\pi$
$199$	6.22328	−	10.7790i	0.441157	−	0.764106i	0.997776	+	0.0666623i	$0.0212350\pi$
$200$	0.0192006			0.00135769
$201$	−16.9198	+	29.3059i	−1.19343	+	2.06708i
$202$	0.919708	−	1.59298i	0.0647104	−	0.112082i
$203$	0.607142			0.0426130
$204$	4.44836	−	7.70479i	0.311448	−	0.539443i
$205$	−10.2395	−	17.7354i	−0.715160	−	1.23869i
$206$	−0.0803776	−	0.139218i	−0.00560017	−	0.00969979i
$207$	6.73935			0.468417
$208$	−10.0633	−	8.65698i	−0.697766	−	0.600254i
$209$	10.7485			0.743491
$210$	0.857556	+	1.48533i	0.0591770	+	0.102498i
$211$	12.1961	+	21.1243i	0.839617	+	1.45426i	0.890215	+	0.455540i	$0.150554\pi$
$211$	12.1961	+	21.1243i	0.839617	+	1.45426i	−0.0505979	+	0.998719i	$0.516113\pi$
$212$	8.17136	−	14.1532i	0.561211	−	0.972046i
$213$	17.3232			1.18696
$214$	−1.03493	+	1.79255i	−0.0707465	+	0.122536i
$215$	1.37381	−	2.37950i	0.0936927	−	0.162281i
$216$	15.2804			1.03970
$217$	0.857556	−	1.48533i	0.0582147	−	0.100831i
$218$	0.262904	+	0.455363i	0.0178061	+	0.0308411i
$219$	−6.58396	−	11.4037i	−0.444903	−	0.770594i
$220$	14.4295			0.972835
$221$	0.921313	−	4.87414i	0.0619742	−	0.327870i
$222$	−1.19417			−0.0801473
$223$	−11.3247	−	19.6149i	−0.758357	−	1.31351i	−0.943688	−	0.330837i	$-0.892669\pi$
$223$	−11.3247	−	19.6149i	−0.758357	−	1.31351i	0.185331	−	0.982676i	$-0.440664\pi$
$224$	1.33896	+	2.31915i	0.0894630	+	0.154954i
$225$	0.0845083	−	0.146373i	0.00563389	−	0.00975818i
$226$	−2.19903			−0.146278
$227$	−0.642530	+	1.11289i	−0.0426462	+	0.0738654i	−0.886561	−	0.462612i	$-0.846912\pi$
$227$	−0.642530	+	1.11289i	−0.0426462	+	0.0738654i	0.843914	+	0.536478i	$0.180246\pi$
$228$	−10.4609	+	18.1187i	−0.692787	+	1.19994i
$229$	−4.64451			−0.306918			−0.153459	−	0.988155i	$-0.549041\pi$
$229$	−4.64451			−0.306918			−0.153459	+	0.988155i	$0.549041\pi$
$230$	0.216438	−	0.374882i	0.0142715	−	0.0247190i
$231$	−5.51868	−	9.55864i	−0.363103	−	0.628912i
$232$	−0.277178	−	0.480086i	−0.0181976	−	0.0315192i
$233$	11.8877			0.778790			0.389395	−	0.921071i	$-0.372684\pi$
$233$	11.8877			0.778790			0.389395	+	0.921071i	$0.372684\pi$
$234$	6.32799	−	2.21556i	0.413674	−	0.144836i
$235$	3.63304			0.236993
$236$	8.58622	+	14.8718i	0.558915	+	0.968070i
$237$	10.7151	+	18.5591i	0.696021	+	1.20554i
$238$	−0.159151	+	0.275657i	−0.0103162	+	0.0178682i
$239$	−4.17783			−0.270242			−0.135121	−	0.990829i	$-0.543142\pi$
$239$	−4.17783			−0.270242			−0.135121	+	0.990829i	$0.543142\pi$
$240$	−13.6465	+	23.6364i	−0.880877	+	1.52572i
$241$	−2.01671	+	3.49304i	−0.129907	+	0.225006i	−0.923641	−	0.383260i	$-0.874801\pi$
$241$	−2.01671	+	3.49304i	−0.129907	+	0.225006i	0.793733	+	0.608266i	$0.208135\pi$
$242$	0.00864462			0.000555697
$243$	27.2010	−	47.1135i	1.74495	−	3.02233i
$244$	5.32036	+	9.21514i	0.340601	+	0.589939i
$245$	1.11568	+	1.93242i	0.0712782	+	0.123457i
$246$	7.05444			0.449775
$247$	−2.16658	+	11.4621i	−0.137856	+	0.729317i
$248$	−1.56600			−0.0994410
$249$	−7.70855	−	13.3516i	−0.488509	−	0.846123i
$250$	−1.29605	−	2.24483i	−0.0819695	−	0.141975i
$251$	−13.9343	+	24.1348i	−0.879523	+	1.52338i	−0.0276571	+	0.999617i	$0.508805\pi$
$251$	−13.9343	+	24.1348i	−0.879523	+	1.52338i	−0.851866	+	0.523760i	$0.824529\pi$
$252$	15.6445			0.985511
$253$	−1.39286	+	2.41250i	−0.0875683	+	0.151673i
$254$	−2.13239	+	3.69340i	−0.133798	+	0.231745i
$255$	−10.1989			−0.638678
$256$	−5.94377	+	10.2949i	−0.371486	+	0.643432i
$257$	3.57032	+	6.18398i	0.222710	+	0.385746i	0.955630	−	0.294569i	$-0.0951762\pi$
$257$	3.57032	+	6.18398i	0.222710	+	0.385746i	−0.732920	+	0.680315i	$0.761843\pi$
$258$	0.473236	+	0.819669i	0.0294624	+	0.0510304i
$259$	−1.55361			−0.0965369
$260$	−2.90855	+	15.3874i	−0.180380	+	0.954289i
$261$	−4.87982			−0.302053
$262$	0.202250	+	0.350308i	0.0124951	+	0.0216421i
$263$	−10.6596	−	18.4630i	−0.657300	−	1.13848i	−0.981312	−	0.192423i	$-0.938365\pi$
$263$	−10.6596	−	18.4630i	−0.657300	−	1.13848i	0.324012	−	0.946053i	$-0.394968\pi$
$264$	−5.03888	+	8.72760i	−0.310122	+	0.537147i
$265$	−18.7347			−1.15086
$266$	0.374262	−	0.648241i	0.0229475	−	0.0397462i
$267$	15.1632	−	26.2634i	0.927972	−	1.60729i
$268$	19.8263			1.21108
$269$	−1.39438	+	2.41513i	−0.0850167	+	0.147253i	−0.905398	−	0.424563i	$-0.860428\pi$
$269$	−1.39438	+	2.41513i	−0.0850167	+	0.147253i	0.820382	+	0.571816i	$0.193761\pi$
$270$	−4.31982	−	7.48215i	−0.262896	−	0.455349i
$271$	7.73737	+	13.4015i	0.470012	+	0.814085i	0.999412	−	0.0342877i	$-0.0109163\pi$
$271$	7.73737	+	13.4015i	0.470012	+	0.814085i	−0.529400	+	0.848372i	$0.677583\pi$
$272$	−5.06521			−0.307123
$273$	11.3056	−	3.95833i	0.684248	−	0.239569i
$274$	−4.16524			−0.251631
$275$	0.0349316	+	0.0605033i	0.00210645	+	0.00364849i
$276$	−2.71116	−	4.69587i	−0.163193	−	0.282658i
$277$	−2.76477	+	4.78873i	−0.166119	+	0.287727i	−0.937052	−	0.349189i	$-0.886457\pi$
$277$	−2.76477	+	4.78873i	−0.166119	+	0.287727i	0.770933	+	0.636916i	$0.219790\pi$
$278$	3.22006			0.193127
$279$	−6.89249	+	11.9381i	−0.412642	+	0.714718i
$280$	1.01868	−	1.76441i	0.0608779	−	0.105444i
$281$	−31.4871			−1.87836			−0.939182	−	0.343419i	$-0.888415\pi$
$281$	−31.4871			−1.87836			−0.939182	+	0.343419i	$0.888415\pi$
$282$	−0.625738	+	1.08381i	−0.0372621	+	0.0645399i
$283$	3.67559	+	6.36631i	0.218491	+	0.378438i	0.954347	−	0.298700i	$-0.0965531\pi$
$283$	3.67559	+	6.36631i	0.218491	+	0.378438i	−0.735856	+	0.677138i	$0.763220\pi$
$284$	−5.07473	−	8.78969i	−0.301130	−	0.521572i
$285$	23.9838			1.42068
$286$	−0.514731	+	2.72315i	−0.0304367	+	0.161023i
$287$	9.17783			0.541750
$288$	−10.7617	−	18.6398i	−0.634140	−	1.09836i
$289$	7.55361	+	13.0832i	0.444330	+	0.769603i
$290$	−0.156718	+	0.271444i	−0.00920281	+	0.0159397i
$291$	51.0261			2.99120
$292$	−3.85747	+	6.68133i	−0.225741	+	0.390995i
$293$	6.76675	−	11.7204i	0.395318	−	0.684710i	−0.597824	−	0.801627i	$-0.703968\pi$
$293$	6.76675	−	11.7204i	0.395318	−	0.684710i	0.993142	+	0.116917i	$0.0373012\pi$
$294$	−0.768639			−0.0448279
$295$	9.84291	−	17.0484i	0.573076	−	0.992597i
$296$	0.709271	+	1.22849i	0.0412255	+	0.0714047i
$297$	27.7996	+	48.1503i	1.61310	+	2.79397i
$298$	−3.68565			−0.213504
$299$	−2.29191	−	1.97162i	−0.132545	−	0.114022i
$300$	−0.135987			−0.00785120
$301$	0.615680	+	1.06639i	0.0354872	+	0.0614657i
$302$	1.61370	+	2.79502i	0.0928583	+	0.160835i
$303$	−13.2067	+	22.8746i	−0.758703	+	1.31411i
$304$	11.9114			0.683168
$305$	6.09906	−	10.5639i	0.349231	−	0.604886i
$306$	1.27915	−	2.21556i	0.0731243	−	0.126655i
$307$	−3.30609			−0.188688			−0.0943442	−	0.995540i	$-0.530075\pi$
$307$	−3.30609			−0.188688			−0.0943442	+	0.995540i	$0.530075\pi$
$308$	−3.23334	+	5.60030i	−0.184236	+	0.319107i
$309$	1.15419	+	1.99912i	0.0656597	+	0.113726i
$310$	0.442713	+	0.766801i	0.0251444	+	0.0435514i
$311$	−34.3063			−1.94533			−0.972665	−	0.232214i	$-0.925403\pi$
$311$	−34.3063			−1.94533			−0.972665	+	0.232214i	$0.925403\pi$
$312$	−8.29134	−	7.13263i	−0.469405	−	0.403806i
$313$	7.21428			0.407775			0.203888	−	0.978994i	$-0.434642\pi$
$313$	7.21428			0.407775			0.203888	+	0.978994i	$0.434642\pi$
$314$	1.50091	+	2.59966i	0.0847015	+	0.146707i
$315$	−8.96713	−	15.5315i	−0.505241	−	0.875102i
$316$	6.27787	−	10.8736i	0.353158	−	0.611687i
$317$	−8.04040			−0.451594			−0.225797	−	0.974174i	$-0.572499\pi$
$317$	−8.04040			−0.451594			−0.225797	+	0.974174i	$0.572499\pi$
$318$	3.22677	−	5.58893i	0.180948	−	0.313412i
$319$	1.00854	−	1.74684i	0.0564673	−	0.0978043i
$320$	15.0479			0.841204
$321$	14.8612	−	25.7404i	0.829472	−	1.43669i
$322$	0.0969983	+	0.168006i	0.00540550	+	0.00936261i
$323$	2.22554	+	3.85475i	0.123832	+	0.214484i
$324$	−61.2888			−3.40493
$325$	−0.0715613	+	0.0250551i	−0.00396950	+	0.00138981i
$326$	4.25899			0.235884
$327$	−3.77520	−	6.53884i	−0.208769	−	0.361599i
$328$	−4.18995	−	7.25721i	−0.231351	−	0.400712i
$329$	−0.814085	+	1.41004i	−0.0448820	+	0.0777379i
$330$	5.69803			0.313666
$331$	−0.446843	+	0.773955i	−0.0245607	+	0.0425404i	−0.878045	−	0.478579i	$-0.841152\pi$
$331$	−0.446843	+	0.773955i	−0.0245607	+	0.0425404i	0.853484	+	0.521119i	$0.174485\pi$
$332$	−4.51636	+	7.82256i	−0.247867	+	0.429319i
$333$	12.4870			0.684281
$334$	2.14001	−	3.70661i	0.117096	−	0.202817i
$335$	−11.3640	−	19.6831i	−0.620883	−	1.07540i
$336$	−6.11577	−	10.5928i	−0.333642	−	0.577886i
$337$	15.0717			0.821007			0.410504	−	0.911859i	$-0.365353\pi$
$337$	15.0717			0.821007			0.410504	+	0.911859i	$0.365353\pi$
$338$	−2.80018	−	1.09781i	−0.152310	−	0.0597129i
$339$	31.5773			1.71504
$340$	2.98770	+	5.17485i	0.162031	+	0.280646i
$341$	−2.84902	−	4.93464i	−0.154283	−	0.267226i
$342$	−3.00808	+	5.21015i	−0.162658	+	0.281733i
$343$	−1.00000			−0.0539949
$344$	0.562153	−	0.973677i	0.0303092	−	0.0524971i
$345$	−3.10797	+	5.38316i	−0.167327	+	0.289820i
$346$	−3.97897			−0.213911
$347$	8.20818	−	14.2170i	0.440638	−	0.763207i	−0.557099	−	0.830446i	$-0.688086\pi$
$347$	8.20818	−	14.2170i	0.440638	−	0.763207i	0.997737	+	0.0672387i	$0.0214189\pi$
$348$	1.96309	+	3.40018i	0.105233	+	0.182269i
$349$	−17.1861	−	29.7672i	−0.919950	−	1.59340i	−0.799488	−	0.600682i	$-0.794896\pi$
$349$	−17.1861	−	29.7672i	−0.919950	−	1.59340i	−0.120462	−	0.992718i	$-0.538438\pi$
$350$	0.00486525			0.000260059
$351$	−56.9506	+	19.9396i	−3.03980	+	1.06430i
$352$	8.89672			0.474197
$353$	11.9581	+	20.7121i	0.636467	+	1.10239i	0.986202	+	0.165545i	$0.0529383\pi$
$353$	11.9581	+	20.7121i	0.636467	+	1.10239i	−0.349735	+	0.936849i	$0.613728\pi$
$354$	3.39060	+	5.87269i	0.180208	+	0.312130i
$355$	−5.81747	+	10.0762i	−0.308759	+	0.534787i
$356$	−17.7679			−0.941697
$357$	2.28535	−	3.95833i	0.120953	−	0.209497i
$358$	−1.67605	+	2.90300i	−0.0885819	+	0.153428i
$359$	−6.17875			−0.326102			−0.163051	−	0.986618i	$-0.552133\pi$
$359$	−6.17875			−0.326102			−0.163051	+	0.986618i	$0.552133\pi$
$360$	−8.18752	+	14.1812i	−0.431520	+	0.747415i
$361$	4.26638	+	7.38958i	0.224546	+	0.388925i
$362$	−0.792970	−	1.37347i	−0.0416776	−	0.0721877i
$363$	−0.124133			−0.00651531
$364$	−5.32036	−	4.57685i	−0.278863	−	0.239892i
$365$	8.84411			0.462922
$366$	2.10095	+	3.63895i	0.109818	+	0.190211i
$367$	−9.92798	−	17.1958i	−0.518236	−	0.897612i	−0.999776	−	0.0211872i	$-0.993255\pi$
$367$	−9.92798	−	17.1958i	−0.518236	−	0.897612i	0.481539	−	0.876425i	$-0.340078\pi$
$368$	−1.54356	+	2.67352i	−0.0804634	+	0.139367i
$369$	−73.7656			−3.84008
$370$	0.401026	−	0.694598i	0.0208484	−	0.0361104i
$371$	4.19803	−	7.27121i	0.217951	−	0.377502i
$372$	11.0911			0.575045
$373$	−15.0975	+	26.1497i	−0.781721	+	1.35398i	0.149217	+	0.988804i	$0.452325\pi$
$373$	−15.0975	+	26.1497i	−0.781721	+	1.35398i	−0.930938	+	0.365176i	$0.881009\pi$
$374$	0.528739	+	0.915804i	0.0273405	+	0.0473551i
$375$	18.6108	+	32.2349i	0.961058	+	1.66460i
$376$	1.48662			0.0766664
$377$	1.65952	+	1.42761i	0.0854697	+	0.0735254i
$378$	3.87192			0.199150
$379$	2.16121	+	3.74333i	0.111014	+	0.192282i	0.916179	−	0.400768i	$-0.131257\pi$
$379$	2.16121	+	3.74333i	0.111014	+	0.192282i	−0.805165	+	0.593050i	$0.797923\pi$
$380$	−7.02594	−	12.1693i	−0.360423	−	0.624271i
$381$	30.6203	−	53.0358i	1.56872	−	2.71711i
$382$	−0.659755			−0.0337560
$383$	8.67407	−	15.0239i	0.443224	−	0.767687i	−0.554702	−	0.832049i	$-0.687168\pi$
$383$	8.67407	−	15.0239i	0.443224	−	0.767687i	0.997927	+	0.0643617i	$0.0205011\pi$
$384$	−11.4885	+	19.8987i	−0.586271	+	1.01545i
$385$	7.41314			0.377809
$386$	1.16264	−	2.01376i	0.0591771	−	0.102498i
$387$	−4.94845	−	8.57096i	−0.251544	−	0.435687i
$388$	−14.9478	−	25.8904i	−0.758860	−	1.31438i
$389$	−25.3474			−1.28516			−0.642582	−	0.766217i	$-0.722137\pi$
$389$	−25.3474			−1.28516			−0.642582	+	0.766217i	$0.722137\pi$
$390$	−1.14855	+	6.07632i	−0.0581591	+	0.307687i
$391$	−1.15360			−0.0583398
$392$	0.456530	+	0.790732i	0.0230582	+	0.0399380i
$393$	−2.90423	−	5.03028i	−0.146499	−	0.253744i
$394$	2.94026	−	5.09268i	0.148128	−	0.256566i
$395$	−14.3934			−0.724211
$396$	25.9875	−	45.0117i	1.30592	−	2.26192i
$397$	13.5375	−	23.4476i	0.679425	−	1.17680i	−0.295729	−	0.955272i	$-0.595563\pi$
$397$	13.5375	−	23.4476i	0.679425	−	1.17680i	0.975154	−	0.221527i	$-0.0711041\pi$
$398$	−2.87965			−0.144344
$399$	−5.37426	+	9.30850i	−0.269050	+	0.466008i
$400$	0.0387110	+	0.0670494i	0.00193555	+	0.00335247i
$401$	14.6429	+	25.3622i	0.731232	+	1.26653i	0.956357	+	0.292201i	$0.0943875\pi$
$401$	14.6429	+	25.3622i	0.731232	+	1.26653i	−0.225125	+	0.974330i	$0.572279\pi$
$402$	7.82916			0.390483
$403$	5.83653	−	2.04349i	0.290738	−	0.101793i
$404$	15.4753			0.769924
$405$	35.1296	+	60.8462i	1.74560	+	3.02347i
$406$	−0.0702344	−	0.121650i	−0.00348567	−	0.00603736i
$407$	−2.58075	+	4.46999i	−0.127923	+	0.221569i
$408$	−4.17331			−0.206610
$409$	−11.6856	+	20.2401i	−0.577817	+	1.00081i	0.417912	+	0.908487i	$0.362762\pi$
$409$	−11.6856	+	20.2401i	−0.577817	+	1.00081i	−0.995729	+	0.0923213i	$0.970571\pi$
$410$	−2.36903	+	4.10327i	−0.116998	+	0.202646i
$411$	59.8112			2.95027
$412$	0.676229	−	1.17126i	0.0333154	−	0.0577040i
$413$	4.41117	+	7.64037i	0.217059	+	0.375958i
$414$	−0.779611	−	1.35033i	−0.0383158	−	0.0663649i
$415$	10.3548			0.508295
$416$	−1.79331	+	9.48738i	−0.0879242	+	0.465157i
$417$	−46.2389			−2.26433
$418$	−1.24339	−	2.15362i	−0.0608164	−	0.105337i
$419$	−7.30320	−	12.6495i	−0.356785	−	0.617969i	0.630637	−	0.776078i	$-0.282794\pi$
$419$	−7.30320	−	12.6495i	−0.356785	−	0.617969i	−0.987422	+	0.158109i	$0.949460\pi$
$420$	−7.21474	+	12.4963i	−0.352043	+	0.609757i
$421$	10.2728			0.500668			0.250334	−	0.968160i	$-0.419460\pi$
$421$	10.2728			0.500668			0.250334	+	0.968160i	$0.419460\pi$
$422$	2.82171	−	4.88734i	0.137359	−	0.237912i
$423$	6.54310	−	11.3330i	0.318136	−	0.551028i
$424$	−7.66611			−0.372299
$425$	−0.0144656	+	0.0250551i	−0.000701682	+	0.00121535i
$426$	−2.00395	−	3.47095i	−0.0970917	−	0.168168i
$427$	2.73334	+	4.73428i	0.132275	+	0.229108i
$428$	−17.4141			−0.841740
$429$	7.39134	−	39.1034i	0.356857	−	1.88793i
$430$	−0.635689			−0.0306557
$431$	6.25087	+	10.8268i	0.301094	+	0.521510i	0.976384	−	0.216042i	$-0.0693149\pi$
$431$	6.25087	+	10.8268i	0.301094	+	0.521510i	−0.675290	+	0.737552i	$0.735982\pi$
$432$	30.8073	+	53.3599i	1.48222	+	2.56728i
$433$	5.47361	−	9.48057i	0.263045	−	0.455607i	−0.704005	−	0.710195i	$-0.748607\pi$
$433$	5.47361	−	9.48057i	0.263045	−	0.455607i	0.967050	+	0.254588i	$0.0819400\pi$
$434$	−0.396810			−0.0190475
$435$	2.25041	−	3.89783i	0.107899	−	0.186887i
$436$	−2.21185	+	3.83104i	−0.105928	+	0.183473i
$437$	2.71282			0.129772
$438$	−1.52327	+	2.63838i	−0.0727846	+	0.126067i
$439$	8.95896	+	15.5174i	0.427588	+	0.740604i	0.996658	−	0.0816849i	$-0.0260301\pi$
$439$	8.95896	+	15.5174i	0.427588	+	0.740604i	−0.569070	+	0.822289i	$0.692697\pi$
$440$	−3.38432	−	5.86181i	−0.161341	−	0.279451i
$441$	8.03736			0.382732
$442$	−1.08318	+	0.379244i	−0.0515217	+	0.0180388i
$443$	27.7194			1.31699			0.658494	−	0.752586i	$-0.271194\pi$
$443$	27.7194			1.31699			0.658494	+	0.752586i	$0.271194\pi$
$444$	−5.02336	−	8.70071i	−0.238398	−	0.412917i
$445$	10.1842	+	17.6396i	0.482778	+	0.836196i
$446$	−2.62009	+	4.53813i	−0.124065	+	0.214887i
$447$	52.9245			2.50324
$448$	−3.37192	+	5.84033i	−0.159308	+	0.275930i
$449$	0.0829898	−	0.143743i	0.00391653	−	0.00678363i	−0.864060	−	0.503388i	$-0.832087\pi$
$449$	0.0829898	−	0.143743i	0.00391653	−	0.00678363i	0.867977	+	0.496604i	$0.165420\pi$
$450$	−0.0391038			−0.00184337
$451$	15.2455	−	26.4061i	0.717884	−	1.24341i
$452$	−9.25039	−	16.0222i	−0.435102	−	0.753619i
$453$	−23.1722	−	40.1354i	−1.08872	−	1.88573i
$454$	0.297313			0.0139536
$455$	−1.49426	+	7.90530i	−0.0700522	+	0.370606i
$456$	9.81404			0.459584
$457$	−15.8677	−	27.4837i	−0.742260	−	1.28563i	−0.951464	−	0.307760i	$-0.900421\pi$
$457$	−15.8677	−	27.4837i	−0.742260	−	1.28563i	0.209205	−	0.977872i	$-0.432913\pi$
$458$	0.537278	+	0.930593i	0.0251054	+	0.0434838i
$459$	−11.5121	+	19.9396i	−0.537340	+	0.930700i
$460$	3.64185			0.169802
$461$	−14.5328	+	25.1715i	−0.676859	+	1.17235i	0.299063	+	0.954233i	$0.403326\pi$
$461$	−14.5328	+	25.1715i	−0.676859	+	1.17235i	−0.975922	+	0.218121i	$0.930007\pi$
$462$	−1.27681	+	2.21149i	−0.0594024	+	0.102888i
$463$	6.31904			0.293671			0.146835	−	0.989161i	$-0.453091\pi$
$463$	6.31904			0.293671			0.146835	+	0.989161i	$0.453091\pi$
$464$	1.11766	−	1.93584i	0.0518859	−	0.0898690i
$465$	−6.35718	−	11.0110i	−0.294807	−	0.510621i
$466$	−1.37518	−	2.38188i	−0.0637038	−	0.110338i
$467$	−34.6409			−1.60299			−0.801495	−	0.598002i	$-0.795962\pi$
$467$	−34.6409			−1.60299			−0.801495	+	0.598002i	$0.795962\pi$
$468$	42.7617	+	36.7858i	1.97666	+	1.70042i
$469$	10.1857			0.470334
$470$	−0.420271	−	0.727931i	−0.0193857	−	0.0335769i
$471$	−21.5526	−	37.3301i	−0.993089	−	1.72008i
$472$	4.02766	−	6.97611i	0.185388	−	0.321101i
$473$	4.09089			0.188099
$474$	2.47906	−	4.29385i	0.113867	−	0.197223i
$475$	0.0340175	−	0.0589200i	0.00156083	−	0.00270343i
$476$	−2.67792			−0.122742
$477$	−33.7411	+	58.4413i	−1.54490	+	2.67585i
$478$	0.483293	+	0.837089i	0.0221053	+	0.0382876i
$479$	3.57115	+	6.18541i	0.163170	+	0.282619i	0.936004	−	0.351990i	$-0.114495\pi$
$479$	3.57115	+	6.18541i	0.163170	+	0.282619i	−0.772834	+	0.634608i	$0.781161\pi$
$480$	19.8518			0.906107
$481$	−4.24655	−	3.65310i	−0.193626	−	0.166567i
$482$	0.933174			0.0425049
$483$	−1.39286	−	2.41250i	−0.0633773	−	0.109773i
$484$	0.0363642	+	0.0629847i	0.00165292	+	0.00286294i
$485$	−17.1356	+	29.6797i	−0.778087	+	1.34769i
$486$	−12.5865			−0.570935
$487$	9.25013	−	16.0217i	0.419163	−	0.726012i	−0.576692	−	0.816962i	$-0.695657\pi$
$487$	9.25013	−	16.0217i	0.419163	−	0.726012i	0.995856	+	0.0909493i	$0.0289901\pi$
$488$	2.49570	−	4.32267i	0.112975	−	0.195678i
$489$	−61.1575			−2.76564
$490$	0.258125	−	0.447085i	0.0116609	−	0.0201972i
$491$	7.63904	+	13.2312i	0.344745	+	0.597116i	0.985307	−	0.170790i	$-0.0546321\pi$
$491$	7.63904	+	13.2312i	0.344745	+	0.597116i	−0.640563	+	0.767906i	$0.721299\pi$
$492$	29.6750	+	51.3986i	1.33785	+	2.31723i
$493$	0.835294			0.0376197
$494$	2.54723	−	0.891838i	0.114605	−	0.0401257i
$495$	−59.5821			−2.67802
$496$	−3.15726	−	5.46854i	−0.141765	−	0.245545i
$497$	−2.60714	−	4.51570i	−0.116946	−	0.202557i
$498$	−1.78346	+	3.08904i	−0.0799186	+	0.138423i
$499$	12.4783			0.558606			0.279303	−	0.960203i	$-0.409897\pi$
$499$	12.4783			0.558606			0.279303	+	0.960203i	$0.409897\pi$
$500$	10.9039	−	18.8861i	0.487636	−	0.844610i
$501$	−30.7297	+	53.2255i	−1.37290	+	2.37794i
$502$	6.44768			0.287774
$503$	1.29004	−	2.23441i	0.0575200	−	0.0996276i	−0.835832	−	0.548986i	$-0.815014\pi$
$503$	1.29004	−	2.23441i	0.0575200	−	0.0996276i	0.893352	+	0.449358i	$0.148347\pi$
$504$	−3.66929	−	6.35540i	−0.163443	−	0.283092i
$505$	−8.87013	−	15.3635i	−0.394716	−	0.683668i
$506$	0.644506			0.0286518
$507$	40.2095	+	15.7641i	1.78577	+	0.700108i
$508$	−35.8802			−1.59192
$509$	−17.8404	−	30.9005i	−0.790761	−	1.36964i	−0.925496	−	0.378757i	$-0.876352\pi$
$509$	−17.8404	−	30.9005i	−0.790761	−	1.36964i	0.134735	−	0.990882i	$-0.456982\pi$
$510$	1.17981	+	2.04349i	0.0522428	+	0.0904872i
$511$	−1.98177	+	3.43253i	−0.0876686	+	0.151846i
$512$	16.5825			0.732850
$513$	27.0721	−	46.8903i	1.19526	−	2.07026i
$514$	0.826032	−	1.43073i	0.0364347	−	0.0631068i
$515$	−1.55040			−0.0683190
$516$	−3.98140	+	6.89599i	−0.175272	+	0.303579i
$517$	2.70460	+	4.68450i	0.118948	+	0.206024i
$518$	0.179723	+	0.311289i	0.00789656	+	0.0136772i
$519$	57.1365			2.50801
$520$	6.93315	−	2.42744i	0.304039	−	0.106450i
$521$	−20.9637			−0.918437			−0.459219	−	0.888323i	$-0.651871\pi$
$521$	−20.9637			−0.918437			−0.459219	+	0.888323i	$0.651871\pi$
$522$	0.564499	+	0.977742i	0.0247075	+	0.0427946i
$523$	11.4131	+	19.7681i	0.499062	+	0.864401i	0.999999	−	0.00108279i	$-0.000344663\pi$
$523$	11.4131	+	19.7681i	0.499062	+	0.864401i	−0.500937	+	0.865484i	$0.667011\pi$
$524$	−1.70156	+	2.94719i	−0.0743330	+	0.128749i
$525$	−0.0698632			−0.00304908
$526$	−2.46622	+	4.27161i	−0.107532	+	0.186251i
$527$	1.17981	−	2.04349i	0.0513933	−	0.0890158i
$528$	−40.6362			−1.76847
$529$	11.1485	−	19.3097i	0.484716	−	0.839552i
$530$	2.16723	+	3.75376i	0.0941386	+	0.163053i
$531$	−35.4542	−	61.4084i	−1.53858	−	2.66490i
$532$	6.29744			0.273029
$533$	25.0861	+	21.5803i	1.08660	+	0.934749i
$534$	−7.01634			−0.303627
$535$	9.98140	+	17.2883i	0.431534	+	0.747438i
$536$	−4.65009	−	8.05419i	−0.200853	−	0.347888i
$537$	24.0674	−	41.6860i	1.03859	−	1.79888i
$538$	0.645208			0.0278169
$539$	−1.66113	+	2.87716i	−0.0715498	+	0.123928i
$540$	36.3433	−	62.9484i	1.56397	−	2.70887i
$541$	30.2191			1.29922			0.649611	−	0.760266i	$-0.274932\pi$
$541$	30.2191			1.29922			0.649611	+	0.760266i	$0.274932\pi$
$542$	1.79013	−	3.10059i	0.0768925	−	0.133182i
$543$	11.3868	+	19.7224i	0.488652	+	0.846371i
$544$	1.84211	+	3.19064i	0.0789800	+	0.136797i
$545$	5.07116			0.217225
$546$	−2.10095	−	1.80734i	−0.0899123	−	0.0773472i
$547$	−16.8223			−0.719271			−0.359636	−	0.933093i	$-0.617099\pi$
$547$	−16.8223			−0.719271			−0.359636	+	0.933093i	$0.617099\pi$
$548$	−17.5214	−	30.3479i	−0.748476	−	1.29640i
$549$	−21.9688	−	38.0511i	−0.937606	−	1.62398i
$550$	0.00808180	−	0.0139981i	0.000344609	−	0.000596881i
$551$	−1.96429			−0.0836817
$552$	−1.27176	+	2.20276i	−0.0541298	+	0.0937555i
$553$	3.22525	−	5.58630i	0.137152	−	0.237554i
$554$	1.27932			0.0543531
$555$	−5.75858	+	9.97416i	−0.244438	+	0.423379i
$556$	13.5454	+	23.4614i	0.574454	+	0.994984i
$557$	5.24591	+	9.08619i	0.222276	+	0.384994i	0.955499	−	0.294995i	$-0.0953179\pi$
$557$	5.24591	+	9.08619i	0.222276	+	0.384994i	−0.733222	+	0.679989i	$0.761985\pi$
$558$	3.18930			0.135014
$559$	−0.824600	+	4.36249i	−0.0348768	+	0.184513i
$560$	8.21520			0.347155
$561$	−7.59250	−	13.1506i	−0.320555	−	0.555218i
$562$	3.64244	+	6.30890i	0.153647	+	0.266125i
$563$	−15.4737	+	26.8012i	−0.652138	+	1.12954i	0.330465	+	0.943818i	$0.392795\pi$
$563$	−15.4737	+	26.8012i	−0.652138	+	1.12954i	−0.982603	+	0.185718i	$0.940539\pi$
$564$	−10.5288			−0.443344
$565$	−10.6043	+	18.3672i	−0.446126	+	0.772713i
$566$	0.850388	−	1.47292i	0.0357445	−	0.0619112i
$567$	−31.4871			−1.32234
$568$	−2.38047	+	4.12310i	−0.0998825	+	0.173002i
$569$	18.4545	+	31.9641i	0.773651	+	1.34000i	0.935549	+	0.353196i	$0.114905\pi$
$569$	18.4545	+	31.9641i	0.773651	+	1.34000i	−0.161898	+	0.986807i	$0.551762\pi$
$570$	−2.77446	−	4.80551i	−0.116209	−	0.201280i
$571$	−1.77093			−0.0741113			−0.0370556	−	0.999313i	$-0.511798\pi$
$571$	−1.77093			−0.0741113			−0.0370556	+	0.999313i	$0.511798\pi$
$572$	−22.0061	+	7.70479i	−0.920121	+	0.322153i
$573$	9.47383			0.395775
$574$	−1.06170	−	1.83891i	−0.0443143	−	0.0767546i
$575$	0.00881638	+	0.0152704i	0.000367668	+	0.000636820i
$576$	27.1013	−	46.9409i	1.12922	−	1.95587i
$577$	−9.83999			−0.409644			−0.204822	−	0.978799i	$-0.565662\pi$
$577$	−9.83999			−0.409644			−0.204822	+	0.978799i	$0.565662\pi$
$578$	1.74761	−	3.02695i	0.0726910	−	0.125905i
$579$	−16.6951	+	28.9168i	−0.693826	+	1.20174i
$580$	−2.63699			−0.109495
$581$	−2.32028	+	4.01884i	−0.0962613	+	0.166730i
$582$	−5.90272	−	10.2238i	−0.244675	−	0.423790i
$583$	−13.9469	−	24.1568i	−0.577623	−	1.00047i
$584$	3.61896			0.149753
$585$	12.0100	−	63.5378i	0.496550	−	2.62696i
$586$	−3.13112			−0.129345
$587$	7.56917	+	13.1102i	0.312413	+	0.541116i	0.978884	−	0.204415i	$-0.0655293\pi$
$587$	7.56917	+	13.1102i	0.312413	+	0.541116i	−0.666471	+	0.745531i	$0.732196\pi$
$588$	−3.23334	−	5.60030i	−0.133341	−	0.230953i
$589$	−2.77446	+	4.80551i	−0.114320	+	0.198007i
$590$	−4.55453			−0.187507
$591$	−42.2210	+	73.1289i	−1.73674	+	3.00812i
$592$	−2.85997	+	4.95361i	−0.117544	+	0.203592i
$593$	9.17148			0.376628			0.188314	−	0.982109i	$-0.439698\pi$
$593$	9.17148			0.376628			0.188314	+	0.982109i	$0.439698\pi$
$594$	6.43174	−	11.1401i	0.263898	−	0.457084i
$595$	1.53493	+	2.65858i	0.0629261	+	0.108991i
$596$	−15.5040	−	26.8536i	−0.635067	−	1.09997i
$597$	41.3506			1.69237
$598$	−0.129913	+	0.687294i	−0.00531253	+	0.0281056i
$599$	−18.5811			−0.759202			−0.379601	−	0.925150i	$-0.623939\pi$
$599$	−18.5811			−0.759202			−0.379601	+	0.925150i	$0.623939\pi$
$600$	0.0318946	+	0.0552431i	0.00130209	+	0.00225529i
$601$	6.70179	+	11.6078i	0.273372	+	0.473494i	0.969723	−	0.244207i	$-0.0785277\pi$
$601$	6.70179	+	11.6078i	0.273372	+	0.473494i	−0.696351	+	0.717701i	$0.745194\pi$
$602$	0.142444	−	0.246721i	0.00580560	−	0.0100556i
$603$	−81.8665			−3.33386
$604$	−13.5763	+	23.5149i	−0.552413	+	0.956808i
$605$	0.0416865	−	0.0722032i	0.00169480	−	0.00293548i
$606$	6.11101			0.248243
$607$	−6.31812	+	10.9433i	−0.256445	+	0.444175i	−0.965287	−	0.261192i	$-0.915884\pi$
$607$	−6.31812	+	10.9433i	−0.256445	+	0.444175i	0.708842	+	0.705367i	$0.249218\pi$
$608$	−4.33195	−	7.50316i	−0.175684	−	0.304293i
$609$	1.00854	+	1.74684i	0.0408681	+	0.0707856i
$610$	−2.82217			−0.114266
$611$	−5.54067	+	1.93990i	−0.224151	+	0.0784800i
$612$	21.5234			0.870032
$613$	−12.8540	−	22.2637i	−0.519167	−	0.899223i	−0.999752	−	0.0222753i	$-0.992909\pi$
$613$	−12.8540	−	22.2637i	−0.519167	−	0.899223i	0.480585	−	0.876948i	$-0.340424\pi$
$614$	0.382450	+	0.662422i	0.0154344	+	0.0267332i
$615$	34.0183	−	58.9214i	1.37175	−	2.37594i
$616$	3.03341			0.122220
$617$	3.29810	−	5.71248i	0.132777	−	0.229976i	−0.791969	−	0.610561i	$-0.790944\pi$
$617$	3.29810	−	5.71248i	0.132777	−	0.229976i	0.924746	+	0.380585i	$0.124277\pi$
$618$	0.267035	−	0.462518i	0.0107417	−	0.0186052i
$619$	−21.0124			−0.844559			−0.422280	−	0.906466i	$-0.638770\pi$
$619$	−21.0124			−0.844559			−0.422280	+	0.906466i	$0.638770\pi$
$620$	−3.72461	+	6.45121i	−0.149584	+	0.259087i
$621$	7.01634	+	12.1526i	0.281556	+	0.487669i
$622$	3.96856	+	6.87375i	0.159125	+	0.275612i
$623$	−9.12826			−0.365716
$624$	8.19103	−	43.3341i	0.327904	−	1.73475i
$625$	−24.8944			−0.995777
$626$	−0.834551	−	1.44549i	−0.0333554	−	0.0577732i
$627$	17.8547	+	30.9252i	0.713046	+	1.23503i
$628$	−12.6274	+	21.8713i	−0.503888	+	0.872760i
$629$	−2.13743			−0.0852250
$630$	−2.07464	+	3.59339i	−0.0826557	+	0.143164i
$631$	−13.0105	+	22.5349i	−0.517940	+	0.897099i	0.481842	+	0.876258i	$0.339968\pi$
$631$	−13.0105	+	22.5349i	−0.517940	+	0.897099i	−0.999783	+	0.0208412i	$0.993366\pi$
$632$	−5.88970			−0.234280
$633$	−40.5187	+	70.1804i	−1.61047	+	2.78942i
$634$	0.930117	+	1.61101i	0.0369397	+	0.0639814i
$635$	20.5658	+	35.6210i	0.816130	+	1.41358i
$636$	54.2946			2.15292
$637$	−2.73334	−	2.35136i	−0.108299	−	0.0931641i
$638$	−0.466673			−0.0184758
$639$	20.9545	+	36.2943i	0.828949	+	1.43578i
$640$	−7.71615	−	13.3648i	−0.305008	−	0.528289i
$641$	−9.26694	+	16.0508i	−0.366022	+	0.633969i	−0.988940	−	0.148319i	$-0.952614\pi$
$641$	−9.26694	+	16.0508i	−0.366022	+	0.633969i	0.622917	+	0.782288i	$0.285947\pi$
$642$	−6.87661			−0.271398
$643$	7.22328	−	12.5111i	0.284858	−	0.493389i	−0.687716	−	0.725979i	$-0.741387\pi$
$643$	7.22328	−	12.5111i	0.284858	−	0.493389i	0.972575	+	0.232590i	$0.0747201\pi$
$644$	−0.816061	+	1.41346i	−0.0321573	+	0.0556981i
$645$	9.12826			0.359425
$646$	0.514903	−	0.891838i	0.0202586	−	0.0350889i
$647$	−14.6438	−	25.3637i	−0.575706	−	0.997152i	−0.995965	−	0.0897473i	$-0.971394\pi$
$647$	−14.6438	−	25.3637i	−0.575706	−	0.997152i	0.420259	−	0.907404i	$-0.361939\pi$
$648$	14.3748	+	24.8979i	0.564696	+	0.978082i
$649$	29.3100			1.15052
$650$	0.0132984	+	0.0114399i	0.000521605	+	0.000448711i
$651$	5.69803			0.223324
$652$	17.9158	+	31.0310i	0.701636	+	1.21527i
$653$	15.4807	+	26.8134i	0.605808	+	1.04929i	0.991923	+	0.126840i	$0.0404836\pi$
$653$	15.4807	+	26.8134i	0.605808	+	1.04929i	−0.386115	+	0.922451i	$0.626183\pi$
$654$	−0.873434	+	1.51283i	−0.0341540	+	0.0591564i
$655$	3.90121			0.152433
$656$	16.8950	−	29.2630i	0.659639	−	1.14253i
$657$	15.9282	−	27.5885i	0.621420	−	1.07633i
$658$	0.376695			0.0146851
$659$	18.5414	−	32.1146i	0.722270	−	1.25101i	−0.237817	−	0.971310i	$-0.576432\pi$
$659$	18.5414	−	32.1146i	0.722270	−	1.25101i	0.960088	−	0.279699i	$-0.0902347\pi$
$660$	23.9692	+	41.5159i	0.933000	+	1.61600i
$661$	10.2009	+	17.6685i	0.396770	+	0.687226i	0.993325	−	0.115346i	$-0.0367977\pi$
$661$	10.2009	+	17.6685i	0.396770	+	0.687226i	−0.596555	+	0.802572i	$0.703464\pi$
$662$	0.206764			0.00803611
$663$	15.5541	−	5.44580i	0.604070	−	0.211497i
$664$	4.23710			0.164431
$665$	−3.60957	−	6.25197i	−0.139973	−	0.242441i
$666$	−1.44450	−	2.50194i	−0.0559731	−	0.0969483i
$667$	0.254545	−	0.440885i	0.00985601	−	0.0170711i
$668$	36.0085			1.39321
$669$	37.6235	−	65.1658i	1.45461	−	2.51945i
$670$	−2.62919	+	4.55389i	−0.101574	+	0.175932i
$671$	18.1617			0.701123
$672$	−4.44836	+	7.70479i	−0.171599	+	0.297219i
$673$	−7.25551	−	12.5669i	−0.279679	−	0.484419i	0.691626	−	0.722256i	$-0.256895\pi$
$673$	−7.25551	−	12.5669i	−0.279679	−	0.484419i	−0.971305	+	0.237837i	$0.923562\pi$
$674$	−1.74350	−	3.01983i	−0.0671571	−	0.116319i
$675$	0.351926			0.0135457
$676$	−3.78055	−	25.0201i	−0.145406	−	0.962313i
$677$	−3.51476			−0.135083			−0.0675417	−	0.997716i	$-0.521516\pi$
$677$	−3.51476			−0.135083			−0.0675417	+	0.997716i	$0.521516\pi$
$678$	−3.65287	−	6.32696i	−0.140288	−	0.242985i
$679$	−7.67944	−	13.3012i	−0.294710	−	0.510452i
$680$	1.40148	−	2.42744i	0.0537444	−	0.0930881i
$681$	−4.26930			−0.163600
$682$	−0.659151	+	1.14168i	−0.0252402	+	0.0437173i
$683$	13.5376	−	23.4479i	0.518003	−	0.897208i	−0.481778	−	0.876293i	$-0.660009\pi$
$683$	13.5376	−	23.4479i	0.518003	−	0.897208i	0.999781	−	0.0209144i	$-0.00665773\pi$
$684$	−50.6149			−1.93531
$685$	−20.0858	+	34.7897i	−0.767440	+	1.32925i
$686$	0.115680	+	0.200364i	0.00441670	+	0.00764995i
$687$	−7.71511	−	13.3630i	−0.294350	−	0.509829i
$688$	4.53350			0.172838
$689$	28.5718	−	10.0036i	1.08850	−	0.381106i
$690$	1.43812			0.0547485
$691$	−14.8702	−	25.7560i	−0.565690	−	0.979803i	−0.996985	−	0.0775926i	$-0.975277\pi$
$691$	−14.8702	−	25.7560i	−0.565690	−	0.979803i	0.431295	−	0.902211i	$-0.358057\pi$
$692$	−16.7378	−	28.9908i	−0.636277	−	1.10206i
$693$	13.3511	−	23.1247i	0.507166	−	0.878436i
$694$	−3.79810			−0.144174
$695$	15.5280	−	26.8952i	0.589009	−	1.02019i
$696$	0.920856	−	1.59497i	0.0349049	−	0.0604571i
$697$	12.6267			0.478270
$698$	−3.97619	+	6.88696i	−0.150501	+	0.260675i
$699$	19.7470	+	34.2028i	0.746900	+	1.29367i
$700$	0.0204660	+	0.0354482i	0.000773544	+	0.00133982i
$701$	18.2888			0.690760			0.345380	−	0.938463i	$-0.387750\pi$
$701$	18.2888			0.690760			0.345380	+	0.938463i	$0.387750\pi$
$702$	10.5832	+	9.10425i	0.399439	+	0.343618i
$703$	5.02642			0.189575
$704$	11.2024	+	19.4030i	0.422205	+	0.731280i
$705$	6.03493	+	10.4528i	0.227289	+	0.393676i
$706$	2.76664	−	4.79197i	0.104124	−	0.180348i
$707$	7.95042			0.299006
$708$	−28.5256	+	49.4078i	−1.07206	+	1.85686i
$709$	14.3402	−	24.8379i	0.538557	−	0.932808i	−0.460425	−	0.887699i	$-0.652303\pi$
$709$	14.3402	−	24.8379i	0.538557	−	0.932808i	0.998982	−	0.0451098i	$-0.0143638\pi$
$710$	2.69187			0.101024
$711$	−25.9225	+	44.8992i	−0.972171	+	1.68385i
$712$	4.16732	+	7.21801i	0.156177	+	0.270506i
$713$	−0.719062	−	1.24545i	−0.0269291	−	0.0466426i
$714$	−1.05748			−0.0395752
$715$	20.2626	+	17.4309i	0.757779	+	0.651880i
$716$	−28.2017			−1.05395
$717$	−6.93991	−	12.0203i	−0.259176	−	0.448905i
$718$	0.714760	+	1.23800i	0.0266746	+	0.0462018i
$719$	−12.7381	+	22.0631i	−0.475052	+	0.822813i	−0.999592	−	0.0285723i	$-0.990904\pi$
$719$	−12.7381	+	22.0631i	−0.475052	+	0.822813i	0.524540	+	0.851386i	$0.324237\pi$
$720$	−66.0285			−2.46074
$721$	0.347412	−	0.601736i	0.0129383	−	0.0224098i
$722$	0.987073	−	1.70966i	0.0367350	−	0.0636270i
$723$	−13.4000			−0.498352
$724$	6.67138	−	11.5552i	0.247940	−	0.429444i
$725$	−0.00638375	−	0.0110570i	−0.000237086	−	0.000410646i
$726$	0.0143598	+	0.0248719i	0.000532942	+	0.000923083i
$727$	−9.02572			−0.334746			−0.167373	−	0.985894i	$-0.553528\pi$
$727$	−9.02572			−0.334746			−0.167373	+	0.985894i	$0.553528\pi$
$728$	−0.611444	+	3.23480i	−0.0226616	+	0.119890i
$729$	86.2759			3.19540
$730$	−1.02309	−	1.77204i	−0.0378663	−	0.0655863i
$731$	0.847041	+	1.46712i	0.0313290	+	0.0542633i
$732$	−17.6756	+	30.6150i	−0.653309	+	1.13156i
$733$	−7.57069			−0.279630			−0.139815	−	0.990178i	$-0.544651\pi$
$733$	−7.57069			−0.279630			−0.139815	+	0.990178i	$0.544651\pi$
$734$	−2.29695	+	3.97843i	−0.0847818	+	0.146846i
$735$	−3.70657	+	6.41997i	−0.136719	+	0.236804i
$736$	2.24544			0.0827681
$737$	16.9198	−	29.3059i	0.623249	−	1.07950i
$738$	8.53323	+	14.7800i	0.314113	+	0.544059i
$739$	3.18648	+	5.51914i	0.117216	+	0.203025i	0.918664	−	0.395041i	$-0.129270\pi$
$739$	3.18648	+	5.51914i	0.117216	+	0.203025i	−0.801447	+	0.598066i	$0.795936\pi$
$740$	6.74778			0.248053
$741$	−36.5772	+	12.8064i	−1.34370	+	0.470457i
$742$	−1.94252			−0.0713122
$743$	11.4148	+	19.7711i	0.418770	+	0.725330i	0.995816	−	0.0913811i	$-0.0291281\pi$
$743$	11.4148	+	19.7711i	0.418770	+	0.725330i	−0.577046	+	0.816711i	$0.695795\pi$
$744$	−2.60132	−	4.50562i	−0.0953690	−	0.165184i
$745$	−17.7731	+	30.7840i	−0.651157	+	1.12784i
$746$	6.98596			0.255774
$747$	18.6489	−	32.3009i	0.682328	−	1.18183i
$748$	−4.44836	+	7.70479i	−0.162648	+	0.281715i
$749$	−8.94647			−0.326897
$750$	4.30581	−	7.45788i	0.157226	−	0.272323i
$751$	−19.6848	−	34.0950i	−0.718307	−	1.24414i	−0.961670	−	0.274209i	$-0.911584\pi$
$751$	−19.6848	−	34.0950i	−0.718307	−	1.24414i	0.243363	−	0.969935i	$-0.421749\pi$
$752$	2.99722	+	5.19133i	0.109297	+	0.189308i
$753$	−92.5863			−3.37403
$754$	0.0940671	−	0.497655i	0.00342572	−	0.0181235i
$755$	31.1268			1.13282
$756$	16.2875	+	28.2108i	0.592370	+	1.02602i
$757$	−4.36357	−	7.55792i	−0.158597	−	0.274697i	0.775766	−	0.631020i	$-0.217364\pi$
$757$	−4.36357	−	7.55792i	−0.158597	−	0.274697i	−0.934363	+	0.356323i	$0.884030\pi$
$758$	0.500020	−	0.866060i	0.0181615	−	0.0314567i
$759$	−9.25486			−0.335930
$760$	−3.29575	+	5.70841i	−0.119550	+	0.207066i
$761$	11.4195	−	19.7792i	0.413958	−	0.716996i	−0.581361	−	0.813646i	$-0.697480\pi$
$761$	11.4195	−	19.7792i	0.413958	−	0.716996i	0.995318	+	0.0966503i	$0.0308128\pi$
$762$	−14.1687			−0.513276
$763$	−1.13634	+	1.96820i	−0.0411382	+	0.0712535i
$764$	−2.77531	−	4.80697i	−0.100407	−	0.173910i
$765$	−12.3368	−	21.3680i	−0.446038	−	0.772561i
$766$	−4.01368			−0.145020
$767$	−5.90801	+	31.2559i	−0.213326	+	1.12859i
$768$	−39.4934			−1.42510
$769$	−17.4174	−	30.1679i	−0.628089	−	1.08788i	−0.987935	−	0.154871i	$-0.950504\pi$
$769$	−17.4174	−	30.1679i	−0.628089	−	1.08788i	0.359846	−	0.933012i	$-0.382829\pi$
$770$	−0.857556	−	1.48533i	−0.0309042	−	0.0535276i
$771$	−11.8615	+	20.5447i	−0.427182	+	0.739900i
$772$	19.5630			0.704088
$773$	16.6372	−	28.8164i	0.598397	−	1.03645i	−0.394661	−	0.918827i	$-0.629138\pi$
$773$	16.6372	−	28.8164i	0.598397	−	1.03645i	0.993058	−	0.117627i	$-0.0375289\pi$
$774$	−1.14488	+	1.98299i	−0.0411518	+	0.0712769i
$775$	−0.0360668			−0.00129556
$776$	−7.01178	+	12.1448i	−0.251708	+	0.435971i
$777$	−2.58075	−	4.46999i	−0.0925838	−	0.160360i
$778$	2.93220	+	5.07872i	0.105124	+	0.182081i
$779$	−29.6932			−1.06387
$780$	−49.1035	+	17.1922i	−1.75819	+	0.615578i
$781$	−17.3232			−0.619872
$782$	0.133448	+	0.231139i	0.00477210	+	0.00826553i
$783$	−5.08038	−	8.79947i	−0.181558	−	0.314467i
$784$	−1.84085	+	3.18844i	−0.0657446	+	0.113873i
$785$	28.9512			1.03331
$786$	−0.671926	+	1.16381i	−0.0239668	+	0.0415117i
$787$	13.9079	−	24.0891i	0.495762	−	0.858685i	−0.504226	−	0.863572i	$-0.668222\pi$
$787$	13.9079	−	24.0891i	0.495762	−	0.858685i	0.999988	+	0.00488682i	$0.00155553\pi$
$788$	49.4737			1.76243
$789$	35.4139	−	61.3387i	1.26077	−	2.18372i
$790$	1.66504	+	2.88393i	0.0592393	+	0.102606i
$791$	−4.75239	−	8.23138i	−0.168976	−	0.292674i
$792$	−24.3806			−0.866329
$793$	−3.66084	+	19.3674i	−0.130000	+	0.687757i
$794$	−6.26407			−0.222304
$795$	−31.1206	−	53.9025i	−1.10374	−	1.91173i
$796$	−12.1134	−	20.9811i	−0.429349	−	0.743655i
$797$	−17.9343	+	31.0630i	−0.635264	+	1.10031i	0.351195	+	0.936302i	$0.385775\pi$
$797$	−17.9343	+	31.0630i	−0.635264	+	1.10031i	−0.986459	+	0.164007i	$0.947558\pi$
$798$	2.48679			0.0880313
$799$	−1.12000	+	1.93990i	−0.0396228	+	0.0686288i
$800$	0.0281568	−	0.0487690i	0.000995493	−	0.00172424i
$801$	73.3671			2.59230
$802$	3.38779	−	5.86783i	0.119627	−	0.207200i
$803$	6.58396	+	11.4037i	0.232343	+	0.402430i
$804$	32.9339	+	57.0432i	1.16149	+	2.01176i
$805$	1.87100			0.0659441
$806$	−1.08461	−	0.933040i	−0.0382039	−	0.0328649i
$807$	−9.26495			−0.326142
$808$	−3.62960	−	6.28666i	−0.127689	−	0.221164i
$809$	8.91223	+	15.4364i	0.313337	+	0.542716i	0.979083	−	0.203463i	$-0.0652196\pi$
$809$	8.91223	+	15.4364i	0.313337	+	0.542716i	−0.665745	+	0.746179i	$0.731886\pi$
$810$	8.12761	−	14.0774i	0.285575	−	0.494630i
$811$	25.2152			0.885425			0.442713	−	0.896664i	$-0.354016\pi$
$811$	25.2152			0.885425			0.442713	+	0.896664i	$0.354016\pi$
$812$	0.590892	−	1.02346i	0.0207362	−	0.0359162i
$813$	−25.7055	+	44.5233i	−0.901532	+	1.56150i
$814$	1.19417			0.0418556
$815$	20.5379	−	35.5728i	0.719413	−	1.24606i
$816$	−8.41395	−	14.5734i	−0.294547	−	0.510171i
$817$	−1.99192	−	3.45010i	−0.0696884	−	0.120704i
$818$	5.40719			0.189058
$819$	21.9688	+	18.8987i	0.767653	+	0.660374i
$820$	−39.8619			−1.39204
$821$	5.22797	+	9.05511i	0.182457	+	0.316026i	0.942717	−	0.333594i	$-0.108261\pi$
$821$	5.22797	+	9.05511i	0.182457	+	0.316026i	−0.760259	+	0.649620i	$0.774928\pi$
$822$	−6.91899	−	11.9840i	−0.241327	−	0.417991i
$823$	16.6203	−	28.7871i	0.579346	−	1.00346i	−0.416209	−	0.909269i	$-0.636641\pi$
$823$	16.6203	−	28.7871i	0.579346	−	1.00346i	0.995554	−	0.0941873i	$-0.0300253\pi$
$824$	−0.634416			−0.0221009
$825$	−0.116052	+	0.201007i	−0.00404040	+	0.00699817i
$826$	1.02057	−	1.76768i	0.0355102	−	0.0615055i
$827$	−37.9927			−1.32113			−0.660567	−	0.750767i	$-0.729684\pi$
$827$	−37.9927			−1.32113			−0.660567	+	0.750767i	$0.729684\pi$
$828$	6.55898	−	11.3605i	0.227940	−	0.394804i
$829$	−8.34721	−	14.4578i	−0.289911	−	0.502140i	0.683877	−	0.729597i	$-0.260292\pi$
$829$	−8.34721	−	14.4578i	−0.289911	−	0.502140i	−0.973788	+	0.227457i	$0.926959\pi$
$830$	−1.19784	−	2.07472i	−0.0415777	−	0.0720147i
$831$	−18.3706			−0.637268
$832$	−22.9493	+	8.03501i	−0.795623	+	0.278564i
$833$	−1.37578			−0.0476680
$834$	5.34893	+	9.26462i	0.185218	+	0.320808i
$835$	−20.6394	−	35.7484i	−0.714254	−	1.23712i
$836$	10.4609	−	18.1187i	0.361796	−	0.626649i
$837$	−28.7031			−0.992123
$838$	−1.68967	+	2.92660i	−0.0583688	+	0.101098i
$839$	23.3206	−	40.3924i	0.805115	−	1.39450i	−0.111098	−	0.993809i	$-0.535437\pi$
$839$	23.3206	−	40.3924i	0.805115	−	1.39450i	0.916213	−	0.400691i	$-0.131230\pi$
$840$	6.76864			0.233540
$841$	14.3157	−	24.7955i	0.493644	−	0.855017i
$842$	−1.18837	−	2.05831i	−0.0409538	−	0.0709341i
$843$	−52.3041	−	90.5934i	−1.80145	−	3.12020i
$844$	47.4789			1.63429
$845$	−22.6725	+	18.0943i	−0.779958	+	0.622463i
$846$	−3.02763			−0.104092
$847$	0.0186821	+	0.0323584i	0.000641925	+	0.00111185i
$848$	−15.4559	−	26.7704i	−0.530758	−	0.919299i
$849$	−12.2112	+	21.1505i	−0.419089	+	0.725883i
$850$	0.00669352			0.000229586
$851$	−0.651354	+	1.12818i	−0.0223281	+	0.0386735i
$852$	16.8595	−	29.2016i	0.577598	−	1.00043i
$853$	39.5640			1.35464			0.677322	−	0.735686i	$-0.263140\pi$
$853$	39.5640			1.35464			0.677322	+	0.735686i	$0.263140\pi$
$854$	0.632387	−	1.09533i	0.0216398	−	0.0374813i
$855$	29.0115	+	50.2493i	0.992171	+	1.71849i
$856$	4.08433	+	7.07426i	0.139599	+	0.241793i
$857$	−19.5613			−0.668201			−0.334101	−	0.942537i	$-0.608433\pi$
$857$	−19.5613			−0.668201			−0.334101	+	0.942537i	$0.608433\pi$
$858$	−8.68995	+	3.04253i	−0.296670	+	0.103870i
$859$	−10.1632			−0.346762			−0.173381	−	0.984855i	$-0.555469\pi$
$859$	−10.1632			−0.346762			−0.173381	+	0.984855i	$0.555469\pi$
$860$	−2.67407	−	4.63163i	−0.0911851	−	0.157937i
$861$	15.2455	+	26.4061i	0.519567	+	0.899916i
$862$	1.44621	−	2.50490i	0.0492580	−	0.0853174i
$863$	26.8903			0.915356			0.457678	−	0.889118i	$-0.348681\pi$
$863$	26.8903			0.915356			0.457678	+	0.889118i	$0.348681\pi$
$864$	22.4080	−	38.8118i	0.762336	−	1.32041i
$865$	−19.1876	+	33.2339i	−0.652398	+	1.12999i
$866$	−2.53276			−0.0860666
$867$	−25.0950	+	43.4658i	−0.852271	+	1.47618i
$868$	−1.66921	−	2.89115i	−0.0566566	−	0.0981321i
$869$	−10.7151	−	18.5591i	−0.363485	−	0.629575i
$870$	−1.04132			−0.0353039
$871$	27.8410	+	23.9503i	0.943358	+	0.811524i
$872$	2.07509			0.0702713
$873$	61.7224	+	106.906i	2.08899	+	3.61823i
$874$	−0.313820	−	0.543552i	−0.0106151	−	0.0183859i
$875$	5.60186	−	9.70271i	0.189378	−	0.328012i
$876$	−25.6310			−0.865991
$877$	0.850801	−	1.47363i	0.0287295	−	0.0497610i	−0.851303	−	0.524674i	$-0.824187\pi$
$877$	0.850801	−	1.47363i	0.0287295	−	0.0497610i	0.880033	+	0.474913i	$0.157521\pi$
$878$	2.07275	−	3.59011i	0.0699520	−	0.121160i
$879$	44.9617			1.51652
$880$	13.6465	−	23.6364i	0.460023	−	0.796783i
$881$	5.65448	+	9.79384i	0.190504	+	0.329963i	0.945417	−	0.325862i	$-0.105654\pi$
$881$	5.65448	+	9.79384i	0.190504	+	0.329963i	−0.754913	+	0.655825i	$0.772321\pi$
$882$	−0.929766	−	1.61040i	−0.0313068	−	0.0542250i
$883$	−46.9068			−1.57854			−0.789270	−	0.614047i	$-0.789541\pi$
$883$	−46.9068			−1.57854			−0.789270	+	0.614047i	$0.789541\pi$
$884$	−7.31965	−	6.29674i	−0.246187	−	0.211782i
$885$	65.4013			2.19844
$886$	−3.20659	−	5.55398i	−0.107728	−	0.186590i
$887$	1.22346	+	2.11909i	0.0410797	+	0.0711522i	0.885834	−	0.464002i	$-0.153587\pi$
$887$	1.22346	+	2.11909i	0.0410797	+	0.0711522i	−0.844755	+	0.535154i	$0.820254\pi$
$888$	−2.35638	+	4.08136i	−0.0790748	+	0.136962i
$889$	−18.4334			−0.618237
$890$	2.35623	−	4.08111i	0.0789810	−	0.136799i
$891$	−52.3041	+	90.5934i	−1.75225	+	3.03499i
$892$	−44.0864			−1.47612
$893$	2.63382	−	4.56191i	0.0881374	−	0.152658i
$894$	−6.12233	−	10.6042i	−0.204761	−	0.354657i
$895$	16.1647	+	27.9980i	0.540325	+	0.935871i
$896$	6.91610			0.231051
$897$	1.86550	−	9.86928i	0.0622872	−	0.329526i
$898$	−0.0384012			−0.00128146
$899$	0.520658	+	0.901806i	0.0173649	+	0.0300769i
$900$	−0.164493	−	0.284910i	−0.00548310	−	0.00949701i
$901$	5.77557	−	10.0036i	0.192412	−	0.333268i
$902$	−7.05444			−0.234887
$903$	−2.04545	+	3.54282i	−0.0680682	+	0.117898i
$904$	−4.33921	+	7.51574i	−0.144320	+	0.249970i
$905$	−15.2956			−0.508443
$906$	−5.36114	+	9.28576i	−0.178112	+	0.308499i
$907$	20.7083	+	35.8678i	0.687607	+	1.19097i	0.972610	+	0.232443i	$0.0746719\pi$
$907$	20.7083	+	35.8678i	0.687607	+	1.19097i	−0.285003	+	0.958526i	$0.591995\pi$
$908$	1.25067	+	2.16622i	0.0415048	+	0.0718885i
$909$	−63.9004			−2.11944
$910$	1.75680	−	0.615091i	0.0582373	−	0.0203901i
$911$	−11.9951			−0.397416			−0.198708	−	0.980059i	$-0.563675\pi$
$911$	−11.9951			−0.397416			−0.198708	+	0.980059i	$0.563675\pi$
$912$	19.7864	+	34.2711i	0.655194	+	1.13483i
$913$	7.70855	+	13.3516i	0.255116	+	0.441873i
$914$	−3.67116	+	6.35864i	−0.121431	+	0.210325i
$915$	40.5252			1.33972
$916$	−4.52020	+	7.82922i	−0.149352	+	0.258685i
$917$	−0.874176	+	1.51412i	−0.0288678	+	0.0500006i
$918$	5.32691			0.175814
$919$	−22.4708	+	38.9206i	−0.741243	+	1.28387i	0.210686	+	0.977554i	$0.432430\pi$
$919$	−22.4708	+	38.9206i	−0.741243	+	1.28387i	−0.951930	+	0.306317i	$0.900903\pi$
$920$	−0.854167	−	1.47946i	−0.0281611	−	0.0487764i
$921$	−5.49183	−	9.51213i	−0.180962	−	0.313435i
$922$	6.72463			0.221464
$923$	3.49182	−	18.4732i	0.114935	−	0.608054i
$924$	−21.4839			−0.706769
$925$	0.0163354	+	0.0282937i	0.000537103	+	0.000930290i
$926$	−0.730990	−	1.26611i	−0.0240218	−	0.0416070i
$927$	−2.79228	+	4.83637i	−0.0917105	+	0.158847i
$928$	−1.62588			−0.0533720
$929$	−14.1298	+	24.4735i	−0.463582	+	0.802948i	−0.999136	−	0.0415530i	$-0.986769\pi$
$929$	−14.1298	+	24.4735i	−0.463582	+	0.802948i	0.535554	+	0.844501i	$0.320103\pi$
$930$	−1.47080	+	2.54751i	−0.0482295	+	0.0835360i
$931$	3.23531			0.106033
$932$	11.5696	−	20.0391i	0.378973	−	0.656401i
$933$	−56.9870	−	98.7044i	−1.86567	−	3.23144i
$934$	4.00727	+	6.94080i	0.131122	+	0.227110i
$935$	10.1989			0.333538
$936$	4.91440	−	25.9993i	0.160632	−	0.849813i
$937$	32.4601			1.06042			0.530212	−	0.847865i	$-0.322112\pi$
$937$	32.4601			1.06042			0.530212	+	0.847865i	$0.322112\pi$
$938$	−1.17829	−	2.04086i	−0.0384725	−	0.0666364i
$939$	11.9838	+	20.7566i	0.391078	+	0.677366i
$940$	3.53580	−	6.12419i	0.115325	−	0.199749i
$941$	−12.6051			−0.410913			−0.205457	−	0.978666i	$-0.565868\pi$
$941$	−12.6051			−0.410913			−0.205457	+	0.978666i	$0.565868\pi$
$942$	−4.98642	+	8.63673i	−0.162466	+	0.281400i
$943$	3.84782	−	6.66462i	0.125302	−	0.217030i
$944$	32.4812			1.05717
$945$	18.6714	−	32.3397i	0.607379	−	1.05201i
$946$	−0.473236	−	0.819669i	−0.0153862	−	0.0266497i
$947$	6.64010	+	11.5010i	0.215774	+	0.373732i	0.953512	−	0.301356i	$-0.0974392\pi$
$947$	6.64010	+	11.5010i	0.215774	+	0.373732i	−0.737738	+	0.675088i	$0.764106\pi$
$948$	41.7133			1.35479
$949$	−13.4880	+	4.72242i	−0.437838	+	0.153296i
$950$	−0.0157406			−0.000510693
$951$	−13.3561	−	23.1335i	−0.433102	−	0.750155i
$952$	0.628085	+	1.08787i	0.0203563	+	0.0352582i
$953$	29.2159	−	50.6035i	0.946397	−	1.63921i	0.193467	−	0.981107i	$-0.438027\pi$
$953$	29.2159	−	50.6035i	0.946397	−	1.63921i	0.752930	−	0.658101i	$-0.228640\pi$
$954$	15.6127			0.505481
$955$	−3.18151	+	5.51053i	−0.102951	+	0.178317i
$956$	−4.06602	+	7.04255i	−0.131504	+	0.227772i
$957$	6.70124			0.216620
$958$	0.826224	−	1.43106i	0.0266941	−	0.0462355i
$959$	−9.00160	−	15.5912i	−0.290677	−	0.503467i
$960$	24.9965	+	43.2952i	0.806759	+	1.39735i
$961$	−28.0584			−0.905109
$962$	−0.240708	+	1.27345i	−0.00776074	+	0.0410576i
$963$	71.9061			2.31714
$964$	3.92546	+	6.79910i	0.126431	+	0.218984i
$965$	−11.2131	−	19.4217i	−0.360964	−	0.625207i
$966$	−0.322253	+	0.558158i	−0.0103683	+	0.0179585i
$967$	33.2182			1.06823			0.534113	−	0.845413i	$-0.320646\pi$
$967$	33.2182			1.06823			0.534113	+	0.845413i	$0.320646\pi$
$968$	0.0170579	−	0.0295451i	0.000548261	−	0.000949616i
$969$	−7.39381	+	12.8064i	−0.237523	+	0.411402i
$970$	7.92901			0.254585
$971$	−8.38890	+	14.5300i	−0.269213	+	0.466290i	−0.968659	−	0.248395i	$-0.920097\pi$
$971$	−8.38890	+	14.5300i	−0.269213	+	0.466290i	0.699446	+	0.714685i	$0.253430\pi$
$972$	−52.9460	−	91.7052i	−1.69824	−	2.94144i
$973$	6.95896	+	12.0533i	0.223094	+	0.386410i
$974$	−4.28023			−0.137148
$975$	−0.190960	−	0.164273i	−0.00611560	−	0.00526095i
$976$	20.1266			0.644238
$977$	25.0211	+	43.3378i	0.800496	+	1.38650i	0.919290	+	0.393581i	$0.128764\pi$
$977$	25.0211	+	43.3378i	0.800496	+	1.38650i	−0.118793	+	0.992919i	$0.537903\pi$
$978$	7.07473	+	12.2538i	0.226225	+	0.391833i
$979$	−15.1632	+	26.2634i	−0.484618	+	0.839382i
$980$	4.34328			0.138741
$981$	9.13316	−	15.8191i	0.291599	−	0.505065i
$982$	1.76737	−	3.06118i	0.0563992	−	0.0976862i
$983$	16.6741			0.531822			0.265911	−	0.963998i	$-0.414327\pi$
$983$	16.6741			0.531822			0.265911	+	0.963998i	$0.414327\pi$
$984$	13.9201	−	24.1103i	0.443756	−	0.768608i
$985$	−28.3574	−	49.1164i	−0.903540	−	1.56498i
$986$	−0.0966271	−	0.167363i	−0.00307723	−	0.00532993i
$987$	−5.40919			−0.172177
$988$	17.2130	+	14.8075i	0.547620	+	0.471090i
$989$	1.03250			0.0328316
$990$	6.89249	+	11.9381i	0.219058	+	0.379419i
$991$	−10.1642	−	17.6050i	−0.322878	−	0.559241i	0.658203	−	0.752841i	$-0.271317\pi$
$991$	−10.1642	−	17.6050i	−0.322878	−	0.559241i	−0.981081	+	0.193600i	$0.937984\pi$
$992$	−2.29646	+	3.97759i	−0.0729128	+	0.126289i
$993$	−2.96905			−0.0942201
$994$	−0.603190	+	1.04476i	−0.0191320	+	0.0331377i
$995$	−13.8864	+	24.0519i	−0.440228	+	0.762497i
$996$	−30.0089			−0.950870
$997$	−3.13823	+	5.43557i	−0.0993887	+	0.172146i	−0.911432	−	0.411451i	$-0.865022\pi$
$997$	−3.13823	+	5.43557i	−0.0993887	+	0.172146i	0.812043	+	0.583597i	$0.198355\pi$
$998$	−1.44350	−	2.50021i	−0.0456931	−	0.0791427i
$999$	13.0002	+	22.5170i	0.411307	+	0.712405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.f.c.29.2	yes	8
3.2	odd	2		819.2.o.h.757.3		8
4.3	odd	2		1456.2.s.q.1121.1		8
7.2	even	3		637.2.g.k.263.2		8
7.3	odd	6		637.2.h.i.471.3		8
7.4	even	3		637.2.h.h.471.3		8
7.5	odd	6		637.2.g.j.263.2		8
7.6	odd	2		637.2.f.i.393.2		8
13.2	odd	12		1183.2.c.g.337.4		8
13.3	even	3		1183.2.a.k.1.3		4
13.9	even	3	inner	91.2.f.c.22.2	✓	8
13.10	even	6		1183.2.a.l.1.2		4
13.11	odd	12		1183.2.c.g.337.5		8
39.35	odd	6		819.2.o.h.568.3		8
52.35	odd	6		1456.2.s.q.113.1		8
91.9	even	3		637.2.h.h.165.3		8
91.48	odd	6		637.2.f.i.295.2		8
91.55	odd	6		8281.2.a.bp.1.3		4
91.61	odd	6		637.2.h.i.165.3		8
91.62	odd	6		8281.2.a.bt.1.2		4
91.74	even	3		637.2.g.k.373.2		8
91.87	odd	6		637.2.g.j.373.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.2	✓	8	13.9	even	3	inner
91.2.f.c.29.2	yes	8	1.1	even	1	trivial
637.2.f.i.295.2		8	91.48	odd	6
637.2.f.i.393.2		8	7.6	odd	2
637.2.g.j.263.2		8	7.5	odd	6
637.2.g.j.373.2		8	91.87	odd	6
637.2.g.k.263.2		8	7.2	even	3
637.2.g.k.373.2		8	91.74	even	3
637.2.h.h.165.3		8	91.9	even	3
637.2.h.h.471.3		8	7.4	even	3
637.2.h.i.165.3		8	91.61	odd	6
637.2.h.i.471.3		8	7.3	odd	6
819.2.o.h.568.3		8	39.35	odd	6
819.2.o.h.757.3		8	3.2	odd	2
1183.2.a.k.1.3		4	13.3	even	3
1183.2.a.l.1.2		4	13.10	even	6
1183.2.c.g.337.4		8	13.2	odd	12
1183.2.c.g.337.5		8	13.11	odd	12
1456.2.s.q.113.1		8	52.35	odd	6
1456.2.s.q.1121.1		8	4.3	odd	2
8281.2.a.bp.1.3		4	91.55	odd	6
8281.2.a.bt.1.2		4	91.62	odd	6

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.115680 - 0.200364i) q^{2} +(1.66113 + 2.87716i) q^{3} +(0.973236 - 1.68569i) q^{4} -2.23136 q^{5} +(0.384320 - 0.665661i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.913059 q^{8} +(-4.01868 + 6.96056i) q^{9} +O(q^{10})\)	\(q+(-0.115680 - 0.200364i) q^{2} +(1.66113 + 2.87716i) q^{3} +(0.973236 - 1.68569i) q^{4} -2.23136 q^{5} +(0.384320 - 0.665661i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.913059 q^{8} +(-4.01868 + 6.96056i) q^{9} +(0.258125 + 0.447085i) q^{10} +(-1.66113 - 2.87716i) q^{11} +6.46667 q^{12} +(3.40300 - 1.19146i) q^{13} -0.231361 q^{14} +(-3.70657 - 6.41997i) q^{15} +(-1.84085 - 3.18844i) q^{16} +(0.687890 - 1.19146i) q^{17} +1.85953 q^{18} +(-1.61766 + 2.80186i) q^{19} +(-2.17164 + 3.76139i) q^{20} +3.32225 q^{21} +(-0.384320 + 0.665661i) q^{22} +(-0.419251 - 0.726164i) q^{23} +(-1.51671 - 2.62701i) q^{24} -0.0210289 q^{25} +(-0.632387 - 0.544012i) q^{26} -16.7354 q^{27} +(-0.973236 - 1.68569i) q^{28} +(0.303571 + 0.525800i) q^{29} +(-0.857556 + 1.48533i) q^{30} +1.71511 q^{31} +(-1.33896 + 2.31915i) q^{32} +(5.51868 - 9.55864i) q^{33} -0.318302 q^{34} +(-1.11568 + 1.93242i) q^{35} +(7.82225 + 13.5485i) q^{36} +(-0.776807 - 1.34547i) q^{37} +0.748524 q^{38} +(9.08083 + 7.81180i) q^{39} +2.03736 q^{40} +(4.58892 + 7.94824i) q^{41} +(-0.384320 - 0.665661i) q^{42} +(-0.615680 + 1.06639i) q^{43} -6.46667 q^{44} +(8.96713 - 15.5315i) q^{45} +(-0.0969983 + 0.168006i) q^{46} -1.62817 q^{47} +(6.11577 - 10.5928i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.00243263 + 0.00421343i) q^{50} +4.57069 q^{51} +(1.30348 - 6.89599i) q^{52} +8.39607 q^{53} +(1.93596 + 3.35318i) q^{54} +(3.70657 + 6.41997i) q^{55} +(-0.456530 + 0.790732i) q^{56} -10.7485 q^{57} +(0.0702344 - 0.121650i) q^{58} +(-4.41117 + 7.64037i) q^{59} -14.4295 q^{60} +(-2.73334 + 4.73428i) q^{61} +(-0.198405 - 0.343647i) q^{62} +(4.01868 + 6.96056i) q^{63} -6.74383 q^{64} +(-7.59332 + 2.65858i) q^{65} -2.55361 q^{66} +(5.09287 + 8.82111i) q^{67} +(-1.33896 - 2.31915i) q^{68} +(1.39286 - 2.41250i) q^{69} +0.516249 q^{70} +(2.60714 - 4.51570i) q^{71} +(3.66929 - 6.35540i) q^{72} -3.96355 q^{73} +(-0.179723 + 0.311289i) q^{74} +(-0.0349316 - 0.0605033i) q^{75} +(3.14872 + 5.45375i) q^{76} -3.32225 q^{77} +(0.514731 - 2.72315i) q^{78} +6.45051 q^{79} +(4.10760 + 7.11457i) q^{80} +(-15.7436 - 27.2687i) q^{81} +(1.06170 - 1.83891i) q^{82} -4.64055 q^{83} +(3.23334 - 5.60030i) q^{84} +(-1.53493 + 2.65858i) q^{85} +0.284889 q^{86} +(-1.00854 + 1.74684i) q^{87} +(1.51671 + 2.62701i) q^{88} +(-4.56413 - 7.90530i) q^{89} -4.14929 q^{90} +(0.669665 - 3.54282i) q^{91} -1.63212 q^{92} +(2.84902 + 4.93464i) q^{93} +(0.188347 + 0.326227i) q^{94} +(3.60957 - 6.25197i) q^{95} -8.89672 q^{96} +(7.67944 - 13.3012i) q^{97} +(-0.115680 + 0.200364i) q^{98} +26.7022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 3 * q^15 - 19 * q^16 + 4 * q^17 - 6 * q^18 - q^19 + 2 * q^20 - 2 * q^21 - 5 * q^22 + 2 * q^23 + 3 * q^24 + 10 * q^25 + 12 * q^26 - 52 * q^27 + 5 * q^28 - q^29 + 4 * q^30 - 8 * q^31 + 33 * q^32 + 19 * q^33 + 6 * q^34 - 7 * q^35 + 34 * q^36 + 10 * q^37 - 46 * q^38 + 20 * q^39 - 34 * q^40 + 22 * q^41 - 5 * q^42 - 3 * q^43 - 24 * q^44 + 11 * q^45 - 24 * q^46 + 4 * q^47 - 11 * q^48 - 4 * q^49 - 43 * q^50 + 14 * q^51 + 65 * q^52 + 4 * q^53 - 5 * q^54 + 3 * q^55 - 6 * q^56 - 34 * q^57 + 11 * q^58 + 8 * q^59 - 22 * q^60 - 8 * q^61 + 5 * q^62 + 7 * q^63 + 28 * q^64 + 7 * q^65 + 12 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 22 * q^70 + 14 * q^71 - 5 * q^72 - 16 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 + 2 * q^77 - q^78 - 52 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 + 12 * q^84 - 5 * q^85 + 24 * q^86 - 13 * q^87 - 3 * q^88 + q^89 + 52 * q^90 - 4 * q^91 + 24 * q^92 + 7 * q^93 - 33 * q^94 - 21 * q^95 - 116 * q^96 - 3 * q^97 + q^98 + 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more