LMFDB - Embedded newform 637.2.f.i.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, 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("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.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:	$5.08647060876$
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:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.2
Root			$-0.115680 + 0.200364i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.i.393.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.115680 + 0.200364i) q^{2} +(-1.66113 + 2.87716i) q^{3} +(0.973236 + 1.68569i) q^{4} +2.23136 q^{5} +(-0.384320 - 0.665661i) q^{6} -0.913059 q^{8} +(-4.01868 - 6.96056i) q^{9} +O(q^{10})$	\(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} -0.913059 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} +(-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} +(-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} +(0.303571 - 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} +(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} +(-0.615680 - 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} +(0.00243263 - 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} -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} -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} +(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} +(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} +(-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} -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} +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} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + q^2 + q^3 - 5 * q^4 + 14 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9	$ 8 q + q^{2} + q^{3} - 5 q^{4} + 14 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9} - 11 q^{10} + q^{11} - 24 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} - 6 q^{18} + q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} - 3 q^{24} + 10 q^{25} - 12 q^{26} + 52 q^{27} - q^{29} + 4 q^{30} + 8 q^{31} + 33 q^{32} - 19 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} + 46 q^{38} + 20 q^{39} + 34 q^{40} - 22 q^{41} - 3 q^{43} - 24 q^{44} - 11 q^{45} - 24 q^{46} - 4 q^{47} + 11 q^{48} - 43 q^{50} + 14 q^{51} - 65 q^{52} + 4 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} + 11 q^{58} - 8 q^{59} - 22 q^{60} + 8 q^{61} - 5 q^{62} + 28 q^{64} + 7 q^{65} - 12 q^{66} + 6 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} - 5 q^{72} + 16 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} - 52 q^{79} + 7 q^{80} - 24 q^{81} - 14 q^{82} - 5 q^{85} + 24 q^{86} + 13 q^{87} - 3 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} + 33 q^{94} - 21 q^{95} + 116 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) $ 8 * q + q^2 + q^3 - 5 * q^4 + 14 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9 - 11 * q^10 + q^11 - 24 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 - 6 * q^18 + q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 - 3 * q^24 + 10 * q^25 - 12 * q^26 + 52 * q^27 - q^29 + 4 * q^30 + 8 * q^31 + 33 * q^32 - 19 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 + 46 * q^38 + 20 * q^39 + 34 * q^40 - 22 * q^41 - 3 * q^43 - 24 * q^44 - 11 * q^45 - 24 * q^46 - 4 * q^47 + 11 * q^48 - 43 * q^50 + 14 * q^51 - 65 * q^52 + 4 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 + 11 * q^58 - 8 * q^59 - 22 * q^60 + 8 * q^61 - 5 * q^62 + 28 * q^64 + 7 * q^65 - 12 * q^66 + 6 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 - 5 * q^72 + 16 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 - 52 * q^79 + 7 * q^80 - 24 * q^81 - 14 * q^82 - 5 * q^85 + 24 * q^86 + 13 * q^87 - 3 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 + 33 * q^94 - 21 * q^95 + 116 * q^96 + 3 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	−0.904022	−	0.427485i	$-0.859400\pi$
$2$	−0.115680	+	0.200364i	−0.0817984	+	0.141679i	0.822224	+	0.569164i	$0.192733\pi$
$3$	−1.66113	+	2.87716i	−0.959052	+	1.66113i	−0.234241	+	0.972179i	$0.575260\pi$
$3$	−1.66113	+	2.87716i	−0.959052	+	1.66113i	−0.724811	+	0.688948i	$0.758073\pi$
$4$	0.973236	+	1.68569i	0.486618	+	0.842847i
$5$	2.23136			0.997895			0.498947	−	0.866632i	$-0.333720\pi$
$5$	2.23136			0.997895			0.498947	+	0.866632i	$0.333720\pi$
$6$	−0.384320	−	0.665661i	−0.156898	−	0.271755i
$7$		0			0
$7$		0			0
$8$	−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	0.499151	+	0.866515i	$0.333645\pi$
$11$	−1.66113	+	2.87716i	−0.500848	+	0.867495i	−1.00000		0.000980003i	$0.999688\pi$
$12$	−6.46667			−1.86677
$13$	−3.40300	−	1.19146i	−0.943823	−	0.330452i
$13$	−3.40300	−	1.19146i	−0.943823	−	0.330452i
$14$		0			0
$15$	−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	$-0.220022\pi$
$17$	−0.687890	−	1.19146i	−0.166838	−	0.288972i	−0.937306	+	0.348506i	$0.886689\pi$
$18$	1.85953			0.438296
$19$	1.61766	+	2.80186i	0.371116	+	0.642791i	0.989737	−	0.142898i	$-0.0456420\pi$
$19$	1.61766	+	2.80186i	0.371116	+	0.642791i	−0.618622	+	0.785689i	$0.712309\pi$
$20$	2.17164	+	3.76139i	0.485594	+	0.841073i
$21$		0			0
$22$	−0.384320	−	0.665661i	−0.0819372	−	0.141919i
$23$	−0.419251	+	0.726164i	−0.0874199	+	0.151416i	−0.906420	−	0.422378i	$-0.861196\pi$
$23$	−0.419251	+	0.726164i	−0.0874199	+	0.151416i	0.819000	+	0.573794i	$0.194529\pi$
$24$	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			0
$29$	0.303571	−	0.525800i	0.0563717	−	0.0976386i	−0.836462	−	0.548024i	$-0.815380\pi$
$29$	0.303571	−	0.525800i	0.0563717	−	0.0976386i	0.892834	+	0.450386i	$0.148713\pi$
$30$	−0.857556	−	1.48533i	−0.156568	−	0.271183i
$31$	−1.71511			−0.308043			−0.154022	−	0.988067i	$-0.549223\pi$
$31$	−1.71511			−0.308043			−0.154022	+	0.988067i	$0.549223\pi$
$32$	−1.33896	−	2.31915i	−0.236697	−	0.409971i
$33$	−5.51868	−	9.55864i	−0.960679	−	1.66395i
$34$	0.318302			0.0545883
$35$		0			0
$36$	7.82225	−	13.5485i	1.30371	−	2.25809i
$37$	−0.776807	+	1.34547i	−0.127706	+	0.221194i	−0.922788	−	0.385309i	$-0.874095\pi$
$37$	−0.776807	+	1.34547i	−0.127706	+	0.221194i	0.795081	+	0.606503i	$0.207428\pi$
$38$	−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	0.245644	+	0.969360i	$0.421001\pi$
$41$	−4.58892	+	7.94824i	−0.716668	+	1.24131i	−0.962313	+	0.271946i	$0.912333\pi$
$42$		0			0
$43$	−0.615680	−	1.06639i	−0.0938904	−	0.162623i	0.815255	−	0.579103i	$-0.196597\pi$
$43$	−0.615680	−	1.06639i	−0.0938904	−	0.162623i	−0.909145	+	0.416480i	$0.863264\pi$
$44$	−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	$-0.462112\pi$
$47$	1.62817			0.237493			0.118747	+	0.992925i	$0.462112\pi$
$48$	−6.11577	−	10.5928i	−0.882735	−	1.52894i
$49$		0			0
$50$	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			0
$57$	−10.7485			−1.42368
$58$	0.0702344	+	0.121650i	0.00922223	+	0.0159734i
$59$	4.41117	+	7.64037i	0.574285	+	0.994691i	0.996119	+	0.0880181i	$0.0280533\pi$
$59$	4.41117	+	7.64037i	0.574285	+	0.994691i	−0.421834	+	0.906673i	$0.638613\pi$
$60$	−14.4295			−1.86284
$61$	2.73334	+	4.73428i	0.349968	+	0.606162i	0.986243	−	0.165300i	$-0.0528592\pi$
$61$	2.73334	+	4.73428i	0.349968	+	0.606162i	−0.636276	+	0.771462i	$0.719526\pi$
$62$	0.198405	−	0.343647i	0.0251974	−	0.0436432i
$63$		0			0
$64$	−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	−0.366884	−	0.930267i	$-0.619575\pi$
$67$	5.09287	−	8.82111i	0.622193	−	1.07767i	0.989077	−	0.147403i	$-0.0470913\pi$
$68$	1.33896	−	2.31915i	0.162373	−	0.281238i
$69$	−1.39286	−	2.41250i	−0.167680	−	0.290431i
$70$		0			0
$71$	2.60714	+	4.51570i	0.309411	+	0.535915i	0.978234	−	0.207507i	$-0.0665349\pi$
$71$	2.60714	+	4.51570i	0.309411	+	0.535915i	−0.668823	+	0.743422i	$0.733202\pi$
$72$	3.66929	+	6.35540i	0.432430	+	0.748992i
$73$	3.96355			0.463898			0.231949	−	0.972728i	$-0.425490\pi$
$73$	3.96355			0.463898			0.231949	+	0.972728i	$0.425490\pi$
$74$	−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
$77$		0			0
$78$	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	$-0.418029\pi$
$83$	4.64055			0.509367			0.254684	+	0.967024i	$0.418029\pi$
$84$		0			0
$85$	−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	$-0.672591\pi$
$89$	4.56413	−	7.90530i	0.483797	−	0.837960i	0.999827	+	0.0186101i	$0.00592411\pi$
$90$	4.14929			0.437373
$91$		0			0
$92$	−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	−0.932098	−	0.362206i	$-0.882024\pi$
$97$	−7.67944	−	13.3012i	−0.779729	−	1.35053i	0.152369	−	0.988324i	$-0.451310\pi$
$98$		0			0
$99$	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	$-0.962779\pi$
$101$	−3.97521	+	6.88527i	−0.395548	+	0.685110i	0.597623	+	0.801777i	$0.296112\pi$
$102$	−0.528739	+	0.915804i	−0.0523530	+	0.0906781i
$103$	−0.694825			−0.0684631			−0.0342316	−	0.999414i	$-0.510898\pi$
$103$	−0.694825			−0.0684631			−0.0342316	+	0.999414i	$0.510898\pi$
$104$	3.10714	+	1.08787i	0.304680	+	0.106675i
$105$		0			0
$106$	−0.971261	+	1.68227i	−0.0943372	+	0.163397i
$107$	−4.47324	+	7.74787i	−0.432444	+	0.749015i	−0.997083	−	0.0763228i	$-0.975682\pi$
$107$	−4.47324	+	7.74787i	−0.432444	+	0.749015i	0.564639	+	0.825338i	$0.309015\pi$
$108$	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
$112$		0			0
$113$	4.75239	+	8.23138i	0.447067	+	0.774343i	0.998194	−	0.0600786i	$-0.0191351\pi$
$113$	4.75239	+	8.23138i	0.447067	+	0.774343i	−0.551126	+	0.834422i	$0.685802\pi$
$114$	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			0
$120$	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			0
$127$	−9.21672	+	15.9638i	−0.817851	+	1.41656i	0.0894111	+	0.995995i	$0.471502\pi$
$127$	−9.21672	+	15.9638i	−0.817851	+	1.41656i	−0.907262	+	0.420565i	$0.861832\pi$
$128$	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	$-0.475665\pi$
$131$	1.74835			0.152754			0.0763771	+	0.997079i	$0.475665\pi$
$132$	10.7420	−	18.6056i	0.934968	−	1.61941i
$133$		0			0
$134$	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	0.938074	+	0.346436i	$0.112608\pi$
$137$	9.00160	+	15.5912i	0.769059	+	1.33205i	−0.169015	+	0.985614i	$0.554059\pi$
$138$	0.644506			0.0548640
$139$	6.95896	+	12.0533i	0.590251	+	1.02235i	0.994198	+	0.107563i	$0.0343048\pi$
$139$	6.95896	+	12.0533i	0.590251	+	1.02235i	−0.403947	+	0.914782i	$0.632362\pi$
$140$		0			0
$141$	−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
$147$		0			0
$148$	−3.02407			−0.248577
$149$	7.96515	+	13.7961i	0.652531	+	1.13022i	0.982507	+	0.186227i	$0.0596261\pi$
$149$	7.96515	+	13.7961i	0.652531	+	1.13022i	−0.329976	+	0.943989i	$0.607041\pi$
$150$	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			0
$155$	−3.82703			−0.307395
$156$	22.0061	+	7.70479i	1.76190	+	0.616877i
$157$	12.9747			1.03549			0.517745	−	0.855535i	$-0.326771\pi$
$157$	12.9747			1.03549			0.517745	+	0.855535i	$0.326771\pi$
$158$	−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			0
$162$	−3.64244	−	6.30890i	−0.286177	−	0.495674i
$163$	−9.20423	−	15.9422i	−0.720931	−	1.24869i	−0.960627	−	0.277841i	$-0.910381\pi$
$163$	−9.20423	−	15.9422i	−0.720931	−	1.24869i	0.239697	−	0.970848i	$-0.422952\pi$
$164$	−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	0.246904	+	0.969040i	$0.420587\pi$
$167$	−9.24967	+	16.0209i	−0.715761	+	1.23973i	−0.962665	+	0.270695i	$0.912747\pi$
$168$		0			0
$169$	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	−0.982200	−	0.187840i	$-0.939851\pi$
$173$	−8.59906	−	14.8940i	−0.653774	−	1.13237i	0.328425	−	0.944530i	$-0.393482\pi$
$174$	−0.466673			−0.0353784
$175$		0			0
$176$	−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	0.457355	+	0.889284i	$0.348797\pi$
$179$	−7.24431	+	12.5475i	−0.541465	+	0.937845i	−0.998820	+	0.0485608i	$0.984537\pi$
$180$	17.4543	−	30.2317i	1.30096	−	2.25334i
$181$	−6.85484			−0.509516			−0.254758	−	0.967005i	$-0.581996\pi$
$181$	−6.85484			−0.509516			−0.254758	+	0.967005i	$0.581996\pi$
$182$		0			0
$183$	−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
$189$		0			0
$190$	−1.67023			−0.121171
$191$	1.42581	+	2.46958i	0.103168	+	0.178693i	0.912988	−	0.407986i	$-0.133769\pi$
$191$	1.42581	+	2.46958i	0.103168	+	0.178693i	−0.809820	+	0.586678i	$0.800435\pi$
$192$	11.2024	−	19.4030i	0.808460	−	1.40029i
$193$	5.02525	−	8.70398i	0.361725	−	0.626526i	−0.626520	−	0.779406i	$-0.715521\pi$
$193$	5.02525	−	8.70398i	0.361725	−	0.626526i	0.988245	+	0.152879i	$0.0488546\pi$
$194$	3.55344			0.255122
$195$	20.2626	−	17.4309i	1.45104	−	1.24826i
$196$		0			0
$197$	12.7085	−	22.0119i	0.905447	−	1.56828i	0.0851299	−	0.996370i	$-0.472869\pi$
$197$	12.7085	−	22.0119i	0.905447	−	1.56828i	0.820317	−	0.571910i	$-0.193797\pi$
$198$	−3.08892	+	5.35016i	−0.219520	+	0.380219i
$199$	−6.22328	−	10.7790i	−0.441157	−	0.764106i	0.556619	−	0.830768i	$-0.312098\pi$
$199$	−6.22328	−	10.7790i	−0.441157	−	0.764106i	−0.997776	+	0.0666623i	$0.978765\pi$
$200$	0.0192006			0.00135769
$201$	16.9198	+	29.3059i	1.19343	+	2.06708i
$202$	−0.919708	−	1.59298i	−0.0647104	−	0.112082i
$203$		0			0
$204$	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			0
$211$	12.1961	−	21.1243i	0.839617	−	1.45426i	−0.0505979	−	0.998719i	$-0.516113\pi$
$211$	12.1961	−	21.1243i	0.839617	−	1.45426i	0.890215	−	0.455540i	$-0.150554\pi$
$212$	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			0
$218$	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	−0.185331	−	0.982676i	$-0.559336\pi$
$223$	11.3247	−	19.6149i	0.758357	−	1.31351i	0.943688	−	0.330837i	$-0.107331\pi$
$224$		0			0
$225$	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	$-0.153088\pi$
$227$	0.642530	+	1.11289i	0.0426462	+	0.0738654i	−0.843914	+	0.536478i	$0.819754\pi$
$228$	−10.4609	−	18.1187i	−0.692787	−	1.19994i
$229$	4.64451			0.306918			0.153459	−	0.988155i	$-0.450959\pi$
$229$	4.64451			0.306918			0.153459	+	0.988155i	$0.450959\pi$
$230$	−0.216438	−	0.374882i	−0.0142715	−	0.0247190i
$231$		0			0
$232$	−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			0
$239$	−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	$-0.125199\pi$
$241$	2.01671	+	3.49304i	0.129907	+	0.225006i	−0.793733	+	0.608266i	$0.791865\pi$
$242$	0.00864462			0.000555697
$243$	−27.2010	−	47.1135i	−1.74495	−	3.02233i
$244$	−5.32036	+	9.21514i	−0.340601	+	0.589939i
$245$		0			0
$246$	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	0.851866	+	0.523760i	$0.175471\pi$
$251$	13.9343	+	24.1348i	0.879523	+	1.52338i	0.0276571	+	0.999617i	$0.491195\pi$
$252$		0			0
$253$	−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	$-0.904824\pi$
$257$	−3.57032	+	6.18398i	−0.222710	+	0.385746i	0.732920	+	0.680315i	$0.238157\pi$
$258$	−0.473236	+	0.819669i	−0.0294624	+	0.0510304i
$259$		0			0
$260$	−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	0.324012	+	0.946053i	$0.394968\pi$
$263$	−10.6596	+	18.4630i	−0.657300	+	1.13848i	−0.981312	+	0.192423i	$0.938365\pi$
$264$	5.03888	+	8.72760i	0.310122	+	0.537147i
$265$	18.7347			1.15086
$266$		0			0
$267$	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	$-0.139572\pi$
$269$	1.39438	+	2.41513i	0.0850167	+	0.147253i	−0.820382	+	0.571816i	$0.806239\pi$
$270$	−4.31982	+	7.48215i	−0.262896	+	0.455349i
$271$	−7.73737	+	13.4015i	−0.470012	+	0.814085i	−0.999412	−	0.0342877i	$-0.989084\pi$
$271$	−7.73737	+	13.4015i	−0.470012	+	0.814085i	0.529400	+	0.848372i	$0.322417\pi$
$272$	5.06521			0.307123
$273$		0			0
$274$	−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	0.770933	−	0.636916i	$-0.219790\pi$
$277$	−2.76477	−	4.78873i	−0.166119	−	0.287727i	−0.937052	+	0.349189i	$0.886457\pi$
$278$	−3.22006			−0.193127
$279$	6.89249	+	11.9381i	0.412642	+	0.714718i
$280$		0			0
$281$	−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	$-0.903447\pi$
$283$	−3.67559	+	6.36631i	−0.218491	+	0.378438i	0.735856	+	0.677138i	$0.236780\pi$
$284$	−5.07473	+	8.78969i	−0.301130	+	0.521572i
$285$	−23.9838			−1.42068
$286$	0.514731	+	2.72315i	0.0304367	+	0.161023i
$287$		0			0
$288$	−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	$-0.296032\pi$
$293$	−6.76675	−	11.7204i	−0.395318	−	0.684710i	−0.993142	+	0.116917i	$0.962699\pi$
$294$		0			0
$295$	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			0
$302$	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	$-0.469925\pi$
$307$	3.30609			0.188688			0.0943442	+	0.995540i	$0.469925\pi$
$308$		0			0
$309$	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	$-0.0745969\pi$
$311$	34.3063			1.94533			0.972665	+	0.232214i	$0.0745969\pi$
$312$	−8.29134	+	7.13263i	−0.469405	+	0.403806i
$313$	−7.21428			−0.407775			−0.203888	−	0.978994i	$-0.565358\pi$
$313$	−7.21428			−0.407775			−0.203888	+	0.978994i	$0.565358\pi$
$314$	−1.50091	+	2.59966i	−0.0847015	+	0.146707i
$315$		0			0
$316$	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			0
$323$	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			0
$330$	5.69803			0.313666
$331$	−0.446843	−	0.773955i	−0.0245607	−	0.0425404i	0.853484	−	0.521119i	$-0.174485\pi$
$331$	−0.446843	−	0.773955i	−0.0245607	−	0.0425404i	−0.878045	+	0.478579i	$0.841152\pi$
$332$	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
$336$		0			0
$337$	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
$343$		0			0
$344$	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	0.997737	−	0.0672387i	$-0.0214189\pi$
$347$	8.20818	+	14.2170i	0.440638	+	0.763207i	−0.557099	+	0.830446i	$0.688086\pi$
$348$	−1.96309	+	3.40018i	−0.105233	+	0.182269i
$349$	17.1861	−	29.7672i	0.919950	−	1.59340i	0.120462	−	0.992718i	$-0.461562\pi$
$349$	17.1861	−	29.7672i	0.919950	−	1.59340i	0.799488	−	0.600682i	$-0.205104\pi$
$350$		0			0
$351$	−56.9506	−	19.9396i	−3.03980	−	1.06430i
$352$	8.89672			0.474197
$353$	−11.9581	+	20.7121i	−0.636467	+	1.10239i	0.349735	+	0.936849i	$0.386272\pi$
$353$	−11.9581	+	20.7121i	−0.636467	+	1.10239i	−0.986202	+	0.165545i	$0.947062\pi$
$354$	3.39060	−	5.87269i	0.180208	−	0.312130i
$355$	5.81747	+	10.0762i	0.308759	+	0.534787i
$356$	17.7679			0.941697
$357$		0			0
$358$	−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
$364$		0			0
$365$	8.84411			0.462922
$366$	2.10095	−	3.63895i	0.109818	−	0.190211i
$367$	9.92798	−	17.1958i	0.518236	−	0.897612i	−0.481539	−	0.876425i	$-0.659922\pi$
$367$	9.92798	−	17.1958i	0.518236	−	0.897612i	0.999776	−	0.0211872i	$-0.00674460\pi$
$368$	−1.54356	−	2.67352i	−0.0804634	−	0.139367i
$369$	73.7656			3.84008
$370$	−0.401026	−	0.694598i	−0.0208484	−	0.0361104i
$371$		0			0
$372$	11.0911			0.575045
$373$	−15.0975	−	26.1497i	−0.781721	−	1.35398i	−0.930938	−	0.365176i	$-0.881009\pi$
$373$	−15.0975	−	26.1497i	−0.781721	−	1.35398i	0.149217	−	0.988804i	$-0.452325\pi$
$374$	−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
$378$		0			0
$379$	2.16121	−	3.74333i	0.111014	−	0.192282i	−0.805165	−	0.593050i	$-0.797923\pi$
$379$	2.16121	−	3.74333i	0.111014	−	0.192282i	0.916179	+	0.400768i	$0.131257\pi$
$380$	−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	$-0.312832\pi$
$383$	−8.67407	−	15.0239i	−0.443224	−	0.767687i	−0.997927	+	0.0643617i	$0.979499\pi$
$384$	11.4885	+	19.8987i	0.586271	+	1.01545i
$385$		0			0
$386$	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			0
$393$	−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	−0.975154	−	0.221527i	$-0.928896\pi$
$397$	−13.5375	−	23.4476i	−0.679425	−	1.17680i	0.295729	−	0.955272i	$-0.404437\pi$
$398$	2.87965			0.144344
$399$		0			0
$400$	0.0387110	−	0.0670494i	0.00193555	−	0.00335247i
$401$	14.6429	−	25.3622i	0.731232	−	1.26653i	−0.225125	−	0.974330i	$-0.572279\pi$
$401$	14.6429	−	25.3622i	0.731232	−	1.26653i	0.956357	−	0.292201i	$-0.0943875\pi$
$402$	−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			0
$407$	−2.58075	−	4.46999i	−0.127923	−	0.221569i
$408$	−4.17331			−0.206610
$409$	11.6856	+	20.2401i	0.577817	+	1.00081i	0.995729	+	0.0923213i	$0.0294287\pi$
$409$	11.6856	+	20.2401i	0.577817	+	1.00081i	−0.417912	+	0.908487i	$0.637238\pi$
$410$	−2.36903	−	4.10327i	−0.116998	−	0.202646i
$411$	−59.8112			−2.95027
$412$	−0.676229	−	1.17126i	−0.0333154	−	0.0577040i
$413$		0			0
$414$	−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	$-0.717206\pi$
$419$	7.30320	−	12.6495i	0.356785	−	0.617969i	0.987422	+	0.158109i	$0.0505397\pi$
$420$		0			0
$421$	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
$427$		0			0
$428$	−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	−0.675290	−	0.737552i	$-0.735982\pi$
$431$	6.25087	−	10.8268i	0.301094	−	0.521510i	0.976384	+	0.216042i	$0.0693149\pi$
$432$	−30.8073	+	53.3599i	−1.48222	+	2.56728i
$433$	−5.47361	−	9.48057i	−0.263045	−	0.455607i	0.704005	−	0.710195i	$-0.251393\pi$
$433$	−5.47361	−	9.48057i	−0.263045	−	0.455607i	−0.967050	+	0.254588i	$0.918060\pi$
$434$		0			0
$435$	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	$-0.973970\pi$
$439$	−8.95896	+	15.5174i	−0.427588	+	0.740604i	0.569070	+	0.822289i	$0.307303\pi$
$440$	3.38432	−	5.86181i	0.161341	−	0.279451i
$441$		0			0
$442$	−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
$448$		0			0
$449$	0.0829898	+	0.143743i	0.00391653	+	0.00678363i	0.867977	−	0.496604i	$-0.165420\pi$
$449$	0.0829898	+	0.143743i	0.00391653	+	0.00678363i	−0.864060	+	0.503388i	$0.832087\pi$
$450$	−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
$455$		0			0
$456$	9.81404			0.459584
$457$	−15.8677	+	27.4837i	−0.742260	+	1.28563i	0.209205	+	0.977872i	$0.432913\pi$
$457$	−15.8677	+	27.4837i	−0.742260	+	1.28563i	−0.951464	+	0.307760i	$0.900421\pi$
$458$	−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	0.975922	+	0.218121i	$0.0699926\pi$
$461$	14.5328	+	25.1715i	0.676859	+	1.17235i	−0.299063	+	0.954233i	$0.596674\pi$
$462$		0			0
$463$	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	$-0.204038\pi$
$467$	34.6409			1.60299			0.801495	+	0.598002i	$0.204038\pi$
$468$	−42.7617	+	36.7858i	−1.97666	+	1.70042i
$469$		0			0
$470$	−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
$476$		0			0
$477$	−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	$-0.885505\pi$
$479$	−3.57115	+	6.18541i	−0.163170	+	0.282619i	0.772834	+	0.634608i	$0.218839\pi$
$480$	19.8518			0.906107
$481$	4.24655	−	3.65310i	0.193626	−	0.166567i
$482$	−0.933174			−0.0425049
$483$		0			0
$484$	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	0.995856	−	0.0909493i	$-0.0289901\pi$
$487$	9.25013	+	16.0217i	0.419163	+	0.726012i	−0.576692	+	0.816962i	$0.695657\pi$
$488$	−2.49570	−	4.32267i	−0.112975	−	0.195678i
$489$	61.1575			2.76564
$490$		0			0
$491$	7.63904	−	13.2312i	0.344745	−	0.597116i	−0.640563	−	0.767906i	$-0.721299\pi$
$491$	7.63904	−	13.2312i	0.344745	−	0.597116i	0.985307	+	0.170790i	$0.0546321\pi$
$492$	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
$497$		0			0
$498$	−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	$-0.184986\pi$
$503$	−1.29004	−	2.23441i	−0.0575200	−	0.0996276i	−0.893352	+	0.449358i	$0.851653\pi$
$504$		0			0
$505$	−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	−0.134735	−	0.990882i	$-0.543018\pi$
$509$	17.8404	−	30.9005i	0.790761	−	1.36964i	0.925496	−	0.378757i	$-0.123648\pi$
$510$	−1.17981	+	2.04349i	−0.0522428	+	0.0904872i
$511$		0			0
$512$	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			0
$519$	57.1365			2.50801
$520$	6.93315	+	2.42744i	0.304039	+	0.106450i
$521$	20.9637			0.918437			0.459219	−	0.888323i	$-0.348129\pi$
$521$	20.9637			0.918437			0.459219	+	0.888323i	$0.348129\pi$
$522$	0.564499	−	0.977742i	0.0247075	−	0.0427946i
$523$	−11.4131	+	19.7681i	−0.499062	+	0.864401i	−0.999999	−	0.00108279i	$-0.999655\pi$
$523$	−11.4131	+	19.7681i	−0.499062	+	0.864401i	0.500937	+	0.865484i	$0.332989\pi$
$524$	1.70156	+	2.94719i	0.0743330	+	0.128749i
$525$		0			0
$526$	−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
$532$		0			0
$533$	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
$539$		0			0
$540$	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
$546$		0			0
$547$	−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
$553$		0			0
$554$	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	−0.733222	−	0.679989i	$-0.761985\pi$
$557$	5.24591	−	9.08619i	0.222276	−	0.384994i	0.955499	+	0.294995i	$0.0953179\pi$
$558$	−3.18930			−0.135014
$559$	0.824600	+	4.36249i	0.0348768	+	0.184513i
$560$		0			0
$561$	−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	0.982603	+	0.185718i	$0.0594612\pi$
$563$	15.4737	+	26.8012i	0.652138	+	1.12954i	−0.330465	+	0.943818i	$0.607205\pi$
$564$	−10.5288			−0.443344
$565$	10.6043	+	18.3672i	0.446126	+	0.772713i
$566$	−0.850388	−	1.47292i	−0.0357445	−	0.0619112i
$567$		0			0
$568$	−2.38047	−	4.12310i	−0.0998825	−	0.173002i
$569$	18.4545	−	31.9641i	0.773651	−	1.34000i	−0.161898	−	0.986807i	$-0.551762\pi$
$569$	18.4545	−	31.9641i	0.773651	−	1.34000i	0.935549	−	0.353196i	$-0.114905\pi$
$570$	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
$574$		0			0
$575$	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	$-0.434338\pi$
$577$	9.83999			0.409644			0.204822	+	0.978799i	$0.434338\pi$
$578$	1.74761	+	3.02695i	0.0726910	+	0.125905i
$579$	16.6951	+	28.9168i	0.693826	+	1.20174i
$580$	2.63699			0.109495
$581$		0			0
$582$	−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	$-0.934471\pi$
$587$	−7.56917	+	13.1102i	−0.312413	+	0.541116i	0.666471	+	0.745531i	$0.267804\pi$
$588$		0			0
$589$	−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	$-0.560302\pi$
$593$	−9.17148			−0.376628			−0.188314	+	0.982109i	$0.560302\pi$
$594$	−6.43174	−	11.1401i	−0.263898	−	0.457084i
$595$		0			0
$596$	−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	$-0.921472\pi$
$601$	−6.70179	+	11.6078i	−0.273372	+	0.473494i	0.696351	+	0.717701i	$0.254806\pi$
$602$		0			0
$603$	−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	$-0.0841155\pi$
$607$	6.31812	+	10.9433i	0.256445	+	0.444175i	−0.708842	+	0.705367i	$0.750782\pi$
$608$	4.33195	−	7.50316i	0.175684	−	0.304293i
$609$		0			0
$610$	−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	0.480585	+	0.876948i	$0.340424\pi$
$613$	−12.8540	+	22.2637i	−0.519167	+	0.899223i	−0.999752	+	0.0222753i	$0.992909\pi$
$614$	−0.382450	+	0.662422i	−0.0154344	+	0.0267332i
$615$	−34.0183	−	58.9214i	−1.37175	−	2.37594i
$616$		0			0
$617$	3.29810	+	5.71248i	0.132777	+	0.229976i	0.924746	−	0.380585i	$-0.124277\pi$
$617$	3.29810	+	5.71248i	0.132777	+	0.229976i	−0.791969	+	0.610561i	$0.790944\pi$
$618$	0.267035	+	0.462518i	0.0107417	+	0.0186052i
$619$	21.0124			0.844559			0.422280	−	0.906466i	$-0.361230\pi$
$619$	21.0124			0.844559			0.422280	+	0.906466i	$0.361230\pi$
$620$	−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
$623$		0			0
$624$	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
$630$		0			0
$631$	−13.0105	−	22.5349i	−0.517940	−	0.897099i	−0.999783	−	0.0208412i	$-0.993366\pi$
$631$	−13.0105	−	22.5349i	−0.517940	−	0.897099i	0.481842	−	0.876258i	$-0.339968\pi$
$632$	−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
$637$		0			0
$638$	−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	0.622917	−	0.782288i	$-0.285947\pi$
$641$	−9.26694	−	16.0508i	−0.366022	−	0.633969i	−0.988940	+	0.148319i	$0.952614\pi$
$642$	6.87661			0.271398
$643$	−7.22328	−	12.5111i	−0.284858	−	0.493389i	0.687716	−	0.725979i	$-0.258613\pi$
$643$	−7.22328	−	12.5111i	−0.284858	−	0.493389i	−0.972575	+	0.232590i	$0.925280\pi$
$644$		0			0
$645$	9.12826			0.359425
$646$	0.514903	+	0.891838i	0.0202586	+	0.0350889i
$647$	14.6438	−	25.3637i	0.575706	−	0.997152i	−0.420259	−	0.907404i	$-0.638061\pi$
$647$	14.6438	−	25.3637i	0.575706	−	0.997152i	0.995965	−	0.0897473i	$-0.0286059\pi$
$648$	14.3748	−	24.8979i	0.564696	−	0.978082i
$649$	−29.3100			−1.15052
$650$	−0.0132984	+	0.0114399i	−0.000521605	+	0.000448711i
$651$		0			0
$652$	17.9158	−	31.0310i	0.701636	−	1.21527i
$653$	15.4807	−	26.8134i	0.605808	−	1.04929i	−0.386115	−	0.922451i	$-0.626183\pi$
$653$	15.4807	−	26.8134i	0.605808	−	1.04929i	0.991923	−	0.126840i	$-0.0404836\pi$
$654$	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			0
$659$	18.5414	+	32.1146i	0.722270	+	1.25101i	0.960088	+	0.279699i	$0.0902347\pi$
$659$	18.5414	+	32.1146i	0.722270	+	1.25101i	−0.237817	+	0.971310i	$0.576432\pi$
$660$	23.9692	−	41.5159i	0.933000	−	1.61600i
$661$	−10.2009	+	17.6685i	−0.396770	+	0.687226i	−0.993325	−	0.115346i	$-0.963202\pi$
$661$	−10.2009	+	17.6685i	−0.396770	+	0.687226i	0.596555	+	0.802572i	$0.296536\pi$
$662$	0.206764			0.00803611
$663$	−15.5541	−	5.44580i	−0.604070	−	0.211497i
$664$	−4.23710			−0.164431
$665$		0			0
$666$	−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
$672$		0			0
$673$	−7.25551	+	12.5669i	−0.279679	+	0.484419i	−0.971305	−	0.237837i	$-0.923562\pi$
$673$	−7.25551	+	12.5669i	−0.279679	+	0.484419i	0.691626	+	0.722256i	$0.256895\pi$
$674$	−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	$-0.478484\pi$
$677$	3.51476			0.135083			0.0675417	+	0.997716i	$0.478484\pi$
$678$	3.65287	−	6.32696i	0.140288	−	0.242985i
$679$		0			0
$680$	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	0.999781	+	0.0209144i	$0.00665773\pi$
$683$	13.5376	+	23.4479i	0.518003	+	0.897208i	−0.481778	+	0.876293i	$0.660009\pi$
$684$	50.6149			1.93531
$685$	20.0858	+	34.7897i	0.767440	+	1.32925i
$686$		0			0
$687$	−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	−0.431295	−	0.902211i	$-0.641943\pi$
$691$	14.8702	−	25.7560i	0.565690	−	0.979803i	0.996985	−	0.0775926i	$-0.0247233\pi$
$692$	16.7378	−	28.9908i	0.636277	−	1.10206i
$693$		0			0
$694$	−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			0
$701$	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
$707$		0			0
$708$	−28.5256	−	49.4078i	−1.07206	−	1.85686i
$709$	14.3402	+	24.8379i	0.538557	+	0.932808i	0.998982	+	0.0451098i	$0.0143638\pi$
$709$	14.3402	+	24.8379i	0.538557	+	0.932808i	−0.460425	+	0.887699i	$0.652303\pi$
$710$	−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
$714$		0			0
$715$	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	$-0.00909607\pi$
$719$	12.7381	+	22.0631i	0.475052	+	0.822813i	−0.524540	+	0.851386i	$0.675763\pi$
$720$	66.0285			2.46074
$721$		0			0
$722$	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	$-0.446472\pi$
$727$	9.02572			0.334746			0.167373	+	0.985894i	$0.446472\pi$
$728$		0			0
$729$	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	$-0.455349\pi$
$733$	7.57069			0.279630			0.139815	+	0.990178i	$0.455349\pi$
$734$	2.29695	+	3.97843i	0.0847818	+	0.146846i
$735$		0			0
$736$	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	−0.801447	−	0.598066i	$-0.795936\pi$
$739$	3.18648	−	5.51914i	0.117216	−	0.203025i	0.918664	+	0.395041i	$0.129270\pi$
$740$	−6.74778			−0.248053
$741$	36.5772	+	12.8064i	1.34370	+	0.470457i
$742$		0			0
$743$	11.4148	−	19.7711i	0.418770	−	0.725330i	−0.577046	−	0.816711i	$-0.695795\pi$
$743$	11.4148	−	19.7711i	0.418770	−	0.725330i	0.995816	+	0.0913811i	$0.0291281\pi$
$744$	−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
$749$		0			0
$750$	4.30581	+	7.45788i	0.157226	+	0.272323i
$751$	−19.6848	+	34.0950i	−0.718307	+	1.24414i	0.243363	+	0.969935i	$0.421749\pi$
$751$	−19.6848	+	34.0950i	−0.718307	+	1.24414i	−0.961670	+	0.274209i	$0.911584\pi$
$752$	−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
$756$		0			0
$757$	−4.36357	+	7.55792i	−0.158597	+	0.274697i	−0.934363	−	0.356323i	$-0.884030\pi$
$757$	−4.36357	+	7.55792i	−0.158597	+	0.274697i	0.775766	+	0.631020i	$0.217364\pi$
$758$	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	$-0.302520\pi$
$761$	−11.4195	−	19.7792i	−0.413958	−	0.716996i	−0.995318	+	0.0966503i	$0.969187\pi$
$762$	14.1687			0.513276
$763$		0			0
$764$	−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	−0.359846	−	0.933012i	$-0.617171\pi$
$769$	17.4174	−	30.1679i	0.628089	−	1.08788i	0.987935	−	0.154871i	$-0.0494960\pi$
$770$		0			0
$771$	−11.8615	−	20.5447i	−0.427182	−	0.739900i
$772$	19.5630			0.704088
$773$	−16.6372	−	28.8164i	−0.598397	−	1.03645i	−0.993058	−	0.117627i	$-0.962471\pi$
$773$	−16.6372	−	28.8164i	−0.598397	−	1.03645i	0.394661	−	0.918827i	$-0.370862\pi$
$774$	−1.14488	−	1.98299i	−0.0411518	−	0.0712769i
$775$	0.0360668			0.00129556
$776$	7.01178	+	12.1448i	0.251708	+	0.435971i
$777$		0			0
$778$	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
$784$		0			0
$785$	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	$-0.331778\pi$
$787$	−13.9079	−	24.0891i	−0.495762	−	0.858685i	−0.999988	+	0.00488682i	$0.998444\pi$
$788$	49.4737			1.76243
$789$	−35.4139	−	61.3387i	−1.26077	−	2.18372i
$790$	−1.66504	+	2.88393i	−0.0592393	+	0.102606i
$791$		0			0
$792$	−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	0.986459	+	0.164007i	$0.0524421\pi$
$797$	17.9343	+	31.0630i	0.635264	+	1.10031i	−0.351195	+	0.936302i	$0.614225\pi$
$798$		0			0
$799$	−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
$805$		0			0
$806$	−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	−0.665745	−	0.746179i	$-0.731886\pi$
$809$	8.91223	−	15.4364i	0.313337	−	0.542716i	0.979083	+	0.203463i	$0.0652196\pi$
$810$	−8.12761	−	14.0774i	−0.285575	−	0.494630i
$811$	−25.2152			−0.885425			−0.442713	−	0.896664i	$-0.645984\pi$
$811$	−25.2152			−0.885425			−0.442713	+	0.896664i	$0.645984\pi$
$812$		0			0
$813$	−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
$819$		0			0
$820$	−39.8619			−1.39204
$821$	5.22797	−	9.05511i	0.182457	−	0.316026i	−0.760259	−	0.649620i	$-0.774928\pi$
$821$	5.22797	−	9.05511i	0.182457	−	0.316026i	0.942717	+	0.333594i	$0.108261\pi$
$822$	6.91899	−	11.9840i	0.241327	−	0.417991i
$823$	16.6203	+	28.7871i	0.579346	+	1.00346i	0.995554	+	0.0941873i	$0.0300253\pi$
$823$	16.6203	+	28.7871i	0.579346	+	1.00346i	−0.416209	+	0.909269i	$0.636641\pi$
$824$	0.634416			0.0221009
$825$	0.116052	+	0.201007i	0.00404040	+	0.00699817i
$826$		0			0
$827$	−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	$-0.739708\pi$
$829$	8.34721	−	14.4578i	0.289911	−	0.502140i	0.973788	+	0.227457i	$0.0730411\pi$
$830$	−1.19784	+	2.07472i	−0.0415777	+	0.0720147i
$831$	18.3706			0.637268
$832$	22.9493	+	8.03501i	0.795623	+	0.278564i
$833$		0			0
$834$	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	−0.916213	−	0.400691i	$-0.868770\pi$
$839$	−23.3206	−	40.3924i	−0.805115	−	1.39450i	0.111098	−	0.993809i	$-0.464563\pi$
$840$		0			0
$841$	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			0
$848$	−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	$-0.736860\pi$
$853$	−39.5640			−1.35464			−0.677322	+	0.735686i	$0.736860\pi$
$854$		0			0
$855$	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	$-0.391567\pi$
$857$	19.5613			0.668201			0.334101	+	0.942537i	$0.391567\pi$
$858$	−8.68995	−	3.04253i	−0.296670	−	0.103870i
$859$	10.1632			0.346762			0.173381	−	0.984855i	$-0.444531\pi$
$859$	10.1632			0.346762			0.173381	+	0.984855i	$0.444531\pi$
$860$	2.67407	−	4.63163i	0.0911851	−	0.157937i
$861$		0			0
$862$	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
$868$		0			0
$869$	−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
$875$		0			0
$876$	−25.6310			−0.865991
$877$	0.850801	+	1.47363i	0.0287295	+	0.0497610i	0.880033	−	0.474913i	$-0.157521\pi$
$877$	0.850801	+	1.47363i	0.0287295	+	0.0497610i	−0.851303	+	0.524674i	$0.824187\pi$
$878$	−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	$-0.894346\pi$
$881$	−5.65448	+	9.79384i	−0.190504	+	0.329963i	0.754913	+	0.655825i	$0.227679\pi$
$882$		0			0
$883$	−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	$-0.846413\pi$
$887$	−1.22346	+	2.11909i	−0.0410797	+	0.0711522i	0.844755	+	0.535154i	$0.179746\pi$
$888$	2.35638	+	4.08136i	0.0790748	+	0.136962i
$889$		0			0
$890$	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
$896$		0			0
$897$	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
$903$		0			0
$904$	−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	−0.285003	−	0.958526i	$-0.591995\pi$
$907$	20.7083	−	35.8678i	0.687607	−	1.19097i	0.972610	−	0.232443i	$-0.0746719\pi$
$908$	−1.25067	+	2.16622i	−0.0415048	+	0.0718885i
$909$	63.9004			2.11944
$910$		0			0
$911$	−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			0
$918$	5.32691			0.175814
$919$	−22.4708	−	38.9206i	−0.741243	−	1.28387i	−0.951930	−	0.306317i	$-0.900903\pi$
$919$	−22.4708	−	38.9206i	−0.741243	−	1.28387i	0.210686	−	0.977554i	$-0.432430\pi$
$920$	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
$924$		0			0
$925$	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	$-0.0132305\pi$
$929$	14.1298	+	24.4735i	0.463582	+	0.802948i	−0.535554	+	0.844501i	$0.679897\pi$
$930$	1.47080	+	2.54751i	0.0482295	+	0.0835360i
$931$		0			0
$932$	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	$-0.677888\pi$
$937$	−32.4601			−1.06042			−0.530212	+	0.847865i	$0.677888\pi$
$938$		0			0
$939$	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	$-0.434132\pi$
$941$	12.6051			0.410913			0.205457	+	0.978666i	$0.434132\pi$
$942$	−4.98642	−	8.63673i	−0.162466	−	0.281400i
$943$	−3.84782	−	6.66462i	−0.125302	−	0.217030i
$944$	−32.4812			−1.05717
$945$		0			0
$946$	−0.473236	+	0.819669i	−0.0153862	+	0.0266497i
$947$	6.64010	−	11.5010i	0.215774	−	0.373732i	−0.737738	−	0.675088i	$-0.764106\pi$
$947$	6.64010	−	11.5010i	0.215774	−	0.373732i	0.953512	+	0.301356i	$0.0974392\pi$
$948$	−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			0
$953$	29.2159	+	50.6035i	0.946397	+	1.63921i	0.752930	+	0.658101i	$0.228640\pi$
$953$	29.2159	+	50.6035i	0.946397	+	1.63921i	0.193467	+	0.981107i	$0.438027\pi$
$954$	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
$959$		0			0
$960$	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			0
$967$	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	$-0.0799032\pi$
$971$	8.38890	+	14.5300i	0.269213	+	0.466290i	−0.699446	+	0.714685i	$0.746570\pi$
$972$	52.9460	−	91.7052i	1.69824	−	2.94144i
$973$		0			0
$974$	−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	−0.118793	−	0.992919i	$-0.537903\pi$
$977$	25.0211	−	43.3378i	0.800496	−	1.38650i	0.919290	−	0.393581i	$-0.128764\pi$
$978$	−7.07473	+	12.2538i	−0.226225	+	0.391833i
$979$	15.1632	+	26.2634i	0.484618	+	0.839382i
$980$		0			0
$981$	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	$-0.585673\pi$
$983$	−16.6741			−0.531822			−0.265911	+	0.963998i	$0.585673\pi$
$984$	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
$987$		0			0
$988$	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	−0.981081	−	0.193600i	$-0.937984\pi$
$991$	−10.1642	+	17.6050i	−0.322878	+	0.559241i	0.658203	+	0.752841i	$0.271317\pi$
$992$	2.29646	+	3.97759i	0.0729128	+	0.126289i
$993$	2.96905			0.0942201
$994$		0			0
$995$	−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	$-0.134978\pi$
$997$	3.13823	+	5.43557i	0.0993887	+	0.172146i	−0.812043	+	0.583597i	$0.801645\pi$
$998$	−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	637.2.f.i.295.2		8
7.2	even	3		637.2.h.i.165.3		8
7.3	odd	6		637.2.g.k.373.2		8
7.4	even	3		637.2.g.j.373.2		8
7.5	odd	6		637.2.h.h.165.3		8
7.6	odd	2		91.2.f.c.22.2	✓	8
13.3	even	3	inner	637.2.f.i.393.2		8
13.4	even	6		8281.2.a.bt.1.2		4
13.9	even	3		8281.2.a.bp.1.3		4
21.20	even	2		819.2.o.h.568.3		8
28.27	even	2		1456.2.s.q.113.1		8
91.3	odd	6		637.2.h.h.471.3		8
91.6	even	12		1183.2.c.g.337.4		8
91.16	even	3		637.2.g.j.263.2		8
91.20	even	12		1183.2.c.g.337.5		8
91.48	odd	6		1183.2.a.k.1.3		4
91.55	odd	6		91.2.f.c.29.2	yes	8
91.68	odd	6		637.2.g.k.263.2		8
91.69	odd	6		1183.2.a.l.1.2		4
91.81	even	3		637.2.h.i.471.3		8
273.146	even	6		819.2.o.h.757.3		8
364.55	even	6		1456.2.s.q.1121.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.2	✓	8	7.6	odd	2
91.2.f.c.29.2	yes	8	91.55	odd	6
637.2.f.i.295.2		8	1.1	even	1	trivial
637.2.f.i.393.2		8	13.3	even	3	inner
637.2.g.j.263.2		8	91.16	even	3
637.2.g.j.373.2		8	7.4	even	3
637.2.g.k.263.2		8	91.68	odd	6
637.2.g.k.373.2		8	7.3	odd	6
637.2.h.h.165.3		8	7.5	odd	6
637.2.h.h.471.3		8	91.3	odd	6
637.2.h.i.165.3		8	7.2	even	3
637.2.h.i.471.3		8	91.81	even	3
819.2.o.h.568.3		8	21.20	even	2
819.2.o.h.757.3		8	273.146	even	6
1183.2.a.k.1.3		4	91.48	odd	6
1183.2.a.l.1.2		4	91.69	odd	6
1183.2.c.g.337.4		8	91.6	even	12
1183.2.c.g.337.5		8	91.20	even	12
1456.2.s.q.113.1		8	28.27	even	2
1456.2.s.q.1121.1		8	364.55	even	6
8281.2.a.bp.1.3		4	13.9	even	3
8281.2.a.bt.1.2		4	13.4	even	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.115680 + 0.200364i) q^{2} +(-1.66113 + 2.87716i) q^{3} +(0.973236 + 1.68569i) q^{4} +2.23136 q^{5} +(-0.384320 - 0.665661i) q^{6} -0.913059 q^{8} +(-4.01868 - 6.96056i) q^{9} +O(q^{10})\)	\(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} -0.913059 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} +(-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} +(-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} +(0.303571 - 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} +(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} +(-0.615680 - 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} +(0.00243263 - 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} -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} -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} +(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} +(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} +(-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} -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} +26.7022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{3} - 5 q^{4} + 14 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + q^2 + q^3 - 5 * q^4 + 14 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} + q^{3} - 5 q^{4} + 14 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9} - 11 q^{10} + q^{11} - 24 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} - 6 q^{18} + q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} - 3 q^{24} + 10 q^{25} - 12 q^{26} + 52 q^{27} - q^{29} + 4 q^{30} + 8 q^{31} + 33 q^{32} - 19 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} + 46 q^{38} + 20 q^{39} + 34 q^{40} - 22 q^{41} - 3 q^{43} - 24 q^{44} - 11 q^{45} - 24 q^{46} - 4 q^{47} + 11 q^{48} - 43 q^{50} + 14 q^{51} - 65 q^{52} + 4 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} + 11 q^{58} - 8 q^{59} - 22 q^{60} + 8 q^{61} - 5 q^{62} + 28 q^{64} + 7 q^{65} - 12 q^{66} + 6 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} - 5 q^{72} + 16 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} - 52 q^{79} + 7 q^{80} - 24 q^{81} - 14 q^{82} - 5 q^{85} + 24 q^{86} + 13 q^{87} - 3 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} + 33 q^{94} - 21 q^{95} + 116 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 + q^3 - 5 * q^4 + 14 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9 - 11 * q^10 + q^11 - 24 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 - 6 * q^18 + q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 - 3 * q^24 + 10 * q^25 - 12 * q^26 + 52 * q^27 - q^29 + 4 * q^30 + 8 * q^31 + 33 * q^32 - 19 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 + 46 * q^38 + 20 * q^39 + 34 * q^40 - 22 * q^41 - 3 * q^43 - 24 * q^44 - 11 * q^45 - 24 * q^46 - 4 * q^47 + 11 * q^48 - 43 * q^50 + 14 * q^51 - 65 * q^52 + 4 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 + 11 * q^58 - 8 * q^59 - 22 * q^60 + 8 * q^61 - 5 * q^62 + 28 * q^64 + 7 * q^65 - 12 * q^66 + 6 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 - 5 * q^72 + 16 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 - 52 * q^79 + 7 * q^80 - 24 * q^81 - 14 * q^82 - 5 * q^85 + 24 * q^86 + 13 * q^87 - 3 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 + 33 * q^94 - 21 * q^95 + 116 * q^96 + 3 * q^97 + 46 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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