LMFDB - Embedded newform 637.2.h.h.165.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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([4, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not 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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.3
Root			$-0.115680 - 0.200364i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.h.471.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.231361 q^{2} +(1.66113 + 2.87716i) q^{3} -1.94647 q^{4} +(1.11568 + 1.93242i) q^{5} +(0.384320 + 0.665661i) q^{6} -0.913059 q^{8} +(-4.01868 + 6.96056i) q^{9} +O(q^{10})$	\(q+0.231361 q^{2} +(1.66113 + 2.87716i) q^{3} -1.94647 q^{4} +(1.11568 + 1.93242i) 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} +(-3.23334 - 5.60030i) q^{12} +(3.40300 + 1.19146i) q^{13} +(-3.70657 + 6.41997i) q^{15} +3.68170 q^{16} -1.37578 q^{17} +(-0.929766 + 1.61040i) q^{18} +(-1.61766 + 2.80186i) q^{19} +(-2.17164 - 3.76139i) q^{20} +(-0.384320 - 0.665661i) q^{22} +0.838502 q^{23} +(-1.51671 - 2.62701i) q^{24} +(0.0105144 - 0.0182115i) q^{25} +(0.787321 + 0.275657i) q^{26} -16.7354 q^{27} +(0.303571 - 0.525800i) q^{29} +(-0.857556 + 1.48533i) q^{30} +(-0.857556 + 1.48533i) q^{31} +2.67792 q^{32} +(5.51868 - 9.55864i) q^{33} -0.318302 q^{34} +(7.82225 - 13.5485i) q^{36} +1.55361 q^{37} +(-0.374262 + 0.648241i) q^{38} +(2.22480 + 11.7701i) q^{39} +(-1.01868 - 1.76441i) q^{40} +(4.58892 - 7.94824i) q^{41} +(-0.615680 - 1.06639i) q^{43} +(3.23334 + 5.60030i) q^{44} -17.9343 q^{45} +0.193997 q^{46} +(0.814085 + 1.41004i) q^{47} +(6.11577 + 10.5928i) q^{48} +(0.00243263 - 0.00421343i) q^{50} +(-2.28535 - 3.95833i) q^{51} +(-6.62385 - 2.31915i) q^{52} +(-4.19803 + 7.27121i) q^{53} -3.87192 q^{54} +(3.70657 - 6.41997i) q^{55} -10.7485 q^{57} +(0.0702344 - 0.121650i) q^{58} +8.82234 q^{59} +(7.21474 - 12.4963i) q^{60} +(-2.73334 + 4.73428i) q^{61} +(-0.198405 + 0.343647i) q^{62} -6.74383 q^{64} +(1.49426 + 7.90530i) q^{65} +(1.27681 - 2.21149i) q^{66} +(5.09287 + 8.82111i) q^{67} +2.67792 q^{68} +(1.39286 + 2.41250i) q^{69} +(2.60714 + 4.51570i) q^{71} +(3.66929 - 6.35540i) q^{72} +(1.98177 - 3.43253i) q^{73} +0.359445 q^{74} +0.0698632 q^{75} +(3.14872 - 5.45375i) q^{76} +(0.514731 + 2.72315i) q^{78} +(-3.22525 - 5.58630i) 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} +(-0.142444 - 0.246721i) q^{86} +2.01708 q^{87} +(1.51671 + 2.62701i) q^{88} +9.12826 q^{89} -4.14929 q^{90} -1.63212 q^{92} -5.69803 q^{93} +(0.188347 + 0.326227i) q^{94} -7.21915 q^{95} +(4.44836 + 7.70479i) q^{96} +(7.67944 + 13.3012i) q^{97} +26.7022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - q^{3} + 10 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - q^3 + 10 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 - 7 * q^9	$ 8 q - 2 q^{2} - q^{3} + 10 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} - 12 q^{12} + 4 q^{13} - 3 q^{15} + 38 q^{16} - 8 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} - 5 q^{22} - 4 q^{23} + 3 q^{24} - 5 q^{25} - 15 q^{26} - 52 q^{27} - q^{29} + 4 q^{30} + 4 q^{31} - 66 q^{32} + 19 q^{33} + 6 q^{34} + 34 q^{36} - 20 q^{37} + 23 q^{38} - q^{39} + 17 q^{40} + 22 q^{41} - 3 q^{43} + 12 q^{44} - 22 q^{45} + 48 q^{46} - 2 q^{47} - 11 q^{48} - 43 q^{50} - 7 q^{51} - 31 q^{52} - 2 q^{53} + 10 q^{54} + 3 q^{55} - 34 q^{57} + 11 q^{58} - 16 q^{59} + 11 q^{60} - 8 q^{61} + 5 q^{62} + 28 q^{64} - 11 q^{65} - 6 q^{66} + 6 q^{67} - 66 q^{68} + 18 q^{69} + 14 q^{71} - 5 q^{72} + 8 q^{73} + 40 q^{74} - 14 q^{75} - 32 q^{76} - q^{78} + 26 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} - 5 q^{85} - 12 q^{86} + 26 q^{87} - 3 q^{88} - 2 q^{89} + 52 q^{90} + 24 q^{92} - 14 q^{93} - 33 q^{94} + 42 q^{95} + 58 q^{96} - 3 q^{97} + 46 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - q^3 + 10 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 - 12 * q^12 + 4 * q^13 - 3 * q^15 + 38 * q^16 - 8 * q^17 + 3 * q^18 - q^19 + 2 * q^20 - 5 * q^22 - 4 * q^23 + 3 * q^24 - 5 * q^25 - 15 * q^26 - 52 * q^27 - q^29 + 4 * q^30 + 4 * q^31 - 66 * q^32 + 19 * q^33 + 6 * q^34 + 34 * q^36 - 20 * q^37 + 23 * q^38 - q^39 + 17 * q^40 + 22 * q^41 - 3 * q^43 + 12 * q^44 - 22 * q^45 + 48 * q^46 - 2 * q^47 - 11 * q^48 - 43 * q^50 - 7 * q^51 - 31 * q^52 - 2 * q^53 + 10 * q^54 + 3 * q^55 - 34 * q^57 + 11 * q^58 - 16 * q^59 + 11 * q^60 - 8 * q^61 + 5 * q^62 + 28 * q^64 - 11 * q^65 - 6 * q^66 + 6 * q^67 - 66 * q^68 + 18 * q^69 + 14 * q^71 - 5 * q^72 + 8 * q^73 + 40 * q^74 - 14 * q^75 - 32 * q^76 - q^78 + 26 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 - 5 * q^85 - 12 * q^86 + 26 * q^87 - 3 * q^88 - 2 * q^89 + 52 * q^90 + 24 * q^92 - 14 * q^93 - 33 * q^94 + 42 * q^95 + 58 * q^96 - 3 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.231361			0.163597			0.0817984	−	0.996649i	$-0.473934\pi$
$2$	0.231361			0.163597			0.0817984	+	0.996649i	$0.473934\pi$
$3$	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	$0.424740\pi$
$4$	−1.94647			−0.973236
$5$	1.11568	+	1.93242i	0.498947	+	0.864202i	0.999999	−	0.00121496i	$-0.000386732\pi$
$5$	1.11568	+	1.93242i	0.498947	+	0.864202i	−0.501052	+	0.865417i	$0.667053\pi$
$6$	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	−1.00000		0.000980003i	$-0.999688\pi$
$11$	−1.66113	−	2.87716i	−0.500848	−	0.867495i	0.499151	−	0.866515i	$-0.333645\pi$
$12$	−3.23334	−	5.60030i	−0.933384	−	1.61667i
$13$	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
$16$	3.68170			0.920425
$17$	−1.37578			−0.333676			−0.166838	−	0.985984i	$-0.553356\pi$
$17$	−1.37578			−0.333676			−0.166838	+	0.985984i	$0.553356\pi$
$18$	−0.929766	+	1.61040i	−0.219148	+	0.379575i
$19$	−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
$21$		0			0
$22$	−0.384320	−	0.665661i	−0.0819372	−	0.141919i
$23$	0.838502			0.174840			0.0874199	−	0.996172i	$-0.472138\pi$
$23$	0.838502			0.174840			0.0874199	+	0.996172i	$0.472138\pi$
$24$	−1.51671	−	2.62701i	−0.309596	−	0.536237i
$25$	0.0105144	−	0.0182115i	0.00210289	−	0.00364231i
$26$	0.787321	+	0.275657i	0.154406	+	0.0540609i
$27$	−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
$31$	−0.857556	+	1.48533i	−0.154022	+	0.266773i	−0.932702	−	0.360647i	$-0.882556\pi$
$31$	−0.857556	+	1.48533i	−0.154022	+	0.266773i	0.778681	+	0.627420i	$0.215889\pi$
$32$	2.67792			0.473394
$33$	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
$37$	1.55361			0.255413			0.127706	−	0.991812i	$-0.459239\pi$
$37$	1.55361			0.255413			0.127706	+	0.991812i	$0.459239\pi$
$38$	−0.374262	+	0.648241i	−0.0607133	+	0.105159i
$39$	2.22480	+	11.7701i	0.356253	+	1.88473i
$40$	−1.01868	−	1.76441i	−0.161068	−	0.278978i
$41$	4.58892	−	7.94824i	0.716668	−	1.24131i	−0.245644	−	0.969360i	$-0.578999\pi$
$41$	4.58892	−	7.94824i	0.716668	−	1.24131i	0.962313	−	0.271946i	$-0.0876672\pi$
$42$		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	$0.863264\pi$
$44$	3.23334	+	5.60030i	0.487444	+	0.844277i
$45$	−17.9343			−2.67348
$46$	0.193997			0.0286032
$47$	0.814085	+	1.41004i	0.118747	+	0.205675i	0.919271	−	0.393625i	$-0.128779\pi$
$47$	0.814085	+	1.41004i	0.118747	+	0.205675i	−0.800525	+	0.599300i	$0.795446\pi$
$48$	6.11577	+	10.5928i	0.882735	+	1.52894i
$49$		0			0
$50$	0.00243263	−	0.00421343i	0.000344025	−	0.000595870i
$51$	−2.28535	−	3.95833i	−0.320012	−	0.554278i
$52$	−6.62385	−	2.31915i	−0.918562	−	0.321608i
$53$	−4.19803	+	7.27121i	−0.576644	+	0.998777i	0.419217	+	0.907886i	$0.362305\pi$
$53$	−4.19803	+	7.27121i	−0.576644	+	0.998777i	−0.995861	+	0.0908909i	$0.971029\pi$
$54$	−3.87192			−0.526901
$55$	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
$59$	8.82234			1.14857			0.574285	−	0.818655i	$-0.305280\pi$
$59$	8.82234			1.14857			0.574285	+	0.818655i	$0.305280\pi$
$60$	7.21474	−	12.4963i	0.931419	−	1.61326i
$61$	−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
$63$		0			0
$64$	−6.74383			−0.842979
$65$	1.49426	+	7.90530i	0.185341	+	0.980532i
$66$	1.27681	−	2.21149i	0.157164	−	0.272216i
$67$	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	$0.619575\pi$
$68$	2.67792			0.324745
$69$	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
$73$	1.98177	−	3.43253i	0.231949	−	0.401748i	−0.726432	−	0.687238i	$-0.758823\pi$
$73$	1.98177	−	3.43253i	0.231949	−	0.401748i	0.958382	+	0.285490i	$0.0921563\pi$
$74$	0.359445			0.0417847
$75$	0.0698632			0.00806711
$76$	3.14872	−	5.45375i	0.361183	−	0.625588i
$77$		0			0
$78$	0.514731	+	2.72315i	0.0582818	+	0.308336i
$79$	−3.22525	−	5.58630i	−0.362869	−	0.628508i	0.625562	−	0.780174i	$-0.284870\pi$
$79$	−3.22525	−	5.58630i	−0.362869	−	0.628508i	−0.988432	+	0.151666i	$0.951536\pi$
$80$	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	$0.581971\pi$
$84$		0			0
$85$	−1.53493	−	2.65858i	−0.166487	−	0.288363i
$86$	−0.142444	−	0.246721i	−0.0153602	−	0.0266046i
$87$	2.01708			0.216253
$88$	1.51671	+	2.62701i	0.161681	+	0.280041i
$89$	9.12826			0.967593			0.483797	−	0.875180i	$-0.339257\pi$
$89$	9.12826			0.967593			0.483797	+	0.875180i	$0.339257\pi$
$90$	−4.14929			−0.437373
$91$		0			0
$92$	−1.63212			−0.170160
$93$	−5.69803			−0.590859
$94$	0.188347	+	0.326227i	0.0194266	+	0.0336478i
$95$	−7.21915			−0.740669
$96$	4.44836	+	7.70479i	0.454009	+	0.786367i
$97$	7.67944	+	13.3012i	0.779729	+	1.35053i	0.932098	+	0.362206i	$0.117976\pi$
$97$	7.67944	+	13.3012i	0.779729	+	1.35053i	−0.152369	+	0.988324i	$0.548690\pi$
$98$		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	$-0.0372212\pi$
$101$	3.97521	+	6.88527i	0.395548	+	0.685110i	−0.597623	+	0.801777i	$0.703888\pi$
$102$	−0.528739	−	0.915804i	−0.0523530	−	0.0906781i
$103$	−0.347412	−	0.601736i	−0.0342316	−	0.0592908i	0.848402	−	0.529352i	$-0.177565\pi$
$103$	−0.347412	−	0.601736i	−0.0342316	−	0.0592908i	−0.882634	+	0.470062i	$0.844232\pi$
$104$	−3.10714	−	1.08787i	−0.304680	−	0.106675i
$105$		0			0
$106$	−0.971261	+	1.68227i	−0.0943372	+	0.163397i
$107$	8.94647			0.864888			0.432444	−	0.901661i	$-0.357651\pi$
$107$	8.94647			0.864888			0.432444	+	0.901661i	$0.357651\pi$
$108$	32.5750			3.13453
$109$	1.13634	−	1.96820i	0.108841	−	0.188519i	−0.806460	−	0.591289i	$-0.798619\pi$
$109$	1.13634	−	1.96820i	0.108841	−	0.188519i	0.915301	+	0.402770i	$0.131953\pi$
$110$	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	$0.685802\pi$
$114$	−2.48679			−0.232909
$115$	0.935501	+	1.62033i	0.0872359	+	0.151097i
$116$	−0.590892	+	1.02346i	−0.0548630	+	0.0950254i
$117$	−21.9688	+	18.8987i	−2.03102	+	1.74719i
$118$	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
$122$	−0.632387	+	1.09533i	−0.0572536	+	0.0991662i
$123$	30.4911			2.74929
$124$	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	$0.861832\pi$
$128$	−6.91610			−0.611302
$129$	2.04545	−	3.54282i	0.180091	−	0.311928i
$130$	0.345714	+	1.82898i	0.0303212	+	0.160412i
$131$	0.874176	+	1.51412i	0.0763771	+	0.132289i	0.901684	−	0.432395i	$-0.142331\pi$
$131$	0.874176	+	1.51412i	0.0763771	+	0.132289i	−0.825307	+	0.564684i	$0.808998\pi$
$132$	−10.7420	+	18.6056i	−0.934968	+	1.61941i
$133$		0			0
$134$	1.17829	+	2.04086i	0.101789	+	0.176303i
$135$	−18.6714	−	32.3397i	−1.60697	−	2.78336i
$136$	1.25617			0.107716
$137$	−18.0032			−1.53812			−0.769059	−	0.639178i	$-0.779275\pi$
$137$	−18.0032			−1.53812			−0.769059	+	0.639178i	$0.779275\pi$
$138$	0.322253	+	0.558158i	0.0274320	+	0.0475136i
$139$	−6.95896	−	12.0533i	−0.590251	−	1.02235i	−0.994198	−	0.107563i	$-0.965695\pi$
$139$	−6.95896	−	12.0533i	−0.590251	−	1.02235i	0.403947	−	0.914782i	$-0.367638\pi$
$140$		0			0
$141$	−2.70460	+	4.68450i	−0.227768	+	0.394506i
$142$	0.603190	+	1.04476i	0.0506186	+	0.0876740i
$143$	−2.22480	−	11.7701i	−0.186047	−	0.984268i
$144$	−14.7956	+	25.6267i	−1.23296	+	2.13556i
$145$	1.35475			0.112506
$146$	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	−0.329976	−	0.943989i	$-0.607041\pi$
$149$	7.96515	−	13.7961i	0.652531	−	1.13022i	0.982507	−	0.186227i	$-0.0596261\pi$
$150$	0.0161636			0.00131975
$151$	6.97484	−	12.0808i	0.567604	−	0.983120i	−0.429198	−	0.903211i	$-0.641204\pi$
$151$	6.97484	−	12.0808i	0.567604	−	0.983120i	0.996802	−	0.0799092i	$-0.0254630\pi$
$152$	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
$156$	−4.33051	−	22.9102i	−0.346718	−	1.83429i
$157$	6.48733	−	11.2364i	0.517745	−	0.896761i	−0.482042	−	0.876148i	$-0.660105\pi$
$157$	6.48733	−	11.2364i	0.517745	−	0.896761i	0.999788	−	0.0206132i	$-0.00656186\pi$
$158$	−0.746198	−	1.29245i	−0.0593643	−	0.102822i
$159$	−27.8939			−2.21213
$160$	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	0.239697	+	0.970848i	$0.422952\pi$
$163$	−9.20423	+	15.9422i	−0.720931	+	1.24869i	−0.960627	+	0.277841i	$0.910381\pi$
$164$	−8.93220	+	15.4710i	−0.697488	+	1.20808i
$165$	24.6283			1.91731
$166$	−1.07364			−0.0833308
$167$	9.24967	−	16.0209i	0.715761	−	1.23973i	−0.246904	−	0.969040i	$-0.579413\pi$
$167$	9.24967	−	16.0209i	0.715761	−	1.23973i	0.962665	−	0.270695i	$-0.0872534\pi$
$168$		0			0
$169$	10.1608	+	8.10909i	0.781603	+	0.623776i
$170$	−0.355123	−	0.615091i	−0.0272367	−	0.0471753i
$171$	−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			0
$176$	−6.11577	−	10.5928i	−0.460993	−	0.798464i
$177$	14.6550	+	25.3832i	1.10154	+	1.90792i
$178$	2.11192			0.158295
$179$	−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	$-0.348797\pi$
$180$	34.9085			2.60193
$181$	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			0
$183$	−18.1617			−1.34255
$184$	−0.765602			−0.0564409
$185$	1.73334	+	3.00223i	0.127437	+	0.220728i
$186$	−1.31830			−0.0966626
$187$	2.28535	+	3.95833i	0.167121	+	0.289462i
$188$	−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	−0.809820	−	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	$0.715521\pi$
$194$	1.77672	+	3.07737i	0.127561	+	0.220942i
$195$	−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	$-0.193797\pi$
$198$	6.17783			0.439039
$199$	−12.4466			−0.882313			−0.441157	−	0.897430i	$-0.645432\pi$
$199$	−12.4466			−0.882313			−0.441157	+	0.897430i	$0.645432\pi$
$200$	−0.00960030	+	0.0166282i	−0.000678843	+	0.00117579i
$201$	−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
$205$	20.4791			1.43032
$206$	−0.0803776	−	0.139218i	−0.00560017	−	0.00969979i
$207$	−3.36967	+	5.83645i	−0.234209	+	0.405661i
$208$	12.5288	+	4.38660i	0.868718	+	0.304156i
$209$	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
$213$	−8.66158	+	15.0023i	−0.593482	+	1.02794i
$214$	2.06986			0.141493
$215$	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
$219$	13.1679			0.889805
$220$	−7.21474	+	12.4963i	−0.486418	+	0.842500i
$221$	−4.68178	−	1.63919i	−0.314931	−	0.110264i
$222$	0.597084	+	1.03418i	0.0400737	+	0.0694096i
$223$	−11.3247	+	19.6149i	−0.758357	+	1.31351i	0.185331	+	0.982676i	$0.440664\pi$
$223$	−11.3247	+	19.6149i	−0.758357	+	1.31351i	−0.943688	+	0.330837i	$0.892669\pi$
$224$		0			0
$225$	0.0845083	+	0.146373i	0.00563389	+	0.00975818i
$226$	1.09952	+	1.90442i	0.0731388	+	0.126680i
$227$	1.28506			0.0852925			0.0426462	−	0.999090i	$-0.486421\pi$
$227$	1.28506			0.0852925			0.0426462	+	0.999090i	$0.486421\pi$
$228$	20.9217			1.38557
$229$	2.32225	+	4.02226i	0.153459	+	0.265798i	0.932497	−	0.361178i	$-0.117625\pi$
$229$	2.32225	+	4.02226i	0.153459	+	0.265798i	−0.779038	+	0.626977i	$0.784292\pi$
$230$	0.216438	+	0.374882i	0.0142715	+	0.0247190i
$231$		0			0
$232$	−0.277178	+	0.480086i	−0.0181976	+	0.0315192i
$233$	−5.94386	−	10.2951i	−0.389395	−	0.674452i	0.602973	−	0.797762i	$-0.293983\pi$
$233$	−5.94386	−	10.2951i	−0.389395	−	0.674452i	−0.992368	+	0.123309i	$0.960649\pi$
$234$	−5.08272	+	4.37242i	−0.332268	+	0.285834i
$235$	−1.81652	+	3.14630i	−0.118497	+	0.205242i
$236$	−17.1724			−1.11783
$237$	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
$241$	4.03341			0.259815			0.129907	−	0.991526i	$-0.458532\pi$
$241$	4.03341			0.259815			0.129907	+	0.991526i	$0.458532\pi$
$242$	−0.00432231	+	0.00748646i	−0.000277849	+	0.000481248i
$243$	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
$247$	−8.84320	+	7.60737i	−0.562679	+	0.484045i
$248$	0.782999	−	1.35619i	0.0497205	−	0.0861184i
$249$	−7.70855	−	13.3516i	−0.488509	−	0.846123i
$250$	2.59210			0.163939
$251$	−13.9343	−	24.1348i	−0.879523	−	1.52338i	−0.851866	−	0.523760i	$-0.824529\pi$
$251$	−13.9343	−	24.1348i	−0.879523	−	1.52338i	−0.0276571	−	0.999617i	$-0.508805\pi$
$252$		0			0
$253$	−1.39286	−	2.41250i	−0.0875683	−	0.151673i
$254$	−2.13239	+	3.69340i	−0.133798	+	0.231745i
$255$	5.09943	−	8.83247i	0.319339	−	0.553111i
$256$	11.8875			0.742972
$257$	−7.14064			−0.445421			−0.222710	−	0.974885i	$-0.571490\pi$
$257$	−7.14064			−0.445421			−0.222710	+	0.974885i	$0.571490\pi$
$258$	0.473236	−	0.819669i	0.0294624	−	0.0510304i
$259$		0			0
$260$	−2.90855	−	15.3874i	−0.180380	−	0.954289i
$261$	2.43991	+	4.22605i	0.151027	+	0.261586i
$262$	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			0
$267$	15.1632	+	26.2634i	0.927972	+	1.60729i
$268$	−9.91313	−	17.1700i	−0.605540	−	1.04883i
$269$	2.78875			0.170033			0.0850167	−	0.996380i	$-0.472906\pi$
$269$	2.78875			0.170033			0.0850167	+	0.996380i	$0.472906\pi$
$270$	−4.31982	−	7.48215i	−0.262896	−	0.455349i
$271$	−15.4747			−0.940024			−0.470012	−	0.882660i	$-0.655750\pi$
$271$	−15.4747			−0.940024			−0.470012	+	0.882660i	$0.655750\pi$
$272$	−5.06521			−0.307123
$273$		0			0
$274$	−4.16524			−0.251631
$275$	−0.0698632			−0.00421291
$276$	−2.71116	−	4.69587i	−0.163193	−	0.282658i
$277$	5.52955			0.332238			0.166119	−	0.986106i	$-0.446876\pi$
$277$	5.52955			0.332238			0.166119	+	0.986106i	$0.446876\pi$
$278$	−1.61003	−	2.78866i	−0.0965633	−	0.167252i
$279$	−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	$-0.0965531\pi$
$283$	3.67559	+	6.36631i	0.218491	+	0.378438i	−0.735856	+	0.677138i	$0.763220\pi$
$284$	−5.07473	−	8.78969i	−0.301130	−	0.521572i
$285$	−11.9919	−	20.7706i	−0.710340	−	1.23034i
$286$	−0.514731	−	2.72315i	−0.0304367	−	0.161023i
$287$		0			0
$288$	−10.7617	+	18.6398i	−0.634140	+	1.09836i
$289$	−15.1072			−0.888660
$290$	0.313437			0.0184056
$291$	−25.5130	+	44.1899i	−1.49560	+	2.59046i
$292$	−3.85747	+	6.68133i	−0.225741	+	0.390995i
$293$	6.76675	+	11.7204i	0.395318	+	0.684710i	0.993142	−	0.116917i	$-0.0373012\pi$
$293$	6.76675	+	11.7204i	0.395318	+	0.684710i	−0.597824	+	0.801627i	$0.703968\pi$
$294$		0			0
$295$	9.84291	+	17.0484i	0.573076	+	0.992597i
$296$	−1.41854			−0.0824510
$297$	27.7996	+	48.1503i	1.61310	+	2.79397i
$298$	1.84282	−	3.19187i	0.106752	−	0.184900i
$299$	2.85342	+	0.999043i	0.165018	+	0.0577761i
$300$	−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
$304$	−5.95572	+	10.3156i	−0.341584	+	0.591641i
$305$	−12.1981			−0.698462
$306$	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	$0.530075\pi$
$308$		0			0
$309$	1.15419	−	1.99912i	0.0656597	−	0.113726i
$310$	−0.885425			−0.0502888
$311$	17.1531	−	29.7101i	0.972665	−	1.68470i	0.285229	−	0.958459i	$-0.407930\pi$
$311$	17.1531	−	29.7101i	0.972665	−	1.68470i	0.687435	−	0.726246i	$-0.258736\pi$
$312$	−2.03137	−	10.7468i	−0.115004	−	0.608419i
$313$	−3.60714	−	6.24775i	−0.203888	−	0.353144i	0.745890	−	0.666069i	$-0.232024\pi$
$313$	−3.60714	−	6.24775i	−0.203888	−	0.353144i	−0.949778	+	0.312925i	$0.898691\pi$
$314$	1.50091	−	2.59966i	0.0847015	−	0.146707i
$315$		0			0
$316$	6.27787	+	10.8736i	0.353158	+	0.611687i
$317$	4.02020	+	6.96319i	0.225797	+	0.391092i	0.956558	−	0.291541i	$-0.0941681\pi$
$317$	4.02020	+	6.96319i	0.225797	+	0.391092i	−0.730761	+	0.682633i	$0.760835\pi$
$318$	−6.45355			−0.361897
$319$	−2.01708			−0.112935
$320$	−7.52396	−	13.0319i	−0.420602	−	0.728504i
$321$	14.8612	+	25.7404i	0.829472	+	1.43669i
$322$		0			0
$323$	2.22554	−	3.85475i	0.123832	−	0.214484i
$324$	30.6444	+	53.0777i	1.70247	+	2.94876i
$325$	0.0574790	−	0.0494463i	0.00318836	−	0.00274279i
$326$	−2.12950	+	3.68840i	−0.117942	+	0.204281i
$327$	7.55040			0.417538
$328$	−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	−0.878045	−	0.478579i	$-0.841152\pi$
$331$	−0.446843	+	0.773955i	−0.0245607	+	0.0425404i	0.853484	+	0.521119i	$0.174485\pi$
$332$	9.03271			0.495734
$333$	−6.24348	+	10.8140i	−0.342141	+	0.592605i
$334$	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	$0.365353\pi$
$338$	2.35082	+	1.87613i	0.127868	+	0.102048i
$339$	−15.7886	+	27.3467i	−0.857521	+	1.48527i
$340$	2.98770	+	5.17485i	0.162031	+	0.280646i
$341$	5.69803			0.308566
$342$	−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
$346$	1.98949	−	3.44589i	0.106955	−	0.185252i
$347$	−16.4164			−0.881276			−0.440638	−	0.897685i	$-0.645248\pi$
$347$	−16.4164			−0.881276			−0.440638	+	0.897685i	$0.645248\pi$
$348$	−3.92619			−0.210466
$349$	−17.1861	+	29.7672i	−0.919950	+	1.59340i	−0.120462	+	0.992718i	$0.538438\pi$
$349$	−17.1861	+	29.7672i	−0.919950	+	1.59340i	−0.799488	+	0.600682i	$0.794896\pi$
$350$		0			0
$351$	−56.9506	−	19.9396i	−3.03980	−	1.06430i
$352$	−4.44836	−	7.70479i	−0.237098	−	0.410667i
$353$	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
$357$		0			0
$358$	−1.67605	−	2.90300i	−0.0885819	−	0.153428i
$359$	3.08937	+	5.35095i	0.163051	+	0.282412i	0.935961	−	0.352103i	$-0.114533\pi$
$359$	3.08937	+	5.35095i	0.163051	+	0.282412i	−0.772911	+	0.634515i	$0.781200\pi$
$360$	16.3750			0.863040
$361$	4.26638	+	7.38958i	0.224546	+	0.388925i
$362$	1.58594			0.0833552
$363$	−0.124133			−0.00651531
$364$		0			0
$365$	8.84411			0.462922
$366$	−4.20190			−0.219637
$367$	−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	$-0.340078\pi$
$368$	3.08711			0.160927
$369$	36.8828	+	63.8829i	1.92004	+	3.32561i
$370$	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	0.149217	+	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
$376$	−0.743308	−	1.28745i	−0.0383332	−	0.0663950i
$377$	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	$0.131257\pi$
$380$	14.0519			0.720846
$381$	−61.2405			−3.13745
$382$	0.329878	−	0.571365i	0.0168780	−	0.0292336i
$383$	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
$385$		0			0
$386$	1.16264	+	2.01376i	0.0591771	+	0.102498i
$387$	9.89690			0.503087
$388$	−14.9478	−	25.8904i	−0.758860	−	1.31438i
$389$	12.6737	−	21.9515i	0.642582	−	1.11299i	−0.342272	−	0.939601i	$-0.611196\pi$
$389$	12.6737	−	21.9515i	0.642582	−	1.11299i	0.984854	−	0.173384i	$-0.0554702\pi$
$390$	−4.68798	+	4.03284i	−0.237385	+	0.204211i
$391$	−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
$395$	7.19671	−	12.4651i	0.362106	−	0.627185i
$396$	−51.9750			−2.61184
$397$	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
$399$		0			0
$400$	0.0387110	−	0.0670494i	0.00193555	−	0.00335247i
$401$	−29.2858			−1.46246			−0.731232	−	0.682129i	$-0.761054\pi$
$401$	−29.2858			−1.46246			−0.731232	+	0.682129i	$0.761054\pi$
$402$	−3.91458	+	6.78025i	−0.195241	+	0.338168i
$403$	−4.68798	+	4.03284i	−0.233525	+	0.200890i
$404$	−7.73764	−	13.4020i	−0.384962	−	0.666774i
$405$	35.1296	−	60.8462i	1.74560	−	3.02347i
$406$		0			0
$407$	−2.58075	−	4.46999i	−0.127923	−	0.221569i
$408$	2.08666	+	3.61419i	0.103305	+	0.178929i
$409$	23.3713			1.15563			0.577817	−	0.816166i	$-0.303905\pi$
$409$	23.3713			1.15563			0.577817	+	0.816166i	$0.303905\pi$
$410$	4.73805			0.233996
$411$	−29.9056	−	51.7980i	−1.47513	−	2.55501i
$412$	0.676229	+	1.17126i	0.0333154	+	0.0577040i
$413$		0			0
$414$	−0.779611	+	1.35033i	−0.0383158	+	0.0663649i
$415$	−5.17738	−	8.96748i	−0.254147	−	0.440196i
$416$	9.11296	+	3.19064i	0.446800	+	0.156434i
$417$	23.1194	−	40.0440i	1.13216	−	1.96096i
$418$	2.48679			0.121633
$419$	−7.30320	+	12.6495i	−0.356785	+	0.617969i	−0.987422	−	0.158109i	$-0.949460\pi$
$419$	−7.30320	+	12.6495i	−0.356785	+	0.617969i	0.630637	+	0.776078i	$0.282794\pi$
$420$		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
$423$	−13.0862			−0.636273
$424$	3.83305	−	6.63904i	0.186149	−	0.322420i
$425$	−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
$429$	30.1688	−	25.9528i	1.45656	−	1.25301i
$430$	0.317845	−	0.550523i	0.0153278	−	0.0265486i
$431$	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	$0.735982\pi$
$432$	−61.6147			−2.96444
$433$	5.47361	+	9.48057i	0.263045	+	0.455607i	0.967050	−	0.254588i	$-0.0819400\pi$
$433$	5.47361	+	9.48057i	0.263045	+	0.455607i	−0.704005	+	0.710195i	$0.748607\pi$
$434$		0			0
$435$	2.25041	+	3.89783i	0.107899	+	0.186887i
$436$	−2.21185	+	3.83104i	−0.105928	+	0.183473i
$437$	−1.35641	+	2.34937i	−0.0648858	+	0.112386i
$438$	3.04654			0.145569
$439$	−17.9179			−0.855176			−0.427588	−	0.903974i	$-0.640637\pi$
$439$	−17.9179			−0.855176			−0.427588	+	0.903974i	$0.640637\pi$
$440$	−3.38432	+	5.86181i	−0.161341	+	0.279451i
$441$		0			0
$442$	−1.08318	−	0.379244i	−0.0515217	−	0.0180388i
$443$	−13.8597	−	24.0057i	−0.658494	−	1.14055i	−0.981005	−	0.193980i	$-0.937860\pi$
$443$	−13.8597	−	24.0057i	−0.658494	−	1.14055i	0.322511	−	0.946566i	$-0.395473\pi$
$444$	−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	$0.832087\pi$
$450$	0.0195519	+	0.0338649i	0.000921686	+	0.00159641i
$451$	−30.4911			−1.43577
$452$	−9.25039	−	16.0222i	−0.435102	−	0.753619i
$453$	46.3444			2.17745
$454$	0.297313			0.0139536
$455$		0			0
$456$	9.81404			0.459584
$457$	31.7354			1.48452			0.742260	−	0.670112i	$-0.233754\pi$
$457$	31.7354			1.48452			0.742260	+	0.670112i	$0.233754\pi$
$458$	0.537278	+	0.930593i	0.0251054	+	0.0434838i
$459$	23.0242			1.07468
$460$	−1.82093	−	3.15394i	−0.0849011	−	0.147053i
$461$	−14.5328	−	25.1715i	−0.676859	−	1.17235i	−0.975922	−	0.218121i	$-0.930007\pi$
$461$	−14.5328	−	25.1715i	−0.676859	−	1.17235i	0.299063	−	0.954233i	$-0.403326\pi$
$462$		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
$467$	17.3204	+	29.9999i	0.801495	+	1.38823i	0.918632	+	0.395114i	$0.129295\pi$
$467$	17.3204	+	29.9999i	0.801495	+	1.38823i	−0.117137	+	0.993116i	$0.537372\pi$
$468$	42.7617	−	36.7858i	1.97666	−	1.70042i
$469$		0			0
$470$	−0.420271	+	0.727931i	−0.0193857	+	0.0335769i
$471$	43.1051			1.98618
$472$	−8.05532			−0.370776
$473$	−2.04545	+	3.54282i	−0.0940497	+	0.162899i
$474$	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
$478$	−0.966587			−0.0442107
$479$	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	$0.781161\pi$
$480$	−9.92590	+	17.1922i	−0.453053	+	0.784711i
$481$	5.28695	+	1.85107i	0.241064	+	0.0844015i
$482$	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
$486$	6.29325	−	10.9002i	0.285468	−	0.494444i
$487$	−18.5003			−0.838327			−0.419163	−	0.907911i	$-0.637677\pi$
$487$	−18.5003			−0.838327			−0.419163	+	0.907911i	$0.637677\pi$
$488$	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	$0.0546321\pi$
$492$	−59.3500			−2.67571
$493$	−0.417647	+	0.723386i	−0.0188099	+	0.0325796i
$494$	−2.04597	+	1.76005i	−0.0920525	+	0.0791883i
$495$	29.7911	+	51.5997i	1.33901	+	2.31923i
$496$	−3.15726	+	5.46854i	−0.141765	+	0.245545i
$497$		0			0
$498$	−1.78346	−	3.08904i	−0.0799186	−	0.138423i
$499$	−6.23916	−	10.8065i	−0.279303	−	0.483767i	0.691909	−	0.721985i	$-0.256770\pi$
$499$	−6.23916	−	10.8065i	−0.279303	−	0.483767i	−0.971212	+	0.238218i	$0.923437\pi$
$500$	−21.8077			−0.975272
$501$	61.4595			2.74581
$502$	−3.22384	−	5.58386i	−0.143887	−	0.249220i
$503$	1.29004	+	2.23441i	0.0575200	+	0.0996276i	0.893352	−	0.449358i	$-0.148347\pi$
$503$	1.29004	+	2.23441i	0.0575200	+	0.0996276i	−0.835832	+	0.548986i	$0.815014\pi$
$504$		0			0
$505$	−8.87013	+	15.3635i	−0.394716	+	0.683668i
$506$	−0.322253	−	0.558158i	−0.0143259	−	0.0248132i
$507$	−6.45266	+	42.7045i	−0.286573	+	1.89658i
$508$	17.9401	−	31.0731i	0.795962	−	1.37865i
$509$	35.6808			1.58152			0.790761	−	0.612125i	$-0.209685\pi$
$509$	35.6808			1.58152			0.790761	+	0.612125i	$0.209685\pi$
$510$	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
$514$	−1.65206			−0.0728694
$515$	0.775202	−	1.34269i	0.0341595	−	0.0591660i
$516$	−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
$520$	−1.36435	−	7.21801i	−0.0598308	−	0.316531i
$521$	10.4819	−	18.1551i	0.459219	−	0.795390i	−0.539701	−	0.841857i	$-0.681463\pi$
$521$	10.4819	−	18.1551i	0.459219	−	0.795390i	0.998920	+	0.0464666i	$0.0147961\pi$
$522$	0.564499	+	0.977742i	0.0247075	+	0.0427946i
$523$	−22.8263			−0.998124			−0.499062	−	0.866566i	$-0.666322\pi$
$523$	−22.8263			−0.998124			−0.499062	+	0.866566i	$0.666322\pi$
$524$	−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
$528$	20.3181	−	35.1920i	0.884233	−	1.53154i
$529$	−22.2969			−0.969431
$530$	−4.33447			−0.188277
$531$	−35.4542	+	61.4084i	−1.53858	+	2.66490i
$532$		0			0
$533$	25.0861	−	21.5803i	1.08660	−	0.934749i
$534$	3.50817	+	6.07632i	0.151813	+	0.262948i
$535$	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
$541$	−15.1096	−	26.1706i	−0.649611	−	1.12516i	−0.983216	−	0.182447i	$-0.941598\pi$
$541$	−15.1096	−	26.1706i	−0.649611	−	1.12516i	0.333604	−	0.942713i	$-0.391735\pi$
$542$	−3.58025			−0.153785
$543$	11.3868	+	19.7224i	0.488652	+	0.846371i
$544$	−3.68423			−0.157960
$545$	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	$0.617099\pi$
$548$	35.0427			1.49695
$549$	−21.9688	−	38.0511i	−0.937606	−	1.62398i
$550$	−0.0161636			−0.000689219
$551$	0.982146	+	1.70113i	0.0418408	+	0.0724704i
$552$	−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	0.955499	−	0.294995i	$-0.0953179\pi$
$557$	5.24591	+	9.08619i	0.222276	+	0.384994i	−0.733222	+	0.679989i	$0.761985\pi$
$558$	−1.59465	−	2.76202i	−0.0675070	−	0.116926i
$559$	−0.824600	−	4.36249i	−0.0348768	−	0.184513i
$560$		0			0
$561$	−7.59250	+	13.1506i	−0.320555	+	0.555218i
$562$	−7.28489			−0.307294
$563$	30.9474			1.30428			0.652138	−	0.758100i	$-0.273872\pi$
$563$	30.9474			1.30428			0.652138	+	0.758100i	$0.273872\pi$
$564$	5.26442	−	9.11825i	0.221672	−	0.383947i
$565$	−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
$569$	−36.9089			−1.54730			−0.773651	−	0.633612i	$-0.781572\pi$
$569$	−36.9089			−1.54730			−0.773651	+	0.633612i	$0.781572\pi$
$570$	−2.77446	−	4.80551i	−0.116209	−	0.201280i
$571$	0.885467	−	1.53367i	0.0370556	−	0.0641822i	−0.846903	−	0.531748i	$-0.821535\pi$
$571$	0.885467	−	1.53367i	0.0370556	−	0.0641822i	0.883958	+	0.467565i	$0.154869\pi$
$572$	4.33051	+	22.9102i	0.181068	+	0.957925i
$573$	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
$577$	4.91999	−	8.52168i	0.204822	−	0.354762i	−0.745254	−	0.666781i	$-0.767672\pi$
$577$	4.91999	−	8.52168i	0.204822	−	0.354762i	0.950076	+	0.312019i	$0.101005\pi$
$578$	−3.49522			−0.145382
$579$	−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
$583$	27.8939			1.15525
$584$	−1.80948	+	3.13411i	−0.0748767	+	0.129690i
$585$	−61.0303	−	21.3680i	−2.52329	−	0.883457i
$586$	1.56556	+	2.71163i	0.0646727	+	0.112016i
$587$	7.56917	−	13.1102i	0.312413	−	0.541116i	−0.666471	−	0.745531i	$-0.732196\pi$
$587$	7.56917	−	13.1102i	0.312413	−	0.541116i	0.978884	+	0.204415i	$0.0655293\pi$
$588$		0			0
$589$	−2.77446	−	4.80551i	−0.114320	−	0.198007i
$590$	2.27726	+	3.94434i	0.0937535	+	0.162386i
$591$	84.4420			3.47348
$592$	5.71994			0.235088
$593$	−4.58574	−	7.94274i	−0.188314	−	0.326169i	0.756374	−	0.654139i	$-0.226969\pi$
$593$	−4.58574	−	7.94274i	−0.188314	−	0.326169i	−0.944688	+	0.327970i	$0.893636\pi$
$594$	6.43174	+	11.1401i	0.263898	+	0.457084i
$595$		0			0
$596$	−15.5040	+	26.8536i	−0.635067	+	1.09997i
$597$	−20.6753	−	35.8107i	−0.846184	−	1.46563i
$598$	0.660171	+	0.231139i	0.0269964	+	0.00945199i
$599$	9.29053	−	16.0917i	0.379601	−	0.657488i	−0.611403	−	0.791319i	$-0.709395\pi$
$599$	9.29053	−	16.0917i	0.379601	−	0.657488i	0.991004	+	0.133831i	$0.0427280\pi$
$600$	−0.0637892			−0.00260418
$601$	6.70179	−	11.6078i	0.273372	−	0.473494i	−0.696351	−	0.717701i	$-0.745194\pi$
$601$	6.70179	−	11.6078i	0.273372	−	0.473494i	0.969723	+	0.244207i	$0.0785277\pi$
$602$		0			0
$603$	−81.8665			−3.33386
$604$	−13.5763	+	23.5149i	−0.552413	+	0.956808i
$605$	−0.0833731			−0.00338960
$606$	−3.05550	+	5.29229i	−0.124121	+	0.214984i
$607$	−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
$609$		0			0
$610$	−2.82217			−0.114266
$611$	1.09033	+	5.76831i	0.0441100	+	0.233361i
$612$	−10.7617	+	18.6398i	−0.435016	+	0.753470i
$613$	−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	$-0.340424\pi$
$614$	−0.764900			−0.0308688
$615$	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
$619$	10.5062	−	18.1973i	0.422280	−	0.731410i	−0.573883	−	0.818938i	$-0.694563\pi$
$619$	10.5062	−	18.1973i	0.422280	−	0.731410i	0.996162	+	0.0875280i	$0.0278967\pi$
$620$	7.44921			0.299168
$621$	−14.0327			−0.563112
$622$	3.96856	−	6.87375i	0.159125	−	0.275612i
$623$		0			0
$624$	8.19103	+	43.3341i	0.327904	+	1.73475i
$625$	12.4472	+	21.5592i	0.497888	+	0.862368i
$626$	−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	$-0.339968\pi$
$632$	2.94485	+	5.10063i	0.117140	+	0.202892i
$633$	81.0373			3.22095
$634$	0.930117	+	1.61101i	0.0369397	+	0.0639814i
$635$	−41.1316			−1.63226
$636$	54.2946			2.15292
$637$		0			0
$638$	−0.466673			−0.0184758
$639$	−41.9091			−1.65790
$640$	−7.71615	−	13.3648i	−0.305008	−	0.528289i
$641$	18.5339			0.732044			0.366022	−	0.930606i	$-0.380719\pi$
$641$	18.5339			0.732044			0.366022	+	0.930606i	$0.380719\pi$
$642$	3.43830	+	5.95532i	0.135699	+	0.235038i
$643$	7.22328	+	12.5111i	0.284858	+	0.493389i	0.972575	−	0.232590i	$-0.0747201\pi$
$643$	7.22328	+	12.5111i	0.284858	+	0.493389i	−0.687716	+	0.725979i	$0.741387\pi$
$644$		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	−0.995965	−	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
$649$	−14.6550	−	25.3832i	−0.575260	−	0.996379i
$650$	0.0132984	−	0.0114399i	0.000521605	−	0.000448711i
$651$		0			0
$652$	17.9158	−	31.0310i	0.701636	−	1.21527i
$653$	−30.9615			−1.21162			−0.605808	−	0.795611i	$-0.707150\pi$
$653$	−30.9615			−1.21162			−0.605808	+	0.795611i	$0.707150\pi$
$654$	1.74687			0.0683079
$655$	−1.95060	+	3.37854i	−0.0762164	+	0.132011i
$656$	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	$0.576432\pi$
$660$	−47.9384			−1.86600
$661$	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	$0.703464\pi$
$662$	−0.103382	+	0.179063i	−0.00401806	+	0.00695948i
$663$	−3.06083	−	16.1931i	−0.118873	−	0.628889i
$664$	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
$668$	−18.0042	+	31.1842i	−0.696605	+	1.20655i
$669$	−75.2469			−2.90921
$670$	−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	$0.256895\pi$
$674$	3.48700			0.134314
$675$	−0.175963	+	0.304777i	−0.00677283	+	0.0117309i
$676$	−19.7778	−	15.7841i	−0.760684	−	0.607081i
$677$	1.75738	+	3.04388i	0.0675417	+	0.116986i	0.897819	−	0.440365i	$-0.145151\pi$
$677$	1.75738	+	3.04388i	0.0675417	+	0.116986i	−0.830277	+	0.557351i	$0.811818\pi$
$678$	−3.65287	+	6.32696i	−0.140288	+	0.242985i
$679$		0			0
$680$	1.40148	+	2.42744i	0.0537444	+	0.0930881i
$681$	2.13465	+	3.69732i	0.0817999	+	0.141682i
$682$	1.31830			0.0504804
$683$	−27.0753			−1.03601			−0.518003	−	0.855379i	$-0.673324\pi$
$683$	−27.0753			−1.03601			−0.518003	+	0.855379i	$0.673324\pi$
$684$	25.3074	+	43.8338i	0.967654	+	1.67603i
$685$	−20.0858	−	34.7897i	−0.767440	−	1.32925i
$686$		0			0
$687$	−7.71511	+	13.3630i	−0.294350	+	0.509829i
$688$	−2.26675	−	3.92613i	−0.0864190	−	0.149682i
$689$	−22.9493	+	19.7421i	−0.874298	+	0.752116i
$690$	−0.719062	+	1.24545i	−0.0273742	+	0.0474136i
$691$	29.7404			1.13138			0.565690	−	0.824618i	$-0.308610\pi$
$691$	29.7404			1.13138			0.565690	+	0.824618i	$0.308610\pi$
$692$	−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
$696$	−1.84171			−0.0698099
$697$	−6.31334	+	10.9350i	−0.239135	+	0.414194i
$698$	−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	$0.387750\pi$
$702$	−13.1761	−	4.61324i	−0.497301	−	0.174115i
$703$	−2.51321	+	4.35301i	−0.0947876	+	0.164177i
$704$	11.2024	+	19.4030i	0.422205	+	0.731280i
$705$	−12.0699			−0.454577
$706$	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	−0.460425	−	0.887699i	$-0.652303\pi$
$709$	14.3402	−	24.8379i	0.538557	−	0.932808i	0.998982	−	0.0451098i	$-0.0143638\pi$
$710$	−1.34594	+	2.33123i	−0.0505121	+	0.0874895i
$711$	51.8451			1.94434
$712$	−8.33464			−0.312354
$713$	−0.719062	+	1.24545i	−0.0269291	+	0.0466426i
$714$		0			0
$715$	20.2626	−	17.4309i	0.757779	−	0.651880i
$716$	14.1008	+	24.4234i	0.526973	+	0.912744i
$717$	−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			0
$722$	0.987073	+	1.70966i	0.0367350	+	0.0636270i
$723$	6.70001	+	11.6048i	0.249176	+	0.431586i
$724$	−13.3428			−0.495879
$725$	−0.00638375	−	0.0110570i	−0.000237086	−	0.000410646i
$726$	−0.0287196			−0.00106588
$727$	−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			0
$729$	86.2759			3.19540
$730$	2.04618			0.0757325
$731$	0.847041	+	1.46712i	0.0313290	+	0.0542633i
$732$	35.3512			1.30662
$733$	3.78535	+	6.55641i	0.139815	+	0.242167i	0.927426	−	0.374006i	$-0.122016\pi$
$733$	3.78535	+	6.55641i	0.139815	+	0.242167i	−0.787612	+	0.616172i	$0.788683\pi$
$734$	−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	0.918664	−	0.395041i	$-0.129270\pi$
$739$	3.18648	+	5.51914i	0.117216	+	0.203025i	−0.801447	+	0.598066i	$0.795936\pi$
$740$	−3.37389	−	5.84375i	−0.124027	−	0.214821i
$741$	−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	$0.0291281\pi$
$744$	5.20264			0.190738
$745$	35.5463			1.30231
$746$	−3.49298	+	6.05002i	−0.127887	+	0.221507i
$747$	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
$751$	39.3695			1.43661			0.718307	−	0.695726i	$-0.244917\pi$
$751$	39.3695			1.43661			0.718307	+	0.695726i	$0.244917\pi$
$752$	2.99722	+	5.19133i	0.109297	+	0.189308i
$753$	46.2931	−	80.1821i	1.68702	−	2.92200i
$754$	0.383948	−	0.330292i	0.0139826	−	0.0120285i
$755$	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
$759$	4.62743	−	8.01494i	0.167965	−	0.290924i
$760$	6.59151			0.239099
$761$	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
$763$		0			0
$764$	−2.77531	+	4.80697i	−0.100407	+	0.173910i
$765$	24.6736			0.892076
$766$	2.00684	−	3.47595i	0.0725101	−	0.125591i
$767$	30.0224	+	10.5115i	1.08405	+	0.379547i
$768$	19.7467	+	34.2023i	0.712548	+	1.23417i
$769$	−17.4174	+	30.1679i	−0.628089	+	1.08788i	0.359846	+	0.933012i	$0.382829\pi$
$769$	−17.4174	+	30.1679i	−0.628089	+	1.08788i	−0.987935	+	0.154871i	$0.950504\pi$
$770$		0			0
$771$	−11.8615	−	20.5447i	−0.427182	−	0.739900i
$772$	−9.78150	−	16.9421i	−0.352044	−	0.609758i
$773$	−33.2743			−1.19679			−0.598397	−	0.801200i	$-0.704196\pi$
$773$	−33.2743			−1.19679			−0.598397	+	0.801200i	$0.704196\pi$
$774$	2.28975			0.0823035
$775$	0.0180334	+	0.0312348i	0.000647780	+	0.00112199i
$776$	−7.01178	−	12.1448i	−0.251708	−	0.435971i
$777$		0			0
$778$	2.93220	−	5.07872i	0.105124	−	0.182081i
$779$	14.8466	+	25.7150i	0.531934	+	0.921336i
$780$	39.4406	−	33.9288i	1.41220	−	1.21485i
$781$	8.66158	−	15.0023i	0.309936	−	0.536825i
$782$	−0.266897			−0.00954421
$783$	−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
$787$	−27.8157			−0.991524			−0.495762	−	0.868458i	$-0.665111\pi$
$787$	−27.8157			−0.991524			−0.495762	+	0.868458i	$0.665111\pi$
$788$	−24.7368	+	42.8455i	−0.881213	+	1.52631i
$789$	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
$793$	−14.9423	+	12.8541i	−0.530615	+	0.456462i
$794$	3.13204	−	5.42484i	0.111152	−	0.192521i
$795$	−31.1206	−	53.9025i	−1.10374	−	1.91173i
$796$	24.2269			0.858699
$797$	−17.9343	−	31.0630i	−0.635264	−	1.10031i	−0.986459	−	0.164007i	$-0.947558\pi$
$797$	−17.9343	−	31.0630i	−0.635264	−	1.10031i	0.351195	−	0.936302i	$-0.385775\pi$
$798$		0			0
$799$	−1.12000	−	1.93990i	−0.0396228	−	0.0686288i
$800$	0.0281568	−	0.0487690i	0.000995493	−	0.00172424i
$801$	−36.6836	+	63.5378i	−1.29615	+	2.24500i
$802$	−6.77559			−0.239254
$803$	−13.1679			−0.464686
$804$	32.9339	−	57.0432i	1.16149	−	2.01176i
$805$		0			0
$806$	−1.08461	+	0.933040i	−0.0382039	+	0.0328649i
$807$	4.63247	+	8.02368i	0.163071	+	0.282447i
$808$	−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			0
$813$	−25.7055	−	44.5233i	−0.901532	−	1.56150i
$814$	−0.597084	−	1.03418i	−0.0209278	−	0.0362480i
$815$	−41.0759			−1.43883
$816$	−8.41395	−	14.5734i	−0.294547	−	0.510171i
$817$	3.98384			0.139377
$818$	5.40719			0.189058
$819$		0			0
$820$	−39.8619			−1.39204
$821$	−10.4559			−0.364915			−0.182457	−	0.983214i	$-0.558405\pi$
$821$	−10.4559			−0.364915			−0.182457	+	0.983214i	$0.558405\pi$
$822$	−6.91899	−	11.9840i	−0.241327	−	0.417991i
$823$	−33.2405			−1.15869			−0.579346	−	0.815082i	$-0.696692\pi$
$823$	−33.2405			−1.15869			−0.579346	+	0.815082i	$0.696692\pi$
$824$	0.317208	+	0.549420i	0.0110505	+	0.0191400i
$825$	−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	$-0.260292\pi$
$829$	−8.34721	−	14.4578i	−0.289911	−	0.502140i	−0.973788	+	0.227457i	$0.926959\pi$
$830$	−1.19784	−	2.07472i	−0.0415777	−	0.0720147i
$831$	9.18528	+	15.9094i	0.318634	+	0.551890i
$832$	−22.9493	−	8.03501i	−0.795623	−	0.278564i
$833$		0			0
$834$	5.34893	−	9.26462i	0.185218	−	0.320808i
$835$	41.2787			1.42851
$836$	−20.9217			−0.723592
$837$	14.3515	−	24.8576i	0.496062	−	0.859204i
$838$	−1.68967	+	2.92660i	−0.0583688	+	0.101098i
$839$	23.3206	+	40.3924i	0.805115	+	1.39450i	0.916213	+	0.400691i	$0.131230\pi$
$839$	23.3206	+	40.3924i	0.805115	+	1.39450i	−0.111098	+	0.993809i	$0.535437\pi$
$840$		0			0
$841$	14.3157	+	24.7955i	0.493644	+	0.855017i
$842$	2.37673			0.0819077
$843$	−52.3041	−	90.5934i	−1.80145	−	3.12020i
$844$	−23.7395	+	41.1179i	−0.817146	+	1.41534i
$845$	−4.33387	+	28.6821i	−0.149090	+	0.986695i
$846$	−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
$850$	−0.00334676	+	0.00579676i	−0.000114793	+	0.000198827i
$851$	1.30271			0.0446563
$852$	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			0
$855$	29.0115	−	50.2493i	0.992171	−	1.71849i
$856$	−8.16866			−0.279199
$857$	9.78065	−	16.9406i	0.334101	−	0.578679i	−0.649211	−	0.760608i	$-0.724901\pi$
$857$	9.78065	−	16.9406i	0.334101	−	0.578679i	0.983312	+	0.181929i	$0.0582341\pi$
$858$	6.97989	−	6.00445i	0.238289	−	0.204989i
$859$	5.08158	+	8.80155i	0.173381	+	0.300305i	0.939600	−	0.342275i	$-0.111197\pi$
$859$	5.08158	+	8.80155i	0.173381	+	0.300305i	−0.766219	+	0.642580i	$0.777864\pi$
$860$	−2.67407	+	4.63163i	−0.0911851	+	0.157937i
$861$		0			0
$862$	1.44621	+	2.50490i	0.0492580	+	0.0853174i
$863$	−13.4451	−	23.2877i	−0.457678	−	0.792722i	0.541160	−	0.840920i	$-0.317985\pi$
$863$	−13.4451	−	23.2877i	−0.457678	−	0.792722i	−0.998838	+	0.0481982i	$0.984652\pi$
$864$	−44.8160			−1.52467
$865$	38.3752			1.30480
$866$	1.26638	+	2.19343i	0.0430333	+	0.0745358i
$867$	−25.0950	−	43.4658i	−0.852271	−	1.47618i
$868$		0			0
$869$	−10.7151	+	18.5591i	−0.363485	+	0.629575i
$870$	0.520658	+	0.901806i	0.0176519	+	0.0305741i
$871$	6.82103	+	36.0862i	0.231122	+	1.22273i
$872$	−1.03754	+	1.79708i	−0.0351357	+	0.0608568i
$873$	−123.445			−4.17798
$874$	−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	−0.851303	−	0.524674i	$-0.824187\pi$
$877$	0.850801	−	1.47363i	0.0287295	−	0.0497610i	0.880033	+	0.474913i	$0.157521\pi$
$878$	−4.14551			−0.139904
$879$	−22.4809	+	38.9380i	−0.758260	+	1.31335i
$880$	13.6465	−	23.6364i	0.460023	−	0.796783i
$881$	5.65448	−	9.79384i	0.190504	−	0.329963i	−0.754913	−	0.655825i	$-0.772321\pi$
$881$	5.65448	−	9.79384i	0.190504	−	0.329963i	0.945417	+	0.325862i	$0.105654\pi$
$882$		0			0
$883$	−46.9068			−1.57854			−0.789270	−	0.614047i	$-0.789541\pi$
$883$	−46.9068			−1.57854			−0.789270	+	0.614047i	$0.789541\pi$
$884$	9.11296	+	3.19064i	0.306502	+	0.107313i
$885$	−32.7006	+	56.6392i	−1.09922	+	1.90390i
$886$	−3.20659	−	5.55398i	−0.107728	−	0.186590i
$887$	−2.44692			−0.0821594			−0.0410797	−	0.999156i	$-0.513080\pi$
$887$	−2.44692			−0.0821594			−0.0410797	+	0.999156i	$0.513080\pi$
$888$	−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
$892$	22.0432	−	38.1799i	0.738060	−	1.27836i
$893$	−5.26764			−0.176275
$894$	12.2447			0.409523
$895$	16.1647	−	27.9980i	0.540325	−	0.935871i
$896$		0			0
$897$	1.86550	+	9.86928i	0.0622872	+	0.329526i
$898$	0.0192006	+	0.0332564i	0.000640732	+	0.00110978i
$899$	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
$905$	7.64781	+	13.2464i	0.254222	+	0.440325i
$906$	10.7223			0.356224
$907$	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	$0.591995\pi$
$908$	−2.50133			−0.0830097
$909$	−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	$0.563675\pi$
$912$	−39.5728			−1.31039
$913$	7.70855	+	13.3516i	0.255116	+	0.441873i
$914$	7.34233			0.242863
$915$	−20.2626	−	35.0959i	−0.669862	−	1.16023i
$916$	−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	0.210686	+	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
$922$	−3.36232	−	5.82370i	−0.110732	−	0.191793i
$923$	3.49182	+	18.4732i	0.114935	+	0.608054i
$924$		0			0
$925$	0.0163354	−	0.0282937i	0.000537103	−	0.000930290i
$926$	1.46198			0.0480436
$927$	5.58456			0.183421
$928$	0.812938	−	1.40805i	0.0266860	−	0.0462215i
$929$	−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
$931$		0			0
$932$	11.5696	+	20.0391i	0.378973	+	0.656401i
$933$	113.974			3.73134
$934$	4.00727	+	6.94080i	0.131122	+	0.227110i
$935$	−5.09943	+	8.83247i	−0.166769	+	0.288853i
$936$	20.0588	−	17.2556i	0.655643	−	0.564018i
$937$	32.4601			1.06042			0.530212	−	0.847865i	$-0.322112\pi$
$937$	32.4601			1.06042			0.530212	+	0.847865i	$0.322112\pi$
$938$		0			0
$939$	11.9838	−	20.7566i	0.391078	−	0.677366i
$940$	3.53580	−	6.12419i	0.115325	−	0.199749i
$941$	6.30253	−	10.9163i	0.205457	−	0.355861i	−0.744822	−	0.667264i	$-0.767465\pi$
$941$	6.30253	−	10.9163i	0.205457	−	0.355861i	0.950278	+	0.311402i	$0.100799\pi$
$942$	9.97283			0.324932
$943$	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
$947$	−13.2802			−0.431548			−0.215774	−	0.976443i	$-0.569228\pi$
$947$	−13.2802			−0.431548			−0.215774	+	0.976443i	$0.569228\pi$
$948$	−20.8567	+	36.1248i	−0.677393	+	1.17328i
$949$	10.8337	−	9.31971i	0.351677	−	0.302531i
$950$	0.00787031	+	0.0136318i	0.000255347	+	0.000442273i
$951$	−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	$0.438027\pi$
$954$	−7.80637	−	13.5210i	−0.252741	−	0.437760i
$955$	6.36301			0.205902
$956$	8.13204			0.263009
$957$	−3.35062	−	5.80345i	−0.108310	−	0.187599i
$958$	0.826224	+	1.43106i	0.0266941	+	0.0462355i
$959$		0			0
$960$	24.9965	−	43.2952i	0.806759	−	1.39735i
$961$	14.0292	+	24.2993i	0.452555	+	0.783848i
$962$	1.22319	+	0.428265i	0.0394373	+	0.0138078i
$963$	−35.9530	+	62.2725i	−1.15857	+	2.00670i
$964$	−7.85093			−0.252861
$965$	−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
$969$	14.7876			0.475047
$970$	−3.96451	+	6.86673i	−0.127293	+	0.220477i
$971$	−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
$973$		0			0
$974$	−4.28023			−0.137148
$975$	0.237745	+	0.0832393i	0.00761392	+	0.00266579i
$976$	−10.0633	+	17.4302i	−0.322119	+	0.557927i
$977$	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	$0.537903\pi$
$978$	−14.1495			−0.452450
$979$	−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
$983$	−8.33707	+	14.4402i	−0.265911	+	0.460572i	−0.967802	−	0.251713i	$-0.919006\pi$
$983$	−8.33707	+	14.4402i	−0.265911	+	0.460572i	0.701891	+	0.712285i	$0.252339\pi$
$984$	−27.8402			−0.887512
$985$	56.7147			1.80708
$986$	−0.0966271	+	0.167363i	−0.00307723	+	0.00532993i
$987$		0			0
$988$	17.2130	−	14.8075i	0.547620	−	0.471090i
$989$	−0.516249	−	0.894170i	−0.0164158	−	0.0284330i
$990$	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			0
$995$	−13.8864	−	24.0519i	−0.440228	−	0.762497i
$996$	15.0045	+	25.9885i	0.475435	+	0.823478i
$997$	6.27646			0.198777			0.0993887	−	0.995049i	$-0.468311\pi$
$997$	6.27646			0.198777			0.0993887	+	0.995049i	$0.468311\pi$
$998$	−1.44350	−	2.50021i	−0.0456931	−	0.0791427i
$999$	−26.0003			−0.822614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.h.165.3		8
7.2	even	3		637.2.g.k.373.2		8
7.3	odd	6		637.2.f.i.295.2		8
7.4	even	3		91.2.f.c.22.2	✓	8
7.5	odd	6		637.2.g.j.373.2		8
7.6	odd	2		637.2.h.i.165.3		8
13.3	even	3		637.2.g.k.263.2		8
21.11	odd	6		819.2.o.h.568.3		8
28.11	odd	6		1456.2.s.q.113.1		8
91.3	odd	6		637.2.f.i.393.2		8
91.4	even	6		1183.2.a.l.1.2		4
91.16	even	3	inner	637.2.h.h.471.3		8
91.17	odd	6		8281.2.a.bt.1.2		4
91.32	odd	12		1183.2.c.g.337.4		8
91.46	odd	12		1183.2.c.g.337.5		8
91.55	odd	6		637.2.g.j.263.2		8
91.68	odd	6		637.2.h.i.471.3		8
91.74	even	3		1183.2.a.k.1.3		4
91.81	even	3		91.2.f.c.29.2	yes	8
91.87	odd	6		8281.2.a.bp.1.3		4
273.263	odd	6		819.2.o.h.757.3		8
364.263	odd	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	7.4	even	3
91.2.f.c.29.2	yes	8	91.81	even	3
637.2.f.i.295.2		8	7.3	odd	6
637.2.f.i.393.2		8	91.3	odd	6
637.2.g.j.263.2		8	91.55	odd	6
637.2.g.j.373.2		8	7.5	odd	6
637.2.g.k.263.2		8	13.3	even	3
637.2.g.k.373.2		8	7.2	even	3
637.2.h.h.165.3		8	1.1	even	1	trivial
637.2.h.h.471.3		8	91.16	even	3	inner
637.2.h.i.165.3		8	7.6	odd	2
637.2.h.i.471.3		8	91.68	odd	6
819.2.o.h.568.3		8	21.11	odd	6
819.2.o.h.757.3		8	273.263	odd	6
1183.2.a.k.1.3		4	91.74	even	3
1183.2.a.l.1.2		4	91.4	even	6
1183.2.c.g.337.4		8	91.32	odd	12
1183.2.c.g.337.5		8	91.46	odd	12
1456.2.s.q.113.1		8	28.11	odd	6
1456.2.s.q.1121.1		8	364.263	odd	6
8281.2.a.bp.1.3		4	91.87	odd	6
8281.2.a.bt.1.2		4	91.17	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.231361 q^{2} +(1.66113 + 2.87716i) q^{3} -1.94647 q^{4} +(1.11568 + 1.93242i) q^{5} +(0.384320 + 0.665661i) q^{6} -0.913059 q^{8} +(-4.01868 + 6.96056i) q^{9} +O(q^{10})\)	\(q+0.231361 q^{2} +(1.66113 + 2.87716i) q^{3} -1.94647 q^{4} +(1.11568 + 1.93242i) 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} +(-3.23334 - 5.60030i) q^{12} +(3.40300 + 1.19146i) q^{13} +(-3.70657 + 6.41997i) q^{15} +3.68170 q^{16} -1.37578 q^{17} +(-0.929766 + 1.61040i) q^{18} +(-1.61766 + 2.80186i) q^{19} +(-2.17164 - 3.76139i) q^{20} +(-0.384320 - 0.665661i) q^{22} +0.838502 q^{23} +(-1.51671 - 2.62701i) q^{24} +(0.0105144 - 0.0182115i) q^{25} +(0.787321 + 0.275657i) q^{26} -16.7354 q^{27} +(0.303571 - 0.525800i) q^{29} +(-0.857556 + 1.48533i) q^{30} +(-0.857556 + 1.48533i) q^{31} +2.67792 q^{32} +(5.51868 - 9.55864i) q^{33} -0.318302 q^{34} +(7.82225 - 13.5485i) q^{36} +1.55361 q^{37} +(-0.374262 + 0.648241i) q^{38} +(2.22480 + 11.7701i) q^{39} +(-1.01868 - 1.76441i) q^{40} +(4.58892 - 7.94824i) q^{41} +(-0.615680 - 1.06639i) q^{43} +(3.23334 + 5.60030i) q^{44} -17.9343 q^{45} +0.193997 q^{46} +(0.814085 + 1.41004i) q^{47} +(6.11577 + 10.5928i) q^{48} +(0.00243263 - 0.00421343i) q^{50} +(-2.28535 - 3.95833i) q^{51} +(-6.62385 - 2.31915i) q^{52} +(-4.19803 + 7.27121i) q^{53} -3.87192 q^{54} +(3.70657 - 6.41997i) q^{55} -10.7485 q^{57} +(0.0702344 - 0.121650i) q^{58} +8.82234 q^{59} +(7.21474 - 12.4963i) q^{60} +(-2.73334 + 4.73428i) q^{61} +(-0.198405 + 0.343647i) q^{62} -6.74383 q^{64} +(1.49426 + 7.90530i) q^{65} +(1.27681 - 2.21149i) q^{66} +(5.09287 + 8.82111i) q^{67} +2.67792 q^{68} +(1.39286 + 2.41250i) q^{69} +(2.60714 + 4.51570i) q^{71} +(3.66929 - 6.35540i) q^{72} +(1.98177 - 3.43253i) q^{73} +0.359445 q^{74} +0.0698632 q^{75} +(3.14872 - 5.45375i) q^{76} +(0.514731 + 2.72315i) q^{78} +(-3.22525 - 5.58630i) 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} +(-0.142444 - 0.246721i) q^{86} +2.01708 q^{87} +(1.51671 + 2.62701i) q^{88} +9.12826 q^{89} -4.14929 q^{90} -1.63212 q^{92} -5.69803 q^{93} +(0.188347 + 0.326227i) q^{94} -7.21915 q^{95} +(4.44836 + 7.70479i) q^{96} +(7.67944 + 13.3012i) q^{97} +26.7022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - q^{3} + 10 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - q^3 + 10 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 - 7 * q^9	\( 8 q - 2 q^{2} - q^{3} + 10 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} - 12 q^{12} + 4 q^{13} - 3 q^{15} + 38 q^{16} - 8 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} - 5 q^{22} - 4 q^{23} + 3 q^{24} - 5 q^{25} - 15 q^{26} - 52 q^{27} - q^{29} + 4 q^{30} + 4 q^{31} - 66 q^{32} + 19 q^{33} + 6 q^{34} + 34 q^{36} - 20 q^{37} + 23 q^{38} - q^{39} + 17 q^{40} + 22 q^{41} - 3 q^{43} + 12 q^{44} - 22 q^{45} + 48 q^{46} - 2 q^{47} - 11 q^{48} - 43 q^{50} - 7 q^{51} - 31 q^{52} - 2 q^{53} + 10 q^{54} + 3 q^{55} - 34 q^{57} + 11 q^{58} - 16 q^{59} + 11 q^{60} - 8 q^{61} + 5 q^{62} + 28 q^{64} - 11 q^{65} - 6 q^{66} + 6 q^{67} - 66 q^{68} + 18 q^{69} + 14 q^{71} - 5 q^{72} + 8 q^{73} + 40 q^{74} - 14 q^{75} - 32 q^{76} - q^{78} + 26 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} - 5 q^{85} - 12 q^{86} + 26 q^{87} - 3 q^{88} - 2 q^{89} + 52 q^{90} + 24 q^{92} - 14 q^{93} - 33 q^{94} + 42 q^{95} + 58 q^{96} - 3 q^{97} + 46 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 + 10 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 - 12 * q^12 + 4 * q^13 - 3 * q^15 + 38 * q^16 - 8 * q^17 + 3 * q^18 - q^19 + 2 * q^20 - 5 * q^22 - 4 * q^23 + 3 * q^24 - 5 * q^25 - 15 * q^26 - 52 * q^27 - q^29 + 4 * q^30 + 4 * q^31 - 66 * q^32 + 19 * q^33 + 6 * q^34 + 34 * q^36 - 20 * q^37 + 23 * q^38 - q^39 + 17 * q^40 + 22 * q^41 - 3 * q^43 + 12 * q^44 - 22 * q^45 + 48 * q^46 - 2 * q^47 - 11 * q^48 - 43 * q^50 - 7 * q^51 - 31 * q^52 - 2 * q^53 + 10 * q^54 + 3 * q^55 - 34 * q^57 + 11 * q^58 - 16 * q^59 + 11 * q^60 - 8 * q^61 + 5 * q^62 + 28 * q^64 - 11 * q^65 - 6 * q^66 + 6 * q^67 - 66 * q^68 + 18 * q^69 + 14 * q^71 - 5 * q^72 + 8 * q^73 + 40 * q^74 - 14 * q^75 - 32 * q^76 - q^78 + 26 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 - 5 * q^85 - 12 * q^86 + 26 * q^87 - 3 * q^88 - 2 * q^89 + 52 * q^90 + 24 * q^92 - 14 * q^93 - 33 * q^94 + 42 * q^95 + 58 * q^96 - 3 * q^97 + 46 * q^99

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