LMFDB - Embedded newform 637.2.h.i.165.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(165,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,-2,1,10,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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:	8.0.59066497296.1
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.i.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} +(-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} - 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}+ \cdots + 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

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	$-0.758073\pi$
$3$	−1.66113	−	2.87716i	−0.959052	−	1.66113i	−0.234241	−	0.972179i	$-0.575260\pi$
$4$	−1.94647			−0.973236
$5$	−1.11568	−	1.93242i	−0.498947	−	0.864202i	0.501052	−	0.865417i	$-0.332947\pi$
$5$	−1.11568	−	1.93242i	−0.498947	−	0.864202i	−0.999999	+	0.00121496i	$0.999613\pi$
$6$	−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	$-0.446644\pi$
$17$	1.37578			0.333676			0.166838	+	0.985984i	$0.446644\pi$
$18$	−0.929766	+	1.61040i	−0.219148	+	0.379575i
$19$	1.61766	−	2.80186i	0.371116	−	0.642791i	−0.618622	−	0.785689i	$-0.712309\pi$
$19$	1.61766	−	2.80186i	0.371116	−	0.642791i	0.989737	+	0.142898i	$0.0456420\pi$
$20$	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	−0.778681	−	0.627420i	$-0.784111\pi$
$31$	0.857556	−	1.48533i	0.154022	−	0.266773i	0.932702	+	0.360647i	$0.117444\pi$
$32$	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	$0.421001\pi$
$41$	−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	$0.863264\pi$
$44$	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	0.800525	−	0.599300i	$-0.204554\pi$
$47$	−0.814085	−	1.41004i	−0.118747	−	0.205675i	−0.919271	+	0.393625i	$0.871221\pi$
$48$	−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	$-0.694720\pi$
$59$	−8.82234			−1.14857			−0.574285	+	0.818655i	$0.694720\pi$
$60$	7.21474	−	12.4963i	0.931419	−	1.61326i
$61$	2.73334	−	4.73428i	0.349968	−	0.606162i	−0.636276	−	0.771462i	$-0.719526\pi$
$61$	2.73334	−	4.73428i	0.349968	−	0.606162i	0.986243	+	0.165300i	$0.0528592\pi$
$62$	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	−0.958382	−	0.285490i	$-0.907844\pi$
$73$	−1.98177	+	3.43253i	−0.231949	+	0.401748i	0.726432	+	0.687238i	$0.241177\pi$
$74$	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	$-0.418029\pi$
$83$	4.64055			0.509367			0.254684	+	0.967024i	$0.418029\pi$
$84$		0			0
$85$	−1.53493	−	2.65858i	−0.166487	−	0.288363i
$86$	−0.142444	−	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	$-0.660743\pi$
$89$	−9.12826			−0.967593			−0.483797	+	0.875180i	$0.660743\pi$
$90$	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	$-0.882024\pi$
$97$	−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	0.597623	−	0.801777i	$-0.296112\pi$
$101$	−3.97521	−	6.88527i	−0.395548	−	0.685110i	−0.993171	+	0.116668i	$0.962779\pi$
$102$	−0.528739	−	0.915804i	−0.0523530	−	0.0906781i
$103$	0.347412	+	0.601736i	0.0342316	+	0.0592908i	0.882634	−	0.470062i	$-0.155768\pi$
$103$	0.347412	+	0.601736i	0.0342316	+	0.0592908i	−0.848402	+	0.529352i	$0.822435\pi$
$104$	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	0.825307	−	0.564684i	$-0.191002\pi$
$131$	−0.874176	−	1.51412i	−0.0763771	−	0.132289i	−0.901684	+	0.432395i	$0.857669\pi$
$132$	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	$0.0343048\pi$
$139$	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
$142$	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	$0.339895\pi$
$157$	−6.48733	+	11.2364i	−0.517745	+	0.896761i	−0.999788	+	0.0206132i	$0.993438\pi$
$158$	−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	$0.420587\pi$
$167$	−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
$170$	−0.355123	−	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	$0.393482\pi$
$173$	−8.59906	+	14.8940i	−0.653774	+	1.13237i	−0.982200	+	0.187840i	$0.939851\pi$
$174$	−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	$-0.581996\pi$
$181$	−6.85484			−0.509516			−0.254758	+	0.967005i	$0.581996\pi$
$182$		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	$-0.354568\pi$
$199$	12.4466			0.882313			0.441157	+	0.897430i	$0.354568\pi$
$200$	−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	$-0.559336\pi$
$223$	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
$226$	1.09952	+	1.90442i	0.0731388	+	0.126680i
$227$	−1.28506			−0.0852925			−0.0426462	−	0.999090i	$-0.513579\pi$
$227$	−1.28506			−0.0852925			−0.0426462	+	0.999090i	$0.513579\pi$
$228$	20.9217			1.38557
$229$	−2.32225	−	4.02226i	−0.153459	−	0.265798i	0.779038	−	0.626977i	$-0.215708\pi$
$229$	−2.32225	−	4.02226i	−0.153459	−	0.265798i	−0.932497	+	0.361178i	$0.882375\pi$
$230$	−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	$-0.541468\pi$
$241$	−4.03341			−0.259815			−0.129907	+	0.991526i	$0.541468\pi$
$242$	−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	$0.175471\pi$
$251$	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
$255$	−5.09943	+	8.83247i	−0.319339	+	0.553111i
$256$	11.8875			0.742972
$257$	7.14064			0.445421			0.222710	−	0.974885i	$-0.428510\pi$
$257$	7.14064			0.445421			0.222710	+	0.974885i	$0.428510\pi$
$258$	−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	$-0.527094\pi$
$269$	−2.78875			−0.170033			−0.0850167	+	0.996380i	$0.527094\pi$
$270$	−4.31982	−	7.48215i	−0.262896	−	0.455349i
$271$	15.4747			0.940024			0.470012	−	0.882660i	$-0.344250\pi$
$271$	15.4747			0.940024			0.470012	+	0.882660i	$0.344250\pi$
$272$	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	0.735856	−	0.677138i	$-0.236780\pi$
$283$	−3.67559	−	6.36631i	−0.218491	−	0.378438i	−0.954347	+	0.298700i	$0.903447\pi$
$284$	−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	0.597824	−	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
$296$	−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	$-0.469925\pi$
$307$	3.30609			0.188688			0.0943442	+	0.995540i	$0.469925\pi$
$308$		0			0
$309$	1.15419	−	1.99912i	0.0656597	−	0.113726i
$310$	−0.885425			−0.0502888
$311$	−17.1531	+	29.7101i	−0.972665	+	1.68470i	−0.285229	+	0.958459i	$0.592070\pi$
$311$	−17.1531	+	29.7101i	−0.972665	+	1.68470i	−0.687435	+	0.726246i	$0.741264\pi$
$312$	−2.03137	−	10.7468i	−0.115004	−	0.608419i
$313$	3.60714	+	6.24775i	0.203888	+	0.353144i	0.949778	−	0.312925i	$-0.101309\pi$
$313$	3.60714	+	6.24775i	0.203888	+	0.353144i	−0.745890	+	0.666069i	$0.767976\pi$
$314$	−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	$-0.461562\pi$
$349$	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
$352$	−4.44836	−	7.70479i	−0.237098	−	0.410667i
$353$	−11.9581	−	20.7121i	−0.636467	−	1.10239i	−0.986202	−	0.165545i	$-0.947062\pi$
$353$	−11.9581	−	20.7121i	−0.636467	−	1.10239i	0.349735	−	0.936849i	$-0.386272\pi$
$354$	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	$0.00674460\pi$
$367$	9.92798	+	17.1958i	0.518236	+	0.897612i	−0.481539	+	0.876425i	$0.659922\pi$
$368$	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	−0.997927	−	0.0643617i	$-0.979499\pi$
$383$	−8.67407	+	15.0239i	−0.443224	+	0.767687i	0.554702	+	0.832049i	$0.312832\pi$
$384$	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	$0.404437\pi$
$397$	−13.5375	+	23.4476i	−0.679425	+	1.17680i	−0.975154	+	0.221527i	$0.928896\pi$
$398$	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	$-0.696095\pi$
$409$	−23.3713			−1.15563			−0.577817	+	0.816166i	$0.696095\pi$
$410$	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	−0.630637	−	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
$423$	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	0.704005	−	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
$437$	1.35641	−	2.34937i	0.0648858	−	0.112386i
$438$	3.04654			0.145569
$439$	17.9179			0.855176			0.427588	−	0.903974i	$-0.359363\pi$
$439$	17.9179			0.855176			0.427588	+	0.903974i	$0.359363\pi$
$440$	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	$0.0699926\pi$
$461$	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
$467$	−17.3204	−	29.9999i	−0.801495	−	1.38823i	−0.918632	−	0.395114i	$-0.870705\pi$
$467$	−17.3204	−	29.9999i	−0.801495	−	1.38823i	0.117137	−	0.993116i	$-0.462628\pi$
$468$	−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	0.772834	−	0.634608i	$-0.218839\pi$
$479$	−3.57115	−	6.18541i	−0.163170	−	0.282619i	−0.936004	+	0.351990i	$0.885505\pi$
$480$	−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	0.835832	−	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
$506$	−0.322253	−	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	$-0.790315\pi$
$509$	−35.6808			−1.58152			−0.790761	+	0.612125i	$0.790315\pi$
$510$	−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	−0.998920	−	0.0464666i	$-0.985204\pi$
$521$	−10.4819	+	18.1551i	−0.459219	+	0.795390i	0.539701	+	0.841857i	$0.318537\pi$
$522$	0.564499	+	0.977742i	0.0247075	+	0.0427946i
$523$	22.8263			0.998124			0.499062	−	0.866566i	$-0.333678\pi$
$523$	22.8263			0.998124			0.499062	+	0.866566i	$0.333678\pi$
$524$	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	$-0.726128\pi$
$563$	−30.9474			−1.30428			−0.652138	+	0.758100i	$0.726128\pi$
$564$	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	−0.950076	−	0.312019i	$-0.898995\pi$
$577$	−4.91999	+	8.52168i	−0.204822	+	0.354762i	0.745254	+	0.666781i	$0.232328\pi$
$578$	−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	−0.978884	−	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
$590$	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	0.944688	−	0.327970i	$-0.106364\pi$
$593$	4.58574	+	7.94274i	0.188314	+	0.326169i	−0.756374	+	0.654139i	$0.773031\pi$
$594$	−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	−0.969723	−	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
$605$	0.0833731			0.00338960
$606$	−3.05550	+	5.29229i	−0.124121	+	0.214984i
$607$	6.31812	−	10.9433i	0.256445	−	0.444175i	−0.708842	−	0.705367i	$-0.750782\pi$
$607$	6.31812	−	10.9433i	0.256445	−	0.444175i	0.965287	+	0.261192i	$0.0841155\pi$
$608$	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	−0.996162	−	0.0875280i	$-0.972103\pi$
$619$	−10.5062	+	18.1973i	−0.422280	+	0.731410i	0.573883	+	0.818938i	$0.305437\pi$
$620$	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	0.687716	−	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	0.995965	+	0.0897473i	$0.0286059\pi$
$647$	14.6438	+	25.3637i	0.575706	+	0.997152i	−0.420259	+	0.907404i	$0.638061\pi$
$648$	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	0.596555	−	0.802572i	$-0.296536\pi$
$661$	−10.2009	−	17.6685i	−0.396770	−	0.687226i	−0.993325	+	0.115346i	$0.963202\pi$
$662$	−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	0.830277	−	0.557351i	$-0.188182\pi$
$677$	−1.75738	−	3.04388i	−0.0675417	−	0.116986i	−0.897819	+	0.440365i	$0.854849\pi$
$678$	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	$-0.691390\pi$
$691$	−29.7404			−1.13138			−0.565690	+	0.824618i	$0.691390\pi$
$692$	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	−0.524540	−	0.851386i	$-0.675763\pi$
$719$	12.7381	−	22.0631i	0.475052	−	0.822813i	0.999592	+	0.0285723i	$0.00909607\pi$
$720$	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	$-0.446472\pi$
$727$	9.02572			0.334746			0.167373	+	0.985894i	$0.446472\pi$
$728$		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	0.787612	−	0.616172i	$-0.211317\pi$
$733$	−3.78535	−	6.55641i	−0.139815	−	0.242167i	−0.927426	+	0.374006i	$0.877984\pi$
$734$	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	−0.995318	−	0.0966503i	$-0.969187\pi$
$761$	−11.4195	+	19.7792i	−0.413958	+	0.716996i	0.581361	+	0.813646i	$0.302520\pi$
$762$	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	$-0.617171\pi$
$769$	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
$772$	−9.78150	−	16.9421i	−0.352044	−	0.609758i
$773$	33.2743			1.19679			0.598397	−	0.801200i	$-0.295804\pi$
$773$	33.2743			1.19679			0.598397	+	0.801200i	$0.295804\pi$
$774$	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	$-0.334889\pi$
$787$	27.8157			0.991524			0.495762	+	0.868458i	$0.334889\pi$
$788$	−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	$0.0524421\pi$
$797$	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
$801$	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	$-0.645984\pi$
$811$	−25.2152			−0.885425			−0.442713	+	0.896664i	$0.645984\pi$
$812$		0			0
$813$	−25.7055	−	44.5233i	−0.901532	−	1.56150i
$814$	−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	0.973788	−	0.227457i	$-0.0730411\pi$
$829$	8.34721	+	14.4578i	0.289911	+	0.502140i	−0.683877	+	0.729597i	$0.739708\pi$
$830$	−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	$-0.868770\pi$
$839$	−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
$842$	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	$-0.736860\pi$
$853$	−39.5640			−1.35464			−0.677322	+	0.735686i	$0.736860\pi$
$854$		0			0
$855$	29.0115	−	50.2493i	0.992171	−	1.71849i
$856$	−8.16866			−0.279199
$857$	−9.78065	+	16.9406i	−0.334101	+	0.578679i	−0.983312	−	0.181929i	$-0.941766\pi$
$857$	−9.78065	+	16.9406i	−0.334101	+	0.578679i	0.649211	+	0.760608i	$0.275099\pi$
$858$	6.97989	−	6.00445i	0.238289	−	0.204989i
$859$	−5.08158	−	8.80155i	−0.173381	−	0.300305i	0.766219	−	0.642580i	$-0.222136\pi$
$859$	−5.08158	−	8.80155i	−0.173381	−	0.300305i	−0.939600	+	0.342275i	$0.888803\pi$
$860$	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	−0.945417	−	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	$0.789541\pi$
$884$	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	$-0.486920\pi$
$887$	2.44692			0.0821594			0.0410797	+	0.999156i	$0.486920\pi$
$888$	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	−0.535554	−	0.844501i	$-0.679897\pi$
$929$	14.1298	−	24.4735i	0.463582	−	0.802948i	0.999136	+	0.0415530i	$0.0132305\pi$
$930$	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	$-0.677888\pi$
$937$	−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
$941$	−6.30253	+	10.9163i	−0.205457	+	0.355861i	−0.950278	−	0.311402i	$-0.899201\pi$
$941$	−6.30253	+	10.9163i	−0.205457	+	0.355861i	0.744822	+	0.667264i	$0.232535\pi$
$942$	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	−0.699446	−	0.714685i	$-0.746570\pi$
$971$	8.38890	−	14.5300i	0.269213	−	0.466290i	0.968659	+	0.248395i	$0.0799032\pi$
$972$	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	−0.701891	−	0.712285i	$-0.747661\pi$
$983$	8.33707	−	14.4402i	0.265911	−	0.460572i	0.967802	+	0.251713i	$0.0809939\pi$
$984$	−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	$-0.531689\pi$
$997$	−6.27646			−0.198777			−0.0993887	+	0.995049i	$0.531689\pi$
$998$	−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.i.165.3		8
7.2	even	3		637.2.g.j.373.2		8
7.3	odd	6		91.2.f.c.22.2	✓	8
7.4	even	3		637.2.f.i.295.2		8
7.5	odd	6		637.2.g.k.373.2		8
7.6	odd	2		637.2.h.h.165.3		8
13.3	even	3		637.2.g.j.263.2		8
21.17	even	6		819.2.o.h.568.3		8
28.3	even	6		1456.2.s.q.113.1		8
91.3	odd	6		91.2.f.c.29.2	yes	8
91.4	even	6		8281.2.a.bt.1.2		4
91.16	even	3	inner	637.2.h.i.471.3		8
91.17	odd	6		1183.2.a.l.1.2		4
91.45	even	12		1183.2.c.g.337.4		8
91.55	odd	6		637.2.g.k.263.2		8
91.59	even	12		1183.2.c.g.337.5		8
91.68	odd	6		637.2.h.h.471.3		8
91.74	even	3		8281.2.a.bp.1.3		4
91.81	even	3		637.2.f.i.393.2		8
91.87	odd	6		1183.2.a.k.1.3		4
273.185	even	6		819.2.o.h.757.3		8
364.3	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	7.3	odd	6
91.2.f.c.29.2	yes	8	91.3	odd	6
637.2.f.i.295.2		8	7.4	even	3
637.2.f.i.393.2		8	91.81	even	3
637.2.g.j.263.2		8	13.3	even	3
637.2.g.j.373.2		8	7.2	even	3
637.2.g.k.263.2		8	91.55	odd	6
637.2.g.k.373.2		8	7.5	odd	6
637.2.h.h.165.3		8	7.6	odd	2
637.2.h.h.471.3		8	91.68	odd	6
637.2.h.i.165.3		8	1.1	even	1	trivial
637.2.h.i.471.3		8	91.16	even	3	inner
819.2.o.h.568.3		8	21.17	even	6
819.2.o.h.757.3		8	273.185	even	6
1183.2.a.k.1.3		4	91.87	odd	6
1183.2.a.l.1.2		4	91.17	odd	6
1183.2.c.g.337.4		8	91.45	even	12
1183.2.c.g.337.5		8	91.59	even	12
1456.2.s.q.113.1		8	28.3	even	6
1456.2.s.q.1121.1		8	364.3	even	6
8281.2.a.bp.1.3		4	91.74	even	3
8281.2.a.bt.1.2		4	91.4	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 $\F_{q}$
Belyi maps

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + q^{3} + 10 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9} - 11 q^{10} + q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} + 38 q^{16} + 8 q^{17} + 3 q^{18} + q^{19} - 2 q^{20} - 5 q^{22} - 4 q^{23}+ \cdots + 46 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more