LMFDB - Embedded newform 644.2.i.a.277.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 13 x^{12} - 8 x^{11} + 130 x^{10} - 78 x^{9} + 505 x^{8} - 519 x^{7} + 1508 x^{6} - 955 x^{5} + \cdots + 1 $ x^14 + 13x^12 - 8x^11 + 130x^10 - 78x^9 + 505x^8 - 519x^7 + 1508x^6 - 955x^5 + 1023x^4 + 156x^3 + 107x^2 - 9x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.7
Root			$-1.52632 + 2.64366i$ of defining polynomial
Character	$\chi$	$=$	644.277
Dual form			644.2.i.a.93.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09449 - 1.89572i) q^{3} +(0.0359834 + 0.0623251i) q^{5} +(0.105282 + 2.64366i) q^{7} +(-0.895837 - 1.55164i) q^{9} +O(q^{10})$	\(q+(1.09449 - 1.89572i) q^{3} +(0.0359834 + 0.0623251i) q^{5} +(0.105282 + 2.64366i) q^{7} +(-0.895837 - 1.55164i) q^{9} +(2.19197 - 3.79660i) q^{11} +1.85129 q^{13} +0.157535 q^{15} +(2.43468 - 4.21699i) q^{17} +(-0.857370 - 1.48501i) q^{19} +(5.12686 + 2.69388i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.49741 - 4.32564i) q^{25} +2.64501 q^{27} -2.32535 q^{29} +(-1.89152 + 3.27621i) q^{31} +(-4.79820 - 8.31072i) q^{33} +(-0.160978 + 0.101689i) q^{35} +(2.57924 + 4.46737i) q^{37} +(2.02622 - 3.50952i) q^{39} +0.793289 q^{41} -8.05385 q^{43} +(0.0644706 - 0.111666i) q^{45} +(-2.52839 - 4.37931i) q^{47} +(-6.97783 + 0.556658i) q^{49} +(-5.32949 - 9.23095i) q^{51} +(0.179049 - 0.310123i) q^{53} +0.315498 q^{55} -3.75355 q^{57} +(-1.42319 + 2.46503i) q^{59} +(4.95073 + 8.57492i) q^{61} +(4.00768 - 2.53164i) q^{63} +(0.0666156 + 0.115382i) q^{65} +(-6.18427 + 10.7115i) q^{67} +2.18899 q^{69} -5.98797 q^{71} +(3.07196 - 5.32079i) q^{73} +(-5.46680 - 9.46878i) q^{75} +(10.2677 + 5.39510i) q^{77} +(-3.64675 - 6.31635i) q^{79} +(5.58246 - 9.66911i) q^{81} +10.8670 q^{83} +0.350433 q^{85} +(-2.54508 + 4.40821i) q^{87} +(8.92519 + 15.4589i) q^{89} +(0.194907 + 4.89416i) q^{91} +(4.14052 + 7.17159i) q^{93} +(0.0617022 - 0.106871i) q^{95} +9.62586 q^{97} -7.85459 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.09449	−	1.89572i	0.631907	−	1.09449i	−0.355255	−	0.934770i	$-0.615606\pi$
$3$	1.09449	−	1.89572i	0.631907	−	1.09449i	0.987162	−	0.159725i	$-0.0510608\pi$
$4$		0			0
$5$	0.0359834	+	0.0623251i	0.0160923	+	0.0278726i	0.873959	−	0.485999i	$-0.161544\pi$
$5$	0.0359834	+	0.0623251i	0.0160923	+	0.0278726i	−0.857867	+	0.513872i	$0.828211\pi$
$6$		0			0
$7$	0.105282	+	2.64366i	0.0397928	+	0.999208i
$7$	0.105282	+	2.64366i	0.0397928	+	0.999208i
$8$		0			0
$9$	−0.895837	−	1.55164i	−0.298612	−	0.517212i
$10$		0			0
$11$	2.19197	−	3.79660i	0.660904	−	1.14472i	−0.319475	−	0.947595i	$-0.603506\pi$
$11$	2.19197	−	3.79660i	0.660904	−	1.14472i	0.980379	−	0.197124i	$-0.0631602\pi$
$12$		0			0
$13$	1.85129			0.513454			0.256727	−	0.966484i	$-0.417356\pi$
$13$	1.85129			0.513454			0.256727	+	0.966484i	$0.417356\pi$
$14$		0			0
$15$	0.157535			0.0406753
$16$		0			0
$17$	2.43468	−	4.21699i	0.590497	−	1.02277i	−0.403668	−	0.914905i	$-0.632265\pi$
$17$	2.43468	−	4.21699i	0.590497	−	1.02277i	0.994165	−	0.107866i	$-0.0344017\pi$
$18$		0			0
$19$	−0.857370	−	1.48501i	−0.196694	−	0.340684i	0.750760	−	0.660575i	$-0.229687\pi$
$19$	−0.857370	−	1.48501i	−0.196694	−	0.340684i	−0.947455	+	0.319890i	$0.896354\pi$
$20$		0			0
$21$	5.12686	+	2.69388i	1.11877	+	0.587853i
$22$		0			0
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$		0			0
$25$	2.49741	−	4.32564i	0.499482	−	0.865128i
$26$		0			0
$27$	2.64501			0.509033
$28$		0			0
$29$	−2.32535			−0.431806			−0.215903	−	0.976415i	$-0.569270\pi$
$29$	−2.32535			−0.431806			−0.215903	+	0.976415i	$0.569270\pi$
$30$		0			0
$31$	−1.89152	+	3.27621i	−0.339727	+	0.588425i	−0.984381	−	0.176050i	$-0.943668\pi$
$31$	−1.89152	+	3.27621i	−0.339727	+	0.588425i	0.644654	+	0.764474i	$0.277001\pi$
$32$		0			0
$33$	−4.79820	−	8.31072i	−0.835259	−	1.44671i
$34$		0			0
$35$	−0.160978	+	0.101689i	−0.0272102	+	0.0171887i
$36$		0			0
$37$	2.57924	+	4.46737i	0.424024	+	0.734431i	0.996329	−	0.0856097i	$-0.0272838\pi$
$37$	2.57924	+	4.46737i	0.424024	+	0.734431i	−0.572305	+	0.820041i	$0.693950\pi$
$38$		0			0
$39$	2.02622	−	3.50952i	0.324455	−	0.561973i
$40$		0			0
$41$	0.793289			0.123891			0.0619455	−	0.998080i	$-0.480270\pi$
$41$	0.793289			0.123891			0.0619455	+	0.998080i	$0.480270\pi$
$42$		0			0
$43$	−8.05385			−1.22820			−0.614100	−	0.789228i	$-0.710481\pi$
$43$	−8.05385			−1.22820			−0.614100	+	0.789228i	$0.710481\pi$
$44$		0			0
$45$	0.0644706	−	0.111666i	0.00961071	−	0.0166462i
$46$		0			0
$47$	−2.52839	−	4.37931i	−0.368804	−	0.638788i	0.620575	−	0.784147i	$-0.286899\pi$
$47$	−2.52839	−	4.37931i	−0.368804	−	0.638788i	−0.989379	+	0.145360i	$0.953566\pi$
$48$		0			0
$49$	−6.97783	+	0.556658i	−0.996833	+	0.0795226i
$50$		0			0
$51$	−5.32949	−	9.23095i	−0.746278	−	1.29259i
$52$		0			0
$53$	0.179049	−	0.310123i	0.0245943	−	0.0425986i	−0.853466	−	0.521148i	$-0.825504\pi$
$53$	0.179049	−	0.310123i	0.0245943	−	0.0425986i	0.878061	+	0.478549i	$0.158837\pi$
$54$		0			0
$55$	0.315498			0.0425418
$56$		0			0
$57$	−3.75355			−0.497170
$58$		0			0
$59$	−1.42319	+	2.46503i	−0.185283	+	0.320920i	−0.943672	−	0.330883i	$-0.892654\pi$
$59$	−1.42319	+	2.46503i	−0.185283	+	0.320920i	0.758389	+	0.651803i	$0.225987\pi$
$60$		0			0
$61$	4.95073	+	8.57492i	0.633876	+	1.09791i	0.986752	+	0.162236i	$0.0518706\pi$
$61$	4.95073	+	8.57492i	0.633876	+	1.09791i	−0.352876	+	0.935670i	$0.614796\pi$
$62$		0			0
$63$	4.00768	−	2.53164i	0.504920	−	0.318957i
$64$		0			0
$65$	0.0666156	+	0.115382i	0.00826265	+	0.0143113i
$66$		0			0
$67$	−6.18427	+	10.7115i	−0.755529	+	1.30862i	0.189581	+	0.981865i	$0.439287\pi$
$67$	−6.18427	+	10.7115i	−0.755529	+	1.30862i	−0.945111	+	0.326750i	$0.894046\pi$
$68$		0			0
$69$	2.18899			0.263523
$70$		0			0
$71$	−5.98797			−0.710641			−0.355320	−	0.934745i	$-0.615628\pi$
$71$	−5.98797			−0.710641			−0.355320	+	0.934745i	$0.615628\pi$
$72$		0			0
$73$	3.07196	−	5.32079i	0.359546	−	0.622752i	−0.628339	−	0.777940i	$-0.716265\pi$
$73$	3.07196	−	5.32079i	0.359546	−	0.622752i	0.987885	+	0.155188i	$0.0495983\pi$
$74$		0			0
$75$	−5.46680	−	9.46878i	−0.631252	−	1.09336i
$76$		0			0
$77$	10.2677	+	5.39510i	1.17011	+	0.614829i
$78$		0			0
$79$	−3.64675	−	6.31635i	−0.410291	−	0.710645i	0.584630	−	0.811300i	$-0.301240\pi$
$79$	−3.64675	−	6.31635i	−0.410291	−	0.710645i	−0.994921	+	0.100655i	$0.967906\pi$
$80$		0			0
$81$	5.58246	−	9.66911i	0.620274	−	1.07435i
$82$		0			0
$83$	10.8670			1.19281			0.596405	−	0.802684i	$-0.296595\pi$
$83$	10.8670			1.19281			0.596405	+	0.802684i	$0.296595\pi$
$84$		0			0
$85$	0.350433			0.0380098
$86$		0			0
$87$	−2.54508	+	4.40821i	−0.272861	+	0.472610i
$88$		0			0
$89$	8.92519	+	15.4589i	0.946068	+	1.63864i	0.753599	+	0.657335i	$0.228316\pi$
$89$	8.92519	+	15.4589i	0.946068	+	1.63864i	0.192469	+	0.981303i	$0.438351\pi$
$90$		0			0
$91$	0.194907	+	4.89416i	0.0204318	+	0.513048i
$92$		0			0
$93$	4.14052	+	7.17159i	0.429352	+	0.743659i
$94$		0			0
$95$	0.0617022	−	0.106871i	0.00633052	−	0.0109648i
$96$		0			0
$97$	9.62586			0.977358			0.488679	−	0.872464i	$-0.337479\pi$
$97$	9.62586			0.977358			0.488679	+	0.872464i	$0.337479\pi$
$98$		0			0
$99$	−7.85459			−0.789416
$100$		0			0
$101$	−3.81908	+	6.61483i	−0.380012	+	0.658200i	−0.991064	−	0.133391i	$-0.957414\pi$
$101$	−3.81908	+	6.61483i	−0.380012	+	0.658200i	0.611051	+	0.791591i	$0.290747\pi$
$102$		0			0
$103$	−3.76424	−	6.51985i	−0.370901	−	0.642420i	0.618803	−	0.785546i	$-0.287618\pi$
$103$	−3.76424	−	6.51985i	−0.370901	−	0.642420i	−0.989704	+	0.143126i	$0.954284\pi$
$104$		0			0
$105$	0.0165855	+	0.416467i	0.00161858	+	0.0406431i
$106$		0			0
$107$	8.05004	+	13.9431i	0.778227	+	1.34793i	0.932963	+	0.359973i	$0.117214\pi$
$107$	8.05004	+	13.9431i	0.778227	+	1.34793i	−0.154736	+	0.987956i	$0.549453\pi$
$108$		0			0
$109$	−5.56558	+	9.63986i	−0.533085	+	0.923331i	0.466168	+	0.884696i	$0.345634\pi$
$109$	−5.56558	+	9.63986i	−0.533085	+	0.923331i	−0.999253	+	0.0386348i	$0.987699\pi$
$110$		0			0
$111$	11.2919			1.07178
$112$		0			0
$113$	−5.17210			−0.486551			−0.243275	−	0.969957i	$-0.578222\pi$
$113$	−5.17210			−0.486551			−0.243275	+	0.969957i	$0.578222\pi$
$114$		0			0
$115$	−0.0359834	+	0.0623251i	−0.00335547	+	0.00581185i
$116$		0			0
$117$	−1.65845	−	2.87252i	−0.153324	−	0.265565i
$118$		0			0
$119$	11.4046	+	5.99249i	1.04546	+	0.549331i
$120$		0			0
$121$	−4.10946	−	7.11780i	−0.373587	−	0.647072i
$122$		0			0
$123$	0.868251	−	1.50385i	0.0782875	−	0.135598i
$124$		0			0
$125$	0.719296			0.0643358
$126$		0			0
$127$	−10.9213			−0.969110			−0.484555	−	0.874761i	$-0.661018\pi$
$127$	−10.9213			−0.969110			−0.484555	+	0.874761i	$0.661018\pi$
$128$		0			0
$129$	−8.81489	+	15.2678i	−0.776108	+	1.34426i
$130$		0			0
$131$	−3.20469	−	5.55068i	−0.279995	−	0.484965i	0.691388	−	0.722483i	$-0.256999\pi$
$131$	−3.20469	−	5.55068i	−0.279995	−	0.484965i	−0.971383	+	0.237518i	$0.923666\pi$
$132$		0			0
$133$	3.83559	−	2.42294i	0.332587	−	0.210095i
$134$		0			0
$135$	0.0951766	+	0.164851i	0.00819150	+	0.0141881i
$136$		0			0
$137$	1.14554	−	1.98412i	0.0978697	−	0.169515i	−0.812933	−	0.582357i	$-0.802131\pi$
$137$	1.14554	−	1.98412i	0.0978697	−	0.169515i	0.910803	+	0.412842i	$0.135464\pi$
$138$		0			0
$139$	−7.99375			−0.678021			−0.339011	−	0.940783i	$-0.610092\pi$
$139$	−7.99375			−0.678021			−0.339011	+	0.940783i	$0.610092\pi$
$140$		0			0
$141$	−11.0693			−0.932199
$142$		0			0
$143$	4.05796	−	7.02860i	0.339344	−	0.587761i
$144$		0			0
$145$	−0.0836740	−	0.144928i	−0.00694875	−	0.0120356i
$146$		0			0
$147$	−6.58193	+	13.8373i	−0.542869	+	1.14128i
$148$		0			0
$149$	1.57003	+	2.71938i	0.128622	+	0.222780i	0.923143	−	0.384457i	$-0.125611\pi$
$149$	1.57003	+	2.71938i	0.128622	+	0.222780i	−0.794521	+	0.607237i	$0.792278\pi$
$150$		0			0
$151$	2.36555	−	4.09726i	0.192506	−	0.333430i	−0.753574	−	0.657363i	$-0.771672\pi$
$151$	2.36555	−	4.09726i	0.192506	−	0.333430i	0.946080	+	0.323933i	$0.105005\pi$
$152$		0			0
$153$	−8.72432			−0.705319
$154$		0			0
$155$	−0.272254			−0.0218679
$156$		0			0
$157$	−6.45525	+	11.1808i	−0.515185	+	0.892327i	0.484660	+	0.874703i	$0.338943\pi$
$157$	−6.45525	+	11.1808i	−0.515185	+	0.892327i	−0.999845	+	0.0176237i	$0.994390\pi$
$158$		0			0
$159$	−0.391937	−	0.678855i	−0.0310826	−	0.0538367i
$160$		0			0
$161$	−2.23683	+	1.41300i	−0.176287	+	0.111360i
$162$		0			0
$163$	−12.0576	−	20.8844i	−0.944425	−	1.63579i	−0.756898	−	0.653533i	$-0.773286\pi$
$163$	−12.0576	−	20.8844i	−0.944425	−	1.63579i	−0.187527	−	0.982259i	$-0.560047\pi$
$164$		0			0
$165$	0.345311	−	0.598097i	0.0268824	−	0.0465618i
$166$		0			0
$167$	−0.219228			−0.0169644			−0.00848218	−	0.999964i	$-0.502700\pi$
$167$	−0.219228			−0.0169644			−0.00848218	+	0.999964i	$0.502700\pi$
$168$		0			0
$169$	−9.57274			−0.736365
$170$		0			0
$171$	−1.53613	+	2.66065i	−0.117471	+	0.203465i
$172$		0			0
$173$	9.40504	+	16.2900i	0.715052	+	1.23851i	0.962939	+	0.269718i	$0.0869305\pi$
$173$	9.40504	+	16.2900i	0.715052	+	1.23851i	−0.247887	+	0.968789i	$0.579736\pi$
$174$		0			0
$175$	11.6984	+	6.14688i	0.884319	+	0.464661i
$176$		0			0
$177$	3.11534	+	5.39593i	0.234163	+	0.405583i
$178$		0			0
$179$	−2.88526	+	4.99742i	−0.215655	+	0.373525i	−0.953475	−	0.301472i	$-0.902522\pi$
$179$	−2.88526	+	4.99742i	−0.215655	+	0.373525i	0.737820	+	0.674997i	$0.235855\pi$
$180$		0			0
$181$	17.6999			1.31562			0.657811	−	0.753183i	$-0.271483\pi$
$181$	17.6999			1.31562			0.657811	+	0.753183i	$0.271483\pi$
$182$		0			0
$183$	21.6742			1.60220
$184$		0			0
$185$	−0.185620	+	0.321503i	−0.0136470	+	0.0236373i
$186$		0			0
$187$	−10.6735	−	18.4870i	−0.780524	−	1.35191i
$188$		0			0
$189$	0.278472	+	6.99250i	0.0202558	+	0.508630i
$190$		0			0
$191$	−7.20243	−	12.4750i	−0.521150	−	0.902658i	−0.999697	−	0.0245962i	$-0.992170\pi$
$191$	−7.20243	−	12.4750i	−0.521150	−	0.902658i	0.478548	−	0.878062i	$-0.341163\pi$
$192$		0			0
$193$	−9.35317	+	16.2002i	−0.673256	+	1.16611i	0.303719	+	0.952762i	$0.401772\pi$
$193$	−9.35317	+	16.2002i	−0.673256	+	1.16611i	−0.976975	+	0.213352i	$0.931562\pi$
$194$		0			0
$195$	0.291642			0.0208849
$196$		0			0
$197$	−14.9181			−1.06287			−0.531437	−	0.847098i	$-0.678348\pi$
$197$	−14.9181			−1.06287			−0.531437	+	0.847098i	$0.678348\pi$
$198$		0			0
$199$	−8.42710	+	14.5962i	−0.597382	+	1.03470i	0.395824	+	0.918326i	$0.370459\pi$
$199$	−8.42710	+	14.5962i	−0.597382	+	1.03470i	−0.993206	+	0.116369i	$0.962874\pi$
$200$		0			0
$201$	13.5373	+	23.4473i	0.954848	+	1.65385i
$202$		0			0
$203$	−0.244817	−	6.14742i	−0.0171828	−	0.431464i
$204$		0			0
$205$	0.0285453	+	0.0494418i	0.00199369	+	0.00345317i
$206$		0			0
$207$	0.895837	−	1.55164i	0.0622650	−	0.107846i
$208$		0			0
$209$	−7.51732			−0.519984
$210$		0			0
$211$	10.9538			0.754090			0.377045	−	0.926195i	$-0.376940\pi$
$211$	10.9538			0.754090			0.377045	+	0.926195i	$0.376940\pi$
$212$		0			0
$213$	−6.55380	+	11.3515i	−0.449059	+	0.777792i
$214$		0			0
$215$	−0.289805	−	0.501957i	−0.0197645	−	0.0342332i
$216$		0			0
$217$	−8.86031	−	4.65560i	−0.601477	−	0.316043i
$218$		0			0
$219$	−6.72449	−	11.6472i	−0.454399	−	0.787042i
$220$		0			0
$221$	4.50729	−	7.80686i	0.303193	−	0.525146i
$222$		0			0
$223$	−16.1219			−1.07960			−0.539800	−	0.841793i	$-0.681500\pi$
$223$	−16.1219			−1.07960			−0.539800	+	0.841793i	$0.681500\pi$
$224$		0			0
$225$	−8.94909			−0.596606
$226$		0			0
$227$	−8.01464	+	13.8818i	−0.531950	+	0.921365i	0.467354	+	0.884070i	$0.345207\pi$
$227$	−8.01464	+	13.8818i	−0.531950	+	0.921365i	−0.999304	+	0.0372947i	$0.988126\pi$
$228$		0			0
$229$	−4.46768	−	7.73825i	−0.295233	−	0.511358i	0.679806	−	0.733392i	$-0.262064\pi$
$229$	−4.46768	−	7.73825i	−0.295233	−	0.511358i	−0.975039	+	0.222034i	$0.928730\pi$
$230$		0			0
$231$	21.4655	−	13.5598i	1.41233	−	0.892166i
$232$		0			0
$233$	−12.2060	−	21.1414i	−0.799641	−	1.38502i	−0.919850	−	0.392270i	$-0.871690\pi$
$233$	−12.2060	−	21.1414i	−0.799641	−	1.38502i	0.120210	−	0.992749i	$-0.461643\pi$
$234$		0			0
$235$	0.181961	−	0.315165i	0.0118698	−	0.0205591i
$236$		0			0
$237$	−15.9654			−1.03706
$238$		0			0
$239$	16.9555			1.09676			0.548380	−	0.836229i	$-0.315245\pi$
$239$	16.9555			1.09676			0.548380	+	0.836229i	$0.315245\pi$
$240$		0			0
$241$	−9.62452	+	16.6702i	−0.619970	+	1.07382i	0.369521	+	0.929223i	$0.379522\pi$
$241$	−9.62452	+	16.6702i	−0.619970	+	1.07382i	−0.989491	+	0.144597i	$0.953811\pi$
$242$		0			0
$243$	−8.25243	−	14.2936i	−0.529394	−	0.916937i
$244$		0			0
$245$	−0.285780	−	0.414864i	−0.0182578	−	0.0265047i
$246$		0			0
$247$	−1.58724	−	2.74917i	−0.100993	−	0.174926i
$248$		0			0
$249$	11.8939	−	20.6008i	0.753744	−	1.30552i
$250$		0			0
$251$	0.385635			0.0243411			0.0121705	−	0.999926i	$-0.496126\pi$
$251$	0.385635			0.0243411			0.0121705	+	0.999926i	$0.496126\pi$
$252$		0			0
$253$	4.38394			0.275616
$254$		0			0
$255$	0.383547	−	0.664323i	0.0240186	−	0.0416015i
$256$		0			0
$257$	7.08077	+	12.2643i	0.441686	+	0.765023i	0.997815	−	0.0660734i	$-0.0210471\pi$
$257$	7.08077	+	12.2643i	0.441686	+	0.765023i	−0.556129	+	0.831096i	$0.687714\pi$
$258$		0			0
$259$	−11.5386	+	7.28895i	−0.716977	+	0.452913i
$260$		0			0
$261$	2.08313	+	3.60809i	0.128943	+	0.223335i
$262$		0			0
$263$	5.13891	−	8.90085i	0.316879	−	0.548850i	−0.662957	−	0.748658i	$-0.730699\pi$
$263$	5.13891	−	8.90085i	0.316879	−	0.548850i	0.979835	+	0.199808i	$0.0640319\pi$
$264$		0			0
$265$	0.0257712			0.00158311
$266$		0			0
$267$	39.0743			2.39131
$268$		0			0
$269$	1.73021	−	2.99682i	0.105493	−	0.182719i	−0.808447	−	0.588570i	$-0.799691\pi$
$269$	1.73021	−	2.99682i	0.105493	−	0.182719i	0.913940	+	0.405850i	$0.133025\pi$
$270$		0			0
$271$	−4.75759	−	8.24038i	−0.289003	−	0.500567i	0.684569	−	0.728948i	$-0.259990\pi$
$271$	−4.75759	−	8.24038i	−0.289003	−	0.500567i	−0.973572	+	0.228380i	$0.926657\pi$
$272$		0			0
$273$	9.49129	+	4.98714i	0.574439	+	0.301836i
$274$		0			0
$275$	−10.9485	−	18.9634i	−0.660219	−	1.14353i
$276$		0			0
$277$	3.77368	−	6.53620i	0.226738	−	0.392722i	−0.730101	−	0.683339i	$-0.760527\pi$
$277$	3.77368	−	6.53620i	0.226738	−	0.392722i	0.956840	+	0.290617i	$0.0938605\pi$
$278$		0			0
$279$	6.77798			0.405787
$280$		0			0
$281$	23.9373			1.42798			0.713990	−	0.700156i	$-0.246886\pi$
$281$	23.9373			1.42798			0.713990	+	0.700156i	$0.246886\pi$
$282$		0			0
$283$	−14.5164	+	25.1431i	−0.862910	+	1.49460i	0.00619731	+	0.999981i	$0.498027\pi$
$283$	−14.5164	+	25.1431i	−0.862910	+	1.49460i	−0.869107	+	0.494623i	$0.835306\pi$
$284$		0			0
$285$	−0.135066	−	0.233940i	−0.00800059	−	0.0138574i
$286$		0			0
$287$	0.0835190	+	2.09718i	0.00492997	+	0.123793i
$288$		0			0
$289$	−3.35536	−	5.81165i	−0.197374	−	0.341862i
$290$		0			0
$291$	10.5355	−	18.2479i	0.617599	−	1.06971i
$292$		0			0
$293$	23.8421			1.39287			0.696434	−	0.717621i	$-0.254769\pi$
$293$	23.8421			1.39287			0.696434	+	0.717621i	$0.254769\pi$
$294$		0			0
$295$	−0.204845			−0.0119265
$296$		0			0
$297$	5.79779	−	10.0421i	0.336422	−	0.582699i
$298$		0			0
$299$	0.925643	+	1.60326i	0.0535313	+	0.0927189i
$300$		0			0
$301$	−0.847924	−	21.2916i	−0.0488735	−	1.22723i
$302$		0			0
$303$	8.35991	+	14.4798i	0.480265	+	0.831843i
$304$		0			0
$305$	−0.356289	+	0.617110i	−0.0204010	+	0.0353356i
$306$		0			0
$307$	−9.57258			−0.546336			−0.273168	−	0.961966i	$-0.588072\pi$
$307$	−9.57258			−0.546336			−0.273168	+	0.961966i	$0.588072\pi$
$308$		0			0
$309$	−16.4797			−0.937500
$310$		0			0
$311$	15.7457	−	27.2723i	0.892857	−	1.54647i	0.0564216	−	0.998407i	$-0.482031\pi$
$311$	15.7457	−	27.2723i	0.892857	−	1.54647i	0.836435	−	0.548066i	$-0.184636\pi$
$312$		0			0
$313$	−8.70556	−	15.0785i	−0.492068	−	0.852286i	0.507891	−	0.861422i	$-0.330425\pi$
$313$	−8.70556	−	15.0785i	−0.492068	−	0.852286i	−0.999958	+	0.00913551i	$0.997092\pi$
$314$		0			0
$315$	0.301995	+	0.158682i	0.0170155	+	0.00894069i
$316$		0			0
$317$	−13.2838	−	23.0082i	−0.746091	−	1.29227i	−0.949683	−	0.313212i	$-0.898595\pi$
$317$	−13.2838	−	23.0082i	−0.746091	−	1.29227i	0.203592	−	0.979056i	$-0.434738\pi$
$318$		0			0
$319$	−5.09709	+	8.82842i	−0.285382	+	0.494297i
$320$		0			0
$321$	35.2429			1.96707
$322$		0			0
$323$	−8.34970			−0.464589
$324$		0			0
$325$	4.62342	−	8.00800i	0.256461	−	0.444204i
$326$		0			0
$327$	12.1830	+	21.1015i	0.673721	+	1.16692i
$328$		0			0
$329$	11.3112	−	7.14526i	0.623606	−	0.393931i
$330$		0			0
$331$	2.84844	+	4.93364i	0.156564	+	0.271177i	0.933627	−	0.358245i	$-0.116625\pi$
$331$	2.84844	+	4.93364i	0.156564	+	0.271177i	−0.777063	+	0.629422i	$0.783292\pi$
$332$		0			0
$333$	4.62116	−	8.00408i	0.253238	−	0.438621i
$334$		0			0
$335$	−0.890125			−0.0486327
$336$		0			0
$337$	3.86498			0.210539			0.105269	−	0.994444i	$-0.466429\pi$
$337$	3.86498			0.210539			0.105269	+	0.994444i	$0.466429\pi$
$338$		0			0
$339$	−5.66084	+	9.80486i	−0.307455	+	0.532527i
$340$		0			0
$341$	8.29231	+	14.3627i	0.449054	+	0.777784i
$342$		0			0
$343$	−2.20625	−	18.3884i	−0.119126	−	0.992879i
$344$		0			0
$345$	0.0787673	+	0.136429i	0.00424069	+	0.00734509i
$346$		0			0
$347$	−12.1197	+	20.9919i	−0.650619	+	1.12690i	0.332354	+	0.943155i	$0.392157\pi$
$347$	−12.1197	+	20.9919i	−0.650619	+	1.12690i	−0.982973	+	0.183750i	$0.941176\pi$
$348$		0			0
$349$	35.6339			1.90744			0.953721	−	0.300694i	$-0.0972183\pi$
$349$	35.6339			1.90744			0.953721	+	0.300694i	$0.0972183\pi$
$350$		0			0
$351$	4.89667			0.261365
$352$		0			0
$353$	−3.97145	+	6.87876i	−0.211379	+	0.366119i	−0.952146	−	0.305642i	$-0.901129\pi$
$353$	−3.97145	+	6.87876i	−0.211379	+	0.366119i	0.740767	+	0.671762i	$0.234462\pi$
$354$		0			0
$355$	−0.215467	−	0.373201i	−0.0114358	−	0.0198074i
$356$		0			0
$357$	23.8424	−	15.0612i	1.26187	−	0.797123i
$358$		0			0
$359$	13.2126	+	22.8850i	0.697336	+	1.20782i	0.969387	+	0.245539i	$0.0789649\pi$
$359$	13.2126	+	22.8850i	0.697336	+	1.20782i	−0.272050	+	0.962283i	$0.587702\pi$
$360$		0			0
$361$	8.02983	−	13.9081i	0.422623	−	0.732004i
$362$		0			0
$363$	−17.9911			−0.944290
$364$		0			0
$365$	0.442159			0.0231436
$366$		0			0
$367$	−3.03963	+	5.26480i	−0.158668	+	0.274820i	−0.934388	−	0.356256i	$-0.884053\pi$
$367$	−3.03963	+	5.26480i	−0.158668	+	0.274820i	0.775721	+	0.631076i	$0.217386\pi$
$368$		0			0
$369$	−0.710658	−	1.23090i	−0.0369954	−	0.0640779i
$370$		0			0
$371$	0.838708	+	0.440694i	0.0435435	+	0.0228797i
$372$		0			0
$373$	−11.1196	−	19.2597i	−0.575752	−	0.997231i	−0.995960	−	0.0898032i	$-0.971376\pi$
$373$	−11.1196	−	19.2597i	−0.575752	−	0.997231i	0.420208	−	0.907428i	$-0.361957\pi$
$374$		0			0
$375$	0.787265	−	1.36358i	0.0406542	−	0.0704152i
$376$		0			0
$377$	−4.30488			−0.221713
$378$		0			0
$379$	7.87561			0.404543			0.202271	−	0.979330i	$-0.435168\pi$
$379$	7.87561			0.404543			0.202271	+	0.979330i	$0.435168\pi$
$380$		0			0
$381$	−11.9533	+	20.7037i	−0.612387	+	1.06069i
$382$		0			0
$383$	−8.59475	−	14.8865i	−0.439171	−	0.760667i	0.558454	−	0.829535i	$-0.311395\pi$
$383$	−8.59475	−	14.8865i	−0.439171	−	0.760667i	−0.997626	+	0.0688681i	$0.978061\pi$
$384$		0			0
$385$	0.0332163	+	0.834069i	0.00169286	+	0.0425081i
$386$		0			0
$387$	7.21494	+	12.4966i	0.366756	+	0.635240i
$388$		0			0
$389$	13.9997	−	24.2483i	0.709815	−	1.22944i	−0.255110	−	0.966912i	$-0.582112\pi$
$389$	13.9997	−	24.2483i	0.709815	−	1.22944i	0.964925	−	0.262524i	$-0.0845550\pi$
$390$		0			0
$391$	4.86936			0.246254
$392$		0			0
$393$	−14.0300			−0.707722
$394$		0			0
$395$	0.262445	−	0.454568i	0.0132050	−	0.0228718i
$396$		0			0
$397$	1.82027	+	3.15280i	0.0913567	+	0.158235i	0.908082	−	0.418792i	$-0.137546\pi$
$397$	1.82027	+	3.15280i	0.0913567	+	0.158235i	−0.816726	+	0.577026i	$0.804213\pi$
$398$		0			0
$399$	−0.395181	−	9.92309i	−0.0197838	−	0.496776i
$400$		0			0
$401$	−13.1249	−	22.7331i	−0.655428	−	1.13523i	−0.981786	−	0.189989i	$-0.939155\pi$
$401$	−13.1249	−	22.7331i	−0.655428	−	1.13523i	0.326358	−	0.945246i	$-0.394178\pi$
$402$		0			0
$403$	−3.50174	+	6.06520i	−0.174434	+	0.302129i
$404$		0			0
$405$	0.803505			0.0399265
$406$		0			0
$407$	22.6145			1.12096
$408$		0			0
$409$	10.8595	−	18.8092i	0.536967	−	0.930054i	−0.462099	−	0.886829i	$-0.652903\pi$
$409$	10.8595	−	18.8092i	0.536967	−	0.930054i	0.999065	−	0.0432251i	$-0.0137633\pi$
$410$		0			0
$411$	−2.50756	−	4.34323i	−0.123689	−	0.214236i
$412$		0			0
$413$	−6.66653	−	3.50289i	−0.328039	−	0.172366i
$414$		0			0
$415$	0.391032	+	0.677288i	0.0191950	+	0.0332467i
$416$		0			0
$417$	−8.74912	+	15.1539i	−0.428446	+	0.742090i
$418$		0			0
$419$	30.5363			1.49179			0.745897	−	0.666061i	$-0.232021\pi$
$419$	30.5363			1.49179			0.745897	+	0.666061i	$0.232021\pi$
$420$		0			0
$421$	−27.6624			−1.34818			−0.674092	−	0.738647i	$-0.735465\pi$
$421$	−27.6624			−1.34818			−0.674092	+	0.738647i	$0.735465\pi$
$422$		0			0
$423$	−4.53006	+	7.84629i	−0.220259	+	0.381500i
$424$		0			0
$425$	−12.1608	−	21.0631i	−0.589886	−	1.02171i
$426$		0			0
$427$	−22.1479	+	13.9908i	−1.07181	+	0.677063i
$428$		0			0
$429$	−8.88283	−	15.3855i	−0.428867	−	0.742820i
$430$		0			0
$431$	−17.0725	+	29.5704i	−0.822352	+	1.42435i	0.0815751	+	0.996667i	$0.474005\pi$
$431$	−17.0725	+	29.5704i	−0.822352	+	1.42435i	−0.903927	+	0.427687i	$0.859328\pi$
$432$		0			0
$433$	−2.44775			−0.117631			−0.0588157	−	0.998269i	$-0.518732\pi$
$433$	−2.44775			−0.117631			−0.0588157	+	0.998269i	$0.518732\pi$
$434$		0			0
$435$	−0.366323			−0.0175638
$436$		0			0
$437$	0.857370	−	1.48501i	0.0410136	−	0.0710376i
$438$		0			0
$439$	6.69148	+	11.5900i	0.319367	+	0.553159i	0.980356	−	0.197236i	$-0.0631965\pi$
$439$	6.69148	+	11.5900i	0.319367	+	0.553159i	−0.660989	+	0.750395i	$0.729863\pi$
$440$		0			0
$441$	7.11473	+	10.3284i	0.338797	+	0.491827i
$442$		0			0
$443$	−14.5674	−	25.2315i	−0.692119	−	1.19879i	−0.971142	−	0.238501i	$-0.923344\pi$
$443$	−14.5674	−	25.2315i	−0.692119	−	1.19879i	0.279023	−	0.960284i	$-0.409990\pi$
$444$		0			0
$445$	−0.642318	+	1.11253i	−0.0304488	+	0.0527388i
$446$		0			0
$447$	6.87358			0.325109
$448$		0			0
$449$	15.9823			0.754252			0.377126	−	0.926162i	$-0.376912\pi$
$449$	15.9823			0.754252			0.377126	+	0.926162i	$0.376912\pi$
$450$		0			0
$451$	1.73887	−	3.01180i	0.0818800	−	0.141820i
$452$		0			0
$453$	−5.17817	−	8.96885i	−0.243292	−	0.421393i
$454$		0			0
$455$	−0.298016	+	0.188256i	−0.0139712	+	0.00882559i
$456$		0			0
$457$	−2.35634	−	4.08129i	−0.110225	−	0.190915i	0.805636	−	0.592411i	$-0.201824\pi$
$457$	−2.35634	−	4.08129i	−0.110225	−	0.190915i	−0.915861	+	0.401496i	$0.868490\pi$
$458$		0			0
$459$	6.43976	−	11.1540i	0.300582	−	0.520624i
$460$		0			0
$461$	−4.47502			−0.208422			−0.104211	−	0.994555i	$-0.533232\pi$
$461$	−4.47502			−0.208422			−0.104211	+	0.994555i	$0.533232\pi$
$462$		0			0
$463$	−22.7700			−1.05821			−0.529106	−	0.848556i	$-0.677473\pi$
$463$	−22.7700			−1.05821			−0.529106	+	0.848556i	$0.677473\pi$
$464$		0			0
$465$	−0.297980	+	0.516117i	−0.0138185	+	0.0239343i
$466$		0			0
$467$	−5.82068	−	10.0817i	−0.269349	−	0.466526i	0.699345	−	0.714784i	$-0.253475\pi$
$467$	−5.82068	−	10.0817i	−0.269349	−	0.466526i	−0.968694	+	0.248258i	$0.920142\pi$
$468$		0			0
$469$	−28.9686	−	15.2214i	−1.33764	−	0.702857i
$470$		0			0
$471$	14.1305	+	24.4747i	0.651098	+	1.12773i
$472$		0			0
$473$	−17.6538	+	30.5773i	−0.811722	+	1.40594i
$474$		0			0
$475$	−8.56482			−0.392981
$476$		0			0
$477$	−0.641596			−0.0293767
$478$		0			0
$479$	6.07916	−	10.5294i	0.277764	−	0.481102i	−0.693065	−	0.720875i	$-0.743740\pi$
$479$	6.07916	−	10.5294i	0.277764	−	0.481102i	0.970829	+	0.239774i	$0.0770733\pi$
$480$		0			0
$481$	4.77491	+	8.27038i	0.217717	+	0.377097i
$482$		0			0
$483$	0.230461	+	5.78693i	0.0104863	+	0.263315i
$484$		0			0
$485$	0.346372	+	0.599933i	0.0157279	+	0.0272416i
$486$		0			0
$487$	−5.94597	+	10.2987i	−0.269437	+	0.466679i	−0.968717	−	0.248169i	$-0.920171\pi$
$487$	−5.94597	+	10.2987i	−0.269437	+	0.466679i	0.699279	+	0.714849i	$0.253504\pi$
$488$		0			0
$489$	−52.7880			−2.38715
$490$		0			0
$491$	−24.0688			−1.08621			−0.543105	−	0.839665i	$-0.682751\pi$
$491$	−24.0688			−1.08621			−0.543105	+	0.839665i	$0.682751\pi$
$492$		0			0
$493$	−5.66148	+	9.80598i	−0.254980	+	0.441639i
$494$		0			0
$495$	−0.282635	−	0.489538i	−0.0127035	−	0.0220031i
$496$		0			0
$497$	−0.630424	−	15.8301i	−0.0282784	−	0.710078i
$498$		0			0
$499$	11.5890	+	20.0727i	0.518793	+	0.898576i	0.999762	+	0.0218382i	$0.00695188\pi$
$499$	11.5890	+	20.0727i	0.518793	+	0.898576i	−0.480968	+	0.876738i	$0.659715\pi$
$500$		0			0
$501$	−0.239944	+	0.415595i	−0.0107199	+	0.0185674i
$502$		0			0
$503$	−22.4748			−1.00210			−0.501051	−	0.865418i	$-0.667053\pi$
$503$	−22.4748			−1.00210			−0.501051	+	0.865418i	$0.667053\pi$
$504$		0			0
$505$	−0.549694			−0.0244610
$506$		0			0
$507$	−10.4773	+	18.1472i	−0.465314	+	0.805947i
$508$		0			0
$509$	4.85291	+	8.40548i	0.215101	+	0.372566i	0.953304	−	0.302013i	$-0.0976585\pi$
$509$	4.85291	+	8.40548i	0.215101	+	0.372566i	−0.738203	+	0.674579i	$0.764325\pi$
$510$		0			0
$511$	14.3898	+	7.56102i	0.636566	+	0.334480i
$512$		0			0
$513$	−2.26775	−	3.92787i	−0.100124	−	0.173419i
$514$		0			0
$515$	0.270900	−	0.469213i	0.0119373	−	0.0206760i
$516$		0			0
$517$	−22.1687			−0.974976
$518$		0			0
$519$	41.1751			1.80739
$520$		0			0
$521$	−6.69399	+	11.5943i	−0.293269	+	0.507957i	−0.974581	−	0.224036i	$-0.928077\pi$
$521$	−6.69399	+	11.5943i	−0.293269	+	0.507957i	0.681312	+	0.731994i	$0.261410\pi$
$522$		0			0
$523$	−0.474027	−	0.821038i	−0.0207277	−	0.0359015i	0.855475	−	0.517843i	$-0.173265\pi$
$523$	−0.474027	−	0.821038i	−0.0207277	−	0.0359015i	−0.876203	+	0.481942i	$0.839932\pi$
$524$		0			0
$525$	24.4566	−	15.4492i	1.06738	−	0.674260i
$526$		0			0
$527$	9.21050	+	15.9531i	0.401216	+	0.694926i
$528$		0			0
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$		0			0
$531$	5.09978			0.221311
$532$		0			0
$533$	1.46860			0.0636123
$534$		0			0
$535$	−0.579336	+	1.00344i	−0.0250469	+	0.0433825i
$536$		0			0
$537$	6.31581	+	10.9393i	0.272547	+	0.472066i
$538$		0			0
$539$	−13.1818	+	27.7122i	−0.567780	+	1.19365i
$540$		0			0
$541$	11.6379	+	20.1574i	0.500351	+	0.866634i	1.00000		0.000405820i	$0.000129176\pi$
$541$	11.6379	+	20.1574i	0.500351	+	0.866634i	−0.499649	+	0.866228i	$0.666537\pi$
$542$		0			0
$543$	19.3724	−	33.5540i	0.831351	−	1.43994i
$544$		0			0
$545$	−0.801074			−0.0343142
$546$		0			0
$547$	0.308688			0.0131985			0.00659927	−	0.999978i	$-0.497899\pi$
$547$	0.308688			0.0131985			0.00659927	+	0.999978i	$0.497899\pi$
$548$		0			0
$549$	8.87010	−	15.3635i	0.378567	−	0.655697i
$550$		0			0
$551$	1.99368	+	3.45316i	0.0849338	+	0.147110i
$552$		0			0
$553$	16.3143	−	10.3057i	0.693756	−	0.438245i
$554$		0			0
$555$	0.406319	+	0.703766i	0.0172473	+	0.0298732i
$556$		0			0
$557$	0.998466	−	1.72939i	0.0423063	−	0.0732767i	−0.844097	−	0.536191i	$-0.819863\pi$
$557$	0.998466	−	1.72939i	0.0423063	−	0.0732767i	0.886403	+	0.462914i	$0.153196\pi$
$558$		0			0
$559$	−14.9100			−0.630625
$560$		0			0
$561$	−46.7284			−1.97287
$562$		0			0
$563$	11.7294	−	20.3159i	0.494334	−	0.856211i	−0.505645	−	0.862742i	$-0.668745\pi$
$563$	11.7294	−	20.3159i	0.494334	−	0.856211i	0.999979	+	0.00653041i	$0.00207871\pi$
$564$		0			0
$565$	−0.186110	−	0.322352i	−0.00782971	−	0.0135614i
$566$		0			0
$567$	26.1495	+	13.7401i	1.09818	+	0.577031i
$568$		0			0
$569$	−0.862149	−	1.49329i	−0.0361432	−	0.0626018i	0.847388	−	0.530974i	$-0.178174\pi$
$569$	−0.862149	−	1.49329i	−0.0361432	−	0.0626018i	−0.883531	+	0.468372i	$0.844841\pi$
$570$		0			0
$571$	−17.6562	+	30.5814i	−0.738889	+	1.27979i	0.214107	+	0.976810i	$0.431316\pi$
$571$	−17.6562	+	30.5814i	−0.738889	+	1.27979i	−0.952996	+	0.302983i	$0.902018\pi$
$572$		0			0
$573$	−31.5321			−1.31727
$574$		0			0
$575$	4.99482			0.208298
$576$		0			0
$577$	10.3554	−	17.9361i	0.431101	−	0.746690i	−0.565867	−	0.824497i	$-0.691458\pi$
$577$	10.3554	−	17.9361i	0.431101	−	0.746690i	0.996968	+	0.0778069i	$0.0247918\pi$
$578$		0			0
$579$	20.4740	+	35.4620i	0.850870	+	1.47375i
$580$		0			0
$581$	1.14410	+	28.7286i	0.0474652	+	1.19186i
$582$		0			0
$583$	−0.784941	−	1.35956i	−0.0325089	−	0.0563071i
$584$		0			0
$585$	0.119353	−	0.206726i	0.00493466	−	0.00854708i
$586$		0			0
$587$	−24.7352			−1.02093			−0.510466	−	0.859898i	$-0.670527\pi$
$587$	−24.7352			−1.02093			−0.510466	+	0.859898i	$0.670527\pi$
$588$		0			0
$589$	6.48693			0.267289
$590$		0			0
$591$	−16.3278	+	28.2806i	−0.671637	+	1.16331i
$592$		0			0
$593$	21.6774	+	37.5463i	0.890184	+	1.54184i	0.839655	+	0.543121i	$0.182757\pi$
$593$	21.6774	+	37.5463i	0.890184	+	1.54184i	0.0505290	+	0.998723i	$0.483909\pi$
$594$		0			0
$595$	0.0368942	+	0.926424i	0.00151252	+	0.0379797i
$596$		0			0
$597$	18.4468	+	31.9509i	0.754979	+	1.30766i
$598$		0			0
$599$	21.7989	−	37.7567i	0.890677	−	1.54270i	0.0516117	−	0.998667i	$-0.483564\pi$
$599$	21.7989	−	37.7567i	0.890677	−	1.54270i	0.839065	−	0.544031i	$-0.183102\pi$
$600$		0			0
$601$	7.71021			0.314506			0.157253	−	0.987558i	$-0.449736\pi$
$601$	7.71021			0.314506			0.157253	+	0.987558i	$0.449736\pi$
$602$		0			0
$603$	22.1604			0.902442
$604$		0			0
$605$	0.295745	−	0.512245i	0.0120237	−	0.0208257i
$606$		0			0
$607$	−5.63511	−	9.76030i	−0.228722	−	0.396158i	0.728708	−	0.684825i	$-0.240121\pi$
$607$	−5.63511	−	9.76030i	−0.228722	−	0.396158i	−0.957430	+	0.288667i	$0.906788\pi$
$608$		0			0
$609$	−11.9217	−	6.26421i	−0.483093	−	0.253839i
$610$		0			0
$611$	−4.68078	−	8.10735i	−0.189364	−	0.327988i
$612$		0			0
$613$	−11.6094	+	20.1080i	−0.468899	+	0.812156i	−0.999368	−	0.0355479i	$-0.988682\pi$
$613$	−11.6094	+	20.1080i	−0.468899	+	0.812156i	0.530469	+	0.847704i	$0.322016\pi$
$614$		0			0
$615$	0.124971			0.00503930
$616$		0			0
$617$	33.7330			1.35804			0.679020	−	0.734120i	$-0.262405\pi$
$617$	33.7330			1.35804			0.679020	+	0.734120i	$0.262405\pi$
$618$		0			0
$619$	1.08403	−	1.87759i	0.0435707	−	0.0754666i	−0.843418	−	0.537258i	$-0.819460\pi$
$619$	1.08403	−	1.87759i	0.0435707	−	0.0754666i	0.886988	+	0.461792i	$0.152793\pi$
$620$		0			0
$621$	1.32251	+	2.29065i	0.0530703	+	0.0919205i
$622$		0			0
$623$	−39.9283	+	25.2227i	−1.59969	+	1.01052i
$624$		0			0
$625$	−12.4612	−	21.5834i	−0.498447	−	0.863335i
$626$		0			0
$627$	−8.22766	+	14.2507i	−0.328581	+	0.569119i
$628$		0			0
$629$	25.1185			1.00154
$630$		0			0
$631$	10.9250			0.434919			0.217460	−	0.976069i	$-0.430223\pi$
$631$	10.9250			0.434919			0.217460	+	0.976069i	$0.430223\pi$
$632$		0			0
$633$	11.9889	−	20.7653i	0.476515	−	0.825348i
$634$		0			0
$635$	−0.392986	−	0.680672i	−0.0155952	−	0.0270116i
$636$		0			0
$637$	−12.9180	+	1.03053i	−0.511828	+	0.0408312i
$638$		0			0
$639$	5.36424	+	9.29114i	0.212206	+	0.367552i
$640$		0			0
$641$	7.98407	−	13.8288i	0.315352	−	0.546205i	−0.664160	−	0.747590i	$-0.731211\pi$
$641$	7.98407	−	13.8288i	0.315352	−	0.546205i	0.979512	+	0.201385i	$0.0645442\pi$
$642$		0			0
$643$	49.9442			1.96961			0.984803	−	0.173677i	$-0.0555649\pi$
$643$	49.9442			1.96961			0.984803	+	0.173677i	$0.0555649\pi$
$644$		0			0
$645$	−1.26876			−0.0499574
$646$		0			0
$647$	−9.89589	+	17.1402i	−0.389048	+	0.673851i	−0.992322	−	0.123684i	$-0.960529\pi$
$647$	−9.89589	+	17.1402i	−0.389048	+	0.673851i	0.603274	+	0.797534i	$0.293863\pi$
$648$		0			0
$649$	6.23917	+	10.8066i	0.244909	+	0.424194i
$650$		0			0
$651$	−18.5233	+	11.7011i	−0.725985	+	0.458604i
$652$		0			0
$653$	−4.54862	−	7.87844i	−0.178001	−	0.308307i	0.763195	−	0.646169i	$-0.223630\pi$
$653$	−4.54862	−	7.87844i	−0.178001	−	0.308307i	−0.941196	+	0.337862i	$0.890296\pi$
$654$		0			0
$655$	0.230631	−	0.399465i	0.00901150	−	0.0156084i
$656$		0			0
$657$	−11.0079			−0.429459
$658$		0			0
$659$	−18.4716			−0.719551			−0.359775	−	0.933039i	$-0.617147\pi$
$659$	−18.4716			−0.719551			−0.359775	+	0.933039i	$0.617147\pi$
$660$		0			0
$661$	19.3905	−	33.5853i	0.754202	−	1.30632i	−0.191567	−	0.981479i	$-0.561357\pi$
$661$	19.3905	−	33.5853i	0.754202	−	1.30632i	0.945770	−	0.324837i	$-0.105310\pi$
$662$		0			0
$663$	−9.86641	−	17.0891i	−0.383180	−	0.663687i
$664$		0			0
$665$	0.289027	+	0.151868i	0.0112080	+	0.00588918i
$666$		0			0
$667$	−1.16267	−	2.01381i	−0.0450189	−	0.0779751i
$668$		0			0
$669$	−17.6453	+	30.5625i	−0.682206	+	1.18162i
$670$		0			0
$671$	43.4074			1.67573
$672$		0			0
$673$	−33.6340			−1.29650			−0.648249	−	0.761429i	$-0.724498\pi$
$673$	−33.6340			−1.29650			−0.648249	+	0.761429i	$0.724498\pi$
$674$		0			0
$675$	6.60568	−	11.4414i	0.254253	−	0.440379i
$676$		0			0
$677$	−13.3864	−	23.1859i	−0.514481	−	0.891108i	−0.999859	−	0.0168031i	$-0.994651\pi$
$677$	−13.3864	−	23.1859i	−0.514481	−	0.891108i	0.485377	−	0.874305i	$-0.338682\pi$
$678$		0			0
$679$	1.01343	+	25.4475i	0.0388918	+	0.976584i
$680$		0			0
$681$	17.5440	+	30.3870i	0.672286	+	1.16443i
$682$		0			0
$683$	15.9979	−	27.7092i	0.612142	−	1.06026i	−0.378736	−	0.925505i	$-0.623641\pi$
$683$	15.9979	−	27.7092i	0.612142	−	1.06026i	0.990879	−	0.134757i	$-0.0430254\pi$
$684$		0			0
$685$	0.164881			0.00629978
$686$		0			0
$687$	−19.5594			−0.746238
$688$		0			0
$689$	0.331471	−	0.574125i	0.0126281	−	0.0218724i
$690$		0			0
$691$	−3.51130	−	6.08175i	−0.133576	−	0.231361i	0.791477	−	0.611200i	$-0.209313\pi$
$691$	−3.51130	−	6.08175i	−0.133576	−	0.231361i	−0.925053	+	0.379839i	$0.875979\pi$
$692$		0			0
$693$	−0.826946	−	20.7648i	−0.0314131	−	0.788791i
$694$		0			0
$695$	−0.287643	−	0.498211i	−0.0109109	−	0.0188982i
$696$		0			0
$697$	1.93141	−	3.34529i	0.0731572	−	0.126712i
$698$		0			0
$699$	−53.4375			−2.02119
$700$		0			0
$701$	−10.9934			−0.415216			−0.207608	−	0.978212i	$-0.566568\pi$
$701$	−10.9934			−0.415216			−0.207608	+	0.978212i	$0.566568\pi$
$702$		0			0
$703$	4.42272	−	7.66038i	0.166806	−	0.288917i
$704$		0			0
$705$	−0.398310	−	0.689893i	−0.0150012	−	0.0259829i
$706$		0			0
$707$	−17.8894	−	9.39990i	−0.672801	−	0.353520i
$708$		0			0
$709$	−5.31289	−	9.20220i	−0.199530	−	0.345596i	0.748846	−	0.662744i	$-0.230608\pi$
$709$	−5.31289	−	9.20220i	−0.199530	−	0.345596i	−0.948376	+	0.317148i	$0.897275\pi$
$710$		0			0
$711$	−6.53378	+	11.3168i	−0.245036	+	0.424415i
$712$		0			0
$713$	−3.78304			−0.141676
$714$		0			0
$715$	0.584077			0.0218433
$716$		0			0
$717$	18.5577	−	32.1429i	0.693050	−	1.20040i
$718$		0			0
$719$	3.52935	+	6.11302i	0.131623	+	0.227977i	0.924302	−	0.381661i	$-0.124648\pi$
$719$	3.52935	+	6.11302i	0.131623	+	0.227977i	−0.792680	+	0.609638i	$0.791315\pi$
$720$		0			0
$721$	16.8399	−	10.6378i	0.627152	−	0.396171i
$722$		0			0
$723$	21.0680	+	36.4908i	0.783526	+	1.35711i
$724$		0			0
$725$	−5.80735	+	10.0586i	−0.215680	+	0.373568i
$726$		0			0
$727$	33.7235			1.25073			0.625367	−	0.780330i	$-0.284949\pi$
$727$	33.7235			1.25073			0.625367	+	0.780330i	$0.284949\pi$
$728$		0			0
$729$	−2.63421			−0.0975632
$730$		0			0
$731$	−19.6086	+	33.9630i	−0.725249	+	1.25617i
$732$		0			0
$733$	−19.8218	−	34.3324i	−0.732135	−	1.26809i	−0.955969	−	0.293467i	$-0.905191\pi$
$733$	−19.8218	−	34.3324i	−0.732135	−	1.26809i	0.223834	−	0.974627i	$-0.428142\pi$
$734$		0			0
$735$	−1.09925	+	0.0876930i	−0.0405465	+	0.00323460i
$736$		0			0
$737$	27.1115	+	46.9585i	0.998664	+	1.72974i
$738$		0			0
$739$	−7.51682	+	13.0195i	−0.276511	+	0.478931i	−0.970515	−	0.241040i	$-0.922511\pi$
$739$	−7.51682	+	13.0195i	−0.276511	+	0.478931i	0.694004	+	0.719971i	$0.255845\pi$
$740$		0			0
$741$	−6.94889			−0.255274
$742$		0			0
$743$	−0.734579			−0.0269491			−0.0134745	−	0.999909i	$-0.504289\pi$
$743$	−0.734579			−0.0269491			−0.0134745	+	0.999909i	$0.504289\pi$
$744$		0			0
$745$	−0.112990	+	0.195705i	−0.00413965	+	0.00717008i
$746$		0			0
$747$	−9.73507	−	16.8616i	−0.356188	−	0.616935i
$748$		0			0
$749$	−36.0132	+	22.7495i	−1.31589	+	0.831249i
$750$		0			0
$751$	10.6869	+	18.5102i	0.389970	+	0.675447i	0.992445	−	0.122690i	$-0.0391521\pi$
$751$	10.6869	+	18.5102i	0.389970	+	0.675447i	−0.602475	+	0.798138i	$0.705819\pi$
$752$		0			0
$753$	0.422076	−	0.731056i	0.0153813	−	0.0266412i
$754$		0			0
$755$	0.340483			0.0123914
$756$		0			0
$757$	−13.7206			−0.498683			−0.249342	−	0.968416i	$-0.580214\pi$
$757$	−13.7206			−0.498683			−0.249342	+	0.968416i	$0.580214\pi$
$758$		0			0
$759$	4.79820	−	8.31072i	0.174164	−	0.301660i
$760$		0			0
$761$	19.9169	+	34.4971i	0.721987	+	1.25052i	0.960202	+	0.279305i	$0.0901041\pi$
$761$	19.9169	+	34.4971i	0.721987	+	1.25052i	−0.238216	+	0.971212i	$0.576563\pi$
$762$		0			0
$763$	−26.0704	−	13.6986i	−0.943813	−	0.495921i
$764$		0			0
$765$	−0.313931	−	0.543744i	−0.0113502	−	0.0196591i
$766$		0			0
$767$	−2.63473	+	4.56348i	−0.0951344	+	0.164778i
$768$		0			0
$769$	1.46079			0.0526775			0.0263387	−	0.999653i	$-0.491615\pi$
$769$	1.46079			0.0526775			0.0263387	+	0.999653i	$0.491615\pi$
$770$		0			0
$771$	30.9995			1.11642
$772$		0			0
$773$	7.60609	−	13.1741i	0.273572	−	0.473841i	−0.696202	−	0.717846i	$-0.745128\pi$
$773$	7.60609	−	13.1741i	0.273572	−	0.473841i	0.969774	+	0.244005i	$0.0784615\pi$
$774$		0			0
$775$	9.44781	+	16.3641i	0.339375	+	0.587815i
$776$		0			0
$777$	1.18883	+	29.8518i	0.0426489	+	1.07093i
$778$		0			0
$779$	−0.680142	−	1.17804i	−0.0243686	−	0.0422077i
$780$		0			0
$781$	−13.1254	+	22.7339i	−0.469665	+	0.813484i
$782$		0			0
$783$	−6.15057			−0.219804
$784$		0			0
$785$	−0.929128			−0.0331620
$786$		0			0
$787$	13.9325	−	24.1317i	0.496639	−	0.860204i	−0.503354	−	0.864081i	$-0.667901\pi$
$787$	13.9325	−	24.1317i	0.496639	−	0.860204i	0.999992	+	0.00387666i	$0.00123398\pi$
$788$		0			0
$789$	−11.2490	−	19.4839i	−0.400475	−	0.693644i
$790$		0			0
$791$	−0.544529	−	13.6733i	−0.0193612	−	0.486165i
$792$		0			0
$793$	9.16522	+	15.8746i	0.325467	+	0.563725i
$794$		0			0
$795$	0.0282065	−	0.0488550i	0.00100038	−	0.00173271i
$796$		0			0
$797$	−50.7212			−1.79664			−0.898318	−	0.439346i	$-0.855210\pi$
$797$	−50.7212			−1.79664			−0.898318	+	0.439346i	$0.855210\pi$
$798$		0			0
$799$	−24.6233			−0.871111
$800$		0			0
$801$	15.9910	−	27.6973i	0.565015	−	0.978635i
$802$		0			0
$803$	−13.4673	−	23.3260i	−0.475250	−	0.823158i
$804$		0			0
$805$	−0.168555	−	0.0885661i	−0.00594077	−	0.00312154i
$806$		0			0
$807$	−3.78742	−	6.56000i	−0.133323	−	0.230923i
$808$		0			0
$809$	15.0296	−	26.0320i	0.528411	−	0.915235i	−0.471040	−	0.882112i	$-0.656121\pi$
$809$	15.0296	−	26.0320i	0.528411	−	0.915235i	0.999451	−	0.0331235i	$-0.0105455\pi$
$810$		0			0
$811$	31.1143			1.09257			0.546285	−	0.837599i	$-0.316041\pi$
$811$	31.1143			1.09257			0.546285	+	0.837599i	$0.316041\pi$
$812$		0			0
$813$	−20.8286			−0.730491
$814$		0			0
$815$	0.867748	−	1.50298i	0.0303959	−	0.0526472i
$816$		0			0
$817$	6.90513	+	11.9600i	0.241580	+	0.418429i
$818$		0			0
$819$	7.41935	−	4.68680i	0.259253	−	0.163770i
$820$		0			0
$821$	−7.11940	−	12.3312i	−0.248469	−	0.430361i	0.714632	−	0.699500i	$-0.246594\pi$
$821$	−7.11940	−	12.3312i	−0.248469	−	0.430361i	−0.963101	+	0.269140i	$0.913261\pi$
$822$		0			0
$823$	22.1535	−	38.3711i	0.772224	−	1.33753i	−0.164118	−	0.986441i	$-0.552478\pi$
$823$	22.1535	−	38.3711i	0.772224	−	1.33753i	0.936342	−	0.351090i	$-0.114189\pi$
$824$		0			0
$825$	−47.9323			−1.66879
$826$		0			0
$827$	49.3690			1.71673			0.858365	−	0.513040i	$-0.171481\pi$
$827$	49.3690			1.71673			0.858365	+	0.513040i	$0.171481\pi$
$828$		0			0
$829$	11.2800	−	19.5375i	0.391771	−	0.678567i	−0.600912	−	0.799315i	$-0.705196\pi$
$829$	11.2800	−	19.5375i	0.391771	−	0.678567i	0.992683	+	0.120748i	$0.0385293\pi$
$830$		0			0
$831$	−8.26054	−	14.3077i	−0.286555	−	0.496328i
$832$		0			0
$833$	−14.6414	+	30.7808i	−0.507294	+	1.06649i
$834$		0			0
$835$	−0.00788857	−	0.0136634i	−0.000272995	−	0.000472842i
$836$		0			0
$837$	−5.00309	+	8.66561i	−0.172932	+	0.299527i
$838$		0			0
$839$	20.8102			0.718446			0.359223	−	0.933252i	$-0.383042\pi$
$839$	20.8102			0.718446			0.359223	+	0.933252i	$0.383042\pi$
$840$		0			0
$841$	−23.5928			−0.813543
$842$		0			0
$843$	26.1992	−	45.3784i	0.902350	−	1.56292i
$844$		0			0
$845$	−0.344460	−	0.596622i	−0.0118498	−	0.0205244i
$846$		0			0
$847$	18.3844	−	11.6134i	0.631694	−	0.399040i
$848$		0			0
$849$	31.7762	+	55.0381i	1.09056	+	1.88890i
$850$		0			0
$851$	−2.57924	+	4.46737i	−0.0884152	+	0.153140i
$852$		0			0
$853$	47.1257			1.61355			0.806776	−	0.590858i	$-0.201210\pi$
$853$	47.1257			1.61355			0.806776	+	0.590858i	$0.201210\pi$
$854$		0			0
$855$	−0.221101			−0.00756148
$856$		0			0
$857$	20.3491	−	35.2456i	0.695111	−	1.20397i	−0.275032	−	0.961435i	$-0.588689\pi$
$857$	20.3491	−	35.2456i	0.695111	−	1.20397i	0.970143	−	0.242533i	$-0.0779781\pi$
$858$		0			0
$859$	−2.57186	−	4.45460i	−0.0877509	−	0.151989i	0.818809	−	0.574066i	$-0.194635\pi$
$859$	−2.57186	−	4.45460i	−0.0877509	−	0.151989i	−0.906560	+	0.422077i	$0.861301\pi$
$860$		0			0
$861$	4.06708	+	2.13703i	0.138606	+	0.0728297i
$862$		0			0
$863$	20.4100	+	35.3511i	0.694764	+	1.20337i	0.970260	+	0.242065i	$0.0778246\pi$
$863$	20.4100	+	35.3511i	0.694764	+	1.20337i	−0.275496	+	0.961302i	$0.588842\pi$
$864$		0			0
$865$	−0.676851	+	1.17234i	−0.0230136	+	0.0398608i
$866$		0			0
$867$	−14.6897			−0.498888
$868$		0			0
$869$	−31.9742			−1.08465
$870$		0			0
$871$	−11.4489	+	19.8300i	−0.387930	+	0.671914i
$872$		0			0
$873$	−8.62321	−	14.9358i	−0.291851	−	0.505501i
$874$		0			0
$875$	0.0757288	+	1.90157i	0.00256010	+	0.0642848i
$876$		0			0
$877$	23.1334	+	40.0683i	0.781161	+	1.35301i	0.931266	+	0.364340i	$0.118705\pi$
$877$	23.1334	+	40.0683i	0.781161	+	1.35301i	−0.150105	+	0.988670i	$0.547961\pi$
$878$		0			0
$879$	26.0950	−	45.1979i	0.880163	−	1.52449i
$880$		0			0
$881$	−43.7278			−1.47323			−0.736614	−	0.676314i	$-0.763576\pi$
$881$	−43.7278			−1.47323			−0.736614	+	0.676314i	$0.763576\pi$
$882$		0			0
$883$	−35.5479			−1.19628			−0.598140	−	0.801391i	$-0.704094\pi$
$883$	−35.5479			−1.19628			−0.598140	+	0.801391i	$0.704094\pi$
$884$		0			0
$885$	−0.224201	+	0.388328i	−0.00753644	+	0.0130535i
$886$		0			0
$887$	−20.3329	−	35.2176i	−0.682712	−	1.18249i	−0.974150	−	0.225902i	$-0.927467\pi$
$887$	−20.3329	−	35.2176i	−0.682712	−	1.18249i	0.291438	−	0.956590i	$-0.405866\pi$
$888$		0			0
$889$	−1.14982	−	28.8722i	−0.0385636	−	0.968342i
$890$		0			0
$891$	−24.4732	−	42.3888i	−0.819882	−	1.42008i
$892$		0			0
$893$	−4.33554	+	7.50937i	−0.145083	+	0.251292i
$894$		0			0
$895$	−0.415287			−0.0138815
$896$		0			0
$897$	4.05244			0.135307
$898$		0			0
$899$	4.39844	−	7.61833i	0.146696	−	0.254085i
$900$		0			0
$901$	−0.871856	−	1.51010i	−0.0290457	−	0.0503087i
$902$		0			0
$903$	−41.2910	−	21.6961i	−1.37408	−	0.722001i
$904$		0			0
$905$	0.636903	+	1.10315i	0.0211714	+	0.0366699i
$906$		0			0
$907$	−25.9837	+	45.0052i	−0.862776	+	1.49437i	0.00646228	+	0.999979i	$0.497943\pi$
$907$	−25.9837	+	45.0052i	−0.862776	+	1.49437i	−0.869238	+	0.494393i	$0.835390\pi$
$908$		0			0
$909$	13.6851			0.453905
$910$		0			0
$911$	−25.1337			−0.832717			−0.416359	−	0.909200i	$-0.636694\pi$
$911$	−25.1337			−0.832717			−0.416359	+	0.909200i	$0.636694\pi$
$912$		0			0
$913$	23.8202	−	41.2577i	0.788332	−	1.36543i
$914$		0			0
$915$	0.779912	+	1.35085i	0.0257831	+	0.0446576i
$916$		0			0
$917$	14.3367	−	9.05647i	0.473439	−	0.299071i
$918$		0			0
$919$	21.2803	+	36.8586i	0.701972	+	1.21585i	0.967773	+	0.251824i	$0.0810304\pi$
$919$	21.2803	+	36.8586i	0.701972	+	1.21585i	−0.265801	+	0.964028i	$0.585636\pi$
$920$		0			0
$921$	−10.4771	+	18.1469i	−0.345234	+	0.597962i
$922$		0			0
$923$	−11.0854			−0.364881
$924$		0			0
$925$	25.7657			0.847170
$926$		0			0
$927$	−6.74428	+	11.6814i	−0.221511	+	0.383669i
$928$		0			0
$929$	−19.4519	−	33.6918i	−0.638198	−	1.10539i	−0.985828	−	0.167759i	$-0.946347\pi$
$929$	−19.4519	−	33.6918i	−0.638198	−	1.10539i	0.347630	−	0.937632i	$-0.386986\pi$
$930$		0			0
$931$	6.80923	+	9.88488i	0.223163	+	0.323964i
$932$		0			0
$933$	−34.4672	−	59.6989i	−1.12840	−	1.95445i
$934$		0			0
$935$	0.768138	−	1.33045i	0.0251208	−	0.0435105i
$936$		0			0
$937$	36.2132			1.18303			0.591516	−	0.806293i	$-0.298530\pi$
$937$	36.2132			1.18303			0.591516	+	0.806293i	$0.298530\pi$
$938$		0			0
$939$	−38.1128			−1.24376
$940$		0			0
$941$	−14.1321	+	24.4775i	−0.460694	+	0.797945i	−0.998996	−	0.0448070i	$-0.985733\pi$
$941$	−14.1321	+	24.4775i	−0.460694	+	0.797945i	0.538302	+	0.842752i	$0.319066\pi$
$942$		0			0
$943$	0.396645	+	0.687008i	0.0129165	+	0.0223721i
$944$		0			0
$945$	−0.425788	+	0.268970i	−0.0138509	+	0.00874959i
$946$		0			0
$947$	−28.3440	−	49.0933i	−0.921056	−	1.59532i	−0.797784	−	0.602944i	$-0.793994\pi$
$947$	−28.3440	−	49.0933i	−0.921056	−	1.59532i	−0.123273	−	0.992373i	$-0.539339\pi$
$948$		0			0
$949$	5.68708	−	9.85031i	0.184610	−	0.319754i
$950$		0			0
$951$	−58.1561			−1.88584
$952$		0			0
$953$	25.5848			0.828773			0.414386	−	0.910101i	$-0.363996\pi$
$953$	25.5848			0.828773			0.414386	+	0.910101i	$0.363996\pi$
$954$		0			0
$955$	0.518336	−	0.897785i	0.0167730	−	0.0290516i
$956$		0			0
$957$	11.1575	+	19.3253i	0.360670	+	0.624699i
$958$		0			0
$959$	5.36595	+	2.81951i	0.173275	+	0.0910467i
$960$		0			0
$961$	8.34430	+	14.4528i	0.269171	+	0.466218i
$962$		0			0
$963$	14.4231	−	24.9815i	0.464777	−	0.805017i
$964$		0			0
$965$	−1.34624			−0.0433369
$966$		0			0
$967$	37.3732			1.20184			0.600920	−	0.799309i	$-0.294801\pi$
$967$	37.3732			1.20184			0.600920	+	0.799309i	$0.294801\pi$
$968$		0			0
$969$	−9.13870	+	15.8287i	−0.293577	+	0.508491i
$970$		0			0
$971$	4.29467	+	7.43858i	0.137822	+	0.238715i	0.926672	−	0.375871i	$-0.122656\pi$
$971$	4.29467	+	7.43858i	0.137822	+	0.238715i	−0.788850	+	0.614586i	$0.789323\pi$
$972$		0			0
$973$	−0.841597	−	21.1327i	−0.0269804	−	0.677484i
$974$		0			0
$975$	−10.1206	−	17.5294i	−0.324119	−	0.561391i
$976$		0			0
$977$	−8.86739	+	15.3588i	−0.283693	+	0.491371i	−0.972291	−	0.233772i	$-0.924893\pi$
$977$	−8.86739	+	15.3588i	−0.283693	+	0.491371i	0.688598	+	0.725143i	$0.258226\pi$
$978$		0			0
$979$	78.2549			2.50104
$980$		0			0
$981$	19.9434			0.636744
$982$		0			0
$983$	25.6603	−	44.4449i	0.818436	−	1.41757i	−0.0883989	−	0.996085i	$-0.528175\pi$
$983$	25.6603	−	44.4449i	0.818436	−	1.41757i	0.906835	−	0.421487i	$-0.138492\pi$
$984$		0			0
$985$	−0.536806	−	0.929775i	−0.0171040	−	0.0296251i
$986$		0			0
$987$	−1.16539	−	29.2633i	−0.0370948	−	0.931461i
$988$		0			0
$989$	−4.02692	−	6.97484i	−0.128049	−	0.221787i
$990$		0			0
$991$	−12.9788	+	22.4799i	−0.412284	+	0.714097i	−0.995139	−	0.0984790i	$-0.968602\pi$
$991$	−12.9788	+	22.4799i	−0.412284	+	0.714097i	0.582855	+	0.812576i	$0.301936\pi$
$992$		0			0
$993$	12.4704			0.395736
$994$		0			0
$995$	−1.21294			−0.0384529
$996$		0			0
$997$	9.60484	−	16.6361i	0.304188	−	0.526870i	−0.672892	−	0.739741i	$-0.734948\pi$
$997$	9.60484	−	16.6361i	0.304188	−	0.526870i	0.977080	+	0.212871i	$0.0682815\pi$
$998$		0			0
$999$	6.82212	+	11.8163i	0.215842	+	0.373850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.i.a.277.7	yes	14
7.2	even	3	inner	644.2.i.a.93.7	✓	14
7.3	odd	6		4508.2.a.l.1.7		7
7.4	even	3		4508.2.a.m.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.i.a.93.7	✓	14	7.2	even	3	inner
644.2.i.a.277.7	yes	14	1.1	even	1	trivial
4508.2.a.l.1.7		7	7.3	odd	6
4508.2.a.m.1.1		7	7.4	even	3

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09449 - 1.89572i) q^{3} +(0.0359834 + 0.0623251i) q^{5} +(0.105282 + 2.64366i) q^{7} +(-0.895837 - 1.55164i) q^{9} +O(q^{10})\)	\(q+(1.09449 - 1.89572i) q^{3} +(0.0359834 + 0.0623251i) q^{5} +(0.105282 + 2.64366i) q^{7} +(-0.895837 - 1.55164i) q^{9} +(2.19197 - 3.79660i) q^{11} +1.85129 q^{13} +0.157535 q^{15} +(2.43468 - 4.21699i) q^{17} +(-0.857370 - 1.48501i) q^{19} +(5.12686 + 2.69388i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.49741 - 4.32564i) q^{25} +2.64501 q^{27} -2.32535 q^{29} +(-1.89152 + 3.27621i) q^{31} +(-4.79820 - 8.31072i) q^{33} +(-0.160978 + 0.101689i) q^{35} +(2.57924 + 4.46737i) q^{37} +(2.02622 - 3.50952i) q^{39} +0.793289 q^{41} -8.05385 q^{43} +(0.0644706 - 0.111666i) q^{45} +(-2.52839 - 4.37931i) q^{47} +(-6.97783 + 0.556658i) q^{49} +(-5.32949 - 9.23095i) q^{51} +(0.179049 - 0.310123i) q^{53} +0.315498 q^{55} -3.75355 q^{57} +(-1.42319 + 2.46503i) q^{59} +(4.95073 + 8.57492i) q^{61} +(4.00768 - 2.53164i) q^{63} +(0.0666156 + 0.115382i) q^{65} +(-6.18427 + 10.7115i) q^{67} +2.18899 q^{69} -5.98797 q^{71} +(3.07196 - 5.32079i) q^{73} +(-5.46680 - 9.46878i) q^{75} +(10.2677 + 5.39510i) q^{77} +(-3.64675 - 6.31635i) q^{79} +(5.58246 - 9.66911i) q^{81} +10.8670 q^{83} +0.350433 q^{85} +(-2.54508 + 4.40821i) q^{87} +(8.92519 + 15.4589i) q^{89} +(0.194907 + 4.89416i) q^{91} +(4.14052 + 7.17159i) q^{93} +(0.0617022 - 0.106871i) q^{95} +9.62586 q^{97} -7.85459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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