LMFDB - Embedded newform 512.2.g.a.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(65,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("512.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.g (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			65.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	512.65
Dual form			512.2.g.a.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292893 + 0.707107i) q^{3} +(-2.70711 + 1.12132i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(1.70711 + 1.70711i) q^{9} +O(q^{10})$	\(q+(-0.292893 + 0.707107i) q^{3} +(-2.70711 + 1.12132i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(1.70711 + 1.70711i) q^{9} +(-1.70711 - 4.12132i) q^{11} +(-0.707107 - 0.292893i) q^{13} -2.24264i q^{15} -2.82843i q^{17} +(-3.70711 - 1.53553i) q^{19} +(-0.414214 - 1.00000i) q^{21} +(-5.82843 - 5.82843i) q^{23} +(2.53553 - 2.53553i) q^{25} +(-3.82843 + 1.58579i) q^{27} +(-1.29289 + 3.12132i) q^{29} -4.00000 q^{31} +3.41421 q^{33} +(1.58579 - 3.82843i) q^{35} +(-0.707107 + 0.292893i) q^{37} +(0.414214 - 0.414214i) q^{39} +(0.171573 + 0.171573i) q^{41} +(1.94975 + 4.70711i) q^{43} +(-6.53553 - 2.70711i) q^{45} -0.343146i q^{47} +5.00000i q^{49} +(2.00000 + 0.828427i) q^{51} +(-0.464466 - 1.12132i) q^{53} +(9.24264 + 9.24264i) q^{55} +(2.17157 - 2.17157i) q^{57} +(4.53553 - 1.87868i) q^{59} +(0.707107 - 1.70711i) q^{61} -3.41421 q^{63} +2.24264 q^{65} +(-2.29289 + 5.53553i) q^{67} +(5.82843 - 2.41421i) q^{69} +(5.82843 - 5.82843i) q^{71} +(-7.00000 - 7.00000i) q^{73} +(1.05025 + 2.53553i) q^{75} +(5.82843 + 2.41421i) q^{77} +6.00000i q^{79} +4.07107i q^{81} +(-4.53553 - 1.87868i) q^{83} +(3.17157 + 7.65685i) q^{85} +(-1.82843 - 1.82843i) q^{87} +(-8.65685 + 8.65685i) q^{89} +(1.00000 - 0.414214i) q^{91} +(1.17157 - 2.82843i) q^{93} +11.7574 q^{95} -18.4853 q^{97} +(4.12132 - 9.94975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 8 q^{5} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 8 * q^5 - 4 * q^7 + 4 * q^9	$ 4 q - 4 q^{3} - 8 q^{5} - 4 q^{7} + 4 q^{9} - 4 q^{11} - 12 q^{19} + 4 q^{21} - 12 q^{23} - 4 q^{25} - 4 q^{27} - 8 q^{29} - 16 q^{31} + 8 q^{33} + 12 q^{35} - 4 q^{39} + 12 q^{41} - 12 q^{43} - 12 q^{45} + 8 q^{51} - 16 q^{53} + 20 q^{55} + 20 q^{57} + 4 q^{59} - 8 q^{63} - 8 q^{65} - 12 q^{67} + 12 q^{69} + 12 q^{71} - 28 q^{73} + 24 q^{75} + 12 q^{77} - 4 q^{83} + 24 q^{85} + 4 q^{87} - 12 q^{89} + 4 q^{91} + 16 q^{93} + 64 q^{95} - 40 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 8 * q^5 - 4 * q^7 + 4 * q^9 - 4 * q^11 - 12 * q^19 + 4 * q^21 - 12 * q^23 - 4 * q^25 - 4 * q^27 - 8 * q^29 - 16 * q^31 + 8 * q^33 + 12 * q^35 - 4 * q^39 + 12 * q^41 - 12 * q^43 - 12 * q^45 + 8 * q^51 - 16 * q^53 + 20 * q^55 + 20 * q^57 + 4 * q^59 - 8 * q^63 - 8 * q^65 - 12 * q^67 + 12 * q^69 + 12 * q^71 - 28 * q^73 + 24 * q^75 + 12 * q^77 - 4 * q^83 + 24 * q^85 + 4 * q^87 - 12 * q^89 + 4 * q^91 + 16 * q^93 + 64 * q^95 - 40 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.292893	+	0.707107i	−0.169102	+	0.408248i	−0.985599	−	0.169102i	$-0.945913\pi$
$3$	−0.292893	+	0.707107i	−0.169102	+	0.408248i	0.816497	+	0.577350i	$0.195913\pi$
$4$		0			0
$5$	−2.70711	+	1.12132i	−1.21065	+	0.501470i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−2.70711	+	1.12132i	−1.21065	+	0.501470i	−0.316228	+	0.948683i	$0.602416\pi$
$6$		0			0
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$		0			0
$9$	1.70711	+	1.70711i	0.569036	+	0.569036i
$10$		0			0
$11$	−1.70711	−	4.12132i	−0.514712	−	1.24262i	−0.941113	−	0.338091i	$-0.890219\pi$
$11$	−1.70711	−	4.12132i	−0.514712	−	1.24262i	0.426401	−	0.904534i	$-0.359781\pi$
$12$		0			0
$13$	−0.707107	−	0.292893i	−0.196116	−	0.0812340i	0.282464	−	0.959278i	$-0.408848\pi$
$13$	−0.707107	−	0.292893i	−0.196116	−	0.0812340i	−0.478580	+	0.878044i	$0.658848\pi$
$14$		0			0
$15$		−	2.24264i		−	0.579047i
$16$		0			0
$17$		−	2.82843i		−	0.685994i	−0.939336	−	0.342997i	$-0.888558\pi$
$17$		−	2.82843i		−	0.685994i	0.939336	−	0.342997i	$-0.111442\pi$
$18$		0			0
$19$	−3.70711	−	1.53553i	−0.850469	−	0.352276i	−0.0854961	−	0.996339i	$-0.527248\pi$
$19$	−3.70711	−	1.53553i	−0.850469	−	0.352276i	−0.764973	+	0.644063i	$0.777248\pi$
$20$		0			0
$21$	−0.414214	−	1.00000i	−0.0903888	−	0.218218i
$22$		0			0
$23$	−5.82843	−	5.82843i	−1.21531	−	1.21531i	−0.969256	−	0.246055i	$-0.920866\pi$
$23$	−5.82843	−	5.82843i	−1.21531	−	1.21531i	−0.246055	−	0.969256i	$-0.579134\pi$
$24$		0			0
$25$	2.53553	−	2.53553i	0.507107	−	0.507107i
$26$		0			0
$27$	−3.82843	+	1.58579i	−0.736781	+	0.305185i
$28$		0			0
$29$	−1.29289	+	3.12132i	−0.240084	+	0.579615i	−0.997291	−	0.0735609i	$-0.976564\pi$
$29$	−1.29289	+	3.12132i	−0.240084	+	0.579615i	0.757206	+	0.653176i	$0.226564\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$	3.41421			0.594338
$34$		0			0
$35$	1.58579	−	3.82843i	0.268047	−	0.647122i
$36$		0			0
$37$	−0.707107	+	0.292893i	−0.116248	+	0.0481513i	−0.440049	−	0.897974i	$-0.645039\pi$
$37$	−0.707107	+	0.292893i	−0.116248	+	0.0481513i	0.323802	+	0.946125i	$0.395039\pi$
$38$		0			0
$39$	0.414214	−	0.414214i	0.0663273	−	0.0663273i
$40$		0			0
$41$	0.171573	+	0.171573i	0.0267952	+	0.0267952i	0.720377	−	0.693582i	$-0.243969\pi$
$41$	0.171573	+	0.171573i	0.0267952	+	0.0267952i	−0.693582	+	0.720377i	$0.743969\pi$
$42$		0			0
$43$	1.94975	+	4.70711i	0.297334	+	0.717827i	0.999980	+	0.00628798i	$0.00200154\pi$
$43$	1.94975	+	4.70711i	0.297334	+	0.717827i	−0.702647	+	0.711539i	$0.747998\pi$
$44$		0			0
$45$	−6.53553	−	2.70711i	−0.974260	−	0.403552i
$46$		0			0
$47$		−	0.343146i		−	0.0500530i	−0.999687	−	0.0250265i	$-0.992033\pi$
$47$		−	0.343146i		−	0.0500530i	0.999687	−	0.0250265i	$-0.00796701\pi$
$48$		0			0
$49$			5.00000i			0.714286i
$50$		0			0
$51$	2.00000	+	0.828427i	0.280056	+	0.116003i
$52$		0			0
$53$	−0.464466	−	1.12132i	−0.0637993	−	0.154025i	0.888764	−	0.458364i	$-0.151564\pi$
$53$	−0.464466	−	1.12132i	−0.0637993	−	0.154025i	−0.952564	+	0.304339i	$0.901564\pi$
$54$		0			0
$55$	9.24264	+	9.24264i	1.24628	+	1.24628i
$56$		0			0
$57$	2.17157	−	2.17157i	0.287632	−	0.287632i
$58$		0			0
$59$	4.53553	−	1.87868i	0.590476	−	0.244583i	−0.0673793	−	0.997727i	$-0.521464\pi$
$59$	4.53553	−	1.87868i	0.590476	−	0.244583i	0.657855	+	0.753144i	$0.271464\pi$
$60$		0			0
$61$	0.707107	−	1.70711i	0.0905357	−	0.218573i	−0.872125	−	0.489283i	$-0.837259\pi$
$61$	0.707107	−	1.70711i	0.0905357	−	0.218573i	0.962661	+	0.270710i	$0.0872585\pi$
$62$		0			0
$63$	−3.41421			−0.430150
$64$		0			0
$65$	2.24264			0.278165
$66$		0			0
$67$	−2.29289	+	5.53553i	−0.280121	+	0.676273i	−0.999838	−	0.0179949i	$-0.994272\pi$
$67$	−2.29289	+	5.53553i	−0.280121	+	0.676273i	0.719717	+	0.694268i	$0.244272\pi$
$68$		0			0
$69$	5.82843	−	2.41421i	0.701660	−	0.290637i
$70$		0			0
$71$	5.82843	−	5.82843i	0.691707	−	0.691707i	−0.270900	−	0.962607i	$-0.587321\pi$
$71$	5.82843	−	5.82843i	0.691707	−	0.691707i	0.962607	+	0.270900i	$0.0873214\pi$
$72$		0			0
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	0.166717	−	0.986005i	$-0.446683\pi$
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	−0.986005	+	0.166717i	$0.946683\pi$
$74$		0			0
$75$	1.05025	+	2.53553i	0.121273	+	0.292778i
$76$		0			0
$77$	5.82843	+	2.41421i	0.664211	+	0.275125i
$78$		0			0
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$		0			0
$81$			4.07107i			0.452341i
$82$		0			0
$83$	−4.53553	−	1.87868i	−0.497840	−	0.206212i	0.119612	−	0.992821i	$-0.461835\pi$
$83$	−4.53553	−	1.87868i	−0.497840	−	0.206212i	−0.617452	+	0.786609i	$0.711835\pi$
$84$		0			0
$85$	3.17157	+	7.65685i	0.344005	+	0.830502i
$86$		0			0
$87$	−1.82843	−	1.82843i	−0.196028	−	0.196028i
$88$		0			0
$89$	−8.65685	+	8.65685i	−0.917625	+	0.917625i	−0.996856	−	0.0792315i	$-0.974753\pi$
$89$	−8.65685	+	8.65685i	−0.917625	+	0.917625i	0.0792315	+	0.996856i	$0.474753\pi$
$90$		0			0
$91$	1.00000	−	0.414214i	0.104828	−	0.0434214i
$92$		0			0
$93$	1.17157	−	2.82843i	0.121486	−	0.293294i
$94$		0			0
$95$	11.7574			1.20628
$96$		0			0
$97$	−18.4853			−1.87690			−0.938448	−	0.345421i	$-0.887736\pi$
$97$	−18.4853			−1.87690			−0.938448	+	0.345421i	$0.887736\pi$
$98$		0			0
$99$	4.12132	−	9.94975i	0.414208	−	0.999987i
$100$		0			0
$101$	3.29289	−	1.36396i	0.327655	−	0.135719i	−0.212791	−	0.977098i	$-0.568255\pi$
$101$	3.29289	−	1.36396i	0.327655	−	0.135719i	0.540446	+	0.841379i	$0.318255\pi$
$102$		0			0
$103$	−9.48528	+	9.48528i	−0.934613	+	0.934613i	−0.997990	−	0.0633771i	$-0.979813\pi$
$103$	−9.48528	+	9.48528i	−0.934613	+	0.934613i	0.0633771	+	0.997990i	$0.479813\pi$
$104$		0			0
$105$	2.24264	+	2.24264i	0.218859	+	0.218859i
$106$		0			0
$107$	−1.70711	−	4.12132i	−0.165032	−	0.398423i	0.819630	−	0.572893i	$-0.194179\pi$
$107$	−1.70711	−	4.12132i	−0.165032	−	0.398423i	−0.984663	+	0.174470i	$0.944179\pi$
$108$		0			0
$109$	13.7782	+	5.70711i	1.31971	+	0.546642i	0.927702	−	0.373320i	$-0.121781\pi$
$109$	13.7782	+	5.70711i	1.31971	+	0.546642i	0.392007	+	0.919962i	$0.371781\pi$
$110$		0			0
$111$		−	0.585786i		−	0.0556004i
$112$		0			0
$113$		−	6.34315i		−	0.596713i	−0.954455	−	0.298356i	$-0.903562\pi$
$113$		−	6.34315i		−	0.596713i	0.954455	−	0.298356i	$-0.0964384\pi$
$114$		0			0
$115$	22.3137	+	9.24264i	2.08076	+	0.861881i
$116$		0			0
$117$	−0.707107	−	1.70711i	−0.0653720	−	0.157822i
$118$		0			0
$119$	2.82843	+	2.82843i	0.259281	+	0.259281i
$120$		0			0
$121$	−6.29289	+	6.29289i	−0.572081	+	0.572081i
$122$		0			0
$123$	−0.171573	+	0.0710678i	−0.0154702	+	0.00640797i
$124$		0			0
$125$	1.58579	−	3.82843i	0.141837	−	0.342425i
$126$		0			0
$127$	12.9706			1.15095			0.575476	−	0.817819i	$-0.304817\pi$
$127$	12.9706			1.15095			0.575476	+	0.817819i	$0.304817\pi$
$128$		0			0
$129$	−3.89949			−0.343331
$130$		0			0
$131$	−6.77817	+	16.3640i	−0.592212	+	1.42973i	0.289150	+	0.957284i	$0.406627\pi$
$131$	−6.77817	+	16.3640i	−0.592212	+	1.42973i	−0.881362	+	0.472442i	$0.843373\pi$
$132$		0			0
$133$	5.24264	−	2.17157i	0.454595	−	0.188299i
$134$		0			0
$135$	8.58579	−	8.58579i	0.738947	−	0.738947i
$136$		0			0
$137$	8.65685	+	8.65685i	0.739605	+	0.739605i	0.972502	−	0.232897i	$-0.0748204\pi$
$137$	8.65685	+	8.65685i	0.739605	+	0.739605i	−0.232897	+	0.972502i	$0.574820\pi$
$138$		0			0
$139$	5.46447	+	13.1924i	0.463490	+	1.11896i	0.966955	+	0.254948i	$0.0820584\pi$
$139$	5.46447	+	13.1924i	0.463490	+	1.11896i	−0.503465	+	0.864016i	$0.667942\pi$
$140$		0			0
$141$	0.242641	+	0.100505i	0.0204340	+	0.00846405i
$142$		0			0
$143$			3.41421i			0.285511i
$144$		0			0
$145$		−	9.89949i		−	0.822108i
$146$		0			0
$147$	−3.53553	−	1.46447i	−0.291606	−	0.120787i
$148$		0			0
$149$	−6.46447	−	15.6066i	−0.529590	−	1.27854i	−0.931792	−	0.362992i	$-0.881755\pi$
$149$	−6.46447	−	15.6066i	−0.529590	−	1.27854i	0.402203	−	0.915551i	$-0.368245\pi$
$150$		0			0
$151$	1.48528	+	1.48528i	0.120870	+	0.120870i	0.764955	−	0.644084i	$-0.222761\pi$
$151$	1.48528	+	1.48528i	0.120870	+	0.120870i	−0.644084	+	0.764955i	$0.722761\pi$
$152$		0			0
$153$	4.82843	−	4.82843i	0.390355	−	0.390355i
$154$		0			0
$155$	10.8284	−	4.48528i	0.869760	−	0.360266i
$156$		0			0
$157$	0.707107	−	1.70711i	0.0564333	−	0.136242i	−0.893148	−	0.449763i	$-0.851509\pi$
$157$	0.707107	−	1.70711i	0.0564333	−	0.136242i	0.949581	+	0.313521i	$0.101509\pi$
$158$		0			0
$159$	0.928932			0.0736691
$160$		0			0
$161$	11.6569			0.918689
$162$		0			0
$163$	0.192388	−	0.464466i	0.0150690	−	0.0363798i	−0.916166	−	0.400799i	$-0.868733\pi$
$163$	0.192388	−	0.464466i	0.0150690	−	0.0363798i	0.931235	+	0.364419i	$0.118733\pi$
$164$		0			0
$165$	−9.24264	+	3.82843i	−0.719539	+	0.298043i
$166$		0			0
$167$	−14.6569	+	14.6569i	−1.13418	+	1.13418i	−0.144707	+	0.989475i	$0.546224\pi$
$167$	−14.6569	+	14.6569i	−1.13418	+	1.13418i	−0.989475	+	0.144707i	$0.953776\pi$
$168$		0			0
$169$	−8.77817	−	8.77817i	−0.675244	−	0.675244i
$170$		0			0
$171$	−3.70711	−	8.94975i	−0.283490	−	0.684404i
$172$		0			0
$173$	−7.53553	−	3.12132i	−0.572916	−	0.237310i	0.0773656	−	0.997003i	$-0.475349\pi$
$173$	−7.53553	−	3.12132i	−0.572916	−	0.237310i	−0.650282	+	0.759693i	$0.725349\pi$
$174$		0			0
$175$			5.07107i			0.383337i
$176$		0			0
$177$			3.75736i			0.282420i
$178$		0			0
$179$	3.94975	+	1.63604i	0.295218	+	0.122283i	0.525377	−	0.850870i	$-0.323924\pi$
$179$	3.94975	+	1.63604i	0.295218	+	0.122283i	−0.230159	+	0.973153i	$0.573924\pi$
$180$		0			0
$181$	6.70711	+	16.1924i	0.498535	+	1.20357i	0.950272	+	0.311420i	$0.100804\pi$
$181$	6.70711	+	16.1924i	0.498535	+	1.20357i	−0.451737	+	0.892151i	$0.649196\pi$
$182$		0			0
$183$	1.00000	+	1.00000i	0.0739221	+	0.0739221i
$184$		0			0
$185$	1.58579	−	1.58579i	0.116589	−	0.116589i
$186$		0			0
$187$	−11.6569	+	4.82843i	−0.852434	+	0.353090i
$188$		0			0
$189$	2.24264	−	5.41421i	0.163128	−	0.393826i
$190$		0			0
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$		0			0
$193$	−1.51472			−0.109032			−0.0545159	−	0.998513i	$-0.517362\pi$
$193$	−1.51472			−0.109032			−0.0545159	+	0.998513i	$0.517362\pi$
$194$		0			0
$195$	−0.656854	+	1.58579i	−0.0470383	+	0.113561i
$196$		0			0
$197$	−11.1924	+	4.63604i	−0.797425	+	0.330304i	−0.743924	−	0.668264i	$-0.767038\pi$
$197$	−11.1924	+	4.63604i	−0.797425	+	0.330304i	−0.0535002	+	0.998568i	$0.517038\pi$
$198$		0			0
$199$	15.9706	−	15.9706i	1.13212	−	1.13212i	0.142300	−	0.989824i	$-0.454550\pi$
$199$	15.9706	−	15.9706i	1.13212	−	1.13212i	0.989824	−	0.142300i	$-0.0454496\pi$
$200$		0			0
$201$	−3.24264	−	3.24264i	−0.228718	−	0.228718i
$202$		0			0
$203$	−1.82843	−	4.41421i	−0.128330	−	0.309817i
$204$		0			0
$205$	−0.656854	−	0.272078i	−0.0458767	−	0.0190027i
$206$		0			0
$207$		−	19.8995i		−	1.38311i
$208$		0			0
$209$			17.8995i			1.23813i
$210$		0			0
$211$	−18.1924	−	7.53553i	−1.25242	−	0.518768i	−0.344842	−	0.938661i	$-0.612068\pi$
$211$	−18.1924	−	7.53553i	−1.25242	−	0.518768i	−0.907574	+	0.419893i	$0.862068\pi$
$212$		0			0
$213$	2.41421	+	5.82843i	0.165419	+	0.399357i
$214$		0			0
$215$	−10.5563	−	10.5563i	−0.719937	−	0.719937i
$216$		0			0
$217$	4.00000	−	4.00000i	0.271538	−	0.271538i
$218$		0			0
$219$	7.00000	−	2.89949i	0.473016	−	0.195930i
$220$		0			0
$221$	−0.828427	+	2.00000i	−0.0557260	+	0.134535i
$222$		0			0
$223$	−20.9706			−1.40429			−0.702146	−	0.712033i	$-0.747775\pi$
$223$	−20.9706			−1.40429			−0.702146	+	0.712033i	$0.747775\pi$
$224$		0			0
$225$	8.65685			0.577124
$226$		0			0
$227$	7.70711	−	18.6066i	0.511539	−	1.23496i	−0.431449	−	0.902137i	$-0.641998\pi$
$227$	7.70711	−	18.6066i	0.511539	−	1.23496i	0.942988	−	0.332826i	$-0.108002\pi$
$228$		0			0
$229$	22.2635	−	9.22183i	1.47121	−	0.609395i	0.504076	−	0.863659i	$-0.331833\pi$
$229$	22.2635	−	9.22183i	1.47121	−	0.609395i	0.967135	+	0.254264i	$0.0818332\pi$
$230$		0			0
$231$	−3.41421	+	3.41421i	−0.224639	+	0.224639i
$232$		0			0
$233$	2.65685	+	2.65685i	0.174056	+	0.174056i	0.788759	−	0.614703i	$-0.210724\pi$
$233$	2.65685	+	2.65685i	0.174056	+	0.174056i	−0.614703	+	0.788759i	$0.710724\pi$
$234$		0			0
$235$	0.384776	+	0.928932i	0.0251000	+	0.0605969i
$236$		0			0
$237$	−4.24264	−	1.75736i	−0.275589	−	0.114153i
$238$		0			0
$239$		−	5.31371i		−	0.343715i	−0.985122	−	0.171858i	$-0.945023\pi$
$239$		−	5.31371i		−	0.343715i	0.985122	−	0.171858i	$-0.0549769\pi$
$240$		0			0
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$		0			0
$243$	−14.3640	−	5.94975i	−0.921449	−	0.381676i
$244$		0			0
$245$	−5.60660	−	13.5355i	−0.358193	−	0.864754i
$246$		0			0
$247$	2.17157	+	2.17157i	0.138174	+	0.138174i
$248$		0			0
$249$	2.65685	−	2.65685i	0.168371	−	0.168371i
$250$		0			0
$251$	−15.9497	+	6.60660i	−1.00674	+	0.417005i	−0.824264	−	0.566205i	$-0.808411\pi$
$251$	−15.9497	+	6.60660i	−1.00674	+	0.417005i	−0.182475	+	0.983210i	$0.558411\pi$
$252$		0			0
$253$	−14.0711	+	33.9706i	−0.884640	+	2.13571i
$254$		0			0
$255$	−6.34315			−0.397223
$256$		0			0
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$		0			0
$259$	0.414214	−	1.00000i	0.0257380	−	0.0621370i
$260$		0			0
$261$	−7.53553	+	3.12132i	−0.466438	+	0.193205i
$262$		0			0
$263$	5.82843	−	5.82843i	0.359396	−	0.359396i	−0.504194	−	0.863590i	$-0.668210\pi$
$263$	5.82843	−	5.82843i	0.359396	−	0.359396i	0.863590	+	0.504194i	$0.168210\pi$
$264$		0			0
$265$	2.51472	+	2.51472i	0.154478	+	0.154478i
$266$		0			0
$267$	−3.58579	−	8.65685i	−0.219447	−	0.529791i
$268$		0			0
$269$	−22.0208	−	9.12132i	−1.34263	−	0.556137i	−0.408401	−	0.912803i	$-0.633913\pi$
$269$	−22.0208	−	9.12132i	−1.34263	−	0.556137i	−0.934232	+	0.356666i	$0.883913\pi$
$270$		0			0
$271$			18.0000i			1.09342i	0.837321	+	0.546711i	$0.184120\pi$
$271$			18.0000i			1.09342i	−0.837321	+	0.546711i	$0.815880\pi$
$272$		0			0
$273$			0.828427i			0.0501387i
$274$		0			0
$275$	−14.7782	−	6.12132i	−0.891157	−	0.369130i
$276$		0			0
$277$	0.707107	+	1.70711i	0.0424859	+	0.102570i	0.943698	−	0.330808i	$-0.107321\pi$
$277$	0.707107	+	1.70711i	0.0424859	+	0.102570i	−0.901212	+	0.433378i	$0.857321\pi$
$278$		0			0
$279$	−6.82843	−	6.82843i	−0.408807	−	0.408807i
$280$		0			0
$281$	11.8284	−	11.8284i	0.705625	−	0.705625i	−0.259987	−	0.965612i	$-0.583718\pi$
$281$	11.8284	−	11.8284i	0.705625	−	0.705625i	0.965612	+	0.259987i	$0.0837184\pi$
$282$		0			0
$283$	−13.9497	+	5.77817i	−0.829226	+	0.343477i	−0.756596	−	0.653882i	$-0.773139\pi$
$283$	−13.9497	+	5.77817i	−0.829226	+	0.343477i	−0.0726300	+	0.997359i	$0.523139\pi$
$284$		0			0
$285$	−3.44365	+	8.31371i	−0.203984	+	0.492462i
$286$		0			0
$287$	−0.343146			−0.0202553
$288$		0			0
$289$	9.00000			0.529412
$290$		0			0
$291$	5.41421	−	13.0711i	0.317387	−	0.766240i
$292$		0			0
$293$	−23.1924	+	9.60660i	−1.35491	+	0.561224i	−0.937656	−	0.347565i	$-0.887009\pi$
$293$	−23.1924	+	9.60660i	−1.35491	+	0.561224i	−0.417258	+	0.908788i	$0.637009\pi$
$294$		0			0
$295$	−10.1716	+	10.1716i	−0.592212	+	0.592212i
$296$		0			0
$297$	13.0711	+	13.0711i	0.758460	+	0.758460i
$298$		0			0
$299$	2.41421	+	5.82843i	0.139618	+	0.337067i
$300$		0			0
$301$	−6.65685	−	2.75736i	−0.383695	−	0.158932i
$302$		0			0
$303$			2.72792i			0.156715i
$304$		0			0
$305$			5.41421i			0.310017i
$306$		0			0
$307$	16.7782	+	6.94975i	0.957581	+	0.396643i	0.806075	−	0.591813i	$-0.201588\pi$
$307$	16.7782	+	6.94975i	0.957581	+	0.396643i	0.151506	+	0.988456i	$0.451588\pi$
$308$		0			0
$309$	−3.92893	−	9.48528i	−0.223509	−	0.539599i
$310$		0			0
$311$	2.65685	+	2.65685i	0.150656	+	0.150656i	0.778411	−	0.627755i	$-0.216026\pi$
$311$	2.65685	+	2.65685i	0.150656	+	0.150656i	−0.627755	+	0.778411i	$0.716026\pi$
$312$		0			0
$313$	7.48528	−	7.48528i	0.423093	−	0.423093i	−0.463174	−	0.886267i	$-0.653290\pi$
$313$	7.48528	−	7.48528i	0.423093	−	0.423093i	0.886267	+	0.463174i	$0.153290\pi$
$314$		0			0
$315$	9.24264	−	3.82843i	0.520764	−	0.215707i
$316$		0			0
$317$	7.19239	−	17.3640i	0.403965	−	0.975257i	−0.582729	−	0.812667i	$-0.698015\pi$
$317$	7.19239	−	17.3640i	0.403965	−	0.975257i	0.986694	−	0.162591i	$-0.0519850\pi$
$318$		0			0
$319$	15.0711			0.843818
$320$		0			0
$321$	3.41421			0.190563
$322$		0			0
$323$	−4.34315	+	10.4853i	−0.241659	+	0.583417i
$324$		0			0
$325$	−2.53553	+	1.05025i	−0.140646	+	0.0582575i
$326$		0			0
$327$	−8.07107	+	8.07107i	−0.446331	+	0.446331i
$328$		0			0
$329$	0.343146	+	0.343146i	0.0189182	+	0.0189182i
$330$		0			0
$331$	−0.535534	−	1.29289i	−0.0294356	−	0.0710638i	0.908478	−	0.417932i	$-0.137245\pi$
$331$	−0.535534	−	1.29289i	−0.0294356	−	0.0710638i	−0.937914	+	0.346868i	$0.887245\pi$
$332$		0			0
$333$	−1.70711	−	0.707107i	−0.0935489	−	0.0387492i
$334$		0			0
$335$		−	17.5563i		−	0.959206i
$336$		0			0
$337$		−	16.9706i		−	0.924445i	−0.886764	−	0.462223i	$-0.847052\pi$
$337$		−	16.9706i		−	0.924445i	0.886764	−	0.462223i	$-0.152948\pi$
$338$		0			0
$339$	4.48528	+	1.85786i	0.243607	+	0.100905i
$340$		0			0
$341$	6.82843	+	16.4853i	0.369780	+	0.892728i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$	−13.0711	+	13.0711i	−0.703723	+	0.703723i
$346$		0			0
$347$	−3.94975	+	1.63604i	−0.212034	+	0.0878272i	−0.486172	−	0.873863i	$-0.661607\pi$
$347$	−3.94975	+	1.63604i	−0.212034	+	0.0878272i	0.274139	+	0.961690i	$0.411607\pi$
$348$		0			0
$349$	10.2218	−	24.6777i	0.547162	−	1.32097i	−0.372419	−	0.928065i	$-0.621472\pi$
$349$	10.2218	−	24.6777i	0.547162	−	1.32097i	0.919581	−	0.392901i	$-0.128528\pi$
$350$		0			0
$351$	3.17157			0.169286
$352$		0			0
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$	−9.24264	+	22.3137i	−0.490548	+	1.18429i
$356$		0			0
$357$	−2.82843	+	1.17157i	−0.149696	+	0.0620062i
$358$		0			0
$359$	17.8284	−	17.8284i	0.940948	−	0.940948i	−0.0574027	−	0.998351i	$-0.518282\pi$
$359$	17.8284	−	17.8284i	0.940948	−	0.940948i	0.998351	+	0.0574027i	$0.0182819\pi$
$360$		0			0
$361$	−2.05025	−	2.05025i	−0.107908	−	0.107908i
$362$		0			0
$363$	−2.60660	−	6.29289i	−0.136811	−	0.330291i
$364$		0			0
$365$	26.7990	+	11.1005i	1.40272	+	0.581027i
$366$		0			0
$367$		−	6.00000i		−	0.313197i	−0.987662	−	0.156599i	$-0.949947\pi$
$367$		−	6.00000i		−	0.313197i	0.987662	−	0.156599i	$-0.0500529\pi$
$368$		0			0
$369$			0.585786i			0.0304948i
$370$		0			0
$371$	1.58579	+	0.656854i	0.0823299	+	0.0341022i
$372$		0			0
$373$	−4.26346	−	10.2929i	−0.220753	−	0.532946i	0.774239	−	0.632893i	$-0.218133\pi$
$373$	−4.26346	−	10.2929i	−0.220753	−	0.532946i	−0.994993	+	0.0999471i	$0.968133\pi$
$374$		0			0
$375$	2.24264	+	2.24264i	0.115809	+	0.115809i
$376$		0			0
$377$	1.82843	−	1.82843i	0.0941688	−	0.0941688i
$378$		0			0
$379$	33.0208	−	13.6777i	1.69617	−	0.702575i	0.696281	−	0.717769i	$-0.254837\pi$
$379$	33.0208	−	13.6777i	1.69617	−	0.702575i	0.999885	+	0.0151948i	$0.00483684\pi$
$380$		0			0
$381$	−3.79899	+	9.17157i	−0.194628	+	0.469874i
$382$		0			0
$383$	−16.9706			−0.867155			−0.433578	−	0.901116i	$-0.642749\pi$
$383$	−16.9706			−0.867155			−0.433578	+	0.901116i	$0.642749\pi$
$384$		0			0
$385$	−18.4853			−0.942097
$386$		0			0
$387$	−4.70711	+	11.3640i	−0.239276	+	0.577663i
$388$		0			0
$389$	20.2635	−	8.39340i	1.02740	−	0.425562i	0.195625	−	0.980679i	$-0.437326\pi$
$389$	20.2635	−	8.39340i	1.02740	−	0.425562i	0.831773	+	0.555117i	$0.187326\pi$
$390$		0			0
$391$	−16.4853	+	16.4853i	−0.833697	+	0.833697i
$392$		0			0
$393$	−9.58579	−	9.58579i	−0.483539	−	0.483539i
$394$		0			0
$395$	−6.72792	−	16.2426i	−0.338518	−	0.817256i
$396$		0			0
$397$	22.2635	+	9.22183i	1.11737	+	0.462830i	0.863470	−	0.504400i	$-0.168286\pi$
$397$	22.2635	+	9.22183i	1.11737	+	0.462830i	0.253901	+	0.967230i	$0.418286\pi$
$398$		0			0
$399$			4.34315i			0.217429i
$400$		0			0
$401$		−	2.82843i		−	0.141245i	−0.997503	−	0.0706225i	$-0.977501\pi$
$401$		−	2.82843i		−	0.141245i	0.997503	−	0.0706225i	$-0.0224986\pi$
$402$		0			0
$403$	2.82843	+	1.17157i	0.140894	+	0.0583602i
$404$		0			0
$405$	−4.56497	−	11.0208i	−0.226835	−	0.547629i
$406$		0			0
$407$	2.41421	+	2.41421i	0.119668	+	0.119668i
$408$		0			0
$409$	−21.4853	+	21.4853i	−1.06238	+	1.06238i	−0.0644584	+	0.997920i	$0.520532\pi$
$409$	−21.4853	+	21.4853i	−1.06238	+	1.06238i	−0.997920	+	0.0644584i	$0.979468\pi$
$410$		0			0
$411$	−8.65685	+	3.58579i	−0.427011	+	0.176874i
$412$		0			0
$413$	−2.65685	+	6.41421i	−0.130735	+	0.315623i
$414$		0			0
$415$	14.3848			0.706121
$416$		0			0
$417$	−10.9289			−0.535192
$418$		0			0
$419$	5.22183	−	12.6066i	0.255103	−	0.615873i	−0.743499	−	0.668737i	$-0.766835\pi$
$419$	5.22183	−	12.6066i	0.255103	−	0.615873i	0.998602	+	0.0528644i	$0.0168351\pi$
$420$		0			0
$421$	−15.1924	+	6.29289i	−0.740432	+	0.306697i	−0.720831	−	0.693111i	$-0.756240\pi$
$421$	−15.1924	+	6.29289i	−0.740432	+	0.306697i	−0.0196009	+	0.999808i	$0.506240\pi$
$422$		0			0
$423$	0.585786	−	0.585786i	0.0284819	−	0.0284819i
$424$		0			0
$425$	−7.17157	−	7.17157i	−0.347872	−	0.347872i
$426$		0			0
$427$	1.00000	+	2.41421i	0.0483934	+	0.116832i
$428$		0			0
$429$	−2.41421	−	1.00000i	−0.116559	−	0.0482805i
$430$		0			0
$431$		−	12.3431i		−	0.594548i	−0.954792	−	0.297274i	$-0.903922\pi$
$431$		−	12.3431i		−	0.594548i	0.954792	−	0.297274i	$-0.0960775\pi$
$432$		0			0
$433$		−	15.5147i		−	0.745590i	−0.927914	−	0.372795i	$-0.878400\pi$
$433$		−	15.5147i		−	0.745590i	0.927914	−	0.372795i	$-0.121600\pi$
$434$		0			0
$435$	7.00000	+	2.89949i	0.335624	+	0.139020i
$436$		0			0
$437$	12.6569	+	30.5563i	0.605459	+	1.46171i
$438$		0			0
$439$	17.0000	+	17.0000i	0.811366	+	0.811366i	0.984839	−	0.173473i	$-0.0554989\pi$
$439$	17.0000	+	17.0000i	0.811366	+	0.811366i	−0.173473	+	0.984839i	$0.555499\pi$
$440$		0			0
$441$	−8.53553	+	8.53553i	−0.406454	+	0.406454i
$442$		0			0
$443$	−1.46447	+	0.606602i	−0.0695789	+	0.0288205i	−0.417201	−	0.908814i	$-0.636989\pi$
$443$	−1.46447	+	0.606602i	−0.0695789	+	0.0288205i	0.347623	+	0.937635i	$0.386989\pi$
$444$		0			0
$445$	13.7279	−	33.1421i	0.650766	−	1.57109i
$446$		0			0
$447$	12.9289			0.611518
$448$		0			0
$449$	−19.4558			−0.918178			−0.459089	−	0.888390i	$-0.651824\pi$
$449$	−19.4558			−0.918178			−0.459089	+	0.888390i	$0.651824\pi$
$450$		0			0
$451$	0.414214	−	1.00000i	0.0195046	−	0.0470882i
$452$		0			0
$453$	−1.48528	+	0.615224i	−0.0697846	+	0.0289057i
$454$		0			0
$455$	−2.24264	+	2.24264i	−0.105137	+	0.105137i
$456$		0			0
$457$	7.48528	+	7.48528i	0.350147	+	0.350147i	0.860164	−	0.510017i	$-0.170361\pi$
$457$	7.48528	+	7.48528i	0.350147	+	0.350147i	−0.510017	+	0.860164i	$0.670361\pi$
$458$		0			0
$459$	4.48528	+	10.8284i	0.209355	+	0.505428i
$460$		0			0
$461$	−1.53553	−	0.636039i	−0.0715169	−	0.0296233i	0.346638	−	0.937999i	$-0.387323\pi$
$461$	−1.53553	−	0.636039i	−0.0715169	−	0.0296233i	−0.418155	+	0.908376i	$0.637323\pi$
$462$		0			0
$463$			22.9706i			1.06753i	0.845632	+	0.533766i	$0.179224\pi$
$463$			22.9706i			1.06753i	−0.845632	+	0.533766i	$0.820776\pi$
$464$		0			0
$465$			8.97056i			0.416000i
$466$		0			0
$467$	21.9497	+	9.09188i	1.01571	+	0.420722i	0.827536	−	0.561413i	$-0.189742\pi$
$467$	21.9497	+	9.09188i	1.01571	+	0.420722i	0.188177	+	0.982135i	$0.439742\pi$
$468$		0			0
$469$	−3.24264	−	7.82843i	−0.149731	−	0.361483i
$470$		0			0
$471$	1.00000	+	1.00000i	0.0460776	+	0.0460776i
$472$		0			0
$473$	16.0711	−	16.0711i	0.738948	−	0.738948i
$474$		0			0
$475$	−13.2929	+	5.50610i	−0.609920	+	0.252637i
$476$		0			0
$477$	1.12132	−	2.70711i	0.0513417	−	0.123950i
$478$		0			0
$479$	28.9706			1.32370			0.661849	−	0.749637i	$-0.269772\pi$
$479$	28.9706			1.32370			0.661849	+	0.749637i	$0.269772\pi$
$480$		0			0
$481$	0.585786			0.0267096
$482$		0			0
$483$	−3.41421	+	8.24264i	−0.155352	+	0.375053i
$484$		0			0
$485$	50.0416	−	20.7279i	2.27227	−	0.941206i
$486$		0			0
$487$	11.0000	−	11.0000i	0.498458	−	0.498458i	−0.412500	−	0.910958i	$-0.635344\pi$
$487$	11.0000	−	11.0000i	0.498458	−	0.498458i	0.910958	+	0.412500i	$0.135344\pi$
$488$		0			0
$489$	0.272078	+	0.272078i	0.0123038	+	0.0123038i
$490$		0			0
$491$	16.2929	+	39.3345i	0.735288	+	1.77514i	0.624102	+	0.781343i	$0.285465\pi$
$491$	16.2929	+	39.3345i	0.735288	+	1.77514i	0.111186	+	0.993800i	$0.464535\pi$
$492$		0			0
$493$	8.82843	+	3.65685i	0.397612	+	0.164696i
$494$		0			0
$495$			31.5563i			1.41835i
$496$		0			0
$497$			11.6569i			0.522881i
$498$		0			0
$499$	2.29289	+	0.949747i	0.102644	+	0.0425165i	0.433415	−	0.901195i	$-0.357309\pi$
$499$	2.29289	+	0.949747i	0.102644	+	0.0425165i	−0.330771	+	0.943711i	$0.607309\pi$
$500$		0			0
$501$	−6.07107	−	14.6569i	−0.271235	−	0.654820i
$502$		0			0
$503$	11.1421	+	11.1421i	0.496803	+	0.496803i	0.910441	−	0.413638i	$-0.135742\pi$
$503$	11.1421	+	11.1421i	0.496803	+	0.496803i	−0.413638	+	0.910441i	$0.635742\pi$
$504$		0			0
$505$	−7.38478	+	7.38478i	−0.328618	+	0.328618i
$506$		0			0
$507$	8.77817	−	3.63604i	0.389852	−	0.161482i
$508$		0			0
$509$	−10.8076	+	26.0919i	−0.479039	+	1.15650i	0.481021	+	0.876709i	$0.340266\pi$
$509$	−10.8076	+	26.0919i	−0.479039	+	1.15650i	−0.960060	+	0.279793i	$0.909734\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$		0			0
$513$	16.6274			0.734118
$514$		0			0
$515$	15.0416	−	36.3137i	0.662813	−	1.60017i
$516$		0			0
$517$	−1.41421	+	0.585786i	−0.0621970	+	0.0257629i
$518$		0			0
$519$	4.41421	−	4.41421i	0.193762	−	0.193762i
$520$		0			0
$521$	−3.34315	−	3.34315i	−0.146466	−	0.146466i	0.630071	−	0.776537i	$-0.283026\pi$
$521$	−3.34315	−	3.34315i	−0.146466	−	0.146466i	−0.776537	+	0.630071i	$0.783026\pi$
$522$		0			0
$523$	7.94975	+	19.1924i	0.347618	+	0.839225i	0.996900	+	0.0786768i	$0.0250695\pi$
$523$	7.94975	+	19.1924i	0.347618	+	0.839225i	−0.649282	+	0.760548i	$0.724930\pi$
$524$		0			0
$525$	−3.58579	−	1.48528i	−0.156497	−	0.0648230i
$526$		0			0
$527$			11.3137i			0.492833i
$528$		0			0
$529$			44.9411i			1.95396i
$530$		0			0
$531$	10.9497	+	4.53553i	0.475179	+	0.196825i
$532$		0			0
$533$	−0.0710678	−	0.171573i	−0.00307829	−	0.00743165i
$534$		0			0
$535$	9.24264	+	9.24264i	0.399594	+	0.399594i
$536$		0			0
$537$	−2.31371	+	2.31371i	−0.0998439	+	0.0998439i
$538$		0			0
$539$	20.6066	−	8.53553i	0.887589	−	0.367651i
$540$		0			0
$541$	−11.2929	+	27.2635i	−0.485519	+	1.17215i	0.471433	+	0.881902i	$0.343737\pi$
$541$	−11.2929	+	27.2635i	−0.485519	+	1.17215i	−0.956952	+	0.290246i	$0.906263\pi$
$542$		0			0
$543$	−13.4142			−0.575659
$544$		0			0
$545$	−43.6985			−1.87184
$546$		0			0
$547$	−7.26346	+	17.5355i	−0.310563	+	0.749765i	0.689122	+	0.724646i	$0.257997\pi$
$547$	−7.26346	+	17.5355i	−0.310563	+	0.749765i	−0.999684	+	0.0251195i	$0.992003\pi$
$548$		0			0
$549$	4.12132	−	1.70711i	0.175894	−	0.0728575i
$550$		0			0
$551$	9.58579	−	9.58579i	0.408368	−	0.408368i
$552$		0			0
$553$	−6.00000	−	6.00000i	−0.255146	−	0.255146i
$554$		0			0
$555$	0.656854	+	1.58579i	0.0278819	+	0.0673129i
$556$		0			0
$557$	−36.5061	−	15.1213i	−1.54681	−	0.640711i	−0.564077	−	0.825722i	$-0.690768\pi$
$557$	−36.5061	−	15.1213i	−1.54681	−	0.640711i	−0.982736	+	0.185012i	$0.940768\pi$
$558$		0			0
$559$		−	3.89949i		−	0.164931i
$560$		0			0
$561$		−	9.65685i		−	0.407713i
$562$		0			0
$563$	−19.0208	−	7.87868i	−0.801632	−	0.332047i	−0.0560220	−	0.998430i	$-0.517842\pi$
$563$	−19.0208	−	7.87868i	−0.801632	−	0.332047i	−0.745610	+	0.666383i	$0.767842\pi$
$564$		0			0
$565$	7.11270	+	17.1716i	0.299233	+	0.722414i
$566$		0			0
$567$	−4.07107	−	4.07107i	−0.170969	−	0.170969i
$568$		0			0
$569$	−14.6569	+	14.6569i	−0.614447	+	0.614447i	−0.944102	−	0.329654i	$-0.893068\pi$
$569$	−14.6569	+	14.6569i	−0.614447	+	0.614447i	0.329654	+	0.944102i	$0.393068\pi$
$570$		0			0
$571$	6.53553	−	2.70711i	0.273504	−	0.113289i	−0.241716	−	0.970347i	$-0.577710\pi$
$571$	6.53553	−	2.70711i	0.273504	−	0.113289i	0.515220	+	0.857058i	$0.327710\pi$
$572$		0			0
$573$	3.51472	−	8.48528i	0.146829	−	0.354478i
$574$		0			0
$575$	−29.5563			−1.23258
$576$		0			0
$577$	18.9706			0.789755			0.394877	−	0.918734i	$-0.370787\pi$
$577$	18.9706			0.789755			0.394877	+	0.918734i	$0.370787\pi$
$578$		0			0
$579$	0.443651	−	1.07107i	0.0184375	−	0.0445121i
$580$		0			0
$581$	6.41421	−	2.65685i	0.266106	−	0.110225i
$582$		0			0
$583$	−3.82843	+	3.82843i	−0.158557	+	0.158557i
$584$		0			0
$585$	3.82843	+	3.82843i	0.158286	+	0.158286i
$586$		0			0
$587$	−5.22183	−	12.6066i	−0.215528	−	0.520330i	0.778728	−	0.627362i	$-0.215865\pi$
$587$	−5.22183	−	12.6066i	−0.215528	−	0.520330i	−0.994256	+	0.107032i	$0.965865\pi$
$588$		0			0
$589$	14.8284	+	6.14214i	0.610995	+	0.253082i
$590$		0			0
$591$		−	9.27208i		−	0.381402i
$592$		0			0
$593$		−	28.2843i		−	1.16150i	−0.814083	−	0.580748i	$-0.802760\pi$
$593$		−	28.2843i		−	1.16150i	0.814083	−	0.580748i	$-0.197240\pi$
$594$		0			0
$595$	−10.8284	−	4.48528i	−0.443922	−	0.183879i
$596$		0			0
$597$	6.61522	+	15.9706i	0.270743	+	0.653632i
$598$		0			0
$599$	26.6569	+	26.6569i	1.08917	+	1.08917i	0.995614	+	0.0935555i	$0.0298232\pi$
$599$	26.6569	+	26.6569i	1.08917	+	1.08917i	0.0935555	+	0.995614i	$0.470177\pi$
$600$		0			0
$601$	21.9706	−	21.9706i	0.896198	−	0.896198i	−0.0988995	−	0.995097i	$-0.531532\pi$
$601$	21.9706	−	21.9706i	0.896198	−	0.896198i	0.995097	+	0.0988995i	$0.0315322\pi$
$602$		0			0
$603$	−13.3640	+	5.53553i	−0.544223	+	0.225424i
$604$		0			0
$605$	9.97918	−	24.0919i	0.405712	−	0.979474i
$606$		0			0
$607$	−32.9706			−1.33823			−0.669117	−	0.743157i	$-0.733327\pi$
$607$	−32.9706			−1.33823			−0.669117	+	0.743157i	$0.733327\pi$
$608$		0			0
$609$	3.65685			0.148183
$610$		0			0
$611$	−0.100505	+	0.242641i	−0.00406600	+	0.00981619i
$612$		0			0
$613$	−3.19239	+	1.32233i	−0.128939	+	0.0534084i	−0.446220	−	0.894923i	$-0.647230\pi$
$613$	−3.19239	+	1.32233i	−0.128939	+	0.0534084i	0.317281	+	0.948332i	$0.397230\pi$
$614$		0			0
$615$	0.384776	−	0.384776i	0.0155157	−	0.0155157i
$616$		0			0
$617$	−22.7990	−	22.7990i	−0.917853	−	0.917853i	0.0790202	−	0.996873i	$-0.474821\pi$
$617$	−22.7990	−	22.7990i	−0.917853	−	0.917853i	−0.996873	+	0.0790202i	$0.974821\pi$
$618$		0			0
$619$	−9.02082	−	21.7782i	−0.362577	−	0.875339i	−0.994922	−	0.100651i	$-0.967907\pi$
$619$	−9.02082	−	21.7782i	−0.362577	−	0.875339i	0.632345	−	0.774687i	$-0.282093\pi$
$620$		0			0
$621$	31.5563	+	13.0711i	1.26631	+	0.524524i
$622$		0			0
$623$		−	17.3137i		−	0.693659i
$624$		0			0
$625$			30.0711i			1.20284i
$626$		0			0
$627$	−12.6569	−	5.24264i	−0.505466	−	0.209371i
$628$		0			0
$629$	0.828427	+	2.00000i	0.0330316	+	0.0797452i
$630$		0			0
$631$	−32.4558	−	32.4558i	−1.29205	−	1.29205i	−0.933519	−	0.358528i	$-0.883279\pi$
$631$	−32.4558	−	32.4558i	−1.29205	−	1.29205i	−0.358528	−	0.933519i	$-0.616721\pi$
$632$		0			0
$633$	10.6569	−	10.6569i	0.423572	−	0.423572i
$634$		0			0
$635$	−35.1127	+	14.5442i	−1.39340	+	0.577167i
$636$		0			0
$637$	1.46447	−	3.53553i	0.0580243	−	0.140083i
$638$		0			0
$639$	19.8995			0.787212
$640$		0			0
$641$	7.45584			0.294488			0.147244	−	0.989100i	$-0.452960\pi$
$641$	7.45584			0.294488			0.147244	+	0.989100i	$0.452960\pi$
$642$		0			0
$643$	4.73654	−	11.4350i	0.186791	−	0.450954i	−0.802547	−	0.596588i	$-0.796522\pi$
$643$	4.73654	−	11.4350i	0.186791	−	0.450954i	0.989338	+	0.145635i	$0.0465225\pi$
$644$		0			0
$645$	10.5563	−	4.37258i	0.415656	−	0.172170i
$646$		0			0
$647$	−6.17157	+	6.17157i	−0.242630	+	0.242630i	−0.817937	−	0.575308i	$-0.804882\pi$
$647$	−6.17157	+	6.17157i	−0.242630	+	0.242630i	0.575308	+	0.817937i	$0.304882\pi$
$648$		0			0
$649$	−15.4853	−	15.4853i	−0.607850	−	0.607850i
$650$		0			0
$651$	1.65685	+	4.00000i	0.0649372	+	0.156772i
$652$		0			0
$653$	−5.05025	−	2.09188i	−0.197632	−	0.0818617i	0.281672	−	0.959511i	$-0.409111\pi$
$653$	−5.05025	−	2.09188i	−0.197632	−	0.0818617i	−0.479304	+	0.877649i	$0.659111\pi$
$654$		0			0
$655$		−	51.8995i		−	2.02788i
$656$		0			0
$657$		−	23.8995i		−	0.932408i
$658$		0			0
$659$	24.4350	+	10.1213i	0.951854	+	0.394271i	0.803927	−	0.594728i	$-0.202740\pi$
$659$	24.4350	+	10.1213i	0.951854	+	0.394271i	0.147926	+	0.988998i	$0.452740\pi$
$660$		0			0
$661$	−17.2929	−	41.7487i	−0.672616	−	1.62384i	−0.777149	−	0.629316i	$-0.783335\pi$
$661$	−17.2929	−	41.7487i	−0.672616	−	1.62384i	0.104534	−	0.994521i	$-0.466665\pi$
$662$		0			0
$663$	−1.17157	−	1.17157i	−0.0455001	−	0.0455001i
$664$		0			0
$665$	−11.7574	+	11.7574i	−0.455931	+	0.455931i
$666$		0			0
$667$	25.7279	−	10.6569i	0.996189	−	0.412635i
$668$		0			0
$669$	6.14214	−	14.8284i	0.237469	−	0.573300i
$670$		0			0
$671$	−8.24264			−0.318204
$672$		0			0
$673$	22.4853			0.866744			0.433372	−	0.901215i	$-0.357324\pi$
$673$	22.4853			0.866744			0.433372	+	0.901215i	$0.357324\pi$
$674$		0			0
$675$	−5.68629	+	13.7279i	−0.218865	+	0.528388i
$676$		0			0
$677$	−37.6777	+	15.6066i	−1.44807	+	0.599810i	−0.961740	−	0.273964i	$-0.911665\pi$
$677$	−37.6777	+	15.6066i	−1.44807	+	0.599810i	−0.486331	+	0.873775i	$0.661665\pi$
$678$		0			0
$679$	18.4853	−	18.4853i	0.709400	−	0.709400i
$680$		0			0
$681$	10.8995	+	10.8995i	0.417670	+	0.417670i
$682$		0			0
$683$	−4.19239	−	10.1213i	−0.160417	−	0.387282i	0.823150	−	0.567824i	$-0.192215\pi$
$683$	−4.19239	−	10.1213i	−0.160417	−	0.387282i	−0.983567	+	0.180543i	$0.942215\pi$
$684$		0			0
$685$	−33.1421	−	13.7279i	−1.26630	−	0.524517i
$686$		0			0
$687$			18.4437i			0.703669i
$688$		0			0
$689$			0.928932i			0.0353895i
$690$		0			0
$691$	−30.1924	−	12.5061i	−1.14857	−	0.475754i	−0.274518	−	0.961582i	$-0.588518\pi$
$691$	−30.1924	−	12.5061i	−1.14857	−	0.475754i	−0.874055	+	0.485828i	$0.838518\pi$
$692$		0			0
$693$	5.82843	+	14.0711i	0.221404	+	0.534516i
$694$		0			0
$695$	−29.5858	−	29.5858i	−1.12225	−	1.12225i
$696$		0			0
$697$	0.485281	−	0.485281i	0.0183813	−	0.0183813i
$698$		0			0
$699$	−2.65685	+	1.10051i	−0.100491	+	0.0416249i
$700$		0			0
$701$	1.19239	−	2.87868i	0.0450359	−	0.108726i	−0.899761	−	0.436383i	$-0.856259\pi$
$701$	1.19239	−	2.87868i	0.0450359	−	0.108726i	0.944797	+	0.327657i	$0.106259\pi$
$702$		0			0
$703$	3.07107			0.115828
$704$		0			0
$705$	−0.769553			−0.0289830
$706$		0			0
$707$	−1.92893	+	4.65685i	−0.0725450	+	0.175139i
$708$		0			0
$709$	−21.1924	+	8.77817i	−0.795897	+	0.329671i	−0.743312	−	0.668945i	$-0.766746\pi$
$709$	−21.1924	+	8.77817i	−0.795897	+	0.329671i	−0.0525851	+	0.998616i	$0.516746\pi$
$710$		0			0
$711$	−10.2426	+	10.2426i	−0.384129	+	0.384129i
$712$		0			0
$713$	23.3137	+	23.3137i	0.873105	+	0.873105i
$714$		0			0
$715$	−3.82843	−	9.24264i	−0.143175	−	0.345655i
$716$		0			0
$717$	3.75736	+	1.55635i	0.140321	+	0.0581229i
$718$		0			0
$719$			35.6569i			1.32978i	0.746943	+	0.664888i	$0.231521\pi$
$719$			35.6569i			1.32978i	−0.746943	+	0.664888i	$0.768479\pi$
$720$		0			0
$721$		−	18.9706i		−	0.706501i
$722$		0			0
$723$	6.00000	+	2.48528i	0.223142	+	0.0924286i
$724$		0			0
$725$	4.63604	+	11.1924i	0.172178	+	0.415675i
$726$		0			0
$727$	9.97056	+	9.97056i	0.369788	+	0.369788i	0.867400	−	0.497612i	$-0.165790\pi$
$727$	9.97056	+	9.97056i	0.369788	+	0.369788i	−0.497612	+	0.867400i	$0.665790\pi$
$728$		0			0
$729$	−0.221825	+	0.221825i	−0.00821576	+	0.00821576i
$730$		0			0
$731$	13.3137	−	5.51472i	0.492425	−	0.203969i
$732$		0			0
$733$	−13.7782	+	33.2635i	−0.508908	+	1.22861i	0.435604	+	0.900138i	$0.356535\pi$
$733$	−13.7782	+	33.2635i	−0.508908	+	1.22861i	−0.944513	+	0.328475i	$0.893465\pi$
$734$		0			0
$735$	11.2132			0.413605
$736$		0			0
$737$	26.7279			0.984536
$738$		0			0
$739$	0.192388	−	0.464466i	0.00707711	−	0.0170857i	−0.920301	−	0.391210i	$-0.872057\pi$
$739$	0.192388	−	0.464466i	0.00707711	−	0.0170857i	0.927379	+	0.374124i	$0.122057\pi$
$740$		0			0
$741$	−2.17157	+	0.899495i	−0.0797747	+	0.0330438i
$742$		0			0
$743$	−31.6274	+	31.6274i	−1.16030	+	1.16030i	−0.175887	+	0.984410i	$0.556279\pi$
$743$	−31.6274	+	31.6274i	−1.16030	+	1.16030i	−0.984410	+	0.175887i	$0.943721\pi$
$744$		0			0
$745$	35.0000	+	35.0000i	1.28230	+	1.28230i
$746$		0			0
$747$	−4.53553	−	10.9497i	−0.165947	−	0.400630i
$748$		0			0
$749$	5.82843	+	2.41421i	0.212966	+	0.0882134i
$750$		0			0
$751$		−	10.9706i		−	0.400322i	−0.979763	−	0.200161i	$-0.935854\pi$
$751$		−	10.9706i		−	0.400322i	0.979763	−	0.200161i	$-0.0641464\pi$
$752$		0			0
$753$		−	13.2132i		−	0.481516i
$754$		0			0
$755$	−5.68629	−	2.35534i	−0.206945	−	0.0857196i
$756$		0			0
$757$	−13.7782	−	33.2635i	−0.500776	−	1.20898i	−0.949062	−	0.315090i	$-0.897965\pi$
$757$	−13.7782	−	33.2635i	−0.500776	−	1.20898i	0.448285	−	0.893890i	$-0.352035\pi$
$758$		0			0
$759$	−19.8995	−	19.8995i	−0.722306	−	0.722306i
$760$		0			0
$761$	29.8284	−	29.8284i	1.08128	−	1.08128i	0.0848892	−	0.996390i	$-0.472946\pi$
$761$	29.8284	−	29.8284i	1.08128	−	1.08128i	0.996390	−	0.0848892i	$-0.0270536\pi$
$762$		0			0
$763$	−19.4853	+	8.07107i	−0.705415	+	0.292192i
$764$		0			0
$765$	−7.65685	+	18.4853i	−0.276834	+	0.668337i
$766$		0			0
$767$	−3.75736			−0.135670
$768$		0			0
$769$	5.51472			0.198866			0.0994329	−	0.995044i	$-0.468297\pi$
$769$	5.51472			0.198866			0.0994329	+	0.995044i	$0.468297\pi$
$770$		0			0
$771$	−1.75736	+	4.24264i	−0.0632897	+	0.152795i
$772$		0			0
$773$	−29.1924	+	12.0919i	−1.04998	+	0.434915i	−0.839884	−	0.542766i	$-0.817377\pi$
$773$	−29.1924	+	12.0919i	−1.04998	+	0.434915i	−0.210094	+	0.977681i	$0.567377\pi$
$774$		0			0
$775$	−10.1421	+	10.1421i	−0.364316	+	0.364316i
$776$		0			0
$777$	0.585786	+	0.585786i	0.0210150	+	0.0210150i
$778$		0			0
$779$	−0.372583	−	0.899495i	−0.0133492	−	0.0322278i
$780$		0			0
$781$	−33.9706	−	14.0711i	−1.21556	−	0.503502i
$782$		0			0
$783$		−	14.0000i		−	0.500319i
$784$		0			0
$785$			5.41421i			0.193242i
$786$		0			0
$787$	2.29289	+	0.949747i	0.0817328	+	0.0338548i	0.423175	−	0.906048i	$-0.360915\pi$
$787$	2.29289	+	0.949747i	0.0817328	+	0.0338548i	−0.341442	+	0.939903i	$0.610915\pi$
$788$		0			0
$789$	2.41421	+	5.82843i	0.0859483	+	0.207498i
$790$		0			0
$791$	6.34315	+	6.34315i	0.225536	+	0.225536i
$792$		0			0
$793$	−1.00000	+	1.00000i	−0.0355110	+	0.0355110i
$794$		0			0
$795$	−2.51472	+	1.04163i	−0.0891879	+	0.0369428i
$796$		0			0
$797$	−10.8076	+	26.0919i	−0.382825	+	0.924222i	0.608592	+	0.793484i	$0.291735\pi$
$797$	−10.8076	+	26.0919i	−0.382825	+	0.924222i	−0.991417	+	0.130738i	$0.958265\pi$
$798$		0			0
$799$	−0.970563			−0.0343360
$800$		0			0
$801$	−29.5563			−1.04432
$802$		0			0
$803$	−16.8995	+	40.7990i	−0.596370	+	1.43977i
$804$		0			0
$805$	−31.5563	+	13.0711i	−1.11222	+	0.460695i
$806$		0			0
$807$	12.8995	−	12.8995i	0.454084	−	0.454084i
$808$		0			0
$809$	29.1421	+	29.1421i	1.02458	+	1.02458i	0.999690	+	0.0248928i	$0.00792444\pi$
$809$	29.1421	+	29.1421i	1.02458	+	1.02458i	0.0248928	+	0.999690i	$0.492076\pi$
$810$		0			0
$811$	−17.5061	−	42.2635i	−0.614722	−	1.48407i	−0.857758	−	0.514053i	$-0.828143\pi$
$811$	−17.5061	−	42.2635i	−0.614722	−	1.48407i	0.243036	−	0.970017i	$-0.421857\pi$
$812$		0			0
$813$	−12.7279	−	5.27208i	−0.446388	−	0.184900i
$814$		0			0
$815$			1.47309i			0.0516000i
$816$		0			0
$817$		−	20.4437i		−	0.715233i
$818$		0			0
$819$	2.41421	+	1.00000i	0.0843594	+	0.0349428i
$820$		0			0
$821$	−8.94975	−	21.6066i	−0.312348	−	0.754076i	−0.999617	−	0.0276723i	$-0.991191\pi$
$821$	−8.94975	−	21.6066i	−0.312348	−	0.754076i	0.687269	−	0.726403i	$-0.258809\pi$
$822$		0			0
$823$	−35.9706	−	35.9706i	−1.25385	−	1.25385i	−0.953978	−	0.299877i	$-0.903054\pi$
$823$	−35.9706	−	35.9706i	−1.25385	−	1.25385i	−0.299877	−	0.953978i	$-0.596946\pi$
$824$		0			0
$825$	8.65685	−	8.65685i	0.301393	−	0.301393i
$826$		0			0
$827$	−38.9203	+	16.1213i	−1.35339	+	0.560593i	−0.937235	−	0.348699i	$-0.886623\pi$
$827$	−38.9203	+	16.1213i	−1.35339	+	0.560593i	−0.416157	+	0.909293i	$0.636623\pi$
$828$		0			0
$829$	14.1630	−	34.1924i	0.491900	−	1.18755i	−0.461853	−	0.886957i	$-0.652815\pi$
$829$	14.1630	−	34.1924i	0.491900	−	1.18755i	0.953752	−	0.300594i	$-0.0971849\pi$
$830$		0			0
$831$	−1.41421			−0.0490585
$832$		0			0
$833$	14.1421			0.489996
$834$		0			0
$835$	23.2426	−	56.1127i	0.804345	−	1.94186i
$836$		0			0
$837$	15.3137	−	6.34315i	0.529319	−	0.219251i
$838$		0			0
$839$	−9.68629	+	9.68629i	−0.334408	+	0.334408i	−0.854258	−	0.519850i	$-0.825988\pi$
$839$	−9.68629	+	9.68629i	−0.334408	+	0.334408i	0.519850	+	0.854258i	$0.325988\pi$
$840$		0			0
$841$	12.4350	+	12.4350i	0.428794	+	0.428794i
$842$		0			0
$843$	4.89949	+	11.8284i	0.168748	+	0.407393i
$844$		0			0
$845$	33.6066	+	13.9203i	1.15610	+	0.478873i
$846$		0			0
$847$		−	12.5858i		−	0.432453i
$848$		0			0
$849$		−	11.5563i		−	0.396613i
$850$		0			0
$851$	5.82843	+	2.41421i	0.199796	+	0.0827582i
$852$		0			0
$853$	21.1924	+	51.1630i	0.725614	+	1.75179i	0.656686	+	0.754164i	$0.271958\pi$
$853$	21.1924	+	51.1630i	0.725614	+	1.75179i	0.0689279	+	0.997622i	$0.478042\pi$
$854$		0			0
$855$	20.0711	+	20.0711i	0.686416	+	0.686416i
$856$		0			0
$857$	−9.68629	+	9.68629i	−0.330877	+	0.330877i	−0.852920	−	0.522042i	$-0.825170\pi$
$857$	−9.68629	+	9.68629i	−0.330877	+	0.330877i	0.522042	+	0.852920i	$0.325170\pi$
$858$		0			0
$859$	4.05025	−	1.67767i	0.138193	−	0.0572413i	−0.312515	−	0.949913i	$-0.601172\pi$
$859$	4.05025	−	1.67767i	0.138193	−	0.0572413i	0.450708	+	0.892671i	$0.351172\pi$
$860$		0			0
$861$	0.100505	−	0.242641i	0.00342520	−	0.00826917i
$862$		0			0
$863$	21.9411			0.746885			0.373442	−	0.927653i	$-0.378177\pi$
$863$	21.9411			0.746885			0.373442	+	0.927653i	$0.378177\pi$
$864$		0			0
$865$	23.8995			0.812607
$866$		0			0
$867$	−2.63604	+	6.36396i	−0.0895246	+	0.216131i
$868$		0			0
$869$	24.7279	−	10.2426i	0.838837	−	0.347458i
$870$		0			0
$871$	3.24264	−	3.24264i	0.109873	−	0.109873i
$872$		0			0
$873$	−31.5563	−	31.5563i	−1.06802	−	1.06802i
$874$		0			0
$875$	2.24264	+	5.41421i	0.0758151	+	0.183034i
$876$		0			0
$877$	1.77817	+	0.736544i	0.0600447	+	0.0248713i	0.412504	−	0.910956i	$-0.364654\pi$
$877$	1.77817	+	0.736544i	0.0600447	+	0.0248713i	−0.352459	+	0.935827i	$0.614654\pi$
$878$		0			0
$879$		−	19.2132i		−	0.648045i
$880$		0			0
$881$			22.6274i			0.762337i	0.924506	+	0.381169i	$0.124478\pi$
$881$			22.6274i			0.762337i	−0.924506	+	0.381169i	$0.875522\pi$
$882$		0			0
$883$	−49.6482	−	20.5650i	−1.67080	−	0.692066i	−0.671973	−	0.740575i	$-0.734553\pi$
$883$	−49.6482	−	20.5650i	−1.67080	−	0.692066i	−0.998823	+	0.0485090i	$0.984553\pi$
$884$		0			0
$885$	−4.21320	−	10.1716i	−0.141625	−	0.341914i
$886$		0			0
$887$	−2.31371	−	2.31371i	−0.0776867	−	0.0776867i	0.667196	−	0.744882i	$-0.267494\pi$
$887$	−2.31371	−	2.31371i	−0.0776867	−	0.0776867i	−0.744882	+	0.667196i	$0.767494\pi$
$888$		0			0
$889$	−12.9706	+	12.9706i	−0.435019	+	0.435019i
$890$		0			0
$891$	16.7782	−	6.94975i	0.562090	−	0.232825i
$892$		0			0
$893$	−0.526912	+	1.27208i	−0.0176324	+	0.0425685i
$894$		0			0
$895$	−12.5269			−0.418728
$896$		0			0
$897$	−4.82843			−0.161216
$898$		0			0
$899$	5.17157	−	12.4853i	0.172482	−	0.416407i
$900$		0			0
$901$	−3.17157	+	1.31371i	−0.105660	+	0.0437660i
$902$		0			0
$903$	3.89949	−	3.89949i	0.129767	−	0.129767i
$904$		0			0
$905$	−36.3137	−	36.3137i	−1.20711	−	1.20711i
$906$		0			0
$907$	−6.53553	−	15.7782i	−0.217009	−	0.523906i	0.777461	−	0.628932i	$-0.216507\pi$
$907$	−6.53553	−	15.7782i	−0.217009	−	0.523906i	−0.994469	+	0.105026i	$0.966507\pi$
$908$		0			0
$909$	7.94975	+	3.29289i	0.263676	+	0.109218i
$910$		0			0
$911$			33.5980i			1.11315i	0.830797	+	0.556575i	$0.187885\pi$
$911$			33.5980i			1.11315i	−0.830797	+	0.556575i	$0.812115\pi$
$912$		0			0
$913$			21.8995i			0.724767i
$914$		0			0
$915$	−3.82843	−	1.58579i	−0.126564	−	0.0524245i
$916$		0			0
$917$	−9.58579	−	23.1421i	−0.316551	−	0.764221i
$918$		0			0
$919$	8.51472	+	8.51472i	0.280875	+	0.280875i	0.833458	−	0.552583i	$-0.186358\pi$
$919$	8.51472	+	8.51472i	0.280875	+	0.280875i	−0.552583	+	0.833458i	$0.686358\pi$
$920$		0			0
$921$	−9.82843	+	9.82843i	−0.323858	+	0.323858i
$922$		0			0
$923$	−5.82843	+	2.41421i	−0.191845	+	0.0794648i
$924$		0			0
$925$	−1.05025	+	2.53553i	−0.0345321	+	0.0833678i
$926$		0			0
$927$	−32.3848			−1.06366
$928$		0			0
$929$	−9.51472			−0.312168			−0.156084	−	0.987744i	$-0.549887\pi$
$929$	−9.51472			−0.312168			−0.156084	+	0.987744i	$0.549887\pi$
$930$		0			0
$931$	7.67767	−	18.5355i	0.251625	−	0.607478i
$932$		0			0
$933$	−2.65685	+	1.10051i	−0.0869815	+	0.0360289i
$934$		0			0
$935$	26.1421	−	26.1421i	0.854939	−	0.854939i
$936$		0			0
$937$	−19.0000	−	19.0000i	−0.620703	−	0.620703i	0.325008	−	0.945711i	$-0.394633\pi$
$937$	−19.0000	−	19.0000i	−0.620703	−	0.620703i	−0.945711	+	0.325008i	$0.894633\pi$
$938$		0			0
$939$	3.10051	+	7.48528i	0.101181	+	0.244273i
$940$		0			0
$941$	−1.53553	−	0.636039i	−0.0500570	−	0.0207343i	0.357514	−	0.933908i	$-0.383624\pi$
$941$	−1.53553	−	0.636039i	−0.0500570	−	0.0207343i	−0.407571	+	0.913173i	$0.633624\pi$
$942$		0			0
$943$		−	2.00000i		−	0.0651290i
$944$		0			0
$945$			17.1716i			0.558591i
$946$		0			0
$947$	−22.5355	−	9.33452i	−0.732306	−	0.303331i	−0.0148070	−	0.999890i	$-0.504713\pi$
$947$	−22.5355	−	9.33452i	−0.732306	−	0.303331i	−0.717499	+	0.696559i	$0.754713\pi$
$948$		0			0
$949$	2.89949	+	7.00000i	0.0941216	+	0.227230i
$950$		0			0
$951$	10.1716	+	10.1716i	0.329836	+	0.329836i
$952$		0			0
$953$	−14.6569	+	14.6569i	−0.474782	+	0.474782i	−0.903458	−	0.428676i	$-0.858980\pi$
$953$	−14.6569	+	14.6569i	−0.474782	+	0.474782i	0.428676	+	0.903458i	$0.358980\pi$
$954$		0			0
$955$	32.4853	−	13.4558i	1.05120	−	0.435421i
$956$		0			0
$957$	−4.41421	+	10.6569i	−0.142691	+	0.344487i
$958$		0			0
$959$	−17.3137			−0.559089
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	4.12132	−	9.94975i	0.132808	−	0.320626i
$964$		0			0
$965$	4.10051	−	1.69848i	0.132000	−	0.0546762i
$966$		0			0
$967$	6.02944	−	6.02944i	0.193894	−	0.193894i	−0.603483	−	0.797376i	$-0.706221\pi$
$967$	6.02944	−	6.02944i	0.193894	−	0.193894i	0.797376	+	0.603483i	$0.206221\pi$
$968$		0			0
$969$	−6.14214	−	6.14214i	−0.197314	−	0.197314i
$970$		0			0
$971$	9.26346	+	22.3640i	0.297278	+	0.717694i	0.999981	+	0.00620964i	$0.00197660\pi$
$971$	9.26346	+	22.3640i	0.297278	+	0.717694i	−0.702702	+	0.711484i	$0.748023\pi$
$972$		0			0
$973$	−18.6569	−	7.72792i	−0.598111	−	0.247746i
$974$		0			0
$975$		−	2.10051i		−	0.0672700i
$976$		0			0
$977$			14.1421i			0.452447i	0.974075	+	0.226224i	$0.0726380\pi$
$977$			14.1421i			0.452447i	−0.974075	+	0.226224i	$0.927362\pi$
$978$		0			0
$979$	50.4558	+	20.8995i	1.61258	+	0.667951i
$980$		0			0
$981$	13.7782	+	33.2635i	0.439903	+	1.06202i
$982$		0			0
$983$	19.6274	+	19.6274i	0.626017	+	0.626017i	0.947064	−	0.321046i	$-0.104034\pi$
$983$	19.6274	+	19.6274i	0.626017	+	0.626017i	−0.321046	+	0.947064i	$0.604034\pi$
$984$		0			0
$985$	25.1005	−	25.1005i	0.799769	−	0.799769i
$986$		0			0
$987$	−0.343146	+	0.142136i	−0.0109224	+	0.00452423i
$988$		0			0
$989$	16.0711	−	38.7990i	0.511030	−	1.23374i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	1.07107			0.0339893
$994$		0			0
$995$	−25.3259	+	61.1421i	−0.802885	+	1.93834i
$996$		0			0
$997$	48.7487	−	20.1924i	1.54389	−	0.639499i	0.561690	−	0.827348i	$-0.310151\pi$
$997$	48.7487	−	20.1924i	1.54389	−	0.639499i	0.982198	+	0.187848i	$0.0601514\pi$
$998$		0			0
$999$	2.24264	−	2.24264i	0.0709540	−	0.0709540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.g.a.65.1		4
4.3	odd	2		512.2.g.c.65.1		4
8.3	odd	2		512.2.g.b.65.1		4
8.5	even	2		512.2.g.d.65.1		4
16.3	odd	4		128.2.g.a.81.1		4
16.5	even	4		256.2.g.b.161.1		4
16.11	odd	4		256.2.g.a.161.1		4
16.13	even	4		32.2.g.a.29.1	yes	4
32.3	odd	8		128.2.g.a.49.1		4
32.5	even	8	inner	512.2.g.a.449.1		4
32.11	odd	8		512.2.g.b.449.1		4
32.13	even	8		256.2.g.b.97.1		4
32.19	odd	8		256.2.g.a.97.1		4
32.21	even	8		512.2.g.d.449.1		4
32.27	odd	8		512.2.g.c.449.1		4
32.29	even	8		32.2.g.a.21.1	✓	4
48.29	odd	4		288.2.v.a.253.1		4
48.35	even	4		1152.2.v.a.721.1		4
64.5	even	16		4096.2.a.e.1.2		4
64.27	odd	16		4096.2.a.f.1.2		4
64.37	even	16		4096.2.a.e.1.3		4
64.59	odd	16		4096.2.a.f.1.3		4
80.13	odd	4		800.2.ba.b.349.1		4
80.29	even	4		800.2.y.a.701.1		4
80.77	odd	4		800.2.ba.a.349.1		4
96.29	odd	8		288.2.v.a.181.1		4
96.35	even	8		1152.2.v.a.433.1		4
160.29	even	8		800.2.y.a.501.1		4
160.93	odd	8		800.2.ba.a.149.1		4
160.157	odd	8		800.2.ba.b.149.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.21.1	✓	4	32.29	even	8
32.2.g.a.29.1	yes	4	16.13	even	4
128.2.g.a.49.1		4	32.3	odd	8
128.2.g.a.81.1		4	16.3	odd	4
256.2.g.a.97.1		4	32.19	odd	8
256.2.g.a.161.1		4	16.11	odd	4
256.2.g.b.97.1		4	32.13	even	8
256.2.g.b.161.1		4	16.5	even	4
288.2.v.a.181.1		4	96.29	odd	8
288.2.v.a.253.1		4	48.29	odd	4
512.2.g.a.65.1		4	1.1	even	1	trivial
512.2.g.a.449.1		4	32.5	even	8	inner
512.2.g.b.65.1		4	8.3	odd	2
512.2.g.b.449.1		4	32.11	odd	8
512.2.g.c.65.1		4	4.3	odd	2
512.2.g.c.449.1		4	32.27	odd	8
512.2.g.d.65.1		4	8.5	even	2
512.2.g.d.449.1		4	32.21	even	8
800.2.y.a.501.1		4	160.29	even	8
800.2.y.a.701.1		4	80.29	even	4
800.2.ba.a.149.1		4	160.93	odd	8
800.2.ba.a.349.1		4	80.77	odd	4
800.2.ba.b.149.1		4	160.157	odd	8
800.2.ba.b.349.1		4	80.13	odd	4
1152.2.v.a.433.1		4	96.35	even	8
1152.2.v.a.721.1		4	48.35	even	4
4096.2.a.e.1.2		4	64.5	even	16
4096.2.a.e.1.3		4	64.37	even	16
4096.2.a.f.1.2		4	64.27	odd	16
4096.2.a.f.1.3		4	64.59	odd	16

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.292893 + 0.707107i) q^{3} +(-2.70711 + 1.12132i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(1.70711 + 1.70711i) q^{9} +O(q^{10})\)	\(q+(-0.292893 + 0.707107i) q^{3} +(-2.70711 + 1.12132i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(1.70711 + 1.70711i) q^{9} +(-1.70711 - 4.12132i) q^{11} +(-0.707107 - 0.292893i) q^{13} -2.24264i q^{15} -2.82843i q^{17} +(-3.70711 - 1.53553i) q^{19} +(-0.414214 - 1.00000i) q^{21} +(-5.82843 - 5.82843i) q^{23} +(2.53553 - 2.53553i) q^{25} +(-3.82843 + 1.58579i) q^{27} +(-1.29289 + 3.12132i) q^{29} -4.00000 q^{31} +3.41421 q^{33} +(1.58579 - 3.82843i) q^{35} +(-0.707107 + 0.292893i) q^{37} +(0.414214 - 0.414214i) q^{39} +(0.171573 + 0.171573i) q^{41} +(1.94975 + 4.70711i) q^{43} +(-6.53553 - 2.70711i) q^{45} -0.343146i q^{47} +5.00000i q^{49} +(2.00000 + 0.828427i) q^{51} +(-0.464466 - 1.12132i) q^{53} +(9.24264 + 9.24264i) q^{55} +(2.17157 - 2.17157i) q^{57} +(4.53553 - 1.87868i) q^{59} +(0.707107 - 1.70711i) q^{61} -3.41421 q^{63} +2.24264 q^{65} +(-2.29289 + 5.53553i) q^{67} +(5.82843 - 2.41421i) q^{69} +(5.82843 - 5.82843i) q^{71} +(-7.00000 - 7.00000i) q^{73} +(1.05025 + 2.53553i) q^{75} +(5.82843 + 2.41421i) q^{77} +6.00000i q^{79} +4.07107i q^{81} +(-4.53553 - 1.87868i) q^{83} +(3.17157 + 7.65685i) q^{85} +(-1.82843 - 1.82843i) q^{87} +(-8.65685 + 8.65685i) q^{89} +(1.00000 - 0.414214i) q^{91} +(1.17157 - 2.82843i) q^{93} +11.7574 q^{95} -18.4853 q^{97} +(4.12132 - 9.94975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 8 q^{5} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 8 * q^5 - 4 * q^7 + 4 * q^9	\( 4 q - 4 q^{3} - 8 q^{5} - 4 q^{7} + 4 q^{9} - 4 q^{11} - 12 q^{19} + 4 q^{21} - 12 q^{23} - 4 q^{25} - 4 q^{27} - 8 q^{29} - 16 q^{31} + 8 q^{33} + 12 q^{35} - 4 q^{39} + 12 q^{41} - 12 q^{43} - 12 q^{45} + 8 q^{51} - 16 q^{53} + 20 q^{55} + 20 q^{57} + 4 q^{59} - 8 q^{63} - 8 q^{65} - 12 q^{67} + 12 q^{69} + 12 q^{71} - 28 q^{73} + 24 q^{75} + 12 q^{77} - 4 q^{83} + 24 q^{85} + 4 q^{87} - 12 q^{89} + 4 q^{91} + 16 q^{93} + 64 q^{95} - 40 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 8 * q^5 - 4 * q^7 + 4 * q^9 - 4 * q^11 - 12 * q^19 + 4 * q^21 - 12 * q^23 - 4 * q^25 - 4 * q^27 - 8 * q^29 - 16 * q^31 + 8 * q^33 + 12 * q^35 - 4 * q^39 + 12 * q^41 - 12 * q^43 - 12 * q^45 + 8 * q^51 - 16 * q^53 + 20 * q^55 + 20 * q^57 + 4 * q^59 - 8 * q^63 - 8 * q^65 - 12 * q^67 + 12 * q^69 + 12 * q^71 - 28 * q^73 + 24 * q^75 + 12 * q^77 - 4 * q^83 + 24 * q^85 + 4 * q^87 - 12 * q^89 + 4 * q^91 + 16 * q^93 + 64 * q^95 - 40 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more