LMFDB - Embedded newform 512.2.g.g.193.2

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:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			193.2
Root			$0.500000 - 0.691860i$ of defining polynomial
Character	$\chi$	$=$	512.193
Dual form			512.2.g.g.321.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.60607 - 1.07947i) q^{3} +(-0.292893 + 0.707107i) q^{5} +(1.68554 + 1.68554i) q^{7} +(3.50504 - 3.50504i) q^{9} +O(q^{10})$	\(q+(2.60607 - 1.07947i) q^{3} +(-0.292893 + 0.707107i) q^{5} +(1.68554 + 1.68554i) q^{7} +(3.50504 - 3.50504i) q^{9} +(0.808140 + 0.334743i) q^{11} +(-0.451835 - 1.09083i) q^{13} +2.15894i q^{15} -0.224777i q^{17} +(-1.19186 - 2.87740i) q^{19} +(6.21215 + 2.57316i) q^{21} +(-3.68554 + 3.68554i) q^{23} +(3.12132 + 3.12132i) q^{25} +(2.11239 - 5.09976i) q^{27} +(5.66398 - 2.34610i) q^{29} -6.82843 q^{31} +2.46742 q^{33} +(-1.68554 + 0.698175i) q^{35} +(4.09083 - 9.87613i) q^{37} +(-2.35503 - 2.35503i) q^{39} +(-6.37109 + 6.37109i) q^{41} +(-4.60607 - 1.90790i) q^{43} +(1.45183 + 3.50504i) q^{45} +0.542661i q^{47} -1.31788i q^{49} +(-0.242641 - 0.585786i) q^{51} +(-9.46191 - 3.91925i) q^{53} +(-0.473398 + 0.473398i) q^{55} +(-6.21215 - 6.21215i) q^{57} +(-1.39393 + 3.36524i) q^{59} +(0.962379 - 0.398630i) q^{61} +11.8158 q^{63} +0.903670 q^{65} +(-3.57558 + 1.48105i) q^{67} +(-5.62636 + 13.5832i) q^{69} +(-5.39978 - 5.39978i) q^{71} +(5.15894 - 5.15894i) q^{73} +(11.5038 + 4.76501i) q^{75} +(0.797933 + 1.92638i) q^{77} +8.39218i q^{79} -0.699980i q^{81} +(4.64665 + 11.2180i) q^{83} +(0.158942 + 0.0658358i) q^{85} +(12.2282 - 12.2282i) q^{87} +(5.92638 + 5.92638i) q^{89} +(1.07705 - 2.60022i) q^{91} +(-17.7954 + 7.37109i) q^{93} +2.38372 q^{95} -4.19951 q^{97} +(4.00585 - 1.65928i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 8 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q + 4 * q^3 - 8 * q^5 - 8 * q^7	$ 8 q + 4 q^{3} - 8 q^{5} - 8 q^{7} + 12 q^{11} - 4 q^{19} + 16 q^{21} - 8 q^{23} + 8 q^{25} + 16 q^{27} + 8 q^{29} - 32 q^{31} - 16 q^{33} + 8 q^{35} + 16 q^{37} + 16 q^{39} - 8 q^{41} - 20 q^{43} + 8 q^{45} + 32 q^{51} - 16 q^{53} - 16 q^{55} - 16 q^{57} - 28 q^{59} + 40 q^{63} - 12 q^{67} - 24 q^{71} + 32 q^{73} + 20 q^{75} - 16 q^{77} - 36 q^{83} - 8 q^{85} + 56 q^{87} + 16 q^{89} - 32 q^{93} + 8 q^{95} + 32 q^{97} - 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 8 * q^5 - 8 * q^7 + 12 * q^11 - 4 * q^19 + 16 * q^21 - 8 * q^23 + 8 * q^25 + 16 * q^27 + 8 * q^29 - 32 * q^31 - 16 * q^33 + 8 * q^35 + 16 * q^37 + 16 * q^39 - 8 * q^41 - 20 * q^43 + 8 * q^45 + 32 * q^51 - 16 * q^53 - 16 * q^55 - 16 * q^57 - 28 * q^59 + 40 * q^63 - 12 * q^67 - 24 * q^71 + 32 * q^73 + 20 * q^75 - 16 * q^77 - 36 * q^83 - 8 * q^85 + 56 * q^87 + 16 * q^89 - 32 * q^93 + 8 * q^95 + 32 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	2.60607	−	1.07947i	1.50462	−	0.623233i	0.530178	−	0.847886i	$-0.322125\pi$
$3$	2.60607	−	1.07947i	1.50462	−	0.623233i	0.974439	+	0.224653i	$0.0721250\pi$
$4$		0			0
$5$	−0.292893	+	0.707107i	−0.130986	+	0.316228i	−0.975742	−	0.218924i	$-0.929745\pi$
$5$	−0.292893	+	0.707107i	−0.130986	+	0.316228i	0.844756	+	0.535151i	$0.179745\pi$
$6$		0			0
$7$	1.68554	+	1.68554i	0.637076	+	0.637076i	0.949833	−	0.312757i	$-0.101253\pi$
$7$	1.68554	+	1.68554i	0.637076	+	0.637076i	−0.312757	+	0.949833i	$0.601253\pi$
$8$		0			0
$9$	3.50504	−	3.50504i	1.16835	−	1.16835i
$10$		0			0
$11$	0.808140	+	0.334743i	0.243664	+	0.100929i	0.501173	−	0.865347i	$-0.332902\pi$
$11$	0.808140	+	0.334743i	0.243664	+	0.100929i	−0.257510	+	0.966276i	$0.582902\pi$
$12$		0			0
$13$	−0.451835	−	1.09083i	−0.125316	−	0.302541i	0.848753	−	0.528789i	$-0.177354\pi$
$13$	−0.451835	−	1.09083i	−0.125316	−	0.302541i	−0.974070	+	0.226249i	$0.927354\pi$
$14$		0			0
$15$			2.15894i			0.557436i
$16$		0			0
$17$		−	0.224777i		−	0.0545165i	−0.999628	−	0.0272583i	$-0.991322\pi$
$17$		−	0.224777i		−	0.0545165i	0.999628	−	0.0272583i	$-0.00867765\pi$
$18$		0			0
$19$	−1.19186	−	2.87740i	−0.273431	−	0.660122i	0.726194	−	0.687490i	$-0.241287\pi$
$19$	−1.19186	−	2.87740i	−0.273431	−	0.660122i	−0.999625	+	0.0273681i	$0.991287\pi$
$20$		0			0
$21$	6.21215	+	2.57316i	1.35560	+	0.561509i
$22$		0			0
$23$	−3.68554	+	3.68554i	−0.768489	+	0.768489i	−0.977840	−	0.209351i	$-0.932865\pi$
$23$	−3.68554	+	3.68554i	−0.768489	+	0.768489i	0.209351	+	0.977840i	$0.432865\pi$
$24$		0			0
$25$	3.12132	+	3.12132i	0.624264	+	0.624264i
$26$		0			0
$27$	2.11239	−	5.09976i	0.406529	−	0.981449i
$28$		0			0
$29$	5.66398	−	2.34610i	1.05177	−	0.435659i	0.211250	−	0.977432i	$-0.432247\pi$
$29$	5.66398	−	2.34610i	1.05177	−	0.435659i	0.840525	+	0.541773i	$0.182247\pi$
$30$		0			0
$31$	−6.82843			−1.22642			−0.613211	−	0.789919i	$-0.710122\pi$
$31$	−6.82843			−1.22642			−0.613211	+	0.789919i	$0.710122\pi$
$32$		0			0
$33$	2.46742			0.429522
$34$		0			0
$35$	−1.68554	+	0.698175i	−0.284909	+	0.118013i
$36$		0			0
$37$	4.09083	−	9.87613i	0.672528	−	1.62363i	−0.104773	−	0.994496i	$-0.533412\pi$
$37$	4.09083	−	9.87613i	0.672528	−	1.62363i	0.777301	−	0.629129i	$-0.216588\pi$
$38$		0			0
$39$	−2.35503	−	2.35503i	−0.377107	−	0.377107i
$40$		0			0
$41$	−6.37109	+	6.37109i	−0.994997	+	0.994997i	−0.999988	−	0.00499079i	$-0.998411\pi$
$41$	−6.37109	+	6.37109i	−0.994997	+	0.994997i	0.00499079	+	0.999988i	$0.498411\pi$
$42$		0			0
$43$	−4.60607	−	1.90790i	−0.702420	−	0.290952i	0.00274415	−	0.999996i	$-0.499127\pi$
$43$	−4.60607	−	1.90790i	−0.702420	−	0.290952i	−0.705164	+	0.709045i	$0.749127\pi$
$44$		0			0
$45$	1.45183	+	3.50504i	0.216427	+	0.522500i
$46$		0			0
$47$			0.542661i			0.0791552i	0.999216	+	0.0395776i	$0.0126012\pi$
$47$			0.542661i			0.0791552i	−0.999216	+	0.0395776i	$0.987399\pi$
$48$		0			0
$49$		−	1.31788i		−	0.188269i
$50$		0			0
$51$	−0.242641	−	0.585786i	−0.0339765	−	0.0820265i
$52$		0			0
$53$	−9.46191	−	3.91925i	−1.29969	−	0.538351i	−0.377834	−	0.925873i	$-0.623331\pi$
$53$	−9.46191	−	3.91925i	−1.29969	−	0.538351i	−0.921860	+	0.387523i	$0.873331\pi$
$54$		0			0
$55$	−0.473398	+	0.473398i	−0.0638329	+	0.0638329i
$56$		0			0
$57$	−6.21215	−	6.21215i	−0.822819	−	0.822819i
$58$		0			0
$59$	−1.39393	+	3.36524i	−0.181474	+	0.438117i	−0.988271	−	0.152712i	$-0.951199\pi$
$59$	−1.39393	+	3.36524i	−0.181474	+	0.438117i	0.806797	+	0.590829i	$0.201199\pi$
$60$		0			0
$61$	0.962379	−	0.398630i	0.123220	−	0.0510394i	−0.320222	−	0.947343i	$-0.603757\pi$
$61$	0.962379	−	0.398630i	0.123220	−	0.0510394i	0.443442	+	0.896303i	$0.353757\pi$
$62$		0			0
$63$	11.8158			1.48865
$64$		0			0
$65$	0.903670			0.112086
$66$		0			0
$67$	−3.57558	+	1.48105i	−0.436826	+	0.180939i	−0.590249	−	0.807221i	$-0.700970\pi$
$67$	−3.57558	+	1.48105i	−0.436826	+	0.180939i	0.153423	+	0.988161i	$0.450970\pi$
$68$		0			0
$69$	−5.62636	+	13.5832i	−0.677334	+	1.63523i
$70$		0			0
$71$	−5.39978	−	5.39978i	−0.640836	−	0.640836i	0.309925	−	0.950761i	$-0.399696\pi$
$71$	−5.39978	−	5.39978i	−0.640836	−	0.640836i	−0.950761	+	0.309925i	$0.899696\pi$
$72$		0			0
$73$	5.15894	−	5.15894i	0.603808	−	0.603808i	−0.337513	−	0.941321i	$-0.609586\pi$
$73$	5.15894	−	5.15894i	0.603808	−	0.603808i	0.941321	+	0.337513i	$0.109586\pi$
$74$		0			0
$75$	11.5038	+	4.76501i	1.32834	+	0.550217i
$76$		0			0
$77$	0.797933	+	1.92638i	0.0909329	+	0.219531i
$78$		0			0
$79$			8.39218i			0.944194i	0.881547	+	0.472097i	$0.156503\pi$
$79$			8.39218i			0.944194i	−0.881547	+	0.472097i	$0.843497\pi$
$80$		0			0
$81$		−	0.699980i		−	0.0777755i
$82$		0			0
$83$	4.64665	+	11.2180i	0.510036	+	1.23134i	0.943862	+	0.330339i	$0.107163\pi$
$83$	4.64665	+	11.2180i	0.510036	+	1.23134i	−0.433827	+	0.900996i	$0.642837\pi$
$84$		0			0
$85$	0.158942	+	0.0658358i	0.0172396	+	0.00714089i
$86$		0			0
$87$	12.2282	−	12.2282i	1.31100	−	1.31100i
$88$		0			0
$89$	5.92638	+	5.92638i	0.628195	+	0.628195i	0.947614	−	0.319419i	$-0.103488\pi$
$89$	5.92638	+	5.92638i	0.628195	+	0.628195i	−0.319419	+	0.947614i	$0.603488\pi$
$90$		0			0
$91$	1.07705	−	2.60022i	0.112905	−	0.272577i
$92$		0			0
$93$	−17.7954	+	7.37109i	−1.84529	+	0.764346i
$94$		0			0
$95$	2.38372			0.244564
$96$		0			0
$97$	−4.19951			−0.426396			−0.213198	−	0.977009i	$-0.568388\pi$
$97$	−4.19951			−0.426396			−0.213198	+	0.977009i	$0.568388\pi$
$98$		0			0
$99$	4.00585	−	1.65928i	0.402603	−	0.166764i
$100$		0			0
$101$	−1.84819	+	4.46191i	−0.183901	+	0.443977i	−0.988764	−	0.149484i	$-0.952239\pi$
$101$	−1.84819	+	4.46191i	−0.183901	+	0.443977i	0.804863	+	0.593461i	$0.202239\pi$
$102$		0			0
$103$	10.9635	+	10.9635i	1.08027	+	1.08027i	0.996484	+	0.0837844i	$0.0267007\pi$
$103$	10.9635	+	10.9635i	1.08027	+	1.08027i	0.0837844	+	0.996484i	$0.473299\pi$
$104$		0			0
$105$	−3.63899	+	3.63899i	−0.355129	+	0.355129i
$106$		0			0
$107$	−8.08128	−	3.34737i	−0.781246	−	0.323603i	−0.0438280	−	0.999039i	$-0.513955\pi$
$107$	−8.08128	−	3.34737i	−0.781246	−	0.323603i	−0.737418	+	0.675436i	$0.763955\pi$
$108$		0			0
$109$	−3.57088	−	8.62086i	−0.342028	−	0.825728i	−0.997511	−	0.0705180i	$-0.977535\pi$
$109$	−3.57088	−	8.62086i	−0.342028	−	0.825728i	0.655483	−	0.755210i	$-0.272465\pi$
$110$		0			0
$111$		−	30.1538i		−	2.86208i
$112$		0			0
$113$			2.42429i			0.228058i	0.993477	+	0.114029i	$0.0363757\pi$
$113$			2.42429i			0.228058i	−0.993477	+	0.114029i	$0.963624\pi$
$114$		0			0
$115$	−1.52660	−	3.68554i	−0.142356	−	0.343679i
$116$		0			0
$117$	−5.40709	−	2.23969i	−0.499885	−	0.207059i
$118$		0			0
$119$	0.378872	−	0.378872i	0.0347312	−	0.0347312i
$120$		0			0
$121$	−7.23714	−	7.23714i	−0.657921	−	0.657921i
$122$		0			0
$123$	−9.72612	+	23.4809i	−0.876974	+	2.11720i
$124$		0			0
$125$	−6.65685	+	2.75736i	−0.595407	+	0.246626i
$126$		0			0
$127$	2.19266			0.194567			0.0972836	−	0.995257i	$-0.468985\pi$
$127$	2.19266			0.194567			0.0972836	+	0.995257i	$0.468985\pi$
$128$		0			0
$129$	−14.0633			−1.23820
$130$		0			0
$131$	−7.63657	+	3.16317i	−0.667210	+	0.276367i	−0.690469	−	0.723362i	$-0.742596\pi$
$131$	−7.63657	+	3.16317i	−0.667210	+	0.276367i	0.0232589	+	0.999729i	$0.492596\pi$
$132$		0			0
$133$	2.84106	−	6.85892i	0.246351	−	0.594744i
$134$		0			0
$135$	2.98737	+	2.98737i	0.257112	+	0.257112i
$136$		0			0
$137$	−7.76744	+	7.76744i	−0.663617	+	0.663617i	−0.956231	−	0.292614i	$-0.905475\pi$
$137$	−7.76744	+	7.76744i	−0.663617	+	0.663617i	0.292614	+	0.956231i	$0.405475\pi$
$138$		0			0
$139$	−0.862967	−	0.357453i	−0.0731959	−	0.0303188i	0.345785	−	0.938314i	$-0.387613\pi$
$139$	−0.862967	−	0.357453i	−0.0731959	−	0.0303188i	−0.418981	+	0.907995i	$0.637613\pi$
$140$		0			0
$141$	0.585786	+	1.41421i	0.0493321	+	0.119098i
$142$		0			0
$143$		−	1.03279i		−	0.0863662i
$144$		0			0
$145$			4.69220i			0.389666i
$146$		0			0
$147$	−1.42262	−	3.43450i	−0.117335	−	0.283273i
$148$		0			0
$149$	5.66398	+	2.34610i	0.464011	+	0.192200i	0.602426	−	0.798175i	$-0.294201\pi$
$149$	5.66398	+	2.34610i	0.464011	+	0.192200i	−0.138415	+	0.990374i	$0.544201\pi$
$150$		0			0
$151$	−8.17083	+	8.17083i	−0.664932	+	0.664932i	−0.956538	−	0.291606i	$-0.905810\pi$
$151$	−8.17083	+	8.17083i	−0.664932	+	0.664932i	0.291606	+	0.956538i	$0.405810\pi$
$152$		0			0
$153$	−0.787854	−	0.787854i	−0.0636942	−	0.0636942i
$154$		0			0
$155$	2.00000	−	4.82843i	0.160644	−	0.387829i
$156$		0			0
$157$	11.7908	−	4.88391i	0.941009	−	0.389779i	0.141164	−	0.989986i	$-0.454915\pi$
$157$	11.7908	−	4.88391i	0.941009	−	0.389779i	0.799844	+	0.600208i	$0.204915\pi$
$158$		0			0
$159$	−28.8892			−2.29106
$160$		0			0
$161$	−12.4243			−0.979171
$162$		0			0
$163$	−1.81822	+	0.753131i	−0.142414	+	0.0589898i	−0.452752	−	0.891636i	$-0.649558\pi$
$163$	−1.81822	+	0.753131i	−0.142414	+	0.0589898i	0.310338	+	0.950626i	$0.399558\pi$
$164$		0			0
$165$	−0.722690	+	1.74473i	−0.0562613	+	0.135827i
$166$		0			0
$167$	−15.1630	−	15.1630i	−1.17335	−	1.17335i	−0.981406	−	0.191946i	$-0.938520\pi$
$167$	−15.1630	−	15.1630i	−1.17335	−	1.17335i	−0.191946	−	0.981406i	$-0.561480\pi$
$168$		0			0
$169$	8.20664	−	8.20664i	0.631280	−	0.631280i
$170$		0			0
$171$	−14.2629	−	5.90790i	−1.09071	−	0.451788i
$172$		0			0
$173$	−1.88391	−	4.54817i	−0.143231	−	0.345791i	0.835942	−	0.548818i	$-0.184922\pi$
$173$	−1.88391	−	4.54817i	−0.143231	−	0.345791i	−0.979173	+	0.203027i	$0.934922\pi$
$174$		0			0
$175$			10.5222i			0.795407i
$176$		0			0
$177$			10.2748i			0.772298i
$178$		0			0
$179$	3.01505	+	7.27899i	0.225356	+	0.544057i	0.995601	−	0.0936904i	$-0.0298664\pi$
$179$	3.01505	+	7.27899i	0.225356	+	0.544057i	−0.770246	+	0.637747i	$0.779866\pi$
$180$		0			0
$181$	14.7782	+	6.12132i	1.09845	+	0.454994i	0.856947	−	0.515405i	$-0.172359\pi$
$181$	14.7782	+	6.12132i	1.09845	+	0.454994i	0.241506	+	0.970399i	$0.422359\pi$
$182$		0			0
$183$	2.07772	−	2.07772i	0.153589	−	0.153589i
$184$		0			0
$185$	5.78530	+	5.78530i	0.425344	+	0.425344i
$186$		0			0
$187$	0.0752426	−	0.181652i	0.00550228	−	0.0132837i
$188$		0			0
$189$	12.1564	−	5.03534i	0.884247	−	0.366267i
$190$		0			0
$191$	15.4642			1.11895			0.559475	−	0.828847i	$-0.311003\pi$
$191$	15.4642			1.11895			0.559475	+	0.828847i	$0.311003\pi$
$192$		0			0
$193$	13.2206			0.951640			0.475820	−	0.879543i	$-0.342151\pi$
$193$	13.2206			0.951640			0.475820	+	0.879543i	$0.342151\pi$
$194$		0			0
$195$	2.35503	−	0.975485i	0.168647	−	0.0698559i
$196$		0			0
$197$	0.249768	−	0.602992i	0.0177952	−	0.0429614i	−0.914732	−	0.404061i	$-0.867598\pi$
$197$	0.249768	−	0.602992i	0.0177952	−	0.0429614i	0.932527	+	0.361099i	$0.117598\pi$
$198$		0			0
$199$	−1.86490	−	1.86490i	−0.132199	−	0.132199i	0.637911	−	0.770110i	$-0.279799\pi$
$199$	−1.86490	−	1.86490i	−0.132199	−	0.132199i	−0.770110	+	0.637911i	$0.779799\pi$
$200$		0			0
$201$	−7.71947	+	7.71947i	−0.544489	+	0.544489i
$202$		0			0
$203$	13.5013	+	5.59244i	0.947608	+	0.392512i
$204$		0			0
$205$	−2.63899	−	6.37109i	−0.184315	−	0.444976i
$206$		0			0
$207$			25.8360i			1.79572i
$208$		0			0
$209$		−	2.72431i		−	0.188445i
$210$		0			0
$211$	−7.88406	−	19.0338i	−0.542761	−	1.31034i	−0.922768	−	0.385357i	$-0.874078\pi$
$211$	−7.88406	−	19.0338i	−0.542761	−	1.31034i	0.380007	−	0.924984i	$-0.375922\pi$
$212$		0			0
$213$	−19.9011	−	8.24331i	−1.36360	−	0.564822i
$214$		0			0
$215$	2.69818	−	2.69818i	0.184014	−	0.184014i
$216$		0			0
$217$	−11.5096	−	11.5096i	−0.781324	−	0.781324i
$218$		0			0
$219$	7.87565	−	19.0135i	0.532187	−	1.28481i
$220$		0			0
$221$	−0.245193	+	0.101562i	−0.0164935	+	0.00683182i
$222$		0			0
$223$	17.2119			1.15259			0.576297	−	0.817241i	$-0.304497\pi$
$223$	17.2119			1.15259			0.576297	+	0.817241i	$0.304497\pi$
$224$		0			0
$225$	21.8807			1.45871
$226$		0			0
$227$	1.52075	−	0.629916i	0.100936	−	0.0418090i	−0.331644	−	0.943405i	$-0.607603\pi$
$227$	1.52075	−	0.629916i	0.100936	−	0.0418090i	0.432580	+	0.901596i	$0.357603\pi$
$228$		0			0
$229$	−1.01491	+	2.45021i	−0.0670672	+	0.161915i	−0.953859	−	0.300254i	$-0.902929\pi$
$229$	−1.01491	+	2.45021i	−0.0670672	+	0.161915i	0.886792	+	0.462169i	$0.152929\pi$
$230$		0			0
$231$	4.15894	+	4.15894i	0.273638	+	0.273638i
$232$		0			0
$233$	10.9475	−	10.9475i	0.717192	−	0.717192i	−0.250837	−	0.968029i	$-0.580706\pi$
$233$	10.9475	−	10.9475i	0.717192	−	0.717192i	0.968029	+	0.250837i	$0.0807058\pi$
$234$		0			0
$235$	−0.383719	−	0.158942i	−0.0250311	−	0.0103682i
$236$		0			0
$237$	9.05911	+	21.8706i	0.588452	+	1.42065i
$238$		0			0
$239$		−	18.2858i		−	1.18281i	−0.806375	−	0.591404i	$-0.798574\pi$
$239$		−	18.2858i		−	1.18281i	0.806375	−	0.591404i	$-0.201426\pi$
$240$		0			0
$241$		−	27.8155i		−	1.79176i	−0.444300	−	0.895878i	$-0.646548\pi$
$241$		−	27.8155i		−	1.79176i	0.444300	−	0.895878i	$-0.353452\pi$
$242$		0			0
$243$	5.58156	+	13.4751i	0.358057	+	0.864426i
$244$		0			0
$245$	0.931884	+	0.385999i	0.0595359	+	0.0246606i
$246$		0			0
$247$	−2.60022	+	2.60022i	−0.165448	+	0.165448i
$248$		0			0
$249$	24.2190	+	24.2190i	1.53482	+	1.53482i
$250$		0			0
$251$	3.88406	−	9.37694i	0.245159	−	0.591867i	−0.752621	−	0.658454i	$-0.771211\pi$
$251$	3.88406	−	9.37694i	0.245159	−	0.591867i	0.997781	+	0.0665866i	$0.0212109\pi$
$252$		0			0
$253$	−4.21215	+	1.74473i	−0.264815	+	0.109690i
$254$		0			0
$255$	0.485281			0.0303895
$256$		0			0
$257$	20.0656			1.25166			0.625828	−	0.779961i	$-0.284761\pi$
$257$	20.0656			1.25166			0.625828	+	0.779961i	$0.284761\pi$
$258$		0			0
$259$	23.5419	−	9.75138i	1.46282	−	0.605921i
$260$		0			0
$261$	11.6293	−	28.0756i	0.719836	−	1.73784i
$262$		0			0
$263$	17.9782	+	17.9782i	1.10858	+	1.10858i	0.993337	+	0.115244i	$0.0367650\pi$
$263$	17.9782	+	17.9782i	1.10858	+	1.10858i	0.115244	+	0.993337i	$0.463235\pi$
$264$		0			0
$265$	5.54266	−	5.54266i	0.340483	−	0.340483i
$266$		0			0
$267$	21.8419	+	9.04722i	1.33670	+	0.553681i
$268$		0			0
$269$	10.6286	+	25.6598i	0.648040	+	1.56451i	0.815582	+	0.578641i	$0.196417\pi$
$269$	10.6286	+	25.6598i	0.648040	+	1.56451i	−0.167543	+	0.985865i	$0.553583\pi$
$270$		0			0
$271$			16.4921i			1.00183i	0.865498	+	0.500913i	$0.167002\pi$
$271$			16.4921i			1.00183i	−0.865498	+	0.500913i	$0.832998\pi$
$272$		0			0
$273$		−	7.93901i		−	0.480491i
$274$		0			0
$275$	1.47763	+	3.56730i	0.0891042	+	0.215117i
$276$		0			0
$277$	−5.60044	−	2.31978i	−0.336498	−	0.139382i	0.208035	−	0.978121i	$-0.433293\pi$
$277$	−5.60044	−	2.31978i	−0.336498	−	0.139382i	−0.544533	+	0.838739i	$0.683293\pi$
$278$		0			0
$279$	−23.9339	+	23.9339i	−1.43289	+	1.43289i
$280$		0			0
$281$	−9.80801	−	9.80801i	−0.585097	−	0.585097i	0.351203	−	0.936299i	$-0.385773\pi$
$281$	−9.80801	−	9.80801i	−0.585097	−	0.585097i	−0.936299	+	0.351203i	$0.885773\pi$
$282$		0			0
$283$	8.84871	−	21.3627i	0.526001	−	1.26988i	−0.408121	−	0.912928i	$-0.633816\pi$
$283$	8.84871	−	21.3627i	0.526001	−	1.26988i	0.934123	−	0.356952i	$-0.116184\pi$
$284$		0			0
$285$	6.21215	−	2.57316i	0.367976	−	0.152421i
$286$		0			0
$287$	−21.4775			−1.26778
$288$		0			0
$289$	16.9495			0.997028
$290$		0			0
$291$	−10.9442	+	4.53325i	−0.641563	+	0.265744i
$292$		0			0
$293$	−8.46715	+	20.4415i	−0.494656	+	1.19421i	0.457670	+	0.889122i	$0.348684\pi$
$293$	−8.46715	+	20.4415i	−0.494656	+	1.19421i	−0.952326	+	0.305083i	$0.901316\pi$
$294$		0			0
$295$	−1.97131	−	1.97131i	−0.114774	−	0.114774i
$296$		0			0
$297$	3.41421	−	3.41421i	0.198113	−	0.198113i
$298$		0			0
$299$	5.68554	+	2.35503i	0.328803	+	0.136195i
$300$		0			0
$301$	−4.54789	−	10.9796i	−0.262136	−	0.632853i
$302$		0			0
$303$			13.6231i			0.782629i
$304$		0			0
$305$			0.797261i			0.0456510i
$306$		0			0
$307$	−6.46984	−	15.6196i	−0.369253	−	0.891456i	−0.993873	−	0.110527i	$-0.964746\pi$
$307$	−6.46984	−	15.6196i	−0.369253	−	0.891456i	0.624620	−	0.780929i	$-0.285254\pi$
$308$		0			0
$309$	40.4066	+	16.7369i	2.29865	+	0.952131i
$310$		0			0
$311$	7.24929	−	7.24929i	0.411070	−	0.411070i	−0.471041	−	0.882111i	$-0.656122\pi$
$311$	7.24929	−	7.24929i	0.411070	−	0.411070i	0.882111	+	0.471041i	$0.156122\pi$
$312$		0			0
$313$	10.1596	+	10.1596i	0.574255	+	0.574255i	0.933315	−	0.359059i	$-0.116902\pi$
$313$	10.1596	+	10.1596i	0.574255	+	0.574255i	−0.359059	+	0.933315i	$0.616902\pi$
$314$		0			0
$315$	−3.46077	+	8.35503i	−0.194992	+	0.470753i
$316$		0			0
$317$	−3.24198	+	1.34287i	−0.182088	+	0.0754233i	−0.471865	−	0.881671i	$-0.656419\pi$
$317$	−3.24198	+	1.34287i	−0.182088	+	0.0754233i	0.289777	+	0.957094i	$0.406419\pi$
$318$		0			0
$319$	5.36263			0.300250
$320$		0			0
$321$	−24.6738			−1.37716
$322$		0			0
$323$	−0.646775	+	0.267903i	−0.0359875	+	0.0149065i
$324$		0			0
$325$	1.99450	−	4.81514i	0.110635	−	0.267096i
$326$		0			0
$327$	−18.6119	−	18.6119i	−1.02924	−	1.02924i
$328$		0			0
$329$	−0.914679	+	0.914679i	−0.0504279	+	0.0504279i
$330$		0			0
$331$	−15.5299	−	6.43270i	−0.853601	−	0.353573i	−0.0873991	−	0.996173i	$-0.527856\pi$
$331$	−15.5299	−	6.43270i	−0.853601	−	0.353573i	−0.766201	+	0.642600i	$0.777856\pi$
$332$		0			0
$333$	−20.2777	−	48.9547i	−1.11121	−	2.68270i
$334$		0			0
$335$		−	2.96211i		−	0.161837i
$336$		0			0
$337$			2.10641i			0.114743i	0.998353	+	0.0573717i	$0.0182720\pi$
$337$			2.10641i			0.114743i	−0.998353	+	0.0573717i	$0.981728\pi$
$338$		0			0
$339$	2.61695	+	6.31788i	0.142133	+	0.343140i
$340$		0			0
$341$	−5.51833	−	2.28577i	−0.298834	−	0.123781i
$342$		0			0
$343$	14.0202	−	14.0202i	0.757017	−	0.757017i
$344$		0			0
$345$	−7.95687	−	7.95687i	−0.428384	−	0.428384i
$346$		0			0
$347$	−5.13193	+	12.3896i	−0.275496	+	0.665107i	−0.999700	−	0.0244788i	$-0.992207\pi$
$347$	−5.13193	+	12.3896i	−0.275496	+	0.665107i	0.724204	+	0.689586i	$0.242207\pi$
$348$		0			0
$349$	18.1658	−	7.52453i	0.972394	−	0.402779i	0.160791	−	0.986988i	$-0.448596\pi$
$349$	18.1658	−	7.52453i	0.972394	−	0.402779i	0.811603	+	0.584210i	$0.198596\pi$
$350$		0			0
$351$	−6.51740			−0.347873
$352$		0			0
$353$	−28.7013			−1.52762			−0.763809	−	0.645442i	$-0.776673\pi$
$353$	−28.7013			−1.52762			−0.763809	+	0.645442i	$0.776673\pi$
$354$		0			0
$355$	5.39978	−	2.23666i	0.286590	−	0.118710i
$356$		0			0
$357$	0.578387	−	1.39635i	0.0306115	−	0.0739027i
$358$		0			0
$359$	6.39199	+	6.39199i	0.337356	+	0.337356i	0.855372	−	0.518015i	$-0.173329\pi$
$359$	6.39199	+	6.39199i	0.337356	+	0.337356i	−0.518015	+	0.855372i	$0.673329\pi$
$360$		0			0
$361$	6.57611	−	6.57611i	0.346111	−	0.346111i
$362$		0			0
$363$	−26.6728	−	11.0482i	−1.39996	−	0.579882i
$364$		0			0
$365$	2.13690	+	5.15894i	0.111851	+	0.270031i
$366$		0			0
$367$		−	14.5985i		−	0.762038i	−0.924567	−	0.381019i	$-0.875573\pi$
$367$		−	14.5985i		−	0.762038i	0.924567	−	0.381019i	$-0.124427\pi$
$368$		0			0
$369$			44.6618i			2.32500i
$370$		0			0
$371$	−9.34240	−	22.5545i	−0.485033	−	1.17097i
$372$		0			0
$373$	−14.5761	−	6.03762i	−0.754722	−	0.312616i	−0.0280555	−	0.999606i	$-0.508932\pi$
$373$	−14.5761	−	6.03762i	−0.754722	−	0.312616i	−0.726667	+	0.686990i	$0.758932\pi$
$374$		0			0
$375$	−14.3718	+	14.3718i	−0.742154	+	0.742154i
$376$		0			0
$377$	−5.11837	−	5.11837i	−0.263609	−	0.263609i
$378$		0			0
$379$	−2.35403	+	5.68312i	−0.120918	+	0.291922i	−0.972736	−	0.231916i	$-0.925500\pi$
$379$	−2.35403	+	5.68312i	−0.120918	+	0.291922i	0.851818	+	0.523839i	$0.175500\pi$
$380$		0			0
$381$	5.71423	−	2.36691i	0.292749	−	0.121261i
$382$		0			0
$383$	−12.4633			−0.636843			−0.318422	−	0.947949i	$-0.603153\pi$
$383$	−12.4633			−0.636843			−0.318422	+	0.947949i	$0.603153\pi$
$384$		0			0
$385$	−1.59587			−0.0813328
$386$		0			0
$387$	−22.8317	+	9.45721i	−1.16060	+	0.480737i
$388$		0			0
$389$	5.85275	−	14.1298i	0.296746	−	0.716408i	−0.703239	−	0.710953i	$-0.748264\pi$
$389$	5.85275	−	14.1298i	0.296746	−	0.716408i	0.999985	−	0.00545476i	$-0.00173631\pi$
$390$		0			0
$391$	0.828427	+	0.828427i	0.0418954	+	0.0418954i
$392$		0			0
$393$	−16.4869	+	16.4869i	−0.831654	+	0.831654i
$394$		0			0
$395$	−5.93416	−	2.45801i	−0.298580	−	0.123676i
$396$		0			0
$397$	10.5929	+	25.5736i	0.531643	+	1.28350i	0.930434	+	0.366458i	$0.119430\pi$
$397$	10.5929	+	25.5736i	0.531643	+	1.28350i	−0.398791	+	0.917042i	$0.630570\pi$
$398$		0			0
$399$		−	20.9417i		−	1.04840i
$400$		0			0
$401$			16.5018i			0.824062i	0.911170	+	0.412031i	$0.135180\pi$
$401$			16.5018i			0.824062i	−0.911170	+	0.412031i	$0.864820\pi$
$402$		0			0
$403$	3.08532	+	7.44862i	0.153691	+	0.371042i
$404$		0			0
$405$	0.494961	+	0.205019i	0.0245948	+	0.0101875i
$406$		0			0
$407$	6.61192	−	6.61192i	0.327741	−	0.327741i
$408$		0			0
$409$	−1.28577	−	1.28577i	−0.0635771	−	0.0635771i	0.674603	−	0.738180i	$-0.264315\pi$
$409$	−1.28577	−	1.28577i	−0.0635771	−	0.0635771i	−0.738180	+	0.674603i	$0.764315\pi$
$410$		0			0
$411$	−11.8578	+	28.6272i	−0.584902	+	1.41208i
$412$		0			0
$413$	−8.02178	+	3.32273i	−0.394726	+	0.163501i
$414$		0			0
$415$	−9.29329			−0.456190
$416$		0			0
$417$	−2.63482			−0.129028
$418$		0			0
$419$	36.1858	−	14.9887i	1.76779	−	0.732244i	0.772535	−	0.634972i	$-0.218988\pi$
$419$	36.1858	−	14.9887i	1.76779	−	0.732244i	0.995258	−	0.0972723i	$-0.0310118\pi$
$420$		0			0
$421$	−5.63872	+	13.6131i	−0.274814	+	0.663460i	−0.999677	−	0.0254334i	$-0.991903\pi$
$421$	−5.63872	+	13.6131i	−0.274814	+	0.663460i	0.724862	+	0.688894i	$0.241903\pi$
$422$		0			0
$423$	1.90205	+	1.90205i	0.0924807	+	0.0924807i
$424$		0			0
$425$	0.701602	−	0.701602i	0.0340327	−	0.0340327i
$426$		0			0
$427$	2.29404	+	0.950223i	0.111016	+	0.0459845i
$428$		0			0
$429$	−1.11487	−	2.69152i	−0.0538262	−	0.129948i
$430$		0			0
$431$			2.85730i			0.137631i	0.997629	+	0.0688156i	$0.0219220\pi$
$431$			2.85730i			0.137631i	−0.997629	+	0.0688156i	$0.978078\pi$
$432$		0			0
$433$		−	22.5174i		−	1.08212i	−0.840985	−	0.541059i	$-0.818024\pi$
$433$		−	22.5174i		−	1.08212i	0.840985	−	0.541059i	$-0.181976\pi$
$434$		0			0
$435$	5.06509	+	12.2282i	0.242852	+	0.586298i
$436$		0			0
$437$	14.9974	+	6.21215i	0.717425	+	0.297167i
$438$		0			0
$439$	−8.87727	+	8.87727i	−0.423689	+	0.423689i	−0.886472	−	0.462783i	$-0.846851\pi$
$439$	−8.87727	+	8.87727i	−0.423689	+	0.423689i	0.462783	+	0.886472i	$0.346851\pi$
$440$		0			0
$441$	−4.61923	−	4.61923i	−0.219963	−	0.219963i
$442$		0			0
$443$	−9.83247	+	23.7377i	−0.467155	+	1.12781i	0.498245	+	0.867036i	$0.333978\pi$
$443$	−9.83247	+	23.7377i	−0.467155	+	1.12781i	−0.965400	+	0.260775i	$0.916022\pi$
$444$		0			0
$445$	−5.92638	+	2.45479i	−0.280937	+	0.116368i
$446$		0			0
$447$	17.2933			0.817945
$448$		0			0
$449$	8.83528			0.416963			0.208481	−	0.978026i	$-0.433148\pi$
$449$	8.83528			0.416963			0.208481	+	0.978026i	$0.433148\pi$
$450$		0			0
$451$	−7.28141	+	3.01606i	−0.342868	+	0.142021i
$452$		0			0
$453$	−12.4736	+	30.1139i	−0.586061	+	1.41488i
$454$		0			0
$455$	1.52318	+	1.52318i	0.0714075	+	0.0714075i
$456$		0			0
$457$	−7.58808	+	7.58808i	−0.354955	+	0.354955i	−0.861950	−	0.506994i	$-0.830757\pi$
$457$	−7.58808	+	7.58808i	−0.354955	+	0.354955i	0.506994	+	0.861950i	$0.330757\pi$
$458$		0			0
$459$	−1.14631	−	0.474817i	−0.0535052	−	0.0221626i
$460$		0			0
$461$	−6.31816	−	15.2534i	−0.294266	−	0.710421i	−0.999998	−	0.00194197i	$-0.999382\pi$
$461$	−6.31816	−	15.2534i	−0.294266	−	0.710421i	0.705732	−	0.708479i	$-0.250618\pi$
$462$		0			0
$463$		−	18.7996i		−	0.873689i	−0.899537	−	0.436845i	$-0.856096\pi$
$463$		−	18.7996i		−	0.873689i	0.899537	−	0.436845i	$-0.143904\pi$
$464$		0			0
$465$		−	14.7422i		−	0.683652i
$466$		0			0
$467$	3.84804	+	9.28999i	0.178066	+	0.429890i	0.987561	−	0.157238i	$-0.0502588\pi$
$467$	3.84804	+	9.28999i	0.178066	+	0.429890i	−0.809495	+	0.587127i	$0.800259\pi$
$468$		0			0
$469$	−8.52318	−	3.53041i	−0.393564	−	0.163019i
$470$		0			0
$471$	25.4557	−	25.4557i	1.17293	−	1.17293i
$472$		0			0
$473$	−3.08370	−	3.08370i	−0.141789	−	0.141789i
$474$		0			0
$475$	5.26112	−	12.7015i	0.241397	−	0.582784i
$476$		0			0
$477$	−46.9015	+	19.4272i	−2.14747	+	0.889512i
$478$		0			0
$479$	14.7779			0.675220			0.337610	−	0.941286i	$-0.390382\pi$
$479$	14.7779			0.675220			0.337610	+	0.941286i	$0.390382\pi$
$480$		0			0
$481$	−12.6215			−0.575491
$482$		0			0
$483$	−32.3786	+	13.4117i	−1.47328	+	0.610252i
$484$		0			0
$485$	1.23001	−	2.96951i	0.0558519	−	0.134838i
$486$		0			0
$487$	13.0855	+	13.0855i	0.592961	+	0.592961i	0.938430	−	0.345469i	$-0.112280\pi$
$487$	13.0855	+	13.0855i	0.592961	+	0.592961i	−0.345469	+	0.938430i	$0.612280\pi$
$488$		0			0
$489$	−3.92543	+	3.92543i	−0.177514	+	0.177514i
$490$		0			0
$491$	28.4741	+	11.7944i	1.28502	+	0.532273i	0.917497	−	0.397742i	$-0.130206\pi$
$491$	28.4741	+	11.7944i	1.28502	+	0.532273i	0.367523	+	0.930015i	$0.380206\pi$
$492$		0			0
$493$	−0.527350	−	1.27314i	−0.0237506	−	0.0573391i
$494$		0			0
$495$			3.31856i			0.149158i
$496$		0			0
$497$		−	18.2031i		−	0.816522i
$498$		0			0
$499$	9.28886	+	22.4253i	0.415827	+	1.00389i	0.983544	+	0.180670i	$0.0578267\pi$
$499$	9.28886	+	22.4253i	0.415827	+	1.00389i	−0.567717	+	0.823224i	$0.692173\pi$
$500$		0			0
$501$	−55.8841	−	23.1479i	−2.49672	−	1.03417i
$502$		0			0
$503$	23.5062	−	23.5062i	1.04809	−	1.04809i	0.0493053	−	0.998784i	$-0.484299\pi$
$503$	23.5062	−	23.5062i	1.04809	−	1.04809i	0.998784	−	0.0493053i	$-0.0157007\pi$
$504$		0			0
$505$	−2.61373	−	2.61373i	−0.116309	−	0.116309i
$506$		0			0
$507$	12.5283	−	30.2459i	0.556400	−	1.34327i
$508$		0			0
$509$	−31.7834	+	13.1651i	−1.40877	+	0.583534i	−0.952014	−	0.306056i	$-0.900991\pi$
$509$	−31.7834	+	13.1651i	−1.40877	+	0.583534i	−0.456761	+	0.889589i	$0.650991\pi$
$510$		0			0
$511$	17.3912			0.769343
$512$		0			0
$513$	−17.1917			−0.759033
$514$		0			0
$515$	−10.9635	+	4.54124i	−0.483111	+	0.200111i
$516$		0			0
$517$	−0.181652	+	0.438546i	−0.00798903	+	0.0192872i
$518$		0			0
$519$	−9.81922	−	9.81922i	−0.431016	−	0.431016i
$520$		0			0
$521$	10.8936	−	10.8936i	0.477257	−	0.477257i	−0.426996	−	0.904253i	$-0.640428\pi$
$521$	10.8936	−	10.8936i	0.477257	−	0.477257i	0.904253	+	0.426996i	$0.140428\pi$
$522$		0			0
$523$	15.6600	+	6.48657i	0.684763	+	0.283638i	0.697816	−	0.716277i	$-0.254155\pi$
$523$	15.6600	+	6.48657i	0.684763	+	0.283638i	−0.0130536	+	0.999915i	$0.504155\pi$
$524$		0			0
$525$	11.3585	+	27.4217i	0.495724	+	1.19678i
$526$		0			0
$527$			1.53488i			0.0668603i
$528$		0			0
$529$		−	4.16647i		−	0.181151i
$530$		0			0
$531$	6.90952	+	16.6811i	0.299848	+	0.723896i
$532$		0			0
$533$	9.82843	+	4.07107i	0.425716	+	0.176338i
$534$		0			0
$535$	4.73390	−	4.73390i	0.204664	−	0.204664i
$536$		0			0
$537$	15.7149	+	15.7149i	0.678148	+	0.678148i
$538$		0			0
$539$	0.441152	−	1.06503i	0.0190018	−	0.0458743i
$540$		0			0
$541$	2.66006	−	1.10183i	0.114365	−	0.0473716i	−0.324767	−	0.945794i	$-0.605286\pi$
$541$	2.66006	−	1.10183i	0.114365	−	0.0473716i	0.439132	+	0.898422i	$0.355286\pi$
$542$		0			0
$543$	45.1208			1.93632
$544$		0			0
$545$	7.14175			0.305919
$546$		0			0
$547$	−25.1462	+	10.4159i	−1.07517	+	0.445351i	−0.848813	−	0.528693i	$-0.822682\pi$
$547$	−25.1462	+	10.4159i	−1.07517	+	0.445351i	−0.226360	+	0.974044i	$0.572682\pi$
$548$		0			0
$549$	1.97596	−	4.77039i	0.0843319	−	0.203595i
$550$		0			0
$551$	−13.5013	−	13.5013i	−0.575176	−	0.575176i
$552$		0			0
$553$	−14.1454	+	14.1454i	−0.601523	+	0.601523i
$554$		0			0
$555$	21.3220	+	8.83185i	0.905068	+	0.374891i
$556$		0			0
$557$	−10.9504	−	26.4367i	−0.463984	−	1.12016i	−0.966748	−	0.255733i	$-0.917683\pi$
$557$	−10.9504	−	26.4367i	−0.463984	−	1.12016i	0.502763	−	0.864424i	$-0.332317\pi$
$558$		0			0
$559$			5.88648i			0.248972i
$560$		0			0
$561$		−	0.554620i		−	0.0234161i
$562$		0			0
$563$	−9.49093	−	22.9131i	−0.399995	−	0.965673i	−0.987666	−	0.156574i	$-0.949955\pi$
$563$	−9.49093	−	22.9131i	−0.399995	−	0.965673i	0.587671	−	0.809100i	$-0.300045\pi$
$564$		0			0
$565$	−1.71423	−	0.710059i	−0.0721184	−	0.0298724i
$566$		0			0
$567$	1.17985	−	1.17985i	0.0495489	−	0.0495489i
$568$		0			0
$569$	−12.2981	−	12.2981i	−0.515565	−	0.515565i	0.400661	−	0.916226i	$-0.368780\pi$
$569$	−12.2981	−	12.2981i	−0.515565	−	0.515565i	−0.916226	+	0.400661i	$0.868780\pi$
$570$		0			0
$571$	2.04555	−	4.93839i	0.0856036	−	0.206665i	−0.875281	−	0.483615i	$-0.839324\pi$
$571$	2.04555	−	4.93839i	0.0856036	−	0.206665i	0.960884	+	0.276950i	$0.0893235\pi$
$572$		0			0
$573$	40.3008	−	16.6931i	1.68359	−	0.697366i
$574$		0			0
$575$	−23.0075			−0.959480
$576$		0			0
$577$	2.06423			0.0859352			0.0429676	−	0.999076i	$-0.486319\pi$
$577$	2.06423			0.0859352			0.0429676	+	0.999076i	$0.486319\pi$
$578$		0			0
$579$	34.4539	−	14.2713i	1.43185	−	0.593093i
$580$		0			0
$581$	−11.0763	+	26.7406i	−0.459522	+	1.10939i
$582$		0			0
$583$	−6.33461	−	6.33461i	−0.262353	−	0.262353i
$584$		0			0
$585$	3.16740	−	3.16740i	0.130956	−	0.130956i
$586$		0			0
$587$	−21.1056	−	8.74223i	−0.871122	−	0.360830i	−0.0980746	−	0.995179i	$-0.531268\pi$
$587$	−21.1056	−	8.74223i	−0.871122	−	0.360830i	−0.773047	+	0.634349i	$0.781268\pi$
$588$		0			0
$589$	8.13853	+	19.6481i	0.335342	+	0.809588i
$590$		0			0
$591$		−	1.84106i		−	0.0757310i
$592$		0			0
$593$			24.2771i			0.996939i	0.866907	+	0.498470i	$0.166104\pi$
$593$			24.2771i			0.996939i	−0.866907	+	0.498470i	$0.833896\pi$
$594$		0			0
$595$	0.156934	+	0.378872i	0.00643367	+	0.0155322i
$596$		0			0
$597$	−6.87318	−	2.84696i	−0.281300	−	0.116518i
$598$		0			0
$599$	−33.3626	+	33.3626i	−1.36316	+	1.36316i	−0.493295	+	0.869862i	$0.664208\pi$
$599$	−33.3626	+	33.3626i	−1.36316	+	1.36316i	−0.869862	+	0.493295i	$0.835792\pi$
$600$		0			0
$601$	21.0676	+	21.0676i	0.859365	+	0.859365i	0.991263	−	0.131898i	$-0.0421073\pi$
$601$	21.0676	+	21.0676i	0.859365	+	0.859365i	−0.131898	+	0.991263i	$0.542107\pi$
$602$		0			0
$603$	−7.34139	+	17.7237i	−0.298965	+	0.721765i
$604$		0			0
$605$	7.23714	−	2.99772i	0.294231	−	0.121875i
$606$		0			0
$607$	−3.82750			−0.155353			−0.0776767	−	0.996979i	$-0.524750\pi$
$607$	−3.82750			−0.155353			−0.0776767	+	0.996979i	$0.524750\pi$
$608$		0			0
$609$	41.2224			1.67041
$610$		0			0
$611$	0.591948	−	0.245193i	0.0239477	−	0.00991945i
$612$		0			0
$613$	12.0488	−	29.0883i	0.486645	−	1.17486i	−0.469753	−	0.882798i	$-0.655657\pi$
$613$	12.0488	−	29.0883i	0.486645	−	1.17486i	0.956398	−	0.292067i	$-0.0943429\pi$
$614$		0			0
$615$	−13.7548	−	13.7548i	−0.554647	−	0.554647i
$616$		0			0
$617$	−22.2479	+	22.2479i	−0.895666	+	0.895666i	−0.995049	−	0.0993836i	$-0.968313\pi$
$617$	−22.2479	+	22.2479i	−0.895666	+	0.895666i	0.0993836	+	0.995049i	$0.468313\pi$
$618$		0			0
$619$	−6.53408	−	2.70650i	−0.262627	−	0.108784i	0.247485	−	0.968892i	$-0.420396\pi$
$619$	−6.53408	−	2.70650i	−0.262627	−	0.108784i	−0.510112	+	0.860108i	$0.670396\pi$
$620$		0			0
$621$	11.0101	+	26.5807i	0.441819	+	1.06665i
$622$		0			0
$623$			19.9783i			0.800416i
$624$		0			0
$625$			16.5563i			0.662254i
$626$		0			0
$627$	−2.94082	−	7.09976i	−0.117445	−	0.283537i
$628$		0			0
$629$	−2.21993	−	0.919525i	−0.0885144	−	0.0366639i
$630$		0			0
$631$	1.24929	−	1.24929i	0.0497335	−	0.0497335i	−0.681803	−	0.731536i	$-0.738804\pi$
$631$	1.24929	−	1.24929i	0.0497335	−	0.0497335i	0.731536	+	0.681803i	$0.238804\pi$
$632$		0			0
$633$	−41.0928	−	41.0928i	−1.63329	−	1.63329i
$634$		0			0
$635$	−0.642215	+	1.55045i	−0.0254855	+	0.0615275i
$636$		0			0
$637$	−1.43758	+	0.595466i	−0.0569590	+	0.0235932i
$638$		0			0
$639$	−37.8529			−1.49744
$640$		0			0
$641$	11.2362			0.443802			0.221901	−	0.975069i	$-0.428774\pi$
$641$	11.2362			0.443802			0.221901	+	0.975069i	$0.428774\pi$
$642$		0			0
$643$	−13.8682	+	5.74440i	−0.546908	+	0.226537i	−0.638991	−	0.769215i	$-0.720648\pi$
$643$	−13.8682	+	5.74440i	−0.546908	+	0.226537i	0.0920822	+	0.995751i	$0.470648\pi$
$644$		0			0
$645$	4.11904	−	9.94424i	0.162187	−	0.391554i
$646$		0			0
$647$	13.9424	+	13.9424i	0.548134	+	0.548134i	0.925901	−	0.377767i	$-0.123308\pi$
$647$	13.9424	+	13.9424i	0.548134	+	0.548134i	−0.377767	+	0.925901i	$0.623308\pi$
$648$		0			0
$649$	−2.25298	+	2.25298i	−0.0884371	+	0.0884371i
$650$		0			0
$651$	−42.4192	−	17.5706i	−1.66254	−	0.688646i
$652$		0			0
$653$	0.149807	+	0.361667i	0.00586241	+	0.0141531i	0.926784	−	0.375596i	$-0.122562\pi$
$653$	0.149807	+	0.361667i	0.00586241	+	0.0141531i	−0.920921	+	0.389749i	$0.872562\pi$
$654$		0			0
$655$		−	6.32634i		−	0.247191i
$656$		0			0
$657$		−	36.1646i		−	1.41091i
$658$		0			0
$659$	−7.66613	−	18.5077i	−0.298630	−	0.720957i	−0.999967	−	0.00812687i	$-0.997413\pi$
$659$	−7.66613	−	18.5077i	−0.298630	−	0.720957i	0.701337	−	0.712830i	$-0.252587\pi$
$660$		0			0
$661$	29.9699	+	12.4139i	1.16569	+	0.482846i	0.879767	−	0.475405i	$-0.157698\pi$
$661$	29.9699	+	12.4139i	1.16569	+	0.482846i	0.285927	+	0.958251i	$0.407698\pi$
$662$		0			0
$663$	−0.529357	+	0.529357i	−0.0205585	+	0.0205585i
$664$		0			0
$665$	4.01786	+	4.01786i	0.155806	+	0.155806i
$666$		0			0
$667$	−12.2282	+	29.5215i	−0.473478	+	1.14308i
$668$		0			0
$669$	44.8554	−	18.5797i	1.73421	−	0.718334i
$670$		0			0
$671$	0.911176			0.0351755
$672$		0			0
$673$	−47.5269			−1.83203			−0.916014	−	0.401146i	$-0.868612\pi$
$673$	−47.5269			−1.83203			−0.916014	+	0.401146i	$0.868612\pi$
$674$		0			0
$675$	22.5114	−	9.32453i	0.866465	−	0.358902i
$676$		0			0
$677$	17.3078	−	41.7848i	0.665194	−	1.60592i	−0.124360	−	0.992237i	$-0.539688\pi$
$677$	17.3078	−	41.7848i	0.665194	−	1.60592i	0.789553	−	0.613682i	$-0.210312\pi$
$678$		0			0
$679$	−7.07847	−	7.07847i	−0.271647	−	0.271647i
$680$		0			0
$681$	3.28321	−	3.28321i	0.125813	−	0.125813i
$682$		0			0
$683$	−32.0496	−	13.2754i	−1.22634	−	0.507968i	−0.326922	−	0.945051i	$-0.606012\pi$
$683$	−32.0496	−	13.2754i	−1.22634	−	0.507968i	−0.899421	+	0.437083i	$0.856012\pi$
$684$		0			0
$685$	−3.21738	−	7.76744i	−0.122930	−	0.296779i
$686$		0			0
$687$			7.48100i			0.285418i
$688$		0			0
$689$			12.0922i			0.460674i
$690$		0			0
$691$	19.1067	+	46.1276i	0.726852	+	1.75478i	0.652812	+	0.757520i	$0.273589\pi$
$691$	19.1067	+	46.1276i	0.726852	+	1.75478i	0.0740401	+	0.997255i	$0.476411\pi$
$692$		0			0
$693$	9.54882	+	3.95525i	0.362730	+	0.150248i
$694$		0			0
$695$	0.505515	−	0.505515i	0.0191753	−	0.0191753i
$696$		0			0
$697$	1.43208	+	1.43208i	0.0542438	+	0.0542438i
$698$		0			0
$699$	16.7124	−	40.3474i	0.632122	−	1.52608i
$700$		0			0
$701$	12.9050	−	5.34543i	0.487415	−	0.201894i	−0.125422	−	0.992104i	$-0.540028\pi$
$701$	12.9050	−	5.34543i	0.487415	−	0.201894i	0.612837	+	0.790210i	$0.290028\pi$
$702$		0			0
$703$	−33.2933			−1.25568
$704$		0			0
$705$	−1.17157			−0.0441240
$706$		0			0
$707$	−10.6359	+	4.40555i	−0.400006	+	0.165688i
$708$		0			0
$709$	−12.8826	+	31.1013i	−0.483815	+	1.16803i	0.473968	+	0.880542i	$0.342821\pi$
$709$	−12.8826	+	31.1013i	−0.483815	+	1.16803i	−0.957783	+	0.287491i	$0.907179\pi$
$710$		0			0
$711$	29.4149	+	29.4149i	1.10315	+	1.10315i
$712$		0			0
$713$	25.1665	−	25.1665i	0.942492	−	0.942492i
$714$		0			0
$715$	0.730292	+	0.302497i	0.0273114	+	0.0113127i
$716$		0			0
$717$	−19.7390	−	47.6540i	−0.737165	−	1.77967i
$718$		0			0
$719$			0.571168i			0.0213010i	0.999943	+	0.0106505i	$0.00339022\pi$
$719$			0.571168i			0.0213010i	−0.999943	+	0.0106505i	$0.996610\pi$
$720$		0			0
$721$			36.9590i			1.37643i
$722$		0			0
$723$	−30.0261	−	72.4893i	−1.11668	−	2.69591i
$724$		0			0
$725$	25.0020	+	10.3562i	0.928552	+	0.384619i
$726$		0			0
$727$	−23.0479	+	23.0479i	−0.854800	+	0.854800i	−0.990720	−	0.135920i	$-0.956601\pi$
$727$	−23.0479	+	23.0479i	−0.854800	+	0.854800i	0.135920	+	0.990720i	$0.456601\pi$
$728$		0			0
$729$	30.5768	+	30.5768i	1.13247	+	1.13247i
$730$		0			0
$731$	−0.428852	+	1.03534i	−0.0158617	+	0.0382935i
$732$		0			0
$733$	−28.7029	+	11.8891i	−1.06017	+	0.439136i	−0.843511	−	0.537112i	$-0.819515\pi$
$733$	−28.7029	+	11.8891i	−1.06017	+	0.439136i	−0.216656	+	0.976248i	$0.569515\pi$
$734$		0			0
$735$	2.84523			0.104948
$736$		0			0
$737$	−3.38534			−0.124701
$738$		0			0
$739$	−6.94437	+	2.87645i	−0.255453	+	0.105812i	−0.506735	−	0.862102i	$-0.669148\pi$
$739$	−6.94437	+	2.87645i	−0.255453	+	0.105812i	0.251282	+	0.967914i	$0.419148\pi$
$740$		0			0
$741$	−3.96951	+	9.58323i	−0.145823	+	0.352049i
$742$		0			0
$743$	−16.6576	−	16.6576i	−0.611108	−	0.611108i	0.332127	−	0.943235i	$-0.392234\pi$
$743$	−16.6576	−	16.6576i	−0.611108	−	0.611108i	−0.943235	+	0.332127i	$0.892234\pi$
$744$		0			0
$745$	−3.31788	+	3.31788i	−0.121558	+	0.121558i
$746$		0			0
$747$	55.6062	+	23.0328i	2.03452	+	0.842728i
$748$		0			0
$749$	−7.97920	−	19.2635i	−0.291554	−	0.703873i
$750$		0			0
$751$			31.1077i			1.13514i	0.823326	+	0.567569i	$0.192116\pi$
$751$			31.1077i			1.13514i	−0.823326	+	0.567569i	$0.807884\pi$
$752$		0			0
$753$		−	28.6297i		−	1.04332i
$754$		0			0
$755$	−3.38447	−	8.17083i	−0.123173	−	0.297367i
$756$		0			0
$757$	−5.69056	−	2.35711i	−0.206827	−	0.0856705i	0.276865	−	0.960909i	$-0.410704\pi$
$757$	−5.69056	−	2.35711i	−0.206827	−	0.0856705i	−0.483692	+	0.875238i	$0.660704\pi$
$758$		0			0
$759$	−9.09378	+	9.09378i	−0.330083	+	0.330083i
$760$		0			0
$761$	14.2913	+	14.2913i	0.518059	+	0.518059i	0.916984	−	0.398925i	$-0.130617\pi$
$761$	14.2913	+	14.2913i	0.518059	+	0.518059i	−0.398925	+	0.916984i	$0.630617\pi$
$762$		0			0
$763$	8.51196	−	20.5497i	0.308154	−	0.743949i
$764$		0			0
$765$	0.787854	−	0.326340i	0.0284849	−	0.0117988i
$766$		0			0
$767$	4.30071			0.155290
$768$		0			0
$769$	8.95004			0.322747			0.161373	−	0.986893i	$-0.448408\pi$
$769$	8.95004			0.322747			0.161373	+	0.986893i	$0.448408\pi$
$770$		0			0
$771$	52.2924	−	21.6602i	1.88326	−	0.780073i
$772$		0			0
$773$	11.0293	−	26.6270i	0.396695	−	0.957707i	−0.591749	−	0.806122i	$-0.701562\pi$
$773$	11.0293	−	26.6270i	0.396695	−	0.957707i	0.988444	−	0.151585i	$-0.0484377\pi$
$774$		0			0
$775$	−21.3137	−	21.3137i	−0.765611	−	0.765611i
$776$		0			0
$777$	50.8256	−	50.8256i	1.82336	−	1.82336i
$778$		0			0
$779$	25.9256	+	10.7387i	0.928882	+	0.384756i
$780$		0			0
$781$	−2.55624	−	6.17132i	−0.0914695	−	0.220827i
$782$		0			0
$783$		−	33.8408i		−	1.20937i
$784$		0			0
$785$			9.76782i			0.348629i
$786$		0			0
$787$	1.84348	+	4.45056i	0.0657130	+	0.158645i	0.953324	−	0.301948i	$-0.0976368\pi$
$787$	1.84348	+	4.45056i	0.0657130	+	0.158645i	−0.887611	+	0.460593i	$0.847637\pi$
$788$		0			0
$789$	66.2593	+	27.4455i	2.35889	+	0.977086i
$790$		0			0
$791$	−4.08625	+	4.08625i	−0.145290	+	0.145290i
$792$		0			0
$793$	−0.869673	−	0.869673i	−0.0308830	−	0.0308830i
$794$		0			0
$795$	8.46144	−	20.4277i	0.300096	−	0.724497i
$796$		0			0
$797$	36.2064	−	14.9972i	1.28250	−	0.531227i	0.365756	−	0.930711i	$-0.380811\pi$
$797$	36.2064	−	14.9972i	1.28250	−	0.531227i	0.916740	+	0.399484i	$0.130811\pi$
$798$		0			0
$799$	0.121978			0.00431527
$800$		0			0
$801$	41.5444			1.46790
$802$		0			0
$803$	5.89607	−	2.44223i	0.208068	−	0.0861845i
$804$		0			0
$805$	3.63899	−	8.78530i	0.128258	−	0.309641i
$806$		0			0
$807$	55.3980	+	55.3980i	1.95010	+	1.95010i
$808$		0			0
$809$	18.3458	−	18.3458i	0.645005	−	0.645005i	−0.306777	−	0.951782i	$-0.599250\pi$
$809$	18.3458	−	18.3458i	0.645005	−	0.645005i	0.951782	+	0.306777i	$0.0992505\pi$
$810$		0			0
$811$	35.1209	+	14.5476i	1.23326	+	0.510834i	0.901603	−	0.432565i	$-0.142391\pi$
$811$	35.1209	+	14.5476i	1.23326	+	0.510834i	0.331660	+	0.943399i	$0.392391\pi$
$812$		0			0
$813$	17.8028	+	42.9797i	0.624371	+	1.50736i
$814$		0			0
$815$		−	1.50626i		−	0.0527621i
$816$		0			0
$817$			15.5275i			0.543238i
$818$		0			0
$819$	−5.33879	−	12.8890i	−0.186552	−	0.450377i
$820$		0			0
$821$	−24.6248	−	10.1999i	−0.859410	−	0.355979i	−0.0909335	−	0.995857i	$-0.528985\pi$
$821$	−24.6248	−	10.1999i	−0.859410	−	0.355979i	−0.768477	+	0.639877i	$0.778985\pi$
$822$		0			0
$823$	−1.53506	+	1.53506i	−0.0535088	+	0.0535088i	−0.733355	−	0.679846i	$-0.762047\pi$
$823$	−1.53506	+	1.53506i	−0.0535088	+	0.0535088i	0.679846	+	0.733355i	$0.262047\pi$
$824$		0			0
$825$	7.70160	+	7.70160i	0.268135	+	0.268135i
$826$		0			0
$827$	7.71287	−	18.6205i	0.268203	−	0.647499i	−0.731196	−	0.682167i	$-0.761038\pi$
$827$	7.71287	−	18.6205i	0.268203	−	0.647499i	0.999399	+	0.0346687i	$0.0110376\pi$
$828$		0			0
$829$	−24.1110	+	9.98710i	−0.837409	+	0.346866i	−0.759831	−	0.650120i	$-0.774719\pi$
$829$	−24.1110	+	9.98710i	−0.837409	+	0.346866i	−0.0775776	+	0.996986i	$0.524719\pi$
$830$		0			0
$831$	−17.0993			−0.593168
$832$		0			0
$833$	−0.296230			−0.0102638
$834$		0			0
$835$	15.1630	−	6.28074i	0.524739	−	0.217354i
$836$		0			0
$837$	−14.4243	+	34.8233i	−0.498576	+	1.20367i
$838$		0			0
$839$	31.2561	+	31.2561i	1.07908	+	1.07908i	0.996592	+	0.0824901i	$0.0262873\pi$
$839$	31.2561	+	31.2561i	1.07908	+	1.07908i	0.0824901	+	0.996592i	$0.473713\pi$
$840$		0			0
$841$	6.07041	−	6.07041i	0.209324	−	0.209324i
$842$		0			0
$843$	−36.1479	−	14.9729i	−1.24500	−	0.515695i
$844$		0			0
$845$	3.39930	+	8.20664i	0.116940	+	0.282317i
$846$		0			0
$847$		−	24.3970i		−	0.838292i
$848$		0			0
$849$		−	65.2246i		−	2.23850i
$850$		0			0
$851$	21.3220	+	51.4758i	0.730908	+	1.76457i
$852$		0			0
$853$	−18.6692	−	7.73304i	−0.639222	−	0.264774i	0.0394438	−	0.999222i	$-0.487441\pi$
$853$	−18.6692	−	7.73304i	−0.639222	−	0.264774i	−0.678666	+	0.734447i	$0.737441\pi$
$854$		0			0
$855$	8.35503	−	8.35503i	0.285736	−	0.285736i
$856$		0			0
$857$	−4.21699	−	4.21699i	−0.144050	−	0.144050i	0.631404	−	0.775454i	$-0.282479\pi$
$857$	−4.21699	−	4.21699i	−0.144050	−	0.144050i	−0.775454	+	0.631404i	$0.782479\pi$
$858$		0			0
$859$	−13.4192	+	32.3968i	−0.457857	+	1.10536i	0.511407	+	0.859339i	$0.329125\pi$
$859$	−13.4192	+	32.3968i	−0.457857	+	1.10536i	−0.969263	+	0.246025i	$0.920875\pi$
$860$		0			0
$861$	−55.9719	+	23.1843i	−1.90752	+	0.790120i
$862$		0			0
$863$	18.7779			0.639207			0.319604	−	0.947551i	$-0.396450\pi$
$863$	18.7779			0.639207			0.319604	+	0.947551i	$0.396450\pi$
$864$		0			0
$865$	3.76782			0.128110
$866$		0			0
$867$	44.1716	−	18.2965i	1.50015	−	0.621380i
$868$		0			0
$869$	−2.80922	+	6.78206i	−0.0952963	+	0.230066i
$870$		0			0
$871$	3.23114	+	3.23114i	0.109483	+	0.109483i
$872$		0			0
$873$	−14.7195	+	14.7195i	−0.498178	+	0.498178i
$874$		0			0
$875$	−15.8681	−	6.57277i	−0.536439	−	0.222200i
$876$		0			0
$877$	−2.31816	−	5.59652i	−0.0782786	−	0.188981i	0.879895	−	0.475167i	$-0.157612\pi$
$877$	−2.31816	−	5.59652i	−0.0782786	−	0.188981i	−0.958174	+	0.286186i	$0.907612\pi$
$878$		0			0
$879$			62.4121i			2.10511i
$880$		0			0
$881$		−	16.3413i		−	0.550552i	−0.961365	−	0.275276i	$-0.911231\pi$
$881$		−	16.3413i		−	0.550552i	0.961365	−	0.275276i	$-0.0887692\pi$
$882$		0			0
$883$	−0.151958	−	0.366860i	−0.00511380	−	0.0123458i	0.921302	−	0.388848i	$-0.127127\pi$
$883$	−0.151958	−	0.366860i	−0.00511380	−	0.0123458i	−0.926416	+	0.376502i	$0.877127\pi$
$884$		0			0
$885$	−7.26535	−	3.00941i	−0.244222	−	0.101160i
$886$		0			0
$887$	−6.38554	+	6.38554i	−0.214406	+	0.214406i	−0.806136	−	0.591730i	$-0.798445\pi$
$887$	−6.38554	+	6.38554i	−0.214406	+	0.214406i	0.591730	+	0.806136i	$0.298445\pi$
$888$		0			0
$889$	3.69583	+	3.69583i	0.123954	+	0.123954i
$890$		0			0
$891$	0.234313	−	0.565682i	0.00784979	−	0.0189511i
$892$		0			0
$893$	1.56145	−	0.646775i	0.0522521	−	0.0216435i
$894$		0			0
$895$	−6.03011			−0.201564
$896$		0			0
$897$	17.3591			0.579604
$898$		0			0
$899$	−38.6761	+	16.0202i	−1.28992	+	0.534302i
$900$		0			0
$901$	−0.880960	+	2.12682i	−0.0293490	+	0.0708548i
$902$		0			0
$903$	−23.7043	−	23.7043i	−0.788829	−	0.788829i
$904$		0			0
$905$	−8.65685	+	8.65685i	−0.287764	+	0.287764i
$906$		0			0
$907$	−35.3230	−	14.6313i	−1.17288	−	0.485823i	−0.290737	−	0.956803i	$-0.593900\pi$
$907$	−35.3230	−	14.6313i	−1.17288	−	0.485823i	−0.882144	+	0.470980i	$0.843900\pi$
$908$		0			0
$909$	9.16122	+	22.1171i	0.303859	+	0.733579i
$910$		0			0
$911$			30.2904i			1.00356i	0.864994	+	0.501782i	$0.167322\pi$
$911$			30.2904i			1.00356i	−0.864994	+	0.501782i	$0.832678\pi$
$912$		0			0
$913$			10.6211i			0.351509i
$914$		0			0
$915$	0.860620	+	2.07772i	0.0284512	+	0.0686873i
$916$		0			0
$917$	−18.2034	−	7.54011i	−0.601130	−	0.248996i
$918$		0			0
$919$	42.1116	−	42.1116i	1.38913	−	1.38913i	0.561987	−	0.827146i	$-0.310037\pi$
$919$	42.1116	−	42.1116i	1.38913	−	1.38913i	0.827146	−	0.561987i	$-0.189963\pi$
$920$		0			0
$921$	−33.7218	−	33.7218i	−1.11117	−	1.11117i
$922$		0			0
$923$	−3.45041	+	8.33002i	−0.113572	+	0.274186i
$924$		0			0
$925$	43.5953	−	18.0578i	1.43341	−	0.593736i
$926$		0			0
$927$	76.8552			2.52426
$928$		0			0
$929$	25.2271			0.827674			0.413837	−	0.910351i	$-0.364188\pi$
$929$	25.2271			0.827674			0.413837	+	0.910351i	$0.364188\pi$
$930$		0			0
$931$	−3.79208	+	1.57073i	−0.124280	+	0.0514787i
$932$		0			0
$933$	11.0668	−	26.7176i	0.362310	−	0.874694i
$934$		0			0
$935$	0.106409	+	0.106409i	0.00347995	+	0.00347995i
$936$		0			0
$937$	−30.3001	+	30.3001i	−0.989863	+	0.989863i	−0.999949	−	0.0100865i	$-0.996789\pi$
$937$	−30.3001	+	30.3001i	−0.989863	+	0.989863i	0.0100865	+	0.999949i	$0.496789\pi$
$938$		0			0
$939$	37.4437	+	15.5097i	1.22193	+	0.506140i
$940$		0			0
$941$	0.438818	+	1.05940i	0.0143051	+	0.0345355i	0.930871	−	0.365349i	$-0.119050\pi$
$941$	0.438818	+	1.05940i	0.0143051	+	0.0345355i	−0.916566	+	0.399884i	$0.869050\pi$
$942$		0			0
$943$		−	46.9618i		−	1.52929i
$944$		0			0
$945$			10.0707i			0.327599i
$946$		0			0
$947$	−10.4790	−	25.2985i	−0.340520	−	0.822089i	−0.997663	−	0.0683231i	$-0.978235\pi$
$947$	−10.4790	−	25.2985i	−0.340520	−	0.822089i	0.657143	−	0.753766i	$-0.271765\pi$
$948$		0			0
$949$	−7.95850	−	3.29652i	−0.258344	−	0.107009i
$950$		0			0
$951$	−6.99925	+	6.99925i	−0.226966	+	0.226966i
$952$		0			0
$953$	−8.84307	−	8.84307i	−0.286455	−	0.286455i	0.549222	−	0.835677i	$-0.314924\pi$
$953$	−8.84307	−	8.84307i	−0.286455	−	0.286455i	−0.835677	+	0.549222i	$0.814924\pi$
$954$		0			0
$955$	−4.52936	+	10.9348i	−0.146567	+	0.353843i
$956$		0			0
$957$	13.9754	−	5.78880i	0.451761	−	0.187125i
$958$		0			0
$959$	−26.1847			−0.845549
$960$		0			0
$961$	15.6274			0.504110
$962$		0			0
$963$	−40.0579	+	16.5925i	−1.29085	+	0.534686i
$964$		0			0
$965$	−3.87222	+	9.34838i	−0.124651	+	0.300935i
$966$		0			0
$967$	−33.2189	−	33.2189i	−1.06825	−	1.06825i	−0.997494	−	0.0707549i	$-0.977459\pi$
$967$	−33.2189	−	33.2189i	−1.06825	−	1.06825i	−0.0707549	−	0.997494i	$-0.522541\pi$
$968$		0			0
$969$	−1.39635	+	1.39635i	−0.0448572	+	0.0448572i
$970$		0			0
$971$	2.81729	+	1.16696i	0.0904111	+	0.0374495i	0.427431	−	0.904048i	$-0.359419\pi$
$971$	2.81729	+	1.16696i	0.0904111	+	0.0374495i	−0.337019	+	0.941498i	$0.609419\pi$
$972$		0			0
$973$	−0.852067	−	2.05707i	−0.0273160	−	0.0659467i
$974$		0			0
$975$		−	14.7016i		−	0.470828i
$976$		0			0
$977$			13.5807i			0.434484i	0.976118	+	0.217242i	$0.0697061\pi$
$977$			13.5807i			0.434484i	−0.976118	+	0.217242i	$0.930294\pi$
$978$		0			0
$979$	2.80553	+	6.77316i	0.0896653	+	0.216471i
$980$		0			0
$981$	−42.7325	−	17.7004i	−1.36434	−	0.565130i
$982$		0			0
$983$	−29.0855	+	29.0855i	−0.927684	+	0.927684i	−0.997556	−	0.0698724i	$-0.977741\pi$
$983$	−29.0855	+	29.0855i	−0.927684	+	0.927684i	0.0698724	+	0.997556i	$0.477741\pi$
$984$		0			0
$985$	0.353225	+	0.353225i	0.0112547	+	0.0112547i
$986$		0			0
$987$	−1.39635	+	3.37109i	−0.0444463	+	0.107303i
$988$		0			0
$989$	24.0075	−	9.94424i	0.763395	−	0.316209i
$990$		0			0
$991$	−6.64680			−0.211143			−0.105571	−	0.994412i	$-0.533667\pi$
$991$	−6.64680			−0.211143			−0.105571	+	0.994412i	$0.533667\pi$
$992$		0			0
$993$	−47.4160			−1.50470
$994$		0			0
$995$	1.86490	−	0.772467i	0.0591213	−	0.0244889i
$996$		0			0
$997$	−18.2353	+	44.0238i	−0.577516	+	1.39425i	0.317519	+	0.948252i	$0.397150\pi$
$997$	−18.2353	+	44.0238i	−0.577516	+	1.39425i	−0.895035	+	0.445996i	$0.852850\pi$
$998$		0			0
$999$	−41.7244	−	41.7244i	−1.32010	−	1.32010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.g.g.193.2		8
4.3	odd	2		512.2.g.e.193.1		8
8.3	odd	2		512.2.g.h.193.2		8
8.5	even	2		512.2.g.f.193.1		8
16.3	odd	4		32.2.g.b.5.1	✓	8
16.5	even	4		256.2.g.c.225.1		8
16.11	odd	4		256.2.g.d.225.2		8
16.13	even	4		128.2.g.b.113.2		8
32.3	odd	8		512.2.g.e.321.1		8
32.5	even	8		256.2.g.c.33.1		8
32.11	odd	8		32.2.g.b.13.1	yes	8
32.13	even	8		512.2.g.f.321.1		8
32.19	odd	8		512.2.g.h.321.2		8
32.21	even	8		128.2.g.b.17.2		8
32.27	odd	8		256.2.g.d.33.2		8
32.29	even	8	inner	512.2.g.g.321.2		8
48.29	odd	4		1152.2.v.b.1009.1		8
48.35	even	4		288.2.v.b.37.2		8
64.3	odd	16		4096.2.a.k.1.8		8
64.29	even	16		4096.2.a.q.1.8		8
64.35	odd	16		4096.2.a.k.1.1		8
64.61	even	16		4096.2.a.q.1.1		8
80.3	even	4		800.2.ba.d.549.1		8
80.19	odd	4		800.2.y.b.101.2		8
80.67	even	4		800.2.ba.c.549.2		8
96.11	even	8		288.2.v.b.109.2		8
96.53	odd	8		1152.2.v.b.145.1		8
160.43	even	8		800.2.ba.c.749.2		8
160.107	even	8		800.2.ba.d.749.1		8
160.139	odd	8		800.2.y.b.301.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.5.1	✓	8	16.3	odd	4
32.2.g.b.13.1	yes	8	32.11	odd	8
128.2.g.b.17.2		8	32.21	even	8
128.2.g.b.113.2		8	16.13	even	4
256.2.g.c.33.1		8	32.5	even	8
256.2.g.c.225.1		8	16.5	even	4
256.2.g.d.33.2		8	32.27	odd	8
256.2.g.d.225.2		8	16.11	odd	4
288.2.v.b.37.2		8	48.35	even	4
288.2.v.b.109.2		8	96.11	even	8
512.2.g.e.193.1		8	4.3	odd	2
512.2.g.e.321.1		8	32.3	odd	8
512.2.g.f.193.1		8	8.5	even	2
512.2.g.f.321.1		8	32.13	even	8
512.2.g.g.193.2		8	1.1	even	1	trivial
512.2.g.g.321.2		8	32.29	even	8	inner
512.2.g.h.193.2		8	8.3	odd	2
512.2.g.h.321.2		8	32.19	odd	8
800.2.y.b.101.2		8	80.19	odd	4
800.2.y.b.301.2		8	160.139	odd	8
800.2.ba.c.549.2		8	80.67	even	4
800.2.ba.c.749.2		8	160.43	even	8
800.2.ba.d.549.1		8	80.3	even	4
800.2.ba.d.749.1		8	160.107	even	8
1152.2.v.b.145.1		8	96.53	odd	8
1152.2.v.b.1009.1		8	48.29	odd	4
4096.2.a.k.1.1		8	64.35	odd	16
4096.2.a.k.1.8		8	64.3	odd	16
4096.2.a.q.1.1		8	64.61	even	16
4096.2.a.q.1.8		8	64.29	even	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)

\(f(q)\)	\(=\)	\(q+(2.60607 - 1.07947i) q^{3} +(-0.292893 + 0.707107i) q^{5} +(1.68554 + 1.68554i) q^{7} +(3.50504 - 3.50504i) q^{9} +O(q^{10})\)	\(q+(2.60607 - 1.07947i) q^{3} +(-0.292893 + 0.707107i) q^{5} +(1.68554 + 1.68554i) q^{7} +(3.50504 - 3.50504i) q^{9} +(0.808140 + 0.334743i) q^{11} +(-0.451835 - 1.09083i) q^{13} +2.15894i q^{15} -0.224777i q^{17} +(-1.19186 - 2.87740i) q^{19} +(6.21215 + 2.57316i) q^{21} +(-3.68554 + 3.68554i) q^{23} +(3.12132 + 3.12132i) q^{25} +(2.11239 - 5.09976i) q^{27} +(5.66398 - 2.34610i) q^{29} -6.82843 q^{31} +2.46742 q^{33} +(-1.68554 + 0.698175i) q^{35} +(4.09083 - 9.87613i) q^{37} +(-2.35503 - 2.35503i) q^{39} +(-6.37109 + 6.37109i) q^{41} +(-4.60607 - 1.90790i) q^{43} +(1.45183 + 3.50504i) q^{45} +0.542661i q^{47} -1.31788i q^{49} +(-0.242641 - 0.585786i) q^{51} +(-9.46191 - 3.91925i) q^{53} +(-0.473398 + 0.473398i) q^{55} +(-6.21215 - 6.21215i) q^{57} +(-1.39393 + 3.36524i) q^{59} +(0.962379 - 0.398630i) q^{61} +11.8158 q^{63} +0.903670 q^{65} +(-3.57558 + 1.48105i) q^{67} +(-5.62636 + 13.5832i) q^{69} +(-5.39978 - 5.39978i) q^{71} +(5.15894 - 5.15894i) q^{73} +(11.5038 + 4.76501i) q^{75} +(0.797933 + 1.92638i) q^{77} +8.39218i q^{79} -0.699980i q^{81} +(4.64665 + 11.2180i) q^{83} +(0.158942 + 0.0658358i) q^{85} +(12.2282 - 12.2282i) q^{87} +(5.92638 + 5.92638i) q^{89} +(1.07705 - 2.60022i) q^{91} +(-17.7954 + 7.37109i) q^{93} +2.38372 q^{95} -4.19951 q^{97} +(4.00585 - 1.65928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 8 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q + 4 * q^3 - 8 * q^5 - 8 * q^7	\( 8 q + 4 q^{3} - 8 q^{5} - 8 q^{7} + 12 q^{11} - 4 q^{19} + 16 q^{21} - 8 q^{23} + 8 q^{25} + 16 q^{27} + 8 q^{29} - 32 q^{31} - 16 q^{33} + 8 q^{35} + 16 q^{37} + 16 q^{39} - 8 q^{41} - 20 q^{43} + 8 q^{45} + 32 q^{51} - 16 q^{53} - 16 q^{55} - 16 q^{57} - 28 q^{59} + 40 q^{63} - 12 q^{67} - 24 q^{71} + 32 q^{73} + 20 q^{75} - 16 q^{77} - 36 q^{83} - 8 q^{85} + 56 q^{87} + 16 q^{89} - 32 q^{93} + 8 q^{95} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 8 * q^5 - 8 * q^7 + 12 * q^11 - 4 * q^19 + 16 * q^21 - 8 * q^23 + 8 * q^25 + 16 * q^27 + 8 * q^29 - 32 * q^31 - 16 * q^33 + 8 * q^35 + 16 * q^37 + 16 * q^39 - 8 * q^41 - 20 * q^43 + 8 * q^45 + 32 * q^51 - 16 * q^53 - 16 * q^55 - 16 * q^57 - 28 * q^59 + 40 * q^63 - 12 * q^67 - 24 * q^71 + 32 * q^73 + 20 * q^75 - 16 * q^77 - 36 * q^83 - 8 * q^85 + 56 * q^87 + 16 * q^89 - 32 * q^93 + 8 * q^95 + 32 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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