LMFDB - Embedded newform 256.2.g.c.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(33,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, 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("256.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.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:	$2.04417029174$
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			225.1
Root			$0.500000 - 2.10607i$ of defining polynomial
Character	$\chi$	$=$	256.225
Dual form			256.2.g.c.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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
$3$	−1.07947	−	2.60607i	−0.623233	−	1.50462i	−0.847886	−	0.530178i	$-0.822125\pi$
$3$	−1.07947	−	2.60607i	−0.623233	−	1.50462i	0.224653	−	0.974439i	$-0.427875\pi$
$4$		0			0
$5$	−0.707107	−	0.292893i	−0.316228	−	0.130986i	0.218924	−	0.975742i	$-0.429745\pi$
$5$	−0.707107	−	0.292893i	−0.316228	−	0.130986i	−0.535151	+	0.844756i	$0.679745\pi$
$6$		0			0
$7$	−1.68554	−	1.68554i	−0.637076	−	0.637076i	0.312757	−	0.949833i	$-0.398747\pi$
$7$	−1.68554	−	1.68554i	−0.637076	−	0.637076i	−0.949833	+	0.312757i	$0.898747\pi$
$8$		0			0
$9$	−3.50504	+	3.50504i	−1.16835	+	1.16835i
$10$		0			0
$11$	−0.334743	+	0.808140i	−0.100929	+	0.243664i	−0.966276	−	0.257510i	$-0.917098\pi$
$11$	−0.334743	+	0.808140i	−0.100929	+	0.243664i	0.865347	+	0.501173i	$0.167098\pi$
$12$		0			0
$13$	−1.09083	+	0.451835i	−0.302541	+	0.125316i	−0.528789	−	0.848753i	$-0.677354\pi$
$13$	−1.09083	+	0.451835i	−0.302541	+	0.125316i	0.226249	+	0.974070i	$0.427354\pi$
$14$		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
$19$	−2.87740	+	1.19186i	−0.660122	+	0.273431i	−0.687490	−	0.726194i	$-0.741287\pi$
$19$	−2.87740	+	1.19186i	−0.660122	+	0.273431i	0.0273681	+	0.999625i	$0.491287\pi$
$20$		0			0
$21$	−2.57316	+	6.21215i	−0.561509	+	1.35560i
$22$		0			0
$23$	3.68554	−	3.68554i	0.768489	−	0.768489i	−0.209351	−	0.977840i	$-0.567135\pi$
$23$	3.68554	−	3.68554i	0.768489	−	0.768489i	0.977840	+	0.209351i	$0.0671353\pi$
$24$		0			0
$25$	−3.12132	−	3.12132i	−0.624264	−	0.624264i
$26$		0			0
$27$	5.09976	+	2.11239i	0.981449	+	0.406529i
$28$		0			0
$29$	−2.34610	−	5.66398i	−0.435659	−	1.05177i	−0.977432	−	0.211250i	$-0.932247\pi$
$29$	−2.34610	−	5.66398i	−0.435659	−	1.05177i	0.541773	−	0.840525i	$-0.317753\pi$
$30$		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
$35$	0.698175	+	1.68554i	0.118013	+	0.284909i
$36$		0			0
$37$	9.87613	+	4.09083i	1.62363	+	0.672528i	0.994496	−	0.104773i	$-0.0334116\pi$
$37$	9.87613	+	4.09083i	1.62363	+	0.672528i	0.629129	+	0.777301i	$0.283412\pi$
$38$		0			0
$39$	2.35503	+	2.35503i	0.377107	+	0.377107i
$40$		0			0
$41$	6.37109	−	6.37109i	0.994997	−	0.994997i	−0.00499079	−	0.999988i	$-0.501589\pi$
$41$	6.37109	−	6.37109i	0.994997	−	0.994997i	0.999988	+	0.00499079i	$0.00158862\pi$
$42$		0			0
$43$	1.90790	−	4.60607i	0.290952	−	0.702420i	−0.709045	−	0.705164i	$-0.750873\pi$
$43$	1.90790	−	4.60607i	0.290952	−	0.702420i	0.999996	+	0.00274415i	$0.000873491\pi$
$44$		0			0
$45$	3.50504	−	1.45183i	0.522500	−	0.216427i
$46$		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
$51$	−0.585786	+	0.242641i	−0.0820265	+	0.0339765i
$52$		0			0
$53$	3.91925	−	9.46191i	0.538351	−	1.29969i	−0.387523	−	0.921860i	$-0.626669\pi$
$53$	3.91925	−	9.46191i	0.538351	−	1.29969i	0.925873	−	0.377834i	$-0.123331\pi$
$54$		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
$59$	−3.36524	−	1.39393i	−0.438117	−	0.181474i	0.152712	−	0.988271i	$-0.451199\pi$
$59$	−3.36524	−	1.39393i	−0.438117	−	0.181474i	−0.590829	+	0.806797i	$0.701199\pi$
$60$		0			0
$61$	−0.398630	−	0.962379i	−0.0510394	−	0.123220i	0.896303	−	0.443442i	$-0.146243\pi$
$61$	−0.398630	−	0.962379i	−0.0510394	−	0.123220i	−0.947343	+	0.320222i	$0.896243\pi$
$62$		0			0
$63$	11.8158			1.48865
$64$		0			0
$65$	0.903670			0.112086
$66$		0			0
$67$	1.48105	+	3.57558i	0.180939	+	0.436826i	0.988161	−	0.153423i	$-0.0490296\pi$
$67$	1.48105	+	3.57558i	0.180939	+	0.436826i	−0.807221	+	0.590249i	$0.799030\pi$
$68$		0			0
$69$	−13.5832	−	5.62636i	−1.63523	−	0.677334i
$70$		0			0
$71$	5.39978	+	5.39978i	0.640836	+	0.640836i	0.950761	−	0.309925i	$-0.100304\pi$
$71$	5.39978	+	5.39978i	0.640836	+	0.640836i	−0.309925	+	0.950761i	$0.600304\pi$
$72$		0			0
$73$	−5.15894	+	5.15894i	−0.603808	+	0.603808i	−0.941321	−	0.337513i	$-0.890414\pi$
$73$	−5.15894	+	5.15894i	−0.603808	+	0.603808i	0.337513	+	0.941321i	$0.390414\pi$
$74$		0			0
$75$	−4.76501	+	11.5038i	−0.550217	+	1.32834i
$76$		0			0
$77$	1.92638	−	0.797933i	0.219531	−	0.0909329i
$78$		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
$83$	11.2180	−	4.64665i	1.23134	−	0.510036i	0.330339	−	0.943862i	$-0.392837\pi$
$83$	11.2180	−	4.64665i	1.23134	−	0.510036i	0.900996	+	0.433827i	$0.142837\pi$
$84$		0			0
$85$	−0.0658358	+	0.158942i	−0.00714089	+	0.0172396i
$86$		0			0
$87$	−12.2282	+	12.2282i	−1.31100	+	1.31100i
$88$		0			0
$89$	−5.92638	−	5.92638i	−0.628195	−	0.628195i	0.319419	−	0.947614i	$-0.396512\pi$
$89$	−5.92638	−	5.92638i	−0.628195	−	0.628195i	−0.947614	+	0.319419i	$0.896512\pi$
$90$		0			0
$91$	2.60022	+	1.07705i	0.272577	+	0.112905i
$92$		0			0
$93$	7.37109	+	17.7954i	0.764346	+	1.84529i
$94$		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
$99$	−1.65928	−	4.00585i	−0.166764	−	0.402603i
$100$		0			0
$101$	−4.46191	−	1.84819i	−0.443977	−	0.183901i	0.149484	−	0.988764i	$-0.452239\pi$
$101$	−4.46191	−	1.84819i	−0.443977	−	0.183901i	−0.593461	+	0.804863i	$0.702239\pi$
$102$		0			0
$103$	−10.9635	−	10.9635i	−1.08027	−	1.08027i	−0.996484	−	0.0837844i	$-0.973299\pi$
$103$	−10.9635	−	10.9635i	−1.08027	−	1.08027i	−0.0837844	−	0.996484i	$-0.526701\pi$
$104$		0			0
$105$	3.63899	−	3.63899i	0.355129	−	0.355129i
$106$		0			0
$107$	3.34737	−	8.08128i	0.323603	−	0.781246i	−0.675436	−	0.737418i	$-0.736045\pi$
$107$	3.34737	−	8.08128i	0.323603	−	0.781246i	0.999039	−	0.0438280i	$-0.0139554\pi$
$108$		0			0
$109$	−8.62086	+	3.57088i	−0.825728	+	0.342028i	−0.755210	−	0.655483i	$-0.772465\pi$
$109$	−8.62086	+	3.57088i	−0.825728	+	0.342028i	−0.0705180	+	0.997511i	$0.522465\pi$
$110$		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
$115$	−3.68554	+	1.52660i	−0.343679	+	0.142356i
$116$		0			0
$117$	2.23969	−	5.40709i	0.207059	−	0.499885i
$118$		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
$123$	−23.4809	−	9.72612i	−2.11720	−	0.876974i
$124$		0			0
$125$	2.75736	+	6.65685i	0.246626	+	0.595407i
$126$		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
$131$	3.16317	+	7.63657i	0.276367	+	0.667210i	0.999729	−	0.0232589i	$-0.00740422\pi$
$131$	3.16317	+	7.63657i	0.276367	+	0.667210i	−0.723362	+	0.690469i	$0.757404\pi$
$132$		0			0
$133$	6.85892	+	2.84106i	0.594744	+	0.246351i
$134$		0			0
$135$	−2.98737	−	2.98737i	−0.257112	−	0.257112i
$136$		0			0
$137$	7.76744	−	7.76744i	0.663617	−	0.663617i	−0.292614	−	0.956231i	$-0.594525\pi$
$137$	7.76744	−	7.76744i	0.663617	−	0.663617i	0.956231	+	0.292614i	$0.0945250\pi$
$138$		0			0
$139$	0.357453	−	0.862967i	0.0303188	−	0.0731959i	−0.907995	−	0.418981i	$-0.862387\pi$
$139$	0.357453	−	0.862967i	0.0303188	−	0.0731959i	0.938314	+	0.345785i	$0.112387\pi$
$140$		0			0
$141$	1.41421	−	0.585786i	0.119098	−	0.0493321i
$142$		0			0
$143$		−	1.03279i		−	0.0863662i
$144$		0			0
$145$			4.69220i			0.389666i
$146$		0			0
$147$	−3.43450	+	1.42262i	−0.283273	+	0.117335i
$148$		0			0
$149$	−2.34610	+	5.66398i	−0.192200	+	0.464011i	−0.990374	−	0.138415i	$-0.955799\pi$
$149$	−2.34610	+	5.66398i	−0.192200	+	0.464011i	0.798175	+	0.602426i	$0.205799\pi$
$150$		0			0
$151$	8.17083	−	8.17083i	0.664932	−	0.664932i	−0.291606	−	0.956538i	$-0.594190\pi$
$151$	8.17083	−	8.17083i	0.664932	−	0.664932i	0.956538	+	0.291606i	$0.0941897\pi$
$152$		0			0
$153$	0.787854	+	0.787854i	0.0636942	+	0.0636942i
$154$		0			0
$155$	4.82843	+	2.00000i	0.387829	+	0.160644i
$156$		0			0
$157$	−4.88391	−	11.7908i	−0.389779	−	0.941009i	−0.989986	−	0.141164i	$-0.954915\pi$
$157$	−4.88391	−	11.7908i	−0.389779	−	0.941009i	0.600208	−	0.799844i	$-0.295085\pi$
$158$		0			0
$159$	−28.8892			−2.29106
$160$		0			0
$161$	−12.4243			−0.979171
$162$		0			0
$163$	0.753131	+	1.81822i	0.0589898	+	0.142414i	0.950626	−	0.310338i	$-0.100442\pi$
$163$	0.753131	+	1.81822i	0.0589898	+	0.142414i	−0.891636	+	0.452752i	$0.850442\pi$
$164$		0			0
$165$	−1.74473	−	0.722690i	−0.135827	−	0.0562613i
$166$		0			0
$167$	15.1630	+	15.1630i	1.17335	+	1.17335i	0.981406	+	0.191946i	$0.0614798\pi$
$167$	15.1630	+	15.1630i	1.17335	+	1.17335i	0.191946	+	0.981406i	$0.438520\pi$
$168$		0			0
$169$	−8.20664	+	8.20664i	−0.631280	+	0.631280i
$170$		0			0
$171$	5.90790	−	14.2629i	0.451788	−	1.09071i
$172$		0			0
$173$	−4.54817	+	1.88391i	−0.345791	+	0.143231i	−0.548818	−	0.835942i	$-0.684922\pi$
$173$	−4.54817	+	1.88391i	−0.345791	+	0.143231i	0.203027	+	0.979173i	$0.434922\pi$
$174$		0			0
$175$			10.5222i			0.795407i
$176$		0			0
$177$			10.2748i			0.772298i
$178$		0			0
$179$	7.27899	−	3.01505i	0.544057	−	0.225356i	−0.0936904	−	0.995601i	$-0.529866\pi$
$179$	7.27899	−	3.01505i	0.544057	−	0.225356i	0.637747	+	0.770246i	$0.279866\pi$
$180$		0			0
$181$	−6.12132	+	14.7782i	−0.454994	+	1.09845i	0.515405	+	0.856947i	$0.327641\pi$
$181$	−6.12132	+	14.7782i	−0.454994	+	1.09845i	−0.970399	+	0.241506i	$0.922359\pi$
$182$		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
$187$	0.181652	+	0.0752426i	0.0132837	+	0.00550228i
$188$		0			0
$189$	−5.03534	−	12.1564i	−0.366267	−	0.884247i
$190$		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
$195$	−0.975485	−	2.35503i	−0.0698559	−	0.168647i
$196$		0			0
$197$	0.602992	+	0.249768i	0.0429614	+	0.0177952i	0.404061	−	0.914732i	$-0.367598\pi$
$197$	0.602992	+	0.249768i	0.0429614	+	0.0177952i	−0.361099	+	0.932527i	$0.617598\pi$
$198$		0			0
$199$	1.86490	+	1.86490i	0.132199	+	0.132199i	0.770110	−	0.637911i	$-0.220201\pi$
$199$	1.86490	+	1.86490i	0.132199	+	0.132199i	−0.637911	+	0.770110i	$0.720201\pi$
$200$		0			0
$201$	7.71947	−	7.71947i	0.544489	−	0.544489i
$202$		0			0
$203$	−5.59244	+	13.5013i	−0.392512	+	0.947608i
$204$		0			0
$205$	−6.37109	+	2.63899i	−0.444976	+	0.184315i
$206$		0			0
$207$			25.8360i			1.79572i
$208$		0			0
$209$		−	2.72431i		−	0.188445i
$210$		0			0
$211$	−19.0338	+	7.88406i	−1.31034	+	0.542761i	−0.924984	−	0.380007i	$-0.875922\pi$
$211$	−19.0338	+	7.88406i	−1.31034	+	0.542761i	−0.385357	+	0.922768i	$0.625922\pi$
$212$		0			0
$213$	8.24331	−	19.9011i	0.564822	−	1.36360i
$214$		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
$219$	19.0135	+	7.87565i	1.28481	+	0.532187i
$220$		0			0
$221$	0.101562	+	0.245193i	0.00683182	+	0.0164935i
$222$		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
$227$	−0.629916	−	1.52075i	−0.0418090	−	0.100936i	0.901596	−	0.432580i	$-0.142397\pi$
$227$	−0.629916	−	1.52075i	−0.0418090	−	0.100936i	−0.943405	+	0.331644i	$0.892397\pi$
$228$		0			0
$229$	−2.45021	−	1.01491i	−0.161915	−	0.0670672i	0.300254	−	0.953859i	$-0.402929\pi$
$229$	−2.45021	−	1.01491i	−0.161915	−	0.0670672i	−0.462169	+	0.886792i	$0.652929\pi$
$230$		0			0
$231$	−4.15894	−	4.15894i	−0.273638	−	0.273638i
$232$		0			0
$233$	−10.9475	+	10.9475i	−0.717192	+	0.717192i	−0.968029	−	0.250837i	$-0.919294\pi$
$233$	−10.9475	+	10.9475i	−0.717192	+	0.717192i	0.250837	+	0.968029i	$0.419294\pi$
$234$		0			0
$235$	0.158942	−	0.383719i	0.0103682	−	0.0250311i
$236$		0			0
$237$	21.8706	−	9.05911i	1.42065	−	0.588452i
$238$		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
$243$	13.4751	−	5.58156i	0.864426	−	0.358057i
$244$		0			0
$245$	−0.385999	+	0.931884i	−0.0246606	+	0.0595359i
$246$		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
$251$	9.37694	+	3.88406i	0.591867	+	0.245159i	0.658454	−	0.752621i	$-0.271211\pi$
$251$	9.37694	+	3.88406i	0.591867	+	0.245159i	−0.0665866	+	0.997781i	$0.521211\pi$
$252$		0			0
$253$	1.74473	+	4.21215i	0.109690	+	0.264815i
$254$		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
$259$	−9.75138	−	23.5419i	−0.605921	−	1.46282i
$260$		0			0
$261$	28.0756	+	11.6293i	1.73784	+	0.719836i
$262$		0			0
$263$	−17.9782	−	17.9782i	−1.10858	−	1.10858i	−0.993337	−	0.115244i	$-0.963235\pi$
$263$	−17.9782	−	17.9782i	−1.10858	−	1.10858i	−0.115244	−	0.993337i	$-0.536765\pi$
$264$		0			0
$265$	−5.54266	+	5.54266i	−0.340483	+	0.340483i
$266$		0			0
$267$	−9.04722	+	21.8419i	−0.553681	+	1.33670i
$268$		0			0
$269$	25.6598	−	10.6286i	1.56451	−	0.648040i	0.578641	−	0.815582i	$-0.303583\pi$
$269$	25.6598	−	10.6286i	1.56451	−	0.648040i	0.985865	+	0.167543i	$0.0535832\pi$
$270$		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
$275$	3.56730	−	1.47763i	0.215117	−	0.0891042i
$276$		0			0
$277$	2.31978	−	5.60044i	0.139382	−	0.336498i	−0.838739	−	0.544533i	$-0.816707\pi$
$277$	2.31978	−	5.60044i	0.139382	−	0.336498i	0.978121	+	0.208035i	$0.0667069\pi$
$278$		0			0
$279$	23.9339	−	23.9339i	1.43289	−	1.43289i
$280$		0			0
$281$	9.80801	+	9.80801i	0.585097	+	0.585097i	0.936299	−	0.351203i	$-0.114227\pi$
$281$	9.80801	+	9.80801i	0.585097	+	0.585097i	−0.351203	+	0.936299i	$0.614227\pi$
$282$		0			0
$283$	21.3627	+	8.84871i	1.26988	+	0.526001i	0.912928	−	0.408121i	$-0.133816\pi$
$283$	21.3627	+	8.84871i	1.26988	+	0.526001i	0.356952	+	0.934123i	$0.383816\pi$
$284$		0			0
$285$	−2.57316	−	6.21215i	−0.152421	−	0.367976i
$286$		0			0
$287$	−21.4775			−1.26778
$288$		0			0
$289$	16.9495			0.997028
$290$		0			0
$291$	4.53325	+	10.9442i	0.265744	+	0.641563i
$292$		0			0
$293$	−20.4415	−	8.46715i	−1.19421	−	0.494656i	−0.305083	−	0.952326i	$-0.598684\pi$
$293$	−20.4415	−	8.46715i	−1.19421	−	0.494656i	−0.889122	+	0.457670i	$0.848684\pi$
$294$		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
$299$	−2.35503	+	5.68554i	−0.136195	+	0.328803i
$300$		0			0
$301$	−10.9796	+	4.54789i	−0.632853	+	0.262136i
$302$		0			0
$303$			13.6231i			0.782629i
$304$		0			0
$305$			0.797261i			0.0456510i
$306$		0			0
$307$	−15.6196	+	6.46984i	−0.891456	+	0.369253i	−0.780929	−	0.624620i	$-0.785254\pi$
$307$	−15.6196	+	6.46984i	−0.891456	+	0.369253i	−0.110527	+	0.993873i	$0.535254\pi$
$308$		0			0
$309$	−16.7369	+	40.4066i	−0.952131	+	2.29865i
$310$		0			0
$311$	−7.24929	+	7.24929i	−0.411070	+	0.411070i	−0.882111	−	0.471041i	$-0.843878\pi$
$311$	−7.24929	+	7.24929i	−0.411070	+	0.411070i	0.471041	+	0.882111i	$0.343878\pi$
$312$		0			0
$313$	−10.1596	−	10.1596i	−0.574255	−	0.574255i	0.359059	−	0.933315i	$-0.383098\pi$
$313$	−10.1596	−	10.1596i	−0.574255	−	0.574255i	−0.933315	+	0.359059i	$0.883098\pi$
$314$		0			0
$315$	−8.35503	−	3.46077i	−0.470753	−	0.194992i
$316$		0			0
$317$	1.34287	+	3.24198i	0.0754233	+	0.182088i	0.957094	−	0.289777i	$-0.0935811\pi$
$317$	1.34287	+	3.24198i	0.0754233	+	0.182088i	−0.881671	+	0.471865i	$0.843581\pi$
$318$		0			0
$319$	5.36263			0.300250
$320$		0			0
$321$	−24.6738			−1.37716
$322$		0			0
$323$	0.267903	+	0.646775i	0.0149065	+	0.0359875i
$324$		0			0
$325$	4.81514	+	1.99450i	0.267096	+	0.110635i
$326$		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
$331$	6.43270	−	15.5299i	0.353573	−	0.853601i	−0.642600	−	0.766201i	$-0.722144\pi$
$331$	6.43270	−	15.5299i	0.353573	−	0.853601i	0.996173	−	0.0873991i	$-0.0278555\pi$
$332$		0			0
$333$	−48.9547	+	20.2777i	−2.68270	+	1.11121i
$334$		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
$339$	6.31788	−	2.61695i	0.343140	−	0.142133i
$340$		0			0
$341$	2.28577	−	5.51833i	0.123781	−	0.298834i
$342$		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
$347$	−12.3896	−	5.13193i	−0.665107	−	0.275496i	0.0244788	−	0.999700i	$-0.492207\pi$
$347$	−12.3896	−	5.13193i	−0.665107	−	0.275496i	−0.689586	+	0.724204i	$0.742207\pi$
$348$		0			0
$349$	−7.52453	−	18.1658i	−0.402779	−	0.972394i	−0.986988	−	0.160791i	$-0.948596\pi$
$349$	−7.52453	−	18.1658i	−0.402779	−	0.972394i	0.584210	−	0.811603i	$-0.301404\pi$
$350$		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
$355$	−2.23666	−	5.39978i	−0.118710	−	0.286590i
$356$		0			0
$357$	1.39635	+	0.578387i	0.0739027	+	0.0306115i
$358$		0			0
$359$	−6.39199	−	6.39199i	−0.337356	−	0.337356i	0.518015	−	0.855372i	$-0.326671\pi$
$359$	−6.39199	−	6.39199i	−0.337356	−	0.337356i	−0.855372	+	0.518015i	$0.826671\pi$
$360$		0			0
$361$	−6.57611	+	6.57611i	−0.346111	+	0.346111i
$362$		0			0
$363$	11.0482	−	26.6728i	0.579882	−	1.39996i
$364$		0			0
$365$	5.15894	−	2.13690i	0.270031	−	0.111851i
$366$		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
$371$	−22.5545	+	9.34240i	−1.17097	+	0.485033i
$372$		0			0
$373$	6.03762	−	14.5761i	0.312616	−	0.754722i	−0.686990	−	0.726667i	$-0.741068\pi$
$373$	6.03762	−	14.5761i	0.312616	−	0.754722i	0.999606	−	0.0280555i	$-0.00893152\pi$
$374$		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
$379$	−5.68312	−	2.35403i	−0.291922	−	0.120918i	0.231916	−	0.972736i	$-0.425500\pi$
$379$	−5.68312	−	2.35403i	−0.291922	−	0.120918i	−0.523839	+	0.851818i	$0.675500\pi$
$380$		0			0
$381$	−2.36691	−	5.71423i	−0.121261	−	0.292749i
$382$		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
$387$	9.45721	+	22.8317i	0.480737	+	1.16060i
$388$		0			0
$389$	14.1298	+	5.85275i	0.716408	+	0.296746i	0.710953	−	0.703239i	$-0.248264\pi$
$389$	14.1298	+	5.85275i	0.716408	+	0.296746i	0.00545476	+	0.999985i	$0.498264\pi$
$390$		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
$395$	2.45801	−	5.93416i	0.123676	−	0.298580i
$396$		0			0
$397$	25.5736	−	10.5929i	1.28350	−	0.531643i	0.366458	−	0.930434i	$-0.380570\pi$
$397$	25.5736	−	10.5929i	1.28350	−	0.531643i	0.917042	+	0.398791i	$0.130570\pi$
$398$		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
$403$	7.44862	−	3.08532i	0.371042	−	0.153691i
$404$		0			0
$405$	−0.205019	+	0.494961i	−0.0101875	+	0.0245948i
$406$		0			0
$407$	−6.61192	+	6.61192i	−0.327741	+	0.327741i
$408$		0			0
$409$	1.28577	+	1.28577i	0.0635771	+	0.0635771i	0.738180	−	0.674603i	$-0.235685\pi$
$409$	1.28577	+	1.28577i	0.0635771	+	0.0635771i	−0.674603	+	0.738180i	$0.735685\pi$
$410$		0			0
$411$	−28.6272	−	11.8578i	−1.41208	−	0.584902i
$412$		0			0
$413$	3.32273	+	8.02178i	0.163501	+	0.394726i
$414$		0			0
$415$	−9.29329			−0.456190
$416$		0			0
$417$	−2.63482			−0.129028
$418$		0			0
$419$	−14.9887	−	36.1858i	−0.732244	−	1.76779i	−0.634972	−	0.772535i	$-0.718988\pi$
$419$	−14.9887	−	36.1858i	−0.732244	−	1.76779i	−0.0972723	−	0.995258i	$-0.531012\pi$
$420$		0			0
$421$	−13.6131	−	5.63872i	−0.663460	−	0.274814i	0.0254334	−	0.999677i	$-0.491903\pi$
$421$	−13.6131	−	5.63872i	−0.663460	−	0.274814i	−0.688894	+	0.724862i	$0.741903\pi$
$422$		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
$427$	−0.950223	+	2.29404i	−0.0459845	+	0.111016i
$428$		0			0
$429$	−2.69152	+	1.11487i	−0.129948	+	0.0538262i
$430$		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
$435$	12.2282	−	5.06509i	0.586298	−	0.242852i
$436$		0			0
$437$	−6.21215	+	14.9974i	−0.297167	+	0.717425i
$438$		0			0
$439$	8.87727	−	8.87727i	0.423689	−	0.423689i	−0.462783	−	0.886472i	$-0.653149\pi$
$439$	8.87727	−	8.87727i	0.423689	−	0.423689i	0.886472	+	0.462783i	$0.153149\pi$
$440$		0			0
$441$	4.61923	+	4.61923i	0.219963	+	0.219963i
$442$		0			0
$443$	−23.7377	−	9.83247i	−1.12781	−	0.467155i	−0.260775	−	0.965400i	$-0.583978\pi$
$443$	−23.7377	−	9.83247i	−1.12781	−	0.467155i	−0.867036	+	0.498245i	$0.833978\pi$
$444$		0			0
$445$	2.45479	+	5.92638i	0.116368	+	0.280937i
$446$		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
$451$	3.01606	+	7.28141i	0.142021	+	0.342868i
$452$		0			0
$453$	−30.1139	−	12.4736i	−1.41488	−	0.586061i
$454$		0			0
$455$	−1.52318	−	1.52318i	−0.0714075	−	0.0714075i
$456$		0			0
$457$	7.58808	−	7.58808i	0.354955	−	0.354955i	−0.506994	−	0.861950i	$-0.669243\pi$
$457$	7.58808	−	7.58808i	0.354955	−	0.354955i	0.861950	+	0.506994i	$0.169243\pi$
$458$		0			0
$459$	0.474817	−	1.14631i	0.0221626	−	0.0535052i
$460$		0			0
$461$	−15.2534	+	6.31816i	−0.710421	+	0.294266i	−0.708479	−	0.705732i	$-0.750618\pi$
$461$	−15.2534	+	6.31816i	−0.710421	+	0.294266i	−0.00194197	+	0.999998i	$0.500618\pi$
$462$		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
$467$	9.28999	−	3.84804i	0.429890	−	0.178066i	−0.157238	−	0.987561i	$-0.550259\pi$
$467$	9.28999	−	3.84804i	0.429890	−	0.178066i	0.587127	+	0.809495i	$0.300259\pi$
$468$		0			0
$469$	3.53041	−	8.52318i	0.163019	−	0.393564i
$470$		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
$475$	12.7015	+	5.26112i	0.582784	+	0.241397i
$476$		0			0
$477$	19.4272	+	46.9015i	0.889512	+	2.14747i
$478$		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
$483$	13.4117	+	32.3786i	0.610252	+	1.47328i
$484$		0			0
$485$	2.96951	+	1.23001i	0.134838	+	0.0558519i
$486$		0			0
$487$	−13.0855	−	13.0855i	−0.592961	−	0.592961i	0.345469	−	0.938430i	$-0.387720\pi$
$487$	−13.0855	−	13.0855i	−0.592961	−	0.592961i	−0.938430	+	0.345469i	$0.887720\pi$
$488$		0			0
$489$	3.92543	−	3.92543i	0.177514	−	0.177514i
$490$		0			0
$491$	−11.7944	+	28.4741i	−0.532273	+	1.28502i	0.397742	+	0.917497i	$0.369794\pi$
$491$	−11.7944	+	28.4741i	−0.532273	+	1.28502i	−0.930015	+	0.367523i	$0.880206\pi$
$492$		0			0
$493$	−1.27314	+	0.527350i	−0.0573391	+	0.0237506i
$494$		0			0
$495$			3.31856i			0.149158i
$496$		0			0
$497$		−	18.2031i		−	0.816522i
$498$		0			0
$499$	22.4253	−	9.28886i	1.00389	−	0.415827i	0.180670	−	0.983544i	$-0.442173\pi$
$499$	22.4253	−	9.28886i	1.00389	−	0.415827i	0.823224	+	0.567717i	$0.192173\pi$
$500$		0			0
$501$	23.1479	−	55.8841i	1.03417	−	2.49672i
$502$		0			0
$503$	−23.5062	+	23.5062i	−1.04809	+	1.04809i	−0.0493053	+	0.998784i	$0.515701\pi$
$503$	−23.5062	+	23.5062i	−1.04809	+	1.04809i	−0.998784	+	0.0493053i	$0.984299\pi$
$504$		0			0
$505$	2.61373	+	2.61373i	0.116309	+	0.116309i
$506$		0			0
$507$	30.2459	+	12.5283i	1.34327	+	0.556400i
$508$		0			0
$509$	13.1651	+	31.7834i	0.583534	+	1.40877i	0.889589	+	0.456761i	$0.150991\pi$
$509$	13.1651	+	31.7834i	0.583534	+	1.40877i	−0.306056	+	0.952014i	$0.599009\pi$
$510$		0			0
$511$	17.3912			0.769343
$512$		0			0
$513$	−17.1917			−0.759033
$514$		0			0
$515$	4.54124	+	10.9635i	0.200111	+	0.483111i
$516$		0			0
$517$	−0.438546	−	0.181652i	−0.0192872	−	0.00798903i
$518$		0			0
$519$	9.81922	+	9.81922i	0.431016	+	0.431016i
$520$		0			0
$521$	−10.8936	+	10.8936i	−0.477257	+	0.477257i	−0.904253	−	0.426996i	$-0.859572\pi$
$521$	−10.8936	+	10.8936i	−0.477257	+	0.477257i	0.426996	+	0.904253i	$0.359572\pi$
$522$		0			0
$523$	−6.48657	+	15.6600i	−0.283638	+	0.684763i	−0.999915	−	0.0130536i	$-0.995845\pi$
$523$	−6.48657	+	15.6600i	−0.283638	+	0.684763i	0.716277	+	0.697816i	$0.245845\pi$
$524$		0			0
$525$	27.4217	−	11.3585i	1.19678	−	0.495724i
$526$		0			0
$527$			1.53488i			0.0668603i
$528$		0			0
$529$		−	4.16647i		−	0.181151i
$530$		0			0
$531$	16.6811	−	6.90952i	0.723896	−	0.299848i
$532$		0			0
$533$	−4.07107	+	9.82843i	−0.176338	+	0.425716i
$534$		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
$539$	1.06503	+	0.441152i	0.0458743	+	0.0190018i
$540$		0			0
$541$	−1.10183	−	2.66006i	−0.0473716	−	0.114365i	0.898422	−	0.439132i	$-0.144714\pi$
$541$	−1.10183	−	2.66006i	−0.0473716	−	0.114365i	−0.945794	+	0.324767i	$0.894714\pi$
$542$		0			0
$543$	45.1208			1.93632
$544$		0			0
$545$	7.14175			0.305919
$546$		0			0
$547$	10.4159	+	25.1462i	0.445351	+	1.07517i	0.974044	+	0.226360i	$0.0726825\pi$
$547$	10.4159	+	25.1462i	0.445351	+	1.07517i	−0.528693	+	0.848813i	$0.677318\pi$
$548$		0			0
$549$	4.77039	+	1.97596i	0.203595	+	0.0843319i
$550$		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
$555$	−8.83185	+	21.3220i	−0.374891	+	0.905068i
$556$		0			0
$557$	−26.4367	+	10.9504i	−1.12016	+	0.463984i	−0.864424	−	0.502763i	$-0.832317\pi$
$557$	−26.4367	+	10.9504i	−1.12016	+	0.463984i	−0.255733	+	0.966748i	$0.582317\pi$
$558$		0			0
$559$			5.88648i			0.248972i
$560$		0			0
$561$		−	0.554620i		−	0.0234161i
$562$		0			0
$563$	−22.9131	+	9.49093i	−0.965673	+	0.399995i	−0.809100	−	0.587671i	$-0.800045\pi$
$563$	−22.9131	+	9.49093i	−0.965673	+	0.399995i	−0.156574	+	0.987666i	$0.550045\pi$
$564$		0			0
$565$	0.710059	−	1.71423i	0.0298724	−	0.0721184i
$566$		0			0
$567$	−1.17985	+	1.17985i	−0.0495489	+	0.0495489i
$568$		0			0
$569$	12.2981	+	12.2981i	0.515565	+	0.515565i	0.916226	−	0.400661i	$-0.131220\pi$
$569$	12.2981	+	12.2981i	0.515565	+	0.515565i	−0.400661	+	0.916226i	$0.631220\pi$
$570$		0			0
$571$	4.93839	+	2.04555i	0.206665	+	0.0856036i	0.483615	−	0.875281i	$-0.339324\pi$
$571$	4.93839	+	2.04555i	0.206665	+	0.0856036i	−0.276950	+	0.960884i	$0.589324\pi$
$572$		0			0
$573$	−16.6931	−	40.3008i	−0.697366	−	1.68359i
$574$		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
$579$	−14.2713	−	34.4539i	−0.593093	−	1.43185i
$580$		0			0
$581$	−26.7406	−	11.0763i	−1.10939	−	0.459522i
$582$		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
$587$	8.74223	−	21.1056i	0.360830	−	0.871122i	−0.634349	−	0.773047i	$-0.718732\pi$
$587$	8.74223	−	21.1056i	0.360830	−	0.871122i	0.995179	−	0.0980746i	$-0.0312684\pi$
$588$		0			0
$589$	19.6481	−	8.13853i	0.809588	−	0.335342i
$590$		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
$595$	0.378872	−	0.156934i	0.0155322	−	0.00643367i
$596$		0			0
$597$	2.84696	−	6.87318i	0.116518	−	0.281300i
$598$		0			0
$599$	33.3626	−	33.3626i	1.36316	−	1.36316i	0.493295	−	0.869862i	$-0.335792\pi$
$599$	33.3626	−	33.3626i	1.36316	−	1.36316i	0.869862	−	0.493295i	$-0.164208\pi$
$600$		0			0
$601$	−21.0676	−	21.0676i	−0.859365	−	0.859365i	0.131898	−	0.991263i	$-0.457893\pi$
$601$	−21.0676	−	21.0676i	−0.859365	−	0.859365i	−0.991263	+	0.131898i	$0.957893\pi$
$602$		0			0
$603$	−17.7237	−	7.34139i	−0.721765	−	0.298965i
$604$		0			0
$605$	−2.99772	−	7.23714i	−0.121875	−	0.294231i
$606$		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
$611$	−0.245193	−	0.591948i	−0.00991945	−	0.0239477i
$612$		0			0
$613$	29.0883	+	12.0488i	1.17486	+	0.486645i	0.882798	−	0.469753i	$-0.155657\pi$
$613$	29.0883	+	12.0488i	1.17486	+	0.486645i	0.292067	+	0.956398i	$0.405657\pi$
$614$		0			0
$615$	13.7548	+	13.7548i	0.554647	+	0.554647i
$616$		0			0
$617$	22.2479	−	22.2479i	0.895666	−	0.895666i	−0.0993836	−	0.995049i	$-0.531687\pi$
$617$	22.2479	−	22.2479i	0.895666	−	0.895666i	0.995049	+	0.0993836i	$0.0316871\pi$
$618$		0			0
$619$	2.70650	−	6.53408i	0.108784	−	0.262627i	−0.860108	−	0.510112i	$-0.829604\pi$
$619$	2.70650	−	6.53408i	0.108784	−	0.262627i	0.968892	+	0.247485i	$0.0796041\pi$
$620$		0			0
$621$	26.5807	−	11.0101i	1.06665	−	0.441819i
$622$		0			0
$623$			19.9783i			0.800416i
$624$		0			0
$625$			16.5563i			0.662254i
$626$		0			0
$627$	−7.09976	+	2.94082i	−0.283537	+	0.117445i
$628$		0			0
$629$	0.919525	−	2.21993i	0.0366639	−	0.0885144i
$630$		0			0
$631$	−1.24929	+	1.24929i	−0.0497335	+	0.0497335i	−0.731536	−	0.681803i	$-0.761196\pi$
$631$	−1.24929	+	1.24929i	−0.0497335	+	0.0497335i	0.681803	+	0.731536i	$0.261196\pi$
$632$		0			0
$633$	41.0928	+	41.0928i	1.63329	+	1.63329i
$634$		0			0
$635$	−1.55045	−	0.642215i	−0.0615275	−	0.0254855i
$636$		0			0
$637$	0.595466	+	1.43758i	0.0235932	+	0.0569590i
$638$		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
$643$	5.74440	+	13.8682i	0.226537	+	0.546908i	0.995751	−	0.0920822i	$-0.0293523\pi$
$643$	5.74440	+	13.8682i	0.226537	+	0.546908i	−0.769215	+	0.638991i	$0.779352\pi$
$644$		0			0
$645$	9.94424	+	4.11904i	0.391554	+	0.162187i
$646$		0			0
$647$	−13.9424	−	13.9424i	−0.548134	−	0.548134i	0.377767	−	0.925901i	$-0.376692\pi$
$647$	−13.9424	−	13.9424i	−0.548134	−	0.548134i	−0.925901	+	0.377767i	$0.876692\pi$
$648$		0			0
$649$	2.25298	−	2.25298i	0.0884371	−	0.0884371i
$650$		0			0
$651$	17.5706	−	42.4192i	0.688646	−	1.66254i
$652$		0			0
$653$	0.361667	−	0.149807i	0.0141531	−	0.00586241i	−0.375596	−	0.926784i	$-0.622562\pi$
$653$	0.361667	−	0.149807i	0.0141531	−	0.00586241i	0.389749	+	0.920921i	$0.372562\pi$
$654$		0			0
$655$		−	6.32634i		−	0.247191i
$656$		0			0
$657$		−	36.1646i		−	1.41091i
$658$		0			0
$659$	−18.5077	+	7.66613i	−0.720957	+	0.298630i	−0.712830	−	0.701337i	$-0.752587\pi$
$659$	−18.5077	+	7.66613i	−0.720957	+	0.298630i	−0.00812687	+	0.999967i	$0.502587\pi$
$660$		0			0
$661$	−12.4139	+	29.9699i	−0.482846	+	1.16569i	0.475405	+	0.879767i	$0.342302\pi$
$661$	−12.4139	+	29.9699i	−0.482846	+	1.16569i	−0.958251	+	0.285927i	$0.907698\pi$
$662$		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
$667$	−29.5215	−	12.2282i	−1.14308	−	0.473478i
$668$		0			0
$669$	−18.5797	−	44.8554i	−0.718334	−	1.73421i
$670$		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
$675$	−9.32453	−	22.5114i	−0.358902	−	0.866465i
$676$		0			0
$677$	41.7848	+	17.3078i	1.60592	+	0.665194i	0.992237	−	0.124360i	$-0.0396877\pi$
$677$	41.7848	+	17.3078i	1.60592	+	0.665194i	0.613682	+	0.789553i	$0.289688\pi$
$678$		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
$683$	13.2754	−	32.0496i	0.507968	−	1.22634i	−0.437083	−	0.899421i	$-0.643988\pi$
$683$	13.2754	−	32.0496i	0.507968	−	1.22634i	0.945051	−	0.326922i	$-0.106012\pi$
$684$		0			0
$685$	−7.76744	+	3.21738i	−0.296779	+	0.122930i
$686$		0			0
$687$			7.48100i			0.285418i
$688$		0			0
$689$			12.0922i			0.460674i
$690$		0			0
$691$	46.1276	−	19.1067i	1.75478	−	0.726852i	0.757520	−	0.652812i	$-0.226411\pi$
$691$	46.1276	−	19.1067i	1.75478	−	0.726852i	0.997255	−	0.0740401i	$-0.0235893\pi$
$692$		0			0
$693$	−3.95525	+	9.54882i	−0.150248	+	0.362730i
$694$		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
$699$	40.3474	+	16.7124i	1.52608	+	0.632122i
$700$		0			0
$701$	−5.34543	−	12.9050i	−0.201894	−	0.487415i	0.790210	−	0.612837i	$-0.209972\pi$
$701$	−5.34543	−	12.9050i	−0.201894	−	0.487415i	−0.992104	+	0.125422i	$0.959972\pi$
$702$		0			0
$703$	−33.2933			−1.25568
$704$		0			0
$705$	−1.17157			−0.0441240
$706$		0			0
$707$	4.40555	+	10.6359i	0.165688	+	0.400006i
$708$		0			0
$709$	−31.1013	−	12.8826i	−1.16803	−	0.483815i	−0.287491	−	0.957783i	$-0.592821\pi$
$709$	−31.1013	−	12.8826i	−1.16803	−	0.483815i	−0.880542	+	0.473968i	$0.842821\pi$
$710$		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
$715$	−0.302497	+	0.730292i	−0.0113127	+	0.0273114i
$716$		0			0
$717$	−47.6540	+	19.7390i	−1.77967	+	0.737165i
$718$		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
$723$	−72.4893	+	30.0261i	−2.69591	+	1.11668i
$724$		0			0
$725$	−10.3562	+	25.0020i	−0.384619	+	0.928552i
$726$		0			0
$727$	23.0479	−	23.0479i	0.854800	−	0.854800i	−0.135920	−	0.990720i	$-0.543399\pi$
$727$	23.0479	−	23.0479i	0.854800	−	0.854800i	0.990720	+	0.135920i	$0.0433990\pi$
$728$		0			0
$729$	−30.5768	−	30.5768i	−1.13247	−	1.13247i
$730$		0			0
$731$	−1.03534	−	0.428852i	−0.0382935	−	0.0158617i
$732$		0			0
$733$	11.8891	+	28.7029i	0.439136	+	1.06017i	0.976248	+	0.216656i	$0.0695151\pi$
$733$	11.8891	+	28.7029i	0.439136	+	1.06017i	−0.537112	+	0.843511i	$0.680485\pi$
$734$		0			0
$735$	2.84523			0.104948
$736$		0			0
$737$	−3.38534			−0.124701
$738$		0			0
$739$	2.87645	+	6.94437i	0.105812	+	0.255453i	0.967914	−	0.251282i	$-0.0808522\pi$
$739$	2.87645	+	6.94437i	0.105812	+	0.255453i	−0.862102	+	0.506735i	$0.830852\pi$
$740$		0			0
$741$	−9.58323	−	3.96951i	−0.352049	−	0.145823i
$742$		0			0
$743$	16.6576	+	16.6576i	0.611108	+	0.611108i	0.943235	−	0.332127i	$-0.107766\pi$
$743$	16.6576	+	16.6576i	0.611108	+	0.611108i	−0.332127	+	0.943235i	$0.607766\pi$
$744$		0			0
$745$	3.31788	−	3.31788i	0.121558	−	0.121558i
$746$		0			0
$747$	−23.0328	+	55.6062i	−0.842728	+	2.03452i
$748$		0			0
$749$	−19.2635	+	7.97920i	−0.703873	+	0.291554i
$750$		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
$755$	−8.17083	+	3.38447i	−0.297367	+	0.123173i
$756$		0			0
$757$	2.35711	−	5.69056i	0.0856705	−	0.206827i	−0.875238	−	0.483692i	$-0.839296\pi$
$757$	2.35711	−	5.69056i	0.0856705	−	0.206827i	0.960909	+	0.276865i	$0.0892955\pi$
$758$		0			0
$759$	9.09378	−	9.09378i	0.330083	−	0.330083i
$760$		0			0
$761$	−14.2913	−	14.2913i	−0.518059	−	0.518059i	0.398925	−	0.916984i	$-0.369383\pi$
$761$	−14.2913	−	14.2913i	−0.518059	−	0.518059i	−0.916984	+	0.398925i	$0.869383\pi$
$762$		0			0
$763$	20.5497	+	8.51196i	0.743949	+	0.308154i
$764$		0			0
$765$	−0.326340	−	0.787854i	−0.0117988	−	0.0284849i
$766$		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
$771$	−21.6602	−	52.2924i	−0.780073	−	1.88326i
$772$		0			0
$773$	26.6270	+	11.0293i	0.957707	+	0.396695i	0.806122	−	0.591749i	$-0.201562\pi$
$773$	26.6270	+	11.0293i	0.957707	+	0.396695i	0.151585	+	0.988444i	$0.451562\pi$
$774$		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
$779$	−10.7387	+	25.9256i	−0.384756	+	0.928882i
$780$		0			0
$781$	−6.17132	+	2.55624i	−0.220827	+	0.0914695i
$782$		0			0
$783$		−	33.8408i		−	1.20937i
$784$		0			0
$785$			9.76782i			0.348629i
$786$		0			0
$787$	4.45056	−	1.84348i	0.158645	−	0.0657130i	−0.301948	−	0.953324i	$-0.597637\pi$
$787$	4.45056	−	1.84348i	0.158645	−	0.0657130i	0.460593	+	0.887611i	$0.347637\pi$
$788$		0			0
$789$	−27.4455	+	66.2593i	−0.977086	+	2.35889i
$790$		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
$795$	20.4277	+	8.46144i	0.724497	+	0.300096i
$796$		0			0
$797$	−14.9972	−	36.2064i	−0.531227	−	1.28250i	−0.930711	−	0.365756i	$-0.880811\pi$
$797$	−14.9972	−	36.2064i	−0.531227	−	1.28250i	0.399484	−	0.916740i	$-0.369189\pi$
$798$		0			0
$799$	0.121978			0.00431527
$800$		0			0
$801$	41.5444			1.46790
$802$		0			0
$803$	−2.44223	−	5.89607i	−0.0861845	−	0.208068i
$804$		0			0
$805$	8.78530	+	3.63899i	0.309641	+	0.128258i
$806$		0			0
$807$	−55.3980	−	55.3980i	−1.95010	−	1.95010i
$808$		0			0
$809$	−18.3458	+	18.3458i	−0.645005	+	0.645005i	−0.951782	−	0.306777i	$-0.900750\pi$
$809$	−18.3458	+	18.3458i	−0.645005	+	0.645005i	0.306777	+	0.951782i	$0.400750\pi$
$810$		0			0
$811$	−14.5476	+	35.1209i	−0.510834	+	1.23326i	0.432565	+	0.901603i	$0.357609\pi$
$811$	−14.5476	+	35.1209i	−0.510834	+	1.23326i	−0.943399	+	0.331660i	$0.892391\pi$
$812$		0			0
$813$	42.9797	−	17.8028i	1.50736	−	0.624371i
$814$		0			0
$815$		−	1.50626i		−	0.0527621i
$816$		0			0
$817$			15.5275i			0.543238i
$818$		0			0
$819$	−12.8890	+	5.33879i	−0.450377	+	0.186552i
$820$		0			0
$821$	10.1999	−	24.6248i	0.355979	−	0.859410i	−0.639877	−	0.768477i	$-0.721015\pi$
$821$	10.1999	−	24.6248i	0.355979	−	0.859410i	0.995857	−	0.0909335i	$-0.0289851\pi$
$822$		0			0
$823$	1.53506	−	1.53506i	0.0535088	−	0.0535088i	−0.679846	−	0.733355i	$-0.737953\pi$
$823$	1.53506	−	1.53506i	0.0535088	−	0.0535088i	0.733355	+	0.679846i	$0.237953\pi$
$824$		0			0
$825$	−7.70160	−	7.70160i	−0.268135	−	0.268135i
$826$		0			0
$827$	18.6205	+	7.71287i	0.647499	+	0.268203i	0.682167	−	0.731196i	$-0.261038\pi$
$827$	18.6205	+	7.71287i	0.647499	+	0.268203i	−0.0346687	+	0.999399i	$0.511038\pi$
$828$		0			0
$829$	9.98710	+	24.1110i	0.346866	+	0.837409i	0.996986	+	0.0775776i	$0.0247186\pi$
$829$	9.98710	+	24.1110i	0.346866	+	0.837409i	−0.650120	+	0.759831i	$0.725281\pi$
$830$		0			0
$831$	−17.0993			−0.593168
$832$		0			0
$833$	−0.296230			−0.0102638
$834$		0			0
$835$	−6.28074	−	15.1630i	−0.217354	−	0.524739i
$836$		0			0
$837$	−34.8233	−	14.4243i	−1.20367	−	0.498576i
$838$		0			0
$839$	−31.2561	−	31.2561i	−1.07908	−	1.07908i	−0.996592	−	0.0824901i	$-0.973713\pi$
$839$	−31.2561	−	31.2561i	−1.07908	−	1.07908i	−0.0824901	−	0.996592i	$-0.526287\pi$
$840$		0			0
$841$	−6.07041	+	6.07041i	−0.209324	+	0.209324i
$842$		0			0
$843$	14.9729	−	36.1479i	0.515695	−	1.24500i
$844$		0			0
$845$	8.20664	−	3.39930i	0.282317	−	0.116940i
$846$		0			0
$847$		−	24.3970i		−	0.838292i
$848$		0			0
$849$		−	65.2246i		−	2.23850i
$850$		0			0
$851$	51.4758	−	21.3220i	1.76457	−	0.730908i
$852$		0			0
$853$	7.73304	−	18.6692i	0.264774	−	0.639222i	−0.734447	−	0.678666i	$-0.762559\pi$
$853$	7.73304	−	18.6692i	0.264774	−	0.639222i	0.999222	+	0.0394438i	$0.0125586\pi$
$854$		0			0
$855$	−8.35503	+	8.35503i	−0.285736	+	0.285736i
$856$		0			0
$857$	4.21699	+	4.21699i	0.144050	+	0.144050i	0.775454	−	0.631404i	$-0.217521\pi$
$857$	4.21699	+	4.21699i	0.144050	+	0.144050i	−0.631404	+	0.775454i	$0.717521\pi$
$858$		0			0
$859$	−32.3968	−	13.4192i	−1.10536	−	0.457857i	−0.246025	−	0.969263i	$-0.579125\pi$
$859$	−32.3968	−	13.4192i	−1.10536	−	0.457857i	−0.859339	+	0.511407i	$0.829125\pi$
$860$		0			0
$861$	23.1843	+	55.9719i	0.790120	+	1.90752i
$862$		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
$867$	−18.2965	−	44.1716i	−0.621380	−	1.50015i
$868$		0			0
$869$	−6.78206	−	2.80922i	−0.230066	−	0.0952963i
$870$		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
$875$	6.57277	−	15.8681i	0.222200	−	0.536439i
$876$		0			0
$877$	−5.59652	+	2.31816i	−0.188981	+	0.0782786i	−0.475167	−	0.879895i	$-0.657612\pi$
$877$	−5.59652	+	2.31816i	−0.188981	+	0.0782786i	0.286186	+	0.958174i	$0.407612\pi$
$878$		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
$883$	−0.366860	+	0.151958i	−0.0123458	+	0.00511380i	−0.388848	−	0.921302i	$-0.627127\pi$
$883$	−0.366860	+	0.151958i	−0.0123458	+	0.00511380i	0.376502	+	0.926416i	$0.377127\pi$
$884$		0			0
$885$	3.00941	−	7.26535i	0.101160	−	0.244222i
$886$		0			0
$887$	6.38554	−	6.38554i	0.214406	−	0.214406i	−0.591730	−	0.806136i	$-0.701555\pi$
$887$	6.38554	−	6.38554i	0.214406	−	0.214406i	0.806136	+	0.591730i	$0.201555\pi$
$888$		0			0
$889$	−3.69583	−	3.69583i	−0.123954	−	0.123954i
$890$		0			0
$891$	0.565682	+	0.234313i	0.0189511	+	0.00784979i
$892$		0			0
$893$	−0.646775	−	1.56145i	−0.0216435	−	0.0522521i
$894$		0			0
$895$	−6.03011			−0.201564
$896$		0			0
$897$	17.3591			0.579604
$898$		0			0
$899$	16.0202	+	38.6761i	0.534302	+	1.28992i
$900$		0			0
$901$	−2.12682	−	0.880960i	−0.0708548	−	0.0293490i
$902$		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
$907$	14.6313	−	35.3230i	0.485823	−	1.17288i	−0.470980	−	0.882144i	$-0.656100\pi$
$907$	14.6313	−	35.3230i	0.485823	−	1.17288i	0.956803	−	0.290737i	$-0.0939004\pi$
$908$		0			0
$909$	22.1171	−	9.16122i	0.733579	−	0.303859i
$910$		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
$915$	2.07772	−	0.860620i	0.0686873	−	0.0284512i
$916$		0			0
$917$	7.54011	−	18.2034i	0.248996	−	0.601130i
$918$		0			0
$919$	−42.1116	+	42.1116i	−1.38913	+	1.38913i	−0.561987	+	0.827146i	$0.689963\pi$
$919$	−42.1116	+	42.1116i	−1.38913	+	1.38913i	−0.827146	+	0.561987i	$0.810037\pi$
$920$		0			0
$921$	33.7218	+	33.7218i	1.11117	+	1.11117i
$922$		0			0
$923$	−8.33002	−	3.45041i	−0.274186	−	0.113572i
$924$		0			0
$925$	−18.0578	−	43.5953i	−0.593736	−	1.43341i
$926$		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
$931$	1.57073	+	3.79208i	0.0514787	+	0.124280i
$932$		0			0
$933$	26.7176	+	11.0668i	0.874694	+	0.362310i
$934$		0			0
$935$	−0.106409	−	0.106409i	−0.00347995	−	0.00347995i
$936$		0			0
$937$	30.3001	−	30.3001i	0.989863	−	0.989863i	−0.0100865	−	0.999949i	$-0.503211\pi$
$937$	30.3001	−	30.3001i	0.989863	−	0.989863i	0.999949	+	0.0100865i	$0.00321068\pi$
$938$		0			0
$939$	−15.5097	+	37.4437i	−0.506140	+	1.22193i
$940$		0			0
$941$	1.05940	−	0.438818i	0.0345355	−	0.0143051i	−0.365349	−	0.930871i	$-0.619050\pi$
$941$	1.05940	−	0.438818i	0.0345355	−	0.0143051i	0.399884	+	0.916566i	$0.369050\pi$
$942$		0			0
$943$		−	46.9618i		−	1.52929i
$944$		0			0
$945$			10.0707i			0.327599i
$946$		0			0
$947$	−25.2985	+	10.4790i	−0.822089	+	0.340520i	−0.753766	−	0.657143i	$-0.771765\pi$
$947$	−25.2985	+	10.4790i	−0.822089	+	0.340520i	−0.0683231	+	0.997663i	$0.521765\pi$
$948$		0			0
$949$	3.29652	−	7.95850i	0.107009	−	0.258344i
$950$		0			0
$951$	6.99925	−	6.99925i	0.226966	−	0.226966i
$952$		0			0
$953$	8.84307	+	8.84307i	0.286455	+	0.286455i	0.835677	−	0.549222i	$-0.185076\pi$
$953$	8.84307	+	8.84307i	0.286455	+	0.286455i	−0.549222	+	0.835677i	$0.685076\pi$
$954$		0			0
$955$	−10.9348	−	4.52936i	−0.353843	−	0.146567i
$956$		0			0
$957$	−5.78880	−	13.9754i	−0.187125	−	0.451761i
$958$		0			0
$959$	−26.1847			−0.845549
$960$		0			0
$961$	15.6274			0.504110
$962$		0			0
$963$	16.5925	+	40.0579i	0.534686	+	1.29085i
$964$		0			0
$965$	−9.34838	−	3.87222i	−0.300935	−	0.124651i
$966$		0			0
$967$	33.2189	+	33.2189i	1.06825	+	1.06825i	0.997494	+	0.0707549i	$0.0225408\pi$
$967$	33.2189	+	33.2189i	1.06825	+	1.06825i	0.0707549	+	0.997494i	$0.477459\pi$
$968$		0			0
$969$	1.39635	−	1.39635i	0.0448572	−	0.0448572i
$970$		0			0
$971$	−1.16696	+	2.81729i	−0.0374495	+	0.0904111i	−0.941498	−	0.337019i	$-0.890581\pi$
$971$	−1.16696	+	2.81729i	−0.0374495	+	0.0904111i	0.904048	+	0.427431i	$0.140581\pi$
$972$		0			0
$973$	−2.05707	+	0.852067i	−0.0659467	+	0.0273160i
$974$		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
$979$	6.77316	−	2.80553i	0.216471	−	0.0896653i
$980$		0			0
$981$	17.7004	−	42.7325i	0.565130	−	1.36434i
$982$		0			0
$983$	29.0855	−	29.0855i	0.927684	−	0.927684i	−0.0698724	−	0.997556i	$-0.522259\pi$
$983$	29.0855	−	29.0855i	0.927684	−	0.927684i	0.997556	+	0.0698724i	$0.0222592\pi$
$984$		0			0
$985$	−0.353225	−	0.353225i	−0.0112547	−	0.0112547i
$986$		0			0
$987$	−3.37109	−	1.39635i	−0.107303	−	0.0444463i
$988$		0			0
$989$	−9.94424	−	24.0075i	−0.316209	−	0.763395i
$990$		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
$995$	−0.772467	−	1.86490i	−0.0244889	−	0.0591213i
$996$		0			0
$997$	−44.0238	−	18.2353i	−1.39425	−	0.577516i	−0.445996	−	0.895035i	$-0.647150\pi$
$997$	−44.0238	−	18.2353i	−1.39425	−	0.577516i	−0.948252	+	0.317519i	$0.897150\pi$
$998$		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	256.2.g.c.225.1		8
4.3	odd	2		256.2.g.d.225.2		8
8.3	odd	2		32.2.g.b.5.1	✓	8
8.5	even	2		128.2.g.b.113.2		8
16.3	odd	4		512.2.g.e.193.1		8
16.5	even	4		512.2.g.f.193.1		8
16.11	odd	4		512.2.g.h.193.2		8
16.13	even	4		512.2.g.g.193.2		8
24.5	odd	2		1152.2.v.b.1009.1		8
24.11	even	2		288.2.v.b.37.2		8
32.3	odd	8		32.2.g.b.13.1	yes	8
32.5	even	8		512.2.g.g.321.2		8
32.11	odd	8		512.2.g.h.321.2		8
32.13	even	8	inner	256.2.g.c.33.1		8
32.19	odd	8		256.2.g.d.33.2		8
32.21	even	8		512.2.g.f.321.1		8
32.27	odd	8		512.2.g.e.321.1		8
32.29	even	8		128.2.g.b.17.2		8
40.3	even	4		800.2.ba.d.549.1		8
40.19	odd	2		800.2.y.b.101.2		8
40.27	even	4		800.2.ba.c.549.2		8
64.13	even	16		4096.2.a.q.1.1		8
64.19	odd	16		4096.2.a.k.1.1		8
64.45	even	16		4096.2.a.q.1.8		8
64.51	odd	16		4096.2.a.k.1.8		8
96.29	odd	8		1152.2.v.b.145.1		8
96.35	even	8		288.2.v.b.109.2		8
160.3	even	8		800.2.ba.c.749.2		8
160.67	even	8		800.2.ba.d.749.1		8
160.99	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	8.3	odd	2
32.2.g.b.13.1	yes	8	32.3	odd	8
128.2.g.b.17.2		8	32.29	even	8
128.2.g.b.113.2		8	8.5	even	2
256.2.g.c.33.1		8	32.13	even	8	inner
256.2.g.c.225.1		8	1.1	even	1	trivial
256.2.g.d.33.2		8	32.19	odd	8
256.2.g.d.225.2		8	4.3	odd	2
288.2.v.b.37.2		8	24.11	even	2
288.2.v.b.109.2		8	96.35	even	8
512.2.g.e.193.1		8	16.3	odd	4
512.2.g.e.321.1		8	32.27	odd	8
512.2.g.f.193.1		8	16.5	even	4
512.2.g.f.321.1		8	32.21	even	8
512.2.g.g.193.2		8	16.13	even	4
512.2.g.g.321.2		8	32.5	even	8
512.2.g.h.193.2		8	16.11	odd	4
512.2.g.h.321.2		8	32.11	odd	8
800.2.y.b.101.2		8	40.19	odd	2
800.2.y.b.301.2		8	160.99	odd	8
800.2.ba.c.549.2		8	40.27	even	4
800.2.ba.c.749.2		8	160.3	even	8
800.2.ba.d.549.1		8	40.3	even	4
800.2.ba.d.749.1		8	160.67	even	8
1152.2.v.b.145.1		8	96.29	odd	8
1152.2.v.b.1009.1		8	24.5	odd	2
4096.2.a.k.1.1		8	64.19	odd	16
4096.2.a.k.1.8		8	64.51	odd	16
4096.2.a.q.1.1		8	64.13	even	16
4096.2.a.q.1.8		8	64.45	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.g (of order \(8\), degree \(4\), not minimal)

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

Introduction

L-functions

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Database

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