LMFDB - Embedded newform 128.2.g.b.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, 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("128.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.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:	$1.02208514587$
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			113.2
Root			$0.500000 + 2.10607i$ of defining polynomial
Character	$\chi$	$=$	128.113
Dual form			128.2.g.b.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07947 + 2.60607i) q^{3} +(0.707107 + 0.292893i) q^{5} +(-1.68554 - 1.68554i) q^{7} +(-3.50504 + 3.50504i) q^{9} +O(q^{10})$	\(q+(1.07947 + 2.60607i) q^{3} +(0.707107 + 0.292893i) q^{5} +(-1.68554 - 1.68554i) q^{7} +(-3.50504 + 3.50504i) q^{9} +(0.334743 - 0.808140i) q^{11} +(1.09083 - 0.451835i) q^{13} +2.15894i q^{15} -0.224777i q^{17} +(2.87740 - 1.19186i) q^{19} +(2.57316 - 6.21215i) q^{21} +(3.68554 - 3.68554i) q^{23} +(-3.12132 - 3.12132i) q^{25} +(-5.09976 - 2.11239i) q^{27} +(2.34610 + 5.66398i) q^{29} -6.82843 q^{31} +2.46742 q^{33} +(-0.698175 - 1.68554i) q^{35} +(-9.87613 - 4.09083i) q^{37} +(2.35503 + 2.35503i) q^{39} +(6.37109 - 6.37109i) q^{41} +(-1.90790 + 4.60607i) q^{43} +(-3.50504 + 1.45183i) q^{45} +0.542661i q^{47} -1.31788i q^{49} +(0.585786 - 0.242641i) q^{51} +(-3.91925 + 9.46191i) q^{53} +(0.473398 - 0.473398i) q^{55} +(6.21215 + 6.21215i) q^{57} +(3.36524 + 1.39393i) q^{59} +(0.398630 + 0.962379i) q^{61} +11.8158 q^{63} +0.903670 q^{65} +(-1.48105 - 3.57558i) q^{67} +(13.5832 + 5.62636i) q^{69} +(5.39978 + 5.39978i) q^{71} +(-5.15894 + 5.15894i) q^{73} +(4.76501 - 11.5038i) q^{75} +(-1.92638 + 0.797933i) q^{77} +8.39218i q^{79} -0.699980i q^{81} +(-11.2180 + 4.64665i) q^{83} +(0.0658358 - 0.158942i) q^{85} +(-12.2282 + 12.2282i) q^{87} +(-5.92638 - 5.92638i) q^{89} +(-2.60022 - 1.07705i) q^{91} +(-7.37109 - 17.7954i) q^{93} +2.38372 q^{95} -4.19951 q^{97} +(1.65928 + 4.00585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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	$0.177875\pi$
$3$	1.07947	+	2.60607i	0.623233	+	1.50462i	−0.224653	+	0.974439i	$0.572125\pi$
$4$		0			0
$5$	0.707107	+	0.292893i	0.316228	+	0.130986i	0.535151	−	0.844756i	$-0.320255\pi$
$5$	0.707107	+	0.292893i	0.316228	+	0.130986i	−0.218924	+	0.975742i	$0.570255\pi$
$6$		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	−0.865347	−	0.501173i	$-0.832902\pi$
$11$	0.334743	−	0.808140i	0.100929	−	0.243664i	0.966276	+	0.257510i	$0.0829019\pi$
$12$		0			0
$13$	1.09083	−	0.451835i	0.302541	−	0.125316i	−0.226249	−	0.974070i	$-0.572646\pi$
$13$	1.09083	−	0.451835i	0.302541	−	0.125316i	0.528789	+	0.848753i	$0.322646\pi$
$14$		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	−0.0273681	−	0.999625i	$-0.508713\pi$
$19$	2.87740	−	1.19186i	0.660122	−	0.273431i	0.687490	+	0.726194i	$0.258713\pi$
$20$		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	$0.0677534\pi$
$29$	2.34610	+	5.66398i	0.435659	+	1.05177i	−0.541773	+	0.840525i	$0.682247\pi$
$30$		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	−0.629129	−	0.777301i	$-0.716588\pi$
$37$	−9.87613	−	4.09083i	−1.62363	−	0.672528i	−0.994496	+	0.104773i	$0.966588\pi$
$38$		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	−0.999996	−	0.00274415i	$-0.999127\pi$
$43$	−1.90790	+	4.60607i	−0.290952	+	0.702420i	0.709045	+	0.705164i	$0.249127\pi$
$44$		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	$0.373331\pi$
$53$	−3.91925	+	9.46191i	−0.538351	+	1.29969i	−0.925873	+	0.377834i	$0.876669\pi$
$54$		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	0.590829	−	0.806797i	$-0.298801\pi$
$59$	3.36524	+	1.39393i	0.438117	+	0.181474i	−0.152712	+	0.988271i	$0.548801\pi$
$60$		0			0
$61$	0.398630	+	0.962379i	0.0510394	+	0.123220i	0.947343	−	0.320222i	$-0.103757\pi$
$61$	0.398630	+	0.962379i	0.0510394	+	0.123220i	−0.896303	+	0.443442i	$0.853757\pi$
$62$		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	0.807221	−	0.590249i	$-0.200970\pi$
$67$	−1.48105	−	3.57558i	−0.180939	−	0.436826i	−0.988161	+	0.153423i	$0.950970\pi$
$68$		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	−0.900996	−	0.433827i	$-0.857163\pi$
$83$	−11.2180	+	4.64665i	−1.23134	+	0.510036i	−0.330339	+	0.943862i	$0.607163\pi$
$84$		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	0.593461	−	0.804863i	$-0.297761\pi$
$101$	4.46191	+	1.84819i	0.443977	+	0.183901i	−0.149484	+	0.988764i	$0.547761\pi$
$102$		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	$0.263955\pi$
$107$	−3.34737	+	8.08128i	−0.323603	+	0.781246i	−0.999039	+	0.0438280i	$0.986045\pi$
$108$		0			0
$109$	8.62086	−	3.57088i	0.825728	−	0.342028i	0.0705180	−	0.997511i	$-0.477535\pi$
$109$	8.62086	−	3.57088i	0.825728	−	0.342028i	0.755210	+	0.655483i	$0.227535\pi$
$110$		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	0.723362	−	0.690469i	$-0.242596\pi$
$131$	−3.16317	−	7.63657i	−0.276367	−	0.667210i	−0.999729	+	0.0232589i	$0.992596\pi$
$132$		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	−0.938314	−	0.345785i	$-0.887613\pi$
$139$	−0.357453	+	0.862967i	−0.0303188	+	0.0731959i	0.907995	+	0.418981i	$0.137613\pi$
$140$		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	−0.798175	−	0.602426i	$-0.794201\pi$
$149$	2.34610	−	5.66398i	0.192200	−	0.464011i	0.990374	+	0.138415i	$0.0442007\pi$
$150$		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	$0.0450846\pi$
$157$	4.88391	+	11.7908i	0.389779	+	0.941009i	−0.600208	+	0.799844i	$0.704915\pi$
$158$		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	0.891636	−	0.452752i	$-0.149558\pi$
$163$	−0.753131	−	1.81822i	−0.0589898	−	0.142414i	−0.950626	+	0.310338i	$0.899558\pi$
$164$		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	−0.203027	−	0.979173i	$-0.565078\pi$
$173$	4.54817	−	1.88391i	0.345791	−	0.143231i	0.548818	+	0.835942i	$0.315078\pi$
$174$		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	−0.637747	−	0.770246i	$-0.720134\pi$
$179$	−7.27899	+	3.01505i	−0.544057	+	0.225356i	0.0936904	+	0.995601i	$0.470134\pi$
$180$		0			0
$181$	6.12132	−	14.7782i	0.454994	−	1.09845i	−0.515405	−	0.856947i	$-0.672359\pi$
$181$	6.12132	−	14.7782i	0.454994	−	1.09845i	0.970399	−	0.241506i	$-0.0776415\pi$
$182$		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	0.361099	−	0.932527i	$-0.382402\pi$
$197$	−0.602992	−	0.249768i	−0.0429614	−	0.0177952i	−0.404061	+	0.914732i	$0.632402\pi$
$198$		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	0.385357	−	0.922768i	$-0.374078\pi$
$211$	19.0338	−	7.88406i	1.31034	−	0.542761i	0.924984	+	0.380007i	$0.124078\pi$
$212$		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	0.943405	−	0.331644i	$-0.107603\pi$
$227$	0.629916	+	1.52075i	0.0418090	+	0.100936i	−0.901596	+	0.432580i	$0.857603\pi$
$228$		0			0
$229$	2.45021	+	1.01491i	0.161915	+	0.0670672i	0.462169	−	0.886792i	$-0.347071\pi$
$229$	2.45021	+	1.01491i	0.161915	+	0.0670672i	−0.300254	+	0.953859i	$0.597071\pi$
$230$		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	0.0665866	−	0.997781i	$-0.478789\pi$
$251$	−9.37694	−	3.88406i	−0.591867	−	0.245159i	−0.658454	+	0.752621i	$0.728789\pi$
$252$		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	−0.985865	−	0.167543i	$-0.946417\pi$
$269$	−25.6598	+	10.6286i	−1.56451	+	0.648040i	−0.578641	+	0.815582i	$0.696417\pi$
$270$		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	−0.978121	−	0.208035i	$-0.933293\pi$
$277$	−2.31978	+	5.60044i	−0.139382	+	0.336498i	0.838739	+	0.544533i	$0.183293\pi$
$278$		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	−0.356952	−	0.934123i	$-0.616184\pi$
$283$	−21.3627	−	8.84871i	−1.26988	−	0.526001i	−0.912928	+	0.408121i	$0.866184\pi$
$284$		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	0.889122	−	0.457670i	$-0.151316\pi$
$293$	20.4415	+	8.46715i	1.19421	+	0.494656i	0.305083	+	0.952326i	$0.401316\pi$
$294$		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	0.110527	−	0.993873i	$-0.464746\pi$
$307$	15.6196	−	6.46984i	0.891456	−	0.369253i	0.780929	+	0.624620i	$0.214746\pi$
$308$		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	0.881671	−	0.471865i	$-0.156419\pi$
$317$	−1.34287	−	3.24198i	−0.0754233	−	0.182088i	−0.957094	+	0.289777i	$0.906419\pi$
$318$		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	$0.277856\pi$
$331$	−6.43270	+	15.5299i	−0.353573	+	0.853601i	−0.996173	+	0.0873991i	$0.972144\pi$
$332$		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	0.689586	−	0.724204i	$-0.257793\pi$
$347$	12.3896	+	5.13193i	0.665107	+	0.275496i	−0.0244788	+	0.999700i	$0.507793\pi$
$348$		0			0
$349$	7.52453	+	18.1658i	0.402779	+	0.972394i	0.986988	+	0.160791i	$0.0514045\pi$
$349$	7.52453	+	18.1658i	0.402779	+	0.972394i	−0.584210	+	0.811603i	$0.698596\pi$
$350$		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	$0.258932\pi$
$373$	−6.03762	+	14.5761i	−0.312616	+	0.754722i	−0.999606	+	0.0280555i	$0.991068\pi$
$374$		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	0.523839	−	0.851818i	$-0.324500\pi$
$379$	5.68312	+	2.35403i	0.291922	+	0.120918i	−0.231916	+	0.972736i	$0.574500\pi$
$380$		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	−0.00545476	−	0.999985i	$-0.501736\pi$
$389$	−14.1298	−	5.85275i	−0.716408	−	0.296746i	−0.710953	+	0.703239i	$0.751736\pi$
$390$		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	−0.917042	−	0.398791i	$-0.869430\pi$
$397$	−25.5736	+	10.5929i	−1.28350	+	0.531643i	−0.366458	+	0.930434i	$0.619430\pi$
$398$		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	$0.281012\pi$
$419$	14.9887	+	36.1858i	0.732244	+	1.76779i	0.0972723	+	0.995258i	$0.468988\pi$
$420$		0			0
$421$	13.6131	+	5.63872i	0.663460	+	0.274814i	0.688894	−	0.724862i	$-0.258097\pi$
$421$	13.6131	+	5.63872i	0.663460	+	0.274814i	−0.0254334	+	0.999677i	$0.508097\pi$
$422$		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	0.867036	−	0.498245i	$-0.166022\pi$
$443$	23.7377	+	9.83247i	1.12781	+	0.467155i	0.260775	+	0.965400i	$0.416022\pi$
$444$		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	0.00194197	−	0.999998i	$-0.499382\pi$
$461$	15.2534	−	6.31816i	0.710421	−	0.294266i	0.708479	+	0.705732i	$0.249382\pi$
$462$		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	−0.587127	−	0.809495i	$-0.699741\pi$
$467$	−9.28999	+	3.84804i	−0.429890	+	0.178066i	0.157238	+	0.987561i	$0.449741\pi$
$468$		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	$-0.630206\pi$
$491$	11.7944	−	28.4741i	0.532273	−	1.28502i	0.930015	−	0.367523i	$-0.119794\pi$
$492$		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	−0.823224	−	0.567717i	$-0.807827\pi$
$499$	−22.4253	+	9.28886i	−1.00389	+	0.415827i	−0.180670	+	0.983544i	$0.557827\pi$
$500$		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	$-0.849009\pi$
$509$	−13.1651	−	31.7834i	−0.583534	−	1.40877i	0.306056	−	0.952014i	$-0.400991\pi$
$510$		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	−0.716277	−	0.697816i	$-0.754155\pi$
$523$	6.48657	−	15.6600i	0.283638	−	0.684763i	0.999915	+	0.0130536i	$0.00415520\pi$
$524$		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	0.945794	−	0.324767i	$-0.105286\pi$
$541$	1.10183	+	2.66006i	0.0473716	+	0.114365i	−0.898422	+	0.439132i	$0.855286\pi$
$542$		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	$-0.927318\pi$
$547$	−10.4159	−	25.1462i	−0.445351	−	1.07517i	0.528693	−	0.848813i	$-0.322682\pi$
$548$		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	0.255733	−	0.966748i	$-0.417683\pi$
$557$	26.4367	−	10.9504i	1.12016	−	0.463984i	0.864424	+	0.502763i	$0.167683\pi$
$558$		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	0.156574	−	0.987666i	$-0.449955\pi$
$563$	22.9131	−	9.49093i	0.965673	−	0.399995i	0.809100	+	0.587671i	$0.199955\pi$
$564$		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	0.276950	−	0.960884i	$-0.410676\pi$
$571$	−4.93839	−	2.04555i	−0.206665	−	0.0856036i	−0.483615	+	0.875281i	$0.660676\pi$
$572$		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	$0.281268\pi$
$587$	−8.74223	+	21.1056i	−0.360830	+	0.871122i	−0.995179	+	0.0980746i	$0.968732\pi$
$588$		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	−0.292067	−	0.956398i	$-0.594343\pi$
$613$	−29.0883	−	12.0488i	−1.17486	−	0.486645i	−0.882798	+	0.469753i	$0.844343\pi$
$614$		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	−0.968892	−	0.247485i	$-0.920396\pi$
$619$	−2.70650	+	6.53408i	−0.108784	+	0.262627i	0.860108	+	0.510112i	$0.170396\pi$
$620$		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	0.769215	−	0.638991i	$-0.220648\pi$
$643$	−5.74440	−	13.8682i	−0.226537	−	0.546908i	−0.995751	+	0.0920822i	$0.970648\pi$
$644$		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	−0.389749	−	0.920921i	$-0.627438\pi$
$653$	−0.361667	+	0.149807i	−0.0141531	+	0.00586241i	0.375596	+	0.926784i	$0.377438\pi$
$654$		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	0.00812687	−	0.999967i	$-0.497413\pi$
$659$	18.5077	−	7.66613i	0.720957	−	0.298630i	0.712830	+	0.701337i	$0.247413\pi$
$660$		0			0
$661$	12.4139	−	29.9699i	0.482846	−	1.16569i	−0.475405	−	0.879767i	$-0.657698\pi$
$661$	12.4139	−	29.9699i	0.482846	−	1.16569i	0.958251	−	0.285927i	$-0.0923015\pi$
$662$		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	−0.613682	−	0.789553i	$-0.710312\pi$
$677$	−41.7848	−	17.3078i	−1.60592	−	0.665194i	−0.992237	+	0.124360i	$0.960312\pi$
$678$		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	$0.356012\pi$
$683$	−13.2754	+	32.0496i	−0.507968	+	1.22634i	−0.945051	+	0.326922i	$0.893988\pi$
$684$		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	$0.773589\pi$
$691$	−46.1276	+	19.1067i	−1.75478	+	0.726852i	−0.997255	+	0.0740401i	$0.976411\pi$
$692$		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	0.992104	−	0.125422i	$-0.0400283\pi$
$701$	5.34543	+	12.9050i	0.201894	+	0.487415i	−0.790210	+	0.612837i	$0.790028\pi$
$702$		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	0.880542	−	0.473968i	$-0.157179\pi$
$709$	31.1013	+	12.8826i	1.16803	+	0.483815i	0.287491	+	0.957783i	$0.407179\pi$
$710$		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	$-0.930485\pi$
$733$	−11.8891	−	28.7029i	−0.439136	−	1.06017i	0.537112	−	0.843511i	$-0.319515\pi$
$734$		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	0.862102	−	0.506735i	$-0.169148\pi$
$739$	−2.87645	−	6.94437i	−0.105812	−	0.255453i	−0.967914	+	0.251282i	$0.919148\pi$
$740$		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	−0.960909	−	0.276865i	$-0.910704\pi$
$757$	−2.35711	+	5.69056i	−0.0856705	+	0.206827i	0.875238	+	0.483692i	$0.160704\pi$
$758$		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	−0.151585	−	0.988444i	$-0.548438\pi$
$773$	−26.6270	−	11.0293i	−0.957707	−	0.396695i	−0.806122	+	0.591749i	$0.798438\pi$
$774$		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	−0.460593	−	0.887611i	$-0.652363\pi$
$787$	−4.45056	+	1.84348i	−0.158645	+	0.0657130i	0.301948	+	0.953324i	$0.402363\pi$
$788$		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	$0.119189\pi$
$797$	14.9972	+	36.2064i	0.531227	+	1.28250i	−0.399484	+	0.916740i	$0.630811\pi$
$798$		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	$-0.642391\pi$
$811$	14.5476	−	35.1209i	0.510834	−	1.23326i	0.943399	−	0.331660i	$-0.107609\pi$
$812$		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	$0.278985\pi$
$821$	−10.1999	+	24.6248i	−0.355979	+	0.859410i	−0.995857	+	0.0909335i	$0.971015\pi$
$822$		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	0.0346687	−	0.999399i	$-0.488962\pi$
$827$	−18.6205	−	7.71287i	−0.647499	−	0.268203i	−0.682167	+	0.731196i	$0.738962\pi$
$828$		0			0
$829$	−9.98710	−	24.1110i	−0.346866	−	0.837409i	−0.996986	−	0.0775776i	$-0.975281\pi$
$829$	−9.98710	−	24.1110i	−0.346866	−	0.837409i	0.650120	−	0.759831i	$-0.274719\pi$
$830$		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	−0.999222	−	0.0394438i	$-0.987441\pi$
$853$	−7.73304	+	18.6692i	−0.264774	+	0.639222i	0.734447	+	0.678666i	$0.237441\pi$
$854$		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	0.859339	−	0.511407i	$-0.170875\pi$
$859$	32.3968	+	13.4192i	1.10536	+	0.457857i	0.246025	+	0.969263i	$0.420875\pi$
$860$		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	−0.286186	−	0.958174i	$-0.592388\pi$
$877$	5.59652	−	2.31816i	0.188981	−	0.0782786i	0.475167	+	0.879895i	$0.342388\pi$
$878$		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	−0.376502	−	0.926416i	$-0.622873\pi$
$883$	0.366860	−	0.151958i	0.0123458	−	0.00511380i	0.388848	+	0.921302i	$0.372873\pi$
$884$		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	$0.343900\pi$
$907$	−14.6313	+	35.3230i	−0.485823	+	1.17288i	−0.956803	+	0.290737i	$0.906100\pi$
$908$		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	−0.399884	−	0.916566i	$-0.630950\pi$
$941$	−1.05940	+	0.438818i	−0.0345355	+	0.0143051i	0.365349	+	0.930871i	$0.380950\pi$
$942$		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	0.0683231	−	0.997663i	$-0.478235\pi$
$947$	25.2985	−	10.4790i	0.822089	−	0.340520i	0.753766	+	0.657143i	$0.228235\pi$
$948$		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	−0.904048	−	0.427431i	$-0.859419\pi$
$971$	1.16696	−	2.81729i	0.0374495	−	0.0904111i	0.941498	+	0.337019i	$0.109419\pi$
$972$		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	0.948252	−	0.317519i	$-0.102850\pi$
$997$	44.0238	+	18.2353i	1.39425	+	0.577516i	0.445996	+	0.895035i	$0.352850\pi$
$998$		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	128.2.g.b.113.2		8
3.2	odd	2		1152.2.v.b.1009.1		8
4.3	odd	2		32.2.g.b.5.1	✓	8
8.3	odd	2		256.2.g.d.225.2		8
8.5	even	2		256.2.g.c.225.1		8
12.11	even	2		288.2.v.b.37.2		8
16.3	odd	4		512.2.g.h.193.2		8
16.5	even	4		512.2.g.g.193.2		8
16.11	odd	4		512.2.g.e.193.1		8
16.13	even	4		512.2.g.f.193.1		8
20.3	even	4		800.2.ba.d.549.1		8
20.7	even	4		800.2.ba.c.549.2		8
20.19	odd	2		800.2.y.b.101.2		8
32.3	odd	8		256.2.g.d.33.2		8
32.5	even	8		512.2.g.f.321.1		8
32.11	odd	8		512.2.g.e.321.1		8
32.13	even	8	inner	128.2.g.b.17.2		8
32.19	odd	8		32.2.g.b.13.1	yes	8
32.21	even	8		512.2.g.g.321.2		8
32.27	odd	8		512.2.g.h.321.2		8
32.29	even	8		256.2.g.c.33.1		8
64.13	even	16		4096.2.a.q.1.8		8
64.19	odd	16		4096.2.a.k.1.8		8
64.45	even	16		4096.2.a.q.1.1		8
64.51	odd	16		4096.2.a.k.1.1		8
96.77	odd	8		1152.2.v.b.145.1		8
96.83	even	8		288.2.v.b.109.2		8
160.19	odd	8		800.2.y.b.301.2		8
160.83	even	8		800.2.ba.c.749.2		8
160.147	even	8		800.2.ba.d.749.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.5.1	✓	8	4.3	odd	2
32.2.g.b.13.1	yes	8	32.19	odd	8
128.2.g.b.17.2		8	32.13	even	8	inner
128.2.g.b.113.2		8	1.1	even	1	trivial
256.2.g.c.33.1		8	32.29	even	8
256.2.g.c.225.1		8	8.5	even	2
256.2.g.d.33.2		8	32.3	odd	8
256.2.g.d.225.2		8	8.3	odd	2
288.2.v.b.37.2		8	12.11	even	2
288.2.v.b.109.2		8	96.83	even	8
512.2.g.e.193.1		8	16.11	odd	4
512.2.g.e.321.1		8	32.11	odd	8
512.2.g.f.193.1		8	16.13	even	4
512.2.g.f.321.1		8	32.5	even	8
512.2.g.g.193.2		8	16.5	even	4
512.2.g.g.321.2		8	32.21	even	8
512.2.g.h.193.2		8	16.3	odd	4
512.2.g.h.321.2		8	32.27	odd	8
800.2.y.b.101.2		8	20.19	odd	2
800.2.y.b.301.2		8	160.19	odd	8
800.2.ba.c.549.2		8	20.7	even	4
800.2.ba.c.749.2		8	160.83	even	8
800.2.ba.d.549.1		8	20.3	even	4
800.2.ba.d.749.1		8	160.147	even	8
1152.2.v.b.145.1		8	96.77	odd	8
1152.2.v.b.1009.1		8	3.2	odd	2
4096.2.a.k.1.1		8	64.51	odd	16
4096.2.a.k.1.8		8	64.19	odd	16
4096.2.a.q.1.1		8	64.45	even	16
4096.2.a.q.1.8		8	64.13	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.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

Modular forms

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Database

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