LMFDB - Embedded newform 512.2.i.b.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	512.33
Dual form			512.2.i.b.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.51381 + 1.67967i) q^{3} +(2.28487 - 0.454489i) q^{5} +(0.303950 + 0.733799i) q^{7} +(2.34987 - 5.67309i) q^{9} +O(q^{10})$	\(q+(-2.51381 + 1.67967i) q^{3} +(2.28487 - 0.454489i) q^{5} +(0.303950 + 0.733799i) q^{7} +(2.34987 - 5.67309i) q^{9} +(2.41516 - 3.61454i) q^{11} +(0.174791 + 0.0347682i) q^{13} +(-4.98033 + 4.98033i) q^{15} +(0.422266 + 0.422266i) q^{17} +(0.424489 - 2.13405i) q^{19} +(-1.99661 - 1.33409i) q^{21} +(6.39382 + 2.64841i) q^{23} +(0.394679 - 0.163481i) q^{25} +(1.85234 + 9.31236i) q^{27} +(5.22657 + 7.82211i) q^{29} -1.80802i q^{31} +13.1429i q^{33} +(1.02799 + 1.53849i) q^{35} +(0.559507 + 2.81283i) q^{37} +(-0.497791 + 0.206192i) q^{39} +(-4.83885 - 2.00432i) q^{41} +(6.27110 + 4.19021i) q^{43} +(2.79080 - 14.0303i) q^{45} +(2.42967 + 2.42967i) q^{47} +(4.50367 - 4.50367i) q^{49} +(-1.77076 - 0.352226i) q^{51} +(0.350569 - 0.524664i) q^{53} +(3.87556 - 9.35642i) q^{55} +(2.51742 + 6.07759i) q^{57} +(-8.25271 + 1.64157i) q^{59} +(2.67124 - 1.78487i) q^{61} +4.87715 q^{63} +0.415178 q^{65} +(-0.879840 + 0.587891i) q^{67} +(-20.5213 + 4.08194i) q^{69} +(-0.458776 - 1.10758i) q^{71} +(-0.783268 + 1.89098i) q^{73} +(-0.717551 + 1.07389i) q^{75} +(3.38643 + 0.673603i) q^{77} +(-5.97434 + 5.97434i) q^{79} +(-7.27213 - 7.27213i) q^{81} +(1.56393 - 7.86242i) q^{83} +(1.15674 + 0.772908i) q^{85} +(-26.2772 - 10.8844i) q^{87} +(6.64632 - 2.75300i) q^{89} +(0.0276149 + 0.138830i) q^{91} +(3.03687 + 4.54500i) q^{93} -5.06895i q^{95} -9.60392i q^{97} +(-14.8303 - 22.1951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.51381	+	1.67967i	−1.45135	+	0.969758i	−0.454471	+	0.890761i	$0.650172\pi$
$3$	−2.51381	+	1.67967i	−1.45135	+	0.969758i	−0.996875	+	0.0789971i	$0.974828\pi$
$4$		0			0
$5$	2.28487	−	0.454489i	1.02183	−	0.203254i	0.344383	−	0.938829i	$-0.388088\pi$
$5$	2.28487	−	0.454489i	1.02183	−	0.203254i	0.677443	+	0.735576i	$0.263088\pi$
$6$		0			0
$7$	0.303950	+	0.733799i	0.114882	+	0.277350i	0.970854	−	0.239673i	$-0.0770402\pi$
$7$	0.303950	+	0.733799i	0.114882	+	0.277350i	−0.855972	+	0.517023i	$0.827040\pi$
$8$		0			0
$9$	2.34987	−	5.67309i	0.783291	−	1.89103i
$10$		0			0
$11$	2.41516	−	3.61454i	0.728198	−	1.08983i	−0.263923	−	0.964544i	$-0.585017\pi$
$11$	2.41516	−	3.61454i	0.728198	−	1.08983i	0.992121	−	0.125281i	$-0.0399834\pi$
$12$		0			0
$13$	0.174791	+	0.0347682i	0.0484784	+	0.00964295i	0.219270	−	0.975664i	$-0.429632\pi$
$13$	0.174791	+	0.0347682i	0.0484784	+	0.00964295i	−0.170792	+	0.985307i	$0.554632\pi$
$14$		0			0
$15$	−4.98033	+	4.98033i	−1.28592	+	1.28592i
$16$		0			0
$17$	0.422266	+	0.422266i	0.102415	+	0.102415i	0.756457	−	0.654043i	$-0.226928\pi$
$17$	0.422266	+	0.422266i	0.102415	+	0.102415i	−0.654043	+	0.756457i	$0.726928\pi$
$18$		0			0
$19$	0.424489	−	2.13405i	0.0973844	−	0.489584i	−0.901053	−	0.433708i	$-0.857205\pi$
$19$	0.424489	−	2.13405i	0.0973844	−	0.489584i	0.998438	−	0.0558761i	$-0.0177952\pi$
$20$		0			0
$21$	−1.99661	−	1.33409i	−0.435696	−	0.291123i
$22$		0			0
$23$	6.39382	+	2.64841i	1.33320	+	0.552231i	0.931568	−	0.363568i	$-0.118442\pi$
$23$	6.39382	+	2.64841i	1.33320	+	0.552231i	0.401636	+	0.915799i	$0.368442\pi$
$24$		0			0
$25$	0.394679	−	0.163481i	0.0789358	−	0.0326963i
$26$		0			0
$27$	1.85234	+	9.31236i	0.356484	+	1.79216i
$28$		0			0
$29$	5.22657	+	7.82211i	0.970550	+	1.45253i	0.890097	+	0.455772i	$0.150637\pi$
$29$	5.22657	+	7.82211i	0.970550	+	1.45253i	0.0804529	+	0.996758i	$0.474363\pi$
$30$		0			0
$31$		−	1.80802i		−	0.324729i	−0.986731	−	0.162365i	$-0.948088\pi$
$31$		−	1.80802i		−	0.324729i	0.986731	−	0.162365i	$-0.0519121\pi$
$32$		0			0
$33$			13.1429i			2.28789i
$34$		0			0
$35$	1.02799	+	1.53849i	0.173762	+	0.260053i
$36$		0			0
$37$	0.559507	+	2.81283i	0.0919823	+	0.462426i	0.999133	+	0.0416214i	$0.0132523\pi$
$37$	0.559507	+	2.81283i	0.0919823	+	0.462426i	−0.907151	+	0.420805i	$0.861748\pi$
$38$		0			0
$39$	−0.497791	+	0.206192i	−0.0797103	+	0.0330171i
$40$		0			0
$41$	−4.83885	−	2.00432i	−0.755701	−	0.313022i	−0.0286356	−	0.999590i	$-0.509116\pi$
$41$	−4.83885	−	2.00432i	−0.755701	−	0.313022i	−0.727065	+	0.686568i	$0.759116\pi$
$42$		0			0
$43$	6.27110	+	4.19021i	0.956334	+	0.639002i	0.932675	−	0.360718i	$-0.117468\pi$
$43$	6.27110	+	4.19021i	0.956334	+	0.639002i	0.0236588	+	0.999720i	$0.492468\pi$
$44$		0			0
$45$	2.79080	−	14.0303i	0.416027	−	2.09151i
$46$		0			0
$47$	2.42967	+	2.42967i	0.354403	+	0.354403i	0.861745	−	0.507342i	$-0.169372\pi$
$47$	2.42967	+	2.42967i	0.354403	+	0.354403i	−0.507342	+	0.861745i	$0.669372\pi$
$48$		0			0
$49$	4.50367	−	4.50367i	0.643382	−	0.643382i
$50$		0			0
$51$	−1.77076	−	0.352226i	−0.247956	−	0.0493216i
$52$		0			0
$53$	0.350569	−	0.524664i	0.0481544	−	0.0720682i	−0.806611	−	0.591082i	$-0.798701\pi$
$53$	0.350569	−	0.524664i	0.0481544	−	0.0720682i	0.854766	+	0.519014i	$0.173701\pi$
$54$		0			0
$55$	3.87556	−	9.35642i	0.522580	−	1.26162i
$56$		0			0
$57$	2.51742	+	6.07759i	0.333440	+	0.804996i
$58$		0			0
$59$	−8.25271	+	1.64157i	−1.07441	+	0.213714i	−0.700429	−	0.713722i	$-0.747008\pi$
$59$	−8.25271	+	1.64157i	−1.07441	+	0.213714i	−0.373982	+	0.927436i	$0.622008\pi$
$60$		0			0
$61$	2.67124	−	1.78487i	0.342018	−	0.228529i	−0.372684	−	0.927958i	$-0.621562\pi$
$61$	2.67124	−	1.78487i	0.342018	−	0.228529i	0.714702	+	0.699429i	$0.246562\pi$
$62$		0			0
$63$	4.87715			0.614463
$64$		0			0
$65$	0.415178			0.0514964
$66$		0			0
$67$	−0.879840	+	0.587891i	−0.107490	+	0.0718223i	−0.608153	−	0.793820i	$-0.708089\pi$
$67$	−0.879840	+	0.587891i	−0.107490	+	0.0718223i	0.500664	+	0.865642i	$0.333089\pi$
$68$		0			0
$69$	−20.5213	+	4.08194i	−2.47047	+	0.491407i
$70$		0			0
$71$	−0.458776	−	1.10758i	−0.0544467	−	0.131446i	0.894316	−	0.447437i	$-0.147663\pi$
$71$	−0.458776	−	1.10758i	−0.0544467	−	0.131446i	−0.948762	+	0.315991i	$0.897663\pi$
$72$		0			0
$73$	−0.783268	+	1.89098i	−0.0916746	+	0.221322i	−0.963065	−	0.269267i	$-0.913218\pi$
$73$	−0.783268	+	1.89098i	−0.0916746	+	0.221322i	0.871391	+	0.490589i	$0.163218\pi$
$74$		0			0
$75$	−0.717551	+	1.07389i	−0.0828557	+	0.124002i
$76$		0			0
$77$	3.38643	+	0.673603i	0.385920	+	0.0767642i
$78$		0			0
$79$	−5.97434	+	5.97434i	−0.672166	+	0.672166i	−0.958215	−	0.286049i	$-0.907658\pi$
$79$	−5.97434	+	5.97434i	−0.672166	+	0.672166i	0.286049	+	0.958215i	$0.407658\pi$
$80$		0			0
$81$	−7.27213	−	7.27213i	−0.808014	−	0.808014i
$82$		0			0
$83$	1.56393	−	7.86242i	0.171664	−	0.863012i	−0.794930	−	0.606701i	$-0.792493\pi$
$83$	1.56393	−	7.86242i	0.171664	−	0.863012i	0.966594	−	0.256312i	$-0.0825074\pi$
$84$		0			0
$85$	1.15674	+	0.772908i	0.125466	+	0.0838336i
$86$		0			0
$87$	−26.2772	−	10.8844i	−2.81721	−	1.16693i
$88$		0			0
$89$	6.64632	−	2.75300i	0.704509	−	0.291817i	−0.00152141	−	0.999999i	$-0.500484\pi$
$89$	6.64632	−	2.75300i	0.704509	−	0.291817i	0.706030	+	0.708182i	$0.250484\pi$
$90$		0			0
$91$	0.0276149	+	0.138830i	0.00289483	+	0.0145533i
$92$		0			0
$93$	3.03687	+	4.54500i	0.314909	+	0.471295i
$94$		0			0
$95$		−	5.06895i		−	0.520064i
$96$		0			0
$97$		−	9.60392i		−	0.975130i	−0.873087	−	0.487565i	$-0.837885\pi$
$97$		−	9.60392i		−	0.975130i	0.873087	−	0.487565i	$-0.162115\pi$
$98$		0			0
$99$	−14.8303	−	22.1951i	−1.49050	−	2.23069i
$100$		0			0
$101$	−3.03083	−	15.2370i	−0.301579	−	1.51614i	−0.773099	−	0.634285i	$-0.781295\pi$
$101$	−3.03083	−	15.2370i	−0.301579	−	1.51614i	0.471520	−	0.881855i	$-0.343705\pi$
$102$		0			0
$103$	13.0558	−	5.40788i	1.28642	−	0.532854i	0.368506	−	0.929625i	$-0.379869\pi$
$103$	13.0558	−	5.40788i	1.28642	−	0.532854i	0.917917	+	0.396771i	$0.129869\pi$
$104$		0			0
$105$	−5.16833	−	2.14079i	−0.504377	−	0.208920i
$106$		0			0
$107$	−12.1990	−	8.15112i	−1.17932	−	0.787999i	−0.197970	−	0.980208i	$-0.563435\pi$
$107$	−12.1990	−	8.15112i	−1.17932	−	0.787999i	−0.981354	+	0.192209i	$0.938435\pi$
$108$		0			0
$109$	−1.31130	+	6.59237i	−0.125600	+	0.631435i	0.865781	+	0.500424i	$0.166822\pi$
$109$	−1.31130	+	6.59237i	−0.125600	+	0.631435i	−0.991381	+	0.131011i	$0.958178\pi$
$110$		0			0
$111$	−6.13112	−	6.13112i	−0.581940	−	0.581940i
$112$		0			0
$113$	−5.92301	+	5.92301i	−0.557190	+	0.557190i	−0.928506	−	0.371317i	$-0.878906\pi$
$113$	−5.92301	+	5.92301i	−0.557190	+	0.557190i	0.371317	+	0.928506i	$0.378906\pi$
$114$		0			0
$115$	15.8127	+	3.14535i	1.47455	+	0.293305i
$116$		0			0
$117$	0.607980	−	0.909907i	0.0562078	−	0.0841209i
$118$		0			0
$119$	−0.181511	+	0.438206i	−0.0166391	+	0.0401703i
$120$		0			0
$121$	−3.02239	−	7.29671i	−0.274763	−	0.663337i
$122$		0			0
$123$	15.5305	−	3.08921i	1.40034	−	0.278545i
$124$		0			0
$125$	−8.85761	+	5.91847i	−0.792249	+	0.529364i
$126$		0			0
$127$	7.95115			0.705551			0.352775	−	0.935708i	$-0.385238\pi$
$127$	7.95115			0.705551			0.352775	+	0.935708i	$0.385238\pi$
$128$		0			0
$129$	−22.8025			−2.00765
$130$		0			0
$131$	−2.99684	+	2.00242i	−0.261835	+	0.174953i	−0.679558	−	0.733622i	$-0.737828\pi$
$131$	−2.99684	+	2.00242i	−0.261835	+	0.174953i	0.417723	+	0.908575i	$0.362828\pi$
$132$		0			0
$133$	1.69499	−	0.337154i	0.146974	−	0.0292349i
$134$		0			0
$135$	8.46473	+	20.4357i	0.728528	+	1.75882i
$136$		0			0
$137$	−5.13309	+	12.3924i	−0.438550	+	1.05875i	0.537900	+	0.843008i	$0.319218\pi$
$137$	−5.13309	+	12.3924i	−0.438550	+	1.05875i	−0.976450	+	0.215744i	$0.930782\pi$
$138$		0			0
$139$	7.12464	−	10.6628i	0.604304	−	0.904405i	−0.395598	−	0.918424i	$-0.629462\pi$
$139$	7.12464	−	10.6628i	0.604304	−	0.904405i	0.999902	+	0.0140189i	$0.00446249\pi$
$140$		0			0
$141$	−10.1887	−	2.02667i	−0.858047	−	0.170676i
$142$		0			0
$143$	0.547820	−	0.547820i	0.0458110	−	0.0458110i
$144$		0			0
$145$	15.4971	+	15.4971i	1.28696	+	1.28696i
$146$		0			0
$147$	−3.75667	+	18.8860i	−0.309845	+	1.55769i
$148$		0			0
$149$	18.3515	+	12.2621i	1.50341	+	1.00455i	0.989149	+	0.146914i	$0.0469341\pi$
$149$	18.3515	+	12.2621i	1.50341	+	1.00455i	0.514262	+	0.857633i	$0.328066\pi$
$150$		0			0
$151$	2.57112	+	1.06499i	0.209235	+	0.0866679i	0.484839	−	0.874603i	$-0.338878\pi$
$151$	2.57112	+	1.06499i	0.209235	+	0.0866679i	−0.275605	+	0.961271i	$0.588878\pi$
$152$		0			0
$153$	3.38782	−	1.40328i	0.273889	−	0.113449i
$154$		0			0
$155$	−0.821724	−	4.13109i	−0.0660025	−	0.331817i
$156$		0			0
$157$	−10.9729	−	16.4222i	−0.875736	−	1.31063i	−0.949632	−	0.313366i	$-0.898543\pi$
$157$	−10.9729	−	16.4222i	−0.875736	−	1.31063i	0.0738963	−	0.997266i	$-0.476457\pi$
$158$		0			0
$159$			1.90774i			0.151294i
$160$		0			0
$161$			5.49676i			0.433206i
$162$		0			0
$163$	7.08796	+	10.6079i	0.555172	+	0.830873i	0.997832	−	0.0658161i	$-0.0209651\pi$
$163$	7.08796	+	10.6079i	0.555172	+	0.830873i	−0.442660	+	0.896690i	$0.645965\pi$
$164$		0			0
$165$	5.97332	+	30.0299i	0.465022	+	2.33782i
$166$		0			0
$167$	−4.60049	+	1.90558i	−0.355996	+	0.147459i	−0.553512	−	0.832841i	$-0.686713\pi$
$167$	−4.60049	+	1.90558i	−0.355996	+	0.147459i	0.197516	+	0.980300i	$0.436713\pi$
$168$		0			0
$169$	−11.9811	−	4.96273i	−0.921622	−	0.381748i
$170$		0			0
$171$	−11.1092	−	7.42291i	−0.849539	−	0.567644i
$172$		0			0
$173$	−4.04445	+	20.3328i	−0.307494	+	1.54587i	0.449998	+	0.893029i	$0.351425\pi$
$173$	−4.04445	+	20.3328i	−0.307494	+	1.54587i	−0.757492	+	0.652845i	$0.773575\pi$
$174$		0			0
$175$	0.239925	+	0.239925i	0.0181366	+	0.0181366i
$176$		0			0
$177$	17.9884	−	17.9884i	1.35209	−	1.35209i
$178$		0			0
$179$	6.57810	+	1.30847i	0.491670	+	0.0977993i	0.434698	−	0.900576i	$-0.356855\pi$
$179$	6.57810	+	1.30847i	0.491670	+	0.0977993i	0.0569725	+	0.998376i	$0.481855\pi$
$180$		0			0
$181$	12.0521	−	18.0372i	0.895822	−	1.34069i	−0.0440013	−	0.999031i	$-0.514011\pi$
$181$	12.0521	−	18.0372i	0.895822	−	1.34069i	0.939823	−	0.341661i	$-0.110989\pi$
$182$		0			0
$183$	−3.71700	+	8.97362i	−0.274768	+	0.663349i
$184$		0			0
$185$	2.55680	+	6.17266i	0.187980	+	0.453823i
$186$		0			0
$187$	2.54614	−	0.506458i	0.186192	−	0.0370359i
$188$		0			0
$189$	−6.27038	+	4.18973i	−0.456103	+	0.304758i
$190$		0			0
$191$	−12.1977			−0.882592			−0.441296	−	0.897362i	$-0.645481\pi$
$191$	−12.1977			−0.882592			−0.441296	+	0.897362i	$0.645481\pi$
$192$		0			0
$193$	16.3911			1.17986			0.589929	−	0.807455i	$-0.299156\pi$
$193$	16.3911			1.17986			0.589929	+	0.807455i	$0.299156\pi$
$194$		0			0
$195$	−1.04368	+	0.697362i	−0.0747392	+	0.0499391i
$196$		0			0
$197$	−12.9559	+	2.57710i	−0.923073	+	0.183611i	−0.633676	−	0.773599i	$-0.718455\pi$
$197$	−12.9559	+	2.57710i	−0.923073	+	0.183611i	−0.289397	+	0.957209i	$0.593455\pi$
$198$		0			0
$199$	1.44670	+	3.49265i	0.102554	+	0.247587i	0.966825	−	0.255439i	$-0.0822199\pi$
$199$	1.44670	+	3.49265i	0.102554	+	0.247587i	−0.864271	+	0.503026i	$0.832220\pi$
$200$		0			0
$201$	1.22428	−	2.95569i	0.0863544	−	0.208478i
$202$		0			0
$203$	−4.15125	+	6.21278i	−0.291360	+	0.436052i
$204$		0			0
$205$	−11.9671	−	2.38040i	−0.835817	−	0.166254i
$206$		0			0
$207$	30.0493	−	30.0493i	2.08857	−	2.08857i
$208$		0			0
$209$	−6.68840	−	6.68840i	−0.462646	−	0.462646i
$210$		0			0
$211$	−1.24095	+	6.23870i	−0.0854309	+	0.429490i	0.914272	+	0.405102i	$0.132764\pi$
$211$	−1.24095	+	6.23870i	−0.0854309	+	0.429490i	−0.999703	+	0.0243884i	$0.992236\pi$
$212$		0			0
$213$	3.01365	+	2.01366i	0.206492	+	0.137973i
$214$		0			0
$215$	16.2331	+	6.72395i	1.10709	+	0.458570i
$216$		0			0
$217$	1.32672	−	0.549546i	0.0900637	−	0.0373056i
$218$		0			0
$219$	−1.20723	−	6.06918i	−0.0815773	−	0.410117i
$220$		0			0
$221$	0.0591270	+	0.0884899i	0.00397731	+	0.00595247i
$222$		0			0
$223$			5.65324i			0.378569i	0.981922	+	0.189284i	$0.0606168\pi$
$223$			5.65324i			0.378569i	−0.981922	+	0.189284i	$0.939383\pi$
$224$		0			0
$225$		−	2.62321i		−	0.174881i
$226$		0			0
$227$	3.62832	+	5.43017i	0.240820	+	0.360413i	0.932117	−	0.362158i	$-0.117960\pi$
$227$	3.62832	+	5.43017i	0.240820	+	0.360413i	−0.691296	+	0.722571i	$0.742960\pi$
$228$		0			0
$229$	−4.22963	−	21.2638i	−0.279502	−	1.40515i	−0.824096	−	0.566451i	$-0.808316\pi$
$229$	−4.22963	−	21.2638i	−0.279502	−	1.40515i	0.544594	−	0.838700i	$-0.316684\pi$
$230$		0			0
$231$	−9.64427	+	3.99479i	−0.634546	+	0.262838i
$232$		0			0
$233$	3.58263	+	1.48397i	0.234706	+	0.0972182i	0.496936	−	0.867787i	$-0.334458\pi$
$233$	3.58263	+	1.48397i	0.234706	+	0.0972182i	−0.262231	+	0.965005i	$0.584458\pi$
$234$		0			0
$235$	6.65573	+	4.44722i	0.434172	+	0.290104i
$236$		0			0
$237$	4.98340	−	25.0533i	0.323707	−	1.62738i
$238$		0			0
$239$	−16.2539	−	16.2539i	−1.05138	−	1.05138i	−0.998607	−	0.0527693i	$-0.983195\pi$
$239$	−16.2539	−	16.2539i	−1.05138	−	1.05138i	−0.0527693	−	0.998607i	$-0.516805\pi$
$240$		0			0
$241$	−4.71850	+	4.71850i	−0.303945	+	0.303945i	−0.842555	−	0.538610i	$-0.818950\pi$
$241$	−4.71850	+	4.71850i	−0.303945	+	0.303945i	0.538610	+	0.842555i	$0.318950\pi$
$242$		0			0
$243$	2.55844	+	0.508905i	0.164124	+	0.0326463i
$244$		0			0
$245$	8.24344	−	12.3372i	0.526654	−	0.788194i
$246$		0			0
$247$	0.148394	−	0.358255i	0.00944208	−	0.0227952i
$248$		0			0
$249$	9.27485	+	22.3915i	0.587770	+	1.41900i
$250$		0			0
$251$	−24.3591	+	4.84533i	−1.53753	+	0.305834i	−0.889913	−	0.456130i	$-0.849235\pi$
$251$	−24.3591	+	4.84533i	−1.53753	+	0.305834i	−0.647620	+	0.761964i	$0.724235\pi$
$252$		0			0
$253$	25.0149	−	16.7144i	1.57267	−	1.05083i
$254$		0			0
$255$	−4.20605			−0.263393
$256$		0			0
$257$	−17.0757			−1.06515			−0.532576	−	0.846382i	$-0.678776\pi$
$257$	−17.0757			−1.06515			−0.532576	+	0.846382i	$0.678776\pi$
$258$		0			0
$259$	−1.89399	+	1.26552i	−0.117687	+	0.0786358i
$260$		0			0
$261$	56.6573	−	11.2698i	3.50700	−	0.697586i
$262$		0			0
$263$	−6.67352	−	16.1113i	−0.411507	−	0.993465i	−0.984734	−	0.174069i	$-0.944309\pi$
$263$	−6.67352	−	16.1113i	−0.411507	−	0.993465i	0.573227	−	0.819397i	$-0.305691\pi$
$264$		0			0
$265$	0.562552	−	1.35812i	0.0345573	−	0.0834287i
$266$		0			0
$267$	−12.0834	+	18.0841i	−0.739494	+	1.10673i
$268$		0			0
$269$	3.60444	+	0.716968i	0.219767	+	0.0437143i	0.303745	−	0.952753i	$-0.401763\pi$
$269$	3.60444	+	0.716968i	0.219767	+	0.0437143i	−0.0839787	+	0.996468i	$0.526763\pi$
$270$		0			0
$271$	−20.5532	+	20.5532i	−1.24852	+	1.24852i	−0.292145	+	0.956374i	$0.594369\pi$
$271$	−20.5532	+	20.5532i	−1.24852	+	1.24852i	−0.956374	+	0.292145i	$0.905631\pi$
$272$		0			0
$273$	−0.302606	−	0.302606i	−0.0183146	−	0.0183146i
$274$		0			0
$275$	0.362302	−	1.82142i	0.0218477	−	0.109836i
$276$		0			0
$277$	−15.0658	−	10.0667i	−0.905217	−	0.604846i	0.0134373	−	0.999910i	$-0.495723\pi$
$277$	−15.0658	−	10.0667i	−0.905217	−	0.604846i	−0.918654	+	0.395063i	$0.870723\pi$
$278$		0			0
$279$	−10.2570	−	4.24861i	−0.614073	−	0.254357i
$280$		0			0
$281$	4.52217	−	1.87315i	0.269770	−	0.111743i	−0.243698	−	0.969851i	$-0.578360\pi$
$281$	4.52217	−	1.87315i	0.269770	−	0.111743i	0.513468	+	0.858109i	$0.328360\pi$
$282$		0			0
$283$	0.721894	+	3.62921i	0.0429121	+	0.215734i	0.996292	−	0.0860399i	$-0.0274213\pi$
$283$	0.721894	+	3.62921i	0.0429121	+	0.215734i	−0.953380	+	0.301774i	$0.902421\pi$
$284$		0			0
$285$	8.51417	+	12.7424i	0.504336	+	0.754792i
$286$		0			0
$287$		−	4.15995i		−	0.245554i
$288$		0			0
$289$		−	16.6434i		−	0.979023i
$290$		0			0
$291$	16.1314	+	24.1424i	0.945640	+	1.41525i
$292$		0			0
$293$	0.201266	+	1.01183i	0.0117581	+	0.0591118i	0.986219	−	0.165446i	$-0.0529063\pi$
$293$	0.201266	+	1.01183i	0.0117581	+	0.0591118i	−0.974461	+	0.224558i	$0.927906\pi$
$294$		0			0
$295$	−18.1103	+	7.50154i	−1.05442	+	0.436756i
$296$		0			0
$297$	38.1336	+	15.7955i	2.21274	+	0.916545i
$298$		0			0
$299$	1.02550	+	0.685220i	0.0593065	+	0.0396273i
$300$		0			0
$301$	−1.16868	+	5.87534i	−0.0673615	+	0.338649i
$302$		0			0
$303$	33.2121	+	33.2121i	1.90799	+	1.90799i
$304$		0			0
$305$	5.29225	−	5.29225i	0.303033	−	0.303033i
$306$		0			0
$307$	−14.4531	−	2.87489i	−0.824880	−	0.164079i	−0.235438	−	0.971889i	$-0.575652\pi$
$307$	−14.4531	−	2.87489i	−0.824880	−	0.164079i	−0.589442	+	0.807811i	$0.700652\pi$
$308$		0			0
$309$	−23.7362	+	35.5237i	−1.35031	+	2.02088i
$310$		0			0
$311$	−12.5822	+	30.3761i	−0.713470	+	1.72247i	−0.0223281	+	0.999751i	$0.507108\pi$
$311$	−12.5822	+	30.3761i	−0.713470	+	1.72247i	−0.691142	+	0.722719i	$0.742892\pi$
$312$		0			0
$313$	−6.07425	−	14.6645i	−0.343337	−	0.828889i	−0.997374	−	0.0724262i	$-0.976926\pi$
$313$	−6.07425	−	14.6645i	−0.343337	−	0.828889i	0.654037	−	0.756463i	$-0.273074\pi$
$314$		0			0
$315$	11.1437	−	2.21661i	0.627874	−	0.124892i
$316$		0			0
$317$	−12.7506	+	8.51970i	−0.716147	+	0.478514i	−0.859486	−	0.511160i	$-0.829216\pi$
$317$	−12.7506	+	8.51970i	−0.716147	+	0.478514i	0.143339	+	0.989674i	$0.454216\pi$
$318$		0			0
$319$	40.8963			2.28976
$320$		0			0
$321$	44.3572			2.47578
$322$		0			0
$323$	1.08038	−	0.721889i	0.0601141	−	0.0401670i
$324$		0			0
$325$	0.0746705	−	0.0148529i	0.00414197	−	0.000823889i
$326$		0			0
$327$	−7.77665	−	18.7745i	−0.430050	−	1.03823i
$328$		0			0
$329$	−1.04439	+	2.52138i	−0.0575791	+	0.139008i
$330$		0			0
$331$	16.0230	−	23.9801i	0.880702	−	1.31806i	−0.0666189	−	0.997778i	$-0.521221\pi$
$331$	16.0230	−	23.9801i	0.880702	−	1.31806i	0.947321	−	0.320285i	$-0.103779\pi$
$332$		0			0
$333$	17.2722	+	3.43566i	0.946511	+	0.188273i
$334$		0			0
$335$	−1.74313	+	1.74313i	−0.0952375	+	0.0952375i
$336$		0			0
$337$	−21.0382	−	21.0382i	−1.14602	−	1.14602i	−0.987328	−	0.158695i	$-0.949271\pi$
$337$	−21.0382	−	21.0382i	−1.14602	−	1.14602i	−0.158695	−	0.987328i	$-0.550729\pi$
$338$		0			0
$339$	4.94058	−	24.8380i	0.268336	−	1.34901i
$340$		0			0
$341$	−6.53515	−	4.36665i	−0.353898	−	0.236467i
$342$		0			0
$343$	9.81027	+	4.06355i	0.529705	+	0.219411i
$344$		0			0
$345$	−45.0333	+	18.6534i	−2.42451	+	1.00427i
$346$		0			0
$347$	2.53390	+	12.7388i	0.136027	+	0.683853i	0.987266	+	0.159076i	$0.0508514\pi$
$347$	2.53390	+	12.7388i	0.136027	+	0.683853i	−0.851240	+	0.524777i	$0.824149\pi$
$348$		0			0
$349$	−4.24727	−	6.35649i	−0.227351	−	0.340255i	0.700203	−	0.713944i	$-0.253093\pi$
$349$	−4.24727	−	6.35649i	−0.227351	−	0.340255i	−0.927554	+	0.373689i	$0.878093\pi$
$350$		0			0
$351$			1.69212i			0.0903188i
$352$		0			0
$353$		−	26.8538i		−	1.42928i	−0.699491	−	0.714642i	$-0.746590\pi$
$353$		−	26.8538i		−	1.42928i	0.699491	−	0.714642i	$-0.253410\pi$
$354$		0			0
$355$	−1.55163	−	2.32218i	−0.0823519	−	0.123248i
$356$		0			0
$357$	−0.279759	−	1.40644i	−0.0148064	−	0.0744368i
$358$		0			0
$359$	−2.56193	+	1.06119i	−0.135214	+	0.0560073i	−0.449264	−	0.893399i	$-0.648314\pi$
$359$	−2.56193	+	1.06119i	−0.135214	+	0.0560073i	0.314051	+	0.949406i	$0.398314\pi$
$360$		0			0
$361$	13.1797	+	5.45923i	0.693670	+	0.287328i
$362$		0			0
$363$	19.8538	+	13.2659i	1.04205	+	0.696278i
$364$		0			0
$365$	−0.930238	+	4.67662i	−0.0486909	+	0.244786i
$366$		0			0
$367$	13.2056	+	13.2056i	0.689329	+	0.689329i	0.962084	−	0.272755i	$-0.0879347\pi$
$367$	13.2056	+	13.2056i	0.689329	+	0.689329i	−0.272755	+	0.962084i	$0.587935\pi$
$368$		0			0
$369$	−22.7413	+	22.7413i	−1.18387	+	1.18387i
$370$		0			0
$371$	0.491553	+	0.0977761i	0.0255202	+	0.00507628i
$372$		0			0
$373$	−20.4728	+	30.6397i	−1.06004	+	1.58646i	−0.280770	+	0.959775i	$0.590590\pi$
$373$	−20.4728	+	30.6397i	−1.06004	+	1.58646i	−0.779271	+	0.626688i	$0.784410\pi$
$374$		0			0
$375$	12.3252	−	29.7557i	0.636472	−	1.53658i
$376$		0			0
$377$	0.641599	+	1.54896i	0.0330440	+	0.0797753i
$378$		0			0
$379$	−26.5748	+	5.28606i	−1.36506	+	0.271527i	−0.822631	−	0.568576i	$-0.807494\pi$
$379$	−26.5748	+	5.28606i	−1.36506	+	0.271527i	−0.542427	+	0.840103i	$0.682494\pi$
$380$		0			0
$381$	−19.9876	+	13.3553i	−1.02400	+	0.684214i
$382$		0			0
$383$	−12.4669			−0.637027			−0.318514	−	0.947918i	$-0.603184\pi$
$383$	−12.4669			−0.637027			−0.318514	+	0.947918i	$0.603184\pi$
$384$		0			0
$385$	8.04371			0.409945
$386$		0			0
$387$	38.5078	−	25.7301i	1.95746	−	1.30793i
$388$		0			0
$389$	−6.19647	+	1.23255i	−0.314173	+	0.0624930i	−0.349659	−	0.936877i	$-0.613702\pi$
$389$	−6.19647	+	1.23255i	−0.314173	+	0.0624930i	0.0354851	+	0.999370i	$0.488702\pi$
$390$		0			0
$391$	1.58156	+	3.81823i	0.0799830	+	0.193096i
$392$		0			0
$393$	4.17006	−	10.0674i	0.210352	−	0.507834i
$394$		0			0
$395$	−10.9353	+	16.3659i	−0.550216	+	0.823457i
$396$		0			0
$397$	24.4366	+	4.86075i	1.22644	+	0.243954i	0.765476	−	0.643465i	$-0.222504\pi$
$397$	24.4366	+	4.86075i	1.22644	+	0.243954i	0.460964	+	0.887419i	$0.347504\pi$
$398$		0			0
$399$	−3.69456	+	3.69456i	−0.184959	+	0.184959i
$400$		0			0
$401$	0.213936	+	0.213936i	0.0106835	+	0.0106835i	0.712428	−	0.701745i	$-0.247595\pi$
$401$	0.213936	+	0.213936i	0.0106835	+	0.0106835i	−0.701745	+	0.712428i	$0.747595\pi$
$402$		0			0
$403$	0.0628614	−	0.316026i	0.00313135	−	0.0157424i
$404$		0			0
$405$	−19.9210	−	13.3108i	−0.989882	−	0.661418i
$406$		0			0
$407$	11.5184	+	4.77107i	0.570945	+	0.236493i
$408$		0			0
$409$	−8.00529	+	3.31590i	−0.395836	+	0.163961i	−0.571717	−	0.820451i	$-0.693723\pi$
$409$	−8.00529	+	3.31590i	−0.395836	+	0.163961i	0.175881	+	0.984411i	$0.443723\pi$
$410$		0			0
$411$	−7.91153	−	39.7739i	−0.390247	−	1.96190i
$412$		0			0
$413$	−3.71299	−	5.55688i	−0.182704	−	0.273436i
$414$		0			0
$415$		−	18.6754i		−	0.916739i
$416$		0			0
$417$			38.7712i			1.89863i
$418$		0			0
$419$	9.47052	+	14.1736i	0.462665	+	0.692427i	0.987294	−	0.158904i	$-0.0507959\pi$
$419$	9.47052	+	14.1736i	0.462665	+	0.692427i	−0.524629	+	0.851331i	$0.675796\pi$
$420$		0			0
$421$	4.60289	+	23.1403i	0.224331	+	1.12779i	0.914638	+	0.404273i	$0.132475\pi$
$421$	4.60289	+	23.1403i	0.224331	+	1.12779i	−0.690307	+	0.723517i	$0.742525\pi$
$422$		0			0
$423$	19.4931	−	8.07431i	0.947788	−	0.392587i
$424$		0			0
$425$	0.235692	+	0.0976269i	0.0114327	+	0.00473560i
$426$		0			0
$427$	2.12166	+	1.41765i	0.102674	+	0.0686047i
$428$		0			0
$429$	−0.456955	+	2.29727i	−0.0220620	+	0.110913i
$430$		0			0
$431$	−6.06685	−	6.06685i	−0.292230	−	0.292230i	0.545731	−	0.837961i	$-0.316252\pi$
$431$	−6.06685	−	6.06685i	−0.292230	−	0.292230i	−0.837961	+	0.545731i	$0.816252\pi$
$432$		0			0
$433$	−19.0094	+	19.0094i	−0.913533	+	0.913533i	−0.996548	−	0.0830154i	$-0.973545\pi$
$433$	−19.0094	+	19.0094i	−0.913533	+	0.913533i	0.0830154	+	0.996548i	$0.473545\pi$
$434$		0			0
$435$	−64.9867	−	12.9267i	−3.11588	−	0.619786i
$436$		0			0
$437$	8.36594	−	12.5205i	0.400197	−	0.598937i
$438$		0			0
$439$	1.00267	−	2.42067i	0.0478550	−	0.115532i	−0.898144	−	0.439701i	$-0.855085\pi$
$439$	1.00267	−	2.42067i	0.0478550	−	0.115532i	0.945999	+	0.324169i	$0.105085\pi$
$440$		0			0
$441$	−14.9667	−	36.1328i	−0.712700	−	1.72061i
$442$		0			0
$443$	10.3515	−	2.05904i	0.491815	−	0.0978280i	0.0570485	−	0.998371i	$-0.481831\pi$
$443$	10.3515	−	2.05904i	0.491815	−	0.0978280i	0.434766	+	0.900543i	$0.356831\pi$
$444$		0			0
$445$	13.9348	−	9.31093i	0.660572	−	0.441380i
$446$		0			0
$447$	−66.7283			−3.15614
$448$		0			0
$449$	−16.5623			−0.781622			−0.390811	−	0.920471i	$-0.627805\pi$
$449$	−16.5623			−0.781622			−0.390811	+	0.920471i	$0.627805\pi$
$450$		0			0
$451$	−18.9313	+	12.6495i	−0.891438	+	0.595640i
$452$		0			0
$453$	−8.25213	+	1.64145i	−0.387719	+	0.0771221i
$454$		0			0
$455$	0.126193	+	0.304657i	0.00591602	+	0.0142825i
$456$		0			0
$457$	3.37664	−	8.15192i	0.157952	−	0.381331i	−0.825015	−	0.565111i	$-0.808833\pi$
$457$	3.37664	−	8.15192i	0.157952	−	0.381331i	0.982967	+	0.183780i	$0.0588334\pi$
$458$		0			0
$459$	−3.15011	+	4.71447i	−0.147034	+	0.220053i
$460$		0			0
$461$	−25.6514	−	5.10238i	−1.19470	−	0.237641i	−0.442620	−	0.896709i	$-0.645951\pi$
$461$	−25.6514	−	5.10238i	−1.19470	−	0.237641i	−0.752084	+	0.659068i	$0.770951\pi$
$462$		0			0
$463$	10.3091	−	10.3091i	0.479105	−	0.479105i	−0.425741	−	0.904845i	$-0.639986\pi$
$463$	10.3091	−	10.3091i	0.479105	−	0.479105i	0.904845	+	0.425741i	$0.139986\pi$
$464$		0			0
$465$	9.00452	+	9.00452i	0.417575	+	0.417575i
$466$		0			0
$467$	4.65749	−	23.4148i	0.215523	−	1.08351i	−0.709822	−	0.704381i	$-0.751225\pi$
$467$	4.65749	−	23.4148i	0.215523	−	1.08351i	0.925345	−	0.379126i	$-0.123775\pi$
$468$		0			0
$469$	−0.698821	−	0.466937i	−0.0322685	−	0.0215612i
$470$		0			0
$471$	55.1677	+	22.8512i	2.54199	+	1.05293i
$472$		0			0
$473$	30.2914	−	12.5471i	1.39280	−	0.576917i
$474$		0			0
$475$	−0.181341	−	0.911661i	−0.00832048	−	0.0418299i
$476$		0			0
$477$	−2.15268	−	3.22171i	−0.0985642	−	0.147512i
$478$		0			0
$479$		−	7.22838i		−	0.330273i	−0.986271	−	0.165136i	$-0.947194\pi$
$479$		−	7.22838i		−	0.330273i	0.986271	−	0.165136i	$-0.0528065\pi$
$480$		0			0
$481$			0.511111i			0.0233047i
$482$		0			0
$483$	−9.23275	−	13.8178i	−0.420105	−	0.628731i
$484$		0			0
$485$	−4.36488	−	21.9437i	−0.198199	−	0.996413i
$486$		0			0
$487$	−13.5574	+	5.61566i	−0.614345	+	0.254470i	−0.668085	−	0.744085i	$-0.732886\pi$
$487$	−13.5574	+	5.61566i	−0.614345	+	0.254470i	0.0537402	+	0.998555i	$0.482886\pi$
$488$		0			0
$489$	−35.6355	−	14.7607i	−1.61149	−	0.667502i
$490$		0			0
$491$	16.6130	+	11.1005i	0.749734	+	0.500956i	0.870769	−	0.491692i	$-0.163621\pi$
$491$	16.6130	+	11.1005i	0.749734	+	0.500956i	−0.121035	+	0.992648i	$0.538621\pi$
$492$		0			0
$493$	−1.09601	+	5.51001i	−0.0493618	+	0.248159i
$494$		0			0
$495$	−43.9728	−	43.9728i	−1.97643	−	1.97643i
$496$		0			0
$497$	0.673299	−	0.673299i	0.0302016	−	0.0302016i
$498$		0			0
$499$	1.73704	+	0.345518i	0.0777605	+	0.0154675i	0.233817	−	0.972281i	$-0.424878\pi$
$499$	1.73704	+	0.345518i	0.0777605	+	0.0154675i	−0.156057	+	0.987748i	$0.549878\pi$
$500$		0			0
$501$	8.36397	−	12.5176i	0.373675	−	0.559244i
$502$		0			0
$503$	−6.27595	+	15.1515i	−0.279831	+	0.675571i	−0.999831	−	0.0184028i	$-0.994142\pi$
$503$	−6.27595	+	15.1515i	−0.279831	+	0.675571i	0.720000	+	0.693974i	$0.244142\pi$
$504$		0			0
$505$	−13.8501	−	33.4372i	−0.616322	−	1.48793i
$506$		0			0
$507$	38.4539	−	7.64895i	1.70780	−	0.339702i
$508$		0			0
$509$	0.961984	−	0.642777i	0.0426392	−	0.0284906i	−0.534068	−	0.845442i	$-0.679337\pi$
$509$	0.961984	−	0.642777i	0.0426392	−	0.0284906i	0.576707	+	0.816951i	$0.304337\pi$
$510$		0			0
$511$	−1.62567			−0.0719154
$512$		0			0
$513$	20.6593			0.912131
$514$		0			0
$515$	27.3729	−	18.2900i	1.20620	−	0.805954i
$516$		0			0
$517$	14.6502	−	2.91410i	0.644313	−	0.128162i
$518$		0			0
$519$	−23.9855	−	57.9060i	−1.05285	−	2.54179i
$520$		0			0
$521$	1.84213	−	4.44729i	0.0807050	−	0.194839i	−0.878376	−	0.477970i	$-0.841373\pi$
$521$	1.84213	−	4.44729i	0.0807050	−	0.194839i	0.959081	+	0.283130i	$0.0913729\pi$
$522$		0			0
$523$	1.19764	−	1.79239i	0.0523691	−	0.0783759i	−0.804361	−	0.594141i	$-0.797492\pi$
$523$	1.19764	−	1.79239i	0.0523691	−	0.0783759i	0.856730	+	0.515765i	$0.172492\pi$
$524$		0			0
$525$	−1.00612	−	0.200130i	−0.0439107	−	0.00873438i
$526$		0			0
$527$	0.763464	−	0.763464i	0.0332570	−	0.0332570i
$528$		0			0
$529$	17.6034	+	17.6034i	0.765367	+	0.765367i
$530$		0			0
$531$	−10.0801	+	50.6759i	−0.437437	+	2.19915i
$532$		0			0
$533$	−0.776102	−	0.518575i	−0.0336167	−	0.0224620i
$534$		0			0
$535$	−31.5778	−	13.0799i	−1.36523	−	0.565496i
$536$		0			0
$537$	−18.7338	+	7.75981i	−0.808425	+	0.334861i
$538$		0			0
$539$	−5.40162	−	27.1558i	−0.232664	−	1.16968i
$540$		0			0
$541$	−5.84519	−	8.74795i	−0.251304	−	0.376104i	0.684273	−	0.729226i	$-0.260120\pi$
$541$	−5.84519	−	8.74795i	−0.251304	−	0.376104i	−0.935577	+	0.353123i	$0.885120\pi$
$542$		0			0
$543$			65.5854i			2.81454i
$544$		0			0
$545$			15.6587i			0.670745i
$546$		0			0
$547$	−17.4357	−	26.0944i	−0.745498	−	1.11572i	−0.989301	−	0.145892i	$-0.953395\pi$
$547$	−17.4357	−	26.0944i	−0.745498	−	1.11572i	0.243803	−	0.969825i	$-0.421605\pi$
$548$		0			0
$549$	−3.84864	−	19.3484i	−0.164256	−	0.825771i
$550$		0			0
$551$	18.9114	−	7.83336i	0.805653	−	0.333712i
$552$		0			0
$553$	−6.19987	−	2.56807i	−0.263645	−	0.109205i
$554$		0			0
$555$	−16.7953	−	11.2223i	−0.712923	−	0.476360i
$556$		0			0
$557$	1.91577	−	9.63121i	0.0811736	−	0.408087i	−0.918739	−	0.394865i	$-0.870791\pi$
$557$	1.91577	−	9.63121i	0.0811736	−	0.408087i	0.999913	−	0.0132219i	$-0.00420879\pi$
$558$		0			0
$559$	0.950448	+	0.950448i	0.0401997	+	0.0401997i
$560$		0			0
$561$	−5.54981	+	5.54981i	−0.234313	+	0.234313i
$562$		0			0
$563$	−9.75123	−	1.93964i	−0.410965	−	0.0817461i	−0.0147220	−	0.999892i	$-0.504686\pi$
$563$	−9.75123	−	1.93964i	−0.410965	−	0.0817461i	−0.396243	+	0.918146i	$0.629686\pi$
$564$		0			0
$565$	−10.8414	+	16.2253i	−0.456100	+	0.682602i
$566$		0			0
$567$	3.12592	−	7.54664i	0.131276	−	0.316929i
$568$		0			0
$569$	12.1558	+	29.3467i	0.509599	+	1.23028i	0.944115	+	0.329616i	$0.106919\pi$
$569$	12.1558	+	29.3467i	0.509599	+	1.23028i	−0.434517	+	0.900664i	$0.643081\pi$
$570$		0			0
$571$	14.9708	−	2.97788i	0.626510	−	0.124621i	0.128383	−	0.991725i	$-0.459021\pi$
$571$	14.9708	−	2.97788i	0.626510	−	0.124621i	0.498127	+	0.867104i	$0.334021\pi$
$572$		0			0
$573$	30.6626	−	20.4881i	1.28095	−	0.855901i
$574$		0			0
$575$	2.95647			0.123293
$576$		0			0
$577$	−29.9355			−1.24623			−0.623116	−	0.782129i	$-0.714134\pi$
$577$	−29.9355			−1.24623			−0.623116	+	0.782129i	$0.714134\pi$
$578$		0			0
$579$	−41.2041	+	27.5317i	−1.71238	+	1.14418i
$580$		0			0
$581$	6.24479	−	1.24217i	0.259078	−	0.0515337i
$582$		0			0
$583$	−1.04974	−	2.53429i	−0.0434758	−	0.104960i
$584$		0			0
$585$	0.975614	−	2.35534i	0.0403367	−	0.0973814i
$586$		0			0
$587$	−15.2402	+	22.8085i	−0.629029	+	0.941408i	0.370890	+	0.928677i	$0.379053\pi$
$587$	−15.2402	+	22.8085i	−0.629029	+	0.941408i	−0.999919	+	0.0127316i	$0.995947\pi$
$588$		0			0
$589$	−3.85840	−	0.767483i	−0.158982	−	0.0316236i
$590$		0			0
$591$	28.2400	−	28.2400i	1.16164	−	1.16164i
$592$		0			0
$593$	23.4309	+	23.4309i	0.962194	+	0.962194i	0.999311	−	0.0371172i	$-0.0118175\pi$
$593$	23.4309	+	23.4309i	0.962194	+	0.962194i	−0.0371172	+	0.999311i	$0.511817\pi$
$594$		0			0
$595$	−0.215569	+	1.08374i	−0.00883747	+	0.0444290i
$596$		0			0
$597$	−9.50323	−	6.34986i	−0.388941	−	0.259882i
$598$		0			0
$599$	−14.1017	−	5.84110i	−0.576179	−	0.238661i	0.0755132	−	0.997145i	$-0.475940\pi$
$599$	−14.1017	−	5.84110i	−0.576179	−	0.238661i	−0.651692	+	0.758484i	$0.725940\pi$
$600$		0			0
$601$	16.4696	−	6.82193i	0.671809	−	0.278272i	−0.0205894	−	0.999788i	$-0.506554\pi$
$601$	16.4696	−	6.82193i	0.671809	−	0.278272i	0.692398	+	0.721516i	$0.256554\pi$
$602$		0			0
$603$	1.26765	+	6.37288i	0.0516225	+	0.259524i
$604$		0			0
$605$	−10.2221	−	15.2984i	−0.415586	−	0.621968i
$606$		0			0
$607$			10.7750i			0.437344i	0.975798	+	0.218672i	$0.0701724\pi$
$607$			10.7750i			0.437344i	−0.975798	+	0.218672i	$0.929828\pi$
$608$		0			0
$609$		−	22.5904i		−	0.915411i
$610$		0			0
$611$	0.340210	+	0.509160i	0.0137634	+	0.0205984i
$612$		0			0
$613$	3.48904	+	17.5406i	0.140921	+	0.708457i	0.985043	+	0.172307i	$0.0551220\pi$
$613$	3.48904	+	17.5406i	0.140921	+	0.708457i	−0.844122	+	0.536150i	$0.819878\pi$
$614$		0			0
$615$	34.0812	−	14.1169i	1.37429	−	0.569248i
$616$		0			0
$617$	32.6001	+	13.5034i	1.31243	+	0.543626i	0.925592	−	0.378523i	$-0.123568\pi$
$617$	32.6001	+	13.5034i	1.31243	+	0.543626i	0.386837	+	0.922148i	$0.373568\pi$
$618$		0			0
$619$	−1.79801	−	1.20140i	−0.0722683	−	0.0482881i	0.518911	−	0.854828i	$-0.326338\pi$
$619$	−1.79801	−	1.20140i	−0.0722683	−	0.0482881i	−0.591180	+	0.806540i	$0.701338\pi$
$620$		0			0
$621$	−12.8194	+	64.4473i	−0.514423	+	2.58618i
$622$		0			0
$623$	4.04029	+	4.04029i	0.161871	+	0.161871i
$624$		0			0
$625$	−19.0590	+	19.0590i	−0.762360	+	0.762360i
$626$		0			0
$627$	28.0476	+	5.57902i	1.12012	+	0.222805i
$628$		0			0
$629$	−0.951501	+	1.42402i	−0.0379388	+	0.0567795i
$630$		0			0
$631$	9.48652	−	22.9025i	0.377652	−	0.911733i	−0.614753	−	0.788720i	$-0.710744\pi$
$631$	9.48652	−	22.9025i	0.377652	−	0.911733i	0.992405	−	0.123014i	$-0.0392558\pi$
$632$		0			0
$633$	−7.35945	−	17.7673i	−0.292512	−	0.706186i
$634$		0			0
$635$	18.1674	−	3.61371i	0.720950	−	0.143406i
$636$		0			0
$637$	0.943787	−	0.630619i	0.0373942	−	0.0249860i
$638$		0			0
$639$	−7.36149			−0.291216
$640$		0			0
$641$	−22.8856			−0.903928			−0.451964	−	0.892036i	$-0.649277\pi$
$641$	−22.8856			−0.903928			−0.451964	+	0.892036i	$0.649277\pi$
$642$		0			0
$643$	−10.6628	+	7.12468i	−0.420501	+	0.280970i	−0.747765	−	0.663963i	$-0.768873\pi$
$643$	−10.6628	+	7.12468i	−0.420501	+	0.280970i	0.327264	+	0.944933i	$0.393873\pi$
$644$		0			0
$645$	−52.1008	+	10.3635i	−2.05147	+	0.408062i
$646$		0			0
$647$	16.6415	+	40.1760i	0.654243	+	1.57948i	0.806561	+	0.591151i	$0.201326\pi$
$647$	16.6415	+	40.1760i	0.654243	+	1.57948i	−0.152318	+	0.988332i	$0.548674\pi$
$648$		0			0
$649$	−13.9981	+	33.7944i	−0.549474	+	1.32655i
$650$		0			0
$651$	−2.41206	+	3.60991i	−0.0945362	+	0.141483i
$652$		0			0
$653$	15.7287	+	3.12864i	0.615512	+	0.122433i	0.492993	−	0.870033i	$-0.335903\pi$
$653$	15.7287	+	3.12864i	0.615512	+	0.122433i	0.122519	+	0.992466i	$0.460903\pi$
$654$		0			0
$655$	−5.93731	+	5.93731i	−0.231990	+	0.231990i
$656$		0			0
$657$	8.88710	+	8.88710i	0.346719	+	0.346719i
$658$		0			0
$659$	3.67625	−	18.4817i	0.143206	−	0.719947i	−0.840734	−	0.541448i	$-0.817876\pi$
$659$	3.67625	−	18.4817i	0.143206	−	0.719947i	0.983940	−	0.178498i	$-0.0571238\pi$
$660$		0			0
$661$	−1.08878	−	0.727500i	−0.0423487	−	0.0282965i	0.534216	−	0.845348i	$-0.320607\pi$
$661$	−1.08878	−	0.727500i	−0.0423487	−	0.0282965i	−0.576564	+	0.817052i	$0.695607\pi$
$662$		0			0
$663$	−0.297268	−	0.123132i	−0.0115449	−	0.00478206i
$664$		0			0
$665$	3.71959	−	1.54071i	0.144240	−	0.0597460i
$666$		0			0
$667$	12.7016	+	63.8553i	0.491808	+	2.47249i
$668$		0			0
$669$	−9.49558	−	14.2111i	−0.367120	−	0.549435i
$670$		0			0
$671$		−	13.9661i		−	0.539154i
$672$		0			0
$673$		−	29.4054i		−	1.13349i	−0.823892	−	0.566747i	$-0.808202\pi$
$673$		−	29.4054i		−	1.13349i	0.823892	−	0.566747i	$-0.191798\pi$
$674$		0			0
$675$	2.25348	+	3.37257i	0.0867364	+	0.129810i
$676$		0			0
$677$	−0.168449	−	0.846851i	−0.00647403	−	0.0325471i	0.977413	−	0.211337i	$-0.0677818\pi$
$677$	−0.168449	−	0.846851i	−0.00647403	−	0.0325471i	−0.983887	+	0.178790i	$0.942782\pi$
$678$		0			0
$679$	7.04734	−	2.91911i	0.270452	−	0.112025i
$680$		0			0
$681$	−18.2418	−	7.55600i	−0.699027	−	0.289546i
$682$		0			0
$683$	24.3032	+	16.2389i	0.929937	+	0.621364i	0.925550	−	0.378626i	$-0.123603\pi$
$683$	24.3032	+	16.2389i	0.929937	+	0.621364i	0.00438760	+	0.999990i	$0.498603\pi$
$684$		0			0
$685$	−6.09625	+	30.6479i	−0.232926	+	1.17100i
$686$		0			0
$687$	46.3486	+	46.3486i	1.76831	+	1.76831i
$688$		0			0
$689$	0.0795181	−	0.0795181i	0.00302940	−	0.00302940i
$690$		0			0
$691$	36.6353	+	7.28722i	1.39367	+	0.277219i	0.834123	−	0.551578i	$-0.185974\pi$
$691$	36.6353	+	7.28722i	1.39367	+	0.277219i	0.559550	+	0.828797i	$0.310974\pi$
$692$		0			0
$693$	11.7791	−	17.6287i	0.447451	−	0.669658i
$694$		0			0
$695$	11.4328	−	27.6011i	0.433670	−	1.04697i
$696$		0			0
$697$	−1.19693	−	2.88963i	−0.0453368	−	0.109453i
$698$		0			0
$699$	−11.4986	+	2.28722i	−0.434917	+	0.0865104i
$700$		0			0
$701$	8.75861	−	5.85232i	0.330808	−	0.221039i	−0.379062	−	0.925371i	$-0.623753\pi$
$701$	8.75861	−	5.85232i	0.330808	−	0.221039i	0.709871	+	0.704332i	$0.248753\pi$
$702$		0			0
$703$	6.24022			0.235354
$704$		0			0
$705$	−24.2011			−0.911465
$706$		0			0
$707$	10.2597	−	6.85531i	0.385855	−	0.257820i
$708$		0			0
$709$	14.6656	−	2.91717i	0.550778	−	0.109557i	0.0881469	−	0.996107i	$-0.471906\pi$
$709$	14.6656	−	2.91717i	0.550778	−	0.109557i	0.462631	+	0.886551i	$0.346906\pi$
$710$		0			0
$711$	19.8541	+	47.9319i	0.744585	+	1.79759i
$712$		0			0
$713$	4.78837	−	11.5601i	0.179326	−	0.432931i
$714$		0			0
$715$	1.00272	−	1.50068i	0.0374996	−	0.0561221i
$716$		0			0
$717$	68.1603	+	13.5579i	2.54549	+	0.506330i
$718$		0			0
$719$	24.2122	−	24.2122i	0.902963	−	0.902963i	−0.0927286	−	0.995691i	$-0.529559\pi$
$719$	24.2122	−	24.2122i	0.902963	−	0.902963i	0.995691	+	0.0927286i	$0.0295589\pi$
$720$		0			0
$721$	7.93659	+	7.93659i	0.295574	+	0.295574i
$722$		0			0
$723$	3.93586	−	19.7869i	0.146376	−	0.735883i
$724$		0			0
$725$	3.34159	+	2.23278i	0.124103	+	0.0829233i
$726$		0			0
$727$	−20.4528	−	8.47184i	−0.758553	−	0.314203i	−0.0303271	−	0.999540i	$-0.509655\pi$
$727$	−20.4528	−	8.47184i	−0.758553	−	0.314203i	−0.728226	+	0.685337i	$0.759655\pi$
$728$		0			0
$729$	21.2183	−	8.78890i	0.785862	−	0.325515i
$730$		0			0
$731$	0.878686	+	4.41746i	0.0324994	+	0.163385i
$732$		0			0
$733$	−2.00568	−	3.00171i	−0.0740814	−	0.110871i	0.792579	−	0.609769i	$-0.208738\pi$
$733$	−2.00568	−	3.00171i	−0.0740814	−	0.110871i	−0.866660	+	0.498899i	$0.833738\pi$
$734$		0			0
$735$			44.8595i			1.65467i
$736$		0			0
$737$			4.60007i			0.169446i
$738$		0			0
$739$	−19.0522	−	28.5137i	−0.700847	−	1.04889i	−0.995635	−	0.0933295i	$-0.970249\pi$
$739$	−19.0522	−	28.5137i	−0.700847	−	1.04889i	0.294788	−	0.955563i	$-0.404751\pi$
$740$		0			0
$741$	0.228717	+	1.14984i	0.00840211	+	0.0422403i
$742$		0			0
$743$	−41.6805	+	17.2646i	−1.52911	+	0.633378i	−0.979391	−	0.201973i	$-0.935265\pi$
$743$	−41.6805	+	17.2646i	−1.52911	+	0.633378i	−0.549718	+	0.835351i	$0.685265\pi$
$744$		0			0
$745$	47.5037	+	19.6767i	1.74040	+	0.720898i
$746$		0			0
$747$	−40.9292	−	27.3480i	−1.49752	−	1.00061i
$748$		0			0
$749$	2.27340	−	11.4292i	0.0830683	−	0.417612i
$750$		0			0
$751$	−30.7983	−	30.7983i	−1.12385	−	1.12385i	−0.991158	−	0.132689i	$-0.957639\pi$
$751$	−30.7983	−	30.7983i	−1.12385	−	1.12385i	−0.132689	−	0.991158i	$-0.542361\pi$
$752$		0			0
$753$	53.0955	−	53.0955i	1.93491	−	1.93491i
$754$		0			0
$755$	6.35871	+	1.26483i	0.231417	+	0.0460317i
$756$		0			0
$757$	−11.2220	+	16.7948i	−0.407869	+	0.610419i	−0.977361	−	0.211578i	$-0.932140\pi$
$757$	−11.2220	+	16.7948i	−0.407869	+	0.610419i	0.569492	+	0.821997i	$0.307140\pi$
$758$		0			0
$759$	−34.8078	+	84.0335i	−1.26344	+	3.05022i
$760$		0			0
$761$	10.6346	+	25.6742i	0.385504	+	0.930689i	0.990880	+	0.134749i	$0.0430228\pi$
$761$	10.6346	+	25.6742i	0.385504	+	0.930689i	−0.605376	+	0.795940i	$0.706977\pi$
$762$		0			0
$763$	−5.23605	+	1.04151i	−0.189558	+	0.0377054i
$764$		0			0
$765$	7.10297	−	4.74605i	0.256808	−	0.171594i
$766$		0			0
$767$	−1.49958			−0.0541466
$768$		0			0
$769$	52.8993			1.90760			0.953798	−	0.300448i	$-0.0971361\pi$
$769$	52.8993			1.90760			0.953798	+	0.300448i	$0.0971361\pi$
$770$		0			0
$771$	42.9249	−	28.6815i	1.54590	−	1.03294i
$772$		0			0
$773$	−21.6566	+	4.30777i	−0.778934	+	0.154940i	−0.568516	−	0.822672i	$-0.692482\pi$
$773$	−21.6566	+	4.30777i	−0.778934	+	0.154940i	−0.210418	+	0.977612i	$0.567482\pi$
$774$		0			0
$775$	−0.295577	−	0.713586i	−0.0106174	−	0.0256328i
$776$		0			0
$777$	2.63546	−	6.36256i	0.0945466	−	0.228256i
$778$		0			0
$779$	−6.33134	+	9.47552i	−0.226844	+	0.339496i
$780$		0			0
$781$	−5.11142	−	1.01672i	−0.182901	−	0.0363813i
$782$		0			0
$783$	−63.1609	+	63.1609i	−2.25719	+	2.25719i
$784$		0			0
$785$	−32.5355	−	32.5355i	−1.16124	−	1.16124i
$786$		0			0
$787$	−4.63019	+	23.2775i	−0.165048	+	0.829754i	0.806192	+	0.591654i	$0.201525\pi$
$787$	−4.63019	+	23.2775i	−0.165048	+	0.829754i	−0.971241	+	0.238101i	$0.923475\pi$
$788$		0			0
$789$	43.8376	+	29.2914i	1.56066	+	1.04280i
$790$		0			0
$791$	−6.14659	−	2.54600i	−0.218548	−	0.0905254i
$792$		0			0
$793$	0.528967	−	0.219105i	0.0187842	−	0.00778066i
$794$		0			0
$795$	0.867049	+	4.35895i	0.0307511	+	0.154596i
$796$		0			0
$797$	25.5956	+	38.3065i	0.906643	+	1.35689i	0.934004	+	0.357262i	$0.116290\pi$
$797$	25.5956	+	38.3065i	0.906643	+	1.35689i	−0.0273612	+	0.999626i	$0.508710\pi$
$798$		0			0
$799$			2.05193i			0.0725921i
$800$		0			0
$801$		−	44.1744i		−	1.56083i
$802$		0			0
$803$	4.94329	+	7.39816i	0.174445	+	0.261075i
$804$		0			0
$805$	2.49822	+	12.5594i	0.0880507	+	0.442661i
$806$		0			0
$807$	−10.2651	+	4.25196i	−0.361350	+	0.149676i
$808$		0			0
$809$	−19.2600	−	7.97776i	−0.677146	−	0.280483i	0.0174870	−	0.999847i	$-0.494433\pi$
$809$	−19.2600	−	7.97776i	−0.677146	−	0.280483i	−0.694633	+	0.719364i	$0.744433\pi$
$810$		0			0
$811$	−3.44040	−	2.29880i	−0.120809	−	0.0807219i	0.493698	−	0.869634i	$-0.335645\pi$
$811$	−3.44040	−	2.29880i	−0.120809	−	0.0807219i	−0.614507	+	0.788912i	$0.710645\pi$
$812$		0			0
$813$	17.1441	−	86.1894i	0.601271	−	3.02280i
$814$		0			0
$815$	21.0162	+	21.0162i	0.736167	+	0.736167i
$816$		0			0
$817$	11.6041	−	11.6041i	0.405977	−	0.405977i
$818$		0			0
$819$	0.852484	+	0.169570i	0.0297882	+	0.00592524i
$820$		0			0
$821$	4.72002	−	7.06401i	0.164730	−	0.246536i	−0.739916	−	0.672699i	$-0.765135\pi$
$821$	4.72002	−	7.06401i	0.164730	−	0.246536i	0.904646	+	0.426163i	$0.140135\pi$
$822$		0			0
$823$	6.08212	−	14.6835i	0.212009	−	0.511836i	−0.781723	−	0.623626i	$-0.785659\pi$
$823$	6.08212	−	14.6835i	0.212009	−	0.511836i	0.993732	+	0.111791i	$0.0356587\pi$
$824$		0			0
$825$	2.14862	+	5.18724i	0.0748055	+	0.180596i
$826$		0			0
$827$	−13.0143	+	2.58870i	−0.452551	+	0.0900181i	−0.416103	−	0.909317i	$-0.636604\pi$
$827$	−13.0143	+	2.58870i	−0.452551	+	0.0900181i	−0.0364484	+	0.999336i	$0.511604\pi$
$828$		0			0
$829$	−0.266055	+	0.177772i	−0.00924047	+	0.00617428i	−0.560182	−	0.828370i	$-0.689269\pi$
$829$	−0.266055	+	0.177772i	−0.00924047	+	0.00617428i	0.550941	+	0.834544i	$0.314269\pi$
$830$		0			0
$831$	54.7812			1.90034
$832$		0			0
$833$	3.80349			0.131783
$834$		0			0
$835$	−9.64545	+	6.44489i	−0.333795	+	0.223034i
$836$		0			0
$837$	16.8369	−	3.34907i	0.581968	−	0.115761i
$838$		0			0
$839$	−11.9276	−	28.7957i	−0.411785	−	0.994137i	−0.984658	−	0.174493i	$-0.944171\pi$
$839$	−11.9276	−	28.7957i	−0.411785	−	0.994137i	0.572874	−	0.819644i	$-0.305829\pi$
$840$		0			0
$841$	−22.7706	+	54.9731i	−0.785194	+	1.89563i
$842$		0			0
$843$	−8.22160	+	12.3045i	−0.283167	+	0.423789i
$844$		0			0
$845$	−29.6308	−	5.89392i	−1.01933	−	0.202757i
$846$		0			0
$847$	4.43566	−	4.43566i	0.152411	−	0.152411i
$848$		0			0
$849$	−7.91057	−	7.91057i	−0.271490	−	0.271490i
$850$		0			0
$851$	−3.87213	+	19.4665i	−0.132735	+	0.667304i
$852$		0			0
$853$	5.25349	+	3.51027i	0.179876	+	0.120189i	0.642249	−	0.766496i	$-0.278002\pi$
$853$	5.25349	+	3.51027i	0.179876	+	0.120189i	−0.462373	+	0.886686i	$0.653002\pi$
$854$		0			0
$855$	−28.7566	−	11.9114i	−0.983456	−	0.407361i
$856$		0			0
$857$	−11.1977	+	4.63825i	−0.382507	+	0.158439i	−0.565647	−	0.824647i	$-0.691374\pi$
$857$	−11.1977	+	4.63825i	−0.382507	+	0.158439i	0.183141	+	0.983087i	$0.441374\pi$
$858$		0			0
$859$	−10.3238	−	51.9011i	−0.352243	−	1.77084i	−0.597984	−	0.801508i	$-0.704031\pi$
$859$	−10.3238	−	51.9011i	−0.352243	−	1.77084i	0.245741	−	0.969335i	$-0.420969\pi$
$860$		0			0
$861$	6.98735	+	10.4573i	0.238128	+	0.356384i
$862$		0			0
$863$		−	44.3164i		−	1.50855i	−0.656559	−	0.754275i	$-0.727989\pi$
$863$		−	44.3164i		−	1.50855i	0.656559	−	0.754275i	$-0.272011\pi$
$864$		0			0
$865$			48.2960i			1.64211i
$866$		0			0
$867$	27.9554	+	41.8382i	0.949415	+	1.42090i
$868$		0			0
$869$	7.16552	+	36.0235i	0.243074	+	1.22201i
$870$		0			0
$871$	−0.174228	+	0.0721678i	−0.00590350	+	0.00244531i
$872$		0			0
$873$	−54.4839	−	22.5680i	−1.84400	−	0.763810i
$874$		0			0
$875$	−7.03523	−	4.70079i	−0.237834	−	0.158916i
$876$		0			0
$877$	7.58614	−	38.1381i	0.256166	−	1.28783i	−0.611722	−	0.791073i	$-0.709523\pi$
$877$	7.58614	−	38.1381i	0.256166	−	1.28783i	0.867888	−	0.496760i	$-0.165477\pi$
$878$		0			0
$879$	−2.20549	−	2.20549i	−0.0743892	−	0.0743892i
$880$		0			0
$881$	18.0489	−	18.0489i	0.608084	−	0.608084i	−0.334361	−	0.942445i	$-0.608520\pi$
$881$	18.0489	−	18.0489i	0.608084	−	0.608084i	0.942445	+	0.334361i	$0.108520\pi$
$882$		0			0
$883$	−7.66573	−	1.52481i	−0.257972	−	0.0513139i	0.0644097	−	0.997924i	$-0.479484\pi$
$883$	−7.66573	−	1.52481i	−0.257972	−	0.0513139i	−0.322382	+	0.946610i	$0.604484\pi$
$884$		0			0
$885$	32.9257	−	49.2768i	1.10678	−	1.65642i
$886$		0			0
$887$	−5.60114	+	13.5223i	−0.188068	+	0.454036i	−0.989587	−	0.143933i	$-0.954025\pi$
$887$	−5.60114	+	13.5223i	−0.188068	+	0.454036i	0.801520	+	0.597968i	$0.204025\pi$
$888$		0			0
$889$	2.41675	+	5.83455i	0.0810552	+	0.195684i
$890$		0			0
$891$	−43.8488	+	8.72206i	−1.46899	+	0.292200i
$892$		0			0
$893$	6.21639	−	4.15366i	0.208024	−	0.138997i
$894$		0			0
$895$	15.6248			0.522279
$896$		0			0
$897$	−3.72886			−0.124503
$898$		0			0
$899$	14.1425	−	9.44972i	0.471679	−	0.315166i
$900$		0			0
$901$	0.369581	−	0.0735143i	0.0123125	−	0.00244912i
$902$		0			0
$903$	−6.93081	−	16.7325i	−0.230643	−	0.556821i
$904$		0			0
$905$	19.3397	−	46.6901i	0.642873	−	1.55203i
$906$		0			0
$907$	18.5691	−	27.7907i	0.616578	−	0.922775i	−0.383421	−	0.923573i	$-0.625254\pi$
$907$	18.5691	−	27.7907i	0.616578	−	0.922775i	1.00000		0.000798948i	$0.000254313\pi$
$908$		0			0
$909$	−93.5631	−	18.6109i	−3.10329	−	0.617283i
$910$		0			0
$911$	19.9890	−	19.9890i	0.662264	−	0.662264i	−0.293649	−	0.955913i	$-0.594870\pi$
$911$	19.9890	−	19.9890i	0.662264	−	0.662264i	0.955913	+	0.293649i	$0.0948698\pi$
$912$		0			0
$913$	−24.6419	−	24.6419i	−0.815527	−	0.815527i
$914$		0			0
$915$	−4.41444	+	22.1929i	−0.145937	+	0.733675i
$916$		0			0
$917$	−2.38027	−	1.59044i	−0.0786033	−	0.0525210i
$918$		0			0
$919$	32.1621	+	13.3220i	1.06093	+	0.439452i	0.843782	−	0.536687i	$-0.180324\pi$
$919$	32.1621	+	13.3220i	1.06093	+	0.439452i	0.217149	+	0.976139i	$0.430324\pi$
$920$		0			0
$921$	41.1611	−	17.0495i	1.35630	−	0.561799i
$922$		0			0
$923$	−0.0416814	−	0.209547i	−0.00137196	−	0.00689732i
$924$		0			0
$925$	0.680671	+	1.01870i	0.0223803	+	0.0334945i
$926$		0			0
$927$		−	86.7744i		−	2.85005i
$928$		0			0
$929$		−	1.74110i		−	0.0571236i	−0.999592	−	0.0285618i	$-0.990907\pi$
$929$		−	1.74110i		−	0.0571236i	0.999592	−	0.0285618i	$-0.00909274\pi$
$930$		0			0
$931$	−7.69930	−	11.5228i	−0.252334	−	0.377645i
$932$		0			0
$933$	−19.3927	−	97.4935i	−0.634887	−	3.19179i
$934$		0			0
$935$	5.58741	−	2.31438i	0.182728	−	0.0756884i
$936$		0			0
$937$	7.06597	+	2.92682i	0.230835	+	0.0956151i	0.495103	−	0.868834i	$-0.335130\pi$
$937$	7.06597	+	2.92682i	0.230835	+	0.0956151i	−0.264268	+	0.964449i	$0.585130\pi$
$938$		0			0
$939$	39.9011	+	26.6611i	1.30212	+	0.870051i
$940$		0			0
$941$	−0.778661	+	3.91459i	−0.0253836	+	0.127612i	−0.991399	−	0.130871i	$-0.958223\pi$
$941$	−0.778661	+	3.91459i	−0.0253836	+	0.127612i	0.966016	+	0.258483i	$0.0832226\pi$
$942$		0			0
$943$	−25.6305	−	25.6305i	−0.834643	−	0.834643i
$944$		0			0
$945$	−12.4228	+	12.4228i	−0.404114	+	0.404114i
$946$		0			0
$947$	−43.5246	−	8.65759i	−1.41436	−	0.281334i	−0.572002	−	0.820252i	$-0.693833\pi$
$947$	−43.5246	−	8.65759i	−1.41436	−	0.281334i	−0.842358	+	0.538918i	$0.818833\pi$
$948$		0			0
$949$	−0.202654	+	0.303294i	−0.00657844	+	0.00984532i
$950$		0			0
$951$	17.7423	−	42.8337i	0.575334	−	1.38898i
$952$		0			0
$953$	11.8200	+	28.5361i	0.382888	+	0.924374i	0.991404	+	0.130833i	$0.0417650\pi$
$953$	11.8200	+	28.5361i	0.382888	+	0.924374i	−0.608516	+	0.793541i	$0.708235\pi$
$954$		0			0
$955$	−27.8701	+	5.54371i	−0.901855	+	0.179390i
$956$		0			0
$957$	−102.805	+	68.6924i	−3.32323	+	2.22051i
$958$		0			0
$959$	−10.6537			−0.344026
$960$		0			0
$961$	27.7311			0.894551
$962$		0			0
$963$	−74.9082	+	50.0521i	−2.41388	+	1.61291i
$964$		0			0
$965$	37.4516	−	7.44958i	1.20561	−	0.239811i
$966$		0			0
$967$	20.2478	+	48.8824i	0.651124	+	1.57195i	0.811149	+	0.584839i	$0.198842\pi$
$967$	20.2478	+	48.8824i	0.651124	+	1.57195i	−0.160025	+	0.987113i	$0.551158\pi$
$968$		0			0
$969$	−1.50334	+	3.62938i	−0.0482941	+	0.116592i
$970$		0			0
$971$	10.4503	−	15.6399i	0.335365	−	0.501909i	−0.625012	−	0.780615i	$-0.714906\pi$
$971$	10.4503	−	15.6399i	0.335365	−	0.501909i	0.960376	+	0.278707i	$0.0899058\pi$
$972$		0			0
$973$	9.98987	+	1.98711i	0.320260	+	0.0637038i
$974$		0			0
$975$	−0.162759	+	0.162759i	−0.00521246	+	0.00521246i
$976$		0			0
$977$	−3.83519	−	3.83519i	−0.122699	−	0.122699i	0.643091	−	0.765790i	$-0.277652\pi$
$977$	−3.83519	−	3.83519i	−0.122699	−	0.122699i	−0.765790	+	0.643091i	$0.777652\pi$
$978$		0			0
$979$	6.10111	−	30.6723i	0.194992	−	0.980292i
$980$		0			0
$981$	34.3177	+	22.9304i	1.09568	+	0.732111i
$982$		0			0
$983$	11.2735	+	4.66965i	0.359570	+	0.148939i	0.555153	−	0.831748i	$-0.312660\pi$
$983$	11.2735	+	4.66965i	0.359570	+	0.148939i	−0.195583	+	0.980687i	$0.562660\pi$
$984$		0			0
$985$	−28.4314	+	11.7767i	−0.905900	+	0.375236i
$986$		0			0
$987$	−1.60970	−	8.09250i	−0.0512372	−	0.257587i
$988$		0			0
$989$	28.9989	+	43.3999i	0.922111	+	1.38004i
$990$		0			0
$991$		−	4.91122i		−	0.156010i	−0.996953	−	0.0780051i	$-0.975145\pi$
$991$		−	4.91122i		−	0.156010i	0.996953	−	0.0780051i	$-0.0248550\pi$
$992$		0			0
$993$			87.1946i			2.76704i
$994$		0			0
$995$	4.89290	+	7.32275i	0.155115	+	0.232147i
$996$		0			0
$997$	7.85511	+	39.4903i	0.248774	+	1.25067i	0.879963	+	0.475042i	$0.157567\pi$
$997$	7.85511	+	39.4903i	0.248774	+	1.25067i	−0.631189	+	0.775629i	$0.717433\pi$
$998$		0			0
$999$	−25.1577	+	10.4206i	−0.795953	+	0.329695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.b.33.1		56
4.3	odd	2		512.2.i.a.33.7		56
8.3	odd	2		256.2.i.a.145.1		56
8.5	even	2		64.2.i.a.13.2	yes	56
24.5	odd	2		576.2.bd.a.397.6		56
64.5	even	16	inner	512.2.i.b.481.1		56
64.27	odd	16		256.2.i.a.113.1		56
64.37	even	16		64.2.i.a.5.2	✓	56
64.59	odd	16		512.2.i.a.481.7		56
192.101	odd	16		576.2.bd.a.325.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.2	✓	56	64.37	even	16
64.2.i.a.13.2	yes	56	8.5	even	2
256.2.i.a.113.1		56	64.27	odd	16
256.2.i.a.145.1		56	8.3	odd	2
512.2.i.a.33.7		56	4.3	odd	2
512.2.i.a.481.7		56	64.59	odd	16
512.2.i.b.33.1		56	1.1	even	1	trivial
512.2.i.b.481.1		56	64.5	even	16	inner
576.2.bd.a.325.6		56	192.101	odd	16
576.2.bd.a.397.6		56	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.51381 + 1.67967i) q^{3} +(2.28487 - 0.454489i) q^{5} +(0.303950 + 0.733799i) q^{7} +(2.34987 - 5.67309i) q^{9} +O(q^{10})\)	\(q+(-2.51381 + 1.67967i) q^{3} +(2.28487 - 0.454489i) q^{5} +(0.303950 + 0.733799i) q^{7} +(2.34987 - 5.67309i) q^{9} +(2.41516 - 3.61454i) q^{11} +(0.174791 + 0.0347682i) q^{13} +(-4.98033 + 4.98033i) q^{15} +(0.422266 + 0.422266i) q^{17} +(0.424489 - 2.13405i) q^{19} +(-1.99661 - 1.33409i) q^{21} +(6.39382 + 2.64841i) q^{23} +(0.394679 - 0.163481i) q^{25} +(1.85234 + 9.31236i) q^{27} +(5.22657 + 7.82211i) q^{29} -1.80802i q^{31} +13.1429i q^{33} +(1.02799 + 1.53849i) q^{35} +(0.559507 + 2.81283i) q^{37} +(-0.497791 + 0.206192i) q^{39} +(-4.83885 - 2.00432i) q^{41} +(6.27110 + 4.19021i) q^{43} +(2.79080 - 14.0303i) q^{45} +(2.42967 + 2.42967i) q^{47} +(4.50367 - 4.50367i) q^{49} +(-1.77076 - 0.352226i) q^{51} +(0.350569 - 0.524664i) q^{53} +(3.87556 - 9.35642i) q^{55} +(2.51742 + 6.07759i) q^{57} +(-8.25271 + 1.64157i) q^{59} +(2.67124 - 1.78487i) q^{61} +4.87715 q^{63} +0.415178 q^{65} +(-0.879840 + 0.587891i) q^{67} +(-20.5213 + 4.08194i) q^{69} +(-0.458776 - 1.10758i) q^{71} +(-0.783268 + 1.89098i) q^{73} +(-0.717551 + 1.07389i) q^{75} +(3.38643 + 0.673603i) q^{77} +(-5.97434 + 5.97434i) q^{79} +(-7.27213 - 7.27213i) q^{81} +(1.56393 - 7.86242i) q^{83} +(1.15674 + 0.772908i) q^{85} +(-26.2772 - 10.8844i) q^{87} +(6.64632 - 2.75300i) q^{89} +(0.0276149 + 0.138830i) q^{91} +(3.03687 + 4.54500i) q^{93} -5.06895i q^{95} -9.60392i q^{97} +(-14.8303 - 22.1951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Introduction

L-functions

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Database

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