LMFDB - Embedded newform 512.2.i.a.33.7

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			33.7
Character	$\chi$	$=$	512.33
Dual form			512.2.i.a.481.7

$q$-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	$-0.349828\pi$
$3$	2.51381	−	1.67967i	1.45135	−	0.969758i	0.996875	−	0.0789971i	$-0.0251718\pi$
$4$		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	0.855972	−	0.517023i	$-0.172960\pi$
$7$	−0.303950	−	0.733799i	−0.114882	−	0.277350i	−0.970854	+	0.239673i	$0.922960\pi$
$8$		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	$0.414983\pi$
$11$	−2.41516	+	3.61454i	−0.728198	+	1.08983i	−0.992121	+	0.125281i	$0.960017\pi$
$12$		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	$0.142795\pi$
$19$	−0.424489	+	2.13405i	−0.0973844	+	0.489584i	−0.998438	+	0.0558761i	$0.982205\pi$
$20$		0			0
$21$	−1.99661	−	1.33409i	−0.435696	−	0.291123i
$22$		0			0
$23$	−6.39382	−	2.64841i	−1.33320	−	0.552231i	−0.401636	−	0.915799i	$-0.631558\pi$
$23$	−6.39382	−	2.64841i	−1.33320	−	0.552231i	−0.931568	+	0.363568i	$0.881558\pi$
$24$		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	$0.0519121\pi$
$31$			1.80802i			0.324729i	−0.986731	+	0.162365i	$0.948088\pi$
$32$		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	−0.0236588	−	0.999720i	$-0.507532\pi$
$43$	−6.27110	−	4.19021i	−0.956334	−	0.639002i	−0.932675	+	0.360718i	$0.882532\pi$
$44$		0			0
$45$	2.79080	−	14.0303i	0.416027	−	2.09151i
$46$		0			0
$47$	−2.42967	−	2.42967i	−0.354403	−	0.354403i	0.507342	−	0.861745i	$-0.330628\pi$
$47$	−2.42967	−	2.42967i	−0.354403	−	0.354403i	−0.861745	+	0.507342i	$0.830628\pi$
$48$		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	0.373982	−	0.927436i	$-0.377992\pi$
$59$	8.25271	−	1.64157i	1.07441	−	0.213714i	0.700429	+	0.713722i	$0.252992\pi$
$60$		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	−0.500664	−	0.865642i	$-0.666911\pi$
$67$	0.879840	−	0.587891i	0.107490	−	0.0718223i	0.608153	+	0.793820i	$0.291911\pi$
$68$		0			0
$69$	−20.5213	+	4.08194i	−2.47047	+	0.491407i
$70$		0			0
$71$	0.458776	+	1.10758i	0.0544467	+	0.131446i	0.948762	−	0.315991i	$-0.102337\pi$
$71$	0.458776	+	1.10758i	0.0544467	+	0.131446i	−0.894316	+	0.447437i	$0.852337\pi$
$72$		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	−0.286049	−	0.958215i	$-0.592342\pi$
$79$	5.97434	−	5.97434i	0.672166	−	0.672166i	0.958215	+	0.286049i	$0.0923420\pi$
$80$		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	$0.207507\pi$
$83$	−1.56393	+	7.86242i	−0.171664	+	0.863012i	−0.966594	+	0.256312i	$0.917493\pi$
$84$		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	−0.917917	−	0.396771i	$-0.870131\pi$
$103$	−13.0558	+	5.40788i	−1.28642	+	0.532854i	−0.368506	+	0.929625i	$0.620131\pi$
$104$		0			0
$105$	−5.16833	−	2.14079i	−0.504377	−	0.208920i
$106$		0			0
$107$	12.1990	+	8.15112i	1.17932	+	0.787999i	0.981354	−	0.192209i	$-0.0615652\pi$
$107$	12.1990	+	8.15112i	1.17932	+	0.787999i	0.197970	+	0.980208i	$0.436565\pi$
$108$		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	$-0.614762\pi$
$127$	−7.95115			−0.705551			−0.352775	+	0.935708i	$0.614762\pi$
$128$		0			0
$129$	−22.8025			−2.00765
$130$		0			0
$131$	2.99684	−	2.00242i	0.261835	−	0.174953i	−0.417723	−	0.908575i	$-0.637172\pi$
$131$	2.99684	−	2.00242i	0.261835	−	0.174953i	0.679558	+	0.733622i	$0.262172\pi$
$132$		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	−0.999902	−	0.0140189i	$-0.995538\pi$
$139$	−7.12464	+	10.6628i	−0.604304	+	0.904405i	0.395598	+	0.918424i	$0.370538\pi$
$140$		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	0.275605	−	0.961271i	$-0.411122\pi$
$151$	−2.57112	−	1.06499i	−0.209235	−	0.0866679i	−0.484839	+	0.874603i	$0.661122\pi$
$152$		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	0.442660	−	0.896690i	$-0.354035\pi$
$163$	−7.08796	−	10.6079i	−0.555172	−	0.830873i	−0.997832	+	0.0658161i	$0.979035\pi$
$164$		0			0
$165$	5.97332	+	30.0299i	0.465022	+	2.33782i
$166$		0			0
$167$	4.60049	−	1.90558i	0.355996	−	0.147459i	−0.197516	−	0.980300i	$-0.563287\pi$
$167$	4.60049	−	1.90558i	0.355996	−	0.147459i	0.553512	+	0.832841i	$0.313287\pi$
$168$		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	−0.0569725	−	0.998376i	$-0.518145\pi$
$179$	−6.57810	−	1.30847i	−0.491670	−	0.0977993i	−0.434698	+	0.900576i	$0.643145\pi$
$180$		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	$-0.354519\pi$
$191$	12.1977			0.882592			0.441296	+	0.897362i	$0.354519\pi$
$192$		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	0.864271	−	0.503026i	$-0.167780\pi$
$199$	−1.44670	−	3.49265i	−0.102554	−	0.247587i	−0.966825	+	0.255439i	$0.917780\pi$
$200$		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	$-0.867236\pi$
$211$	1.24095	−	6.23870i	0.0854309	−	0.429490i	0.999703	−	0.0243884i	$-0.00776383\pi$
$212$		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	$-0.939383\pi$
$223$		−	5.65324i		−	0.378569i	0.981922	−	0.189284i	$-0.0606168\pi$
$224$		0			0
$225$		−	2.62321i		−	0.174881i
$226$		0			0
$227$	−3.62832	−	5.43017i	−0.240820	−	0.360413i	0.691296	−	0.722571i	$-0.257040\pi$
$227$	−3.62832	−	5.43017i	−0.240820	−	0.360413i	−0.932117	+	0.362158i	$0.882040\pi$
$228$		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	$0.0168048\pi$
$239$	16.2539	+	16.2539i	1.05138	+	1.05138i	0.0527693	+	0.998607i	$0.483195\pi$
$240$		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	0.647620	−	0.761964i	$-0.275765\pi$
$251$	24.3591	−	4.84533i	1.53753	−	0.305834i	0.889913	+	0.456130i	$0.150765\pi$
$252$		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	$0.0556914\pi$
$263$	6.67352	+	16.1113i	0.411507	+	0.993465i	−0.573227	+	0.819397i	$0.694309\pi$
$264$		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	$-0.405631\pi$
$271$	20.5532	−	20.5532i	1.24852	−	1.24852i	0.956374	−	0.292145i	$-0.0943691\pi$
$272$		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	0.953380	−	0.301774i	$-0.0975787\pi$
$283$	−0.721894	−	3.62921i	−0.0429121	−	0.215734i	−0.996292	+	0.0860399i	$0.972579\pi$
$284$		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	0.589442	−	0.807811i	$-0.299348\pi$
$307$	14.4531	+	2.87489i	0.824880	+	0.164079i	0.235438	+	0.971889i	$0.424348\pi$
$308$		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	$-0.492892\pi$
$311$	12.5822	−	30.3761i	0.713470	−	1.72247i	0.691142	−	0.722719i	$-0.257108\pi$
$312$		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	$0.478779\pi$
$331$	−16.0230	+	23.9801i	−0.880702	+	1.31806i	−0.947321	+	0.320285i	$0.896221\pi$
$332$		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	$-0.949149\pi$
$347$	−2.53390	−	12.7388i	−0.136027	−	0.683853i	0.851240	−	0.524777i	$-0.175851\pi$
$348$		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	−0.314051	−	0.949406i	$-0.601686\pi$
$359$	2.56193	−	1.06119i	0.135214	−	0.0560073i	0.449264	+	0.893399i	$0.351686\pi$
$360$		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	0.272755	−	0.962084i	$-0.412065\pi$
$367$	−13.2056	−	13.2056i	−0.689329	−	0.689329i	−0.962084	+	0.272755i	$0.912065\pi$
$368$		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	0.542427	−	0.840103i	$-0.317506\pi$
$379$	26.5748	−	5.28606i	1.36506	−	0.271527i	0.822631	+	0.568576i	$0.192506\pi$
$380$		0			0
$381$	−19.9876	+	13.3553i	−1.02400	+	0.684214i
$382$		0			0
$383$	12.4669			0.637027			0.318514	−	0.947918i	$-0.396816\pi$
$383$	12.4669			0.637027			0.318514	+	0.947918i	$0.396816\pi$
$384$		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	0.524629	−	0.851331i	$-0.324204\pi$
$419$	−9.47052	−	14.1736i	−0.462665	−	0.692427i	−0.987294	+	0.158904i	$0.949204\pi$
$420$		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	0.837961	−	0.545731i	$-0.183748\pi$
$431$	6.06685	+	6.06685i	0.292230	+	0.292230i	−0.545731	+	0.837961i	$0.683748\pi$
$432$		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	−0.945999	−	0.324169i	$-0.894915\pi$
$439$	−1.00267	+	2.42067i	−0.0478550	+	0.115532i	0.898144	+	0.439701i	$0.144915\pi$
$440$		0			0
$441$	−14.9667	−	36.1328i	−0.712700	−	1.72061i
$442$		0			0
$443$	−10.3515	+	2.05904i	−0.491815	+	0.0978280i	−0.434766	−	0.900543i	$-0.643169\pi$
$443$	−10.3515	+	2.05904i	−0.491815	+	0.0978280i	−0.0570485	+	0.998371i	$0.518169\pi$
$444$		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	−0.904845	−	0.425741i	$-0.860014\pi$
$463$	−10.3091	+	10.3091i	−0.479105	+	0.479105i	0.425741	+	0.904845i	$0.360014\pi$
$464$		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	$0.248775\pi$
$467$	−4.65749	+	23.4148i	−0.215523	+	1.08351i	−0.925345	+	0.379126i	$0.876225\pi$
$468$		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	$0.0528065\pi$
$479$			7.22838i			0.330273i	−0.986271	+	0.165136i	$0.947194\pi$
$480$		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	−0.0537402	−	0.998555i	$-0.517114\pi$
$487$	13.5574	−	5.61566i	0.614345	−	0.254470i	0.668085	+	0.744085i	$0.267114\pi$
$488$		0			0
$489$	−35.6355	−	14.7607i	−1.61149	−	0.667502i
$490$		0			0
$491$	−16.6130	−	11.1005i	−0.749734	−	0.500956i	0.121035	−	0.992648i	$-0.461379\pi$
$491$	−16.6130	−	11.1005i	−0.749734	−	0.500956i	−0.870769	+	0.491692i	$0.836379\pi$
$492$		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	0.156057	−	0.987748i	$-0.450122\pi$
$499$	−1.73704	−	0.345518i	−0.0777605	−	0.0154675i	−0.233817	+	0.972281i	$0.575122\pi$
$500$		0			0
$501$	8.36397	−	12.5176i	0.373675	−	0.559244i
$502$		0			0
$503$	6.27595	−	15.1515i	0.279831	−	0.675571i	−0.720000	−	0.693974i	$-0.755858\pi$
$503$	6.27595	−	15.1515i	0.279831	−	0.675571i	0.999831	+	0.0184028i	$0.00585812\pi$
$504$		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	−0.856730	−	0.515765i	$-0.827508\pi$
$523$	−1.19764	+	1.79239i	−0.0523691	+	0.0783759i	0.804361	+	0.594141i	$0.202508\pi$
$524$		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	$0.0466051\pi$
$547$	17.4357	+	26.0944i	0.745498	+	1.11572i	−0.243803	+	0.969825i	$0.578395\pi$
$548$		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	0.396243	−	0.918146i	$-0.370314\pi$
$563$	9.75123	+	1.93964i	0.410965	+	0.0817461i	0.0147220	+	0.999892i	$0.495314\pi$
$564$		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	−0.498127	−	0.867104i	$-0.665979\pi$
$571$	−14.9708	+	2.97788i	−0.626510	+	0.124621i	−0.128383	+	0.991725i	$0.540979\pi$
$572$		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	$-0.620947\pi$
$587$	15.2402	−	22.8085i	0.629029	−	0.941408i	0.999919	−	0.0127316i	$-0.00405269\pi$
$588$		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	0.651692	−	0.758484i	$-0.274060\pi$
$599$	14.1017	+	5.84110i	0.576179	+	0.238661i	−0.0755132	+	0.997145i	$0.524060\pi$
$600$		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	$-0.929828\pi$
$607$		−	10.7750i		−	0.437344i	0.975798	−	0.218672i	$-0.0701724\pi$
$608$		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	0.591180	−	0.806540i	$-0.298662\pi$
$619$	1.79801	+	1.20140i	0.0722683	+	0.0482881i	−0.518911	+	0.854828i	$0.673662\pi$
$620$		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	$0.289256\pi$
$631$	−9.48652	+	22.9025i	−0.377652	+	0.911733i	−0.992405	+	0.123014i	$0.960744\pi$
$632$		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	−0.327264	−	0.944933i	$-0.606127\pi$
$643$	10.6628	−	7.12468i	0.420501	−	0.280970i	0.747765	+	0.663963i	$0.231127\pi$
$644$		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	$-0.798674\pi$
$647$	−16.6415	−	40.1760i	−0.654243	−	1.57948i	0.152318	−	0.988332i	$-0.451326\pi$
$648$		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	$0.182124\pi$
$659$	−3.67625	+	18.4817i	−0.143206	+	0.719947i	−0.983940	+	0.178498i	$0.942876\pi$
$660$		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	−0.00438760	−	0.999990i	$-0.501397\pi$
$683$	−24.3032	−	16.2389i	−0.929937	−	0.621364i	−0.925550	+	0.378626i	$0.876397\pi$
$684$		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	−0.559550	−	0.828797i	$-0.689026\pi$
$691$	−36.6353	−	7.28722i	−1.39367	−	0.277219i	−0.834123	+	0.551578i	$0.814026\pi$
$692$		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	−0.995691	−	0.0927286i	$-0.970441\pi$
$719$	−24.2122	+	24.2122i	−0.902963	+	0.902963i	0.0927286	+	0.995691i	$0.470441\pi$
$720$		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	0.728226	−	0.685337i	$-0.240345\pi$
$727$	20.4528	+	8.47184i	0.758553	+	0.314203i	0.0303271	+	0.999540i	$0.490345\pi$
$728$		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	$0.0297510\pi$
$739$	19.0522	+	28.5137i	0.700847	+	1.04889i	−0.294788	+	0.955563i	$0.595249\pi$
$740$		0			0
$741$	0.228717	+	1.14984i	0.00840211	+	0.0422403i
$742$		0			0
$743$	41.6805	−	17.2646i	1.52911	−	0.633378i	0.549718	−	0.835351i	$-0.314735\pi$
$743$	41.6805	−	17.2646i	1.52911	−	0.633378i	0.979391	+	0.201973i	$0.0647353\pi$
$744$		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	$0.0423612\pi$
$751$	30.7983	+	30.7983i	1.12385	+	1.12385i	0.132689	+	0.991158i	$0.457639\pi$
$752$		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	$-0.798475\pi$
$787$	4.63019	−	23.2775i	0.165048	−	0.829754i	0.971241	−	0.238101i	$-0.0765248\pi$
$788$		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	0.614507	−	0.788912i	$-0.289355\pi$
$811$	3.44040	+	2.29880i	0.120809	+	0.0807219i	−0.493698	+	0.869634i	$0.664355\pi$
$812$		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	−0.993732	−	0.111791i	$-0.964341\pi$
$823$	−6.08212	+	14.6835i	−0.212009	+	0.511836i	0.781723	+	0.623626i	$0.214341\pi$
$824$		0			0
$825$	2.14862	+	5.18724i	0.0748055	+	0.180596i
$826$		0			0
$827$	13.0143	−	2.58870i	0.452551	−	0.0900181i	0.0364484	−	0.999336i	$-0.488396\pi$
$827$	13.0143	−	2.58870i	0.452551	−	0.0900181i	0.416103	+	0.909317i	$0.363396\pi$
$828$		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	$0.0558286\pi$
$839$	11.9276	+	28.7957i	0.411785	+	0.994137i	−0.572874	+	0.819644i	$0.694171\pi$
$840$		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	$0.295969\pi$
$859$	10.3238	+	51.9011i	0.352243	+	1.77084i	−0.245741	+	0.969335i	$0.579031\pi$
$860$		0			0
$861$	6.98735	+	10.4573i	0.238128	+	0.356384i
$862$		0			0
$863$			44.3164i			1.50855i	0.656559	+	0.754275i	$0.272011\pi$
$863$			44.3164i			1.50855i	−0.656559	+	0.754275i	$0.727989\pi$
$864$		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	0.322382	−	0.946610i	$-0.395516\pi$
$883$	7.66573	+	1.52481i	0.257972	+	0.0513139i	−0.0644097	+	0.997924i	$0.520516\pi$
$884$		0			0
$885$	32.9257	−	49.2768i	1.10678	−	1.65642i
$886$		0			0
$887$	5.60114	−	13.5223i	0.188068	−	0.454036i	−0.801520	−	0.597968i	$-0.795975\pi$
$887$	5.60114	−	13.5223i	0.188068	−	0.454036i	0.989587	+	0.143933i	$0.0459749\pi$
$888$		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	−1.00000		0.000798948i	$-0.999746\pi$
$907$	−18.5691	+	27.7907i	−0.616578	+	0.922775i	0.383421	+	0.923573i	$0.374746\pi$
$908$		0			0
$909$	−93.5631	−	18.6109i	−3.10329	−	0.617283i
$910$		0			0
$911$	−19.9890	+	19.9890i	−0.662264	+	0.662264i	−0.955913	−	0.293649i	$-0.905130\pi$
$911$	−19.9890	+	19.9890i	−0.662264	+	0.662264i	0.293649	+	0.955913i	$0.405130\pi$
$912$		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	−0.217149	−	0.976139i	$-0.569676\pi$
$919$	−32.1621	−	13.3220i	−1.06093	−	0.439452i	−0.843782	+	0.536687i	$0.819676\pi$
$920$		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	0.842358	−	0.538918i	$-0.181167\pi$
$947$	43.5246	+	8.65759i	1.41436	+	0.281334i	0.572002	+	0.820252i	$0.306167\pi$
$948$		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	$-0.801158\pi$
$967$	−20.2478	−	48.8824i	−0.651124	−	1.57195i	0.160025	−	0.987113i	$-0.448842\pi$
$968$		0			0
$969$	−1.50334	+	3.62938i	−0.0482941	+	0.116592i
$970$		0			0
$971$	−10.4503	+	15.6399i	−0.335365	+	0.501909i	−0.960376	−	0.278707i	$-0.910094\pi$
$971$	−10.4503	+	15.6399i	−0.335365	+	0.501909i	0.625012	+	0.780615i	$0.285094\pi$
$972$		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	0.195583	−	0.980687i	$-0.437340\pi$
$983$	−11.2735	−	4.66965i	−0.359570	−	0.148939i	−0.555153	+	0.831748i	$0.687340\pi$
$984$		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	$0.0248550\pi$
$991$			4.91122i			0.156010i	−0.996953	+	0.0780051i	$0.975145\pi$
$992$		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.a.33.7		56
4.3	odd	2		512.2.i.b.33.1		56
8.3	odd	2		64.2.i.a.13.2	yes	56
8.5	even	2		256.2.i.a.145.1		56
24.11	even	2		576.2.bd.a.397.6		56
64.5	even	16	inner	512.2.i.a.481.7		56
64.27	odd	16		64.2.i.a.5.2	✓	56
64.37	even	16		256.2.i.a.113.1		56
64.59	odd	16		512.2.i.b.481.1		56
192.155	even	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	64.27	odd	16
64.2.i.a.13.2	yes	56	8.3	odd	2
256.2.i.a.113.1		56	64.37	even	16
256.2.i.a.145.1		56	8.5	even	2
512.2.i.a.33.7		56	1.1	even	1	trivial
512.2.i.a.481.7		56	64.5	even	16	inner
512.2.i.b.33.1		56	4.3	odd	2
512.2.i.b.481.1		56	64.59	odd	16
576.2.bd.a.325.6		56	192.155	even	16
576.2.bd.a.397.6		56	24.11	even	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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more