LMFDB - Embedded newform 512.2.i.a.97.7

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			97.7
Character	$\chi$	$=$	512.97
Dual form			512.2.i.a.417.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.553854 + 2.78441i) q^{3} +(-2.59756 + 1.73564i) q^{5} +(1.96508 + 0.813965i) q^{7} +(-4.67456 + 1.93627i) q^{9} +O(q^{10})$	\(q+(0.553854 + 2.78441i) q^{3} +(-2.59756 + 1.73564i) q^{5} +(1.96508 + 0.813965i) q^{7} +(-4.67456 + 1.93627i) q^{9} +(-2.02382 - 0.402563i) q^{11} +(1.99644 + 1.33398i) q^{13} +(-6.27140 - 6.27140i) q^{15} +(-2.31120 + 2.31120i) q^{17} +(2.37703 - 3.55748i) q^{19} +(-1.17804 + 5.92242i) q^{21} +(-0.993213 - 2.39783i) q^{23} +(1.82149 - 4.39746i) q^{25} +(-3.24866 - 4.86196i) q^{27} +(-2.34079 + 0.465613i) q^{29} +1.81094i q^{31} -5.85811i q^{33} +(-6.51718 + 1.29635i) q^{35} +(-1.40742 - 2.10635i) q^{37} +(-2.60861 + 6.29775i) q^{39} +(4.66056 + 11.2516i) q^{41} +(0.452227 - 2.27350i) q^{43} +(8.78181 - 13.1429i) q^{45} +(2.27298 - 2.27298i) q^{47} +(-1.75073 - 1.75073i) q^{49} +(-7.71539 - 5.15526i) q^{51} +(-7.98970 - 1.58925i) q^{53} +(5.95570 - 2.46693i) q^{55} +(11.2220 + 4.64831i) q^{57} +(7.08029 - 4.73090i) q^{59} +(1.95998 + 9.85346i) q^{61} -10.7620 q^{63} -7.50119 q^{65} +(2.88943 + 14.5262i) q^{67} +(6.12645 - 4.09356i) q^{69} +(6.41451 + 2.65698i) q^{71} +(-3.36337 + 1.39315i) q^{73} +(13.2532 + 2.63622i) q^{75} +(-3.64930 - 2.43839i) q^{77} +(10.9490 + 10.9490i) q^{79} +(1.00516 - 1.00516i) q^{81} +(-3.72793 + 5.57925i) q^{83} +(1.99208 - 10.0149i) q^{85} +(-2.59292 - 6.25985i) q^{87} +(-3.10595 + 7.49842i) q^{89} +(2.83736 + 4.24642i) q^{91} +(-5.04240 + 1.00299i) q^{93} +13.3664i q^{95} -8.49286i q^{97} +(10.2399 - 2.03685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$1$

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
$3$	0.553854	+	2.78441i	0.319768	+	1.60758i	0.721898	+	0.691999i	$0.243270\pi$
$3$	0.553854	+	2.78441i	0.319768	+	1.60758i	−0.402131	+	0.915582i	$0.631730\pi$
$4$		0			0
$5$	−2.59756	+	1.73564i	−1.16167	+	0.776200i	−0.978371	−	0.206858i	$-0.933676\pi$
$5$	−2.59756	+	1.73564i	−1.16167	+	0.776200i	−0.183295	+	0.983058i	$0.558676\pi$
$6$		0			0
$7$	1.96508	+	0.813965i	0.742732	+	0.307650i	0.721772	−	0.692131i	$-0.243328\pi$
$7$	1.96508	+	0.813965i	0.742732	+	0.307650i	0.0209598	+	0.999780i	$0.493328\pi$
$8$		0			0
$9$	−4.67456	+	1.93627i	−1.55819	+	0.645422i
$10$		0			0
$11$	−2.02382	−	0.402563i	−0.610205	−	0.121377i	−0.119692	−	0.992811i	$-0.538191\pi$
$11$	−2.02382	−	0.402563i	−0.610205	−	0.121377i	−0.490513	+	0.871434i	$0.663191\pi$
$12$		0			0
$13$	1.99644	+	1.33398i	0.553713	+	0.369979i	0.800724	−	0.599033i	$-0.204448\pi$
$13$	1.99644	+	1.33398i	0.553713	+	0.369979i	−0.247011	+	0.969013i	$0.579448\pi$
$14$		0			0
$15$	−6.27140	−	6.27140i	−1.61927	−	1.61927i
$16$		0			0
$17$	−2.31120	+	2.31120i	−0.560547	+	0.560547i	−0.929463	−	0.368916i	$-0.879729\pi$
$17$	−2.31120	+	2.31120i	−0.560547	+	0.560547i	0.368916	+	0.929463i	$0.379729\pi$
$18$		0			0
$19$	2.37703	−	3.55748i	0.545328	−	0.816142i	−0.451780	−	0.892129i	$-0.649211\pi$
$19$	2.37703	−	3.55748i	0.545328	−	0.816142i	0.997109	+	0.0759875i	$0.0242109\pi$
$20$		0			0
$21$	−1.17804	+	5.92242i	−0.257070	+	1.29238i
$22$		0			0
$23$	−0.993213	−	2.39783i	−0.207099	−	0.499982i	0.785865	−	0.618398i	$-0.212218\pi$
$23$	−0.993213	−	2.39783i	−0.207099	−	0.499982i	−0.992964	+	0.118417i	$0.962218\pi$
$24$		0			0
$25$	1.82149	−	4.39746i	0.364297	−	0.879491i
$26$		0			0
$27$	−3.24866	−	4.86196i	−0.625205	−	0.935685i
$28$		0			0
$29$	−2.34079	+	0.465613i	−0.434674	+	0.0864621i	−0.407577	−	0.913171i	$-0.633626\pi$
$29$	−2.34079	+	0.465613i	−0.434674	+	0.0864621i	−0.0270970	+	0.999633i	$0.508626\pi$
$30$		0			0
$31$			1.81094i			0.325254i	0.986688	+	0.162627i	$0.0519967\pi$
$31$			1.81094i			0.325254i	−0.986688	+	0.162627i	$0.948003\pi$
$32$		0			0
$33$		−	5.85811i		−	1.01977i
$34$		0			0
$35$	−6.51718	+	1.29635i	−1.10160	+	0.219123i
$36$		0			0
$37$	−1.40742	−	2.10635i	−0.231378	−	0.346282i	0.697554	−	0.716533i	$-0.254272\pi$
$37$	−1.40742	−	2.10635i	−0.231378	−	0.346282i	−0.928932	+	0.370250i	$0.879272\pi$
$38$		0			0
$39$	−2.60861	+	6.29775i	−0.417712	+	1.00845i
$40$		0			0
$41$	4.66056	+	11.2516i	0.727858	+	1.75720i	0.649607	+	0.760270i	$0.274933\pi$
$41$	4.66056	+	11.2516i	0.727858	+	1.75720i	0.0782501	+	0.996934i	$0.475067\pi$
$42$		0			0
$43$	0.452227	−	2.27350i	0.0689639	−	0.346705i	−0.930862	−	0.365371i	$-0.880942\pi$
$43$	0.452227	−	2.27350i	0.0689639	−	0.346705i	0.999826	+	0.0186663i	$0.00594202\pi$
$44$		0			0
$45$	8.78181	−	13.1429i	1.30912	−	1.95923i
$46$		0			0
$47$	2.27298	−	2.27298i	0.331549	−	0.331549i	−0.521626	−	0.853174i	$-0.674674\pi$
$47$	2.27298	−	2.27298i	0.331549	−	0.331549i	0.853174	+	0.521626i	$0.174674\pi$
$48$		0			0
$49$	−1.75073	−	1.75073i	−0.250104	−	0.250104i
$50$		0			0
$51$	−7.71539	−	5.15526i	−1.08037	−	0.721881i
$52$		0			0
$53$	−7.98970	−	1.58925i	−1.09747	−	0.218300i	−0.387036	−	0.922065i	$-0.626501\pi$
$53$	−7.98970	−	1.58925i	−1.09747	−	0.218300i	−0.710433	+	0.703764i	$0.751501\pi$
$54$		0			0
$55$	5.95570	−	2.46693i	0.803067	−	0.332641i
$56$		0			0
$57$	11.2220	+	4.64831i	1.48639	+	0.615684i
$58$		0			0
$59$	7.08029	−	4.73090i	0.921775	−	0.615911i	−0.00152111	−	0.999999i	$-0.500484\pi$
$59$	7.08029	−	4.73090i	0.921775	−	0.615911i	0.923296	+	0.384088i	$0.125484\pi$
$60$		0			0
$61$	1.95998	+	9.85346i	0.250949	+	1.26161i	0.876492	+	0.481417i	$0.159878\pi$
$61$	1.95998	+	9.85346i	0.250949	+	1.26161i	−0.625543	+	0.780190i	$0.715122\pi$
$62$		0			0
$63$	−10.7620			−1.35588
$64$		0			0
$65$	−7.50119			−0.930408
$66$		0			0
$67$	2.88943	+	14.5262i	0.353000	+	1.77465i	0.594342	+	0.804212i	$0.297413\pi$
$67$	2.88943	+	14.5262i	0.353000	+	1.77465i	−0.241342	+	0.970440i	$0.577587\pi$
$68$		0			0
$69$	6.12645	−	4.09356i	0.737537	−	0.492807i
$70$		0			0
$71$	6.41451	+	2.65698i	0.761263	+	0.315325i	0.729328	−	0.684165i	$-0.239833\pi$
$71$	6.41451	+	2.65698i	0.761263	+	0.315325i	0.0319351	+	0.999490i	$0.489833\pi$
$72$		0			0
$73$	−3.36337	+	1.39315i	−0.393653	+	0.163056i	−0.570724	−	0.821142i	$-0.693338\pi$
$73$	−3.36337	+	1.39315i	−0.393653	+	0.163056i	0.177072	+	0.984198i	$0.443338\pi$
$74$		0			0
$75$	13.2532	+	2.63622i	1.53034	+	0.304404i
$76$		0			0
$77$	−3.64930	−	2.43839i	−0.415877	−	0.277880i
$78$		0			0
$79$	10.9490	+	10.9490i	1.23186	+	1.23186i	0.963247	+	0.268617i	$0.0865667\pi$
$79$	10.9490	+	10.9490i	1.23186	+	1.23186i	0.268617	+	0.963247i	$0.413433\pi$
$80$		0			0
$81$	1.00516	−	1.00516i	0.111685	−	0.111685i
$82$		0			0
$83$	−3.72793	+	5.57925i	−0.409194	+	0.612402i	−0.977632	−	0.210324i	$-0.932548\pi$
$83$	−3.72793	+	5.57925i	−0.409194	+	0.612402i	0.568438	+	0.822726i	$0.307548\pi$
$84$		0			0
$85$	1.99208	−	10.0149i	0.216072	−	1.08627i
$86$		0			0
$87$	−2.59292	−	6.25985i	−0.277990	−	0.671126i
$88$		0			0
$89$	−3.10595	+	7.49842i	−0.329230	+	0.794831i	0.669420	+	0.742884i	$0.266543\pi$
$89$	−3.10595	+	7.49842i	−0.329230	+	0.794831i	−0.998650	+	0.0519471i	$0.983457\pi$
$90$		0			0
$91$	2.83736	+	4.24642i	0.297437	+	0.445145i
$92$		0			0
$93$	−5.04240	+	1.00299i	−0.522872	+	0.104006i
$94$		0			0
$95$			13.3664i			1.37137i
$96$		0			0
$97$		−	8.49286i		−	0.862319i	−0.902276	−	0.431160i	$-0.858105\pi$
$97$		−	8.49286i		−	0.862319i	0.902276	−	0.431160i	$-0.141895\pi$
$98$		0			0
$99$	10.2399	−	2.03685i	1.02915	−	0.204711i
$100$		0			0
$101$	8.24152	+	12.3343i	0.820062	+	1.22731i	0.971074	+	0.238777i	$0.0767465\pi$
$101$	8.24152	+	12.3343i	0.820062	+	1.22731i	−0.151013	+	0.988532i	$0.548253\pi$
$102$		0			0
$103$	2.14828	−	5.18641i	0.211676	−	0.511032i	−0.782005	−	0.623273i	$-0.785803\pi$
$103$	2.14828	−	5.18641i	0.211676	−	0.511032i	0.993681	+	0.112241i	$0.0358027\pi$
$104$		0			0
$105$	−7.21913	−	17.4285i	−0.704515	−	1.70085i
$106$		0			0
$107$	2.52870	−	12.7126i	0.244458	−	1.22897i	−0.642195	−	0.766541i	$-0.721976\pi$
$107$	2.52870	−	12.7126i	0.244458	−	1.22897i	0.886654	−	0.462434i	$-0.153024\pi$
$108$		0			0
$109$	−5.38971	+	8.06626i	−0.516240	+	0.772608i	−0.994402	−	0.105664i	$-0.966303\pi$
$109$	−5.38971	+	8.06626i	−0.516240	+	0.772608i	0.478162	+	0.878272i	$0.341303\pi$
$110$		0			0
$111$	5.08545	−	5.08545i	0.482689	−	0.482689i
$112$		0			0
$113$	4.75634	+	4.75634i	0.447439	+	0.447439i	0.894502	−	0.447063i	$-0.147530\pi$
$113$	4.75634	+	4.75634i	0.447439	+	0.447439i	−0.447063	+	0.894502i	$0.647530\pi$
$114$		0			0
$115$	6.74169	+	4.50465i	0.628666	+	0.420061i
$116$		0			0
$117$	−11.9154	−	2.37013i	−1.10158	−	0.219118i
$118$		0			0
$119$	−6.42293	+	2.66046i	−0.588789	+	0.243884i
$120$		0			0
$121$	−6.22889	−	2.58009i	−0.566262	−	0.234554i
$122$		0			0
$123$	−28.7478	+	19.2087i	−2.59210	+	1.73199i
$124$		0			0
$125$	−0.146412	−	0.736062i	−0.0130955	−	0.0658354i
$126$		0			0
$127$	−0.302397			−0.0268334			−0.0134167	−	0.999910i	$-0.504271\pi$
$127$	−0.302397			−0.0268334			−0.0134167	+	0.999910i	$0.504271\pi$
$128$		0			0
$129$	6.58082			0.579409
$130$		0			0
$131$	−1.05063	−	5.28186i	−0.0917938	−	0.461478i	−0.999154	−	0.0411246i	$-0.986906\pi$
$131$	−1.05063	−	5.28186i	−0.0917938	−	0.461478i	0.907360	−	0.420354i	$-0.138094\pi$
$132$		0			0
$133$	7.56673	−	5.05593i	0.656119	−	0.438404i
$134$		0			0
$135$	16.8772	+	6.99077i	1.45256	+	0.601669i
$136$		0			0
$137$	15.9084	−	6.58948i	1.35915	−	0.562978i	0.420324	−	0.907374i	$-0.361917\pi$
$137$	15.9084	−	6.58948i	1.35915	−	0.562978i	0.938824	+	0.344397i	$0.111917\pi$
$138$		0			0
$139$	11.7049	+	2.32824i	0.992793	+	0.197479i	0.664654	−	0.747151i	$-0.268579\pi$
$139$	11.7049	+	2.32824i	0.992793	+	0.197479i	0.328138	+	0.944630i	$0.393579\pi$
$140$		0			0
$141$	7.58783	+	5.07002i	0.639010	+	0.426973i
$142$		0			0
$143$	−3.50343	−	3.50343i	−0.292971	−	0.292971i
$144$		0			0
$145$	5.27222	−	5.27222i	0.437834	−	0.437834i
$146$		0			0
$147$	3.90511	−	5.84440i	0.322088	−	0.482038i
$148$		0			0
$149$	2.62919	−	13.2179i	0.215392	−	1.08285i	−0.710106	−	0.704095i	$-0.751353\pi$
$149$	2.62919	−	13.2179i	0.215392	−	1.08285i	0.925498	−	0.378753i	$-0.123647\pi$
$150$		0			0
$151$	0.726711	+	1.75444i	0.0591389	+	0.142774i	0.950687	−	0.310152i	$-0.100380\pi$
$151$	0.726711	+	1.75444i	0.0591389	+	0.142774i	−0.891548	+	0.452926i	$0.850380\pi$
$152$		0			0
$153$	6.32873	−	15.2789i	0.511648	−	1.23523i
$154$		0			0
$155$	−3.14313	−	4.70402i	−0.252462	−	0.377836i
$156$		0			0
$157$	18.2962	−	3.63933i	1.46019	−	0.290450i	0.599828	−	0.800129i	$-0.295236\pi$
$157$	18.2962	−	3.63933i	1.46019	−	0.290450i	0.860365	+	0.509679i	$0.170236\pi$
$158$		0			0
$159$		−	23.1268i		−	1.83408i
$160$		0			0
$161$		−	5.52037i		−	0.435066i
$162$		0			0
$163$	−3.25039	+	0.646543i	−0.254590	+	0.0506412i	−0.320735	−	0.947169i	$-0.603930\pi$
$163$	−3.25039	+	0.646543i	−0.254590	+	0.0506412i	0.0661449	+	0.997810i	$0.478930\pi$
$164$		0			0
$165$	10.1676	+	15.2168i	0.791543	+	1.18463i
$166$		0			0
$167$	−0.0933446	+	0.225354i	−0.00722322	+	0.0174384i	−0.927450	−	0.373947i	$-0.878004\pi$
$167$	−0.0933446	+	0.225354i	−0.00722322	+	0.0174384i	0.920227	+	0.391386i	$0.128004\pi$
$168$		0			0
$169$	−2.76861	−	6.68401i	−0.212970	−	0.514154i
$170$		0			0
$171$	−4.22335	+	21.2322i	−0.322968	+	1.62367i
$172$		0			0
$173$	8.24361	−	12.3374i	0.626750	−	0.937998i	−0.373197	−	0.927752i	$-0.621739\pi$
$173$	8.24361	−	12.3374i	0.626750	−	0.937998i	0.999948	−	0.0102459i	$-0.00326144\pi$
$174$		0			0
$175$	7.15875	−	7.15875i	0.541151	−	0.541151i
$176$		0			0
$177$	17.0942	+	17.0942i	1.28488	+	1.28488i
$178$		0			0
$179$	9.58585	+	6.40506i	0.716480	+	0.478736i	0.859599	−	0.510969i	$-0.170713\pi$
$179$	9.58585	+	6.40506i	0.716480	+	0.478736i	−0.143119	+	0.989705i	$0.545713\pi$
$180$		0			0
$181$	8.33755	+	1.65844i	0.619726	+	0.123271i	0.494961	−	0.868915i	$-0.335182\pi$
$181$	8.33755	+	1.65844i	0.619726	+	0.123271i	0.124765	+	0.992186i	$0.460182\pi$
$182$		0			0
$183$	−26.3506	+	10.9148i	−1.94789	+	0.806842i
$184$		0			0
$185$	7.31172	+	3.02862i	0.537569	+	0.222668i
$186$		0			0
$187$	5.60785	−	3.74704i	0.410086	−	0.274011i
$188$		0			0
$189$	−2.42642	−	12.1985i	−0.176496	−	0.887307i
$190$		0			0
$191$	−6.31207			−0.456725			−0.228363	−	0.973576i	$-0.573337\pi$
$191$	−6.31207			−0.456725			−0.228363	+	0.973576i	$0.573337\pi$
$192$		0			0
$193$	−10.5158			−0.756940			−0.378470	−	0.925614i	$-0.623550\pi$
$193$	−10.5158			−0.756940			−0.378470	+	0.925614i	$0.623550\pi$
$194$		0			0
$195$	−4.15456	−	20.8864i	−0.297515	−	1.49571i
$196$		0			0
$197$	−13.0604	+	8.72666i	−0.930513	+	0.621749i	−0.925708	−	0.378240i	$-0.876530\pi$
$197$	−13.0604	+	8.72666i	−0.930513	+	0.621749i	−0.00480529	+	0.999988i	$0.501530\pi$
$198$		0			0
$199$	−25.4075	−	10.5241i	−1.80109	−	0.746037i	−0.986008	−	0.166695i	$-0.946690\pi$
$199$	−25.4075	−	10.5241i	−1.80109	−	0.746037i	−0.815085	−	0.579342i	$-0.803310\pi$
$200$		0			0
$201$	−38.8465	+	16.0907i	−2.74002	+	1.13495i
$202$		0			0
$203$	−4.97885	−	0.990354i	−0.349447	−	0.0695092i
$204$		0			0
$205$	−31.6348	−	21.1377i	−2.20947	−	1.47632i
$206$		0			0
$207$	9.28566	+	9.28566i	0.645398	+	0.645398i
$208$		0			0
$209$	−6.24279	+	6.24279i	−0.431823	+	0.431823i
$210$		0			0
$211$	12.5416	−	18.7698i	0.863399	−	1.29217i	−0.0916719	−	0.995789i	$-0.529221\pi$
$211$	12.5416	−	18.7698i	0.863399	−	1.29217i	0.955071	−	0.296378i	$-0.0957789\pi$
$212$		0			0
$213$	−3.84542	+	19.3322i	−0.263484	+	1.32462i
$214$		0			0
$215$	2.77128	+	6.69045i	0.189000	+	0.456285i
$216$		0			0
$217$	−1.47404	+	3.55864i	−0.100064	+	0.241576i
$218$		0			0
$219$	−5.74193	−	8.59341i	−0.388004	−	0.580689i
$220$		0			0
$221$	−7.69726	+	1.53108i	−0.517774	+	0.102992i
$222$		0			0
$223$			8.11318i			0.543298i	0.962396	+	0.271649i	$0.0875690\pi$
$223$			8.11318i			0.543298i	−0.962396	+	0.271649i	$0.912431\pi$
$224$		0			0
$225$			24.0831i			1.60554i
$226$		0			0
$227$	−11.3933	+	2.26626i	−0.756197	+	0.150417i	−0.558109	−	0.829767i	$-0.688473\pi$
$227$	−11.3933	+	2.26626i	−0.756197	+	0.150417i	−0.198087	+	0.980184i	$0.563473\pi$
$228$		0			0
$229$	−12.2867	−	18.3883i	−0.811926	−	1.21513i	−0.973594	−	0.228288i	$-0.926687\pi$
$229$	−12.2867	−	18.3883i	−0.811926	−	1.21513i	0.161668	−	0.986845i	$-0.448313\pi$
$230$		0			0
$231$	4.76829	−	11.5117i	0.313731	−	0.757413i
$232$		0			0
$233$	0.609526	+	1.47153i	0.0399314	+	0.0964028i	0.942587	−	0.333961i	$-0.108385\pi$
$233$	0.609526	+	1.47153i	0.0399314	+	0.0964028i	−0.902656	+	0.430364i	$0.858385\pi$
$234$		0			0
$235$	−1.95915	+	9.84930i	−0.127801	+	0.642497i
$236$		0			0
$237$	−24.4225	+	36.5508i	−1.58641	+	2.37423i
$238$		0			0
$239$	1.07033	−	1.07033i	0.0692337	−	0.0692337i	−0.671642	−	0.740876i	$-0.734411\pi$
$239$	1.07033	−	1.07033i	0.0692337	−	0.0692337i	0.740876	+	0.671642i	$0.234411\pi$
$240$		0			0
$241$	11.5889	+	11.5889i	0.746509	+	0.746509i	0.973822	−	0.227313i	$-0.0729940\pi$
$241$	11.5889	+	11.5889i	0.746509	+	0.746509i	−0.227313	+	0.973822i	$0.572994\pi$
$242$		0			0
$243$	−11.2304	−	7.50390i	−0.720429	−	0.481375i
$244$		0			0
$245$	7.58626	+	1.50900i	0.484669	+	0.0964066i
$246$		0			0
$247$	9.49121	−	3.93139i	0.603911	−	0.250148i
$248$		0			0
$249$	−17.5997	−	7.29002i	−1.11533	−	0.461986i
$250$		0			0
$251$	−3.20465	+	2.14128i	−0.202276	+	0.135156i	−0.652583	−	0.757717i	$-0.726315\pi$
$251$	−3.20465	+	2.14128i	−0.202276	+	0.135156i	0.450307	+	0.892874i	$0.351315\pi$
$252$		0			0
$253$	1.04481	+	5.25260i	0.0656865	+	0.330228i
$254$		0			0
$255$	28.9889			1.81535
$256$		0			0
$257$	−12.4093			−0.774071			−0.387035	−	0.922065i	$-0.626501\pi$
$257$	−12.4093			−0.774071			−0.387035	+	0.922065i	$0.626501\pi$
$258$		0			0
$259$	−1.05120	−	5.28475i	−0.0653185	−	0.328378i
$260$		0			0
$261$	10.0406	−	6.70893i	0.621499	−	0.415272i
$262$		0			0
$263$	−1.63628	−	0.677769i	−0.100897	−	0.0417930i	0.331664	−	0.943398i	$-0.392390\pi$
$263$	−1.63628	−	0.677769i	−0.100897	−	0.0417930i	−0.432561	+	0.901605i	$0.642390\pi$
$264$		0			0
$265$	23.5121	−	9.73904i	1.44434	−	0.598264i
$266$		0			0
$267$	−22.5989	−	4.49521i	−1.38303	−	0.275102i
$268$		0			0
$269$	26.2384	+	17.5320i	1.59978	+	1.06894i	0.951547	+	0.307505i	$0.0994939\pi$
$269$	26.2384	+	17.5320i	1.59978	+	1.06894i	0.648238	+	0.761438i	$0.275506\pi$
$270$		0			0
$271$	1.58765	+	1.58765i	0.0964427	+	0.0964427i	0.753682	−	0.657239i	$-0.228276\pi$
$271$	1.58765	+	1.58765i	0.0964427	+	0.0964427i	−0.657239	+	0.753682i	$0.728276\pi$
$272$		0			0
$273$	−10.2523	+	10.2523i	−0.620497	+	0.620497i
$274$		0			0
$275$	−5.45661	+	8.16640i	−0.329046	+	0.492452i
$276$		0			0
$277$	0.970436	−	4.87871i	0.0583079	−	0.293133i	−0.940618	−	0.339466i	$-0.889754\pi$
$277$	0.970436	−	4.87871i	0.0583079	−	0.293133i	0.998926	+	0.0463330i	$0.0147535\pi$
$278$		0			0
$279$	−3.50646	−	8.46533i	−0.209926	−	0.506806i
$280$		0			0
$281$	−0.758051	+	1.83010i	−0.0452216	+	0.109175i	−0.944876	−	0.327428i	$-0.893818\pi$
$281$	−0.758051	+	1.83010i	−0.0452216	+	0.109175i	0.899655	+	0.436602i	$0.143818\pi$
$282$		0			0
$283$	5.42628	+	8.12100i	0.322559	+	0.482744i	0.956944	−	0.290274i	$-0.0937464\pi$
$283$	5.42628	+	8.12100i	0.322559	+	0.482744i	−0.634385	+	0.773018i	$0.718746\pi$
$284$		0			0
$285$	−37.2177	+	7.40306i	−2.20459	+	0.438519i
$286$		0			0
$287$			25.9039i			1.52906i
$288$		0			0
$289$			6.31674i			0.371573i
$290$		0			0
$291$	23.6476	−	4.70380i	1.38625	−	0.275742i
$292$		0			0
$293$	−6.65651	−	9.96217i	−0.388877	−	0.581996i	0.584446	−	0.811432i	$-0.301312\pi$
$293$	−6.65651	−	9.96217i	−0.388877	−	0.581996i	−0.973324	+	0.229436i	$0.926312\pi$
$294$		0			0
$295$	−10.1804	+	24.5776i	−0.592725	+	1.43096i
$296$		0			0
$297$	4.61746	+	11.1475i	0.267932	+	0.646845i
$298$		0			0
$299$	1.21576	−	6.11205i	0.0703093	−	0.353469i
$300$		0			0
$301$	2.73921	−	4.09952i	0.157885	−	0.236292i
$302$		0			0
$303$	−29.7792	+	29.7792i	−1.71077	+	1.71077i
$304$		0			0
$305$	−22.1932	−	22.1932i	−1.27078	−	1.27078i
$306$		0			0
$307$	−9.59801	−	6.41318i	−0.547787	−	0.366020i	0.250669	−	0.968073i	$-0.419350\pi$
$307$	−9.59801	−	6.41318i	−0.547787	−	0.366020i	−0.798456	+	0.602053i	$0.794350\pi$
$308$		0			0
$309$	15.6309	+	3.10919i	0.889213	+	0.176875i
$310$		0			0
$311$	21.5704	−	8.93477i	1.22315	−	0.506644i	0.324738	−	0.945804i	$-0.394724\pi$
$311$	21.5704	−	8.93477i	1.22315	−	0.506644i	0.898409	+	0.439160i	$0.144724\pi$
$312$		0			0
$313$	−1.66011	−	0.687642i	−0.0938352	−	0.0388678i	0.335272	−	0.942121i	$-0.391172\pi$
$313$	−1.66011	−	0.687642i	−0.0938352	−	0.0388678i	−0.429107	+	0.903254i	$0.641172\pi$
$314$		0			0
$315$	27.9549	−	18.6788i	1.57508	−	1.05243i
$316$		0			0
$317$	2.90261	+	14.5924i	0.163027	+	0.819590i	0.972584	+	0.232550i	$0.0747069\pi$
$317$	2.90261	+	14.5924i	0.163027	+	0.819590i	−0.809558	+	0.587040i	$0.800293\pi$
$318$		0			0
$319$	4.92478			0.275735
$320$		0			0
$321$	36.7977			2.05385
$322$		0			0
$323$	2.72825	+	13.7158i	0.151804	+	0.763169i
$324$		0			0
$325$	9.50261	−	6.34944i	0.527110	−	0.352204i
$326$		0			0
$327$	−25.4449	−	10.5396i	−1.40711	−	0.582843i
$328$		0			0
$329$	6.31673	−	2.61648i	0.348253	−	0.144251i
$330$		0			0
$331$	5.51285	+	1.09657i	0.303014	+	0.0602732i	0.344255	−	0.938876i	$-0.388131\pi$
$331$	5.51285	+	1.09657i	0.303014	+	0.0602732i	−0.0412418	+	0.999149i	$0.513131\pi$
$332$		0			0
$333$	10.6575	+	7.12113i	0.584029	+	0.390236i
$334$		0			0
$335$	−32.7176	−	32.7176i	−1.78755	−	1.78755i
$336$		0			0
$337$	2.17791	−	2.17791i	0.118638	−	0.118638i	−0.645295	−	0.763933i	$-0.723266\pi$
$337$	2.17791	−	2.17791i	0.118638	−	0.118638i	0.763933	+	0.645295i	$0.223266\pi$
$338$		0			0
$339$	−10.6093	+	15.8779i	−0.576218	+	0.862371i
$340$		0			0
$341$	0.729016	−	3.66501i	0.0394784	−	0.198471i
$342$		0			0
$343$	−7.71305	−	18.6210i	−0.416466	−	1.00544i
$344$		0			0
$345$	−8.80890	+	21.2666i	−0.474255	+	1.14495i
$346$		0			0
$347$	5.32825	+	7.97430i	0.286036	+	0.428083i	0.946465	−	0.322805i	$-0.104626\pi$
$347$	5.32825	+	7.97430i	0.286036	+	0.428083i	−0.660430	+	0.750888i	$0.729626\pi$
$348$		0			0
$349$	1.63592	−	0.325405i	0.0875689	−	0.0174185i	−0.151111	−	0.988517i	$-0.548285\pi$
$349$	1.63592	−	0.325405i	0.0875689	−	0.0174185i	0.238680	+	0.971098i	$0.423285\pi$
$350$		0			0
$351$		−	14.0403i		−	0.749414i
$352$		0			0
$353$		−	5.92592i		−	0.315405i	−0.987487	−	0.157702i	$-0.949591\pi$
$353$		−	5.92592i		−	0.315405i	0.987487	−	0.157702i	$-0.0504087\pi$
$354$		0			0
$355$	−21.2737	+	4.23159i	−1.12909	+	0.224590i
$356$		0			0
$357$	−10.9652	−	16.4106i	−0.580340	−	0.868539i
$358$		0			0
$359$	12.0537	−	29.1002i	0.636170	−	1.53585i	−0.195573	−	0.980689i	$-0.562657\pi$
$359$	12.0537	−	29.1002i	0.636170	−	1.53585i	0.831743	−	0.555161i	$-0.187343\pi$
$360$		0			0
$361$	0.265606	+	0.641230i	0.0139793	+	0.0337489i
$362$		0			0
$363$	3.73414	−	18.7728i	0.195991	−	0.985315i
$364$		0			0
$365$	6.31856	−	9.45639i	0.330729	−	0.494970i
$366$		0			0
$367$	18.9541	−	18.9541i	0.989396	−	0.989396i	−0.0105483	−	0.999944i	$-0.503358\pi$
$367$	18.9541	−	18.9541i	0.989396	−	0.989396i	0.999944	+	0.0105483i	$0.00335770\pi$
$368$		0			0
$369$	−43.5722	−	43.5722i	−2.26828	−	2.26828i
$370$		0			0
$371$	−14.4068	−	9.62634i	−0.747966	−	0.499775i
$372$		0			0
$373$	21.0597	+	4.18903i	1.09043	+	0.216899i	0.707383	−	0.706830i	$-0.249876\pi$
$373$	21.0597	+	4.18903i	1.09043	+	0.216899i	0.383044	+	0.923730i	$0.374876\pi$
$374$		0			0
$375$	1.96841	−	0.815342i	0.101648	−	0.0421041i
$376$		0			0
$377$	−5.29437	−	2.19300i	−0.272674	−	0.112945i
$378$		0			0
$379$	3.08942	−	2.06428i	0.158693	−	0.106035i	−0.473688	−	0.880693i	$-0.657078\pi$
$379$	3.08942	−	2.06428i	0.158693	−	0.106035i	0.632381	+	0.774657i	$0.282078\pi$
$380$		0			0
$381$	−0.167484	−	0.841999i	−0.00858046	−	0.0431369i
$382$		0			0
$383$	−16.3597			−0.835942			−0.417971	−	0.908460i	$-0.637259\pi$
$383$	−16.3597			−0.835942			−0.417971	+	0.908460i	$0.637259\pi$
$384$		0			0
$385$	13.7115			0.698800
$386$		0			0
$387$	2.28813	+	11.5032i	0.116312	+	0.584742i
$388$		0			0
$389$	−21.6591	+	14.4722i	−1.09816	+	0.733768i	−0.966279	−	0.257498i	$-0.917102\pi$
$389$	−21.6591	+	14.4722i	−1.09816	+	0.733768i	−0.131882	+	0.991265i	$0.542102\pi$
$390$		0			0
$391$	7.83736	+	3.24634i	0.396352	+	0.164174i
$392$		0			0
$393$	14.1250	−	5.85076i	0.712511	−	0.295132i
$394$		0			0
$395$	−47.4444	−	9.43728i	−2.38719	−	0.474841i
$396$		0			0
$397$	−3.68511	−	2.46232i	−0.184951	−	0.123580i	0.459648	−	0.888101i	$-0.347976\pi$
$397$	−3.68511	−	2.46232i	−0.184951	−	0.123580i	−0.644599	+	0.764521i	$0.722976\pi$
$398$		0			0
$399$	18.2686	+	18.2686i	0.914576	+	0.914576i
$400$		0			0
$401$	8.30297	−	8.30297i	0.414630	−	0.414630i	−0.468718	−	0.883348i	$-0.655284\pi$
$401$	8.30297	−	8.30297i	0.414630	−	0.414630i	0.883348	+	0.468718i	$0.155284\pi$
$402$		0			0
$403$	−2.41575	+	3.61543i	−0.120337	+	0.180097i
$404$		0			0
$405$	−0.866379	+	4.35558i	−0.0430507	+	0.216431i
$406$		0			0
$407$	2.00042	+	4.82945i	0.0991573	+	0.239387i
$408$		0			0
$409$	12.9503	−	31.2648i	0.640350	−	1.54594i	−0.185857	−	0.982577i	$-0.559506\pi$
$409$	12.9503	−	31.2648i	0.640350	−	1.54594i	0.826207	−	0.563366i	$-0.190494\pi$
$410$		0			0
$411$	27.1588	+	40.6460i	1.33964	+	2.00492i
$412$		0			0
$413$	17.7641	−	3.53351i	0.874117	−	0.173873i
$414$		0			0
$415$		−	20.9628i		−	1.02902i
$416$		0			0
$417$			33.8806i			1.65914i
$418$		0			0
$419$	15.5325	−	3.08960i	0.758811	−	0.150937i	0.199503	−	0.979897i	$-0.436067\pi$
$419$	15.5325	−	3.08960i	0.758811	−	0.150937i	0.559307	+	0.828960i	$0.311067\pi$
$420$		0			0
$421$	−1.42193	−	2.12807i	−0.0693006	−	0.103716i	0.795201	−	0.606346i	$-0.207366\pi$
$421$	−1.42193	−	2.12807i	−0.0693006	−	0.103716i	−0.864501	+	0.502631i	$0.832366\pi$
$422$		0			0
$423$	−6.22410	+	15.0263i	−0.302626	+	0.730604i
$424$		0			0
$425$	5.95357	+	14.3732i	0.288791	+	0.697203i
$426$		0			0
$427$	−4.16885	+	20.9582i	−0.201745	+	1.01424i
$428$		0			0
$429$	7.81460	−	11.6954i	0.377292	−	0.564658i
$430$		0			0
$431$	−13.2163	+	13.2163i	−0.636606	+	0.636606i	−0.949717	−	0.313111i	$-0.898629\pi$
$431$	−13.2163	+	13.2163i	−0.636606	+	0.636606i	0.313111	+	0.949717i	$0.398629\pi$
$432$		0			0
$433$	−5.42276	−	5.42276i	−0.260601	−	0.260601i	0.564697	−	0.825298i	$-0.308993\pi$
$433$	−5.42276	−	5.42276i	−0.260601	−	0.260601i	−0.825298	+	0.564697i	$0.808993\pi$
$434$		0			0
$435$	17.6001	+	11.7600i	0.843860	+	0.563849i
$436$		0			0
$437$	−10.8911	−	2.16638i	−0.520993	−	0.103632i
$438$		0			0
$439$	15.4472	−	6.39844i	0.737255	−	0.305381i	0.0177256	−	0.999843i	$-0.494357\pi$
$439$	15.4472	−	6.39844i	0.737255	−	0.305381i	0.719530	+	0.694462i	$0.244357\pi$
$440$		0			0
$441$	11.5738	+	4.79401i	0.551132	+	0.228286i
$442$		0			0
$443$	8.77140	−	5.86086i	0.416742	−	0.278458i	−0.329471	−	0.944166i	$-0.606870\pi$
$443$	8.77140	−	5.86086i	0.416742	−	0.278458i	0.746213	+	0.665708i	$0.231870\pi$
$444$		0			0
$445$	−4.94664	−	24.8684i	−0.234493	−	1.17888i
$446$		0			0
$447$	38.2601			1.80964
$448$		0			0
$449$	11.0927			0.523498			0.261749	−	0.965136i	$-0.415701\pi$
$449$	11.0927			0.523498			0.261749	+	0.965136i	$0.415701\pi$
$450$		0			0
$451$	−4.90267	−	24.6474i	−0.230857	−	1.16060i
$452$		0			0
$453$	−4.48258	+	2.99516i	−0.210610	+	0.140725i
$454$		0			0
$455$	−14.7405	−	6.10570i	−0.691044	−	0.286240i
$456$		0			0
$457$	20.2978	−	8.40761i	0.949490	−	0.393292i	0.146451	−	0.989218i	$-0.453215\pi$
$457$	20.2978	−	8.40761i	0.949490	−	0.393292i	0.803039	+	0.595926i	$0.203215\pi$
$458$		0			0
$459$	18.7452	+	3.72866i	0.874953	+	0.174039i
$460$		0			0
$461$	−19.1714	−	12.8099i	−0.892903	−	0.596619i	0.0222379	−	0.999753i	$-0.492921\pi$
$461$	−19.1714	−	12.8099i	−0.892903	−	0.596619i	−0.915141	+	0.403134i	$0.867921\pi$
$462$		0			0
$463$	9.19024	+	9.19024i	0.427107	+	0.427107i	0.887642	−	0.460535i	$-0.152342\pi$
$463$	9.19024	+	9.19024i	0.427107	+	0.427107i	−0.460535	+	0.887642i	$0.652342\pi$
$464$		0			0
$465$	11.3571	−	11.3571i	0.526673	−	0.526673i
$466$		0			0
$467$	0.319653	−	0.478395i	0.0147918	−	0.0221375i	−0.824000	−	0.566590i	$-0.808262\pi$
$467$	0.319653	−	0.478395i	0.0147918	−	0.0221375i	0.838792	+	0.544452i	$0.183262\pi$
$468$		0			0
$469$	−6.14580	+	30.8970i	−0.283787	+	1.42669i
$470$		0			0
$471$	20.2668	+	48.9284i	0.933845	+	2.25450i
$472$		0			0
$473$	−1.83045	+	4.41910i	−0.0841642	+	0.203190i
$474$		0			0
$475$	−11.3141	−	16.9328i	−0.519128	−	0.776930i
$476$		0			0
$477$	40.4255	−	8.04114i	1.85096	−	0.368178i
$478$		0			0
$479$		−	33.0010i		−	1.50786i	−0.656957	−	0.753928i	$-0.728157\pi$
$479$		−	33.0010i		−	1.50786i	0.656957	−	0.753928i	$-0.271843\pi$
$480$		0			0
$481$		−	6.08268i		−	0.277346i
$482$		0			0
$483$	15.3710	−	3.05748i	0.699404	−	0.139120i
$484$		0			0
$485$	14.7405	+	22.0607i	0.669332	+	1.00173i
$486$		0			0
$487$	−14.4792	+	34.9559i	−0.656116	+	1.58400i	0.147637	+	0.989042i	$0.452833\pi$
$487$	−14.4792	+	34.9559i	−0.656116	+	1.58400i	−0.803753	+	0.594963i	$0.797167\pi$
$488$		0			0
$489$	−3.60049	−	8.69235i	−0.162820	−	0.393081i
$490$		0			0
$491$	4.13764	−	20.8013i	0.186729	−	0.938750i	−0.767813	−	0.640674i	$-0.778655\pi$
$491$	4.13764	−	20.8013i	0.186729	−	0.938750i	0.954542	−	0.298076i	$-0.0963450\pi$
$492$		0			0
$493$	4.33391	−	6.48615i	0.195189	−	0.292122i
$494$		0			0
$495$	−23.0637	+	23.0637i	−1.03663	+	1.03663i
$496$		0			0
$497$	10.4424	+	10.4424i	0.468404	+	0.468404i
$498$		0			0
$499$	34.2079	+	22.8570i	1.53135	+	1.02322i	0.982275	+	0.187448i	$0.0600215\pi$
$499$	34.2079	+	22.8570i	1.53135	+	1.02322i	0.549079	+	0.835770i	$0.314979\pi$
$500$		0			0
$501$	−0.679177	−	0.135097i	−0.0303434	−	0.00603568i
$502$		0			0
$503$	16.6755	−	6.90723i	0.743525	−	0.307978i	0.0214284	−	0.999770i	$-0.493179\pi$
$503$	16.6755	−	6.90723i	0.743525	−	0.307978i	0.722097	+	0.691792i	$0.243179\pi$
$504$		0			0
$505$	−42.8157	−	17.7349i	−1.90528	−	0.789191i
$506$		0			0
$507$	17.0776	−	11.4109i	0.758444	−	0.506776i
$508$		0			0
$509$	−4.55107	−	22.8798i	−0.201722	−	1.01413i	−0.940401	−	0.340069i	$-0.889550\pi$
$509$	−4.55107	−	22.8798i	−0.201722	−	1.01413i	0.738678	−	0.674058i	$-0.235450\pi$
$510$		0			0
$511$	−7.74328			−0.342543
$512$		0			0
$513$	−25.0185			−1.10459
$514$		0			0
$515$	3.42142	+	17.2007i	0.150766	+	0.757952i
$516$		0			0
$517$	−5.51513	+	3.68509i	−0.242555	+	0.162070i
$518$		0			0
$519$	38.9183	+	16.1205i	1.70832	+	0.707610i
$520$		0			0
$521$	−25.8128	+	10.6920i	−1.13088	+	0.468426i	−0.868080	−	0.496424i	$-0.834646\pi$
$521$	−25.8128	+	10.6920i	−1.13088	+	0.468426i	−0.262801	+	0.964850i	$0.584646\pi$
$522$		0			0
$523$	−3.91430	−	0.778602i	−0.171160	−	0.0340459i	0.108766	−	0.994067i	$-0.465310\pi$
$523$	−3.91430	−	0.778602i	−0.171160	−	0.0340459i	−0.279926	+	0.960021i	$0.590310\pi$
$524$		0			0
$525$	23.8978	+	15.9680i	1.04299	+	0.696901i
$526$		0			0
$527$	−4.18543	−	4.18543i	−0.182320	−	0.182320i
$528$		0			0
$529$	11.5004	−	11.5004i	0.500015	−	0.500015i
$530$		0			0
$531$	−23.9370	+	35.8242i	−1.03878	+	1.55464i
$532$		0			0
$533$	−5.70486	+	28.6802i	−0.247105	+	1.24228i
$534$		0			0
$535$	15.4960	+	37.4107i	0.669952	+	1.61741i
$536$		0			0
$537$	−12.5252	+	30.2384i	−0.540501	+	1.30488i
$538$		0			0
$539$	2.83838	+	4.24794i	0.122258	+	0.182972i
$540$		0			0
$541$	23.5841	−	4.69116i	1.01396	−	0.201689i	0.339974	−	0.940435i	$-0.389582\pi$
$541$	23.5841	−	4.69116i	1.01396	−	0.201689i	0.673984	+	0.738746i	$0.264582\pi$
$542$		0			0
$543$			24.1337i			1.03568i
$544$		0			0
$545$		−	30.3072i		−	1.29822i
$546$		0			0
$547$	−18.9505	+	3.76948i	−0.810263	+	0.161171i	−0.582800	−	0.812615i	$-0.698043\pi$
$547$	−18.9505	+	3.76948i	−0.810263	+	0.161171i	−0.227463	+	0.973787i	$0.573043\pi$
$548$		0			0
$549$	−28.2409	−	42.2656i	−1.20529	−	1.80385i
$550$		0			0
$551$	−3.90773	+	9.43410i	−0.166475	+	0.401906i
$552$		0			0
$553$	12.6037	+	30.4279i	0.535962	+	1.29393i
$554$		0			0
$555$	−4.38329	+	22.0363i	−0.186060	+	0.935387i
$556$		0			0
$557$	−9.35372	+	13.9988i	−0.396330	+	0.593149i	−0.974944	−	0.222452i	$-0.928594\pi$
$557$	−9.35372	+	13.9988i	−0.396330	+	0.593149i	0.578614	+	0.815602i	$0.303594\pi$
$558$		0			0
$559$	3.93564	−	3.93564i	0.166460	−	0.166460i
$560$		0			0
$561$	13.5392	+	13.5392i	0.571627	+	0.571627i
$562$		0			0
$563$	33.2172	+	22.1950i	1.39994	+	0.935409i	0.999821	+	0.0189460i	$0.00603105\pi$
$563$	33.2172	+	22.1950i	1.39994	+	0.935409i	0.400119	+	0.916463i	$0.368969\pi$
$564$		0			0
$565$	−20.6102	−	4.09962i	−0.867077	−	0.172472i
$566$		0			0
$567$	2.79340	−	1.15706i	0.117312	−	0.0485922i
$568$		0			0
$569$	14.9275	+	6.18318i	0.625794	+	0.259212i	0.672965	−	0.739674i	$-0.265020\pi$
$569$	14.9275	+	6.18318i	0.625794	+	0.259212i	−0.0471707	+	0.998887i	$0.515020\pi$
$570$		0			0
$571$	−10.6636	+	7.12517i	−0.446257	+	0.298179i	−0.758320	−	0.651882i	$-0.773980\pi$
$571$	−10.6636	+	7.12517i	−0.446257	+	0.298179i	0.312064	+	0.950061i	$0.398980\pi$
$572$		0			0
$573$	−3.49596	−	17.5754i	−0.146046	−	0.734223i
$574$		0			0
$575$	−12.3535			−0.515175
$576$		0			0
$577$	−18.6883			−0.778002			−0.389001	−	0.921237i	$-0.627180\pi$
$577$	−18.6883			−0.778002			−0.389001	+	0.921237i	$0.627180\pi$
$578$		0			0
$579$	−5.82419	−	29.2802i	−0.242045	−	1.21684i
$580$		0			0
$581$	−11.8670	+	7.92928i	−0.492327	+	0.328962i
$582$		0			0
$583$	15.5299	+	6.43271i	0.643184	+	0.266416i
$584$		0			0
$585$	35.0648	−	14.5243i	1.44975	−	0.600506i
$586$		0			0
$587$	16.9938	+	3.38028i	0.701409	+	0.139519i	0.532896	−	0.846180i	$-0.321104\pi$
$587$	16.9938	+	3.38028i	0.701409	+	0.139519i	0.168513	+	0.985699i	$0.446104\pi$
$588$		0			0
$589$	6.44237	+	4.30465i	0.265453	+	0.177370i
$590$		0			0
$591$	−31.5322	−	31.5322i	−1.29706	−	1.29706i
$592$		0			0
$593$	−5.79685	+	5.79685i	−0.238048	+	0.238048i	−0.816042	−	0.577993i	$-0.803836\pi$
$593$	−5.79685	+	5.79685i	−0.238048	+	0.238048i	0.577993	+	0.816042i	$0.303836\pi$
$594$		0			0
$595$	12.0664	−	18.0586i	0.494673	−	0.740330i
$596$		0			0
$597$	15.2315	−	76.5739i	0.623384	−	3.13396i
$598$		0			0
$599$	6.07554	+	14.6677i	0.248240	+	0.599304i	0.998055	−	0.0623435i	$-0.0198574\pi$
$599$	6.07554	+	14.6677i	0.248240	+	0.599304i	−0.749815	+	0.661648i	$0.769857\pi$
$600$		0			0
$601$	−9.70092	+	23.4201i	−0.395709	+	0.955325i	0.592963	+	0.805230i	$0.297958\pi$
$601$	−9.70092	+	23.4201i	−0.395709	+	0.955325i	−0.988672	+	0.150095i	$0.952042\pi$
$602$		0			0
$603$	−41.6333	−	62.3087i	−1.69544	−	2.53741i
$604$		0			0
$605$	20.6580	−	4.10914i	0.839868	−	0.167060i
$606$		0			0
$607$		−	0.795354i		−	0.0322824i	−0.999870	−	0.0161412i	$-0.994862\pi$
$607$		−	0.795354i		−	0.0322824i	0.999870	−	0.0161412i	$-0.00513813\pi$
$608$		0			0
$609$		−	14.4117i		−	0.583991i
$610$		0			0
$611$	7.57000	−	1.50577i	0.306249	−	0.0609168i
$612$		0			0
$613$	2.28756	+	3.42358i	0.0923939	+	0.138277i	0.874787	−	0.484508i	$-0.161001\pi$
$613$	2.28756	+	3.42358i	0.0923939	+	0.138277i	−0.782393	+	0.622785i	$0.786001\pi$
$614$		0			0
$615$	41.3350	−	99.7915i	1.66679	−	4.02398i
$616$		0			0
$617$	−16.1612	−	39.0166i	−0.650626	−	1.57075i	−0.811872	−	0.583836i	$-0.801551\pi$
$617$	−16.1612	−	39.0166i	−0.650626	−	1.57075i	0.161246	−	0.986914i	$-0.448449\pi$
$618$		0			0
$619$	2.87121	−	14.4345i	0.115404	−	0.580173i	−0.879202	−	0.476448i	$-0.841924\pi$
$619$	2.87121	−	14.4345i	0.115404	−	0.580173i	0.994606	−	0.103725i	$-0.0330761\pi$
$620$		0			0
$621$	−8.43154	+	12.6187i	−0.338346	+	0.506370i
$622$		0			0
$623$	−12.2069	+	12.2069i	−0.489059	+	0.489059i
$624$		0			0
$625$	18.4862	+	18.4862i	0.739448	+	0.739448i
$626$		0			0
$627$	−20.8401	−	13.9249i	−0.832274	−	0.556107i
$628$		0			0
$629$	8.12102	+	1.61537i	0.323806	+	0.0644090i
$630$		0			0
$631$	−35.2699	+	14.6093i	−1.40407	+	0.581586i	−0.950806	−	0.309788i	$-0.899742\pi$
$631$	−35.2699	+	14.6093i	−1.40407	+	0.581586i	−0.453268	+	0.891374i	$0.649742\pi$
$632$		0			0
$633$	59.2091	+	24.5252i	2.35335	+	0.974790i
$634$		0			0
$635$	0.785496	−	0.524852i	0.0311715	−	0.0208281i
$636$		0			0
$637$	−1.15979	−	5.83067i	−0.0459526	−	0.231020i
$638$		0			0
$639$	−35.1296			−1.38971
$640$		0			0
$641$	11.8042			0.466237			0.233119	−	0.972448i	$-0.425107\pi$
$641$	11.8042			0.466237			0.233119	+	0.972448i	$0.425107\pi$
$642$		0			0
$643$	−2.84656	−	14.3106i	−0.112257	−	0.564355i	−0.995445	−	0.0953360i	$-0.969607\pi$
$643$	−2.84656	−	14.3106i	−0.112257	−	0.564355i	0.883188	−	0.469019i	$-0.155393\pi$
$644$		0			0
$645$	−17.0941	+	11.4219i	−0.673080	+	0.449737i
$646$		0			0
$647$	6.76078	+	2.80041i	0.265794	+	0.110095i	0.511600	−	0.859224i	$-0.329053\pi$
$647$	6.76078	+	2.80041i	0.265794	+	0.110095i	−0.245807	+	0.969319i	$0.579053\pi$
$648$		0			0
$649$	−16.2337	+	6.72422i	−0.637229	+	0.263949i
$650$		0			0
$651$	−10.7251	−	2.13336i	−0.420351	−	0.0836130i
$652$		0			0
$653$	−9.41350	−	6.28990i	−0.368379	−	0.246143i	0.357578	−	0.933883i	$-0.383603\pi$
$653$	−9.41350	−	6.28990i	−0.368379	−	0.246143i	−0.725957	+	0.687741i	$0.758603\pi$
$654$		0			0
$655$	11.8965	+	11.8965i	0.464833	+	0.464833i
$656$		0			0
$657$	13.0248	−	13.0248i	0.508144	−	0.508144i
$658$		0			0
$659$	−6.27371	+	9.38927i	−0.244389	+	0.365754i	−0.933303	−	0.359089i	$-0.883088\pi$
$659$	−6.27371	+	9.38927i	−0.244389	+	0.365754i	0.688914	+	0.724843i	$0.258088\pi$
$660$		0			0
$661$	0.0233980	−	0.117629i	0.000910075	−	0.00457526i	−0.980328	−	0.197377i	$-0.936758\pi$
$661$	0.0233980	−	0.117629i	0.000910075	−	0.00457526i	0.981238	+	0.192802i	$0.0617576\pi$
$662$		0			0
$663$	−8.52632	−	20.5843i	−0.331135	−	0.799430i
$664$		0			0
$665$	−10.8798	+	26.2662i	−0.421901	+	1.01856i
$666$		0			0
$667$	3.44136	+	5.15036i	0.133250	+	0.199423i
$668$		0			0
$669$	−22.5904	+	4.49352i	−0.873396	+	0.173729i
$670$		0			0
$671$		−	20.7306i		−	0.800298i
$672$		0			0
$673$			41.1783i			1.58731i	0.608371	+	0.793653i	$0.291823\pi$
$673$			41.1783i			1.58731i	−0.608371	+	0.793653i	$0.708177\pi$
$674$		0			0
$675$	−27.2977	+	5.42984i	−1.05069	+	0.208995i
$676$		0			0
$677$	13.0241	+	19.4920i	0.500557	+	0.749137i	0.992599	−	0.121435i	$-0.0387495\pi$
$677$	13.0241	+	19.4920i	0.500557	+	0.749137i	−0.492042	+	0.870571i	$0.663749\pi$
$678$		0			0
$679$	6.91289	−	16.6892i	0.265292	−	0.640472i
$680$		0			0
$681$	−12.6204	−	30.4683i	−0.483615	−	1.16755i
$682$		0			0
$683$	2.94439	−	14.8024i	0.112664	−	0.566399i	−0.882677	−	0.469980i	$-0.844261\pi$
$683$	2.94439	−	14.8024i	0.112664	−	0.566399i	0.995341	−	0.0964191i	$-0.0307389\pi$
$684$		0			0
$685$	−29.8862	+	44.7278i	−1.14189	+	1.70896i
$686$		0			0
$687$	44.3956	−	44.3956i	1.69380	−	1.69380i
$688$		0			0
$689$	−13.8309	−	13.8309i	−0.526917	−	0.526917i
$690$		0			0
$691$	−23.4953	−	15.6991i	−0.893805	−	0.597221i	0.0215953	−	0.999767i	$-0.493125\pi$
$691$	−23.4953	−	15.6991i	−0.893805	−	0.597221i	−0.915400	+	0.402546i	$0.868125\pi$
$692$		0			0
$693$	21.7803	+	4.33236i	0.827364	+	0.164573i
$694$		0			0
$695$	−34.4451	+	14.2676i	−1.30658	+	0.541202i
$696$		0			0
$697$	−36.7761	−	15.2332i	−1.39299	−	0.576997i
$698$		0			0
$699$	−3.75975	+	2.51218i	−0.142207	+	0.0950194i
$700$		0			0
$701$	−1.68037	−	8.44781i	−0.0634668	−	0.319069i	0.935990	−	0.352027i	$-0.114507\pi$
$701$	−1.68037	−	8.44781i	−0.0634668	−	0.319069i	−0.999457	+	0.0329575i	$0.989507\pi$
$702$		0			0
$703$	−10.8388			−0.408792
$704$		0			0
$705$	−28.5096			−1.07373
$706$		0			0
$707$	6.15559	+	30.9462i	0.231505	+	1.16385i
$708$		0			0
$709$	9.70687	−	6.48592i	0.364549	−	0.243584i	−0.359782	−	0.933036i	$-0.617149\pi$
$709$	9.70687	−	6.48592i	0.364549	−	0.243584i	0.724331	+	0.689453i	$0.242149\pi$
$710$		0			0
$711$	−72.3823	−	29.9817i	−2.71455	−	1.12440i
$712$		0			0
$713$	4.34231	−	1.79865i	0.162621	−	0.0673598i
$714$		0			0
$715$	15.1811	+	3.01970i	0.567739	+	0.112930i
$716$		0			0
$717$	3.57303	+	2.38743i	0.133437	+	0.0891600i
$718$		0			0
$719$	22.6553	+	22.6553i	0.844899	+	0.844899i	0.989491	−	0.144592i	$-0.0461871\pi$
$719$	22.6553	+	22.6553i	0.844899	+	0.844899i	−0.144592	+	0.989491i	$0.546187\pi$
$720$		0			0
$721$	8.44310	−	8.44310i	0.314438	−	0.314438i
$722$		0			0
$723$	−25.8498	+	38.6869i	−0.961364	+	1.43878i
$724$		0			0
$725$	−2.21621	+	11.1416i	−0.0823080	+	0.413790i
$726$		0			0
$727$	−14.7776	−	35.6764i	−0.548072	−	1.32316i	−0.918911	−	0.394466i	$-0.870930\pi$
$727$	−14.7776	−	35.6764i	−0.548072	−	1.32316i	0.370839	−	0.928697i	$-0.379070\pi$
$728$		0			0
$729$	16.3059	−	39.3660i	0.603923	−	1.45800i
$730$		0			0
$731$	4.20931	+	6.29968i	0.155687	+	0.233002i
$732$		0			0
$733$	−12.4550	+	2.47746i	−0.460037	+	0.0915071i	−0.419668	−	0.907678i	$-0.637853\pi$
$733$	−12.4550	+	2.47746i	−0.460037	+	0.0915071i	−0.0403693	+	0.999185i	$0.512853\pi$
$734$		0			0
$735$			21.9591i			0.809972i
$736$		0			0
$737$		−	30.5615i		−	1.12575i
$738$		0			0
$739$	0.370926	−	0.0737817i	0.0136447	−	0.00271410i	−0.188263	−	0.982119i	$-0.560286\pi$
$739$	0.370926	−	0.0737817i	0.0136447	−	0.00271410i	0.201908	+	0.979405i	$0.435286\pi$
$740$		0			0
$741$	16.2034	+	24.2500i	0.595245	+	0.890847i
$742$		0			0
$743$	10.5484	−	25.4660i	0.386983	−	0.934259i	−0.603593	−	0.797292i	$-0.706265\pi$
$743$	10.5484	−	25.4660i	0.386983	−	0.934259i	0.990576	−	0.136966i	$-0.0437351\pi$
$744$		0			0
$745$	16.1119	+	38.8975i	0.590294	+	1.42510i
$746$		0			0
$747$	6.62354	−	33.2988i	0.242343	−	1.21834i
$748$		0			0
$749$	15.3167	−	22.9231i	0.559661	−	0.837591i
$750$		0			0
$751$	−33.7123	+	33.7123i	−1.23018	+	1.23018i	−0.266286	+	0.963894i	$0.585797\pi$
$751$	−33.7123	+	33.7123i	−1.23018	+	1.23018i	−0.963894	+	0.266286i	$0.914203\pi$
$752$		0			0
$753$	−7.73712	−	7.73712i	−0.281956	−	0.281956i
$754$		0			0
$755$	−4.93274	−	3.29595i	−0.179521	−	0.119952i
$756$		0			0
$757$	−0.880215	−	0.175086i	−0.0319920	−	0.00636360i	0.179068	−	0.983837i	$-0.442692\pi$
$757$	−0.880215	−	0.175086i	−0.0319920	−	0.00636360i	−0.211060	+	0.977473i	$0.567692\pi$
$758$		0			0
$759$	−14.0467	+	5.81835i	−0.509864	+	0.211193i
$760$		0			0
$761$	25.8419	+	10.7040i	0.936766	+	0.388021i	0.798241	−	0.602338i	$-0.205764\pi$
$761$	25.8419	+	10.7040i	0.936766	+	0.388021i	0.138525	+	0.990359i	$0.455764\pi$
$762$		0			0
$763$	−17.1569	+	11.4639i	−0.621121	+	0.415020i
$764$		0			0
$765$	10.0794	+	50.6724i	0.364420	+	1.83206i
$766$		0			0
$767$	20.4463			0.738273
$768$		0			0
$769$	−30.4304			−1.09735			−0.548674	−	0.836036i	$-0.684867\pi$
$769$	−30.4304			−1.09735			−0.548674	+	0.836036i	$0.684867\pi$
$770$		0			0
$771$	−6.87294	−	34.5526i	−0.247523	−	1.24438i
$772$		0			0
$773$	7.79837	−	5.21070i	0.280488	−	0.187416i	−0.407366	−	0.913265i	$-0.633553\pi$
$773$	7.79837	−	5.21070i	0.280488	−	0.187416i	0.687854	+	0.725849i	$0.258553\pi$
$774$		0			0
$775$	7.96352	+	3.29860i	0.286058	+	0.118489i
$776$		0			0
$777$	14.1327	−	5.85396i	0.507008	−	0.210010i
$778$		0			0
$779$	51.1056	+	10.1655i	1.83105	+	0.364218i
$780$		0			0
$781$	−11.9122	−	7.95949i	−0.426253	−	0.284813i
$782$		0			0
$783$	9.86823	+	9.86823i	0.352662	+	0.352662i
$784$		0			0
$785$	−41.2089	+	41.2089i	−1.47081	+	1.47081i
$786$		0			0
$787$	19.4919	−	29.1717i	0.694813	−	1.03986i	−0.301450	−	0.953482i	$-0.597471\pi$
$787$	19.4919	−	29.1717i	0.694813	−	1.03986i	0.996262	−	0.0863785i	$-0.0275294\pi$
$788$		0			0
$789$	0.980928	−	4.93146i	0.0349220	−	0.175565i
$790$		0			0
$791$	5.47512	+	13.2181i	0.194673	+	0.469982i
$792$		0			0
$793$	−9.23134	+	22.2864i	−0.327815	+	0.791414i
$794$		0			0
$795$	40.1398	+	60.0734i	1.42361	+	2.13058i
$796$		0			0
$797$	11.1662	−	2.22109i	0.395526	−	0.0786751i	0.00667994	−	0.999978i	$-0.497874\pi$
$797$	11.1662	−	2.22109i	0.395526	−	0.0786751i	0.388846	+	0.921303i	$0.372874\pi$
$798$		0			0
$799$			10.5066i			0.371698i
$800$		0			0
$801$		−	41.0658i		−	1.45099i
$802$		0			0
$803$	7.36769	−	1.46552i	0.260000	−	0.0517172i
$804$		0			0
$805$	9.58136	+	14.3395i	0.337699	+	0.505402i
$806$		0			0
$807$	−34.2839	+	82.7687i	−1.20685	+	2.91360i
$808$		0			0
$809$	−3.82483	−	9.23396i	−0.134474	−	0.324649i	0.842271	−	0.539055i	$-0.181218\pi$
$809$	−3.82483	−	9.23396i	−0.134474	−	0.324649i	−0.976745	+	0.214406i	$0.931218\pi$
$810$		0			0
$811$	−9.50273	+	47.7735i	−0.333686	+	1.67755i	0.341482	+	0.939888i	$0.389071\pi$
$811$	−9.50273	+	47.7735i	−0.333686	+	1.67755i	−0.675168	+	0.737664i	$0.735929\pi$
$812$		0			0
$813$	−3.54134	+	5.29999i	−0.124200	+	0.185879i
$814$		0			0
$815$	7.32094	−	7.32094i	0.256441	−	0.256441i
$816$		0			0
$817$	−7.01296	−	7.01296i	−0.245352	−	0.245352i
$818$		0			0
$819$	−21.4856	−	14.3562i	−0.750768	−	0.501647i
$820$		0			0
$821$	−13.9146	−	2.76779i	−0.485623	−	0.0965965i	−0.0537945	−	0.998552i	$-0.517132\pi$
$821$	−13.9146	−	2.76779i	−0.485623	−	0.0965965i	−0.431829	+	0.901956i	$0.642132\pi$
$822$		0			0
$823$	42.1742	−	17.4691i	1.47010	−	0.608935i	0.503217	−	0.864160i	$-0.332150\pi$
$823$	42.1742	−	17.4691i	1.47010	−	0.608935i	0.966882	+	0.255225i	$0.0821497\pi$
$824$		0			0
$825$	−25.7608	−	10.6705i	−0.896876	−	0.371498i
$826$		0			0
$827$	−18.5286	+	12.3804i	−0.644302	+	0.430509i	−0.834326	−	0.551271i	$-0.814143\pi$
$827$	−18.5286	+	12.3804i	−0.644302	+	0.430509i	0.190025	+	0.981779i	$0.439143\pi$
$828$		0			0
$829$	8.53766	+	42.9217i	0.296525	+	1.49073i	0.785733	+	0.618565i	$0.212286\pi$
$829$	8.53766	+	42.9217i	0.296525	+	1.49073i	−0.489208	+	0.872167i	$0.662714\pi$
$830$		0			0
$831$	14.1218			0.489881
$832$		0			0
$833$	8.09256			0.280391
$834$		0			0
$835$	−0.148664	−	0.747383i	−0.00514472	−	0.0258643i
$836$		0			0
$837$	8.80471	−	5.88312i	0.304335	−	0.203350i
$838$		0			0
$839$	31.4108	+	13.0108i	1.08442	+	0.449182i	0.852059	−	0.523446i	$-0.175354\pi$
$839$	31.4108	+	13.0108i	1.08442	+	0.449182i	0.232364	+	0.972629i	$0.425354\pi$
$840$		0			0
$841$	−21.5300	+	8.91801i	−0.742414	+	0.307518i
$842$		0			0
$843$	−5.51560	−	1.09712i	−0.189967	−	0.0377868i
$844$		0			0
$845$	18.7926	+	12.5568i	0.646487	+	0.431969i
$846$		0			0
$847$	−10.1402	−	10.1402i	−0.348421	−	0.348421i
$848$		0			0
$849$	−19.6069	+	19.6069i	−0.672906	+	0.672906i
$850$		0			0
$851$	−3.65280	+	5.46680i	−0.125216	+	0.187400i
$852$		0			0
$853$	−10.2217	+	51.3880i	−0.349984	+	1.75949i	0.258583	+	0.965989i	$0.416744\pi$
$853$	−10.2217	+	51.3880i	−0.349984	+	1.75949i	−0.608568	+	0.793502i	$0.708256\pi$
$854$		0			0
$855$	−25.8810	−	62.4822i	−0.885111	−	2.13685i
$856$		0			0
$857$	5.90193	−	14.2485i	0.201606	−	0.486720i	−0.790448	−	0.612529i	$-0.790152\pi$
$857$	5.90193	−	14.2485i	0.201606	−	0.486720i	0.992055	+	0.125808i	$0.0401524\pi$
$858$		0			0
$859$	−32.4534	−	48.5700i	−1.10730	−	1.65719i	−0.622747	−	0.782423i	$-0.713983\pi$
$859$	−32.4534	−	48.5700i	−1.10730	−	1.65719i	−0.484550	−	0.874764i	$-0.661017\pi$
$860$		0			0
$861$	−72.1270	+	14.3470i	−2.45808	+	0.488943i
$862$		0			0
$863$		−	32.8866i		−	1.11947i	−0.828671	−	0.559736i	$-0.810902\pi$
$863$		−	32.8866i		−	1.11947i	0.828671	−	0.559736i	$-0.189098\pi$
$864$		0			0
$865$			46.3552i			1.57612i
$866$		0			0
$867$	−17.5884	+	3.49855i	−0.597334	+	0.118817i
$868$		0			0
$869$	−17.7512	−	26.5666i	−0.602169	−	0.901209i
$870$		0			0
$871$	−13.6090	+	32.8551i	−0.461124	+	1.11325i
$872$		0			0
$873$	16.4444	+	39.7004i	0.556560	+	1.34365i
$874$		0			0
$875$	0.311417	−	1.56560i	0.0105278	−	0.0529269i
$876$		0			0
$877$	−6.14533	+	9.19714i	−0.207513	+	0.310565i	−0.920597	−	0.390513i	$-0.872298\pi$
$877$	−6.14533	+	9.19714i	−0.207513	+	0.310565i	0.713084	+	0.701078i	$0.247298\pi$
$878$		0			0
$879$	24.0520	−	24.0520i	0.811255	−	0.811255i
$880$		0			0
$881$	11.2198	+	11.2198i	0.378006	+	0.378006i	0.870382	−	0.492376i	$-0.163872\pi$
$881$	11.2198	+	11.2198i	0.378006	+	0.378006i	−0.492376	+	0.870382i	$0.663872\pi$
$882$		0			0
$883$	29.8483	+	19.9440i	1.00447	+	0.671168i	0.945003	−	0.327062i	$-0.106059\pi$
$883$	29.8483	+	19.9440i	1.00447	+	0.671168i	0.0594714	+	0.998230i	$0.481059\pi$
$884$		0			0
$885$	−74.0727	−	14.7340i	−2.48993	−	0.495277i
$886$		0			0
$887$	32.5314	−	13.4749i	1.09230	−	0.452444i	0.237489	−	0.971390i	$-0.423676\pi$
$887$	32.5314	−	13.4749i	1.09230	−	0.452444i	0.854807	+	0.518946i	$0.173676\pi$
$888$		0			0
$889$	−0.594236	−	0.246141i	−0.0199300	−	0.00825529i
$890$		0			0
$891$	−2.43891	+	1.62963i	−0.0817067	+	0.0545947i
$892$		0			0
$893$	−2.68314	−	13.4891i	−0.0897878	−	0.451394i
$894$		0			0
$895$	−36.0167			−1.20391
$896$		0			0
$897$	17.6918			0.590713
$898$		0			0
$899$	−0.843195	−	4.23903i	−0.0281221	−	0.141379i
$900$		0			0
$901$	22.1388	−	14.7927i	0.737551	−	0.492816i
$902$		0			0
$903$	12.9319	+	5.35655i	0.430346	+	0.178255i
$904$		0			0
$905$	−24.5358	+	10.1631i	−0.815597	+	0.337831i
$906$		0			0
$907$	−49.0725	−	9.76113i	−1.62943	−	0.324113i	−0.706095	−	0.708117i	$-0.749545\pi$
$907$	−49.0725	−	9.76113i	−1.62943	−	0.324113i	−0.923331	+	0.384004i	$0.874545\pi$
$908$		0			0
$909$	−62.4080	−	41.6997i	−2.06994	−	1.38309i
$910$		0			0
$911$	0.673519	+	0.673519i	0.0223147	+	0.0223147i	0.718176	−	0.695861i	$-0.244977\pi$
$911$	0.673519	+	0.673519i	0.0223147	+	0.0223147i	−0.695861	+	0.718176i	$0.744977\pi$
$912$		0			0
$913$	9.79066	−	9.79066i	0.324024	−	0.324024i
$914$		0			0
$915$	49.5032	−	74.0868i	1.63653	−	2.44923i
$916$		0			0
$917$	2.23468	−	11.2345i	0.0737955	−	0.370995i
$918$		0			0
$919$	−18.8450	−	45.4958i	−0.621639	−	1.50077i	−0.849778	−	0.527140i	$-0.823264\pi$
$919$	−18.8450	−	45.4958i	−0.621639	−	1.50077i	0.228139	−	0.973628i	$-0.426736\pi$
$920$		0			0
$921$	12.5411	−	30.2768i	0.413242	−	0.997654i
$922$		0			0
$923$	9.26185	+	13.8613i	0.304857	+	0.456251i
$924$		0			0
$925$	−11.8262	+	2.35238i	−0.388843	+	0.0773456i
$926$		0			0
$927$			28.4038i			0.932904i
$928$		0			0
$929$			37.0292i			1.21489i	0.794362	+	0.607445i	$0.207805\pi$
$929$			37.0292i			1.21489i	−0.794362	+	0.607445i	$0.792195\pi$
$930$		0			0
$931$	−10.3897	+	2.06664i	−0.340510	+	0.0677316i
$932$		0			0
$933$	36.8250	+	55.1124i	1.20559	+	1.80430i
$934$		0			0
$935$	−8.06323	+	19.4664i	−0.263696	+	0.636618i
$936$		0			0
$937$	−13.0321	−	31.4623i	−0.425740	−	1.02783i	−0.980624	−	0.195900i	$-0.937237\pi$
$937$	−13.0321	−	31.4623i	−0.425740	−	1.02783i	0.554884	−	0.831928i	$-0.312763\pi$
$938$		0			0
$939$	0.995217	−	5.00329i	0.0324777	−	0.163276i
$940$		0			0
$941$	14.1954	−	21.2450i	0.462758	−	0.692566i	−0.524551	−	0.851379i	$-0.675767\pi$
$941$	14.1954	−	21.2450i	0.462758	−	0.692566i	0.987309	+	0.158813i	$0.0507666\pi$
$942$		0			0
$943$	22.3504	−	22.3504i	0.727831	−	0.727831i
$944$		0			0
$945$	27.4749	+	27.4749i	0.893758	+	0.893758i
$946$		0			0
$947$	−43.8404	−	29.2932i	−1.42462	−	0.951902i	−0.998892	−	0.0470518i	$-0.985017\pi$
$947$	−43.8404	−	29.2932i	−1.42462	−	0.951902i	−0.425730	−	0.904850i	$-0.639983\pi$
$948$		0			0
$949$	−8.57321	−	1.70532i	−0.278298	−	0.0553570i
$950$		0			0
$951$	−39.0236	+	16.1641i	−1.26543	+	0.524157i
$952$		0			0
$953$	2.18380	+	0.904560i	0.0707403	+	0.0293016i	0.417773	−	0.908551i	$-0.362811\pi$
$953$	2.18380	+	0.904560i	0.0707403	+	0.0293016i	−0.347033	+	0.937853i	$0.612811\pi$
$954$		0			0
$955$	16.3960	−	10.9555i	0.530562	−	0.354510i
$956$		0			0
$957$	2.72761	+	13.7126i	0.0881711	+	0.443266i
$958$		0			0
$959$	36.6250			1.18268
$960$		0			0
$961$	27.7205			0.894210
$962$		0			0
$963$	12.7945	+	64.3221i	0.412296	+	2.07275i
$964$		0			0
$965$	27.3153	−	18.2515i	0.879312	−	0.587537i
$966$		0			0
$967$	−44.4518	−	18.4125i	−1.42947	−	0.592107i	−0.472251	−	0.881464i	$-0.656559\pi$
$967$	−44.4518	−	18.4125i	−1.42947	−	0.592107i	−0.957221	+	0.289357i	$0.906559\pi$
$968$		0			0
$969$	−36.6794	+	15.1931i	−1.17831	+	0.488074i
$970$		0			0
$971$	−8.20968	−	1.63301i	−0.263461	−	0.0524057i	0.0615920	−	0.998101i	$-0.480382\pi$
$971$	−8.20968	−	1.63301i	−0.263461	−	0.0524057i	−0.325053	+	0.945696i	$0.605382\pi$
$972$		0			0
$973$	21.1059	+	14.1025i	0.676625	+	0.452106i
$974$		0			0
$975$	22.9425	+	22.9425i	0.734749	+	0.734749i
$976$		0			0
$977$	13.9697	−	13.9697i	0.446930	−	0.446930i	−0.447403	−	0.894333i	$-0.647651\pi$
$977$	13.9697	−	13.9697i	0.446930	−	0.446930i	0.894333	+	0.447403i	$0.147651\pi$
$978$		0			0
$979$	9.30447	−	13.9251i	0.297372	−	0.445049i
$980$		0			0
$981$	9.57607	−	48.1421i	0.305740	−	1.53706i
$982$		0			0
$983$	18.1142	+	43.7315i	0.577753	+	1.39482i	0.894825	+	0.446417i	$0.147300\pi$
$983$	18.1142	+	43.7315i	0.577753	+	1.39482i	−0.317072	+	0.948401i	$0.602700\pi$
$984$		0			0
$985$	18.7788	−	45.3361i	0.598344	−	1.44453i
$986$		0			0
$987$	10.7839	+	16.1392i	0.343255	+	0.513718i
$988$		0			0
$989$	−5.90061	+	1.17370i	−0.187628	+	0.0373216i
$990$		0			0
$991$		−	14.8761i		−	0.472553i	−0.971686	−	0.236277i	$-0.924073\pi$
$991$		−	14.8761i		−	0.472553i	0.971686	−	0.236277i	$-0.0759272\pi$
$992$		0			0
$993$			15.9574i			0.506392i
$994$		0			0
$995$	84.2638	−	16.7611i	2.67134	−	0.531363i
$996$		0			0
$997$	−17.6104	−	26.3559i	−0.557728	−	0.834698i	0.440276	−	0.897863i	$-0.354881\pi$
$997$	−17.6104	−	26.3559i	−0.557728	−	0.834698i	−0.998003	+	0.0631644i	$0.979881\pi$
$998$		0			0
$999$	−5.66878	+	13.6856i	−0.179352	+	0.432994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.a.97.7		56
4.3	odd	2		512.2.i.b.97.1		56
8.3	odd	2		64.2.i.a.21.4	✓	56
8.5	even	2		256.2.i.a.177.1		56
24.11	even	2		576.2.bd.a.469.4		56
64.3	odd	16		512.2.i.b.417.1		56
64.29	even	16		256.2.i.a.81.1		56
64.35	odd	16		64.2.i.a.61.4	yes	56
64.61	even	16	inner	512.2.i.a.417.7		56
192.35	even	16		576.2.bd.a.253.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.4	✓	56	8.3	odd	2
64.2.i.a.61.4	yes	56	64.35	odd	16
256.2.i.a.81.1		56	64.29	even	16
256.2.i.a.177.1		56	8.5	even	2
512.2.i.a.97.7		56	1.1	even	1	trivial
512.2.i.a.417.7		56	64.61	even	16	inner
512.2.i.b.97.1		56	4.3	odd	2
512.2.i.b.417.1		56	64.3	odd	16
576.2.bd.a.253.4		56	192.35	even	16
576.2.bd.a.469.4		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)

\(f(q)\)	\(=\)	\(q+(0.553854 + 2.78441i) q^{3} +(-2.59756 + 1.73564i) q^{5} +(1.96508 + 0.813965i) q^{7} +(-4.67456 + 1.93627i) q^{9} +O(q^{10})\)	\(q+(0.553854 + 2.78441i) q^{3} +(-2.59756 + 1.73564i) q^{5} +(1.96508 + 0.813965i) q^{7} +(-4.67456 + 1.93627i) q^{9} +(-2.02382 - 0.402563i) q^{11} +(1.99644 + 1.33398i) q^{13} +(-6.27140 - 6.27140i) q^{15} +(-2.31120 + 2.31120i) q^{17} +(2.37703 - 3.55748i) q^{19} +(-1.17804 + 5.92242i) q^{21} +(-0.993213 - 2.39783i) q^{23} +(1.82149 - 4.39746i) q^{25} +(-3.24866 - 4.86196i) q^{27} +(-2.34079 + 0.465613i) q^{29} +1.81094i q^{31} -5.85811i q^{33} +(-6.51718 + 1.29635i) q^{35} +(-1.40742 - 2.10635i) q^{37} +(-2.60861 + 6.29775i) q^{39} +(4.66056 + 11.2516i) q^{41} +(0.452227 - 2.27350i) q^{43} +(8.78181 - 13.1429i) q^{45} +(2.27298 - 2.27298i) q^{47} +(-1.75073 - 1.75073i) q^{49} +(-7.71539 - 5.15526i) q^{51} +(-7.98970 - 1.58925i) q^{53} +(5.95570 - 2.46693i) q^{55} +(11.2220 + 4.64831i) q^{57} +(7.08029 - 4.73090i) q^{59} +(1.95998 + 9.85346i) q^{61} -10.7620 q^{63} -7.50119 q^{65} +(2.88943 + 14.5262i) q^{67} +(6.12645 - 4.09356i) q^{69} +(6.41451 + 2.65698i) q^{71} +(-3.36337 + 1.39315i) q^{73} +(13.2532 + 2.63622i) q^{75} +(-3.64930 - 2.43839i) q^{77} +(10.9490 + 10.9490i) q^{79} +(1.00516 - 1.00516i) q^{81} +(-3.72793 + 5.57925i) q^{83} +(1.99208 - 10.0149i) q^{85} +(-2.59292 - 6.25985i) q^{87} +(-3.10595 + 7.49842i) q^{89} +(2.83736 + 4.24642i) q^{91} +(-5.04240 + 1.00299i) q^{93} +13.3664i q^{95} -8.49286i q^{97} +(10.2399 - 2.03685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 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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