LMFDB - Embedded newform 656.2.bs.d.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(33,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

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

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

chi := DirichletCharacter("656.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.bs (of order $20$, 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:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			225.1
Character	$\chi$	$=$	656.225
Dual form			656.2.bs.d.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.964912 + 0.964912i) q^{3} +(-2.03721 + 2.80398i) q^{5} +(-1.29765 - 0.661185i) q^{7} +1.13789i q^{9} +O(q^{10})$	\(q+(-0.964912 + 0.964912i) q^{3} +(-2.03721 + 2.80398i) q^{5} +(-1.29765 - 0.661185i) q^{7} +1.13789i q^{9} +(-0.285814 + 1.80456i) q^{11} +(-2.91004 - 5.71127i) q^{13} +(-0.739865 - 4.67132i) q^{15} +(3.14295 + 0.497794i) q^{17} +(-1.51872 + 2.98065i) q^{19} +(1.89010 - 0.614131i) q^{21} +(1.67386 - 5.15161i) q^{23} +(-2.16699 - 6.66932i) q^{25} +(-3.99270 - 3.99270i) q^{27} +(-0.335113 + 0.0530767i) q^{29} +(3.04183 - 2.21002i) q^{31} +(-1.46545 - 2.01702i) q^{33} +(4.49754 - 2.29161i) q^{35} +(0.993200 + 0.721602i) q^{37} +(8.31880 + 2.70294i) q^{39} +(-6.22198 - 1.51227i) q^{41} +(-7.02832 - 2.28364i) q^{43} +(-3.19062 - 2.31812i) q^{45} +(1.40824 - 0.717533i) q^{47} +(-2.86777 - 3.94715i) q^{49} +(-3.51299 + 2.55234i) q^{51} +(1.12895 - 0.178807i) q^{53} +(-4.47768 - 4.47768i) q^{55} +(-1.41064 - 4.34149i) q^{57} +(-4.16549 + 12.8200i) q^{59} +(-4.39785 + 1.42895i) q^{61} +(0.752356 - 1.47658i) q^{63} +(21.9426 + 3.47537i) q^{65} +(-1.04355 - 6.58873i) q^{67} +(3.35573 + 6.58598i) q^{69} +(1.29298 - 8.16358i) q^{71} +8.99466i q^{73} +(8.52627 + 4.34435i) q^{75} +(1.56403 - 2.15271i) q^{77} +(-7.20521 + 7.20521i) q^{79} +4.29154 q^{81} +7.11449 q^{83} +(-7.79865 + 7.79865i) q^{85} +(0.272140 - 0.374569i) q^{87} +(-12.9260 - 6.58613i) q^{89} +9.33529i q^{91} +(-0.802625 + 5.06757i) q^{93} +(-5.26374 - 10.3307i) q^{95} +(0.514313 + 3.24724i) q^{97} +(-2.05339 - 0.325225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$1$	$1$

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
$3$	−0.964912	+	0.964912i	−0.557092	+	0.557092i	−0.928478	−	0.371386i	$-0.878883\pi$
$3$	−0.964912	+	0.964912i	−0.557092	+	0.557092i	0.371386	+	0.928478i	$0.378883\pi$
$4$		0			0
$5$	−2.03721	+	2.80398i	−0.911069	+	1.25398i	0.0557316	+	0.998446i	$0.482251\pi$
$5$	−2.03721	+	2.80398i	−0.911069	+	1.25398i	−0.966800	+	0.255533i	$0.917749\pi$
$6$		0			0
$7$	−1.29765	−	0.661185i	−0.490465	−	0.249905i	0.191224	−	0.981546i	$-0.438754\pi$
$7$	−1.29765	−	0.661185i	−0.490465	−	0.249905i	−0.681689	+	0.731642i	$0.738754\pi$
$8$		0			0
$9$			1.13789i			0.379297i
$10$		0			0
$11$	−0.285814	+	1.80456i	−0.0861761	+	0.544095i	0.906395	+	0.422431i	$0.138823\pi$
$11$	−0.285814	+	1.80456i	−0.0861761	+	0.544095i	−0.992571	+	0.121664i	$0.961177\pi$
$12$		0			0
$13$	−2.91004	−	5.71127i	−0.807099	−	1.58402i	−0.811731	−	0.584031i	$-0.801475\pi$
$13$	−2.91004	−	5.71127i	−0.807099	−	1.58402i	0.00463289	−	0.999989i	$-0.498525\pi$
$14$		0			0
$15$	−0.739865	−	4.67132i	−0.191032	−	1.20613i
$16$		0			0
$17$	3.14295	+	0.497794i	0.762277	+	0.120733i	0.525456	−	0.850821i	$-0.323895\pi$
$17$	3.14295	+	0.497794i	0.762277	+	0.120733i	0.236821	+	0.971553i	$0.423895\pi$
$18$		0			0
$19$	−1.51872	+	2.98065i	−0.348417	+	0.683808i	−0.997005	−	0.0773320i	$-0.975360\pi$
$19$	−1.51872	+	2.98065i	−0.348417	+	0.683808i	0.648588	+	0.761140i	$0.275360\pi$
$20$		0			0
$21$	1.89010	−	0.614131i	0.412454	−	0.134014i
$22$		0			0
$23$	1.67386	−	5.15161i	0.349024	−	1.07419i	−0.610370	−	0.792117i	$-0.708979\pi$
$23$	1.67386	−	5.15161i	0.349024	−	1.07419i	0.959394	−	0.282069i	$-0.0910208\pi$
$24$		0			0
$25$	−2.16699	−	6.66932i	−0.433399	−	1.33386i
$26$		0			0
$27$	−3.99270	−	3.99270i	−0.768395	−	0.768395i
$28$		0			0
$29$	−0.335113	+	0.0530767i	−0.0622289	+	0.00985609i	−0.187471	−	0.982270i	$-0.560029\pi$
$29$	−0.335113	+	0.0530767i	−0.0622289	+	0.00985609i	0.125242	+	0.992126i	$0.460029\pi$
$30$		0			0
$31$	3.04183	−	2.21002i	0.546329	−	0.396931i	−0.280101	−	0.959971i	$-0.590368\pi$
$31$	3.04183	−	2.21002i	0.546329	−	0.396931i	0.826430	+	0.563039i	$0.190368\pi$
$32$		0			0
$33$	−1.46545	−	2.01702i	−0.255103	−	0.351119i
$34$		0			0
$35$	4.49754	−	2.29161i	0.760222	−	0.387353i
$36$		0			0
$37$	0.993200	+	0.721602i	0.163281	+	0.118631i	0.666425	−	0.745572i	$-0.267824\pi$
$37$	0.993200	+	0.721602i	0.163281	+	0.118631i	−0.503144	+	0.864202i	$0.667824\pi$
$38$		0			0
$39$	8.31880	+	2.70294i	1.33207	+	0.432817i
$40$		0			0
$41$	−6.22198	−	1.51227i	−0.971710	−	0.236176i
$41$	−6.22198	−	1.51227i	−0.971710	−	0.236176i
$42$		0			0
$43$	−7.02832	−	2.28364i	−1.07181	−	0.348252i	−0.280617	−	0.959820i	$-0.590539\pi$
$43$	−7.02832	−	2.28364i	−1.07181	−	0.348252i	−0.791192	+	0.611568i	$0.790539\pi$
$44$		0			0
$45$	−3.19062	−	2.31812i	−0.475630	−	0.345565i
$46$		0			0
$47$	1.40824	−	0.717533i	0.205413	−	0.104663i	−0.348258	−	0.937399i	$-0.613227\pi$
$47$	1.40824	−	0.717533i	0.205413	−	0.104663i	0.553671	+	0.832736i	$0.313227\pi$
$48$		0			0
$49$	−2.86777	−	3.94715i	−0.409681	−	0.563878i
$50$		0			0
$51$	−3.51299	+	2.55234i	−0.491918	+	0.357399i
$52$		0			0
$53$	1.12895	−	0.178807i	0.155073	−	0.0245611i	−0.0784154	−	0.996921i	$-0.524986\pi$
$53$	1.12895	−	0.178807i	0.155073	−	0.0245611i	0.233488	+	0.972360i	$0.424986\pi$
$54$		0			0
$55$	−4.47768	−	4.47768i	−0.603771	−	0.603771i
$56$		0			0
$57$	−1.41064	−	4.34149i	−0.186843	−	0.575045i
$58$		0			0
$59$	−4.16549	+	12.8200i	−0.542300	+	1.66903i	0.185024	+	0.982734i	$0.440764\pi$
$59$	−4.16549	+	12.8200i	−0.542300	+	1.66903i	−0.727324	+	0.686294i	$0.759236\pi$
$60$		0			0
$61$	−4.39785	+	1.42895i	−0.563087	+	0.182958i	−0.576710	−	0.816949i	$-0.695664\pi$
$61$	−4.39785	+	1.42895i	−0.563087	+	0.182958i	0.0136225	+	0.999907i	$0.495664\pi$
$62$		0			0
$63$	0.752356	−	1.47658i	0.0947880	−	0.186032i
$64$		0			0
$65$	21.9426	+	3.47537i	2.72165	+	0.431067i
$66$		0			0
$67$	−1.04355	−	6.58873i	−0.127490	−	0.804941i	−0.965713	−	0.259613i	$-0.916405\pi$
$67$	−1.04355	−	6.58873i	−0.127490	−	0.804941i	0.838223	−	0.545328i	$-0.183595\pi$
$68$		0			0
$69$	3.35573	+	6.58598i	0.403982	+	0.792859i
$70$		0			0
$71$	1.29298	−	8.16358i	0.153449	−	0.968839i	−0.784011	−	0.620746i	$-0.786830\pi$
$71$	1.29298	−	8.16358i	0.153449	−	0.968839i	0.937460	−	0.348092i	$-0.113170\pi$
$72$		0			0
$73$			8.99466i			1.05274i	0.850254	+	0.526372i	$0.176448\pi$
$73$			8.99466i			1.05274i	−0.850254	+	0.526372i	$0.823552\pi$
$74$		0			0
$75$	8.52627	+	4.34435i	0.984529	+	0.501642i
$76$		0			0
$77$	1.56403	−	2.15271i	0.178238	−	0.245324i
$78$		0			0
$79$	−7.20521	+	7.20521i	−0.810649	+	0.810649i	−0.984731	−	0.174082i	$-0.944304\pi$
$79$	−7.20521	+	7.20521i	−0.810649	+	0.810649i	0.174082	+	0.984731i	$0.444304\pi$
$80$		0			0
$81$	4.29154			0.476837
$82$		0			0
$83$	7.11449			0.780916			0.390458	−	0.920621i	$-0.372317\pi$
$83$	7.11449			0.780916			0.390458	+	0.920621i	$0.372317\pi$
$84$		0			0
$85$	−7.79865	+	7.79865i	−0.845883	+	0.845883i
$86$		0			0
$87$	0.272140	−	0.374569i	0.0291765	−	0.0401580i
$88$		0			0
$89$	−12.9260	−	6.58613i	−1.37015	−	0.698128i	−0.394798	−	0.918768i	$-0.629186\pi$
$89$	−12.9260	−	6.58613i	−1.37015	−	0.698128i	−0.975355	+	0.220639i	$0.929186\pi$
$90$		0			0
$91$			9.33529i			0.978604i
$92$		0			0
$93$	−0.802625	+	5.06757i	−0.0832283	+	0.525483i
$94$		0			0
$95$	−5.26374	−	10.3307i	−0.540048	−	1.05990i
$96$		0			0
$97$	0.514313	+	3.24724i	0.0522205	+	0.329707i	0.999944	+	0.0106137i	$0.00337850\pi$
$97$	0.514313	+	3.24724i	0.0522205	+	0.329707i	−0.947723	+	0.319094i	$0.896621\pi$
$98$		0			0
$99$	−2.05339	−	0.325225i	−0.206373	−	0.0326863i
$100$		0			0
$101$	2.96889	−	5.82677i	0.295415	−	0.579785i	−0.694821	−	0.719183i	$-0.744516\pi$
$101$	2.96889	−	5.82677i	0.295415	−	0.579785i	0.990237	+	0.139397i	$0.0445165\pi$
$102$		0			0
$103$	−15.6950	+	5.09961i	−1.54647	+	0.502479i	−0.953153	−	0.302488i	$-0.902183\pi$
$103$	−15.6950	+	5.09961i	−1.54647	+	0.502479i	−0.593319	+	0.804967i	$0.702183\pi$
$104$		0			0
$105$	−2.12853	+	6.55093i	−0.207723	+	0.639305i
$106$		0			0
$107$	2.13141	+	6.55981i	0.206051	+	0.634160i	0.999669	+	0.0257432i	$0.00819521\pi$
$107$	2.13141	+	6.55981i	0.206051	+	0.634160i	−0.793617	+	0.608417i	$0.791805\pi$
$108$		0			0
$109$	0.909585	+	0.909585i	0.0871225	+	0.0871225i	0.749325	−	0.662202i	$-0.230378\pi$
$109$	0.909585	+	0.909585i	0.0871225	+	0.0871225i	−0.662202	+	0.749325i	$0.730378\pi$
$110$		0			0
$111$	−1.65463	+	0.262068i	−0.157051	+	0.0248744i
$112$		0			0
$113$	−5.72258	+	4.15770i	−0.538335	+	0.391123i	−0.823466	−	0.567365i	$-0.807963\pi$
$113$	−5.72258	+	4.15770i	−0.538335	+	0.391123i	0.285131	+	0.958489i	$0.407963\pi$
$114$		0			0
$115$	11.0350	+	15.1884i	1.02902	+	1.41633i
$116$		0			0
$117$	6.49879	−	3.31130i	0.600814	−	0.306130i
$118$		0			0
$119$	−3.74931	−	2.72403i	−0.343699	−	0.249712i
$120$		0			0
$121$	7.28688	+	2.36765i	0.662444	+	0.215241i
$122$		0			0
$123$	7.46287	−	4.54446i	0.672904	−	0.409760i
$124$		0			0
$125$	6.63390	+	2.15548i	0.593354	+	0.192792i
$126$		0			0
$127$	−4.45174	−	3.23438i	−0.395028	−	0.287005i	0.372485	−	0.928038i	$-0.378506\pi$
$127$	−4.45174	−	3.23438i	−0.395028	−	0.287005i	−0.767513	+	0.641034i	$0.778506\pi$
$128$		0			0
$129$	8.98522	−	4.57820i	0.791105	−	0.403088i
$130$		0			0
$131$	4.78432	+	6.58506i	0.418008	+	0.575339i	0.965149	−	0.261702i	$-0.0842836\pi$
$131$	4.78432	+	6.58506i	0.418008	+	0.575339i	−0.547140	+	0.837041i	$0.684284\pi$
$132$		0			0
$133$	3.94152	−	2.86368i	0.341773	−	0.248313i
$134$		0			0
$135$	19.3294	−	3.06148i	1.66361	−	0.263490i
$136$		0			0
$137$	0.0757881	+	0.0757881i	0.00647501	+	0.00647501i	0.710337	−	0.703862i	$-0.248543\pi$
$137$	0.0757881	+	0.0757881i	0.00647501	+	0.00647501i	−0.703862	+	0.710337i	$0.748543\pi$
$138$		0			0
$139$	−4.01271	−	12.3499i	−0.340354	−	1.04750i	−0.964024	−	0.265814i	$-0.914359\pi$
$139$	−4.01271	−	12.3499i	−0.340354	−	1.04750i	0.623670	−	0.781688i	$-0.285641\pi$
$140$		0			0
$141$	−0.666469	+	2.05118i	−0.0561268	+	0.172741i
$142$		0			0
$143$	11.1380	−	3.61897i	0.931409	−	0.302633i
$144$		0			0
$145$	0.533870	−	1.04778i	0.0443355	−	0.0870133i
$146$		0			0
$147$	6.57579	+	1.04150i	0.542362	+	0.0859017i
$148$		0			0
$149$	0.0276020	+	0.174272i	0.00226125	+	0.0142769i	0.988793	−	0.149292i	$-0.0476994\pi$
$149$	0.0276020	+	0.174272i	0.00226125	+	0.0142769i	−0.986532	+	0.163569i	$0.947699\pi$
$150$		0			0
$151$	8.96384	+	17.5925i	0.729467	+	1.43166i	0.895281	+	0.445502i	$0.146975\pi$
$151$	8.96384	+	17.5925i	0.729467	+	1.43166i	−0.165814	+	0.986157i	$0.553025\pi$
$152$		0			0
$153$	−0.566435	+	3.57633i	−0.0457935	+	0.289129i
$154$		0			0
$155$			13.0315i			1.04672i
$156$		0			0
$157$	−3.16869	−	1.61453i	−0.252889	−	0.128853i	0.322951	−	0.946416i	$-0.395325\pi$
$157$	−3.16869	−	1.61453i	−0.252889	−	0.128853i	−0.575840	+	0.817562i	$0.695325\pi$
$158$		0			0
$159$	−0.916800	+	1.26187i	−0.0727069	+	0.100073i
$160$		0			0
$161$	−5.57826	+	5.57826i	−0.439628	+	0.439628i
$162$		0			0
$163$	4.06263			0.318210			0.159105	−	0.987262i	$-0.449139\pi$
$163$	4.06263			0.318210			0.159105	+	0.987262i	$0.449139\pi$
$164$		0			0
$165$	8.64114			0.672712
$166$		0			0
$167$	−4.42614	+	4.42614i	−0.342505	+	0.342505i	−0.857308	−	0.514803i	$-0.827865\pi$
$167$	−4.42614	+	4.42614i	−0.342505	+	0.342505i	0.514803	+	0.857308i	$0.327865\pi$
$168$		0			0
$169$	−16.5090	+	22.7227i	−1.26993	+	1.74790i
$170$		0			0
$171$	−3.39165	−	1.72813i	−0.259366	−	0.132154i
$172$		0			0
$173$			5.09639i			0.387472i	0.981054	+	0.193736i	$0.0620605\pi$
$173$			5.09639i			0.387472i	−0.981054	+	0.193736i	$0.937940\pi$
$174$		0			0
$175$	−1.59766	+	10.0872i	−0.120772	+	0.762523i
$176$		0			0
$177$	−8.35089	−	16.3895i	−0.627691	−	1.23191i
$178$		0			0
$179$	−1.40815	−	8.89068i	−0.105250	−	0.664521i	−0.982749	−	0.184943i	$-0.940790\pi$
$179$	−1.40815	−	8.89068i	−0.105250	−	0.664521i	0.877500	−	0.479578i	$-0.159210\pi$
$180$		0			0
$181$	−11.7410	−	1.85960i	−0.872704	−	0.138223i	−0.296012	−	0.955184i	$-0.595657\pi$
$181$	−11.7410	−	1.85960i	−0.872704	−	0.138223i	−0.576692	+	0.816961i	$0.695657\pi$
$182$		0			0
$183$	2.86473	−	5.62235i	0.211767	−	0.415616i
$184$		0			0
$185$	−4.04672	+	1.31486i	−0.297521	+	0.0966703i
$186$		0			0
$187$	−1.79660	+	5.52935i	−0.131380	+	0.404346i
$188$		0			0
$189$	2.54121	+	7.82104i	0.184846	+	0.568897i
$190$		0			0
$191$	−12.4651	−	12.4651i	−0.901943	−	0.901943i	0.0936612	−	0.995604i	$-0.470143\pi$
$191$	−12.4651	−	12.4651i	−0.901943	−	0.901943i	−0.995604	+	0.0936612i	$0.970143\pi$
$192$		0			0
$193$	13.5277	−	2.14258i	0.973749	−	0.154227i	0.350767	−	0.936463i	$-0.385921\pi$
$193$	13.5277	−	2.14258i	0.973749	−	0.154227i	0.622982	+	0.782236i	$0.285921\pi$
$194$		0			0
$195$	−24.5261	+	17.8193i	−1.75635	+	1.27607i
$196$		0			0
$197$	2.51439	+	3.46077i	0.179143	+	0.246569i	0.889140	−	0.457636i	$-0.151304\pi$
$197$	2.51439	+	3.46077i	0.179143	+	0.246569i	−0.709997	+	0.704205i	$0.751304\pi$
$198$		0			0
$199$	−3.37859	+	1.72148i	−0.239502	+	0.122032i	−0.569623	−	0.821906i	$-0.692911\pi$
$199$	−3.37859	+	1.72148i	−0.239502	+	0.122032i	0.330120	+	0.943939i	$0.392911\pi$
$200$		0			0
$201$	7.36448	+	5.35061i	0.519450	+	0.377403i
$202$		0			0
$203$	0.469952	+	0.152697i	0.0329842	+	0.0107172i
$204$		0			0
$205$	16.9159	−	14.3655i	1.18145	−	1.00333i
$206$		0			0
$207$	5.86197	+	1.90467i	0.407435	+	0.132384i
$208$		0			0
$209$	−4.94468	−	3.59252i	−0.342031	−	0.248500i
$210$		0			0
$211$	−1.22845	+	0.625927i	−0.0845701	+	0.0430906i	−0.495764	−	0.868457i	$-0.665112\pi$
$211$	−1.22845	+	0.625927i	−0.0845701	+	0.0430906i	0.411194	+	0.911548i	$0.365112\pi$
$212$		0			0
$213$	6.62952	+	9.12475i	0.454247	+	0.625218i
$214$		0			0
$215$	20.7215	−	15.0550i	1.41319	−	1.02674i
$216$		0			0
$217$	−5.40846	+	0.856616i	−0.367150	+	0.0581509i
$218$		0			0
$219$	−8.67905	−	8.67905i	−0.586476	−	0.586476i
$220$		0			0
$221$	−6.30305	−	19.3988i	−0.423989	−	1.30490i
$222$		0			0
$223$	0.544037	−	1.67437i	0.0364314	−	0.112124i	−0.931187	−	0.364542i	$-0.881226\pi$
$223$	0.544037	−	1.67437i	0.0364314	−	0.112124i	0.967618	+	0.252417i	$0.0812256\pi$
$224$		0			0
$225$	7.58896	−	2.46580i	0.505931	−	0.164387i
$226$		0			0
$227$	−0.0104794	+	0.0205670i	−0.000695544	+	0.00136508i	−0.891354	−	0.453308i	$-0.850244\pi$
$227$	−0.0104794	+	0.0205670i	−0.000695544	+	0.00136508i	0.890658	+	0.454673i	$0.150244\pi$
$228$		0			0
$229$	−23.8647	−	3.77980i	−1.57703	−	0.249776i	−0.694308	−	0.719678i	$-0.744289\pi$
$229$	−23.8647	−	3.77980i	−1.57703	−	0.249776i	−0.882719	+	0.469902i	$0.844289\pi$
$230$		0			0
$231$	0.568018	+	3.58633i	0.0373729	+	0.235963i
$232$		0			0
$233$	8.63167	+	16.9406i	0.565480	+	1.10982i	0.979855	+	0.199710i	$0.0640001\pi$
$233$	8.63167	+	16.9406i	0.565480	+	1.10982i	−0.414375	+	0.910106i	$0.636000\pi$
$234$		0			0
$235$	−0.856929	+	5.41044i	−0.0558999	+	0.352938i
$236$		0			0
$237$		−	13.9048i		−	0.903213i
$238$		0			0
$239$	−15.9440	−	8.12387i	−1.03133	−	0.525490i	−0.145433	−	0.989368i	$-0.546457\pi$
$239$	−15.9440	−	8.12387i	−1.03133	−	0.525490i	−0.885899	+	0.463878i	$0.846457\pi$
$240$		0			0
$241$	−3.38611	+	4.66058i	−0.218118	+	0.300214i	−0.904029	−	0.427472i	$-0.859404\pi$
$241$	−3.38611	+	4.66058i	−0.218118	+	0.300214i	0.685910	+	0.727686i	$0.259404\pi$
$242$		0			0
$243$	7.83714	−	7.83714i	0.502753	−	0.502753i
$244$		0			0
$245$	16.9100			1.08034
$246$		0			0
$247$	21.4428			1.36437
$248$		0			0
$249$	−6.86485	+	6.86485i	−0.435042	+	0.435042i
$250$		0			0
$251$	−14.5918	+	20.0839i	−0.921025	+	1.26768i	0.0422335	+	0.999108i	$0.486553\pi$
$251$	−14.5918	+	20.0839i	−0.921025	+	1.26768i	−0.963259	+	0.268575i	$0.913447\pi$
$252$		0			0
$253$	8.81797	+	4.49298i	0.554381	+	0.282471i
$254$		0			0
$255$		−	15.0500i		−	0.942469i
$256$		0			0
$257$	1.77211	−	11.1887i	0.110541	−	0.697931i	−0.868716	−	0.495311i	$-0.835054\pi$
$257$	1.77211	−	11.1887i	0.110541	−	0.697931i	0.979257	−	0.202620i	$-0.0649457\pi$
$258$		0			0
$259$	−0.811713	−	1.59308i	−0.0504374	−	0.0989889i
$260$		0			0
$261$	−0.0603954	−	0.381322i	−0.00373838	−	0.0236032i
$262$		0			0
$263$	5.50072	+	0.871229i	0.339189	+	0.0537223i	0.323706	−	0.946158i	$-0.395071\pi$
$263$	5.50072	+	0.871229i	0.339189	+	0.0537223i	0.0154834	+	0.999880i	$0.495071\pi$
$264$		0			0
$265$	−1.79853	+	3.52981i	−0.110483	+	0.216835i
$266$		0			0
$267$	18.8275	−	6.11742i	1.15222	−	0.374380i
$268$		0			0
$269$	2.20004	−	6.77102i	0.134139	−	0.412836i	−0.861316	−	0.508069i	$-0.830360\pi$
$269$	2.20004	−	6.77102i	0.134139	−	0.412836i	0.995455	+	0.0952327i	$0.0303595\pi$
$270$		0			0
$271$	−4.59561	−	14.1438i	−0.279164	−	0.859177i	−0.988088	−	0.153892i	$-0.950819\pi$
$271$	−4.59561	−	14.1438i	−0.279164	−	0.859177i	0.708924	−	0.705285i	$-0.249181\pi$
$272$		0			0
$273$	−9.00773	−	9.00773i	−0.545173	−	0.545173i
$274$		0			0
$275$	12.6545	−	2.00428i	0.763097	−	0.120863i
$276$		0			0
$277$	−6.93372	+	5.03764i	−0.416607	+	0.302683i	−0.776271	−	0.630399i	$-0.782891\pi$
$277$	−6.93372	+	5.03764i	−0.416607	+	0.302683i	0.359664	+	0.933082i	$0.382891\pi$
$278$		0			0
$279$	2.51476	+	3.46127i	0.150555	+	0.207221i
$280$		0			0
$281$	10.9370	−	5.57269i	0.652448	−	0.332439i	−0.0962434	−	0.995358i	$-0.530683\pi$
$281$	10.9370	−	5.57269i	0.652448	−	0.332439i	0.748691	+	0.662919i	$0.230683\pi$
$282$		0			0
$283$	−17.0898	−	12.4165i	−1.01588	−	0.738083i	−0.0504491	−	0.998727i	$-0.516065\pi$
$283$	−17.0898	−	12.4165i	−1.01588	−	0.738083i	−0.965435	+	0.260644i	$0.916065\pi$
$284$		0			0
$285$	15.0472	+	4.88914i	0.891321	+	0.289608i
$286$		0			0
$287$	7.07406	+	6.07627i	0.417569	+	0.358671i
$288$		0			0
$289$	−6.53764	−	2.12421i	−0.384567	−	0.124953i
$290$		0			0
$291$	−3.62957	−	2.63704i	−0.212769	−	0.154586i
$292$		0			0
$293$	−23.6770	+	12.0640i	−1.38323	+	0.704789i	−0.977839	−	0.209356i	$-0.932863\pi$
$293$	−23.6770	+	12.0640i	−1.38323	+	0.704789i	−0.405387	+	0.914145i	$0.632863\pi$
$294$		0			0
$295$	−27.4612	−	37.7971i	−1.59885	−	2.20063i
$296$		0			0
$297$	8.34623	−	6.06389i	0.484297	−	0.351862i
$298$		0			0
$299$	−34.2932	+	5.43151i	−1.98323	+	0.314113i
$300$		0			0
$301$	7.61039	+	7.61039i	0.438655	+	0.438655i
$302$		0			0
$303$	2.75760	+	8.48703i	0.158420	+	0.487567i
$304$		0			0
$305$	4.95261	−	15.2426i	0.283586	−	0.872787i
$306$		0			0
$307$	−6.65182	+	2.16131i	−0.379639	+	0.123352i	−0.492619	−	0.870245i	$-0.663960\pi$
$307$	−6.65182	+	2.16131i	−0.379639	+	0.123352i	0.112980	+	0.993597i	$0.463960\pi$
$308$		0			0
$309$	10.2236	−	20.0649i	0.581600	−	1.14145i
$310$		0			0
$311$	3.25192	+	0.515053i	0.184399	+	0.0292060i	0.247951	−	0.968773i	$-0.420243\pi$
$311$	3.25192	+	0.515053i	0.184399	+	0.0292060i	−0.0635517	+	0.997979i	$0.520243\pi$
$312$		0			0
$313$	−1.77802	−	11.2260i	−0.100499	−	0.634528i	−0.985595	−	0.169120i	$-0.945907\pi$
$313$	−1.77802	−	11.2260i	−0.100499	−	0.634528i	0.885096	−	0.465408i	$-0.154093\pi$
$314$		0			0
$315$	2.60760	+	5.11770i	0.146922	+	0.288350i
$316$		0			0
$317$	4.29092	−	27.0918i	0.241002	−	1.52163i	−0.509334	−	0.860569i	$-0.670108\pi$
$317$	4.29092	−	27.0918i	0.241002	−	1.52163i	0.750336	−	0.661057i	$-0.229892\pi$
$318$		0			0
$319$		−	0.619901i		−	0.0347078i
$320$		0			0
$321$	−8.38626	−	4.27301i	−0.468075	−	0.238496i
$322$		0			0
$323$	−6.25700	+	8.61202i	−0.348149	+	0.479185i
$324$		0			0
$325$	−31.7843	+	31.7843i	−1.76307	+	1.76307i
$326$		0			0
$327$	−1.75534			−0.0970705
$328$		0			0
$329$	−2.30182			−0.126903
$330$		0			0
$331$	10.6130	−	10.6130i	0.583344	−	0.583344i	−0.352477	−	0.935821i	$-0.614660\pi$
$331$	10.6130	−	10.6130i	0.583344	−	0.583344i	0.935821	+	0.352477i	$0.114660\pi$
$332$		0			0
$333$	−0.821104	+	1.13015i	−0.0449962	+	0.0619320i
$334$		0			0
$335$	20.6006	+	10.4965i	1.12553	+	0.573487i
$336$		0			0
$337$		−	11.4038i		−	0.621207i	−0.950540	−	0.310603i	$-0.899469\pi$
$337$		−	11.4038i		−	0.621207i	0.950540	−	0.310603i	$-0.100531\pi$
$338$		0			0
$339$	1.50997	−	9.53360i	0.0820105	−	0.517794i
$340$		0			0
$341$	3.11871	+	6.12082i	0.168888	+	0.331461i
$342$		0			0
$343$	2.70637	+	17.0873i	0.146130	+	0.922629i
$344$		0			0
$345$	−25.3033	−	4.00765i	−1.36228	−	0.215765i
$346$		0			0
$347$	15.1544	−	29.7422i	0.813531	−	1.59665i	0.0110717	−	0.999939i	$-0.496476\pi$
$347$	15.1544	−	29.7422i	0.813531	−	1.59665i	0.802460	−	0.596706i	$-0.203524\pi$
$348$		0			0
$349$	−4.88104	+	1.58595i	−0.261276	+	0.0848938i	−0.436726	−	0.899595i	$-0.643862\pi$
$349$	−4.88104	+	1.58595i	−0.261276	+	0.0848938i	0.175450	+	0.984488i	$0.443862\pi$
$350$		0			0
$351$	−11.1845	+	34.4223i	−0.596983	+	1.83732i
$352$		0			0
$353$	7.91928	+	24.3730i	0.421501	+	1.29725i	0.906305	+	0.422624i	$0.138891\pi$
$353$	7.91928	+	24.3730i	0.421501	+	1.29725i	−0.484804	+	0.874623i	$0.661109\pi$
$354$		0			0
$355$	20.2564	+	20.2564i	1.07510	+	1.07510i
$356$		0			0
$357$	6.24620	−	0.989301i	0.330584	−	0.0523594i
$358$		0			0
$359$	1.10482	−	0.802698i	0.0583101	−	0.0423648i	−0.558248	−	0.829674i	$-0.688526\pi$
$359$	1.10482	−	0.802698i	0.0583101	−	0.0423648i	0.616559	+	0.787309i	$0.288526\pi$
$360$		0			0
$361$	4.59015	+	6.31780i	0.241587	+	0.332516i
$362$		0			0
$363$	−9.31577	+	4.74662i	−0.488951	+	0.249133i
$364$		0			0
$365$	−25.2208	−	18.3240i	−1.32012	−	0.959123i
$366$		0			0
$367$	−8.38455	−	2.72431i	−0.437670	−	0.142208i	0.0818904	−	0.996641i	$-0.473904\pi$
$367$	−8.38455	−	2.72431i	−0.437670	−	0.142208i	−0.519560	+	0.854434i	$0.673904\pi$
$368$		0			0
$369$	1.72079	−	7.07993i	0.0895808	−	0.368567i
$370$		0			0
$371$	−1.58320	−	0.514413i	−0.0821956	−	0.0267070i
$372$		0			0
$373$	−13.1261	−	9.53664i	−0.679641	−	0.493788i	0.193597	−	0.981081i	$-0.437984\pi$
$373$	−13.1261	−	9.53664i	−0.679641	−	0.493788i	−0.873239	+	0.487293i	$0.837984\pi$
$374$		0			0
$375$	−8.48098	+	4.32128i	−0.437956	+	0.223150i
$376$		0			0
$377$	1.27833	+	1.75946i	0.0658371	+	0.0906170i
$378$		0			0
$379$	9.20110	−	6.68499i	0.472629	−	0.343385i	−0.325836	−	0.945426i	$-0.605646\pi$
$379$	9.20110	−	6.68499i	0.472629	−	0.343385i	0.798465	+	0.602041i	$0.205646\pi$
$380$		0			0
$381$	7.41643	−	1.17465i	0.379955	−	0.0601790i
$382$		0			0
$383$	−3.21049	−	3.21049i	−0.164048	−	0.164048i	0.620309	−	0.784357i	$-0.287007\pi$
$383$	−3.21049	−	3.21049i	−0.164048	−	0.164048i	−0.784357	+	0.620309i	$0.787007\pi$
$384$		0			0
$385$	2.84988	+	8.77104i	0.145243	+	0.447014i
$386$		0			0
$387$	2.59853	−	7.99746i	0.132091	−	0.406534i
$388$		0			0
$389$	−24.2065	+	7.86516i	−1.22732	+	0.398780i	−0.849742	−	0.527199i	$-0.823242\pi$
$389$	−24.2065	+	7.86516i	−1.22732	+	0.398780i	−0.377576	+	0.925979i	$0.623242\pi$
$390$		0			0
$391$	7.82530	−	15.3580i	0.395742	−	0.776688i
$392$		0			0
$393$	−10.9705	−	1.73755i	−0.553386	−	0.0876478i
$394$		0			0
$395$	−5.52473	−	34.8818i	−0.277980	−	1.75509i
$396$		0			0
$397$	10.4510	+	20.5112i	0.524519	+	1.02943i	0.989558	+	0.144136i	$0.0460402\pi$
$397$	10.4510	+	20.5112i	0.524519	+	1.02943i	−0.465039	+	0.885290i	$0.653960\pi$
$398$		0			0
$399$	−1.04002	+	6.56642i	−0.0520661	+	0.328732i
$400$		0			0
$401$		−	21.8245i		−	1.08986i	−0.838481	−	0.544931i	$-0.816556\pi$
$401$		−	21.8245i		−	1.08986i	0.838481	−	0.544931i	$-0.183444\pi$
$402$		0			0
$403$	−21.4739	−	10.9415i	−1.06969	−	0.545034i
$404$		0			0
$405$	−8.74277	+	12.0334i	−0.434432	+	0.597944i
$406$		0			0
$407$	−1.58604	+	1.58604i	−0.0786173	+	0.0786173i
$408$		0			0
$409$	−3.45570			−0.170874			−0.0854368	−	0.996344i	$-0.527229\pi$
$409$	−3.45570			−0.170874			−0.0854368	+	0.996344i	$0.527229\pi$
$410$		0			0
$411$	−0.146258			−0.00721436
$412$		0			0
$413$	13.8818	−	13.8818i	0.683077	−	0.683077i
$414$		0			0
$415$	−14.4937	+	19.9489i	−0.711468	+	0.979252i
$416$		0			0
$417$	15.7884	+	8.04462i	0.773164	+	0.393947i
$418$		0			0
$419$			18.7536i			0.916172i	0.888908	+	0.458086i	$0.151465\pi$
$419$			18.7536i			0.916172i	−0.888908	+	0.458086i	$0.848535\pi$
$420$		0			0
$421$	−0.976054	+	6.16256i	−0.0475699	+	0.300345i	−0.999990	−	0.00444331i	$-0.998586\pi$
$421$	−0.976054	+	6.16256i	−0.0475699	+	0.300345i	0.952420	+	0.304788i	$0.0985856\pi$
$422$		0			0
$423$	0.816474	+	1.60242i	0.0396983	+	0.0779123i
$424$		0			0
$425$	−3.49080	−	22.0401i	−0.169329	−	1.06910i
$426$		0			0
$427$	6.65167	+	1.05352i	0.321897	+	0.0509834i
$428$		0			0
$429$	−7.25524	+	14.2392i	−0.350286	+	0.687476i
$430$		0			0
$431$	−6.05658	+	1.96790i	−0.291735	+	0.0947906i	−0.451228	−	0.892408i	$-0.649014\pi$
$431$	−6.05658	+	1.96790i	−0.291735	+	0.0947906i	0.159493	+	0.987199i	$0.449014\pi$
$432$		0			0
$433$	−0.625179	+	1.92410i	−0.0300442	+	0.0924664i	−0.964954	−	0.262418i	$-0.915480\pi$
$433$	−0.625179	+	1.92410i	−0.0300442	+	0.0924664i	0.934910	+	0.354885i	$0.115480\pi$
$434$		0			0
$435$	0.495877	+	1.52615i	0.0237755	+	0.0731734i
$436$		0			0
$437$	12.8130	+	12.8130i	0.612931	+	0.612931i
$438$		0			0
$439$	−21.7512	+	3.44505i	−1.03813	+	0.164423i	−0.652154	−	0.758086i	$-0.726135\pi$
$439$	−21.7512	+	3.44505i	−1.03813	+	0.164423i	−0.385974	+	0.922510i	$0.626135\pi$
$440$		0			0
$441$	4.49142	−	3.26321i	0.213877	−	0.155391i
$442$		0			0
$443$	9.35155	+	12.8713i	0.444305	+	0.611534i	0.971162	−	0.238420i	$-0.0766296\pi$
$443$	9.35155	+	12.8713i	0.444305	+	0.611534i	−0.526857	+	0.849954i	$0.676630\pi$
$444$		0			0
$445$	44.8004	−	22.8269i	2.12374	−	1.08210i
$446$		0			0
$447$	−0.194791	−	0.141524i	−0.00921330	−	0.00669385i
$448$		0			0
$449$	21.4180	+	6.95914i	1.01078	+	0.328422i	0.767165	−	0.641450i	$-0.221667\pi$
$449$	21.4180	+	6.95914i	1.01078	+	0.328422i	0.243615	+	0.969872i	$0.421667\pi$
$450$		0			0
$451$	4.50730	−	10.7957i	0.212240	−	0.508350i
$452$		0			0
$453$	−25.6246	−	8.32592i	−1.20395	−	0.391186i
$454$		0			0
$455$	−26.1760	−	19.0180i	−1.22715	−	0.891576i
$456$		0			0
$457$	3.27733	−	1.66988i	0.153307	−	0.0781138i	−0.375654	−	0.926760i	$-0.622582\pi$
$457$	3.27733	−	1.66988i	0.153307	−	0.0781138i	0.528961	+	0.848646i	$0.322582\pi$
$458$		0			0
$459$	−10.5613	−	14.5364i	−0.492959	−	0.678500i
$460$		0			0
$461$	−3.11530	+	2.26340i	−0.145094	+	0.105417i	−0.657964	−	0.753049i	$-0.728582\pi$
$461$	−3.11530	+	2.26340i	−0.145094	+	0.105417i	0.512870	+	0.858466i	$0.328582\pi$
$462$		0			0
$463$	31.3684	−	4.96826i	1.45781	−	0.230895i	0.623342	−	0.781949i	$-0.285774\pi$
$463$	31.3684	−	4.96826i	1.45781	−	0.230895i	0.834469	+	0.551054i	$0.185774\pi$
$464$		0			0
$465$	−12.5743	−	12.5743i	−0.583118	−	0.583118i
$466$		0			0
$467$	−9.68505	−	29.8075i	−0.448171	−	1.37933i	−0.878969	−	0.476879i	$-0.841768\pi$
$467$	−9.68505	−	29.8075i	−0.448171	−	1.37933i	0.430798	−	0.902448i	$-0.358232\pi$
$468$		0			0
$469$	−3.00221	+	9.23984i	−0.138629	+	0.426656i
$470$		0			0
$471$	4.61539	−	1.49963i	0.212666	−	0.0690993i
$472$		0			0
$473$	6.12975	−	12.0303i	0.281846	−	0.553155i
$474$		0			0
$475$	23.1700	+	3.66976i	1.06311	+	0.168380i
$476$		0			0
$477$	0.203463	+	1.28462i	0.00931594	+	0.0588185i
$478$		0			0
$479$	18.7953	+	36.8879i	0.858780	+	1.68545i	0.718711	+	0.695309i	$0.244732\pi$
$479$	18.7953	+	36.8879i	0.858780	+	1.68545i	0.140069	+	0.990142i	$0.455268\pi$
$480$		0			0
$481$	1.23101	−	7.77232i	0.0561294	−	0.354387i
$482$		0			0
$483$		−	10.7650i		−	0.489827i
$484$		0			0
$485$	−10.1530	−	5.17320i	−0.461023	−	0.234903i
$486$		0			0
$487$	−19.1905	+	26.4134i	−0.869602	+	1.19691i	0.109591	+	0.993977i	$0.465046\pi$
$487$	−19.1905	+	26.4134i	−0.869602	+	1.19691i	−0.979194	+	0.202928i	$0.934954\pi$
$488$		0			0
$489$	−3.92008	+	3.92008i	−0.177272	+	0.177272i
$490$		0			0
$491$	40.3633			1.82157			0.910786	−	0.412880i	$-0.135477\pi$
$491$	40.3633			1.82157			0.910786	+	0.412880i	$0.135477\pi$
$492$		0			0
$493$	−1.07966			−0.0486256
$494$		0			0
$495$	5.09511	−	5.09511i	0.229008	−	0.229008i
$496$		0			0
$497$	−7.07548	+	9.73856i	−0.317379	+	0.436834i
$498$		0			0
$499$	9.86612	+	5.02704i	0.441668	+	0.225041i	0.660660	−	0.750686i	$-0.270277\pi$
$499$	9.86612	+	5.02704i	0.441668	+	0.225041i	−0.218992	+	0.975727i	$0.570277\pi$
$500$		0			0
$501$		−	8.54167i		−	0.381613i
$502$		0			0
$503$	−5.39469	+	34.0608i	−0.240538	+	1.51869i	0.511333	+	0.859383i	$0.329152\pi$
$503$	−5.39469	+	34.0608i	−0.240538	+	1.51869i	−0.751870	+	0.659311i	$0.770848\pi$
$504$		0			0
$505$	10.2899	+	20.1951i	0.457895	+	0.898669i
$506$		0			0
$507$	−5.99568	−	37.8552i	−0.266277	−	1.68121i
$508$		0			0
$509$	20.1967	+	3.19884i	0.895202	+	0.141786i	0.587050	−	0.809551i	$-0.300289\pi$
$509$	20.1967	+	3.19884i	0.895202	+	0.141786i	0.308152	+	0.951337i	$0.400289\pi$
$510$		0			0
$511$	5.94713	−	11.6719i	0.263086	−	0.516335i
$512$		0			0
$513$	17.9646	−	5.83706i	0.793157	−	0.257712i
$514$		0			0
$515$	17.6748	−	54.3974i	0.778844	−	2.39704i
$516$		0			0
$517$	0.892336	+	2.74633i	0.0392449	+	0.120783i
$518$		0			0
$519$	−4.91757	−	4.91757i	−0.215857	−	0.215857i
$520$		0			0
$521$	27.5874	−	4.36942i	1.20863	−	0.191428i	0.480577	−	0.876952i	$-0.340427\pi$
$521$	27.5874	−	4.36942i	1.20863	−	0.191428i	0.728050	+	0.685525i	$0.240427\pi$
$522$		0			0
$523$	−29.2671	+	21.2638i	−1.27976	+	0.929800i	−0.999546	−	0.0301373i	$-0.990406\pi$
$523$	−29.2671	+	21.2638i	−1.27976	+	0.929800i	−0.280214	+	0.959937i	$0.590406\pi$
$524$		0			0
$525$	−8.19168	−	11.2749i	−0.357514	−	0.492076i
$526$		0			0
$527$	10.6605	−	5.43177i	0.464377	−	0.236612i
$528$		0			0
$529$	−5.12993	−	3.72711i	−0.223040	−	0.162048i
$530$		0			0
$531$	−14.5878	−	4.73987i	−0.633057	−	0.205693i
$532$		0			0
$533$	9.46924	+	39.9361i	0.410158	+	1.72983i
$534$		0			0
$535$	−22.7357	−	7.38728i	−0.982950	−	0.319380i
$536$		0			0
$537$	9.93746	+	7.21999i	0.428833	+	0.311565i
$538$		0			0
$539$	7.94250	−	4.04691i	0.342108	−	0.174313i
$540$		0			0
$541$	−20.5933	−	28.3442i	−0.885374	−	1.21861i	−0.974903	−	0.222628i	$-0.928536\pi$
$541$	−20.5933	−	28.3442i	−0.885374	−	1.21861i	0.0895294	−	0.995984i	$-0.471464\pi$
$542$		0			0
$543$	13.1234	−	9.53472i	0.563180	−	0.409174i
$544$		0			0
$545$	−4.40348	+	0.697442i	−0.188624	+	0.0298751i
$546$		0			0
$547$	9.29596	+	9.29596i	0.397467	+	0.397467i	0.877339	−	0.479872i	$-0.159317\pi$
$547$	9.29596	+	9.29596i	0.397467	+	0.397467i	−0.479872	+	0.877339i	$0.659317\pi$
$548$		0			0
$549$	−1.62599	−	5.00427i	−0.0693954	−	0.213577i
$550$		0			0
$551$	0.350739	−	1.07946i	0.0149420	−	0.0459866i
$552$		0			0
$553$	14.1138	−	4.58585i	0.600180	−	0.195010i
$554$		0			0
$555$	2.63600	−	5.17345i	0.111892	−	0.219601i
$556$		0			0
$557$	28.1382	+	4.45665i	1.19225	+	0.188834i	0.720855	−	0.693086i	$-0.243749\pi$
$557$	28.1382	+	4.45665i	1.19225	+	0.188834i	0.471399	+	0.881920i	$0.343749\pi$
$558$		0			0
$559$	7.41019	+	46.7861i	0.313418	+	1.97884i
$560$		0			0
$561$	−3.60178	−	7.06890i	−0.152067	−	0.298449i
$562$		0			0
$563$	−2.11661	+	13.3638i	−0.0892046	+	0.563216i	0.902089	+	0.431549i	$0.142033\pi$
$563$	−2.11661	+	13.3638i	−0.0892046	+	0.563216i	−0.991294	+	0.131667i	$0.957967\pi$
$564$		0			0
$565$		−	24.5161i		−	1.03140i
$566$		0			0
$567$	−5.56891	−	2.83750i	−0.233872	−	0.119164i
$568$		0			0
$569$	−26.6643	+	36.7002i	−1.11782	+	1.53855i	−0.308467	+	0.951235i	$0.599816\pi$
$569$	−26.6643	+	36.7002i	−1.11782	+	1.53855i	−0.809357	+	0.587317i	$0.800184\pi$
$570$		0			0
$571$	1.62367	−	1.62367i	0.0679486	−	0.0679486i	−0.672316	−	0.740264i	$-0.734700\pi$
$571$	1.62367	−	1.62367i	0.0679486	−	0.0679486i	0.740264	+	0.672316i	$0.234700\pi$
$572$		0			0
$573$	24.0554			1.00493
$574$		0			0
$575$	−37.9850			−1.58409
$576$		0			0
$577$	−4.24210	+	4.24210i	−0.176601	+	0.176601i	−0.789872	−	0.613271i	$-0.789853\pi$
$577$	−4.24210	+	4.24210i	−0.176601	+	0.176601i	0.613271	+	0.789872i	$0.289853\pi$
$578$		0			0
$579$	−10.9857	+	15.1205i	−0.456549	+	0.628386i
$580$		0			0
$581$	−9.23210	−	4.70399i	−0.383012	−	0.195154i
$582$		0			0
$583$			2.08835i			0.0864908i
$584$		0			0
$585$	−3.95459	+	24.9683i	−0.163502	+	1.03231i
$586$		0			0
$587$	16.5667	+	32.5140i	0.683780	+	1.34199i	0.928111	+	0.372303i	$0.121432\pi$
$587$	16.5667	+	32.5140i	0.683780	+	1.34199i	−0.244331	+	0.969692i	$0.578568\pi$
$588$		0			0
$589$	1.96761	+	12.4230i	0.0810741	+	0.511882i
$590$		0			0
$591$	−5.76550	−	0.913166i	−0.237161	−	0.0375626i
$592$		0			0
$593$	−0.226552	+	0.444634i	−0.00930339	+	0.0182589i	−0.895611	−	0.444837i	$-0.853262\pi$
$593$	−0.226552	+	0.444634i	−0.00930339	+	0.0182589i	0.886308	+	0.463096i	$0.153262\pi$
$594$		0			0
$595$	15.2763	−	4.96356i	0.626266	−	0.203486i
$596$		0			0
$597$	1.59897	−	4.92112i	0.0654414	−	0.201408i
$598$		0			0
$599$	7.58173	+	23.3342i	0.309781	+	0.953409i	0.977850	+	0.209309i	$0.0671214\pi$
$599$	7.58173	+	23.3342i	0.309781	+	0.953409i	−0.668068	+	0.744100i	$0.732879\pi$
$600$		0			0
$601$	5.35213	+	5.35213i	0.218318	+	0.218318i	0.807789	−	0.589471i	$-0.200664\pi$
$601$	5.35213	+	5.35213i	0.218318	+	0.218318i	−0.589471	+	0.807789i	$0.700664\pi$
$602$		0			0
$603$	7.49725	−	1.18745i	0.305312	−	0.0483566i
$604$		0			0
$605$	−21.4838	+	15.6089i	−0.873440	+	0.634591i
$606$		0			0
$607$	−21.2236	−	29.2118i	−0.861440	−	1.18567i	−0.981224	−	0.192870i	$-0.938220\pi$
$607$	−21.2236	−	29.2118i	−0.861440	−	1.18567i	0.119785	−	0.992800i	$-0.461780\pi$
$608$		0			0
$609$	−0.600802	+	0.306124i	−0.0243457	+	0.0124048i
$610$		0			0
$611$	−8.19604	−	5.95477i	−0.331576	−	0.240904i
$612$		0			0
$613$	−30.2951	−	9.84349i	−1.22361	−	0.397575i	−0.375214	−	0.926938i	$-0.622431\pi$
$613$	−30.2951	−	9.84349i	−1.22361	−	0.397575i	−0.848395	+	0.529364i	$0.822431\pi$
$614$		0			0
$615$	−2.46085	+	30.1838i	−0.0992312	+	1.21713i
$616$		0			0
$617$	18.2794	+	5.93935i	0.735903	+	0.239109i	0.652904	−	0.757440i	$-0.273550\pi$
$617$	18.2794	+	5.93935i	0.735903	+	0.239109i	0.0829983	+	0.996550i	$0.473550\pi$
$618$		0			0
$619$	31.0258	+	22.5415i	1.24703	+	0.906021i	0.998046	−	0.0624862i	$-0.0199029\pi$
$619$	31.0258	+	22.5415i	1.24703	+	0.906021i	0.248985	+	0.968507i	$0.419903\pi$
$620$		0			0
$621$	−27.2521	+	13.8856i	−1.09359	+	0.557211i
$622$		0			0
$623$	12.4188	+	17.0930i	0.497547	+	0.684815i
$624$		0			0
$625$	8.80773	−	6.39919i	0.352309	−	0.255968i
$626$		0			0
$627$	8.23765	−	1.30472i	0.328980	−	0.0521053i
$628$		0			0
$629$	2.76237	+	2.76237i	0.110143	+	0.110143i
$630$		0			0
$631$	11.7225	+	36.0782i	0.466666	+	1.43625i	0.856875	+	0.515525i	$0.172403\pi$
$631$	11.7225	+	36.0782i	0.466666	+	1.43625i	−0.390208	+	0.920727i	$0.627597\pi$
$632$		0			0
$633$	0.581383	−	1.78931i	0.0231079	−	0.0711188i
$634$		0			0
$635$	18.1383	−	5.89349i	0.719796	−	0.233876i
$636$		0			0
$637$	−14.1979	+	27.8649i	−0.562541	+	1.10405i
$638$		0			0
$639$	9.28926	+	1.47127i	0.367477	+	0.0582027i
$640$		0			0
$641$	4.45397	+	28.1213i	0.175921	+	1.11072i	0.904723	+	0.426000i	$0.140077\pi$
$641$	4.45397	+	28.1213i	0.175921	+	1.11072i	−0.728802	+	0.684725i	$0.759923\pi$
$642$		0			0
$643$	−14.8198	−	29.0856i	−0.584437	−	1.14702i	−0.974111	−	0.226070i	$-0.927412\pi$
$643$	−14.8198	−	29.0856i	−0.584437	−	1.14702i	0.389674	−	0.920953i	$-0.372588\pi$
$644$		0			0
$645$	−5.46762	+	34.5212i	−0.215287	+	1.35927i
$646$		0			0
$647$			35.7053i			1.40372i	0.712315	+	0.701860i	$0.247647\pi$
$647$			35.7053i			1.40372i	−0.712315	+	0.701860i	$0.752353\pi$
$648$		0			0
$649$	−21.9440	−	11.1810i	−0.861376	−	0.438893i
$650$		0			0
$651$	4.39213	−	6.04525i	0.172141	−	0.236932i
$652$		0			0
$653$	13.7761	−	13.7761i	0.539102	−	0.539102i	−0.384163	−	0.923265i	$-0.625510\pi$
$653$	13.7761	−	13.7761i	0.539102	−	0.539102i	0.923265	+	0.384163i	$0.125510\pi$
$654$		0			0
$655$	−28.2111			−1.10230
$656$		0			0
$657$	−10.2349			−0.399303
$658$		0			0
$659$	−10.7415	+	10.7415i	−0.418431	+	0.418431i	−0.884663	−	0.466231i	$-0.845611\pi$
$659$	−10.7415	+	10.7415i	−0.418431	+	0.418431i	0.466231	+	0.884663i	$0.345611\pi$
$660$		0			0
$661$	−6.05918	+	8.33975i	−0.235675	+	0.324379i	−0.910430	−	0.413663i	$-0.864249\pi$
$661$	−6.05918	+	8.33975i	−0.235675	+	0.324379i	0.674755	+	0.738042i	$0.264249\pi$
$662$		0			0
$663$	24.8000	+	12.6362i	0.963153	+	0.490751i
$664$		0			0
$665$			16.8859i			0.654806i
$666$		0			0
$667$	−0.287502	+	1.81522i	−0.0111321	+	0.0702854i
$668$		0			0
$669$	1.09068	+	2.14057i	0.0421680	+	0.0827593i
$670$		0			0
$671$	−1.32165	−	8.34459i	−0.0510219	−	0.322139i
$672$		0			0
$673$	−22.8825	−	3.62423i	−0.882055	−	0.139704i	−0.301054	−	0.953607i	$-0.597339\pi$
$673$	−22.8825	−	3.62423i	−0.882055	−	0.139704i	−0.581001	+	0.813903i	$0.697339\pi$
$674$		0			0
$675$	−17.9764	+	35.2808i	−0.691914	+	1.35796i
$676$		0			0
$677$	10.7253	−	3.48486i	0.412206	−	0.133934i	−0.0955705	−	0.995423i	$-0.530468\pi$
$677$	10.7253	−	3.48486i	0.412206	−	0.133934i	0.507777	+	0.861489i	$0.330468\pi$
$678$		0			0
$679$	1.47963	−	4.55384i	0.0567830	−	0.174760i
$680$		0			0
$681$	−0.00973365	−	0.0299571i	−0.000372994	−	0.00114796i
$682$		0			0
$683$	6.92268	+	6.92268i	0.264889	+	0.264889i	0.827037	−	0.562148i	$-0.190025\pi$
$683$	6.92268	+	6.92268i	0.264889	+	0.264889i	−0.562148	+	0.827037i	$0.690025\pi$
$684$		0			0
$685$	−0.366905	+	0.0581120i	−0.0140187	+	0.00222035i
$686$		0			0
$687$	26.6745	−	19.3802i	1.01770	−	0.739401i
$688$		0			0
$689$	−4.30649	−	5.92737i	−0.164064	−	0.225815i
$690$		0			0
$691$	32.0987	−	16.3551i	1.22109	−	0.622178i	0.279895	−	0.960031i	$-0.409700\pi$
$691$	32.0987	−	16.3551i	1.22109	−	0.622178i	0.941199	+	0.337852i	$0.109700\pi$
$692$		0			0
$693$	2.44954	+	1.77970i	0.0930505	+	0.0676051i
$694$		0			0
$695$	42.8035	+	13.9077i	1.62363	+	0.527550i
$696$		0			0
$697$	−18.8026	−	7.85023i	−0.712198	−	0.297349i
$698$		0			0
$699$	−24.6750	−	8.01739i	−0.933294	−	0.303246i
$700$		0			0
$701$	41.7632	+	30.3427i	1.57737	+	1.14603i	0.919630	+	0.392787i	$0.128489\pi$
$701$	41.7632	+	30.3427i	1.57737	+	1.14603i	0.657744	+	0.753242i	$0.271511\pi$
$702$		0			0
$703$	−3.65923	+	1.86447i	−0.138011	+	0.0703199i
$704$		0			0
$705$	−4.39374	−	6.04746i	−0.165478	−	0.227760i
$706$		0			0
$707$	−7.70515	+	5.59812i	−0.289782	+	0.210539i
$708$		0			0
$709$	48.3157	−	7.65246i	1.81453	−	0.287394i	0.845438	−	0.534074i	$-0.179340\pi$
$709$	48.3157	−	7.65246i	1.81453	−	0.287394i	0.969097	+	0.246680i	$0.0793395\pi$
$710$		0			0
$711$	−8.19874	−	8.19874i	−0.307477	−	0.307477i
$712$		0			0
$713$	−6.29357	−	19.3696i	−0.235696	−	0.725398i
$714$		0			0
$715$	−12.5430	+	38.6035i	−0.469082	+	1.44369i
$716$		0			0
$717$	23.2234	−	7.54573i	0.867293	−	0.281801i
$718$		0			0
$719$	−9.42790	+	18.5033i	−0.351601	+	0.690056i	−0.997292	−	0.0735426i	$-0.976570\pi$
$719$	−9.42790	+	18.5033i	−0.351601	+	0.690056i	0.645691	+	0.763599i	$0.276570\pi$
$720$		0			0
$721$	23.7384	+	3.75979i	0.884063	+	0.140022i
$722$		0			0
$723$	−1.22975	−	7.76435i	−0.0457350	−	0.288759i
$724$		0			0
$725$	1.08017	+	2.11996i	0.0401166	+	0.0787333i
$726$		0			0
$727$	2.24680	−	14.1858i	0.0833293	−	0.526121i	−0.910348	−	0.413844i	$-0.864186\pi$
$727$	2.24680	−	14.1858i	0.0833293	−	0.526121i	0.993677	−	0.112276i	$-0.0358142\pi$
$728$		0			0
$729$			27.9989i			1.03700i
$730$		0			0
$731$	−20.9529	−	10.6760i	−0.774970	−	0.394867i
$732$		0			0
$733$	14.2196	−	19.5717i	0.525214	−	0.722895i	−0.461177	−	0.887308i	$-0.652573\pi$
$733$	14.2196	−	19.5717i	0.525214	−	0.722895i	0.986392	+	0.164413i	$0.0525728\pi$
$734$		0			0
$735$	−16.3166	+	16.3166i	−0.601848	+	0.601848i
$736$		0			0
$737$	12.1880			0.448951
$738$		0			0
$739$	−0.683852			−0.0251559			−0.0125780	−	0.999921i	$-0.504004\pi$
$739$	−0.683852			−0.0251559			−0.0125780	+	0.999921i	$0.504004\pi$
$740$		0			0
$741$	−20.6904	+	20.6904i	−0.760081	+	0.760081i
$742$		0			0
$743$	17.7873	−	24.4821i	0.652553	−	0.898162i	−0.346654	−	0.937993i	$-0.612682\pi$
$743$	17.7873	−	24.4821i	0.652553	−	0.898162i	0.999206	+	0.0398315i	$0.0126821\pi$
$744$		0			0
$745$	−0.544888	−	0.277634i	−0.0199631	−	0.0101717i
$746$		0			0
$747$			8.09550i			0.296199i
$748$		0			0
$749$	1.57142	−	9.92158i	0.0574186	−	0.362527i
$750$		0			0
$751$	−8.69372	−	17.0624i	−0.317238	−	0.622615i	0.676234	−	0.736687i	$-0.263611\pi$
$751$	−8.69372	−	17.0624i	−0.317238	−	0.622615i	−0.993473	+	0.114072i	$0.963611\pi$
$752$		0			0
$753$	−5.29938	−	33.4590i	−0.193120	−	1.21931i
$754$		0			0
$755$	−67.5904	−	10.7053i	−2.45986	−	0.389604i
$756$		0			0
$757$	16.5655	−	32.5117i	0.602085	−	1.18166i	−0.365901	−	0.930654i	$-0.619239\pi$
$757$	16.5655	−	32.5117i	0.602085	−	1.18166i	0.967986	−	0.251005i	$-0.0807609\pi$
$758$		0			0
$759$	−12.8439	+	4.17324i	−0.466204	+	0.151479i
$760$		0			0
$761$	−5.94946	+	18.3106i	−0.215668	+	0.663758i	0.783438	+	0.621470i	$0.213464\pi$
$761$	−5.94946	+	18.3106i	−0.215668	+	0.663758i	−0.999106	+	0.0422871i	$0.986536\pi$
$762$		0			0
$763$	−0.578918	−	1.78173i	−0.0209582	−	0.0645028i
$764$		0			0
$765$	−8.87401	−	8.87401i	−0.320841	−	0.320841i
$766$		0			0
$767$	85.3404	−	13.5166i	3.08146	−	0.488056i
$768$		0			0
$769$	−14.1385	+	10.2722i	−0.509848	+	0.370427i	−0.812766	−	0.582590i	$-0.802039\pi$
$769$	−14.1385	+	10.2722i	−0.509848	+	0.370427i	0.302918	+	0.953017i	$0.402039\pi$
$770$		0			0
$771$	9.08616	+	12.5060i	0.327230	+	0.450394i
$772$		0			0
$773$	−37.4355	+	19.0743i	−1.34646	+	0.686056i	−0.970618	−	0.240627i	$-0.922647\pi$
$773$	−37.4355	+	19.0743i	−1.34646	+	0.686056i	−0.375843	+	0.926683i	$0.622647\pi$
$774$		0			0
$775$	−21.3310	−	15.4979i	−0.766231	−	0.556700i
$776$		0			0
$777$	2.32041	+	0.753947i	0.0832442	+	0.0270477i
$778$		0			0
$779$	13.9570	−	16.2488i	0.500060	−	0.582175i
$780$		0			0
$781$	14.3621	+	4.66653i	0.513916	+	0.166982i
$782$		0			0
$783$	1.54992	+	1.12609i	0.0553898	+	0.0402430i
$784$		0			0
$785$	10.9824	−	5.59582i	0.391979	−	0.199723i
$786$		0			0
$787$	−12.6296	−	17.3831i	−0.450195	−	0.619640i	0.522244	−	0.852796i	$-0.325095\pi$
$787$	−12.6296	−	17.3831i	−0.450195	−	0.619640i	−0.972439	+	0.233156i	$0.925095\pi$
$788$		0			0
$789$	−6.14837	+	4.46705i	−0.218888	+	0.159031i
$790$		0			0
$791$	10.1749	−	1.61155i	0.361778	−	0.0573000i
$792$		0			0
$793$	20.9590	+	20.9590i	0.744276	+	0.744276i
$794$		0			0
$795$	−1.67054	−	5.14138i	−0.0592478	−	0.182346i
$796$		0			0
$797$	7.95385	−	24.4794i	0.281740	−	0.867106i	−0.705617	−	0.708593i	$-0.749330\pi$
$797$	7.95385	−	24.4794i	0.281740	−	0.867106i	0.987357	−	0.158513i	$-0.0506699\pi$
$798$		0			0
$799$	4.78320	−	1.55416i	0.169217	−	0.0549821i
$800$		0			0
$801$	7.49429	−	14.7084i	0.264798	−	0.519695i
$802$		0			0
$803$	−16.2314	−	2.57080i	−0.572793	−	0.0907215i
$804$		0			0
$805$	−4.27724	−	27.0054i	−0.150753	−	0.951816i
$806$		0			0
$807$	4.41059	+	8.65628i	0.155260	+	0.304715i
$808$		0			0
$809$	−2.48312	+	15.6778i	−0.0873018	+	0.551202i	0.904807	+	0.425822i	$0.140015\pi$
$809$	−2.48312	+	15.6778i	−0.0873018	+	0.551202i	−0.992109	+	0.125380i	$0.959985\pi$
$810$		0			0
$811$		−	46.8407i		−	1.64480i	−0.568910	−	0.822400i	$-0.692635\pi$
$811$		−	46.8407i		−	1.64480i	0.568910	−	0.822400i	$-0.307365\pi$
$812$		0			0
$813$	18.0819	+	9.21320i	0.634161	+	0.323121i
$814$		0			0
$815$	−8.27644	+	11.3915i	−0.289911	+	0.399028i
$816$		0			0
$817$	17.4808	−	17.4808i	0.611574	−	0.611574i
$818$		0			0
$819$	−10.6225			−0.371181
$820$		0			0
$821$	−4.49527			−0.156886			−0.0784431	−	0.996919i	$-0.524995\pi$
$821$	−4.49527			−0.156886			−0.0784431	+	0.996919i	$0.524995\pi$
$822$		0			0
$823$	10.4358	−	10.4358i	0.363769	−	0.363769i	−0.501429	−	0.865199i	$-0.667192\pi$
$823$	10.4358	−	10.4358i	0.363769	−	0.363769i	0.865199	+	0.501429i	$0.167192\pi$
$824$		0			0
$825$	−10.2766	+	14.1445i	−0.357784	+	0.492447i
$826$		0			0
$827$	−32.6277	−	16.6247i	−1.13458	−	0.578096i	−0.217205	−	0.976126i	$-0.569694\pi$
$827$	−32.6277	−	16.6247i	−1.13458	−	0.578096i	−0.917372	+	0.398030i	$0.869694\pi$
$828$		0			0
$829$			24.1722i			0.839534i	0.907632	+	0.419767i	$0.137888\pi$
$829$			24.1722i			0.839534i	−0.907632	+	0.419767i	$0.862112\pi$
$830$		0			0
$831$	1.82955	−	11.5513i	0.0634663	−	0.400711i
$832$		0			0
$833$	−7.04838	−	13.8332i	−0.244212	−	0.479293i
$834$		0			0
$835$	−3.39383	−	21.4278i	−0.117448	−	0.741539i
$836$		0			0
$837$	−20.9691	−	3.32117i	−0.724797	−	0.114797i
$838$		0			0
$839$	13.7897	−	27.0638i	0.476074	−	0.934347i	−0.520674	−	0.853756i	$-0.674319\pi$
$839$	13.7897	−	27.0638i	0.476074	−	0.934347i	0.996747	−	0.0805911i	$-0.0256808\pi$
$840$		0			0
$841$	−27.4712	+	8.92592i	−0.947281	+	0.307790i
$842$		0			0
$843$	−5.17610	+	15.9304i	−0.178274	+	0.548672i
$844$		0			0
$845$	−30.0817	−	92.5821i	−1.03484	−	3.18492i
$846$		0			0
$847$	−7.89036	−	7.89036i	−0.271116	−	0.271116i
$848$		0			0
$849$	28.4710	−	4.50936i	0.977121	−	0.154761i
$850$		0			0
$851$	5.37990	−	3.90872i	0.184420	−	0.133989i
$852$		0			0
$853$	−0.247241	−	0.340298i	−0.00846537	−	0.0116516i	0.804763	−	0.593596i	$-0.202292\pi$
$853$	−0.247241	−	0.340298i	−0.00846537	−	0.0116516i	−0.813229	+	0.581944i	$0.802292\pi$
$854$		0			0
$855$	11.7552	−	5.98955i	0.402018	−	0.204838i
$856$		0			0
$857$	−43.6766	−	31.7329i	−1.49196	−	1.08397i	−0.973449	−	0.228906i	$-0.926485\pi$
$857$	−43.6766	−	31.7329i	−1.49196	−	1.08397i	−0.518514	−	0.855069i	$-0.673515\pi$
$858$		0			0
$859$	39.5195	+	12.8407i	1.34839	+	0.438117i	0.892149	−	0.451741i	$-0.149197\pi$
$859$	39.5195	+	12.8407i	1.34839	+	0.438117i	0.456237	+	0.889858i	$0.349197\pi$
$860$		0			0
$861$	−12.6889	+	0.962779i	−0.432437	+	0.0328114i
$862$		0			0
$863$	−5.06646	−	1.64619i	−0.172464	−	0.0560371i	0.221512	−	0.975158i	$-0.428901\pi$
$863$	−5.06646	−	1.64619i	−0.172464	−	0.0560371i	−0.393976	+	0.919121i	$0.628901\pi$
$864$		0			0
$865$	−14.2902	−	10.3824i	−0.485881	−	0.353013i
$866$		0			0
$867$	8.35792	−	4.25857i	0.283850	−	0.144629i
$868$		0			0
$869$	−10.9429	−	15.0616i	−0.371211	−	0.510929i
$870$		0			0
$871$	−34.5932	+	25.1334i	−1.17215	+	0.851614i
$872$		0			0
$873$	−3.69501	+	0.585231i	−0.125057	+	0.0198071i
$874$		0			0
$875$	−7.18330	−	7.18330i	−0.242840	−	0.242840i
$876$		0			0
$877$	9.32212	+	28.6905i	0.314786	+	0.968811i	0.975843	+	0.218475i	$0.0701082\pi$
$877$	9.32212	+	28.6905i	0.314786	+	0.968811i	−0.661057	+	0.750336i	$0.729892\pi$
$878$		0			0
$879$	11.2055	−	34.4870i	0.377952	−	1.16322i
$880$		0			0
$881$	−11.5811	+	3.76294i	−0.390179	+	0.126777i	−0.497535	−	0.867444i	$-0.665761\pi$
$881$	−11.5811	+	3.76294i	−0.390179	+	0.126777i	0.107356	+	0.994221i	$0.465761\pi$
$882$		0			0
$883$	−5.32064	+	10.4423i	−0.179054	+	0.351413i	−0.963037	−	0.269369i	$-0.913185\pi$
$883$	−5.32064	+	10.4423i	−0.179054	+	0.351413i	0.783983	+	0.620782i	$0.213185\pi$
$884$		0			0
$885$	62.9685	+	9.97323i	2.11666	+	0.335246i
$886$		0			0
$887$	−5.47072	−	34.5408i	−0.183689	−	1.15976i	−0.891385	−	0.453248i	$-0.850265\pi$
$887$	−5.47072	−	34.5408i	−0.183689	−	1.15976i	0.707696	−	0.706517i	$-0.249735\pi$
$888$		0			0
$889$	3.63827	+	7.14052i	0.122024	+	0.239485i
$890$		0			0
$891$	−1.22658	+	7.74432i	−0.0410920	+	0.259445i
$892$		0			0
$893$			5.28719i			0.176929i
$894$		0			0
$895$	27.7980	+	14.1638i	0.929184	+	0.473443i
$896$		0			0
$897$	27.8490	−	38.3309i	0.929852	−	1.27983i
$898$		0			0
$899$	−0.902057	+	0.902057i	−0.0300853	+	0.0300853i
$900$		0			0
$901$	3.63723			0.121174
$902$		0			0
$903$	−14.6867			−0.488743
$904$		0			0
$905$	29.1333	−	29.1333i	0.968422	−	0.968422i
$906$		0			0
$907$	5.59498	−	7.70083i	0.185778	−	0.255702i	−0.705962	−	0.708250i	$-0.749485\pi$
$907$	5.59498	−	7.70083i	0.185778	−	0.255702i	0.891740	+	0.452548i	$0.149485\pi$
$908$		0			0
$909$	6.63022	+	3.37827i	0.219911	+	0.112050i
$910$		0			0
$911$			36.1439i			1.19750i	0.800936	+	0.598750i	$0.204336\pi$
$911$			36.1439i			1.19750i	−0.800936	+	0.598750i	$0.795664\pi$
$912$		0			0
$913$	−2.03342	+	12.8385i	−0.0672963	+	0.424892i
$914$		0			0
$915$	9.92890	+	19.4866i	0.328239	+	0.644206i
$916$		0			0
$917$	−1.85443	−	11.7084i	−0.0612387	−	0.386646i
$918$		0			0
$919$	−55.4813	−	8.78737i	−1.83016	−	0.289869i	−0.856208	−	0.516631i	$-0.827186\pi$
$919$	−55.4813	−	8.78737i	−1.83016	−	0.289869i	−0.973950	+	0.226763i	$0.927186\pi$
$920$		0			0
$921$	4.33295	−	8.50389i	0.142775	−	0.280213i
$922$		0			0
$923$	−50.3870	+	16.3717i	−1.65851	+	0.538882i
$924$		0			0
$925$	2.66034	−	8.18769i	0.0874714	−	0.269209i
$926$		0			0
$927$	−5.80279	−	17.8592i	−0.190589	−	0.586572i
$928$		0			0
$929$	37.3268	+	37.3268i	1.22465	+	1.22465i	0.965959	+	0.258694i	$0.0832921\pi$
$929$	37.3268	+	37.3268i	1.22465	+	1.22465i	0.258694	+	0.965959i	$0.416708\pi$
$930$		0			0
$931$	16.1204	−	2.55322i	0.528324	−	0.0836784i
$932$		0			0
$933$	−3.63480	+	2.64083i	−0.118998	+	0.0864570i
$934$		0			0
$935$	−11.8442	−	16.3021i	−0.387345	−	0.533135i
$936$		0			0
$937$	8.13713	−	4.14608i	0.265829	−	0.135446i	−0.315997	−	0.948760i	$-0.602339\pi$
$937$	8.13713	−	4.14608i	0.265829	−	0.135446i	0.581825	+	0.813314i	$0.302339\pi$
$938$		0			0
$939$	12.5477	+	9.11642i	0.409478	+	0.297503i
$940$		0			0
$941$	−33.6652	−	10.9385i	−1.09745	−	0.356584i	−0.296331	−	0.955085i	$-0.595763\pi$
$941$	−33.6652	−	10.9385i	−1.09745	−	0.356584i	−0.801122	+	0.598501i	$0.795763\pi$
$942$		0			0
$943$	−18.2053	+	29.5219i	−0.592847	+	0.961366i
$944$		0			0
$945$	−27.1070	−	8.80760i	−0.881791	−	0.286511i
$946$		0			0
$947$	21.7998	+	15.8385i	0.708399	+	0.514682i	0.882657	−	0.470018i	$-0.155753\pi$
$947$	21.7998	+	15.8385i	0.708399	+	0.514682i	−0.174258	+	0.984700i	$0.555753\pi$
$948$		0			0
$949$	51.3709	−	26.1748i	1.66757	−	0.849669i
$950$		0			0
$951$	22.0008	+	30.2815i	0.713425	+	0.981946i
$952$		0			0
$953$	−37.0784	+	26.9390i	−1.20109	+	0.872640i	−0.994391	−	0.105765i	$-0.966271\pi$
$953$	−37.0784	+	26.9390i	−1.20109	+	0.872640i	−0.206695	+	0.978405i	$0.566271\pi$
$954$		0			0
$955$	60.3459	−	9.55786i	1.95275	−	0.309285i
$956$		0			0
$957$	0.598150	+	0.598150i	0.0193354	+	0.0193354i
$958$		0			0
$959$	−0.0482364	−	0.148456i	−0.00155763	−	0.00479390i
$960$		0			0
$961$	−5.21097	+	16.0377i	−0.168096	+	0.517346i
$962$		0			0
$963$	−7.46434	+	2.42531i	−0.240535	+	0.0781545i
$964$		0			0
$965$	−21.5511	+	42.2965i	−0.693755	+	1.36157i
$966$		0			0
$967$	−12.8592	−	2.03670i	−0.413524	−	0.0654957i	−0.0537936	−	0.998552i	$-0.517131\pi$
$967$	−12.8592	−	2.03670i	−0.413524	−	0.0654957i	−0.359730	+	0.933056i	$0.617131\pi$
$968$		0			0
$969$	−2.27239	−	14.3473i	−0.0729996	−	0.460901i
$970$		0			0
$971$	−14.6907	−	28.8321i	−0.471447	−	0.925268i	−0.997211	−	0.0746367i	$-0.976220\pi$
$971$	−14.6907	−	28.8321i	−0.471447	−	0.925268i	0.525763	−	0.850631i	$-0.323780\pi$
$972$		0			0
$973$	−2.95845	+	18.6789i	−0.0948437	+	0.598819i
$974$		0			0
$975$		−	61.3380i		−	1.96439i
$976$		0			0
$977$	−33.8782	−	17.2618i	−1.08386	−	0.552254i	−0.181567	−	0.983379i	$-0.558117\pi$
$977$	−33.8782	−	17.2618i	−1.08386	−	0.552254i	−0.902292	+	0.431125i	$0.858117\pi$
$978$		0			0
$979$	15.5795	−	21.4433i	0.497922	−	0.685331i
$980$		0			0
$981$	−1.03501	+	1.03501i	−0.0330453	+	0.0330453i
$982$		0			0
$983$	2.64592			0.0843918			0.0421959	−	0.999109i	$-0.486565\pi$
$983$	2.64592			0.0843918			0.0421959	+	0.999109i	$0.486565\pi$
$984$		0			0
$985$	−14.8263			−0.472404
$986$		0			0
$987$	2.22105	−	2.22105i	0.0706969	−	0.0706969i
$988$		0			0
$989$	−23.5289	+	32.3847i	−0.748175	+	1.02977i
$990$		0			0
$991$	−8.06220	−	4.10790i	−0.256104	−	0.130492i	0.321225	−	0.947003i	$-0.395905\pi$
$991$	−8.06220	−	4.10790i	−0.256104	−	0.130492i	−0.577330	+	0.816511i	$0.695905\pi$
$992$		0			0
$993$			20.4812i			0.649952i
$994$		0			0
$995$	2.05591	−	12.9805i	0.0651768	−	0.411510i
$996$		0			0
$997$	−17.3045	−	33.9621i	−0.548040	−	1.07559i	−0.984421	−	0.175828i	$-0.943740\pi$
$997$	−17.3045	−	33.9621i	−0.548040	−	1.07559i	0.436381	−	0.899762i	$-0.356260\pi$
$998$		0			0
$999$	−1.08441	−	6.84669i	−0.0343092	−	0.216620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.bs.d.225.1		24
4.3	odd	2		41.2.g.a.20.2	✓	24
12.11	even	2		369.2.u.a.307.2		24
41.39	even	20	inner	656.2.bs.d.449.1		24
164.11	even	40		1681.2.a.m.1.12		24
164.39	odd	20		41.2.g.a.39.2	yes	24
164.71	even	40		1681.2.a.m.1.11		24
492.203	even	20		369.2.u.a.244.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.2	✓	24	4.3	odd	2
41.2.g.a.39.2	yes	24	164.39	odd	20
369.2.u.a.244.2		24	492.203	even	20
369.2.u.a.307.2		24	12.11	even	2
656.2.bs.d.225.1		24	1.1	even	1	trivial
656.2.bs.d.449.1		24	41.39	even	20	inner
1681.2.a.m.1.11		24	164.71	even	40
1681.2.a.m.1.12		24	164.11	even	40

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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.bs (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.964912 + 0.964912i) q^{3} +(-2.03721 + 2.80398i) q^{5} +(-1.29765 - 0.661185i) q^{7} +1.13789i q^{9} +O(q^{10})\)	\(q+(-0.964912 + 0.964912i) q^{3} +(-2.03721 + 2.80398i) q^{5} +(-1.29765 - 0.661185i) q^{7} +1.13789i q^{9} +(-0.285814 + 1.80456i) q^{11} +(-2.91004 - 5.71127i) q^{13} +(-0.739865 - 4.67132i) q^{15} +(3.14295 + 0.497794i) q^{17} +(-1.51872 + 2.98065i) q^{19} +(1.89010 - 0.614131i) q^{21} +(1.67386 - 5.15161i) q^{23} +(-2.16699 - 6.66932i) q^{25} +(-3.99270 - 3.99270i) q^{27} +(-0.335113 + 0.0530767i) q^{29} +(3.04183 - 2.21002i) q^{31} +(-1.46545 - 2.01702i) q^{33} +(4.49754 - 2.29161i) q^{35} +(0.993200 + 0.721602i) q^{37} +(8.31880 + 2.70294i) q^{39} +(-6.22198 - 1.51227i) q^{41} +(-7.02832 - 2.28364i) q^{43} +(-3.19062 - 2.31812i) q^{45} +(1.40824 - 0.717533i) q^{47} +(-2.86777 - 3.94715i) q^{49} +(-3.51299 + 2.55234i) q^{51} +(1.12895 - 0.178807i) q^{53} +(-4.47768 - 4.47768i) q^{55} +(-1.41064 - 4.34149i) q^{57} +(-4.16549 + 12.8200i) q^{59} +(-4.39785 + 1.42895i) q^{61} +(0.752356 - 1.47658i) q^{63} +(21.9426 + 3.47537i) q^{65} +(-1.04355 - 6.58873i) q^{67} +(3.35573 + 6.58598i) q^{69} +(1.29298 - 8.16358i) q^{71} +8.99466i q^{73} +(8.52627 + 4.34435i) q^{75} +(1.56403 - 2.15271i) q^{77} +(-7.20521 + 7.20521i) q^{79} +4.29154 q^{81} +7.11449 q^{83} +(-7.79865 + 7.79865i) q^{85} +(0.272140 - 0.374569i) q^{87} +(-12.9260 - 6.58613i) q^{89} +9.33529i q^{91} +(-0.802625 + 5.06757i) q^{93} +(-5.26374 - 10.3307i) q^{95} +(0.514313 + 3.24724i) q^{97} +(-2.05339 - 0.325225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

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Representations

Groups

Database

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