LMFDB - Embedded newform 656.2.bs.d.289.1

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			289.1
Character	$\chi$	$=$	656.289
Dual form			656.2.bs.d.513.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49921 + 1.49921i) q^{3} +(1.72514 + 2.37446i) q^{5} +(1.11329 + 2.18496i) q^{7} -1.49525i q^{9} +O(q^{10})$	\(q+(-1.49921 + 1.49921i) q^{3} +(1.72514 + 2.37446i) q^{5} +(1.11329 + 2.18496i) q^{7} -1.49525i q^{9} +(6.07021 - 0.961426i) q^{11} +(0.531087 + 0.270602i) q^{13} +(-6.14615 - 0.973455i) q^{15} +(0.0921689 + 0.581932i) q^{17} +(1.67787 - 0.854919i) q^{19} +(-4.94477 - 1.60665i) q^{21} +(1.21857 + 3.75036i) q^{23} +(-1.11684 + 3.43727i) q^{25} +(-2.25594 - 2.25594i) q^{27} +(0.785988 - 4.96253i) q^{29} +(-4.03548 - 2.93195i) q^{31} +(-7.65912 + 10.5419i) q^{33} +(-3.26751 + 6.41285i) q^{35} +(-1.87618 + 1.36313i) q^{37} +(-1.20190 + 0.390521i) q^{39} +(-1.29313 + 6.27119i) q^{41} +(-2.50072 + 0.812532i) q^{43} +(3.55040 - 2.57951i) q^{45} +(-2.33269 + 4.57815i) q^{47} +(0.579854 - 0.798101i) q^{49} +(-1.01062 - 0.734256i) q^{51} +(0.818669 - 5.16887i) q^{53} +(12.7548 + 12.7548i) q^{55} +(-1.23378 + 3.79718i) q^{57} +(-3.23058 - 9.94272i) q^{59} +(0.968261 + 0.314607i) q^{61} +(3.26706 - 1.66465i) q^{63} +(0.273668 + 1.72787i) q^{65} +(3.42634 + 0.542679i) q^{67} +(-7.44946 - 3.79569i) q^{69} +(-4.74402 + 0.751379i) q^{71} -0.596626i q^{73} +(-3.47881 - 6.82756i) q^{75} +(8.85861 + 12.1928i) q^{77} +(-3.13817 + 3.13817i) q^{79} +11.2500 q^{81} -3.79458 q^{83} +(-1.22277 + 1.22277i) q^{85} +(6.26151 + 8.61823i) q^{87} +(-5.50333 - 10.8009i) q^{89} +1.46167i q^{91} +(10.4456 - 1.65442i) q^{93} +(4.92454 + 2.50918i) q^{95} +(-10.0255 - 1.58788i) q^{97} +(-1.43757 - 9.07645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$1$	$1$

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
$3$	−1.49921	+	1.49921i	−0.865568	+	0.865568i	−0.991978	−	0.126410i	$-0.959654\pi$
$3$	−1.49921	+	1.49921i	−0.865568	+	0.865568i	0.126410	+	0.991978i	$0.459654\pi$
$4$		0			0
$5$	1.72514	+	2.37446i	0.771508	+	1.06189i	0.996169	+	0.0874522i	$0.0278725\pi$
$5$	1.72514	+	2.37446i	0.771508	+	1.06189i	−0.224661	+	0.974437i	$0.572127\pi$
$6$		0			0
$7$	1.11329	+	2.18496i	0.420786	+	0.825839i	0.999944	+	0.0106232i	$0.00338154\pi$
$7$	1.11329	+	2.18496i	0.420786	+	0.825839i	−0.579158	+	0.815216i	$0.696618\pi$
$8$		0			0
$9$		−	1.49525i		−	0.498415i
$10$		0			0
$11$	6.07021	−	0.961426i	1.83024	−	0.289881i	0.856262	−	0.516541i	$-0.172781\pi$
$11$	6.07021	−	0.961426i	1.83024	−	0.289881i	0.973974	+	0.226660i	$0.0727808\pi$
$12$		0			0
$13$	0.531087	+	0.270602i	0.147297	+	0.0750516i	0.526085	−	0.850432i	$-0.323659\pi$
$13$	0.531087	+	0.270602i	0.147297	+	0.0750516i	−0.378788	+	0.925483i	$0.623659\pi$
$14$		0			0
$15$	−6.14615	−	0.973455i	−1.58693	−	0.251345i
$16$		0			0
$17$	0.0921689	+	0.581932i	0.0223542	+	0.141139i	0.996341	−	0.0854651i	$-0.0272376\pi$
$17$	0.0921689	+	0.581932i	0.0223542	+	0.141139i	−0.973987	+	0.226604i	$0.927238\pi$
$18$		0			0
$19$	1.67787	−	0.854919i	0.384931	−	0.196132i	−0.250807	−	0.968037i	$-0.580696\pi$
$19$	1.67787	−	0.854919i	0.384931	−	0.196132i	0.635738	+	0.771905i	$0.280696\pi$
$20$		0			0
$21$	−4.94477	−	1.60665i	−1.07904	−	0.350601i
$22$		0			0
$23$	1.21857	+	3.75036i	0.254089	+	0.782005i	0.994008	+	0.109309i	$0.0348637\pi$
$23$	1.21857	+	3.75036i	0.254089	+	0.782005i	−0.739919	+	0.672696i	$0.765136\pi$
$24$		0			0
$25$	−1.11684	+	3.43727i	−0.223368	+	0.687455i
$26$		0			0
$27$	−2.25594	−	2.25594i	−0.434155	−	0.434155i
$28$		0			0
$29$	0.785988	−	4.96253i	0.145954	−	0.921519i	−0.800652	−	0.599129i	$-0.795514\pi$
$29$	0.785988	−	4.96253i	0.145954	−	0.921519i	0.946607	−	0.322390i	$-0.104486\pi$
$30$		0			0
$31$	−4.03548	−	2.93195i	−0.724794	−	0.526593i	0.163118	−	0.986606i	$-0.447845\pi$
$31$	−4.03548	−	2.93195i	−0.724794	−	0.526593i	−0.887912	+	0.460013i	$0.847845\pi$
$32$		0			0
$33$	−7.65912	+	10.5419i	−1.33328	+	1.83511i
$34$		0			0
$35$	−3.26751	+	6.41285i	−0.552310	+	1.08397i
$36$		0			0
$37$	−1.87618	+	1.36313i	−0.308443	+	0.224097i	−0.731228	−	0.682133i	$-0.761052\pi$
$37$	−1.87618	+	1.36313i	−0.308443	+	0.224097i	0.422785	+	0.906230i	$0.361052\pi$
$38$		0			0
$39$	−1.20190	+	0.390521i	−0.192458	+	0.0625333i
$40$		0			0
$41$	−1.29313	+	6.27119i	−0.201953	+	0.979395i
$41$	−1.29313	+	6.27119i	−0.201953	+	0.979395i
$42$		0			0
$43$	−2.50072	+	0.812532i	−0.381356	+	0.123910i	−0.493420	−	0.869791i	$-0.664254\pi$
$43$	−2.50072	+	0.812532i	−0.381356	+	0.123910i	0.112065	+	0.993701i	$0.464254\pi$
$44$		0			0
$45$	3.55040	−	2.57951i	0.529262	−	0.384531i
$46$		0			0
$47$	−2.33269	+	4.57815i	−0.340257	+	0.667792i	−0.996207	−	0.0870119i	$-0.972268\pi$
$47$	−2.33269	+	4.57815i	−0.340257	+	0.667792i	0.655950	+	0.754804i	$0.272268\pi$
$48$		0			0
$49$	0.579854	−	0.798101i	0.0828364	−	0.114014i
$50$		0			0
$51$	−1.01062	−	0.734256i	−0.141515	−	0.102816i
$52$		0			0
$53$	0.818669	−	5.16887i	0.112453	−	0.710000i	−0.865459	−	0.500980i	$-0.832973\pi$
$53$	0.818669	−	5.16887i	0.112453	−	0.710000i	0.977912	−	0.209019i	$-0.0670271\pi$
$54$		0			0
$55$	12.7548	+	12.7548i	1.71986	+	1.71986i
$56$		0			0
$57$	−1.23378	+	3.79718i	−0.163418	+	0.502949i
$58$		0			0
$59$	−3.23058	−	9.94272i	−0.420586	−	1.29443i	−0.907158	−	0.420791i	$-0.861753\pi$
$59$	−3.23058	−	9.94272i	−0.420586	−	1.29443i	0.486572	−	0.873641i	$-0.338247\pi$
$60$		0			0
$61$	0.968261	+	0.314607i	0.123973	+	0.0402813i	0.370347	−	0.928894i	$-0.379239\pi$
$61$	0.968261	+	0.314607i	0.123973	+	0.0402813i	−0.246373	+	0.969175i	$0.579239\pi$
$62$		0			0
$63$	3.26706	−	1.66465i	0.411611	−	0.209726i
$64$		0			0
$65$	0.273668	+	1.72787i	0.0339443	+	0.214316i
$66$		0			0
$67$	3.42634	+	0.542679i	0.418594	+	0.0662988i	0.362179	−	0.932109i	$-0.382033\pi$
$67$	3.42634	+	0.542679i	0.418594	+	0.0662988i	0.0564152	+	0.998407i	$0.482033\pi$
$68$		0			0
$69$	−7.44946	−	3.79569i	−0.896809	−	0.456947i
$70$		0			0
$71$	−4.74402	+	0.751379i	−0.563012	+	0.0891723i	−0.431452	−	0.902136i	$-0.641999\pi$
$71$	−4.74402	+	0.751379i	−0.563012	+	0.0891723i	−0.131560	+	0.991308i	$0.541999\pi$
$72$		0			0
$73$		−	0.596626i		−	0.0698297i	−0.999390	−	0.0349149i	$-0.988884\pi$
$73$		−	0.596626i		−	0.0698297i	0.999390	−	0.0349149i	$-0.0111160\pi$
$74$		0			0
$75$	−3.47881	−	6.82756i	−0.401699	−	0.788379i
$76$		0			0
$77$	8.85861	+	12.1928i	1.00953	+	1.38950i
$78$		0			0
$79$	−3.13817	+	3.13817i	−0.353072	+	0.353072i	−0.861251	−	0.508179i	$-0.830319\pi$
$79$	−3.13817	+	3.13817i	−0.353072	+	0.353072i	0.508179	+	0.861251i	$0.330319\pi$
$80$		0			0
$81$	11.2500			1.25000
$82$		0			0
$83$	−3.79458			−0.416509			−0.208254	−	0.978075i	$-0.566778\pi$
$83$	−3.79458			−0.416509			−0.208254	+	0.978075i	$0.566778\pi$
$84$		0			0
$85$	−1.22277	+	1.22277i	−0.132628	+	0.132628i
$86$		0			0
$87$	6.26151	+	8.61823i	0.671304	+	0.923971i
$88$		0			0
$89$	−5.50333	−	10.8009i	−0.583352	−	1.14489i	−0.974463	−	0.224549i	$-0.927909\pi$
$89$	−5.50333	−	10.8009i	−0.583352	−	1.14489i	0.391111	−	0.920343i	$-0.372091\pi$
$90$		0			0
$91$			1.46167i			0.153224i
$92$		0			0
$93$	10.4456	−	1.65442i	1.08316	−	0.171556i
$94$		0			0
$95$	4.92454	+	2.50918i	0.505247	+	0.257436i
$96$		0			0
$97$	−10.0255	−	1.58788i	−1.01793	−	0.161224i	−0.374900	−	0.927065i	$-0.622323\pi$
$97$	−10.0255	−	1.58788i	−1.01793	−	0.161224i	−0.643030	+	0.765841i	$0.722323\pi$
$98$		0			0
$99$	−1.43757	−	9.07645i	−0.144481	−	0.912218i
$100$		0			0
$101$	3.94458	−	2.00986i	0.392500	−	0.199989i	−0.246591	−	0.969120i	$-0.579311\pi$
$101$	3.94458	−	2.00986i	0.392500	−	0.199989i	0.639091	+	0.769131i	$0.279311\pi$
$102$		0			0
$103$	−0.205290	−	0.0667028i	−0.0202278	−	0.00657242i	0.298886	−	0.954289i	$-0.403385\pi$
$103$	−0.205290	−	0.0667028i	−0.0202278	−	0.00657242i	−0.319113	+	0.947717i	$0.603385\pi$
$104$		0			0
$105$	−4.71551	−	14.5129i	−0.460187	−	1.41631i
$106$		0			0
$107$	4.88121	−	15.0228i	0.471885	−	1.45231i	−0.378229	−	0.925712i	$-0.623467\pi$
$107$	4.88121	−	15.0228i	0.471885	−	1.45231i	0.850113	−	0.526600i	$-0.176533\pi$
$108$		0			0
$109$	4.23511	+	4.23511i	0.405650	+	0.405650i	0.880219	−	0.474568i	$-0.157396\pi$
$109$	4.23511	+	4.23511i	0.405650	+	0.405650i	−0.474568	+	0.880219i	$0.657396\pi$
$110$		0			0
$111$	0.769178	−	4.85640i	0.0730072	−	0.460949i
$112$		0			0
$113$	−14.7878	−	10.7440i	−1.39112	−	1.01071i	−0.995741	−	0.0921939i	$-0.970612\pi$
$113$	−14.7878	−	10.7440i	−1.39112	−	1.01071i	−0.395383	−	0.918517i	$-0.629388\pi$
$114$		0			0
$115$	−6.80287	+	9.36335i	−0.634371	+	0.873137i
$116$		0			0
$117$	0.404617	−	0.794106i	0.0374069	−	0.0734151i
$118$		0			0
$119$	−1.16889	+	0.849247i	−0.107152	+	0.0778504i
$120$		0			0
$121$	25.4614	−	8.27292i	2.31468	−	0.752084i
$122$		0			0
$123$	−7.46314	−	11.3405i	−0.672929	−	1.02254i
$124$		0			0
$125$	3.86834	−	1.25690i	0.345995	−	0.112421i
$126$		0			0
$127$	14.7740	−	10.7340i	1.31098	−	0.952485i	0.310985	−	0.950415i	$-0.399341\pi$
$127$	14.7740	−	10.7340i	1.31098	−	0.952485i	0.999998	−	0.00206962i	$-0.000658779\pi$
$128$		0			0
$129$	2.53094	−	4.96725i	0.222837	−	0.437342i
$130$		0			0
$131$	7.96565	−	10.9638i	0.695962	−	0.957909i	−0.304024	−	0.952664i	$-0.598330\pi$
$131$	7.96565	−	10.9638i	0.695962	−	0.957909i	0.999986	−	0.00524501i	$-0.00166955\pi$
$132$		0			0
$133$	3.73594	+	2.71432i	0.323947	+	0.235361i
$134$		0			0
$135$	1.46481	−	9.24844i	0.126071	−	0.795979i
$136$		0			0
$137$	10.5077	+	10.5077i	0.897730	+	0.897730i	0.995235	−	0.0975051i	$-0.0310862\pi$
$137$	10.5077	+	10.5077i	0.897730	+	0.897730i	−0.0975051	+	0.995235i	$0.531086\pi$
$138$		0			0
$139$	−0.195261	+	0.600951i	−0.0165618	+	0.0509720i	−0.958996	−	0.283420i	$-0.908531\pi$
$139$	−0.195261	+	0.600951i	−0.0165618	+	0.0509720i	0.942434	+	0.334392i	$0.108531\pi$
$140$		0			0
$141$	−3.36642	−	10.3608i	−0.283504	−	0.872535i
$142$		0			0
$143$	3.48397	+	1.13201i	0.291344	+	0.0946635i
$144$		0			0
$145$	13.1393	−	6.69479i	1.09116	−	0.555972i
$146$		0			0
$147$	0.327197	+	2.06584i	0.0269868	+	0.170388i
$148$		0			0
$149$	−12.6918	−	2.01019i	−1.03975	−	0.164681i	−0.386866	−	0.922136i	$-0.626443\pi$
$149$	−12.6918	−	2.01019i	−1.03975	−	0.164681i	−0.652887	+	0.757455i	$0.726443\pi$
$150$		0			0
$151$	12.1082	+	6.16943i	0.985350	+	0.502061i	0.870949	−	0.491374i	$-0.163505\pi$
$151$	12.1082	+	6.16943i	0.985350	+	0.502061i	0.114401	+	0.993435i	$0.463505\pi$
$152$		0			0
$153$	0.870131	−	0.137815i	0.0703459	−	0.0111417i
$154$		0			0
$155$		−	14.6401i		−	1.17592i
$156$		0			0
$157$	1.90025	+	3.72944i	0.151656	+	0.297642i	0.954318	−	0.298792i	$-0.0965837\pi$
$157$	1.90025	+	3.72944i	0.151656	+	0.297642i	−0.802662	+	0.596434i	$0.796584\pi$
$158$		0			0
$159$	6.52186	+	8.97657i	0.517217	+	0.711888i
$160$		0			0
$161$	−6.83778	+	6.83778i	−0.538893	+	0.538893i
$162$		0			0
$163$	16.9510			1.32770			0.663851	−	0.747865i	$-0.268921\pi$
$163$	16.9510			1.32770			0.663851	+	0.747865i	$0.268921\pi$
$164$		0			0
$165$	−38.2443			−2.97732
$166$		0			0
$167$	−18.1214	+	18.1214i	−1.40227	+	1.40227i	−0.609446	+	0.792827i	$0.708608\pi$
$167$	−18.1214	+	18.1214i	−1.40227	+	1.40227i	−0.792827	+	0.609446i	$0.791392\pi$
$168$		0			0
$169$	−7.43238	−	10.2298i	−0.571722	−	0.786907i
$170$		0			0
$171$	−1.27831	−	2.50883i	−0.0977552	−	0.191855i
$172$		0			0
$173$			6.83171i			0.519405i	0.965689	+	0.259702i	$0.0836245\pi$
$173$			6.83171i			0.519405i	−0.965689	+	0.259702i	$0.916376\pi$
$174$		0			0
$175$	−8.75369	+	1.38645i	−0.661717	+	0.104806i
$176$		0			0
$177$	19.7495	+	10.0629i	1.48446	+	0.756372i
$178$		0			0
$179$	−15.4408	−	2.44559i	−1.15410	−	0.182792i	−0.450092	−	0.892982i	$-0.648609\pi$
$179$	−15.4408	−	2.44559i	−1.15410	−	0.182792i	−0.704009	+	0.710191i	$0.748609\pi$
$180$		0			0
$181$	3.13498	+	19.7935i	0.233022	+	1.47124i	0.775594	+	0.631232i	$0.217450\pi$
$181$	3.13498	+	19.7935i	0.233022	+	1.47124i	−0.542573	+	0.840009i	$0.682550\pi$
$182$		0			0
$183$	−1.92329	+	0.979963i	−0.142173	+	0.0724409i
$184$		0			0
$185$	−6.47337	−	2.10333i	−0.475932	−	0.154640i
$186$		0			0
$187$	1.11897	+	3.44383i	0.0818271	+	0.251838i
$188$		0			0
$189$	2.41762	−	7.44067i	0.175856	−	0.541229i
$190$		0			0
$191$	4.38486	+	4.38486i	0.317277	+	0.317277i	0.847721	−	0.530443i	$-0.177974\pi$
$191$	4.38486	+	4.38486i	0.317277	+	0.317277i	−0.530443	+	0.847721i	$0.677974\pi$
$192$		0			0
$193$	−2.21890	+	14.0096i	−0.159720	+	1.00843i	0.769430	+	0.638731i	$0.220540\pi$
$193$	−2.21890	+	14.0096i	−0.159720	+	1.00843i	−0.929150	+	0.369702i	$0.879460\pi$
$194$		0			0
$195$	−3.00072	−	2.18015i	−0.214886	−	0.156124i
$196$		0			0
$197$	5.40427	−	7.43834i	0.385038	−	0.529960i	−0.571872	−	0.820343i	$-0.693783\pi$
$197$	5.40427	−	7.43834i	0.385038	−	0.529960i	0.956911	+	0.290383i	$0.0937827\pi$
$198$		0			0
$199$	4.04507	−	7.93889i	0.286747	−	0.562773i	−0.702034	−	0.712143i	$-0.747725\pi$
$199$	4.04507	−	7.93889i	0.286747	−	0.562773i	0.988781	+	0.149370i	$0.0477247\pi$
$200$		0			0
$201$	−5.95038	+	4.32321i	−0.419708	+	0.304935i
$202$		0			0
$203$	11.7180	−	3.80741i	0.822442	−	0.267228i
$204$		0			0
$205$	−17.1215	+	7.74822i	−1.19582	+	0.541159i
$206$		0			0
$207$	5.60772	−	1.82206i	0.389763	−	0.126642i
$208$		0			0
$209$	9.36310	−	6.80269i	0.647659	−	0.470552i
$210$		0			0
$211$	1.13287	−	2.22339i	0.0779901	−	0.153064i	−0.848719	−	0.528845i	$-0.822625\pi$
$211$	1.13287	−	2.22339i	0.0779901	−	0.153064i	0.926709	+	0.375781i	$0.122625\pi$
$212$		0			0
$213$	5.98580	−	8.23875i	0.410140	−	0.564510i
$214$		0			0
$215$	−6.24342	−	4.53611i	−0.425798	−	0.309360i
$216$		0			0
$217$	1.91352	−	12.0815i	0.129898	−	0.820146i
$218$		0			0
$219$	0.894466	+	0.894466i	0.0604424	+	0.0604424i
$220$		0			0
$221$	−0.108522	+	0.333997i	−0.00730000	+	0.0224671i
$222$		0			0
$223$	7.66122	+	23.5788i	0.513034	+	1.57895i	0.786832	+	0.617168i	$0.211720\pi$
$223$	7.66122	+	23.5788i	0.513034	+	1.57895i	−0.273798	+	0.961787i	$0.588280\pi$
$224$		0			0
$225$	5.13957	+	1.66995i	0.342638	+	0.111330i
$226$		0			0
$227$	−2.03948	+	1.03917i	−0.135365	+	0.0689721i	−0.520361	−	0.853946i	$-0.674203\pi$
$227$	−2.03948	+	1.03917i	−0.135365	+	0.0689721i	0.384996	+	0.922918i	$0.374203\pi$
$228$		0			0
$229$	−3.28848	−	20.7626i	−0.217309	−	1.37203i	−0.819224	−	0.573474i	$-0.805596\pi$
$229$	−3.28848	−	20.7626i	−0.217309	−	1.37203i	0.601915	−	0.798560i	$-0.294404\pi$
$230$		0			0
$231$	−31.5605	−	4.99869i	−2.07653	−	0.328890i
$232$		0			0
$233$	−7.76709	−	3.95753i	−0.508839	−	0.259267i	0.180670	−	0.983544i	$-0.442174\pi$
$233$	−7.76709	−	3.95753i	−0.508839	−	0.259267i	−0.689509	+	0.724277i	$0.742174\pi$
$234$		0			0
$235$	−14.8948	+	2.35911i	−0.971633	+	0.153891i
$236$		0			0
$237$		−	9.40955i		−	0.611216i
$238$		0			0
$239$	−10.4691	−	20.5467i	−0.677188	−	1.32906i	−0.932138	−	0.362102i	$-0.882059\pi$
$239$	−10.4691	−	20.5467i	−0.677188	−	1.32906i	0.254950	−	0.966954i	$-0.417941\pi$
$240$		0			0
$241$	3.16869	+	4.36133i	0.204113	+	0.280938i	0.898786	−	0.438389i	$-0.144451\pi$
$241$	3.16869	+	4.36133i	0.204113	+	0.280938i	−0.694672	+	0.719326i	$0.744451\pi$
$242$		0			0
$243$	−10.0982	+	10.0982i	−0.647802	+	0.647802i
$244$		0			0
$245$	2.89539			0.184980
$246$		0			0
$247$	1.12244			0.0714191
$248$		0			0
$249$	5.68886	−	5.68886i	0.360517	−	0.360517i
$250$		0			0
$251$	6.43570	+	8.85798i	0.406218	+	0.559111i	0.962291	−	0.272023i	$-0.0876925\pi$
$251$	6.43570	+	8.85798i	0.406218	+	0.559111i	−0.556073	+	0.831133i	$0.687693\pi$
$252$		0			0
$253$	11.0026	+	21.5939i	0.691730	+	1.35760i
$254$		0			0
$255$		−	3.66636i		−	0.229597i
$256$		0			0
$257$	−11.7305	+	1.85792i	−0.731726	+	0.115894i	−0.511169	−	0.859480i	$-0.670787\pi$
$257$	−11.7305	+	1.85792i	−0.731726	+	0.115894i	−0.220557	+	0.975374i	$0.570787\pi$
$258$		0			0
$259$	−5.06713	−	2.58183i	−0.314856	−	0.160427i
$260$		0			0
$261$	−7.42021	−	1.17525i	−0.459299	−	0.0727459i
$262$		0			0
$263$	1.09630	+	6.92176i	0.0676007	+	0.426814i	0.998158	+	0.0606678i	$0.0193230\pi$
$263$	1.09630	+	6.92176i	0.0676007	+	0.426814i	−0.930557	+	0.366146i	$0.880677\pi$
$264$		0			0
$265$	13.6856	−	6.97316i	0.840699	−	0.428358i
$266$		0			0
$267$	24.4434	+	7.94214i	1.49591	+	0.486051i
$268$		0			0
$269$	9.10933	+	28.0356i	0.555406	+	1.70936i	0.694869	+	0.719136i	$0.255462\pi$
$269$	9.10933	+	28.0356i	0.555406	+	1.70936i	−0.139463	+	0.990227i	$0.544538\pi$
$270$		0			0
$271$	0.323450	−	0.995477i	0.0196482	−	0.0604709i	−0.940752	−	0.339096i	$-0.889879\pi$
$271$	0.323450	−	0.995477i	0.0196482	−	0.0604709i	0.960400	+	0.278625i	$0.0898788\pi$
$272$		0			0
$273$	−2.19134	−	2.19134i	−0.132626	−	0.132626i
$274$		0			0
$275$	−3.47475	+	21.9387i	−0.209535	+	1.32295i
$276$		0			0
$277$	19.6390	+	14.2685i	1.17999	+	0.857314i	0.992171	−	0.124890i	$-0.0398577\pi$
$277$	19.6390	+	14.2685i	1.17999	+	0.857314i	0.187820	+	0.982203i	$0.439858\pi$
$278$		0			0
$279$	−4.38399	+	6.03404i	−0.262462	+	0.361248i
$280$		0			0
$281$	−8.65174	+	16.9800i	−0.516120	+	1.01294i	0.475002	+	0.879985i	$0.342447\pi$
$281$	−8.65174	+	16.9800i	−0.516120	+	1.01294i	−0.991122	+	0.132957i	$0.957553\pi$
$282$		0			0
$283$	−16.9992	+	12.3506i	−1.01050	+	0.734168i	−0.964313	−	0.264765i	$-0.914706\pi$
$283$	−16.9992	+	12.3506i	−1.01050	+	0.734168i	−0.0461826	+	0.998933i	$0.514706\pi$
$284$		0			0
$285$	−11.1447	+	3.62113i	−0.660154	+	0.214497i
$286$		0			0
$287$	−15.1420	+	4.15624i	−0.893801	+	0.245335i
$288$		0			0
$289$	15.8378	−	5.14602i	0.931636	−	0.302707i
$290$		0			0
$291$	17.4108	−	12.6497i	1.02064	−	0.741537i
$292$		0			0
$293$	5.11758	−	10.0438i	0.298972	−	0.586766i	−0.691834	−	0.722057i	$-0.743197\pi$
$293$	5.11758	−	10.0438i	0.298972	−	0.586766i	0.990806	+	0.135291i	$0.0431968\pi$
$294$		0			0
$295$	18.0353	−	24.8235i	1.05006	−	1.44528i
$296$		0			0
$297$	−15.8629	−	11.5251i	−0.920460	−	0.668754i
$298$		0			0
$299$	−0.367692	+	2.32152i	−0.0212642	+	0.134257i
$300$		0			0
$301$	−4.55939	−	4.55939i	−0.262799	−	0.262799i
$302$		0			0
$303$	−2.90054	+	8.92694i	−0.166632	+	0.512839i
$304$		0			0
$305$	0.923368	+	2.84184i	0.0528719	+	0.162723i
$306$		0			0
$307$	−8.99276	−	2.92192i	−0.513244	−	0.166763i	0.0409331	−	0.999162i	$-0.486967\pi$
$307$	−8.99276	−	2.92192i	−0.513244	−	0.166763i	−0.554177	+	0.832399i	$0.686967\pi$
$308$		0			0
$309$	0.407774	−	0.207771i	0.0231974	−	0.0118197i
$310$		0			0
$311$	2.64006	+	16.6687i	0.149704	+	0.945195i	0.942135	+	0.335234i	$0.108815\pi$
$311$	2.64006	+	16.6687i	0.149704	+	0.945195i	−0.792431	+	0.609962i	$0.791185\pi$
$312$		0			0
$313$	−24.1931	−	3.83181i	−1.36747	−	0.216587i	−0.570846	−	0.821057i	$-0.693385\pi$
$313$	−24.1931	−	3.83181i	−1.36747	−	0.216587i	−0.796628	+	0.604471i	$0.793385\pi$
$314$		0			0
$315$	9.58878	+	4.88573i	0.540267	+	0.275280i
$316$		0			0
$317$	−9.70461	+	1.53706i	−0.545065	+	0.0863299i	−0.422894	−	0.906179i	$-0.638986\pi$
$317$	−9.70461	+	1.53706i	−0.545065	+	0.0863299i	−0.122171	+	0.992509i	$0.538986\pi$
$318$		0			0
$319$		−	30.8793i		−	1.72891i
$320$		0			0
$321$	15.2044	+	29.8403i	0.848626	+	1.66552i
$322$		0			0
$323$	0.652152	+	0.897611i	0.0362867	+	0.0499444i
$324$		0			0
$325$	−1.52327	+	1.52327i	−0.0844959	+	0.0844959i
$326$		0			0
$327$	−12.6986			−0.702236
$328$		0			0
$329$	−12.6001			−0.694664
$330$		0			0
$331$	14.3440	−	14.3440i	0.788417	−	0.788417i	−0.192818	−	0.981235i	$-0.561763\pi$
$331$	14.3440	−	14.3440i	0.788417	−	0.788417i	0.981235	+	0.192818i	$0.0617626\pi$
$332$		0			0
$333$	2.03821	+	2.80536i	0.111693	+	0.153733i
$334$		0			0
$335$	4.62236	+	9.07189i	0.252547	+	0.495651i
$336$		0			0
$337$			8.81241i			0.480043i	0.970768	+	0.240021i	$0.0771545\pi$
$337$			8.81241i			0.480043i	−0.970768	+	0.240021i	$0.922846\pi$
$338$		0			0
$339$	38.2775	−	6.06257i	2.07895	−	0.329273i
$340$		0			0
$341$	−27.3151	−	13.9177i	−1.47919	−	0.753687i
$342$		0			0
$343$	19.3437	+	3.06375i	1.04446	+	0.165427i
$344$		0			0
$345$	−3.83869	−	24.2365i	−0.206668	−	1.30485i
$346$		0			0
$347$	4.18176	−	2.13071i	0.224489	−	0.114383i	−0.338129	−	0.941100i	$-0.609794\pi$
$347$	4.18176	−	2.13071i	0.224489	−	0.114383i	0.562618	+	0.826717i	$0.309794\pi$
$348$		0			0
$349$	12.3323	+	4.00699i	0.660130	+	0.214489i	0.619876	−	0.784700i	$-0.287183\pi$
$349$	12.3323	+	4.00699i	0.660130	+	0.214489i	0.0402548	+	0.999189i	$0.487183\pi$
$350$		0			0
$351$	−0.587637	−	1.80856i	−0.0313658	−	0.0965339i
$352$		0			0
$353$	6.12880	−	18.8625i	0.326203	−	1.00395i	−0.644692	−	0.764443i	$-0.723014\pi$
$353$	6.12880	−	18.8625i	0.326203	−	1.00395i	0.970895	−	0.239507i	$-0.0769857\pi$
$354$		0			0
$355$	−9.96824	−	9.96824i	−0.529059	−	0.529059i
$356$		0			0
$357$	0.479209	−	3.02560i	0.0253624	−	0.160132i
$358$		0			0
$359$	1.27423	+	0.925784i	0.0672514	+	0.0488610i	0.620903	−	0.783887i	$-0.286766\pi$
$359$	1.27423	+	0.925784i	0.0672514	+	0.0488610i	−0.553652	+	0.832748i	$0.686766\pi$
$360$		0			0
$361$	−9.08355	+	12.5024i	−0.478081	+	0.658023i
$362$		0			0
$363$	−25.7692	+	50.5748i	−1.35253	+	2.65449i
$364$		0			0
$365$	1.41666	−	1.02926i	0.0741514	−	0.0538742i
$366$		0			0
$367$	10.0426	−	3.26304i	0.524219	−	0.170329i	−0.0349400	−	0.999389i	$-0.511124\pi$
$367$	10.0426	−	3.26304i	0.524219	−	0.170329i	0.559159	+	0.829060i	$0.311124\pi$
$368$		0			0
$369$	9.37697	+	1.93355i	0.488146	+	0.100657i
$370$		0			0
$371$	12.2052	−	3.96572i	0.633664	−	0.205890i
$372$		0			0
$373$	28.7981	−	20.9230i	1.49111	−	1.08335i	0.517349	−	0.855774i	$-0.326919\pi$
$373$	28.7981	−	20.9230i	1.49111	−	1.08335i	0.973760	−	0.227579i	$-0.0730811\pi$
$374$		0			0
$375$	−3.91509	+	7.68380i	−0.202175	+	0.396790i
$376$		0			0
$377$	1.76030	−	2.42285i	0.0906601	−	0.124783i
$378$		0			0
$379$	1.34011	+	0.973646i	0.0688368	+	0.0500129i	0.621671	−	0.783278i	$-0.286454\pi$
$379$	1.34011	+	0.973646i	0.0688368	+	0.0500129i	−0.552835	+	0.833291i	$0.686454\pi$
$380$		0			0
$381$	−6.05690	+	38.2418i	−0.310304	+	1.95918i
$382$		0			0
$383$	−6.91149	−	6.91149i	−0.353161	−	0.353161i	0.508123	−	0.861284i	$-0.330339\pi$
$383$	−6.91149	−	6.91149i	−0.353161	−	0.353161i	−0.861284	+	0.508123i	$0.830339\pi$
$384$		0			0
$385$	−13.6690	+	42.0688i	−0.696635	+	2.14402i
$386$		0			0
$387$	1.21494	+	3.73919i	0.0617587	+	0.190074i
$388$		0			0
$389$	−15.4034	−	5.00488i	−0.780985	−	0.253757i	−0.108724	−	0.994072i	$-0.534677\pi$
$389$	−15.4034	−	5.00488i	−0.780985	−	0.253757i	−0.672261	+	0.740314i	$0.734677\pi$
$390$		0			0
$391$	−2.07014	+	1.05479i	−0.104692	+	0.0533430i
$392$		0			0
$393$	4.49481	+	28.3791i	0.226733	+	1.43154i
$394$		0			0
$395$	−12.8653	−	2.03766i	−0.647321	−	0.102526i
$396$		0			0
$397$	16.0168	+	8.16099i	0.803862	+	0.409588i	0.807106	−	0.590407i	$-0.201033\pi$
$397$	16.0168	+	8.16099i	0.803862	+	0.409588i	−0.00324401	+	0.999995i	$0.501033\pi$
$398$		0			0
$399$	−9.67027	+	1.53162i	−0.484119	+	0.0766769i
$400$		0			0
$401$		−	8.90016i		−	0.444453i	−0.974995	−	0.222226i	$-0.928668\pi$
$401$		−	8.90016i		−	0.444453i	0.974995	−	0.222226i	$-0.0713324\pi$
$402$		0			0
$403$	−1.34980	−	2.64913i	−0.0672383	−	0.131963i
$404$		0			0
$405$	19.4078	+	26.7126i	0.964383	+	1.32736i
$406$		0			0
$407$	−10.0783	+	10.0783i	−0.499562	+	0.499562i
$408$		0			0
$409$	−31.3466			−1.54999			−0.774996	−	0.631966i	$-0.782248\pi$
$409$	−31.3466			−1.54999			−0.774996	+	0.631966i	$0.782248\pi$
$410$		0			0
$411$	−31.5063			−1.55409
$412$		0			0
$413$	18.1279	−	18.1279i	0.892015	−	0.892015i
$414$		0			0
$415$	−6.54619	−	9.01005i	−0.321340	−	0.442286i
$416$		0			0
$417$	−0.608214	−	1.19369i	−0.0297844	−	0.0584551i
$418$		0			0
$419$			7.90991i			0.386424i	0.981157	+	0.193212i	$0.0618906\pi$
$419$			7.90991i			0.386424i	−0.981157	+	0.193212i	$0.938109\pi$
$420$		0			0
$421$	16.1064	−	2.55101i	0.784979	−	0.124329i	0.248937	−	0.968520i	$-0.419919\pi$
$421$	16.1064	−	2.55101i	0.784979	−	0.124329i	0.536042	+	0.844191i	$0.319919\pi$
$422$		0			0
$423$	6.84547	+	3.48794i	0.332838	+	0.169589i
$424$		0			0
$425$	−2.10320	−	0.333114i	−0.102020	−	0.0161584i
$426$		0			0
$427$	0.390555	+	2.46587i	0.0189003	+	0.119332i
$428$		0			0
$429$	−6.92032	+	3.52608i	−0.334116	+	0.170241i
$430$		0			0
$431$	−0.374602	−	0.121716i	−0.0180439	−	0.00586283i	0.299981	−	0.953945i	$-0.403020\pi$
$431$	−0.374602	−	0.121716i	−0.0180439	−	0.00586283i	−0.318025	+	0.948082i	$0.603020\pi$
$432$		0			0
$433$	−5.34527	−	16.4510i	−0.256877	−	0.790587i	−0.993454	−	0.114233i	$-0.963559\pi$
$433$	−5.34527	−	16.4510i	−0.256877	−	0.790587i	0.736577	−	0.676354i	$-0.236441\pi$
$434$		0			0
$435$	−9.66160	+	29.7354i	−0.463238	+	1.42570i
$436$		0			0
$437$	5.25086	+	5.25086i	0.251183	+	0.251183i
$438$		0			0
$439$	−0.0655373	+	0.413787i	−0.00312793	+	0.0197490i	−0.989203	−	0.146552i	$-0.953182\pi$
$439$	−0.0655373	+	0.413787i	−0.00312793	+	0.0197490i	0.986075	+	0.166301i	$0.0531824\pi$
$440$		0			0
$441$	−1.19336	−	0.867025i	−0.0568266	−	0.0412869i
$442$		0			0
$443$	15.5288	−	21.3736i	0.737796	−	1.01549i	−0.260947	−	0.965353i	$-0.584035\pi$
$443$	15.5288	−	21.3736i	0.737796	−	1.01549i	0.998742	−	0.0501355i	$-0.0159653\pi$
$444$		0			0
$445$	16.1522	−	31.7005i	0.765688	−	1.50275i
$446$		0			0
$447$	22.0413	−	16.0140i	1.04252	−	0.757435i
$448$		0			0
$449$	22.1252	−	7.18892i	1.04415	−	0.339266i	0.263783	−	0.964582i	$-0.415030\pi$
$449$	22.1252	−	7.18892i	1.04415	−	0.339266i	0.780372	+	0.625316i	$0.215030\pi$
$450$		0			0
$451$	−1.82028	+	39.3107i	−0.0857138	+	1.85107i
$452$		0			0
$453$	−27.4019	+	8.90343i	−1.28746	+	0.418320i
$454$		0			0
$455$	−3.47066	+	2.52158i	−0.162707	+	0.118214i
$456$		0			0
$457$	−4.13792	+	8.12113i	−0.193564	+	0.379890i	−0.967307	−	0.253609i	$-0.918382\pi$
$457$	−4.13792	+	8.12113i	−0.193564	+	0.379890i	0.773743	+	0.633500i	$0.218382\pi$
$458$		0			0
$459$	1.10487	−	1.52073i	0.0515711	−	0.0709816i
$460$		0			0
$461$	−31.8495	−	23.1400i	−1.48338	−	1.07774i	−0.976449	−	0.215749i	$-0.930781\pi$
$461$	−31.8495	−	23.1400i	−1.48338	−	1.07774i	−0.506929	−	0.861988i	$-0.669219\pi$
$462$		0			0
$463$	−2.77611	+	17.5277i	−0.129017	+	0.814580i	0.835293	+	0.549805i	$0.185298\pi$
$463$	−2.77611	+	17.5277i	−0.129017	+	0.814580i	−0.964310	+	0.264776i	$0.914702\pi$
$464$		0			0
$465$	21.9486	+	21.9486i	1.01784	+	1.01784i
$466$		0			0
$467$	−1.24330	+	3.82647i	−0.0575329	+	0.177068i	−0.975693	−	0.219141i	$-0.929674\pi$
$467$	−1.24330	+	3.82647i	−0.0575329	+	0.177068i	0.918160	+	0.396209i	$0.129674\pi$
$468$		0			0
$469$	2.62879	+	8.09059i	0.121386	+	0.373589i
$470$		0			0
$471$	−8.44007	−	2.74234i	−0.388898	−	0.126361i
$472$		0			0
$473$	−14.3987	+	7.33649i	−0.662052	+	0.337332i
$474$		0			0
$475$	1.06468	+	6.72212i	0.0488508	+	0.308432i
$476$		0			0
$477$	−7.72874	−	1.22411i	−0.353875	−	0.0560482i
$478$		0			0
$479$	−16.7284	−	8.52355i	−0.764340	−	0.389451i	0.0279388	−	0.999610i	$-0.491106\pi$
$479$	−16.7284	−	8.52355i	−0.764340	−	0.389451i	−0.792279	+	0.610159i	$0.791106\pi$
$480$		0			0
$481$	−1.36528	+	0.216240i	−0.0622515	+	0.00985967i
$482$		0			0
$483$		−	20.5025i		−	0.932896i
$484$		0			0
$485$	−13.5250	−	26.5443i	−0.614139	−	1.20532i
$486$		0			0
$487$	−3.29322	−	4.53273i	−0.149230	−	0.205398i	0.727857	−	0.685729i	$-0.240516\pi$
$487$	−3.29322	−	4.53273i	−0.149230	−	0.205398i	−0.877087	+	0.480331i	$0.840516\pi$
$488$		0			0
$489$	−25.4130	+	25.4130i	−1.14922	+	1.14922i
$490$		0			0
$491$	−31.8490			−1.43733			−0.718663	−	0.695358i	$-0.755246\pi$
$491$	−31.8490			−1.43733			−0.718663	+	0.695358i	$0.755246\pi$
$492$		0			0
$493$	2.96030			0.133325
$494$		0			0
$495$	19.0716	−	19.0716i	0.857206	−	0.857206i
$496$		0			0
$497$	−6.92323	−	9.52901i	−0.310549	−	0.427434i
$498$		0			0
$499$	−1.89386	−	3.71692i	−0.0847810	−	0.166392i	0.844723	−	0.535203i	$-0.179765\pi$
$499$	−1.89386	−	3.71692i	−0.0847810	−	0.166392i	−0.929504	+	0.368811i	$0.879765\pi$
$500$		0			0
$501$		−	54.3354i		−	2.42753i
$502$		0			0
$503$	3.67805	−	0.582545i	0.163996	−	0.0259744i	−0.0738965	−	0.997266i	$-0.523543\pi$
$503$	3.67805	−	0.582545i	0.163996	−	0.0259744i	0.237892	+	0.971292i	$0.423543\pi$
$504$		0			0
$505$	11.5773	+	5.89893i	0.515183	+	0.262499i
$506$		0			0
$507$	26.4793	+	4.19390i	1.17599	+	0.186258i
$508$		0			0
$509$	4.30277	+	27.1666i	0.190717	+	1.20414i	0.878328	+	0.478059i	$0.158659\pi$
$509$	4.30277	+	27.1666i	0.190717	+	1.20414i	−0.687611	+	0.726079i	$0.741341\pi$
$510$		0			0
$511$	1.30361	−	0.664220i	0.0576681	−	0.0293834i
$512$		0			0
$513$	−5.71382	−	1.85653i	−0.252271	−	0.0819680i
$514$		0			0
$515$	−0.195772	−	0.602524i	−0.00862674	−	0.0265504i
$516$		0			0
$517$	−9.75833	+	30.0330i	−0.429171	+	1.32085i
$518$		0			0
$519$	−10.2421	−	10.2421i	−0.449580	−	0.449580i
$520$		0			0
$521$	−0.365315	+	2.30651i	−0.0160047	+	0.101050i	−0.994398	−	0.105705i	$-0.966290\pi$
$521$	−0.365315	+	2.30651i	−0.0160047	+	0.101050i	0.978393	+	0.206755i	$0.0662902\pi$
$522$		0			0
$523$	−10.9719	−	7.97156i	−0.479768	−	0.348572i	0.321468	−	0.946921i	$-0.395824\pi$
$523$	−10.9719	−	7.97156i	−0.479768	−	0.348572i	−0.801236	+	0.598349i	$0.795824\pi$
$524$		0			0
$525$	11.0450	−	15.2022i	0.482044	−	0.663477i
$526$		0			0
$527$	1.33425	−	2.61861i	0.0581207	−	0.114068i
$528$		0			0
$529$	6.02708	−	4.37893i	0.262047	−	0.190388i
$530$		0			0
$531$	−14.8668	+	4.83052i	−0.645165	+	0.209627i
$532$		0			0
$533$	−2.38376	+	2.98062i	−0.103252	+	0.129105i
$534$		0			0
$535$	44.0918	−	14.3263i	1.90626	−	0.619380i
$536$		0			0
$537$	26.8154	−	19.4825i	1.15717	−	0.840734i
$538$		0			0
$539$	2.75252	−	5.40213i	0.118559	−	0.232686i
$540$		0			0
$541$	20.2273	−	27.8405i	0.869640	−	1.19696i	−0.109544	−	0.993982i	$-0.534939\pi$
$541$	20.2273	−	27.8405i	0.869640	−	1.19696i	0.979184	−	0.202974i	$-0.0650608\pi$
$542$		0			0
$543$	−34.3746	−	24.9746i	−1.47515	−	1.07176i
$544$		0			0
$545$	−2.74991	+	17.3623i	−0.117793	+	0.743718i
$546$		0			0
$547$	4.29151	+	4.29151i	0.183492	+	0.183492i	0.792875	−	0.609384i	$-0.208583\pi$
$547$	4.29151	+	4.29151i	0.183492	+	0.183492i	−0.609384	+	0.792875i	$0.708583\pi$
$548$		0			0
$549$	0.470415	−	1.44779i	0.0200768	−	0.0617901i
$550$		0			0
$551$	−2.92378	−	8.99846i	−0.124557	−	0.383347i
$552$		0			0
$553$	−10.3505	−	3.36308i	−0.440148	−	0.143013i
$554$		0			0
$555$	12.8583	−	6.55161i	0.545803	−	0.278100i
$556$		0			0
$557$	−1.52108	−	9.60372i	−0.0644502	−	0.406923i	−0.998730	−	0.0503819i	$-0.983956\pi$
$557$	−1.52108	−	9.60372i	−0.0644502	−	0.406923i	0.934280	−	0.356541i	$-0.116044\pi$
$558$		0			0
$559$	−1.54797	−	0.245175i	−0.0654722	−	0.0103698i
$560$		0			0
$561$	−6.84058	−	3.48545i	−0.288810	−	0.147156i
$562$		0			0
$563$	19.5048	−	3.08926i	0.822030	−	0.130197i	0.268769	−	0.963205i	$-0.413383\pi$
$563$	19.5048	−	3.08926i	0.822030	−	0.130197i	0.553261	+	0.833008i	$0.313383\pi$
$564$		0			0
$565$		−	53.6480i		−	2.25699i
$566$		0			0
$567$	12.5245	+	24.5808i	0.525981	+	1.03230i
$568$		0			0
$569$	−21.8076	−	30.0155i	−0.914220	−	1.25832i	−0.965705	−	0.259643i	$-0.916395\pi$
$569$	−21.8076	−	30.0155i	−0.914220	−	1.25832i	0.0514845	−	0.998674i	$-0.483605\pi$
$570$		0			0
$571$	−9.74733	+	9.74733i	−0.407913	+	0.407913i	−0.881010	−	0.473097i	$-0.843136\pi$
$571$	−9.74733	+	9.74733i	−0.407913	+	0.407913i	0.473097	+	0.881010i	$0.343136\pi$
$572$		0			0
$573$	−13.1476			−0.549250
$574$		0			0
$575$	−14.2520			−0.594348
$576$		0			0
$577$	4.93444	−	4.93444i	0.205423	−	0.205423i	−0.596895	−	0.802319i	$-0.703599\pi$
$577$	4.93444	−	4.93444i	0.205423	−	0.205423i	0.802319	+	0.596895i	$0.203599\pi$
$578$		0			0
$579$	−17.6767	−	24.3299i	−0.734618	−	1.01112i
$580$		0			0
$581$	−4.22448	−	8.29101i	−0.175261	−	0.343969i
$582$		0			0
$583$		−	32.1632i		−	1.33206i
$584$		0			0
$585$	2.58359	−	0.409201i	0.106818	−	0.0169184i
$586$		0			0
$587$	−0.548784	−	0.279619i	−0.0226507	−	0.0115411i	0.442628	−	0.896705i	$-0.354046\pi$
$587$	−0.548784	−	0.279619i	−0.0226507	−	0.0115411i	−0.465279	+	0.885164i	$0.654046\pi$
$588$		0			0
$589$	−9.27760	−	1.46943i	−0.382277	−	0.0605467i
$590$		0			0
$591$	3.04949	+	19.2537i	0.125439	+	0.791993i
$592$		0			0
$593$	38.3541	−	19.5424i	1.57501	−	0.802509i	0.575134	−	0.818059i	$-0.304950\pi$
$593$	38.3541	−	19.5424i	1.57501	−	0.802509i	0.999879	+	0.0155502i	$0.00495000\pi$
$594$		0			0
$595$	−4.03300	−	1.31040i	−0.165337	−	0.0537212i
$596$		0			0
$597$	5.83765	+	17.9664i	0.238919	+	0.735317i
$598$		0			0
$599$	13.1007	−	40.3197i	0.535278	−	1.64742i	−0.207769	−	0.978178i	$-0.566620\pi$
$599$	13.1007	−	40.3197i	0.535278	−	1.64742i	0.743047	−	0.669239i	$-0.233380\pi$
$600$		0			0
$601$	13.3208	+	13.3208i	0.543365	+	0.543365i	0.924514	−	0.381148i	$-0.124471\pi$
$601$	13.3208	+	13.3208i	0.543365	+	0.543365i	−0.381148	+	0.924514i	$0.624471\pi$
$602$		0			0
$603$	0.811439	−	5.12322i	0.0330443	−	0.208634i
$604$		0			0
$605$	63.5683	+	46.1851i	2.58442	+	1.87769i
$606$		0			0
$607$	−13.4407	+	18.4996i	−0.545543	+	0.750875i	−0.989399	−	0.145223i	$-0.953610\pi$
$607$	−13.4407	+	18.4996i	−0.545543	+	0.750875i	0.443856	+	0.896098i	$0.353610\pi$
$608$		0			0
$609$	−11.8596	+	23.2758i	−0.480576	+	0.943183i
$610$		0			0
$611$	−2.47772	+	1.80017i	−0.100238	+	0.0728270i
$612$		0			0
$613$	−24.0488	+	7.81393i	−0.971322	+	0.315602i	−0.751350	−	0.659904i	$-0.770597\pi$
$613$	−24.0488	+	7.81393i	−0.971322	+	0.315602i	−0.219973	+	0.975506i	$0.570597\pi$
$614$		0			0
$615$	14.0525	−	37.2849i	0.566651	−	1.50347i
$616$		0			0
$617$	16.1405	−	5.24436i	0.649791	−	0.211130i	0.0344691	−	0.999406i	$-0.489026\pi$
$617$	16.1405	−	5.24436i	0.649791	−	0.211130i	0.615322	+	0.788276i	$0.289026\pi$
$618$		0			0
$619$	−33.6865	+	24.4747i	−1.35397	+	0.983720i	−0.355171	+	0.934801i	$0.615577\pi$
$619$	−33.6865	+	24.4747i	−1.35397	+	0.983720i	−0.998803	+	0.0489186i	$0.984423\pi$
$620$		0			0
$621$	5.71157	−	11.2096i	0.229198	−	0.449826i
$622$		0			0
$623$	17.4727	−	24.0491i	0.700030	−	0.963509i
$624$		0			0
$625$	24.2775	+	17.6386i	0.971100	+	0.705545i
$626$		0			0
$627$	−3.83858	+	24.2359i	−0.153298	+	0.967887i
$628$		0			0
$629$	−0.966173	−	0.966173i	−0.0385238	−	0.0385238i
$630$		0			0
$631$	−7.59021	+	23.3602i	−0.302161	+	0.929957i	0.678560	+	0.734545i	$0.262604\pi$
$631$	−7.59021	+	23.3602i	−0.302161	+	0.929957i	−0.980721	+	0.195412i	$0.937396\pi$
$632$		0			0
$633$	1.63491	+	5.03173i	0.0649818	+	0.199993i
$634$		0			0
$635$	50.9746	+	16.5627i	2.02287	+	0.657269i
$636$		0			0
$637$	0.523921	−	0.266951i	0.0207585	−	0.0105770i
$638$		0			0
$639$	1.12350	+	7.09348i	0.0444449	+	0.280614i
$640$		0			0
$641$	22.7389	+	3.60148i	0.898131	+	0.142250i	0.588396	−	0.808573i	$-0.299760\pi$
$641$	22.7389	+	3.60148i	0.898131	+	0.142250i	0.309735	+	0.950823i	$0.399760\pi$
$642$		0			0
$643$	21.2226	+	10.8135i	0.836939	+	0.426442i	0.819274	−	0.573402i	$-0.194377\pi$
$643$	21.2226	+	10.8135i	0.836939	+	0.426442i	0.0176649	+	0.999844i	$0.494377\pi$
$644$		0			0
$645$	16.1607	−	2.55961i	0.636329	−	0.100785i
$646$		0			0
$647$		−	19.1223i		−	0.751777i	−0.926665	−	0.375889i	$-0.877338\pi$
$647$		−	19.1223i		−	0.751777i	0.926665	−	0.375889i	$-0.122662\pi$
$648$		0			0
$649$	−29.1695	−	57.2484i	−1.14500	−	2.24720i
$650$		0			0
$651$	15.2439	+	20.9814i	0.597456	+	0.822328i
$652$		0			0
$653$	−25.5620	+	25.5620i	−1.00032	+	1.00032i	−0.000318893		1.00000i	$0.500102\pi$
$653$	−25.5620	+	25.5620i	−1.00032	+	1.00032i	−1.00000		0.000318893i	$0.999898\pi$
$654$		0			0
$655$	39.7749			1.55413
$656$		0			0
$657$	−0.892102			−0.0348042
$658$		0			0
$659$	14.3256	−	14.3256i	0.558044	−	0.558044i	−0.370706	−	0.928750i	$-0.620884\pi$
$659$	14.3256	−	14.3256i	0.558044	−	0.558044i	0.928750	+	0.370706i	$0.120884\pi$
$660$		0			0
$661$	−5.30607	−	7.30318i	−0.206382	−	0.284061i	0.693261	−	0.720687i	$-0.256173\pi$
$661$	−5.30607	−	7.30318i	−0.206382	−	0.284061i	−0.899643	+	0.436626i	$0.856173\pi$
$662$		0			0
$663$	−0.338034	−	0.663429i	−0.0131282	−	0.0257654i
$664$		0			0
$665$			13.5534i			0.525578i
$666$		0			0
$667$	19.5691	−	3.09944i	0.757718	−	0.120011i
$668$		0			0
$669$	−46.8353	−	23.8638i	−1.81076	−	0.922627i
$670$		0			0
$671$	6.18002	+	0.978818i	0.238577	+	0.0377869i
$672$		0			0
$673$	1.11504	+	7.04008i	0.0429816	+	0.271375i	0.999814	−	0.0192636i	$-0.00613217\pi$
$673$	1.11504	+	7.04008i	0.0429816	+	0.271375i	−0.956833	+	0.290639i	$0.906132\pi$
$674$		0			0
$675$	10.2738	−	5.23476i	0.395438	−	0.201486i
$676$		0			0
$677$	14.9246	+	4.84928i	0.573597	+	0.186373i	0.581430	−	0.813596i	$-0.302493\pi$
$677$	14.9246	+	4.84928i	0.573597	+	0.186373i	−0.00783293	+	0.999969i	$0.502493\pi$
$678$		0			0
$679$	−7.69183	−	23.6730i	−0.295185	−	0.908487i
$680$		0			0
$681$	1.49968	−	4.61554i	0.0574679	−	0.176868i
$682$		0			0
$683$	−19.3845	−	19.3845i	−0.741729	−	0.741729i	0.231182	−	0.972911i	$-0.425741\pi$
$683$	−19.3845	−	19.3845i	−0.741729	−	0.741729i	−0.972911	+	0.231182i	$0.925741\pi$
$684$		0			0
$685$	−6.82276	+	43.0772i	−0.260684	+	1.64590i
$686$		0			0
$687$	36.0576	+	26.1974i	1.37568	+	0.999493i
$688$		0			0
$689$	1.83349	−	2.52359i	0.0698506	−	0.0961411i
$690$		0			0
$691$	15.4816	−	30.3844i	0.588948	−	1.15588i	−0.383671	−	0.923470i	$-0.625340\pi$
$691$	15.4816	−	30.3844i	0.588948	−	1.15588i	0.972619	−	0.232406i	$-0.0746598\pi$
$692$		0			0
$693$	18.2313	−	13.2458i	0.692549	−	0.503167i
$694$		0			0
$695$	−1.76379	+	0.573089i	−0.0669042	+	0.0217385i
$696$		0			0
$697$	−3.76859	−	0.174505i	−0.142746	−	0.00660984i
$698$		0			0
$699$	17.5776	−	5.71132i	0.664848	−	0.216022i
$700$		0			0
$701$	−21.2988	+	15.4745i	−0.804445	+	0.584464i	−0.912215	−	0.409712i	$-0.865629\pi$
$701$	−21.2988	+	15.4745i	−0.804445	+	0.584464i	0.107769	+	0.994176i	$0.465629\pi$
$702$		0			0
$703$	−1.98264	+	3.89114i	−0.0747765	+	0.146757i
$704$		0			0
$705$	18.7937	−	25.8673i	0.707810	−	0.974218i
$706$		0			0
$707$	8.78296	+	6.38119i	0.330317	+	0.239989i
$708$		0			0
$709$	1.29513	−	8.17714i	0.0486397	−	0.307099i	−0.951360	−	0.308082i	$-0.900313\pi$
$709$	1.29513	−	8.17714i	0.0486397	−	0.307099i	1.00000		0.000982939i	$0.000312879\pi$
$710$		0			0
$711$	4.69234	+	4.69234i	0.175977	+	0.175977i
$712$		0			0
$713$	6.07837	−	18.7073i	0.227637	−	0.700593i
$714$		0			0
$715$	3.32244	+	10.2254i	0.124252	+	0.382409i
$716$		0			0
$717$	46.4991	+	15.1085i	1.73654	+	0.564236i
$718$		0			0
$719$	−12.5280	+	6.38331i	−0.467214	+	0.238057i	−0.671716	−	0.740809i	$-0.734442\pi$
$719$	−12.5280	+	6.38331i	−0.467214	+	0.238057i	0.204502	+	0.978866i	$0.434442\pi$
$720$		0			0
$721$	−0.0828052	−	0.522811i	−0.00308383	−	0.0194705i
$722$		0			0
$723$	−11.2891	−	1.78801i	−0.419845	−	0.0664968i
$724$		0			0
$725$	16.1798	+	8.24400i	0.600901	+	0.306175i
$726$		0			0
$727$	−3.58748	+	0.568201i	−0.133052	+	0.0210734i	−0.222605	−	0.974909i	$-0.571456\pi$
$727$	−3.58748	+	0.568201i	−0.133052	+	0.0210734i	0.0895531	+	0.995982i	$0.471456\pi$
$728$		0			0
$729$			3.47123i			0.128564i
$730$		0			0
$731$	−0.703327	−	1.38036i	−0.0260135	−	0.0510543i
$732$		0			0
$733$	−11.2030	−	15.4196i	−0.413793	−	0.569537i	0.550346	−	0.834937i	$-0.314496\pi$
$733$	−11.2030	−	15.4196i	−0.413793	−	0.569537i	−0.964138	+	0.265400i	$0.914496\pi$
$734$		0			0
$735$	−4.34079	+	4.34079i	−0.160112	+	0.160112i
$736$		0			0
$737$	21.3203			0.785345
$738$		0			0
$739$	−3.70903			−0.136439			−0.0682195	−	0.997670i	$-0.521732\pi$
$739$	−3.70903			−0.136439			−0.0682195	+	0.997670i	$0.521732\pi$
$740$		0			0
$741$	−1.68277	+	1.68277i	−0.0618181	+	0.0618181i
$742$		0			0
$743$	−22.4945	−	30.9610i	−0.825243	−	1.13585i	−0.988790	−	0.149314i	$-0.952293\pi$
$743$	−22.4945	−	30.9610i	−0.825243	−	1.13585i	0.163546	−	0.986536i	$-0.447707\pi$
$744$		0			0
$745$	−17.1221	−	33.6040i	−0.627305	−	1.23116i
$746$		0			0
$747$			5.67382i			0.207594i
$748$		0			0
$749$	38.2586	−	6.05956i	1.39794	−	0.221412i
$750$		0			0
$751$	−45.1176	−	22.9886i	−1.64636	−	0.838864i	−0.996918	−	0.0784569i	$-0.975001\pi$
$751$	−45.1176	−	22.9886i	−1.64636	−	0.838864i	−0.649446	−	0.760407i	$-0.724999\pi$
$752$		0			0
$753$	−22.9284	−	3.63150i	−0.835558	−	0.132339i
$754$		0			0
$755$	6.23932	+	39.3935i	0.227072	+	1.43368i
$756$		0			0
$757$	−16.4699	+	8.39181i	−0.598607	+	0.305006i	−0.726914	−	0.686729i	$-0.759046\pi$
$757$	−16.4699	+	8.39181i	−0.598607	+	0.305006i	0.128306	+	0.991735i	$0.459046\pi$
$758$		0			0
$759$	−48.8690	−	15.8785i	−1.77383	−	0.576353i
$760$		0			0
$761$	−4.05425	−	12.4777i	−0.146967	−	0.452317i	0.850292	−	0.526311i	$-0.176425\pi$
$761$	−4.05425	−	12.4777i	−0.146967	−	0.452317i	−0.997259	+	0.0739945i	$0.976425\pi$
$762$		0			0
$763$	−4.53864	+	13.9685i	−0.164310	+	0.505694i
$764$		0			0
$765$	1.82834	+	1.82834i	0.0661037	+	0.0661037i
$766$		0			0
$767$	0.974801	−	6.15465i	0.0351980	−	0.222232i
$768$		0			0
$769$	−9.65861	−	7.01739i	−0.348298	−	0.253053i	0.399857	−	0.916578i	$-0.369060\pi$
$769$	−9.65861	−	7.01739i	−0.348298	−	0.253053i	−0.748155	+	0.663524i	$0.769060\pi$
$770$		0			0
$771$	14.8010	−	20.3718i	0.533044	−	0.733672i
$772$		0			0
$773$	−6.63677	+	13.0254i	−0.238708	+	0.468491i	−0.979018	−	0.203775i	$-0.934679\pi$
$773$	−6.63677	+	13.0254i	−0.238708	+	0.468491i	0.740310	+	0.672266i	$0.234679\pi$
$774$		0			0
$775$	14.5849	−	10.5965i	0.523905	−	0.380639i
$776$		0			0
$777$	11.4674	−	3.72598i	0.411390	−	0.133669i
$778$		0			0
$779$	3.19165	+	11.6278i	0.114353	+	0.416609i
$780$		0			0
$781$	−28.0748	+	9.12205i	−1.00460	+	0.326413i
$782$		0			0
$783$	−12.9683	+	9.42203i	−0.463450	+	0.336716i
$784$		0			0
$785$	−5.57720	+	10.9459i	−0.199059	+	0.390675i
$786$		0			0
$787$	22.3369	−	30.7442i	0.796226	−	1.09591i	−0.197078	−	0.980388i	$-0.563145\pi$
$787$	22.3369	−	30.7442i	0.796226	−	1.09591i	0.993305	−	0.115524i	$-0.0368546\pi$
$788$		0			0
$789$	−12.0207	−	8.73358i	−0.427950	−	0.310924i
$790$		0			0
$791$	7.01202	−	44.2722i	0.249319	−	1.57414i
$792$		0			0
$793$	0.429097	+	0.429097i	0.0152377	+	0.0152377i
$794$		0			0
$795$	−10.0633	+	30.9717i	−0.356910	+	1.09845i
$796$		0			0
$797$	3.31857	+	10.2135i	0.117550	+	0.361781i	0.992470	−	0.122485i	$-0.0390864\pi$
$797$	3.31857	+	10.2135i	0.117550	+	0.361781i	−0.874920	+	0.484267i	$0.839086\pi$
$798$		0			0
$799$	−2.87917	−	0.935500i	−0.101858	−	0.0330956i
$800$		0			0
$801$	−16.1500	+	8.22883i	−0.570632	+	0.290751i
$802$		0			0
$803$	−0.573611	−	3.62164i	−0.0202423	−	0.127805i
$804$		0			0
$805$	−28.0322	−	4.43986i	−0.988004	−	0.156484i
$806$		0			0
$807$	−55.6880	−	28.3745i	−1.96031	−	0.998829i
$808$		0			0
$809$	25.5063	−	4.03980i	0.896754	−	0.142032i	0.308991	−	0.951065i	$-0.400009\pi$
$809$	25.5063	−	4.03980i	0.896754	−	0.142032i	0.587763	+	0.809033i	$0.300009\pi$
$810$		0			0
$811$			41.1472i			1.44488i	0.691436	+	0.722438i	$0.256978\pi$
$811$			41.1472i			1.44488i	−0.691436	+	0.722438i	$0.743022\pi$
$812$		0			0
$813$	1.00751	+	1.97735i	0.0353348	+	0.0693485i
$814$		0			0
$815$	29.2429	+	40.2493i	1.02433	+	1.40987i
$816$		0			0
$817$	−3.50124	+	3.50124i	−0.122493	+	0.122493i
$818$		0			0
$819$	2.18555			0.0763693
$820$		0			0
$821$	−21.5835			−0.753268			−0.376634	−	0.926362i	$-0.622919\pi$
$821$	−21.5835			−0.753268			−0.376634	+	0.926362i	$0.622919\pi$
$822$		0			0
$823$	−14.2285	+	14.2285i	−0.495975	+	0.495975i	−0.910182	−	0.414208i	$-0.864059\pi$
$823$	−14.2285	+	14.2285i	−0.495975	+	0.495975i	0.414208	+	0.910182i	$0.364059\pi$
$824$		0			0
$825$	−27.6813	−	38.1001i	−0.963740	−	1.32647i
$826$		0			0
$827$	9.37300	+	18.3955i	0.325931	+	0.639676i	0.994588	−	0.103895i	$-0.0331307\pi$
$827$	9.37300	+	18.3955i	0.325931	+	0.639676i	−0.668657	+	0.743571i	$0.733131\pi$
$828$		0			0
$829$			32.8047i			1.13935i	0.821868	+	0.569677i	$0.192932\pi$
$829$			32.8047i			1.13935i	−0.821868	+	0.569677i	$0.807068\pi$
$830$		0			0
$831$	−50.8344	+	8.05138i	−1.76343	+	0.279299i
$832$		0			0
$833$	0.517885	+	0.263876i	0.0179436	+	0.00914275i
$834$		0			0
$835$	−74.2904	−	11.7664i	−2.57092	−	0.407194i
$836$		0			0
$837$	2.48950	+	15.7181i	0.0860497	+	0.543297i
$838$		0			0
$839$	8.20381	−	4.18005i	0.283227	−	0.144311i	−0.306606	−	0.951836i	$-0.599193\pi$
$839$	8.20381	−	4.18005i	0.283227	−	0.144311i	0.589833	+	0.807525i	$0.299193\pi$
$840$		0			0
$841$	3.57168	+	1.16051i	0.123161	+	0.0400175i
$842$		0			0
$843$	−12.4858	−	38.4273i	−0.430033	−	1.32351i
$844$		0			0
$845$	11.4683	−	35.2957i	0.394521	−	1.21421i
$846$		0			0
$847$	46.4221	+	46.4221i	1.59508	+	1.59508i
$848$		0			0
$849$	6.96914	−	44.0014i	0.239180	−	1.51012i
$850$		0			0
$851$	−7.39848	−	5.37531i	−0.253617	−	0.184263i
$852$		0			0
$853$	3.94397	−	5.42840i	0.135039	−	0.185865i	−0.736142	−	0.676827i	$-0.763355\pi$
$853$	3.94397	−	5.42840i	0.135039	−	0.185865i	0.871181	+	0.490962i	$0.163355\pi$
$854$		0			0
$855$	3.75184	−	7.36340i	0.128310	−	0.251823i
$856$		0			0
$857$	−22.0856	+	16.0461i	−0.754428	+	0.548124i	−0.897196	−	0.441632i	$-0.854400\pi$
$857$	−22.0856	+	16.0461i	−0.754428	+	0.548124i	0.142768	+	0.989756i	$0.454400\pi$
$858$		0			0
$859$	−39.2836	+	12.7640i	−1.34034	+	0.435503i	−0.889432	−	0.457068i	$-0.848900\pi$
$859$	−39.2836	+	12.7640i	−1.34034	+	0.435503i	−0.450907	+	0.892571i	$0.648900\pi$
$860$		0			0
$861$	16.4699	−	28.9320i	0.561292	−	0.986000i
$862$		0			0
$863$	−31.0353	+	10.0840i	−1.05646	+	0.343263i	−0.785199	−	0.619244i	$-0.787439\pi$
$863$	−31.0353	+	10.0840i	−1.05646	+	0.343263i	−0.271257	+	0.962507i	$0.587439\pi$
$864$		0			0
$865$	−16.2216	+	11.7857i	−0.551551	+	0.400725i
$866$		0			0
$867$	−16.0292	+	31.4591i	−0.544381	+	1.06841i
$868$		0			0
$869$	−16.0322	+	22.0665i	−0.543856	+	0.748554i
$870$		0			0
$871$	1.67283	+	1.21539i	0.0566818	+	0.0411818i
$872$		0			0
$873$	−2.37427	+	14.9905i	−0.0803567	+	0.507352i
$874$		0			0
$875$	7.05289	+	7.05289i	0.238431	+	0.238431i
$876$		0			0
$877$	−3.53001	+	10.8643i	−0.119200	+	0.366860i	−0.992800	−	0.119785i	$-0.961780\pi$
$877$	−3.53001	+	10.8643i	−0.119200	+	0.366860i	0.873600	+	0.486645i	$0.161780\pi$
$878$		0			0
$879$	7.38546	+	22.7301i	0.249105	+	0.766667i
$880$		0			0
$881$	19.8386	+	6.44595i	0.668379	+	0.217169i	0.623500	−	0.781823i	$-0.285710\pi$
$881$	19.8386	+	6.44595i	0.668379	+	0.217169i	0.0448784	+	0.998992i	$0.485710\pi$
$882$		0			0
$883$	−14.2619	+	7.26681i	−0.479951	+	0.244547i	−0.677190	−	0.735808i	$-0.736803\pi$
$883$	−14.2619	+	7.26681i	−0.479951	+	0.244547i	0.197239	+	0.980355i	$0.436803\pi$
$884$		0			0
$885$	10.1769	+	64.2543i	0.342092	+	2.15988i
$886$		0			0
$887$	−1.51345	−	0.239706i	−0.0508165	−	0.00804855i	0.130974	−	0.991386i	$-0.458189\pi$
$887$	−1.51345	−	0.239706i	−0.0508165	−	0.00804855i	−0.181791	+	0.983337i	$0.558189\pi$
$888$		0			0
$889$	39.9011	+	20.3307i	1.33824	+	0.681868i
$890$		0			0
$891$	68.2897	−	10.8160i	2.28779	−	0.362350i
$892$		0			0
$893$			9.67582i			0.323789i
$894$		0			0
$895$	−20.8307	−	40.8825i	−0.696293	−	1.36655i
$896$		0			0
$897$	−2.92919	−	4.03168i	−0.0978027	−	0.134614i
$898$		0			0
$899$	−17.7217	+	17.7217i	−0.591053	+	0.591053i
$900$		0			0
$901$	3.08339			0.102723
$902$		0			0
$903$	13.6709			0.454940
$904$		0			0
$905$	−41.5905	+	41.5905i	−1.38252	+	1.38252i
$906$		0			0
$907$	10.1296	+	13.9421i	0.336346	+	0.462941i	0.943370	−	0.331743i	$-0.107637\pi$
$907$	10.1296	+	13.9421i	0.336346	+	0.462941i	−0.607023	+	0.794684i	$0.707637\pi$
$908$		0			0
$909$	−3.00524	−	5.89812i	−0.0996775	−	0.195628i
$910$		0			0
$911$			10.8340i			0.358947i	0.983763	+	0.179474i	$0.0574395\pi$
$911$			10.8340i			0.358947i	−0.983763	+	0.179474i	$0.942561\pi$
$912$		0			0
$913$	−23.0339	+	3.64820i	−0.762309	+	0.120738i
$914$		0			0
$915$	−5.64482	−	2.87618i	−0.186612	−	0.0950836i
$916$		0			0
$917$	32.8236	+	5.19874i	1.08393	+	0.171678i
$918$		0			0
$919$	8.24478	+	52.0555i	0.271970	+	1.71715i	0.624222	+	0.781247i	$0.285416\pi$
$919$	8.24478	+	52.0555i	0.271970	+	1.71715i	−0.352251	+	0.935905i	$0.614584\pi$
$920$		0			0
$921$	17.8626	−	9.10144i	0.588592	−	0.299903i
$922$		0			0
$923$	−2.72281	−	0.884696i	−0.0896225	−	0.0291201i
$924$		0			0
$925$	−2.59005	−	7.97135i	−0.0851603	−	0.262096i
$926$		0			0
$927$	−0.0997371	+	0.306959i	−0.00327580	+	0.0100819i
$928$		0			0
$929$	−25.6149	−	25.6149i	−0.840396	−	0.840396i	0.148514	−	0.988910i	$-0.452551\pi$
$929$	−25.6149	−	25.6149i	−0.840396	−	0.840396i	−0.988910	+	0.148514i	$0.952551\pi$
$930$		0			0
$931$	0.290610	−	1.83484i	0.00952437	−	0.0601345i
$932$		0			0
$933$	−28.9478	−	21.0318i	−0.947710	−	0.688552i
$934$		0			0
$935$	−6.24685	+	8.59805i	−0.204294	+	0.281186i
$936$		0			0
$937$	−4.26783	+	8.37609i	−0.139424	+	0.273635i	−0.950151	−	0.311789i	$-0.899072\pi$
$937$	−4.26783	+	8.37609i	−0.139424	+	0.273635i	0.810728	+	0.585424i	$0.199072\pi$
$938$		0			0
$939$	42.0151	−	30.5258i	1.37111	−	0.996171i
$940$		0			0
$941$	−15.1051	+	4.90795i	−0.492413	+	0.159995i	−0.544689	−	0.838638i	$-0.683352\pi$
$941$	−15.1051	+	4.90795i	−0.492413	+	0.159995i	0.0522762	+	0.998633i	$0.483352\pi$
$942$		0			0
$943$	−25.0950	+	2.79215i	−0.817205	+	0.0909250i
$944$		0			0
$945$	21.8383	−	7.09569i	0.710399	−	0.230823i
$946$		0			0
$947$	30.5510	−	22.1966i	0.992775	−	0.721293i	0.0322482	−	0.999480i	$-0.489733\pi$
$947$	30.5510	−	22.1966i	0.992775	−	0.721293i	0.960527	+	0.278186i	$0.0897333\pi$
$948$		0			0
$949$	0.161448	−	0.316860i	0.00524083	−	0.0102857i
$950$		0			0
$951$	12.2449	−	16.8536i	0.397067	−	0.546515i
$952$		0			0
$953$	25.8698	+	18.7955i	0.838006	+	0.608847i	0.921813	−	0.387635i	$-0.126708\pi$
$953$	25.8698	+	18.7955i	0.838006	+	0.608847i	−0.0838068	+	0.996482i	$0.526708\pi$
$954$		0			0
$955$	−2.84715	+	17.9762i	−0.0921315	+	0.581695i
$956$		0			0
$957$	46.2944	+	46.2944i	1.49649	+	1.49649i
$958$		0			0
$959$	−11.2607	+	34.6570i	−0.363628	+	1.11913i
$960$		0			0
$961$	−1.89074	−	5.81911i	−0.0609917	−	0.187713i
$962$		0			0
$963$	−22.4628	−	7.29862i	−0.723855	−	0.235195i
$964$		0			0
$965$	−37.0931	+	18.8999i	−1.19407	+	0.608408i
$966$		0			0
$967$	7.26414	+	45.8640i	0.233599	+	1.47489i	0.773842	+	0.633378i	$0.218332\pi$
$967$	7.26414	+	45.8640i	0.233599	+	1.47489i	−0.540243	+	0.841509i	$0.681668\pi$
$968$		0			0
$969$	−2.32342	−	0.367993i	−0.0746389	−	0.0118216i
$970$		0			0
$971$	45.6829	+	23.2766i	1.46603	+	0.746982i	0.991110	−	0.133045i	$-0.0424753\pi$
$971$	45.6829	+	23.2766i	1.46603	+	0.746982i	0.474925	+	0.880027i	$0.342475\pi$
$972$		0			0
$973$	−1.53044	+	0.242398i	−0.0490636	+	0.00777092i
$974$		0			0
$975$		−	4.56740i		−	0.146274i
$976$		0			0
$977$	5.61016	+	11.0106i	0.179485	+	0.352259i	0.963167	−	0.268903i	$-0.0866610\pi$
$977$	5.61016	+	11.0106i	0.179485	+	0.352259i	−0.783682	+	0.621162i	$0.786661\pi$
$978$		0			0
$979$	−43.7906	−	60.2726i	−1.39955	−	1.92632i
$980$		0			0
$981$	6.33254	−	6.33254i	0.202182	−	0.202182i
$982$		0			0
$983$	33.4651			1.06737			0.533686	−	0.845683i	$-0.320806\pi$
$983$	33.4651			1.06737			0.533686	+	0.845683i	$0.320806\pi$
$984$		0			0
$985$	26.9852			0.859819
$986$		0			0
$987$	18.8901	−	18.8901i	0.601279	−	0.601279i
$988$		0			0
$989$	−6.09458	−	8.38847i	−0.193796	−	0.266738i
$990$		0			0
$991$	−3.03259	−	5.95180i	−0.0963335	−	0.189065i	0.837811	−	0.545961i	$-0.183835\pi$
$991$	−3.03259	−	5.95180i	−0.0963335	−	0.189065i	−0.934144	+	0.356895i	$0.883835\pi$
$992$		0			0
$993$			43.0092i			1.36486i
$994$		0			0
$995$	25.8289	−	4.09089i	0.818830	−	0.129690i
$996$		0			0
$997$	−53.5880	−	27.3044i	−1.69715	−	0.864740i	−0.987006	−	0.160682i	$-0.948631\pi$
$997$	−53.5880	−	27.3044i	−1.69715	−	0.864740i	−0.710142	−	0.704058i	$-0.751369\pi$
$998$		0			0
$999$	7.30769	+	1.15742i	0.231205	+	0.0366193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.bs.d.289.1		24
4.3	odd	2		41.2.g.a.2.1	✓	24
12.11	even	2		369.2.u.a.289.3		24
41.21	even	20	inner	656.2.bs.d.513.1		24
164.103	odd	20		41.2.g.a.21.1	yes	24
164.111	even	40		1681.2.a.m.1.19		24
164.135	even	40		1681.2.a.m.1.20		24
492.431	even	20		369.2.u.a.226.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.2.1	✓	24	4.3	odd	2
41.2.g.a.21.1	yes	24	164.103	odd	20
369.2.u.a.226.3		24	492.431	even	20
369.2.u.a.289.3		24	12.11	even	2
656.2.bs.d.289.1		24	1.1	even	1	trivial
656.2.bs.d.513.1		24	41.21	even	20	inner
1681.2.a.m.1.19		24	164.111	even	40
1681.2.a.m.1.20		24	164.135	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)

\(f(q)\)	\(=\)	\(q+(-1.49921 + 1.49921i) q^{3} +(1.72514 + 2.37446i) q^{5} +(1.11329 + 2.18496i) q^{7} -1.49525i q^{9} +O(q^{10})\)	\(q+(-1.49921 + 1.49921i) q^{3} +(1.72514 + 2.37446i) q^{5} +(1.11329 + 2.18496i) q^{7} -1.49525i q^{9} +(6.07021 - 0.961426i) q^{11} +(0.531087 + 0.270602i) q^{13} +(-6.14615 - 0.973455i) q^{15} +(0.0921689 + 0.581932i) q^{17} +(1.67787 - 0.854919i) q^{19} +(-4.94477 - 1.60665i) q^{21} +(1.21857 + 3.75036i) q^{23} +(-1.11684 + 3.43727i) q^{25} +(-2.25594 - 2.25594i) q^{27} +(0.785988 - 4.96253i) q^{29} +(-4.03548 - 2.93195i) q^{31} +(-7.65912 + 10.5419i) q^{33} +(-3.26751 + 6.41285i) q^{35} +(-1.87618 + 1.36313i) q^{37} +(-1.20190 + 0.390521i) q^{39} +(-1.29313 + 6.27119i) q^{41} +(-2.50072 + 0.812532i) q^{43} +(3.55040 - 2.57951i) q^{45} +(-2.33269 + 4.57815i) q^{47} +(0.579854 - 0.798101i) q^{49} +(-1.01062 - 0.734256i) q^{51} +(0.818669 - 5.16887i) q^{53} +(12.7548 + 12.7548i) q^{55} +(-1.23378 + 3.79718i) q^{57} +(-3.23058 - 9.94272i) q^{59} +(0.968261 + 0.314607i) q^{61} +(3.26706 - 1.66465i) q^{63} +(0.273668 + 1.72787i) q^{65} +(3.42634 + 0.542679i) q^{67} +(-7.44946 - 3.79569i) q^{69} +(-4.74402 + 0.751379i) q^{71} -0.596626i q^{73} +(-3.47881 - 6.82756i) q^{75} +(8.85861 + 12.1928i) q^{77} +(-3.13817 + 3.13817i) q^{79} +11.2500 q^{81} -3.79458 q^{83} +(-1.22277 + 1.22277i) q^{85} +(6.26151 + 8.61823i) q^{87} +(-5.50333 - 10.8009i) q^{89} +1.46167i q^{91} +(10.4456 - 1.65442i) q^{93} +(4.92454 + 2.50918i) q^{95} +(-10.0255 - 1.58788i) q^{97} +(-1.43757 - 9.07645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) \) 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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Database

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