LMFDB - Embedded newform 688.2.bg.c.273.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [688,2,Mod(17,688)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(688, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 0, 38]))

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

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

chi := DirichletCharacter("688.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 688 = 2^{4} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	688.bg (of order $21$, degree $12$, 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:	$5.49370765906$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			273.2
Character	$\chi$	$=$	688.273
Dual form			688.2.bg.c.625.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.528255 - 1.34597i) q^{3} +(0.0684907 + 0.913945i) q^{5} +(0.971539 - 1.68276i) q^{7} +(0.666571 + 0.618487i) q^{9} +O(q^{10})$	\(q+(0.528255 - 1.34597i) q^{3} +(0.0684907 + 0.913945i) q^{5} +(0.971539 - 1.68276i) q^{7} +(0.666571 + 0.618487i) q^{9} +(0.100377 - 0.439781i) q^{11} +(2.90116 - 1.97798i) q^{13} +(1.26632 + 0.390609i) q^{15} +(0.142476 - 1.90121i) q^{17} +(-2.97713 + 2.76237i) q^{19} +(-1.75172 - 2.19659i) q^{21} +(1.77211 - 0.546623i) q^{23} +(4.11355 - 0.620018i) q^{25} +(5.09278 - 2.45255i) q^{27} +(-1.90792 - 4.86129i) q^{29} +(-0.920034 - 0.138673i) q^{31} +(-0.538908 - 0.367421i) q^{33} +(1.60449 + 0.772681i) q^{35} +(0.277212 + 0.480145i) q^{37} +(-1.12975 - 4.94975i) q^{39} +(0.111290 - 0.139553i) q^{41} +(6.30773 + 1.79236i) q^{43} +(-0.519610 + 0.651570i) q^{45} +(-1.72810 - 7.57131i) q^{47} +(1.61222 + 2.79245i) q^{49} +(-2.48371 - 1.19609i) q^{51} +(-8.52328 - 5.81107i) q^{53} +(0.408811 + 0.0616183i) q^{55} +(2.14539 + 5.46636i) q^{57} +(-9.19536 + 4.42825i) q^{59} +(-5.55516 + 0.837306i) q^{61} +(1.68836 - 0.520791i) q^{63} +(2.00646 + 2.51603i) q^{65} +(0.807046 - 0.748830i) q^{67} +(0.200386 - 2.67396i) q^{69} +(5.41606 + 1.67063i) q^{71} +(11.7207 - 7.99101i) q^{73} +(1.33848 - 5.86425i) q^{75} +(-0.642524 - 0.596175i) q^{77} +(-1.13115 + 1.95921i) q^{79} +(-0.406922 - 5.43000i) q^{81} +(-5.11608 + 13.0356i) q^{83} +1.74736 q^{85} -7.55102 q^{87} +(0.143414 - 0.365414i) q^{89} +(-0.509861 - 6.80362i) q^{91} +(-0.672662 + 1.16508i) q^{93} +(-2.72856 - 2.53173i) q^{95} +(-3.76302 + 16.4869i) q^{97} +(0.338908 - 0.231063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 16 q^{3} - 17 q^{5} - 6 q^{7} - q^{9}+O(q^{10}) $ 36 * q + 16 * q^3 - 17 * q^5 - 6 * q^7 - q^9	$ 36 q + 16 q^{3} - 17 q^{5} - 6 q^{7} - q^{9} + 4 q^{11} + 3 q^{15} - 10 q^{17} - 10 q^{19} - 21 q^{21} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 9 q^{29} - 40 q^{31} - 11 q^{33} - 11 q^{35} - 19 q^{37} + q^{39} - 28 q^{41} + 8 q^{43} - 46 q^{45} + 30 q^{47} + 6 q^{49} - 57 q^{51} - 24 q^{53} - 14 q^{55} + 52 q^{57} + q^{59} - 14 q^{61} - 47 q^{63} + 38 q^{65} - 66 q^{67} - 7 q^{69} + 33 q^{71} + 29 q^{73} + 55 q^{75} - 27 q^{77} + 17 q^{79} + 38 q^{81} + 23 q^{83} - 56 q^{85} + 86 q^{87} - 19 q^{89} + 13 q^{91} - 30 q^{93} - q^{95} - 31 q^{97} + 31 q^{99}+O(q^{100}) $ 36 * q + 16 * q^3 - 17 * q^5 - 6 * q^7 - q^9 + 4 * q^11 + 3 * q^15 - 10 * q^17 - 10 * q^19 - 21 * q^21 - 4 * q^23 - 2 * q^25 + 4 * q^27 + 9 * q^29 - 40 * q^31 - 11 * q^33 - 11 * q^35 - 19 * q^37 + q^39 - 28 * q^41 + 8 * q^43 - 46 * q^45 + 30 * q^47 + 6 * q^49 - 57 * q^51 - 24 * q^53 - 14 * q^55 + 52 * q^57 + q^59 - 14 * q^61 - 47 * q^63 + 38 * q^65 - 66 * q^67 - 7 * q^69 + 33 * q^71 + 29 * q^73 + 55 * q^75 - 27 * q^77 + 17 * q^79 + 38 * q^81 + 23 * q^83 - 56 * q^85 + 86 * q^87 - 19 * q^89 + 13 * q^91 - 30 * q^93 - q^95 - 31 * q^97 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/688\mathbb{Z}\right)^\times$.

$n$	$431$	$433$	$517$
$\chi(n)$	$1$	$e\left(\frac{13}{21}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.528255	−	1.34597i	0.304988	−	0.777097i	−0.693412	−	0.720542i	$-0.743893\pi$
$3$	0.528255	−	1.34597i	0.304988	−	0.777097i	0.998399	−	0.0565549i	$-0.0180116\pi$
$4$		0			0
$5$	0.0684907	+	0.913945i	0.0306300	+	0.408729i	0.991353	+	0.131220i	$0.0418895\pi$
$5$	0.0684907	+	0.913945i	0.0306300	+	0.408729i	−0.960723	+	0.277508i	$0.910491\pi$
$6$		0			0
$7$	0.971539	−	1.68276i	0.367207	−	0.636022i	−0.621920	−	0.783080i	$-0.713647\pi$
$7$	0.971539	−	1.68276i	0.367207	−	0.636022i	0.989128	+	0.147059i	$0.0469806\pi$
$8$		0			0
$9$	0.666571	+	0.618487i	0.222190	+	0.206162i
$10$		0			0
$11$	0.100377	−	0.439781i	0.0302648	−	0.132599i	−0.957539	−	0.288305i	$-0.906908\pi$
$11$	0.100377	−	0.439781i	0.0302648	−	0.132599i	0.987803	+	0.155706i	$0.0497653\pi$
$12$		0			0
$13$	2.90116	−	1.97798i	0.804637	−	0.548592i	−0.0897094	−	0.995968i	$-0.528594\pi$
$13$	2.90116	−	1.97798i	0.804637	−	0.548592i	0.894346	+	0.447376i	$0.147641\pi$
$14$		0			0
$15$	1.26632	+	0.390609i	0.326963	+	0.100855i
$16$		0			0
$17$	0.142476	−	1.90121i	0.0345555	−	0.461111i	−0.952908	−	0.303261i	$-0.901925\pi$
$17$	0.142476	−	1.90121i	0.0345555	−	0.461111i	0.987463	−	0.157850i	$-0.0504563\pi$
$18$		0			0
$19$	−2.97713	+	2.76237i	−0.683000	+	0.633731i	−0.943356	−	0.331781i	$-0.892350\pi$
$19$	−2.97713	+	2.76237i	−0.683000	+	0.633731i	0.260357	+	0.965513i	$0.416160\pi$
$20$		0			0
$21$	−1.75172	−	2.19659i	−0.382257	−	0.479335i
$22$		0			0
$23$	1.77211	−	0.546623i	0.369510	−	0.113979i	−0.104438	−	0.994531i	$-0.533304\pi$
$23$	1.77211	−	0.546623i	0.369510	−	0.113979i	0.473949	+	0.880553i	$0.342828\pi$
$24$		0			0
$25$	4.11355	−	0.620018i	0.822710	−	0.124004i
$26$		0			0
$27$	5.09278	−	2.45255i	0.980106	−	0.471994i
$28$		0			0
$29$	−1.90792	−	4.86129i	−0.354291	−	0.902719i	−0.991271	−	0.131839i	$-0.957912\pi$
$29$	−1.90792	−	4.86129i	−0.354291	−	0.902719i	0.636980	−	0.770880i	$-0.280183\pi$
$30$		0			0
$31$	−0.920034	−	0.138673i	−0.165243	−	0.0249064i	0.0658996	−	0.997826i	$-0.479008\pi$
$31$	−0.920034	−	0.138673i	−0.165243	−	0.0249064i	−0.231143	+	0.972920i	$0.574246\pi$
$32$		0			0
$33$	−0.538908	−	0.367421i	−0.0938118	−	0.0639598i
$34$		0			0
$35$	1.60449	+	0.772681i	0.271208	+	0.130607i
$36$		0			0
$37$	0.277212	+	0.480145i	0.0455734	+	0.0789354i	0.887912	−	0.460013i	$-0.152155\pi$
$37$	0.277212	+	0.480145i	0.0455734	+	0.0789354i	−0.842339	+	0.538948i	$0.818822\pi$
$38$		0			0
$39$	−1.12975	−	4.94975i	−0.180904	−	0.792594i
$40$		0			0
$41$	0.111290	−	0.139553i	0.0173806	−	0.0217945i	−0.773065	−	0.634327i	$-0.781277\pi$
$41$	0.111290	−	0.139553i	0.0173806	−	0.0217945i	0.790446	+	0.612532i	$0.209849\pi$
$42$		0			0
$43$	6.30773	+	1.79236i	0.961920	+	0.273333i
$43$	6.30773	+	1.79236i	0.961920	+	0.273333i
$44$		0			0
$45$	−0.519610	+	0.651570i	−0.0774588	+	0.0971303i
$46$		0			0
$47$	−1.72810	−	7.57131i	−0.252069	−	1.10439i	−0.929506	−	0.368807i	$-0.879766\pi$
$47$	−1.72810	−	7.57131i	−0.252069	−	1.10439i	0.677436	−	0.735581i	$-0.263091\pi$
$48$		0			0
$49$	1.61222	+	2.79245i	0.230317	+	0.398922i
$50$		0			0
$51$	−2.48371	−	1.19609i	−0.347789	−	0.167486i
$52$		0			0
$53$	−8.52328	−	5.81107i	−1.17076	−	0.798212i	−0.187834	−	0.982201i	$-0.560147\pi$
$53$	−8.52328	−	5.81107i	−1.17076	−	0.798212i	−0.982928	+	0.183989i	$0.941099\pi$
$54$		0			0
$55$	0.408811	+	0.0616183i	0.0551240	+	0.00830861i
$56$		0			0
$57$	2.14539	+	5.46636i	0.284164	+	0.724037i
$58$		0			0
$59$	−9.19536	+	4.42825i	−1.19713	+	0.576509i	−0.922857	−	0.385142i	$-0.874152\pi$
$59$	−9.19536	+	4.42825i	−1.19713	+	0.576509i	−0.274276	+	0.961651i	$0.588438\pi$
$60$		0			0
$61$	−5.55516	+	0.837306i	−0.711266	+	0.107206i	−0.494702	−	0.869063i	$-0.664723\pi$
$61$	−5.55516	+	0.837306i	−0.711266	+	0.107206i	−0.216563	+	0.976269i	$0.569485\pi$
$62$		0			0
$63$	1.68836	−	0.520791i	0.212714	−	0.0656135i
$64$		0			0
$65$	2.00646	+	2.51603i	0.248871	+	0.312075i
$66$		0			0
$67$	0.807046	−	0.748830i	0.0985964	−	0.0914841i	−0.629335	−	0.777134i	$-0.716673\pi$
$67$	0.807046	−	0.748830i	0.0985964	−	0.0914841i	0.727931	+	0.685650i	$0.240482\pi$
$68$		0			0
$69$	0.200386	−	2.67396i	0.0241236	−	0.321907i
$70$		0			0
$71$	5.41606	+	1.67063i	0.642768	+	0.198268i	0.598968	−	0.800773i	$-0.295578\pi$
$71$	5.41606	+	1.67063i	0.642768	+	0.198268i	0.0437996	+	0.999040i	$0.486054\pi$
$72$		0			0
$73$	11.7207	−	7.99101i	1.37180	−	0.935277i	0.371823	−	0.928304i	$-0.378733\pi$
$73$	11.7207	−	7.99101i	1.37180	−	0.935277i	0.999976	−	0.00697295i	$-0.00221958\pi$
$74$		0			0
$75$	1.33848	−	5.86425i	0.154554	−	0.677145i
$76$		0			0
$77$	−0.642524	−	0.596175i	−0.0732224	−	0.0679404i
$78$		0			0
$79$	−1.13115	+	1.95921i	−0.127264	+	0.220429i	−0.922616	−	0.385720i	$-0.873953\pi$
$79$	−1.13115	+	1.95921i	−0.127264	+	0.220429i	0.795351	+	0.606149i	$0.207286\pi$
$80$		0			0
$81$	−0.406922	−	5.43000i	−0.0452136	−	0.603334i
$82$		0			0
$83$	−5.11608	+	13.0356i	−0.561563	+	1.43084i	0.314786	+	0.949163i	$0.398067\pi$
$83$	−5.11608	+	13.0356i	−0.561563	+	1.43084i	−0.876349	+	0.481676i	$0.840028\pi$
$84$		0			0
$85$	1.74736			0.189528
$86$		0			0
$87$	−7.55102			−0.809554
$88$		0			0
$89$	0.143414	−	0.365414i	0.0152019	−	0.0387338i	−0.923071	−	0.384629i	$-0.874329\pi$
$89$	0.143414	−	0.365414i	0.0152019	−	0.0387338i	0.938273	+	0.345895i	$0.112425\pi$
$90$		0			0
$91$	−0.509861	−	6.80362i	−0.0534480	−	0.713213i
$92$		0			0
$93$	−0.672662	+	1.16508i	−0.0697518	+	0.120814i
$94$		0			0
$95$	−2.72856	−	2.53173i	−0.279944	−	0.259750i
$96$		0			0
$97$	−3.76302	+	16.4869i	−0.382077	+	1.67399i	0.308885	+	0.951099i	$0.400044\pi$
$97$	−3.76302	+	16.4869i	−0.382077	+	1.67399i	−0.690963	+	0.722891i	$0.742813\pi$
$98$		0			0
$99$	0.338908	−	0.231063i	0.0340615	−	0.0232227i
$100$		0			0
$101$	5.90279	+	1.82077i	0.587349	+	0.181173i	0.574165	−	0.818740i	$-0.305327\pi$
$101$	5.90279	+	1.82077i	0.587349	+	0.181173i	0.0131846	+	0.999913i	$0.495803\pi$
$102$		0			0
$103$	−0.712752	+	9.51101i	−0.0702295	+	0.937148i	0.845143	+	0.534540i	$0.179515\pi$
$103$	−0.712752	+	9.51101i	−0.0702295	+	0.937148i	−0.915373	+	0.402608i	$0.868104\pi$
$104$		0			0
$105$	1.88758	−	1.75142i	0.184209	−	0.170921i
$106$		0			0
$107$	2.82868	+	3.54705i	0.273459	+	0.342906i	0.899530	−	0.436860i	$-0.143909\pi$
$107$	2.82868	+	3.54705i	0.273459	+	0.342906i	−0.626071	+	0.779766i	$0.715338\pi$
$108$		0			0
$109$	−15.3056	+	4.72117i	−1.46601	+	0.452206i	−0.922106	−	0.386939i	$-0.873533\pi$
$109$	−15.3056	+	4.72117i	−1.46601	+	0.452206i	−0.543909	+	0.839144i	$0.683056\pi$
$110$		0			0
$111$	0.792700	−	0.119480i	0.0752398	−	0.0113406i
$112$		0			0
$113$	−11.7135	+	5.64091i	−1.10191	+	0.530652i	−0.894258	−	0.447551i	$-0.852296\pi$
$113$	−11.7135	+	5.64091i	−1.10191	+	0.530652i	−0.207652	+	0.978203i	$0.566582\pi$
$114$		0			0
$115$	0.620957	+	1.58217i	0.0579045	+	0.147538i
$116$		0			0
$117$	3.15718	+	0.475869i	0.291882	+	0.0439941i
$118$		0			0
$119$	−3.06085	−	2.08685i	−0.280588	−	0.191301i
$120$		0			0
$121$	9.72733	+	4.68443i	0.884302	+	0.425858i
$122$		0			0
$123$	−0.129045	−	0.223513i	−0.0116356	−	0.0201535i
$124$		0			0
$125$	1.86811	+	8.18474i	0.167089	+	0.732065i
$126$		0			0
$127$	8.20396	−	10.2874i	0.727983	−	0.912862i	−0.270777	−	0.962642i	$-0.587281\pi$
$127$	8.20396	−	10.2874i	0.727983	−	0.912862i	0.998760	+	0.0497798i	$0.0158520\pi$
$128$		0			0
$129$	5.74456	−	7.54319i	0.505780	−	0.664141i
$130$		0			0
$131$	−1.89745	+	2.37933i	−0.165781	+	0.207883i	−0.857782	−	0.514014i	$-0.828158\pi$
$131$	−1.89745	+	2.37933i	−0.165781	+	0.207883i	0.692001	+	0.721897i	$0.256729\pi$
$132$		0			0
$133$	1.75600	+	7.69353i	0.152264	+	0.667113i
$134$		0			0
$135$	2.59031	+	4.48654i	0.222938	+	0.386140i
$136$		0			0
$137$	10.9381	+	5.26750i	0.934503	+	0.450033i	0.838227	−	0.545322i	$-0.183593\pi$
$137$	10.9381	+	5.26750i	0.934503	+	0.450033i	0.0962759	+	0.995355i	$0.469307\pi$
$138$		0			0
$139$	3.71295	+	2.53144i	0.314928	+	0.214714i	0.710459	−	0.703738i	$-0.248487\pi$
$139$	3.71295	+	2.53144i	0.314928	+	0.214714i	−0.395531	+	0.918452i	$0.629440\pi$
$140$		0			0
$141$	−11.1036	−	1.67360i	−0.935095	−	0.140943i
$142$		0			0
$143$	−0.578666	−	1.47442i	−0.0483905	−	0.123297i
$144$		0			0
$145$	4.31228	−	2.07668i	0.358115	−	0.172459i
$146$		0			0
$147$	4.61022	−	0.694879i	0.380245	−	0.0573127i
$148$		0			0
$149$	−8.97878	+	2.76959i	−0.735571	+	0.226893i	−0.639834	−	0.768513i	$-0.720997\pi$
$149$	−8.97878	+	2.76959i	−0.735571	+	0.226893i	−0.0957367	+	0.995407i	$0.530521\pi$
$150$		0			0
$151$	5.17636	+	6.49094i	0.421246	+	0.528226i	0.946493	−	0.322724i	$-0.104599\pi$
$151$	5.17636	+	6.49094i	0.421246	+	0.528226i	−0.525247	+	0.850950i	$0.676027\pi$
$152$		0			0
$153$	1.27084	−	1.17917i	0.102742	−	0.0953303i
$154$		0			0
$155$	0.0637256	−	0.850359i	0.00511856	−	0.0683025i
$156$		0			0
$157$	−9.31783	−	2.87417i	−0.743644	−	0.229384i	−0.100296	−	0.994958i	$-0.531979\pi$
$157$	−9.31783	−	2.87417i	−0.743644	−	0.229384i	−0.643348	+	0.765574i	$0.722455\pi$
$158$		0			0
$159$	−12.3240	+	8.40236i	−0.977356	+	0.666350i
$160$		0			0
$161$	0.801841	−	3.51309i	0.0631939	−	0.276871i
$162$		0			0
$163$	1.63792	+	1.51977i	0.128292	+	0.119037i	0.741709	−	0.670721i	$-0.234015\pi$
$163$	1.63792	+	1.51977i	0.128292	+	0.119037i	−0.613418	+	0.789759i	$0.710206\pi$
$164$		0			0
$165$	0.298893	−	0.517697i	0.0232687	−	0.0403027i
$166$		0			0
$167$	1.74279	+	23.2559i	0.134861	+	1.79959i	0.497292	+	0.867583i	$0.334328\pi$
$167$	1.74279	+	23.2559i	0.134861	+	1.79959i	−0.362431	+	0.932011i	$0.618053\pi$
$168$		0			0
$169$	−0.245104	+	0.624515i	−0.0188542	+	0.0480396i
$170$		0			0
$171$	−3.69296			−0.282407
$172$		0			0
$173$	−1.53451			−0.116666			−0.0583332	−	0.998297i	$-0.518579\pi$
$173$	−1.53451			−0.116666			−0.0583332	+	0.998297i	$0.518579\pi$
$174$		0			0
$175$	2.95314	−	7.52447i	0.223236	−	0.568797i
$176$		0			0
$177$	1.10281	+	14.7159i	0.0828920	+	1.10612i
$178$		0			0
$179$	−3.26451	+	5.65429i	−0.244001	+	0.422621i	−0.961850	−	0.273577i	$-0.911793\pi$
$179$	−3.26451	+	5.65429i	−0.244001	+	0.422621i	0.717850	+	0.696198i	$0.245127\pi$
$180$		0			0
$181$	−13.9680	−	12.9604i	−1.03823	−	0.963336i	−0.0388746	−	0.999244i	$-0.512377\pi$
$181$	−13.9680	−	12.9604i	−1.03823	−	0.963336i	−0.999355	+	0.0359077i	$0.988568\pi$
$182$		0			0
$183$	−1.80755	+	7.91940i	−0.133618	+	0.585419i
$184$		0			0
$185$	−0.419840	+	0.286242i	−0.0308672	+	0.0210449i
$186$		0			0
$187$	−0.821814	−	0.253496i	−0.0600970	−	0.0185375i
$188$		0			0
$189$	0.820788	−	10.9527i	0.0597035	−	0.796688i
$190$		0			0
$191$	−11.7580	+	10.9099i	−0.850781	+	0.789410i	−0.979325	−	0.202294i	$-0.935160\pi$
$191$	−11.7580	+	10.9099i	−0.850781	+	0.789410i	0.128544	+	0.991704i	$0.458970\pi$
$192$		0			0
$193$	−3.90963	−	4.90253i	−0.281422	−	0.352892i	0.620950	−	0.783850i	$-0.286747\pi$
$193$	−3.90963	−	4.90253i	−0.281422	−	0.352892i	−0.902372	+	0.430959i	$0.858176\pi$
$194$		0			0
$195$	4.44642	−	1.37154i	0.318415	−	0.0982180i
$196$		0			0
$197$	−10.7637	+	1.62237i	−0.766884	+	0.115589i	−0.520822	−	0.853665i	$-0.674375\pi$
$197$	−10.7637	+	1.62237i	−0.766884	+	0.115589i	−0.246062	+	0.969254i	$0.579137\pi$
$198$		0			0
$199$	−4.32905	+	2.08476i	−0.306878	+	0.147785i	−0.580984	−	0.813915i	$-0.697332\pi$
$199$	−4.32905	+	2.08476i	−0.306878	+	0.147785i	0.274106	+	0.961699i	$0.411618\pi$
$200$		0			0
$201$	−0.581577	−	1.48183i	−0.0410213	−	0.104520i
$202$		0			0
$203$	−10.0340	−	1.51238i	−0.704247	−	0.106148i
$204$		0			0
$205$	0.135166	+	0.0921548i	0.00944042	+	0.00643637i
$206$		0			0
$207$	1.51932	+	0.731664i	0.105600	+	0.0508542i
$208$		0			0
$209$	0.916002	+	1.58656i	0.0633612	+	0.109745i
$210$		0			0
$211$	−4.43696	−	19.4396i	−0.305453	−	1.33828i	−0.861766	−	0.507305i	$-0.830642\pi$
$211$	−4.43696	−	19.4396i	−0.305453	−	1.33828i	0.556313	−	0.830973i	$-0.312215\pi$
$212$		0			0
$213$	5.10968	−	6.40734i	0.350110	−	0.439024i
$214$		0			0
$215$	−1.20610	+	5.88768i	−0.0822554	+	0.401536i
$216$		0			0
$217$	−1.12720	+	1.41347i	−0.0765195	+	0.0959524i
$218$		0			0
$219$	−4.56417	−	19.9969i	−0.308418	−	1.35127i
$220$		0			0
$221$	−3.34720	−	5.79752i	−0.225157	−	0.389983i
$222$		0			0
$223$	−1.34141	−	0.645989i	−0.0898274	−	0.0432586i	0.388431	−	0.921478i	$-0.373017\pi$
$223$	−1.34141	−	0.645989i	−0.0898274	−	0.0432586i	−0.478258	+	0.878219i	$0.658732\pi$
$224$		0			0
$225$	3.12545	+	2.13089i	0.208363	+	0.142060i
$226$		0			0
$227$	−24.3967	−	3.67721i	−1.61927	−	0.244065i	−0.724067	−	0.689730i	$-0.757729\pi$
$227$	−24.3967	−	3.67721i	−1.61927	−	0.244065i	−0.895200	+	0.445665i	$0.852967\pi$
$228$		0			0
$229$	5.63673	+	14.3622i	0.372486	+	0.949078i	0.987079	+	0.160234i	$0.0512248\pi$
$229$	5.63673	+	14.3622i	0.372486	+	0.949078i	−0.614594	+	0.788844i	$0.710680\pi$
$230$		0			0
$231$	−1.14185	+	0.549886i	−0.0751282	+	0.0361798i
$232$		0			0
$233$	−20.2723	+	3.05556i	−1.32808	+	0.200176i	−0.774476	−	0.632603i	$-0.781987\pi$
$233$	−20.2723	+	3.05556i	−1.32808	+	0.200176i	−0.553606	+	0.832779i	$0.686749\pi$
$234$		0			0
$235$	6.80140	−	2.09795i	0.443674	−	0.136855i
$236$		0			0
$237$	2.03951	+	2.55746i	0.132480	+	0.166125i
$238$		0			0
$239$	9.45056	−	8.76884i	0.611306	−	0.567209i	−0.312573	−	0.949894i	$-0.601191\pi$
$239$	9.45056	−	8.76884i	0.611306	−	0.567209i	0.923879	+	0.382685i	$0.125000\pi$
$240$		0			0
$241$	−0.568011	+	7.57957i	−0.0365888	+	0.488243i	0.948567	+	0.316578i	$0.102534\pi$
$241$	−0.568011	+	7.57957i	−0.0365888	+	0.488243i	−0.985155	+	0.171665i	$0.945085\pi$
$242$		0			0
$243$	8.68070	+	2.67764i	0.556867	+	0.171771i
$244$		0			0
$245$	−2.44172	+	1.66474i	−0.155996	+	0.106356i
$246$		0			0
$247$	−3.17321	+	13.9028i	−0.201907	+	0.884611i
$248$		0			0
$249$	14.8429	+	13.7722i	0.940630	+	0.872777i
$250$		0			0
$251$	7.99653	−	13.8504i	0.504736	−	0.874229i	−0.495249	−	0.868751i	$-0.664923\pi$
$251$	7.99653	−	13.8504i	0.504736	−	0.874229i	0.999985	−	0.00547772i	$-0.00174362\pi$
$252$		0			0
$253$	−0.0625153	−	0.834208i	−0.00393030	−	0.0524462i
$254$		0			0
$255$	0.923050	−	2.35189i	0.0578036	−	0.147281i
$256$		0			0
$257$	−2.70015			−0.168431			−0.0842154	−	0.996448i	$-0.526838\pi$
$257$	−2.70015			−0.168431			−0.0842154	+	0.996448i	$0.526838\pi$
$258$		0			0
$259$	1.07729			0.0669395
$260$		0			0
$261$	1.73489	−	4.42042i	0.107387	−	0.273617i
$262$		0			0
$263$	−1.38065	−	18.4235i	−0.0851345	−	1.13604i	−0.862182	−	0.506599i	$-0.830903\pi$
$263$	−1.38065	−	18.4235i	−0.0851345	−	1.13604i	0.777048	−	0.629442i	$-0.216716\pi$
$264$		0			0
$265$	4.72723	−	8.18781i	0.290392	−	0.502973i
$266$		0			0
$267$	−0.416077	−	0.386063i	−0.0254635	−	0.0236267i
$268$		0			0
$269$	−2.87587	+	12.6000i	−0.175345	+	0.768236i	0.808395	+	0.588640i	$0.200336\pi$
$269$	−2.87587	+	12.6000i	−0.175345	+	0.768236i	−0.983740	+	0.179596i	$0.942521\pi$
$270$		0			0
$271$	12.7456	−	8.68981i	0.774240	−	0.527868i	−0.110543	−	0.993871i	$-0.535259\pi$
$271$	12.7456	−	8.68981i	0.774240	−	0.527868i	0.884783	+	0.466003i	$0.154306\pi$
$272$		0			0
$273$	−9.42681	−	2.90779i	−0.570537	−	0.175987i
$274$		0			0
$275$	0.140234	−	1.87130i	0.00845645	−	0.112843i
$276$		0			0
$277$	17.5390	−	16.2738i	1.05382	−	0.977798i	0.0540310	−	0.998539i	$-0.482793\pi$
$277$	17.5390	−	16.2738i	1.05382	−	0.977798i	0.999785	+	0.0207410i	$0.00660253\pi$
$278$		0			0
$279$	−0.527501	−	0.661465i	−0.0315806	−	0.0396009i
$280$		0			0
$281$	9.50488	−	2.93187i	0.567013	−	0.174900i	0.00202302	−	0.999998i	$-0.499356\pi$
$281$	9.50488	−	2.93187i	0.567013	−	0.174900i	0.564990	+	0.825097i	$0.308880\pi$
$282$		0			0
$283$	−13.7960	+	2.07941i	−0.820084	+	0.123608i	−0.545666	−	0.838003i	$-0.683723\pi$
$283$	−13.7960	+	2.07941i	−0.820084	+	0.123608i	−0.274418	+	0.961610i	$0.588485\pi$
$284$		0			0
$285$	−4.84901	+	2.33516i	−0.287231	+	0.138323i
$286$		0			0
$287$	−0.126711	−	0.322855i	−0.00747953	−	0.0190575i
$288$		0			0
$289$	13.2158	+	1.99197i	0.777402	+	0.117174i
$290$		0			0
$291$	20.2030	+	13.7742i	1.18432	+	0.807458i
$292$		0			0
$293$	15.4513	+	7.44096i	0.902676	+	0.434706i	0.826855	−	0.562416i	$-0.190128\pi$
$293$	15.4513	+	7.44096i	0.902676	+	0.434706i	0.0758211	+	0.997121i	$0.475842\pi$
$294$		0			0
$295$	−4.67697	−	8.10076i	−0.272304	−	0.471644i
$296$		0			0
$297$	−0.567388	−	2.48589i	−0.0329232	−	0.144246i
$298$		0			0
$299$	4.05996	−	5.09103i	0.234794	−	0.294422i
$300$		0			0
$301$	9.14432	−	8.87301i	0.527070	−	0.511432i
$302$		0			0
$303$	5.56888	−	6.98315i	0.319924	−	0.401172i
$304$		0			0
$305$	−1.14573	−	5.01977i	−0.0656042	−	0.287431i
$306$		0			0
$307$	10.5428	+	18.2606i	0.601707	+	1.04219i	0.992563	+	0.121736i	$0.0388460\pi$
$307$	10.5428	+	18.2606i	0.601707	+	1.04219i	−0.390855	+	0.920452i	$0.627821\pi$
$308$		0			0
$309$	12.4250	+	5.98358i	0.706835	+	0.340394i
$310$		0			0
$311$	−5.32355	−	3.62953i	−0.301871	−	0.205812i	0.402906	−	0.915242i	$-0.368000\pi$
$311$	−5.32355	−	3.62953i	−0.301871	−	0.205812i	−0.704776	+	0.709430i	$0.748953\pi$
$312$		0			0
$313$	−6.81682	−	1.02747i	−0.385310	−	0.0580761i	−0.0464687	−	0.998920i	$-0.514797\pi$
$313$	−6.81682	−	1.02747i	−0.385310	−	0.0580761i	−0.338841	+	0.940844i	$0.610035\pi$
$314$		0			0
$315$	0.591612	+	1.50740i	0.0333335	+	0.0849325i
$316$		0			0
$317$	−1.03153	+	0.496760i	−0.0579367	+	0.0279008i	−0.462628	−	0.886553i	$-0.653093\pi$
$317$	−1.03153	+	0.496760i	−0.0579367	+	0.0279008i	0.404691	+	0.914453i	$0.367379\pi$
$318$		0			0
$319$	−2.32941	+	0.351103i	−0.130422	+	0.0196580i
$320$		0			0
$321$	6.26849	−	1.93357i	0.349873	−	0.107922i
$322$		0			0
$323$	4.82767	+	6.05371i	0.268619	+	0.336837i
$324$		0			0
$325$	10.7077	−	9.93527i	0.593955	−	0.551110i
$326$		0			0
$327$	−1.73073	+	23.0949i	−0.0957093	+	1.27715i
$328$		0			0
$329$	−14.4196	−	4.44785i	−0.794977	−	0.245218i
$330$		0			0
$331$	8.16250	−	5.56510i	0.448651	−	0.305885i	−0.317835	−	0.948146i	$-0.602956\pi$
$331$	8.16250	−	5.56510i	0.448651	−	0.305885i	0.766486	+	0.642261i	$0.222003\pi$
$332$		0			0
$333$	−0.112182	+	0.491503i	−0.00614755	+	0.0269342i
$334$		0			0
$335$	0.739664	+	0.686308i	0.0404122	+	0.0374970i
$336$		0			0
$337$	11.5821	−	20.0608i	0.630919	−	1.09278i	−0.356445	−	0.934316i	$-0.616011\pi$
$337$	11.5821	−	20.0608i	0.630919	−	1.09278i	0.987364	−	0.158468i	$-0.0506554\pi$
$338$		0			0
$339$	1.40480	+	18.7458i	0.0762985	+	1.01813i
$340$		0			0
$341$	−0.153336	+	0.390694i	−0.00830362	+	0.0211573i
$342$		0			0
$343$	19.8669			1.07271
$344$		0			0
$345$	2.45758			0.132312
$346$		0			0
$347$	6.10329	−	15.5509i	0.327642	−	0.834818i	−0.668222	−	0.743962i	$-0.732944\pi$
$347$	6.10329	−	15.5509i	0.327642	−	0.834818i	0.995864	−	0.0908560i	$-0.0289603\pi$
$348$		0			0
$349$	−1.53538	−	20.4883i	−0.0821871	−	1.09671i	−0.873993	−	0.485938i	$-0.838478\pi$
$349$	−1.53538	−	20.4883i	−0.0821871	−	1.09671i	0.791806	−	0.610773i	$-0.209141\pi$
$350$		0			0
$351$	9.92386	−	17.1886i	0.529697	−	0.917461i
$352$		0			0
$353$	−7.38749	−	6.85459i	−0.393196	−	0.364833i	0.458657	−	0.888613i	$-0.348331\pi$
$353$	−7.38749	−	6.85459i	−0.393196	−	0.364833i	−0.851853	+	0.523781i	$0.824521\pi$
$354$		0			0
$355$	−1.15592	+	5.06440i	−0.0613497	+	0.268791i
$356$		0			0
$357$	−4.42575	+	3.01742i	−0.234235	+	0.159699i
$358$		0			0
$359$	−14.5648	−	4.49265i	−0.768701	−	0.237113i	−0.114489	−	0.993424i	$-0.536523\pi$
$359$	−14.5648	−	4.49265i	−0.768701	−	0.237113i	−0.654211	+	0.756312i	$0.726999\pi$
$360$		0			0
$361$	−0.187276	+	2.49903i	−0.00985663	+	0.131528i
$362$		0			0
$363$	11.4436	−	10.6181i	0.600634	−	0.557307i
$364$		0			0
$365$	8.10610	+	10.1647i	0.424292	+	0.532046i
$366$		0			0
$367$	11.2654	−	3.47491i	0.588047	−	0.181389i	0.0135684	−	0.999908i	$-0.495681\pi$
$367$	11.2654	−	3.47491i	0.588047	−	0.181389i	0.574479	+	0.818519i	$0.305205\pi$
$368$		0			0
$369$	0.160495	−	0.0241907i	0.00835501	−	0.00125932i
$370$		0			0
$371$	−18.0593	+	8.69691i	−0.937593	+	0.451521i
$372$		0			0
$373$	−4.44434	−	11.3240i	−0.230119	−	0.586335i	0.768444	−	0.639917i	$-0.221031\pi$
$373$	−4.44434	−	11.3240i	−0.230119	−	0.586335i	−0.998563	+	0.0535823i	$0.982936\pi$
$374$		0			0
$375$	12.0033	+	1.80920i	0.619846	+	0.0934267i
$376$		0			0
$377$	−15.1507	−	10.3296i	−0.780300	−	0.531999i
$378$		0			0
$379$	−7.27433	−	3.50313i	−0.373657	−	0.179944i	0.237624	−	0.971357i	$-0.423631\pi$
$379$	−7.27433	−	3.50313i	−0.373657	−	0.179944i	−0.611281	+	0.791413i	$0.709346\pi$
$380$		0			0
$381$	−9.51281	−	16.4767i	−0.487356	−	0.844125i
$382$		0			0
$383$	−5.78751	−	25.3567i	−0.295728	−	1.29567i	−0.876421	−	0.481546i	$-0.840075\pi$
$383$	−5.78751	−	25.3567i	−0.295728	−	1.29567i	0.580693	−	0.814123i	$-0.302782\pi$
$384$		0			0
$385$	0.500864	−	0.628064i	0.0255264	−	0.0320091i
$386$		0			0
$387$	3.09599	+	5.09599i	0.157378	+	0.259044i
$388$		0			0
$389$	−2.28337	+	2.86325i	−0.115771	+	0.145173i	−0.836340	−	0.548211i	$-0.815309\pi$
$389$	−2.28337	+	2.86325i	−0.115771	+	0.145173i	0.720569	+	0.693383i	$0.243881\pi$
$390$		0			0
$391$	−0.786762	−	3.44703i	−0.0397883	−	0.174324i
$392$		0			0
$393$	2.20017	+	3.81080i	0.110984	+	0.192230i
$394$		0			0
$395$	−1.86809	−	0.899623i	−0.0939936	−	0.0452649i
$396$		0			0
$397$	21.5184	+	14.6710i	1.07998	+	0.736315i	0.966356	−	0.257209i	$-0.0828028\pi$
$397$	21.5184	+	14.6710i	1.07998	+	0.736315i	0.113620	+	0.993524i	$0.463755\pi$
$398$		0			0
$399$	11.2829	+	1.70062i	0.564850	+	0.0851375i
$400$		0			0
$401$	−5.05268	−	12.8740i	−0.252319	−	0.642897i	0.747452	−	0.664316i	$-0.231277\pi$
$401$	−5.05268	−	12.8740i	−0.252319	−	0.642897i	−0.999771	+	0.0214185i	$0.993182\pi$
$402$		0			0
$403$	−2.94346	+	1.41749i	−0.146624	+	0.0706104i
$404$		0			0
$405$	4.93485	−	0.743809i	0.245215	−	0.0369602i
$406$		0			0
$407$	0.238984	−	0.0737170i	0.0118460	−	0.00365401i
$408$		0			0
$409$	4.23419	+	5.30951i	0.209367	+	0.262538i	0.875416	−	0.483370i	$-0.160587\pi$
$409$	4.23419	+	5.30951i	0.209367	+	0.262538i	−0.666049	+	0.745908i	$0.732016\pi$
$410$		0			0
$411$	12.8680	−	11.9397i	0.634731	−	0.588944i
$412$		0			0
$413$	−1.48199	+	19.7758i	−0.0729239	+	0.973101i
$414$		0			0
$415$	−12.2642	−	3.78300i	−0.602026	−	0.185700i
$416$		0			0
$417$	5.36863	−	3.66027i	0.262903	−	0.179244i
$418$		0			0
$419$	−2.65456	+	11.6304i	−0.129684	+	0.568181i	0.867776	+	0.496955i	$0.165549\pi$
$419$	−2.65456	+	11.6304i	−0.129684	+	0.568181i	−0.997460	+	0.0712267i	$0.977309\pi$
$420$		0			0
$421$	−5.95716	−	5.52743i	−0.290334	−	0.269391i	0.521535	−	0.853230i	$-0.325359\pi$
$421$	−5.95716	−	5.52743i	−0.290334	−	0.269391i	−0.811869	+	0.583839i	$0.801550\pi$
$422$		0			0
$423$	3.53086	−	6.11562i	0.171676	−	0.297352i
$424$		0			0
$425$	−0.592702	−	7.90905i	−0.0287502	−	0.383645i
$426$		0			0
$427$	−3.98808	+	10.1615i	−0.192997	+	0.491747i
$428$		0			0
$429$	−2.29021			−0.110572
$430$		0			0
$431$	13.4125			0.646056			0.323028	−	0.946389i	$-0.395299\pi$
$431$	13.4125			0.646056			0.323028	+	0.946389i	$0.395299\pi$
$432$		0			0
$433$	3.83290	−	9.76607i	0.184197	−	0.469327i	−0.808711	−	0.588206i	$-0.799835\pi$
$433$	3.83290	−	9.76607i	0.184197	−	0.469327i	0.992909	+	0.118878i	$0.0379298\pi$
$434$		0			0
$435$	−0.517175	−	6.90122i	−0.0247966	−	0.330888i
$436$		0			0
$437$	−3.76582	+	6.52259i	−0.180143	+	0.312018i
$438$		0			0
$439$	−17.6465	−	16.3735i	−0.842220	−	0.781466i	0.135633	−	0.990759i	$-0.456693\pi$
$439$	−17.6465	−	16.3735i	−0.842220	−	0.781466i	−0.977853	+	0.209293i	$0.932884\pi$
$440$		0			0
$441$	−0.652435	+	2.85851i	−0.0310683	+	0.136119i
$442$		0			0
$443$	14.5647	−	9.93004i	0.691990	−	0.471791i	−0.165555	−	0.986201i	$-0.552941\pi$
$443$	14.5647	−	9.93004i	0.691990	−	0.471791i	0.857544	+	0.514410i	$0.171989\pi$
$444$		0			0
$445$	0.343791	+	0.106045i	0.0162972	+	0.00502704i
$446$		0			0
$447$	−1.01530	+	13.5482i	−0.0480220	+	0.640809i
$448$		0			0
$449$	−16.9841	+	15.7590i	−0.801531	+	0.743712i	−0.970290	−	0.241945i	$-0.922214\pi$
$449$	−16.9841	+	15.7590i	−0.801531	+	0.743712i	0.168759	+	0.985657i	$0.446024\pi$
$450$		0			0
$451$	−0.0502019	−	0.0629512i	−0.00236391	−	0.00296425i
$452$		0			0
$453$	11.4711	−	3.53835i	0.538957	−	0.166246i
$454$		0			0
$455$	6.18322	−	0.931970i	0.289874	−	0.0436914i
$456$		0			0
$457$	−20.4097	+	9.82881i	−0.954727	+	0.459772i	−0.845341	−	0.534227i	$-0.820603\pi$
$457$	−20.4097	+	9.82881i	−0.954727	+	0.459772i	−0.109386	+	0.993999i	$0.534889\pi$
$458$		0			0
$459$	−3.93722	−	10.0319i	−0.183773	−	0.468247i
$460$		0			0
$461$	27.2692	+	4.11018i	1.27006	+	0.191430i	0.749274	−	0.662260i	$-0.230403\pi$
$461$	27.2692	+	4.11018i	1.27006	+	0.191430i	0.520781	+	0.853690i	$0.325641\pi$
$462$		0			0
$463$	−8.81026	−	6.00673i	−0.409447	−	0.279156i	0.341030	−	0.940052i	$-0.389224\pi$
$463$	−8.81026	−	6.00673i	−0.409447	−	0.279156i	−0.750478	+	0.660896i	$0.770177\pi$
$464$		0			0
$465$	−1.11089	−	0.534979i	−0.0515165	−	0.0248090i
$466$		0			0
$467$	2.52919	+	4.38068i	0.117037	+	0.202714i	0.918592	−	0.395207i	$-0.129327\pi$
$467$	2.52919	+	4.38068i	0.117037	+	0.202714i	−0.801555	+	0.597921i	$0.795994\pi$
$468$		0			0
$469$	−0.476020	−	2.08558i	−0.0219806	−	0.0963031i
$470$		0			0
$471$	−8.79074	+	11.0232i	−0.405056	+	0.507924i
$472$		0			0
$473$	1.42140	−	2.59411i	0.0653560	−	0.119277i
$474$		0			0
$475$	−10.5338	+	13.2090i	−0.483326	+	0.606071i
$476$		0			0
$477$	−2.08729	−	9.14503i	−0.0955706	−	0.418722i
$478$		0			0
$479$	−17.3338	−	30.0230i	−0.792001	−	1.37179i	−0.924726	−	0.380633i	$-0.875706\pi$
$479$	−17.3338	−	30.0230i	−0.792001	−	1.37179i	0.132726	−	0.991153i	$-0.457627\pi$
$480$		0			0
$481$	1.75395	+	0.844659i	0.0799733	+	0.0385131i
$482$		0			0
$483$	−4.30495	−	2.93506i	−0.195882	−	0.133550i
$484$		0			0
$485$	−15.3258	−	2.31000i	−0.695911	−	0.104892i
$486$		0			0
$487$	8.75751	+	22.3138i	0.396841	+	1.01113i	0.980039	+	0.198804i	$0.0637057\pi$
$487$	8.75751	+	22.3138i	0.396841	+	1.01113i	−0.583199	+	0.812330i	$0.698199\pi$
$488$		0			0
$489$	2.91080	−	1.40177i	0.131631	−	0.0633901i
$490$		0			0
$491$	−2.48484	+	0.374530i	−0.112139	+	0.0169023i	−0.204872	−	0.978789i	$-0.565678\pi$
$491$	−2.48484	+	0.374530i	−0.112139	+	0.0169023i	0.0927327	+	0.995691i	$0.470440\pi$
$492$		0			0
$493$	−9.51415	+	2.93473i	−0.428496	+	0.132174i
$494$		0			0
$495$	0.234391	+	0.293917i	0.0105351	+	0.0132106i
$496$		0			0
$497$	8.07318	−	7.49082i	0.362132	−	0.336009i
$498$		0			0
$499$	−1.13941	+	15.2043i	−0.0510068	+	0.680638i	0.911832	+	0.410563i	$0.134668\pi$
$499$	−1.13941	+	15.2043i	−0.0510068	+	0.680638i	−0.962839	+	0.270076i	$0.912951\pi$
$500$		0			0
$501$	32.2224	+	9.93928i	1.43959	+	0.444054i
$502$		0			0
$503$	−1.84862	+	1.26037i	−0.0824261	+	0.0561971i	−0.603832	−	0.797112i	$-0.706360\pi$
$503$	−1.84862	+	1.26037i	−0.0824261	+	0.0561971i	0.521406	+	0.853309i	$0.325408\pi$
$504$		0			0
$505$	−1.25980	+	5.51953i	−0.0560602	+	0.245616i
$506$		0			0
$507$	0.711102	+	0.659806i	0.0315811	+	0.0293030i
$508$		0			0
$509$	−17.6153	+	30.5107i	−0.780786	+	1.35236i	0.150698	+	0.988580i	$0.451848\pi$
$509$	−17.6153	+	30.5107i	−0.780786	+	1.35236i	−0.931484	+	0.363782i	$0.881485\pi$
$510$		0			0
$511$	−2.05983	−	27.4866i	−0.0911217	−	1.21593i
$512$		0			0
$513$	−8.38699	+	21.3697i	−0.370294	+	0.943495i
$514$		0			0
$515$	−8.74136			−0.385190
$516$		0			0
$517$	−3.50318			−0.154070
$518$		0			0
$519$	−0.810611	+	2.06540i	−0.0355819	+	0.0906611i
$520$		0			0
$521$	−3.20580	−	42.7785i	−0.140449	−	1.87416i	−0.411247	−	0.911524i	$-0.634907\pi$
$521$	−3.20580	−	42.7785i	−0.140449	−	1.87416i	0.270799	−	0.962636i	$-0.412712\pi$
$522$		0			0
$523$	−7.69902	+	13.3351i	−0.336655	+	0.583103i	−0.983801	−	0.179263i	$-0.942629\pi$
$523$	−7.69902	+	13.3351i	−0.336655	+	0.583103i	0.647147	+	0.762366i	$0.275962\pi$
$524$		0			0
$525$	−8.56771	−	7.94967i	−0.373926	−	0.346952i
$526$		0			0
$527$	−0.394729	+	1.72942i	−0.0171947	+	0.0753347i
$528$		0			0
$529$	−16.1619	+	11.0190i	−0.702692	+	0.479087i
$530$		0			0
$531$	−8.86817	−	2.73547i	−0.384846	−	0.118709i
$532$		0			0
$533$	0.0468369	−	0.624995i	0.00202873	−	0.0270715i
$534$		0			0
$535$	−3.04807	+	2.82820i	−0.131780	+	0.122274i
$536$		0			0
$537$	5.88602	+	7.38083i	0.254000	+	0.318507i
$538$		0			0
$539$	1.38990	−	0.428726i	0.0598671	−	0.0184666i
$540$		0			0
$541$	32.2484	−	4.86067i	1.38647	−	0.208976i	0.586952	−	0.809622i	$-0.300328\pi$
$541$	32.2484	−	4.86067i	1.38647	−	0.208976i	0.799516	+	0.600645i	$0.205090\pi$
$542$		0			0
$543$	−24.8229	+	11.9541i	−1.06525	+	0.512999i
$544$		0			0
$545$	−5.36318	−	13.6652i	−0.229733	−	0.585351i
$546$		0			0
$547$	4.56008	+	0.687322i	0.194975	+	0.0293878i	0.245804	−	0.969320i	$-0.420948\pi$
$547$	4.56008	+	0.687322i	0.194975	+	0.0293878i	−0.0508287	+	0.998707i	$0.516186\pi$
$548$		0			0
$549$	−4.22077	−	2.87767i	−0.180138	−	0.122816i
$550$		0			0
$551$	19.1088	+	9.20230i	0.814061	+	0.392031i
$552$		0			0
$553$	2.19792	+	3.80690i	0.0934649	+	0.161886i
$554$		0			0
$555$	0.163491	+	0.716301i	0.00693981	+	0.0304053i
$556$		0			0
$557$	2.71786	−	3.40809i	0.115159	−	0.144405i	−0.720911	−	0.693028i	$-0.756276\pi$
$557$	2.71786	−	3.40809i	0.115159	−	0.144405i	0.836070	+	0.548623i	$0.184848\pi$
$558$		0			0
$559$	21.8450	−	7.27661i	0.923944	−	0.307768i
$560$		0			0
$561$	−0.775325	+	0.972227i	−0.0327343	+	0.0410475i
$562$		0			0
$563$	6.19136	+	27.1261i	0.260935	+	1.14323i	0.920240	+	0.391354i	$0.127993\pi$
$563$	6.19136	+	27.1261i	0.260935	+	1.14323i	−0.659306	+	0.751875i	$0.729150\pi$
$564$		0			0
$565$	−5.95774	−	10.3191i	−0.250644	−	0.434128i
$566$		0			0
$567$	−9.53271	−	4.59071i	−0.400336	−	0.192792i
$568$		0			0
$569$	1.04489	+	0.712395i	0.0438042	+	0.0298652i	0.585024	−	0.811016i	$-0.301085\pi$
$569$	1.04489	+	0.712395i	0.0438042	+	0.0298652i	−0.541220	+	0.840881i	$0.682037\pi$
$570$		0			0
$571$	20.4623	+	3.08420i	0.856322	+	0.129070i	0.562507	−	0.826792i	$-0.309837\pi$
$571$	20.4623	+	3.08420i	0.856322	+	0.129070i	0.293815	+	0.955862i	$0.405075\pi$
$572$		0			0
$573$	8.47312	+	21.5891i	0.353970	+	0.901900i
$574$		0			0
$575$	6.95074	−	3.34730i	0.289866	−	0.139592i
$576$		0			0
$577$	−11.3836	+	1.71580i	−0.473905	+	0.0714297i	−0.381653	−	0.924306i	$-0.624645\pi$
$577$	−11.3836	+	1.71580i	−0.473905	+	0.0714297i	−0.0922528	+	0.995736i	$0.529407\pi$
$578$		0			0
$579$	−8.66394	+	2.67247i	−0.360061	+	0.111064i
$580$		0			0
$581$	16.9652	+	21.2737i	0.703835	+	0.882581i
$582$		0			0
$583$	−3.41114	+	3.16508i	−0.141275	+	0.131084i
$584$		0			0
$585$	−0.218680	+	2.91808i	−0.00904131	+	0.120648i
$586$		0			0
$587$	−29.3343	−	9.04842i	−1.21075	−	0.373468i	−0.377318	−	0.926084i	$-0.623154\pi$
$587$	−29.3343	−	9.04842i	−1.21075	−	0.373468i	−0.833437	+	0.552615i	$0.813630\pi$
$588$		0			0
$589$	3.12212	−	2.12863i	0.128645	−	0.0877086i
$590$		0			0
$591$	−3.50233	+	15.3447i	−0.144066	+	0.631196i
$592$		0			0
$593$	−2.70312	−	2.50813i	−0.111004	−	0.102997i	0.622718	−	0.782446i	$-0.286028\pi$
$593$	−2.70312	−	2.50813i	−0.111004	−	0.102997i	−0.733722	+	0.679449i	$0.762219\pi$
$594$		0			0
$595$	1.69763	−	2.94038i	0.0695959	−	0.120544i
$596$		0			0
$597$	0.519186	+	6.92805i	0.0212489	+	0.283546i
$598$		0			0
$599$	−11.9286	+	30.3935i	−0.487388	+	1.24184i	0.449834	+	0.893112i	$0.351483\pi$
$599$	−11.9286	+	30.3935i	−0.487388	+	1.24184i	−0.937222	+	0.348732i	$0.886612\pi$
$600$		0			0
$601$	−33.8084			−1.37907			−0.689536	−	0.724251i	$-0.742186\pi$
$601$	−33.8084			−1.37907			−0.689536	+	0.724251i	$0.742186\pi$
$602$		0			0
$603$	1.00110			0.0407678
$604$		0			0
$605$	−3.61508	+	9.21108i	−0.146974	+	0.374484i
$606$		0			0
$607$	1.39787	+	18.6532i	0.0567376	+	0.757111i	0.950926	+	0.309419i	$0.100135\pi$
$607$	1.39787	+	18.6532i	0.0567376	+	0.757111i	−0.894188	+	0.447691i	$0.852246\pi$
$608$		0			0
$609$	−7.33611	+	12.7065i	−0.297274	+	0.514894i
$610$		0			0
$611$	−19.9894	−	18.5474i	−0.808683	−	0.750348i
$612$		0			0
$613$	−4.20791	+	18.4361i	−0.169956	+	0.744626i	0.816059	+	0.577969i	$0.196154\pi$
$613$	−4.20791	+	18.4361i	−0.169956	+	0.744626i	−0.986015	+	0.166657i	$0.946703\pi$
$614$		0			0
$615$	0.195440	−	0.133249i	0.00788090	−	0.00537311i
$616$		0			0
$617$	−24.4540	−	7.54305i	−0.984479	−	0.303672i	−0.239601	−	0.970872i	$-0.577017\pi$
$617$	−24.4540	−	7.54305i	−0.984479	−	0.303672i	−0.744879	+	0.667200i	$0.767493\pi$
$618$		0			0
$619$	3.08108	−	41.1142i	0.123839	−	1.65252i	−0.496392	−	0.868099i	$-0.665342\pi$
$619$	3.08108	−	41.1142i	0.123839	−	1.65252i	0.620231	−	0.784419i	$-0.287039\pi$
$620$		0			0
$621$	7.68434	−	7.13002i	0.308362	−	0.286118i
$622$		0			0
$623$	−0.475570	−	0.596346i	−0.0190533	−	0.0238921i
$624$		0			0
$625$	12.5235	−	3.86300i	0.500941	−	0.154520i
$626$		0			0
$627$	2.61935	−	0.394803i	0.104607	−	0.0157669i
$628$		0			0
$629$	0.952352	−	0.458629i	0.0379728	−	0.0182867i
$630$		0			0
$631$	−8.41507	−	21.4412i	−0.334998	−	0.853562i	−0.994774	−	0.102100i	$-0.967444\pi$
$631$	−8.41507	−	21.4412i	−0.334998	−	0.853562i	0.659776	−	0.751463i	$-0.270651\pi$
$632$		0			0
$633$	−28.5090	−	4.29704i	−1.13313	−	0.170792i
$634$		0			0
$635$	9.96405	+	6.79337i	0.395411	+	0.269587i
$636$		0			0
$637$	10.2007	+	4.91240i	0.404167	+	0.194637i
$638$		0			0
$639$	2.57692	+	4.46336i	0.101941	+	0.176568i
$640$		0			0
$641$	−7.22296	−	31.6459i	−0.285290	−	1.24994i	−0.890909	−	0.454182i	$-0.849932\pi$
$641$	−7.22296	−	31.6459i	−0.285290	−	1.24994i	0.605619	−	0.795755i	$-0.292926\pi$
$642$		0			0
$643$	−25.0195	+	31.3734i	−0.986671	+	1.23725i	−0.0152498	+	0.999884i	$0.504854\pi$
$643$	−25.0195	+	31.3734i	−0.986671	+	1.23725i	−0.971421	+	0.237362i	$0.923717\pi$
$644$		0			0
$645$	7.28751	+	4.73357i	0.286946	+	0.186384i
$646$		0			0
$647$	−0.798384	+	1.00114i	−0.0313877	+	0.0393590i	−0.797278	−	0.603613i	$-0.793727\pi$
$647$	−0.798384	+	1.00114i	−0.0313877	+	0.0393590i	0.765890	+	0.642972i	$0.222299\pi$
$648$		0			0
$649$	1.02446	+	4.48844i	0.0402134	+	0.176187i
$650$		0			0
$651$	1.30704	+	2.26385i	0.0512268	+	0.0887274i
$652$		0			0
$653$	15.6506	+	7.53694i	0.612456	+	0.294943i	0.714281	−	0.699859i	$-0.246754\pi$
$653$	15.6506	+	7.53694i	0.612456	+	0.294943i	−0.101825	+	0.994802i	$0.532468\pi$
$654$		0			0
$655$	−2.30453	−	1.57120i	−0.0900455	−	0.0613920i
$656$		0			0
$657$	12.7550	+	1.92250i	0.497619	+	0.0750040i
$658$		0			0
$659$	14.1869	+	36.1477i	0.552645	+	1.40812i	0.885279	+	0.465060i	$0.153967\pi$
$659$	14.1869	+	36.1477i	0.552645	+	1.40812i	−0.332635	+	0.943056i	$0.607938\pi$
$660$		0			0
$661$	−31.3625	+	15.1034i	−1.21986	+	0.587454i	−0.929273	−	0.369395i	$-0.879565\pi$
$661$	−31.3625	+	15.1034i	−1.21986	+	0.587454i	−0.290587	+	0.956848i	$0.593851\pi$
$662$		0			0
$663$	−9.57147	+	1.44267i	−0.371725	+	0.0560285i
$664$		0			0
$665$	−6.91119	+	2.13182i	−0.268005	+	0.0826685i
$666$		0			0
$667$	−6.03833	−	7.57182i	−0.233805	−	0.293182i
$668$		0			0
$669$	−1.57809	+	1.46425i	−0.0610124	+	0.0566112i
$670$		0			0
$671$	−0.189380	+	2.52710i	−0.00731094	+	0.0975577i
$672$		0			0
$673$	20.4975	+	6.32264i	0.790120	+	0.243720i	0.663446	−	0.748225i	$-0.269093\pi$
$673$	20.4975	+	6.32264i	0.790120	+	0.243720i	0.126675	+	0.991944i	$0.459570\pi$
$674$		0			0
$675$	19.4288	−	13.2463i	0.747814	−	0.509851i
$676$		0			0
$677$	−8.90216	+	39.0029i	−0.342138	+	1.49900i	0.452414	+	0.891808i	$0.350563\pi$
$677$	−8.90216	+	39.0029i	−0.342138	+	1.49900i	−0.794552	+	0.607196i	$0.792294\pi$
$678$		0			0
$679$	24.0875	+	22.3499i	0.924393	+	0.857711i
$680$		0			0
$681$	−17.8371	+	30.8948i	−0.683519	+	1.18389i
$682$		0			0
$683$	−0.0581079	−	0.775395i	−0.00222344	−	0.0296697i	0.995982	−	0.0895567i	$-0.0285450\pi$
$683$	−0.0581079	−	0.775395i	−0.00222344	−	0.0296697i	−0.998205	+	0.0598870i	$0.980926\pi$
$684$		0			0
$685$	−4.06505	+	10.3576i	−0.155317	+	0.395742i
$686$		0			0
$687$	22.3087			0.851129
$688$		0			0
$689$	−36.2215			−1.37993
$690$		0			0
$691$	13.6014	−	34.6557i	0.517420	−	1.31836i	−0.398561	−	0.917142i	$-0.630490\pi$
$691$	13.6014	−	34.6557i	0.517420	−	1.31836i	0.915981	−	0.401223i	$-0.131415\pi$
$692$		0			0
$693$	−0.0595610	−	0.794786i	−0.00226253	−	0.0301914i
$694$		0			0
$695$	−2.05930	+	3.56681i	−0.0781136	+	0.135297i
$696$		0			0
$697$	−0.249464	−	0.231468i	−0.00944911	−	0.00876749i
$698$		0			0
$699$	−6.59624	+	28.9000i	−0.249493	+	1.09310i
$700$		0			0
$701$	32.1515	−	21.9205i	1.21434	−	0.827926i	0.225119	−	0.974331i	$-0.427723\pi$
$701$	32.1515	−	21.9205i	1.21434	−	0.827926i	0.989225	+	0.146405i	$0.0467704\pi$
$702$		0			0
$703$	−2.15163	−	0.663691i	−0.0811504	−	0.0250316i
$704$		0			0
$705$	0.769086	−	10.2627i	0.0289655	−	0.386517i
$706$		0			0
$707$	8.79870	−	8.16400i	0.330909	−	0.307039i
$708$		0			0
$709$	4.24430	+	5.32218i	0.159398	+	0.199879i	0.855117	−	0.518436i	$-0.173485\pi$
$709$	4.24430	+	5.32218i	0.159398	+	0.199879i	−0.695719	+	0.718314i	$0.744914\pi$
$710$		0			0
$711$	−1.96574	+	0.606351i	−0.0737210	+	0.0227399i
$712$		0			0
$713$	−1.70620	+	0.257169i	−0.0638978	+	0.00963105i
$714$		0			0
$715$	1.30790	−	0.629853i	0.0489128	−	0.0235552i
$716$		0			0
$717$	−6.81030	−	17.3524i	−0.254335	−	0.648036i
$718$		0			0
$719$	9.10645	+	1.37258i	0.339613	+	0.0511885i	0.316635	−	0.948547i	$-0.397447\pi$
$719$	9.10645	+	1.37258i	0.339613	+	0.0511885i	0.0229784	+	0.999736i	$0.492685\pi$
$720$		0			0
$721$	15.3122	+	10.4397i	0.570258	+	0.388795i
$722$		0			0
$723$	9.90183	+	4.76847i	0.368253	+	0.177341i
$724$		0			0
$725$	−10.8624	−	18.8142i	−0.403419	−	0.698742i
$726$		0			0
$727$	4.20129	+	18.4071i	0.155817	+	0.682680i	0.991129	+	0.132904i	$0.0424301\pi$
$727$	4.20129	+	18.4071i	0.155817	+	0.682680i	−0.835312	+	0.549777i	$0.814713\pi$
$728$		0			0
$729$	18.3748	−	23.0413i	0.680548	−	0.853380i
$730$		0			0
$731$	4.30636	−	11.7369i	0.159276	−	0.434106i
$732$		0			0
$733$	14.2106	−	17.8195i	0.524880	−	0.658178i	−0.446757	−	0.894655i	$-0.647421\pi$
$733$	14.2106	−	17.8195i	0.524880	−	0.658178i	0.971637	+	0.236477i	$0.0759927\pi$
$734$		0			0
$735$	0.950839	+	4.16590i	0.0350722	+	0.153661i
$736$		0			0
$737$	−0.248312	−	0.430089i	−0.00914669	−	0.0158425i
$738$		0			0
$739$	21.1790	+	10.1993i	0.779083	+	0.375187i	0.780775	−	0.624812i	$-0.214824\pi$
$739$	21.1790	+	10.1993i	0.779083	+	0.375187i	−0.00169199	+	0.999999i	$0.500539\pi$
$740$		0			0
$741$	17.0364	+	11.6152i	0.625849	+	0.426697i
$742$		0			0
$743$	−27.3290	−	4.11919i	−1.00260	−	0.151118i	−0.372833	−	0.927899i	$-0.621613\pi$
$743$	−27.3290	−	4.11919i	−1.00260	−	0.151118i	−0.629772	+	0.776780i	$0.716852\pi$
$744$		0			0
$745$	−3.14621	−	8.01642i	−0.115268	−	0.293699i
$746$		0			0
$747$	−11.4726	+	5.52490i	−0.419759	+	0.202145i
$748$		0			0
$749$	8.71699	−	1.31388i	0.318512	−	0.0480079i
$750$		0			0
$751$	19.8284	−	6.11625i	0.723549	−	0.223185i	0.0889600	−	0.996035i	$-0.471646\pi$
$751$	19.8284	−	6.11625i	0.723549	−	0.223185i	0.634589	+	0.772850i	$0.281169\pi$
$752$		0			0
$753$	−14.4180	−	18.0796i	−0.525422	−	0.658858i
$754$		0			0
$755$	−5.57783	+	5.17547i	−0.202998	+	0.188355i
$756$		0			0
$757$	−1.60398	+	21.4036i	−0.0582975	+	0.777926i	0.889069	+	0.457774i	$0.151353\pi$
$757$	−1.60398	+	21.4036i	−0.0582975	+	0.777926i	−0.947366	+	0.320152i	$0.896266\pi$
$758$		0			0
$759$	−1.15584	−	0.356531i	−0.0419545	−	0.0129412i
$760$		0			0
$761$	9.83792	−	6.70738i	0.356624	−	0.243142i	−0.371733	−	0.928340i	$-0.621236\pi$
$761$	9.83792	−	6.70738i	0.356624	−	0.243142i	0.728357	+	0.685197i	$0.240284\pi$
$762$		0			0
$763$	−6.92547	+	30.3425i	−0.250719	+	1.09847i
$764$		0			0
$765$	1.16474	+	1.08072i	0.0421112	+	0.0390735i
$766$		0			0
$767$	−17.9182	+	31.0353i	−0.646989	+	1.12062i
$768$		0			0
$769$	2.45417	+	32.7486i	0.0884996	+	1.18094i	0.847840	+	0.530252i	$0.177903\pi$
$769$	2.45417	+	32.7486i	0.0884996	+	1.18094i	−0.759341	+	0.650693i	$0.774478\pi$
$770$		0			0
$771$	−1.42637	+	3.63433i	−0.0513694	+	0.130887i
$772$		0			0
$773$	16.1263			0.580024			0.290012	−	0.957023i	$-0.406341\pi$
$773$	16.1263			0.580024			0.290012	+	0.957023i	$0.406341\pi$
$774$		0			0
$775$	−3.87059			−0.139036
$776$		0			0
$777$	0.569083	−	1.45000i	0.0204157	−	0.0520185i
$778$		0			0
$779$	0.0541732	+	0.722892i	0.00194096	+	0.0259003i
$780$		0			0
$781$	1.27836	−	2.21419i	0.0457434	−	0.0792298i
$782$		0			0
$783$	−21.6392	−	20.0782i	−0.773320	−	0.717536i
$784$		0			0
$785$	1.98865	−	8.71284i	0.0709779	−	0.310975i
$786$		0			0
$787$	−5.84489	+	3.98498i	−0.208348	+	0.142049i	−0.662999	−	0.748621i	$-0.730716\pi$
$787$	−5.84489	+	3.98498i	−0.208348	+	0.142049i	0.454651	+	0.890670i	$0.349764\pi$
$788$		0			0
$789$	−25.5268	−	7.87398i	−0.908778	−	0.280321i
$790$		0			0
$791$	−1.88782	+	25.1913i	−0.0671233	+	0.895698i
$792$		0			0
$793$	−14.4602	+	13.4171i	−0.513498	+	0.476456i
$794$		0			0
$795$	−8.52337	−	10.6880i	−0.302293	−	0.379063i
$796$		0			0
$797$	47.8168	−	14.7495i	1.69376	−	0.522455i	0.710347	−	0.703852i	$-0.248538\pi$
$797$	47.8168	−	14.7495i	1.69376	−	0.522455i	0.983410	+	0.181397i	$0.0580619\pi$
$798$		0			0
$799$	−14.6408	+	2.20675i	−0.517956	+	0.0780693i
$800$		0			0
$801$	0.321600	−	0.154874i	0.0113632	−	0.00547222i
$802$		0			0
$803$	−2.33781	−	5.95664i	−0.0824994	−	0.210205i
$804$		0			0
$805$	3.26569	+	0.492224i	0.115101	+	0.0173486i
$806$		0			0
$807$	15.4401	+	10.5269i	0.543516	+	0.370563i
$808$		0			0
$809$	22.2720	+	10.7256i	0.783041	+	0.377093i	0.782296	−	0.622907i	$-0.214049\pi$
$809$	22.2720	+	10.7256i	0.783041	+	0.377093i	0.000745138		1.00000i	$0.499763\pi$
$810$		0			0
$811$	−11.1420	−	19.2986i	−0.391249	−	0.677664i	0.601365	−	0.798974i	$-0.294624\pi$
$811$	−11.1420	−	19.2986i	−0.391249	−	0.677664i	−0.992615	+	0.121310i	$0.961290\pi$
$812$		0			0
$813$	−4.96330	−	21.7456i	−0.174071	−	0.762653i
$814$		0			0
$815$	−1.27680	+	1.60106i	−0.0447244	+	0.0560826i
$816$		0			0
$817$	−23.7301	+	12.0882i	−0.830210	+	0.422912i
$818$		0			0
$819$	3.86810	−	4.85044i	0.135162	−	0.169488i
$820$		0			0
$821$	−11.3396	−	49.6819i	−0.395753	−	1.73391i	−0.643830	−	0.765169i	$-0.722656\pi$
$821$	−11.3396	−	49.6819i	−0.395753	−	1.73391i	0.248077	−	0.968740i	$-0.420202\pi$
$822$		0			0
$823$	−7.72992	−	13.3886i	−0.269448	−	0.466698i	0.699271	−	0.714856i	$-0.253508\pi$
$823$	−7.72992	−	13.3886i	−0.269448	−	0.466698i	−0.968719	+	0.248158i	$0.920175\pi$
$824$		0			0
$825$	−2.44463	−	1.17727i	−0.0851111	−	0.0409874i
$826$		0			0
$827$	−15.9404	−	10.8680i	−0.554304	−	0.377918i	0.253531	−	0.967327i	$-0.418408\pi$
$827$	−15.9404	−	10.8680i	−0.554304	−	0.377918i	−0.807834	+	0.589409i	$0.799360\pi$
$828$		0			0
$829$	−32.4810	−	4.89573i	−1.12811	−	0.170036i	−0.441641	−	0.897192i	$-0.645603\pi$
$829$	−32.4810	−	4.89573i	−1.12811	−	0.170036i	−0.686472	+	0.727156i	$0.740841\pi$
$830$		0			0
$831$	−12.6390	−	32.2037i	−0.438443	−	1.11713i
$832$		0			0
$833$	5.53873	−	2.66731i	0.191906	−	0.0924169i
$834$		0			0
$835$	−21.1352	+	3.18562i	−0.731415	+	0.110243i
$836$		0			0
$837$	−5.02563	+	1.55020i	−0.173711	+	0.0535828i
$838$		0			0
$839$	4.90787	+	6.15427i	0.169438	+	0.212469i	0.859300	−	0.511473i	$-0.170900\pi$
$839$	4.90787	+	6.15427i	0.169438	+	0.212469i	−0.689861	+	0.723942i	$0.742328\pi$
$840$		0			0
$841$	1.26652	−	1.17516i	0.0436730	−	0.0405226i
$842$		0			0
$843$	1.07479	−	14.3421i	0.0370177	−	0.493967i
$844$		0			0
$845$	−0.587560	−	0.181238i	−0.0202127	−	0.00623479i
$846$		0			0
$847$	17.3332	−	11.8176i	0.595577	−	0.406058i
$848$		0			0
$849$	−4.48896	+	19.6674i	−0.154061	+	0.674984i
$850$		0			0
$851$	0.753708	+	0.699339i	0.0258368	+	0.0239730i
$852$		0			0
$853$	0.698964	−	1.21064i	0.0239321	−	0.0414516i	−0.853811	−	0.520583i	$-0.825715\pi$
$853$	0.698964	−	1.21064i	0.0239321	−	0.0414516i	0.877743	+	0.479131i	$0.159048\pi$
$854$		0			0
$855$	−0.252933	−	3.37516i	−0.00865013	−	0.115428i
$856$		0			0
$857$	−20.5503	+	52.3614i	−0.701986	+	1.78863i	−0.0926784	+	0.995696i	$0.529543\pi$
$857$	−20.5503	+	52.3614i	−0.701986	+	1.78863i	−0.609307	+	0.792934i	$0.708552\pi$
$858$		0			0
$859$	13.0903			0.446635			0.223317	−	0.974746i	$-0.428311\pi$
$859$	13.0903			0.446635			0.223317	+	0.974746i	$0.428311\pi$
$860$		0			0
$861$	−0.501490			−0.0170907
$862$		0			0
$863$	10.2189	−	26.0374i	0.347856	−	0.886322i	−0.644690	−	0.764445i	$-0.723013\pi$
$863$	10.2189	−	26.0374i	0.347856	−	0.886322i	0.992545	−	0.121877i	$-0.0388914\pi$
$864$		0			0
$865$	−0.105100	−	1.40246i	−0.00357349	−	0.0476849i
$866$		0			0
$867$	9.66245	−	16.7359i	0.328154	−	0.568380i
$868$		0			0
$869$	0.748082	+	0.694119i	0.0253770	+	0.0235464i
$870$		0			0
$871$	0.860202	−	3.76879i	0.0291468	−	0.127701i
$872$		0			0
$873$	−12.7053	+	8.66230i	−0.430008	+	0.293174i
$874$		0			0
$875$	15.5879	+	4.80822i	0.526966	+	0.162547i
$876$		0			0
$877$	−2.80162	+	37.3850i	−0.0946039	+	1.26240i	0.724709	+	0.689055i	$0.241974\pi$
$877$	−2.80162	+	37.3850i	−0.0946039	+	1.26240i	−0.819313	+	0.573347i	$0.805645\pi$
$878$		0			0
$879$	18.1776	−	16.8663i	0.613114	−	0.568886i
$880$		0			0
$881$	20.0677	+	25.1641i	0.676098	+	0.847800i	0.994988	−	0.0999917i	$-0.0318816\pi$
$881$	20.0677	+	25.1641i	0.676098	+	0.847800i	−0.318890	+	0.947792i	$0.603310\pi$
$882$		0			0
$883$	5.12237	−	1.58004i	0.172381	−	0.0531726i	−0.207363	−	0.978264i	$-0.566488\pi$
$883$	5.12237	−	1.58004i	0.172381	−	0.0531726i	0.379744	+	0.925091i	$0.376012\pi$
$884$		0			0
$885$	−13.3740	+	2.01581i	−0.449563	+	0.0677607i
$886$		0			0
$887$	−37.9003	+	18.2518i	−1.27257	+	0.612836i	−0.943470	−	0.331459i	$-0.892459\pi$
$887$	−37.9003	+	18.2518i	−1.27257	+	0.612836i	−0.329098	+	0.944296i	$0.606745\pi$
$888$		0			0
$889$	−9.34077	−	23.7999i	−0.313280	−	0.798223i
$890$		0			0
$891$	−2.42886	−	0.366091i	−0.0813698	−	0.0122645i
$892$		0			0
$893$	26.0595	+	17.7671i	0.872049	+	0.594553i
$894$		0			0
$895$	−5.39130	−	2.59631i	−0.180211	−	0.0867852i
$896$		0			0
$897$	−4.70769	−	8.15395i	−0.157185	−	0.272252i
$898$		0			0
$899$	1.08122	+	4.73713i	0.0360607	+	0.157992i
$900$		0			0
$901$	−12.2624	+	15.3766i	−0.408520	+	0.512268i
$902$		0			0
$903$	−7.11229	−	16.9952i	−0.236682	−	0.565565i
$904$		0			0
$905$	10.8884	−	13.6536i	0.361942	−	0.453861i
$906$		0			0
$907$	−11.0757	−	48.5257i	−0.367762	−	1.61127i	−0.732913	−	0.680322i	$-0.761840\pi$
$907$	−11.0757	−	48.5257i	−0.367762	−	1.61127i	0.365151	−	0.930948i	$-0.381017\pi$
$908$		0			0
$909$	2.80850	+	4.86447i	0.0931522	+	0.161344i
$910$		0			0
$911$	30.3278	+	14.6051i	1.00481	+	0.483889i	0.862567	−	0.505943i	$-0.168856\pi$
$911$	30.3278	+	14.6051i	1.00481	+	0.483889i	0.142239	+	0.989832i	$0.454570\pi$
$912$		0			0
$913$	5.21926	+	3.55843i	0.172732	+	0.117767i
$914$		0			0
$915$	−7.36170	−	1.10960i	−0.243370	−	0.0366821i
$916$		0			0
$917$	2.16038	+	5.50456i	0.0713420	+	0.181776i
$918$		0			0
$919$	1.21942	−	0.587240i	0.0402248	−	0.0193712i	−0.413663	−	0.910430i	$-0.635751\pi$
$919$	1.21942	−	0.587240i	0.0402248	−	0.0193712i	0.453888	+	0.891059i	$0.350037\pi$
$920$		0			0
$921$	30.1475	−	4.54401i	0.993394	−	0.149730i
$922$		0			0
$923$	19.0173	−	5.86606i	0.625963	−	0.193084i
$924$		0			0
$925$	1.43802	+	1.80322i	0.0472819	+	0.0592897i
$926$		0			0
$927$	−6.35754	+	5.89894i	−0.208809	+	0.193746i
$928$		0			0
$929$	2.76821	−	36.9392i	0.0908219	−	1.21193i	−0.746561	−	0.665317i	$-0.768296\pi$
$929$	2.76821	−	36.9392i	0.0908219	−	1.21193i	0.837383	−	0.546617i	$-0.184085\pi$
$930$		0			0
$931$	−12.5136	−	3.85992i	−0.410116	−	0.126504i
$932$		0			0
$933$	−7.69744	+	5.24802i	−0.252003	+	0.171813i
$934$		0			0
$935$	0.175395	−	0.768455i	0.00573602	−	0.0251312i
$936$		0			0
$937$	−1.98566	−	1.84242i	−0.0648686	−	0.0601893i	0.647072	−	0.762429i	$-0.275993\pi$
$937$	−1.98566	−	1.84242i	−0.0648686	−	0.0601893i	−0.711941	+	0.702239i	$0.752184\pi$
$938$		0			0
$939$	−4.98396	+	8.63248i	−0.162646	+	0.281710i
$940$		0			0
$941$	1.22530	+	16.3505i	0.0399436	+	0.533011i	0.980904	+	0.194493i	$0.0623063\pi$
$941$	1.22530	+	16.3505i	0.0399436	+	0.533011i	−0.940960	+	0.338517i	$0.890075\pi$
$942$		0			0
$943$	0.120935	−	0.308137i	0.00393818	−	0.0100343i
$944$		0			0
$945$	10.0663			0.327458
$946$		0			0
$947$	−13.5238			−0.439463			−0.219731	−	0.975560i	$-0.570518\pi$
$947$	−13.5238			−0.439463			−0.219731	+	0.975560i	$0.570518\pi$
$948$		0			0
$949$	18.1975	−	46.3663i	0.590714	−	1.50512i
$950$		0			0
$951$	0.123713	+	1.65083i	0.00401165	+	0.0535318i
$952$		0			0
$953$	15.5635	−	26.9569i	0.504153	−	0.873218i	−0.495836	−	0.868416i	$-0.665138\pi$
$953$	15.5635	−	26.9569i	0.504153	−	0.873218i	0.999988	−	0.00480189i	$-0.00152849\pi$
$954$		0			0
$955$	−10.7763	−	9.99897i	−0.348714	−	0.323559i
$956$		0			0
$957$	−0.757950	+	3.32079i	−0.0245010	+	0.107346i
$958$		0			0
$959$	19.4907	−	13.2885i	0.629387	−	0.429109i
$960$		0			0
$961$	−28.7955	−	8.88224i	−0.928888	−	0.286524i
$962$		0			0
$963$	−0.308291	+	4.11386i	−0.00993455	+	0.132567i
$964$		0			0
$965$	4.21287	−	3.90897i	0.135617	−	0.125834i
$966$		0			0
$967$	0.697559	+	0.874712i	0.0224320	+	0.0281288i	0.792921	−	0.609324i	$-0.208559\pi$
$967$	0.697559	+	0.874712i	0.0224320	+	0.0281288i	−0.770489	+	0.637453i	$0.779988\pi$
$968$		0			0
$969$	10.6984	−	3.30001i	0.343681	−	0.106011i
$970$		0			0
$971$	42.2187	−	6.36345i	1.35486	−	0.204213i	0.568860	−	0.822435i	$-0.307385\pi$
$971$	42.2187	−	6.36345i	1.35486	−	0.204213i	0.786004	+	0.618222i	$0.212147\pi$
$972$		0			0
$973$	7.86708	−	3.78858i	0.252207	−	0.121456i
$974$		0			0
$975$	−7.71621	−	19.6606i	−0.247116	−	0.629642i
$976$		0			0
$977$	11.1357	+	1.67844i	0.356264	+	0.0536981i	0.324736	−	0.945805i	$-0.394725\pi$
$977$	11.1357	+	1.67844i	0.356264	+	0.0536981i	0.0315278	+	0.999503i	$0.489963\pi$
$978$		0			0
$979$	−0.146307	−	0.0997501i	−0.00467598	−	0.00318803i
$980$		0			0
$981$	−13.1223	−	6.31936i	−0.418962	−	0.201762i
$982$		0			0
$983$	4.19746	+	7.27021i	0.133878	+	0.231884i	0.925168	−	0.379557i	$-0.123924\pi$
$983$	4.19746	+	7.27021i	0.133878	+	0.231884i	−0.791290	+	0.611441i	$0.790590\pi$
$984$		0			0
$985$	−2.21997	−	9.72634i	−0.0707342	−	0.309907i
$986$		0			0
$987$	−13.6039	+	17.0587i	−0.433016	+	0.542985i
$988$		0			0
$989$	12.1577	−	0.271687i	0.386593	−	0.00863916i
$990$		0			0
$991$	−25.7233	+	32.2560i	−0.817129	+	1.02465i	0.182016	+	0.983296i	$0.441738\pi$
$991$	−25.7233	+	32.2560i	−0.817129	+	1.02465i	−0.999145	+	0.0413515i	$0.986834\pi$
$992$		0			0
$993$	−3.17858	−	13.9263i	−0.100869	−	0.441937i
$994$		0			0
$995$	−2.20185	−	3.81372i	−0.0698035	−	0.120903i
$996$		0			0
$997$	−54.1007	−	26.0535i	−1.71339	−	0.825124i	−0.991036	−	0.133598i	$-0.957347\pi$
$997$	−54.1007	−	26.0535i	−1.71339	−	0.825124i	−0.722352	−	0.691526i	$-0.756939\pi$
$998$		0			0
$999$	2.58936	+	1.76540i	0.0819237	+	0.0558547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	688.2.bg.c.273.2		36
4.3	odd	2		43.2.g.a.15.1	✓	36
12.11	even	2		387.2.y.c.316.3		36
43.23	even	21	inner	688.2.bg.c.625.2		36
172.23	odd	42		43.2.g.a.23.1	yes	36
172.111	odd	42		1849.2.a.n.1.1		18
172.147	even	42		1849.2.a.o.1.18		18
516.23	even	42		387.2.y.c.109.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.15.1	✓	36	4.3	odd	2
43.2.g.a.23.1	yes	36	172.23	odd	42
387.2.y.c.109.3		36	516.23	even	42
387.2.y.c.316.3		36	12.11	even	2
688.2.bg.c.273.2		36	1.1	even	1	trivial
688.2.bg.c.625.2		36	43.23	even	21	inner
1849.2.a.n.1.1		18	172.111	odd	42
1849.2.a.o.1.18		18	172.147	even	42

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:	\( N \)	\(=\)	\( 688 = 2^{4} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	688.bg (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.528255 - 1.34597i) q^{3} +(0.0684907 + 0.913945i) q^{5} +(0.971539 - 1.68276i) q^{7} +(0.666571 + 0.618487i) q^{9} +O(q^{10})\)	\(q+(0.528255 - 1.34597i) q^{3} +(0.0684907 + 0.913945i) q^{5} +(0.971539 - 1.68276i) q^{7} +(0.666571 + 0.618487i) q^{9} +(0.100377 - 0.439781i) q^{11} +(2.90116 - 1.97798i) q^{13} +(1.26632 + 0.390609i) q^{15} +(0.142476 - 1.90121i) q^{17} +(-2.97713 + 2.76237i) q^{19} +(-1.75172 - 2.19659i) q^{21} +(1.77211 - 0.546623i) q^{23} +(4.11355 - 0.620018i) q^{25} +(5.09278 - 2.45255i) q^{27} +(-1.90792 - 4.86129i) q^{29} +(-0.920034 - 0.138673i) q^{31} +(-0.538908 - 0.367421i) q^{33} +(1.60449 + 0.772681i) q^{35} +(0.277212 + 0.480145i) q^{37} +(-1.12975 - 4.94975i) q^{39} +(0.111290 - 0.139553i) q^{41} +(6.30773 + 1.79236i) q^{43} +(-0.519610 + 0.651570i) q^{45} +(-1.72810 - 7.57131i) q^{47} +(1.61222 + 2.79245i) q^{49} +(-2.48371 - 1.19609i) q^{51} +(-8.52328 - 5.81107i) q^{53} +(0.408811 + 0.0616183i) q^{55} +(2.14539 + 5.46636i) q^{57} +(-9.19536 + 4.42825i) q^{59} +(-5.55516 + 0.837306i) q^{61} +(1.68836 - 0.520791i) q^{63} +(2.00646 + 2.51603i) q^{65} +(0.807046 - 0.748830i) q^{67} +(0.200386 - 2.67396i) q^{69} +(5.41606 + 1.67063i) q^{71} +(11.7207 - 7.99101i) q^{73} +(1.33848 - 5.86425i) q^{75} +(-0.642524 - 0.596175i) q^{77} +(-1.13115 + 1.95921i) q^{79} +(-0.406922 - 5.43000i) q^{81} +(-5.11608 + 13.0356i) q^{83} +1.74736 q^{85} -7.55102 q^{87} +(0.143414 - 0.365414i) q^{89} +(-0.509861 - 6.80362i) q^{91} +(-0.672662 + 1.16508i) q^{93} +(-2.72856 - 2.53173i) q^{95} +(-3.76302 + 16.4869i) q^{97} +(0.338908 - 0.231063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 16 q^{3} - 17 q^{5} - 6 q^{7} - q^{9}+O(q^{10}) \) 36 * q + 16 * q^3 - 17 * q^5 - 6 * q^7 - q^9	\( 36 q + 16 q^{3} - 17 q^{5} - 6 q^{7} - q^{9} + 4 q^{11} + 3 q^{15} - 10 q^{17} - 10 q^{19} - 21 q^{21} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 9 q^{29} - 40 q^{31} - 11 q^{33} - 11 q^{35} - 19 q^{37} + q^{39} - 28 q^{41} + 8 q^{43} - 46 q^{45} + 30 q^{47} + 6 q^{49} - 57 q^{51} - 24 q^{53} - 14 q^{55} + 52 q^{57} + q^{59} - 14 q^{61} - 47 q^{63} + 38 q^{65} - 66 q^{67} - 7 q^{69} + 33 q^{71} + 29 q^{73} + 55 q^{75} - 27 q^{77} + 17 q^{79} + 38 q^{81} + 23 q^{83} - 56 q^{85} + 86 q^{87} - 19 q^{89} + 13 q^{91} - 30 q^{93} - q^{95} - 31 q^{97} + 31 q^{99}+O(q^{100}) \) 36 * q + 16 * q^3 - 17 * q^5 - 6 * q^7 - q^9 + 4 * q^11 + 3 * q^15 - 10 * q^17 - 10 * q^19 - 21 * q^21 - 4 * q^23 - 2 * q^25 + 4 * q^27 + 9 * q^29 - 40 * q^31 - 11 * q^33 - 11 * q^35 - 19 * q^37 + q^39 - 28 * q^41 + 8 * q^43 - 46 * q^45 + 30 * q^47 + 6 * q^49 - 57 * q^51 - 24 * q^53 - 14 * q^55 + 52 * q^57 + q^59 - 14 * q^61 - 47 * q^63 + 38 * q^65 - 66 * q^67 - 7 * q^69 + 33 * q^71 + 29 * q^73 + 55 * q^75 - 27 * q^77 + 17 * q^79 + 38 * q^81 + 23 * q^83 - 56 * q^85 + 86 * q^87 - 19 * q^89 + 13 * q^91 - 30 * q^93 - q^95 - 31 * q^97 + 31 * q^99

Introduction

L-functions

Modular forms

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