LMFDB - Embedded newform 768.2.r.a.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(49,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("768.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.r (of order $16$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 192)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	768.49
Dual form			768.2.r.a.721.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.980785 + 0.195090i) q^{3} +(1.62504 + 2.43205i) q^{5} +(-0.294182 - 0.121854i) q^{7} +(0.923880 - 0.382683i) q^{9} +O(q^{10})$	\(q+(-0.980785 + 0.195090i) q^{3} +(1.62504 + 2.43205i) q^{5} +(-0.294182 - 0.121854i) q^{7} +(0.923880 - 0.382683i) q^{9} +(1.07988 - 5.42890i) q^{11} +(2.67591 - 4.00478i) q^{13} +(-2.06829 - 2.06829i) q^{15} +(0.394520 - 0.394520i) q^{17} +(2.13690 + 1.42783i) q^{19} +(0.312302 + 0.0621207i) q^{21} +(3.37395 + 8.14543i) q^{23} +(-1.36068 + 3.28498i) q^{25} +(-0.831470 + 0.555570i) q^{27} +(0.411462 + 2.06856i) q^{29} +1.31001i q^{31} +5.53526i q^{33} +(-0.181703 - 0.913483i) q^{35} +(1.47533 - 0.985786i) q^{37} +(-1.84320 + 4.44987i) q^{39} +(4.39934 + 10.6209i) q^{41} +(2.25285 + 0.448119i) q^{43} +(2.43205 + 1.62504i) q^{45} +(5.23873 - 5.23873i) q^{47} +(-4.87805 - 4.87805i) q^{49} +(-0.309973 + 0.463907i) q^{51} +(1.88714 - 9.48728i) q^{53} +(14.9582 - 6.19589i) q^{55} +(-2.37440 - 0.983508i) q^{57} +(0.373863 + 0.559526i) q^{59} +(0.868572 - 0.172770i) q^{61} -0.318420 q^{63} +14.0883 q^{65} +(-10.3046 + 2.04972i) q^{67} +(-4.89821 - 7.33069i) q^{69} +(12.4243 + 5.14631i) q^{71} +(-14.5155 + 6.01250i) q^{73} +(0.693670 - 3.48732i) q^{75} +(-0.979213 + 1.46550i) q^{77} +(2.55934 + 2.55934i) q^{79} +(0.707107 - 0.707107i) q^{81} +(-0.585536 - 0.391243i) q^{83} +(1.60061 + 0.318380i) q^{85} +(-0.807113 - 1.94854i) q^{87} +(3.72369 - 8.98978i) q^{89} +(-1.27520 + 0.852063i) q^{91} +(-0.255570 - 1.28484i) q^{93} +7.51734i q^{95} +0.565484i q^{97} +(-1.07988 - 5.42890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 32 q^{51} + 64 q^{55} + 128 q^{59} + 32 q^{63} + 32 q^{67} + 128 q^{71} + 64 q^{75} + 32 q^{79}+O(q^{100}) $ 128 * q + 32 * q^51 + 64 * q^55 + 128 * q^59 + 32 * q^63 + 32 * q^67 + 128 * q^71 + 64 * q^75 + 32 * q^79

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

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
$3$	−0.980785	+	0.195090i	−0.566257	+	0.112635i
$3$	−0.980785	+	0.195090i	−0.566257	+	0.112635i
$4$		0			0
$5$	1.62504	+	2.43205i	0.726742	+	1.08765i	0.992337	+	0.123561i	$0.0394316\pi$
$5$	1.62504	+	2.43205i	0.726742	+	1.08765i	−0.265595	+	0.964085i	$0.585568\pi$
$6$		0			0
$7$	−0.294182	−	0.121854i	−0.111190	−	0.0460565i	0.326395	−	0.945234i	$-0.394166\pi$
$7$	−0.294182	−	0.121854i	−0.111190	−	0.0460565i	−0.437585	+	0.899177i	$0.644166\pi$
$8$		0			0
$9$	0.923880	−	0.382683i	0.307960	−	0.127561i
$10$		0			0
$11$	1.07988	−	5.42890i	0.325595	−	1.63687i	−0.377666	−	0.925942i	$-0.623273\pi$
$11$	1.07988	−	5.42890i	0.325595	−	1.63687i	0.703260	−	0.710932i	$-0.251727\pi$
$12$		0			0
$13$	2.67591	−	4.00478i	0.742163	−	1.11073i	−0.247718	−	0.968832i	$-0.579681\pi$
$13$	2.67591	−	4.00478i	0.742163	−	1.11073i	0.989882	−	0.141894i	$-0.0453192\pi$
$14$		0			0
$15$	−2.06829	−	2.06829i	−0.534030	−	0.534030i
$16$		0			0
$17$	0.394520	−	0.394520i	0.0956853	−	0.0956853i	−0.657644	−	0.753329i	$-0.728447\pi$
$17$	0.394520	−	0.394520i	0.0956853	−	0.0956853i	0.753329	+	0.657644i	$0.228447\pi$
$18$		0			0
$19$	2.13690	+	1.42783i	0.490239	+	0.327567i	0.775999	−	0.630734i	$-0.217246\pi$
$19$	2.13690	+	1.42783i	0.490239	+	0.327567i	−0.285760	+	0.958301i	$0.592246\pi$
$20$		0			0
$21$	0.312302	+	0.0621207i	0.0681498	+	0.0135558i
$22$		0			0
$23$	3.37395	+	8.14543i	0.703516	+	1.69844i	0.715599	+	0.698512i	$0.246154\pi$
$23$	3.37395	+	8.14543i	0.703516	+	1.69844i	−0.0120823	+	0.999927i	$0.503846\pi$
$24$		0			0
$25$	−1.36068	+	3.28498i	−0.272137	+	0.656996i
$26$		0			0
$27$	−0.831470	+	0.555570i	−0.160016	+	0.106920i
$28$		0			0
$29$	0.411462	+	2.06856i	0.0764067	+	0.384122i	1.00000		0.000747904i	$0.000238065\pi$
$29$	0.411462	+	2.06856i	0.0764067	+	0.384122i	−0.923593	+	0.383374i	$0.874762\pi$
$30$		0			0
$31$			1.31001i			0.235285i	0.993056	+	0.117642i	$0.0375336\pi$
$31$			1.31001i			0.235285i	−0.993056	+	0.117642i	$0.962466\pi$
$32$		0			0
$33$			5.53526i			0.963565i
$34$		0			0
$35$	−0.181703	−	0.913483i	−0.0307134	−	0.154407i
$36$		0			0
$37$	1.47533	−	0.985786i	0.242543	−	0.162062i	−0.428358	−	0.903609i	$-0.640908\pi$
$37$	1.47533	−	0.985786i	0.242543	−	0.162062i	0.670901	+	0.741547i	$0.265908\pi$
$38$		0			0
$39$	−1.84320	+	4.44987i	−0.295148	+	0.712550i
$40$		0			0
$41$	4.39934	+	10.6209i	0.687061	+	1.65871i	0.750621	+	0.660733i	$0.229755\pi$
$41$	4.39934	+	10.6209i	0.687061	+	1.65871i	−0.0635600	+	0.997978i	$0.520245\pi$
$42$		0			0
$43$	2.25285	+	0.448119i	0.343556	+	0.0683376i	0.363853	−	0.931456i	$-0.381461\pi$
$43$	2.25285	+	0.448119i	0.343556	+	0.0683376i	−0.0202967	+	0.999794i	$0.506461\pi$
$44$		0			0
$45$	2.43205	+	1.62504i	0.362549	+	0.242247i
$46$		0			0
$47$	5.23873	−	5.23873i	0.764147	−	0.764147i	−0.212922	−	0.977069i	$-0.568298\pi$
$47$	5.23873	−	5.23873i	0.764147	−	0.764147i	0.977069	+	0.212922i	$0.0682980\pi$
$48$		0			0
$49$	−4.87805	−	4.87805i	−0.696865	−	0.696865i
$50$		0			0
$51$	−0.309973	+	0.463907i	−0.0434049	+	0.0649600i
$52$		0			0
$53$	1.88714	−	9.48728i	0.259218	−	1.30318i	−0.603447	−	0.797403i	$-0.706206\pi$
$53$	1.88714	−	9.48728i	0.259218	−	1.30318i	0.862665	−	0.505775i	$-0.168794\pi$
$54$		0			0
$55$	14.9582	−	6.19589i	2.01696	−	0.835453i
$56$		0			0
$57$	−2.37440	−	0.983508i	−0.314497	−	0.130269i
$58$		0			0
$59$	0.373863	+	0.559526i	0.0486728	+	0.0728441i	0.855008	−	0.518615i	$-0.173552\pi$
$59$	0.373863	+	0.559526i	0.0486728	+	0.0728441i	−0.806335	+	0.591459i	$0.798552\pi$
$60$		0			0
$61$	0.868572	−	0.172770i	0.111209	−	0.0221209i	−0.139172	−	0.990268i	$-0.544444\pi$
$61$	0.868572	−	0.172770i	0.111209	−	0.0221209i	0.250381	+	0.968147i	$0.419444\pi$
$62$		0			0
$63$	−0.318420			−0.0401172
$64$		0			0
$65$	14.0883			1.74744
$66$		0			0
$67$	−10.3046	+	2.04972i	−1.25891	+	0.250413i	−0.779068	−	0.626940i	$-0.784307\pi$
$67$	−10.3046	+	2.04972i	−1.25891	+	0.250413i	−0.479845	+	0.877353i	$0.659307\pi$
$68$		0			0
$69$	−4.89821	−	7.33069i	−0.589675	−	0.882511i
$70$		0			0
$71$	12.4243	+	5.14631i	1.47449	+	0.610755i	0.967878	−	0.251419i	$-0.0808971\pi$
$71$	12.4243	+	5.14631i	1.47449	+	0.610755i	0.506614	+	0.862173i	$0.330897\pi$
$72$		0			0
$73$	−14.5155	+	6.01250i	−1.69891	+	0.703710i	−0.999935	−	0.0114397i	$-0.996359\pi$
$73$	−14.5155	+	6.01250i	−1.69891	+	0.703710i	−0.698971	+	0.715150i	$0.746359\pi$
$74$		0			0
$75$	0.693670	−	3.48732i	0.0800982	−	0.402681i
$76$		0			0
$77$	−0.979213	+	1.46550i	−0.111592	+	0.167009i
$78$		0			0
$79$	2.55934	+	2.55934i	0.287948	+	0.287948i	0.836268	−	0.548320i	$-0.184733\pi$
$79$	2.55934	+	2.55934i	0.287948	+	0.287948i	−0.548320	+	0.836268i	$0.684733\pi$
$80$		0			0
$81$	0.707107	−	0.707107i	0.0785674	−	0.0785674i
$82$		0			0
$83$	−0.585536	−	0.391243i	−0.0642710	−	0.0429445i	0.523020	−	0.852321i	$-0.324805\pi$
$83$	−0.585536	−	0.391243i	−0.0642710	−	0.0429445i	−0.587291	+	0.809376i	$0.699805\pi$
$84$		0			0
$85$	1.60061	+	0.318380i	0.173610	+	0.0345332i
$86$		0			0
$87$	−0.807113	−	1.94854i	−0.0865316	−	0.208906i
$88$		0			0
$89$	3.72369	−	8.98978i	0.394710	−	0.952915i	−0.594189	−	0.804326i	$-0.702527\pi$
$89$	3.72369	−	8.98978i	0.394710	−	0.952915i	0.988899	−	0.148589i	$-0.0474733\pi$
$90$		0			0
$91$	−1.27520	+	0.852063i	−0.133678	+	0.0893205i
$92$		0			0
$93$	−0.255570	−	1.28484i	−0.0265014	−	0.133232i
$94$		0			0
$95$			7.51734i			0.771263i
$96$		0			0
$97$			0.565484i			0.0574162i	0.999588	+	0.0287081i	$0.00913933\pi$
$97$			0.565484i			0.0574162i	−0.999588	+	0.0287081i	$0.990861\pi$
$98$		0			0
$99$	−1.07988	−	5.42890i	−0.108532	−	0.545625i
$100$		0			0
$101$	9.22776	−	6.16579i	0.918196	−	0.613519i	−0.00410457	−	0.999992i	$-0.501307\pi$
$101$	9.22776	−	6.16579i	0.918196	−	0.613519i	0.922301	+	0.386472i	$0.126307\pi$
$102$		0			0
$103$	−3.23367	+	7.80677i	−0.318623	+	0.769223i	0.680705	+	0.732558i	$0.261674\pi$
$103$	−3.23367	+	7.80677i	−0.318623	+	0.769223i	−0.999328	+	0.0366656i	$0.988326\pi$
$104$		0			0
$105$	0.356424	+	0.860483i	0.0347834	+	0.0839745i
$106$		0			0
$107$	−8.21391	−	1.63385i	−0.794069	−	0.157950i	−0.218644	−	0.975805i	$-0.570163\pi$
$107$	−8.21391	−	1.63385i	−0.794069	−	0.157950i	−0.575425	+	0.817855i	$0.695163\pi$
$108$		0			0
$109$	0.453546	+	0.303050i	0.0434419	+	0.0290269i	0.577102	−	0.816672i	$-0.304184\pi$
$109$	0.453546	+	0.303050i	0.0434419	+	0.0290269i	−0.533660	+	0.845699i	$0.679184\pi$
$110$		0			0
$111$	−1.25467	+	1.25467i	−0.119088	+	0.119088i
$112$		0			0
$113$	1.13400	+	1.13400i	0.106678	+	0.106678i	0.758431	−	0.651753i	$-0.225966\pi$
$113$	1.13400	+	1.13400i	0.106678	+	0.106678i	−0.651753	+	0.758431i	$0.725966\pi$
$114$		0			0
$115$	−14.3273	+	21.4423i	−1.33603	+	1.99950i
$116$		0			0
$117$	0.939654	−	4.72396i	0.0868711	−	0.436730i
$118$		0			0
$119$	−0.164135	+	0.0679868i	−0.0150462	+	0.00623234i
$120$		0			0
$121$	−18.1441	−	7.51555i	−1.64947	−	0.683231i
$122$		0			0
$123$	−6.38684	−	9.55859i	−0.575882	−	0.861869i
$124$		0			0
$125$	4.14359	−	0.824210i	0.370614	−	0.0737196i
$126$		0			0
$127$	−6.16120			−0.546718			−0.273359	−	0.961912i	$-0.588135\pi$
$127$	−6.16120			−0.546718			−0.273359	+	0.961912i	$0.588135\pi$
$128$		0			0
$129$	−2.29698			−0.202238
$130$		0			0
$131$	18.7962	−	3.73880i	1.64223	−	0.326660i	0.714423	−	0.699714i	$-0.246689\pi$
$131$	18.7962	−	3.73880i	1.64223	−	0.326660i	0.927810	+	0.373054i	$0.121689\pi$
$132$		0			0
$133$	−0.454650	−	0.680432i	−0.0394232	−	0.0590010i
$134$		0			0
$135$	−2.70235	−	1.11935i	−0.232581	−	0.0963383i
$136$		0			0
$137$	−20.4158	+	8.45651i	−1.74424	+	0.722488i	−0.745830	+	0.666137i	$0.767947\pi$
$137$	−20.4158	+	8.45651i	−1.74424	+	0.722488i	−0.998411	+	0.0563516i	$0.982053\pi$
$138$		0			0
$139$	1.51500	−	7.61643i	0.128501	−	0.646018i	−0.861819	−	0.507215i	$-0.830675\pi$
$139$	1.51500	−	7.61643i	0.128501	−	0.646018i	0.990320	−	0.138802i	$-0.0443252\pi$
$140$		0			0
$141$	−4.11604	+	6.16010i	−0.346633	+	0.518774i
$142$		0			0
$143$	−18.8519	−	18.8519i	−1.57647	−	1.57647i
$144$		0			0
$145$	−4.36220	+	4.36220i	−0.362261	+	0.362261i
$146$		0			0
$147$	5.73598	+	3.83266i	0.473096	+	0.316113i
$148$		0			0
$149$	−14.4464	−	2.87356i	−1.18349	−	0.235411i	−0.436165	−	0.899867i	$-0.643664\pi$
$149$	−14.4464	−	2.87356i	−1.18349	−	0.235411i	−0.747328	+	0.664455i	$0.768664\pi$
$150$		0			0
$151$	−7.33383	−	17.7054i	−0.596819	−	1.44085i	−0.876806	−	0.480845i	$-0.840330\pi$
$151$	−7.33383	−	17.7054i	−0.596819	−	1.44085i	0.279987	−	0.960004i	$-0.409670\pi$
$152$		0			0
$153$	0.213513	−	0.515466i	0.0172615	−	0.0416729i
$154$		0			0
$155$	−3.18601	+	2.12882i	−0.255906	+	0.170991i
$156$		0			0
$157$	2.49692	+	12.5529i	0.199276	+	1.00183i	0.942861	+	0.333187i	$0.108124\pi$
$157$	2.49692	+	12.5529i	0.199276	+	1.00183i	−0.743584	+	0.668642i	$0.766876\pi$
$158$		0			0
$159$			9.67315i			0.767131i
$160$		0			0
$161$		−	2.80737i		−	0.221251i
$162$		0			0
$163$	−1.62246	−	8.15667i	−0.127081	−	0.638880i	−0.990847	−	0.134987i	$-0.956901\pi$
$163$	−1.62246	−	8.15667i	−0.127081	−	0.638880i	0.863766	−	0.503893i	$-0.168099\pi$
$164$		0			0
$165$	−13.4620	+	8.99504i	−1.04802	+	0.700263i
$166$		0			0
$167$	−2.16239	+	5.22048i	−0.167331	+	0.403973i	−0.985195	−	0.171439i	$-0.945158\pi$
$167$	−2.16239	+	5.22048i	−0.167331	+	0.403973i	0.817864	+	0.575412i	$0.195158\pi$
$168$		0			0
$169$	−3.90289	−	9.42242i	−0.300222	−	0.724801i
$170$		0			0
$171$	2.52065	+	0.501388i	0.192759	+	0.0383421i
$172$		0			0
$173$	1.03110	+	0.688961i	0.0783933	+	0.0523808i	0.594149	−	0.804355i	$-0.297489\pi$
$173$	1.03110	+	0.688961i	0.0783933	+	0.0523808i	−0.515756	+	0.856736i	$0.672489\pi$
$174$		0			0
$175$	0.800577	−	0.800577i	0.0605179	−	0.0605179i
$176$		0			0
$177$	−0.475838	−	0.475838i	−0.0357661	−	0.0357661i
$178$		0			0
$179$	−2.80532	+	4.19846i	−0.209680	+	0.313808i	−0.921371	−	0.388685i	$-0.872930\pi$
$179$	−2.80532	+	4.19846i	−0.209680	+	0.313808i	0.711691	+	0.702492i	$0.247930\pi$
$180$		0			0
$181$	2.72985	−	13.7239i	0.202908	−	1.02009i	−0.736278	−	0.676679i	$-0.763419\pi$
$181$	2.72985	−	13.7239i	0.202908	−	1.02009i	0.939186	−	0.343408i	$-0.111581\pi$
$182$		0			0
$183$	−0.818177	+	0.338900i	−0.0604814	+	0.0250522i
$184$		0			0
$185$	4.79496	+	1.98614i	0.352533	+	0.146024i
$186$		0			0
$187$	−1.71578	−	2.56784i	−0.125470	−	0.187779i
$188$		0			0
$189$	0.312302	−	0.0621207i	0.0227166	−	0.00451862i
$190$		0			0
$191$	3.22178			0.233120			0.116560	−	0.993184i	$-0.462813\pi$
$191$	3.22178			0.233120			0.116560	+	0.993184i	$0.462813\pi$
$192$		0			0
$193$	20.2935			1.46076			0.730381	−	0.683040i	$-0.239343\pi$
$193$	20.2935			1.46076			0.730381	+	0.683040i	$0.239343\pi$
$194$		0			0
$195$	−13.8176	+	2.74849i	−0.989498	+	0.196823i
$196$		0			0
$197$	10.1421	+	15.1788i	0.722597	+	1.08144i	0.992933	+	0.118677i	$0.0378652\pi$
$197$	10.1421	+	15.1788i	0.722597	+	1.08144i	−0.270336	+	0.962766i	$0.587135\pi$
$198$		0			0
$199$	−11.3372	−	4.69603i	−0.803674	−	0.332893i	−0.0572470	−	0.998360i	$-0.518232\pi$
$199$	−11.3372	−	4.69603i	−0.803674	−	0.332893i	−0.746427	+	0.665467i	$0.768232\pi$
$200$		0			0
$201$	9.70677	−	4.02067i	0.684663	−	0.283597i
$202$		0			0
$203$	0.131018	−	0.658672i	0.00919566	−	0.0462297i
$204$		0			0
$205$	−18.6815	+	27.9589i	−1.30477	+	1.95273i
$206$		0			0
$207$	6.23424	+	6.23424i	0.433310	+	0.433310i
$208$		0			0
$209$	10.0591	−	10.0591i	0.695805	−	0.695805i
$210$		0			0
$211$	−10.3269	−	6.90024i	−0.710935	−	0.475032i	0.146772	−	0.989170i	$-0.453112\pi$
$211$	−10.3269	−	6.90024i	−0.710935	−	0.475032i	−0.857707	+	0.514139i	$0.828112\pi$
$212$		0			0
$213$	−13.1896	−	2.62357i	−0.903734	−	0.179764i
$214$		0			0
$215$	2.57113	+	6.20726i	0.175350	+	0.423331i
$216$		0			0
$217$	0.159630	−	0.385381i	0.0108364	−	0.0261614i
$218$		0			0
$219$	13.0636	−	8.72880i	0.882754	−	0.589837i
$220$		0			0
$221$	−0.524267	−	2.63567i	−0.0352660	−	0.177294i
$222$		0			0
$223$		−	16.4720i		−	1.10305i	−0.834158	−	0.551525i	$-0.814046\pi$
$223$		−	16.4720i		−	1.10305i	0.834158	−	0.551525i	$-0.185954\pi$
$224$		0			0
$225$			3.55564i			0.237042i
$226$		0			0
$227$	−1.40712	−	7.07407i	−0.0933939	−	0.469523i	−0.998972	−	0.0453422i	$-0.985562\pi$
$227$	−1.40712	−	7.07407i	−0.0933939	−	0.469523i	0.905578	−	0.424181i	$-0.139438\pi$
$228$		0			0
$229$	4.56486	−	3.05014i	0.301654	−	0.201559i	−0.395526	−	0.918455i	$-0.629438\pi$
$229$	4.56486	−	3.05014i	0.301654	−	0.201559i	0.697180	+	0.716896i	$0.254438\pi$
$230$		0			0
$231$	0.674494	−	1.62837i	0.0443784	−	0.107139i
$232$		0			0
$233$	3.73176	+	9.00926i	0.244476	+	0.590216i	0.997717	−	0.0675274i	$-0.0215110\pi$
$233$	3.73176	+	9.00926i	0.244476	+	0.590216i	−0.753242	+	0.657744i	$0.771511\pi$
$234$		0			0
$235$	21.2540	+	4.22769i	1.38646	+	0.275784i
$236$		0			0
$237$	−3.00946	−	2.01086i	−0.195486	−	0.130619i
$238$		0			0
$239$	−15.5694	+	15.5694i	−1.00710	+	1.00710i	−0.00712806	+	0.999975i	$0.502269\pi$
$239$	−15.5694	+	15.5694i	−1.00710	+	1.00710i	−0.999975	+	0.00712806i	$0.997731\pi$
$240$		0			0
$241$	−9.69865	−	9.69865i	−0.624745	−	0.624745i	0.321996	−	0.946741i	$-0.395646\pi$
$241$	−9.69865	−	9.69865i	−0.624745	−	0.624745i	−0.946741	+	0.321996i	$0.895646\pi$
$242$		0			0
$243$	−0.555570	+	0.831470i	−0.0356398	+	0.0533388i
$244$		0			0
$245$	3.93662	−	19.7907i	0.251501	−	1.26438i
$246$		0			0
$247$	11.4363	−	4.73707i	0.727675	−	0.301413i
$248$		0			0
$249$	0.650613	+	0.269493i	0.0412309	+	0.0170784i
$250$		0			0
$251$	−5.88752	−	8.81130i	−0.371617	−	0.556165i	0.597781	−	0.801660i	$-0.296049\pi$
$251$	−5.88752	−	8.81130i	−0.371617	−	0.556165i	−0.969398	+	0.245495i	$0.921049\pi$
$252$		0			0
$253$	47.8641	−	9.52077i	3.00919	−	0.598566i
$254$		0			0
$255$	−1.63196			−0.102198
$256$		0			0
$257$	−13.3850			−0.834934			−0.417467	−	0.908692i	$-0.637082\pi$
$257$	−13.3850			−0.834934			−0.417467	+	0.908692i	$0.637082\pi$
$258$		0			0
$259$	−0.554139	+	0.110225i	−0.0344325	+	0.00684905i
$260$		0			0
$261$	1.17175	+	1.75364i	0.0725292	+	0.108548i
$262$		0			0
$263$	1.95063	+	0.807975i	0.120281	+	0.0498219i	0.442012	−	0.897009i	$-0.354265\pi$
$263$	1.95063	+	0.807975i	0.120281	+	0.0498219i	−0.321731	+	0.946831i	$0.604265\pi$
$264$		0			0
$265$	26.1402	−	10.8276i	1.60578	−	0.665137i
$266$		0			0
$267$	−1.89832	+	9.54350i	−0.116175	+	0.584053i
$268$		0			0
$269$	−3.24219	+	4.85228i	−0.197680	+	0.295849i	−0.917045	−	0.398783i	$-0.869433\pi$
$269$	−3.24219	+	4.85228i	−0.197680	+	0.295849i	0.719365	+	0.694632i	$0.244433\pi$
$270$		0			0
$271$	−12.0904	−	12.0904i	−0.734438	−	0.734438i	0.237058	−	0.971496i	$-0.423817\pi$
$271$	−12.0904	−	12.0904i	−0.734438	−	0.734438i	−0.971496	+	0.237058i	$0.923817\pi$
$272$		0			0
$273$	1.08447	−	1.08447i	0.0656352	−	0.0656352i
$274$		0			0
$275$	16.3645	+	10.9344i	0.986814	+	0.659368i
$276$		0			0
$277$	−19.1137	−	3.80195i	−1.14843	−	0.228437i	−0.416056	−	0.909339i	$-0.636588\pi$
$277$	−19.1137	−	3.80195i	−1.14843	−	0.228437i	−0.732375	+	0.680902i	$0.761588\pi$
$278$		0			0
$279$	0.501319	+	1.21029i	0.0300132	+	0.0724582i
$280$		0			0
$281$	−4.87231	+	11.7628i	−0.290658	+	0.701710i	−0.999995	−	0.00315921i	$-0.998994\pi$
$281$	−4.87231	+	11.7628i	−0.290658	+	0.701710i	0.709337	+	0.704869i	$0.248994\pi$
$282$		0			0
$283$	−14.6616	+	9.79655i	−0.871540	+	0.582344i	−0.908926	−	0.416957i	$-0.863097\pi$
$283$	−14.6616	+	9.79655i	−0.871540	+	0.582344i	0.0373867	+	0.999301i	$0.488097\pi$
$284$		0			0
$285$	−1.46656	−	7.37290i	−0.0868715	−	0.436733i
$286$		0			0
$287$		−	3.66056i		−	0.216076i
$288$		0			0
$289$			16.6887i			0.981689i
$290$		0			0
$291$	−0.110320	−	0.554618i	−0.00646710	−	0.0325123i
$292$		0			0
$293$	−13.2983	+	8.88565i	−0.776896	+	0.519105i	−0.879662	−	0.475600i	$-0.842231\pi$
$293$	−13.2983	+	8.88565i	−0.776896	+	0.519105i	0.102765	+	0.994706i	$0.467231\pi$
$294$		0			0
$295$	−0.753251	+	1.81851i	−0.0438560	+	0.105878i
$296$		0			0
$297$	2.11825	+	5.11391i	0.122913	+	0.296739i
$298$		0			0
$299$	41.6490	+	8.28450i	2.40862	+	0.479105i
$300$		0			0
$301$	−0.608142	−	0.406348i	−0.0350527	−	0.0234215i
$302$		0			0
$303$	−7.84756	+	7.84756i	−0.450831	+	0.450831i
$304$		0			0
$305$	1.83165	+	1.83165i	0.104880	+	0.104880i
$306$		0			0
$307$	−7.73866	+	11.5817i	−0.441668	+	0.661004i	−0.983796	−	0.179293i	$-0.942619\pi$
$307$	−7.73866	+	11.5817i	−0.441668	+	0.661004i	0.542127	+	0.840296i	$0.317619\pi$
$308$		0			0
$309$	1.64851	−	8.28762i	0.0937804	−	0.471466i
$310$		0			0
$311$	9.17931	−	3.80219i	0.520511	−	0.215603i	−0.106930	−	0.994266i	$-0.534102\pi$
$311$	9.17931	−	3.80219i	0.520511	−	0.215603i	0.627441	+	0.778664i	$0.284102\pi$
$312$		0			0
$313$	14.8947	+	6.16958i	0.841897	+	0.348725i	0.761601	−	0.648046i	$-0.224414\pi$
$313$	14.8947	+	6.16958i	0.841897	+	0.348725i	0.0802956	+	0.996771i	$0.474414\pi$
$314$		0			0
$315$	−0.517447	−	0.774414i	−0.0291548	−	0.0436333i
$316$		0			0
$317$	−30.4022	+	6.04738i	−1.70756	+	0.339654i	−0.949794	−	0.312875i	$-0.898708\pi$
$317$	−30.4022	+	6.04738i	−1.70756	+	0.339654i	−0.757764	+	0.652529i	$0.773708\pi$
$318$		0			0
$319$	11.6743			0.653637
$320$		0			0
$321$	8.37483			0.467437
$322$		0			0
$323$	1.40636	−	0.279742i	0.0782519	−	0.0155653i
$324$		0			0
$325$	9.51456	+	14.2395i	0.527773	+	0.789868i
$326$		0			0
$327$	−0.503954	−	0.208744i	−0.0278687	−	0.0115436i
$328$		0			0
$329$	−2.17950	+	0.902779i	−0.120160	+	0.0497718i
$330$		0			0
$331$	1.73426	−	8.71873i	0.0953238	−	0.479225i	−0.903404	−	0.428791i	$-0.858940\pi$
$331$	1.73426	−	8.71873i	0.0953238	−	0.479225i	0.998727	−	0.0504338i	$-0.0160604\pi$
$332$		0			0
$333$	0.985786	−	1.47533i	0.0540208	−	0.0808478i
$334$		0			0
$335$	−21.7305	−	21.7305i	−1.18727	−	1.18727i
$336$		0			0
$337$	−8.25556	+	8.25556i	−0.449709	+	0.449709i	−0.895258	−	0.445549i	$-0.853009\pi$
$337$	−8.25556	+	8.25556i	−0.449709	+	0.449709i	0.445549	+	0.895258i	$0.353009\pi$
$338$		0			0
$339$	−1.33344	−	0.890978i	−0.0724227	−	0.0483913i
$340$		0			0
$341$	7.11191	+	1.41465i	0.385131	+	0.0766074i
$342$		0			0
$343$	1.69360	+	4.08872i	0.0914459	+	0.220770i
$344$		0			0
$345$	9.86880	−	23.8254i	0.531318	−	1.28272i
$346$		0			0
$347$	−11.1318	+	7.43806i	−0.597588	+	0.399296i	−0.817253	−	0.576280i	$-0.804504\pi$
$347$	−11.1318	+	7.43806i	−0.597588	+	0.399296i	0.219664	+	0.975576i	$0.429504\pi$
$348$		0			0
$349$	0.867225	+	4.35983i	0.0464215	+	0.233377i	0.997030	−	0.0770164i	$-0.0245394\pi$
$349$	0.867225	+	4.35983i	0.0464215	+	0.233377i	−0.950608	+	0.310393i	$0.899539\pi$
$350$		0			0
$351$			4.81651i			0.257086i
$352$		0			0
$353$		−	31.4850i		−	1.67578i	−0.545839	−	0.837890i	$-0.683789\pi$
$353$		−	31.4850i		−	1.67578i	0.545839	−	0.837890i	$-0.316211\pi$
$354$		0			0
$355$	7.67394	+	38.5795i	0.407290	+	2.04759i
$356$		0			0
$357$	0.147717	−	0.0987016i	0.00781803	−	0.00522384i
$358$		0			0
$359$	−6.61491	+	15.9698i	−0.349122	+	0.842854i	0.647603	+	0.761978i	$0.275772\pi$
$359$	−6.61491	+	15.9698i	−0.349122	+	0.842854i	−0.996724	+	0.0808758i	$0.974228\pi$
$360$		0			0
$361$	−4.74334	−	11.4514i	−0.249650	−	0.602707i
$362$		0			0
$363$	19.2617	+	3.83139i	1.01098	+	0.201096i
$364$		0			0
$365$	−38.2110	−	25.5318i	−2.00005	−	1.33639i
$366$		0			0
$367$	−2.68230	+	2.68230i	−0.140015	+	0.140015i	−0.773640	−	0.633625i	$-0.781566\pi$
$367$	−2.68230	+	2.68230i	−0.140015	+	0.140015i	0.633625	+	0.773640i	$0.281566\pi$
$368$		0			0
$369$	8.12891	+	8.12891i	0.423174	+	0.423174i
$370$		0			0
$371$	−1.71123	+	2.56103i	−0.0888424	+	0.132962i
$372$		0			0
$373$	−6.63396	+	33.3511i	−0.343493	+	1.72686i	0.293475	+	0.955967i	$0.405188\pi$
$373$	−6.63396	+	33.3511i	−0.343493	+	1.72686i	−0.636968	+	0.770890i	$0.719812\pi$
$374$		0			0
$375$	−3.90317	+	1.61675i	−0.201559	+	0.0834885i
$376$		0			0
$377$	9.38517	+	3.88746i	0.483361	+	0.200215i
$378$		0			0
$379$	2.07239	+	3.10156i	0.106452	+	0.159316i	0.880871	−	0.473357i	$-0.156958\pi$
$379$	2.07239	+	3.10156i	0.106452	+	0.159316i	−0.774419	+	0.632673i	$0.781958\pi$
$380$		0			0
$381$	6.04281	−	1.20199i	0.309583	−	0.0615798i
$382$		0			0
$383$	23.4907			1.20032			0.600159	−	0.799880i	$-0.295104\pi$
$383$	23.4907			1.20032			0.600159	+	0.799880i	$0.295104\pi$
$384$		0			0
$385$	−5.15543			−0.262745
$386$		0			0
$387$	2.25285	−	0.448119i	0.114519	−	0.0227792i
$388$		0			0
$389$	9.39612	+	14.0623i	0.476402	+	0.712987i	0.989370	−	0.145422i	$-0.0464538\pi$
$389$	9.39612	+	14.0623i	0.476402	+	0.712987i	−0.512967	+	0.858408i	$0.671454\pi$
$390$		0			0
$391$	4.54463	+	1.88245i	0.229832	+	0.0951994i
$392$		0			0
$393$	−17.7056	+	7.33392i	−0.893132	+	0.369947i
$394$		0			0
$395$	−2.06540	+	10.3835i	−0.103922	+	0.522449i
$396$		0			0
$397$	5.92073	−	8.86099i	0.297153	−	0.444720i	−0.652609	−	0.757695i	$-0.726325\pi$
$397$	5.92073	−	8.86099i	0.297153	−	0.444720i	0.949762	+	0.312975i	$0.101325\pi$
$398$		0			0
$399$	0.578660	+	0.578660i	0.0289692	+	0.0289692i
$400$		0			0
$401$	12.3125	−	12.3125i	0.614859	−	0.614859i	−0.329349	−	0.944208i	$-0.606829\pi$
$401$	12.3125	−	12.3125i	0.614859	−	0.614859i	0.944208	+	0.329349i	$0.106829\pi$
$402$		0			0
$403$	5.24630	+	3.50547i	0.261337	+	0.174620i
$404$		0			0
$405$	2.86880	+	0.570640i	0.142552	+	0.0283553i
$406$		0			0
$407$	−3.75856	−	9.07396i	−0.186305	−	0.449780i
$408$		0			0
$409$	11.9692	−	28.8963i	0.591841	−	1.42883i	−0.289882	−	0.957062i	$-0.593616\pi$
$409$	11.9692	−	28.8963i	0.591841	−	1.42883i	0.881723	−	0.471767i	$-0.156384\pi$
$410$		0			0
$411$	18.3737	−	12.2769i	0.906310	−	0.605577i
$412$		0			0
$413$	−0.0418032	−	0.210159i	−0.00205700	−	0.0103413i
$414$		0			0
$415$		−	2.05984i		−	0.101114i
$416$		0			0
$417$			7.76565i			0.380285i
$418$		0			0
$419$	−6.14582	−	30.8971i	−0.300243	−	1.50942i	−0.776500	−	0.630117i	$-0.783007\pi$
$419$	−6.14582	−	30.8971i	−0.300243	−	1.50942i	0.476257	−	0.879306i	$-0.341993\pi$
$420$		0			0
$421$	−2.09636	+	1.40074i	−0.102170	+	0.0682681i	−0.605606	−	0.795765i	$-0.707069\pi$
$421$	−2.09636	+	1.40074i	−0.102170	+	0.0682681i	0.503435	+	0.864033i	$0.332069\pi$
$422$		0			0
$423$	2.83518	−	6.84473i	0.137851	−	0.332802i
$424$		0			0
$425$	0.759174	+	1.83281i	0.0368254	+	0.0889043i
$426$		0			0
$427$	−0.276571	−	0.0550134i	−0.0133842	−	0.00266228i
$428$		0			0
$429$	22.1675	+	14.8118i	1.07026	+	0.715122i
$430$		0			0
$431$	12.1380	−	12.1380i	0.584669	−	0.584669i	−0.351514	−	0.936183i	$-0.614333\pi$
$431$	12.1380	−	12.1380i	0.584669	−	0.584669i	0.936183	+	0.351514i	$0.114333\pi$
$432$		0			0
$433$	−22.3743	−	22.3743i	−1.07524	−	1.07524i	−0.996929	−	0.0783126i	$-0.975047\pi$
$433$	−22.3743	−	22.3743i	−1.07524	−	1.07524i	−0.0783126	−	0.996929i	$-0.524953\pi$
$434$		0			0
$435$	3.42736	−	5.12941i	0.164329	−	0.245936i
$436$		0			0
$437$	−4.42051	+	22.2234i	−0.211462	+	1.06309i
$438$		0			0
$439$	0.796259	−	0.329821i	0.0380034	−	0.0157415i	−0.363601	−	0.931555i	$-0.618453\pi$
$439$	0.796259	−	0.329821i	0.0380034	−	0.0157415i	0.401604	+	0.915813i	$0.368453\pi$
$440$		0			0
$441$	−6.37348	−	2.63998i	−0.303499	−	0.125713i
$442$		0			0
$443$	−6.32934	−	9.47253i	−0.300716	−	0.450053i	0.650082	−	0.759864i	$-0.274734\pi$
$443$	−6.32934	−	9.47253i	−0.300716	−	0.450053i	−0.950798	+	0.309810i	$0.899734\pi$
$444$		0			0
$445$	27.9148	−	5.55259i	1.32329	−	0.263218i
$446$		0			0
$447$	14.7294			0.696677
$448$		0			0
$449$	23.1176			1.09099			0.545495	−	0.838114i	$-0.316342\pi$
$449$	23.1176			1.09099			0.545495	+	0.838114i	$0.316342\pi$
$450$		0			0
$451$	62.4107	−	12.4143i	2.93881	−	0.584565i
$452$		0			0
$453$	10.6471	+	15.9345i	0.500243	+	0.748667i
$454$		0			0
$455$	−4.14452	−	1.71672i	−0.194298	−	0.0804809i
$456$		0			0
$457$	−17.1139	+	7.08880i	−0.800553	+	0.331600i	−0.745178	−	0.666866i	$-0.767635\pi$
$457$	−17.1139	+	7.08880i	−0.800553	+	0.331600i	−0.0553752	+	0.998466i	$0.517635\pi$
$458$		0			0
$459$	−0.108848	+	0.547216i	−0.00508059	+	0.0255418i
$460$		0			0
$461$	−9.72599	+	14.5560i	−0.452984	+	0.677939i	−0.985730	−	0.168337i	$-0.946160\pi$
$461$	−9.72599	+	14.5560i	−0.452984	+	0.677939i	0.532745	+	0.846276i	$0.321160\pi$
$462$		0			0
$463$	15.4991	+	15.4991i	0.720304	+	0.720304i	0.968667	−	0.248363i	$-0.0798925\pi$
$463$	15.4991	+	15.4991i	0.720304	+	0.720304i	−0.248363	+	0.968667i	$0.579893\pi$
$464$		0			0
$465$	2.70948	−	2.70948i	0.125649	−	0.125649i
$466$		0			0
$467$	19.4918	+	13.0240i	0.901971	+	0.602678i	0.917733	−	0.397198i	$-0.130017\pi$
$467$	19.4918	+	13.0240i	0.901971	+	0.602678i	−0.0157622	+	0.999876i	$0.505017\pi$
$468$		0			0
$469$	3.28121	+	0.652673i	0.151512	+	0.0301376i
$470$		0			0
$471$	−4.89789	−	11.8246i	−0.225683	−	0.544847i
$472$		0			0
$473$	4.86559	−	11.7466i	0.223720	−	0.540108i
$474$		0			0
$475$	−7.59805	+	5.07685i	−0.348622	+	0.232942i
$476$		0			0
$477$	−1.88714	−	9.48728i	−0.0864061	−	0.434393i
$478$		0			0
$479$			13.5004i			0.616849i	0.951249	+	0.308424i	$0.0998017\pi$
$479$			13.5004i			0.616849i	−0.951249	+	0.308424i	$0.900198\pi$
$480$		0			0
$481$		−	8.54626i		−	0.389676i
$482$		0			0
$483$	0.547690	+	2.75342i	0.0249208	+	0.125285i
$484$		0			0
$485$	−1.37529	+	0.918937i	−0.0624485	+	0.0417268i
$486$		0			0
$487$	−4.80481	+	11.5998i	−0.217727	+	0.525639i	−0.994572	−	0.104053i	$-0.966819\pi$
$487$	−4.80481	+	11.5998i	−0.217727	+	0.525639i	0.776845	+	0.629692i	$0.216819\pi$
$488$		0			0
$489$	3.18258	+	7.68342i	0.143921	+	0.347456i
$490$		0			0
$491$	−31.5600	−	6.27768i	−1.42428	−	0.283308i	−0.577999	−	0.816037i	$-0.696166\pi$
$491$	−31.5600	−	6.27768i	−1.42428	−	0.283308i	−0.846286	+	0.532730i	$0.821166\pi$
$492$		0			0
$493$	0.978420	+	0.653759i	0.0440658	+	0.0294438i
$494$		0			0
$495$	11.4485	−	11.4485i	0.514572	−	0.514572i
$496$		0			0
$497$	−3.02790	−	3.02790i	−0.135820	−	0.135820i
$498$		0			0
$499$	12.7702	−	19.1119i	0.571671	−	0.855565i	−0.427147	−	0.904182i	$-0.640481\pi$
$499$	12.7702	−	19.1119i	0.571671	−	0.855565i	0.998818	+	0.0486167i	$0.0154813\pi$
$500$		0			0
$501$	1.10238	−	5.54203i	0.0492506	−	0.247600i
$502$		0			0
$503$	−26.6111	+	11.0227i	−1.18653	+	0.491476i	−0.886623	−	0.462493i	$-0.846955\pi$
$503$	−26.6111	+	11.0227i	−1.18653	+	0.491476i	−0.299905	+	0.953969i	$0.596955\pi$
$504$		0			0
$505$	29.9910	+	12.4227i	1.33458	+	0.552803i
$506$		0			0
$507$	5.66612	+	8.47995i	0.251641	+	0.376608i
$508$		0			0
$509$	−6.48058	+	1.28907i	−0.287247	+	0.0571370i	−0.336611	−	0.941644i	$-0.609281\pi$
$509$	−6.48058	+	1.28907i	−0.287247	+	0.0571370i	0.0493638	+	0.998781i	$0.484281\pi$
$510$		0			0
$511$	5.00283			0.221312
$512$		0			0
$513$	−2.57003			−0.113470
$514$		0			0
$515$	−24.2413	+	4.82189i	−1.06820	+	0.212478i
$516$		0			0
$517$	−22.7834	−	34.0977i	−1.00201	−	1.49962i
$518$		0			0
$519$	−1.14570	−	0.474565i	−0.0502907	−	0.0208311i
$520$		0			0
$521$	−4.49853	+	1.86335i	−0.197084	+	0.0816349i	−0.479042	−	0.877792i	$-0.659016\pi$
$521$	−4.49853	+	1.86335i	−0.197084	+	0.0816349i	0.281958	+	0.959427i	$0.409016\pi$
$522$		0			0
$523$	−2.98320	+	14.9975i	−0.130446	+	0.655797i	0.859127	+	0.511763i	$0.171007\pi$
$523$	−2.98320	+	14.9975i	−0.130446	+	0.655797i	−0.989573	+	0.144034i	$0.953993\pi$
$524$		0			0
$525$	−0.629009	+	0.941379i	−0.0274522	+	0.0410851i
$526$		0			0
$527$	0.516826	+	0.516826i	0.0225133	+	0.0225133i
$528$		0			0
$529$	−38.7010	+	38.7010i	−1.68265	+	1.68265i
$530$		0			0
$531$	0.559526	+	0.373863i	0.0242814	+	0.0162243i
$532$		0			0
$533$	54.3067	+	10.8023i	2.35229	+	0.467899i
$534$		0			0
$535$	−9.37437	−	22.6317i	−0.405289	−	0.978455i
$536$		0			0
$537$	1.93234	−	4.66508i	0.0833866	−	0.201313i
$538$		0			0
$539$	−31.7501	+	21.2148i	−1.36758	+	0.913785i
$540$		0			0
$541$	2.50762	+	12.6067i	0.107811	+	0.542002i	0.996507	+	0.0835060i	$0.0266118\pi$
$541$	2.50762	+	12.6067i	0.107811	+	0.542002i	−0.888696	+	0.458496i	$0.848388\pi$
$542$		0			0
$543$			13.9927i			0.600485i
$544$		0			0
$545$			1.59552i			0.0683444i
$546$		0			0
$547$	−4.22387	−	21.2348i	−0.180600	−	0.907936i	−0.959698	−	0.281034i	$-0.909323\pi$
$547$	−4.22387	−	21.2348i	−0.180600	−	0.907936i	0.779098	−	0.626902i	$-0.215677\pi$
$548$		0			0
$549$	0.736340	−	0.492006i	0.0314262	−	0.0209983i
$550$		0			0
$551$	−2.07430	+	5.00781i	−0.0883683	+	0.213340i
$552$		0			0
$553$	−0.441045	−	1.06478i	−0.0187551	−	0.0452789i
$554$		0			0
$555$	−5.09031	−	1.01253i	−0.216072	−	0.0429793i
$556$		0			0
$557$	17.0377	+	11.3842i	0.721909	+	0.482364i	0.861444	−	0.507853i	$-0.169561\pi$
$557$	17.0377	+	11.3842i	0.721909	+	0.482364i	−0.139535	+	0.990217i	$0.544561\pi$
$558$		0			0
$559$	7.82304	−	7.82304i	0.330879	−	0.330879i
$560$		0			0
$561$	2.18377	+	2.18377i	0.0921989	+	0.0921989i
$562$		0			0
$563$	16.4974	−	24.6900i	0.695281	−	1.04056i	−0.300935	−	0.953645i	$-0.597299\pi$
$563$	16.4974	−	24.6900i	0.695281	−	1.04056i	0.996216	−	0.0869163i	$-0.0277013\pi$
$564$		0			0
$565$	−0.915145	+	4.60075i	−0.0385005	+	0.193555i
$566$		0			0
$567$	−0.294182	+	0.121854i	−0.0123545	+	0.00511739i
$568$		0			0
$569$	−23.1377	−	9.58394i	−0.969982	−	0.401780i	−0.159277	−	0.987234i	$-0.550916\pi$
$569$	−23.1377	−	9.58394i	−0.969982	−	0.401780i	−0.810706	+	0.585454i	$0.800916\pi$
$570$		0			0
$571$	19.8386	+	29.6906i	0.830222	+	1.24251i	0.967724	+	0.252013i	$0.0810926\pi$
$571$	19.8386	+	29.6906i	0.830222	+	1.24251i	−0.137502	+	0.990501i	$0.543907\pi$
$572$		0			0
$573$	−3.15988	+	0.628538i	−0.132006	+	0.0262576i
$574$		0			0
$575$	−31.3484			−1.30732
$576$		0			0
$577$	41.3597			1.72183			0.860914	−	0.508751i	$-0.169893\pi$
$577$	41.3597			1.72183			0.860914	+	0.508751i	$0.169893\pi$
$578$		0			0
$579$	−19.9036	+	3.95907i	−0.827166	+	0.164534i
$580$		0			0
$581$	0.124580	+	0.186447i	0.00516843	+	0.00773511i
$582$		0			0
$583$	−49.4676	−	20.4902i	−2.04874	−	0.848616i
$584$		0			0
$585$	13.0159	−	5.39136i	0.538141	−	0.222905i
$586$		0			0
$587$	−6.18128	+	31.0754i	−0.255129	+	1.28262i	0.614502	+	0.788915i	$0.289357\pi$
$587$	−6.18128	+	31.0754i	−0.255129	+	1.28262i	−0.869631	+	0.493703i	$0.835643\pi$
$588$		0			0
$589$	−1.87047	+	2.79936i	−0.0770715	+	0.115346i
$590$		0			0
$591$	−12.9085	−	12.9085i	−0.530984	−	0.530984i
$592$		0			0
$593$	−0.502147	+	0.502147i	−0.0206207	+	0.0206207i	−0.717342	−	0.696721i	$-0.754641\pi$
$593$	−0.502147	+	0.502147i	−0.0206207	+	0.0206207i	0.696721	+	0.717342i	$0.254641\pi$
$594$		0			0
$595$	−0.432073	−	0.288702i	−0.0177133	−	0.0118356i
$596$		0			0
$597$	12.0355	+	2.39401i	0.492581	+	0.0979805i
$598$		0			0
$599$	7.67530	+	18.5298i	0.313604	+	0.757108i	0.999566	+	0.0294698i	$0.00938188\pi$
$599$	7.67530	+	18.5298i	0.313604	+	0.757108i	−0.685961	+	0.727638i	$0.740618\pi$
$600$		0			0
$601$	−8.64504	+	20.8710i	−0.352639	+	0.851345i	0.643654	+	0.765317i	$0.277418\pi$
$601$	−8.64504	+	20.8710i	−0.352639	+	0.851345i	−0.996293	+	0.0860284i	$0.972582\pi$
$602$		0			0
$603$	−8.73586	+	5.83712i	−0.355752	+	0.237706i
$604$		0			0
$605$	−11.2068	−	56.3405i	−0.455622	−	2.29057i
$606$		0			0
$607$			18.5694i			0.753711i	0.926272	+	0.376855i	$0.122995\pi$
$607$			18.5694i			0.753711i	−0.926272	+	0.376855i	$0.877005\pi$
$608$		0			0
$609$			0.671576i			0.0272136i
$610$		0			0
$611$	−6.96160	−	34.9983i	−0.281636	−	1.41588i
$612$		0			0
$613$	24.5393	−	16.3967i	0.991135	−	0.662255i	0.0494587	−	0.998776i	$-0.484250\pi$
$613$	24.5393	−	16.3967i	0.991135	−	0.662255i	0.941676	+	0.336521i	$0.109250\pi$
$614$		0			0
$615$	12.8681	−	31.0663i	0.518890	−	1.25271i
$616$		0			0
$617$	13.0190	+	31.4307i	0.524126	+	1.26535i	0.935320	+	0.353804i	$0.115112\pi$
$617$	13.0190	+	31.4307i	0.524126	+	1.26535i	−0.411194	+	0.911548i	$0.634888\pi$
$618$		0			0
$619$	−20.5706	−	4.09174i	−0.826802	−	0.164461i	−0.236487	−	0.971635i	$-0.575996\pi$
$619$	−20.5706	−	4.09174i	−0.826802	−	0.164461i	−0.590314	+	0.807174i	$0.700996\pi$
$620$		0			0
$621$	−7.33069	−	4.89821i	−0.294170	−	0.196558i
$622$		0			0
$623$	−2.19088	+	2.19088i	−0.0877759	+	0.0877759i
$624$		0			0
$625$	21.3091	+	21.3091i	0.852364	+	0.852364i
$626$		0			0
$627$	−7.90341	+	11.8283i	−0.315632	+	0.472377i
$628$		0			0
$629$	0.193136	−	0.970962i	0.00770085	−	0.0387148i
$630$		0			0
$631$	37.1648	−	15.3942i	1.47951	−	0.612832i	0.510503	−	0.859876i	$-0.329459\pi$
$631$	37.1648	−	15.3942i	1.47951	−	0.612832i	0.969004	+	0.247044i	$0.0794591\pi$
$632$		0			0
$633$	11.4747	+	4.75297i	0.456077	+	0.188913i
$634$		0			0
$635$	−10.0122	−	14.9843i	−0.397323	−	0.594636i
$636$		0			0
$637$	−32.5888	+	6.48231i	−1.29121	+	0.256838i
$638$		0			0
$639$	13.4480			0.531993
$640$		0			0
$641$	−35.5138			−1.40271			−0.701356	−	0.712811i	$-0.747422\pi$
$641$	−35.5138			−1.40271			−0.701356	+	0.712811i	$0.747422\pi$
$642$		0			0
$643$	−21.5451	+	4.28559i	−0.849656	+	0.169007i	−0.600667	−	0.799499i	$-0.705098\pi$
$643$	−21.5451	+	4.28559i	−0.849656	+	0.169007i	−0.248989	+	0.968506i	$0.580098\pi$
$644$		0			0
$645$	−3.73270	−	5.58638i	−0.146975	−	0.219964i
$646$		0			0
$647$	−12.8162	−	5.30863i	−0.503856	−	0.208704i	0.116253	−	0.993220i	$-0.462912\pi$
$647$	−12.8162	−	5.30863i	−0.503856	−	0.208704i	−0.620109	+	0.784516i	$0.712912\pi$
$648$		0			0
$649$	3.44133	−	1.42545i	0.135084	−	0.0559537i
$650$		0			0
$651$	−0.0813787	+	0.409118i	−0.00318948	+	0.0160346i
$652$		0			0
$653$	−4.45389	+	6.66572i	−0.174294	+	0.260850i	−0.908324	−	0.418268i	$-0.862637\pi$
$653$	−4.45389	+	6.66572i	−0.174294	+	0.260850i	0.734029	+	0.679118i	$0.237637\pi$
$654$		0			0
$655$	39.6376	+	39.6376i	1.54877	+	1.54877i
$656$		0			0
$657$	−11.1097	+	11.1097i	−0.433429	+	0.433429i
$658$		0			0
$659$	−17.4455	−	11.6567i	−0.679579	−	0.454080i	0.167272	−	0.985911i	$-0.446504\pi$
$659$	−17.4455	−	11.6567i	−0.679579	−	0.454080i	−0.846851	+	0.531831i	$0.821504\pi$
$660$		0			0
$661$	−14.4368	−	2.87166i	−0.561527	−	0.111695i	−0.0938378	−	0.995588i	$-0.529913\pi$
$661$	−14.4368	−	2.87166i	−0.561527	−	0.111695i	−0.467690	+	0.883893i	$0.654913\pi$
$662$		0			0
$663$	1.02839	+	2.48274i	0.0399392	+	0.0964218i
$664$		0			0
$665$	0.916019	−	2.21147i	0.0355217	−	0.0857569i
$666$		0			0
$667$	−15.4611	+	10.3308i	−0.598655	+	0.400008i
$668$		0			0
$669$	3.21354	+	16.1555i	0.124243	+	0.624609i
$670$		0			0
$671$		−	4.90196i		−	0.189238i
$672$		0			0
$673$		−	9.82761i		−	0.378826i	−0.981897	−	0.189413i	$-0.939341\pi$
$673$		−	9.82761i		−	0.378826i	0.981897	−	0.189413i	$-0.0606586\pi$
$674$		0			0
$675$	−0.693670	−	3.48732i	−0.0266994	−	0.134227i
$676$		0			0
$677$	−18.3376	+	12.2528i	−0.704770	+	0.470912i	−0.855593	−	0.517648i	$-0.826808\pi$
$677$	−18.3376	+	12.2528i	−0.704770	+	0.470912i	0.150823	+	0.988561i	$0.451808\pi$
$678$		0			0
$679$	0.0689066	−	0.166355i	0.00264439	−	0.00638413i
$680$		0			0
$681$	2.76017	+	6.66363i	0.105770	+	0.255351i
$682$		0			0
$683$	−39.0856	−	7.77460i	−1.49557	−	0.297487i	−0.621548	−	0.783376i	$-0.713496\pi$
$683$	−39.0856	−	7.77460i	−1.49557	−	0.297487i	−0.874020	+	0.485889i	$0.838496\pi$
$684$		0			0
$685$	−53.7433	−	35.9101i	−2.05342	−	1.37205i
$686$		0			0
$687$	−3.88209	+	3.88209i	−0.148111	+	0.148111i
$688$		0			0
$689$	−32.9447	−	32.9447i	−1.25509	−	1.25509i
$690$		0			0
$691$	−0.586959	+	0.878446i	−0.0223290	+	0.0334177i	−0.842466	−	0.538749i	$-0.818897\pi$
$691$	−0.586959	+	0.878446i	−0.0223290	+	0.0334177i	0.820137	+	0.572167i	$0.193897\pi$
$692$		0			0
$693$	−0.343854	+	1.72867i	−0.0130619	+	0.0656668i
$694$		0			0
$695$	20.9855	−	8.69248i	0.796025	−	0.329724i
$696$		0			0
$697$	5.92580	+	2.45455i	0.224456	+	0.0929726i
$698$		0			0
$699$	−5.41767	−	8.10812i	−0.204915	−	0.306677i
$700$		0			0
$701$	7.02983	−	1.39832i	0.265513	−	0.0528138i	−0.0605384	−	0.998166i	$-0.519282\pi$
$701$	7.02983	−	1.39832i	0.265513	−	0.0528138i	0.326051	+	0.945352i	$0.394282\pi$
$702$		0			0
$703$	4.56018			0.171990
$704$		0			0
$705$	−21.6704			−0.816155
$706$		0			0
$707$	−3.46597	+	0.689424i	−0.130351	+	0.0259284i
$708$		0			0
$709$	16.3103	+	24.4101i	0.612546	+	0.916740i	0.999987	−	0.00515478i	$-0.00164083\pi$
$709$	16.3103	+	24.4101i	0.612546	+	0.916740i	−0.387441	+	0.921895i	$0.626641\pi$
$710$		0			0
$711$	3.34394	+	1.38510i	0.125407	+	0.0519454i
$712$		0			0
$713$	−10.6706	+	4.41990i	−0.399617	+	0.165527i
$714$		0			0
$715$	15.2136	−	76.4839i	0.568956	−	2.86034i
$716$		0			0
$717$	12.2328	−	18.3077i	0.456843	−	0.683714i
$718$		0			0
$719$	−2.72562	−	2.72562i	−0.101649	−	0.101649i	0.654454	−	0.756102i	$-0.272899\pi$
$719$	−2.72562	−	2.72562i	−0.101649	−	0.101649i	−0.756102	+	0.654454i	$0.772899\pi$
$720$		0			0
$721$	1.90257	−	1.90257i	0.0708555	−	0.0708555i
$722$		0			0
$723$	11.4044	+	7.62018i	0.424135	+	0.283398i
$724$		0			0
$725$	−7.35505	−	1.46301i	−0.273160	−	0.0543349i
$726$		0			0
$727$	16.6313	+	40.1516i	0.616823	+	1.48914i	0.855374	+	0.518011i	$0.173328\pi$
$727$	16.6313	+	40.1516i	0.616823	+	1.48914i	−0.238551	+	0.971130i	$0.576672\pi$
$728$		0			0
$729$	0.382683	−	0.923880i	0.0141735	−	0.0342178i
$730$		0			0
$731$	1.06559	−	0.712003i	0.0394122	−	0.0263344i
$732$		0			0
$733$	−1.23293	−	6.19836i	−0.0455393	−	0.228942i	0.951313	−	0.308228i	$-0.0997359\pi$
$733$	−1.23293	−	6.19836i	−0.0455393	−	0.228942i	−0.996852	+	0.0792861i	$0.974736\pi$
$734$		0			0
$735$			20.1784i			0.744293i
$736$		0			0
$737$			58.1563i			2.14222i
$738$		0			0
$739$	−3.58939	−	18.0451i	−0.132038	−	0.663799i	−0.988940	−	0.148319i	$-0.952614\pi$
$739$	−3.58939	−	18.0451i	−0.132038	−	0.663799i	0.856902	−	0.515480i	$-0.172386\pi$
$740$		0			0
$741$	−10.2924	+	6.87716i	−0.378101	+	0.252639i
$742$		0			0
$743$	7.10234	−	17.1466i	0.260560	−	0.629047i	−0.738414	−	0.674348i	$-0.764425\pi$
$743$	7.10234	−	17.1466i	0.260560	−	0.629047i	0.998973	+	0.0453012i	$0.0144248\pi$
$744$		0			0
$745$	−16.4874	−	39.8040i	−0.604050	−	1.45831i
$746$		0			0
$747$	−0.690687	−	0.137386i	−0.0252709	−	0.00502670i
$748$		0			0
$749$	2.21729	+	1.48155i	0.0810181	+	0.0541346i
$750$		0			0
$751$	12.0765	−	12.0765i	0.440679	−	0.440679i	−0.451561	−	0.892240i	$-0.649133\pi$
$751$	12.0765	−	12.0765i	0.440679	−	0.440679i	0.892240	+	0.451561i	$0.149133\pi$
$752$		0			0
$753$	7.49340	+	7.49340i	0.273075	+	0.273075i
$754$		0			0
$755$	31.1427	−	46.6084i	1.13340	−	1.69625i
$756$		0			0
$757$	3.15311	−	15.8517i	0.114602	−	0.576142i	−0.880225	−	0.474556i	$-0.842609\pi$
$757$	3.15311	−	15.8517i	0.114602	−	0.576142i	0.994827	−	0.101585i	$-0.0323915\pi$
$758$		0			0
$759$	−45.0870	+	18.6757i	−1.63656	+	0.677883i
$760$		0			0
$761$	−12.7704	−	5.28967i	−0.462927	−	0.191751i	0.139015	−	0.990290i	$-0.455606\pi$
$761$	−12.7704	−	5.28967i	−0.462927	−	0.191751i	−0.601942	+	0.798540i	$0.705606\pi$
$762$		0			0
$763$	−0.0964972	−	0.144418i	−0.00349343	−	0.00522829i
$764$		0			0
$765$	1.60061	−	0.318380i	0.0578701	−	0.0115111i
$766$		0			0
$767$	3.24120			0.117033
$768$		0			0
$769$	−36.5971			−1.31973			−0.659863	−	0.751386i	$-0.729386\pi$
$769$	−36.5971			−1.31973			−0.659863	+	0.751386i	$0.729386\pi$
$770$		0			0
$771$	13.1278	−	2.61129i	0.472787	−	0.0940432i
$772$		0			0
$773$	−19.3354	−	28.9374i	−0.695445	−	1.04081i	−0.996199	−	0.0871053i	$-0.972238\pi$
$773$	−19.3354	−	28.9374i	−0.695445	−	1.04081i	0.300754	−	0.953702i	$-0.402762\pi$
$774$		0			0
$775$	−4.30336	−	1.78251i	−0.154581	−	0.0640296i
$776$		0			0
$777$	0.521987	−	0.216214i	0.0187262	−	0.00775664i
$778$		0			0
$779$	−5.76396	+	28.9774i	−0.206515	+	1.03822i
$780$		0			0
$781$	41.3555	−	61.8928i	1.47982	−	2.21470i
$782$		0			0
$783$	−1.49135	−	1.49135i	−0.0532965	−	0.0532965i
$784$		0			0
$785$	−26.4716	+	26.4716i	−0.944814	+	0.944814i
$786$		0			0
$787$	−39.0123	−	26.0672i	−1.39064	−	0.929195i	−0.999962	−	0.00866684i	$-0.997241\pi$
$787$	−39.0123	−	26.0672i	−1.39064	−	0.929195i	−0.390676	−	0.920528i	$-0.627759\pi$
$788$		0			0
$789$	−2.07077	−	0.411902i	−0.0737215	−	0.0146641i
$790$		0			0
$791$	−0.195420	−	0.471785i	−0.00694833	−	0.0167747i
$792$		0			0
$793$	1.63231	−	3.94076i	0.0579652	−	0.139940i
$794$		0			0
$795$	−23.5256	+	15.7193i	−0.834367	+	0.557506i
$796$		0			0
$797$	−4.26222	−	21.4276i	−0.150976	−	0.759005i	−0.979876	−	0.199609i	$-0.936033\pi$
$797$	−4.26222	−	21.4276i	−0.150976	−	0.759005i	0.828900	−	0.559397i	$-0.188967\pi$
$798$		0			0
$799$		−	4.13357i		−	0.146235i
$800$		0			0
$801$		−	9.73047i		−	0.343809i
$802$		0			0
$803$	16.9664	+	85.2957i	0.598730	+	3.01002i
$804$		0			0
$805$	6.82765	−	4.56209i	0.240643	−	0.160793i
$806$		0			0
$807$	2.23326	−	5.39157i	0.0786145	−	0.189792i
$808$		0			0
$809$	3.30815	+	7.98658i	0.116308	+	0.280793i	0.971304	−	0.237842i	$-0.0764402\pi$
$809$	3.30815	+	7.98658i	0.116308	+	0.280793i	−0.854995	+	0.518636i	$0.826440\pi$
$810$		0			0
$811$	28.3926	+	5.64764i	0.996998	+	0.198315i	0.666511	−	0.745495i	$-0.267787\pi$
$811$	28.3926	+	5.64764i	0.996998	+	0.198315i	0.330487	+	0.943810i	$0.392787\pi$
$812$		0			0
$813$	14.2168	+	9.49934i	0.498604	+	0.333157i
$814$		0			0
$815$	17.2009	−	17.2009i	0.602520	−	0.602520i
$816$		0			0
$817$	4.17428	+	4.17428i	0.146039	+	0.146039i
$818$		0			0
$819$	−0.852063	+	1.27520i	−0.0297735	+	0.0445592i
$820$		0			0
$821$	−0.523141	+	2.63001i	−0.0182578	+	0.0917879i	−0.988840	−	0.148983i	$-0.952400\pi$
$821$	−0.523141	+	2.63001i	−0.0182578	+	0.0917879i	0.970582	+	0.240771i	$0.0774001\pi$
$822$		0			0
$823$	−28.2090	+	11.6845i	−0.983304	+	0.407298i	−0.815648	−	0.578548i	$-0.803620\pi$
$823$	−28.2090	+	11.6845i	−0.983304	+	0.407298i	−0.167655	+	0.985846i	$0.553620\pi$
$824$		0			0
$825$	−18.1832	−	7.53173i	−0.633058	−	0.262221i
$826$		0			0
$827$	3.65599	+	5.47157i	0.127131	+	0.190265i	0.889575	−	0.456789i	$-0.151001\pi$
$827$	3.65599	+	5.47157i	0.127131	+	0.190265i	−0.762444	+	0.647054i	$0.776001\pi$
$828$		0			0
$829$	−39.2725	+	7.81178i	−1.36399	+	0.271314i	−0.822199	−	0.569200i	$-0.807253\pi$
$829$	−39.2725	+	7.81178i	−1.36399	+	0.271314i	−0.541790	+	0.840514i	$0.682253\pi$
$830$		0			0
$831$	19.4882			0.676037
$832$		0			0
$833$	−3.84898			−0.133359
$834$		0			0
$835$	−16.2104	+	3.22446i	−0.560986	+	0.111587i
$836$		0			0
$837$	−0.727802	−	1.08923i	−0.0251565	−	0.0376494i
$838$		0			0
$839$	0.387077	+	0.160333i	0.0133634	+	0.00553530i	0.389355	−	0.921088i	$-0.372698\pi$
$839$	0.387077	+	0.160333i	0.0133634	+	0.00553530i	−0.375992	+	0.926623i	$0.622698\pi$
$840$		0			0
$841$	22.6829	−	9.39555i	0.782168	−	0.323984i
$842$		0			0
$843$	2.48388	−	12.4873i	0.0855495	−	0.430086i
$844$		0			0
$845$	16.5734	−	24.8039i	0.570143	−	0.853279i
$846$		0			0
$847$	4.42187	+	4.42187i	0.151937	+	0.151937i
$848$		0			0
$849$	12.4686	−	12.4686i	0.427923	−	0.427923i
$850$		0			0
$851$	13.0073	+	8.69123i	0.445886	+	0.297932i
$852$		0			0
$853$	−35.1220	−	6.98620i	−1.20255	−	0.239203i	−0.447148	−	0.894460i	$-0.647560\pi$
$853$	−35.1220	−	6.98620i	−1.20255	−	0.239203i	−0.755406	+	0.655257i	$0.772560\pi$
$854$		0			0
$855$	2.87676	+	6.94512i	0.0983832	+	0.237518i
$856$		0			0
$857$	−10.0446	+	24.2499i	−0.343118	+	0.828361i	0.654279	+	0.756253i	$0.272972\pi$
$857$	−10.0446	+	24.2499i	−0.343118	+	0.828361i	−0.997397	+	0.0721071i	$0.977028\pi$
$858$		0			0
$859$	12.8731	−	8.60156i	0.439226	−	0.293482i	−0.316228	−	0.948683i	$-0.602416\pi$
$859$	12.8731	−	8.60156i	0.439226	−	0.293482i	0.755454	+	0.655202i	$0.227416\pi$
$860$		0			0
$861$	0.714140	+	3.59023i	0.0243378	+	0.122355i
$862$		0			0
$863$		−	18.1277i		−	0.617073i	−0.951213	−	0.308536i	$-0.900161\pi$
$863$		−	18.1277i		−	0.617073i	0.951213	−	0.308536i	$-0.0998392\pi$
$864$		0			0
$865$			3.62729i			0.123331i
$866$		0			0
$867$	−3.25581	−	16.3680i	−0.110573	−	0.555888i
$868$		0			0
$869$	16.6581	−	11.1306i	0.565089	−	0.377580i
$870$		0			0
$871$	−19.3656	+	46.7527i	−0.656179	+	1.58416i
$872$		0			0
$873$	0.216401	+	0.522439i	0.00732408	+	0.0176819i
$874$		0			0
$875$	−1.31940	−	0.262445i	−0.0446039	−	0.00887227i
$876$		0			0
$877$	−9.44491	−	6.31089i	−0.318932	−	0.213104i	0.385791	−	0.922586i	$-0.373929\pi$
$877$	−9.44491	−	6.31089i	−0.318932	−	0.213104i	−0.704723	+	0.709483i	$0.748929\pi$
$878$		0			0
$879$	11.3093	−	11.3093i	0.381453	−	0.381453i
$880$		0			0
$881$	−13.7251	−	13.7251i	−0.462412	−	0.462412i	0.437034	−	0.899445i	$-0.356029\pi$
$881$	−13.7251	−	13.7251i	−0.462412	−	0.462412i	−0.899445	+	0.437034i	$0.856029\pi$
$882$		0			0
$883$	−2.77069	+	4.14663i	−0.0932411	+	0.139545i	−0.875158	−	0.483838i	$-0.839242\pi$
$883$	−2.77069	+	4.14663i	−0.0932411	+	0.139545i	0.781916	+	0.623383i	$0.214242\pi$
$884$		0			0
$885$	0.384004	−	1.93052i	0.0129081	−	0.0648937i
$886$		0			0
$887$	−21.8529	+	9.05179i	−0.733750	+	0.303929i	−0.718092	−	0.695948i	$-0.754984\pi$
$887$	−21.8529	+	9.05179i	−0.733750	+	0.303929i	−0.0156581	+	0.999877i	$0.504984\pi$
$888$		0			0
$889$	1.81251	+	0.750767i	0.0607897	+	0.0251799i
$890$		0			0
$891$	−3.07522	−	4.60240i	−0.103024	−	0.154186i
$892$		0			0
$893$	18.6747	−	3.71462i	0.624924	−	0.124305i
$894$		0			0
$895$	−14.7696			−0.493695
$896$		0			0
$897$	−42.4650			−1.41786
$898$		0			0
$899$	−2.70984	+	0.539020i	−0.0903781	+	0.0179773i
$900$		0			0
$901$	−2.99841	−	4.48744i	−0.0998916	−	0.149498i
$902$		0			0
$903$	0.675731	+	0.279897i	0.0224869	+	0.00931439i
$904$		0			0
$905$	37.8132	−	15.6628i	1.25695	−	0.520648i
$906$		0			0
$907$	0.516883	−	2.59855i	0.0171628	−	0.0862833i	−0.971255	−	0.238043i	$-0.923494\pi$
$907$	0.516883	−	2.59855i	0.0171628	−	0.0862833i	0.988417	+	0.151760i	$0.0484940\pi$
$908$		0			0
$909$	6.16579	−	9.22776i	0.204506	−	0.306065i
$910$		0			0
$911$	30.6239	+	30.6239i	1.01461	+	1.01461i	0.999892	+	0.0147224i	$0.00468644\pi$
$911$	30.6239	+	30.6239i	1.01461	+	1.01461i	0.0147224	+	0.999892i	$0.495314\pi$
$912$		0			0
$913$	−2.75632	+	2.75632i	−0.0912210	+	0.0912210i
$914$		0			0
$915$	−2.15380	−	1.43912i	−0.0712023	−	0.0475758i
$916$		0			0
$917$	−5.98509	−	1.19051i	−0.197645	−	0.0393141i
$918$		0			0
$919$	−4.08571	−	9.86378i	−0.134775	−	0.325376i	0.842055	−	0.539392i	$-0.181346\pi$
$919$	−4.08571	−	9.86378i	−0.134775	−	0.325376i	−0.976830	+	0.214015i	$0.931346\pi$
$920$		0			0
$921$	5.33048	−	12.8689i	0.175645	−	0.424045i
$922$		0			0
$923$	53.8561	−	35.9855i	1.77270	−	1.18448i
$924$		0			0
$925$	1.23083	+	6.18779i	0.0404693	+	0.203453i
$926$		0			0
$927$			8.44998i			0.277534i
$928$		0			0
$929$		−	2.01972i		−	0.0662650i	−0.999451	−	0.0331325i	$-0.989452\pi$
$929$		−	2.01972i		−	0.0662650i	0.999451	−	0.0331325i	$-0.0105483\pi$
$930$		0			0
$931$	−3.45888	−	17.3890i	−0.113360	−	0.569900i
$932$		0			0
$933$	−8.26116	+	5.51993i	−0.270458	+	0.180714i
$934$		0			0
$935$	3.45691	−	8.34572i	0.113053	−	0.272934i
$936$		0			0
$937$	9.96228	+	24.0511i	0.325453	+	0.785714i	0.998919	+	0.0464951i	$0.0148052\pi$
$937$	9.96228	+	24.0511i	0.325453	+	0.785714i	−0.673465	+	0.739219i	$0.735195\pi$
$938$		0			0
$939$	−15.8121	−	3.14522i	−0.516008	−	0.102640i
$940$		0			0
$941$	19.7754	+	13.2135i	0.644659	+	0.430747i	0.834455	−	0.551076i	$-0.185783\pi$
$941$	19.7754	+	13.2135i	0.644659	+	0.430747i	−0.189796	+	0.981824i	$0.560783\pi$
$942$		0			0
$943$	−71.6689	+	71.6689i	−2.33386	+	2.33386i
$944$		0			0
$945$	0.658585	+	0.658585i	0.0214238	+	0.0214238i
$946$		0			0
$947$	−14.6312	+	21.8971i	−0.475450	+	0.711561i	−0.989231	−	0.146360i	$-0.953244\pi$
$947$	−14.6312	+	21.8971i	−0.475450	+	0.711561i	0.513782	+	0.857921i	$0.328244\pi$
$948$		0			0
$949$	−14.7633	+	74.2201i	−0.479237	+	2.40929i
$950$		0			0
$951$	28.6383	−	11.8624i	0.928659	−	0.384663i
$952$		0			0
$953$	−16.4109	−	6.79760i	−0.531600	−	0.220196i	0.100704	−	0.994916i	$-0.467890\pi$
$953$	−16.4109	−	6.79760i	−0.531600	−	0.220196i	−0.632304	+	0.774721i	$0.717890\pi$
$954$		0			0
$955$	5.23554	+	7.83553i	0.169418	+	0.253552i
$956$		0			0
$957$	−11.4500	+	2.27755i	−0.370127	+	0.0736227i
$958$		0			0
$959$	7.03642			0.227218
$960$		0			0
$961$	29.2839			0.944641
$962$		0			0
$963$	−8.21391	+	1.63385i	−0.264690	+	0.0526500i
$964$		0			0
$965$	32.9779	+	49.3549i	1.06160	+	1.58879i
$966$		0			0
$967$	30.9379	+	12.8149i	0.994897	+	0.412100i	0.819923	−	0.572473i	$-0.194016\pi$
$967$	30.9379	+	12.8149i	0.994897	+	0.412100i	0.174974	+	0.984573i	$0.444016\pi$
$968$		0			0
$969$	−1.32476	+	0.548734i	−0.0425575	+	0.0176279i
$970$		0			0
$971$	−9.31325	+	46.8209i	−0.298876	+	1.50255i	0.481056	+	0.876690i	$0.340253\pi$
$971$	−9.31325	+	46.8209i	−0.298876	+	1.50255i	−0.779933	+	0.625864i	$0.784747\pi$
$972$		0			0
$973$	−1.37378	+	2.05601i	−0.0440414	+	0.0659126i
$974$		0			0
$975$	−12.1097	−	12.1097i	−0.387822	−	0.387822i
$976$		0			0
$977$	26.4810	−	26.4810i	0.847201	−	0.847201i	−0.142582	−	0.989783i	$-0.545540\pi$
$977$	26.4810	−	26.4810i	0.847201	−	0.847201i	0.989783	+	0.142582i	$0.0455405\pi$
$978$		0			0
$979$	−44.7835	−	29.9234i	−1.43129	−	0.956355i
$980$		0			0
$981$	0.534994	+	0.106417i	0.0170811	+	0.00339763i
$982$		0			0
$983$	−9.39257	−	22.6757i	−0.299577	−	0.723242i	−0.999955	−	0.00947017i	$-0.996986\pi$
$983$	−9.39257	−	22.6757i	−0.299577	−	0.723242i	0.700379	−	0.713771i	$-0.253014\pi$
$984$		0			0
$985$	−20.4341	+	49.3323i	−0.651085	+	1.57186i
$986$		0			0
$987$	1.96150	−	1.31063i	0.0624352	−	0.0417179i
$988$		0			0
$989$	3.95087	+	19.8623i	0.125630	+	0.631586i
$990$		0			0
$991$		−	9.05267i		−	0.287567i	−0.989609	−	0.143784i	$-0.954073\pi$
$991$		−	9.05267i		−	0.287567i	0.989609	−	0.143784i	$-0.0459270\pi$
$992$		0			0
$993$			8.88954i			0.282101i
$994$		0			0
$995$	−7.00250	−	35.2039i	−0.221994	−	1.11604i
$996$		0			0
$997$	11.0204	−	7.36360i	0.349020	−	0.233207i	−0.368686	−	0.929554i	$-0.620192\pi$
$997$	11.0204	−	7.36360i	0.349020	−	0.233207i	0.717706	+	0.696346i	$0.245192\pi$
$998$		0			0
$999$	−0.679021	+	1.63930i	−0.0214833	+	0.0518652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.r.a.49.7		128
4.3	odd	2		192.2.r.a.181.6	yes	128
12.11	even	2		576.2.bd.b.181.11		128
64.29	even	16	inner	768.2.r.a.721.7		128
64.35	odd	16		192.2.r.a.157.6	✓	128
192.35	even	16		576.2.bd.b.541.11		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.6	✓	128	64.35	odd	16
192.2.r.a.181.6	yes	128	4.3	odd	2
576.2.bd.b.181.11		128	12.11	even	2
576.2.bd.b.541.11		128	192.35	even	16
768.2.r.a.49.7		128	1.1	even	1	trivial
768.2.r.a.721.7		128	64.29	even	16	inner

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.r (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.980785 + 0.195090i) q^{3} +(1.62504 + 2.43205i) q^{5} +(-0.294182 - 0.121854i) q^{7} +(0.923880 - 0.382683i) q^{9} +O(q^{10})\)	\(q+(-0.980785 + 0.195090i) q^{3} +(1.62504 + 2.43205i) q^{5} +(-0.294182 - 0.121854i) q^{7} +(0.923880 - 0.382683i) q^{9} +(1.07988 - 5.42890i) q^{11} +(2.67591 - 4.00478i) q^{13} +(-2.06829 - 2.06829i) q^{15} +(0.394520 - 0.394520i) q^{17} +(2.13690 + 1.42783i) q^{19} +(0.312302 + 0.0621207i) q^{21} +(3.37395 + 8.14543i) q^{23} +(-1.36068 + 3.28498i) q^{25} +(-0.831470 + 0.555570i) q^{27} +(0.411462 + 2.06856i) q^{29} +1.31001i q^{31} +5.53526i q^{33} +(-0.181703 - 0.913483i) q^{35} +(1.47533 - 0.985786i) q^{37} +(-1.84320 + 4.44987i) q^{39} +(4.39934 + 10.6209i) q^{41} +(2.25285 + 0.448119i) q^{43} +(2.43205 + 1.62504i) q^{45} +(5.23873 - 5.23873i) q^{47} +(-4.87805 - 4.87805i) q^{49} +(-0.309973 + 0.463907i) q^{51} +(1.88714 - 9.48728i) q^{53} +(14.9582 - 6.19589i) q^{55} +(-2.37440 - 0.983508i) q^{57} +(0.373863 + 0.559526i) q^{59} +(0.868572 - 0.172770i) q^{61} -0.318420 q^{63} +14.0883 q^{65} +(-10.3046 + 2.04972i) q^{67} +(-4.89821 - 7.33069i) q^{69} +(12.4243 + 5.14631i) q^{71} +(-14.5155 + 6.01250i) q^{73} +(0.693670 - 3.48732i) q^{75} +(-0.979213 + 1.46550i) q^{77} +(2.55934 + 2.55934i) q^{79} +(0.707107 - 0.707107i) q^{81} +(-0.585536 - 0.391243i) q^{83} +(1.60061 + 0.318380i) q^{85} +(-0.807113 - 1.94854i) q^{87} +(3.72369 - 8.98978i) q^{89} +(-1.27520 + 0.852063i) q^{91} +(-0.255570 - 1.28484i) q^{93} +7.51734i q^{95} +0.565484i q^{97} +(-1.07988 - 5.42890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 32 q^{51} + 64 q^{55} + 128 q^{59} + 32 q^{63} + 32 q^{67} + 128 q^{71} + 64 q^{75} + 32 q^{79}+O(q^{100}) \) 128 * q + 32 * q^51 + 64 * q^55 + 128 * q^59 + 32 * q^63 + 32 * q^67 + 128 * q^71 + 64 * q^75 + 32 * q^79

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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