LMFDB - Embedded newform 1680.2.dx.h.271.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(31,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.dx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,6,0,0,0,-2,0,-6,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 35 x^{10} - 120 x^{9} + 328 x^{8} - 658 x^{7} + 1045 x^{6} - 1270 x^{5} + 1183 x^{4} + \cdots + 13 $ x^12 - 6x^11 + 35x^10 - 120x^9 + 328x^8 - 658x^7 + 1045x^6 - 1270x^5 + 1183x^4 - 810x^3 + 376x^2 - 104*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.3
Root			$0.500000 + 1.45168i$ of defining polynomial
Character	$\chi$	$=$	1680.271
Dual form			1680.2.dx.h.31.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(2.26392 - 1.36919i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.87494 - 1.08250i) q^{11} -0.624468i q^{13} -1.00000i q^{15} +(-0.335186 + 0.193520i) q^{17} +(-1.76076 + 3.04972i) q^{19} +(2.31771 + 1.27602i) q^{21} +(3.87150 + 2.23521i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +9.47323 q^{29} +(-4.73346 - 8.19859i) q^{31} +(1.87494 + 1.08250i) q^{33} +(-2.64520 + 0.0537914i) q^{35} +(1.85852 - 3.21904i) q^{37} +(0.540805 - 0.312234i) q^{39} -4.80729i q^{41} -8.75451i q^{43} +(0.866025 - 0.500000i) q^{45} +(0.432944 - 0.749882i) q^{47} +(3.25065 - 6.19946i) q^{49} +(-0.335186 - 0.193520i) q^{51} +(6.63542 + 11.4929i) q^{53} -2.16500 q^{55} -3.52151 q^{57} +(2.30789 + 3.99737i) q^{59} +(4.08660 + 2.35940i) q^{61} +(0.0537914 + 2.64520i) q^{63} +(-0.312234 + 0.540805i) q^{65} +(-7.20299 + 4.15865i) q^{67} +4.47042i q^{69} +1.64174i q^{71} +(14.2438 - 8.22367i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(2.76257 - 5.01783i) q^{77} +(1.03740 + 0.598945i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.472163 q^{83} +0.387040 q^{85} +(4.73662 + 8.20406i) q^{87} +(5.00002 + 2.88676i) q^{89} +(-0.855013 - 1.41374i) q^{91} +(4.73346 - 8.19859i) q^{93} +(3.04972 - 1.76076i) q^{95} -2.92471i q^{97} +2.16500i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 2 q^{7} - 6 q^{9} + 10 q^{19} - 4 q^{21} + 12 q^{23} + 6 q^{25} - 12 q^{27} + 8 q^{29} - 2 q^{31} - 4 q^{35} - 10 q^{37} + 6 q^{39} + 2 q^{49} + 16 q^{53} + 20 q^{57} + 24 q^{61} - 2 q^{63}+ \cdots + 24 q^{95}+O(q^{100}) $ 12 * q + 6 * q^3 - 2 * q^7 - 6 * q^9 + 10 * q^19 - 4 * q^21 + 12 * q^23 + 6 * q^25 - 12 * q^27 + 8 * q^29 - 2 * q^31 - 4 * q^35 - 10 * q^37 + 6 * q^39 + 2 * q^49 + 16 * q^53 + 20 * q^57 + 24 * q^61 - 2 * q^63 + 4 * q^65 - 6 * q^67 + 30 * q^73 - 6 * q^75 + 36 * q^77 + 42 * q^79 - 6 * q^81 - 64 * q^83 - 8 * q^85 + 4 * q^87 + 14 * q^91 + 2 * q^93 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$		0			0
$7$	2.26392	−	1.36919i	0.855681	−	0.517504i
$7$	2.26392	−	1.36919i	0.855681	−	0.517504i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.87494	−	1.08250i	0.565316	−	0.326385i	−0.189960	−	0.981792i	$-0.560836\pi$
$11$	1.87494	−	1.08250i	0.565316	−	0.326385i	0.755276	+	0.655406i	$0.227503\pi$
$12$		0			0
$13$		−	0.624468i		−	0.173196i	−0.996243	−	0.0865981i	$-0.972400\pi$
$13$		−	0.624468i		−	0.173196i	0.996243	−	0.0865981i	$-0.0275996\pi$
$14$		0			0
$15$		−	1.00000i		−	0.258199i
$16$		0			0
$17$	−0.335186	+	0.193520i	−0.0812946	+	0.0469355i	−0.540096	−	0.841603i	$-0.681612\pi$
$17$	−0.335186	+	0.193520i	−0.0812946	+	0.0469355i	0.458802	+	0.888539i	$0.348279\pi$
$18$		0			0
$19$	−1.76076	+	3.04972i	−0.403945	+	0.699654i	−0.994198	−	0.107565i	$-0.965695\pi$
$19$	−1.76076	+	3.04972i	−0.403945	+	0.699654i	0.590253	+	0.807219i	$0.299028\pi$
$20$		0			0
$21$	2.31771	+	1.27602i	0.505766	+	0.278450i
$22$		0			0
$23$	3.87150	+	2.23521i	0.807264	+	0.466074i	0.846005	−	0.533175i	$-0.179001\pi$
$23$	3.87150	+	2.23521i	0.807264	+	0.466074i	−0.0387410	+	0.999249i	$0.512335\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	9.47323			1.75914			0.879568	−	0.475774i	$-0.157832\pi$
$29$	9.47323			1.75914			0.879568	+	0.475774i	$0.157832\pi$
$30$		0			0
$31$	−4.73346	−	8.19859i	−0.850154	−	1.47251i	−0.881069	−	0.472988i	$-0.843176\pi$
$31$	−4.73346	−	8.19859i	−0.850154	−	1.47251i	0.0309153	−	0.999522i	$-0.490158\pi$
$32$		0			0
$33$	1.87494	+	1.08250i	0.326385	+	0.188439i
$34$		0			0
$35$	−2.64520	+	0.0537914i	−0.447121	+	0.00909240i
$36$		0			0
$37$	1.85852	−	3.21904i	0.305538	−	0.529207i	−0.671843	−	0.740694i	$-0.734497\pi$
$37$	1.85852	−	3.21904i	0.305538	−	0.529207i	0.977381	+	0.211486i	$0.0678304\pi$
$38$		0			0
$39$	0.540805	−	0.312234i	0.0865981	−	0.0499975i
$40$		0			0
$41$		−	4.80729i		−	0.750773i	−0.926868	−	0.375387i	$-0.877510\pi$
$41$		−	4.80729i		−	0.750773i	0.926868	−	0.375387i	$-0.122490\pi$
$42$		0			0
$43$		−	8.75451i		−	1.33505i	−0.744587	−	0.667525i	$-0.767354\pi$
$43$		−	8.75451i		−	1.33505i	0.744587	−	0.667525i	$-0.232646\pi$
$44$		0			0
$45$	0.866025	−	0.500000i	0.129099	−	0.0745356i
$46$		0			0
$47$	0.432944	−	0.749882i	0.0631514	−	0.109381i	−0.832721	−	0.553693i	$-0.813218\pi$
$47$	0.432944	−	0.749882i	0.0631514	−	0.109381i	0.895872	+	0.444311i	$0.146552\pi$
$48$		0			0
$49$	3.25065	−	6.19946i	0.464379	−	0.885636i
$50$		0			0
$51$	−0.335186	−	0.193520i	−0.0469355	−	0.0270982i
$52$		0			0
$53$	6.63542	+	11.4929i	0.911445	+	1.57867i	0.812024	+	0.583624i	$0.198366\pi$
$53$	6.63542	+	11.4929i	0.911445	+	1.57867i	0.0994207	+	0.995045i	$0.468301\pi$
$54$		0			0
$55$	−2.16500			−0.291928
$56$		0			0
$57$	−3.52151			−0.466436
$58$		0			0
$59$	2.30789	+	3.99737i	0.300461	+	0.520414i	0.976240	−	0.216690i	$-0.0695261\pi$
$59$	2.30789	+	3.99737i	0.300461	+	0.520414i	−0.675779	+	0.737104i	$0.736193\pi$
$60$		0			0
$61$	4.08660	+	2.35940i	0.523236	+	0.302091i	0.738258	−	0.674519i	$-0.235649\pi$
$61$	4.08660	+	2.35940i	0.523236	+	0.302091i	−0.215022	+	0.976609i	$0.568982\pi$
$62$		0			0
$63$	0.0537914	+	2.64520i	0.00677708	+	0.333264i
$64$		0			0
$65$	−0.312234	+	0.540805i	−0.0387279	+	0.0670786i
$66$		0			0
$67$	−7.20299	+	4.15865i	−0.879986	+	0.508060i	−0.870654	−	0.491896i	$-0.836304\pi$
$67$	−7.20299	+	4.15865i	−0.879986	+	0.508060i	−0.00933200	+	0.999956i	$0.502971\pi$
$68$		0			0
$69$			4.47042i			0.538176i
$70$		0			0
$71$			1.64174i			0.194839i	0.995243	+	0.0974195i	$0.0310589\pi$
$71$			1.64174i			0.194839i	−0.995243	+	0.0974195i	$0.968941\pi$
$72$		0			0
$73$	14.2438	−	8.22367i	1.66711	−	0.962508i	0.697930	−	0.716166i	$-0.254105\pi$
$73$	14.2438	−	8.22367i	1.66711	−	0.962508i	0.969183	−	0.246342i	$-0.0792285\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$	2.76257	−	5.01783i	0.314824	−	0.571835i
$78$		0			0
$79$	1.03740	+	0.598945i	0.116717	+	0.0673866i	0.557222	−	0.830364i	$-0.311867\pi$
$79$	1.03740	+	0.598945i	0.116717	+	0.0673866i	−0.440505	+	0.897750i	$0.645201\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−0.472163			−0.0518266			−0.0259133	−	0.999664i	$-0.508249\pi$
$83$	−0.472163			−0.0518266			−0.0259133	+	0.999664i	$0.508249\pi$
$84$		0			0
$85$	0.387040			0.0419804
$86$		0			0
$87$	4.73662	+	8.20406i	0.507819	+	0.879568i
$88$		0			0
$89$	5.00002	+	2.88676i	0.530001	+	0.305996i	0.741017	−	0.671486i	$-0.234344\pi$
$89$	5.00002	+	2.88676i	0.530001	+	0.305996i	−0.211016	+	0.977483i	$0.567677\pi$
$90$		0			0
$91$	−0.855013	−	1.41374i	−0.0896298	−	0.148201i
$92$		0			0
$93$	4.73346	−	8.19859i	0.490837	−	0.850154i
$94$		0			0
$95$	3.04972	−	1.76076i	0.312895	−	0.180650i
$96$		0			0
$97$		−	2.92471i		−	0.296960i	−0.988915	−	0.148480i	$-0.952562\pi$
$97$		−	2.92471i		−	0.296960i	0.988915	−	0.148480i	$-0.0474380\pi$
$98$		0			0
$99$			2.16500i			0.217590i
$100$		0			0
$101$	10.1093	−	5.83659i	1.00591	−	0.580763i	0.0959186	−	0.995389i	$-0.469421\pi$
$101$	10.1093	−	5.83659i	1.00591	−	0.580763i	0.909992	+	0.414627i	$0.136088\pi$
$102$		0			0
$103$	−0.0474683	+	0.0822176i	−0.00467720	+	0.00810114i	−0.868355	−	0.495944i	$-0.834822\pi$
$103$	−0.0474683	+	0.0822176i	−0.00467720	+	0.00810114i	0.863677	+	0.504045i	$0.168155\pi$
$104$		0			0
$105$	−1.36919	−	2.26392i	−0.133619	−	0.220936i
$106$		0			0
$107$	10.1493	+	5.85968i	0.981166	+	0.566477i	0.902622	−	0.430434i	$-0.141639\pi$
$107$	10.1493	+	5.85968i	0.981166	+	0.566477i	0.0785443	+	0.996911i	$0.474973\pi$
$108$		0			0
$109$	7.02019	+	12.1593i	0.672412	+	1.16465i	0.977218	+	0.212237i	$0.0680749\pi$
$109$	7.02019	+	12.1593i	0.672412	+	1.16465i	−0.304806	+	0.952414i	$0.598592\pi$
$110$		0			0
$111$	3.71703			0.352805
$112$		0			0
$113$	−11.4871			−1.08062			−0.540309	−	0.841467i	$-0.681692\pi$
$113$	−11.4871			−1.08062			−0.540309	+	0.841467i	$0.681692\pi$
$114$		0			0
$115$	−2.23521	−	3.87150i	−0.208435	−	0.361019i
$116$		0			0
$117$	0.540805	+	0.312234i	0.0499975	+	0.0288660i
$118$		0			0
$119$	−0.493870	+	0.897046i	−0.0452729	+	0.0822321i
$120$		0			0
$121$	−3.15640	+	5.46704i	−0.286945	+	0.497004i
$122$		0			0
$123$	4.16324	−	2.40365i	0.375387	−	0.216730i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	9.75839i		−	0.865917i	−0.901414	−	0.432958i	$-0.857470\pi$
$127$		−	9.75839i		−	0.865917i	0.901414	−	0.432958i	$-0.142530\pi$
$128$		0			0
$129$	7.58163	−	4.37726i	0.667525	−	0.385396i
$130$		0			0
$131$	−6.20248	+	10.7430i	−0.541913	+	0.938620i	0.456881	+	0.889528i	$0.348966\pi$
$131$	−6.20248	+	10.7430i	−0.541913	+	0.938620i	−0.998794	+	0.0490929i	$0.984367\pi$
$132$		0			0
$133$	0.189427	+	9.31512i	0.0164254	+	0.807724i
$134$		0			0
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$		0			0
$137$	−3.73318	−	6.46605i	−0.318947	−	0.552432i	0.661322	−	0.750102i	$-0.269996\pi$
$137$	−3.73318	−	6.46605i	−0.318947	−	0.552432i	−0.980269	+	0.197670i	$0.936663\pi$
$138$		0			0
$139$	−15.4516			−1.31059			−0.655294	−	0.755374i	$-0.727455\pi$
$139$	−15.4516			−1.31059			−0.655294	+	0.755374i	$0.727455\pi$
$140$		0			0
$141$	0.865889			0.0729210
$142$		0			0
$143$	−0.675985	−	1.17084i	−0.0565287	−	0.0979106i
$144$		0			0
$145$	−8.20406	−	4.73662i	−0.681310	−	0.393355i
$146$		0			0
$147$	6.99421	−	0.284578i	0.576873	−	0.0234716i
$148$		0			0
$149$	1.31904	−	2.28464i	0.108060	−	0.187165i	−0.806924	−	0.590655i	$-0.798870\pi$
$149$	1.31904	−	2.28464i	0.108060	−	0.187165i	0.914984	+	0.403490i	$0.132203\pi$
$150$		0			0
$151$	3.67537	−	2.12197i	0.299097	−	0.172684i	−0.342940	−	0.939357i	$-0.611423\pi$
$151$	3.67537	−	2.12197i	0.299097	−	0.172684i	0.642037	+	0.766673i	$0.278089\pi$
$152$		0			0
$153$		−	0.387040i		−	0.0312903i
$154$		0			0
$155$			9.46691i			0.760401i
$156$		0			0
$157$	−8.84051	+	5.10407i	−0.705549	+	0.407349i	−0.809411	−	0.587243i	$-0.800213\pi$
$157$	−8.84051	+	5.10407i	−0.705549	+	0.407349i	0.103862	+	0.994592i	$0.466880\pi$
$158$		0			0
$159$	−6.63542	+	11.4929i	−0.526223	+	0.911445i
$160$		0			0
$161$	11.8252	−	0.240470i	0.931955	−	0.0189517i
$162$		0			0
$163$	−2.18219	−	1.25989i	−0.170922	−	0.0986820i	0.412098	−	0.911139i	$-0.364796\pi$
$163$	−2.18219	−	1.25989i	−0.170922	−	0.0986820i	−0.583021	+	0.812457i	$0.698129\pi$
$164$		0			0
$165$	−1.08250	−	1.87494i	−0.0842723	−	0.145964i
$166$		0			0
$167$	−6.00269			−0.464502			−0.232251	−	0.972656i	$-0.574609\pi$
$167$	−6.00269			−0.464502			−0.232251	+	0.972656i	$0.574609\pi$
$168$		0			0
$169$	12.6100			0.970003
$170$		0			0
$171$	−1.76076	−	3.04972i	−0.134648	−	0.233218i
$172$		0			0
$173$	8.04871	+	4.64693i	0.611932	+	0.353299i	0.773721	−	0.633526i	$-0.218393\pi$
$173$	8.04871	+	4.64693i	0.611932	+	0.353299i	−0.161789	+	0.986825i	$0.551726\pi$
$174$		0			0
$175$	2.31771	+	1.27602i	0.175202	+	0.0964579i
$176$		0			0
$177$	−2.30789	+	3.99737i	−0.173471	+	0.300461i
$178$		0			0
$179$	−10.9947	+	6.34782i	−0.821786	+	0.474458i	−0.851032	−	0.525114i	$-0.824023\pi$
$179$	−10.9947	+	6.34782i	−0.821786	+	0.474458i	0.0292459	+	0.999572i	$0.490689\pi$
$180$		0			0
$181$			12.8039i			0.951704i	0.879525	+	0.475852i	$0.157860\pi$
$181$			12.8039i			0.951704i	−0.879525	+	0.475852i	$0.842140\pi$
$182$		0			0
$183$			4.71880i			0.348824i
$184$		0			0
$185$	−3.21904	+	1.85852i	−0.236669	+	0.136641i
$186$		0			0
$187$	−0.418970	+	0.725677i	−0.0306381	+	0.0530667i
$188$		0			0
$189$	−2.26392	+	1.36919i	−0.164676	+	0.0995937i
$190$		0			0
$191$	22.0574	+	12.7349i	1.59602	+	0.921462i	0.992244	+	0.124308i	$0.0396711\pi$
$191$	22.0574	+	12.7349i	1.59602	+	0.921462i	0.603776	+	0.797154i	$0.293662\pi$
$192$		0			0
$193$	−2.75726	−	4.77571i	−0.198472	−	0.343763i	0.749561	−	0.661935i	$-0.230264\pi$
$193$	−2.75726	−	4.77571i	−0.198472	−	0.343763i	−0.948033	+	0.318172i	$0.896931\pi$
$194$		0			0
$195$	−0.624468			−0.0447191
$196$		0			0
$197$	−18.1310			−1.29178			−0.645890	−	0.763430i	$-0.723514\pi$
$197$	−18.1310			−1.29178			−0.645890	+	0.763430i	$0.723514\pi$
$198$		0			0
$199$	−12.7094	−	22.0133i	−0.900944	−	1.56048i	−0.826271	−	0.563273i	$-0.809542\pi$
$199$	−12.7094	−	22.0133i	−0.900944	−	1.56048i	−0.0746728	−	0.997208i	$-0.523791\pi$
$200$		0			0
$201$	−7.20299	−	4.15865i	−0.508060	−	0.293329i
$202$		0			0
$203$	21.4466	−	12.9706i	1.50526	−	0.910360i
$204$		0			0
$205$	−2.40365	+	4.16324i	−0.167878	+	0.290773i
$206$		0			0
$207$	−3.87150	+	2.23521i	−0.269088	+	0.155358i
$208$		0			0
$209$			7.62406i			0.527367i
$210$		0			0
$211$		−	17.8978i		−	1.23214i	−0.787692	−	0.616069i	$-0.788724\pi$
$211$		−	17.8978i		−	1.23214i	0.787692	−	0.616069i	$-0.211276\pi$
$212$		0			0
$213$	−1.42179	+	0.820871i	−0.0974195	+	0.0562452i
$214$		0			0
$215$	−4.37726	+	7.58163i	−0.298526	+	0.517063i
$216$		0			0
$217$	−21.9416	−	12.0799i	−1.48949	−	0.820040i
$218$		0			0
$219$	14.2438	+	8.22367i	0.962508	+	0.555704i
$220$		0			0
$221$	0.120847	+	0.209313i	0.00812905	+	0.0140799i
$222$		0			0
$223$	−5.65034			−0.378375			−0.189187	−	0.981941i	$-0.560585\pi$
$223$	−5.65034			−0.378375			−0.189187	+	0.981941i	$0.560585\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−11.5695	−	20.0390i	−0.767896	−	1.33003i	−0.938702	−	0.344730i	$-0.887970\pi$
$227$	−11.5695	−	20.0390i	−0.767896	−	1.33003i	0.170806	−	0.985305i	$-0.445363\pi$
$228$		0			0
$229$	15.9897	+	9.23168i	1.05663	+	0.610046i	0.924499	−	0.381186i	$-0.124484\pi$
$229$	15.9897	+	9.23168i	1.05663	+	0.610046i	0.132133	+	0.991232i	$0.457817\pi$
$230$		0			0
$231$	5.72685	−	0.116458i	0.376799	−	0.00766238i
$232$		0			0
$233$	6.10122	−	10.5676i	0.399704	−	0.692308i	−0.593985	−	0.804476i	$-0.702446\pi$
$233$	6.10122	−	10.5676i	0.399704	−	0.692308i	0.993689	+	0.112168i	$0.0357796\pi$
$234$		0			0
$235$	−0.749882	+	0.432944i	−0.0489169	+	0.0282422i
$236$		0			0
$237$			1.19789i			0.0778114i
$238$		0			0
$239$		−	10.9016i		−	0.705163i	−0.935781	−	0.352581i	$-0.885304\pi$
$239$		−	10.9016i		−	0.705163i	0.935781	−	0.352581i	$-0.114696\pi$
$240$		0			0
$241$	−5.24772	+	3.02977i	−0.338036	+	0.195165i	−0.659403	−	0.751790i	$-0.729191\pi$
$241$	−5.24772	+	3.02977i	−0.338036	+	0.195165i	0.321367	+	0.946955i	$0.395858\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−5.91488	+	3.74356i	−0.377888	+	0.239167i
$246$		0			0
$247$	1.90445	+	1.09954i	0.121177	+	0.0699618i
$248$		0			0
$249$	−0.236081	−	0.408905i	−0.0149611	−	0.0259133i
$250$		0			0
$251$	−13.0474			−0.823543			−0.411771	−	0.911287i	$-0.635090\pi$
$251$	−13.0474			−0.823543			−0.411771	+	0.911287i	$0.635090\pi$
$252$		0			0
$253$	9.67845			0.608479
$254$		0			0
$255$	0.193520	+	0.335186i	0.0121187	+	0.0209902i
$256$		0			0
$257$	−26.5382	−	15.3218i	−1.65541	−	0.955749i	−0.974794	−	0.223105i	$-0.928381\pi$
$257$	−26.5382	−	15.3218i	−1.65541	−	0.955749i	−0.680612	−	0.732644i	$-0.738286\pi$
$258$		0			0
$259$	−0.199944	−	9.83230i	−0.0124239	−	0.610950i
$260$		0			0
$261$	−4.73662	+	8.20406i	−0.293189	+	0.507819i
$262$		0			0
$263$	−14.5348	+	8.39167i	−0.896254	+	0.517452i	−0.875983	−	0.482342i	$-0.839786\pi$
$263$	−14.5348	+	8.39167i	−0.896254	+	0.517452i	−0.0202710	+	0.999795i	$0.506453\pi$
$264$		0			0
$265$		−	13.2708i		−	0.815221i
$266$		0			0
$267$			5.77352i			0.353334i
$268$		0			0
$269$	4.28678	−	2.47497i	0.261370	−	0.150902i	−0.363590	−	0.931559i	$-0.618449\pi$
$269$	4.28678	−	2.47497i	0.261370	−	0.150902i	0.624959	+	0.780657i	$0.285116\pi$
$270$		0			0
$271$	−2.87212	+	4.97466i	−0.174469	+	0.302189i	−0.939977	−	0.341237i	$-0.889154\pi$
$271$	−2.87212	+	4.97466i	−0.174469	+	0.302189i	0.765508	+	0.643426i	$0.222487\pi$
$272$		0			0
$273$	0.796832	−	1.44734i	0.0482265	−	0.0875967i
$274$		0			0
$275$	1.87494	+	1.08250i	0.113063	+	0.0652771i
$276$		0			0
$277$	−4.56118	−	7.90020i	−0.274055	−	0.474677i	0.695841	−	0.718196i	$-0.255032\pi$
$277$	−4.56118	−	7.90020i	−0.274055	−	0.474677i	−0.969896	+	0.243518i	$0.921698\pi$
$278$		0			0
$279$	9.46691			0.566769
$280$		0			0
$281$	−4.78334			−0.285350			−0.142675	−	0.989770i	$-0.545570\pi$
$281$	−4.78334			−0.285350			−0.142675	+	0.989770i	$0.545570\pi$
$282$		0			0
$283$	0.176678	+	0.306014i	0.0105024	+	0.0181907i	0.871229	−	0.490877i	$-0.163324\pi$
$283$	0.176678	+	0.306014i	0.0105024	+	0.0181907i	−0.860726	+	0.509068i	$0.829990\pi$
$284$		0			0
$285$	3.04972	+	1.76076i	0.180650	+	0.104298i
$286$		0			0
$287$	−6.58208	−	10.8833i	−0.388528	−	0.642422i
$288$		0			0
$289$	−8.42510	+	14.5927i	−0.495594	+	0.858394i
$290$		0			0
$291$	2.53288	−	1.46236i	0.148480	−	0.0857248i
$292$		0			0
$293$			18.1101i			1.05800i	0.848621	+	0.529001i	$0.177433\pi$
$293$			18.1101i			1.05800i	−0.848621	+	0.529001i	$0.822567\pi$
$294$		0			0
$295$		−	4.61577i		−	0.268741i
$296$		0			0
$297$	−1.87494	+	1.08250i	−0.108795	+	0.0628129i
$298$		0			0
$299$	1.39582	−	2.41763i	0.0807223	−	0.139815i
$300$		0			0
$301$	−11.9866	−	19.8195i	−0.690894	−	1.14238i
$302$		0			0
$303$	10.1093	+	5.83659i	0.580763	+	0.335303i
$304$		0			0
$305$	−2.35940	−	4.08660i	−0.135099	−	0.233998i
$306$		0			0
$307$	−8.94552			−0.510548			−0.255274	−	0.966869i	$-0.582166\pi$
$307$	−8.94552			−0.510548			−0.255274	+	0.966869i	$0.582166\pi$
$308$		0			0
$309$	−0.0949367			−0.00540076
$310$		0			0
$311$	11.3699	+	19.6932i	0.644727	+	1.11670i	0.984365	+	0.176143i	$0.0563622\pi$
$311$	11.3699	+	19.6932i	0.644727	+	1.11670i	−0.339638	+	0.940556i	$0.610304\pi$
$312$		0			0
$313$	−2.01263	−	1.16199i	−0.113761	−	0.0656797i	0.442040	−	0.896995i	$-0.354255\pi$
$313$	−2.01263	−	1.16199i	−0.113761	−	0.0656797i	−0.555801	+	0.831316i	$0.687588\pi$
$314$		0			0
$315$	1.27602	−	2.31771i	0.0718954	−	0.130588i
$316$		0			0
$317$	−3.20795	+	5.55634i	−0.180177	+	0.312075i	−0.941941	−	0.335780i	$-0.891000\pi$
$317$	−3.20795	+	5.55634i	−0.180177	+	0.312075i	0.761764	+	0.647855i	$0.224334\pi$
$318$		0			0
$319$	17.7618	−	10.2548i	0.994467	−	0.574156i
$320$		0			0
$321$			11.7194i			0.654111i
$322$		0			0
$323$		−	1.36297i		−	0.0758375i
$324$		0			0
$325$	0.540805	−	0.312234i	0.0299985	−	0.0173196i
$326$		0			0
$327$	−7.02019	+	12.1593i	−0.388217	+	0.672412i
$328$		0			0
$329$	−0.0465774	−	2.29045i	−0.00256789	−	0.126277i
$330$		0			0
$331$	−13.1467	−	7.59025i	−0.722608	−	0.417198i	0.0931036	−	0.995656i	$-0.470321\pi$
$331$	−13.1467	−	7.59025i	−0.722608	−	0.417198i	−0.815712	+	0.578458i	$0.803655\pi$
$332$		0			0
$333$	1.85852	+	3.21904i	0.101846	+	0.176402i
$334$		0			0
$335$	8.31730			0.454423
$336$		0			0
$337$	−20.9205			−1.13961			−0.569807	−	0.821779i	$-0.692982\pi$
$337$	−20.9205			−1.13961			−0.569807	+	0.821779i	$0.692982\pi$
$338$		0			0
$339$	−5.74356	−	9.94814i	−0.311947	−	0.540309i
$340$		0			0
$341$	−17.7499	−	10.2479i	−0.961211	−	0.554955i
$342$		0			0
$343$	−1.12900	−	18.4858i	−0.0609601	−	0.998140i
$344$		0			0
$345$	2.23521	−	3.87150i	0.120340	−	0.208435i
$346$		0			0
$347$	23.0621	−	13.3149i	1.23804	−	0.714783i	0.269347	−	0.963043i	$-0.413192\pi$
$347$	23.0621	−	13.3149i	1.23804	−	0.714783i	0.968693	+	0.248261i	$0.0798589\pi$
$348$		0			0
$349$		−	21.5362i		−	1.15281i	−0.817165	−	0.576404i	$-0.804455\pi$
$349$		−	21.5362i		−	1.15281i	0.817165	−	0.576404i	$-0.195545\pi$
$350$		0			0
$351$			0.624468i			0.0333316i
$352$		0			0
$353$	−8.12477	+	4.69084i	−0.432438	+	0.249668i	−0.700385	−	0.713766i	$-0.746988\pi$
$353$	−8.12477	+	4.69084i	−0.432438	+	0.249668i	0.267947	+	0.963434i	$0.413655\pi$
$354$		0			0
$355$	0.820871	−	1.42179i	0.0435673	−	0.0754608i
$356$		0			0
$357$	−1.02380	+	0.0208194i	−0.0541852	+	0.00110188i
$358$		0			0
$359$	13.3749	+	7.72199i	0.705899	+	0.407551i	0.809541	−	0.587064i	$-0.199716\pi$
$359$	13.3749	+	7.72199i	0.705899	+	0.407551i	−0.103642	+	0.994615i	$0.533050\pi$
$360$		0			0
$361$	3.29947	+	5.71485i	0.173656	+	0.300782i
$362$		0			0
$363$	−6.31280			−0.331336
$364$		0			0
$365$	−16.4473			−0.860893
$366$		0			0
$367$	−10.9725	−	19.0050i	−0.572761	−	0.992051i	−0.996281	−	0.0861645i	$-0.972539\pi$
$367$	−10.9725	−	19.0050i	−0.572761	−	0.992051i	0.423520	−	0.905887i	$-0.360794\pi$
$368$		0			0
$369$	4.16324	+	2.40365i	0.216730	+	0.125129i
$370$		0			0
$371$	30.7580	+	16.9338i	1.59687	+	0.879160i
$372$		0			0
$373$	−14.7767	+	25.5940i	−0.765108	+	1.32521i	0.175081	+	0.984554i	$0.443981\pi$
$373$	−14.7767	+	25.5940i	−0.765108	+	1.32521i	−0.940189	+	0.340652i	$0.889352\pi$
$374$		0			0
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$		0			0
$377$		−	5.91573i		−	0.304676i
$378$		0			0
$379$			31.4003i			1.61293i	0.591284	+	0.806463i	$0.298621\pi$
$379$			31.4003i			1.61293i	−0.591284	+	0.806463i	$0.701379\pi$
$380$		0			0
$381$	8.45101	−	4.87919i	0.432958	−	0.249969i
$382$		0			0
$383$	−9.28472	+	16.0816i	−0.474427	+	0.821732i	−0.999571	−	0.0292814i	$-0.990678\pi$
$383$	−9.28472	+	16.0816i	−0.474427	+	0.821732i	0.525144	+	0.851013i	$0.324011\pi$
$384$		0			0
$385$	−4.90137	+	2.96428i	−0.249797	+	0.151074i
$386$		0			0
$387$	7.58163	+	4.37726i	0.385396	+	0.222508i
$388$		0			0
$389$	18.0827	+	31.3202i	0.916832	+	1.58800i	0.804197	+	0.594362i	$0.202595\pi$
$389$	18.0827	+	31.3202i	0.916832	+	1.58800i	0.112634	+	0.993637i	$0.464071\pi$
$390$		0			0
$391$	−1.73023			−0.0875016
$392$		0			0
$393$	−12.4050			−0.625747
$394$		0			0
$395$	−0.598945	−	1.03740i	−0.0301362	−	0.0521974i
$396$		0			0
$397$	−22.8204	−	13.1754i	−1.14533	−	0.661254i	−0.197582	−	0.980286i	$-0.563309\pi$
$397$	−22.8204	−	13.1754i	−1.14533	−	0.661254i	−0.947744	+	0.319032i	$0.896642\pi$
$398$		0			0
$399$	−7.97242	+	4.82161i	−0.399120	+	0.241382i
$400$		0			0
$401$	−0.195516	+	0.338644i	−0.00976361	+	0.0169111i	−0.870866	−	0.491521i	$-0.836441\pi$
$401$	−0.195516	+	0.338644i	−0.00976361	+	0.0169111i	0.861102	+	0.508432i	$0.169775\pi$
$402$		0			0
$403$	−5.11975	+	2.95589i	−0.255033	+	0.147243i
$404$		0			0
$405$			1.00000i			0.0496904i
$406$		0			0
$407$		−	8.04735i		−	0.398892i
$408$		0			0
$409$	3.09564	−	1.78727i	0.153070	−	0.0883748i	−0.421509	−	0.906824i	$-0.638499\pi$
$409$	3.09564	−	1.78727i	0.153070	−	0.0883748i	0.574578	+	0.818450i	$0.305166\pi$
$410$		0			0
$411$	3.73318	−	6.46605i	0.184144	−	0.318947i
$412$		0			0
$413$	10.6980	+	5.88980i	0.526415	+	0.289818i
$414$		0			0
$415$	0.408905	+	0.236081i	0.0200724	+	0.0115888i
$416$		0			0
$417$	−7.72580	−	13.3815i	−0.378334	−	0.655294i
$418$		0			0
$419$	8.40368			0.410547			0.205273	−	0.978705i	$-0.434192\pi$
$419$	8.40368			0.410547			0.205273	+	0.978705i	$0.434192\pi$
$420$		0			0
$421$	13.1746			0.642089			0.321045	−	0.947064i	$-0.395966\pi$
$421$	13.1746			0.642089			0.321045	+	0.947064i	$0.395966\pi$
$422$		0			0
$423$	0.432944	+	0.749882i	0.0210505	+	0.0364605i
$424$		0			0
$425$	−0.335186	−	0.193520i	−0.0162589	−	0.00938709i
$426$		0			0
$427$	12.4822	−	0.253831i	0.604056	−	0.0122837i
$428$		0			0
$429$	0.675985	−	1.17084i	0.0326369	−	0.0565287i
$430$		0			0
$431$	−30.6869	+	17.7171i	−1.47813	+	0.853401i	−0.999694	−	0.0247194i	$-0.992131\pi$
$431$	−30.6869	+	17.7171i	−1.47813	+	0.853401i	−0.478440	+	0.878120i	$0.658797\pi$
$432$		0			0
$433$		−	24.7571i		−	1.18975i	−0.803818	−	0.594875i	$-0.797202\pi$
$433$		−	24.7571i		−	1.18975i	0.803818	−	0.594875i	$-0.202798\pi$
$434$		0			0
$435$		−	9.47323i		−	0.454207i
$436$		0			0
$437$	−13.6335	+	7.87133i	−0.652181	+	0.376537i
$438$		0			0
$439$	−8.62200	+	14.9337i	−0.411506	+	0.712749i	−0.995055	−	0.0993292i	$-0.968330\pi$
$439$	−8.62200	+	14.9337i	−0.411506	+	0.712749i	0.583549	+	0.812078i	$0.301664\pi$
$440$		0			0
$441$	3.74356	+	5.91488i	0.178265	+	0.281661i
$442$		0			0
$443$	2.77380	+	1.60145i	0.131787	+	0.0760873i	0.564444	−	0.825471i	$-0.309091\pi$
$443$	2.77380	+	1.60145i	0.131787	+	0.0760873i	−0.432657	+	0.901559i	$0.642424\pi$
$444$		0			0
$445$	−2.88676	−	5.00002i	−0.136846	−	0.237024i
$446$		0			0
$447$	2.63808			0.124777
$448$		0			0
$449$	−6.87442			−0.324424			−0.162212	−	0.986756i	$-0.551863\pi$
$449$	−6.87442			−0.324424			−0.162212	+	0.986756i	$0.551863\pi$
$450$		0			0
$451$	−5.20388	−	9.01339i	−0.245041	−	0.424424i
$452$		0			0
$453$	3.67537	+	2.12197i	0.172684	+	0.0996990i
$454$		0			0
$455$	0.0335910	+	1.65185i	0.00157477	+	0.0774397i
$456$		0			0
$457$	−6.71794	+	11.6358i	−0.314252	+	0.544301i	−0.979278	−	0.202519i	$-0.935087\pi$
$457$	−6.71794	+	11.6358i	−0.314252	+	0.544301i	0.665026	+	0.746820i	$0.268420\pi$
$458$		0			0
$459$	0.335186	−	0.193520i	0.0156452	−	0.00903274i
$460$		0			0
$461$			17.4847i			0.814342i	0.913352	+	0.407171i	$0.133485\pi$
$461$			17.4847i			0.814342i	−0.913352	+	0.407171i	$0.866515\pi$
$462$		0			0
$463$		−	27.1433i		−	1.26146i	−0.776003	−	0.630729i	$-0.782756\pi$
$463$		−	27.1433i		−	1.26146i	0.776003	−	0.630729i	$-0.217244\pi$
$464$		0			0
$465$	−8.19859	+	4.73346i	−0.380200	+	0.219509i
$466$		0			0
$467$	−3.82517	+	6.62539i	−0.177008	+	0.306586i	−0.940854	−	0.338812i	$-0.889975\pi$
$467$	−3.82517	+	6.62539i	−0.177008	+	0.306586i	0.763847	+	0.645398i	$0.223308\pi$
$468$		0			0
$469$	−10.6130	+	19.2771i	−0.490064	+	0.890133i
$470$		0			0
$471$	−8.84051	−	5.10407i	−0.407349	−	0.235183i
$472$		0			0
$473$	−9.47674	−	16.4142i	−0.435741	−	0.754725i
$474$		0			0
$475$	−3.52151			−0.161578
$476$		0			0
$477$	−13.2708			−0.607630
$478$		0			0
$479$	−17.5088	−	30.3262i	−0.799999	−	1.38564i	−0.919616	−	0.392818i	$-0.871500\pi$
$479$	−17.5088	−	30.3262i	−0.799999	−	1.38564i	0.119618	−	0.992820i	$-0.461833\pi$
$480$		0			0
$481$	−2.01019	−	1.16058i	−0.0916567	−	0.0529180i
$482$		0			0
$483$	6.12085	+	10.1207i	0.278508	+	0.460507i
$484$		0			0
$485$	−1.46236	+	2.53288i	−0.0664022	+	0.115012i
$486$		0			0
$487$	−20.2636	+	11.6992i	−0.918230	+	0.530140i	−0.883070	−	0.469241i	$-0.844527\pi$
$487$	−20.2636	+	11.6992i	−0.918230	+	0.530140i	−0.0351600	+	0.999382i	$0.511194\pi$
$488$		0			0
$489$		−	2.51978i		−	0.113948i
$490$		0			0
$491$			6.69380i			0.302087i	0.988527	+	0.151044i	$0.0482634\pi$
$491$			6.69380i			0.302087i	−0.988527	+	0.151044i	$0.951737\pi$
$492$		0			0
$493$	−3.17530	+	1.83326i	−0.143008	+	0.0825659i
$494$		0			0
$495$	1.08250	−	1.87494i	0.0486546	−	0.0842723i
$496$		0			0
$497$	2.24785	+	3.71677i	0.100830	+	0.166720i
$498$		0			0
$499$	25.1746	+	14.5345i	1.12697	+	0.650655i	0.943171	−	0.332309i	$-0.107828\pi$
$499$	25.1746	+	14.5345i	1.12697	+	0.650655i	0.183797	+	0.982964i	$0.441161\pi$
$500$		0			0
$501$	−3.00135	−	5.19849i	−0.134090	−	0.232251i
$502$		0			0
$503$	−2.45562			−0.109491			−0.0547454	−	0.998500i	$-0.517435\pi$
$503$	−2.45562			−0.109491			−0.0547454	+	0.998500i	$0.517435\pi$
$504$		0			0
$505$	−11.6732			−0.519450
$506$		0			0
$507$	6.30502	+	10.9206i	0.280016	+	0.485002i
$508$		0			0
$509$	10.7499	+	6.20647i	0.476482	+	0.275097i	0.718949	−	0.695063i	$-0.244623\pi$
$509$	10.7499	+	6.20647i	0.476482	+	0.275097i	−0.242467	+	0.970160i	$0.577957\pi$
$510$		0			0
$511$	20.9871	−	38.1202i	0.928415	−	1.68634i
$512$		0			0
$513$	1.76076	−	3.04972i	0.0777393	−	0.134648i
$514$		0			0
$515$	0.0822176	−	0.0474683i	0.00362294	−	0.00209171i
$516$		0			0
$517$		−	1.87465i		−	0.0824468i
$518$		0			0
$519$			9.29386i			0.407955i
$520$		0			0
$521$	−29.1390	+	16.8234i	−1.27660	+	0.737048i	−0.976222	−	0.216771i	$-0.930447\pi$
$521$	−29.1390	+	16.8234i	−1.27660	+	0.737048i	−0.300382	+	0.953819i	$0.597114\pi$
$522$		0			0
$523$	−18.1358	+	31.4121i	−0.793022	+	1.37356i	0.131065	+	0.991374i	$0.458160\pi$
$523$	−18.1358	+	31.4121i	−0.793022	+	1.37356i	−0.924087	+	0.382181i	$0.875173\pi$
$524$		0			0
$525$	0.0537914	+	2.64520i	0.00234765	+	0.115446i
$526$		0			0
$527$	3.17318	+	1.83204i	0.138226	+	0.0798047i
$528$		0			0
$529$	−1.50765	−	2.61133i	−0.0655501	−	0.113536i
$530$		0			0
$531$	−4.61577			−0.200307
$532$		0			0
$533$	−3.00200			−0.130031
$534$		0			0
$535$	−5.85968	−	10.1493i	−0.253336	−	0.438791i
$536$		0			0
$537$	−10.9947	−	6.34782i	−0.474458	−	0.273929i
$538$		0			0
$539$	−0.616111	−	15.1424i	−0.0265378	−	0.652231i
$540$		0			0
$541$	13.3803	−	23.1753i	0.575263	−	0.996386i	−0.420749	−	0.907177i	$-0.638233\pi$
$541$	13.3803	−	23.1753i	0.575263	−	0.996386i	0.996013	−	0.0892087i	$-0.0284338\pi$
$542$		0			0
$543$	−11.0885	+	6.40193i	−0.475852	+	0.274733i
$544$		0			0
$545$		−	14.0404i		−	0.601423i
$546$		0			0
$547$			23.0776i			0.986726i	0.869824	+	0.493363i	$0.164233\pi$
$547$			23.0776i			0.986726i	−0.869824	+	0.493363i	$0.835767\pi$
$548$		0			0
$549$	−4.08660	+	2.35940i	−0.174412	+	0.100697i
$550$		0			0
$551$	−16.6801	+	28.8907i	−0.710595	+	1.23079i
$552$		0			0
$553$	3.16867	−	0.0644362i	0.134745	−	0.00274011i
$554$		0			0
$555$	−3.21904	−	1.85852i	−0.136641	−	0.0788896i
$556$		0			0
$557$	−15.5815	−	26.9879i	−0.660207	−	1.14351i	−0.980561	−	0.196215i	$-0.937135\pi$
$557$	−15.5815	−	26.9879i	−0.660207	−	1.14351i	0.320354	−	0.947298i	$-0.396198\pi$
$558$		0			0
$559$	−5.46691			−0.231226
$560$		0			0
$561$	−0.837939			−0.0353778
$562$		0			0
$563$	−0.480238	−	0.831797i	−0.0202396	−	0.0350561i	0.855728	−	0.517426i	$-0.173110\pi$
$563$	−0.480238	−	0.831797i	−0.0202396	−	0.0350561i	−0.875968	+	0.482370i	$0.839776\pi$
$564$		0			0
$565$	9.94814	+	5.74356i	0.418521	+	0.241633i
$566$		0			0
$567$	−2.31771	−	1.27602i	−0.0973347	−	0.0535877i
$568$		0			0
$569$	8.85745	−	15.3415i	0.371323	−	0.643151i	−0.618446	−	0.785827i	$-0.712237\pi$
$569$	8.85745	−	15.3415i	0.371323	−	0.643151i	0.989769	+	0.142676i	$0.0455708\pi$
$570$		0			0
$571$	−25.2165	+	14.5587i	−1.05528	+	0.609264i	−0.924122	−	0.382098i	$-0.875202\pi$
$571$	−25.2165	+	14.5587i	−1.05528	+	0.609264i	−0.131155	+	0.991362i	$0.541869\pi$
$572$		0			0
$573$			25.4697i			1.06401i
$574$		0			0
$575$			4.47042i			0.186430i
$576$		0			0
$577$	−21.0379	+	12.1463i	−0.875820	+	0.505655i	−0.869278	−	0.494323i	$-0.835416\pi$
$577$	−21.0379	+	12.1463i	−0.875820	+	0.505655i	−0.00654236	+	0.999979i	$0.502083\pi$
$578$		0			0
$579$	2.75726	−	4.77571i	0.114588	−	0.198472i
$580$		0			0
$581$	−1.06894	+	0.646479i	−0.0443470	+	0.0268205i
$582$		0			0
$583$	24.8820	+	14.3657i	1.03051	+	0.594965i
$584$		0			0
$585$	−0.312234	−	0.540805i	−0.0129093	−	0.0223595i
$586$		0			0
$587$	−8.36534			−0.345275			−0.172637	−	0.984985i	$-0.555229\pi$
$587$	−8.36534			−0.345275			−0.172637	+	0.984985i	$0.555229\pi$
$588$		0			0
$589$	33.3379			1.37366
$590$		0			0
$591$	−9.06550	−	15.7019i	−0.372905	−	0.645890i
$592$		0			0
$593$	26.0968	+	15.0670i	1.07167	+	0.618728i	0.928637	−	0.370990i	$-0.120982\pi$
$593$	26.0968	+	15.0670i	1.07167	+	0.618728i	0.143031	+	0.989718i	$0.454315\pi$
$594$		0			0
$595$	0.876227	−	0.529930i	0.0359218	−	0.0217250i
$596$		0			0
$597$	12.7094	−	22.0133i	0.520160	−	0.900944i
$598$		0			0
$599$	36.7001	−	21.1888i	1.49952	−	0.865751i	0.499525	−	0.866300i	$-0.333508\pi$
$599$	36.7001	−	21.1888i	1.49952	−	0.865751i	1.00000		0.000548741i	$0.000174670\pi$
$600$		0			0
$601$		−	12.3666i		−	0.504446i	−0.967669	−	0.252223i	$-0.918838\pi$
$601$		−	12.3666i		−	0.504446i	0.967669	−	0.252223i	$-0.0811616\pi$
$602$		0			0
$603$		−	8.31730i		−	0.338707i
$604$		0			0
$605$	5.46704	−	3.15640i	0.222267	−	0.128326i
$606$		0			0
$607$	−14.2387	+	24.6621i	−0.577929	+	1.00100i	0.417787	+	0.908545i	$0.362806\pi$
$607$	−14.2387	+	24.6621i	−0.577929	+	1.00100i	−0.995717	+	0.0924583i	$0.970528\pi$
$608$		0			0
$609$	21.9562	+	12.0880i	0.889711	+	0.489831i
$610$		0			0
$611$	−0.468277	−	0.270360i	−0.0189445	−	0.0109376i
$612$		0			0
$613$	21.0904	+	36.5297i	0.851834	+	1.47542i	0.879552	+	0.475804i	$0.157843\pi$
$613$	21.0904	+	36.5297i	0.851834	+	1.47542i	−0.0277177	+	0.999616i	$0.508824\pi$
$614$		0			0
$615$	−4.80729			−0.193849
$616$		0			0
$617$	10.2278			0.411756			0.205878	−	0.978578i	$-0.433995\pi$
$617$	10.2278			0.411756			0.205878	+	0.978578i	$0.433995\pi$
$618$		0			0
$619$	−6.95024	−	12.0382i	−0.279354	−	0.483855i	0.691870	−	0.722022i	$-0.256787\pi$
$619$	−6.95024	−	12.0382i	−0.279354	−	0.483855i	−0.971224	+	0.238167i	$0.923454\pi$
$620$		0			0
$621$	−3.87150	−	2.23521i	−0.155358	−	0.0896960i
$622$		0			0
$623$	15.2722	−	0.310566i	0.611866	−	0.0124426i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−6.60263	+	3.81203i	−0.263684	+	0.152238i
$628$		0			0
$629$			1.43864i			0.0573623i
$630$		0			0
$631$		−	30.4667i		−	1.21286i	−0.795137	−	0.606430i	$-0.792601\pi$
$631$		−	30.4667i		−	1.21286i	0.795137	−	0.606430i	$-0.207399\pi$
$632$		0			0
$633$	15.5000	−	8.94892i	0.616069	−	0.355688i
$634$		0			0
$635$	−4.87919	+	8.45101i	−0.193625	+	0.335368i
$636$		0			0
$637$	−3.87136	−	2.02993i	−0.153389	−	0.0804287i
$638$		0			0
$639$	−1.42179	−	0.820871i	−0.0562452	−	0.0324732i
$640$		0			0
$641$	−0.573997	−	0.994192i	−0.0226715	−	0.0392682i	0.854467	−	0.519506i	$-0.173884\pi$
$641$	−0.573997	−	0.994192i	−0.0226715	−	0.0392682i	−0.877139	+	0.480237i	$0.840551\pi$
$642$		0			0
$643$	−28.5026			−1.12403			−0.562017	−	0.827126i	$-0.689974\pi$
$643$	−28.5026			−1.12403			−0.562017	+	0.827126i	$0.689974\pi$
$644$		0			0
$645$	−8.75451			−0.344709
$646$		0			0
$647$	−8.77664	−	15.2016i	−0.345046	−	0.597636i	0.640317	−	0.768111i	$-0.278803\pi$
$647$	−8.77664	−	15.2016i	−0.345046	−	0.597636i	−0.985362	+	0.170475i	$0.945470\pi$
$648$		0			0
$649$	8.65430	+	4.99656i	0.339711	+	0.196132i
$650$		0			0
$651$	−0.509238	−	25.0419i	−0.0199586	−	0.981470i
$652$		0			0
$653$	5.21286	−	9.02893i	0.203995	−	0.353329i	−0.745817	−	0.666151i	$-0.767941\pi$
$653$	5.21286	−	9.02893i	0.203995	−	0.353329i	0.949812	+	0.312821i	$0.101274\pi$
$654$		0			0
$655$	10.7430	−	6.20248i	0.419764	−	0.242351i
$656$		0			0
$657$			16.4473i			0.641672i
$658$		0			0
$659$			0.397054i			0.0154670i	0.999970	+	0.00773351i	$0.00246168\pi$
$659$			0.397054i			0.0154670i	−0.999970	+	0.00773351i	$0.997538\pi$
$660$		0			0
$661$	−11.3038	+	6.52627i	−0.439668	+	0.253843i	−0.703457	−	0.710738i	$-0.748361\pi$
$661$	−11.3038	+	6.52627i	−0.439668	+	0.253843i	0.263789	+	0.964581i	$0.415028\pi$
$662$		0			0
$663$	−0.120847	+	0.209313i	−0.00469331	+	0.00812905i
$664$		0			0
$665$	4.49351	−	8.16185i	0.174251	−	0.316503i
$666$		0			0
$667$	36.6756	+	21.1747i	1.42009	+	0.819887i
$668$		0			0
$669$	−2.82517	−	4.89334i	−0.109227	−	0.189187i
$670$		0			0
$671$	10.2162			0.394392
$672$		0			0
$673$	−2.94900			−0.113675			−0.0568377	−	0.998383i	$-0.518102\pi$
$673$	−2.94900			−0.113675			−0.0568377	+	0.998383i	$0.518102\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$		0			0
$677$	−30.4674	−	17.5904i	−1.17096	−	0.676053i	−0.217053	−	0.976160i	$-0.569644\pi$
$677$	−30.4674	−	17.5904i	−1.17096	−	0.676053i	−0.953906	+	0.300107i	$0.902978\pi$
$678$		0			0
$679$	−4.00448	−	6.62131i	−0.153678	−	0.254103i
$680$		0			0
$681$	11.5695	−	20.0390i	0.443345	−	0.767896i
$682$		0			0
$683$	−24.0692	+	13.8964i	−0.920984	+	0.531730i	−0.883949	−	0.467584i	$-0.845125\pi$
$683$	−24.0692	+	13.8964i	−0.920984	+	0.531730i	−0.0370352	+	0.999314i	$0.511791\pi$
$684$		0			0
$685$			7.46636i			0.285275i
$686$		0			0
$687$			18.4634i			0.704421i
$688$		0			0
$689$	7.17694	−	4.14361i	0.273420	−	0.157859i
$690$		0			0
$691$	−3.01643	+	5.22460i	−0.114750	+	0.198753i	−0.917680	−	0.397321i	$-0.869940\pi$
$691$	−3.01643	+	5.22460i	−0.114750	+	0.198753i	0.802930	+	0.596074i	$0.203273\pi$
$692$		0			0
$693$	2.96428	+	4.90137i	0.112604	+	0.186188i
$694$		0			0
$695$	13.3815	+	7.72580i	0.507589	+	0.293056i
$696$		0			0
$697$	0.930307	+	1.61134i	0.0352379	+	0.0610338i
$698$		0			0
$699$	12.2024			0.461538
$700$		0			0
$701$	26.3380			0.994773			0.497386	−	0.867529i	$-0.334293\pi$
$701$	26.3380			0.994773			0.497386	+	0.867529i	$0.334293\pi$
$702$		0			0
$703$	6.54479	+	11.3359i	0.246841	+	0.427542i
$704$		0			0
$705$	−0.749882	−	0.432944i	−0.0282422	−	0.0163056i
$706$		0			0
$707$	14.8952	−	27.0551i	0.560191	−	1.01751i
$708$		0			0
$709$	−3.02042	+	5.23152i	−0.113434	+	0.196474i	−0.917153	−	0.398536i	$-0.869518\pi$
$709$	−3.02042	+	5.23152i	−0.113434	+	0.196474i	0.803718	+	0.595010i	$0.202852\pi$
$710$		0			0
$711$	−1.03740	+	0.598945i	−0.0389057	+	0.0224622i
$712$		0			0
$713$		−	42.3211i		−	1.58494i
$714$		0			0
$715$			1.35197i			0.0505608i
$716$		0			0
$717$	9.44102	−	5.45078i	0.352581	−	0.203563i
$718$		0			0
$719$	−18.3181	+	31.7279i	−0.683150	+	1.18325i	0.290865	+	0.956764i	$0.406057\pi$
$719$	−18.3181	+	31.7279i	−0.683150	+	1.18325i	−0.974014	+	0.226486i	$0.927276\pi$
$720$		0			0
$721$	0.00510678	+	0.251127i	0.000190186	+	0.00935246i
$722$		0			0
$723$	−5.24772	−	3.02977i	−0.195165	−	0.112679i
$724$		0			0
$725$	4.73662	+	8.20406i	0.175914	+	0.304691i
$726$		0			0
$727$	43.2058			1.60241			0.801207	−	0.598387i	$-0.204191\pi$
$727$	43.2058			1.60241			0.801207	+	0.598387i	$0.204191\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	1.69417	+	2.93439i	0.0626612	+	0.108532i
$732$		0			0
$733$	20.7209	+	11.9632i	0.765345	+	0.441872i	0.831212	−	0.555956i	$-0.187648\pi$
$733$	20.7209	+	11.9632i	0.765345	+	0.441872i	−0.0658665	+	0.997828i	$0.520981\pi$
$734$		0			0
$735$	−6.19946	−	3.25065i	−0.228670	−	0.119902i
$736$		0			0
$737$	−9.00346	+	15.5944i	−0.331647	+	0.574429i
$738$		0			0
$739$	33.0290	−	19.0693i	1.21499	−	0.701476i	0.251149	−	0.967948i	$-0.419192\pi$
$739$	33.0290	−	19.0693i	1.21499	−	0.701476i	0.963842	+	0.266473i	$0.0858582\pi$
$740$		0			0
$741$			2.19907i			0.0807850i
$742$		0			0
$743$		−	11.9035i		−	0.436698i	−0.975871	−	0.218349i	$-0.929933\pi$
$743$		−	11.9035i		−	0.436698i	0.975871	−	0.218349i	$-0.0700671\pi$
$744$		0			0
$745$	−2.28464	+	1.31904i	−0.0837028	+	0.0483258i
$746$		0			0
$747$	0.236081	−	0.408905i	0.00863777	−	0.0149611i
$748$		0			0
$749$	31.0001	−	0.630401i	1.13272	−	0.0230343i
$750$		0			0
$751$	13.0940	+	7.55980i	0.477805	+	0.275861i	0.719501	−	0.694491i	$-0.244370\pi$
$751$	13.0940	+	7.55980i	0.477805	+	0.275861i	−0.241696	+	0.970352i	$0.577704\pi$
$752$		0			0
$753$	−6.52369	−	11.2994i	−0.237736	−	0.411771i
$754$		0			0
$755$	−4.24395			−0.154453
$756$		0			0
$757$	51.2575			1.86299			0.931493	−	0.363760i	$-0.118507\pi$
$757$	51.2575			1.86299			0.931493	+	0.363760i	$0.118507\pi$
$758$		0			0
$759$	4.83922	+	8.38178i	0.175653	+	0.304239i
$760$		0			0
$761$	30.3632	+	17.5302i	1.10066	+	0.635468i	0.936395	−	0.350947i	$-0.114140\pi$
$761$	30.3632	+	17.5302i	1.10066	+	0.635468i	0.164268	+	0.986416i	$0.447474\pi$
$762$		0			0
$763$	32.5415	+	17.9158i	1.17808	+	0.648594i
$764$		0			0
$765$	−0.193520	+	0.335186i	−0.00699673	+	0.0121187i
$766$		0			0
$767$	2.49623	−	1.44120i	0.0901337	−	0.0520387i
$768$		0			0
$769$			28.9855i			1.04524i	0.852564	+	0.522622i	$0.175046\pi$
$769$			28.9855i			1.04524i	−0.852564	+	0.522622i	$0.824954\pi$
$770$		0			0
$771$		−	30.6436i		−	1.10360i
$772$		0			0
$773$	23.2430	−	13.4194i	0.835994	−	0.482661i	−0.0199066	−	0.999802i	$-0.506337\pi$
$773$	23.2430	−	13.4194i	0.835994	−	0.482661i	0.855901	+	0.517141i	$0.173004\pi$
$774$		0			0
$775$	4.73346	−	8.19859i	0.170031	−	0.294502i
$776$		0			0
$777$	8.41505	−	5.08931i	0.301888	−	0.182578i
$778$		0			0
$779$	14.6609	+	8.46448i	0.525281	+	0.303271i
$780$		0			0
$781$	1.77718	+	3.07817i	0.0635926	+	0.110146i
$782$		0			0
$783$	−9.47323			−0.338546
$784$		0			0
$785$	10.2081			0.364344
$786$		0			0
$787$	14.0089	+	24.2642i	0.499365	+	0.864925i	1.00000		0.000733319i	$-0.000233423\pi$
$787$	14.0089	+	24.2642i	0.499365	+	0.864925i	−0.500635	+	0.865659i	$0.666900\pi$
$788$		0			0
$789$	−14.5348	−	8.39167i	−0.517452	−	0.298751i
$790$		0			0
$791$	−26.0059	+	15.7280i	−0.924663	+	0.559224i
$792$		0			0
$793$	1.47337	−	2.55195i	0.0523210	−	0.0906225i
$794$		0			0
$795$	11.4929	−	6.63542i	0.407611	−	0.235334i
$796$		0			0
$797$		−	2.37503i		−	0.0841279i	−0.999115	−	0.0420640i	$-0.986607\pi$
$797$		−	2.37503i		−	0.0841279i	0.999115	−	0.0420640i	$-0.0133933\pi$
$798$		0			0
$799$			0.335133i			0.0118562i
$800$		0			0
$801$	−5.00002	+	2.88676i	−0.176667	+	0.101999i
$802$		0			0
$803$	17.8042	−	30.8378i	0.628297	−	1.08824i
$804$		0			0
$805$	−10.3611	−	5.70434i	−0.365182	−	0.201052i
$806$		0			0
$807$	4.28678	+	2.47497i	0.150902	+	0.0871232i
$808$		0			0
$809$	−8.04097	−	13.9274i	−0.282705	−	0.489660i	0.689345	−	0.724434i	$-0.257899\pi$
$809$	−8.04097	−	13.9274i	−0.282705	−	0.489660i	−0.972050	+	0.234773i	$0.924565\pi$
$810$		0			0
$811$	−18.8656			−0.662461			−0.331231	−	0.943550i	$-0.607464\pi$
$811$	−18.8656			−0.662461			−0.331231	+	0.943550i	$0.607464\pi$
$812$		0			0
$813$	−5.74424			−0.201459
$814$		0			0
$815$	1.25989	+	2.18219i	0.0441319	+	0.0764388i
$816$		0			0
$817$	26.6988	+	15.4146i	0.934073	+	0.539287i
$818$		0			0
$819$	1.65185	−	0.0335910i	0.0577202	−	0.00117376i
$820$		0			0
$821$	8.83796	−	15.3078i	0.308447	−	0.534246i	−0.669576	−	0.742744i	$-0.733524\pi$
$821$	8.83796	−	15.3078i	0.308447	−	0.534246i	0.978023	+	0.208498i	$0.0668575\pi$
$822$		0			0
$823$	−29.6861	+	17.1393i	−1.03479	+	0.597439i	−0.918354	−	0.395759i	$-0.870481\pi$
$823$	−29.6861	+	17.1393i	−1.03479	+	0.597439i	−0.116440	+	0.993198i	$0.537148\pi$
$824$		0			0
$825$			2.16500i			0.0753755i
$826$		0			0
$827$		−	53.5653i		−	1.86265i	−0.364190	−	0.931325i	$-0.618654\pi$
$827$		−	53.5653i		−	1.86265i	0.364190	−	0.931325i	$-0.381346\pi$
$828$		0			0
$829$	14.4270	−	8.32945i	0.501072	−	0.289294i	−0.228084	−	0.973641i	$-0.573246\pi$
$829$	14.4270	−	8.32945i	0.501072	−	0.289294i	0.729156	+	0.684347i	$0.239913\pi$
$830$		0			0
$831$	4.56118	−	7.90020i	0.158226	−	0.274055i
$832$		0			0
$833$	0.110143	+	2.70704i	0.00381624	+	0.0937933i
$834$		0			0
$835$	5.19849	+	3.00135i	0.179901	+	0.103866i
$836$		0			0
$837$	4.73346	+	8.19859i	0.163612	+	0.283385i
$838$		0			0
$839$	−0.646377			−0.0223154			−0.0111577	−	0.999938i	$-0.503552\pi$
$839$	−0.646377			−0.0223154			−0.0111577	+	0.999938i	$0.503552\pi$
$840$		0			0
$841$	60.7422			2.09456
$842$		0			0
$843$	−2.39167	−	4.14249i	−0.0823734	−	0.142675i
$844$		0			0
$845$	−10.9206	−	6.30502i	−0.375681	−	0.216899i
$846$		0			0
$847$	0.339574	+	16.6986i	0.0116679	+	0.573772i
$848$		0			0
$849$	−0.176678	+	0.306014i	−0.00606356	+	0.0105024i
$850$		0			0
$851$	14.3905	−	8.30835i	0.493300	−	0.284807i
$852$		0			0
$853$		−	39.5869i		−	1.35543i	−0.735324	−	0.677715i	$-0.762970\pi$
$853$		−	39.5869i		−	1.35543i	0.735324	−	0.677715i	$-0.237030\pi$
$854$		0			0
$855$			3.52151i			0.120433i
$856$		0			0
$857$	24.2101	−	13.9777i	0.827003	−	0.477470i	−0.0258226	−	0.999667i	$-0.508221\pi$
$857$	24.2101	−	13.9777i	0.827003	−	0.477470i	0.852825	+	0.522196i	$0.174887\pi$
$858$		0			0
$859$	−4.44220	+	7.69412i	−0.151566	+	0.262520i	−0.931803	−	0.362964i	$-0.881765\pi$
$859$	−4.44220	+	7.69412i	−0.151566	+	0.262520i	0.780237	+	0.625484i	$0.215098\pi$
$860$		0			0
$861$	6.13419	−	11.1419i	0.209053	−	0.379715i
$862$		0			0
$863$	−43.5484	−	25.1427i	−1.48241	−	0.855868i	−0.482606	−	0.875838i	$-0.660310\pi$
$863$	−43.5484	−	25.1427i	−1.48241	−	0.855868i	−0.999801	+	0.0199703i	$0.993643\pi$
$864$		0			0
$865$	−4.64693	−	8.04871i	−0.158000	−	0.273665i
$866$		0			0
$867$	−16.8502			−0.572263
$868$		0			0
$869$	2.59343			0.0879760
$870$		0			0
$871$	2.59694	+	4.49804i	0.0879941	+	0.152410i
$872$		0			0
$873$	2.53288	+	1.46236i	0.0857248	+	0.0494933i
$874$		0			0
$875$	−1.36919	−	2.26392i	−0.0462870	−	0.0765344i
$876$		0			0
$877$	0.478486	−	0.828762i	0.0161573	−	0.0279853i	−0.857834	−	0.513927i	$-0.828190\pi$
$877$	0.478486	−	0.828762i	0.0161573	−	0.0279853i	0.873991	+	0.485942i	$0.161523\pi$
$878$		0			0
$879$	−15.6838	+	9.05504i	−0.529001	+	0.305419i
$880$		0			0
$881$			58.9964i			1.98764i	0.111000	+	0.993820i	$0.464594\pi$
$881$			58.9964i			1.98764i	−0.111000	+	0.993820i	$0.535406\pi$
$882$		0			0
$883$			18.1642i			0.611274i	0.952148	+	0.305637i	$0.0988694\pi$
$883$			18.1642i			0.611274i	−0.952148	+	0.305637i	$0.901131\pi$
$884$		0			0
$885$	3.99737	−	2.30789i	0.134370	−	0.0775787i
$886$		0			0
$887$	7.97320	−	13.8100i	0.267714	−	0.463694i	−0.700557	−	0.713596i	$-0.747065\pi$
$887$	7.97320	−	13.8100i	0.267714	−	0.463694i	0.968271	+	0.249902i	$0.0803985\pi$
$888$		0			0
$889$	−13.3611	−	22.0922i	−0.448115	−	0.740948i
$890$		0			0
$891$	−1.87494	−	1.08250i	−0.0628129	−	0.0362650i
$892$		0			0
$893$	1.52462	+	2.64072i	0.0510195	+	0.0883683i
$894$		0			0
$895$	12.6956			0.424369
$896$		0			0
$897$	2.79164			0.0932101
$898$		0			0
$899$	−44.8411	−	77.6671i	−1.49554	−	2.59034i
$900$		0			0
$901$	−4.44820	−	2.56817i	−0.148191	−	0.0855582i
$902$		0			0
$903$	11.1709	−	20.2904i	0.371745	−	0.675223i
$904$		0			0
$905$	6.40193	−	11.0885i	0.212807	−	0.368593i
$906$		0			0
$907$	−30.2636	+	17.4727i	−1.00489	+	0.580172i	−0.909691	−	0.415287i	$-0.863681\pi$
$907$	−30.2636	+	17.4727i	−1.00489	+	0.580172i	−0.0951964	+	0.995459i	$0.530348\pi$
$908$		0			0
$909$			11.6732i			0.387175i
$910$		0			0
$911$			25.7541i			0.853270i	0.904424	+	0.426635i	$0.140301\pi$
$911$			25.7541i			0.853270i	−0.904424	+	0.426635i	$0.859699\pi$
$912$		0			0
$913$	−0.885278	+	0.511115i	−0.0292984	+	0.0169154i
$914$		0			0
$915$	2.35940	−	4.08660i	0.0779994	−	0.135099i
$916$		0			0
$917$	0.667280	+	32.8136i	0.0220355	+	1.08360i
$918$		0			0
$919$	13.7854	+	7.95898i	0.454737	+	0.262543i	0.709829	−	0.704374i	$-0.248772\pi$
$919$	13.7854	+	7.95898i	0.454737	+	0.262543i	−0.255092	+	0.966917i	$0.582106\pi$
$920$		0			0
$921$	−4.47276	−	7.74705i	−0.147382	−	0.255274i
$922$		0			0
$923$	1.02522			0.0337454
$924$		0			0
$925$	3.71703			0.122215
$926$		0			0
$927$	−0.0474683	−	0.0822176i	−0.00155907	−	0.00270038i
$928$		0			0
$929$	5.43070	+	3.13542i	0.178175	+	0.102870i	0.586435	−	0.809996i	$-0.300531\pi$
$929$	5.43070	+	3.13542i	0.178175	+	0.102870i	−0.408260	+	0.912866i	$0.633864\pi$
$930$		0			0
$931$	13.1830	+	20.8293i	0.432055	+	0.682653i
$932$		0			0
$933$	−11.3699	+	19.6932i	−0.372233	+	0.644727i
$934$		0			0
$935$	0.725677	−	0.418970i	0.0237322	−	0.0137018i
$936$		0			0
$937$		−	54.4941i		−	1.78024i	−0.455722	−	0.890122i	$-0.650619\pi$
$937$		−	54.4941i		−	1.78024i	0.455722	−	0.890122i	$-0.349381\pi$
$938$		0			0
$939$		−	2.32399i		−	0.0758404i
$940$		0			0
$941$	7.19924	−	4.15649i	0.234689	−	0.135498i	−0.378045	−	0.925787i	$-0.623403\pi$
$941$	7.19924	−	4.15649i	0.234689	−	0.135498i	0.612733	+	0.790290i	$0.290070\pi$
$942$		0			0
$943$	10.7453	−	18.6114i	0.349916	−	0.606072i
$944$		0			0
$945$	2.64520	−	0.0537914i	0.0860485	−	0.00174983i
$946$		0			0
$947$	−36.4305	−	21.0332i	−1.18383	−	0.683487i	−0.226935	−	0.973910i	$-0.572871\pi$
$947$	−36.4305	−	21.0332i	−1.18383	−	0.683487i	−0.956898	+	0.290423i	$0.906204\pi$
$948$		0			0
$949$	−5.13542	−	8.89481i	−0.166703	−	0.288738i
$950$		0			0
$951$	−6.41591			−0.208050
$952$		0			0
$953$	−22.1029			−0.715983			−0.357992	−	0.933725i	$-0.616538\pi$
$953$	−22.1029			−0.715983			−0.357992	+	0.933725i	$0.616538\pi$
$954$		0			0
$955$	−12.7349	−	22.0574i	−0.412090	−	0.713762i
$956$		0			0
$957$	17.7618	+	10.2548i	0.574156	+	0.331489i
$958$		0			0
$959$	−17.3048	−	9.52720i	−0.558803	−	0.307649i
$960$		0			0
$961$	−29.3112	+	50.7685i	−0.945523	+	1.63769i
$962$		0			0
$963$	−10.1493	+	5.85968i	−0.327055	+	0.188826i
$964$		0			0
$965$			5.51451i			0.177518i
$966$		0			0
$967$		−	15.6608i		−	0.503618i	−0.967777	−	0.251809i	$-0.918975\pi$
$967$		−	15.6608i		−	0.503618i	0.967777	−	0.251809i	$-0.0810254\pi$
$968$		0			0
$969$	1.18036	−	0.681483i	0.0379187	−	0.0218924i
$970$		0			0
$971$	−14.4680	+	25.0594i	−0.464301	+	0.804193i	−0.999170	−	0.0407421i	$-0.987028\pi$
$971$	−14.4680	+	25.0594i	−0.464301	+	0.804193i	0.534869	+	0.844935i	$0.320361\pi$
$972$		0			0
$973$	−34.9812	+	21.1561i	−1.12145	+	0.678235i
$974$		0			0
$975$	0.540805	+	0.312234i	0.0173196	+	0.00999949i
$976$		0			0
$977$	16.1804	+	28.0253i	0.517657	+	0.896608i	0.999790	+	0.0205097i	$0.00652890\pi$
$977$	16.1804	+	28.0253i	0.517657	+	0.896608i	−0.482133	+	0.876098i	$0.660138\pi$
$978$		0			0
$979$	12.4997			0.399491
$980$		0			0
$981$	−14.0404			−0.448275
$982$		0			0
$983$	3.87039	+	6.70370i	0.123446	+	0.213815i	0.921124	−	0.389268i	$-0.127272\pi$
$983$	3.87039	+	6.70370i	0.123446	+	0.213815i	−0.797678	+	0.603083i	$0.793939\pi$
$984$		0			0
$985$	15.7019	+	9.06550i	0.500304	+	0.288851i
$986$		0			0
$987$	1.96030	−	1.18556i	0.0623971	−	0.0377369i
$988$		0			0
$989$	19.5682	−	33.8931i	0.622232	−	1.07774i
$990$		0			0
$991$	27.5944	−	15.9317i	0.876566	−	0.506086i	0.00704159	−	0.999975i	$-0.497759\pi$
$991$	27.5944	−	15.9317i	0.876566	−	0.506086i	0.869525	+	0.493889i	$0.164425\pi$
$992$		0			0
$993$		−	15.1805i		−	0.481739i
$994$		0			0
$995$			25.4188i			0.805829i
$996$		0			0
$997$	−5.13220	+	2.96307i	−0.162538	+	0.0938415i	−0.579063	−	0.815283i	$-0.696581\pi$
$997$	−5.13220	+	2.96307i	−0.162538	+	0.0938415i	0.416524	+	0.909125i	$0.363248\pi$
$998$		0			0
$999$	−1.85852	+	3.21904i	−0.0588008	+	0.101846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.dx.h.271.3	yes	12
4.3	odd	2		1680.2.dx.f.271.1	yes	12
7.3	odd	6		1680.2.dx.f.31.1	✓	12
28.3	even	6	inner	1680.2.dx.h.31.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.dx.f.31.1	✓	12	7.3	odd	6
1680.2.dx.f.271.1	yes	12	4.3	odd	2
1680.2.dx.h.31.3	yes	12	28.3	even	6	inner
1680.2.dx.h.271.3	yes	12	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.dx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(2.26392 - 1.36919i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.87494 - 1.08250i) q^{11} -0.624468i q^{13} -1.00000i q^{15} +(-0.335186 + 0.193520i) q^{17} +(-1.76076 + 3.04972i) q^{19} +(2.31771 + 1.27602i) q^{21} +(3.87150 + 2.23521i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +9.47323 q^{29} +(-4.73346 - 8.19859i) q^{31} +(1.87494 + 1.08250i) q^{33} +(-2.64520 + 0.0537914i) q^{35} +(1.85852 - 3.21904i) q^{37} +(0.540805 - 0.312234i) q^{39} -4.80729i q^{41} -8.75451i q^{43} +(0.866025 - 0.500000i) q^{45} +(0.432944 - 0.749882i) q^{47} +(3.25065 - 6.19946i) q^{49} +(-0.335186 - 0.193520i) q^{51} +(6.63542 + 11.4929i) q^{53} -2.16500 q^{55} -3.52151 q^{57} +(2.30789 + 3.99737i) q^{59} +(4.08660 + 2.35940i) q^{61} +(0.0537914 + 2.64520i) q^{63} +(-0.312234 + 0.540805i) q^{65} +(-7.20299 + 4.15865i) q^{67} +4.47042i q^{69} +1.64174i q^{71} +(14.2438 - 8.22367i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(2.76257 - 5.01783i) q^{77} +(1.03740 + 0.598945i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.472163 q^{83} +0.387040 q^{85} +(4.73662 + 8.20406i) q^{87} +(5.00002 + 2.88676i) q^{89} +(-0.855013 - 1.41374i) q^{91} +(4.73346 - 8.19859i) q^{93} +(3.04972 - 1.76076i) q^{95} -2.92471i q^{97} +2.16500i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 2 q^{7} - 6 q^{9} + 10 q^{19} - 4 q^{21} + 12 q^{23} + 6 q^{25} - 12 q^{27} + 8 q^{29} - 2 q^{31} - 4 q^{35} - 10 q^{37} + 6 q^{39} + 2 q^{49} + 16 q^{53} + 20 q^{57} + 24 q^{61} - 2 q^{63}+ \cdots + 24 q^{95}+O(q^{100}) \) 12 * q + 6 * q^3 - 2 * q^7 - 6 * q^9 + 10 * q^19 - 4 * q^21 + 12 * q^23 + 6 * q^25 - 12 * q^27 + 8 * q^29 - 2 * q^31 - 4 * q^35 - 10 * q^37 + 6 * q^39 + 2 * q^49 + 16 * q^53 + 20 * q^57 + 24 * q^61 - 2 * q^63 + 4 * q^65 - 6 * q^67 + 30 * q^73 - 6 * q^75 + 36 * q^77 + 42 * q^79 - 6 * q^81 - 64 * q^83 - 8 * q^85 + 4 * q^87 + 14 * q^91 + 2 * q^93 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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