LMFDB - Embedded newform 722.2.e.c.595.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			595.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	722.595
Dual form			722.2.e.c.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.694593 - 3.93923i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.53209 - 1.28558i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.694593 - 3.93923i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.53209 - 1.28558i) q^{9} +(-3.06418 - 2.57115i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.939693 - 0.342020i) q^{13} +(0.520945 + 2.95442i) q^{14} +(0.694593 - 3.93923i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.29813 - 1.92836i) q^{17} -2.00000 q^{18} -4.00000 q^{20} +(-2.29813 + 1.92836i) q^{21} +(-1.87939 - 0.684040i) q^{22} +(-0.173648 + 0.984808i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-10.3366 + 3.76222i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.50000 - 4.33013i) q^{27} +(2.29813 + 1.92836i) q^{28} +(-3.83022 - 3.21394i) q^{29} +(-2.00000 - 3.46410i) q^{30} +(4.00000 - 6.92820i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.347296 - 1.96962i) q^{33} +(0.520945 - 2.95442i) q^{34} +(11.2763 + 4.10424i) q^{35} +(-1.53209 + 1.28558i) q^{36} -2.00000 q^{37} +1.00000 q^{39} +(-3.06418 + 2.57115i) q^{40} +(7.51754 + 2.73616i) q^{41} +(-0.520945 + 2.95442i) q^{42} +(0.694593 + 3.93923i) q^{43} +(-1.87939 + 0.684040i) q^{44} +(-4.00000 + 6.92820i) q^{45} +(0.500000 + 0.866025i) q^{46} +(6.12836 + 5.14230i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(-5.50000 + 9.52628i) q^{50} +(2.81908 - 1.02606i) q^{51} +(-0.173648 - 0.984808i) q^{52} +(-0.173648 + 0.984808i) q^{53} +(-4.69846 - 1.71010i) q^{54} +(-6.12836 + 5.14230i) q^{55} +3.00000 q^{56} -5.00000 q^{58} +(11.4907 - 9.64181i) q^{59} +(-3.75877 - 1.36808i) q^{60} +(0.347296 - 1.96962i) q^{61} +(-1.38919 - 7.87846i) q^{62} +(5.63816 - 2.05212i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.00000 - 3.46410i) q^{65} +(-1.53209 - 1.28558i) q^{66} +(2.29813 + 1.92836i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-0.500000 + 0.866025i) q^{69} +(11.2763 - 4.10424i) q^{70} +(0.347296 + 1.96962i) q^{71} +(-0.347296 + 1.96962i) q^{72} +(-8.45723 - 3.07818i) q^{73} +(-1.53209 + 1.28558i) q^{74} -11.0000 q^{75} +6.00000 q^{77} +(0.766044 - 0.642788i) q^{78} +(9.39693 + 3.42020i) q^{79} +(-0.694593 + 3.93923i) q^{80} +(0.173648 + 0.984808i) q^{81} +(7.51754 - 2.73616i) q^{82} +(3.00000 - 5.19615i) q^{83} +(1.50000 + 2.59808i) q^{84} +(-9.19253 - 7.71345i) q^{85} +(3.06418 + 2.57115i) q^{86} +(-2.50000 - 4.33013i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(1.38919 + 7.87846i) q^{90} +(-0.520945 + 2.95442i) q^{91} +(0.939693 + 0.342020i) q^{92} +(6.12836 - 5.14230i) q^{93} +8.00000 q^{94} -1.00000 q^{96} +(-1.53209 + 1.28558i) q^{97} +(-1.87939 - 0.684040i) q^{98} +(-0.694593 + 3.93923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 9 * q^7 - 3 * q^8	$ 6 q - 9 q^{7} - 3 q^{8} - 6 q^{11} + 3 q^{12} - 12 q^{18} - 24 q^{20} + 3 q^{26} - 15 q^{27} - 12 q^{30} + 24 q^{31} - 12 q^{37} + 6 q^{39} - 24 q^{45} + 3 q^{46} - 6 q^{49} - 33 q^{50} + 18 q^{56} - 30 q^{58} - 3 q^{64} - 12 q^{65} - 9 q^{68} - 3 q^{69} - 66 q^{75} + 36 q^{77} + 18 q^{83} + 9 q^{84} - 15 q^{87} - 6 q^{88} + 48 q^{94} - 6 q^{96}+O(q^{100}) $ 6 * q - 9 * q^7 - 3 * q^8 - 6 * q^11 + 3 * q^12 - 12 * q^18 - 24 * q^20 + 3 * q^26 - 15 * q^27 - 12 * q^30 + 24 * q^31 - 12 * q^37 + 6 * q^39 - 24 * q^45 + 3 * q^46 - 6 * q^49 - 33 * q^50 + 18 * q^56 - 30 * q^58 - 3 * q^64 - 12 * q^65 - 9 * q^68 - 3 * q^69 - 66 * q^75 + 36 * q^77 + 18 * q^83 + 9 * q^84 - 15 * q^87 - 6 * q^88 + 48 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i	0.598725	−	0.800954i	$-0.295674\pi$
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i	−0.0561935	+	0.998420i	$0.517896\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.694593	−	3.93923i	−0.310631	−	1.76168i	−0.595735	−	0.803181i	$-0.703139\pi$
$5$	−0.694593	−	3.93923i	−0.310631	−	1.76168i	0.285104	−	0.958497i	$-0.407972\pi$
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−1.53209	−	1.28558i	−0.510696	−	0.428525i
$10$	−3.06418	−	2.57115i	−0.968978	−	0.813069i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.939693	−	0.342020i	0.260624	−	0.0948593i	−0.208404	−	0.978043i	$-0.566827\pi$
$13$	0.939693	−	0.342020i	0.260624	−	0.0948593i	0.469027	+	0.883184i	$0.344605\pi$
$14$	0.520945	+	2.95442i	0.139228	+	0.789603i
$15$	0.694593	−	3.93923i	0.179343	−	1.01711i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.29813	−	1.92836i	0.557379	−	0.467697i	−0.320051	−	0.947400i	$-0.603700\pi$
$17$	2.29813	−	1.92836i	0.557379	−	0.467697i	0.877431	+	0.479703i	$0.159256\pi$
$18$	−2.00000			−0.471405
$19$		0			0
$19$		0			0
$20$	−4.00000			−0.894427
$21$	−2.29813	+	1.92836i	−0.501494	+	0.420803i
$22$	−1.87939	−	0.684040i	−0.400686	−	0.145838i
$23$	−0.173648	+	0.984808i	−0.0362081	+	0.205347i	−0.997545	−	0.0700286i	$-0.977691\pi$
$23$	−0.173648	+	0.984808i	−0.0362081	+	0.205347i	0.961337	+	0.275375i	$0.0888021\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	−10.3366	+	3.76222i	−2.06732	+	0.752444i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	−2.50000	−	4.33013i	−0.481125	−	0.833333i
$28$	2.29813	+	1.92836i	0.434306	+	0.364426i
$29$	−3.83022	−	3.21394i	−0.711254	−	0.596813i	0.213696	−	0.976900i	$-0.431450\pi$
$29$	−3.83022	−	3.21394i	−0.711254	−	0.596813i	−0.924951	+	0.380087i	$0.875894\pi$
$30$	−2.00000	−	3.46410i	−0.365148	−	0.632456i
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−0.347296	−	1.96962i	−0.0604565	−	0.342866i
$34$	0.520945	−	2.95442i	0.0893413	−	0.506679i
$35$	11.2763	+	4.10424i	1.90604	+	0.693743i
$36$	−1.53209	+	1.28558i	−0.255348	+	0.214263i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		0			0
$39$	1.00000			0.160128
$40$	−3.06418	+	2.57115i	−0.484489	+	0.406535i
$41$	7.51754	+	2.73616i	1.17404	+	0.427317i	0.854094	−	0.520118i	$-0.174112\pi$
$41$	7.51754	+	2.73616i	1.17404	+	0.427317i	0.319948	+	0.947435i	$0.396334\pi$
$42$	−0.520945	+	2.95442i	−0.0803835	+	0.455877i
$43$	0.694593	+	3.93923i	0.105924	+	0.600727i	0.990847	+	0.134989i	$0.0431000\pi$
$43$	0.694593	+	3.93923i	0.105924	+	0.600727i	−0.884923	+	0.465738i	$0.845789\pi$
$44$	−1.87939	+	0.684040i	−0.283328	+	0.103123i
$45$	−4.00000	+	6.92820i	−0.596285	+	1.03280i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	6.12836	+	5.14230i	0.893913	+	0.750082i	0.968991	−	0.247096i	$-0.0794763\pi$
$47$	6.12836	+	5.14230i	0.893913	+	0.750082i	−0.0750785	+	0.997178i	$0.523921\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	−5.50000	+	9.52628i	−0.777817	+	1.34722i
$51$	2.81908	−	1.02606i	0.394750	−	0.143677i
$52$	−0.173648	−	0.984808i	−0.0240807	−	0.136568i
$53$	−0.173648	+	0.984808i	−0.0238524	+	0.135274i	−0.994409	−	0.105601i	$-0.966323\pi$
$53$	−0.173648	+	0.984808i	−0.0238524	+	0.135274i	0.970556	+	0.240875i	$0.0774344\pi$
$54$	−4.69846	−	1.71010i	−0.639380	−	0.232715i
$55$	−6.12836	+	5.14230i	−0.826347	+	0.693388i
$56$	3.00000			0.400892
$57$		0			0
$58$	−5.00000			−0.656532
$59$	11.4907	−	9.64181i	1.49596	−	1.25526i	0.609205	−	0.793013i	$-0.291489\pi$
$59$	11.4907	−	9.64181i	1.49596	−	1.25526i	0.886753	−	0.462244i	$-0.152956\pi$
$60$	−3.75877	−	1.36808i	−0.485255	−	0.176618i
$61$	0.347296	−	1.96962i	0.0444667	−	0.252183i	−0.954469	−	0.298311i	$-0.903577\pi$
$61$	0.347296	−	1.96962i	0.0444667	−	0.252183i	0.998936	+	0.0461272i	$0.0146880\pi$
$62$	−1.38919	−	7.87846i	−0.176427	−	1.00057i
$63$	5.63816	−	2.05212i	0.710341	−	0.258543i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$	−1.53209	−	1.28558i	−0.188587	−	0.158243i
$67$	2.29813	+	1.92836i	0.280762	+	0.235587i	0.772283	−	0.635278i	$-0.219115\pi$
$67$	2.29813	+	1.92836i	0.280762	+	0.235587i	−0.491522	+	0.870865i	$0.663559\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	−0.500000	+	0.866025i	−0.0601929	+	0.104257i
$70$	11.2763	−	4.10424i	1.34778	−	0.490551i
$71$	0.347296	+	1.96962i	0.0412165	+	0.233750i	0.998456	−	0.0555458i	$-0.0176899\pi$
$71$	0.347296	+	1.96962i	0.0412165	+	0.233750i	−0.957240	+	0.289296i	$0.906579\pi$
$72$	−0.347296	+	1.96962i	−0.0409293	+	0.232121i
$73$	−8.45723	−	3.07818i	−0.989844	−	0.360274i	−0.204184	−	0.978932i	$-0.565454\pi$
$73$	−8.45723	−	3.07818i	−0.989844	−	0.360274i	−0.785660	+	0.618659i	$0.787676\pi$
$74$	−1.53209	+	1.28558i	−0.178102	+	0.149445i
$75$	−11.0000			−1.27017
$76$		0			0
$77$	6.00000			0.683763
$78$	0.766044	−	0.642788i	0.0867375	−	0.0727814i
$79$	9.39693	+	3.42020i	1.05724	+	0.384803i	0.811389	−	0.584506i	$-0.198712\pi$
$79$	9.39693	+	3.42020i	1.05724	+	0.384803i	0.245847	+	0.969309i	$0.420934\pi$
$80$	−0.694593	+	3.93923i	−0.0776578	+	0.440419i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	7.51754	−	2.73616i	0.830174	−	0.302158i
$83$	3.00000	−	5.19615i	0.329293	−	0.570352i	−0.653079	−	0.757290i	$-0.726523\pi$
$83$	3.00000	−	5.19615i	0.329293	−	0.570352i	0.982372	+	0.186938i	$0.0598564\pi$
$84$	1.50000	+	2.59808i	0.163663	+	0.283473i
$85$	−9.19253	−	7.71345i	−0.997070	−	0.836641i
$86$	3.06418	+	2.57115i	0.330419	+	0.277254i
$87$	−2.50000	−	4.33013i	−0.268028	−	0.464238i
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$89$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$90$	1.38919	+	7.87846i	0.146433	+	0.830463i
$91$	−0.520945	+	2.95442i	−0.0546098	+	0.309708i
$92$	0.939693	+	0.342020i	0.0979697	+	0.0356581i
$93$	6.12836	−	5.14230i	0.635481	−	0.533232i
$94$	8.00000			0.825137
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−1.53209	+	1.28558i	−0.155560	+	0.130530i	−0.717246	−	0.696820i	$-0.754597\pi$
$97$	−1.53209	+	1.28558i	−0.155560	+	0.130530i	0.561686	+	0.827351i	$0.310153\pi$
$98$	−1.87939	−	0.684040i	−0.189847	−	0.0690985i
$99$	−0.694593	+	3.93923i	−0.0698092	+	0.395908i
$100$	1.91013	+	10.8329i	0.191013	+	1.08329i
$101$	−1.87939	+	0.684040i	−0.187006	+	0.0680646i	−0.433826	−	0.900997i	$-0.642837\pi$
$101$	−1.87939	+	0.684040i	−0.187006	+	0.0680646i	0.246820	+	0.969061i	$0.420614\pi$
$102$	1.50000	−	2.59808i	0.148522	−	0.257248i
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	0.975124	−	0.221660i	$-0.0711475\pi$
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	−0.679525	+	0.733652i	$0.737814\pi$
$104$	−0.766044	−	0.642788i	−0.0751168	−	0.0630305i
$105$	9.19253	+	7.71345i	0.897099	+	0.752756i
$106$	0.500000	+	0.866025i	0.0485643	+	0.0841158i
$107$	3.50000	−	6.06218i	0.338358	−	0.586053i	−0.645766	−	0.763535i	$-0.723462\pi$
$107$	3.50000	−	6.06218i	0.338358	−	0.586053i	0.984124	+	0.177482i	$0.0567953\pi$
$108$	−4.69846	+	1.71010i	−0.452110	+	0.164555i
$109$	−2.60472	−	14.7721i	−0.249487	−	1.41491i	−0.809836	−	0.586656i	$-0.800444\pi$
$109$	−2.60472	−	14.7721i	−0.249487	−	1.41491i	0.560349	−	0.828256i	$-0.310667\pi$
$110$	−1.38919	+	7.87846i	−0.132454	+	0.751182i
$111$	−1.87939	−	0.684040i	−0.178383	−	0.0649262i
$112$	2.29813	−	1.92836i	0.217153	−	0.182213i
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$	4.00000			0.373002
$116$	−3.83022	+	3.21394i	−0.355627	+	0.298407i
$117$	−1.87939	−	0.684040i	−0.173749	−	0.0632395i
$118$	2.60472	−	14.7721i	0.239784	−	1.35988i
$119$	1.56283	+	8.86327i	0.143265	+	0.812495i
$120$	−3.75877	+	1.36808i	−0.343127	+	0.124888i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$	6.12836	+	5.14230i	0.552575	+	0.463666i
$124$	−6.12836	−	5.14230i	−0.550343	−	0.461792i
$125$	12.0000	+	20.7846i	1.07331	+	1.85903i
$126$	3.00000	−	5.19615i	0.267261	−	0.462910i
$127$	−16.9145	+	6.15636i	−1.50092	+	0.546289i	−0.956298	−	0.292395i	$-0.905548\pi$
$127$	−16.9145	+	6.15636i	−1.50092	+	0.546289i	−0.544619	+	0.838684i	$0.683326\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−0.694593	+	3.93923i	−0.0611555	+	0.346830i
$130$	−3.75877	−	1.36808i	−0.329666	−	0.119989i
$131$	9.19253	−	7.71345i	0.803155	−	0.673927i	−0.145808	−	0.989313i	$-0.546578\pi$
$131$	9.19253	−	7.71345i	0.803155	−	0.673927i	0.948964	+	0.315385i	$0.102134\pi$
$132$	−2.00000			−0.174078
$133$		0			0
$134$	3.00000			0.259161
$135$	−15.3209	+	12.8558i	−1.31861	+	1.10645i
$136$	−2.81908	−	1.02606i	−0.241734	−	0.0879840i
$137$	−2.95202	+	16.7417i	−0.252208	+	1.43034i	0.550931	+	0.834551i	$0.314273\pi$
$137$	−2.95202	+	16.7417i	−0.252208	+	1.43034i	−0.803139	+	0.595792i	$0.796838\pi$
$138$	0.173648	+	0.984808i	0.0147819	+	0.0838324i
$139$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$139$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$140$	6.00000	−	10.3923i	0.507093	−	0.878310i
$141$	4.00000	+	6.92820i	0.336861	+	0.583460i
$142$	1.53209	+	1.28558i	0.128570	+	0.107883i
$143$	−1.53209	−	1.28558i	−0.128120	−	0.107505i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	−10.0000	+	17.3205i	−0.830455	+	1.43839i
$146$	−8.45723	+	3.07818i	−0.699926	+	0.254752i
$147$	−0.347296	−	1.96962i	−0.0286445	−	0.162451i
$148$	−0.347296	+	1.96962i	−0.0285476	+	0.161901i
$149$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$149$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$150$	−8.42649	+	7.07066i	−0.688020	+	0.577317i
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	4.59627	−	3.85673i	0.370378	−	0.310784i
$155$	−30.0702	−	10.9446i	−2.41529	−	0.879095i
$156$	0.173648	−	0.984808i	0.0139030	−	0.0788477i
$157$	−0.347296	−	1.96962i	−0.0277173	−	0.157192i	0.967808	−	0.251690i	$-0.0809865\pi$
$157$	−0.347296	−	1.96962i	−0.0277173	−	0.157192i	−0.995525	+	0.0944981i	$0.969875\pi$
$158$	9.39693	−	3.42020i	0.747579	−	0.272097i
$159$	−0.500000	+	0.866025i	−0.0396526	+	0.0686803i
$160$	2.00000	+	3.46410i	0.158114	+	0.273861i
$161$	−2.29813	−	1.92836i	−0.181118	−	0.151976i
$162$	0.766044	+	0.642788i	0.0601861	+	0.0505022i
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	4.00000	−	6.92820i	0.312348	−	0.541002i
$165$	−7.51754	+	2.73616i	−0.585240	+	0.213010i
$166$	−1.04189	−	5.90885i	−0.0808663	−	0.458615i
$167$	−2.08378	+	11.8177i	−0.161248	+	0.914481i	0.791602	+	0.611037i	$0.209247\pi$
$167$	−2.08378	+	11.8177i	−0.161248	+	0.914481i	−0.952849	+	0.303443i	$0.901864\pi$
$168$	2.81908	+	1.02606i	0.217497	+	0.0791623i
$169$	−9.19253	+	7.71345i	−0.707118	+	0.593342i
$170$	−12.0000			−0.920358
$171$		0			0
$172$	4.00000			0.304997
$173$	−4.59627	+	3.85673i	−0.349448	+	0.293221i	−0.800568	−	0.599242i	$-0.795469\pi$
$173$	−4.59627	+	3.85673i	−0.349448	+	0.293221i	0.451121	+	0.892463i	$0.351024\pi$
$174$	−4.69846	−	1.71010i	−0.356190	−	0.129642i
$175$	5.73039	−	32.4987i	0.433177	−	2.45667i
$176$	0.347296	+	1.96962i	0.0261784	+	0.148465i
$177$	14.0954	−	5.13030i	1.05947	−	0.385617i
$178$		0			0
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	6.12836	+	5.14230i	0.456781	+	0.383284i
$181$	16.8530	+	14.1413i	1.25267	+	1.05112i	0.996423	+	0.0845058i	$0.0269311\pi$
$181$	16.8530	+	14.1413i	1.25267	+	1.05112i	0.256249	+	0.966611i	$0.417513\pi$
$182$	1.50000	+	2.59808i	0.111187	+	0.192582i
$183$	1.00000	−	1.73205i	0.0739221	−	0.128037i
$184$	0.939693	−	0.342020i	0.0692751	−	0.0252141i
$185$	1.38919	+	7.87846i	0.102135	+	0.579236i
$186$	1.38919	−	7.87846i	0.101860	−	0.577677i
$187$	−5.63816	−	2.05212i	−0.412303	−	0.150066i
$188$	6.12836	−	5.14230i	0.446956	−	0.375041i
$189$	15.0000			1.09109
$190$		0			0
$191$	7.00000			0.506502			0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000			0.506502			0.253251	+	0.967401i	$0.418500\pi$
$192$	−0.766044	+	0.642788i	−0.0552845	+	0.0463892i
$193$	5.63816	+	2.05212i	0.405843	+	0.147715i	0.536872	−	0.843664i	$-0.319606\pi$
$193$	5.63816	+	2.05212i	0.405843	+	0.147715i	−0.131029	+	0.991379i	$0.541828\pi$
$194$	−0.347296	+	1.96962i	−0.0249344	+	0.141410i
$195$	−0.694593	−	3.93923i	−0.0497408	−	0.282094i
$196$	−1.87939	+	0.684040i	−0.134242	+	0.0488600i
$197$	−4.00000	+	6.92820i	−0.284988	+	0.493614i	−0.972606	−	0.232458i	$-0.925323\pi$
$197$	−4.00000	+	6.92820i	−0.284988	+	0.493614i	0.687618	+	0.726073i	$0.258656\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	−19.1511	−	16.0697i	−1.35759	−	1.13915i	−0.976720	−	0.214520i	$-0.931181\pi$
$199$	−19.1511	−	16.0697i	−1.35759	−	1.13915i	−0.380867	−	0.924630i	$-0.624374\pi$
$200$	8.42649	+	7.07066i	0.595843	+	0.499971i
$201$	1.50000	+	2.59808i	0.105802	+	0.183254i
$202$	−1.00000	+	1.73205i	−0.0703598	+	0.121867i
$203$	14.0954	−	5.13030i	0.989302	−	0.360077i
$204$	−0.520945	−	2.95442i	−0.0364734	−	0.206851i
$205$	5.55674	−	31.5138i	0.388100	−	2.20102i
$206$	5.63816	+	2.05212i	0.392829	+	0.142978i
$207$	1.53209	−	1.28558i	0.106488	−	0.0893537i
$208$	−1.00000			−0.0693375
$209$		0			0
$210$	12.0000			0.828079
$211$	20.6832	−	17.3553i	1.42389	−	1.19479i	0.474674	−	0.880162i	$-0.342566\pi$
$211$	20.6832	−	17.3553i	1.42389	−	1.19479i	0.949216	−	0.314624i	$-0.101878\pi$
$212$	0.939693	+	0.342020i	0.0645384	+	0.0234900i
$213$	−0.347296	+	1.96962i	−0.0237964	+	0.134956i
$214$	−1.21554	−	6.89365i	−0.0830924	−	0.471241i
$215$	15.0351	−	5.47232i	1.02538	−	0.373209i
$216$	−2.50000	+	4.33013i	−0.170103	+	0.294628i
$217$	12.0000	+	20.7846i	0.814613	+	1.41095i
$218$	−11.4907	−	9.64181i	−0.778246	−	0.653026i
$219$	−6.89440	−	5.78509i	−0.465880	−	0.390920i
$220$	4.00000	+	6.92820i	0.269680	+	0.467099i
$221$	1.50000	−	2.59808i	0.100901	−	0.174766i
$222$	−1.87939	+	0.684040i	−0.126136	+	0.0459098i
$223$	2.43107	+	13.7873i	0.162797	+	0.923266i	0.951307	+	0.308245i	$0.0997416\pi$
$223$	2.43107	+	13.7873i	0.162797	+	0.923266i	−0.788510	+	0.615022i	$0.789147\pi$
$224$	0.520945	−	2.95442i	0.0348071	−	0.197401i
$225$	20.6732	+	7.52444i	1.37822	+	0.501630i
$226$	10.7246	−	8.99903i	0.713391	−	0.598606i
$227$	−17.0000			−1.12833			−0.564165	−	0.825662i	$-0.690802\pi$
$227$	−17.0000			−1.12833			−0.564165	+	0.825662i	$0.690802\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	3.06418	−	2.57115i	0.202046	−	0.169537i
$231$	5.63816	+	2.05212i	0.370963	+	0.135020i
$232$	−0.868241	+	4.92404i	−0.0570028	+	0.323279i
$233$	−1.04189	−	5.90885i	−0.0682564	−	0.387101i	−0.999729	−	0.0232893i	$-0.992586\pi$
$233$	−1.04189	−	5.90885i	−0.0682564	−	0.387101i	0.931472	−	0.363812i	$-0.118525\pi$
$234$	−1.87939	+	0.684040i	−0.122859	+	0.0447171i
$235$	16.0000	−	27.7128i	1.04372	−	1.80778i
$236$	−7.50000	−	12.9904i	−0.488208	−	0.845602i
$237$	7.66044	+	6.42788i	0.497599	+	0.417535i
$238$	6.89440	+	5.78509i	0.446898	+	0.374992i
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$	−2.00000	+	3.46410i	−0.129099	+	0.223607i
$241$	7.51754	−	2.73616i	0.484247	−	0.176252i	−0.0883481	−	0.996090i	$-0.528159\pi$
$241$	7.51754	−	2.73616i	0.484247	−	0.176252i	0.572596	+	0.819838i	$0.305937\pi$
$242$	−1.21554	−	6.89365i	−0.0781377	−	0.443141i
$243$	−2.77837	+	15.7569i	−0.178233	+	1.01081i
$244$	−1.87939	−	0.684040i	−0.120315	−	0.0437912i
$245$	−6.12836	+	5.14230i	−0.391526	+	0.328530i
$246$	8.00000			0.510061
$247$		0			0
$248$	−8.00000			−0.508001
$249$	4.59627	−	3.85673i	0.291277	−	0.244410i
$250$	22.5526	+	8.20848i	1.42635	+	0.519150i
$251$	0.347296	−	1.96962i	0.0219212	−	0.124321i	−0.971883	−	0.235462i	$-0.924340\pi$
$251$	0.347296	−	1.96962i	0.0219212	−	0.124321i	0.993805	+	0.111141i	$0.0354506\pi$
$252$	−1.04189	−	5.90885i	−0.0656328	−	0.372222i
$253$	1.87939	−	0.684040i	0.118156	−	0.0430052i
$254$	−9.00000	+	15.5885i	−0.564710	+	0.978107i
$255$	−6.00000	−	10.3923i	−0.375735	−	0.650791i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	6.12836	+	5.14230i	0.382276	+	0.320768i	0.813595	−	0.581432i	$-0.197507\pi$
$257$	6.12836	+	5.14230i	0.382276	+	0.320768i	−0.431319	+	0.902199i	$0.641952\pi$
$258$	2.00000	+	3.46410i	0.124515	+	0.215666i
$259$	3.00000	−	5.19615i	0.186411	−	0.322873i
$260$	−3.75877	+	1.36808i	−0.233109	+	0.0848448i
$261$	1.73648	+	9.84808i	0.107486	+	0.609581i
$262$	2.08378	−	11.8177i	0.128736	−	0.730100i
$263$	−22.5526	−	8.20848i	−1.39065	−	0.506157i	−0.465264	−	0.885172i	$-0.654041\pi$
$263$	−22.5526	−	8.20848i	−1.39065	−	0.506157i	−0.925390	+	0.379015i	$0.876263\pi$
$264$	−1.53209	+	1.28558i	−0.0942936	+	0.0791217i
$265$	4.00000			0.245718
$266$		0			0
$267$		0			0
$268$	2.29813	−	1.92836i	0.140381	−	0.117794i
$269$	−28.1908	−	10.2606i	−1.71882	−	0.625600i	−0.721086	−	0.692846i	$-0.756357\pi$
$269$	−28.1908	−	10.2606i	−1.71882	−	0.625600i	−0.997736	+	0.0672458i	$0.978579\pi$
$270$	−3.47296	+	19.6962i	−0.211358	+	1.19867i
$271$	1.21554	+	6.89365i	0.0738386	+	0.418760i	0.999212	+	0.0397017i	$0.0126408\pi$
$271$	1.21554	+	6.89365i	0.0738386	+	0.418760i	−0.925373	+	0.379058i	$0.876248\pi$
$272$	−2.81908	+	1.02606i	−0.170932	+	0.0622141i
$273$	−1.50000	+	2.59808i	−0.0907841	+	0.157243i
$274$	8.50000	+	14.7224i	0.513504	+	0.889415i
$275$	16.8530	+	14.1413i	1.01627	+	0.852754i
$276$	0.766044	+	0.642788i	0.0461105	+	0.0386913i
$277$	−14.0000	−	24.2487i	−0.841178	−	1.45696i	−0.888899	−	0.458103i	$-0.848529\pi$
$277$	−14.0000	−	24.2487i	−0.841178	−	1.45696i	0.0477206	−	0.998861i	$-0.484804\pi$
$278$		0			0
$279$	−15.0351	+	5.47232i	−0.900127	+	0.327619i
$280$	−2.08378	−	11.8177i	−0.124530	−	0.706242i
$281$	−1.38919	+	7.87846i	−0.0828719	+	0.469990i	0.914924	+	0.403627i	$0.132251\pi$
$281$	−1.38919	+	7.87846i	−0.0828719	+	0.469990i	−0.997796	+	0.0663628i	$0.978861\pi$
$282$	7.51754	+	2.73616i	0.447663	+	0.162936i
$283$	−4.59627	+	3.85673i	−0.273220	+	0.229259i	−0.769094	−	0.639136i	$-0.779292\pi$
$283$	−4.59627	+	3.85673i	−0.273220	+	0.229259i	0.495874	+	0.868394i	$0.334848\pi$
$284$	2.00000			0.118678
$285$		0			0
$286$	−2.00000			−0.118262
$287$	−18.3851	+	15.4269i	−1.08524	+	0.910621i
$288$	1.87939	+	0.684040i	0.110744	+	0.0403075i
$289$	−1.38919	+	7.87846i	−0.0817168	+	0.463439i
$290$	3.47296	+	19.6962i	0.203939	+	1.15660i
$291$	−1.87939	+	0.684040i	−0.110172	+	0.0400992i
$292$	−4.50000	+	7.79423i	−0.263343	+	0.456123i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$	−1.53209	−	1.28558i	−0.0893532	−	0.0749763i
$295$	−45.9627	−	38.5673i	−2.67605	−	2.24547i
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	−5.00000	+	8.66025i	−0.290129	+	0.502519i
$298$		0			0
$299$	0.173648	+	0.984808i	0.0100423	+	0.0569529i
$300$	−1.91013	+	10.8329i	−0.110281	+	0.625437i
$301$	−11.2763	−	4.10424i	−0.649956	−	0.236565i
$302$	1.53209	−	1.28558i	0.0881618	−	0.0739765i
$303$	−2.00000			−0.114897
$304$		0			0
$305$	−8.00000			−0.458079
$306$	−4.59627	+	3.85673i	−0.262751	+	0.220474i
$307$	11.2763	+	4.10424i	0.643573	+	0.234241i	0.643128	−	0.765758i	$-0.277636\pi$
$307$	11.2763	+	4.10424i	0.643573	+	0.234241i	0.000444803		1.00000i	$0.499858\pi$
$308$	1.04189	−	5.90885i	0.0593671	−	0.336688i
$309$	1.04189	+	5.90885i	0.0592710	+	0.336143i
$310$	−30.0702	+	10.9446i	−1.70787	+	0.621614i
$311$	−3.50000	+	6.06218i	−0.198467	+	0.343755i	−0.948031	−	0.318177i	$-0.896930\pi$
$311$	−3.50000	+	6.06218i	−0.198467	+	0.343755i	0.749565	+	0.661931i	$0.230263\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	22.2153	+	18.6408i	1.25568	+	1.05364i	0.996128	+	0.0879141i	$0.0280201\pi$
$313$	22.2153	+	18.6408i	1.25568	+	1.05364i	0.259554	+	0.965729i	$0.416424\pi$
$314$	−1.53209	−	1.28558i	−0.0864608	−	0.0725492i
$315$	−12.0000	−	20.7846i	−0.676123	−	1.17108i
$316$	5.00000	−	8.66025i	0.281272	−	0.487177i
$317$	25.3717	−	9.23454i	1.42502	−	0.518664i	0.489518	−	0.871993i	$-0.337173\pi$
$317$	25.3717	−	9.23454i	1.42502	−	0.518664i	0.935499	+	0.353330i	$0.114951\pi$
$318$	0.173648	+	0.984808i	0.00973771	+	0.0552253i
$319$	−1.73648	+	9.84808i	−0.0972243	+	0.551386i
$320$	3.75877	+	1.36808i	0.210122	+	0.0764780i
$321$	5.36231	−	4.49951i	0.299295	−	0.251138i
$322$	−3.00000			−0.167183
$323$		0			0
$324$	1.00000			0.0555556
$325$	−8.42649	+	7.07066i	−0.467418	+	0.392210i
$326$	15.0351	+	5.47232i	0.832716	+	0.303084i
$327$	2.60472	−	14.7721i	0.144041	−	0.816900i
$328$	−1.38919	−	7.87846i	−0.0767049	−	0.435015i
$329$	−22.5526	+	8.20848i	−1.24337	+	0.452548i
$330$	−4.00000	+	6.92820i	−0.220193	+	0.381385i
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$	−4.59627	−	3.85673i	−0.252253	−	0.211665i
$333$	3.06418	+	2.57115i	0.167916	+	0.140898i
$334$	6.00000	+	10.3923i	0.328305	+	0.568642i
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$	2.81908	−	1.02606i	0.153793	−	0.0559762i
$337$	−5.55674	−	31.5138i	−0.302695	−	1.71667i	−0.634161	−	0.773201i	$-0.718654\pi$
$337$	−5.55674	−	31.5138i	−0.302695	−	1.71667i	0.331466	−	0.943467i	$-0.392457\pi$
$338$	−2.08378	+	11.8177i	−0.113343	+	0.642798i
$339$	13.1557	+	4.78828i	0.714519	+	0.260064i
$340$	−9.19253	+	7.71345i	−0.498535	+	0.418321i
$341$	−16.0000			−0.866449
$342$		0			0
$343$	−15.0000			−0.809924
$344$	3.06418	−	2.57115i	0.165209	−	0.138627i
$345$	3.75877	+	1.36808i	0.202365	+	0.0736550i
$346$	−1.04189	+	5.90885i	−0.0560123	+	0.317662i
$347$	−0.347296	−	1.96962i	−0.0186438	−	0.105735i	0.974066	−	0.226265i	$-0.0726515\pi$
$347$	−0.347296	−	1.96962i	−0.0186438	−	0.105735i	−0.992710	+	0.120531i	$0.961540\pi$
$348$	−4.69846	+	1.71010i	−0.251864	+	0.0916710i
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$	−16.5000	−	28.5788i	−0.881962	−	1.52760i
$351$	−3.83022	−	3.21394i	−0.204442	−	0.171547i
$352$	1.53209	+	1.28558i	0.0816606	+	0.0685214i
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$	7.50000	−	12.9904i	0.398621	−	0.690431i
$355$	7.51754	−	2.73616i	0.398990	−	0.145220i
$356$		0			0
$357$	−1.56283	+	8.86327i	−0.0827139	+	0.469094i
$358$		0			0
$359$	−11.4907	+	9.64181i	−0.606454	+	0.508875i	−0.893513	−	0.449037i	$-0.851767\pi$
$359$	−11.4907	+	9.64181i	−0.606454	+	0.508875i	0.287059	+	0.957913i	$0.407323\pi$
$360$	8.00000			0.421637
$361$		0			0
$362$	22.0000			1.15629
$363$	5.36231	−	4.49951i	0.281448	−	0.236163i
$364$	2.81908	+	1.02606i	0.147760	+	0.0537802i
$365$	−6.25133	+	35.4531i	−0.327210	+	1.85570i
$366$	−0.347296	−	1.96962i	−0.0181535	−	0.102953i
$367$	−26.3114	+	9.57656i	−1.37344	+	0.499893i	−0.920184	−	0.391486i	$-0.871961\pi$
$367$	−26.3114	+	9.57656i	−1.37344	+	0.499893i	−0.453260	+	0.891379i	$0.649739\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	−8.00000	−	13.8564i	−0.416463	−	0.721336i
$370$	6.12836	+	5.14230i	0.318598	+	0.267335i
$371$	−2.29813	−	1.92836i	−0.119313	−	0.100116i
$372$	−4.00000	−	6.92820i	−0.207390	−	0.359211i
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$	−5.63816	+	2.05212i	−0.291542	+	0.106113i
$375$	4.16756	+	23.6354i	0.215212	+	1.22053i
$376$	1.38919	−	7.87846i	0.0716418	−	0.406301i
$377$	−4.69846	−	1.71010i	−0.241983	−	0.0880747i
$378$	11.4907	−	9.64181i	0.591016	−	0.495921i
$379$	15.0000			0.770498			0.385249	−	0.922813i	$-0.374116\pi$
$379$	15.0000			0.770498			0.385249	+	0.922813i	$0.374116\pi$
$380$		0			0
$381$	−18.0000			−0.922168
$382$	5.36231	−	4.49951i	0.274360	−	0.230215i
$383$	24.4320	+	8.89252i	1.24842	+	0.454387i	0.879867	−	0.475221i	$-0.157632\pi$
$383$	24.4320	+	8.89252i	1.24842	+	0.454387i	0.368551	+	0.929608i	$0.379854\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	−4.16756	−	23.6354i	−0.212398	−	1.20457i
$386$	5.63816	−	2.05212i	0.286975	−	0.104450i
$387$	4.00000	−	6.92820i	0.203331	−	0.352180i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	−22.9813	−	19.2836i	−1.16520	−	0.977719i	−0.165236	−	0.986254i	$-0.552839\pi$
$389$	−22.9813	−	19.2836i	−1.16520	−	0.977719i	−0.999964	+	0.00853524i	$0.997283\pi$
$390$	−3.06418	−	2.57115i	−0.155161	−	0.130195i
$391$	1.50000	+	2.59808i	0.0758583	+	0.131390i
$392$	−1.00000	+	1.73205i	−0.0505076	+	0.0874818i
$393$	11.2763	−	4.10424i	0.568815	−	0.207032i
$394$	1.38919	+	7.87846i	0.0699862	+	0.396911i
$395$	6.94593	−	39.3923i	0.349488	−	1.98204i
$396$	3.75877	+	1.36808i	0.188885	+	0.0687486i
$397$	6.12836	−	5.14230i	0.307573	−	0.258085i	−0.475915	−	0.879491i	$-0.657883\pi$
$397$	6.12836	−	5.14230i	0.307573	−	0.258085i	0.783488	+	0.621407i	$0.213439\pi$
$398$	−25.0000			−1.25314
$399$		0			0
$400$	11.0000			0.550000
$401$	−6.12836	+	5.14230i	−0.306035	+	0.256794i	−0.782851	−	0.622209i	$-0.786235\pi$
$401$	−6.12836	+	5.14230i	−0.306035	+	0.256794i	0.476816	+	0.879003i	$0.341791\pi$
$402$	2.81908	+	1.02606i	0.140603	+	0.0511752i
$403$	1.38919	−	7.87846i	0.0692003	−	0.392454i
$404$	0.347296	+	1.96962i	0.0172786	+	0.0979920i
$405$	3.75877	−	1.36808i	0.186775	−	0.0679805i
$406$	7.50000	−	12.9904i	0.372219	−	0.644702i
$407$	2.00000	+	3.46410i	0.0991363	+	0.171709i
$408$	−2.29813	−	1.92836i	−0.113775	−	0.0954682i
$409$	−15.3209	−	12.8558i	−0.757569	−	0.635676i	0.179924	−	0.983681i	$-0.442415\pi$
$409$	−15.3209	−	12.8558i	−0.757569	−	0.635676i	−0.937493	+	0.348005i	$0.886859\pi$
$410$	−16.0000	−	27.7128i	−0.790184	−	1.36864i
$411$	−8.50000	+	14.7224i	−0.419274	+	0.726204i
$412$	5.63816	−	2.05212i	0.277772	−	0.101101i
$413$	7.81417	+	44.3163i	0.384510	+	2.18066i
$414$	0.347296	−	1.96962i	0.0170687	−	0.0968013i
$415$	−22.5526	−	8.20848i	−1.10706	−	0.402939i
$416$	−0.766044	+	0.642788i	−0.0375584	+	0.0315153i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	9.19253	−	7.71345i	0.448550	−	0.376378i
$421$	12.2160	+	4.44626i	0.595372	+	0.216698i	0.622090	−	0.782945i	$-0.286284\pi$
$421$	12.2160	+	4.44626i	0.595372	+	0.216698i	−0.0267188	+	0.999643i	$0.508506\pi$
$422$	4.68850	−	26.5898i	0.228233	−	1.29437i
$423$	−2.77837	−	15.7569i	−0.135089	−	0.766128i
$424$	0.939693	−	0.342020i	0.0456355	−	0.0166100i
$425$	−16.5000	+	28.5788i	−0.800368	+	1.38628i
$426$	1.00000	+	1.73205i	0.0484502	+	0.0839181i
$427$	4.59627	+	3.85673i	0.222429	+	0.186640i
$428$	−5.36231	−	4.49951i	−0.259197	−	0.217492i
$429$	−1.00000	−	1.73205i	−0.0482805	−	0.0836242i
$430$	8.00000	−	13.8564i	0.385794	−	0.668215i
$431$	16.9145	−	6.15636i	0.814741	−	0.296542i	0.0991604	−	0.995071i	$-0.468384\pi$
$431$	16.9145	−	6.15636i	0.814741	−	0.296542i	0.715581	+	0.698530i	$0.246162\pi$
$432$	0.868241	+	4.92404i	0.0417733	+	0.236908i
$433$	2.43107	−	13.7873i	0.116830	−	0.662576i	−0.868998	−	0.494816i	$-0.835236\pi$
$433$	2.43107	−	13.7873i	0.116830	−	0.662576i	0.985828	−	0.167760i	$-0.0536534\pi$
$434$	22.5526	+	8.20848i	1.08256	+	0.394020i
$435$	−15.3209	+	12.8558i	−0.734580	+	0.616386i
$436$	−15.0000			−0.718370
$437$		0			0
$438$	−9.00000			−0.430037
$439$	15.3209	−	12.8558i	0.731226	−	0.613572i	−0.199239	−	0.979951i	$-0.563847\pi$
$439$	15.3209	−	12.8558i	0.731226	−	0.613572i	0.930466	+	0.366379i	$0.119403\pi$
$440$	7.51754	+	2.73616i	0.358385	+	0.130441i
$441$	−0.694593	+	3.93923i	−0.0330758	+	0.187582i
$442$	−0.520945	−	2.95442i	−0.0247788	−	0.140528i
$443$	24.4320	−	8.89252i	1.16080	−	0.422497i	0.311417	−	0.950273i	$-0.399197\pi$
$443$	24.4320	−	8.89252i	1.16080	−	0.422497i	0.849383	+	0.527777i	$0.176974\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$		0			0
$446$	10.7246	+	8.99903i	0.507826	+	0.426116i
$447$		0			0
$448$	−1.50000	−	2.59808i	−0.0708683	−	0.122748i
$449$	−5.00000	+	8.66025i	−0.235965	+	0.408703i	−0.959553	−	0.281529i	$-0.909158\pi$
$449$	−5.00000	+	8.66025i	−0.235965	+	0.408703i	0.723588	+	0.690232i	$0.242492\pi$
$450$	20.6732	−	7.52444i	0.974546	−	0.354706i
$451$	−2.77837	−	15.7569i	−0.130828	−	0.741965i
$452$	2.43107	−	13.7873i	0.114348	−	0.648500i
$453$	1.87939	+	0.684040i	0.0883012	+	0.0321390i
$454$	−13.0228	+	10.9274i	−0.611188	+	0.512848i
$455$	12.0000			0.562569
$456$		0			0
$457$	−7.00000			−0.327446			−0.163723	−	0.986506i	$-0.552350\pi$
$457$	−7.00000			−0.327446			−0.163723	+	0.986506i	$0.552350\pi$
$458$	−7.66044	+	6.42788i	−0.357949	+	0.300355i
$459$	−14.0954	−	5.13030i	−0.657916	−	0.239462i
$460$	0.694593	−	3.93923i	0.0323856	−	0.183668i
$461$	−4.86215	−	27.5746i	−0.226453	−	1.28428i	−0.859888	−	0.510482i	$-0.829467\pi$
$461$	−4.86215	−	27.5746i	−0.226453	−	1.28428i	0.633435	−	0.773796i	$-0.281644\pi$
$462$	5.63816	−	2.05212i	0.262311	−	0.0954733i
$463$	−2.00000	+	3.46410i	−0.0929479	+	0.160990i	−0.908750	−	0.417340i	$-0.862962\pi$
$463$	−2.00000	+	3.46410i	−0.0929479	+	0.160990i	0.815802	+	0.578331i	$0.196296\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$	−24.5134	−	20.5692i	−1.13678	−	0.953874i
$466$	−4.59627	−	3.85673i	−0.212918	−	0.178659i
$467$	1.00000	+	1.73205i	0.0462745	+	0.0801498i	0.888235	−	0.459390i	$-0.151932\pi$
$467$	1.00000	+	1.73205i	0.0462745	+	0.0801498i	−0.841960	+	0.539539i	$0.818598\pi$
$468$	−1.00000	+	1.73205i	−0.0462250	+	0.0800641i
$469$	−8.45723	+	3.07818i	−0.390519	+	0.142137i
$470$	−5.55674	−	31.5138i	−0.256313	−	1.45363i
$471$	0.347296	−	1.96962i	0.0160026	−	0.0907551i
$472$	−14.0954	−	5.13030i	−0.648793	−	0.236141i
$473$	6.12836	−	5.14230i	0.281782	−	0.236443i
$474$	10.0000			0.459315
$475$		0			0
$476$	9.00000			0.412514
$477$	1.53209	−	1.28558i	0.0701495	−	0.0588624i
$478$	−14.0954	−	5.13030i	−0.644708	−	0.234655i
$479$	−3.47296	+	19.6962i	−0.158684	+	0.899940i	0.796657	+	0.604432i	$0.206600\pi$
$479$	−3.47296	+	19.6962i	−0.158684	+	0.899940i	−0.955340	+	0.295508i	$0.904511\pi$
$480$	0.694593	+	3.93923i	0.0317037	+	0.179800i
$481$	−1.87939	+	0.684040i	−0.0856926	+	0.0311896i
$482$	4.00000	−	6.92820i	0.182195	−	0.315571i
$483$	−1.50000	−	2.59808i	−0.0682524	−	0.118217i
$484$	−5.36231	−	4.49951i	−0.243741	−	0.204523i
$485$	6.12836	+	5.14230i	0.278274	+	0.233500i
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$	−1.87939	+	0.684040i	−0.0850758	+	0.0309650i
$489$	2.77837	+	15.7569i	0.125642	+	0.712553i
$490$	−1.38919	+	7.87846i	−0.0627570	+	0.355913i
$491$	26.3114	+	9.57656i	1.18742	+	0.432184i	0.858816	−	0.512285i	$-0.171201\pi$
$491$	26.3114	+	9.57656i	1.18742	+	0.432184i	0.328601	+	0.944469i	$0.393423\pi$
$492$	6.12836	−	5.14230i	0.276288	−	0.231833i
$493$	−15.0000			−0.675566
$494$		0			0
$495$	16.0000			0.719147
$496$	−6.12836	+	5.14230i	−0.275171	+	0.230896i
$497$	−5.63816	−	2.05212i	−0.252906	−	0.0920502i
$498$	1.04189	−	5.90885i	0.0466882	−	0.264782i
$499$	6.94593	+	39.3923i	0.310942	+	1.76344i	0.594122	+	0.804375i	$0.297500\pi$
$499$	6.94593	+	39.3923i	0.310942	+	1.76344i	−0.283179	+	0.959067i	$0.591389\pi$
$500$	22.5526	−	8.20848i	1.00858	−	0.367095i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$	−1.00000	−	1.73205i	−0.0446322	−	0.0773052i
$503$	29.8757	+	25.0687i	1.33209	+	1.11776i	0.983583	+	0.180454i	$0.0577566\pi$
$503$	29.8757	+	25.0687i	1.33209	+	1.11776i	0.348510	+	0.937305i	$0.386688\pi$
$504$	−4.59627	−	3.85673i	−0.204734	−	0.171792i
$505$	4.00000	+	6.92820i	0.177998	+	0.308301i
$506$	1.00000	−	1.73205i	0.0444554	−	0.0769991i
$507$	−11.2763	+	4.10424i	−0.500799	+	0.182276i
$508$	3.12567	+	17.7265i	0.138679	+	0.786488i
$509$	−5.20945	+	29.5442i	−0.230905	+	1.30953i	0.620165	+	0.784472i	$0.287066\pi$
$509$	−5.20945	+	29.5442i	−0.230905	+	1.30953i	−0.851069	+	0.525053i	$0.824045\pi$
$510$	−11.2763	−	4.10424i	−0.499323	−	0.181739i
$511$	20.6832	−	17.3553i	0.914971	−	0.767752i
$512$	1.00000			0.0441942
$513$		0			0
$514$	8.00000			0.352865
$515$	18.3851	−	15.4269i	0.810143	−	0.679791i
$516$	3.75877	+	1.36808i	0.165471	+	0.0602264i
$517$	2.77837	−	15.7569i	0.122193	−	0.692989i
$518$	−1.04189	−	5.90885i	−0.0457780	−	0.259620i
$519$	−5.63816	+	2.05212i	−0.247488	+	0.0900781i
$520$	−2.00000	+	3.46410i	−0.0877058	+	0.151911i
$521$	14.0000	+	24.2487i	0.613351	+	1.06236i	0.990671	+	0.136272i	$0.0435123\pi$
$521$	14.0000	+	24.2487i	0.613351	+	1.06236i	−0.377320	+	0.926083i	$0.623154\pi$
$522$	7.66044	+	6.42788i	0.335289	+	0.281340i
$523$	22.2153	+	18.6408i	0.971407	+	0.815107i	0.982771	−	0.184828i	$-0.0591729\pi$
$523$	22.2153	+	18.6408i	0.971407	+	0.815107i	−0.0113641	+	0.999935i	$0.503617\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$	16.5000	−	28.5788i	0.720119	−	1.24728i
$526$	−22.5526	+	8.20848i	−0.983341	+	0.357907i
$527$	−4.16756	−	23.6354i	−0.181542	−	1.02957i
$528$	−0.347296	+	1.96962i	−0.0151141	+	0.0857165i
$529$	20.6732	+	7.52444i	0.898836	+	0.327150i
$530$	3.06418	−	2.57115i	0.133099	−	0.111684i
$531$	−30.0000			−1.30189
$532$		0			0
$533$	8.00000			0.346518
$534$		0			0
$535$	−26.3114	−	9.57656i	−1.13754	−	0.414031i
$536$	0.520945	−	2.95442i	0.0225014	−	0.127612i
$537$		0			0
$538$	−28.1908	+	10.2606i	−1.21539	+	0.442366i
$539$	−2.00000	+	3.46410i	−0.0861461	+	0.149209i
$540$	10.0000	+	17.3205i	0.430331	+	0.745356i
$541$	1.53209	+	1.28558i	0.0658696	+	0.0552712i	0.675128	−	0.737701i	$-0.264088\pi$
$541$	1.53209	+	1.28558i	0.0658696	+	0.0552712i	−0.609258	+	0.792972i	$0.708533\pi$
$542$	5.36231	+	4.49951i	0.230331	+	0.193271i
$543$	11.0000	+	19.0526i	0.472055	+	0.817624i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	−56.3816	+	20.5212i	−2.41512	+	0.879032i
$546$	0.520945	+	2.95442i	0.0222944	+	0.126438i
$547$	4.86215	−	27.5746i	0.207890	−	1.17901i	−0.684936	−	0.728604i	$-0.740170\pi$
$547$	4.86215	−	27.5746i	0.207890	−	1.17901i	0.892826	−	0.450402i	$-0.148719\pi$
$548$	15.9748	+	5.81434i	0.682409	+	0.248376i
$549$	−3.06418	+	2.57115i	−0.130776	+	0.109734i
$550$	22.0000			0.938083
$551$		0			0
$552$	1.00000			0.0425628
$553$	−22.9813	+	19.2836i	−0.977266	+	0.820023i
$554$	−26.3114	−	9.57656i	−1.11786	−	0.406869i
$555$	−1.38919	+	7.87846i	−0.0589676	+	0.334422i
$556$		0			0
$557$	−26.3114	+	9.57656i	−1.11485	+	0.405772i	−0.832770	−	0.553619i	$-0.813246\pi$
$557$	−26.3114	+	9.57656i	−1.11485	+	0.405772i	−0.282079	+	0.959391i	$0.591024\pi$
$558$	−8.00000	+	13.8564i	−0.338667	+	0.586588i
$559$	2.00000	+	3.46410i	0.0845910	+	0.146516i
$560$	−9.19253	−	7.71345i	−0.388455	−	0.325953i
$561$	−4.59627	−	3.85673i	−0.194055	−	0.162831i
$562$	4.00000	+	6.92820i	0.168730	+	0.292249i
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$	7.51754	−	2.73616i	0.316546	−	0.115213i
$565$	−9.72430	−	55.1492i	−0.409104	−	2.32015i
$566$	−1.04189	+	5.90885i	−0.0437939	+	0.248367i
$567$	−2.81908	−	1.02606i	−0.118390	−	0.0430905i
$568$	1.53209	−	1.28558i	0.0642850	−	0.0539415i
$569$	40.0000			1.67689			0.838444	−	0.544988i	$-0.183466\pi$
$569$	40.0000			1.67689			0.838444	+	0.544988i	$0.183466\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$	−1.53209	+	1.28558i	−0.0640599	+	0.0537526i
$573$	6.57785	+	2.39414i	0.274794	+	0.100017i
$574$	−4.16756	+	23.6354i	−0.173950	+	0.986522i
$575$	−1.91013	−	10.8329i	−0.0796579	−	0.451763i
$576$	1.87939	−	0.684040i	0.0783077	−	0.0285017i
$577$	18.5000	−	32.0429i	0.770165	−	1.33397i	−0.167307	−	0.985905i	$-0.553507\pi$
$577$	18.5000	−	32.0429i	0.770165	−	1.33397i	0.937472	−	0.348060i	$-0.113160\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	4.59627	+	3.85673i	0.191014	+	0.160280i
$580$	15.3209	+	12.8558i	0.636165	+	0.533806i
$581$	9.00000	+	15.5885i	0.373383	+	0.646718i
$582$	−1.00000	+	1.73205i	−0.0414513	+	0.0717958i
$583$	1.87939	−	0.684040i	0.0778362	−	0.0283301i
$584$	1.56283	+	8.86327i	0.0646705	+	0.366765i
$585$	−1.38919	+	7.87846i	−0.0574357	+	0.325734i
$586$	−8.45723	−	3.07818i	−0.349365	−	0.127158i
$587$	−9.19253	+	7.71345i	−0.379416	+	0.318368i	−0.812473	−	0.582998i	$-0.801879\pi$
$587$	−9.19253	+	7.71345i	−0.379416	+	0.318368i	0.433057	+	0.901367i	$0.357435\pi$
$588$	−2.00000			−0.0824786
$589$		0			0
$590$	−60.0000			−2.47016
$591$	−6.12836	+	5.14230i	−0.252087	+	0.211526i
$592$	1.87939	+	0.684040i	0.0772423	+	0.0281139i
$593$	5.90404	−	33.4835i	0.242450	−	1.37500i	−0.583892	−	0.811832i	$-0.698471\pi$
$593$	5.90404	−	33.4835i	0.242450	−	1.37500i	0.826341	−	0.563169i	$-0.190418\pi$
$594$	1.73648	+	9.84808i	0.0712487	+	0.404072i
$595$	33.8289	−	12.3127i	1.38685	−	0.504773i
$596$		0			0
$597$	−12.5000	−	21.6506i	−0.511591	−	0.886102i
$598$	0.766044	+	0.642788i	0.0313259	+	0.0262855i
$599$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$599$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$600$	5.50000	+	9.52628i	0.224537	+	0.388909i
$601$	4.00000	−	6.92820i	0.163163	−	0.282607i	−0.772838	−	0.634603i	$-0.781164\pi$
$601$	4.00000	−	6.92820i	0.163163	−	0.282607i	0.936002	+	0.351996i	$0.114497\pi$
$602$	−11.2763	+	4.10424i	−0.459588	+	0.167276i
$603$	−1.04189	−	5.90885i	−0.0424290	−	0.240627i
$604$	0.347296	−	1.96962i	0.0141313	−	0.0801425i
$605$	−26.3114	−	9.57656i	−1.06971	−	0.389343i
$606$	−1.53209	+	1.28558i	−0.0622369	+	0.0522229i
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$		0			0
$609$	15.0000			0.607831
$610$	−6.12836	+	5.14230i	−0.248130	+	0.208206i
$611$	7.51754	+	2.73616i	0.304127	+	0.110693i
$612$	−1.04189	+	5.90885i	−0.0421159	+	0.238851i
$613$	5.90404	+	33.4835i	0.238462	+	1.35238i	0.835199	+	0.549948i	$0.185352\pi$
$613$	5.90404	+	33.4835i	0.238462	+	1.35238i	−0.596737	+	0.802437i	$0.703537\pi$
$614$	11.2763	−	4.10424i	0.455075	−	0.165634i
$615$	16.0000	−	27.7128i	0.645182	−	1.11749i
$616$	−3.00000	−	5.19615i	−0.120873	−	0.209359i
$617$	13.7888	+	11.5702i	0.555116	+	0.465798i	0.876669	−	0.481094i	$-0.159760\pi$
$617$	13.7888	+	11.5702i	0.555116	+	0.465798i	−0.321553	+	0.946892i	$0.604205\pi$
$618$	4.59627	+	3.85673i	0.184889	+	0.155140i
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	0.747873	−	0.663842i	$-0.231075\pi$
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$620$	−16.0000	+	27.7128i	−0.642575	+	1.11297i
$621$	4.69846	−	1.71010i	0.188543	−	0.0686240i
$622$	1.21554	+	6.89365i	0.0487386	+	0.276410i
$623$		0			0
$624$	−0.939693	−	0.342020i	−0.0376178	−	0.0136918i
$625$	31.4078	−	26.3543i	1.25631	−	1.05417i
$626$	29.0000			1.15907
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	−4.59627	+	3.85673i	−0.183265	+	0.153778i
$630$	−22.5526	−	8.20848i	−0.898518	−	0.327034i
$631$	5.55674	−	31.5138i	0.221210	−	1.25455i	−0.648588	−	0.761140i	$-0.724640\pi$
$631$	5.55674	−	31.5138i	0.221210	−	1.25455i	0.869799	−	0.493407i	$-0.164249\pi$
$632$	−1.73648	−	9.84808i	−0.0690735	−	0.391735i
$633$	25.3717	−	9.23454i	1.00843	−	0.367040i
$634$	13.5000	−	23.3827i	0.536153	−	0.928645i
$635$	36.0000	+	62.3538i	1.42862	+	2.47444i
$636$	0.766044	+	0.642788i	0.0303756	+	0.0254882i
$637$	−1.53209	−	1.28558i	−0.0607036	−	0.0509363i
$638$	5.00000	+	8.66025i	0.197952	+	0.342863i
$639$	2.00000	−	3.46410i	0.0791188	−	0.137038i
$640$	3.75877	−	1.36808i	0.148578	−	0.0540781i
$641$	7.29322	+	41.3619i	0.288065	+	1.63370i	0.694127	+	0.719852i	$0.255791\pi$
$641$	7.29322	+	41.3619i	0.288065	+	1.63370i	−0.406062	+	0.913845i	$0.633098\pi$
$642$	1.21554	−	6.89365i	0.0479734	−	0.272071i
$643$	24.4320	+	8.89252i	0.963504	+	0.350687i	0.775406	−	0.631463i	$-0.217545\pi$
$643$	24.4320	+	8.89252i	0.963504	+	0.350687i	0.188099	+	0.982150i	$0.439768\pi$
$644$	−2.29813	+	1.92836i	−0.0905591	+	0.0759881i
$645$	16.0000			0.629999
$646$		0			0
$647$	23.0000			0.904223			0.452112	−	0.891961i	$-0.350671\pi$
$647$	23.0000			0.904223			0.452112	+	0.891961i	$0.350671\pi$
$648$	0.766044	−	0.642788i	0.0300931	−	0.0252511i
$649$	−28.1908	−	10.2606i	−1.10658	−	0.402764i
$650$	−1.91013	+	10.8329i	−0.0749215	+	0.424901i
$651$	4.16756	+	23.6354i	0.163339	+	0.926344i
$652$	15.0351	−	5.47232i	0.588819	−	0.214313i
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$	−7.50000	−	12.9904i	−0.293273	−	0.507964i
$655$	−36.7701	−	30.8538i	−1.43673	−	1.20556i
$656$	−6.12836	−	5.14230i	−0.239272	−	0.200773i
$657$	9.00000	+	15.5885i	0.351123	+	0.608164i
$658$	−12.0000	+	20.7846i	−0.467809	+	0.810268i
$659$	−4.69846	+	1.71010i	−0.183026	+	0.0666161i	−0.431907	−	0.901918i	$-0.642159\pi$
$659$	−4.69846	+	1.71010i	−0.183026	+	0.0666161i	0.248881	+	0.968534i	$0.419937\pi$
$660$	1.38919	+	7.87846i	0.0540740	+	0.306669i
$661$	−3.99391	+	22.6506i	−0.155345	+	0.881005i	0.803125	+	0.595811i	$0.203169\pi$
$661$	−3.99391	+	22.6506i	−0.155345	+	0.881005i	−0.958470	+	0.285194i	$0.907942\pi$
$662$	−15.9748	−	5.81434i	−0.620877	−	0.225981i
$663$	2.29813	−	1.92836i	0.0892521	−	0.0748914i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	3.83022	−	3.21394i	0.148307	−	0.124444i
$668$	11.2763	+	4.10424i	0.436294	+	0.158798i
$669$	−2.43107	+	13.7873i	−0.0939908	+	0.533048i
$670$	−2.08378	−	11.8177i	−0.0805034	−	0.456557i
$671$	−3.75877	+	1.36808i	−0.145106	+	0.0528142i
$672$	1.50000	−	2.59808i	0.0578638	−	0.100223i
$673$	−22.0000	−	38.1051i	−0.848038	−	1.46884i	−0.882957	−	0.469454i	$-0.844451\pi$
$673$	−22.0000	−	38.1051i	−0.848038	−	1.46884i	0.0349191	−	0.999390i	$-0.488883\pi$
$674$	−24.5134	−	20.5692i	−0.944222	−	0.792296i
$675$	42.1324	+	35.3533i	1.62168	+	1.36075i
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	−6.50000	+	11.2583i	−0.249815	+	0.432693i	−0.963474	−	0.267800i	$-0.913703\pi$
$677$	−6.50000	+	11.2583i	−0.249815	+	0.432693i	0.713659	+	0.700493i	$0.247037\pi$
$678$	13.1557	−	4.78828i	0.505241	−	0.183893i
$679$	−1.04189	−	5.90885i	−0.0399840	−	0.226761i
$680$	−2.08378	+	11.8177i	−0.0799092	+	0.453188i
$681$	−15.9748	−	5.81434i	−0.612155	−	0.222806i
$682$	−12.2567	+	10.2846i	−0.469334	+	0.393818i
$683$	4.00000			0.153056			0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$		0			0
$685$	68.0000			2.59815
$686$	−11.4907	+	9.64181i	−0.438716	+	0.368126i
$687$	−9.39693	−	3.42020i	−0.358515	−	0.130489i
$688$	0.694593	−	3.93923i	0.0264811	−	0.150182i
$689$	0.173648	+	0.984808i	0.00661547	+	0.0375182i
$690$	3.75877	−	1.36808i	0.143094	−	0.0520819i
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	0.121470	+	0.992595i	$0.461239\pi$
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	−0.920348	+	0.391102i	$0.872094\pi$
$692$	3.00000	+	5.19615i	0.114043	+	0.197528i
$693$	−9.19253	−	7.71345i	−0.349195	−	0.293010i
$694$	−1.53209	−	1.28558i	−0.0581573	−	0.0487998i
$695$		0			0
$696$	−2.50000	+	4.33013i	−0.0947623	+	0.164133i
$697$	22.5526	−	8.20848i	0.854242	−	0.310918i
$698$	1.73648	+	9.84808i	0.0657268	+	0.372755i
$699$	1.04189	−	5.90885i	0.0394079	−	0.223493i
$700$	−31.0099	−	11.2867i	−1.17206	−	0.426596i
$701$	−21.4492	+	17.9981i	−0.810127	+	0.679777i	−0.950638	−	0.310302i	$-0.899570\pi$
$701$	−21.4492	+	17.9981i	−0.810127	+	0.679777i	0.140511	+	0.990079i	$0.455125\pi$
$702$	−5.00000			−0.188713
$703$		0			0
$704$	2.00000			0.0753778
$705$	24.5134	−	20.5692i	0.923229	−	0.774681i
$706$	−8.45723	−	3.07818i	−0.318292	−	0.115849i
$707$	1.04189	−	5.90885i	0.0391843	−	0.222225i
$708$	−2.60472	−	14.7721i	−0.0978915	−	0.555170i
$709$	28.1908	−	10.2606i	1.05873	−	0.385345i	0.246777	−	0.969072i	$-0.420628\pi$
$709$	28.1908	−	10.2606i	1.05873	−	0.385345i	0.811950	+	0.583727i	$0.198406\pi$
$710$	4.00000	−	6.92820i	0.150117	−	0.260011i
$711$	−10.0000	−	17.3205i	−0.375029	−	0.649570i
$712$		0			0
$713$	6.12836	+	5.14230i	0.229509	+	0.192581i
$714$	4.50000	+	7.79423i	0.168408	+	0.291692i
$715$	−4.00000	+	6.92820i	−0.149592	+	0.259100i
$716$		0			0
$717$	−2.60472	−	14.7721i	−0.0972752	−	0.551675i
$718$	−2.60472	+	14.7721i	−0.0972074	+	0.551290i
$719$	4.69846	+	1.71010i	0.175223	+	0.0637760i	0.428142	−	0.903712i	$-0.359168\pi$
$719$	4.69846	+	1.71010i	0.175223	+	0.0637760i	−0.252919	+	0.967488i	$0.581391\pi$
$720$	6.12836	−	5.14230i	0.228390	−	0.191642i
$721$	−18.0000			−0.670355
$722$		0			0
$723$	8.00000			0.297523
$724$	16.8530	−	14.1413i	0.626336	−	0.525558i
$725$	51.6831	+	18.8111i	1.91946	+	0.698627i
$726$	1.21554	−	6.89365i	0.0451128	−	0.255848i
$727$	−2.95202	−	16.7417i	−0.109484	−	0.620916i	−0.989334	−	0.145664i	$-0.953468\pi$
$727$	−2.95202	−	16.7417i	−0.109484	−	0.620916i	0.879850	−	0.475252i	$-0.157643\pi$
$728$	2.81908	−	1.02606i	0.104482	−	0.0380283i
$729$	−6.50000	+	11.2583i	−0.240741	+	0.416975i
$730$	18.0000	+	31.1769i	0.666210	+	1.15391i
$731$	9.19253	+	7.71345i	0.339998	+	0.285292i
$732$	−1.53209	−	1.28558i	−0.0566276	−	0.0475162i
$733$	18.0000	+	31.1769i	0.664845	+	1.15155i	0.979327	+	0.202282i	$0.0648358\pi$
$733$	18.0000	+	31.1769i	0.664845	+	1.15155i	−0.314482	+	0.949263i	$0.601831\pi$
$734$	−14.0000	+	24.2487i	−0.516749	+	0.895036i
$735$	−7.51754	+	2.73616i	−0.277289	+	0.100925i
$736$	−0.173648	−	0.984808i	−0.00640076	−	0.0363005i
$737$	1.04189	−	5.90885i	0.0383785	−	0.217655i
$738$	−15.0351	−	5.47232i	−0.553449	−	0.201439i
$739$	−30.6418	+	25.7115i	−1.12718	+	0.945813i	−0.998945	−	0.0459313i	$-0.985374\pi$
$739$	−30.6418	+	25.7115i	−1.12718	+	0.945813i	−0.128231	+	0.991744i	$0.540930\pi$
$740$	8.00000			0.294086
$741$		0			0
$742$	−3.00000			−0.110133
$743$	−12.2567	+	10.2846i	−0.449655	+	0.377305i	−0.839308	−	0.543656i	$-0.817039\pi$
$743$	−12.2567	+	10.2846i	−0.449655	+	0.377305i	0.389653	+	0.920962i	$0.372595\pi$
$744$	−7.51754	−	2.73616i	−0.275606	−	0.100313i
$745$		0			0
$746$	5.03580	+	28.5594i	0.184374	+	1.04563i
$747$	−11.2763	+	4.10424i	−0.412579	+	0.150166i
$748$	−3.00000	+	5.19615i	−0.109691	+	0.189990i
$749$	10.5000	+	18.1865i	0.383662	+	0.664521i
$750$	18.3851	+	15.4269i	0.671328	+	0.563311i
$751$	24.5134	+	20.5692i	0.894507	+	0.750581i	0.969109	−	0.246633i	$-0.0793241\pi$
$751$	24.5134	+	20.5692i	0.894507	+	0.750581i	−0.0746016	+	0.997213i	$0.523769\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$	1.00000	−	1.73205i	0.0364420	−	0.0631194i
$754$	−4.69846	+	1.71010i	−0.171108	+	0.0622782i
$755$	−1.38919	−	7.87846i	−0.0505576	−	0.286727i
$756$	2.60472	−	14.7721i	0.0947328	−	0.537257i
$757$	1.87939	+	0.684040i	0.0683074	+	0.0248619i	0.375948	−	0.926641i	$-0.377317\pi$
$757$	1.87939	+	0.684040i	0.0683074	+	0.0248619i	−0.307640	+	0.951503i	$0.599539\pi$
$758$	11.4907	−	9.64181i	0.417360	−	0.350206i
$759$	2.00000			0.0725954
$760$		0			0
$761$	27.0000			0.978749			0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000			0.978749			0.489375	+	0.872074i	$0.337225\pi$
$762$	−13.7888	+	11.5702i	−0.499516	+	0.419143i
$763$	42.2862	+	15.3909i	1.53086	+	0.557188i
$764$	1.21554	−	6.89365i	0.0439766	−	0.249404i
$765$	4.16756	+	23.6354i	0.150678	+	0.854539i
$766$	24.4320	−	8.89252i	0.882764	−	0.321300i
$767$	7.50000	−	12.9904i	0.270809	−	0.469055i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−26.8116	−	22.4976i	−0.966849	−	0.811283i	0.0152043	−	0.999884i	$-0.495160\pi$
$769$	−26.8116	−	22.4976i	−0.966849	−	0.811283i	−0.982054	+	0.188601i	$0.939605\pi$
$770$	−18.3851	−	15.4269i	−0.662552	−	0.555947i
$771$	4.00000	+	6.92820i	0.144056	+	0.249513i
$772$	3.00000	−	5.19615i	0.107972	−	0.187014i
$773$	−8.45723	+	3.07818i	−0.304186	+	0.110714i	−0.489603	−	0.871945i	$-0.662858\pi$
$773$	−8.45723	+	3.07818i	−0.304186	+	0.110714i	0.185418	+	0.982660i	$0.440636\pi$
$774$	−1.38919	−	7.87846i	−0.0499332	−	0.283185i
$775$	−15.2810	+	86.6631i	−0.548911	+	3.11303i
$776$	1.87939	+	0.684040i	0.0674660	+	0.0245556i
$777$	4.59627	−	3.85673i	0.164890	−	0.138359i
$778$	−30.0000			−1.07555
$779$		0			0
$780$	−4.00000			−0.143223
$781$	3.06418	−	2.57115i	0.109645	−	0.0920030i
$782$	2.81908	+	1.02606i	0.100810	+	0.0366918i
$783$	−4.34120	+	24.6202i	−0.155142	+	0.879854i
$784$	0.347296	+	1.96962i	0.0124034	+	0.0703434i
$785$	−7.51754	+	2.73616i	−0.268313	+	0.0976578i
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	8.50000	+	14.7224i	0.302992	+	0.524798i	0.976812	−	0.214097i	$-0.0686810\pi$
$787$	8.50000	+	14.7224i	0.302992	+	0.524798i	−0.673820	+	0.738896i	$0.735348\pi$
$788$	6.12836	+	5.14230i	0.218314	+	0.183187i
$789$	−18.3851	−	15.4269i	−0.654526	−	0.549212i
$790$	−20.0000	−	34.6410i	−0.711568	−	1.23247i
$791$	−21.0000	+	36.3731i	−0.746674	+	1.29328i
$792$	3.75877	−	1.36808i	0.133562	−	0.0486126i
$793$	−0.347296	−	1.96962i	−0.0123329	−	0.0699431i
$794$	1.38919	−	7.87846i	0.0493003	−	0.279596i
$795$	3.75877	+	1.36808i	0.133310	+	0.0485208i
$796$	−19.1511	+	16.0697i	−0.678793	+	0.569575i
$797$	3.00000			0.106265			0.0531327	−	0.998587i	$-0.483079\pi$
$797$	3.00000			0.106265			0.0531327	+	0.998587i	$0.483079\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	8.42649	−	7.07066i	0.297921	−	0.249986i
$801$		0			0
$802$	−1.38919	+	7.87846i	−0.0490538	+	0.278198i
$803$	3.12567	+	17.7265i	0.110302	+	0.625556i
$804$	2.81908	−	1.02606i	0.0994212	−	0.0361864i
$805$	−6.00000	+	10.3923i	−0.211472	+	0.366281i
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	−22.9813	−	19.2836i	−0.808981	−	0.678816i
$808$	1.53209	+	1.28558i	0.0538987	+	0.0452264i
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	0.967219	−	0.253946i	$-0.0817284\pi$
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	−0.703533	+	0.710663i	$0.748395\pi$
$810$	2.00000	−	3.46410i	0.0702728	−	0.121716i
$811$	2.81908	−	1.02606i	0.0989912	−	0.0360299i	−0.292050	−	0.956403i	$-0.594337\pi$
$811$	2.81908	−	1.02606i	0.0989912	−	0.0360299i	0.391041	+	0.920373i	$0.372115\pi$
$812$	−2.60472	−	14.7721i	−0.0914078	−	0.518400i
$813$	−1.21554	+	6.89365i	−0.0426308	+	0.241771i
$814$	3.75877	+	1.36808i	0.131745	+	0.0479512i
$815$	49.0268	−	41.1384i	1.71734	−	1.44102i
$816$	−3.00000			−0.105021
$817$		0			0
$818$	−20.0000			−0.699284
$819$	4.59627	−	3.85673i	0.160607	−	0.134765i
$820$	−30.0702	−	10.9446i	−1.05010	−	0.382204i
$821$	2.08378	−	11.8177i	0.0727244	−	0.412440i	−0.926612	−	0.376019i	$-0.877293\pi$
$821$	2.08378	−	11.8177i	0.0727244	−	0.412440i	0.999337	−	0.0364218i	$-0.0115960\pi$
$822$	2.95202	+	16.7417i	0.102963	+	0.583935i
$823$	−27.2511	+	9.91858i	−0.949913	+	0.345740i	−0.770073	−	0.637956i	$-0.779780\pi$
$823$	−27.2511	+	9.91858i	−0.949913	+	0.345740i	−0.179840	+	0.983696i	$0.557558\pi$
$824$	3.00000	−	5.19615i	0.104510	−	0.181017i
$825$	11.0000	+	19.0526i	0.382971	+	0.663325i
$826$	34.4720	+	28.9254i	1.19943	+	1.00644i
$827$	17.6190	+	14.7841i	0.612673	+	0.514094i	0.895491	−	0.445080i	$-0.146825\pi$
$827$	17.6190	+	14.7841i	0.612673	+	0.514094i	−0.282818	+	0.959174i	$0.591269\pi$
$828$	−1.00000	−	1.73205i	−0.0347524	−	0.0601929i
$829$	7.50000	−	12.9904i	0.260486	−	0.451175i	−0.705885	−	0.708326i	$-0.749451\pi$
$829$	7.50000	−	12.9904i	0.260486	−	0.451175i	0.966371	+	0.257152i	$0.0827840\pi$
$830$	−22.5526	+	8.20848i	−0.782813	+	0.284921i
$831$	−4.86215	−	27.5746i	−0.168666	−	0.956553i
$832$	−0.173648	+	0.984808i	−0.00602017	+	0.0341421i
$833$	−5.63816	−	2.05212i	−0.195351	−	0.0711018i
$834$		0			0
$835$	48.0000			1.66111
$836$		0			0
$837$	−40.0000			−1.38260
$838$		0			0
$839$	−18.7939	−	6.84040i	−0.648836	−	0.236157i	−0.00342687	−	0.999994i	$-0.501091\pi$
$839$	−18.7939	−	6.84040i	−0.648836	−	0.236157i	−0.645409	+	0.763837i	$0.723313\pi$
$840$	2.08378	−	11.8177i	0.0718972	−	0.407749i
$841$	−0.694593	−	3.93923i	−0.0239515	−	0.135836i
$842$	12.2160	−	4.44626i	0.420991	−	0.153228i
$843$	−4.00000	+	6.92820i	−0.137767	+	0.238620i
$844$	−13.5000	−	23.3827i	−0.464689	−	0.804865i
$845$	36.7701	+	30.8538i	1.26493	+	1.06140i
$846$	−12.2567	−	10.2846i	−0.421394	−	0.353592i
$847$	10.5000	+	18.1865i	0.360784	+	0.624897i
$848$	0.500000	−	0.866025i	0.0171701	−	0.0297394i
$849$	−5.63816	+	2.05212i	−0.193501	+	0.0704286i
$850$	5.73039	+	32.4987i	0.196551	+	1.11469i
$851$	0.347296	−	1.96962i	0.0119052	−	0.0675175i
$852$	1.87939	+	0.684040i	0.0643867	+	0.0234348i
$853$	−4.59627	+	3.85673i	−0.157373	+	0.132052i	−0.718074	−	0.695967i	$-0.754976\pi$
$853$	−4.59627	+	3.85673i	−0.157373	+	0.132052i	0.560701	+	0.828018i	$0.310532\pi$
$854$	6.00000			0.205316
$855$		0			0
$856$	−7.00000			−0.239255
$857$	−9.19253	+	7.71345i	−0.314011	+	0.263486i	−0.786147	−	0.618039i	$-0.787927\pi$
$857$	−9.19253	+	7.71345i	−0.314011	+	0.263486i	0.472137	+	0.881525i	$0.343483\pi$
$858$	−1.87939	−	0.684040i	−0.0641612	−	0.0233528i
$859$	−8.68241	+	49.2404i	−0.296240	+	1.68006i	0.365880	+	0.930662i	$0.380768\pi$
$859$	−8.68241	+	49.2404i	−0.296240	+	1.68006i	−0.662120	+	0.749398i	$0.730343\pi$
$860$	−2.77837	−	15.7569i	−0.0947417	−	0.537307i
$861$	−22.5526	+	8.20848i	−0.768591	+	0.279744i
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.800799	−	0.598933i	$-0.795592\pi$
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.118291	−	0.992979i	$-0.537742\pi$
$864$	3.83022	+	3.21394i	0.130307	+	0.109340i
$865$	18.3851	+	15.4269i	0.625111	+	0.524530i
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$	−4.00000	+	6.92820i	−0.135847	+	0.235294i
$868$	22.5526	−	8.20848i	0.765486	−	0.278614i
$869$	−3.47296	−	19.6962i	−0.117812	−	0.668146i
$870$	−3.47296	+	19.6962i	−0.117744	+	0.667762i
$871$	2.81908	+	1.02606i	0.0955208	+	0.0347667i
$872$	−11.4907	+	9.64181i	−0.389123	+	0.326513i
$873$	4.00000			0.135379
$874$		0			0
$875$	−72.0000			−2.43404
$876$	−6.89440	+	5.78509i	−0.232940	+	0.195460i
$877$	−12.2160	−	4.44626i	−0.412505	−	0.150140i	0.127427	−	0.991848i	$-0.459328\pi$
$877$	−12.2160	−	4.44626i	−0.412505	−	0.150140i	−0.539933	+	0.841708i	$0.681550\pi$
$878$	3.47296	−	19.6962i	0.117207	−	0.664713i
$879$	−1.56283	−	8.86327i	−0.0527131	−	0.298951i
$880$	7.51754	−	2.73616i	0.253416	−	0.0922360i
$881$	9.00000	−	15.5885i	0.303218	−	0.525188i	−0.673645	−	0.739055i	$-0.735272\pi$
$881$	9.00000	−	15.5885i	0.303218	−	0.525188i	0.976863	+	0.213866i	$0.0686057\pi$
$882$	2.00000	+	3.46410i	0.0673435	+	0.116642i
$883$	26.0455	+	21.8548i	0.876501	+	0.735472i	0.965457	−	0.260564i	$-0.0839084\pi$
$883$	26.0455	+	21.8548i	0.876501	+	0.735472i	−0.0889554	+	0.996036i	$0.528353\pi$
$884$	−2.29813	−	1.92836i	−0.0772946	−	0.0648579i
$885$	−30.0000	−	51.9615i	−1.00844	−	1.74667i
$886$	13.0000	−	22.5167i	0.436744	−	0.756462i
$887$	1.87939	−	0.684040i	0.0631036	−	0.0229678i	−0.310276	−	0.950647i	$-0.600421\pi$
$887$	1.87939	−	0.684040i	0.0631036	−	0.0229678i	0.373379	+	0.927679i	$0.378199\pi$
$888$	0.347296	+	1.96962i	0.0116545	+	0.0660960i
$889$	9.37700	−	53.1796i	0.314495	−	1.78359i
$890$		0			0
$891$	1.53209	−	1.28558i	0.0513269	−	0.0430684i
$892$	14.0000			0.468755
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−2.81908	−	1.02606i	−0.0941788	−	0.0342783i
$897$	−0.173648	+	0.984808i	−0.00579794	+	0.0328818i
$898$	1.73648	+	9.84808i	0.0579471	+	0.328635i
$899$	−37.5877	+	13.6808i	−1.25362	+	0.456280i
$900$	11.0000	−	19.0526i	0.366667	−	0.635085i
$901$	1.50000	+	2.59808i	0.0499722	+	0.0865545i
$902$	−12.2567	−	10.2846i	−0.408104	−	0.342440i
$903$	−9.19253	−	7.71345i	−0.305908	−	0.256688i
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	44.0000	−	76.2102i	1.46261	−	2.53331i
$906$	1.87939	−	0.684040i	0.0624384	−	0.0227257i
$907$	9.20335	+	52.1948i	0.305592	+	1.73310i	0.620703	+	0.784045i	$0.286847\pi$
$907$	9.20335	+	52.1948i	0.305592	+	1.73310i	−0.315111	+	0.949055i	$0.602042\pi$
$908$	−2.95202	+	16.7417i	−0.0979662	+	0.555594i
$909$	3.75877	+	1.36808i	0.124671	+	0.0453764i
$910$	9.19253	−	7.71345i	0.304730	−	0.255698i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	−12.0000			−0.397142
$914$	−5.36231	+	4.49951i	−0.177369	+	0.148831i
$915$	−7.51754	−	2.73616i	−0.248522	−	0.0904547i
$916$	−1.73648	+	9.84808i	−0.0573750	+	0.325390i
$917$	6.25133	+	35.4531i	0.206437	+	1.17076i
$918$	−14.0954	+	5.13030i	−0.465217	+	0.169325i
$919$	−2.50000	+	4.33013i	−0.0824674	+	0.142838i	−0.904309	−	0.426878i	$-0.859613\pi$
$919$	−2.50000	+	4.33013i	−0.0824674	+	0.142838i	0.821842	+	0.569716i	$0.192947\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$	9.19253	+	7.71345i	0.302904	+	0.254167i
$922$	−21.4492	−	17.9981i	−0.706393	−	0.592734i
$923$	1.00000	+	1.73205i	0.0329154	+	0.0570111i
$924$	3.00000	−	5.19615i	0.0986928	−	0.170941i
$925$	20.6732	−	7.52444i	0.679732	−	0.247402i
$926$	0.694593	+	3.93923i	0.0228257	+	0.129451i
$927$	2.08378	−	11.8177i	0.0684403	−	0.388144i
$928$	4.69846	+	1.71010i	0.154235	+	0.0561368i
$929$	−42.1324	+	35.3533i	−1.38232	+	1.15990i	−0.413976	+	0.910288i	$0.635860\pi$
$929$	−42.1324	+	35.3533i	−1.38232	+	1.15990i	−0.968345	+	0.249617i	$0.919695\pi$
$930$	−32.0000			−1.04932
$931$		0			0
$932$	−6.00000			−0.196537
$933$	−5.36231	+	4.49951i	−0.175554	+	0.147307i
$934$	1.87939	+	0.684040i	0.0614954	+	0.0223825i
$935$	−4.16756	+	23.6354i	−0.136294	+	0.772960i
$936$	0.347296	+	1.96962i	0.0113517	+	0.0643789i
$937$	6.57785	−	2.39414i	0.214889	−	0.0782132i	−0.232333	−	0.972636i	$-0.574636\pi$
$937$	6.57785	−	2.39414i	0.214889	−	0.0782132i	0.447222	+	0.894423i	$0.352414\pi$
$938$	−4.50000	+	7.79423i	−0.146930	+	0.254491i
$939$	14.5000	+	25.1147i	0.473190	+	0.819588i
$940$	−24.5134	−	20.5692i	−0.799540	−	0.670893i
$941$	5.36231	+	4.49951i	0.174806	+	0.146680i	0.725993	−	0.687702i	$-0.241380\pi$
$941$	5.36231	+	4.49951i	0.174806	+	0.146680i	−0.551187	+	0.834382i	$0.685825\pi$
$942$	−1.00000	−	1.73205i	−0.0325818	−	0.0564333i
$943$	−4.00000	+	6.92820i	−0.130258	+	0.225613i
$944$	−14.0954	+	5.13030i	−0.458766	+	0.166977i
$945$	−10.4189	−	59.0885i	−0.338927	−	1.92215i
$946$	1.38919	−	7.87846i	0.0451663	−	0.256151i
$947$	11.2763	+	4.10424i	0.366431	+	0.133370i	0.518672	−	0.854973i	$-0.326427\pi$
$947$	11.2763	+	4.10424i	0.366431	+	0.133370i	−0.152241	+	0.988343i	$0.548649\pi$
$948$	7.66044	−	6.42788i	0.248800	−	0.208768i
$949$	−9.00000			−0.292152
$950$		0			0
$951$	27.0000			0.875535
$952$	6.89440	−	5.78509i	0.223449	−	0.187496i
$953$	43.2259	+	15.7329i	1.40022	+	0.509639i	0.928245	−	0.371971i	$-0.121318\pi$
$953$	43.2259	+	15.7329i	1.40022	+	0.509639i	0.471978	+	0.881610i	$0.343540\pi$
$954$	0.347296	−	1.96962i	0.0112441	−	0.0637687i
$955$	−4.86215	−	27.5746i	−0.157335	−	0.892294i
$956$	−14.0954	+	5.13030i	−0.455877	+	0.165926i
$957$	−5.00000	+	8.66025i	−0.161627	+	0.279946i
$958$	10.0000	+	17.3205i	0.323085	+	0.559600i
$959$	−39.0683	−	32.7822i	−1.26158	−	1.05859i
$960$	3.06418	+	2.57115i	0.0988959	+	0.0829835i
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−1.00000	+	1.73205i	−0.0322413	+	0.0558436i
$963$	−13.1557	+	4.78828i	−0.423936	+	0.154300i
$964$	−1.38919	−	7.87846i	−0.0447426	−	0.253748i
$965$	4.16756	−	23.6354i	0.134158	−	0.760850i
$966$	−2.81908	−	1.02606i	−0.0907023	−	0.0330130i
$967$	36.7701	−	30.8538i	1.18245	−	0.992191i	0.182488	−	0.983208i	$-0.441585\pi$
$967$	36.7701	−	30.8538i	1.18245	−	0.992191i	0.999960	−	0.00898343i	$-0.00285955\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	8.00000			0.256865
$971$	−21.4492	+	17.9981i	−0.688339	+	0.577585i	−0.918430	−	0.395584i	$-0.870542\pi$
$971$	−21.4492	+	17.9981i	−0.688339	+	0.577585i	0.230091	+	0.973169i	$0.426098\pi$
$972$	15.0351	+	5.47232i	0.482250	+	0.175525i
$973$		0			0
$974$	−0.347296	−	1.96962i	−0.0111281	−	0.0631106i
$975$	−10.3366	+	3.76222i	−0.331037	+	0.120488i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−4.00000	−	6.92820i	−0.127971	−	0.221653i	0.794919	−	0.606715i	$-0.207513\pi$
$977$	−4.00000	−	6.92820i	−0.127971	−	0.221653i	−0.922890	+	0.385063i	$0.874180\pi$
$978$	12.2567	+	10.2846i	0.391926	+	0.328865i
$979$		0			0
$980$	4.00000	+	6.92820i	0.127775	+	0.221313i
$981$	−15.0000	+	25.9808i	−0.478913	+	0.829502i
$982$	26.3114	−	9.57656i	0.839630	−	0.305600i
$983$	−1.04189	−	5.90885i	−0.0332311	−	0.188463i	0.963674	−	0.267083i	$-0.0860598\pi$
$983$	−1.04189	−	5.90885i	−0.0332311	−	0.188463i	−0.996905	+	0.0786200i	$0.974949\pi$
$984$	1.38919	−	7.87846i	0.0442856	−	0.251156i
$985$	30.0702	+	10.9446i	0.958115	+	0.348725i
$986$	−11.4907	+	9.64181i	−0.365937	+	0.307058i
$987$	−24.0000			−0.763928
$988$		0			0
$989$	−4.00000			−0.127193
$990$	12.2567	−	10.2846i	0.389544	−	0.326866i
$991$	7.51754	+	2.73616i	0.238803	+	0.0869170i	0.458649	−	0.888617i	$-0.348333\pi$
$991$	7.51754	+	2.73616i	0.238803	+	0.0869170i	−0.219847	+	0.975534i	$0.570556\pi$
$992$	−1.38919	+	7.87846i	−0.0441067	+	0.250141i
$993$	−2.95202	−	16.7417i	−0.0936795	−	0.531283i
$994$	−5.63816	+	2.05212i	−0.178831	+	0.0650893i
$995$	−50.0000	+	86.6025i	−1.58511	+	2.74549i
$996$	−3.00000	−	5.19615i	−0.0950586	−	0.164646i
$997$	21.4492	+	17.9981i	0.679304	+	0.570004i	0.915803	−	0.401628i	$-0.131555\pi$
$997$	21.4492	+	17.9981i	0.679304	+	0.570004i	−0.236499	+	0.971632i	$0.576000\pi$
$998$	30.6418	+	25.7115i	0.969949	+	0.813883i
$999$	5.00000	+	8.66025i	0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.c.595.1		6
19.2	odd	18		722.2.e.d.423.1		6
19.3	odd	18		722.2.e.d.415.1		6
19.4	even	9		38.2.a.b.1.1	✓	1
19.5	even	9	inner	722.2.e.c.245.1		6
19.6	even	9		722.2.c.d.653.1		2
19.7	even	3	inner	722.2.e.c.389.1		6
19.8	odd	6		722.2.e.d.99.1		6
19.9	even	9		722.2.c.d.429.1		2
19.10	odd	18		722.2.c.f.429.1		2
19.11	even	3	inner	722.2.e.c.99.1		6
19.12	odd	6		722.2.e.d.389.1		6
19.13	odd	18		722.2.c.f.653.1		2
19.14	odd	18		722.2.e.d.245.1		6
19.15	odd	18		722.2.a.b.1.1		1
19.16	even	9	inner	722.2.e.c.415.1		6
19.17	even	9	inner	722.2.e.c.423.1		6
19.18	odd	2		722.2.e.d.595.1		6
57.23	odd	18		342.2.a.d.1.1		1
57.53	even	18		6498.2.a.y.1.1		1
76.15	even	18		5776.2.a.d.1.1		1
76.23	odd	18		304.2.a.d.1.1		1
95.4	even	18		950.2.a.b.1.1		1
95.23	odd	36		950.2.b.c.799.1		2
95.42	odd	36		950.2.b.c.799.2		2
133.118	odd	18		1862.2.a.f.1.1		1
152.61	even	18		1216.2.a.n.1.1		1
152.99	odd	18		1216.2.a.g.1.1		1
209.175	odd	18		4598.2.a.a.1.1		1
228.23	even	18		2736.2.a.w.1.1		1
247.194	even	18		6422.2.a.b.1.1		1
285.194	odd	18		8550.2.a.u.1.1		1
380.99	odd	18		7600.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.a.b.1.1	✓	1	19.4	even	9
304.2.a.d.1.1		1	76.23	odd	18
342.2.a.d.1.1		1	57.23	odd	18
722.2.a.b.1.1		1	19.15	odd	18
722.2.c.d.429.1		2	19.9	even	9
722.2.c.d.653.1		2	19.6	even	9
722.2.c.f.429.1		2	19.10	odd	18
722.2.c.f.653.1		2	19.13	odd	18
722.2.e.c.99.1		6	19.11	even	3	inner
722.2.e.c.245.1		6	19.5	even	9	inner
722.2.e.c.389.1		6	19.7	even	3	inner
722.2.e.c.415.1		6	19.16	even	9	inner
722.2.e.c.423.1		6	19.17	even	9	inner
722.2.e.c.595.1		6	1.1	even	1	trivial
722.2.e.d.99.1		6	19.8	odd	6
722.2.e.d.245.1		6	19.14	odd	18
722.2.e.d.389.1		6	19.12	odd	6
722.2.e.d.415.1		6	19.3	odd	18
722.2.e.d.423.1		6	19.2	odd	18
722.2.e.d.595.1		6	19.18	odd	2
950.2.a.b.1.1		1	95.4	even	18
950.2.b.c.799.1		2	95.23	odd	36
950.2.b.c.799.2		2	95.42	odd	36
1216.2.a.g.1.1		1	152.99	odd	18
1216.2.a.n.1.1		1	152.61	even	18
1862.2.a.f.1.1		1	133.118	odd	18
2736.2.a.w.1.1		1	228.23	even	18
4598.2.a.a.1.1		1	209.175	odd	18
5776.2.a.d.1.1		1	76.15	even	18
6422.2.a.b.1.1		1	247.194	even	18
6498.2.a.y.1.1		1	57.53	even	18
7600.2.a.h.1.1		1	380.99	odd	18
8550.2.a.u.1.1		1	285.194	odd	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.694593 - 3.93923i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.53209 - 1.28558i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.694593 - 3.93923i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.53209 - 1.28558i) q^{9} +(-3.06418 - 2.57115i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.939693 - 0.342020i) q^{13} +(0.520945 + 2.95442i) q^{14} +(0.694593 - 3.93923i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.29813 - 1.92836i) q^{17} -2.00000 q^{18} -4.00000 q^{20} +(-2.29813 + 1.92836i) q^{21} +(-1.87939 - 0.684040i) q^{22} +(-0.173648 + 0.984808i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-10.3366 + 3.76222i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.50000 - 4.33013i) q^{27} +(2.29813 + 1.92836i) q^{28} +(-3.83022 - 3.21394i) q^{29} +(-2.00000 - 3.46410i) q^{30} +(4.00000 - 6.92820i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.347296 - 1.96962i) q^{33} +(0.520945 - 2.95442i) q^{34} +(11.2763 + 4.10424i) q^{35} +(-1.53209 + 1.28558i) q^{36} -2.00000 q^{37} +1.00000 q^{39} +(-3.06418 + 2.57115i) q^{40} +(7.51754 + 2.73616i) q^{41} +(-0.520945 + 2.95442i) q^{42} +(0.694593 + 3.93923i) q^{43} +(-1.87939 + 0.684040i) q^{44} +(-4.00000 + 6.92820i) q^{45} +(0.500000 + 0.866025i) q^{46} +(6.12836 + 5.14230i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(-5.50000 + 9.52628i) q^{50} +(2.81908 - 1.02606i) q^{51} +(-0.173648 - 0.984808i) q^{52} +(-0.173648 + 0.984808i) q^{53} +(-4.69846 - 1.71010i) q^{54} +(-6.12836 + 5.14230i) q^{55} +3.00000 q^{56} -5.00000 q^{58} +(11.4907 - 9.64181i) q^{59} +(-3.75877 - 1.36808i) q^{60} +(0.347296 - 1.96962i) q^{61} +(-1.38919 - 7.87846i) q^{62} +(5.63816 - 2.05212i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.00000 - 3.46410i) q^{65} +(-1.53209 - 1.28558i) q^{66} +(2.29813 + 1.92836i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-0.500000 + 0.866025i) q^{69} +(11.2763 - 4.10424i) q^{70} +(0.347296 + 1.96962i) q^{71} +(-0.347296 + 1.96962i) q^{72} +(-8.45723 - 3.07818i) q^{73} +(-1.53209 + 1.28558i) q^{74} -11.0000 q^{75} +6.00000 q^{77} +(0.766044 - 0.642788i) q^{78} +(9.39693 + 3.42020i) q^{79} +(-0.694593 + 3.93923i) q^{80} +(0.173648 + 0.984808i) q^{81} +(7.51754 - 2.73616i) q^{82} +(3.00000 - 5.19615i) q^{83} +(1.50000 + 2.59808i) q^{84} +(-9.19253 - 7.71345i) q^{85} +(3.06418 + 2.57115i) q^{86} +(-2.50000 - 4.33013i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(1.38919 + 7.87846i) q^{90} +(-0.520945 + 2.95442i) q^{91} +(0.939693 + 0.342020i) q^{92} +(6.12836 - 5.14230i) q^{93} +8.00000 q^{94} -1.00000 q^{96} +(-1.53209 + 1.28558i) q^{97} +(-1.87939 - 0.684040i) q^{98} +(-0.694593 + 3.93923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 9 * q^7 - 3 * q^8	\( 6 q - 9 q^{7} - 3 q^{8} - 6 q^{11} + 3 q^{12} - 12 q^{18} - 24 q^{20} + 3 q^{26} - 15 q^{27} - 12 q^{30} + 24 q^{31} - 12 q^{37} + 6 q^{39} - 24 q^{45} + 3 q^{46} - 6 q^{49} - 33 q^{50} + 18 q^{56} - 30 q^{58} - 3 q^{64} - 12 q^{65} - 9 q^{68} - 3 q^{69} - 66 q^{75} + 36 q^{77} + 18 q^{83} + 9 q^{84} - 15 q^{87} - 6 q^{88} + 48 q^{94} - 6 q^{96}+O(q^{100}) \) 6 * q - 9 * q^7 - 3 * q^8 - 6 * q^11 + 3 * q^12 - 12 * q^18 - 24 * q^20 + 3 * q^26 - 15 * q^27 - 12 * q^30 + 24 * q^31 - 12 * q^37 + 6 * q^39 - 24 * q^45 + 3 * q^46 - 6 * q^49 - 33 * q^50 + 18 * q^56 - 30 * q^58 - 3 * q^64 - 12 * q^65 - 9 * q^68 - 3 * q^69 - 66 * q^75 + 36 * q^77 + 18 * q^83 + 9 * q^84 - 15 * q^87 - 6 * q^88 + 48 * q^94 - 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more