LMFDB - Embedded newform 798.2.j.l.457.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(457,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("798.457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.4
Root			$0.385731i$ of defining polynomial
Character	$\chi$	$=$	798.457
Dual form			798.2.j.l.571.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.73065 - 2.99758i) q^{5} +1.00000 q^{6} +(-2.36975 - 1.17656i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.73065 - 2.99758i) q^{5} +1.00000 q^{6} +(-2.36975 - 1.17656i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.73065 - 2.99758i) q^{10} +(-0.139098 - 0.240925i) q^{11} +(0.500000 - 0.866025i) q^{12} +6.92261 q^{13} +(-2.20380 + 1.46399i) q^{14} +3.46130 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.89876 - 5.02079i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -3.46130 q^{20} +(-0.165947 - 2.64054i) q^{21} -0.278197 q^{22} +(-1.54617 + 2.67804i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.49031 - 6.04539i) q^{25} +(3.46130 - 5.99515i) q^{26} -1.00000 q^{27} +(0.165947 + 2.64054i) q^{28} -8.55364 q^{29} +(1.73065 - 2.99758i) q^{30} +(-3.67480 - 6.36493i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.139098 - 0.240925i) q^{33} -5.79751 q^{34} +(-7.62803 + 5.06730i) q^{35} +1.00000 q^{36} +(2.62056 - 4.53894i) q^{37} +(0.500000 + 0.866025i) q^{38} +(3.46130 + 5.99515i) q^{39} +(-1.73065 + 2.99758i) q^{40} +8.88553 q^{41} +(-2.36975 - 1.17656i) q^{42} +10.3705 q^{43} +(-0.139098 + 0.240925i) q^{44} +(1.73065 + 2.99758i) q^{45} +(1.54617 + 2.67804i) q^{46} +(0.896599 - 1.55296i) q^{47} -1.00000 q^{48} +(4.23143 + 5.57629i) q^{49} -6.98062 q^{50} +(2.89876 - 5.02079i) q^{51} +(-3.46130 - 5.99515i) q^{52} +(-4.19411 - 7.26442i) q^{53} +(-0.500000 + 0.866025i) q^{54} -0.962923 q^{55} +(2.36975 + 1.17656i) q^{56} -1.00000 q^{57} +(-4.27682 + 7.40767i) q^{58} +(3.89738 + 6.75046i) q^{59} +(-1.73065 - 2.99758i) q^{60} +(-4.56470 + 7.90630i) q^{61} -7.34959 q^{62} +(2.20380 - 1.46399i) q^{63} +1.00000 q^{64} +(11.9806 - 20.7510i) q^{65} +(-0.139098 - 0.240925i) q^{66} +(6.86891 + 11.8973i) q^{67} +(-2.89876 + 5.02079i) q^{68} -3.09233 q^{69} +(0.574394 + 9.13972i) q^{70} +0.684727 q^{71} +(0.500000 - 0.866025i) q^{72} +(0.962682 + 1.66741i) q^{73} +(-2.62056 - 4.53894i) q^{74} +(3.49031 - 6.04539i) q^{75} +1.00000 q^{76} +(0.0461660 + 0.734590i) q^{77} +6.92261 q^{78} +(-0.703803 + 1.21902i) q^{79} +(1.73065 + 2.99758i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.44277 - 7.69509i) q^{82} -0.146030 q^{83} +(-2.20380 + 1.46399i) q^{84} -20.0670 q^{85} +(5.18526 - 8.98114i) q^{86} +(-4.27682 - 7.40767i) q^{87} +(0.139098 + 0.240925i) q^{88} +(6.85037 - 11.8652i) q^{89} +3.46130 q^{90} +(-16.4048 - 8.14484i) q^{91} +3.09233 q^{92} +(3.67480 - 6.36493i) q^{93} +(-0.896599 - 1.55296i) q^{94} +(1.73065 + 2.99758i) q^{95} +(-0.500000 + 0.866025i) q^{96} +4.09233 q^{97} +(6.94492 - 0.876382i) q^{98} +0.278197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{11} + 4 q^{12} - q^{14} - 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} - 4 q^{25} - 8 q^{27} + q^{28} - 6 q^{29} - 9 q^{31} + 4 q^{32} - 2 q^{33} - 20 q^{34} - 9 q^{35} + 8 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{41} - 2 q^{42} + 42 q^{43} + 2 q^{44} - 5 q^{46} - 7 q^{47} - 8 q^{48} - 4 q^{49} - 8 q^{50} + 10 q^{51} + 7 q^{53} - 4 q^{54} + 2 q^{56} - 8 q^{57} - 3 q^{58} - 7 q^{59} - 23 q^{61} - 18 q^{62} + q^{63} + 8 q^{64} + 48 q^{65} + 2 q^{66} - 6 q^{67} - 10 q^{68} + 10 q^{69} + 15 q^{70} + 4 q^{71} + 4 q^{72} + 5 q^{73} - 14 q^{74} + 4 q^{75} + 8 q^{76} - 17 q^{77} + 11 q^{79} - 4 q^{81} + 4 q^{82} + 28 q^{83} - q^{84} + 12 q^{85} + 21 q^{86} - 3 q^{87} - 2 q^{88} - 10 q^{89} - 48 q^{91} - 10 q^{92} + 9 q^{93} + 7 q^{94} - 4 q^{96} - 2 q^{97} + 25 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^11 + 4 * q^12 - q^14 - 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 - 4 * q^25 - 8 * q^27 + q^28 - 6 * q^29 - 9 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 - 9 * q^35 + 8 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^41 - 2 * q^42 + 42 * q^43 + 2 * q^44 - 5 * q^46 - 7 * q^47 - 8 * q^48 - 4 * q^49 - 8 * q^50 + 10 * q^51 + 7 * q^53 - 4 * q^54 + 2 * q^56 - 8 * q^57 - 3 * q^58 - 7 * q^59 - 23 * q^61 - 18 * q^62 + q^63 + 8 * q^64 + 48 * q^65 + 2 * q^66 - 6 * q^67 - 10 * q^68 + 10 * q^69 + 15 * q^70 + 4 * q^71 + 4 * q^72 + 5 * q^73 - 14 * q^74 + 4 * q^75 + 8 * q^76 - 17 * q^77 + 11 * q^79 - 4 * q^81 + 4 * q^82 + 28 * q^83 - q^84 + 12 * q^85 + 21 * q^86 - 3 * q^87 - 2 * q^88 - 10 * q^89 - 48 * q^91 - 10 * q^92 + 9 * q^93 + 7 * q^94 - 4 * q^96 - 2 * q^97 + 25 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.73065	−	2.99758i	0.773971	−	1.34056i	−0.161400	−	0.986889i	$-0.551601\pi$
$5$	1.73065	−	2.99758i	0.773971	−	1.34056i	0.935371	−	0.353668i	$-0.115066\pi$
$6$	1.00000			0.408248
$7$	−2.36975	−	1.17656i	−0.895681	−	0.444696i
$7$	−2.36975	−	1.17656i	−0.895681	−	0.444696i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.73065	−	2.99758i	−0.547280	−	0.947917i
$11$	−0.139098	−	0.240925i	−0.0419397	−	0.0726418i	0.844294	−	0.535881i	$-0.180020\pi$
$11$	−0.139098	−	0.240925i	−0.0419397	−	0.0726418i	−0.886233	+	0.463239i	$0.846687\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	6.92261			1.91999			0.959993	−	0.280025i	$-0.0903427\pi$
$13$	6.92261			1.91999			0.959993	+	0.280025i	$0.0903427\pi$
$14$	−2.20380	+	1.46399i	−0.588991	+	0.391267i
$15$	3.46130			0.893705
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.89876	−	5.02079i	−0.703052	−	1.21772i	−0.967390	−	0.253291i	$-0.918487\pi$
$17$	−2.89876	−	5.02079i	−0.703052	−	1.21772i	0.264338	−	0.964430i	$-0.414846\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	−3.46130			−0.773971
$21$	−0.165947	−	2.64054i	−0.0362127	−	0.576213i
$22$	−0.278197			−0.0593118
$23$	−1.54617	+	2.67804i	−0.322398	+	0.558410i	−0.980982	−	0.194097i	$-0.937822\pi$
$23$	−1.54617	+	2.67804i	−0.322398	+	0.558410i	0.658584	+	0.752507i	$0.271156\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−3.49031	−	6.04539i	−0.698062	−	1.20908i
$26$	3.46130	−	5.99515i	0.678817	−	1.17575i
$27$	−1.00000			−0.192450
$28$	0.165947	+	2.64054i	0.0313611	+	0.499016i
$29$	−8.55364			−1.58837			−0.794185	−	0.607676i	$-0.792102\pi$
$29$	−8.55364			−1.58837			−0.794185	+	0.607676i	$0.792102\pi$
$30$	1.73065	−	2.99758i	0.315972	−	0.547280i
$31$	−3.67480	−	6.36493i	−0.660013	−	1.14318i	−0.980612	−	0.195961i	$-0.937218\pi$
$31$	−3.67480	−	6.36493i	−0.660013	−	1.14318i	0.320599	−	0.947215i	$-0.396116\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.139098	−	0.240925i	0.0242139	−	0.0419397i
$34$	−5.79751			−0.994265
$35$	−7.62803	+	5.06730i	−1.28937	+	0.856530i
$36$	1.00000			0.166667
$37$	2.62056	−	4.53894i	0.430817	−	0.746198i	−0.566126	−	0.824318i	$-0.691559\pi$
$37$	2.62056	−	4.53894i	0.430817	−	0.746198i	0.996944	+	0.0781207i	$0.0248920\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	3.46130	+	5.99515i	0.554252	+	0.959993i
$40$	−1.73065	+	2.99758i	−0.273640	+	0.473958i
$41$	8.88553			1.38769			0.693843	−	0.720126i	$-0.255916\pi$
$41$	8.88553			1.38769			0.693843	+	0.720126i	$0.255916\pi$
$42$	−2.36975	−	1.17656i	−0.365660	−	0.181547i
$43$	10.3705			1.58149			0.790745	−	0.612145i	$-0.209693\pi$
$43$	10.3705			1.58149			0.790745	+	0.612145i	$0.209693\pi$
$44$	−0.139098	+	0.240925i	−0.0209699	+	0.0363209i
$45$	1.73065	+	2.99758i	0.257990	+	0.446852i
$46$	1.54617	+	2.67804i	0.227970	+	0.394855i
$47$	0.896599	−	1.55296i	0.130782	−	0.226522i	−0.793196	−	0.608966i	$-0.791584\pi$
$47$	0.896599	−	1.55296i	0.130782	−	0.226522i	0.923978	+	0.382445i	$0.124918\pi$
$48$	−1.00000			−0.144338
$49$	4.23143	+	5.57629i	0.604490	+	0.796613i
$50$	−6.98062			−0.987209
$51$	2.89876	−	5.02079i	0.405907	−	0.703052i
$52$	−3.46130	−	5.99515i	−0.479996	−	0.831378i
$53$	−4.19411	−	7.26442i	−0.576106	−	0.997844i	−0.995921	−	0.0902346i	$-0.971238\pi$
$53$	−4.19411	−	7.26442i	−0.576106	−	0.997844i	0.419815	−	0.907610i	$-0.362095\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−0.962923			−0.129841
$56$	2.36975	+	1.17656i	0.316671	+	0.157224i
$57$	−1.00000			−0.132453
$58$	−4.27682	+	7.40767i	−0.561574	+	0.972674i
$59$	3.89738	+	6.75046i	0.507395	+	0.878835i	0.999963	+	0.00856059i	$0.00272495\pi$
$59$	3.89738	+	6.75046i	0.507395	+	0.878835i	−0.492568	+	0.870274i	$0.663942\pi$
$60$	−1.73065	−	2.99758i	−0.223426	−	0.386985i
$61$	−4.56470	+	7.90630i	−0.584450	+	1.01230i	0.410493	+	0.911864i	$0.365357\pi$
$61$	−4.56470	+	7.90630i	−0.584450	+	1.01230i	−0.994944	+	0.100434i	$0.967977\pi$
$62$	−7.34959			−0.933399
$63$	2.20380	−	1.46399i	0.277653	−	0.184445i
$64$	1.00000			0.125000
$65$	11.9806	−	20.7510i	1.48601	−	2.57385i
$66$	−0.139098	−	0.240925i	−0.0171218	−	0.0296559i
$67$	6.86891	+	11.8973i	0.839171	+	1.45349i	0.890589	+	0.454809i	$0.150293\pi$
$67$	6.86891	+	11.8973i	0.839171	+	1.45349i	−0.0514182	+	0.998677i	$0.516374\pi$
$68$	−2.89876	+	5.02079i	−0.351526	+	0.608861i
$69$	−3.09233			−0.372273
$70$	0.574394	+	9.13972i	0.0686532	+	1.09241i
$71$	0.684727			0.0812621			0.0406311	−	0.999174i	$-0.487063\pi$
$71$	0.684727			0.0812621			0.0406311	+	0.999174i	$0.487063\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	0.962682	+	1.66741i	0.112673	+	0.195156i	0.916847	−	0.399238i	$-0.130725\pi$
$73$	0.962682	+	1.66741i	0.112673	+	0.195156i	−0.804174	+	0.594394i	$0.797392\pi$
$74$	−2.62056	−	4.53894i	−0.304634	−	0.527641i
$75$	3.49031	−	6.04539i	0.403026	−	0.698062i
$76$	1.00000			0.114708
$77$	0.0461660	+	0.734590i	0.00526111	+	0.0837143i
$78$	6.92261			0.783831
$79$	−0.703803	+	1.21902i	−0.0791840	+	0.137151i	−0.902898	−	0.429855i	$-0.858565\pi$
$79$	−0.703803	+	1.21902i	−0.0791840	+	0.137151i	0.823714	+	0.567005i	$0.191898\pi$
$80$	1.73065	+	2.99758i	0.193493	+	0.335139i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.44277	−	7.69509i	0.490621	−	0.849781i
$83$	−0.146030			−0.0160289			−0.00801443	−	0.999968i	$-0.502551\pi$
$83$	−0.146030			−0.0160289			−0.00801443	+	0.999968i	$0.502551\pi$
$84$	−2.20380	+	1.46399i	−0.240455	+	0.159734i
$85$	−20.0670			−2.17657
$86$	5.18526	−	8.98114i	0.559141	−	0.968461i
$87$	−4.27682	−	7.40767i	−0.458523	−	0.794185i
$88$	0.139098	+	0.240925i	0.0148279	+	0.0256827i
$89$	6.85037	−	11.8652i	0.726138	−	1.25771i	−0.232366	−	0.972628i	$-0.574647\pi$
$89$	6.85037	−	11.8652i	0.726138	−	1.25771i	0.958504	−	0.285079i	$-0.0920199\pi$
$90$	3.46130			0.364853
$91$	−16.4048	−	8.14484i	−1.71970	−	0.853811i
$92$	3.09233			0.322398
$93$	3.67480	−	6.36493i	0.381059	−	0.660013i
$94$	−0.896599	−	1.55296i	−0.0924771	−	0.160175i
$95$	1.73065	+	2.99758i	0.177561	+	0.307545i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	4.09233			0.415513			0.207757	−	0.978181i	$-0.433384\pi$
$97$	4.09233			0.415513			0.207757	+	0.978181i	$0.433384\pi$
$98$	6.94492	−	0.876382i	0.701543	−	0.0885279i
$99$	0.278197			0.0279598
$100$	−3.49031	+	6.04539i	−0.349031	+	0.604539i
$101$	1.22849	+	2.12781i	0.122240	+	0.211725i	0.920651	−	0.390388i	$-0.127659\pi$
$101$	1.22849	+	2.12781i	0.122240	+	0.211725i	−0.798411	+	0.602113i	$0.794326\pi$
$102$	−2.89876	−	5.02079i	−0.287020	−	0.497133i
$103$	−8.67342	+	15.0228i	−0.854617	+	1.48024i	0.0223826	+	0.999749i	$0.492875\pi$
$103$	−8.67342	+	15.0228i	−0.854617	+	1.48024i	−0.877000	+	0.480491i	$0.840459\pi$
$104$	−6.92261			−0.678817
$105$	−8.20242	−	4.07242i	−0.800475	−	0.397427i
$106$	−8.38823			−0.814737
$107$	5.73896	−	9.94017i	0.554806	−	0.960953i	−0.443112	−	0.896466i	$-0.646126\pi$
$107$	5.73896	−	9.94017i	0.554806	−	0.960953i	0.997919	−	0.0644867i	$-0.0205410\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	9.34068	+	16.1785i	0.894675	+	1.54962i	0.834206	+	0.551452i	$0.185926\pi$
$109$	9.34068	+	16.1785i	0.894675	+	1.54962i	0.0604685	+	0.998170i	$0.480741\pi$
$110$	−0.481462	+	0.833916i	−0.0459056	+	0.0795108i
$111$	5.24112			0.497465
$112$	2.20380	−	1.46399i	0.208240	−	0.138334i
$113$	3.29913			0.310356			0.155178	−	0.987886i	$-0.450405\pi$
$113$	3.29913			0.310356			0.155178	+	0.987886i	$0.450405\pi$
$114$	−0.500000	+	0.866025i	−0.0468293	+	0.0811107i
$115$	5.35175	+	9.26950i	0.499053	+	0.864386i
$116$	4.27682	+	7.40767i	0.397093	+	0.687784i
$117$	−3.46130	+	5.99515i	−0.319998	+	0.554252i
$118$	7.79476			0.717565
$119$	0.962082	+	15.3086i	0.0881939	+	1.40334i
$120$	−3.46130			−0.315972
$121$	5.46130	−	9.45925i	0.496482	−	0.859932i
$122$	4.56470	+	7.90630i	0.413269	+	0.715803i
$123$	4.44277	+	7.69509i	0.400591	+	0.693843i
$124$	−3.67480	+	6.36493i	−0.330006	+	0.571588i
$125$	−6.85553			−0.613177
$126$	−0.165947	−	2.64054i	−0.0147838	−	0.235238i
$127$	−3.45699			−0.306758			−0.153379	−	0.988167i	$-0.549016\pi$
$127$	−3.45699			−0.306758			−0.153379	+	0.988167i	$0.549016\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	5.18526	+	8.98114i	0.456537	+	0.790745i
$130$	−11.9806	−	20.7510i	−1.05077	−	1.81999i
$131$	−9.24781	+	16.0177i	−0.807985	+	1.39947i	0.106272	+	0.994337i	$0.466108\pi$
$131$	−9.24781	+	16.0177i	−0.807985	+	1.39947i	−0.914257	+	0.405134i	$0.867225\pi$
$132$	−0.278197			−0.0242139
$133$	2.20380	−	1.46399i	0.191094	−	0.126944i
$134$	13.7378			1.18677
$135$	−1.73065	+	2.99758i	−0.148951	+	0.257990i
$136$	2.89876	+	5.02079i	0.248566	+	0.430530i
$137$	6.08402	+	10.5378i	0.519793	+	0.900308i	0.999735	+	0.0230078i	$0.00732427\pi$
$137$	6.08402	+	10.5378i	0.519793	+	0.900308i	−0.479942	+	0.877300i	$0.659342\pi$
$138$	−1.54617	+	2.67804i	−0.131618	+	0.227970i
$139$	−2.91829			−0.247526			−0.123763	−	0.992312i	$-0.539496\pi$
$139$	−2.91829			−0.247526			−0.123763	+	0.992312i	$0.539496\pi$
$140$	8.20242	+	4.07242i	0.693231	+	0.344182i
$141$	1.79320			0.151015
$142$	0.342363	−	0.592991i	0.0287305	−	0.0497627i
$143$	−0.962923	−	1.66783i	−0.0805237	−	0.139471i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−14.8034	+	25.6402i	−1.22935	+	2.12930i
$146$	1.92536			0.159344
$147$	−2.71349	+	6.45267i	−0.223805	+	0.532207i
$148$	−5.24112			−0.430817
$149$	2.08246	−	3.60693i	0.170602	−	0.295491i	−0.768028	−	0.640416i	$-0.778762\pi$
$149$	2.08246	−	3.60693i	0.170602	−	0.295491i	0.938631	+	0.344924i	$0.112095\pi$
$150$	−3.49031	−	6.04539i	−0.284983	−	0.493604i
$151$	−9.63772	−	16.6930i	−0.784306	−	1.35846i	−0.929413	−	0.369043i	$-0.879686\pi$
$151$	−9.63772	−	16.6930i	−0.784306	−	1.35846i	0.145106	−	0.989416i	$-0.453648\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$	5.79751			0.468701
$154$	0.659257	+	0.327314i	0.0531244	+	0.0263757i
$155$	−25.4392			−2.04332
$156$	3.46130	−	5.99515i	0.277126	−	0.479996i
$157$	10.7284	+	18.5822i	0.856222	+	1.48302i	0.875507	+	0.483206i	$0.160528\pi$
$157$	10.7284	+	18.5822i	0.856222	+	1.48302i	−0.0192847	+	0.999814i	$0.506139\pi$
$158$	0.703803	+	1.21902i	0.0559915	+	0.0969802i
$159$	4.19411	−	7.26442i	0.332615	−	0.576106i
$160$	3.46130			0.273640
$161$	6.81489	−	4.52713i	0.537089	−	0.356788i
$162$	−1.00000			−0.0785674
$163$	−7.97231	+	13.8084i	−0.624439	+	1.08156i	0.364209	+	0.931317i	$0.381339\pi$
$163$	−7.97231	+	13.8084i	−0.624439	+	1.08156i	−0.988649	+	0.150244i	$0.951994\pi$
$164$	−4.44277	−	7.69509i	−0.346922	−	0.600886i
$165$	−0.481462	−	0.833916i	−0.0374817	−	0.0649203i
$166$	−0.0730150	+	0.126466i	−0.00566706	+	0.00981564i
$167$	17.6073			1.36250			0.681248	−	0.732053i	$-0.261437\pi$
$167$	17.6073			1.36250			0.681248	+	0.732053i	$0.261437\pi$
$168$	0.165947	+	2.64054i	0.0128031	+	0.203722i
$169$	34.9225			2.68634
$170$	−10.0335	+	17.3785i	−0.769533	+	1.33287i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−5.18526	−	8.98114i	−0.395373	−	0.684806i
$173$	−5.00531	+	8.66945i	−0.380547	+	0.659126i	−0.991140	−	0.132818i	$-0.957598\pi$
$173$	−5.00531	+	8.66945i	−0.380547	+	0.659126i	0.610594	+	0.791944i	$0.290931\pi$
$174$	−8.55364			−0.648449
$175$	1.15842	+	18.4326i	0.0875680	+	1.39338i
$176$	0.278197			0.0209699
$177$	−3.89738	+	6.75046i	−0.292945	+	0.507395i
$178$	−6.85037	−	11.8652i	−0.513457	−	0.889334i
$179$	−3.12941	−	5.42029i	−0.233903	−	0.405132i	0.725050	−	0.688696i	$-0.241816\pi$
$179$	−3.12941	−	5.42029i	−0.233903	−	0.405132i	−0.958953	+	0.283564i	$0.908483\pi$
$180$	1.73065	−	2.99758i	0.128995	−	0.223426i
$181$	−4.25019			−0.315914			−0.157957	−	0.987446i	$-0.550491\pi$
$181$	−4.25019			−0.315914			−0.157957	+	0.987446i	$0.550491\pi$
$182$	−15.2561	+	10.1346i	−1.13085	+	0.751226i
$183$	−9.12941			−0.674865
$184$	1.54617	−	2.67804i	0.113985	−	0.197428i
$185$	−9.07055	−	15.7107i	−0.666880	−	1.15507i
$186$	−3.67480	−	6.36493i	−0.269449	−	0.466700i
$187$	−0.806425	+	1.39677i	−0.0589716	+	0.102142i
$188$	−1.79320			−0.130782
$189$	2.36975	+	1.17656i	0.172374	+	0.0855819i
$190$	3.46130			0.251109
$191$	5.47393	−	9.48112i	0.396080	−	0.686030i	−0.597159	−	0.802123i	$-0.703704\pi$
$191$	5.47393	−	9.48112i	0.396080	−	0.686030i	0.993238	+	0.116093i	$0.0370371\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−10.6449	−	18.4376i	−0.766240	−	1.32717i	−0.939588	−	0.342306i	$-0.888792\pi$
$193$	−10.6449	−	18.4376i	−0.766240	−	1.32717i	0.173348	−	0.984861i	$-0.444541\pi$
$194$	2.04617	−	3.54406i	0.146906	−	0.254449i
$195$	23.9612			1.71590
$196$	2.71349	−	6.45267i	0.193821	−	0.460905i
$197$	−6.63103			−0.472441			−0.236221	−	0.971699i	$-0.575909\pi$
$197$	−6.63103			−0.472441			−0.236221	+	0.971699i	$0.575909\pi$
$198$	0.139098	−	0.240925i	0.00988529	−	0.0171218i
$199$	3.93523	+	6.81602i	0.278961	+	0.483175i	0.971127	−	0.238564i	$-0.0766766\pi$
$199$	3.93523	+	6.81602i	0.278961	+	0.483175i	−0.692166	+	0.721739i	$0.743343\pi$
$200$	3.49031	+	6.04539i	0.246802	+	0.427474i
$201$	−6.86891	+	11.8973i	−0.484495	+	0.839171i
$202$	2.45699			0.172873
$203$	20.2700	+	10.0638i	1.42267	+	0.706343i
$204$	−5.79751			−0.405907
$205$	15.3778	−	26.6351i	1.07403	−	1.86027i
$206$	8.67342	+	15.0228i	0.604306	+	1.04669i
$207$	−1.54617	−	2.67804i	−0.107466	−	0.186137i
$208$	−3.46130	+	5.99515i	−0.239998	+	0.415689i
$209$	0.278197			0.0192433
$210$	−7.62803	+	5.06730i	−0.526384	+	0.349677i
$211$	14.9123			1.02660			0.513302	−	0.858208i	$-0.328422\pi$
$211$	14.9123			1.02660			0.513302	+	0.858208i	$0.328422\pi$
$212$	−4.19411	+	7.26442i	−0.288053	+	0.498922i
$213$	0.342363	+	0.592991i	0.0234583	+	0.0406311i
$214$	−5.73896	−	9.94017i	−0.392307	−	0.679496i
$215$	17.9478	−	31.0865i	1.22403	−	2.12008i
$216$	1.00000			0.0680414
$217$	1.21965	+	19.4069i	0.0827949	+	1.31743i
$218$	18.6814			1.26526
$219$	−0.962682	+	1.66741i	−0.0650520	+	0.112673i
$220$	0.481462	+	0.833916i	0.0324601	+	0.0562226i
$221$	−20.0670	−	34.7570i	−1.34985	−	2.33801i
$222$	2.62056	−	4.53894i	0.175880	−	0.304634i
$223$	3.92861			0.263079			0.131539	−	0.991311i	$-0.458008\pi$
$223$	3.92861			0.263079			0.131539	+	0.991311i	$0.458008\pi$
$224$	−0.165947	−	2.64054i	−0.0110878	−	0.176429i
$225$	6.98062			0.465375
$226$	1.64957	−	2.85713i	0.109728	−	0.190054i
$227$	3.51985	+	6.09657i	0.233621	+	0.404643i	0.958871	−	0.283842i	$-0.0916092\pi$
$227$	3.51985	+	6.09657i	0.233621	+	0.404643i	−0.725250	+	0.688486i	$0.758276\pi$
$228$	0.500000	+	0.866025i	0.0331133	+	0.0573539i
$229$	−2.94199	+	5.09567i	−0.194412	+	0.336731i	−0.946708	−	0.322094i	$-0.895613\pi$
$229$	−2.94199	+	5.09567i	−0.194412	+	0.336731i	0.752296	+	0.658826i	$0.228947\pi$
$230$	10.7035			0.705768
$231$	−0.613091	+	0.407276i	−0.0403384	+	0.0267968i
$232$	8.55364			0.561574
$233$	−1.40329	+	2.43057i	−0.0919326	+	0.159232i	−0.908324	−	0.418267i	$-0.862638\pi$
$233$	−1.40329	+	2.43057i	−0.0919326	+	0.159232i	0.816392	+	0.577499i	$0.195971\pi$
$234$	3.46130	+	5.99515i	0.226272	+	0.391915i
$235$	−3.10340	−	5.37525i	−0.202444	−	0.350643i
$236$	3.89738	−	6.75046i	0.253698	−	0.439417i
$237$	−1.40761			−0.0914338
$238$	13.7387	+	6.82110i	0.890545	+	0.442146i
$239$	−12.4016			−0.802193			−0.401097	−	0.916036i	$-0.631371\pi$
$239$	−12.4016			−0.802193			−0.401097	+	0.916036i	$0.631371\pi$
$240$	−1.73065	+	2.99758i	−0.111713	+	0.193493i
$241$	7.59824	+	13.1605i	0.489446	+	0.847745i	0.999926	−	0.0121442i	$-0.00386573\pi$
$241$	7.59824	+	13.1605i	0.489446	+	0.847745i	−0.510480	+	0.859889i	$0.670532\pi$
$242$	−5.46130	−	9.45925i	−0.351066	−	0.608064i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	9.12941			0.584450
$245$	24.0385	−	3.03342i	1.53576	−	0.193798i
$246$	8.88553			0.566521
$247$	−3.46130	+	5.99515i	−0.220237	+	0.381462i
$248$	3.67480	+	6.36493i	0.233350	+	0.404174i
$249$	−0.0730150	−	0.126466i	−0.00462714	−	0.00801443i
$250$	−3.42776	+	5.93706i	−0.216791	+	0.375493i
$251$	5.91198			0.373161			0.186581	−	0.982440i	$-0.440259\pi$
$251$	5.91198			0.373161			0.186581	+	0.982440i	$0.440259\pi$
$252$	−2.36975	−	1.17656i	−0.149280	−	0.0741161i
$253$	0.860277			0.0540851
$254$	−1.72849	+	2.99384i	−0.108455	+	0.187850i
$255$	−10.0335	−	17.3785i	−0.628321	−	1.08828i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.702424	+	1.21663i	−0.0438160	+	0.0758915i	−0.887102	−	0.461574i	$-0.847285\pi$
$257$	−0.702424	+	1.21663i	−0.0438160	+	0.0758915i	0.843286	+	0.537466i	$0.180618\pi$
$258$	10.3705			0.645641
$259$	−11.5504	+	7.67292i	−0.717707	+	0.476772i
$260$	−23.9612			−1.48601
$261$	4.27682	−	7.40767i	0.264728	−	0.458523i
$262$	9.24781	+	16.0177i	0.571332	+	0.989575i
$263$	5.38907	+	9.33414i	0.332304	+	0.575568i	0.982963	−	0.183802i	$-0.0588406\pi$
$263$	5.38907	+	9.33414i	0.332304	+	0.575568i	−0.650659	+	0.759370i	$0.725507\pi$
$264$	−0.139098	+	0.240925i	−0.00856091	+	0.0148279i
$265$	−29.0342			−1.78356
$266$	−0.165947	−	2.64054i	−0.0101749	−	0.161902i
$267$	13.7007			0.838472
$268$	6.86891	−	11.8973i	0.419585	−	0.726743i
$269$	−11.2231	−	19.4390i	−0.684286	−	1.18522i	−0.973661	−	0.228002i	$-0.926781\pi$
$269$	−11.2231	−	19.4390i	−0.684286	−	1.18522i	0.289375	−	0.957216i	$-0.406553\pi$
$270$	1.73065	+	2.99758i	0.105324	+	0.182427i
$271$	1.13826	−	1.97152i	0.0691442	−	0.119761i	−0.829381	−	0.558684i	$-0.811306\pi$
$271$	1.13826	−	1.97152i	0.0691442	−	0.119761i	0.898525	+	0.438923i	$0.144640\pi$
$272$	5.79751			0.351526
$273$	−1.14879	−	18.2794i	−0.0695278	−	1.10632i
$274$	12.1680			0.735098
$275$	−0.970993	+	1.68181i	−0.0585531	+	0.101417i
$276$	1.54617	+	2.67804i	0.0930683	+	0.161199i
$277$	−13.7260	−	23.7742i	−0.824717	−	1.42845i	−0.902135	−	0.431454i	$-0.858001\pi$
$277$	−13.7260	−	23.7742i	−0.824717	−	1.42845i	0.0774178	−	0.996999i	$-0.475332\pi$
$278$	−1.45915	+	2.52731i	−0.0875137	+	0.151578i
$279$	7.34959			0.440009
$280$	7.62803	−	5.06730i	0.455862	−	0.302829i
$281$	8.14279			0.485758			0.242879	−	0.970057i	$-0.421908\pi$
$281$	8.14279			0.485758			0.242879	+	0.970057i	$0.421908\pi$
$282$	0.896599	−	1.55296i	0.0533917	−	0.0924771i
$283$	4.09293	+	7.08917i	0.243300	+	0.421407i	0.961652	−	0.274272i	$-0.0884369\pi$
$283$	4.09293	+	7.08917i	0.243300	+	0.421407i	−0.718353	+	0.695679i	$0.755104\pi$
$284$	−0.342363	−	0.592991i	−0.0203155	−	0.0351875i
$285$	−1.73065	+	2.99758i	−0.102515	+	0.177561i
$286$	−1.92585			−0.113878
$287$	−21.0565	−	10.4543i	−1.24293	−	0.617099i
$288$	−1.00000			−0.0589256
$289$	−8.30558	+	14.3857i	−0.488564	+	0.846217i
$290$	14.8034	+	25.6402i	0.869283	+	1.50564i
$291$	2.04617	+	3.54406i	0.119948	+	0.207757i
$292$	0.962682	−	1.66741i	0.0563367	−	0.0975781i
$293$	−19.3421			−1.12998			−0.564988	−	0.825099i	$-0.691119\pi$
$293$	−19.3421			−1.12998			−0.564988	+	0.825099i	$0.691119\pi$
$294$	4.23143	+	5.57629i	0.246782	+	0.325216i
$295$	26.9800			1.57084
$296$	−2.62056	+	4.53894i	−0.152317	+	0.263821i
$297$	0.139098	+	0.240925i	0.00807131	+	0.0139799i
$298$	−2.08246	−	3.60693i	−0.120634	−	0.208944i
$299$	−10.7035	+	18.5390i	−0.618999	+	1.07214i
$300$	−6.98062			−0.403026
$301$	−24.5756	−	12.2015i	−1.41651	−	0.703283i
$302$	−19.2754			−1.10918
$303$	−1.22849	+	2.12781i	−0.0705751	+	0.122240i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	15.7998	+	27.3661i	0.904695	+	1.56698i
$306$	2.89876	−	5.02079i	0.165711	−	0.287020i
$307$	−11.7007			−0.667797			−0.333898	−	0.942609i	$-0.608364\pi$
$307$	−11.7007			−0.667797			−0.333898	+	0.942609i	$0.608364\pi$
$308$	0.613091	−	0.407276i	0.0349341	−	0.0232067i
$309$	−17.3468			−0.986827
$310$	−12.7196	+	22.0310i	−0.722424	+	1.25127i
$311$	−6.92776	−	11.9992i	−0.392837	−	0.680414i	0.599985	−	0.800011i	$-0.295173\pi$
$311$	−6.92776	−	11.9992i	−0.392837	−	0.680414i	−0.992823	+	0.119597i	$0.961840\pi$
$312$	−3.46130	−	5.99515i	−0.195958	−	0.339409i
$313$	0.985994	−	1.70779i	0.0557317	−	0.0965301i	−0.836814	−	0.547488i	$-0.815584\pi$
$313$	0.985994	−	1.70779i	0.0557317	−	0.0965301i	0.892545	+	0.450958i	$0.148918\pi$
$314$	21.4569			1.21088
$315$	−0.574394	−	9.13972i	−0.0323634	−	0.514965i
$316$	1.40761			0.0791840
$317$	−9.95023	+	17.2343i	−0.558861	+	0.967975i	0.438731	+	0.898618i	$0.355428\pi$
$317$	−9.95023	+	17.2343i	−0.558861	+	0.967975i	−0.997592	+	0.0693570i	$0.977905\pi$
$318$	−4.19411	−	7.26442i	−0.235194	−	0.407368i
$319$	1.18980	+	2.06079i	0.0666158	+	0.115382i
$320$	1.73065	−	2.99758i	0.0967464	−	0.167570i
$321$	11.4779			0.640635
$322$	−0.513164	−	8.16543i	−0.0285975	−	0.455042i
$323$	5.79751			0.322582
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−24.1620	−	41.8499i	−1.34027	−	2.32141i
$326$	7.97231	+	13.8084i	0.441545	+	0.764779i
$327$	−9.34068	+	16.1785i	−0.516541	+	0.894675i
$328$	−8.88553			−0.490621
$329$	−3.95185	+	2.62522i	−0.217873	+	0.144733i
$330$	−0.962923			−0.0530072
$331$	2.33381	−	4.04228i	0.128278	−	0.222184i	−0.794732	−	0.606961i	$-0.792388\pi$
$331$	2.33381	−	4.04228i	0.128278	−	0.222184i	0.923009	+	0.384777i	$0.125722\pi$
$332$	0.0730150	+	0.126466i	0.00400722	+	0.00694070i
$333$	2.62056	+	4.53894i	0.143606	+	0.248733i
$334$	8.80367	−	15.2484i	0.481715	−	0.834355i
$335$	47.5508			2.59798
$336$	2.36975	+	1.17656i	0.129280	+	0.0641864i
$337$	−11.4639			−0.624480			−0.312240	−	0.950003i	$-0.601079\pi$
$337$	−11.4639			−0.624480			−0.312240	+	0.950003i	$0.601079\pi$
$338$	17.4612	−	30.2438i	0.949766	−	1.64504i
$339$	1.64957	+	2.85713i	0.0895922	+	0.155178i
$340$	10.0335	+	17.3785i	0.544142	+	0.942481i
$341$	−1.02232	+	1.77070i	−0.0553615	+	0.0958890i
$342$	−1.00000			−0.0540738
$343$	−3.46661	−	18.1929i	−0.187180	−	0.982326i
$344$	−10.3705			−0.559141
$345$	−5.35175	+	9.26950i	−0.288129	+	0.499053i
$346$	5.00531	+	8.66945i	0.269087	+	0.466073i
$347$	−3.92129	−	6.79187i	−0.210506	−	0.364607i	0.741367	−	0.671100i	$-0.234178\pi$
$347$	−3.92129	−	6.79187i	−0.210506	−	0.364607i	−0.951873	+	0.306493i	$0.900844\pi$
$348$	−4.27682	+	7.40767i	−0.229261	+	0.397093i
$349$	21.2991			1.14012			0.570058	−	0.821604i	$-0.306921\pi$
$349$	21.2991			1.14012			0.570058	+	0.821604i	$0.306921\pi$
$350$	16.5423	+	8.21309i	0.884224	+	0.439008i
$351$	−6.92261			−0.369501
$352$	0.139098	−	0.240925i	0.00741397	−	0.0128414i
$353$	−4.35850	−	7.54915i	−0.231980	−	0.401801i	0.726411	−	0.687261i	$-0.241187\pi$
$353$	−4.35850	−	7.54915i	−0.231980	−	0.401801i	−0.958391	+	0.285460i	$0.907854\pi$
$354$	3.89738	+	6.75046i	0.207143	+	0.358783i
$355$	1.18502	−	2.05252i	0.0628945	−	0.108936i
$356$	−13.7007			−0.726138
$357$	−12.7766	+	8.48748i	−0.676208	+	0.449205i
$358$	−6.25882			−0.330789
$359$	−0.585642	+	1.01436i	−0.0309090	+	0.0535359i	−0.881066	−	0.472993i	$-0.843174\pi$
$359$	−0.585642	+	1.01436i	−0.0309090	+	0.0535359i	0.850157	+	0.526529i	$0.176507\pi$
$360$	−1.73065	−	2.99758i	−0.0912134	−	0.157986i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−2.12509	+	3.68077i	−0.111692	+	0.193457i
$363$	10.9226			0.573288
$364$	1.14879	+	18.2794i	0.0602129	+	0.958103i
$365$	6.66427			0.348824
$366$	−4.56470	+	7.90630i	−0.238601	+	0.413269i
$367$	−2.50647	−	4.34134i	−0.130837	−	0.226616i	0.793163	−	0.609010i	$-0.208433\pi$
$367$	−2.50647	−	4.34134i	−0.130837	−	0.226616i	−0.923999	+	0.382394i	$0.875100\pi$
$368$	−1.54617	−	2.67804i	−0.0805995	−	0.139602i
$369$	−4.44277	+	7.69509i	−0.231281	+	0.400591i
$370$	−18.1411			−0.943111
$371$	1.39200	+	22.1495i	0.0722692	+	1.14994i
$372$	−7.34959			−0.381059
$373$	−0.932921	+	1.61587i	−0.0483048	+	0.0836664i	−0.889167	−	0.457583i	$-0.848715\pi$
$373$	−0.932921	+	1.61587i	−0.0483048	+	0.0836664i	0.840862	+	0.541250i	$0.182049\pi$
$374$	0.806425	+	1.39677i	0.0416992	+	0.0722252i
$375$	−3.42776	−	5.93706i	−0.177009	−	0.306589i
$376$	−0.896599	+	1.55296i	−0.0462386	+	0.0800875i
$377$	−59.2135			−3.04965
$378$	2.20380	−	1.46399i	0.113351	−	0.0752993i
$379$	−11.8065			−0.606457			−0.303228	−	0.952918i	$-0.598065\pi$
$379$	−11.8065			−0.606457			−0.303228	+	0.952918i	$0.598065\pi$
$380$	1.73065	−	2.99758i	0.0887806	−	0.153772i
$381$	−1.72849	−	2.99384i	−0.0885534	−	0.153379i
$382$	−5.47393	−	9.48112i	−0.280071	−	0.485097i
$383$	−2.76320	+	4.78600i	−0.141193	+	0.244553i	−0.927946	−	0.372715i	$-0.878427\pi$
$383$	−2.76320	+	4.78600i	−0.141193	+	0.244553i	0.786753	+	0.617268i	$0.211760\pi$
$384$	1.00000			0.0510310
$385$	2.28189	+	1.13293i	0.116296	+	0.0577396i
$386$	−21.2899			−1.08363
$387$	−5.18526	+	8.98114i	−0.263582	+	0.456537i
$388$	−2.04617	−	3.54406i	−0.103878	−	0.179923i
$389$	−0.632104	−	1.09484i	−0.0320490	−	0.0555104i	0.849556	−	0.527498i	$-0.176870\pi$
$389$	−0.632104	−	1.09484i	−0.0320490	−	0.0555104i	−0.881605	+	0.471988i	$0.843537\pi$
$390$	11.9806	−	20.7510i	0.606662	−	1.05077i
$391$	17.9278			0.906650
$392$	−4.23143	−	5.57629i	−0.213720	−	0.281645i
$393$	−18.4956			−0.932981
$394$	−3.31551	+	5.74264i	−0.167033	+	0.289310i
$395$	2.43607	+	4.21940i	0.122572	+	0.212301i
$396$	−0.139098	−	0.240925i	−0.00698996	−	0.0121070i
$397$	0.702424	−	1.21663i	0.0352536	−	0.0610611i	−0.847860	−	0.530220i	$-0.822109\pi$
$397$	0.702424	−	1.21663i	0.0352536	−	0.0610611i	0.883114	+	0.469159i	$0.155443\pi$
$398$	7.87047			0.394511
$399$	2.36975	+	1.17656i	0.118636	+	0.0589015i
$400$	6.98062			0.349031
$401$	2.38559	−	4.13197i	0.119131	−	0.206341i	−0.800293	−	0.599610i	$-0.795323\pi$
$401$	2.38559	−	4.13197i	0.119131	−	0.206341i	0.919423	+	0.393269i	$0.128656\pi$
$402$	6.86891	+	11.8973i	0.342590	+	0.593383i
$403$	−25.4392	−	44.0619i	−1.26722	−	2.19488i
$404$	1.22849	−	2.12781i	0.0611198	−	0.105863i
$405$	−3.46130			−0.171994
$406$	18.8505	−	12.5224i	0.935536	−	0.621476i
$407$	−1.45806			−0.0722735
$408$	−2.89876	+	5.02079i	−0.143510	+	0.248566i
$409$	9.04448	+	15.6655i	0.447221	+	0.774609i	0.998204	−	0.0599071i	$-0.0190804\pi$
$409$	9.04448	+	15.6655i	0.447221	+	0.774609i	−0.550983	+	0.834516i	$0.685747\pi$
$410$	−15.3778	−	26.6351i	−0.759453	−	1.31541i
$411$	−6.08402	+	10.5378i	−0.300103	+	0.519793i
$412$	17.3468			0.854617
$413$	−1.29352	−	20.5824i	−0.0636499	−	1.01279i
$414$	−3.09233			−0.151980
$415$	−0.252727	+	0.437736i	−0.0124059	+	0.0214876i
$416$	3.46130	+	5.99515i	0.169704	+	0.293937i
$417$	−1.45915	−	2.52731i	−0.0714547	−	0.123763i
$418$	0.139098	−	0.240925i	0.00680353	−	0.0117841i
$419$	2.70518			0.132157			0.0660784	−	0.997814i	$-0.478951\pi$
$419$	2.70518			0.132157			0.0660784	+	0.997814i	$0.478951\pi$
$420$	0.574394	+	9.13972i	0.0280276	+	0.445972i
$421$	6.14064			0.299276			0.149638	−	0.988741i	$-0.452189\pi$
$421$	6.14064			0.299276			0.149638	+	0.988741i	$0.452189\pi$
$422$	7.45615	−	12.9144i	0.362960	−	0.628664i
$423$	0.896599	+	1.55296i	0.0435941	+	0.0755073i
$424$	4.19411	+	7.26442i	0.203684	+	0.352791i
$425$	−20.2351	+	35.0483i	−0.981548	+	1.70009i
$426$	0.684727			0.0331751
$427$	20.1194	−	13.3653i	0.973647	−	0.646793i
$428$	−11.4779			−0.554806
$429$	0.962923	−	1.66783i	0.0464904	−	0.0805237i
$430$	−17.9478	−	31.0865i	−0.865518	−	1.49912i
$431$	−10.6383	−	18.4260i	−0.512427	−	0.887549i	−0.999896	−	0.0144092i	$-0.995413\pi$
$431$	−10.6383	−	18.4260i	−0.512427	−	0.887549i	0.487469	−	0.873140i	$-0.337920\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−9.42099			−0.452744			−0.226372	−	0.974041i	$-0.572686\pi$
$433$	−9.42099			−0.452744			−0.226372	+	0.974041i	$0.572686\pi$
$434$	17.4167	+	8.64721i	0.836028	+	0.415079i
$435$	−29.6067			−1.41953
$436$	9.34068	−	16.1785i	0.447337	−	0.774811i
$437$	−1.54617	−	2.67804i	−0.0739632	−	0.128108i
$438$	0.962682	+	1.66741i	0.0459987	+	0.0796722i
$439$	−6.29620	+	10.9053i	−0.300501	+	0.520483i	−0.976250	−	0.216649i	$-0.930487\pi$
$439$	−6.29620	+	10.9053i	−0.300501	+	0.520483i	0.675748	+	0.737132i	$0.263821\pi$
$440$	0.962923			0.0459056
$441$	−6.94492	+	0.876382i	−0.330711	+	0.0417325i
$442$	−40.1339			−1.90898
$443$	11.6473	−	20.1738i	0.553382	−	0.958486i	−0.444645	−	0.895707i	$-0.646670\pi$
$443$	11.6473	−	20.1738i	0.553382	−	0.958486i	0.998027	−	0.0627792i	$-0.0199964\pi$
$444$	−2.62056	−	4.53894i	−0.124366	−	0.215409i
$445$	−23.7112	−	41.0690i	−1.12402	−	1.94686i
$446$	1.96430	−	3.40227i	0.0930124	−	0.161102i
$447$	4.16493			0.196994
$448$	−2.36975	−	1.17656i	−0.111960	−	0.0555871i
$449$	−0.486074			−0.0229393			−0.0114696	−	0.999934i	$-0.503651\pi$
$449$	−0.486074			−0.0229393			−0.0114696	+	0.999934i	$0.503651\pi$
$450$	3.49031	−	6.04539i	0.164535	−	0.284983i
$451$	−1.23596	−	2.14075i	−0.0581992	−	0.100804i
$452$	−1.64957	−	2.85713i	−0.0775891	−	0.134388i
$453$	9.63772	−	16.6930i	0.452820	−	0.784306i
$454$	7.03971			0.330390
$455$	−52.8058	+	35.0789i	−2.47558	+	1.64452i
$456$	1.00000			0.0468293
$457$	−7.22987	+	12.5225i	−0.338199	+	0.585778i	−0.984094	−	0.177648i	$-0.943151\pi$
$457$	−7.22987	+	12.5225i	−0.338199	+	0.585778i	0.645895	+	0.763426i	$0.276484\pi$
$458$	2.94199	+	5.09567i	0.137470	+	0.238105i
$459$	2.89876	+	5.02079i	0.135302	+	0.234351i
$460$	5.35175	−	9.26950i	0.249527	−	0.432193i
$461$	18.0188			0.839218			0.419609	−	0.907705i	$-0.362167\pi$
$461$	18.0188			0.839218			0.419609	+	0.907705i	$0.362167\pi$
$462$	0.0461660	+	0.734590i	0.00214784	+	0.0341762i
$463$	23.3408			1.08474			0.542370	−	0.840140i	$-0.317527\pi$
$463$	23.3408			1.08474			0.542370	+	0.840140i	$0.317527\pi$
$464$	4.27682	−	7.40767i	0.198546	−	0.343892i
$465$	−12.7196	−	22.0310i	−0.589857	−	1.02166i
$466$	1.40329	+	2.43057i	0.0650061	+	0.112594i
$467$	4.07439	−	7.05706i	0.188540	−	0.326562i	−0.756223	−	0.654314i	$-0.772958\pi$
$467$	4.07439	−	7.05706i	0.188540	−	0.326562i	0.944764	+	0.327752i	$0.106291\pi$
$468$	6.92261			0.319998
$469$	−2.27975	−	36.2753i	−0.105269	−	1.67504i
$470$	−6.20680			−0.286298
$471$	−10.7284	+	18.5822i	−0.494340	+	0.856222i
$472$	−3.89738	−	6.75046i	−0.179391	−	0.310715i
$473$	−1.44252	−	2.49852i	−0.0663273	−	0.114882i
$474$	−0.703803	+	1.21902i	−0.0323267	+	0.0559915i
$475$	6.98062			0.320293
$476$	12.7766	−	8.48748i	0.585613	−	0.389023i
$477$	8.38823			0.384070
$478$	−6.20080	+	10.7401i	−0.283618	+	0.491241i
$479$	−13.5813	−	23.5235i	−0.620547	−	1.07482i	−0.989384	−	0.145324i	$-0.953577\pi$
$479$	−13.5813	−	23.5235i	−0.620547	−	1.07482i	0.368837	−	0.929494i	$-0.379756\pi$
$480$	1.73065	+	2.99758i	0.0789931	+	0.136820i
$481$	18.1411	−	31.4213i	0.827163	−	1.43269i
$482$	15.1965			0.692181
$483$	7.32805	+	3.63830i	0.333438	+	0.165549i
$484$	−10.9226			−0.496482
$485$	7.08240	−	12.2671i	0.321595	−	0.557019i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	5.97117	+	10.3424i	0.270580	+	0.468658i	0.969010	−	0.247020i	$-0.0794513\pi$
$487$	5.97117	+	10.3424i	0.270580	+	0.468658i	−0.698431	+	0.715678i	$0.746118\pi$
$488$	4.56470	−	7.90630i	0.206634	−	0.357901i
$489$	−15.9446			−0.721041
$490$	9.39222	−	22.3346i	0.424297	−	1.00898i
$491$	−7.00863			−0.316295			−0.158148	−	0.987415i	$-0.550552\pi$
$491$	−7.00863			−0.316295			−0.158148	+	0.987415i	$0.550552\pi$
$492$	4.44277	−	7.69509i	0.200295	−	0.346922i
$493$	24.7949	+	42.9460i	1.11671	+	1.93419i
$494$	3.46130	+	5.99515i	0.155731	+	0.269735i
$495$	0.481462	−	0.833916i	0.0216401	−	0.0374817i
$496$	7.34959			0.330006
$497$	−1.62263	−	0.805620i	−0.0727850	−	0.0361370i
$498$	−0.146030			−0.00654376
$499$	4.56302	−	7.90339i	0.204269	−	0.353804i	−0.745631	−	0.666359i	$-0.767852\pi$
$499$	4.56302	−	7.90339i	0.204269	−	0.353804i	0.949900	+	0.312555i	$0.101185\pi$
$500$	3.42776	+	5.93706i	0.153294	+	0.265513i
$501$	8.80367	+	15.2484i	0.393319	+	0.681248i
$502$	2.95599	−	5.11993i	0.131932	−	0.228514i
$503$	−24.1190			−1.07541			−0.537706	−	0.843133i	$-0.680709\pi$
$503$	−24.1190			−1.07541			−0.537706	+	0.843133i	$0.680709\pi$
$504$	−2.20380	+	1.46399i	−0.0981652	+	0.0652111i
$505$	8.50438			0.378440
$506$	0.430138	−	0.745022i	0.0191220	−	0.0331203i
$507$	17.4612	+	30.2438i	0.775481	+	1.34317i
$508$	1.72849	+	2.99384i	0.0766895	+	0.132830i
$509$	18.7531	−	32.4813i	0.831215	−	1.43971i	−0.0658607	−	0.997829i	$-0.520979\pi$
$509$	18.7531	−	32.4813i	0.831215	−	1.43971i	0.897075	−	0.441877i	$-0.145687\pi$
$510$	−20.0670			−0.888580
$511$	−0.319509	−	5.08401i	−0.0141343	−	0.224903i
$512$	−1.00000			−0.0441942
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$	0.702424	+	1.21663i	0.0309826	+	0.0536634i
$515$	30.0213	+	51.9985i	1.32290	+	2.29133i
$516$	5.18526	−	8.98114i	0.228269	−	0.395373i
$517$	−0.498862			−0.0219399
$518$	0.869750	+	13.8394i	0.0382146	+	0.608068i
$519$	−10.0106			−0.439418
$520$	−11.9806	+	20.7510i	−0.525385	+	0.909993i
$521$	−21.1025	−	36.5506i	−0.924516	−	1.60131i	−0.792338	−	0.610083i	$-0.791136\pi$
$521$	−21.1025	−	36.5506i	−0.924516	−	1.60131i	−0.132179	−	0.991226i	$-0.542197\pi$
$522$	−4.27682	−	7.40767i	−0.187191	−	0.324225i
$523$	−9.54692	+	16.5358i	−0.417458	+	0.723058i	−0.995683	−	0.0928192i	$-0.970412\pi$
$523$	−9.54692	+	16.5358i	−0.417458	+	0.723058i	0.578225	+	0.815877i	$0.303745\pi$
$524$	18.4956			0.807985
$525$	−15.3839	+	10.2195i	−0.671409	+	0.446017i
$526$	10.7781			0.469949
$527$	−21.3047	+	36.9008i	−0.928046	+	1.60742i
$528$	0.139098	+	0.240925i	0.00605348	+	0.0104849i
$529$	6.71874	+	11.6372i	0.292119	+	0.505965i
$530$	−14.5171	+	25.1443i	−0.630582	+	1.09220i
$531$	−7.79476			−0.338264
$532$	−2.36975	−	1.17656i	−0.102742	−	0.0510102i
$533$	61.5110			2.66434
$534$	6.85037	−	11.8652i	0.296445	−	0.513457i
$535$	−19.8643	−	34.4060i	−0.858808	−	1.48750i
$536$	−6.86891	−	11.8973i	−0.296692	−	0.513885i
$537$	3.12941	−	5.42029i	0.135044	−	0.233903i
$538$	−22.4462			−0.967726
$539$	0.754885	−	1.79511i	0.0325152	−	0.0773210i
$540$	3.46130			0.148951
$541$	−0.393062	+	0.680803i	−0.0168991	+	0.0292700i	−0.874351	−	0.485294i	$-0.838713\pi$
$541$	−0.393062	+	0.680803i	−0.0168991	+	0.0292700i	0.857452	+	0.514564i	$0.172046\pi$
$542$	−1.13826	−	1.97152i	−0.0488923	−	0.0846840i
$543$	−2.12509	−	3.68077i	−0.0911965	−	0.157957i
$544$	2.89876	−	5.02079i	0.124283	−	0.215265i
$545$	64.6619			2.76981
$546$	−16.4048	−	8.14484i	−0.702063	−	0.348567i
$547$	0.670738			0.0286787			0.0143394	−	0.999897i	$-0.495435\pi$
$547$	0.670738			0.0286787			0.0143394	+	0.999897i	$0.495435\pi$
$548$	6.08402	−	10.5378i	0.259897	−	0.450154i
$549$	−4.56470	−	7.90630i	−0.194817	−	0.337433i
$550$	0.970993	+	1.68181i	0.0414033	+	0.0717126i
$551$	4.27682	−	7.40767i	0.182199	−	0.315577i
$552$	3.09233			0.131618
$553$	3.10208	−	2.06071i	0.131914	−	0.0876305i
$554$	−27.4521			−1.16633
$555$	9.07055	−	15.7107i	0.385024	−	0.666880i
$556$	1.45915	+	2.52731i	0.0618815	+	0.107182i
$557$	−3.07649	−	5.32864i	−0.130355	−	0.225782i	0.793458	−	0.608624i	$-0.208278\pi$
$557$	−3.07649	−	5.32864i	−0.130355	−	0.225782i	−0.923813	+	0.382843i	$0.874945\pi$
$558$	3.67480	−	6.36493i	0.155567	−	0.269449i
$559$	71.7911			3.03644
$560$	−0.574394	−	9.13972i	−0.0242726	−	0.386224i
$561$	−1.61285			−0.0680946
$562$	4.07139	−	7.05186i	0.171741	−	0.297465i
$563$	11.8377	+	20.5035i	0.498899	+	0.864118i	0.999999	−	0.00127111i	$-0.000404608\pi$
$563$	11.8377	+	20.5035i	0.498899	+	0.864118i	−0.501100	+	0.865389i	$0.667071\pi$
$564$	−0.896599	−	1.55296i	−0.0377536	−	0.0653912i
$565$	5.70965	−	9.88941i	0.240207	−	0.416050i
$566$	8.18586			0.344078
$567$	0.165947	+	2.64054i	0.00696913	+	0.110892i
$568$	−0.684727			−0.0287305
$569$	−18.3345	+	31.7563i	−0.768623	+	1.33129i	0.169686	+	0.985498i	$0.445725\pi$
$569$	−18.3345	+	31.7563i	−0.768623	+	1.33129i	−0.938309	+	0.345797i	$0.887609\pi$
$570$	1.73065	+	2.99758i	0.0724890	+	0.125555i
$571$	8.86399	+	15.3529i	0.370947	+	0.642498i	0.989711	−	0.143078i	$-0.0457000\pi$
$571$	8.86399	+	15.3529i	0.370947	+	0.642498i	−0.618765	+	0.785576i	$0.712367\pi$
$572$	−0.962923	+	1.66783i	−0.0402619	+	0.0697356i
$573$	10.9479			0.457353
$574$	−19.5820	+	13.0083i	−0.817335	+	0.542955i
$575$	21.5864			0.900215
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	0.616028	+	1.06699i	0.0256456	+	0.0444194i	0.878563	−	0.477626i	$-0.158503\pi$
$577$	0.616028	+	1.06699i	0.0256456	+	0.0444194i	−0.852918	+	0.522045i	$0.825169\pi$
$578$	8.30558	+	14.3857i	0.345467	+	0.598366i
$579$	10.6449	−	18.4376i	0.442389	−	0.766240i
$580$	29.6067			1.22935
$581$	0.346054	+	0.171812i	0.0143568	+	0.00712798i
$582$	4.09233			0.169633
$583$	−1.16679	+	2.02094i	−0.0483235	+	0.0836987i
$584$	−0.962682	−	1.66741i	−0.0398361	−	0.0689981i
$585$	11.9806	+	20.7510i	0.495338	+	0.857950i
$586$	−9.67104	+	16.7507i	−0.399507	+	0.691967i
$587$	−10.0714			−0.415691			−0.207845	−	0.978162i	$-0.566645\pi$
$587$	−10.0714			−0.415691			−0.207845	+	0.978162i	$0.566645\pi$
$588$	6.94492	−	0.876382i	0.286404	−	0.0361414i
$589$	7.34959			0.302835
$590$	13.4900	−	23.3654i	0.555375	−	0.961937i
$591$	−3.31551	−	5.74264i	−0.136382	−	0.236221i
$592$	2.62056	+	4.53894i	0.107704	+	0.186549i
$593$	−14.1317	+	24.4769i	−0.580320	+	1.00514i	0.415121	+	0.909766i	$0.363739\pi$
$593$	−14.1317	+	24.4769i	−0.580320	+	1.00514i	−0.995441	+	0.0953778i	$0.969594\pi$
$594$	0.278197			0.0114146
$595$	47.5537	+	23.6099i	1.94951	+	0.967912i
$596$	−4.16493			−0.170602
$597$	−3.93523	+	6.81602i	−0.161058	+	0.278961i
$598$	10.7035	+	18.5390i	0.437699	+	0.758116i
$599$	−2.13988	−	3.70638i	−0.0874330	−	0.151438i	0.818992	−	0.573804i	$-0.194533\pi$
$599$	−2.13988	−	3.70638i	−0.0874330	−	0.151438i	−0.906425	+	0.422366i	$0.861200\pi$
$600$	−3.49031	+	6.04539i	−0.142491	+	0.246802i
$601$	−47.6366			−1.94314			−0.971569	−	0.236757i	$-0.923915\pi$
$601$	−47.6366			−1.94314			−0.971569	+	0.236757i	$0.923915\pi$
$602$	−22.8546	+	15.1823i	−0.931484	+	0.618785i
$603$	−13.7378			−0.559447
$604$	−9.63772	+	16.6930i	−0.392153	+	0.679229i
$605$	−18.9032	−	32.7413i	−0.768525	−	1.33113i
$606$	1.22849	+	2.12781i	0.0499041	+	0.0864365i
$607$	10.3465	−	17.9207i	0.419953	−	0.727379i	−0.575982	−	0.817463i	$-0.695380\pi$
$607$	10.3465	−	17.9207i	0.419953	−	0.727379i	0.995934	+	0.0900833i	$0.0287133\pi$
$608$	−1.00000			−0.0405554
$609$	1.41945	+	22.5862i	0.0575191	+	0.915240i
$610$	31.5997			1.27943
$611$	6.20680	−	10.7505i	0.251100	−	0.434919i
$612$	−2.89876	−	5.02079i	−0.117175	−	0.202954i
$613$	−0.836989	−	1.44971i	−0.0338057	−	0.0585532i	0.848628	−	0.528991i	$-0.177429\pi$
$613$	−0.836989	−	1.44971i	−0.0338057	−	0.0585532i	−0.882433	+	0.470438i	$0.844096\pi$
$614$	−5.85037	+	10.1331i	−0.236102	+	0.408940i
$615$	30.7555			1.24018
$616$	−0.0461660	−	0.734590i	−0.00186008	−	0.0295975i
$617$	−13.5252			−0.544504			−0.272252	−	0.962226i	$-0.587768\pi$
$617$	−13.5252			−0.544504			−0.272252	+	0.962226i	$0.587768\pi$
$618$	−8.67342	+	15.0228i	−0.348896	+	0.604306i
$619$	−22.5780	−	39.1062i	−0.907485	−	1.57181i	−0.817547	−	0.575862i	$-0.804666\pi$
$619$	−22.5780	−	39.1062i	−0.907485	−	1.57181i	−0.0899383	−	0.995947i	$-0.528667\pi$
$620$	12.7196	+	22.0310i	0.510831	+	0.884785i
$621$	1.54617	−	2.67804i	0.0620455	−	0.107466i
$622$	−13.8555			−0.555556
$623$	−30.1937	+	20.0577i	−1.20969	+	0.803594i
$624$	−6.92261			−0.277126
$625$	5.58702	−	9.67700i	0.223481	−	0.387080i
$626$	−0.985994	−	1.70779i	−0.0394083	−	0.0682571i
$627$	0.139098	+	0.240925i	0.00555505	+	0.00962164i
$628$	10.7284	−	18.5822i	0.428111	−	0.741510i
$629$	−30.3855			−1.21155
$630$	−8.20242	−	4.07242i	−0.326792	−	0.162249i
$631$	−3.01542			−0.120042			−0.0600210	−	0.998197i	$-0.519117\pi$
$631$	−3.01542			−0.120042			−0.0600210	+	0.998197i	$0.519117\pi$
$632$	0.703803	−	1.21902i	0.0279958	−	0.0484901i
$633$	7.45615	+	12.9144i	0.296355	+	0.513302i
$634$	9.95023	+	17.2343i	0.395174	+	0.684462i
$635$	−5.98284	+	10.3626i	−0.237422	+	0.411227i
$636$	−8.38823			−0.332615
$637$	29.2925	+	38.6025i	1.16061	+	1.52948i
$638$	2.37959			0.0942090
$639$	−0.342363	+	0.592991i	−0.0135437	+	0.0234583i
$640$	−1.73065	−	2.99758i	−0.0684100	−	0.118490i
$641$	−7.99808	−	13.8531i	−0.315905	−	0.547164i	0.663724	−	0.747977i	$-0.268975\pi$
$641$	−7.99808	−	13.8531i	−0.315905	−	0.547164i	−0.979630	+	0.200813i	$0.935642\pi$
$642$	5.73896	−	9.94017i	0.226499	−	0.392307i
$643$	−20.9315			−0.825460			−0.412730	−	0.910854i	$-0.635425\pi$
$643$	−20.9315			−0.825460			−0.412730	+	0.910854i	$0.635425\pi$
$644$	−7.32805	−	3.63830i	−0.288766	−	0.143369i
$645$	35.8955			1.41339
$646$	2.89876	−	5.02079i	0.114050	−	0.197541i
$647$	−21.7099	−	37.6026i	−0.853504	−	1.47831i	−0.878026	−	0.478613i	$-0.841140\pi$
$647$	−21.7099	−	37.6026i	−0.853504	−	1.47831i	0.0245220	−	0.999699i	$-0.492194\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	1.08424	−	1.87796i	0.0425601	−	0.0737162i
$650$	−48.3241			−1.89543
$651$	−16.1970	+	10.7597i	−0.634812	+	0.421706i
$652$	15.9446			0.624439
$653$	3.03110	−	5.25002i	0.118616	−	0.205449i	−0.800603	−	0.599195i	$-0.795488\pi$
$653$	3.03110	−	5.25002i	0.118616	−	0.205449i	0.919220	+	0.393745i	$0.128821\pi$
$654$	9.34068	+	16.1785i	0.365250	+	0.632631i
$655$	32.0095	+	55.4420i	1.25071	+	2.16630i
$656$	−4.44277	+	7.69509i	−0.173461	+	0.300443i
$657$	−1.92536			−0.0751156
$658$	0.297576	+	4.73501i	0.0116007	+	0.184590i
$659$	−0.570382			−0.0222189			−0.0111095	−	0.999938i	$-0.503536\pi$
$659$	−0.570382			−0.0222189			−0.0111095	+	0.999938i	$0.503536\pi$
$660$	−0.481462	+	0.833916i	−0.0187409	+	0.0324601i
$661$	8.81981	+	15.2764i	0.343051	+	0.594181i	0.984998	−	0.172568i	$-0.0552064\pi$
$661$	8.81981	+	15.2764i	0.343051	+	0.594181i	−0.641947	+	0.766749i	$0.721873\pi$
$662$	−2.33381	−	4.04228i	−0.0907062	−	0.157108i
$663$	20.0670	−	34.7570i	0.779336	−	1.34985i
$664$	0.146030			0.00566706
$665$	−0.574394	−	9.13972i	−0.0222740	−	0.354423i
$666$	5.24112			0.203089
$667$	13.2253	−	22.9070i	0.512087	−	0.886961i
$668$	−8.80367	−	15.2484i	−0.340624	−	0.589978i
$669$	1.96430	+	3.40227i	0.0759443	+	0.131539i
$670$	23.7754	−	41.1802i	0.918523	−	1.59093i
$671$	2.53977			0.0980468
$672$	2.20380	−	1.46399i	0.0850135	−	0.0564745i
$673$	−39.1296			−1.50833			−0.754167	−	0.656682i	$-0.771959\pi$
$673$	−39.1296			−1.50833			−0.754167	+	0.656682i	$0.771959\pi$
$674$	−5.73197	+	9.92806i	−0.220787	+	0.382415i
$675$	3.49031	+	6.04539i	0.134342	+	0.232687i
$676$	−17.4612	−	30.2438i	−0.671586	−	1.16322i
$677$	−17.7074	+	30.6702i	−0.680552	+	1.17875i	0.294261	+	0.955725i	$0.404927\pi$
$677$	−17.7074	+	30.6702i	−0.680552	+	1.17875i	−0.974813	+	0.223025i	$0.928407\pi$
$678$	3.29913			0.126702
$679$	−9.69780	−	4.81486i	−0.372168	−	0.184777i
$680$	20.0670			0.769533
$681$	−3.51985	+	6.09657i	−0.134881	+	0.233621i
$682$	1.02232	+	1.77070i	0.0391465	+	0.0678038i
$683$	18.1449	+	31.4279i	0.694295	+	1.20255i	0.970418	+	0.241431i	$0.0776169\pi$
$683$	18.1449	+	31.4279i	0.694295	+	1.20255i	−0.276123	+	0.961122i	$0.589050\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$	42.1173			1.60922
$686$	−17.4888	−	6.09429i	−0.667727	−	0.232681i
$687$	−5.88397			−0.224488
$688$	−5.18526	+	8.98114i	−0.197686	+	0.342403i
$689$	−29.0342	−	50.2887i	−1.10611	−	1.91585i
$690$	5.35175	+	9.26950i	0.203738	+	0.352884i
$691$	−16.8574	+	29.1978i	−0.641284	+	1.11074i	0.343862	+	0.939020i	$0.388265\pi$
$691$	−16.8574	+	29.1978i	−0.641284	+	1.11074i	−0.985146	+	0.171717i	$0.945069\pi$
$692$	10.0106			0.380547
$693$	−0.659257	−	0.327314i	−0.0250431	−	0.0124336i
$694$	−7.84258			−0.297700
$695$	−5.05054	+	8.74780i	−0.191578	+	0.331823i
$696$	4.27682	+	7.40767i	0.162112	+	0.280787i
$697$	−25.7570	−	44.6124i	−0.975616	−	1.68982i
$698$	10.6496	−	18.4456i	0.403092	−	0.698176i
$699$	−2.80658			−0.106155
$700$	15.3839	−	10.2195i	0.581457	−	0.386262i
$701$	12.6976			0.479583			0.239791	−	0.970824i	$-0.422921\pi$
$701$	12.6976			0.479583			0.239791	+	0.970824i	$0.422921\pi$
$702$	−3.46130	+	5.99515i	−0.130638	+	0.226272i
$703$	2.62056	+	4.53894i	0.0988363	+	0.171189i
$704$	−0.139098	−	0.240925i	−0.00524247	−	0.00908022i
$705$	3.10340	−	5.37525i	0.116881	−	0.202444i
$706$	−8.71701			−0.328069
$707$	−0.407731	−	6.48778i	−0.0153343	−	0.243998i
$708$	7.79476			0.292945
$709$	10.6396	−	18.4283i	0.399578	−	0.692089i	−0.594096	−	0.804394i	$-0.702490\pi$
$709$	10.6396	−	18.4283i	0.399578	−	0.692089i	0.993674	+	0.112305i	$0.0358235\pi$
$710$	−1.18502	−	2.05252i	−0.0444731	−	0.0770297i
$711$	−0.703803	−	1.21902i	−0.0263947	−	0.0457169i
$712$	−6.85037	+	11.8652i	−0.256728	+	0.444667i
$713$	22.7274			0.851147
$714$	0.962082	+	15.3086i	0.0360050	+	0.572909i
$715$	−6.66594			−0.249292
$716$	−3.12941	+	5.42029i	−0.116951	+	0.202566i
$717$	−6.20080	−	10.7401i	−0.231573	−	0.401097i
$718$	0.585642	+	1.01436i	0.0218559	+	0.0378556i
$719$	−24.1116	+	41.7625i	−0.899210	+	1.55748i	−0.0707049	+	0.997497i	$0.522525\pi$
$719$	−24.1116	+	41.7625i	−0.899210	+	1.55748i	−0.828506	+	0.559981i	$0.810808\pi$
$720$	−3.46130			−0.128995
$721$	38.2290	−	25.3955i	1.42372	−	0.945778i
$722$	−1.00000			−0.0372161
$723$	−7.59824	+	13.1605i	−0.282582	+	0.489446i
$724$	2.12509	+	3.68077i	0.0789784	+	0.136795i
$725$	29.8548	+	51.7101i	1.10878	+	1.92046i
$726$	5.46130	−	9.45925i	0.202688	−	0.351066i
$727$	49.2945			1.82823			0.914116	−	0.405452i	$-0.132886\pi$
$727$	49.2945			1.82823			0.914116	+	0.405452i	$0.132886\pi$
$728$	16.4048	+	8.14484i	0.608004	+	0.301868i
$729$	1.00000			0.0370370
$730$	3.33214	−	5.77143i	0.123328	−	0.213610i
$731$	−30.0616	−	52.0683i	−1.11187	−	1.92582i
$732$	4.56470	+	7.90630i	0.168716	+	0.292225i
$733$	0.462145	−	0.800458i	0.0170697	−	0.0295656i	−0.857364	−	0.514710i	$-0.827900\pi$
$733$	0.462145	−	0.800458i	0.0170697	−	0.0295656i	0.874434	+	0.485144i	$0.161233\pi$
$734$	−5.01295			−0.185031
$735$	14.6463	+	19.3012i	0.540236	+	0.711936i
$736$	−3.09233			−0.113985
$737$	1.91091	−	3.30979i	0.0703892	−	0.121918i
$738$	4.44277	+	7.69509i	0.163540	+	0.283260i
$739$	−1.17588	−	2.03668i	−0.0432554	−	0.0749205i	0.843587	−	0.536992i	$-0.180440\pi$
$739$	−1.17588	−	2.03668i	−0.0432554	−	0.0749205i	−0.886843	+	0.462072i	$0.847106\pi$
$740$	−9.07055	+	15.7107i	−0.333440	+	0.577535i
$741$	−6.92261			−0.254308
$742$	19.8780	+	9.86922i	0.729744	+	0.362310i
$743$	−50.4616			−1.85126			−0.925628	−	0.378433i	$-0.876463\pi$
$743$	−50.4616			−1.85126			−0.925628	+	0.378433i	$0.876463\pi$
$744$	−3.67480	+	6.36493i	−0.134725	+	0.233350i
$745$	−7.20804	−	12.4847i	−0.264082	−	0.457404i
$746$	0.932921	+	1.61587i	0.0341567	+	0.0591611i
$747$	0.0730150	−	0.126466i	0.00267148	−	0.00462714i
$748$	1.61285			0.0589716
$749$	−25.2951	+	16.8035i	−0.924262	+	0.613987i
$750$	−6.85553			−0.250328
$751$	3.11141	−	5.38912i	0.113537	−	0.196652i	−0.803657	−	0.595093i	$-0.797115\pi$
$751$	3.11141	−	5.38912i	0.113537	−	0.196652i	0.917194	+	0.398441i	$0.130449\pi$
$752$	0.896599	+	1.55296i	0.0326956	+	0.0566304i
$753$	2.95599	+	5.11993i	0.107722	+	0.186581i
$754$	−29.6067	+	51.2804i	−1.07821	+	1.86752i
$755$	−66.7181			−2.42812
$756$	−0.165947	−	2.64054i	−0.00603545	−	0.0960356i
$757$	19.9762			0.726047			0.363023	−	0.931780i	$-0.381745\pi$
$757$	19.9762			0.726047			0.363023	+	0.931780i	$0.381745\pi$
$758$	−5.90323	+	10.2247i	−0.214415	+	0.371377i
$759$	0.430138	+	0.745022i	0.0156130	+	0.0270426i
$760$	−1.73065	−	2.99758i	−0.0627773	−	0.108734i
$761$	−7.65272	+	13.2549i	−0.277411	+	0.480490i	−0.970741	−	0.240131i	$-0.922810\pi$
$761$	−7.65272	+	13.2549i	−0.277411	+	0.480490i	0.693330	+	0.720621i	$0.256143\pi$
$762$	−3.45699			−0.125233
$763$	−3.10012	−	49.3289i	−0.112232	−	1.78583i
$764$	−10.9479			−0.396080
$765$	10.0335	−	17.3785i	0.362761	−	0.628321i
$766$	2.76320	+	4.78600i	0.0998383	+	0.172925i
$767$	26.9800	+	46.7308i	0.974192	+	1.68735i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−18.0461			−0.650761			−0.325380	−	0.945583i	$-0.605492\pi$
$769$	−18.0461			−0.650761			−0.325380	+	0.945583i	$0.605492\pi$
$770$	2.12209	−	1.40971i	0.0764749	−	0.0508023i
$771$	−1.40485			−0.0505943
$772$	−10.6449	+	18.4376i	−0.383120	+	0.663583i
$773$	20.1390	+	34.8818i	0.724351	+	1.25461i	0.959241	+	0.282590i	$0.0911937\pi$
$773$	20.1390	+	34.8818i	0.724351	+	1.25461i	−0.234890	+	0.972022i	$0.575473\pi$
$774$	5.18526	+	8.98114i	0.186380	+	0.322820i
$775$	−25.6524	+	44.4312i	−0.921460	+	1.59602i
$776$	−4.09233			−0.146906
$777$	−12.4201	−	6.16647i	−0.445570	−	0.221221i
$778$	−1.26421			−0.0453241
$779$	−4.44277	+	7.69509i	−0.159179	+	0.275705i
$780$	−11.9806	−	20.7510i	−0.428975	−	0.743007i
$781$	−0.0952444	−	0.164968i	−0.00340811	−	0.00590302i
$782$	8.96392	−	15.5260i	0.320549	−	0.555207i
$783$	8.55364			0.305682
$784$	−6.94492	+	0.876382i	−0.248033	+	0.0312994i
$785$	74.2687			2.65076
$786$	−9.24781	+	16.0177i	−0.329858	+	0.571332i
$787$	11.1428	+	19.2999i	0.397198	+	0.687966i	0.993379	−	0.114883i	$-0.0366494\pi$
$787$	11.1428	+	19.2999i	0.397198	+	0.687966i	−0.596181	+	0.802850i	$0.703316\pi$
$788$	3.31551	+	5.74264i	0.118110	+	0.204573i
$789$	−5.38907	+	9.33414i	−0.191856	+	0.332304i
$790$	4.87215			0.173343
$791$	−7.81812	−	3.88162i	−0.277980	−	0.138014i
$792$	−0.278197			−0.00988529
$793$	−31.5997	+	54.7322i	−1.12214	+	1.94360i
$794$	−0.702424	−	1.21663i	−0.0249281	−	0.0431767i
$795$	−14.5171	−	25.1443i	−0.514868	−	0.891778i
$796$	3.93523	−	6.81602i	0.139481	−	0.241588i
$797$	−11.6159			−0.411457			−0.205728	−	0.978609i	$-0.565956\pi$
$797$	−11.6159			−0.411457			−0.205728	+	0.978609i	$0.565956\pi$
$798$	2.20380	−	1.46399i	0.0780138	−	0.0518245i
$799$	−10.3961			−0.367787
$800$	3.49031	−	6.04539i	0.123401	−	0.213737i
$801$	6.85037	+	11.8652i	0.242046	+	0.419236i
$802$	−2.38559	−	4.13197i	−0.0842382	−	0.145905i
$803$	0.267815	−	0.463869i	0.00945099	−	0.0163696i
$804$	13.7378			0.484495
$805$	−1.77622	−	28.2630i	−0.0626034	−	0.996141i
$806$	−50.8783			−1.79211
$807$	11.2231	−	19.4390i	0.395073	−	0.684286i
$808$	−1.22849	−	2.12781i	−0.0432183	−	0.0748562i
$809$	10.9978	+	19.0488i	0.386664	+	0.669721i	0.991998	−	0.126250i	$-0.0402941\pi$
$809$	10.9978	+	19.0488i	0.386664	+	0.669721i	−0.605335	+	0.795971i	$0.706961\pi$
$810$	−1.73065	+	2.99758i	−0.0608089	+	0.105324i
$811$	24.2399			0.851177			0.425588	−	0.904917i	$-0.360067\pi$
$811$	24.2399			0.851177			0.425588	+	0.904917i	$0.360067\pi$
$812$	−1.41945	−	22.5862i	−0.0498130	−	0.792621i
$813$	2.27651			0.0798408
$814$	−0.729031	+	1.26272i	−0.0255525	+	0.0442583i
$815$	27.5946	+	47.7952i	0.966596	+	1.67419i
$816$	2.89876	+	5.02079i	0.101477	+	0.175763i
$817$	−5.18526	+	8.98114i	−0.181409	+	0.314210i
$818$	18.0890			0.632466
$819$	15.2561	−	10.1346i	0.533090	−	0.354131i
$820$	−30.7555			−1.07403
$821$	6.71658	−	11.6335i	0.234410	−	0.406011i	−0.724691	−	0.689074i	$-0.758017\pi$
$821$	6.71658	−	11.6335i	0.234410	−	0.406011i	0.959101	+	0.283064i	$0.0913507\pi$
$822$	6.08402	+	10.5378i	0.212205	+	0.367549i
$823$	−4.76827	−	8.25888i	−0.166211	−	0.287886i	0.770873	−	0.636988i	$-0.219820\pi$
$823$	−4.76827	−	8.25888i	−0.166211	−	0.287886i	−0.937085	+	0.349102i	$0.886487\pi$
$824$	8.67342	−	15.0228i	0.302153	−	0.523344i
$825$	−1.94199			−0.0676113
$826$	−18.4716	−	9.17097i	−0.642710	−	0.319099i
$827$	46.7140			1.62440			0.812202	−	0.583376i	$-0.198268\pi$
$827$	46.7140			1.62440			0.812202	+	0.583376i	$0.198268\pi$
$828$	−1.54617	+	2.67804i	−0.0537330	+	0.0930683i
$829$	−8.66379	−	15.0061i	−0.300906	−	0.521184i	0.675436	−	0.737419i	$-0.263956\pi$
$829$	−8.66379	−	15.0061i	−0.300906	−	0.521184i	−0.976341	+	0.216235i	$0.930622\pi$
$830$	0.252727	+	0.437736i	0.00877228	+	0.0151940i
$831$	13.7260	−	23.7742i	0.476151	−	0.824717i
$832$	6.92261			0.239998
$833$	15.7315	−	37.4094i	0.545065	−	1.29616i
$834$	−2.91829			−0.101052
$835$	30.4722	−	52.7793i	1.05453	−	1.82650i
$836$	−0.139098	−	0.240925i	−0.00481082	−	0.00833258i
$837$	3.67480	+	6.36493i	0.127020	+	0.220004i
$838$	1.35259	−	2.34276i	0.0467245	−	0.0809292i
$839$	−26.5740			−0.917435			−0.458718	−	0.888582i	$-0.651691\pi$
$839$	−26.5740			−0.917435			−0.458718	+	0.888582i	$0.651691\pi$
$840$	8.20242	+	4.07242i	0.283010	+	0.140512i
$841$	44.1647			1.52292
$842$	3.07032	−	5.31795i	0.105810	−	0.183269i
$843$	4.07139	+	7.05186i	0.140226	+	0.242879i
$844$	−7.45615	−	12.9144i	−0.256651	−	0.444533i
$845$	60.4386	−	104.683i	2.07915	−	3.60120i
$846$	1.79320			0.0616514
$847$	−24.0713	+	15.9905i	−0.827099	+	0.549441i
$848$	8.38823			0.288053
$849$	−4.09293	+	7.08917i	−0.140469	+	0.243300i
$850$	20.2351	+	35.0483i	0.694059	+	1.20215i
$851$	8.10364	+	14.0359i	0.277789	+	0.481145i
$852$	0.342363	−	0.592991i	0.0117292	−	0.0203155i
$853$	−4.35464			−0.149100			−0.0745500	−	0.997217i	$-0.523752\pi$
$853$	−4.35464			−0.149100			−0.0745500	+	0.997217i	$0.523752\pi$
$854$	−1.51500	−	24.1066i	−0.0518423	−	0.824910i
$855$	−3.46130			−0.118374
$856$	−5.73896	+	9.94017i	−0.196154	+	0.339748i
$857$	22.3505	+	38.7123i	0.763480	+	1.32239i	0.941046	+	0.338277i	$0.109844\pi$
$857$	22.3505	+	38.7123i	0.763480	+	1.32239i	−0.177567	+	0.984109i	$0.556822\pi$
$858$	−0.962923	−	1.66783i	−0.0328737	−	0.0569389i
$859$	−2.71025	+	4.69429i	−0.0924726	+	0.160167i	−0.908551	−	0.417774i	$-0.862810\pi$
$859$	−2.71025	+	4.69429i	−0.0924726	+	0.160167i	0.816078	+	0.577941i	$0.196144\pi$
$860$	−35.8955			−1.22403
$861$	−1.47453	−	23.4626i	−0.0502519	−	0.799604i
$862$	−21.2765			−0.724681
$863$	20.8794	−	36.1641i	0.710742	−	1.23104i	−0.253837	−	0.967247i	$-0.581693\pi$
$863$	20.8794	−	36.1641i	0.710742	−	1.23104i	0.964579	−	0.263795i	$-0.0849741\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	17.3249	+	30.0076i	0.589064	+	1.02029i
$866$	−4.71049	+	8.15881i	−0.160069	+	0.277248i
$867$	−16.6112			−0.564145
$868$	16.1970	−	10.7597i	0.549764	−	0.365208i
$869$	0.391591			0.0132838
$870$	−14.8034	+	25.6402i	−0.501881	+	0.869283i
$871$	47.5508	+	82.3603i	1.61120	+	2.79067i
$872$	−9.34068	−	16.1785i	−0.316315	−	0.547874i
$873$	−2.04617	+	3.54406i	−0.0692522	+	0.119948i
$874$	−3.09233			−0.104600
$875$	16.2459	+	8.06591i	0.549211	+	0.272678i
$876$	1.92536			0.0650520
$877$	−17.9700	+	31.1250i	−0.606805	+	1.05102i	0.384959	+	0.922934i	$0.374216\pi$
$877$	−17.9700	+	31.1250i	−0.606805	+	1.05102i	−0.991763	+	0.128083i	$0.959118\pi$
$878$	6.29620	+	10.9053i	0.212486	+	0.368037i
$879$	−9.67104	−	16.7507i	−0.326196	−	0.564988i
$880$	0.481462	−	0.833916i	0.0162301	−	0.0281113i
$881$	49.3541			1.66278			0.831391	−	0.555688i	$-0.187545\pi$
$881$	49.3541			1.66278			0.831391	+	0.555688i	$0.187545\pi$
$882$	−2.71349	+	6.45267i	−0.0913680	+	0.217273i
$883$	12.0927			0.406951			0.203476	−	0.979080i	$-0.434776\pi$
$883$	12.0927			0.406951			0.203476	+	0.979080i	$0.434776\pi$
$884$	−20.0670	+	34.7570i	−0.674925	+	1.16900i
$885$	13.4900	+	23.3654i	0.453462	+	0.785419i
$886$	−11.6473	−	20.1738i	−0.391300	−	0.677752i
$887$	−13.7810	+	23.8695i	−0.462722	+	0.801458i	−0.999096	−	0.0425224i	$-0.986461\pi$
$887$	−13.7810	+	23.8695i	−0.462722	+	0.801458i	0.536373	+	0.843981i	$0.319794\pi$
$888$	−5.24112			−0.175880
$889$	8.19220	+	4.06734i	0.274757	+	0.136414i
$890$	−47.4224			−1.58960
$891$	−0.139098	+	0.240925i	−0.00465997	+	0.00807131i
$892$	−1.96430	−	3.40227i	−0.0657697	−	0.113916i
$893$	0.896599	+	1.55296i	0.0300035	+	0.0519677i
$894$	2.08246	−	3.60693i	0.0696480	−	0.120634i
$895$	−21.6637			−0.724136
$896$	−2.20380	+	1.46399i	−0.0736239	+	0.0489083i
$897$	−21.4070			−0.714759
$898$	−0.243037	+	0.420953i	−0.00811025	+	0.0140474i
$899$	31.4329	+	54.4433i	1.04834	+	1.81579i
$900$	−3.49031	−	6.04539i	−0.116344	−	0.201513i
$901$	−24.3154	+	42.1156i	−0.810064	+	1.40307i
$902$	−2.47193			−0.0823061
$903$	−1.72096	−	27.3838i	−0.0572700	−	0.911276i
$904$	−3.29913			−0.109728
$905$	−7.35559	+	12.7403i	−0.244508	+	0.423500i
$906$	−9.63772	−	16.6930i	−0.320192	−	0.554588i
$907$	−20.1839	−	34.9596i	−0.670197	−	1.16082i	−0.977848	−	0.209316i	$-0.932876\pi$
$907$	−20.1839	−	34.9596i	−0.670197	−	1.16082i	0.307651	−	0.951499i	$-0.400457\pi$
$908$	3.51985	−	6.09657i	0.116810	−	0.202322i
$909$	−2.45699			−0.0814931
$910$	3.97630	+	63.2707i	0.131813	+	2.09740i
$911$	−6.02988			−0.199779			−0.0998894	−	0.994999i	$-0.531849\pi$
$911$	−6.02988			−0.199779			−0.0998894	+	0.994999i	$0.531849\pi$
$912$	0.500000	−	0.866025i	0.0165567	−	0.0286770i
$913$	0.0203125	+	0.0351823i	0.000672247	+	0.00116437i
$914$	7.22987	+	12.5225i	0.239143	+	0.414208i
$915$	−15.7998	+	27.3661i	−0.522326	+	0.904695i
$916$	5.88397			0.194412
$917$	40.7607	−	27.0773i	1.34604	−	0.894172i
$918$	5.79751			0.191346
$919$	−25.7574	+	44.6132i	−0.849659	+	1.47165i	0.0318529	+	0.999493i	$0.489859\pi$
$919$	−25.7574	+	44.6132i	−0.849659	+	1.47165i	−0.881512	+	0.472161i	$0.843474\pi$
$920$	−5.35175	−	9.26950i	−0.176442	−	0.305606i
$921$	−5.85037	−	10.1331i	−0.192776	−	0.333898i
$922$	9.00939	−	15.6047i	0.296708	−	0.513914i
$923$	4.74009			0.156022
$924$	0.659257	+	0.327314i	0.0216880	+	0.0107678i
$925$	−36.5863			−1.20295
$926$	11.6704	−	20.2138i	0.383514	−	0.664265i
$927$	−8.67342	−	15.0228i	−0.284872	−	0.493413i
$928$	−4.27682	−	7.40767i	−0.140393	−	0.243169i
$929$	4.34268	−	7.52175i	0.142479	−	0.246781i	−0.785951	−	0.618289i	$-0.787826\pi$
$929$	4.34268	−	7.52175i	0.142479	−	0.246781i	0.928430	+	0.371509i	$0.121159\pi$
$930$	−25.4392			−0.834183
$931$	−6.94492	+	0.876382i	−0.227611	+	0.0287223i
$932$	2.80658			0.0919326
$933$	6.92776	−	11.9992i	0.226805	−	0.392837i
$934$	−4.07439	−	7.05706i	−0.133318	−	0.230914i
$935$	2.79128	+	4.83464i	0.0912847	+	0.158110i
$936$	3.46130	−	5.99515i	0.113136	−	0.195958i
$937$	−59.2801			−1.93660			−0.968298	−	0.249799i	$-0.919635\pi$
$937$	−59.2801			−1.93660			−0.968298	+	0.249799i	$0.919635\pi$
$938$	−32.5552	−	16.1633i	−1.06296	−	0.527751i
$939$	1.97199			0.0643534
$940$	−3.10340	+	5.37525i	−0.101222	+	0.175321i
$941$	7.11409	+	12.3220i	0.231913	+	0.401684i	0.958371	−	0.285526i	$-0.0921683\pi$
$941$	7.11409	+	12.3220i	0.231913	+	0.401684i	−0.726458	+	0.687211i	$0.758835\pi$
$942$	10.7284	+	18.5822i	0.349551	+	0.605440i
$943$	−13.7385	+	23.7958i	−0.447387	+	0.774897i
$944$	−7.79476			−0.253698
$945$	7.62803	−	5.06730i	0.248140	−	0.164839i
$946$	−2.88505			−0.0938010
$947$	−7.80403	+	13.5170i	−0.253597	+	0.439242i	−0.964513	−	0.264034i	$-0.914947\pi$
$947$	−7.80403	+	13.5170i	−0.253597	+	0.439242i	0.710917	+	0.703276i	$0.248280\pi$
$948$	0.703803	+	1.21902i	0.0228584	+	0.0395920i
$949$	6.66427	+	11.5429i	0.216331	+	0.374697i
$950$	3.49031	−	6.04539i	0.113241	−	0.196138i
$951$	−19.9005			−0.645317
$952$	−0.962082	−	15.3086i	−0.0311813	−	0.496154i
$953$	9.11279			0.295192			0.147596	−	0.989048i	$-0.452846\pi$
$953$	9.11279			0.295192			0.147596	+	0.989048i	$0.452846\pi$
$954$	4.19411	−	7.26442i	0.135789	−	0.235194i
$955$	−18.9469	−	32.8170i	−0.613108	−	1.06193i
$956$	6.20080	+	10.7401i	0.200548	+	0.347360i
$957$	−1.18980	+	2.06079i	−0.0384607	+	0.0666158i
$958$	−27.1627			−0.877585
$959$	−2.01925	−	32.1302i	−0.0652051	−	1.03754i
$960$	3.46130			0.111713
$961$	−11.5082	+	19.9329i	−0.371234	+	0.642996i
$962$	−18.1411	−	31.4213i	−0.584893	−	1.01306i
$963$	5.73896	+	9.94017i	0.184935	+	0.320318i
$964$	7.59824	−	13.1605i	0.244723	−	0.423873i
$965$	−73.6908			−2.37219
$966$	6.81489	−	4.52713i	0.219265	−	0.145658i
$967$	−4.04494			−0.130077			−0.0650383	−	0.997883i	$-0.520717\pi$
$967$	−4.04494			−0.130077			−0.0650383	+	0.997883i	$0.520717\pi$
$968$	−5.46130	+	9.45925i	−0.175533	+	0.304032i
$969$	2.89876	+	5.02079i	0.0931215	+	0.161291i
$970$	−7.08240	−	12.2671i	−0.227402	−	0.393872i
$971$	−9.04293	+	15.6628i	−0.290201	+	0.502643i	−0.973857	−	0.227161i	$-0.927056\pi$
$971$	−9.04293	+	15.6628i	−0.290201	+	0.502643i	0.683656	+	0.729805i	$0.260389\pi$
$972$	−1.00000			−0.0320750
$973$	6.91562	+	3.43353i	0.221705	+	0.110074i
$974$	11.9423			0.382657
$975$	24.1620	−	41.8499i	0.773805	−	1.34027i
$976$	−4.56470	−	7.90630i	−0.146113	−	0.253074i
$977$	21.5756	+	37.3701i	0.690266	+	1.19558i	0.971751	+	0.236010i	$0.0758399\pi$
$977$	21.5756	+	37.3701i	0.690266	+	1.19558i	−0.281484	+	0.959566i	$0.590827\pi$
$978$	−7.97231	+	13.8084i	−0.254926	+	0.441545i
$979$	−3.81150			−0.121816
$980$	−14.6463	−	19.3012i	−0.467858	−	0.616555i
$981$	−18.6814			−0.596450
$982$	−3.50432	+	6.06965i	−0.111827	+	0.193690i
$983$	15.7958	+	27.3592i	0.503809	+	0.872622i	0.999990	+	0.00440358i	$0.00140171\pi$
$983$	15.7958	+	27.3592i	0.503809	+	0.872622i	−0.496182	+	0.868219i	$0.665265\pi$
$984$	−4.44277	−	7.69509i	−0.141630	−	0.245311i
$985$	−11.4760	+	19.8770i	−0.365656	+	0.633334i
$986$	49.5898			1.57926
$987$	−4.24943	−	2.10980i	−0.135261	−	0.0671556i
$988$	6.92261			0.220237
$989$	−16.0346	+	27.7727i	−0.509869	+	0.883120i
$990$	−0.481462	−	0.833916i	−0.0153019	−	0.0265036i
$991$	−18.3975	−	31.8655i	−0.584417	−	1.01224i	−0.994948	−	0.100394i	$-0.967990\pi$
$991$	−18.3975	−	31.8655i	−0.584417	−	1.01224i	0.410530	−	0.911847i	$-0.365344\pi$
$992$	3.67480	−	6.36493i	0.116675	−	0.202087i
$993$	4.66762			0.148123
$994$	−1.50900	+	1.00243i	−0.0478627	+	0.0317951i
$995$	27.2421			0.863632
$996$	−0.0730150	+	0.126466i	−0.00231357	+	0.00400722i
$997$	21.1562	+	36.6436i	0.670023	+	1.16051i	0.977897	+	0.209086i	$0.0670490\pi$
$997$	21.1562	+	36.6436i	0.670023	+	1.16051i	−0.307875	+	0.951427i	$0.599618\pi$
$998$	−4.56302	−	7.90339i	−0.144440	−	0.250177i
$999$	−2.62056	+	4.53894i	−0.0829109	+	0.143606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.j.l.457.4	✓	8
7.2	even	3		5586.2.a.bw.1.1		4
7.4	even	3	inner	798.2.j.l.571.4	yes	8
7.5	odd	6		5586.2.a.bz.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.l.457.4	✓	8	1.1	even	1	trivial
798.2.j.l.571.4	yes	8	7.4	even	3	inner
5586.2.a.bw.1.1		4	7.2	even	3
5586.2.a.bz.1.4		4	7.5	odd	6

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.73065 - 2.99758i) q^{5} +1.00000 q^{6} +(-2.36975 - 1.17656i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.73065 - 2.99758i) q^{5} +1.00000 q^{6} +(-2.36975 - 1.17656i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.73065 - 2.99758i) q^{10} +(-0.139098 - 0.240925i) q^{11} +(0.500000 - 0.866025i) q^{12} +6.92261 q^{13} +(-2.20380 + 1.46399i) q^{14} +3.46130 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.89876 - 5.02079i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -3.46130 q^{20} +(-0.165947 - 2.64054i) q^{21} -0.278197 q^{22} +(-1.54617 + 2.67804i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.49031 - 6.04539i) q^{25} +(3.46130 - 5.99515i) q^{26} -1.00000 q^{27} +(0.165947 + 2.64054i) q^{28} -8.55364 q^{29} +(1.73065 - 2.99758i) q^{30} +(-3.67480 - 6.36493i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.139098 - 0.240925i) q^{33} -5.79751 q^{34} +(-7.62803 + 5.06730i) q^{35} +1.00000 q^{36} +(2.62056 - 4.53894i) q^{37} +(0.500000 + 0.866025i) q^{38} +(3.46130 + 5.99515i) q^{39} +(-1.73065 + 2.99758i) q^{40} +8.88553 q^{41} +(-2.36975 - 1.17656i) q^{42} +10.3705 q^{43} +(-0.139098 + 0.240925i) q^{44} +(1.73065 + 2.99758i) q^{45} +(1.54617 + 2.67804i) q^{46} +(0.896599 - 1.55296i) q^{47} -1.00000 q^{48} +(4.23143 + 5.57629i) q^{49} -6.98062 q^{50} +(2.89876 - 5.02079i) q^{51} +(-3.46130 - 5.99515i) q^{52} +(-4.19411 - 7.26442i) q^{53} +(-0.500000 + 0.866025i) q^{54} -0.962923 q^{55} +(2.36975 + 1.17656i) q^{56} -1.00000 q^{57} +(-4.27682 + 7.40767i) q^{58} +(3.89738 + 6.75046i) q^{59} +(-1.73065 - 2.99758i) q^{60} +(-4.56470 + 7.90630i) q^{61} -7.34959 q^{62} +(2.20380 - 1.46399i) q^{63} +1.00000 q^{64} +(11.9806 - 20.7510i) q^{65} +(-0.139098 - 0.240925i) q^{66} +(6.86891 + 11.8973i) q^{67} +(-2.89876 + 5.02079i) q^{68} -3.09233 q^{69} +(0.574394 + 9.13972i) q^{70} +0.684727 q^{71} +(0.500000 - 0.866025i) q^{72} +(0.962682 + 1.66741i) q^{73} +(-2.62056 - 4.53894i) q^{74} +(3.49031 - 6.04539i) q^{75} +1.00000 q^{76} +(0.0461660 + 0.734590i) q^{77} +6.92261 q^{78} +(-0.703803 + 1.21902i) q^{79} +(1.73065 + 2.99758i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.44277 - 7.69509i) q^{82} -0.146030 q^{83} +(-2.20380 + 1.46399i) q^{84} -20.0670 q^{85} +(5.18526 - 8.98114i) q^{86} +(-4.27682 - 7.40767i) q^{87} +(0.139098 + 0.240925i) q^{88} +(6.85037 - 11.8652i) q^{89} +3.46130 q^{90} +(-16.4048 - 8.14484i) q^{91} +3.09233 q^{92} +(3.67480 - 6.36493i) q^{93} +(-0.896599 - 1.55296i) q^{94} +(1.73065 + 2.99758i) q^{95} +(-0.500000 + 0.866025i) q^{96} +4.09233 q^{97} +(6.94492 - 0.876382i) q^{98} +0.278197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{11} + 4 q^{12} - q^{14} - 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} - 4 q^{25} - 8 q^{27} + q^{28} - 6 q^{29} - 9 q^{31} + 4 q^{32} - 2 q^{33} - 20 q^{34} - 9 q^{35} + 8 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{41} - 2 q^{42} + 42 q^{43} + 2 q^{44} - 5 q^{46} - 7 q^{47} - 8 q^{48} - 4 q^{49} - 8 q^{50} + 10 q^{51} + 7 q^{53} - 4 q^{54} + 2 q^{56} - 8 q^{57} - 3 q^{58} - 7 q^{59} - 23 q^{61} - 18 q^{62} + q^{63} + 8 q^{64} + 48 q^{65} + 2 q^{66} - 6 q^{67} - 10 q^{68} + 10 q^{69} + 15 q^{70} + 4 q^{71} + 4 q^{72} + 5 q^{73} - 14 q^{74} + 4 q^{75} + 8 q^{76} - 17 q^{77} + 11 q^{79} - 4 q^{81} + 4 q^{82} + 28 q^{83} - q^{84} + 12 q^{85} + 21 q^{86} - 3 q^{87} - 2 q^{88} - 10 q^{89} - 48 q^{91} - 10 q^{92} + 9 q^{93} + 7 q^{94} - 4 q^{96} - 2 q^{97} + 25 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^11 + 4 * q^12 - q^14 - 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 - 4 * q^25 - 8 * q^27 + q^28 - 6 * q^29 - 9 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 - 9 * q^35 + 8 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^41 - 2 * q^42 + 42 * q^43 + 2 * q^44 - 5 * q^46 - 7 * q^47 - 8 * q^48 - 4 * q^49 - 8 * q^50 + 10 * q^51 + 7 * q^53 - 4 * q^54 + 2 * q^56 - 8 * q^57 - 3 * q^58 - 7 * q^59 - 23 * q^61 - 18 * q^62 + q^63 + 8 * q^64 + 48 * q^65 + 2 * q^66 - 6 * q^67 - 10 * q^68 + 10 * q^69 + 15 * q^70 + 4 * q^71 + 4 * q^72 + 5 * q^73 - 14 * q^74 + 4 * q^75 + 8 * q^76 - 17 * q^77 + 11 * q^79 - 4 * q^81 + 4 * q^82 + 28 * q^83 - q^84 + 12 * q^85 + 21 * q^86 - 3 * q^87 - 2 * q^88 - 10 * q^89 - 48 * q^91 - 10 * q^92 + 9 * q^93 + 7 * q^94 - 4 * q^96 - 2 * q^97 + 25 * q^98 - 4 * q^99

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