LMFDB - Embedded newform 798.2.j.h.457.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	798.457
Dual form			798.2.j.h.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.792893 - 1.37333i) q^{5} -1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.792893 - 1.37333i) q^{5} -1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.792893 + 1.37333i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.82843 q^{13} +(1.00000 - 2.44949i) q^{14} +1.58579 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.12132 + 3.67423i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -1.58579 q^{20} +(-1.62132 - 2.09077i) q^{21} -1.00000 q^{22} +(-1.70711 + 2.95680i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.24264 + 2.15232i) q^{25} +(-1.41421 + 2.44949i) q^{26} -1.00000 q^{27} +(1.62132 + 2.09077i) q^{28} +2.17157 q^{29} +(-0.792893 + 1.37333i) q^{30} +(5.32843 + 9.22911i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -4.24264 q^{34} +(-1.58579 + 3.88437i) q^{35} +1.00000 q^{36} +(-0.121320 + 0.210133i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(1.41421 + 2.44949i) q^{39} +(0.792893 - 1.37333i) q^{40} -0.585786 q^{41} +(2.62132 - 0.358719i) q^{42} +6.24264 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.792893 + 1.37333i) q^{45} +(-1.70711 - 2.95680i) q^{46} +(-1.58579 + 2.74666i) q^{47} -1.00000 q^{48} +(6.74264 - 1.88064i) q^{49} -2.48528 q^{50} +(-2.12132 + 3.67423i) q^{51} +(-1.41421 - 2.44949i) q^{52} +(-0.914214 - 1.58346i) q^{53} +(0.500000 - 0.866025i) q^{54} +1.58579 q^{55} +(-2.62132 + 0.358719i) q^{56} -1.00000 q^{57} +(-1.08579 + 1.88064i) q^{58} +(-3.03553 - 5.25770i) q^{59} +(-0.792893 - 1.37333i) q^{60} +(2.41421 - 4.18154i) q^{61} -10.6569 q^{62} +(1.00000 - 2.44949i) q^{63} +1.00000 q^{64} +(2.24264 - 3.88437i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(1.00000 + 1.73205i) q^{67} +(2.12132 - 3.67423i) q^{68} -3.41421 q^{69} +(-2.57107 - 3.31552i) q^{70} -7.89949 q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.41421 + 12.8418i) q^{73} +(-0.121320 - 0.210133i) q^{74} +(-1.24264 + 2.15232i) q^{75} +1.00000 q^{76} +(-1.62132 - 2.09077i) q^{77} -2.82843 q^{78} +(0.0857864 - 0.148586i) q^{79} +(0.792893 + 1.37333i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.292893 - 0.507306i) q^{82} -17.1421 q^{83} +(-1.00000 + 2.44949i) q^{84} +6.72792 q^{85} +(-3.12132 + 5.40629i) q^{86} +(1.08579 + 1.88064i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.87868 + 3.25397i) q^{89} -1.58579 q^{90} +(-7.41421 + 1.01461i) q^{91} +3.41421 q^{92} +(-5.32843 + 9.22911i) q^{93} +(-1.58579 - 2.74666i) q^{94} +(0.792893 + 1.37333i) q^{95} +(0.500000 - 0.866025i) q^{96} -5.58579 q^{97} +(-1.74264 + 6.77962i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 6 q^{10} + 2 q^{11} + 2 q^{12} + 4 q^{14} + 12 q^{15} - 2 q^{16} - 2 q^{18} - 2 q^{19} - 12 q^{20} + 2 q^{21} - 4 q^{22} - 4 q^{23} + 2 q^{24} - 12 q^{25} - 4 q^{27} - 2 q^{28} + 20 q^{29} - 6 q^{30} + 10 q^{31} - 2 q^{32} - 2 q^{33} - 12 q^{35} + 4 q^{36} + 8 q^{37} - 2 q^{38} + 6 q^{40} - 8 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + 6 q^{45} - 4 q^{46} - 12 q^{47} - 4 q^{48} + 10 q^{49} + 24 q^{50} + 2 q^{53} + 2 q^{54} + 12 q^{55} - 2 q^{56} - 4 q^{57} - 10 q^{58} + 2 q^{59} - 6 q^{60} + 4 q^{61} - 20 q^{62} + 4 q^{63} + 4 q^{64} - 8 q^{65} - 2 q^{66} + 4 q^{67} - 8 q^{69} + 18 q^{70} + 8 q^{71} - 2 q^{72} + 24 q^{73} + 8 q^{74} + 12 q^{75} + 4 q^{76} + 2 q^{77} + 6 q^{79} + 6 q^{80} - 2 q^{81} + 4 q^{82} - 12 q^{83} - 4 q^{84} - 24 q^{85} - 4 q^{86} + 10 q^{87} + 2 q^{88} - 16 q^{89} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 10 q^{93} - 12 q^{94} + 6 q^{95} + 2 q^{96} - 28 q^{97} + 10 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 6 * q^10 + 2 * q^11 + 2 * q^12 + 4 * q^14 + 12 * q^15 - 2 * q^16 - 2 * q^18 - 2 * q^19 - 12 * q^20 + 2 * q^21 - 4 * q^22 - 4 * q^23 + 2 * q^24 - 12 * q^25 - 4 * q^27 - 2 * q^28 + 20 * q^29 - 6 * q^30 + 10 * q^31 - 2 * q^32 - 2 * q^33 - 12 * q^35 + 4 * q^36 + 8 * q^37 - 2 * q^38 + 6 * q^40 - 8 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + 6 * q^45 - 4 * q^46 - 12 * q^47 - 4 * q^48 + 10 * q^49 + 24 * q^50 + 2 * q^53 + 2 * q^54 + 12 * q^55 - 2 * q^56 - 4 * q^57 - 10 * q^58 + 2 * q^59 - 6 * q^60 + 4 * q^61 - 20 * q^62 + 4 * q^63 + 4 * q^64 - 8 * q^65 - 2 * q^66 + 4 * q^67 - 8 * q^69 + 18 * q^70 + 8 * q^71 - 2 * q^72 + 24 * q^73 + 8 * q^74 + 12 * q^75 + 4 * q^76 + 2 * q^77 + 6 * q^79 + 6 * q^80 - 2 * q^81 + 4 * q^82 - 12 * q^83 - 4 * q^84 - 24 * q^85 - 4 * q^86 + 10 * q^87 + 2 * q^88 - 16 * q^89 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 10 * q^93 - 12 * q^94 + 6 * q^95 + 2 * q^96 - 28 * q^97 + 10 * 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
$5$	0.792893	−	1.37333i	0.354593	−	0.614172i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$	0.792893	−	1.37333i	0.354593	−	0.614172i	0.987048	+	0.160424i	$0.0512862\pi$
$6$	−1.00000			−0.408248
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.792893	+	1.37333i	0.250735	+	0.434286i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$	1.00000	−	2.44949i	0.267261	−	0.654654i
$15$	1.58579			0.409448
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.12132	+	3.67423i	0.514496	+	0.891133i	0.999859	+	0.0168199i	$0.00535420\pi$
$17$	2.12132	+	3.67423i	0.514496	+	0.891133i	−0.485363	+	0.874313i	$0.661312\pi$
$18$	−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
$20$	−1.58579			−0.354593
$21$	−1.62132	−	2.09077i	−0.353801	−	0.456243i
$22$	−1.00000			−0.213201
$23$	−1.70711	+	2.95680i	−0.355956	+	0.616535i	−0.987281	−	0.158984i	$-0.949178\pi$
$23$	−1.70711	+	2.95680i	−0.355956	+	0.616535i	0.631325	+	0.775519i	$0.282511\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.24264	+	2.15232i	0.248528	+	0.430463i
$26$	−1.41421	+	2.44949i	−0.277350	+	0.480384i
$27$	−1.00000			−0.192450
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$	2.17157			0.403251			0.201625	−	0.979463i	$-0.435378\pi$
$29$	2.17157			0.403251			0.201625	+	0.979463i	$0.435378\pi$
$30$	−0.792893	+	1.37333i	−0.144762	+	0.250735i
$31$	5.32843	+	9.22911i	0.957014	+	1.65760i	0.729691	+	0.683777i	$0.239664\pi$
$31$	5.32843	+	9.22911i	0.957014	+	1.65760i	0.227323	+	0.973819i	$0.427003\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	−4.24264			−0.727607
$35$	−1.58579	+	3.88437i	−0.268047	+	0.656578i
$36$	1.00000			0.166667
$37$	−0.121320	+	0.210133i	−0.0199449	+	0.0345457i	−0.875826	−	0.482628i	$-0.839682\pi$
$37$	−0.121320	+	0.210133i	−0.0199449	+	0.0345457i	0.855881	+	0.517173i	$0.173016\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$	1.41421	+	2.44949i	0.226455	+	0.392232i
$40$	0.792893	−	1.37333i	0.125367	−	0.217143i
$41$	−0.585786			−0.0914845			−0.0457422	−	0.998953i	$-0.514565\pi$
$41$	−0.585786			−0.0914845			−0.0457422	+	0.998953i	$0.514565\pi$
$42$	2.62132	−	0.358719i	0.404479	−	0.0553516i
$43$	6.24264			0.951994			0.475997	−	0.879447i	$-0.342087\pi$
$43$	6.24264			0.951994			0.475997	+	0.879447i	$0.342087\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	0.792893	+	1.37333i	0.118198	+	0.204724i
$46$	−1.70711	−	2.95680i	−0.251699	−	0.435956i
$47$	−1.58579	+	2.74666i	−0.231311	+	0.400642i	−0.958194	−	0.286119i	$-0.907635\pi$
$47$	−1.58579	+	2.74666i	−0.231311	+	0.400642i	0.726883	+	0.686761i	$0.240968\pi$
$48$	−1.00000			−0.144338
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	−2.48528			−0.351472
$51$	−2.12132	+	3.67423i	−0.297044	+	0.514496i
$52$	−1.41421	−	2.44949i	−0.196116	−	0.339683i
$53$	−0.914214	−	1.58346i	−0.125577	−	0.217506i	0.796381	−	0.604795i	$-0.206745\pi$
$53$	−0.914214	−	1.58346i	−0.125577	−	0.217506i	−0.921958	+	0.387289i	$0.873412\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.58579			0.213827
$56$	−2.62132	+	0.358719i	−0.350289	+	0.0479359i
$57$	−1.00000			−0.132453
$58$	−1.08579	+	1.88064i	−0.142571	+	0.246940i
$59$	−3.03553	−	5.25770i	−0.395193	−	0.684494i	0.597933	−	0.801546i	$-0.295989\pi$
$59$	−3.03553	−	5.25770i	−0.395193	−	0.684494i	−0.993126	+	0.117052i	$0.962656\pi$
$60$	−0.792893	−	1.37333i	−0.102362	−	0.177296i
$61$	2.41421	−	4.18154i	0.309108	−	0.535391i	−0.669059	−	0.743209i	$-0.733303\pi$
$61$	2.41421	−	4.18154i	0.309108	−	0.535391i	0.978168	+	0.207818i	$0.0666361\pi$
$62$	−10.6569			−1.35342
$63$	1.00000	−	2.44949i	0.125988	−	0.308607i
$64$	1.00000			0.125000
$65$	2.24264	−	3.88437i	0.278165	−	0.481797i
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	2.12132	−	3.67423i	0.257248	−	0.445566i
$69$	−3.41421			−0.411023
$70$	−2.57107	−	3.31552i	−0.307301	−	0.396280i
$71$	−7.89949			−0.937498			−0.468749	−	0.883332i	$-0.655295\pi$
$71$	−7.89949			−0.937498			−0.468749	+	0.883332i	$0.655295\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	7.41421	+	12.8418i	0.867768	+	1.50302i	0.864272	+	0.503024i	$0.167779\pi$
$73$	7.41421	+	12.8418i	0.867768	+	1.50302i	0.00349590	+	0.999994i	$0.498887\pi$
$74$	−0.121320	−	0.210133i	−0.0141032	−	0.0244275i
$75$	−1.24264	+	2.15232i	−0.143488	+	0.248528i
$76$	1.00000			0.114708
$77$	−1.62132	−	2.09077i	−0.184767	−	0.238265i
$78$	−2.82843			−0.320256
$79$	0.0857864	−	0.148586i	0.00965173	−	0.0167173i	−0.861159	−	0.508335i	$-0.830261\pi$
$79$	0.0857864	−	0.148586i	0.00965173	−	0.0167173i	0.870811	+	0.491618i	$0.163594\pi$
$80$	0.792893	+	1.37333i	0.0886482	+	0.153543i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.292893	−	0.507306i	0.0323446	−	0.0560226i
$83$	−17.1421			−1.88159			−0.940797	−	0.338971i	$-0.889921\pi$
$83$	−17.1421			−1.88159			−0.940797	+	0.338971i	$0.889921\pi$
$84$	−1.00000	+	2.44949i	−0.109109	+	0.267261i
$85$	6.72792			0.729746
$86$	−3.12132	+	5.40629i	−0.336581	+	0.582975i
$87$	1.08579	+	1.88064i	0.116409	+	0.201625i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−1.87868	+	3.25397i	−0.199140	+	0.344920i	−0.948250	−	0.317526i	$-0.897148\pi$
$89$	−1.87868	+	3.25397i	−0.199140	+	0.344920i	0.749110	+	0.662446i	$0.230481\pi$
$90$	−1.58579			−0.167157
$91$	−7.41421	+	1.01461i	−0.777221	+	0.106360i
$92$	3.41421			0.355956
$93$	−5.32843	+	9.22911i	−0.552532	+	0.957014i
$94$	−1.58579	−	2.74666i	−0.163561	−	0.283297i
$95$	0.792893	+	1.37333i	0.0813491	+	0.140901i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−5.58579			−0.567151			−0.283575	−	0.958950i	$-0.591521\pi$
$97$	−5.58579			−0.567151			−0.283575	+	0.958950i	$0.591521\pi$
$98$	−1.74264	+	6.77962i	−0.176033	+	0.684845i
$99$	−1.00000			−0.100504
$100$	1.24264	−	2.15232i	0.124264	−	0.215232i
$101$	−7.48528	−	12.9649i	−0.744813	−	1.29005i	−0.950282	−	0.311391i	$-0.899205\pi$
$101$	−7.48528	−	12.9649i	−0.744813	−	1.29005i	0.205469	−	0.978664i	$-0.434128\pi$
$102$	−2.12132	−	3.67423i	−0.210042	−	0.363803i
$103$	9.24264	−	16.0087i	0.910704	−	1.57739i	0.0976330	−	0.995222i	$-0.468873\pi$
$103$	9.24264	−	16.0087i	0.910704	−	1.57739i	0.813071	−	0.582164i	$-0.197794\pi$
$104$	2.82843			0.277350
$105$	−4.15685	+	0.568852i	−0.405667	+	0.0555143i
$106$	1.82843			0.177593
$107$	−5.86396	+	10.1567i	−0.566891	+	0.981883i	0.429981	+	0.902838i	$0.358520\pi$
$107$	−5.86396	+	10.1567i	−0.566891	+	0.981883i	−0.996871	+	0.0790450i	$0.974813\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−0.878680	−	1.52192i	−0.0841622	−	0.145773i	0.820872	−	0.571113i	$-0.193488\pi$
$109$	−0.878680	−	1.52192i	−0.0841622	−	0.145773i	−0.905034	+	0.425339i	$0.860155\pi$
$110$	−0.792893	+	1.37333i	−0.0755994	+	0.130942i
$111$	−0.242641			−0.0230304
$112$	1.00000	−	2.44949i	0.0944911	−	0.231455i
$113$	10.2426			0.963547			0.481773	−	0.876296i	$-0.339993\pi$
$113$	10.2426			0.963547			0.481773	+	0.876296i	$0.339993\pi$
$114$	0.500000	−	0.866025i	0.0468293	−	0.0811107i
$115$	2.70711	+	4.68885i	0.252439	+	0.437237i
$116$	−1.08579	−	1.88064i	−0.100813	−	0.174613i
$117$	−1.41421	+	2.44949i	−0.130744	+	0.226455i
$118$	6.07107			0.558887
$119$	−6.87868	−	8.87039i	−0.630568	−	0.813147i
$120$	1.58579			0.144762
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	2.41421	+	4.18154i	0.218573	+	0.378579i
$123$	−0.292893	−	0.507306i	−0.0264093	−	0.0457422i
$124$	5.32843	−	9.22911i	0.478507	−	0.828798i
$125$	11.8701			1.06169
$126$	1.62132	+	2.09077i	0.144439	+	0.186261i
$127$	−5.82843			−0.517189			−0.258595	−	0.965986i	$-0.583259\pi$
$127$	−5.82843			−0.517189			−0.258595	+	0.965986i	$0.583259\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.12132	+	5.40629i	0.274817	+	0.475997i
$130$	2.24264	+	3.88437i	0.196693	+	0.340682i
$131$	−2.15685	+	3.73578i	−0.188445	+	0.326397i	−0.944732	−	0.327843i	$-0.893678\pi$
$131$	−2.15685	+	3.73578i	−0.188445	+	0.326397i	0.756287	+	0.654240i	$0.227011\pi$
$132$	1.00000			0.0870388
$133$	1.00000	−	2.44949i	0.0867110	−	0.212398i
$134$	−2.00000			−0.172774
$135$	−0.792893	+	1.37333i	−0.0682414	+	0.118198i
$136$	2.12132	+	3.67423i	0.181902	+	0.315063i
$137$	0.171573	+	0.297173i	0.0146585	+	0.0253892i	0.873262	−	0.487252i	$-0.162001\pi$
$137$	0.171573	+	0.297173i	0.0146585	+	0.0253892i	−0.858603	+	0.512641i	$0.828667\pi$
$138$	1.70711	−	2.95680i	0.145319	−	0.251699i
$139$	7.89949			0.670026			0.335013	−	0.942213i	$-0.391259\pi$
$139$	7.89949			0.670026			0.335013	+	0.942213i	$0.391259\pi$
$140$	4.15685	−	0.568852i	0.351318	−	0.0480768i
$141$	−3.17157			−0.267095
$142$	3.94975	−	6.84116i	0.331455	−	0.574098i
$143$	1.41421	+	2.44949i	0.118262	+	0.204837i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.72183	−	2.98229i	0.142990	−	0.247666i
$146$	−14.8284			−1.22721
$147$	5.00000	+	4.89898i	0.412393	+	0.404061i
$148$	0.242641			0.0199449
$149$	9.24264	−	16.0087i	0.757187	−	1.31149i	−0.187093	−	0.982342i	$-0.559907\pi$
$149$	9.24264	−	16.0087i	0.757187	−	1.31149i	0.944280	−	0.329144i	$-0.106760\pi$
$150$	−1.24264	−	2.15232i	−0.101461	−	0.175736i
$151$	5.67157	+	9.82345i	0.461546	+	0.799421i	0.999038	−	0.0438475i	$-0.0139616\pi$
$151$	5.67157	+	9.82345i	0.461546	+	0.799421i	−0.537492	+	0.843269i	$0.680628\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	−4.24264			−0.342997
$154$	2.62132	−	0.358719i	0.211232	−	0.0289064i
$155$	16.8995			1.35740
$156$	1.41421	−	2.44949i	0.113228	−	0.196116i
$157$	2.24264	+	3.88437i	0.178982	+	0.310006i	0.941532	−	0.336923i	$-0.109386\pi$
$157$	2.24264	+	3.88437i	0.178982	+	0.310006i	−0.762550	+	0.646929i	$0.776053\pi$
$158$	0.0857864	+	0.148586i	0.00682480	+	0.0118209i
$159$	0.914214	−	1.58346i	0.0725019	−	0.125577i
$160$	−1.58579			−0.125367
$161$	3.41421	−	8.36308i	0.269078	−	0.659103i
$162$	1.00000			0.0785674
$163$	5.41421	−	9.37769i	0.424074	−	0.734518i	−0.572260	−	0.820073i	$-0.693933\pi$
$163$	5.41421	−	9.37769i	0.424074	−	0.734518i	0.996333	+	0.0855550i	$0.0272663\pi$
$164$	0.292893	+	0.507306i	0.0228711	+	0.0396139i
$165$	0.792893	+	1.37333i	0.0617267	+	0.106914i
$166$	8.57107	−	14.8455i	0.665244	−	1.15224i
$167$	−6.72792			−0.520622			−0.260311	−	0.965525i	$-0.583825\pi$
$167$	−6.72792			−0.520622			−0.260311	+	0.965525i	$0.583825\pi$
$168$	−1.62132	−	2.09077i	−0.125088	−	0.161306i
$169$	−5.00000			−0.384615
$170$	−3.36396	+	5.82655i	−0.258004	+	0.446876i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−3.12132	−	5.40629i	−0.237998	−	0.412225i
$173$	7.89949	−	13.6823i	0.600587	−	1.04025i	−0.392145	−	0.919904i	$-0.628267\pi$
$173$	7.89949	−	13.6823i	0.600587	−	1.04025i	0.992732	−	0.120344i	$-0.0383999\pi$
$174$	−2.17157			−0.164627
$175$	−4.02944	−	5.19615i	−0.304597	−	0.392792i
$176$	−1.00000			−0.0753778
$177$	3.03553	−	5.25770i	0.228165	−	0.395193i
$178$	−1.87868	−	3.25397i	−0.140813	−	0.243895i
$179$	3.75736	+	6.50794i	0.280838	+	0.486426i	0.971591	−	0.236665i	$-0.0760542\pi$
$179$	3.75736	+	6.50794i	0.280838	+	0.486426i	−0.690753	+	0.723091i	$0.742721\pi$
$180$	0.792893	−	1.37333i	0.0590988	−	0.102362i
$181$	−20.4853			−1.52266			−0.761329	−	0.648365i	$-0.775453\pi$
$181$	−20.4853			−1.52266			−0.761329	+	0.648365i	$0.775453\pi$
$182$	2.82843	−	6.92820i	0.209657	−	0.513553i
$183$	4.82843			0.356928
$184$	−1.70711	+	2.95680i	−0.125850	+	0.217978i
$185$	0.192388	+	0.333226i	0.0141447	+	0.0244993i
$186$	−5.32843	−	9.22911i	−0.390699	−	0.676711i
$187$	−2.12132	+	3.67423i	−0.155126	+	0.268687i
$188$	3.17157			0.231311
$189$	2.62132	−	0.358719i	0.190673	−	0.0260930i
$190$	−1.58579			−0.115045
$191$	9.07107	−	15.7116i	0.656359	−	1.13685i	−0.325192	−	0.945648i	$-0.605429\pi$
$191$	9.07107	−	15.7116i	0.656359	−	1.13685i	0.981551	−	0.191200i	$-0.0612378\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	11.8640	+	20.5490i	0.853987	+	1.47915i	0.877582	+	0.479427i	$0.159155\pi$
$193$	11.8640	+	20.5490i	0.853987	+	1.47915i	−0.0235954	+	0.999722i	$0.507511\pi$
$194$	2.79289	−	4.83743i	0.200518	−	0.347307i
$195$	4.48528			0.321198
$196$	−5.00000	−	4.89898i	−0.357143	−	0.349927i
$197$	1.17157			0.0834711			0.0417356	−	0.999129i	$-0.486711\pi$
$197$	1.17157			0.0834711			0.0417356	+	0.999129i	$0.486711\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−4.24264	−	7.34847i	−0.300753	−	0.520919i	0.675554	−	0.737311i	$-0.263905\pi$
$199$	−4.24264	−	7.34847i	−0.300753	−	0.520919i	−0.976307	+	0.216391i	$0.930571\pi$
$200$	1.24264	+	2.15232i	0.0878680	+	0.152192i
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	14.9706			1.05333
$203$	−5.69239	+	0.778985i	−0.399527	+	0.0546741i
$204$	4.24264			0.297044
$205$	−0.464466	+	0.804479i	−0.0324397	+	0.0561872i
$206$	9.24264	+	16.0087i	0.643965	+	1.11538i
$207$	−1.70711	−	2.95680i	−0.118652	−	0.205512i
$208$	−1.41421	+	2.44949i	−0.0980581	+	0.169842i
$209$	−1.00000			−0.0691714
$210$	1.58579	−	3.88437i	0.109430	−	0.268047i
$211$	−15.0711			−1.03754			−0.518768	−	0.854915i	$-0.673609\pi$
$211$	−15.0711			−1.03754			−0.518768	+	0.854915i	$0.673609\pi$
$212$	−0.914214	+	1.58346i	−0.0627884	+	0.108753i
$213$	−3.94975	−	6.84116i	−0.270632	−	0.468749i
$214$	−5.86396	−	10.1567i	−0.400852	−	0.694296i
$215$	4.94975	−	8.57321i	0.337570	−	0.584688i
$216$	−1.00000			−0.0680414
$217$	−17.2782	−	22.2810i	−1.17292	−	1.51254i
$218$	1.75736			0.119023
$219$	−7.41421	+	12.8418i	−0.501006	+	0.867768i
$220$	−0.792893	−	1.37333i	−0.0534568	−	0.0925900i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$	0.121320	−	0.210133i	0.00814249	−	0.0141032i
$223$	23.4853			1.57269			0.786345	−	0.617787i	$-0.211971\pi$
$223$	23.4853			1.57269			0.786345	+	0.617787i	$0.211971\pi$
$224$	1.62132	+	2.09077i	0.108329	+	0.139695i
$225$	−2.48528			−0.165685
$226$	−5.12132	+	8.87039i	−0.340665	+	0.590049i
$227$	−0.550253	−	0.953065i	−0.0365215	−	0.0632572i	0.847187	−	0.531295i	$-0.178294\pi$
$227$	−0.550253	−	0.953065i	−0.0365215	−	0.0632572i	−0.883708	+	0.468038i	$0.844961\pi$
$228$	0.500000	+	0.866025i	0.0331133	+	0.0573539i
$229$	9.89949	−	17.1464i	0.654177	−	1.13307i	−0.327922	−	0.944705i	$-0.606348\pi$
$229$	9.89949	−	17.1464i	0.654177	−	1.13307i	0.982099	−	0.188363i	$-0.0603182\pi$
$230$	−5.41421			−0.357003
$231$	1.00000	−	2.44949i	0.0657952	−	0.161165i
$232$	2.17157			0.142571
$233$	2.58579	−	4.47871i	0.169401	−	0.293410i	−0.768809	−	0.639479i	$-0.779150\pi$
$233$	2.58579	−	4.47871i	0.169401	−	0.293410i	0.938209	+	0.346069i	$0.112484\pi$
$234$	−1.41421	−	2.44949i	−0.0924500	−	0.160128i
$235$	2.51472	+	4.35562i	0.164042	+	0.284129i
$236$	−3.03553	+	5.25770i	−0.197596	+	0.342247i
$237$	0.171573			0.0111449
$238$	11.1213	−	1.52192i	0.720888	−	0.0986513i
$239$	28.2843			1.82956			0.914779	−	0.403955i	$-0.132365\pi$
$239$	28.2843			1.82956			0.914779	+	0.403955i	$0.132365\pi$
$240$	−0.792893	+	1.37333i	−0.0511810	+	0.0886482i
$241$	−0.278175	−	0.481813i	−0.0179188	−	0.0310363i	0.856927	−	0.515438i	$-0.172371\pi$
$241$	−0.278175	−	0.481813i	−0.0179188	−	0.0310363i	−0.874846	+	0.484402i	$0.839037\pi$
$242$	5.00000	+	8.66025i	0.321412	+	0.556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.82843			−0.309108
$245$	2.76346	−	10.7510i	0.176551	−	0.686858i
$246$	0.585786			0.0373484
$247$	−1.41421	+	2.44949i	−0.0899843	+	0.155857i
$248$	5.32843	+	9.22911i	0.338355	+	0.586049i
$249$	−8.57107	−	14.8455i	−0.543169	−	0.940797i
$250$	−5.93503	+	10.2798i	−0.375364	+	0.650150i
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$	−2.62132	+	0.358719i	−0.165128	+	0.0225972i
$253$	−3.41421			−0.214650
$254$	2.91421	−	5.04757i	0.182854	−	0.316712i
$255$	3.36396	+	5.82655i	0.210659	+	0.364873i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	−6.24264			−0.388650
$259$	0.242641	−	0.594346i	0.0150770	−	0.0369309i
$260$	−4.48528			−0.278165
$261$	−1.08579	+	1.88064i	−0.0672085	+	0.116409i
$262$	−2.15685	−	3.73578i	−0.133251	−	0.230797i
$263$	5.77817	+	10.0081i	0.356298	+	0.617125i	0.987339	−	0.158624i	$-0.0507056\pi$
$263$	5.77817	+	10.0081i	0.356298	+	0.617125i	−0.631042	+	0.775749i	$0.717372\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	−2.89949			−0.178115
$266$	1.62132	+	2.09077i	0.0994095	+	0.128193i
$267$	−3.75736			−0.229947
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	−0.500000	−	0.866025i	−0.0304855	−	0.0528025i	0.850380	−	0.526169i	$-0.176372\pi$
$269$	−0.500000	−	0.866025i	−0.0304855	−	0.0528025i	−0.880866	+	0.473366i	$0.843039\pi$
$270$	−0.792893	−	1.37333i	−0.0482539	−	0.0835783i
$271$	−4.44975	+	7.70719i	−0.270303	+	0.468178i	−0.968939	−	0.247298i	$-0.920457\pi$
$271$	−4.44975	+	7.70719i	−0.270303	+	0.468178i	0.698636	+	0.715477i	$0.253791\pi$
$272$	−4.24264			−0.257248
$273$	−4.58579	−	5.91359i	−0.277544	−	0.357907i
$274$	−0.343146			−0.0207302
$275$	−1.24264	+	2.15232i	−0.0749341	+	0.129790i
$276$	1.70711	+	2.95680i	0.102756	+	0.177978i
$277$	6.87868	+	11.9142i	0.413300	+	0.715856i	0.995248	−	0.0973694i	$-0.0310428\pi$
$277$	6.87868	+	11.9142i	0.413300	+	0.715856i	−0.581949	+	0.813226i	$0.697709\pi$
$278$	−3.94975	+	6.84116i	−0.236890	+	0.410306i
$279$	−10.6569			−0.638009
$280$	−1.58579	+	3.88437i	−0.0947689	+	0.232135i
$281$	−1.31371			−0.0783693			−0.0391846	−	0.999232i	$-0.512476\pi$
$281$	−1.31371			−0.0783693			−0.0391846	+	0.999232i	$0.512476\pi$
$282$	1.58579	−	2.74666i	0.0944322	−	0.163561i
$283$	−10.7782	−	18.6683i	−0.640696	−	1.10972i	−0.985278	−	0.170962i	$-0.945313\pi$
$283$	−10.7782	−	18.6683i	−0.640696	−	1.10972i	0.344582	−	0.938756i	$-0.388021\pi$
$284$	3.94975	+	6.84116i	0.234374	+	0.405948i
$285$	−0.792893	+	1.37333i	−0.0469669	+	0.0813491i
$286$	−2.82843			−0.167248
$287$	1.53553	−	0.210133i	0.0906397	−	0.0124038i
$288$	1.00000			0.0589256
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	1.72183	+	2.98229i	0.101109	+	0.175126i
$291$	−2.79289	−	4.83743i	−0.163722	−	0.283575i
$292$	7.41421	−	12.8418i	0.433884	−	0.751509i
$293$	−23.0000			−1.34367			−0.671837	−	0.740699i	$-0.734495\pi$
$293$	−23.0000			−1.34367			−0.671837	+	0.740699i	$0.734495\pi$
$294$	−6.74264	+	1.88064i	−0.393239	+	0.109681i
$295$	−9.62742			−0.560530
$296$	−0.121320	+	0.210133i	−0.00705160	+	0.0122137i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	9.24264	+	16.0087i	0.535412	+	0.927360i
$299$	−4.82843	+	8.36308i	−0.279235	+	0.483649i
$300$	2.48528			0.143488
$301$	−16.3640	+	2.23936i	−0.943203	+	0.129074i
$302$	−11.3431			−0.652725
$303$	7.48528	−	12.9649i	0.430018	−	0.744813i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	−3.82843	−	6.63103i	−0.219215	−	0.379692i
$306$	2.12132	−	3.67423i	0.121268	−	0.210042i
$307$	7.41421			0.423152			0.211576	−	0.977362i	$-0.432140\pi$
$307$	7.41421			0.423152			0.211576	+	0.977362i	$0.432140\pi$
$308$	−1.00000	+	2.44949i	−0.0569803	+	0.139573i
$309$	18.4853			1.05159
$310$	−8.44975	+	14.6354i	−0.479913	+	0.831234i
$311$	−11.1213	−	19.2627i	−0.630632	−	1.09229i	−0.987423	−	0.158103i	$-0.949462\pi$
$311$	−11.1213	−	19.2627i	−0.630632	−	1.09229i	0.356790	−	0.934184i	$-0.383871\pi$
$312$	1.41421	+	2.44949i	0.0800641	+	0.138675i
$313$	1.91421	−	3.31552i	0.108198	−	0.187404i	−0.806842	−	0.590767i	$-0.798825\pi$
$313$	1.91421	−	3.31552i	0.108198	−	0.187404i	0.915040	+	0.403363i	$0.132159\pi$
$314$	−4.48528			−0.253119
$315$	−2.57107	−	3.31552i	−0.144863	−	0.186808i
$316$	−0.171573			−0.00965173
$317$	4.74264	−	8.21449i	0.266373	−	0.461372i	−0.701549	−	0.712621i	$-0.747508\pi$
$317$	4.74264	−	8.21449i	0.266373	−	0.461372i	0.967922	+	0.251249i	$0.0808413\pi$
$318$	0.914214	+	1.58346i	0.0512666	+	0.0887963i
$319$	1.08579	+	1.88064i	0.0607924	+	0.105295i
$320$	0.792893	−	1.37333i	0.0443241	−	0.0767716i
$321$	−11.7279			−0.654589
$322$	5.53553	+	7.13834i	0.308483	+	0.397804i
$323$	−4.24264			−0.236067
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	3.51472	+	6.08767i	0.194962	+	0.337683i
$326$	5.41421	+	9.37769i	0.299866	+	0.519382i
$327$	0.878680	−	1.52192i	0.0485911	−	0.0841622i
$328$	−0.585786			−0.0323446
$329$	3.17157	−	7.76874i	0.174854	−	0.428304i
$330$	−1.58579			−0.0872947
$331$	2.19239	−	3.79733i	0.120505	−	0.208720i	−0.799462	−	0.600716i	$-0.794882\pi$
$331$	2.19239	−	3.79733i	0.120505	−	0.208720i	0.919967	+	0.391996i	$0.128215\pi$
$332$	8.57107	+	14.8455i	0.470398	+	0.814754i
$333$	−0.121320	−	0.210133i	−0.00664831	−	0.0115152i
$334$	3.36396	−	5.82655i	0.184068	−	0.318815i
$335$	3.17157			0.173282
$336$	2.62132	−	0.358719i	0.143005	−	0.0195698i
$337$	2.07107			0.112818			0.0564091	−	0.998408i	$-0.482035\pi$
$337$	2.07107			0.112818			0.0564091	+	0.998408i	$0.482035\pi$
$338$	2.50000	−	4.33013i	0.135982	−	0.235528i
$339$	5.12132	+	8.87039i	0.278152	+	0.481773i
$340$	−3.36396	−	5.82655i	−0.182436	−	0.315989i
$341$	−5.32843	+	9.22911i	−0.288551	+	0.499784i
$342$	1.00000			0.0540738
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	6.24264			0.336581
$345$	−2.70711	+	4.68885i	−0.145746	+	0.252439i
$346$	7.89949	+	13.6823i	0.424679	+	0.735566i
$347$	17.0000	+	29.4449i	0.912608	+	1.58068i	0.810366	+	0.585923i	$0.199268\pi$
$347$	17.0000	+	29.4449i	0.912608	+	1.58068i	0.102241	+	0.994760i	$0.467399\pi$
$348$	1.08579	−	1.88064i	0.0582043	−	0.100813i
$349$	−7.75736			−0.415242			−0.207621	−	0.978209i	$-0.566572\pi$
$349$	−7.75736			−0.415242			−0.207621	+	0.978209i	$0.566572\pi$
$350$	6.51472	−	0.891519i	0.348226	−	0.0476537i
$351$	−2.82843			−0.150970
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−7.05025	−	12.2114i	−0.375247	−	0.649947i	0.615117	−	0.788436i	$-0.289109\pi$
$353$	−7.05025	−	12.2114i	−0.375247	−	0.649947i	−0.990364	+	0.138489i	$0.955775\pi$
$354$	3.03553	+	5.25770i	0.161337	+	0.279444i
$355$	−6.26346	+	10.8486i	−0.332430	+	0.575785i
$356$	3.75736			0.199140
$357$	4.24264	−	10.3923i	0.224544	−	0.550019i
$358$	−7.51472			−0.397165
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$	0.792893	+	1.37333i	0.0417891	+	0.0723809i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	10.2426	−	17.7408i	0.538341	−	0.932434i
$363$	10.0000			0.524864
$364$	4.58579	+	5.91359i	0.240361	+	0.309956i
$365$	23.5147			1.23082
$366$	−2.41421	+	4.18154i	−0.126193	+	0.218573i
$367$	−2.62132	−	4.54026i	−0.136832	−	0.237000i	0.789464	−	0.613797i	$-0.210359\pi$
$367$	−2.62132	−	4.54026i	−0.136832	−	0.237000i	−0.926296	+	0.376797i	$0.877025\pi$
$368$	−1.70711	−	2.95680i	−0.0889891	−	0.154134i
$369$	0.292893	−	0.507306i	0.0152474	−	0.0264093i
$370$	−0.384776			−0.0200036
$371$	2.96447	+	3.82282i	0.153907	+	0.198471i
$372$	10.6569			0.552532
$373$	−0.242641	+	0.420266i	−0.0125635	+	0.0217605i	−0.872239	−	0.489080i	$-0.837333\pi$
$373$	−0.242641	+	0.420266i	−0.0125635	+	0.0217605i	0.859675	+	0.510841i	$0.170666\pi$
$374$	−2.12132	−	3.67423i	−0.109691	−	0.189990i
$375$	5.93503	+	10.2798i	0.306484	+	0.530845i
$376$	−1.58579	+	2.74666i	−0.0817807	+	0.141648i
$377$	6.14214			0.316336
$378$	−1.00000	+	2.44949i	−0.0514344	+	0.125988i
$379$	3.31371			0.170214			0.0851069	−	0.996372i	$-0.472877\pi$
$379$	3.31371			0.170214			0.0851069	+	0.996372i	$0.472877\pi$
$380$	0.792893	−	1.37333i	0.0406746	−	0.0704504i
$381$	−2.91421	−	5.04757i	−0.149300	−	0.258595i
$382$	9.07107	+	15.7116i	0.464116	+	0.803873i
$383$	−7.82843	+	13.5592i	−0.400014	+	0.692844i	−0.993727	−	0.111832i	$-0.964328\pi$
$383$	−7.82843	+	13.5592i	−0.400014	+	0.692844i	0.593713	+	0.804677i	$0.297661\pi$
$384$	−1.00000			−0.0510310
$385$	−4.15685	+	0.568852i	−0.211853	+	0.0289914i
$386$	−23.7279			−1.20772
$387$	−3.12132	+	5.40629i	−0.158666	+	0.274817i
$388$	2.79289	+	4.83743i	0.141788	+	0.245583i
$389$	−11.5858	−	20.0672i	−0.587423	−	1.01745i	−0.994569	−	0.104083i	$-0.966809\pi$
$389$	−11.5858	−	20.0672i	−0.587423	−	1.01745i	0.407146	−	0.913363i	$-0.366524\pi$
$390$	−2.24264	+	3.88437i	−0.113561	+	0.196693i
$391$	−14.4853			−0.732552
$392$	6.74264	−	1.88064i	0.340555	−	0.0949865i
$393$	−4.31371			−0.217598
$394$	−0.585786	+	1.01461i	−0.0295115	+	0.0511154i
$395$	−0.136039	−	0.235626i	−0.00684486	−	0.0118557i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	5.41421	−	9.37769i	0.271732	−	0.470653i	−0.697574	−	0.716513i	$-0.745737\pi$
$397$	5.41421	−	9.37769i	0.271732	−	0.470653i	0.969305	+	0.245860i	$0.0790704\pi$
$398$	8.48528			0.425329
$399$	2.62132	−	0.358719i	0.131230	−	0.0179584i
$400$	−2.48528			−0.124264
$401$	−7.07107	+	12.2474i	−0.353112	+	0.611608i	−0.986793	−	0.161986i	$-0.948210\pi$
$401$	−7.07107	+	12.2474i	−0.353112	+	0.611608i	0.633681	+	0.773595i	$0.281543\pi$
$402$	−1.00000	−	1.73205i	−0.0498755	−	0.0863868i
$403$	15.0711	+	26.1039i	0.750743	+	1.30033i
$404$	−7.48528	+	12.9649i	−0.372407	+	0.645027i
$405$	−1.58579			−0.0787984
$406$	2.17157	−	5.31925i	0.107773	−	0.263990i
$407$	−0.242641			−0.0120273
$408$	−2.12132	+	3.67423i	−0.105021	+	0.181902i
$409$	−15.4497	−	26.7597i	−0.763941	−	1.32318i	−0.940805	−	0.338949i	$-0.889929\pi$
$409$	−15.4497	−	26.7597i	−0.763941	−	1.32318i	0.176864	−	0.984235i	$-0.443405\pi$
$410$	−0.464466	−	0.804479i	−0.0229383	−	0.0397304i
$411$	−0.171573	+	0.297173i	−0.00846307	+	0.0146585i
$412$	−18.4853			−0.910704
$413$	9.84315	+	12.6932i	0.484350	+	0.624592i
$414$	3.41421			0.167799
$415$	−13.5919	+	23.5418i	−0.667199	+	1.15562i
$416$	−1.41421	−	2.44949i	−0.0693375	−	0.120096i
$417$	3.94975	+	6.84116i	0.193420	+	0.335013i
$418$	0.500000	−	0.866025i	0.0244558	−	0.0423587i
$419$	−30.9706			−1.51301			−0.756505	−	0.653987i	$-0.773095\pi$
$419$	−30.9706			−1.51301			−0.756505	+	0.653987i	$0.773095\pi$
$420$	2.57107	+	3.31552i	0.125455	+	0.161781i
$421$	15.1716			0.739417			0.369709	−	0.929148i	$-0.379458\pi$
$421$	15.1716			0.739417			0.369709	+	0.929148i	$0.379458\pi$
$422$	7.53553	−	13.0519i	0.366824	−	0.635358i
$423$	−1.58579	−	2.74666i	−0.0771036	−	0.133547i
$424$	−0.914214	−	1.58346i	−0.0443981	−	0.0768998i
$425$	−5.27208	+	9.13151i	−0.255733	+	0.442943i
$426$	7.89949			0.382732
$427$	−4.82843	+	11.8272i	−0.233664	+	0.572357i
$428$	11.7279			0.566891
$429$	−1.41421	+	2.44949i	−0.0682789	+	0.118262i
$430$	4.94975	+	8.57321i	0.238698	+	0.413437i
$431$	7.05025	+	12.2114i	0.339599	+	0.588202i	0.984357	−	0.176184i	$-0.0563754\pi$
$431$	7.05025	+	12.2114i	0.339599	+	0.588202i	−0.644759	+	0.764386i	$0.723042\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−30.8284			−1.48152			−0.740760	−	0.671770i	$-0.765534\pi$
$433$	−30.8284			−1.48152			−0.740760	+	0.671770i	$0.765534\pi$
$434$	27.9350	−	3.82282i	1.34092	−	0.183501i
$435$	3.44365			0.165110
$436$	−0.878680	+	1.52192i	−0.0420811	+	0.0728866i
$437$	−1.70711	−	2.95680i	−0.0816620	−	0.141443i
$438$	−7.41421	−	12.8418i	−0.354265	−	0.613605i
$439$	−11.2279	+	19.4473i	−0.535879	+	0.928170i	0.463241	+	0.886232i	$0.346687\pi$
$439$	−11.2279	+	19.4473i	−0.535879	+	0.928170i	−0.999120	+	0.0419380i	$0.986647\pi$
$440$	1.58579			0.0755994
$441$	−1.74264	+	6.77962i	−0.0829829	+	0.322839i
$442$	−12.0000			−0.570782
$443$	7.32843	−	12.6932i	0.348184	−	0.603073i	−0.637743	−	0.770249i	$-0.720132\pi$
$443$	7.32843	−	12.6932i	0.348184	−	0.603073i	0.985927	+	0.167177i	$0.0534651\pi$
$444$	0.121320	+	0.210133i	0.00575761	+	0.00997247i
$445$	2.97918	+	5.16010i	0.141227	+	0.244612i
$446$	−11.7426	+	20.3389i	−0.556030	+	0.963072i
$447$	18.4853			0.874324
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$	14.2426			0.672152			0.336076	−	0.941835i	$-0.390900\pi$
$449$	14.2426			0.672152			0.336076	+	0.941835i	$0.390900\pi$
$450$	1.24264	−	2.15232i	0.0585786	−	0.101461i
$451$	−0.292893	−	0.507306i	−0.0137918	−	0.0238881i
$452$	−5.12132	−	8.87039i	−0.240887	−	0.417228i
$453$	−5.67157	+	9.82345i	−0.266474	+	0.461546i
$454$	1.10051			0.0516493
$455$	−4.48528	+	10.9867i	−0.210273	+	0.515062i
$456$	−1.00000			−0.0468293
$457$	−18.0563	+	31.2745i	−0.844640	+	1.46296i	0.0412927	+	0.999147i	$0.486852\pi$
$457$	−18.0563	+	31.2745i	−0.844640	+	1.46296i	−0.885933	+	0.463813i	$0.846481\pi$
$458$	9.89949	+	17.1464i	0.462573	+	0.801200i
$459$	−2.12132	−	3.67423i	−0.0990148	−	0.171499i
$460$	2.70711	−	4.68885i	0.126220	−	0.218619i
$461$	−17.3137			−0.806380			−0.403190	−	0.915116i	$-0.632099\pi$
$461$	−17.3137			−0.806380			−0.403190	+	0.915116i	$0.632099\pi$
$462$	1.62132	+	2.09077i	0.0754306	+	0.0972714i
$463$	1.65685			0.0770005			0.0385003	−	0.999259i	$-0.487742\pi$
$463$	1.65685			0.0770005			0.0385003	+	0.999259i	$0.487742\pi$
$464$	−1.08579	+	1.88064i	−0.0504064	+	0.0873064i
$465$	8.44975	+	14.6354i	0.391848	+	0.678700i
$466$	2.58579	+	4.47871i	0.119784	+	0.207472i
$467$	7.58579	−	13.1390i	0.351028	−	0.607999i	−0.635402	−	0.772182i	$-0.719165\pi$
$467$	7.58579	−	13.1390i	0.351028	−	0.607999i	0.986430	+	0.164183i	$0.0524987\pi$
$468$	2.82843			0.130744
$469$	−3.24264	−	4.18154i	−0.149731	−	0.193086i
$470$	−5.02944			−0.231991
$471$	−2.24264	+	3.88437i	−0.103335	+	0.178982i
$472$	−3.03553	−	5.25770i	−0.139722	−	0.242005i
$473$	3.12132	+	5.40629i	0.143518	+	0.248581i
$474$	−0.0857864	+	0.148586i	−0.00394030	+	0.00682480i
$475$	−2.48528			−0.114033
$476$	−4.24264	+	10.3923i	−0.194461	+	0.476331i
$477$	1.82843			0.0837179
$478$	−14.1421	+	24.4949i	−0.646846	+	1.12037i
$479$	−0.656854	−	1.13770i	−0.0300124	−	0.0519831i	0.850629	−	0.525766i	$-0.176221\pi$
$479$	−0.656854	−	1.13770i	−0.0300124	−	0.0519831i	−0.880641	+	0.473783i	$0.842888\pi$
$480$	−0.792893	−	1.37333i	−0.0361905	−	0.0626837i
$481$	−0.343146	+	0.594346i	−0.0156461	+	0.0270998i
$482$	0.556349			0.0253410
$483$	8.94975	−	1.22474i	0.407228	−	0.0557278i
$484$	−10.0000			−0.454545
$485$	−4.42893	+	7.67114i	−0.201107	+	0.348328i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	19.3995	+	33.6009i	0.879075	+	1.52260i	0.852357	+	0.522960i	$0.175172\pi$
$487$	19.3995	+	33.6009i	0.879075	+	1.52260i	0.0267175	+	0.999643i	$0.491495\pi$
$488$	2.41421	−	4.18154i	0.109286	−	0.189289i
$489$	10.8284			0.489678
$490$	7.92893	+	7.76874i	0.358193	+	0.350956i
$491$	−9.14214			−0.412579			−0.206289	−	0.978491i	$-0.566139\pi$
$491$	−9.14214			−0.412579			−0.206289	+	0.978491i	$0.566139\pi$
$492$	−0.292893	+	0.507306i	−0.0132046	+	0.0228711i
$493$	4.60660	+	7.97887i	0.207471	+	0.359350i
$494$	−1.41421	−	2.44949i	−0.0636285	−	0.110208i
$495$	−0.792893	+	1.37333i	−0.0356379	+	0.0617267i
$496$	−10.6569			−0.478507
$497$	20.7071	−	2.83370i	0.928841	−	0.127109i
$498$	17.1421			0.768157
$499$	−4.65685	+	8.06591i	−0.208469	+	0.361080i	−0.951233	−	0.308475i	$-0.900182\pi$
$499$	−4.65685	+	8.06591i	−0.208469	+	0.361080i	0.742763	+	0.669554i	$0.233515\pi$
$500$	−5.93503	−	10.2798i	−0.265423	−	0.459725i
$501$	−3.36396	−	5.82655i	−0.150291	−	0.260311i
$502$	10.5000	−	18.1865i	0.468638	−	0.811705i
$503$	9.75736			0.435059			0.217530	−	0.976054i	$-0.430200\pi$
$503$	9.75736			0.435059			0.217530	+	0.976054i	$0.430200\pi$
$504$	1.00000	−	2.44949i	0.0445435	−	0.109109i
$505$	−23.7401			−1.05642
$506$	1.70711	−	2.95680i	0.0758902	−	0.131446i
$507$	−2.50000	−	4.33013i	−0.111029	−	0.192308i
$508$	2.91421	+	5.04757i	0.129297	+	0.223950i
$509$	7.15685	−	12.3960i	0.317222	−	0.549445i	−0.662685	−	0.748898i	$-0.730583\pi$
$509$	7.15685	−	12.3960i	0.317222	−	0.549445i	0.979907	+	0.199453i	$0.0639166\pi$
$510$	−6.72792			−0.297917
$511$	−24.0416	−	31.0028i	−1.06354	−	1.37148i
$512$	1.00000			0.0441942
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	−14.6569	−	25.3864i	−0.645858	−	1.11866i
$516$	3.12132	−	5.40629i	0.137408	−	0.237998i
$517$	−3.17157			−0.139486
$518$	0.393398	+	0.507306i	0.0172849	+	0.0222897i
$519$	15.7990			0.693499
$520$	2.24264	−	3.88437i	0.0983463	−	0.170341i
$521$	−17.9706	−	31.1259i	−0.787305	−	1.36365i	−0.927613	−	0.373544i	$-0.878143\pi$
$521$	−17.9706	−	31.1259i	−0.787305	−	1.36365i	0.140308	−	0.990108i	$-0.455191\pi$
$522$	−1.08579	−	1.88064i	−0.0475236	−	0.0823133i
$523$	−2.05025	+	3.55114i	−0.0896513	+	0.155281i	−0.907364	−	0.420346i	$-0.861909\pi$
$523$	−2.05025	+	3.55114i	−0.0896513	+	0.155281i	0.817712	+	0.575627i	$0.195242\pi$
$524$	4.31371			0.188445
$525$	2.48528	−	6.08767i	0.108467	−	0.265688i
$526$	−11.5563			−0.503881
$527$	−22.6066	+	39.1558i	−0.984759	+	1.70565i
$528$	−0.500000	−	0.866025i	−0.0217597	−	0.0376889i
$529$	5.67157	+	9.82345i	0.246590	+	0.427107i
$530$	1.44975	−	2.51104i	0.0629730	−	0.109072i
$531$	6.07107			0.263462
$532$	−2.62132	+	0.358719i	−0.113649	+	0.0155525i
$533$	−1.65685			−0.0717663
$534$	1.87868	−	3.25397i	0.0812984	−	0.140813i
$535$	9.29899	+	16.1063i	0.402030	+	0.696337i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−3.75736	+	6.50794i	−0.162142	+	0.280838i
$538$	1.00000			0.0431131
$539$	5.00000	+	4.89898i	0.215365	+	0.211014i
$540$	1.58579			0.0682414
$541$	15.1924	−	26.3140i	0.653172	−	1.13133i	−0.329177	−	0.944268i	$-0.606771\pi$
$541$	15.1924	−	26.3140i	0.653172	−	1.13133i	0.982349	−	0.187058i	$-0.0598954\pi$
$542$	−4.44975	−	7.70719i	−0.191133	−	0.331052i
$543$	−10.2426	−	17.7408i	−0.439554	−	0.761329i
$544$	2.12132	−	3.67423i	0.0909509	−	0.157532i
$545$	−2.78680			−0.119373
$546$	7.41421	−	1.01461i	0.317299	−	0.0434214i
$547$	10.7279			0.458693			0.229346	−	0.973345i	$-0.426341\pi$
$547$	10.7279			0.458693			0.229346	+	0.973345i	$0.426341\pi$
$548$	0.171573	−	0.297173i	0.00732923	−	0.0126946i
$549$	2.41421	+	4.18154i	0.103036	+	0.178464i
$550$	−1.24264	−	2.15232i	−0.0529864	−	0.0917751i
$551$	−1.08579	+	1.88064i	−0.0462561	+	0.0801178i
$552$	−3.41421			−0.145319
$553$	−0.171573	+	0.420266i	−0.00729602	+	0.0178715i
$554$	−13.7574			−0.584494
$555$	−0.192388	+	0.333226i	−0.00816642	+	0.0141447i
$556$	−3.94975	−	6.84116i	−0.167507	−	0.290130i
$557$	−12.2071	−	21.1433i	−0.517232	−	0.895872i	−0.999800	−	0.0200131i	$-0.993629\pi$
$557$	−12.2071	−	21.1433i	−0.517232	−	0.895872i	0.482568	−	0.875859i	$-0.339704\pi$
$558$	5.32843	−	9.22911i	0.225570	−	0.390699i
$559$	17.6569			0.746805
$560$	−2.57107	−	3.31552i	−0.108647	−	0.140106i
$561$	−4.24264			−0.179124
$562$	0.656854	−	1.13770i	0.0277077	−	0.0479912i
$563$	17.4497	+	30.2238i	0.735419	+	1.27378i	0.954539	+	0.298085i	$0.0963480\pi$
$563$	17.4497	+	30.2238i	0.735419	+	1.27378i	−0.219120	+	0.975698i	$0.570319\pi$
$564$	1.58579	+	2.74666i	0.0667737	+	0.115655i
$565$	8.12132	−	14.0665i	0.341667	−	0.591784i
$566$	21.5563			0.906081
$567$	1.62132	+	2.09077i	0.0680891	+	0.0878041i
$568$	−7.89949			−0.331455
$569$	11.3137	−	19.5959i	0.474295	−	0.821504i	−0.525271	−	0.850935i	$-0.676036\pi$
$569$	11.3137	−	19.5959i	0.474295	−	0.821504i	0.999567	+	0.0294311i	$0.00936956\pi$
$570$	−0.792893	−	1.37333i	−0.0332106	−	0.0575225i
$571$	−17.2635	−	29.9012i	−0.722453	−	1.25133i	−0.960014	−	0.279953i	$-0.909681\pi$
$571$	−17.2635	−	29.9012i	−0.722453	−	1.25133i	0.237561	−	0.971373i	$-0.423652\pi$
$572$	1.41421	−	2.44949i	0.0591312	−	0.102418i
$573$	18.1421			0.757899
$574$	−0.585786	+	1.43488i	−0.0244503	+	0.0598906i
$575$	−8.48528			−0.353861
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.74264	−	13.4106i	−0.322330	−	0.558293i	0.658638	−	0.752460i	$-0.271133\pi$
$577$	−7.74264	−	13.4106i	−0.322330	−	0.558293i	−0.980968	+	0.194167i	$0.937800\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	−11.8640	+	20.5490i	−0.493049	+	0.853987i
$580$	−3.44365			−0.142990
$581$	44.9350	−	6.14922i	1.86422	−	0.255113i
$582$	5.58579			0.231538
$583$	0.914214	−	1.58346i	0.0378629	−	0.0655804i
$584$	7.41421	+	12.8418i	0.306802	+	0.531397i
$585$	2.24264	+	3.88437i	0.0927218	+	0.160599i
$586$	11.5000	−	19.9186i	0.475061	−	0.822829i
$587$	23.6274			0.975208			0.487604	−	0.873065i	$-0.337871\pi$
$587$	23.6274			0.975208			0.487604	+	0.873065i	$0.337871\pi$
$588$	1.74264	−	6.77962i	0.0718653	−	0.279587i
$589$	−10.6569			−0.439108
$590$	4.81371	−	8.33759i	0.198177	−	0.343253i
$591$	0.585786	+	1.01461i	0.0240960	+	0.0417356i
$592$	−0.121320	−	0.210133i	−0.00498624	−	0.00863641i
$593$	−14.3848	+	24.9152i	−0.590712	+	1.02314i	0.403425	+	0.915013i	$0.367820\pi$
$593$	−14.3848	+	24.9152i	−0.590712	+	1.02314i	−0.994137	+	0.108130i	$0.965514\pi$
$594$	1.00000			0.0410305
$595$	−17.6360	+	2.41344i	−0.723007	+	0.0989413i
$596$	−18.4853			−0.757187
$597$	4.24264	−	7.34847i	0.173640	−	0.300753i
$598$	−4.82843	−	8.36308i	−0.197449	−	0.341992i
$599$	−19.1213	−	33.1191i	−0.781276	−	1.35321i	−0.931199	−	0.364512i	$-0.881236\pi$
$599$	−19.1213	−	33.1191i	−0.781276	−	1.35321i	0.149923	−	0.988698i	$-0.452098\pi$
$600$	−1.24264	+	2.15232i	−0.0507306	+	0.0878680i
$601$	−29.5858			−1.20683			−0.603415	−	0.797428i	$-0.706194\pi$
$601$	−29.5858			−1.20683			−0.603415	+	0.797428i	$0.706194\pi$
$602$	6.24264	−	15.2913i	0.254431	−	0.623226i
$603$	−2.00000			−0.0814463
$604$	5.67157	−	9.82345i	0.230773	−	0.399711i
$605$	−7.92893	−	13.7333i	−0.322357	−	0.558339i
$606$	7.48528	+	12.9649i	0.304069	+	0.526663i
$607$	8.39949	−	14.5484i	0.340925	−	0.590499i	−0.643680	−	0.765295i	$-0.722593\pi$
$607$	8.39949	−	14.5484i	0.340925	−	0.590499i	0.984605	+	0.174796i	$0.0559264\pi$
$608$	1.00000			0.0405554
$609$	−3.52082	−	4.54026i	−0.142671	−	0.183981i
$610$	7.65685			0.310017
$611$	−4.48528	+	7.76874i	−0.181455	+	0.314289i
$612$	2.12132	+	3.67423i	0.0857493	+	0.148522i
$613$	12.6777	+	21.9584i	0.512046	+	0.886890i	0.999902	+	0.0139661i	$0.00444570\pi$
$613$	12.6777	+	21.9584i	0.512046	+	0.886890i	−0.487856	+	0.872924i	$0.662221\pi$
$614$	−3.70711	+	6.42090i	−0.149607	+	0.259126i
$615$	−0.928932			−0.0374582
$616$	−1.62132	−	2.09077i	−0.0653249	−	0.0842395i
$617$	30.5269			1.22897			0.614484	−	0.788930i	$-0.289364\pi$
$617$	30.5269			1.22897			0.614484	+	0.788930i	$0.289364\pi$
$618$	−9.24264	+	16.0087i	−0.371794	+	0.643965i
$619$	2.89949	+	5.02207i	0.116541	+	0.201854i	0.918395	−	0.395666i	$-0.129486\pi$
$619$	2.89949	+	5.02207i	0.116541	+	0.201854i	−0.801854	+	0.597520i	$0.796153\pi$
$620$	−8.44975	−	14.6354i	−0.339350	−	0.587771i
$621$	1.70711	−	2.95680i	0.0685038	−	0.118652i
$622$	22.2426			0.891849
$623$	3.75736	−	9.20361i	0.150535	−	0.368735i
$624$	−2.82843			−0.113228
$625$	3.19848	−	5.53994i	0.127939	−	0.221598i
$626$	1.91421	+	3.31552i	0.0765074	+	0.132515i
$627$	−0.500000	−	0.866025i	−0.0199681	−	0.0345857i
$628$	2.24264	−	3.88437i	0.0894911	−	0.155003i
$629$	−1.02944			−0.0410464
$630$	4.15685	−	0.568852i	0.165613	−	0.0226636i
$631$	−6.55635			−0.261004			−0.130502	−	0.991448i	$-0.541659\pi$
$631$	−6.55635			−0.261004			−0.130502	+	0.991448i	$0.541659\pi$
$632$	0.0857864	−	0.148586i	0.00341240	−	0.00591045i
$633$	−7.53553	−	13.0519i	−0.299511	−	0.518768i
$634$	4.74264	+	8.21449i	0.188354	+	0.326239i
$635$	−4.62132	+	8.00436i	−0.183392	+	0.317643i
$636$	−1.82843			−0.0725019
$637$	19.0711	−	5.31925i	0.755623	−	0.210756i
$638$	−2.17157			−0.0859734
$639$	3.94975	−	6.84116i	0.156250	−	0.270632i
$640$	0.792893	+	1.37333i	0.0313419	+	0.0542857i
$641$	9.29289	+	16.0958i	0.367047	+	0.635744i	0.989102	−	0.147229i	$-0.0470354\pi$
$641$	9.29289	+	16.0958i	0.367047	+	0.635744i	−0.622055	+	0.782973i	$0.713702\pi$
$642$	5.86396	−	10.1567i	0.231432	−	0.400852i
$643$	42.2426			1.66589			0.832944	−	0.553358i	$-0.186654\pi$
$643$	42.2426			1.66589			0.832944	+	0.553358i	$0.186654\pi$
$644$	−8.94975	+	1.22474i	−0.352669	+	0.0482617i
$645$	9.89949			0.389792
$646$	2.12132	−	3.67423i	0.0834622	−	0.144561i
$647$	−21.6777	−	37.5468i	−0.852237	−	1.47612i	−0.879185	−	0.476481i	$-0.841912\pi$
$647$	−21.6777	−	37.5468i	−0.852237	−	1.47612i	0.0269476	−	0.999637i	$-0.491421\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	3.03553	−	5.25770i	0.119155	−	0.206383i
$650$	−7.02944			−0.275717
$651$	10.6569	−	26.1039i	0.417675	−	1.02309i
$652$	−10.8284			−0.424074
$653$	13.1066	−	22.7013i	0.512901	−	0.888371i	−0.486987	−	0.873409i	$-0.661904\pi$
$653$	13.1066	−	22.7013i	0.512901	−	0.888371i	0.999888	−	0.0149614i	$-0.00476253\pi$
$654$	0.878680	+	1.52192i	0.0343591	+	0.0595117i
$655$	3.42031	+	5.92415i	0.133643	+	0.231476i
$656$	0.292893	−	0.507306i	0.0114356	−	0.0198070i
$657$	−14.8284			−0.578512
$658$	5.14214	+	6.63103i	0.200461	+	0.258504i
$659$	2.97056			0.115717			0.0578583	−	0.998325i	$-0.481573\pi$
$659$	2.97056			0.115717			0.0578583	+	0.998325i	$0.481573\pi$
$660$	0.792893	−	1.37333i	0.0308633	−	0.0534568i
$661$	−16.1924	−	28.0460i	−0.629811	−	1.09086i	−0.987589	−	0.157058i	$-0.949799\pi$
$661$	−16.1924	−	28.0460i	−0.629811	−	1.09086i	0.357778	−	0.933806i	$-0.383534\pi$
$662$	2.19239	+	3.79733i	0.0852096	+	0.147587i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$	−17.1421			−0.665244
$665$	−2.57107	−	3.31552i	−0.0997017	−	0.128570i
$666$	0.242641			0.00940214
$667$	−3.70711	+	6.42090i	−0.143540	+	0.248618i
$668$	3.36396	+	5.82655i	0.130156	+	0.225436i
$669$	11.7426	+	20.3389i	0.453997	+	0.786345i
$670$	−1.58579	+	2.74666i	−0.0612643	+	0.106113i
$671$	4.82843			0.186399
$672$	−1.00000	+	2.44949i	−0.0385758	+	0.0944911i
$673$	−2.27208			−0.0875822			−0.0437911	−	0.999041i	$-0.513944\pi$
$673$	−2.27208			−0.0875822			−0.0437911	+	0.999041i	$0.513944\pi$
$674$	−1.03553	+	1.79360i	−0.0398873	+	0.0690868i
$675$	−1.24264	−	2.15232i	−0.0478293	−	0.0828427i
$676$	2.50000	+	4.33013i	0.0961538	+	0.166543i
$677$	11.1569	−	19.3242i	0.428793	−	0.742691i	−0.567973	−	0.823047i	$-0.692272\pi$
$677$	11.1569	−	19.3242i	0.428793	−	0.742691i	0.996766	+	0.0803560i	$0.0256057\pi$
$678$	−10.2426			−0.393366
$679$	14.6421	−	2.00373i	0.561914	−	0.0768961i
$680$	6.72792			0.258004
$681$	0.550253	−	0.953065i	0.0210857	−	0.0365215i
$682$	−5.32843	−	9.22911i	−0.204036	−	0.353401i
$683$	−15.6213	−	27.0569i	−0.597733	−	1.03530i	−0.993155	−	0.116805i	$-0.962735\pi$
$683$	−15.6213	−	27.0569i	−0.597733	−	1.03530i	0.395422	−	0.918500i	$-0.370598\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$	0.544156			0.0207911
$686$	2.13604	−	18.3967i	0.0815543	−	0.702388i
$687$	19.7990			0.755379
$688$	−3.12132	+	5.40629i	−0.118999	+	0.206113i
$689$	−2.58579	−	4.47871i	−0.0985106	−	0.170625i
$690$	−2.70711	−	4.68885i	−0.103058	−	0.178501i
$691$	−10.2218	+	17.7047i	−0.388857	+	0.673519i	−0.992296	−	0.123889i	$-0.960463\pi$
$691$	−10.2218	+	17.7047i	−0.388857	+	0.673519i	0.603439	+	0.797409i	$0.293797\pi$
$692$	−15.7990			−0.600587
$693$	2.62132	−	0.358719i	0.0995757	−	0.0136266i
$694$	−34.0000			−1.29062
$695$	6.26346	−	10.8486i	0.237586	−	0.411512i
$696$	1.08579	+	1.88064i	0.0411566	+	0.0712854i
$697$	−1.24264	−	2.15232i	−0.0470684	−	0.0815248i
$698$	3.87868	−	6.71807i	0.146810	−	0.254283i
$699$	5.17157			0.195607
$700$	−2.48528	+	6.08767i	−0.0939348	+	0.230092i
$701$	41.0416			1.55012			0.775060	−	0.631887i	$-0.217719\pi$
$701$	41.0416			1.55012			0.775060	+	0.631887i	$0.217719\pi$
$702$	1.41421	−	2.44949i	0.0533761	−	0.0924500i
$703$	−0.121320	−	0.210133i	−0.00457568	−	0.00792532i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−2.51472	+	4.35562i	−0.0947098	+	0.164042i
$706$	14.1005			0.530680
$707$	24.2721	+	31.3000i	0.912845	+	1.17716i
$708$	−6.07107			−0.228165
$709$	25.1924	−	43.6345i	0.946120	−	1.63873i	0.192627	−	0.981272i	$-0.438299\pi$
$709$	25.1924	−	43.6345i	0.946120	−	1.63873i	0.753493	−	0.657456i	$-0.228367\pi$
$710$	−6.26346	−	10.8486i	−0.235063	−	0.407142i
$711$	0.0857864	+	0.148586i	0.00321724	+	0.00557243i
$712$	−1.87868	+	3.25397i	−0.0704065	+	0.121948i
$713$	−36.3848			−1.36262
$714$	6.87868	+	8.87039i	0.257428	+	0.331966i
$715$	4.48528			0.167740
$716$	3.75736	−	6.50794i	0.140419	−	0.243213i
$717$	14.1421	+	24.4949i	0.528148	+	0.914779i
$718$	−5.00000	−	8.66025i	−0.186598	−	0.323198i
$719$	−4.41421	+	7.64564i	−0.164622	+	0.285134i	−0.936521	−	0.350611i	$-0.885974\pi$
$719$	−4.41421	+	7.64564i	−0.164622	+	0.285134i	0.771899	+	0.635746i	$0.219307\pi$
$720$	−1.58579			−0.0590988
$721$	−18.4853	+	45.2795i	−0.688428	+	1.68630i
$722$	1.00000			0.0372161
$723$	0.278175	−	0.481813i	0.0103454	−	0.0179188i
$724$	10.2426	+	17.7408i	0.380665	+	0.659331i
$725$	2.69848	+	4.67391i	0.100219	+	0.173585i
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$	43.7279			1.62178			0.810889	−	0.585199i	$-0.198984\pi$
$727$	43.7279			1.62178			0.810889	+	0.585199i	$0.198984\pi$
$728$	−7.41421	+	1.01461i	−0.274789	+	0.0376040i
$729$	1.00000			0.0370370
$730$	−11.7574	+	20.3643i	−0.435159	+	0.753718i
$731$	13.2426	+	22.9369i	0.489797	+	0.848353i
$732$	−2.41421	−	4.18154i	−0.0892319	−	0.154554i
$733$	−17.0919	+	29.6040i	−0.631303	+	1.09345i	0.355982	+	0.934493i	$0.384146\pi$
$733$	−17.0919	+	29.6040i	−0.631303	+	1.09345i	−0.987286	+	0.158956i	$0.949187\pi$
$734$	5.24264			0.193509
$735$	10.6924	−	2.98229i	0.394395	−	0.110003i
$736$	3.41421			0.125850
$737$	−1.00000	+	1.73205i	−0.0368355	+	0.0638009i
$738$	0.292893	+	0.507306i	0.0107815	+	0.0186742i
$739$	−16.7782	−	29.0607i	−0.617195	−	1.06901i	−0.989995	−	0.141102i	$-0.954936\pi$
$739$	−16.7782	−	29.0607i	−0.617195	−	1.06901i	0.372800	−	0.927912i	$-0.378398\pi$
$740$	0.192388	−	0.333226i	0.00707233	−	0.0122496i
$741$	−2.82843			−0.103905
$742$	−4.79289	+	0.655892i	−0.175953	+	0.0240786i
$743$	−48.9117			−1.79440			−0.897198	−	0.441629i	$-0.854401\pi$
$743$	−48.9117			−1.79440			−0.897198	+	0.441629i	$0.854401\pi$
$744$	−5.32843	+	9.22911i	−0.195350	+	0.338355i
$745$	−14.6569	−	25.3864i	−0.536986	−	0.930086i
$746$	−0.242641	−	0.420266i	−0.00888371	−	0.0153870i
$747$	8.57107	−	14.8455i	0.313599	−	0.543169i
$748$	4.24264			0.155126
$749$	11.7279	−	28.7274i	0.428529	−	1.04968i
$750$	−11.8701			−0.433433
$751$	8.05635	−	13.9540i	0.293980	−	0.509189i	−0.680767	−	0.732500i	$-0.738353\pi$
$751$	8.05635	−	13.9540i	0.293980	−	0.509189i	0.974747	+	0.223311i	$0.0716866\pi$
$752$	−1.58579	−	2.74666i	−0.0578277	−	0.100160i
$753$	−10.5000	−	18.1865i	−0.382641	−	0.662754i
$754$	−3.07107	+	5.31925i	−0.111842	+	0.193715i
$755$	17.9878			0.654643
$756$	−1.62132	−	2.09077i	−0.0589669	−	0.0760406i
$757$	1.21320			0.0440946			0.0220473	−	0.999757i	$-0.492982\pi$
$757$	1.21320			0.0440946			0.0220473	+	0.999757i	$0.492982\pi$
$758$	−1.65685	+	2.86976i	−0.0601797	+	0.104234i
$759$	−1.70711	−	2.95680i	−0.0619641	−	0.107325i
$760$	0.792893	+	1.37333i	0.0287613	+	0.0498160i
$761$	−3.07107	+	5.31925i	−0.111326	+	0.192822i	−0.916305	−	0.400481i	$-0.868843\pi$
$761$	−3.07107	+	5.31925i	−0.111326	+	0.192822i	0.804979	+	0.593303i	$0.202176\pi$
$762$	5.82843			0.211142
$763$	2.84924	+	3.67423i	0.103150	+	0.133016i
$764$	−18.1421			−0.656359
$765$	−3.36396	+	5.82655i	−0.121624	+	0.210659i
$766$	−7.82843	−	13.5592i	−0.282853	−	0.489915i
$767$	−8.58579	−	14.8710i	−0.310015	−	0.536961i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	33.3431			1.20238			0.601192	−	0.799104i	$-0.294693\pi$
$769$	33.3431			1.20238			0.601192	+	0.799104i	$0.294693\pi$
$770$	1.58579	−	3.88437i	0.0571478	−	0.139983i
$771$	−6.00000			−0.216085
$772$	11.8640	−	20.5490i	0.426993	−	0.739574i
$773$	17.3137	+	29.9882i	0.622731	+	1.07860i	0.988975	+	0.148083i	$0.0473102\pi$
$773$	17.3137	+	29.9882i	0.622731	+	1.07860i	−0.366244	+	0.930519i	$0.619357\pi$
$774$	−3.12132	−	5.40629i	−0.112194	−	0.194325i
$775$	−13.2426	+	22.9369i	−0.475690	+	0.823919i
$776$	−5.58579			−0.200518
$777$	0.636039	−	0.0870399i	0.0228178	−	0.00312254i
$778$	23.1716			0.830741
$779$	0.292893	−	0.507306i	0.0104940	−	0.0181761i
$780$	−2.24264	−	3.88437i	−0.0802994	−	0.139083i
$781$	−3.94975	−	6.84116i	−0.141333	−	0.244796i
$782$	7.24264	−	12.5446i	0.258996	−	0.448595i
$783$	−2.17157			−0.0776057
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$	7.11270			0.253863
$786$	2.15685	−	3.73578i	0.0769324	−	0.133251i
$787$	−9.34315	−	16.1828i	−0.333047	−	0.576855i	0.650061	−	0.759882i	$-0.274744\pi$
$787$	−9.34315	−	16.1828i	−0.333047	−	0.576855i	−0.983108	+	0.183028i	$0.941410\pi$
$788$	−0.585786	−	1.01461i	−0.0208678	−	0.0361441i
$789$	−5.77817	+	10.0081i	−0.205708	+	0.356298i
$790$	0.272078			0.00968010
$791$	−26.8492	+	3.67423i	−0.954649	+	0.130641i
$792$	−1.00000			−0.0355335
$793$	6.82843	−	11.8272i	0.242485	−	0.419996i
$794$	5.41421	+	9.37769i	0.192143	+	0.332802i
$795$	−1.44975	−	2.51104i	−0.0514172	−	0.0890573i
$796$	−4.24264	+	7.34847i	−0.150376	+	0.260460i
$797$	−9.00000			−0.318796			−0.159398	−	0.987214i	$-0.550955\pi$
$797$	−9.00000			−0.318796			−0.159398	+	0.987214i	$0.550955\pi$
$798$	−1.00000	+	2.44949i	−0.0353996	+	0.0867110i
$799$	−13.4558			−0.476034
$800$	1.24264	−	2.15232i	0.0439340	−	0.0760959i
$801$	−1.87868	−	3.25397i	−0.0663799	−	0.114973i
$802$	−7.07107	−	12.2474i	−0.249688	−	0.432472i
$803$	−7.41421	+	12.8418i	−0.261642	+	0.453177i
$804$	2.00000			0.0705346
$805$	−8.77817	−	11.3199i	−0.309390	−	0.398973i
$806$	−30.1421			−1.06171
$807$	0.500000	−	0.866025i	0.0176008	−	0.0304855i
$808$	−7.48528	−	12.9649i	−0.263331	−	0.456103i
$809$	25.4350	+	44.0548i	0.894248	+	1.54888i	0.834733	+	0.550656i	$0.185622\pi$
$809$	25.4350	+	44.0548i	0.894248	+	1.54888i	0.0595154	+	0.998227i	$0.481044\pi$
$810$	0.792893	−	1.37333i	0.0278594	−	0.0482539i
$811$	3.55635			0.124880			0.0624402	−	0.998049i	$-0.480112\pi$
$811$	3.55635			0.124880			0.0624402	+	0.998049i	$0.480112\pi$
$812$	3.52082	+	4.54026i	0.123556	+	0.159332i
$813$	−8.89949			−0.312119
$814$	0.121320	−	0.210133i	0.00425228	−	0.00736516i
$815$	−8.58579	−	14.8710i	−0.300747	−	0.520909i
$816$	−2.12132	−	3.67423i	−0.0742611	−	0.128624i
$817$	−3.12132	+	5.40629i	−0.109201	+	0.189142i
$818$	30.8995			1.08038
$819$	2.82843	−	6.92820i	0.0988332	−	0.242091i
$820$	0.928932			0.0324397
$821$	−15.5919	+	27.0059i	−0.544160	+	0.942514i	0.454499	+	0.890747i	$0.349818\pi$
$821$	−15.5919	+	27.0059i	−0.544160	+	0.942514i	−0.998659	+	0.0517662i	$0.983515\pi$
$822$	−0.171573	−	0.297173i	−0.00598429	−	0.0103651i
$823$	−12.1421	−	21.0308i	−0.423248	−	0.733087i	0.573007	−	0.819551i	$-0.305777\pi$
$823$	−12.1421	−	21.0308i	−0.423248	−	0.733087i	−0.996255	+	0.0864631i	$0.972444\pi$
$824$	9.24264	−	16.0087i	0.321983	−	0.557690i
$825$	−2.48528			−0.0865264
$826$	−15.9142	+	2.17781i	−0.553726	+	0.0757757i
$827$	27.7279			0.964194			0.482097	−	0.876118i	$-0.339875\pi$
$827$	27.7279			0.964194			0.482097	+	0.876118i	$0.339875\pi$
$828$	−1.70711	+	2.95680i	−0.0593261	+	0.102756i
$829$	24.4853	+	42.4098i	0.850409	+	1.47295i	0.880840	+	0.473415i	$0.156979\pi$
$829$	24.4853	+	42.4098i	0.850409	+	1.47295i	−0.0304307	+	0.999537i	$0.509688\pi$
$830$	−13.5919	−	23.5418i	−0.471781	−	0.817149i
$831$	−6.87868	+	11.9142i	−0.238619	+	0.413300i
$832$	2.82843			0.0980581
$833$	21.2132	+	20.7846i	0.734994	+	0.720144i
$834$	−7.89949			−0.273537
$835$	−5.33452	+	9.23967i	−0.184609	+	0.319752i
$836$	0.500000	+	0.866025i	0.0172929	+	0.0299521i
$837$	−5.32843	−	9.22911i	−0.184177	−	0.319005i
$838$	15.4853	−	26.8213i	0.534930	−	0.926526i
$839$	53.2132			1.83712			0.918562	−	0.395277i	$-0.129351\pi$
$839$	53.2132			1.83712			0.918562	+	0.395277i	$0.129351\pi$
$840$	−4.15685	+	0.568852i	−0.143425	+	0.0196273i
$841$	−24.2843			−0.837389
$842$	−7.58579	+	13.1390i	−0.261423	+	0.452799i
$843$	−0.656854	−	1.13770i	−0.0226233	−	0.0391846i
$844$	7.53553	+	13.0519i	0.259384	+	0.449266i
$845$	−3.96447	+	6.86666i	−0.136382	+	0.236220i
$846$	3.17157			0.109041
$847$	−10.0000	+	24.4949i	−0.343604	+	0.841655i
$848$	1.82843			0.0627884
$849$	10.7782	−	18.6683i	0.369906	−	0.640696i
$850$	−5.27208	−	9.13151i	−0.180831	−	0.313208i
$851$	−0.414214	−	0.717439i	−0.0141991	−	0.0245935i
$852$	−3.94975	+	6.84116i	−0.135316	+	0.234374i
$853$	57.4975			1.96868			0.984338	−	0.176291i	$-0.0564101\pi$
$853$	57.4975			1.96868			0.984338	+	0.176291i	$0.0564101\pi$
$854$	−7.82843	−	10.0951i	−0.267883	−	0.345448i
$855$	−1.58579			−0.0542328
$856$	−5.86396	+	10.1567i	−0.200426	+	0.347148i
$857$	9.34315	+	16.1828i	0.319156	+	0.552794i	0.980312	−	0.197454i	$-0.0632673\pi$
$857$	9.34315	+	16.1828i	0.319156	+	0.552794i	−0.661156	+	0.750248i	$0.729934\pi$
$858$	−1.41421	−	2.44949i	−0.0482805	−	0.0836242i
$859$	24.2132	−	41.9385i	0.826144	−	1.43092i	−0.0748981	−	0.997191i	$-0.523863\pi$
$859$	24.2132	−	41.9385i	0.826144	−	1.43092i	0.901042	−	0.433732i	$-0.142804\pi$
$860$	−9.89949			−0.337570
$861$	0.949747	+	1.22474i	0.0323673	+	0.0417392i
$862$	−14.1005			−0.480265
$863$	−19.1213	+	33.1191i	−0.650897	+	1.12739i	0.332008	+	0.943277i	$0.392274\pi$
$863$	−19.1213	+	33.1191i	−0.650897	+	1.12739i	−0.982906	+	0.184111i	$0.941060\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−12.5269	−	21.6972i	−0.425928	−	0.737729i
$866$	15.4142	−	26.6982i	0.523796	−	0.907242i
$867$	−1.00000			−0.0339618
$868$	−10.6569	+	26.1039i	−0.361717	+	0.886023i
$869$	0.171573			0.00582021
$870$	−1.72183	+	2.98229i	−0.0583753	+	0.101109i
$871$	2.82843	+	4.89898i	0.0958376	+	0.165996i
$872$	−0.878680	−	1.52192i	−0.0297558	−	0.0515386i
$873$	2.79289	−	4.83743i	0.0945251	−	0.163722i
$874$	3.41421			0.115487
$875$	−31.1152	+	4.25802i	−1.05189	+	0.143947i
$876$	14.8284			0.501006
$877$	−20.3640	+	35.2714i	−0.687642	+	1.19103i	0.284957	+	0.958540i	$0.408021\pi$
$877$	−20.3640	+	35.2714i	−0.687642	+	1.19103i	−0.972599	+	0.232491i	$0.925313\pi$
$878$	−11.2279	−	19.4473i	−0.378924	−	0.656316i
$879$	−11.5000	−	19.9186i	−0.387885	−	0.671837i
$880$	−0.792893	+	1.37333i	−0.0267284	+	0.0462950i
$881$	−23.9411			−0.806597			−0.403299	−	0.915068i	$-0.632136\pi$
$881$	−23.9411			−0.806597			−0.403299	+	0.915068i	$0.632136\pi$
$882$	−5.00000	−	4.89898i	−0.168359	−	0.164957i
$883$	46.8701			1.57730			0.788652	−	0.614840i	$-0.210780\pi$
$883$	46.8701			1.57730			0.788652	+	0.614840i	$0.210780\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$	−4.81371	−	8.33759i	−0.161811	−	0.280265i
$886$	7.32843	+	12.6932i	0.246203	+	0.426437i
$887$	25.5355	−	44.2288i	0.857399	−	1.48506i	−0.0170018	−	0.999855i	$-0.505412\pi$
$887$	25.5355	−	44.2288i	0.857399	−	1.48506i	0.874401	−	0.485204i	$-0.161255\pi$
$888$	−0.242641			−0.00814249
$889$	15.2782	−	2.09077i	0.512414	−	0.0701222i
$890$	−5.95837			−0.199725
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−11.7426	−	20.3389i	−0.393173	−	0.680995i
$893$	−1.58579	−	2.74666i	−0.0530663	−	0.0919136i
$894$	−9.24264	+	16.0087i	−0.309120	+	0.535412i
$895$	11.9167			0.398333
$896$	1.00000	−	2.44949i	0.0334077	−	0.0818317i
$897$	−9.65685			−0.322433
$898$	−7.12132	+	12.3345i	−0.237642	+	0.411607i
$899$	11.5711	+	20.0417i	0.385917	+	0.668427i
$900$	1.24264	+	2.15232i	0.0414214	+	0.0717439i
$901$	3.87868	−	6.71807i	0.129218	−	0.223811i
$902$	0.585786			0.0195046
$903$	−10.1213	−	13.0519i	−0.336816	−	0.434341i
$904$	10.2426			0.340665
$905$	−16.2426	+	28.1331i	−0.539924	+	0.935175i
$906$	−5.67157	−	9.82345i	−0.188425	−	0.326362i
$907$	−8.05025	−	13.9434i	−0.267304	−	0.462985i	0.700861	−	0.713298i	$-0.252800\pi$
$907$	−8.05025	−	13.9434i	−0.267304	−	0.462985i	−0.968165	+	0.250314i	$0.919466\pi$
$908$	−0.550253	+	0.953065i	−0.0182608	+	0.0316286i
$909$	14.9706			0.496542
$910$	−7.27208	−	9.37769i	−0.241067	−	0.310867i
$911$	−28.8284			−0.955128			−0.477564	−	0.878597i	$-0.658480\pi$
$911$	−28.8284			−0.955128			−0.477564	+	0.878597i	$0.658480\pi$
$912$	0.500000	−	0.866025i	0.0165567	−	0.0286770i
$913$	−8.57107	−	14.8455i	−0.283661	−	0.491315i
$914$	−18.0563	−	31.2745i	−0.597251	−	1.03447i
$915$	3.82843	−	6.63103i	0.126564	−	0.219215i
$916$	−19.7990			−0.654177
$917$	4.31371	−	10.5664i	0.142451	−	0.348933i
$918$	4.24264			0.140028
$919$	20.1716	−	34.9382i	0.665399	−	1.15250i	−0.313778	−	0.949496i	$-0.601595\pi$
$919$	20.1716	−	34.9382i	0.665399	−	1.15250i	0.979177	−	0.203008i	$-0.0650718\pi$
$920$	2.70711	+	4.68885i	0.0892507	+	0.154587i
$921$	3.70711	+	6.42090i	0.122153	+	0.211576i
$922$	8.65685	−	14.9941i	0.285098	−	0.493805i
$923$	−22.3431			−0.735434
$924$	−2.62132	+	0.358719i	−0.0862351	+	0.0118010i
$925$	−0.603030			−0.0198275
$926$	−0.828427	+	1.43488i	−0.0272238	+	0.0471530i
$927$	9.24264	+	16.0087i	0.303568	+	0.525795i
$928$	−1.08579	−	1.88064i	−0.0356427	−	0.0617349i
$929$	1.46447	−	2.53653i	0.0480476	−	0.0832208i	−0.841001	−	0.541033i	$-0.818033\pi$
$929$	1.46447	−	2.53653i	0.0480476	−	0.0832208i	0.889049	+	0.457812i	$0.151367\pi$
$930$	−16.8995			−0.554156
$931$	−1.74264	+	6.77962i	−0.0571127	+	0.222193i
$932$	−5.17157			−0.169401
$933$	11.1213	−	19.2627i	0.364096	−	0.630632i
$934$	7.58579	+	13.1390i	0.248215	+	0.429920i
$935$	3.36396	+	5.82655i	0.110013	+	0.190549i
$936$	−1.41421	+	2.44949i	−0.0462250	+	0.0800641i
$937$	0.857864			0.0280252			0.0140126	−	0.999902i	$-0.495540\pi$
$937$	0.857864			0.0280252			0.0140126	+	0.999902i	$0.495540\pi$
$938$	5.24264	−	0.717439i	0.171178	−	0.0234252i
$939$	3.82843			0.124936
$940$	2.51472	−	4.35562i	0.0820211	−	0.142065i
$941$	13.1569	+	22.7883i	0.428901	+	0.742879i	0.996776	−	0.0802364i	$-0.0255675\pi$
$941$	13.1569	+	22.7883i	0.428901	+	0.742879i	−0.567875	+	0.823115i	$0.692234\pi$
$942$	−2.24264	−	3.88437i	−0.0730692	−	0.126560i
$943$	1.00000	−	1.73205i	0.0325645	−	0.0564033i
$944$	6.07107			0.197596
$945$	1.58579	−	3.88437i	0.0515856	−	0.126358i
$946$	−6.24264			−0.202966
$947$	15.8284	−	27.4156i	0.514355	−	0.890889i	−0.485507	−	0.874233i	$-0.661365\pi$
$947$	15.8284	−	27.4156i	0.514355	−	0.890889i	0.999861	−	0.0166555i	$-0.00530187\pi$
$948$	−0.0857864	−	0.148586i	−0.00278621	−	0.00482586i
$949$	20.9706	+	36.3221i	0.680733	+	1.17906i
$950$	1.24264	−	2.15232i	0.0403166	−	0.0698304i
$951$	9.48528			0.307581
$952$	−6.87868	−	8.87039i	−0.222939	−	0.287491i
$953$	39.1716			1.26889			0.634446	−	0.772967i	$-0.281228\pi$
$953$	39.1716			1.26889			0.634446	+	0.772967i	$0.281228\pi$
$954$	−0.914214	+	1.58346i	−0.0295988	+	0.0512666i
$955$	−14.3848	−	24.9152i	−0.465480	−	0.806236i
$956$	−14.1421	−	24.4949i	−0.457389	−	0.792222i
$957$	−1.08579	+	1.88064i	−0.0350985	+	0.0607924i
$958$	1.31371			0.0424440
$959$	−0.556349	−	0.717439i	−0.0179655	−	0.0231673i
$960$	1.58579			0.0511810
$961$	−41.2843	+	71.5065i	−1.33175	+	2.30666i
$962$	−0.343146	−	0.594346i	−0.0110635	−	0.0191625i
$963$	−5.86396	−	10.1567i	−0.188964	−	0.327294i
$964$	−0.278175	+	0.481813i	−0.00895940	+	0.0155181i
$965$	37.6274			1.21127
$966$	−3.41421	+	8.36308i	−0.109851	+	0.269078i
$967$	−30.5563			−0.982626			−0.491313	−	0.870983i	$-0.663483\pi$
$967$	−30.5563			−0.982626			−0.491313	+	0.870983i	$0.663483\pi$
$968$	5.00000	−	8.66025i	0.160706	−	0.278351i
$969$	−2.12132	−	3.67423i	−0.0681466	−	0.118033i
$970$	−4.42893	−	7.67114i	−0.142204	−	0.246305i
$971$	−18.5208	+	32.0790i	−0.594361	+	1.02946i	0.399275	+	0.916831i	$0.369262\pi$
$971$	−18.5208	+	32.0790i	−0.594361	+	1.02946i	−0.993637	+	0.112633i	$0.964072\pi$
$972$	−1.00000			−0.0320750
$973$	−20.7071	+	2.83370i	−0.663839	+	0.0908443i
$974$	−38.7990			−1.24320
$975$	−3.51472	+	6.08767i	−0.112561	+	0.194962i
$976$	2.41421	+	4.18154i	0.0772771	+	0.133848i
$977$	1.00000	+	1.73205i	0.0319928	+	0.0554132i	0.881579	−	0.472037i	$-0.156481\pi$
$977$	1.00000	+	1.73205i	0.0319928	+	0.0554132i	−0.849586	+	0.527451i	$0.823148\pi$
$978$	−5.41421	+	9.37769i	−0.173127	+	0.299866i
$979$	−3.75736			−0.120086
$980$	−10.6924	+	2.98229i	−0.341556	+	0.0952657i
$981$	1.75736			0.0561082
$982$	4.57107	−	7.91732i	0.145869	−	0.252652i
$983$	−24.4853	−	42.4098i	−0.780959	−	1.35266i	−0.931384	−	0.364039i	$-0.881397\pi$
$983$	−24.4853	−	42.4098i	−0.780959	−	1.35266i	0.150424	−	0.988622i	$-0.451936\pi$
$984$	−0.292893	−	0.507306i	−0.00933709	−	0.0161723i
$985$	0.928932	−	1.60896i	0.0295982	−	0.0512657i
$986$	−9.21320			−0.293408
$987$	8.31371	−	1.13770i	0.264628	−	0.0362135i
$988$	2.82843			0.0899843
$989$	−10.6569	+	18.4582i	−0.338868	+	0.586937i
$990$	−0.792893	−	1.37333i	−0.0251998	−	0.0436473i
$991$	5.81371	+	10.0696i	0.184679	+	0.319873i	0.943468	−	0.331463i	$-0.107542\pi$
$991$	5.81371	+	10.0696i	0.184679	+	0.319873i	−0.758790	+	0.651336i	$0.774209\pi$
$992$	5.32843	−	9.22911i	0.169178	−	0.293024i
$993$	4.38478			0.139147
$994$	−7.89949	+	19.3497i	−0.250557	+	0.613736i
$995$	−13.4558			−0.426579
$996$	−8.57107	+	14.8455i	−0.271585	+	0.470398i
$997$	−1.58579	−	2.74666i	−0.0502224	−	0.0869877i	0.839821	−	0.542863i	$-0.182660\pi$
$997$	−1.58579	−	2.74666i	−0.0502224	−	0.0869877i	−0.890044	+	0.455875i	$0.849326\pi$
$998$	−4.65685	−	8.06591i	−0.147410	−	0.255322i
$999$	0.121320	−	0.210133i	0.00383841	−	0.00664831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.j.h.457.1	✓	4
7.2	even	3		5586.2.a.bg.1.2		2
7.4	even	3	inner	798.2.j.h.571.1	yes	4
7.5	odd	6		5586.2.a.br.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.h.457.1	✓	4	1.1	even	1	trivial
798.2.j.h.571.1	yes	4	7.4	even	3	inner
5586.2.a.bg.1.2		2	7.2	even	3
5586.2.a.br.1.1		2	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.792893 - 1.37333i) q^{5} -1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.792893 - 1.37333i) q^{5} -1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.792893 + 1.37333i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.82843 q^{13} +(1.00000 - 2.44949i) q^{14} +1.58579 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.12132 + 3.67423i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -1.58579 q^{20} +(-1.62132 - 2.09077i) q^{21} -1.00000 q^{22} +(-1.70711 + 2.95680i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.24264 + 2.15232i) q^{25} +(-1.41421 + 2.44949i) q^{26} -1.00000 q^{27} +(1.62132 + 2.09077i) q^{28} +2.17157 q^{29} +(-0.792893 + 1.37333i) q^{30} +(5.32843 + 9.22911i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -4.24264 q^{34} +(-1.58579 + 3.88437i) q^{35} +1.00000 q^{36} +(-0.121320 + 0.210133i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(1.41421 + 2.44949i) q^{39} +(0.792893 - 1.37333i) q^{40} -0.585786 q^{41} +(2.62132 - 0.358719i) q^{42} +6.24264 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.792893 + 1.37333i) q^{45} +(-1.70711 - 2.95680i) q^{46} +(-1.58579 + 2.74666i) q^{47} -1.00000 q^{48} +(6.74264 - 1.88064i) q^{49} -2.48528 q^{50} +(-2.12132 + 3.67423i) q^{51} +(-1.41421 - 2.44949i) q^{52} +(-0.914214 - 1.58346i) q^{53} +(0.500000 - 0.866025i) q^{54} +1.58579 q^{55} +(-2.62132 + 0.358719i) q^{56} -1.00000 q^{57} +(-1.08579 + 1.88064i) q^{58} +(-3.03553 - 5.25770i) q^{59} +(-0.792893 - 1.37333i) q^{60} +(2.41421 - 4.18154i) q^{61} -10.6569 q^{62} +(1.00000 - 2.44949i) q^{63} +1.00000 q^{64} +(2.24264 - 3.88437i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(1.00000 + 1.73205i) q^{67} +(2.12132 - 3.67423i) q^{68} -3.41421 q^{69} +(-2.57107 - 3.31552i) q^{70} -7.89949 q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.41421 + 12.8418i) q^{73} +(-0.121320 - 0.210133i) q^{74} +(-1.24264 + 2.15232i) q^{75} +1.00000 q^{76} +(-1.62132 - 2.09077i) q^{77} -2.82843 q^{78} +(0.0857864 - 0.148586i) q^{79} +(0.792893 + 1.37333i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.292893 - 0.507306i) q^{82} -17.1421 q^{83} +(-1.00000 + 2.44949i) q^{84} +6.72792 q^{85} +(-3.12132 + 5.40629i) q^{86} +(1.08579 + 1.88064i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.87868 + 3.25397i) q^{89} -1.58579 q^{90} +(-7.41421 + 1.01461i) q^{91} +3.41421 q^{92} +(-5.32843 + 9.22911i) q^{93} +(-1.58579 - 2.74666i) q^{94} +(0.792893 + 1.37333i) q^{95} +(0.500000 - 0.866025i) q^{96} -5.58579 q^{97} +(-1.74264 + 6.77962i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 6 q^{10} + 2 q^{11} + 2 q^{12} + 4 q^{14} + 12 q^{15} - 2 q^{16} - 2 q^{18} - 2 q^{19} - 12 q^{20} + 2 q^{21} - 4 q^{22} - 4 q^{23} + 2 q^{24} - 12 q^{25} - 4 q^{27} - 2 q^{28} + 20 q^{29} - 6 q^{30} + 10 q^{31} - 2 q^{32} - 2 q^{33} - 12 q^{35} + 4 q^{36} + 8 q^{37} - 2 q^{38} + 6 q^{40} - 8 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + 6 q^{45} - 4 q^{46} - 12 q^{47} - 4 q^{48} + 10 q^{49} + 24 q^{50} + 2 q^{53} + 2 q^{54} + 12 q^{55} - 2 q^{56} - 4 q^{57} - 10 q^{58} + 2 q^{59} - 6 q^{60} + 4 q^{61} - 20 q^{62} + 4 q^{63} + 4 q^{64} - 8 q^{65} - 2 q^{66} + 4 q^{67} - 8 q^{69} + 18 q^{70} + 8 q^{71} - 2 q^{72} + 24 q^{73} + 8 q^{74} + 12 q^{75} + 4 q^{76} + 2 q^{77} + 6 q^{79} + 6 q^{80} - 2 q^{81} + 4 q^{82} - 12 q^{83} - 4 q^{84} - 24 q^{85} - 4 q^{86} + 10 q^{87} + 2 q^{88} - 16 q^{89} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 10 q^{93} - 12 q^{94} + 6 q^{95} + 2 q^{96} - 28 q^{97} + 10 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 6 * q^10 + 2 * q^11 + 2 * q^12 + 4 * q^14 + 12 * q^15 - 2 * q^16 - 2 * q^18 - 2 * q^19 - 12 * q^20 + 2 * q^21 - 4 * q^22 - 4 * q^23 + 2 * q^24 - 12 * q^25 - 4 * q^27 - 2 * q^28 + 20 * q^29 - 6 * q^30 + 10 * q^31 - 2 * q^32 - 2 * q^33 - 12 * q^35 + 4 * q^36 + 8 * q^37 - 2 * q^38 + 6 * q^40 - 8 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + 6 * q^45 - 4 * q^46 - 12 * q^47 - 4 * q^48 + 10 * q^49 + 24 * q^50 + 2 * q^53 + 2 * q^54 + 12 * q^55 - 2 * q^56 - 4 * q^57 - 10 * q^58 + 2 * q^59 - 6 * q^60 + 4 * q^61 - 20 * q^62 + 4 * q^63 + 4 * q^64 - 8 * q^65 - 2 * q^66 + 4 * q^67 - 8 * q^69 + 18 * q^70 + 8 * q^71 - 2 * q^72 + 24 * q^73 + 8 * q^74 + 12 * q^75 + 4 * q^76 + 2 * q^77 + 6 * q^79 + 6 * q^80 - 2 * q^81 + 4 * q^82 - 12 * q^83 - 4 * q^84 - 24 * q^85 - 4 * q^86 + 10 * q^87 + 2 * q^88 - 16 * q^89 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 10 * q^93 - 12 * q^94 + 6 * q^95 + 2 * q^96 - 28 * q^97 + 10 * q^98 - 4 * q^99

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