LMFDB - Embedded newform 798.2.j.h.571.1

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			571.1
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	798.571
Dual form			798.2.j.h.457.1

$q$-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 $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	0.987048	−	0.160424i	$-0.0512862\pi$
$5$	0.792893	+	1.37333i	0.354593	+	0.614172i	−0.632456	+	0.774597i	$0.717953\pi$
$6$	−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	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$	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	−0.485363	−	0.874313i	$-0.661312\pi$
$17$	2.12132	−	3.67423i	0.514496	−	0.891133i	0.999859	−	0.0168199i	$-0.00535420\pi$
$18$	−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	0.631325	−	0.775519i	$-0.282511\pi$
$23$	−1.70711	−	2.95680i	−0.355956	−	0.616535i	−0.987281	+	0.158984i	$0.949178\pi$
$24$	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	0.227323	−	0.973819i	$-0.427003\pi$
$31$	5.32843	−	9.22911i	0.957014	−	1.65760i	0.729691	−	0.683777i	$-0.239664\pi$
$32$	−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	0.855881	−	0.517173i	$-0.173016\pi$
$37$	−0.121320	−	0.210133i	−0.0199449	−	0.0345457i	−0.875826	+	0.482628i	$0.839682\pi$
$38$	−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	0.726883	−	0.686761i	$-0.240968\pi$
$47$	−1.58579	−	2.74666i	−0.231311	−	0.400642i	−0.958194	+	0.286119i	$0.907635\pi$
$48$	−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	−0.921958	−	0.387289i	$-0.873412\pi$
$53$	−0.914214	+	1.58346i	−0.125577	+	0.217506i	0.796381	+	0.604795i	$0.206745\pi$
$54$	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	−0.993126	−	0.117052i	$-0.962656\pi$
$59$	−3.03553	+	5.25770i	−0.395193	+	0.684494i	0.597933	+	0.801546i	$0.295989\pi$
$60$	−0.792893	+	1.37333i	−0.102362	+	0.177296i
$61$	2.41421	+	4.18154i	0.309108	+	0.535391i	0.978168	−	0.207818i	$-0.0666361\pi$
$61$	2.41421	+	4.18154i	0.309108	+	0.535391i	−0.669059	+	0.743209i	$0.733303\pi$
$62$	−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	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	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	0.00349590	−	0.999994i	$-0.498887\pi$
$73$	7.41421	−	12.8418i	0.867768	−	1.50302i	0.864272	−	0.503024i	$-0.167779\pi$
$74$	−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	0.870811	−	0.491618i	$-0.163594\pi$
$79$	0.0857864	+	0.148586i	0.00965173	+	0.0167173i	−0.861159	+	0.508335i	$0.830261\pi$
$80$	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	0.749110	−	0.662446i	$-0.230481\pi$
$89$	−1.87868	−	3.25397i	−0.199140	−	0.344920i	−0.948250	+	0.317526i	$0.897148\pi$
$90$	−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	0.205469	+	0.978664i	$0.434128\pi$
$101$	−7.48528	+	12.9649i	−0.744813	+	1.29005i	−0.950282	+	0.311391i	$0.899205\pi$
$102$	−2.12132	+	3.67423i	−0.210042	+	0.363803i
$103$	9.24264	+	16.0087i	0.910704	+	1.57739i	0.813071	+	0.582164i	$0.197794\pi$
$103$	9.24264	+	16.0087i	0.910704	+	1.57739i	0.0976330	+	0.995222i	$0.468873\pi$
$104$	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	−0.996871	−	0.0790450i	$-0.974813\pi$
$107$	−5.86396	−	10.1567i	−0.566891	−	0.981883i	0.429981	−	0.902838i	$-0.358520\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−0.878680	+	1.52192i	−0.0841622	+	0.145773i	−0.905034	−	0.425339i	$-0.860155\pi$
$109$	−0.878680	+	1.52192i	−0.0841622	+	0.145773i	0.820872	+	0.571113i	$0.193488\pi$
$110$	−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	0.756287	−	0.654240i	$-0.227011\pi$
$131$	−2.15685	−	3.73578i	−0.188445	−	0.326397i	−0.944732	+	0.327843i	$0.893678\pi$
$132$	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	−0.858603	−	0.512641i	$-0.828667\pi$
$137$	0.171573	−	0.297173i	0.0146585	−	0.0253892i	0.873262	+	0.487252i	$0.162001\pi$
$138$	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	0.944280	+	0.329144i	$0.106760\pi$
$149$	9.24264	+	16.0087i	0.757187	+	1.31149i	−0.187093	+	0.982342i	$0.559907\pi$
$150$	−1.24264	+	2.15232i	−0.101461	+	0.175736i
$151$	5.67157	−	9.82345i	0.461546	−	0.799421i	−0.537492	−	0.843269i	$-0.680628\pi$
$151$	5.67157	−	9.82345i	0.461546	−	0.799421i	0.999038	+	0.0438475i	$0.0139616\pi$
$152$	−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	−0.762550	−	0.646929i	$-0.776053\pi$
$157$	2.24264	−	3.88437i	0.178982	−	0.310006i	0.941532	+	0.336923i	$0.109386\pi$
$158$	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	0.996333	−	0.0855550i	$-0.0272663\pi$
$163$	5.41421	+	9.37769i	0.424074	+	0.734518i	−0.572260	+	0.820073i	$0.693933\pi$
$164$	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	0.992732	+	0.120344i	$0.0383999\pi$
$173$	7.89949	+	13.6823i	0.600587	+	1.04025i	−0.392145	+	0.919904i	$0.628267\pi$
$174$	−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	−0.690753	−	0.723091i	$-0.742721\pi$
$179$	3.75736	−	6.50794i	0.280838	−	0.486426i	0.971591	+	0.236665i	$0.0760542\pi$
$180$	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	0.981551	+	0.191200i	$0.0612378\pi$
$191$	9.07107	+	15.7116i	0.656359	+	1.13685i	−0.325192	+	0.945648i	$0.605429\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	11.8640	−	20.5490i	0.853987	−	1.47915i	−0.0235954	−	0.999722i	$-0.507511\pi$
$193$	11.8640	−	20.5490i	0.853987	−	1.47915i	0.877582	−	0.479427i	$-0.159155\pi$
$194$	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	−0.976307	−	0.216391i	$-0.930571\pi$
$199$	−4.24264	+	7.34847i	−0.300753	+	0.520919i	0.675554	+	0.737311i	$0.263905\pi$
$200$	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	−0.883708	−	0.468038i	$-0.844961\pi$
$227$	−0.550253	+	0.953065i	−0.0365215	+	0.0632572i	0.847187	+	0.531295i	$0.178294\pi$
$228$	0.500000	−	0.866025i	0.0331133	−	0.0573539i
$229$	9.89949	+	17.1464i	0.654177	+	1.13307i	0.982099	+	0.188363i	$0.0603182\pi$
$229$	9.89949	+	17.1464i	0.654177	+	1.13307i	−0.327922	+	0.944705i	$0.606348\pi$
$230$	−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	0.938209	−	0.346069i	$-0.112484\pi$
$233$	2.58579	+	4.47871i	0.169401	+	0.293410i	−0.768809	+	0.639479i	$0.779150\pi$
$234$	−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	−0.874846	−	0.484402i	$-0.839037\pi$
$241$	−0.278175	+	0.481813i	−0.0179188	+	0.0310363i	0.856927	+	0.515438i	$0.172371\pi$
$242$	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	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	−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	−0.631042	−	0.775749i	$-0.717372\pi$
$263$	5.77817	−	10.0081i	0.356298	−	0.617125i	0.987339	+	0.158624i	$0.0507056\pi$
$264$	−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	−0.880866	−	0.473366i	$-0.843039\pi$
$269$	−0.500000	+	0.866025i	−0.0304855	+	0.0528025i	0.850380	+	0.526169i	$0.176372\pi$
$270$	−0.792893	+	1.37333i	−0.0482539	+	0.0835783i
$271$	−4.44975	−	7.70719i	−0.270303	−	0.468178i	0.698636	−	0.715477i	$-0.253791\pi$
$271$	−4.44975	−	7.70719i	−0.270303	−	0.468178i	−0.968939	+	0.247298i	$0.920457\pi$
$272$	−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	−0.581949	−	0.813226i	$-0.697709\pi$
$277$	6.87868	−	11.9142i	0.413300	−	0.715856i	0.995248	+	0.0973694i	$0.0310428\pi$
$278$	−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	0.344582	+	0.938756i	$0.388021\pi$
$283$	−10.7782	+	18.6683i	−0.640696	+	1.10972i	−0.985278	+	0.170962i	$0.945313\pi$
$284$	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	0.356790	+	0.934184i	$0.383871\pi$
$311$	−11.1213	+	19.2627i	−0.630632	+	1.09229i	−0.987423	+	0.158103i	$0.949462\pi$
$312$	1.41421	−	2.44949i	0.0800641	−	0.138675i
$313$	1.91421	+	3.31552i	0.108198	+	0.187404i	0.915040	−	0.403363i	$-0.132159\pi$
$313$	1.91421	+	3.31552i	0.108198	+	0.187404i	−0.806842	+	0.590767i	$0.798825\pi$
$314$	−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	0.967922	−	0.251249i	$-0.0808413\pi$
$317$	4.74264	+	8.21449i	0.266373	+	0.461372i	−0.701549	+	0.712621i	$0.747508\pi$
$318$	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	0.919967	−	0.391996i	$-0.128215\pi$
$331$	2.19239	+	3.79733i	0.120505	+	0.208720i	−0.799462	+	0.600716i	$0.794882\pi$
$332$	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	0.102241	−	0.994760i	$-0.467399\pi$
$347$	17.0000	−	29.4449i	0.912608	−	1.58068i	0.810366	−	0.585923i	$-0.199268\pi$
$348$	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	−0.990364	−	0.138489i	$-0.955775\pi$
$353$	−7.05025	+	12.2114i	−0.375247	+	0.649947i	0.615117	+	0.788436i	$0.289109\pi$
$354$	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	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$	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	−0.926296	−	0.376797i	$-0.877025\pi$
$367$	−2.62132	+	4.54026i	−0.136832	+	0.237000i	0.789464	+	0.613797i	$0.210359\pi$
$368$	−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	0.859675	−	0.510841i	$-0.170666\pi$
$373$	−0.242641	−	0.420266i	−0.0125635	−	0.0217605i	−0.872239	+	0.489080i	$0.837333\pi$
$374$	−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	0.593713	−	0.804677i	$-0.297661\pi$
$383$	−7.82843	−	13.5592i	−0.400014	−	0.692844i	−0.993727	+	0.111832i	$0.964328\pi$
$384$	−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	0.407146	+	0.913363i	$0.366524\pi$
$389$	−11.5858	+	20.0672i	−0.587423	+	1.01745i	−0.994569	+	0.104083i	$0.966809\pi$
$390$	−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	0.969305	−	0.245860i	$-0.0790704\pi$
$397$	5.41421	+	9.37769i	0.271732	+	0.470653i	−0.697574	+	0.716513i	$0.745737\pi$
$398$	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	0.633681	−	0.773595i	$-0.281543\pi$
$401$	−7.07107	−	12.2474i	−0.353112	−	0.611608i	−0.986793	+	0.161986i	$0.948210\pi$
$402$	−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	0.176864	+	0.984235i	$0.443405\pi$
$409$	−15.4497	+	26.7597i	−0.763941	+	1.32318i	−0.940805	+	0.338949i	$0.889929\pi$
$410$	−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	−0.644759	−	0.764386i	$-0.723042\pi$
$431$	7.05025	−	12.2114i	0.339599	−	0.588202i	0.984357	+	0.176184i	$0.0563754\pi$
$432$	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	−0.999120	−	0.0419380i	$-0.986647\pi$
$439$	−11.2279	−	19.4473i	−0.535879	−	0.928170i	0.463241	−	0.886232i	$-0.346687\pi$
$440$	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	0.985927	−	0.167177i	$-0.0534651\pi$
$443$	7.32843	+	12.6932i	0.348184	+	0.603073i	−0.637743	+	0.770249i	$0.720132\pi$
$444$	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	−0.885933	−	0.463813i	$-0.846481\pi$
$457$	−18.0563	−	31.2745i	−0.844640	−	1.46296i	0.0412927	−	0.999147i	$-0.486852\pi$
$458$	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	0.986430	−	0.164183i	$-0.0524987\pi$
$467$	7.58579	+	13.1390i	0.351028	+	0.607999i	−0.635402	+	0.772182i	$0.719165\pi$
$468$	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	−0.880641	−	0.473783i	$-0.842888\pi$
$479$	−0.656854	+	1.13770i	−0.0300124	+	0.0519831i	0.850629	+	0.525766i	$0.176221\pi$
$480$	−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	0.0267175	−	0.999643i	$-0.491495\pi$
$487$	19.3995	−	33.6009i	0.879075	−	1.52260i	0.852357	−	0.522960i	$-0.175172\pi$
$488$	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	0.742763	−	0.669554i	$-0.233515\pi$
$499$	−4.65685	−	8.06591i	−0.208469	−	0.361080i	−0.951233	+	0.308475i	$0.900182\pi$
$500$	−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	0.979907	−	0.199453i	$-0.0639166\pi$
$509$	7.15685	+	12.3960i	0.317222	+	0.549445i	−0.662685	+	0.748898i	$0.730583\pi$
$510$	−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	0.140308	+	0.990108i	$0.455191\pi$
$521$	−17.9706	+	31.1259i	−0.787305	+	1.36365i	−0.927613	+	0.373544i	$0.878143\pi$
$522$	−1.08579	+	1.88064i	−0.0475236	+	0.0823133i
$523$	−2.05025	−	3.55114i	−0.0896513	−	0.155281i	0.817712	−	0.575627i	$-0.195242\pi$
$523$	−2.05025	−	3.55114i	−0.0896513	−	0.155281i	−0.907364	+	0.420346i	$0.861909\pi$
$524$	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	0.982349	+	0.187058i	$0.0598954\pi$
$541$	15.1924	+	26.3140i	0.653172	+	1.13133i	−0.329177	+	0.944268i	$0.606771\pi$
$542$	−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	0.482568	+	0.875859i	$0.339704\pi$
$557$	−12.2071	+	21.1433i	−0.517232	+	0.895872i	−0.999800	+	0.0200131i	$0.993629\pi$
$558$	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	−0.219120	−	0.975698i	$-0.570319\pi$
$563$	17.4497	−	30.2238i	0.735419	−	1.27378i	0.954539	−	0.298085i	$-0.0963480\pi$
$564$	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	0.999567	−	0.0294311i	$-0.00936956\pi$
$569$	11.3137	+	19.5959i	0.474295	+	0.821504i	−0.525271	+	0.850935i	$0.676036\pi$
$570$	−0.792893	+	1.37333i	−0.0332106	+	0.0575225i
$571$	−17.2635	+	29.9012i	−0.722453	+	1.25133i	0.237561	+	0.971373i	$0.423652\pi$
$571$	−17.2635	+	29.9012i	−0.722453	+	1.25133i	−0.960014	+	0.279953i	$0.909681\pi$
$572$	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	−0.980968	−	0.194167i	$-0.937800\pi$
$577$	−7.74264	+	13.4106i	−0.322330	+	0.558293i	0.658638	+	0.752460i	$0.271133\pi$
$578$	−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	−0.994137	−	0.108130i	$-0.965514\pi$
$593$	−14.3848	−	24.9152i	−0.590712	−	1.02314i	0.403425	−	0.915013i	$-0.367820\pi$
$594$	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	0.149923	+	0.988698i	$0.452098\pi$
$599$	−19.1213	+	33.1191i	−0.781276	+	1.35321i	−0.931199	+	0.364512i	$0.881236\pi$
$600$	−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	0.984605	−	0.174796i	$-0.0559264\pi$
$607$	8.39949	+	14.5484i	0.340925	+	0.590499i	−0.643680	+	0.765295i	$0.722593\pi$
$608$	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	−0.487856	−	0.872924i	$-0.662221\pi$
$613$	12.6777	−	21.9584i	0.512046	−	0.886890i	0.999902	−	0.0139661i	$-0.00444570\pi$
$614$	−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	−0.801854	−	0.597520i	$-0.796153\pi$
$619$	2.89949	−	5.02207i	0.116541	−	0.201854i	0.918395	+	0.395666i	$0.129486\pi$
$620$	−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	−0.622055	−	0.782973i	$-0.713702\pi$
$641$	9.29289	−	16.0958i	0.367047	−	0.635744i	0.989102	+	0.147229i	$0.0470354\pi$
$642$	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	0.0269476	+	0.999637i	$0.491421\pi$
$647$	−21.6777	+	37.5468i	−0.852237	+	1.47612i	−0.879185	+	0.476481i	$0.841912\pi$
$648$	−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	0.999888	+	0.0149614i	$0.00476253\pi$
$653$	13.1066	+	22.7013i	0.512901	+	0.888371i	−0.486987	+	0.873409i	$0.661904\pi$
$654$	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	0.357778	+	0.933806i	$0.383534\pi$
$661$	−16.1924	+	28.0460i	−0.629811	+	1.09086i	−0.987589	+	0.157058i	$0.949799\pi$
$662$	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	0.996766	−	0.0803560i	$-0.0256057\pi$
$677$	11.1569	+	19.3242i	0.428793	+	0.742691i	−0.567973	+	0.823047i	$0.692272\pi$
$678$	−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	0.395422	+	0.918500i	$0.370598\pi$
$683$	−15.6213	+	27.0569i	−0.597733	+	1.03530i	−0.993155	+	0.116805i	$0.962735\pi$
$684$	−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	0.603439	−	0.797409i	$-0.293797\pi$
$691$	−10.2218	−	17.7047i	−0.388857	−	0.673519i	−0.992296	+	0.123889i	$0.960463\pi$
$692$	−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	0.753493	+	0.657456i	$0.228367\pi$
$709$	25.1924	+	43.6345i	0.946120	+	1.63873i	0.192627	+	0.981272i	$0.438299\pi$
$710$	−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	0.771899	−	0.635746i	$-0.219307\pi$
$719$	−4.41421	−	7.64564i	−0.164622	−	0.285134i	−0.936521	+	0.350611i	$0.885974\pi$
$720$	−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	−0.987286	−	0.158956i	$-0.949187\pi$
$733$	−17.0919	−	29.6040i	−0.631303	−	1.09345i	0.355982	−	0.934493i	$-0.384146\pi$
$734$	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	0.372800	+	0.927912i	$0.378398\pi$
$739$	−16.7782	+	29.0607i	−0.617195	+	1.06901i	−0.989995	+	0.141102i	$0.954936\pi$
$740$	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	0.974747	−	0.223311i	$-0.0716866\pi$
$751$	8.05635	+	13.9540i	0.293980	+	0.509189i	−0.680767	+	0.732500i	$0.738353\pi$
$752$	−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	0.804979	−	0.593303i	$-0.202176\pi$
$761$	−3.07107	−	5.31925i	−0.111326	−	0.192822i	−0.916305	+	0.400481i	$0.868843\pi$
$762$	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	$0.294693\pi$

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

Introduction

L-functions

Modular forms

Varieties

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