LMFDB - Embedded newform 231.2.i.d.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.i (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:	$1.84454428669$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.d.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(1.00000 + 1.73205i) q^{5} -2.41421 q^{6} +(1.00000 - 2.44949i) q^{7} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(1.00000 + 1.73205i) q^{5} -2.41421 q^{6} +(1.00000 - 2.44949i) q^{7} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.41421 + 4.18154i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.91421 - 3.31552i) q^{12} -0.828427 q^{13} +(6.32843 - 0.866025i) q^{14} -2.00000 q^{15} +(-1.50000 - 2.59808i) q^{16} +(2.20711 - 3.82282i) q^{17} +(1.20711 - 2.09077i) q^{18} +(-3.62132 - 6.27231i) q^{19} -7.65685 q^{20} +(1.62132 + 2.09077i) q^{21} -2.41421 q^{22} +(3.50000 + 6.06218i) q^{23} +(2.20711 - 3.82282i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(6.20711 + 8.00436i) q^{28} +3.24264 q^{29} +(-2.41421 - 4.18154i) q^{30} +(-2.82843 + 4.89898i) q^{31} +(-0.792893 + 1.37333i) q^{32} +(-0.500000 - 0.866025i) q^{33} +10.6569 q^{34} +(5.24264 - 0.717439i) q^{35} +3.82843 q^{36} +(4.74264 + 8.21449i) q^{37} +(8.74264 - 15.1427i) q^{38} +(0.414214 - 0.717439i) q^{39} +(-4.41421 - 7.64564i) q^{40} -1.17157 q^{41} +(-2.41421 + 5.91359i) q^{42} -2.75736 q^{43} +(-1.91421 - 3.31552i) q^{44} +(1.00000 - 1.73205i) q^{45} +(-8.44975 + 14.6354i) q^{46} +(-4.91421 - 8.51167i) q^{47} +3.00000 q^{48} +(-5.00000 - 4.89898i) q^{49} +2.41421 q^{50} +(2.20711 + 3.82282i) q^{51} +(1.58579 - 2.74666i) q^{52} +(3.58579 - 6.21076i) q^{53} +(1.20711 + 2.09077i) q^{54} -2.00000 q^{55} +(-4.41421 + 10.8126i) q^{56} +7.24264 q^{57} +(3.91421 + 6.77962i) q^{58} +(4.32843 - 7.49706i) q^{59} +(3.82843 - 6.63103i) q^{60} +(2.00000 + 3.46410i) q^{61} -13.6569 q^{62} +(-2.62132 + 0.358719i) q^{63} -9.82843 q^{64} +(-0.828427 - 1.43488i) q^{65} +(1.20711 - 2.09077i) q^{66} +(1.58579 - 2.74666i) q^{67} +(8.44975 + 14.6354i) q^{68} -7.00000 q^{69} +(7.82843 + 10.0951i) q^{70} -4.17157 q^{71} +(2.20711 + 3.82282i) q^{72} +(-0.171573 + 0.297173i) q^{73} +(-11.4497 + 19.8315i) q^{74} +(0.500000 + 0.866025i) q^{75} +27.7279 q^{76} +(1.62132 + 2.09077i) q^{77} +2.00000 q^{78} +(-6.65685 - 11.5300i) q^{79} +(3.00000 - 5.19615i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.41421 - 2.44949i) q^{82} -2.82843 q^{83} +(-10.0355 + 1.37333i) q^{84} +8.82843 q^{85} +(-3.32843 - 5.76500i) q^{86} +(-1.62132 + 2.80821i) q^{87} +(2.20711 - 3.82282i) q^{88} +(7.07107 + 12.2474i) q^{89} +4.82843 q^{90} +(-0.828427 + 2.02922i) q^{91} -26.7990 q^{92} +(-2.82843 - 4.89898i) q^{93} +(11.8640 - 20.5490i) q^{94} +(7.24264 - 12.5446i) q^{95} +(-0.792893 - 1.37333i) q^{96} -11.4853 q^{97} +(4.20711 - 16.3674i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 12 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 12 q^{8} - 2 q^{9} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 8 q^{13} + 14 q^{14} - 8 q^{15} - 6 q^{16} + 6 q^{17} + 2 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} - 4 q^{22} + 14 q^{23} + 6 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{27} + 22 q^{28} - 4 q^{29} - 4 q^{30} - 6 q^{32} - 2 q^{33} + 20 q^{34} + 4 q^{35} + 4 q^{36} + 2 q^{37} + 18 q^{38} - 4 q^{39} - 12 q^{40} - 16 q^{41} - 4 q^{42} - 28 q^{43} - 2 q^{44} + 4 q^{45} - 14 q^{46} - 14 q^{47} + 12 q^{48} - 20 q^{49} + 4 q^{50} + 6 q^{51} + 12 q^{52} + 20 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 12 q^{57} + 10 q^{58} + 6 q^{59} + 4 q^{60} + 8 q^{61} - 32 q^{62} - 2 q^{63} - 28 q^{64} + 8 q^{65} + 2 q^{66} + 12 q^{67} + 14 q^{68} - 28 q^{69} + 20 q^{70} - 28 q^{71} + 6 q^{72} - 12 q^{73} - 26 q^{74} + 2 q^{75} + 60 q^{76} - 2 q^{77} + 8 q^{78} - 4 q^{79} + 12 q^{80} - 2 q^{81} - 26 q^{84} + 24 q^{85} - 2 q^{86} + 2 q^{87} + 6 q^{88} + 8 q^{90} + 8 q^{91} - 28 q^{92} + 22 q^{94} + 12 q^{95} - 6 q^{96} - 12 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 12 * q^8 - 2 * q^9 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 8 * q^13 + 14 * q^14 - 8 * q^15 - 6 * q^16 + 6 * q^17 + 2 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 - 4 * q^22 + 14 * q^23 + 6 * q^24 + 2 * q^25 - 4 * q^26 + 4 * q^27 + 22 * q^28 - 4 * q^29 - 4 * q^30 - 6 * q^32 - 2 * q^33 + 20 * q^34 + 4 * q^35 + 4 * q^36 + 2 * q^37 + 18 * q^38 - 4 * q^39 - 12 * q^40 - 16 * q^41 - 4 * q^42 - 28 * q^43 - 2 * q^44 + 4 * q^45 - 14 * q^46 - 14 * q^47 + 12 * q^48 - 20 * q^49 + 4 * q^50 + 6 * q^51 + 12 * q^52 + 20 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 12 * q^57 + 10 * q^58 + 6 * q^59 + 4 * q^60 + 8 * q^61 - 32 * q^62 - 2 * q^63 - 28 * q^64 + 8 * q^65 + 2 * q^66 + 12 * q^67 + 14 * q^68 - 28 * q^69 + 20 * q^70 - 28 * q^71 + 6 * q^72 - 12 * q^73 - 26 * q^74 + 2 * q^75 + 60 * q^76 - 2 * q^77 + 8 * q^78 - 4 * q^79 + 12 * q^80 - 2 * q^81 - 26 * q^84 + 24 * q^85 - 2 * q^86 + 2 * q^87 + 6 * q^88 + 8 * q^90 + 8 * q^91 - 28 * q^92 + 22 * q^94 + 12 * q^95 - 6 * q^96 - 12 * q^97 + 14 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.20711	+	2.09077i	0.853553	+	1.47840i	0.877981	+	0.478696i	$0.158890\pi$
$2$	1.20711	+	2.09077i	0.853553	+	1.47840i	−0.0244272	+	0.999702i	$0.507776\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.91421	+	3.31552i	−0.957107	+	1.65776i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	−2.41421			−0.985599
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$	−4.41421			−1.56066
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.41421	+	4.18154i	−0.763441	+	1.32232i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−1.91421	−	3.31552i	−0.552586	−	0.957107i
$13$	−0.828427			−0.229764			−0.114882	−	0.993379i	$-0.536649\pi$
$13$	−0.828427			−0.229764			−0.114882	+	0.993379i	$0.536649\pi$
$14$	6.32843	−	0.866025i	1.69134	−	0.231455i
$15$	−2.00000			−0.516398
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	2.20711	−	3.82282i	0.535302	−	0.927170i	−0.463847	−	0.885916i	$-0.653531\pi$
$17$	2.20711	−	3.82282i	0.535302	−	0.927170i	0.999149	−	0.0412548i	$-0.0131355\pi$
$18$	1.20711	−	2.09077i	0.284518	−	0.492799i
$19$	−3.62132	−	6.27231i	−0.830788	−	1.43897i	−0.897414	−	0.441189i	$-0.854557\pi$
$19$	−3.62132	−	6.27231i	−0.830788	−	1.43897i	0.0666264	−	0.997778i	$-0.478776\pi$
$20$	−7.65685			−1.71212
$21$	1.62132	+	2.09077i	0.353801	+	0.456243i
$22$	−2.41421			−0.514712
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	0.956967	+	0.290196i	$0.0937204\pi$
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$24$	2.20711	−	3.82282i	0.450524	−	0.780330i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	1.00000			0.192450
$28$	6.20711	+	8.00436i	1.17303	+	1.51268i
$29$	3.24264			0.602143			0.301072	−	0.953602i	$-0.402656\pi$
$29$	3.24264			0.602143			0.301072	+	0.953602i	$0.402656\pi$
$30$	−2.41421	−	4.18154i	−0.440773	−	0.763441i
$31$	−2.82843	+	4.89898i	−0.508001	+	0.879883i	0.491957	+	0.870620i	$0.336282\pi$
$31$	−2.82843	+	4.89898i	−0.508001	+	0.879883i	−0.999957	+	0.00926296i	$0.997051\pi$
$32$	−0.792893	+	1.37333i	−0.140165	+	0.242773i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	10.6569			1.82764
$35$	5.24264	−	0.717439i	0.886168	−	0.121269i
$36$	3.82843			0.638071
$37$	4.74264	+	8.21449i	0.779685	+	1.35045i	0.932123	+	0.362142i	$0.117954\pi$
$37$	4.74264	+	8.21449i	0.779685	+	1.35045i	−0.152438	+	0.988313i	$0.548712\pi$
$38$	8.74264	−	15.1427i	1.41824	−	2.45647i
$39$	0.414214	−	0.717439i	0.0663273	−	0.114882i
$40$	−4.41421	−	7.64564i	−0.697948	−	1.20888i
$41$	−1.17157			−0.182969			−0.0914845	−	0.995807i	$-0.529161\pi$
$41$	−1.17157			−0.182969			−0.0914845	+	0.995807i	$0.529161\pi$
$42$	−2.41421	+	5.91359i	−0.372521	+	0.912487i
$43$	−2.75736			−0.420493			−0.210247	−	0.977648i	$-0.567427\pi$
$43$	−2.75736			−0.420493			−0.210247	+	0.977648i	$0.567427\pi$
$44$	−1.91421	−	3.31552i	−0.288579	−	0.499833i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	−8.44975	+	14.6354i	−1.24585	+	2.15787i
$47$	−4.91421	−	8.51167i	−0.716812	−	1.24155i	−0.962257	−	0.272144i	$-0.912267\pi$
$47$	−4.91421	−	8.51167i	−0.716812	−	1.24155i	0.245445	−	0.969411i	$-0.421066\pi$
$48$	3.00000			0.433013
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$	2.41421			0.341421
$51$	2.20711	+	3.82282i	0.309057	+	0.535302i
$52$	1.58579	−	2.74666i	0.219909	−	0.380894i
$53$	3.58579	−	6.21076i	0.492546	−	0.853114i	−0.507417	−	0.861700i	$-0.669400\pi$
$53$	3.58579	−	6.21076i	0.492546	−	0.853114i	0.999963	+	0.00858626i	$0.00273313\pi$
$54$	1.20711	+	2.09077i	0.164266	+	0.284518i
$55$	−2.00000			−0.269680
$56$	−4.41421	+	10.8126i	−0.589874	+	1.44489i
$57$	7.24264			0.959311
$58$	3.91421	+	6.77962i	0.513961	+	0.890207i
$59$	4.32843	−	7.49706i	0.563513	−	0.976034i	−0.433673	−	0.901070i	$-0.642783\pi$
$59$	4.32843	−	7.49706i	0.563513	−	0.976034i	0.997186	−	0.0749632i	$-0.0238839\pi$
$60$	3.82843	−	6.63103i	0.494248	−	0.856062i
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	−13.6569			−1.73442
$63$	−2.62132	+	0.358719i	−0.330255	+	0.0451944i
$64$	−9.82843			−1.22855
$65$	−0.828427	−	1.43488i	−0.102754	−	0.177975i
$66$	1.20711	−	2.09077i	0.148585	−	0.257356i
$67$	1.58579	−	2.74666i	0.193735	−	0.335558i	−0.752750	−	0.658306i	$-0.771273\pi$
$67$	1.58579	−	2.74666i	0.193735	−	0.335558i	0.946485	+	0.322748i	$0.104607\pi$
$68$	8.44975	+	14.6354i	1.02468	+	1.77480i
$69$	−7.00000			−0.842701
$70$	7.82843	+	10.0951i	0.935676	+	1.20660i
$71$	−4.17157			−0.495075			−0.247537	−	0.968878i	$-0.579621\pi$
$71$	−4.17157			−0.495075			−0.247537	+	0.968878i	$0.579621\pi$
$72$	2.20711	+	3.82282i	0.260110	+	0.450524i
$73$	−0.171573	+	0.297173i	−0.0200811	+	0.0347815i	−0.875891	−	0.482508i	$-0.839726\pi$
$73$	−0.171573	+	0.297173i	−0.0200811	+	0.0347815i	0.855810	+	0.517290i	$0.173059\pi$
$74$	−11.4497	+	19.8315i	−1.33101	+	2.30537i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	27.7279			3.18061
$77$	1.62132	+	2.09077i	0.184767	+	0.238265i
$78$	2.00000			0.226455
$79$	−6.65685	−	11.5300i	−0.748955	−	1.29723i	−0.948324	−	0.317303i	$-0.897223\pi$
$79$	−6.65685	−	11.5300i	−0.748955	−	1.29723i	0.199370	−	0.979924i	$-0.436111\pi$
$80$	3.00000	−	5.19615i	0.335410	−	0.580948i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.41421	−	2.44949i	−0.156174	−	0.270501i
$83$	−2.82843			−0.310460			−0.155230	−	0.987878i	$-0.549612\pi$
$83$	−2.82843			−0.310460			−0.155230	+	0.987878i	$0.549612\pi$
$84$	−10.0355	+	1.37333i	−1.09497	+	0.149843i
$85$	8.82843			0.957577
$86$	−3.32843	−	5.76500i	−0.358914	−	0.621656i
$87$	−1.62132	+	2.80821i	−0.173824	+	0.301072i
$88$	2.20711	−	3.82282i	0.235278	−	0.407514i
$89$	7.07107	+	12.2474i	0.749532	+	1.29823i	0.948047	+	0.318129i	$0.103055\pi$
$89$	7.07107	+	12.2474i	0.749532	+	1.29823i	−0.198516	+	0.980098i	$0.563612\pi$
$90$	4.82843			0.508961
$91$	−0.828427	+	2.02922i	−0.0868428	+	0.212720i
$92$	−26.7990			−2.79399
$93$	−2.82843	−	4.89898i	−0.293294	−	0.508001i
$94$	11.8640	−	20.5490i	1.22367	−	2.11947i
$95$	7.24264	−	12.5446i	0.743079	−	1.28705i
$96$	−0.792893	−	1.37333i	−0.0809243	−	0.140165i
$97$	−11.4853			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$97$	−11.4853			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$98$	4.20711	−	16.3674i	0.424982	−	1.65336i
$99$	1.00000			0.100504
$100$	1.91421	+	3.31552i	0.191421	+	0.331552i
$101$	−2.44975	+	4.24309i	−0.243759	+	0.422203i	−0.961782	−	0.273816i	$-0.911714\pi$
$101$	−2.44975	+	4.24309i	−0.243759	+	0.422203i	0.718023	+	0.696019i	$0.245047\pi$
$102$	−5.32843	+	9.22911i	−0.527593	+	0.913818i
$103$	−6.24264	−	10.8126i	−0.615106	−	1.06539i	−0.990366	−	0.138475i	$-0.955780\pi$
$103$	−6.24264	−	10.8126i	−0.615106	−	1.06539i	0.375260	−	0.926919i	$-0.377553\pi$
$104$	3.65685			0.358584
$105$	−2.00000	+	4.89898i	−0.195180	+	0.478091i
$106$	17.3137			1.68166
$107$	−4.82843	−	8.36308i	−0.466782	−	0.808490i	0.532498	−	0.846431i	$-0.321253\pi$
$107$	−4.82843	−	8.36308i	−0.466782	−	0.808490i	−0.999280	+	0.0379415i	$0.987920\pi$
$108$	−1.91421	+	3.31552i	−0.184195	+	0.319036i
$109$	3.41421	−	5.91359i	0.327022	−	0.566419i	−0.654897	−	0.755718i	$-0.727288\pi$
$109$	3.41421	−	5.91359i	0.327022	−	0.566419i	0.981920	+	0.189299i	$0.0606214\pi$
$110$	−2.41421	−	4.18154i	−0.230186	−	0.398694i
$111$	−9.48528			−0.900303
$112$	−7.86396	+	1.07616i	−0.743074	+	0.101687i
$113$	−7.65685			−0.720296			−0.360148	−	0.932895i	$-0.617274\pi$
$113$	−7.65685			−0.720296			−0.360148	+	0.932895i	$0.617274\pi$
$114$	8.74264	+	15.1427i	0.818823	+	1.41824i
$115$	−7.00000	+	12.1244i	−0.652753	+	1.13060i
$116$	−6.20711	+	10.7510i	−0.576315	+	0.998208i
$117$	0.414214	+	0.717439i	0.0382941	+	0.0663273i
$118$	20.8995			1.92395
$119$	−7.15685	−	9.22911i	−0.656068	−	0.846031i
$120$	8.82843			0.805921
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−4.82843	+	8.36308i	−0.437145	+	0.757158i
$123$	0.585786	−	1.01461i	0.0528186	−	0.0914845i
$124$	−10.8284	−	18.7554i	−0.972421	−	1.68428i
$125$	12.0000			1.07331
$126$	−3.91421	−	5.04757i	−0.348706	−	0.449673i
$127$	−16.0711			−1.42608			−0.713038	−	0.701125i	$-0.752681\pi$
$127$	−16.0711			−1.42608			−0.713038	+	0.701125i	$0.752681\pi$
$128$	−10.2782	−	17.8023i	−0.908471	−	1.57352i
$129$	1.37868	−	2.38794i	0.121386	−	0.210247i
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	2.58579	+	4.47871i	0.225921	+	0.391307i	0.956595	−	0.291419i	$-0.0941275\pi$
$131$	2.58579	+	4.47871i	0.225921	+	0.391307i	−0.730674	+	0.682726i	$0.760794\pi$
$132$	3.82843			0.333222
$133$	−18.9853	+	2.59808i	−1.64623	+	0.225282i
$134$	7.65685			0.661451
$135$	1.00000	+	1.73205i	0.0860663	+	0.149071i
$136$	−9.74264	+	16.8747i	−0.835425	+	1.44700i
$137$	−0.242641	+	0.420266i	−0.0207302	+	0.0359057i	−0.876204	−	0.481940i	$-0.839932\pi$
$137$	−0.242641	+	0.420266i	−0.0207302	+	0.0359057i	0.855474	+	0.517845i	$0.173266\pi$
$138$	−8.44975	−	14.6354i	−0.719290	−	1.24585i
$139$	8.41421			0.713684			0.356842	−	0.934165i	$-0.383853\pi$
$139$	8.41421			0.713684			0.356842	+	0.934165i	$0.383853\pi$
$140$	−7.65685	+	18.7554i	−0.647122	+	1.58512i
$141$	9.82843			0.827703
$142$	−5.03553	−	8.72180i	−0.422573	−	0.731917i
$143$	0.414214	−	0.717439i	0.0346383	−	0.0599953i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	3.24264	+	5.61642i	0.269287	+	0.466418i
$146$	−0.828427			−0.0685611
$147$	6.74264	−	1.88064i	0.556124	−	0.155112i
$148$	−36.3137			−2.98497
$149$	11.1066	+	19.2372i	0.909888	+	1.57597i	0.814218	+	0.580560i	$0.197166\pi$
$149$	11.1066	+	19.2372i	0.909888	+	1.57597i	0.0956705	+	0.995413i	$0.469500\pi$
$150$	−1.20711	+	2.09077i	−0.0985599	+	0.170711i
$151$	9.44975	−	16.3674i	0.769010	−	1.33196i	−0.169091	−	0.985600i	$-0.554083\pi$
$151$	9.44975	−	16.3674i	0.769010	−	1.33196i	0.938101	−	0.346363i	$-0.112583\pi$
$152$	15.9853	+	27.6873i	1.29658	+	2.24574i
$153$	−4.41421			−0.356868
$154$	−2.41421	+	5.91359i	−0.194543	+	0.476531i
$155$	−11.3137			−0.908739
$156$	1.58579	+	2.74666i	0.126965	+	0.219909i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	16.0711	−	27.8359i	1.27855	−	2.21451i
$159$	3.58579	+	6.21076i	0.284371	+	0.492546i
$160$	−3.17157			−0.250735
$161$	18.3492	−	2.51104i	1.44612	−	0.197897i
$162$	−2.41421			−0.189679
$163$	10.4853	+	18.1610i	0.821271	+	1.42248i	0.904736	+	0.425972i	$0.140068\pi$
$163$	10.4853	+	18.1610i	0.821271	+	1.42248i	−0.0834658	+	0.996511i	$0.526599\pi$
$164$	2.24264	−	3.88437i	0.175121	−	0.303318i
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$	−3.41421	−	5.91359i	−0.264994	−	0.458984i
$167$	5.17157			0.400188			0.200094	−	0.979777i	$-0.435875\pi$
$167$	5.17157			0.400188			0.200094	+	0.979777i	$0.435875\pi$
$168$	−7.15685	−	9.22911i	−0.552163	−	0.712041i
$169$	−12.3137			−0.947208
$170$	10.6569	+	18.4582i	0.817343	+	1.41568i
$171$	−3.62132	+	6.27231i	−0.276929	+	0.479656i
$172$	5.27817	−	9.14207i	0.402457	−	0.697076i
$173$	7.41421	+	12.8418i	0.563692	+	0.976344i	0.997170	+	0.0751793i	$0.0239529\pi$
$173$	7.41421	+	12.8418i	0.563692	+	0.976344i	−0.433478	+	0.901164i	$0.642714\pi$
$174$	−7.82843			−0.593472
$175$	−1.62132	−	2.09077i	−0.122560	−	0.158047i
$176$	3.00000			0.226134
$177$	4.32843	+	7.49706i	0.325345	+	0.563513i
$178$	−17.0711	+	29.5680i	−1.27953	+	2.21621i
$179$	−8.91421	+	15.4399i	−0.666280	+	1.15403i	0.312657	+	0.949866i	$0.398781\pi$
$179$	−8.91421	+	15.4399i	−0.666280	+	1.15403i	−0.978937	+	0.204164i	$0.934552\pi$
$180$	3.82843	+	6.63103i	0.285354	+	0.494248i
$181$	−11.6569			−0.866447			−0.433224	−	0.901286i	$-0.642624\pi$
$181$	−11.6569			−0.866447			−0.433224	+	0.901286i	$0.642624\pi$
$182$	−5.24264	+	0.717439i	−0.388610	+	0.0531801i
$183$	−4.00000			−0.295689
$184$	−15.4497	−	26.7597i	−1.13897	−	1.97275i
$185$	−9.48528	+	16.4290i	−0.697372	+	1.20788i
$186$	6.82843	−	11.8272i	0.500685	−	0.867211i
$187$	2.20711	+	3.82282i	0.161400	+	0.279552i
$188$	37.6274			2.74426
$189$	1.00000	−	2.44949i	0.0727393	−	0.178174i
$190$	34.9706			2.53703
$191$	10.8284	+	18.7554i	0.783517	+	1.35709i	0.929881	+	0.367861i	$0.119910\pi$
$191$	10.8284	+	18.7554i	0.783517	+	1.35709i	−0.146363	+	0.989231i	$0.546757\pi$
$192$	4.91421	−	8.51167i	0.354653	−	0.614277i
$193$	6.07107	−	10.5154i	0.437005	−	0.756915i	−0.560452	−	0.828187i	$-0.689373\pi$
$193$	6.07107	−	10.5154i	0.437005	−	0.756915i	0.997457	+	0.0712721i	$0.0227059\pi$
$194$	−13.8640	−	24.0131i	−0.995374	−	1.72404i
$195$	1.65685			0.118650
$196$	25.8137	−	7.19988i	1.84384	−	0.514277i
$197$	−16.4142			−1.16946			−0.584732	−	0.811226i	$-0.698800\pi$
$197$	−16.4142			−1.16946			−0.584732	+	0.811226i	$0.698800\pi$
$198$	1.20711	+	2.09077i	0.0857853	+	0.148585i
$199$	9.89949	−	17.1464i	0.701757	−	1.21548i	−0.266093	−	0.963947i	$-0.585733\pi$
$199$	9.89949	−	17.1464i	0.701757	−	1.21548i	0.967849	−	0.251531i	$-0.0809339\pi$
$200$	−2.20711	+	3.82282i	−0.156066	+	0.270314i
$201$	1.58579	+	2.74666i	0.111853	+	0.193735i
$202$	−11.8284			−0.832245
$203$	3.24264	−	7.94282i	0.227589	−	0.557476i
$204$	−16.8995			−1.18320
$205$	−1.17157	−	2.02922i	−0.0818262	−	0.141727i
$206$	15.0711	−	26.1039i	1.05005	−	1.81874i
$207$	3.50000	−	6.06218i	0.243267	−	0.421350i
$208$	1.24264	+	2.15232i	0.0861616	+	0.149236i
$209$	7.24264			0.500984
$210$	−12.6569	+	1.73205i	−0.873406	+	0.119523i
$211$	14.9706			1.03062			0.515308	−	0.857005i	$-0.327678\pi$
$211$	14.9706			1.03062			0.515308	+	0.857005i	$0.327678\pi$
$212$	13.7279	+	23.7775i	0.942838	+	1.63304i
$213$	2.08579	−	3.61269i	0.142916	−	0.247537i
$214$	11.6569	−	20.1903i	0.796846	−	1.38018i
$215$	−2.75736	−	4.77589i	−0.188050	−	0.325713i
$216$	−4.41421			−0.300349
$217$	9.17157	+	11.8272i	0.622607	+	0.802881i
$218$	16.4853			1.11652
$219$	−0.171573	−	0.297173i	−0.0115938	−	0.0200811i
$220$	3.82843	−	6.63103i	0.258113	−	0.447064i
$221$	−1.82843	+	3.16693i	−0.122993	+	0.213031i
$222$	−11.4497	−	19.8315i	−0.768457	−	1.33101i
$223$	−22.9706			−1.53822			−0.769111	−	0.639115i	$-0.779301\pi$
$223$	−22.9706			−1.53822			−0.769111	+	0.639115i	$0.779301\pi$
$224$	2.57107	+	3.31552i	0.171787	+	0.221527i
$225$	−1.00000			−0.0666667
$226$	−9.24264	−	16.0087i	−0.614811	−	1.06488i
$227$	−7.48528	+	12.9649i	−0.496816	+	0.860510i	−0.999993	−	0.00367316i	$-0.998831\pi$
$227$	−7.48528	+	12.9649i	−0.496816	+	0.860510i	0.503178	+	0.864183i	$0.332164\pi$
$228$	−13.8640	+	24.0131i	−0.918163	+	1.59031i
$229$	7.82843	+	13.5592i	0.517317	+	0.896019i	0.999798	+	0.0201128i	$0.00640252\pi$
$229$	7.82843	+	13.5592i	0.517317	+	0.896019i	−0.482481	+	0.875907i	$0.660264\pi$
$230$	−33.7990			−2.22864
$231$	−2.62132	+	0.358719i	−0.172470	+	0.0236020i
$232$	−14.3137			−0.939741
$233$	−5.20711	−	9.01897i	−0.341129	−	0.590853i	0.643514	−	0.765435i	$-0.277476\pi$
$233$	−5.20711	−	9.01897i	−0.341129	−	0.590853i	−0.984643	+	0.174582i	$0.944143\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$	9.82843	−	17.0233i	0.641136	−	1.11048i
$236$	16.5711	+	28.7019i	1.07868	+	1.86834i
$237$	13.3137			0.864818
$238$	10.6569	−	26.1039i	0.690781	−	1.69206i
$239$	−6.48528			−0.419498			−0.209749	−	0.977755i	$-0.567265\pi$
$239$	−6.48528			−0.419498			−0.209749	+	0.977755i	$0.567265\pi$
$240$	3.00000	+	5.19615i	0.193649	+	0.335410i
$241$	−3.65685	+	6.33386i	−0.235559	+	0.408000i	−0.959435	−	0.281930i	$-0.909025\pi$
$241$	−3.65685	+	6.33386i	−0.235559	+	0.408000i	0.723876	+	0.689930i	$0.242359\pi$
$242$	1.20711	−	2.09077i	0.0775958	−	0.134400i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−15.3137			−0.980360
$245$	3.48528	−	13.5592i	0.222666	−	0.866268i
$246$	2.82843			0.180334
$247$	3.00000	+	5.19615i	0.190885	+	0.330623i
$248$	12.4853	−	21.6251i	0.792816	−	1.37320i
$249$	1.41421	−	2.44949i	0.0896221	−	0.155230i
$250$	14.4853	+	25.0892i	0.916130	+	1.58678i
$251$	−2.51472			−0.158728			−0.0793638	−	0.996846i	$-0.525289\pi$
$251$	−2.51472			−0.158728			−0.0793638	+	0.996846i	$0.525289\pi$
$252$	3.82843	−	9.37769i	0.241168	−	0.590739i
$253$	−7.00000			−0.440086
$254$	−19.3995	−	33.6009i	−1.21723	−	2.10831i
$255$	−4.41421	+	7.64564i	−0.276429	+	0.478789i
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	−10.7279	−	18.5813i	−0.669189	−	1.15907i	−0.978131	−	0.207989i	$-0.933308\pi$
$257$	−10.7279	−	18.5813i	−0.669189	−	1.15907i	0.308942	−	0.951081i	$-0.400025\pi$
$258$	6.65685			0.414438
$259$	24.8640	−	3.40256i	1.54497	−	0.211424i
$260$	6.34315			0.393385
$261$	−1.62132	−	2.80821i	−0.100357	−	0.173824i
$262$	−6.24264	+	10.8126i	−0.385672	+	0.668003i
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$	2.20711	+	3.82282i	0.135838	+	0.235278i
$265$	14.3431			0.881092
$266$	−28.3492	−	36.5577i	−1.73820	−	2.24150i
$267$	−14.1421			−0.865485
$268$	6.07107	+	10.5154i	0.370849	+	0.642330i
$269$	13.8995	−	24.0746i	0.847467	−	1.46786i	−0.0359941	−	0.999352i	$-0.511460\pi$
$269$	13.8995	−	24.0746i	0.847467	−	1.46786i	0.883461	−	0.468504i	$-0.155207\pi$
$270$	−2.41421	+	4.18154i	−0.146924	+	0.254480i
$271$	11.4853	+	19.8931i	0.697681	+	1.20842i	0.969268	+	0.246005i	$0.0791181\pi$
$271$	11.4853	+	19.8931i	0.697681	+	1.20842i	−0.271587	+	0.962414i	$0.587549\pi$
$272$	−13.2426			−0.802953
$273$	−1.34315	−	1.73205i	−0.0812909	−	0.104828i
$274$	−1.17157			−0.0707773
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	13.3995	−	23.2086i	0.806555	−	1.39699i
$277$	12.8284	−	22.2195i	0.770785	−	1.33504i	−0.166348	−	0.986067i	$-0.553197\pi$
$277$	12.8284	−	22.2195i	0.770785	−	1.33504i	0.937133	−	0.348972i	$-0.113469\pi$
$278$	10.1569	+	17.5922i	0.609168	+	1.05511i
$279$	5.65685			0.338667
$280$	−23.1421	+	3.16693i	−1.38301	+	0.189260i
$281$	14.4142			0.859880			0.429940	−	0.902857i	$-0.358535\pi$
$281$	14.4142			0.859880			0.429940	+	0.902857i	$0.358535\pi$
$282$	11.8640	+	20.5490i	0.706489	+	1.22367i
$283$	−10.1716	+	17.6177i	−0.604637	+	1.04726i	0.387471	+	0.921882i	$0.373349\pi$
$283$	−10.1716	+	17.6177i	−0.604637	+	1.04726i	−0.992109	+	0.125381i	$0.959985\pi$
$284$	7.98528	−	13.8309i	0.473839	−	0.820714i
$285$	7.24264	+	12.5446i	0.429017	+	0.743079i
$286$	2.00000			0.118262
$287$	−1.17157	+	2.86976i	−0.0691558	+	0.169396i
$288$	1.58579			0.0934434
$289$	−1.24264	−	2.15232i	−0.0730965	−	0.126607i
$290$	−7.82843	+	13.5592i	−0.459701	+	0.796226i
$291$	5.74264	−	9.94655i	0.336640	−	0.583077i
$292$	−0.656854	−	1.13770i	−0.0384395	−	0.0665791i
$293$	5.72792			0.334629			0.167314	−	0.985904i	$-0.446491\pi$
$293$	5.72792			0.334629			0.167314	+	0.985904i	$0.446491\pi$
$294$	12.0711	+	11.8272i	0.703999	+	0.689775i
$295$	17.3137			1.00804
$296$	−20.9350	−	36.2605i	−1.21682	−	2.10760i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	−26.8137	+	46.4427i	−1.55328	+	2.69035i
$299$	−2.89949	−	5.02207i	−0.167682	−	0.290434i
$300$	−3.82843			−0.221034
$301$	−2.75736	+	6.75412i	−0.158932	+	0.389301i
$302$	45.6274			2.62556
$303$	−2.44975	−	4.24309i	−0.140734	−	0.243759i
$304$	−10.8640	+	18.8169i	−0.623091	+	1.07923i
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$	−5.32843	−	9.22911i	−0.304606	−	0.527593i
$307$	−17.3137			−0.988146			−0.494073	−	0.869421i	$-0.664492\pi$
$307$	−17.3137			−0.988146			−0.494073	+	0.869421i	$0.664492\pi$
$308$	−10.0355	+	1.37333i	−0.571828	+	0.0782528i
$309$	12.4853			0.710263
$310$	−13.6569	−	23.6544i	−0.775657	−	1.34348i
$311$	−14.8137	+	25.6581i	−0.840008	+	1.45494i	0.0498782	+	0.998755i	$0.484117\pi$
$311$	−14.8137	+	25.6581i	−0.840008	+	1.45494i	−0.889887	+	0.456182i	$0.849217\pi$
$312$	−1.82843	+	3.16693i	−0.103514	+	0.179292i
$313$	−2.39949	−	4.15605i	−0.135627	−	0.234914i	0.790210	−	0.612837i	$-0.209972\pi$
$313$	−2.39949	−	4.15605i	−0.135627	−	0.234914i	−0.925837	+	0.377923i	$0.876638\pi$
$314$	−16.8995			−0.953694
$315$	−3.24264	−	4.18154i	−0.182702	−	0.235603i
$316$	50.9706			2.86732
$317$	12.6569	+	21.9223i	0.710880	+	1.23128i	0.964527	+	0.263983i	$0.0850363\pi$
$317$	12.6569	+	21.9223i	0.710880	+	1.23128i	−0.253648	+	0.967297i	$0.581630\pi$
$318$	−8.65685	+	14.9941i	−0.485452	+	0.840828i
$319$	−1.62132	+	2.80821i	−0.0907765	+	0.157230i
$320$	−9.82843	−	17.0233i	−0.549426	−	0.951633i
$321$	9.65685			0.538993
$322$	27.3995	+	35.3330i	1.52691	+	1.96903i
$323$	−31.9706			−1.77889
$324$	−1.91421	−	3.31552i	−0.106345	−	0.184195i
$325$	−0.414214	+	0.717439i	−0.0229764	+	0.0397964i
$326$	−25.3137	+	43.8446i	−1.40200	+	2.42833i
$327$	3.41421	+	5.91359i	0.188806	+	0.327022i
$328$	5.17157			0.285552
$329$	−25.7635	+	3.52565i	−1.42039	+	0.194375i
$330$	4.82843			0.265796
$331$	−11.2426	−	19.4728i	−0.617951	−	1.07032i	−0.989859	−	0.142053i	$-0.954629\pi$
$331$	−11.2426	−	19.4728i	−0.617951	−	1.07032i	0.371908	−	0.928270i	$-0.378704\pi$
$332$	5.41421	−	9.37769i	0.297144	−	0.514668i
$333$	4.74264	−	8.21449i	0.259895	−	0.450152i
$334$	6.24264	+	10.8126i	0.341582	+	0.591638i
$335$	6.34315			0.346563
$336$	3.00000	−	7.34847i	0.163663	−	0.400892i
$337$	3.85786			0.210151			0.105076	−	0.994464i	$-0.466492\pi$
$337$	3.85786			0.210151			0.105076	+	0.994464i	$0.466492\pi$
$338$	−14.8640	−	25.7451i	−0.808493	−	1.40035i
$339$	3.82843	−	6.63103i	0.207932	−	0.360148i
$340$	−16.8995	+	29.2708i	−0.916504	+	1.58743i
$341$	−2.82843	−	4.89898i	−0.153168	−	0.265295i
$342$	−17.4853			−0.945496
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	12.1716			0.656247
$345$	−7.00000	−	12.1244i	−0.376867	−	0.652753i
$346$	−17.8995	+	31.0028i	−0.962283	+	1.66672i
$347$	−7.48528	+	12.9649i	−0.401831	+	0.695992i	−0.993947	−	0.109861i	$-0.964959\pi$
$347$	−7.48528	+	12.9649i	−0.401831	+	0.695992i	0.592116	+	0.805853i	$0.298293\pi$
$348$	−6.20711	−	10.7510i	−0.332736	−	0.576315i
$349$	10.9706			0.587241			0.293620	−	0.955922i	$-0.405140\pi$
$349$	10.9706			0.587241			0.293620	+	0.955922i	$0.405140\pi$
$350$	2.41421	−	5.91359i	0.129045	−	0.316095i
$351$	−0.828427			−0.0442182
$352$	−0.792893	−	1.37333i	−0.0422614	−	0.0731988i
$353$	−6.65685	+	11.5300i	−0.354309	+	0.613680i	−0.986999	−	0.160724i	$-0.948617\pi$
$353$	−6.65685	+	11.5300i	−0.354309	+	0.613680i	0.632691	+	0.774405i	$0.281950\pi$
$354$	−10.4497	+	18.0995i	−0.555398	+	0.961977i
$355$	−4.17157	−	7.22538i	−0.221404	−	0.383483i
$356$	−54.1421			−2.86953
$357$	11.5711	−	1.58346i	0.612406	−	0.0838058i
$358$	−43.0416			−2.27482
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	0.952063	−	0.305903i	$-0.0989582\pi$
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	−0.740951	+	0.671559i	$0.765625\pi$
$360$	−4.41421	+	7.64564i	−0.232649	+	0.402961i
$361$	−16.7279	+	28.9736i	−0.880417	+	1.52493i
$362$	−14.0711	−	24.3718i	−0.739559	−	1.28095i
$363$	1.00000			0.0524864
$364$	−5.14214	−	6.63103i	−0.269521	−	0.347560i
$365$	−0.686292			−0.0359221
$366$	−4.82843	−	8.36308i	−0.252386	−	0.437145i
$367$	2.07107	−	3.58719i	0.108109	−	0.187250i	−0.806895	−	0.590695i	$-0.798854\pi$
$367$	2.07107	−	3.58719i	0.108109	−	0.187250i	0.915004	+	0.403445i	$0.132187\pi$
$368$	10.5000	−	18.1865i	0.547350	−	0.948039i
$369$	0.585786	+	1.01461i	0.0304948	+	0.0528186i
$370$	−45.7990			−2.38098
$371$	−11.6274	−	14.9941i	−0.603665	−	0.778455i
$372$	21.6569			1.12286
$373$	0.828427	+	1.43488i	0.0428943	+	0.0742952i	0.886675	−	0.462392i	$-0.153009\pi$
$373$	0.828427	+	1.43488i	0.0428943	+	0.0742952i	−0.843781	+	0.536687i	$0.819675\pi$
$374$	−5.32843	+	9.22911i	−0.275526	+	0.477226i
$375$	−6.00000	+	10.3923i	−0.309839	+	0.536656i
$376$	21.6924	+	37.5723i	1.11870	+	1.93764i
$377$	−2.68629			−0.138351
$378$	6.32843	−	0.866025i	0.325499	−	0.0445435i
$379$	18.8284			0.967151			0.483576	−	0.875303i	$-0.339338\pi$
$379$	18.8284			0.967151			0.483576	+	0.875303i	$0.339338\pi$
$380$	27.7279	+	48.0262i	1.42241	+	2.46369i
$381$	8.03553	−	13.9180i	0.411673	−	0.713038i
$382$	−26.1421	+	45.2795i	−1.33755	+	2.31670i
$383$	−1.15685	−	2.00373i	−0.0591125	−	0.102386i	0.834955	−	0.550319i	$-0.185494\pi$
$383$	−1.15685	−	2.00373i	−0.0591125	−	0.102386i	−0.894067	+	0.447933i	$0.852160\pi$
$384$	20.5563			1.04901
$385$	−2.00000	+	4.89898i	−0.101929	+	0.249675i
$386$	29.3137			1.49203
$387$	1.37868	+	2.38794i	0.0700822	+	0.121386i
$388$	21.9853	−	38.0796i	1.11613	−	1.93320i
$389$	5.89949	−	10.2182i	0.299116	−	0.518085i	−0.676818	−	0.736151i	$-0.736641\pi$
$389$	5.89949	−	10.2182i	0.299116	−	0.518085i	0.975934	+	0.218066i	$0.0699748\pi$
$390$	2.00000	+	3.46410i	0.101274	+	0.175412i
$391$	30.8995			1.56265
$392$	22.0711	+	21.6251i	1.11476	+	1.09223i
$393$	−5.17157			−0.260871
$394$	−19.8137	−	34.3183i	−0.998200	−	1.72893i
$395$	13.3137	−	23.0600i	0.669885	−	1.16028i
$396$	−1.91421	+	3.31552i	−0.0961929	+	0.166611i
$397$	−8.74264	−	15.1427i	−0.438781	−	0.759990i	0.558815	−	0.829292i	$-0.311256\pi$
$397$	−8.74264	−	15.1427i	−0.438781	−	0.759990i	−0.997596	+	0.0693020i	$0.977923\pi$
$398$	47.7990			2.39595
$399$	7.24264	−	17.7408i	0.362586	−	0.888150i
$400$	−3.00000			−0.150000
$401$	−3.75736	−	6.50794i	−0.187634	−	0.324991i	0.756827	−	0.653615i	$-0.226748\pi$
$401$	−3.75736	−	6.50794i	−0.187634	−	0.324991i	−0.944461	+	0.328624i	$0.893415\pi$
$402$	−3.82843	+	6.63103i	−0.190945	+	0.330726i
$403$	2.34315	−	4.05845i	0.116720	−	0.202166i
$404$	−9.37868	−	16.2443i	−0.466607	−	0.808187i
$405$	−2.00000			−0.0993808
$406$	20.5208	−	2.80821i	1.01843	−	0.139369i
$407$	−9.48528			−0.470168
$408$	−9.74264	−	16.8747i	−0.482333	−	0.835425i
$409$	3.89949	−	6.75412i	0.192818	−	0.333970i	−0.753365	−	0.657602i	$-0.771571\pi$
$409$	3.89949	−	6.75412i	0.192818	−	0.333970i	0.946183	+	0.323632i	$0.104904\pi$
$410$	2.82843	−	4.89898i	0.139686	−	0.241943i
$411$	−0.242641	−	0.420266i	−0.0119686	−	0.0207302i
$412$	47.7990			2.35489
$413$	−14.0355	−	18.0995i	−0.690643	−	0.890618i
$414$	16.8995			0.830565
$415$	−2.82843	−	4.89898i	−0.138842	−	0.240481i
$416$	0.656854	−	1.13770i	0.0322049	−	0.0557806i
$417$	−4.20711	+	7.28692i	−0.206023	+	0.356842i
$418$	8.74264	+	15.1427i	0.427617	+	0.740654i
$419$	14.7990			0.722978			0.361489	−	0.932376i	$-0.382269\pi$
$419$	14.7990			0.722978			0.361489	+	0.932376i	$0.382269\pi$
$420$	−12.4142	−	16.0087i	−0.605752	−	0.781146i
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	18.0711	+	31.3000i	0.879686	+	1.52366i
$423$	−4.91421	+	8.51167i	−0.238937	+	0.413851i
$424$	−15.8284	+	27.4156i	−0.768696	+	1.33142i
$425$	−2.20711	−	3.82282i	−0.107060	−	0.185434i
$426$	10.0711			0.487945
$427$	10.4853	−	1.43488i	0.507418	−	0.0694386i
$428$	36.9706			1.78704
$429$	0.414214	+	0.717439i	0.0199984	+	0.0346383i
$430$	6.65685	−	11.5300i	0.321022	−	0.556026i
$431$	−3.48528	+	6.03668i	−0.167880	+	0.290777i	−0.937674	−	0.347515i	$-0.887025\pi$
$431$	−3.48528	+	6.03668i	−0.167880	+	0.290777i	0.769794	+	0.638292i	$0.220359\pi$
$432$	−1.50000	−	2.59808i	−0.0721688	−	0.125000i
$433$	0.857864			0.0412263			0.0206132	−	0.999788i	$-0.493438\pi$
$433$	0.857864			0.0412263			0.0206132	+	0.999788i	$0.493438\pi$
$434$	−13.6569	+	33.4523i	−0.655550	+	1.60576i
$435$	−6.48528			−0.310945
$436$	13.0711	+	22.6398i	0.625991	+	1.08425i
$437$	25.3492	−	43.9062i	1.21262	−	2.10032i
$438$	0.414214	−	0.717439i	0.0197919	−	0.0342806i
$439$	−15.4497	−	26.7597i	−0.737376	−	1.27717i	−0.953673	−	0.300845i	$-0.902731\pi$
$439$	−15.4497	−	26.7597i	−0.737376	−	1.27717i	0.216297	−	0.976328i	$-0.430602\pi$
$440$	8.82843			0.420879
$441$	−1.74264	+	6.77962i	−0.0829829	+	0.322839i
$442$	−8.82843			−0.419925
$443$	−16.8137	−	29.1222i	−0.798843	−	1.38364i	−0.920370	−	0.391049i	$-0.872112\pi$
$443$	−16.8137	−	29.1222i	−0.798843	−	1.38364i	0.121526	−	0.992588i	$-0.461221\pi$
$444$	18.1569	−	31.4486i	0.861686	−	1.49248i
$445$	−14.1421	+	24.4949i	−0.670402	+	1.16117i
$446$	−27.7279	−	48.0262i	−1.31296	−	2.27411i
$447$	−22.2132			−1.05065
$448$	−9.82843	+	24.0746i	−0.464350	+	1.13742i
$449$	−4.00000			−0.188772			−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000			−0.188772			−0.0943858	+	0.995536i	$0.530089\pi$
$450$	−1.20711	−	2.09077i	−0.0569036	−	0.0985599i
$451$	0.585786	−	1.01461i	0.0275836	−	0.0477762i
$452$	14.6569	−	25.3864i	0.689400	−	1.19408i
$453$	9.44975	+	16.3674i	0.443988	+	0.769010i
$454$	−36.1421			−1.69623
$455$	−4.34315	+	0.594346i	−0.203610	+	0.0278634i
$456$	−31.9706			−1.49716
$457$	−9.41421	−	16.3059i	−0.440378	−	0.762758i	0.557339	−	0.830285i	$-0.311822\pi$
$457$	−9.41421	−	16.3059i	−0.440378	−	0.762758i	−0.997717	+	0.0675273i	$0.978489\pi$
$458$	−18.8995	+	32.7349i	−0.883115	+	1.52960i
$459$	2.20711	−	3.82282i	0.103019	−	0.178434i
$460$	−26.7990	−	46.4172i	−1.24951	−	2.16421i
$461$	6.75736			0.314722			0.157361	−	0.987541i	$-0.449701\pi$
$461$	6.75736			0.314722			0.157361	+	0.987541i	$0.449701\pi$
$462$	−3.91421	−	5.04757i	−0.182106	−	0.234834i
$463$	18.6274			0.865689			0.432845	−	0.901468i	$-0.357510\pi$
$463$	18.6274			0.865689			0.432845	+	0.901468i	$0.357510\pi$
$464$	−4.86396	−	8.42463i	−0.225804	−	0.391104i
$465$	5.65685	−	9.79796i	0.262330	−	0.454369i
$466$	12.5711	−	21.7737i	0.582343	−	1.00865i
$467$	4.15685	+	7.19988i	0.192356	+	0.333171i	0.946031	−	0.324077i	$-0.105054\pi$
$467$	4.15685	+	7.19988i	0.192356	+	0.333171i	−0.753674	+	0.657248i	$0.771720\pi$
$468$	−3.17157			−0.146606
$469$	−5.14214	−	6.63103i	−0.237442	−	0.306193i
$470$	47.4558			2.18897
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	−19.1066	+	33.0936i	−0.879453	+	1.52326i
$473$	1.37868	−	2.38794i	0.0633918	−	0.109798i
$474$	16.0711	+	27.8359i	0.738169	+	1.27855i
$475$	−7.24264			−0.332315
$476$	44.2990	−	6.06218i	2.03044	−	0.277859i
$477$	−7.17157			−0.328364
$478$	−7.82843	−	13.5592i	−0.358064	−	0.620185i
$479$	−7.00000	+	12.1244i	−0.319838	+	0.553976i	−0.980454	−	0.196748i	$-0.936962\pi$
$479$	−7.00000	+	12.1244i	−0.319838	+	0.553976i	0.660616	+	0.750724i	$0.270295\pi$
$480$	1.58579	−	2.74666i	0.0723809	−	0.125367i
$481$	−3.92893	−	6.80511i	−0.179144	−	0.310286i
$482$	−17.6569			−0.804248
$483$	−7.00000	+	17.1464i	−0.318511	+	0.780189i
$484$	3.82843			0.174019
$485$	−11.4853	−	19.8931i	−0.521520	−	0.903299i
$486$	1.20711	−	2.09077i	0.0547555	−	0.0948393i
$487$	16.3137	−	28.2562i	0.739245	−	1.28041i	−0.213591	−	0.976923i	$-0.568516\pi$
$487$	16.3137	−	28.2562i	0.739245	−	1.28041i	0.952836	−	0.303486i	$-0.0981506\pi$
$488$	−8.82843	−	15.2913i	−0.399644	−	0.692204i
$489$	−20.9706			−0.948322
$490$	32.5563	−	9.08052i	1.47075	−	0.410216i
$491$	−1.51472			−0.0683583			−0.0341791	−	0.999416i	$-0.510882\pi$
$491$	−1.51472			−0.0683583			−0.0341791	+	0.999416i	$0.510882\pi$
$492$	2.24264	+	3.88437i	0.101106	+	0.175121i
$493$	7.15685	−	12.3960i	0.322329	−	0.558289i
$494$	−7.24264	+	12.5446i	−0.325862	+	0.564409i
$495$	1.00000	+	1.73205i	0.0449467	+	0.0778499i
$496$	16.9706			0.762001
$497$	−4.17157	+	10.2182i	−0.187121	+	0.458350i
$498$	6.82843			0.305989
$499$	15.8995	+	27.5387i	0.711759	+	1.23280i	0.964196	+	0.265190i	$0.0854346\pi$
$499$	15.8995	+	27.5387i	0.711759	+	1.23280i	−0.252437	+	0.967613i	$0.581232\pi$
$500$	−22.9706	+	39.7862i	−1.02727	+	1.77929i
$501$	−2.58579	+	4.47871i	−0.115524	+	0.200094i
$502$	−3.03553	−	5.25770i	−0.135483	−	0.234663i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	11.5711	−	1.58346i	0.515416	−	0.0705331i
$505$	−9.79899			−0.436049
$506$	−8.44975	−	14.6354i	−0.375637	−	0.650623i
$507$	6.15685	−	10.6640i	0.273435	−	0.473604i
$508$	30.7635	−	53.2839i	1.36491	−	2.36409i
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$	−21.3137			−0.943787
$511$	0.556349	+	0.717439i	0.0246114	+	0.0317376i
$512$	31.2426			1.38074
$513$	−3.62132	−	6.27231i	−0.159885	−	0.276929i
$514$	25.8995	−	44.8592i	1.14238	−	1.97866i
$515$	12.4853	−	21.6251i	0.550167	−	0.952918i
$516$	5.27817	+	9.14207i	0.232359	+	0.402457i
$517$	9.82843			0.432254
$518$	37.1274	+	47.8776i	1.63129	+	2.10362i
$519$	−14.8284			−0.650896
$520$	3.65685	+	6.33386i	0.160364	+	0.277758i
$521$	−15.5858	+	26.9954i	−0.682826	+	1.18269i	0.291289	+	0.956635i	$0.405916\pi$
$521$	−15.5858	+	26.9954i	−0.682826	+	1.18269i	−0.974115	+	0.226054i	$0.927418\pi$
$522$	3.91421	−	6.77962i	0.171320	−	0.296736i
$523$	11.1421	+	19.2987i	0.487212	+	0.843875i	0.999892	−	0.0147044i	$-0.00468072\pi$
$523$	11.1421	+	19.2987i	0.487212	+	0.843875i	−0.512680	+	0.858580i	$0.671347\pi$
$524$	−19.7990			−0.864923
$525$	2.62132	−	0.358719i	0.114404	−	0.0156558i
$526$	−43.4558			−1.89476
$527$	12.4853	+	21.6251i	0.543867	+	0.942006i
$528$	−1.50000	+	2.59808i	−0.0652791	+	0.113067i
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$	17.3137	+	29.9882i	0.752059	+	1.30261i
$531$	−8.65685			−0.375675
$532$	27.7279	−	67.9193i	1.20216	−	2.94467i
$533$	0.970563			0.0420397
$534$	−17.0711	−	29.5680i	−0.738737	−	1.27953i
$535$	9.65685	−	16.7262i	0.417502	−	0.723135i
$536$	−7.00000	+	12.1244i	−0.302354	+	0.523692i
$537$	−8.91421	−	15.4399i	−0.384677	−	0.666280i
$538$	67.1127			2.89343
$539$	6.74264	−	1.88064i	0.290426	−	0.0810048i
$540$	−7.65685			−0.329499
$541$	−9.82843	−	17.0233i	−0.422557	−	0.731890i	0.573632	−	0.819113i	$-0.305534\pi$
$541$	−9.82843	−	17.0233i	−0.422557	−	0.731890i	−0.996189	+	0.0872230i	$0.972201\pi$
$542$	−27.7279	+	48.0262i	−1.19102	+	2.06290i
$543$	5.82843	−	10.0951i	0.250122	−	0.433224i
$544$	3.50000	+	6.06218i	0.150061	+	0.259914i
$545$	13.6569			0.584995
$546$	2.00000	−	4.89898i	0.0855921	−	0.209657i
$547$	−24.2132			−1.03528			−0.517641	−	0.855598i	$-0.673190\pi$
$547$	−24.2132			−1.03528			−0.517641	+	0.855598i	$0.673190\pi$
$548$	−0.928932	−	1.60896i	−0.0396820	−	0.0687313i
$549$	2.00000	−	3.46410i	0.0853579	−	0.147844i
$550$	−1.20711	+	2.09077i	−0.0514712	+	0.0891507i
$551$	−11.7426	−	20.3389i	−0.500253	−	0.866464i
$552$	30.8995			1.31517
$553$	−34.8995	+	4.77589i	−1.48408	+	0.203091i
$554$	61.9411			2.63163
$555$	−9.48528	−	16.4290i	−0.402628	−	0.697372i
$556$	−16.1066	+	27.8975i	−0.683072	+	1.18312i
$557$	4.27817	−	7.41002i	0.181272	−	0.313972i	−0.761042	−	0.648703i	$-0.775312\pi$
$557$	4.27817	−	7.41002i	0.181272	−	0.313972i	0.942314	+	0.334730i	$0.108645\pi$
$558$	6.82843	+	11.8272i	0.289070	+	0.500685i
$559$	2.28427			0.0966144
$560$	−9.72792	−	12.5446i	−0.411080	−	0.530107i
$561$	−4.41421			−0.186368
$562$	17.3995	+	30.1368i	0.733953	+	1.27124i
$563$	−12.4142	+	21.5020i	−0.523197	+	0.906203i	0.476439	+	0.879208i	$0.341927\pi$
$563$	−12.4142	+	21.5020i	−0.523197	+	0.906203i	−0.999636	+	0.0269957i	$0.991406\pi$
$564$	−18.8137	+	32.5863i	−0.792200	+	1.37213i
$565$	−7.65685	−	13.2621i	−0.322126	−	0.557939i
$566$	−49.1127			−2.06436
$567$	1.62132	+	2.09077i	0.0680891	+	0.0878041i
$568$	18.4142			0.772643
$569$	−0.621320	−	1.07616i	−0.0260471	−	0.0451149i	0.852708	−	0.522388i	$-0.174959\pi$
$569$	−0.621320	−	1.07616i	−0.0260471	−	0.0451149i	−0.878755	+	0.477273i	$0.841625\pi$
$570$	−17.4853	+	30.2854i	−0.732378	+	1.26852i
$571$	1.96447	−	3.40256i	0.0822103	−	0.142392i	−0.821989	−	0.569504i	$-0.807135\pi$
$571$	1.96447	−	3.40256i	0.0822103	−	0.142392i	0.904199	+	0.427111i	$0.140469\pi$
$572$	1.58579	+	2.74666i	0.0663051	+	0.114844i
$573$	−21.6569			−0.904728
$574$	−7.41421	+	1.01461i	−0.309463	+	0.0423491i
$575$	7.00000			0.291920
$576$	4.91421	+	8.51167i	0.204759	+	0.354653i
$577$	−3.82843	+	6.63103i	−0.159380	+	0.276053i	−0.934645	−	0.355582i	$-0.884283\pi$
$577$	−3.82843	+	6.63103i	−0.159380	+	0.276053i	0.775266	+	0.631635i	$0.217616\pi$
$578$	3.00000	−	5.19615i	0.124784	−	0.216131i
$579$	6.07107	+	10.5154i	0.252305	+	0.437005i
$580$	−24.8284			−1.03094
$581$	−2.82843	+	6.92820i	−0.117343	+	0.287430i
$582$	27.7279			1.14936
$583$	3.58579	+	6.21076i	0.148508	+	0.257224i
$584$	0.757359	−	1.31178i	0.0313398	−	0.0542820i
$585$	−0.828427	+	1.43488i	−0.0342512	+	0.0593249i
$586$	6.91421	+	11.9758i	0.285624	+	0.494714i
$587$	8.68629			0.358522			0.179261	−	0.983802i	$-0.442629\pi$
$587$	8.68629			0.358522			0.179261	+	0.983802i	$0.442629\pi$
$588$	−6.67157	+	25.9553i	−0.275131	+	1.07038i
$589$	40.9706			1.68816
$590$	20.8995	+	36.1990i	0.860419	+	1.49029i
$591$	8.20711	−	14.2151i	0.337595	−	0.584732i
$592$	14.2279	−	24.6435i	0.584764	−	1.01284i
$593$	11.1360	+	19.2882i	0.457302	+	0.792071i	0.998817	−	0.0486202i	$-0.0154824\pi$
$593$	11.1360	+	19.2882i	0.457302	+	0.792071i	−0.541515	+	0.840691i	$0.682149\pi$
$594$	−2.41421			−0.0990564
$595$	8.82843	−	21.6251i	0.361930	−	0.886544i
$596$	−85.0416			−3.48344
$597$	9.89949	+	17.1464i	0.405159	+	0.701757i
$598$	7.00000	−	12.1244i	0.286251	−	0.495802i
$599$	0.686292	−	1.18869i	0.0280411	−	0.0485686i	−0.851664	−	0.524088i	$-0.824406\pi$
$599$	0.686292	−	1.18869i	0.0280411	−	0.0485686i	0.879705	+	0.475519i	$0.157740\pi$
$600$	−2.20711	−	3.82282i	−0.0901048	−	0.156066i
$601$	−14.4853			−0.590867			−0.295433	−	0.955363i	$-0.595464\pi$
$601$	−14.4853			−0.590867			−0.295433	+	0.955363i	$0.595464\pi$
$602$	−17.4497	+	2.38794i	−0.711199	+	0.0973253i
$603$	−3.17157			−0.129156
$604$	36.1777	+	62.6616i	1.47205	+	2.54966i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$	5.91421	−	10.2437i	0.240249	−	0.416123i
$607$	9.34315	+	16.1828i	0.379227	+	0.656840i	0.990950	−	0.134232i	$-0.0428568\pi$
$607$	9.34315	+	16.1828i	0.379227	+	0.656840i	−0.611723	+	0.791072i	$0.709523\pi$
$608$	11.4853			0.465790
$609$	5.25736	+	6.77962i	0.213039	+	0.274724i
$610$	−19.3137			−0.781989
$611$	4.07107	+	7.05130i	0.164698	+	0.285265i
$612$	8.44975	−	14.6354i	0.341561	−	0.591601i
$613$	−12.5858	+	21.7992i	−0.508335	+	0.880462i	0.491618	+	0.870811i	$0.336406\pi$
$613$	−12.5858	+	21.7992i	−0.508335	+	0.880462i	−0.999953	+	0.00965147i	$0.996928\pi$
$614$	−20.8995	−	36.1990i	−0.843435	−	1.46087i
$615$	2.34315			0.0944848
$616$	−7.15685	−	9.22911i	−0.288358	−	0.371851i
$617$	13.1716			0.530268			0.265134	−	0.964212i	$-0.414584\pi$
$617$	13.1716			0.530268			0.265134	+	0.964212i	$0.414584\pi$
$618$	15.0711	+	26.1039i	0.606247	+	1.05005i
$619$	−17.3137	+	29.9882i	−0.695897	+	1.20533i	0.273981	+	0.961735i	$0.411660\pi$
$619$	−17.3137	+	29.9882i	−0.695897	+	1.20533i	−0.969877	+	0.243593i	$0.921674\pi$
$620$	21.6569	−	37.5108i	0.869760	−	1.50647i
$621$	3.50000	+	6.06218i	0.140450	+	0.243267i
$622$	−71.5269			−2.86797
$623$	37.0711	−	5.07306i	1.48522	−	0.203248i
$624$	−2.48528			−0.0994909
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	5.79289	−	10.0336i	0.231531	−	0.401023i
$627$	−3.62132	+	6.27231i	−0.144622	+	0.250492i
$628$	−13.3995	−	23.2086i	−0.534698	−	0.926124i
$629$	41.8701			1.66947
$630$	4.82843	−	11.8272i	0.192369	−	0.471206i
$631$	26.2843			1.04636			0.523180	−	0.852222i	$-0.324745\pi$
$631$	26.2843			1.04636			0.523180	+	0.852222i	$0.324745\pi$
$632$	29.3848	+	50.8959i	1.16886	+	2.02453i
$633$	−7.48528	+	12.9649i	−0.297513	+	0.515308i
$634$	−30.5563	+	52.9251i	−1.21355	+	2.10193i
$635$	−16.0711	−	27.8359i	−0.637761	−	1.10463i
$636$	−27.4558			−1.08870
$637$	4.14214	+	4.05845i	0.164117	+	0.160802i
$638$	−7.82843			−0.309930
$639$	2.08579	+	3.61269i	0.0825124	+	0.142916i
$640$	20.5563	−	35.6046i	0.812561	−	1.40740i
$641$	6.24264	−	10.8126i	0.246569	−	0.427071i	−0.716002	−	0.698098i	$-0.754030\pi$
$641$	6.24264	−	10.8126i	0.246569	−	0.427071i	0.962572	+	0.271027i	$0.0873633\pi$
$642$	11.6569	+	20.1903i	0.460059	+	0.796846i
$643$	2.00000			0.0788723			0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000			0.0788723			0.0394362	+	0.999222i	$0.487444\pi$
$644$	−26.7990	+	65.6439i	−1.05603	+	2.58673i
$645$	5.51472			0.217142
$646$	−38.5919	−	66.8431i	−1.51838	−	2.62991i
$647$	9.65685	−	16.7262i	0.379650	−	0.657573i	−0.611361	−	0.791352i	$-0.709378\pi$
$647$	9.65685	−	16.7262i	0.379650	−	0.657573i	0.991011	+	0.133778i	$0.0427110\pi$
$648$	2.20711	−	3.82282i	0.0867033	−	0.150175i
$649$	4.32843	+	7.49706i	0.169906	+	0.294285i
$650$	−2.00000			−0.0784465
$651$	−14.8284	+	2.02922i	−0.581172	+	0.0795315i
$652$	−80.2843			−3.14417
$653$	−15.5563	−	26.9444i	−0.608767	−	1.05442i	−0.991444	−	0.130533i	$-0.958331\pi$
$653$	−15.5563	−	26.9444i	−0.608767	−	1.05442i	0.382677	−	0.923882i	$-0.375002\pi$
$654$	−8.24264	+	14.2767i	−0.322313	+	0.558262i
$655$	−5.17157	+	8.95743i	−0.202070	+	0.349996i
$656$	1.75736	+	3.04384i	0.0686134	+	0.118842i
$657$	0.343146			0.0133874
$658$	−38.4706	−	49.6096i	−1.49974	−	1.93398i
$659$	34.4853			1.34336			0.671678	−	0.740843i	$-0.265574\pi$
$659$	34.4853			1.34336			0.671678	+	0.740843i	$0.265574\pi$
$660$	3.82843	+	6.63103i	0.149021	+	0.258113i
$661$	−5.98528	+	10.3668i	−0.232800	+	0.403222i	−0.958631	−	0.284651i	$-0.908122\pi$
$661$	−5.98528	+	10.3668i	−0.232800	+	0.403222i	0.725831	+	0.687873i	$0.241456\pi$
$662$	27.1421	−	47.0116i	1.05491	−	1.82716i
$663$	−1.82843	−	3.16693i	−0.0710102	−	0.122993i
$664$	12.4853			0.484523
$665$	−23.4853	−	30.2854i	−0.910720	−	1.17442i
$666$	22.8995			0.887337
$667$	11.3492	+	19.6575i	0.439444	+	0.761140i
$668$	−9.89949	+	17.1464i	−0.383023	+	0.663415i
$669$	11.4853	−	19.8931i	0.444047	−	0.769111i
$670$	7.65685	+	13.2621i	0.295810	+	0.512358i
$671$	−4.00000			−0.154418
$672$	−4.15685	+	0.568852i	−0.160354	+	0.0219440i
$673$	27.1716			1.04739			0.523694	−	0.851907i	$-0.324554\pi$
$673$	27.1716			1.04739			0.523694	+	0.851907i	$0.324554\pi$
$674$	4.65685	+	8.06591i	0.179375	+	0.310687i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	23.5711	−	40.8263i	0.906580	−	1.57024i
$677$	16.0061	+	27.7234i	0.615164	+	1.06550i	0.990356	+	0.138548i	$0.0442437\pi$
$677$	16.0061	+	27.7234i	0.615164	+	1.06550i	−0.375191	+	0.926947i	$0.622423\pi$
$678$	18.4853			0.709923
$679$	−11.4853	+	28.1331i	−0.440765	+	1.07965i
$680$	−38.9706			−1.49445
$681$	−7.48528	−	12.9649i	−0.286837	−	0.496816i
$682$	6.82843	−	11.8272i	0.261474	−	0.452886i
$683$	−1.60051	+	2.77216i	−0.0612416	+	0.106074i	−0.895021	−	0.446025i	$-0.852839\pi$
$683$	−1.60051	+	2.77216i	−0.0612416	+	0.106074i	0.833779	+	0.552098i	$0.186173\pi$
$684$	−13.8640	−	24.0131i	−0.530102	−	0.918163i
$685$	−0.970563			−0.0370833
$686$	−35.8848	−	26.6727i	−1.37009	−	1.01837i
$687$	−15.6569			−0.597346
$688$	4.13604	+	7.16383i	0.157685	+	0.273118i
$689$	−2.97056	+	5.14517i	−0.113169	+	0.196015i
$690$	16.8995	−	29.2708i	0.643353	−	1.11432i
$691$	5.72792	+	9.92105i	0.217900	+	0.377415i	0.954166	−	0.299278i	$-0.0967459\pi$
$691$	5.72792	+	9.92105i	0.217900	+	0.377415i	−0.736265	+	0.676693i	$0.763413\pi$
$692$	−56.7696			−2.15805
$693$	1.00000	−	2.44949i	0.0379869	−	0.0930484i
$694$	−36.1421			−1.37194
$695$	8.41421	+	14.5738i	0.319169	+	0.552817i
$696$	7.15685	−	12.3960i	0.271280	−	0.469871i
$697$	−2.58579	+	4.47871i	−0.0979436	+	0.169643i
$698$	13.2426	+	22.9369i	0.501241	+	0.868175i
$699$	10.4142			0.393902
$700$	10.0355	−	1.37333i	0.379308	−	0.0519070i
$701$	−2.89949			−0.109512			−0.0547562	−	0.998500i	$-0.517438\pi$
$701$	−2.89949			−0.109512			−0.0547562	+	0.998500i	$0.517438\pi$
$702$	−1.00000	−	1.73205i	−0.0377426	−	0.0653720i
$703$	34.3492	−	59.4946i	1.29551	−	2.24388i
$704$	4.91421	−	8.51167i	0.185211	−	0.320796i
$705$	9.82843	+	17.0233i	0.370160	+	0.641136i
$706$	−32.1421			−1.20969
$707$	7.94365	+	10.2437i	0.298752	+	0.385255i
$708$	−33.1421			−1.24556
$709$	−12.8848	−	22.3171i	−0.483898	−	0.838136i	0.515931	−	0.856630i	$-0.327446\pi$
$709$	−12.8848	−	22.3171i	−0.483898	−	0.838136i	−0.999829	+	0.0184943i	$0.994113\pi$
$710$	10.0711	−	17.4436i	0.377960	−	0.654647i
$711$	−6.65685	+	11.5300i	−0.249652	+	0.432409i
$712$	−31.2132	−	54.0629i	−1.16976	−	2.02609i
$713$	−39.5980			−1.48296
$714$	17.2782	+	22.2810i	0.646619	+	0.833847i
$715$	1.65685			0.0619628
$716$	−34.1274	−	59.1104i	−1.27540	−	2.20906i
$717$	3.24264	−	5.61642i	0.121099	−	0.209749i
$718$	−9.65685	+	16.7262i	−0.360391	+	0.624215i
$719$	−5.60051	−	9.70036i	−0.208864	−	0.361762i	0.742493	−	0.669854i	$-0.233643\pi$
$719$	−5.60051	−	9.70036i	−0.208864	−	0.361762i	−0.951357	+	0.308091i	$0.900310\pi$
$720$	−6.00000			−0.223607
$721$	−32.7279	+	4.47871i	−1.21885	+	0.166796i
$722$	−80.7696			−3.00593
$723$	−3.65685	−	6.33386i	−0.136000	−	0.235559i
$724$	22.3137	−	38.6485i	0.829282	−	1.43636i
$725$	1.62132	−	2.80821i	0.0602143	−	0.104294i
$726$	1.20711	+	2.09077i	0.0447999	+	0.0775958i
$727$	46.0833			1.70913			0.854567	−	0.519342i	$-0.173823\pi$
$727$	46.0833			1.70913			0.854567	+	0.519342i	$0.173823\pi$
$728$	3.65685	−	8.95743i	0.135532	−	0.331984i
$729$	1.00000			0.0370370
$730$	−0.828427	−	1.43488i	−0.0306615	−	0.0531072i
$731$	−6.08579	+	10.5409i	−0.225091	+	0.389869i
$732$	7.65685	−	13.2621i	0.283005	−	0.490180i
$733$	−4.82843	−	8.36308i	−0.178342	−	0.308897i	0.762971	−	0.646433i	$-0.223740\pi$
$733$	−4.82843	−	8.36308i	−0.178342	−	0.308897i	−0.941313	+	0.337536i	$0.890407\pi$
$734$	10.0000			0.369107
$735$	10.0000	+	9.79796i	0.368856	+	0.361403i
$736$	−11.1005			−0.409170
$737$	1.58579	+	2.74666i	0.0584132	+	0.101175i
$738$	−1.41421	+	2.44949i	−0.0520579	+	0.0901670i
$739$	19.8284	−	34.3438i	0.729400	−	1.26336i	−0.227736	−	0.973723i	$-0.573132\pi$
$739$	19.8284	−	34.3438i	0.729400	−	1.26336i	0.957137	−	0.289636i	$-0.0935342\pi$
$740$	−36.3137	−	62.8972i	−1.33492	−	2.31215i
$741$	−6.00000			−0.220416
$742$	17.3137	−	42.4098i	0.635606	−	1.55691i
$743$	33.7990			1.23996			0.619982	−	0.784616i	$-0.287140\pi$
$743$	33.7990			1.23996			0.619982	+	0.784616i	$0.287140\pi$
$744$	12.4853	+	21.6251i	0.457733	+	0.792816i
$745$	−22.2132	+	38.4744i	−0.813829	+	1.40959i
$746$	−2.00000	+	3.46410i	−0.0732252	+	0.126830i
$747$	1.41421	+	2.44949i	0.0517434	+	0.0896221i
$748$	−16.8995			−0.617907
$749$	−25.3137	+	3.46410i	−0.924943	+	0.126576i
$750$	−28.9706			−1.05786
$751$	14.6569	+	25.3864i	0.534836	+	0.926363i	0.999171	+	0.0407039i	$0.0129600\pi$
$751$	14.6569	+	25.3864i	0.534836	+	0.926363i	−0.464335	+	0.885660i	$0.653707\pi$
$752$	−14.7426	+	25.5350i	−0.537609	+	0.931166i
$753$	1.25736	−	2.17781i	0.0458207	−	0.0793638i
$754$	−3.24264	−	5.61642i	−0.118090	−	0.204538i
$755$	37.7990			1.37565
$756$	6.20711	+	8.00436i	0.225750	+	0.291116i
$757$	−7.68629			−0.279363			−0.139682	−	0.990196i	$-0.544608\pi$
$757$	−7.68629			−0.279363			−0.139682	+	0.990196i	$0.544608\pi$
$758$	22.7279	+	39.3659i	0.825515	+	1.42983i
$759$	3.50000	−	6.06218i	0.127042	−	0.220043i
$760$	−31.9706	+	55.3746i	−1.15969	+	2.00865i
$761$	0.100505	+	0.174080i	0.00364331	+	0.00631039i	0.867841	−	0.496841i	$-0.165507\pi$
$761$	0.100505	+	0.174080i	0.00364331	+	0.00631039i	−0.864198	+	0.503152i	$0.832174\pi$
$762$	38.7990			1.40554
$763$	−11.0711	−	14.2767i	−0.400800	−	0.516850i
$764$	−82.9117			−2.99964
$765$	−4.41421	−	7.64564i	−0.159596	−	0.276429i
$766$	2.79289	−	4.83743i	0.100911	−	0.174784i
$767$	−3.58579	+	6.21076i	−0.129475	+	0.224258i
$768$	14.9853	+	25.9553i	0.540735	+	0.936580i
$769$	33.7990			1.21882			0.609411	−	0.792854i	$-0.291406\pi$
$769$	33.7990			1.21882			0.609411	+	0.792854i	$0.291406\pi$
$770$	−12.6569	+	1.73205i	−0.456121	+	0.0624188i

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(1.00000 + 1.73205i) q^{5} -2.41421 q^{6} +(1.00000 - 2.44949i) q^{7} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(1.00000 + 1.73205i) q^{5} -2.41421 q^{6} +(1.00000 - 2.44949i) q^{7} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.41421 + 4.18154i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.91421 - 3.31552i) q^{12} -0.828427 q^{13} +(6.32843 - 0.866025i) q^{14} -2.00000 q^{15} +(-1.50000 - 2.59808i) q^{16} +(2.20711 - 3.82282i) q^{17} +(1.20711 - 2.09077i) q^{18} +(-3.62132 - 6.27231i) q^{19} -7.65685 q^{20} +(1.62132 + 2.09077i) q^{21} -2.41421 q^{22} +(3.50000 + 6.06218i) q^{23} +(2.20711 - 3.82282i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(6.20711 + 8.00436i) q^{28} +3.24264 q^{29} +(-2.41421 - 4.18154i) q^{30} +(-2.82843 + 4.89898i) q^{31} +(-0.792893 + 1.37333i) q^{32} +(-0.500000 - 0.866025i) q^{33} +10.6569 q^{34} +(5.24264 - 0.717439i) q^{35} +3.82843 q^{36} +(4.74264 + 8.21449i) q^{37} +(8.74264 - 15.1427i) q^{38} +(0.414214 - 0.717439i) q^{39} +(-4.41421 - 7.64564i) q^{40} -1.17157 q^{41} +(-2.41421 + 5.91359i) q^{42} -2.75736 q^{43} +(-1.91421 - 3.31552i) q^{44} +(1.00000 - 1.73205i) q^{45} +(-8.44975 + 14.6354i) q^{46} +(-4.91421 - 8.51167i) q^{47} +3.00000 q^{48} +(-5.00000 - 4.89898i) q^{49} +2.41421 q^{50} +(2.20711 + 3.82282i) q^{51} +(1.58579 - 2.74666i) q^{52} +(3.58579 - 6.21076i) q^{53} +(1.20711 + 2.09077i) q^{54} -2.00000 q^{55} +(-4.41421 + 10.8126i) q^{56} +7.24264 q^{57} +(3.91421 + 6.77962i) q^{58} +(4.32843 - 7.49706i) q^{59} +(3.82843 - 6.63103i) q^{60} +(2.00000 + 3.46410i) q^{61} -13.6569 q^{62} +(-2.62132 + 0.358719i) q^{63} -9.82843 q^{64} +(-0.828427 - 1.43488i) q^{65} +(1.20711 - 2.09077i) q^{66} +(1.58579 - 2.74666i) q^{67} +(8.44975 + 14.6354i) q^{68} -7.00000 q^{69} +(7.82843 + 10.0951i) q^{70} -4.17157 q^{71} +(2.20711 + 3.82282i) q^{72} +(-0.171573 + 0.297173i) q^{73} +(-11.4497 + 19.8315i) q^{74} +(0.500000 + 0.866025i) q^{75} +27.7279 q^{76} +(1.62132 + 2.09077i) q^{77} +2.00000 q^{78} +(-6.65685 - 11.5300i) q^{79} +(3.00000 - 5.19615i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.41421 - 2.44949i) q^{82} -2.82843 q^{83} +(-10.0355 + 1.37333i) q^{84} +8.82843 q^{85} +(-3.32843 - 5.76500i) q^{86} +(-1.62132 + 2.80821i) q^{87} +(2.20711 - 3.82282i) q^{88} +(7.07107 + 12.2474i) q^{89} +4.82843 q^{90} +(-0.828427 + 2.02922i) q^{91} -26.7990 q^{92} +(-2.82843 - 4.89898i) q^{93} +(11.8640 - 20.5490i) q^{94} +(7.24264 - 12.5446i) q^{95} +(-0.792893 - 1.37333i) q^{96} -11.4853 q^{97} +(4.20711 - 16.3674i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 12 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 12 q^{8} - 2 q^{9} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 8 q^{13} + 14 q^{14} - 8 q^{15} - 6 q^{16} + 6 q^{17} + 2 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} - 4 q^{22} + 14 q^{23} + 6 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{27} + 22 q^{28} - 4 q^{29} - 4 q^{30} - 6 q^{32} - 2 q^{33} + 20 q^{34} + 4 q^{35} + 4 q^{36} + 2 q^{37} + 18 q^{38} - 4 q^{39} - 12 q^{40} - 16 q^{41} - 4 q^{42} - 28 q^{43} - 2 q^{44} + 4 q^{45} - 14 q^{46} - 14 q^{47} + 12 q^{48} - 20 q^{49} + 4 q^{50} + 6 q^{51} + 12 q^{52} + 20 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 12 q^{57} + 10 q^{58} + 6 q^{59} + 4 q^{60} + 8 q^{61} - 32 q^{62} - 2 q^{63} - 28 q^{64} + 8 q^{65} + 2 q^{66} + 12 q^{67} + 14 q^{68} - 28 q^{69} + 20 q^{70} - 28 q^{71} + 6 q^{72} - 12 q^{73} - 26 q^{74} + 2 q^{75} + 60 q^{76} - 2 q^{77} + 8 q^{78} - 4 q^{79} + 12 q^{80} - 2 q^{81} - 26 q^{84} + 24 q^{85} - 2 q^{86} + 2 q^{87} + 6 q^{88} + 8 q^{90} + 8 q^{91} - 28 q^{92} + 22 q^{94} + 12 q^{95} - 6 q^{96} - 12 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 12 * q^8 - 2 * q^9 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 8 * q^13 + 14 * q^14 - 8 * q^15 - 6 * q^16 + 6 * q^17 + 2 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 - 4 * q^22 + 14 * q^23 + 6 * q^24 + 2 * q^25 - 4 * q^26 + 4 * q^27 + 22 * q^28 - 4 * q^29 - 4 * q^30 - 6 * q^32 - 2 * q^33 + 20 * q^34 + 4 * q^35 + 4 * q^36 + 2 * q^37 + 18 * q^38 - 4 * q^39 - 12 * q^40 - 16 * q^41 - 4 * q^42 - 28 * q^43 - 2 * q^44 + 4 * q^45 - 14 * q^46 - 14 * q^47 + 12 * q^48 - 20 * q^49 + 4 * q^50 + 6 * q^51 + 12 * q^52 + 20 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 12 * q^57 + 10 * q^58 + 6 * q^59 + 4 * q^60 + 8 * q^61 - 32 * q^62 - 2 * q^63 - 28 * q^64 + 8 * q^65 + 2 * q^66 + 12 * q^67 + 14 * q^68 - 28 * q^69 + 20 * q^70 - 28 * q^71 + 6 * q^72 - 12 * q^73 - 26 * q^74 + 2 * q^75 + 60 * q^76 - 2 * q^77 + 8 * q^78 - 4 * q^79 + 12 * q^80 - 2 * q^81 - 26 * q^84 + 24 * q^85 - 2 * q^86 + 2 * q^87 + 6 * q^88 + 8 * q^90 + 8 * q^91 - 28 * q^92 + 22 * q^94 + 12 * q^95 - 6 * q^96 - 12 * q^97 + 14 * q^98 + 4 * q^99

Introduction

L-functions

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