LMFDB - Embedded newform 762.2.e.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [762,2,Mod(19,762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(762, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("762.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 762 = 2 \cdot 3 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	762.e (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:	$6.08460063402$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
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			361.1
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	762.361
Dual form			762.2.e.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} -2.30278 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} -2.30278 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -2.30278 q^{10} +(2.65139 - 4.59234i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.15139 + 1.99426i) q^{15} +1.00000 q^{16} +(-3.45416 + 5.98279i) q^{17} +(-0.500000 + 0.866025i) q^{18} -4.90833 q^{19} -2.30278 q^{20} +(-0.500000 + 0.866025i) q^{21} +(2.65139 - 4.59234i) q^{22} +(-2.80278 - 4.85455i) q^{23} +(-0.500000 - 0.866025i) q^{24} +0.302776 q^{25} +(-1.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-0.151388 + 0.262211i) q^{29} +(1.15139 + 1.99426i) q^{30} +(-3.95416 - 6.84881i) q^{31} +1.00000 q^{32} -5.30278 q^{33} +(-3.45416 + 5.98279i) q^{34} +(1.15139 + 1.99426i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.65139 - 4.59234i) q^{37} -4.90833 q^{38} +(-1.50000 + 2.59808i) q^{39} -2.30278 q^{40} +(0.802776 - 1.39045i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(6.10555 - 10.5751i) q^{43} +(2.65139 - 4.59234i) q^{44} +(1.15139 - 1.99426i) q^{45} +(-2.80278 - 4.85455i) q^{46} -0.394449 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +0.302776 q^{50} +6.90833 q^{51} +(-1.50000 - 2.59808i) q^{52} +(-4.90833 + 8.50147i) q^{53} +1.00000 q^{54} +(-6.10555 + 10.5751i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(2.45416 + 4.25074i) q^{57} +(-0.151388 + 0.262211i) q^{58} +(-6.15139 + 10.6545i) q^{59} +(1.15139 + 1.99426i) q^{60} +5.30278 q^{61} +(-3.95416 - 6.84881i) q^{62} +1.00000 q^{63} +1.00000 q^{64} +(3.45416 + 5.98279i) q^{65} -5.30278 q^{66} +(2.50000 + 4.33013i) q^{67} +(-3.45416 + 5.98279i) q^{68} +(-2.80278 + 4.85455i) q^{69} +(1.15139 + 1.99426i) q^{70} +(5.80278 + 10.0507i) q^{71} +(-0.500000 + 0.866025i) q^{72} +0.697224 q^{73} +(2.65139 - 4.59234i) q^{74} +(-0.151388 - 0.262211i) q^{75} -4.90833 q^{76} -5.30278 q^{77} +(-1.50000 + 2.59808i) q^{78} +(2.84861 + 4.93394i) q^{79} -2.30278 q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.802776 - 1.39045i) q^{82} +(8.21110 - 14.2220i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(7.95416 - 13.7770i) q^{85} +(6.10555 - 10.5751i) q^{86} +0.302776 q^{87} +(2.65139 - 4.59234i) q^{88} +1.51388 q^{89} +(1.15139 - 1.99426i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(-2.80278 - 4.85455i) q^{92} +(-3.95416 + 6.84881i) q^{93} -0.394449 q^{94} +11.3028 q^{95} +(-0.500000 - 0.866025i) q^{96} +(4.00000 + 6.92820i) q^{97} +(3.00000 - 5.19615i) q^{98} +(2.65139 + 4.59234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - 2 q^{10} + 7 q^{11} - 2 q^{12} - 6 q^{13} - 2 q^{14} + q^{15} + 4 q^{16} - 3 q^{17} - 2 q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{21} + 7 q^{22} - 4 q^{23} - 2 q^{24} - 6 q^{25} - 6 q^{26} + 4 q^{27} - 2 q^{28} + 3 q^{29} + q^{30} - 5 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + q^{35} - 2 q^{36} + 7 q^{37} + 2 q^{38} - 6 q^{39} - 2 q^{40} - 4 q^{41} - 2 q^{42} + 10 q^{43} + 7 q^{44} + q^{45} - 4 q^{46} - 16 q^{47} - 2 q^{48} + 12 q^{49} - 6 q^{50} + 6 q^{51} - 6 q^{52} + 2 q^{53} + 4 q^{54} - 10 q^{55} - 2 q^{56} - q^{57} + 3 q^{58} - 21 q^{59} + q^{60} + 14 q^{61} - 5 q^{62} + 4 q^{63} + 4 q^{64} + 3 q^{65} - 14 q^{66} + 10 q^{67} - 3 q^{68} - 4 q^{69} + q^{70} + 16 q^{71} - 2 q^{72} + 10 q^{73} + 7 q^{74} + 3 q^{75} + 2 q^{76} - 14 q^{77} - 6 q^{78} + 15 q^{79} - 2 q^{80} - 2 q^{81} - 4 q^{82} + 4 q^{83} - 2 q^{84} + 21 q^{85} + 10 q^{86} - 6 q^{87} + 7 q^{88} - 30 q^{89} + q^{90} - 6 q^{91} - 4 q^{92} - 5 q^{93} - 16 q^{94} + 38 q^{95} - 2 q^{96} + 16 q^{97} + 12 q^{98} + 7 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 - 2 * q^10 + 7 * q^11 - 2 * q^12 - 6 * q^13 - 2 * q^14 + q^15 + 4 * q^16 - 3 * q^17 - 2 * q^18 + 2 * q^19 - 2 * q^20 - 2 * q^21 + 7 * q^22 - 4 * q^23 - 2 * q^24 - 6 * q^25 - 6 * q^26 + 4 * q^27 - 2 * q^28 + 3 * q^29 + q^30 - 5 * q^31 + 4 * q^32 - 14 * q^33 - 3 * q^34 + q^35 - 2 * q^36 + 7 * q^37 + 2 * q^38 - 6 * q^39 - 2 * q^40 - 4 * q^41 - 2 * q^42 + 10 * q^43 + 7 * q^44 + q^45 - 4 * q^46 - 16 * q^47 - 2 * q^48 + 12 * q^49 - 6 * q^50 + 6 * q^51 - 6 * q^52 + 2 * q^53 + 4 * q^54 - 10 * q^55 - 2 * q^56 - q^57 + 3 * q^58 - 21 * q^59 + q^60 + 14 * q^61 - 5 * q^62 + 4 * q^63 + 4 * q^64 + 3 * q^65 - 14 * q^66 + 10 * q^67 - 3 * q^68 - 4 * q^69 + q^70 + 16 * q^71 - 2 * q^72 + 10 * q^73 + 7 * q^74 + 3 * q^75 + 2 * q^76 - 14 * q^77 - 6 * q^78 + 15 * q^79 - 2 * q^80 - 2 * q^81 - 4 * q^82 + 4 * q^83 - 2 * q^84 + 21 * q^85 + 10 * q^86 - 6 * q^87 + 7 * q^88 - 30 * q^89 + q^90 - 6 * q^91 - 4 * q^92 - 5 * q^93 - 16 * q^94 + 38 * q^95 - 2 * q^96 + 16 * q^97 + 12 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/762\mathbb{Z}\right)^\times$.

$n$	$509$	$511$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	−2.30278			−1.02983			−0.514916	−	0.857240i	$-0.672177\pi$
$5$	−2.30278			−1.02983			−0.514916	+	0.857240i	$0.672177\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.30278			−0.728202
$11$	2.65139	−	4.59234i	0.799424	−	1.38464i	−0.120569	−	0.992705i	$-0.538472\pi$
$11$	2.65139	−	4.59234i	0.799424	−	1.38464i	0.919992	−	0.391937i	$-0.128195\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	0.579510	−	0.814965i	$-0.303244\pi$
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	−0.995535	+	0.0943882i	$0.969911\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	1.15139	+	1.99426i	0.297287	+	0.514916i
$16$	1.00000			0.250000
$17$	−3.45416	+	5.98279i	−0.837758	+	1.45104i	0.0540075	+	0.998541i	$0.482800\pi$
$17$	−3.45416	+	5.98279i	−0.837758	+	1.45104i	−0.891765	+	0.452498i	$0.850533\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−4.90833			−1.12605			−0.563024	−	0.826441i	$-0.690362\pi$
$19$	−4.90833			−1.12605			−0.563024	+	0.826441i	$0.690362\pi$
$20$	−2.30278			−0.514916
$21$	−0.500000	+	0.866025i	−0.109109	+	0.188982i
$22$	2.65139	−	4.59234i	0.565278	−	0.979090i
$23$	−2.80278	−	4.85455i	−0.584419	−	1.01224i	−0.994948	−	0.100396i	$-0.967989\pi$
$23$	−2.80278	−	4.85455i	−0.584419	−	1.01224i	0.410528	−	0.911848i	$-0.365344\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	0.302776			0.0605551
$26$	−1.50000	−	2.59808i	−0.294174	−	0.509525i
$27$	1.00000			0.192450
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	−0.151388	+	0.262211i	−0.0281120	+	0.0486914i	−0.879739	−	0.475457i	$-0.842283\pi$
$29$	−0.151388	+	0.262211i	−0.0281120	+	0.0486914i	0.851627	+	0.524148i	$0.175616\pi$
$30$	1.15139	+	1.99426i	0.210214	+	0.364101i
$31$	−3.95416	−	6.84881i	−0.710189	−	1.23008i	−0.964786	−	0.263036i	$-0.915276\pi$
$31$	−3.95416	−	6.84881i	−0.710189	−	1.23008i	0.254597	−	0.967047i	$-0.418057\pi$
$32$	1.00000			0.176777
$33$	−5.30278			−0.923095
$34$	−3.45416	+	5.98279i	−0.592384	+	1.02604i
$35$	1.15139	+	1.99426i	0.194620	+	0.337092i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.65139	−	4.59234i	0.435885	−	0.754976i	−0.561482	−	0.827489i	$-0.689769\pi$
$37$	2.65139	−	4.59234i	0.435885	−	0.754976i	0.997367	+	0.0725132i	$0.0231019\pi$
$38$	−4.90833			−0.796236
$39$	−1.50000	+	2.59808i	−0.240192	+	0.416025i
$40$	−2.30278			−0.364101
$41$	0.802776	−	1.39045i	0.125372	−	0.217152i	−0.796506	−	0.604631i	$-0.793321\pi$
$41$	0.802776	−	1.39045i	0.125372	−	0.217152i	0.921878	+	0.387479i	$0.126654\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	6.10555	−	10.5751i	0.931088	−	1.61269i	0.149622	−	0.988743i	$-0.452194\pi$
$43$	6.10555	−	10.5751i	0.931088	−	1.61269i	0.781466	−	0.623948i	$-0.214472\pi$
$44$	2.65139	−	4.59234i	0.399712	−	0.692321i
$45$	1.15139	−	1.99426i	0.171639	−	0.297287i
$46$	−2.80278	−	4.85455i	−0.413247	−	0.715764i
$47$	−0.394449			−0.0575363			−0.0287681	−	0.999586i	$-0.509158\pi$
$47$	−0.394449			−0.0575363			−0.0287681	+	0.999586i	$0.509158\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	0.302776			0.0428189
$51$	6.90833			0.967359
$52$	−1.50000	−	2.59808i	−0.208013	−	0.360288i
$53$	−4.90833	+	8.50147i	−0.674211	+	1.16777i	0.302488	+	0.953153i	$0.402183\pi$
$53$	−4.90833	+	8.50147i	−0.674211	+	1.16777i	−0.976699	+	0.214614i	$0.931151\pi$
$54$	1.00000			0.136083
$55$	−6.10555	+	10.5751i	−0.823272	+	1.42595i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	2.45416	+	4.25074i	0.325062	+	0.563024i
$58$	−0.151388	+	0.262211i	−0.0198782	+	0.0344300i
$59$	−6.15139	+	10.6545i	−0.800842	+	1.38710i	0.118220	+	0.992987i	$0.462281\pi$
$59$	−6.15139	+	10.6545i	−0.800842	+	1.38710i	−0.919062	+	0.394112i	$0.871052\pi$
$60$	1.15139	+	1.99426i	0.148644	+	0.257458i
$61$	5.30278			0.678951			0.339475	−	0.940615i	$-0.389750\pi$
$61$	5.30278			0.678951			0.339475	+	0.940615i	$0.389750\pi$
$62$	−3.95416	−	6.84881i	−0.502179	−	0.869800i
$63$	1.00000			0.125988
$64$	1.00000			0.125000
$65$	3.45416	+	5.98279i	0.428436	+	0.742073i
$66$	−5.30278			−0.652727
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	−3.45416	+	5.98279i	−0.418879	+	0.725519i
$69$	−2.80278	+	4.85455i	−0.337415	+	0.584419i
$70$	1.15139	+	1.99426i	0.137617	+	0.238360i
$71$	5.80278	+	10.0507i	0.688663	+	1.19280i	0.972271	+	0.233859i	$0.0751353\pi$
$71$	5.80278	+	10.0507i	0.688663	+	1.19280i	−0.283608	+	0.958940i	$0.591531\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	0.697224			0.0816039			0.0408020	−	0.999167i	$-0.487009\pi$
$73$	0.697224			0.0816039			0.0408020	+	0.999167i	$0.487009\pi$
$74$	2.65139	−	4.59234i	0.308218	−	0.533848i
$75$	−0.151388	−	0.262211i	−0.0174808	−	0.0302776i
$76$	−4.90833			−0.563024
$77$	−5.30278			−0.604307
$78$	−1.50000	+	2.59808i	−0.169842	+	0.294174i
$79$	2.84861	+	4.93394i	0.320494	+	0.555112i	0.980590	−	0.196069i	$-0.0628178\pi$
$79$	2.84861	+	4.93394i	0.320494	+	0.555112i	−0.660096	+	0.751181i	$0.729484\pi$
$80$	−2.30278			−0.257458
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.802776	−	1.39045i	0.0886517	−	0.153549i
$83$	8.21110	−	14.2220i	0.901286	−	1.56107i	0.0754586	−	0.997149i	$-0.475958\pi$
$83$	8.21110	−	14.2220i	0.901286	−	1.56107i	0.825827	−	0.563924i	$-0.190709\pi$
$84$	−0.500000	+	0.866025i	−0.0545545	+	0.0944911i
$85$	7.95416	−	13.7770i	0.862750	−	1.49433i
$86$	6.10555	−	10.5751i	0.658379	−	1.14035i
$87$	0.302776			0.0324610
$88$	2.65139	−	4.59234i	0.282639	−	0.489545i
$89$	1.51388			0.160471			0.0802354	−	0.996776i	$-0.474433\pi$
$89$	1.51388			0.160471			0.0802354	+	0.996776i	$0.474433\pi$
$90$	1.15139	−	1.99426i	0.121367	−	0.210214i
$91$	−1.50000	+	2.59808i	−0.157243	+	0.272352i
$92$	−2.80278	−	4.85455i	−0.292210	−	0.506122i
$93$	−3.95416	+	6.84881i	−0.410028	+	0.710189i
$94$	−0.394449			−0.0406843
$95$	11.3028			1.15964
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	0.994453	−	0.105180i	$-0.0335417\pi$
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	−0.588315	+	0.808632i	$0.700208\pi$
$98$	3.00000	−	5.19615i	0.303046	−	0.524891i
$99$	2.65139	+	4.59234i	0.266475	+	0.461547i
$100$	0.302776			0.0302776
$101$	−0.454163	−	0.786634i	−0.0451910	−	0.0782730i	0.842545	−	0.538626i	$-0.181056\pi$
$101$	−0.454163	−	0.786634i	−0.0451910	−	0.0782730i	−0.887736	+	0.460353i	$0.847723\pi$
$102$	6.90833			0.684026
$103$	0.651388	+	1.12824i	0.0641831	+	0.111168i	0.896331	−	0.443385i	$-0.146222\pi$
$103$	0.651388	+	1.12824i	0.0641831	+	0.111168i	−0.832148	+	0.554553i	$0.812889\pi$
$104$	−1.50000	−	2.59808i	−0.147087	−	0.254762i
$105$	1.15139	−	1.99426i	0.112364	−	0.194620i
$106$	−4.90833	+	8.50147i	−0.476739	+	0.825736i
$107$	7.60555			0.735256			0.367628	−	0.929973i	$-0.380170\pi$
$107$	7.60555			0.735256			0.367628	+	0.929973i	$0.380170\pi$
$108$	1.00000			0.0962250
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−6.10555	+	10.5751i	−0.582141	+	1.00830i
$111$	−5.30278			−0.503317
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−0.651388	−	1.12824i	−0.0612774	−	0.106136i	0.833759	−	0.552128i	$-0.186184\pi$
$113$	−0.651388	−	1.12824i	−0.0612774	−	0.106136i	−0.895037	+	0.445993i	$0.852851\pi$
$114$	2.45416	+	4.25074i	0.229853	+	0.398118i
$115$	6.45416	+	11.1789i	0.601854	+	1.04244i
$116$	−0.151388	+	0.262211i	−0.0140560	+	0.0243457i
$117$	3.00000			0.277350
$118$	−6.15139	+	10.6545i	−0.566281	+	0.980828i
$119$	6.90833			0.633285
$120$	1.15139	+	1.99426i	0.105107	+	0.182050i
$121$	−8.55971	−	14.8259i	−0.778156	−	1.34781i
$122$	5.30278			0.480091
$123$	−1.60555			−0.144768
$124$	−3.95416	−	6.84881i	−0.355094	−	0.615041i
$125$	10.8167			0.967471
$126$	1.00000			0.0890871
$127$	−3.89445	−	10.5751i	−0.345576	−	0.938391i
$127$	−3.89445	−	10.5751i	−0.345576	−	0.938391i
$128$	1.00000			0.0883883
$129$	−12.2111			−1.07513
$130$	3.45416	+	5.98279i	0.302950	+	0.524725i
$131$	16.4222			1.43481			0.717407	−	0.696654i	$-0.245329\pi$
$131$	16.4222			1.43481			0.717407	+	0.696654i	$0.245329\pi$
$132$	−5.30278			−0.461547
$133$	2.45416	+	4.25074i	0.212803	+	0.368586i
$134$	2.50000	+	4.33013i	0.215967	+	0.374066i
$135$	−2.30278			−0.198191
$136$	−3.45416	+	5.98279i	−0.296192	+	0.513020i
$137$	−20.5139			−1.75262			−0.876309	−	0.481749i	$-0.840002\pi$
$137$	−20.5139			−1.75262			−0.876309	+	0.481749i	$0.840002\pi$
$138$	−2.80278	+	4.85455i	−0.238588	+	0.413247i
$139$	5.30278	+	9.18468i	0.449776	+	0.779034i	0.998371	−	0.0570537i	$-0.0181706\pi$
$139$	5.30278	+	9.18468i	0.449776	+	0.779034i	−0.548596	+	0.836088i	$0.684837\pi$
$140$	1.15139	+	1.99426i	0.0973100	+	0.168546i
$141$	0.197224	+	0.341603i	0.0166093	+	0.0287681i
$142$	5.80278	+	10.0507i	0.486958	+	0.843436i
$143$	−15.9083			−1.33032
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.348612	−	0.603814i	0.0289507	−	0.0501440i
$146$	0.697224			0.0577027
$147$	−6.00000			−0.494872
$148$	2.65139	−	4.59234i	0.217943	−	0.377488i
$149$	2.55971	−	4.43356i	0.209700	−	0.363211i	−0.741920	−	0.670488i	$-0.766085\pi$
$149$	2.55971	−	4.43356i	0.209700	−	0.363211i	0.951620	+	0.307277i	$0.0994179\pi$
$150$	−0.151388	−	0.262211i	−0.0123608	−	0.0214095i
$151$	6.19722	+	10.7339i	0.504323	+	0.873513i	0.999988	+	0.00499895i	$0.00159122\pi$
$151$	6.19722	+	10.7339i	0.504323	+	0.873513i	−0.495665	+	0.868514i	$0.665075\pi$
$152$	−4.90833			−0.398118
$153$	−3.45416	−	5.98279i	−0.279253	−	0.483680i
$154$	−5.30278			−0.427310
$155$	9.10555	+	15.7713i	0.731375	+	1.26678i
$156$	−1.50000	+	2.59808i	−0.120096	+	0.208013i
$157$	−10.8625	−	18.8144i	−0.866921	−	1.50155i	−0.865127	−	0.501553i	$-0.832762\pi$
$157$	−10.8625	−	18.8144i	−0.866921	−	1.50155i	−0.00179420	−	0.999998i	$-0.500571\pi$
$158$	2.84861	+	4.93394i	0.226623	+	0.392523i
$159$	9.81665			0.778511
$160$	−2.30278			−0.182050
$161$	−2.80278	+	4.85455i	−0.220890	+	0.382592i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	11.7111	−	20.2842i	0.917284	−	1.58878i	0.113762	−	0.993508i	$-0.463710\pi$
$163$	11.7111	−	20.2842i	0.917284	−	1.58878i	0.803522	−	0.595275i	$-0.202957\pi$
$164$	0.802776	−	1.39045i	0.0626862	−	0.108576i
$165$	12.2111			0.950633
$166$	8.21110	−	14.2220i	0.637305	−	1.10384i
$167$	−9.30278			−0.719870			−0.359935	−	0.932977i	$-0.617201\pi$
$167$	−9.30278			−0.719870			−0.359935	+	0.932977i	$0.617201\pi$
$168$	−0.500000	+	0.866025i	−0.0385758	+	0.0668153i
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$	7.95416	−	13.7770i	0.610056	−	1.05665i
$171$	2.45416	−	4.25074i	0.187675	−	0.325062i
$172$	6.10555	−	10.5751i	0.465544	−	0.806346i
$173$	3.05971	+	5.29958i	0.232626	+	0.402920i	0.958580	−	0.284823i	$-0.0919349\pi$
$173$	3.05971	+	5.29958i	0.232626	+	0.402920i	−0.725954	+	0.687743i	$0.758602\pi$
$174$	0.302776			0.0229534
$175$	−0.151388	−	0.262211i	−0.0114438	−	0.0198213i
$176$	2.65139	−	4.59234i	0.199856	−	0.346161i
$177$	12.3028			0.924733
$178$	1.51388			0.113470
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	0.995009	−	0.0997838i	$-0.0318151\pi$
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	−0.583920	+	0.811811i	$0.698482\pi$
$180$	1.15139	−	1.99426i	0.0858194	−	0.148644i
$181$	−2.51388			−0.186855			−0.0934275	−	0.995626i	$-0.529782\pi$
$181$	−2.51388			−0.186855			−0.0934275	+	0.995626i	$0.529782\pi$
$182$	−1.50000	+	2.59808i	−0.111187	+	0.192582i
$183$	−2.65139	−	4.59234i	−0.195996	−	0.339475i
$184$	−2.80278	−	4.85455i	−0.206623	−	0.357882i
$185$	−6.10555	+	10.5751i	−0.448889	+	0.777499i
$186$	−3.95416	+	6.84881i	−0.289933	+	0.502179i
$187$	18.3167	+	31.7254i	1.33945	+	2.31999i
$188$	−0.394449			−0.0287681
$189$	−0.500000	−	0.866025i	−0.0363696	−	0.0629941i
$190$	11.3028			0.819990
$191$	−10.2111			−0.738849			−0.369425	−	0.929261i	$-0.620445\pi$
$191$	−10.2111			−0.738849			−0.369425	+	0.929261i	$0.620445\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−4.60555			−0.331515			−0.165757	−	0.986167i	$-0.553007\pi$
$193$	−4.60555			−0.331515			−0.165757	+	0.986167i	$0.553007\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$	3.45416	−	5.98279i	0.247358	−	0.428436i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−7.60555	−	13.1732i	−0.541873	−	0.938552i	−0.998797	−	0.0490457i	$-0.984382\pi$
$197$	−7.60555	−	13.1732i	−0.541873	−	0.938552i	0.456923	−	0.889506i	$-0.348951\pi$
$198$	2.65139	+	4.59234i	0.188426	+	0.326363i
$199$	10.8028	−	18.7110i	0.765788	−	1.32638i	−0.174040	−	0.984739i	$-0.555682\pi$
$199$	10.8028	−	18.7110i	0.765788	−	1.32638i	0.939829	−	0.341646i	$-0.110984\pi$
$200$	0.302776			0.0214095
$201$	2.50000	−	4.33013i	0.176336	−	0.305424i
$202$	−0.454163	−	0.786634i	−0.0319548	−	0.0553474i
$203$	0.302776			0.0212507
$204$	6.90833			0.483680
$205$	−1.84861	+	3.20189i	−0.129113	+	0.223630i
$206$	0.651388	+	1.12824i	0.0453843	+	0.0786080i
$207$	5.60555			0.389613
$208$	−1.50000	−	2.59808i	−0.104006	−	0.180144i
$209$	−13.0139	+	22.5407i	−0.900189	+	1.55917i
$210$	1.15139	−	1.99426i	0.0794533	−	0.137617i
$211$	−9.71110	+	16.8201i	−0.668540	+	1.15795i	0.309773	+	0.950811i	$0.399747\pi$
$211$	−9.71110	+	16.8201i	−0.668540	+	1.15795i	−0.978313	+	0.207134i	$0.933586\pi$
$212$	−4.90833	+	8.50147i	−0.337105	+	0.583883i
$213$	5.80278	−	10.0507i	0.397600	−	0.688663i
$214$	7.60555			0.519905
$215$	−14.0597	+	24.3521i	−0.958865	+	1.66080i
$216$	1.00000			0.0680414
$217$	−3.95416	+	6.84881i	−0.268426	+	0.464928i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−0.348612	−	0.603814i	−0.0235570	−	0.0408020i
$220$	−6.10555	+	10.5751i	−0.411636	+	0.712975i
$221$	20.7250			1.39411
$222$	−5.30278			−0.355899
$223$	−11.2111	−	19.4182i	−0.750751	−	1.30034i	−0.947459	−	0.319877i	$-0.896359\pi$
$223$	−11.2111	−	19.4182i	−0.750751	−	1.30034i	0.196708	−	0.980462i	$-0.436975\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−0.151388	+	0.262211i	−0.0100925	+	0.0174808i
$226$	−0.651388	−	1.12824i	−0.0433297	−	0.0750492i
$227$	−13.2111			−0.876852			−0.438426	−	0.898767i	$-0.644464\pi$
$227$	−13.2111			−0.876852			−0.438426	+	0.898767i	$0.644464\pi$
$228$	2.45416	+	4.25074i	0.162531	+	0.281512i
$229$	4.30278			0.284335			0.142168	−	0.989843i	$-0.454593\pi$
$229$	4.30278			0.284335			0.142168	+	0.989843i	$0.454593\pi$
$230$	6.45416	+	11.1789i	0.425575	+	0.737117i
$231$	2.65139	+	4.59234i	0.174449	+	0.302154i
$232$	−0.151388	+	0.262211i	−0.00993910	+	0.0172150i
$233$	0.605551	−	1.04885i	0.0396710	−	0.0687122i	−0.845508	−	0.533962i	$-0.820702\pi$
$233$	0.605551	−	1.04885i	0.0396710	−	0.0687122i	0.885179	+	0.465250i	$0.154036\pi$
$234$	3.00000			0.196116
$235$	0.908327			0.0592527
$236$	−6.15139	+	10.6545i	−0.400421	+	0.693550i
$237$	2.84861	−	4.93394i	0.185037	−	0.320494i
$238$	6.90833			0.447800
$239$	−9.90833	−	17.1617i	−0.640916	−	1.11010i	−0.985229	−	0.171245i	$-0.945221\pi$
$239$	−9.90833	−	17.1617i	−0.640916	−	1.11010i	0.344312	−	0.938855i	$-0.388112\pi$
$240$	1.15139	+	1.99426i	0.0743218	+	0.128729i
$241$	−5.19722	−	9.00186i	−0.334783	−	0.579861i	0.648660	−	0.761078i	$-0.275330\pi$
$241$	−5.19722	−	9.00186i	−0.334783	−	0.579861i	−0.983443	+	0.181217i	$0.941996\pi$
$242$	−8.55971	−	14.8259i	−0.550239	−	0.953042i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	5.30278			0.339475
$245$	−6.90833	+	11.9656i	−0.441357	+	0.764452i
$246$	−1.60555			−0.102366
$247$	7.36249	+	12.7522i	0.468464	+	0.811404i
$248$	−3.95416	−	6.84881i	−0.251090	−	0.434900i
$249$	−16.4222			−1.04071
$250$	10.8167			0.684105
$251$	5.40833	+	9.36750i	0.341371	+	0.591271i	0.984687	−	0.174329i	$-0.0557756\pi$
$251$	5.40833	+	9.36750i	0.341371	+	0.591271i	−0.643317	+	0.765600i	$0.722442\pi$
$252$	1.00000			0.0629941
$253$	−29.7250			−1.86879
$254$	−3.89445	−	10.5751i	−0.244359	−	0.663542i
$255$	−15.9083			−0.996218
$256$	1.00000			0.0625000
$257$	14.5139	+	25.1388i	0.905351	+	1.56811i	0.820446	+	0.571725i	$0.193725\pi$
$257$	14.5139	+	25.1388i	0.905351	+	1.56811i	0.0849053	+	0.996389i	$0.472941\pi$
$258$	−12.2111			−0.760230
$259$	−5.30278			−0.329498
$260$	3.45416	+	5.98279i	0.214218	+	0.371037i
$261$	−0.151388	−	0.262211i	−0.00937067	−	0.0162305i
$262$	16.4222			1.01457
$263$	2.74306	−	4.75112i	0.169144	−	0.292967i	−0.768975	−	0.639279i	$-0.779233\pi$
$263$	2.74306	−	4.75112i	0.169144	−	0.292967i	0.938119	+	0.346312i	$0.112566\pi$
$264$	−5.30278			−0.326363
$265$	11.3028	−	19.5770i	0.694324	−	1.20260i
$266$	2.45416	+	4.25074i	0.150474	+	0.260629i
$267$	−0.756939	−	1.31106i	−0.0463239	−	0.0802354i
$268$	2.50000	+	4.33013i	0.152712	+	0.264505i
$269$	−8.95416	−	15.5091i	−0.545945	−	0.945604i	−0.998547	−	0.0538917i	$-0.982837\pi$
$269$	−8.95416	−	15.5091i	−0.545945	−	0.945604i	0.452602	−	0.891713i	$-0.350496\pi$
$270$	−2.30278			−0.140142
$271$	10.4083	−	18.0278i	0.632261	−	1.09511i	−0.354828	−	0.934932i	$-0.615460\pi$
$271$	10.4083	−	18.0278i	0.632261	−	1.09511i	0.987088	−	0.160176i	$-0.0512062\pi$
$272$	−3.45416	+	5.98279i	−0.209439	+	0.362760i
$273$	3.00000			0.181568
$274$	−20.5139			−1.23929
$275$	0.802776	−	1.39045i	0.0484092	−	0.0838472i
$276$	−2.80278	+	4.85455i	−0.168707	+	0.292210i
$277$	−9.01388	−	15.6125i	−0.541591	−	0.938064i	−0.998813	−	0.0487110i	$-0.984489\pi$
$277$	−9.01388	−	15.6125i	−0.541591	−	0.938064i	0.457221	−	0.889353i	$-0.348845\pi$
$278$	5.30278	+	9.18468i	0.318039	+	0.550860i
$279$	7.90833			0.473459
$280$	1.15139	+	1.99426i	0.0688086	+	0.119180i
$281$	29.5416			1.76231			0.881153	−	0.472831i	$-0.156768\pi$
$281$	29.5416			1.76231			0.881153	+	0.472831i	$0.156768\pi$
$282$	0.197224	+	0.341603i	0.0117445	+	0.0203421i
$283$	−14.9680	+	25.9254i	−0.889758	+	1.54111i	−0.0495962	+	0.998769i	$0.515793\pi$
$283$	−14.9680	+	25.9254i	−0.889758	+	1.54111i	−0.840162	+	0.542336i	$0.817540\pi$
$284$	5.80278	+	10.0507i	0.344331	+	0.596399i
$285$	−5.65139	−	9.78849i	−0.334759	−	0.579820i
$286$	−15.9083			−0.940679
$287$	−1.60555			−0.0947727
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−15.3625	−	26.6086i	−0.903676	−	1.56521i
$290$	0.348612	−	0.603814i	0.0204712	−	0.0354572i
$291$	4.00000	−	6.92820i	0.234484	−	0.406138i
$292$	0.697224			0.0408020
$293$	−0.908327	+	1.57327i	−0.0530650	+	0.0919113i	−0.891338	−	0.453340i	$-0.850232\pi$
$293$	−0.908327	+	1.57327i	−0.0530650	+	0.0919113i	0.838273	+	0.545251i	$0.183566\pi$
$294$	−6.00000			−0.349927
$295$	14.1653	−	24.5350i	0.824734	−	1.42848i
$296$	2.65139	−	4.59234i	0.154109	−	0.266924i
$297$	2.65139	−	4.59234i	0.153849	−	0.266475i
$298$	2.55971	−	4.43356i	0.148280	−	0.256829i
$299$	−8.40833	+	14.5636i	−0.486266	+	0.842238i
$300$	−0.151388	−	0.262211i	−0.00874038	−	0.0151388i
$301$	−12.2111			−0.703836
$302$	6.19722	+	10.7339i	0.356610	+	0.617667i
$303$	−0.454163	+	0.786634i	−0.0260910	+	0.0451910i
$304$	−4.90833			−0.281512
$305$	−12.2111			−0.699206
$306$	−3.45416	−	5.98279i	−0.197461	−	0.342013i
$307$	−7.65139	+	13.2526i	−0.436688	+	0.756365i	−0.997432	−	0.0716239i	$-0.977182\pi$
$307$	−7.65139	+	13.2526i	−0.436688	+	0.756365i	0.560744	+	0.827989i	$0.310515\pi$
$308$	−5.30278			−0.302154
$309$	0.651388	−	1.12824i	0.0370562	−	0.0641831i
$310$	9.10555	+	15.7713i	0.517161	+	0.895748i
$311$	6.60555	+	11.4412i	0.374566	+	0.648768i	0.990262	−	0.139216i	$-0.0444582\pi$
$311$	6.60555	+	11.4412i	0.374566	+	0.648768i	−0.615696	+	0.787984i	$0.711125\pi$
$312$	−1.50000	+	2.59808i	−0.0849208	+	0.147087i
$313$	−8.51388	+	14.7465i	−0.481233	+	0.833520i	−0.999768	−	0.0215365i	$-0.993144\pi$
$313$	−8.51388	+	14.7465i	−0.481233	+	0.833520i	0.518535	+	0.855056i	$0.326478\pi$
$314$	−10.8625	−	18.8144i	−0.613006	−	1.06176i
$315$	−2.30278			−0.129747
$316$	2.84861	+	4.93394i	0.160247	+	0.277556i
$317$	16.8167			0.944517			0.472259	−	0.881460i	$-0.343439\pi$
$317$	16.8167			0.944517			0.472259	+	0.881460i	$0.343439\pi$
$318$	9.81665			0.550491
$319$	0.802776	+	1.39045i	0.0449468	+	0.0778502i
$320$	−2.30278			−0.128729
$321$	−3.80278	−	6.58660i	−0.212250	−	0.367628i
$322$	−2.80278	+	4.85455i	−0.156193	+	0.270533i
$323$	16.9542	−	29.3655i	0.943355	−	1.63394i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−0.454163	−	0.786634i	−0.0251925	−	0.0436346i
$326$	11.7111	−	20.2842i	0.648618	−	1.12344i
$327$	−2.00000			−0.110600
$328$	0.802776	−	1.39045i	0.0443259	−	0.0767747i
$329$	0.197224	+	0.341603i	0.0108733	+	0.0188332i
$330$	12.2111			0.672199
$331$	8.09167			0.444759			0.222379	−	0.974960i	$-0.428618\pi$
$331$	8.09167			0.444759			0.222379	+	0.974960i	$0.428618\pi$
$332$	8.21110	−	14.2220i	0.450643	−	0.780536i
$333$	2.65139	+	4.59234i	0.145295	+	0.251659i
$334$	−9.30278			−0.509025
$335$	−5.75694	−	9.97131i	−0.314535	−	0.544791i
$336$	−0.500000	+	0.866025i	−0.0272772	+	0.0472456i
$337$	−7.86249	+	13.6182i	−0.428297	+	0.741832i	−0.996722	−	0.0809028i	$-0.974220\pi$
$337$	−7.86249	+	13.6182i	−0.428297	+	0.741832i	0.568425	+	0.822735i	$0.307553\pi$
$338$	2.00000	−	3.46410i	0.108786	−	0.188422i
$339$	−0.651388	+	1.12824i	−0.0353785	+	0.0612774i
$340$	7.95416	−	13.7770i	0.431375	−	0.747164i
$341$	−41.9361			−2.27097
$342$	2.45416	−	4.25074i	0.132706	−	0.229853i
$343$	−13.0000			−0.701934
$344$	6.10555	−	10.5751i	0.329189	−	0.570173i
$345$	6.45416	−	11.1789i	0.347480	−	0.601854i
$346$	3.05971	+	5.29958i	0.164491	+	0.284907i
$347$	−0.137510	+	0.238174i	−0.00738190	+	0.0127858i	−0.869693	−	0.493593i	$-0.835683\pi$
$347$	−0.137510	+	0.238174i	−0.00738190	+	0.0127858i	0.862311	+	0.506379i	$0.169016\pi$
$348$	0.302776			0.0162305
$349$	10.9083			0.583909			0.291955	−	0.956432i	$-0.405694\pi$
$349$	10.9083			0.583909			0.291955	+	0.956432i	$0.405694\pi$
$350$	−0.151388	−	0.262211i	−0.00809202	−	0.0140158i
$351$	−1.50000	−	2.59808i	−0.0800641	−	0.138675i
$352$	2.65139	−	4.59234i	0.141319	−	0.244772i
$353$	−11.7569	−	20.3636i	−0.625759	−	1.08385i	−0.988394	−	0.151915i	$-0.951456\pi$
$353$	−11.7569	−	20.3636i	−0.625759	−	1.08385i	0.362635	−	0.931931i	$-0.381877\pi$
$354$	12.3028			0.653885
$355$	−13.3625	−	23.1445i	−0.709207	−	1.22838i
$356$	1.51388			0.0802354
$357$	−3.45416	−	5.98279i	−0.182814	−	0.316643i
$358$	5.50000	+	9.52628i	0.290684	+	0.503480i
$359$	8.95416	−	15.5091i	0.472583	−	0.818537i	−0.526925	−	0.849912i	$-0.676655\pi$
$359$	8.95416	−	15.5091i	0.472583	−	0.818537i	0.999508	+	0.0313746i	$0.00998848\pi$
$360$	1.15139	−	1.99426i	0.0606835	−	0.105107i
$361$	5.09167			0.267983
$362$	−2.51388			−0.132127
$363$	−8.55971	+	14.8259i	−0.449269	+	0.778156i
$364$	−1.50000	+	2.59808i	−0.0786214	+	0.136176i
$365$	−1.60555			−0.0840384
$366$	−2.65139	−	4.59234i	−0.138590	−	0.240045i
$367$	13.5139	+	23.4067i	0.705419	+	1.22182i	0.966540	+	0.256515i	$0.0825743\pi$
$367$	13.5139	+	23.4067i	0.705419	+	1.22182i	−0.261122	+	0.965306i	$0.584092\pi$
$368$	−2.80278	−	4.85455i	−0.146105	−	0.253061i
$369$	0.802776	+	1.39045i	0.0417908	+	0.0723838i
$370$	−6.10555	+	10.5751i	−0.317412	+	0.549775i
$371$	9.81665			0.509655
$372$	−3.95416	+	6.84881i	−0.205014	+	0.355094i
$373$	−28.2389			−1.46215			−0.731076	−	0.682296i	$-0.760982\pi$
$373$	−28.2389			−1.46215			−0.731076	+	0.682296i	$0.760982\pi$
$374$	18.3167	+	31.7254i	0.947132	+	1.64048i
$375$	−5.40833	−	9.36750i	−0.279285	−	0.483735i
$376$	−0.394449			−0.0203421
$377$	0.908327			0.0467812
$378$	−0.500000	−	0.866025i	−0.0257172	−	0.0445435i
$379$	18.5139			0.950994			0.475497	−	0.879717i	$-0.342268\pi$
$379$	18.5139			0.950994			0.475497	+	0.879717i	$0.342268\pi$
$380$	11.3028			0.579820
$381$	−7.21110	+	8.66025i	−0.369436	+	0.443678i
$382$	−10.2111			−0.522445
$383$	−33.4222			−1.70779			−0.853897	−	0.520441i	$-0.825767\pi$
$383$	−33.4222			−1.70779			−0.853897	+	0.520441i	$0.825767\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	12.2111			0.622335
$386$	−4.60555			−0.234416
$387$	6.10555	+	10.5751i	0.310363	+	0.537564i
$388$	4.00000	+	6.92820i	0.203069	+	0.351726i
$389$	−3.60555			−0.182809			−0.0914044	−	0.995814i	$-0.529136\pi$
$389$	−3.60555			−0.182809			−0.0914044	+	0.995814i	$0.529136\pi$
$390$	3.45416	−	5.98279i	0.174908	−	0.302950i
$391$	38.7250			1.95841
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$	−8.21110	−	14.2220i	−0.414195	−	0.717407i
$394$	−7.60555	−	13.1732i	−0.383162	−	0.663656i
$395$	−6.55971	−	11.3618i	−0.330055	−	0.571672i
$396$	2.65139	+	4.59234i	0.133237	+	0.230774i
$397$	4.72498			0.237140			0.118570	−	0.992946i	$-0.462169\pi$
$397$	4.72498			0.237140			0.118570	+	0.992946i	$0.462169\pi$
$398$	10.8028	−	18.7110i	0.541494	−	0.937895i
$399$	2.45416	−	4.25074i	0.122862	−	0.212803i
$400$	0.302776			0.0151388
$401$	−9.30278			−0.464558			−0.232279	−	0.972649i	$-0.574618\pi$
$401$	−9.30278			−0.464558			−0.232279	+	0.972649i	$0.574618\pi$
$402$	2.50000	−	4.33013i	0.124689	−	0.215967i
$403$	−11.8625	+	20.5464i	−0.590913	+	1.02349i
$404$	−0.454163	−	0.786634i	−0.0225955	−	0.0391365i
$405$	1.15139	+	1.99426i	0.0572129	+	0.0990957i
$406$	0.302776			0.0150265
$407$	−14.0597	−	24.3521i	−0.696914	−	1.20709i
$408$	6.90833			0.342013
$409$	−1.24306	−	2.15304i	−0.0614654	−	0.106461i	0.833655	−	0.552285i	$-0.186244\pi$
$409$	−1.24306	−	2.15304i	−0.0614654	−	0.106461i	−0.895121	+	0.445824i	$0.852911\pi$
$410$	−1.84861	+	3.20189i	−0.0912964	+	0.158130i
$411$	10.2569	+	17.7655i	0.505937	+	0.876309i
$412$	0.651388	+	1.12824i	0.0320916	+	0.0555842i
$413$	12.3028			0.605380
$414$	5.60555			0.275498
$415$	−18.9083	+	32.7502i	−0.928173	+	1.60764i
$416$	−1.50000	−	2.59808i	−0.0735436	−	0.127381i
$417$	5.30278	−	9.18468i	0.259678	−	0.449776i
$418$	−13.0139	+	22.5407i	−0.636530	+	1.10250i
$419$	36.1194			1.76455			0.882275	−	0.470735i	$-0.156011\pi$
$419$	36.1194			1.76455			0.882275	+	0.470735i	$0.156011\pi$
$420$	1.15139	−	1.99426i	0.0561820	−	0.0973100i
$421$	14.6333			0.713184			0.356592	−	0.934260i	$-0.383939\pi$
$421$	14.6333			0.713184			0.356592	+	0.934260i	$0.383939\pi$
$422$	−9.71110	+	16.8201i	−0.472729	+	0.818791i
$423$	0.197224	−	0.341603i	0.00958938	−	0.0166093i
$424$	−4.90833	+	8.50147i	−0.238369	+	0.412868i
$425$	−1.04584	+	1.81144i	−0.0507305	+	0.0878678i
$426$	5.80278	−	10.0507i	0.281145	−	0.486958i
$427$	−2.65139	−	4.59234i	−0.128310	−	0.222239i
$428$	7.60555			0.367628
$429$	7.95416	+	13.7770i	0.384031	+	0.665161i
$430$	−14.0597	+	24.3521i	−0.678020	+	1.17436i
$431$	−19.7250			−0.950119			−0.475059	−	0.879954i	$-0.657573\pi$
$431$	−19.7250			−0.950119			−0.475059	+	0.879954i	$0.657573\pi$
$432$	1.00000			0.0481125
$433$	2.51388	+	4.35416i	0.120809	+	0.209248i	0.920087	−	0.391714i	$-0.128118\pi$
$433$	2.51388	+	4.35416i	0.120809	+	0.209248i	−0.799278	+	0.600962i	$0.794784\pi$
$434$	−3.95416	+	6.84881i	−0.189806	+	0.328753i
$435$	−0.697224			−0.0334293
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	13.7569	+	23.8277i	0.658084	+	1.13983i
$438$	−0.348612	−	0.603814i	−0.0166573	−	0.0288513i
$439$	14.4222	−	24.9800i	0.688334	−	1.19223i	−0.284042	−	0.958812i	$-0.591676\pi$
$439$	14.4222	−	24.9800i	0.688334	−	1.19223i	0.972376	−	0.233418i	$-0.0749911\pi$
$440$	−6.10555	+	10.5751i	−0.291071	+	0.504149i
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$	20.7250			0.985787
$443$	14.2111	+	24.6144i	0.675190	+	1.16946i	0.976413	+	0.215910i	$0.0692716\pi$
$443$	14.2111	+	24.6144i	0.675190	+	1.16946i	−0.301224	+	0.953554i	$0.597395\pi$
$444$	−5.30278			−0.251659
$445$	−3.48612			−0.165258
$446$	−11.2111	−	19.4182i	−0.530861	−	0.919478i
$447$	−5.11943			−0.242141
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−0.908327	+	1.57327i	−0.0428666	+	0.0742471i	−0.886663	−	0.462417i	$-0.846982\pi$
$449$	−0.908327	+	1.57327i	−0.0428666	+	0.0742471i	0.843796	+	0.536664i	$0.180316\pi$
$450$	−0.151388	+	0.262211i	−0.00713649	+	0.0123608i
$451$	−4.25694	−	7.37323i	−0.200451	−	0.347192i
$452$	−0.651388	−	1.12824i	−0.0306387	−	0.0530678i
$453$	6.19722	−	10.7339i	0.291171	−	0.504323i
$454$	−13.2111			−0.620028
$455$	3.45416	−	5.98279i	0.161934	−	0.280477i
$456$	2.45416	+	4.25074i	0.114927	+	0.199059i
$457$	7.69722			0.360061			0.180030	−	0.983661i	$-0.442380\pi$
$457$	7.69722			0.360061			0.180030	+	0.983661i	$0.442380\pi$
$458$	4.30278			0.201056
$459$	−3.45416	+	5.98279i	−0.161227	+	0.279253i
$460$	6.45416	+	11.1789i	0.300927	+	0.521221i
$461$	−38.4500			−1.79079			−0.895397	−	0.445269i	$-0.853108\pi$
$461$	−38.4500			−1.79079			−0.895397	+	0.445269i	$0.853108\pi$
$462$	2.65139	+	4.59234i	0.123354	+	0.213655i
$463$	9.50000	−	16.4545i	0.441502	−	0.764705i	−0.556299	−	0.830982i	$-0.687779\pi$
$463$	9.50000	−	16.4545i	0.441502	−	0.764705i	0.997801	+	0.0662777i	$0.0211123\pi$
$464$	−0.151388	+	0.262211i	−0.00702800	+	0.0121729i
$465$	9.10555	−	15.7713i	0.422260	−	0.731375i
$466$	0.605551	−	1.04885i	0.0280516	−	0.0485868i
$467$	16.5000	−	28.5788i	0.763529	−	1.32247i	−0.177492	−	0.984122i	$-0.556798\pi$
$467$	16.5000	−	28.5788i	0.763529	−	1.32247i	0.941021	−	0.338349i	$-0.109868\pi$
$468$	3.00000			0.138675
$469$	2.50000	−	4.33013i	0.115439	−	0.199947i
$470$	0.908327			0.0418980
$471$	−10.8625	+	18.8144i	−0.500517	+	0.866921i
$472$	−6.15139	+	10.6545i	−0.283141	+	0.490414i
$473$	−32.3764	−	56.0775i	−1.48867	−	2.57845i
$474$	2.84861	−	4.93394i	0.130841	−	0.226623i
$475$	−1.48612			−0.0681879
$476$	6.90833			0.316643
$477$	−4.90833	−	8.50147i	−0.224737	−	0.389256i
$478$	−9.90833	−	17.1617i	−0.453196	−	0.784959i
$479$	7.89445	−	13.6736i	0.360707	−	0.624762i	−0.627371	−	0.778721i	$-0.715869\pi$
$479$	7.89445	−	13.6736i	0.360707	−	0.624762i	0.988077	+	0.153959i	$0.0492022\pi$
$480$	1.15139	+	1.99426i	0.0525534	+	0.0910252i
$481$	−15.9083			−0.725357
$482$	−5.19722	−	9.00186i	−0.236727	−	0.410023i
$483$	5.60555			0.255061
$484$	−8.55971	−	14.8259i	−0.389078	−	0.673903i
$485$	−9.21110	−	15.9541i	−0.418255	−	0.724438i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−12.4083	+	21.4919i	−0.562275	+	0.973889i	0.435023	+	0.900420i	$0.356740\pi$
$487$	−12.4083	+	21.4919i	−0.562275	+	0.973889i	−0.997297	+	0.0734692i	$0.976593\pi$
$488$	5.30278			0.240045
$489$	−23.4222			−1.05919
$490$	−6.90833	+	11.9656i	−0.312086	+	0.540549i
$491$	−5.95416	+	10.3129i	−0.268708	+	0.465415i	−0.968528	−	0.248903i	$-0.919930\pi$
$491$	−5.95416	+	10.3129i	−0.268708	+	0.465415i	0.699821	+	0.714319i	$0.253263\pi$
$492$	−1.60555			−0.0723838
$493$	−1.04584	−	1.81144i	−0.0471021	−	0.0815832i
$494$	7.36249	+	12.7522i	0.331254	+	0.573749i
$495$	−6.10555	−	10.5751i	−0.274424	−	0.475317i
$496$	−3.95416	−	6.84881i	−0.177547	−	0.307521i
$497$	5.80278	−	10.0507i	0.260290	−	0.450836i
$498$	−16.4222			−0.735897
$499$	−6.59167	+	11.4171i	−0.295084	+	0.511100i	−0.975004	−	0.222186i	$-0.928681\pi$
$499$	−6.59167	+	11.4171i	−0.295084	+	0.511100i	0.679921	+	0.733286i	$0.262014\pi$
$500$	10.8167			0.483735
$501$	4.65139	+	8.05644i	0.207809	+	0.359935i
$502$	5.40833	+	9.36750i	0.241385	+	0.418092i
$503$	−24.6333			−1.09834			−0.549172	−	0.835709i	$-0.685057\pi$
$503$	−24.6333			−1.09834			−0.549172	+	0.835709i	$0.685057\pi$
$504$	1.00000			0.0445435
$505$	1.04584	+	1.81144i	0.0465391	+	0.0806081i
$506$	−29.7250			−1.32144
$507$	−4.00000			−0.177646
$508$	−3.89445	−	10.5751i	−0.172788	−	0.469195i
$509$	3.00000			0.132973			0.0664863	−	0.997787i	$-0.478821\pi$
$509$	3.00000			0.132973			0.0664863	+	0.997787i	$0.478821\pi$
$510$	−15.9083			−0.704433
$511$	−0.348612	−	0.603814i	−0.0154217	−	0.0267112i
$512$	1.00000			0.0441942
$513$	−4.90833			−0.216708
$514$	14.5139	+	25.1388i	0.640180	+	1.10882i
$515$	−1.50000	−	2.59808i	−0.0660979	−	0.114485i
$516$	−12.2111			−0.537564
$517$	−1.04584	+	1.81144i	−0.0459958	+	0.0796671i
$518$	−5.30278			−0.232991
$519$	3.05971	−	5.29958i	0.134307	−	0.232626i
$520$	3.45416	+	5.98279i	0.151475	+	0.262363i
$521$	4.10555	+	7.11102i	0.179867	+	0.311540i	0.941835	−	0.336076i	$-0.109100\pi$
$521$	4.10555	+	7.11102i	0.179867	+	0.311540i	−0.761968	+	0.647615i	$0.775766\pi$
$522$	−0.151388	−	0.262211i	−0.00662606	−	0.0114767i
$523$	−3.09167	−	5.35493i	−0.135189	−	0.234155i	0.790480	−	0.612487i	$-0.209831\pi$
$523$	−3.09167	−	5.35493i	−0.135189	−	0.234155i	−0.925670	+	0.378332i	$0.876498\pi$
$524$	16.4222			0.717407
$525$	−0.151388	+	0.262211i	−0.00660711	+	0.0114438i
$526$	2.74306	−	4.75112i	0.119603	−	0.207159i
$527$	54.6333			2.37986
$528$	−5.30278			−0.230774
$529$	−4.21110	+	7.29384i	−0.183091	+	0.317124i
$530$	11.3028	−	19.5770i	0.490961	−	0.850370i
$531$	−6.15139	−	10.6545i	−0.266947	−	0.462367i
$532$	2.45416	+	4.25074i	0.106401	+	0.184293i
$533$	−4.81665			−0.208632
$534$	−0.756939	−	1.31106i	−0.0327560	−	0.0567350i
$535$	−17.5139			−0.757191
$536$	2.50000	+	4.33013i	0.107984	+	0.187033i
$537$	5.50000	−	9.52628i	0.237343	−	0.411089i
$538$	−8.95416	−	15.5091i	−0.386041	−	0.668643i
$539$	−15.9083	−	27.5540i	−0.685220	−	1.18684i
$540$	−2.30278			−0.0990957
$541$	28.1194			1.20895			0.604474	−	0.796625i	$-0.293383\pi$
$541$	28.1194			1.20895			0.604474	+	0.796625i	$0.293383\pi$
$542$	10.4083	−	18.0278i	0.447076	−	0.774358i
$543$	1.25694	+	2.17708i	0.0539404	+	0.0934275i
$544$	−3.45416	+	5.98279i	−0.148096	+	0.256510i
$545$	−2.30278	+	3.98852i	−0.0986401	+	0.170850i
$546$	3.00000			0.128388
$547$	−14.8486	+	25.7186i	−0.634881	+	1.09965i	0.351660	+	0.936128i	$0.385617\pi$
$547$	−14.8486	+	25.7186i	−0.634881	+	1.09965i	−0.986540	+	0.163518i	$0.947716\pi$
$548$	−20.5139			−0.876309
$549$	−2.65139	+	4.59234i	−0.113158	+	0.195996i
$550$	0.802776	−	1.39045i	0.0342305	−	0.0592889i
$551$	0.743061	−	1.28702i	0.0316555	−	0.0548289i
$552$	−2.80278	+	4.85455i	−0.119294	+	0.206623i
$553$	2.84861	−	4.93394i	0.121135	−	0.209813i
$554$	−9.01388	−	15.6125i	−0.382963	−	0.663311i
$555$	12.2111			0.518332
$556$	5.30278	+	9.18468i	0.224888	+	0.389517i
$557$	13.8486	−	23.9865i	0.586785	−	1.01634i	−0.407866	−	0.913042i	$-0.633727\pi$
$557$	13.8486	−	23.9865i	0.586785	−	1.01634i	0.994650	−	0.103299i	$-0.0329398\pi$
$558$	7.90833			0.334786
$559$	−36.6333			−1.54942
$560$	1.15139	+	1.99426i	0.0486550	+	0.0842730i
$561$	18.3167	−	31.7254i	0.773330	−	1.33945i
$562$	29.5416			1.24614
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	−0.997876	−	0.0651433i	$-0.979250\pi$
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	0.555354	+	0.831614i	$0.312583\pi$
$564$	0.197224	+	0.341603i	0.00830464	+	0.0143841i
$565$	1.50000	+	2.59808i	0.0631055	+	0.109302i
$566$	−14.9680	+	25.9254i	−0.629154	+	1.08973i
$567$	−0.500000	+	0.866025i	−0.0209980	+	0.0363696i
$568$	5.80278	+	10.0507i	0.243479	+	0.421718i
$569$	37.3305			1.56498			0.782489	−	0.622665i	$-0.213950\pi$
$569$	37.3305			1.56498			0.782489	+	0.622665i	$0.213950\pi$
$570$	−5.65139	−	9.78849i	−0.236711	−	0.409995i
$571$	−34.3028			−1.43553			−0.717763	−	0.696287i	$-0.754834\pi$
$571$	−34.3028			−1.43553			−0.717763	+	0.696287i	$0.754834\pi$
$572$	−15.9083			−0.665161
$573$	5.10555	+	8.84307i	0.213287	+	0.369425i
$574$	−1.60555			−0.0670144
$575$	−0.848612	−	1.46984i	−0.0353896	−	0.0612965i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	4.05971	−	7.03163i	0.169008	−	0.292731i	−0.769063	−	0.639173i	$-0.779277\pi$
$577$	4.05971	−	7.03163i	0.169008	−	0.292731i	0.938071	+	0.346442i	$0.112610\pi$
$578$	−15.3625	−	26.6086i	−0.638995	−	1.10677i
$579$	2.30278	+	3.98852i	0.0957001	+	0.165757i
$580$	0.348612	−	0.603814i	0.0144753	−	0.0250720i
$581$	−16.4222			−0.681308
$582$	4.00000	−	6.92820i	0.165805	−	0.287183i
$583$	26.0278	+	45.0814i	1.07796	+	1.86708i
$584$	0.697224			0.0288513
$585$	−6.90833			−0.285624
$586$	−0.908327	+	1.57327i	−0.0375226	+	0.0649911i
$587$	−10.1194	−	17.5274i	−0.417674	−	0.723432i	0.578031	−	0.816014i	$-0.303821\pi$
$587$	−10.1194	−	17.5274i	−0.417674	−	0.723432i	−0.995705	+	0.0925827i	$0.970488\pi$
$588$	−6.00000			−0.247436
$589$	19.4083	+	33.6162i	0.799706	+	1.38513i
$590$	14.1653	−	24.5350i	0.583175	−	1.01009i
$591$	−7.60555	+	13.1732i	−0.312851	+	0.541873i
$592$	2.65139	−	4.59234i	0.108971	−	0.188744i
$593$	−1.86249	+	3.22593i	−0.0764833	+	0.132473i	−0.901730	−	0.432299i	$-0.857703\pi$
$593$	−1.86249	+	3.22593i	−0.0764833	+	0.132473i	0.825247	+	0.564772i	$0.191036\pi$
$594$	2.65139	−	4.59234i	0.108788	−	0.188426i
$595$	−15.9083			−0.652178
$596$	2.55971	−	4.43356i	0.104850	−	0.181606i
$597$	−21.6056			−0.884256
$598$	−8.40833	+	14.5636i	−0.343842	+	0.595552i
$599$	20.8764	−	36.1589i	0.852985	−	1.47741i	−0.0255163	−	0.999674i	$-0.508123\pi$
$599$	20.8764	−	36.1589i	0.852985	−	1.47741i	0.878502	−	0.477739i	$-0.158544\pi$
$600$	−0.151388	−	0.262211i	−0.00618038	−	0.0107047i
$601$	9.57359	−	16.5819i	0.390515	−	0.676392i	−0.602003	−	0.798494i	$-0.705630\pi$
$601$	9.57359	−	16.5819i	0.390515	−	0.676392i	0.992518	+	0.122102i	$0.0389636\pi$
$602$	−12.2111			−0.497687
$603$	−5.00000			−0.203616
$604$	6.19722	+	10.7339i	0.252161	+	0.436757i
$605$	19.7111	+	34.1406i	0.801370	+	1.38801i
$606$	−0.454163	+	0.786634i	−0.0184491	+	0.0319548i
$607$	−9.50000	−	16.4545i	−0.385593	−	0.667867i	0.606258	−	0.795268i	$-0.292670\pi$
$607$	−9.50000	−	16.4545i	−0.385593	−	0.667867i	−0.991851	+	0.127401i	$0.959336\pi$
$608$	−4.90833			−0.199059
$609$	−0.151388	−	0.262211i	−0.00613454	−	0.0106253i
$610$	−12.2111			−0.494413
$611$	0.591673	+	1.02481i	0.0239365	+	0.0414593i
$612$	−3.45416	−	5.98279i	−0.139626	−	0.241840i
$613$	−15.4222	+	26.7120i	−0.622897	+	1.07889i	0.366047	+	0.930597i	$0.380711\pi$
$613$	−15.4222	+	26.7120i	−0.622897	+	1.07889i	−0.988944	+	0.148293i	$0.952622\pi$
$614$	−7.65139	+	13.2526i	−0.308785	+	0.534831i
$615$	3.69722			0.149086
$616$	−5.30278			−0.213655
$617$	3.10555	−	5.37897i	0.125025	−	0.216549i	−0.796718	−	0.604351i	$-0.793432\pi$
$617$	3.10555	−	5.37897i	0.125025	−	0.216549i	0.921743	+	0.387802i	$0.126766\pi$
$618$	0.651388	−	1.12824i	0.0262027	−	0.0453843i
$619$	25.9361			1.04246			0.521230	−	0.853416i	$-0.325474\pi$
$619$	25.9361			1.04246			0.521230	+	0.853416i	$0.325474\pi$
$620$	9.10555	+	15.7713i	0.365688	+	0.633390i
$621$	−2.80278	−	4.85455i	−0.112472	−	0.194806i
$622$	6.60555	+	11.4412i	0.264858	+	0.458748i
$623$	−0.756939	−	1.31106i	−0.0303261	−	0.0525264i
$624$	−1.50000	+	2.59808i	−0.0600481	+	0.104006i
$625$	−26.4222			−1.05689
$626$	−8.51388	+	14.7465i	−0.340283	+	0.589387i
$627$	26.0278			1.03945
$628$	−10.8625	−	18.8144i	−0.433461	−	0.750776i
$629$	18.3167	+	31.7254i	0.730333	+	1.26497i
$630$	−2.30278			−0.0917448
$631$	−26.6333			−1.06026			−0.530128	−	0.847918i	$-0.677856\pi$
$631$	−26.6333			−1.06026			−0.530128	+	0.847918i	$0.677856\pi$
$632$	2.84861	+	4.93394i	0.113312	+	0.196262i
$633$	19.4222			0.771963
$634$	16.8167			0.667875
$635$	8.96804	+	24.3521i	0.355886	+	0.966385i
$636$	9.81665			0.389256
$637$	−18.0000			−0.713186
$638$	0.802776	+	1.39045i	0.0317822	+	0.0550484i
$639$	−11.6056			−0.459109
$640$	−2.30278			−0.0910252
$641$	−5.40833	−	9.36750i	−0.213616	−	0.369994i	0.739228	−	0.673456i	$-0.235191\pi$
$641$	−5.40833	−	9.36750i	−0.213616	−	0.369994i	−0.952844	+	0.303462i	$0.901857\pi$
$642$	−3.80278	−	6.58660i	−0.150084	−	0.259952i
$643$	−9.27502			−0.365771			−0.182886	−	0.983134i	$-0.558544\pi$
$643$	−9.27502			−0.365771			−0.182886	+	0.983134i	$0.558544\pi$
$644$	−2.80278	+	4.85455i	−0.110445	+	0.191296i
$645$	28.1194			1.10720
$646$	16.9542	−	29.3655i	0.667053	−	1.15537i
$647$	−2.80278	−	4.85455i	−0.110188	−	0.190852i	0.805658	−	0.592381i	$-0.201812\pi$
$647$	−2.80278	−	4.85455i	−0.110188	−	0.190852i	−0.915846	+	0.401529i	$0.868479\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	32.6194	+	56.4985i	1.28042	+	2.21776i
$650$	−0.454163	−	0.786634i	−0.0178138	−	0.0308543i
$651$	7.90833			0.309952
$652$	11.7111	−	20.2842i	0.458642	−	0.794392i
$653$	−14.4083	+	24.9560i	−0.563841	+	0.976602i	0.433315	+	0.901243i	$0.357344\pi$
$653$	−14.4083	+	24.9560i	−0.563841	+	0.976602i	−0.997156	+	0.0753594i	$0.975990\pi$
$654$	−2.00000			−0.0782062
$655$	−37.8167			−1.47762
$656$	0.802776	−	1.39045i	0.0313431	−	0.0542879i
$657$	−0.348612	+	0.603814i	−0.0136007	+	0.0235570i
$658$	0.197224	+	0.341603i	0.00768861	+	0.0133171i
$659$	14.6972	+	25.4563i	0.572523	+	0.991638i	0.996306	+	0.0858746i	$0.0273684\pi$
$659$	14.6972	+	25.4563i	0.572523	+	0.991638i	−0.423783	+	0.905764i	$0.639298\pi$
$660$	12.2111			0.475317
$661$	−0.637510	−	1.10420i	−0.0247963	−	0.0429484i	0.853361	−	0.521320i	$-0.174560\pi$
$661$	−0.637510	−	1.10420i	−0.0247963	−	0.0429484i	−0.878157	+	0.478372i	$0.841227\pi$
$662$	8.09167			0.314492
$663$	−10.3625	−	17.9484i	−0.402446	−	0.697057i
$664$	8.21110	−	14.2220i	0.318653	−	0.551922i
$665$	−5.65139	−	9.78849i	−0.219151	−	0.379581i
$666$	2.65139	+	4.59234i	0.102739	+	0.177949i
$667$	1.69722			0.0657168
$668$	−9.30278			−0.359935
$669$	−11.2111	+	19.4182i	−0.433446	+	0.750751i
$670$	−5.75694	−	9.97131i	−0.222410	−	0.385225i
$671$	14.0597	−	24.3521i	0.542769	−	0.940104i
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	−15.3305			−0.590949			−0.295474	−	0.955351i	$-0.595478\pi$
$673$	−15.3305			−0.590949			−0.295474	+	0.955351i	$0.595478\pi$
$674$	−7.86249	+	13.6182i	−0.302852	+	0.524555i
$675$	0.302776			0.0116538
$676$	2.00000	−	3.46410i	0.0769231	−	0.133235i
$677$	10.7708	−	18.6556i	0.413956	−	0.716993i	−0.581362	−	0.813645i	$-0.697480\pi$
$677$	10.7708	−	18.6556i	0.413956	−	0.716993i	0.995318	+	0.0966519i	$0.0308134\pi$
$678$	−0.651388	+	1.12824i	−0.0250164	+	0.0433297i
$679$	4.00000	−	6.92820i	0.153506	−	0.265880i
$680$	7.95416	−	13.7770i	0.305028	−	0.528324i
$681$	6.60555	+	11.4412i	0.253125	+	0.438426i
$682$	−41.9361			−1.60582
$683$	−10.6056	−	18.3694i	−0.405810	−	0.702884i	0.588605	−	0.808421i	$-0.299677\pi$
$683$	−10.6056	−	18.3694i	−0.405810	−	0.702884i	−0.994415	+	0.105537i	$0.966344\pi$
$684$	2.45416	−	4.25074i	0.0938373	−	0.162531i
$685$	47.2389			1.80490
$686$	−13.0000			−0.496342
$687$	−2.15139	−	3.72631i	−0.0820806	−	0.142168i
$688$	6.10555	−	10.5751i	0.232772	−	0.403173i
$689$	29.4500			1.12195
$690$	6.45416	−	11.1789i	0.245706	−	0.425575i
$691$	7.19722	+	12.4660i	0.273795	+	0.474227i	0.969830	−	0.243780i	$-0.0783876\pi$
$691$	7.19722	+	12.4660i	0.273795	+	0.474227i	−0.696035	+	0.718008i	$0.745054\pi$
$692$	3.05971	+	5.29958i	0.116313	+	0.201460i
$693$	2.65139	−	4.59234i	0.100718	−	0.174449i
$694$	−0.137510	+	0.238174i	−0.00521979	+	0.00904095i
$695$	−12.2111	−	21.1503i	−0.463194	−	0.802275i
$696$	0.302776			0.0114767
$697$	5.54584	+	9.60567i	0.210064	+	0.363841i
$698$	10.9083			0.412886
$699$	−1.21110			−0.0458081
$700$	−0.151388	−	0.262211i	−0.00572192	−	0.00991066i
$701$	33.5416			1.26685			0.633425	−	0.773804i	$-0.281649\pi$
$701$	33.5416			1.26685			0.633425	+	0.773804i	$0.281649\pi$
$702$	−1.50000	−	2.59808i	−0.0566139	−	0.0980581i
$703$	−13.0139	+	22.5407i	−0.490828	+	0.850139i
$704$	2.65139	−	4.59234i	0.0999279	−	0.173080i
$705$	−0.454163	−	0.786634i	−0.0171048	−	0.0296264i
$706$	−11.7569	−	20.3636i	−0.442478	−	0.766395i
$707$	−0.454163	+	0.786634i	−0.0170806	+	0.0295844i
$708$	12.3028			0.462367
$709$	2.86249	−	4.95798i	0.107503	−	0.186201i	−0.807255	−	0.590203i	$-0.799048\pi$
$709$	2.86249	−	4.95798i	0.107503	−	0.186201i	0.914758	+	0.404002i	$0.132381\pi$
$710$	−13.3625	−	23.1445i	−0.501485	−	0.868598i
$711$	−5.69722			−0.213663
$712$	1.51388			0.0567350
$713$	−22.1653	+	38.3914i	−0.830096	+	1.43777i
$714$	−3.45416	−	5.98279i	−0.129269	−	0.223900i
$715$	36.6333			1.37001
$716$	5.50000	+	9.52628i	0.205545	+	0.356014i
$717$	−9.90833	+	17.1617i	−0.370033	+	0.640916i
$718$	8.95416	−	15.5091i	0.334166	−	0.578793i
$719$	−7.60555	+	13.1732i	−0.283639	+	0.491278i	−0.972278	−	0.233827i	$-0.924875\pi$
$719$	−7.60555	+	13.1732i	−0.283639	+	0.491278i	0.688639	+	0.725104i	$0.258208\pi$
$720$	1.15139	−	1.99426i	0.0429097	−	0.0743218i
$721$	0.651388	−	1.12824i	0.0242590	−	0.0420177i
$722$	5.09167			0.189492
$723$	−5.19722	+	9.00186i	−0.193287	+	0.334783i
$724$	−2.51388			−0.0934275
$725$	−0.0458365	+	0.0793912i	−0.00170233	+	0.00294852i
$726$	−8.55971	+	14.8259i	−0.317681	+	0.550239i
$727$	4.80278	+	8.31865i	0.178125	+	0.308522i	0.941238	−	0.337743i	$-0.109663\pi$
$727$	4.80278	+	8.31865i	0.178125	+	0.308522i	−0.763113	+	0.646265i	$0.776330\pi$
$728$	−1.50000	+	2.59808i	−0.0555937	+	0.0962911i
$729$	1.00000			0.0370370
$730$	−1.60555			−0.0594241
$731$	42.1791	+	73.0564i	1.56005	+	2.70209i
$732$	−2.65139	−	4.59234i	−0.0979981	−	0.169738i
$733$	21.7569	−	37.6841i	0.803611	−	1.39189i	−0.113614	−	0.993525i	$-0.536243\pi$
$733$	21.7569	−	37.6841i	0.803611	−	1.39189i	0.917225	−	0.398370i	$-0.130424\pi$
$734$	13.5139	+	23.4067i	0.498806	+	0.863958i
$735$	13.8167			0.509635
$736$	−2.80278	−	4.85455i	−0.103312	−	0.178941i
$737$	26.5139			0.976651
$738$	0.802776	+	1.39045i	0.0295506	+	0.0511831i
$739$	19.5736	+	33.9025i	0.720026	+	1.24712i	0.960989	+	0.276588i	$0.0892036\pi$
$739$	19.5736	+	33.9025i	0.720026	+	1.24712i	−0.240962	+	0.970534i	$0.577463\pi$
$740$	−6.10555	+	10.5751i	−0.224445	+	0.388749i
$741$	7.36249	−	12.7522i	0.270468	−	0.468464i
$742$	9.81665			0.360381
$743$	12.3944			0.454708			0.227354	−	0.973812i	$-0.426993\pi$
$743$	12.3944			0.454708			0.227354	+	0.973812i	$0.426993\pi$
$744$	−3.95416	+	6.84881i	−0.144967	+	0.251090i
$745$	−5.89445	+	10.2095i	−0.215956	+	0.374047i
$746$	−28.2389			−1.03390
$747$	8.21110	+	14.2220i	0.300429	+	0.520357i
$748$	18.3167	+	31.7254i	0.669723	+	1.15999i
$749$	−3.80278	−	6.58660i	−0.138950	−	0.240669i
$750$	−5.40833	−	9.36750i	−0.197484	−	0.342053i
$751$	−3.05971	+	5.29958i	−0.111651	+	0.193384i	−0.916436	−	0.400182i	$-0.868947\pi$
$751$	−3.05971	+	5.29958i	−0.111651	+	0.193384i	0.804785	+	0.593566i	$0.202280\pi$
$752$	−0.394449			−0.0143841
$753$	5.40833	−	9.36750i	0.197090	−	0.341371i
$754$	0.908327			0.0330793
$755$	−14.2708	−	24.7178i	−0.519368	−	0.899572i
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	14.8167			0.538520			0.269260	−	0.963067i	$-0.413221\pi$
$757$	14.8167			0.538520			0.269260	+	0.963067i	$0.413221\pi$
$758$	18.5139			0.672454
$759$	14.8625	+	25.7426i	0.539474	+	0.934397i
$760$	11.3028			0.409995
$761$	−32.0917			−1.16332			−0.581661	−	0.813431i	$-0.697597\pi$
$761$	−32.0917			−1.16332			−0.581661	+	0.813431i	$0.697597\pi$
$762$	−7.21110	+	8.66025i	−0.261231	+	0.313728i
$763$	−2.00000			−0.0724049
$764$	−10.2111			−0.369425
$765$	7.95416	+	13.7770i	0.287583	+	0.498109i
$766$	−33.4222			−1.20759
$767$	36.9083			1.33268
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	8.28890	+	14.3568i	0.298905	+	0.517719i	0.975886	−	0.218282i	$-0.0700452\pi$
$769$	8.28890	+	14.3568i	0.298905	+	0.517719i	−0.676980	+	0.736001i	$0.736712\pi$
$770$	12.2111			0.440058
$771$	14.5139	−	25.1388i	0.522705	−	0.905351i
$772$	−4.60555			−0.165757
$773$	24.4083	−	42.2765i	0.877906	−	1.52058i	0.0242725	−	0.999705i	$-0.492273\pi$
$773$	24.4083	−	42.2765i	0.877906	−	1.52058i	0.853634	−	0.520873i	$-0.174394\pi$
$774$	6.10555	+	10.5751i	0.219460	+	0.380115i
$775$	−1.19722	−	2.07365i	−0.0430056	−	0.0744878i
$776$	4.00000	+	6.92820i	0.143592	+	0.248708i
$777$	2.65139	+	4.59234i	0.0951180	+	0.164749i
$778$	−3.60555			−0.129265
$779$	−3.94029	+	6.82477i	−0.141175	+	0.244523i
$780$	3.45416	−	5.98279i	0.123679	−	0.214218i
$781$	61.5416			2.20213
$782$	38.7250			1.38480
$783$	−0.151388	+	0.262211i	−0.00541016	+	0.00937067i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	25.0139	+	43.3253i	0.892784	+	1.54635i
$786$	−8.21110	−	14.2220i	−0.292880	−	0.507284i
$787$	47.6611			1.69893			0.849467	−	0.527642i	$-0.176924\pi$
$787$	47.6611			1.69893			0.849467	+	0.527642i	$0.176924\pi$
$788$	−7.60555	−	13.1732i	−0.270937	−	0.469276i
$789$	−5.48612			−0.195311
$790$	−6.55971	−	11.3618i	−0.233384	−	0.404233i
$791$	−0.651388	+	1.12824i	−0.0231607	+	0.0401155i
$792$	2.65139	+	4.59234i	0.0942130	+	0.163182i
$793$	−7.95416	−	13.7770i	−0.282461	−	0.489236i
$794$	4.72498			0.167683
$795$	−22.6056			−0.801736
$796$	10.8028	−	18.7110i	0.382894	−	0.663192i
$797$	17.6972	+	30.6525i	0.626868	+	1.08577i	0.988176	+	0.153321i	$0.0489967\pi$
$797$	17.6972	+	30.6525i	0.626868	+	1.08577i	−0.361309	+	0.932446i	$0.617670\pi$
$798$	2.45416	−	4.25074i	0.0868764	−	0.150474i
$799$	1.36249	−	2.35990i	0.0482014	−	0.0834874i
$800$	0.302776			0.0107047
$801$	−0.756939	+	1.31106i	−0.0267451	+	0.0463239i
$802$	−9.30278			−0.328492
$803$	1.84861	−	3.20189i	0.0652361	−	0.112992i
$804$	2.50000	−	4.33013i	0.0881682	−	0.152712i
$805$	6.45416	−	11.1789i	0.227479	−	0.394006i
$806$	−11.8625	+	20.5464i	−0.417838	+	0.723717i
$807$	−8.95416	+	15.5091i	−0.315201	+	0.545945i
$808$	−0.454163	−	0.786634i	−0.0159774	−	0.0276737i
$809$	−54.1194			−1.90274			−0.951369	−	0.308054i	$-0.900322\pi$
$809$	−54.1194			−1.90274			−0.951369	+	0.308054i	$0.900322\pi$
$810$	1.15139	+	1.99426i	0.0404556	+	0.0700712i
$811$	23.1791	−	40.1475i	0.813930	−	1.40977i	−0.0961640	−	0.995366i	$-0.530657\pi$
$811$	23.1791	−	40.1475i	0.813930	−	1.40977i	0.910094	−	0.414402i	$-0.136009\pi$
$812$	0.302776			0.0106253
$813$	−20.8167			−0.730072
$814$	−14.0597	−	24.3521i	−0.492793	−	0.853542i
$815$	−26.9680	+	46.7100i	−0.944649	+	1.63618i
$816$	6.90833			0.241840
$817$	−29.9680	+	51.9062i	−1.04845	+	1.81597i
$818$	−1.24306	−	2.15304i	−0.0434626	−	0.0752794i
$819$	−1.50000	−	2.59808i	−0.0524142	−	0.0907841i
$820$	−1.84861	+	3.20189i	−0.0645563	+	0.111815i
$821$	19.3764	−	33.5609i	0.676240	−	1.17128i	−0.299865	−	0.953982i	$-0.596942\pi$
$821$	19.3764	−	33.5609i	0.676240	−	1.17128i	0.976105	−	0.217300i	$-0.0697251\pi$
$822$	10.2569	+	17.7655i	0.357752	+	0.619644i
$823$	16.5778			0.577866			0.288933	−	0.957349i	$-0.406700\pi$
$823$	16.5778			0.577866			0.288933	+	0.957349i	$0.406700\pi$
$824$	0.651388	+	1.12824i	0.0226922	+	0.0393040i
$825$	−1.60555			−0.0558981
$826$	12.3028			0.428068
$827$	−17.6194	−	30.5177i	−0.612688	−	1.06121i	−0.990785	−	0.135440i	$-0.956755\pi$
$827$	−17.6194	−	30.5177i	−0.612688	−	1.06121i	0.378098	−	0.925766i	$-0.376578\pi$
$828$	5.60555			0.194806
$829$	13.0917	+	22.6754i	0.454693	+	0.787551i	0.998670	−	0.0515489i	$-0.0164158\pi$
$829$	13.0917	+	22.6754i	0.454693	+	0.787551i	−0.543978	+	0.839100i	$0.683082\pi$
$830$	−18.9083	+	32.7502i	−0.656318	+	1.13678i
$831$	−9.01388	+	15.6125i	−0.312688	+	0.541591i
$832$	−1.50000	−	2.59808i	−0.0520031	−	0.0900721i
$833$	20.7250	+	35.8967i	0.718078	+	1.24375i
$834$	5.30278	−	9.18468i	0.183620	−	0.318039i
$835$	21.4222			0.741346
$836$	−13.0139	+	22.5407i	−0.450094	+	0.779586i
$837$	−3.95416	−	6.84881i	−0.136676	−	0.236730i
$838$	36.1194			1.24772
$839$	31.8167			1.09843			0.549216	−	0.835680i	$-0.314926\pi$
$839$	31.8167			1.09843			0.549216	+	0.835680i	$0.314926\pi$
$840$	1.15139	−	1.99426i	0.0397267	−	0.0688086i
$841$	14.4542	+	25.0353i	0.498419	+	0.863288i
$842$	14.6333			0.504297
$843$	−14.7708	−	25.5838i	−0.508734	−	0.881153i
$844$	−9.71110	+	16.8201i	−0.334270	+	0.578973i
$845$	−4.60555	+	7.97705i	−0.158436	+	0.274419i
$846$	0.197224	−	0.341603i	0.00678071	−	0.0117445i
$847$	−8.55971	+	14.8259i	−0.294115	+	0.509423i
$848$	−4.90833	+	8.50147i	−0.168553	+	0.291942i
$849$	29.9361			1.02740
$850$	−1.04584	+	1.81144i	−0.0358719	+	0.0621319i
$851$	−29.7250			−1.01896
$852$	5.80278	−	10.0507i	0.198800	−	0.344331i
$853$	−10.5458	+	18.2659i	−0.361083	+	0.625413i	−0.988139	−	0.153560i	$-0.950926\pi$
$853$	−10.5458	+	18.2659i	−0.361083	+	0.625413i	0.627057	+	0.778974i	$0.284259\pi$
$854$	−2.65139	−	4.59234i	−0.0907286	−	0.157147i
$855$	−5.65139	+	9.78849i	−0.193273	+	0.334759i
$856$	7.60555			0.259952
$857$	−9.06392			−0.309617			−0.154809	−	0.987944i	$-0.549476\pi$
$857$	−9.06392			−0.309617			−0.154809	+	0.987944i	$0.549476\pi$
$858$	7.95416	+	13.7770i	0.271551	+	0.470340i
$859$	−5.61943	−	9.73314i	−0.191732	−	0.332090i	0.754092	−	0.656769i	$-0.228077\pi$
$859$	−5.61943	−	9.73314i	−0.191732	−	0.332090i	−0.945824	+	0.324678i	$0.894744\pi$
$860$	−14.0597	+	24.3521i	−0.479432	+	0.830401i
$861$	0.802776	+	1.39045i	0.0273585	+	0.0473863i
$862$	−19.7250			−0.671836
$863$	−3.78890	−	6.56256i	−0.128976	−	0.223392i	0.794304	−	0.607520i	$-0.207836\pi$
$863$	−3.78890	−	6.56256i	−0.128976	−	0.223392i	−0.923280	+	0.384128i	$0.874502\pi$
$864$	1.00000			0.0340207
$865$	−7.04584	−	12.2037i	−0.239566	−	0.414940i
$866$	2.51388	+	4.35416i	0.0854251	+	0.147961i
$867$	−15.3625	+	26.6086i	−0.521738	+	0.903676i
$868$	−3.95416	+	6.84881i	−0.134213	+	0.232464i
$869$	30.2111			1.02484
$870$	−0.697224			−0.0236381
$871$	7.50000	−	12.9904i	0.254128	−	0.440162i
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$	−8.00000			−0.270759
$874$	13.7569	+	23.8277i	0.465335	+	0.805985i
$875$	−5.40833	−	9.36750i	−0.182835	−	0.316679i
$876$	−0.348612	−	0.603814i	−0.0117785	−	0.0204010i
$877$	15.3625	+	26.6086i	0.518754	+	0.898509i	0.999763	+	0.0217929i	$0.00693744\pi$
$877$	15.3625	+	26.6086i	0.518754	+	0.898509i	−0.481008	+	0.876716i	$0.659729\pi$
$878$	14.4222	−	24.9800i	0.486726	−	0.843034i
$879$	1.81665			0.0612742
$880$	−6.10555	+	10.5751i	−0.205818	+	0.356487i
$881$	−11.7250			−0.395025			−0.197512	−	0.980300i	$-0.563286\pi$
$881$	−11.7250			−0.395025			−0.197512	+	0.980300i	$0.563286\pi$
$882$	3.00000	+	5.19615i	0.101015	+	0.174964i
$883$	−7.65139	−	13.2526i	−0.257490	−	0.445985i	0.708079	−	0.706133i	$-0.249562\pi$
$883$	−7.65139	−	13.2526i	−0.257490	−	0.445985i	−0.965569	+	0.260148i	$0.916229\pi$
$884$	20.7250			0.697057
$885$	−28.3305			−0.952320
$886$	14.2111	+	24.6144i	0.477431	+	0.826935i
$887$	−25.9361			−0.870848			−0.435424	−	0.900225i	$-0.643402\pi$
$887$	−25.9361			−0.870848			−0.435424	+	0.900225i	$0.643402\pi$
$888$	−5.30278			−0.177949
$889$	−7.21110	+	8.66025i	−0.241853	+	0.290456i
$890$	−3.48612			−0.116855
$891$	−5.30278			−0.177650
$892$	−11.2111	−	19.4182i	−0.375375	−	0.650169i
$893$	1.93608			0.0647886
$894$	−5.11943			−0.171219
$895$	−12.6653	−	21.9369i	−0.423353	−	0.733269i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	16.8167			0.561492
$898$	−0.908327	+	1.57327i	−0.0303113	+	0.0525006i
$899$	2.39445			0.0798593
$900$	−0.151388	+	0.262211i	−0.00504626	+	0.00874038i
$901$	−33.9083	−	58.7309i	−1.12965	−	1.95661i
$902$	−4.25694	−	7.37323i	−0.141741	−	0.245502i
$903$	6.10555	+	10.5751i	0.203180	+	0.351918i
$904$	−0.651388	−	1.12824i	−0.0216648	−	0.0375246i
$905$	5.78890			0.192429
$906$	6.19722	−	10.7339i	0.205889	−	0.356610i
$907$	12.0736	−	20.9121i	0.400897	−	0.694374i	−0.592937	−	0.805249i	$-0.702032\pi$
$907$	12.0736	−	20.9121i	0.400897	−	0.694374i	0.993834	+	0.110875i	$0.0353652\pi$
$908$	−13.2111			−0.438426
$909$	0.908327			0.0301273
$910$	3.45416	−	5.98279i	0.114504	−	0.198327i
$911$	13.5000	−	23.3827i	0.447275	−	0.774703i	−0.550933	−	0.834550i	$-0.685728\pi$
$911$	13.5000	−	23.3827i	0.447275	−	0.774703i	0.998208	+	0.0598468i	$0.0190612\pi$
$912$	2.45416	+	4.25074i	0.0812655	+	0.140756i
$913$	−43.5416	−	75.4163i	−1.44102	−	2.49592i
$914$	7.69722			0.254602
$915$	6.10555	+	10.5751i	0.201843	+	0.349603i
$916$	4.30278			0.142168
$917$	−8.21110	−	14.2220i	−0.271154	−	0.469653i
$918$	−3.45416	+	5.98279i	−0.114004	+	0.197461i
$919$	−1.03196	−	1.78740i	−0.0340412	−	0.0589610i	0.848503	−	0.529191i	$-0.177504\pi$
$919$	−1.03196	−	1.78740i	−0.0340412	−	0.0589610i	−0.882544	+	0.470230i	$0.844171\pi$
$920$	6.45416	+	11.1789i	0.212787	+	0.368559i
$921$	15.3028			0.504244
$922$	−38.4500			−1.26628
$923$	17.4083	−	30.1521i	0.573002	−	0.992469i
$924$	2.65139	+	4.59234i	0.0872243	+	0.151077i
$925$	0.802776	−	1.39045i	0.0263951	−	0.0457177i
$926$	9.50000	−	16.4545i	0.312189	−	0.540728i
$927$	−1.30278			−0.0427888
$928$	−0.151388	+	0.262211i	−0.00496955	+	0.00860751i
$929$	−49.6972			−1.63051			−0.815257	−	0.579100i	$-0.803404\pi$
$929$	−49.6972			−1.63051			−0.815257	+	0.579100i	$0.803404\pi$
$930$	9.10555	−	15.7713i	0.298583	−	0.517161i
$931$	−14.7250	+	25.5044i	−0.482592	+	0.835873i
$932$	0.605551	−	1.04885i	0.0198355	−	0.0343561i
$933$	6.60555	−	11.4412i	0.216256	−	0.374566i
$934$	16.5000	−	28.5788i	0.539896	−	0.935128i
$935$	−42.1791	−	73.0564i	−1.37941	−	2.38920i
$936$	3.00000			0.0980581
$937$	9.34861	+	16.1923i	0.305406	+	0.528978i	0.977352	−	0.211622i	$-0.0678745\pi$
$937$	9.34861	+	16.1923i	0.305406	+	0.528978i	−0.671946	+	0.740600i	$0.734541\pi$
$938$	2.50000	−	4.33013i	0.0816279	−	0.141384i
$939$	17.0278			0.555680
$940$	0.908327			0.0296264
$941$	12.1056	+	20.9674i	0.394630	+	0.683519i	0.993054	−	0.117661i	$-0.0375396\pi$
$941$	12.1056	+	20.9674i	0.394630	+	0.683519i	−0.598424	+	0.801179i	$0.704206\pi$
$942$	−10.8625	+	18.8144i	−0.353919	+	0.613006i
$943$	−9.00000			−0.293080
$944$	−6.15139	+	10.6545i	−0.200211	+	0.346775i
$945$	1.15139	+	1.99426i	0.0374546	+	0.0648734i
$946$	−32.3764	−	56.0775i	−1.05265	−	1.82324i
$947$	13.4680	−	23.3273i	0.437653	−	0.758036i	−0.559855	−	0.828590i	$-0.689143\pi$
$947$	13.4680	−	23.3273i	0.437653	−	0.758036i	0.997508	+	0.0705539i	$0.0224767\pi$
$948$	2.84861	−	4.93394i	0.0925186	−	0.160247i
$949$	−1.04584	−	1.81144i	−0.0339493	−	0.0588019i
$950$	−1.48612			−0.0482162
$951$	−8.40833	−	14.5636i	−0.272659	−	0.472259i
$952$	6.90833			0.223900
$953$	−2.21110			−0.0716246			−0.0358123	−	0.999359i	$-0.511402\pi$
$953$	−2.21110			−0.0716246			−0.0358123	+	0.999359i	$0.511402\pi$
$954$	−4.90833	−	8.50147i	−0.158913	−	0.275245i
$955$	23.5139			0.760891
$956$	−9.90833	−	17.1617i	−0.320458	−	0.555050i
$957$	0.802776	−	1.39045i	0.0259501	−	0.0449468i
$958$	7.89445	−	13.6736i	0.255058	−	0.441774i
$959$	10.2569	+	17.7655i	0.331214	+	0.573679i
$960$	1.15139	+	1.99426i	0.0371609	+	0.0643645i
$961$	−15.7708	+	27.3159i	−0.508736	+	0.881157i
$962$	−15.9083			−0.512905
$963$	−3.80278	+	6.58660i	−0.122543	+	0.212250i
$964$	−5.19722	−	9.00186i	−0.167391	−	0.289930i
$965$	10.6056			0.341405
$966$	5.60555			0.180356
$967$	−14.5139	+	25.1388i	−0.466735	+	0.808408i	−0.999278	−	0.0379944i	$-0.987903\pi$
$967$	−14.5139	+	25.1388i	−0.466735	+	0.808408i	0.532543	+	0.846403i	$0.321236\pi$
$968$	−8.55971	−	14.8259i	−0.275120	−	0.476521i
$969$	−33.9083			−1.08929
$970$	−9.21110	−	15.9541i	−0.295751	−	0.512255i
$971$	16.4680	−	28.5235i	0.528485	−	0.915362i	−0.470964	−	0.882153i	$-0.656094\pi$
$971$	16.4680	−	28.5235i	0.528485	−	0.915362i	0.999448	−	0.0332097i	$-0.0105729\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	5.30278	−	9.18468i	0.169999	−	0.294447i
$974$	−12.4083	+	21.4919i	−0.397588	+	0.688643i
$975$	−0.454163	+	0.786634i	−0.0145449	+	0.0251925i
$976$	5.30278			0.169738
$977$	−17.6056	+	30.4937i	−0.563251	+	0.975580i	0.433959	+	0.900933i	$0.357116\pi$
$977$	−17.6056	+	30.4937i	−0.563251	+	0.975580i	−0.997210	+	0.0746473i	$0.976217\pi$
$978$	−23.4222			−0.748960
$979$	4.01388	−	6.95224i	0.128284	−	0.222195i
$980$	−6.90833	+	11.9656i	−0.220678	+	0.382226i
$981$	1.00000	+	1.73205i	0.0319275	+	0.0553001i
$982$	−5.95416	+	10.3129i	−0.190005	+	0.329098i
$983$	15.1194			0.482235			0.241117	−	0.970496i	$-0.422486\pi$
$983$	15.1194			0.482235			0.241117	+	0.970496i	$0.422486\pi$
$984$	−1.60555			−0.0511831
$985$	17.5139	+	30.3349i	0.558039	+	0.966551i
$986$	−1.04584	−	1.81144i	−0.0333062	−	0.0576881i
$987$	0.197224	−	0.341603i	0.00627772	−	0.0108733i
$988$	7.36249	+	12.7522i	0.234232	+	0.405702i
$989$	−68.4500			−2.17658
$990$	−6.10555	−	10.5751i	−0.194047	−	0.336100i
$991$	−14.3583			−0.456106			−0.228053	−	0.973649i	$-0.573236\pi$
$991$	−14.3583			−0.456106			−0.228053	+	0.973649i	$0.573236\pi$
$992$	−3.95416	−	6.84881i	−0.125545	−	0.217450i
$993$	−4.04584	−	7.00759i	−0.128391	−	0.222379i
$994$	5.80278	−	10.0507i	0.184053	−	0.318789i
$995$	−24.8764	+	43.0871i	−0.788634	+	1.36595i
$996$	−16.4222			−0.520357
$997$	−31.5139			−0.998055			−0.499027	−	0.866586i	$-0.666309\pi$
$997$	−31.5139			−0.998055			−0.499027	+	0.866586i	$0.666309\pi$
$998$	−6.59167	+	11.4171i	−0.208656	+	0.361402i
$999$	2.65139	−	4.59234i	0.0838862	−	0.145295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	762.2.e.c.361.1	yes	4
127.19	even	3	inner	762.2.e.c.19.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
762.2.e.c.19.1	✓	4	127.19	even	3	inner
762.2.e.c.361.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 762 = 2 \cdot 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	762.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} -2.30278 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} -2.30278 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -2.30278 q^{10} +(2.65139 - 4.59234i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.15139 + 1.99426i) q^{15} +1.00000 q^{16} +(-3.45416 + 5.98279i) q^{17} +(-0.500000 + 0.866025i) q^{18} -4.90833 q^{19} -2.30278 q^{20} +(-0.500000 + 0.866025i) q^{21} +(2.65139 - 4.59234i) q^{22} +(-2.80278 - 4.85455i) q^{23} +(-0.500000 - 0.866025i) q^{24} +0.302776 q^{25} +(-1.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-0.151388 + 0.262211i) q^{29} +(1.15139 + 1.99426i) q^{30} +(-3.95416 - 6.84881i) q^{31} +1.00000 q^{32} -5.30278 q^{33} +(-3.45416 + 5.98279i) q^{34} +(1.15139 + 1.99426i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.65139 - 4.59234i) q^{37} -4.90833 q^{38} +(-1.50000 + 2.59808i) q^{39} -2.30278 q^{40} +(0.802776 - 1.39045i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(6.10555 - 10.5751i) q^{43} +(2.65139 - 4.59234i) q^{44} +(1.15139 - 1.99426i) q^{45} +(-2.80278 - 4.85455i) q^{46} -0.394449 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +0.302776 q^{50} +6.90833 q^{51} +(-1.50000 - 2.59808i) q^{52} +(-4.90833 + 8.50147i) q^{53} +1.00000 q^{54} +(-6.10555 + 10.5751i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(2.45416 + 4.25074i) q^{57} +(-0.151388 + 0.262211i) q^{58} +(-6.15139 + 10.6545i) q^{59} +(1.15139 + 1.99426i) q^{60} +5.30278 q^{61} +(-3.95416 - 6.84881i) q^{62} +1.00000 q^{63} +1.00000 q^{64} +(3.45416 + 5.98279i) q^{65} -5.30278 q^{66} +(2.50000 + 4.33013i) q^{67} +(-3.45416 + 5.98279i) q^{68} +(-2.80278 + 4.85455i) q^{69} +(1.15139 + 1.99426i) q^{70} +(5.80278 + 10.0507i) q^{71} +(-0.500000 + 0.866025i) q^{72} +0.697224 q^{73} +(2.65139 - 4.59234i) q^{74} +(-0.151388 - 0.262211i) q^{75} -4.90833 q^{76} -5.30278 q^{77} +(-1.50000 + 2.59808i) q^{78} +(2.84861 + 4.93394i) q^{79} -2.30278 q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.802776 - 1.39045i) q^{82} +(8.21110 - 14.2220i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(7.95416 - 13.7770i) q^{85} +(6.10555 - 10.5751i) q^{86} +0.302776 q^{87} +(2.65139 - 4.59234i) q^{88} +1.51388 q^{89} +(1.15139 - 1.99426i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(-2.80278 - 4.85455i) q^{92} +(-3.95416 + 6.84881i) q^{93} -0.394449 q^{94} +11.3028 q^{95} +(-0.500000 - 0.866025i) q^{96} +(4.00000 + 6.92820i) q^{97} +(3.00000 - 5.19615i) q^{98} +(2.65139 + 4.59234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - 2 q^{10} + 7 q^{11} - 2 q^{12} - 6 q^{13} - 2 q^{14} + q^{15} + 4 q^{16} - 3 q^{17} - 2 q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{21} + 7 q^{22} - 4 q^{23} - 2 q^{24} - 6 q^{25} - 6 q^{26} + 4 q^{27} - 2 q^{28} + 3 q^{29} + q^{30} - 5 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + q^{35} - 2 q^{36} + 7 q^{37} + 2 q^{38} - 6 q^{39} - 2 q^{40} - 4 q^{41} - 2 q^{42} + 10 q^{43} + 7 q^{44} + q^{45} - 4 q^{46} - 16 q^{47} - 2 q^{48} + 12 q^{49} - 6 q^{50} + 6 q^{51} - 6 q^{52} + 2 q^{53} + 4 q^{54} - 10 q^{55} - 2 q^{56} - q^{57} + 3 q^{58} - 21 q^{59} + q^{60} + 14 q^{61} - 5 q^{62} + 4 q^{63} + 4 q^{64} + 3 q^{65} - 14 q^{66} + 10 q^{67} - 3 q^{68} - 4 q^{69} + q^{70} + 16 q^{71} - 2 q^{72} + 10 q^{73} + 7 q^{74} + 3 q^{75} + 2 q^{76} - 14 q^{77} - 6 q^{78} + 15 q^{79} - 2 q^{80} - 2 q^{81} - 4 q^{82} + 4 q^{83} - 2 q^{84} + 21 q^{85} + 10 q^{86} - 6 q^{87} + 7 q^{88} - 30 q^{89} + q^{90} - 6 q^{91} - 4 q^{92} - 5 q^{93} - 16 q^{94} + 38 q^{95} - 2 q^{96} + 16 q^{97} + 12 q^{98} + 7 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 - 2 * q^10 + 7 * q^11 - 2 * q^12 - 6 * q^13 - 2 * q^14 + q^15 + 4 * q^16 - 3 * q^17 - 2 * q^18 + 2 * q^19 - 2 * q^20 - 2 * q^21 + 7 * q^22 - 4 * q^23 - 2 * q^24 - 6 * q^25 - 6 * q^26 + 4 * q^27 - 2 * q^28 + 3 * q^29 + q^30 - 5 * q^31 + 4 * q^32 - 14 * q^33 - 3 * q^34 + q^35 - 2 * q^36 + 7 * q^37 + 2 * q^38 - 6 * q^39 - 2 * q^40 - 4 * q^41 - 2 * q^42 + 10 * q^43 + 7 * q^44 + q^45 - 4 * q^46 - 16 * q^47 - 2 * q^48 + 12 * q^49 - 6 * q^50 + 6 * q^51 - 6 * q^52 + 2 * q^53 + 4 * q^54 - 10 * q^55 - 2 * q^56 - q^57 + 3 * q^58 - 21 * q^59 + q^60 + 14 * q^61 - 5 * q^62 + 4 * q^63 + 4 * q^64 + 3 * q^65 - 14 * q^66 + 10 * q^67 - 3 * q^68 - 4 * q^69 + q^70 + 16 * q^71 - 2 * q^72 + 10 * q^73 + 7 * q^74 + 3 * q^75 + 2 * q^76 - 14 * q^77 - 6 * q^78 + 15 * q^79 - 2 * q^80 - 2 * q^81 - 4 * q^82 + 4 * q^83 - 2 * q^84 + 21 * q^85 + 10 * q^86 - 6 * q^87 + 7 * q^88 - 30 * q^89 + q^90 - 6 * q^91 - 4 * q^92 - 5 * q^93 - 16 * q^94 + 38 * q^95 - 2 * q^96 + 16 * q^97 + 12 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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