LMFDB - Embedded newform 273.2.k.c.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
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			211.3
Root			$0.900969 + 1.56052i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.c.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12349 + 1.94594i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.52446 + 2.64044i) q^{4} +1.69202 q^{5} +(1.12349 - 1.94594i) q^{6} +(-0.500000 + 0.866025i) q^{7} -2.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.12349 + 1.94594i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.52446 + 2.64044i) q^{4} +1.69202 q^{5} +(1.12349 - 1.94594i) q^{6} +(-0.500000 + 0.866025i) q^{7} -2.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.90097 + 3.29257i) q^{10} +(2.64795 + 4.58638i) q^{11} +3.04892 q^{12} +(-3.20291 + 1.65571i) q^{13} -2.24698 q^{14} +(-0.846011 - 1.46533i) q^{15} +(0.400969 + 0.694498i) q^{16} +(1.12349 - 1.94594i) q^{17} -2.24698 q^{18} +(3.74698 - 6.48996i) q^{19} +(-2.57942 + 4.46768i) q^{20} +1.00000 q^{21} +(-5.94989 + 10.3055i) q^{22} +(-3.38135 - 5.85668i) q^{23} +(1.17845 + 2.04113i) q^{24} -2.13706 q^{25} +(-6.82036 - 4.37249i) q^{26} +1.00000 q^{27} +(-1.52446 - 2.64044i) q^{28} +(-3.78232 - 6.55118i) q^{29} +(1.90097 - 3.29257i) q^{30} +3.89977 q^{31} +(-3.25786 + 5.64279i) q^{32} +(2.64795 - 4.58638i) q^{33} +5.04892 q^{34} +(-0.846011 + 1.46533i) q^{35} +(-1.52446 - 2.64044i) q^{36} +(4.78501 + 8.28788i) q^{37} +16.8388 q^{38} +(3.03534 + 1.94594i) q^{39} -3.98792 q^{40} +(-3.49396 - 6.05171i) q^{41} +(1.12349 + 1.94594i) q^{42} +(3.13437 - 5.42890i) q^{43} -16.1468 q^{44} +(-0.846011 + 1.46533i) q^{45} +(7.59783 - 13.1598i) q^{46} -1.70410 q^{47} +(0.400969 - 0.694498i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.40097 - 4.15860i) q^{50} -2.24698 q^{51} +(0.510885 - 10.9812i) q^{52} -4.20775 q^{53} +(1.12349 + 1.94594i) q^{54} +(4.48039 + 7.76026i) q^{55} +(1.17845 - 2.04113i) q^{56} -7.49396 q^{57} +(8.49880 - 14.7204i) q^{58} +(3.13437 - 5.42890i) q^{59} +5.15883 q^{60} +(-3.08211 + 5.33836i) q^{61} +(4.38135 + 7.58873i) q^{62} +(-0.500000 - 0.866025i) q^{63} -13.0368 q^{64} +(-5.41939 + 2.80150i) q^{65} +11.8998 q^{66} +(1.48643 + 2.57457i) q^{67} +(3.42543 + 5.93301i) q^{68} +(-3.38135 + 5.85668i) q^{69} -3.80194 q^{70} +(4.18933 - 7.25614i) q^{71} +(1.17845 - 2.04113i) q^{72} -4.37867 q^{73} +(-10.7518 + 18.6227i) q^{74} +(1.06853 + 1.85075i) q^{75} +(11.4242 + 19.7873i) q^{76} -5.29590 q^{77} +(-0.376510 + 8.09285i) q^{78} +5.40581 q^{79} +(0.678448 + 1.17511i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.85086 - 13.5981i) q^{82} +0.131687 q^{83} +(-1.52446 + 2.64044i) q^{84} +(1.90097 - 3.29257i) q^{85} +14.0858 q^{86} +(-3.78232 + 6.55118i) q^{87} +(-6.24094 - 10.8096i) q^{88} +(2.94504 + 5.10096i) q^{89} -3.80194 q^{90} +(0.167563 - 3.60166i) q^{91} +20.6189 q^{92} +(-1.94989 - 3.37730i) q^{93} +(-1.91454 - 3.31608i) q^{94} +(6.33997 - 10.9812i) q^{95} +6.51573 q^{96} +(0.187177 - 0.324200i) q^{97} +(1.12349 - 1.94594i) q^{98} -5.29590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} + 2 q^{11} - 6 q^{13} - 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 13 q^{19} - 7 q^{20} + 6 q^{21} - 13 q^{22} - 3 q^{23} + 3 q^{24} - 2 q^{25} - 4 q^{26} + 6 q^{27} - q^{29} + 7 q^{30} - 22 q^{31} - 7 q^{32} + 2 q^{33} + 12 q^{34} + 4 q^{37} + 36 q^{38} + 6 q^{39} + 14 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 42 q^{44} + 9 q^{46} - 38 q^{47} - 2 q^{48} - 3 q^{49} - 10 q^{50} - 4 q^{51} + 10 q^{53} + 2 q^{54} + 14 q^{55} + 3 q^{56} - 26 q^{57} + 10 q^{58} + 11 q^{59} + 14 q^{60} - 7 q^{61} + 9 q^{62} - 3 q^{63} - 22 q^{64} + 26 q^{66} + 15 q^{67} + 7 q^{68} - 3 q^{69} - 14 q^{70} + 18 q^{71} + 3 q^{72} - 12 q^{73} - 33 q^{74} + q^{75} + 14 q^{76} - 4 q^{77} - 7 q^{78} + 6 q^{79} - 3 q^{81} + 20 q^{82} - 4 q^{83} + 7 q^{85} + 10 q^{86} - q^{87} - 9 q^{88} + 17 q^{89} - 14 q^{90} + 56 q^{92} + 11 q^{93} - q^{94} + 14 q^{95} + 14 q^{96} + 13 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 + 2 * q^11 - 6 * q^13 - 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 13 * q^19 - 7 * q^20 + 6 * q^21 - 13 * q^22 - 3 * q^23 + 3 * q^24 - 2 * q^25 - 4 * q^26 + 6 * q^27 - q^29 + 7 * q^30 - 22 * q^31 - 7 * q^32 + 2 * q^33 + 12 * q^34 + 4 * q^37 + 36 * q^38 + 6 * q^39 + 14 * q^40 - 2 * q^41 + 2 * q^42 + 11 * q^43 - 42 * q^44 + 9 * q^46 - 38 * q^47 - 2 * q^48 - 3 * q^49 - 10 * q^50 - 4 * q^51 + 10 * q^53 + 2 * q^54 + 14 * q^55 + 3 * q^56 - 26 * q^57 + 10 * q^58 + 11 * q^59 + 14 * q^60 - 7 * q^61 + 9 * q^62 - 3 * q^63 - 22 * q^64 + 26 * q^66 + 15 * q^67 + 7 * q^68 - 3 * q^69 - 14 * q^70 + 18 * q^71 + 3 * q^72 - 12 * q^73 - 33 * q^74 + q^75 + 14 * q^76 - 4 * q^77 - 7 * q^78 + 6 * q^79 - 3 * q^81 + 20 * q^82 - 4 * q^83 + 7 * q^85 + 10 * q^86 - q^87 - 9 * q^88 + 17 * q^89 - 14 * q^90 + 56 * q^92 + 11 * q^93 - q^94 + 14 * q^95 + 14 * q^96 + 13 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.12349	+	1.94594i	0.794427	+	1.37599i	0.923202	+	0.384315i	$0.125562\pi$
$2$	1.12349	+	1.94594i	0.794427	+	1.37599i	−0.128775	+	0.991674i	$0.541104\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.52446	+	2.64044i	−0.762229	+	1.32022i
$5$	1.69202			0.756695			0.378348	−	0.925664i	$-0.376492\pi$
$5$	1.69202			0.756695			0.378348	+	0.925664i	$0.376492\pi$
$6$	1.12349	−	1.94594i	0.458663	−	0.794427i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−2.35690			−0.833289
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.90097	+	3.29257i	0.601139	+	1.04120i
$11$	2.64795	+	4.58638i	0.798387	+	1.38285i	0.920666	+	0.390350i	$0.127646\pi$
$11$	2.64795	+	4.58638i	0.798387	+	1.38285i	−0.122280	+	0.992496i	$0.539021\pi$
$12$	3.04892			0.880147
$13$	−3.20291	+	1.65571i	−0.888326	+	0.459212i
$13$	−3.20291	+	1.65571i	−0.888326	+	0.459212i
$14$	−2.24698			−0.600531
$15$	−0.846011	−	1.46533i	−0.218439	−	0.378348i
$16$	0.400969	+	0.694498i	0.100242	+	0.173625i
$17$	1.12349	−	1.94594i	0.272486	−	0.471960i	−0.697012	−	0.717060i	$-0.745487\pi$
$17$	1.12349	−	1.94594i	0.272486	−	0.471960i	0.969498	+	0.245100i	$0.0788207\pi$
$18$	−2.24698			−0.529618
$19$	3.74698	−	6.48996i	0.859616	−	1.48890i	−0.0126794	−	0.999920i	$-0.504036\pi$
$19$	3.74698	−	6.48996i	0.859616	−	1.48890i	0.872295	−	0.488979i	$-0.162631\pi$
$20$	−2.57942	+	4.46768i	−0.576775	+	0.999004i
$21$	1.00000			0.218218
$22$	−5.94989	+	10.3055i	−1.26852	+	2.19714i
$23$	−3.38135	−	5.85668i	−0.705061	−	1.22120i	−0.966669	−	0.256028i	$-0.917586\pi$
$23$	−3.38135	−	5.85668i	−0.705061	−	1.22120i	0.261608	−	0.965174i	$-0.415747\pi$
$24$	1.17845	+	2.04113i	0.240550	+	0.416644i
$25$	−2.13706			−0.427413
$26$	−6.82036	−	4.37249i	−1.33758	−	0.857516i
$27$	1.00000			0.192450
$28$	−1.52446	−	2.64044i	−0.288096	−	0.498996i
$29$	−3.78232	−	6.55118i	−0.702360	−	1.21652i	−0.967636	−	0.252350i	$-0.918796\pi$
$29$	−3.78232	−	6.55118i	−0.702360	−	1.21652i	0.265276	−	0.964172i	$-0.414537\pi$
$30$	1.90097	−	3.29257i	0.347068	−	0.601139i
$31$	3.89977			0.700420			0.350210	−	0.936671i	$-0.386110\pi$
$31$	3.89977			0.700420			0.350210	+	0.936671i	$0.386110\pi$
$32$	−3.25786	+	5.64279i	−0.575915	+	0.997513i
$33$	2.64795	−	4.58638i	0.460949	−	0.798387i
$34$	5.04892			0.865882
$35$	−0.846011	+	1.46533i	−0.143002	+	0.247687i
$36$	−1.52446	−	2.64044i	−0.254076	−	0.440073i
$37$	4.78501	+	8.28788i	0.786651	+	1.36252i	0.928008	+	0.372561i	$0.121520\pi$
$37$	4.78501	+	8.28788i	0.786651	+	1.36252i	−0.141357	+	0.989959i	$0.545146\pi$
$38$	16.8388			2.73161
$39$	3.03534	+	1.94594i	0.486044	+	0.311600i
$40$	−3.98792			−0.630545
$41$	−3.49396	−	6.05171i	−0.545665	−	0.945119i	−0.998565	−	0.0535578i	$-0.982944\pi$
$41$	−3.49396	−	6.05171i	−0.545665	−	0.945119i	0.452900	−	0.891561i	$-0.350389\pi$
$42$	1.12349	+	1.94594i	0.173358	+	0.300265i
$43$	3.13437	−	5.42890i	0.477988	−	0.827899i	−0.521694	−	0.853133i	$-0.674700\pi$
$43$	3.13437	−	5.42890i	0.477988	−	0.827899i	0.999682	+	0.0252338i	$0.00803301\pi$
$44$	−16.1468			−2.43421
$45$	−0.846011	+	1.46533i	−0.126116	+	0.218439i
$46$	7.59783	−	13.1598i	1.12024	−	1.94031i
$47$	−1.70410			−0.248569			−0.124284	−	0.992247i	$-0.539664\pi$
$47$	−1.70410			−0.248569			−0.124284	+	0.992247i	$0.539664\pi$
$48$	0.400969	−	0.694498i	0.0578749	−	0.100242i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.40097	−	4.15860i	−0.339548	−	0.588115i
$51$	−2.24698			−0.314640
$52$	0.510885	−	10.9812i	0.0708470	−	1.52281i
$53$	−4.20775			−0.577979			−0.288990	−	0.957332i	$-0.593319\pi$
$53$	−4.20775			−0.577979			−0.288990	+	0.957332i	$0.593319\pi$
$54$	1.12349	+	1.94594i	0.152888	+	0.264809i
$55$	4.48039	+	7.76026i	0.604135	+	1.04639i
$56$	1.17845	−	2.04113i	0.157477	−	0.272758i
$57$	−7.49396			−0.992599
$58$	8.49880	−	14.7204i	1.11595	−	1.93288i
$59$	3.13437	−	5.42890i	0.408061	−	0.706782i	−0.586612	−	0.809868i	$-0.699538\pi$
$59$	3.13437	−	5.42890i	0.408061	−	0.706782i	0.994672	+	0.103086i	$0.0328718\pi$
$60$	5.15883			0.666003
$61$	−3.08211	+	5.33836i	−0.394623	+	0.683507i	−0.993053	−	0.117668i	$-0.962458\pi$
$61$	−3.08211	+	5.33836i	−0.394623	+	0.683507i	0.598430	+	0.801175i	$0.295792\pi$
$62$	4.38135	+	7.58873i	0.556433	+	0.963770i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	−13.0368			−1.62960
$65$	−5.41939	+	2.80150i	−0.672192	+	0.347484i
$66$	11.8998			1.46476
$67$	1.48643	+	2.57457i	0.181596	+	0.314533i	0.942424	−	0.334420i	$-0.108540\pi$
$67$	1.48643	+	2.57457i	0.181596	+	0.314533i	−0.760828	+	0.648953i	$0.775207\pi$
$68$	3.42543	+	5.93301i	0.415394	+	0.719484i
$69$	−3.38135	+	5.85668i	−0.407067	+	0.705061i
$70$	−3.80194			−0.454418
$71$	4.18933	−	7.25614i	0.497182	−	0.861145i	−0.502812	−	0.864396i	$-0.667701\pi$
$71$	4.18933	−	7.25614i	0.497182	−	0.861145i	0.999995	+	0.00325048i	$0.00103466\pi$
$72$	1.17845	−	2.04113i	0.138881	−	0.240550i
$73$	−4.37867			−0.512484			−0.256242	−	0.966613i	$-0.582484\pi$
$73$	−4.37867			−0.512484			−0.256242	+	0.966613i	$0.582484\pi$
$74$	−10.7518	+	18.6227i	−1.24987	+	2.16485i
$75$	1.06853	+	1.85075i	0.123383	+	0.213706i
$76$	11.4242	+	19.7873i	1.31045	+	2.26976i
$77$	−5.29590			−0.603523
$78$	−0.376510	+	8.09285i	−0.0426314	+	0.916334i
$79$	5.40581			0.608202			0.304101	−	0.952640i	$-0.401644\pi$
$79$	5.40581			0.608202			0.304101	+	0.952640i	$0.401644\pi$
$80$	0.678448	+	1.17511i	0.0758528	+	0.131381i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.85086	−	13.5981i	0.866982	−	1.50166i
$83$	0.131687			0.0144545			0.00722724	−	0.999974i	$-0.497699\pi$
$83$	0.131687			0.0144545			0.00722724	+	0.999974i	$0.497699\pi$
$84$	−1.52446	+	2.64044i	−0.166332	+	0.288096i
$85$	1.90097	−	3.29257i	0.206189	−	0.357130i
$86$	14.0858			1.51891
$87$	−3.78232	+	6.55118i	−0.405508	+	0.702360i
$88$	−6.24094	−	10.8096i	−0.665286	−	1.15231i
$89$	2.94504	+	5.10096i	0.312174	+	0.540701i	0.978833	−	0.204662i	$-0.0656095\pi$
$89$	2.94504	+	5.10096i	0.312174	+	0.540701i	−0.666659	+	0.745363i	$0.732276\pi$
$90$	−3.80194			−0.400759
$91$	0.167563	−	3.60166i	0.0175654	−	0.377556i
$92$	20.6189			2.14967
$93$	−1.94989	−	3.37730i	−0.202194	−	0.350210i
$94$	−1.91454	−	3.31608i	−0.197470	−	0.342028i
$95$	6.33997	−	10.9812i	0.650467	−	1.12664i
$96$	6.51573			0.665009
$97$	0.187177	−	0.324200i	0.0190050	−	0.0329176i	−0.856367	−	0.516368i	$-0.827284\pi$
$97$	0.187177	−	0.324200i	0.0190050	−	0.0329176i	0.875371	+	0.483451i	$0.160617\pi$
$98$	1.12349	−	1.94594i	0.113490	−	0.196570i
$99$	−5.29590			−0.532258
$100$	3.25786	−	5.64279i	0.325786	−	0.564279i
$101$	7.01238	+	12.1458i	0.697758	+	1.20855i	0.969242	+	0.246109i	$0.0791521\pi$
$101$	7.01238	+	12.1458i	0.697758	+	1.20855i	−0.271485	+	0.962443i	$0.587515\pi$
$102$	−2.52446	−	4.37249i	−0.249959	−	0.432941i
$103$	−14.9215			−1.47026			−0.735132	−	0.677924i	$-0.762880\pi$
$103$	−14.9215			−1.47026			−0.735132	+	0.677924i	$0.762880\pi$
$104$	7.54892	−	3.90235i	0.740232	−	0.382656i
$105$	1.69202			0.165124
$106$	−4.72737	−	8.18804i	−0.459162	−	0.795292i
$107$	−4.06734	−	7.04483i	−0.393204	−	0.681050i	0.599666	−	0.800250i	$-0.295300\pi$
$107$	−4.06734	−	7.04483i	−0.393204	−	0.681050i	−0.992870	+	0.119201i	$0.961967\pi$
$108$	−1.52446	+	2.64044i	−0.146691	+	0.254076i
$109$	−7.86294			−0.753133			−0.376566	−	0.926390i	$-0.622895\pi$
$109$	−7.86294			−0.753133			−0.376566	+	0.926390i	$0.622895\pi$
$110$	−10.0673	+	17.4371i	−0.959883	+	1.66257i
$111$	4.78501	−	8.28788i	0.454173	−	0.786651i
$112$	−0.801938			−0.0757760
$113$	−3.05011	+	5.28295i	−0.286931	+	0.496978i	−0.973076	−	0.230487i	$-0.925968\pi$
$113$	−3.05011	+	5.28295i	−0.286931	+	0.496978i	0.686145	+	0.727465i	$0.259302\pi$
$114$	−8.41939	−	14.5828i	−0.788548	−	1.36580i
$115$	−5.72132	−	9.90962i	−0.533516	−	0.924077i
$116$	23.0640			2.14144
$117$	0.167563	−	3.60166i	0.0154912	−	0.332973i
$118$	14.0858			1.29670
$119$	1.12349	+	1.94594i	0.102990	+	0.178384i
$120$	1.99396	+	3.45364i	0.182023	+	0.315273i
$121$	−8.52326	+	14.7627i	−0.774842	+	1.34207i
$122$	−13.8509			−1.25400
$123$	−3.49396	+	6.05171i	−0.315040	+	0.545665i
$124$	−5.94504	+	10.2971i	−0.533881	+	0.924708i
$125$	−12.0761			−1.08012
$126$	1.12349	−	1.94594i	0.100088	−	0.173358i
$127$	10.0538	+	17.4136i	0.892127	+	1.54521i	0.837320	+	0.546712i	$0.184121\pi$
$127$	10.0538	+	17.4136i	0.892127	+	1.54521i	0.0548067	+	0.998497i	$0.482546\pi$
$128$	−8.13102	−	14.0833i	−0.718688	−	1.24480i
$129$	−6.26875			−0.551933
$130$	−11.5402	−	7.39835i	−1.01214	−	0.648878i
$131$	−3.69202			−0.322573			−0.161287	−	0.986908i	$-0.551564\pi$
$131$	−3.69202			−0.322573			−0.161287	+	0.986908i	$0.551564\pi$
$132$	8.07338	+	13.9835i	0.702697	+	1.21711i
$133$	3.74698	+	6.48996i	0.324904	+	0.562751i
$134$	−3.33997	+	5.78500i	−0.288529	+	0.499748i
$135$	1.69202			0.145626
$136$	−2.64795	+	4.58638i	−0.227060	+	0.393279i
$137$	0.923272	−	1.59915i	0.0788804	−	0.136625i	−0.823887	−	0.566754i	$-0.808199\pi$
$137$	0.923272	−	1.59915i	0.0788804	−	0.136625i	0.902767	+	0.430130i	$0.141532\pi$
$138$	−15.1957			−1.29354
$139$	7.25451	−	12.5652i	0.615320	−	1.06576i	−0.375009	−	0.927021i	$-0.622360\pi$
$139$	7.25451	−	12.5652i	0.615320	−	1.06576i	0.990328	−	0.138744i	$-0.0443064\pi$
$140$	−2.57942	−	4.46768i	−0.218001	−	0.377588i
$141$	0.852052	+	1.47580i	0.0717557	+	0.124284i
$142$	18.8267			1.57990
$143$	−16.0749	−	10.3055i	−1.34425	−	0.861790i
$144$	−0.801938			−0.0668281
$145$	−6.39977	−	11.0847i	−0.531472	−	0.920537i
$146$	−4.91939	−	8.52063i	−0.407131	−	0.705172i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$	−29.1782			−2.39843
$149$	−6.20291	+	10.7437i	−0.508162	+	0.880162i	0.491793	+	0.870712i	$0.336342\pi$
$149$	−6.20291	+	10.7437i	−0.508162	+	0.880162i	−0.999955	+	0.00945034i	$0.996992\pi$
$150$	−2.40097	+	4.15860i	−0.196038	+	0.339548i
$151$	1.32975			0.108213			0.0541067	−	0.998535i	$-0.482769\pi$
$151$	1.32975			0.108213			0.0541067	+	0.998535i	$0.482769\pi$
$152$	−8.83124	+	15.2962i	−0.716308	+	1.24068i
$153$	1.12349	+	1.94594i	0.0908288	+	0.157320i
$154$	−5.94989	−	10.3055i	−0.479455	−	0.830441i
$155$	6.59850			0.530004
$156$	−9.76540	+	5.04814i	−0.781858	+	0.404174i
$157$	−8.43727			−0.673368			−0.336684	−	0.941618i	$-0.609305\pi$
$157$	−8.43727			−0.673368			−0.336684	+	0.941618i	$0.609305\pi$
$158$	6.07338	+	10.5194i	0.483172	+	0.836878i
$159$	2.10388	+	3.64402i	0.166848	+	0.288990i
$160$	−5.51238	+	9.54772i	−0.435792	+	0.754813i
$161$	6.76271			0.532976
$162$	1.12349	−	1.94594i	0.0882697	−	0.152888i
$163$	−7.09179	+	12.2833i	−0.555472	+	0.962106i	0.442394	+	0.896821i	$0.354129\pi$
$163$	−7.09179	+	12.2833i	−0.555472	+	0.962106i	−0.997867	+	0.0652854i	$0.979204\pi$
$164$	21.3056			1.66369
$165$	4.48039	−	7.76026i	0.348798	−	0.604135i
$166$	0.147948	+	0.256254i	0.0114830	+	0.0198892i
$167$	−4.43900	−	7.68858i	−0.343500	−	0.594960i	0.641580	−	0.767056i	$-0.278279\pi$
$167$	−4.43900	−	7.68858i	−0.343500	−	0.594960i	−0.985080	+	0.172096i	$0.944946\pi$
$168$	−2.35690			−0.181838
$169$	7.51722	−	10.6062i	0.578248	−	0.815861i
$170$	8.54288			0.655209
$171$	3.74698	+	6.48996i	0.286539	+	0.496300i
$172$	9.55645	+	16.5523i	0.728672	+	1.26210i
$173$	12.1615	−	21.0644i	0.924623	−	1.60149i	0.132458	−	0.991189i	$-0.457713\pi$
$173$	12.1615	−	21.0644i	0.924623	−	1.60149i	0.792166	−	0.610306i	$-0.208954\pi$
$174$	−16.9976			−1.28859
$175$	1.06853	−	1.85075i	0.0807734	−	0.139904i
$176$	−2.12349	+	3.67799i	−0.160064	+	0.277239i
$177$	−6.26875			−0.471188
$178$	−6.61745	+	11.4618i	−0.495999	+	0.859095i
$179$	6.43512	+	11.1459i	0.480983	+	0.833087i	0.999762	−	0.0218213i	$-0.00694648\pi$
$179$	6.43512	+	11.1459i	0.480983	+	0.833087i	−0.518779	+	0.854909i	$0.673613\pi$
$180$	−2.57942	−	4.46768i	−0.192258	−	0.333001i
$181$	9.25667			0.688043			0.344021	−	0.938962i	$-0.388211\pi$
$181$	9.25667			0.688043			0.344021	+	0.938962i	$0.388211\pi$
$182$	7.19687	−	3.72036i	0.533467	−	0.275771i
$183$	6.16421			0.455672
$184$	7.96950	+	13.8036i	0.587519	+	1.01761i
$185$	8.09634	+	14.0233i	0.595255	+	1.03101i
$186$	4.38135	−	7.58873i	0.321257	−	0.556433i
$187$	11.8998			0.870198
$188$	2.59783	−	4.49958i	0.189467	−	0.328166i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	28.4916			2.06700
$191$	1.68933	−	2.92601i	0.122236	−	0.211719i	−0.798413	−	0.602110i	$-0.794327\pi$
$191$	1.68933	−	2.92601i	0.122236	−	0.211719i	0.920649	+	0.390391i	$0.127660\pi$
$192$	6.51842	+	11.2902i	0.470426	+	0.814802i
$193$	12.4574	+	21.5769i	0.896705	+	1.55314i	0.831681	+	0.555254i	$0.187379\pi$
$193$	12.4574	+	21.5769i	0.896705	+	1.55314i	0.0650240	+	0.997884i	$0.479288\pi$
$194$	0.841166			0.0603922
$195$	5.13587	+	3.29257i	0.367787	+	0.235786i
$196$	3.04892			0.217780
$197$	−8.41454	−	14.5744i	−0.599511	−	1.03838i	−0.992893	−	0.119009i	$-0.962028\pi$
$197$	−8.41454	−	14.5744i	−0.599511	−	1.03838i	0.393382	−	0.919375i	$-0.371305\pi$
$198$	−5.94989	−	10.3055i	−0.422840	−	0.732380i
$199$	−8.15010	+	14.1164i	−0.577746	+	1.00068i	0.417992	+	0.908451i	$0.362734\pi$
$199$	−8.15010	+	14.1164i	−0.577746	+	1.00068i	−0.995737	+	0.0922339i	$0.970599\pi$
$200$	5.03684			0.356158
$201$	1.48643	−	2.57457i	0.104844	−	0.181596i
$202$	−15.7567	+	27.2914i	−1.10864	+	1.92021i
$203$	7.56465			0.530934
$204$	3.42543	−	5.93301i	0.239828	−	0.415394i
$205$	−5.91185	−	10.2396i	−0.412902	−	0.715167i
$206$	−16.7642	−	29.0364i	−1.16802	−	2.02307i
$207$	6.76271			0.470041
$208$	−2.43416	−	1.56052i	−0.168778	−	0.108203i
$209$	39.6872			2.74522
$210$	1.90097	+	3.29257i	0.131179	+	0.227209i
$211$	6.76540	+	11.7180i	0.465749	+	0.806701i	0.999235	−	0.0391078i	$-0.0124516\pi$
$211$	6.76540	+	11.7180i	0.465749	+	0.806701i	−0.533486	+	0.845809i	$0.679118\pi$
$212$	6.41454	−	11.1103i	0.440553	−	0.763059i
$213$	−8.37867			−0.574097
$214$	9.13922	−	15.8296i	0.624744	−	1.08209i
$215$	5.30343	−	9.18581i	0.361691	−	0.626467i
$216$	−2.35690			−0.160366
$217$	−1.94989	+	3.37730i	−0.132367	+	0.229266i
$218$	−8.83393	−	15.3008i	−0.598309	−	1.03630i
$219$	2.18933	+	3.79204i	0.147941	+	0.256242i
$220$	−27.3207			−1.84196
$221$	−0.376510	+	8.09285i	−0.0253268	+	0.544384i
$222$	21.5036			1.44323
$223$	4.80798	+	8.32766i	0.321966	+	0.557662i	0.980894	−	0.194545i	$-0.0623230\pi$
$223$	4.80798	+	8.32766i	0.321966	+	0.557662i	−0.658928	+	0.752206i	$0.728990\pi$
$224$	−3.25786	−	5.64279i	−0.217675	−	0.377025i
$225$	1.06853	−	1.85075i	0.0712354	−	0.123383i
$226$	−13.7071			−0.911782
$227$	−5.66905	+	9.81909i	−0.376268	+	0.651716i	−0.990516	−	0.137397i	$-0.956126\pi$
$227$	−5.66905	+	9.81909i	−0.376268	+	0.651716i	0.614248	+	0.789113i	$0.289460\pi$
$228$	11.4242	−	19.7873i	0.756588	−	1.31045i
$229$	−5.28083			−0.348967			−0.174484	−	0.984660i	$-0.555826\pi$
$229$	−5.28083			−0.348967			−0.174484	+	0.984660i	$0.555826\pi$
$230$	12.8557	−	22.2667i	0.847680	−	1.46822i
$231$	2.64795	+	4.58638i	0.174222	+	0.301762i
$232$	8.91454	+	15.4404i	0.585268	+	1.01371i
$233$	3.09783			0.202946			0.101473	−	0.994838i	$-0.467644\pi$
$233$	3.09783			0.202946			0.101473	+	0.994838i	$0.467644\pi$
$234$	7.19687	−	3.72036i	0.470474	−	0.243207i
$235$	−2.88338			−0.188091
$236$	9.55645	+	16.5523i	0.622072	+	1.07746i
$237$	−2.70291	−	4.68157i	−0.175573	−	0.304101i
$238$	−2.52446	+	4.37249i	−0.163636	+	0.283426i
$239$	10.7138			0.693018			0.346509	−	0.938047i	$-0.387367\pi$
$239$	10.7138			0.693018			0.346509	+	0.938047i	$0.387367\pi$
$240$	0.678448	−	1.17511i	0.0437936	−	0.0758528i
$241$	−8.11410	+	14.0540i	−0.522675	+	0.905300i	0.476977	+	0.878916i	$0.341733\pi$
$241$	−8.11410	+	14.0540i	−0.522675	+	0.905300i	−0.999652	+	0.0263837i	$0.991601\pi$
$242$	−38.3032			−2.46222
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−9.39708	−	16.2762i	−0.601587	−	1.04198i
$245$	−0.846011	−	1.46533i	−0.0540496	−	0.0936167i
$246$	−15.7017			−1.00110
$247$	−1.25571	+	26.9907i	−0.0798988	+	1.71737i
$248$	−9.19136			−0.583652
$249$	−0.0658433	−	0.114044i	−0.00417265	−	0.00722724i
$250$	−13.5673	−	23.4993i	−0.858074	−	1.48623i
$251$	10.9717	−	19.0035i	0.692525	−	1.19949i	−0.278483	−	0.960441i	$-0.589832\pi$
$251$	10.9717	−	19.0035i	0.692525	−	1.19949i	0.971008	−	0.239047i	$-0.0768350\pi$
$252$	3.04892			0.192064
$253$	17.9073	−	31.0164i	1.12582	−	1.94998i
$254$	−22.5906	+	39.1281i	−1.41746	+	2.45511i
$255$	−3.80194			−0.238087
$256$	5.23341	−	9.06453i	0.327088	−	0.566533i
$257$	−10.7714	−	18.6567i	−0.671904	−	1.16377i	−0.977364	−	0.211567i	$-0.932143\pi$
$257$	−10.7714	−	18.6567i	−0.671904	−	1.16377i	0.305460	−	0.952205i	$-0.401190\pi$
$258$	−7.04288	−	12.1986i	−0.438470	−	0.759453i
$259$	−9.57002			−0.594652
$260$	0.864429	−	18.5803i	0.0536096	−	1.15230i
$261$	7.56465			0.468240
$262$	−4.14795	−	7.18446i	−0.256261	−	0.443857i
$263$	6.27748	+	10.8729i	0.387086	+	0.670453i	0.992056	−	0.125796i	$-0.0401483\pi$
$263$	6.27748	+	10.8729i	0.387086	+	0.670453i	−0.604970	+	0.796248i	$0.706815\pi$
$264$	−6.24094	+	10.8096i	−0.384103	+	0.665286i
$265$	−7.11960			−0.437354
$266$	−8.41939	+	14.5828i	−0.516226	+	0.894129i
$267$	2.94504	−	5.10096i	0.180234	−	0.312174i
$268$	−9.06398			−0.553671
$269$	−0.358092	+	0.620234i	−0.0218333	+	0.0378163i	−0.876736	−	0.480973i	$-0.840284\pi$
$269$	−0.358092	+	0.620234i	−0.0218333	+	0.0378163i	0.854902	+	0.518789i	$0.173617\pi$
$270$	1.90097	+	3.29257i	0.115689	+	0.200380i
$271$	−2.50753	−	4.34317i	−0.152322	−	0.263829i	0.779759	−	0.626080i	$-0.215342\pi$
$271$	−2.50753	−	4.34317i	−0.152322	−	0.263829i	−0.932081	+	0.362251i	$0.882008\pi$
$272$	1.80194			0.109259
$273$	−3.20291	+	1.65571i	−0.193849	+	0.100208i
$274$	4.14914			0.250659
$275$	−5.65883	−	9.80139i	−0.341241	−	0.591046i
$276$	−10.3095	−	17.8565i	−0.620557	−	1.07484i
$277$	5.26875	−	9.12574i	0.316568	−	0.548313i	−0.663201	−	0.748441i	$-0.730803\pi$
$277$	5.26875	−	9.12574i	0.316568	−	0.548313i	0.979770	+	0.200128i	$0.0641360\pi$
$278$	32.6015			1.95531
$279$	−1.94989	+	3.37730i	−0.116737	+	0.202194i
$280$	1.99396	−	3.45364i	0.119162	−	0.206394i
$281$	−3.04461			−0.181626			−0.0908130	−	0.995868i	$-0.528947\pi$
$281$	−3.04461			−0.181626			−0.0908130	+	0.995868i	$0.528947\pi$
$282$	−1.91454	+	3.31608i	−0.114009	+	0.197470i
$283$	−2.17845	−	3.77318i	−0.129495	−	0.224292i	0.793986	−	0.607936i	$-0.208002\pi$
$283$	−2.17845	−	3.77318i	−0.129495	−	0.224292i	−0.923481	+	0.383644i	$0.874669\pi$
$284$	12.7729	+	22.1234i	0.757934	+	1.31278i
$285$	−12.6799			−0.751095
$286$	1.99396	−	42.8589i	0.117905	−	2.53430i
$287$	6.98792			0.412484
$288$	−3.25786	−	5.64279i	−0.191972	−	0.332504i
$289$	5.97554	+	10.3499i	0.351502	+	0.608820i
$290$	14.3802	−	24.9072i	0.844432	−	1.46260i
$291$	−0.374354			−0.0219450
$292$	6.67510	−	11.5616i	0.390630	−	0.676592i
$293$	−13.8611	+	24.0081i	−0.809773	+	1.40257i	0.103249	+	0.994656i	$0.467076\pi$
$293$	−13.8611	+	24.0081i	−0.809773	+	1.40257i	−0.913021	+	0.407912i	$0.866257\pi$
$294$	−2.24698			−0.131047
$295$	5.30343	−	9.18581i	0.308778	−	0.534819i
$296$	−11.2778	−	19.5337i	−0.655507	−	1.13537i
$297$	2.64795	+	4.58638i	0.153650	+	0.266129i
$298$	−27.8756			−1.61479
$299$	20.5271	+	13.1598i	1.18712	+	0.761053i
$300$	−6.51573			−0.376186
$301$	3.13437	+	5.42890i	0.180662	+	0.312916i
$302$	1.49396	+	2.58761i	0.0859677	+	0.148900i
$303$	7.01238	−	12.1458i	0.402851	−	0.697758i
$304$	6.00969			0.344679
$305$	−5.21499	+	9.03262i	−0.298609	+	0.517207i
$306$	−2.52446	+	4.37249i	−0.144314	+	0.249959i
$307$	−16.5332			−0.943599			−0.471799	−	0.881706i	$-0.656395\pi$
$307$	−16.5332			−0.943599			−0.471799	+	0.881706i	$0.656395\pi$
$308$	8.07338	−	13.9835i	0.460023	−	0.796784i
$309$	7.46077	+	12.9224i	0.424428	+	0.735132i
$310$	7.41335	+	12.8403i	0.421050	+	0.729280i
$311$	−25.7482			−1.46005			−0.730024	−	0.683421i	$-0.760491\pi$
$311$	−25.7482			−1.46005			−0.730024	+	0.683421i	$0.760491\pi$
$312$	−7.15399	−	4.58638i	−0.405015	−	0.259653i
$313$	−24.1618			−1.36571			−0.682853	−	0.730555i	$-0.739261\pi$
$313$	−24.1618			−1.36571			−0.682853	+	0.730555i	$0.739261\pi$
$314$	−9.47919	−	16.4184i	−0.534942	−	0.926546i
$315$	−0.846011	−	1.46533i	−0.0476673	−	0.0825622i
$316$	−8.24094	+	14.2737i	−0.463589	+	0.802960i
$317$	−4.11423			−0.231078			−0.115539	−	0.993303i	$-0.536860\pi$
$317$	−4.11423			−0.231078			−0.115539	+	0.993303i	$0.536860\pi$
$318$	−4.72737	+	8.18804i	−0.265097	+	0.459162i
$319$	20.0308	−	34.6944i	1.12151	−	1.94251i
$320$	−22.0586			−1.23311
$321$	−4.06734	+	7.04483i	−0.227017	+	0.393204i
$322$	7.59783	+	13.1598i	0.423411	+	0.733369i
$323$	−8.41939	−	14.5828i	−0.468467	−	0.811409i
$324$	3.04892			0.169384
$325$	6.84481	−	3.53837i	0.379682	−	0.196273i
$326$	−31.8702			−1.76513
$327$	3.93147	+	6.80950i	0.217411	+	0.376566i
$328$	8.23490	+	14.2633i	0.454696	+	0.787557i
$329$	0.852052	−	1.47580i	0.0469751	−	0.0813633i
$330$	20.1347			1.10838
$331$	12.4133	−	21.5005i	0.682299	−	1.18178i	−0.291978	−	0.956425i	$-0.594313\pi$
$331$	12.4133	−	21.5005i	0.682299	−	1.18178i	0.974277	−	0.225352i	$-0.0723532\pi$
$332$	−0.200751	+	0.347710i	−0.0110176	+	0.0190831i
$333$	−9.57002			−0.524434
$334$	9.97434	−	17.2761i	0.545772	−	0.945305i
$335$	2.51507	+	4.35622i	0.137413	+	0.238006i
$336$	0.400969	+	0.694498i	0.0218746	+	0.0378880i
$337$	32.7415			1.78354			0.891772	−	0.452484i	$-0.149462\pi$
$337$	32.7415			1.78354			0.891772	+	0.452484i	$0.149462\pi$
$338$	29.0846	+	2.71212i	1.58199	+	0.147520i
$339$	6.10023			0.331319
$340$	5.79590	+	10.0388i	0.314327	+	0.544430i
$341$	10.3264	+	17.8858i	0.559206	+	0.968573i
$342$	−8.41939	+	14.5828i	−0.455268	+	0.788548i
$343$	1.00000			0.0539949
$344$	−7.38740	+	12.7953i	−0.398302	+	0.689879i
$345$	−5.72132	+	9.90962i	−0.308026	+	0.533516i
$346$	54.6534			2.93818
$347$	−0.151301	+	0.262061i	−0.00812226	+	0.0140682i	−0.870058	−	0.492949i	$-0.835919\pi$
$347$	−0.151301	+	0.262061i	−0.00812226	+	0.0140682i	0.861936	+	0.507018i	$0.169252\pi$
$348$	−11.5320	−	19.9740i	−0.618180	−	1.07072i
$349$	−13.9901	−	24.2315i	−0.748872	−	1.29708i	−0.948364	−	0.317184i	$-0.897263\pi$
$349$	−13.9901	−	24.2315i	−0.748872	−	1.29708i	0.199492	−	0.979899i	$-0.436071\pi$
$350$	4.80194			0.256674
$351$	−3.20291	+	1.65571i	−0.170959	+	0.0883755i
$352$	−34.5066			−1.83921
$353$	−0.0621954	−	0.107726i	−0.00331033	−	0.00573365i	0.864365	−	0.502864i	$-0.167720\pi$
$353$	−0.0621954	−	0.107726i	−0.00331033	−	0.00573365i	−0.867676	+	0.497130i	$0.834387\pi$
$354$	−7.04288	−	12.1986i	−0.374325	−	0.648349i
$355$	7.08844	−	12.2775i	0.376215	−	0.651624i
$356$	−17.9584			−0.951792
$357$	1.12349	−	1.94594i	0.0594614	−	0.102990i
$358$	−14.4596	+	25.0447i	−0.764212	+	1.32365i
$359$	20.5241			1.08322			0.541610	−	0.840630i	$-0.317815\pi$
$359$	20.5241			1.08322			0.541610	+	0.840630i	$0.317815\pi$
$360$	1.99396	−	3.45364i	0.105091	−	0.182023i
$361$	−18.5797	−	32.1810i	−0.977880	−	1.69374i
$362$	10.3998	+	18.0129i	0.546600	+	0.946739i
$363$	17.0465			0.894710
$364$	9.25451	+	5.93301i	0.485068	+	0.310974i
$365$	−7.40880			−0.387794
$366$	6.92543	+	11.9952i	0.361998	+	0.626999i
$367$	7.68263	+	13.3067i	0.401030	+	0.694604i	0.993850	−	0.110730i	$-0.0353190\pi$
$367$	7.68263	+	13.3067i	0.401030	+	0.694604i	−0.592821	+	0.805335i	$0.701986\pi$
$368$	2.71164	−	4.69669i	0.141354	−	0.244832i
$369$	6.98792			0.363777
$370$	−18.1923	+	31.5100i	−0.945774	+	1.63813i
$371$	2.10388	−	3.64402i	0.109228	−	0.189188i
$372$	11.8901			0.616472
$373$	2.42596	−	4.20189i	0.125611	−	0.217565i	−0.796360	−	0.604822i	$-0.793244\pi$
$373$	2.42596	−	4.20189i	0.125611	−	0.217565i	0.921972	+	0.387257i	$0.126577\pi$
$374$	13.3693	+	23.1563i	0.691309	+	1.19738i
$375$	6.03803	+	10.4582i	0.311803	+	0.540058i
$376$	4.01639			0.207130
$377$	22.9613	+	14.7204i	1.18257	+	0.758137i
$378$	−2.24698			−0.115572
$379$	2.67456	+	4.63248i	0.137383	+	0.237954i	0.926505	−	0.376282i	$-0.122798\pi$
$379$	2.67456	+	4.63248i	0.137383	+	0.237954i	−0.789122	+	0.614236i	$0.789464\pi$
$380$	19.3300	+	33.4806i	0.991610	+	1.71752i
$381$	10.0538	−	17.4136i	0.515070	−	0.892127i
$382$	7.59179			0.388430
$383$	0.670251	−	1.16091i	0.0342482	−	0.0593197i	−0.848393	−	0.529367i	$-0.822430\pi$
$383$	0.670251	−	1.16091i	0.0342482	−	0.0593197i	0.882641	+	0.470047i	$0.155763\pi$
$384$	−8.13102	+	14.0833i	−0.414935	+	0.718688i
$385$	−8.96077			−0.456683
$386$	−27.9916	+	48.4828i	−1.42473	+	2.46771i
$387$	3.13437	+	5.42890i	0.159329	+	0.275966i
$388$	0.570688	+	0.988460i	0.0289723	+	0.0501814i
$389$	−17.1051			−0.867265			−0.433632	−	0.901090i	$-0.642768\pi$
$389$	−17.1051			−0.867265			−0.433632	+	0.901090i	$0.642768\pi$
$390$	−0.637063	+	13.6933i	−0.0322590	+	0.693386i
$391$	−15.1957			−0.768478
$392$	1.17845	+	2.04113i	0.0595206	+	0.103093i
$393$	1.84601	+	3.19738i	0.0931189	+	0.161287i
$394$	18.9073	−	32.7484i	0.952536	−	1.64984i
$395$	9.14675			0.460223
$396$	8.07338	−	13.9835i	0.405702	−	0.702697i
$397$	−5.01022	+	8.67796i	−0.251456	+	0.435534i	−0.963927	−	0.266167i	$-0.914243\pi$
$397$	−5.01022	+	8.67796i	−0.251456	+	0.435534i	0.712471	+	0.701701i	$0.247576\pi$
$398$	−36.6262			−1.83591
$399$	3.74698	−	6.48996i	0.187584	−	0.324904i
$400$	−0.856896	−	1.48419i	−0.0428448	−	0.0742094i
$401$	4.41335	+	7.64414i	0.220392	+	0.381730i	0.954927	−	0.296841i	$-0.0959330\pi$
$401$	4.41335	+	7.64414i	0.220392	+	0.381730i	−0.734535	+	0.678571i	$0.762600\pi$
$402$	6.67994			0.333165
$403$	−12.4906	+	6.45691i	−0.622201	+	0.321642i
$404$	−42.7603			−2.12741
$405$	−0.846011	−	1.46533i	−0.0420386	−	0.0728130i
$406$	8.49880	+	14.7204i	0.421789	+	0.730559i
$407$	−25.3409	+	43.8918i	−1.25610	+	2.17563i
$408$	5.29590			0.262186
$409$	−0.261217	+	0.452441i	−0.0129164	+	0.0223718i	−0.872411	−	0.488772i	$-0.837445\pi$
$409$	−0.261217	+	0.452441i	−0.0129164	+	0.0223718i	0.859495	+	0.511144i	$0.170778\pi$
$410$	13.2838	−	23.0082i	0.656041	−	1.13630i
$411$	−1.84654			−0.0910833
$412$	22.7473	−	39.3994i	1.12068	−	1.94107i
$413$	3.13437	+	5.42890i	0.154233	+	0.267139i
$414$	7.59783	+	13.1598i	0.373413	+	0.646771i
$415$	0.222816			0.0109376
$416$	1.09179	−	23.4674i	0.0535296	−	1.15058i
$417$	−14.5090			−0.710510
$418$	44.5882	+	77.2290i	2.18088	+	3.77740i
$419$	−5.53266	−	9.58284i	−0.270288	−	0.468152i	0.698648	−	0.715466i	$-0.253786\pi$
$419$	−5.53266	−	9.58284i	−0.270288	−	0.468152i	−0.968935	+	0.247314i	$0.920452\pi$
$420$	−2.57942	+	4.46768i	−0.125863	+	0.218001i
$421$	−5.26444			−0.256573			−0.128287	−	0.991737i	$-0.540948\pi$
$421$	−5.26444			−0.256573			−0.128287	+	0.991737i	$0.540948\pi$
$422$	−15.2017	+	26.3301i	−0.740008	+	1.28173i
$423$	0.852052	−	1.47580i	0.0414282	−	0.0717557i
$424$	9.91723			0.481623
$425$	−2.40097	+	4.15860i	−0.116464	+	0.201722i
$426$	−9.41335	−	16.3044i	−0.456078	−	0.789950i
$427$	−3.08211	−	5.33836i	−0.149154	−	0.258341i
$428$	24.8019			1.19885
$429$	−0.887395	+	19.0740i	−0.0428439	+	0.920901i
$430$	23.8334			1.14935
$431$	5.02595	+	8.70520i	0.242092	+	0.419315i	0.961310	−	0.275469i	$-0.0888332\pi$
$431$	5.02595	+	8.70520i	0.242092	+	0.419315i	−0.719218	+	0.694784i	$0.755500\pi$
$432$	0.400969	+	0.694498i	0.0192916	+	0.0334141i
$433$	−14.0700	+	24.3700i	−0.676162	+	1.17115i	0.299966	+	0.953950i	$0.403025\pi$
$433$	−14.0700	+	24.3700i	−0.676162	+	1.17115i	−0.976128	+	0.217197i	$0.930309\pi$
$434$	−8.76271			−0.420623
$435$	−6.39977	+	11.0847i	−0.306846	+	0.531472i
$436$	11.9867	−	20.7616i	0.574060	−	0.994301i
$437$	−50.6795			−2.42433
$438$	−4.91939	+	8.52063i	−0.235057	+	0.407131i
$439$	13.2860	+	23.0120i	0.634105	+	1.09830i	0.986704	+	0.162527i	$0.0519646\pi$
$439$	13.2860	+	23.0120i	0.634105	+	1.09830i	−0.352599	+	0.935774i	$0.614702\pi$
$440$	−10.5598	−	18.2901i	−0.503419	−	0.871947i
$441$	1.00000			0.0476190
$442$	−16.1712	+	8.35956i	−0.769186	+	0.397624i
$443$	−35.1957			−1.67220			−0.836098	−	0.548580i	$-0.815169\pi$
$443$	−35.1957			−1.67220			−0.836098	+	0.548580i	$0.815169\pi$
$444$	14.5891	+	25.2691i	0.692368	+	1.19922i
$445$	4.98307	+	8.63094i	0.236220	+	0.409146i
$446$	−10.8034	+	18.7121i	−0.511557	+	0.886043i
$447$	12.4058			0.586775
$448$	6.51842	−	11.2902i	0.307966	−	0.533413i
$449$	10.5990	−	18.3581i	0.500199	−	0.866370i	−0.499801	−	0.866140i	$-0.666593\pi$
$449$	10.5990	−	18.3581i	0.500199	−	0.866370i	1.00000		0.000230038i	$-7.32232e-5\pi$
$450$	4.80194			0.226366
$451$	18.5036	−	32.0493i	0.871303	−	1.50914i
$452$	−9.29954	−	16.1073i	−0.437414	−	0.757623i
$453$	−0.664874	−	1.15160i	−0.0312385	−	0.0541067i
$454$	−25.4765			−1.19567
$455$	0.283520	−	6.09408i	0.0132916	−	0.285695i
$456$	17.6625			0.827121
$457$	−18.1199	−	31.3846i	−0.847613	−	1.46811i	−0.883332	−	0.468747i	$-0.844706\pi$
$457$	−18.1199	−	31.3846i	−0.847613	−	1.46811i	0.0357191	−	0.999362i	$-0.488628\pi$
$458$	−5.93296	−	10.2762i	−0.277229	−	0.480175i
$459$	1.12349	−	1.94594i	0.0524400	−	0.0908288i
$460$	34.8877			1.62665
$461$	16.6613	−	28.8582i	0.775993	−	1.34406i	−0.158241	−	0.987401i	$-0.550582\pi$
$461$	16.6613	−	28.8582i	0.775993	−	1.34406i	0.934234	−	0.356659i	$-0.116084\pi$
$462$	−5.94989	+	10.3055i	−0.276814	+	0.479455i
$463$	−31.3497			−1.45694			−0.728472	−	0.685075i	$-0.759769\pi$
$463$	−31.3497			−1.45694			−0.728472	+	0.685075i	$0.759769\pi$
$464$	3.03319	−	5.25364i	0.140812	−	0.243894i
$465$	−3.29925	−	5.71447i	−0.152999	−	0.265002i
$466$	3.48039	+	6.02820i	0.161226	+	0.279251i
$467$	1.57540			0.0729008			0.0364504	−	0.999335i	$-0.488395\pi$
$467$	1.57540			0.0729008			0.0364504	+	0.999335i	$0.488395\pi$
$468$	9.25451	+	5.93301i	0.427790	+	0.274254i
$469$	−2.97285			−0.137274
$470$	−3.23945	−	5.61089i	−0.149425	−	0.258811i
$471$	4.21864	+	7.30689i	0.194384	+	0.336684i
$472$	−7.38740	+	12.7953i	−0.340032	+	0.588953i
$473$	33.1987			1.52648
$474$	6.07338	−	10.5194i	0.278959	−	0.483172i
$475$	−8.00753	+	13.8695i	−0.367411	+	0.636374i
$476$	−6.85086			−0.314008
$477$	2.10388	−	3.64402i	0.0963298	−	0.166848i
$478$	12.0368	+	20.8484i	0.550552	+	0.953584i
$479$	9.82036	+	17.0094i	0.448704	+	0.777177i	0.998302	−	0.0582517i	$-0.0185526\pi$
$479$	9.82036	+	17.0094i	0.448704	+	0.777177i	−0.549598	+	0.835429i	$0.685219\pi$
$480$	11.0248			0.503209
$481$	−29.0483	−	18.6227i	−1.32449	−	0.849122i
$482$	−36.4644			−1.66091
$483$	−3.38135	−	5.85668i	−0.153857	−	0.266488i
$484$	−25.9867	−	45.0103i	−1.18121	−	2.04592i
$485$	0.316708	−	0.548554i	0.0143810	−	0.0249085i
$486$	−2.24698			−0.101925
$487$	9.54072	−	16.5250i	0.432331	−	0.748820i	−0.564742	−	0.825267i	$-0.691024\pi$
$487$	9.54072	−	16.5250i	0.432331	−	0.748820i	0.997074	+	0.0764475i	$0.0243578\pi$
$488$	7.26420	−	12.5820i	0.328835	−	0.569559i
$489$	14.1836			0.641404
$490$	1.90097	−	3.29257i	0.0858770	−	0.148743i
$491$	−7.92908	−	13.7336i	−0.357834	−	0.619787i	0.629765	−	0.776786i	$-0.283151\pi$
$491$	−7.92908	−	13.7336i	−0.357834	−	0.619787i	−0.987599	+	0.156999i	$0.949818\pi$
$492$	−10.6528	−	18.4512i	−0.480265	−	0.831843i
$493$	−16.9976			−0.765534
$494$	−53.9330	+	27.8802i	−2.42656	+	1.25439i
$495$	−8.96077			−0.402757
$496$	1.56369	+	2.70839i	0.0702116	+	0.121610i
$497$	4.18933	+	7.25614i	0.187917	+	0.325482i
$498$	0.147948	−	0.256254i	0.00662973	−	0.0114830i
$499$	17.1806			0.769109			0.384555	−	0.923102i	$-0.374355\pi$
$499$	17.1806			0.769109			0.384555	+	0.923102i	$0.374355\pi$
$500$	18.4095	−	31.8861i	0.823296	−	1.42599i
$501$	−4.43900	+	7.68858i	−0.198320	+	0.343500i
$502$	49.3062			2.20064
$503$	−3.72521	+	6.45225i	−0.166099	+	0.287692i	−0.937045	−	0.349209i	$-0.886450\pi$
$503$	−3.72521	+	6.45225i	−0.166099	+	0.287692i	0.770946	+	0.636900i	$0.219784\pi$
$504$	1.17845	+	2.04113i	0.0524922	+	0.0909192i
$505$	11.8651	+	20.5509i	0.527990	+	0.914505i
$506$	80.4747			3.57754
$507$	−12.9438	−	1.20701i	−0.574856	−	0.0536051i
$508$	−61.3062			−2.72002
$509$	6.11960	+	10.5995i	0.271247	+	0.469813i	0.969181	−	0.246348i	$-0.0792307\pi$
$509$	6.11960	+	10.5995i	0.271247	+	0.469813i	−0.697935	+	0.716161i	$0.745897\pi$
$510$	−4.27144	−	7.39835i	−0.189142	−	0.327604i
$511$	2.18933	−	3.79204i	0.0968504	−	0.167750i
$512$	−9.00538			−0.397985
$513$	3.74698	−	6.48996i	0.165433	−	0.286539i
$514$	24.2032	−	41.9212i	1.06756	−	1.84906i
$515$	−25.2476			−1.11254
$516$	9.55645	−	16.5523i	0.420699	−	0.728672i
$517$	−4.51238	−	7.81567i	−0.198454	−	0.343733i
$518$	−10.7518	−	18.6227i	−0.472408	−	0.818235i
$519$	−24.3230			−1.06766
$520$	12.7729	−	6.60285i	0.560130	−	0.289554i
$521$	42.0646			1.84288			0.921441	−	0.388518i	$-0.127013\pi$
$521$	42.0646			1.84288			0.921441	+	0.388518i	$0.127013\pi$
$522$	8.49880	+	14.7204i	0.371983	+	0.644293i
$523$	−1.02297	−	1.77183i	−0.0447312	−	0.0774767i	0.842793	−	0.538238i	$-0.180910\pi$
$523$	−1.02297	−	1.77183i	−0.0447312	−	0.0774767i	−0.887524	+	0.460761i	$0.847576\pi$
$524$	5.62833	−	9.74856i	0.245875	−	0.425868i
$525$	−2.13706			−0.0932691
$526$	−14.1054	+	24.4312i	−0.615023	+	1.06525i
$527$	4.38135	−	7.58873i	0.190855	−	0.330570i
$528$	4.24698			0.184826
$529$	−11.3671	+	19.6884i	−0.494222	+	0.856018i
$530$	−7.99880	−	13.8543i	−0.347446	−	0.601794i
$531$	3.13437	+	5.42890i	0.136020	+	0.235594i
$532$	−22.8485			−0.990606
$533$	21.2107	+	13.5981i	0.918739	+	0.588998i
$534$	13.2349			0.572730
$535$	−6.88202	−	11.9200i	−0.297536	−	0.515347i
$536$	−3.50335	−	6.06798i	−0.151322	−	0.262097i
$537$	6.43512	−	11.1459i	0.277696	−	0.480983i
$538$	−1.60925			−0.0693798
$539$	2.64795	−	4.58638i	0.114055	−	0.197549i
$540$	−2.57942	+	4.46768i	−0.111000	+	0.192258i
$541$	−25.8495			−1.11136			−0.555679	−	0.831397i	$-0.687542\pi$
$541$	−25.8495			−1.11136			−0.555679	+	0.831397i	$0.687542\pi$
$542$	5.63437	−	9.75902i	0.242017	−	0.419186i
$543$	−4.62833	−	8.01651i	−0.198621	−	0.344021i
$544$	7.32036	+	12.6792i	0.313858	+	0.543617i
$545$	−13.3043			−0.569892
$546$	−6.82036	−	4.37249i	−0.291884	−	0.187125i
$547$	22.6866			0.970011			0.485005	−	0.874511i	$-0.338818\pi$
$547$	22.6866			0.970011			0.485005	+	0.874511i	$0.338818\pi$
$548$	2.81498	+	4.87569i	0.120250	+	0.208279i
$549$	−3.08211	−	5.33836i	−0.131541	−	0.227836i
$550$	12.7153	−	22.0235i	0.542182	−	0.939086i
$551$	−56.6892			−2.41504
$552$	7.96950	−	13.8036i	0.339204	−	0.587519i
$553$	−2.70291	+	4.68157i	−0.114939	+	0.199081i
$554$	23.6775			1.00596
$555$	8.09634	−	14.0233i	0.343671	−	0.595255i
$556$	22.1184	+	38.3102i	0.938029	+	1.62471i
$557$	−5.04138	−	8.73193i	−0.213610	−	0.369984i	0.739231	−	0.673451i	$-0.235189\pi$
$557$	−5.04138	−	8.73193i	−0.213610	−	0.369984i	−0.952842	+	0.303468i	$0.901856\pi$
$558$	−8.76271			−0.370955
$559$	−1.05041	+	22.5779i	−0.0444276	+	0.954942i
$560$	−1.35690			−0.0573393
$561$	−5.94989	−	10.3055i	−0.251204	−	0.435099i
$562$	−3.42058	−	5.92462i	−0.144289	−	0.249915i
$563$	−1.44893	+	2.50961i	−0.0610650	+	0.105768i	−0.894942	−	0.446183i	$-0.852783\pi$
$563$	−1.44893	+	2.50961i	−0.0610650	+	0.105768i	0.833877	+	0.551951i	$0.186116\pi$
$564$	−5.19567			−0.218777
$565$	−5.16086	+	8.93887i	−0.217119	+	0.376061i
$566$	4.89493	−	8.47826i	0.205749	−	0.356368i
$567$	1.00000			0.0419961
$568$	−9.87382	+	17.1020i	−0.414296	+	0.717582i
$569$	−14.1984	−	24.5923i	−0.595226	−	1.03096i	−0.993515	−	0.113702i	$-0.963729\pi$
$569$	−14.1984	−	24.5923i	−0.595226	−	1.03096i	0.398289	−	0.917260i	$-0.369604\pi$
$570$	−14.2458	−	24.6744i	−0.596690	−	1.03350i
$571$	39.6262			1.65831			0.829153	−	0.559021i	$-0.188823\pi$
$571$	39.6262			1.65831			0.829153	+	0.559021i	$0.188823\pi$
$572$	51.7165	−	26.7344i	2.16238	−	1.11782i
$573$	−3.37867			−0.141146
$574$	7.85086	+	13.5981i	0.327688	+	0.567573i
$575$	7.22617	+	12.5161i	0.301352	+	0.521957i
$576$	6.51842	−	11.2902i	0.271601	−	0.470426i
$577$	−12.8170			−0.533579			−0.266789	−	0.963755i	$-0.585963\pi$
$577$	−12.8170			−0.533579			−0.266789	+	0.963755i	$0.585963\pi$
$578$	−13.4269	+	23.2561i	−0.558486	+	0.967327i
$579$	12.4574	−	21.5769i	0.517713	−	0.896705i
$580$	39.0248			1.62041
$581$	−0.0658433	+	0.114044i	−0.00273164	+	0.00473134i
$582$	−0.420583	−	0.728471i	−0.0174337	−	0.0301961i
$583$	−11.1419	−	19.2984i	−0.461451	−	0.799256i
$584$	10.3201			0.427047
$585$	0.283520	−	6.09408i	0.0117221	−	0.251959i
$586$	−62.2911			−2.57322
$587$	−24.1063	−	41.7534i	−0.994975	−	1.72335i	−0.584200	−	0.811609i	$-0.698592\pi$
$587$	−24.1063	−	41.7534i	−0.994975	−	1.72335i	−0.410774	−	0.911737i	$-0.634742\pi$
$588$	−1.52446	−	2.64044i	−0.0628676	−	0.108890i
$589$	14.6124	−	25.3094i	0.602092	−	1.04285i
$590$	23.8334			0.981205
$591$	−8.41454	+	14.5744i	−0.346128	+	0.599511i
$592$	−3.83728	+	6.64637i	−0.157711	+	0.273164i
$593$	15.5539			0.638722			0.319361	−	0.947633i	$-0.396532\pi$
$593$	15.5539			0.638722			0.319361	+	0.947633i	$0.396532\pi$
$594$	−5.94989	+	10.3055i	−0.244127	+	0.422840i
$595$	1.90097	+	3.29257i	0.0779321	+	0.134982i
$596$	−18.9121	−	32.7568i	−0.774672	−	1.34177i
$597$	16.3002			0.667123
$598$	−2.54623	+	54.7296i	−0.104123	+	2.23806i
$599$	−16.0422			−0.655467			−0.327734	−	0.944770i	$-0.606285\pi$
$599$	−16.0422			−0.655467			−0.327734	+	0.944770i	$0.606285\pi$
$600$	−2.51842	−	4.36203i	−0.102814	−	0.178079i
$601$	−11.8828	−	20.5817i	−0.484711	−	0.839545i	0.515134	−	0.857109i	$-0.327742\pi$
$601$	−11.8828	−	20.5817i	−0.484711	−	0.839545i	−0.999846	+	0.0175647i	$0.994409\pi$
$602$	−7.04288	+	12.1986i	−0.287046	+	0.497179i
$603$	−2.97285			−0.121064
$604$	−2.02715	+	3.51112i	−0.0824834	+	0.142866i
$605$	−14.4215	+	24.9788i	−0.586319	+	1.01553i
$606$	31.5133			1.28014
$607$	−21.3168	+	36.9217i	−0.865221	+	1.49861i	0.00160687	+	0.999999i	$0.499489\pi$
$607$	−21.3168	+	36.9217i	−0.865221	+	1.49861i	−0.866828	+	0.498608i	$0.833845\pi$
$608$	24.4143	+	42.2868i	0.990131	+	1.71496i
$609$	−3.78232	−	6.55118i	−0.153267	−	0.265467i
$610$	−23.4359			−0.948894
$611$	5.45808	−	2.82151i	0.220810	−	0.114146i
$612$	−6.85086			−0.276929
$613$	9.78262	+	16.9440i	0.395116	+	0.684361i	0.993116	−	0.117135i	$-0.0373710\pi$
$613$	9.78262	+	16.9440i	0.395116	+	0.684361i	−0.598000	+	0.801496i	$0.704038\pi$
$614$	−18.5749	−	32.1726i	−0.749621	−	1.29838i
$615$	−5.91185	+	10.2396i	−0.238389	+	0.412902i
$616$	12.4819			0.502909
$617$	−22.5695	+	39.0915i	−0.908614	+	1.57376i	−0.0926216	+	0.995701i	$0.529525\pi$
$617$	−22.5695	+	39.0915i	−0.908614	+	1.57376i	−0.815992	+	0.578063i	$0.803809\pi$
$618$	−16.7642	+	29.0364i	−0.674355	+	1.16802i
$619$	−2.87071			−0.115383			−0.0576917	−	0.998334i	$-0.518374\pi$
$619$	−2.87071			−0.115383			−0.0576917	+	0.998334i	$0.518374\pi$
$620$	−10.0591	+	17.4229i	−0.403985	+	0.699722i
$621$	−3.38135	−	5.85668i	−0.135689	−	0.235020i
$622$	−28.9279	−	50.1046i	−1.15990	−	2.00901i
$623$	−5.89008			−0.235981
$624$	−0.134375	+	2.88830i	−0.00537930	+	0.115625i
$625$	−9.74764			−0.389906
$626$	−27.1456	−	47.0175i	−1.08495	−	1.87920i
$627$	−19.8436	−	34.3702i	−0.792478	−	1.37261i
$628$	12.8623	−	22.2781i	0.513261	−	0.888993i
$629$	21.5036			0.857407
$630$	1.90097	−	3.29257i	0.0757364	−	0.131179i
$631$	−9.72497	+	16.8441i	−0.387145	+	0.670555i	−0.992064	−	0.125732i	$-0.959872\pi$
$631$	−9.72497	+	16.8441i	−0.387145	+	0.670555i	0.604919	+	0.796287i	$0.293205\pi$
$632$	−12.7409			−0.506807
$633$	6.76540	−	11.7180i	0.268900	−	0.465749i
$634$	−4.62229	−	8.00605i	−0.183575	−	0.317961i
$635$	17.0112	+	29.4642i	0.675068	+	1.16925i
$636$	−12.8291			−0.508706
$637$	3.03534	+	1.94594i	0.120265	+	0.0771010i
$638$	90.0176			3.56383
$639$	4.18933	+	7.25614i	0.165727	+	0.287048i
$640$	−13.7579	−	23.8293i	−0.543827	−	0.941937i
$641$	1.43565	−	2.48662i	0.0567047	−	0.0982154i	−0.836280	−	0.548303i	$-0.815274\pi$
$641$	1.43565	−	2.48662i	0.0567047	−	0.0982154i	0.892984	+	0.450088i	$0.148607\pi$
$642$	−18.2784			−0.721392
$643$	13.3237	−	23.0773i	0.525436	−	0.910081i	−0.474125	−	0.880457i	$-0.657236\pi$
$643$	13.3237	−	23.0773i	0.525436	−	0.910081i	0.999561	−	0.0296241i	$-0.00943101\pi$
$644$	−10.3095	+	17.8565i	−0.406250	+	0.703646i
$645$	−10.6069			−0.417645
$646$	18.9182	−	32.7673i	0.744326	−	1.28921i
$647$	−3.90193	−	6.75834i	−0.153401	−	0.265698i	0.779075	−	0.626931i	$-0.215689\pi$
$647$	−3.90193	−	6.75834i	−0.153401	−	0.265698i	−0.932476	+	0.361233i	$0.882356\pi$
$648$	1.17845	+	2.04113i	0.0462938	+	0.0801832i
$649$	33.1987			1.30316
$650$	14.5755	+	9.34429i	0.571699	+	0.366513i
$651$	3.89977			0.152844
$652$	−21.6223	−	37.4509i	−0.846794	−	1.46669i
$653$	7.78621	+	13.4861i	0.304698	+	0.527752i	0.977194	−	0.212348i	$-0.0681112\pi$
$653$	7.78621	+	13.4861i	0.304698	+	0.527752i	−0.672496	+	0.740101i	$0.734778\pi$
$654$	−8.83393	+	15.3008i	−0.345434	+	0.598309i
$655$	−6.24698			−0.244090
$656$	2.80194	−	4.85310i	0.109397	−	0.189482i
$657$	2.18933	−	3.79204i	0.0854140	−	0.147941i
$658$	3.82908			0.149273
$659$	14.9083	−	25.8219i	0.580744	−	1.00588i	−0.414648	−	0.909982i	$-0.636095\pi$
$659$	14.9083	−	25.8219i	0.580744	−	1.00588i	0.995391	−	0.0958954i	$-0.0305714\pi$
$660$	13.6603	+	23.6604i	0.531727	+	0.920979i
$661$	−7.53199	−	13.0458i	−0.292961	−	0.507422i	0.681548	−	0.731774i	$-0.261307\pi$
$661$	−7.53199	−	13.0458i	−0.292961	−	0.507422i	−0.974508	+	0.224351i	$0.927974\pi$
$662$	55.7851			2.16815
$663$	7.19687	−	3.72036i	0.279503	−	0.144487i
$664$	−0.310371			−0.0120447
$665$	6.33997	+	10.9812i	0.245853	+	0.425831i
$666$	−10.7518	−	18.6227i	−0.416625	−	0.721615i
$667$	−25.5788	+	44.3037i	−0.990413	+	1.71545i
$668$	27.0683			1.04730
$669$	4.80798	−	8.32766i	0.185887	−	0.321966i
$670$	−5.65130	+	9.78834i	−0.218329	+	0.378157i
$671$	−32.6450			−1.26025
$672$	−3.25786	+	5.64279i	−0.125675	+	0.217675i
$673$	8.10590	+	14.0398i	0.312459	+	0.541196i	0.978894	−	0.204368i	$-0.0655138\pi$
$673$	8.10590	+	14.0398i	0.312459	+	0.541196i	−0.666435	+	0.745563i	$0.732180\pi$
$674$	36.7848	+	63.7131i	1.41690	+	2.45414i
$675$	−2.13706			−0.0822556
$676$	16.5453	+	36.0175i	0.636359	+	1.38529i
$677$	5.36419			0.206163			0.103081	−	0.994673i	$-0.467130\pi$
$677$	5.36419			0.206163			0.103081	+	0.994673i	$0.467130\pi$
$678$	6.85354	+	11.8707i	0.263209	+	0.455891i
$679$	0.187177	+	0.324200i	0.00718320	+	0.0124417i
$680$	−4.48039	+	7.76026i	−0.171815	+	0.297592i
$681$	11.3381			0.434477
$682$	−23.2032	+	40.1891i	−0.888497	+	1.53892i
$683$	23.9460	−	41.4757i	0.916268	−	1.58702i	0.111235	−	0.993794i	$-0.464520\pi$
$683$	23.9460	−	41.4757i	0.916268	−	1.58702i	0.805034	−	0.593229i	$-0.202147\pi$
$684$	−22.8485			−0.873633
$685$	1.56220	−	2.70580i	0.0596884	−	0.103383i
$686$	1.12349	+	1.94594i	0.0428950	+	0.0742964i
$687$	2.64042	+	4.57333i	0.100738	+	0.174484i
$688$	5.02715			0.191658
$689$	13.4770	−	6.96683i	0.513434	−	0.265415i
$690$	−25.7114			−0.978816
$691$	5.87771	+	10.1805i	0.223598	+	0.387284i	0.955898	−	0.293699i	$-0.0948862\pi$
$691$	5.87771	+	10.1805i	0.223598	+	0.387284i	−0.732300	+	0.680983i	$0.761553\pi$
$692$	37.0795	+	64.2235i	1.40955	+	2.44141i
$693$	2.64795	−	4.58638i	0.100587	−	0.174222i
$694$	−0.679940			−0.0258102
$695$	12.2748	−	21.2606i	0.465609	−	0.806459i
$696$	8.91454	−	15.4404i	0.337905	−	0.585268i
$697$	−15.7017			−0.594745
$698$	31.4354	−	54.4477i	1.18985	−	2.06088i
$699$	−1.54892	−	2.68280i	−0.0585854	−	0.101473i
$700$	3.25786	+	5.64279i	0.123136	+	0.213277i
$701$	−8.59611			−0.324670			−0.162335	−	0.986736i	$-0.551903\pi$
$701$	−8.59611			−0.324670			−0.162335	+	0.986736i	$0.551903\pi$
$702$	−6.82036	−	4.37249i	−0.257418	−	0.165029i
$703$	71.7174			2.70487
$704$	−34.5209	−	59.7919i	−1.30105	−	2.25349i
$705$	1.44169	+	2.49708i	0.0542972	+	0.0940455i
$706$	0.139752	−	0.242057i	0.00525963	−	0.00910994i
$707$	−14.0248			−0.527455
$708$	9.55645	−	16.5523i	0.359153	−	0.622072i
$709$	14.5178	−	25.1455i	0.545226	−	0.944359i	−0.453367	−	0.891324i	$-0.649777\pi$
$709$	14.5178	−	25.1455i	0.545226	−	0.944359i	0.998593	−	0.0530347i	$-0.0168894\pi$
$710$	31.8552			1.19550
$711$	−2.70291	+	4.68157i	−0.101367	+	0.175573i
$712$	−6.94116	−	12.0224i	−0.260131	−	0.450560i
$713$	−13.1865	−	22.8397i	−0.493839	−	0.855354i
$714$	5.04892			0.188951
$715$	−27.1990	−	17.4371i	−1.01719	−	0.652112i
$716$	−39.2403			−1.46648
$717$	−5.35690	−	9.27842i	−0.200057	−	0.346509i
$718$	23.0586	+	39.9387i	0.860540	+	1.49050i
$719$	−20.0281	+	34.6897i	−0.746922	+	1.29371i	0.202369	+	0.979309i	$0.435136\pi$
$719$	−20.0281	+	34.6897i	−0.746922	+	1.29371i	−0.949291	+	0.314398i	$0.898197\pi$
$720$	−1.35690			−0.0505685
$721$	7.46077	−	12.9224i	0.277854	−	0.481257i
$722$	41.7482	−	72.3101i	1.55371	−	2.69110i
$723$	16.2282			0.603533
$724$	−14.1114	+	24.4417i	−0.524446	+	0.908368i
$725$	8.08306	+	14.0003i	0.300197	+	0.519957i
$726$	19.1516	+	33.1715i	0.710782	+	1.23111i
$727$	−12.4004			−0.459907			−0.229953	−	0.973202i	$-0.573857\pi$
$727$	−12.4004			−0.459907			−0.229953	+	0.973202i	$0.573857\pi$
$728$	−0.394928	+	8.48873i	−0.0146370	+	0.314613i
$729$	1.00000			0.0370370
$730$	−8.32371	−	14.4171i	−0.308074	−	0.533600i
$731$	−7.04288	−	12.1986i	−0.260490	−	0.451182i
$732$	−9.39708	+	16.2762i	−0.347326	+	0.601587i
$733$	39.9245			1.47465			0.737323	−	0.675540i	$-0.236090\pi$
$733$	39.9245			1.47465			0.737323	+	0.675540i	$0.236090\pi$
$734$	−17.2627	+	29.8999i	−0.637178	+	1.10363i
$735$	−0.846011	+	1.46533i	−0.0312056	+	0.0540496i
$736$	44.0640			1.62422
$737$	−7.87196	+	13.6346i	−0.289967	+	0.502238i
$738$	7.85086	+	13.5981i	0.288994	+	0.500552i
$739$	13.0516	+	22.6060i	0.480111	+	0.831577i	0.999740	−	0.0228155i	$-0.00726302\pi$
$739$	13.0516	+	22.6060i	0.480111	+	0.831577i	−0.519629	+	0.854392i	$0.673930\pi$
$740$	−49.3702			−1.81488
$741$	24.0025	−	12.4079i	0.881752	−	0.455814i
$742$	9.45473			0.347094
$743$	−8.67480	−	15.0252i	−0.318248	−	0.551221i	0.661875	−	0.749614i	$-0.269761\pi$
$743$	−8.67480	−	15.0252i	−0.318248	−	0.551221i	−0.980122	+	0.198393i	$0.936428\pi$
$744$	4.59568	+	7.95995i	0.168486	+	0.291826i
$745$	−10.4955	+	18.1787i	−0.384524	+	0.666014i
$746$	10.9022			0.399157
$747$	−0.0658433	+	0.114044i	−0.00240908	+	0.00417265i
$748$	−18.1407	+	31.4206i	−0.663290	+	1.14885i
$749$	8.13467			0.297234
$750$	−13.5673	+	23.4993i	−0.495409	+	0.858074i
$751$	8.59634	+	14.8893i	0.313685	+	0.543318i	0.979157	−	0.203104i	$-0.0651031\pi$
$751$	8.59634	+	14.8893i	0.313685	+	0.543318i	−0.665472	+	0.746423i	$0.731770\pi$
$752$	−0.683292	−	1.18350i	−0.0249171	−	0.0431577i
$753$	−21.9433			−0.799659
$754$	−2.84817	+	61.2195i	−0.103724	+	2.22948i
$755$	2.24996			0.0818846
$756$	−1.52446	−	2.64044i	−0.0554440	−	0.0960319i
$757$	−0.651169	−	1.12786i	−0.0236672	−	0.0409927i	0.853949	−	0.520356i	$-0.174201\pi$
$757$	−0.651169	−	1.12786i	−0.0236672	−	0.0409927i	−0.877616	+	0.479364i	$0.840868\pi$
$758$	−6.00969	+	10.4091i	−0.218282	+	0.378075i
$759$	−35.8146			−1.29999
$760$	−14.9426	+	25.8814i	−0.542027	+	0.938818i
$761$	2.08695	−	3.61470i	0.0756519	−	0.131033i	−0.825718	−	0.564084i	$-0.809230\pi$
$761$	2.08695	−	3.61470i	0.0756519	−	0.131033i	0.901370	+	0.433051i	$0.142563\pi$
$762$	45.1812			1.63674
$763$	3.93147	−	6.80950i	0.142329	−	0.246521i
$764$	5.15064	+	8.92116i	0.186344	+	0.322756i
$765$	1.90097	+	3.29257i	0.0687297	+	0.119043i
$766$	3.01208			0.108831
$767$	−1.05041	+	22.5779i	−0.0379281	+	0.815240i
$768$	−10.4668			−0.377689
$769$	5.83340	+	10.1037i	0.210358	+	0.364350i	0.951826	−	0.306637i	$-0.0992038\pi$
$769$	5.83340	+	10.1037i	0.210358	+	0.364350i	−0.741469	+	0.670987i	$0.765870\pi$
$770$	−10.0673	−	17.4371i	−0.362802	−	0.628391i
$771$	−10.7714	+	18.6567i	−0.387924	+	0.671904i
$772$	−75.9633			−2.73398
$773$	1.83297	−	3.17480i	0.0659273	−	0.114189i	−0.831178	−	0.556007i	$-0.812333\pi$
$773$	1.83297	−	3.17480i	0.0659273	−	0.114189i	0.897105	+	0.441817i	$0.145666\pi$
$774$	−7.04288	+	12.1986i	−0.253151	+	0.438470i
$775$	−8.33406			−0.299368
$776$	−0.441157	+	0.764106i	−0.0158366	+	0.0274298i
$777$	4.78501	+	8.28788i	0.171661	+	0.297326i
$778$	−19.2174	−	33.2856i	−0.688979	−	1.19335i
$779$	−52.3672			−1.87625
$780$	−16.5233	+	8.54155i	−0.591628	+	0.305837i
$781$	44.3726			1.58777
$782$	−17.0722	−	29.5699i	−0.610500	−	1.05742i
$783$	−3.78232	−	6.55118i	−0.135169	−	0.234120i
$784$	0.400969	−	0.694498i	0.0143203	−	0.0248035i
$785$	−14.2760			−0.509534
$786$	−4.14795	+	7.18446i	−0.147952	+	0.256261i
$787$	10.3886	−	17.9936i	0.370313	−	0.641401i	−0.619300	−	0.785154i	$-0.712584\pi$
$787$	10.3886	−	17.9936i	0.370313	−	0.641401i	0.989614	+	0.143753i	$0.0459170\pi$
$788$	51.3105			1.82786
$789$	6.27748	−	10.8729i	0.223484	−	0.387086i
$790$	10.2763	+	17.7990i	0.365614	+	0.633262i
$791$	−3.05011	−	5.28295i	−0.108450	−	0.187840i
$792$	12.4819			0.443524
$793$	1.03289	−	22.2014i	0.0366791	−	0.788394i
$794$	−22.5157			−0.799053
$795$	3.55980	+	6.16576i	0.126253	+	0.218677i
$796$	−24.8490	−	43.0397i	−0.880749	−	1.52550i
$797$	6.68867	−	11.5851i	0.236925	−	0.410366i	−0.722906	−	0.690947i	$-0.757194\pi$
$797$	6.68867	−	11.5851i	0.236925	−	0.410366i	0.959830	+	0.280581i	$0.0905272\pi$
$798$	16.8388			0.596086
$799$	−1.91454	+	3.31608i	−0.0677316	+	0.117315i
$800$	6.96226	−	12.0590i	0.246153	−	0.426350i
$801$	−5.89008			−0.208116
$802$	−9.91670	+	17.1762i	−0.350171	+	0.606514i
$803$	−11.5945	−	20.0822i	−0.409160	−	0.708687i
$804$	4.53199	+	7.84964i	0.159831	+	0.276835i
$805$	11.4426			0.403300
$806$	−26.5978	−	17.0517i	−0.936869	−	0.600621i
$807$	0.716185			0.0252109
$808$	−16.5274	−	28.6264i	−0.581433	−	1.00707i
$809$	5.94182	+	10.2915i	0.208903	+	0.361831i	0.951369	−	0.308053i	$-0.0996773\pi$
$809$	5.94182	+	10.2915i	0.208903	+	0.361831i	−0.742466	+	0.669884i	$0.766344\pi$
$810$	1.90097	−	3.29257i	0.0667932	−	0.115689i
$811$	−0.178211			−0.00625783			−0.00312892	−	0.999995i	$-0.500996\pi$
$811$	−0.178211			−0.00625783			−0.00312892	+	0.999995i	$0.500996\pi$
$812$	−11.5320	+	19.9740i	−0.404694	+	0.700950i
$813$	−2.50753	+	4.34317i	−0.0879430	+	0.152322i
$814$	−113.881			−3.99153
$815$	−11.9995	+	20.7837i	−0.420323	+	0.728021i
$816$	−0.900969	−	1.56052i	−0.0315402	−	0.0546293i
$817$	−23.4889	−	40.6839i	−0.821772	−	1.42335i
$818$	−1.17390			−0.0410444
$819$	3.03534	+	1.94594i	0.106063	+	0.0679967i
$820$	36.0495			1.25890
$821$	15.7778	+	27.3279i	0.550648	+	0.953751i	0.998228	+	0.0595065i	$0.0189527\pi$
$821$	15.7778	+	27.3279i	0.550648	+	0.953751i	−0.447580	+	0.894244i	$0.647714\pi$
$822$	−2.07457	−	3.59326i	−0.0723590	−	0.125330i
$823$	−18.7470	+	32.4707i	−0.653479	+	1.13186i	0.328794	+	0.944402i	$0.393358\pi$
$823$	−18.7470	+	32.4707i	−0.653479	+	1.13186i	−0.982273	+	0.187457i	$0.939976\pi$
$824$	35.1685			1.22515
$825$	−5.65883	+	9.80139i	−0.197015	+	0.341241i
$826$	−7.04288	+	12.1986i	−0.245053	+	0.424444i
$827$	40.3749			1.40397			0.701987	−	0.712190i	$-0.252296\pi$
$827$	40.3749			1.40397			0.701987	+	0.712190i	$0.252296\pi$
$828$	−10.3095	+	17.8565i	−0.358279	+	0.620557i
$829$	17.4276	+	30.1855i	0.605285	+	1.04838i	0.992006	+	0.126188i	$0.0402742\pi$
$829$	17.4276	+	30.1855i	0.605285	+	1.04838i	−0.386721	+	0.922197i	$0.626392\pi$
$830$	0.250332	+	0.433588i	0.00868915	+	0.0150500i
$831$	−10.5375			−0.365542
$832$	41.7558	−	21.5853i	1.44762	−	0.748335i
$833$	−2.24698			−0.0778532
$834$	−16.3007	−	28.2337i	−0.564449	−	0.977653i
$835$	−7.51089	−	13.0092i	−0.259925	−	0.450203i
$836$	−60.5016	+	104.792i	−2.09249	+	3.62430i
$837$	3.89977			0.134796
$838$	12.4318	−	21.5324i	0.429448	−	0.743826i
$839$	−11.9629	+	20.7204i	−0.413006	+	0.715348i	−0.995217	−	0.0976903i	$-0.968855\pi$
$839$	−11.9629	+	20.7204i	−0.413006	+	0.715348i	0.582211	+	0.813038i	$0.302188\pi$
$840$	−3.98792			−0.137596
$841$	−14.1119	+	24.4426i	−0.486619	+	0.842848i
$842$	−5.91454	−	10.2443i	−0.203829	−	0.353041i
$843$	1.52230	+	2.63671i	0.0524309	+	0.0908130i
$844$	−41.2543			−1.42003
$845$	12.7193	−	17.9459i	0.437557	−	0.617358i
$846$	3.82908			0.131647
$847$	−8.52326	−	14.7627i	−0.292863	−	0.507253i
$848$	−1.68718	−	2.92228i	−0.0579379	−	0.100351i
$849$	−2.17845	+	3.77318i	−0.0747641	+	0.129495i
$850$	−10.7899			−0.370089
$851$	32.3596	−	56.0485i	1.10927	−	1.92132i
$852$	12.7729	−	22.1234i	0.437593	−	0.757934i
$853$	39.9101			1.36649			0.683247	−	0.730187i	$-0.260567\pi$
$853$	39.9101			1.36649			0.683247	+	0.730187i	$0.260567\pi$
$854$	6.92543	−	11.9952i	0.236983	−	0.410467i
$855$	6.33997	+	10.9812i	0.216822	+	0.375547i
$856$	9.58629	+	16.6039i	0.327652	+	0.567511i
$857$	−12.0392			−0.411252			−0.205626	−	0.978631i	$-0.565923\pi$
$857$	−12.0392			−0.411252			−0.205626	+	0.978631i	$0.565923\pi$
$858$	−38.1139	+	19.7026i	−1.30119	+	0.672636i
$859$	13.6993			0.467415			0.233707	−	0.972307i	$-0.424914\pi$
$859$	13.6993			0.467415			0.233707	+	0.972307i	$0.424914\pi$
$860$	16.1697	+	28.0068i	0.551383	+	0.955023i
$861$	−3.49396	−	6.05171i	−0.119074	−	0.206242i
$862$	−11.2932	+	19.5604i	−0.384648	+	0.666230i
$863$	7.45712			0.253843			0.126922	−	0.991913i	$-0.459490\pi$
$863$	7.45712			0.253843			0.126922	+	0.991913i	$0.459490\pi$
$864$	−3.25786	+	5.64279i	−0.110835	+	0.191972i
$865$	20.5776	−	35.6414i	0.699658	−	1.21184i
$866$	−63.2301			−2.14865
$867$	5.97554	−	10.3499i	0.202940	−	0.351502i
$868$	−5.94504	−	10.2971i	−0.201788	−	0.349507i
$869$	14.3143	+	24.7931i	0.485580	+	0.841049i
$870$	−28.7603			−0.975066
$871$	−9.02363	−	5.78500i	−0.305754	−	0.196017i
$872$	18.5321			0.627577
$873$	0.187177	+	0.324200i	0.00633499	+	0.0109725i
$874$	−56.9379	−	98.6193i	−1.92595	−	3.33585i
$875$	6.03803	−	10.4582i	0.204123	−	0.353551i
$876$	−13.3502			−0.451061
$877$	−17.4743	+	30.2665i	−0.590067	+	1.02203i	0.404156	+	0.914690i	$0.367565\pi$
$877$	−17.4743	+	30.2665i	−0.590067	+	1.02203i	−0.994223	+	0.107336i	$0.965768\pi$
$878$	−29.8533	+	51.7074i	−1.00750	+	1.74504i
$879$	27.7222			0.935045
$880$	−3.59299	+	6.22324i	−0.121120	+	0.209785i
$881$	22.7896	+	39.4728i	0.767802	+	1.32987i	0.938753	+	0.344592i	$0.111983\pi$
$881$	22.7896	+	39.4728i	0.767802	+	1.32987i	−0.170951	+	0.985280i	$0.554684\pi$
$882$	1.12349	+	1.94594i	0.0378299	+	0.0655233i
$883$	5.39240			0.181469			0.0907344	−	0.995875i	$-0.471079\pi$
$883$	5.39240			0.181469			0.0907344	+	0.995875i	$0.471079\pi$
$884$	−20.7947	−	13.3314i	−0.699401	−	0.448382i
$885$	−10.6069			−0.356546
$886$	−39.5420	−	68.4887i	−1.32844	−	2.30092i
$887$	21.4263	+	37.1114i	0.719423	+	1.24608i	0.961229	+	0.275753i	$0.0889271\pi$
$887$	21.4263	+	37.1114i	0.719423	+	1.24608i	−0.241805	+	0.970325i	$0.577740\pi$
$888$	−11.2778	+	19.5337i	−0.378457	+	0.655507i
$889$	−20.1075			−0.674385
$890$	−11.1969	+	19.3935i	−0.375320	+	0.650073i
$891$	2.64795	−	4.58638i	0.0887096	−	0.153650i
$892$	−29.3183			−0.981648
$893$	−6.38524	+	11.0596i	−0.213674	+	0.370094i
$894$	13.9378	+	24.1410i	0.466150	+	0.807395i
$895$	10.8884	+	18.8592i	0.363958	+	0.630393i
$896$	16.2620			0.543277
$897$	1.13318	−	24.3569i	0.0378357	−	0.813255i
$898$	47.6316			1.58949
$899$	−14.7502	−	25.5481i	−0.491947	−	0.852077i
$900$	3.25786	+	5.64279i	0.108595	+	0.188093i
$901$	−4.72737	+	8.18804i	−0.157491	+	0.272783i
$902$	83.1546			2.76875
$903$	3.13437	−	5.42890i	0.104305	−	0.180662i
$904$	7.18880	−	12.4514i	0.239096	−	0.414126i
$905$	15.6625			0.520639
$906$	1.49396	−	2.58761i	0.0496335	−	0.0859677i
$907$	−19.3061	−	33.4392i	−0.641049	−	1.11033i	−0.985199	−	0.171415i	$-0.945166\pi$
$907$	−19.3061	−	33.4392i	−0.641049	−	1.11033i	0.344150	−	0.938915i	$-0.388167\pi$
$908$	−17.2845	−	29.9376i	−0.573606	−	0.993514i
$909$	−14.0248			−0.465172
$910$	12.1773	−	6.29492i	0.403672	−	0.208675i
$911$	−2.88663			−0.0956382			−0.0478191	−	0.998856i	$-0.515227\pi$
$911$	−2.88663			−0.0956382			−0.0478191	+	0.998856i	$0.515227\pi$
$912$	−3.00484	−	5.20454i	−0.0995003	−	0.172340i
$913$	0.348699	+	0.603965i	0.0115403	+	0.0199883i
$914$	40.7150	−	70.5205i	1.34673	−	2.33261i
$915$	10.4300			0.344804
$916$	8.05041	−	13.9437i	0.265993	−	0.460713i
$917$	1.84601	−	3.19738i	0.0609606	−	0.105587i
$918$	5.04892			0.166639
$919$	18.6691	−	32.3358i	0.615835	−	1.06666i	−0.374402	−	0.927266i	$-0.622152\pi$
$919$	18.6691	−	32.3358i	0.615835	−	1.06666i	0.990237	−	0.139392i	$-0.0445147\pi$
$920$	13.4846	+	23.3560i	0.444573	+	0.770023i
$921$	8.26659	+	14.3182i	0.272394	+	0.471799i
$922$	74.8751			2.46588
$923$	−1.40395	+	30.1771i	−0.0462117	+	0.993290i
$924$	−16.1468			−0.531189
$925$	−10.2259	−	17.7117i	−0.336225	−	0.582358i
$926$	−35.2211	−	61.0047i	−1.15744	−	2.00474i
$927$	7.46077	−	12.9224i	0.245044	−	0.424428i
$928$	49.2892			1.61800
$929$	0.964124	−	1.66991i	0.0316319	−	0.0547880i	−0.849776	−	0.527144i	$-0.823263\pi$
$929$	0.964124	−	1.66991i	0.0316319	−	0.0547880i	0.881408	+	0.472356i	$0.156596\pi$
$930$	7.41335	−	12.8403i	0.243093	−	0.421050i
$931$	−7.49396			−0.245605
$932$	−4.72252	+	8.17965i	−0.154691	+	0.267933i
$933$	12.8741	+	22.2986i	0.421480	+	0.730024i
$934$	1.76995	+	3.06564i	0.0579144	+	0.100311i
$935$	20.1347			0.658474
$936$	−0.394928	+	8.48873i	−0.0129086	+	0.277463i
$937$	49.0810			1.60341			0.801703	−	0.597723i	$-0.203928\pi$
$937$	49.0810			1.60341			0.801703	+	0.597723i	$0.203928\pi$
$938$	−3.33997	−	5.78500i	−0.109054	−	0.188887i
$939$	12.0809	+	20.9247i	0.394246	+	0.682853i
$940$	4.39559	−	7.61339i	0.143368	−	0.248321i
$941$	8.92394			0.290912			0.145456	−	0.989365i	$-0.453535\pi$
$941$	8.92394			0.290912			0.145456	+	0.989365i	$0.453535\pi$
$942$	−9.47919	+	16.4184i	−0.308849	+	0.534942i
$943$	−23.6286	+	40.9260i	−0.769454	+	1.33273i
$944$	5.02715			0.163620
$945$	−0.846011	+	1.46533i	−0.0275207	+	0.0476673i
$946$	37.2983	+	64.6026i	1.21267	+	2.10041i
$947$	−26.4850	−	45.8734i	−0.860647	−	1.49068i	−0.871306	−	0.490741i	$-0.836726\pi$
$947$	−26.4850	−	45.8734i	−0.860647	−	1.49068i	0.0106591	−	0.999943i	$-0.496607\pi$
$948$	16.4819			0.535306
$949$	14.0245	−	7.24982i	0.455253	−	0.235339i
$950$	−35.9855			−1.16752
$951$	2.05711	+	3.56303i	0.0667065	+	0.115539i
$952$	−2.64795	−	4.58638i	−0.0858205	−	0.148645i
$953$	−5.20493	+	9.01520i	−0.168604	+	0.292031i	−0.937929	−	0.346826i	$-0.887259\pi$
$953$	−5.20493	+	9.01520i	−0.168604	+	0.292031i	0.769325	+	0.638857i	$0.220593\pi$
$954$	9.45473			0.306108
$955$	2.85839	−	4.95087i	0.0924953	−	0.160206i
$956$	−16.3327	+	28.2891i	−0.528238	+	0.914936i
$957$	−40.0616			−1.29501
$958$	−22.0661	+	38.2197i	−0.712925	+	1.23482i
$959$	0.923272	+	1.59915i	0.0298140	+	0.0516394i
$960$	11.0293	+	19.1033i	0.355969	+	0.616557i
$961$	−15.7918			−0.509412
$962$	3.60321	−	77.4487i	0.116172	−	2.49705i
$963$	8.13467			0.262136
$964$	−24.7392	−	42.8496i	−0.796796	−	1.38009i
$965$	21.0782	+	36.5085i	0.678532	+	1.17525i
$966$	7.59783	−	13.1598i	0.244456	−	0.423411i
$967$	51.0689			1.64226			0.821132	−	0.570738i	$-0.193343\pi$
$967$	51.0689			1.64226			0.821132	+	0.570738i	$0.193343\pi$
$968$	20.0884	−	34.7942i	0.645667	−	1.11833i
$969$	−8.41939	+	14.5828i	−0.270470	+	0.468467i
$970$	1.42327			0.0456985
$971$	−22.3853	+	38.7725i	−0.718378	+	1.24427i	0.243264	+	0.969960i	$0.421782\pi$
$971$	−22.3853	+	38.7725i	−0.718378	+	1.24427i	−0.961642	+	0.274308i	$0.911551\pi$
$972$	−1.52446	−	2.64044i	−0.0488970	−	0.0846921i
$973$	7.25451	+	12.5652i	0.232569	+	0.402821i
$974$	42.8756			1.37382
$975$	−6.48672	−	4.15860i	−0.207741	−	0.133182i
$976$	−4.94331			−0.158232
$977$	8.07338	+	13.9835i	0.258290	+	0.447372i	0.965784	−	0.259348i	$-0.0835076\pi$
$977$	8.07338	+	13.9835i	0.258290	+	0.447372i	−0.707494	+	0.706720i	$0.750174\pi$
$978$	15.9351	+	27.6004i	0.509549	+	0.882564i
$979$	−15.5966	+	27.0142i	−0.498471	+	0.863377i
$980$	5.15883			0.164793
$981$	3.93147	−	6.80950i	0.125522	−	0.217411i
$982$	17.8165	−	30.8590i	0.568546	−	0.984751i
$983$	53.2198			1.69745			0.848725	−	0.528835i	$-0.177371\pi$
$983$	53.2198			1.69745			0.848725	+	0.528835i	$0.177371\pi$
$984$	8.23490	−	14.2633i	0.262519	−	0.454696i
$985$	−14.2376	−	24.6602i	−0.453647	−	0.785740i
$986$	−19.0966	−	33.0763i	−0.608161	−	1.05337i
$987$	−1.70410			−0.0542422
$988$	−69.3529	−	44.4618i	−2.20641	−	1.41452i
$989$	−42.3937			−1.34804
$990$	−10.0673	−	17.4371i	−0.319961	−	0.554189i
$991$	−13.0468	−	22.5977i	−0.414444	−	0.717838i	0.580926	−	0.813956i	$-0.302691\pi$
$991$	−13.0468	−	22.5977i	−0.414444	−	0.717838i	−0.995370	+	0.0961183i	$0.969357\pi$
$992$	−12.7049	+	22.0056i	−0.403382	+	0.698678i
$993$	−24.8267			−0.787851
$994$	−9.41335	+	16.3044i	−0.298573	+	0.517144i
$995$	−13.7902	+	23.8852i	−0.437177	+	0.757213i
$996$	0.401501			0.0127221
$997$	−1.73663	+	3.00793i	−0.0549995	+	0.0952620i	−0.892214	−	0.451612i	$-0.850849\pi$
$997$	−1.73663	+	3.00793i	−0.0549995	+	0.0952620i	0.837215	+	0.546874i	$0.184182\pi$
$998$	19.3022	+	33.4324i	0.611002	+	1.05829i
$999$	4.78501	+	8.28788i	0.151391	+	0.262217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.k.c.211.3	yes	6
3.2	odd	2		819.2.o.e.757.1		6
13.3	even	3		3549.2.a.i.1.1		3
13.9	even	3	inner	273.2.k.c.22.3	✓	6
13.10	even	6		3549.2.a.u.1.3		3
39.35	odd	6		819.2.o.e.568.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.c.22.3	✓	6	13.9	even	3	inner
273.2.k.c.211.3	yes	6	1.1	even	1	trivial
819.2.o.e.568.1		6	39.35	odd	6
819.2.o.e.757.1		6	3.2	odd	2
3549.2.a.i.1.1		3	13.3	even	3
3549.2.a.u.1.3		3	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12349 + 1.94594i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.52446 + 2.64044i) q^{4} +1.69202 q^{5} +(1.12349 - 1.94594i) q^{6} +(-0.500000 + 0.866025i) q^{7} -2.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.12349 + 1.94594i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.52446 + 2.64044i) q^{4} +1.69202 q^{5} +(1.12349 - 1.94594i) q^{6} +(-0.500000 + 0.866025i) q^{7} -2.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.90097 + 3.29257i) q^{10} +(2.64795 + 4.58638i) q^{11} +3.04892 q^{12} +(-3.20291 + 1.65571i) q^{13} -2.24698 q^{14} +(-0.846011 - 1.46533i) q^{15} +(0.400969 + 0.694498i) q^{16} +(1.12349 - 1.94594i) q^{17} -2.24698 q^{18} +(3.74698 - 6.48996i) q^{19} +(-2.57942 + 4.46768i) q^{20} +1.00000 q^{21} +(-5.94989 + 10.3055i) q^{22} +(-3.38135 - 5.85668i) q^{23} +(1.17845 + 2.04113i) q^{24} -2.13706 q^{25} +(-6.82036 - 4.37249i) q^{26} +1.00000 q^{27} +(-1.52446 - 2.64044i) q^{28} +(-3.78232 - 6.55118i) q^{29} +(1.90097 - 3.29257i) q^{30} +3.89977 q^{31} +(-3.25786 + 5.64279i) q^{32} +(2.64795 - 4.58638i) q^{33} +5.04892 q^{34} +(-0.846011 + 1.46533i) q^{35} +(-1.52446 - 2.64044i) q^{36} +(4.78501 + 8.28788i) q^{37} +16.8388 q^{38} +(3.03534 + 1.94594i) q^{39} -3.98792 q^{40} +(-3.49396 - 6.05171i) q^{41} +(1.12349 + 1.94594i) q^{42} +(3.13437 - 5.42890i) q^{43} -16.1468 q^{44} +(-0.846011 + 1.46533i) q^{45} +(7.59783 - 13.1598i) q^{46} -1.70410 q^{47} +(0.400969 - 0.694498i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.40097 - 4.15860i) q^{50} -2.24698 q^{51} +(0.510885 - 10.9812i) q^{52} -4.20775 q^{53} +(1.12349 + 1.94594i) q^{54} +(4.48039 + 7.76026i) q^{55} +(1.17845 - 2.04113i) q^{56} -7.49396 q^{57} +(8.49880 - 14.7204i) q^{58} +(3.13437 - 5.42890i) q^{59} +5.15883 q^{60} +(-3.08211 + 5.33836i) q^{61} +(4.38135 + 7.58873i) q^{62} +(-0.500000 - 0.866025i) q^{63} -13.0368 q^{64} +(-5.41939 + 2.80150i) q^{65} +11.8998 q^{66} +(1.48643 + 2.57457i) q^{67} +(3.42543 + 5.93301i) q^{68} +(-3.38135 + 5.85668i) q^{69} -3.80194 q^{70} +(4.18933 - 7.25614i) q^{71} +(1.17845 - 2.04113i) q^{72} -4.37867 q^{73} +(-10.7518 + 18.6227i) q^{74} +(1.06853 + 1.85075i) q^{75} +(11.4242 + 19.7873i) q^{76} -5.29590 q^{77} +(-0.376510 + 8.09285i) q^{78} +5.40581 q^{79} +(0.678448 + 1.17511i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.85086 - 13.5981i) q^{82} +0.131687 q^{83} +(-1.52446 + 2.64044i) q^{84} +(1.90097 - 3.29257i) q^{85} +14.0858 q^{86} +(-3.78232 + 6.55118i) q^{87} +(-6.24094 - 10.8096i) q^{88} +(2.94504 + 5.10096i) q^{89} -3.80194 q^{90} +(0.167563 - 3.60166i) q^{91} +20.6189 q^{92} +(-1.94989 - 3.37730i) q^{93} +(-1.91454 - 3.31608i) q^{94} +(6.33997 - 10.9812i) q^{95} +6.51573 q^{96} +(0.187177 - 0.324200i) q^{97} +(1.12349 - 1.94594i) q^{98} -5.29590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} + 2 q^{11} - 6 q^{13} - 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 13 q^{19} - 7 q^{20} + 6 q^{21} - 13 q^{22} - 3 q^{23} + 3 q^{24} - 2 q^{25} - 4 q^{26} + 6 q^{27} - q^{29} + 7 q^{30} - 22 q^{31} - 7 q^{32} + 2 q^{33} + 12 q^{34} + 4 q^{37} + 36 q^{38} + 6 q^{39} + 14 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 42 q^{44} + 9 q^{46} - 38 q^{47} - 2 q^{48} - 3 q^{49} - 10 q^{50} - 4 q^{51} + 10 q^{53} + 2 q^{54} + 14 q^{55} + 3 q^{56} - 26 q^{57} + 10 q^{58} + 11 q^{59} + 14 q^{60} - 7 q^{61} + 9 q^{62} - 3 q^{63} - 22 q^{64} + 26 q^{66} + 15 q^{67} + 7 q^{68} - 3 q^{69} - 14 q^{70} + 18 q^{71} + 3 q^{72} - 12 q^{73} - 33 q^{74} + q^{75} + 14 q^{76} - 4 q^{77} - 7 q^{78} + 6 q^{79} - 3 q^{81} + 20 q^{82} - 4 q^{83} + 7 q^{85} + 10 q^{86} - q^{87} - 9 q^{88} + 17 q^{89} - 14 q^{90} + 56 q^{92} + 11 q^{93} - q^{94} + 14 q^{95} + 14 q^{96} + 13 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 + 2 * q^11 - 6 * q^13 - 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 13 * q^19 - 7 * q^20 + 6 * q^21 - 13 * q^22 - 3 * q^23 + 3 * q^24 - 2 * q^25 - 4 * q^26 + 6 * q^27 - q^29 + 7 * q^30 - 22 * q^31 - 7 * q^32 + 2 * q^33 + 12 * q^34 + 4 * q^37 + 36 * q^38 + 6 * q^39 + 14 * q^40 - 2 * q^41 + 2 * q^42 + 11 * q^43 - 42 * q^44 + 9 * q^46 - 38 * q^47 - 2 * q^48 - 3 * q^49 - 10 * q^50 - 4 * q^51 + 10 * q^53 + 2 * q^54 + 14 * q^55 + 3 * q^56 - 26 * q^57 + 10 * q^58 + 11 * q^59 + 14 * q^60 - 7 * q^61 + 9 * q^62 - 3 * q^63 - 22 * q^64 + 26 * q^66 + 15 * q^67 + 7 * q^68 - 3 * q^69 - 14 * q^70 + 18 * q^71 + 3 * q^72 - 12 * q^73 - 33 * q^74 + q^75 + 14 * q^76 - 4 * q^77 - 7 * q^78 + 6 * q^79 - 3 * q^81 + 20 * q^82 - 4 * q^83 + 7 * q^85 + 10 * q^86 - q^87 - 9 * q^88 + 17 * q^89 - 14 * q^90 + 56 * q^92 + 11 * q^93 - q^94 + 14 * q^95 + 14 * q^96 + 13 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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