LMFDB - Embedded newform 169.2.c.c.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(22,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34947179416$
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			22.1
Root			$0.222521 - 0.385418i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.2.c.c.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.400969 + 0.694498i) q^{2} +(1.12349 - 1.94594i) q^{3} +(0.678448 + 1.17511i) q^{4} +0.246980 q^{5} +(0.900969 + 1.56052i) q^{6} +(1.17845 + 2.04113i) q^{7} -2.69202 q^{8} +(-1.02446 - 1.77441i) q^{9} +O(q^{10})$	\(q+(-0.400969 + 0.694498i) q^{2} +(1.12349 - 1.94594i) q^{3} +(0.678448 + 1.17511i) q^{4} +0.246980 q^{5} +(0.900969 + 1.56052i) q^{6} +(1.17845 + 2.04113i) q^{7} -2.69202 q^{8} +(-1.02446 - 1.77441i) q^{9} +(-0.0990311 + 0.171527i) q^{10} +(2.12349 - 3.67799i) q^{11} +3.04892 q^{12} -1.89008 q^{14} +(0.277479 - 0.480608i) q^{15} +(-0.277479 + 0.480608i) q^{16} +(-1.07942 - 1.86960i) q^{17} +1.64310 q^{18} +(0.0440730 + 0.0763367i) q^{19} +(0.167563 + 0.290227i) q^{20} +5.29590 q^{21} +(1.70291 + 2.94952i) q^{22} +(-0.746980 + 1.29381i) q^{23} +(-3.02446 + 5.23852i) q^{24} -4.93900 q^{25} +2.13706 q^{27} +(-1.59903 + 2.76960i) q^{28} +(-2.31551 + 4.01058i) q^{29} +(0.222521 + 0.385418i) q^{30} -6.63102 q^{31} +(-2.91454 - 5.04814i) q^{32} +(-4.77144 - 8.26437i) q^{33} +1.73125 q^{34} +(0.291053 + 0.504118i) q^{35} +(1.39008 - 2.40770i) q^{36} +(-2.84601 + 4.92944i) q^{37} -0.0706876 q^{38} -0.664874 q^{40} +(5.79590 - 10.0388i) q^{41} +(-2.12349 + 3.67799i) q^{42} +(0.147948 + 0.256254i) q^{43} +5.76271 q^{44} +(-0.253020 - 0.438244i) q^{45} +(-0.599031 - 1.03755i) q^{46} -7.35690 q^{47} +(0.623490 + 1.07992i) q^{48} +(0.722521 - 1.25144i) q^{49} +(1.98039 - 3.43013i) q^{50} -4.85086 q^{51} -10.3937 q^{53} +(-0.856896 + 1.48419i) q^{54} +(0.524459 - 0.908389i) q^{55} +(-3.17241 - 5.49477i) q^{56} +0.198062 q^{57} +(-1.85690 - 3.21624i) q^{58} +(3.39008 + 5.87180i) q^{59} +0.753020 q^{60} +(-1.73609 - 3.00700i) q^{61} +(2.65883 - 4.60523i) q^{62} +(2.41454 - 4.18211i) q^{63} +3.56465 q^{64} +7.65279 q^{66} +(-3.83997 + 6.65102i) q^{67} +(1.46466 - 2.53686i) q^{68} +(1.67845 + 2.90716i) q^{69} -0.466812 q^{70} +(4.33244 + 7.50400i) q^{71} +(2.75786 + 4.77676i) q^{72} +6.73556 q^{73} +(-2.28232 - 3.95310i) q^{74} +(-5.54892 + 9.61101i) q^{75} +(-0.0598025 + 0.103581i) q^{76} +10.0097 q^{77} +9.97046 q^{79} +(-0.0685317 + 0.118700i) q^{80} +(5.47434 - 9.48184i) q^{81} +(4.64795 + 8.05048i) q^{82} +1.60925 q^{83} +(3.59299 + 6.22324i) q^{84} +(-0.266594 - 0.461754i) q^{85} -0.237291 q^{86} +(5.20291 + 9.01170i) q^{87} +(-5.71648 + 9.90123i) q^{88} +(1.44235 - 2.49823i) q^{89} +0.405813 q^{90} -2.02715 q^{92} +(-7.44989 + 12.9036i) q^{93} +(2.94989 - 5.10935i) q^{94} +(0.0108851 + 0.0188536i) q^{95} -13.0978 q^{96} +(4.02930 + 6.97896i) q^{97} +(0.579417 + 1.00358i) q^{98} -8.70171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 2 q^{3} - 8 q^{5} + q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 + q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9	$ 6 q + 2 q^{2} + 2 q^{3} - 8 q^{5} + q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 5 q^{10} + 8 q^{11} - 10 q^{14} + 2 q^{15} - 2 q^{16} + 2 q^{17} + 18 q^{18} + 4 q^{19} + 4 q^{21} - 3 q^{22} + 5 q^{23} - 9 q^{24} - 10 q^{25} + 2 q^{27} - 14 q^{28} + q^{29} + q^{30} - 10 q^{31} - 7 q^{32} - 10 q^{33} + 26 q^{34} - 4 q^{35} + 7 q^{36} - 12 q^{37} + 24 q^{38} - 6 q^{40} + 7 q^{41} - 8 q^{42} - 13 q^{43} - 11 q^{45} - 8 q^{46} - 36 q^{47} - q^{48} + 4 q^{49} - q^{50} - 2 q^{51} + 2 q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} + 10 q^{57} - 3 q^{58} + 19 q^{59} + 14 q^{60} - 4 q^{61} - q^{62} + 4 q^{63} - 22 q^{64} + 10 q^{66} + q^{67} + 21 q^{68} + 6 q^{69} + 4 q^{70} + 27 q^{71} + 4 q^{72} + 18 q^{73} + 8 q^{74} - 15 q^{75} + 21 q^{76} + 16 q^{77} - 10 q^{79} + 5 q^{80} + q^{81} + 14 q^{82} - 14 q^{83} + 7 q^{84} - 5 q^{85} - 36 q^{86} + 18 q^{87} - 15 q^{88} + 11 q^{89} - 24 q^{90} - 22 q^{93} - 5 q^{94} - 3 q^{95} - 42 q^{96} - 7 q^{97} - 5 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 + q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 5 * q^10 + 8 * q^11 - 10 * q^14 + 2 * q^15 - 2 * q^16 + 2 * q^17 + 18 * q^18 + 4 * q^19 + 4 * q^21 - 3 * q^22 + 5 * q^23 - 9 * q^24 - 10 * q^25 + 2 * q^27 - 14 * q^28 + q^29 + q^30 - 10 * q^31 - 7 * q^32 - 10 * q^33 + 26 * q^34 - 4 * q^35 + 7 * q^36 - 12 * q^37 + 24 * q^38 - 6 * q^40 + 7 * q^41 - 8 * q^42 - 13 * q^43 - 11 * q^45 - 8 * q^46 - 36 * q^47 - q^48 + 4 * q^49 - q^50 - 2 * q^51 + 2 * q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 + 10 * q^57 - 3 * q^58 + 19 * q^59 + 14 * q^60 - 4 * q^61 - q^62 + 4 * q^63 - 22 * q^64 + 10 * q^66 + q^67 + 21 * q^68 + 6 * q^69 + 4 * q^70 + 27 * q^71 + 4 * q^72 + 18 * q^73 + 8 * q^74 - 15 * q^75 + 21 * q^76 + 16 * q^77 - 10 * q^79 + 5 * q^80 + q^81 + 14 * q^82 - 14 * q^83 + 7 * q^84 - 5 * q^85 - 36 * q^86 + 18 * q^87 - 15 * q^88 + 11 * q^89 - 24 * q^90 - 22 * q^93 - 5 * q^94 - 3 * q^95 - 42 * q^96 - 7 * q^97 - 5 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.400969	+	0.694498i	−0.283528	+	0.491085i	−0.972251	−	0.233940i	$-0.924838\pi$
$2$	−0.400969	+	0.694498i	−0.283528	+	0.491085i	0.688723	+	0.725024i	$0.258171\pi$
$3$	1.12349	−	1.94594i	0.648647	−	1.12349i	−0.334799	−	0.942290i	$-0.608668\pi$
$3$	1.12349	−	1.94594i	0.648647	−	1.12349i	0.983446	−	0.181200i	$-0.0579982\pi$
$4$	0.678448	+	1.17511i	0.339224	+	0.587553i
$5$	0.246980			0.110453			0.0552263	−	0.998474i	$-0.482412\pi$
$5$	0.246980			0.110453			0.0552263	+	0.998474i	$0.482412\pi$
$6$	0.900969	+	1.56052i	0.367819	+	0.637081i
$7$	1.17845	+	2.04113i	0.445411	+	0.771475i	0.998081	−	0.0619254i	$-0.0197241\pi$
$7$	1.17845	+	2.04113i	0.445411	+	0.771475i	−0.552669	+	0.833401i	$0.686391\pi$
$8$	−2.69202			−0.951773
$9$	−1.02446	−	1.77441i	−0.341486	−	0.591471i
$10$	−0.0990311	+	0.171527i	−0.0313164	+	0.0542416i
$11$	2.12349	−	3.67799i	0.640256	−	1.10896i	−0.345119	−	0.938559i	$-0.612161\pi$
$11$	2.12349	−	3.67799i	0.640256	−	1.10896i	0.985375	−	0.170397i	$-0.0545052\pi$
$12$	3.04892			0.880147
$13$		0			0
$13$		0			0
$14$	−1.89008			−0.505146
$15$	0.277479	−	0.480608i	0.0716448	−	0.124092i
$16$	−0.277479	+	0.480608i	−0.0693698	+	0.120152i
$17$	−1.07942	−	1.86960i	−0.261797	−	0.453446i	0.704922	−	0.709284i	$-0.250982\pi$
$17$	−1.07942	−	1.86960i	−0.261797	−	0.453446i	−0.966720	+	0.255839i	$0.917648\pi$
$18$	1.64310			0.387283
$19$	0.0440730	+	0.0763367i	0.0101110	+	0.0175128i	0.871037	−	0.491218i	$-0.163448\pi$
$19$	0.0440730	+	0.0763367i	0.0101110	+	0.0175128i	−0.860926	+	0.508731i	$0.830115\pi$
$20$	0.167563	+	0.290227i	0.0374682	+	0.0648968i
$21$	5.29590			1.15566
$22$	1.70291	+	2.94952i	0.363061	+	0.628840i
$23$	−0.746980	+	1.29381i	−0.155756	+	0.269777i	−0.933334	−	0.359009i	$-0.883115\pi$
$23$	−0.746980	+	1.29381i	−0.155756	+	0.269777i	0.777578	+	0.628786i	$0.216448\pi$
$24$	−3.02446	+	5.23852i	−0.617365	+	1.06931i
$25$	−4.93900			−0.987800
$26$		0			0
$27$	2.13706			0.411278
$28$	−1.59903	+	2.76960i	−0.302188	+	0.523406i
$29$	−2.31551	+	4.01058i	−0.429980	+	0.744747i	−0.996871	−	0.0790460i	$-0.974813\pi$
$29$	−2.31551	+	4.01058i	−0.429980	+	0.744747i	0.566891	+	0.823793i	$0.308146\pi$
$30$	0.222521	+	0.385418i	0.0406266	+	0.0703673i
$31$	−6.63102			−1.19097			−0.595483	−	0.803368i	$-0.703039\pi$
$31$	−6.63102			−1.19097			−0.595483	+	0.803368i	$0.703039\pi$
$32$	−2.91454	−	5.04814i	−0.515223	−	0.892393i
$33$	−4.77144	−	8.26437i	−0.830601	−	1.43864i
$34$	1.73125			0.296907
$35$	0.291053	+	0.504118i	0.0491969	+	0.0852115i
$36$	1.39008	−	2.40770i	0.231681	−	0.401283i
$37$	−2.84601	+	4.92944i	−0.467881	+	0.810394i	−0.999326	−	0.0366986i	$-0.988316\pi$
$37$	−2.84601	+	4.92944i	−0.467881	+	0.810394i	0.531445	+	0.847093i	$0.321649\pi$
$38$	−0.0706876			−0.0114670
$39$		0			0
$40$	−0.664874			−0.105126
$41$	5.79590	−	10.0388i	0.905167	−	1.56780i	0.0844742	−	0.996426i	$-0.473079\pi$
$41$	5.79590	−	10.0388i	0.905167	−	1.56780i	0.820693	−	0.571370i	$-0.193588\pi$
$42$	−2.12349	+	3.67799i	−0.327662	+	0.567527i
$43$	0.147948	+	0.256254i	0.0225619	+	0.0390784i	0.877086	−	0.480334i	$-0.159484\pi$
$43$	0.147948	+	0.256254i	0.0225619	+	0.0390784i	−0.854524	+	0.519412i	$0.826151\pi$
$44$	5.76271			0.868761
$45$	−0.253020	−	0.438244i	−0.0377181	−	0.0653296i
$46$	−0.599031	−	1.03755i	−0.0883223	−	0.152979i
$47$	−7.35690			−1.07311			−0.536557	−	0.843864i	$-0.680275\pi$
$47$	−7.35690			−1.07311			−0.536557	+	0.843864i	$0.680275\pi$
$48$	0.623490	+	1.07992i	0.0899930	+	0.155872i
$49$	0.722521	−	1.25144i	0.103217	−	0.178778i
$50$	1.98039	−	3.43013i	0.280069	−	0.485093i
$51$	−4.85086			−0.679256
$52$		0			0
$53$	−10.3937			−1.42769			−0.713844	−	0.700304i	$-0.753048\pi$
$53$	−10.3937			−1.42769			−0.713844	+	0.700304i	$0.753048\pi$
$54$	−0.856896	+	1.48419i	−0.116609	+	0.201972i
$55$	0.524459	−	0.908389i	0.0707180	−	0.122487i
$56$	−3.17241	−	5.49477i	−0.423931	−	0.734270i
$57$	0.198062			0.0262340
$58$	−1.85690	−	3.21624i	−0.243822	−	0.422313i
$59$	3.39008	+	5.87180i	0.441351	+	0.764443i	0.997790	−	0.0664458i	$-0.0211659\pi$
$59$	3.39008	+	5.87180i	0.441351	+	0.764443i	−0.556439	+	0.830889i	$0.687833\pi$
$60$	0.753020			0.0972145
$61$	−1.73609	−	3.00700i	−0.222284	−	0.385007i	0.733217	−	0.679995i	$-0.238018\pi$
$61$	−1.73609	−	3.00700i	−0.222284	−	0.385007i	−0.955501	+	0.294987i	$0.904685\pi$
$62$	2.65883	−	4.60523i	0.337672	−	0.584865i
$63$	2.41454	−	4.18211i	0.304204	−	0.526896i
$64$	3.56465			0.445581
$65$		0			0
$66$	7.65279			0.941994
$67$	−3.83997	+	6.65102i	−0.469127	+	0.812552i	−0.999377	−	0.0352895i	$-0.988765\pi$
$67$	−3.83997	+	6.65102i	−0.469127	+	0.812552i	0.530250	+	0.847841i	$0.322098\pi$
$68$	1.46466	−	2.53686i	0.177616	−	0.307639i
$69$	1.67845	+	2.90716i	0.202061	+	0.349981i
$70$	−0.466812			−0.0557947
$71$	4.33244	+	7.50400i	0.514166	+	0.890561i	0.999865	+	0.0164351i	$0.00523170\pi$
$71$	4.33244	+	7.50400i	0.514166	+	0.890561i	−0.485699	+	0.874126i	$0.661435\pi$
$72$	2.75786	+	4.77676i	0.325017	+	0.562947i
$73$	6.73556			0.788338			0.394169	−	0.919038i	$-0.371032\pi$
$73$	6.73556			0.788338			0.394169	+	0.919038i	$0.371032\pi$
$74$	−2.28232	−	3.95310i	−0.265315	−	0.459539i
$75$	−5.54892	+	9.61101i	−0.640734	+	1.10978i
$76$	−0.0598025	+	0.103581i	−0.00685981	+	0.0118815i
$77$	10.0097			1.14071
$78$		0			0
$79$	9.97046			1.12176			0.560882	−	0.827896i	$-0.310462\pi$
$79$	9.97046			1.12176			0.560882	+	0.827896i	$0.310462\pi$
$80$	−0.0685317	+	0.118700i	−0.00766207	+	0.0132711i
$81$	5.47434	−	9.48184i	0.608261	−	1.05354i
$82$	4.64795	+	8.05048i	0.513280	+	0.889027i
$83$	1.60925			0.176638			0.0883192	−	0.996092i	$-0.471850\pi$
$83$	1.60925			0.176638			0.0883192	+	0.996092i	$0.471850\pi$
$84$	3.59299	+	6.22324i	0.392027	+	0.679011i
$85$	−0.266594	−	0.461754i	−0.0289162	−	0.0500843i
$86$	−0.237291			−0.0255877
$87$	5.20291	+	9.01170i	0.557810	+	0.966156i
$88$	−5.71648	+	9.90123i	−0.609379	+	1.05548i
$89$	1.44235	−	2.49823i	0.152889	−	0.264812i	−0.779399	−	0.626528i	$-0.784476\pi$
$89$	1.44235	−	2.49823i	0.152889	−	0.264812i	0.932288	+	0.361716i	$0.117809\pi$
$90$	0.405813			0.0427765
$91$		0			0
$92$	−2.02715			−0.211345
$93$	−7.44989	+	12.9036i	−0.772517	+	1.33804i
$94$	2.94989	−	5.10935i	0.304258	−	0.526990i
$95$	0.0108851	+	0.0188536i	0.00111679	+	0.00193434i
$96$	−13.0978			−1.33679
$97$	4.02930	+	6.97896i	0.409114	+	0.708606i	0.994791	−	0.101939i	$-0.0325046\pi$
$97$	4.02930	+	6.97896i	0.409114	+	0.708606i	−0.585677	+	0.810545i	$0.699171\pi$
$98$	0.579417	+	1.00358i	0.0585299	+	0.101377i
$99$	−8.70171			−0.874555
$100$	−3.35086	−	5.80385i	−0.335086	−	0.580385i
$101$	6.67725	−	11.5653i	0.664411	−	1.15079i	−0.315033	−	0.949081i	$-0.602016\pi$
$101$	6.67725	−	11.5653i	0.664411	−	1.15079i	0.979445	−	0.201714i	$-0.0646510\pi$
$102$	1.94504	−	3.36891i	0.192588	−	0.333572i
$103$	1.36227			0.134229			0.0671144	−	0.997745i	$-0.478621\pi$
$103$	1.36227			0.134229			0.0671144	+	0.997745i	$0.478621\pi$
$104$		0			0
$105$	1.30798			0.127646
$106$	4.16756	−	7.21843i	0.404789	−	0.701116i
$107$	−1.63437	+	2.83082i	−0.158001	+	0.273666i	−0.934148	−	0.356887i	$-0.883838\pi$
$107$	−1.63437	+	2.83082i	−0.158001	+	0.273666i	0.776147	+	0.630552i	$0.217172\pi$
$108$	1.44989	+	2.51128i	0.139515	+	0.241648i
$109$	15.7017			1.50395			0.751976	−	0.659191i	$-0.229101\pi$
$109$	15.7017			1.50395			0.751976	+	0.659191i	$0.229101\pi$
$110$	0.420583	+	0.728471i	0.0401010	+	0.0694570i
$111$	6.39493	+	11.0763i	0.606980	+	1.05132i
$112$	−1.30798			−0.123592
$113$	−6.02446	−	10.4347i	−0.566733	−	0.981611i	−0.996886	−	0.0788549i	$-0.974874\pi$
$113$	−6.02446	−	10.4347i	−0.566733	−	0.981611i	0.430153	−	0.902756i	$-0.358460\pi$
$114$	−0.0794168	+	0.137554i	−0.00743806	+	0.0128831i
$115$	−0.184489	+	0.319544i	−0.0172037	+	0.0297976i
$116$	−6.28382			−0.583438
$117$		0			0
$118$	−5.43727			−0.500541
$119$	2.54407	−	4.40646i	0.233215	−	0.403940i
$120$	−0.746980	+	1.29381i	−0.0681896	+	0.118108i
$121$	−3.51842	−	6.09408i	−0.319856	−	0.554007i
$122$	2.78448			0.252095
$123$	−13.0233	−	22.5570i	−1.17427	−	2.03389i
$124$	−4.49880	−	7.79216i	−0.404004	−	0.699756i
$125$	−2.45473			−0.219558
$126$	1.93631	+	3.35379i	0.172500	+	0.298780i
$127$	4.90366	−	8.49338i	0.435129	−	0.753666i	−0.562177	−	0.827017i	$-0.690036\pi$
$127$	4.90366	−	8.49338i	0.435129	−	0.753666i	0.997306	+	0.0733510i	$0.0233694\pi$
$128$	4.39977	−	7.62063i	0.388889	−	0.673575i
$129$	0.664874			0.0585389
$130$		0			0
$131$	−6.57673			−0.574611			−0.287306	−	0.957839i	$-0.592760\pi$
$131$	−6.57673			−0.574611			−0.287306	+	0.957839i	$0.592760\pi$
$132$	6.47434	−	11.2139i	0.563519	−	0.976044i
$133$	−0.103875	+	0.179918i	−0.00900715	+	0.0156008i
$134$	−3.07942	−	5.33371i	−0.266021	−	0.460762i
$135$	0.527811			0.0454267
$136$	2.90581	+	5.03302i	0.249171	+	0.431578i
$137$	−3.10992	−	5.38653i	−0.265698	−	0.460203i	0.702048	−	0.712129i	$-0.252269\pi$
$137$	−3.10992	−	5.38653i	−0.265698	−	0.460203i	−0.967746	+	0.251927i	$0.918936\pi$
$138$	−2.69202			−0.229160
$139$	7.35354	+	12.7367i	0.623719	+	1.08031i	0.988787	+	0.149333i	$0.0477125\pi$
$139$	7.35354	+	12.7367i	0.623719	+	1.08031i	−0.365068	+	0.930981i	$0.618954\pi$
$140$	−0.394928	+	0.684035i	−0.0333775	+	0.0578116i
$141$	−8.26540	+	14.3161i	−0.696072	+	1.20563i
$142$	−6.94869			−0.583121
$143$		0			0
$144$	1.13706			0.0947553
$145$	−0.571884	+	0.990532i	−0.0474924	+	0.0822592i
$146$	−2.70075	+	4.67784i	−0.223516	+	0.387141i
$147$	−1.62349	−	2.81197i	−0.133903	−	0.231927i
$148$	−7.72348			−0.634866
$149$	−2.16756	−	3.75433i	−0.177574	−	0.307567i	0.763475	−	0.645837i	$-0.223491\pi$
$149$	−2.16756	−	3.75433i	−0.177574	−	0.307567i	−0.941049	+	0.338270i	$0.890158\pi$
$150$	−4.44989	−	7.70743i	−0.363332	−	0.629309i
$151$	3.94438			0.320989			0.160494	−	0.987037i	$-0.448691\pi$
$151$	3.94438			0.320989			0.160494	+	0.987037i	$0.448691\pi$
$152$	−0.118645	−	0.205500i	−0.00962342	−	0.0166682i
$153$	−2.21164	+	3.83067i	−0.178800	+	0.309691i
$154$	−4.01357	+	6.95171i	−0.323423	+	0.560185i
$155$	−1.63773			−0.131545
$156$		0			0
$157$	4.45473			0.355526			0.177763	−	0.984073i	$-0.443114\pi$
$157$	4.45473			0.355526			0.177763	+	0.984073i	$0.443114\pi$
$158$	−3.99784	+	6.92447i	−0.318051	+	0.550881i
$159$	−11.6773	+	20.2256i	−0.926066	+	1.60399i
$160$	−0.719833	−	1.24679i	−0.0569078	−	0.0985671i
$161$	−3.52111			−0.277502
$162$	4.39008	+	7.60385i	0.344918	+	0.597415i
$163$	−8.07942	−	13.9940i	−0.632829	−	1.09609i	−0.986971	−	0.160900i	$-0.948560\pi$
$163$	−8.07942	−	13.9940i	−0.632829	−	1.09609i	0.354142	−	0.935192i	$-0.384773\pi$
$164$	15.7289			1.22822
$165$	−1.17845	−	2.04113i	−0.0917420	−	0.158902i
$166$	−0.645260	+	1.11762i	−0.0500819	+	0.0867444i
$167$	−8.05861	+	13.9579i	−0.623594	+	1.08010i	0.365217	+	0.930922i	$0.380995\pi$
$167$	−8.05861	+	13.9579i	−0.623594	+	1.08010i	−0.988811	+	0.149174i	$0.952339\pi$
$168$	−14.2567			−1.09993
$169$		0			0
$170$	0.427583			0.0327942
$171$	0.0903019	−	0.156408i	0.00690556	−	0.0119608i
$172$	−0.200751	+	0.347710i	−0.0153071	+	0.0265127i
$173$	10.7681	+	18.6509i	0.818682	+	1.41800i	0.906653	+	0.421876i	$0.138628\pi$
$173$	10.7681	+	18.6509i	0.818682	+	1.41800i	−0.0879709	+	0.996123i	$0.528038\pi$
$174$	−8.34481			−0.632619
$175$	−5.82036	−	10.0812i	−0.439978	−	0.762063i
$176$	1.17845	+	2.04113i	0.0888289	+	0.153856i
$177$	15.2349			1.14513
$178$	1.15668	+	2.00342i	0.0866967	+	0.150163i
$179$	−5.71648	+	9.90123i	−0.427270	+	0.740053i	−0.996629	−	0.0820356i	$-0.973858\pi$
$179$	−5.71648	+	9.90123i	−0.427270	+	0.740053i	0.569360	+	0.822089i	$0.307191\pi$
$180$	0.343322	−	0.594652i	0.0255897	−	0.0443227i
$181$	20.9705			1.55872			0.779361	−	0.626575i	$-0.215544\pi$
$181$	20.9705			1.55872			0.779361	+	0.626575i	$0.215544\pi$
$182$		0			0
$183$	−7.80194			−0.576736
$184$	2.01089	−	3.48296i	0.148244	−	0.256767i
$185$	−0.702907	+	1.21747i	−0.0516787	+	0.0895102i
$186$	−5.97434	−	10.3479i	−0.438060	−	0.758743i
$187$	−9.16852			−0.670469
$188$	−4.99127	−	8.64513i	−0.364026	−	0.630511i
$189$	2.51842	+	4.36203i	0.183188	+	0.317291i
$190$	−0.0174584			−0.00126657
$191$	7.21864	+	12.5030i	0.522322	+	0.904689i	0.999663	+	0.0259702i	$0.00826749\pi$
$191$	7.21864	+	12.5030i	0.522322	+	0.904689i	−0.477341	+	0.878718i	$0.658399\pi$
$192$	4.00484	−	6.93659i	0.289025	−	0.500606i
$193$	6.78986	−	11.7604i	0.488745	−	0.846530i	−0.511172	−	0.859479i	$-0.670788\pi$
$193$	6.78986	−	11.7604i	0.488745	−	0.846530i	0.999916	+	0.0129483i	$0.00412168\pi$
$194$	−6.46250			−0.463980
$195$		0			0
$196$	1.96077			0.140055
$197$	0.280167	−	0.485264i	0.0199611	−	0.0345736i	−0.855872	−	0.517187i	$-0.826979\pi$
$197$	0.280167	−	0.485264i	0.0199611	−	0.0345736i	0.875833	+	0.482614i	$0.160312\pi$
$198$	3.48911	−	6.04332i	0.247961	−	0.429480i
$199$	−5.74578	−	9.95199i	−0.407308	−	0.705478i	0.587279	−	0.809384i	$-0.300199\pi$
$199$	−5.74578	−	9.95199i	−0.407308	−	0.705478i	−0.994587	+	0.103907i	$0.966866\pi$
$200$	13.2959			0.940162
$201$	8.62833	+	14.9447i	0.608596	+	1.05412i
$202$	5.35474	+	9.27468i	0.376758	+	0.652564i
$203$	−10.9148			−0.766071
$204$	−3.29105	−	5.70027i	−0.230420	−	0.399099i
$205$	1.43147	−	2.47938i	0.0999781	−	0.173167i
$206$	−0.546229	+	0.946096i	−0.0380576	+	0.0659177i
$207$	3.06100			0.212754
$208$		0			0
$209$	0.374354			0.0258946
$210$	−0.524459	+	0.908389i	−0.0361911	+	0.0626848i
$211$	−4.39224	+	7.60758i	−0.302374	+	0.523728i	−0.976673	−	0.214731i	$-0.931113\pi$
$211$	−4.39224	+	7.60758i	−0.302374	+	0.523728i	0.674299	+	0.738458i	$0.264446\pi$
$212$	−7.05161	−	12.2137i	−0.484306	−	0.838843i
$213$	19.4698			1.33405
$214$	−1.31067	−	2.27014i	−0.0895953	−	0.155184i
$215$	0.0365403	+	0.0632896i	0.00249202	+	0.00431631i
$216$	−5.75302			−0.391443
$217$	−7.81431	−	13.5348i	−0.530470	−	0.918801i
$218$	−6.29590	+	10.9048i	−0.426412	+	0.738567i
$219$	7.56734	−	13.1070i	0.511353	−	0.885690i
$220$	1.42327			0.0959570
$221$		0			0
$222$	−10.2567			−0.688383
$223$	1.12953	−	1.95640i	0.0756390	−	0.131011i	−0.825725	−	0.564073i	$-0.809234\pi$
$223$	1.12953	−	1.95640i	0.0756390	−	0.131011i	0.901364	+	0.433062i	$0.142567\pi$
$224$	6.86927	−	11.8979i	0.458973	−	0.794964i
$225$	5.05980	+	8.76383i	0.337320	+	0.584256i
$226$	9.66248			0.642739
$227$	3.48307	+	6.03286i	0.231180	+	0.400415i	0.958156	−	0.286248i	$-0.0924081\pi$
$227$	3.48307	+	6.03286i	0.231180	+	0.400415i	−0.726976	+	0.686663i	$0.759075\pi$
$228$	0.134375	+	0.232744i	0.00889920	+	0.0154139i
$229$	−24.1739			−1.59746			−0.798728	−	0.601692i	$-0.794493\pi$
$229$	−24.1739			−1.59746			−0.798728	+	0.601692i	$0.794493\pi$
$230$	−0.147948	−	0.256254i	−0.00975543	−	0.0168969i
$231$	11.2458	−	19.4783i	0.739918	−	1.28158i
$232$	6.23341	−	10.7966i	0.409243	−	0.708830i
$233$	−3.06100			−0.200533			−0.100266	−	0.994961i	$-0.531969\pi$
$233$	−3.06100			−0.200533			−0.100266	+	0.994961i	$0.531969\pi$
$234$		0			0
$235$	−1.81700			−0.118528
$236$	−4.59999	+	7.96742i	−0.299434	+	0.518635i
$237$	11.2017	−	19.4019i	0.727629	−	1.26029i
$238$	2.04019	+	3.53371i	0.132246	+	0.229056i
$239$	−25.1468			−1.62661			−0.813304	−	0.581839i	$-0.802333\pi$
$239$	−25.1468			−1.62661			−0.813304	+	0.581839i	$0.802333\pi$
$240$	0.153989	+	0.266717i	0.00993996	+	0.0172165i
$241$	10.1332	+	17.5512i	0.652735	+	1.13057i	0.982456	+	0.186492i	$0.0597120\pi$
$241$	10.1332	+	17.5512i	0.652735	+	1.13057i	−0.329721	+	0.944078i	$0.606955\pi$
$242$	5.64310			0.362752
$243$	−9.09515	−	15.7533i	−0.583454	−	1.01057i
$244$	2.35570	−	4.08019i	0.150808	−	0.261207i
$245$	0.178448	−	0.309081i	0.0114006	−	0.0197465i
$246$	20.8877			1.33175
$247$		0			0
$248$	17.8509			1.13353
$249$	1.80798	−	3.13151i	0.114576	−	0.198451i
$250$	0.984271	−	1.70481i	0.0622507	−	0.107821i
$251$	11.8605	+	20.5431i	0.748631	+	1.29667i	0.948479	+	0.316840i	$0.102622\pi$
$251$	11.8605	+	20.5431i	0.748631	+	1.29667i	−0.199848	+	0.979827i	$0.564045\pi$
$252$	6.55257			0.412773
$253$	3.17241	+	5.49477i	0.199448	+	0.345453i
$254$	3.93243	+	6.81116i	0.246742	+	0.427370i
$255$	−1.19806			−0.0750256
$256$	7.09299	+	12.2854i	0.443312	+	0.767839i
$257$	−7.11207	+	12.3185i	−0.443639	+	0.768405i	−0.997956	−	0.0639003i	$-0.979646\pi$
$257$	−7.11207	+	12.3185i	−0.443639	+	0.768405i	0.554317	+	0.832305i	$0.312979\pi$
$258$	−0.266594	+	0.461754i	−0.0165974	+	0.0287476i
$259$	−13.4155			−0.833599
$260$		0			0
$261$	9.48858			0.587329
$262$	2.63706	−	4.56753i	0.162918	−	0.282183i
$263$	8.54772	−	14.8051i	0.527075	−	0.912921i	−0.472427	−	0.881370i	$-0.656622\pi$
$263$	8.54772	−	14.8051i	0.527075	−	0.912921i	0.999502	−	0.0315510i	$-0.0100447\pi$
$264$	12.8448	+	22.2479i	0.790544	+	1.36926i
$265$	−2.56704			−0.157692
$266$	−0.0833017	−	0.144283i	−0.00510755	−	0.00884654i
$267$	−3.24094	−	5.61347i	−0.198342	−	0.343539i
$268$	−10.4209			−0.636556
$269$	3.23341	+	5.60042i	0.197144	+	0.341464i	0.947601	−	0.319455i	$-0.103500\pi$
$269$	3.23341	+	5.60042i	0.197144	+	0.341464i	−0.750457	+	0.660919i	$0.770167\pi$
$270$	−0.211636	+	0.366564i	−0.0128797	+	0.0223084i
$271$	−3.22401	+	5.58415i	−0.195845	+	0.339213i	−0.947177	−	0.320711i	$-0.896078\pi$
$271$	−3.22401	+	5.58415i	−0.195845	+	0.339213i	0.751332	+	0.659924i	$0.229412\pi$
$272$	1.19806			0.0726432
$273$		0			0
$274$	4.98792			0.301331
$275$	−10.4879	+	18.1656i	−0.632445	+	1.09543i
$276$	−2.27748	+	3.94471i	−0.137088	+	0.237444i
$277$	−6.73005	−	11.6568i	−0.404370	−	0.700389i	0.589878	−	0.807492i	$-0.299176\pi$
$277$	−6.73005	−	11.6568i	−0.404370	−	0.700389i	−0.994248	+	0.107103i	$0.965842\pi$
$278$	−11.7942			−0.707367
$279$	6.79321	+	11.7662i	0.406699	+	0.704423i
$280$	−0.783520	−	1.35710i	−0.0468243	−	0.0811020i
$281$	5.03684			0.300472			0.150236	−	0.988650i	$-0.451997\pi$
$281$	5.03684			0.300472			0.150236	+	0.988650i	$0.451997\pi$
$282$	−6.62833	−	11.4806i	−0.394712	−	0.683660i
$283$	−11.0640	+	19.1634i	−0.657686	+	1.13914i	0.323528	+	0.946219i	$0.395131\pi$
$283$	−11.0640	+	19.1634i	−0.657686	+	1.13914i	−0.981213	+	0.192926i	$0.938202\pi$
$284$	−5.87867	+	10.1821i	−0.348835	+	0.604199i
$285$	0.0489173			0.00289761
$286$		0			0
$287$	27.3207			1.61269
$288$	−5.97166	+	10.3432i	−0.351883	+	0.609480i
$289$	6.16972	−	10.6863i	0.362925	−	0.628604i
$290$	−0.458615	−	0.794345i	−0.0269308	−	0.0466456i
$291$	18.1075			1.06148
$292$	4.56973	+	7.91500i	0.267423	+	0.463190i
$293$	−7.47315	−	12.9439i	−0.436586	−	0.756189i	0.560838	−	0.827926i	$-0.310479\pi$
$293$	−7.47315	−	12.9439i	−0.436586	−	0.756189i	−0.997424	+	0.0717367i	$0.977146\pi$
$294$	2.60388			0.151861
$295$	0.837282	+	1.45021i	0.0487484	+	0.0844347i
$296$	7.66152	−	13.2701i	0.445317	−	0.771312i
$297$	4.53803	−	7.86010i	0.263323	−	0.456089i
$298$	3.47650			0.201388
$299$		0			0
$300$	−15.0586			−0.869409
$301$	−0.348699	+	0.603965i	−0.0200987	+	0.0348119i
$302$	−1.58157	+	2.73936i	−0.0910093	+	0.157633i
$303$	−15.0036	−	25.9871i	−0.861937	−	1.49292i
$304$	−0.0489173			−0.00280560
$305$	−0.428780	−	0.742669i	−0.0245519	−	0.0425251i
$306$	−1.77359	−	3.07196i	−0.101390	−	0.175612i
$307$	19.1293			1.09177			0.545883	−	0.837861i	$-0.316194\pi$
$307$	19.1293			1.09177			0.545883	+	0.837861i	$0.316194\pi$
$308$	6.79105	+	11.7624i	0.386956	+	0.670228i
$309$	1.53050	−	2.65090i	0.0870671	−	0.150805i
$310$	0.656678	−	1.13740i	0.0372968	−	0.0645999i
$311$	−0.269815			−0.0152998			−0.00764990	−	0.999971i	$-0.502435\pi$
$311$	−0.269815			−0.0152998			−0.00764990	+	0.999971i	$0.502435\pi$
$312$		0			0
$313$	−23.3937			−1.32229			−0.661146	−	0.750257i	$-0.729930\pi$
$313$	−23.3937			−1.32229			−0.661146	+	0.750257i	$0.729930\pi$
$314$	−1.78621	+	3.09380i	−0.100802	+	0.174593i
$315$	0.596343	−	1.03290i	0.0336001	−	0.0581971i
$316$	6.76444	+	11.7164i	0.380529	+	0.659096i
$317$	−13.9952			−0.786050			−0.393025	−	0.919528i	$-0.628571\pi$
$317$	−13.9952			−0.786050			−0.393025	+	0.919528i	$0.628571\pi$
$318$	−9.36443	−	16.2197i	−0.525131	−	0.909554i
$319$	9.83393	+	17.0329i	0.550594	+	0.953657i
$320$	0.880395			0.0492156
$321$	3.67241	+	6.36080i	0.204974	+	0.355025i
$322$	1.41185	−	2.44540i	0.0786795	−	0.136277i
$323$	0.0951463	−	0.164798i	0.00529408	−	0.00916962i
$324$	14.8562			0.825346
$325$		0			0
$326$	12.9584			0.717698
$327$	17.6407	−	30.5546i	0.975534	−	1.68967i
$328$	−15.6027	+	27.0246i	−0.861514	+	1.49219i
$329$	−8.66972	−	15.0164i	−0.477977	−	0.827881i
$330$	1.89008			0.104046
$331$	−8.91066	−	15.4337i	−0.489774	−	0.848314i	0.510157	−	0.860081i	$-0.329587\pi$
$331$	−8.91066	−	15.4337i	−0.489774	−	0.848314i	−0.999931	+	0.0117680i	$0.996254\pi$
$332$	1.09179	+	1.89104i	0.0599200	+	0.103784i
$333$	11.6625			0.639100
$334$	−6.46250	−	11.1934i	−0.353612	−	0.612474i
$335$	−0.948394	+	1.64267i	−0.0518163	+	0.0897485i
$336$	−1.46950	+	2.54525i	−0.0801678	+	0.138855i
$337$	−27.8485			−1.51700			−0.758501	−	0.651672i	$-0.774068\pi$
$337$	−27.8485			−1.51700			−0.758501	+	0.651672i	$0.774068\pi$
$338$		0			0
$339$	−27.0737			−1.47044
$340$	0.361740	−	0.626552i	0.0196181	−	0.0339796i
$341$	−14.0809	+	24.3888i	−0.762524	+	1.32073i
$342$	0.0724165	+	0.125429i	0.00391584	+	0.00678243i
$343$	19.9041			1.07472
$344$	−0.398280	−	0.689842i	−0.0214738	−	0.0371938i
$345$	0.414542	+	0.718009i	0.0223182	+	0.0386563i
$346$	−17.2707			−0.928477
$347$	−0.751824	−	1.30220i	−0.0403600	−	0.0699056i	0.845140	−	0.534545i	$-0.179517\pi$
$347$	−0.751824	−	1.30220i	−0.0403600	−	0.0699056i	−0.885500	+	0.464640i	$0.846184\pi$
$348$	−7.05980	+	12.2279i	−0.378445	+	0.655486i
$349$	7.09299	−	12.2854i	0.379679	−	0.657623i	−0.611336	−	0.791371i	$-0.709368\pi$
$349$	7.09299	−	12.2854i	0.379679	−	0.657623i	0.991015	+	0.133747i	$0.0427011\pi$
$350$	9.33513			0.498983
$351$		0			0
$352$	−24.7560			−1.31950
$353$	3.58426	−	6.20812i	0.190771	−	0.330425i	−0.754735	−	0.656030i	$-0.772235\pi$
$353$	3.58426	−	6.20812i	0.190771	−	0.330425i	0.945506	+	0.325605i	$0.105568\pi$
$354$	−6.10872	+	10.5806i	−0.324675	+	0.562353i
$355$	1.07002	+	1.85334i	0.0567910	+	0.0983648i
$356$	3.91425			0.207455
$357$	−5.71648	−	9.90123i	−0.302548	−	0.524029i
$358$	−4.58426	−	7.94017i	−0.242286	−	0.419651i
$359$	19.8853			1.04951			0.524753	−	0.851255i	$-0.324158\pi$
$359$	19.8853			1.04951			0.524753	+	0.851255i	$0.324158\pi$
$360$	0.681136	+	1.17976i	0.0358990	+	0.0621790i
$361$	9.49612	−	16.4478i	0.499796	−	0.865671i
$362$	−8.40850	+	14.5640i	−0.441941	+	0.765464i
$363$	−15.8116			−0.829895
$364$		0			0
$365$	1.66355			0.0870740
$366$	3.12833	−	5.41843i	0.163521	−	0.283226i
$367$	−0.541917	+	0.938628i	−0.0282878	+	0.0489960i	−0.879823	−	0.475302i	$-0.842339\pi$
$367$	−0.541917	+	0.938628i	−0.0282878	+	0.0489960i	0.851535	+	0.524298i	$0.175672\pi$
$368$	−0.414542	−	0.718009i	−0.0216095	−	0.0374288i
$369$	−23.7506			−1.23641
$370$	−0.563687	−	0.976335i	−0.0293047	−	0.0507572i
$371$	−12.2485	−	21.2150i	−0.635909	−	1.10143i
$372$	−20.2174			−1.04823
$373$	3.06518	+	5.30905i	0.158709	+	0.274892i	0.934403	−	0.356217i	$-0.115934\pi$
$373$	3.06518	+	5.30905i	0.158709	+	0.274892i	−0.775694	+	0.631109i	$0.782600\pi$
$374$	3.67629	−	6.36752i	0.190097	−	0.329257i
$375$	−2.75786	+	4.77676i	−0.142416	+	0.246671i
$376$	19.8049			1.02136
$377$		0			0
$378$	−4.03923			−0.207756
$379$	1.20440	−	2.08608i	0.0618658	−	0.107155i	−0.833434	−	0.552620i	$-0.813628\pi$
$379$	1.20440	−	2.08608i	0.0618658	−	0.107155i	0.895299	+	0.445465i	$0.146962\pi$
$380$	−0.0147700	+	0.0255824i	−0.000757685	+	0.00131235i
$381$	−11.0184	−	19.0845i	−0.564491	−	0.977726i
$382$	−11.5778			−0.592371
$383$	15.1957	+	26.3197i	0.776462	+	1.34487i	0.933969	+	0.357354i	$0.116321\pi$
$383$	15.1957	+	26.3197i	0.776462	+	1.34487i	−0.157506	+	0.987518i	$0.550345\pi$
$384$	−9.88620	−	17.1234i	−0.504503	−	0.873825i
$385$	2.47219			0.125994
$386$	5.44504	+	9.43109i	0.277145	+	0.480030i
$387$	0.303134	−	0.525044i	0.0154092	−	0.0266895i
$388$	−5.46734	+	9.46972i	−0.277562	+	0.480752i
$389$	−15.9409			−0.808237			−0.404118	−	0.914707i	$-0.632422\pi$
$389$	−15.9409			−0.808237			−0.404118	+	0.914707i	$0.632422\pi$
$390$		0			0
$391$	3.22521			0.163106
$392$	−1.94504	+	3.36891i	−0.0982394	+	0.170156i
$393$	−7.38889	+	12.7979i	−0.372720	+	0.645570i
$394$	0.224677	+	0.389152i	0.0113191	+	0.0196052i
$395$	2.46250			0.123902
$396$	−5.90366	−	10.2254i	−0.296670	−	0.513847i
$397$	−8.45742	−	14.6487i	−0.424466	−	0.735196i	0.571905	−	0.820320i	$-0.306205\pi$
$397$	−8.45742	−	14.6487i	−0.424466	−	0.735196i	−0.996370	+	0.0851239i	$0.972871\pi$
$398$	9.21552			0.461932
$399$	0.233406	+	0.404271i	0.0116849	+	0.0202389i
$400$	1.37047	−	2.37372i	0.0685235	−	0.118686i
$401$	−13.3312	+	23.0904i	−0.665730	+	1.15308i	0.313356	+	0.949636i	$0.398547\pi$
$401$	−13.3312	+	23.0904i	−0.665730	+	1.15308i	−0.979087	+	0.203443i	$0.934787\pi$
$402$	−13.8388			−0.690215
$403$		0			0
$404$	18.1207			0.901537
$405$	1.35205	−	2.34182i	0.0671840	−	0.116366i
$406$	4.37651	−	7.58034i	0.217203	−	0.376206i
$407$	12.0869	+	20.9352i	0.599128	+	1.03772i
$408$	13.0586			0.646497
$409$	−14.2582	−	24.6959i	−0.705021	−	1.22113i	−0.966684	−	0.255972i	$-0.917604\pi$
$409$	−14.2582	−	24.6959i	−0.705021	−	1.22113i	0.261663	−	0.965159i	$-0.415729\pi$
$410$	1.14795	+	1.98831i	0.0566931	+	0.0981954i
$411$	−13.9758			−0.689377
$412$	0.924231	+	1.60082i	0.0455336	+	0.0788665i
$413$	−7.99007	+	13.8392i	−0.393166	+	0.680983i
$414$	−1.22737	+	2.12586i	−0.0603217	+	0.104480i
$415$	0.397452			0.0195102
$416$		0			0
$417$	33.0465			1.61830
$418$	−0.150104	+	0.259988i	−0.00734185	+	0.0127165i
$419$	14.8046	−	25.6424i	0.723253	−	1.25271i	−0.236436	−	0.971647i	$-0.575979\pi$
$419$	14.8046	−	25.6424i	0.723253	−	1.25271i	0.959689	−	0.281064i	$-0.0906874\pi$
$420$	0.887395	+	1.53701i	0.0433005	+	0.0749986i
$421$	−11.6606			−0.568301			−0.284151	−	0.958780i	$-0.591712\pi$
$421$	−11.6606			−0.568301			−0.284151	+	0.958780i	$0.591712\pi$
$422$	−3.52230	−	6.10081i	−0.171463	−	0.296983i
$423$	7.53684	+	13.0542i	0.366453	+	0.634716i
$424$	27.9801			1.35884
$425$	5.33124	+	9.23398i	0.258603	+	0.447914i
$426$	−7.80678	+	13.5217i	−0.378240	+	0.655131i
$427$	4.09179	−	7.08719i	0.198016	−	0.342973i
$428$	−4.43535			−0.214391
$429$		0			0
$430$	−0.0586060			−0.00282623
$431$	−2.17456	+	3.76645i	−0.104745	+	0.181424i	−0.913634	−	0.406538i	$-0.866736\pi$
$431$	−2.17456	+	3.76645i	−0.104745	+	0.181424i	0.808889	+	0.587961i	$0.200069\pi$
$432$	−0.592990	+	1.02709i	−0.0285303	+	0.0494159i
$433$	7.19418	+	12.4607i	0.345730	+	0.598822i	0.985486	−	0.169756i	$-0.0542979\pi$
$433$	7.19418	+	12.4607i	0.345730	+	0.598822i	−0.639756	+	0.768578i	$0.720965\pi$
$434$	12.5332			0.601612
$435$	1.28501	+	2.22571i	0.0616116	+	0.106714i
$436$	10.6528	+	18.4512i	0.510176	+	0.883651i
$437$	−0.131687			−0.00629942
$438$	6.06853	+	10.5110i	0.289966	+	0.502235i
$439$	10.1163	−	17.5219i	0.482822	−	0.836273i	−0.516983	−	0.855996i	$-0.672945\pi$
$439$	10.1163	−	17.5219i	0.482822	−	0.836273i	0.999805	+	0.0197227i	$0.00627834\pi$
$440$	−1.41185	+	2.44540i	−0.0673075	+	0.116580i
$441$	−2.96077			−0.140989
$442$		0			0
$443$	8.12200			0.385888			0.192944	−	0.981210i	$-0.438196\pi$
$443$	8.12200			0.385888			0.192944	+	0.981210i	$0.438196\pi$
$444$	−8.67725	+	15.0294i	−0.411804	+	0.713266i
$445$	0.356232	−	0.617012i	0.0168870	−	0.0292492i
$446$	0.905813	+	1.56891i	0.0428915	+	0.0742903i
$447$	−9.74094			−0.460731
$448$	4.20075	+	7.27591i	0.198467	+	0.343755i
$449$	−6.24578	−	10.8180i	−0.294757	−	0.510534i	0.680172	−	0.733053i	$-0.261905\pi$
$449$	−6.24578	−	10.8180i	−0.294757	−	0.510534i	−0.974928	+	0.222519i	$0.928572\pi$
$450$	−8.11529			−0.382559
$451$	−24.6151	−	42.6345i	−1.15908	−	2.00758i
$452$	8.17456	−	14.1588i	0.384499	−	0.665972i
$453$	4.43147	−	7.67553i	0.208209	−	0.360628i
$454$	−5.58642			−0.262184
$455$		0			0
$456$	−0.533188			−0.0249688
$457$	−2.99061	+	5.17988i	−0.139895	+	0.242305i	−0.927457	−	0.373931i	$-0.878010\pi$
$457$	−2.99061	+	5.17988i	−0.139895	+	0.242305i	0.787562	+	0.616236i	$0.211343\pi$
$458$	9.69298	−	16.7887i	0.452923	−	0.784486i
$459$	−2.30678	−	3.99546i	−0.107671	−	0.186492i
$460$	−0.500664			−0.0233436
$461$	1.02834	+	1.78114i	0.0478947	+	0.0829561i	0.888979	−	0.457948i	$-0.151415\pi$
$461$	1.02834	+	1.78114i	0.0478947	+	0.0829561i	−0.841084	+	0.540904i	$0.818082\pi$
$462$	9.01842	+	15.6204i	0.419575	+	0.726725i
$463$	−8.44935			−0.392675			−0.196337	−	0.980536i	$-0.562905\pi$
$463$	−8.44935			−0.392675			−0.196337	+	0.980536i	$0.562905\pi$
$464$	−1.28501	−	2.22571i	−0.0596552	−	0.103326i
$465$	−1.83997	+	3.18692i	−0.0853266	+	0.147790i
$466$	1.22737	−	2.12586i	0.0568566	−	0.0984785i
$467$	33.5139			1.55084			0.775420	−	0.631446i	$-0.217538\pi$
$467$	33.5139			1.55084			0.775420	+	0.631446i	$0.217538\pi$
$468$		0			0
$469$	−18.1008			−0.835818
$470$	0.728562	−	1.26191i	0.0336060	−	0.0582074i
$471$	5.00484	−	8.66864i	0.230611	−	0.399430i
$472$	−9.12618	−	15.8070i	−0.420066	−	0.727576i
$473$	1.25667			0.0577817
$474$	8.98307	+	15.5591i	0.412606	+	0.714655i
$475$	−0.217677	−	0.377027i	−0.00998769	−	0.0172992i
$476$	6.90408			0.316448
$477$	10.6479	+	18.4428i	0.487536	+	0.844437i
$478$	10.0831	−	17.4644i	0.461189	−	0.798802i
$479$	12.3656	−	21.4179i	0.565000	−	0.978608i	−0.432050	−	0.901850i	$-0.642210\pi$
$479$	12.3656	−	21.4179i	0.565000	−	0.978608i	0.997050	−	0.0767587i	$-0.0244571\pi$
$480$	−3.23490			−0.147652
$481$		0			0
$482$	−16.2524			−0.740275
$483$	−3.95593	+	6.85187i	−0.180001	+	0.311771i
$484$	4.77413	−	8.26903i	0.217006	−	0.375865i
$485$	0.995156	+	1.72366i	0.0451877	+	0.0782674i
$486$	14.5875			0.661702
$487$	18.8778	+	32.6972i	0.855433	+	1.48165i	0.876243	+	0.481870i	$0.160042\pi$
$487$	18.8778	+	32.6972i	0.855433	+	1.48165i	−0.0208094	+	0.999783i	$0.506624\pi$
$488$	4.67360	+	8.09492i	0.211564	+	0.366440i
$489$	−36.3086			−1.64193
$490$	0.143104	+	0.247864i	0.00646479	+	0.0111973i
$491$	−15.6555	+	27.1161i	−0.706522	+	1.22373i	0.259617	+	0.965712i	$0.416404\pi$
$491$	−15.6555	+	27.1161i	−0.706522	+	1.22373i	−0.966139	+	0.258020i	$0.916930\pi$
$492$	17.6712	−	30.6074i	0.796680	−	1.37989i
$493$	9.99761			0.450270
$494$		0			0
$495$	−2.14914			−0.0965969
$496$	1.83997	−	3.18692i	0.0826171	−	0.143097i
$497$	−10.2111	+	17.6861i	−0.458031	+	0.793332i
$498$	1.44989	+	2.51128i	0.0649710	+	0.112533i
$499$	21.4873			0.961902			0.480951	−	0.876748i	$-0.340292\pi$
$499$	21.4873			0.961902			0.480951	+	0.876748i	$0.340292\pi$
$500$	−1.66541	−	2.88457i	−0.0744793	−	0.129002i
$501$	18.1075	+	31.3632i	0.808984	+	1.40120i
$502$	−19.0228			−0.849031
$503$	−18.7962	−	32.5560i	−0.838081	−	1.45160i	−0.891497	−	0.453026i	$-0.850344\pi$
$503$	−18.7962	−	32.5560i	−0.838081	−	1.45160i	0.0534164	−	0.998572i	$-0.482989\pi$
$504$	−6.50000	+	11.2583i	−0.289533	+	0.501486i
$505$	1.64914	−	2.85640i	0.0733860	−	0.127108i
$506$	−5.08815			−0.226196
$507$		0			0
$508$	13.3075			0.590425
$509$	8.55376	−	14.8155i	0.379139	−	0.656688i	−0.611798	−	0.791014i	$-0.709554\pi$
$509$	8.55376	−	14.8155i	0.379139	−	0.656688i	0.990937	+	0.134326i	$0.0428869\pi$
$510$	0.480386	−	0.832052i	0.0212718	−	0.0368439i
$511$	7.93751	+	13.7482i	0.351135	+	0.608183i
$512$	6.22282			0.275012
$513$	0.0941868	+	0.163136i	0.00415845	+	0.00720264i
$514$	−5.70344	−	9.87865i	−0.251568	−	0.435728i
$515$	0.336454			0.0148259
$516$	0.451083	+	0.781298i	0.0198578	+	0.0343947i
$517$	−15.6223	+	27.0586i	−0.687068	+	1.19004i
$518$	5.37920	−	9.31705i	0.236348	−	0.409367i
$519$	48.3913			2.12414
$520$		0			0
$521$	−19.8465			−0.869493			−0.434746	−	0.900553i	$-0.643162\pi$
$521$	−19.8465			−0.869493			−0.434746	+	0.900553i	$0.643162\pi$
$522$	−3.80463	+	6.58981i	−0.166524	+	0.288428i
$523$	5.71499	−	9.89865i	0.249899	−	0.432838i	−0.713599	−	0.700555i	$-0.752936\pi$
$523$	5.71499	−	9.89865i	0.249899	−	0.432838i	0.963498	+	0.267717i	$0.0862693\pi$
$524$	−4.46197	−	7.72835i	−0.194922	−	0.337615i
$525$	−26.1564			−1.14156
$526$	6.85474	+	11.8728i	0.298881	+	0.517677i
$527$	7.15764	+	12.3974i	0.311792	+	0.540039i
$528$	5.29590			0.230474
$529$	10.3840	+	17.9857i	0.451480	+	0.781987i
$530$	1.02930	−	1.78281i	0.0447101	−	0.0774401i
$531$	6.94600	−	12.0308i	0.301431	−	0.522093i
$532$	−0.281896			−0.0122218
$533$		0			0
$534$	5.19806			0.224942
$535$	−0.403657	+	0.699155i	−0.0174516	+	0.0302271i
$536$	10.3373	−	17.9047i	0.446503	−	0.773365i
$537$	12.8448	+	22.2479i	0.554295	+	0.960066i
$538$	−5.18598			−0.223584
$539$	−3.06853	−	5.31485i	−0.132171	−	0.228927i
$540$	0.358092	+	0.620234i	0.0154098	+	0.0266906i
$541$	16.1884			0.695993			0.347996	−	0.937496i	$-0.386862\pi$
$541$	16.1884			0.695993			0.347996	+	0.937496i	$0.386862\pi$
$542$	−2.58546	−	4.47814i	−0.111055	−	0.192353i
$543$	23.5601	−	40.8073i	1.01106	−	1.75121i
$544$	−6.29201	+	10.8981i	−0.269768	+	0.467252i
$545$	3.87800			0.166115
$546$		0			0
$547$	5.33081			0.227929			0.113965	−	0.993485i	$-0.463645\pi$
$547$	5.33081			0.227929			0.113965	+	0.993485i	$0.463645\pi$
$548$	4.21983	−	7.30896i	0.180262	−	0.312223i
$549$	−3.55711	+	6.16110i	−0.151814	+	0.262949i
$550$	−8.41066	−	14.5677i	−0.358632	−	0.621168i
$551$	−0.408206			−0.0173902
$552$	−4.51842	−	7.82613i	−0.192317	−	0.333102i
$553$	11.7497	+	20.3510i	0.499647	+	0.865413i
$554$	10.7942			0.458600
$555$	1.57942	+	2.73563i	0.0670425	+	0.116121i
$556$	−9.97799	+	17.2824i	−0.423161	+	0.732937i
$557$	−3.69537	+	6.40058i	−0.156578	+	0.271201i	−0.933633	−	0.358232i	$-0.883380\pi$
$557$	−3.69537	+	6.40058i	−0.156578	+	0.271201i	0.777054	+	0.629433i	$0.216713\pi$
$558$	−10.8955			−0.461242
$559$		0			0
$560$	−0.323044			−0.0136511
$561$	−10.3007	+	17.8414i	−0.434898	+	0.753265i
$562$	−2.01961	+	3.49807i	−0.0851923	+	0.147557i
$563$	4.73945	+	8.20896i	0.199744	+	0.345967i	0.948445	−	0.316941i	$-0.102656\pi$
$563$	4.73945	+	8.20896i	0.199744	+	0.345967i	−0.748701	+	0.662907i	$0.769322\pi$
$564$	−22.4306			−0.944497
$565$	−1.48792	−	2.57715i	−0.0625972	−	0.108422i
$566$	−8.87263	−	15.3678i	−0.372944	−	0.645958i
$567$	25.8049			1.08370
$568$	−11.6630	−	20.2009i	−0.489369	−	0.847612i
$569$	5.07188	−	8.78476i	0.212624	−	0.368276i	−0.739911	−	0.672705i	$-0.765132\pi$
$569$	5.07188	−	8.78476i	0.212624	−	0.368276i	0.952535	+	0.304429i	$0.0984656\pi$
$570$	−0.0196143	+	0.0339730i	−0.000821554	+	0.00142297i
$571$	−14.0925			−0.589751			−0.294876	−	0.955536i	$-0.595278\pi$
$571$	−14.0925			−0.589751			−0.294876	+	0.955536i	$0.595278\pi$
$572$		0			0
$573$	32.4403			1.35521
$574$	−10.9547	+	18.9741i	−0.457242	+	0.791966i
$575$	3.68933	−	6.39011i	0.153856	−	0.266486i
$576$	−3.65183	−	6.32516i	−0.152160	−	0.263548i
$577$	25.1545			1.04720			0.523598	−	0.851965i	$-0.324589\pi$
$577$	25.1545			1.04720			0.523598	+	0.851965i	$0.324589\pi$
$578$	4.94773	+	8.56972i	0.205798	+	0.356453i
$579$	−15.2567	−	26.4253i	−0.634045	−	1.09820i
$580$	−1.55197			−0.0644422
$581$	1.89642	+	3.28470i	0.0786768	+	0.136272i
$582$	−7.26055	+	12.5756i	−0.300960	+	0.521277i
$583$	−22.0710	+	38.2281i	−0.914087	+	1.58324i
$584$	−18.1323			−0.750319
$585$		0			0
$586$	11.9860			0.495137
$587$	−21.9177	+	37.9625i	−0.904639	+	1.56688i	−0.0832369	+	0.996530i	$0.526526\pi$
$587$	−21.9177	+	37.9625i	−0.904639	+	1.56688i	−0.821402	+	0.570350i	$0.806808\pi$
$588$	2.20291	−	3.81555i	0.0908463	−	0.157350i
$589$	−0.292249	−	0.506190i	−0.0120419	−	0.0208572i
$590$	−1.34290			−0.0552861
$591$	−0.629531	−	1.09038i	−0.0258954	−	0.0448522i
$592$	−1.57942	−	2.73563i	−0.0649136	−	0.112434i
$593$	−24.9965			−1.02648			−0.513242	−	0.858244i	$-0.671556\pi$
$593$	−24.9965			−1.02648			−0.513242	+	0.858244i	$0.671556\pi$
$594$	3.63922	+	6.30331i	0.149319	+	0.258628i
$595$	0.628334	−	1.08831i	0.0257592	−	0.0446162i
$596$	2.94116	−	5.09423i	0.120474	−	0.208668i
$597$	−25.8213			−1.05680
$598$		0			0
$599$	−6.24027			−0.254971			−0.127485	−	0.991840i	$-0.540691\pi$
$599$	−6.24027			−0.254971			−0.127485	+	0.991840i	$0.540691\pi$
$600$	14.9378	−	25.8730i	0.609833	−	1.05626i
$601$	−3.16487	+	5.48172i	−0.129098	+	0.223604i	−0.923327	−	0.384014i	$-0.874541\pi$
$601$	−3.16487	+	5.48172i	−0.129098	+	0.223604i	0.794229	+	0.607618i	$0.207875\pi$
$602$	−0.279635	−	0.484342i	−0.0113971	−	0.0197403i
$603$	15.7356			0.640802
$604$	2.67606	+	4.63506i	0.108887	+	0.188598i
$605$	−0.868977	−	1.50511i	−0.0353290	−	0.0611915i
$606$	24.0640			0.977532
$607$	21.8240	+	37.8003i	0.885809	+	1.53427i	0.844784	+	0.535108i	$0.179729\pi$
$607$	21.8240	+	37.8003i	0.885809	+	1.53427i	0.0410253	+	0.999158i	$0.486938\pi$
$608$	0.256905	−	0.444973i	0.0104189	−	0.0180460i
$609$	−12.2627	+	21.2396i	−0.496910	+	0.860673i
$610$	0.687710			0.0278445
$611$		0			0
$612$	−6.00192			−0.242613
$613$	12.9770	−	22.4769i	0.524137	−	0.907833i	−0.475468	−	0.879733i	$-0.657721\pi$
$613$	12.9770	−	22.4769i	0.524137	−	0.907833i	0.999605	−	0.0280995i	$-0.00894552\pi$
$614$	−7.67025	+	13.2853i	−0.309546	+	0.536150i
$615$	−3.21648	−	5.57111i	−0.129701	−	0.224649i
$616$	−26.9463			−1.08570
$617$	−22.9698	−	39.7849i	−0.924729	−	1.60168i	−0.791996	−	0.610526i	$-0.790958\pi$
$617$	−22.9698	−	39.7849i	−0.924729	−	1.60168i	−0.132733	−	0.991152i	$-0.542375\pi$
$618$	1.22737	+	2.12586i	0.0493719	+	0.0855146i
$619$	6.73556			0.270725			0.135363	−	0.990796i	$-0.456780\pi$
$619$	6.73556			0.270725			0.135363	+	0.990796i	$0.456780\pi$
$620$	−1.11111	−	1.92450i	−0.0446234	−	0.0772899i
$621$	−1.59634	+	2.76495i	−0.0640590	+	0.110953i
$622$	0.108187	−	0.187386i	0.00433792	−	0.00751349i
$623$	6.79895			0.272394
$624$		0			0
$625$	24.0887			0.963549
$626$	9.38016	−	16.2469i	0.374907	−	0.649357i
$627$	0.420583	−	0.728471i	0.0167965	−	0.0290923i
$628$	3.02230	+	5.23478i	0.120603	+	0.208891i
$629$	12.2881			0.489960
$630$	0.478230	+	0.828318i	0.0190531	+	0.0330010i
$631$	−22.5499	−	39.0575i	−0.897696	−	1.55486i	−0.830432	−	0.557121i	$-0.811906\pi$
$631$	−22.5499	−	39.0575i	−0.897696	−	1.55486i	−0.0672649	−	0.997735i	$-0.521427\pi$
$632$	−26.8407			−1.06767
$633$	9.86927	+	17.0941i	0.392268	+	0.679429i
$634$	5.61165	−	9.71965i	0.222867	−	0.386017i
$635$	1.21110	−	2.09769i	0.0480612	−	0.0832444i
$636$	−31.6896			−1.25658
$637$		0			0
$638$	−15.7724			−0.624435
$639$	8.87681	−	15.3751i	0.351161	−	0.608229i
$640$	1.08665	−	1.88214i	0.0429538	−	0.0743981i
$641$	−16.2911	−	28.2169i	−0.643458	−	1.11450i	−0.984655	−	0.174510i	$-0.944166\pi$
$641$	−16.2911	−	28.2169i	−0.643458	−	1.11450i	0.341197	−	0.939992i	$-0.389168\pi$
$642$	−5.89008			−0.232463
$643$	−12.7877	−	22.1489i	−0.504298	−	0.873469i	−0.999988	−	0.00496965i	$-0.998418\pi$
$643$	−12.7877	−	22.1489i	−0.504298	−	0.873469i	0.495690	−	0.868500i	$-0.334915\pi$
$644$	−2.38889	−	4.13767i	−0.0941353	−	0.163047i
$645$	0.164210			0.00646578
$646$	0.0763014	+	0.132158i	0.00300204	+	0.00519968i
$647$	15.0858	−	26.1293i	0.593082	−	1.02725i	−0.400732	−	0.916195i	$-0.631244\pi$
$647$	15.0858	−	26.1293i	0.593082	−	1.02725i	0.993814	−	0.111053i	$-0.0354224\pi$
$648$	−14.7371	+	25.5253i	−0.578926	+	1.00273i
$649$	28.7952			1.13031
$650$		0			0
$651$	−35.1172			−1.37635
$652$	10.9629	−	18.9883i	0.429341	−	0.743641i
$653$	−18.4514	+	31.9587i	−0.722058	+	1.25064i	0.238115	+	0.971237i	$0.423470\pi$
$653$	−18.4514	+	31.9587i	−0.722058	+	1.25064i	−0.960173	+	0.279405i	$0.909863\pi$
$654$	14.1468	+	24.5029i	0.553182	+	0.958139i
$655$	−1.62432			−0.0634673
$656$	3.21648	+	5.57111i	0.125582	+	0.217515i
$657$	−6.90030	−	11.9517i	−0.269207	−	0.466279i
$658$	13.9051			0.542079
$659$	−11.8433	−	20.5132i	−0.461350	−	0.799082i	0.537678	−	0.843150i	$-0.319302\pi$
$659$	−11.8433	−	20.5132i	−0.461350	−	0.799082i	−0.999029	+	0.0440679i	$0.985968\pi$
$660$	1.59903	−	2.76960i	0.0622422	−	0.107807i
$661$	15.8795	−	27.5041i	0.617641	−	1.06979i	−0.372274	−	0.928123i	$-0.621422\pi$
$661$	15.8795	−	27.5041i	0.617641	−	1.06979i	0.989915	−	0.141662i	$-0.0452447\pi$
$662$	14.2916			0.555458
$663$		0			0
$664$	−4.33214			−0.168120
$665$	−0.0256551	+	0.0444360i	−0.000994863	+	0.00172315i
$666$	−4.67629	+	8.09958i	−0.181203	+	0.313852i
$667$	−3.45928	−	5.99165i	−0.133944	−	0.231998i
$668$	−21.8694			−0.846152
$669$	−2.53803	−	4.39600i	−0.0981260	−	0.169959i
$670$	−0.760553	−	1.31732i	−0.0293827	−	0.0508924i
$671$	−14.7463			−0.569275
$672$	−15.4351	−	26.7344i	−0.595423	−	1.03130i
$673$	3.75116	−	6.49720i	0.144597	−	0.250449i	−0.784626	−	0.619970i	$-0.787145\pi$
$673$	3.75116	−	6.49720i	0.144597	−	0.250449i	0.929222	+	0.369521i	$0.120478\pi$
$674$	11.1664	−	19.3407i	0.430112	−	0.744976i
$675$	−10.5550			−0.406261
$676$		0			0
$677$	−35.0315			−1.34637			−0.673184	−	0.739475i	$-0.735074\pi$
$677$	−35.0315			−1.34637			−0.673184	+	0.739475i	$0.735074\pi$
$678$	10.8557	−	18.8026i	0.416911	−	0.722110i
$679$	−9.49665	+	16.4487i	−0.364448	+	0.631242i
$680$	0.717677	+	1.24305i	0.0275216	+	0.0476689i
$681$	15.6528			0.599816
$682$	−11.2920	−	19.5583i	−0.432393	−	0.748927i
$683$	12.0417	+	20.8568i	0.460762	+	0.798063i	0.998999	−	0.0447302i	$-0.0142428\pi$
$683$	12.0417	+	20.8568i	0.460762	+	0.798063i	−0.538237	+	0.842794i	$0.680909\pi$
$684$	0.245061			0.00937013
$685$	−0.768086	−	1.33036i	−0.0293471	−	0.0508306i
$686$	−7.98092	+	13.8234i	−0.304713	+	0.527778i
$687$	−27.1591	+	47.0410i	−1.03619	+	1.79473i
$688$	−0.164210			−0.00626046
$689$		0			0
$690$	−0.664874			−0.0253113
$691$	−1.00724	+	1.74459i	−0.0383171	+	0.0663672i	−0.884548	−	0.466449i	$-0.845533\pi$
$691$	−1.00724	+	1.74459i	−0.0383171	+	0.0663672i	0.846231	+	0.532816i	$0.178866\pi$
$692$	−14.6112	+	25.3073i	−0.555433	+	0.962039i
$693$	−10.2545	−	17.7613i	−0.389537	−	0.674697i
$694$	1.20583			0.0457728
$695$	1.81618	+	3.14571i	0.0688915	+	0.119323i
$696$	−14.0063	−	24.2597i	−0.530909	−	0.919561i
$697$	−25.0248			−0.947880
$698$	5.68814	+	9.85214i	0.215299	+	0.372909i
$699$	−3.43900	+	5.95652i	−0.130075	+	0.225296i
$700$	7.89762	−	13.6791i	0.298502	−	0.517020i
$701$	−48.8189			−1.84387			−0.921933	−	0.387350i	$-0.873390\pi$
$701$	−48.8189			−1.84387			−0.921933	+	0.387350i	$0.873390\pi$
$702$		0			0
$703$	−0.501729			−0.0189231
$704$	7.56949	−	13.1107i	0.285286	−	0.494130i
$705$	−2.04138	+	3.53578i	−0.0768830	+	0.133165i
$706$	2.87435	+	4.97853i	0.108178	+	0.187369i
$707$	31.4752			1.18375
$708$	10.3361	+	17.9026i	0.388454	+	0.672822i
$709$	10.4030	+	18.0185i	0.390693	+	0.676699i	0.992541	−	0.121911i	$-0.0389022\pi$
$709$	10.4030	+	18.0185i	0.390693	+	0.676699i	−0.601848	+	0.798610i	$0.705569\pi$
$710$	−1.71618			−0.0644073
$711$	−10.2143	−	17.6917i	−0.383067	−	0.663492i
$712$	−3.88285	+	6.72529i	−0.145516	+	0.252041i
$713$	4.95324	−	8.57926i	0.185500	−	0.321296i
$714$	9.16852			0.343123
$715$		0			0
$716$	−15.5133			−0.579761
$717$	−28.2521	+	48.9341i	−1.05509	+	1.82748i
$718$	−7.97339	+	13.8103i	−0.297564	+	0.515396i
$719$	−10.7153	−	18.5594i	−0.399613	−	0.692149i	0.594065	−	0.804417i	$-0.297522\pi$
$719$	−10.7153	−	18.5594i	−0.399613	−	0.692149i	−0.993678	+	0.112267i	$0.964189\pi$
$720$	0.280831			0.0104660
$721$	1.60537	+	2.78058i	0.0597870	+	0.103554i
$722$	7.61529	+	13.1901i	0.283412	+	0.490884i
$723$	45.5381			1.69358
$724$	14.2274	+	24.6425i	0.528756	+	0.915832i
$725$	11.4363	−	19.8083i	0.424734	−	0.735661i
$726$	6.33997	−	10.9812i	0.235298	−	0.407549i
$727$	13.4862			0.500175			0.250088	−	0.968223i	$-0.419541\pi$
$727$	13.4862			0.500175			0.250088	+	0.968223i	$0.419541\pi$
$728$		0			0
$729$	−8.02715			−0.297302
$730$	−0.667030	+	1.15533i	−0.0246879	+	0.0427607i
$731$	0.319396	−	0.553210i	0.0118133	−	0.0204612i
$732$	−5.29321	−	9.16811i	−0.195643	−	0.338863i
$733$	−43.5424			−1.60828			−0.804138	−	0.594443i	$-0.797373\pi$
$733$	−43.5424			−1.60828			−0.804138	+	0.594443i	$0.797373\pi$
$734$	−0.434584	−	0.752721i	−0.0160408	−	0.0277834i
$735$	−0.400969	−	0.694498i	−0.0147900	−	0.0256170i
$736$	8.70841			0.320996
$737$	16.3083	+	28.2468i	0.600723	+	1.04048i
$738$	9.52326	−	16.4948i	0.350556	−	0.607181i
$739$	−10.0271	+	17.3675i	−0.368855	+	0.638875i	−0.989387	−	0.145306i	$-0.953583\pi$
$739$	−10.0271	+	17.3675i	−0.368855	+	0.638875i	0.620532	+	0.784181i	$0.286917\pi$
$740$	−1.90754			−0.0701226
$741$		0			0
$742$	19.6450			0.721191
$743$	16.5843	−	28.7248i	0.608418	−	1.05381i	−0.383084	−	0.923714i	$-0.625138\pi$
$743$	16.5843	−	28.7248i	0.608418	−	1.05381i	0.991501	−	0.130096i	$-0.0415287\pi$
$744$	20.0553	−	34.7367i	0.735261	−	1.27351i
$745$	−0.535344	−	0.927243i	−0.0196135	−	0.0339715i
$746$	−4.91617			−0.179994
$747$	−1.64861	−	2.85548i	−0.0603196	−	0.104477i
$748$	−6.22037	−	10.7740i	−0.227439	−	0.393936i
$749$	−7.70410			−0.281502
$750$	−2.21164	−	3.83067i	−0.0807575	−	0.139876i
$751$	−19.6407	+	34.0187i	−0.716700	+	1.24136i	0.245601	+	0.969371i	$0.421015\pi$
$751$	−19.6407	+	34.0187i	−0.716700	+	1.24136i	−0.962300	+	0.271989i	$0.912318\pi$
$752$	2.04138	−	3.53578i	0.0744416	−	0.128937i
$753$	53.3008			1.94239
$754$		0			0
$755$	0.974181			0.0354541
$756$	−3.41723	+	5.91882i	−0.124283	+	0.215265i
$757$	23.3213	−	40.3937i	0.847628	−	1.46813i	−0.0356920	−	0.999363i	$-0.511364\pi$
$757$	23.3213	−	40.3937i	0.847628	−	1.46813i	0.883320	−	0.468771i	$-0.155303\pi$
$758$	0.965853	+	1.67291i	0.0350813	+	0.0607627i
$759$	14.2567			0.517484
$760$	−0.0293030	−	0.0507543i	−0.00106293	−	0.00184105i
$761$	10.9492	+	18.9646i	0.396909	+	0.687467i	0.993343	−	0.115196i	$-0.0367495\pi$
$761$	10.9492	+	18.9646i	0.396909	+	0.687467i	−0.596434	+	0.802662i	$0.703416\pi$
$762$	17.6722			0.640195
$763$	18.5036	+	32.0493i	0.669877	+	1.16026i
$764$	−9.79494	+	16.9653i	−0.354368	+	0.613784i
$765$	−0.546229	+	0.946096i	−0.0197489	+	0.0342062i
$766$	−24.3720			−0.880595
$767$		0			0
$768$	31.8756			1.15021
$769$	−23.3548	+	40.4517i	−0.842196	+	1.45873i	0.0458390	+	0.998949i	$0.485404\pi$
$769$	−23.3548	+	40.4517i	−0.842196	+	1.45873i	−0.888035	+	0.459777i	$0.847929\pi$
$770$	−0.991271	+	1.71693i	−0.0357229	+	0.0618739i
$771$	15.9807	+	27.6794i	0.575530	+	0.996848i
$772$	18.4263			0.663175
$773$	15.1208	+	26.1900i	0.543857	+	0.941989i	0.998678	+	0.0514055i	$0.0163701\pi$
$773$	15.1208	+	26.1900i	0.543857	+	0.941989i	−0.454820	+	0.890583i	$0.650297\pi$
$774$	0.243095	+	0.421052i	0.00873786	+	0.0151344i
$775$	32.7506			1.17644
$776$	−10.8470	−	18.7875i	−0.389384	−	0.674432i
$777$	−15.0722	+	26.1058i	−0.540711	+	0.936540i
$778$	6.39181	−	11.0709i	0.229158	−	0.396913i
$779$	1.02177			0.0366087
$780$		0			0
$781$	36.7995			1.31679
$782$	−1.29321	+	2.23990i	−0.0462450	+	0.0800988i
$783$	−4.94839	+	8.57087i	−0.176841	+	0.306298i
$784$	0.400969	+	0.694498i	0.0143203	+	0.0248035i
$785$	1.10023			0.0392688
$786$	−5.92543	−	10.2631i	−0.211353	−	0.366074i
$787$	−14.3512	−	24.8569i	−0.511563	−	0.886054i	−0.999910	−	0.0134040i	$-0.995733\pi$
$787$	−14.3512	−	24.8569i	−0.511563	−	0.886054i	0.488347	−	0.872650i	$-0.337600\pi$
$788$	0.760316			0.0270851
$789$	−19.2066	−	33.2667i	−0.683771	−	1.18433i
$790$	−0.987386	+	1.71020i	−0.0351296	+	0.0608463i
$791$	14.1990	−	24.5934i	0.504859	−	0.874442i
$792$	23.4252			0.832378
$793$		0			0
$794$	13.5646			0.481391
$795$	−2.88404	+	4.99531i	−0.102286	+	0.177165i
$796$	7.79643	−	13.5038i	0.276337	−	0.478630i
$797$	9.27091	+	16.0577i	0.328392	+	0.568792i	0.982193	−	0.187875i	$-0.0601599\pi$
$797$	9.27091	+	16.0577i	0.328392	+	0.568792i	−0.653801	+	0.756667i	$0.726827\pi$
$798$	−0.374354			−0.0132520
$799$	7.94116	+	13.7545i	0.280938	+	0.486599i
$800$	14.3949	+	24.9327i	0.508938	+	0.881506i
$801$	−5.91053			−0.208838
$802$	−10.6908	−	18.5171i	−0.377506	−	0.653860i
$803$	14.3029	−	24.7733i	0.504738	−	0.874232i
$804$	−11.7078	+	20.2784i	−0.412901	+	0.715165i
$805$	−0.869641			−0.0306508
$806$		0			0
$807$	14.5308			0.511508
$808$	−17.9753	+	31.1341i	−0.632369	+	1.09530i
$809$	5.03385	−	8.71889i	0.176981	−	0.306540i	−0.763864	−	0.645377i	$-0.776700\pi$
$809$	5.03385	−	8.71889i	0.176981	−	0.306540i	0.940845	+	0.338837i	$0.110034\pi$
$810$	1.08426	+	1.87800i	0.0380971	+	0.0659860i
$811$	−10.0285			−0.352147			−0.176074	−	0.984377i	$-0.556340\pi$
$811$	−10.0285			−0.352147			−0.176074	+	0.984377i	$0.556340\pi$
$812$	−7.40515	−	12.8261i	−0.259870	−	0.450108i
$813$	7.24429	+	12.5475i	0.254068	+	0.440059i
$814$	−19.3860			−0.679478
$815$	−1.99545	−	3.45622i	−0.0698976	−	0.121066i
$816$	1.34601	−	2.33136i	0.0471198	−	0.0816139i
$817$	−0.0130411	+	0.0225878i	−0.000456249	+	0.000790247i
$818$	22.8683			0.799572
$819$		0			0
$820$	3.88471			0.135660
$821$	13.0852	−	22.6643i	0.456677	−	0.790988i	−0.542106	−	0.840310i	$-0.682373\pi$
$821$	13.0852	−	22.6643i	0.456677	−	0.790988i	0.998783	+	0.0493220i	$0.0157061\pi$
$822$	5.60388	−	9.70620i	0.195458	−	0.338542i
$823$	−0.911190	−	1.57823i	−0.0317621	−	0.0550135i	0.849707	−	0.527255i	$-0.176779\pi$
$823$	−0.911190	−	1.57823i	−0.0317621	−	0.0550135i	−0.881470	+	0.472241i	$0.843445\pi$
$824$	−3.66727			−0.127755
$825$	23.5661	+	40.8177i	0.820468	+	1.42109i
$826$	−6.40754	−	11.0982i	−0.222947	−	0.386155i
$827$	−32.2941			−1.12298			−0.561488	−	0.827485i	$-0.689771\pi$
$827$	−32.2941			−1.12298			−0.561488	+	0.827485i	$0.689771\pi$
$828$	2.07673	+	3.59700i	0.0721713	+	0.125004i
$829$	−7.55011	+	13.0772i	−0.262226	+	0.454189i	−0.966833	−	0.255409i	$-0.917790\pi$
$829$	−7.55011	+	13.0772i	−0.262226	+	0.454189i	0.704607	+	0.709598i	$0.251123\pi$
$830$	−0.159366	+	0.276030i	−0.00553168	+	0.00958115i
$831$	−30.2446			−1.04917
$832$		0			0
$833$	−3.11960			−0.108088
$834$	−13.2506	+	22.9508i	−0.458832	+	0.794720i
$835$	−1.99031	+	3.44732i	−0.0688776	+	0.119299i
$836$	0.253980	+	0.439906i	0.00878408	+	0.0152145i
$837$	−14.1709			−0.489818
$838$	11.8724	+	20.5636i	0.410125	+	0.710357i
$839$	16.4983	+	28.5758i	0.569584	+	0.986548i	0.996607	+	0.0823071i	$0.0262288\pi$
$839$	16.4983	+	28.5758i	0.569584	+	0.986548i	−0.427023	+	0.904241i	$0.640438\pi$
$840$	−3.52111			−0.121490
$841$	3.77682	+	6.54164i	0.130235	+	0.225574i
$842$	4.67552	−	8.09824i	0.161129	−	0.279084i
$843$	5.65883	−	9.80139i	0.194901	−	0.337578i
$844$	−11.9196			−0.410290
$845$		0			0
$846$	−12.0881			−0.415599
$847$	8.29254	−	14.3631i	0.284935	−	0.493522i
$848$	2.88404	−	4.99531i	0.0990384	−	0.171540i
$849$	24.8605	+	43.0597i	0.853212	+	1.47781i
$850$	−8.55065			−0.293285
$851$	−4.25182	−	7.36438i	−0.145751	−	0.252448i
$852$	13.2092	+	22.8791i	0.452541	+	0.783824i
$853$	−37.7802			−1.29357			−0.646784	−	0.762673i	$-0.723887\pi$
$853$	−37.7802			−1.29357			−0.646784	+	0.762673i	$0.723887\pi$
$854$	3.28136	+	5.68349i	0.112286	+	0.194485i
$855$	0.0223027	−	0.0386295i	0.000762737	−	0.00132110i
$856$	4.39977	−	7.62063i	0.150381	−	0.260468i
$857$	27.3623			0.934677			0.467339	−	0.884078i	$-0.345213\pi$
$857$	27.3623			0.934677			0.467339	+	0.884078i	$0.345213\pi$
$858$		0			0
$859$	−20.0629			−0.684538			−0.342269	−	0.939602i	$-0.611195\pi$
$859$	−20.0629			−0.684538			−0.342269	+	0.939602i	$0.611195\pi$
$860$	−0.0495813	+	0.0858774i	−0.00169071	+	0.00292839i
$861$	30.6945	−	53.1644i	1.04606	−	1.81184i
$862$	−1.74386	−	3.02046i	−0.0593962	−	0.102877i
$863$	−6.14483			−0.209173			−0.104586	−	0.994516i	$-0.533352\pi$
$863$	−6.14483			−0.209173			−0.104586	+	0.994516i	$0.533352\pi$
$864$	−6.22856	−	10.7882i	−0.211900	−	0.367022i
$865$	2.65950	+	4.60638i	0.0904256	+	0.156622i
$866$	−11.5386			−0.392096
$867$	−13.8632	−	24.0118i	−0.470820	−	0.815484i
$868$	10.6032	−	18.3653i	0.359896	−	0.623359i
$869$	21.1722	−	36.6713i	0.718217	−	1.24399i
$870$	−2.06100			−0.0698744
$871$		0			0
$872$	−42.2693			−1.43142
$873$	8.25571	−	14.2993i	0.279413	−	0.483958i
$874$	0.0528022	−	0.0914561i	0.00178606	−	0.00309355i
$875$	−2.89277	−	5.01043i	−0.0977935	−	0.169383i
$876$	20.5362			0.693853
$877$	6.75385	+	11.6980i	0.228061	+	0.395014i	0.957233	−	0.289317i	$-0.0934280\pi$
$877$	6.75385	+	11.6980i	0.228061	+	0.395014i	−0.729172	+	0.684330i	$0.760095\pi$
$878$	8.11260	+	14.0514i	0.273787	+	0.474213i
$879$	−33.5840			−1.13276
$880$	0.291053	+	0.504118i	0.00981138	+	0.0169938i
$881$	2.61715	−	4.53304i	0.0881741	−	0.152722i	−0.818565	−	0.574414i	$-0.805230\pi$
$881$	2.61715	−	4.53304i	0.0881741	−	0.152722i	0.906739	+	0.421691i	$0.138563\pi$
$882$	1.18718	−	2.05625i	0.0399743	−	0.0692376i
$883$	−4.57301			−0.153894			−0.0769470	−	0.997035i	$-0.524517\pi$
$883$	−4.57301			−0.153894			−0.0769470	+	0.997035i	$0.524517\pi$
$884$		0			0
$885$	3.76271			0.126482
$886$	−3.25667	+	5.64071i	−0.109410	+	0.189504i
$887$	0.820356	−	1.42090i	0.0275448	−	0.0477091i	−0.851924	−	0.523665i	$-0.824564\pi$
$887$	0.820356	−	1.42090i	0.0275448	−	0.0477091i	0.879469	+	0.475956i	$0.157898\pi$
$888$	−17.2153	−	29.8177i	−0.577707	−	1.00062i
$889$	23.1148			0.775246
$890$	0.285676	+	0.494805i	0.00957587	+	0.0165859i
$891$	−23.2494	−	40.2692i	−0.778885	−	1.34907i
$892$	3.06531			0.102634
$893$	−0.324240	−	0.561601i	−0.0108503	−	0.0187933i
$894$	3.90581	−	6.76507i	0.130630	−	0.226258i
$895$	−1.41185	+	2.44540i	−0.0471931	+	0.0817408i
$896$	20.7396			0.692862
$897$		0			0
$898$	10.0175			0.334287
$899$	15.3542	−	26.5943i	0.512091	−	0.886968i
$900$	−6.86563	+	11.8916i	−0.228854	+	0.396387i
$901$	11.2192	+	19.4322i	0.373765	+	0.647379i
$902$	39.4795			1.31452
$903$	0.783520	+	1.35710i	0.0260739	+	0.0451613i
$904$	16.2180	+	28.0904i	0.539402	+	0.934271i
$905$	5.17928			0.172165
$906$	3.55376	+	6.15530i	0.118066	+	0.204496i
$907$	−4.05107	+	7.01666i	−0.134514	+	0.232985i	−0.925412	−	0.378964i	$-0.876281\pi$
$907$	−4.05107	+	7.01666i	−0.134514	+	0.232985i	0.790898	+	0.611948i	$0.209614\pi$
$908$	−4.72617	+	8.18596i	−0.156843	+	0.271661i
$909$	−27.3623			−0.907549
$910$		0			0
$911$	−9.18119			−0.304187			−0.152093	−	0.988366i	$-0.548601\pi$
$911$	−9.18119			−0.304187			−0.152093	+	0.988366i	$0.548601\pi$
$912$	−0.0549581	+	0.0951903i	−0.00181985	+	0.00315207i
$913$	3.41723	−	5.91882i	0.113094	−	0.195884i
$914$	−2.39828	−	4.15394i	−0.0793281	−	0.137400i
$915$	−1.92692			−0.0637020
$916$	−16.4007	−	28.4069i	−0.541895	−	0.938590i
$917$	−7.75033	−	13.4240i	−0.255939	−	0.443299i
$918$	3.69979			0.122111
$919$	−13.7518	−	23.8189i	−0.453631	−	0.785712i	0.544978	−	0.838451i	$-0.316538\pi$
$919$	−13.7518	−	23.8189i	−0.453631	−	0.785712i	−0.998608	+	0.0527390i	$0.983205\pi$
$920$	0.496648	−	0.860219i	0.0163740	−	0.0283606i
$921$	21.4916	−	37.2245i	0.708171	−	1.22659i
$922$	−1.64933			−0.0543180
$923$		0			0
$924$	30.5187			1.00399
$925$	14.0565	−	24.3465i	0.462173	−	0.800508i
$926$	3.38793	−	5.86806i	0.111334	−	0.192837i
$927$	−1.39559	−	2.41724i	−0.0458373	−	0.0793925i
$928$	26.9946			0.886142
$929$	−12.1066	−	20.9692i	−0.397203	−	0.687977i	0.596176	−	0.802854i	$-0.296686\pi$
$929$	−12.1066	−	20.9692i	−0.397203	−	0.687977i	−0.993380	+	0.114877i	$0.963353\pi$
$930$	−1.47554	−	2.55571i	−0.0483849	−	0.0838051i
$931$	0.127375			0.00417454
$932$	−2.07673	−	3.59700i	−0.0680255	−	0.117824i
$933$	−0.303134	+	0.525044i	−0.00992417	+	0.0171892i
$934$	−13.4380	+	23.2754i	−0.439706	+	0.761593i
$935$	−2.26444			−0.0740550
$936$		0			0
$937$	11.1830			0.365333			0.182666	−	0.983175i	$-0.441527\pi$
$937$	11.1830			0.365333			0.182666	+	0.983175i	$0.441527\pi$
$938$	7.25786	−	12.5710i	0.236978	−	0.410457i
$939$	−26.2826	+	45.5228i	−0.857701	+	1.48558i
$940$	−1.23274	−	2.13517i	−0.0402076	−	0.0696416i
$941$	−15.9638			−0.520404			−0.260202	−	0.965554i	$-0.583789\pi$
$941$	−15.9638			−0.520404			−0.260202	+	0.965554i	$0.583789\pi$
$942$	4.01357	+	6.95171i	0.130769	+	0.226499i
$943$	8.65883	+	14.9975i	0.281970	+	0.488387i
$944$	−3.76271			−0.122466
$945$	0.621998	+	1.07733i	0.0202336	+	0.0350456i
$946$	−0.503885	+	0.872754i	−0.0163827	+	0.0283757i
$947$	−3.25733	+	5.64186i	−0.105849	+	0.183336i	−0.914085	−	0.405523i	$-0.867089\pi$
$947$	−3.25733	+	5.64186i	−0.105849	+	0.183336i	0.808236	+	0.588859i	$0.200423\pi$
$948$	30.3991			0.987317
$949$		0			0
$950$	0.349126			0.0113271
$951$	−15.7235	+	27.2339i	−0.509869	+	0.883119i
$952$	−6.84870	+	11.8623i	−0.221968	+	0.384459i
$953$	−23.8235	−	41.2635i	−0.771718	−	1.33665i	−0.936621	−	0.350345i	$-0.886064\pi$
$953$	−23.8235	−	41.2635i	−0.771718	−	1.33665i	0.164903	−	0.986310i	$-0.447269\pi$
$954$	−17.0780			−0.552920
$955$	1.78286	+	3.08800i	0.0576919	+	0.0999252i
$956$	−17.0608	−	29.5501i	−0.551784	−	0.955719i
$957$	44.1933			1.42857
$958$	9.91646	+	17.1758i	0.320386	+	0.554925i
$959$	7.32975	−	12.6955i	0.236690	−	0.409959i
$960$	0.989115	−	1.71320i	0.0319235	−	0.0552932i
$961$	12.9705			0.418402
$962$		0			0
$963$	6.69740			0.215821
$964$	−13.7497	+	23.8151i	−0.442847	+	0.767033i
$965$	1.67696	−	2.90457i	0.0539831	−	0.0935015i
$966$	−3.17241	−	5.49477i	−0.102071	−	0.176791i
$967$	−43.8122			−1.40891			−0.704453	−	0.709751i	$-0.748808\pi$
$967$	−43.8122			−1.40891			−0.704453	+	0.709751i	$0.748808\pi$
$968$	9.47166	+	16.4054i	0.304431	+	0.527289i
$969$	−0.213792	−	0.370298i	−0.00686798	−	0.0118957i
$970$	−1.59611			−0.0512479
$971$	−2.14742	−	3.71943i	−0.0689139	−	0.119362i	0.829510	−	0.558492i	$-0.188620\pi$
$971$	−2.14742	−	3.71943i	−0.0689139	−	0.119362i	−0.898423	+	0.439130i	$0.855287\pi$
$972$	12.3412	−	21.3755i	0.395843	−	0.685620i
$973$	−17.3315	+	30.0191i	−0.555624	+	0.962368i
$974$	−30.2776			−0.970156
$975$		0			0
$976$	1.92692			0.0616792
$977$	−13.4010	+	23.2112i	−0.428735	+	0.742591i	−0.996761	−	0.0804198i	$-0.974374\pi$
$977$	−13.4010	+	23.2112i	−0.428735	+	0.742591i	0.568026	+	0.823011i	$0.307707\pi$
$978$	14.5586	−	25.2162i	0.465533	−	0.806327i
$979$	−6.12565	−	10.6099i	−0.195776	−	0.339095i
$980$	0.484271			0.0154695
$981$	−16.0858	−	27.8613i	−0.513579	−	0.889544i
$982$	−12.5547	−	21.7454i	−0.400637	−	0.693924i
$983$	27.2495			0.869124			0.434562	−	0.900642i	$-0.356903\pi$
$983$	27.2495			0.869124			0.434562	+	0.900642i	$0.356903\pi$
$984$	35.0589	+	60.7238i	1.11764	+	1.93580i
$985$	0.0691957	−	0.119850i	0.00220476	−	0.00381875i
$986$	−4.00873	+	6.94332i	−0.127664	+	0.221120i
$987$	−38.9614			−1.24015
$988$		0			0
$989$	−0.442058			−0.0140566
$990$	0.861740	−	1.49258i	0.0273879	−	0.0474372i
$991$	−12.1945	+	21.1214i	−0.387370	+	0.670945i	−0.992095	−	0.125490i	$-0.959950\pi$
$991$	−12.1945	+	21.1214i	−0.387370	+	0.670945i	0.604725	+	0.796435i	$0.293283\pi$
$992$	19.3264	+	33.4743i	0.613614	+	1.06281i
$993$	−40.0441			−1.27076
$994$	−8.18867	−	14.1832i	−0.259729	−	0.449863i
$995$	−1.41909	−	2.45794i	−0.0449882	−	0.0779219i
$996$	4.90648			0.155468
$997$	−15.6603	−	27.1245i	−0.495967	−	0.859041i	0.504022	−	0.863691i	$-0.331853\pi$
$997$	−15.6603	−	27.1245i	−0.495967	−	0.859041i	−0.999989	+	0.00465010i	$0.998520\pi$
$998$	−8.61572	+	14.9229i	−0.272726	+	0.472375i
$999$	−6.08211	+	10.5345i	−0.192429	+	0.333297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.c.c.22.1		6
13.2	odd	12		169.2.e.b.23.2		12
13.3	even	3	inner	169.2.c.c.146.1		6
13.4	even	6		169.2.a.c.1.1	yes	3
13.5	odd	4		169.2.e.b.147.5		12
13.6	odd	12		169.2.b.b.168.2		6
13.7	odd	12		169.2.b.b.168.5		6
13.8	odd	4		169.2.e.b.147.2		12
13.9	even	3		169.2.a.b.1.3	✓	3
13.10	even	6		169.2.c.b.146.3		6
13.11	odd	12		169.2.e.b.23.5		12
13.12	even	2		169.2.c.b.22.3		6
39.17	odd	6		1521.2.a.o.1.3		3
39.20	even	12		1521.2.b.l.1351.2		6
39.32	even	12		1521.2.b.l.1351.5		6
39.35	odd	6		1521.2.a.r.1.1		3
52.7	even	12		2704.2.f.o.337.6		6
52.19	even	12		2704.2.f.o.337.5		6
52.35	odd	6		2704.2.a.z.1.3		3
52.43	odd	6		2704.2.a.ba.1.3		3
65.4	even	6		4225.2.a.bb.1.3		3
65.9	even	6		4225.2.a.bg.1.1		3
91.48	odd	6		8281.2.a.bf.1.3		3
91.69	odd	6		8281.2.a.bj.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.a.b.1.3	✓	3	13.9	even	3
169.2.a.c.1.1	yes	3	13.4	even	6
169.2.b.b.168.2		6	13.6	odd	12
169.2.b.b.168.5		6	13.7	odd	12
169.2.c.b.22.3		6	13.12	even	2
169.2.c.b.146.3		6	13.10	even	6
169.2.c.c.22.1		6	1.1	even	1	trivial
169.2.c.c.146.1		6	13.3	even	3	inner
169.2.e.b.23.2		12	13.2	odd	12
169.2.e.b.23.5		12	13.11	odd	12
169.2.e.b.147.2		12	13.8	odd	4
169.2.e.b.147.5		12	13.5	odd	4
1521.2.a.o.1.3		3	39.17	odd	6
1521.2.a.r.1.1		3	39.35	odd	6
1521.2.b.l.1351.2		6	39.20	even	12
1521.2.b.l.1351.5		6	39.32	even	12
2704.2.a.z.1.3		3	52.35	odd	6
2704.2.a.ba.1.3		3	52.43	odd	6
2704.2.f.o.337.5		6	52.19	even	12
2704.2.f.o.337.6		6	52.7	even	12
4225.2.a.bb.1.3		3	65.4	even	6
4225.2.a.bg.1.1		3	65.9	even	6
8281.2.a.bf.1.3		3	91.48	odd	6
8281.2.a.bj.1.1		3	91.69	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.400969 + 0.694498i) q^{2} +(1.12349 - 1.94594i) q^{3} +(0.678448 + 1.17511i) q^{4} +0.246980 q^{5} +(0.900969 + 1.56052i) q^{6} +(1.17845 + 2.04113i) q^{7} -2.69202 q^{8} +(-1.02446 - 1.77441i) q^{9} +O(q^{10})\)	\(q+(-0.400969 + 0.694498i) q^{2} +(1.12349 - 1.94594i) q^{3} +(0.678448 + 1.17511i) q^{4} +0.246980 q^{5} +(0.900969 + 1.56052i) q^{6} +(1.17845 + 2.04113i) q^{7} -2.69202 q^{8} +(-1.02446 - 1.77441i) q^{9} +(-0.0990311 + 0.171527i) q^{10} +(2.12349 - 3.67799i) q^{11} +3.04892 q^{12} -1.89008 q^{14} +(0.277479 - 0.480608i) q^{15} +(-0.277479 + 0.480608i) q^{16} +(-1.07942 - 1.86960i) q^{17} +1.64310 q^{18} +(0.0440730 + 0.0763367i) q^{19} +(0.167563 + 0.290227i) q^{20} +5.29590 q^{21} +(1.70291 + 2.94952i) q^{22} +(-0.746980 + 1.29381i) q^{23} +(-3.02446 + 5.23852i) q^{24} -4.93900 q^{25} +2.13706 q^{27} +(-1.59903 + 2.76960i) q^{28} +(-2.31551 + 4.01058i) q^{29} +(0.222521 + 0.385418i) q^{30} -6.63102 q^{31} +(-2.91454 - 5.04814i) q^{32} +(-4.77144 - 8.26437i) q^{33} +1.73125 q^{34} +(0.291053 + 0.504118i) q^{35} +(1.39008 - 2.40770i) q^{36} +(-2.84601 + 4.92944i) q^{37} -0.0706876 q^{38} -0.664874 q^{40} +(5.79590 - 10.0388i) q^{41} +(-2.12349 + 3.67799i) q^{42} +(0.147948 + 0.256254i) q^{43} +5.76271 q^{44} +(-0.253020 - 0.438244i) q^{45} +(-0.599031 - 1.03755i) q^{46} -7.35690 q^{47} +(0.623490 + 1.07992i) q^{48} +(0.722521 - 1.25144i) q^{49} +(1.98039 - 3.43013i) q^{50} -4.85086 q^{51} -10.3937 q^{53} +(-0.856896 + 1.48419i) q^{54} +(0.524459 - 0.908389i) q^{55} +(-3.17241 - 5.49477i) q^{56} +0.198062 q^{57} +(-1.85690 - 3.21624i) q^{58} +(3.39008 + 5.87180i) q^{59} +0.753020 q^{60} +(-1.73609 - 3.00700i) q^{61} +(2.65883 - 4.60523i) q^{62} +(2.41454 - 4.18211i) q^{63} +3.56465 q^{64} +7.65279 q^{66} +(-3.83997 + 6.65102i) q^{67} +(1.46466 - 2.53686i) q^{68} +(1.67845 + 2.90716i) q^{69} -0.466812 q^{70} +(4.33244 + 7.50400i) q^{71} +(2.75786 + 4.77676i) q^{72} +6.73556 q^{73} +(-2.28232 - 3.95310i) q^{74} +(-5.54892 + 9.61101i) q^{75} +(-0.0598025 + 0.103581i) q^{76} +10.0097 q^{77} +9.97046 q^{79} +(-0.0685317 + 0.118700i) q^{80} +(5.47434 - 9.48184i) q^{81} +(4.64795 + 8.05048i) q^{82} +1.60925 q^{83} +(3.59299 + 6.22324i) q^{84} +(-0.266594 - 0.461754i) q^{85} -0.237291 q^{86} +(5.20291 + 9.01170i) q^{87} +(-5.71648 + 9.90123i) q^{88} +(1.44235 - 2.49823i) q^{89} +0.405813 q^{90} -2.02715 q^{92} +(-7.44989 + 12.9036i) q^{93} +(2.94989 - 5.10935i) q^{94} +(0.0108851 + 0.0188536i) q^{95} -13.0978 q^{96} +(4.02930 + 6.97896i) q^{97} +(0.579417 + 1.00358i) q^{98} -8.70171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 2 q^{3} - 8 q^{5} + q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 + q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9	\( 6 q + 2 q^{2} + 2 q^{3} - 8 q^{5} + q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 5 q^{10} + 8 q^{11} - 10 q^{14} + 2 q^{15} - 2 q^{16} + 2 q^{17} + 18 q^{18} + 4 q^{19} + 4 q^{21} - 3 q^{22} + 5 q^{23} - 9 q^{24} - 10 q^{25} + 2 q^{27} - 14 q^{28} + q^{29} + q^{30} - 10 q^{31} - 7 q^{32} - 10 q^{33} + 26 q^{34} - 4 q^{35} + 7 q^{36} - 12 q^{37} + 24 q^{38} - 6 q^{40} + 7 q^{41} - 8 q^{42} - 13 q^{43} - 11 q^{45} - 8 q^{46} - 36 q^{47} - q^{48} + 4 q^{49} - q^{50} - 2 q^{51} + 2 q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} + 10 q^{57} - 3 q^{58} + 19 q^{59} + 14 q^{60} - 4 q^{61} - q^{62} + 4 q^{63} - 22 q^{64} + 10 q^{66} + q^{67} + 21 q^{68} + 6 q^{69} + 4 q^{70} + 27 q^{71} + 4 q^{72} + 18 q^{73} + 8 q^{74} - 15 q^{75} + 21 q^{76} + 16 q^{77} - 10 q^{79} + 5 q^{80} + q^{81} + 14 q^{82} - 14 q^{83} + 7 q^{84} - 5 q^{85} - 36 q^{86} + 18 q^{87} - 15 q^{88} + 11 q^{89} - 24 q^{90} - 22 q^{93} - 5 q^{94} - 3 q^{95} - 42 q^{96} - 7 q^{97} - 5 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 + q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 5 * q^10 + 8 * q^11 - 10 * q^14 + 2 * q^15 - 2 * q^16 + 2 * q^17 + 18 * q^18 + 4 * q^19 + 4 * q^21 - 3 * q^22 + 5 * q^23 - 9 * q^24 - 10 * q^25 + 2 * q^27 - 14 * q^28 + q^29 + q^30 - 10 * q^31 - 7 * q^32 - 10 * q^33 + 26 * q^34 - 4 * q^35 + 7 * q^36 - 12 * q^37 + 24 * q^38 - 6 * q^40 + 7 * q^41 - 8 * q^42 - 13 * q^43 - 11 * q^45 - 8 * q^46 - 36 * q^47 - q^48 + 4 * q^49 - q^50 - 2 * q^51 + 2 * q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 + 10 * q^57 - 3 * q^58 + 19 * q^59 + 14 * q^60 - 4 * q^61 - q^62 + 4 * q^63 - 22 * q^64 + 10 * q^66 + q^67 + 21 * q^68 + 6 * q^69 + 4 * q^70 + 27 * q^71 + 4 * q^72 + 18 * q^73 + 8 * q^74 - 15 * q^75 + 21 * q^76 + 16 * q^77 - 10 * q^79 + 5 * q^80 + q^81 + 14 * q^82 - 14 * q^83 + 7 * q^84 - 5 * q^85 - 36 * q^86 + 18 * q^87 - 15 * q^88 + 11 * q^89 - 24 * q^90 - 22 * q^93 - 5 * q^94 - 3 * q^95 - 42 * q^96 - 7 * q^97 - 5 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more