LMFDB - Embedded newform 169.2.e.b.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(23,169)]

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([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Root			$1.56052 + 0.900969i$ of defining polynomial
Character	$\chi$	$=$	169.23
Dual form			169.2.e.b.147.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.694498	+	0.400969i	−0.491085	+	0.283528i	−0.725024	−	0.688723i	$-0.758171\pi$
$2$	−0.694498	+	0.400969i	−0.491085	+	0.283528i	0.233940	+	0.972251i	$0.424838\pi$
$3$	1.12349	+	1.94594i	0.648647	+	1.12349i	0.983446	+	0.181200i	$0.0579982\pi$
$3$	1.12349	+	1.94594i	0.648647	+	1.12349i	−0.334799	+	0.942290i	$0.608668\pi$
$4$	−0.678448	+	1.17511i	−0.339224	+	0.587553i
$5$		−	0.246980i		−	0.110453i	−0.998474	−	0.0552263i	$-0.982412\pi$
$5$		−	0.246980i		−	0.110453i	0.998474	−	0.0552263i	$-0.0175880\pi$
$6$	−1.56052	−	0.900969i	−0.637081	−	0.367819i
$7$	2.04113	+	1.17845i	0.771475	+	0.445411i	0.833401	−	0.552669i	$-0.186391\pi$
$7$	2.04113	+	1.17845i	0.771475	+	0.445411i	−0.0619254	+	0.998081i	$0.519724\pi$
$8$		−	2.69202i		−	0.951773i
$9$	−1.02446	+	1.77441i	−0.341486	+	0.591471i
$10$	0.0990311	+	0.171527i	0.0313164	+	0.0542416i
$11$	−3.67799	+	2.12349i	−1.10896	+	0.640256i	−0.938559	−	0.345119i	$-0.887839\pi$
$11$	−3.67799	+	2.12349i	−1.10896	+	0.640256i	−0.170397	+	0.985375i	$0.554505\pi$
$12$	−3.04892			−0.880147
$13$		0			0
$13$		0			0
$14$	−1.89008			−0.505146
$15$	0.480608	−	0.277479i	0.124092	−	0.0716448i
$16$	−0.277479	−	0.480608i	−0.0693698	−	0.120152i
$17$	1.07942	−	1.86960i	0.261797	−	0.453446i	−0.704922	−	0.709284i	$-0.749018\pi$
$17$	1.07942	−	1.86960i	0.261797	−	0.453446i	0.966720	+	0.255839i	$0.0823516\pi$
$18$		−	1.64310i		−	0.387283i
$19$	−0.0763367	−	0.0440730i	−0.0175128	−	0.0101110i	0.491218	−	0.871037i	$-0.336552\pi$
$19$	−0.0763367	−	0.0440730i	−0.0175128	−	0.0101110i	−0.508731	+	0.860926i	$0.669885\pi$
$20$	0.290227	+	0.167563i	0.0648968	+	0.0374682i
$21$			5.29590i			1.15566i
$22$	1.70291	−	2.94952i	0.363061	−	0.628840i
$23$	0.746980	+	1.29381i	0.155756	+	0.269777i	0.933334	−	0.359009i	$-0.116885\pi$
$23$	0.746980	+	1.29381i	0.155756	+	0.269777i	−0.777578	+	0.628786i	$0.783552\pi$
$24$	5.23852	−	3.02446i	1.06931	−	0.617365i
$25$	4.93900			0.987800
$26$		0			0
$27$	2.13706			0.411278
$28$	−2.76960	+	1.59903i	−0.523406	+	0.302188i
$29$	−2.31551	−	4.01058i	−0.429980	−	0.744747i	0.566891	−	0.823793i	$-0.308146\pi$
$29$	−2.31551	−	4.01058i	−0.429980	−	0.744747i	−0.996871	+	0.0790460i	$0.974813\pi$
$30$	−0.222521	+	0.385418i	−0.0406266	+	0.0703673i
$31$			6.63102i			1.19097i	0.803368	+	0.595483i	$0.203039\pi$
$31$			6.63102i			1.19097i	−0.803368	+	0.595483i	$0.796961\pi$
$32$	5.04814	+	2.91454i	0.892393	+	0.515223i
$33$	−8.26437	−	4.77144i	−1.43864	−	0.830601i
$34$			1.73125i			0.296907i
$35$	0.291053	−	0.504118i	0.0491969	−	0.0852115i
$36$	−1.39008	−	2.40770i	−0.231681	−	0.401283i
$37$	4.92944	−	2.84601i	0.810394	−	0.467881i	−0.0366986	−	0.999326i	$-0.511684\pi$
$37$	4.92944	−	2.84601i	0.810394	−	0.467881i	0.847093	+	0.531445i	$0.178351\pi$
$38$	0.0706876			0.0114670
$39$		0			0
$40$	−0.664874			−0.105126
$41$	10.0388	−	5.79590i	1.56780	−	0.905167i	0.571370	−	0.820693i	$-0.306412\pi$
$41$	10.0388	−	5.79590i	1.56780	−	0.905167i	0.996426	−	0.0844742i	$-0.0269210\pi$
$42$	−2.12349	−	3.67799i	−0.327662	−	0.567527i
$43$	−0.147948	+	0.256254i	−0.0225619	+	0.0390784i	−0.877086	−	0.480334i	$-0.840516\pi$
$43$	−0.147948	+	0.256254i	−0.0225619	+	0.0390784i	0.854524	+	0.519412i	$0.173849\pi$
$44$		−	5.76271i		−	0.868761i
$45$	0.438244	+	0.253020i	0.0653296	+	0.0377181i
$46$	−1.03755	−	0.599031i	−0.152979	−	0.0883223i
$47$		−	7.35690i		−	1.07311i	−0.843864	−	0.536557i	$-0.819725\pi$
$47$		−	7.35690i		−	1.07311i	0.843864	−	0.536557i	$-0.180275\pi$
$48$	0.623490	−	1.07992i	0.0899930	−	0.155872i
$49$	−0.722521	−	1.25144i	−0.103217	−	0.178778i
$50$	−3.43013	+	1.98039i	−0.485093	+	0.280069i
$51$	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	$0.753048\pi$
$54$	−1.48419	+	0.856896i	−0.201972	+	0.116609i
$55$	0.524459	+	0.908389i	0.0707180	+	0.122487i
$56$	3.17241	−	5.49477i	0.423931	−	0.734270i
$57$		−	0.198062i		−	0.0262340i
$58$	3.21624	+	1.85690i	0.422313	+	0.243822i
$59$	5.87180	+	3.39008i	0.764443	+	0.441351i	0.830889	−	0.556439i	$-0.187833\pi$
$59$	5.87180	+	3.39008i	0.764443	+	0.441351i	−0.0664458	+	0.997790i	$0.521166\pi$
$60$			0.753020i			0.0972145i
$61$	−1.73609	+	3.00700i	−0.222284	+	0.385007i	−0.955501	−	0.294987i	$-0.904685\pi$
$61$	−1.73609	+	3.00700i	−0.222284	+	0.385007i	0.733217	+	0.679995i	$0.238018\pi$
$62$	−2.65883	−	4.60523i	−0.337672	−	0.584865i
$63$	−4.18211	+	2.41454i	−0.526896	+	0.304204i
$64$	−3.56465			−0.445581
$65$		0			0
$66$	7.65279			0.941994
$67$	−6.65102	+	3.83997i	−0.812552	+	0.469127i	−0.847841	−	0.530250i	$-0.822098\pi$
$67$	−6.65102	+	3.83997i	−0.812552	+	0.469127i	0.0352895	+	0.999377i	$0.488765\pi$
$68$	1.46466	+	2.53686i	0.177616	+	0.307639i
$69$	−1.67845	+	2.90716i	−0.202061	+	0.349981i
$70$			0.466812i			0.0557947i
$71$	−7.50400	−	4.33244i	−0.890561	−	0.514166i	−0.0164351	−	0.999865i	$-0.505232\pi$
$71$	−7.50400	−	4.33244i	−0.890561	−	0.514166i	−0.874126	+	0.485699i	$0.838565\pi$
$72$	4.77676	+	2.75786i	0.562947	+	0.325017i
$73$			6.73556i			0.788338i	0.919038	+	0.394169i	$0.128968\pi$
$73$			6.73556i			0.788338i	−0.919038	+	0.394169i	$0.871032\pi$
$74$	−2.28232	+	3.95310i	−0.265315	+	0.459539i
$75$	5.54892	+	9.61101i	0.640734	+	1.10978i
$76$	0.103581	−	0.0598025i	0.0118815	−	0.00685981i
$77$	−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	$0.310462\pi$
$80$	−0.118700	+	0.0685317i	−0.0132711	+	0.00766207i
$81$	5.47434	+	9.48184i	0.608261	+	1.05354i
$82$	−4.64795	+	8.05048i	−0.513280	+	0.889027i
$83$		−	1.60925i		−	0.176638i	−0.996092	−	0.0883192i	$-0.971850\pi$
$83$		−	1.60925i		−	0.176638i	0.996092	−	0.0883192i	$-0.0281495\pi$
$84$	−6.22324	−	3.59299i	−0.679011	−	0.392027i
$85$	−0.461754	−	0.266594i	−0.0500843	−	0.0289162i
$86$		−	0.237291i		−	0.0255877i
$87$	5.20291	−	9.01170i	0.557810	−	0.966156i
$88$	5.71648	+	9.90123i	0.609379	+	1.05548i
$89$	−2.49823	+	1.44235i	−0.264812	+	0.152889i	−0.626528	−	0.779399i	$-0.715524\pi$
$89$	−2.49823	+	1.44235i	−0.264812	+	0.152889i	0.361716	+	0.932288i	$0.382191\pi$
$90$	−0.405813			−0.0427765
$91$		0			0
$92$	−2.02715			−0.211345
$93$	−12.9036	+	7.44989i	−1.33804	+	0.772517i
$94$	2.94989	+	5.10935i	0.304258	+	0.526990i
$95$	−0.0108851	+	0.0188536i	−0.00111679	+	0.00193434i
$96$			13.0978i			1.33679i
$97$	−6.97896	−	4.02930i	−0.708606	−	0.409114i	0.101939	−	0.994791i	$-0.467495\pi$
$97$	−6.97896	−	4.02930i	−0.708606	−	0.409114i	−0.810545	+	0.585677i	$0.800829\pi$
$98$	1.00358	+	0.579417i	0.101377	+	0.0585299i
$99$		−	8.70171i		−	0.874555i
$100$	−3.35086	+	5.80385i	−0.335086	+	0.580385i
$101$	−6.67725	−	11.5653i	−0.664411	−	1.15079i	−0.979445	−	0.201714i	$-0.935349\pi$
$101$	−6.67725	−	11.5653i	−0.664411	−	1.15079i	0.315033	−	0.949081i	$-0.397984\pi$
$102$	−3.36891	+	1.94504i	−0.333572	+	0.192588i
$103$	−1.36227			−0.134229			−0.0671144	−	0.997745i	$-0.521379\pi$
$103$	−1.36227			−0.134229			−0.0671144	+	0.997745i	$0.521379\pi$
$104$		0			0
$105$	1.30798			0.127646
$106$	7.21843	−	4.16756i	0.701116	−	0.404789i
$107$	−1.63437	−	2.83082i	−0.158001	−	0.273666i	0.776147	−	0.630552i	$-0.217172\pi$
$107$	−1.63437	−	2.83082i	−0.158001	−	0.273666i	−0.934148	+	0.356887i	$0.883838\pi$
$108$	−1.44989	+	2.51128i	−0.139515	+	0.241648i
$109$		−	15.7017i		−	1.50395i	−0.659191	−	0.751976i	$-0.729101\pi$
$109$		−	15.7017i		−	1.50395i	0.659191	−	0.751976i	$-0.270899\pi$
$110$	−0.728471	−	0.420583i	−0.0694570	−	0.0401010i
$111$	11.0763	+	6.39493i	1.05132	+	0.606980i
$112$		−	1.30798i		−	0.123592i
$113$	−6.02446	+	10.4347i	−0.566733	+	0.981611i	0.430153	+	0.902756i	$0.358460\pi$
$113$	−6.02446	+	10.4347i	−0.566733	+	0.981611i	−0.996886	+	0.0788549i	$0.974874\pi$
$114$	0.0794168	+	0.137554i	0.00743806	+	0.0128831i
$115$	0.319544	−	0.184489i	0.0297976	−	0.0172037i
$116$	6.28382			0.583438
$117$		0			0
$118$	−5.43727			−0.500541
$119$	4.40646	−	2.54407i	0.403940	−	0.233215i
$120$	−0.746980	−	1.29381i	−0.0681896	−	0.118108i
$121$	3.51842	−	6.09408i	0.319856	−	0.554007i
$122$		−	2.78448i		−	0.252095i
$123$	22.5570	+	13.0233i	2.03389	+	1.17427i
$124$	−7.79216	−	4.49880i	−0.699756	−	0.404004i
$125$		−	2.45473i		−	0.219558i
$126$	1.93631	−	3.35379i	0.172500	−	0.298780i
$127$	−4.90366	−	8.49338i	−0.435129	−	0.753666i	0.562177	−	0.827017i	$-0.309964\pi$
$127$	−4.90366	−	8.49338i	−0.435129	−	0.753666i	−0.997306	+	0.0733510i	$0.976631\pi$
$128$	−7.62063	+	4.39977i	−0.673575	+	0.388889i
$129$	−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	$0.592760\pi$
$132$	11.2139	−	6.47434i	0.976044	−	0.563519i
$133$	−0.103875	−	0.179918i	−0.00900715	−	0.0156008i
$134$	3.07942	−	5.33371i	0.266021	−	0.460762i
$135$		−	0.527811i		−	0.0454267i
$136$	−5.03302	−	2.90581i	−0.431578	−	0.249171i
$137$	−5.38653	−	3.10992i	−0.460203	−	0.265698i	0.251927	−	0.967746i	$-0.418936\pi$
$137$	−5.38653	−	3.10992i	−0.460203	−	0.265698i	−0.712129	+	0.702048i	$0.752269\pi$
$138$		−	2.69202i		−	0.229160i
$139$	7.35354	−	12.7367i	0.623719	−	1.08031i	−0.365068	−	0.930981i	$-0.618954\pi$
$139$	7.35354	−	12.7367i	0.623719	−	1.08031i	0.988787	−	0.149333i	$-0.0477125\pi$
$140$	0.394928	+	0.684035i	0.0333775	+	0.0578116i
$141$	14.3161	−	8.26540i	1.20563	−	0.696072i
$142$	6.94869			0.583121
$143$		0			0
$144$	1.13706			0.0947553
$145$	−0.990532	+	0.571884i	−0.0822592	+	0.0474924i
$146$	−2.70075	−	4.67784i	−0.223516	−	0.387141i
$147$	1.62349	−	2.81197i	0.133903	−	0.231927i
$148$			7.72348i			0.634866i
$149$	3.75433	+	2.16756i	0.307567	+	0.177574i	0.645837	−	0.763475i	$-0.276509\pi$
$149$	3.75433	+	2.16756i	0.307567	+	0.177574i	−0.338270	+	0.941049i	$0.609842\pi$
$150$	−7.70743	−	4.44989i	−0.629309	−	0.363332i
$151$			3.94438i			0.320989i	0.987037	+	0.160494i	$0.0513089\pi$
$151$			3.94438i			0.320989i	−0.987037	+	0.160494i	$0.948691\pi$
$152$	−0.118645	+	0.205500i	−0.00962342	+	0.0166682i
$153$	2.21164	+	3.83067i	0.178800	+	0.309691i
$154$	6.95171	−	4.01357i	0.560185	−	0.323423i
$155$	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	$0.443114\pi$
$158$	−6.92447	+	3.99784i	−0.550881	+	0.318051i
$159$	−11.6773	−	20.2256i	−0.926066	−	1.60399i
$160$	0.719833	−	1.24679i	0.0569078	−	0.0985671i
$161$			3.52111i			0.277502i
$162$	−7.60385	−	4.39008i	−0.597415	−	0.344918i
$163$	−13.9940	−	8.07942i	−1.09609	−	0.632829i	−0.160900	−	0.986971i	$-0.551440\pi$
$163$	−13.9940	−	8.07942i	−1.09609	−	0.632829i	−0.935192	+	0.354142i	$0.884773\pi$
$164$			15.7289i			1.22822i
$165$	−1.17845	+	2.04113i	−0.0917420	+	0.158902i
$166$	0.645260	+	1.11762i	0.0500819	+	0.0867444i
$167$	13.9579	−	8.05861i	1.08010	−	0.623594i	0.149174	−	0.988811i	$-0.452339\pi$
$167$	13.9579	−	8.05861i	1.08010	−	0.623594i	0.930922	+	0.365217i	$0.119005\pi$
$168$	14.2567			1.09993
$169$		0			0
$170$	0.427583			0.0327942
$171$	0.156408	−	0.0903019i	0.0119608	−	0.00690556i
$172$	−0.200751	−	0.347710i	−0.0153071	−	0.0265127i
$173$	−10.7681	+	18.6509i	−0.818682	+	1.41800i	0.0879709	+	0.996123i	$0.471962\pi$
$173$	−10.7681	+	18.6509i	−0.818682	+	1.41800i	−0.906653	+	0.421876i	$0.861372\pi$
$174$			8.34481i			0.632619i
$175$	10.0812	+	5.82036i	0.762063	+	0.439978i
$176$	2.04113	+	1.17845i	0.153856	+	0.0888289i
$177$			15.2349i			1.14513i
$178$	1.15668	−	2.00342i	0.0866967	−	0.150163i
$179$	5.71648	+	9.90123i	0.427270	+	0.740053i	0.996629	−	0.0820356i	$-0.0261421\pi$
$179$	5.71648	+	9.90123i	0.427270	+	0.740053i	−0.569360	+	0.822089i	$0.692809\pi$
$180$	−0.594652	+	0.343322i	−0.0443227	+	0.0255897i
$181$	−20.9705			−1.55872			−0.779361	−	0.626575i	$-0.784456\pi$
$181$	−20.9705			−1.55872			−0.779361	+	0.626575i	$0.784456\pi$
$182$		0			0
$183$	−7.80194			−0.576736
$184$	3.48296	−	2.01089i	0.256767	−	0.148244i
$185$	−0.702907	−	1.21747i	−0.0516787	−	0.0895102i
$186$	5.97434	−	10.3479i	0.438060	−	0.758743i
$187$			9.16852i			0.670469i
$188$	8.64513	+	4.99127i	0.630511	+	0.364026i
$189$	4.36203	+	2.51842i	0.317291	+	0.183188i
$190$		−	0.0174584i		−	0.00126657i
$191$	7.21864	−	12.5030i	0.522322	−	0.904689i	−0.477341	−	0.878718i	$-0.658399\pi$
$191$	7.21864	−	12.5030i	0.522322	−	0.904689i	0.999663	−	0.0259702i	$-0.00826749\pi$
$192$	−4.00484	−	6.93659i	−0.289025	−	0.500606i
$193$	−11.7604	+	6.78986i	−0.846530	+	0.488745i	−0.859479	−	0.511172i	$-0.829212\pi$
$193$	−11.7604	+	6.78986i	−0.846530	+	0.488745i	0.0129483	+	0.999916i	$0.495878\pi$
$194$	6.46250			0.463980
$195$		0			0
$196$	1.96077			0.140055
$197$	0.485264	−	0.280167i	0.0345736	−	0.0199611i	−0.482614	−	0.875833i	$-0.660312\pi$
$197$	0.485264	−	0.280167i	0.0345736	−	0.0199611i	0.517187	+	0.855872i	$0.326979\pi$
$198$	3.48911	+	6.04332i	0.247961	+	0.429480i
$199$	5.74578	−	9.95199i	0.407308	−	0.705478i	−0.587279	−	0.809384i	$-0.699801\pi$
$199$	5.74578	−	9.95199i	0.407308	−	0.705478i	0.994587	+	0.103907i	$0.0331343\pi$
$200$		−	13.2959i		−	0.940162i
$201$	−14.9447	−	8.62833i	−1.05412	−	0.608596i
$202$	9.27468	+	5.35474i	0.652564	+	0.376758i
$203$		−	10.9148i		−	0.766071i
$204$	−3.29105	+	5.70027i	−0.230420	+	0.399099i
$205$	−1.43147	−	2.47938i	−0.0999781	−	0.173167i
$206$	0.946096	−	0.546229i	0.0659177	−	0.0380576i
$207$	−3.06100			−0.212754
$208$		0			0
$209$	0.374354			0.0258946
$210$	−0.908389	+	0.524459i	−0.0626848	+	0.0361911i
$211$	−4.39224	−	7.60758i	−0.302374	−	0.523728i	0.674299	−	0.738458i	$-0.264446\pi$
$211$	−4.39224	−	7.60758i	−0.302374	−	0.523728i	−0.976673	+	0.214731i	$0.931113\pi$
$212$	7.05161	−	12.2137i	0.484306	−	0.838843i
$213$		−	19.4698i		−	1.33405i
$214$	2.27014	+	1.31067i	0.155184	+	0.0895953i
$215$	0.0632896	+	0.0365403i	0.00431631	+	0.00249202i
$216$		−	5.75302i		−	0.391443i
$217$	−7.81431	+	13.5348i	−0.530470	+	0.918801i
$218$	6.29590	+	10.9048i	0.426412	+	0.738567i
$219$	−13.1070	+	7.56734i	−0.885690	+	0.511353i
$220$	−1.42327			−0.0959570
$221$		0			0
$222$	−10.2567			−0.688383
$223$	1.95640	−	1.12953i	0.131011	−	0.0756390i	−0.433062	−	0.901364i	$-0.642567\pi$
$223$	1.95640	−	1.12953i	0.131011	−	0.0756390i	0.564073	+	0.825725i	$0.309234\pi$
$224$	6.86927	+	11.8979i	0.458973	+	0.794964i
$225$	−5.05980	+	8.76383i	−0.337320	+	0.584256i
$226$		−	9.66248i		−	0.642739i
$227$	−6.03286	−	3.48307i	−0.400415	−	0.231180i	0.286248	−	0.958156i	$-0.407592\pi$
$227$	−6.03286	−	3.48307i	−0.400415	−	0.231180i	−0.686663	+	0.726976i	$0.740925\pi$
$228$	0.232744	+	0.134375i	0.0154139	+	0.00889920i
$229$		−	24.1739i		−	1.59746i	−0.601692	−	0.798728i	$-0.705507\pi$
$229$		−	24.1739i		−	1.59746i	0.601692	−	0.798728i	$-0.294493\pi$
$230$	−0.147948	+	0.256254i	−0.00975543	+	0.0168969i
$231$	−11.2458	−	19.4783i	−0.739918	−	1.28158i
$232$	−10.7966	+	6.23341i	−0.708830	+	0.409243i
$233$	3.06100			0.200533			0.100266	−	0.994961i	$-0.468031\pi$
$233$	3.06100			0.200533			0.100266	+	0.994961i	$0.468031\pi$
$234$		0			0
$235$	−1.81700			−0.118528
$236$	−7.96742	+	4.59999i	−0.518635	+	0.299434i
$237$	11.2017	+	19.4019i	0.727629	+	1.26029i
$238$	−2.04019	+	3.53371i	−0.132246	+	0.229056i
$239$			25.1468i			1.62661i	0.581839	+	0.813304i	$0.302333\pi$
$239$			25.1468i			1.62661i	−0.581839	+	0.813304i	$0.697667\pi$
$240$	−0.266717	−	0.153989i	−0.0172165	−	0.00993996i
$241$	17.5512	+	10.1332i	1.13057	+	0.652735i	0.944078	−	0.329721i	$-0.106955\pi$
$241$	17.5512	+	10.1332i	1.13057	+	0.652735i	0.186492	+	0.982456i	$0.440288\pi$
$242$			5.64310i			0.362752i
$243$	−9.09515	+	15.7533i	−0.583454	+	1.01057i
$244$	−2.35570	−	4.08019i	−0.150808	−	0.261207i
$245$	−0.309081	+	0.178448i	−0.0197465	+	0.0114006i
$246$	−20.8877			−1.33175
$247$		0			0
$248$	17.8509			1.13353
$249$	3.13151	−	1.80798i	0.198451	−	0.114576i
$250$	0.984271	+	1.70481i	0.0622507	+	0.107821i
$251$	−11.8605	+	20.5431i	−0.748631	+	1.29667i	0.199848	+	0.979827i	$0.435955\pi$
$251$	−11.8605	+	20.5431i	−0.748631	+	1.29667i	−0.948479	+	0.316840i	$0.897378\pi$
$252$		−	6.55257i		−	0.412773i
$253$	−5.49477	−	3.17241i	−0.345453	−	0.199448i
$254$	6.81116	+	3.93243i	0.427370	+	0.246742i
$255$		−	1.19806i		−	0.0750256i
$256$	7.09299	−	12.2854i	0.443312	−	0.767839i
$257$	7.11207	+	12.3185i	0.443639	+	0.768405i	0.997956	−	0.0639003i	$-0.0203540\pi$
$257$	7.11207	+	12.3185i	0.443639	+	0.768405i	−0.554317	+	0.832305i	$0.687021\pi$
$258$	0.461754	−	0.266594i	0.0287476	−	0.0165974i
$259$	13.4155			0.833599
$260$		0			0
$261$	9.48858			0.587329
$262$	4.56753	−	2.63706i	0.282183	−	0.162918i
$263$	8.54772	+	14.8051i	0.527075	+	0.912921i	0.999502	+	0.0315510i	$0.0100447\pi$
$263$	8.54772	+	14.8051i	0.527075	+	0.912921i	−0.472427	+	0.881370i	$0.656622\pi$
$264$	−12.8448	+	22.2479i	−0.790544	+	1.36926i
$265$			2.56704i			0.157692i
$266$	0.144283	+	0.0833017i	0.00884654	+	0.00510755i
$267$	−5.61347	−	3.24094i	−0.343539	−	0.198342i
$268$		−	10.4209i		−	0.636556i
$269$	3.23341	−	5.60042i	0.197144	−	0.341464i	−0.750457	−	0.660919i	$-0.770167\pi$
$269$	3.23341	−	5.60042i	0.197144	−	0.341464i	0.947601	+	0.319455i	$0.103500\pi$
$270$	0.211636	+	0.366564i	0.0128797	+	0.0223084i
$271$	5.58415	−	3.22401i	0.339213	−	0.195845i	−0.320711	−	0.947177i	$-0.603922\pi$
$271$	5.58415	−	3.22401i	0.339213	−	0.195845i	0.659924	+	0.751332i	$0.270588\pi$
$272$	−1.19806			−0.0726432
$273$		0			0
$274$	4.98792			0.301331
$275$	−18.1656	+	10.4879i	−1.09543	+	0.632445i
$276$	−2.27748	−	3.94471i	−0.137088	−	0.237444i
$277$	6.73005	−	11.6568i	0.404370	−	0.700389i	−0.589878	−	0.807492i	$-0.700824\pi$
$277$	6.73005	−	11.6568i	0.404370	−	0.700389i	0.994248	+	0.107103i	$0.0341576\pi$
$278$			11.7942i			0.707367i
$279$	−11.7662	−	6.79321i	−0.704423	−	0.406699i
$280$	−1.35710	−	0.783520i	−0.0811020	−	0.0468243i
$281$			5.03684i			0.300472i	0.988650	+	0.150236i	$0.0480034\pi$
$281$			5.03684i			0.300472i	−0.988650	+	0.150236i	$0.951997\pi$
$282$	−6.62833	+	11.4806i	−0.394712	+	0.683660i
$283$	11.0640	+	19.1634i	0.657686	+	1.13914i	0.981213	+	0.192926i	$0.0617977\pi$
$283$	11.0640	+	19.1634i	0.657686	+	1.13914i	−0.323528	+	0.946219i	$0.604869\pi$
$284$	10.1821	−	5.87867i	0.604199	−	0.348835i
$285$	−0.0489173			−0.00289761
$286$		0			0
$287$	27.3207			1.61269
$288$	−10.3432	+	5.97166i	−0.609480	+	0.351883i
$289$	6.16972	+	10.6863i	0.362925	+	0.628604i
$290$	0.458615	−	0.794345i	0.0269308	−	0.0466456i
$291$		−	18.1075i		−	1.06148i
$292$	−7.91500	−	4.56973i	−0.463190	−	0.267423i
$293$	−12.9439	−	7.47315i	−0.756189	−	0.436586i	0.0717367	−	0.997424i	$-0.477146\pi$
$293$	−12.9439	−	7.47315i	−0.756189	−	0.436586i	−0.827926	+	0.560838i	$0.810479\pi$
$294$			2.60388i			0.151861i
$295$	0.837282	−	1.45021i	0.0487484	−	0.0844347i
$296$	−7.66152	−	13.2701i	−0.445317	−	0.771312i
$297$	−7.86010	+	4.53803i	−0.456089	+	0.263323i
$298$	−3.47650			−0.201388
$299$		0			0
$300$	−15.0586			−0.869409
$301$	−0.603965	+	0.348699i	−0.0348119	+	0.0200987i
$302$	−1.58157	−	2.73936i	−0.0910093	−	0.157633i
$303$	15.0036	−	25.9871i	0.861937	−	1.49292i
$304$			0.0489173i			0.00280560i
$305$	0.742669	+	0.428780i	0.0425251	+	0.0245519i
$306$	−3.07196	−	1.77359i	−0.175612	−	0.101390i
$307$			19.1293i			1.09177i	0.837861	+	0.545883i	$0.183806\pi$
$307$			19.1293i			1.09177i	−0.837861	+	0.545883i	$0.816194\pi$
$308$	6.79105	−	11.7624i	0.386956	−	0.670228i
$309$	−1.53050	−	2.65090i	−0.0870671	−	0.150805i
$310$	−1.13740	+	0.656678i	−0.0645999	+	0.0372968i
$311$	0.269815			0.0152998			0.00764990	−	0.999971i	$-0.497565\pi$
$311$	0.269815			0.0152998			0.00764990	+	0.999971i	$0.497565\pi$
$312$		0			0
$313$	−23.3937			−1.32229			−0.661146	−	0.750257i	$-0.729930\pi$
$313$	−23.3937			−1.32229			−0.661146	+	0.750257i	$0.729930\pi$
$314$	−3.09380	+	1.78621i	−0.174593	+	0.100802i
$315$	0.596343	+	1.03290i	0.0336001	+	0.0581971i
$316$	−6.76444	+	11.7164i	−0.380529	+	0.659096i
$317$			13.9952i			0.786050i	0.919528	+	0.393025i	$0.128571\pi$
$317$			13.9952i			0.786050i	−0.919528	+	0.393025i	$0.871429\pi$
$318$	16.2197	+	9.36443i	0.909554	+	0.525131i
$319$	17.0329	+	9.83393i	0.953657	+	0.550594i
$320$			0.880395i			0.0492156i
$321$	3.67241	−	6.36080i	0.204974	−	0.355025i
$322$	−1.41185	−	2.44540i	−0.0786795	−	0.136277i
$323$	−0.164798	+	0.0951463i	−0.00916962	+	0.00529408i
$324$	−14.8562			−0.825346
$325$		0			0
$326$	12.9584			0.717698
$327$	30.5546	−	17.6407i	1.68967	−	0.975534i
$328$	−15.6027	−	27.0246i	−0.861514	−	1.49219i
$329$	8.66972	−	15.0164i	0.477977	−	0.827881i
$330$		−	1.89008i		−	0.104046i
$331$	15.4337	+	8.91066i	0.848314	+	0.489774i	0.860081	−	0.510157i	$-0.170413\pi$
$331$	15.4337	+	8.91066i	0.848314	+	0.489774i	−0.0117680	+	0.999931i	$0.503746\pi$
$332$	1.89104	+	1.09179i	0.103784	+	0.0599200i
$333$			11.6625i			0.639100i
$334$	−6.46250	+	11.1934i	−0.353612	+	0.612474i
$335$	0.948394	+	1.64267i	0.0518163	+	0.0897485i
$336$	2.54525	−	1.46950i	0.138855	−	0.0801678i
$337$	27.8485			1.51700			0.758501	−	0.651672i	$-0.225932\pi$
$337$	27.8485			1.51700			0.758501	+	0.651672i	$0.225932\pi$
$338$		0			0
$339$	−27.0737			−1.47044
$340$	0.626552	−	0.361740i	0.0339796	−	0.0196181i
$341$	−14.0809	−	24.3888i	−0.762524	−	1.32073i
$342$	−0.0724165	+	0.125429i	−0.00391584	+	0.00678243i
$343$		−	19.9041i		−	1.07472i
$344$	0.689842	+	0.398280i	0.0371938	+	0.0214738i
$345$	0.718009	+	0.414542i	0.0386563	+	0.0223182i
$346$		−	17.2707i		−	0.928477i
$347$	−0.751824	+	1.30220i	−0.0403600	+	0.0699056i	−0.885500	−	0.464640i	$-0.846184\pi$
$347$	−0.751824	+	1.30220i	−0.0403600	+	0.0699056i	0.845140	+	0.534545i	$0.179517\pi$
$348$	7.05980	+	12.2279i	0.378445	+	0.655486i
$349$	−12.2854	+	7.09299i	−0.657623	+	0.379679i	−0.791371	−	0.611336i	$-0.790632\pi$
$349$	−12.2854	+	7.09299i	−0.657623	+	0.379679i	0.133747	+	0.991015i	$0.457299\pi$
$350$	−9.33513			−0.498983
$351$		0			0
$352$	−24.7560			−1.31950
$353$	6.20812	−	3.58426i	0.330425	−	0.190771i	−0.325605	−	0.945506i	$-0.605568\pi$
$353$	6.20812	−	3.58426i	0.330425	−	0.190771i	0.656030	+	0.754735i	$0.272235\pi$
$354$	−6.10872	−	10.5806i	−0.324675	−	0.562353i
$355$	−1.07002	+	1.85334i	−0.0567910	+	0.0983648i
$356$		−	3.91425i		−	0.207455i
$357$	9.90123	+	5.71648i	0.524029	+	0.302548i
$358$	−7.94017	−	4.58426i	−0.419651	−	0.242286i
$359$			19.8853i			1.04951i	0.851255	+	0.524753i	$0.175842\pi$
$359$			19.8853i			1.04951i	−0.851255	+	0.524753i	$0.824158\pi$
$360$	0.681136	−	1.17976i	0.0358990	−	0.0621790i
$361$	−9.49612	−	16.4478i	−0.499796	−	0.865671i
$362$	14.5640	−	8.40850i	0.765464	−	0.441941i
$363$	15.8116			0.829895
$364$		0			0
$365$	1.66355			0.0870740
$366$	5.41843	−	3.12833i	0.283226	−	0.163521i
$367$	−0.541917	−	0.938628i	−0.0282878	−	0.0489960i	0.851535	−	0.524298i	$-0.175672\pi$
$367$	−0.541917	−	0.938628i	−0.0282878	−	0.0489960i	−0.879823	+	0.475302i	$0.842339\pi$
$368$	0.414542	−	0.718009i	0.0216095	−	0.0374288i
$369$			23.7506i			1.23641i
$370$	0.976335	+	0.563687i	0.0507572	+	0.0293047i
$371$	−21.2150	−	12.2485i	−1.10143	−	0.635909i
$372$		−	20.2174i		−	1.04823i
$373$	3.06518	−	5.30905i	0.158709	−	0.274892i	−0.775694	−	0.631109i	$-0.782600\pi$
$373$	3.06518	−	5.30905i	0.158709	−	0.274892i	0.934403	+	0.356217i	$0.115934\pi$
$374$	−3.67629	−	6.36752i	−0.190097	−	0.329257i
$375$	4.77676	−	2.75786i	0.246671	−	0.142416i
$376$	−19.8049			−1.02136
$377$		0			0
$378$	−4.03923			−0.207756
$379$	2.08608	−	1.20440i	0.107155	−	0.0618658i	−0.445465	−	0.895299i	$-0.646962\pi$
$379$	2.08608	−	1.20440i	0.107155	−	0.0618658i	0.552620	+	0.833434i	$0.313628\pi$
$380$	−0.0147700	−	0.0255824i	−0.000757685	−	0.00131235i
$381$	11.0184	−	19.0845i	0.564491	−	0.977726i
$382$			11.5778i			0.592371i
$383$	−26.3197	−	15.1957i	−1.34487	−	0.776462i	−0.357354	−	0.933969i	$-0.616321\pi$
$383$	−26.3197	−	15.1957i	−1.34487	−	0.776462i	−0.987518	+	0.157506i	$0.949655\pi$
$384$	−17.1234	−	9.88620i	−0.873825	−	0.504503i
$385$			2.47219i			0.125994i
$386$	5.44504	−	9.43109i	0.277145	−	0.480030i
$387$	−0.303134	−	0.525044i	−0.0154092	−	0.0266895i
$388$	9.46972	−	5.46734i	0.480752	−	0.277562i
$389$	15.9409			0.808237			0.404118	−	0.914707i	$-0.367578\pi$
$389$	15.9409			0.808237			0.404118	+	0.914707i	$0.367578\pi$
$390$		0			0
$391$	3.22521			0.163106
$392$	−3.36891	+	1.94504i	−0.170156	+	0.0982394i
$393$	−7.38889	−	12.7979i	−0.372720	−	0.645570i
$394$	−0.224677	+	0.389152i	−0.0113191	+	0.0196052i
$395$		−	2.46250i		−	0.123902i
$396$	10.2254	+	5.90366i	0.513847	+	0.296670i
$397$	−14.6487	−	8.45742i	−0.735196	−	0.424466i	0.0851239	−	0.996370i	$-0.472871\pi$
$397$	−14.6487	−	8.45742i	−0.735196	−	0.424466i	−0.820320	+	0.571905i	$0.806205\pi$
$398$			9.21552i			0.461932i
$399$	0.233406	−	0.404271i	0.0116849	−	0.0202389i
$400$	−1.37047	−	2.37372i	−0.0685235	−	0.118686i
$401$	23.0904	−	13.3312i	1.15308	−	0.665730i	0.203443	−	0.979087i	$-0.434787\pi$
$401$	23.0904	−	13.3312i	1.15308	−	0.665730i	0.949636	+	0.313356i	$0.101453\pi$
$402$	13.8388			0.690215
$403$		0			0
$404$	18.1207			0.901537
$405$	2.34182	−	1.35205i	0.116366	−	0.0671840i
$406$	4.37651	+	7.58034i	0.217203	+	0.376206i
$407$	−12.0869	+	20.9352i	−0.599128	+	1.03772i
$408$		−	13.0586i		−	0.646497i
$409$	24.6959	+	14.2582i	1.22113	+	0.705021i	0.965159	−	0.261663i	$-0.0842710\pi$
$409$	24.6959	+	14.2582i	1.22113	+	0.705021i	0.255972	+	0.966684i	$0.417604\pi$
$410$	1.98831	+	1.14795i	0.0981954	+	0.0566931i
$411$		−	13.9758i		−	0.689377i
$412$	0.924231	−	1.60082i	0.0455336	−	0.0788665i
$413$	7.99007	+	13.8392i	0.393166	+	0.680983i
$414$	2.12586	−	1.22737i	0.104480	−	0.0603217i
$415$	−0.397452			−0.0195102
$416$		0			0
$417$	33.0465			1.61830
$418$	−0.259988	+	0.150104i	−0.0127165	+	0.00734185i
$419$	14.8046	+	25.6424i	0.723253	+	1.25271i	0.959689	+	0.281064i	$0.0906874\pi$
$419$	14.8046	+	25.6424i	0.723253	+	1.25271i	−0.236436	+	0.971647i	$0.575979\pi$
$420$	−0.887395	+	1.53701i	−0.0433005	+	0.0749986i
$421$			11.6606i			0.568301i	0.958780	+	0.284151i	$0.0917115\pi$
$421$			11.6606i			0.568301i	−0.958780	+	0.284151i	$0.908288\pi$
$422$	6.10081	+	3.52230i	0.296983	+	0.171463i
$423$	13.0542	+	7.53684i	0.634716	+	0.366453i
$424$			27.9801i			1.35884i
$425$	5.33124	−	9.23398i	0.258603	−	0.447914i
$426$	7.80678	+	13.5217i	0.378240	+	0.655131i
$427$	−7.08719	+	4.09179i	−0.342973	+	0.198016i
$428$	4.43535			0.214391
$429$		0			0
$430$	−0.0586060			−0.00282623
$431$	−3.76645	+	2.17456i	−0.181424	+	0.104745i	−0.587961	−	0.808889i	$-0.700069\pi$
$431$	−3.76645	+	2.17456i	−0.181424	+	0.104745i	0.406538	+	0.913634i	$0.366736\pi$
$432$	−0.592990	−	1.02709i	−0.0285303	−	0.0494159i
$433$	−7.19418	+	12.4607i	−0.345730	+	0.598822i	−0.985486	−	0.169756i	$-0.945702\pi$
$433$	−7.19418	+	12.4607i	−0.345730	+	0.598822i	0.639756	+	0.768578i	$0.279035\pi$
$434$		−	12.5332i		−	0.601612i
$435$	−2.22571	−	1.28501i	−0.106714	−	0.0616116i
$436$	18.4512	+	10.6528i	0.883651	+	0.510176i
$437$		−	0.131687i		−	0.00629942i
$438$	6.06853	−	10.5110i	0.289966	−	0.502235i
$439$	−10.1163	−	17.5219i	−0.482822	−	0.836273i	0.516983	−	0.855996i	$-0.327055\pi$
$439$	−10.1163	−	17.5219i	−0.482822	−	0.836273i	−0.999805	+	0.0197227i	$0.993722\pi$
$440$	2.44540	−	1.41185i	0.116580	−	0.0673075i
$441$	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	$0.438196\pi$
$444$	−15.0294	+	8.67725i	−0.713266	+	0.411804i
$445$	0.356232	+	0.617012i	0.0168870	+	0.0292492i
$446$	−0.905813	+	1.56891i	−0.0428915	+	0.0742903i
$447$			9.74094i			0.460731i
$448$	−7.27591	−	4.20075i	−0.343755	−	0.198467i
$449$	−10.8180	−	6.24578i	−0.510534	−	0.294757i	0.222519	−	0.974928i	$-0.428572\pi$
$449$	−10.8180	−	6.24578i	−0.510534	−	0.294757i	−0.733053	+	0.680172i	$0.761905\pi$
$450$		−	8.11529i		−	0.382559i
$451$	−24.6151	+	42.6345i	−1.15908	+	2.00758i
$452$	−8.17456	−	14.1588i	−0.384499	−	0.665972i
$453$	−7.67553	+	4.43147i	−0.360628	+	0.208209i
$454$	5.58642			0.262184
$455$		0			0
$456$	−0.533188			−0.0249688
$457$	−5.17988	+	2.99061i	−0.242305	+	0.139895i	−0.616236	−	0.787562i	$-0.711343\pi$
$457$	−5.17988	+	2.99061i	−0.242305	+	0.139895i	0.373931	+	0.927457i	$0.378010\pi$
$458$	9.69298	+	16.7887i	0.452923	+	0.784486i
$459$	2.30678	−	3.99546i	0.107671	−	0.186492i
$460$			0.500664i			0.0233436i
$461$	−1.78114	−	1.02834i	−0.0829561	−	0.0478947i	0.457948	−	0.888979i	$-0.348585\pi$
$461$	−1.78114	−	1.02834i	−0.0829561	−	0.0478947i	−0.540904	+	0.841084i	$0.681918\pi$
$462$	15.6204	+	9.01842i	0.726725	+	0.419575i
$463$		−	8.44935i		−	0.392675i	−0.980536	−	0.196337i	$-0.937095\pi$
$463$		−	8.44935i		−	0.392675i	0.980536	−	0.196337i	$-0.0629048\pi$
$464$	−1.28501	+	2.22571i	−0.0596552	+	0.103326i
$465$	1.83997	+	3.18692i	0.0853266	+	0.147790i
$466$	−2.12586	+	1.22737i	−0.0984785	+	0.0568566i
$467$	−33.5139			−1.55084			−0.775420	−	0.631446i	$-0.782462\pi$
$467$	−33.5139			−1.55084			−0.775420	+	0.631446i	$0.782462\pi$
$468$		0			0
$469$	−18.1008			−0.835818
$470$	1.26191	−	0.728562i	0.0582074	−	0.0336060i
$471$	5.00484	+	8.66864i	0.230611	+	0.399430i
$472$	9.12618	−	15.8070i	0.420066	−	0.727576i
$473$		−	1.25667i		−	0.0577817i
$474$	−15.5591	−	8.98307i	−0.714655	−	0.412606i
$475$	−0.377027	−	0.217677i	−0.0172992	−	0.00998769i
$476$			6.90408i			0.316448i
$477$	10.6479	−	18.4428i	0.487536	−	0.844437i
$478$	−10.0831	−	17.4644i	−0.461189	−	0.798802i
$479$	−21.4179	+	12.3656i	−0.978608	+	0.565000i	−0.901850	−	0.432050i	$-0.857790\pi$
$479$	−21.4179	+	12.3656i	−0.978608	+	0.565000i	−0.0767587	+	0.997050i	$0.524457\pi$
$480$	3.23490			0.147652
$481$		0			0
$482$	−16.2524			−0.740275
$483$	−6.85187	+	3.95593i	−0.311771	+	0.180001i
$484$	4.77413	+	8.26903i	0.217006	+	0.375865i
$485$	−0.995156	+	1.72366i	−0.0451877	+	0.0782674i
$486$		−	14.5875i		−	0.661702i
$487$	−32.6972	−	18.8778i	−1.48165	−	0.855433i	−0.481870	−	0.876243i	$-0.660042\pi$
$487$	−32.6972	−	18.8778i	−1.48165	−	0.855433i	−0.999783	+	0.0208094i	$0.993376\pi$
$488$	8.09492	+	4.67360i	0.366440	+	0.211564i
$489$		−	36.3086i		−	1.64193i
$490$	0.143104	−	0.247864i	0.00646479	−	0.0111973i
$491$	15.6555	+	27.1161i	0.706522	+	1.22373i	0.966139	+	0.258020i	$0.0830702\pi$
$491$	15.6555	+	27.1161i	0.706522	+	1.22373i	−0.259617	+	0.965712i	$0.583596\pi$
$492$	−30.6074	+	17.6712i	−1.37989	+	0.796680i
$493$	−9.99761			−0.450270
$494$		0			0
$495$	−2.14914			−0.0965969
$496$	3.18692	−	1.83997i	0.143097	−	0.0826171i
$497$	−10.2111	−	17.6861i	−0.458031	−	0.793332i
$498$	−1.44989	+	2.51128i	−0.0649710	+	0.112533i
$499$		−	21.4873i		−	0.961902i	−0.876748	−	0.480951i	$-0.840292\pi$
$499$		−	21.4873i		−	0.961902i	0.876748	−	0.480951i	$-0.159708\pi$
$500$	2.88457	+	1.66541i	0.129002	+	0.0744793i
$501$	31.3632	+	18.1075i	1.40120	+	0.808984i
$502$		−	19.0228i		−	0.849031i
$503$	−18.7962	+	32.5560i	−0.838081	+	1.45160i	0.0534164	+	0.998572i	$0.482989\pi$
$503$	−18.7962	+	32.5560i	−0.838081	+	1.45160i	−0.891497	+	0.453026i	$0.850344\pi$
$504$	6.50000	+	11.2583i	0.289533	+	0.501486i
$505$	−2.85640	+	1.64914i	−0.127108	+	0.0733860i
$506$	5.08815			0.226196
$507$		0			0
$508$	13.3075			0.590425
$509$	14.8155	−	8.55376i	0.656688	−	0.379139i	−0.134326	−	0.990937i	$-0.542887\pi$
$509$	14.8155	−	8.55376i	0.656688	−	0.379139i	0.791014	+	0.611798i	$0.209554\pi$
$510$	0.480386	+	0.832052i	0.0212718	+	0.0368439i
$511$	−7.93751	+	13.7482i	−0.351135	+	0.608183i
$512$		−	6.22282i		−	0.275012i
$513$	−0.163136	−	0.0941868i	−0.00720264	−	0.00415845i
$514$	−9.87865	−	5.70344i	−0.435728	−	0.251568i
$515$			0.336454i			0.0148259i
$516$	0.451083	−	0.781298i	0.0198578	−	0.0343947i
$517$	15.6223	+	27.0586i	0.687068	+	1.19004i
$518$	−9.31705	+	5.37920i	−0.409367	+	0.236348i
$519$	−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	$0.643162\pi$
$522$	−6.58981	+	3.80463i	−0.288428	+	0.166524i
$523$	5.71499	+	9.89865i	0.249899	+	0.432838i	0.963498	−	0.267717i	$-0.0862693\pi$
$523$	5.71499	+	9.89865i	0.249899	+	0.432838i	−0.713599	+	0.700555i	$0.752936\pi$
$524$	4.46197	−	7.72835i	0.194922	−	0.337615i
$525$			26.1564i			1.14156i
$526$	−11.8728	−	6.85474i	−0.517677	−	0.298881i
$527$	12.3974	+	7.15764i	0.540039	+	0.311792i
$528$			5.29590i			0.230474i
$529$	10.3840	−	17.9857i	0.451480	−	0.781987i
$530$	−1.02930	−	1.78281i	−0.0447101	−	0.0774401i
$531$	−12.0308	+	6.94600i	−0.522093	+	0.301431i
$532$	0.281896			0.0122218
$533$		0			0
$534$	5.19806			0.224942
$535$	−0.699155	+	0.403657i	−0.0302271	+	0.0174516i
$536$	10.3373	+	17.9047i	0.446503	+	0.773365i
$537$	−12.8448	+	22.2479i	−0.554295	+	0.960066i
$538$			5.18598i			0.223584i
$539$	5.31485	+	3.06853i	0.228927	+	0.132171i
$540$	0.620234	+	0.358092i	0.0266906	+	0.0154098i
$541$			16.1884i			0.695993i	0.937496	+	0.347996i	$0.113138\pi$
$541$			16.1884i			0.695993i	−0.937496	+	0.347996i	$0.886862\pi$
$542$	−2.58546	+	4.47814i	−0.111055	+	0.192353i
$543$	−23.5601	−	40.8073i	−1.01106	−	1.75121i
$544$	10.8981	−	6.29201i	0.467252	−	0.269768i
$545$	−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	$0.463645\pi$
$548$	7.30896	−	4.21983i	0.312223	−	0.180262i
$549$	−3.55711	−	6.16110i	−0.151814	−	0.262949i
$550$	8.41066	−	14.5677i	0.358632	−	0.621168i
$551$			0.408206i			0.0173902i
$552$	7.82613	+	4.51842i	0.333102	+	0.192317i
$553$	20.3510	+	11.7497i	0.865413	+	0.499647i
$554$			10.7942i			0.458600i
$555$	1.57942	−	2.73563i	0.0670425	−	0.116121i
$556$	9.97799	+	17.2824i	0.423161	+	0.732937i
$557$	6.40058	−	3.69537i	0.271201	−	0.156578i	−0.358232	−	0.933633i	$-0.616620\pi$
$557$	6.40058	−	3.69537i	0.271201	−	0.156578i	0.629433	+	0.777054i	$0.283287\pi$
$558$	10.8955			0.461242
$559$		0			0
$560$	−0.323044			−0.0136511
$561$	−17.8414	+	10.3007i	−0.753265	+	0.434898i
$562$	−2.01961	−	3.49807i	−0.0851923	−	0.147557i
$563$	−4.73945	+	8.20896i	−0.199744	+	0.345967i	−0.948445	−	0.316941i	$-0.897344\pi$
$563$	−4.73945	+	8.20896i	−0.199744	+	0.345967i	0.748701	+	0.662907i	$0.230678\pi$
$564$			22.4306i			0.944497i
$565$	2.57715	+	1.48792i	0.108422	+	0.0625972i
$566$	−15.3678	−	8.87263i	−0.645958	−	0.372944i
$567$			25.8049i			1.08370i
$568$	−11.6630	+	20.2009i	−0.489369	+	0.847612i
$569$	−5.07188	−	8.78476i	−0.212624	−	0.368276i	0.739911	−	0.672705i	$-0.234868\pi$
$569$	−5.07188	−	8.78476i	−0.212624	−	0.368276i	−0.952535	+	0.304429i	$0.901534\pi$
$570$	0.0339730	−	0.0196143i	0.00142297	−	0.000821554i
$571$	14.0925			0.589751			0.294876	−	0.955536i	$-0.404722\pi$
$571$	14.0925			0.589751			0.294876	+	0.955536i	$0.404722\pi$
$572$		0			0
$573$	32.4403			1.35521
$574$	−18.9741	+	10.9547i	−0.791966	+	0.457242i
$575$	3.68933	+	6.39011i	0.153856	+	0.266486i
$576$	3.65183	−	6.32516i	0.152160	−	0.263548i
$577$		−	25.1545i		−	1.04720i	−0.851965	−	0.523598i	$-0.824589\pi$
$577$		−	25.1545i		−	1.04720i	0.851965	−	0.523598i	$-0.175411\pi$
$578$	−8.56972	−	4.94773i	−0.356453	−	0.205798i
$579$	−26.4253	−	15.2567i	−1.09820	−	0.634045i
$580$		−	1.55197i		−	0.0644422i
$581$	1.89642	−	3.28470i	0.0786768	−	0.136272i
$582$	7.26055	+	12.5756i	0.300960	+	0.521277i
$583$	38.2281	−	22.0710i	1.58324	−	0.914087i
$584$	18.1323			0.750319
$585$		0			0
$586$	11.9860			0.495137
$587$	−37.9625	+	21.9177i	−1.56688	+	0.904639i	−0.570350	+	0.821402i	$0.693192\pi$
$587$	−37.9625	+	21.9177i	−1.56688	+	0.904639i	−0.996530	+	0.0832369i	$0.973474\pi$
$588$	2.20291	+	3.81555i	0.0908463	+	0.157350i
$589$	0.292249	−	0.506190i	0.0120419	−	0.0208572i
$590$			1.34290i			0.0552861i
$591$	1.09038	+	0.629531i	0.0448522	+	0.0258954i
$592$	−2.73563	−	1.57942i	−0.112434	−	0.0649136i
$593$		−	24.9965i		−	1.02648i	−0.858244	−	0.513242i	$-0.828444\pi$
$593$		−	24.9965i		−	1.02648i	0.858244	−	0.513242i	$-0.171556\pi$
$594$	3.63922	−	6.30331i	0.149319	−	0.258628i
$595$	−0.628334	−	1.08831i	−0.0257592	−	0.0446162i
$596$	−5.09423	+	2.94116i	−0.208668	+	0.120474i
$597$	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	$0.540691\pi$
$600$	25.8730	−	14.9378i	1.05626	−	0.609833i
$601$	−3.16487	−	5.48172i	−0.129098	−	0.223604i	0.794229	−	0.607618i	$-0.207875\pi$
$601$	−3.16487	−	5.48172i	−0.129098	−	0.223604i	−0.923327	+	0.384014i	$0.874541\pi$
$602$	0.279635	−	0.484342i	0.0113971	−	0.0197403i
$603$		−	15.7356i		−	0.640802i
$604$	−4.63506	−	2.67606i	−0.188598	−	0.108887i
$605$	−1.50511	−	0.868977i	−0.0611915	−	0.0353290i
$606$			24.0640i			0.977532i
$607$	21.8240	−	37.8003i	0.885809	−	1.53427i	0.0410253	−	0.999158i	$-0.486938\pi$
$607$	21.8240	−	37.8003i	0.885809	−	1.53427i	0.844784	−	0.535108i	$-0.179729\pi$
$608$	−0.256905	−	0.444973i	−0.0104189	−	0.0180460i
$609$	21.2396	−	12.2627i	0.860673	−	0.496910i
$610$	−0.687710			−0.0278445
$611$		0			0
$612$	−6.00192			−0.242613
$613$	22.4769	−	12.9770i	0.907833	−	0.524137i	0.0280995	−	0.999605i	$-0.491054\pi$
$613$	22.4769	−	12.9770i	0.907833	−	0.524137i	0.879733	+	0.475468i	$0.157721\pi$
$614$	−7.67025	−	13.2853i	−0.309546	−	0.536150i
$615$	3.21648	−	5.57111i	0.129701	−	0.224649i
$616$			26.9463i			1.08570i
$617$	39.7849	+	22.9698i	1.60168	+	0.924729i	0.991152	+	0.132733i	$0.0423753\pi$
$617$	39.7849	+	22.9698i	1.60168	+	0.924729i	0.610526	+	0.791996i	$0.290958\pi$
$618$	2.12586	+	1.22737i	0.0855146	+	0.0493719i
$619$			6.73556i			0.270725i	0.990796	+	0.135363i	$0.0432199\pi$
$619$			6.73556i			0.270725i	−0.990796	+	0.135363i	$0.956780\pi$
$620$	−1.11111	+	1.92450i	−0.0446234	+	0.0772899i
$621$	1.59634	+	2.76495i	0.0640590	+	0.110953i
$622$	−0.187386	+	0.108187i	−0.00751349	+	0.00433792i
$623$	−6.79895			−0.272394
$624$		0			0
$625$	24.0887			0.963549
$626$	16.2469	−	9.38016i	0.649357	−	0.374907i
$627$	0.420583	+	0.728471i	0.0167965	+	0.0290923i
$628$	−3.02230	+	5.23478i	−0.120603	+	0.208891i
$629$		−	12.2881i		−	0.489960i
$630$	−0.828318	−	0.478230i	−0.0330010	−	0.0190531i
$631$	−39.0575	−	22.5499i	−1.55486	−	0.897696i	−0.997735	−	0.0672649i	$-0.978573\pi$
$631$	−39.0575	−	22.5499i	−1.55486	−	0.897696i	−0.557121	−	0.830432i	$-0.688094\pi$
$632$		−	26.8407i		−	1.06767i
$633$	9.86927	−	17.0941i	0.392268	−	0.679429i
$634$	−5.61165	−	9.71965i	−0.222867	−	0.386017i
$635$	−2.09769	+	1.21110i	−0.0832444	+	0.0480612i
$636$	31.6896			1.25658
$637$		0			0
$638$	−15.7724			−0.624435
$639$	15.3751	−	8.87681i	0.608229	−	0.351161i
$640$	1.08665	+	1.88214i	0.0429538	+	0.0743981i
$641$	16.2911	−	28.2169i	0.643458	−	1.11450i	−0.341197	−	0.939992i	$-0.610832\pi$
$641$	16.2911	−	28.2169i	0.643458	−	1.11450i	0.984655	−	0.174510i	$-0.0558342\pi$
$642$			5.89008i			0.232463i
$643$	22.1489	+	12.7877i	0.873469	+	0.504298i	0.868500	−	0.495690i	$-0.165085\pi$
$643$	22.1489	+	12.7877i	0.873469	+	0.504298i	0.00496965	+	0.999988i	$0.498418\pi$
$644$	−4.13767	−	2.38889i	−0.163047	−	0.0941353i
$645$			0.164210i			0.00646578i
$646$	0.0763014	−	0.132158i	0.00300204	−	0.00519968i
$647$	−15.0858	−	26.1293i	−0.593082	−	1.02725i	−0.993814	−	0.111053i	$-0.964578\pi$
$647$	−15.0858	−	26.1293i	−0.593082	−	1.02725i	0.400732	−	0.916195i	$-0.368756\pi$
$648$	25.5253	−	14.7371i	1.00273	−	0.578926i
$649$	−28.7952			−1.13031
$650$		0			0
$651$	−35.1172			−1.37635
$652$	18.9883	−	10.9629i	0.743641	−	0.429341i
$653$	−18.4514	−	31.9587i	−0.722058	−	1.25064i	−0.960173	−	0.279405i	$-0.909863\pi$
$653$	−18.4514	−	31.9587i	−0.722058	−	1.25064i	0.238115	−	0.971237i	$-0.423470\pi$
$654$	−14.1468	+	24.5029i	−0.553182	+	0.958139i
$655$			1.62432i			0.0634673i
$656$	−5.57111	−	3.21648i	−0.217515	−	0.125582i
$657$	−11.9517	−	6.90030i	−0.466279	−	0.269207i
$658$			13.9051i			0.542079i
$659$	−11.8433	+	20.5132i	−0.461350	+	0.799082i	−0.999029	−	0.0440679i	$-0.985968\pi$
$659$	−11.8433	+	20.5132i	−0.461350	+	0.799082i	0.537678	+	0.843150i	$0.319302\pi$
$660$	−1.59903	−	2.76960i	−0.0622422	−	0.107807i
$661$	−27.5041	+	15.8795i	−1.06979	+	0.617641i	−0.928123	−	0.372274i	$-0.878578\pi$
$661$	−27.5041	+	15.8795i	−1.06979	+	0.617641i	−0.141662	+	0.989915i	$0.545245\pi$
$662$	−14.2916			−0.555458
$663$		0			0
$664$	−4.33214			−0.168120
$665$	−0.0444360	+	0.0256551i	−0.00172315	+	0.000994863i
$666$	−4.67629	−	8.09958i	−0.181203	−	0.313852i
$667$	3.45928	−	5.99165i	0.133944	−	0.231998i
$668$			21.8694i			0.846152i
$669$	4.39600	+	2.53803i	0.169959	+	0.0981260i
$670$	−1.31732	−	0.760553i	−0.0508924	−	0.0293827i
$671$		−	14.7463i		−	0.569275i
$672$	−15.4351	+	26.7344i	−0.595423	+	1.03130i
$673$	−3.75116	−	6.49720i	−0.144597	−	0.250449i	0.784626	−	0.619970i	$-0.212855\pi$
$673$	−3.75116	−	6.49720i	−0.144597	−	0.250449i	−0.929222	+	0.369521i	$0.879522\pi$
$674$	−19.3407	+	11.1664i	−0.744976	+	0.430112i
$675$	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	$0.735074\pi$
$678$	18.8026	−	10.8557i	0.722110	−	0.416911i
$679$	−9.49665	−	16.4487i	−0.364448	−	0.631242i
$680$	−0.717677	+	1.24305i	−0.0275216	+	0.0476689i
$681$		−	15.6528i		−	0.599816i
$682$	19.5583	+	11.2920i	0.748927	+	0.432393i
$683$	20.8568	+	12.0417i	0.798063	+	0.460762i	0.842794	−	0.538237i	$-0.180909\pi$
$683$	20.8568	+	12.0417i	0.798063	+	0.460762i	−0.0447302	+	0.998999i	$0.514243\pi$
$684$			0.245061i			0.00937013i
$685$	−0.768086	+	1.33036i	−0.0293471	+	0.0508306i
$686$	7.98092	+	13.8234i	0.304713	+	0.527778i
$687$	47.0410	−	27.1591i	1.79473	−	1.03619i
$688$	0.164210			0.00626046
$689$		0			0
$690$	−0.664874			−0.0253113
$691$	−1.74459	+	1.00724i	−0.0663672	+	0.0383171i	−0.532816	−	0.846231i	$-0.678866\pi$
$691$	−1.74459	+	1.00724i	−0.0663672	+	0.0383171i	0.466449	+	0.884548i	$0.345533\pi$
$692$	−14.6112	−	25.3073i	−0.555433	−	0.962039i
$693$	10.2545	−	17.7613i	0.389537	−	0.674697i
$694$		−	1.20583i		−	0.0457728i
$695$	−3.14571	−	1.81618i	−0.119323	−	0.0688915i
$696$	−24.2597	−	14.0063i	−0.919561	−	0.530909i
$697$		−	25.0248i		−	0.947880i
$698$	5.68814	−	9.85214i	0.215299	−	0.372909i
$699$	3.43900	+	5.95652i	0.130075	+	0.225296i
$700$	−13.6791	+	7.89762i	−0.517020	+	0.298502i
$701$	48.8189			1.84387			0.921933	−	0.387350i	$-0.126610\pi$
$701$	48.8189			1.84387			0.921933	+	0.387350i	$0.126610\pi$
$702$		0			0
$703$	−0.501729			−0.0189231
$704$	13.1107	−	7.56949i	0.494130	−	0.285286i
$705$	−2.04138	−	3.53578i	−0.0768830	−	0.133165i
$706$	−2.87435	+	4.97853i	−0.108178	+	0.187369i
$707$		−	31.4752i		−	1.18375i
$708$	−17.9026	−	10.3361i	−0.672822	−	0.388454i
$709$	18.0185	+	10.4030i	0.676699	+	0.390693i	0.798610	−	0.601848i	$-0.205569\pi$
$709$	18.0185	+	10.4030i	0.676699	+	0.390693i	−0.121911	+	0.992541i	$0.538902\pi$
$710$		−	1.71618i		−	0.0644073i
$711$	−10.2143	+	17.6917i	−0.383067	+	0.663492i
$712$	3.88285	+	6.72529i	0.145516	+	0.252041i
$713$	−8.57926	+	4.95324i	−0.321296	+	0.185500i
$714$	−9.16852			−0.343123
$715$		0			0
$716$	−15.5133			−0.579761
$717$	−48.9341	+	28.2521i	−1.82748	+	1.05509i
$718$	−7.97339	−	13.8103i	−0.297564	−	0.515396i
$719$	10.7153	−	18.5594i	0.399613	−	0.692149i	−0.594065	−	0.804417i	$-0.702478\pi$
$719$	10.7153	−	18.5594i	0.399613	−	0.692149i	0.993678	+	0.112267i	$0.0358113\pi$
$720$		−	0.280831i		−	0.0104660i
$721$	−2.78058	−	1.60537i	−0.103554	−	0.0597870i
$722$	13.1901	+	7.61529i	0.490884	+	0.283412i
$723$			45.5381i			1.69358i
$724$	14.2274	−	24.6425i	0.528756	−	0.915832i
$725$	−11.4363	−	19.8083i	−0.424734	−	0.735661i
$726$	−10.9812	+	6.33997i	−0.407549	+	0.235298i
$727$	−13.4862			−0.500175			−0.250088	−	0.968223i	$-0.580459\pi$
$727$	−13.4862			−0.500175			−0.250088	+	0.968223i	$0.580459\pi$
$728$		0			0
$729$	−8.02715			−0.297302
$730$	−1.15533	+	0.667030i	−0.0427607	+	0.0246879i
$731$	0.319396	+	0.553210i	0.0118133	+	0.0204612i
$732$	5.29321	−	9.16811i	0.195643	−	0.338863i
$733$			43.5424i			1.60828i	0.594443	+	0.804138i	$0.297373\pi$
$733$			43.5424i			1.60828i	−0.594443	+	0.804138i	$0.702627\pi$
$734$	0.752721	+	0.434584i	0.0277834	+	0.0160408i
$735$	−0.694498	−	0.400969i	−0.0256170	−	0.0147900i
$736$			8.70841i			0.320996i
$737$	16.3083	−	28.2468i	0.600723	−	1.04048i
$738$	−9.52326	−	16.4948i	−0.350556	−	0.607181i
$739$	17.3675	−	10.0271i	0.638875	−	0.368855i	−0.145306	−	0.989387i	$-0.546417\pi$
$739$	17.3675	−	10.0271i	0.638875	−	0.368855i	0.784181	+	0.620532i	$0.213083\pi$
$740$	1.90754			0.0701226
$741$		0			0
$742$	19.6450			0.721191
$743$	28.7248	−	16.5843i	1.05381	−	0.608418i	0.130096	−	0.991501i	$-0.458471\pi$
$743$	28.7248	−	16.5843i	1.05381	−	0.608418i	0.923714	+	0.383084i	$0.125138\pi$
$744$	20.0553	+	34.7367i	0.735261	+	1.27351i
$745$	0.535344	−	0.927243i	0.0196135	−	0.0339715i
$746$			4.91617i			0.179994i
$747$	2.85548	+	1.64861i	0.104477	+	0.0603196i
$748$	−10.7740	−	6.22037i	−0.393936	−	0.227439i
$749$		−	7.70410i		−	0.281502i
$750$	−2.21164	+	3.83067i	−0.0807575	+	0.139876i
$751$	19.6407	+	34.0187i	0.716700	+	1.24136i	0.962300	+	0.271989i	$0.0876815\pi$
$751$	19.6407	+	34.0187i	0.716700	+	1.24136i	−0.245601	+	0.969371i	$0.578985\pi$
$752$	−3.53578	+	2.04138i	−0.128937	+	0.0744416i
$753$	−53.3008			−1.94239
$754$		0			0
$755$	0.974181			0.0354541
$756$	−5.91882	+	3.41723i	−0.215265	+	0.124283i
$757$	23.3213	+	40.3937i	0.847628	+	1.46813i	0.883320	+	0.468771i	$0.155303\pi$
$757$	23.3213	+	40.3937i	0.847628	+	1.46813i	−0.0356920	+	0.999363i	$0.511364\pi$
$758$	−0.965853	+	1.67291i	−0.0350813	+	0.0607627i
$759$		−	14.2567i		−	0.517484i
$760$	0.0507543	+	0.0293030i	0.00184105	+	0.00106293i
$761$	18.9646	+	10.9492i	0.687467	+	0.396909i	0.802662	−	0.596434i	$-0.203416\pi$
$761$	18.9646	+	10.9492i	0.687467	+	0.396909i	−0.115196	+	0.993343i	$0.536750\pi$
$762$			17.6722i			0.640195i
$763$	18.5036	−	32.0493i	0.669877	−	1.16026i
$764$	9.79494	+	16.9653i	0.354368	+	0.613784i
$765$	0.946096	−	0.546229i	0.0342062	−	0.0197489i
$766$	24.3720			0.880595
$767$		0			0
$768$	31.8756			1.15021
$769$	−40.4517	+	23.3548i	−1.45873	+	0.842196i	−0.998949	−	0.0458390i	$-0.985404\pi$
$769$	−40.4517	+	23.3548i	−1.45873	+	0.842196i	−0.459777	+	0.888035i	$0.652071\pi$
$770$	−0.991271	−	1.71693i	−0.0357229	−	0.0618739i
$771$	−15.9807	+	27.6794i	−0.575530	+	0.996848i
$772$		−	18.4263i		−	0.663175i
$773$	−26.1900	−	15.1208i	−0.941989	−	0.543857i	−0.0514055	−	0.998678i	$-0.516370\pi$
$773$	−26.1900	−	15.1208i	−0.941989	−	0.543857i	−0.890583	+	0.454820i	$0.849703\pi$
$774$	0.421052	+	0.243095i	0.0151344	+	0.00873786i
$775$			32.7506i			1.17644i
$776$	−10.8470	+	18.7875i	−0.389384	+	0.674432i
$777$	15.0722	+	26.1058i	0.540711	+	0.936540i
$778$	−11.0709	+	6.39181i	−0.396913	+	0.229158i
$779$	−1.02177			−0.0366087
$780$		0			0
$781$	36.7995			1.31679
$782$	−2.23990	+	1.29321i	−0.0800988	+	0.0462450i
$783$	−4.94839	−	8.57087i	−0.176841	−	0.306298i
$784$	−0.400969	+	0.694498i	−0.0143203	+	0.0248035i
$785$		−	1.10023i		−	0.0392688i
$786$	10.2631	+	5.92543i	0.366074	+	0.211353i
$787$	−24.8569	−	14.3512i	−0.886054	−	0.511563i	−0.0134040	−	0.999910i	$-0.504267\pi$
$787$	−24.8569	−	14.3512i	−0.886054	−	0.511563i	−0.872650	+	0.488347i	$0.837600\pi$
$788$			0.760316i			0.0270851i
$789$	−19.2066	+	33.2667i	−0.683771	+	1.18433i
$790$	0.987386	+	1.71020i	0.0351296	+	0.0608463i
$791$	−24.5934	+	14.1990i	−0.874442	+	0.504859i
$792$	−23.4252			−0.832378
$793$		0			0
$794$	13.5646			0.481391
$795$	−4.99531	+	2.88404i	−0.177165	+	0.102286i
$796$	7.79643	+	13.5038i	0.276337	+	0.478630i
$797$	−9.27091	+	16.0577i	−0.328392	+	0.568792i	−0.982193	−	0.187875i	$-0.939840\pi$
$797$	−9.27091	+	16.0577i	−0.328392	+	0.568792i	0.653801	+	0.756667i	$0.273173\pi$
$798$			0.374354i			0.0132520i
$799$	−13.7545	−	7.94116i	−0.486599	−	0.280938i
$800$	24.9327	+	14.3949i	0.881506	+	0.508938i
$801$		−	5.91053i		−	0.208838i
$802$	−10.6908	+	18.5171i	−0.377506	+	0.653860i
$803$	−14.3029	−	24.7733i	−0.504738	−	0.874232i
$804$	20.2784	−	11.7078i	0.715165	−	0.412901i
$805$	0.869641			0.0306508
$806$		0			0
$807$	14.5308			0.511508
$808$	−31.1341	+	17.9753i	−1.09530	+	0.632369i
$809$	5.03385	+	8.71889i	0.176981	+	0.306540i	0.940845	−	0.338837i	$-0.110034\pi$
$809$	5.03385	+	8.71889i	0.176981	+	0.306540i	−0.763864	+	0.645377i	$0.776700\pi$
$810$	−1.08426	+	1.87800i	−0.0380971	+	0.0659860i
$811$			10.0285i			0.352147i	0.984377	+	0.176074i	$0.0563397\pi$
$811$			10.0285i			0.352147i	−0.984377	+	0.176074i	$0.943660\pi$
$812$	12.8261	+	7.40515i	0.450108	+	0.259870i
$813$	12.5475	+	7.24429i	0.440059	+	0.254068i
$814$		−	19.3860i		−	0.679478i
$815$	−1.99545	+	3.45622i	−0.0698976	+	0.121066i
$816$	−1.34601	−	2.33136i	−0.0471198	−	0.0816139i
$817$	0.0225878	−	0.0130411i	0.000790247	−	0.000456249i
$818$	−22.8683			−0.799572
$819$		0			0
$820$	3.88471			0.135660
$821$	22.6643	−	13.0852i	0.790988	−	0.456677i	−0.0493220	−	0.998783i	$-0.515706\pi$
$821$	22.6643	−	13.0852i	0.790988	−	0.456677i	0.840310	+	0.542106i	$0.182373\pi$
$822$	5.60388	+	9.70620i	0.195458	+	0.338542i
$823$	0.911190	−	1.57823i	0.0317621	−	0.0550135i	−0.849707	−	0.527255i	$-0.823221\pi$
$823$	0.911190	−	1.57823i	0.0317621	−	0.0550135i	0.881470	+	0.472241i	$0.156555\pi$
$824$			3.66727i			0.127755i
$825$	−40.8177	−	23.5661i	−1.42109	−	0.820468i
$826$	−11.0982	−	6.40754i	−0.386155	−	0.222947i
$827$		−	32.2941i		−	1.12298i	−0.827485	−	0.561488i	$-0.810229\pi$
$827$		−	32.2941i		−	1.12298i	0.827485	−	0.561488i	$-0.189771\pi$
$828$	2.07673	−	3.59700i	0.0721713	−	0.125004i
$829$	7.55011	+	13.0772i	0.262226	+	0.454189i	0.966833	−	0.255409i	$-0.0822100\pi$
$829$	7.55011	+	13.0772i	0.262226	+	0.454189i	−0.704607	+	0.709598i	$0.748877\pi$
$830$	0.276030	−	0.159366i	0.00958115	−	0.00553168i
$831$	30.2446			1.04917
$832$		0			0
$833$	−3.11960			−0.108088
$834$	−22.9508	+	13.2506i	−0.794720	+	0.458832i
$835$	−1.99031	−	3.44732i	−0.0688776	−	0.119299i
$836$	−0.253980	+	0.439906i	−0.00878408	+	0.0152145i
$837$			14.1709i			0.489818i
$838$	−20.5636	−	11.8724i	−0.710357	−	0.410125i
$839$	28.5758	+	16.4983i	0.986548	+	0.569584i	0.904241	−	0.427023i	$-0.140438\pi$
$839$	28.5758	+	16.4983i	0.986548	+	0.569584i	0.0823071	+	0.996607i	$0.473771\pi$
$840$		−	3.52111i		−	0.121490i
$841$	3.77682	−	6.54164i	0.130235	−	0.225574i
$842$	−4.67552	−	8.09824i	−0.161129	−	0.279084i
$843$	−9.80139	+	5.65883i	−0.337578	+	0.194901i
$844$	11.9196			0.410290
$845$		0			0
$846$	−12.0881			−0.415599
$847$	14.3631	−	8.29254i	0.493522	−	0.284935i
$848$	2.88404	+	4.99531i	0.0990384	+	0.171540i
$849$	−24.8605	+	43.0597i	−0.853212	+	1.47781i
$850$			8.55065i			0.293285i
$851$	7.36438	+	4.25182i	0.252448	+	0.145751i
$852$	22.8791	+	13.2092i	0.783824	+	0.452541i
$853$		−	37.7802i		−	1.29357i	−0.762673	−	0.646784i	$-0.776113\pi$
$853$		−	37.7802i		−	1.29357i	0.762673	−	0.646784i	$-0.223887\pi$
$854$	3.28136	−	5.68349i	0.112286	−	0.194485i
$855$	−0.0223027	−	0.0386295i	−0.000762737	−	0.00132110i
$856$	−7.62063	+	4.39977i	−0.260468	+	0.150381i
$857$	−27.3623			−0.934677			−0.467339	−	0.884078i	$-0.654787\pi$
$857$	−27.3623			−0.934677			−0.467339	+	0.884078i	$0.654787\pi$
$858$		0			0
$859$	−20.0629			−0.684538			−0.342269	−	0.939602i	$-0.611195\pi$
$859$	−20.0629			−0.684538			−0.342269	+	0.939602i	$0.611195\pi$
$860$	−0.0858774	+	0.0495813i	−0.00292839	+	0.00169071i
$861$	30.6945	+	53.1644i	1.04606	+	1.81184i
$862$	1.74386	−	3.02046i	0.0593962	−	0.102877i
$863$			6.14483i			0.209173i	0.994516	+	0.104586i	$0.0333518\pi$
$863$			6.14483i			0.209173i	−0.994516	+	0.104586i	$0.966648\pi$
$864$	10.7882	+	6.22856i	0.367022	+	0.211900i
$865$	4.60638	+	2.65950i	0.156622	+	0.0904256i
$866$		−	11.5386i		−	0.392096i
$867$	−13.8632	+	24.0118i	−0.470820	+	0.815484i
$868$	−10.6032	−	18.3653i	−0.359896	−	0.623359i
$869$	−36.6713	+	21.1722i	−1.24399	+	0.718217i
$870$	2.06100			0.0698744
$871$		0			0
$872$	−42.2693			−1.43142
$873$	14.2993	−	8.25571i	0.483958	−	0.279413i
$874$	0.0528022	+	0.0914561i	0.00178606	+	0.00309355i
$875$	2.89277	−	5.01043i	0.0977935	−	0.169383i
$876$		−	20.5362i		−	0.693853i
$877$	−11.6980	−	6.75385i	−0.395014	−	0.228061i	0.289317	−	0.957233i	$-0.406572\pi$
$877$	−11.6980	−	6.75385i	−0.395014	−	0.228061i	−0.684330	+	0.729172i	$0.739905\pi$
$878$	14.0514	+	8.11260i	0.474213	+	0.273787i
$879$		−	33.5840i		−	1.13276i
$880$	0.291053	−	0.504118i	0.00981138	−	0.0169938i
$881$	−2.61715	−	4.53304i	−0.0881741	−	0.152722i	0.818565	−	0.574414i	$-0.194770\pi$
$881$	−2.61715	−	4.53304i	−0.0881741	−	0.152722i	−0.906739	+	0.421691i	$0.861437\pi$
$882$	−2.05625	+	1.18718i	−0.0692376	+	0.0399743i
$883$	4.57301			0.153894			0.0769470	−	0.997035i	$-0.475483\pi$
$883$	4.57301			0.153894			0.0769470	+	0.997035i	$0.475483\pi$
$884$		0			0
$885$	3.76271			0.126482
$886$	−5.64071	+	3.25667i	−0.189504	+	0.109410i
$887$	0.820356	+	1.42090i	0.0275448	+	0.0477091i	0.879469	−	0.475956i	$-0.157898\pi$
$887$	0.820356	+	1.42090i	0.0275448	+	0.0477091i	−0.851924	+	0.523665i	$0.824564\pi$
$888$	17.2153	−	29.8177i	0.577707	−	1.00062i
$889$		−	23.1148i		−	0.775246i
$890$	−0.494805	−	0.285676i	−0.0165859	−	0.00957587i
$891$	−40.2692	−	23.2494i	−1.34907	−	0.778885i
$892$			3.06531i			0.102634i
$893$	−0.324240	+	0.561601i	−0.0108503	+	0.0187933i
$894$	−3.90581	−	6.76507i	−0.130630	−	0.226258i
$895$	2.44540	−	1.41185i	0.0817408	−	0.0471931i
$896$	−20.7396			−0.692862
$897$		0			0
$898$	10.0175			0.334287
$899$	26.5943	−	15.3542i	0.886968	−	0.512091i
$900$	−6.86563	−	11.8916i	−0.228854	−	0.396387i
$901$	−11.2192	+	19.4322i	−0.373765	+	0.647379i
$902$		−	39.4795i		−	1.31452i
$903$	−1.35710	−	0.783520i	−0.0451613	−	0.0260739i
$904$	28.0904	+	16.2180i	0.934271	+	0.539402i
$905$			5.17928i			0.172165i
$906$	3.55376	−	6.15530i	0.118066	−	0.204496i
$907$	4.05107	+	7.01666i	0.134514	+	0.232985i	0.925412	−	0.378964i	$-0.123719\pi$
$907$	4.05107	+	7.01666i	0.134514	+	0.232985i	−0.790898	+	0.611948i	$0.790386\pi$
$908$	8.18596	−	4.72617i	0.271661	−	0.156843i
$909$	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	$0.548601\pi$
$912$	−0.0951903	+	0.0549581i	−0.00315207	+	0.00181985i
$913$	3.41723	+	5.91882i	0.113094	+	0.195884i
$914$	2.39828	−	4.15394i	0.0793281	−	0.137400i
$915$			1.92692i			0.0637020i
$916$	28.4069	+	16.4007i	0.938590	+	0.541895i
$917$	−13.4240	−	7.75033i	−0.443299	−	0.255939i
$918$			3.69979i			0.122111i
$919$	−13.7518	+	23.8189i	−0.453631	+	0.785712i	−0.998608	−	0.0527390i	$-0.983205\pi$
$919$	−13.7518	+	23.8189i	−0.453631	+	0.785712i	0.544978	+	0.838451i	$0.316538\pi$
$920$	−0.496648	−	0.860219i	−0.0163740	−	0.0283606i
$921$	−37.2245	+	21.4916i	−1.22659	+	0.708171i
$922$	1.64933			0.0543180
$923$		0			0
$924$	30.5187			1.00399
$925$	24.3465	−	14.0565i	0.800508	−	0.462173i
$926$	3.38793	+	5.86806i	0.111334	+	0.192837i
$927$	1.39559	−	2.41724i	0.0458373	−	0.0793925i
$928$		−	26.9946i		−	0.886142i
$929$	20.9692	+	12.1066i	0.687977	+	0.397203i	0.802854	−	0.596176i	$-0.203314\pi$
$929$	20.9692	+	12.1066i	0.687977	+	0.397203i	−0.114877	+	0.993380i	$0.536647\pi$
$930$	−2.55571	−	1.47554i	−0.0838051	−	0.0483849i
$931$			0.127375i			0.00417454i
$932$	−2.07673	+	3.59700i	−0.0680255	+	0.117824i
$933$	0.303134	+	0.525044i	0.00992417	+	0.0171892i
$934$	23.2754	−	13.4380i	0.761593	−	0.439706i
$935$	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	$0.441527\pi$
$938$	12.5710	−	7.25786i	0.410457	−	0.236978i
$939$	−26.2826	−	45.5228i	−0.857701	−	1.48558i
$940$	1.23274	−	2.13517i	0.0402076	−	0.0696416i
$941$			15.9638i			0.520404i	0.965554	+	0.260202i	$0.0837891\pi$
$941$			15.9638i			0.520404i	−0.965554	+	0.260202i	$0.916211\pi$
$942$	−6.95171	−	4.01357i	−0.226499	−	0.130769i
$943$	14.9975	+	8.65883i	0.488387	+	0.281970i
$944$		−	3.76271i		−	0.122466i
$945$	0.621998	−	1.07733i	0.0202336	−	0.0350456i
$946$	0.503885	+	0.872754i	0.0163827	+	0.0283757i
$947$	5.64186	−	3.25733i	0.183336	−	0.105849i	−0.405523	−	0.914085i	$-0.632911\pi$
$947$	5.64186	−	3.25733i	0.183336	−	0.105849i	0.588859	+	0.808236i	$0.299577\pi$
$948$	−30.3991			−0.987317
$949$		0			0
$950$	0.349126			0.0113271
$951$	−27.2339	+	15.7235i	−0.883119	+	0.509869i
$952$	−6.84870	−	11.8623i	−0.221968	−	0.384459i
$953$	23.8235	−	41.2635i	0.771718	−	1.33665i	−0.164903	−	0.986310i	$-0.552731\pi$
$953$	23.8235	−	41.2635i	0.771718	−	1.33665i	0.936621	−	0.350345i	$-0.113936\pi$
$954$			17.0780i			0.552920i
$955$	−3.08800	−	1.78286i	−0.0999252	−	0.0576919i
$956$	−29.5501	−	17.0608i	−0.955719	−	0.551784i
$957$			44.1933i			1.42857i
$958$	9.91646	−	17.1758i	0.320386	−	0.554925i
$959$	−7.32975	−	12.6955i	−0.236690	−	0.409959i
$960$	−1.71320	+	0.989115i	−0.0552932	+	0.0319235i
$961$	−12.9705			−0.418402
$962$		0			0
$963$	6.69740			0.215821
$964$	−23.8151	+	13.7497i	−0.767033	+	0.442847i
$965$	1.67696	+	2.90457i	0.0539831	+	0.0935015i
$966$	3.17241	−	5.49477i	0.102071	−	0.176791i
$967$			43.8122i			1.40891i	0.709751	+	0.704453i	$0.248808\pi$
$967$			43.8122i			1.40891i	−0.709751	+	0.704453i	$0.751192\pi$
$968$	−16.4054	−	9.47166i	−0.527289	−	0.304431i
$969$	−0.370298	−	0.213792i	−0.0118957	−	0.00686798i
$970$		−	1.59611i		−	0.0512479i
$971$	−2.14742	+	3.71943i	−0.0689139	+	0.119362i	−0.898423	−	0.439130i	$-0.855287\pi$
$971$	−2.14742	+	3.71943i	−0.0689139	+	0.119362i	0.829510	+	0.558492i	$0.188620\pi$
$972$	−12.3412	−	21.3755i	−0.395843	−	0.685620i
$973$	30.0191	−	17.3315i	0.962368	−	0.555624i
$974$	30.2776			0.970156
$975$		0			0
$976$	1.92692			0.0616792
$977$	−23.2112	+	13.4010i	−0.742591	+	0.428735i	−0.823011	−	0.568026i	$-0.807707\pi$
$977$	−23.2112	+	13.4010i	−0.742591	+	0.428735i	0.0804198	+	0.996761i	$0.474374\pi$
$978$	14.5586	+	25.2162i	0.465533	+	0.806327i
$979$	6.12565	−	10.6099i	0.195776	−	0.339095i
$980$		−	0.484271i		−	0.0154695i
$981$	27.8613	+	16.0858i	0.889544	+	0.513579i
$982$	−21.7454	−	12.5547i	−0.693924	−	0.400637i
$983$			27.2495i			0.869124i	0.900642	+	0.434562i	$0.143097\pi$
$983$			27.2495i			0.869124i	−0.900642	+	0.434562i	$0.856903\pi$
$984$	35.0589	−	60.7238i	1.11764	−	1.93580i
$985$	−0.0691957	−	0.119850i	−0.00220476	−	0.00381875i
$986$	6.94332	−	4.00873i	0.221120	−	0.127664i
$987$	38.9614			1.24015
$988$		0			0
$989$	−0.442058			−0.0140566
$990$	1.49258	−	0.861740i	0.0474372	−	0.0273879i
$991$	−12.1945	−	21.1214i	−0.387370	−	0.670945i	0.604725	−	0.796435i	$-0.293283\pi$
$991$	−12.1945	−	21.1214i	−0.387370	−	0.670945i	−0.992095	+	0.125490i	$0.959950\pi$
$992$	−19.3264	+	33.4743i	−0.613614	+	1.06281i
$993$			40.0441i			1.27076i
$994$	14.1832	+	8.18867i	0.449863	+	0.259729i
$995$	−2.45794	−	1.41909i	−0.0779219	−	0.0449882i
$996$			4.90648i			0.155468i
$997$	−15.6603	+	27.1245i	−0.495967	+	0.859041i	−0.999989	−	0.00465010i	$-0.998520\pi$
$997$	−15.6603	+	27.1245i	−0.495967	+	0.859041i	0.504022	+	0.863691i	$0.331853\pi$
$998$	8.61572	+	14.9229i	0.272726	+	0.472375i
$999$	10.5345	−	6.08211i	0.333297	−	0.192429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.e.b.23.2		12
13.2	odd	12		169.2.a.c.1.1	yes	3
13.3	even	3		169.2.b.b.168.2		6
13.4	even	6	inner	169.2.e.b.147.2		12
13.5	odd	4		169.2.c.b.146.3		6
13.6	odd	12		169.2.c.b.22.3		6
13.7	odd	12		169.2.c.c.22.1		6
13.8	odd	4		169.2.c.c.146.1		6
13.9	even	3	inner	169.2.e.b.147.5		12
13.10	even	6		169.2.b.b.168.5		6
13.11	odd	12		169.2.a.b.1.3	✓	3
13.12	even	2	inner	169.2.e.b.23.5		12
39.2	even	12		1521.2.a.o.1.3		3
39.11	even	12		1521.2.a.r.1.1		3
39.23	odd	6		1521.2.b.l.1351.2		6
39.29	odd	6		1521.2.b.l.1351.5		6
52.3	odd	6		2704.2.f.o.337.5		6
52.11	even	12		2704.2.a.z.1.3		3
52.15	even	12		2704.2.a.ba.1.3		3
52.23	odd	6		2704.2.f.o.337.6		6
65.24	odd	12		4225.2.a.bg.1.1		3
65.54	odd	12		4225.2.a.bb.1.3		3
91.41	even	12		8281.2.a.bj.1.1		3
91.76	even	12		8281.2.a.bf.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.a.b.1.3	✓	3	13.11	odd	12
169.2.a.c.1.1	yes	3	13.2	odd	12
169.2.b.b.168.2		6	13.3	even	3
169.2.b.b.168.5		6	13.10	even	6
169.2.c.b.22.3		6	13.6	odd	12
169.2.c.b.146.3		6	13.5	odd	4
169.2.c.c.22.1		6	13.7	odd	12
169.2.c.c.146.1		6	13.8	odd	4
169.2.e.b.23.2		12	1.1	even	1	trivial
169.2.e.b.23.5		12	13.12	even	2	inner
169.2.e.b.147.2		12	13.4	even	6	inner
169.2.e.b.147.5		12	13.9	even	3	inner
1521.2.a.o.1.3		3	39.2	even	12
1521.2.a.r.1.1		3	39.11	even	12
1521.2.b.l.1351.2		6	39.23	odd	6
1521.2.b.l.1351.5		6	39.29	odd	6
2704.2.a.z.1.3		3	52.11	even	12
2704.2.a.ba.1.3		3	52.15	even	12
2704.2.f.o.337.5		6	52.3	odd	6
2704.2.f.o.337.6		6	52.23	odd	6
4225.2.a.bb.1.3		3	65.54	odd	12
4225.2.a.bg.1.1		3	65.24	odd	12
8281.2.a.bf.1.3		3	91.76	even	12
8281.2.a.bj.1.1		3	91.41	even	12

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.e (of order \(6\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

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