LMFDB - Embedded newform 169.2.e.b.147.4

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			147.4
Root			$0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	169.147
Dual form			169.2.e.b.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.480608 + 0.277479i) q^{2} +(-0.400969 + 0.694498i) q^{3} +(-0.846011 - 1.46533i) q^{4} -2.80194i q^{5} +(-0.385418 + 0.222521i) q^{6} +(2.33136 - 1.34601i) q^{7} -2.04892i q^{8} +(1.17845 + 2.04113i) q^{9} +O(q^{10})$	\(q+(0.480608 + 0.277479i) q^{2} +(-0.400969 + 0.694498i) q^{3} +(-0.846011 - 1.46533i) q^{4} -2.80194i q^{5} +(-0.385418 + 0.222521i) q^{6} +(2.33136 - 1.34601i) q^{7} -2.04892i q^{8} +(1.17845 + 2.04113i) q^{9} +(0.777479 - 1.34663i) q^{10} +(-1.03755 - 0.599031i) q^{11} +1.35690 q^{12} +1.49396 q^{14} +(1.94594 + 1.12349i) q^{15} +(-1.12349 + 1.94594i) q^{16} +(0.568532 + 0.984726i) q^{17} +1.30798i q^{18} +(1.67922 - 0.969501i) q^{19} +(-4.10577 + 2.37047i) q^{20} +2.15883i q^{21} +(-0.332437 - 0.575798i) q^{22} +(-2.30194 + 3.98707i) q^{23} +(1.42297 + 0.821552i) q^{24} -2.85086 q^{25} -4.29590 q^{27} +(-3.94471 - 2.27748i) q^{28} +(3.94989 - 6.84140i) q^{29} +(0.623490 + 1.07992i) q^{30} +5.89977i q^{31} +(-4.62874 + 2.67241i) q^{32} +(0.832052 - 0.480386i) q^{33} +0.631023i q^{34} +(-3.77144 - 6.53232i) q^{35} +(1.99396 - 3.45364i) q^{36} +(0.823662 + 0.475541i) q^{37} +1.07606 q^{38} -5.74094 q^{40} +(-2.87318 - 1.65883i) q^{41} +(-0.599031 + 1.03755i) q^{42} +(3.57942 + 6.19973i) q^{43} +2.02715i q^{44} +(5.71912 - 3.30194i) q^{45} +(-2.21266 + 1.27748i) q^{46} +7.69202i q^{47} +(-0.900969 - 1.56052i) q^{48} +(0.123490 - 0.213891i) q^{49} +(-1.37014 - 0.791053i) q^{50} -0.911854 q^{51} +5.87263 q^{53} +(-2.06464 - 1.19202i) q^{54} +(-1.67845 + 2.90716i) q^{55} +(-2.75786 - 4.77676i) q^{56} +1.55496i q^{57} +(3.79669 - 2.19202i) q^{58} +(0.0104630 - 0.00604079i) q^{59} -3.80194i q^{60} +(4.01842 + 6.96010i) q^{61} +(-1.63706 + 2.83548i) q^{62} +(5.49477 + 3.17241i) q^{63} +1.52781 q^{64} +0.533188 q^{66} +(8.01651 + 4.62833i) q^{67} +(0.961968 - 1.66618i) q^{68} +(-1.84601 - 3.19738i) q^{69} -4.18598i q^{70} +(-11.9000 + 6.87047i) q^{71} +(4.18211 - 2.41454i) q^{72} -12.8170i q^{73} +(0.263906 + 0.457098i) q^{74} +(1.14310 - 1.97991i) q^{75} +(-2.84128 - 1.64042i) q^{76} -3.22521 q^{77} +0.807315 q^{79} +(5.45241 + 3.14795i) q^{80} +(-1.81282 + 3.13990i) q^{81} +(-0.920583 - 1.59450i) q^{82} -16.3327i q^{83} +(3.16341 - 1.82640i) q^{84} +(2.75914 - 1.59299i) q^{85} +3.97285i q^{86} +(3.16756 + 5.48638i) q^{87} +(-1.22737 + 2.12586i) q^{88} +(-12.7556 - 7.36443i) q^{89} +3.66487 q^{90} +7.78986 q^{92} +(-4.09738 - 2.36563i) q^{93} +(-2.13437 + 3.69685i) q^{94} +(-2.71648 - 4.70508i) q^{95} -4.28621i q^{96} +(2.71212 - 1.56584i) q^{97} +(0.118700 - 0.0685317i) q^{98} -2.82371i 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.480608	+	0.277479i	0.339841	+	0.196207i	0.660202	−	0.751088i	$-0.270471\pi$
$2$	0.480608	+	0.277479i	0.339841	+	0.196207i	−0.320361	+	0.947296i	$0.603804\pi$
$3$	−0.400969	+	0.694498i	−0.231499	+	0.400969i	−0.958250	−	0.285933i	$-0.907696\pi$
$3$	−0.400969	+	0.694498i	−0.231499	+	0.400969i	0.726750	+	0.686902i	$0.241030\pi$
$4$	−0.846011	−	1.46533i	−0.423005	−	0.732667i
$5$		−	2.80194i		−	1.25306i	−0.779395	−	0.626532i	$-0.784474\pi$
$5$		−	2.80194i		−	1.25306i	0.779395	−	0.626532i	$-0.215526\pi$
$6$	−0.385418	+	0.222521i	−0.157346	+	0.0908438i
$7$	2.33136	−	1.34601i	0.881171	−	0.508744i	0.0101266	−	0.999949i	$-0.496777\pi$
$7$	2.33136	−	1.34601i	0.881171	−	0.508744i	0.871044	+	0.491204i	$0.163443\pi$
$8$		−	2.04892i		−	0.724402i
$9$	1.17845	+	2.04113i	0.392816	+	0.680377i
$10$	0.777479	−	1.34663i	0.245860	−	0.425843i
$11$	−1.03755	−	0.599031i	−0.312834	−	0.180615i	0.335360	−	0.942090i	$-0.391142\pi$
$11$	−1.03755	−	0.599031i	−0.312834	−	0.180615i	−0.648194	+	0.761475i	$0.724475\pi$
$12$	1.35690			0.391702
$13$		0			0
$13$		0			0
$14$	1.49396			0.399277
$15$	1.94594	+	1.12349i	0.502440	+	0.290084i
$16$	−1.12349	+	1.94594i	−0.280872	+	0.486485i
$17$	0.568532	+	0.984726i	0.137889	+	0.238831i	0.926697	−	0.375808i	$-0.122635\pi$
$17$	0.568532	+	0.984726i	0.137889	+	0.238831i	−0.788808	+	0.614639i	$0.789302\pi$
$18$			1.30798i			0.308293i
$19$	1.67922	−	0.969501i	0.385240	−	0.222419i	−0.294855	−	0.955542i	$-0.595271\pi$
$19$	1.67922	−	0.969501i	0.385240	−	0.222419i	0.680096	+	0.733123i	$0.261938\pi$
$20$	−4.10577	+	2.37047i	−0.918079	+	0.530053i
$21$			2.15883i			0.471096i
$22$	−0.332437	−	0.575798i	−0.0708758	−	0.122761i
$23$	−2.30194	+	3.98707i	−0.479987	+	0.831362i	−0.999736	−	0.0229566i	$-0.992692\pi$
$23$	−2.30194	+	3.98707i	−0.479987	+	0.831362i	0.519749	+	0.854319i	$0.326025\pi$
$24$	1.42297	+	0.821552i	0.290463	+	0.167699i
$25$	−2.85086			−0.570171
$26$		0			0
$27$	−4.29590			−0.826746
$28$	−3.94471	−	2.27748i	−0.745480	−	0.430403i
$29$	3.94989	−	6.84140i	0.733475	−	1.27042i	−0.221914	−	0.975066i	$-0.571230\pi$
$29$	3.94989	−	6.84140i	0.733475	−	1.27042i	0.955389	−	0.295350i	$-0.0954364\pi$
$30$	0.623490	+	1.07992i	0.113833	+	0.197165i
$31$			5.89977i			1.05963i	0.848113	+	0.529815i	$0.177739\pi$
$31$			5.89977i			1.05963i	−0.848113	+	0.529815i	$0.822261\pi$
$32$	−4.62874	+	2.67241i	−0.818254	+	0.472419i
$33$	0.832052	−	0.480386i	0.144842	−	0.0836244i
$34$			0.631023i			0.108219i
$35$	−3.77144	−	6.53232i	−0.637489	−	1.10416i
$36$	1.99396	−	3.45364i	0.332327	−	0.575606i
$37$	0.823662	+	0.475541i	0.135409	+	0.0781785i	0.566174	−	0.824286i	$-0.308423\pi$
$37$	0.823662	+	0.475541i	0.135409	+	0.0781785i	−0.430765	+	0.902464i	$0.641756\pi$
$38$	1.07606			0.174561
$39$		0			0
$40$	−5.74094			−0.907722
$41$	−2.87318	−	1.65883i	−0.448716	−	0.259066i	0.258572	−	0.965992i	$-0.416748\pi$
$41$	−2.87318	−	1.65883i	−0.448716	−	0.259066i	−0.707288	+	0.706926i	$0.750081\pi$
$42$	−0.599031	+	1.03755i	−0.0924325	+	0.160098i
$43$	3.57942	+	6.19973i	0.545856	+	0.945450i	0.998553	+	0.0537856i	$0.0171288\pi$
$43$	3.57942	+	6.19973i	0.545856	+	0.945450i	−0.452697	+	0.891665i	$0.649538\pi$
$44$			2.02715i			0.305604i
$45$	5.71912	−	3.30194i	0.852557	−	0.492224i
$46$	−2.21266	+	1.27748i	−0.326239	+	0.188354i
$47$			7.69202i			1.12200i	0.827817	+	0.560998i	$0.189583\pi$
$47$			7.69202i			1.12200i	−0.827817	+	0.560998i	$0.810417\pi$
$48$	−0.900969	−	1.56052i	−0.130044	−	0.225242i
$49$	0.123490	−	0.213891i	0.0176414	−	0.0305558i
$50$	−1.37014	−	0.791053i	−0.193768	−	0.111872i
$51$	−0.911854			−0.127685
$52$		0			0
$53$	5.87263			0.806667			0.403334	−	0.915053i	$-0.367851\pi$
$53$	5.87263			0.806667			0.403334	+	0.915053i	$0.367851\pi$
$54$	−2.06464	−	1.19202i	−0.280962	−	0.162214i
$55$	−1.67845	+	2.90716i	−0.226322	+	0.392001i
$56$	−2.75786	−	4.77676i	−0.368535	−	0.638322i
$57$			1.55496i			0.205959i
$58$	3.79669	−	2.19202i	0.498530	−	0.287827i
$59$	0.0104630	−	0.00604079i	0.00136216	−	0.000786444i	−0.499319	−	0.866418i	$-0.666416\pi$
$59$	0.0104630	−	0.00604079i	0.00136216	−	0.000786444i	0.500681	+	0.865632i	$0.333083\pi$
$60$		−	3.80194i		−	0.490828i
$61$	4.01842	+	6.96010i	0.514506	+	0.891150i	0.999858	+	0.0168315i	$0.00535789\pi$
$61$	4.01842	+	6.96010i	0.514506	+	0.891150i	−0.485353	+	0.874318i	$0.661309\pi$
$62$	−1.63706	+	2.83548i	−0.207907	+	0.360106i
$63$	5.49477	+	3.17241i	0.692276	+	0.399686i
$64$	1.52781			0.190976
$65$		0			0
$66$	0.533188			0.0656309
$67$	8.01651	+	4.62833i	0.979373	+	0.565441i	0.902081	−	0.431567i	$-0.142039\pi$
$67$	8.01651	+	4.62833i	0.979373	+	0.565441i	0.0772919	+	0.997009i	$0.475373\pi$
$68$	0.961968	−	1.66618i	0.116656	−	0.202054i
$69$	−1.84601	−	3.19738i	−0.222234	−	0.384920i
$70$		−	4.18598i		−	0.500320i
$71$	−11.9000	+	6.87047i	−1.41227	+	0.815375i	−0.995602	−	0.0936838i	$-0.970136\pi$
$71$	−11.9000	+	6.87047i	−1.41227	+	0.815375i	−0.416668	+	0.909059i	$0.636802\pi$
$72$	4.18211	−	2.41454i	0.492866	−	0.284557i
$73$		−	12.8170i		−	1.50012i	−0.661372	−	0.750058i	$-0.730025\pi$
$73$		−	12.8170i		−	1.50012i	0.661372	−	0.750058i	$-0.269975\pi$
$74$	0.263906	+	0.457098i	0.0306784	+	0.0531365i
$75$	1.14310	−	1.97991i	0.131994	−	0.228621i
$76$	−2.84128	−	1.64042i	−0.325918	−	0.188169i
$77$	−3.22521			−0.367547
$78$		0			0
$79$	0.807315			0.0908300			0.0454150	−	0.998968i	$-0.485539\pi$
$79$	0.807315			0.0908300			0.0454150	+	0.998968i	$0.485539\pi$
$80$	5.45241	+	3.14795i	0.609598	+	0.351951i
$81$	−1.81282	+	3.13990i	−0.201425	+	0.348878i
$82$	−0.920583	−	1.59450i	−0.101661	−	0.176083i
$83$		−	16.3327i		−	1.79275i	−0.443296	−	0.896375i	$-0.646191\pi$
$83$		−	16.3327i		−	1.79275i	0.443296	−	0.896375i	$-0.353809\pi$
$84$	3.16341	−	1.82640i	0.345156	−	0.199276i
$85$	2.75914	−	1.59299i	0.299271	−	0.172784i
$86$			3.97285i			0.428404i
$87$	3.16756	+	5.48638i	0.339598	+	0.588202i
$88$	−1.22737	+	2.12586i	−0.130838	+	0.226617i
$89$	−12.7556	−	7.36443i	−1.35209	−	0.780628i	−0.363546	−	0.931576i	$-0.618434\pi$
$89$	−12.7556	−	7.36443i	−1.35209	−	0.780628i	−0.988542	+	0.150949i	$0.951767\pi$
$90$	3.66487			0.386312
$91$		0			0
$92$	7.78986			0.812149
$93$	−4.09738	−	2.36563i	−0.424879	−	0.245304i
$94$	−2.13437	+	3.69685i	−0.220144	+	0.381301i
$95$	−2.71648	−	4.70508i	−0.278705	−	0.482731i
$96$		−	4.28621i		−	0.437459i
$97$	2.71212	−	1.56584i	0.275374	−	0.158987i	−0.355953	−	0.934504i	$-0.615844\pi$
$97$	2.71212	−	1.56584i	0.275374	−	0.158987i	0.631327	+	0.775516i	$0.282510\pi$
$98$	0.118700	−	0.0685317i	0.0119905	−	0.00692274i
$99$		−	2.82371i		−	0.283793i
$100$	2.41185	+	4.17745i	0.241185	+	0.417745i
$101$	2.64526	−	4.58172i	0.263213	−	0.455899i	−0.703881	−	0.710318i	$-0.748551\pi$
$101$	2.64526	−	4.58172i	0.263213	−	0.455899i	0.967094	+	0.254420i	$0.0818844\pi$
$102$	−0.438244	−	0.253020i	−0.0433926	−	0.0250528i
$103$	13.5308			1.33323			0.666614	−	0.745403i	$-0.267743\pi$
$103$	13.5308			1.33323			0.666614	+	0.745403i	$0.267743\pi$
$104$		0			0
$105$	6.04892			0.590314
$106$	2.82243	+	1.62953i	0.274139	+	0.158274i
$107$	−2.81551	+	4.87661i	−0.272186	+	0.471440i	−0.969421	−	0.245403i	$-0.921080\pi$
$107$	−2.81551	+	4.87661i	−0.272186	+	0.471440i	0.697236	+	0.716842i	$0.254413\pi$
$108$	3.63437	+	6.29492i	0.349718	+	0.605729i
$109$			4.17629i			0.400016i	0.979794	+	0.200008i	$0.0640969\pi$
$109$			4.17629i			0.400016i	−0.979794	+	0.200008i	$0.935903\pi$
$110$	−1.61335	+	0.931468i	−0.153827	+	0.0888120i
$111$	−0.660525	+	0.381355i	−0.0626943	+	0.0361966i
$112$			6.04892i			0.571569i
$113$	−3.82155	−	6.61912i	−0.359501	−	0.622675i	0.628376	−	0.777910i	$-0.283720\pi$
$113$	−3.82155	−	6.61912i	−0.359501	−	0.622675i	−0.987878	+	0.155235i	$0.950387\pi$
$114$	−0.431468	+	0.747325i	−0.0404107	+	0.0699934i
$115$	11.1715	+	6.44989i	1.04175	+	0.601455i
$116$	−13.3666			−1.24106
$117$		0			0
$118$	0.00670477			0.000617224
$119$	2.65090	+	1.53050i	0.243008	+	0.140301i
$120$	2.30194	−	3.98707i	0.210137	−	0.363968i
$121$	−4.78232	−	8.28323i	−0.434757	−	0.753021i
$122$			4.46011i			0.403799i
$123$	2.30411	−	1.33028i	0.207755	−	0.119947i
$124$	8.64513	−	4.99127i	0.776356	−	0.448229i
$125$		−	6.02177i		−	0.538604i
$126$	1.76055	+	3.04937i	0.156843	+	0.271659i
$127$	3.38889	−	5.86972i	0.300715	−	0.520854i	−0.675583	−	0.737284i	$-0.736108\pi$
$127$	3.38889	−	5.86972i	0.300715	−	0.520854i	0.976298	+	0.216430i	$0.0694413\pi$
$128$	9.99177	+	5.76875i	0.883156	+	0.509890i
$129$	−5.74094			−0.505461
$130$		0			0
$131$	−13.6799			−1.19522			−0.597611	−	0.801786i	$-0.703883\pi$
$131$	−13.6799			−1.19522			−0.597611	+	0.801786i	$0.703883\pi$
$132$	−1.40785	−	0.812823i	−0.122538	−	0.0707471i
$133$	2.60992	−	4.52051i	0.226308	−	0.391978i
$134$	2.56853	+	4.44883i	0.221887	+	0.384320i
$135$			12.0368i			1.03597i
$136$	2.01762	−	1.16487i	0.173010	−	0.0998872i
$137$	−11.2479	+	6.49396i	−0.960970	+	0.554816i	−0.896471	−	0.443101i	$-0.853878\pi$
$137$	−11.2479	+	6.49396i	−0.960970	+	0.554816i	−0.0644987	+	0.997918i	$0.520545\pi$
$138$		−	2.04892i		−	0.174415i
$139$	−6.02326	−	10.4326i	−0.510886	−	0.884881i	−0.999920	−	0.0126165i	$-0.995984\pi$
$139$	−6.02326	−	10.4326i	−0.510886	−	0.884881i	0.489034	−	0.872265i	$-0.337349\pi$
$140$	−6.38135	+	11.0528i	−0.539323	+	0.934135i
$141$	−5.34210	−	3.08426i	−0.449886	−	0.259742i
$142$	−7.62565			−0.639930
$143$		0			0
$144$	−5.29590			−0.441325
$145$	−19.1692	−	11.0673i	−1.59191	−	0.919092i
$146$	3.55645	−	6.15995i	0.294334	−	0.509801i
$147$	0.0990311	+	0.171527i	0.00816795	+	0.0141473i
$148$		−	1.60925i		−	0.132280i
$149$	−0.641672	+	0.370469i	−0.0525678	+	0.0303500i	−0.526054	−	0.850451i	$-0.676329\pi$
$149$	−0.641672	+	0.370469i	−0.0525678	+	0.0303500i	0.473486	+	0.880801i	$0.342996\pi$
$150$	1.09877	−	0.634375i	0.0897142	−	0.0517965i
$151$			19.0737i			1.55219i	0.630614	+	0.776097i	$0.282803\pi$
$151$			19.0737i			1.55219i	−0.630614	+	0.776097i	$0.717197\pi$
$152$	−1.98643	−	3.44059i	−0.161120	−	0.279069i
$153$	−1.33997	+	2.32090i	−0.108330	+	0.187633i
$154$	−1.55006	−	0.894928i	−0.124907	−	0.0721154i
$155$	16.5308			1.32779
$156$		0			0
$157$	−4.02177			−0.320972			−0.160486	−	0.987038i	$-0.551306\pi$
$157$	−4.02177			−0.320972			−0.160486	+	0.987038i	$0.551306\pi$
$158$	0.388002	+	0.224013i	0.0308678	+	0.0178215i
$159$	−2.35474	+	4.07853i	−0.186743	+	0.323448i
$160$	7.48792	+	12.9695i	0.591972	+	1.02533i
$161$			12.3937i			0.976763i
$162$	−1.74251	+	1.00604i	−0.136905	+	0.0790420i
$163$	−13.1091	+	7.56853i	−1.02678	+	0.592813i	−0.916061	−	0.401038i	$-0.868649\pi$
$163$	−13.1091	+	7.56853i	−1.02678	+	0.592813i	−0.110721	+	0.993852i	$0.535316\pi$
$164$			5.61356i			0.438346i
$165$	−1.34601	−	2.33136i	−0.104787	−	0.181496i
$166$	4.53199	−	7.84964i	0.351751	−	0.609250i
$167$	−5.42424	−	3.13169i	−0.419740	−	0.242337i	0.275226	−	0.961380i	$-0.411247\pi$
$167$	−5.42424	−	3.13169i	−0.419740	−	0.242337i	−0.694966	+	0.719042i	$0.744581\pi$
$168$	4.42327			0.341263
$169$		0			0
$170$	1.76809			0.135606
$171$	3.95776	+	2.28501i	0.302657	+	0.174739i
$172$	6.05645	−	10.4901i	0.461800	−	0.799861i
$173$	8.19567	+	14.1953i	0.623105	+	1.07925i	0.988904	+	0.148556i	$0.0474625\pi$
$173$	8.19567	+	14.1953i	0.623105	+	1.07925i	−0.365799	+	0.930694i	$0.619204\pi$
$174$			3.51573i			0.266527i
$175$	−6.64637	+	3.83728i	−0.502418	+	0.290071i
$176$	2.33136	−	1.34601i	0.175733	−	0.101459i
$177$			0.00968868i			0.000728246i
$178$	−4.08695	−	7.07880i	−0.306330	−	0.530579i
$179$	−1.22737	+	2.12586i	−0.0917376	+	0.158894i	−0.908242	−	0.418445i	$-0.862575\pi$
$179$	−1.22737	+	2.12586i	−0.0917376	+	0.158894i	0.816505	+	0.577339i	$0.195909\pi$
$180$	−9.67688	−	5.58695i	−0.721272	−	0.416427i
$181$	−11.8073			−0.877631			−0.438815	−	0.898577i	$-0.644602\pi$
$181$	−11.8073			−0.877631			−0.438815	+	0.898577i	$0.644602\pi$
$182$		0			0
$183$	−6.44504			−0.476431
$184$	8.16918	+	4.71648i	0.602240	+	0.347704i
$185$	1.33244	−	2.30785i	0.0979627	−	0.169676i
$186$	−1.31282	−	2.27388i	−0.0962608	−	0.166729i
$187$		−	1.36227i		−	0.0996192i
$188$	11.2714	−	6.50753i	0.822050	−	0.474611i
$189$	−10.0153	+	5.78232i	−0.728504	+	0.420602i
$190$		−	3.01507i		−	0.218736i
$191$	4.49665	+	7.78842i	0.325366	+	0.563550i	0.981586	−	0.191019i	$-0.0611792\pi$
$191$	4.49665	+	7.78842i	0.325366	+	0.563550i	−0.656220	+	0.754569i	$0.727846\pi$
$192$	−0.612605	+	1.06106i	−0.0442109	+	0.0765756i
$193$	11.7134	+	6.76271i	0.843146	+	0.486790i	0.858332	−	0.513094i	$-0.171501\pi$
$193$	11.7134	+	6.76271i	0.843146	+	0.486790i	−0.0151865	+	0.999885i	$0.504834\pi$
$194$	1.73795			0.124778
$195$		0			0
$196$	−0.417895			−0.0298496
$197$	−11.2374	−	6.48792i	−0.800632	−	0.462245i	0.0430602	−	0.999072i	$-0.486289\pi$
$197$	−11.2374	−	6.48792i	−0.800632	−	0.462245i	−0.843692	+	0.536827i	$0.819623\pi$
$198$	0.783520	−	1.35710i	0.0556823	−	0.0964446i
$199$	−6.79321	−	11.7662i	−0.481558	−	0.834083i	0.518218	−	0.855248i	$-0.326596\pi$
$199$	−6.79321	−	11.7662i	−0.481558	−	0.834083i	−0.999776	+	0.0211659i	$0.993262\pi$
$200$			5.84117i			0.413033i
$201$	−6.42874	+	3.71164i	−0.453448	+	0.261799i
$202$	2.54267	−	1.46801i	0.178901	−	0.103289i
$203$		−	21.2664i		−	1.49261i
$204$	0.771438	+	1.33617i	0.0540115	+	0.0935506i
$205$	−4.64795	+	8.05048i	−0.324627	+	0.562270i
$206$	6.50301	+	3.75451i	0.453086	+	0.261589i
$207$	−10.8509			−0.754187
$208$		0			0
$209$	−2.32304			−0.160688
$210$	2.90716	+	1.67845i	0.200613	+	0.115824i
$211$	−5.23005	+	9.05872i	−0.360052	+	0.623628i	−0.987969	−	0.154652i	$-0.950574\pi$
$211$	−5.23005	+	9.05872i	−0.360052	+	0.623628i	0.627917	+	0.778280i	$0.283908\pi$
$212$	−4.96830	−	8.60536i	−0.341225	−	0.591018i
$213$		−	11.0194i		−	0.755035i
$214$	−2.70631	+	1.56249i	−0.185000	+	0.106810i
$215$	17.3713	−	10.0293i	1.18471	−	0.683993i
$216$			8.80194i			0.598896i
$217$	7.94116	+	13.7545i	0.539081	+	0.933715i
$218$	−1.15883	+	2.00716i	−0.0784861	+	0.135942i
$219$	8.90139	+	5.13922i	0.601500	+	0.347276i
$220$	5.67994			0.382941
$221$		0			0
$222$	−0.423272			−0.0284081
$223$	9.87772	+	5.70291i	0.661461	+	0.381895i	0.792834	−	0.609438i	$-0.208605\pi$
$223$	9.87772	+	5.70291i	0.661461	+	0.381895i	−0.131372	+	0.991333i	$0.541938\pi$
$224$	−7.19418	+	12.4607i	−0.480681	+	0.832564i
$225$	−3.35958	−	5.81897i	−0.223972	−	0.387931i
$226$		−	4.24160i		−	0.282147i
$227$	9.21513	−	5.32036i	0.611629	−	0.353124i	−0.161973	−	0.986795i	$-0.551786\pi$
$227$	9.21513	−	5.32036i	0.611629	−	0.353124i	0.773603	+	0.633671i	$0.218453\pi$
$228$	2.27853	−	1.31551i	0.150899	−	0.0871219i
$229$			1.13946i			0.0752974i	0.999291	+	0.0376487i	$0.0119868\pi$
$229$			1.13946i			0.0752974i	−0.999291	+	0.0376487i	$0.988013\pi$
$230$	3.57942	+	6.19973i	0.236020	+	0.408798i
$231$	1.29321	−	2.23990i	0.0850869	−	0.147375i
$232$	−14.0175	−	8.09299i	−0.920292	−	0.531331i
$233$	10.8509			0.710863			0.355432	−	0.934702i	$-0.384334\pi$
$233$	10.8509			0.710863			0.355432	+	0.934702i	$0.384334\pi$
$234$		0			0
$235$	21.5526			1.40593
$236$	−0.0177036	−	0.0102212i	−0.00115240	−	0.000665340i
$237$	−0.323708	+	0.560679i	−0.0210271	+	0.0364200i
$238$	0.849363	+	1.47114i	0.0550560	+	0.0953598i
$239$		−	11.9293i		−	0.771643i	−0.922573	−	0.385822i	$-0.873918\pi$
$239$		−	11.9293i		−	0.771643i	0.922573	−	0.385822i	$-0.126082\pi$
$240$	−4.37249	+	2.52446i	−0.282243	+	0.162953i
$241$	3.15968	−	1.82424i	0.203533	−	0.117510i	−0.394770	−	0.918780i	$-0.629176\pi$
$241$	3.15968	−	1.82424i	0.203533	−	0.117510i	0.598302	+	0.801271i	$0.295842\pi$
$242$		−	5.30798i		−	0.341210i
$243$	−7.89762	−	13.6791i	−0.506632	−	0.877513i
$244$	6.79925	−	11.7766i	0.435277	−	0.753922i
$245$	−0.599308	−	0.346011i	−0.0382884	−	0.0221058i
$246$	1.47650			0.0941383
$247$		0			0
$248$	12.0881			0.767598
$249$	11.3431	+	6.54892i	0.718837	+	0.415021i
$250$	1.67092	−	2.89411i	0.105678	−	0.183040i
$251$	0.686645	+	1.18930i	0.0433406	+	0.0750682i	0.886882	−	0.461996i	$-0.152867\pi$
$251$	0.686645	+	1.18930i	0.0433406	+	0.0750682i	−0.843541	+	0.537064i	$0.819533\pi$
$252$		−	10.7356i		−	0.676277i
$253$	4.77676	−	2.75786i	0.300312	−	0.173385i
$254$	3.25745	−	1.88069i	0.204391	−	0.118005i
$255$			2.55496i			0.159998i
$256$	1.67360	+	2.89877i	0.104600	+	0.181173i
$257$	14.7180	−	25.4923i	0.918082	−	1.59016i	0.115756	−	0.993278i	$-0.463071\pi$
$257$	14.7180	−	25.4923i	0.918082	−	1.59016i	0.802325	−	0.596887i	$-0.203596\pi$
$258$	−2.75914	−	1.59299i	−0.171777	−	0.0991752i
$259$	2.56033			0.159091
$260$		0			0
$261$	18.6189			1.15248
$262$	−6.57469	−	3.79590i	−0.406185	−	0.234511i
$263$	−5.34817	+	9.26330i	−0.329782	+	0.571199i	−0.982468	−	0.186429i	$-0.940309\pi$
$263$	−5.34817	+	9.26330i	−0.329782	+	0.571199i	0.652686	+	0.757628i	$0.273642\pi$
$264$	−0.984271	−	1.70481i	−0.0605777	−	0.104924i
$265$		−	16.4547i		−	1.01081i
$266$	2.50869	−	1.44839i	0.153818	−	0.0888067i
$267$	10.2292	−	5.90581i	0.626015	−	0.361430i
$268$		−	15.6625i		−	0.956738i
$269$	5.09299	+	8.82132i	0.310525	+	0.537845i	0.978476	−	0.206360i	$-0.0661618\pi$
$269$	5.09299	+	8.82132i	0.310525	+	0.537845i	−0.667951	+	0.744205i	$0.732828\pi$
$270$	−3.33997	+	5.78500i	−0.203264	+	0.352064i
$271$	−25.5065	−	14.7262i	−1.54941	−	0.894551i	−0.998187	−	0.0601918i	$-0.980829\pi$
$271$	−25.5065	−	14.7262i	−1.54941	−	0.894551i	−0.551221	−	0.834359i	$-0.685838\pi$
$272$	−2.55496			−0.154917
$273$		0			0
$274$	−7.20775			−0.435436
$275$	2.95791	+	1.70775i	0.178369	+	0.102981i
$276$	−3.12349	+	5.41004i	−0.188012	+	0.325646i
$277$	−5.12229	−	8.87207i	−0.307769	−	0.533071i	0.670105	−	0.742266i	$-0.266249\pi$
$277$	−5.12229	−	8.87207i	−0.307769	−	0.533071i	−0.977874	+	0.209195i	$0.932916\pi$
$278$		−	6.68532i		−	0.400959i
$279$	−12.0422	+	6.95257i	−0.720948	+	0.416240i
$280$	−13.3842	+	7.72737i	−0.799858	+	0.461798i
$281$			11.5646i			0.689889i	0.938623	+	0.344944i	$0.112102\pi$
$281$			11.5646i			0.689889i	−0.938623	+	0.344944i	$0.887898\pi$
$282$	−1.71164	−	2.96464i	−0.101926	−	0.176542i
$283$	−15.3545	+	26.5948i	−0.912730	+	1.58090i	−0.102540	+	0.994729i	$0.532697\pi$
$283$	−15.3545	+	26.5948i	−0.912730	+	1.58090i	−0.810191	+	0.586167i	$0.800636\pi$
$284$	20.1351	+	11.6250i	1.19480	+	0.689816i
$285$	4.35690			0.258080
$286$		0			0
$287$	−8.93123			−0.527194
$288$	−10.9095	−	6.29859i	−0.642847	−	0.371148i
$289$	7.85354	−	13.6027i	0.461973	−	0.800161i
$290$	−6.14191	−	10.6381i	−0.360665	−	0.624691i
$291$			2.51142i			0.147222i
$292$	−18.7812	+	10.8433i	−1.09909	+	0.634557i
$293$	16.1152	−	9.30409i	0.941458	−	0.543551i	0.0510409	−	0.998697i	$-0.483746\pi$
$293$	16.1152	−	9.30409i	0.941458	−	0.543551i	0.890417	+	0.455146i	$0.150413\pi$
$294$			0.109916i			0.00641045i
$295$	−0.0169259	−	0.0293166i	−0.000985465	−	0.00170688i
$296$	0.974345	−	1.68761i	0.0566326	−	0.0980906i
$297$	4.45722	+	2.57338i	0.258634	+	0.149322i
$298$	−0.411190			−0.0238196
$299$		0			0
$300$	−3.86831			−0.223337
$301$	16.6898	+	9.63587i	0.961985	+	0.555402i
$302$	−5.29254	+	9.16696i	−0.304552	+	0.527499i
$303$	2.12133	+	3.67426i	0.121867	+	0.211081i
$304$			4.35690i			0.249885i
$305$	19.5018	−	11.2594i	1.11667	−	0.644709i
$306$	−1.28800	+	0.743627i	−0.0736301	+	0.0425103i
$307$		−	8.94438i		−	0.510483i	−0.966877	−	0.255241i	$-0.917845\pi$
$307$		−	8.94438i		−	0.510483i	0.966877	−	0.255241i	$-0.0821549\pi$
$308$	2.72856	+	4.72601i	0.155474	+	0.269289i
$309$	−5.42543	+	9.39712i	−0.308642	+	0.534583i
$310$	7.94483	+	4.58695i	0.451236	+	0.260521i
$311$	−21.0398			−1.19306			−0.596529	−	0.802591i	$-0.703454\pi$
$311$	−21.0398			−1.19306			−0.596529	+	0.802591i	$0.703454\pi$
$312$		0			0
$313$	−7.12737			−0.402863			−0.201432	−	0.979503i	$-0.564559\pi$
$313$	−7.12737			−0.402863			−0.201432	+	0.979503i	$0.564559\pi$
$314$	−1.93289	−	1.11596i	−0.109080	−	0.0629771i
$315$	8.88889	−	15.3960i	0.500832	−	0.867467i
$316$	−0.682997	−	1.18299i	−0.0384216	−	0.0665481i
$317$			23.9651i			1.34601i	0.739636	+	0.673007i	$0.234997\pi$
$317$			23.9651i			1.34601i	−0.739636	+	0.673007i	$0.765003\pi$
$318$	−2.26341	+	1.30678i	−0.126926	+	0.0732807i
$319$	−8.19643	+	4.73221i	−0.458912	+	0.264953i
$320$		−	4.28083i		−	0.239306i
$321$	−2.25786	−	3.91074i	−0.126022	−	0.218276i
$322$	−3.43900	+	5.95652i	−0.191648	+	0.331944i
$323$	1.90938	+	1.10238i	0.106241	+	0.0613383i
$324$	6.13467			0.340815
$325$		0			0
$326$	−8.40044			−0.465257
$327$	−2.90043	−	1.67456i	−0.160394	−	0.0926035i
$328$	−3.39881	+	5.88692i	−0.187668	+	0.325051i
$329$	10.3535	+	17.9329i	0.570809	+	0.988671i
$330$		−	1.49396i		−	0.0822397i
$331$	2.50754	−	1.44773i	0.137827	−	0.0795745i	−0.429501	−	0.903066i	$-0.641311\pi$
$331$	2.50754	−	1.44773i	0.137827	−	0.0795745i	0.567328	+	0.823492i	$0.307977\pi$
$332$	−23.9329	+	13.8177i	−1.31349	+	0.758343i
$333$			2.24160i			0.122839i
$334$	−1.73795	−	3.01023i	−0.0950967	−	0.164712i
$335$	12.9683	−	22.4618i	0.708534	−	1.22722i
$336$	−4.20096	−	2.42543i	−0.229181	−	0.132318i
$337$	3.10560			0.169173			0.0845865	−	0.996416i	$-0.473043\pi$
$337$	3.10560			0.169173			0.0845865	+	0.996416i	$0.473043\pi$
$338$		0			0
$339$	6.12929			0.332898
$340$	−4.66852	−	2.69537i	−0.253186	−	0.146177i
$341$	3.53415	−	6.12132i	0.191385	−	0.331488i
$342$	1.26809	+	2.19639i	0.0685702	+	0.118767i
$343$			18.1793i			0.981589i
$344$	12.7027	−	7.33393i	0.684886	−	0.395419i
$345$	−8.95887	+	5.17241i	−0.482329	+	0.278473i
$346$			9.09651i			0.489031i
$347$	5.68933	+	9.85421i	0.305419	+	0.529002i	0.977355	−	0.211608i	$-0.0678700\pi$
$347$	5.68933	+	9.85421i	0.305419	+	0.529002i	−0.671935	+	0.740610i	$0.734537\pi$
$348$	5.35958	−	9.28307i	0.287304	−	0.497625i
$349$	−2.89877	−	1.67360i	−0.155167	−	0.0895859i	0.420406	−	0.907336i	$-0.361888\pi$
$349$	−2.89877	−	1.67360i	−0.155167	−	0.0895859i	−0.575573	+	0.817750i	$0.695221\pi$
$350$	−4.25906			−0.227656
$351$		0			0
$352$	6.40342			0.341303
$353$	−0.552288	−	0.318864i	−0.0293953	−	0.0169714i	0.485230	−	0.874386i	$-0.338736\pi$
$353$	−0.552288	−	0.318864i	−0.0293953	−	0.0169714i	−0.514626	+	0.857415i	$0.672069\pi$
$354$	−0.00268841	+	0.00465646i	−0.000142887	+	0.000247488i
$355$	19.2506	+	33.3431i	1.02172	+	1.76967i
$356$			24.9215i			1.32084i
$357$	−2.12586	+	1.22737i	−0.112512	+	0.0649591i
$358$	−1.17976	+	0.681136i	−0.0623524	+	0.0359992i
$359$			21.4590i			1.13256i	0.824211	+	0.566282i	$0.191619\pi$
$359$			21.4590i			1.13256i	−0.824211	+	0.566282i	$0.808381\pi$
$360$	−6.76540	−	11.7180i	−0.356568	−	0.617593i
$361$	−7.62014	+	13.1985i	−0.401060	+	0.694656i
$362$	−5.67469	−	3.27628i	−0.298255	−	0.172198i
$363$	7.67025			0.402584
$364$		0			0
$365$	−35.9124			−1.87974
$366$	−3.09754	−	1.78836i	−0.161911	−	0.0934793i
$367$	4.69351	−	8.12940i	0.244999	−	0.424351i	−0.717132	−	0.696937i	$-0.754546\pi$
$367$	4.69351	−	8.12940i	0.244999	−	0.424351i	0.962131	+	0.272586i	$0.0878789\pi$
$368$	−5.17241	−	8.95887i	−0.269630	−	0.467013i
$369$		−	7.81940i		−	0.407062i
$370$	1.28076	−	0.739447i	0.0665835	−	0.0384420i
$371$	13.6912	−	7.90462i	0.710812	−	0.410387i
$372$			8.00538i			0.415059i
$373$	−13.8632	−	24.0118i	−0.717811	−	1.24329i	−0.961865	−	0.273523i	$-0.911811\pi$
$373$	−13.8632	−	24.0118i	−0.717811	−	1.24329i	0.244054	−	0.969762i	$-0.421522\pi$
$374$	0.378002	−	0.654719i	0.0195460	−	0.0338547i
$375$	4.18211	+	2.41454i	0.215963	+	0.124686i
$376$	15.7603			0.812776
$377$		0			0
$378$	−6.41789			−0.330101
$379$	−31.0645	−	17.9351i	−1.59568	−	0.921265i	−0.992307	−	0.123805i	$-0.960490\pi$
$379$	−31.0645	−	17.9351i	−1.59568	−	0.921265i	−0.603371	−	0.797460i	$-0.706176\pi$
$380$	−4.59634	+	7.96110i	−0.235787	+	0.408396i
$381$	2.71768	+	4.70715i	0.139231	+	0.241155i
$382$			4.99090i			0.255357i
$383$	4.20470	−	2.42758i	0.214850	−	0.124044i	−0.388713	−	0.921359i	$-0.627080\pi$
$383$	4.20470	−	2.42758i	0.214850	−	0.124044i	0.603563	+	0.797315i	$0.293747\pi$
$384$	−8.01278	+	4.62618i	−0.408900	+	0.236079i
$385$			9.03684i			0.460560i
$386$	3.75302	+	6.50042i	0.191024	+	0.330863i
$387$	−8.43631	+	14.6121i	−0.428842	+	0.742776i
$388$	−4.58897	−	2.64944i	−0.232969	−	0.134505i
$389$	−2.38537			−0.120943			−0.0604716	−	0.998170i	$-0.519260\pi$
$389$	−2.38537			−0.120943			−0.0604716	+	0.998170i	$0.519260\pi$
$390$		0			0
$391$	−5.23490			−0.264740
$392$	−0.438244	−	0.253020i	−0.0221347	−	0.0127795i
$393$	5.48523	−	9.50070i	0.276693	−	0.479247i
$394$	−3.60052	−	6.23629i	−0.181392	−	0.314180i
$395$		−	2.26205i		−	0.113816i
$396$	−4.13767	+	2.38889i	−0.207926	+	0.120046i
$397$	13.2211	−	7.63318i	0.663546	−	0.383098i	−0.130081	−	0.991503i	$-0.541524\pi$
$397$	13.2211	−	7.63318i	0.663546	−	0.383098i	0.793627	+	0.608405i	$0.208190\pi$
$398$		−	7.53989i		−	0.377941i
$399$	2.09299	+	3.62517i	0.104781	+	0.181485i
$400$	3.20291	−	5.54760i	0.160145	−	0.277380i
$401$	11.0491	+	6.37920i	0.551766	+	0.318562i	0.749834	−	0.661626i	$-0.230133\pi$
$401$	11.0491	+	6.37920i	0.551766	+	0.318562i	−0.198068	+	0.980188i	$0.563467\pi$
$402$	−4.11960			−0.205467
$403$		0			0
$404$	−8.95167			−0.445362
$405$	8.79781	+	5.07942i	0.437167	+	0.252398i
$406$	5.90097	−	10.2208i	0.292860	−	0.507249i
$407$	−0.569728	−	0.986798i	−0.0282404	−	0.0489138i
$408$			1.86831i			0.0924953i
$409$	−21.9614	+	12.6794i	−1.08592	+	0.626956i	−0.932487	−	0.361203i	$-0.882366\pi$
$409$	−21.9614	+	12.6794i	−1.08592	+	0.626956i	−0.153433	+	0.988159i	$0.549033\pi$
$410$	−4.46768	+	2.57942i	−0.220643	+	0.127388i
$411$		−	10.4155i		−	0.513759i
$412$	−11.4472	−	19.8271i	−0.563963	−	0.976812i
$413$	0.0162619	−	0.0281665i	0.000800198	−	0.00138598i
$414$	−5.21501	−	3.01089i	−0.256304	−	0.147977i
$415$	−45.7633			−2.24643
$416$		0			0
$417$	9.66056			0.473080
$418$	−1.11647	−	0.644596i	−0.0546085	−	0.0315282i
$419$	5.83363	−	10.1041i	0.284992	−	0.493620i	−0.687616	−	0.726075i	$-0.741343\pi$
$419$	5.83363	−	10.1041i	0.284992	−	0.493620i	0.972607	+	0.232455i	$0.0746758\pi$
$420$	−5.11745	−	8.86368i	−0.249706	−	0.432503i
$421$		−	8.29291i		−	0.404172i	−0.979368	−	0.202086i	$-0.935228\pi$
$421$		−	8.29291i		−	0.404172i	0.979368	−	0.202086i	$-0.0647720\pi$
$422$	−5.02721	+	2.90246i	−0.244721	+	0.141290i
$423$	−15.7004	+	9.06465i	−0.763381	+	0.440738i
$424$		−	12.0325i		−	0.584351i
$425$	−1.62080	−	2.80731i	−0.0786204	−	0.136175i
$426$	3.05765	−	5.29600i	0.148143	−	0.256592i
$427$	18.7367	+	10.8177i	0.906735	+	0.523504i
$428$	9.52781			0.460544
$429$		0			0
$430$	11.1317			0.536818
$431$	−0.807392	−	0.466148i	−0.0388907	−	0.0224536i	0.480429	−	0.877034i	$-0.340481\pi$
$431$	−0.807392	−	0.466148i	−0.0388907	−	0.0224536i	−0.519319	+	0.854580i	$0.673814\pi$
$432$	4.82640	−	8.35956i	0.232210	−	0.402200i
$433$	−6.67510	−	11.5616i	−0.320785	−	0.555615i	0.659866	−	0.751384i	$-0.270613\pi$
$433$	−6.67510	−	11.5616i	−0.320785	−	0.555615i	−0.980650	+	0.195768i	$0.937280\pi$
$434$			8.81402i			0.423086i
$435$	15.3725	−	8.87531i	0.737055	−	0.425539i
$436$	6.11966	−	3.53319i	0.293079	−	0.169209i
$437$			8.92692i			0.427032i
$438$	2.85205	+	4.93990i	0.136276	+	0.236037i
$439$	6.99612	−	12.1176i	0.333906	−	0.578343i	−0.649368	−	0.760475i	$-0.724966\pi$
$439$	6.99612	−	12.1176i	0.333906	−	0.578343i	0.983274	+	0.182132i	$0.0582997\pi$
$440$	5.95652	+	3.43900i	0.283966	+	0.163948i
$441$	0.582105			0.0277193
$442$		0			0
$443$	23.7017			1.12610			0.563051	−	0.826422i	$-0.309627\pi$
$443$	23.7017			1.12610			0.563051	+	0.826422i	$0.309627\pi$
$444$	1.11762	+	0.645260i	0.0530401	+	0.0306227i
$445$	−20.6347	+	35.7403i	−0.978177	+	1.69425i
$446$	3.16487	+	5.48172i	0.149861	+	0.259567i
$447$		−	0.594187i		−	0.0281041i
$448$	3.56188	−	2.05645i	0.168283	−	0.0971581i
$449$	10.9002	−	6.29321i	0.514410	−	0.296995i	−0.220234	−	0.975447i	$-0.570682\pi$
$449$	10.9002	−	6.29321i	0.514410	−	0.296995i	0.734645	+	0.678452i	$0.237349\pi$
$450$		−	3.72886i		−	0.175780i
$451$	1.98739	+	3.44225i	0.0935823	+	0.162089i
$452$	−6.46615	+	11.1997i	−0.304142	+	0.526789i
$453$	−13.2466	−	7.64795i	−0.622381	−	0.359332i
$454$	5.90515			0.277142
$455$		0			0
$456$	3.18598			0.149197
$457$	29.1316	+	16.8192i	1.36272	+	0.786767i	0.989985	−	0.141171i	$-0.0450866\pi$
$457$	29.1316	+	16.8192i	1.36272	+	0.786767i	0.372735	+	0.927938i	$0.378420\pi$
$458$	−0.316175	+	0.547632i	−0.0147739	+	0.0255891i
$459$	−2.44235	−	4.23028i	−0.113999	−	0.197453i
$460$		−	21.8267i		−	1.01767i
$461$	−1.21489	+	0.701415i	−0.0565829	+	0.0326681i	−0.528025	−	0.849229i	$-0.677067\pi$
$461$	−1.21489	+	0.701415i	−0.0565829	+	0.0326681i	0.471442	+	0.881897i	$0.343734\pi$
$462$	1.24305	−	0.717677i	0.0578320	−	0.0333893i
$463$			15.2010i			0.706453i	0.935538	+	0.353226i	$0.114915\pi$
$463$			15.2010i			0.706453i	−0.935538	+	0.353226i	$0.885085\pi$
$464$	8.87531	+	15.3725i	0.412026	+	0.713650i
$465$	−6.62833	+	11.4806i	−0.307382	+	0.532401i
$466$	5.21501	+	3.01089i	0.241580	+	0.139477i
$467$	39.3414			1.82050			0.910250	−	0.414058i	$-0.135889\pi$
$467$	39.3414			1.82050			0.910250	+	0.414058i	$0.135889\pi$
$468$		0			0
$469$	24.9191			1.15066
$470$	10.3583	+	5.98039i	0.477794	+	0.275855i
$471$	1.61260	−	2.79311i	0.0743049	−	0.128700i
$472$	−0.0123771	−	0.0214377i	−0.000569701	−	0.000986752i
$473$		−	8.57673i		−	0.394358i
$474$	−0.311153	+	0.179644i	−0.0142917	+	0.00825134i
$475$	−4.78722	+	2.76391i	−0.219653	+	0.126817i
$476$		−	5.17928i		−	0.237392i
$477$	6.92058	+	11.9868i	0.316872	+	0.548838i
$478$	3.31013	−	5.73332i	0.151402	−	0.262236i
$479$	−19.3721	−	11.1845i	−0.885134	−	0.511032i	−0.0127862	−	0.999918i	$-0.504070\pi$
$479$	−19.3721	−	11.1845i	−0.885134	−	0.511032i	−0.872348	+	0.488886i	$0.837403\pi$
$480$	−12.0097			−0.548165
$481$		0			0
$482$	2.02475			0.0922250
$483$	−8.60743	−	4.96950i	−0.391652	−	0.226120i
$484$	−8.09179	+	14.0154i	−0.367809	+	0.637064i
$485$	−4.38740	−	7.59919i	−0.199221	−	0.345062i
$486$		−	8.76569i		−	0.397620i
$487$	19.8497	−	11.4602i	0.899476	−	0.519313i	0.0224462	−	0.999748i	$-0.492855\pi$
$487$	19.8497	−	11.4602i	0.899476	−	0.519313i	0.877030	+	0.480435i	$0.159521\pi$
$488$	14.2607	−	8.23341i	0.645551	−	0.372709i
$489$		−	12.1390i		−	0.548944i
$490$	−0.192021	−	0.332591i	−0.00867465	−	0.0150249i
$491$	0.921780	−	1.59657i	0.0415993	−	0.0720522i	−0.844476	−	0.535593i	$-0.820088\pi$
$491$	0.921780	−	1.59657i	0.0415993	−	0.0720522i	0.886075	+	0.463541i	$0.153421\pi$
$492$	−3.89861	−	2.25086i	−0.175763	−	0.101477i
$493$	8.98254			0.404553
$494$		0			0
$495$	−7.91185			−0.355611
$496$	−11.4806	−	6.62833i	−0.515495	−	0.297621i
$497$	−18.4955	+	32.0351i	−0.829634	+	1.43697i
$498$	3.63437	+	6.29492i	0.162860	+	0.282082i
$499$		−	12.0344i		−	0.538736i	−0.963037	−	0.269368i	$-0.913185\pi$
$499$		−	12.0344i		−	0.538736i	0.963037	−	0.269368i	$-0.0868147\pi$
$500$	−8.82390	+	5.09448i	−0.394617	+	0.227832i
$501$	4.34990	−	2.51142i	0.194339	−	0.112202i
$502$			0.762118i			0.0340150i
$503$	15.2528	+	26.4186i	0.680088	+	1.17795i	0.974954	+	0.222408i	$0.0713918\pi$
$503$	15.2528	+	26.4186i	0.680088	+	1.17795i	−0.294866	+	0.955539i	$0.595275\pi$
$504$	6.50000	−	11.2583i	0.289533	−	0.501486i
$505$	−12.8377	−	7.41185i	−0.571270	−	0.329823i
$506$	3.06100			0.136078
$507$		0			0
$508$	−11.4681			−0.508816
$509$	1.30893	+	0.755709i	0.0580171	+	0.0334962i	0.528728	−	0.848791i	$-0.322669\pi$
$509$	1.30893	+	0.755709i	0.0580171	+	0.0334962i	−0.470711	+	0.882288i	$0.656002\pi$
$510$	−0.708947	+	1.22793i	−0.0313927	+	0.0543738i
$511$	−17.2518	−	29.8810i	−0.763176	−	1.32186i
$512$		−	21.2174i		−	0.937687i
$513$	−7.21377	+	4.16487i	−0.318496	+	0.183884i
$514$	14.1471	−	8.16786i	0.624004	−	0.360269i
$515$		−	37.9124i		−	1.67062i
$516$	4.85690	+	8.41239i	0.213813	+	0.370335i
$517$	4.60776	−	7.98088i	0.202649	−	0.350998i
$518$	1.23052	+	0.710439i	0.0540658	+	0.0312149i
$519$	−13.1448			−0.576994
$520$		0			0
$521$	−5.64012			−0.247098			−0.123549	−	0.992338i	$-0.539428\pi$
$521$	−5.64012			−0.247098			−0.123549	+	0.992338i	$0.539428\pi$
$522$	8.94841	+	5.16637i	0.391661	+	0.226126i
$523$	15.8753	−	27.4968i	0.694179	−	1.20235i	−0.276278	−	0.961078i	$-0.589101\pi$
$523$	15.8753	−	27.4968i	0.694179	−	1.20235i	0.970457	−	0.241275i	$-0.0775657\pi$
$524$	11.5734	+	20.0457i	0.505585	+	0.875699i
$525$		−	6.15452i		−	0.268605i
$526$	−5.14074	+	2.96801i	−0.224147	+	0.129411i
$527$	−5.80966	+	3.35421i	−0.253073	+	0.146112i
$528$			2.15883i			0.0939512i
$529$	0.902165	+	1.56260i	0.0392246	+	0.0679390i
$530$	4.56584	−	7.90827i	0.198328	−	0.343513i
$531$	0.0246601	+	0.0142375i	0.00107016	+	0.000617856i
$532$	−8.83207			−0.382919
$533$		0			0
$534$	6.55496			0.283661
$535$	13.6640	+	7.88889i	0.590744	+	0.341066i
$536$	9.48307	−	16.4252i	0.409606	−	0.709459i
$537$	−0.984271	−	1.70481i	−0.0424744	−	0.0735678i
$538$			5.65279i			0.243709i
$539$	−0.256254	+	0.147948i	−0.0110377	+	0.00637259i
$540$	17.6380	−	10.1833i	0.759018	−	0.438219i
$541$		−	24.3297i		−	1.04602i	−0.852327	−	0.523009i	$-0.824809\pi$
$541$		−	24.3297i		−	1.04602i	0.852327	−	0.523009i	$-0.175191\pi$
$542$	−8.17241	−	14.1550i	−0.351035	−	0.608010i
$543$	4.73437	−	8.20016i	0.203171	−	0.351903i
$544$	−5.26318	−	3.03870i	−0.225657	−	0.130283i
$545$	11.7017			0.501246
$546$		0			0
$547$	−8.18896			−0.350135			−0.175067	−	0.984556i	$-0.556014\pi$
$547$	−8.18896			−0.350135			−0.175067	+	0.984556i	$0.556014\pi$
$548$	19.0316	+	10.9879i	0.812991	+	0.469381i
$549$	−9.47099	+	16.4042i	−0.404212	+	0.700116i
$550$	0.947730	+	1.64152i	0.0404114	+	0.0699945i
$551$		−	15.3177i		−	0.652555i
$552$	−6.55118	+	3.78232i	−0.278837	+	0.160986i
$553$	1.88214	−	1.08665i	0.0800367	−	0.0462092i
$554$		−	5.68532i		−	0.241546i
$555$	1.06853	+	1.85075i	0.0453566	+	0.0785600i
$556$	−10.1915	+	17.6522i	−0.432215	+	0.748619i
$557$	21.9388	+	12.6664i	0.929576	+	0.536691i	0.886678	−	0.462388i	$-0.153007\pi$
$557$	21.9388	+	12.6664i	0.929576	+	0.536691i	0.0428988	+	0.999079i	$0.486341\pi$
$558$	−7.71678			−0.326677
$559$		0			0
$560$	16.9487			0.716213
$561$	0.946096	+	0.546229i	0.0399442	+	0.0230618i
$562$	−3.20895	+	5.55806i	−0.135361	+	0.234453i
$563$	−12.6969	−	21.9916i	−0.535109	−	0.926836i	−0.999158	−	0.0410266i	$-0.986937\pi$
$563$	−12.6969	−	21.9916i	−0.535109	−	0.926836i	0.464049	−	0.885810i	$-0.346396\pi$
$564$			10.4373i			0.439488i
$565$	−18.5464	+	10.7078i	−0.780252	+	0.450478i
$566$	−14.7590	+	8.52111i	−0.620367	+	0.358169i
$567$			9.76032i			0.409895i
$568$	14.0770	+	24.3821i	0.590659	+	1.02305i
$569$	−15.5673	+	26.9634i	−0.652617	+	1.13037i	0.329869	+	0.944027i	$0.392995\pi$
$569$	−15.5673	+	26.9634i	−0.652617	+	1.13037i	−0.982486	+	0.186338i	$0.940338\pi$
$570$	2.09396	+	1.20895i	0.0877063	+	0.0506372i
$571$	20.5090			0.858276			0.429138	−	0.903239i	$-0.358817\pi$
$571$	20.5090			0.858276			0.429138	+	0.903239i	$0.358817\pi$
$572$		0			0
$573$	−7.21206			−0.301288
$574$	−4.29242	−	2.47823i	−0.179162	−	0.103439i
$575$	6.56249	−	11.3666i	0.273675	−	0.474019i
$576$	1.80045	+	3.11846i	0.0750186	+	0.129936i
$577$			15.6890i			0.653143i	0.945172	+	0.326572i	$0.105893\pi$
$577$			15.6890i			0.653143i	−0.945172	+	0.326572i	$0.894107\pi$
$578$	7.54895	−	4.35839i	0.313995	−	0.181285i
$579$	−9.39338	+	5.42327i	−0.390376	+	0.225383i
$580$			37.4523i			1.55512i
$581$	−21.9840	−	38.0775i	−0.912051	−	1.57972i
$582$	−0.696866	+	1.20701i	−0.0288860	+	0.0500320i
$583$	−6.09316	−	3.51789i	−0.252353	−	0.145696i
$584$	−26.2610			−1.08669
$585$		0			0
$586$	10.3268			0.426595
$587$	−26.4733	−	15.2843i	−1.09267	−	0.630853i	−0.158383	−	0.987378i	$-0.550628\pi$
$587$	−26.4733	−	15.2843i	−1.09267	−	0.630853i	−0.934286	+	0.356525i	$0.883961\pi$
$588$	0.167563	−	0.290227i	0.00691017	−	0.0119688i
$589$	5.71983	+	9.90704i	0.235682	+	0.408212i
$590$		−	0.0187864i		−	0.000773422i
$591$	9.01170	−	5.20291i	0.370692	−	0.214019i
$592$	−1.85075	+	1.06853i	−0.0760654	+	0.0439164i
$593$			29.6883i			1.21915i	0.792727	+	0.609576i	$0.208660\pi$
$593$			29.6883i			1.21915i	−0.792727	+	0.609576i	$0.791340\pi$
$594$	1.42812	+	2.47357i	0.0585963	+	0.101492i
$595$	4.28836	−	7.42766i	0.175806	−	0.304505i
$596$	1.08572	+	0.626842i	0.0444729	+	0.0256765i
$597$	10.8955			0.445922
$598$		0			0
$599$	24.2325			0.990113			0.495057	−	0.868861i	$-0.335147\pi$
$599$	24.2325			0.990113			0.495057	+	0.868861i	$0.335147\pi$
$600$	−4.05668	−	2.34213i	−0.165613	−	0.0956169i
$601$	−8.24094	+	14.2737i	−0.336155	+	0.582237i	−0.983706	−	0.179785i	$-0.942460\pi$
$601$	−8.24094	+	14.2737i	−0.336155	+	0.582237i	0.647551	+	0.762022i	$0.275793\pi$
$602$	5.34750	+	9.26215i	0.217948	+	0.377497i
$603$			21.8170i			0.888457i
$604$	27.9493	−	16.1365i	1.13724	−	0.656586i
$605$	−23.2091	+	13.3998i	−0.943584	+	0.544778i
$606$			2.35450i			0.0956451i
$607$	−0.715948	−	1.24006i	−0.0290594	−	0.0503324i	0.851130	−	0.524955i	$-0.175918\pi$
$607$	−0.715948	−	1.24006i	−0.0290594	−	0.0503324i	−0.880189	+	0.474623i	$0.842585\pi$
$608$	−5.18180	+	8.97514i	−0.210150	+	0.363990i
$609$	14.7695	+	8.52715i	0.598488	+	0.345537i
$610$	12.4969			0.505986
$611$		0			0
$612$	4.53452			0.183297
$613$	−3.33287	−	1.92423i	−0.134613	−	0.0777190i	0.431181	−	0.902265i	$-0.358097\pi$
$613$	−3.33287	−	1.92423i	−0.134613	−	0.0777190i	−0.565794	+	0.824546i	$0.691430\pi$
$614$	2.48188	−	4.29874i	0.100160	−	0.173483i
$615$	−3.72737	−	6.45599i	−0.150302	−	0.260330i
$616$			6.60819i			0.266251i
$617$	−13.0239	+	7.51938i	−0.524324	+	0.302719i	−0.738702	−	0.674032i	$-0.764561\pi$
$617$	−13.0239	+	7.51938i	−0.524324	+	0.302719i	0.214378	+	0.976751i	$0.431228\pi$
$618$	−5.21501	+	3.01089i	−0.209778	+	0.121116i
$619$		−	12.8170i		−	0.515159i	−0.966257	−	0.257579i	$-0.917075\pi$
$619$		−	12.8170i		−	0.515159i	0.966257	−	0.257579i	$-0.0829249\pi$
$620$	−13.9852	−	24.2231i	−0.561660	−	0.972824i
$621$	9.88889	−	17.1281i	0.396827	−	0.687325i
$622$	−10.1119	−	5.83811i	−0.405450	−	0.234087i
$623$	−39.6504			−1.58856
$624$		0			0
$625$	−31.1269			−1.24508
$626$	−3.42547	−	1.97770i	−0.136909	−	0.0790447i
$627$	0.931468	−	1.61335i	0.0371993	−	0.0644310i
$628$	3.40246	+	5.89324i	0.135773	+	0.235166i
$629$			1.08144i			0.0431199i
$630$	8.54414	−	4.93296i	0.340407	−	0.196534i
$631$	−22.3016	+	12.8758i	−0.887813	+	0.512579i	−0.873227	−	0.487314i	$-0.837977\pi$
$631$	−22.3016	+	12.8758i	−0.887813	+	0.512579i	−0.0145868	+	0.999894i	$0.504643\pi$
$632$		−	1.65412i		−	0.0657974i
$633$	−4.19418	−	7.26453i	−0.166704	−	0.288739i
$634$	−6.64981	+	11.5178i	−0.264098	+	0.457431i
$635$	−16.4466	−	9.49545i	−0.652664	−	0.376815i
$636$	7.96854			0.315973
$637$		0			0
$638$	−5.25236			−0.207943
$639$	−28.0471	−	16.1930i	−1.10952	−	0.640584i
$640$	16.1637	−	27.9963i	0.638925	−	1.10665i
$641$	12.2286	+	21.1805i	0.482999	+	0.836579i	0.999809	−	0.0195209i	$-0.00621408\pi$
$641$	12.2286	+	21.1805i	0.482999	+	0.836579i	−0.516810	+	0.856100i	$0.672881\pi$
$642$		−	2.50604i		−	0.0989055i
$643$	−8.63726	+	4.98672i	−0.340620	+	0.196657i	−0.660546	−	0.750785i	$-0.729675\pi$
$643$	−8.63726	+	4.98672i	−0.340620	+	0.196657i	0.319926	+	0.947442i	$0.396342\pi$
$644$	18.1610	−	10.4852i	0.715642	−	0.413176i
$645$			16.0858i			0.633376i
$646$	0.611777	+	1.05963i	0.0240700	+	0.0416905i
$647$	5.92154	−	10.2564i	0.232800	−	0.403221i	−0.725831	−	0.687873i	$-0.758545\pi$
$647$	5.92154	−	10.2564i	0.232800	−	0.403221i	0.958631	+	0.284652i	$0.0918780\pi$
$648$	6.43340	+	3.71432i	0.252728	+	0.145912i
$649$	−0.0144745			−0.000568173
$650$		0			0
$651$	−12.7366			−0.499188
$652$	22.1808	+	12.8061i	0.868669	+	0.501526i
$653$	3.73705	−	6.47277i	0.146242	−	0.253299i	−0.783593	−	0.621274i	$-0.786615\pi$
$653$	3.73705	−	6.47277i	0.146242	−	0.253299i	0.929836	+	0.367975i	$0.119949\pi$
$654$	−0.929312	−	1.60962i	−0.0363390	−	0.0629410i
$655$			38.3303i			1.49769i
$656$	6.45599	−	3.72737i	0.252064	−	0.145529i
$657$	26.1612	−	15.1042i	1.02065	−	0.589270i
$658$			11.4916i			0.447988i
$659$	−17.0869	−	29.5955i	−0.665613	−	1.15288i	−0.979119	−	0.203289i	$-0.934837\pi$
$659$	−17.0869	−	29.5955i	−0.665613	−	1.15288i	0.313506	−	0.949586i	$-0.398497\pi$
$660$	−2.27748	+	3.94471i	−0.0886508	+	0.153548i
$661$	29.1061	+	16.8044i	1.13209	+	0.653615i	0.944461	−	0.328624i	$-0.106585\pi$
$661$	29.1061	+	16.8044i	1.13209	+	0.653615i	0.187634	+	0.982239i	$0.439918\pi$
$662$	1.60686			0.0624524
$663$		0			0
$664$	−33.4644			−1.29867
$665$	−12.6662	−	7.31282i	−0.491173	−	0.283579i
$666$	−0.621998	+	1.07733i	−0.0241019	+	0.0417458i
$667$	18.1848	+	31.4970i	0.704118	+	1.21957i
$668$			10.5978i			0.410040i
$669$	−7.92132	+	4.57338i	−0.306256	+	0.176817i
$670$	12.4653	−	7.19687i	0.481578	−	0.278039i
$671$		−	9.62863i		−	0.371709i
$672$	−5.76928	−	9.99269i	−0.222555	−	0.385476i
$673$	24.0160	−	41.5970i	0.925750	−	1.60345i	0.135399	−	0.990791i	$-0.456768\pi$
$673$	24.0160	−	41.5970i	0.925750	−	1.60345i	0.790351	−	0.612654i	$-0.209898\pi$
$674$	1.49258	+	0.861740i	0.0574919	+	0.0331930i
$675$	12.2470			0.471386
$676$		0			0
$677$	−33.6582			−1.29359			−0.646794	−	0.762665i	$-0.723891\pi$
$677$	−33.6582			−1.29359			−0.646794	+	0.762665i	$0.723891\pi$
$678$	2.94579	+	1.70075i	0.113132	+	0.0653169i
$679$	4.21528	−	7.30109i	0.161768	−	0.280190i
$680$	−3.26391	−	5.65325i	−0.125165	−	0.216792i
$681$			8.53319i			0.326992i
$682$	3.39708	−	1.96130i	0.130081	−	0.0751022i
$683$	−13.7733	+	7.95204i	−0.527022	+	0.304276i	−0.739803	−	0.672824i	$-0.765081\pi$
$683$	−13.7733	+	7.95204i	−0.527022	+	0.304276i	0.212781	+	0.977100i	$0.431748\pi$
$684$		−	7.73258i		−	0.295663i
$685$	18.1957	+	31.5158i	0.695221	+	1.20416i
$686$	−5.04437	+	8.73710i	−0.192595	+	0.333584i
$687$	−0.791351	−	0.456886i	−0.0301919	−	0.0174313i
$688$	−16.0858			−0.613264
$689$		0			0
$690$	−5.74094			−0.218554
$691$	−28.7436	−	16.5951i	−1.09346	−	0.631309i	−0.158964	−	0.987284i	$-0.550815\pi$
$691$	−28.7436	−	16.5951i	−1.09346	−	0.631309i	−0.934495	+	0.355975i	$0.884149\pi$
$692$	13.8672	−	24.0188i	0.527154	−	0.913057i
$693$	−3.80074	−	6.58308i	−0.144378	−	0.250070i
$694$			6.31468i			0.239702i
$695$	−29.2315	+	16.8768i	−1.10881	+	0.640174i
$696$	11.2411	−	6.49007i	0.426094	−	0.246006i
$697$		−	3.77240i		−	0.142890i
$698$	−0.928780	−	1.60869i	−0.0351548	−	0.0608900i
$699$	−4.35086	+	7.53590i	−0.164564	+	0.285034i
$700$	11.2458	+	6.49276i	0.425051	+	0.245403i
$701$	14.9129			0.563253			0.281627	−	0.959524i	$-0.409126\pi$
$701$	14.9129			0.563253			0.281627	+	0.959524i	$0.409126\pi$
$702$		0			0
$703$	1.84415			0.0695534
$704$	−1.58518	−	0.915206i	−0.0597439	−	0.0344931i
$705$	−8.64191	+	14.9682i	−0.325473	+	0.563736i
$706$	−0.176956	−	0.306497i	−0.00665983	−	0.0115352i
$707$		−	14.2422i		−	0.535633i
$708$	0.0141971	−	0.00819673i	0.000533561	−	0.000308052i
$709$	−33.2824	+	19.2156i	−1.24995	+	0.721656i	−0.971098	−	0.238679i	$-0.923286\pi$
$709$	−33.2824	+	19.2156i	−1.24995	+	0.721656i	−0.278847	+	0.960336i	$0.589952\pi$
$710$			21.3666i			0.801874i
$711$	0.951378	+	1.64784i	0.0356795	+	0.0617987i
$712$	−15.0891	+	26.1351i	−0.565488	+	0.979454i
$713$	−23.5228	−	13.5809i	−0.880937	−	0.508609i
$714$	−1.36227			−0.0509818
$715$		0			0
$716$	4.15346			0.155222
$717$	8.28489	+	4.78328i	0.309405	+	0.178635i
$718$	−5.95444	+	10.3134i	−0.222218	+	0.384892i
$719$	−5.71864	−	9.90497i	−0.213269	−	0.369393i	0.739467	−	0.673193i	$-0.235078\pi$
$719$	−5.71864	−	9.90497i	−0.213269	−	0.369393i	−0.952736	+	0.303800i	$0.901744\pi$
$720$			14.8388i			0.553008i
$721$	31.5451	−	18.2126i	1.17480	−	0.678272i
$722$	−7.32460	+	4.22886i	−0.272593	+	0.157382i
$723$			2.92585i			0.108814i
$724$	9.98911	+	17.3017i	0.371243	+	0.643011i
$725$	−11.2606	+	19.5039i	−0.418206	+	0.724355i
$726$	3.68638	+	2.12833i	0.136815	+	0.0789899i
$727$	−3.63640			−0.134867			−0.0674333	−	0.997724i	$-0.521481\pi$
$727$	−3.63640			−0.134867			−0.0674333	+	0.997724i	$0.521481\pi$
$728$		0			0
$729$	1.78986			0.0662910
$730$	−17.2598	−	9.96495i	−0.638814	−	0.368819i
$731$	−4.07002	+	7.04949i	−0.150535	+	0.260735i
$732$	5.45257	+	9.44414i	0.201533	+	0.349065i
$733$		−	3.52217i		−	0.130094i	−0.997882	−	0.0650472i	$-0.979280\pi$
$733$		−	3.52217i		−	0.130094i	0.997882	−	0.0650472i	$-0.0207198\pi$
$734$	4.51148	−	2.60470i	0.166522	−	0.0961414i
$735$	0.480608	−	0.277479i	0.0177275	−	0.0102350i
$736$		−	24.6069i		−	0.907021i
$737$	−5.54503	−	9.60428i	−0.204254	−	0.353778i
$738$	2.16972	−	3.75806i	0.0798685	−	0.138336i
$739$	0.363980	+	0.210144i	0.0133892	+	0.00773027i	0.506680	−	0.862134i	$-0.330873\pi$
$739$	0.363980	+	0.210144i	0.0133892	+	0.00773027i	−0.493290	+	0.869865i	$0.664206\pi$
$740$	−4.50902			−0.165755
$741$		0			0
$742$	8.77346			0.322084
$743$	21.9644	+	12.6811i	0.805795	+	0.465226i	0.845493	−	0.533986i	$-0.179306\pi$
$743$	21.9644	+	12.6811i	0.805795	+	0.465226i	−0.0396987	+	0.999212i	$0.512640\pi$
$744$	−4.84697	+	8.39520i	−0.177699	+	0.307783i
$745$	1.03803	+	1.79792i	0.0380306	+	0.0658709i
$746$		−	15.3870i		−	0.563359i
$747$	33.3373	−	19.2473i	1.21975	−	0.704221i
$748$	−1.99618	+	1.15250i	−0.0729877	+	0.0421395i
$749$			15.1588i			0.553892i
$750$	1.33997	+	2.32090i	0.0489288	+	0.0847471i
$751$	0.325437	−	0.563673i	0.0118754	−	0.0205687i	−0.860027	−	0.510249i	$-0.829553\pi$
$751$	0.325437	−	0.563673i	0.0118754	−	0.0205687i	0.871902	+	0.489680i	$0.162887\pi$
$752$	−14.9682	−	8.64191i	−0.545835	−	0.315138i
$753$	−1.10129			−0.0401333
$754$		0			0
$755$	53.4432			1.94500
$756$	16.9461	+	9.78382i	0.616322	+	0.355834i
$757$	8.39546	−	14.5414i	0.305138	−	0.528515i	−0.672154	−	0.740411i	$-0.734631\pi$
$757$	8.39546	−	14.5414i	0.305138	−	0.528515i	0.977292	+	0.211897i	$0.0679640\pi$
$758$	−9.95324	−	17.2395i	−0.361518	−	0.626167i
$759$			4.42327i			0.160555i
$760$	−9.64032	+	5.56584i	−0.349691	+	0.201894i
$761$	−26.7794	+	15.4611i	−0.970751	+	0.560463i	−0.899465	−	0.436993i	$-0.856044\pi$
$761$	−26.7794	+	15.4611i	−0.970751	+	0.560463i	−0.0712857	+	0.997456i	$0.522710\pi$
$762$			3.01639i			0.109272i
$763$	5.62133	+	9.73644i	0.203506	+	0.352483i
$764$	7.60842	−	13.1782i	0.275263	−	0.476770i
$765$	6.50301	+	3.75451i	0.235117	+	0.135745i
$766$	2.69441			0.0973531
$767$		0			0
$768$	−2.68425			−0.0968596
$769$	37.9050	+	21.8845i	1.36689	+	0.789174i	0.990530	−	0.137299i	$-0.0438422\pi$
$769$	37.9050	+	21.8845i	1.36689	+	0.789174i	0.376360	+	0.926473i	$0.377176\pi$
$770$	−2.50753	+	4.34317i	−0.0903652	+	0.156517i
$771$	11.8029	+	20.4432i	0.425071	+	0.736245i
$772$		−	22.8853i		−	0.823660i
$773$	−36.7376	+	21.2104i	−1.32136	+	0.762886i	−0.983945	−	0.178470i	$-0.942885\pi$
$773$	−36.7376	+	21.2104i	−1.32136	+	0.762886i	−0.337413	+	0.941357i	$0.609552\pi$
$774$	−8.10912	+	4.68180i	−0.291476	+	0.168284i
$775$		−	16.8194i		−	0.604171i
$776$	−3.20828	−	5.55691i	−0.115171	−	0.199481i
$777$	−1.02661	+	1.77815i	−0.0368296	+	0.0637907i
$778$	−1.14643	−	0.661890i	−0.0411014	−	0.0237299i
$779$	−6.43296			−0.230485
$780$		0			0
$781$	16.4625			0.589075
$782$	−2.51593	−	1.45257i	−0.0899696	−	0.0519440i
$783$	−16.9683	+	29.3900i	−0.606398	+	1.05031i
$784$	0.277479	+	0.480608i	0.00990997	+	0.0171646i
$785$			11.2687i			0.402199i
$786$	5.27249	−	3.04407i	0.188063	−	0.108578i
$787$	31.1870	−	18.0058i	1.11170	−	0.641838i	0.172427	−	0.985022i	$-0.444839\pi$
$787$	31.1870	−	18.0058i	1.11170	−	0.641838i	0.939268	+	0.343185i	$0.111506\pi$
$788$			21.9554i			0.782129i
$789$	−4.28890	−	7.42859i	−0.152689	−	0.264465i
$790$	0.627670	−	1.08716i	0.0223315	−	0.0386793i
$791$	−17.8188	−	10.2877i	−0.633564	−	0.365789i
$792$	−5.78554			−0.205580
$793$		0			0
$794$	8.47219			0.300667
$795$	11.4278	+	6.59783i	0.405302	+	0.234001i
$796$	−11.4943	+	19.9086i	−0.407403	+	0.705643i
$797$	−15.8550	−	27.4617i	−0.561614	−	0.972744i	−0.997356	−	0.0726725i	$-0.976847\pi$
$797$	−15.8550	−	27.4617i	−0.561614	−	0.972744i	0.435742	−	0.900072i	$-0.356486\pi$
$798$			2.32304i			0.0822349i
$799$	−7.57453	+	4.37316i	−0.267968	+	0.154711i
$800$	13.1959	−	7.61865i	0.466545	−	0.269360i
$801$		−	34.7144i		−	1.22657i
$802$	3.54019	+	6.13179i	0.125008	+	0.216521i
$803$	−7.67778	+	13.2983i	−0.270943	+	0.469287i
$804$	10.8776	+	6.28017i	0.383622	+	0.221484i
$805$	34.7265			1.22395
$806$		0			0
$807$	−8.16852			−0.287546
$808$	−9.38758	−	5.41992i	−0.330254	−	0.190672i
$809$	22.6407	−	39.2149i	0.796005	−	1.37872i	−0.126194	−	0.992006i	$-0.540276\pi$
$809$	22.6407	−	39.2149i	0.796005	−	1.37872i	0.922199	−	0.386716i	$-0.126390\pi$
$810$	2.81886	+	4.88242i	0.0990448	+	0.171551i
$811$		−	42.8635i		−	1.50514i	−0.658511	−	0.752571i	$-0.728813\pi$
$811$		−	42.8635i		−	1.50514i	0.658511	−	0.752571i	$-0.271187\pi$
$812$	−31.1623	+	17.9916i	−1.09358	+	0.631380i
$813$	20.4546	−	11.8095i	0.717374	−	0.414176i
$814$		−	0.632351i		−	0.0221639i
$815$	21.2066	+	36.7308i	0.742833	+	1.28662i
$816$	1.02446	−	1.77441i	0.0358632	−	0.0621169i
$817$	12.0213	+	6.94049i	0.420572	+	0.242817i
$818$	−14.0731			−0.492054
$819$		0			0
$820$	15.7289			0.549276
$821$	6.77904	+	3.91388i	0.236590	+	0.136595i	0.613608	−	0.789610i	$-0.289717\pi$
$821$	6.77904	+	3.91388i	0.236590	+	0.136595i	−0.377018	+	0.926206i	$0.623051\pi$
$822$	2.89008	−	5.00577i	0.100803	−	0.174596i
$823$	−18.3877	−	31.8484i	−0.640955	−	1.11017i	−0.985220	−	0.171294i	$-0.945205\pi$
$823$	−18.3877	−	31.8484i	−0.640955	−	1.11017i	0.344265	−	0.938872i	$-0.388128\pi$
$824$		−	27.7235i		−	0.965793i
$825$	−2.37206	+	1.36951i	−0.0825846	+	0.0476802i
$826$	0.0156312	−	0.00902470i	0.000543880	−	0.000314009i
$827$		−	47.3293i		−	1.64580i	−0.568186	−	0.822900i	$-0.692355\pi$
$827$		−	47.3293i		−	1.64580i	0.568186	−	0.822900i	$-0.307645\pi$
$828$	9.17994	+	15.9001i	0.319025	+	0.552567i
$829$	12.6344	−	21.8834i	0.438810	−	0.760041i	−0.558788	−	0.829311i	$-0.688733\pi$
$829$	12.6344	−	21.8834i	0.438810	−	0.760041i	0.997598	+	0.0692694i	$0.0220668\pi$
$830$	−21.9942	−	12.6984i	−0.763430	−	0.440766i
$831$	8.21552			0.284993
$832$		0			0
$833$	0.280831			0.00973023
$834$	4.64294	+	2.68060i	0.160772	+	0.0928217i
$835$	−8.77479	+	15.1984i	−0.303664	+	0.525962i
$836$	1.96532	+	3.40403i	0.0679720	+	0.117731i
$837$		−	25.3448i		−	0.876045i
$838$	5.60738	−	3.23742i	0.193704	−	0.111835i
$839$	32.6390	−	18.8442i	1.12682	−	0.650572i	0.183690	−	0.982984i	$-0.441196\pi$
$839$	32.6390	−	18.8442i	1.12682	−	0.650572i	0.943134	+	0.332412i	$0.107862\pi$
$840$		−	12.3937i		−	0.427624i
$841$	−16.7032	−	28.9308i	−0.575972	−	0.997614i
$842$	2.30111	−	3.98564i	0.0793015	−	0.137354i
$843$	−8.03163	−	4.63706i	−0.276624	−	0.159709i
$844$	17.6987			0.609215
$845$		0			0
$846$	−10.0610			−0.345904
$847$	−22.2986	−	12.8741i	−0.766190	−	0.442360i
$848$	−6.59783	+	11.4278i	−0.226571	+	0.392432i
$849$	−12.3134	−	21.3274i	−0.422593	−	0.731953i
$850$		−	1.79895i		−	0.0617036i
$851$	−3.79204	+	2.18933i	−0.129989	+	0.0750494i
$852$	−16.1471	+	9.32251i	−0.553189	+	0.319384i
$853$			31.0121i			1.06183i	0.847424	+	0.530917i	$0.178152\pi$
$853$			31.0121i			1.06183i	−0.847424	+	0.530917i	$0.821848\pi$
$854$	6.00335	+	10.3981i	0.205430	+	0.355816i
$855$	6.40246	−	11.0894i	0.218960	−	0.379249i
$856$	9.99177	+	5.76875i	0.341512	+	0.197172i
$857$	−12.4692			−0.425940			−0.212970	−	0.977059i	$-0.568314\pi$
$857$	−12.4692			−0.425940			−0.212970	+	0.977059i	$0.568314\pi$
$858$		0			0
$859$	−17.3163			−0.590826			−0.295413	−	0.955370i	$-0.595457\pi$
$859$	−17.3163			−0.590826			−0.295413	+	0.955370i	$0.595457\pi$
$860$	−29.3925	−	16.9698i	−1.00228	−	0.578665i
$861$	3.58115	−	6.20273i	0.122045	−	0.211388i
$862$	−0.258693	−	0.448069i	−0.00881111	−	0.0152613i
$863$		−	3.46383i		−	0.117910i	−0.998261	−	0.0589550i	$-0.981223\pi$
$863$		−	3.46383i		−	0.117910i	0.998261	−	0.0589550i	$-0.0187769\pi$
$864$	19.8846	−	11.4804i	0.676488	−	0.390571i
$865$	39.7744	−	22.9638i	1.35237	−	0.780791i
$866$		−	7.40880i		−	0.251761i
$867$	6.29805	+	10.9085i	0.213893	+	0.370474i
$868$	13.4366	−	23.2729i	0.456068	−	0.789933i
$869$	−0.837631	−	0.483607i	−0.0284147	−	0.0164052i
$870$	9.85086			0.333975
$871$		0			0
$872$	8.55688			0.289772
$873$	6.39218	+	3.69053i	0.216343	+	0.124905i
$874$	−2.47703	+	4.29035i	−0.0837869	+	0.145123i
$875$	−8.10537	−	14.0389i	−0.274011	−	0.474602i
$876$		−	17.3913i		−	0.587599i
$877$	49.5842	−	28.6274i	1.67434	−	0.966680i	0.709175	−	0.705033i	$-0.249068\pi$
$877$	49.5842	−	28.6274i	1.67434	−	0.966680i	0.965164	−	0.261647i	$-0.0842656\pi$
$878$	6.72478	−	3.88255i	0.226950	−	0.131030i
$879$			14.9226i			0.503327i
$880$	−3.77144	−	6.53232i	−0.127135	−	0.220205i
$881$	−21.5891	+	37.3934i	−0.727355	+	1.25982i	0.230642	+	0.973039i	$0.425917\pi$
$881$	−21.5891	+	37.3934i	−0.727355	+	1.25982i	−0.957997	+	0.286778i	$0.907416\pi$
$882$	0.279764	+	0.161522i	0.00942015	+	0.00543873i
$883$	−49.9560			−1.68115			−0.840576	−	0.541693i	$-0.817784\pi$
$883$	−49.9560			−1.68115			−0.840576	+	0.541693i	$0.817784\pi$
$884$		0			0
$885$	0.0271471			0.000912539
$886$	11.3912	+	6.57673i	0.382696	+	0.220950i
$887$	−8.83728	+	15.3066i	−0.296727	+	0.513946i	−0.975385	−	0.220508i	$-0.929228\pi$
$887$	−8.83728	+	15.3066i	−0.296727	+	0.513946i	0.678658	+	0.734454i	$0.262562\pi$
$888$	0.781364	+	1.35336i	0.0262209	+	0.0454159i
$889$		−	18.2459i		−	0.611948i
$890$	−19.8344	+	11.4514i	−0.664850	+	0.383851i
$891$	3.76180	−	2.17187i	0.126025	−	0.0727605i
$892$		−	19.2989i		−	0.646174i
$893$	7.45742	+	12.9166i	0.249553	+	0.432238i
$894$	0.164874	−	0.285571i	0.00551422	−	0.00955092i
$895$	5.95652	+	3.43900i	0.199105	+	0.114953i
$896$	31.0592			1.03761
$897$		0			0
$898$	6.98493			0.233090
$899$	40.3627	+	23.3034i	1.34617	+	0.777213i
$900$	−5.68449	+	9.84582i	−0.189483	+	0.328194i
$901$	3.33877	+	5.78293i	0.111231	+	0.192657i
$902$			2.20583i			0.0734462i
$903$	−13.3842	+	7.72737i	−0.445398	+	0.257151i
$904$	−13.5620	+	7.83004i	−0.451067	+	0.260423i
$905$			33.0834i			1.09973i
$906$	−4.24429	−	7.35133i	−0.141007	−	0.244232i
$907$	3.86712	−	6.69804i	0.128406	−	0.222405i	−0.794653	−	0.607063i	$-0.792347\pi$
$907$	3.86712	−	6.69804i	0.128406	−	0.222405i	0.923059	+	0.384658i	$0.125681\pi$
$908$	−15.5922	−	9.00216i	−0.517445	−	0.298747i
$909$	12.4692			0.413577
$910$		0			0
$911$	39.6179			1.31260			0.656299	−	0.754501i	$-0.272121\pi$
$911$	39.6179			1.31260			0.656299	+	0.754501i	$0.272121\pi$
$912$	−3.02586	−	1.74698i	−0.100196	−	0.0578483i
$913$	−9.78382	+	16.9461i	−0.323797	+	0.560833i
$914$	9.33393	+	16.1668i	0.308739	+	0.534752i
$915$			18.0586i			0.596999i
$916$	1.66968	−	0.963992i	0.0551679	−	0.0318512i
$917$	−31.8929	+	18.4133i	−1.05319	+	0.608062i
$918$		−	2.71081i		−	0.0894700i
$919$	−7.31067	−	12.6624i	−0.241157	−	0.417696i	0.719887	−	0.694091i	$-0.244193\pi$
$919$	−7.31067	−	12.6624i	−0.241157	−	0.417696i	−0.961044	+	0.276395i	$0.910860\pi$
$920$	13.2153	−	22.8895i	0.435695	−	0.754646i
$921$	6.21186	+	3.58642i	0.204688	+	0.118176i
$922$	−0.778512			−0.0256389
$923$		0			0
$924$	−4.37627			−0.143969
$925$	−2.34814	−	1.35570i	−0.0772064	−	0.0445751i
$926$	−4.21797	+	7.30574i	−0.138611	+	0.240082i
$927$	15.9453	+	27.6181i	0.523714	+	0.907099i
$928$			42.2228i			1.38603i
$929$	3.08076	−	1.77868i	0.101076	−	0.0583565i	−0.448610	−	0.893728i	$-0.648081\pi$
$929$	3.08076	−	1.77868i	0.101076	−	0.0583565i	0.549686	+	0.835371i	$0.314747\pi$
$930$	−6.37126	+	3.67845i	−0.208922	+	0.120621i
$931$		−	0.478894i		−	0.0156951i
$932$	−9.17994	−	15.9001i	−0.300699	−	0.520826i
$933$	8.43631	−	14.6121i	0.276192	−	0.478379i
$934$	18.9078	+	10.9164i	0.618681	+	0.357196i
$935$	−3.81700			−0.124829
$936$		0			0
$937$	34.5526			1.12878			0.564392	−	0.825507i	$-0.309111\pi$
$937$	34.5526			1.12878			0.564392	+	0.825507i	$0.309111\pi$
$938$	11.9763	+	6.91454i	0.391041	+	0.225768i
$939$	2.85786	−	4.94995i	0.0932626	−	0.161536i
$940$	−18.2337	−	31.5817i	−0.594718	−	1.03008i
$941$			20.6233i			0.672299i	0.941809	+	0.336149i	$0.109125\pi$
$941$			20.6233i			0.672299i	−0.941809	+	0.336149i	$0.890875\pi$
$942$	1.55006	−	0.894928i	0.0505037	−	0.0291583i
$943$	13.2278	−	7.63706i	0.430756	−	0.248697i
$944$			0.0271471i			0.000883562i
$945$	16.2017	+	28.0622i	0.527042	+	0.912863i
$946$	2.37986	−	4.12204i	0.0773760	−	0.134019i
$947$	25.5477	+	14.7500i	0.830188	+	0.479309i	0.853917	−	0.520409i	$-0.174221\pi$
$947$	25.5477	+	14.7500i	0.830188	+	0.479309i	−0.0237289	+	0.999718i	$0.507554\pi$
$948$	1.09544			0.0355783
$949$		0			0
$950$	−3.06770			−0.0995295
$951$	−16.6437	−	9.60925i	−0.539709	−	0.311601i
$952$	3.13587	−	5.43148i	0.101634	−	0.176035i
$953$	13.1195	+	22.7236i	0.424981	+	0.736089i	0.996419	−	0.0845563i	$-0.0269473\pi$
$953$	13.1195	+	22.7236i	0.424981	+	0.736089i	−0.571437	+	0.820646i	$0.693614\pi$
$954$			7.68127i			0.248690i
$955$	21.8227	−	12.5993i	0.706165	−	0.407705i
$956$	−17.4804	+	10.0923i	−0.565357	+	0.326409i
$957$		−	7.58987i		−	0.245346i
$958$	−6.20692	−	10.7507i	−0.200537	−	0.347340i
$959$	−17.4819	+	30.2795i	−0.564519	+	0.977776i
$960$	2.97303	+	1.71648i	0.0959542	+	0.0553992i
$961$	−3.80731			−0.122817
$962$		0			0
$963$	−13.2717			−0.427676
$964$	−5.34624	−	3.08665i	−0.172191	−	0.0994144i
$965$	18.9487	−	32.8201i	0.609980	−	1.05652i
$966$	−2.75786	−	4.77676i	−0.0887328	−	0.153690i
$967$			17.5176i			0.563330i	0.959513	+	0.281665i	$0.0908866\pi$
$967$			17.5176i			0.563330i	−0.959513	+	0.281665i	$0.909113\pi$
$968$	−16.9716	+	9.79859i	−0.545489	+	0.314938i
$969$	−1.53121	+	0.884043i	−0.0491895	+	0.0283996i
$970$		−	4.86964i		−	0.156355i
$971$	−10.2560	−	17.7639i	−0.329131	−	0.570071i	0.653209	−	0.757178i	$-0.273422\pi$
$971$	−10.2560	−	17.7639i	−0.329131	−	0.570071i	−0.982340	+	0.187106i	$0.940089\pi$
$972$	−13.3629	+	23.1453i	−0.428616	+	0.742385i
$973$	−28.0848	−	16.2148i	−0.900356	−	0.519821i
$974$	12.7199			0.407572
$975$		0			0
$976$	−18.0586			−0.578042
$977$	−22.0361	−	12.7225i	−0.704996	−	0.407030i	0.104210	−	0.994555i	$-0.466769\pi$
$977$	−22.0361	−	12.7225i	−0.704996	−	0.407030i	−0.809205	+	0.587526i	$0.800102\pi$
$978$	3.36831	−	5.83409i	0.107707	−	0.186554i
$979$	8.82304	+	15.2820i	0.281986	+	0.488414i
$980$			1.17092i			0.0374035i
$981$	−8.52436	+	4.92154i	−0.272162	+	0.157133i
$982$	0.886029	−	0.511549i	0.0282743	−	0.0163242i
$983$			39.5244i			1.26063i	0.776339	+	0.630316i	$0.217074\pi$
$983$			39.5244i			1.26063i	−0.776339	+	0.630316i	$0.782926\pi$
$984$	−2.72564	−	4.72094i	−0.0868901	−	0.150498i
$985$	−18.1787	+	31.4865i	−0.579223	+	1.00324i
$986$	4.31708	+	2.49247i	0.137484	+	0.0793763i
$987$	−16.6058			−0.528568
$988$		0			0
$989$	−32.9584			−1.04802
$990$	−3.80250	−	2.19537i	−0.120851	−	0.0697736i
$991$	14.9189	−	25.8402i	0.473913	−	0.820841i	−0.525641	−	0.850707i	$-0.676174\pi$
$991$	14.9189	−	25.8402i	0.473913	−	0.820841i	0.999554	+	0.0298651i	$0.00950777\pi$
$992$	−15.7666	−	27.3085i	−0.500590	−	0.867047i
$993$			2.32198i			0.0736858i
$994$	−17.7781	+	10.2642i	−0.563888	+	0.325561i
$995$	−32.9681	+	19.0341i	−1.04516	+	0.603423i
$996$		−	22.1618i		−	0.702224i
$997$	2.46562	+	4.27057i	0.0780868	+	0.135250i	0.902424	−	0.430848i	$-0.141786\pi$
$997$	2.46562	+	4.27057i	0.0780868	+	0.135250i	−0.824338	+	0.566098i	$0.808452\pi$
$998$	3.33931	−	5.78385i	0.105704	−	0.183084i
$999$	−3.53837	−	2.04288i	−0.111949	−	0.0646338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.e.b.147.4		12
13.2	odd	12		169.2.c.c.146.2		6
13.3	even	3	inner	169.2.e.b.23.3		12
13.4	even	6		169.2.b.b.168.4		6
13.5	odd	4		169.2.c.c.22.2		6
13.6	odd	12		169.2.a.b.1.2	✓	3
13.7	odd	12		169.2.a.c.1.2	yes	3
13.8	odd	4		169.2.c.b.22.2		6
13.9	even	3		169.2.b.b.168.3		6
13.10	even	6	inner	169.2.e.b.23.4		12
13.11	odd	12		169.2.c.b.146.2		6
13.12	even	2	inner	169.2.e.b.147.3		12
39.17	odd	6		1521.2.b.l.1351.3		6
39.20	even	12		1521.2.a.o.1.2		3
39.32	even	12		1521.2.a.r.1.2		3
39.35	odd	6		1521.2.b.l.1351.4		6
52.7	even	12		2704.2.a.ba.1.1		3
52.19	even	12		2704.2.a.z.1.1		3
52.35	odd	6		2704.2.f.o.337.1		6
52.43	odd	6		2704.2.f.o.337.2		6
65.19	odd	12		4225.2.a.bg.1.2		3
65.59	odd	12		4225.2.a.bb.1.2		3
91.6	even	12		8281.2.a.bf.1.2		3
91.20	even	12		8281.2.a.bj.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.a.b.1.2	✓	3	13.6	odd	12
169.2.a.c.1.2	yes	3	13.7	odd	12
169.2.b.b.168.3		6	13.9	even	3
169.2.b.b.168.4		6	13.4	even	6
169.2.c.b.22.2		6	13.8	odd	4
169.2.c.b.146.2		6	13.11	odd	12
169.2.c.c.22.2		6	13.5	odd	4
169.2.c.c.146.2		6	13.2	odd	12
169.2.e.b.23.3		12	13.3	even	3	inner
169.2.e.b.23.4		12	13.10	even	6	inner
169.2.e.b.147.3		12	13.12	even	2	inner
169.2.e.b.147.4		12	1.1	even	1	trivial
1521.2.a.o.1.2		3	39.20	even	12
1521.2.a.r.1.2		3	39.32	even	12
1521.2.b.l.1351.3		6	39.17	odd	6
1521.2.b.l.1351.4		6	39.35	odd	6
2704.2.a.z.1.1		3	52.19	even	12
2704.2.a.ba.1.1		3	52.7	even	12
2704.2.f.o.337.1		6	52.35	odd	6
2704.2.f.o.337.2		6	52.43	odd	6
4225.2.a.bb.1.2		3	65.59	odd	12
4225.2.a.bg.1.2		3	65.19	odd	12
8281.2.a.bf.1.2		3	91.6	even	12
8281.2.a.bj.1.2		3	91.20	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)

\(f(q)\)	\(=\)	\(q+(0.480608 + 0.277479i) q^{2} +(-0.400969 + 0.694498i) q^{3} +(-0.846011 - 1.46533i) q^{4} -2.80194i q^{5} +(-0.385418 + 0.222521i) q^{6} +(2.33136 - 1.34601i) q^{7} -2.04892i q^{8} +(1.17845 + 2.04113i) q^{9} +O(q^{10})\)	\(q+(0.480608 + 0.277479i) q^{2} +(-0.400969 + 0.694498i) q^{3} +(-0.846011 - 1.46533i) q^{4} -2.80194i q^{5} +(-0.385418 + 0.222521i) q^{6} +(2.33136 - 1.34601i) q^{7} -2.04892i q^{8} +(1.17845 + 2.04113i) q^{9} +(0.777479 - 1.34663i) q^{10} +(-1.03755 - 0.599031i) q^{11} +1.35690 q^{12} +1.49396 q^{14} +(1.94594 + 1.12349i) q^{15} +(-1.12349 + 1.94594i) q^{16} +(0.568532 + 0.984726i) q^{17} +1.30798i q^{18} +(1.67922 - 0.969501i) q^{19} +(-4.10577 + 2.37047i) q^{20} +2.15883i q^{21} +(-0.332437 - 0.575798i) q^{22} +(-2.30194 + 3.98707i) q^{23} +(1.42297 + 0.821552i) q^{24} -2.85086 q^{25} -4.29590 q^{27} +(-3.94471 - 2.27748i) q^{28} +(3.94989 - 6.84140i) q^{29} +(0.623490 + 1.07992i) q^{30} +5.89977i q^{31} +(-4.62874 + 2.67241i) q^{32} +(0.832052 - 0.480386i) q^{33} +0.631023i q^{34} +(-3.77144 - 6.53232i) q^{35} +(1.99396 - 3.45364i) q^{36} +(0.823662 + 0.475541i) q^{37} +1.07606 q^{38} -5.74094 q^{40} +(-2.87318 - 1.65883i) q^{41} +(-0.599031 + 1.03755i) q^{42} +(3.57942 + 6.19973i) q^{43} +2.02715i q^{44} +(5.71912 - 3.30194i) q^{45} +(-2.21266 + 1.27748i) q^{46} +7.69202i q^{47} +(-0.900969 - 1.56052i) q^{48} +(0.123490 - 0.213891i) q^{49} +(-1.37014 - 0.791053i) q^{50} -0.911854 q^{51} +5.87263 q^{53} +(-2.06464 - 1.19202i) q^{54} +(-1.67845 + 2.90716i) q^{55} +(-2.75786 - 4.77676i) q^{56} +1.55496i q^{57} +(3.79669 - 2.19202i) q^{58} +(0.0104630 - 0.00604079i) q^{59} -3.80194i q^{60} +(4.01842 + 6.96010i) q^{61} +(-1.63706 + 2.83548i) q^{62} +(5.49477 + 3.17241i) q^{63} +1.52781 q^{64} +0.533188 q^{66} +(8.01651 + 4.62833i) q^{67} +(0.961968 - 1.66618i) q^{68} +(-1.84601 - 3.19738i) q^{69} -4.18598i q^{70} +(-11.9000 + 6.87047i) q^{71} +(4.18211 - 2.41454i) q^{72} -12.8170i q^{73} +(0.263906 + 0.457098i) q^{74} +(1.14310 - 1.97991i) q^{75} +(-2.84128 - 1.64042i) q^{76} -3.22521 q^{77} +0.807315 q^{79} +(5.45241 + 3.14795i) q^{80} +(-1.81282 + 3.13990i) q^{81} +(-0.920583 - 1.59450i) q^{82} -16.3327i q^{83} +(3.16341 - 1.82640i) q^{84} +(2.75914 - 1.59299i) q^{85} +3.97285i q^{86} +(3.16756 + 5.48638i) q^{87} +(-1.22737 + 2.12586i) q^{88} +(-12.7556 - 7.36443i) q^{89} +3.66487 q^{90} +7.78986 q^{92} +(-4.09738 - 2.36563i) q^{93} +(-2.13437 + 3.69685i) q^{94} +(-2.71648 - 4.70508i) q^{95} -4.28621i q^{96} +(2.71212 - 1.56584i) q^{97} +(0.118700 - 0.0685317i) q^{98} -2.82371i 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

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