LMFDB - Embedded newform 169.2.e.b.23.6

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			23.6
Root			$-1.07992 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	169.23
Dual form			169.2.e.b.147.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94594 - 1.12349i) q^{2} +(0.277479 + 0.480608i) q^{3} +(1.52446 - 2.64044i) q^{4} +1.44504i q^{5} +(1.07992 + 0.623490i) q^{6} +(-1.77441 - 1.02446i) q^{7} -2.35690i q^{8} +(1.34601 - 2.33136i) q^{9} +O(q^{10})$	\(q+(1.94594 - 1.12349i) q^{2} +(0.277479 + 0.480608i) q^{3} +(1.52446 - 2.64044i) q^{4} +1.44504i q^{5} +(1.07992 + 0.623490i) q^{6} +(-1.77441 - 1.02446i) q^{7} -2.35690i q^{8} +(1.34601 - 2.33136i) q^{9} +(1.62349 + 2.81197i) q^{10} +(-2.21266 + 1.27748i) q^{11} +1.69202 q^{12} -4.60388 q^{14} +(-0.694498 + 0.400969i) q^{15} +(0.400969 + 0.694498i) q^{16} +(-2.64795 + 4.58638i) q^{17} -6.04892i q^{18} +(-5.06699 - 2.92543i) q^{19} +(3.81555 + 2.20291i) q^{20} -1.13706i q^{21} +(-2.87047 + 4.97180i) q^{22} +(-0.945042 - 1.63686i) q^{23} +(1.13274 - 0.653989i) q^{24} +2.91185 q^{25} +3.15883 q^{27} +(-5.41004 + 3.12349i) q^{28} +(-1.13437 - 1.96480i) q^{29} +(-0.900969 + 1.56052i) q^{30} +4.26875i q^{31} +(5.64279 + 3.25786i) q^{32} +(-1.22793 - 0.708947i) q^{33} +11.8998i q^{34} +(1.48039 - 2.56410i) q^{35} +(-4.10388 - 7.10812i) q^{36} +(4.63921 - 2.67845i) q^{37} -13.1468 q^{38} +3.40581 q^{40} +(-1.10343 + 0.637063i) q^{41} +(-1.27748 - 2.21266i) q^{42} +(3.06853 - 5.31485i) q^{43} +7.78986i q^{44} +(3.36891 + 1.94504i) q^{45} +(-3.67799 - 2.12349i) q^{46} -2.95108i q^{47} +(-0.222521 + 0.385418i) q^{48} +(-1.40097 - 2.42655i) q^{49} +(5.66630 - 3.27144i) q^{50} -2.93900 q^{51} +5.52111 q^{53} +(6.14691 - 3.54892i) q^{54} +(-1.84601 - 3.19738i) q^{55} +(-2.41454 + 4.18211i) q^{56} -3.24698i q^{57} +(-4.41485 - 2.54892i) q^{58} +(10.5722 + 6.10388i) q^{59} +2.44504i q^{60} +(-4.28232 + 7.41720i) q^{61} +(4.79590 + 8.30674i) q^{62} +(-4.77676 + 2.75786i) q^{63} +13.0368 q^{64} -3.18598 q^{66} +(-0.499461 + 0.288364i) q^{67} +(8.07338 + 13.9835i) q^{68} +(0.524459 - 0.908389i) q^{69} -6.65279i q^{70} +(-3.97868 - 2.29709i) q^{71} +(-5.49477 - 3.17241i) q^{72} -10.5526i q^{73} +(6.01842 - 10.4242i) q^{74} +(0.807979 + 1.39946i) q^{75} +(-15.4488 + 8.91939i) q^{76} +5.23490 q^{77} -15.7778 q^{79} +(-1.00358 + 0.579417i) q^{80} +(-3.16152 - 5.47592i) q^{81} +(-1.43147 + 2.47938i) q^{82} -7.72348i q^{83} +(-3.00235 - 1.73341i) q^{84} +(-6.62751 - 3.82640i) q^{85} -13.7899i q^{86} +(0.629531 - 1.09038i) q^{87} +(3.01089 + 5.21501i) q^{88} +(5.72751 - 3.30678i) q^{89} +8.74094 q^{90} -5.76271 q^{92} +(-2.05159 + 1.18449i) q^{93} +(-3.31551 - 5.74263i) q^{94} +(4.22737 - 7.32201i) q^{95} +3.61596i q^{96} +(10.3290 + 5.96346i) q^{97} +(-5.45241 - 3.14795i) q^{98} +6.87800i 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 $

$2$	1.94594	−	1.12349i	1.37599	−	0.794427i	0.384315	−	0.923202i	$-0.374438\pi$
$2$	1.94594	−	1.12349i	1.37599	−	0.794427i	0.991674	+	0.128775i	$0.0411045\pi$
$3$	0.277479	+	0.480608i	0.160203	+	0.277479i	0.934941	−	0.354803i	$-0.115452\pi$
$3$	0.277479	+	0.480608i	0.160203	+	0.277479i	−0.774739	+	0.632282i	$0.782119\pi$
$4$	1.52446	−	2.64044i	0.762229	−	1.32022i
$5$			1.44504i			0.646242i	0.946358	+	0.323121i	$0.104732\pi$
$5$			1.44504i			0.646242i	−0.946358	+	0.323121i	$0.895268\pi$
$6$	1.07992	+	0.623490i	0.440874	+	0.254539i
$7$	−1.77441	−	1.02446i	−0.670666	−	0.387209i	0.125663	−	0.992073i	$-0.459894\pi$
$7$	−1.77441	−	1.02446i	−0.670666	−	0.387209i	−0.796329	+	0.604864i	$0.793227\pi$
$8$		−	2.35690i		−	0.833289i
$9$	1.34601	−	2.33136i	0.448670	−	0.777120i
$10$	1.62349	+	2.81197i	0.513393	+	0.889222i
$11$	−2.21266	+	1.27748i	−0.667142	+	0.385174i	−0.794993	−	0.606619i	$-0.792525\pi$
$11$	−2.21266	+	1.27748i	−0.667142	+	0.385174i	0.127851	+	0.991793i	$0.459192\pi$
$12$	1.69202			0.488445
$13$		0			0
$13$		0			0
$14$	−4.60388			−1.23044
$15$	−0.694498	+	0.400969i	−0.179319	+	0.103530i
$16$	0.400969	+	0.694498i	0.100242	+	0.173625i
$17$	−2.64795	+	4.58638i	−0.642222	+	1.11236i	0.342714	+	0.939440i	$0.388654\pi$
$17$	−2.64795	+	4.58638i	−0.642222	+	1.11236i	−0.984936	+	0.172921i	$0.944679\pi$
$18$		−	6.04892i		−	1.42574i
$19$	−5.06699	−	2.92543i	−1.16245	−	0.671139i	−0.210558	−	0.977581i	$-0.567528\pi$
$19$	−5.06699	−	2.92543i	−1.16245	−	0.671139i	−0.951889	+	0.306442i	$0.900861\pi$
$20$	3.81555	+	2.20291i	0.853182	+	0.492585i
$21$		−	1.13706i		−	0.248128i
$22$	−2.87047	+	4.97180i	−0.611986	+	1.05999i
$23$	−0.945042	−	1.63686i	−0.197055	−	0.341309i	0.750517	−	0.660851i	$-0.229804\pi$
$23$	−0.945042	−	1.63686i	−0.197055	−	0.341309i	−0.947572	+	0.319542i	$0.896471\pi$
$24$	1.13274	−	0.653989i	0.231220	−	0.133495i
$25$	2.91185			0.582371
$26$		0			0
$27$	3.15883			0.607918
$28$	−5.41004	+	3.12349i	−1.02240	+	0.590284i
$29$	−1.13437	−	1.96480i	−0.210648	−	0.364853i	0.741269	−	0.671208i	$-0.234224\pi$
$29$	−1.13437	−	1.96480i	−0.210648	−	0.364853i	−0.951918	+	0.306354i	$0.900891\pi$
$30$	−0.900969	+	1.56052i	−0.164494	+	0.284911i
$31$			4.26875i			0.766690i	0.923605	+	0.383345i	$0.125228\pi$
$31$			4.26875i			0.766690i	−0.923605	+	0.383345i	$0.874772\pi$
$32$	5.64279	+	3.25786i	0.997513	+	0.575915i
$33$	−1.22793	−	0.708947i	−0.213756	−	0.123412i
$34$			11.8998i			2.04079i
$35$	1.48039	−	2.56410i	0.250231	−	0.433413i
$36$	−4.10388	−	7.10812i	−0.683979	−	1.18469i
$37$	4.63921	−	2.67845i	0.762681	−	0.440334i	−0.0675764	−	0.997714i	$-0.521527\pi$
$37$	4.63921	−	2.67845i	0.762681	−	0.440334i	0.830258	+	0.557380i	$0.188193\pi$
$38$	−13.1468			−2.13268
$39$		0			0
$40$	3.40581			0.538506
$41$	−1.10343	+	0.637063i	−0.172326	+	0.0994926i	−0.583682	−	0.811982i	$-0.698389\pi$
$41$	−1.10343	+	0.637063i	−0.172326	+	0.0994926i	0.411356	+	0.911475i	$0.365055\pi$
$42$	−1.27748	−	2.21266i	−0.197119	−	0.341421i
$43$	3.06853	−	5.31485i	0.467947	−	0.810507i	−0.531382	−	0.847132i	$-0.678327\pi$
$43$	3.06853	−	5.31485i	0.467947	−	0.810507i	0.999329	+	0.0366246i	$0.0116606\pi$
$44$			7.78986i			1.17437i
$45$	3.36891	+	1.94504i	0.502208	+	0.289950i
$46$	−3.67799	−	2.12349i	−0.542290	−	0.313091i
$47$		−	2.95108i		−	0.430460i	−0.976563	−	0.215230i	$-0.930950\pi$
$47$		−	2.95108i		−	0.430460i	0.976563	−	0.215230i	$-0.0690501\pi$
$48$	−0.222521	+	0.385418i	−0.0321181	+	0.0556302i
$49$	−1.40097	−	2.42655i	−0.200138	−	0.346650i
$50$	5.66630	−	3.27144i	0.801335	−	0.462651i
$51$	−2.93900			−0.411542
$52$		0			0
$53$	5.52111			0.758382			0.379191	−	0.925318i	$-0.376202\pi$
$53$	5.52111			0.758382			0.379191	+	0.925318i	$0.376202\pi$
$54$	6.14691	−	3.54892i	0.836488	−	0.482946i
$55$	−1.84601	−	3.19738i	−0.248916	−	0.431135i
$56$	−2.41454	+	4.18211i	−0.322657	+	0.558858i
$57$		−	3.24698i		−	0.430073i
$58$	−4.41485	−	2.54892i	−0.579699	−	0.334689i
$59$	10.5722	+	6.10388i	1.37639	+	0.794657i	0.991722	−	0.128400i	$-0.0409841\pi$
$59$	10.5722	+	6.10388i	1.37639	+	0.794657i	0.384664	+	0.923057i	$0.374317\pi$
$60$			2.44504i			0.315654i
$61$	−4.28232	+	7.41720i	−0.548295	+	0.949675i	0.450096	+	0.892980i	$0.351390\pi$
$61$	−4.28232	+	7.41720i	−0.548295	+	0.949675i	−0.998392	+	0.0566953i	$0.981944\pi$
$62$	4.79590	+	8.30674i	0.609080	+	1.05496i
$63$	−4.77676	+	2.75786i	−0.601815	+	0.347458i
$64$	13.0368			1.62960
$65$		0			0
$66$	−3.18598			−0.392167
$67$	−0.499461	+	0.288364i	−0.0610189	+	0.0352293i	−0.530199	−	0.847873i	$-0.677883\pi$
$67$	−0.499461	+	0.288364i	−0.0610189	+	0.0352293i	0.469180	+	0.883102i	$0.344549\pi$
$68$	8.07338	+	13.9835i	0.979041	+	1.69575i
$69$	0.524459	−	0.908389i	0.0631374	−	0.109357i
$70$		−	6.65279i		−	0.795161i
$71$	−3.97868	−	2.29709i	−0.472183	−	0.272615i	0.244970	−	0.969531i	$-0.421222\pi$
$71$	−3.97868	−	2.29709i	−0.472183	−	0.272615i	−0.717153	+	0.696916i	$0.754555\pi$
$72$	−5.49477	−	3.17241i	−0.647565	−	0.373872i
$73$		−	10.5526i		−	1.23508i	−0.786538	−	0.617542i	$-0.788128\pi$
$73$		−	10.5526i		−	1.23508i	0.786538	−	0.617542i	$-0.211872\pi$
$74$	6.01842	−	10.4242i	0.699627	−	1.21179i
$75$	0.807979	+	1.39946i	0.0932973	+	0.161596i
$76$	−15.4488	+	8.91939i	−1.77210	+	1.02312i
$77$	5.23490			0.596572
$78$		0			0
$79$	−15.7778			−1.77514			−0.887569	−	0.460674i	$-0.847608\pi$
$79$	−15.7778			−1.77514			−0.887569	+	0.460674i	$0.847608\pi$
$80$	−1.00358	+	0.579417i	−0.112204	+	0.0647808i
$81$	−3.16152	−	5.47592i	−0.351280	−	0.608435i
$82$	−1.43147	+	2.47938i	−0.158079	+	0.273801i
$83$		−	7.72348i		−	0.847762i	−0.905718	−	0.423881i	$-0.860667\pi$
$83$		−	7.72348i		−	0.847762i	0.905718	−	0.423881i	$-0.139333\pi$
$84$	−3.00235	−	1.73341i	−0.327583	−	0.189130i
$85$	−6.62751	−	3.82640i	−0.718855	−	0.415031i
$86$		−	13.7899i		−	1.48700i
$87$	0.629531	−	1.09038i	0.0674928	−	0.116901i
$88$	3.01089	+	5.21501i	0.320961	+	0.555922i
$89$	5.72751	−	3.30678i	0.607115	−	0.350518i	−0.164720	−	0.986340i	$-0.552672\pi$
$89$	5.72751	−	3.30678i	0.607115	−	0.350518i	0.771836	+	0.635822i	$0.219339\pi$
$90$	8.74094			0.921376
$91$		0			0
$92$	−5.76271			−0.600804
$93$	−2.05159	+	1.18449i	−0.212740	+	0.122826i
$94$	−3.31551	−	5.74263i	−0.341969	−	0.592307i
$95$	4.22737	−	7.32201i	0.433719	−	0.751223i
$96$			3.61596i			0.369052i
$97$	10.3290	+	5.96346i	1.04875	+	0.605498i	0.922300	−	0.386475i	$-0.126307\pi$
$97$	10.3290	+	5.96346i	1.04875	+	0.605498i	0.126453	+	0.991973i	$0.459641\pi$
$98$	−5.45241	−	3.14795i	−0.550776	−	0.317991i
$99$			6.87800i			0.691265i
$100$	4.43900	−	7.68858i	0.443900	−	0.768858i
$101$	6.53199	+	11.3137i	0.649957	+	1.12576i	0.983133	+	0.182894i	$0.0585466\pi$
$101$	6.53199	+	11.3137i	0.649957	+	1.12576i	−0.333175	+	0.942865i	$0.608120\pi$
$102$	−5.71912	+	3.30194i	−0.566278	+	0.326941i
$103$	−9.16852			−0.903401			−0.451701	−	0.892170i	$-0.649182\pi$
$103$	−9.16852			−0.903401			−0.451701	+	0.892170i	$0.649182\pi$
$104$		0			0
$105$	1.64310			0.160351
$106$	10.7437	−	6.20291i	1.04353	−	0.602480i
$107$	3.44989	+	5.97538i	0.333513	+	0.577662i	0.983198	−	0.182542i	$-0.0584325\pi$
$107$	3.44989	+	5.97538i	0.333513	+	0.577662i	−0.649685	+	0.760204i	$0.725099\pi$
$108$	4.81551	−	8.34071i	0.463373	−	0.802585i
$109$		−	0.121998i		−	0.0116853i	−0.999983	−	0.00584264i	$-0.998140\pi$
$109$		−	0.121998i		−	0.0116853i	0.999983	−	0.00584264i	$-0.00185978\pi$
$110$	−7.18446	−	4.14795i	−0.685011	−	0.395491i
$111$	2.57457	+	1.48643i	0.244367	+	0.141085i
$112$		−	1.64310i		−	0.155259i
$113$	−3.65399	+	6.32890i	−0.343738	+	0.595372i	−0.985124	−	0.171847i	$-0.945027\pi$
$113$	−3.65399	+	6.32890i	−0.343738	+	0.595372i	0.641385	+	0.767219i	$0.278360\pi$
$114$	−3.64795	−	6.31843i	−0.341662	−	0.591775i
$115$	2.36533	−	1.36563i	0.220568	−	0.127345i
$116$	−6.91723			−0.642249
$117$		0			0
$118$	27.4306			2.52519
$119$	9.39712	−	5.42543i	0.861432	−	0.497348i
$120$	0.945042	+	1.63686i	0.0862701	+	0.149424i
$121$	−2.23609	+	3.87303i	−0.203281	+	0.352094i
$122$			19.2446i			1.74232i
$123$	−0.612355	−	0.353543i	−0.0552142	−	0.0318779i
$124$	11.2714	+	6.50753i	1.01220	+	0.584394i
$125$			11.4330i			1.02260i
$126$	−6.19687	+	10.7333i	−0.552061	+	0.956197i
$127$	−9.48523	−	16.4289i	−0.841678	−	1.45783i	−0.888475	−	0.458925i	$-0.848235\pi$
$127$	−9.48523	−	16.4289i	−0.841678	−	1.45783i	0.0467971	−	0.998904i	$-0.485099\pi$
$128$	14.0833	−	8.13102i	1.24480	−	0.718688i
$129$	3.40581			0.299865
$130$		0			0
$131$	3.25667			0.284536			0.142268	−	0.989828i	$-0.454560\pi$
$131$	3.25667			0.284536			0.142268	+	0.989828i	$0.454560\pi$
$132$	−3.74387	+	2.16152i	−0.325862	+	0.188136i
$133$	5.99396	+	10.3818i	0.519742	+	0.900220i
$134$	−0.647948	+	1.12228i	−0.0559742	+	0.0969502i
$135$			4.56465i			0.392862i
$136$	10.8096	+	6.24094i	0.926918	+	0.535156i
$137$	−0.686108	−	0.396125i	−0.0586181	−	0.0338432i	0.470405	−	0.882451i	$-0.344108\pi$
$137$	−0.686108	−	0.396125i	−0.0586181	−	0.0338432i	−0.529023	+	0.848608i	$0.677441\pi$
$138$		−	2.35690i		−	0.200632i
$139$	5.66972	−	9.82024i	0.480899	−	0.832942i	−0.518861	−	0.854859i	$-0.673644\pi$
$139$	5.66972	−	9.82024i	0.480899	−	0.832942i	0.999760	+	0.0219169i	$0.00697694\pi$
$140$	−4.51357	−	7.81774i	−0.381467	−	0.660720i
$141$	1.41831	−	0.818864i	0.119444	−	0.0689608i
$142$	−10.3230			−0.866291
$143$		0			0
$144$	2.15883			0.179903
$145$	2.83921	−	1.63922i	0.235784	−	0.136130i
$146$	−11.8557	−	20.5347i	−0.981185	−	1.69946i
$147$	0.777479	−	1.34663i	0.0641254	−	0.111068i
$148$		−	16.3327i		−	1.34254i
$149$	7.27965	+	4.20291i	0.596372	+	0.344316i	0.767613	−	0.640914i	$-0.221444\pi$
$149$	7.27965	+	4.20291i	0.596372	+	0.344316i	−0.171241	+	0.985229i	$0.554778\pi$
$150$	3.14456	+	1.81551i	0.256752	+	0.148236i
$151$			14.1293i			1.14983i	0.818215	+	0.574913i	$0.194964\pi$
$151$			14.1293i			1.14983i	−0.818215	+	0.574913i	$0.805036\pi$
$152$	−6.89493	+	11.9424i	−0.559253	+	0.968654i
$153$	7.12833	+	12.3466i	0.576292	+	0.998166i
$154$	10.1868	−	5.88135i	0.820876	−	0.473933i
$155$	−6.16852			−0.495468
$156$		0			0
$157$	−9.43296			−0.752832			−0.376416	−	0.926451i	$-0.622844\pi$
$157$	−9.43296			−0.752832			−0.376416	+	0.926451i	$0.622844\pi$
$158$	−30.7026	+	17.7262i	−2.44257	+	1.41022i
$159$	1.53199	+	2.65349i	0.121495	+	0.210435i
$160$	−4.70775	+	8.15406i	−0.372180	+	0.644635i
$161$			3.87263i			0.305206i
$162$	−12.3043	−	7.10388i	−0.966715	−	0.558133i
$163$	−7.53797	−	4.35205i	−0.590420	−	0.340879i	0.174844	−	0.984596i	$-0.444058\pi$
$163$	−7.53797	−	4.35205i	−0.590420	−	0.340879i	−0.765263	+	0.643717i	$0.777391\pi$
$164$			3.88471i			0.303345i
$165$	1.02446	−	1.77441i	0.0797540	−	0.138138i
$166$	−8.67725	−	15.0294i	−0.673485	−	1.16651i
$167$	−20.6580	+	11.9269i	−1.59857	+	0.922933i	−0.606803	+	0.794853i	$0.707548\pi$
$167$	−20.6580	+	11.9269i	−1.59857	+	0.922933i	−0.991764	+	0.128080i	$0.959119\pi$
$168$	−2.67994			−0.206762
$169$		0			0
$170$	−17.1957			−1.31885
$171$	−13.6404	+	7.87531i	−1.04311	+	0.602240i
$172$	−9.35570	−	16.2045i	−0.713365	−	1.23559i
$173$	−9.42758	+	16.3291i	−0.716766	+	1.24147i	0.245509	+	0.969394i	$0.421045\pi$
$173$	−9.42758	+	16.3291i	−0.716766	+	1.24147i	−0.962274	+	0.272081i	$0.912288\pi$
$174$		−	2.82908i		−	0.214472i
$175$	−5.16684	−	2.98307i	−0.390576	−	0.225499i
$176$	−1.77441	−	1.02446i	−0.133752	−	0.0772215i
$177$			6.77479i			0.509224i
$178$	7.43027	−	12.8696i	0.556922	−	0.964618i
$179$	3.01089	+	5.21501i	0.225044	+	0.389788i	0.956333	−	0.292280i	$-0.0944140\pi$
$179$	3.01089	+	5.21501i	0.225044	+	0.389788i	−0.731289	+	0.682068i	$0.761081\pi$
$180$	10.2715	−	5.93027i	0.765595	−	0.442016i
$181$	4.77777			0.355129			0.177565	−	0.984109i	$-0.443178\pi$
$181$	4.77777			0.355129			0.177565	+	0.984109i	$0.443178\pi$
$182$		0			0
$183$	−4.75302			−0.351353
$184$	−3.85791	+	2.22737i	−0.284409	+	0.164204i
$185$	3.87047	+	6.70385i	0.284563	+	0.492877i
$186$	−2.66152	+	4.60989i	−0.195152	+	0.338014i
$187$		−	13.5308i		−	0.989470i
$188$	−7.79216	−	4.49880i	−0.568301	−	0.328109i
$189$	−5.60508	−	3.23609i	−0.407710	−	0.235391i
$190$		−	18.9976i		−	1.37823i
$191$	−9.21528	+	15.9613i	−0.666795	+	1.15492i	0.312001	+	0.950082i	$0.399001\pi$
$191$	−9.21528	+	15.9613i	−0.666795	+	1.15492i	−0.978795	+	0.204840i	$0.934333\pi$
$192$	3.61745	+	6.26561i	0.261067	+	0.452181i
$193$	5.24317	−	3.02715i	0.377412	−	0.217899i	−0.299280	−	0.954165i	$-0.596746\pi$
$193$	5.24317	−	3.02715i	0.377412	−	0.217899i	0.676692	+	0.736267i	$0.263413\pi$
$194$	26.7995			1.92410
$195$		0			0
$196$	−8.54288			−0.610205
$197$	9.88611	−	5.70775i	0.704357	−	0.406660i	−0.104611	−	0.994513i	$-0.533360\pi$
$197$	9.88611	−	5.70775i	0.704357	−	0.406660i	0.808968	+	0.587853i	$0.200027\pi$
$198$	7.72737	+	13.3842i	0.549160	+	0.951173i
$199$	−6.95257	+	12.0422i	−0.492855	+	0.853650i	−0.999966	−	0.00823084i	$-0.997380\pi$
$199$	−6.95257	+	12.0422i	−0.492855	+	0.853650i	0.507111	+	0.861881i	$0.330713\pi$
$200$		−	6.86294i		−	0.485283i
$201$	−0.277180	−	0.160030i	−0.0195508	−	0.0112876i
$202$	25.4217	+	14.6773i	1.78867	+	1.03269i
$203$			4.64848i			0.326259i
$204$	−4.48039	+	7.76026i	−0.313690	+	0.543327i
$205$	−0.920583	−	1.59450i	−0.0642963	−	0.111364i
$206$	−17.8414	+	10.3007i	−1.24307	+	0.717687i
$207$	−5.08815			−0.353651
$208$		0			0
$209$	14.9487			1.03402
$210$	3.19738	−	1.84601i	0.220640	−	0.127387i
$211$	6.62229	+	11.4701i	0.455897	+	0.789638i	0.998739	−	0.0501974i	$-0.0159850\pi$
$211$	6.62229	+	11.4701i	0.455897	+	0.789638i	−0.542842	+	0.839835i	$0.682652\pi$
$212$	8.41670	−	14.5781i	0.578061	−	1.00123i
$213$		−	2.54958i		−	0.174694i
$214$	13.4266	+	7.75182i	0.917820	+	0.529904i
$215$	7.68018	+	4.43416i	0.523784	+	0.302407i
$216$		−	7.44504i		−	0.506571i
$217$	4.37316	−	7.57453i	0.296869	−	0.514193i
$218$	−0.137063	−	0.237401i	−0.00928310	−	0.0160788i
$219$	5.07165	−	2.92812i	0.342710	−	0.197864i
$220$	−11.2567			−0.758924
$221$		0			0
$222$	6.67994			0.448328
$223$	6.35241	−	3.66756i	0.425389	−	0.245598i	−0.271992	−	0.962300i	$-0.587682\pi$
$223$	6.35241	−	3.66756i	0.425389	−	0.245598i	0.697380	+	0.716701i	$0.254349\pi$
$224$	−6.67510	−	11.5616i	−0.445999	−	0.772492i
$225$	3.91939	−	6.78858i	0.261292	−	0.452572i
$226$			16.4209i			1.09230i
$227$	−7.51239	−	4.33728i	−0.498615	−	0.287875i	0.229526	−	0.973302i	$-0.426282\pi$
$227$	−7.51239	−	4.33728i	−0.498615	−	0.287875i	−0.728141	+	0.685427i	$0.759616\pi$
$228$	−8.57345	−	4.94989i	−0.567791	−	0.327814i
$229$		−	13.6866i		−	0.904439i	−0.891907	−	0.452219i	$-0.850632\pi$
$229$		−	13.6866i		−	0.904439i	0.891907	−	0.452219i	$-0.149368\pi$
$230$	3.06853	−	5.31485i	0.202333	−	0.350451i
$231$	1.45257	+	2.51593i	0.0955724	+	0.165536i
$232$	−4.63082	+	2.67360i	−0.304028	+	0.175531i
$233$	5.08815			0.333336			0.166668	−	0.986013i	$-0.446699\pi$
$233$	5.08815			0.333336			0.166668	+	0.986013i	$0.446699\pi$
$234$		0			0
$235$	4.26444			0.278181
$236$	32.2338	−	18.6102i	2.09824	−	1.21142i
$237$	−4.37800	−	7.58292i	−0.284382	−	0.492564i
$238$	12.1908	−	21.1151i	0.790214	−	1.36869i
$239$			10.9239i			0.706611i	0.935508	+	0.353305i	$0.114942\pi$
$239$			10.9239i			0.706611i	−0.935508	+	0.353305i	$0.885058\pi$
$240$	−0.556945	−	0.321552i	−0.0359506	−	0.0207561i
$241$	−10.3186	−	5.95742i	−0.664676	−	0.383751i	0.129380	−	0.991595i	$-0.458701\pi$
$241$	−10.3186	−	5.95742i	−0.664676	−	0.383751i	−0.794056	+	0.607844i	$0.792035\pi$
$242$			10.0489i			0.645969i
$243$	6.49276	−	11.2458i	0.416511	−	0.721418i
$244$	13.0565	+	22.6144i	0.835854	+	1.44774i
$245$	3.50647	−	2.02446i	0.224020	−	0.129338i
$246$	−1.58881			−0.101299
$247$		0			0
$248$	10.0610			0.638874
$249$	3.71197	−	2.14310i	0.235236	−	0.135814i
$250$	12.8448	+	22.2479i	0.812377	+	1.40708i
$251$	11.1739	−	19.3538i	0.705290	−	1.22160i	−0.261296	−	0.965259i	$-0.584150\pi$
$251$	11.1739	−	19.3538i	0.705290	−	1.22160i	0.966587	−	0.256340i	$-0.0825167\pi$
$252$			16.8170i			1.05937i
$253$	4.18211	+	2.41454i	0.262927	+	0.151801i
$254$	−36.9154	−	21.3131i	−2.31628	−	1.33730i
$255$		−	4.24698i		−	0.265956i
$256$	5.23341	−	9.06453i	0.327088	−	0.566533i
$257$	−9.33004	−	16.1601i	−0.581992	−	1.00804i	−0.995243	−	0.0974228i	$-0.968940\pi$
$257$	−9.33004	−	16.1601i	−0.581992	−	1.00804i	0.413251	−	0.910617i	$-0.364393\pi$
$258$	6.62751	−	3.82640i	0.412611	−	0.238221i
$259$	−10.9758			−0.682005
$260$		0			0
$261$	−6.10752			−0.378046
$262$	6.33729	−	3.65883i	0.391519	−	0.226043i
$263$	−7.19955	−	12.4700i	−0.443944	−	0.768933i	0.554034	−	0.832494i	$-0.313088\pi$
$263$	−7.19955	−	12.4700i	−0.443944	−	0.768933i	−0.997978	+	0.0635610i	$0.979754\pi$
$264$	−1.67092	+	2.89411i	−0.102838	+	0.178120i
$265$			7.97823i			0.490099i
$266$	23.3278	+	13.4683i	1.43032	+	0.825795i
$267$	3.17853	+	1.83513i	0.194523	+	0.112308i
$268$			1.75840i			0.107411i
$269$	−0.326396	+	0.565335i	−0.0199007	+	0.0344691i	−0.875804	−	0.482666i	$-0.839668\pi$
$269$	−0.326396	+	0.565335i	−0.0199007	+	0.0344691i	0.855904	+	0.517136i	$0.173002\pi$
$270$	5.12833	+	8.88254i	0.312100	+	0.540574i
$271$	−1.72832	+	0.997844i	−0.104988	+	0.0606147i	−0.551574	−	0.834126i	$-0.685973\pi$
$271$	−1.72832	+	0.997844i	−0.104988	+	0.0606147i	0.446587	+	0.894740i	$0.352639\pi$
$272$	−4.24698			−0.257511
$273$		0			0
$274$	−1.78017			−0.107544
$275$	−6.44294	+	3.71983i	−0.388524	+	0.224314i
$276$	−1.59903	−	2.76960i	−0.0962504	−	0.166711i
$277$	5.89224	−	10.2057i	0.354030	−	0.613199i	−0.632921	−	0.774216i	$-0.718144\pi$
$277$	5.89224	−	10.2057i	0.354030	−	0.613199i	0.986952	+	0.161018i	$0.0514776\pi$
$278$		−	25.4795i		−	1.52816i
$279$	9.95199	+	5.74578i	0.595810	+	0.343991i
$280$	−6.04332	−	3.48911i	−0.361158	−	0.208514i
$281$		−	6.47219i		−	0.386098i	−0.981189	−	0.193049i	$-0.938162\pi$
$281$		−	6.47219i		−	0.386098i	0.981189	−	0.193049i	$-0.0618377\pi$
$282$	1.83997	−	3.18692i	0.109569	−	0.189778i
$283$	3.29052	+	5.69935i	0.195601	+	0.338791i	0.947097	−	0.320946i	$-0.104001\pi$
$283$	3.29052	+	5.69935i	0.195601	+	0.338791i	−0.751496	+	0.659737i	$0.770668\pi$
$284$	−12.1307	+	7.00365i	−0.719823	+	0.415590i
$285$	4.69202			0.277931
$286$		0			0
$287$	2.61058			0.154098
$288$	15.1905	−	8.77024i	0.895109	−	0.516791i
$289$	−5.52326	−	9.56657i	−0.324898	−	0.562739i
$290$	3.68329	−	6.37965i	0.216290	−	0.374626i
$291$			6.61894i			0.388009i
$292$	−27.8634	−	16.0869i	−1.63058	−	0.941418i
$293$	21.0774	+	12.1691i	1.23136	+	0.710924i	0.967313	−	0.253587i	$-0.0816104\pi$
$293$	21.0774	+	12.1691i	1.23136	+	0.710924i	0.264044	+	0.964511i	$0.414944\pi$
$294$		−	3.49396i		−	0.203772i
$295$	−8.82036	+	15.2773i	−0.513541	+	0.889479i
$296$	−6.31282	−	10.9341i	−0.366925	−	0.635533i
$297$	−6.98942	+	4.03534i	−0.405567	+	0.234154i
$298$	18.8877			1.09413
$299$		0			0
$300$	4.92692			0.284456
$301$	−10.8897	+	6.28717i	−0.627672	+	0.362386i
$302$	15.8741	+	27.4948i	0.913453	+	1.58215i
$303$	−3.62498	+	6.27865i	−0.208250	+	0.360699i
$304$		−	4.69202i		−	0.269106i
$305$	−10.7182	−	6.18814i	−0.613720	−	0.354332i
$306$	27.7426	+	16.0172i	1.58594	+	0.915644i
$307$		−	14.0737i		−	0.803227i	−0.915809	−	0.401613i	$-0.868450\pi$
$307$		−	14.0737i		−	0.803227i	0.915809	−	0.401613i	$-0.131550\pi$
$308$	7.98039	−	13.8224i	0.454725	−	0.787606i
$309$	−2.54407	−	4.40646i	−0.144727	−	0.250675i
$310$	−12.0036	+	6.93027i	−0.681758	+	0.393613i
$311$	29.7700			1.68810			0.844051	−	0.536263i	$-0.180164\pi$
$311$	29.7700			1.68810			0.844051	+	0.536263i	$0.180164\pi$
$312$		0			0
$313$	−7.47889			−0.422732			−0.211366	−	0.977407i	$-0.567791\pi$
$313$	−7.47889			−0.422732			−0.211366	+	0.977407i	$0.567791\pi$
$314$	−18.3560	+	10.5978i	−1.03589	+	0.598070i
$315$	−3.98523	−	6.90262i	−0.224542	−	0.388919i
$316$	−24.0526	+	41.6603i	−1.35306	+	2.34357i
$317$		−	30.0301i		−	1.68666i	−0.537396	−	0.843330i	$-0.680592\pi$
$317$		−	30.0301i		−	1.68666i	0.537396	−	0.843330i	$-0.319408\pi$
$318$	5.96233	+	3.44235i	0.334351	+	0.193038i
$319$	5.01997	+	2.89828i	0.281064	+	0.162273i
$320$			18.8388i			1.05312i
$321$	−1.91454	+	3.31608i	−0.106859	+	0.185086i
$322$	4.35086	+	7.53590i	0.242464	+	0.419959i
$323$	26.8343	−	15.4928i	1.49310	−	0.862040i
$324$	−19.2784			−1.07102
$325$		0			0
$326$	−19.5579			−1.08321
$327$	0.0586331	−	0.0338518i	0.00324242	−	0.00187201i
$328$	1.50149	+	2.60066i	0.0829060	+	0.143597i
$329$	−3.02326	+	5.23644i	−0.166678	+	0.288694i
$330$		−	4.60388i		−	0.253435i
$331$	−13.6111	−	7.85839i	−0.748135	−	0.431936i	0.0768845	−	0.997040i	$-0.475503\pi$
$331$	−13.6111	−	7.85839i	−0.748135	−	0.431936i	−0.825020	+	0.565104i	$0.808836\pi$
$332$	−20.3934	−	11.7741i	−1.11923	−	0.646189i
$333$		−	14.4209i		−	0.790259i
$334$	−26.7995	+	46.4182i	−1.46641	+	2.53989i
$335$	−0.416698	−	0.721743i	−0.0227667	−	0.0394330i
$336$	0.789689	−	0.455927i	0.0430811	−	0.0248729i
$337$	−1.95407			−0.106445			−0.0532224	−	0.998583i	$-0.516949\pi$
$337$	−1.95407			−0.106445			−0.0532224	+	0.998583i	$0.516949\pi$
$338$		0			0
$339$	−4.05562			−0.220271
$340$	−20.2067	+	11.6664i	−1.09586	+	0.632698i
$341$	−5.45324	−	9.44529i	−0.295309	−	0.511491i
$342$	−17.6957	+	30.6498i	−0.956872	+	1.65735i
$343$			20.0834i			1.08440i
$344$	−12.5266	−	7.23221i	−0.675387	−	0.389935i
$345$	1.31266	+	0.757865i	0.0706713	+	0.0408021i
$346$			42.3672i			2.27767i
$347$	8.56249	−	14.8307i	0.459659	−	0.796152i	−0.539284	−	0.842124i	$-0.681305\pi$
$347$	8.56249	−	14.8307i	0.459659	−	0.796152i	0.998943	+	0.0459718i	$0.0146384\pi$
$348$	−1.91939	−	3.32448i	−0.102890	−	0.178211i
$349$	−9.06453	+	5.23341i	−0.485213	+	0.280138i	−0.722586	−	0.691281i	$-0.757047\pi$
$349$	−9.06453	+	5.23341i	−0.485213	+	0.280138i	0.237373	+	0.971418i	$0.423713\pi$
$350$	−13.4058			−0.716571
$351$		0			0
$352$	−16.6474			−0.887310
$353$	−13.4501	+	7.76540i	−0.715875	+	0.413310i	−0.813232	−	0.581939i	$-0.802294\pi$
$353$	−13.4501	+	7.76540i	−0.715875	+	0.413310i	0.0973578	+	0.995249i	$0.468961\pi$
$354$	7.61141	+	13.1833i	0.404542	+	0.700687i
$355$	3.31940	−	5.74936i	0.176175	−	0.305144i
$356$		−	20.1642i		−	1.06870i
$357$	5.21501	+	3.01089i	0.276007	+	0.159353i
$358$	11.7180	+	6.76540i	0.619316	+	0.357562i
$359$		−	21.4263i		−	1.13083i	−0.824805	−	0.565417i	$-0.808715\pi$
$359$		−	21.4263i		−	1.13083i	0.824805	−	0.565417i	$-0.191285\pi$
$360$	4.58426	−	7.94017i	0.241612	−	0.418484i
$361$	7.61625	+	13.1917i	0.400855	+	0.694302i
$362$	9.29727	−	5.36778i	0.488654	−	0.282124i
$363$	−2.48188			−0.130265
$364$		0			0
$365$	15.2489			0.798164
$366$	−9.24910	+	5.33997i	−0.483458	+	0.279125i
$367$	−17.1516	−	29.7074i	−0.895306	−	1.55072i	−0.833425	−	0.552632i	$-0.813624\pi$
$367$	−17.1516	−	29.7074i	−0.895306	−	1.55072i	−0.0618807	−	0.998084i	$-0.519710\pi$
$368$	0.757865	−	1.31266i	0.0395064	−	0.0684271i
$369$			3.42998i			0.178557i
$370$	15.0634	+	8.69687i	0.783110	+	0.452129i
$371$	−9.79673	−	5.65615i	−0.508621	−	0.293652i
$372$			7.22282i			0.374486i
$373$	6.29805	−	10.9085i	0.326101	−	0.564823i	−0.655634	−	0.755079i	$-0.727598\pi$
$373$	6.29805	−	10.9085i	0.326101	−	0.564823i	0.981735	+	0.190256i	$0.0609318\pi$
$374$	−15.2017	−	26.3301i	−0.786062	−	1.36150i
$375$	−5.49477	+	3.17241i	−0.283749	+	0.163822i
$376$	−6.95539			−0.358697
$377$		0			0
$378$	−14.5429			−0.748005
$379$	−14.3228	+	8.26928i	−0.735714	+	0.424765i	−0.820509	−	0.571634i	$-0.806310\pi$
$379$	−14.3228	+	8.26928i	−0.735714	+	0.424765i	0.0847951	+	0.996398i	$0.472976\pi$
$380$	−12.8889	−	22.3242i	−0.661186	−	1.14521i
$381$	5.26391	−	9.11735i	0.269678	−	0.467096i
$382$			41.4131i			2.11888i
$383$	6.52652	+	3.76809i	0.333489	+	0.192540i	0.657389	−	0.753551i	$-0.271661\pi$
$383$	6.52652	+	3.76809i	0.333489	+	0.192540i	−0.323900	+	0.946091i	$0.604994\pi$
$384$	7.81567	+	4.51238i	0.398842	+	0.230271i
$385$			7.56465i			0.385530i
$386$	6.80194	−	11.7813i	0.346210	−	0.599652i
$387$	−8.26055	−	14.3077i	−0.419908	−	0.727301i
$388$	31.4923	−	18.1821i	1.59878	−	0.923056i
$389$	−35.5555			−1.80274			−0.901369	−	0.433052i	$-0.857437\pi$
$389$	−35.5555			−1.80274			−0.901369	+	0.433052i	$0.857437\pi$
$390$		0			0
$391$	10.0097			0.506212
$392$	−5.71912	+	3.30194i	−0.288859	+	0.166773i
$393$	0.903657	+	1.56518i	0.0455835	+	0.0789529i
$394$	12.8252	−	22.2139i	0.646124	−	1.11912i
$395$		−	22.7995i		−	1.14717i
$396$	18.1610	+	10.4852i	0.912622	+	0.526903i
$397$	−1.17045	−	0.675760i	−0.0587432	−	0.0339154i	0.470341	−	0.882485i	$-0.344131\pi$
$397$	−1.17045	−	0.675760i	−0.0587432	−	0.0339154i	−0.529084	+	0.848569i	$0.677464\pi$
$398$			31.2446i			1.56615i
$399$	−3.32640	+	5.76149i	−0.166528	+	0.288435i
$400$	1.16756	+	2.02228i	0.0583781	+	0.101114i
$401$	0.501534	−	0.289561i	0.0250454	−	0.0144600i	−0.487425	−	0.873165i	$-0.662064\pi$
$401$	0.501534	−	0.289561i	0.0250454	−	0.0144600i	0.512470	+	0.858705i	$0.328730\pi$
$402$	−0.719169			−0.0358689
$403$		0			0
$404$	39.8310			1.98167
$405$	7.91293	−	4.56853i	0.393197	−	0.227012i
$406$	5.22252	+	9.04567i	0.259189	+	0.448929i
$407$	−6.84332	+	11.8530i	−0.339211	+	0.587531i
$408$			6.92692i			0.342934i
$409$	−13.1268	−	7.57875i	−0.649078	−	0.374745i	0.139025	−	0.990289i	$-0.455603\pi$
$409$	−13.1268	−	7.57875i	−0.649078	−	0.374745i	−0.788103	+	0.615544i	$0.788936\pi$
$410$	−3.58280	−	2.06853i	−0.176942	−	0.102157i
$411$		−	0.439665i		−	0.0216871i
$412$	−13.9770	+	24.2089i	−0.688599	+	1.19269i
$413$	−12.5063	−	21.6616i	−0.615397	−	1.06590i
$414$	−9.90123	+	5.71648i	−0.486619	+	0.280950i
$415$	11.1608			0.547860
$416$		0			0
$417$	6.29291			0.308165
$418$	29.0893	−	16.7947i	1.42280	−	0.821456i
$419$	17.8617	+	30.9374i	0.872603	+	1.51139i	0.859294	+	0.511481i	$0.170903\pi$
$419$	17.8617	+	30.9374i	0.872603	+	1.51139i	0.0133088	+	0.999911i	$0.495764\pi$
$420$	2.50484	−	4.33852i	0.122224	−	0.211698i
$421$			35.0465i			1.70806i	0.520221	+	0.854032i	$0.325849\pi$
$421$			35.0465i			1.70806i	−0.520221	+	0.854032i	$0.674151\pi$
$422$	25.7732	+	14.8802i	1.25462	+	0.724355i
$423$	−6.88003	−	3.97219i	−0.334519	−	0.193134i
$424$		−	13.0127i		−	0.631951i
$425$	−7.71044	+	13.3549i	−0.374011	+	0.647806i
$426$	−2.86443	−	4.96134i	−0.138782	−	0.240378i
$427$	15.1972	−	8.77413i	0.735446	−	0.424610i
$428$	21.0368			1.01685
$429$		0			0
$430$	19.9269			0.960961
$431$	29.6886	−	17.1407i	1.43005	−	0.825639i	0.432925	−	0.901430i	$-0.357481\pi$
$431$	29.6886	−	17.1407i	1.43005	−	0.825639i	0.997124	+	0.0757909i	$0.0241482\pi$
$432$	1.26659	+	2.19381i	0.0609390	+	0.105549i
$433$	6.86927	−	11.8979i	0.330116	−	0.571778i	−0.652418	−	0.757859i	$-0.726245\pi$
$433$	6.86927	−	11.8979i	0.330116	−	0.571778i	0.982534	+	0.186081i	$0.0595787\pi$
$434$		−	19.6528i		−	0.943364i
$435$	1.57564	+	0.909698i	0.0755463	+	0.0436167i
$436$	−0.322128	−	0.185981i	−0.0154271	−	0.00890686i
$437$			11.0586i			0.529005i
$438$	6.57942	−	11.3959i	0.314377	−	0.544516i
$439$	5.12014	+	8.86834i	0.244371	+	0.423263i	0.961955	−	0.273210i	$-0.0880853\pi$
$439$	5.12014	+	8.86834i	0.244371	+	0.423263i	−0.717584	+	0.696472i	$0.754752\pi$
$440$	−7.53590	+	4.35086i	−0.359260	+	0.207419i
$441$	−7.54288			−0.359185
$442$		0			0
$443$	12.1763			0.578513			0.289257	−	0.957252i	$-0.406592\pi$
$443$	12.1763			0.578513			0.289257	+	0.957252i	$0.406592\pi$
$444$	7.84964	−	4.53199i	0.372527	−	0.215079i
$445$	4.77844	+	8.27650i	0.226520	+	0.392344i
$446$	8.24094	−	14.2737i	0.390220	−	0.675880i
$447$			4.66487i			0.220641i
$448$	−23.1327	−	13.3557i	−1.09292	−	0.630997i
$449$	11.1762	+	6.45257i	0.527437	+	0.304516i	0.739972	−	0.672638i	$-0.234839\pi$
$449$	11.1762	+	6.45257i	0.527437	+	0.304516i	−0.212535	+	0.977153i	$0.568172\pi$
$450$		−	17.6136i		−	0.830311i
$451$	1.62767	−	2.81921i	0.0766440	−	0.132751i
$452$	11.1407	+	19.2963i	0.524015	+	0.907621i
$453$	−6.79065	+	3.92058i	−0.319053	+	0.184205i
$454$	−19.4916			−0.914785
$455$		0			0
$456$	−7.65279			−0.358375
$457$	−4.03317	+	2.32855i	−0.188664	+	0.108925i	−0.591357	−	0.806410i	$-0.701408\pi$
$457$	−4.03317	+	2.32855i	−0.188664	+	0.108925i	0.402693	+	0.915335i	$0.368074\pi$
$458$	−15.3768	−	26.6334i	−0.718511	−	1.24450i
$459$	−8.36443	+	14.4876i	−0.390418	+	0.676224i
$460$		−	8.32736i		−	0.388265i
$461$	−27.3149	−	15.7702i	−1.27218	−	0.734493i	−0.296782	−	0.954945i	$-0.595913\pi$
$461$	−27.3149	−	15.7702i	−1.27218	−	0.734493i	−0.975398	+	0.220452i	$0.929247\pi$
$462$	5.65325	+	3.26391i	0.263013	+	0.151851i
$463$			17.6504i			0.820284i	0.912022	+	0.410142i	$0.134521\pi$
$463$			17.6504i			0.820284i	−0.912022	+	0.410142i	$0.865479\pi$
$464$	0.909698	−	1.57564i	0.0422317	−	0.0731474i
$465$	−1.71164	−	2.96464i	−0.0793752	−	0.137482i
$466$	9.90123	−	5.71648i	0.458666	−	0.264811i
$467$	32.1726			1.48877			0.744385	−	0.667751i	$-0.232743\pi$
$467$	32.1726			1.48877			0.744385	+	0.667751i	$0.232743\pi$
$468$		0			0
$469$	1.18167			0.0545644
$470$	8.29835	−	4.79105i	0.382774	−	0.220995i
$471$	−2.61745	−	4.53355i	−0.120606	−	0.208895i
$472$	14.3862	−	24.9176i	0.662178	−	1.14693i
$473$			15.6799i			0.720964i
$474$	−17.0387	−	9.83728i	−0.782612	−	0.451841i
$475$	−14.7543	−	8.51842i	−0.676975	−	0.390852i
$476$		−	33.0834i		−	1.51637i
$477$	7.43147	−	12.8717i	0.340264	−	0.589354i
$478$	12.2729	+	21.2573i	0.561351	+	0.972288i
$479$	−30.2241	+	17.4499i	−1.38097	+	0.797306i	−0.992275	−	0.124059i	$-0.960409\pi$
$479$	−30.2241	+	17.4499i	−1.38097	+	0.797306i	−0.388699	+	0.921365i	$0.627075\pi$
$480$	−5.22521			−0.238497
$481$		0			0
$482$	−26.7724			−1.21945
$483$	−1.86121	+	1.07457i	−0.0846882	+	0.0488947i
$484$	6.81767	+	11.8085i	0.309894	+	0.536752i
$485$	−8.61745	+	14.9259i	−0.391298	+	0.677748i
$486$		−	29.1782i		−	1.32355i
$487$	36.2302	+	20.9175i	1.64175	+	0.947864i	0.980212	+	0.197950i	$0.0634284\pi$
$487$	36.2302	+	20.9175i	1.64175	+	0.947864i	0.661536	+	0.749914i	$0.269905\pi$
$488$	17.4816	+	10.0930i	0.791354	+	0.456888i
$489$		−	4.83041i		−	0.218439i
$490$	4.54892	−	7.87896i	0.205499	−	0.355935i
$491$	10.9227	+	18.9187i	0.492936	+	0.853791i	0.999967	−	0.00813732i	$-0.00259022\pi$
$491$	10.9227	+	18.9187i	0.492936	+	0.853791i	−0.507031	+	0.861928i	$0.669257\pi$
$492$	−1.86702	+	1.07792i	−0.0841718	+	0.0485966i
$493$	12.0151			0.541131
$494$		0			0
$495$	−9.93900			−0.446725
$496$	−2.96464	+	1.71164i	−0.133116	+	0.0768547i
$497$	4.70655	+	8.15199i	0.211118	+	0.365667i
$498$	4.81551	−	8.34071i	0.215788	−	0.373756i
$499$		−	23.5472i		−	1.05412i	−0.849829	−	0.527058i	$-0.823295\pi$
$499$		−	23.5472i		−	1.05412i	0.849829	−	0.527058i	$-0.176705\pi$
$500$	30.1880	+	17.4291i	1.35005	+	0.779452i
$501$	−11.4643	−	6.61894i	−0.512189	−	0.295712i
$502$		−	50.2150i		−	2.24121i
$503$	3.54341	−	6.13736i	0.157993	−	0.273652i	−0.776152	−	0.630546i	$-0.782831\pi$
$503$	3.54341	−	6.13736i	0.157993	−	0.273652i	0.934145	+	0.356894i	$0.116164\pi$
$504$	6.50000	+	11.2583i	0.289533	+	0.501486i
$505$	−16.3488	+	9.43900i	−0.727513	+	0.420030i
$506$	10.8509			0.482379
$507$		0			0
$508$	−57.8394			−2.56621
$509$	−6.59820	+	3.80947i	−0.292460	+	0.168852i	−0.639051	−	0.769165i	$-0.720673\pi$
$509$	−6.59820	+	3.80947i	−0.292460	+	0.168852i	0.346591	+	0.938016i	$0.387339\pi$
$510$	−4.77144	−	8.26437i	−0.211283	−	0.365953i
$511$	−10.8107	+	18.7246i	−0.478236	+	0.828329i
$512$			9.00538i			0.397985i
$513$	−16.0058	−	9.24094i	−0.706672	−	0.407997i
$514$	−36.3114	−	20.9644i	−1.60163	−	0.924701i
$515$		−	13.2489i		−	0.583816i
$516$	5.19202	−	8.99284i	0.228566	−	0.395888i
$517$	3.76995	+	6.52974i	0.165802	+	0.287178i
$518$	−21.3583	+	12.3312i	−0.938431	+	0.541804i
$519$	−10.4638			−0.459311
$520$		0			0
$521$	−39.5133			−1.73111			−0.865555	−	0.500813i	$-0.833034\pi$
$521$	−39.5133			−1.73111			−0.865555	+	0.500813i	$0.833034\pi$
$522$	−11.8849	+	6.86174i	−0.520187	+	0.300330i
$523$	7.90970	+	13.7000i	0.345867	+	0.599059i	0.985511	−	0.169612i	$-0.0542515\pi$
$523$	7.90970	+	13.7000i	0.345867	+	0.599059i	−0.639644	+	0.768671i	$0.720918\pi$
$524$	4.96466	−	8.59904i	0.216882	−	0.375651i
$525$		−	3.31096i		−	0.144502i
$526$	−28.0198	−	16.1773i	−1.22172	−	0.705362i
$527$	−19.5781	−	11.3034i	−0.852836	−	0.492385i
$528$		−	1.13706i		−	0.0494843i
$529$	9.71379	−	16.8248i	0.422339	−	0.731512i
$530$	8.96346	+	15.5252i	0.389348	+	0.674370i
$531$	28.4606	−	16.4318i	1.23509	−	0.713078i
$532$	36.5502			1.58465
$533$		0			0
$534$	8.24698			0.356882
$535$	−8.63467	+	4.98523i	−0.373309	+	0.215530i
$536$	0.679644	+	1.17718i	0.0293562	+	0.0508464i
$537$	−1.67092	+	2.89411i	−0.0721053	+	0.124890i
$538$			1.46681i			0.0632388i
$539$	6.19973	+	3.57942i	0.267041	+	0.154176i
$540$	12.0527	+	6.95862i	0.518665	+	0.299451i
$541$			34.4819i			1.48249i	0.671234	+	0.741246i	$0.265765\pi$
$541$			34.4819i			1.48249i	−0.671234	+	0.741246i	$0.734235\pi$
$542$	−2.24214	+	3.88349i	−0.0963080	+	0.166810i
$543$	1.32573	+	2.29624i	0.0568926	+	0.0985409i
$544$	−29.8836	+	17.2533i	−1.28125	+	0.739730i
$545$	0.176292			0.00755152
$546$		0			0
$547$	36.8582			1.57594			0.787970	−	0.615713i	$-0.211132\pi$
$547$	36.8582			1.57594			0.787970	+	0.615713i	$0.211132\pi$
$548$	−2.09189	+	1.20775i	−0.0893609	+	0.0515926i
$549$	11.5281	+	19.9673i	0.492008	+	0.852182i
$550$	−8.35839	+	14.4772i	−0.356403	+	0.617308i
$551$			13.2741i			0.565497i
$552$	−2.14098	−	1.23609i	−0.0911261	−	0.0526117i
$553$	27.9963	+	16.1637i	1.19052	+	0.687350i
$554$		−	26.4795i		−	1.12501i
$555$	−2.14795	+	3.72036i	−0.0911753	+	0.157920i
$556$	−17.2865	−	29.9411i	−0.733111	−	1.26979i
$557$	1.10550	−	0.638260i	0.0468415	−	0.0270439i	−0.476396	−	0.879231i	$-0.658057\pi$
$557$	1.10550	−	0.638260i	0.0468415	−	0.0270439i	0.523238	+	0.852187i	$0.324724\pi$
$558$	25.8213			1.09310
$559$		0			0
$560$	2.37435			0.100335
$561$	6.50301	−	3.75451i	0.274557	−	0.158516i
$562$	−7.27144	−	12.5945i	−0.306727	−	0.531267i
$563$	−4.56369	+	7.90454i	−0.192336	+	0.333137i	−0.946024	−	0.324096i	$-0.894940\pi$
$563$	−4.56369	+	7.90454i	−0.192336	+	0.333137i	0.753688	+	0.657233i	$0.228273\pi$
$564$		−	4.99330i		−	0.210256i
$565$	−9.14552	−	5.28017i	−0.384755	−	0.222138i
$566$	12.8063	+	7.39373i	0.538290	+	0.310782i
$567$			12.9554i			0.544075i
$568$	−5.41401	+	9.37734i	−0.227167	+	0.393464i
$569$	−2.86078	−	4.95502i	−0.119930	−	0.207725i	0.799810	−	0.600254i	$-0.204934\pi$
$569$	−2.86078	−	4.95502i	−0.119930	−	0.207725i	−0.919740	+	0.392529i	$0.871600\pi$
$570$	9.13040	−	5.27144i	0.382430	−	0.220796i
$571$	−7.60148			−0.318112			−0.159056	−	0.987270i	$-0.550845\pi$
$571$	−7.60148			−0.318112			−0.159056	+	0.987270i	$0.550845\pi$
$572$		0			0
$573$	−10.2282			−0.427289
$574$	5.08004	−	2.93296i	0.212037	−	0.122419i
$575$	−2.75182	−	4.76630i	−0.114759	−	0.198768i
$576$	17.5477	−	30.3935i	0.731155	−	1.26640i
$577$		−	45.1564i		−	1.87989i	−0.341330	−	0.939944i	$-0.610877\pi$
$577$		−	45.1564i		−	1.87989i	0.341330	−	0.939944i	$-0.389123\pi$
$578$	−21.4959	−	12.4107i	−0.894111	−	0.516215i
$579$	2.90974	+	1.67994i	0.120925	+	0.0698159i
$580$		−	9.99569i		−	0.415048i
$581$	−7.91239	+	13.7047i	−0.328261	+	0.568565i
$582$	7.43631	+	12.8801i	0.308245	+	0.533896i
$583$	−12.2163	+	7.05310i	−0.505948	+	0.292109i
$584$	−24.8713			−1.02918
$585$		0			0
$586$	54.6872			2.25911
$587$	28.0627	−	16.2020i	1.15827	−	0.668728i	0.207382	−	0.978260i	$-0.433506\pi$
$587$	28.0627	−	16.2020i	1.15827	−	0.668728i	0.950889	+	0.309532i	$0.100172\pi$
$588$	−2.37047	−	4.10577i	−0.0977565	−	0.169319i
$589$	12.4879	−	21.6297i	0.514556	−	0.891237i
$590$			39.6383i			1.63188i
$591$	5.48638	+	3.16756i	0.225680	+	0.130296i
$592$	3.72036	+	2.14795i	0.152906	+	0.0882801i
$593$			36.6848i			1.50647i	0.657754	+	0.753233i	$0.271507\pi$
$593$			36.6848i			1.50647i	−0.657754	+	0.753233i	$0.728493\pi$
$594$	−9.06734	+	15.7051i	−0.372037	+	0.644387i
$595$	7.83997	+	13.5792i	0.321407	+	0.556694i
$596$	22.1950	−	12.8143i	0.909144	−	0.524895i
$597$	−7.71678			−0.315827
$598$		0			0
$599$	−9.99223			−0.408271			−0.204136	−	0.978943i	$-0.565438\pi$
$599$	−9.99223			−0.408271			−0.204136	+	0.978943i	$0.565438\pi$
$600$	3.29838	−	1.90432i	0.134656	−	0.0777436i
$601$	0.905813	+	1.56891i	0.0369489	+	0.0639974i	0.883908	−	0.467660i	$-0.154903\pi$
$601$	0.905813	+	1.56891i	0.0369489	+	0.0639974i	−0.846960	+	0.531657i	$0.821569\pi$
$602$	−14.1271	+	24.4689i	−0.575779	+	0.997279i
$603$			1.55257i			0.0632253i
$604$	37.3076	+	21.5395i	1.51802	+	0.876431i
$605$	−5.59669	−	3.23125i	−0.227538	−	0.131369i
$606$			16.2905i			0.661757i
$607$	−5.60806	+	9.71344i	−0.227624	+	0.394256i	−0.957103	−	0.289746i	$-0.906429\pi$
$607$	−5.60806	+	9.71344i	−0.227624	+	0.394256i	0.729479	+	0.684003i	$0.239762\pi$
$608$	−19.0613	−	33.0151i	−0.773038	−	1.33894i
$609$	−2.23410	+	1.28986i	−0.0905302	+	0.0522676i
$610$	−27.8092			−1.12596
$611$		0			0
$612$	43.4674			1.75707
$613$	18.0951	−	10.4472i	0.730853	−	0.421958i	−0.0878810	−	0.996131i	$-0.528010\pi$
$613$	18.0951	−	10.4472i	0.730853	−	0.421958i	0.818734	+	0.574173i	$0.194676\pi$
$614$	−15.8116	−	27.3865i	−0.638105	−	1.10523i
$615$	0.510885	−	0.884879i	0.0206009	−	0.0356818i
$616$		−	12.3381i		−	0.497117i
$617$	10.4782	+	6.04958i	0.421836	+	0.243547i	0.695862	−	0.718175i	$-0.255022\pi$
$617$	10.4782	+	6.04958i	0.421836	+	0.243547i	−0.274027	+	0.961722i	$0.588356\pi$
$618$	−9.90123	−	5.71648i	−0.398286	−	0.229951i
$619$		−	10.5526i		−	0.424143i	−0.977254	−	0.212072i	$-0.931979\pi$
$619$		−	10.5526i		−	0.424143i	0.977254	−	0.212072i	$-0.0680210\pi$
$620$	−9.40366	+	16.2876i	−0.377660	+	0.654126i
$621$	−2.98523	−	5.17057i	−0.119793	−	0.207488i
$622$	57.9307	−	33.4463i	2.32281	−	1.34107i
$623$	−13.5506			−0.542895
$624$		0			0
$625$	−1.96184			−0.0784735
$626$	−14.5535	+	8.40246i	−0.581674	+	0.335830i
$627$	4.14795	+	7.18446i	0.165653	+	0.286920i
$628$	−14.3802	+	24.9072i	−0.573831	+	0.993904i
$629$			28.3696i			1.13117i
$630$	−15.5100	−	8.95473i	−0.617935	−	0.356765i
$631$	11.9957	+	6.92572i	0.477541	+	0.275709i	0.719391	−	0.694605i	$-0.244421\pi$
$631$	11.9957	+	6.92572i	0.477541	+	0.275709i	−0.241850	+	0.970314i	$0.577754\pi$
$632$			37.1866i			1.47920i
$633$	−3.67510	+	6.36545i	−0.146072	+	0.253004i
$634$	−33.7385	−	58.4369i	−1.33993	−	2.32082i
$635$	23.7404	−	13.7066i	0.942111	−	0.543928i
$636$	9.34183			0.370428
$637$		0			0
$638$	13.0248			0.515655
$639$	−10.7107	+	6.18382i	−0.423709	+	0.244628i
$640$	11.7497	+	20.3510i	0.464446	+	0.804445i
$641$	17.4804	−	30.2769i	0.690434	−	1.19587i	−0.281262	−	0.959631i	$-0.590753\pi$
$641$	17.4804	−	30.2769i	0.690434	−	1.19587i	0.971696	−	0.236235i	$-0.0759136\pi$
$642$			8.60388i			0.339568i
$643$	28.9236	+	16.6990i	1.14063	+	0.658545i	0.946587	−	0.322447i	$-0.104505\pi$
$643$	28.9236	+	16.6990i	1.14063	+	0.658545i	0.194046	+	0.980992i	$0.437839\pi$
$644$	10.2254	+	5.90366i	0.402939	+	0.232637i
$645$			4.92154i			0.193786i
$646$	34.8119	−	60.2960i	1.36966	−	2.37232i
$647$	1.16421	+	2.01647i	0.0457698	+	0.0792757i	0.888003	−	0.459838i	$-0.152093\pi$
$647$	1.16421	+	2.01647i	0.0457698	+	0.0792757i	−0.842233	+	0.539114i	$0.818759\pi$
$648$	−12.9062	+	7.45138i	−0.507002	+	0.292718i
$649$	−31.1903			−1.22433
$650$		0			0
$651$	4.85384			0.190237
$652$	−22.9827	+	13.2690i	−0.900070	+	0.519656i
$653$	−7.28568	−	12.6192i	−0.285111	−	0.493826i	0.687525	−	0.726160i	$-0.258697\pi$
$653$	−7.28568	−	12.6192i	−0.285111	−	0.493826i	−0.972636	+	0.232334i	$0.925364\pi$
$654$	0.0760644	−	0.131747i	0.00297435	−	0.00515173i
$655$			4.70602i			0.183879i
$656$	−0.884879	−	0.510885i	−0.0345487	−	0.0199467i
$657$	−24.6018	−	14.2039i	−0.959808	−	0.554146i
$658$			13.5864i			0.529654i
$659$	−5.56973	+	9.64705i	−0.216966	+	0.375796i	−0.953879	−	0.300192i	$-0.902949\pi$
$659$	−5.56973	+	9.64705i	−0.216966	+	0.375796i	0.736913	+	0.675988i	$0.236283\pi$
$660$	−3.12349	−	5.41004i	−0.121582	−	0.210586i
$661$	−11.9943	+	6.92490i	−0.466523	+	0.269347i	−0.714783	−	0.699346i	$-0.753475\pi$
$661$	−11.9943	+	6.92490i	−0.466523	+	0.269347i	0.248260	+	0.968693i	$0.420141\pi$
$662$	−35.3153			−1.37257
$663$		0			0
$664$	−18.2034			−0.706430
$665$	−15.0022	+	8.66152i	−0.581760	+	0.335879i
$666$	−16.2017	−	28.0622i	−0.627804	−	1.08739i
$667$	−2.14406	+	3.71363i	−0.0830185	+	0.143792i
$668$			72.7284i			2.81395i
$669$	3.52532	+	2.03534i	0.136297	+	0.0786909i
$670$	−1.62174	−	0.936313i	−0.0626533	−	0.0361729i
$671$		−	21.8823i		−	0.844757i
$672$	3.70440	−	6.41621i	0.142900	−	0.247511i
$673$	−3.26487	−	5.65491i	−0.125851	−	0.217981i	0.796214	−	0.605015i	$-0.206833\pi$
$673$	−3.26487	−	5.65491i	−0.125851	−	0.217981i	−0.922065	+	0.387034i	$0.873500\pi$
$674$	−3.80250	+	2.19537i	−0.146467	+	0.0845626i
$675$	9.19806			0.354034
$676$		0			0
$677$	−11.3104			−0.434693			−0.217346	−	0.976095i	$-0.569740\pi$
$677$	−11.3104			−0.434693			−0.217346	+	0.976095i	$0.569740\pi$
$678$	−7.89200	+	4.55645i	−0.303091	+	0.174989i
$679$	−12.2186	−	21.1633i	−0.468908	−	0.812173i
$680$	−9.01842	+	15.6204i	−0.345841	+	0.599013i
$681$		−	4.81402i		−	0.184474i
$682$	−21.2234	−	12.2533i	−0.812685	−	0.469204i
$683$	−12.2796	−	7.08964i	−0.469866	−	0.271277i	0.246317	−	0.969189i	$-0.420779\pi$
$683$	−12.2796	−	7.08964i	−0.469866	−	0.271277i	−0.716184	+	0.697912i	$0.754113\pi$
$684$			48.0224i			1.83618i
$685$	0.572417	−	0.991455i	0.0218709	−	0.0378815i
$686$	22.5635	+	39.0810i	0.861477	+	1.49212i
$687$	6.57791	−	3.79776i	0.250963	−	0.144893i
$688$	4.92154			0.187632
$689$		0			0
$690$	3.40581			0.129657
$691$	−26.6695	+	15.3976i	−1.01455	+	0.585753i	−0.912522	−	0.409028i	$-0.865868\pi$
$691$	−26.6695	+	15.3976i	−1.01455	+	0.585753i	−0.102032	+	0.994781i	$0.532534\pi$
$692$	28.7439	+	49.7859i	1.09268	+	1.89258i
$693$	7.04623	−	12.2044i	0.267664	−	0.463608i
$694$		−	38.4795i		−	1.46066i
$695$	14.1907	+	8.19298i	0.538282	+	0.310777i
$696$	−2.56991	−	1.48374i	−0.0974122	−	0.0562409i
$697$		−	6.74764i		−	0.255585i
$698$	−11.7594	+	20.3678i	−0.445098	+	0.770933i
$699$	1.41185	+	2.44540i	0.0534012	+	0.0924936i
$700$	−15.7533	+	9.09515i	−0.595417	+	0.343764i
$701$	−6.73184			−0.254258			−0.127129	−	0.991886i	$-0.540576\pi$
$701$	−6.73184			−0.254258			−0.127129	+	0.991886i	$0.540576\pi$
$702$		0			0
$703$	−31.3424			−1.18210
$704$	−28.8461	+	16.6543i	−1.08718	+	0.627682i
$705$	1.18329	+	2.04952i	0.0445654	+	0.0771895i
$706$	−17.4487	+	30.2220i	−0.656690	+	1.13742i
$707$		−	26.7670i		−	1.00668i
$708$	17.8884	+	10.3279i	0.672288	+	0.388146i
$709$	41.2446	+	23.8126i	1.54897	+	0.894300i	0.998220	+	0.0596324i	$0.0189929\pi$
$709$	41.2446	+	23.8126i	1.54897	+	0.894300i	0.550753	+	0.834668i	$0.314340\pi$
$710$		−	14.9172i		−	0.559834i
$711$	−21.2371	+	36.7837i	−0.796452	+	1.37949i
$712$	−7.79374	−	13.4992i	−0.292083	−	0.505902i
$713$	6.98735	−	4.03415i	0.261678	−	0.151080i
$714$	13.5308			0.506377
$715$		0			0
$716$	18.3599			0.686141
$717$	−5.25013	+	3.03116i	−0.196070	+	0.113201i
$718$	−24.0722	−	41.6942i	−0.898366	−	1.55602i
$719$	−2.99665	+	5.19035i	−0.111756	+	0.193567i	−0.916478	−	0.400084i	$-0.868981\pi$
$719$	−2.99665	+	5.19035i	−0.111756	+	0.193567i	0.804722	+	0.593651i	$0.202314\pi$
$720$			3.11960i			0.116261i
$721$	16.2688	+	9.39277i	0.605880	+	0.349805i
$722$	29.6416	+	17.1136i	1.10314	+	0.636901i
$723$		−	6.61224i		−	0.245912i
$724$	7.28352	−	12.6154i	0.270690	−	0.468849i
$725$	−3.30313	−	5.72120i	−0.122675	−	0.212480i
$726$	−4.82959	+	2.78836i	−0.179243	+	0.103486i
$727$	24.1226			0.894657			0.447329	−	0.894370i	$-0.352375\pi$
$727$	24.1226			0.894657			0.447329	+	0.894370i	$0.352375\pi$
$728$		0			0
$729$	−11.7627			−0.435656
$730$	29.6735	−	17.1320i	1.09826	−	0.634083i
$731$	16.2506	+	28.1469i	0.601051	+	1.04105i
$732$	−7.24578	+	12.5501i	−0.267812	+	0.463864i
$733$		−	36.0646i		−	1.33208i	−0.745918	−	0.666038i	$-0.767989\pi$
$733$		−	36.0646i		−	1.33208i	0.745918	−	0.666038i	$-0.232011\pi$
$734$	−66.7520	−	38.5393i	−2.46386	−	1.42251i
$735$	1.94594	+	1.12349i	0.0717771	+	0.0414405i
$736$		−	12.3153i		−	0.453947i
$737$	0.736758	−	1.27610i	0.0271388	−	0.0470059i
$738$	3.85354	+	6.67453i	0.141851	+	0.245693i
$739$	23.8377	−	13.7627i	0.876884	−	0.506269i	0.00725452	−	0.999974i	$-0.497691\pi$
$739$	23.8377	−	13.7627i	0.876884	−	0.506269i	0.869630	+	0.493704i	$0.164357\pi$
$740$	23.6015			0.867608
$741$		0			0
$742$	−25.4185			−0.933142
$743$	9.06660	−	5.23460i	0.332621	−	0.192039i	−0.324383	−	0.945926i	$-0.605157\pi$
$743$	9.06660	−	5.23460i	0.332621	−	0.192039i	0.657004	+	0.753887i	$0.271823\pi$
$744$	2.79172	+	4.83539i	0.102349	+	0.177274i
$745$	−6.07338	+	10.5194i	−0.222511	+	0.385401i
$746$		−	28.3032i		−	1.03625i
$747$	−18.0062	−	10.3959i	−0.658813	−	0.380366i
$748$	−35.7273	−	20.6271i	−1.30632	−	0.754203i
$749$		−	14.1371i		−	0.516557i
$750$	−7.12833	+	12.3466i	−0.260290	+	0.450835i
$751$	2.03385	+	3.52273i	0.0742163	+	0.128546i	0.900745	−	0.434348i	$-0.143021\pi$
$751$	2.03385	+	3.52273i	0.0742163	+	0.128546i	−0.826529	+	0.562894i	$0.809688\pi$
$752$	2.04952	−	1.18329i	0.0747384	−	0.0431502i
$753$	12.4021			0.451957
$754$		0			0
$755$	−20.4174			−0.743066
$756$	−17.0894	+	9.86658i	−0.621536	+	0.358844i
$757$	−10.2168	−	17.6960i	−0.371335	−	0.643171i	0.618436	−	0.785835i	$-0.287767\pi$
$757$	−10.2168	−	17.6960i	−0.371335	−	0.643171i	−0.989771	+	0.142664i	$0.954433\pi$
$758$	−18.5809	+	32.1831i	−0.674889	+	1.16894i
$759$			2.67994i			0.0972757i
$760$	−17.2572	−	9.96346i	−0.625985	−	0.361413i
$761$	23.4032	+	13.5118i	0.848365	+	0.489804i	0.860099	−	0.510127i	$-0.170402\pi$
$761$	23.4032	+	13.5118i	0.848365	+	0.489804i	−0.0117336	+	0.999931i	$0.503735\pi$
$762$		−	23.6558i		−	0.856958i
$763$	−0.124982	+	0.216475i	−0.00452464	+	0.00783691i
$764$	28.0966	+	48.6648i	1.01650	+	1.76063i
$765$	−17.8414	+	10.3007i	−0.645057	+	0.372424i
$766$	16.9336			0.611837
$767$		0			0
$768$	5.80864			0.209601
$769$	32.8576	−	18.9703i	1.18487	−	0.684088i	0.227737	−	0.973723i	$-0.426867\pi$
$769$	32.8576	−	18.9703i	1.18487	−	0.684088i	0.957137	+	0.289635i	$0.0935339\pi$
$770$	8.49880	+	14.7204i	0.306276	+	0.530485i
$771$	5.17778	−	8.96818i	0.186473	−	0.322981i
$772$		−	18.4590i		−	0.664355i
$773$	−14.1487	−	8.16876i	−0.508894	−	0.293810i	0.223485	−	0.974707i	$-0.428257\pi$
$773$	−14.1487	−	8.16876i	−0.508894	−	0.293810i	−0.732379	+	0.680897i	$0.761590\pi$
$774$	−32.1491	−	18.5613i	−1.15558	−	0.667172i
$775$			12.4300i			0.446498i
$776$	14.0553	−	24.3444i	0.504554	−	0.873914i
$777$	−3.04556	−	5.27507i	−0.109259	−	0.189242i
$778$	−69.1890	+	39.9463i	−2.48055	+	1.43214i
$779$	7.45473			0.267093
$780$		0			0
$781$	11.7380			0.420017
$782$	19.4783	−	11.2458i	0.696541	−	0.402148i
$783$	−3.58330	−	6.20646i	−0.128057	−	0.221801i
$784$	1.12349	−	1.94594i	0.0401246	−	0.0694979i
$785$		−	13.6310i		−	0.486512i
$786$	3.51693	+	2.03050i	0.125445	+	0.0724255i
$787$	16.1866	+	9.34535i	0.576991	+	0.333126i	0.759936	−	0.649997i	$-0.225230\pi$
$787$	16.1866	+	9.34535i	0.576991	+	0.333126i	−0.182946	+	0.983123i	$0.558563\pi$
$788$		−	34.8049i		−	1.23987i
$789$	3.99545	−	6.92032i	0.142242	−	0.246370i
$790$	−25.6151	−	44.3666i	−0.911343	−	1.57849i
$791$	12.9674	−	7.48672i	0.461067	−	0.266197i
$792$	16.2107			0.576023
$793$		0			0
$794$	−3.03684			−0.107773
$795$	−3.83440	+	2.21379i	−0.135992	+	0.0785151i
$796$	21.1978	+	36.7157i	0.751337	+	1.30135i
$797$	14.6259	−	25.3329i	0.518077	−	0.897336i	−0.481702	−	0.876335i	$-0.659981\pi$
$797$	14.6259	−	25.3329i	0.518077	−	0.897336i	0.999779	−	0.0210013i	$-0.00668543\pi$
$798$			14.9487i			0.529178i
$799$	13.5348	+	7.81431i	0.478826	+	0.276451i
$800$	16.4310	+	9.48643i	0.580923	+	0.335396i
$801$		−	17.8039i		−	0.629068i
$802$	0.650637	−	1.12694i	0.0229748	−	0.0397935i
$803$	13.4807	+	23.3492i	0.475723	+	0.823976i
$804$	−0.845099	+	0.487918i	−0.0298044	+	0.0172076i
$805$	−5.59611			−0.197237
$806$		0			0
$807$	−0.362273			−0.0127526
$808$	26.6653	−	15.3952i	0.938082	−	0.541602i
$809$	3.32544	+	5.75983i	0.116916	+	0.202505i	0.918544	−	0.395319i	$-0.129366\pi$
$809$	3.32544	+	5.75983i	0.116916	+	0.202505i	−0.801628	+	0.597823i	$0.796032\pi$
$810$	10.2654	−	17.7802i	0.360689	−	0.624732i
$811$		−	3.89200i		−	0.136667i	−0.997663	−	0.0683333i	$-0.978232\pi$
$811$		−	3.89200i		−	0.136667i	0.997663	−	0.0683333i	$-0.0217681\pi$
$812$	12.2740	+	7.08642i	0.430734	+	0.248684i
$813$	−0.959143	−	0.553762i	−0.0336386	−	0.0194213i
$814$			30.7536i			1.07791i
$815$	6.28890	−	10.8927i	0.220290	−	0.381554i
$816$	−1.17845	−	2.04113i	−0.0412539	−	0.0714539i
$817$	−31.0964	+	17.9535i	−1.08793	+	0.628115i
$818$	−34.0586			−1.19083
$819$		0			0
$820$	−5.61356			−0.196034
$821$	−39.8356	+	22.9991i	−1.39027	+	0.802674i	−0.993345	−	0.115176i	$-0.963257\pi$
$821$	−39.8356	+	22.9991i	−1.39027	+	0.802674i	−0.396927	+	0.917850i	$0.629923\pi$
$822$	−0.493959	−	0.855562i	−0.0172288	−	0.0298412i
$823$	3.97650	−	6.88750i	0.138612	−	0.240083i	−0.788359	−	0.615215i	$-0.789069\pi$
$823$	3.97650	−	6.88750i	0.138612	−	0.240083i	0.926971	+	0.375132i	$0.122403\pi$
$824$			21.6093i			0.752794i
$825$	−3.57556	−	2.06435i	−0.124485	−	0.0718715i
$826$	−48.6732	−	28.1015i	−1.69356	−	0.977776i
$827$			27.9648i			0.972432i	0.873839	+	0.486216i	$0.161623\pi$
$827$			27.9648i			0.972432i	−0.873839	+	0.486216i	$0.838377\pi$
$828$	−7.75667	+	13.4349i	−0.269563	+	0.466897i
$829$	13.8155	+	23.9292i	0.479833	+	0.831094i	0.999732	−	0.0231329i	$-0.00736408\pi$
$829$	13.8155	+	23.9292i	0.479833	+	0.831094i	−0.519900	+	0.854227i	$0.674031\pi$
$830$	21.7182	−	12.5390i	0.753849	−	0.435235i
$831$	6.53989			0.226866
$832$		0			0
$833$	14.8388			0.514133
$834$	12.2456	−	7.07002i	0.424032	−	0.244815i
$835$	−17.2349	−	29.8517i	−0.596438	−	1.03306i
$836$	22.7887	−	39.4711i	0.788162	−	1.36514i
$837$			13.4843i			0.466085i
$838$	69.5158	+	40.1350i	2.40138	+	1.38644i
$839$	−24.8418	−	14.3424i	−0.857634	−	0.495155i	0.00558509	−	0.999984i	$-0.498222\pi$
$839$	−24.8418	−	14.3424i	−0.857634	−	0.495155i	−0.863219	+	0.504829i	$0.831556\pi$
$840$		−	3.87263i		−	0.133618i
$841$	11.9264	−	20.6571i	0.411255	−	0.712314i
$842$	39.3744	+	68.1985i	1.35693	+	2.35027i
$843$	3.11058	−	1.79590i	0.107134	−	0.0618540i
$844$	40.3817			1.38999
$845$		0			0
$846$	−17.8509			−0.613725
$847$	7.93552	−	4.58157i	0.272668	−	0.157425i
$848$	2.21379	+	3.83440i	0.0760219	+	0.131674i
$849$	−1.82610	+	3.16290i	−0.0626716	+	0.108550i
$850$			34.6504i			1.18850i
$851$	−8.76849	−	5.06249i	−0.300580	−	0.173540i
$852$	−6.73202	−	3.88673i	−0.230635	−	0.133157i
$853$		−	43.2078i		−	1.47941i	−0.672934	−	0.739703i	$-0.734966\pi$
$853$		−	43.2078i		−	1.47941i	0.672934	−	0.739703i	$-0.265034\pi$
$854$	19.7153	−	34.1479i	0.674643	−	1.16852i
$855$	−11.3802	−	19.7110i	−0.389193	−	0.674102i
$856$	14.0833	−	8.13102i	0.481359	−	0.277913i
$857$	−35.1685			−1.20133			−0.600667	−	0.799499i	$-0.705098\pi$
$857$	−35.1685			−1.20133			−0.600667	+	0.799499i	$0.705098\pi$
$858$		0			0
$859$	27.3793			0.934168			0.467084	−	0.884213i	$-0.345305\pi$
$859$	27.3793			0.934168			0.467084	+	0.884213i	$0.345305\pi$
$860$	23.4162	−	13.5194i	0.798487	−	0.461007i
$861$	0.724381	+	1.25467i	0.0246869	+	0.0427589i
$862$	38.5148	−	66.7096i	1.31182	−	2.27214i
$863$			41.3913i			1.40898i	0.709715	+	0.704489i	$0.248824\pi$
$863$			41.3913i			1.40898i	−0.709715	+	0.704489i	$0.751176\pi$
$864$	17.8246	+	10.2911i	0.606406	+	0.350109i
$865$	−23.5962	−	13.6233i	−0.802294	−	0.463204i
$866$		−	30.8702i		−	1.04901i
$867$	3.06518	−	5.30905i	0.104099	−	0.180305i
$868$	−13.3334	−	23.0941i	−0.452565	−	0.783866i
$869$	34.9108	−	20.1558i	1.18427	−	0.683738i
$870$	4.08815			0.138601
$871$		0			0
$872$	−0.287536			−0.00973721
$873$	27.8059	−	16.0538i	0.941088	−	0.543338i
$874$	12.4242	+	21.5194i	0.420256	+	0.727905i
$875$	11.7126	−	20.2868i	0.395958	−	0.685819i
$876$		−	17.8552i		−	0.603270i
$877$	−21.4317	−	12.3736i	−0.723696	−	0.417826i	0.0924153	−	0.995721i	$-0.470541\pi$
$877$	−21.4317	−	12.3736i	−0.723696	−	0.417826i	−0.816112	+	0.577894i	$0.803875\pi$
$878$	19.9270	+	11.5048i	0.672503	+	0.388270i
$879$			13.5066i			0.455567i
$880$	1.48039	−	2.56410i	0.0499038	−	0.0864359i
$881$	−14.2937	−	24.7575i	−0.481568	−	0.834101i	0.518208	−	0.855255i	$-0.326599\pi$
$881$	−14.2937	−	24.7575i	−0.481568	−	0.834101i	−0.999776	+	0.0211538i	$0.993266\pi$
$882$	−14.6780	+	8.47434i	−0.494234	+	0.285346i
$883$	−9.61702			−0.323639			−0.161819	−	0.986820i	$-0.551736\pi$
$883$	−9.61702			−0.323639			−0.161819	+	0.986820i	$0.551736\pi$
$884$		0			0
$885$	−9.78986			−0.329082
$886$	23.6944	−	13.6799i	0.796027	−	0.459587i
$887$	−7.98307	−	13.8271i	−0.268045	−	0.464268i	0.700312	−	0.713837i	$-0.253044\pi$
$887$	−7.98307	−	13.8271i	−0.268045	−	0.464268i	−0.968357	+	0.249569i	$0.919711\pi$
$888$	3.50335	−	6.06798i	0.117565	−	0.203628i
$889$			38.8689i			1.30362i
$890$	18.5971	+	10.7371i	0.623377	+	0.359907i
$891$	13.9907	+	8.07756i	0.468707	+	0.270608i
$892$		−	22.3642i		−	0.748809i
$893$	−8.63318	+	14.9531i	−0.288898	+	0.500387i
$894$	5.24094	+	9.07757i	0.175283	+	0.303599i
$895$	−7.53590	+	4.35086i	−0.251897	+	0.145433i
$896$	−33.3196			−1.11313
$897$		0			0
$898$	28.9976			0.967663
$899$	8.38722	−	4.84236i	0.279729	−	0.161502i
$900$	−11.9499	−	20.6978i	−0.398330	−	0.689927i
$901$	−14.6196	+	25.3219i	−0.487050	+	0.843595i
$902$		−	7.31468i		−	0.243552i
$903$	−6.04332	−	3.48911i	−0.201109	−	0.116110i
$904$	14.9165	+	8.61207i	0.496117	+	0.286433i
$905$			6.90408i			0.229500i
$906$	−8.80947	+	15.2585i	−0.292675	+	0.506928i
$907$	−14.4182	−	24.9730i	−0.478748	−	0.829216i	0.520955	−	0.853584i	$-0.325576\pi$
$907$	−14.4182	−	24.9730i	−0.478748	−	0.829216i	−0.999703	+	0.0243681i	$0.992243\pi$
$908$	−22.9047	+	13.2240i	−0.760118	+	0.438854i
$909$	35.1685			1.16647
$910$		0			0
$911$	38.5633			1.27766			0.638830	−	0.769348i	$-0.279419\pi$
$911$	38.5633			1.27766			0.638830	+	0.769348i	$0.279419\pi$
$912$	2.25502	−	1.30194i	0.0746713	−	0.0431115i
$913$	9.86658	+	17.0894i	0.326536	+	0.565577i
$914$	−5.23221	+	9.06245i	−0.173066	+	0.299759i
$915$		−	6.86831i		−	0.227059i
$916$	−36.1388	−	20.8647i	−1.19406	−	0.689390i
$917$	−5.77868	−	3.33632i	−0.190829	−	0.110175i
$918$			37.5894i			1.24064i
$919$	−4.43751	+	7.68599i	−0.146380	+	0.253537i	−0.929887	−	0.367845i	$-0.880096\pi$
$919$	−4.43751	+	7.68599i	−0.146380	+	0.253537i	0.783507	+	0.621383i	$0.213429\pi$
$920$	−3.21864	−	5.57484i	−0.106115	−	0.183797i
$921$	6.76392	−	3.90515i	0.222879	−	0.128679i
$922$	−70.8708			−2.33401
$923$		0			0
$924$	8.85756			0.291392
$925$	13.5087	−	7.79925i	0.444163	−	0.256438i
$926$	19.8300	+	34.3466i	0.651656	+	1.12870i
$927$	−12.3409	+	21.3751i	−0.405329	+	0.702051i
$928$		−	14.7826i		−	0.485261i
$929$	20.9834	+	12.1148i	0.688442	+	0.397472i	0.803028	−	0.595941i	$-0.203221\pi$
$929$	20.9834	+	12.1148i	0.688442	+	0.397472i	−0.114586	+	0.993413i	$0.536554\pi$
$930$	−6.66149	−	3.84601i	−0.218439	−	0.126116i
$931$			16.3937i			0.537283i
$932$	7.75667	−	13.4349i	0.254078	−	0.440076i
$933$	8.26055	+	14.3077i	0.270438	+	0.468413i
$934$	62.6059	−	36.1456i	2.04853	−	1.18272i
$935$	19.5526			0.639437
$936$		0			0
$937$	17.2644			0.564005			0.282002	−	0.959414i	$-0.409001\pi$
$937$	17.2644			0.564005			0.282002	+	0.959414i	$0.409001\pi$
$938$	2.29946	−	1.32759i	0.0750800	−	0.0433474i
$939$	−2.07524	−	3.59441i	−0.0677228	−	0.117299i
$940$	6.50096	−	11.2600i	0.212038	−	0.367260i
$941$		−	4.34050i		−	0.141496i	−0.997494	−	0.0707482i	$-0.977461\pi$
$941$		−	4.34050i		−	0.141496i	0.997494	−	0.0707482i	$-0.0225387\pi$
$942$	−10.1868	−	5.88135i	−0.331904	−	0.191625i
$943$	2.08557	+	1.20410i	0.0679154	+	0.0392110i
$944$			9.78986i			0.318633i
$945$	4.67629	−	8.09958i	0.152120	−	0.263479i
$946$	17.6163	+	30.5122i	0.572754	+	0.992039i
$947$	−38.9838	+	22.5073i	−1.26680	+	0.731389i	−0.974382	−	0.224901i	$-0.927794\pi$
$947$	−38.9838	+	22.5073i	−1.26680	+	0.731389i	−0.292421	+	0.956290i	$0.594461\pi$
$948$	−26.6963			−0.867057
$949$		0			0
$950$	−38.2814			−1.24201
$951$	14.4327	−	8.33273i	0.468013	−	0.270207i
$952$	−12.7872	−	22.1480i	−0.414434	−	0.717822i
$953$	−23.4429	+	40.6044i	−0.759391	+	1.31530i	0.183770	+	0.982969i	$0.441170\pi$
$953$	−23.4429	+	40.6044i	−0.759391	+	1.31530i	−0.943161	+	0.332335i	$0.892163\pi$
$954$		−	33.3967i		−	1.08126i
$955$	−23.0648	−	13.3165i	−0.746360	−	0.430911i
$956$	28.8440	+	16.6531i	0.932881	+	0.538599i
$957$			3.21685i			0.103986i
$958$	−39.2095	+	67.9129i	−1.26680	+	2.19417i
$959$	0.811626	+	1.40578i	0.0262088	+	0.0453949i
$960$	−9.05406	+	5.22737i	−0.292219	+	0.168712i
$961$	12.7778			0.412186
$962$		0			0
$963$	18.5743			0.598550
$964$	−31.4604	+	18.1637i	−1.01327	+	0.585013i
$965$	4.37435	+	7.57660i	0.140815	+	0.243900i
$966$	−2.41454	+	4.18211i	−0.0776866	+	0.134557i
$967$		−	6.29457i		−	0.202420i	−0.994865	−	0.101210i	$-0.967729\pi$
$967$		−	6.29457i		−	0.202420i	0.994865	−	0.101210i	$-0.0322714\pi$
$968$	9.12833	+	5.27024i	0.293396	+	0.169392i
$969$	14.8919	+	8.59783i	0.478396	+	0.276202i
$970$			38.7265i			1.24343i
$971$	20.9034	−	36.2058i	0.670823	−	1.16190i	−0.306848	−	0.951758i	$-0.599274\pi$
$971$	20.9034	−	36.2058i	0.670823	−	1.16190i	0.977671	−	0.210141i	$-0.0673922\pi$
$972$	−19.7959	−	34.2875i	−0.634954	−	1.09977i
$973$	−20.1209	+	11.6168i	−0.645045	+	0.372417i
$974$	94.0025			3.01203
$975$		0			0
$976$	−6.86831			−0.219849
$977$	−20.5707	+	11.8765i	−0.658116	+	0.379963i	−0.791559	−	0.611093i	$-0.790730\pi$
$977$	−20.5707	+	11.8765i	−0.658116	+	0.379963i	0.133443	+	0.991056i	$0.457397\pi$
$978$	−5.42692	−	9.39970i	−0.173534	−	0.300569i
$979$	−8.44869	+	14.6336i	−0.270021	+	0.467691i
$980$		−	12.3448i		−	0.394341i
$981$	−0.284421	−	0.164210i	−0.00908086	−	0.00524284i
$982$	42.5100	+	24.5432i	1.35655	+	0.783204i
$983$		−	55.7251i		−	1.77736i	−0.458532	−	0.888678i	$-0.651625\pi$
$983$		−	55.7251i		−	1.77736i	0.458532	−	0.888678i	$-0.348375\pi$
$984$	−0.833265	+	1.44326i	−0.0265635	+	0.0460094i
$985$	8.24794	+	14.2858i	0.262801	+	0.455185i
$986$	23.3806	−	13.4988i	0.744590	−	0.429889i
$987$	−3.35557			−0.106809
$988$		0			0
$989$	−11.5996			−0.368845
$990$	−19.3407	+	11.1664i	−0.614688	+	0.354890i
$991$	17.7756	+	30.7883i	0.564661	+	0.978022i	0.997081	+	0.0763495i	$0.0243265\pi$
$991$	17.7756	+	30.7883i	0.564661	+	0.978022i	−0.432420	+	0.901672i	$0.642340\pi$
$992$	−13.9070	+	24.0876i	−0.441548	+	0.764784i
$993$		−	8.72215i		−	0.276789i
$994$	18.3174	+	10.5755i	0.580991	+	0.335436i
$995$	−17.4015	−	10.0468i	−0.551665	−	0.318504i
$996$		−	13.0683i		−	0.414085i
$997$	−3.30529	+	5.72493i	−0.104680	+	0.181310i	−0.913607	−	0.406598i	$-0.866715\pi$
$997$	−3.30529	+	5.72493i	−0.104680	+	0.181310i	0.808928	+	0.587908i	$0.200048\pi$
$998$	−26.4550	−	45.8214i	−0.837419	−	1.45045i
$999$	14.6545	−	8.46077i	0.463647	−	0.267687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.e.b.23.6		12
13.2	odd	12		169.2.a.c.1.3	yes	3
13.3	even	3		169.2.b.b.168.6		6
13.4	even	6	inner	169.2.e.b.147.6		12
13.5	odd	4		169.2.c.b.146.1		6
13.6	odd	12		169.2.c.b.22.1		6
13.7	odd	12		169.2.c.c.22.3		6
13.8	odd	4		169.2.c.c.146.3		6
13.9	even	3	inner	169.2.e.b.147.1		12
13.10	even	6		169.2.b.b.168.1		6
13.11	odd	12		169.2.a.b.1.1	✓	3
13.12	even	2	inner	169.2.e.b.23.1		12
39.2	even	12		1521.2.a.o.1.1		3
39.11	even	12		1521.2.a.r.1.3		3
39.23	odd	6		1521.2.b.l.1351.6		6
39.29	odd	6		1521.2.b.l.1351.1		6
52.3	odd	6		2704.2.f.o.337.4		6
52.11	even	12		2704.2.a.z.1.2		3
52.15	even	12		2704.2.a.ba.1.2		3
52.23	odd	6		2704.2.f.o.337.3		6
65.24	odd	12		4225.2.a.bg.1.3		3
65.54	odd	12		4225.2.a.bb.1.1		3
91.41	even	12		8281.2.a.bj.1.3		3
91.76	even	12		8281.2.a.bf.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.a.b.1.1	✓	3	13.11	odd	12
169.2.a.c.1.3	yes	3	13.2	odd	12
169.2.b.b.168.1		6	13.10	even	6
169.2.b.b.168.6		6	13.3	even	3
169.2.c.b.22.1		6	13.6	odd	12
169.2.c.b.146.1		6	13.5	odd	4
169.2.c.c.22.3		6	13.7	odd	12
169.2.c.c.146.3		6	13.8	odd	4
169.2.e.b.23.1		12	13.12	even	2	inner
169.2.e.b.23.6		12	1.1	even	1	trivial
169.2.e.b.147.1		12	13.9	even	3	inner
169.2.e.b.147.6		12	13.4	even	6	inner
1521.2.a.o.1.1		3	39.2	even	12
1521.2.a.r.1.3		3	39.11	even	12
1521.2.b.l.1351.1		6	39.29	odd	6
1521.2.b.l.1351.6		6	39.23	odd	6
2704.2.a.z.1.2		3	52.11	even	12
2704.2.a.ba.1.2		3	52.15	even	12
2704.2.f.o.337.3		6	52.23	odd	6
2704.2.f.o.337.4		6	52.3	odd	6
4225.2.a.bb.1.1		3	65.54	odd	12
4225.2.a.bg.1.3		3	65.24	odd	12
8281.2.a.bf.1.1		3	91.76	even	12
8281.2.a.bj.1.3		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)

\(f(q)\)	\(=\)	\(q+(1.94594 - 1.12349i) q^{2} +(0.277479 + 0.480608i) q^{3} +(1.52446 - 2.64044i) q^{4} +1.44504i q^{5} +(1.07992 + 0.623490i) q^{6} +(-1.77441 - 1.02446i) q^{7} -2.35690i q^{8} +(1.34601 - 2.33136i) q^{9} +O(q^{10})\)	\(q+(1.94594 - 1.12349i) q^{2} +(0.277479 + 0.480608i) q^{3} +(1.52446 - 2.64044i) q^{4} +1.44504i q^{5} +(1.07992 + 0.623490i) q^{6} +(-1.77441 - 1.02446i) q^{7} -2.35690i q^{8} +(1.34601 - 2.33136i) q^{9} +(1.62349 + 2.81197i) q^{10} +(-2.21266 + 1.27748i) q^{11} +1.69202 q^{12} -4.60388 q^{14} +(-0.694498 + 0.400969i) q^{15} +(0.400969 + 0.694498i) q^{16} +(-2.64795 + 4.58638i) q^{17} -6.04892i q^{18} +(-5.06699 - 2.92543i) q^{19} +(3.81555 + 2.20291i) q^{20} -1.13706i q^{21} +(-2.87047 + 4.97180i) q^{22} +(-0.945042 - 1.63686i) q^{23} +(1.13274 - 0.653989i) q^{24} +2.91185 q^{25} +3.15883 q^{27} +(-5.41004 + 3.12349i) q^{28} +(-1.13437 - 1.96480i) q^{29} +(-0.900969 + 1.56052i) q^{30} +4.26875i q^{31} +(5.64279 + 3.25786i) q^{32} +(-1.22793 - 0.708947i) q^{33} +11.8998i q^{34} +(1.48039 - 2.56410i) q^{35} +(-4.10388 - 7.10812i) q^{36} +(4.63921 - 2.67845i) q^{37} -13.1468 q^{38} +3.40581 q^{40} +(-1.10343 + 0.637063i) q^{41} +(-1.27748 - 2.21266i) q^{42} +(3.06853 - 5.31485i) q^{43} +7.78986i q^{44} +(3.36891 + 1.94504i) q^{45} +(-3.67799 - 2.12349i) q^{46} -2.95108i q^{47} +(-0.222521 + 0.385418i) q^{48} +(-1.40097 - 2.42655i) q^{49} +(5.66630 - 3.27144i) q^{50} -2.93900 q^{51} +5.52111 q^{53} +(6.14691 - 3.54892i) q^{54} +(-1.84601 - 3.19738i) q^{55} +(-2.41454 + 4.18211i) q^{56} -3.24698i q^{57} +(-4.41485 - 2.54892i) q^{58} +(10.5722 + 6.10388i) q^{59} +2.44504i q^{60} +(-4.28232 + 7.41720i) q^{61} +(4.79590 + 8.30674i) q^{62} +(-4.77676 + 2.75786i) q^{63} +13.0368 q^{64} -3.18598 q^{66} +(-0.499461 + 0.288364i) q^{67} +(8.07338 + 13.9835i) q^{68} +(0.524459 - 0.908389i) q^{69} -6.65279i q^{70} +(-3.97868 - 2.29709i) q^{71} +(-5.49477 - 3.17241i) q^{72} -10.5526i q^{73} +(6.01842 - 10.4242i) q^{74} +(0.807979 + 1.39946i) q^{75} +(-15.4488 + 8.91939i) q^{76} +5.23490 q^{77} -15.7778 q^{79} +(-1.00358 + 0.579417i) q^{80} +(-3.16152 - 5.47592i) q^{81} +(-1.43147 + 2.47938i) q^{82} -7.72348i q^{83} +(-3.00235 - 1.73341i) q^{84} +(-6.62751 - 3.82640i) q^{85} -13.7899i q^{86} +(0.629531 - 1.09038i) q^{87} +(3.01089 + 5.21501i) q^{88} +(5.72751 - 3.30678i) q^{89} +8.74094 q^{90} -5.76271 q^{92} +(-2.05159 + 1.18449i) q^{93} +(-3.31551 - 5.74263i) q^{94} +(4.22737 - 7.32201i) q^{95} +3.61596i q^{96} +(10.3290 + 5.96346i) q^{97} +(-5.45241 - 3.14795i) q^{98} +6.87800i 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more