LMFDB - Embedded newform 56.2.m.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,2,Mod(3,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("56.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$56 = 2^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	56.m (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.447162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4$ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Root			$1.09935 - 0.468876i$ of defining polynomial
Character	$\chi$	$=$	56.19
Dual form			56.2.m.a.3.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13090 + 0.849154i) q^{2} +(-2.27230 + 1.31191i) q^{3} +(0.557875 + 1.92062i) q^{4} +(1.03926 - 1.80005i) q^{5} +(-3.68377 - 0.445890i) q^{6} +(1.25203 - 2.33076i) q^{7} +(-1.00000 + 2.64575i) q^{8} +(1.94224 - 3.36406i) q^{9} +(2.70382 - 1.15319i) q^{10} +(-0.669938 - 1.16037i) q^{11} +(-3.78735 - 3.63234i) q^{12} -2.50406 q^{13} +(3.39509 - 1.57269i) q^{14} +5.45368i q^{15} +(-3.37755 + 2.14293i) q^{16} +(-2.78212 + 1.60626i) q^{17} +(5.05309 - 2.15516i) q^{18} +(3.55442 + 2.05215i) q^{19} +(4.03699 + 0.991819i) q^{20} +(0.212768 + 6.93874i) q^{21} +(0.227697 - 1.88114i) q^{22} +(-5.54952 - 3.20402i) q^{23} +(-1.19870 - 7.32386i) q^{24} +(0.339877 + 0.588684i) q^{25} +(-2.83184 - 2.12633i) q^{26} +2.32073i q^{27} +(5.17497 + 1.10440i) q^{28} -4.66151i q^{29} +(-4.63102 + 6.16758i) q^{30} +(2.21897 + 3.84337i) q^{31} +(-5.63935 - 0.444621i) q^{32} +(3.04461 + 1.75780i) q^{33} +(-4.51026 - 0.545930i) q^{34} +(-2.89430 - 4.67598i) q^{35} +(7.54461 + 1.85358i) q^{36} +(5.50178 + 3.17646i) q^{37} +(2.27711 + 5.33903i) q^{38} +(5.68997 - 3.28511i) q^{39} +(3.72323 + 4.54968i) q^{40} +5.55076i q^{41} +(-5.65144 + 8.02770i) q^{42} +(1.85488 - 1.93404i) q^{44} +(-4.03699 - 6.99227i) q^{45} +(-3.55526 - 8.33583i) q^{46} +(-0.565988 + 0.980320i) q^{47} +(4.86348 - 9.30045i) q^{48} +(-3.86485 - 5.83634i) q^{49} +(-0.115516 + 0.954351i) q^{50} +(4.21455 - 7.29981i) q^{51} +(-1.39695 - 4.80934i) q^{52} +(-7.43567 + 4.29299i) q^{53} +(-1.97066 + 2.62452i) q^{54} -2.78496 q^{55} +(4.91457 + 5.64331i) q^{56} -10.7690 q^{57} +(3.95834 - 5.27171i) q^{58} +(6.29193 - 3.63265i) q^{59} +(-10.4744 + 3.04247i) q^{60} +(2.57219 - 4.45517i) q^{61} +(-0.754178 + 6.23073i) q^{62} +(-5.40907 - 8.73879i) q^{63} +(-6.00000 - 5.29150i) q^{64} +(-2.60236 + 4.50743i) q^{65} +(1.95050 + 4.57324i) q^{66} +(3.93243 + 6.81116i) q^{67} +(-4.63708 - 4.44730i) q^{68} +16.8136 q^{69} +(0.697459 - 7.74577i) q^{70} -5.29150i q^{71} +(6.95823 + 8.50275i) q^{72} +(0.480369 - 0.277341i) q^{73} +(3.52467 + 8.26412i) q^{74} +(-1.54461 - 0.891779i) q^{75} +(-1.95847 + 7.97153i) q^{76} +(-3.54332 + 0.108651i) q^{77} +(9.22436 + 1.11653i) q^{78} +(5.26862 + 3.04184i) q^{79} +(0.347228 + 8.30683i) q^{80} +(2.78212 + 4.81877i) q^{81} +(-4.71345 + 6.27736i) q^{82} -0.503175i q^{83} +(-13.2080 + 4.27959i) q^{84} +6.67728i q^{85} +(6.11551 + 10.5924i) q^{87} +(3.73998 - 0.612123i) q^{88} +(1.50000 + 0.866025i) q^{89} +(1.37208 - 11.3356i) q^{90} +(-3.13515 + 5.83634i) q^{91} +(3.05776 - 12.4460i) q^{92} +(-10.0844 - 5.82221i) q^{93} +(-1.47252 + 0.628034i) q^{94} +(7.38794 - 4.26543i) q^{95} +(13.3976 - 6.38804i) q^{96} -17.2234i q^{97} +(0.585189 - 9.88218i) q^{98} -5.20473 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 6 q^{3} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 18 q^{12} + 6 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 24 q^{22} + 6 q^{24} + 6 q^{26} + 6 q^{28} - 12 q^{30} - 6 q^{33} + 18 q^{35} + 48 q^{36} - 24 q^{38}+ \cdots - 24 q^{99}+O(q^{100})$ 12 * q - 6 * q^3 - 12 * q^8 + 6 * q^10 - 6 * q^11 - 18 * q^12 + 6 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 24 * q^22 + 6 * q^24 + 6 * q^26 + 6 * q^28 - 12 * q^30 - 6 * q^33 + 18 * q^35 + 48 * q^36 - 24 * q^38 + 42 * q^40 - 30 * q^42 + 6 * q^44 - 18 * q^46 - 12 * q^49 - 48 * q^50 + 6 * q^51 - 24 * q^52 - 36 * q^54 - 36 * q^57 + 18 * q^58 + 42 * q^59 - 6 * q^60 - 72 * q^64 - 12 * q^65 + 12 * q^66 + 30 * q^67 - 36 * q^68 + 30 * q^70 + 18 * q^73 + 12 * q^74 + 24 * q^75 + 60 * q^78 + 36 * q^80 + 6 * q^81 + 54 * q^82 + 12 * q^84 + 6 * q^88 + 18 * q^89 - 72 * q^91 + 60 * q^92 - 12 * q^94 + 60 * q^96 - 6 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$ .

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	1.13090	+	0.849154i	0.799668	+	0.600443i
$2$	1.13090	+	0.849154i	0.799668	+	0.600443i
$3$	−2.27230	+	1.31191i	−1.31191	+	0.757434i	−0.982413	−	0.186720i	$-0.940214\pi$
$3$	−2.27230	+	1.31191i	−1.31191	+	0.757434i	−0.329502	+	0.944155i	$0.606881\pi$
$4$	0.557875	+	1.92062i	0.278937	+	0.960309i
$5$	1.03926	−	1.80005i	0.464771	−	0.805007i	−0.534420	−	0.845219i	$-0.679470\pi$
$5$	1.03926	−	1.80005i	0.464771	−	0.805007i	0.999191	+	0.0402117i	$0.0128032\pi$
$6$	−3.68377	−	0.445890i	−1.50389	−	0.182034i
$7$	1.25203	−	2.33076i	0.473222	−	0.880943i
$7$	1.25203	−	2.33076i	0.473222	−	0.880943i
$8$	−1.00000	+	2.64575i	−0.353553	+	0.935414i
$9$	1.94224	−	3.36406i	0.647414	−	1.12135i
$10$	2.70382	−	1.15319i	0.855023	−	0.364670i
$11$	−0.669938	−	1.16037i	−0.201994	−	0.349864i	0.747177	−	0.664625i	$-0.231409\pi$
$11$	−0.669938	−	1.16037i	−0.201994	−	0.349864i	−0.949171	+	0.314761i	$0.898075\pi$
$12$	−3.78735	−	3.63234i	−1.09331	−	1.04857i
$13$	−2.50406			−0.694500			−0.347250	−	0.937773i	$-0.612884\pi$
$13$	−2.50406			−0.694500			−0.347250	+	0.937773i	$0.612884\pi$
$14$	3.39509	−	1.57269i	0.907376	−	0.420319i
$15$			5.45368i			1.40814i
$16$	−3.37755	+	2.14293i	−0.844388	+	0.535732i
$17$	−2.78212	+	1.60626i	−0.674763	+	0.389575i	−0.797879	−	0.602818i	$-0.794045\pi$
$17$	−2.78212	+	1.60626i	−0.674763	+	0.389575i	0.123116	+	0.992392i	$0.460711\pi$
$18$	5.05309	−	2.15516i	1.19102	−	0.507976i
$19$	3.55442	+	2.05215i	0.815440	+	0.470795i	0.848842	−	0.528647i	$-0.177301\pi$
$19$	3.55442	+	2.05215i	0.815440	+	0.470795i	−0.0334012	+	0.999442i	$0.510634\pi$
$20$	4.03699	+	0.991819i	0.902698	+	0.221778i
$21$	0.212768	+	6.93874i	0.0464297	+	1.51416i
$22$	0.227697	−	1.88114i	0.0485451	−	0.401061i
$23$	−5.54952	−	3.20402i	−1.15716	−	0.668084i	−0.206535	−	0.978439i	$-0.566219\pi$
$23$	−5.54952	−	3.20402i	−1.15716	−	0.668084i	−0.950621	+	0.310355i	$0.899552\pi$
$24$	−1.19870	−	7.32386i	−0.244683	−	1.49498i
$25$	0.339877	+	0.588684i	0.0679754	+	0.117737i
$26$	−2.83184	−	2.12633i	−0.555369	−	0.417007i
$27$			2.32073i			0.446626i
$28$	5.17497	+	1.10440i	0.977977	+	0.208712i
$29$		−	4.66151i		−	0.865621i	−0.901485	−	0.432811i	$-0.857522\pi$
$29$		−	4.66151i		−	0.865621i	0.901485	−	0.432811i	$-0.142478\pi$
$30$	−4.63102	+	6.16758i	−0.845504	+	1.12604i
$31$	2.21897	+	3.84337i	0.398539	+	0.690290i	0.993546	−	0.113430i	$-0.0361839\pi$
$31$	2.21897	+	3.84337i	0.398539	+	0.690290i	−0.595007	+	0.803721i	$0.702851\pi$
$32$	−5.63935	−	0.444621i	−0.996906	−	0.0785986i
$33$	3.04461	+	1.75780i	0.529998	+	0.305994i
$34$	−4.51026	−	0.545930i	−0.773503	−	0.0936262i
$35$	−2.89430	−	4.67598i	−0.489226	−	0.790384i
$36$	7.54461	+	1.85358i	1.25743	+	0.308930i
$37$	5.50178	+	3.17646i	0.904488	+	0.522206i	0.878653	−	0.477460i	$-0.158442\pi$
$37$	5.50178	+	3.17646i	0.904488	+	0.522206i	0.0258343	+	0.999666i	$0.491776\pi$
$38$	2.27711	+	5.33903i	0.369396	+	0.866105i
$39$	5.68997	−	3.28511i	0.911125	−	0.526038i
$40$	3.72323	+	4.54968i	0.588694	+	0.719367i
$41$			5.55076i			0.866882i	0.901182	+	0.433441i	$0.142701\pi$
$41$			5.55076i			0.866882i	−0.901182	+	0.433441i	$0.857299\pi$
$42$	−5.65144	+	8.02770i	−0.872036	+	1.23870i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	1.85488	−	1.93404i	0.279634	−	0.291567i
$45$	−4.03699	−	6.99227i	−0.601799	−	1.04235i
$46$	−3.55526	−	8.33583i	−0.524194	−	1.22905i
$47$	−0.565988	+	0.980320i	−0.0825579	+	0.142994i	−0.904348	−	0.426796i	$-0.859642\pi$
$47$	−0.565988	+	0.980320i	−0.0825579	+	0.142994i	0.821790	+	0.569790i	$0.192976\pi$
$48$	4.86348	−	9.30045i	0.701983	−	1.34240i
$49$	−3.86485	−	5.83634i	−0.552122	−	0.833763i
$50$	−0.115516	+	0.954351i	−0.0163365	+	0.134966i
$51$	4.21455	−	7.29981i	0.590154	−	1.02218i
$52$	−1.39695	−	4.80934i	−0.193722	−	0.666935i
$53$	−7.43567	+	4.29299i	−1.02137	+	0.589687i	−0.914500	−	0.404586i	$-0.867416\pi$
$53$	−7.43567	+	4.29299i	−1.02137	+	0.589687i	−0.106868	+	0.994273i	$0.534082\pi$
$54$	−1.97066	+	2.62452i	−0.268173	+	0.357152i
$55$	−2.78496			−0.375524
$56$	4.91457	+	5.64331i	0.656738	+	0.754119i
$57$	−10.7690			−1.42638
$58$	3.95834	−	5.27171i	0.519756	−	0.692210i
$59$	6.29193	−	3.63265i	0.819140	−	0.472931i	−0.0309798	−	0.999520i	$-0.509863\pi$
$59$	6.29193	−	3.63265i	0.819140	−	0.472931i	0.850120	+	0.526589i	$0.176529\pi$
$60$	−10.4744	+	3.04247i	−1.35225	+	0.392781i
$61$	2.57219	−	4.45517i	0.329336	−	0.570426i	−0.653045	−	0.757319i	$-0.726509\pi$
$61$	2.57219	−	4.45517i	0.329336	−	0.570426i	0.982380	+	0.186893i	$0.0598419\pi$
$62$	−0.754178	+	6.23073i	−0.0957807	+	0.791303i
$63$	−5.40907	−	8.73879i	−0.681479	−	1.10098i
$64$	−6.00000	−	5.29150i	−0.750000	−	0.661438i
$65$	−2.60236	+	4.50743i	−0.322784	+	0.559078i
$66$	1.95050	+	4.57324i	0.240090	+	0.562927i
$67$	3.93243	+	6.81116i	0.480422	+	0.832116i	0.999748	−	0.0224607i	$-0.00715005\pi$
$67$	3.93243	+	6.81116i	0.480422	+	0.832116i	−0.519325	+	0.854577i	$0.673817\pi$
$68$	−4.63708	−	4.44730i	−0.562329	−	0.539314i
$69$	16.8136			2.02412
$70$	0.697459	−	7.74577i	0.0833622	−	0.925797i
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$	6.95823	+	8.50275i	0.820035	+	1.00206i
$73$	0.480369	−	0.277341i	0.0562230	−	0.0324604i	−0.471625	−	0.881799i	$-0.656332\pi$
$73$	0.480369	−	0.277341i	0.0562230	−	0.0324604i	0.527848	+	0.849339i	$0.322999\pi$
$74$	3.52467	+	8.26412i	0.409735	+	0.960685i
$75$	−1.54461	−	0.891779i	−0.178356	−	0.102974i
$76$	−1.95847	+	7.97153i	−0.224652	+	0.914397i
$77$	−3.54332	+	0.108651i	−0.403798	+	0.0123820i
$78$	9.22436	+	1.11653i	1.04445	+	0.126422i
$79$	5.26862	+	3.04184i	0.592766	+	0.342233i	0.766190	−	0.642614i	$-0.222150\pi$
$79$	5.26862	+	3.04184i	0.592766	+	0.342233i	−0.173425	+	0.984847i	$0.555483\pi$
$80$	0.347228	+	8.30683i	0.0388212	+	0.928731i
$81$	2.78212	+	4.81877i	0.309124	+	0.535419i
$82$	−4.71345	+	6.27736i	−0.520513	+	0.693218i
$83$		−	0.503175i		−	0.0552307i	−0.999619	−	0.0276153i	$-0.991209\pi$
$83$		−	0.503175i		−	0.0552307i	0.999619	−	0.0276153i	$-0.00879135\pi$
$84$	−13.2080	+	4.27959i	−1.44111	+	0.466942i
$85$			6.67728i			0.724252i
$86$		0			0
$87$	6.11551	+	10.5924i	0.655651	+	1.13562i
$88$	3.73998	−	0.612123i	0.398683	−	0.0652525i
$89$	1.50000	+	0.866025i	0.159000	+	0.0917985i	0.577389	−	0.816469i	$-0.304072\pi$
$89$	1.50000	+	0.866025i	0.159000	+	0.0917985i	−0.418389	+	0.908268i	$0.637405\pi$
$90$	1.37208	−	11.3356i	0.144630	−	1.19488i
$91$	−3.13515	+	5.83634i	−0.328653	+	0.611815i
$92$	3.05776	−	12.4460i	0.318793	−	1.29758i
$93$	−10.0844	−	5.82221i	−1.04570	−	0.603735i
$94$	−1.47252	+	0.628034i	−0.151879	+	0.0647768i
$95$	7.38794	−	4.26543i	0.757986	−	0.437624i
$96$	13.3976	−	6.38804i	1.36739	−	0.651977i
$97$		−	17.2234i		−	1.74878i	−0.485228	−	0.874388i	$-0.661263\pi$
$97$		−	17.2234i		−	1.74878i	0.485228	−	0.874388i	$-0.338737\pi$
$98$	0.585189	−	9.88218i	0.0591130	−	0.998251i
$99$	−5.20473			−0.523095
$100$	−0.941029	+	0.981186i	−0.0941029	+	0.0981186i
$101$	−0.613725	−	1.06300i	−0.0610679	−	0.105773i	0.833875	−	0.551953i	$-0.186117\pi$
$101$	−0.613725	−	1.06300i	−0.0610679	−	0.105773i	−0.894943	+	0.446180i	$0.852784\pi$
$102$	10.9649	−	4.67656i	1.08569	−	0.463049i
$103$	−7.62804	+	13.2122i	−0.751613	+	1.30183i	0.195427	+	0.980718i	$0.437391\pi$
$103$	−7.62804	+	13.2122i	−0.751613	+	1.30183i	−0.947041	+	0.321114i	$0.895943\pi$
$104$	2.50406	−	6.62511i	0.245543	−	0.649645i
$105$	12.7112	+	6.82816i	1.24049	+	0.666360i
$106$	−12.0544	−	1.45909i	−1.17083	−	0.141719i
$107$	−5.55442	+	9.62054i	−0.536966	+	0.930053i	0.462099	+	0.886828i	$0.347096\pi$
$107$	−5.55442	+	9.62054i	−0.536966	+	0.930053i	−0.999065	+	0.0432246i	$0.986237\pi$
$108$	−4.45725	+	1.29468i	−0.428899	+	0.124581i
$109$	−10.9109	+	6.29938i	−1.04507	+	0.603372i	−0.921265	−	0.388935i	$-0.872843\pi$
$109$	−10.9109	+	6.29938i	−1.04507	+	0.603372i	−0.123805	+	0.992307i	$0.539510\pi$
$110$	−3.14952	−	2.36486i	−0.300295	−	0.225481i
$111$	−16.6690			−1.58215
$112$	0.765858	+	10.5553i	0.0723668	+	0.997378i
$113$	20.0629			1.88736			0.943680	−	0.330860i	$-0.107339\pi$
$113$	20.0629			1.88736			0.943680	+	0.330860i	$0.107339\pi$
$114$	−12.1786	−	9.14451i	−1.14063	−	0.856462i
$115$	−11.5348	+	6.65961i	−1.07562	+	0.621012i
$116$	8.95299	−	2.60054i	0.831264	−	0.241454i
$117$	−4.86348	+	8.42380i	−0.449629	+	0.778780i
$118$	10.2002	+	1.23465i	0.939008	+	0.113659i
$119$	0.260504	+	8.49552i	0.0238804	+	0.778783i
$120$	−14.4291	−	5.45368i	−1.31719	−	0.497851i
$121$	4.60236	−	7.97153i	0.418397	−	0.724685i
$122$	6.69202	−	2.85417i	0.605867	−	0.258404i
$123$	−7.28212	−	12.6130i	−0.656607	−	1.13728i
$124$	−6.14375	+	6.40592i	−0.551725	+	0.575269i
$125$	11.8055			1.05591
$126$	1.30346	−	14.4758i	0.116121	−	1.28961i
$127$		−	14.6145i		−	1.29683i	−0.761287	−	0.648415i	$-0.775432\pi$
$127$		−	14.6145i		−	1.29683i	0.761287	−	0.648415i	$-0.224568\pi$
$128$	−2.29211	−	11.0791i	−0.202595	−	0.979263i
$129$		0			0
$130$	−6.77052	+	2.88765i	−0.593814	+	0.253263i
$131$	−5.27230	−	3.04397i	−0.460643	−	0.265953i	0.251671	−	0.967813i	$-0.419020\pi$
$131$	−5.27230	−	3.04397i	−0.460643	−	0.265953i	−0.712315	+	0.701860i	$0.752353\pi$
$132$	−1.67756	+	6.82816i	−0.146013	+	0.594315i
$133$	9.23329	−	5.71515i	0.800628	−	0.495566i
$134$	−1.33654	+	11.0420i	−0.115460	+	0.953882i
$135$	4.17744	+	2.41185i	0.359537	+	0.207579i
$136$	−1.46764	−	8.96705i	−0.125849	−	0.768918i
$137$	−6.98685	−	12.1016i	−0.596927	−	1.03391i	−0.993272	−	0.115806i	$-0.963055\pi$
$137$	−6.98685	−	12.1016i	−0.596927	−	1.03391i	0.396345	−	0.918102i	$-0.370278\pi$
$138$	19.0145	+	14.2773i	1.61862	+	1.21537i
$139$			0.503175i			0.0426788i	0.999772	+	0.0213394i	$0.00679305\pi$
$139$			0.503175i			0.0426788i	−0.999772	+	0.0213394i	$0.993207\pi$
$140$	7.36611	−	8.16745i	0.622550	−	0.690276i
$141$		−	2.97011i		−	0.250129i
$142$	4.49330	−	5.98417i	0.377069	−	0.502180i
$143$	1.67756	+	2.90562i	0.140285	+	0.242981i
$144$	0.648923	+	15.5244i	0.0540769	+	1.29370i
$145$	−8.39096	−	4.84452i	−0.696832	−	0.402316i
$146$	0.778756	+	0.0942619i	0.0644503	+	0.00780117i
$147$	16.4389	+	8.19159i	1.35586	+	0.675631i
$148$	−3.03146	+	12.3389i	−0.249184	+	1.01425i
$149$	4.77077	+	2.75440i	0.390836	+	0.225649i	0.682522	−	0.730865i	$-0.260883\pi$
$149$	4.77077	+	2.75440i	0.390836	+	0.225649i	−0.291686	+	0.956514i	$0.594216\pi$
$150$	−0.989540	−	2.32012i	−0.0807956	−	0.189437i
$151$	6.09511	−	3.51901i	0.496013	−	0.286373i	−0.231053	−	0.972941i	$-0.574217\pi$
$151$	6.09511	−	3.51901i	0.496013	−	0.286373i	0.727066	+	0.686568i	$0.240884\pi$
$152$	−8.98389	+	7.35197i	−0.728690	+	0.596324i
$153$			12.4790i			1.00886i
$154$	−4.09940	−	2.88595i	−0.330339	−	0.232556i
$155$	9.22436			0.740918
$156$	9.48373	+	9.09559i	0.759306	+	0.728230i
$157$	−7.15477	−	12.3924i	−0.571013	−	0.989023i	−0.996462	−	0.0840409i	$-0.973217\pi$
$157$	−7.15477	−	12.3924i	−0.571013	−	0.989023i	0.425450	−	0.904982i	$-0.360116\pi$
$158$	3.37530	+	7.91388i	0.268524	+	0.629595i
$159$	11.2641	−	19.5099i	0.893299	−	1.54724i
$160$	−6.66110	+	9.68905i	−0.526606	+	0.765987i
$161$	−14.4159	+	8.92306i	−1.13614	+	0.703236i
$162$	−0.945578	+	7.81200i	−0.0742916	+	0.613769i
$163$	−4.15679	+	7.19977i	−0.325585	+	0.563929i	−0.981631	−	0.190792i	$-0.938894\pi$
$163$	−4.15679	+	7.19977i	−0.325585	+	0.563929i	0.656046	+	0.754721i	$0.272228\pi$
$164$	−10.6609	+	3.09663i	−0.832475	+	0.241806i
$165$	6.32828	−	3.65363i	0.492656	−	0.284435i
$166$	0.427273	−	0.569041i	0.0331628	−	0.0441662i
$167$	−2.50406			−0.193770			−0.0968848	−	0.995296i	$-0.530888\pi$
$167$	−2.50406			−0.193770			−0.0968848	+	0.995296i	$0.530888\pi$
$168$	−18.5709	−	6.37581i	−1.43278	−	0.491904i
$169$	−6.72971			−0.517670
$170$	−5.67004	+	7.55134i	−0.434872	+	0.579161i
$171$	13.8071	−	7.97153i	1.05585	−	0.609598i
$172$		0			0
$173$	2.71682	−	4.70568i	0.206556	−	0.357766i	−0.744071	−	0.668100i	$-0.767108\pi$
$173$	2.71682	−	4.70568i	0.206556	−	0.357766i	0.950627	+	0.310334i	$0.100441\pi$
$174$	−2.07852	+	17.1719i	−0.157572	+	1.30180i
$175$	1.79761	−	0.0551216i	0.135887	−	0.00416680i
$176$	4.74934	+	2.48357i	0.357995	+	0.187206i
$177$	−9.53146	+	16.5090i	−0.716428	+	1.24089i
$178$	0.960963	+	2.25312i	0.0720272	+	0.168879i
$179$	−1.75915	−	3.04694i	−0.131485	−	0.227739i	0.792764	−	0.609529i	$-0.208641\pi$
$179$	−1.75915	−	3.04694i	−0.131485	−	0.227739i	−0.924249	+	0.381790i	$0.875308\pi$
$180$	11.1773	−	11.6543i	0.833110	−	0.868662i
$181$	−22.1981			−1.64997			−0.824985	−	0.565154i	$-0.808817\pi$
$181$	−22.1981			−1.64997			−0.824985	+	0.565154i	$0.808817\pi$
$182$	−8.50150	+	3.93811i	−0.630173	+	0.291912i
$183$			13.4980i			0.997801i
$184$	14.0266	−	11.4786i	1.03405	−	0.846216i
$185$	11.4356	−	6.60233i	0.840760	−	0.485413i
$186$	−6.46046	−	15.1475i	−0.473704	−	1.11067i
$187$	3.72770	+	2.15219i	0.272596	+	0.157383i
$188$	−2.19857	−	0.540152i	−0.160347	−	0.0393946i
$189$	5.40907	+	2.90562i	0.393452	+	0.211353i
$190$	11.9770	+	1.44972i	0.868905	+	0.105174i
$191$	−1.13615	−	0.655958i	−0.0822091	−	0.0474635i	0.458332	−	0.888781i	$-0.348447\pi$
$191$	−1.13615	−	0.655958i	−0.0822091	−	0.0474635i	−0.540541	+	0.841318i	$0.681780\pi$
$192$	20.5758	+	4.15241i	1.48493	+	0.299674i
$193$	5.64697	+	9.78084i	0.406478	+	0.704040i	0.994492	−	0.104810i	$-0.0334235\pi$
$193$	5.64697	+	9.78084i	0.406478	+	0.704040i	−0.588014	+	0.808851i	$0.700090\pi$
$194$	14.6254	−	19.4780i	1.05004	−	1.39844i
$195$		−	13.6563i		−	0.977950i
$196$	9.05329	−	10.6789i	0.646663	−	0.762776i
$197$			5.92149i			0.421889i	0.977498	+	0.210944i	$0.0676539\pi$
$197$			5.92149i			0.421889i	−0.977498	+	0.210944i	$0.932346\pi$
$198$	−5.88603	−	4.41962i	−0.418302	−	0.314089i
$199$	−9.30560	−	16.1178i	−0.659657	−	1.14256i	−0.980704	−	0.195496i	$-0.937368\pi$
$199$	−9.30560	−	16.1178i	−0.659657	−	1.14256i	0.321048	−	0.947063i	$-0.395965\pi$
$200$	−1.89739	+	0.310546i	−0.134166	+	0.0219589i
$201$	−17.8713	−	10.3180i	−1.26055	−	0.727777i
$202$	0.208591	−	1.72330i	0.0146764	−	0.121251i
$203$	−10.8649	−	5.83634i	−0.762563	−	0.409631i
$204$	16.3713	+	4.02216i	1.14622	+	0.281607i
$205$	9.99164	+	5.76868i	0.697847	+	0.402902i
$206$	−19.8457	+	8.46426i	−1.38272	+	0.589733i
$207$	−21.5570	+	12.4460i	−1.49832	+	0.865054i
$208$	8.45758	−	5.36601i	0.586427	−	0.372066i
$209$		−	5.49925i		−	0.380391i
$210$	8.57696	+	18.5158i	0.591866	+	1.27771i
$211$	5.72971			0.394449			0.197225	−	0.980358i	$-0.436807\pi$
$211$	5.72971			0.394449			0.197225	+	0.980358i	$0.436807\pi$
$212$	−12.3934	−	11.8861i	−0.851180	−	0.816344i
$213$	6.94200	+	12.0239i	0.475658	+	0.823864i
$214$	−14.4508	+	6.16332i	−0.987838	+	0.421316i
$215$		0			0
$216$	−6.14009	−	2.32073i	−0.417780	−	0.157906i
$217$	11.7362	−	0.359875i	0.796704	−	0.0244299i
$218$	−17.6882	−	2.14101i	−1.19800	−	0.145008i
$219$	−0.727697	+	1.26041i	−0.0491732	+	0.0851704i
$220$	−1.55366	−	5.34885i	−0.104748	−	0.360619i
$221$	6.96658	−	4.02216i	0.468623	−	0.270560i
$222$	−18.8510	−	14.1545i	−1.26519	−	0.949989i
$223$	20.8668			1.39734			0.698672	−	0.715442i	$-0.253775\pi$
$223$	20.8668			1.39734			0.698672	+	0.715442i	$0.253775\pi$
$224$	−8.09693	+	12.5873i	−0.540999	+	0.841023i
$225$	2.64049			0.176033
$226$	22.6892	+	17.0365i	1.50926	+	1.13325i
$227$	14.2775	−	8.24309i	0.947628	−	0.547113i	0.0552847	−	0.998471i	$-0.482393\pi$
$227$	14.2775	−	8.24309i	0.947628	−	0.547113i	0.892343	+	0.451357i	$0.149060\pi$
$228$	−6.00773	−	20.6831i	−0.397872	−	1.36977i
$229$	4.24976	−	7.36079i	0.280832	−	0.486415i	−0.690758	−	0.723086i	$-0.742723\pi$
$229$	4.24976	−	7.36079i	0.280832	−	0.486415i	0.971590	+	0.236671i	$0.0760564\pi$
$230$	−18.6997	−	2.26345i	−1.23302	−	0.149247i
$231$	7.90895	−	4.89542i	0.520371	−	0.322095i
$232$	12.3332	+	4.66151i	0.809715	+	0.306043i
$233$	−2.23751	+	3.87548i	−0.146584	+	0.253891i	−0.929963	−	0.367653i	$-0.880161\pi$
$233$	−2.23751	+	3.87548i	−0.146584	+	0.253891i	0.783379	+	0.621545i	$0.213495\pi$
$234$	−12.6532	+	5.39664i	−0.827167	+	0.352789i
$235$	1.17642	+	2.03762i	0.0767410	+	0.132919i
$236$	10.4870	+	10.0578i	0.682649	+	0.654710i
$237$	−15.9625			−1.03688
$238$	−6.91940	+	9.82880i	−0.448518	+	0.637107i
$239$			24.5675i			1.58914i	0.607171	+	0.794571i	$0.292304\pi$
$239$			24.5675i			1.58914i	−0.607171	+	0.794571i	$0.707696\pi$
$240$	−11.6869	−	18.4201i	−0.754383	−	1.18901i
$241$	−5.02498	+	2.90117i	−0.323687	+	0.186881i	−0.653035	−	0.757328i	$-0.726505\pi$
$241$	−5.02498	+	2.90117i	−0.323687	+	0.186881i	0.329348	+	0.944209i	$0.393171\pi$
$242$	11.9739	−	5.10690i	0.769710	−	0.328284i
$243$	−18.6731	−	10.7809i	−1.19788	−	0.691596i
$244$	9.99164	+	2.45478i	0.639649	+	0.157151i
$245$	−14.5223	+	0.891454i	−0.927796	+	0.0569529i
$246$	2.47502	−	20.4477i	0.157802	−	1.30370i
$247$	−8.90047	−	5.13869i	−0.566323	−	0.326967i
$248$	−12.3876	+	2.02748i	−0.786612	+	0.128745i
$249$	0.660123	+	1.14337i	0.0418336	+	0.0724579i
$250$	13.3508	+	10.0247i	0.844381	+	0.634016i
$251$			18.8010i			1.18671i	0.804942	+	0.593353i	$0.202196\pi$
$251$			18.8010i			1.18671i	−0.804942	+	0.593353i	$0.797804\pi$
$252$	13.7663	−	15.2639i	0.867196	−	0.961536i
$253$			8.58598i			0.539796i
$254$	12.4100	−	16.5276i	0.778672	−	1.03703i
$255$	−8.76002	−	15.1728i	−0.548574	−	0.950157i
$256$	6.81571	−	14.4757i	0.425982	−	0.904732i
$257$	10.9106	+	6.29923i	0.680584	+	0.392935i	0.800075	−	0.599900i	$-0.204793\pi$
$257$	10.9106	+	6.29923i	0.680584	+	0.392935i	−0.119491	+	0.992835i	$0.538126\pi$
$258$		0			0
$259$	14.2919	−	8.84631i	0.888058	−	0.549683i
$260$	−10.1088	−	2.48357i	−0.626924	−	0.154024i
$261$	−15.6816	−	9.05379i	−0.970668	−	0.560415i
$262$	−3.37766	−	7.91942i	−0.208672	−	0.489264i
$263$	−4.27292	+	2.46697i	−0.263479	+	0.152120i	−0.625921	−	0.779887i	$-0.715277\pi$
$263$	−4.27292	+	2.46697i	−0.263479	+	0.152120i	0.362441	+	0.932007i	$0.381943\pi$
$264$	−7.69532	+	6.29747i	−0.473614	+	0.387582i
$265$			17.8461i			1.09628i
$266$	15.2950	+	1.37722i	0.937795	+	0.0844426i
$267$	−4.54461			−0.278125
$268$	−10.8878	+	11.3525i	−0.665081	+	0.693462i
$269$	13.1502	+	22.7769i	0.801783	+	1.38873i	0.918441	+	0.395558i	$0.129449\pi$
$269$	13.1502	+	22.7769i	0.801783	+	1.38873i	−0.116658	+	0.993172i	$0.537218\pi$
$270$	2.67624	+	6.27485i	0.162871	+	0.381875i
$271$	−14.0490	+	24.3336i	−0.853418	+	1.47816i	0.0246868	+	0.999695i	$0.492141\pi$
$271$	−14.0490	+	24.3336i	−0.853418	+	1.47816i	−0.878105	+	0.478468i	$0.841192\pi$
$272$	5.95465	−	11.3871i	0.361054	−	0.690444i
$273$	−0.532782	−	17.3750i	−0.0322454	−	1.05158i
$274$	2.37467	−	19.6186i	0.143459	−	1.18520i
$275$	0.455393	−	0.788764i	0.0274612	−	0.0475643i
$276$	9.37988	+	32.2925i	0.564602	+	1.94378i
$277$	23.3982	−	13.5090i	1.40586	−	0.811675i	0.410876	−	0.911691i	$-0.365223\pi$
$277$	23.3982	−	13.5090i	1.40586	−	0.811675i	0.994986	+	0.100017i	$0.0318897\pi$
$278$	−0.427273	+	0.569041i	−0.0256261	+	0.0341288i
$279$	17.2391			1.03208
$280$	15.2658	−	2.98162i	0.912304	−	0.178186i
$281$	−20.0629			−1.19685			−0.598426	−	0.801178i	$-0.704207\pi$
$281$	−20.0629			−1.19685			−0.598426	+	0.801178i	$0.704207\pi$
$282$	2.52208	−	3.35890i	0.150188	−	0.200020i
$283$	−4.75248	+	2.74385i	−0.282506	+	0.163105i	−0.634557	−	0.772876i	$-0.718817\pi$
$283$	−4.75248	+	2.74385i	−0.282506	+	0.163105i	0.352052	+	0.935981i	$0.385484\pi$
$284$	10.1630	−	2.95200i	0.603061	−	0.175169i
$285$	−11.1918	+	19.3847i	−0.662943	+	1.14825i
$286$	−0.570165	+	4.71048i	−0.0337146	+	0.278537i
$287$	12.9375	+	6.94970i	0.763674	+	0.410228i
$288$	−12.4487	+	18.1076i	−0.733548	+	1.06700i
$289$	−3.33988	+	5.78484i	−0.196463	+	0.340284i
$290$	−5.37560	−	12.6039i	−0.315666	−	0.740126i
$291$	22.5957	+	39.1369i	1.32458	+	2.29425i
$292$	0.800653	+	0.767885i	0.0468547	+	0.0449370i
$293$	−13.6931			−0.799957			−0.399978	−	0.916525i	$-0.630982\pi$
$293$	−13.6931			−0.799957			−0.399978	+	0.916525i	$0.630982\pi$
$294$	11.6349	+	23.2230i	0.678559	+	1.35440i
$295$		−	15.1011i		−	0.879218i
$296$	−13.9059	+	11.3799i	−0.808264	+	0.661443i
$297$	2.69291	−	1.55475i	0.156258	−	0.0902157i
$298$	3.05635	+	7.16607i	0.177050	+	0.415119i
$299$	13.8963	+	8.02304i	0.803644	+	0.463984i
$300$	0.851071	−	3.46410i	0.0491366	−	0.200000i
$301$		0			0
$302$	9.88115	+	1.19603i	0.568596	+	0.0688238i
$303$	2.78914	+	1.61031i	0.160232	+	0.0925099i
$304$	−16.4028	+	0.685643i	−0.940768	+	0.0393243i
$305$	−5.34636	−	9.26016i	−0.306131	−	0.530235i
$306$	−10.5966	+	14.1125i	−0.605765	+	0.806756i
$307$		−	24.4197i		−	1.39371i	−0.717213	−	0.696854i	$-0.754583\pi$
$307$		−	24.4197i		−	1.39371i	0.717213	−	0.696854i	$-0.245417\pi$
$308$	−2.18540	−	6.74474i	−0.124525	−	0.384317i
$309$		−	40.0294i		−	2.27719i
$310$	10.4318	+	7.83290i	0.592489	+	0.444879i
$311$	−8.61539	−	14.9223i	−0.488534	−	0.846165i	0.511379	−	0.859355i	$-0.329135\pi$
$311$	−8.61539	−	14.9223i	−0.488534	−	0.846165i	−0.999913	+	0.0131898i	$0.995801\pi$
$312$	3.00160	+	18.3394i	0.169932	+	1.03826i
$313$	15.0446	+	8.68601i	0.850371	+	0.490962i	0.860776	−	0.508984i	$-0.169979\pi$
$313$	15.0446	+	8.68601i	0.850371	+	0.490962i	−0.0104047	+	0.999946i	$0.503312\pi$
$314$	2.43174	−	20.0901i	0.137231	−	1.13375i
$315$	−21.3517	+	0.654723i	−1.20303	+	0.0368894i
$316$	−2.90298	+	11.8160i	−0.163305	+	0.664700i
$317$	16.7863	+	9.69155i	0.942810	+	0.544332i	0.890840	−	0.454317i	$-0.150117\pi$
$317$	16.7863	+	9.69155i	0.942810	+	0.544332i	0.0519701	+	0.998649i	$0.483450\pi$
$318$	29.3055	−	12.4989i	1.64337	−	0.700903i
$319$	−5.40907	+	3.12293i	−0.302850	+	0.174850i
$320$	−15.7605	+	5.30106i	−0.881041	+	0.296338i
$321$		−	29.1477i		−	1.62687i
$322$	−23.8801	−	2.15025i	−1.33078	−	0.119829i
$323$	−13.1851			−0.733639
$324$	−7.70295	+	8.03166i	−0.427942	+	0.446203i
$325$	−0.851071	−	1.47410i	−0.0472089	−	0.0817682i
$326$	−10.8146	+	4.61247i	−0.598967	+	0.255461i
$327$	16.5285	−	28.6282i	0.914029	−	1.58314i
$328$	−14.6859	−	5.55076i	−0.810894	−	0.306489i
$329$	1.57625	+	2.54657i	0.0869018	+	0.140397i
$330$	10.2592	+	1.24179i	0.564748	+	0.0683580i
$331$	10.4008	−	18.0147i	0.571678	−	0.990176i	−0.424715	−	0.905327i	$-0.639626\pi$
$331$	10.4008	−	18.0147i	0.571678	−	0.990176i	0.996394	−	0.0848492i	$-0.0270409\pi$
$332$	0.966408	−	0.280709i	0.0530385	−	0.0154059i
$333$	21.3716	−	12.3389i	1.17116	−	0.676167i
$334$	−2.83184	−	2.12633i	−0.154951	−	0.116348i
$335$	16.3473			0.893146
$336$	−15.5879	−	22.9800i	−0.850388	−	1.25366i
$337$	10.3332			0.562886			0.281443	−	0.959578i	$-0.409187\pi$
$337$	10.3332			0.562886			0.281443	+	0.959578i	$0.409187\pi$
$338$	−7.61063	−	5.71456i	−0.413964	−	0.310831i
$339$	−45.5890	+	26.3208i	−2.47606	+	1.42955i
$340$	−12.8245	+	3.72508i	−0.695506	+	0.202021i
$341$	2.97315	−	5.14965i	0.161005	−	0.278869i
$342$	22.3835	+	2.70934i	1.21036	+	0.146504i
$343$	−18.4420	+	1.70077i	−0.995774	+	0.0918328i
$344$		0			0
$345$	17.4737	−	30.2653i	0.940752	−	1.62943i
$346$	7.06830	−	3.01465i	0.379994	−	0.162069i
$347$	−16.8169	−	29.1277i	−0.902779	−	1.56366i	−0.823871	−	0.566777i	$-0.808190\pi$
$347$	−16.8169	−	29.1277i	−0.902779	−	1.56366i	−0.0789080	−	0.996882i	$-0.525143\pi$
$348$	−16.9322	+	17.6548i	−0.907662	+	0.946395i
$349$	−13.3546			−0.714858			−0.357429	−	0.933940i	$-0.616347\pi$
$349$	−13.3546			−0.714858			−0.357429	+	0.933940i	$0.616347\pi$
$350$	2.07973	+	1.46411i	0.111166	+	0.0782602i
$351$		−	5.81125i		−	0.310182i
$352$	3.26210	+	6.84159i	0.173870	+	0.364658i
$353$	6.80175	−	3.92699i	0.362021	−	0.209013i	−0.307946	−	0.951404i	$-0.599642\pi$
$353$	6.80175	−	3.92699i	0.362021	−	0.209013i	0.669967	+	0.742391i	$0.266308\pi$
$354$	−24.7978	+	10.5763i	−1.31799	+	0.562126i
$355$	−9.52498	−	5.49925i	−0.505533	−	0.291870i
$356$	−0.826492	+	3.36406i	−0.0438040	+	0.178295i
$357$	−11.7373	−	18.9626i	−0.621206	−	1.00361i
$358$	0.597895	−	4.93958i	0.0315997	−	0.261065i
$359$	−0.140453	−	0.0810905i	−0.00741282	−	0.00427979i	0.496289	−	0.868157i	$-0.334696\pi$
$359$	−0.140453	−	0.0810905i	−0.00741282	−	0.00427979i	−0.503702	+	0.863878i	$0.668029\pi$
$360$	22.5368	−	3.68860i	1.18779	−	0.194406i
$361$	−1.07739	−	1.86609i	−0.0567047	−	0.0982154i
$362$	−25.1038	−	18.8496i	−1.31943	−	0.990713i
$363$			24.1516i			1.26763i
$364$	−12.9584	−	2.76547i	−0.679205	−	0.144950i
$365$		−	1.15292i		−	0.0603466i
$366$	−11.4619	+	15.2649i	−0.599122	+	0.797909i
$367$	10.1321	+	17.5493i	0.528891	+	0.916066i	0.999432	+	0.0336883i	$0.0107254\pi$
$367$	10.1321	+	17.5493i	0.528891	+	0.916066i	−0.470541	+	0.882378i	$0.655941\pi$
$368$	25.6098	−	1.07050i	1.33500	−	0.0558034i
$369$	18.6731	+	10.7809i	0.972082	+	0.561232i
$370$	18.5389	+	2.24398i	0.963791	+	0.116659i
$371$	0.696241	+	22.7057i	0.0361470	+	1.17882i
$372$	5.55643	−	22.6163i	0.288088	−	1.17260i
$373$	−5.78269	−	3.33864i	−0.299416	−	0.172868i	0.342764	−	0.939421i	$-0.388637\pi$
$373$	−5.78269	−	3.33864i	−0.299416	−	0.172868i	−0.642181	+	0.766553i	$0.721970\pi$
$374$	2.38812	+	5.59930i	0.123487	+	0.289533i
$375$	−26.8256	+	15.4878i	−1.38527	+	0.799786i
$376$	−2.02770	−	2.47778i	−0.104570	−	0.127782i
$377$			11.6727i			0.601174i
$378$	3.64980	+	7.87911i	0.187725	+	0.405257i
$379$	−4.60350			−0.236466			−0.118233	−	0.992986i	$-0.537723\pi$
$379$	−4.60350			−0.236466			−0.118233	+	0.992986i	$0.537723\pi$
$380$	12.3138	+	11.8098i	0.631685	+	0.605832i
$381$	19.1730	+	33.2086i	0.982264	+	1.70133i
$382$	−0.727867	−	1.70659i	−0.0372409	−	0.0873169i
$383$	5.71038	−	9.89066i	0.291787	−	0.505389i	−0.682446	−	0.730936i	$-0.739084\pi$
$383$	5.71038	−	9.89066i	0.291787	−	0.505389i	0.974232	+	0.225547i	$0.0724170\pi$
$384$	19.7432	+	22.1680i	1.00752	+	1.13126i
$385$	−3.48685	+	6.49107i	−0.177706	+	0.330815i
$386$	−1.91928	+	15.8563i	−0.0976885	+	0.807065i
$387$		0			0
$388$	33.0797	−	9.60852i	1.67937	−	0.487799i
$389$	−26.0307	+	15.0288i	−1.31981	+	0.761991i	−0.983697	−	0.179832i	$-0.942445\pi$
$389$	−26.0307	+	15.0288i	−1.31981	+	0.761991i	−0.336109	+	0.941823i	$0.609111\pi$
$390$	11.5963	−	15.4440i	0.587203	−	0.782035i
$391$	20.5859			1.04107
$392$	19.3064	−	4.38910i	0.975119	−	0.221683i
$393$	15.9737			0.805766
$394$	−5.02826	+	6.69662i	−0.253320	+	0.337371i
$395$	10.9509	−	6.32252i	0.551001	−	0.318120i
$396$	−2.90359	−	9.99630i	−0.145911	−	0.502333i
$397$	−2.17124	+	3.76069i	−0.108971	+	0.188744i	−0.915354	−	0.402651i	$-0.868089\pi$
$397$	−2.17124	+	3.76069i	−0.108971	+	0.188744i	0.806383	+	0.591394i	$0.201422\pi$
$398$	3.16276	−	26.1295i	0.158535	−	1.30975i
$399$	−13.4830	+	25.0998i	−0.674997	+	1.25656i
$400$	−2.40946	−	1.25998i	−0.120473	−	0.0629989i
$401$	9.98685	−	17.2977i	0.498719	−	0.863807i	−0.501279	−	0.865285i	$-0.667137\pi$
$401$	9.98685	−	17.2977i	0.498719	−	0.863807i	0.999999	+	0.00147805i	$0.000470479\pi$
$402$	−11.4491	−	26.8442i	−0.571030	−	1.33887i
$403$	−5.55643	−	9.62402i	−0.276786	−	0.479407i
$404$	1.69924	−	1.77175i	0.0845404	−	0.0881480i
$405$	11.5654			0.574688
$406$	−7.33112	−	15.8263i	−0.363837	−	0.785444i
$407$		−	8.51212i		−	0.421930i
$408$	15.0989	+	18.4504i	0.747508	+	0.913433i
$409$	−26.4356	+	15.2626i	−1.30715	+	0.754686i	−0.981620	−	0.190844i	$-0.938878\pi$
$409$	−26.4356	+	15.2626i	−1.30715	+	0.754686i	−0.325534	+	0.945530i	$0.605544\pi$
$410$	6.40106	+	15.0082i	0.316126	+	0.741205i
$411$	31.7525	+	18.3323i	1.56623	+	0.904266i
$412$	−29.6310	−	7.27983i	−1.45981	−	0.358652i
$413$	−0.589147	−	19.2131i	−0.0289900	−	0.945417i
$414$	−34.9474	−	4.23009i	−1.71757	−	0.207898i
$415$	−0.905741	−	0.522930i	−0.0444611	−	0.0256696i
$416$	14.1213	+	1.11336i	0.692351	+	0.0545867i
$417$	−0.660123	−	1.14337i	−0.0323264	−	0.0559909i
$418$	4.66971	−	6.21911i	0.228403	−	0.304186i
$419$		−	2.08070i		−	0.101649i	−0.998708	−	0.0508245i	$-0.983815\pi$
$419$		−	2.08070i		−	0.101649i	0.998708	−	0.0508245i	$-0.0161849\pi$
$420$	−6.02304	+	28.2226i	−0.293894	+	1.37712i
$421$			30.4039i			1.48180i	0.671618	+	0.740898i	$0.265600\pi$
$421$			30.4039i			1.48180i	−0.671618	+	0.740898i	$0.734400\pi$
$422$	6.47973	+	4.86540i	0.315428	+	0.236844i
$423$	2.19857	+	3.80804i	0.106898	+	0.185153i
$424$	−3.92251	−	23.9659i	−0.190494	−	1.16389i
$425$	−1.89116	−	1.09186i	−0.0917345	−	0.0529630i
$426$	−2.35943	+	19.4927i	−0.114315	+	0.944423i
$427$	−7.16346	−	11.5732i	−0.346664	−	0.560064i
$428$	−21.5761	−	5.30087i	−1.04292	−	0.256227i
$429$	−7.62386	−	4.40164i	−0.368084	−	0.212513i
$430$		0			0
$431$	2.32280	−	1.34107i	0.111885	−	0.0645970i	−0.443013	−	0.896515i	$-0.646090\pi$
$431$	2.32280	−	1.34107i	0.111885	−	0.0645970i	0.554898	+	0.831918i	$0.312757\pi$
$432$	−4.97317	−	7.83840i	−0.239272	−	0.377125i
$433$			29.4673i			1.41611i	0.706158	+	0.708054i	$0.250427\pi$
$433$			29.4673i			1.41611i	−0.706158	+	0.708054i	$0.749573\pi$
$434$	13.5781	+	9.55885i	0.651767	+	0.458839i
$435$	25.4224			1.21891
$436$	−18.1856	−	17.4413i	−0.870932	−	0.835288i
$437$	−13.1502	−	22.7769i	−0.629061	−	1.08957i
$438$	−1.89323	+	0.807470i	−0.0904622	+	0.0385824i
$439$	−3.77648	+	6.54106i	−0.180242	+	0.312188i	−0.941963	−	0.335717i	$-0.891021\pi$
$439$	−3.77648	+	6.54106i	−0.180242	+	0.312188i	0.761721	+	0.647905i	$0.224355\pi$
$440$	2.78496	−	7.36831i	0.132768	−	0.351271i
$441$	−27.1403	+	1.66601i	−1.29240	+	0.0793339i
$442$	11.2939	+	1.36704i	0.537198	+	0.0650234i
$443$	3.75915	−	6.51104i	0.178603	−	0.309349i	−0.762799	−	0.646635i	$-0.776176\pi$
$443$	3.75915	−	6.51104i	0.178603	−	0.309349i	0.941402	+	0.337286i	$0.109509\pi$
$444$	−9.29919	−	32.0147i	−0.441320	−	1.51935i
$445$	3.11778	−	1.80005i	0.147797	−	0.0853306i
$446$	23.5983	+	17.7191i	1.11741	+	0.839025i
$447$	−14.4542			−0.683659
$448$	−19.8454	+	7.35943i	−0.937606	+	0.347700i
$449$	−14.3332			−0.676426			−0.338213	−	0.941070i	$-0.609822\pi$
$449$	−14.3332			−0.676426			−0.338213	+	0.941070i	$0.609822\pi$
$450$	2.98614	+	2.24218i	0.140768	+	0.105698i
$451$	6.44092	−	3.71866i	0.303291	−	0.175105i
$452$	11.1926	+	38.5332i	0.526455	+	1.81245i
$453$	−9.23329	+	15.9925i	−0.433818	+	0.751394i
$454$	23.1460	+	2.80164i	1.08630	+	0.131487i
$455$	7.24749	+	11.7089i	0.339767	+	0.548922i
$456$	10.7690	−	28.4920i	0.504303	−	1.33426i
$457$	−6.48037	+	11.2243i	−0.303139	+	0.525052i	−0.976845	−	0.213947i	$-0.931368\pi$
$457$	−6.48037	+	11.2243i	−0.303139	+	0.525052i	0.673706	+	0.738999i	$0.264701\pi$
$458$	11.0565	−	4.71563i	0.516636	−	0.220347i
$459$	−3.72770	−	6.45656i	−0.173994	−	0.301366i
$460$	−19.2255	−	18.4387i	−0.896396	−	0.859709i
$461$	33.3871			1.55499			0.777496	−	0.628888i	$-0.216490\pi$
$461$	33.3871			1.55499			0.777496	+	0.628888i	$0.216490\pi$
$462$	13.1012	+	1.17968i	0.609523	+	0.0548837i
$463$		−	29.7739i		−	1.38371i	−0.722036	−	0.691855i	$-0.756794\pi$
$463$		−	29.7739i		−	1.38371i	0.722036	−	0.691855i	$-0.243206\pi$
$464$	9.98929	+	15.7445i	0.463741	+	0.730920i
$465$	−20.9605	+	12.1016i	−0.972022	+	0.561197i
$466$	−5.82129	+	2.48280i	−0.269666	+	0.115013i
$467$	23.5399	+	13.5908i	1.08930	+	0.628907i	0.933390	−	0.358865i	$-0.116836\pi$
$467$	23.5399	+	13.5908i	1.08930	+	0.628907i	0.155909	+	0.987771i	$0.450169\pi$
$468$	−18.8921	−	4.64147i	−0.873288	−	0.214552i
$469$	20.7987	−	0.637765i	0.960393	−	0.0294492i
$470$	−0.399837	+	3.30330i	−0.0184431	+	0.152370i
$471$	32.5156	+	18.7729i	1.49824	+	0.865009i
$472$	3.31915	+	20.2795i	0.152776	+	0.933442i
$473$		0			0
$474$	−18.0520	−	13.5546i	−0.829157	−	0.622585i
$475$			2.78991i			0.128010i
$476$	−16.1713	+	5.23977i	−0.741211	+	0.240164i
$477$			33.3521i			1.52709i
$478$	−20.8616	+	27.7835i	−0.954189	+	1.27079i
$479$	−17.2187	−	29.8237i	−0.786744	−	1.36268i	−0.927952	−	0.372700i	$-0.878432\pi$
$479$	−17.2187	−	29.8237i	−0.786744	−	1.36268i	0.141208	−	0.989980i	$-0.454901\pi$
$480$	2.42482	−	30.7553i	0.110677	−	1.40378i
$481$	−13.7768	−	7.95402i	−0.628167	−	0.362672i
$482$	−8.14629	−	0.986041i	−0.371053	−	0.0449129i
$483$	21.0511	−	39.1884i	0.957858	−	1.78313i
$484$	17.8778	+	4.39227i	0.812628	+	0.199649i
$485$	−31.0031	−	17.8996i	−1.40778	−	0.812781i
$486$	−11.9628	−	28.0485i	−0.542642	−	1.27230i
$487$	−6.82613	+	3.94107i	−0.309321	+	0.178587i	−0.646623	−	0.762810i	$-0.723819\pi$
$487$	−6.82613	+	3.94107i	−0.309321	+	0.178587i	0.337301	+	0.941397i	$0.390486\pi$
$488$	9.21508	+	11.2606i	0.417147	+	0.509741i
$489$		−	21.8134i		−	0.986436i
$490$	−17.1803	−	11.3235i	−0.776126	−	0.511545i
$491$	−8.06291			−0.363874			−0.181937	−	0.983310i	$-0.558237\pi$
$491$	−8.06291			−0.363874			−0.181937	+	0.983310i	$0.558237\pi$
$492$	20.1623	−	21.0226i	0.908985	−	0.947774i
$493$	7.48759	+	12.9689i	0.337224	+	0.584089i
$494$	−5.70201	−	13.3692i	−0.256546	−	0.601510i
$495$	−5.40907	+	9.36878i	−0.243120	+	0.421095i
$496$	−15.7308	−	8.22609i	−0.706333	−	0.369362i
$497$	−12.3332	−	6.62511i	−0.553220	−	0.297177i
$498$	−0.224361	+	1.85358i	−0.0100538	+	0.0830610i
$499$	12.0216	−	20.8221i	0.538163	−	0.932125i	−0.460841	−	0.887483i	$-0.652452\pi$
$499$	12.0216	−	20.8221i	0.538163	−	0.932125i	0.999003	−	0.0446419i	$-0.0142147\pi$
$500$	6.58598	+	22.6738i	0.294534	+	1.01400i
$501$	5.68997	−	3.28511i	0.254209	−	0.146768i
$502$	−15.9649	+	21.2620i	−0.712549	+	0.948971i
$503$	−40.8993			−1.82361			−0.911804	−	0.410626i	$-0.865310\pi$
$503$	−40.8993			−1.82361			−0.911804	+	0.410626i	$0.865310\pi$
$504$	28.5297	−	5.57226i	1.27082	−	0.248208i
$505$	−2.55128			−0.113530
$506$	−7.29082	+	9.70989i	−0.324116	+	0.431657i
$507$	15.2919	−	8.82880i	0.679139	−	0.392101i
$508$	28.0689	−	8.15308i	1.24536	−	0.361734i
$509$	−2.02661	+	3.51019i	−0.0898278	+	0.155586i	−0.907438	−	0.420186i	$-0.861965\pi$
$509$	−2.02661	+	3.51019i	−0.0898278	+	0.155586i	0.817610	+	0.575772i	$0.195298\pi$
$510$	2.97733	−	24.5975i	0.131838	−	1.08920i
$511$	−0.0449795	−	1.46686i	−0.00198978	−	0.0648902i
$512$	20.0000	−	10.5830i	0.883883	−	0.467707i
$513$	−4.76249	+	8.24887i	−0.210269	+	0.364197i
$514$	6.98978	+	16.3886i	0.308306	+	0.722870i
$515$	15.8550	+	27.4617i	0.698656	+	1.21011i
$516$		0			0
$517$	1.51671			0.0667048
$518$	23.6746	+	2.13175i	1.04020	+	0.0936639i
$519$			14.2570i			0.625811i
$520$	−9.32317	−	11.3926i	−0.408848	−	0.499600i
$521$	27.1927	−	15.6997i	1.19133	−	0.687817i	0.232725	−	0.972543i	$-0.425236\pi$
$521$	27.1927	−	15.6997i	1.19133	−	0.687817i	0.958609	+	0.284725i	$0.0919024\pi$
$522$	−10.0463	−	23.5550i	−0.439715	−	1.03098i
$523$	−11.7132	−	6.76263i	−0.512183	−	0.295709i	0.221547	−	0.975150i	$-0.428889\pi$
$523$	−11.7132	−	6.76263i	−0.512183	−	0.295709i	−0.733731	+	0.679440i	$0.762223\pi$
$524$	2.90501	−	11.8242i	0.126906	−	0.516544i
$525$	−4.01241	+	2.48357i	−0.175116	+	0.108392i
$526$	−6.92708	−	0.838466i	−0.302035	−	0.0365588i
$527$	−12.3469	−	7.12848i	−0.537839	−	0.310522i
$528$	−14.0502	+	0.587301i	−0.611455	+	0.0255590i
$529$	9.03146	+	15.6429i	0.392672	+	0.680128i
$530$	−15.1541	+	20.1822i	−0.658253	+	0.876659i
$531$		−	28.2219i		−	1.22473i
$532$	16.1276	+	14.5453i	0.699222	+	0.630618i
$533$		−	13.8994i		−	0.602050i
$534$	−5.13950	−	3.85907i	−0.222408	−	0.166998i
$535$	11.5450	+	19.9965i	0.499133	+	0.864524i
$536$	−21.9531	+	3.59306i	−0.948228	+	0.155197i
$537$	7.99465	+	4.61572i	0.344995	+	0.199183i
$538$	−4.46946	+	36.9249i	−0.192692	+	1.59195i
$539$	−4.18309	+	8.39464i	−0.180178	+	0.361583i
$540$	−2.30175	+	9.36878i	−0.0990515	+	0.403168i
$541$	−27.1543	−	15.6775i	−1.16745	−	0.674030i	−0.214375	−	0.976751i	$-0.568771\pi$
$541$	−27.1543	−	15.6775i	−1.16745	−	0.674030i	−0.953079	+	0.302722i	$0.902105\pi$
$542$	−36.5511	+	15.5891i	−1.57000	+	0.669611i
$543$	50.4408	−	29.1220i	2.16462	−	1.24974i
$544$	16.4035	−	7.82126i	0.703295	−	0.335334i
$545$			26.1868i			1.12172i
$546$	14.1515	−	20.1018i	0.605629	−	0.860278i
$547$	−44.7293			−1.91249			−0.956244	−	0.292571i	$-0.905489\pi$
$547$	−44.7293			−1.91249			−0.956244	+	0.292571i	$0.905489\pi$
$548$	19.3447	−	20.1702i	0.826366	−	0.861630i
$549$	−9.99164	−	17.3060i	−0.426433	−	0.738604i
$550$	1.18479	−	0.505315i	0.0505195	−	0.0215467i
$551$	9.56611	−	16.5690i	0.407530	−	0.705863i
$552$	−16.8136	+	44.4846i	−0.715634	+	1.89339i
$553$	13.6862	−	8.47140i	0.581998	−	0.360240i
$554$	37.9322	+	4.59138i	1.61159	+	0.195069i
$555$	−17.3234	+	30.0050i	−0.735337	+	1.27364i
$556$	−0.966408	+	0.280709i	−0.0409848	+	0.0119047i
$557$	10.5345	−	6.08208i	0.446360	−	0.257706i	−0.259932	−	0.965627i	$-0.583700\pi$
$557$	10.5345	−	6.08208i	0.446360	−	0.257706i	0.706292	+	0.707921i	$0.250367\pi$
$558$	19.4958	+	14.6387i	0.825321	+	0.619705i
$559$		0			0
$560$	19.7959	+	9.59107i	0.836531	+	0.405297i
$561$	−11.2939			−0.476831
$562$	−22.6892	−	17.0365i	−0.957085	−	0.718641i
$563$	−31.4311	+	18.1468i	−1.32466	+	0.764794i	−0.984469	−	0.175561i	$-0.943826\pi$
$563$	−31.4311	+	18.1468i	−1.32466	+	0.764794i	−0.340194	+	0.940355i	$0.610493\pi$
$564$	5.70445	−	1.65695i	0.240201	−	0.0697702i
$565$	20.8506	−	36.1143i	0.877191	−	1.51934i
$566$	−7.70453	−	0.932570i	−0.323846	−	0.0391988i
$567$	14.7147	−	0.451207i	0.617958	−	0.0189489i
$568$	14.0000	+	5.29150i	0.587427	+	0.222027i
$569$	−6.01830	+	10.4240i	−0.252300	+	0.436997i	−0.964159	−	0.265326i	$-0.914520\pi$
$569$	−6.01830	+	10.4240i	−0.252300	+	0.436997i	0.711858	+	0.702323i	$0.247854\pi$
$570$	−29.1174	+	12.4186i	−1.21959	+	0.520160i
$571$	−4.10570	−	7.11128i	−0.171818	−	0.297598i	0.767237	−	0.641363i	$-0.221631\pi$
$571$	−4.10570	−	7.11128i	−0.171818	−	0.297598i	−0.939056	+	0.343765i	$0.888298\pi$
$572$	−4.64473	+	4.84293i	−0.194206	+	0.202493i
$573$	3.44225			0.143802
$574$	8.72962	+	18.8453i	0.364367	+	0.786588i
$575$		−	4.35589i		−	0.181653i
$576$	−29.4544	+	9.90699i	−1.22727	+	0.412791i
$577$	14.5500	−	8.40042i	0.605722	−	0.349714i	−0.165567	−	0.986199i	$-0.552945\pi$
$577$	14.5500	−	8.40042i	0.605722	−	0.349714i	0.771289	+	0.636485i	$0.219612\pi$
$578$	−8.68929	+	3.70601i	−0.361427	+	0.154150i
$579$	−25.6633	−	14.8167i	−1.06653	−	0.615761i
$580$	4.62338	−	18.8185i	0.191975	−	0.781395i
$581$	−1.17278	−	0.629989i	−0.0486551	−	0.0261364i
$582$	−7.67975	+	63.4472i	−0.318336	+	2.62997i
$583$	9.96289	+	5.75208i	0.412621	+	0.238227i
$584$	0.253407	+	1.54828i	0.0104861	+	0.0640682i
$585$	10.1088	+	17.5090i	0.417949	+	0.723909i
$586$	−15.4855	−	11.6275i	−0.639700	−	0.480328i
$587$			25.4261i			1.04945i	0.851273	+	0.524723i	$0.175831\pi$
$587$			25.4261i			1.04945i	−0.851273	+	0.524723i	$0.824169\pi$
$588$	−6.56206	+	36.1427i	−0.270615	+	1.49050i
$589$			18.2146i			0.750521i
$590$	12.8231	−	17.0778i	0.527920	−	0.703083i
$591$	−7.76849	−	13.4554i	−0.319553	−	0.553482i
$592$	−25.3895	+	1.06129i	−1.04350	+	0.0436186i
$593$	−19.0694	−	11.0097i	−0.783086	−	0.452115i	0.0544368	−	0.998517i	$-0.482664\pi$
$593$	−19.0694	−	11.0097i	−0.783086	−	0.452115i	−0.837523	+	0.546402i	$0.815997\pi$
$594$	4.36563	+	0.528423i	0.179124	+	0.0216815i
$595$	15.5631	+	8.36013i	0.638025	+	0.342732i
$596$	−2.62867	+	10.6994i	−0.107674	+	0.438266i
$597$	42.2903	+	24.4163i	1.73083	+	0.999294i
$598$	8.90256	+	20.8734i	0.364053	+	0.853576i
$599$	−0.500607	+	0.289026i	−0.0204543	+	0.0118093i	−0.510192	−	0.860060i	$-0.670426\pi$
$599$	−0.500607	+	0.289026i	−0.0204543	+	0.0118093i	0.489738	+	0.871870i	$0.337092\pi$
$600$	3.90403	−	3.19487i	0.159381	−	0.130430i
$601$		−	27.3186i		−	1.11435i	−0.830395	−	0.557175i	$-0.811885\pi$
$601$		−	27.3186i		−	1.11435i	0.830395	−	0.557175i	$-0.188115\pi$
$602$		0			0
$603$	30.5509			1.24413
$604$	10.1590	+	9.74321i	0.413363	+	0.396446i
$605$	−9.56611	−	16.5690i	−0.388918	−	0.673625i
$606$	1.78684	+	4.18951i	0.0725853	+	0.170187i
$607$	5.99963	−	10.3917i	0.243518	−	0.421785i	−0.718196	−	0.695841i	$-0.755032\pi$
$607$	5.99963	−	10.3917i	0.243518	−	0.421785i	0.961714	+	0.274056i	$0.0883653\pi$
$608$	−19.1322	−	13.1532i	−0.775914	−	0.533431i
$609$	32.3450	−	0.991819i	1.31069	−	0.0401905i
$610$	1.81710	−	15.0122i	0.0735723	−	0.607826i
$611$	1.41727	−	2.45478i	0.0573364	−	0.0993096i
$612$	−23.9673	+	6.96170i	−0.968821	+	0.281410i
$613$	−3.96050	+	2.28659i	−0.159963	+	0.0923547i	−0.577845	−	0.816147i	$-0.696106\pi$
$613$	−3.96050	+	2.28659i	−0.159963	+	0.0923547i	0.417882	+	0.908501i	$0.362773\pi$
$614$	20.7361	−	27.6163i	0.836841	−	1.11450i
$615$	−30.2721			−1.22069
$616$	3.25585	−	9.48338i	0.131182	−	0.382096i
$617$	5.12621			0.206373			0.103187	−	0.994662i	$-0.467096\pi$
$617$	5.12621			0.206373			0.103187	+	0.994662i	$0.467096\pi$
$618$	33.9911	−	45.2693i	1.36732	−	1.82100i
$619$	39.5293	−	22.8222i	1.58881	−	0.917303i	0.595312	−	0.803495i	$-0.297028\pi$
$619$	39.5293	−	22.8222i	1.58881	−	0.917303i	0.993503	−	0.113808i	$-0.0363049\pi$
$620$	5.14604	+	17.7165i	0.206670	+	0.711511i
$621$	7.43567	−	12.8790i	0.298383	−	0.516815i
$622$	2.92817	−	24.1914i	0.117409	−	0.969988i
$623$	3.89654	−	2.41185i	0.156111	−	0.0966286i
$624$	−12.1784	+	23.2888i	−0.487527	+	0.932299i
$625$	10.5696	−	18.3071i	0.422783	−	0.732282i
$626$	9.63820	+	22.5982i	0.385220	+	0.903206i
$627$	7.21455	+	12.4960i	0.288121	+	0.499041i
$628$	19.8097	−	20.6550i	0.790491	−	0.824224i
$629$	−20.4088			−0.813753
$630$	−24.7026	−	17.3905i	−0.984176	−	0.692852i
$631$			17.1345i			0.682113i	0.940043	+	0.341057i	$0.110785\pi$
$631$			17.1345i			0.682113i	−0.940043	+	0.341057i	$0.889215\pi$
$632$	−13.3166	+	10.8976i	−0.529704	+	0.433484i
$633$	−13.0196	+	7.51689i	−0.517484	+	0.298769i
$634$	10.7540	+	25.2143i	0.427095	+	1.00139i
$635$	−26.3069	−	15.1883i	−1.04396	−	0.602729i
$636$	43.7551	+	10.7499i	1.73500	+	0.426261i
$637$	9.67781	+	14.6145i	0.383449	+	0.579049i
$638$	−8.76897	−	1.06141i	−0.347167	−	0.0420217i
$639$	−17.8009	−	10.2774i	−0.704194	−	0.406567i
$640$	−22.3250	−	7.38815i	−0.882474	−	0.292042i
$641$	−4.02498	−	6.97146i	−0.158977	−	0.275356i	0.775523	−	0.631319i	$-0.217486\pi$
$641$	−4.02498	−	6.97146i	−0.158977	−	0.275356i	−0.934500	+	0.355963i	$0.884153\pi$
$642$	24.7509	−	32.9632i	0.976840	−	1.30095i
$643$			22.2710i			0.878283i	0.898418	+	0.439142i	$0.144717\pi$
$643$			22.2710i			0.878283i	−0.898418	+	0.439142i	$0.855283\pi$
$644$	−25.1801	−	22.7096i	−0.992235	−	0.894882i
$645$		0			0
$646$	−14.9110	−	11.1962i	−0.586667	−	0.440508i
$647$	18.9125	+	32.7574i	0.743528	+	1.28783i	0.950879	+	0.309561i	$0.100182\pi$
$647$	18.9125	+	32.7574i	0.743528	+	1.28783i	−0.207352	+	0.978266i	$0.566484\pi$
$648$	−15.5314	+	2.54202i	−0.610131	+	0.0998601i
$649$	−8.43042	−	4.86730i	−0.330923	−	0.191058i
$650$	0.289259	−	2.38975i	0.0113457	−	0.0937337i
$651$	−26.1960	+	16.2146i	−1.02670	+	0.635501i
$652$	−16.1470	−	3.96704i	−0.632364	−	0.155361i
$653$	25.6130	+	14.7877i	1.00231	+	0.578686i	0.908932	−	0.416944i	$-0.136899\pi$
$653$	25.6130	+	14.7877i	1.00231	+	0.578686i	0.0933818	+	0.995630i	$0.470232\pi$
$654$	43.0019	−	18.3404i	1.68151	−	0.717168i
$655$	−10.9586	+	6.32694i	−0.428188	+	0.247214i
$656$	−11.8949	−	18.7480i	−0.464417	−	0.731985i
$657$		−	2.15466i		−	0.0840611i
$658$	−0.379841	+	4.21840i	−0.0148077	+	0.164450i
$659$	18.3961			0.716611			0.358305	−	0.933604i	$-0.383355\pi$
$659$	18.3961			0.716611			0.358305	+	0.933604i	$0.383355\pi$
$660$	10.5476	+	10.1159i	0.410566	+	0.393762i
$661$	5.92732	+	10.2664i	0.230546	+	0.399317i	0.957969	−	0.286872i	$-0.0926154\pi$
$661$	5.92732	+	10.2664i	0.230546	+	0.399317i	−0.727423	+	0.686189i	$0.759282\pi$
$662$	27.0595	−	11.5410i	1.05170	−	0.448552i
$663$	−10.5535	+	18.2791i	−0.409862	+	0.709902i
$664$	1.33128	+	0.503175i	0.0516635	+	0.0195270i
$665$	−0.691771	−	22.5599i	−0.0268257	−	0.874836i
$666$	34.6468	+	4.19370i	1.34254	+	0.162503i
$667$	−14.9356	+	25.8692i	−0.578308	+	1.00166i
$668$	−1.39695	−	4.80934i	−0.0540496	−	0.186079i
$669$	−47.4157	+	27.3755i	−1.83320	+	1.05840i
$670$	18.4871	+	13.8813i	0.714220	+	0.536283i
$671$	−6.89285			−0.266095
$672$	1.88524	−	39.2246i	0.0727246	−	1.51312i
$673$	10.8738			0.419154			0.209577	−	0.977792i	$-0.432791\pi$
$673$	10.8738			0.419154			0.209577	+	0.977792i	$0.432791\pi$
$674$	11.6858	+	8.77448i	0.450121	+	0.337980i
$675$	−1.36618	+	0.788764i	−0.0525843	+	0.0303595i
$676$	−3.75433	−	12.9252i	−0.144397	−	0.497123i
$677$	−22.7163	+	39.3458i	−0.873060	+	1.51218i	−0.0142443	+	0.999899i	$0.504534\pi$
$677$	−22.7163	+	39.3458i	−0.873060	+	1.51218i	−0.858815	+	0.512285i	$0.828799\pi$
$678$	−73.9071	−	8.94584i	−2.83839	−	0.343563i
$679$	−40.1437	−	21.5642i	−1.54057	−	0.827559i
$680$	−17.6664	−	6.67728i	−0.677476	−	0.256062i
$681$	−21.6285	+	37.4616i	−0.828805	+	1.43553i
$682$	7.73518	−	3.29908i	0.296196	−	0.126328i
$683$	−12.3693	−	21.4243i	−0.473299	−	0.819778i	0.526234	−	0.850340i	$-0.323604\pi$
$683$	−12.3693	−	21.4243i	−0.473299	−	0.819778i	−0.999533	+	0.0305620i	$0.990270\pi$
$684$	23.0129	+	22.0710i	0.879920	+	0.843908i
$685$	−29.0446			−1.10974
$686$	−22.3003	−	13.7367i	−0.851429	−	0.524470i
$687$			22.3013i			0.850847i
$688$		0			0
$689$	18.6193	−	10.7499i	0.709340	−	0.409538i
$690$	45.4610	−	19.3892i	1.73067	−	0.738136i
$691$	−4.10457	−	2.36977i	−0.156145	−	0.0901504i	0.419892	−	0.907574i	$-0.362068\pi$
$691$	−4.10457	−	2.36977i	−0.156145	−	0.0901504i	−0.576037	+	0.817424i	$0.695401\pi$
$692$	10.5535	+	2.59280i	0.401182	+	0.0985636i
$693$	−6.51647	+	12.1310i	−0.247540	+	0.460817i
$694$	5.71568	−	47.2207i	0.216964	−	1.79247i
$695$	0.905741	+	0.522930i	0.0343567	+	0.0198359i
$696$	−34.1403	+	5.58774i	−1.29408	+	0.211803i
$697$	−8.91594	−	15.4429i	−0.337715	−	0.584940i
$698$	−15.1028	−	11.3401i	−0.571649	−	0.429231i
$699$		−	11.7417i		−	0.444112i
$700$	1.10871	+	3.42178i	0.0419053	+	0.129331i
$701$		−	39.8121i		−	1.50368i	−0.659345	−	0.751840i	$-0.729166\pi$
$701$		−	39.8121i		−	1.50368i	0.659345	−	0.751840i	$-0.270834\pi$
$702$	4.93465	−	6.57195i	0.186246	−	0.248042i
$703$	13.0371	+	22.5809i	0.491704	+	0.851656i
$704$	−2.12046	+	10.5072i	−0.0799177	+	0.396004i
$705$	−5.34636	−	3.08672i	−0.201355	−	0.116253i
$706$	11.0267	+	1.33469i	0.414996	+	0.0502319i
$707$	−3.24600	+	0.0995345i	−0.122078	+	0.00374338i
$708$	−37.0248	−	9.09636i	−1.39148	−	0.341862i
$709$	4.97242	+	2.87083i	0.186743	+	0.107816i	0.590457	−	0.807069i	$-0.298948\pi$
$709$	4.97242	+	2.87083i	0.186743	+	0.107816i	−0.403714	+	0.914885i	$0.632281\pi$
$710$	−6.10210	−	14.3073i	−0.229008	−	0.536943i
$711$	20.4659	−	11.8160i	0.767529	−	0.443133i
$712$	−3.79129	+	3.10260i	−0.142085	+	0.116275i
$713$		−	28.4385i		−	1.06503i
$714$	2.82843	−	31.4117i	0.105851	−	1.17555i
$715$	6.97370			0.260801
$716$	4.87062	−	5.07847i	0.182024	−	0.189791i
$717$	−32.2305	−	55.8249i	−1.20367	−	2.08482i
$718$	−0.0899800	−	0.210971i	−0.00335802	−	0.00787338i
$719$	−7.62804	+	13.2122i	−0.284478	+	0.492730i	−0.972482	−	0.232976i	$-0.925154\pi$
$719$	−7.62804	+	13.2122i	−0.284478	+	0.492730i	0.688005	+	0.725706i	$0.258487\pi$
$720$	28.6191	+	14.9658i	1.06657	+	0.557741i
$721$	21.2438	+	34.3211i	0.791160	+	1.27818i
$722$	0.366180	−	3.02523i	0.0136278	−	0.112588i
$723$	7.61218	−	13.1847i	0.283100	−	0.490344i
$724$	−12.3837	−	42.6341i	−0.460238	−	1.58448i
$725$	2.74416	−	1.58434i	0.101915	−	0.0588409i
$726$	−20.5085	+	27.3131i	−0.761141	+	1.01369i
$727$	40.8993			1.51687			0.758435	−	0.651749i	$-0.225964\pi$
$727$	40.8993			1.51687			0.758435	+	0.651749i	$0.225964\pi$
$728$	−12.3064	−	14.1312i	−0.456104	−	0.523736i
$729$	39.8818			1.47710
$730$	0.979006	−	1.30384i	0.0362346	−	0.0482572i
$731$		0			0
$732$	−25.9245	+	7.53019i	−0.958197	+	0.278324i
$733$	12.2037	−	21.1374i	0.450753	−	0.780728i	−0.547680	−	0.836688i	$-0.684489\pi$
$733$	12.2037	−	21.1374i	0.450753	−	0.780728i	0.998433	+	0.0559605i	$0.0178221\pi$
$734$	−3.44367	+	28.4502i	−0.127108	+	1.05012i
$735$	31.8296	−	21.0777i	1.17405	−	0.777462i
$736$	29.8711	+	20.5360i	1.10106	+	0.756968i
$737$	5.26897	−	9.12612i	0.194085	−	0.336165i
$738$	11.9628	+	28.0485i	0.440355	+	1.03248i
$739$	15.3996	+	26.6730i	0.566485	+	0.981181i	0.996910	+	0.0785545i	$0.0250305\pi$
$739$	15.3996	+	26.6730i	0.566485	+	0.981181i	−0.430425	+	0.902626i	$0.641636\pi$
$740$	19.0602	+	18.2801i	0.700666	+	0.671990i
$741$	26.9661			0.990624
$742$	−18.4932	+	26.2691i	−0.678909	+	0.964369i
$743$			23.9376i			0.878184i	0.898442	+	0.439092i	$0.144700\pi$
$743$			23.9376i			0.878184i	−0.898442	+	0.439092i	$0.855300\pi$
$744$	25.4885	−	20.8585i	0.934453	−	0.764710i
$745$	9.91613	−	5.72508i	0.363299	−	0.209751i
$746$	−3.70463	−	8.68606i	−0.135636	−	0.318019i
$747$	−1.69271	−	0.977288i	−0.0619331	−	0.0357571i
$748$	−2.05394	+	8.36013i	−0.0750996	+	0.305677i
$749$	15.4689	+	24.9912i	0.565219	+	0.913158i
$750$	−43.4887	−	5.26394i	−1.58798	−	0.192212i
$751$	−11.9543	−	6.90181i	−0.436218	−	0.251851i	0.265774	−	0.964035i	$-0.414373\pi$
$751$	−11.9543	−	6.90181i	−0.436218	−	0.251851i	−0.701992	+	0.712185i	$0.747706\pi$
$752$	−0.189102	−	4.52395i	−0.00689586	−	0.164972i
$753$	−24.6653	−	42.7215i	−0.898853	−	1.55686i
$754$	−9.91191	+	13.2007i	−0.360970	+	0.480740i
$755$		−	14.6287i		−	0.532392i
$756$	−2.56301	+	12.0097i	−0.0932159	+	0.436790i
$757$			2.14156i			0.0778362i	0.999242	+	0.0389181i	$0.0123911\pi$
$757$			2.14156i			0.0778362i	−0.999242	+	0.0389181i	$0.987609\pi$
$758$	−5.20610	−	3.90908i	−0.189094	−	0.141984i
$759$	−11.2641	−	19.5099i	−0.408860	−	0.708166i
$760$	3.89732	+	23.8121i	0.141371	+	0.863755i
$761$	36.8321	+	21.2650i	1.33516	+	0.770856i	0.986086	−	0.166239i	$-0.0531622\pi$
$761$	36.8321	+	21.2650i	1.33516	+	0.770856i	0.349076	+	0.937094i	$0.386496\pi$
$762$	−6.51647	+	53.8365i	−0.236067	+	1.95029i
$763$	1.02164	+	33.3175i	0.0369859	+	1.20618i
$764$	0.626015	−	2.54806i	0.0226484	−	0.0921855i
$765$	22.4628	+	12.9689i	0.812143	+	0.468891i
$766$	14.8566	−	6.33637i	0.536789	−	0.228942i
$767$	−15.7554	+	9.09636i	−0.568893	+	0.328450i
$768$	3.50354	+	41.8348i	0.126423	+	1.50958i
$769$			15.6459i			0.564206i	0.959384	+	0.282103i	$0.0910320\pi$
$769$			15.6459i			0.564206i	−0.959384	+	0.282103i	$0.908968\pi$
$770$	−9.45520	+	4.37988i	−0.340742	+	0.157840i
$771$	−33.0562			−1.19049
$772$	−15.6350	+	16.3022i	−0.562715	+	0.586728i
$773$	15.2125	+	26.3489i	0.547156	+	0.947703i	0.998468	+	0.0553362i	$0.0176230\pi$
$773$	15.2125	+	26.3489i	0.547156	+	0.947703i	−0.451311	+	0.892367i	$0.649044\pi$
$774$		0			0
$775$	−1.50836	+	2.61255i	−0.0541817	+	0.0938455i
$776$	45.5689	+	17.2234i	1.63583	+	0.618286i
$777$	−20.8700	+	38.8513i	−0.748707	+	1.39378i
$778$	−42.1999	−	5.10794i	−1.51294	−	0.183129i
$779$	−11.3910	+	19.7297i	−0.408124	+	0.706891i
$780$	26.2286	−	7.61852i	0.939134	−	0.272787i
$781$	−6.14009	+	3.54498i	−0.219710	+	0.126849i
$782$	23.2806	+	17.4806i	0.832513	+	0.625105i
$783$	10.8181			0.386609
$784$	25.5606	+	11.4304i	0.912879	+	0.408230i
$785$	−29.7427			−1.06156
$786$	18.0647	+	13.5641i	0.644346	+	0.483817i
$787$	−28.3722	+	16.3807i	−1.01136	+	0.583909i	−0.911590	−	0.411102i	$-0.865144\pi$
$787$	−28.3722	+	16.3807i	−1.01136	+	0.583909i	−0.0997704	+	0.995010i	$0.531811\pi$
$788$	−11.3729	+	3.30345i	−0.405144	+	0.117681i
$789$	6.47291	−	11.2114i	0.230442	−	0.399137i
$790$	17.7532	+	2.14888i	0.631631	+	0.0764536i
$791$	25.1193	−	46.7618i	0.893140	−	1.66266i
$792$	5.20473	−	13.7704i	0.184942	−	0.489311i
$793$	−6.44092	+	11.1560i	−0.228724	+	0.396161i
$794$	−5.64886	+	2.40926i	−0.200471	+	0.0855013i
$795$	−23.4126	−	40.5518i	−0.830359	−	1.43822i
$796$	25.7647	−	26.8642i	0.913207	−	0.952177i
$797$	28.3790			1.00523			0.502617	−	0.864509i	$-0.332370\pi$
$797$	28.3790			1.00523			0.502617	+	0.864509i	$0.332370\pi$
$798$	−36.5616	+	16.9363i	−1.29427	+	0.599537i
$799$		−	3.63649i		−	0.128650i
$800$	−1.65494	−	3.47091i	−0.0585111	−	0.122715i
$801$	5.82673	−	3.36406i	0.205877	−	0.118863i
$802$	25.9826	−	11.0816i	0.917477	−	0.391307i
$803$	−0.643636	−	0.371603i	−0.0227134	−	0.0131136i
$804$	9.84701	−	40.0802i	0.347277	−	1.41352i
$805$	1.08006	+	35.2228i	0.0380672	+	1.24144i
$806$	1.88850	−	15.6021i	0.0665197	−	0.549560i
$807$	−59.7626	−	34.5040i	−2.10374	−	1.21460i
$808$	3.42617	−	0.560761i	0.120532	−	0.0197275i
$809$	4.08387	+	7.07347i	0.143581	+	0.248690i	0.928843	−	0.370474i	$-0.120805\pi$
$809$	4.08387	+	7.07347i	0.143581	+	0.248690i	−0.785262	+	0.619164i	$0.787472\pi$
$810$	13.0793	+	9.82079i	0.459560	+	0.345067i
$811$		−	22.2710i		−	0.782041i	−0.920382	−	0.391021i	$-0.872122\pi$
$811$		−	22.2710i		−	0.782041i	0.920382	−	0.391021i	$-0.127878\pi$
$812$	5.14816	−	24.1232i	0.180665	−	0.846558i
$813$		−	73.7246i		−	2.58563i
$814$	7.22810	−	9.62637i	0.253345	−	0.337404i
$815$	8.63997	+	14.9649i	0.302645	+	0.524196i
$816$	1.40812	+	33.6869i	0.0492942	+	1.17928i
$817$		0			0
$818$	−42.8563	−	5.18740i	−1.49844	−	0.181373i
$819$	13.5446	+	21.8824i	0.473287	+	0.764634i
$820$	−5.50535	+	22.4083i	−0.192255	+	0.782533i
$821$	−4.52231	−	2.61096i	−0.157830	−	0.0911230i	0.419005	−	0.907984i	$-0.362379\pi$
$821$	−4.52231	−	2.61096i	−0.157830	−	0.0911230i	−0.576835	+	0.816861i	$0.695712\pi$
$822$	20.3420	+	47.6948i	0.709508	+	1.66355i
$823$	8.29368	−	4.78836i	0.289099	−	0.166912i	−0.348436	−	0.937333i	$-0.613287\pi$
$823$	8.29368	−	4.78836i	0.289099	−	0.166912i	0.637536	+	0.770421i	$0.279954\pi$
$824$	−27.3280	−	33.3941i	−0.952017	−	1.16334i
$825$			2.38975i			0.0832004i
$826$	15.6487	−	22.2284i	0.544486	−	0.773426i
$827$	40.6664			1.41411			0.707055	−	0.707159i	$-0.250023\pi$
$827$	40.6664			1.41411			0.707055	+	0.707159i	$0.250023\pi$
$828$	−35.9300	−	34.4595i	−1.24866	−	1.19755i
$829$	−16.6171	−	28.7816i	−0.577134	−	0.999625i	−0.995806	−	0.0914880i	$-0.970838\pi$
$829$	−16.6171	−	28.7816i	−0.577134	−	0.999625i	0.418672	−	0.908137i	$-0.362496\pi$
$830$	−0.580256	−	1.36050i	−0.0201410	−	0.0472235i
$831$	−35.4452	+	61.3929i	−1.22958	+	2.12970i
$832$	15.0243	+	13.2502i	0.520875	+	0.459369i
$833$	20.1271	+	10.0295i	0.697364	+	0.347500i
$834$	0.224361	−	1.85358i	0.00776897	−	0.0641843i
$835$	−2.60236	+	4.50743i	−0.0900586	+	0.155986i
$836$	10.5620	−	3.06789i	0.365293	−	0.106105i
$837$	−8.91945	+	5.14965i	−0.308301	+	0.177998i
$838$	1.76684	−	2.35307i	0.0610344	−	0.0812855i
$839$	15.0243			0.518698			0.259349	−	0.965784i	$-0.416492\pi$
$839$	15.0243			0.518698			0.259349	+	0.965784i	$0.416492\pi$
$840$	−30.7768	+	26.8025i	−1.06190	+	0.924775i
$841$	7.27029			0.250700
$842$	−25.8176	+	34.3838i	−0.889733	+	1.18494i
$843$	45.5890	−	26.3208i	1.57017	−	0.906538i
$844$	3.19646	+	11.0046i	0.110027	+	0.378793i
$845$	−6.99392	+	12.1138i	−0.240598	+	0.416728i
$846$	−0.747244	+	6.17344i	−0.0256908	+	0.212247i
$847$	−12.8174	−	20.7076i	−0.440411	−	0.711521i
$848$	15.9148	−	30.4339i	0.546517	−	1.04510i
$849$	7.19938	−	12.4697i	0.247082	−	0.427959i
$850$	−1.21155	−	2.84067i	−0.0415559	−	0.0974341i
$851$	−20.3548	−	35.2556i	−0.697755	−	1.20855i
$852$	−19.2206	+	20.0408i	−0.658485	+	0.686585i
$853$	12.5203			0.428686			0.214343	−	0.976758i	$-0.431239\pi$
$853$	12.5203			0.428686			0.214343	+	0.976758i	$0.431239\pi$
$854$	1.72623	−	19.1710i	0.0590703	−	0.656017i
$855$		−	33.1380i		−	1.13329i
$856$	−19.8991	−	24.3162i	−0.680139	−	0.831109i
$857$	−46.8265	+	27.0353i	−1.59956	+	0.923509i	−0.607993	+	0.793942i	$0.708025\pi$
$857$	−46.8265	+	27.0353i	−1.59956	+	0.923509i	−0.991571	+	0.129566i	$0.958641\pi$
$858$	−4.88417	−	11.4517i	−0.166743	−	0.390953i
$859$	17.0990	+	9.87213i	0.583411	+	0.336833i	0.762488	−	0.647002i	$-0.223978\pi$
$859$	17.0990	+	9.87213i	0.583411	+	0.336833i	−0.179077	+	0.983835i	$0.557311\pi$
$860$		0			0
$861$	−38.5152	+	1.18102i	−1.31260	+	0.0402491i
$862$	3.76563	+	0.455798i	0.128258	+	0.0155246i
$863$	26.3755	+	15.2279i	0.897833	+	0.518364i	0.876497	−	0.481408i	$-0.159874\pi$
$863$	26.3755	+	15.2279i	0.897833	+	0.518364i	0.0213367	+	0.999772i	$0.493208\pi$
$864$	1.03185	−	13.0874i	0.0351042	−	0.445244i
$865$	−5.64697	−	9.78084i	−0.192003	−	0.332559i
$866$	−25.0223	+	33.3246i	−0.850292	+	1.13242i
$867$		−	17.5265i		−	0.595232i
$868$	7.23850	+	22.3400i	0.245691	+	0.758268i
$869$		−	8.15137i		−	0.276516i
$870$	28.7502	+	21.5876i	0.974724	+	0.731887i
$871$	−9.84701	−	17.0555i	−0.333653	−	0.577905i
$872$	−5.75575	−	35.1668i	−0.194914	−	1.19090i
$873$	−57.9407	−	33.4521i	−1.96100	−	1.13218i
$874$	4.46946	−	36.9249i	0.151182	−	1.24900i
$875$	14.7808	−	27.5157i	0.499682	−	0.930201i
$876$	−2.82673	−	0.694478i	−0.0955062	−	0.0234642i
$877$	−18.3275	−	10.5814i	−0.618877	−	0.357309i	0.157555	−	0.987510i	$-0.449639\pi$
$877$	−18.3275	−	10.5814i	−0.618877	−	0.357309i	−0.776432	+	0.630201i	$0.782972\pi$
$878$	−9.82520	+	4.19048i	−0.331584	+	0.141422i
$879$	31.1148	−	17.9641i	1.04948	−	0.605915i
$880$	9.40635	−	5.96797i	0.317088	−	0.201180i
$881$			11.5367i			0.388681i	0.980934	+	0.194340i	$0.0622566\pi$
$881$			11.5367i			0.388681i	−0.980934	+	0.194340i	$0.937743\pi$
$882$	−32.1077	−	21.1622i	−1.08112	−	0.712568i
$883$	49.8555			1.67777			0.838886	−	0.544307i	$-0.183207\pi$
$883$	49.8555			1.67777			0.838886	+	0.544307i	$0.183207\pi$
$884$	11.6115	+	11.1363i	0.390537	+	0.374554i
$885$	19.8113	+	34.3142i	0.665950	+	1.15346i
$886$	9.78011	−	4.17125i	0.328569	−	0.140136i
$887$	5.56575	−	9.64015i	0.186879	−	0.323685i	−0.757329	−	0.653034i	$-0.773496\pi$
$887$	5.56575	−	9.64015i	0.186879	−	0.323685i	0.944208	+	0.329349i	$0.106829\pi$
$888$	16.6690	−	44.1019i	0.559374	−	1.47996i
$889$	−34.0629	−	18.2978i	−1.14243	−	0.613688i
$890$	5.05442	+	0.611796i	0.169425	+	0.0205074i
$891$	3.72770	−	6.45656i	0.124883	−	0.216303i
$892$	11.6411	+	40.0772i	0.389772	+	1.34188i
$893$	−4.02352	+	2.32298i	−0.134642	+	0.0777356i
$894$	−16.3462	−	12.2738i	−0.546700	−	0.410498i
$895$	−7.31287			−0.244442
$896$	−28.6924	−	8.52899i	−0.958547	−	0.284934i
$897$	−42.1022			−1.40575
$898$	−16.2094	−	12.1711i	−0.540916	−	0.406155i
$899$	17.9159	−	10.3438i	0.597530	−	0.344984i
$900$	1.47306	+	5.07138i	0.0491021	+	0.169046i
$901$	13.7913	−	23.8872i	0.459454	−	0.795798i
$902$	10.4418	+	1.26389i	0.347672	+	0.0420829i
$903$		0			0
$904$	−20.0629	+	53.0815i	−0.667282	+	1.76546i
$905$	−23.0696	+	39.9577i	−0.766859	+	1.32824i
$906$	−24.0221	+	10.2455i	−0.798079	+	0.340383i
$907$	7.20674	+	12.4824i	0.239296	+	0.414473i	0.960512	−	0.278237i	$-0.0897501\pi$
$907$	7.20674	+	12.4824i	0.239296	+	0.414473i	−0.721217	+	0.692710i	$0.756417\pi$
$908$	23.7969	+	22.8229i	0.789727	+	0.757406i
$909$	−4.76801			−0.158145
$910$	−1.74647	+	19.3958i	−0.0578951	+	0.642966i
$911$			19.1909i			0.635823i	0.948120	+	0.317911i	$0.102981\pi$
$911$			19.1909i			0.635823i	−0.948120	+	0.317911i	$0.897019\pi$
$912$	36.3727	−	23.0771i	1.20442	−	0.764160i
$913$	−0.583868	+	0.337096i	−0.0193232	+	0.0111563i
$914$	−16.8598	+	7.19077i	−0.557674	+	0.237850i
$915$	24.2971	+	14.0279i	0.803237	+	0.463749i
$916$	16.5081	+	4.05576i	0.545443	+	0.134006i
$917$	−13.6958	+	8.47733i	−0.452276	+	0.279946i
$918$	1.26696	−	10.4671i	0.0418158	−	0.345466i
$919$	22.4285	+	12.9491i	0.739848	+	0.427151i	0.822014	−	0.569467i	$-0.192850\pi$
$919$	22.4285	+	12.9491i	0.739848	+	0.427151i	−0.0821662	+	0.996619i	$0.526184\pi$
$920$	−6.08489	−	37.1778i	−0.200613	−	1.22572i
$921$	32.0366	+	55.4890i	1.05564	+	1.82843i
$922$	37.7575	+	28.3508i	1.24348	+	0.933683i
$923$			13.2502i			0.436136i
$924$	13.8144	+	12.4590i	0.454461	+	0.409872i
$925$			4.31842i			0.141989i
$926$	25.2826	−	33.6713i	0.830839	−	1.10651i
$927$	29.6310	+	51.3224i	0.973210	+	1.68565i
$928$	−2.07261	+	26.2879i	−0.0680366	+	0.862943i
$929$	−36.7480	−	21.2165i	−1.20566	−	0.696090i	−0.243854	−	0.969812i	$-0.578412\pi$
$929$	−36.7480	−	21.2165i	−1.20566	−	0.696090i	−0.961809	+	0.273722i	$0.911745\pi$
$930$	−33.9804	−	4.11305i	−1.11426	−	0.134872i
$931$	−1.76029	−	28.6761i	−0.0576910	−	0.939820i
$932$	−8.69158	−	2.13537i	−0.284702	−	0.0699464i
$933$	39.1536	+	22.6053i	1.28183	+	0.740065i
$934$	15.0807	+	35.3589i	0.493455	+	1.15698i
$935$	7.74809	−	4.47336i	0.253390	−	0.146295i
$936$	−17.4238	−	21.2914i	−0.569514	−	0.695930i
$937$		−	46.5547i		−	1.52088i	−0.649410	−	0.760439i	$-0.724984\pi$
$937$		−	46.5547i		−	1.52088i	0.649410	−	0.760439i	$-0.275016\pi$
$938$	24.0628	+	16.9400i	0.785678	+	0.553111i
$939$	−45.5812			−1.48749
$940$	−3.25719	+	3.39618i	−0.106238	+	0.110771i
$941$	−1.48937	−	2.57967i	−0.0485522	−	0.0840949i	0.840728	−	0.541458i	$-0.182127\pi$
$941$	−1.48937	−	2.57967i	−0.0485522	−	0.0840949i	−0.889280	+	0.457363i	$0.848794\pi$
$942$	20.8309	+	48.8411i	0.678706	+	1.59133i
$943$	17.7847	−	30.8040i	0.579150	−	1.00312i
$944$	−13.4668	+	25.7526i	−0.438308	+	0.838177i
$945$	10.8517	−	6.71690i	0.353006	−	0.218501i
$946$		0			0
$947$	13.5270	−	23.4294i	0.439568	−	0.761354i	−0.558088	−	0.829782i	$-0.688465\pi$
$947$	13.5270	−	23.4294i	0.439568	−	0.761354i	0.997656	+	0.0684276i	$0.0217982\pi$
$948$	−8.90509	−	30.6579i	−0.289224	−	0.995723i
$949$	−1.20287	+	0.694478i	−0.0390469	+	0.0225437i
$950$	−2.36906	+	3.15511i	−0.0768625	+	0.102365i
$951$	−50.8580			−1.64918
$952$	−22.7375	−	7.80629i	−0.736928	−	0.253003i
$953$	28.7293			0.930634			0.465317	−	0.885144i	$-0.345940\pi$
$953$	28.7293			0.930634			0.465317	+	0.885144i	$0.345940\pi$
$954$	−28.3211	+	37.7179i	−0.916928	+	1.22116i
$955$	−2.36152	+	1.36342i	−0.0764169	+	0.0441193i
$956$	−47.1849	+	13.7056i	−1.52607	+	0.443271i
$957$	8.19403	−	14.1925i	0.264875	−	0.458778i
$958$	5.85225	−	48.3490i	0.189078	−	1.56209i
$959$	−36.9536	+	1.13313i	−1.19329	+	0.0365908i
$960$	28.8582	−	32.7221i	0.931394	−	1.05610i
$961$	5.65232	−	9.79010i	0.182333	−	0.315810i
$962$	−8.82598	−	20.6938i	−0.284561	−	0.667195i
$963$	21.5761	+	37.3708i	0.695279	+	1.20426i
$964$	−8.37535	−	8.03257i	−0.269752	−	0.258712i
$965$	23.4747			0.755677
$966$	57.0837	−	26.4426i	1.83664	−	0.850776i
$967$		−	13.3546i		−	0.429453i	−0.976674	−	0.214727i	$-0.931114\pi$
$967$		−	13.3546i		−	0.429453i	0.976674	−	0.214727i	$-0.0688861\pi$
$968$	16.4883	+	20.1482i	0.529955	+	0.647589i
$969$	29.9605	−	17.2977i	0.962471	−	0.555683i
$970$	−19.8619	−	46.5691i	−0.637726	−	1.49524i
$971$	−1.71876	−	0.992325i	−0.0551575	−	0.0318452i	0.472168	−	0.881509i	$-0.343472\pi$
$971$	−1.71876	−	0.992325i	−0.0551575	−	0.0318452i	−0.527325	+	0.849664i	$0.676805\pi$
$972$	10.2888	−	41.8783i	0.330013	−	1.34325i
$973$	1.17278	+	0.629989i	0.0375976	+	0.0201965i
$974$	−11.0662	−	1.33948i	−0.354585	−	0.0429196i
$975$	3.86778	+	2.23306i	0.123868	+	0.0715153i
$976$	0.859396	+	20.5596i	0.0275086	+	0.658097i
$977$	31.2242	+	54.0818i	0.998950	+	1.73023i	0.539158	+	0.842205i	$0.318743\pi$
$977$	31.2242	+	54.0818i	0.998950	+	1.73023i	0.459792	+	0.888027i	$0.347924\pi$
$978$	18.5229	−	24.6688i	0.592298	−	0.788821i
$979$		−	2.32073i		−	0.0741710i
$980$	−9.81377	−	27.3945i	−0.313489	−	0.875085i
$981$			48.9397i			1.56252i
$982$	−9.11836	−	6.84665i	−0.290978	−	0.218486i
$983$	−3.64021	−	6.30503i	−0.116105	−	0.201099i	0.802116	−	0.597168i	$-0.203707\pi$
$983$	−3.64021	−	6.30503i	−0.116105	−	0.201099i	−0.918221	+	0.396069i	$0.870374\pi$
$984$	40.6530	−	6.65368i	1.29597	−	0.212111i
$985$	10.6590	+	6.15397i	0.339624	+	0.196082i
$986$	−2.54486	+	21.0246i	−0.0810448	+	0.669561i
$987$	−6.92261	−	3.71866i	−0.220349	−	0.118366i
$988$	4.90411	−	19.9612i	0.156021	−	0.635049i
$989$		0			0
$990$	−14.0727	+	6.00203i	−0.447258	+	0.190757i
$991$	−31.3345	+	18.0910i	−0.995373	+	0.574679i	−0.906876	−	0.421398i	$-0.861540\pi$
$991$	−31.3345	+	18.0910i	−0.995373	+	0.574679i	−0.0884967	+	0.996076i	$0.528206\pi$
$992$	−10.8047	−	22.6607i	−0.343051	−	0.719479i
$993$			54.5797i			1.73204i
$994$	−8.32190	−	17.9651i	−0.263955	−	0.569819i
$995$	−38.6838			−1.22636
$996$	−1.82771	+	1.90570i	−0.0579131	+	0.0603844i
$997$	−17.1218	−	29.6559i	−0.542254	−	0.939211i	−0.998774	−	0.0494984i	$-0.984238\pi$
$997$	−17.1218	−	29.6559i	−0.542254	−	0.939211i	0.456520	−	0.889713i	$-0.349096\pi$
$998$	31.2765	−	13.3395i	0.990039	−	0.422255i
$999$	−7.37171	+	12.7682i	−0.233231	+	0.403967i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.2.m.a.19.6	yes	12
3.2	odd	2		504.2.bk.a.19.1		12
4.3	odd	2		224.2.q.a.47.6		12
7.2	even	3		392.2.e.e.195.5		12
7.3	odd	6	inner	56.2.m.a.3.2	✓	12
7.4	even	3		392.2.m.g.227.2		12
7.5	odd	6		392.2.e.e.195.6		12
7.6	odd	2		392.2.m.g.19.6		12
8.3	odd	2	inner	56.2.m.a.19.1	yes	12
8.5	even	2		224.2.q.a.47.5		12
12.11	even	2		2016.2.bs.a.271.2		12
21.17	even	6		504.2.bk.a.451.5		12
24.5	odd	2		2016.2.bs.a.271.5		12
24.11	even	2		504.2.bk.a.19.6		12
28.3	even	6		224.2.q.a.143.5		12
28.11	odd	6		1568.2.q.g.815.2		12
28.19	even	6		1568.2.e.e.783.2		12
28.23	odd	6		1568.2.e.e.783.11		12
28.27	even	2		1568.2.q.g.1391.1		12
56.3	even	6	inner	56.2.m.a.3.5	yes	12
56.5	odd	6		1568.2.e.e.783.1		12
56.11	odd	6		392.2.m.g.227.5		12
56.13	odd	2		1568.2.q.g.1391.2		12
56.19	even	6		392.2.e.e.195.8		12
56.27	even	2		392.2.m.g.19.1		12
56.37	even	6		1568.2.e.e.783.12		12
56.45	odd	6		224.2.q.a.143.6		12
56.51	odd	6		392.2.e.e.195.7		12
56.53	even	6		1568.2.q.g.815.1		12
84.59	odd	6		2016.2.bs.a.1711.5		12
168.59	odd	6		504.2.bk.a.451.2		12
168.101	even	6		2016.2.bs.a.1711.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.2	✓	12	7.3	odd	6	inner
56.2.m.a.3.5	yes	12	56.3	even	6	inner
56.2.m.a.19.1	yes	12	8.3	odd	2	inner
56.2.m.a.19.6	yes	12	1.1	even	1	trivial
224.2.q.a.47.5		12	8.5	even	2
224.2.q.a.47.6		12	4.3	odd	2
224.2.q.a.143.5		12	28.3	even	6
224.2.q.a.143.6		12	56.45	odd	6
392.2.e.e.195.5		12	7.2	even	3
392.2.e.e.195.6		12	7.5	odd	6
392.2.e.e.195.7		12	56.51	odd	6
392.2.e.e.195.8		12	56.19	even	6
392.2.m.g.19.1		12	56.27	even	2
392.2.m.g.19.6		12	7.6	odd	2
392.2.m.g.227.2		12	7.4	even	3
392.2.m.g.227.5		12	56.11	odd	6
504.2.bk.a.19.1		12	3.2	odd	2
504.2.bk.a.19.6		12	24.11	even	2
504.2.bk.a.451.2		12	168.59	odd	6
504.2.bk.a.451.5		12	21.17	even	6
1568.2.e.e.783.1		12	56.5	odd	6
1568.2.e.e.783.2		12	28.19	even	6
1568.2.e.e.783.11		12	28.23	odd	6
1568.2.e.e.783.12		12	56.37	even	6
1568.2.q.g.815.1		12	56.53	even	6
1568.2.q.g.815.2		12	28.11	odd	6
1568.2.q.g.1391.1		12	28.27	even	2
1568.2.q.g.1391.2		12	56.13	odd	2
2016.2.bs.a.271.2		12	12.11	even	2
2016.2.bs.a.271.5		12	24.5	odd	2
2016.2.bs.a.1711.2		12	168.101	even	6
2016.2.bs.a.1711.5		12	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	56.2.m.a.19.6

Level	$56$
Weight	$2$
Character	56.19
Analytic conductor	$0.447$
Analytic rank	$0$
Dimension	$12$
Inner twists	$4$