LMFDB - Embedded newform 336.2.w.b.85.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (of order $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			85.10
Character	$\chi$	$=$	336.85
Dual form			336.2.w.b.253.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.647888 - 1.25708i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.16048 - 1.62889i) q^{4} +(2.52107 + 2.52107i) q^{5} +(-0.430761 - 1.34701i) q^{6} -1.00000i q^{7} +(-2.79950 + 0.403476i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.647888 - 1.25708i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.16048 - 1.62889i) q^{4} +(2.52107 + 2.52107i) q^{5} +(-0.430761 - 1.34701i) q^{6} -1.00000i q^{7} +(-2.79950 + 0.403476i) q^{8} -1.00000i q^{9} +(4.80254 - 1.53580i) q^{10} +(-1.92584 - 1.92584i) q^{11} +(-1.97238 - 0.331214i) q^{12} +(4.58005 - 4.58005i) q^{13} +(-1.25708 - 0.647888i) q^{14} +3.56533 q^{15} +(-1.30656 + 3.78059i) q^{16} +3.46521 q^{17} +(-1.25708 - 0.647888i) q^{18} +(-3.90337 + 3.90337i) q^{19} +(1.18089 - 7.03219i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(-3.66867 + 1.17320i) q^{22} +2.95507i q^{23} +(-1.69425 + 2.26485i) q^{24} +7.71155i q^{25} +(-2.79011 - 8.72483i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.62889 + 1.16048i) q^{28} +(-1.67222 + 1.67222i) q^{29} +(2.30993 - 4.48189i) q^{30} -7.77268 q^{31} +(3.90599 + 4.09185i) q^{32} -2.72356 q^{33} +(2.24507 - 4.35603i) q^{34} +(2.52107 - 2.52107i) q^{35} +(-1.62889 + 1.16048i) q^{36} +(-3.39526 - 3.39526i) q^{37} +(2.37789 + 7.43578i) q^{38} -6.47717i q^{39} +(-8.07492 - 6.04054i) q^{40} +8.22116i q^{41} +(-1.34701 + 0.430761i) q^{42} +(3.36600 + 3.36600i) q^{43} +(-0.902080 + 5.37190i) q^{44} +(2.52107 - 2.52107i) q^{45} +(3.71475 + 1.91455i) q^{46} +5.44032 q^{47} +(1.74940 + 3.59716i) q^{48} -1.00000 q^{49} +(9.69401 + 4.99622i) q^{50} +(2.45027 - 2.45027i) q^{51} +(-12.7755 - 2.14533i) q^{52} +(0.328423 + 0.328423i) q^{53} +(-1.34701 + 0.430761i) q^{54} -9.71036i q^{55} +(0.403476 + 2.79950i) q^{56} +5.52020i q^{57} +(1.01870 + 3.18552i) q^{58} +(4.92858 + 4.92858i) q^{59} +(-4.13750 - 5.80752i) q^{60} +(-10.0529 + 10.0529i) q^{61} +(-5.03583 + 9.77085i) q^{62} -1.00000 q^{63} +(7.67441 - 2.25906i) q^{64} +23.0932 q^{65} +(-1.76456 + 3.42372i) q^{66} +(-5.72344 + 5.72344i) q^{67} +(-4.02131 - 5.64444i) q^{68} +(2.08955 + 2.08955i) q^{69} +(-1.53580 - 4.80254i) q^{70} -5.86339i q^{71} +(0.403476 + 2.79950i) q^{72} -6.93302i q^{73} +(-6.46786 + 2.06836i) q^{74} +(5.45289 + 5.45289i) q^{75} +(10.8880 + 1.82837i) q^{76} +(-1.92584 + 1.92584i) q^{77} +(-8.14229 - 4.19648i) q^{78} +8.37696 q^{79} +(-12.8251 + 6.23720i) q^{80} -1.00000 q^{81} +(10.3346 + 5.32639i) q^{82} +(3.79326 - 3.79326i) q^{83} +(-0.331214 + 1.97238i) q^{84} +(8.73601 + 8.73601i) q^{85} +(6.41211 - 2.05053i) q^{86} +2.36488i q^{87} +(6.16844 + 4.61437i) q^{88} -7.71391i q^{89} +(-1.53580 - 4.80254i) q^{90} +(-4.58005 - 4.58005i) q^{91} +(4.81348 - 3.42931i) q^{92} +(-5.49612 + 5.49612i) q^{93} +(3.52472 - 6.83890i) q^{94} -19.6813 q^{95} +(5.65533 + 0.131425i) q^{96} -12.3113 q^{97} +(-0.647888 + 1.25708i) q^{98} +(-1.92584 + 1.92584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) $ 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

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 $

$2$	0.647888	−	1.25708i	0.458126	−	0.888887i
$2$	0.647888	−	1.25708i	0.458126	−	0.888887i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.16048	−	1.62889i	−0.580241	−	0.814445i
$5$	2.52107	+	2.52107i	1.12746	+	1.12746i	0.990590	+	0.136866i	$0.0437028\pi$
$5$	2.52107	+	2.52107i	1.12746	+	1.12746i	0.136866	+	0.990590i	$0.456297\pi$
$6$	−0.430761	−	1.34701i	−0.175858	−	0.549916i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.79950	+	0.403476i	−0.989773	+	0.142650i
$9$		−	1.00000i		−	0.333333i
$10$	4.80254	−	1.53580i	1.51870	−	0.485664i
$11$	−1.92584	−	1.92584i	−0.580664	−	0.580664i	0.354422	−	0.935086i	$-0.384678\pi$
$11$	−1.92584	−	1.92584i	−0.580664	−	0.580664i	−0.935086	+	0.354422i	$0.884678\pi$
$12$	−1.97238	−	0.331214i	−0.569378	−	0.0956133i
$13$	4.58005	−	4.58005i	1.27028	−	1.27028i	0.324335	−	0.945942i	$-0.394860\pi$
$13$	4.58005	−	4.58005i	1.27028	−	1.27028i	0.945942	−	0.324335i	$-0.105140\pi$
$14$	−1.25708	−	0.647888i	−0.335968	−	0.173155i
$15$	3.56533			0.920563
$16$	−1.30656	+	3.78059i	−0.326641	+	0.945149i
$17$	3.46521			0.840436			0.420218	−	0.907423i	$-0.361954\pi$
$17$	3.46521			0.840436			0.420218	+	0.907423i	$0.361954\pi$
$18$	−1.25708	−	0.647888i	−0.296296	−	0.152709i
$19$	−3.90337	+	3.90337i	−0.895495	+	0.895495i	−0.995034	−	0.0995391i	$-0.968263\pi$
$19$	−3.90337	+	3.90337i	−0.895495	+	0.895495i	0.0995391	+	0.995034i	$0.468263\pi$
$20$	1.18089	−	7.03219i	0.264054	−	1.57245i
$21$	−0.707107	−	0.707107i	−0.154303	−	0.154303i
$22$	−3.66867	+	1.17320i	−0.782162	+	0.250127i
$23$			2.95507i			0.616175i	0.951358	+	0.308087i	$0.0996889\pi$
$23$			2.95507i			0.616175i	−0.951358	+	0.308087i	$0.900311\pi$
$24$	−1.69425	+	2.26485i	−0.345836	+	0.462310i
$25$			7.71155i			1.54231i
$26$	−2.79011	−	8.72483i	−0.547186	−	1.71108i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.62889	+	1.16048i	−0.307831	+	0.219310i
$29$	−1.67222	+	1.67222i	−0.310523	+	0.310523i	−0.845112	−	0.534589i	$-0.820466\pi$
$29$	−1.67222	+	1.67222i	−0.310523	+	0.310523i	0.534589	+	0.845112i	$0.320466\pi$
$30$	2.30993	−	4.48189i	0.421734	−	0.818277i
$31$	−7.77268			−1.39601			−0.698007	−	0.716090i	$-0.745930\pi$
$31$	−7.77268			−1.39601			−0.698007	+	0.716090i	$0.745930\pi$
$32$	3.90599	+	4.09185i	0.690488	+	0.723344i
$33$	−2.72356			−0.474110
$34$	2.24507	−	4.35603i	0.385026	−	0.747053i
$35$	2.52107	−	2.52107i	0.426138	−	0.426138i
$36$	−1.62889	+	1.16048i	−0.271482	+	0.193414i
$37$	−3.39526	−	3.39526i	−0.558178	−	0.558178i	0.370610	−	0.928788i	$-0.379149\pi$
$37$	−3.39526	−	3.39526i	−0.558178	−	0.558178i	−0.928788	+	0.370610i	$0.879149\pi$
$38$	2.37789	+	7.43578i	0.385744	+	1.20624i
$39$		−	6.47717i		−	1.03718i
$40$	−8.07492	−	6.04054i	−1.27676	−	0.955093i
$41$			8.22116i			1.28393i	0.766734	+	0.641965i	$0.221880\pi$
$41$			8.22116i			1.28393i	−0.766734	+	0.641965i	$0.778120\pi$
$42$	−1.34701	+	0.430761i	−0.207849	+	0.0664679i
$43$	3.36600	+	3.36600i	0.513310	+	0.513310i	0.915539	−	0.402229i	$-0.131764\pi$
$43$	3.36600	+	3.36600i	0.513310	+	0.513310i	−0.402229	+	0.915539i	$0.631764\pi$
$44$	−0.902080	+	5.37190i	−0.135994	+	0.809844i
$45$	2.52107	−	2.52107i	0.375818	−	0.375818i
$46$	3.71475	+	1.91455i	0.547710	+	0.282286i
$47$	5.44032			0.793552			0.396776	−	0.917915i	$-0.370129\pi$
$47$	5.44032			0.793552			0.396776	+	0.917915i	$0.370129\pi$
$48$	1.74940	+	3.59716i	0.252505	+	0.519206i
$49$	−1.00000			−0.142857
$50$	9.69401	+	4.99622i	1.37094	+	0.706573i
$51$	2.45027	−	2.45027i	0.343106	−	0.343106i
$52$	−12.7755	−	2.14533i	−1.77164	−	0.297504i
$53$	0.328423	+	0.328423i	0.0451124	+	0.0451124i	0.729303	−	0.684191i	$-0.239844\pi$
$53$	0.328423	+	0.328423i	0.0451124	+	0.0451124i	−0.684191	+	0.729303i	$0.739844\pi$
$54$	−1.34701	+	0.430761i	−0.183305	+	0.0586192i
$55$		−	9.71036i		−	1.30935i
$56$	0.403476	+	2.79950i	0.0539168	+	0.374099i
$57$			5.52020i			0.731168i
$58$	1.01870	+	3.18552i	0.133761	+	0.418279i
$59$	4.92858	+	4.92858i	0.641647	+	0.641647i	0.950960	−	0.309314i	$-0.100099\pi$
$59$	4.92858	+	4.92858i	0.641647	+	0.641647i	−0.309314	+	0.950960i	$0.600099\pi$
$60$	−4.13750	−	5.80752i	−0.534149	−	0.749748i
$61$	−10.0529	+	10.0529i	−1.28715	+	1.28715i	−0.350633	+	0.936513i	$0.614033\pi$
$61$	−10.0529	+	10.0529i	−1.28715	+	1.28715i	−0.936513	+	0.350633i	$0.885967\pi$
$62$	−5.03583	+	9.77085i	−0.639551	+	1.24090i
$63$	−1.00000			−0.125988
$64$	7.67441	−	2.25906i	0.959302	−	0.282383i
$65$	23.0932			2.86436
$66$	−1.76456	+	3.42372i	−0.217202	+	0.421430i
$67$	−5.72344	+	5.72344i	−0.699230	+	0.699230i	−0.964244	−	0.265015i	$-0.914623\pi$
$67$	−5.72344	+	5.72344i	−0.699230	+	0.699230i	0.265015	+	0.964244i	$0.414623\pi$
$68$	−4.02131	−	5.64444i	−0.487655	−	0.684489i
$69$	2.08955	+	2.08955i	0.251552	+	0.251552i
$70$	−1.53580	−	4.80254i	−0.183564	−	0.574014i
$71$		−	5.86339i		−	0.695857i	−0.937521	−	0.347928i	$-0.886885\pi$
$71$		−	5.86339i		−	0.695857i	0.937521	−	0.347928i	$-0.113115\pi$
$72$	0.403476	+	2.79950i	0.0475501	+	0.329924i
$73$		−	6.93302i		−	0.811449i	−0.913995	−	0.405724i	$-0.867019\pi$
$73$		−	6.93302i		−	0.811449i	0.913995	−	0.405724i	$-0.132981\pi$
$74$	−6.46786	+	2.06836i	−0.751873	+	0.240441i
$75$	5.45289	+	5.45289i	0.629646	+	0.629646i
$76$	10.8880	+	1.82837i	1.24893	+	0.209728i
$77$	−1.92584	+	1.92584i	−0.219470	+	0.219470i
$78$	−8.14229	−	4.19648i	−0.921933	−	0.475158i
$79$	8.37696			0.942482			0.471241	−	0.882005i	$-0.343806\pi$
$79$	8.37696			0.942482			0.471241	+	0.882005i	$0.343806\pi$
$80$	−12.8251	+	6.23720i	−1.43389	+	0.697340i
$81$	−1.00000			−0.111111
$82$	10.3346	+	5.32639i	1.14127	+	0.588202i
$83$	3.79326	−	3.79326i	0.416365	−	0.416365i	−0.467584	−	0.883949i	$-0.654875\pi$
$83$	3.79326	−	3.79326i	0.416365	−	0.416365i	0.883949	+	0.467584i	$0.154875\pi$
$84$	−0.331214	+	1.97238i	−0.0361384	+	0.215205i
$85$	8.73601	+	8.73601i	0.947554	+	0.947554i
$86$	6.41211	−	2.05053i	0.691436	−	0.221114i
$87$			2.36488i			0.253541i
$88$	6.16844	+	4.61437i	0.657558	+	0.491894i
$89$		−	7.71391i		−	0.817673i	−0.912608	−	0.408836i	$-0.865935\pi$
$89$		−	7.71391i		−	0.817673i	0.912608	−	0.408836i	$-0.134065\pi$
$90$	−1.53580	−	4.80254i	−0.161888	−	0.506232i
$91$	−4.58005	−	4.58005i	−0.480120	−	0.480120i
$92$	4.81348	−	3.42931i	0.501840	−	0.357530i
$93$	−5.49612	+	5.49612i	−0.569921	+	0.569921i
$94$	3.52472	−	6.83890i	0.363547	−	0.705379i
$95$	−19.6813			−2.01926
$96$	5.65533	+	0.131425i	0.577194	+	0.0134135i
$97$	−12.3113			−1.25003			−0.625014	−	0.780614i	$-0.714907\pi$
$97$	−12.3113			−1.25003			−0.625014	+	0.780614i	$0.714907\pi$
$98$	−0.647888	+	1.25708i	−0.0654466	+	0.126984i
$99$	−1.92584	+	1.92584i	−0.193555	+	0.193555i
$100$	12.5613	−	8.94912i	1.25613	−	0.894912i
$101$	−4.87076	−	4.87076i	−0.484658	−	0.484658i	0.421957	−	0.906616i	$-0.361343\pi$
$101$	−4.87076	−	4.87076i	−0.484658	−	0.484658i	−0.906616	+	0.421957i	$0.861343\pi$
$102$	−1.49268	−	4.66768i	−0.147797	−	0.462169i
$103$		−	17.4531i		−	1.71970i	−0.510546	−	0.859850i	$-0.670557\pi$
$103$		−	17.4531i		−	1.71970i	0.510546	−	0.859850i	$-0.329443\pi$
$104$	−10.9739	+	14.6698i	−1.07608	+	1.43849i
$105$		−	3.56533i		−	0.347940i
$106$	0.625634	−	0.200072i	0.0607670	−	0.0194327i
$107$	−3.39105	−	3.39105i	−0.327825	−	0.327825i	0.523934	−	0.851759i	$-0.324464\pi$
$107$	−3.39105	−	3.39105i	−0.327825	−	0.327825i	−0.851759	+	0.523934i	$0.824464\pi$
$108$	−0.331214	+	1.97238i	−0.0318711	+	0.189793i
$109$	−7.49212	+	7.49212i	−0.717615	+	0.717615i	−0.968116	−	0.250501i	$-0.919405\pi$
$109$	−7.49212	+	7.49212i	−0.717615	+	0.717615i	0.250501	+	0.968116i	$0.419405\pi$
$110$	−12.2067	−	6.29123i	−1.16386	−	0.599845i
$111$	−4.80163			−0.455750
$112$	3.78059	+	1.30656i	0.357233	+	0.123459i
$113$	17.0029			1.59950			0.799749	−	0.600334i	$-0.204966\pi$
$113$	17.0029			1.59950			0.799749	+	0.600334i	$0.204966\pi$
$114$	6.93931	+	3.57647i	0.649926	+	0.334967i
$115$	−7.44993	+	7.44993i	−0.694709	+	0.694709i
$116$	4.66444	+	0.783280i	0.433083	+	0.0727258i
$117$	−4.58005	−	4.58005i	−0.423426	−	0.423426i
$118$	9.38877	−	3.00243i	0.864306	−	0.276396i
$119$		−	3.46521i		−	0.317655i
$120$	−9.98114	+	1.43852i	−0.911149	+	0.131319i
$121$		−	3.58225i		−	0.325659i
$122$	6.12413	+	19.1505i	0.554452	+	1.73380i
$123$	5.81324	+	5.81324i	0.524162	+	0.524162i
$124$	9.02006	+	12.6608i	0.810025	+	1.13698i
$125$	−6.83600	+	6.83600i	−0.611431	+	0.611431i
$126$	−0.647888	+	1.25708i	−0.0577185	+	0.111989i
$127$	−3.49439			−0.310077			−0.155038	−	0.987908i	$-0.549550\pi$
$127$	−3.49439			−0.310077			−0.155038	+	0.987908i	$0.549550\pi$
$128$	2.13234	−	11.1109i	0.188474	−	0.982078i
$129$	4.76024			0.419116
$130$	14.9618	−	29.0299i	1.31224	−	2.54609i
$131$	−1.97326	+	1.97326i	−0.172405	+	0.172405i	−0.788035	−	0.615630i	$-0.788901\pi$
$131$	−1.97326	+	1.97326i	−0.172405	+	0.172405i	0.615630	+	0.788035i	$0.288901\pi$
$132$	3.16064	+	4.43637i	0.275098	+	0.386137i
$133$	3.90337	+	3.90337i	0.338465	+	0.338465i
$134$	3.48665	+	10.9030i	0.301201	+	0.941871i
$135$		−	3.56533i		−	0.306854i
$136$	−9.70085	+	1.39813i	−0.831841	+	0.119889i
$137$			19.5147i			1.66725i	0.552328	+	0.833627i	$0.313739\pi$
$137$			19.5147i			1.66725i	−0.552328	+	0.833627i	$0.686261\pi$
$138$	3.98052	−	1.27293i	0.338844	−	0.108359i
$139$	11.6873	+	11.6873i	0.991304	+	0.991304i	0.999963	−	0.00865832i	$-0.00275606\pi$
$139$	11.6873	+	11.6873i	0.991304	+	0.991304i	−0.00865832	+	0.999963i	$0.502756\pi$
$140$	−7.03219	−	1.18089i	−0.594329	−	0.0998031i
$141$	3.84689	−	3.84689i	0.323966	−	0.323966i
$142$	−7.37073	−	3.79882i	−0.618538	−	0.318790i
$143$	−17.6409			−1.47521
$144$	3.78059	+	1.30656i	0.315050	+	0.108880i
$145$	−8.43155			−0.700202
$146$	−8.71534	−	4.49182i	−0.721287	−	0.371746i
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$	−1.59037	+	9.47065i	−0.130727	+	0.778483i
$149$	1.95708	+	1.95708i	0.160330	+	0.160330i	0.782713	−	0.622383i	$-0.213835\pi$
$149$	1.95708	+	1.95708i	0.160330	+	0.160330i	−0.622383	+	0.782713i	$0.713835\pi$
$150$	10.3876	−	3.32184i	0.848141	−	0.271227i
$151$		−	1.15152i		−	0.0937094i	−0.998902	−	0.0468547i	$-0.985080\pi$
$151$		−	1.15152i		−	0.0937094i	0.998902	−	0.0468547i	$-0.0149198\pi$
$152$	9.35257	−	12.5024i	0.758594	−	1.01408i
$153$		−	3.46521i		−	0.280145i
$154$	1.17320	+	3.66867i	0.0945393	+	0.295629i
$155$	−19.5954	−	19.5954i	−1.57394	−	1.57394i
$156$	−10.5506	+	7.51664i	−0.844723	+	0.601813i
$157$	2.92934	−	2.92934i	0.233787	−	0.233787i	−0.580484	−	0.814271i	$-0.697137\pi$
$157$	2.92934	−	2.92934i	0.233787	−	0.233787i	0.814271	+	0.580484i	$0.197137\pi$
$158$	5.42733	−	10.5305i	0.431775	−	0.837760i
$159$	0.464461			0.0368341
$160$	−0.468571	+	20.1631i	−0.0370438	+	1.59403i
$161$	2.95507			0.232892
$162$	−0.647888	+	1.25708i	−0.0509029	+	0.0987652i
$163$	−4.56066	+	4.56066i	−0.357218	+	0.357218i	−0.862787	−	0.505568i	$-0.831283\pi$
$163$	−4.56066	+	4.56066i	−0.357218	+	0.357218i	0.505568	+	0.862787i	$0.331283\pi$
$164$	13.3914	−	9.54051i	1.04569	−	0.744988i
$165$	−6.86626	−	6.86626i	−0.534538	−	0.534538i
$166$	−2.31081	−	7.22603i	−0.179354	−	0.560849i
$167$		−	16.4718i		−	1.27463i	−0.770603	−	0.637315i	$-0.780045\pi$
$167$		−	16.4718i		−	1.27463i	0.770603	−	0.637315i	$-0.219955\pi$
$168$	2.26485	+	1.69425i	0.174737	+	0.130714i
$169$		−	28.9537i		−	2.22721i
$170$	16.6418	−	5.32188i	1.27637	−	0.408169i
$171$	3.90337	+	3.90337i	0.298498	+	0.298498i
$172$	1.57666	−	9.38902i	0.120219	−	0.715906i
$173$	−2.40066	+	2.40066i	−0.182519	+	0.182519i	−0.792452	−	0.609934i	$-0.791196\pi$
$173$	−2.40066	+	2.40066i	−0.182519	+	0.182519i	0.609934	+	0.792452i	$0.291196\pi$
$174$	2.97283	+	1.53217i	0.225370	+	0.116154i
$175$	7.71155			0.582939
$176$	9.79707	−	4.76460i	0.738482	−	0.359145i
$177$	6.97007			0.523902
$178$	−9.69697	−	4.99775i	−0.726819	−	0.374597i
$179$	−7.49093	+	7.49093i	−0.559899	+	0.559899i	−0.929279	−	0.369380i	$-0.879570\pi$
$179$	−7.49093	+	7.49093i	−0.559899	+	0.559899i	0.369380	+	0.929279i	$0.379570\pi$
$180$	−7.03219	−	1.18089i	−0.524149	−	0.0880181i
$181$	−12.6190	−	12.6190i	−0.937965	−	0.937965i	0.0602204	−	0.998185i	$-0.480820\pi$
$181$	−12.6190	−	12.6190i	−0.937965	−	0.937965i	−0.998185	+	0.0602204i	$0.980820\pi$
$182$	−8.72483	+	2.79011i	−0.646727	+	0.206817i
$183$			14.2170i			1.05095i
$184$	−1.19230	−	8.27272i	−0.0878976	−	0.609873i
$185$		−	17.1194i		−	1.25864i
$186$	3.34817	+	10.4699i	0.245500	+	0.767691i
$187$	−6.67345	−	6.67345i	−0.488011	−	0.488011i
$188$	−6.31339	−	8.86168i	−0.460452	−	0.646305i
$189$	−0.707107	+	0.707107i	−0.0514344	+	0.0514344i
$190$	−12.7513	+	24.7409i	−0.925076	+	1.79489i
$191$	4.74528			0.343357			0.171678	−	0.985153i	$-0.445081\pi$
$191$	4.74528			0.343357			0.171678	+	0.985153i	$0.445081\pi$
$192$	3.82923	−	7.02403i	0.276351	−	0.506916i
$193$	5.12759			0.369092			0.184546	−	0.982824i	$-0.440919\pi$
$193$	5.12759			0.369092			0.184546	+	0.982824i	$0.440919\pi$
$194$	−7.97637	+	15.4763i	−0.572670	+	1.11113i
$195$	16.3294	−	16.3294i	1.16937	−	1.16937i
$196$	1.16048	+	1.62889i	0.0828916	+	0.116349i
$197$	−14.3400	−	14.3400i	−1.02168	−	1.02168i	−0.999760	−	0.0219215i	$-0.993022\pi$
$197$	−14.3400	−	14.3400i	−1.02168	−	1.02168i	−0.0219215	−	0.999760i	$-0.506978\pi$
$198$	1.17320	+	3.66867i	0.0833758	+	0.260721i
$199$		−	27.4844i		−	1.94831i	−0.225872	−	0.974157i	$-0.572523\pi$
$199$		−	27.4844i		−	1.94831i	0.225872	−	0.974157i	$-0.427477\pi$
$200$	−3.11143	−	21.5885i	−0.220011	−	1.52654i
$201$			8.09417i			0.570919i
$202$	−9.27862	+	2.96721i	−0.652841	+	0.208772i
$203$	1.67222	+	1.67222i	0.117367	+	0.117367i
$204$	−6.83471	−	1.14773i	−0.478526	−	0.0803568i
$205$	−20.7261	+	20.7261i	−1.44757	+	1.44757i
$206$	−21.9398	−	11.3076i	−1.52862	−	0.787840i
$207$	2.95507			0.205392
$208$	11.3312	+	23.2994i	0.785676	+	1.61552i
$209$	15.0346			1.03996
$210$	−4.48189	−	2.30993i	−0.309280	−	0.159400i
$211$	2.28552	−	2.28552i	0.157342	−	0.157342i	−0.624046	−	0.781388i	$-0.714512\pi$
$211$	2.28552	−	2.28552i	0.157342	−	0.157342i	0.781388	+	0.624046i	$0.214512\pi$
$212$	0.153836	−	0.916094i	0.0105655	−	0.0629176i
$213$	−4.14605	−	4.14605i	−0.284082	−	0.284082i
$214$	−6.45983	+	2.06579i	−0.441585	+	0.141214i
$215$			16.9718i			1.15747i
$216$	2.26485	+	1.69425i	0.154103	+	0.115279i
$217$			7.77268i			0.527644i
$218$	4.56411	+	14.2722i	0.309121	+	0.966637i
$219$	−4.90239	−	4.90239i	−0.331273	−	0.331273i
$220$	−15.8171	+	11.2687i	−1.06639	+	0.759736i
$221$	15.8708	−	15.8708i	1.06759	−	1.06759i
$222$	−3.11092	+	6.03601i	−0.208791	+	0.405111i
$223$	28.0134			1.87592			0.937958	−	0.346748i	$-0.112714\pi$
$223$	28.0134			1.87592			0.937958	+	0.346748i	$0.112714\pi$
$224$	4.09185	−	3.90599i	0.273398	−	0.260980i
$225$	7.71155			0.514103
$226$	11.0160	−	21.3740i	0.732772	−	1.42177i
$227$	−14.2413	+	14.2413i	−0.945226	+	0.945226i	−0.998576	−	0.0533501i	$-0.983010\pi$
$227$	−14.2413	+	14.2413i	−0.945226	+	0.945226i	0.0533501	+	0.998576i	$0.483010\pi$
$228$	8.99180	−	6.40609i	0.595496	−	0.424254i
$229$	−14.3396	−	14.3396i	−0.947586	−	0.947586i	0.0511070	−	0.998693i	$-0.483725\pi$
$229$	−14.3396	−	14.3396i	−0.947586	−	0.947586i	−0.998693	+	0.0511070i	$0.983725\pi$
$230$	4.53841	+	14.1918i	0.299254	+	0.935783i
$231$			2.72356i			0.179197i
$232$	4.00668	−	5.35608i	0.263051	−	0.351644i
$233$		−	4.41313i		−	0.289113i	−0.989497	−	0.144557i	$-0.953824\pi$
$233$		−	4.41313i		−	0.289113i	0.989497	−	0.144557i	$-0.0461756\pi$
$234$	−8.72483	+	2.79011i	−0.570360	+	0.182395i
$235$	13.7154	+	13.7154i	0.894695	+	0.894695i
$236$	2.30858	−	13.7476i	0.150276	−	0.894895i
$237$	5.92341	−	5.92341i	0.384767	−	0.384767i
$238$	−4.35603	−	2.24507i	−0.282359	−	0.145526i
$239$	8.17969			0.529100			0.264550	−	0.964372i	$-0.414777\pi$
$239$	8.17969			0.529100			0.264550	+	0.964372i	$0.414777\pi$
$240$	−4.65832	+	13.4791i	−0.300693	+	0.870069i
$241$	−9.93205			−0.639779			−0.319890	−	0.947455i	$-0.603646\pi$
$241$	−9.93205			−0.639779			−0.319890	+	0.947455i	$0.603646\pi$
$242$	−4.50316	−	2.32090i	−0.289474	−	0.149193i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	28.0414	+	4.70887i	1.79516	+	0.301454i
$245$	−2.52107	−	2.52107i	−0.161065	−	0.161065i
$246$	11.0740	−	3.54136i	0.706053	−	0.225789i
$247$			35.7553i			2.27505i
$248$	21.7596	−	3.13609i	1.38174	−	0.199142i
$249$		−	5.36448i		−	0.339960i
$250$	4.16441	+	13.0223i	0.263381	+	0.823605i
$251$	8.90034	+	8.90034i	0.561784	+	0.561784i	0.929814	−	0.368030i	$-0.119968\pi$
$251$	8.90034	+	8.90034i	0.561784	+	0.561784i	−0.368030	+	0.929814i	$0.619968\pi$
$252$	1.16048	+	1.62889i	0.0731035	+	0.102610i
$253$	5.69101	−	5.69101i	0.357790	−	0.357790i
$254$	−2.26397	+	4.39271i	−0.142054	+	0.275623i
$255$	12.3546			0.773674
$256$	−12.5858	−	9.87917i	−0.786612	−	0.617448i
$257$	−12.5379			−0.782093			−0.391047	−	0.920371i	$-0.627887\pi$
$257$	−12.5379			−0.782093			−0.391047	+	0.920371i	$0.627887\pi$
$258$	3.08410	−	5.98399i	0.192008	−	0.372547i
$259$	−3.39526	+	3.39526i	−0.210971	+	0.210971i
$260$	−26.7993	−	37.6163i	−1.66202	−	2.33286i
$261$	1.67222	+	1.67222i	0.103508	+	0.103508i
$262$	1.20209	+	3.75900i	0.0742653	+	0.232231i
$263$			23.1368i			1.42668i	0.700820	+	0.713338i	$0.252817\pi$
$263$			23.1368i			1.42668i	−0.700820	+	0.713338i	$0.747183\pi$
$264$	7.62460	−	1.09889i	0.469261	−	0.0676320i
$265$			1.65595i			0.101724i
$266$	7.43578	−	2.37789i	0.455917	−	0.145798i
$267$	−5.45456	−	5.45456i	−0.333814	−	0.333814i
$268$	15.9648	+	2.68090i	0.975206	+	0.163762i
$269$	15.8990	−	15.8990i	0.969378	−	0.969378i	−0.0301671	−	0.999545i	$-0.509604\pi$
$269$	15.8990	−	15.8990i	0.969378	−	0.969378i	0.999545	+	0.0301671i	$0.00960393\pi$
$270$	−4.48189	−	2.30993i	−0.272759	−	0.140578i
$271$	7.68120			0.466600			0.233300	−	0.972405i	$-0.425048\pi$
$271$	7.68120			0.466600			0.233300	+	0.972405i	$0.425048\pi$
$272$	−4.52751	+	13.1005i	−0.274521	+	0.794337i
$273$	−6.47717			−0.392016
$274$	24.5315	+	12.6433i	1.48200	+	0.763812i
$275$	14.8512	−	14.8512i	0.895564	−	0.895564i
$276$	0.978761	−	5.82853i	0.0589145	−	0.350836i
$277$	12.4381	+	12.4381i	0.747335	+	0.747335i	0.973978	−	0.226643i	$-0.0727749\pi$
$277$	12.4381	+	12.4381i	0.747335	+	0.747335i	−0.226643	+	0.973978i	$0.572775\pi$
$278$	22.2639	−	7.11977i	1.33530	−	0.427015i
$279$			7.77268i			0.465338i
$280$	−6.04054	+	8.07492i	−0.360991	+	0.482569i
$281$		−	1.20110i		−	0.0716518i	−0.999358	−	0.0358259i	$-0.988594\pi$
$281$		−	1.20110i		−	0.0716518i	0.999358	−	0.0358259i	$-0.0114062\pi$
$282$	−2.34348	−	7.32818i	−0.139552	−	0.436387i
$283$	6.33676	+	6.33676i	0.376681	+	0.376681i	0.869903	−	0.493222i	$-0.164181\pi$
$283$	6.33676	+	6.33676i	0.376681	+	0.376681i	−0.493222	+	0.869903i	$0.664181\pi$
$284$	−9.55082	+	6.80436i	−0.566737	+	0.403765i
$285$	−13.9168	+	13.9168i	−0.824359	+	0.824359i
$286$	−11.4293	+	22.1760i	−0.675831	+	1.31129i
$287$	8.22116			0.485280
$288$	4.09185	−	3.90599i	0.241115	−	0.230163i
$289$	−4.99235			−0.293668
$290$	−5.46270	+	10.5991i	−0.320781	+	0.622401i
$291$	−8.70543	+	8.70543i	−0.510322	+	0.510322i
$292$	−11.2931	+	8.04565i	−0.660880	+	0.470836i
$293$	−2.11692	−	2.11692i	−0.123672	−	0.123672i	0.642562	−	0.766234i	$-0.277872\pi$
$293$	−2.11692	−	2.11692i	−0.123672	−	0.123672i	−0.766234	+	0.642562i	$0.777872\pi$
$294$	0.430761	+	1.34701i	0.0251225	+	0.0785594i
$295$			24.8506i			1.44686i
$296$	10.8750	+	8.13514i	0.632094	+	0.472845i
$297$			2.72356i			0.158037i
$298$	3.72816	−	1.19223i	0.215966	−	0.0690639i
$299$	13.5344	+	13.5344i	0.782713	+	0.782713i
$300$	2.55418	−	15.2101i	0.147465	−	0.878158i
$301$	3.36600	−	3.36600i	0.194013	−	0.194013i
$302$	−1.44755	−	0.746056i	−0.0832971	−	0.0429307i
$303$	−6.88829			−0.395722
$304$	−9.65706	−	19.8571i	−0.553870	−	1.13888i
$305$	−50.6882			−2.90240
$306$	−4.35603	−	2.24507i	−0.249018	−	0.128342i
$307$	3.01708	−	3.01708i	0.172194	−	0.172194i	−0.615749	−	0.787943i	$-0.711146\pi$
$307$	3.01708	−	3.01708i	0.172194	−	0.172194i	0.787943	+	0.615749i	$0.211146\pi$
$308$	5.37190	+	0.902080i	0.306092	+	0.0514008i
$309$	−12.3412	−	12.3412i	−0.702065	−	0.702065i
$310$	−37.3286	+	11.9373i	−2.12012	+	0.677994i
$311$		−	21.4417i		−	1.21584i	−0.793997	−	0.607922i	$-0.792003\pi$
$311$		−	21.4417i		−	1.21584i	0.793997	−	0.607922i	$-0.207997\pi$
$312$	2.61338	+	18.1328i	0.147954	+	1.02657i
$313$			6.68883i			0.378075i	0.981970	+	0.189038i	$0.0605368\pi$
$313$			6.68883i			0.378075i	−0.981970	+	0.189038i	$0.939463\pi$
$314$	−1.78452	−	5.58029i	−0.100706	−	0.314914i
$315$	−2.52107	−	2.52107i	−0.142046	−	0.142046i
$316$	−9.72131	−	13.6451i	−0.546867	−	0.767599i
$317$	−12.9359	+	12.9359i	−0.726553	+	0.726553i	−0.969931	−	0.243378i	$-0.921744\pi$
$317$	−12.9359	+	12.9359i	−0.726553	+	0.726553i	0.243378	+	0.969931i	$0.421744\pi$
$318$	0.300918	−	0.583862i	0.0168747	−	0.0327414i
$319$	6.44087			0.360619
$320$	25.0430	+	13.6525i	1.39994	+	0.763195i
$321$	−4.79567			−0.267668
$322$	1.91455	−	3.71475i	0.106694	−	0.207015i
$323$	−13.5260	+	13.5260i	−0.752606	+	0.752606i
$324$	1.16048	+	1.62889i	0.0644712	+	0.0904939i
$325$	35.3193	+	35.3193i	1.95916	+	1.95916i
$326$	2.77830	+	8.68790i	0.153876	+	0.481178i
$327$			10.5955i			0.585930i
$328$	−3.31704	−	23.0151i	−0.183153	−	1.27080i
$329$		−	5.44032i		−	0.299935i
$330$	−13.0800	+	4.18285i	−0.720030	+	0.230258i
$331$	3.36420	+	3.36420i	0.184913	+	0.184913i	0.793493	−	0.608580i	$-0.208260\pi$
$331$	3.36420	+	3.36420i	0.184913	+	0.184913i	−0.608580	+	0.793493i	$0.708260\pi$
$332$	−10.5808	−	1.77679i	−0.580698	−	0.0975142i
$333$	−3.39526	+	3.39526i	−0.186059	+	0.186059i
$334$	−20.7064	−	10.6719i	−1.13300	−	0.583941i
$335$	−28.8583			−1.57670
$336$	3.59716	−	1.74940i	0.196241	−	0.0954378i
$337$	2.45981			0.133995			0.0669973	−	0.997753i	$-0.478658\pi$
$337$	2.45981			0.133995			0.0669973	+	0.997753i	$0.478658\pi$
$338$	−36.3970	−	18.7588i	−1.97974	−	1.02034i
$339$	12.0229	−	12.0229i	0.652993	−	0.652993i
$340$	4.09202	−	24.3680i	0.221921	−	1.32154i
$341$	14.9690	+	14.9690i	0.810615	+	0.810615i
$342$	7.43578	−	2.37789i	0.402081	−	0.128581i
$343$			1.00000i			0.0539949i
$344$	−10.7812	−	8.06502i	−0.581284	−	0.434837i
$345$			10.5358i			0.567228i
$346$	1.46245	+	4.57316i	0.0786219	+	0.245855i
$347$	−11.6653	−	11.6653i	−0.626228	−	0.626228i	0.320889	−	0.947117i	$-0.396018\pi$
$347$	−11.6653	−	11.6653i	−0.626228	−	0.626228i	−0.947117	+	0.320889i	$0.896018\pi$
$348$	3.85212	−	2.74440i	0.206495	−	0.147115i
$349$	21.1040	−	21.1040i	1.12967	−	1.12967i	0.139443	−	0.990230i	$-0.455469\pi$
$349$	21.1040	−	21.1040i	1.12967	−	1.12967i	0.990230	−	0.139443i	$-0.0445313\pi$
$350$	4.99622	−	9.69401i	0.267059	−	0.518167i
$351$	−6.47717			−0.345726
$352$	0.357942	−	15.4026i	0.0190784	−	0.820961i
$353$	19.4701			1.03629			0.518144	−	0.855294i	$-0.326623\pi$
$353$	19.4701			1.03629			0.518144	+	0.855294i	$0.326623\pi$
$354$	4.51582	−	8.76190i	0.240013	−	0.465690i
$355$	14.7820	−	14.7820i	0.784547	−	0.784547i
$356$	−12.5651	+	8.95185i	−0.665949	+	0.474447i
$357$	−2.45027	−	2.45027i	−0.129682	−	0.129682i
$358$	4.56339	+	14.2700i	0.241183	+	0.754191i
$359$		−	3.61484i		−	0.190784i	−0.995440	−	0.0953920i	$-0.969590\pi$
$359$		−	3.61484i		−	0.190784i	0.995440	−	0.0953920i	$-0.0304105\pi$
$360$	−6.04054	+	8.07492i	−0.318364	+	0.425586i
$361$		−	11.4726i		−	0.603821i
$362$	−24.0388	+	7.68736i	−1.26345	+	0.404039i
$363$	−2.53303	−	2.53303i	−0.132950	−	0.132950i
$364$	−2.14533	+	12.7755i	−0.112446	+	0.669616i
$365$	17.4786	−	17.4786i	0.914872	−	0.914872i
$366$	17.8718	+	9.21102i	0.934176	+	0.481468i
$367$	3.31431			0.173006			0.0865029	−	0.996252i	$-0.472431\pi$
$367$	3.31431			0.173006			0.0865029	+	0.996252i	$0.472431\pi$
$368$	−11.1719	−	3.86099i	−0.582377	−	0.201268i
$369$	8.22116			0.427976
$370$	−21.5204	−	11.0914i	−1.11879	−	0.576616i
$371$	0.328423	−	0.328423i	0.0170509	−	0.0170509i
$372$	15.3307	+	2.57442i	0.794860	+	0.133478i
$373$	0.855422	+	0.855422i	0.0442921	+	0.0442921i	0.728906	−	0.684614i	$-0.240029\pi$
$373$	0.855422	+	0.855422i	0.0442921	+	0.0442921i	−0.684614	+	0.728906i	$0.740029\pi$
$374$	−12.7127	+	4.06539i	−0.657357	+	0.210216i
$375$			9.66757i			0.499231i
$376$	−15.2302	+	2.19504i	−0.785437	+	0.113201i
$377$			15.3177i			0.788901i
$378$	0.430761	+	1.34701i	0.0221560	+	0.0692829i
$379$	−8.16854	−	8.16854i	−0.419590	−	0.419590i	0.465472	−	0.885062i	$-0.345884\pi$
$379$	−8.16854	−	8.16854i	−0.419590	−	0.419590i	−0.885062	+	0.465472i	$0.845884\pi$
$380$	22.8398	+	32.0587i	1.17166	+	1.64458i
$381$	−2.47091	+	2.47091i	−0.126588	+	0.126588i
$382$	3.07441	−	5.96519i	0.157301	−	0.305205i
$383$	7.22345			0.369101			0.184551	−	0.982823i	$-0.440917\pi$
$383$	7.22345			0.369101			0.184551	+	0.982823i	$0.440917\pi$
$384$	−6.34883	−	9.36442i	−0.323987	−	0.477876i
$385$	−9.71036			−0.494886
$386$	3.32210	−	6.44577i	0.169091	−	0.328081i
$387$	3.36600	−	3.36600i	0.171103	−	0.171103i
$388$	14.2871	+	20.0538i	0.725317	+	1.01808i
$389$	23.5977	+	23.5977i	1.19645	+	1.19645i	0.975223	+	0.221226i	$0.0710058\pi$
$389$	23.5977	+	23.5977i	1.19645	+	1.19645i	0.221226	+	0.975223i	$0.428994\pi$
$390$	−9.94766	−	31.1069i	−0.503719	−	1.57516i
$391$			10.2399i			0.517855i
$392$	2.79950	−	0.403476i	0.141396	−	0.0203786i
$393$			2.79061i			0.140768i
$394$	−27.3172	+	8.73575i	−1.37622	+	0.440101i
$395$	21.1189	+	21.1189i	1.06261	+	1.06261i
$396$	5.37190	+	0.902080i	0.269948	+	0.0453312i
$397$	18.0441	−	18.0441i	0.905605	−	0.905605i	−0.0903084	−	0.995914i	$-0.528785\pi$
$397$	18.0441	−	18.0441i	0.905605	−	0.905605i	0.995914	+	0.0903084i	$0.0287853\pi$
$398$	−34.5499	−	17.8068i	−1.73183	−	0.892573i
$399$	5.52020			0.276356
$400$	−29.1543	−	10.0756i	−1.45771	−	0.503781i
$401$	−13.0759			−0.652977			−0.326488	−	0.945201i	$-0.605865\pi$
$401$	−13.0759			−0.652977			−0.326488	+	0.945201i	$0.605865\pi$
$402$	10.1750	+	5.24411i	0.507482	+	0.261553i
$403$	−35.5993	+	35.5993i	−1.77333	+	1.77333i
$404$	−2.28150	+	13.5864i	−0.113509	+	0.675946i
$405$	−2.52107	−	2.52107i	−0.125273	−	0.125273i
$406$	3.18552	−	1.01870i	0.158095	−	0.0505571i
$407$			13.0775i			0.648228i
$408$	−5.87091	+	7.84816i	−0.290653	+	0.388542i
$409$			19.8586i			0.981943i	0.871176	+	0.490971i	$0.163358\pi$
$409$			19.8586i			0.981943i	−0.871176	+	0.490971i	$0.836642\pi$
$410$	12.6261	+	39.4825i	0.623558	+	1.94990i
$411$	13.7990	+	13.7990i	0.680653	+	0.680653i
$412$	−28.4291	+	20.2540i	−1.40060	+	0.997841i
$413$	4.92858	−	4.92858i	0.242520	−	0.242520i
$414$	1.91455	−	3.71475i	0.0940952	−	0.182570i
$415$	19.1261			0.938865
$416$	36.6305	+	0.851259i	1.79596	+	0.0417364i
$417$	16.5283			0.809396
$418$	9.74072	−	18.8996i	0.476434	−	0.924410i
$419$	2.58100	−	2.58100i	0.126090	−	0.126090i	−0.641246	−	0.767336i	$-0.721582\pi$
$419$	2.58100	−	2.58100i	0.126090	−	0.126090i	0.767336	+	0.641246i	$0.221582\pi$
$420$	−5.80752	+	4.13750i	−0.283378	+	0.201889i
$421$	−11.1745	−	11.1745i	−0.544613	−	0.544613i	0.380265	−	0.924878i	$-0.375833\pi$
$421$	−11.1745	−	11.1745i	−0.544613	−	0.544613i	−0.924878	+	0.380265i	$0.875833\pi$
$422$	−1.39231	−	4.35384i	−0.0677768	−	0.211942i
$423$		−	5.44032i		−	0.264517i
$424$	−1.05193	−	0.786910i	−0.0510863	−	0.0382157i
$425$			26.7221i			1.29621i
$426$	−7.89807	+	2.52572i	−0.382663	+	0.122372i
$427$	10.0529	+	10.0529i	0.486495	+	0.486495i
$428$	−1.58839	+	9.45890i	−0.0767779	+	0.457213i
$429$	−12.4740	+	12.4740i	−0.602251	+	0.602251i
$430$	21.3349	+	10.9958i	1.02886	+	0.530266i
$431$	9.16149			0.441293			0.220647	−	0.975354i	$-0.429183\pi$
$431$	9.16149			0.441293			0.220647	+	0.975354i	$0.429183\pi$
$432$	3.59716	−	1.74940i	0.173069	−	0.0841683i
$433$	21.7281			1.04419			0.522093	−	0.852889i	$-0.325151\pi$
$433$	21.7281			1.04419			0.522093	+	0.852889i	$0.325151\pi$
$434$	9.77085	+	5.03583i	0.469016	+	0.241727i
$435$	−5.96201	+	5.96201i	−0.285856	+	0.285856i
$436$	20.8983	+	3.50937i	1.00085	+	0.168068i
$437$	−11.5347	−	11.5347i	−0.551781	−	0.551781i
$438$	−9.33887	+	2.98648i	−0.446229	+	0.142699i
$439$		−	24.5142i		−	1.17000i	−0.811034	−	0.584999i	$-0.801095\pi$
$439$		−	24.5142i		−	1.17000i	0.811034	−	0.584999i	$-0.198905\pi$
$440$	3.91790	+	27.1842i	0.186779	+	1.29595i
$441$			1.00000i			0.0476190i
$442$	−9.66831	−	30.2333i	−0.459875	−	1.43805i
$443$	−18.2529	−	18.2529i	−0.867223	−	0.867223i	0.124941	−	0.992164i	$-0.460126\pi$
$443$	−18.2529	−	18.2529i	−0.867223	−	0.867223i	−0.992164	+	0.124941i	$0.960126\pi$
$444$	5.57220	+	7.82132i	0.264445	+	0.371184i
$445$	19.4473	−	19.4473i	0.921889	−	0.921889i
$446$	18.1496	−	35.2150i	0.859406	−	1.66748i
$447$	2.76772			0.130909
$448$	−2.25906	−	7.67441i	−0.106731	−	0.362582i
$449$	32.9471			1.55487			0.777435	−	0.628963i	$-0.216520\pi$
$449$	32.9471			1.55487			0.777435	+	0.628963i	$0.216520\pi$
$450$	4.99622	−	9.69401i	0.235524	−	0.456980i
$451$	15.8327	−	15.8327i	0.745531	−	0.745531i
$452$	−19.7316	−	27.6959i	−0.928095	−	1.30270i
$453$	−0.814248	−	0.814248i	−0.0382567	−	0.0382567i
$454$	8.67561	+	27.1291i	0.407167	+	1.27323i
$455$		−	23.0932i		−	1.08263i
$456$	−2.22727	−	15.4538i	−0.104301	−	0.723691i
$457$		−	34.1570i		−	1.59780i	−0.601466	−	0.798898i	$-0.705416\pi$
$457$		−	34.1570i		−	1.59780i	0.601466	−	0.798898i	$-0.294584\pi$
$458$	−27.3164	+	8.73550i	−1.27641	+	0.408183i
$459$	−2.45027	−	2.45027i	−0.114369	−	0.114369i
$460$	20.7806	+	3.48960i	0.968901	+	0.162704i
$461$	−22.8828	+	22.8828i	−1.06576	+	1.06576i	−0.0680762	+	0.997680i	$0.521686\pi$
$461$	−22.8828	+	22.8828i	−1.06576	+	1.06576i	−0.997680	+	0.0680762i	$0.978314\pi$
$462$	3.42372	+	1.76456i	0.159286	+	0.0820947i
$463$	−26.3130			−1.22287			−0.611435	−	0.791294i	$-0.709408\pi$
$463$	−26.3130			−1.22287			−0.611435	+	0.791294i	$0.709408\pi$
$464$	−4.13712	−	8.50684i	−0.192061	−	0.394920i
$465$	−27.7121			−1.28512
$466$	−5.54764	−	2.85921i	−0.256989	−	0.132450i
$467$	13.0060	−	13.0060i	0.601848	−	0.601848i	−0.338955	−	0.940803i	$-0.610073\pi$
$467$	13.0060	−	13.0060i	0.601848	−	0.601848i	0.940803	+	0.338955i	$0.110073\pi$
$468$	−2.14533	+	12.7755i	−0.0991679	+	0.590546i
$469$	5.72344	+	5.72344i	0.264284	+	0.264284i
$470$	26.1274	−	8.35527i	1.20517	−	0.385400i
$471$		−	4.14271i		−	0.190886i
$472$	−15.7861	−	11.8090i	−0.726616	−	0.543553i
$473$		−	12.9648i		−	0.596121i
$474$	−3.60847	−	11.2839i	−0.165743	−	0.518286i
$475$	−30.1010	−	30.1010i	−1.38113	−	1.38113i
$476$	−5.64444	+	4.02131i	−0.258712	+	0.184316i
$477$	0.328423	−	0.328423i	0.0150375	−	0.0150375i
$478$	5.29952	−	10.2825i	0.242395	−	0.470310i
$479$	1.50155			0.0686076			0.0343038	−	0.999411i	$-0.489079\pi$
$479$	1.50155			0.0686076			0.0343038	+	0.999411i	$0.489079\pi$
$480$	13.9261	+	14.5888i	0.635638	+	0.665884i
$481$	−31.1010			−1.41808
$482$	−6.43485	+	12.4853i	−0.293100	+	0.568692i
$483$	2.08955	−	2.08955i	0.0950778	−	0.0950778i
$484$	−5.83509	+	4.15713i	−0.265231	+	0.188961i
$485$	−31.0377	−	31.0377i	−1.40935	−	1.40935i
$486$	0.430761	+	1.34701i	0.0195397	+	0.0611018i
$487$		−	30.4382i		−	1.37929i	−0.724149	−	0.689643i	$-0.757767\pi$
$487$		−	30.4382i		−	1.37929i	0.724149	−	0.689643i	$-0.242233\pi$
$488$	24.0871	−	32.1993i	1.09037	−	1.45759i
$489$			6.44975i			0.291668i
$490$	−4.80254	+	1.53580i	−0.216957	+	0.0693806i
$491$	25.6902	+	25.6902i	1.15938	+	1.15938i	0.984608	+	0.174776i	$0.0559202\pi$
$491$	25.6902	+	25.6902i	1.15938	+	1.15938i	0.174776	+	0.984608i	$0.444080\pi$
$492$	2.72296	−	16.2153i	0.122761	−	0.731041i
$493$	−5.79458	+	5.79458i	−0.260975	+	0.260975i
$494$	44.9471	+	23.1654i	2.02227	+	1.04226i
$495$	−9.71036			−0.436448
$496$	10.1555	−	29.3854i	0.455995	−	1.31944i
$497$	−5.86339			−0.263009
$498$	−6.74356	−	3.47558i	−0.302186	−	0.155745i
$499$	11.0748	−	11.0748i	0.495778	−	0.495778i	−0.414343	−	0.910121i	$-0.635989\pi$
$499$	11.0748	−	11.0748i	0.495778	−	0.495778i	0.910121	+	0.414343i	$0.135989\pi$
$500$	19.0682	+	3.20204i	0.852754	+	0.143199i
$501$	−11.6474	−	11.6474i	−0.520366	−	0.520366i
$502$	16.9548	−	5.42198i	0.756731	−	0.241995i
$503$			28.3042i			1.26202i	0.775773	+	0.631012i	$0.217360\pi$
$503$			28.3042i			1.26202i	−0.775773	+	0.631012i	$0.782640\pi$
$504$	2.79950	−	0.403476i	0.124700	−	0.0179723i
$505$		−	24.5590i		−	1.09286i
$506$	−3.46689	−	10.8412i	−0.154122	−	0.481948i
$507$	−20.4734	−	20.4734i	−0.909254	−	0.909254i
$508$	4.05518	+	5.69197i	0.179919	+	0.252540i
$509$	−11.2539	+	11.2539i	−0.498819	+	0.498819i	−0.911070	−	0.412251i	$-0.864743\pi$
$509$	−11.2539	+	11.2539i	−0.498819	+	0.498819i	0.412251	+	0.911070i	$0.364743\pi$
$510$	8.00439	−	15.5307i	0.354440	−	0.687709i
$511$	−6.93302			−0.306699
$512$	−20.5731	+	9.42070i	−0.909209	+	0.416340i
$513$	5.52020			0.243723
$514$	−8.12316	+	15.7611i	−0.358297	+	0.695193i
$515$	44.0003	−	44.0003i	1.93889	−	1.93889i
$516$	−5.52418	−	7.75391i	−0.243188	−	0.341347i
$517$	−10.4772	−	10.4772i	−0.460787	−	0.460787i
$518$	2.06836	+	6.46786i	0.0908783	+	0.284181i
$519$			3.39504i			0.149026i
$520$	−64.6495	+	9.31757i	−2.83507	+	0.408602i
$521$		−	6.03072i		−	0.264211i	−0.991236	−	0.132105i	$-0.957826\pi$
$521$		−	6.03072i		−	0.264211i	0.991236	−	0.132105i	$-0.0421737\pi$
$522$	3.18552	−	1.01870i	0.139426	−	0.0445871i
$523$	1.76817	+	1.76817i	0.0773167	+	0.0773167i	0.744708	−	0.667391i	$-0.232589\pi$
$523$	1.76817	+	1.76817i	0.0773167	+	0.0773167i	−0.667391	+	0.744708i	$0.732589\pi$
$524$	5.50416	+	0.924291i	0.240450	+	0.0403779i
$525$	5.45289	−	5.45289i	0.237984	−	0.237984i
$526$	29.0847	+	14.9900i	1.26815	+	0.653597i
$527$	−26.9339			−1.17326
$528$	3.55850	−	10.2967i	0.154864	−	0.448104i
$529$	14.2676			0.620329
$530$	2.08166	+	1.07287i	0.0904215	+	0.0466026i
$531$	4.92858	−	4.92858i	0.213882	−	0.213882i
$532$	1.82837	−	10.8880i	0.0792698	−	0.472053i
$533$	37.6533	+	37.6533i	1.63095	+	1.63095i
$534$	−10.3907	+	3.32285i	−0.449651	+	0.143794i
$535$		−	17.0981i		−	0.739216i
$536$	13.7135	−	18.3321i	0.592333	−	0.791824i
$537$			10.5938i			0.457155i
$538$	−9.68547	−	30.2870i	−0.417570	−	1.30576i
$539$	1.92584	+	1.92584i	0.0829520	+	0.0829520i
$540$	−5.80752	+	4.13750i	−0.249916	+	0.178050i
$541$	−17.5520	+	17.5520i	−0.754618	+	0.754618i	−0.975337	−	0.220719i	$-0.929160\pi$
$541$	−17.5520	+	17.5520i	−0.754618	+	0.754618i	0.220719	+	0.975337i	$0.429160\pi$
$542$	4.97656	−	9.65585i	0.213761	−	0.414754i
$543$	−17.8460			−0.765845
$544$	13.5351	+	14.1791i	0.580311	+	0.607924i
$545$	−37.7763			−1.61816
$546$	−4.19648	+	8.14229i	−0.179593	+	0.348458i
$547$	−17.1725	+	17.1725i	−0.734241	+	0.734241i	−0.971457	−	0.237216i	$-0.923765\pi$
$547$	−17.1725	+	17.1725i	−0.734241	+	0.734241i	0.237216	+	0.971457i	$0.423765\pi$
$548$	31.7873	−	22.6465i	1.35789	−	0.967409i
$549$	10.0529	+	10.0529i	0.429049	+	0.429049i
$550$	−9.04721	−	28.2911i	−0.385774	−	1.20634i
$551$		−	13.0546i		−	0.556144i
$552$	−6.69278	−	5.00661i	−0.284864	−	0.213096i
$553$		−	8.37696i		−	0.356225i
$554$	23.6942	−	7.57717i	1.00667	−	0.321923i
$555$	−12.1052	−	12.1052i	−0.513838	−	0.513838i
$556$	5.47442	−	32.6002i	0.232167	−	1.38256i
$557$	5.10327	−	5.10327i	0.216232	−	0.216232i	−0.590676	−	0.806909i	$-0.701139\pi$
$557$	5.10327	−	5.10327i	0.216232	−	0.216232i	0.806909	+	0.590676i	$0.201139\pi$
$558$	9.77085	+	5.03583i	0.413633	+	0.213184i
$559$	30.8329			1.30409
$560$	6.23720	+	12.8251i	0.263570	+	0.541958i
$561$	−9.43768			−0.398459
$562$	−1.50988	−	0.778181i	−0.0636904	−	0.0328256i
$563$	−23.6448	+	23.6448i	−0.996510	+	0.996510i	−0.999994	−	0.00348354i	$-0.998891\pi$
$563$	−23.6448	+	23.6448i	−0.996510	+	0.996510i	0.00348354	+	0.999994i	$0.498891\pi$
$564$	−10.7304	−	1.80191i	−0.451831	−	0.0758742i
$565$	42.8655	+	42.8655i	1.80336	+	1.80336i
$566$	12.0713	−	3.86028i	0.507394	−	0.162260i
$567$			1.00000i			0.0419961i
$568$	2.36574	+	16.4146i	0.0992643	+	0.688740i
$569$			21.0293i			0.881593i	0.897607	+	0.440796i	$0.145304\pi$
$569$			21.0293i			0.881593i	−0.897607	+	0.440796i	$0.854696\pi$
$570$	8.47794	+	26.5110i	0.355102	+	1.11042i
$571$	12.2157	+	12.2157i	0.511212	+	0.511212i	0.914898	−	0.403686i	$-0.132271\pi$
$571$	12.2157	+	12.2157i	0.511212	+	0.511212i	−0.403686	+	0.914898i	$0.632271\pi$
$572$	20.4720	+	28.7351i	0.855976	+	1.20148i
$573$	3.35542	−	3.35542i	0.140175	−	0.140175i
$574$	5.32639	−	10.3346i	0.222319	−	0.431359i
$575$	−22.7882			−0.950333
$576$	−2.25906	−	7.67441i	−0.0941277	−	0.319767i
$577$	2.94188			0.122472			0.0612360	−	0.998123i	$-0.480496\pi$
$577$	2.94188			0.122472			0.0612360	+	0.998123i	$0.480496\pi$
$578$	−3.23448	+	6.27576i	−0.134537	+	0.261037i
$579$	3.62575	−	3.62575i	0.150681	−	0.150681i
$580$	9.78467	+	13.7341i	0.406286	+	0.570276i
$581$	−3.79326	−	3.79326i	−0.157371	−	0.157371i
$582$	5.30325	+	16.5835i	0.219827	+	0.687410i
$583$		−	1.26498i		−	0.0523903i
$584$	2.79731	+	19.4090i	0.115754	+	0.803150i
$585$		−	23.0932i		−	0.954787i
$586$	−4.03266	+	1.28960i	−0.166588	+	0.0532731i
$587$	−18.5609	−	18.5609i	−0.766088	−	0.766088i	0.211327	−	0.977415i	$-0.432221\pi$
$587$	−18.5609	−	18.5609i	−0.766088	−	0.766088i	−0.977415	+	0.211327i	$0.932221\pi$
$588$	1.97238	+	0.331214i	0.0813397	+	0.0136590i
$589$	30.3397	−	30.3397i	1.25012	−	1.25012i
$590$	31.2390	+	16.1004i	1.28609	+	0.662842i
$591$	−20.2798			−0.834199
$592$	17.2722	−	8.39999i	0.709885	−	0.345237i
$593$	−23.9692			−0.984296			−0.492148	−	0.870512i	$-0.663788\pi$
$593$	−23.9692			−0.984296			−0.492148	+	0.870512i	$0.663788\pi$
$594$	3.42372	+	1.76456i	0.140477	+	0.0724007i
$595$	8.73601	−	8.73601i	0.358142	−	0.358142i
$596$	0.916709	−	5.45901i	0.0375499	−	0.223610i
$597$	−19.4344	−	19.4344i	−0.795396	−	0.795396i
$598$	25.7825	−	8.24498i	1.05432	−	0.337162i
$599$			16.9472i			0.692446i	0.938152	+	0.346223i	$0.112536\pi$
$599$			16.9472i			0.692446i	−0.938152	+	0.346223i	$0.887464\pi$
$600$	−17.4655	−	13.0653i	−0.713026	−	0.533387i
$601$		−	15.3244i		−	0.625095i	−0.949902	−	0.312548i	$-0.898818\pi$
$601$		−	15.3244i		−	0.625095i	0.949902	−	0.312548i	$-0.101182\pi$
$602$	−2.05053	−	6.41211i	−0.0835733	−	0.261338i
$603$	5.72344	+	5.72344i	0.233077	+	0.233077i
$604$	−1.87570	+	1.33632i	−0.0763211	+	0.0543740i
$605$	9.03108	−	9.03108i	0.367166	−	0.367166i
$606$	−4.46284	+	8.65911i	−0.181291	+	0.351752i
$607$	−8.08892			−0.328319			−0.164160	−	0.986434i	$-0.552491\pi$
$607$	−8.08892			−0.328319			−0.164160	+	0.986434i	$0.552491\pi$
$608$	−31.2185	−	0.725490i	−1.26608	−	0.0294225i
$609$	2.36488			0.0958296
$610$	−32.8403	+	63.7189i	−1.32966	+	2.57990i
$611$	24.9169	−	24.9169i	1.00803	−	1.00803i
$612$	−5.64444	+	4.02131i	−0.228163	+	0.162552i
$613$	6.32208	+	6.32208i	0.255346	+	0.255346i	0.823158	−	0.567812i	$-0.192210\pi$
$613$	6.32208	+	6.32208i	0.255346	+	0.255346i	−0.567812	+	0.823158i	$0.692210\pi$
$614$	−1.83797	−	5.74743i	−0.0741744	−	0.231947i
$615$			29.3111i			1.18194i
$616$	4.61437	−	6.16844i	0.185918	−	0.248533i
$617$			21.3532i			0.859648i	0.902913	+	0.429824i	$0.141424\pi$
$617$			21.3532i			0.859648i	−0.902913	+	0.429824i	$0.858576\pi$
$618$	−23.5095	+	7.51810i	−0.945691	+	0.302422i
$619$	−9.02529	−	9.02529i	−0.362757	−	0.362757i	0.502070	−	0.864827i	$-0.332572\pi$
$619$	−9.02529	−	9.02529i	−0.362757	−	0.362757i	−0.864827	+	0.502070i	$0.832572\pi$
$620$	−9.17866	+	54.6590i	−0.368624	+	2.19516i
$621$	2.08955	−	2.08955i	0.0838508	−	0.0838508i
$622$	−26.9538	−	13.8918i	−1.08075	−	0.557010i
$623$	−7.71391			−0.309051
$624$	24.4875	+	8.46283i	0.980286	+	0.338784i
$625$	4.08972			0.163589
$626$	8.40837	+	4.33361i	0.336066	+	0.173206i
$627$	10.6310	−	10.6310i	0.424563	−	0.424563i
$628$	−8.17102	−	1.37213i	−0.326059	−	0.0547538i
$629$	−11.7653	−	11.7653i	−0.469113	−	0.469113i
$630$	−4.80254	+	1.53580i	−0.191338	+	0.0611879i
$631$			19.6858i			0.783679i	0.920034	+	0.391840i	$0.128161\pi$
$631$			19.6858i			0.783679i	−0.920034	+	0.391840i	$0.871839\pi$
$632$	−23.4513	+	3.37991i	−0.932843	+	0.134445i
$633$		−	3.23222i		−	0.128469i
$634$	7.88041	+	24.6425i	0.312971	+	0.978677i
$635$	−8.80959	−	8.80959i	−0.349598	−	0.349598i
$636$	−0.538998	−	0.756555i	−0.0213727	−	0.0299994i
$637$	−4.58005	+	4.58005i	−0.181468	+	0.181468i
$638$	4.17296	−	8.09666i	0.165209	−	0.320550i
$639$	−5.86339			−0.231952
$640$	33.3872	−	22.6356i	1.31975	−	0.894753i
$641$	−24.6366			−0.973087			−0.486543	−	0.873656i	$-0.661742\pi$
$641$	−24.6366			−0.973087			−0.486543	+	0.873656i	$0.661742\pi$
$642$	−3.10706	+	6.02852i	−0.122626	+	0.237927i
$643$	1.42148	−	1.42148i	0.0560577	−	0.0560577i	−0.678522	−	0.734580i	$-0.737379\pi$
$643$	1.42148	−	1.42148i	0.0560577	−	0.0560577i	0.734580	+	0.678522i	$0.237379\pi$
$644$	−3.42931	−	4.81348i	−0.135134	−	0.189678i
$645$	12.0009	+	12.0009i	0.472534	+	0.472534i
$646$	8.23987	+	25.7665i	0.324193	+	1.01377i
$647$			44.3806i			1.74478i	0.488810	+	0.872390i	$0.337431\pi$
$647$			44.3806i			1.74478i	−0.488810	+	0.872390i	$0.662569\pi$
$648$	2.79950	−	0.403476i	0.109975	−	0.0158500i
$649$		−	18.9834i		−	0.745162i
$650$	67.2820	−	21.5161i	2.63902	−	0.843931i
$651$	5.49612	+	5.49612i	0.215410	+	0.215410i
$652$	12.7214	+	2.13625i	0.498208	+	0.0836619i
$653$	18.3917	−	18.3917i	0.719721	−	0.719721i	−0.248827	−	0.968548i	$-0.580045\pi$
$653$	18.3917	−	18.3917i	0.719721	−	0.719721i	0.968548	+	0.248827i	$0.0800451\pi$
$654$	13.3193	+	6.86467i	0.520826	+	0.268430i
$655$	−9.94945			−0.388757
$656$	−31.0809	−	10.7415i	−1.21350	−	0.419384i
$657$	−6.93302			−0.270483
$658$	−6.83890	−	3.52472i	−0.266608	−	0.137408i
$659$	−6.96690	+	6.96690i	−0.271392	+	0.271392i	−0.829660	−	0.558269i	$-0.811466\pi$
$659$	−6.96690	+	6.96690i	−0.271392	+	0.271392i	0.558269	+	0.829660i	$0.311466\pi$
$660$	−3.21621	+	19.1526i	−0.125191	+	0.745512i
$661$	4.96284	+	4.96284i	0.193032	+	0.193032i	0.797005	−	0.603973i	$-0.206416\pi$
$661$	4.96284	+	4.96284i	0.193032	+	0.193032i	−0.603973	+	0.797005i	$0.706416\pi$
$662$	6.40868	−	2.04943i	0.249080	−	0.0796534i
$663$		−	22.4447i		−	0.871681i
$664$	−9.08875	+	12.1497i	−0.352712	+	0.471501i
$665$			19.6813i			0.763209i
$666$	2.06836	+	6.46786i	0.0801471	+	0.250624i
$667$	−4.94153	−	4.94153i	−0.191337	−	0.191337i
$668$	−26.8308	+	19.1153i	−1.03812	+	0.739593i
$669$	19.8085	−	19.8085i	0.765840	−	0.765840i
$670$	−18.6970	+	36.2771i	−0.722327	+	1.40151i
$671$	38.7208			1.49480
$672$	0.131425	−	5.65533i	0.00506981	−	0.218159i
$673$	−26.7130			−1.02971			−0.514856	−	0.857277i	$-0.672154\pi$
$673$	−26.7130			−1.02971			−0.514856	+	0.857277i	$0.672154\pi$
$674$	1.59368	−	3.09217i	0.0613864	−	0.119106i
$675$	5.45289	−	5.45289i	0.209882	−	0.209882i
$676$	−47.1624	+	33.6002i	−1.81394	+	1.29232i
$677$	−6.42651	−	6.42651i	−0.246991	−	0.246991i	0.572744	−	0.819735i	$-0.305879\pi$
$677$	−6.42651	−	6.42651i	−0.246991	−	0.246991i	−0.819735	+	0.572744i	$0.805879\pi$
$678$	−7.32419	−	22.9031i	−0.281284	−	0.879590i
$679$			12.3113i			0.472466i
$680$	−27.9813	−	20.9317i	−1.07303	−	0.802694i
$681$			20.1402i			0.771774i
$682$	28.5154	−	9.11892i	1.09191	−	0.349182i
$683$	−22.0657	−	22.0657i	−0.844319	−	0.844319i	0.145098	−	0.989417i	$-0.453650\pi$
$683$	−22.0657	−	22.0657i	−0.844319	−	0.844319i	−0.989417	+	0.145098i	$0.953650\pi$
$684$	1.82837	−	10.8880i	0.0699094	−	0.416311i
$685$	−49.1979	+	49.1979i	−1.87975	+	1.87975i
$686$	1.25708	+	0.647888i	0.0479954	+	0.0247365i
$687$	−20.2792			−0.773701
$688$	−17.1234	+	8.32759i	−0.652822	+	0.317486i
$689$	3.00839			0.114610
$690$	13.2443	+	6.82601i	0.504202	+	0.259862i
$691$	−15.0844	+	15.0844i	−0.573838	+	0.573838i	−0.933199	−	0.359360i	$-0.882995\pi$
$691$	−15.0844	+	15.0844i	−0.573838	+	0.573838i	0.359360	+	0.933199i	$0.382995\pi$
$692$	6.69632	+	1.12449i	0.254556	+	0.0427465i
$693$	1.92584	+	1.92584i	0.0731568	+	0.0731568i
$694$	−22.2220	+	7.10639i	−0.843537	+	0.269755i
$695$			58.9289i			2.23530i
$696$	−0.954171	−	6.62047i	−0.0361678	−	0.250948i
$697$			28.4880i			1.07906i
$698$	−12.8563	−	40.2024i	−0.486619	−	1.52169i
$699$	−3.12055	−	3.12055i	−0.118030	−	0.118030i
$700$	−8.94912	−	12.5613i	−0.338245	−	0.474771i
$701$	−20.0801	+	20.0801i	−0.758414	+	0.758414i	−0.976034	−	0.217620i	$-0.930171\pi$
$701$	−20.0801	+	20.0801i	−0.758414	+	0.758414i	0.217620	+	0.976034i	$0.430171\pi$
$702$	−4.19648	+	8.14229i	−0.158386	+	0.307311i
$703$	26.5059			0.999691
$704$	−19.1303	−	10.4291i	−0.721002	−	0.393062i
$705$	19.3965			0.730515
$706$	12.6144	−	24.4754i	0.474750	−	0.921143i
$707$	−4.87076	+	4.87076i	−0.183184	+	0.183184i
$708$	−8.08864	−	11.3535i	−0.303990	−	0.426689i
$709$	4.64626	+	4.64626i	0.174494	+	0.174494i	0.788951	−	0.614457i	$-0.210625\pi$
$709$	4.64626	+	4.64626i	0.174494	+	0.174494i	−0.614457	+	0.788951i	$0.710625\pi$
$710$	−9.00502	−	28.1592i	−0.337953	−	1.05680i
$711$		−	8.37696i		−	0.314161i
$712$	3.11238	+	21.5951i	0.116641	+	0.809311i
$713$		−	22.9688i		−	0.860189i
$714$	−4.66768	+	1.49268i	−0.174683	+	0.0558620i
$715$	−44.4739	−	44.4739i	−1.66323	−	1.66323i
$716$	20.8950	+	3.50881i	0.780883	+	0.131130i
$717$	5.78392	−	5.78392i	0.216004	−	0.216004i
$718$	−4.54413	−	2.34201i	−0.169586	−	0.0874032i
$719$	0.854284			0.0318594			0.0159297	−	0.999873i	$-0.494929\pi$
$719$	0.854284			0.0318594			0.0159297	+	0.999873i	$0.494929\pi$
$720$	6.23720	+	12.8251i	0.232447	+	0.477962i
$721$	−17.4531			−0.649986
$722$	−14.4219	−	7.43296i	−0.536729	−	0.276626i
$723$	−7.02302	+	7.02302i	−0.261189	+	0.261189i
$724$	−5.91085	+	35.1992i	−0.219675	+	1.30817i
$725$	−12.8954	−	12.8954i	−0.478923	−	0.478923i
$726$	−4.82533	+	1.54309i	−0.179085	+	0.0572695i
$727$		−	13.5320i		−	0.501876i	−0.968003	−	0.250938i	$-0.919261\pi$
$727$		−	13.5320i		−	0.501876i	0.968003	−	0.250938i	$-0.0807390\pi$
$728$	14.6698	+	10.9739i	0.543699	+	0.406720i
$729$			1.00000i			0.0370370i
$730$	−10.6478	−	33.2961i	−0.394091	−	1.23235i
$731$	11.6639	+	11.6639i	0.431404	+	0.431404i
$732$	23.1579	−	16.4986i	0.855941	−	0.609804i
$733$	18.6813	−	18.6813i	0.690008	−	0.690008i	−0.272226	−	0.962233i	$-0.587760\pi$
$733$	18.6813	−	18.6813i	0.690008	−	0.690008i	0.962233	+	0.272226i	$0.0877597\pi$
$734$	2.14730	−	4.16634i	0.0792584	−	0.153783i
$735$	−3.56533			−0.131509
$736$	−12.0917	+	11.5425i	−0.445706	+	0.425461i
$737$	22.0449			0.812035
$738$	5.32639	−	10.3346i	0.196067	−	0.380423i
$739$	−1.08158	+	1.08158i	−0.0397865	+	0.0397865i	−0.726720	−	0.686934i	$-0.758956\pi$
$739$	−1.08158	+	1.08158i	−0.0397865	+	0.0397865i	0.686934	+	0.726720i	$0.258956\pi$
$740$	−27.8856	+	19.8667i	−1.02509	+	0.730315i
$741$	25.2828	+	25.2828i	0.928786	+	0.928786i
$742$	−0.200072	−	0.625634i	−0.00734486	−	0.0229678i
$743$		−	19.7858i		−	0.725870i	−0.931814	−	0.362935i	$-0.881775\pi$
$743$		−	19.7858i		−	0.725870i	0.931814	−	0.362935i	$-0.118225\pi$
$744$	13.1688	−	17.6039i	0.482793	−	0.645392i
$745$			9.86783i			0.361529i
$746$	1.62955	−	0.521113i	0.0596620	−	0.0190793i
$747$	−3.79326	−	3.79326i	−0.138788	−	0.138788i
$748$	−3.12589	+	18.6147i	−0.114294	+	0.680622i
$749$	−3.39105	+	3.39105i	−0.123906	+	0.123906i
$750$	12.1529	+	6.26350i	0.443760	+	0.228711i
$751$	−34.3944			−1.25507			−0.627535	−	0.778588i	$-0.715936\pi$
$751$	−34.3944			−1.25507			−0.627535	+	0.778588i	$0.715936\pi$
$752$	−7.10812	+	20.5676i	−0.259207	+	0.750025i
$753$	12.5870			0.458695
$754$	19.2555	+	9.92415i	0.701244	+	0.361416i
$755$	2.90306	−	2.90306i	0.105653	−	0.105653i
$756$	1.97238	+	0.331214i	0.0717349	+	0.0120461i
$757$	16.8007	+	16.8007i	0.610630	+	0.610630i	0.943110	−	0.332480i	$-0.107885\pi$
$757$	16.8007	+	16.8007i	0.610630	+	0.610630i	−0.332480	+	0.943110i	$0.607885\pi$
$758$	−15.5608	+	4.97618i	−0.565193	+	0.180743i
$759$		−	8.04830i		−	0.292135i
$760$	55.0979	−	7.94094i	1.99861	−	0.288048i
$761$		−	10.1708i		−	0.368691i	−0.982862	−	0.184345i	$-0.940983\pi$
$761$		−	10.1708i		−	0.368691i	0.982862	−	0.184345i	$-0.0590165\pi$
$762$	1.50525	+	4.70699i	0.0545293	+	0.170516i
$763$	7.49212	+	7.49212i	0.271233	+	0.271233i
$764$	−5.50682	−	7.72954i	−0.199230	−	0.279645i
$765$	8.73601	−	8.73601i	0.315851	−	0.315851i
$766$	4.67999	−	9.08043i	0.169095	−	0.328089i
$767$	45.1463			1.63014
$768$	−15.8851	+	1.91387i	−0.573205	+	0.0690607i
$769$	−0.122808			−0.00442857			−0.00221429	−	0.999998i	$-0.500705\pi$
$769$	−0.122808			−0.00442857			−0.00221429	+	0.999998i	$0.500705\pi$
$770$	−6.29123	+	12.2067i	−0.226720	+	0.439898i
$771$	−8.86564	+	8.86564i	−0.319288	+	0.319288i
$772$	−5.95047	−	8.35228i	−0.214162	−	0.300605i
$773$	10.6653	+	10.6653i	0.383603	+	0.383603i	0.872399	−	0.488795i	$-0.162563\pi$
$773$	10.6653	+	10.6653i	0.383603	+	0.383603i	−0.488795	+	0.872399i	$0.662563\pi$
$774$	−2.05053	−	6.41211i	−0.0737047	−	0.230479i
$775$		−	59.9394i		−	2.15309i
$776$	34.4656	−	4.96733i	1.23724	−	0.178317i
$777$			4.80163i			0.172257i
$778$	44.9527	−	14.3754i	1.61163	−	0.515384i
$779$	−32.0902	−	32.0902i	−1.14975	−	1.14975i
$780$	−45.5487	−	7.64880i	−1.63090	−	0.273871i
$781$	−11.2920	+	11.2920i	−0.404059	+	0.404059i
$782$	12.8724	+	6.63433i	0.460315	+	0.237243i
$783$	2.36488			0.0845138
$784$	1.30656	−	3.78059i	0.0466630	−	0.135021i
$785$	14.7701			0.527168
$786$	3.50802	+	1.80801i	0.125127	+	0.0644894i
$787$	−30.1798	+	30.1798i	−1.07580	+	1.07580i	−0.0789136	+	0.996881i	$0.525145\pi$
$787$	−30.1798	+	30.1798i	−1.07580	+	1.07580i	−0.996881	+	0.0789136i	$0.974855\pi$
$788$	−6.71696	+	39.9995i	−0.239282	+	1.42492i
$789$	16.3602	+	16.3602i	0.582438	+	0.582438i
$790$	40.2307	−	12.8654i	1.43134	−	0.457729i
$791$		−	17.0029i		−	0.604554i
$792$	4.61437	−	6.16844i	0.163965	−	0.219186i
$793$			92.0858i			3.27006i
$794$	−10.9922	−	34.3733i	−0.390100	−	1.21986i
$795$	1.17094	+	1.17094i	0.0415288	+	0.0415288i
$796$	−44.7690	+	31.8951i	−1.58679	+	1.13049i
$797$	−32.9541	+	32.9541i	−1.16729	+	1.16729i	−0.184454	+	0.982841i	$0.559052\pi$
$797$	−32.9541	+	32.9541i	−1.16729	+	1.16729i	−0.982841	+	0.184454i	$0.940948\pi$
$798$	3.57647	−	6.93931i	0.126606	−	0.245649i
$799$	18.8518			0.666930
$800$	−31.5545	+	30.1212i	−1.11562	+	1.06495i
$801$	−7.71391			−0.272558
$802$	−8.47169	+	16.4373i	−0.299146	+	0.580423i
$803$	−13.3519	+	13.3519i	−0.471179	+	0.471179i
$804$	13.1845	−	9.39314i	0.464982	−	0.331270i
$805$	7.44993	+	7.44993i	0.262575	+	0.262575i
$806$	21.6867	+	67.8153i	0.763880	+	2.38869i
$807$		−	22.4846i		−	0.791494i
$808$	15.6009	+	11.6705i	0.548839	+	0.410565i
$809$			26.3206i			0.925384i	0.886519	+	0.462692i	$0.153116\pi$
$809$			26.3206i			0.925384i	−0.886519	+	0.462692i	$0.846884\pi$
$810$	−4.80254	+	1.53580i	−0.168744	+	0.0539627i
$811$	−31.7501	−	31.7501i	−1.11490	−	1.11490i	−0.992479	−	0.122418i	$-0.960935\pi$
$811$	−31.7501	−	31.7501i	−1.11490	−	1.11490i	−0.122418	−	0.992479i	$-0.539065\pi$
$812$	0.783280	−	4.66444i	0.0274878	−	0.163690i
$813$	5.43143	−	5.43143i	0.190488	−	0.190488i
$814$	16.4394	+	8.47276i	0.576201	+	0.296970i
$815$	−22.9955			−0.805496
$816$	6.06205	+	12.4649i	0.212214	+	0.436359i
$817$	−26.2775			−0.919333
$818$	24.9637	+	12.8661i	0.872836	+	0.449854i
$819$	−4.58005	+	4.58005i	−0.160040	+	0.160040i
$820$	57.8128	+	9.70826i	2.01891	+	0.339027i
$821$	−15.3479	−	15.3479i	−0.535645	−	0.535645i	0.386601	−	0.922247i	$-0.373649\pi$
$821$	−15.3479	−	15.3479i	−0.535645	−	0.535645i	−0.922247	+	0.386601i	$0.873649\pi$
$822$	26.2866	−	8.40617i	0.916849	−	0.293199i
$823$			27.3589i			0.953671i	0.878993	+	0.476835i	$0.158216\pi$
$823$			27.3589i			0.953671i	−0.878993	+	0.476835i	$0.841784\pi$
$824$	7.04189	+	48.8598i	0.245316	+	1.70211i
$825$		−	21.0028i		−	0.731225i
$826$	−3.00243	−	9.38877i	−0.104468	−	0.326677i
$827$	−8.79578	−	8.79578i	−0.305859	−	0.305859i	0.537442	−	0.843301i	$-0.319391\pi$
$827$	−8.79578	−	8.79578i	−0.305859	−	0.305859i	−0.843301	+	0.537442i	$0.819391\pi$
$828$	−3.42931	−	4.81348i	−0.119177	−	0.167280i
$829$	20.2525	−	20.2525i	0.703400	−	0.703400i	−0.261739	−	0.965139i	$-0.584296\pi$
$829$	20.2525	−	20.2525i	0.703400	−	0.703400i	0.965139	+	0.261739i	$0.0842960\pi$
$830$	12.3916	−	24.0430i	0.430119	−	0.834545i
$831$	17.5902			0.610197
$832$	24.8026	−	45.4958i	0.859874	−	1.57728i
$833$	−3.46521			−0.120062
$834$	10.7085	−	20.7774i	0.370806	−	0.719462i
$835$	41.5266	−	41.5266i	1.43709	−	1.43709i
$836$	−17.4473	−	24.4897i	−0.603429	−	0.846992i
$837$	5.49612	+	5.49612i	0.189974	+	0.189974i
$838$	−1.57231	−	4.91670i	−0.0543146	−	0.169845i
$839$			2.30778i			0.0796735i	0.999206	+	0.0398367i	$0.0126838\pi$
$839$			2.30778i			0.0796735i	−0.999206	+	0.0398367i	$0.987316\pi$
$840$	1.43852	+	9.98114i	0.0496338	+	0.344382i
$841$			23.4074i			0.807150i
$842$	−21.2871	+	6.80739i	−0.733601	+	0.234598i
$843$	−0.849308	−	0.849308i	−0.0292517	−	0.0292517i
$844$	−6.37518	−	1.07056i	−0.219443	−	0.0368501i
$845$	72.9942	−	72.9942i	2.51108	−	2.51108i
$846$	−6.83890	−	3.52472i	−0.235126	−	0.121182i
$847$	−3.58225			−0.123087
$848$	−1.67074	+	0.812529i	−0.0573735	+	0.0279024i
$849$	8.96153			0.307559
$850$	33.5917	+	17.3129i	1.15219	+	0.593829i
$851$	10.0332	−	10.0332i	0.343935	−	0.343935i
$852$	−1.94204	+	11.5649i	−0.0665332	+	0.396206i
$853$	2.26956	+	2.26956i	0.0777083	+	0.0777083i	0.744893	−	0.667184i	$-0.232501\pi$
$853$	2.26956	+	2.26956i	0.0777083	+	0.0777083i	−0.667184	+	0.744893i	$0.732501\pi$
$854$	19.1505	−	6.12413i	0.655316	−	0.209563i
$855$			19.6813i			0.673087i
$856$	10.8615	+	8.12504i	0.371237	+	0.277708i
$857$		−	52.3948i		−	1.78977i	−0.446295	−	0.894886i	$-0.647257\pi$
$857$		−	52.3948i		−	1.78977i	0.446295	−	0.894886i	$-0.352743\pi$
$858$	7.59902	+	23.7626i	0.259426	+	0.811240i
$859$	8.49759	+	8.49759i	0.289934	+	0.289934i	0.837054	−	0.547120i	$-0.184276\pi$
$859$	8.49759	+	8.49759i	0.289934	+	0.289934i	−0.547120	+	0.837054i	$0.684276\pi$
$860$	27.6452	−	19.6955i	0.942694	−	0.671611i
$861$	5.81324	−	5.81324i	0.198115	−	0.198115i
$862$	5.93562	−	11.5167i	0.202168	−	0.392260i
$863$	41.8326			1.42400			0.711999	−	0.702180i	$-0.247790\pi$
$863$	41.8326			1.42400			0.711999	+	0.702180i	$0.247790\pi$
$864$	0.131425	−	5.65533i	0.00447115	−	0.192398i
$865$	−12.1044			−0.411563
$866$	14.0774	−	27.3139i	0.478369	−	0.928163i
$867$	−3.53012	+	3.53012i	−0.119889	+	0.119889i
$868$	12.6608	−	9.02006i	0.429737	−	0.306161i
$869$	−16.1327	−	16.1327i	−0.547265	−	0.547265i
$870$	3.63199	+	11.3574i	0.123136	+	0.385052i
$871$			52.4273i			1.77643i
$872$	17.9513	−	23.9971i	0.607908	−	0.812644i
$873$			12.3113i			0.416676i
$874$	−21.9733	+	7.02682i	−0.743257	+	0.237686i
$875$	6.83600	+	6.83600i	0.231099	+	0.231099i
$876$	−2.29632	+	13.6746i	−0.0775853	+	0.462021i
$877$	−1.08296	+	1.08296i	−0.0365690	+	0.0365690i	−0.725155	−	0.688586i	$-0.758232\pi$
$877$	−1.08296	+	1.08296i	−0.0365690	+	0.0365690i	0.688586	+	0.725155i	$0.258232\pi$
$878$	−30.8162	−	15.8824i	−1.04000	−	0.536006i
$879$	−2.99378			−0.100978
$880$	36.7109	+	12.6872i	1.23753	+	0.427685i
$881$	54.3963			1.83266			0.916329	−	0.400426i	$-0.131138\pi$
$881$	54.3963			1.83266			0.916329	+	0.400426i	$0.131138\pi$
$882$	1.25708	+	0.647888i	0.0423280	+	0.0218155i
$883$	4.04981	−	4.04981i	0.136287	−	0.136287i	−0.635672	−	0.771959i	$-0.719277\pi$
$883$	4.04981	−	4.04981i	0.136287	−	0.136287i	0.771959	+	0.635672i	$0.219277\pi$
$884$	−44.2696	−	7.43401i	−1.48895	−	0.250033i
$885$	17.5720	+	17.5720i	0.590676	+	0.590676i
$886$	−34.7712	+	11.1195i	−1.16816	+	0.373566i
$887$		−	6.43683i		−	0.216128i	−0.994144	−	0.108064i	$-0.965535\pi$
$887$		−	6.43683i		−	0.216128i	0.994144	−	0.108064i	$-0.0344651\pi$
$888$	13.4422	−	1.93734i	0.451090	−	0.0650130i
$889$			3.49439i			0.117198i
$890$	−11.8471	−	37.0464i	−0.397114	−	1.24180i
$891$	1.92584	+	1.92584i	0.0645182	+	0.0645182i
$892$	−32.5091	−	45.6307i	−1.08848	−	1.52783i
$893$	−21.2356	+	21.2356i	−0.710622	+	0.710622i
$894$	1.79317	−	3.47924i	0.0599727	−	0.116363i
$895$	−37.7703			−1.26252
$896$	−11.1109	−	2.13234i	−0.371191	−	0.0712366i
$897$	19.1405			0.639082
$898$	21.3460	−	41.4170i	0.712327	−	1.38210i
$899$	12.9976	−	12.9976i	0.433495	−	0.433495i
$900$	−8.94912	−	12.5613i	−0.298304	−	0.418709i
$901$	1.13805	+	1.13805i	0.0379141	+	0.0379141i
$902$	−9.64508	−	30.1607i	−0.321146	−	1.00424i
$903$		−	4.76024i		−	0.158411i
$904$	−47.5997	+	6.86027i	−1.58314	+	0.228169i
$905$		−	63.6268i		−	2.11503i
$906$	−1.55111	+	0.496030i	−0.0515323	+	0.0164795i
$907$	13.9333	+	13.9333i	0.462649	+	0.462649i	0.899523	−	0.436874i	$-0.143914\pi$
$907$	13.9333	+	13.9333i	0.462649	+	0.462649i	−0.436874	+	0.899523i	$0.643914\pi$
$908$	39.7242	+	6.67072i	1.31829	+	0.221375i
$909$	−4.87076	+	4.87076i	−0.161553	+	0.161553i
$910$	−29.0299	−	14.9618i	−0.962333	−	0.495980i
$911$	14.6467			0.485268			0.242634	−	0.970118i	$-0.421989\pi$
$911$	14.6467			0.485268			0.242634	+	0.970118i	$0.421989\pi$
$912$	−20.8696	−	7.21249i	−0.691063	−	0.238829i
$913$	−14.6105			−0.483536
$914$	−42.9379	−	22.1299i	−1.42026	−	0.731992i
$915$	−35.8420	+	35.8420i	−1.18490	+	1.18490i
$916$	−6.71677	+	39.9984i	−0.221928	+	1.32159i
$917$	1.97326	+	1.97326i	0.0651629	+	0.0651629i
$918$	−4.66768	+	1.49268i	−0.154056	+	0.0492656i
$919$			8.89244i			0.293335i	0.989186	+	0.146667i	$0.0468547\pi$
$919$			8.89244i			0.293335i	−0.989186	+	0.146667i	$0.953145\pi$
$920$	17.8502	−	23.8620i	0.588504	−	0.786705i
$921$		−	4.26679i		−	0.140596i
$922$	13.9399	+	43.5908i	0.459086	+	1.43559i
$923$	−26.8546	−	26.8546i	−0.883931	−	0.883931i
$924$	4.43637	−	3.16064i	0.145946	−	0.103977i
$925$	26.1828	−	26.1828i	0.860884	−	0.860884i
$926$	−17.0479	+	33.0775i	−0.560229	+	1.08699i
$927$	−17.4531			−0.573233
$928$	−13.3741	−	0.310803i	−0.439028	−	0.0102026i
$929$	−19.6067			−0.643276			−0.321638	−	0.946863i	$-0.604233\pi$
$929$	−19.6067			−0.643276			−0.321638	+	0.946863i	$0.604233\pi$
$930$	−17.9544	+	34.8363i	−0.588747	+	1.14233i
$931$	3.90337	−	3.90337i	0.127928	−	0.127928i
$932$	−7.18849	+	5.12135i	−0.235467	+	0.167755i
$933$	−15.1615	−	15.1615i	−0.496366	−	0.496366i
$934$	−7.92313	−	24.7761i	−0.259253	−	0.810697i
$935$		−	33.6484i		−	1.10042i
$936$	14.6698	+	10.9739i	0.479497	+	0.358694i
$937$			42.1339i			1.37646i	0.725495	+	0.688228i	$0.241611\pi$
$937$			42.1339i			1.37646i	−0.725495	+	0.688228i	$0.758389\pi$
$938$	10.9030	−	3.48665i	0.355994	−	0.113843i
$939$	4.72972	+	4.72972i	0.154349	+	0.154349i
$940$	6.42440	−	38.2574i	0.209541	−	1.24782i
$941$	−7.17940	+	7.17940i	−0.234042	+	0.234042i	−0.814377	−	0.580336i	$-0.802921\pi$
$941$	−7.17940	+	7.17940i	−0.234042	+	0.234042i	0.580336	+	0.814377i	$0.302921\pi$
$942$	−5.20771	−	2.68402i	−0.169676	−	0.0874499i
$943$	−24.2941			−0.791125
$944$	−25.0725	+	12.1935i	−0.816039	+	0.396863i
$945$	−3.56533			−0.115980
$946$	−16.2977	−	8.39973i	−0.529885	−	0.273099i
$947$	−18.0082	+	18.0082i	−0.585187	+	0.585187i	−0.936324	−	0.351137i	$-0.885795\pi$
$947$	−18.0082	+	18.0082i	−0.585187	+	0.585187i	0.351137	+	0.936324i	$0.385795\pi$
$948$	−16.5226	−	2.77457i	−0.536629	−	0.0901138i
$949$	−31.7536	−	31.7536i	−1.03076	−	1.03076i
$950$	−57.3414	+	18.3372i	−1.86040	+	0.594937i
$951$			18.2941i			0.593228i
$952$	1.39813	+	9.70085i	0.0453136	+	0.314406i
$953$			35.0009i			1.13379i	0.823790	+	0.566895i	$0.191855\pi$
$953$			35.0009i			1.13379i	−0.823790	+	0.566895i	$0.808145\pi$
$954$	−0.200072	−	0.625634i	−0.00647756	−	0.0202557i
$955$	11.9632	+	11.9632i	0.387119	+	0.387119i
$956$	−9.49239	−	13.3238i	−0.307006	−	0.430923i
$957$	4.55438	−	4.55438i	0.147222	−	0.147222i
$958$	0.972837	−	1.88756i	0.0314309	−	0.0609845i
$959$	19.5147			0.630162
$960$	27.3618	−	8.05430i	0.883098	−	0.259952i
$961$	29.4146			0.948858
$962$	−20.1499	+	39.0963i	−0.649660	+	1.26051i
$963$	−3.39105	+	3.39105i	−0.109275	+	0.109275i
$964$	11.5260	+	16.1782i	0.371226	+	0.521065i
$965$	12.9270	+	12.9270i	0.416135	+	0.416135i
$966$	−1.27293	−	3.98052i	−0.0409558	−	0.128071i
$967$		−	26.2043i		−	0.842674i	−0.906904	−	0.421337i	$-0.861561\pi$
$967$		−	26.2043i		−	0.842674i	0.906904	−	0.421337i	$-0.138439\pi$
$968$	1.44535	+	10.0285i	0.0464554	+	0.322328i
$969$			19.1286i			0.614500i
$970$	−59.1257	+	18.9078i	−1.89841	+	0.607093i
$971$	6.83895	+	6.83895i	0.219472	+	0.219472i	0.808276	−	0.588804i	$-0.200401\pi$
$971$	6.83895	+	6.83895i	0.219472	+	0.219472i	−0.588804	+	0.808276i	$0.700401\pi$
$972$	1.97238	+	0.331214i	0.0632642	+	0.0106237i
$973$	11.6873	−	11.6873i	0.374678	−	0.374678i
$974$	−38.2631	−	19.7205i	−1.22603	−	0.631887i
$975$	49.9490			1.59965
$976$	−24.8713	−	51.1408i	−0.796110	−	1.63698i
$977$	57.7642			1.84804			0.924021	−	0.382343i	$-0.124883\pi$
$977$	57.7642			1.84804			0.924021	+	0.382343i	$0.124883\pi$
$978$	8.10783	+	4.17871i	0.259260	+	0.133621i
$979$	−14.8558	+	14.8558i	−0.474793	+	0.474793i
$980$	−1.18089	+	7.03219i	−0.0377220	+	0.224635i
$981$	7.49212	+	7.49212i	0.239205	+	0.239205i
$982$	48.9390	−	15.6502i	1.56171	−	0.499418i
$983$			1.74731i			0.0557305i	0.999612	+	0.0278652i	$0.00887093\pi$
$983$			1.74731i			0.0557305i	−0.999612	+	0.0278652i	$0.991129\pi$
$984$	−18.6197	−	13.9287i	−0.593573	−	0.444030i
$985$		−	72.3041i		−	2.30380i
$986$	3.52999	+	11.0385i	0.112418	+	0.351537i
$987$	−3.84689	−	3.84689i	−0.122448	−	0.122448i
$988$	58.2414	−	41.4933i	1.85290	−	1.32008i
$989$	−9.94677	+	9.94677i	−0.316289	+	0.316289i
$990$	−6.29123	+	12.2067i	−0.199948	+	0.387953i
$991$	37.0380			1.17655			0.588276	−	0.808660i	$-0.299807\pi$
$991$	37.0380			1.17655			0.588276	+	0.808660i	$0.299807\pi$
$992$	−30.3600	−	31.8047i	−0.963931	−	1.00980i
$993$	4.75770			0.150981
$994$	−3.79882	+	7.37073i	−0.120491	+	0.233785i
$995$	69.2899	−	69.2899i	2.19664	−	2.19664i
$996$	−8.73815	+	6.22539i	−0.276879	+	0.197259i
$997$	−11.7705	−	11.7705i	−0.372775	−	0.372775i	0.495712	−	0.868487i	$-0.334907\pi$
$997$	−11.7705	−	11.7705i	−0.372775	−	0.372775i	−0.868487	+	0.495712i	$0.834907\pi$
$998$	−6.74666	−	21.0972i	−0.213562	−	0.667820i
$999$			4.80163i			0.151917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.85.10	✓	28
4.3	odd	2		1344.2.w.b.1009.7		28
8.3	odd	2		2688.2.w.c.2017.8		28
8.5	even	2		2688.2.w.d.2017.7		28
16.3	odd	4		1344.2.w.b.337.7		28
16.5	even	4		2688.2.w.d.673.7		28
16.11	odd	4		2688.2.w.c.673.8		28
16.13	even	4	inner	336.2.w.b.253.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.10	✓	28	1.1	even	1	trivial
336.2.w.b.253.10	yes	28	16.13	even	4	inner
1344.2.w.b.337.7		28	16.3	odd	4
1344.2.w.b.1009.7		28	4.3	odd	2
2688.2.w.c.673.8		28	16.11	odd	4
2688.2.w.c.2017.8		28	8.3	odd	2
2688.2.w.d.673.7		28	16.5	even	4
2688.2.w.d.2017.7		28	8.5	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.647888 - 1.25708i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.16048 - 1.62889i) q^{4} +(2.52107 + 2.52107i) q^{5} +(-0.430761 - 1.34701i) q^{6} -1.00000i q^{7} +(-2.79950 + 0.403476i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.647888 - 1.25708i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.16048 - 1.62889i) q^{4} +(2.52107 + 2.52107i) q^{5} +(-0.430761 - 1.34701i) q^{6} -1.00000i q^{7} +(-2.79950 + 0.403476i) q^{8} -1.00000i q^{9} +(4.80254 - 1.53580i) q^{10} +(-1.92584 - 1.92584i) q^{11} +(-1.97238 - 0.331214i) q^{12} +(4.58005 - 4.58005i) q^{13} +(-1.25708 - 0.647888i) q^{14} +3.56533 q^{15} +(-1.30656 + 3.78059i) q^{16} +3.46521 q^{17} +(-1.25708 - 0.647888i) q^{18} +(-3.90337 + 3.90337i) q^{19} +(1.18089 - 7.03219i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(-3.66867 + 1.17320i) q^{22} +2.95507i q^{23} +(-1.69425 + 2.26485i) q^{24} +7.71155i q^{25} +(-2.79011 - 8.72483i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.62889 + 1.16048i) q^{28} +(-1.67222 + 1.67222i) q^{29} +(2.30993 - 4.48189i) q^{30} -7.77268 q^{31} +(3.90599 + 4.09185i) q^{32} -2.72356 q^{33} +(2.24507 - 4.35603i) q^{34} +(2.52107 - 2.52107i) q^{35} +(-1.62889 + 1.16048i) q^{36} +(-3.39526 - 3.39526i) q^{37} +(2.37789 + 7.43578i) q^{38} -6.47717i q^{39} +(-8.07492 - 6.04054i) q^{40} +8.22116i q^{41} +(-1.34701 + 0.430761i) q^{42} +(3.36600 + 3.36600i) q^{43} +(-0.902080 + 5.37190i) q^{44} +(2.52107 - 2.52107i) q^{45} +(3.71475 + 1.91455i) q^{46} +5.44032 q^{47} +(1.74940 + 3.59716i) q^{48} -1.00000 q^{49} +(9.69401 + 4.99622i) q^{50} +(2.45027 - 2.45027i) q^{51} +(-12.7755 - 2.14533i) q^{52} +(0.328423 + 0.328423i) q^{53} +(-1.34701 + 0.430761i) q^{54} -9.71036i q^{55} +(0.403476 + 2.79950i) q^{56} +5.52020i q^{57} +(1.01870 + 3.18552i) q^{58} +(4.92858 + 4.92858i) q^{59} +(-4.13750 - 5.80752i) q^{60} +(-10.0529 + 10.0529i) q^{61} +(-5.03583 + 9.77085i) q^{62} -1.00000 q^{63} +(7.67441 - 2.25906i) q^{64} +23.0932 q^{65} +(-1.76456 + 3.42372i) q^{66} +(-5.72344 + 5.72344i) q^{67} +(-4.02131 - 5.64444i) q^{68} +(2.08955 + 2.08955i) q^{69} +(-1.53580 - 4.80254i) q^{70} -5.86339i q^{71} +(0.403476 + 2.79950i) q^{72} -6.93302i q^{73} +(-6.46786 + 2.06836i) q^{74} +(5.45289 + 5.45289i) q^{75} +(10.8880 + 1.82837i) q^{76} +(-1.92584 + 1.92584i) q^{77} +(-8.14229 - 4.19648i) q^{78} +8.37696 q^{79} +(-12.8251 + 6.23720i) q^{80} -1.00000 q^{81} +(10.3346 + 5.32639i) q^{82} +(3.79326 - 3.79326i) q^{83} +(-0.331214 + 1.97238i) q^{84} +(8.73601 + 8.73601i) q^{85} +(6.41211 - 2.05053i) q^{86} +2.36488i q^{87} +(6.16844 + 4.61437i) q^{88} -7.71391i q^{89} +(-1.53580 - 4.80254i) q^{90} +(-4.58005 - 4.58005i) q^{91} +(4.81348 - 3.42931i) q^{92} +(-5.49612 + 5.49612i) q^{93} +(3.52472 - 6.83890i) q^{94} -19.6813 q^{95} +(5.65533 + 0.131425i) q^{96} -12.3113 q^{97} +(-0.647888 + 1.25708i) q^{98} +(-1.92584 + 1.92584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) \) 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

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