LMFDB - Embedded newform 714.2.w.e.83.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(83,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 4, 3]))

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

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

chi := DirichletCharacter("714.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.w (of order $8$, degree $4$, 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:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.16
Character	$\chi$	$=$	714.83
Dual form			714.2.w.e.671.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.39247 + 1.03006i) q^{3} -1.00000i q^{4} +(-2.17160 + 0.899506i) q^{5} +(1.71299 - 0.256259i) q^{6} +(-1.14112 + 2.38702i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.877938 + 2.86866i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.39247 + 1.03006i) q^{3} -1.00000i q^{4} +(-2.17160 + 0.899506i) q^{5} +(1.71299 - 0.256259i) q^{6} +(-1.14112 + 2.38702i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.877938 + 2.86866i) q^{9} +(-0.899506 + 2.17160i) q^{10} +(5.47402 + 2.26741i) q^{11} +(1.03006 - 1.39247i) q^{12} -5.36946 q^{13} +(0.880980 + 2.49477i) q^{14} +(-3.95043 - 0.984351i) q^{15} -1.00000 q^{16} +(4.12265 + 0.0610632i) q^{17} +(2.64925 + 1.40765i) q^{18} +(-2.88066 + 2.88066i) q^{19} +(0.899506 + 2.17160i) q^{20} +(-4.04775 + 2.14842i) q^{21} +(5.47402 - 2.26741i) q^{22} +(-5.51535 - 2.28453i) q^{23} +(-0.256259 - 1.71299i) q^{24} +(0.371197 - 0.371197i) q^{25} +(-3.79678 + 3.79678i) q^{26} +(-1.73240 + 4.89886i) q^{27} +(2.38702 + 1.14112i) q^{28} +(2.90750 + 7.01932i) q^{29} +(-3.48942 + 2.09734i) q^{30} +(7.49615 - 3.10501i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.28682 + 8.79589i) q^{33} +(2.95833 - 2.87198i) q^{34} +(0.330923 - 6.21008i) q^{35} +(2.86866 - 0.877938i) q^{36} +(0.629663 + 1.52014i) q^{37} +4.07387i q^{38} +(-7.47680 - 5.53088i) q^{39} +(2.17160 + 0.899506i) q^{40} +(7.15235 + 2.96260i) q^{41} +(-1.34303 + 4.38135i) q^{42} +(5.86162 - 5.86162i) q^{43} +(2.26741 - 5.47402i) q^{44} +(-4.48691 - 5.43987i) q^{45} +(-5.51535 + 2.28453i) q^{46} -1.85665i q^{47} +(-1.39247 - 1.03006i) q^{48} +(-4.39569 - 5.44775i) q^{49} -0.524952i q^{50} +(5.67777 + 4.33162i) q^{51} +5.36946i q^{52} +(-1.10030 + 1.10030i) q^{53} +(2.23902 + 4.68901i) q^{54} -13.9269 q^{55} +(2.49477 - 0.880980i) q^{56} +(-6.97850 + 1.04397i) q^{57} +(7.01932 + 2.90750i) q^{58} +(4.84410 - 4.84410i) q^{59} +(-0.984351 + 3.95043i) q^{60} +(0.313858 - 0.757721i) q^{61} +(3.10501 - 7.49615i) q^{62} +(-7.84938 - 1.17784i) q^{63} +1.00000i q^{64} +(11.6603 - 4.82986i) q^{65} +(9.95798 + 2.48129i) q^{66} -1.51487 q^{67} +(0.0610632 - 4.12265i) q^{68} +(-5.32673 - 8.86229i) q^{69} +(-4.15719 - 4.62519i) q^{70} +(-4.66942 + 1.93414i) q^{71} +(1.40765 - 2.64925i) q^{72} +(-3.49013 - 8.42592i) q^{73} +(1.52014 + 0.629663i) q^{74} +(0.899237 - 0.134524i) q^{75} +(2.88066 + 2.88066i) q^{76} +(-11.6589 + 10.4792i) q^{77} +(-9.19782 + 1.37597i) q^{78} +(3.91211 - 9.44467i) q^{79} +(2.17160 - 0.899506i) q^{80} +(-7.45845 + 5.03702i) q^{81} +(7.15235 - 2.96260i) q^{82} +(-0.354747 - 0.354747i) q^{83} +(2.14842 + 4.04775i) q^{84} +(-9.00768 + 3.57575i) q^{85} -8.28958i q^{86} +(-3.18175 + 12.7691i) q^{87} +(-2.26741 - 5.47402i) q^{88} -12.9846i q^{89} +(-7.01929 - 0.673848i) q^{90} +(6.12720 - 12.8170i) q^{91} +(-2.28453 + 5.51535i) q^{92} +(13.6365 + 3.39789i) q^{93} +(-1.31285 - 1.31285i) q^{94} +(3.66447 - 8.84681i) q^{95} +(-1.71299 + 0.256259i) q^{96} +(-0.646996 - 1.56199i) q^{97} +(-6.96036 - 0.743920i) q^{98} +(-1.69859 + 17.6938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 16 q^{7}+O(q^{10}) $ 80 * q - 16 * q^7	$ 80 q - 16 q^{7} - 16 q^{14} - 16 q^{15} - 80 q^{16} + 16 q^{18} - 32 q^{21} - 16 q^{23} - 32 q^{25} + 64 q^{29} - 16 q^{30} - 48 q^{37} + 16 q^{39} - 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{46} + 16 q^{49} + 104 q^{51} - 80 q^{53} - 16 q^{57} - 16 q^{58} - 48 q^{60} + 56 q^{63} + 80 q^{65} - 144 q^{67} + 8 q^{70} + 16 q^{71} - 32 q^{74} - 24 q^{77} + 32 q^{78} + 32 q^{79} - 16 q^{84} + 208 q^{85} + 16 q^{88} - 8 q^{91} + 16 q^{92} + 48 q^{93} - 16 q^{95} - 16 q^{98} + 80 q^{99}+O(q^{100}) $ 80 * q - 16 * q^7 - 16 * q^14 - 16 * q^15 - 80 * q^16 + 16 * q^18 - 32 * q^21 - 16 * q^23 - 32 * q^25 + 64 * q^29 - 16 * q^30 - 48 * q^37 + 16 * q^39 - 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^46 + 16 * q^49 + 104 * q^51 - 80 * q^53 - 16 * q^57 - 16 * q^58 - 48 * q^60 + 56 * q^63 + 80 * q^65 - 144 * q^67 + 8 * q^70 + 16 * q^71 - 32 * q^74 - 24 * q^77 + 32 * q^78 + 32 * q^79 - 16 * q^84 + 208 * q^85 + 16 * q^88 - 8 * q^91 + 16 * q^92 + 48 * q^93 - 16 * q^95 - 16 * q^98 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.39247	+	1.03006i	0.803942	+	0.594707i
$3$	1.39247	+	1.03006i	0.803942	+	0.594707i
$4$		−	1.00000i		−	0.500000i
$5$	−2.17160	+	0.899506i	−0.971169	+	0.402271i	−0.811147	−	0.584842i	$-0.801156\pi$
$5$	−2.17160	+	0.899506i	−0.971169	+	0.402271i	−0.160022	+	0.987114i	$0.551156\pi$
$6$	1.71299	−	0.256259i	0.699325	−	0.104617i
$7$	−1.14112	+	2.38702i	−0.431303	+	0.902207i
$7$	−1.14112	+	2.38702i	−0.431303	+	0.902207i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.877938	+	2.86866i	0.292646	+	0.956221i
$10$	−0.899506	+	2.17160i	−0.284449	+	0.686720i
$11$	5.47402	+	2.26741i	1.65048	+	0.683651i	0.997292	−	0.0735450i	$-0.0234313\pi$
$11$	5.47402	+	2.26741i	1.65048	+	0.683651i	0.653188	+	0.757196i	$0.273431\pi$
$12$	1.03006	−	1.39247i	0.297354	−	0.401971i
$13$	−5.36946			−1.48922			−0.744610	−	0.667500i	$-0.767364\pi$
$13$	−5.36946			−1.48922			−0.744610	+	0.667500i	$0.767364\pi$
$14$	0.880980	+	2.49477i	0.235452	+	0.666755i
$15$	−3.95043	−	0.984351i	−1.02000	−	0.254158i
$16$	−1.00000			−0.250000
$17$	4.12265	+	0.0610632i	0.999890	+	0.0148100i
$17$	4.12265	+	0.0610632i	0.999890	+	0.0148100i
$18$	2.64925	+	1.40765i	0.624433	+	0.331787i
$19$	−2.88066	+	2.88066i	−0.660869	+	0.660869i	−0.955585	−	0.294716i	$-0.904775\pi$
$19$	−2.88066	+	2.88066i	−0.660869	+	0.660869i	0.294716	+	0.955585i	$0.404775\pi$
$20$	0.899506	+	2.17160i	0.201136	+	0.485584i
$21$	−4.04775	+	2.14842i	−0.883292	+	0.468823i
$22$	5.47402	−	2.26741i	1.16707	−	0.483414i
$23$	−5.51535	−	2.28453i	−1.15003	−	0.476358i	−0.275486	−	0.961305i	$-0.588839\pi$
$23$	−5.51535	−	2.28453i	−1.15003	−	0.476358i	−0.874543	+	0.484948i	$0.838839\pi$
$24$	−0.256259	−	1.71299i	−0.0523087	−	0.349662i
$25$	0.371197	−	0.371197i	0.0742394	−	0.0742394i
$26$	−3.79678	+	3.79678i	−0.744610	+	0.744610i
$27$	−1.73240	+	4.89886i	−0.333401	+	0.942785i
$28$	2.38702	+	1.14112i	0.451104	+	0.215652i
$29$	2.90750	+	7.01932i	0.539909	+	1.30346i	0.924786	+	0.380487i	$0.124244\pi$
$29$	2.90750	+	7.01932i	0.539909	+	1.30346i	−0.384877	+	0.922968i	$0.625756\pi$
$30$	−3.48942	+	2.09734i	−0.637078	+	0.382919i
$31$	7.49615	−	3.10501i	1.34635	−	0.557676i	0.411075	−	0.911602i	$-0.365154\pi$
$31$	7.49615	−	3.10501i	1.34635	−	0.557676i	0.935273	+	0.353926i	$0.115154\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	5.28682	+	8.79589i	0.920318	+	1.53117i
$34$	2.95833	−	2.87198i	0.507350	−	0.492540i
$35$	0.330923	−	6.21008i	0.0559362	−	1.04970i
$36$	2.86866	−	0.877938i	0.478110	−	0.146323i
$37$	0.629663	+	1.52014i	0.103516	+	0.249909i	0.967148	−	0.254212i	$-0.0818162\pi$
$37$	0.629663	+	1.52014i	0.103516	+	0.249909i	−0.863633	+	0.504122i	$0.831816\pi$
$38$			4.07387i			0.660869i
$39$	−7.47680	−	5.53088i	−1.19725	−	0.885650i
$40$	2.17160	+	0.899506i	0.343360	+	0.142224i
$41$	7.15235	+	2.96260i	1.11701	+	0.462681i	0.863346	−	0.504612i	$-0.168364\pi$
$41$	7.15235	+	2.96260i	1.11701	+	0.462681i	0.253664	+	0.967292i	$0.418364\pi$
$42$	−1.34303	+	4.38135i	−0.207235	+	0.676058i
$43$	5.86162	−	5.86162i	0.893889	−	0.893889i	−0.100998	−	0.994887i	$-0.532204\pi$
$43$	5.86162	−	5.86162i	0.893889	−	0.893889i	0.994887	+	0.100998i	$0.0322035\pi$
$44$	2.26741	−	5.47402i	0.341826	−	0.825240i
$45$	−4.48691	−	5.43987i	−0.668869	−	0.810928i
$46$	−5.51535	+	2.28453i	−0.813193	+	0.336836i
$47$		−	1.85665i		−	0.270821i	−0.990790	−	0.135410i	$-0.956765\pi$
$47$		−	1.85665i		−	0.270821i	0.990790	−	0.135410i	$-0.0432353\pi$
$48$	−1.39247	−	1.03006i	−0.200986	−	0.148677i
$49$	−4.39569	−	5.44775i	−0.627955	−	0.778250i
$50$		−	0.524952i		−	0.0742394i
$51$	5.67777	+	4.33162i	0.795046	+	0.606549i
$52$			5.36946i			0.744610i
$53$	−1.10030	+	1.10030i	−0.151138	+	0.151138i	−0.778626	−	0.627488i	$-0.784083\pi$
$53$	−1.10030	+	1.10030i	−0.151138	+	0.151138i	0.627488	+	0.778626i	$0.284083\pi$
$54$	2.23902	+	4.68901i	0.304692	+	0.638093i
$55$	−13.9269			−1.87791
$56$	2.49477	−	0.880980i	0.333378	−	0.117726i
$57$	−6.97850	+	1.04397i	−0.924324	+	0.138277i
$58$	7.01932	+	2.90750i	0.921682	+	0.381773i
$59$	4.84410	−	4.84410i	0.630648	−	0.630648i	−0.317583	−	0.948231i	$-0.602871\pi$
$59$	4.84410	−	4.84410i	0.630648	−	0.630648i	0.948231	+	0.317583i	$0.102871\pi$
$60$	−0.984351	+	3.95043i	−0.127079	+	0.509999i
$61$	0.313858	−	0.757721i	0.0401854	−	0.0970162i	−0.902512	−	0.430664i	$-0.858280\pi$
$61$	0.313858	−	0.757721i	0.0401854	−	0.0970162i	0.942698	+	0.333647i	$0.108280\pi$
$62$	3.10501	−	7.49615i	0.394336	−	0.952012i
$63$	−7.84938	−	1.17784i	−0.988928	−	0.148394i
$64$			1.00000i			0.125000i
$65$	11.6603	−	4.82986i	1.44628	−	0.599070i
$66$	9.95798	+	2.48129i	1.22574	+	0.305425i
$67$	−1.51487			−0.185071			−0.0925355	−	0.995709i	$-0.529497\pi$
$67$	−1.51487			−0.185071			−0.0925355	+	0.995709i	$0.529497\pi$
$68$	0.0610632	−	4.12265i	0.00740500	−	0.499945i
$69$	−5.32673	−	8.86229i	−0.641263	−	1.06689i
$70$	−4.15719	−	4.62519i	−0.496880	−	0.552816i
$71$	−4.66942	+	1.93414i	−0.554158	+	0.229540i	−0.642147	−	0.766582i	$-0.721956\pi$
$71$	−4.66942	+	1.93414i	−0.554158	+	0.229540i	0.0879889	+	0.996121i	$0.471956\pi$
$72$	1.40765	−	2.64925i	0.165894	−	0.312217i
$73$	−3.49013	−	8.42592i	−0.408489	−	0.986179i	−0.985536	−	0.169468i	$-0.945795\pi$
$73$	−3.49013	−	8.42592i	−0.408489	−	0.986179i	0.577047	−	0.816711i	$-0.304205\pi$
$74$	1.52014	+	0.629663i	0.176713	+	0.0731968i
$75$	0.899237	−	0.134524i	0.103835	−	0.0155335i
$76$	2.88066	+	2.88066i	0.330435	+	0.330435i
$77$	−11.6589	+	10.4792i	−1.32865	+	1.19421i
$78$	−9.19782	+	1.37597i	−1.04145	+	0.155798i
$79$	3.91211	−	9.44467i	0.440147	−	1.06261i	−0.535750	−	0.844377i	$-0.679971\pi$
$79$	3.91211	−	9.44467i	0.440147	−	1.06261i	0.975897	−	0.218232i	$-0.0700289\pi$
$80$	2.17160	−	0.899506i	0.242792	−	0.100568i
$81$	−7.45845	+	5.03702i	−0.828716	+	0.559669i
$82$	7.15235	−	2.96260i	0.789845	−	0.327165i
$83$	−0.354747	−	0.354747i	−0.0389385	−	0.0389385i	0.687369	−	0.726308i	$-0.258765\pi$
$83$	−0.354747	−	0.354747i	−0.0389385	−	0.0389385i	−0.726308	+	0.687369i	$0.758765\pi$
$84$	2.14842	+	4.04775i	0.234412	+	0.441646i
$85$	−9.00768	+	3.57575i	−0.977020	+	0.387844i
$86$		−	8.28958i		−	0.893889i
$87$	−3.18175	+	12.7691i	−0.341119	+	1.36899i
$88$	−2.26741	−	5.47402i	−0.241707	−	0.583533i
$89$		−	12.9846i		−	1.37637i	−0.725537	−	0.688183i	$-0.758408\pi$
$89$		−	12.9846i		−	1.37637i	0.725537	−	0.688183i	$-0.241592\pi$
$90$	−7.01929	−	0.673848i	−0.739899	−	0.0710298i
$91$	6.12720	−	12.8170i	0.642305	−	1.34358i
$92$	−2.28453	+	5.51535i	−0.238179	+	0.575014i
$93$	13.6365	+	3.39789i	1.41404	+	0.352344i
$94$	−1.31285	−	1.31285i	−0.135410	−	0.135410i
$95$	3.66447	−	8.84681i	0.375967	−	0.907664i
$96$	−1.71299	+	0.256259i	−0.174831	+	0.0261543i
$97$	−0.646996	−	1.56199i	−0.0656925	−	0.158596i	0.887624	−	0.460569i	$-0.152355\pi$
$97$	−0.646996	−	1.56199i	−0.0656925	−	0.158596i	−0.953316	+	0.301973i	$0.902355\pi$
$98$	−6.96036	−	0.743920i	−0.703102	−	0.0751473i
$99$	−1.69859	+	17.6938i	−0.170715	+	1.77829i
$100$	−0.371197	−	0.371197i	−0.0371197	−	0.0371197i
$101$	8.13441			0.809404			0.404702	−	0.914449i	$-0.367375\pi$
$101$	8.13441			0.809404			0.404702	+	0.914449i	$0.367375\pi$
$102$	7.07771	−	0.951867i	0.700798	−	0.0942489i
$103$			7.03501i			0.693180i	0.938017	+	0.346590i	$0.112660\pi$
$103$			7.03501i			0.693180i	−0.938017	+	0.346590i	$0.887340\pi$
$104$	3.79678	+	3.79678i	0.372305	+	0.372305i
$105$	6.85758	−	8.30648i	0.669231	−	0.810629i
$106$			1.55606i			0.151138i
$107$	2.00613	+	4.84323i	0.193940	+	0.468213i	0.990697	−	0.136087i	$-0.0434528\pi$
$107$	2.00613	+	4.84323i	0.193940	+	0.468213i	−0.796757	+	0.604300i	$0.793453\pi$
$108$	4.89886	+	1.73240i	0.471393	+	0.166701i
$109$	−7.29879	−	3.02326i	−0.699097	−	0.289575i	0.00468746	−	0.999989i	$-0.498508\pi$
$109$	−7.29879	−	3.02326i	−0.699097	−	0.289575i	−0.703784	+	0.710414i	$0.748508\pi$
$110$	−9.84783	+	9.84783i	−0.938953	+	0.938953i
$111$	−0.689055	+	2.76534i	−0.0654022	+	0.262474i
$112$	1.14112	−	2.38702i	0.107826	−	0.225552i
$113$	−2.97676	−	1.23302i	−0.280030	−	0.115992i	0.238248	−	0.971204i	$-0.423427\pi$
$113$	−2.97676	−	1.23302i	−0.280030	−	0.115992i	−0.518278	+	0.855212i	$0.673427\pi$
$114$	−4.19635	+	5.67274i	−0.393024	+	0.531301i
$115$	14.0321			1.30850
$116$	7.01932	−	2.90750i	0.651728	−	0.269954i
$117$	−4.71405	−	15.4032i	−0.435814	−	1.42402i
$118$		−	6.85059i		−	0.630648i
$119$	−4.85021	+	9.77116i	−0.444618	+	0.895720i
$120$	2.09734	+	3.48942i	0.191460	+	0.318539i
$121$	17.0456	+	17.0456i	1.54960	+	1.54960i
$122$	−0.313858	−	0.757721i	−0.0284154	−	0.0686008i
$123$	6.90776	+	11.4927i	0.622852	+	1.03626i
$124$	−3.10501	−	7.49615i	−0.278838	−	0.673174i
$125$	4.02533	−	9.71801i	0.360037	−	0.869205i
$126$	−6.38320	+	4.71749i	−0.568661	+	0.420267i
$127$	6.26091	−	6.26091i	0.555566	−	0.555566i	−0.372476	−	0.928042i	$-0.621491\pi$
$127$	6.26091	−	6.26091i	0.555566	−	0.555566i	0.928042	+	0.372476i	$0.121491\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	14.2000	−	2.12428i	1.25024	−	0.187033i
$130$	4.82986	−	11.6603i	0.423607	−	1.02268i
$131$	−4.60717	+	1.90835i	−0.402531	+	0.166734i	−0.574758	−	0.818324i	$-0.694904\pi$
$131$	−4.60717	+	1.90835i	−0.402531	+	0.166734i	0.172227	+	0.985057i	$0.444904\pi$
$132$	8.79589	−	5.28682i	0.765584	−	0.460159i
$133$	−3.58900	−	10.1634i	−0.311206	−	0.881276i
$134$	−1.07118	+	1.07118i	−0.0925355	+	0.0925355i
$135$	−0.644464	−	12.1967i	−0.0554667	−	1.04972i
$136$	−2.87198	−	2.95833i	−0.246270	−	0.253675i
$137$			14.8692i			1.27036i	0.772362	+	0.635182i	$0.219075\pi$
$137$			14.8692i			1.27036i	−0.772362	+	0.635182i	$0.780925\pi$
$138$	−10.0332	−	2.50002i	−0.854079	−	0.212816i
$139$	−6.60225	+	2.73474i	−0.559995	+	0.231958i	−0.644683	−	0.764450i	$-0.723011\pi$
$139$	−6.60225	+	2.73474i	−0.559995	+	0.231958i	0.0846879	+	0.996408i	$0.473011\pi$
$140$	−6.21008	−	0.330923i	−0.524848	−	0.0279681i
$141$	1.91247	−	2.58533i	0.161059	−	0.217724i
$142$	−1.93414	+	4.66942i	−0.162309	+	0.391849i
$143$	−29.3925	−	12.1748i	−2.45793	−	1.01811i
$144$	−0.877938	−	2.86866i	−0.0731615	−	0.239055i
$145$	−12.6278	−	12.6278i	−1.04868	−	1.04868i
$146$	−8.42592	−	3.49013i	−0.697334	−	0.288845i
$147$	−0.509329	−	12.1137i	−0.0420087	−	0.999117i
$148$	1.52014	−	0.629663i	0.124955	−	0.0517579i
$149$	21.9200			1.79576			0.897878	−	0.440245i	$-0.145108\pi$
$149$	21.9200			1.79576			0.897878	+	0.440245i	$0.145108\pi$
$150$	0.540734	−	0.730979i	0.0441507	−	0.0596842i
$151$	6.02678	+	6.02678i	0.490453	+	0.490453i	0.908449	−	0.417996i	$-0.137267\pi$
$151$	6.02678	+	6.02678i	0.490453	+	0.490453i	−0.417996	+	0.908449i	$0.637267\pi$
$152$	4.07387			0.330435
$153$	3.44427	+	11.8801i	0.278452	+	0.960450i
$154$	−0.834169	+	15.6540i	−0.0672193	+	1.26143i
$155$	−13.4857	+	13.4857i	−1.08319	+	1.08319i
$156$	−5.53088	+	7.47680i	−0.442825	+	0.598623i
$157$	−7.50820			−0.599219			−0.299610	−	0.954062i	$-0.596856\pi$
$157$	−7.50820			−0.599219			−0.299610	+	0.954062i	$0.596856\pi$
$158$	−3.91211	−	9.44467i	−0.311231	−	0.751378i
$159$	−2.66551	+	0.398755i	−0.211389	+	0.0316233i
$160$	0.899506	−	2.17160i	0.0711122	−	0.171680i
$161$	11.7469	−	10.5583i	0.925784	−	0.832110i
$162$	−1.71221	+	8.83563i	−0.134524	+	0.694193i
$163$	−11.1182	−	4.60531i	−0.870844	−	0.360715i	−0.0979051	−	0.995196i	$-0.531214\pi$
$163$	−11.1182	−	4.60531i	−0.870844	−	0.360715i	−0.772939	+	0.634480i	$0.781214\pi$
$164$	2.96260	−	7.15235i	0.231340	−	0.558505i
$165$	−19.3928	−	14.3456i	−1.50973	−	1.11681i
$166$	−0.501688			−0.0389385
$167$	−0.452987	−	1.09361i	−0.0350532	−	0.0846259i	0.905383	−	0.424595i	$-0.139583\pi$
$167$	−0.452987	−	1.09361i	−0.0350532	−	0.0846259i	−0.940437	+	0.339969i	$0.889583\pi$
$168$	4.38135	+	1.34303i	0.338029	+	0.103617i
$169$	15.8311			1.21777
$170$	−3.84095	+	8.89782i	−0.294588	+	0.682432i
$171$	−10.7927	−	5.73460i	−0.825338	−	0.438536i
$172$	−5.86162	−	5.86162i	−0.446944	−	0.446944i
$173$	3.77394	+	9.11111i	0.286928	+	0.692705i	0.999965	−	0.00842187i	$-0.00268079\pi$
$173$	3.77394	+	9.11111i	0.286928	+	0.692705i	−0.713037	+	0.701127i	$0.752681\pi$
$174$	6.77928	+	11.2789i	0.513936	+	0.855055i
$175$	0.462472	+	1.30963i	0.0349596	+	0.0989990i
$176$	−5.47402	−	2.26741i	−0.412620	−	0.170913i
$177$	11.7350	−	1.75553i	0.882055	−	0.131953i
$178$	−9.18151	−	9.18151i	−0.688183	−	0.688183i
$179$	12.1206	+	12.1206i	0.905933	+	0.905933i	0.995941	−	0.0900079i	$-0.0286892\pi$
$179$	12.1206	+	12.1206i	0.905933	+	0.905933i	−0.0900079	+	0.995941i	$0.528689\pi$
$180$	−5.43987	+	4.48691i	−0.405464	+	0.334434i
$181$	19.5197	+	8.08533i	1.45089	+	0.600978i	0.962411	−	0.271598i	$-0.0875520\pi$
$181$	19.5197	+	8.08533i	1.45089	+	0.600978i	0.488479	+	0.872576i	$0.337552\pi$
$182$	−4.73039	−	13.3956i	−0.350640	−	0.992945i
$183$	1.21754	−	0.731809i	0.0900030	−	0.0540968i
$184$	2.28453	+	5.51535i	0.168418	+	0.406597i
$185$	−2.73475	−	2.73475i	−0.201063	−	0.201063i
$186$	12.0451	−	7.23980i	0.883192	−	0.530848i
$187$	22.4290	+	9.68202i	1.64017	+	0.708020i
$188$	−1.85665			−0.135410
$189$	−9.71676	−	9.72546i	−0.706790	−	0.707423i
$190$	−3.66447	−	8.84681i	−0.265849	−	0.641815i
$191$	−2.28750			−0.165518			−0.0827590	−	0.996570i	$-0.526373\pi$
$191$	−2.28750			−0.165518			−0.0827590	+	0.996570i	$0.526373\pi$
$192$	−1.03006	+	1.39247i	−0.0743384	+	0.100493i
$193$	−1.03302	+	2.49394i	−0.0743585	+	0.179517i	−0.956688	−	0.291114i	$-0.905974\pi$
$193$	−1.03302	+	2.49394i	−0.0743585	+	0.179517i	0.882330	+	0.470632i	$0.155974\pi$
$194$	−1.56199	−	0.646996i	−0.112144	−	0.0464516i
$195$	21.2117	+	5.28543i	1.51900	+	0.378498i
$196$	−5.44775	+	4.39569i	−0.389125	+	0.313978i
$197$	3.71607	−	8.97138i	0.264759	−	0.639184i	−0.734462	−	0.678650i	$-0.762565\pi$
$197$	3.71607	−	8.97138i	0.264759	−	0.639184i	0.999221	+	0.0394654i	$0.0125655\pi$
$198$	11.3103	+	13.7125i	0.803788	+	0.974503i
$199$	4.60877	+	11.1265i	0.326707	+	0.788740i	0.998833	+	0.0483031i	$0.0153813\pi$
$199$	4.60877	+	11.1265i	0.326707	+	0.788740i	−0.672126	+	0.740437i	$0.734619\pi$
$200$	−0.524952			−0.0371197
$201$	−2.10941	−	1.56041i	−0.148786	−	0.110063i
$202$	5.75190	−	5.75190i	0.404702	−	0.404702i
$203$	−20.0730	−	1.06965i	−1.40885	−	0.0750749i
$204$	4.33162	−	5.67777i	0.303274	−	0.397523i
$205$	−18.1969			−1.27093
$206$	4.97450	+	4.97450i	0.346590	+	0.346590i
$207$	1.71141	−	17.8273i	0.118952	−	1.23909i
$208$	5.36946			0.372305
$209$	−22.3005	+	9.23715i	−1.54255	+	0.638947i
$210$	−1.02452	−	10.7226i	−0.0706988	−	0.739930i
$211$	−10.9121	−	4.51995i	−0.751222	−	0.311166i	−0.0259818	−	0.999662i	$-0.508271\pi$
$211$	−10.9121	−	4.51995i	−0.751222	−	0.311166i	−0.725240	+	0.688496i	$0.758271\pi$
$212$	1.10030	+	1.10030i	0.0755689	+	0.0755689i
$213$	−8.49430	−	2.11657i	−0.582020	−	0.145025i
$214$	4.84323	+	2.00613i	0.331076	+	0.137136i
$215$	−7.45653	+	18.0017i	−0.508531	+	1.22770i
$216$	4.68901	−	2.23902i	0.319047	−	0.152346i
$217$	−1.14232	+	21.4366i	−0.0775454	+	1.45521i
$218$	−7.29879	+	3.02326i	−0.494336	+	0.204761i
$219$	3.81933	−	15.3279i	0.258087	−	1.03576i
$220$			13.9269i			0.938953i
$221$	−22.1364	−	0.327876i	−1.48906	−	0.0220553i
$222$	1.46815	+	2.44263i	0.0985361	+	0.163938i
$223$	3.79748	−	3.79748i	0.254298	−	0.254298i	−0.568432	−	0.822730i	$-0.692450\pi$
$223$	3.79748	−	3.79748i	0.254298	−	0.254298i	0.822730	+	0.568432i	$0.192450\pi$
$224$	−0.880980	−	2.49477i	−0.0588630	−	0.166689i
$225$	1.39073	+	0.738951i	0.0927151	+	0.0492634i
$226$	−2.97676	+	1.23302i	−0.198011	+	0.0820189i
$227$	2.41386	−	5.82758i	0.160214	−	0.386790i	−0.823304	−	0.567600i	$-0.807872\pi$
$227$	2.41386	−	5.82758i	0.160214	−	0.386790i	0.983518	+	0.180810i	$0.0578719\pi$
$228$	1.04397	+	6.97850i	0.0691384	+	0.462162i
$229$	−15.2356	−	15.2356i	−1.00680	−	1.00680i	−0.999977	−	0.00682023i	$-0.997829\pi$
$229$	−15.2356	−	15.2356i	−1.00680	−	1.00680i	−0.00682023	−	0.999977i	$-0.502171\pi$
$230$	9.92217	−	9.92217i	0.654248	−	0.654248i
$231$	−27.0288	+	2.58255i	−1.77837	+	0.169919i
$232$	2.90750	−	7.01932i	0.190887	−	0.460841i
$233$	−8.25203	−	19.9222i	−0.540608	−	1.30514i	−0.924294	−	0.381680i	$-0.875346\pi$
$233$	−8.25203	−	19.9222i	−0.540608	−	1.30514i	0.383686	−	0.923464i	$-0.374654\pi$
$234$	−14.2250	−	7.55834i	−0.929919	−	0.494104i
$235$	1.67007	+	4.03191i	0.108943	+	0.263013i
$236$	−4.84410	−	4.84410i	−0.315324	−	0.315324i
$237$	15.1761	−	9.12169i	0.985794	−	0.592517i
$238$	3.47964	+	10.3389i	0.225551	+	0.670169i
$239$			22.4045i			1.44923i	0.689155	+	0.724614i	$0.257982\pi$
$239$			22.4045i			1.44923i	−0.689155	+	0.724614i	$0.742018\pi$
$240$	3.95043	+	0.984351i	0.254999	+	0.0635396i
$241$	5.00778	−	2.07429i	0.322580	−	0.133617i	−0.215517	−	0.976500i	$-0.569144\pi$
$241$	5.00778	−	2.07429i	0.322580	−	0.133617i	0.538096	+	0.842883i	$0.319144\pi$
$242$	24.1061			1.54960
$243$	−15.5741	−	0.668786i	−0.999079	−	0.0429026i
$244$	−0.757721	−	0.313858i	−0.0485081	−	0.0200927i
$245$	14.4459	+	7.87638i	0.922918	+	0.503203i
$246$	13.0111	+	3.24205i	0.829557	+	0.206705i
$247$	15.4676	−	15.4676i	0.984179	−	0.984179i
$248$	−7.49615	−	3.10501i	−0.476006	−	0.197168i
$249$	−0.128562	−	0.859386i	−0.00814730	−	0.0544614i
$250$	−4.02533	−	9.71801i	−0.254584	−	0.614621i
$251$			11.8836i			0.750086i	0.927007	+	0.375043i	$0.122372\pi$
$251$			11.8836i			0.750086i	−0.927007	+	0.375043i	$0.877628\pi$
$252$	−1.17784	+	7.84938i	−0.0741969	+	0.494464i
$253$	−25.0111	−	25.0111i	−1.57244	−	1.57244i
$254$		−	8.85426i		−	0.555566i
$255$	−16.2262	−	4.29936i	−1.01612	−	0.269237i
$256$	1.00000			0.0625000
$257$	8.46277	+	8.46277i	0.527893	+	0.527893i	0.919944	−	0.392051i	$-0.128234\pi$
$257$	8.46277	+	8.46277i	0.527893	+	0.527893i	−0.392051	+	0.919944i	$0.628234\pi$
$258$	8.53880	−	11.5430i	0.531602	−	0.718635i
$259$	−4.34712	−	0.231649i	−0.270117	−	0.0143940i
$260$	−4.82986	−	11.6603i	−0.299535	−	0.723142i
$261$	−17.5835	+	14.5032i	−1.08839	+	0.897723i
$262$	−1.90835	+	4.60717i	−0.117899	+	0.284632i
$263$	−7.70634	−	7.70634i	−0.475193	−	0.475193i	0.428397	−	0.903591i	$-0.359078\pi$
$263$	−7.70634	−	7.70634i	−0.475193	−	0.475193i	−0.903591	+	0.428397i	$0.859078\pi$
$264$	2.48129	−	9.95798i	0.152713	−	0.612872i
$265$	1.39968	−	3.37914i	0.0859819	−	0.207579i
$266$	−9.72439	−	4.64878i	−0.596241	−	0.285035i
$267$	13.3750	−	18.0807i	0.818536	−	1.10652i
$268$			1.51487i			0.0925355i
$269$	−4.73887	−	11.4406i	−0.288934	−	0.697548i	0.711050	−	0.703141i	$-0.248220\pi$
$269$	−4.73887	−	11.4406i	−0.288934	−	0.697548i	−0.999984	+	0.00559287i	$0.998220\pi$
$270$	−9.08004	−	8.16863i	−0.552594	−	0.497127i
$271$			10.2680i			0.623737i	0.950125	+	0.311868i	$0.100955\pi$
$271$			10.2680i			0.623737i	−0.950125	+	0.311868i	$0.899045\pi$
$272$	−4.12265	−	0.0610632i	−0.249973	−	0.00370250i
$273$	21.7342	−	11.5358i	1.31542	−	0.698180i
$274$	10.5141	+	10.5141i	0.635182	+	0.635182i
$275$	2.87360	−	1.19028i	0.173284	−	0.0717768i
$276$	−8.86229	+	5.32673i	−0.533447	+	0.320632i
$277$	21.6725	−	8.97704i	1.30217	−	0.539378i	0.379582	−	0.925158i	$-0.376068\pi$
$277$	21.6725	−	8.97704i	1.30217	−	0.539378i	0.922591	+	0.385780i	$0.126068\pi$
$278$	−2.73474	+	6.60225i	−0.164019	+	0.395976i
$279$	15.4884	+	18.7779i	0.927265	+	1.12420i
$280$	−4.62519	+	4.15719i	−0.276408	+	0.248440i
$281$	−13.7591	−	13.7591i	−0.820796	−	0.820796i	0.165426	−	0.986222i	$-0.447100\pi$
$281$	−13.7591	−	13.7591i	−0.820796	−	0.820796i	−0.986222	+	0.165426i	$0.947100\pi$
$282$	−0.475785	−	3.18043i	−0.0283326	−	0.189392i
$283$	10.6909	+	4.42830i	0.635506	+	0.263235i	0.677091	−	0.735900i	$-0.263240\pi$
$283$	10.6909	+	4.42830i	0.635506	+	0.263235i	−0.0415843	+	0.999135i	$0.513240\pi$
$284$	1.93414	+	4.66942i	0.114770	+	0.277079i
$285$	14.2154	−	8.54427i	0.842050	−	0.506119i
$286$	−29.3925	+	12.1748i	−1.73802	+	0.719910i
$287$	−15.2335	+	13.6921i	−0.899204	+	0.808219i
$288$	−2.64925	−	1.40765i	−0.156108	−	0.0829468i
$289$	16.9925	+	0.503485i	0.999561	+	0.0296167i
$290$	−17.8585			−1.04868
$291$	0.708024	−	2.84147i	0.0415051	−	0.166570i
$292$	−8.42592	+	3.49013i	−0.493090	+	0.204244i
$293$			17.0240i			0.994555i	0.867592	+	0.497277i	$0.165667\pi$
$293$			17.0240i			0.994555i	−0.867592	+	0.497277i	$0.834333\pi$
$294$	−8.92580	−	8.20550i	−0.520563	−	0.478554i
$295$	−6.16214	+	14.8767i	−0.358774	+	0.866157i
$296$	0.629663	−	1.52014i	0.0365984	−	0.0883563i
$297$	−20.5909	+	22.8884i	−1.19481	+	1.32812i
$298$	15.4998	−	15.4998i	0.897878	−	0.897878i
$299$	29.6144	+	12.2667i	1.71265	+	0.709401i
$300$	−0.134524	−	0.899237i	−0.00776673	−	0.0519175i
$301$	7.30296	+	20.6806i	0.420936	+	1.19201i
$302$	8.52316			0.490453
$303$	11.3269	+	8.37896i	0.650714	+	0.481359i
$304$	2.88066	−	2.88066i	0.165217	−	0.165217i
$305$			1.92778i			0.110385i
$306$	10.8360	+	5.96504i	0.619451	+	0.340999i
$307$		−	1.77632i		−	0.101380i	−0.998714	−	0.0506899i	$-0.983858\pi$
$307$		−	1.77632i		−	0.101380i	0.998714	−	0.0506899i	$-0.0161420\pi$
$308$	10.4792	+	11.6589i	0.597107	+	0.664326i
$309$	−7.24650	+	9.79603i	−0.412239	+	0.557276i
$310$			19.0716i			1.08319i
$311$	20.5593	−	8.51594i	1.16581	−	0.482895i	0.286005	−	0.958228i	$-0.407672\pi$
$311$	20.5593	−	8.51594i	1.16581	−	0.482895i	0.879806	+	0.475333i	$0.157672\pi$
$312$	1.37597	+	9.19782i	0.0778991	+	0.520724i
$313$	6.81435	−	16.4513i	0.385170	−	0.929883i	−0.605778	−	0.795634i	$-0.707138\pi$
$313$	6.81435	−	16.4513i	0.385170	−	0.929883i	0.990948	−	0.134249i	$-0.0428621\pi$
$314$	−5.30910	+	5.30910i	−0.299610	+	0.299610i
$315$	18.1052	−	4.50276i	1.02011	−	0.253702i
$316$	−9.44467	−	3.91211i	−0.531304	−	0.220073i
$317$	31.9626	+	13.2394i	1.79520	+	0.743596i	0.988224	+	0.153012i	$0.0488973\pi$
$317$	31.9626	+	13.2394i	1.79520	+	0.743596i	0.806976	+	0.590584i	$0.201103\pi$
$318$	−1.60284	+	2.16676i	−0.0898828	+	0.121506i
$319$			45.0164i			2.52044i
$320$	−0.899506	−	2.17160i	−0.0502839	−	0.121396i
$321$	−2.19536	+	8.81049i	−0.122533	+	0.491754i
$322$	0.840466	−	15.7721i	0.0468374	−	0.878947i
$323$	−12.0519	+	11.7001i	−0.670584	+	0.651009i
$324$	5.03702	+	7.45845i	0.279834	+	0.414358i
$325$	−1.99313	+	1.99313i	−0.110559	+	0.110559i
$326$	−11.1182	+	4.60531i	−0.615780	+	0.255064i
$327$	−7.04919	−	11.7280i	−0.389821	−	0.648560i
$328$	−2.96260	−	7.15235i	−0.163582	−	0.394923i
$329$	4.43186	+	2.11867i	0.244336	+	0.116806i
$330$	−23.8567	+	3.56890i	−1.31327	+	0.196462i
$331$	−18.8095	+	18.8095i	−1.03386	+	1.03386i	−0.0344549	+	0.999406i	$0.510969\pi$
$331$	−18.8095	+	18.8095i	−1.03386	+	1.03386i	−0.999406	+	0.0344549i	$0.989031\pi$
$332$	−0.354747	+	0.354747i	−0.0194693	+	0.0194693i
$333$	−3.80796	+	3.14088i	−0.208675	+	0.172119i
$334$	−1.09361	−	0.452987i	−0.0598395	−	0.0247864i
$335$	3.28969	−	1.36264i	0.179735	−	0.0744487i
$336$	4.04775	−	2.14842i	0.220823	−	0.117206i
$337$	−2.38017	−	5.74623i	−0.129656	−	0.313017i	0.845698	−	0.533661i	$-0.179184\pi$
$337$	−2.38017	−	5.74623i	−0.129656	−	0.313017i	−0.975354	+	0.220644i	$0.929184\pi$
$338$	11.1943	−	11.1943i	0.608887	−	0.608887i
$339$	−2.87496	−	4.78319i	−0.156147	−	0.259787i
$340$	3.57575	+	9.00768i	0.193922	+	0.488510i
$341$	48.0744			2.60338
$342$	−11.6866	+	3.57661i	−0.631937	+	0.193401i
$343$	18.0199	−	4.27603i	0.972981	−	0.230884i
$344$	−8.28958			−0.446944
$345$	19.5392	+	14.4539i	1.05196	+	0.778173i
$346$	9.11111	+	3.77394i	0.489816	+	0.202889i
$347$	5.42421	−	13.0952i	0.291187	−	0.702987i	−0.708810	−	0.705399i	$-0.750768\pi$
$347$	5.42421	−	13.0952i	0.291187	−	0.702987i	0.999997	+	0.00241195i	$0.000767750\pi$
$348$	12.7691	+	3.18175i	0.684495	+	0.170559i
$349$	−20.3612	−	20.3612i	−1.08991	−	1.08991i	−0.995537	−	0.0943718i	$-0.969916\pi$
$349$	−20.3612	−	20.3612i	−1.08991	−	1.08991i	−0.0943718	−	0.995537i	$-0.530084\pi$
$350$	1.25307	+	0.599034i	0.0669793	+	0.0320197i
$351$	9.30206	−	26.3042i	0.496507	−	1.40401i
$352$	−5.47402	+	2.26741i	−0.291766	+	0.120854i
$353$			19.4872i			1.03720i	0.855018	+	0.518599i	$0.173546\pi$
$353$			19.4872i			1.03720i	−0.855018	+	0.518599i	$0.826454\pi$
$354$	7.05654	−	9.53923i	0.375051	−	0.507004i
$355$	8.40033	−	8.40033i	0.445843	−	0.445843i
$356$	−12.9846			−0.688183
$357$	−16.8187	+	8.61001i	−0.890138	+	0.455690i
$358$	17.1411			0.905933
$359$	11.0834	−	11.0834i	0.584961	−	0.584961i	−0.351301	−	0.936263i	$-0.614261\pi$
$359$	11.0834	−	11.0834i	0.584961	−	0.584961i	0.936263	+	0.351301i	$0.114261\pi$
$360$	−0.673848	+	7.01929i	−0.0355149	+	0.369949i
$361$			2.40358i			0.126504i
$362$	19.5197	−	8.08533i	1.02593	−	0.424956i
$363$	6.17740	+	41.2934i	0.324230	+	2.16734i
$364$	−12.8170	−	6.12720i	−0.671792	−	0.321153i
$365$	15.1583	+	15.1583i	0.793423	+	0.793423i
$366$	0.343463	−	1.37840i	0.0179531	−	0.0720499i
$367$	−5.32202	+	12.8485i	−0.277807	+	0.670686i	−0.999774	−	0.0212415i	$-0.993238\pi$
$367$	−5.32202	+	12.8485i	−0.277807	+	0.670686i	0.721967	+	0.691927i	$0.243238\pi$
$368$	5.51535	+	2.28453i	0.287507	+	0.119089i
$369$	−2.21938	+	23.1187i	−0.115536	+	1.20351i
$370$	−3.86752			−0.201063
$371$	−1.37086	−	3.88201i	−0.0711714	−	0.201544i
$372$	3.39789	−	13.6365i	0.176172	−	0.707020i
$373$	30.0648			1.55670			0.778348	−	0.627833i	$-0.216058\pi$
$373$	30.0648			1.55670			0.778348	+	0.627833i	$0.216058\pi$
$374$	22.7059	−	9.01350i	1.17410	−	0.466077i
$375$	15.6153	−	9.38568i	0.806371	−	0.484674i
$376$	−1.31285	+	1.31285i	−0.0677052	+	0.0677052i
$377$	−15.6117	−	37.6899i	−0.804043	−	1.94113i
$378$	−13.7477	−	0.00614997i	−0.707107	−	0.000316320i
$379$	−21.3314	+	8.83574i	−1.09572	+	0.453861i	−0.855997	−	0.516980i	$-0.827056\pi$
$379$	−21.3314	+	8.83574i	−1.09572	+	0.453861i	−0.239721	+	0.970842i	$0.577056\pi$
$380$	−8.84681	−	3.66447i	−0.453832	−	0.187983i
$381$	15.1672	−	2.26899i	0.777042	−	0.116244i
$382$	−1.61751	+	1.61751i	−0.0827590	+	0.0827590i
$383$	6.03339	−	6.03339i	0.308292	−	0.308292i	−0.535955	−	0.844247i	$-0.680048\pi$
$383$	6.03339	−	6.03339i	0.308292	−	0.308292i	0.844247	+	0.535955i	$0.180048\pi$
$384$	0.256259	+	1.71299i	0.0130772	+	0.0874156i
$385$	15.8923	−	33.2438i	0.809947	−	1.69426i
$386$	1.03302	+	2.49394i	0.0525794	+	0.126938i
$387$	21.9612	+	11.6689i	1.11635	+	0.593162i
$388$	−1.56199	+	0.646996i	−0.0792979	+	0.0328463i
$389$	0.632878	−	0.632878i	0.0320882	−	0.0320882i	−0.690881	−	0.722969i	$-0.742777\pi$
$389$	0.632878	−	0.632878i	0.0320882	−	0.0320882i	0.722969	+	0.690881i	$0.242777\pi$
$390$	18.7363	−	11.2616i	0.948749	−	0.570251i
$391$	−22.5984	−	9.75511i	−1.14285	−	0.493337i
$392$	−0.743920	+	6.96036i	−0.0375736	+	0.351551i
$393$	−8.38107	−	2.08836i	−0.422769	−	0.105344i
$394$	−3.71607	−	8.97138i	−0.187213	−	0.451972i
$395$			24.0290i			1.20903i
$396$	17.6938	+	1.69859i	0.889145	+	0.0853574i
$397$	17.5497	+	7.26932i	0.880794	+	0.364837i	0.776805	−	0.629742i	$-0.216839\pi$
$397$	17.5497	+	7.26932i	0.880794	+	0.364837i	0.103989	+	0.994578i	$0.466839\pi$
$398$	11.1265	+	4.60877i	0.557723	+	0.231017i
$399$	5.47134	−	17.8491i	0.273910	−	0.893571i
$400$	−0.371197	+	0.371197i	−0.0185598	+	0.0185598i
$401$	0.0106900	−	0.0258079i	0.000533832	−	0.00128878i	−0.923612	−	0.383328i	$-0.874778\pi$
$401$	0.0106900	−	0.0258079i	0.000533832	−	0.00128878i	0.924146	+	0.382039i	$0.124778\pi$
$402$	−2.59496	+	0.388200i	−0.129425	+	0.0193616i
$403$	−40.2503	+	16.6722i	−2.00501	+	0.830502i
$404$		−	8.13441i		−	0.404702i
$405$	11.6659	−	17.6473i	0.579685	−	0.876901i
$406$	−14.9501	+	13.4374i	−0.741963	+	0.666888i
$407$			9.74898i			0.483239i
$408$	−0.951867	−	7.07771i	−0.0471245	−	0.350399i
$409$		−	6.91010i		−	0.341682i	−0.985299	−	0.170841i	$-0.945351\pi$
$409$		−	6.91010i		−	0.341682i	0.985299	−	0.170841i	$-0.0546485\pi$
$410$	−12.8672	+	12.8672i	−0.635464	+	0.635464i
$411$	−15.3163	+	20.7049i	−0.755495	+	1.02130i
$412$	7.03501			0.346590
$413$	6.03523	+	17.0906i	0.296974	+	0.840975i
$414$	−11.3957	−	13.8160i	−0.560067	−	0.679019i
$415$	1.08947	+	0.451271i	0.0534797	+	0.0221520i
$416$	3.79678	−	3.79678i	0.186152	−	0.186152i
$417$	−12.0104	−	2.99269i	−0.588151	−	0.146553i
$418$	−9.23715	+	22.3005i	−0.451804	+	1.09075i
$419$	0.884988	−	2.13655i	0.0432345	−	0.104377i	−0.900787	−	0.434261i	$-0.857010\pi$
$419$	0.884988	−	2.13655i	0.0432345	−	0.104377i	0.944022	+	0.329884i	$0.107010\pi$
$420$	−8.30648	−	6.85758i	−0.405315	−	0.334616i
$421$		−	12.4741i		−	0.607953i	−0.952680	−	0.303976i	$-0.901686\pi$
$421$		−	12.4741i		−	0.607953i	0.952680	−	0.303976i	$-0.0983144\pi$
$422$	−10.9121	+	4.51995i	−0.531194	+	0.220028i
$423$	5.32611	−	1.63003i	0.258964	−	0.0792546i
$424$	1.55606			0.0755689
$425$	1.55298	−	1.50765i	0.0753307	−	0.0731318i
$426$	−7.50302	+	4.50973i	−0.363522	+	0.218497i
$427$	1.45054	+	1.61384i	0.0701966	+	0.0780990i
$428$	4.84323	−	2.00613i	0.234106	−	0.0969701i
$429$	−28.3874	−	47.2292i	−1.37056	−	2.28025i
$430$	7.45653	+	18.0017i	0.359586	+	0.868117i
$431$	−22.0300	−	9.12512i	−1.06115	−	0.439541i	−0.217289	−	0.976107i	$-0.569721\pi$
$431$	−22.0300	−	9.12512i	−1.06115	−	0.439541i	−0.843858	+	0.536566i	$0.819721\pi$
$432$	1.73240	−	4.89886i	0.0833503	−	0.235696i
$433$	−13.9525	−	13.9525i	−0.670516	−	0.670516i	0.287319	−	0.957835i	$-0.407236\pi$
$433$	−13.9525	−	13.9525i	−0.670516	−	0.670516i	−0.957835	+	0.287319i	$0.907236\pi$
$434$	14.3502	+	15.9657i	0.688833	+	0.766379i
$435$	−4.57639	−	30.5913i	−0.219421	−	1.46674i
$436$	−3.02326	+	7.29879i	−0.144788	+	0.349549i
$437$	22.4688	−	9.30688i	1.07483	−	0.445209i
$438$	−8.13777	−	13.5391i	−0.388838	−	0.646925i
$439$	−28.0103	+	11.6022i	−1.33686	+	0.553745i	−0.932604	−	0.360901i	$-0.882469\pi$
$439$	−28.0103	+	11.6022i	−1.33686	+	0.553745i	−0.404255	+	0.914646i	$0.632469\pi$
$440$	9.84783	+	9.84783i	0.469477	+	0.469477i
$441$	11.7686	−	17.3925i	0.560410	−	0.828215i
$442$	−15.8847	+	15.4210i	−0.755556	+	0.733500i
$443$			30.3350i			1.44126i	0.693319	+	0.720630i	$0.256148\pi$
$443$			30.3350i			1.44126i	−0.693319	+	0.720630i	$0.743852\pi$
$444$	2.76534	+	0.689055i	0.131237	+	0.0327011i
$445$	11.6797	+	28.1974i	0.553673	+	1.33668i
$446$		−	5.37045i		−	0.254298i
$447$	30.5229	+	22.5790i	1.44368	+	1.06795i
$448$	−2.38702	−	1.14112i	−0.112776	−	0.0539129i
$449$	9.76445	−	23.5735i	0.460813	−	1.11250i	−0.507251	−	0.861798i	$-0.669338\pi$
$449$	9.76445	−	23.5735i	0.460813	−	1.11250i	0.968064	−	0.250702i	$-0.0806616\pi$
$450$	1.50591	−	0.460875i	0.0709893	−	0.0217259i
$451$	32.4347	+	32.4347i	1.52729	+	1.52729i
$452$	−1.23302	+	2.97676i	−0.0579962	+	0.140015i
$453$	2.18414	+	14.6001i	0.102620	+	0.685971i
$454$	−2.41386	−	5.82758i	−0.113288	−	0.273502i
$455$	−1.77688	+	33.3448i	−0.0833013	+	1.56323i
$456$	5.67274	+	4.19635i	0.265650	+	0.196512i
$457$	−26.6848	−	26.6848i	−1.24826	−	1.24826i	−0.956488	−	0.291773i	$-0.905755\pi$
$457$	−26.6848	−	26.6848i	−1.24826	−	1.24826i	−0.291773	−	0.956488i	$-0.594245\pi$
$458$	−21.5464			−1.00680
$459$	−7.44124	+	20.0905i	−0.347327	+	0.937744i
$460$		−	14.0321i		−	0.654248i
$461$	−2.00831	−	2.00831i	−0.0935363	−	0.0935363i	0.658790	−	0.752327i	$-0.271068\pi$
$461$	−2.00831	−	2.00831i	−0.0935363	−	0.0935363i	−0.752327	+	0.658790i	$0.771068\pi$
$462$	−17.2861	+	20.9384i	−0.804224	+	0.974143i
$463$			37.3051i			1.73371i	0.498558	+	0.866857i	$0.333863\pi$
$463$			37.3051i			1.73371i	−0.498558	+	0.866857i	$0.666137\pi$
$464$	−2.90750	−	7.01932i	−0.134977	−	0.325864i
$465$	−32.6694	+	4.88727i	−1.51501	+	0.226642i
$466$	−19.9222	−	8.25203i	−0.922876	−	0.382268i
$467$	−12.3119	+	12.3119i	−0.569727	+	0.569727i	−0.932052	−	0.362325i	$-0.881983\pi$
$467$	−12.3119	+	12.3119i	−0.569727	+	0.569727i	0.362325	+	0.932052i	$0.381983\pi$
$468$	−15.4032	+	4.71405i	−0.712011	+	0.217907i
$469$	1.72865	−	3.61602i	0.0798217	−	0.166972i
$470$	4.03191	+	1.67007i	0.185978	+	0.0770346i
$471$	−10.4549	−	7.73392i	−0.481738	−	0.356360i
$472$	−6.85059			−0.315324
$473$	45.3774	−	18.7959i	2.08645	−	0.864237i
$474$	4.28112	−	17.1811i	0.196638	−	0.789156i
$475$			2.13859i			0.0981250i
$476$	9.77116	+	4.85021i	0.447860	+	0.222309i
$477$	−4.12239	−	2.19039i	−0.188751	−	0.100291i
$478$	15.8424	+	15.8424i	0.724614	+	0.724614i
$479$	−1.86302	−	4.49774i	−0.0851237	−	0.205507i	0.875586	−	0.483063i	$-0.160476\pi$
$479$	−1.86302	−	4.49774i	−0.0851237	−	0.205507i	−0.960710	+	0.277556i	$0.910476\pi$
$480$	3.48942	−	2.09734i	0.159269	−	0.0957298i
$481$	−3.38095	−	8.16233i	−0.154158	−	0.372170i
$482$	2.07429	−	5.00778i	0.0944814	−	0.228098i
$483$	27.2329	−	2.60205i	1.23914	−	0.118397i
$484$	17.0456	−	17.0456i	0.774799	−	0.774799i
$485$	2.81003	+	2.81003i	0.127597	+	0.127597i
$486$	−11.4855	+	10.5397i	−0.520991	+	0.478088i
$487$	7.10307	−	17.1483i	0.321871	−	0.777065i	−0.677275	−	0.735730i	$-0.736839\pi$
$487$	7.10307	−	17.1483i	0.321871	−	0.777065i	0.999145	−	0.0413345i	$-0.0131609\pi$
$488$	−0.757721	+	0.313858i	−0.0343004	+	0.0142077i
$489$	−10.7380	−	17.8652i	−0.485588	−	0.807892i
$490$	15.7843	−	4.64539i	0.713060	−	0.209857i
$491$	10.4959	−	10.4959i	0.473675	−	0.473675i	−0.429427	−	0.903102i	$-0.641284\pi$
$491$	10.4959	−	10.4959i	0.473675	−	0.473675i	0.903102	+	0.429427i	$0.141284\pi$
$492$	11.4927	−	6.90776i	0.518131	−	0.311426i
$493$	11.5580	+	29.1158i	0.520545	+	1.31131i
$494$		−	21.8745i		−	0.984179i
$495$	−12.2270	−	39.9517i	−0.549562	−	1.79569i
$496$	−7.49615	+	3.10501i	−0.336587	+	0.139419i
$497$	0.711558	−	13.3531i	0.0319177	−	0.598966i
$498$	−0.698585	−	0.516771i	−0.0313043	−	0.0231570i
$499$	2.22049	−	5.36073i	0.0994026	−	0.239979i	−0.866353	−	0.499432i	$-0.833542\pi$
$499$	2.22049	−	5.36073i	0.0994026	−	0.239979i	0.965756	+	0.259453i	$0.0835422\pi$
$500$	−9.71801	−	4.02533i	−0.434603	−	0.180018i
$501$	0.495715	−	1.98942i	0.0221469	−	0.0888807i
$502$	8.40297	+	8.40297i	0.375043	+	0.375043i
$503$	−14.1472	−	5.85995i	−0.630791	−	0.261282i	0.0442980	−	0.999018i	$-0.485895\pi$
$503$	−14.1472	−	5.85995i	−0.630791	−	0.261282i	−0.675089	+	0.737736i	$0.735895\pi$
$504$	4.71749	+	6.38320i	0.210134	+	0.284331i
$505$	−17.6647	+	7.31695i	−0.786068	+	0.325600i
$506$	−35.3711			−1.57244
$507$	22.0443	+	16.3070i	0.979021	+	0.724220i
$508$	−6.26091	−	6.26091i	−0.277783	−	0.277783i
$509$	−21.1819			−0.938871			−0.469436	−	0.882967i	$-0.655543\pi$
$509$	−21.1819			−0.938871			−0.469436	+	0.882967i	$0.655543\pi$
$510$	−14.5137	+	8.43351i	−0.642679	+	0.373442i
$511$	24.0955	+	1.28400i	1.06592	+	0.0568008i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−9.12148	−	19.1024i	−0.402723	−	0.843392i
$514$	11.9682			0.527893
$515$	−6.32803	−	15.2772i	−0.278846	−	0.673194i
$516$	−2.12428	−	14.2000i	−0.0935163	−	0.625119i
$517$	4.20980	−	10.1634i	0.185147	−	0.446984i
$518$	−3.23768	+	2.91008i	−0.142255	+	0.127861i
$519$	−4.12992	+	16.5743i	−0.181283	+	0.727533i
$520$	−11.6603	−	4.82986i	−0.511338	−	0.211803i
$521$	−9.50660	+	22.9510i	−0.416492	+	1.00550i	0.566864	+	0.823811i	$0.308156\pi$
$521$	−9.50660	+	22.9510i	−0.416492	+	1.00550i	−0.983356	+	0.181689i	$0.941844\pi$
$522$	−2.17810	+	22.6887i	−0.0953328	+	0.993056i
$523$	−18.9549			−0.828842			−0.414421	−	0.910085i	$-0.636016\pi$
$523$	−18.9549			−0.828842			−0.414421	+	0.910085i	$0.636016\pi$
$524$	1.90835	+	4.60717i	0.0833668	+	0.201265i
$525$	−0.705028	+	2.30000i	−0.0307699	+	0.100380i
$526$	−10.8984			−0.475193
$527$	31.0936	−	12.3431i	1.35446	−	0.537675i
$528$	−5.28682	−	8.79589i	−0.230079	−	0.382792i
$529$	8.93649	+	8.93649i	0.388543	+	0.388543i
$530$	−1.39968	−	3.37914i	−0.0607984	−	0.146780i
$531$	18.1489	+	9.64326i	0.787595	+	0.418482i
$532$	−10.1634	+	3.58900i	−0.440638	+	0.155603i
$533$	−38.4043	−	15.9076i	−1.66347	−	0.689033i
$534$	−3.32743	−	22.2425i	−0.143992	−	0.962528i
$535$	−8.71303	−	8.71303i	−0.376697	−	0.376697i
$536$	1.07118	+	1.07118i	0.0462677	+	0.0462677i
$537$	4.39255	+	29.3624i	0.189553	+	1.26708i
$538$	−11.4406	−	4.73887i	−0.493241	−	0.204307i
$539$	−11.7098	−	39.7879i	−0.504376	−	1.71379i
$540$	−12.1967	+	0.644464i	−0.524860	+	0.0277333i
$541$	10.2826	+	24.8244i	0.442084	+	1.06729i	0.975216	+	0.221254i	$0.0710148\pi$
$541$	10.2826	+	24.8244i	0.442084	+	1.06729i	−0.533132	+	0.846032i	$0.678985\pi$
$542$	7.26057	+	7.26057i	0.311868	+	0.311868i
$543$	18.8522	+	31.3651i	0.809025	+	1.34601i
$544$	−2.95833	+	2.87198i	−0.126838	+	0.123135i
$545$	18.5695			0.795429
$546$	7.21136	−	23.5255i	0.308618	−	1.00680i
$547$	12.2863	+	29.6618i	0.525326	+	1.26825i	0.934556	+	0.355817i	$0.115797\pi$
$547$	12.2863	+	29.6618i	0.525326	+	1.26825i	−0.409230	+	0.912431i	$0.634203\pi$
$548$	14.8692			0.635182
$549$	2.44919	+	0.235121i	0.104529	+	0.0100347i
$550$	1.19028	−	2.87360i	0.0507538	−	0.122531i
$551$	−28.5958	−	11.8448i	−1.21822	−	0.504604i
$552$	−2.50002	+	10.0332i	−0.106408	+	0.427040i
$553$	18.0804	+	20.1158i	0.768856	+	0.855410i
$554$	8.97704	−	21.6725i	0.381398	−	0.920775i
$555$	−0.991087	−	6.62502i	−0.0420693	−	0.281216i
$556$	2.73474	+	6.60225i	0.115979	+	0.279998i
$557$	−29.5709			−1.25296			−0.626479	−	0.779438i	$-0.715505\pi$
$557$	−29.5709			−1.25296			−0.626479	+	0.779438i	$0.715505\pi$
$558$	24.2299	+	2.32606i	1.02573	+	0.0984699i
$559$	−31.4737	+	31.4737i	−1.33120	+	1.33120i
$560$	−0.330923	+	6.21008i	−0.0139841	+	0.262424i
$561$	21.2586	+	36.5852i	0.897540	+	1.54463i
$562$	−19.4582			−0.820796
$563$	−17.1122	−	17.1122i	−0.721194	−	0.721194i	0.247655	−	0.968848i	$-0.420340\pi$
$563$	−17.1122	−	17.1122i	−0.721194	−	0.721194i	−0.968848	+	0.247655i	$0.920340\pi$
$564$	−2.58533	−	1.91247i	−0.108862	−	0.0805296i
$565$	7.57344			0.318617
$566$	10.6909	−	4.42830i	0.449371	−	0.186136i
$567$	−3.51245	−	23.5513i	−0.147509	−	0.989061i
$568$	4.66942	+	1.93414i	0.195924	+	0.0811545i
$569$	−13.2216	−	13.2216i	−0.554279	−	0.554279i	0.373394	−	0.927673i	$-0.378194\pi$
$569$	−13.2216	−	13.2216i	−0.554279	−	0.554279i	−0.927673	+	0.373394i	$0.878194\pi$
$570$	4.01012	−	16.0935i	0.167965	−	0.674084i
$571$	7.77314	+	3.21974i	0.325296	+	0.134742i	0.539354	−	0.842079i	$-0.318668\pi$
$571$	7.77314	+	3.21974i	0.325296	+	0.134742i	−0.214059	+	0.976821i	$0.568668\pi$
$572$	−12.1748	+	29.3925i	−0.509053	+	1.22896i
$573$	−3.18528	−	2.35627i	−0.133067	−	0.0984348i
$574$	−1.08993	+	20.4535i	−0.0454926	+	0.853711i
$575$	−2.89529	+	1.19927i	−0.120742	+	0.0500130i
$576$	−2.86866	+	0.877938i	−0.119528	+	0.0365808i
$577$		−	42.0634i		−	1.75112i	−0.483107	−	0.875561i	$-0.660492\pi$
$577$		−	42.0634i		−	1.75112i	0.483107	−	0.875561i	$-0.339508\pi$
$578$	12.3716	−	11.6595i	0.514589	−	0.484972i
$579$	−4.00736	+	2.40865i	−0.166540	+	0.100100i
$580$	−12.6278	+	12.6278i	−0.524342	+	0.524342i
$581$	1.25160	−	0.441977i	0.0519249	−	0.0183363i
$582$	−1.50857	−	2.50987i	−0.0625323	−	0.104037i
$583$	−8.51790	+	3.52823i	−0.352776	+	0.146124i
$584$	−3.49013	+	8.42592i	−0.144423	+	0.348667i
$585$	24.0923	+	29.2092i	0.996092	+	1.20765i
$586$	12.0378	+	12.0378i	0.497277	+	0.497277i
$587$	11.6620	−	11.6620i	0.481341	−	0.481341i	−0.424219	−	0.905560i	$-0.639451\pi$
$587$	11.6620	−	11.6620i	0.481341	−	0.481341i	0.905560	+	0.424219i	$0.139451\pi$
$588$	−12.1137	+	0.509329i	−0.499559	+	0.0210044i
$589$	−12.6494	+	30.5383i	−0.521209	+	1.25831i
$590$	6.16214	+	14.8767i	0.253691	+	0.612465i
$591$	14.4156	−	8.66458i	0.592978	−	0.356413i
$592$	−0.629663	−	1.52014i	−0.0258790	−	0.0624774i
$593$	−16.6268	−	16.6268i	−0.682782	−	0.682782i	0.277844	−	0.960626i	$-0.410380\pi$
$593$	−16.6268	−	16.6268i	−0.682782	−	0.682782i	−0.960626	+	0.277844i	$0.910380\pi$
$594$	1.62452	+	30.7445i	0.0666550	+	1.26146i
$595$	1.74349	−	25.5818i	0.0714761	−	1.04875i
$596$		−	21.9200i		−	0.897878i
$597$	−5.04349	+	20.2407i	−0.206416	+	0.828396i
$598$	29.6144	−	12.2667i	1.21102	−	0.501622i
$599$	−23.4765			−0.959222			−0.479611	−	0.877481i	$-0.659222\pi$
$599$	−23.4765			−0.959222			−0.479611	+	0.877481i	$0.659222\pi$
$600$	−0.730979	−	0.540734i	−0.0298421	−	0.0220754i
$601$	−12.0006	−	4.97080i	−0.489514	−	0.202763i	0.124253	−	0.992251i	$-0.460346\pi$
$601$	−12.0006	−	4.97080i	−0.489514	−	0.202763i	−0.613767	+	0.789487i	$0.710346\pi$
$602$	19.7874	+	9.45942i	0.806473	+	0.385537i
$603$	−1.32996	−	4.34565i	−0.0541603	−	0.176969i
$604$	6.02678	−	6.02678i	0.245226	−	0.245226i
$605$	−52.3487	−	21.6836i	−2.12828	−	0.881562i
$606$	13.9342	−	2.08452i	0.566036	−	0.0846777i
$607$	−14.5647	−	35.1622i	−0.591161	−	1.42719i	−0.882382	−	0.470533i	$-0.844062\pi$
$607$	−14.5647	−	35.1622i	−0.591161	−	1.42719i	0.291221	−	0.956656i	$-0.405938\pi$
$608$		−	4.07387i		−	0.165217i
$609$	−26.8493	−	22.1660i	−1.08799	−	0.898210i
$610$	1.36315	+	1.36315i	0.0551923	+	0.0551923i
$611$			9.96922i			0.403312i
$612$	11.8801	−	3.44427i	0.480225	−	0.139226i
$613$	−36.8561			−1.48860			−0.744302	−	0.667843i	$-0.767218\pi$
$613$	−36.8561			−1.48860			−0.744302	+	0.667843i	$0.767218\pi$
$614$	−1.25605	−	1.25605i	−0.0506899	−	0.0506899i
$615$	−25.3386	−	18.7440i	−1.02175	−	0.755830i
$616$	15.6540	+	0.834169i	0.630716	+	0.0336096i
$617$	−5.58712	−	13.4885i	−0.224929	−	0.543027i	0.770617	−	0.637298i	$-0.219948\pi$
$617$	−5.58712	−	13.4885i	−0.224929	−	0.543027i	−0.995547	+	0.0942711i	$0.969948\pi$
$618$	1.80278	+	12.0509i	0.0725186	+	0.484758i
$619$	−8.87140	+	21.4175i	−0.356572	+	0.860840i	0.639205	+	0.769036i	$0.279263\pi$
$619$	−8.87140	+	21.4175i	−0.356572	+	0.860840i	−0.995777	+	0.0918040i	$0.970737\pi$
$620$	13.4857	+	13.4857i	0.541597	+	0.541597i
$621$	20.7464	−	23.0611i	0.832524	−	0.925412i
$622$	8.51594	−	20.5593i	0.341458	−	0.824353i
$623$	30.9945	+	14.8170i	1.24177	+	0.593632i
$624$	7.47680	+	5.53088i	0.299312	+	0.221412i
$625$			27.3492i			1.09397i
$626$	−6.81435	−	16.4513i	−0.272356	−	0.657526i
$627$	−40.5675	−	10.1084i	−1.62011	−	0.403692i
$628$			7.50820i			0.299610i
$629$	2.50306	+	6.30546i	0.0998034	+	0.251415i
$630$	9.61835	−	15.9862i	0.383204	−	0.636906i
$631$	−33.7116	−	33.7116i	−1.34204	−	1.34204i	−0.894028	−	0.448012i	$-0.852132\pi$
$631$	−33.7116	−	33.7116i	−1.34204	−	1.34204i	−0.448012	−	0.894028i	$-0.647868\pi$
$632$	−9.44467	+	3.91211i	−0.375689	+	0.155615i
$633$	−10.5390	−	17.5341i	−0.418886	−	0.696917i
$634$	31.9626	−	13.2394i	1.26940	−	0.525802i
$635$	−7.96446	+	19.2279i	−0.316060	+	0.763036i
$636$	0.398755	+	2.66551i	0.0158116	+	0.105694i
$637$	23.6024	+	29.2514i	0.935163	+	1.15898i
$638$	31.8314	+	31.8314i	1.26022	+	1.26022i
$639$	−9.64784	−	11.6969i	−0.381663	−	0.462723i
$640$	−2.17160	−	0.899506i	−0.0858400	−	0.0355561i
$641$	14.0504	+	33.9205i	0.554956	+	1.33978i	0.913717	+	0.406352i	$0.133199\pi$
$641$	14.0504	+	33.9205i	0.554956	+	1.33978i	−0.358761	+	0.933429i	$0.616801\pi$
$642$	4.67761	+	7.78231i	0.184610	+	0.307143i
$643$	27.0479	−	11.2036i	1.06666	−	0.441826i	0.220851	−	0.975307i	$-0.429116\pi$
$643$	27.0479	−	11.2036i	1.06666	−	0.441826i	0.845812	+	0.533481i	$0.179116\pi$
$644$	−10.5583	−	11.7469i	−0.416055	−	0.462892i
$645$	−28.9258	+	17.3860i	−1.13895	+	0.684575i
$646$	−0.248763	+	16.7952i	−0.00978747	+	0.660797i
$647$	−3.96349			−0.155821			−0.0779104	−	0.996960i	$-0.524825\pi$
$647$	−3.96349			−0.155821			−0.0779104	+	0.996960i	$0.524825\pi$
$648$	8.83563	+	1.71221i	0.347096	+	0.0672620i
$649$	37.5003	−	15.5331i	1.47201	−	0.609728i
$650$			2.81871i			0.110559i
$651$	−23.6717	+	28.6732i	−0.927767	+	1.12379i
$652$	−4.60531	+	11.1182i	−0.180358	+	0.435422i
$653$	−1.15672	+	2.79258i	−0.0452661	+	0.109282i	−0.944895	−	0.327373i	$-0.893837\pi$
$653$	−1.15672	+	2.79258i	−0.0452661	+	0.109282i	0.899629	+	0.436655i	$0.143837\pi$
$654$	−13.2775	−	3.30842i	−0.519191	−	0.129370i
$655$	8.28836	−	8.28836i	0.323853	−	0.323853i
$656$	−7.15235	−	2.96260i	−0.279252	−	0.115670i
$657$	21.1070	−	17.4094i	0.823462	−	0.679207i
$658$	4.63192	−	1.63568i	0.180571	−	0.0637653i
$659$	0.0195045			0.000759789			0.000379894	−	1.00000i	$-0.499879\pi$
$659$	0.0195045			0.000759789			0.000379894		1.00000i	$0.499879\pi$
$660$	−14.3456	+	19.3928i	−0.558403	+	0.754864i
$661$	−11.6303	+	11.6303i	−0.452368	+	0.452368i	−0.896140	−	0.443772i	$-0.853640\pi$
$661$	−11.6303	+	11.6303i	−0.452368	+	0.452368i	0.443772	+	0.896140i	$0.353640\pi$
$662$			26.6006i			1.03386i
$663$	−30.4865	−	23.2585i	−1.18400	−	0.903284i
$664$			0.501688i			0.0194693i
$665$	16.9359	+	18.8424i	0.656745	+	0.730678i
$666$	−0.471700	+	4.91357i	−0.0182780	+	0.190397i
$667$		−	45.3562i		−	1.75620i
$668$	−1.09361	+	0.452987i	−0.0423129	+	0.0175266i
$669$	9.19952	−	1.37623i	0.355674	−	0.0532080i
$670$	1.36264	−	3.28969i	0.0526432	−	0.127092i
$671$	3.43613	−	3.43613i	0.132650	−	0.132650i
$672$	1.34303	−	4.38135i	0.0518086	−	0.169014i
$673$	−25.5749	−	10.5935i	−0.985839	−	0.408348i	−0.169254	−	0.985572i	$-0.554136\pi$
$673$	−25.5749	−	10.5935i	−0.985839	−	0.408348i	−0.816586	+	0.577224i	$0.804136\pi$
$674$	−5.74623	−	2.38017i	−0.221337	−	0.0916806i
$675$	1.17538	+	2.46150i	0.0452403	+	0.0947433i
$676$		−	15.8311i		−	0.608887i
$677$	0.965419	+	2.33073i	0.0371041	+	0.0895771i	0.941345	−	0.337445i	$-0.109563\pi$
$677$	0.965419	+	2.33073i	0.0371041	+	0.0895771i	−0.904241	+	0.427022i	$0.859563\pi$
$678$	−5.41513	−	1.34932i	−0.207967	−	0.0518203i
$679$	4.46679	+	0.238026i	0.171420	+	0.00913462i
$680$	8.89782	+	3.84095i	0.341216	+	0.147294i
$681$	9.36401	−	5.62829i	0.358830	−	0.215677i
$682$	33.9937	−	33.9937i	1.30169	−	1.30169i
$683$	−3.08077	+	1.27610i	−0.117882	+	0.0488284i	−0.440845	−	0.897583i	$-0.645321\pi$
$683$	−3.08077	+	1.27610i	−0.117882	+	0.0488284i	0.322963	+	0.946412i	$0.395321\pi$
$684$	−5.73460	+	10.7927i	−0.219268	+	0.412669i
$685$	−13.3750	−	32.2900i	−0.511031	−	1.23374i
$686$	9.71836	−	15.7656i	0.371049	−	0.601933i
$687$	−5.52146	−	36.9087i	−0.210657	−	1.40816i
$688$	−5.86162	+	5.86162i	−0.223472	+	0.223472i
$689$	5.90802	−	5.90802i	0.225077	−	0.225077i
$690$	24.0368	−	3.59585i	0.915064	−	0.136892i
$691$	−10.7796	−	4.46505i	−0.410075	−	0.169859i	0.168103	−	0.985769i	$-0.446236\pi$
$691$	−10.7796	−	4.46505i	−0.410075	−	0.169859i	−0.578178	+	0.815911i	$0.696236\pi$
$692$	9.11111	−	3.77394i	0.346352	−	0.143464i
$693$	−40.2970	−	24.2453i	−1.53076	−	0.921003i
$694$	−5.42421	−	13.0952i	−0.205900	−	0.497087i
$695$	11.8775	−	11.8775i	0.450540	−	0.450540i
$696$	11.2789	−	6.77928i	0.427527	−	0.256968i
$697$	29.3058	+	12.6505i	1.11004	+	0.479173i
$698$	−28.7951			−1.08991
$699$	9.03040	−	36.2411i	0.341561	−	1.37076i
$700$	1.30963	−	0.462472i	0.0494995	−	0.0174798i
$701$	36.9852			1.39691			0.698456	−	0.715653i	$-0.253871\pi$
$701$	36.9852			1.39691			0.698456	+	0.715653i	$0.253871\pi$
$702$	−12.0223	−	25.1774i	−0.453753	−	0.950261i
$703$	−6.19285	−	2.56516i	−0.233568	−	0.0967470i
$704$	−2.26741	+	5.47402i	−0.0854564	+	0.206310i
$705$	−1.82760	+	7.33458i	−0.0688314	+	0.276236i
$706$	13.7795	+	13.7795i	0.518599	+	0.518599i
$707$	−9.28235	+	19.4170i	−0.349099	+	0.730250i
$708$	−1.75553	−	11.7350i	−0.0659767	−	0.441028i
$709$	−5.24881	+	2.17413i	−0.197123	+	0.0816511i	−0.479061	−	0.877782i	$-0.659023\pi$
$709$	−5.24881	+	2.17413i	−0.197123	+	0.0816511i	0.281938	+	0.959433i	$0.409023\pi$
$710$		−	11.8799i		−	0.445843i
$711$	30.5282	+	2.93069i	1.14490	+	0.109909i
$712$	−9.18151	+	9.18151i	−0.344092	+	0.344092i
$713$	−48.4373			−1.81399
$714$	−5.80440	+	17.9808i	−0.217224	+	0.672914i
$715$	74.7801			2.79662
$716$	12.1206	−	12.1206i	0.452967	−	0.452967i
$717$	−23.0781	+	31.1976i	−0.861866	+	1.16509i
$718$		−	15.6743i		−	0.584961i
$719$	42.1357	−	17.4532i	1.57140	−	0.650894i	0.584377	−	0.811483i	$-0.301339\pi$
$719$	42.1357	−	17.4532i	1.57140	−	0.650894i	0.987022	+	0.160588i	$0.0513391\pi$
$720$	4.48691	+	5.43987i	0.167217	+	0.202732i
$721$	−16.7927	−	8.02779i	−0.625392	−	0.298971i
$722$	1.69959	+	1.69959i	0.0632520	+	0.0632520i
$723$	9.10983	+	2.26995i	0.338798	+	0.0844203i
$724$	8.08533	−	19.5197i	0.300489	−	0.725445i
$725$	3.68481	+	1.52630i	0.136850	+	0.0566852i
$726$	33.5670	+	24.8308i	1.24579	+	0.921557i
$727$	25.6052			0.949645			0.474823	−	0.880081i	$-0.342512\pi$
$727$	25.6052			0.949645			0.474823	+	0.880081i	$0.342512\pi$
$728$	−13.3956	+	4.73039i	−0.496472	+	0.175320i
$729$	−20.9976	−	16.9736i	−0.777687	−	0.628651i
$730$	21.4371			0.793423
$731$	24.5234	−	23.8075i	0.907029	−	0.880552i
$732$	−0.731809	−	1.21754i	−0.0270484	−	0.0450015i
$733$	−16.5350	+	16.5350i	−0.610736	+	0.610736i	−0.943138	−	0.332402i	$-0.892141\pi$
$733$	−16.5350	+	16.5350i	−0.610736	+	0.610736i	0.332402	+	0.943138i	$0.392141\pi$
$734$	5.32202	+	12.8485i	0.196439	+	0.474246i
$735$	12.0024	+	25.8478i	0.442714	+	0.953412i
$736$	5.51535	−	2.28453i	0.203298	−	0.0842089i
$737$	−8.29244	−	3.43484i	−0.305456	−	0.126524i
$738$	14.7780	+	17.9167i	0.543987	+	0.659523i
$739$	13.6325	−	13.6325i	0.501481	−	0.501481i	−0.410417	−	0.911898i	$-0.634617\pi$
$739$	13.6325	−	13.6325i	0.501481	−	0.501481i	0.911898	+	0.410417i	$0.134617\pi$
$740$	−2.73475	+	2.73475i	−0.100531	+	0.100531i
$741$	37.4707	−	5.60554i	1.37652	−	0.205925i
$742$	−3.71434	−	1.77565i	−0.136358	−	0.0651862i
$743$	−6.19140	−	14.9474i	−0.227140	−	0.548365i	0.768687	−	0.639625i	$-0.220911\pi$
$743$	−6.19140	−	14.9474i	−0.227140	−	0.548365i	−0.995827	+	0.0912601i	$0.970911\pi$
$744$	−7.23980	−	12.0451i	−0.265424	−	0.441596i
$745$	−47.6014	+	19.7172i	−1.74398	+	0.722381i
$746$	21.2590	−	21.2590i	0.778348	−	0.778348i
$747$	0.706203	−	1.32910i	0.0258386	−	0.0486291i
$748$	9.68202	−	22.4290i	0.354010	−	0.820087i
$749$	−13.8501	−	0.738045i	−0.506072	−	0.0269676i
$750$	4.40502	−	17.6784i	0.160849	−	0.645523i
$751$	−5.88306	−	14.2030i	−0.214676	−	0.518274i	0.779455	−	0.626458i	$-0.215496\pi$
$751$	−5.88306	−	14.2030i	−0.214676	−	0.518274i	−0.994131	+	0.108185i	$0.965496\pi$
$752$			1.85665i			0.0677052i
$753$	−12.2409	+	16.5475i	−0.446082	+	0.603026i
$754$	−37.6899	−	15.6117i	−1.37259	−	0.568544i
$755$	−18.5089	−	7.66663i	−0.673607	−	0.279017i
$756$	−9.72546	+	9.71676i	−0.353712	+	0.353395i
$757$	38.2088	−	38.2088i	1.38872	−	1.38872i	0.560714	−	0.828010i	$-0.310527\pi$
$757$	38.2088	−	38.2088i	1.38872	−	1.38872i	0.828010	−	0.560714i	$-0.189473\pi$
$758$	−8.83574	+	21.3314i	−0.320928	+	0.774790i
$759$	−9.06417	−	60.5903i	−0.329008	−	2.19929i
$760$	−8.84681	+	3.66447i	−0.320908	+	0.132924i
$761$			26.0236i			0.943353i	0.881772	+	0.471677i	$0.156351\pi$
$761$			26.0236i			0.943353i	−0.881772	+	0.471677i	$0.843649\pi$
$762$	9.12045	−	12.3293i	0.330399	−	0.446643i
$763$	15.5454	−	13.9724i	0.562780	−	0.505835i
$764$			2.28750i			0.0827590i
$765$	−18.1658	−	22.7007i	−0.656786	−	0.820745i
$766$		−	8.53251i		−	0.308292i
$767$	−26.0102	+	26.0102i	−0.939173	+	0.939173i
$768$	1.39247	+	1.03006i	0.0502464	+	0.0371692i
$769$	25.7888			0.929967			0.464983	−	0.885319i	$-0.346060\pi$
$769$	25.7888			0.929967			0.464983	+	0.885319i	$0.346060\pi$
$770$	−12.2694	−	34.7445i	−0.442157	−	1.25210i
$771$	3.06695	+	20.5013i	0.110454	+	0.738337i
$772$	2.49394	+	1.03302i	0.0897587	+	0.0371793i
$773$	8.04860	−	8.04860i	0.289488	−	0.289488i	−0.547390	−	0.836878i	$-0.684378\pi$
$773$	8.04860	−	8.04860i	0.289488	−	0.289488i	0.836878	+	0.547390i	$0.184378\pi$
$774$	23.7800	−	7.27774i	0.854755	−	0.261593i
$775$	1.62998	−	3.93512i	0.0585506	−	0.141354i
$776$	−0.646996	+	1.56199i	−0.0232258	+	0.0560721i
$777$	−5.81461	−	4.80037i	−0.208598	−	0.172212i
$778$		−	0.895025i		−	0.0320882i
$779$	−29.1378	+	12.0693i	−1.04397	+	0.432426i
$780$	5.28543	−	21.2117i	0.189249	−	0.759500i
$781$	−29.9460			−1.07155
$782$	−22.8774	+	9.08154i	−0.818093	+	0.324755i
$783$	−39.4236	+	2.08312i	−1.40888	+	0.0744447i
$784$	4.39569	+	5.44775i	0.156989	+	0.194562i
$785$	16.3048	−	6.75367i	0.581943	−	0.241049i
$786$	−7.40301	+	4.44962i	−0.264056	+	0.158713i
$787$	−0.538972	−	1.30119i	−0.0192123	−	0.0463825i	0.913982	−	0.405754i	$-0.132991\pi$
$787$	−0.538972	−	1.30119i	−0.0192123	−	0.0463825i	−0.933195	+	0.359372i	$0.882991\pi$
$788$	−8.97138	−	3.71607i	−0.319592	−	0.132379i
$789$	−2.79282	−	18.6689i	−0.0994270	−	0.664629i
$790$	16.9911	+	16.9911i	0.604515	+	0.604515i
$791$	6.34007	−	5.69856i	0.225427	−	0.202617i
$792$	13.7125	−	11.3103i	0.487251	−	0.401894i
$793$	−1.68525	+	4.06855i	−0.0598449	+	0.144478i
$794$	17.5497	−	7.26932i	0.622815	−	0.257979i
$795$	5.42974	−	3.26358i	0.192573	−	0.115747i
$796$	11.1265	−	4.60877i	0.394370	−	0.163353i
$797$	−8.72874	−	8.72874i	−0.309188	−	0.309188i	0.535407	−	0.844594i	$-0.320158\pi$
$797$	−8.72874	−	8.72874i	−0.309188	−	0.309188i	−0.844594	+	0.535407i	$0.820158\pi$
$798$	−8.75237	−	16.4900i	−0.309831	−	0.583740i
$799$	0.113373	−	7.65434i	0.00401085	−	0.270791i
$800$			0.524952i			0.0185598i
$801$	37.2485	−	11.3997i	1.31611	−	0.402788i
$802$	−0.0106900	−	0.0258079i	−0.000377476	−	0.000911308i
$803$		−	54.0372i		−	1.90693i
$804$	−1.56041	+	2.10941i	−0.0550315	+	0.0743932i
$805$	−16.0123	+	33.4948i	−0.564359	+	1.18054i
$806$	−16.6722	+	40.2503i	−0.587253	+	1.41775i
$807$	5.18586	−	20.8121i	0.182551	−	0.732619i
$808$	−5.75190	−	5.75190i	−0.202351	−	0.202351i
$809$	10.8381	−	26.1655i	0.381047	−	0.919929i	−0.610717	−	0.791849i	$-0.709119\pi$
$809$	10.8381	−	26.1655i	0.381047	−	0.919929i	0.991764	−	0.128080i	$-0.0408814\pi$
$810$	−4.22947	−	20.7276i	−0.148608	−	0.728293i
$811$	−12.4044	−	29.9469i	−0.435578	−	1.05158i	−0.977459	−	0.211123i	$-0.932288\pi$
$811$	−12.4044	−	29.9469i	−0.435578	−	1.05158i	0.541882	−	0.840455i	$-0.317712\pi$
$812$	−1.06965	+	20.0730i	−0.0375375	+	0.704425i
$813$	−10.5767	+	14.2979i	−0.370941	+	0.501448i
$814$	6.89357	+	6.89357i	0.241620	+	0.241620i
$815$	28.2868			0.990842
$816$	−5.67777	−	4.33162i	−0.198762	−	0.151637i
$817$			33.7707i			1.18149i
$818$	−4.88618	−	4.88618i	−0.170841	−	0.170841i
$819$	42.1469	+	6.32435i	1.47273	+	0.220991i
$820$			18.1969i			0.635464i
$821$	17.1888	+	41.4974i	0.599892	+	1.44827i	0.873691	+	0.486481i	$0.161720\pi$
$821$	17.1888	+	41.4974i	0.599892	+	1.44827i	−0.273799	+	0.961787i	$0.588280\pi$
$822$	3.81038	+	25.4708i	0.132902	+	0.888397i
$823$	−14.7054	−	6.09116i	−0.512596	−	0.212324i	0.111365	−	0.993780i	$-0.464478\pi$
$823$	−14.7054	−	6.09116i	−0.512596	−	0.212324i	−0.623961	+	0.781455i	$0.714478\pi$
$824$	4.97450	−	4.97450i	0.173295	−	0.173295i
$825$	5.22746	+	1.30256i	0.181997	+	0.0453492i
$826$	16.3525	+	7.81735i	0.568975	+	0.272000i
$827$	−29.4613	−	12.2033i	−1.02447	−	0.424349i	−0.193756	−	0.981050i	$-0.562067\pi$
$827$	−29.4613	−	12.2033i	−1.02447	−	0.424349i	−0.830713	+	0.556701i	$0.812067\pi$
$828$	−17.8273	−	1.71141i	−0.619543	−	0.0594758i
$829$	30.2985			1.05231			0.526155	−	0.850388i	$-0.323633\pi$
$829$	30.2985			1.05231			0.526155	+	0.850388i	$0.323633\pi$
$830$	1.08947	−	0.451271i	0.0378159	−	0.0156639i
$831$	39.4252	+	9.82379i	1.36764	+	0.340783i
$832$		−	5.36946i		−	0.186152i
$833$	−17.7892	−	22.7276i	−0.616360	−	0.787464i
$834$	−10.6088	+	6.37647i	−0.367352	+	0.220799i
$835$	1.96741	+	1.96741i	0.0680851	+	0.0680851i
$836$	9.23715	+	22.3005i	0.319474	+	0.771277i
$837$	2.22463	+	42.1017i	0.0768944	+	1.45525i
$838$	−0.884988	−	2.13655i	−0.0305714	−	0.0738059i
$839$	−3.00626	+	7.25776i	−0.103788	+	0.250566i	−0.967239	−	0.253866i	$-0.918298\pi$
$839$	−3.00626	+	7.25776i	−0.103788	+	0.250566i	0.863452	+	0.504431i	$0.168298\pi$
$840$	−10.7226	+	1.02452i	−0.369965	+	0.0353494i
$841$	−20.3112	+	20.3112i	−0.700387	+	0.700387i
$842$	−8.82055	−	8.82055i	−0.303976	−	0.303976i
$843$	−4.98635	−	33.3317i	−0.171739	−	1.14801i
$844$	−4.51995	+	10.9121i	−0.155583	+	0.375611i
$845$	−34.3787	+	14.2401i	−1.18266	+	0.489876i
$846$	2.61353	−	4.91873i	0.0898549	−	0.169110i
$847$	−60.1391	+	21.2370i	−2.06640	+	0.729711i
$848$	1.10030	−	1.10030i	0.0377845	−	0.0377845i
$849$	10.3253	+	17.1786i	0.354362	+	0.589566i
$850$	0.0320552	−	2.16419i	0.00109949	−	0.0742313i
$851$		−	9.82258i		−	0.336714i
$852$	−2.11657	+	8.49430i	−0.0725126	+	0.291010i
$853$	−27.3508	+	11.3291i	−0.936473	+	0.387900i	−0.798130	−	0.602485i	$-0.794177\pi$
$853$	−27.3508	+	11.3291i	−0.936473	+	0.387900i	−0.138342	+	0.990384i	$0.544177\pi$
$854$	2.16684	+	0.115467i	0.0741478	+	0.00395119i
$855$	28.5957	+	2.74517i	0.977952	+	0.0938828i
$856$	2.00613	−	4.84323i	0.0685682	−	0.165538i
$857$	13.3957	+	5.54869i	0.457589	+	0.189540i	0.599558	−	0.800332i	$-0.295343\pi$
$857$	13.3957	+	5.54869i	0.457589	+	0.189540i	−0.141969	+	0.989871i	$0.545343\pi$
$858$	−53.4690	−	13.3232i	−1.82540	−	0.454845i
$859$	13.8122	+	13.8122i	0.471265	+	0.471265i	0.902324	−	0.431059i	$-0.141860\pi$
$859$	13.8122	+	13.8122i	0.471265	+	0.471265i	−0.431059	+	0.902324i	$0.641860\pi$
$860$	18.0017	+	7.45653i	0.613851	+	0.254265i
$861$	−35.3159	+	3.37436i	−1.20356	+	0.114998i
$862$	−22.0300	+	9.12512i	−0.750344	+	0.310803i
$863$	−8.51418			−0.289826			−0.144913	−	0.989444i	$-0.546290\pi$
$863$	−8.51418			−0.289826			−0.144913	+	0.989444i	$0.546290\pi$
$864$	−2.23902	−	4.68901i	−0.0761730	−	0.159523i
$865$	−16.3910	−	16.3910i	−0.557310	−	0.557310i
$866$	−19.7319			−0.670516
$867$	23.1430	+	18.2045i	0.785976	+	0.618257i
$868$	21.4366	+	1.14232i	0.727606	+	0.0387727i
$869$	42.8300	−	42.8300i	1.45291	−	1.45291i
$870$	−24.8673	−	18.3953i	−0.843082	−	0.623661i
$871$	8.13404			0.275611
$872$	3.02326	+	7.29879i	0.102380	+	0.247168i
$873$	3.91279	−	3.22734i	0.132428	−	0.109229i
$874$	9.30688	−	22.4688i	0.314810	−	0.760019i
$875$	18.6036	+	20.6980i	0.628918	+	0.699719i
$876$	−15.3279	−	3.81933i	−0.517881	−	0.129043i
$877$	−15.3816	−	6.37128i	−0.519401	−	0.215143i	0.107553	−	0.994199i	$-0.465698\pi$
$877$	−15.3816	−	6.37128i	−0.519401	−	0.215143i	−0.626954	+	0.779057i	$0.715698\pi$
$878$	−11.6022	+	28.0103i	−0.391557	+	0.945302i
$879$	−17.5358	+	23.7054i	−0.591469	+	0.799565i
$880$	13.9269			0.469477
$881$	16.6337	+	40.1573i	0.560404	+	1.35294i	0.909444	+	0.415827i	$0.136508\pi$
$881$	16.6337	+	40.1573i	0.560404	+	1.35294i	−0.349039	+	0.937108i	$0.613492\pi$
$882$	−3.97671	−	20.6200i	−0.133903	−	0.694313i
$883$	49.7234			1.67333			0.836663	−	0.547718i	$-0.184503\pi$
$883$	49.7234			1.67333			0.836663	+	0.547718i	$0.184503\pi$
$884$	−0.327876	+	22.1364i	−0.0110277	+	0.744528i
$885$	−23.9046	+	14.3680i	−0.803543	+	0.482974i
$886$	21.4501	+	21.4501i	0.720630	+	0.720630i
$887$	−5.97069	−	14.4145i	−0.200476	−	0.483992i	0.791385	−	0.611318i	$-0.209360\pi$
$887$	−5.97069	−	14.4145i	−0.200476	−	0.483992i	−0.991861	+	0.127326i	$0.959360\pi$
$888$	2.44263	−	1.46815i	0.0819692	−	0.0492681i
$889$	7.80043	+	22.0893i	0.261618	+	0.740852i
$890$	28.1974	+	11.6797i	0.945178	+	0.391506i
$891$	−52.2487	+	10.6614i	−1.75040	+	0.357169i
$892$	−3.79748	−	3.79748i	−0.127149	−	0.127149i
$893$	5.34839	+	5.34839i	0.178977	+	0.178977i
$894$	37.5487	−	5.61720i	1.25582	−	0.187867i
$895$	−37.2235	−	15.4185i	−1.24424	−	0.515383i
$896$	−2.49477	+	0.880980i	−0.0833444	+	0.0294315i
$897$	28.6017	+	47.5857i	0.954982	+	1.58884i
$898$	−9.76445	−	23.5735i	−0.325844	−	0.786657i
$899$	43.5901	+	43.5901i	1.45381	+	1.45381i
$900$	0.738951	−	1.39073i	0.0246317	−	0.0463576i
$901$	−4.60334	+	4.46897i	−0.153360	+	0.148883i
$902$	45.8696			1.52729
$903$	−11.1332	+	36.3196i	−0.370489	+	1.20864i
$904$	1.23302	+	2.97676i	0.0410095	+	0.0990056i
$905$	−49.6618			−1.65081
$906$	11.8682	+	8.77939i	0.394295	+	0.291676i
$907$	−0.120435	+	0.290756i	−0.00399898	+	0.00965440i	−0.925866	−	0.377851i	$-0.876663\pi$
$907$	−0.120435	+	0.290756i	−0.00399898	+	0.00965440i	0.921867	+	0.387505i	$0.126663\pi$
$908$	−5.82758	−	2.41386i	−0.193395	−	0.0801069i
$909$	7.14151	+	23.3349i	0.236869	+	0.773969i
$910$	22.3219	+	24.8348i	0.739963	+	0.823265i
$911$	−5.19629	+	12.5449i	−0.172161	+	0.415633i	−0.986284	−	0.165060i	$-0.947218\pi$
$911$	−5.19629	+	12.5449i	−0.172161	+	0.415633i	0.814123	+	0.580693i	$0.197218\pi$
$912$	6.97850	−	1.04397i	0.231081	−	0.0345692i
$913$	−1.13753	−	2.74625i	−0.0376469	−	0.0908876i
$914$	−37.7380			−1.24826
$915$	−1.98574	+	2.68438i	−0.0656465	+	0.0887428i
$916$	−15.2356	+	15.2356i	−0.503398	+	0.503398i
$917$	0.702073	−	13.1751i	0.0231845	−	0.435079i
$918$	8.94438	+	19.4679i	0.295208	+	0.642536i
$919$	−57.6519			−1.90176			−0.950880	−	0.309559i	$-0.899819\pi$
$919$	−57.6519			−1.90176			−0.950880	+	0.309559i	$0.899819\pi$
$920$	−9.92217	−	9.92217i	−0.327124	−	0.327124i
$921$	1.82972	−	2.47347i	0.0602914	−	0.0815036i
$922$	−2.84018			−0.0935363
$923$	25.0722	−	10.3853i	0.825263	−	0.341835i
$924$	2.58255	+	27.0288i	0.0849597	+	0.889183i
$925$	0.798000	+	0.330543i	0.0262381	+	0.0108682i
$926$	26.3787	+	26.3787i	0.866857	+	0.866857i
$927$	−20.1811	+	6.17630i	−0.662833	+	0.202856i
$928$	−7.01932	−	2.90750i	−0.230420	−	0.0954433i
$929$	9.77251	−	23.5929i	0.320626	−	0.774059i	−0.678592	−	0.734515i	$-0.737410\pi$
$929$	9.77251	−	23.5929i	0.320626	−	0.774059i	0.999218	−	0.0395437i	$-0.0125904\pi$
$930$	−19.6450	+	26.5566i	−0.644184	+	0.870825i
$931$	28.3556	+	3.03063i	0.929317	+	0.0993250i
$932$	−19.9222	+	8.25203i	−0.652572	+	0.270304i
$933$	37.4002	+	9.31921i	1.22443	+	0.305097i
$934$			17.4117i			0.569727i
$935$	−57.4159	−	0.850423i	−1.87770	−	0.0278118i
$936$	−7.55834	+	14.2250i	−0.247052	+	0.464959i
$937$	−35.8690	+	35.8690i	−1.17179	+	1.17179i	−0.190006	+	0.981783i	$0.560851\pi$
$937$	−35.8690	+	35.8690i	−1.17179	+	1.17179i	−0.981783	+	0.190006i	$0.939149\pi$
$938$	−1.33457	−	3.77925i	−0.0435753	−	0.123397i
$939$	26.4347	−	15.8887i	0.862663	−	0.518508i
$940$	4.03191	−	1.67007i	0.131506	−	0.0544717i
$941$	20.3217	−	49.0609i	0.662468	−	1.59934i	−0.131455	−	0.991322i	$-0.541965\pi$
$941$	20.3217	−	49.0609i	0.662468	−	1.59934i	0.793923	−	0.608018i	$-0.208035\pi$
$942$	−12.8615	+	1.92404i	−0.419049	+	0.0626888i
$943$	−32.6795	−	32.6795i	−1.06419	−	1.06419i
$944$	−4.84410	+	4.84410i	−0.157662	+	0.157662i
$945$	29.8490	+	12.3795i	0.970988	+	0.402706i
$946$	18.7959	−	45.3774i	0.611108	−	1.47535i
$947$	−13.7193	−	33.1213i	−0.445817	−	1.07630i	−0.973874	−	0.227088i	$-0.927079\pi$
$947$	−13.7193	−	33.1213i	−0.445817	−	1.07630i	0.528057	−	0.849209i	$-0.322921\pi$
$948$	−9.12169	−	15.1761i	−0.296259	−	0.492897i
$949$	18.7401	+	45.2426i	0.608330	+	1.46864i
$950$	1.51221	+	1.51221i	0.0490625	+	0.0490625i
$951$	30.8696	+	51.3589i	1.00101	+	1.66543i
$952$	10.3389	−	3.47964i	0.335085	−	0.112776i
$953$		−	15.1280i		−	0.490045i	−0.969517	−	0.245023i	$-0.921205\pi$
$953$		−	15.1280i		−	0.490045i	0.969517	−	0.245023i	$-0.0787954\pi$
$954$	−4.46381	+	1.36612i	−0.144521	+	0.0442299i
$955$	4.96754	−	2.05762i	0.160746	−	0.0665831i
$956$	22.4045			0.724614
$957$	−46.3698	+	62.6840i	−1.49892	+	2.02628i
$958$	−4.49774	−	1.86302i	−0.145315	−	0.0601915i
$959$	−35.4931	−	16.9676i	−1.14613	−	0.547912i
$960$	0.984351	−	3.95043i	0.0317698	−	0.127500i
$961$	24.6309	−	24.6309i	0.794544	−	0.794544i
$962$	−8.16233	−	3.38095i	−0.263164	−	0.109006i
$963$	−12.1323	+	10.0070i	−0.390959	+	0.322470i
$964$	−2.07429	−	5.00778i	−0.0668084	−	0.161290i
$965$		−	6.34504i		−	0.204254i
$966$	17.4166	−	21.0965i	0.560371	−	0.678768i
$967$	3.28759	+	3.28759i	0.105722	+	0.105722i	0.757989	−	0.652267i	$-0.226182\pi$
$967$	3.28759	+	3.28759i	0.105722	+	0.105722i	−0.652267	+	0.757989i	$0.726182\pi$
$968$		−	24.1061i		−	0.774799i
$969$	−28.8337	+	3.87778i	−0.926271	+	0.124572i
$970$	3.97399			0.127597
$971$	33.7288	+	33.7288i	1.08241	+	1.08241i	0.996285	+	0.0861227i	$0.0274477\pi$
$971$	33.7288	+	33.7288i	1.08241	+	1.08241i	0.0861227	+	0.996285i	$0.472552\pi$
$972$	−0.668786	+	15.5741i	−0.0214513	+	0.499540i
$973$	1.00610	−	18.8803i	0.0322540	−	0.605276i
$974$	−7.10307	−	17.1483i	−0.227597	−	0.549468i
$975$	−4.82841	+	0.722319i	−0.154633	+	0.0231327i
$976$	−0.313858	+	0.757721i	−0.0100464	+	0.0242540i
$977$	−27.3853	−	27.3853i	−0.876133	−	0.876133i	0.116999	−	0.993132i	$-0.462673\pi$
$977$	−27.3853	−	27.3853i	−0.876133	−	0.876133i	−0.993132	+	0.116999i	$0.962673\pi$
$978$	−20.2255	−	5.03970i	−0.646740	−	0.161152i
$979$	29.4415	−	71.0781i	0.940955	−	2.27167i
$980$	7.87638	−	14.4459i	0.251602	−	0.461459i
$981$	2.26482	−	23.5920i	0.0723101	−	0.753234i
$982$		−	14.8435i		−	0.473675i
$983$	4.99286	+	12.0538i	0.159248	+	0.384458i	0.983284	−	0.182079i	$-0.0582828\pi$
$983$	4.99286	+	12.0538i	0.159248	+	0.384458i	−0.824036	+	0.566537i	$0.808283\pi$
$984$	3.24205	−	13.0111i	0.103353	−	0.414779i
$985$			22.8249i			0.727261i
$986$	28.7607	+	12.4152i	0.915927	+	0.395381i
$987$	3.98887	+	7.51527i	0.126967	+	0.239214i
$988$	−15.4676	−	15.4676i	−0.492090	−	0.492090i
$989$	−45.7199	+	18.9378i	−1.45381	+	0.602187i
$990$	−36.8959	−	19.6043i	−1.17263	−	0.623066i
$991$	−27.7868	+	11.5097i	−0.882676	+	0.365616i	−0.777534	−	0.628841i	$-0.783530\pi$
$991$	−27.7868	+	11.5097i	−0.882676	+	0.365616i	−0.105142	+	0.994457i	$0.533530\pi$
$992$	−3.10501	+	7.49615i	−0.0985841	+	0.238003i
$993$	−45.5665	+	6.81664i	−1.44601	+	0.216320i
$994$	−8.93889	−	9.94518i	−0.283524	−	0.315442i
$995$	−20.0168	−	20.0168i	−0.634575	−	0.634575i
$996$	−0.859386	+	0.128562i	−0.0272307	+	0.00407365i
$997$	1.69374	+	0.701569i	0.0536412	+	0.0222189i	0.409343	−	0.912381i	$-0.365758\pi$
$997$	1.69374	+	0.701569i	0.0536412	+	0.0222189i	−0.355702	+	0.934600i	$0.615758\pi$
$998$	−2.22049	−	5.36073i	−0.0702882	−	0.169691i
$999$	−8.53777	+	0.451131i	−0.270123	+	0.0142732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.w.e.83.16	yes	80
3.2	odd	2		714.2.w.f.83.12	yes	80
7.6	odd	2	inner	714.2.w.e.83.5	✓	80
17.8	even	8		714.2.w.f.671.9	yes	80
21.20	even	2		714.2.w.f.83.9	yes	80
51.8	odd	8	inner	714.2.w.e.671.5	yes	80
119.76	odd	8		714.2.w.f.671.12	yes	80
357.314	even	8	inner	714.2.w.e.671.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.w.e.83.5	✓	80	7.6	odd	2	inner
714.2.w.e.83.16	yes	80	1.1	even	1	trivial
714.2.w.e.671.5	yes	80	51.8	odd	8	inner
714.2.w.e.671.16	yes	80	357.314	even	8	inner
714.2.w.f.83.9	yes	80	21.20	even	2
714.2.w.f.83.12	yes	80	3.2	odd	2
714.2.w.f.671.9	yes	80	17.8	even	8
714.2.w.f.671.12	yes	80	119.76	odd	8

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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.39247 + 1.03006i) q^{3} -1.00000i q^{4} +(-2.17160 + 0.899506i) q^{5} +(1.71299 - 0.256259i) q^{6} +(-1.14112 + 2.38702i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.877938 + 2.86866i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.39247 + 1.03006i) q^{3} -1.00000i q^{4} +(-2.17160 + 0.899506i) q^{5} +(1.71299 - 0.256259i) q^{6} +(-1.14112 + 2.38702i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.877938 + 2.86866i) q^{9} +(-0.899506 + 2.17160i) q^{10} +(5.47402 + 2.26741i) q^{11} +(1.03006 - 1.39247i) q^{12} -5.36946 q^{13} +(0.880980 + 2.49477i) q^{14} +(-3.95043 - 0.984351i) q^{15} -1.00000 q^{16} +(4.12265 + 0.0610632i) q^{17} +(2.64925 + 1.40765i) q^{18} +(-2.88066 + 2.88066i) q^{19} +(0.899506 + 2.17160i) q^{20} +(-4.04775 + 2.14842i) q^{21} +(5.47402 - 2.26741i) q^{22} +(-5.51535 - 2.28453i) q^{23} +(-0.256259 - 1.71299i) q^{24} +(0.371197 - 0.371197i) q^{25} +(-3.79678 + 3.79678i) q^{26} +(-1.73240 + 4.89886i) q^{27} +(2.38702 + 1.14112i) q^{28} +(2.90750 + 7.01932i) q^{29} +(-3.48942 + 2.09734i) q^{30} +(7.49615 - 3.10501i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.28682 + 8.79589i) q^{33} +(2.95833 - 2.87198i) q^{34} +(0.330923 - 6.21008i) q^{35} +(2.86866 - 0.877938i) q^{36} +(0.629663 + 1.52014i) q^{37} +4.07387i q^{38} +(-7.47680 - 5.53088i) q^{39} +(2.17160 + 0.899506i) q^{40} +(7.15235 + 2.96260i) q^{41} +(-1.34303 + 4.38135i) q^{42} +(5.86162 - 5.86162i) q^{43} +(2.26741 - 5.47402i) q^{44} +(-4.48691 - 5.43987i) q^{45} +(-5.51535 + 2.28453i) q^{46} -1.85665i q^{47} +(-1.39247 - 1.03006i) q^{48} +(-4.39569 - 5.44775i) q^{49} -0.524952i q^{50} +(5.67777 + 4.33162i) q^{51} +5.36946i q^{52} +(-1.10030 + 1.10030i) q^{53} +(2.23902 + 4.68901i) q^{54} -13.9269 q^{55} +(2.49477 - 0.880980i) q^{56} +(-6.97850 + 1.04397i) q^{57} +(7.01932 + 2.90750i) q^{58} +(4.84410 - 4.84410i) q^{59} +(-0.984351 + 3.95043i) q^{60} +(0.313858 - 0.757721i) q^{61} +(3.10501 - 7.49615i) q^{62} +(-7.84938 - 1.17784i) q^{63} +1.00000i q^{64} +(11.6603 - 4.82986i) q^{65} +(9.95798 + 2.48129i) q^{66} -1.51487 q^{67} +(0.0610632 - 4.12265i) q^{68} +(-5.32673 - 8.86229i) q^{69} +(-4.15719 - 4.62519i) q^{70} +(-4.66942 + 1.93414i) q^{71} +(1.40765 - 2.64925i) q^{72} +(-3.49013 - 8.42592i) q^{73} +(1.52014 + 0.629663i) q^{74} +(0.899237 - 0.134524i) q^{75} +(2.88066 + 2.88066i) q^{76} +(-11.6589 + 10.4792i) q^{77} +(-9.19782 + 1.37597i) q^{78} +(3.91211 - 9.44467i) q^{79} +(2.17160 - 0.899506i) q^{80} +(-7.45845 + 5.03702i) q^{81} +(7.15235 - 2.96260i) q^{82} +(-0.354747 - 0.354747i) q^{83} +(2.14842 + 4.04775i) q^{84} +(-9.00768 + 3.57575i) q^{85} -8.28958i q^{86} +(-3.18175 + 12.7691i) q^{87} +(-2.26741 - 5.47402i) q^{88} -12.9846i q^{89} +(-7.01929 - 0.673848i) q^{90} +(6.12720 - 12.8170i) q^{91} +(-2.28453 + 5.51535i) q^{92} +(13.6365 + 3.39789i) q^{93} +(-1.31285 - 1.31285i) q^{94} +(3.66447 - 8.84681i) q^{95} +(-1.71299 + 0.256259i) q^{96} +(-0.646996 - 1.56199i) q^{97} +(-6.96036 - 0.743920i) q^{98} +(-1.69859 + 17.6938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 16 q^{7}+O(q^{10}) \) 80 * q - 16 * q^7	\( 80 q - 16 q^{7} - 16 q^{14} - 16 q^{15} - 80 q^{16} + 16 q^{18} - 32 q^{21} - 16 q^{23} - 32 q^{25} + 64 q^{29} - 16 q^{30} - 48 q^{37} + 16 q^{39} - 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{46} + 16 q^{49} + 104 q^{51} - 80 q^{53} - 16 q^{57} - 16 q^{58} - 48 q^{60} + 56 q^{63} + 80 q^{65} - 144 q^{67} + 8 q^{70} + 16 q^{71} - 32 q^{74} - 24 q^{77} + 32 q^{78} + 32 q^{79} - 16 q^{84} + 208 q^{85} + 16 q^{88} - 8 q^{91} + 16 q^{92} + 48 q^{93} - 16 q^{95} - 16 q^{98} + 80 q^{99}+O(q^{100}) \) 80 * q - 16 * q^7 - 16 * q^14 - 16 * q^15 - 80 * q^16 + 16 * q^18 - 32 * q^21 - 16 * q^23 - 32 * q^25 + 64 * q^29 - 16 * q^30 - 48 * q^37 + 16 * q^39 - 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^46 + 16 * q^49 + 104 * q^51 - 80 * q^53 - 16 * q^57 - 16 * q^58 - 48 * q^60 + 56 * q^63 + 80 * q^65 - 144 * q^67 + 8 * q^70 + 16 * q^71 - 32 * q^74 - 24 * q^77 + 32 * q^78 + 32 * q^79 - 16 * q^84 + 208 * q^85 + 16 * q^88 - 8 * q^91 + 16 * q^92 + 48 * q^93 - 16 * q^95 - 16 * q^98 + 80 * q^99

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