LMFDB - Embedded newform 252.2.bi.c.139.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.5
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33347 + 0.471009i) q^{2} +(-1.61200 - 0.633613i) q^{3} +(1.55630 - 1.25616i) q^{4} +(-3.16954 - 1.82994i) q^{5} +(2.44799 + 0.0856414i) q^{6} +(-2.26193 + 1.37246i) q^{7} +(-1.48363 + 2.40808i) q^{8} +(2.19707 + 2.04277i) q^{9} +O(q^{10})$	\(q+(-1.33347 + 0.471009i) q^{2} +(-1.61200 - 0.633613i) q^{3} +(1.55630 - 1.25616i) q^{4} +(-3.16954 - 1.82994i) q^{5} +(2.44799 + 0.0856414i) q^{6} +(-2.26193 + 1.37246i) q^{7} +(-1.48363 + 2.40808i) q^{8} +(2.19707 + 2.04277i) q^{9} +(5.08842 + 0.947288i) q^{10} +(1.96543 - 1.13474i) q^{11} +(-3.30467 + 1.03883i) q^{12} +(3.84091 + 2.21755i) q^{13} +(2.36979 - 2.89553i) q^{14} +(3.94982 + 4.95812i) q^{15} +(0.844147 - 3.90991i) q^{16} +3.25685i q^{17} +(-3.89189 - 1.68913i) q^{18} +2.37901 q^{19} +(-7.23145 + 1.13351i) q^{20} +(4.51584 - 0.779212i) q^{21} +(-2.08637 + 2.43888i) q^{22} +(-1.52279 - 0.879184i) q^{23} +(3.91739 - 2.94177i) q^{24} +(4.19733 + 7.27000i) q^{25} +(-6.16624 - 1.14794i) q^{26} +(-2.24734 - 4.68502i) q^{27} +(-1.79623 + 4.97731i) q^{28} +(3.73260 + 6.46506i) q^{29} +(-7.60230 - 4.75111i) q^{30} +(-3.37549 + 5.84652i) q^{31} +(0.715956 + 5.61136i) q^{32} +(-3.88725 + 0.583877i) q^{33} +(-1.53401 - 4.34293i) q^{34} +(9.68082 - 0.210880i) q^{35} +(5.98533 + 0.419299i) q^{36} -8.82337 q^{37} +(-3.17234 + 1.12053i) q^{38} +(-4.78647 - 6.00834i) q^{39} +(9.10905 - 4.91758i) q^{40} +(-2.24519 - 1.29626i) q^{41} +(-5.65474 + 3.16606i) q^{42} +(6.27685 - 3.62394i) q^{43} +(1.63339 - 4.23488i) q^{44} +(-3.22557 - 10.4951i) q^{45} +(2.44471 + 0.455120i) q^{46} +(3.95897 + 6.85713i) q^{47} +(-3.83814 + 5.76790i) q^{48} +(3.23270 - 6.20884i) q^{49} +(-9.02127 - 7.71736i) q^{50} +(2.06359 - 5.25004i) q^{51} +(8.76321 - 1.37360i) q^{52} +2.84881 q^{53} +(5.20346 + 5.18883i) q^{54} -8.30601 q^{55} +(0.0508652 - 7.48314i) q^{56} +(-3.83495 - 1.50737i) q^{57} +(-8.02242 - 6.86289i) q^{58} +(0.278774 - 0.482851i) q^{59} +(12.3753 + 2.75473i) q^{60} +(-0.335560 + 0.193736i) q^{61} +(1.74736 - 9.38606i) q^{62} +(-7.77324 - 1.60521i) q^{63} +(-3.59771 - 7.14538i) q^{64} +(-8.11596 - 14.0572i) q^{65} +(4.90853 - 2.60951i) q^{66} +(-2.07581 - 1.19847i) q^{67} +(4.09112 + 5.06865i) q^{68} +(1.89767 + 2.38210i) q^{69} +(-12.8098 + 4.84095i) q^{70} +9.43272i q^{71} +(-8.17877 + 2.26002i) q^{72} +12.5047i q^{73} +(11.7657 - 4.15589i) q^{74} +(-2.15972 - 14.3787i) q^{75} +(3.70245 - 2.98840i) q^{76} +(-2.88828 + 5.26418i) q^{77} +(9.21261 + 5.75749i) q^{78} +(2.20999 - 1.27594i) q^{79} +(-9.83045 + 10.8479i) q^{80} +(0.654220 + 8.97619i) q^{81} +(3.60446 + 0.671026i) q^{82} +(4.18556 + 7.24960i) q^{83} +(6.04920 - 6.88529i) q^{84} +(5.95984 - 10.3227i) q^{85} +(-6.66311 + 7.78889i) q^{86} +(-1.92060 - 12.7867i) q^{87} +(-0.183413 + 6.41644i) q^{88} +2.43473i q^{89} +(9.24451 + 12.4757i) q^{90} +(-11.7314 + 0.255548i) q^{91} +(-3.47431 + 0.544587i) q^{92} +(9.14571 - 7.28581i) q^{93} +(-8.50894 - 7.27909i) q^{94} +(-7.54036 - 4.35343i) q^{95} +(2.40132 - 9.49914i) q^{96} +(5.47279 - 3.15972i) q^{97} +(-1.38630 + 9.80195i) q^{98} +(6.63619 + 1.52181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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 $

$2$	−1.33347	+	0.471009i	−0.942908	+	0.333054i
$2$	−1.33347	+	0.471009i	−0.942908	+	0.333054i
$3$	−1.61200	−	0.633613i	−0.930687	−	0.365817i
$3$	−1.61200	−	0.633613i	−0.930687	−	0.365817i
$4$	1.55630	−	1.25616i	0.778151	−	0.628078i
$5$	−3.16954	−	1.82994i	−1.41746	−	0.818372i	−0.421387	−	0.906881i	$-0.638457\pi$
$5$	−3.16954	−	1.82994i	−1.41746	−	0.818372i	−0.996075	+	0.0885084i	$0.971790\pi$
$6$	2.44799	+	0.0856414i	0.999389	+	0.0349629i
$7$	−2.26193	+	1.37246i	−0.854931	+	0.518742i
$7$	−2.26193	+	1.37246i	−0.854931	+	0.518742i
$8$	−1.48363	+	2.40808i	−0.524541	+	0.851385i
$9$	2.19707	+	2.04277i	0.732356	+	0.680922i
$10$	5.08842	+	0.947288i	1.60910	+	0.299559i
$11$	1.96543	−	1.13474i	0.592599	−	0.342137i	−0.173526	−	0.984829i	$-0.555516\pi$
$11$	1.96543	−	1.13474i	0.592599	−	0.342137i	0.766125	+	0.642692i	$0.222183\pi$
$12$	−3.30467	+	1.03883i	−0.953976	+	0.299883i
$13$	3.84091	+	2.21755i	1.06528	+	0.615038i	0.926887	−	0.375340i	$-0.122474\pi$
$13$	3.84091	+	2.21755i	1.06528	+	0.615038i	0.138390	+	0.990378i	$0.455807\pi$
$14$	2.36979	−	2.89553i	0.633352	−	0.773864i
$15$	3.94982	+	4.95812i	1.01984	+	1.28018i
$16$	0.844147	−	3.90991i	0.211037	−	0.977478i
$17$			3.25685i			0.789903i	0.918702	+	0.394952i	$0.129239\pi$
$17$			3.25685i			0.789903i	−0.918702	+	0.394952i	$0.870761\pi$
$18$	−3.89189	−	1.68913i	−0.917328	−	0.398133i
$19$	2.37901			0.545781			0.272891	−	0.962045i	$-0.412020\pi$
$19$	2.37901			0.545781			0.272891	+	0.962045i	$0.412020\pi$
$20$	−7.23145	+	1.13351i	−1.61700	+	0.253460i
$21$	4.51584	−	0.779212i	0.985437	−	0.170038i
$22$	−2.08637	+	2.43888i	−0.444816	+	0.519971i
$23$	−1.52279	−	0.879184i	−0.317524	−	0.183323i	0.332764	−	0.943010i	$-0.392019\pi$
$23$	−1.52279	−	0.879184i	−0.317524	−	0.183323i	−0.650288	+	0.759687i	$0.725352\pi$
$24$	3.91739	−	2.94177i	0.799634	−	0.600487i
$25$	4.19733	+	7.27000i	0.839467	+	1.45400i
$26$	−6.16624	−	1.14794i	−1.20930	−	0.225130i
$27$	−2.24734	−	4.68502i	−0.432502	−	0.901633i
$28$	−1.79623	+	4.97731i	−0.339455	+	0.940622i
$29$	3.73260	+	6.46506i	0.693127	+	1.20053i	0.970808	+	0.239858i	$0.0771008\pi$
$29$	3.73260	+	6.46506i	0.693127	+	1.20053i	−0.277681	+	0.960673i	$0.589566\pi$
$30$	−7.60230	−	4.75111i	−1.38798	−	0.867431i
$31$	−3.37549	+	5.84652i	−0.606256	+	1.05007i	0.385596	+	0.922668i	$0.373996\pi$
$31$	−3.37549	+	5.84652i	−0.606256	+	1.05007i	−0.991852	+	0.127398i	$0.959338\pi$
$32$	0.715956	+	5.61136i	0.126564	+	0.991958i
$33$	−3.88725	+	0.583877i	−0.676684	+	0.101640i
$34$	−1.53401	−	4.34293i	−0.263080	−	0.744806i
$35$	9.68082	−	0.210880i	1.63636	−	0.0356451i
$36$	5.98533	+	0.419299i	0.997555	+	0.0698831i
$37$	−8.82337			−1.45055			−0.725277	−	0.688458i	$-0.758288\pi$
$37$	−8.82337			−1.45055			−0.725277	+	0.688458i	$0.758288\pi$
$38$	−3.17234	+	1.12053i	−0.514621	+	0.181774i
$39$	−4.78647	−	6.00834i	−0.766448	−	0.962104i
$40$	9.10905	−	4.91758i	1.44027	−	0.777537i
$41$	−2.24519	−	1.29626i	−0.350640	−	0.202442i	0.314327	−	0.949315i	$-0.398221\pi$
$41$	−2.24519	−	1.29626i	−0.350640	−	0.202442i	−0.664967	+	0.746872i	$0.731555\pi$
$42$	−5.65474	+	3.16606i	−0.872545	+	0.488534i
$43$	6.27685	−	3.62394i	0.957211	−	0.552646i	0.0618977	−	0.998082i	$-0.480285\pi$
$43$	6.27685	−	3.62394i	0.957211	−	0.552646i	0.895314	+	0.445436i	$0.146951\pi$
$44$	1.63339	−	4.23488i	0.246243	−	0.638432i
$45$	−3.22557	−	10.4951i	−0.480840	−	1.56452i
$46$	2.44471	+	0.455120i	0.360452	+	0.0671038i
$47$	3.95897	+	6.85713i	0.577475	+	1.00022i	0.995768	+	0.0919034i	$0.0292951\pi$
$47$	3.95897	+	6.85713i	0.577475	+	1.00022i	−0.418293	+	0.908312i	$0.637372\pi$
$48$	−3.83814	+	5.76790i	−0.553987	+	0.832525i
$49$	3.23270	−	6.20884i	0.461814	−	0.886977i
$50$	−9.02127	−	7.71736i	−1.27580	−	1.09140i
$51$	2.06359	−	5.25004i	0.288960	−	0.735153i
$52$	8.76321	−	1.37360i	1.21524	−	0.190485i
$53$	2.84881			0.391314			0.195657	−	0.980672i	$-0.437316\pi$
$53$	2.84881			0.391314			0.195657	+	0.980672i	$0.437316\pi$
$54$	5.20346	+	5.18883i	0.708101	+	0.706111i
$55$	−8.30601			−1.11998
$56$	0.0508652	−	7.48314i	0.00679715	−	0.999977i
$57$	−3.83495	−	1.50737i	−0.507951	−	0.199656i
$58$	−8.02242	−	6.86289i	−1.05340	−	0.901142i
$59$	0.278774	−	0.482851i	0.0362933	−	0.0628618i	−0.847308	−	0.531101i	$-0.821778\pi$
$59$	0.278774	−	0.482851i	0.0362933	−	0.0628618i	0.883601	+	0.468240i	$0.155112\pi$
$60$	12.3753	+	2.75473i	1.59764	+	0.355635i
$61$	−0.335560	+	0.193736i	−0.0429641	+	0.0248053i	−0.521328	−	0.853356i	$-0.674563\pi$
$61$	−0.335560	+	0.193736i	−0.0429641	+	0.0248053i	0.478364	+	0.878162i	$0.341230\pi$
$62$	1.74736	−	9.38606i	0.221915	−	1.19203i
$63$	−7.77324	−	1.60521i	−0.979337	−	0.202237i
$64$	−3.59771	−	7.14538i	−0.449714	−	0.893173i
$65$	−8.11596	−	14.0572i	−1.00666	−	1.74359i
$66$	4.90853	−	2.60951i	0.604199	−	0.321209i
$67$	−2.07581	−	1.19847i	−0.253601	−	0.146416i	0.367811	−	0.929900i	$-0.380107\pi$
$67$	−2.07581	−	1.19847i	−0.253601	−	0.146416i	−0.621412	+	0.783484i	$0.713441\pi$
$68$	4.09112	+	5.06865i	0.496121	+	0.614664i
$69$	1.89767	+	2.38210i	0.228453	+	0.286772i
$70$	−12.8098	+	4.84095i	−1.53106	+	0.578605i
$71$			9.43272i			1.11946i	0.828676	+	0.559729i	$0.189095\pi$
$71$			9.43272i			1.11946i	−0.828676	+	0.559729i	$0.810905\pi$
$72$	−8.17877	+	2.26002i	−0.963877	+	0.266346i
$73$			12.5047i			1.46356i	0.681539	+	0.731782i	$0.261311\pi$
$73$			12.5047i			1.46356i	−0.681539	+	0.731782i	$0.738689\pi$
$74$	11.7657	−	4.15589i	1.36774	−	0.483112i
$75$	−2.15972	−	14.3787i	−0.249384	−	1.66031i
$76$	3.70245	−	2.98840i	0.424700	−	0.342793i
$77$	−2.88828	+	5.26418i	−0.329150	+	0.599910i
$78$	9.21261	+	5.75749i	1.04312	+	0.651907i
$79$	2.20999	−	1.27594i	0.248643	−	0.143554i	−0.370500	−	0.928833i	$-0.620814\pi$
$79$	2.20999	−	1.27594i	0.248643	−	0.143554i	0.619143	+	0.785278i	$0.287480\pi$
$80$	−9.83045	+	10.8479i	−1.09908	+	1.21283i
$81$	0.654220	+	8.97619i	0.0726911	+	0.997355i
$82$	3.60446	+	0.671026i	0.398046	+	0.0741024i
$83$	4.18556	+	7.24960i	0.459425	+	0.795747i	0.998931	−	0.0462348i	$-0.0147222\pi$
$83$	4.18556	+	7.24960i	0.459425	+	0.795747i	−0.539506	+	0.841982i	$0.681389\pi$
$84$	6.04920	−	6.88529i	0.660022	−	0.751247i
$85$	5.95984	−	10.3227i	0.646435	−	1.11966i
$86$	−6.66311	+	7.78889i	−0.718501	+	0.839897i
$87$	−1.92060	−	12.7867i	−0.205910	−	1.37088i
$88$	−0.183413	+	6.41644i	−0.0195518	+	0.683995i
$89$			2.43473i			0.258081i	0.991639	+	0.129041i	$0.0411897\pi$
$89$			2.43473i			0.258081i	−0.991639	+	0.129041i	$0.958810\pi$
$90$	9.24451	+	12.4757i	0.974457	+	1.31505i
$91$	−11.7314	+	0.255548i	−1.22978	+	0.0267887i
$92$	−3.47431	+	0.544587i	−0.362222	+	0.0567772i
$93$	9.14571	−	7.28581i	0.948366	−	0.755504i
$94$	−8.50894	−	7.27909i	−0.877631	−	0.750781i
$95$	−7.54036	−	4.35343i	−0.773624	−	0.446652i
$96$	2.40132	−	9.49914i	0.245083	−	0.969502i
$97$	5.47279	−	3.15972i	0.555678	−	0.320821i	−0.195731	−	0.980658i	$-0.562708\pi$
$97$	5.47279	−	3.15972i	0.555678	−	0.320821i	0.751409	+	0.659837i	$0.229375\pi$
$98$	−1.38630	+	9.80195i	−0.140037	+	0.990146i
$99$	6.63619	+	1.52181i	0.666962	+	0.152947i
$100$	15.6646	+	6.04180i	1.56646	+	0.604180i
$101$	9.39921	−	5.42664i	0.935256	−	0.539970i	0.0467861	−	0.998905i	$-0.485102\pi$
$101$	9.39921	−	5.42664i	0.935256	−	0.539970i	0.888470	+	0.458934i	$0.151769\pi$
$102$	−0.278922	+	7.97276i	−0.0276173	+	0.789420i
$103$	−2.53157	+	4.38481i	−0.249443	+	0.432048i	−0.963371	−	0.268171i	$-0.913581\pi$
$103$	−2.53157	+	4.38481i	−0.249443	+	0.432048i	0.713928	+	0.700219i	$0.246914\pi$
$104$	−11.0385	+	5.95921i	−1.08242	+	0.584349i
$105$	−15.7391	−	5.79396i	−1.53598	−	0.565432i
$106$	−3.79881	+	1.34181i	−0.368973	+	0.130328i
$107$			4.42246i			0.427536i	0.976884	+	0.213768i	$0.0685736\pi$
$107$			4.42246i			0.427536i	−0.976884	+	0.213768i	$0.931426\pi$
$108$	−9.38266	−	4.46829i	−0.902847	−	0.429962i
$109$	−11.9091			−1.14068			−0.570341	−	0.821408i	$-0.693189\pi$
$109$	−11.9091			−1.14068			−0.570341	+	0.821408i	$0.693189\pi$
$110$	11.0758	−	3.91221i	1.05604	−	0.373014i
$111$	14.2232	+	5.59060i	1.35001	+	0.530637i
$112$	3.45680	+	10.0025i	0.326637	+	0.945150i
$113$	0.733151	−	1.26985i	0.0689690	−	0.119458i	−0.829479	−	0.558538i	$-0.811362\pi$
$113$	0.733151	−	1.26985i	0.0689690	−	0.119458i	0.898448	+	0.439080i	$0.144696\pi$
$114$	5.82379	+	0.203741i	0.545448	+	0.0190821i
$115$	3.21770	+	5.57322i	0.300052	+	0.519706i
$116$	13.9302	+	5.37285i	1.29338	+	0.498856i
$117$	3.90881	+	12.7182i	0.361370	+	1.17580i
$118$	−0.144311	+	0.775173i	−0.0132849	+	0.0713605i
$119$	−4.46991	−	7.36679i	−0.409756	−	0.675313i
$120$	−17.7996	+	2.15550i	−1.62487	+	0.196770i
$121$	−2.92473	+	5.06578i	−0.265884	+	0.460525i
$122$	0.356209	−	0.416394i	0.0322497	−	0.0376985i
$123$	2.79792	+	3.51216i	0.252280	+	0.316681i
$124$	2.09086	+	13.3391i	0.187765	+	1.19788i
$125$		−	12.4241i		−	1.11124i
$126$	11.1215	−	1.52076i	0.990780	−	0.135480i
$127$			8.76631i			0.777884i	0.921262	+	0.388942i	$0.127159\pi$
$127$			8.76631i			0.777884i	−0.921262	+	0.388942i	$0.872841\pi$
$128$	8.16299	+	7.83362i	0.721513	+	0.692401i
$129$	−12.4144	+	1.86469i	−1.09303	+	0.164177i
$130$	17.4435	+	14.9223i	1.52990	+	1.30877i
$131$	−5.18441	+	8.97967i	−0.452964	+	0.784557i	−0.998569	−	0.0534857i	$-0.982967\pi$
$131$	−5.18441	+	8.97967i	−0.452964	+	0.784557i	0.545604	+	0.838043i	$0.316300\pi$
$132$	−5.31629	+	5.79168i	−0.462724	+	0.504101i
$133$	−5.38115	+	3.26509i	−0.466605	+	0.283120i
$134$	3.33253	+	0.620402i	0.287886	+	0.0535946i
$135$	−1.45024	+	18.9619i	−0.124817	+	1.63198i
$136$	−7.84277	−	4.83195i	−0.672512	−	0.414337i
$137$	0.0843932	+	0.146173i	0.00721020	+	0.0124884i	0.869608	−	0.493743i	$-0.164372\pi$
$137$	0.0843932	+	0.146173i	0.00721020	+	0.0124884i	−0.862398	+	0.506231i	$0.831038\pi$
$138$	−3.65249	−	2.28265i	−0.310920	−	0.194312i
$139$	0.755866	−	1.30920i	0.0641117	−	0.111045i	−0.832188	−	0.554494i	$-0.812912\pi$
$139$	0.755866	−	1.30920i	0.0641117	−	0.111045i	0.896300	+	0.443449i	$0.146245\pi$
$140$	14.8014	−	12.4888i	1.25094	−	1.05550i
$141$	−2.03707	−	13.5621i	−0.171552	−	1.14214i
$142$	−4.44290	−	12.5783i	−0.372839	−	1.05555i
$143$	10.0654			0.841710
$144$	9.84168	−	6.86595i	0.820140	−	0.572163i
$145$		−	27.3217i		−	2.26894i
$146$	−5.88982	−	16.6747i	−0.487445	−	1.38001i
$147$	−9.14510	+	7.96035i	−0.754275	+	0.656558i
$148$	−13.7318	+	11.0835i	−1.12875	+	0.911060i
$149$	3.17247	−	5.49488i	0.259899	−	0.450158i	−0.706316	−	0.707897i	$-0.749644\pi$
$149$	3.17247	−	5.49488i	0.259899	−	0.450158i	0.966215	+	0.257739i	$0.0829774\pi$
$150$	9.65243	+	18.1564i	0.788118	+	1.48246i
$151$	−8.75881	+	5.05690i	−0.712782	+	0.411525i	−0.812090	−	0.583532i	$-0.801670\pi$
$151$	−8.75881	+	5.05690i	−0.712782	+	0.411525i	0.0993084	+	0.995057i	$0.468337\pi$
$152$	−3.52955	+	5.72884i	−0.286285	+	0.464670i
$153$	−6.65299	+	7.15553i	−0.537862	+	0.578491i
$154$	1.37197	−	8.38006i	0.110556	−	0.675284i
$155$	21.3975	−	12.3539i	1.71869	−	0.992286i
$156$	−14.9966	−	3.33824i	−1.20069	−	0.267273i
$157$	−12.9272	−	7.46350i	−1.03170	−	0.595652i	−0.114229	−	0.993454i	$-0.536440\pi$
$157$	−12.9272	−	7.46350i	−1.03170	−	0.595652i	−0.917471	+	0.397802i	$0.869773\pi$
$158$	−2.34598	+	2.74235i	−0.186636	+	0.218170i
$159$	−4.59227	−	1.80504i	−0.364190	−	0.143149i
$160$	7.99919	−	19.0956i	0.632391	−	1.50964i
$161$	4.65110	−	0.101316i	0.366558	−	0.00798482i
$162$	−5.10025	−	11.6614i	−0.400714	−	0.916203i
$163$			8.61263i			0.674594i	0.941398	+	0.337297i	$0.109513\pi$
$163$			8.61263i			0.674594i	−0.941398	+	0.337297i	$0.890487\pi$
$164$	−5.12251	+	0.802936i	−0.400001	+	0.0626988i
$165$	13.3893	+	5.26280i	1.04235	+	0.409708i
$166$	−8.99596	−	7.69571i	−0.698222	−	0.597303i
$167$	12.3340	−	21.3631i	0.954434	−	1.65313i	0.218776	−	0.975775i	$-0.429794\pi$
$167$	12.3340	−	21.3631i	0.954434	−	1.65313i	0.735658	−	0.677353i	$-0.236873\pi$
$168$	−4.82341	+	12.0306i	−0.372134	+	0.928179i
$169$	3.33507	+	5.77651i	0.256544	+	0.444347i
$170$	−3.08518	+	16.5722i	−0.236623	+	1.27103i
$171$	5.22684	+	4.85975i	0.399706	+	0.371634i
$172$	5.21644	−	13.5247i	0.397750	−	1.03125i
$173$	−8.38273	+	4.83977i	−0.637327	+	0.367961i	−0.783584	−	0.621286i	$-0.786611\pi$
$173$	−8.38273	+	4.83977i	−0.637327	+	0.367961i	0.146257	+	0.989247i	$0.453277\pi$
$174$	8.58371	+	16.1461i	0.650729	+	1.22403i
$175$	−19.4719	−	10.6836i	−1.47194	−	0.807603i
$176$	−2.77763	−	8.64254i	−0.209371	−	0.651456i
$177$	−0.755323	+	0.601719i	−0.0567736	+	0.0452280i
$178$	−1.14678	−	3.24665i	−0.0859548	−	0.243347i
$179$		−	3.46442i		−	0.258943i	−0.991583	−	0.129472i	$-0.958672\pi$
$179$		−	3.46442i		−	0.258943i	0.991583	−	0.129472i	$-0.0413281\pi$
$180$	−18.2035	−	12.2818i	−1.35681	−	0.915428i
$181$			12.3588i			0.918625i	0.888275	+	0.459313i	$0.151904\pi$
$181$			12.3588i			0.918625i	−0.888275	+	0.459313i	$0.848096\pi$
$182$	15.5231	−	5.86636i	1.15065	−	0.434843i
$183$	0.663676	−	0.0996862i	0.0490603	−	0.00736901i
$184$	4.37640	−	2.36263i	0.322632	−	0.174175i
$185$	27.9661	+	16.1462i	2.05610	+	1.18709i
$186$	−8.76387	+	14.0231i	−0.642598	+	1.02823i
$187$	3.69569	+	6.40112i	0.270255	+	0.468096i
$188$	14.7750	+	5.69868i	1.07758	+	0.415619i
$189$	11.5134	+	7.51282i	0.837474	+	0.546477i
$190$	12.1054	+	2.25360i	0.878216	+	0.163494i
$191$	−3.06238	+	1.76806i	−0.221586	+	0.127933i	−0.606684	−	0.794943i	$-0.707501\pi$
$191$	−3.06238	+	1.76806i	−0.221586	+	0.127933i	0.385098	+	0.922875i	$0.374167\pi$
$192$	1.27209	+	13.7979i	0.0918051	+	0.995777i
$193$	7.23020	−	12.5231i	0.520441	−	0.901431i	−0.479276	−	0.877664i	$-0.659101\pi$
$193$	7.23020	−	12.5231i	0.520441	−	0.901431i	0.999718	−	0.0237669i	$-0.00756594\pi$
$194$	−5.80956	+	6.79113i	−0.417102	+	0.487575i
$195$	4.17604	+	27.8026i	0.299052	+	1.99099i
$196$	−2.76821	−	13.7236i	−0.197730	−	0.980257i
$197$	−11.6967			−0.833353			−0.416677	−	0.909055i	$-0.636805\pi$
$197$	−11.6967			−0.833353			−0.416677	+	0.909055i	$0.636805\pi$
$198$	−9.56597	+	1.09642i	−0.679824	+	0.0779189i
$199$	18.5032			1.31165			0.655827	−	0.754911i	$-0.272320\pi$
$199$	18.5032			1.31165			0.655827	+	0.754911i	$0.272320\pi$
$200$	−23.7340	−	0.678431i	−1.67825	−	0.0479724i
$201$	2.58683	+	3.24719i	0.182461	+	0.229039i
$202$	−9.97760	+	11.6634i	−0.702021	+	0.820633i
$203$	−17.3159	−	9.50068i	−1.21534	−	0.666817i
$204$	−3.38330	−	10.7628i	−0.236879	−	0.753549i
$205$	4.74416	+	8.21712i	0.331346	+	0.573909i
$206$	1.31050	−	7.03942i	0.0913067	−	0.490460i
$207$	−1.54971	−	5.04233i	−0.107712	−	0.350466i
$208$	11.9127	−	13.1457i	0.825999	−	0.911489i
$209$	4.67576	−	2.69955i	0.323429	−	0.186732i
$210$	23.7166	+	0.312847i	1.63660	+	0.0215885i
$211$	11.5414	+	6.66345i	0.794546	+	0.458731i	0.841560	−	0.540163i	$-0.181637\pi$
$211$	11.5414	+	6.66345i	0.794546	+	0.458731i	−0.0470148	+	0.998894i	$0.514971\pi$
$212$	4.43360	−	3.57854i	0.304501	−	0.245775i
$213$	5.97670	−	15.2055i	0.409517	−	1.04186i
$214$	−2.08302	−	5.89724i	−0.142392	−	0.403127i
$215$	−26.5263			−1.80908
$216$	14.6161	+	1.53903i	0.994502	+	0.104718i
$217$	−0.388987	−	17.8572i	−0.0264062	−	1.21222i
$218$	15.8804	−	5.60928i	1.07556	−	0.379908i
$219$	7.92314	−	20.1575i	0.535396	−	1.36212i
$220$	−12.9267	+	10.4336i	−0.871515	+	0.703436i
$221$	−7.22224	+	12.5093i	−0.485821	+	0.841466i
$222$	−21.5995	−	0.755646i	−1.44967	−	0.0507156i
$223$	−9.84503	−	17.0521i	−0.659272	−	1.14189i	−0.980804	−	0.194994i	$-0.937531\pi$
$223$	−9.84503	−	17.0521i	−0.659272	−	1.14189i	0.321532	−	0.946899i	$-0.395802\pi$
$224$	−9.32083	−	11.7099i	−0.622774	−	0.782402i
$225$	−5.62907	+	24.5469i	−0.375271	+	1.63646i
$226$	−0.379524	+	2.03864i	−0.0252456	+	0.135608i
$227$	−8.84757	−	15.3244i	−0.587234	−	1.01712i	−0.994593	−	0.103851i	$-0.966884\pi$
$227$	−8.84757	−	15.3244i	−0.587234	−	1.01712i	0.407359	−	0.913268i	$-0.366450\pi$
$228$	−7.86183	+	2.47137i	−0.520662	+	0.163671i
$229$	11.7943	+	6.80946i	0.779391	+	0.449982i	0.836215	−	0.548402i	$-0.184764\pi$
$229$	11.7943	+	6.80946i	0.779391	+	0.449982i	−0.0568231	+	0.998384i	$0.518097\pi$
$230$	−6.91576	−	5.91618i	−0.456012	−	0.390101i
$231$	7.99136	−	6.65580i	0.525793	−	0.437919i
$232$	−21.1062	−	0.603315i	−1.38569	−	0.0396096i
$233$	11.3654			0.744572			0.372286	−	0.928118i	$-0.378574\pi$
$233$	11.3654			0.744572			0.372286	+	0.928118i	$0.378574\pi$
$234$	−11.2027	−	15.1183i	−0.732342	−	0.988313i
$235$		−	28.9786i		−	1.89036i
$236$	−0.172679	−	1.10164i	−0.0112405	−	0.0717109i
$237$	−4.37094	+	0.656529i	−0.283923	+	0.0426462i
$238$	9.43033	+	7.71805i	0.611277	+	0.500287i
$239$	9.83584	+	5.67873i	0.636228	+	0.367326i	0.783160	−	0.621820i	$-0.213607\pi$
$239$	9.83584	+	5.67873i	0.636228	+	0.367326i	−0.146932	+	0.989147i	$0.546940\pi$
$240$	22.7200	−	11.2581i	1.46657	−	0.726706i
$241$	−14.0257	+	8.09777i	−0.903478	+	0.521623i	−0.878327	−	0.478061i	$-0.841340\pi$
$241$	−14.0257	+	8.09777i	−0.903478	+	0.521623i	−0.0251507	+	0.999684i	$0.508007\pi$
$242$	1.51402	−	8.13265i	0.0973249	−	0.522786i
$243$	4.63283	−	14.8841i	0.297196	−	0.954816i
$244$	−0.278871	+	0.723027i	−0.0178529	+	0.0462871i
$245$	−21.6080	+	13.7635i	−1.38048	+	0.879321i
$246$	−5.38520	−	3.36552i	−0.343348	−	0.214578i
$247$	9.13755	+	5.27557i	0.581408	+	0.335676i
$248$	−9.07093	−	16.8025i	−0.576004	−	1.06696i
$249$	−2.15367	−	14.3384i	−0.136483	−	0.908657i
$250$	5.85184	+	16.5671i	0.370103	+	1.04780i
$251$	−17.8171			−1.12460			−0.562301	−	0.826932i	$-0.690084\pi$
$251$	−17.8171			−1.12460			−0.562301	+	0.826932i	$0.690084\pi$
$252$	−14.1139	+	7.26621i	−0.889092	+	0.457728i
$253$	−3.99058			−0.250886
$254$	−4.12901	−	11.6896i	−0.259077	−	0.733473i
$255$	−16.1479	+	12.8640i	−1.01122	+	0.805575i
$256$	−14.5748	−	6.60108i	−0.910927	−	0.412568i
$257$	5.11189	+	2.95135i	0.318871	+	0.184100i	0.650889	−	0.759173i	$-0.274396\pi$
$257$	5.11189	+	2.95135i	0.318871	+	0.184100i	−0.332018	+	0.943273i	$0.607730\pi$
$258$	15.6760	−	8.33383i	0.975948	−	0.518841i
$259$	19.9579	−	12.1097i	1.24012	−	0.752463i
$260$	−30.2890	−	11.6824i	−1.87844	−	0.724512i
$261$	−5.00581	+	21.8290i	−0.309852	+	1.35118i
$262$	2.68377	−	14.4161i	0.165804	−	0.890627i
$263$	−20.1597	+	11.6392i	−1.24310	+	0.717703i	−0.969724	−	0.244204i	$-0.921473\pi$
$263$	−20.1597	+	11.6392i	−1.24310	+	0.717703i	−0.273375	+	0.961908i	$0.588140\pi$
$264$	4.36120	−	10.2271i	0.268413	−	0.629433i
$265$	−9.02941	−	5.21313i	−0.554672	−	0.320240i
$266$	5.63774	−	6.88849i	0.345672	−	0.422360i
$267$	1.54268	−	3.92478i	0.0944104	−	0.240193i
$268$	−4.73605	+	0.742360i	−0.289300	+	0.0453469i
$269$		−	18.4617i		−	1.12563i	−0.826582	−	0.562816i	$-0.809718\pi$
$269$		−	18.4617i		−	1.12563i	0.826582	−	0.562816i	$-0.190282\pi$
$270$	−6.99736	−	25.9682i	−0.425846	−	1.58038i
$271$	24.5106			1.48891			0.744457	−	0.667670i	$-0.232708\pi$
$271$	24.5106			1.48891			0.744457	+	0.667670i	$0.232708\pi$
$272$	12.7340	+	2.74927i	0.772113	+	0.166699i
$273$	19.0729	+	7.02123i	1.15434	+	0.424944i
$274$	−0.181385	−	0.155168i	−0.0109579	−	0.00937406i
$275$	16.4991	+	9.52577i	0.994935	+	0.574426i
$276$	5.94564	+	1.32350i	0.357886	+	0.0796652i
$277$	5.38832	+	9.33284i	0.323753	+	0.560756i	0.981259	−	0.192693i	$-0.0617220\pi$
$277$	5.38832	+	9.33284i	0.323753	+	0.560756i	−0.657506	+	0.753449i	$0.728389\pi$
$278$	−0.391283	+	2.10180i	−0.0234676	+	0.126058i
$279$	−19.3592	+	5.94987i	−1.15901	+	0.356209i
$280$	−13.8549	+	23.6251i	−0.827988	+	1.41187i
$281$	5.07419	+	8.78875i	0.302701	+	0.524293i	0.976747	−	0.214396i	$-0.0687784\pi$
$281$	5.07419	+	8.78875i	0.302701	+	0.524293i	−0.674046	+	0.738689i	$0.735445\pi$
$282$	9.10426	+	17.1253i	0.542151	+	1.01979i
$283$	6.79544	−	11.7700i	0.403947	−	0.699657i	−0.590251	−	0.807220i	$-0.700971\pi$
$283$	6.79544	−	11.7700i	0.403947	−	0.699657i	0.994198	+	0.107563i	$0.0343047\pi$
$284$	11.8490	+	14.6802i	0.703107	+	0.871107i
$285$	9.39665	+	11.7954i	0.556609	+	0.698698i
$286$	−13.4219	+	4.74088i	−0.793655	+	0.280334i
$287$	6.85755	−	0.149380i	0.404789	−	0.00881761i
$288$	−9.88970	+	13.7911i	−0.582756	+	0.812647i
$289$	6.39290			0.376053
$290$	12.8688	+	36.4328i	0.755680	+	2.13941i
$291$	−10.8242	+	1.62582i	−0.634523	+	0.0953073i
$292$	15.7078	+	19.4611i	0.919231	+	1.13887i
$293$	−16.6445	−	9.60969i	−0.972381	−	0.561404i	−0.0724194	−	0.997374i	$-0.523072\pi$
$293$	−16.6445	−	9.60969i	−0.972381	−	0.561404i	−0.899961	+	0.435970i	$0.856405\pi$
$294$	8.44535	−	14.9223i	0.492543	−	0.870288i
$295$	−1.76717	+	1.02028i	−0.102889	+	0.0594028i
$296$	13.0906	−	21.2474i	0.760874	−	1.23498i
$297$	−9.73328	−	6.65792i	−0.564782	−	0.386332i
$298$	−1.64227	+	8.82154i	−0.0951340	+	0.511018i
$299$	−3.89927	−	6.75374i	−0.225501	−	0.390579i
$300$	−21.4231	−	19.6646i	−1.23686	−	1.13534i
$301$	−9.22411	+	16.8119i	−0.531669	+	0.969020i
$302$	9.29779	−	10.8687i	0.535028	−	0.625425i
$303$	−18.5899	+	2.79226i	−1.06796	+	0.160411i
$304$	2.00823	−	9.30170i	0.115180	−	0.533489i
$305$	1.41810			0.0812000
$306$	5.50126	−	12.6753i	0.314486	−	0.724600i
$307$	−6.50328			−0.371162			−0.185581	−	0.982629i	$-0.559417\pi$
$307$	−6.50328			−0.371162			−0.185581	+	0.982629i	$0.559417\pi$
$308$	2.11760	+	11.8208i	0.120661	+	0.673552i
$309$	6.85916	−	5.46427i	0.390204	−	0.310851i
$310$	−22.7142	+	26.5520i	−1.29008	+	1.50805i
$311$	−13.2350	+	22.9236i	−0.750486	+	1.29988i	0.197101	+	0.980383i	$0.436847\pi$
$311$	−13.2350	+	22.9236i	−0.750486	+	1.29988i	−0.947587	+	0.319497i	$0.896486\pi$
$312$	21.5699	−	2.61208i	1.22115	−	0.147880i
$313$	30.1889	−	17.4296i	1.70638	−	0.985179i	0.767424	−	0.641140i	$-0.221538\pi$
$313$	30.1889	−	17.4296i	1.70638	−	0.985179i	0.938956	−	0.344038i	$-0.111795\pi$
$314$	20.7534	+	3.86357i	1.17118	+	0.218034i
$315$	21.7002	+	19.3123i	1.22267	+	1.08813i
$316$	1.83663	−	4.76183i	0.103319	−	0.267874i
$317$	12.0492	+	20.8699i	0.676751	+	1.17217i	0.975954	+	0.217978i	$0.0699461\pi$
$317$	12.0492	+	20.8699i	0.676751	+	1.17217i	−0.299202	+	0.954190i	$0.596721\pi$
$318$	6.97385	+	0.243976i	0.391074	+	0.0136815i
$319$	14.6723	+	8.47107i	0.821493	+	0.474289i
$320$	−1.67250	+	29.2312i	−0.0934956	+	1.63407i
$321$	2.80213	−	7.12900i	0.156400	−	0.397902i
$322$	−6.15440	+	2.32581i	−0.342971	+	0.129612i
$323$			7.74807i			0.431114i
$324$	12.2937	+	13.1479i	0.682981	+	0.730436i
$325$			37.2312i			2.06522i
$326$	−4.05663	−	11.4847i	−0.224676	−	0.636080i
$327$	19.1974	+	7.54574i	1.06162	+	0.417281i
$328$	6.45253	−	3.48344i	0.356282	−	0.192341i
$329$	−18.3661	−	10.0769i	−1.01255	−	0.555555i
$330$	−20.3331	−	0.711338i	−1.11930	−	0.0391579i
$331$	−8.47411	+	4.89253i	−0.465779	+	0.268918i	−0.714471	−	0.699665i	$-0.753333\pi$
$331$	−8.47411	+	4.89253i	−0.465779	+	0.268918i	0.248692	+	0.968583i	$0.419999\pi$
$332$	15.6206	+	6.02485i	0.857293	+	0.330657i
$333$	−19.3855	−	18.0241i	−1.06232	−	0.987713i
$334$	−6.38484	+	34.2966i	−0.349363	+	1.87663i
$335$	4.38625	+	7.59720i	0.239646	+	0.415079i
$336$	0.765384	−	18.3143i	0.0417551	−	0.999128i
$337$	−1.61835	+	2.80306i	−0.0881569	+	0.152692i	−0.906732	−	0.421707i	$-0.861431\pi$
$337$	−1.61835	+	2.80306i	−0.0881569	+	0.152692i	0.818575	+	0.574399i	$0.194764\pi$
$338$	−7.16801	−	6.13197i	−0.389888	−	0.333535i
$339$	−1.98643	+	1.58247i	−0.107888	+	0.0859479i
$340$	−3.69166	−	23.5518i	−0.200209	−	1.27727i
$341$			15.3212i			0.829690i
$342$	−9.25883	−	4.01846i	−0.500660	−	0.217293i
$343$	1.20924	+	18.4807i	0.0652929	+	0.997866i
$344$	−0.585752	+	20.4918i	−0.0315816	+	1.10484i
$345$	−1.65566	−	11.0228i	−0.0891376	−	0.593448i
$346$	8.89857	−	10.4020i	0.478390	−	0.559217i
$347$	7.17390	+	4.14185i	0.385115	+	0.222346i	0.680041	−	0.733174i	$-0.261962\pi$
$347$	7.17390	+	4.14185i	0.385115	+	0.222346i	−0.294926	+	0.955520i	$0.595295\pi$
$348$	−19.0511	−	17.4874i	−1.02125	−	0.937421i
$349$	−23.6369	+	13.6467i	−1.26525	+	0.730494i	−0.974086	−	0.226179i	$-0.927377\pi$
$349$	−23.6369	+	13.6467i	−1.26525	+	0.730494i	−0.291166	+	0.956673i	$0.594043\pi$
$350$	30.9973	+	5.07483i	1.65688	+	0.271261i
$351$	1.75743	−	22.9784i	0.0938045	−	1.22649i
$352$	7.77460	+	10.2163i	0.414388	+	0.544531i
$353$	20.5575	−	11.8689i	1.09417	−	0.631718i	0.159484	−	0.987200i	$-0.449017\pi$
$353$	20.5575	−	11.8689i	1.09417	−	0.631718i	0.934683	+	0.355483i	$0.115684\pi$
$354$	0.723788	−	1.15814i	0.0384689	−	0.0615544i
$355$	17.2613	−	29.8974i	0.916134	−	1.58679i
$356$	3.05840	+	3.78918i	0.162095	+	0.200826i
$357$	2.53778	+	14.7074i	0.134314	+	0.778400i
$358$	1.63177	+	4.61972i	0.0862420	+	0.244160i
$359$		−	23.8835i		−	1.26052i	−0.776383	−	0.630262i	$-0.782948\pi$
$359$		−	23.8835i		−	1.26052i	0.776383	−	0.630262i	$-0.217052\pi$
$360$	30.0587	+	7.80340i	1.58423	+	0.411275i
$361$	−13.3403			−0.702123
$362$	−5.82112	−	16.4802i	−0.305951	−	0.866179i
$363$	7.92439	−	6.31287i	0.415923	−	0.331340i
$364$	−17.9366	+	15.1342i	−0.940132	+	0.793246i
$365$	22.8828	−	39.6341i	1.19774	−	2.07455i
$366$	−0.838041	+	0.445526i	−0.0438051	+	0.0232880i
$367$	−7.37363	−	12.7715i	−0.384900	−	0.666667i	0.606855	−	0.794813i	$-0.292431\pi$
$367$	−7.37363	−	12.7715i	−0.384900	−	0.666667i	−0.991755	+	0.128146i	$0.959098\pi$
$368$	−4.72299	+	5.21182i	−0.246203	+	0.271685i
$369$	−2.28488	−	7.43438i	−0.118946	−	0.387019i
$370$	−44.8970	−	8.35828i	−2.33408	−	0.434526i
$371$	−6.44381	+	3.90988i	−0.334546	+	0.202991i
$372$	5.08136	−	22.8273i	0.263456	−	1.18354i
$373$	16.5636	−	28.6890i	0.857630	−	1.48546i	−0.0165533	−	0.999863i	$-0.505269\pi$
$373$	16.5636	−	28.6890i	0.857630	−	1.48546i	0.874183	−	0.485596i	$-0.161397\pi$
$374$	−7.94308	−	6.79501i	−0.410727	−	0.351362i
$375$	−7.87205	+	20.0275i	−0.406511	+	1.03422i
$376$	−22.3862	−	0.639903i	−1.15448	−	0.0330005i
$377$			33.1090i			1.70520i
$378$	−18.8914	−	4.59525i	−0.971667	−	0.236354i
$379$			10.7387i			0.551610i	0.961214	+	0.275805i	$0.0889444\pi$
$379$			10.7387i			0.551610i	−0.961214	+	0.275805i	$0.911056\pi$
$380$	−17.2037	+	2.69662i	−0.882529	+	0.138333i
$381$	5.55445	−	14.1313i	0.284563	−	0.723967i
$382$	3.25082	−	3.80007i	0.166327	−	0.194429i
$383$	−11.5745	+	20.0477i	−0.591432	+	1.02439i	0.402608	+	0.915372i	$0.368104\pi$
$383$	−11.5745	+	20.0477i	−0.591432	+	1.02439i	−0.994040	+	0.109017i	$0.965230\pi$
$384$	−8.19522	−	17.8000i	−0.418211	−	0.908350i
$385$	18.7877	−	11.3997i	0.957508	−	0.580982i
$386$	−3.74280	+	20.1047i	−0.190504	+	1.02330i
$387$	21.1935	+	4.86009i	1.07733	+	0.247052i
$388$	4.54821	−	11.7921i	0.230901	−	0.598655i
$389$	−12.7845	−	22.1435i	−0.648202	−	1.12272i	−0.983552	−	0.180625i	$-0.942188\pi$
$389$	−12.7845	−	22.1435i	−0.648202	−	1.12272i	0.335350	−	0.942094i	$-0.391145\pi$
$390$	−18.6639	−	35.1071i	−0.945084	−	1.77772i
$391$	2.86338	−	4.95951i	0.144807	−	0.250813i
$392$	10.1553	+	16.9962i	0.512919	+	0.858437i
$393$	14.0469	−	11.1903i	0.708572	−	0.564475i
$394$	15.5972	−	5.50923i	0.785775	−	0.277551i
$395$	−9.33954			−0.469923
$396$	12.2395	−	5.96770i	0.615060	−	0.299888i
$397$		−	6.99709i		−	0.351174i	−0.984464	−	0.175587i	$-0.943818\pi$
$397$		−	6.99709i		−	0.351174i	0.984464	−	0.175587i	$-0.0561823\pi$
$398$	−24.6735	+	8.71515i	−1.23677	+	0.436851i
$399$	10.7432	−	1.85375i	0.537833	−	0.0928036i
$400$	31.9682	−	10.2743i	1.59841	−	0.513713i
$401$	−17.3130	+	29.9870i	−0.864570	+	1.49748i	0.00290293	+	0.999996i	$0.499076\pi$
$401$	−17.3130	+	29.9870i	−0.864570	+	1.49748i	−0.867473	+	0.497484i	$0.834257\pi$
$402$	−4.97893	−	3.11162i	−0.248326	−	0.155193i
$403$	−25.9299	+	14.9706i	−1.29166	+	0.745741i
$404$	7.81130	−	20.2523i	0.388627	−	1.00759i
$405$	14.3523	−	29.6476i	0.713170	−	1.47320i
$406$	27.5653	+	4.51294i	1.36804	+	0.223974i
$407$	−17.3417	+	10.0122i	−0.859596	+	0.496288i
$408$	9.58093	+	12.7584i	0.474327	+	0.631634i
$409$	28.8194	+	16.6389i	1.42503	+	0.822740i	0.996723	−	0.0808935i	$-0.0257774\pi$
$409$	28.8194	+	16.6389i	1.42503	+	0.822740i	0.428306	+	0.903634i	$0.359111\pi$
$410$	−10.1965	−	8.72277i	−0.503572	−	0.430787i
$411$	−0.0434243	−	0.289104i	−0.00214196	−	0.0142604i
$412$	1.56812	+	10.0041i	0.0772555	+	0.492868i
$413$	0.0321255	+	1.47478i	0.00158079	+	0.0725693i
$414$	4.44148	+	5.99389i	0.218287	+	0.294584i
$415$		−	30.6372i		−	1.50392i
$416$	−9.69357	+	23.1404i	−0.475266	+	1.13455i
$417$	−2.04798	+	1.63150i	−0.100290	+	0.0798948i
$418$	−4.96349	+	5.80211i	−0.242772	+	0.283790i
$419$	10.8501	−	18.7930i	0.530064	−	0.918097i	−0.469321	−	0.883028i	$-0.655501\pi$
$419$	10.8501	−	18.7930i	0.530064	−	0.918097i	0.999385	−	0.0350699i	$-0.0111654\pi$
$420$	−31.7728	+	10.7536i	−1.55036	+	0.524720i
$421$	0.917280	+	1.58878i	0.0447055	+	0.0774322i	0.887512	−	0.460784i	$-0.152432\pi$
$421$	0.917280	+	1.58878i	0.0447055	+	0.0774322i	−0.842807	+	0.538216i	$0.819098\pi$
$422$	−18.5287	−	3.44942i	−0.901965	−	0.167915i
$423$	−5.30939	+	23.1528i	−0.258151	+	1.12573i
$424$	−4.22656	+	6.86016i	−0.205260	+	0.333159i
$425$	−23.6773	+	13.6701i	−1.14852	+	0.663098i
$426$	−0.807831	+	23.0912i	−0.0391395	+	1.11877i
$427$	0.493121	−	0.898762i	0.0238638	−	0.0434941i
$428$	5.55530	+	6.88269i	0.268526	+	0.332687i
$429$	−16.2254	−	6.37756i	−0.783368	−	0.307912i
$430$	35.3722	−	12.4941i	1.70580	−	0.602521i
$431$		−	16.8296i		−	0.810654i	−0.914172	−	0.405327i	$-0.867158\pi$
$431$		−	16.8296i		−	0.810654i	0.914172	−	0.405327i	$-0.132842\pi$
$432$	−20.2151	+	4.83207i	−0.972600	+	0.232483i
$433$			4.35936i			0.209497i	0.994499	+	0.104749i	$0.0334038\pi$
$433$			4.35936i			0.209497i	−0.994499	+	0.104749i	$0.966596\pi$
$434$	8.92959	+	23.6288i	0.428634	+	1.13422i
$435$	−17.3114	+	44.0425i	−0.830018	+	2.11168i
$436$	−18.5341	+	14.9596i	−0.887622	+	0.716437i
$437$	−3.62273	−	2.09158i	−0.173299	−	0.100054i
$438$	−1.07092	+	30.6114i	−0.0511705	+	1.46267i
$439$	11.6841	+	20.2374i	0.557649	+	0.965877i	0.997692	+	0.0679003i	$0.0216300\pi$
$439$	11.6841	+	20.2374i	0.557649	+	0.965877i	−0.440043	+	0.897977i	$0.645037\pi$
$440$	12.3230	−	20.0016i	0.587477	−	0.953537i
$441$	19.7857	−	7.03760i	0.942174	−	0.335124i
$442$	3.73868	−	20.0825i	0.177831	−	0.955229i
$443$	6.40279	−	3.69665i	0.304206	−	0.175633i	−0.340125	−	0.940380i	$-0.610469\pi$
$443$	6.40279	−	3.69665i	0.304206	−	0.175633i	0.644331	+	0.764747i	$0.277136\pi$
$444$	29.1583	−	9.16594i	1.38379	−	0.434996i
$445$	4.45541	−	7.71699i	0.211206	−	0.365820i
$446$	21.1598	+	18.1014i	1.00194	+	0.857127i
$447$	−8.59564	+	6.84761i	−0.406560	+	0.323881i
$448$	17.9445	+	11.2247i	0.847800	+	0.530316i
$449$	−24.0534			−1.13515			−0.567575	−	0.823322i	$-0.692118\pi$
$449$	−24.0534			−1.13515			−0.567575	+	0.823322i	$0.692118\pi$
$450$	−4.05558	−	35.3839i	−0.191182	−	1.66801i
$451$	−5.88369			−0.277052
$452$	−0.454131	−	2.89723i	−0.0213605	−	0.136274i
$453$	17.3233	−	2.60201i	0.813919	−	0.122253i
$454$	19.0159	+	16.2674i	0.892463	+	0.763469i
$455$	37.6508	+	20.6577i	1.76510	+	0.968450i
$456$	9.31950	−	6.99850i	0.436425	−	0.327735i
$457$	−1.41440	−	2.44981i	−0.0661629	−	0.114597i	0.831046	−	0.556203i	$-0.187742\pi$
$457$	−1.41440	−	2.44981i	−0.0661629	−	0.114597i	−0.897209	+	0.441606i	$0.854409\pi$
$458$	−18.9347	−	3.52500i	−0.884762	−	0.164712i
$459$	15.2584	−	7.31928i	0.712203	−	0.341635i
$460$	12.0086	+	4.63168i	0.559902	+	0.215953i
$461$	14.4516	−	8.34364i	0.673079	−	0.388602i	−0.124164	−	0.992262i	$-0.539625\pi$
$461$	14.4516	−	8.34364i	0.673079	−	0.388602i	0.797242	+	0.603660i	$0.206291\pi$
$462$	−7.52133	+	12.6393i	−0.349924	+	0.588035i
$463$	−24.1320	−	13.9326i	−1.12151	−	0.647503i	−0.179722	−	0.983717i	$-0.557520\pi$
$463$	−24.1320	−	13.9326i	−1.12151	−	0.647503i	−0.941785	+	0.336215i	$0.890853\pi$
$464$	28.4287	−	9.13669i	1.31977	−	0.424160i
$465$	−42.3203	+	6.35664i	−1.96256	+	0.294782i
$466$	−15.1555	+	5.35320i	−0.702063	+	0.247982i
$467$	4.54857			0.210483			0.105241	−	0.994447i	$-0.466438\pi$
$467$	4.54857			0.210483			0.105241	+	0.994447i	$0.466438\pi$
$468$	22.0593	+	14.8833i	1.01969	+	0.687979i
$469$	6.34020	−	0.138110i	0.292763	−	0.00637733i
$470$	13.6492	+	38.6422i	0.629590	+	1.78243i
$471$	16.1096	+	20.2220i	0.742290	+	0.931779i
$472$	0.749147	+	1.38768i	0.0344823	+	0.0638731i
$473$	8.22447	−	14.2452i	0.378162	−	0.654995i
$474$	5.51931	−	2.93422i	0.253510	−	0.134773i
$475$	9.98548	+	17.2954i	0.458165	+	0.793566i
$476$	−16.2104	−	5.85005i	−0.743001	−	0.268137i
$477$	6.25902	+	5.81944i	0.286581	+	0.266454i
$478$	−15.7906	−	2.93966i	−0.722243	−	0.134457i
$479$	−12.9746	−	22.4727i	−0.592827	−	1.02681i	−0.993850	−	0.110738i	$-0.964679\pi$
$479$	−12.9746	−	22.4727i	−0.592827	−	1.02681i	0.401023	−	0.916068i	$-0.368655\pi$
$480$	−24.9939	+	25.7137i	−1.14081	+	1.17366i
$481$	−33.8898	−	19.5663i	−1.54524	−	0.892145i
$482$	14.8888	−	17.4044i	0.678168	−	0.792749i
$483$	−7.56176	−	2.78368i	−0.344072	−	0.126662i
$484$	1.81165	+	11.5578i	0.0823475	+	0.525354i
$485$	−23.1283			−1.05020
$486$	0.832793	+	22.0297i	0.0377762	+	0.999286i
$487$			17.2694i			0.782553i	0.920273	+	0.391276i	$0.127966\pi$
$487$			17.2694i			0.782553i	−0.920273	+	0.391276i	$0.872034\pi$
$488$	0.0313143	−	1.09549i	0.00141753	−	0.0495904i
$489$	5.45708	−	13.8835i	0.246778	−	0.627835i
$490$	22.3309	−	28.5309i	1.00881	−	1.28889i
$491$	−31.7529	−	18.3326i	−1.43299	−	0.827337i	−0.435643	−	0.900120i	$-0.643479\pi$
$491$	−31.7529	−	18.3326i	−1.43299	−	0.827337i	−0.997348	+	0.0727822i	$0.976812\pi$
$492$	8.76622	+	1.95136i	0.395212	+	0.0879740i
$493$	−21.0558	+	12.1565i	−0.948303	+	0.547503i
$494$	−14.6695	−	2.73096i	−0.660013	−	0.122872i
$495$	−18.2489	−	16.9672i	−0.820226	−	0.762621i
$496$	20.0100	+	18.1332i	0.898474	+	0.814204i
$497$	−12.9460	−	21.3362i	−0.580710	−	0.957059i
$498$	9.62535	+	18.1054i	0.431322	+	0.811323i
$499$	−12.1400	−	7.00904i	−0.543461	−	0.313768i	0.203019	−	0.979175i	$-0.434925\pi$
$499$	−12.1400	−	7.00904i	−0.543461	−	0.313768i	−0.746481	+	0.665407i	$0.768258\pi$
$500$	−15.6065	−	19.3356i	−0.697946	−	0.864713i
$501$	−33.4183	+	26.6223i	−1.49302	+	1.18940i
$502$	23.7586	−	8.39199i	1.06040	−	0.374553i
$503$	−6.75881			−0.301361			−0.150680	−	0.988583i	$-0.548146\pi$
$503$	−6.75881			−0.301361			−0.150680	+	0.988583i	$0.548146\pi$
$504$	15.3981	−	16.3371i	0.685884	−	0.727711i
$505$	−39.7216			−1.76759
$506$	5.32134	−	1.87960i	0.236562	−	0.0835584i
$507$	−1.71605	−	11.4249i	−0.0762124	−	0.507396i
$508$	11.0118	+	13.6430i	0.488572	+	0.605311i
$509$	−35.2759	−	20.3666i	−1.56358	−	0.902732i	−0.996891	−	0.0787981i	$-0.974892\pi$
$509$	−35.2759	−	20.3666i	−1.56358	−	0.902732i	−0.566686	−	0.823934i	$-0.691775\pi$
$510$	15.4737	−	24.7596i	0.685186	−	1.09637i
$511$	−17.1622	−	28.2848i	−0.759211	−	1.25125i
$512$	22.5443	+	1.93750i	0.996327	+	0.0856260i
$513$	−5.34644	−	11.1457i	−0.236051	−	0.492094i
$514$	−8.20669	−	1.52780i	−0.361981	−	0.0673885i
$515$	16.0479	−	9.26523i	0.707153	−	0.408275i
$516$	−16.9783	+	18.4965i	−0.747427	+	0.814263i
$517$	15.5621	+	8.98480i	0.684422	+	0.395151i
$518$	−20.9095	+	25.5484i	−0.918711	+	1.12253i
$519$	16.5795	−	2.49029i	0.727758	−	0.109311i
$520$	45.8920	+	1.31181i	2.01250	+	0.0575268i
$521$			7.37937i			0.323296i	0.986848	+	0.161648i	$0.0516809\pi$
$521$			7.37937i			0.323296i	−0.986848	+	0.161648i	$0.948319\pi$
$522$	−3.60654	−	31.4662i	−0.157854	−	1.37724i
$523$	−15.2943			−0.668772			−0.334386	−	0.942436i	$-0.608529\pi$
$523$	−15.2943			−0.668772			−0.334386	+	0.942436i	$0.608529\pi$
$524$	3.21135	+	20.4875i	0.140288	+	0.895001i
$525$	24.6194	+	29.5595i	1.07448	+	1.29008i
$526$	21.4002	−	25.0159i	0.933094	−	1.09075i
$527$	−19.0413	−	10.9935i	−0.829450	−	0.478883i
$528$	−0.998505	+	15.6917i	−0.0434544	+	0.682893i
$529$	−9.95407	−	17.2410i	−0.432786	−	0.749607i
$530$	14.4959	+	2.69864i	0.629662	+	0.117221i
$531$	1.59884	−	0.491386i	0.0693836	−	0.0213243i
$532$	−4.27323	+	11.8410i	−0.185268	+	0.513374i
$533$	−5.74906	−	9.95767i	−0.249019	−	0.431314i
$534$	−0.208514	+	5.96021i	−0.00902328	+	0.257923i
$535$	8.09283	−	14.0172i	0.349883	−	0.606016i
$536$	5.96574	−	3.22064i	0.257681	−	0.139110i
$537$	−2.19511	+	5.58464i	−0.0947258	+	0.240995i
$538$	8.69564	+	24.6182i	0.374896	+	1.06137i
$539$	−0.691785	−	15.8713i	−0.0297973	−	0.683625i
$540$	21.5621	+	31.3321i	0.927883	+	1.34832i
$541$	16.4287			0.706324			0.353162	−	0.935562i	$-0.385106\pi$
$541$	16.4287			0.706324			0.353162	+	0.935562i	$0.385106\pi$
$542$	−32.6843	+	11.5447i	−1.40391	+	0.495888i
$543$	7.83072	−	19.9224i	0.336049	−	0.854953i
$544$	−18.2754	+	2.33176i	−0.783551	+	0.0999735i
$545$	37.7463	+	21.7928i	1.61687	+	0.933503i
$546$	−28.7403	−	0.379114i	−1.22997	−	0.0162246i
$547$	24.8523	−	14.3485i	1.06261	−	0.613496i	0.136455	−	0.990646i	$-0.456429\pi$
$547$	24.8523	−	14.3485i	1.06261	−	0.613496i	0.926152	+	0.377150i	$0.123096\pi$
$548$	0.314958	+	0.121479i	0.0134543	+	0.00518932i
$549$	−1.13301	−	0.259820i	−0.0483555	−	0.0110889i
$550$	−26.4879	−	4.93113i	−1.12945	−	0.210264i
$551$	8.87988	+	15.3804i	0.378296	+	0.655227i
$552$	−8.55173	+	1.03560i	−0.363986	+	0.0440781i
$553$	−3.24767	+	5.91921i	−0.138105	+	0.251710i
$554$	−11.5810	−	9.90715i	−0.492031	−	0.420915i
$555$	−34.8507	−	43.7473i	−1.47933	−	1.85697i
$556$	−0.468201	−	2.98699i	−0.0198562	−	0.126677i
$557$	24.7566			1.04897			0.524485	−	0.851420i	$-0.324258\pi$
$557$	24.7566			1.04897			0.524485	+	0.851420i	$0.324258\pi$
$558$	23.0126	−	17.0524i	0.974200	−	0.721884i
$559$	32.1451			1.35959
$560$	7.34752	−	38.0292i	0.310489	−	1.60703i
$561$	−1.90160	−	12.6602i	−0.0802857	−	0.534515i
$562$	−10.9059	−	9.32957i	−0.460036	−	0.393544i
$563$	1.07636	−	1.86431i	0.0453633	−	0.0785715i	−0.842452	−	0.538771i	$-0.818889\pi$
$563$	1.07636	−	1.86431i	0.0453633	−	0.0785715i	0.887816	+	0.460200i	$0.152222\pi$
$564$	−20.2064	−	18.5479i	−0.850845	−	0.781007i
$565$	−4.64751	+	2.68324i	−0.195522	+	0.112885i
$566$	−3.51774	+	18.8958i	−0.147862	+	0.794248i
$567$	−13.7993	−	19.4057i	−0.579515	−	0.814961i
$568$	−22.7148	−	13.9946i	−0.953090	−	0.587202i
$569$	23.4597	+	40.6335i	0.983484	+	1.70344i	0.648489	+	0.761224i	$0.275401\pi$
$569$	23.4597	+	40.6335i	0.983484	+	1.70344i	0.334994	+	0.942220i	$0.391266\pi$
$570$	−18.0859	−	11.3029i	−0.757535	−	0.473427i
$571$	8.36084	+	4.82713i	0.349890	+	0.202009i	0.664637	−	0.747166i	$-0.268586\pi$
$571$	8.36084	+	4.82713i	0.349890	+	0.202009i	−0.314747	+	0.949176i	$0.601920\pi$
$572$	15.6648	−	12.6437i	0.654977	−	0.528659i
$573$	6.05681	−	0.909752i	0.253027	−	0.0380054i
$574$	−9.07401	+	3.42916i	−0.378742	+	0.143130i
$575$		−	14.7609i		−	0.615573i
$576$	6.69192	−	23.0482i	0.278830	−	0.960340i
$577$		−	28.4843i		−	1.18582i	−0.805269	−	0.592909i	$-0.797979\pi$
$577$		−	28.4843i		−	1.18582i	0.805269	−	0.592909i	$-0.202021\pi$
$578$	−8.52476	+	3.01111i	−0.354583	+	0.125246i
$579$	−19.5899	+	15.6060i	−0.814127	+	0.648564i
$580$	−34.3203	−	42.5208i	−1.42507	−	1.76558i
$581$	−19.4173	−	10.6536i	−0.805564	−	0.441986i
$582$	13.6679	−	7.26626i	0.566555	−	0.301196i
$583$	5.59912	−	3.23266i	0.231892	−	0.133883i
$584$	−30.1123	−	18.5523i	−1.24606	−	0.767699i
$585$	10.8843	−	47.4637i	0.450012	−	1.96238i
$586$	26.7212	+	4.97457i	1.10384	+	0.205498i
$587$	1.98771	+	3.44281i	0.0820415	+	0.142100i	0.904127	−	0.427264i	$-0.140523\pi$
$587$	1.98771	+	3.44281i	0.0820415	+	0.142100i	−0.822085	+	0.569364i	$0.807189\pi$
$588$	−4.23310	+	23.8764i	−0.174570	+	0.984645i
$589$	−8.03030	+	13.9089i	−0.330883	+	0.573106i
$590$	1.87592	−	2.19287i	0.0772303	−	0.0902788i
$591$	18.8550	+	7.41116i	0.775591	+	0.304855i
$592$	−7.44823	+	34.4986i	−0.306120	+	1.41788i
$593$			1.41069i			0.0579302i	0.999580	+	0.0289651i	$0.00922116\pi$
$593$			1.41069i			0.0579302i	−0.999580	+	0.0289651i	$0.990779\pi$
$594$	16.1150	+	4.29370i	0.661207	+	0.176173i
$595$	0.686804	+	31.5290i	0.0281562	+	1.29256i
$596$	−1.96510	−	12.5368i	−0.0804938	−	0.513527i
$597$	−29.8270	−	11.7238i	−1.22074	−	0.479825i
$598$	8.38065	+	7.16934i	0.342710	+	0.293176i
$599$	25.5912	+	14.7751i	1.04563	+	0.603694i	0.921422	−	0.388562i	$-0.127028\pi$
$599$	25.5912	+	14.7751i	1.04563	+	0.603694i	0.124206	+	0.992256i	$0.460361\pi$
$600$	37.8293	+	16.1318i	1.54437	+	0.658579i
$601$	1.59490	−	0.920819i	0.0650575	−	0.0375610i	−0.467118	−	0.884195i	$-0.654708\pi$
$601$	1.59490	−	0.920819i	0.0650575	−	0.0375610i	0.532176	+	0.846634i	$0.321374\pi$
$602$	4.38157	−	26.7628i	0.178579	−	1.09077i
$603$	−2.11251	−	6.87351i	−0.0860279	−	0.279911i
$604$	−7.27909	+	18.8725i	−0.296182	+	0.767911i
$605$	18.5401	−	10.7041i	0.753762	−	0.435185i
$606$	23.4739	−	12.4794i	0.953563	−	0.506941i
$607$	−21.9193	+	37.9654i	−0.889678	+	1.54097i	−0.0494224	+	0.998778i	$0.515738\pi$
$607$	−21.9193	+	37.9654i	−0.889678	+	1.54097i	−0.840256	+	0.542190i	$0.817595\pi$
$608$	1.70326	+	13.3495i	0.0690764	+	0.541392i
$609$	21.8935	+	26.2867i	0.887169	+	1.06519i
$610$	−1.89099	+	0.667937i	−0.0765641	+	0.0270440i
$611$			35.1168i			1.42068i
$612$	−1.36560	+	19.4934i	−0.0552009	+	0.787972i
$613$	13.5016			0.545324			0.272662	−	0.962110i	$-0.412096\pi$
$613$	13.5016			0.545324			0.272662	+	0.962110i	$0.412096\pi$
$614$	8.67194	−	3.06310i	0.349971	−	0.123617i
$615$	−2.44109	−	16.2519i	−0.0984343	−	0.655342i
$616$	−8.39145	−	14.7653i	−0.338101	−	0.594911i
$617$	−7.72808	+	13.3854i	−0.311121	+	0.538877i	−0.978605	−	0.205746i	$-0.934038\pi$
$617$	−7.72808	+	13.3854i	−0.311121	+	0.538877i	0.667484	+	0.744624i	$0.267371\pi$
$618$	−6.57279	+	10.5172i	−0.264396	+	0.423063i
$619$	21.2265	+	36.7654i	0.853167	+	1.47773i	0.878335	+	0.478045i	$0.158654\pi$
$619$	21.2265	+	36.7654i	0.853167	+	1.47773i	−0.0251688	+	0.999683i	$0.508012\pi$
$620$	17.7826	−	46.1049i	0.714167	−	1.85162i
$621$	−0.696760	+	9.11014i	−0.0279600	+	0.365578i
$622$	6.85124	−	36.8018i	0.274710	−	1.47562i
$623$	−3.34158	−	5.50721i	−0.133877	−	0.220642i
$624$	−27.5326	+	13.6427i	−1.10218	+	0.546147i
$625$	−1.74856	+	3.02860i	−0.0699425	+	0.121144i
$626$	−32.0466	+	37.4611i	−1.28084	+	1.49725i
$627$	−9.24779	+	1.38905i	−0.369321	+	0.0554732i
$628$	−29.4939	+	4.62307i	−1.17693	+	0.184481i
$629$		−	28.7364i		−	1.14580i
$630$	−38.0329	−	15.5315i	−1.51527	−	0.618789i
$631$		−	9.06801i		−	0.360992i	−0.983576	−	0.180496i	$-0.942230\pi$
$631$		−	9.06801i		−	0.360992i	0.983576	−	0.180496i	$-0.0577703\pi$
$632$	−0.206235	+	7.21484i	−0.00820358	+	0.286991i
$633$	−14.3827	−	18.0543i	−0.571662	−	0.717593i
$634$	−25.8972	−	22.1541i	−1.02851	−	0.879852i
$635$	16.0418	−	27.7852i	0.636599	−	1.10262i
$636$	−9.41436	+	2.95941i	−0.373304	+	0.117348i
$637$	26.1849	−	16.6789i	1.03748	−	0.660843i
$638$	−23.5551	−	4.38515i	−0.932556	−	0.173610i
$639$	−19.2688	+	20.7243i	−0.762263	+	0.819842i
$640$	−11.5379	−	39.7667i	−0.456076	−	1.57192i
$641$	−3.09934	−	5.36821i	−0.122416	−	0.212032i	0.798304	−	0.602255i	$-0.205731\pi$
$641$	−3.09934	−	5.36821i	−0.122416	−	0.212032i	−0.920720	+	0.390224i	$0.872398\pi$
$642$	−0.378746	+	10.8262i	−0.0149479	+	0.427274i
$643$	−16.0245	+	27.7553i	−0.631946	+	1.09456i	0.355207	+	0.934788i	$0.384410\pi$
$643$	−16.0245	+	27.7553i	−0.631946	+	1.09456i	−0.987153	+	0.159776i	$0.948923\pi$
$644$	7.11125	−	6.00019i	0.280222	−	0.236440i
$645$	42.7604	+	16.8074i	1.68369	+	0.661792i
$646$	−3.64941	−	10.3318i	−0.143584	−	0.406501i
$647$	31.9271			1.25518			0.627592	−	0.778543i	$-0.284041\pi$
$647$	31.9271			1.25518			0.627592	+	0.778543i	$0.284041\pi$
$648$	−22.5860	−	11.7419i	−0.887262	−	0.461265i
$649$		−	1.26534i		−	0.0496691i
$650$	−17.5362	−	49.6468i	−0.687828	−	1.94731i
$651$	−10.6875	+	29.0322i	−0.418876	+	1.13786i
$652$	10.8188	+	13.4039i	0.423697	+	0.524935i
$653$	20.5776	−	35.6414i	0.805262	−	1.39476i	−0.110851	−	0.993837i	$-0.535358\pi$
$653$	20.5776	−	35.6414i	0.805262	−	1.39476i	0.916114	−	0.400918i	$-0.131309\pi$
$654$	−29.1533	−	1.01991i	−1.13998	−	0.0398816i
$655$	32.8644	−	18.9743i	1.28412	−	0.741387i
$656$	−6.96355	+	7.68427i	−0.271881	+	0.300021i
$657$	−25.5441	+	27.4737i	−0.996572	+	1.07185i
$658$	29.2370	+	4.78663i	1.13978	+	0.186602i
$659$	−34.8561	+	20.1242i	−1.35780	+	0.783926i	−0.989327	−	0.145713i	$-0.953452\pi$
$659$	−34.8561	+	20.1242i	−1.35780	+	0.783926i	−0.368472	+	0.929639i	$0.620119\pi$
$660$	27.4486	−	8.62850i	1.06844	−	0.335864i
$661$	15.3891	+	8.88491i	0.598567	+	0.345583i	0.768478	−	0.639877i	$-0.221015\pi$
$661$	15.3891	+	8.88491i	0.598567	+	0.345583i	−0.169911	+	0.985459i	$0.554348\pi$
$662$	8.99557	−	10.5154i	0.349623	−	0.408694i
$663$	19.5683	−	15.5888i	0.759969	−	0.605420i
$664$	−23.6674	−	0.676528i	−0.918474	−	0.0262544i
$665$	23.0307	−	0.501683i	0.893093	−	0.0194545i
$666$	34.3396	+	14.9039i	1.33063	+	0.577513i
$667$		−	13.1266i		−	0.508263i
$668$	−7.63997	−	48.7409i	−0.295599	−	1.88584i
$669$	5.06573	+	33.7259i	0.195852	+	1.30392i
$670$	−9.42729	−	8.06470i	−0.364208	−	0.311567i
$671$	−0.439680	+	0.761548i	−0.0169737	+	0.0293992i
$672$	7.60559	+	24.7822i	0.293392	+	0.955992i
$673$	7.70235	+	13.3409i	0.296904	+	0.514253i	0.975426	−	0.220327i	$-0.0707125\pi$
$673$	7.70235	+	13.3409i	0.296904	+	0.514253i	−0.678522	+	0.734580i	$0.737379\pi$
$674$	0.837756	−	4.50006i	0.0322691	−	0.173336i
$675$	24.6272	−	36.0028i	0.947903	−	1.38575i
$676$	12.4466	+	4.80062i	0.478714	+	0.184639i
$677$	1.45386	−	0.839389i	0.0558766	−	0.0322604i	−0.471801	−	0.881705i	$-0.656396\pi$
$677$	1.45386	−	0.839389i	0.0558766	−	0.0322604i	0.527678	+	0.849444i	$0.323063\pi$
$678$	1.90350	−	3.04581i	0.0731035	−	0.116973i
$679$	−8.04250	+	14.6583i	−0.308643	+	0.562533i
$680$	16.0158	+	29.6669i	0.614179	+	1.13767i
$681$	4.55249	+	30.3089i	0.174452	+	1.16144i
$682$	−7.21643	−	20.4304i	−0.276331	−	0.782322i
$683$			23.5509i			0.901150i	0.892739	+	0.450575i	$0.148781\pi$
$683$			23.5509i			0.901150i	−0.892739	+	0.450575i	$0.851219\pi$
$684$	14.2391	+	0.997514i	0.544447	+	0.0381409i
$685$		−	0.617737i		−	0.0236025i
$686$	−10.3171	−	24.0740i	−0.393908	−	0.919150i
$687$	−14.6979	−	18.4499i	−0.560758	−	0.703907i
$688$	−8.87071	−	27.6011i	−0.338193	−	1.05228i
$689$	10.9420	+	6.31737i	0.416857	+	0.240673i
$690$	7.39961	+	13.9188i	0.281698	+	0.529879i
$691$	−21.3374	−	36.9574i	−0.811713	−	1.40593i	−0.911665	−	0.410935i	$-0.865202\pi$
$691$	−21.3374	−	36.9574i	−0.811713	−	1.40593i	0.0999520	−	0.994992i	$-0.468131\pi$
$692$	−6.96655	+	18.0621i	−0.264828	+	0.686620i
$693$	−17.0992	+	5.66569i	−0.649547	+	0.215222i
$694$	−11.5171	−	2.14408i	−0.437181	−	0.0813882i
$695$	−4.79150	+	2.76637i	−0.181752	+	0.104935i
$696$	33.6408	+	14.3457i	1.27515	+	0.543772i
$697$	4.22174	−	7.31227i	0.159910	−	0.276972i
$698$	25.0914	−	29.3307i	0.949723	−	1.11018i
$699$	−18.3210	−	7.20127i	−0.692963	−	0.272377i
$700$	−43.7244	+	7.83285i	−1.65263	+	0.296054i
$701$	−1.35789			−0.0512869			−0.0256434	−	0.999671i	$-0.508163\pi$
$701$	−1.35789			−0.0512869			−0.0256434	+	0.999671i	$0.508163\pi$
$702$	8.47953	+	31.4688i	0.320039	+	1.18771i
$703$	−20.9908			−0.791685
$704$	−15.1792	−	9.96127i	−0.572088	−	0.375429i
$705$	−18.3612	+	46.7135i	−0.691524	+	1.75933i
$706$	−21.8226	+	25.5096i	−0.821303	+	0.960068i
$707$	−13.8125	+	25.1748i	−0.519474	+	0.946794i
$708$	−0.419658	+	1.88526i	−0.0157717	+	0.0708524i
$709$	−3.58536	−	6.21002i	−0.134651	−	0.233222i	0.790813	−	0.612058i	$-0.209658\pi$
$709$	−3.58536	−	6.21002i	−0.134651	−	0.233222i	−0.925464	+	0.378835i	$0.876325\pi$
$710$	−8.93551	+	47.9976i	−0.335344	+	1.80132i
$711$	7.46194	+	1.71117i	0.279844	+	0.0641737i
$712$	−5.86303	−	3.61223i	−0.219726	−	0.135374i
$713$	10.2803	−	5.93535i	0.385001	−	0.222281i
$714$	−10.3114	−	18.4167i	−0.385894	−	0.689226i
$715$	−31.9027	−	18.4190i	−1.19309	−	0.688832i
$716$	−4.35186	−	5.39169i	−0.162636	−	0.201497i
$717$	−12.2572	−	15.3862i	−0.457755	−	0.574608i
$718$	11.2493	+	31.8480i	0.419822	+	1.18856i
$719$	19.8003			0.738427			0.369213	−	0.929345i	$-0.379627\pi$
$719$	19.8003			0.738427			0.369213	+	0.929345i	$0.379627\pi$
$720$	−43.7579	+	3.75227i	−1.63076	+	0.139839i
$721$	−0.291735	−	13.3926i	−0.0108648	−	0.498768i
$722$	17.7890	−	6.28342i	0.662037	−	0.233845i
$723$	27.7403	−	4.16668i	1.03167	−	0.154960i
$724$	15.5246	+	19.2341i	0.576968	+	0.714829i
$725$	−31.3340	+	54.2720i	−1.16371	+	2.01561i
$726$	−7.59355	+	12.1505i	−0.281823	+	0.450947i
$727$	2.03980	+	3.53303i	0.0756519	+	0.131033i	0.901370	−	0.433051i	$-0.142563\pi$
$727$	2.03980	+	3.53303i	0.0756519	+	0.131033i	−0.825718	+	0.564084i	$0.809230\pi$
$728$	16.7896	−	28.6293i	0.622265	−	1.06107i
$729$	−16.8989	+	21.0577i	−0.625885	+	0.779916i
$730$	−11.8455	+	63.6291i	−0.438423	+	2.35502i
$731$	11.8027	+	20.4428i	0.436537	+	0.756104i
$732$	0.907659	−	0.988822i	0.0335480	−	0.0365479i
$733$	−22.5634	−	13.0270i	−0.833397	−	0.481162i	0.0216173	−	0.999766i	$-0.493118\pi$
$733$	−22.5634	−	13.0270i	−0.833397	−	0.481162i	−0.855014	+	0.518604i	$0.826452\pi$
$734$	15.8480	+	13.5574i	0.584961	+	0.500413i
$735$	43.5527	−	8.49571i	1.60647	−	0.313369i
$736$	3.84317	−	9.17440i	0.141661	−	0.338173i
$737$	−5.43981			−0.200378
$738$	6.54849	+	8.83735i	0.241053	+	0.325307i
$739$			13.0991i			0.481858i	0.970543	+	0.240929i	$0.0774520\pi$
$739$			13.0991i			0.481858i	−0.970543	+	0.240929i	$0.922548\pi$
$740$	63.8057	−	10.0013i	2.34555	−	0.367657i
$741$	−11.3870	−	14.2939i	−0.418313	−	0.525098i
$742$	6.75107	−	8.24881i	0.247839	−	0.302823i
$743$	14.3230	+	8.26939i	0.525460	+	0.303375i	0.739166	−	0.673524i	$-0.235220\pi$
$743$	14.3230	+	8.26939i	0.525460	+	0.303375i	−0.213706	+	0.976898i	$0.568553\pi$
$744$	3.97602	+	32.8330i	0.145768	+	1.20372i
$745$	−20.1106	+	11.6108i	−0.736794	+	0.425388i
$746$	−8.57434	+	46.0576i	−0.313929	+	1.68629i
$747$	−5.61327	+	24.4780i	−0.205379	+	0.895603i
$748$	13.7924	+	5.31971i	0.504300	+	0.194508i
$749$	−6.06966	−	10.0033i	−0.221781	−	0.365514i
$750$	1.06401	−	30.4140i	0.0388523	−	1.11056i
$751$	46.5897	+	26.8986i	1.70008	+	0.981543i	0.945662	+	0.325152i	$0.105416\pi$
$751$	46.5897	+	26.8986i	1.70008	+	0.981543i	0.754421	+	0.656391i	$0.227918\pi$
$752$	30.1527	−	9.69078i	1.09956	−	0.353386i
$753$	28.7210	+	11.2891i	1.04665	+	0.411399i
$754$	−15.5946	−	44.1499i	−0.567922	−	1.60784i
$755$	37.0152			1.34712
$756$	27.3555	−	2.77036i	0.994911	−	0.100757i
$757$	47.1829			1.71489			0.857445	−	0.514575i	$-0.172050\pi$
$757$	47.1829			1.71489			0.857445	+	0.514575i	$0.172050\pi$
$758$	−5.05802	−	14.3198i	−0.183716	−	0.520117i
$759$	6.43281	+	2.52849i	0.233496	+	0.0917783i
$760$	21.6705	−	11.6989i	0.786071	−	0.424365i
$761$	15.9384	+	9.20205i	0.577767	+	0.333574i	0.760246	−	0.649636i	$-0.225079\pi$
$761$	15.9384	+	9.20205i	0.577767	+	0.333574i	−0.182478	+	0.983210i	$0.558412\pi$
$762$	−0.750759	+	21.4599i	−0.0271971	+	0.777408i
$763$	26.9375	−	16.3447i	0.975204	−	0.591719i
$764$	−2.54502	+	6.59846i	−0.0920755	+	0.238724i
$765$	34.1811	−	10.5052i	1.23582	−	0.379817i
$766$	5.99170	−	32.1848i	0.216489	−	1.16288i
$767$	2.14149	−	1.23639i	0.0773248	−	0.0446435i
$768$	19.3120	+	19.8757i	0.696863	+	0.717204i
$769$	−24.3013	−	14.0304i	−0.876327	−	0.505948i	−0.00688139	−	0.999976i	$-0.502190\pi$
$769$	−24.3013	−	14.0304i	−0.876327	−	0.505948i	−0.869446	+	0.494029i	$0.835524\pi$
$770$	−19.6835	+	24.0503i	−0.709344	+	0.866714i
$771$	−6.37034	−	7.99654i	−0.229422	−	0.287988i
$772$	−4.47856	−	28.5719i	−0.161187	−	1.02833i
$773$		−	12.5378i		−	0.450954i	−0.974249	−	0.225477i	$-0.927606\pi$
$773$		−	12.5378i		−	0.450954i	0.974249	−	0.225477i	$-0.0723940\pi$
$774$	−30.5502	+	3.50155i	−1.09810	+	0.125861i
$775$	−56.6722			−2.03573
$776$	−0.510717	+	17.8668i	−0.0183337	+	0.641379i
$777$	−39.8449	+	6.87528i	−1.42943	+	0.246649i
$778$	27.4776	+	23.5061i	0.985120	+	0.842734i
$779$	−5.34133	−	3.08382i	−0.191373	−	0.110489i
$780$	41.4236	+	38.0235i	1.48320	+	1.36146i
$781$	10.7037	+	18.5393i	0.383008	+	0.663390i
$782$	−1.48226	+	7.96205i	−0.0530055	+	0.284722i
$783$	21.9005	−	32.0165i	0.782660	−	1.14418i
$784$	−21.5471	−	17.8807i	−0.769541	−	0.638598i
$785$	27.3155	+	47.3118i	0.974931	+	1.68863i
$786$	−13.4604	+	21.5382i	−0.480118	+	0.768241i
$787$	−18.2298	+	31.5750i	−0.649824	+	1.12553i	0.333341	+	0.942806i	$0.391824\pi$
$787$	−18.2298	+	31.5750i	−0.649824	+	1.12553i	−0.983165	+	0.182721i	$0.941509\pi$
$788$	−18.2035	+	14.6928i	−0.648474	+	0.523411i
$789$	39.8721	−	5.98891i	1.41948	−	0.213211i
$790$	12.4540	−	4.39900i	0.443094	−	0.156510i
$791$	0.0844874	+	3.87855i	0.00300403	+	0.137905i
$792$	−13.5103	+	13.7227i	−0.480066	+	0.487615i
$793$	−1.71848			−0.0610249
$794$	3.29569	+	9.33043i	0.116960	+	0.331124i
$795$	11.2523	+	14.1247i	0.399077	+	0.500952i
$796$	28.7965	−	23.2428i	1.02066	−	0.823821i
$797$	37.3540	+	21.5664i	1.32315	+	0.763920i	0.984230	−	0.176896i	$-0.0566055\pi$
$797$	37.3540	+	21.5664i	1.32315	+	0.763920i	0.338919	+	0.940816i	$0.389939\pi$
$798$	−13.4527	+	7.53207i	−0.476219	+	0.266633i
$799$	−22.3327	+	12.8938i	−0.790073	+	0.456149i
$800$	−37.7895	+	28.7578i	−1.33606	+	1.01674i
$801$	−4.97359	+	5.34927i	−0.175733	+	0.189007i
$802$	8.96228	−	48.1414i	0.316469	−	1.69993i
$803$	14.1896	+	24.5771i	0.500739	+	0.867306i
$804$	8.10487	+	1.80414i	0.285837	+	0.0636272i
$805$	−14.9273	−	8.19010i	−0.526117	−	0.288663i
$806$	27.5255	−	32.1762i	0.969545	−	1.13336i
$807$	−11.6976	+	29.7603i	−0.411775	+	1.04761i
$808$	−0.877128	+	30.6852i	−0.0308573	+	1.07950i
$809$	5.55160			0.195184			0.0975919	−	0.995227i	$-0.468886\pi$
$809$	5.55160			0.195184			0.0975919	+	0.995227i	$0.468886\pi$
$810$	−5.17410	+	46.2943i	−0.181799	+	1.62662i
$811$	−24.2871			−0.852837			−0.426419	−	0.904526i	$-0.640225\pi$
$811$	−24.2871			−0.852837			−0.426419	+	0.904526i	$0.640225\pi$
$812$	−38.8832	+	6.96559i	−1.36453	+	0.244444i
$813$	−39.5111	−	15.5303i	−1.38571	−	0.544670i
$814$	18.4088	−	21.5191i	0.645230	−	0.754246i
$815$	15.7606	−	27.2981i	0.552069	−	0.956211i
$816$	−18.7852	−	12.5003i	−0.657614	−	0.437596i
$817$	14.9327	−	8.62138i	0.522428	−	0.301624i
$818$	−46.2670	−	8.61332i	−1.61769	−	0.301158i
$819$	−26.2967	−	23.4030i	−0.918881	−	0.817768i
$820$	17.7053	+	6.82892i	0.618297	+	0.238476i
$821$	−12.9220	−	22.3815i	−0.450981	−	0.781121i	0.547467	−	0.836828i	$-0.315592\pi$
$821$	−12.9220	−	22.3815i	−0.450981	−	0.781121i	−0.998447	+	0.0557061i	$0.982259\pi$
$822$	0.194075	+	0.365059i	0.00676916	+	0.0127329i
$823$	7.07009	+	4.08192i	0.246448	+	0.142287i	0.618137	−	0.786071i	$-0.287888\pi$
$823$	7.07009	+	4.08192i	0.246448	+	0.142287i	−0.371689	+	0.928357i	$0.621221\pi$
$824$	−6.80308	−	12.6016i	−0.236996	−	0.438999i
$825$	−20.5609	−	25.8096i	−0.715838	−	0.898574i
$826$	−0.737474	−	1.95145i	−0.0256600	−	0.0678997i
$827$		−	25.8783i		−	0.899875i	−0.893060	−	0.449938i	$-0.851446\pi$
$827$		−	25.8783i		−	0.899875i	0.893060	−	0.449938i	$-0.148554\pi$
$828$	−8.74577	−	5.90071i	−0.303937	−	0.205064i
$829$			38.7076i			1.34437i	0.740383	+	0.672185i	$0.234644\pi$
$829$			38.7076i			1.34437i	−0.740383	+	0.672185i	$0.765356\pi$
$830$	14.4304	+	40.8539i	0.500887	+	1.41806i
$831$	−2.77254	−	18.4586i	−0.0961784	−	0.640323i
$832$	2.02677	−	35.4229i	0.0702655	−	1.22807i
$833$	20.2213	+	10.5284i	0.700626	+	0.364788i
$834$	1.96248	−	3.14017i	0.0679550	−	0.108735i
$835$	−78.1863	+	45.1409i	−2.70575	+	1.56217i
$836$	3.88584	−	10.0748i	0.134395	−	0.348444i
$837$	34.9770	+	2.67510i	1.20898	+	0.0924650i
$838$	−5.61670	+	30.1705i	−0.194026	+	1.04222i
$839$	−5.28225	−	9.14913i	−0.182364	−	0.315863i	0.760321	−	0.649547i	$-0.225041\pi$
$839$	−5.28225	−	9.14913i	−0.182364	−	0.315863i	−0.942685	+	0.333684i	$0.891708\pi$
$840$	37.3032	−	29.3049i	1.28708	−	1.01111i
$841$	−13.3646	+	23.1482i	−0.460850	+	0.798215i
$842$	−1.97149	−	1.68654i	−0.0679422	−	0.0581221i
$843$	−2.61091	−	17.3825i	−0.0899244	−	0.598685i
$844$	26.3323	−	4.12750i	0.906395	−	0.142074i
$845$		−	24.4119i		−	0.839793i
$846$	−3.82526	−	33.3744i	−0.131515	−	1.14744i
$847$	−0.337042	−	15.4725i	−0.0115809	−	0.531642i
$848$	2.40481	−	11.1386i	0.0825816	−	0.382500i
$849$	−18.4119	+	14.6676i	−0.631894	+	0.503391i
$850$	25.1343	−	29.3810i	0.862101	−	1.00776i
$851$	13.4362	+	7.75737i	0.460585	+	0.265919i
$852$	−9.79895	−	31.1720i	−0.335707	−	1.06794i
$853$	−25.1074	+	14.4958i	−0.859661	+	0.496326i	−0.863899	−	0.503665i	$-0.831985\pi$
$853$	−25.1074	+	14.4958i	−0.859661	+	0.496326i	0.00423747	+	0.999991i	$0.498651\pi$
$854$	−0.234238	+	1.43074i	−0.00801547	+	0.0489589i
$855$	−7.67365	−	24.9680i	−0.262433	−	0.853886i
$856$	−10.6497	−	6.56128i	−0.363998	−	0.224260i
$857$	14.4122	−	8.32088i	0.492311	−	0.284236i	−0.233222	−	0.972424i	$-0.574927\pi$
$857$	14.4122	−	8.32088i	0.492311	−	0.284236i	0.725533	+	0.688188i	$0.241593\pi$
$858$	24.6400	+	0.862013i	0.841195	+	0.0294286i
$859$	−1.23313	+	2.13585i	−0.0420740	+	0.0728742i	−0.886296	−	0.463120i	$-0.846730\pi$
$859$	−1.23313	+	2.13585i	−0.0420740	+	0.0728742i	0.844222	+	0.535994i	$0.180063\pi$
$860$	−41.2830	+	33.3212i	−1.40774	+	1.13624i
$861$	−11.1490	−	4.10424i	−0.379957	−	0.139872i
$862$	7.92690	+	22.4418i	0.269991	+	0.764372i
$863$		−	26.6113i		−	0.905857i	−0.891547	−	0.452929i	$-0.850379\pi$
$863$		−	26.6113i		−	0.905857i	0.891547	−	0.452929i	$-0.149621\pi$
$864$	24.6804	−	15.9649i	0.839643	−	0.543138i
$865$	35.4259			1.20452
$866$	−2.05330	−	5.81309i	−0.0697739	−	0.197537i
$867$	−10.3053	−	4.05062i	−0.349987	−	0.137566i
$868$	−23.0368	−	27.3025i	−0.781919	−	0.926707i
$869$	2.89572	−	5.01553i	0.0982304	−	0.170140i
$870$	2.33987	−	66.8833i	0.0793290	−	2.26756i
$871$	−5.31534	−	9.20643i	−0.180103	−	0.311948i
$872$	17.6686	−	28.6780i	0.598334	−	0.971160i
$873$	18.4787	+	4.23751i	0.625408	+	0.143418i
$874$	5.81597	+	1.08273i	0.196728	+	0.0366240i
$875$	17.0515	+	28.1024i	0.576447	+	0.950035i
$876$	−12.9902	−	41.3239i	−0.438898	−	1.39620i
$877$	−25.0364	+	43.3644i	−0.845420	+	1.46431i	0.0398359	+	0.999206i	$0.487316\pi$
$877$	−25.0364	+	43.3644i	−0.845420	+	1.46431i	−0.885256	+	0.465104i	$0.846017\pi$
$878$	−25.1124	−	21.4827i	−0.847501	−	0.725006i
$879$	20.7420	+	26.0370i	0.699611	+	0.878205i
$880$	−7.01150	+	32.4758i	−0.236358	+	1.09476i
$881$			9.88180i			0.332926i	0.986048	+	0.166463i	$0.0532347\pi$
$881$			9.88180i			0.332926i	−0.986048	+	0.166463i	$0.946765\pi$
$882$	−23.0689	+	18.7037i	−0.776769	+	0.629785i
$883$		−	6.15276i		−	0.207057i	−0.994626	−	0.103529i	$-0.966987\pi$
$883$		−	6.15276i		−	0.207057i	0.994626	−	0.103529i	$-0.0330133\pi$
$884$	4.47363	+	28.5405i	0.150464	+	0.959920i
$885$	3.49514	−	0.524980i	0.117488	−	0.0176470i
$886$	−6.79679	+	7.94516i	−0.228343	+	0.266923i
$887$	13.5919	−	23.5418i	0.456370	−	0.790456i	−0.542396	−	0.840123i	$-0.682483\pi$
$887$	13.5919	−	23.5418i	0.456370	−	0.790456i	0.998766	+	0.0496668i	$0.0158159\pi$
$888$	−34.5646	+	25.9564i	−1.15991	+	0.871039i
$889$	−12.0314	−	19.8288i	−0.403521	−	0.665037i
$890$	−2.30639	+	12.3889i	−0.0773105	+	0.415278i
$891$	11.4715	+	16.8997i	0.384309	+	0.566161i
$892$	−36.7419	−	14.1713i	−1.23021	−	0.474490i
$893$	9.41840	+	16.3131i	0.315175	+	0.545899i
$894$	8.23677	−	13.1797i	0.275479	−	0.440796i
$895$	−6.33968	+	10.9806i	−0.211912	+	0.367042i
$896$	−29.2155	−	6.51575i	−0.976021	−	0.217676i
$897$	2.00636	+	13.3576i	0.0669903	+	0.445998i
$898$	32.0746	−	11.3294i	1.07034	−	0.378066i
$899$	−50.3974			−1.68085
$900$	22.0741	+	45.2733i	0.735805	+	1.50911i
$901$			9.27815i			0.309100i
$902$	7.84574	−	2.77127i	0.261235	−	0.0922732i
$903$	25.5215	−	21.2562i	0.849301	−	0.707361i
$904$	1.97019	+	3.64948i	0.0655276	+	0.121380i
$905$	22.6159	−	39.1719i	0.751778	−	1.30212i
$906$	−21.8746	+	11.6291i	−0.726734	+	0.386352i
$907$	−12.8198	+	7.40152i	−0.425675	+	0.245763i	−0.697502	−	0.716583i	$-0.745705\pi$
$907$	−12.8198	+	7.40152i	−0.425675	+	0.245763i	0.271828	+	0.962346i	$0.412372\pi$
$908$	−33.0194	−	12.7355i	−1.09579	−	0.422643i
$909$	31.7360	+	7.27769i	1.05262	+	0.241386i
$910$	−59.9363	−	9.81268i	−1.98687	−	0.325287i
$911$	43.3054	−	25.0024i	1.43477	−	0.828366i	0.437292	−	0.899319i	$-0.355937\pi$
$911$	43.3054	−	25.0024i	1.43477	−	0.828366i	0.997480	+	0.0709534i	$0.0226042\pi$
$912$	−9.13094	+	13.7219i	−0.302356	+	0.454377i
$913$	16.4528	+	9.49905i	0.544509	+	0.314373i
$914$	3.03995	+	2.60057i	0.100553	+	0.0860191i
$915$	−2.28597	−	0.898525i	−0.0755718	−	0.0297043i
$916$	26.9093	−	4.21794i	0.889108	−	0.139365i
$917$	−0.597445	−	27.4268i	−0.0197294	−	0.905714i
$918$	−16.8993	+	16.9469i	−0.557759	+	0.559332i
$919$		−	13.7069i		−	0.452148i	−0.974110	−	0.226074i	$-0.927411\pi$
$919$		−	13.7069i		−	0.452148i	0.974110	−	0.226074i	$-0.0725892\pi$
$920$	−18.1946	−	0.520090i	−0.599860	−	0.0171469i
$921$	10.4833	+	4.12056i	0.345435	+	0.135777i
$922$	−15.3409	+	17.9329i	−0.505226	+	0.590587i
$923$	−20.9175	+	36.2302i	−0.688509	+	1.19253i
$924$	4.07625	−	20.3968i	0.134099	−	0.671006i
$925$	−37.0346	−	64.1459i	−1.21769	−	2.10910i
$926$	38.7417	+	7.21237i	1.27313	+	0.237013i
$927$	−14.5192	+	4.46232i	−0.476872	+	0.146562i
$928$	−33.6054	+	25.5737i	−1.10315	+	0.839497i
$929$	−11.4091	+	6.58706i	−0.374321	+	0.216114i	−0.675344	−	0.737502i	$-0.736005\pi$
$929$	−11.4091	+	6.58706i	−0.374321	+	0.216114i	0.301024	+	0.953617i	$0.402672\pi$
$930$	53.4389	−	28.4096i	1.75233	−	0.931589i
$931$	7.69060	−	14.7709i	0.252049	−	0.484095i
$932$	17.6880	−	14.2767i	0.579389	−	0.467649i
$933$	35.8595	−	28.5670i	1.17399	−	0.935241i
$934$	−6.06540	+	2.14242i	−0.198466	+	0.0701021i
$935$		−	27.0515i		−	0.884678i
$936$	−36.4257	−	9.45631i	−1.19061	−	0.309089i
$937$		−	5.56332i		−	0.181746i	−0.995863	−	0.0908728i	$-0.971034\pi$
$937$		−	5.56332i		−	0.181746i	0.995863	−	0.0908728i	$-0.0289657\pi$
$938$	−8.38944	+	3.17046i	−0.273925	+	0.103519i
$939$	−59.7081	+	8.96834i	−1.94850	+	0.292671i
$940$	−36.4017	−	45.0995i	−1.18729	−	1.47098i
$941$	15.1652	+	8.75562i	0.494371	+	0.285425i	0.726386	−	0.687287i	$-0.241199\pi$
$941$	15.1652	+	8.75562i	0.494371	+	0.285425i	−0.232015	+	0.972712i	$0.574532\pi$
$942$	−31.0064	−	19.3777i	−1.01024	−	0.631359i
$943$	2.27931	+	3.94788i	0.0742245	+	0.128561i
$944$	−1.65258	−	1.49758i	−0.0537868	−	0.0487420i
$945$	−22.7441	−	44.8809i	−0.739866	−	1.45998i
$946$	−4.25750	+	22.8694i	−0.138423	+	0.743548i
$947$	16.9009	−	9.75776i	0.549206	−	0.317084i	−0.199595	−	0.979878i	$-0.563963\pi$
$947$	16.9009	−	9.75776i	0.549206	−	0.317084i	0.748802	+	0.662794i	$0.230629\pi$
$948$	−5.97780	+	6.51234i	−0.194150	+	0.211511i
$949$	−27.7298	+	48.0294i	−0.900147	+	1.55910i
$950$	−21.4616	−	18.3596i	−0.696307	−	0.595666i
$951$	−6.19988	−	41.2767i	−0.201045	−	1.33849i
$952$	24.3715	+	0.165661i	0.789885	+	0.00536909i
$953$	−29.2232			−0.946631			−0.473316	−	0.880893i	$-0.656943\pi$
$953$	−29.2232			−0.946631			−0.473316	+	0.880893i	$0.656943\pi$
$954$	−11.0872	−	4.81201i	−0.358963	−	0.155795i
$955$	12.9418			0.418786
$956$	22.4409	−	3.51754i	0.725790	−	0.113765i
$957$	−18.2844	−	22.9519i	−0.591050	−	0.741930i
$958$	27.8862	+	23.8556i	0.900962	+	0.770740i
$959$	−0.391509	−	0.214808i	−0.0126425	−	0.00693652i
$960$	21.2173	−	46.0608i	0.684786	−	1.48661i
$961$	−7.28784	−	12.6229i	−0.235092	−	0.407191i
$962$	54.4070	+	10.1287i	1.75415	+	0.326563i
$963$	−9.03406	+	9.71646i	−0.291118	+	0.313108i
$964$	−11.6562	+	30.2211i	−0.375422	+	0.973355i
$965$	−45.8329	+	26.4616i	−1.47541	+	0.851830i
$966$	11.3945	+	0.150306i	0.366613	+	0.00483601i
$967$	−20.7917	−	12.0041i	−0.668616	−	0.386026i	0.126936	−	0.991911i	$-0.459486\pi$
$967$	−20.7917	−	12.0041i	−0.668616	−	0.386026i	−0.795552	+	0.605885i	$0.792819\pi$
$968$	−7.85960	−	14.5587i	−0.252617	−	0.467934i
$969$	4.90928	−	12.4899i	0.157709	−	0.401233i
$970$	30.8410	−	10.8936i	0.990245	−	0.349774i
$971$	40.8430			1.31071			0.655356	−	0.755320i	$-0.272518\pi$
$971$	40.8430			1.31071			0.655356	+	0.755320i	$0.272518\pi$
$972$	−11.4867	−	28.9837i	−0.368435	−	0.929653i
$973$	0.0871050	+	3.99872i	0.00279246	+	0.128193i
$974$	−8.13406	−	23.0283i	−0.260632	−	0.737875i
$975$	23.5902	−	60.0166i	0.755491	−	1.92207i
$976$	0.474228	+	1.47555i	0.0151797	+	0.0472313i
$977$	6.50642	−	11.2694i	0.208159	−	0.360541i	−0.742976	−	0.669318i	$-0.766586\pi$
$977$	6.50642	−	11.2694i	0.208159	−	0.360541i	0.951135	+	0.308777i	$0.0999196\pi$
$978$	−0.737598	+	21.0837i	−0.0235858	+	0.674181i
$979$	2.76279	+	4.78529i	0.0882992	+	0.152939i
$980$	−16.3393	+	48.5632i	−0.521941	+	1.55129i
$981$	−26.1650	−	24.3274i	−0.835385	−	0.776715i
$982$	50.9765	+	9.49007i	1.62673	+	0.302840i
$983$	24.3270	+	42.1356i	0.775910	+	1.34392i	0.934282	+	0.356536i	$0.116042\pi$
$983$	24.3270	+	42.1356i	0.775910	+	1.34392i	−0.158371	+	0.987380i	$0.550624\pi$
$984$	−12.6086	+	1.52688i	−0.401948	+	0.0486752i
$985$	37.0731	+	21.4042i	1.18125	+	0.681993i
$986$	22.3514	−	26.1279i	0.711815	−	0.832081i
$987$	23.2212	+	27.8808i	0.739140	+	0.887457i
$988$	20.8477	−	3.26781i	0.663254	−	0.103963i
$989$	−12.7445			−0.405250
$990$	32.3261	+	14.0300i	1.02739	+	0.445902i
$991$		−	54.2040i		−	1.72185i	−0.508733	−	0.860924i	$-0.669886\pi$
$991$		−	54.2040i		−	1.72185i	0.508733	−	0.860924i	$-0.330114\pi$
$992$	−35.2236	−	14.7552i	−1.11835	−	0.468480i
$993$	16.7602	−	2.51743i	0.531869	−	0.0798884i
$994$	27.3127	+	22.3535i	0.866308	+	0.709011i
$995$	−58.6466	−	33.8596i	−1.85922	−	1.07342i
$996$	−21.3630	−	19.6095i	−0.676911	−	0.621350i
$997$	15.7773	−	9.10904i	0.499673	−	0.288486i	−0.228906	−	0.973449i	$-0.573515\pi$
$997$	15.7773	−	9.10904i	0.499673	−	0.288486i	0.728578	+	0.684962i	$0.240181\pi$
$998$	19.4897	+	3.62831i	0.616935	+	0.114852i
$999$	19.8292	+	41.3377i	0.627367	+	1.30787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.139.5	✓	80
3.2	odd	2		756.2.bi.c.307.36		80
4.3	odd	2	inner	252.2.bi.c.139.36	yes	80
7.6	odd	2	inner	252.2.bi.c.139.6	yes	80
9.2	odd	6		756.2.bi.c.559.5		80
9.7	even	3	inner	252.2.bi.c.223.35	yes	80
12.11	even	2		756.2.bi.c.307.6		80
21.20	even	2		756.2.bi.c.307.35		80
28.27	even	2	inner	252.2.bi.c.139.35	yes	80
36.7	odd	6	inner	252.2.bi.c.223.6	yes	80
36.11	even	6		756.2.bi.c.559.35		80
63.20	even	6		756.2.bi.c.559.6		80
63.34	odd	6	inner	252.2.bi.c.223.36	yes	80
84.83	odd	2		756.2.bi.c.307.5		80
252.83	odd	6		756.2.bi.c.559.36		80
252.223	even	6	inner	252.2.bi.c.223.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.5	✓	80	1.1	even	1	trivial
252.2.bi.c.139.6	yes	80	7.6	odd	2	inner
252.2.bi.c.139.35	yes	80	28.27	even	2	inner
252.2.bi.c.139.36	yes	80	4.3	odd	2	inner
252.2.bi.c.223.5	yes	80	252.223	even	6	inner
252.2.bi.c.223.6	yes	80	36.7	odd	6	inner
252.2.bi.c.223.35	yes	80	9.7	even	3	inner
252.2.bi.c.223.36	yes	80	63.34	odd	6	inner
756.2.bi.c.307.5		80	84.83	odd	2
756.2.bi.c.307.6		80	12.11	even	2
756.2.bi.c.307.35		80	21.20	even	2
756.2.bi.c.307.36		80	3.2	odd	2
756.2.bi.c.559.5		80	9.2	odd	6
756.2.bi.c.559.6		80	63.20	even	6
756.2.bi.c.559.35		80	36.11	even	6
756.2.bi.c.559.36		80	252.83	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33347 + 0.471009i) q^{2} +(-1.61200 - 0.633613i) q^{3} +(1.55630 - 1.25616i) q^{4} +(-3.16954 - 1.82994i) q^{5} +(2.44799 + 0.0856414i) q^{6} +(-2.26193 + 1.37246i) q^{7} +(-1.48363 + 2.40808i) q^{8} +(2.19707 + 2.04277i) q^{9} +O(q^{10})\)	\(q+(-1.33347 + 0.471009i) q^{2} +(-1.61200 - 0.633613i) q^{3} +(1.55630 - 1.25616i) q^{4} +(-3.16954 - 1.82994i) q^{5} +(2.44799 + 0.0856414i) q^{6} +(-2.26193 + 1.37246i) q^{7} +(-1.48363 + 2.40808i) q^{8} +(2.19707 + 2.04277i) q^{9} +(5.08842 + 0.947288i) q^{10} +(1.96543 - 1.13474i) q^{11} +(-3.30467 + 1.03883i) q^{12} +(3.84091 + 2.21755i) q^{13} +(2.36979 - 2.89553i) q^{14} +(3.94982 + 4.95812i) q^{15} +(0.844147 - 3.90991i) q^{16} +3.25685i q^{17} +(-3.89189 - 1.68913i) q^{18} +2.37901 q^{19} +(-7.23145 + 1.13351i) q^{20} +(4.51584 - 0.779212i) q^{21} +(-2.08637 + 2.43888i) q^{22} +(-1.52279 - 0.879184i) q^{23} +(3.91739 - 2.94177i) q^{24} +(4.19733 + 7.27000i) q^{25} +(-6.16624 - 1.14794i) q^{26} +(-2.24734 - 4.68502i) q^{27} +(-1.79623 + 4.97731i) q^{28} +(3.73260 + 6.46506i) q^{29} +(-7.60230 - 4.75111i) q^{30} +(-3.37549 + 5.84652i) q^{31} +(0.715956 + 5.61136i) q^{32} +(-3.88725 + 0.583877i) q^{33} +(-1.53401 - 4.34293i) q^{34} +(9.68082 - 0.210880i) q^{35} +(5.98533 + 0.419299i) q^{36} -8.82337 q^{37} +(-3.17234 + 1.12053i) q^{38} +(-4.78647 - 6.00834i) q^{39} +(9.10905 - 4.91758i) q^{40} +(-2.24519 - 1.29626i) q^{41} +(-5.65474 + 3.16606i) q^{42} +(6.27685 - 3.62394i) q^{43} +(1.63339 - 4.23488i) q^{44} +(-3.22557 - 10.4951i) q^{45} +(2.44471 + 0.455120i) q^{46} +(3.95897 + 6.85713i) q^{47} +(-3.83814 + 5.76790i) q^{48} +(3.23270 - 6.20884i) q^{49} +(-9.02127 - 7.71736i) q^{50} +(2.06359 - 5.25004i) q^{51} +(8.76321 - 1.37360i) q^{52} +2.84881 q^{53} +(5.20346 + 5.18883i) q^{54} -8.30601 q^{55} +(0.0508652 - 7.48314i) q^{56} +(-3.83495 - 1.50737i) q^{57} +(-8.02242 - 6.86289i) q^{58} +(0.278774 - 0.482851i) q^{59} +(12.3753 + 2.75473i) q^{60} +(-0.335560 + 0.193736i) q^{61} +(1.74736 - 9.38606i) q^{62} +(-7.77324 - 1.60521i) q^{63} +(-3.59771 - 7.14538i) q^{64} +(-8.11596 - 14.0572i) q^{65} +(4.90853 - 2.60951i) q^{66} +(-2.07581 - 1.19847i) q^{67} +(4.09112 + 5.06865i) q^{68} +(1.89767 + 2.38210i) q^{69} +(-12.8098 + 4.84095i) q^{70} +9.43272i q^{71} +(-8.17877 + 2.26002i) q^{72} +12.5047i q^{73} +(11.7657 - 4.15589i) q^{74} +(-2.15972 - 14.3787i) q^{75} +(3.70245 - 2.98840i) q^{76} +(-2.88828 + 5.26418i) q^{77} +(9.21261 + 5.75749i) q^{78} +(2.20999 - 1.27594i) q^{79} +(-9.83045 + 10.8479i) q^{80} +(0.654220 + 8.97619i) q^{81} +(3.60446 + 0.671026i) q^{82} +(4.18556 + 7.24960i) q^{83} +(6.04920 - 6.88529i) q^{84} +(5.95984 - 10.3227i) q^{85} +(-6.66311 + 7.78889i) q^{86} +(-1.92060 - 12.7867i) q^{87} +(-0.183413 + 6.41644i) q^{88} +2.43473i q^{89} +(9.24451 + 12.4757i) q^{90} +(-11.7314 + 0.255548i) q^{91} +(-3.47431 + 0.544587i) q^{92} +(9.14571 - 7.28581i) q^{93} +(-8.50894 - 7.27909i) q^{94} +(-7.54036 - 4.35343i) q^{95} +(2.40132 - 9.49914i) q^{96} +(5.47279 - 3.15972i) q^{97} +(-1.38630 + 9.80195i) q^{98} +(6.63619 + 1.52181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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