LMFDB - Embedded newform 861.2.l.a.524.93

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(419,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("861.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$108$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			524.93
Character	$\chi$	$=$	861.524
Dual form			861.2.l.a.419.93

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09764 q^{2} +(-1.51490 - 0.839690i) q^{3} +2.40008 q^{4} +2.02468i q^{5} +(-3.17771 - 1.76136i) q^{6} +(1.67336 - 2.04936i) q^{7} +0.839219 q^{8} +(1.58984 + 2.54409i) q^{9} +O(q^{10})$	\(q+2.09764 q^{2} +(-1.51490 - 0.839690i) q^{3} +2.40008 q^{4} +2.02468i q^{5} +(-3.17771 - 1.76136i) q^{6} +(1.67336 - 2.04936i) q^{7} +0.839219 q^{8} +(1.58984 + 2.54409i) q^{9} +4.24705i q^{10} +(1.97738 + 1.97738i) q^{11} +(-3.63588 - 2.01532i) q^{12} +(0.746924 + 0.746924i) q^{13} +(3.51011 - 4.29880i) q^{14} +(1.70011 - 3.06719i) q^{15} -3.03978 q^{16} +(4.42368 + 4.42368i) q^{17} +(3.33491 + 5.33658i) q^{18} +(3.72167 - 3.72167i) q^{19} +4.85939i q^{20} +(-4.25580 + 1.69946i) q^{21} +(4.14783 + 4.14783i) q^{22} -1.99753i q^{23} +(-1.27133 - 0.704684i) q^{24} +0.900666 q^{25} +(1.56678 + 1.56678i) q^{26} +(-0.272199 - 5.18902i) q^{27} +(4.01620 - 4.91861i) q^{28} +(2.41447 + 2.41447i) q^{29} +(3.56620 - 6.43385i) q^{30} -6.69591i q^{31} -8.05479 q^{32} +(-1.33515 - 4.65593i) q^{33} +(9.27928 + 9.27928i) q^{34} +(4.14929 + 3.38803i) q^{35} +(3.81574 + 6.10602i) q^{36} -0.270291 q^{37} +(7.80672 - 7.80672i) q^{38} +(-0.504330 - 1.75870i) q^{39} +1.69915i q^{40} +(0.494936 + 6.38397i) q^{41} +(-8.92712 + 3.56485i) q^{42} +9.03578i q^{43} +(4.74587 + 4.74587i) q^{44} +(-5.15098 + 3.21892i) q^{45} -4.19010i q^{46} +(-3.64140 - 3.64140i) q^{47} +(4.60496 + 2.55247i) q^{48} +(-1.39972 - 6.85863i) q^{49} +1.88927 q^{50} +(-2.98691 - 10.4160i) q^{51} +(1.79268 + 1.79268i) q^{52} +(2.30499 + 2.30499i) q^{53} +(-0.570974 - 10.8847i) q^{54} +(-4.00357 + 4.00357i) q^{55} +(1.40432 - 1.71986i) q^{56} +(-8.76301 + 2.51291i) q^{57} +(5.06467 + 5.06467i) q^{58} +2.66949 q^{59} +(4.08039 - 7.36149i) q^{60} -0.289048 q^{61} -14.0456i q^{62} +(7.87413 + 0.999040i) q^{63} -10.8165 q^{64} +(-1.51228 + 1.51228i) q^{65} +(-2.80065 - 9.76644i) q^{66} +(-5.92249 - 5.92249i) q^{67} +(10.6172 + 10.6172i) q^{68} +(-1.67731 + 3.02606i) q^{69} +(8.70371 + 7.10685i) q^{70} +(-6.99899 - 6.99899i) q^{71} +(1.33423 + 2.13505i) q^{72} -0.182166 q^{73} -0.566972 q^{74} +(-1.36442 - 0.756280i) q^{75} +(8.93231 - 8.93231i) q^{76} +(7.36124 - 0.743483i) q^{77} +(-1.05790 - 3.68911i) q^{78} +(-10.5205 + 10.5205i) q^{79} -6.15459i q^{80} +(-3.94481 + 8.08940i) q^{81} +(1.03820 + 13.3912i) q^{82} +5.98025 q^{83} +(-10.2143 + 4.07884i) q^{84} +(-8.95655 + 8.95655i) q^{85} +18.9538i q^{86} +(-1.63027 - 5.68508i) q^{87} +(1.65946 + 1.65946i) q^{88} +(-3.63097 + 3.63097i) q^{89} +(-10.8049 + 6.75212i) q^{90} +(2.78059 - 0.280839i) q^{91} -4.79424i q^{92} +(-5.62249 + 10.1436i) q^{93} +(-7.63834 - 7.63834i) q^{94} +(7.53520 + 7.53520i) q^{95} +(12.2022 + 6.76353i) q^{96} +(-4.74709 + 4.74709i) q^{97} +(-2.93610 - 14.3869i) q^{98} +(-1.88692 + 8.17437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 192 q^{4} - 4 q^{7}+O(q^{10}) $ 216 * q + 192 * q^4 - 4 * q^7	$ 216 q + 192 q^{4} - 4 q^{7} + 20 q^{15} + 144 q^{16} - 24 q^{18} - 56 q^{22} - 200 q^{25} - 40 q^{28} + 32 q^{30} + 16 q^{37} + 4 q^{42} - 16 q^{51} - 64 q^{57} - 32 q^{58} + 40 q^{60} - 6 q^{63} + 48 q^{64} - 48 q^{67} + 48 q^{70} - 92 q^{72} + 28 q^{78} + 8 q^{79} - 120 q^{81} + 16 q^{85} - 144 q^{88} - 16 q^{93} + 56 q^{99}+O(q^{100}) $ 216 * q + 192 * q^4 - 4 * q^7 + 20 * q^15 + 144 * q^16 - 24 * q^18 - 56 * q^22 - 200 * q^25 - 40 * q^28 + 32 * q^30 + 16 * q^37 + 4 * q^42 - 16 * q^51 - 64 * q^57 - 32 * q^58 + 40 * q^60 - 6 * q^63 + 48 * q^64 - 48 * q^67 + 48 * q^70 - 92 * q^72 + 28 * q^78 + 8 * q^79 - 120 * q^81 + 16 * q^85 - 144 * q^88 - 16 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	2.09764			1.48325			0.741626	−	0.670813i	$-0.234055\pi$
$2$	2.09764			1.48325			0.741626	+	0.670813i	$0.234055\pi$
$3$	−1.51490	−	0.839690i	−0.874628	−	0.484795i
$3$	−1.51490	−	0.839690i	−0.874628	−	0.484795i
$4$	2.40008			1.20004
$5$			2.02468i			0.905465i	0.891646	+	0.452733i	$0.149551\pi$
$5$			2.02468i			0.905465i	−0.891646	+	0.452733i	$0.850449\pi$
$6$	−3.17771	−	1.76136i	−1.29729	−	0.719074i
$7$	1.67336	−	2.04936i	0.632472	−	0.774584i
$7$	1.67336	−	2.04936i	0.632472	−	0.774584i
$8$	0.839219			0.296709
$9$	1.58984	+	2.54409i	0.529947	+	0.848031i
$10$			4.24705i			1.34303i
$11$	1.97738	+	1.97738i	0.596203	+	0.596203i	0.939300	−	0.343097i	$-0.111476\pi$
$11$	1.97738	+	1.97738i	0.596203	+	0.596203i	−0.343097	+	0.939300i	$0.611476\pi$
$12$	−3.63588	−	2.01532i	−1.04959	−	0.581774i
$13$	0.746924	+	0.746924i	0.207160	+	0.207160i	0.803059	−	0.595900i	$-0.203204\pi$
$13$	0.746924	+	0.746924i	0.207160	+	0.207160i	−0.595900	+	0.803059i	$0.703204\pi$
$14$	3.51011	−	4.29880i	0.938115	−	1.14890i
$15$	1.70011	−	3.06719i	0.438965	−	0.791945i
$16$	−3.03978			−0.759945
$17$	4.42368	+	4.42368i	1.07290	+	1.07290i	0.997125	+	0.0757755i	$0.0241432\pi$
$17$	4.42368	+	4.42368i	1.07290	+	1.07290i	0.0757755	+	0.997125i	$0.475857\pi$
$18$	3.33491	+	5.33658i	0.786045	+	1.25784i
$19$	3.72167	−	3.72167i	0.853810	−	0.853810i	−0.136790	−	0.990600i	$-0.543678\pi$
$19$	3.72167	−	3.72167i	0.853810	−	0.853810i	0.990600	+	0.136790i	$0.0436785\pi$
$20$			4.85939i			1.08659i
$21$	−4.25580	+	1.69946i	−0.928692	+	0.370853i
$22$	4.14783	+	4.14783i	0.884320	+	0.884320i
$23$		−	1.99753i		−	0.416514i	−0.978074	−	0.208257i	$-0.933221\pi$
$23$		−	1.99753i		−	0.416514i	0.978074	−	0.208257i	$-0.0667791\pi$
$24$	−1.27133	−	0.704684i	−0.259510	−	0.143843i
$25$	0.900666			0.180133
$26$	1.56678	+	1.56678i	0.307270	+	0.307270i
$27$	−0.272199	−	5.18902i	−0.0523847	−	0.998627i
$28$	4.01620	−	4.91861i	0.758991	−	0.929531i
$29$	2.41447	+	2.41447i	0.448355	+	0.448355i	0.894807	−	0.446452i	$-0.147313\pi$
$29$	2.41447	+	2.41447i	0.448355	+	0.448355i	−0.446452	+	0.894807i	$0.647313\pi$
$30$	3.56620	−	6.43385i	0.651097	−	1.17465i
$31$		−	6.69591i		−	1.20262i	−0.799016	−	0.601310i	$-0.794646\pi$
$31$		−	6.69591i		−	1.20262i	0.799016	−	0.601310i	$-0.205354\pi$
$32$	−8.05479			−1.42390
$33$	−1.33515	−	4.65593i	−0.232419	−	0.810493i
$34$	9.27928	+	9.27928i	1.59138	+	1.59138i
$35$	4.14929	+	3.38803i	0.701358	+	0.572681i
$36$	3.81574	+	6.10602i	0.635957	+	1.01767i
$37$	−0.270291			−0.0444356			−0.0222178	−	0.999753i	$-0.507073\pi$
$37$	−0.270291			−0.0444356			−0.0222178	+	0.999753i	$0.507073\pi$
$38$	7.80672	−	7.80672i	1.26642	−	1.26642i
$39$	−0.504330	−	1.75870i	−0.0807574	−	0.281617i
$40$			1.69915i			0.268660i
$41$	0.494936	+	6.38397i	0.0772961	+	0.997008i
$41$	0.494936	+	6.38397i	0.0772961	+	0.997008i
$42$	−8.92712	+	3.56485i	−1.37748	+	0.550069i
$43$			9.03578i			1.37794i	0.724788	+	0.688972i	$0.241938\pi$
$43$			9.03578i			1.37794i	−0.724788	+	0.688972i	$0.758062\pi$
$44$	4.74587	+	4.74587i	0.715468	+	0.715468i
$45$	−5.15098	+	3.21892i	−0.767862	+	0.479848i
$46$		−	4.19010i		−	0.617796i
$47$	−3.64140	−	3.64140i	−0.531153	−	0.531153i	0.389762	−	0.920916i	$-0.372557\pi$
$47$	−3.64140	−	3.64140i	−0.531153	−	0.531153i	−0.920916	+	0.389762i	$0.872557\pi$
$48$	4.60496	+	2.55247i	0.664669	+	0.368418i
$49$	−1.39972	−	6.85863i	−0.199960	−	0.979804i
$50$	1.88927			0.267183
$51$	−2.98691	−	10.4160i	−0.418251	−	1.45853i
$52$	1.79268	+	1.79268i	0.248600	+	0.248600i
$53$	2.30499	+	2.30499i	0.316615	+	0.316615i	0.847465	−	0.530851i	$-0.178127\pi$
$53$	2.30499	+	2.30499i	0.316615	+	0.316615i	−0.530851	+	0.847465i	$0.678127\pi$
$54$	−0.570974	−	10.8847i	−0.0776998	−	1.48122i
$55$	−4.00357	+	4.00357i	−0.539841	+	0.539841i
$56$	1.40432	−	1.71986i	0.187660	−	0.229826i
$57$	−8.76301	+	2.51291i	−1.16069	+	0.332843i
$58$	5.06467	+	5.06467i	0.665024	+	0.665024i
$59$	2.66949			0.347538			0.173769	−	0.984786i	$-0.444405\pi$
$59$	2.66949			0.347538			0.173769	+	0.984786i	$0.444405\pi$
$60$	4.08039	−	7.36149i	0.526776	−	0.950365i
$61$	−0.289048			−0.0370088			−0.0185044	−	0.999829i	$-0.505890\pi$
$61$	−0.289048			−0.0370088			−0.0185044	+	0.999829i	$0.505890\pi$
$62$		−	14.0456i		−	1.78379i
$63$	7.87413	+	0.999040i	0.992047	+	0.125867i
$64$	−10.8165			−1.35206
$65$	−1.51228	+	1.51228i	−0.187576	+	0.187576i
$66$	−2.80065	−	9.76644i	−0.344737	−	1.20217i
$67$	−5.92249	−	5.92249i	−0.723548	−	0.723548i	0.245778	−	0.969326i	$-0.420956\pi$
$67$	−5.92249	−	5.92249i	−0.723548	−	0.723548i	−0.969326	+	0.245778i	$0.920956\pi$
$68$	10.6172	+	10.6172i	1.28752	+	1.28752i
$69$	−1.67731	+	3.02606i	−0.201924	+	0.364295i
$70$	8.70371	+	7.10685i	1.04029	+	0.849431i
$71$	−6.99899	−	6.99899i	−0.830628	−	0.830628i	0.156975	−	0.987603i	$-0.449826\pi$
$71$	−6.99899	−	6.99899i	−0.830628	−	0.830628i	−0.987603	+	0.156975i	$0.949826\pi$
$72$	1.33423	+	2.13505i	0.157240	+	0.251618i
$73$	−0.182166			−0.0213209			−0.0106604	−	0.999943i	$-0.503393\pi$
$73$	−0.182166			−0.0213209			−0.0106604	+	0.999943i	$0.503393\pi$
$74$	−0.566972			−0.0659092
$75$	−1.36442	−	0.756280i	−0.157549	−	0.0873277i
$76$	8.93231	−	8.93231i	1.02461	−	1.02461i
$77$	7.36124	−	0.743483i	0.838891	−	0.0847277i
$78$	−1.05790	−	3.68911i	−0.119784	−	0.417710i
$79$	−10.5205	+	10.5205i	−1.18365	+	1.18365i	−0.204863	+	0.978791i	$0.565675\pi$
$79$	−10.5205	+	10.5205i	−1.18365	+	1.18365i	−0.978791	+	0.204863i	$0.934325\pi$
$80$		−	6.15459i		−	0.688104i
$81$	−3.94481	+	8.08940i	−0.438313	+	0.898823i
$82$	1.03820	+	13.3912i	0.114650	+	1.47882i
$83$	5.98025			0.656418			0.328209	−	0.944605i	$-0.393555\pi$
$83$	5.98025			0.656418			0.328209	+	0.944605i	$0.393555\pi$
$84$	−10.2143	+	4.07884i	−1.11447	+	0.445038i
$85$	−8.95655	+	8.95655i	−0.971474	+	0.971474i
$86$			18.9538i			2.04384i
$87$	−1.63027	−	5.68508i	−0.174783	−	0.609505i
$88$	1.65946	+	1.65946i	0.176899	+	0.176899i
$89$	−3.63097	+	3.63097i	−0.384882	+	0.384882i	−0.872857	−	0.487975i	$-0.837736\pi$
$89$	−3.63097	+	3.63097i	−0.384882	+	0.384882i	0.487975	+	0.872857i	$0.337736\pi$
$90$	−10.8049	+	6.75212i	−1.13893	+	0.711736i
$91$	2.78059	−	0.280839i	0.291485	−	0.0294399i
$92$		−	4.79424i		−	0.499834i
$93$	−5.62249	+	10.1436i	−0.583025	+	1.05184i
$94$	−7.63834	−	7.63834i	−0.787835	−	0.787835i
$95$	7.53520	+	7.53520i	0.773095	+	0.773095i
$96$	12.2022	+	6.76353i	1.24538	+	0.690300i
$97$	−4.74709	+	4.74709i	−0.481994	+	0.481994i	−0.905768	−	0.423774i	$-0.860705\pi$
$97$	−4.74709	+	4.74709i	−0.481994	+	0.481994i	0.423774	+	0.905768i	$0.360705\pi$
$98$	−2.93610	−	14.3869i	−0.296591	−	1.45330i
$99$	−1.88692	+	8.17437i	−0.189643	+	0.821555i
$100$	2.16167			0.216167
$101$	−12.8845	−	12.8845i	−1.28205	−	1.28205i	−0.939499	−	0.342553i	$-0.888708\pi$
$101$	−12.8845	−	12.8845i	−1.28205	−	1.28205i	−0.342553	−	0.939499i	$-0.611292\pi$
$102$	−6.26545	−	21.8489i	−0.620372	−	2.16336i
$103$	−3.44740			−0.339682			−0.169841	−	0.985471i	$-0.554325\pi$
$103$	−3.44740			−0.339682			−0.169841	+	0.985471i	$0.554325\pi$
$104$	0.626833	+	0.626833i	0.0614661	+	0.0614661i
$105$	−3.44087	−	8.61664i	−0.335794	−	0.840898i
$106$	4.83503	+	4.83503i	0.469620	+	0.469620i
$107$		−	10.6153i		−	1.02622i	−0.858322	−	0.513111i	$-0.828493\pi$
$107$		−	10.6153i		−	1.02622i	0.858322	−	0.513111i	$-0.171507\pi$
$108$	−0.653299	−	12.4541i	−0.0628637	−	1.19839i
$109$	1.84035	+	1.84035i	0.176274	+	0.176274i	0.789729	−	0.613456i	$-0.210221\pi$
$109$	1.84035	+	1.84035i	0.176274	+	0.176274i	−0.613456	+	0.789729i	$0.710221\pi$
$110$	−8.39803	+	8.39803i	−0.800721	+	0.800721i
$111$	0.409464	+	0.226961i	0.0388646	+	0.0215422i
$112$	−5.08665	+	6.22959i	−0.480644	+	0.588641i
$113$		−	16.8845i		−	1.58836i	−0.607685	−	0.794178i	$-0.707902\pi$
$113$		−	16.8845i		−	1.58836i	0.607685	−	0.794178i	$-0.292098\pi$
$114$	−18.3816	+	5.27117i	−1.72160	+	0.493690i
$115$	4.04437			0.377139
$116$	5.79491	+	5.79491i	0.538044	+	0.538044i
$117$	−0.712754	+	3.08773i	−0.0658941	+	0.285461i
$118$	5.59962			0.515487
$119$	16.4681	−	1.66327i	1.50963	−	0.152472i
$120$	1.42676	−	2.57404i	0.130245	−	0.234977i
$121$		−	3.17991i		−	0.289083i
$122$	−0.606317			−0.0548934
$123$	4.61078	−	10.0867i	0.415740	−	0.909484i
$124$		−	16.0707i		−	1.44319i
$125$			11.9470i			1.06857i
$126$	16.5171	+	2.09562i	1.47146	+	0.186693i
$127$	−20.2414			−1.79613			−0.898065	−	0.439862i	$-0.855027\pi$
$127$	−20.2414			−1.79613			−0.898065	+	0.439862i	$0.855027\pi$
$128$	−6.57943			−0.581545
$129$	7.58726	−	13.6883i	0.668021	−	1.20519i
$130$	−3.17222	+	3.17222i	−0.278222	+	0.278222i
$131$			0.739441i			0.0646053i	0.999478	+	0.0323026i	$0.0102840\pi$
$131$			0.739441i			0.0646053i	−0.999478	+	0.0323026i	$0.989716\pi$
$132$	−3.20446	−	11.1746i	−0.278912	−	0.972623i
$133$	−1.39932	−	13.8547i	−0.121337	−	1.20136i
$134$	−12.4232	−	12.4232i	−1.07320	−	1.07320i
$135$	10.5061	−	0.551116i	0.904222	−	0.0474325i
$136$	3.71244	+	3.71244i	0.318339	+	0.318339i
$137$	1.12158	−	1.12158i	0.0958226	−	0.0958226i	−0.657570	−	0.753393i	$-0.728416\pi$
$137$	1.12158	−	1.12158i	0.0958226	−	0.0958226i	0.753393	+	0.657570i	$0.228416\pi$
$138$	−3.51838	+	6.34758i	−0.299505	+	0.540342i
$139$		−	1.50267i		−	0.127455i	−0.997967	−	0.0637273i	$-0.979701\pi$
$139$		−	1.50267i		−	0.127455i	0.997967	−	0.0637273i	$-0.0202988\pi$
$140$	9.95863	+	8.13153i	0.841658	+	0.687239i
$141$	2.45871	+	8.57401i	0.207061	+	0.722062i
$142$	−14.6813	−	14.6813i	−1.23203	−	1.23203i
$143$			2.95391i			0.247018i
$144$	−4.83277	−	7.73348i	−0.402730	−	0.644457i
$145$	−4.88853	+	4.88853i	−0.405970	+	0.405970i
$146$	−0.382117			−0.0316242
$147$	−3.63869	+	11.5655i	−0.300114	+	0.953903i
$148$	−0.648720			−0.0533244
$149$	−1.30698	+	1.30698i	−0.107072	+	0.107072i	−0.758613	−	0.651541i	$-0.774123\pi$
$149$	−1.30698	+	1.30698i	−0.107072	+	0.107072i	0.651541	+	0.758613i	$0.274123\pi$
$150$	−2.86205	−	1.58640i	−0.233686	−	0.129529i
$151$	4.62897	−	4.62897i	0.376701	−	0.376701i	−0.493210	−	0.869910i	$-0.664177\pi$
$151$	4.62897	−	4.62897i	0.376701	−	0.376701i	0.869910	+	0.493210i	$0.164177\pi$
$152$	3.12330	−	3.12330i	0.253333	−	0.253333i
$153$	−4.22131	+	18.2872i	−0.341272	+	1.47843i
$154$	15.4412	−	1.55956i	1.24429	−	0.125673i
$155$	13.5571			1.08893
$156$	−1.21043	−	4.22102i	−0.0969121	−	0.337952i
$157$	6.56100	+	6.56100i	0.523625	+	0.523625i	0.918664	−	0.395039i	$-0.129269\pi$
$157$	6.56100	+	6.56100i	0.523625	+	0.523625i	−0.395039	+	0.918664i	$0.629269\pi$
$158$	−22.0683	+	22.0683i	−1.75566	+	1.75566i
$159$	−1.55635	−	5.42731i	−0.123427	−	0.430414i
$160$		−	16.3084i		−	1.28929i
$161$	−4.09366	−	3.34260i	−0.322625	−	0.263434i
$162$	−8.27479	+	16.9686i	−0.650129	+	1.33318i
$163$	13.4110			1.05043			0.525217	−	0.850968i	$-0.323984\pi$
$163$	13.4110			1.05043			0.525217	+	0.850968i	$0.323984\pi$
$164$	1.18789	+	15.3220i	0.0927583	+	1.19645i
$165$	9.42677	−	2.70325i	0.733873	−	0.210448i
$166$	12.5444			0.973634
$167$	−1.56671	+	1.56671i	−0.121235	+	0.121235i	−0.765121	−	0.643886i	$-0.777321\pi$
$167$	−1.56671	+	1.56671i	−0.121235	+	0.121235i	0.643886	+	0.765121i	$0.277321\pi$
$168$	−3.57155	+	1.42622i	−0.275551	+	0.110035i
$169$		−	11.8842i		−	0.914170i
$170$	−18.7876	+	18.7876i	−1.44094	+	1.44094i
$171$	15.3851	+	3.55141i	1.17653	+	0.271583i
$172$			21.6866i			1.65359i
$173$		−	5.85099i		−	0.444842i	−0.974951	−	0.222421i	$-0.928604\pi$
$173$		−	5.85099i		−	0.444842i	0.974951	−	0.222421i	$-0.0713960\pi$
$174$	−3.41971	−	11.9252i	−0.259248	−	0.904049i
$175$	1.50714	−	1.84578i	0.113929	−	0.139528i
$176$	−6.01081	−	6.01081i	−0.453082	−	0.453082i
$177$	−4.04401	−	2.24155i	−0.303967	−	0.168485i
$178$	−7.61646	+	7.61646i	−0.570878	+	0.570878i
$179$	−2.75075	+	2.75075i	−0.205601	+	0.205601i	−0.802395	−	0.596794i	$-0.796441\pi$
$179$	−2.75075	+	2.75075i	−0.205601	+	0.205601i	0.596794	+	0.802395i	$0.296441\pi$
$180$	−12.3627	+	7.72566i	−0.921465	+	0.575837i
$181$	−14.9636	+	14.9636i	−1.11224	+	1.11224i	−0.119388	+	0.992848i	$0.538093\pi$
$181$	−14.9636	+	14.9636i	−1.11224	+	1.11224i	−0.992848	+	0.119388i	$0.961907\pi$
$182$	5.83266	−	0.589097i	0.432346	−	0.0436668i
$183$	0.437878	+	0.242711i	0.0323689	+	0.0179417i
$184$		−	1.67637i		−	0.123584i
$185$		−	0.547253i		−	0.0402349i
$186$	−11.7939	+	21.2776i	−0.864773	+	1.56015i
$187$			17.4946i			1.27933i
$188$	−8.73966	−	8.73966i	−0.637405	−	0.637405i
$189$	−11.0896	−	8.12527i	−0.806652	−	0.591027i
$190$	15.8061	+	15.8061i	1.14670	+	1.14670i
$191$	−13.0600	+	13.0600i	−0.944989	+	0.944989i	−0.998564	−	0.0535744i	$-0.982939\pi$
$191$	−13.0600	+	13.0600i	−0.944989	+	0.944989i	0.0535744	+	0.998564i	$0.482939\pi$
$192$	16.3859	+	9.08248i	1.18255	+	0.655472i
$193$	17.8816	−	17.8816i	1.28715	−	1.28715i	0.350633	−	0.936513i	$-0.385966\pi$
$193$	17.8816	−	17.8816i	1.28715	−	1.28715i	0.936513	−	0.350633i	$-0.114034\pi$
$194$	−9.95766	+	9.95766i	−0.714918	+	0.714918i
$195$	3.56081	−	1.02111i	0.254995	−	0.0731230i
$196$	−3.35943	−	16.4612i	−0.239959	−	1.17580i
$197$	−10.7115			−0.763160			−0.381580	−	0.924336i	$-0.624620\pi$
$197$	−10.7115			−0.763160			−0.381580	+	0.924336i	$0.624620\pi$
$198$	−3.95808	+	17.1469i	−0.281288	+	1.21857i
$199$	−11.8741	+	11.8741i	−0.841730	+	0.841730i	−0.989084	−	0.147354i	$-0.952924\pi$
$199$	−11.8741	+	11.8741i	−0.841730	+	0.841730i	0.147354	+	0.989084i	$0.452924\pi$
$200$	0.755856			0.0534471
$201$	3.99892	+	13.9450i	0.282062	+	0.983607i
$202$	−27.0269	−	27.0269i	−1.90161	−	1.90161i
$203$	8.98838	−	0.907824i	0.630861	−	0.0637167i
$204$	−7.16882	−	24.9991i	−0.501918	−	1.75029i
$205$	−12.9255	+	1.00209i	−0.902756	+	0.0699889i
$206$	−7.23139			−0.503835
$207$	5.08191	−	3.17576i	0.353217	−	0.220731i
$208$	−2.27049	−	2.27049i	−0.157430	−	0.157430i
$209$	14.7183			1.01809
$210$	−7.21769	−	18.0746i	−0.498068	−	1.24726i
$211$	18.9647	+	18.9647i	1.30558	+	1.30558i	0.924571	+	0.381010i	$0.124424\pi$
$211$	18.9647	+	18.9647i	1.30558	+	1.30558i	0.381010	+	0.924571i	$0.375576\pi$
$212$	5.53216	+	5.53216i	0.379950	+	0.379950i
$213$	4.72579	+	16.4798i	0.323805	+	1.12917i
$214$		−	22.2671i		−	1.52215i
$215$	−18.2946			−1.24768
$216$	−0.228435	−	4.35472i	−0.0155430	−	0.296301i
$217$	−13.7223	−	11.2047i	−0.931530	−	0.760623i
$218$	3.86039	+	3.86039i	0.261458	+	0.261458i
$219$	0.275963	+	0.152963i	0.0186478	+	0.0103363i
$220$	−9.60888	+	9.60888i	−0.647831	+	0.647831i
$221$			6.60831i			0.444523i
$222$	0.858906	+	0.476081i	0.0576460	+	0.0319525i
$223$		−	3.63008i		−	0.243088i	−0.992586	−	0.121544i	$-0.961215\pi$
$223$		−	3.63008i		−	0.243088i	0.992586	−	0.121544i	$-0.0387845\pi$
$224$	−13.4786	+	16.5071i	−0.900576	+	1.10293i
$225$	1.43191	+	2.29138i	0.0954610	+	0.152758i
$226$		−	35.4175i		−	2.35593i
$227$	−0.712916	−	0.712916i	−0.0473179	−	0.0473179i	0.683052	−	0.730370i	$-0.260652\pi$
$227$	−0.712916	−	0.712916i	−0.0473179	−	0.0473179i	−0.730370	+	0.683052i	$0.760652\pi$
$228$	−21.0319	+	6.03118i	−1.39287	+	0.399424i
$229$	15.7588	−	15.7588i	1.04137	−	1.04137i	0.0422653	−	0.999106i	$-0.486543\pi$
$229$	15.7588	−	15.7588i	1.04137	−	1.04137i	0.999106	−	0.0422653i	$-0.0134575\pi$
$230$	8.48361			0.559393
$231$	−11.7758	−	5.05486i	−0.774793	−	0.332585i
$232$	2.02627	+	2.02627i	0.133031	+	0.133031i
$233$	5.53838	+	5.53838i	0.362831	+	0.362831i	0.864854	−	0.502023i	$-0.167411\pi$
$233$	5.53838	+	5.53838i	0.362831	+	0.362831i	−0.502023	+	0.864854i	$0.667411\pi$
$234$	−1.49510	+	6.47694i	−0.0977376	+	0.423411i
$235$	7.37268	−	7.37268i	0.480941	−	0.480941i
$236$	6.40699			0.417060
$237$	24.7716	−	7.10357i	1.60909	−	0.461426i
$238$	34.5441	−	3.48895i	2.23916	−	0.226155i
$239$	9.25443	+	9.25443i	0.598620	+	0.598620i	0.939945	−	0.341326i	$-0.110876\pi$
$239$	9.25443	+	9.25443i	0.598620	+	0.598620i	−0.341326	+	0.939945i	$0.610876\pi$
$240$	−5.16795	+	9.32358i	−0.333589	+	0.601834i
$241$	−23.2848			−1.49990			−0.749952	−	0.661493i	$-0.769923\pi$
$241$	−23.2848			−1.49990			−0.749952	+	0.661493i	$0.769923\pi$
$242$		−	6.67030i		−	0.428783i
$243$	12.7686	−	8.94221i	0.819105	−	0.573643i
$244$	−0.693738			−0.0444120
$245$	13.8865	−	2.83398i	0.887178	−	0.181056i
$246$	9.67173	−	21.1581i	0.616647	−	1.34899i
$247$	5.55962			0.353750
$248$		−	5.61934i		−	0.356828i
$249$	−9.05948	−	5.02156i	−0.574121	−	0.318228i
$250$			25.0604i			1.58496i
$251$		−	11.6411i		−	0.734777i	−0.930067	−	0.367389i	$-0.880252\pi$
$251$		−	11.6411i		−	0.734777i	0.930067	−	0.367389i	$-0.119748\pi$
$252$	18.8985	+	2.39777i	1.19050	+	0.151046i
$253$	3.94989	−	3.94989i	0.248327	−	0.248327i
$254$	−42.4590			−2.66412
$255$	21.0890	−	6.04754i	1.32064	−	0.378712i
$256$	7.83168			0.489480
$257$	−9.52431	+	9.52431i	−0.594110	+	0.594110i	−0.938739	−	0.344629i	$-0.888005\pi$
$257$	−9.52431	+	9.52431i	−0.594110	+	0.594110i	0.344629	+	0.938739i	$0.388005\pi$
$258$	15.9153	−	28.7131i	0.990844	−	1.78760i
$259$	−0.452295	+	0.553922i	−0.0281042	+	0.0344191i
$260$	−3.62960	+	3.62960i	−0.225098	+	0.225098i
$261$	−2.30401	+	9.98125i	−0.142615	+	0.617824i
$262$			1.55108i			0.0958260i
$263$	20.0529	−	20.0529i	1.23652	−	1.23652i	0.275103	−	0.961415i	$-0.411288\pi$
$263$	20.0529	−	20.0529i	1.23652	−	1.23652i	0.961415	−	0.275103i	$-0.0887118\pi$
$264$	−1.12048	−	3.90734i	−0.0689609	−	0.240480i
$265$	−4.66687	+	4.66687i	−0.286684	+	0.286684i
$266$	−2.93527	−	29.0622i	−0.179973	−	1.78192i
$267$	8.54945	−	2.45166i	0.523218	−	0.150039i
$268$	−14.2144	−	14.2144i	−0.868286	−	0.868286i
$269$	14.6784			0.894960			0.447480	−	0.894294i	$-0.352322\pi$
$269$	14.6784			0.894960			0.447480	+	0.894294i	$0.352322\pi$
$270$	22.0380	−	1.15604i	1.34119	−	0.0703544i
$271$		−	27.6481i		−	1.67950i	−0.542974	−	0.839750i	$-0.682702\pi$
$271$		−	27.6481i		−	1.67950i	0.542974	−	0.839750i	$-0.317298\pi$
$272$	−13.4470	−	13.4470i	−0.815345	−	0.815345i
$273$	−4.44813	−	1.90939i	−0.269213	−	0.115562i
$274$	2.35266	−	2.35266i	0.142129	−	0.142129i
$275$	1.78096	+	1.78096i	0.107396	+	0.107396i
$276$	−4.02567	+	7.26279i	−0.242317	+	0.437168i
$277$	14.0195			0.842353			0.421176	−	0.906979i	$-0.361617\pi$
$277$	14.0195			0.842353			0.421176	+	0.906979i	$0.361617\pi$
$278$		−	3.15205i		−	0.189047i
$279$	17.0350	−	10.6454i	1.01986	−	0.637325i
$280$	3.48217	+	2.84330i	0.208099	+	0.169919i
$281$	−15.4895	+	15.4895i	−0.924025	+	0.924025i	−0.997311	−	0.0732859i	$-0.976651\pi$
$281$	−15.4895	+	15.4895i	−0.924025	+	0.924025i	0.0732859	+	0.997311i	$0.476651\pi$
$282$	5.15748	+	17.9852i	0.307123	+	1.07100i
$283$		−	24.3610i		−	1.44811i	−0.689741	−	0.724056i	$-0.742275\pi$
$283$		−	24.3610i		−	1.44811i	0.689741	−	0.724056i	$-0.257725\pi$
$284$	−16.7981	−	16.7981i	−0.996786	−	0.996786i
$285$	−5.08784	−	17.7423i	−0.301377	−	1.05096i
$286$			6.19623i			0.366391i
$287$	13.9112	+	9.66839i	0.821154	+	0.570707i
$288$	−12.8058	−	20.4921i	−0.754591	−	1.20751i
$289$			22.1379i			1.30223i
$290$	−10.2544	+	10.2544i	−0.602156	+	0.602156i
$291$	11.1774	−	3.20528i	0.655233	−	0.187897i
$292$	−0.437212			−0.0255859
$293$	−0.456694	−	0.456694i	−0.0266803	−	0.0266803i	0.693641	−	0.720321i	$-0.256006\pi$
$293$	−0.456694	−	0.456694i	−0.0266803	−	0.0266803i	−0.720321	+	0.693641i	$0.756006\pi$
$294$	−7.63266	+	24.2601i	−0.445145	+	1.41488i
$295$			5.40487i			0.314684i
$296$	−0.226833			−0.0131844
$297$	9.72243	−	10.7989i	0.564153	−	0.626617i
$298$	−2.74156	+	2.74156i	−0.158814	+	0.158814i
$299$	1.49201	−	1.49201i	0.0862849	−	0.0862849i
$300$	−3.27471	−	1.81513i	−0.189065	−	0.104797i
$301$	18.5175	+	15.1201i	1.06733	+	0.871510i
$302$	9.70991	−	9.70991i	0.558742	−	0.558742i
$303$	8.69970	+	30.3376i	0.499785	+	1.74285i
$304$	−11.3131	+	11.3131i	−0.648849	+	0.648849i
$305$		−	0.585230i		−	0.0335102i
$306$	−8.85477	+	38.3599i	−0.506193	+	2.19289i
$307$	1.98590			0.113342			0.0566708	−	0.998393i	$-0.481951\pi$
$307$	1.98590			0.113342			0.0566708	+	0.998393i	$0.481951\pi$
$308$	17.6676	−	1.78442i	1.00670	−	0.101677i
$309$	5.22246	+	2.89475i	0.297096	+	0.164676i
$310$	28.4378			1.61516
$311$	21.3389	+	21.3389i	1.21002	+	1.21002i	0.971020	+	0.238999i	$0.0768191\pi$
$311$	21.3389	+	21.3389i	1.21002	+	1.21002i	0.238999	+	0.971020i	$0.423181\pi$
$312$	−0.423244	−	1.47594i	−0.0239615	−	0.0835584i
$313$	13.3139	−	13.3139i	0.752545	−	0.752545i	−0.222409	−	0.974954i	$-0.571392\pi$
$313$	13.3139	−	13.3139i	0.752545	−	0.752545i	0.974954	+	0.222409i	$0.0713919\pi$
$314$	13.7626	+	13.7626i	0.776668	+	0.776668i
$315$	−2.02274	+	15.9426i	−0.113968	+	0.898264i
$316$	−25.2501	+	25.2501i	−1.42043	+	1.42043i
$317$	−2.25572	−	2.25572i	−0.126694	−	0.126694i	0.640917	−	0.767610i	$-0.278554\pi$
$317$	−2.25572	−	2.25572i	−0.126694	−	0.126694i	−0.767610	+	0.640917i	$0.778554\pi$
$318$	−3.26466	−	11.3845i	−0.183073	−	0.638412i
$319$			9.54865i			0.534622i
$320$		−	21.8999i		−	1.22424i
$321$	−8.91358	+	16.0811i	−0.497507	+	0.897561i
$322$	−8.58700	−	7.01155i	−0.478535	−	0.390739i
$323$	32.9270			1.83211
$324$	−9.46786	+	19.4152i	−0.525992	+	1.07862i
$325$	0.672729	+	0.672729i	0.0373163	+	0.0373163i
$326$	28.1315			1.55806
$327$	−1.24262	−	4.33327i	−0.0687171	−	0.239630i
$328$	0.415360	+	5.35755i	0.0229344	+	0.295821i
$329$	−13.5559	+	1.36914i	−0.747362	+	0.0754833i
$330$	19.7739	−	5.67043i	1.08852	−	0.312147i
$331$	−0.756244	+	0.756244i	−0.0415669	+	0.0415669i	−0.727585	−	0.686018i	$-0.759357\pi$
$331$	−0.756244	+	0.756244i	−0.0415669	+	0.0415669i	0.686018	+	0.727585i	$0.259357\pi$
$332$	14.3531			0.787728
$333$	−0.429720	−	0.687645i	−0.0235485	−	0.0376827i
$334$	−3.28638	+	3.28638i	−0.179823	+	0.179823i
$335$	11.9912	−	11.9912i	0.655147	−	0.655147i
$336$	12.9367	−	5.16599i	0.705755	−	0.281828i
$337$		−	24.2200i		−	1.31935i	−0.751553	−	0.659673i	$-0.770695\pi$
$337$		−	24.2200i		−	1.31935i	0.751553	−	0.659673i	$-0.229305\pi$
$338$		−	24.9287i		−	1.35595i
$339$	−14.1777	+	25.5783i	−0.770028	+	1.38922i
$340$	−21.4964	+	21.4964i	−1.16581	+	1.16581i
$341$	13.2404	−	13.2404i	0.717006	−	0.717006i
$342$	32.2724	+	7.44957i	1.74509	+	0.402827i
$343$	−16.3980	−	8.60845i	−0.885409	−	0.464813i
$344$			7.58300i			0.408848i
$345$	−6.12681	−	3.39602i	−0.329856	−	0.182835i
$346$		−	12.2732i		−	0.659813i
$347$	24.5046	−	24.5046i	1.31547	−	1.31547i	0.398158	−	0.917317i	$-0.369650\pi$
$347$	24.5046	−	24.5046i	1.31547	−	1.31547i	0.917317	−	0.398158i	$-0.130350\pi$
$348$	−3.91278	−	13.6446i	−0.209747	−	0.731429i
$349$	−36.0130			−1.92773			−0.963865	−	0.266391i	$-0.914169\pi$
$349$	−36.0130			−1.92773			−0.963865	+	0.266391i	$0.914169\pi$
$350$	3.16143	−	3.87178i	0.168986	−	0.206956i
$351$	3.67249	−	4.07912i	0.196023	−	0.217727i
$352$	−15.9274	−	15.9274i	−0.848934	−	0.848934i
$353$	32.7351			1.74231			0.871157	−	0.491005i	$-0.163370\pi$
$353$	32.7351			1.74231			0.871157	+	0.491005i	$0.163370\pi$
$354$	−8.48287	−	4.70195i	−0.450859	−	0.249906i
$355$	14.1707	−	14.1707i	0.752104	−	0.752104i
$356$	−8.71461	+	8.71461i	−0.461874	+	0.461874i
$357$	−26.3442	−	11.3084i	−1.39428	−	0.598505i
$358$	−5.77008	+	5.77008i	−0.304958	+	0.304958i
$359$			18.7389i			0.989003i	0.869177	+	0.494501i	$0.164649\pi$
$359$			18.7389i			0.989003i	−0.869177	+	0.494501i	$0.835351\pi$
$360$	−4.32280	+	2.70138i	−0.227832	+	0.142375i
$361$		−	8.70170i		−	0.457984i
$362$	−31.3882	+	31.3882i	−1.64973	+	1.64973i
$363$	−2.67014	+	4.81725i	−0.140146	+	0.252840i
$364$	6.67363	−	0.674035i	0.349793	−	0.0353290i
$365$		−	0.368827i		−	0.0193053i
$366$	0.918510	+	0.509119i	0.0480113	+	0.0266121i
$367$	−16.5886			−0.865919			−0.432959	−	0.901413i	$-0.642531\pi$
$367$	−16.5886			−0.865919			−0.432959	+	0.901413i	$0.642531\pi$
$368$			6.07206i			0.316528i
$369$	−15.4545	+	11.4087i	−0.804531	+	0.593911i
$370$		−	1.14794i		−	0.0596785i
$371$	8.58083	−	0.866661i	0.445495	−	0.0449948i
$372$	−13.4944	+	24.3455i	−0.699653	+	1.26226i
$373$	−5.77490			−0.299013			−0.149507	−	0.988761i	$-0.547768\pi$
$373$	−5.77490			−0.299013			−0.149507	+	0.988761i	$0.547768\pi$
$374$			36.6974i			1.89758i
$375$	10.0318	−	18.0985i	0.518037	−	0.934600i
$376$	−3.05594	−	3.05594i	−0.157598	−	0.157598i
$377$			3.60685i			0.185762i
$378$	−23.2620	−	17.0439i	−1.19647	−	0.876642i
$379$	−14.3455			−0.736879			−0.368440	−	0.929652i	$-0.620108\pi$
$379$	−14.3455			−0.736879			−0.368440	+	0.929652i	$0.620108\pi$
$380$	18.0851	+	18.0851i	0.927745	+	0.927745i
$381$	30.6636	+	16.9965i	1.57095	+	0.870756i
$382$	−27.3952	+	27.3952i	−1.40166	+	1.40166i
$383$	−12.8310	−	12.8310i	−0.655633	−	0.655633i	0.298711	−	0.954344i	$-0.403443\pi$
$383$	−12.8310	−	12.8310i	−0.655633	−	0.655633i	−0.954344	+	0.298711i	$0.903443\pi$
$384$	9.96717	+	5.52468i	0.508635	+	0.281930i
$385$	1.50532	+	14.9042i	0.0767180	+	0.759586i
$386$	37.5091	−	37.5091i	1.90916	−	1.90916i
$387$	−22.9879	+	14.3655i	−1.16854	+	0.730237i
$388$	−11.3934	+	11.3934i	−0.578411	+	0.578411i
$389$	8.45760			0.428817			0.214409	−	0.976744i	$-0.431218\pi$
$389$	8.45760			0.428817			0.214409	+	0.976744i	$0.431218\pi$
$390$	7.46928	−	2.14191i	0.378222	−	0.108460i
$391$	8.83645	−	8.83645i	0.446879	−	0.446879i
$392$	−1.17467	−	5.75589i	−0.0593298	−	0.290717i
$393$	0.620902	−	1.12018i	0.0313203	−	0.0565056i
$394$	−22.4688			−1.13196
$395$	−21.3008	−	21.3008i	−1.07176	−	1.07176i
$396$	−4.52876	+	19.6191i	−0.227579	+	0.985898i
$397$	2.63287	+	2.63287i	0.132140	+	0.132140i	0.770083	−	0.637943i	$-0.220215\pi$
$397$	2.63287	+	2.63287i	0.132140	+	0.132140i	−0.637943	+	0.770083i	$0.720215\pi$
$398$	−24.9075	+	24.9075i	−1.24850	+	1.24850i
$399$	−9.51385	+	22.1635i	−0.476288	+	1.10956i
$400$	−2.73783			−0.136891
$401$	−14.8737			−0.742756			−0.371378	−	0.928482i	$-0.621115\pi$
$401$	−14.8737			−0.742756			−0.371378	+	0.928482i	$0.621115\pi$
$402$	8.38828	+	29.2516i	0.418370	+	1.45894i
$403$	5.00133	−	5.00133i	0.249134	−	0.249134i
$404$	−30.9237	−	30.9237i	−1.53851	−	1.53851i
$405$	−16.3785	−	7.98699i	−0.813852	−	0.396877i
$406$	18.8544	−	1.90428i	0.935726	−	0.0945080i
$407$	−0.534469	−	0.534469i	−0.0264926	−	0.0264926i
$408$	−2.50667	−	8.74127i	−0.124099	−	0.432757i
$409$		−	36.2004i		−	1.78999i	−0.446073	−	0.894997i	$-0.647178\pi$
$409$		−	36.2004i		−	1.78999i	0.446073	−	0.894997i	$-0.352822\pi$
$410$	−27.1130	+	2.10202i	−1.33902	+	0.103811i
$411$	−2.64085	+	0.757298i	−0.130264	+	0.0373548i
$412$	−8.27403			−0.407632
$413$	4.46703	−	5.47074i	0.219808	−	0.269197i
$414$	10.6600	−	6.66159i	0.523910	−	0.327399i
$415$			12.1081i			0.594364i
$416$	−6.01632	−	6.01632i	−0.294974	−	0.294974i
$417$	−1.26177	+	2.27639i	−0.0617894	+	0.111475i
$418$	30.8737			1.51008
$419$			13.2363i			0.646637i	0.946290	+	0.323319i	$0.104799\pi$
$419$			13.2363i			0.646637i	−0.946290	+	0.323319i	$0.895201\pi$
$420$	−8.25835	−	20.6806i	−0.402966	−	1.00911i
$421$	17.6887	−	17.6887i	0.862093	−	0.862093i	−0.129488	−	0.991581i	$-0.541333\pi$
$421$	17.6887	−	17.6887i	0.862093	−	0.862093i	0.991581	+	0.129488i	$0.0413332\pi$
$422$	39.7810	+	39.7810i	1.93651	+	1.93651i
$423$	3.47482	−	15.0533i	0.168951	−	0.731918i
$424$	1.93439	+	1.93439i	0.0939424	+	0.0939424i
$425$	3.98426	+	3.98426i	0.193265	+	0.193265i
$426$	9.91298	+	34.5685i	0.480285	+	1.67485i
$427$	−0.483682	+	0.592362i	−0.0234070	+	0.0286664i
$428$		−	25.4776i		−	1.23151i
$429$	2.48037	−	4.47488i	0.119753	−	0.216049i
$430$	−38.3754			−1.85062
$431$	−24.6794			−1.18877			−0.594383	−	0.804182i	$-0.702604\pi$
$431$	−24.6794			−1.18877			−0.594383	+	0.804182i	$0.702604\pi$
$432$	0.827425	+	15.7735i	0.0398095	+	0.758902i
$433$			20.0591i			0.963978i	0.876177	+	0.481989i	$0.160086\pi$
$433$			20.0591i			0.963978i	−0.876177	+	0.481989i	$0.839914\pi$
$434$	−28.7844	−	23.5033i	−1.38169	−	1.12820i
$435$	11.5105	−	3.30078i	0.551885	−	0.158260i
$436$	4.41699	+	4.41699i	0.211535	+	0.211535i
$437$	−7.43417	−	7.43417i	−0.355624	−	0.355624i
$438$	0.578869	+	0.320860i	0.0276594	+	0.0153313i
$439$	−5.00937	−	5.00937i	−0.239084	−	0.239084i	0.577387	−	0.816471i	$-0.304073\pi$
$439$	−5.00937	−	5.00937i	−0.239084	−	0.239084i	−0.816471	+	0.577387i	$0.804073\pi$
$440$	−3.35987	+	3.35987i	−0.160176	+	0.160176i
$441$	15.2237	−	14.4651i	0.724936	−	0.688816i
$442$			13.8618i			0.659340i
$443$	−17.0431			−0.809743			−0.404872	−	0.914374i	$-0.632684\pi$
$443$	−17.0431			−0.809743			−0.404872	+	0.914374i	$0.632684\pi$
$444$	0.982745	+	0.544724i	0.0466390	+	0.0258514i
$445$	−7.35156	−	7.35156i	−0.348497	−	0.348497i
$446$		−	7.61458i		−	0.360561i
$447$	3.07739	−	0.882482i	0.145556	−	0.0417400i
$448$	−18.0999	+	22.1668i	−0.855138	+	1.04728i
$449$	−24.0362			−1.13434			−0.567170	−	0.823601i	$-0.691962\pi$
$449$	−24.0362			−1.13434			−0.567170	+	0.823601i	$0.691962\pi$
$450$	3.00364	+	4.80648i	0.141593	+	0.226579i
$451$	−11.6449	+	13.6022i	−0.548335	+	0.640504i
$452$		−	40.5240i		−	1.90609i
$453$	−10.8993	+	3.12553i	−0.512095	+	0.146850i
$454$	−1.49544	−	1.49544i	−0.0701844	−	0.0701844i
$455$	0.568609	+	5.62980i	0.0266568	+	0.263929i
$456$	−7.35409	+	2.10888i	−0.344387	+	0.0987574i
$457$	2.87058	+	2.87058i	0.134280	+	0.134280i	0.771052	−	0.636772i	$-0.219731\pi$
$457$	2.87058	+	2.87058i	0.134280	+	0.134280i	−0.636772	+	0.771052i	$0.719731\pi$
$458$	33.0563	−	33.0563i	1.54462	−	1.54462i
$459$	21.7504	−	24.1587i	1.01522	−	1.12763i
$460$	9.70680			0.452582
$461$	−26.4473			−1.23177			−0.615887	−	0.787834i	$-0.711202\pi$
$461$	−26.4473			−1.23177			−0.615887	+	0.787834i	$0.711202\pi$
$462$	−24.7014	−	10.6033i	−1.14921	−	0.493308i
$463$	−3.77660	+	3.77660i	−0.175514	+	0.175514i	−0.789397	−	0.613883i	$-0.789607\pi$
$463$	−3.77660	+	3.77660i	−0.175514	+	0.175514i	0.613883	+	0.789397i	$0.289607\pi$
$464$	−7.33945	−	7.33945i	−0.340725	−	0.340725i
$465$	−20.5376	−	11.3837i	−0.952409	−	0.527909i
$466$	11.6175	+	11.6175i	0.538171	+	0.538171i
$467$	25.0661			1.15992			0.579959	−	0.814645i	$-0.303068\pi$
$467$	25.0661			1.15992			0.579959	+	0.814645i	$0.303068\pi$
$468$	−1.71067	+	7.41081i	−0.0790755	+	0.342565i
$469$	−22.0478	+	2.22682i	−1.01807	+	0.102825i
$470$	15.4652	−	15.4652i	0.713357	−	0.713357i
$471$	−4.43005	−	15.4485i	−0.204126	−	0.711828i
$472$	2.24029			0.103118
$473$	−17.8672	+	17.8672i	−0.821535	+	0.821535i
$474$	51.9617	−	14.9007i	2.38668	−	0.684412i
$475$	3.35198	−	3.35198i	0.153800	−	0.153800i
$476$	39.5248	−	3.99199i	1.81162	−	0.182973i
$477$	−2.19954	+	9.52868i	−0.100710	+	0.436288i
$478$	19.4124	+	19.4124i	0.887904	+	0.887904i
$479$	−2.40299	+	2.40299i	−0.109795	+	0.109795i	−0.759870	−	0.650075i	$-0.774738\pi$
$479$	−2.40299	+	2.40299i	−0.109795	+	0.109795i	0.650075	+	0.759870i	$0.274738\pi$
$480$	−13.6940	+	24.7056i	−0.625042	+	1.12765i
$481$	−0.201887	−	0.201887i	−0.00920525	−	0.00920525i
$482$	−48.8430			−2.22474
$483$	3.39473	+	8.50110i	0.154466	+	0.386813i
$484$		−	7.63204i		−	0.346911i
$485$	−9.61134	−	9.61134i	−0.436428	−	0.436428i
$486$	26.7839	−	18.7575i	1.21494	−	0.850858i
$487$			17.8432i			0.808552i	0.914637	+	0.404276i	$0.132476\pi$
$487$			17.8432i			0.808552i	−0.914637	+	0.404276i	$0.867524\pi$
$488$	−0.242575			−0.0109808
$489$	−20.3164	−	11.2611i	−0.918738	−	0.509245i
$490$	29.1289	−	5.94466i	1.31591	−	0.268552i
$491$			26.6222i			1.20144i	0.799458	+	0.600722i	$0.205120\pi$
$491$			26.6222i			1.20144i	−0.799458	+	0.600722i	$0.794880\pi$
$492$	11.0662	−	24.2088i	0.498904	−	1.09142i
$493$			21.3617i			0.962081i
$494$	11.6621			0.524701
$495$	−16.5505	−	3.82041i	−0.743889	−	0.171715i
$496$			20.3541i			0.913925i
$497$	−26.0553	+	2.63158i	−1.16874	+	0.118042i
$498$	−19.0035	−	10.5334i	−0.851567	−	0.472013i
$499$	−8.28943	+	8.28943i	−0.371086	+	0.371086i	−0.867873	−	0.496787i	$-0.834513\pi$
$499$	−8.28943	+	8.28943i	−0.371086	+	0.371086i	0.496787	+	0.867873i	$0.334513\pi$
$500$			28.6737i			1.28233i
$501$	3.68895	−	1.05786i	0.164810	−	0.0472615i
$502$		−	24.4187i		−	1.08986i
$503$	−27.5862	+	27.5862i	−1.23001	+	1.23001i	−0.266048	+	0.963960i	$0.585718\pi$
$503$	−27.5862	+	27.5862i	−1.23001	+	1.23001i	−0.963960	+	0.266048i	$0.914282\pi$
$504$	6.60812	+	0.838414i	0.294349	+	0.0373459i
$505$	26.0869	−	26.0869i	1.16085	−	1.16085i
$506$	8.28543	−	8.28543i	0.368332	−	0.368332i
$507$	−9.97905	+	18.0034i	−0.443185	+	0.799558i
$508$	−48.5809			−2.15543
$509$	20.4064	+	20.4064i	0.904499	+	0.904499i	0.995821	−	0.0913223i	$-0.0291094\pi$
$509$	20.4064	+	20.4064i	0.904499	+	0.904499i	−0.0913223	+	0.995821i	$0.529109\pi$
$510$	44.2370	−	12.6855i	1.95885	−	0.561725i
$511$	−0.304829	+	0.373322i	−0.0134848	+	0.0165148i
$512$	29.5869			1.30757
$513$	−20.3249	−	18.2988i	−0.897365	−	0.807911i
$514$	−19.9785	+	19.9785i	−0.881215	+	0.881215i
$515$		−	6.97988i		−	0.307570i
$516$	18.2100	−	32.8530i	0.801651	−	1.44627i
$517$		−	14.4009i		−	0.633351i
$518$	−0.948750	+	1.16193i	−0.0416857	+	0.0510522i
$519$	−4.91302	+	8.86365i	−0.215657	+	0.389071i
$520$	−1.26914	+	1.26914i	−0.0556554	+	0.0556554i
$521$	−26.5644	+	26.5644i	−1.16381	+	1.16381i	−0.180171	+	0.983635i	$0.557665\pi$
$521$	−26.5644	+	26.5644i	−1.16381	+	1.16381i	−0.983635	+	0.180171i	$0.942335\pi$
$522$	−4.83298	+	20.9370i	−0.211534	+	0.916389i
$523$			22.8925i			1.00102i	0.865731	+	0.500510i	$0.166854\pi$
$523$			22.8925i			1.00102i	−0.865731	+	0.500510i	$0.833146\pi$
$524$			1.77472i			0.0775289i
$525$	−3.83305	+	1.53065i	−0.167288	+	0.0668029i
$526$	42.0638	−	42.0638i	1.83407	−	1.83407i
$527$	29.6206	−	29.6206i	1.29029	−	1.29029i
$528$	4.05855	+	14.1530i	0.176626	+	0.615930i
$529$	19.0099			0.826516
$530$	−9.78940	+	9.78940i	−0.425224	+	0.425224i
$531$	4.24407	+	6.79143i	0.184177	+	0.294723i
$532$	−3.35849	−	33.2525i	−0.145609	−	1.44168i
$533$	−4.39866	+	5.13802i	−0.190527	+	0.222552i
$534$	17.9336	−	5.14270i	0.776064	−	0.222546i
$535$	21.4926			0.929207
$536$	−4.97027	−	4.97027i	−0.214683	−	0.214683i
$537$	6.47690	−	1.85733i	0.279499	−	0.0801499i
$538$	30.7900			1.32745
$539$	10.7944	−	16.3299i	0.464946	−	0.703379i
$540$	25.2155	−	1.32272i	1.08510	−	0.0569209i
$541$			0.180347i			0.00775374i	0.999992	+	0.00387687i	$0.00123405\pi$
$541$			0.180347i			0.00775374i	−0.999992	+	0.00387687i	$0.998766\pi$
$542$		−	57.9956i		−	2.49112i
$543$	35.2331	−	10.1036i	1.51200	−	0.433585i
$544$	−35.6318	−	35.6318i	−1.52770	−	1.52770i
$545$	−3.72612	+	3.72612i	−0.159610	+	0.159610i
$546$	−9.33056	−	4.00521i	−0.399311	−	0.171407i
$547$	5.59800	+	5.59800i	0.239353	+	0.239353i	0.816582	−	0.577229i	$-0.195866\pi$
$547$	5.59800	+	5.59800i	0.239353	+	0.239353i	−0.577229	+	0.816582i	$0.695866\pi$
$548$	2.69187	−	2.69187i	0.114991	−	0.114991i
$549$	−0.459540	−	0.735365i	−0.0196127	−	0.0313846i
$550$	3.73581	+	3.73581i	0.159295	+	0.159295i
$551$	17.9717			0.765621
$552$	−1.40763	+	2.53953i	−0.0599127	+	0.108090i
$553$	3.95566	+	39.1650i	0.168212	+	1.66547i
$554$	29.4079			1.24942
$555$	−0.459523	+	0.829034i	−0.0195057	+	0.0351905i
$556$		−	3.60652i		−	0.152950i
$557$	−17.6104	+	17.6104i	−0.746179	+	0.746179i	−0.973759	−	0.227581i	$-0.926918\pi$
$557$	−17.6104	+	17.6104i	−0.746179	+	0.746179i	0.227581	+	0.973759i	$0.426918\pi$
$558$	35.7332	−	22.3302i	1.51271	−	0.945314i
$559$	−6.74904	+	6.74904i	−0.285454	+	0.285454i
$560$	−12.6129	−	10.2989i	−0.532994	−	0.435206i
$561$	14.6901	−	26.5026i	0.620215	−	1.11894i
$562$	−32.4913	+	32.4913i	−1.37056	+	1.37056i
$563$	−16.4094	+	16.4094i	−0.691572	+	0.691572i	−0.962578	−	0.271006i	$-0.912644\pi$
$563$	−16.4094	+	16.4094i	−0.691572	+	0.691572i	0.271006	+	0.962578i	$0.412644\pi$
$564$	5.90110	+	20.5783i	0.248481	+	0.866503i
$565$	34.1856			1.43820
$566$		−	51.1006i		−	2.14792i
$567$	9.97696	+	21.6208i	0.418993	+	0.907989i
$568$	−5.87369	−	5.87369i	−0.246455	−	0.246455i
$569$	−17.7056			−0.742258			−0.371129	−	0.928581i	$-0.621029\pi$
$569$	−17.7056			−0.742258			−0.371129	+	0.928581i	$0.621029\pi$
$570$	−10.6724	−	37.2169i	−0.447019	−	1.55884i
$571$	11.8022	−	11.8022i	0.493907	−	0.493907i	−0.415628	−	0.909535i	$-0.636438\pi$
$571$	11.8022	−	11.8022i	0.493907	−	0.493907i	0.909535	+	0.415628i	$0.136438\pi$
$572$			7.08962i			0.296432i
$573$	30.7510	−	8.81824i	1.28464	−	0.368387i
$574$	29.1807	+	20.2808i	1.21798	+	0.846503i
$575$		−	1.79911i		−	0.0750281i
$576$	−17.1965	−	27.5181i	−0.716519	−	1.14659i
$577$	−7.53826	−	7.53826i	−0.313822	−	0.313822i	0.532566	−	0.846388i	$-0.321228\pi$
$577$	−7.53826	−	7.53826i	−0.313822	−	0.313822i	−0.846388	+	0.532566i	$0.821228\pi$
$578$			46.4373i			1.93154i
$579$	−42.1038	+	12.0738i	−1.74978	+	0.501771i
$580$	−11.7328	+	11.7328i	−0.487180	+	0.487180i
$581$	10.0071	−	12.2557i	0.415166	−	0.508451i
$582$	23.4462	−	6.72350i	0.971877	−	0.278698i
$583$			9.11570i			0.377534i
$584$	−0.152877			−0.00632609
$585$	−6.25168	−	1.44310i	−0.258475	−	0.0596648i
$586$	−0.957978	−	0.957978i	−0.0395737	−	0.0395737i
$587$	−0.248981	+	0.248981i	−0.0102765	+	0.0102765i	−0.712226	−	0.701950i	$-0.752313\pi$
$587$	−0.248981	+	0.248981i	−0.0102765	+	0.0102765i	0.701950	+	0.712226i	$0.252313\pi$
$588$	−8.73315	+	27.7580i	−0.360149	+	1.14472i
$589$	−24.9200	−	24.9200i	−1.02681	−	1.02681i
$590$			11.3375i			0.466756i
$591$	16.2268	+	8.99431i	0.667481	+	0.369977i
$592$	0.821625			0.0337686
$593$	−5.71596	−	5.71596i	−0.234726	−	0.234726i	0.579936	−	0.814662i	$-0.303078\pi$
$593$	−5.71596	−	5.71596i	−0.234726	−	0.234726i	−0.814662	+	0.579936i	$0.803078\pi$
$594$	20.3941	−	22.6522i	0.836781	−	0.929431i
$595$	3.36760	+	33.3427i	0.138058	+	1.36692i
$596$	−3.13684	+	3.13684i	−0.128490	+	0.128490i
$597$	27.9585	−	8.01748i	1.14427	−	0.328133i
$598$	3.12969	−	3.12969i	0.127982	−	0.127982i
$599$			22.2767i			0.910201i	0.890440	+	0.455101i	$0.150397\pi$
$599$			22.2767i			0.910201i	−0.890440	+	0.455101i	$0.849603\pi$
$600$	−1.14505	−	0.634685i	−0.0467463	−	0.0259109i
$601$	8.30614	−	8.30614i	0.338814	−	0.338814i	−0.517107	−	0.855921i	$-0.672991\pi$
$601$	8.30614	−	8.30614i	0.338814	−	0.338814i	0.855921	+	0.517107i	$0.172991\pi$
$602$	38.8430	+	31.7165i	1.58312	+	1.29267i
$603$	5.65155	−	24.4832i	0.230149	−	0.997033i
$604$	11.1099	−	11.1099i	0.452056	−	0.452056i
$605$	6.43831			0.261755
$606$	18.2488	+	63.6373i	0.741307	+	2.58509i
$607$	−4.35516			−0.176771			−0.0883853	−	0.996086i	$-0.528171\pi$
$607$	−4.35516			−0.176771			−0.0883853	+	0.996086i	$0.528171\pi$
$608$	−29.9773	+	29.9773i	−1.21574	+	1.21574i
$609$	−14.3788	−	6.17219i	−0.582658	−	0.250110i
$610$		−	1.22760i		−	0.0497040i
$611$		−	5.43971i		−	0.220067i
$612$	−10.1315	+	43.8907i	−0.409540	+	1.77418i
$613$		−	28.9830i		−	1.17061i	−0.810812	−	0.585307i	$-0.800974\pi$
$613$		−	28.9830i		−	1.17061i	0.810812	−	0.585307i	$-0.199026\pi$
$614$	4.16570			0.168114
$615$	20.4223	+	9.33535i	0.823506	+	0.376438i
$616$	6.17769	−	0.623945i	0.248906	−	0.0251395i
$617$	−17.7686			−0.715335			−0.357668	−	0.933849i	$-0.616428\pi$
$617$	−17.7686			−0.715335			−0.357668	+	0.933849i	$0.616428\pi$
$618$	10.9548	+	6.07213i	0.440668	+	0.244257i
$619$			46.7719i			1.87992i	0.341283	+	0.939961i	$0.389139\pi$
$619$			46.7719i			1.87992i	−0.341283	+	0.939961i	$0.610861\pi$
$620$	32.5381			1.30676
$621$	−10.3652	+	0.543726i	−0.415943	+	0.0218190i
$622$	44.7613	+	44.7613i	1.79476	+	1.79476i
$623$	1.36522	+	13.5171i	0.0546964	+	0.541550i
$624$	1.53305	+	5.34606i	0.0613712	+	0.214014i
$625$	−19.6855			−0.787419
$626$	27.9277	−	27.9277i	1.11621	−	1.11621i
$627$	−22.2968	−	12.3589i	−0.890449	−	0.493565i
$628$	15.7469	+	15.7469i	0.628370	+	0.628370i
$629$	−1.19568	−	1.19568i	−0.0476749	−	0.0476749i
$630$	−4.24297	+	33.4418i	−0.169044	+	1.33235i
$631$	28.0636			1.11720			0.558598	−	0.829439i	$-0.311340\pi$
$631$	28.0636			1.11720			0.558598	+	0.829439i	$0.311340\pi$
$632$	−8.82905	+	8.82905i	−0.351201	+	0.351201i
$633$	−12.8051	−	44.6540i	−0.508958	−	1.77484i
$634$	−4.73167	−	4.73167i	−0.187919	−	0.187919i
$635$		−	40.9823i		−	1.62633i
$636$	−3.73537	−	13.0260i	−0.148117	−	0.516513i
$637$	4.07739	−	6.16836i	0.161552	−	0.244399i
$638$			20.0296i			0.792980i
$639$	6.67880	−	28.9334i	0.264209	−	1.14459i
$640$		−	13.3212i		−	0.526568i
$641$	6.94341	−	6.94341i	0.274248	−	0.274248i	−0.556559	−	0.830808i	$-0.687879\pi$
$641$	6.94341	−	6.94341i	0.274248	−	0.274248i	0.830808	+	0.556559i	$0.187879\pi$
$642$	−18.6974	+	33.7324i	−0.737929	+	1.33131i
$643$	26.5169	+	26.5169i	1.04573	+	1.04573i	0.998903	+	0.0468220i	$0.0149094\pi$
$643$	26.5169	+	26.5169i	1.04573	+	1.04573i	0.0468220	+	0.998903i	$0.485091\pi$
$644$	−9.82510	−	8.02250i	−0.387163	−	0.316131i
$645$	27.7144	+	15.3618i	1.09126	+	0.604869i
$646$	69.0689			2.71748
$647$		−	42.1882i		−	1.65859i	−0.558813	−	0.829294i	$-0.688743\pi$
$647$		−	42.1882i		−	1.65859i	0.558813	−	0.829294i	$-0.311257\pi$
$648$	−3.31056	+	6.78878i	−0.130051	+	0.266689i
$649$	5.27861	+	5.27861i	0.207203	+	0.207203i
$650$	1.41114	+	1.41114i	0.0553495	+	0.0553495i
$651$	11.3794	+	28.4964i	0.445995	+	1.11686i
$652$	32.1876			1.26056
$653$	29.7126	+	29.7126i	1.16275	+	1.16275i	0.983872	+	0.178873i	$0.0572451\pi$
$653$	29.7126	+	29.7126i	1.16275	+	1.16275i	0.178873	+	0.983872i	$0.442755\pi$
$654$	−2.60657	−	9.08962i	−0.101925	−	0.355432i
$655$	−1.49713			−0.0584978
$656$	−1.50450	−	19.4059i	−0.0587408	−	0.757671i
$657$	−0.289614	−	0.463446i	−0.0112989	−	0.0180808i
$658$	−28.4354	+	2.87197i	−1.10853	+	0.111961i
$659$	−10.2150	−	10.2150i	−0.397918	−	0.397918i	0.479580	−	0.877498i	$-0.340789\pi$
$659$	−10.2150	−	10.2150i	−0.397918	−	0.397918i	−0.877498	+	0.479580i	$0.840789\pi$
$660$	22.6250	−	6.48801i	0.880676	−	0.252545i
$661$	−16.9744			−0.660227			−0.330114	−	0.943941i	$-0.607087\pi$
$661$	−16.9744			−0.660227			−0.330114	+	0.943941i	$0.607087\pi$
$662$	−1.58632	+	1.58632i	−0.0616543	+	0.0616543i
$663$	5.54893	−	10.0109i	0.215503	−	0.388792i
$664$	5.01875			0.194765
$665$	28.0514	−	2.83319i	1.08779	−	0.109866i
$666$	−0.901396	−	1.44243i	−0.0349284	−	0.0558930i
$667$	4.82298	−	4.82298i	0.186746	−	0.186746i
$668$	−3.76022	+	3.76022i	−0.145487	+	0.145487i
$669$	−3.04814	+	5.49920i	−0.117848	+	0.212611i
$670$	25.1531	−	25.1531i	0.971749	−	0.971749i
$671$	−0.571558	−	0.571558i	−0.0220648	−	0.0220648i
$672$	34.2796	−	13.6888i	1.32236	−	0.528057i
$673$	10.9588	+	10.9588i	0.422429	+	0.422429i	0.886039	−	0.463610i	$-0.153446\pi$
$673$	10.9588	+	10.9588i	0.422429	+	0.422429i	−0.463610	+	0.886039i	$0.653446\pi$
$674$		−	50.8047i		−	1.95692i
$675$	−0.245160	−	4.67357i	−0.00943622	−	0.179886i
$676$		−	28.5230i		−	1.09704i
$677$		−	3.40048i		−	0.130691i	−0.997863	−	0.0653455i	$-0.979185\pi$
$677$		−	3.40048i		−	0.130691i	0.997863	−	0.0653455i	$-0.0208150\pi$
$678$	−29.7397	+	53.6539i	−1.14215	+	2.06056i
$679$	1.78487	+	17.6721i	0.0684971	+	0.678192i
$680$	−7.51651	+	7.51651i	−0.288245	+	0.288245i
$681$	0.481367	+	1.67862i	0.0184460	+	0.0643250i
$682$	27.7735	−	27.7735i	1.06350	−	1.06350i
$683$	5.94637	−	5.94637i	0.227532	−	0.227532i	−0.584129	−	0.811661i	$-0.698564\pi$
$683$	5.94637	−	5.94637i	0.227532	−	0.227532i	0.811661	+	0.584129i	$0.198564\pi$
$684$	36.9256	+	8.52367i	1.41188	+	0.325911i
$685$	2.27083	+	2.27083i	0.0867641	+	0.0867641i
$686$	−34.3971	−	18.0574i	−1.31329	−	0.689435i
$687$	−37.1055	+	10.6405i	−1.41566	+	0.405960i
$688$		−	27.4668i		−	1.04716i
$689$			3.44331i			0.131180i
$690$	−12.8518	−	7.12361i	−0.489261	−	0.271191i
$691$	−16.5238	+	16.5238i	−0.628596	+	0.628596i	−0.947715	−	0.319119i	$-0.896613\pi$
$691$	−16.5238	+	16.5238i	−0.628596	+	0.628596i	0.319119	+	0.947715i	$0.396613\pi$
$692$		−	14.0428i		−	0.533828i
$693$	13.5947	+	17.5457i	0.516419	+	0.666504i
$694$	51.4017	−	51.4017i	1.95118	−	1.95118i
$695$	3.04242			0.115406
$696$	−1.36815	−	4.77103i	−0.0518598	−	0.180845i
$697$	−26.0512	+	30.4301i	−0.986760	+	1.15262i
$698$	−75.5421			−2.85931
$699$	−3.73957	−	13.0406i	−0.141443	−	0.493241i
$700$	3.61725	−	4.43003i	0.136719	−	0.167439i
$701$			15.4407i			0.583188i	0.956542	+	0.291594i	$0.0941857\pi$
$701$			15.4407i			0.583188i	−0.956542	+	0.291594i	$0.905814\pi$
$702$	7.70355	−	8.55650i	0.290752	−	0.322944i
$703$	−1.00593	+	1.00593i	−0.0379395	+	0.0379395i
$704$	−21.3883	−	21.3883i	−0.806102	−	0.806102i
$705$	−17.3596	+	4.97810i	−0.653802	+	0.187486i
$706$	68.6663			2.58429
$707$	−47.9652	+	4.84447i	−1.80392	+	0.182195i
$708$	−9.70595	−	5.37989i	−0.364772	−	0.202189i
$709$	−17.2082	+	17.2082i	−0.646268	+	0.646268i	−0.952089	−	0.305821i	$-0.901069\pi$
$709$	−17.2082	+	17.2082i	−0.646268	+	0.646268i	0.305821	+	0.952089i	$0.401069\pi$
$710$	29.7250	−	29.7250i	1.11556	−	1.11556i
$711$	−43.4912	−	10.0393i	−1.63105	−	0.376501i
$712$	−3.04718	+	3.04718i	−0.114198	+	0.114198i
$713$	−13.3753			−0.500909
$714$	−55.2605	−	23.7210i	−2.06807	−	0.887735i
$715$	−5.98073			−0.223667
$716$	−6.60202	+	6.60202i	−0.246729	+	0.246729i
$717$	−6.24868	−	21.7904i	−0.233361	−	0.813777i
$718$			39.3075i			1.46694i
$719$	18.4919	+	18.4919i	0.689631	+	0.689631i	0.962150	−	0.272520i	$-0.0878569\pi$
$719$	18.4919	+	18.4919i	0.689631	+	0.689631i	−0.272520	+	0.962150i	$0.587857\pi$
$720$	15.6578	−	9.78481i	0.583533	−	0.364658i
$721$	−5.76875	+	7.06495i	−0.214839	+	0.263112i
$722$		−	18.2530i		−	0.679306i
$723$	35.2741	+	19.5520i	1.31186	+	0.727146i
$724$	−35.9138	+	35.9138i	−1.33473	+	1.33473i
$725$	2.17463	+	2.17463i	0.0807636	+	0.0807636i
$726$	−5.60099	+	10.1048i	−0.207872	+	0.375026i
$727$	−7.97693	−	7.97693i	−0.295848	−	0.295848i	0.543537	−	0.839385i	$-0.317085\pi$
$727$	−7.97693	−	7.97693i	−0.295848	−	0.295848i	−0.839385	+	0.543537i	$0.817085\pi$
$728$	2.33352	−	0.235685i	0.0864861	−	0.00873507i
$729$	−26.8518	+	2.82489i	−0.994512	+	0.104626i
$730$		−	0.773665i		−	0.0286346i
$731$	−39.9714	+	39.9714i	−1.47840	+	1.47840i
$732$	1.05094	+	0.582525i	0.0388440	+	0.0215307i
$733$	35.3200			1.30457			0.652287	−	0.757972i	$-0.273810\pi$
$733$	35.3200			1.30457			0.652287	+	0.757972i	$0.273810\pi$
$734$	−34.7969			−1.28438
$735$	−23.4164	−	7.36719i	−0.863726	−	0.271743i
$736$			16.0897i			0.593075i
$737$		−	23.4221i		−	0.862763i
$738$	−32.4180	+	23.9312i	−1.19332	+	0.880920i
$739$	−39.8911			−1.46742			−0.733709	−	0.679464i	$-0.762212\pi$
$739$	−39.8911			−1.46742			−0.733709	+	0.679464i	$0.762212\pi$
$740$		−	1.31345i		−	0.0482834i
$741$	−8.42226	−	4.66835i	−0.309399	−	0.171496i
$742$	17.9995	−	1.81794i	0.660781	−	0.0667387i
$743$	−45.3144			−1.66243			−0.831213	−	0.555954i	$-0.812353\pi$
$743$	−45.3144			−1.66243			−0.831213	+	0.555954i	$0.812353\pi$
$744$	−4.71850	+	8.51273i	−0.172989	+	0.312092i
$745$	−2.64621	−	2.64621i	−0.0969496	−	0.0969496i
$746$	−12.1136			−0.443512
$747$	9.50765	+	15.2143i	0.347867	+	0.556663i
$748$			41.9885i			1.53525i
$749$	−21.7546	−	17.7633i	−0.794894	−	0.649056i
$750$	21.0430	−	37.9640i	0.768381	−	1.38625i
$751$	13.5274	−	13.5274i	0.493623	−	0.493623i	−0.415823	−	0.909446i	$-0.636506\pi$
$751$	13.5274	−	13.5274i	0.493623	−	0.493623i	0.909446	+	0.415823i	$0.136506\pi$
$752$	11.0691	+	11.0691i	0.403647	+	0.403647i
$753$	−9.77489	+	17.6350i	−0.356217	+	0.642657i
$754$			7.56586i			0.275532i
$755$	9.37220	+	9.37220i	0.341089	+	0.341089i
$756$	−26.6160	−	19.5013i	−0.968014	−	0.709255i
$757$	−25.7757	−	25.7757i	−0.936834	−	0.936834i	0.0612862	−	0.998120i	$-0.480480\pi$
$757$	−25.7757	−	25.7757i	−0.936834	−	0.936834i	−0.998120	+	0.0612862i	$0.980480\pi$
$758$	−30.0917			−1.09298
$759$	−9.30037	+	2.66700i	−0.337582	+	0.0968060i
$760$	6.32369	+	6.32369i	0.229384	+	0.229384i
$761$	4.53345			0.164337			0.0821687	−	0.996618i	$-0.473815\pi$
$761$	4.53345			0.164337			0.0821687	+	0.996618i	$0.473815\pi$
$762$	64.3212	+	35.6524i	2.33011	+	1.29155i
$763$	6.85110	−	0.691959i	0.248027	−	0.0250506i
$764$	−31.3451	+	31.3451i	−1.13402	+	1.13402i
$765$	−37.0258	−	8.54680i	−1.33867	−	0.309010i
$766$	−26.9147	−	26.9147i	−0.972469	−	0.972469i
$767$	1.99391	+	1.99391i	0.0719959	+	0.0719959i
$768$	−11.8642	−	6.57619i	−0.428113	−	0.237298i
$769$		−	50.9062i		−	1.83573i	−0.396898	−	0.917863i	$-0.629913\pi$
$769$		−	50.9062i		−	1.83573i	0.396898	−	0.917863i	$-0.370087\pi$
$770$	3.15761	+	31.2635i	0.113792	+	1.12666i
$771$	22.4258	−	6.43090i	0.807647	−	0.231603i
$772$	42.9173	−	42.9173i	1.54463	−	1.54463i
$773$	−2.67907	−	2.67907i	−0.0963594	−	0.0963594i	0.657284	−	0.753643i	$-0.271705\pi$
$773$	−2.67907	−	2.67907i	−0.0963594	−	0.0963594i	−0.753643	+	0.657284i	$0.771705\pi$
$774$	−48.2202	+	30.1335i	−1.73324	+	1.08313i
$775$		−	6.03077i		−	0.216632i
$776$	−3.98385	+	3.98385i	−0.143012	+	0.143012i
$777$	1.15030	−	0.459349i	0.0412669	−	0.0164791i
$778$	17.7410			0.636044
$779$	25.6010	+	21.9170i	0.917252	+	0.785260i
$780$	8.54622	−	2.45074i	0.306004	−	0.0877505i
$781$		−	27.6794i		−	0.990446i
$782$	18.5357	−	18.5357i	0.662834	−	0.662834i
$783$	11.8715	−	13.1859i	0.424253	−	0.471227i
$784$	4.25483	+	20.8487i	0.151958	+	0.744597i
$785$	−13.2839	+	13.2839i	−0.474124	+	0.474124i
$786$	1.30243	−	2.34973i	0.0464560	−	0.0838121i
$787$	−9.80042			−0.349347			−0.174674	−	0.984626i	$-0.555887\pi$
$787$	−9.80042			−0.349347			−0.174674	+	0.984626i	$0.555887\pi$
$788$	−25.7084			−0.915823
$789$	−47.2165	+	13.5399i	−1.68095	+	0.482034i
$790$	−44.6812	−	44.6812i	−1.58969	−	1.58969i
$791$	−34.6023	−	28.2538i	−1.23031	−	1.00459i
$792$	−1.58354	+	6.86009i	−0.0562687	+	0.243763i
$793$	−0.215897	−	0.215897i	−0.00766672	−	0.00766672i
$794$	5.52281	+	5.52281i	0.195997	+	0.195997i
$795$	10.9886	−	3.15112i	0.389724	−	0.111759i
$796$	−28.4987	+	28.4987i	−1.01011	+	1.01011i
$797$	23.2344			0.823005			0.411503	−	0.911409i	$-0.365004\pi$
$797$	23.2344			0.823005			0.411503	+	0.911409i	$0.365004\pi$
$798$	−19.9566	+	46.4910i	−0.706456	+	1.64576i
$799$		−	32.2168i		−	1.13975i
$800$	−7.25467			−0.256491
$801$	−15.0102	−	3.46486i	−0.530359	−	0.122425i
$802$	−31.1996			−1.10169
$803$	−0.360211	−	0.360211i	−0.0127116	−	0.0127116i
$804$	9.59773	+	33.4692i	0.338486	+	1.18037i
$805$	6.76769	−	8.28835i	0.238530	−	0.292126i
$806$	10.4910	−	10.4910i	0.369529	−	0.369529i
$807$	−22.2364	−	12.3253i	−0.782757	−	0.433873i
$808$	−10.8129	−	10.8129i	−0.380396	−	0.380396i
$809$	−11.8811	−	11.8811i	−0.417718	−	0.417718i	0.466698	−	0.884416i	$-0.345443\pi$
$809$	−11.8811	−	11.8811i	−0.417718	−	0.417718i	−0.884416	+	0.466698i	$0.845443\pi$
$810$	−34.3561	−	16.7538i	−1.20715	−	0.588669i
$811$	−23.3444			−0.819734			−0.409867	−	0.912145i	$-0.634425\pi$
$811$	−23.3444			−0.819734			−0.409867	+	0.912145i	$0.634425\pi$
$812$	21.5728	−	2.17885i	0.757058	−	0.0764626i
$813$	−23.2158	+	41.8840i	−0.814214	+	1.46894i
$814$	−1.12112	−	1.12112i	−0.0392953	−	0.0392953i
$815$			27.1531i			0.951131i
$816$	9.07955	+	31.6622i	0.317848	+	1.10840i
$817$	33.6282	+	33.6282i	1.17650	+	1.17650i
$818$		−	75.9352i		−	2.65501i
$819$	5.13517	+	6.62759i	0.179437	+	0.231587i
$820$	−31.0222	+	2.40509i	−1.08334	+	0.0839894i
$821$			32.9035i			1.14834i	0.818736	+	0.574170i	$0.194675\pi$
$821$			32.9035i			1.14834i	−0.818736	+	0.574170i	$0.805325\pi$
$822$	−5.53954	+	1.58854i	−0.193214	+	0.0554065i
$823$	15.6209	−	15.6209i	0.544511	−	0.544511i	−0.380337	−	0.924848i	$-0.624192\pi$
$823$	15.6209	−	15.6209i	0.544511	−	0.544511i	0.924848	+	0.380337i	$0.124192\pi$
$824$	−2.89312			−0.100787
$825$	−1.20252	−	4.19343i	−0.0418664	−	0.145997i
$826$	9.37020	−	11.4756i	0.326031	−	0.399288i
$827$	26.9798	+	26.9798i	0.938178	+	0.938178i	0.998197	−	0.0600191i	$-0.0191162\pi$
$827$	26.9798	+	26.9798i	0.938178	+	0.938178i	−0.0600191	+	0.998197i	$0.519116\pi$
$828$	12.1970	−	7.62207i	0.423874	−	0.264885i
$829$	52.2940			1.81625			0.908123	−	0.418704i	$-0.137515\pi$
$829$	52.2940			1.81625			0.908123	+	0.418704i	$0.137515\pi$
$830$			25.3984i			0.881592i
$831$	−21.2382	−	11.7721i	−0.736745	−	0.408369i
$832$	−8.07908	−	8.07908i	−0.280092	−	0.280092i
$833$	24.1485	−	36.5323i	0.836696	−	1.26577i
$834$	−2.64674	+	4.77504i	−0.0916493	+	0.165346i
$835$	−3.17208	−	3.17208i	−0.109774	−	0.109774i
$836$	35.3252			1.22175
$837$	−34.7452	+	1.82262i	−1.20097	+	0.0629989i
$838$			27.7650i			0.959126i
$839$	−20.5029	−	20.5029i	−0.707838	−	0.707838i	0.258242	−	0.966080i	$-0.416857\pi$
$839$	−20.5029	−	20.5029i	−0.707838	−	0.707838i	−0.966080	+	0.258242i	$0.916857\pi$
$840$	−2.88764	−	7.23125i	−0.0996332	−	0.249502i
$841$		−	17.3407i		−	0.597955i
$842$	37.1044	−	37.1044i	1.27870	−	1.27870i
$843$	36.4714	−	10.4586i	1.25614	−	0.360215i
$844$	45.5167	+	45.5167i	1.56675	+	1.56675i
$845$	24.0617			0.827749
$846$	7.28890	−	31.5764i	0.250598	−	1.08562i
$847$	−6.51677	−	5.32115i	−0.223919	−	0.182837i
$848$	−7.00667	−	7.00667i	−0.240610	−	0.240610i
$849$	−20.4557	+	36.9045i	−0.702038	+	1.26656i
$850$	8.35752	+	8.35752i	0.286661	+	0.286661i
$851$			0.539915i			0.0185081i
$852$	11.3423	+	39.5527i	0.388579	+	1.35505i
$853$	−30.2203			−1.03472			−0.517362	−	0.855767i	$-0.673086\pi$
$853$	−30.2203			−1.03472			−0.517362	+	0.855767i	$0.673086\pi$
$854$	−1.01459	+	1.24256i	−0.0347185	+	0.0425195i
$855$	−7.19048	+	31.1500i	−0.245909	+	1.06531i
$856$		−	8.90858i		−	0.304489i
$857$	34.3852			1.17458			0.587289	−	0.809377i	$-0.300195\pi$
$857$	34.3852			1.17458			0.587289	+	0.809377i	$0.300195\pi$
$858$	5.20291	−	9.38667i	0.177625	−	0.320455i
$859$	50.9572			1.73864			0.869318	−	0.494253i	$-0.164558\pi$
$859$	50.9572			1.73864			0.869318	+	0.494253i	$0.164558\pi$
$860$	−43.9084			−1.49726
$861$	−12.9557	−	26.3278i	−0.441528	−	0.897248i
$862$	−51.7684			−1.76324
$863$	−26.2677			−0.894162			−0.447081	−	0.894494i	$-0.647536\pi$
$863$	−26.2677			−0.894162			−0.447081	+	0.894494i	$0.647536\pi$
$864$	2.19251	+	41.7965i	0.0745906	+	1.42194i
$865$	11.8464			0.402789
$866$			42.0767i			1.42982i
$867$	18.5890	−	33.5367i	0.631315	−	1.13897i
$868$	−32.9346	−	26.8921i	−1.11787	−	0.912778i
$869$	−41.6063			−1.41140
$870$	24.1448	−	6.92383i	0.818585	−	0.234740i
$871$		−	8.84731i		−	0.299780i
$872$	1.54446	+	1.54446i	0.0523019	+	0.0523019i
$873$	−19.6241	−	4.52992i	−0.664176	−	0.153314i
$874$	−15.5942	−	15.5942i	−0.527481	−	0.527481i
$875$	24.4836	+	19.9916i	0.827696	+	0.675840i
$876$	0.662332	+	0.367122i	0.0223781	+	0.0124039i
$877$	3.17121			0.107084			0.0535420	−	0.998566i	$-0.482949\pi$
$877$	3.17121			0.107084			0.0535420	+	0.998566i	$0.482949\pi$
$878$	−10.5078	−	10.5078i	−0.354622	−	0.354622i
$879$	0.308364	+	1.07533i	0.0104009	+	0.0362699i
$880$	12.1700	−	12.1700i	0.410250	−	0.410250i
$881$		−	8.27262i		−	0.278712i	−0.990242	−	0.139356i	$-0.955497\pi$
$881$		−	8.27262i		−	0.278712i	0.990242	−	0.139356i	$-0.0445032\pi$
$882$	31.9337	−	30.3426i	1.07526	−	1.02169i
$883$	−27.3976	−	27.3976i	−0.922001	−	0.922001i	0.0751695	−	0.997171i	$-0.476050\pi$
$883$	−27.3976	−	27.3976i	−0.922001	−	0.922001i	−0.997171	+	0.0751695i	$0.976050\pi$
$884$			15.8605i			0.533445i
$885$	4.53842	−	8.18784i	0.152557	−	0.275231i
$886$	−35.7503			−1.20105
$887$	−8.33058	−	8.33058i	−0.279714	−	0.279714i	0.553281	−	0.832995i	$-0.313376\pi$
$887$	−8.33058	−	8.33058i	−0.279714	−	0.279714i	−0.832995	+	0.553281i	$0.813376\pi$
$888$	0.343630	+	0.190470i	0.0115315	+	0.00639175i
$889$	−33.8711	+	41.4818i	−1.13600	+	1.39125i
$890$	−15.4209	−	15.4209i	−0.516910	−	0.516910i
$891$	−23.7963	+	8.19544i	−0.797205	+	0.274558i
$892$		−	8.71247i		−	0.291715i
$893$	−27.1042			−0.907009
$894$	6.45525	−	1.85113i	0.215896	−	0.0619109i
$895$	−5.56940	−	5.56940i	−0.186164	−	0.186164i
$896$	−11.0098	+	13.4836i	−0.367810	+	0.450455i
$897$	−3.51306	+	1.00742i	−0.117298	+	0.0336366i
$898$	−50.4192			−1.68251
$899$	16.1670	−	16.1670i	0.539201	−	0.539201i
$900$	3.43671	+	5.49948i	0.114557	+	0.183316i
$901$			20.3931i			0.679393i
$902$	−24.4267	+	28.5325i	−0.813320	+	0.950029i
$903$	−15.3560	−	38.4545i	−0.511015	−	1.27968i
$904$		−	14.1698i		−	0.471279i
$905$	−30.2965	−	30.2965i	−1.00709	−	1.00709i
$906$	−22.8628	+	6.55622i	−0.759567	+	0.217816i
$907$			52.6134i			1.74700i	0.486825	+	0.873499i	$0.338155\pi$
$907$			52.6134i			1.74700i	−0.486825	+	0.873499i	$0.661845\pi$
$908$	−1.71105	−	1.71105i	−0.0567833	−	0.0567833i
$909$	12.2950	−	53.2635i	0.407800	−	1.76664i
$910$	1.19273	+	11.8093i	0.0395387	+	0.391474i
$911$	38.5428			1.27698			0.638491	−	0.769630i	$-0.279559\pi$
$911$	38.5428			1.27698			0.638491	+	0.769630i	$0.279559\pi$
$912$	26.6376	−	7.63869i	0.882060	−	0.252942i
$913$	11.8253	+	11.8253i	0.391359	+	0.391359i
$914$	6.02142	+	6.02142i	0.199171	+	0.199171i
$915$	−0.491412	+	0.886564i	−0.0162456	+	0.0293089i
$916$	37.8224	−	37.8224i	1.24969	−	1.24969i
$917$	1.51538	+	1.23735i	0.0500422	+	0.0408610i
$918$	45.6245	−	50.6761i	1.50583	−	1.67256i
$919$	−12.9944	−	12.9944i	−0.428645	−	0.428645i	0.459521	−	0.888167i	$-0.348021\pi$
$919$	−12.9944	−	12.9944i	−0.428645	−	0.428645i	−0.888167	+	0.459521i	$0.848021\pi$
$920$	3.39411			0.111901
$921$	−3.00844	−	1.66754i	−0.0991316	−	0.0549474i
$922$	−55.4769			−1.82703
$923$		−	10.4554i		−	0.344145i
$924$	−28.2629	−	12.1321i	−0.929782	−	0.399115i
$925$	−0.243442			−0.00800432
$926$	−7.92194	+	7.92194i	−0.260331	+	0.260331i
$927$	−5.48081	−	8.77050i	−0.180014	−	0.288061i
$928$	−19.4480	−	19.4480i	−0.638413	−	0.638413i
$929$	23.8842	+	23.8842i	0.783616	+	0.783616i	0.980439	−	0.196823i	$-0.0630626\pi$
$929$	23.8842	+	23.8842i	0.783616	+	0.783616i	−0.196823	+	0.980439i	$0.563063\pi$
$930$	−43.0804	−	23.8790i	−1.41266	−	0.783022i
$931$	−30.7349	−	20.3163i	−1.00729	−	0.665839i
$932$	13.2925	+	13.2925i	0.435412	+	0.435412i
$933$	−14.4082	−	50.2444i	−0.471704	−	1.64493i
$934$	52.5795			1.72045
$935$	−35.4210			−1.15839
$936$	−0.598157	+	2.59129i	−0.0195514	+	0.0846989i
$937$	9.00990	−	9.00990i	0.294341	−	0.294341i	−0.544452	−	0.838792i	$-0.683262\pi$
$937$	9.00990	−	9.00990i	0.294341	−	0.294341i	0.838792	+	0.544452i	$0.183262\pi$
$938$	−46.2482	+	4.67105i	−1.51006	+	0.152515i
$939$	−31.3487	+	8.98965i	−1.02303	+	0.293366i
$940$	17.6950	−	17.6950i	0.577148	−	0.577148i
$941$			12.3856i			0.403760i	0.979410	+	0.201880i	$0.0647051\pi$
$941$			12.3856i			0.403760i	−0.979410	+	0.201880i	$0.935295\pi$
$942$	−9.29263	−	32.4053i	−0.302770	−	1.05582i
$943$	12.7522	−	0.988652i	0.415268	−	0.0321949i
$944$	−8.11467			−0.264110
$945$	16.4511	−	22.4530i	0.535154	−	0.730395i
$946$	−37.4789	+	37.4789i	−1.21854	+	1.21854i
$947$		−	17.7611i		−	0.577157i	−0.957456	−	0.288579i	$-0.906817\pi$
$947$		−	17.7611i		−	0.577157i	0.957456	−	0.288579i	$-0.0931827\pi$
$948$	59.4537	−	17.0491i	1.93097	−	0.553730i
$949$	−0.136064	−	0.136064i	−0.00441682	−	0.00441682i
$950$	7.03124	−	7.03124i	0.228124	−	0.228124i
$951$	1.52308	+	5.31129i	0.0493893	+	0.172230i
$952$	13.8204	−	1.39585i	0.447921	−	0.0452398i
$953$			54.6021i			1.76874i	0.466790	+	0.884368i	$0.345411\pi$
$953$			54.6021i			1.76874i	−0.466790	+	0.884368i	$0.654589\pi$
$954$	−4.61384	+	19.9877i	−0.149379	+	0.647126i
$955$	−26.4424	−	26.4424i	−0.855655	−	0.855655i
$956$	22.2114	+	22.2114i	0.718367	+	0.718367i
$957$	8.01791	−	14.4652i	0.259182	−	0.467595i
$958$	−5.04059	+	5.04059i	−0.162854	+	0.162854i
$959$	−0.421705	−	4.17531i	−0.0136176	−	0.134828i
$960$	−18.3891	+	33.1761i	−0.593507	+	1.07076i
$961$	−13.8352			−0.446296
$962$	−0.423485	−	0.423485i	−0.0136537	−	0.0136537i
$963$	27.0063	−	16.8767i	0.870267	−	0.543843i
$964$	−55.8853			−1.79994
$965$	36.2046	+	36.2046i	1.16547	+	1.16547i
$966$	7.12091	+	17.8322i	0.229112	+	0.573742i
$967$	23.5981	+	23.5981i	0.758862	+	0.758862i	0.976115	−	0.217253i	$-0.0697097\pi$
$967$	23.5981	+	23.5981i	0.758862	+	0.758862i	−0.217253	+	0.976115i	$0.569710\pi$
$968$		−	2.66865i		−	0.0857735i
$969$	−49.8811	−	27.6485i	−1.60241	−	0.888197i
$970$	−20.1611	−	20.1611i	−0.647334	−	0.647334i
$971$	−17.2598	+	17.2598i	−0.553893	+	0.553893i	−0.927562	−	0.373669i	$-0.878100\pi$
$971$	−17.2598	+	17.2598i	−0.553893	+	0.553893i	0.373669	+	0.927562i	$0.378100\pi$
$972$	30.6456	−	21.4620i	0.982959	−	0.688394i
$973$	−3.07950	−	2.51451i	−0.0987242	−	0.0806114i
$974$			37.4285i			1.19929i
$975$	−0.454233	−	1.58400i	−0.0145471	−	0.0507286i
$976$	0.878642			0.0281246
$977$	11.8320	+	11.8320i	0.378539	+	0.378539i	0.870575	−	0.492036i	$-0.163747\pi$
$977$	11.8320	+	11.8320i	0.378539	+	0.378539i	−0.492036	+	0.870575i	$0.663747\pi$
$978$	−42.6164	−	23.6217i	−1.36272	−	0.755340i
$979$	−14.3596			−0.458936
$980$	33.3288	−	6.80178i	1.06465	−	0.217275i
$981$	−1.75616	+	7.60788i	−0.0560698	+	0.242901i
$982$			55.8437i			1.78205i
$983$	9.95976			0.317667			0.158834	−	0.987305i	$-0.449227\pi$
$983$	9.95976			0.317667			0.158834	+	0.987305i	$0.449227\pi$
$984$	3.86945	−	8.46492i	0.123354	−	0.269852i
$985$		−	21.6873i		−	0.691015i
$986$			44.8090i			1.42701i
$987$	21.6855	+	9.30866i	0.690258	+	0.296298i
$988$	13.3435			0.424514
$989$	18.0493			0.573934
$990$	−34.7169	−	8.01384i	−1.10338	−	0.254697i
$991$	0.311106	−	0.311106i	0.00988259	−	0.00988259i	−0.702148	−	0.712031i	$-0.747776\pi$
$991$	0.311106	−	0.311106i	0.00988259	−	0.00988259i	0.712031	+	0.702148i	$0.247776\pi$
$992$			53.9341i			1.71241i
$993$	1.78064	−	0.510623i	0.0565070	−	0.0162041i
$994$	−54.6545	+	5.52009i	−1.73354	+	0.175087i
$995$	−24.0412	−	24.0412i	−0.762157	−	0.762157i
$996$	−21.7435	−	12.0521i	−0.688968	−	0.381887i
$997$	38.1817	+	38.1817i	1.20923	+	1.20923i	0.971278	+	0.237947i	$0.0764746\pi$
$997$	38.1817	+	38.1817i	1.20923	+	1.20923i	0.237947	+	0.971278i	$0.423525\pi$
$998$	−17.3882	+	17.3882i	−0.550414	+	0.550414i
$999$	0.0735729	+	1.40254i	0.00232774	+	0.0443746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.l.a.524.93	yes	216
3.2	odd	2	inner	861.2.l.a.524.15	yes	216
7.6	odd	2	inner	861.2.l.a.524.94	yes	216
21.20	even	2	inner	861.2.l.a.524.16	yes	216
41.9	even	4	inner	861.2.l.a.419.16	yes	216
123.50	odd	4	inner	861.2.l.a.419.94	yes	216
287.132	odd	4	inner	861.2.l.a.419.15	✓	216
861.419	even	4	inner	861.2.l.a.419.93	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.l.a.419.15	✓	216	287.132	odd	4	inner
861.2.l.a.419.16	yes	216	41.9	even	4	inner
861.2.l.a.419.93	yes	216	861.419	even	4	inner
861.2.l.a.419.94	yes	216	123.50	odd	4	inner
861.2.l.a.524.15	yes	216	3.2	odd	2	inner
861.2.l.a.524.16	yes	216	21.20	even	2	inner
861.2.l.a.524.93	yes	216	1.1	even	1	trivial
861.2.l.a.524.94	yes	216	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.09764 q^{2} +(-1.51490 - 0.839690i) q^{3} +2.40008 q^{4} +2.02468i q^{5} +(-3.17771 - 1.76136i) q^{6} +(1.67336 - 2.04936i) q^{7} +0.839219 q^{8} +(1.58984 + 2.54409i) q^{9} +O(q^{10})\)	\(q+2.09764 q^{2} +(-1.51490 - 0.839690i) q^{3} +2.40008 q^{4} +2.02468i q^{5} +(-3.17771 - 1.76136i) q^{6} +(1.67336 - 2.04936i) q^{7} +0.839219 q^{8} +(1.58984 + 2.54409i) q^{9} +4.24705i q^{10} +(1.97738 + 1.97738i) q^{11} +(-3.63588 - 2.01532i) q^{12} +(0.746924 + 0.746924i) q^{13} +(3.51011 - 4.29880i) q^{14} +(1.70011 - 3.06719i) q^{15} -3.03978 q^{16} +(4.42368 + 4.42368i) q^{17} +(3.33491 + 5.33658i) q^{18} +(3.72167 - 3.72167i) q^{19} +4.85939i q^{20} +(-4.25580 + 1.69946i) q^{21} +(4.14783 + 4.14783i) q^{22} -1.99753i q^{23} +(-1.27133 - 0.704684i) q^{24} +0.900666 q^{25} +(1.56678 + 1.56678i) q^{26} +(-0.272199 - 5.18902i) q^{27} +(4.01620 - 4.91861i) q^{28} +(2.41447 + 2.41447i) q^{29} +(3.56620 - 6.43385i) q^{30} -6.69591i q^{31} -8.05479 q^{32} +(-1.33515 - 4.65593i) q^{33} +(9.27928 + 9.27928i) q^{34} +(4.14929 + 3.38803i) q^{35} +(3.81574 + 6.10602i) q^{36} -0.270291 q^{37} +(7.80672 - 7.80672i) q^{38} +(-0.504330 - 1.75870i) q^{39} +1.69915i q^{40} +(0.494936 + 6.38397i) q^{41} +(-8.92712 + 3.56485i) q^{42} +9.03578i q^{43} +(4.74587 + 4.74587i) q^{44} +(-5.15098 + 3.21892i) q^{45} -4.19010i q^{46} +(-3.64140 - 3.64140i) q^{47} +(4.60496 + 2.55247i) q^{48} +(-1.39972 - 6.85863i) q^{49} +1.88927 q^{50} +(-2.98691 - 10.4160i) q^{51} +(1.79268 + 1.79268i) q^{52} +(2.30499 + 2.30499i) q^{53} +(-0.570974 - 10.8847i) q^{54} +(-4.00357 + 4.00357i) q^{55} +(1.40432 - 1.71986i) q^{56} +(-8.76301 + 2.51291i) q^{57} +(5.06467 + 5.06467i) q^{58} +2.66949 q^{59} +(4.08039 - 7.36149i) q^{60} -0.289048 q^{61} -14.0456i q^{62} +(7.87413 + 0.999040i) q^{63} -10.8165 q^{64} +(-1.51228 + 1.51228i) q^{65} +(-2.80065 - 9.76644i) q^{66} +(-5.92249 - 5.92249i) q^{67} +(10.6172 + 10.6172i) q^{68} +(-1.67731 + 3.02606i) q^{69} +(8.70371 + 7.10685i) q^{70} +(-6.99899 - 6.99899i) q^{71} +(1.33423 + 2.13505i) q^{72} -0.182166 q^{73} -0.566972 q^{74} +(-1.36442 - 0.756280i) q^{75} +(8.93231 - 8.93231i) q^{76} +(7.36124 - 0.743483i) q^{77} +(-1.05790 - 3.68911i) q^{78} +(-10.5205 + 10.5205i) q^{79} -6.15459i q^{80} +(-3.94481 + 8.08940i) q^{81} +(1.03820 + 13.3912i) q^{82} +5.98025 q^{83} +(-10.2143 + 4.07884i) q^{84} +(-8.95655 + 8.95655i) q^{85} +18.9538i q^{86} +(-1.63027 - 5.68508i) q^{87} +(1.65946 + 1.65946i) q^{88} +(-3.63097 + 3.63097i) q^{89} +(-10.8049 + 6.75212i) q^{90} +(2.78059 - 0.280839i) q^{91} -4.79424i q^{92} +(-5.62249 + 10.1436i) q^{93} +(-7.63834 - 7.63834i) q^{94} +(7.53520 + 7.53520i) q^{95} +(12.2022 + 6.76353i) q^{96} +(-4.74709 + 4.74709i) q^{97} +(-2.93610 - 14.3869i) q^{98} +(-1.88692 + 8.17437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 192 q^{4} - 4 q^{7}+O(q^{10}) \) 216 * q + 192 * q^4 - 4 * q^7	\( 216 q + 192 q^{4} - 4 q^{7} + 20 q^{15} + 144 q^{16} - 24 q^{18} - 56 q^{22} - 200 q^{25} - 40 q^{28} + 32 q^{30} + 16 q^{37} + 4 q^{42} - 16 q^{51} - 64 q^{57} - 32 q^{58} + 40 q^{60} - 6 q^{63} + 48 q^{64} - 48 q^{67} + 48 q^{70} - 92 q^{72} + 28 q^{78} + 8 q^{79} - 120 q^{81} + 16 q^{85} - 144 q^{88} - 16 q^{93} + 56 q^{99}+O(q^{100}) \) 216 * q + 192 * q^4 - 4 * q^7 + 20 * q^15 + 144 * q^16 - 24 * q^18 - 56 * q^22 - 200 * q^25 - 40 * q^28 + 32 * q^30 + 16 * q^37 + 4 * q^42 - 16 * q^51 - 64 * q^57 - 32 * q^58 + 40 * q^60 - 6 * q^63 + 48 * q^64 - 48 * q^67 + 48 * q^70 - 92 * q^72 + 28 * q^78 + 8 * q^79 - 120 * q^81 + 16 * q^85 - 144 * q^88 - 16 * q^93 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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