LMFDB - Embedded newform 861.2.l.a.419.94

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			419.94
Character	$\chi$	$=$	861.419
Dual form			861.2.l.a.524.94

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09764 q^{2} +(1.51490 - 0.839690i) q^{3} +2.40008 q^{4} +2.02468i q^{5} +(3.17771 - 1.76136i) q^{6} +(2.04936 + 1.67336i) q^{7} +0.839219 q^{8} +(1.58984 - 2.54409i) q^{9} +O(q^{10})$	\(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} +(2.04936 + 1.67336i) 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} +(4.29880 + 3.51011i) 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} +(4.50967 + 0.814152i) 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} +(4.91861 + 4.01620i) 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} +(-3.38803 + 4.14929i) 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} +(9.45966 + 1.70779i) 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} +(1.71986 + 1.40432i) 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} +(7.51534 - 2.55337i) 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} +(-7.10685 + 8.70371i) 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} +(10.8236 + 1.95403i) 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 $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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
$7$	2.04936	+	1.67336i	0.774584	+	0.632472i
$7$	2.04936	+	1.67336i	0.774584	+	0.632472i
$8$	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	−0.343097	−	0.939300i	$-0.611476\pi$
$11$	1.97738	−	1.97738i	0.596203	−	0.596203i	0.939300	+	0.343097i	$0.111476\pi$
$12$	3.63588	−	2.01532i	1.04959	−	0.581774i
$13$	−0.746924	+	0.746924i	−0.207160	+	0.207160i	−0.803059	−	0.595900i	$-0.796796\pi$
$13$	−0.746924	+	0.746924i	−0.207160	+	0.207160i	0.595900	+	0.803059i	$0.296796\pi$
$14$	4.29880	+	3.51011i	1.14890	+	0.938115i
$15$	1.70011	+	3.06719i	0.438965	+	0.791945i
$16$	−3.03978			−0.759945
$17$	−4.42368	+	4.42368i	−1.07290	+	1.07290i	−0.0757755	+	0.997125i	$0.524143\pi$
$17$	−4.42368	+	4.42368i	−1.07290	+	1.07290i	−0.997125	+	0.0757755i	$0.975857\pi$
$18$	3.33491	−	5.33658i	0.786045	−	1.25784i
$19$	−3.72167	−	3.72167i	−0.853810	−	0.853810i	0.136790	−	0.990600i	$-0.456322\pi$
$19$	−3.72167	−	3.72167i	−0.853810	−	0.853810i	−0.990600	+	0.136790i	$0.956322\pi$
$20$			4.85939i			1.08659i
$21$	4.50967	+	0.814152i	0.984091	+	0.177662i
$22$	4.14783	−	4.14783i	0.884320	−	0.884320i
$23$			1.99753i			0.416514i	0.978074	+	0.208257i	$0.0667791\pi$
$23$			1.99753i			0.416514i	−0.978074	+	0.208257i	$0.933221\pi$
$24$	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
$28$	4.91861	+	4.01620i	0.929531	+	0.758991i
$29$	2.41447	−	2.41447i	0.448355	−	0.448355i	−0.446452	−	0.894807i	$-0.647313\pi$
$29$	2.41447	−	2.41447i	0.448355	−	0.448355i	0.894807	+	0.446452i	$0.147313\pi$
$30$	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
$35$	−3.38803	+	4.14929i	−0.572681	+	0.701358i
$36$	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
$42$	9.45966	+	1.70779i	1.45966	+	0.263518i
$43$		−	9.03578i		−	1.37794i	−0.724788	−	0.688972i	$-0.758062\pi$
$43$		−	9.03578i		−	1.37794i	0.724788	−	0.688972i	$-0.241938\pi$
$44$	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	$-0.627443\pi$
$47$	3.64140	−	3.64140i	0.531153	−	0.531153i	0.920916	+	0.389762i	$0.127443\pi$
$48$	−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	−0.530851	−	0.847465i	$-0.678127\pi$
$53$	2.30499	−	2.30499i	0.316615	−	0.316615i	0.847465	+	0.530851i	$0.178127\pi$
$54$	0.570974	−	10.8847i	0.0776998	−	1.48122i
$55$	4.00357	+	4.00357i	0.539841	+	0.539841i
$56$	1.71986	+	1.40432i	0.229826	+	0.187660i
$57$	−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	$-0.555595\pi$
$59$	−2.66949			−0.347538			−0.173769	+	0.984786i	$0.555595\pi$
$60$	4.08039	+	7.36149i	0.526776	+	0.950365i
$61$	0.289048			0.0370088			0.0185044	−	0.999829i	$-0.494110\pi$
$61$	0.289048			0.0370088			0.0185044	+	0.999829i	$0.494110\pi$
$62$		−	14.0456i		−	1.78379i
$63$	7.51534	−	2.55337i	0.946844	−	0.321695i
$64$	−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	−0.969326	−	0.245778i	$-0.920956\pi$
$67$	−5.92249	+	5.92249i	−0.723548	+	0.723548i	0.245778	+	0.969326i	$0.420956\pi$
$68$	−10.6172	+	10.6172i	−1.28752	+	1.28752i
$69$	1.67731	+	3.02606i	0.201924	+	0.364295i
$70$	−7.10685	+	8.70371i	−0.849431	+	1.04029i
$71$	−6.99899	+	6.99899i	−0.830628	+	0.830628i	−0.987603	−	0.156975i	$-0.949826\pi$
$71$	−6.99899	+	6.99899i	−0.830628	+	0.830628i	0.156975	+	0.987603i	$0.449826\pi$
$72$	1.33423	−	2.13505i	0.157240	−	0.251618i
$73$	0.182166			0.0213209			0.0106604	−	0.999943i	$-0.496607\pi$
$73$	0.182166			0.0213209			0.0106604	+	0.999943i	$0.496607\pi$
$74$	−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	−0.978791	−	0.204863i	$-0.934325\pi$
$79$	−10.5205	−	10.5205i	−1.18365	−	1.18365i	−0.204863	−	0.978791i	$-0.565675\pi$
$80$		−	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	$-0.606445\pi$
$83$	−5.98025			−0.656418			−0.328209	+	0.944605i	$0.606445\pi$
$84$	10.8236	+	1.95403i	1.18095	+	0.213202i
$85$	−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	$-0.162264\pi$
$89$	3.63097	+	3.63097i	0.384882	+	0.384882i	−0.487975	+	0.872857i	$0.662264\pi$
$90$	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	$-0.139295\pi$
$97$	4.74709	+	4.74709i	0.481994	+	0.481994i	−0.423774	+	0.905768i	$0.639295\pi$
$98$	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	0.342553	−	0.939499i	$-0.388708\pi$
$101$	12.8845	−	12.8845i	1.28205	−	1.28205i	0.939499	−	0.342553i	$-0.111292\pi$
$102$	−6.26545	+	21.8489i	−0.620372	+	2.16336i
$103$	3.44740			0.339682			0.169841	−	0.985471i	$-0.445675\pi$
$103$	3.44740			0.339682			0.169841	+	0.985471i	$0.445675\pi$
$104$	−0.626833	+	0.626833i	−0.0614661	+	0.0614661i
$105$	−1.64840	+	9.13065i	−0.160867	+	0.891060i
$106$	4.83503	−	4.83503i	0.469620	−	0.469620i
$107$			10.6153i			1.02622i	0.858322	+	0.513111i	$0.171507\pi$
$107$			10.6153i			1.02622i	−0.858322	+	0.513111i	$0.828493\pi$
$108$	0.653299	−	12.4541i	0.0628637	−	1.19839i
$109$	1.84035	−	1.84035i	0.176274	−	0.176274i	−0.613456	−	0.789729i	$-0.710221\pi$
$109$	1.84035	−	1.84035i	0.176274	−	0.176274i	0.789729	+	0.613456i	$0.210221\pi$
$110$	8.39803	+	8.39803i	0.800721	+	0.800721i
$111$	−0.409464	+	0.226961i	−0.0388646	+	0.0215422i
$112$	−6.22959	−	5.08665i	−0.588641	−	0.480644i
$113$			16.8845i			1.58836i	0.607685	+	0.794178i	$0.292098\pi$
$113$			16.8845i			1.58836i	−0.607685	+	0.794178i	$0.707902\pi$
$114$	−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
$126$	15.7644	−	5.35604i	1.40441	−	0.477154i
$127$	−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	0.753393	−	0.657570i	$-0.228416\pi$
$137$	1.12158	+	1.12158i	0.0958226	+	0.0958226i	−0.657570	+	0.753393i	$0.728416\pi$
$138$	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	$-0.0202988\pi$
$140$	−8.13153	+	9.95863i	−0.687239	+	0.841658i
$141$	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
$147$	7.87955	+	9.21480i	0.649895	+	0.760024i
$148$	−0.648720			−0.0533244
$149$	−1.30698	−	1.30698i	−0.107072	−	0.107072i	0.651541	−	0.758613i	$-0.274123\pi$
$149$	−1.30698	−	1.30698i	−0.107072	−	0.107072i	−0.758613	+	0.651541i	$0.774123\pi$
$150$	2.86205	−	1.58640i	0.233686	−	0.129529i
$151$	4.62897	+	4.62897i	0.376701	+	0.376701i	0.869910	−	0.493210i	$-0.164177\pi$
$151$	4.62897	+	4.62897i	0.376701	+	0.376701i	−0.493210	+	0.869910i	$0.664177\pi$
$152$	−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	$-0.870731\pi$
$157$	−6.56100	+	6.56100i	−0.523625	+	0.523625i	0.395039	+	0.918664i	$0.370731\pi$
$158$	−22.0683	−	22.0683i	−1.75566	−	1.75566i
$159$	1.55635	−	5.42731i	0.123427	−	0.430414i
$160$		−	16.3084i		−	1.28929i
$161$	−3.34260	+	4.09366i	−0.263434	+	0.322625i
$162$	−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	$-0.222679\pi$
$167$	1.56671	+	1.56671i	0.121235	+	0.121235i	−0.643886	+	0.765121i	$0.722679\pi$
$168$	3.78461	+	0.683252i	0.291989	+	0.0527140i
$169$			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
$175$	1.84578	+	1.50714i	0.139528	+	0.113929i
$176$	−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	0.596794	−	0.802395i	$-0.296441\pi$
$179$	−2.75075	−	2.75075i	−0.205601	−	0.205601i	−0.802395	+	0.596794i	$0.796441\pi$
$180$	12.3627	+	7.72566i	0.921465	+	0.575837i
$181$	14.9636	+	14.9636i	1.11224	+	1.11224i	0.992848	+	0.119388i	$0.0380931\pi$
$181$	14.9636	+	14.9636i	1.11224	+	1.11224i	0.119388	+	0.992848i	$0.461907\pi$
$182$	−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
$189$	9.24094	−	10.1787i	0.672179	−	0.740388i
$190$	15.8061	−	15.8061i	1.14670	−	1.14670i
$191$	−13.0600	−	13.0600i	−0.944989	−	0.944989i	0.0535744	−	0.998564i	$-0.482939\pi$
$191$	−13.0600	−	13.0600i	−0.944989	−	0.944989i	−0.998564	+	0.0535744i	$0.982939\pi$
$192$	−16.3859	+	9.08248i	−1.18255	+	0.655472i
$193$	17.8816	+	17.8816i	1.28715	+	1.28715i	0.936513	+	0.350633i	$0.114034\pi$
$193$	17.8816	+	17.8816i	1.28715	+	1.28715i	0.350633	+	0.936513i	$0.385966\pi$
$194$	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	$-0.0470756\pi$
$199$	11.8741	+	11.8741i	0.841730	+	0.841730i	−0.147354	+	0.989084i	$0.547076\pi$
$200$	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
$210$	−3.45774	+	19.1528i	−0.238607	+	1.32167i
$211$	18.9647	−	18.9647i	1.30558	−	1.30558i	0.381010	−	0.924571i	$-0.375576\pi$
$211$	18.9647	−	18.9647i	1.30558	−	1.30558i	0.924571	−	0.381010i	$-0.124424\pi$
$212$	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
$217$	11.2047	−	13.7223i	0.760623	−	0.931530i
$218$	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	$-0.0387845\pi$
$224$	−16.5071	−	13.4786i	−1.10293	−	0.900576i
$225$	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	$-0.739348\pi$
$227$	0.712916	−	0.712916i	0.0473179	−	0.0473179i	0.730370	+	0.683052i	$0.239348\pi$
$228$	−21.0319	−	6.03118i	−1.39287	−	0.399424i
$229$	−15.7588	−	15.7588i	−1.04137	−	1.04137i	−0.999106	−	0.0422653i	$-0.986543\pi$
$229$	−15.7588	−	15.7588i	−1.04137	−	1.04137i	−0.0422653	−	0.999106i	$-0.513457\pi$
$230$	−8.48361			−0.559393
$231$	10.5272	−	7.30746i	0.692642	−	0.480796i
$232$	2.02627	−	2.02627i	0.133031	−	0.133031i
$233$	5.53838	−	5.53838i	0.362831	−	0.362831i	−0.502023	−	0.864854i	$-0.667411\pi$
$233$	5.53838	−	5.53838i	0.362831	−	0.362831i	0.864854	+	0.502023i	$0.167411\pi$
$234$	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	−0.341326	−	0.939945i	$-0.610876\pi$
$239$	9.25443	−	9.25443i	0.598620	−	0.598620i	0.939945	+	0.341326i	$0.110876\pi$
$240$	−5.16795	−	9.32358i	−0.333589	−	0.601834i
$241$	23.2848			1.49990			0.749952	−	0.661493i	$-0.230077\pi$
$241$	23.2848			1.49990			0.749952	+	0.661493i	$0.230077\pi$
$242$			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	$-0.119748\pi$
$252$	18.0374	−	6.12829i	1.13625	−	0.386046i
$253$	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	$-0.111995\pi$
$257$	9.52431	+	9.52431i	0.594110	+	0.594110i	−0.344629	+	0.938739i	$0.611995\pi$
$258$	−15.9153	−	28.7131i	−0.990844	−	1.78760i
$259$	−0.553922	−	0.452295i	−0.0344191	−	0.0281042i
$260$	−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	0.961415	+	0.275103i	$0.0887118\pi$
$263$	20.0529	+	20.0529i	1.23652	+	1.23652i	0.275103	+	0.961415i	$0.411288\pi$
$264$	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	$-0.647678\pi$
$269$	−14.6784			−0.894960			−0.447480	+	0.894294i	$0.647678\pi$
$270$	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
$273$	−3.97649	+	2.76027i	−0.240668	+	0.167059i
$274$	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
$280$	−2.84330	+	3.48217i	−0.169919	+	0.208099i
$281$	−15.4895	−	15.4895i	−0.924025	−	0.924025i	0.0732859	−	0.997311i	$-0.476651\pi$
$281$	−15.4895	−	15.4895i	−0.924025	−	0.924025i	−0.997311	+	0.0732859i	$0.976651\pi$
$282$	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
$287$	−11.6970	+	12.2548i	−0.690452	+	0.723379i
$288$	−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	$-0.743994\pi$
$293$	0.456694	−	0.456694i	0.0266803	−	0.0266803i	0.720321	+	0.693641i	$0.243994\pi$
$294$	16.5284	+	19.3293i	0.963958	+	1.12731i
$295$		−	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
$301$	15.1201	−	18.5175i	0.871510	−	1.06733i
$302$	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	$-0.518049\pi$
$307$	−1.98590			−0.113342			−0.0566708	+	0.998393i	$0.518049\pi$
$308$	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	−0.238999	+	0.971020i	$0.576819\pi$
$311$	−21.3389	+	21.3389i	−1.21002	+	1.21002i	−0.971020	+	0.238999i	$0.923181\pi$
$312$	−0.423244	+	1.47594i	−0.0239615	+	0.0835584i
$313$	−13.3139	−	13.3139i	−0.752545	−	0.752545i	0.222409	−	0.974954i	$-0.428608\pi$
$313$	−13.3139	−	13.3139i	−0.752545	−	0.752545i	−0.974954	+	0.222409i	$0.928608\pi$
$314$	−13.7626	+	13.7626i	−0.776668	+	0.776668i
$315$	5.16976	+	15.2162i	0.291283	+	0.857334i
$316$	−25.2501	−	25.2501i	−1.42043	−	1.42043i
$317$	−2.25572	+	2.25572i	−0.126694	+	0.126694i	−0.767610	−	0.640917i	$-0.778554\pi$
$317$	−2.25572	+	2.25572i	−0.126694	+	0.126694i	0.640917	+	0.767610i	$0.278554\pi$
$318$	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
$322$	−7.01155	+	8.58700i	−0.390739	+	0.478535i
$323$	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	0.686018	−	0.727585i	$-0.259357\pi$
$331$	−0.756244	−	0.756244i	−0.0415669	−	0.0415669i	−0.727585	+	0.686018i	$0.759357\pi$
$332$	−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
$336$	−13.7084	−	2.47484i	−0.747855	−	0.135014i
$337$			24.2200i			1.31935i	0.751553	+	0.659673i	$0.229305\pi$
$337$			24.2200i			1.31935i	−0.751553	+	0.659673i	$0.770695\pi$
$338$			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
$343$	−8.60845	+	16.3980i	−0.464813	+	0.885409i
$344$		−	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	0.917317	+	0.398158i	$0.130350\pi$
$347$	24.5046	+	24.5046i	1.31547	+	1.31547i	0.398158	+	0.917317i	$0.369650\pi$
$348$	3.91278	−	13.6446i	0.209747	−	0.731429i
$349$	36.0130			1.92773			0.963865	−	0.266391i	$-0.0858311\pi$
$349$	36.0130			1.92773			0.963865	+	0.266391i	$0.0858311\pi$
$350$	3.87178	+	3.16143i	0.206956	+	0.168986i
$351$	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	$-0.836630\pi$
$353$	−32.7351			−1.74231			−0.871157	+	0.491005i	$0.836630\pi$
$354$	−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
$357$	−23.5509	+	16.3478i	−1.24645	+	0.865218i
$358$	−5.77008	−	5.77008i	−0.304958	−	0.304958i
$359$		−	18.7389i		−	0.989003i	−0.869177	−	0.494501i	$-0.835351\pi$
$359$		−	18.7389i		−	0.989003i	0.869177	−	0.494501i	$-0.164649\pi$
$360$	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	$-0.357469\pi$
$367$	16.5886			0.865919			0.432959	+	0.901413i	$0.357469\pi$
$368$		−	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
$378$	19.3841	−	21.3511i	0.997012	−	1.09818i
$379$	−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	$-0.596557\pi$
$383$	12.8310	−	12.8310i	0.655633	−	0.655633i	0.954344	+	0.298711i	$0.0965566\pi$
$384$	−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	$-0.779785\pi$
$397$	−2.63287	+	2.63287i	−0.132140	+	0.132140i	0.637943	+	0.770083i	$0.279785\pi$
$398$	24.9075	+	24.9075i	1.24850	+	1.24850i
$399$	−13.7535	−	19.8135i	−0.688537	−	0.991918i
$400$	−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
$413$	−5.47074	−	4.46703i	−0.269197	−	0.219808i
$414$	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	$0.895201\pi$
$420$	−3.95628	+	21.9143i	−0.193047	+	1.06931i
$421$	17.6887	+	17.6887i	0.862093	+	0.862093i	0.991581	−	0.129488i	$-0.0413332\pi$
$421$	17.6887	+	17.6887i	0.862093	+	0.862093i	−0.129488	+	0.991581i	$0.541333\pi$
$422$	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
$427$	0.592362	+	0.483682i	0.0286664	+	0.0234070i
$428$			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	$0.839914\pi$
$434$	23.5033	−	28.7844i	1.12820	−	1.38169i
$435$	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	$-0.695927\pi$
$439$	5.00937	−	5.00937i	0.239084	−	0.239084i	0.816471	+	0.577387i	$0.195927\pi$
$440$	3.35987	+	3.35987i	0.160176	+	0.160176i
$441$	19.6743	+	7.34312i	0.936872	+	0.349672i
$442$		−	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
$448$	−22.1668	−	18.0999i	−1.04728	−	0.855138i
$449$	−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	−0.636772	−	0.771052i	$-0.719731\pi$
$457$	2.87058	−	2.87058i	0.134280	−	0.134280i	0.771052	+	0.636772i	$0.219731\pi$
$458$	−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	$-0.288798\pi$
$461$	26.4473			1.23177			0.615887	+	0.787834i	$0.288798\pi$
$462$	22.0823	−	15.3284i	1.02736	−	0.713142i
$463$	−3.77660	−	3.77660i	−0.175514	−	0.175514i	0.613883	−	0.789397i	$-0.289607\pi$
$463$	−3.77660	−	3.77660i	−0.175514	−	0.175514i	−0.789397	+	0.613883i	$0.789607\pi$
$464$	−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	$-0.696932\pi$
$467$	−25.0661			−1.15992			−0.579959	+	0.814645i	$0.696932\pi$
$468$	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	$-0.225262\pi$
$479$	2.40299	+	2.40299i	0.109795	+	0.109795i	−0.650075	+	0.759870i	$0.725262\pi$
$480$	−13.6940	−	24.7056i	−0.625042	−	1.12765i
$481$	0.201887	−	0.201887i	0.00920525	−	0.00920525i
$482$	48.8430			2.22474
$483$	−1.62630	+	9.00822i	−0.0739990	+	0.409888i
$484$			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	$-0.867524\pi$
$487$		−	17.8432i		−	0.808552i	0.914637	−	0.404276i	$-0.132476\pi$
$488$	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	$-0.794880\pi$
$491$		−	26.6222i		−	1.20144i	0.799458	−	0.600722i	$-0.205120\pi$
$492$	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	0.496787	−	0.867873i	$-0.334513\pi$
$499$	−8.28943	−	8.28943i	−0.371086	−	0.371086i	−0.867873	+	0.496787i	$0.834513\pi$
$500$			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	0.963960	+	0.266048i	$0.0857181\pi$
$503$	27.5862	+	27.5862i	1.23001	+	1.23001i	0.266048	+	0.963960i	$0.414282\pi$
$504$	6.30702	−	2.14284i	0.280937	−	0.0954496i
$505$	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	$-0.970891\pi$
$509$	−20.4064	+	20.4064i	−0.904499	+	0.904499i	0.0913223	+	0.995821i	$0.470891\pi$
$510$	−44.2370	−	12.6855i	−1.95885	−	0.561725i
$511$	0.373322	+	0.304829i	0.0165148	+	0.0134848i
$512$	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
$518$	−1.16193	−	0.948750i	−0.0510522	−	0.0416857i
$519$	−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	0.983635	+	0.180171i	$0.0576652\pi$
$521$	26.5644	+	26.5644i	1.16381	+	1.16381i	0.180171	+	0.983635i	$0.442335\pi$
$522$	−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
$525$	4.06171	+	0.733278i	0.177267	+	0.0320029i
$526$	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
$539$	16.3299	+	10.7944i	0.703379	+	0.464946i
$540$	25.2155	+	1.32272i	1.08510	+	0.0569209i
$541$		−	0.180347i		−	0.00775374i	−0.999992	−	0.00387687i	$-0.998766\pi$
$541$		−	0.180347i		−	0.00775374i	0.999992	−	0.00387687i	$-0.00123405\pi$
$542$		−	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
$546$	−8.34124	+	5.79005i	−0.356972	+	0.247791i
$547$	5.59800	−	5.59800i	0.239353	−	0.239353i	−0.577229	−	0.816582i	$-0.695866\pi$
$547$	5.59800	−	5.59800i	0.239353	−	0.239353i	0.816582	+	0.577229i	$0.195866\pi$
$548$	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	0.227581	−	0.973759i	$-0.426918\pi$
$557$	−17.6104	−	17.6104i	−0.746179	−	0.746179i	−0.973759	+	0.227581i	$0.926918\pi$
$558$	−35.7332	−	22.3302i	−1.51271	−	0.945314i
$559$	6.74904	+	6.74904i	0.285454	+	0.285454i
$560$	10.2989	−	12.6129i	0.435206	−	0.532994i
$561$	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	$-0.0873562\pi$
$563$	16.4094	+	16.4094i	0.691572	+	0.691572i	−0.271006	+	0.962578i	$0.587356\pi$
$564$	5.90110	−	20.5783i	0.248481	−	0.866503i
$565$	−34.1856			−1.43820
$566$		−	51.1006i		−	2.14792i
$567$	5.45218	−	23.1792i	0.228970	−	0.973434i
$568$	−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	0.909535	−	0.415628i	$-0.136438\pi$
$571$	11.8022	+	11.8022i	0.493907	+	0.493907i	−0.415628	+	0.909535i	$0.636438\pi$
$572$			7.08962i			0.296432i
$573$	−30.7510	−	8.81824i	−1.28464	−	0.368387i
$574$	−24.5360	+	25.7061i	−1.02411	+	1.07295i
$575$			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	$-0.678772\pi$
$577$	7.53826	−	7.53826i	0.313822	−	0.313822i	0.846388	+	0.532566i	$0.178772\pi$
$578$		−	46.4373i		−	1.93154i
$579$	42.1038	+	12.0738i	1.74978	+	0.501771i
$580$	11.7328	+	11.7328i	0.487180	+	0.487180i
$581$	−12.2557	−	10.0071i	−0.508451	−	0.415166i
$582$	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	$-0.247687\pi$
$587$	0.248981	+	0.248981i	0.0102765	+	0.0102765i	−0.701950	+	0.712226i	$0.747687\pi$
$588$	18.9116	+	22.1163i	0.779899	+	0.912059i
$589$	−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	$-0.696922\pi$
$593$	5.71596	−	5.71596i	0.234726	−	0.234726i	0.814662	+	0.579936i	$0.196922\pi$
$594$	−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	$-0.849603\pi$
$599$		−	22.2767i		−	0.910201i	0.890440	−	0.455101i	$-0.150397\pi$
$600$	1.14505	−	0.634685i	0.0467463	−	0.0259109i
$601$	−8.30614	−	8.30614i	−0.338814	−	0.338814i	0.517107	−	0.855921i	$-0.327009\pi$
$601$	−8.30614	−	8.30614i	−0.338814	−	0.338814i	−0.855921	+	0.517107i	$0.827009\pi$
$602$	31.7165	−	38.8430i	1.29267	−	1.58312i
$603$	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	$-0.471829\pi$
$607$	4.35516			0.176771			0.0883853	+	0.996086i	$0.471829\pi$
$608$	29.9773	+	29.9773i	1.21574	+	1.21574i
$609$	12.8542	−	8.92272i	0.520879	−	0.361567i
$610$			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	$0.199026\pi$
$613$			28.9830i			1.17061i	−0.810812	+	0.585307i	$0.800974\pi$
$614$	−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
$630$	10.8443	+	31.9180i	0.432047	+	1.27164i
$631$	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
$637$	−6.16836	−	4.07739i	−0.244399	−	0.161552i
$638$		−	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	0.830808	−	0.556559i	$-0.187879\pi$
$641$	6.94341	+	6.94341i	0.274248	+	0.274248i	−0.556559	+	0.830808i	$0.687879\pi$
$642$	18.6974	+	33.7324i	0.737929	+	1.33131i
$643$	−26.5169	+	26.5169i	−1.04573	+	1.04573i	−0.0468220	+	0.998903i	$0.514909\pi$
$643$	−26.5169	+	26.5169i	−1.04573	+	1.04573i	−0.998903	+	0.0468220i	$0.985091\pi$
$644$	−8.02250	+	9.82510i	−0.316131	+	0.387163i
$645$	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
$651$	5.45148	−	30.1964i	0.213660	−	1.18349i
$652$	32.1876			1.26056
$653$	29.7126	−	29.7126i	1.16275	−	1.16275i	0.178873	−	0.983872i	$-0.442755\pi$
$653$	29.7126	−	29.7126i	1.16275	−	1.16275i	0.983872	−	0.178873i	$-0.0572451\pi$
$654$	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	−0.877498	−	0.479580i	$-0.840789\pi$
$659$	−10.2150	+	10.2150i	−0.397918	+	0.397918i	0.479580	+	0.877498i	$0.340789\pi$
$660$	22.6250	+	6.48801i	0.880676	+	0.252545i
$661$	16.9744			0.660227			0.330114	−	0.943941i	$-0.392913\pi$
$661$	16.9744			0.660227			0.330114	+	0.943941i	$0.392913\pi$
$662$	−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
$672$	−36.3245	−	6.55782i	−1.40125	−	0.252973i
$673$	10.9588	−	10.9588i	0.422429	−	0.422429i	−0.463610	−	0.886039i	$-0.653446\pi$
$673$	10.9588	−	10.9588i	0.422429	−	0.422429i	0.886039	+	0.463610i	$0.153446\pi$
$674$			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	0.811661	−	0.584129i	$-0.198564\pi$
$683$	5.94637	+	5.94637i	0.227532	+	0.227532i	−0.584129	+	0.811661i	$0.698564\pi$
$684$	−36.9256	+	8.52367i	−1.41188	+	0.325911i
$685$	−2.27083	+	2.27083i	−0.0867641	+	0.0867641i
$686$	−18.0574	+	34.3971i	−0.689435	+	1.31329i
$687$	−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	$-0.103387\pi$
$691$	16.5238	+	16.5238i	0.628596	+	0.628596i	−0.319119	+	0.947715i	$0.603387\pi$
$692$		−	14.0428i		−	0.533828i
$693$	9.81171	−	19.9097i	0.372716	−	0.756307i
$694$	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
$700$	4.43003	+	3.61725i	0.167439	+	0.136719i
$701$		−	15.4407i		−	0.583188i	−0.956542	−	0.291594i	$-0.905814\pi$
$701$		−	15.4407i		−	0.583188i	0.956542	−	0.291594i	$-0.0941857\pi$
$702$	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	0.305821	−	0.952089i	$-0.401069\pi$
$709$	−17.2082	−	17.2082i	−0.646268	−	0.646268i	−0.952089	+	0.305821i	$0.901069\pi$
$710$	−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
$714$	−49.4012	+	34.2918i	−1.84880	+	1.28334i
$715$	−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	$-0.912143\pi$
$719$	−18.4919	+	18.4919i	−0.689631	+	0.689631i	0.272520	+	0.962150i	$0.412143\pi$
$720$	−15.6578	−	9.78481i	−0.583533	−	0.364658i
$721$	7.06495	+	5.76875i	0.263112	+	0.214839i
$722$			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	$-0.682915\pi$
$727$	7.97693	−	7.97693i	0.295848	−	0.295848i	0.839385	+	0.543537i	$0.182915\pi$
$728$	−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	$-0.726190\pi$
$733$	−35.3200			−1.30457			−0.652287	+	0.757972i	$0.726190\pi$
$734$	34.7969			1.28438
$735$	−18.6570	+	15.9536i	−0.688175	+	0.588457i
$736$		−	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
$749$	−17.7633	+	21.7546i	−0.649056	+	0.794894i
$750$	21.0430	+	37.9640i	0.768381	+	1.38625i
$751$	13.5274	+	13.5274i	0.493623	+	0.493623i	0.909446	−	0.415823i	$-0.136506\pi$
$751$	13.5274	+	13.5274i	0.493623	+	0.493623i	−0.415823	+	0.909446i	$0.636506\pi$
$752$	−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
$756$	22.1790	−	24.4296i	0.806642	−	0.888495i
$757$	−25.7757	+	25.7757i	−0.936834	+	0.936834i	−0.998120	−	0.0612862i	$-0.980480\pi$
$757$	−25.7757	+	25.7757i	−0.936834	+	0.936834i	0.0612862	+	0.998120i	$0.480480\pi$
$758$	−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	$-0.526185\pi$
$761$	−4.53345			−0.164337			−0.0821687	+	0.996618i	$0.526185\pi$
$762$	−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	$-0.728295\pi$
$773$	2.67907	−	2.67907i	0.0963594	−	0.0963594i	0.753643	+	0.657284i	$0.228295\pi$
$774$	−48.2202	−	30.1335i	−1.73324	−	1.08313i
$775$		−	6.03077i		−	0.216632i
$776$	3.98385	+	3.98385i	0.143012	+	0.143012i
$777$	−1.21892	−	0.220058i	−0.0437287	−	0.00789453i
$778$	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	$-0.444113\pi$
$787$	9.80042			0.349347			0.174674	+	0.984626i	$0.444113\pi$
$788$	−25.7084			−0.915823
$789$	47.2165	+	13.5399i	1.68095	+	0.482034i
$790$	44.6812	−	44.6812i	1.58969	−	1.58969i
$791$	−28.2538	+	34.6023i	−1.00459	+	1.23031i
$792$	−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	$-0.634996\pi$
$797$	−23.2344			−0.823005			−0.411503	+	0.911409i	$0.634996\pi$
$798$	−28.8499	−	41.5616i	−1.02128	−	1.47126i
$799$			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
$805$	−8.28835	−	6.76769i	−0.292126	−	0.238530i
$806$	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	−0.884416	−	0.466698i	$-0.845443\pi$
$809$	−11.8811	+	11.8811i	−0.417718	+	0.417718i	0.466698	+	0.884416i	$0.345443\pi$
$810$	34.3561	−	16.7538i	1.20715	−	0.588669i
$811$	23.3444			0.819734			0.409867	−	0.912145i	$-0.365575\pi$
$811$	23.3444			0.819734			0.409867	+	0.912145i	$0.365575\pi$
$812$	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
$819$	−3.70621	+	7.52056i	−0.129506	+	0.262790i
$820$	−31.0222	−	2.40509i	−1.08334	−	0.0839894i
$821$		−	32.9035i		−	1.14834i	−0.818736	−	0.574170i	$-0.805325\pi$
$821$		−	32.9035i		−	1.14834i	0.818736	−	0.574170i	$-0.194675\pi$
$822$	5.53954	+	1.58854i	0.193214	+	0.0554065i
$823$	15.6209	+	15.6209i	0.544511	+	0.544511i	0.924848	−	0.380337i	$-0.124192\pi$
$823$	15.6209	+	15.6209i	0.544511	+	0.544511i	−0.380337	+	0.924848i	$0.624192\pi$
$824$	2.89312			0.100787
$825$	1.20252	−	4.19343i	0.0418664	−	0.145997i
$826$	−11.4756	−	9.37020i	−0.399288	−	0.326031i
$827$	26.9798	−	26.9798i	0.938178	−	0.938178i	−0.0600191	−	0.998197i	$-0.519116\pi$
$827$	26.9798	−	26.9798i	0.938178	−	0.938178i	0.998197	+	0.0600191i	$0.0191162\pi$
$828$	12.1970	+	7.62207i	0.423874	+	0.264885i
$829$	−52.2940			−1.81625			−0.908123	−	0.418704i	$-0.862485\pi$
$829$	−52.2940			−1.81625			−0.908123	+	0.418704i	$0.862485\pi$
$830$		−	25.3984i		−	0.881592i
$831$	21.2382	−	11.7721i	0.736745	−	0.408369i
$832$	8.07908	−	8.07908i	0.280092	−	0.280092i
$833$	−36.5323	−	24.1485i	−1.26577	−	0.836696i
$834$	−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	$-0.583143\pi$
$839$	20.5029	−	20.5029i	0.707838	−	0.707838i	0.966080	+	0.258242i	$0.0831432\pi$
$840$	−1.38337	+	7.66262i	−0.0477307	+	0.264386i
$841$			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
$847$	−5.32115	+	6.51677i	−0.182837	+	0.223919i
$848$	−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	$-0.326914\pi$
$853$	30.2203			1.03472			0.517362	+	0.855767i	$0.326914\pi$
$854$	1.24256	+	1.01459i	0.0425195	+	0.0347185i
$855$	−7.19048	−	31.1500i	−0.245909	−	1.06531i
$856$			8.90858i			0.304489i
$857$	−34.3852			−1.17458			−0.587289	−	0.809377i	$-0.699805\pi$
$857$	−34.3852			−1.17458			−0.587289	+	0.809377i	$0.699805\pi$
$858$	5.20291	+	9.38667i	0.177625	+	0.320455i
$859$	−50.9572			−1.73864			−0.869318	−	0.494253i	$-0.835442\pi$
$859$	−50.9572			−1.73864			−0.869318	+	0.494253i	$0.835442\pi$
$860$	43.9084			1.49726
$861$	−7.42952	+	28.3867i	−0.253197	+	0.967415i
$862$	−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
$868$	26.8921	−	32.9346i	0.912778	−	1.11787i
$869$	−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
$875$	−19.9916	+	24.4836i	−0.675840	+	0.827696i
$876$	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	$-0.0445032\pi$
$882$	41.2696	+	15.4032i	1.38962	+	0.518652i
$883$	−27.3976	+	27.3976i	−0.922001	+	0.922001i	−0.997171	−	0.0751695i	$-0.976050\pi$
$883$	−27.3976	+	27.3976i	−0.922001	+	0.922001i	0.0751695	+	0.997171i	$0.476050\pi$
$884$		−	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	$-0.686624\pi$
$887$	8.33058	−	8.33058i	0.279714	−	0.279714i	0.832995	+	0.553281i	$0.186624\pi$
$888$	−0.343630	+	0.190470i	−0.0115315	+	0.00639175i
$889$	−41.4818	−	33.8711i	−1.39125	−	1.13600i
$890$	−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
$896$	−13.4836	−	11.0098i	−0.450455	−	0.367810i
$897$	−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
$903$	7.35650	−	40.7484i	0.244809	−	1.35602i
$904$			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	$-0.661845\pi$
$907$		−	52.6134i		−	1.74700i	0.486825	−	0.873499i	$-0.338155\pi$
$908$	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
$917$	−1.23735	+	1.51538i	−0.0408610	+	0.0500422i
$918$	45.6245	+	50.6761i	1.50583	+	1.67256i
$919$	−12.9944	+	12.9944i	−0.428645	+	0.428645i	−0.888167	−	0.459521i	$-0.848021\pi$
$919$	−12.9944	+	12.9944i	−0.428645	+	0.428645i	0.459521	+	0.888167i	$0.348021\pi$
$920$	−3.39411			−0.111901
$921$	−3.00844	+	1.66754i	−0.0991316	+	0.0549474i
$922$	55.4769			1.82703
$923$		−	10.4554i		−	0.344145i
$924$	25.2662	−	17.5385i	0.831197	−	0.576974i
$925$	−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	$-0.936937\pi$
$929$	−23.8842	+	23.8842i	−0.783616	+	0.783616i	0.196823	+	0.980439i	$0.436937\pi$
$930$	43.0804	−	23.8790i	1.41266	−	0.783022i
$931$	20.3163	−	30.7349i	0.665839	−	1.00729i
$932$	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	$-0.316738\pi$
$937$	−9.00990	−	9.00990i	−0.294341	−	0.294341i	−0.838792	+	0.544452i	$0.816738\pi$
$938$	−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
$945$	20.6085	+	18.7100i	0.670396	+	0.608635i
$946$	−37.4789	−	37.4789i	−1.21854	−	1.21854i
$947$			17.7611i			0.577157i	0.957456	+	0.288579i	$0.0931827\pi$
$947$			17.7611i			0.577157i	−0.957456	+	0.288579i	$0.906817\pi$
$948$	−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	$-0.654589\pi$
$953$		−	54.6021i		−	1.76874i	0.466790	−	0.884368i	$-0.345411\pi$
$954$	−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
$966$	−3.41138	+	18.8960i	−0.109759	+	0.607968i
$967$	23.5981	−	23.5981i	0.758862	−	0.758862i	−0.217253	−	0.976115i	$-0.569710\pi$
$967$	23.5981	−	23.5981i	0.758862	−	0.758862i	0.976115	+	0.217253i	$0.0697097\pi$
$968$			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	$-0.121900\pi$
$971$	17.2598	+	17.2598i	0.553893	+	0.553893i	−0.373669	+	0.927562i	$0.621900\pi$
$972$	−30.6456	−	21.4620i	−0.982959	−	0.688394i
$973$	2.51451	−	3.07950i	0.0806114	−	0.0987242i
$974$		−	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	−0.492036	−	0.870575i	$-0.663747\pi$
$977$	11.8320	−	11.8320i	0.378539	−	0.378539i	0.870575	+	0.492036i	$0.163747\pi$
$978$	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	$-0.550773\pi$
$983$	−9.95976			−0.317667			−0.158834	+	0.987305i	$0.550773\pi$
$984$	3.86945	+	8.46492i	0.123354	+	0.269852i
$985$		−	21.6873i		−	0.691015i
$986$			44.8090i			1.42701i
$987$	19.3862	−	13.4569i	0.617070	−	0.428338i
$988$	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	0.712031	−	0.702148i	$-0.247776\pi$
$991$	0.311106	+	0.311106i	0.00988259	+	0.00988259i	−0.702148	+	0.712031i	$0.747776\pi$
$992$			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	−0.237947	+	0.971278i	$0.576475\pi$
$997$	−38.1817	+	38.1817i	−1.20923	+	1.20923i	−0.971278	+	0.237947i	$0.923525\pi$
$998$	−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.419.94	yes	216
3.2	odd	2	inner	861.2.l.a.419.16	yes	216
7.6	odd	2	inner	861.2.l.a.419.93	yes	216
21.20	even	2	inner	861.2.l.a.419.15	✓	216
41.32	even	4	inner	861.2.l.a.524.15	yes	216
123.32	odd	4	inner	861.2.l.a.524.93	yes	216
287.237	odd	4	inner	861.2.l.a.524.16	yes	216
861.524	even	4	inner	861.2.l.a.524.94	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.l.a.419.15	✓	216	21.20	even	2	inner
861.2.l.a.419.16	yes	216	3.2	odd	2	inner
861.2.l.a.419.93	yes	216	7.6	odd	2	inner
861.2.l.a.419.94	yes	216	1.1	even	1	trivial
861.2.l.a.524.15	yes	216	41.32	even	4	inner
861.2.l.a.524.16	yes	216	287.237	odd	4	inner
861.2.l.a.524.93	yes	216	123.32	odd	4	inner
861.2.l.a.524.94	yes	216	861.524	even	4	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)

\(f(q)\)	\(=\)	\(q+2.09764 q^{2} +(1.51490 - 0.839690i) q^{3} +2.40008 q^{4} +2.02468i q^{5} +(3.17771 - 1.76136i) q^{6} +(2.04936 + 1.67336i) q^{7} +0.839219 q^{8} +(1.58984 - 2.54409i) q^{9} +O(q^{10})\)	\(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} +(2.04936 + 1.67336i) 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} +(4.29880 + 3.51011i) 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} +(4.50967 + 0.814152i) 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} +(4.91861 + 4.01620i) 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} +(-3.38803 + 4.14929i) 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} +(9.45966 + 1.70779i) 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} +(1.71986 + 1.40432i) 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} +(7.51534 - 2.55337i) 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} +(-7.10685 + 8.70371i) 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} +(10.8236 + 1.95403i) 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

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Representations

Groups

Database

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