LMFDB - Embedded newform 861.2.l.a.419.16

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			419.16
Character	$\chi$	$=$	861.419
Dual form			861.2.l.a.524.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09764 q^{2} +(0.839690 - 1.51490i) q^{3} +2.40008 q^{4} -2.02468i q^{5} +(-1.76136 + 3.17771i) q^{6} +(2.04936 + 1.67336i) q^{7} -0.839219 q^{8} +(-1.58984 - 2.54409i) q^{9} +O(q^{10})$	\(q-2.09764 q^{2} +(0.839690 - 1.51490i) q^{3} +2.40008 q^{4} -2.02468i q^{5} +(-1.76136 + 3.17771i) 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} +(2.01532 - 3.63588i) q^{12} +(-0.746924 + 0.746924i) q^{13} +(-4.29880 - 3.51011i) q^{14} +(-3.06719 - 1.70011i) 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} +(-0.704684 + 1.27133i) q^{24} +0.900666 q^{25} +(1.56678 - 1.56678i) q^{26} +(-5.18902 + 0.272199i) q^{27} +(4.91861 + 4.01620i) q^{28} +(-2.41447 + 2.41447i) q^{29} +(6.43385 + 3.56620i) 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} +(-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} +(-2.55247 + 4.60496i) 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} +(10.8847 - 0.570974i) 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} +(-7.36149 - 4.08039i) q^{60} +0.289048 q^{61} +14.0456i q^{62} +(0.999040 - 7.87413i) 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} +(-3.02606 - 1.67731i) 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} +(0.756280 - 1.36442i) 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} +(-10.1436 - 5.62249i) q^{93} +(7.63834 - 7.63834i) q^{94} +(-7.53520 + 7.53520i) q^{95} +(6.76353 - 12.2022i) q^{96} +(4.74709 + 4.74709i) q^{97} +(-2.93610 - 14.3869i) q^{98} +(8.17437 + 1.88692i) 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	$-0.765945\pi$
$2$	−2.09764			−1.48325			−0.741626	+	0.670813i	$0.765945\pi$
$3$	0.839690	−	1.51490i	0.484795	−	0.874628i
$3$	0.839690	−	1.51490i	0.484795	−	0.874628i
$4$	2.40008			1.20004
$5$		−	2.02468i		−	0.905465i	−0.891646	−	0.452733i	$-0.850449\pi$
$5$		−	2.02468i		−	0.905465i	0.891646	−	0.452733i	$-0.149551\pi$
$6$	−1.76136	+	3.17771i	−0.719074	+	1.29729i
$7$	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	−0.939300	−	0.343097i	$-0.888524\pi$
$11$	−1.97738	+	1.97738i	−0.596203	+	0.596203i	0.343097	+	0.939300i	$0.388524\pi$
$12$	2.01532	−	3.63588i	0.581774	−	1.04959i
$13$	−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
$15$	−3.06719	−	1.70011i	−0.791945	−	0.438965i
$16$	−3.03978			−0.759945
$17$	4.42368	−	4.42368i	1.07290	−	1.07290i	0.0757755	−	0.997125i	$-0.475857\pi$
$17$	4.42368	−	4.42368i	1.07290	−	1.07290i	0.997125	−	0.0757755i	$-0.0241432\pi$
$18$	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
$21$	4.25580	−	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	$-0.0667791\pi$
$24$	−0.704684	+	1.27133i	−0.143843	+	0.259510i
$25$	0.900666			0.180133
$26$	1.56678	−	1.56678i	0.307270	−	0.307270i
$27$	−5.18902	+	0.272199i	−0.998627	+	0.0523847i
$28$	4.91861	+	4.01620i	0.929531	+	0.758991i
$29$	−2.41447	+	2.41447i	−0.448355	+	0.448355i	−0.894807	−	0.446452i	$-0.852687\pi$
$29$	−2.41447	+	2.41447i	−0.448355	+	0.448355i	0.446452	+	0.894807i	$0.352687\pi$
$30$	6.43385	+	3.56620i	1.17465	+	0.651097i
$31$		−	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
$42$	−8.92712	+	3.56485i	−1.37748	+	0.550069i
$43$		−	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	−0.920916	−	0.389762i	$-0.872557\pi$
$47$	−3.64140	+	3.64140i	−0.531153	+	0.531153i	0.389762	+	0.920916i	$0.372557\pi$
$48$	−2.55247	+	4.60496i	−0.368418	+	0.664669i
$49$	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	$-0.821873\pi$
$53$	−2.30499	+	2.30499i	−0.316615	+	0.316615i	0.530851	+	0.847465i	$0.321873\pi$
$54$	10.8847	−	0.570974i	1.48122	−	0.0776998i
$55$	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	$-0.444405\pi$
$59$	2.66949			0.347538			0.173769	+	0.984786i	$0.444405\pi$
$60$	−7.36149	−	4.08039i	−0.950365	−	0.526776i
$61$	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
$63$	0.999040	−	7.87413i	0.125867	−	0.992047i
$64$	−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
$69$	−3.02606	−	1.67731i	−0.364295	−	0.201924i
$70$	−7.10685	+	8.70371i	−0.849431	+	1.04029i
$71$	6.99899	−	6.99899i	0.830628	−	0.830628i	−0.156975	−	0.987603i	$-0.550174\pi$
$71$	6.99899	−	6.99899i	0.830628	−	0.830628i	0.987603	+	0.156975i	$0.0501741\pi$
$72$	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
$75$	0.756280	−	1.36442i	0.0873277	−	0.157549i
$76$	−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	$-0.393555\pi$
$83$	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	0.487975	−	0.872857i	$-0.337736\pi$
$89$	−3.63097	−	3.63097i	−0.384882	−	0.384882i	−0.872857	+	0.487975i	$0.837736\pi$
$90$	10.8049	−	6.75212i	1.13893	−	0.711736i
$91$	−2.78059	+	0.280839i	−0.291485	+	0.0294399i
$92$		−	4.79424i		−	0.499834i
$93$	−10.1436	−	5.62249i	−1.05184	−	0.583025i
$94$	7.63834	−	7.63834i	0.787835	−	0.787835i
$95$	−7.53520	+	7.53520i	−0.773095	+	0.773095i
$96$	6.76353	−	12.2022i	0.690300	−	1.24538i
$97$	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
$99$	8.17437	+	1.88692i	0.821555	+	0.189643i
$100$	2.16167			0.216167
$101$	−12.8845	+	12.8845i	−1.28205	+	1.28205i	−0.342553	+	0.939499i	$0.611292\pi$
$101$	−12.8845	+	12.8845i	−1.28205	+	1.28205i	−0.939499	+	0.342553i	$0.888708\pi$
$102$	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
$105$	−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	$-0.171507\pi$
$108$	−12.4541	+	0.653299i	−1.19839	+	0.0628637i
$109$	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
$111$	−0.226961	+	0.409464i	−0.0215422	+	0.0388646i
$112$	−6.22959	−	5.08665i	−0.588641	−	0.480644i
$113$		−	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
$117$	3.08773	+	0.712754i	0.285461	+	0.0658941i
$118$	−5.59962			−0.515487
$119$	16.4681	−	1.66327i	1.50963	−	0.152472i
$120$	2.57404	+	1.42676i	0.234977	+	0.130245i
$121$			3.17991i			0.289083i
$122$	−0.606317			−0.0548934
$123$	−9.25548	−	6.11033i	−0.834538	−	0.550950i
$124$		−	16.0707i		−	1.44319i
$125$		−	11.9470i		−	1.06857i
$126$	−2.09562	+	16.5171i	−0.186693	+	1.47146i
$127$	−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
$129$	−13.6883	−	7.58726i	−1.20519	−	0.668021i
$130$	−3.17222	−	3.17222i	−0.278222	−	0.278222i
$131$		−	0.739441i		−	0.0646053i	−0.999478	−	0.0323026i	$-0.989716\pi$
$131$		−	0.739441i		−	0.0646053i	0.999478	−	0.0323026i	$-0.0102840\pi$
$132$	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
$135$	0.551116	+	10.5061i	0.0474325	+	0.904222i
$136$	−3.71244	+	3.71244i	−0.318339	+	0.318339i
$137$	−1.12158	−	1.12158i	−0.0958226	−	0.0958226i	0.657570	−	0.753393i	$-0.271584\pi$
$137$	−1.12158	−	1.12158i	−0.0958226	−	0.0958226i	−0.753393	+	0.657570i	$0.771584\pi$
$138$	6.34758	+	3.51838i	0.540342	+	0.299505i
$139$		−	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
$147$	11.5655	+	3.63869i	0.953903	+	0.300114i
$148$	−0.648720			−0.0533244
$149$	1.30698	+	1.30698i	0.107072	+	0.107072i	0.758613	−	0.651541i	$-0.225877\pi$
$149$	1.30698	+	1.30698i	0.107072	+	0.107072i	−0.651541	+	0.758613i	$0.725877\pi$
$150$	−1.58640	+	2.86205i	−0.129529	+	0.233686i
$151$	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
$153$	−18.2872	−	4.22131i	−1.47843	−	0.341272i
$154$	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	0.643886	−	0.765121i	$-0.277321\pi$
$167$	−1.56671	−	1.56671i	−0.121235	−	0.121235i	−0.765121	+	0.643886i	$0.777321\pi$
$168$	−3.57155	+	1.42622i	−0.275551	+	0.110035i
$169$			11.8842i			0.914170i
$170$	18.7876	+	18.7876i	1.44094	+	1.44094i
$171$	−3.55141	+	15.3851i	−0.271583	+	1.17653i
$172$		−	21.6866i		−	1.65359i
$173$			5.85099i			0.444842i	0.974951	+	0.222421i	$0.0713960\pi$
$173$			5.85099i			0.444842i	−0.974951	+	0.222421i	$0.928604\pi$
$174$	−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
$177$	2.24155	−	4.04401i	0.168485	−	0.303967i
$178$	7.61646	+	7.61646i	0.570878	+	0.570878i
$179$	2.75075	+	2.75075i	0.205601	+	0.205601i	0.802395	−	0.596794i	$-0.203559\pi$
$179$	2.75075	+	2.75075i	0.205601	+	0.205601i	−0.596794	+	0.802395i	$0.703559\pi$
$180$	−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
$183$	0.242711	−	0.437878i	0.0179417	−	0.0323689i
$184$			1.67637i			0.123584i
$185$			0.547253i			0.0402349i
$186$	21.2776	+	11.7939i	1.56015	+	0.864773i
$187$			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	$-0.0170614\pi$
$191$	13.0600	+	13.0600i	0.944989	+	0.944989i	−0.0535744	+	0.998564i	$0.517061\pi$
$192$	−9.08248	+	16.3859i	−0.655472	+	1.18255i
$193$	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	$-0.375380\pi$
$197$	10.7115			0.763160			0.381580	+	0.924336i	$0.375380\pi$
$198$	−17.1469	−	3.95808i	−1.21857	−	0.281288i
$199$	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
$210$	7.21769	+	18.0746i	0.498068	+	1.24726i
$211$	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
$216$	4.35472	−	0.228435i	0.296301	−	0.0155430i
$217$	11.2047	−	13.7223i	0.760623	−	0.931530i
$218$	−3.86039	+	3.86039i	−0.261458	+	0.261458i
$219$	0.152963	−	0.275963i	0.0103363	−	0.0186478i
$220$	9.60888	+	9.60888i	0.647831	+	0.647831i
$221$			6.60831i			0.444523i
$222$	0.476081	−	0.858906i	0.0319525	−	0.0576460i
$223$		−	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	−0.730370	−	0.683052i	$-0.760652\pi$
$227$	−0.712916	+	0.712916i	−0.0473179	+	0.0473179i	0.683052	+	0.730370i	$0.260652\pi$
$228$	−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
$231$	−5.05486	+	11.7758i	−0.332585	+	0.774793i
$232$	2.02627	−	2.02627i	0.133031	−	0.133031i
$233$	−5.53838	+	5.53838i	−0.362831	+	0.362831i	−0.864854	−	0.502023i	$-0.832589\pi$
$233$	−5.53838	+	5.53838i	−0.362831	+	0.362831i	0.502023	+	0.864854i	$0.332589\pi$
$234$	−6.47694	−	1.49510i	−0.423411	−	0.0977376i
$235$	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	$-0.889124\pi$
$239$	−9.25443	+	9.25443i	−0.598620	+	0.598620i	0.341326	+	0.939945i	$0.389124\pi$
$240$	9.32358	+	5.16795i	0.601834	+	0.333589i
$241$	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
$243$	8.94221	+	12.7686i	0.573643	+	0.819105i
$244$	0.693738			0.0444120
$245$	13.8865	−	2.83398i	0.887178	−	0.181056i
$246$	19.4146	+	12.8173i	1.23783	+	0.817199i
$247$	5.55962			0.353750
$248$			5.61934i			0.356828i
$249$	5.02156	−	9.05948i	0.318228	−	0.574121i
$250$			25.0604i			1.58496i
$251$			11.6411i			0.734777i	0.930067	+	0.367389i	$0.119748\pi$
$251$			11.6411i			0.734777i	−0.930067	+	0.367389i	$0.880252\pi$
$252$	2.39777	−	18.8985i	0.151046	−	1.19050i
$253$	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	0.344629	−	0.938739i	$-0.388005\pi$
$257$	−9.52431	−	9.52431i	−0.594110	−	0.594110i	−0.938739	+	0.344629i	$0.888005\pi$
$258$	28.7131	+	15.9153i	1.78760	+	0.990844i
$259$	−0.553922	−	0.452295i	−0.0344191	−	0.0281042i
$260$	3.62960	+	3.62960i	0.225098	+	0.225098i
$261$	9.98125	+	2.30401i	0.617824	+	0.142615i
$262$			1.55108i			0.0958260i
$263$	−20.0529	−	20.0529i	−1.23652	−	1.23652i	−0.961415	−	0.275103i	$-0.911288\pi$
$263$	−20.0529	−	20.0529i	−1.23652	−	1.23652i	−0.275103	−	0.961415i	$-0.588712\pi$
$264$	−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	$0.352322\pi$
$270$	−1.15604	−	22.0380i	−0.0703544	−	1.34119i
$271$		−	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
$273$	−1.90939	+	4.44813i	−0.115562	+	0.269213i
$274$	2.35266	+	2.35266i	0.142129	+	0.142129i
$275$	−1.78096	+	1.78096i	−0.107396	+	0.107396i
$276$	−7.26279	−	4.02567i	−0.437168	−	0.242317i
$277$	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	0.997311	−	0.0732859i	$-0.0233486\pi$
$281$	15.4895	+	15.4895i	0.924025	+	0.924025i	−0.0732859	+	0.997311i	$0.523349\pi$
$282$	−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	−0.720321	−	0.693641i	$-0.756006\pi$
$293$	−0.456694	+	0.456694i	−0.0266803	+	0.0266803i	0.693641	+	0.720321i	$0.256006\pi$
$294$	−24.2601	−	7.63266i	−1.41488	−	0.445145i
$295$		−	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
$300$	1.81513	−	3.27471i	0.104797	−	0.189065i
$301$	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
$306$	38.3599	+	8.85477i	2.19289	+	0.506193i
$307$	−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
$309$	2.89475	−	5.22246i	0.164676	−	0.297096i
$310$	28.4378			1.61516
$311$	21.3389	−	21.3389i	1.21002	−	1.21002i	0.238999	−	0.971020i	$-0.423181\pi$
$311$	21.3389	−	21.3389i	1.21002	−	1.21002i	0.971020	−	0.238999i	$-0.0768191\pi$
$312$	−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
$315$	−15.9426	−	2.02274i	−0.898264	−	0.113968i
$316$	−25.2501	−	25.2501i	−1.42043	−	1.42043i
$317$	2.25572	−	2.25572i	0.126694	−	0.126694i	−0.640917	−	0.767610i	$-0.721446\pi$
$317$	2.25572	−	2.25572i	0.126694	−	0.126694i	0.767610	+	0.640917i	$0.221446\pi$
$318$	−3.26466	−	11.3845i	−0.183073	−	0.638412i
$319$		−	9.54865i		−	0.534622i
$320$			21.8999i			1.22424i
$321$	−16.0811	−	8.91358i	−0.897561	−	0.497507i
$322$	−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
$336$	−12.9367	+	5.16599i	−0.705755	+	0.281828i
$337$			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
$339$	−25.5783	−	14.1777i	−1.38922	−	0.770028i
$340$	−21.4964	−	21.4964i	−1.16581	−	1.16581i
$341$	13.2404	+	13.2404i	0.717006	+	0.717006i
$342$	7.44957	−	32.2724i	0.402827	−	1.74509i
$343$	−8.60845	+	16.3980i	−0.464813	+	0.885409i
$344$			7.58300i			0.408848i
$345$	−3.39602	+	6.12681i	−0.182835	+	0.329856i
$346$		−	12.2732i		−	0.659813i
$347$	−24.5046	−	24.5046i	−1.31547	−	1.31547i	−0.917317	−	0.398158i	$-0.869650\pi$
$347$	−24.5046	−	24.5046i	−1.31547	−	1.31547i	−0.398158	−	0.917317i	$-0.630350\pi$
$348$	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	$-0.163370\pi$
$353$	32.7351			1.74231			0.871157	+	0.491005i	$0.163370\pi$
$354$	−4.70195	+	8.48287i	−0.249906	+	0.450859i
$355$	−14.1707	−	14.1707i	−0.752104	−	0.752104i
$356$	−8.71461	−	8.71461i	−0.461874	−	0.461874i
$357$	11.3084	−	26.3442i	0.598505	−	1.39428i
$358$	−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
$363$	4.81725	+	2.67014i	0.252840	+	0.140146i
$364$	−6.67363	+	0.674035i	−0.349793	+	0.0353290i
$365$		−	0.368827i		−	0.0193053i
$366$	−0.509119	+	0.918510i	−0.0266121	+	0.0480113i
$367$	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
$369$	−17.0283	+	8.89033i	−0.886457	+	0.462812i
$370$		−	1.14794i		−	0.0596785i
$371$	−8.58083	+	0.866661i	−0.445495	+	0.0449948i
$372$	−24.3455	−	13.4944i	−1.26226	−	0.699653i
$373$	−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
$375$	−18.0985	−	10.0318i	−0.934600	−	0.518037i
$376$	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
$381$	−16.9965	+	30.6636i	−0.870756	+	1.57095i
$382$	−27.3952	−	27.3952i	−1.40166	−	1.40166i
$383$	−12.8310	+	12.8310i	−0.655633	+	0.655633i	−0.954344	−	0.298711i	$-0.903443\pi$
$383$	−12.8310	+	12.8310i	−0.655633	+	0.655633i	0.298711	+	0.954344i	$0.403443\pi$
$384$	5.52468	−	9.96717i	0.281930	−	0.508635i
$385$	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	$-0.568782\pi$
$389$	−8.45760			−0.428817			−0.214409	+	0.976744i	$0.568782\pi$
$390$	−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
$393$	−1.12018	−	0.620902i	−0.0565056	−	0.0313203i
$394$	−22.4688			−1.13196
$395$	−21.3008	+	21.3008i	−1.07176	+	1.07176i
$396$	19.6191	+	4.52876i	0.985898	+	0.227579i
$397$	−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
$399$	−22.1635	−	9.51385i	−1.10956	−	0.476288i
$400$	−2.73783			−0.136891
$401$	14.8737			0.742756			0.371378	−	0.928482i	$-0.378885\pi$
$401$	14.8737			0.742756			0.371378	+	0.928482i	$0.378885\pi$
$402$	−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
$417$	−2.27639	−	1.26177i	−0.111475	−	0.0617894i
$418$	−30.8737			−1.51008
$419$		−	13.2363i		−	0.646637i	−0.946290	−	0.323319i	$-0.895201\pi$
$419$		−	13.2363i		−	0.646637i	0.946290	−	0.323319i	$-0.104799\pi$
$420$	−8.25835	−	20.6806i	−0.402966	−	1.00911i
$421$	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
$423$	15.0533	+	3.47482i	0.731918	+	0.168951i
$424$	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
$429$	−4.47488	−	2.48037i	−0.216049	−	0.119753i
$430$	38.3754			1.85062
$431$	24.6794			1.18877			0.594383	−	0.804182i	$-0.297396\pi$
$431$	24.6794			1.18877			0.594383	+	0.804182i	$0.297396\pi$
$432$	15.7735	−	0.827425i	0.758902	−	0.0398095i
$433$			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
$438$	−0.320860	+	0.578869i	−0.0153313	+	0.0276594i
$439$	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
$441$	15.2237	−	14.4651i	0.724936	−	0.688816i
$442$		−	13.8618i		−	0.659340i
$443$	17.0431			0.809743			0.404872	−	0.914374i	$-0.367316\pi$
$443$	17.0431			0.809743			0.404872	+	0.914374i	$0.367316\pi$
$444$	−0.544724	+	0.982745i	−0.0258514	+	0.0466390i
$445$	−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	$-0.308038\pi$
$449$	24.0362			1.13434			0.567170	+	0.823601i	$0.308038\pi$
$450$	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	$-0.711202\pi$
$461$	−26.4473			−1.23177			−0.615887	+	0.787834i	$0.711202\pi$
$462$	10.6033	−	24.7014i	0.493308	−	1.14921i
$463$	−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
$465$	−11.3837	+	20.5376i	−0.527909	+	0.952409i
$466$	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	$0.303068\pi$
$468$	7.41081	+	1.71067i	0.342565	+	0.0790755i
$469$	−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
$477$	9.52868	+	2.19954i	0.436288	+	0.100710i
$478$	19.4124	−	19.4124i	0.887904	−	0.887904i
$479$	−2.40299	−	2.40299i	−0.109795	−	0.109795i	0.650075	−	0.759870i	$-0.274738\pi$
$479$	−2.40299	−	2.40299i	−0.109795	−	0.109795i	−0.759870	+	0.650075i	$0.774738\pi$
$480$	−24.7056	−	13.6940i	−1.12765	−	0.625042i
$481$	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
$486$	−18.7575	−	26.7839i	−0.850858	−	1.21494i
$487$		−	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
$489$	11.2611	−	20.3164i	0.509245	−	0.918738i
$490$	−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	$0.794880\pi$
$492$	−22.2139	−	14.6653i	−1.00148	−	0.661162i
$493$			21.3617i			0.962081i
$494$	−11.6621			−0.524701
$495$	3.82041	−	16.5505i	0.171715	−	0.743889i
$496$			20.3541i			0.913925i
$497$	26.0553	−	2.63158i	1.16874	−	0.118042i
$498$	−10.5334	+	19.0035i	−0.472013	+	0.851567i
$499$	−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	$-0.914282\pi$
$503$	−27.5862	−	27.5862i	−1.23001	−	1.23001i	−0.266048	−	0.963960i	$-0.585718\pi$
$504$	−0.838414	+	6.60812i	−0.0373459	+	0.294349i
$505$	26.0869	+	26.0869i	1.16085	+	1.16085i
$506$	−8.28543	−	8.28543i	−0.368332	−	0.368332i
$507$	18.0034	+	9.97905i	0.799558	+	0.443185i
$508$	−48.5809			−2.15543
$509$	20.4064	−	20.4064i	0.904499	−	0.904499i	−0.0913223	−	0.995821i	$-0.529109\pi$
$509$	20.4064	−	20.4064i	0.904499	−	0.904499i	0.995821	+	0.0913223i	$0.0291094\pi$
$510$	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
$516$	−32.8530	−	18.2100i	−1.44627	−	0.801651i
$517$		−	14.4009i		−	0.633351i
$518$	1.16193	+	0.948750i	0.0510522	+	0.0416857i
$519$	8.86365	+	4.91302i	0.389071	+	0.215657i
$520$	−1.26914	−	1.26914i	−0.0556554	−	0.0556554i
$521$	−26.5644	−	26.5644i	−1.16381	−	1.16381i	−0.983635	−	0.180171i	$-0.942335\pi$
$521$	−26.5644	−	26.5644i	−1.16381	−	1.16381i	−0.180171	−	0.983635i	$-0.557665\pi$
$522$	−20.9370	−	4.83298i	−0.916389	−	0.211534i
$523$			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
$539$	−16.3299	−	10.7944i	−0.703379	−	0.464946i
$540$	1.32272	+	25.2155i	0.0569209	+	1.08510i
$541$		−	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
$546$	4.00521	−	9.33056i	0.171407	−	0.399311i
$547$	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
$552$	2.53953	+	1.40763i	0.108090	+	0.0599127i
$553$	−3.95566	−	39.1650i	−0.168212	−	1.66547i
$554$	−29.4079			−1.24942
$555$	0.829034	+	0.459523i	0.0351905	+	0.0195057i
$556$		−	3.60652i		−	0.152950i
$557$	17.6104	+	17.6104i	0.746179	+	0.746179i	0.973759	−	0.227581i	$-0.0730815\pi$
$557$	17.6104	+	17.6104i	0.746179	+	0.746179i	−0.227581	+	0.973759i	$0.573082\pi$
$558$	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
$561$	26.5026	+	14.6901i	1.11894	+	0.620215i
$562$	−32.4913	−	32.4913i	−1.37056	−	1.37056i
$563$	−16.4094	−	16.4094i	−0.691572	−	0.691572i	0.271006	−	0.962578i	$-0.412644\pi$
$563$	−16.4094	−	16.4094i	−0.691572	−	0.691572i	−0.962578	+	0.271006i	$0.912644\pi$
$564$	5.90110	+	20.5783i	0.248481	+	0.866503i
$565$	−34.1856			−1.43820
$566$			51.1006i			2.14792i
$567$	−21.6208	+	9.97696i	−0.907989	+	0.418993i
$568$	−5.87369	+	5.87369i	−0.246455	+	0.246455i
$569$	17.7056			0.742258			0.371129	−	0.928581i	$-0.378971\pi$
$569$	17.7056			0.742258			0.371129	+	0.928581i	$0.378971\pi$
$570$	−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
$585$	1.44310	−	6.25168i	0.0596648	−	0.258475i
$586$	0.957978	−	0.957978i	0.0395737	−	0.0395737i
$587$	−0.248981	−	0.248981i	−0.0102765	−	0.0102765i	0.701950	−	0.712226i	$-0.252313\pi$
$587$	−0.248981	−	0.248981i	−0.0102765	−	0.0102765i	−0.712226	+	0.701950i	$0.752313\pi$
$588$	27.7580	+	8.73315i	1.14472	+	0.360149i
$589$	−24.9200	+	24.9200i	−1.02681	+	1.02681i
$590$			11.3375i			0.466756i
$591$	8.99431	−	16.2268i	0.369977	−	0.667481i
$592$	0.821625			0.0337686
$593$	−5.71596	+	5.71596i	−0.234726	+	0.234726i	−0.814662	−	0.579936i	$-0.803078\pi$
$593$	−5.71596	+	5.71596i	−0.234726	+	0.234726i	0.579936	+	0.814662i	$0.303078\pi$
$594$	−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	$0.849603\pi$
$600$	−0.634685	+	1.14505i	−0.0259109	+	0.0467463i
$601$	−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
$603$	24.4832	+	5.65155i	0.997033	+	0.230149i
$604$	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
$609$	−6.17219	+	14.3788i	−0.250110	+	0.582658i
$610$			1.22760i			0.0497040i
$611$		−	5.43971i		−	0.220067i
$612$	−43.8907	−	10.1315i	−1.77418	−	0.409540i
$613$			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
$615$	−12.3715	+	18.7394i	−0.498866	+	0.755645i
$616$	6.17769	−	0.623945i	0.248906	−	0.0251395i
$617$	17.7686			0.715335			0.357668	−	0.933849i	$-0.383572\pi$
$617$	17.7686			0.715335			0.357668	+	0.933849i	$0.383572\pi$
$618$	−6.07213	+	10.9548i	−0.244257	+	0.440668i
$619$			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
$621$	0.543726	+	10.3652i	0.0218190	+	0.415943i
$622$	−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
$627$	12.3589	−	22.2968i	0.493565	−	0.890449i
$628$	−15.7469	+	15.7469i	−0.628370	+	0.628370i
$629$	−1.19568	+	1.19568i	−0.0476749	+	0.0476749i
$630$	33.4418	+	4.24297i	1.33235	+	0.169044i
$631$	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
$639$	−28.9334	−	6.67880i	−1.14459	−	0.264209i
$640$		−	13.3212i		−	0.526568i
$641$	−6.94341	−	6.94341i	−0.274248	−	0.274248i	0.556559	−	0.830808i	$-0.312121\pi$
$641$	−6.94341	−	6.94341i	−0.274248	−	0.274248i	−0.830808	+	0.556559i	$0.812121\pi$
$642$	33.7324	+	18.6974i	1.33131	+	0.737929i
$643$	−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
$645$	−15.3618	+	27.7144i	−0.604869	+	1.09126i
$646$	69.0689			2.71748
$647$			42.1882i			1.65859i	0.558813	+	0.829294i	$0.311257\pi$
$647$			42.1882i			1.65859i	−0.558813	+	0.829294i	$0.688743\pi$
$648$	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	−0.178873	+	0.983872i	$0.557245\pi$
$653$	−29.7126	+	29.7126i	−1.16275	+	1.16275i	−0.983872	+	0.178873i	$0.942755\pi$
$654$	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	$-0.659211\pi$
$659$	10.2150	−	10.2150i	0.397918	−	0.397918i	0.877498	+	0.479580i	$0.159211\pi$
$660$	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
$663$	10.0109	+	5.54893i	0.388792	+	0.215503i
$664$	−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
$669$	−5.49920	−	3.04814i	−0.212611	−	0.117848i
$670$	−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	−0.463610	−	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
$675$	−4.67357	+	0.245160i	−0.179886	+	0.00943622i
$676$			28.5230i			1.09704i
$677$			3.40048i			0.130691i	0.997863	+	0.0653455i	$0.0208150\pi$
$677$			3.40048i			0.130691i	−0.997863	+	0.0653455i	$0.979185\pi$
$678$	53.6539	+	29.7397i	2.06056	+	1.14215i
$679$	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	$-0.301436\pi$
$683$	−5.94637	−	5.94637i	−0.227532	−	0.227532i	−0.811661	+	0.584129i	$0.801436\pi$
$684$	−8.52367	+	36.9256i	−0.325911	+	1.41188i
$685$	−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
$690$	7.12361	−	12.8518i	0.271191	−	0.489261i
$691$	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
$693$	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
$700$	4.43003	+	3.61725i	0.167439	+	0.136719i
$701$			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
$708$	5.37989	−	9.70595i	0.202189	−	0.364772i
$709$	−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
$711$	−10.0393	+	43.4912i	−0.376501	+	1.63105i
$712$	3.04718	+	3.04718i	0.114198	+	0.114198i
$713$	−13.3753			−0.500909
$714$	−23.7210	+	55.2605i	−0.887735	+	2.06807i
$715$	−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	−0.272520	−	0.962150i	$-0.587857\pi$
$719$	18.4919	−	18.4919i	0.689631	−	0.689631i	0.962150	+	0.272520i	$0.0878569\pi$
$720$	15.6578	−	9.78481i	0.583533	−	0.364658i
$721$	7.06495	+	5.76875i	0.263112	+	0.214839i
$722$		−	18.2530i		−	0.679306i
$723$	19.5520	−	35.2741i	0.727146	−	1.31186i
$724$	35.9138	+	35.9138i	1.33473	+	1.33473i
$725$	−2.17463	+	2.17463i	−0.0807636	+	0.0807636i
$726$	−10.1048	−	5.60099i	−0.375026	−	0.207872i
$727$	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
$732$	0.582525	−	1.05094i	0.0215307	−	0.0388440i
$733$	−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
$735$	7.36719	−	23.4164i	0.271743	−	0.863726i
$736$		−	16.0897i		−	0.593075i
$737$		−	23.4221i		−	0.862763i
$738$	35.7191	−	18.6487i	1.31484	−	0.686467i
$739$	−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
$741$	4.66835	−	8.42226i	0.171496	−	0.309399i
$742$	17.9995	−	1.81794i	0.660781	−	0.0667387i
$743$	45.3144			1.66243			0.831213	−	0.555954i	$-0.187647\pi$
$743$	45.3144			1.66243			0.831213	+	0.555954i	$0.187647\pi$
$744$	8.51273	+	4.71850i	0.312092	+	0.172989i
$745$	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
$750$	37.9640	+	21.0430i	1.38625	+	0.768381i
$751$	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
$753$	17.6350	+	9.77489i	0.642657	+	0.356217i
$754$			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	−0.998120	−	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	$-0.473815\pi$
$761$	4.53345			0.164337			0.0821687	+	0.996618i	$0.473815\pi$
$762$	35.6524	−	64.3212i	1.29155	−	2.33011i
$763$	6.85110	−	0.691959i	0.248027	−	0.0250506i
$764$	31.3451	+	31.3451i	1.13402	+	1.13402i
$765$	−8.54680	+	37.0258i	−0.309010	+	1.33867i
$766$	26.9147	−	26.9147i	0.972469	−	0.972469i
$767$	−1.99391	+	1.99391i	−0.0719959	+	0.0719959i
$768$	6.57619	−	11.8642i	0.237298	−	0.428113i
$769$		−	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	−0.753643	−	0.657284i	$-0.771705\pi$
$773$	−2.67907	+	2.67907i	−0.0963594	+	0.0963594i	0.657284	+	0.753643i	$0.271705\pi$
$774$	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
$786$	2.34973	+	1.30243i	0.0838121	+	0.0464560i
$787$	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
$792$	−6.86009	−	1.58354i	−0.243763	−	0.0562687i
$793$	−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	$0.365004\pi$
$798$	46.4910	+	19.9566i	1.64576	+	0.706456i
$799$			32.2168i			1.13975i
$800$	7.25467			0.256491
$801$	−3.46486	+	15.0102i	−0.122425	+	0.530359i
$802$	−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
$807$	12.3253	−	22.2364i	0.433873	−	0.782757i
$808$	10.8129	−	10.8129i	0.380396	−	0.380396i
$809$	11.8811	−	11.8811i	0.417718	−	0.417718i	−0.466698	−	0.884416i	$-0.654557\pi$
$809$	11.8811	−	11.8811i	0.417718	−	0.417718i	0.884416	+	0.466698i	$0.154557\pi$
$810$	−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
$813$	−41.8840	−	23.2158i	−1.46894	−	0.814214i
$814$	−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	0.924848	−	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	−0.998197	−	0.0600191i	$-0.980884\pi$
$827$	−26.9798	+	26.9798i	−0.938178	+	0.938178i	0.0600191	+	0.998197i	$0.480884\pi$
$828$	−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
$831$	11.7721	−	21.2382i	0.408369	−	0.736745i
$832$	8.07908	−	8.07908i	0.280092	−	0.280092i
$833$	36.5323	+	24.1485i	1.26577	+	0.836696i
$834$	4.77504	+	2.64674i	0.165346	+	0.0916493i
$835$	−3.17208	+	3.17208i	−0.109774	+	0.109774i
$836$	35.3252			1.22175
$837$	1.82262	+	34.7452i	0.0629989	+	1.20097i
$838$			27.7650i			0.959126i
$839$	−20.5029	+	20.5029i	−0.707838	+	0.707838i	−0.966080	−	0.258242i	$-0.916857\pi$
$839$	−20.5029	+	20.5029i	−0.707838	+	0.707838i	0.258242	+	0.966080i	$0.416857\pi$
$840$	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
$846$	−31.5764	−	7.28890i	−1.08562	−	0.250598i
$847$	−5.32115	+	6.51677i	−0.182837	+	0.223919i
$848$	7.00667	−	7.00667i	0.240610	−	0.240610i
$849$	−36.9045	−	20.4557i	−1.26656	−	0.702038i
$850$	−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
$855$	31.1500	+	7.19048i	1.06531	+	0.245909i
$856$			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	$0.300195\pi$
$858$	9.38667	+	5.20291i	0.320455	+	0.177625i
$859$	−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
$861$	−8.74296	−	28.0100i	−0.297959	−	0.954579i
$862$	−51.7684			−1.76324
$863$	26.2677			0.894162			0.447081	−	0.894494i	$-0.352464\pi$
$863$	26.2677			0.894162			0.447081	+	0.894494i	$0.352464\pi$
$864$	−41.7965	+	2.19251i	−1.42194	+	0.0745906i
$865$	11.8464			0.402789
$866$		−	42.0767i		−	1.42982i
$867$	−33.5367	−	18.5890i	−1.13897	−	0.631315i
$868$	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
$873$	4.52992	−	19.6241i	0.153314	−	0.664176i
$874$	15.5942	−	15.5942i	0.527481	−	0.527481i
$875$	19.9916	−	24.4836i	0.675840	−	0.827696i
$876$	0.367122	−	0.662332i	0.0124039	−	0.0223781i
$877$	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	$0.0445032\pi$
$881$			8.27262i			0.278712i	−0.990242	+	0.139356i	$0.955497\pi$
$882$	−31.9337	+	30.3426i	−1.07526	+	1.02169i
$883$	−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
$885$	−8.18784	−	4.53842i	−0.275231	−	0.152557i
$886$	−35.7503			−1.20105
$887$	−8.33058	+	8.33058i	−0.279714	+	0.279714i	−0.832995	−	0.553281i	$-0.813376\pi$
$887$	−8.33058	+	8.33058i	−0.279714	+	0.279714i	0.553281	+	0.832995i	$0.313376\pi$
$888$	0.190470	−	0.343630i	0.00639175	−	0.0115315i
$889$	−41.4818	−	33.8711i	−1.39125	−	1.13600i
$890$	15.4209	−	15.4209i	0.516910	−	0.516910i
$891$	−8.19544	−	23.7963i	−0.274558	−	0.797205i
$892$		−	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
$903$	−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	$-0.661845\pi$
$907$		−	52.6134i		−	1.74700i	0.486825	−	0.873499i	$-0.338155\pi$
$908$	−1.71105	+	1.71105i	−0.0567833	+	0.0567833i
$909$	53.2635	+	12.2950i	1.76664	+	0.407800i
$910$	−1.19273	−	11.8093i	−0.0395387	−	0.391474i
$911$	−38.5428			−1.27698			−0.638491	−	0.769630i	$-0.720441\pi$
$911$	−38.5428			−1.27698			−0.638491	+	0.769630i	$0.720441\pi$
$912$	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
$915$	−0.886564	−	0.491412i	−0.0293089	−	0.0162456i
$916$	−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
$921$	−1.66754	+	3.00844i	−0.0549474	+	0.0991316i
$922$	55.4769			1.82703
$923$			10.4554i			0.344145i
$924$	−12.1321	+	28.2629i	−0.399115	+	0.929782i
$925$	−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	−0.196823	−	0.980439i	$-0.563063\pi$
$929$	23.8842	−	23.8842i	0.783616	−	0.783616i	0.980439	+	0.196823i	$0.0630626\pi$
$930$	23.8790	−	43.0804i	0.783022	−	1.41266i
$931$	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
$936$	−2.59129	−	0.598157i	−0.0846989	−	0.0195514i
$937$	−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	$-0.935295\pi$
$941$		−	12.3856i		−	0.403760i	0.979410	−	0.201880i	$-0.0647051\pi$
$942$	−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	$0.654589\pi$
$954$	−19.9877	−	4.61384i	−0.647126	−	0.149379i
$955$	26.4424	−	26.4424i	0.855655	−	0.855655i
$956$	−22.2114	+	22.2114i	−0.718367	+	0.718367i
$957$	−14.4652	−	8.01791i	−0.467595	−	0.259182i
$958$	5.04059	+	5.04059i	0.162854	+	0.162854i
$959$	−0.421705	−	4.17531i	−0.0136176	−	0.134828i
$960$	33.1761	+	18.3891i	1.07076	+	0.593507i
$961$	−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	−0.217253	−	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
$969$	−27.6485	+	49.8811i	−0.888197	+	1.60241i
$970$	−20.1611	+	20.1611i	−0.647334	+	0.647334i
$971$	−17.2598	−	17.2598i	−0.553893	−	0.553893i	0.373669	−	0.927562i	$-0.378100\pi$
$971$	−17.2598	−	17.2598i	−0.553893	−	0.553893i	−0.927562	+	0.373669i	$0.878100\pi$
$972$	21.4620	+	30.6456i	0.688394	+	0.982959i
$973$	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	−0.870575	−	0.492036i	$-0.836253\pi$
$977$	−11.8320	+	11.8320i	−0.378539	+	0.378539i	0.492036	+	0.870575i	$0.336253\pi$
$978$	−23.6217	+	42.6164i	−0.755340	+	1.36272i
$979$	14.3596			0.458936
$980$	33.3288	−	6.80178i	1.06465	−	0.217275i
$981$	−7.60788	−	1.75616i	−0.242901	−	0.0560698i
$982$		−	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	$0.449227\pi$
$984$	7.76737	+	5.12791i	0.247615	+	0.163472i
$985$		−	21.6873i		−	0.691015i
$986$		−	44.8090i		−	1.42701i
$987$	−9.30866	+	21.6855i	−0.296298	+	0.690258i
$988$	13.3435			0.424514
$989$	−18.0493			−0.573934
$990$	−8.01384	+	34.7169i	−0.254697	+	1.10338i
$991$	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
$996$	12.0521	−	21.7435i	0.381887	−	0.688968i
$997$	−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
$999$	1.40254	−	0.0735729i	0.0443746	−	0.00232774i

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.09764 q^{2} +(0.839690 - 1.51490i) q^{3} +2.40008 q^{4} -2.02468i q^{5} +(-1.76136 + 3.17771i) q^{6} +(2.04936 + 1.67336i) q^{7} -0.839219 q^{8} +(-1.58984 - 2.54409i) q^{9} +O(q^{10})\)	\(q-2.09764 q^{2} +(0.839690 - 1.51490i) q^{3} +2.40008 q^{4} -2.02468i q^{5} +(-1.76136 + 3.17771i) 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} +(2.01532 - 3.63588i) q^{12} +(-0.746924 + 0.746924i) q^{13} +(-4.29880 - 3.51011i) q^{14} +(-3.06719 - 1.70011i) 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} +(-0.704684 + 1.27133i) q^{24} +0.900666 q^{25} +(1.56678 - 1.56678i) q^{26} +(-5.18902 + 0.272199i) q^{27} +(4.91861 + 4.01620i) q^{28} +(-2.41447 + 2.41447i) q^{29} +(6.43385 + 3.56620i) 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} +(-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} +(-2.55247 + 4.60496i) 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} +(10.8847 - 0.570974i) 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} +(-7.36149 - 4.08039i) q^{60} +0.289048 q^{61} +14.0456i q^{62} +(0.999040 - 7.87413i) 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} +(-3.02606 - 1.67731i) 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} +(0.756280 - 1.36442i) 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} +(-10.1436 - 5.62249i) q^{93} +(7.63834 - 7.63834i) q^{94} +(-7.53520 + 7.53520i) q^{95} +(6.76353 - 12.2022i) q^{96} +(4.74709 + 4.74709i) q^{97} +(-2.93610 - 14.3869i) q^{98} +(8.17437 + 1.88692i) 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

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Database

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