LMFDB - Embedded newform 112.2.j.d.27.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,2,Mod(27,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.5
Root			$-1.36166 - 0.381939i$ of defining polynomial
Character	$\chi$	$=$	112.27
Dual form			112.2.j.d.83.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.192769 + 1.40101i) q^{2} +(-1.03649 + 1.03649i) q^{3} +(-1.92568 + 0.540143i) q^{4} +(-1.68683 + 1.68683i) q^{5} +(-1.65195 - 1.25234i) q^{6} +(1.38554 - 2.25395i) q^{7} +(-1.12796 - 2.59378i) q^{8} +0.851361i q^{9} +(-2.68844 - 2.03810i) q^{10} +(-2.00000 + 2.00000i) q^{11} +(1.43610 - 2.55581i) q^{12} +(4.80976 + 4.80976i) q^{13} +(3.42490 + 1.50667i) q^{14} -3.49678i q^{15} +(3.41649 - 2.08029i) q^{16} +1.13424i q^{17} +(-1.19277 + 0.164116i) q^{18} +(1.21746 - 1.21746i) q^{19} +(2.33717 - 4.15942i) q^{20} +(0.900103 + 3.77231i) q^{21} +(-3.18757 - 2.41649i) q^{22} -1.33620 q^{23} +(3.85756 + 1.51932i) q^{24} -0.690788i q^{25} +(-5.81137 + 7.66571i) q^{26} +(-3.99191 - 3.99191i) q^{27} +(-1.45065 + 5.08877i) q^{28} +(5.26785 - 5.26785i) q^{29} +(4.89903 - 0.674069i) q^{30} +8.31885 q^{31} +(3.57310 + 4.38554i) q^{32} -4.14598i q^{33} +(-1.58908 + 0.218646i) q^{34} +(1.46486 + 6.13919i) q^{35} +(-0.459857 - 1.63945i) q^{36} +(-4.18757 - 4.18757i) q^{37} +(1.94036 + 1.47098i) q^{38} -9.97057 q^{39} +(6.27794 + 2.47259i) q^{40} -1.63570 q^{41} +(-5.11154 + 1.98824i) q^{42} +(-1.33620 + 1.33620i) q^{43} +(2.77107 - 4.93165i) q^{44} +(-1.43610 - 1.43610i) q^{45} +(-0.257578 - 1.87204i) q^{46} -1.93345 q^{47} +(-1.38497 + 5.69738i) q^{48} +(-3.16057 - 6.24586i) q^{49} +(0.967804 - 0.133162i) q^{50} +(-1.17563 - 1.17563i) q^{51} +(-11.8600 - 6.66410i) q^{52} +(6.34814 + 6.34814i) q^{53} +(4.82321 - 6.36224i) q^{54} -6.74732i q^{55} +(-7.40908 - 1.05142i) q^{56} +2.52377i q^{57} +(8.39581 + 6.36486i) q^{58} +(-3.29044 - 3.29044i) q^{59} +(1.88876 + 6.73368i) q^{60} +(-2.04875 - 2.04875i) q^{61} +(1.60361 + 11.6548i) q^{62} +(1.91892 + 1.17959i) q^{63} +(-5.45542 + 5.85136i) q^{64} -16.2265 q^{65} +(5.80857 - 0.799214i) q^{66} +(0.107279 + 0.107279i) q^{67} +(-0.612651 - 2.18418i) q^{68} +(1.38497 - 1.38497i) q^{69} +(-8.31872 + 3.23574i) q^{70} +13.0475 q^{71} +(2.20825 - 0.960300i) q^{72} -6.24586 q^{73} +(5.05961 - 6.67407i) q^{74} +(0.715998 + 0.715998i) q^{75} +(-1.68683 + 3.00203i) q^{76} +(1.73682 + 7.27897i) q^{77} +(-1.92201 - 13.9689i) q^{78} -4.51184i q^{79} +(-2.25395 + 9.27213i) q^{80} +5.72110 q^{81} +(-0.315311 - 2.29163i) q^{82} +(-9.71727 + 9.71727i) q^{83} +(-3.77090 - 6.77807i) q^{84} +(-1.91327 - 1.91327i) q^{85} +(-2.12962 - 1.61446i) q^{86} +10.9202i q^{87} +(7.44348 + 2.93165i) q^{88} +11.6171 q^{89} +(1.73516 - 2.28883i) q^{90} +(17.5051 - 4.17685i) q^{91} +(2.57310 - 0.721742i) q^{92} +(-8.62244 + 8.62244i) q^{93} +(-0.372709 - 2.70879i) q^{94} +4.10728i q^{95} +(-8.24908 - 0.842084i) q^{96} -3.23412i q^{97} +(8.14128 - 5.63201i) q^{98} +(-1.70272 - 1.70272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 8 q^{4} + 8 q^{7} - 16 q^{8} - 32 q^{11} + 20 q^{14} + 16 q^{16} - 12 q^{18} + 16 q^{21} + 16 q^{22} - 32 q^{28} + 48 q^{30} - 24 q^{32} + 8 q^{35} - 16 q^{36} + 16 q^{39} - 40 q^{42} + 16 q^{44}+ \cdots + 64 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 8 * q^4 + 8 * q^7 - 16 * q^8 - 32 * q^11 + 20 * q^14 + 16 * q^16 - 12 * q^18 + 16 * q^21 + 16 * q^22 - 32 * q^28 + 48 * q^30 - 24 * q^32 + 8 * q^35 - 16 * q^36 + 16 * q^39 - 40 * q^42 + 16 * q^44 + 8 * q^46 - 16 * q^49 - 12 * q^50 - 32 * q^51 - 16 * q^56 + 48 * q^58 + 72 * q^60 + 64 * q^64 - 80 * q^65 - 48 * q^67 - 40 * q^70 + 32 * q^71 + 16 * q^72 + 16 * q^74 - 16 * q^77 - 64 * q^78 + 32 * q^81 + 56 * q^84 + 64 * q^85 - 24 * q^86 + 48 * q^88 + 8 * q^91 - 40 * q^92 - 64 * q^93 + 36 * q^98 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.192769	+	1.40101i	0.136308	+	0.990667i
$2$	0.192769	+	1.40101i	0.136308	+	0.990667i
$3$	−1.03649	+	1.03649i	−0.598420	+	0.598420i	−0.939892	−	0.341472i	$-0.889075\pi$
$3$	−1.03649	+	1.03649i	−0.598420	+	0.598420i	0.341472	+	0.939892i	$0.389075\pi$
$4$	−1.92568	+	0.540143i	−0.962840	+	0.270072i
$5$	−1.68683	+	1.68683i	−0.754373	+	0.754373i	−0.975292	−	0.220919i	$-0.929094\pi$
$5$	−1.68683	+	1.68683i	−0.754373	+	0.754373i	0.220919	+	0.975292i	$0.429094\pi$
$6$	−1.65195	−	1.25234i	−0.674404	−	0.511265i
$7$	1.38554	−	2.25395i	0.523684	−	0.851913i
$7$	1.38554	−	2.25395i	0.523684	−	0.851913i
$8$	−1.12796	−	2.59378i	−0.398794	−	0.917041i
$9$			0.851361i			0.283787i
$10$	−2.68844	−	2.03810i	−0.850159	−	0.644505i
$11$	−2.00000	+	2.00000i	−0.603023	+	0.603023i	−0.941113	−	0.338091i	$-0.890219\pi$
$11$	−2.00000	+	2.00000i	−0.603023	+	0.603023i	0.338091	+	0.941113i	$0.390219\pi$
$12$	1.43610	−	2.55581i	0.414567	−	0.737799i
$13$	4.80976	+	4.80976i	1.33399	+	1.33399i	0.901769	+	0.432219i	$0.142269\pi$
$13$	4.80976	+	4.80976i	1.33399	+	1.33399i	0.432219	+	0.901769i	$0.357731\pi$
$14$	3.42490	+	1.50667i	0.915344	+	0.402674i
$15$		−	3.49678i		−	0.902864i
$16$	3.41649	−	2.08029i	0.854123	−	0.520072i
$17$			1.13424i			0.275093i	0.990495	+	0.137547i	$0.0439217\pi$
$17$			1.13424i			0.275093i	−0.990495	+	0.137547i	$0.956078\pi$
$18$	−1.19277	+	0.164116i	−0.281138	+	0.0386824i
$19$	1.21746	−	1.21746i	0.279303	−	0.279303i	−0.553528	−	0.832831i	$-0.686719\pi$
$19$	1.21746	−	1.21746i	0.279303	−	0.279303i	0.832831	+	0.553528i	$0.186719\pi$
$20$	2.33717	−	4.15942i	0.522606	−	0.930076i
$21$	0.900103	+	3.77231i	0.196419	+	0.823184i
$22$	−3.18757	−	2.41649i	−0.679591	−	0.515198i
$23$	−1.33620			−0.278618			−0.139309	−	0.990249i	$-0.544488\pi$
$23$	−1.33620			−0.278618			−0.139309	+	0.990249i	$0.544488\pi$
$24$	3.85756	+	1.51932i	0.787422	+	0.310129i
$25$		−	0.690788i		−	0.138158i
$26$	−5.81137	+	7.66571i	−1.13970	+	1.50337i
$27$	−3.99191	−	3.99191i	−0.768244	−	0.768244i
$28$	−1.45065	+	5.08877i	−0.274147	+	0.961688i
$29$	5.26785	−	5.26785i	0.978215	−	0.978215i	−0.0215522	−	0.999768i	$-0.506861\pi$
$29$	5.26785	−	5.26785i	0.978215	−	0.978215i	0.999768	+	0.0215522i	$0.00686082\pi$
$30$	4.89903	−	0.674069i	0.894437	−	0.123068i
$31$	8.31885			1.49411			0.747055	−	0.664763i	$-0.231467\pi$
$31$	8.31885			1.49411			0.747055	+	0.664763i	$0.231467\pi$
$32$	3.57310	+	4.38554i	0.631641	+	0.775261i
$33$		−	4.14598i		−	0.721722i
$34$	−1.58908	+	0.218646i	−0.272526	+	0.0374974i
$35$	1.46486	+	6.13919i	0.247607	+	1.03771i
$36$	−0.459857	−	1.63945i	−0.0766428	−	0.273242i
$37$	−4.18757	−	4.18757i	−0.688431	−	0.688431i	0.273454	−	0.961885i	$-0.411834\pi$
$37$	−4.18757	−	4.18757i	−0.688431	−	0.688431i	−0.961885	+	0.273454i	$0.911834\pi$
$38$	1.94036	+	1.47098i	0.314768	+	0.238625i
$39$	−9.97057			−1.59657
$40$	6.27794	+	2.47259i	0.992630	+	0.390952i
$41$	−1.63570			−0.255453			−0.127726	−	0.991809i	$-0.540768\pi$
$41$	−1.63570			−0.255453			−0.127726	+	0.991809i	$0.540768\pi$
$42$	−5.11154	+	1.98824i	−0.788728	+	0.306792i
$43$	−1.33620	+	1.33620i	−0.203769	+	0.203769i	−0.801613	−	0.597844i	$-0.796024\pi$
$43$	−1.33620	+	1.33620i	−0.203769	+	0.203769i	0.597844	+	0.801613i	$0.296024\pi$
$44$	2.77107	−	4.93165i	0.417755	−	0.743474i
$45$	−1.43610	−	1.43610i	−0.214081	−	0.214081i
$46$	−0.257578	−	1.87204i	−0.0379779	−	0.276017i
$47$	−1.93345			−0.282023			−0.141012	−	0.990008i	$-0.545035\pi$
$47$	−1.93345			−0.282023			−0.141012	+	0.990008i	$0.545035\pi$
$48$	−1.38497	+	5.69738i	−0.199903	+	0.822345i
$49$	−3.16057	−	6.24586i	−0.451510	−	0.892266i
$50$	0.967804	−	0.133162i	0.136868	−	0.0188320i
$51$	−1.17563	−	1.17563i	−0.164621	−	0.164621i
$52$	−11.8600	−	6.66410i	−1.64469	−	0.924145i
$53$	6.34814	+	6.34814i	0.871984	+	0.871984i	0.992688	−	0.120705i	$-0.0385154\pi$
$53$	6.34814	+	6.34814i	0.871984	+	0.871984i	−0.120705	+	0.992688i	$0.538515\pi$
$54$	4.82321	−	6.36224i	0.656356	−	0.865791i
$55$		−	6.74732i		−	0.909808i
$56$	−7.40908	−	1.05142i	−0.990080	−	0.140502i
$57$			2.52377i			0.334281i
$58$	8.39581	+	6.36486i	1.10242	+	0.835747i
$59$	−3.29044	−	3.29044i	−0.428379	−	0.428379i	0.459697	−	0.888076i	$-0.347958\pi$
$59$	−3.29044	−	3.29044i	−0.428379	−	0.428379i	−0.888076	+	0.459697i	$0.847958\pi$
$60$	1.88876	+	6.73368i	0.243838	+	0.869314i
$61$	−2.04875	−	2.04875i	−0.262316	−	0.262316i	0.563678	−	0.825994i	$-0.309386\pi$
$61$	−2.04875	−	2.04875i	−0.262316	−	0.262316i	−0.825994	+	0.563678i	$0.809386\pi$
$62$	1.60361	+	11.6548i	0.203659	+	1.48016i
$63$	1.91892	+	1.17959i	0.241762	+	0.148615i
$64$	−5.45542	+	5.85136i	−0.681927	+	0.731420i
$65$	−16.2265			−2.01265
$66$	5.80857	−	0.799214i	0.714985	−	0.0983765i
$67$	0.107279	+	0.107279i	0.0131062	+	0.0131062i	0.713630	−	0.700523i	$-0.247050\pi$
$67$	0.107279	+	0.107279i	0.0131062	+	0.0131062i	−0.700523	+	0.713630i	$0.747050\pi$
$68$	−0.612651	−	2.18418i	−0.0742949	−	0.264871i
$69$	1.38497	−	1.38497i	0.166731	−	0.166731i
$70$	−8.31872	+	3.23574i	−0.994277	+	0.386745i
$71$	13.0475			1.54846			0.774229	−	0.632906i	$-0.218138\pi$
$71$	13.0475			1.54846			0.774229	+	0.632906i	$0.218138\pi$
$72$	2.20825	−	0.960300i	0.260244	−	0.113172i
$73$	−6.24586			−0.731023			−0.365511	−	0.930807i	$-0.619106\pi$
$73$	−6.24586			−0.731023			−0.365511	+	0.930807i	$0.619106\pi$
$74$	5.05961	−	6.67407i	0.588167	−	0.775845i
$75$	0.715998	+	0.715998i	0.0826763	+	0.0826763i
$76$	−1.68683	+	3.00203i	−0.193493	+	0.344356i
$77$	1.73682	+	7.27897i	0.197929	+	0.829516i
$78$	−1.92201	−	13.9689i	−0.217625	−	1.58167i
$79$		−	4.51184i		−	0.507621i	−0.967254	−	0.253811i	$-0.918316\pi$
$79$		−	4.51184i		−	0.507621i	0.967254	−	0.253811i	$-0.0816840\pi$
$80$	−2.25395	+	9.27213i	−0.251999	+	1.03666i
$81$	5.72110			0.635678
$82$	−0.315311	−	2.29163i	−0.0348203	−	0.253069i
$83$	−9.71727	+	9.71727i	−1.06661	+	1.06661i	−0.0689912	+	0.997617i	$0.521978\pi$
$83$	−9.71727	+	9.71727i	−1.06661	+	1.06661i	−0.997617	+	0.0689912i	$0.978022\pi$
$84$	−3.77090	−	6.77807i	−0.411439	−	0.739548i
$85$	−1.91327	−	1.91327i	−0.207523	−	0.207523i
$86$	−2.12962	−	1.61446i	−0.229643	−	0.174092i
$87$			10.9202i			1.17077i
$88$	7.44348	+	2.93165i	0.793478	+	0.312515i
$89$	11.6171			1.23141			0.615707	−	0.787975i	$-0.288870\pi$
$89$	11.6171			1.23141			0.615707	+	0.787975i	$0.288870\pi$
$90$	1.73516	−	2.28883i	0.182902	−	0.241264i
$91$	17.5051	−	4.17685i	1.83503	−	0.437853i
$92$	2.57310	−	0.721742i	0.268264	−	0.0752468i
$93$	−8.62244	+	8.62244i	−0.894105	+	0.894105i
$94$	−0.372709	−	2.70879i	−0.0384420	−	0.279391i
$95$			4.10728i			0.421398i
$96$	−8.24908	−	0.842084i	−0.841918	−	0.0859448i
$97$		−	3.23412i		−	0.328376i	−0.986429	−	0.164188i	$-0.947500\pi$
$97$		−	3.23412i		−	0.328376i	0.986429	−	0.164188i	$-0.0525003\pi$
$98$	8.14128	−	5.63201i	0.822393	−	0.568919i
$99$	−1.70272	−	1.70272i	−0.171130	−	0.171130i
$100$	0.373125	+	1.33024i	0.0373125	+	0.133024i
$101$	5.94400	−	5.94400i	0.591450	−	0.591450i	−0.346573	−	0.938023i	$-0.612655\pi$
$101$	5.94400	−	5.94400i	0.591450	−	0.591450i	0.938023	+	0.346573i	$0.112655\pi$
$102$	1.42045	−	1.87370i	0.140646	−	0.185524i
$103$			7.44427i			0.733505i	0.930318	+	0.366753i	$0.119530\pi$
$103$			7.44427i			0.733505i	−0.930318	+	0.366753i	$0.880470\pi$
$104$	7.05026	−	17.9007i	0.691335	−	1.75531i
$105$	−7.88156	−	4.84492i	−0.769161	−	0.472815i
$106$	−7.67011	+	10.1176i	−0.744987	+	0.982704i
$107$	−2.83298	+	2.83298i	−0.273875	+	0.273875i	−0.830658	−	0.556783i	$-0.812035\pi$
$107$	−2.83298	+	2.83298i	−0.273875	+	0.273875i	0.556783	+	0.830658i	$0.312035\pi$
$108$	9.84335	+	5.53094i	0.947177	+	0.532215i
$109$	5.51516	−	5.51516i	0.528256	−	0.528256i	−0.391796	−	0.920052i	$-0.628146\pi$
$109$	5.51516	−	5.51516i	0.528256	−	0.528256i	0.920052	+	0.391796i	$0.128146\pi$
$110$	9.45309	−	1.30067i	0.901317	−	0.124014i
$111$	8.68077			0.823942
$112$	0.0448159	−	10.5829i	0.00423470	−	0.999991i
$113$	13.5173			1.27160			0.635801	−	0.771853i	$-0.280670\pi$
$113$	13.5173			1.27160			0.635801	+	0.771853i	$0.280670\pi$
$114$	−3.53584	+	0.486504i	−0.331161	+	0.0455652i
$115$	2.25395	−	2.25395i	0.210182	−	0.210182i
$116$	−7.29881	+	12.9896i	−0.677677	+	1.20605i
$117$	−4.09484	+	4.09484i	−0.378568	+	0.378568i
$118$	3.97566	−	5.24425i	0.365989	−	0.482772i
$119$	2.55652	+	1.57153i	0.234355	+	0.144062i
$120$	−9.06988	+	3.94422i	−0.827963	+	0.360056i
$121$			3.00000i			0.272727i
$122$	2.47540	−	3.26527i	0.224112	−	0.295623i
$123$	1.69539	−	1.69539i	0.152868	−	0.152868i
$124$	−16.0194	+	4.49337i	−1.43859	+	0.403516i
$125$	−7.26891	−	7.26891i	−0.650151	−	0.650151i
$126$	−1.28272	+	2.91583i	−0.114274	+	0.259763i
$127$			2.87835i			0.255413i	0.991812	+	0.127706i	$0.0407615\pi$
$127$			2.87835i			0.255413i	−0.991812	+	0.127706i	$0.959239\pi$
$128$	−9.24947	−	6.51516i	−0.817546	−	0.575864i
$129$		−	2.76994i		−	0.243879i
$130$	−3.12796	−	22.7335i	−0.274340	−	1.99386i
$131$	5.20937	−	5.20937i	0.455145	−	0.455145i	−0.441913	−	0.897058i	$-0.645700\pi$
$131$	5.20937	−	5.20937i	0.455145	−	0.455145i	0.897058	+	0.441913i	$0.145700\pi$
$132$	2.23942	+	7.98382i	0.194917	+	0.694903i
$133$	−1.05725	−	4.43091i	−0.0916754	−	0.384209i
$134$	−0.129619	+	0.170979i	−0.0111974	+	0.0147704i
$135$	13.4674			1.15908
$136$	2.94197	−	1.27937i	0.252272	−	0.109705i
$137$		−	15.8805i		−	1.35676i	−0.734709	−	0.678382i	$-0.762681\pi$
$137$		−	15.8805i		−	1.35676i	0.734709	−	0.678382i	$-0.237319\pi$
$138$	2.20734	+	1.67338i	0.187901	+	0.142448i
$139$	11.7757	+	11.7757i	0.998804	+	0.998804i	0.999999	−	0.00119539i	$-0.000380504\pi$
$139$	11.7757	+	11.7757i	0.998804	+	0.998804i	−0.00119539	+	0.999999i	$0.500381\pi$
$140$	−6.13690	−	11.0309i	−0.518663	−	0.932280i
$141$	2.00401	−	2.00401i	0.168768	−	0.168768i
$142$	2.51516	+	18.2798i	0.211067	+	1.53401i
$143$	−19.2390			−1.60885
$144$	1.77107	+	2.90867i	0.147590	+	0.242389i
$145$			17.7719i			1.47588i
$146$	−1.20401	−	8.75054i	−0.0996443	−	0.724200i
$147$	9.74971	+	3.19788i	0.804143	+	0.263757i
$148$	10.3258	+	5.80203i	0.848775	+	0.476924i
$149$	−7.72570	−	7.72570i	−0.632914	−	0.632914i	0.315884	−	0.948798i	$-0.397699\pi$
$149$	−7.72570	−	7.72570i	−0.632914	−	0.632914i	−0.948798	+	0.315884i	$0.897699\pi$
$150$	−0.865101	+	1.14114i	−0.0706352	+	0.0931741i
$151$	−20.5443			−1.67187			−0.835936	−	0.548826i	$-0.815075\pi$
$151$	−20.5443			−1.67187			−0.835936	+	0.548826i	$0.815075\pi$
$152$	−4.53105	−	1.78457i	−0.367517	−	0.144748i
$153$	−0.965647			−0.0780679
$154$	−9.86314	+	3.83647i	−0.794794	+	0.309152i
$155$	−14.0325	+	14.0325i	−1.12712	+	1.12712i
$156$	19.2001	−	5.38554i	1.53724	−	0.431188i
$157$	−3.07180	−	3.07180i	−0.245156	−	0.245156i	0.573823	−	0.818979i	$-0.305460\pi$
$157$	−3.07180	−	3.07180i	−0.245156	−	0.245156i	−0.818979	+	0.573823i	$0.805460\pi$
$158$	6.32115	−	0.869741i	0.502883	−	0.0691928i
$159$	−13.1596			−1.04363
$160$	−13.4249	−	1.37044i	−1.06133	−	0.108343i
$161$	−1.85136	+	3.01174i	−0.145908	+	0.237358i
$162$	1.10285	+	8.01534i	0.0866480	+	0.629745i
$163$	3.22893	+	3.22893i	0.252909	+	0.252909i	0.822162	−	0.569253i	$-0.192768\pi$
$163$	3.22893	+	3.22893i	0.252909	+	0.252909i	−0.569253	+	0.822162i	$0.692768\pi$
$164$	3.14983	−	0.883510i	0.245960	−	0.0689906i
$165$	6.99355	+	6.99355i	0.544447	+	0.544447i
$166$	−15.4872	−	11.7408i	−1.20204	−	0.911266i
$167$			6.05037i			0.468192i	0.972214	+	0.234096i	$0.0752130\pi$
$167$			6.05037i			0.468192i	−0.972214	+	0.234096i	$0.924787\pi$
$168$	8.76926	−	6.58968i	0.676563	−	0.508405i
$169$			33.2676i			2.55905i
$170$	2.31170	−	3.04933i	0.177299	−	0.233873i
$171$	1.03649	+	1.03649i	0.0792627	+	0.0792627i
$172$	1.85136	−	3.29484i	0.141165	−	0.251230i
$173$	−4.44784	−	4.44784i	−0.338163	−	0.338163i	0.517513	−	0.855676i	$-0.326858\pi$
$173$	−4.44784	−	4.44784i	−0.338163	−	0.338163i	−0.855676	+	0.517513i	$0.826858\pi$
$174$	−15.2993	+	2.10507i	−1.15984	+	0.159585i
$175$	−1.55700	−	0.957113i	−0.117698	−	0.0723509i
$176$	−2.67241	+	10.9936i	−0.201440	+	0.828670i
$177$	6.82105			0.512701
$178$	2.23942	+	16.2758i	0.167852	+	1.21992i
$179$	−9.36007	−	9.36007i	−0.699605	−	0.699605i	0.264721	−	0.964325i	$-0.414720\pi$
$179$	−9.36007	−	9.36007i	−0.699605	−	0.699605i	−0.964325	+	0.264721i	$0.914720\pi$
$180$	3.54117	+	1.98977i	0.263943	+	0.148309i
$181$	0.190668	−	0.190668i	0.0141722	−	0.0141722i	−0.699985	−	0.714157i	$-0.746810\pi$
$181$	0.190668	−	0.190668i	0.0141722	−	0.0141722i	0.714157	+	0.699985i	$0.246810\pi$
$182$	9.22625	+	23.7197i	0.683895	+	1.75822i
$183$	4.24704			0.313950
$184$	1.50718	+	3.46582i	0.111111	+	0.255504i
$185$	14.1274			1.03867
$186$	−13.7423	−	10.4180i	−1.00763	−	0.763886i
$187$	−2.26848	−	2.26848i	−0.165888	−	0.165888i
$188$	3.72321	−	1.04434i	0.271543	−	0.0761664i
$189$	−14.5285	+	3.46662i	−1.05679	+	0.252160i
$190$	−5.75436	+	0.791755i	−0.417465	+	0.0574399i
$191$			3.90133i			0.282291i	0.989989	+	0.141145i	$0.0450785\pi$
$191$			3.90133i			0.282291i	−0.989989	+	0.141145i	$0.954922\pi$
$192$	−0.410393	−	11.7194i	−0.0296176	−	0.845775i
$193$	9.87523			0.710834			0.355417	−	0.934708i	$-0.384339\pi$
$193$	9.87523			0.710834			0.355417	+	0.934708i	$0.384339\pi$
$194$	4.53105	−	0.623438i	0.325311	−	0.0447602i
$195$	16.8187	−	16.8187i	1.20441	−	1.20441i
$196$	9.45991	+	10.3204i	0.675708	+	0.737169i
$197$	−14.4021	−	14.4021i	−1.02611	−	1.02611i	−0.999650	−	0.0264589i	$-0.991577\pi$
$197$	−14.4021	−	14.4021i	−1.02611	−	1.02611i	−0.0264589	−	0.999650i	$-0.508423\pi$
$198$	2.05731	−	2.71377i	0.146206	−	0.192859i
$199$		−	25.6513i		−	1.81837i	−0.416387	−	0.909187i	$-0.636704\pi$
$199$		−	25.6513i		−	1.81837i	0.416387	−	0.909187i	$-0.363296\pi$
$200$	−1.79175	+	0.779181i	−0.126696	+	0.0550964i
$201$	−0.222388			−0.0156860
$202$	9.47344	+	7.18181i	0.666549	+	0.505310i
$203$	−4.57466	−	19.1723i	−0.321078	−	1.34563i
$204$	2.89890	+	1.62888i	0.202964	+	0.114045i
$205$	2.75914	−	2.75914i	0.192707	−	0.192707i
$206$	−10.4295	+	1.43502i	−0.726659	+	0.0999827i
$207$		−	1.13759i		−	0.0790681i
$208$	26.4382	+	6.42682i	1.83316	+	0.445620i
$209$			4.86982i			0.336853i
$210$	5.26848	−	11.9761i	0.363559	−	0.826431i
$211$	−15.4141	−	15.4141i	−1.06115	−	1.06115i	−0.998004	−	0.0631429i	$-0.979888\pi$
$211$	−15.4141	−	15.4141i	−1.06115	−	1.06115i	−0.0631429	−	0.998004i	$-0.520112\pi$
$212$	−15.6534	−	8.79558i	−1.07508	−	0.604083i
$213$	−13.5237	+	13.5237i	−0.926628	+	0.926628i
$214$	−4.51516	−	3.42294i	−0.308650	−	0.233987i
$215$		−	4.50790i		−	0.307436i
$216$	−5.85144	+	14.8569i	−0.398140	+	1.01088i
$217$	11.5261	−	18.7503i	0.782441	−	1.27285i
$218$	8.78996	+	6.66366i	0.595331	+	0.451320i
$219$	6.47380	−	6.47380i	0.437459	−	0.437459i
$220$	3.64452	+	12.9932i	0.245713	+	0.876000i
$221$	−5.45542	+	5.45542i	−0.366971	+	0.366971i
$222$	1.67338	+	12.1619i	0.112310	+	0.816252i
$223$	−15.4012			−1.03134			−0.515670	−	0.856787i	$-0.672457\pi$
$223$	−15.4012			−1.03134			−0.515670	+	0.856787i	$0.672457\pi$
$224$	14.8354	−	1.97727i	0.991235	−	0.132112i
$225$	0.588110			0.0392073
$226$	2.60572	+	18.9380i	0.173330	+	1.25973i
$227$	7.60285	−	7.60285i	0.504619	−	0.504619i	−0.408251	−	0.912870i	$-0.633861\pi$
$227$	7.60285	−	7.60285i	0.504619	−	0.504619i	0.912870	+	0.408251i	$0.133861\pi$
$228$	−1.36320	−	4.85997i	−0.0902799	−	0.321860i
$229$	17.6096	−	17.6096i	1.16368	−	1.16368i	0.180011	−	0.983665i	$-0.442387\pi$
$229$	17.6096	−	17.6096i	1.16368	−	1.16368i	0.983665	−	0.180011i	$-0.0576134\pi$
$230$	3.59230	+	2.72332i	0.236870	+	0.179571i
$231$	−9.34482	−	5.74440i	−0.614844	−	0.377954i
$232$	−19.6056	−	7.72174i	−1.28717	−	0.506957i
$233$			6.72639i			0.440661i	0.975425	+	0.220330i	$0.0707135\pi$
$233$			6.72639i			0.440661i	−0.975425	+	0.220330i	$0.929286\pi$
$234$	−6.52629	−	4.94757i	−0.426637	−	0.323433i
$235$	3.26141	−	3.26141i	0.212751	−	0.212751i
$236$	8.11365	+	4.55903i	0.528154	+	0.296768i
$237$	4.67649	+	4.67649i	0.303771	+	0.303771i
$238$	−1.70892	+	3.88466i	−0.110773	+	0.251805i
$239$			9.53354i			0.616673i	0.951277	+	0.308337i	$0.0997723\pi$
$239$			9.53354i			0.616673i	−0.951277	+	0.308337i	$0.900228\pi$
$240$	−7.27430	−	11.9467i	−0.469554	−	0.771157i
$241$			21.3762i			1.37696i	0.725255	+	0.688481i	$0.241722\pi$
$241$			21.3762i			1.37696i	−0.725255	+	0.688481i	$0.758278\pi$
$242$	−4.20304	+	0.578306i	−0.270182	+	0.0371749i
$243$	6.04585	−	6.04585i	0.387841	−	0.387841i
$244$	5.05186	+	2.83862i	0.323412	+	0.181724i
$245$	15.8671	+	5.20436i	1.01371	+	0.332494i
$246$	2.70208	+	2.04845i	0.172278	+	0.130604i
$247$	11.7113			0.745174
$248$	−9.38332	−	21.5773i	−0.595841	−	1.37016i
$249$		−	20.1438i		−	1.27656i
$250$	8.78262	−	11.5851i	0.555462	−	0.732703i
$251$	−3.97286	−	3.97286i	−0.250765	−	0.250765i	0.570519	−	0.821284i	$-0.306742\pi$
$251$	−3.97286	−	3.97286i	−0.250765	−	0.250765i	−0.821284	+	0.570519i	$0.806742\pi$
$252$	−4.33238	−	1.23502i	−0.272915	−	0.0777992i
$253$	2.67241	−	2.67241i	0.168013	−	0.168013i
$254$	−4.03261	+	0.554856i	−0.253029	+	0.0348148i
$255$	3.96618			0.248372
$256$	7.34482	−	14.2146i	0.459051	−	0.888410i
$257$		−	6.91591i		−	0.431403i	−0.976459	−	0.215701i	$-0.930796\pi$
$257$		−	6.91591i		−	0.431403i	0.976459	−	0.215701i	$-0.0692038\pi$
$258$	3.88072	−	0.533957i	0.241603	−	0.0332427i
$259$	−15.2406	+	3.63653i	−0.947004	+	0.225963i
$260$	31.2470	−	8.76463i	1.93786	−	0.543559i
$261$	4.48484	+	4.48484i	0.277605	+	0.277605i
$262$	8.30260	+	6.29419i	0.512936	+	0.388857i
$263$	−17.7806			−1.09640			−0.548199	−	0.836348i	$-0.684686\pi$
$263$	−17.7806			−1.09640			−0.548199	+	0.836348i	$0.684686\pi$
$264$	−10.7538	+	4.67649i	−0.661848	+	0.287818i
$265$	−21.4165			−1.31560
$266$	6.00396	−	2.33537i	0.368127	−	0.143190i
$267$	−12.0411	+	12.0411i	−0.736903	+	0.736903i
$268$	−0.264531	−	0.148639i	−0.0161588	−	0.00907957i
$269$	9.95044	+	9.95044i	0.606689	+	0.606689i	0.942079	−	0.335390i	$-0.108868\pi$
$269$	9.95044	+	9.95044i	0.606689	+	0.606689i	−0.335390	+	0.942079i	$0.608868\pi$
$270$	2.59608	+	18.8679i	0.157993	+	1.14827i
$271$	19.6010			1.19067			0.595337	−	0.803476i	$-0.297019\pi$
$271$	19.6010			1.19067			0.595337	+	0.803476i	$0.297019\pi$
$272$	2.35954	+	3.87512i	0.143068	+	0.234963i
$273$	−13.8146	+	22.4732i	−0.836098	+	1.36014i
$274$	22.2488	−	3.06127i	1.34410	−	0.184938i
$275$	1.38158	+	1.38158i	0.0833122	+	0.0833122i
$276$	−1.91892	+	3.41509i	−0.115506	+	0.205564i
$277$	13.6430	+	13.6430i	0.819727	+	0.819727i	0.986068	−	0.166341i	$-0.0531952\pi$
$277$	13.6430	+	13.6430i	0.819727	+	0.819727i	−0.166341	+	0.986068i	$0.553195\pi$
$278$	−14.2280	+	18.7679i	−0.853337	+	1.12563i
$279$			7.08234i			0.424009i
$280$	14.2714	−	10.7243i	0.852881	−	0.640899i
$281$		−	7.16702i		−	0.427548i	−0.976883	−	0.213774i	$-0.931424\pi$
$281$		−	7.16702i		−	0.427548i	0.976883	−	0.213774i	$-0.0685757\pi$
$282$	3.19396	+	2.42134i	0.190198	+	0.144189i
$283$	11.6238	+	11.6238i	0.690964	+	0.690964i	0.962444	−	0.271480i	$-0.0875130\pi$
$283$	11.6238	+	11.6238i	0.690964	+	0.690964i	−0.271480	+	0.962444i	$0.587513\pi$
$284$	−25.1254	+	7.04754i	−1.49092	+	0.418195i
$285$	−4.25717	−	4.25717i	−0.252173	−	0.252173i
$286$	−3.70868	−	26.9542i	−0.219299	−	1.59383i
$287$	−2.26632	+	3.68678i	−0.133777	+	0.217624i
$288$	−3.73368	+	3.04200i	−0.220009	+	0.179252i
$289$	15.7135			0.924324
$290$	−24.8987	+	3.42587i	−1.46210	+	0.201174i
$291$	3.35215	+	3.35215i	0.196507	+	0.196507i
$292$	12.0275	−	3.37366i	0.703858	−	0.197428i
$293$	−0.108531	+	0.108531i	−0.00634048	+	0.00634048i	−0.710270	−	0.703929i	$-0.751427\pi$
$293$	−0.108531	+	0.108531i	−0.00634048	+	0.00634048i	0.703929	+	0.710270i	$0.251427\pi$
$294$	−2.60084	+	14.2759i	−0.151684	+	0.832589i
$295$	11.1008			0.646315
$296$	−6.13823	+	15.5850i	−0.356778	+	0.905862i
$297$	15.9676			0.926537
$298$	9.33454	−	12.3131i	0.540736	−	0.713278i
$299$	−6.42682	−	6.42682i	−0.371673	−	0.371673i
$300$	−1.76552	−	0.992042i	−0.101933	−	0.0572756i
$301$	1.16038	+	4.86310i	0.0668829	+	0.280304i
$302$	−3.96030	−	28.7829i	−0.227890	−	1.65627i
$303$			12.3218i			0.707871i
$304$	1.62677	−	6.69208i	0.0933016	−	0.383817i
$305$	6.91179			0.395768
$306$	−0.186146	−	1.35288i	−0.0106413	−	0.0773393i
$307$	1.23198	−	1.23198i	0.0703130	−	0.0703130i	−0.671076	−	0.741389i	$-0.734167\pi$
$307$	1.23198	−	1.23198i	0.0703130	−	0.0703130i	0.741389	+	0.671076i	$0.234167\pi$
$308$	−7.27625	−	13.0788i	−0.414603	−	0.745236i
$309$	−7.71594	−	7.71594i	−0.438944	−	0.438944i
$310$	−22.3647	−	16.9547i	−1.27023	−	0.962961i
$311$			15.0393i			0.852799i	0.904535	+	0.426399i	$0.140218\pi$
$311$			15.0393i			0.852799i	−0.904535	+	0.426399i	$0.859782\pi$
$312$	11.2464	+	25.8615i	0.636702	+	1.46412i
$313$	−33.6455			−1.90176			−0.950879	−	0.309563i	$-0.899817\pi$
$313$	−33.6455			−1.90176			−0.950879	+	0.309563i	$0.899817\pi$
$314$	3.71148	−	4.89578i	0.209451	−	0.276285i
$315$	−5.22667	+	1.24713i	−0.294489	+	0.0702676i
$316$	2.43704	+	8.68835i	0.137094	+	0.488758i
$317$	4.05086	−	4.05086i	0.227519	−	0.227519i	−0.584136	−	0.811655i	$-0.698567\pi$
$317$	4.05086	−	4.05086i	0.227519	−	0.227519i	0.811655	+	0.584136i	$0.198567\pi$
$318$	−2.53676	−	18.4368i	−0.142254	−	1.03388i
$319$			21.0714i			1.17977i
$320$	−0.667890	−	19.0726i	−0.0373362	−	1.06619i
$321$		−	5.87274i		−	0.327784i
$322$	−4.57637	−	2.01321i	−0.255031	−	0.112192i
$323$	1.38089	+	1.38089i	0.0768345	+	0.0768345i
$324$	−11.0170	+	3.09021i	−0.612056	+	0.171679i
$325$	3.32253	−	3.32253i	0.184301	−	0.184301i
$326$	−3.90133	+	5.14621i	−0.216075	+	0.285022i
$327$			11.4329i			0.632238i
$328$	1.84500	+	4.24264i	0.101873	+	0.234261i
$329$	−2.67887	+	4.35790i	−0.147691	+	0.240259i
$330$	−8.44993	+	11.1462i	−0.465153	+	0.613578i
$331$	11.3981	−	11.3981i	0.626497	−	0.626497i	−0.320688	−	0.947185i	$-0.603914\pi$
$331$	11.3981	−	11.3981i	0.626497	−	0.626497i	0.947185	+	0.320688i	$0.103914\pi$
$332$	13.4636	−	23.9611i	0.738913	−	1.31503i
$333$	3.56513	−	3.56513i	0.195368	−	0.195368i
$334$	−8.47665	+	1.16632i	−0.463822	+	0.0638183i
$335$	−0.361923			−0.0197739
$336$	10.9227	+	11.0156i	0.595881	+	0.600949i
$337$	−11.0356			−0.601148			−0.300574	−	0.953759i	$-0.597178\pi$
$337$	−11.0356			−0.601148			−0.300574	+	0.953759i	$0.597178\pi$
$338$	−46.6084	+	6.41295i	−2.53516	+	0.348818i
$339$	−14.0106	+	14.0106i	−0.760953	+	0.760953i
$340$	4.71778	+	2.65090i	0.255858	+	0.143765i
$341$	−16.6377	+	16.6377i	−0.900982	+	0.900982i
$342$	−1.25234	+	1.65195i	−0.0677187	+	0.0893270i
$343$	−18.4569	−	1.53010i	−0.996581	−	0.0826178i
$344$	4.97301	+	1.95864i	0.268127	+	0.105603i
$345$			4.67241i			0.251554i
$346$	5.37408	−	7.08889i	0.288912	−	0.381101i
$347$	13.6494	−	13.6494i	0.732740	−	0.732740i	−0.238422	−	0.971162i	$-0.576630\pi$
$347$	13.6494	−	13.6494i	0.732740	−	0.732740i	0.971162	+	0.238422i	$0.0766301\pi$
$348$	−5.89847	−	21.0288i	−0.316191	−	1.12726i
$349$	−5.59100	−	5.59100i	−0.299280	−	0.299280i	0.541452	−	0.840732i	$-0.317875\pi$
$349$	−5.59100	−	5.59100i	−0.299280	−	0.299280i	−0.840732	+	0.541452i	$0.817875\pi$
$350$	1.04079	−	2.36588i	0.0556324	−	0.126462i
$351$		−	38.4003i		−	2.04966i
$352$	−15.9173	−	1.62487i	−0.848394	−	0.0866058i
$353$		−	31.8994i		−	1.69783i	−0.528528	−	0.848916i	$-0.677256\pi$
$353$		−	31.8994i		−	1.69783i	0.528528	−	0.848916i	$-0.322744\pi$
$354$	1.31488	+	9.55638i	0.0698853	+	0.507916i
$355$	−22.0090	+	22.0090i	−1.16812	+	1.16812i
$356$	−22.3709	+	6.27492i	−1.18566	+	0.332570i
$357$	−4.27870	+	1.02093i	−0.226453	+	0.0540335i
$358$	11.3093	−	14.9179i	0.597713	−	0.788437i
$359$	8.42050			0.444417			0.222209	−	0.974999i	$-0.428673\pi$
$359$	8.42050			0.444417			0.222209	+	0.974999i	$0.428673\pi$
$360$	−2.10507	+	5.34480i	−0.110947	+	0.281696i
$361$			16.0356i			0.843979i
$362$	0.303883	+	0.230374i	0.0159718	+	0.0121082i
$363$	−3.10948	−	3.10948i	−0.163205	−	0.163205i
$364$	−31.4530	+	17.4985i	−1.64859	+	0.917172i
$365$	10.5357	−	10.5357i	0.551464	−	0.551464i
$366$	0.818696	+	5.95016i	0.0427939	+	0.311020i
$367$	−10.0187			−0.522972			−0.261486	−	0.965207i	$-0.584213\pi$
$367$	−10.0187			−0.522972			−0.261486	+	0.965207i	$0.584213\pi$
$368$	−4.56513	+	2.77969i	−0.237974	+	0.144901i
$369$		−	1.39257i		−	0.0724942i
$370$	2.72332	+	19.7927i	0.141579	+	1.02897i
$371$	23.1040	−	5.51280i	1.19950	−	0.286210i
$372$	11.9467	−	21.2614i	0.619408	−	1.10235i
$373$	−1.13115	−	1.13115i	−0.0585685	−	0.0585685i	0.677216	−	0.735784i	$-0.263186\pi$
$373$	−1.13115	−	1.13115i	−0.0585685	−	0.0585685i	−0.735784	+	0.677216i	$0.763186\pi$
$374$	2.74088	−	3.61546i	0.141727	−	0.186951i
$375$	15.0684			0.778126
$376$	2.18086	+	5.01496i	0.112469	+	0.258627i
$377$	50.6742			2.60985
$378$	−7.65743	−	19.6864i	−0.393856	−	1.01256i
$379$	−12.6191	+	12.6191i	−0.648200	+	0.648200i	−0.952558	−	0.304357i	$-0.901558\pi$
$379$	−12.6191	+	12.6191i	−0.648200	+	0.648200i	0.304357	+	0.952558i	$0.401558\pi$
$380$	−2.21852	−	7.90931i	−0.113808	−	0.405739i
$381$	−2.98340	−	2.98340i	−0.152844	−	0.152844i
$382$	−5.46582	+	0.752055i	−0.279656	+	0.0384785i
$383$	16.6646			0.851521			0.425761	−	0.904836i	$-0.360007\pi$
$383$	16.6646			0.851521			0.425761	+	0.904836i	$0.360007\pi$
$384$	16.3399	−	2.83410i	0.833844	−	0.144627i
$385$	−15.2081	−	9.34866i	−0.775077	−	0.476452i
$386$	1.90363	+	13.8353i	0.0968924	+	0.704200i
$387$	−1.13759	−	1.13759i	−0.0578271	−	0.0578271i
$388$	1.74689	+	6.22789i	0.0886849	+	0.316173i
$389$	2.85997	+	2.85997i	0.145006	+	0.145006i	0.775883	−	0.630877i	$-0.217305\pi$
$389$	2.85997	+	2.85997i	0.145006	+	0.145006i	−0.630877	+	0.775883i	$0.717305\pi$
$390$	26.8053	+	20.3211i	1.35734	+	1.02900i
$391$		−	1.51557i		−	0.0766459i
$392$	−12.6354	+	15.2429i	−0.638185	+	0.769883i
$393$			10.7990i			0.544735i
$394$	17.4013	−	22.9539i	0.876665	−	1.15640i
$395$	7.61070	+	7.61070i	0.382936	+	0.382936i
$396$	4.19861	+	2.35918i	0.210988	+	0.118553i
$397$	12.0302	+	12.0302i	0.603778	+	0.603778i	0.941313	−	0.337535i	$-0.109593\pi$
$397$	12.0302	+	12.0302i	0.603778	+	0.603778i	−0.337535	+	0.941313i	$0.609593\pi$
$398$	35.9379	−	4.94477i	1.80140	−	0.247859i
$399$	5.68845	+	3.49678i	0.284779	+	0.175058i
$400$	−1.43704	−	2.36007i	−0.0718519	−	0.118004i
$401$	3.88812			0.194163			0.0970817	−	0.995276i	$-0.469049\pi$
$401$	3.88812			0.194163			0.0970817	+	0.995276i	$0.469049\pi$
$402$	−0.0428694	−	0.311569i	−0.00213813	−	0.0155396i
$403$	40.0117	+	40.0117i	1.99312	+	1.99312i
$404$	−8.23563	+	14.6569i	−0.409738	+	0.729206i
$405$	−9.65052	+	9.65052i	−0.479538	+	0.479538i
$406$	25.9788	−	10.1050i	1.28930	−	0.501502i
$407$	16.7503			0.830280
$408$	−1.72327	+	4.37540i	−0.0853145	+	0.216614i
$409$	−25.7267			−1.27210			−0.636052	−	0.771646i	$-0.719434\pi$
$409$	−25.7267			−1.27210			−0.636052	+	0.771646i	$0.719434\pi$
$410$	4.39747	+	3.33372i	0.217176	+	0.164641i
$411$	16.4601	+	16.4601i	0.811915	+	0.811915i
$412$	−4.02097	−	14.3353i	−0.198099	−	0.706248i
$413$	−11.9755	+	2.85746i	−0.589277	+	0.140606i
$414$	1.59378	−	0.219292i	0.0783301	−	0.0107776i
$415$		−	32.7827i		−	1.60924i
$416$	−3.90762	+	38.2791i	−0.191587	+	1.87679i
$417$	−24.4109			−1.19541
$418$	−6.82269	+	0.938749i	−0.333709	+	0.0459157i
$419$	−15.4348	+	15.4348i	−0.754038	+	0.754038i	−0.975230	−	0.221192i	$-0.929005\pi$
$419$	−15.4348	+	15.4348i	−0.754038	+	0.754038i	0.221192	+	0.975230i	$0.429005\pi$
$420$	17.7943	+	5.07259i	0.868273	+	0.247517i
$421$	−14.9338	−	14.9338i	−0.727830	−	0.727830i	0.242357	−	0.970187i	$-0.422079\pi$
$421$	−14.9338	−	14.9338i	−0.727830	−	0.727830i	−0.970187	+	0.242357i	$0.922079\pi$
$422$	18.6240	−	24.5667i	0.906600	−	1.19589i
$423$		−	1.64607i		−	0.0800345i
$424$	9.30525	−	23.6261i	0.451903	−	1.14739i
$425$	0.783519			0.0380063
$426$	−21.5538	−	16.3399i	−1.04429	−	0.791673i
$427$	−7.45641	+	1.77916i	−0.360841	+	0.0860996i
$428$	3.92520	−	6.98563i	0.189732	−	0.337663i
$429$	19.9411	−	19.9411i	0.962768	−	0.962768i
$430$	6.31563	−	0.868981i	0.304567	−	0.0419060i
$431$		−	23.6114i		−	1.13732i	−0.822572	−	0.568660i	$-0.807462\pi$
$431$		−	23.6114i		−	1.13732i	0.822572	−	0.568660i	$-0.192538\pi$
$432$	−21.9427	−	5.33401i	−1.05572	−	0.256633i
$433$		−	1.78643i		−	0.0858505i	−0.999078	−	0.0429253i	$-0.986332\pi$
$433$		−	1.78643i		−	0.0858505i	0.999078	−	0.0429253i	$-0.0136677\pi$
$434$	28.4912	+	12.5337i	1.36762	+	0.601638i
$435$	−18.4205	−	18.4205i	−0.883196	−	0.883196i
$436$	−7.64146	+	13.5994i	−0.365959	+	0.651293i
$437$	−1.62677	+	1.62677i	−0.0778189	+	0.0778189i
$438$	10.3178	+	7.82193i	0.493005	+	0.373746i
$439$		−	26.6274i		−	1.27085i	−0.772161	−	0.635427i	$-0.780824\pi$
$439$		−	26.6274i		−	1.27085i	0.772161	−	0.635427i	$-0.219176\pi$
$440$	−17.5011	+	7.61070i	−0.834331	+	0.362826i
$441$	5.31748	−	2.69079i	0.253213	−	0.128133i
$442$	−8.69475	−	6.59148i	−0.413567	−	0.313525i
$443$	−16.9403	+	16.9403i	−0.804856	+	0.804856i	−0.983850	−	0.178994i	$-0.942716\pi$
$443$	−16.9403	+	16.9403i	−0.804856	+	0.804856i	0.178994	+	0.983850i	$0.442716\pi$
$444$	−16.7164	+	4.68886i	−0.793325	+	0.222523i
$445$	−19.5961	+	19.5961i	−0.928946	+	0.928946i
$446$	−2.96887	−	21.5773i	−0.140580	−	1.02171i
$447$	16.0153			0.757497
$448$	5.62999	+	20.4035i	0.265992	+	0.963975i
$449$	−6.76315			−0.319173			−0.159586	−	0.987184i	$-0.551016\pi$
$449$	−6.76315			−0.319173			−0.159586	+	0.987184i	$0.551016\pi$
$450$	0.113369	+	0.823951i	0.00534428	+	0.0388414i
$451$	3.27139	−	3.27139i	0.154044	−	0.154044i
$452$	−26.0300	+	7.30129i	−1.22435	+	0.343424i
$453$	21.2941	−	21.2941i	1.00048	−	1.00048i
$454$	12.1173	+	9.18611i	0.568693	+	0.431125i
$455$	−22.4824	+	36.5737i	−1.05399	+	1.71460i
$456$	6.54611	−	2.84671i	0.306550	−	0.133309i
$457$		−	3.79073i		−	0.177323i	−0.996062	−	0.0886615i	$-0.971741\pi$
$457$		−	3.79073i		−	0.177323i	0.996062	−	0.0886615i	$-0.0282590\pi$
$458$	28.0659	+	21.2767i	1.31143	+	0.994196i
$459$	4.52778	−	4.52778i	0.211339	−	0.211339i
$460$	−3.12293	+	5.55784i	−0.145607	+	0.259136i
$461$	−3.04346	−	3.04346i	−0.141748	−	0.141748i	0.632672	−	0.774420i	$-0.281958\pi$
$461$	−3.04346	−	3.04346i	−0.141748	−	0.141748i	−0.774420	+	0.632672i	$0.781958\pi$
$462$	6.24660	−	14.1996i	0.290618	−	0.660623i
$463$			1.44348i			0.0670844i	0.999437	+	0.0335422i	$0.0106788\pi$
$463$			1.44348i			0.0670844i	−0.999437	+	0.0335422i	$0.989321\pi$
$464$	7.03893	−	28.9562i	0.326774	−	1.34426i
$465$		−	29.0892i		−	1.34898i
$466$	−9.42377	+	1.29664i	−0.436548	+	0.0600656i
$467$	−10.9302	+	10.9302i	−0.505789	+	0.505789i	−0.913231	−	0.407442i	$-0.866421\pi$
$467$	−10.9302	+	10.9302i	−0.505789	+	0.505789i	0.407442	+	0.913231i	$0.366421\pi$
$468$	5.67356	−	10.0972i	0.262260	−	0.466741i
$469$	0.390440	−	0.0931623i	0.0180289	−	0.00430184i
$470$	5.19797	+	3.94058i	0.239765	+	0.181765i
$471$	6.36780			0.293413
$472$	−4.82321	+	12.2462i	−0.222006	+	0.563676i
$473$		−	5.34482i		−	0.245755i
$474$	−5.65035	+	7.45331i	−0.259529	+	0.342342i
$475$	−0.841004	−	0.841004i	−0.0385879	−	0.0385879i
$476$	−5.77189	−	1.64538i	−0.264554	−	0.0754159i
$477$	−5.40456	+	5.40456i	−0.247458	+	0.247458i
$478$	−13.3566	+	1.83777i	−0.610917	+	0.0840575i
$479$	22.3261			1.02011			0.510054	−	0.860142i	$-0.329625\pi$
$479$	22.3261			1.02011			0.510054	+	0.860142i	$0.329625\pi$
$480$	15.3352	−	12.4943i	0.699955	−	0.570286i
$481$		−	40.2824i		−	1.83672i
$482$	−29.9483	+	4.12066i	−1.36411	+	0.187691i
$483$	−1.20272	−	5.04057i	−0.0547258	−	0.229354i
$484$	−1.62043	−	5.77704i	−0.0736559	−	0.262593i
$485$	5.45542	+	5.45542i	0.247718	+	0.247718i
$486$	9.63577	+	7.30487i	0.437087	+	0.331356i
$487$	−5.13887			−0.232865			−0.116432	−	0.993199i	$-0.537146\pi$
$487$	−5.13887			−0.232865			−0.116432	+	0.993199i	$0.537146\pi$
$488$	−3.00311	+	7.62493i	−0.135944	+	0.345164i
$489$	−6.69352			−0.302692
$490$	−4.23271	+	23.2332i	−0.191214	+	1.04957i
$491$	6.24398	−	6.24398i	0.281787	−	0.281787i	−0.552034	−	0.833821i	$-0.686148\pi$
$491$	6.24398	−	6.24398i	0.281787	−	0.281787i	0.833821	+	0.552034i	$0.186148\pi$
$492$	−2.34902	+	4.18053i	−0.105902	+	0.188473i
$493$	5.97500	+	5.97500i	0.269101	+	0.269101i
$494$	2.25758	+	16.4077i	0.101573	+	0.738219i
$495$	5.74440			0.258192
$496$	28.4213	−	17.3056i	1.27615	−	0.777044i
$497$	18.0779	−	29.4085i	0.810903	−	1.31915i
$498$	28.2217	−	3.88309i	1.26464	−	0.174005i
$499$	7.56730	+	7.56730i	0.338759	+	0.338759i	0.855900	−	0.517141i	$-0.173004\pi$
$499$	7.56730	+	7.56730i	0.338759	+	0.338759i	−0.517141	+	0.855900i	$0.673004\pi$
$500$	17.9238	+	10.0713i	0.801579	+	0.450404i
$501$	−6.27117	−	6.27117i	−0.280175	−	0.280175i
$502$	4.80019	−	6.33188i	0.214243	−	0.282606i
$503$		−	11.7969i		−	0.525999i	−0.964796	−	0.263000i	$-0.915288\pi$
$503$		−	11.7969i		−	0.525999i	0.964796	−	0.263000i	$-0.0847118\pi$
$504$	0.895138	−	6.30780i	0.0398726	−	0.280972i
$505$			20.0530i			0.892348i
$506$	4.25924	+	3.22893i	0.189346	+	0.143543i
$507$	−34.4816	−	34.4816i	−1.53138	−	1.53138i
$508$	−1.55472	−	5.54279i	−0.0689797	−	0.245922i
$509$	24.1062	+	24.1062i	1.06849	+	1.06849i	0.997475	+	0.0710131i	$0.0226232\pi$
$509$	24.1062	+	24.1062i	1.06849	+	1.06849i	0.0710131	+	0.997475i	$0.477377\pi$
$510$	0.764555	+	5.55667i	0.0338551	+	0.246054i
$511$	−8.65387	+	14.0779i	−0.382825	+	0.622768i
$512$	21.3306	+	7.55007i	0.942690	+	0.333669i
$513$	−9.71995			−0.429146
$514$	9.68929	−	1.33317i	0.427376	−	0.0588036i
$515$	−12.5572	−	12.5572i	−0.553337	−	0.553337i
$516$	1.49616	+	5.33401i	0.0658648	+	0.234817i
$517$	3.86691	−	3.86691i	0.170066	−	0.170066i
$518$	−8.03274	−	20.6513i	−0.352938	−	0.907365i
$519$	9.22031			0.404727
$520$	18.3028	+	42.0880i	0.802632	+	1.84568i
$521$	−42.1032			−1.84457			−0.922287	−	0.386506i	$-0.873682\pi$
$521$	−42.1032			−1.84457			−0.922287	+	0.386506i	$0.873682\pi$
$522$	−5.41879	+	7.14787i	−0.237174	+	0.312854i
$523$	−6.62683	−	6.62683i	−0.289771	−	0.289771i	0.547219	−	0.836990i	$-0.315687\pi$
$523$	−6.62683	−	6.62683i	−0.289771	−	0.289771i	−0.836990	+	0.547219i	$0.815687\pi$
$524$	−7.21777	+	12.8454i	−0.315310	+	0.561153i
$525$	2.60586	−	0.621781i	0.113729	−	0.0271367i
$526$	−3.42754	−	24.9108i	−0.149448	−	1.08616i
$527$			9.43556i			0.411020i
$528$	−8.62482	−	14.1647i	−0.375347	−	0.616439i
$529$	−21.2146			−0.922372
$530$	−4.12842	−	30.0048i	−0.179327	−	1.30332i
$531$	2.80135	−	2.80135i	0.121568	−	0.121568i
$532$	4.42926	+	7.96145i	0.192033	+	0.345173i
$533$	−7.86731	−	7.86731i	−0.340771	−	0.340771i
$534$	−19.1909	−	14.5486i	−0.830471	−	0.629579i
$535$		−	9.55751i		−	0.413207i
$536$	0.157252	−	0.399265i	0.00679225	−	0.0172456i
$537$	19.4033			0.837315
$538$	−12.0226	+	15.8588i	−0.518330	+	0.683723i
$539$	18.8129	+	6.17058i	0.810328	+	0.265786i
$540$	−25.9338	+	7.27430i	−1.11601	+	0.313036i
$541$	1.70184	−	1.70184i	0.0731676	−	0.0731676i	−0.669576	−	0.742744i	$-0.733524\pi$
$541$	1.70184	−	1.70184i	0.0731676	−	0.0731676i	0.742744	+	0.669576i	$0.233524\pi$
$542$	3.77845	+	27.4612i	0.162298	+	1.17956i
$543$			0.395252i			0.0169619i
$544$	−4.97425	+	4.05275i	−0.213269	+	0.173760i
$545$			18.6063i			0.797005i
$546$	−34.1482	−	15.0223i	−1.46141	−	0.642896i
$547$	8.86974	+	8.86974i	0.379243	+	0.379243i	0.870829	−	0.491586i	$-0.163583\pi$
$547$	8.86974	+	8.86974i	0.379243	+	0.379243i	−0.491586	+	0.870829i	$0.663583\pi$
$548$	8.57775	+	30.5808i	0.366424	+	1.30635i
$549$	1.74423	−	1.74423i	0.0744418	−	0.0744418i
$550$	−1.66928	+	2.20193i	−0.0711785	+	0.0938907i
$551$		−	12.8267i		−	0.546438i
$552$	−5.15449	−	2.03012i	−0.219390	−	0.0864076i
$553$	−10.1694	−	6.25132i	−0.432449	−	0.265833i
$554$	−16.4841	+	21.7439i	−0.700341	+	0.923812i
$555$	−14.6430	+	14.6430i	−0.621560	+	0.621560i
$556$	−29.0369	−	16.3157i	−1.23144	−	0.691940i
$557$	−9.83630	+	9.83630i	−0.416777	+	0.416777i	−0.884091	−	0.467314i	$-0.845222\pi$
$557$	−9.83630	+	9.83630i	−0.416777	+	0.416777i	0.467314	+	0.884091i	$0.345222\pi$
$558$	−9.92246	+	1.36525i	−0.420051	+	0.0577958i
$559$	−12.8536			−0.543651
$560$	17.7760	+	17.9272i	0.751172	+	0.757561i
$561$	4.70253			0.198541
$562$	10.0411	−	1.38158i	0.423558	−	0.0582783i
$563$	−3.26139	+	3.26139i	−0.137451	+	0.137451i	−0.772485	−	0.635034i	$-0.780986\pi$
$563$	−3.26139	+	3.26139i	−0.137451	+	0.137451i	0.635034	+	0.772485i	$0.280986\pi$
$564$	−2.77663	+	4.94154i	−0.116917	+	0.208076i
$565$	−22.8014	+	22.8014i	−0.959263	+	0.959263i
$566$	−14.0444	+	18.5258i	−0.590331	+	0.778699i
$567$	7.92680	−	12.8951i	0.332894	−	0.541542i
$568$	−14.7171	−	33.8425i	−0.617515	−	1.42000i
$569$		−	7.26970i		−	0.304762i	−0.988322	−	0.152381i	$-0.951306\pi$
$569$		−	7.26970i		−	0.304762i	0.988322	−	0.152381i	$-0.0486940\pi$
$570$	5.14371	−	6.78500i	0.215446	−	0.284192i
$571$	−1.22962	+	1.22962i	−0.0514579	+	0.0514579i	−0.732367	−	0.680910i	$-0.761585\pi$
$571$	−1.22962	+	1.22962i	−0.0514579	+	0.0514579i	0.680910	+	0.732367i	$0.261585\pi$
$572$	37.0482	−	10.3918i	1.54906	−	0.434505i
$573$	−4.04371	−	4.04371i	−0.168928	−	0.168928i
$574$	−5.60210	−	2.46445i	−0.233827	−	0.102864i
$575$			0.923034i			0.0384932i
$576$	−4.98162	−	4.64453i	−0.207568	−	0.193522i
$577$			20.1315i			0.838084i	0.907967	+	0.419042i	$0.137634\pi$
$577$			20.1315i			0.838084i	−0.907967	+	0.419042i	$0.862366\pi$
$578$	3.02907	+	22.0148i	0.125993	+	0.915696i
$579$	−10.2356	+	10.2356i	−0.425378	+	0.425378i
$580$	−9.59939	−	34.2231i	−0.398593	−	1.42104i
$581$	8.43859	+	35.3659i	0.350092	+	1.46722i
$582$	−4.05022	+	5.34260i	−0.167887	+	0.221458i
$583$	−25.3926			−1.05165
$584$	7.04508	+	16.2004i	0.291527	+	0.670378i
$585$		−	13.8146i		−	0.571163i
$586$	−0.172976	−	0.131133i	−0.00714556	−	0.00541704i
$587$	−13.6801	−	13.6801i	−0.564639	−	0.564639i	0.365983	−	0.930622i	$-0.380733\pi$
$587$	−13.6801	−	13.6801i	−0.564639	−	0.564639i	−0.930622	+	0.365983i	$0.880733\pi$
$588$	−20.5021	−	0.891860i	−0.845494	−	0.0367797i
$589$	10.1278	−	10.1278i	0.417310	−	0.417310i
$590$	2.13989	+	15.5524i	0.0880980	+	0.640283i
$591$	29.8554			1.22809
$592$	−23.0181	−	5.59544i	−0.946039	−	0.229971i
$593$			24.4282i			1.00315i	0.865115	+	0.501573i	$0.167245\pi$
$593$			24.4282i			1.00315i	−0.865115	+	0.501573i	$0.832755\pi$
$594$	3.07806	+	22.3709i	0.126294	+	0.917889i
$595$	−6.96331	+	1.66150i	−0.285468	+	0.0681150i
$596$	19.0502	+	10.7042i	0.780327	+	0.438463i
$597$	26.5875	+	26.5875i	1.08815	+	1.08815i
$598$	7.76518	−	10.2430i	0.317542	−	0.418866i
$599$	25.1701			1.02842			0.514211	−	0.857664i	$-0.328085\pi$
$599$	25.1701			1.02842			0.514211	+	0.857664i	$0.328085\pi$
$600$	1.04953	−	2.66476i	0.0428467	−	0.108788i
$601$	−9.34866			−0.381340			−0.190670	−	0.981654i	$-0.561066\pi$
$601$	−9.34866			−0.381340			−0.190670	+	0.981654i	$0.561066\pi$
$602$	−6.58958	+	2.56316i	−0.268571	+	0.104466i
$603$	−0.0913331	+	0.0913331i	−0.00371937	+	0.00371937i
$604$	39.5618	−	11.0969i	1.60975	−	0.451525i
$605$	−5.06049	−	5.06049i	−0.205738	−	0.205738i
$606$	−17.2631	+	2.37526i	−0.701264	+	0.0964885i
$607$	−27.5600			−1.11863			−0.559314	−	0.828956i	$-0.688935\pi$
$607$	−27.5600			−1.11863			−0.559314	+	0.828956i	$0.688935\pi$
$608$	9.68929	+	0.989103i	0.392953	+	0.0401134i
$609$	24.6136	+	15.1303i	0.997392	+	0.613112i
$610$	1.33238	+	9.68352i	0.0539464	+	0.392074i
$611$	−9.29945	−	9.29945i	−0.376215	−	0.376215i
$612$	1.85953	−	0.521587i	0.0751669	−	0.0210839i
$613$	−6.51272	−	6.51272i	−0.263046	−	0.263046i	0.563244	−	0.826291i	$-0.309553\pi$
$613$	−6.51272	−	6.51272i	−0.263046	−	0.263046i	−0.826291	+	0.563244i	$0.809553\pi$
$614$	1.96351	+	1.48854i	0.0792410	+	0.0600725i
$615$			5.71967i			0.230639i
$616$	16.9210	−	12.7153i	0.681767	−	0.512315i
$617$		−	18.3569i		−	0.739023i	−0.929226	−	0.369511i	$-0.879525\pi$
$617$		−	18.3569i		−	0.739023i	0.929226	−	0.369511i	$-0.120475\pi$
$618$	9.32274	−	12.2975i	0.375016	−	0.494679i
$619$	12.2627	+	12.2627i	0.492878	+	0.492878i	0.909212	−	0.416334i	$-0.136685\pi$
$619$	12.2627	+	12.2627i	0.492878	+	0.492878i	−0.416334	+	0.909212i	$0.636685\pi$
$620$	19.4425	−	34.6016i	0.780831	−	1.38963i
$621$	5.33401	+	5.33401i	0.214046	+	0.214046i
$622$	−21.0702	+	2.89910i	−0.844839	+	0.116243i
$623$	16.0960	−	26.1844i	0.644872	−	1.04906i
$624$	−34.0644	+	20.7416i	−1.36367	+	0.830330i
$625$	27.9768			1.11907
$626$	−6.48580	−	47.1379i	−0.259225	−	1.88401i
$627$	−5.04754	−	5.04754i	−0.201579	−	0.201579i
$628$	7.57451	+	4.25609i	0.302256	+	0.169836i
$629$	4.74970	−	4.74970i	0.189383	−	0.189383i
$630$	−2.75478	−	7.08223i	−0.109753	−	0.282163i
$631$	−24.0987			−0.959353			−0.479676	−	0.877445i	$-0.659246\pi$
$631$	−24.0987			−0.959353			−0.479676	+	0.877445i	$0.659246\pi$
$632$	−11.7027	+	5.08917i	−0.465509	+	0.202436i
$633$	31.9532			1.27002
$634$	6.45619	+	4.89443i	0.256408	+	0.194383i
$635$	−4.85529	−	4.85529i	−0.192676	−	0.192676i
$636$	25.3412	−	7.10807i	1.00484	−	0.281853i
$637$	14.8395	−	45.2427i	0.587962	−	1.79258i
$638$	−29.5213	+	4.06191i	−1.16876	+	0.160812i
$639$			11.1082i			0.439432i
$640$	26.5922	−	4.61232i	1.05115	−	0.182318i
$641$	−33.0833			−1.30671			−0.653357	−	0.757050i	$-0.726640\pi$
$641$	−33.0833			−1.30671			−0.653357	+	0.757050i	$0.726640\pi$
$642$	8.22778	−	1.13208i	0.324725	−	0.0446796i
$643$	4.99031	−	4.99031i	0.196798	−	0.196798i	−0.601828	−	0.798626i	$-0.705561\pi$
$643$	4.99031	−	4.99031i	0.196798	−	0.196798i	0.798626	+	0.601828i	$0.205561\pi$
$644$	1.93836	−	6.79964i	0.0763821	−	0.267943i
$645$	4.67241	+	4.67241i	0.183976	+	0.183976i
$646$	−1.66845	+	2.20083i	−0.0656442	+	0.0865905i
$647$			16.2489i			0.638809i	0.947618	+	0.319405i	$0.103483\pi$
$647$			16.2489i			0.638809i	−0.947618	+	0.319405i	$0.896517\pi$
$648$	−6.45317	−	14.8393i	−0.253504	−	0.582943i
$649$	13.1618			0.516645
$650$	5.29538	+	4.01443i	0.207702	+	0.157459i
$651$	7.48782	+	31.3812i	0.293471	+	1.22993i
$652$	−7.96196	−	4.47380i	−0.311814	−	0.175207i
$653$	−1.10728	+	1.10728i	−0.0433312	+	0.0433312i	−0.728440	−	0.685109i	$-0.759754\pi$
$653$	−1.10728	+	1.10728i	−0.0433312	+	0.0433312i	0.685109	+	0.728440i	$0.259754\pi$
$654$	−16.0176	+	2.20390i	−0.626337	+	0.0861791i
$655$			17.5746i			0.686698i
$656$	−5.58834	+	3.40272i	−0.218188	+	0.132854i
$657$		−	5.31748i		−	0.207455i
$658$	−6.62189	−	2.91307i	−0.258148	−	0.113563i
$659$	23.8965	+	23.8965i	0.930874	+	0.930874i	0.997761	−	0.0668864i	$-0.0213065\pi$
$659$	23.8965	+	23.8965i	0.930874	+	0.930874i	−0.0668864	+	0.997761i	$0.521307\pi$
$660$	−17.2449	−	9.68983i	−0.671256	−	0.377176i
$661$	17.0306	−	17.0306i	0.662414	−	0.662414i	−0.293534	−	0.955949i	$-0.594831\pi$
$661$	17.0306	−	17.0306i	0.662414	−	0.662414i	0.955949	+	0.293534i	$0.0948314\pi$
$662$	18.1661	+	13.7717i	0.706046	+	0.535253i
$663$		−	11.3090i		−	0.439206i
$664$	36.1652	+	14.2438i	1.40348	+	0.552767i
$665$	9.25760	+	5.69079i	0.358994	+	0.220679i
$666$	5.68204	+	4.30755i	0.220175	+	0.166914i
$667$	−7.03893	+	7.03893i	−0.272548	+	0.272548i
$668$	−3.26807	−	11.6511i	−0.126445	−	0.450794i
$669$	15.9632	−	15.9632i	0.617175	−	0.617175i
$670$	−0.0697674	−	0.507059i	−0.00269535	−	0.0195894i
$671$	8.19501			0.316365
$672$	−13.3274	+	17.4263i	−0.514117	+	0.672233i
$673$	2.21456			0.0853649			0.0426825	−	0.999089i	$-0.486410\pi$
$673$	2.21456			0.0853649			0.0426825	+	0.999089i	$0.486410\pi$
$674$	−2.12732	−	15.4610i	−0.0819413	−	0.595537i
$675$	−2.75757	+	2.75757i	−0.106139	+	0.106139i
$676$	−17.9693	−	64.0627i	−0.691125	−	2.46395i
$677$	−10.3945	+	10.3945i	−0.399493	+	0.399493i	−0.878054	−	0.478561i	$-0.841158\pi$
$677$	−10.3945	+	10.3945i	−0.399493	+	0.399493i	0.478561	+	0.878054i	$0.341158\pi$
$678$	−22.3299	−	16.9283i	−0.857574	−	0.650126i
$679$	−7.28955	−	4.48100i	−0.279747	−	0.171965i
$680$	−2.80451	+	7.12069i	−0.107548	+	0.273066i
$681$			15.7606i			0.603948i
$682$	−26.5169	−	20.1024i	−1.01538	−	0.769761i
$683$	17.8265	−	17.8265i	0.682113	−	0.682113i	−0.278363	−	0.960476i	$-0.589792\pi$
$683$	17.8265	−	17.8265i	0.682113	−	0.682113i	0.960476	+	0.278363i	$0.0897917\pi$
$684$	−2.55581	−	1.43610i	−0.0977239	−	0.0549107i
$685$	26.7877	+	26.7877i	1.02351	+	1.02351i
$686$	−1.41422	−	26.1534i	−0.0539953	−	0.998541i
$687$			36.5045i			1.39273i
$688$	−1.78544	+	7.34482i	−0.0680693	+	0.280019i
$689$			61.0660i			2.32643i
$690$	−6.54611	+	0.900694i	−0.249206	+	0.0342888i
$691$	28.7899	−	28.7899i	1.09522	−	1.09522i	0.100257	−	0.994962i	$-0.468034\pi$
$691$	28.7899	−	28.7899i	1.09522	−	1.09522i	0.994962	−	0.100257i	$-0.0319664\pi$
$692$	10.9676	+	6.16264i	0.416925	+	0.234269i
$693$	−6.19703	+	1.47866i	−0.235406	+	0.0561698i
$694$	21.7542	+	16.4919i	0.825779	+	0.626022i
$695$	−39.7273			−1.50694
$696$	28.3246	−	12.3175i	1.07364	−	0.466895i
$697$		−	1.85527i		−	0.0702734i
$698$	6.75530	−	8.91084i	0.255692	−	0.337280i
$699$	−6.97187	−	6.97187i	−0.263700	−	0.263700i
$700$	3.51527	+	1.00209i	0.132865	+	0.0378754i
$701$	−8.26141	+	8.26141i	−0.312029	+	0.312029i	−0.845695	−	0.533666i	$-0.820814\pi$
$701$	−8.26141	+	8.26141i	−0.312029	+	0.312029i	0.533666	+	0.845695i	$0.320814\pi$
$702$	53.7993	−	7.40237i	2.03052	−	0.279384i
$703$	−10.1963			−0.384562
$704$	−0.791888	−	22.6136i	−0.0298454	−	0.852280i
$705$			6.76085i			0.254628i
$706$	44.6914	−	6.14920i	1.68198	−	0.231428i
$707$	−5.16184	−	21.6331i	−0.194131	−	0.813597i
$708$	−13.1352	+	3.68434i	−0.493649	+	0.138466i
$709$	−26.9918	−	26.9918i	−1.01370	−	1.01370i	−0.999905	−	0.0137939i	$-0.995609\pi$
$709$	−26.9918	−	26.9918i	−1.01370	−	1.01370i	−0.0137939	−	0.999905i	$-0.504391\pi$
$710$	−35.0775	−	26.5922i	−1.31644	−	0.997989i
$711$	3.84120			0.144056
$712$	−13.1037	−	30.1323i	−0.491080	−	1.12926i
$713$	−11.1157			−0.416286
$714$	−2.25514	−	5.79771i	−0.0843964	−	0.216974i
$715$	32.4530	−	32.4530i	1.21367	−	1.21367i
$716$	23.0803	+	12.9687i	0.862551	+	0.484664i
$717$	−9.88145	−	9.88145i	−0.369030	−	0.369030i
$718$	1.62321	+	11.7972i	0.0605776	+	0.440269i
$719$	−6.92495			−0.258257			−0.129129	−	0.991628i	$-0.541218\pi$
$719$	−6.92495			−0.258257			−0.129129	+	0.991628i	$0.541218\pi$
$720$	−7.89393	−	1.91892i	−0.294189	−	0.0715141i
$721$	16.7790	+	10.3143i	0.624882	+	0.384125i
$722$	−22.4661	+	3.09116i	−0.836102	+	0.115041i
$723$	−22.1563	−	22.1563i	−0.824001	−	0.824001i
$724$	−0.264178	+	0.470154i	−0.00981809	+	0.0174731i
$725$	−3.63897	−	3.63897i	−0.135148	−	0.135148i
$726$	3.75702	−	4.95584i	0.139436	−	0.183928i
$727$			39.9958i			1.48336i	0.670752	+	0.741681i	$0.265971\pi$
$727$			39.9958i			1.48336i	−0.670752	+	0.741681i	$0.734029\pi$
$728$	−30.5788	−	40.6930i	−1.13333	−	1.50818i
$729$			29.6963i			1.09986i
$730$	16.7916	+	12.7297i	0.621486	+	0.471148i
$731$	−1.51557	−	1.51557i	−0.0560556	−	0.0560556i
$732$	−8.17844	+	2.29401i	−0.302284	+	0.0847890i
$733$	10.2496	+	10.2496i	0.378579	+	0.378579i	0.870589	−	0.492010i	$-0.163738\pi$
$733$	10.2496	+	10.2496i	0.378579	+	0.378579i	−0.492010	+	0.870589i	$0.663738\pi$
$734$	−1.93129	−	14.0364i	−0.0712853	−	0.518091i
$735$	−21.8404	+	11.0518i	−0.805595	+	0.407652i
$736$	−4.77440	−	5.85997i	−0.175987	−	0.216002i
$737$	−0.429116			−0.0158067
$738$	1.95101	−	0.268443i	0.0718176	−	0.00988154i
$739$	−0.573743	−	0.573743i	−0.0211055	−	0.0211055i	0.696475	−	0.717581i	$-0.254751\pi$
$739$	−0.573743	−	0.573743i	−0.0211055	−	0.0211055i	−0.717581	+	0.696475i	$0.754751\pi$
$740$	−27.2049	+	7.63083i	−1.00007	+	0.280515i
$741$	−12.1387	+	12.1387i	−0.445927	+	0.445927i
$742$	12.1772	+	31.3063i	0.447040	+	1.14929i
$743$	25.9627			0.952477			0.476239	−	0.879316i	$-0.342000\pi$
$743$	25.9627			0.952477			0.476239	+	0.879316i	$0.342000\pi$
$744$	32.0905	+	12.6390i	1.17649	+	0.463367i
$745$	26.0639			0.954907
$746$	1.36670	−	1.80280i	0.0500385	−	0.0660052i
$747$	−8.27290	−	8.27290i	−0.302690	−	0.302690i
$748$	5.59367	+	3.14306i	0.204525	+	0.114922i
$749$	2.46019	+	10.3106i	0.0898935	+	0.376741i
$750$	2.90471	+	21.1110i	0.106065	+	0.770864i
$751$		−	13.9799i		−	0.510133i	−0.966924	−	0.255067i	$-0.917903\pi$
$751$		−	13.9799i		−	0.510133i	0.966924	−	0.255067i	$-0.0820974\pi$
$752$	−6.60562	+	4.02214i	−0.240882	+	0.146672i
$753$	8.23569			0.300125
$754$	9.76840	+	70.9953i	0.355744	+	2.58550i
$755$	34.6548	−	34.6548i	1.26122	−	1.26122i
$756$	26.1048	−	14.5231i	0.949422	−	0.528199i
$757$	31.6014	+	31.6014i	1.14857	+	1.14857i	0.986834	+	0.161737i	$0.0517096\pi$
$757$	31.6014	+	31.6014i	1.14857	+	1.14857i	0.161737	+	0.986834i	$0.448290\pi$
$758$	−20.1121	−	15.2470i	−0.730505	−	0.553796i
$759$			5.53987i			0.201085i
$760$	10.6534	−	4.63284i	0.386439	−	0.168051i
$761$	−35.0216			−1.26953			−0.634765	−	0.772705i	$-0.718903\pi$
$761$	−35.0216			−1.26953			−0.634765	+	0.772705i	$0.718903\pi$
$762$	3.60467	−	4.75488i	0.130584	−	0.172251i
$763$	−4.78943	−	20.0723i	−0.173389	−	0.726667i
$764$	−2.10728	−	7.51272i	−0.0762387	−	0.271801i
$765$	1.62888	−	1.62888i	0.0588923	−	0.0588923i
$766$	3.21241	+	23.3473i	0.116069	+	0.843573i
$767$		−	31.6525i		−	1.14290i
$768$	7.12044	+	22.3462i	0.256937	+	0.806348i
$769$			10.9708i			0.395618i	0.980241	+	0.197809i	$0.0633826\pi$
$769$			10.9708i			0.395618i	−0.980241	+	0.197809i	$0.936617\pi$
$770$	10.1660	−	23.1089i	0.366356	−	0.832787i
$771$	7.16830	+	7.16830i	0.258160	+	0.258160i
$772$	−19.0165	+	5.33404i	−0.684420	+	0.191976i
$773$	7.67303	−	7.67303i	0.275980	−	0.275980i	−0.555522	−	0.831502i	$-0.687482\pi$
$773$	7.67303	−	7.67303i	0.275980	−	0.275980i	0.831502	+	0.555522i	$0.187482\pi$
$774$	1.37449	−	1.81307i	0.0494050	−	0.0651696i
$775$		−	5.74656i		−	0.206423i
$776$	−8.38862	+	3.64796i	−0.301134	+	0.130954i
$777$	12.0275	−	19.5660i	0.431485	−	0.701927i
$778$	−3.45555	+	4.55818i	−0.123887	+	0.163419i
$779$	−1.99139	+	1.99139i	−0.0713488	+	0.0713488i
$780$	−23.3029	+	41.4718i	−0.834377	+	1.48493i
$781$	−26.0951	+	26.0951i	−0.933755	+	0.933755i
$782$	2.12334	−	0.292155i	0.0759305	−	0.0104475i
$783$	−42.0576			−1.50302
$784$	−23.7912	−	14.7640i	−0.849687	−	0.527287i
$785$	10.3632			0.369878
$786$	−15.1295	+	2.08170i	−0.539651	+	0.0742518i
$787$	−18.2461	+	18.2461i	−0.650404	+	0.650404i	−0.953090	−	0.302686i	$-0.902117\pi$
$787$	−18.2461	+	18.2461i	−0.650404	+	0.650404i	0.302686	+	0.953090i	$0.402117\pi$
$788$	35.5131	+	19.9547i	1.26510	+	0.710856i
$789$	18.4295	−	18.4295i	0.656106	−	0.656106i
$790$	−9.19559	+	12.1298i	−0.327164	+	0.431559i
$791$	18.7288	−	30.4674i	0.665918	−	1.08329i
$792$	−2.49589	+	6.33709i	−0.0886876	+	0.225179i
$793$		−	19.7080i		−	0.699852i
$794$	−14.5354	+	19.1735i	−0.515843	+	0.680443i
$795$	22.1980	−	22.1980i	0.787283	−	0.787283i
$796$	13.8554	+	49.3963i	0.491091	+	1.75080i
$797$	−22.4616	−	22.4616i	−0.795630	−	0.795630i	0.186773	−	0.982403i	$-0.440197\pi$
$797$	−22.4616	−	22.4616i	−0.795630	−	0.795630i	−0.982403	+	0.186773i	$0.940197\pi$
$798$	−3.80248	+	8.64366i	−0.134606	+	0.305982i
$799$		−	2.19300i		−	0.0775827i
$800$	3.02948	−	2.46826i	0.107108	−	0.0872661i
$801$			9.89038i			0.349459i
$802$	0.749508	+	5.44731i	0.0264660	+	0.192351i
$803$	12.4917	−	12.4917i	0.440823	−	0.440823i
$804$	0.428248	−	0.120121i	0.0151032	−	0.00423635i
$805$	−1.95736	−	8.20322i	−0.0689877	−	0.289125i
$806$	−48.3439	+	63.7699i	−1.70284	+	2.24620i
$807$	−20.6271			−0.726110
$808$	−22.1220	−	8.71285i	−0.778250	−	0.306517i
$809$			24.7622i			0.870592i	0.900287	+	0.435296i	$0.143356\pi$
$809$			24.7622i			0.870592i	−0.900287	+	0.435296i	$0.856644\pi$
$810$	−15.3808	−	11.6602i	−0.540428	−	0.409698i
$811$	−5.40486	−	5.40486i	−0.189790	−	0.189790i	0.605815	−	0.795605i	$-0.292847\pi$
$811$	−5.40486	−	5.40486i	−0.189790	−	0.189790i	−0.795605	+	0.605815i	$0.792847\pi$
$812$	19.1651	+	34.4487i	0.672564	+	1.20891i
$813$	−20.3163	+	20.3163i	−0.712523	+	0.712523i
$814$	3.22893	+	23.4674i	0.113174	+	0.822530i
$815$	−10.8933			−0.381575
$816$	−6.46219	−	1.57088i	−0.226222	−	0.0549919i
$817$			3.25354i			0.113827i
$818$	−4.95930	−	36.0435i	−0.173398	−	1.26023i
$819$	3.55601	+	14.9031i	0.124257	+	0.520757i
$820$	−3.82289	+	6.80356i	−0.133501	+	0.237590i
$821$	−0.191577	−	0.191577i	−0.00668610	−	0.00668610i	0.703756	−	0.710442i	$-0.251505\pi$
$821$	−0.191577	−	0.191577i	−0.00668610	−	0.00668610i	−0.710442	+	0.703756i	$0.751505\pi$
$822$	−19.8878	+	26.2338i	−0.693666	+	0.915008i
$823$	43.4293			1.51385			0.756925	−	0.653501i	$-0.226701\pi$
$823$	43.4293			1.51385			0.756925	+	0.653501i	$0.226701\pi$
$824$	19.3088	−	8.39683i	0.672654	−	0.292517i
$825$	−2.86399			−0.0997114
$826$	−6.31185	−	16.2270i	−0.219617	−	0.564611i
$827$	−38.0398	+	38.0398i	−1.32277	+	1.32277i	−0.411252	+	0.911522i	$0.634909\pi$
$827$	−38.0398	+	38.0398i	−1.32277	+	1.32277i	−0.911522	+	0.411252i	$0.865091\pi$
$828$	0.614463	+	2.19064i	0.0213541	+	0.0761300i
$829$	−2.08602	−	2.08602i	−0.0724505	−	0.0724505i	0.669953	−	0.742403i	$-0.266314\pi$
$829$	−2.08602	−	2.08602i	−0.0724505	−	0.0724505i	−0.742403	+	0.669953i	$0.766314\pi$
$830$	45.9291	−	6.31949i	1.59422	−	0.219353i
$831$	−28.2817			−0.981083
$832$	−54.3829	+	1.90440i	−1.88539	+	0.0660230i
$833$	7.08430	−	3.58484i	0.245456	−	0.124207i
$834$	−4.70566	−	34.2001i	−0.162944	−	1.18425i
$835$	−10.2059	−	10.2059i	−0.353191	−	0.353191i
$836$	−2.63040	−	9.37772i	−0.0909743	−	0.324335i
$837$	−33.2081	−	33.2081i	−1.14784	−	1.14784i
$838$	−24.5997	−	18.6490i	−0.849782	−	0.644219i
$839$		−	37.7564i		−	1.30350i	−0.758436	−	0.651748i	$-0.774036\pi$
$839$		−	37.7564i		−	1.30350i	0.758436	−	0.651748i	$-0.225964\pi$
$840$	−3.67658	+	25.9079i	−0.126854	+	0.893908i
$841$		−	26.5005i		−	0.913811i
$842$	18.0437	−	23.8013i	0.621827	−	0.820245i
$843$	7.42857	+	7.42857i	0.255854	+	0.255854i
$844$	38.0083	+	21.3568i	1.30830	+	0.735130i
$845$	−56.1167	−	56.1167i	−1.93047	−	1.93047i
$846$	2.30616	−	0.317310i	0.0792875	−	0.0109093i
$847$	6.76185	+	4.15661i	0.232340	+	0.142823i
$848$	34.8943	+	8.48241i	1.19828	+	0.291287i
$849$	−24.0960			−0.826974
$850$	0.151038	+	1.09772i	0.00518056	+	0.0376515i
$851$	5.59544	+	5.59544i	0.191809	+	0.191809i
$852$	18.7376	−	33.3470i	0.641939	−	1.14245i
$853$	37.7120	−	37.7120i	1.29124	−	1.29124i	0.357212	−	0.934023i	$-0.383727\pi$
$853$	37.7120	−	37.7120i	1.29124	−	1.29124i	0.934023	−	0.357212i	$-0.116273\pi$
$854$	−3.92999	−	10.1036i	−0.134481	−	0.345737i
$855$	−3.49678			−0.119587
$856$	10.5436	+	4.15265i	0.360374	+	0.141935i
$857$	−15.3930			−0.525814			−0.262907	−	0.964821i	$-0.584681\pi$
$857$	−15.3930			−0.525814			−0.262907	+	0.964821i	$0.584681\pi$
$858$	31.7819	+	24.0938i	1.08501	+	0.822549i
$859$	34.6738	+	34.6738i	1.18306	+	1.18306i	0.978949	+	0.204106i	$0.0654289\pi$
$859$	34.6738	+	34.6738i	1.18306	+	1.18306i	0.204106	+	0.978949i	$0.434571\pi$
$860$	2.43491	+	8.68077i	0.0830298	+	0.296012i
$861$	−1.47230	−	6.17035i	−0.0501757	−	0.210285i
$862$	33.0799	−	4.55154i	1.12671	−	0.155026i
$863$			45.6641i			1.55443i	0.629238	+	0.777213i	$0.283367\pi$
$863$			45.6641i			1.55443i	−0.629238	+	0.777213i	$0.716633\pi$
$864$	3.24317	−	31.7702i	0.110335	−	1.08084i
$865$	15.0055			0.510202
$866$	2.50282	−	0.344368i	0.0850492	−	0.0117021i
$867$	−16.2869	+	16.2869i	−0.553134	+	0.553134i
$868$	−12.0677	+	42.3327i	−0.409605	+	1.43687i
$869$	9.02367	+	9.02367i	0.306107	+	0.306107i
$870$	22.2565	−	29.3583i	0.754566	−	0.995339i
$871$			1.03197i			0.0349670i
$872$	−20.5260	−	8.08425i	−0.695098	−	0.273767i
$873$	2.75341			0.0931887
$874$	−2.59272	−	1.96554i	−0.0876999	−	0.0664852i
$875$	−26.4551	+	6.31240i	−0.894345	+	0.213398i
$876$	−8.96969	+	15.9632i	−0.303058	+	0.539348i
$877$	−37.0077	+	37.0077i	−1.24966	+	1.24966i	−0.293790	+	0.955870i	$0.594917\pi$
$877$	−37.0077	+	37.0077i	−1.24966	+	1.24966i	−0.955870	+	0.293790i	$0.905083\pi$
$878$	37.3053	−	5.13292i	1.25899	−	0.173228i
$879$		−	0.224984i		−	0.00758854i
$880$	−14.0364	−	23.0522i	−0.473165	−	0.777088i
$881$		−	17.8630i		−	0.601820i	−0.953653	−	0.300910i	$-0.902710\pi$
$881$		−	17.8630i		−	0.601820i	0.953653	−	0.300910i	$-0.0972903\pi$
$882$	4.79488	+	6.93117i	0.161452	+	0.233385i
$883$	−24.7949	−	24.7949i	−0.834416	−	0.834416i	0.153701	−	0.988117i	$-0.450881\pi$
$883$	−24.7949	−	24.7949i	−0.834416	−	0.834416i	−0.988117	+	0.153701i	$0.950881\pi$
$884$	7.55868	−	13.4521i	0.254226	−	0.452443i
$885$	−11.5059	+	11.5059i	−0.386768	+	0.386768i
$886$	−26.9991	−	20.4680i	−0.907052	−	0.687636i
$887$			50.7922i			1.70543i	0.522373	+	0.852717i	$0.325047\pi$
$887$			50.7922i			1.70543i	−0.522373	+	0.852717i	$0.674953\pi$
$888$	−9.79155	−	22.5160i	−0.328583	−	0.755589i
$889$	6.48766	+	3.98807i	0.217589	+	0.133755i
$890$	−31.2320	−	23.6769i	−1.04690	−	0.793653i
$891$	−11.4422	+	11.4422i	−0.383328	+	0.383328i
$892$	29.6578	−	8.31885i	0.993016	−	0.278536i
$893$	−2.35389	+	2.35389i	−0.0787700	+	0.0787700i
$894$	3.08725	+	22.4376i	0.103253	+	0.750427i
$895$	31.5777			1.05553
$896$	−27.5003	+	11.8208i	−0.918721	+	0.394907i
$897$	13.3227			0.444833
$898$	−1.30372	−	9.47527i	−0.0435058	−	0.316194i
$899$	43.8225	−	43.8225i	1.46156	−	1.46156i
$900$	−1.13251	+	0.317664i	−0.0377504	+	0.0105888i
$901$	−7.20031	+	7.20031i	−0.239877	+	0.239877i
$902$	5.21389	+	3.95264i	0.173604	+	0.131609i
$903$	−6.24329	−	3.83785i	−0.207764	−	0.127716i
$904$	−15.2470	−	35.0610i	−0.507107	−	1.16611i
$905$			0.643249i			0.0213823i
$906$	33.9381	+	25.7284i	1.12752	+	0.854770i
$907$	−34.2341	+	34.2341i	−1.13673	+	1.13673i	−0.147693	+	0.989033i	$0.547185\pi$
$907$	−34.2341	+	34.2341i	−1.13673	+	1.13673i	−0.989033	+	0.147693i	$0.952815\pi$
$908$	−10.5340	+	18.7473i	−0.349584	+	0.622151i
$909$	5.06049	+	5.06049i	0.167846	+	0.167846i
$910$	−55.5741	−	24.4479i	−1.84227	−	0.810440i
$911$			7.50342i			0.248599i	0.992245	+	0.124300i	$0.0396684\pi$
$911$			7.50342i			0.248599i	−0.992245	+	0.124300i	$0.960332\pi$
$912$	5.25016	+	8.62244i	0.173850	+	0.285517i
$913$		−	38.8691i		−	1.28638i
$914$	5.31087	−	0.730735i	0.175668	−	0.0241706i
$915$	−7.16403	+	7.16403i	−0.236836	+	0.236836i
$916$	−24.3988	+	43.4222i	−0.806158	+	1.43471i
$917$	−4.52388	−	18.9594i	−0.149392	−	0.626095i
$918$	7.21630	+	5.47067i	0.238173	+	0.180559i
$919$	−29.0806			−0.959281			−0.479640	−	0.877465i	$-0.659233\pi$
$919$	−29.0806			−0.959281			−0.479640	+	0.877465i	$0.659233\pi$
$920$	−8.38862	−	3.30389i	−0.276564	−	0.108926i
$921$			2.55389i			0.0841535i
$922$	3.67724	−	4.85061i	0.121104	−	0.159746i
$923$	62.7555	+	62.7555i	2.06562	+	2.06562i
$924$	21.0979	+	6.01435i	0.694071	+	0.197857i
$925$	−2.89272	+	2.89272i	−0.0951121	+	0.0951121i
$926$	−2.02234	+	0.278258i	−0.0664582	+	0.00914414i
$927$	−6.33776			−0.208159
$928$	41.9249	+	4.27979i	1.37625	+	0.140491i
$929$		−	25.2998i		−	0.830059i	−0.909808	−	0.415029i	$-0.863771\pi$
$929$		−	25.2998i		−	0.830059i	0.909808	−	0.415029i	$-0.136229\pi$
$930$	40.7543	−	5.60748i	1.33639	−	0.183876i
$931$	−11.4519	−	3.75620i	−0.375321	−	0.123104i
$932$	−3.63322	−	12.9529i	−0.119010	−	0.424286i
$933$	−15.5881	−	15.5881i	−0.510332	−	0.510332i
$934$	−17.4204	−	13.2064i	−0.570012	−	0.432125i
$935$	7.65307			0.250282
$936$	15.2399	+	6.00232i	0.498133	+	0.196192i
$937$	17.3615			0.567177			0.283588	−	0.958946i	$-0.408475\pi$
$937$	17.3615			0.567177			0.283588	+	0.958946i	$0.408475\pi$
$938$	0.205786	+	0.529054i	0.00671916	+	0.0172742i
$939$	34.8734	−	34.8734i	1.13805	−	1.13805i
$940$	−4.51880	+	8.04205i	−0.147387	+	0.262303i
$941$	−10.8511	−	10.8511i	−0.353735	−	0.353735i	0.507762	−	0.861497i	$-0.330473\pi$
$941$	−10.8511	−	10.8511i	−0.353735	−	0.353735i	−0.861497	+	0.507762i	$0.830473\pi$
$942$	1.22751	+	8.92137i	0.0399945	+	0.290674i
$943$	2.18562			0.0711737
$944$	−18.0868	−	4.39670i	−0.588676	−	0.143101i
$945$	18.6595	−	30.3547i	0.606994	−	0.987439i
$946$	7.48816	−	1.03031i	0.243461	−	0.0334984i
$947$	−26.4451	−	26.4451i	−0.859349	−	0.859349i	0.131912	−	0.991261i	$-0.457888\pi$
$947$	−26.4451	−	26.4451i	−0.859349	−	0.859349i	−0.991261	+	0.131912i	$0.957888\pi$
$948$	−11.5314	−	6.47945i	−0.374522	−	0.210443i
$949$	−30.0411	−	30.0411i	−0.975175	−	0.975175i
$950$	1.01614	−	1.34038i	0.0329679	−	0.0434876i
$951$			8.39738i			0.272304i
$952$	1.19256	−	8.40367i	0.0386512	−	0.272365i
$953$		−	37.5483i		−	1.21631i	−0.793819	−	0.608154i	$-0.791910\pi$
$953$		−	37.5483i		−	1.21631i	0.793819	−	0.608154i	$-0.208090\pi$
$954$	−8.61369	−	6.53003i	−0.278878	−	0.211418i
$955$	−6.58089	−	6.58089i	−0.212952	−	0.212952i
$956$	−5.14947	−	18.3585i	−0.166546	−	0.593758i
$957$	−21.8404	−	21.8404i	−0.705999	−	0.705999i
$958$	4.30378	+	31.2792i	0.139049	+	1.01059i
$959$	−35.7939	−	22.0031i	−1.15584	−	0.710516i
$960$	20.4609	+	19.0764i	0.660373	+	0.615687i
$961$	38.2032			1.23236
$962$	56.4362	−	7.76518i	1.81957	−	0.250359i
$963$	−2.41189	−	2.41189i	−0.0777221	−	0.0777221i
$964$	−11.5462	−	41.1637i	−0.371878	−	1.32579i
$965$	−16.6578	+	16.6578i	−0.536234	+	0.536234i
$966$	6.83006	−	2.65669i	0.219754	−	0.0854777i
$967$	37.9785			1.22131			0.610653	−	0.791898i	$-0.290907\pi$
$967$	37.9785			1.22131			0.610653	+	0.791898i	$0.290907\pi$
$968$	7.78135	−	3.38388i	0.250102	−	0.108762i
$969$	−2.86256			−0.0919586
$970$	−6.59148	+	8.69475i	−0.211640	+	0.279172i
$971$	6.43134	+	6.43134i	0.206392	+	0.206392i	0.802732	−	0.596340i	$-0.203379\pi$
$971$	6.43134	+	6.43134i	0.206392	+	0.206392i	−0.596340	+	0.802732i	$0.703379\pi$
$972$	−8.37675	+	14.9080i	−0.268684	+	0.478174i
$973$	42.8576	−	10.2262i	1.37395	−	0.327836i
$974$	−0.990614	−	7.19963i	−0.0317413	−	0.230691i
$975$			6.88756i			0.220578i
$976$	−11.2615	−	2.73755i	−0.360473	−	0.0876269i
$977$	−3.72659			−0.119224			−0.0596121	−	0.998222i	$-0.518986\pi$
$977$	−3.72659			−0.119224			−0.0596121	+	0.998222i	$0.518986\pi$
$978$	−1.29030	−	9.37772i	−0.0412593	−	0.299866i
$979$	−23.2343	+	23.2343i	−0.742571	+	0.742571i
$980$	−33.3660	−	1.45145i	−1.06584	−	0.0463648i
$981$	4.69539	+	4.69539i	0.149912	+	0.149912i
$982$	9.95155	+	7.54427i	0.317567	+	0.240747i
$983$		−	17.5847i		−	0.560863i	−0.959874	−	0.280432i	$-0.909522\pi$
$983$		−	17.5847i		−	0.560863i	0.959874	−	0.280432i	$-0.0904776\pi$
$984$	−6.30980	−	2.48514i	−0.201149	−	0.0792234i
$985$	48.5879			1.54814
$986$	−7.21927	+	9.52285i	−0.229908	+	0.303269i
$987$	−1.74031	−	7.29357i	−0.0553946	−	0.232157i
$988$	−22.5523	+	6.32580i	−0.717484	+	0.201250i
$989$	1.78544	−	1.78544i	0.0567738	−	0.0567738i
$990$	1.10734	+	8.04799i	0.0351936	+	0.255782i
$991$			44.7264i			1.42078i	0.703808	+	0.710390i	$0.251482\pi$
$991$			44.7264i			1.42078i	−0.703808	+	0.710390i	$0.748518\pi$
$992$	29.7241	+	36.4826i	0.943741	+	1.15832i
$993$			23.6281i			0.749816i
$994$	44.6865	+	19.6583i	1.41737	+	0.623523i
$995$	43.2694	+	43.2694i	1.37173	+	1.37173i
$996$	10.8805	+	38.7905i	0.344762	+	1.22912i
$997$	0.273521	−	0.273521i	0.00866251	−	0.00866251i	−0.702762	−	0.711425i	$-0.748050\pi$
$997$	0.273521	−	0.273521i	0.00866251	−	0.00866251i	0.711425	+	0.702762i	$0.248050\pi$
$998$	−9.14315	+	12.0606i	−0.289421	+	0.381772i
$999$			33.4328i			1.05777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.j.d.27.5	✓	16
4.3	odd	2		448.2.j.d.335.5		16
7.2	even	3		784.2.w.e.619.7		32
7.3	odd	6		784.2.w.e.411.1		32
7.4	even	3		784.2.w.e.411.2		32
7.5	odd	6		784.2.w.e.619.8		32
7.6	odd	2	inner	112.2.j.d.27.6	yes	16
8.3	odd	2		896.2.j.g.671.4		16
8.5	even	2		896.2.j.h.671.5		16
16.3	odd	4	inner	112.2.j.d.83.6	yes	16
16.5	even	4		896.2.j.g.223.5		16
16.11	odd	4		896.2.j.h.223.4		16
16.13	even	4		448.2.j.d.111.4		16
28.27	even	2		448.2.j.d.335.4		16
56.13	odd	2		896.2.j.h.671.4		16
56.27	even	2		896.2.j.g.671.5		16
112.3	even	12		784.2.w.e.19.7		32
112.13	odd	4		448.2.j.d.111.5		16
112.19	even	12		784.2.w.e.227.2		32
112.27	even	4		896.2.j.h.223.5		16
112.51	odd	12		784.2.w.e.227.1		32
112.67	odd	12		784.2.w.e.19.8		32
112.69	odd	4		896.2.j.g.223.4		16
112.83	even	4	inner	112.2.j.d.83.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.j.d.27.5	✓	16	1.1	even	1	trivial
112.2.j.d.27.6	yes	16	7.6	odd	2	inner
112.2.j.d.83.5	yes	16	112.83	even	4	inner
112.2.j.d.83.6	yes	16	16.3	odd	4	inner
448.2.j.d.111.4		16	16.13	even	4
448.2.j.d.111.5		16	112.13	odd	4
448.2.j.d.335.4		16	28.27	even	2
448.2.j.d.335.5		16	4.3	odd	2
784.2.w.e.19.7		32	112.3	even	12
784.2.w.e.19.8		32	112.67	odd	12
784.2.w.e.227.1		32	112.51	odd	12
784.2.w.e.227.2		32	112.19	even	12
784.2.w.e.411.1		32	7.3	odd	6
784.2.w.e.411.2		32	7.4	even	3
784.2.w.e.619.7		32	7.2	even	3
784.2.w.e.619.8		32	7.5	odd	6
896.2.j.g.223.4		16	112.69	odd	4
896.2.j.g.223.5		16	16.5	even	4
896.2.j.g.671.4		16	8.3	odd	2
896.2.j.g.671.5		16	56.27	even	2
896.2.j.h.223.4		16	16.11	odd	4
896.2.j.h.223.5		16	112.27	even	4
896.2.j.h.671.4		16	56.13	odd	2
896.2.j.h.671.5		16	8.5	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.192769 + 1.40101i) q^{2} +(-1.03649 + 1.03649i) q^{3} +(-1.92568 + 0.540143i) q^{4} +(-1.68683 + 1.68683i) q^{5} +(-1.65195 - 1.25234i) q^{6} +(1.38554 - 2.25395i) q^{7} +(-1.12796 - 2.59378i) q^{8} +0.851361i q^{9} +(-2.68844 - 2.03810i) q^{10} +(-2.00000 + 2.00000i) q^{11} +(1.43610 - 2.55581i) q^{12} +(4.80976 + 4.80976i) q^{13} +(3.42490 + 1.50667i) q^{14} -3.49678i q^{15} +(3.41649 - 2.08029i) q^{16} +1.13424i q^{17} +(-1.19277 + 0.164116i) q^{18} +(1.21746 - 1.21746i) q^{19} +(2.33717 - 4.15942i) q^{20} +(0.900103 + 3.77231i) q^{21} +(-3.18757 - 2.41649i) q^{22} -1.33620 q^{23} +(3.85756 + 1.51932i) q^{24} -0.690788i q^{25} +(-5.81137 + 7.66571i) q^{26} +(-3.99191 - 3.99191i) q^{27} +(-1.45065 + 5.08877i) q^{28} +(5.26785 - 5.26785i) q^{29} +(4.89903 - 0.674069i) q^{30} +8.31885 q^{31} +(3.57310 + 4.38554i) q^{32} -4.14598i q^{33} +(-1.58908 + 0.218646i) q^{34} +(1.46486 + 6.13919i) q^{35} +(-0.459857 - 1.63945i) q^{36} +(-4.18757 - 4.18757i) q^{37} +(1.94036 + 1.47098i) q^{38} -9.97057 q^{39} +(6.27794 + 2.47259i) q^{40} -1.63570 q^{41} +(-5.11154 + 1.98824i) q^{42} +(-1.33620 + 1.33620i) q^{43} +(2.77107 - 4.93165i) q^{44} +(-1.43610 - 1.43610i) q^{45} +(-0.257578 - 1.87204i) q^{46} -1.93345 q^{47} +(-1.38497 + 5.69738i) q^{48} +(-3.16057 - 6.24586i) q^{49} +(0.967804 - 0.133162i) q^{50} +(-1.17563 - 1.17563i) q^{51} +(-11.8600 - 6.66410i) q^{52} +(6.34814 + 6.34814i) q^{53} +(4.82321 - 6.36224i) q^{54} -6.74732i q^{55} +(-7.40908 - 1.05142i) q^{56} +2.52377i q^{57} +(8.39581 + 6.36486i) q^{58} +(-3.29044 - 3.29044i) q^{59} +(1.88876 + 6.73368i) q^{60} +(-2.04875 - 2.04875i) q^{61} +(1.60361 + 11.6548i) q^{62} +(1.91892 + 1.17959i) q^{63} +(-5.45542 + 5.85136i) q^{64} -16.2265 q^{65} +(5.80857 - 0.799214i) q^{66} +(0.107279 + 0.107279i) q^{67} +(-0.612651 - 2.18418i) q^{68} +(1.38497 - 1.38497i) q^{69} +(-8.31872 + 3.23574i) q^{70} +13.0475 q^{71} +(2.20825 - 0.960300i) q^{72} -6.24586 q^{73} +(5.05961 - 6.67407i) q^{74} +(0.715998 + 0.715998i) q^{75} +(-1.68683 + 3.00203i) q^{76} +(1.73682 + 7.27897i) q^{77} +(-1.92201 - 13.9689i) q^{78} -4.51184i q^{79} +(-2.25395 + 9.27213i) q^{80} +5.72110 q^{81} +(-0.315311 - 2.29163i) q^{82} +(-9.71727 + 9.71727i) q^{83} +(-3.77090 - 6.77807i) q^{84} +(-1.91327 - 1.91327i) q^{85} +(-2.12962 - 1.61446i) q^{86} +10.9202i q^{87} +(7.44348 + 2.93165i) q^{88} +11.6171 q^{89} +(1.73516 - 2.28883i) q^{90} +(17.5051 - 4.17685i) q^{91} +(2.57310 - 0.721742i) q^{92} +(-8.62244 + 8.62244i) q^{93} +(-0.372709 - 2.70879i) q^{94} +4.10728i q^{95} +(-8.24908 - 0.842084i) q^{96} -3.23412i q^{97} +(8.14128 - 5.63201i) q^{98} +(-1.70272 - 1.70272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 8 q^{4} + 8 q^{7} - 16 q^{8} - 32 q^{11} + 20 q^{14} + 16 q^{16} - 12 q^{18} + 16 q^{21} + 16 q^{22} - 32 q^{28} + 48 q^{30} - 24 q^{32} + 8 q^{35} - 16 q^{36} + 16 q^{39} - 40 q^{42} + 16 q^{44}+ \cdots + 64 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 8 * q^4 + 8 * q^7 - 16 * q^8 - 32 * q^11 + 20 * q^14 + 16 * q^16 - 12 * q^18 + 16 * q^21 + 16 * q^22 - 32 * q^28 + 48 * q^30 - 24 * q^32 + 8 * q^35 - 16 * q^36 + 16 * q^39 - 40 * q^42 + 16 * q^44 + 8 * q^46 - 16 * q^49 - 12 * q^50 - 32 * q^51 - 16 * q^56 + 48 * q^58 + 72 * q^60 + 64 * q^64 - 80 * q^65 - 48 * q^67 - 40 * q^70 + 32 * q^71 + 16 * q^72 + 16 * q^74 - 16 * q^77 - 64 * q^78 + 32 * q^81 + 56 * q^84 + 64 * q^85 - 24 * q^86 + 48 * q^88 + 8 * q^91 - 40 * q^92 - 64 * q^93 + 36 * q^98 + 64 * q^99

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