LMFDB - Embedded newform 357.2.bl.a.10.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(10,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 8, 9]))

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

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

chi := DirichletCharacter("357.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.15
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.559246 - 0.0736262i) q^{2} +(-0.442289 - 0.896873i) q^{3} +(-1.62452 + 0.435288i) q^{4} +(1.94651 - 1.70704i) q^{5} +(-0.313382 - 0.469009i) q^{6} +(2.53814 - 0.746878i) q^{7} +(-1.91873 + 0.794762i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(0.962895 - 1.09797i) q^{10} +(0.958076 - 0.0627956i) q^{11} +(1.10890 + 1.26446i) q^{12} +(-3.77608 - 3.77608i) q^{13} +(1.36446 - 0.604562i) q^{14} +(-2.39192 - 0.990765i) q^{15} +(1.89848 - 1.09609i) q^{16} +(3.07312 - 2.74881i) q^{17} +(-0.282036 + 0.488501i) q^{18} +(-0.417008 - 3.16749i) q^{19} +(-2.41908 + 3.62041i) q^{20} +(-1.79245 - 1.94606i) q^{21} +(0.531177 - 0.105658i) q^{22} +(-3.58688 - 1.76885i) q^{23} +(1.56143 + 1.36934i) q^{24} +(0.222272 - 1.68832i) q^{25} +(-2.38978 - 1.83374i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-3.79815 + 2.31814i) q^{28} +(0.353142 + 1.77536i) q^{29} +(-1.41062 - 0.377974i) q^{30} +(9.23067 - 4.55206i) q^{31} +(4.27631 - 3.28133i) q^{32} +(-0.480066 - 0.831499i) q^{33} +(1.51625 - 1.76352i) q^{34} +(3.66557 - 5.78652i) q^{35} +(0.643606 - 1.55380i) q^{36} +(-0.606978 + 9.26070i) q^{37} +(-0.466420 - 1.74070i) q^{38} +(-1.71655 + 5.05678i) q^{39} +(-2.37812 + 4.82236i) q^{40} +(-1.08348 + 5.44704i) q^{41} +(-1.14570 - 0.956354i) q^{42} +(-0.368499 - 0.889635i) q^{43} +(-1.52908 + 0.519051i) q^{44} +(0.169328 + 2.58345i) q^{45} +(-2.13618 - 0.725136i) q^{46} +(-3.22686 + 12.0428i) q^{47} +(-1.82273 - 1.21791i) q^{48} +(5.88435 - 3.79137i) q^{49} -0.960552i q^{50} +(-3.82454 - 1.54043i) q^{51} +(7.77799 + 4.49062i) q^{52} +(0.111916 + 0.145852i) q^{53} +(0.562864 + 0.0368921i) q^{54} +(1.75771 - 1.75771i) q^{55} +(-4.27641 + 3.45027i) q^{56} +(-2.65640 + 1.77495i) q^{57} +(0.328206 + 0.966865i) q^{58} +(-11.5804 - 1.52459i) q^{59} +(4.31698 + 0.568341i) q^{60} +(3.35591 + 9.88621i) q^{61} +(4.82707 - 3.22534i) q^{62} +(-0.952586 + 2.46832i) q^{63} +(-0.950284 + 0.950284i) q^{64} +(-13.7961 - 0.904245i) q^{65} +(-0.329695 - 0.429667i) q^{66} +(5.04673 + 2.91373i) q^{67} +(-3.79581 + 5.80317i) q^{68} +3.99932i q^{69} +(1.62392 - 3.50597i) q^{70} +(-3.65486 - 2.44210i) q^{71} +(0.537519 - 2.00605i) q^{72} +(9.25085 + 3.14024i) q^{73} +(0.342380 + 5.22370i) q^{74} +(-1.61252 + 0.547376i) q^{75} +(2.05621 + 4.96412i) q^{76} +(2.38483 - 0.874950i) q^{77} +(-0.587661 + 2.95437i) q^{78} +(6.43131 - 13.0414i) q^{79} +(1.82434 - 5.37432i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.204890 + 3.12601i) q^{82} +(-6.07736 + 14.6721i) q^{83} +(3.75895 + 2.38117i) q^{84} +(1.28952 - 10.5965i) q^{85} +(-0.271582 - 0.470394i) q^{86} +(1.43608 - 1.10195i) q^{87} +(-1.78838 + 0.881930i) q^{88} +(9.93227 + 2.66134i) q^{89} +(0.284906 + 1.43232i) q^{90} +(-12.4045 - 6.76397i) q^{91} +(6.59690 + 1.31220i) q^{92} +(-8.16524 - 6.26541i) q^{93} +(-0.917943 + 6.97247i) q^{94} +(-6.21875 - 5.45370i) q^{95} +(-4.83430 - 2.38401i) q^{96} +(5.25025 - 1.04434i) q^{97} +(3.01166 - 2.55355i) q^{98} +(-0.533421 + 0.798320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) $ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

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 $

$2$	0.559246	−	0.0736262i	0.395447	−	0.0520616i	0.0698192	−	0.997560i	$-0.477758\pi$
$2$	0.559246	−	0.0736262i	0.395447	−	0.0520616i	0.325628	+	0.945498i	$0.394424\pi$
$3$	−0.442289	−	0.896873i	−0.255355	−	0.517810i
$3$	−0.442289	−	0.896873i	−0.255355	−	0.517810i
$4$	−1.62452	+	0.435288i	−0.812258	+	0.217644i
$5$	1.94651	−	1.70704i	0.870505	−	0.763413i	−0.102369	−	0.994746i	$-0.532642\pi$
$5$	1.94651	−	1.70704i	0.870505	−	0.763413i	0.972874	+	0.231334i	$0.0743090\pi$
$6$	−0.313382	−	0.469009i	−0.127937	−	0.191472i
$7$	2.53814	−	0.746878i	0.959328	−	0.282293i
$7$	2.53814	−	0.746878i	0.959328	−	0.282293i
$8$	−1.91873	+	0.794762i	−0.678372	+	0.280991i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	0.962895	−	1.09797i	0.304494	−	0.347209i
$11$	0.958076	−	0.0627956i	0.288871	−	0.0189336i	0.0797210	−	0.996817i	$-0.474597\pi$
$11$	0.958076	−	0.0627956i	0.288871	−	0.0189336i	0.209150	+	0.977884i	$0.432930\pi$
$12$	1.10890	+	1.26446i	0.320113	+	0.365019i
$13$	−3.77608	−	3.77608i	−1.04730	−	1.04730i	−0.998825	−	0.0484722i	$-0.984565\pi$
$13$	−3.77608	−	3.77608i	−1.04730	−	1.04730i	−0.0484722	−	0.998825i	$-0.515435\pi$
$14$	1.36446	−	0.604562i	0.364667	−	0.161576i
$15$	−2.39192	−	0.990765i	−0.617591	−	0.255814i
$16$	1.89848	−	1.09609i	0.474620	−	0.274022i
$17$	3.07312	−	2.74881i	0.745341	−	0.666684i
$17$	3.07312	−	2.74881i	0.745341	−	0.666684i
$18$	−0.282036	+	0.488501i	−0.0664765	+	0.115141i
$19$	−0.417008	−	3.16749i	−0.0956682	−	0.726672i	−0.970304	−	0.241891i	$-0.922233\pi$
$19$	−0.417008	−	3.16749i	−0.0956682	−	0.726672i	0.874635	−	0.484781i	$-0.161101\pi$
$20$	−2.41908	+	3.62041i	−0.540923	+	0.809548i
$21$	−1.79245	−	1.94606i	−0.391144	−	0.424664i
$22$	0.531177	−	0.105658i	0.113247	−	0.0225263i
$23$	−3.58688	−	1.76885i	−0.747916	−	0.368831i	0.0280499	−	0.999607i	$-0.491070\pi$
$23$	−3.58688	−	1.76885i	−0.747916	−	0.368831i	−0.775966	+	0.630775i	$0.782737\pi$
$24$	1.56143	+	1.36934i	0.318726	+	0.279515i
$25$	0.222272	−	1.68832i	0.0444543	−	0.337664i
$26$	−2.38978	−	1.83374i	−0.468674	−	0.359626i
$27$	0.980785	+	0.195090i	0.188752	+	0.0375451i
$28$	−3.79815	+	2.31814i	−0.717783	+	0.438087i
$29$	0.353142	+	1.77536i	0.0655768	+	0.329677i	0.999622	−	0.0274769i	$-0.00874727\pi$
$29$	0.353142	+	1.77536i	0.0655768	+	0.329677i	−0.934046	+	0.357154i	$0.883747\pi$
$30$	−1.41062	−	0.377974i	−0.257542	−	0.0690083i
$31$	9.23067	−	4.55206i	1.65788	−	0.817574i	0.660083	−	0.751193i	$-0.270521\pi$
$31$	9.23067	−	4.55206i	1.65788	−	0.817574i	0.997794	−	0.0663814i	$-0.0211454\pi$
$32$	4.27631	−	3.28133i	0.755952	−	0.580062i
$33$	−0.480066	−	0.831499i	−0.0835688	−	0.144745i
$34$	1.51625	−	1.76352i	0.260034	−	0.302442i
$35$	3.66557	−	5.78652i	0.619594	−	0.978101i
$36$	0.643606	−	1.55380i	0.107268	−	0.258967i
$37$	−0.606978	+	9.26070i	−0.0997866	+	1.52245i	0.595288	+	0.803512i	$0.297038\pi$
$37$	−0.606978	+	9.26070i	−0.0997866	+	1.52245i	−0.695075	+	0.718938i	$0.744629\pi$
$38$	−0.466420	−	1.74070i	−0.0756633	−	0.282379i
$39$	−1.71655	+	5.05678i	−0.274867	+	0.809733i
$40$	−2.37812	+	4.82236i	−0.376014	+	0.762481i
$41$	−1.08348	+	5.44704i	−0.169212	+	0.850685i	0.799149	+	0.601133i	$0.205284\pi$
$41$	−1.08348	+	5.44704i	−0.169212	+	0.850685i	−0.968361	+	0.249553i	$0.919716\pi$
$42$	−1.14570	−	0.956354i	−0.176785	−	0.147569i
$43$	−0.368499	−	0.889635i	−0.0561955	−	0.135668i	0.893288	−	0.449485i	$-0.148392\pi$
$43$	−0.368499	−	0.889635i	−0.0561955	−	0.135668i	−0.949484	+	0.313817i	$0.898392\pi$
$44$	−1.52908	+	0.519051i	−0.230517	+	0.0782499i
$45$	0.169328	+	2.58345i	0.0252420	+	0.385118i
$46$	−2.13618	−	0.725136i	−0.314963	−	0.106915i
$47$	−3.22686	+	12.0428i	−0.470685	+	1.75662i	0.166631	+	0.986019i	$0.446711\pi$
$47$	−3.22686	+	12.0428i	−0.470685	+	1.75662i	−0.637316	+	0.770602i	$0.719956\pi$
$48$	−1.82273	−	1.21791i	−0.263088	−	0.175790i
$49$	5.88435	−	3.79137i	0.840621	−	0.541624i
$50$		−	0.960552i		−	0.135843i
$51$	−3.82454	−	1.54043i	−0.535542	−	0.215703i
$52$	7.77799	+	4.49062i	1.07861	+	0.622737i
$53$	0.111916	+	0.145852i	0.0153729	+	0.0200343i	0.800977	−	0.598696i	$-0.204314\pi$
$53$	0.111916	+	0.145852i	0.0153729	+	0.0200343i	−0.785604	+	0.618730i	$0.787647\pi$
$54$	0.562864	+	0.0368921i	0.0765961	+	0.00502037i
$55$	1.75771	−	1.75771i	0.237009	−	0.237009i
$56$	−4.27641	+	3.45027i	−0.571459	+	0.461062i
$57$	−2.65640	+	1.77495i	−0.351848	+	0.235098i
$58$	0.328206	+	0.966865i	0.0430956	+	0.126956i
$59$	−11.5804	−	1.52459i	−1.50764	−	0.198485i	−0.669038	−	0.743228i	$-0.733294\pi$
$59$	−11.5804	−	1.52459i	−1.50764	−	0.198485i	−0.838603	+	0.544743i	$0.816627\pi$
$60$	4.31698	+	0.568341i	0.557319	+	0.0733725i
$61$	3.35591	+	9.88621i	0.429681	+	1.26580i	0.919195	+	0.393803i	$0.128841\pi$
$61$	3.35591	+	9.88621i	0.429681	+	1.26580i	−0.489514	+	0.871996i	$0.662826\pi$
$62$	4.82707	−	3.22534i	0.613038	−	0.409619i
$63$	−0.952586	+	2.46832i	−0.120015	+	0.310978i
$64$	−0.950284	+	0.950284i	−0.118785	+	0.118785i
$65$	−13.7961	−	0.904245i	−1.71120	−	0.112158i
$66$	−0.329695	−	0.429667i	−0.0405827	−	0.0528884i
$67$	5.04673	+	2.91373i	0.616556	+	0.355969i	0.775527	−	0.631314i	$-0.217484\pi$
$67$	5.04673	+	2.91373i	0.616556	+	0.355969i	−0.158971	+	0.987283i	$0.550818\pi$
$68$	−3.79581	+	5.80317i	−0.460309	+	0.703738i
$69$			3.99932i			0.481461i
$70$	1.62392	−	3.50597i	0.194095	−	0.419044i
$71$	−3.65486	−	2.44210i	−0.433752	−	0.289824i	0.319462	−	0.947599i	$-0.396498\pi$
$71$	−3.65486	−	2.44210i	−0.433752	−	0.289824i	−0.753214	+	0.657775i	$0.771498\pi$
$72$	0.537519	−	2.00605i	0.0633472	−	0.236415i
$73$	9.25085	+	3.14024i	1.08273	+	0.367537i	0.805093	−	0.593149i	$-0.202115\pi$
$73$	9.25085	+	3.14024i	1.08273	+	0.367537i	0.277637	+	0.960686i	$0.410449\pi$
$74$	0.342380	+	5.22370i	0.0398008	+	0.607243i
$75$	−1.61252	+	0.547376i	−0.186197	+	0.0632055i
$76$	2.05621	+	4.96412i	0.235863	+	0.569424i
$77$	2.38483	−	0.874950i	0.271777	−	0.0997098i
$78$	−0.587661	+	2.95437i	−0.0665395	+	0.334517i
$79$	6.43131	−	13.0414i	0.723579	−	1.46727i	−0.154115	−	0.988053i	$-0.549253\pi$
$79$	6.43131	−	13.0414i	0.723579	−	1.46727i	0.877695	−	0.479221i	$-0.159081\pi$
$80$	1.82434	−	5.37432i	0.203967	−	0.600868i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	−0.204890	+	3.12601i	−0.0226263	+	0.345210i
$83$	−6.07736	+	14.6721i	−0.667077	+	1.61047i	0.119399	+	0.992846i	$0.461903\pi$
$83$	−6.07736	+	14.6721i	−0.667077	+	1.61047i	−0.786476	+	0.617620i	$0.788097\pi$
$84$	3.75895	+	2.38117i	0.410135	+	0.259807i
$85$	1.28952	−	10.5965i	0.139868	−	1.14935i
$86$	−0.271582	−	0.470394i	−0.0292854	−	0.0507238i
$87$	1.43608	−	1.10195i	0.153964	−	0.118141i
$88$	−1.78838	+	0.881930i	−0.190642	+	0.0940141i
$89$	9.93227	+	2.66134i	1.05282	+	0.282102i	0.743416	−	0.668829i	$-0.233204\pi$
$89$	9.93227	+	2.66134i	1.05282	+	0.282102i	0.309402	+	0.950931i	$0.399871\pi$
$90$	0.284906	+	1.43232i	0.0300317	+	0.150980i
$91$	−12.4045	−	6.76397i	−1.30035	−	0.709056i
$92$	6.59690	+	1.31220i	0.687774	+	0.136807i
$93$	−8.16524	−	6.26541i	−0.846696	−	0.649693i
$94$	−0.917943	+	6.97247i	−0.0946786	+	0.719155i
$95$	−6.21875	−	5.45370i	−0.638030	−	0.559537i
$96$	−4.83430	−	2.38401i	−0.493398	−	0.243317i
$97$	5.25025	−	1.04434i	0.533082	−	0.106037i	0.0787930	−	0.996891i	$-0.474893\pi$
$97$	5.25025	−	1.04434i	0.533082	−	0.106037i	0.454289	+	0.890854i	$0.349893\pi$
$98$	3.01166	−	2.55355i	0.304223	−	0.257947i
$99$	−0.533421	+	0.798320i	−0.0536108	+	0.0802342i
$100$	0.373822	+	2.83946i	0.0373822	+	0.283946i
$101$	3.62332	−	6.27577i	0.360533	−	0.624462i	−0.627515	−	0.778604i	$-0.715928\pi$
$101$	3.62332	−	6.27577i	0.360533	−	0.624462i	0.988049	+	0.154142i	$0.0492613\pi$
$102$	−2.25227	−	0.579893i	−0.223008	−	0.0574180i
$103$	9.46233	−	5.46308i	0.932351	−	0.538293i	0.0447966	−	0.998996i	$-0.485736\pi$
$103$	9.46233	−	5.46308i	0.932351	−	0.538293i	0.887554	+	0.460703i	$0.152403\pi$
$104$	10.2463	+	4.24418i	1.00474	+	0.416176i
$105$	−6.81101	−	0.728234i	−0.664687	−	0.0710683i
$106$	0.0733273	+	0.0733273i	0.00712218	+	0.00712218i
$107$	−6.98828	−	7.96861i	−0.675583	−	0.770355i	0.307888	−	0.951423i	$-0.400378\pi$
$107$	−6.98828	−	7.96861i	−0.675583	−	0.770355i	−0.983471	+	0.181068i	$0.942045\pi$
$108$	−1.67822	+	0.109996i	−0.161487	+	0.0105844i
$109$	−1.92030	+	2.18968i	−0.183931	+	0.209733i	−0.836456	−	0.548034i	$-0.815376\pi$
$109$	−1.92030	+	2.18968i	−0.183931	+	0.209733i	0.652525	+	0.757767i	$0.273710\pi$
$110$	0.853579	−	1.11241i	0.0813855	−	0.106064i
$111$	8.57413	−	3.55152i	0.813820	−	0.337095i
$112$	3.99997	−	4.19996i	0.377961	−	0.396859i
$113$	7.27876	+	10.8934i	0.684728	+	1.02477i	0.997196	+	0.0748391i	$0.0238443\pi$
$113$	7.27876	+	10.8934i	0.684728	+	1.02477i	−0.312468	+	0.949928i	$0.601156\pi$
$114$	−1.35490	+	1.18821i	−0.126898	+	0.111286i
$115$	−10.0014	+	2.67987i	−0.932635	+	0.249899i
$116$	−1.34648	−	2.73039i	−0.125017	−	0.253510i
$117$	5.29450	−	0.697034i	0.489477	−	0.0644408i
$118$	−6.58855			−0.606525
$119$	5.74699	−	9.27211i	0.526826	−	0.849973i
$120$	5.37686			0.490838
$121$	−9.99193	+	1.31546i	−0.908357	+	0.119587i
$122$	2.60467	+	5.28174i	0.235815	+	0.478186i
$123$	5.36452	−	1.43742i	0.483702	−	0.129608i
$124$	−13.0139	+	11.4129i	−1.16868	+	1.02491i
$125$	4.74246	+	7.09759i	0.424178	+	0.634828i
$126$	−0.350998	+	1.45053i	−0.0312694	+	0.129224i
$127$	−10.9584	+	4.53911i	−0.972398	+	0.402781i	−0.811604	−	0.584207i	$-0.801405\pi$
$127$	−10.9584	+	4.53911i	−0.972398	+	0.402781i	−0.160794	+	0.986988i	$0.551405\pi$
$128$	−7.02413	+	9.15403i	−0.620851	+	0.809109i
$129$	−0.634906	+	0.723972i	−0.0559004	+	0.0637422i
$130$	−7.78200	+	0.510059i	−0.682526	+	0.0447351i
$131$	−6.63518	−	7.56597i	−0.579718	−	0.661042i	0.385433	−	0.922736i	$-0.374052\pi$
$131$	−6.63518	−	7.56597i	−0.579718	−	0.661042i	−0.965151	+	0.261694i	$0.915719\pi$
$132$	1.14182	+	1.14182i	0.0993823	+	0.0993823i
$133$	−3.42415	−	7.72809i	−0.296912	−	0.670110i
$134$	3.03689	+	1.25792i	0.262347	+	0.108668i
$135$	2.24213	−	1.29450i	0.192972	−	0.111413i
$136$	−3.71182	+	7.71660i	−0.318286	+	0.661693i
$137$	−2.26000	+	3.91443i	−0.193084	+	0.334432i	−0.946271	−	0.323375i	$-0.895182\pi$
$137$	−2.26000	+	3.91443i	−0.193084	+	0.334432i	0.753186	+	0.657807i	$0.228516\pi$
$138$	0.294454	+	2.23660i	0.0250656	+	0.190392i
$139$	−1.19426	+	1.78734i	−0.101296	+	0.151600i	−0.878655	−	0.477457i	$-0.841559\pi$
$139$	−1.19426	+	1.78734i	−0.101296	+	0.151600i	0.777359	+	0.629057i	$0.216559\pi$
$140$	−3.43597	+	10.9959i	−0.290392	+	0.929321i
$141$	12.2281	−	2.43231i	1.02979	−	0.204838i
$142$	−2.22377	−	1.09664i	−0.186615	−	0.0920282i
$143$	−3.85490	−	3.38065i	−0.322363	−	0.282704i
$144$	−0.286136	+	2.17342i	−0.0238447	+	0.181118i
$145$	3.71801	+	2.85293i	0.308764	+	0.236923i
$146$	5.40471	+	1.07506i	0.447297	+	0.0889729i
$147$	−6.00295	−	3.60063i	−0.495115	−	0.296975i
$148$	−3.04502	−	15.3084i	−0.250299	−	1.25834i
$149$	9.97363	+	2.67243i	0.817072	+	0.218934i	0.643066	−	0.765811i	$-0.277662\pi$
$149$	9.97363	+	2.67243i	0.817072	+	0.218934i	0.174006	+	0.984745i	$0.444329\pi$
$150$	−0.861493	+	0.424841i	−0.0703406	+	0.0346881i
$151$	6.40253	−	4.91283i	0.521030	−	0.399801i	−0.314489	−	0.949261i	$-0.601833\pi$
$151$	6.40253	−	4.91283i	0.521030	−	0.399801i	0.835520	+	0.549460i	$0.185167\pi$
$152$	3.31752	+	5.74612i	0.269087	+	0.466072i
$153$	0.309980	+	4.11144i	0.0250604	+	0.332390i
$154$	1.26929	−	0.664899i	0.102282	−	0.0535791i
$155$	10.1970	−	24.6178i	0.819044	−	1.97735i
$156$	0.587402	−	8.96202i	0.0470298	−	0.717536i
$157$	0.473522	+	1.76721i	0.0377912	+	0.141039i	0.982244	−	0.187609i	$-0.0600738\pi$
$157$	0.473522	+	1.76721i	0.0377912	+	0.141039i	−0.944453	+	0.328648i	$0.893407\pi$
$158$	2.63650	−	7.76687i	0.209749	−	0.617899i
$159$	0.0813115	−	0.164883i	0.00644842	−	0.0130761i
$160$	2.72251	−	13.6870i	0.215233	−	1.08205i
$161$	−10.4251	−	1.81064i	−0.821615	−	0.142699i
$162$	−0.215861	−	0.521135i	−0.0169596	−	0.0409442i
$163$	−4.57124	+	1.55173i	−0.358047	+	0.121541i	−0.494666	−	0.869083i	$-0.664710\pi$
$163$	−4.57124	+	1.55173i	−0.358047	+	0.121541i	0.136619	+	0.990624i	$0.456376\pi$
$164$	−0.610894	−	9.32044i	−0.0477028	−	0.727804i
$165$	−2.35386	−	0.799026i	−0.183247	−	0.0622041i
$166$	−2.31850	+	8.65274i	−0.179950	+	0.671583i
$167$	−2.02483	−	1.35295i	−0.156686	−	0.104694i	0.474756	−	0.880118i	$-0.342536\pi$
$167$	−2.02483	−	1.35295i	−0.156686	−	0.104694i	−0.631442	+	0.775423i	$0.717536\pi$
$168$	4.98586	+	2.30938i	0.384668	+	0.178172i
$169$			15.5176i			1.19366i
$170$	−0.0590221	−	6.02101i	−0.00452679	−	0.461790i
$171$	2.76680	+	1.59741i	0.211582	+	0.122157i
$172$	0.985879	+	1.28482i	0.0751726	+	0.0979668i
$173$	−15.5591	−	1.01980i	−1.18294	−	0.0775338i	−0.538793	−	0.842438i	$-0.681120\pi$
$173$	−15.5591	−	1.01980i	−1.18294	−	0.0775338i	−0.644144	+	0.764904i	$0.722786\pi$
$174$	0.721993	−	0.721993i	0.0547341	−	0.0547341i
$175$	−0.696812	−	4.45121i	−0.0526740	−	0.336480i
$176$	1.75006	−	1.16935i	0.131916	−	0.0881431i
$177$	3.75452	+	11.0605i	0.282207	+	0.831355i
$178$	5.75053	+	0.757071i	0.431020	+	0.0567449i
$179$	4.93527	+	0.649740i	0.368879	+	0.0485639i	0.312687	−	0.949856i	$-0.398771\pi$
$179$	4.93527	+	0.649740i	0.368879	+	0.0485639i	0.0561919	+	0.998420i	$0.482104\pi$
$180$	−1.39962	−	4.12315i	−0.104322	−	0.307322i
$181$	1.69387	−	1.13181i	0.125905	−	0.0841268i	−0.491023	−	0.871146i	$-0.663377\pi$
$181$	1.69387	−	1.13181i	0.125905	−	0.0841268i	0.616928	+	0.787020i	$0.288377\pi$
$182$	−7.43518	−	2.86943i	−0.551132	−	0.212696i
$183$	7.38239	−	7.38239i	0.545722	−	0.545722i
$184$	8.28805	+	0.543227i	0.611003	+	0.0400473i
$185$	14.6269	+	19.0622i	1.07539	+	1.40148i
$186$	−5.02768	−	2.90273i	−0.368647	−	0.212839i
$187$	2.77167	−	2.82655i	0.202684	−	0.206697i
$188$		−	20.9683i		−	1.52927i
$189$	2.63508	−	0.237359i	0.191674	−	0.0172654i
$190$	−3.87935	−	2.59210i	−0.281437	−	0.188050i
$191$	0.174072	−	0.649645i	0.0125954	−	0.0470066i	−0.959342	−	0.282246i	$-0.908921\pi$
$191$	0.174072	−	0.649645i	0.0125954	−	0.0470066i	0.971938	+	0.235239i	$0.0755873\pi$
$192$	1.27258	+	0.431984i	0.0918408	+	0.0311757i
$193$	−0.118027	−	1.80075i	−0.00849578	−	0.129621i	0.991504	−	0.130075i	$-0.0415219\pi$
$193$	−0.118027	−	1.80075i	−0.00849578	−	0.129621i	−1.00000		0.000454761i	$0.999855\pi$
$194$	2.85929	−	0.970598i	0.205285	−	0.0696849i
$195$	5.29087	+	12.7733i	0.378887	+	0.914714i
$196$	−7.90888	+	8.72052i	−0.564920	+	0.622894i
$197$	−1.20363	+	6.05108i	−0.0857554	+	0.431122i	0.913926	+	0.405881i	$0.133035\pi$
$197$	−1.20363	+	6.05108i	−0.0857554	+	0.431122i	−0.999681	+	0.0252407i	$0.991965\pi$
$198$	−0.239536	+	0.485731i	−0.0170231	+	0.0345194i
$199$	8.04185	−	23.6905i	0.570072	−	1.67938i	−0.152685	−	0.988275i	$-0.548792\pi$
$199$	8.04185	−	23.6905i	0.570072	−	1.67938i	0.722757	−	0.691103i	$-0.242875\pi$
$200$	0.915335	+	3.41608i	0.0647240	+	0.241553i
$201$	0.381134	−	5.81498i	0.0268831	−	0.410157i
$202$	1.56427	−	3.77647i	0.110061	−	0.265712i
$203$	2.22230	+	4.24237i	0.155975	+	0.297756i
$204$	6.88355	+	0.837678i	0.481945	+	0.0586492i
$205$	7.18932	+	12.4523i	0.502124	+	0.869705i
$206$	4.88955	−	3.75188i	0.340671	−	0.261406i
$207$	3.58688	−	1.76885i	0.249305	−	0.122944i
$208$	−11.3077	−	3.02990i	−0.784050	−	0.210085i
$209$	−0.598430	−	3.00851i	−0.0413943	−	0.208103i
$210$	−3.86265	+	0.0942069i	−0.266548	+	0.00650089i
$211$	−14.0629	−	2.79728i	−0.968130	−	0.192573i	−0.314391	−	0.949294i	$-0.601800\pi$
$211$	−14.0629	−	2.79728i	−0.968130	−	0.192573i	−0.653738	+	0.756721i	$0.726800\pi$
$212$	−0.245298	−	0.188223i	−0.0168471	−	0.0129272i
$213$	−0.573749	+	4.35806i	−0.0393127	+	0.298609i
$214$	−4.49487	−	3.94189i	−0.307263	−	0.269462i
$215$	−2.23593	−	1.10264i	−0.152489	−	0.0751993i
$216$	−2.03691	+	0.405166i	−0.138594	+	0.0275681i
$217$	20.0289	−	18.4480i	1.35965	−	1.25233i
$218$	−0.912702	+	1.36595i	−0.0618160	+	0.0925141i
$219$	−1.27515	−	9.68573i	−0.0861667	−	0.654501i
$220$	−2.09032	+	3.62054i	−0.140929	+	0.244096i
$221$	−21.9841	−	1.22462i	−1.47881	−	0.0823770i
$222$	4.53357	−	2.61746i	0.304273	−	0.175672i
$223$	−1.19419	−	0.494648i	−0.0799686	−	0.0331241i	0.342341	−	0.939576i	$-0.388780\pi$
$223$	−1.19419	−	0.494648i	−0.0799686	−	0.0331241i	−0.422309	+	0.906452i	$0.638780\pi$
$224$	8.40314	−	11.5224i	0.561458	−	0.769870i
$225$	1.20412	+	1.20412i	0.0802750	+	0.0802750i
$226$	4.87266	+	5.55620i	0.324124	+	0.369593i
$227$	0.0159556	−	0.00104578i	0.00105901	−	6.94111e-5i	−0.0648736	−	0.997893i	$-0.520664\pi$
$227$	0.0159556	−	0.00104578i	0.00105901	−	6.94111e-5i	0.0659326	+	0.997824i	$0.478998\pi$
$228$	3.54275	−	4.03973i	0.234624	−	0.267538i
$229$	−2.99180	+	3.89899i	−0.197704	+	0.257653i	−0.881676	−	0.471855i	$-0.843584\pi$
$229$	−2.99180	+	3.89899i	−0.197704	+	0.257653i	0.683972	+	0.729508i	$0.260251\pi$
$230$	−5.39593	+	2.23507i	−0.355797	+	0.147376i
$231$	−1.83950	−	1.75191i	−0.121030	−	0.115267i
$232$	−2.08857	−	3.12577i	−0.137122	−	0.205217i
$233$	11.6916	−	10.2533i	0.765943	−	0.671714i	−0.184423	−	0.982847i	$-0.559042\pi$
$233$	11.6916	−	10.2533i	0.765943	−	0.671714i	0.950366	+	0.311133i	$0.100708\pi$
$234$	2.90961	−	0.779628i	0.190207	−	0.0509658i
$235$	14.2764	+	28.9498i	0.931293	+	1.88848i
$236$	19.4762	−	2.56409i	1.26779	−	0.166908i
$237$	−14.5410			−0.944538
$238$	2.53131	−	5.60852i	0.164081	−	0.363547i
$239$	−17.9141			−1.15877			−0.579384	−	0.815055i	$-0.696707\pi$
$239$	−17.9141			−1.15877			−0.579384	+	0.815055i	$0.696707\pi$
$240$	−5.62697	+	0.740805i	−0.363219	+	0.0478187i
$241$	−8.25636	−	16.7423i	−0.531839	−	1.07846i	−0.982585	−	0.185811i	$-0.940509\pi$
$241$	−8.25636	−	16.7423i	−0.531839	−	1.07846i	0.450746	−	0.892652i	$-0.351158\pi$
$242$	−5.49110	+	1.47133i	−0.352981	+	0.0945810i
$243$	−0.751840	+	0.659346i	−0.0482305	+	0.0422971i
$244$	−9.75508	−	14.5995i	−0.624505	−	0.934638i
$245$	4.98191	−	17.4248i	0.318283	−	1.11323i
$246$	2.89426	−	1.19884i	0.184531	−	0.0764352i
$247$	−10.3860	+	13.5354i	−0.660848	+	0.861234i
$248$	−14.0933	+	16.0703i	−0.894926	+	1.02047i
$249$	15.8469	−	1.03866i	1.00426	−	0.0658225i
$250$	3.17477	+	3.62013i	0.200790	+	0.228957i
$251$	2.44973	+	2.44973i	0.154625	+	0.154625i	0.780180	−	0.625555i	$-0.215127\pi$
$251$	2.44973	+	2.44973i	0.154625	+	0.154625i	−0.625555	+	0.780180i	$0.715127\pi$
$252$	0.473064	−	4.42447i	0.0298002	−	0.278715i
$253$	−3.54758	−	1.46945i	−0.223034	−	0.0923838i
$254$	−5.79423	+	3.34530i	−0.363562	+	0.209903i
$255$	−10.0741	+	3.53019i	−0.630863	+	0.221069i
$256$	−1.91034	+	3.30880i	−0.119396	+	0.206800i
$257$	−2.91195	−	22.1184i	−0.181642	−	1.37971i	−0.802905	−	0.596107i	$-0.796713\pi$
$257$	−2.91195	−	22.1184i	−0.181642	−	1.37971i	0.621263	−	0.783602i	$-0.286620\pi$
$258$	−0.301766	+	0.451624i	−0.0187871	+	0.0281169i
$259$	5.37601	+	23.9583i	0.334049	+	1.48870i
$260$	22.8056	−	4.53632i	1.41434	−	0.281330i
$261$	−1.62347	−	0.800607i	−0.100490	−	0.0495563i
$262$	−4.26775	−	3.74272i	−0.263663	−	0.231226i
$263$	−0.344039	+	2.61323i	−0.0212143	+	0.161139i	−0.998773	−	0.0495250i	$-0.984229\pi$
$263$	−0.344039	+	2.61323i	−0.0212143	+	0.161139i	0.977559	+	0.210664i	$0.0675626\pi$
$264$	1.58196	+	1.21388i	0.0973628	+	0.0747091i
$265$	0.466822	+	0.0928567i	0.0286766	+	0.00570414i
$266$	−2.48393	−	4.06980i	−0.152300	−	0.249535i
$267$	−2.00604	−	10.0851i	−0.122768	−	0.617196i
$268$	−9.46680	−	2.53662i	−0.578277	−	0.154949i
$269$	5.22766	−	2.57800i	0.318736	−	0.157183i	−0.275882	−	0.961191i	$-0.588970\pi$
$269$	5.22766	−	2.57800i	0.318736	−	0.157183i	0.594618	+	0.804008i	$0.297303\pi$
$270$	1.15860	−	0.889022i	0.0705099	−	0.0541042i
$271$	−0.375161	−	0.649798i	−0.0227894	−	0.0394724i	0.854406	−	0.519606i	$-0.173921\pi$
$271$	−0.375161	−	0.649798i	−0.0227894	−	0.0394724i	−0.877195	+	0.480134i	$0.840588\pi$
$272$	2.82132	−	8.58696i	0.171067	−	0.520661i
$273$	−0.580043	+	14.1169i	−0.0351058	+	0.854393i
$274$	−0.975690	+	2.35552i	−0.0589436	+	0.142302i
$275$	0.106934	−	1.63150i	0.00644836	−	0.0983830i
$276$	−1.74085	−	6.49695i	−0.104787	−	0.391071i
$277$	−2.80472	+	8.26244i	−0.168519	+	0.496442i	−0.998077	−	0.0619785i	$-0.980259\pi$
$277$	−2.80472	+	8.26244i	−0.168519	+	0.496442i	0.829558	+	0.558420i	$0.188592\pi$
$278$	−0.536292	+	1.08749i	−0.0321647	+	0.0652235i
$279$	−2.00788	+	10.0943i	−0.120209	+	0.604330i
$280$	−2.43431	+	14.0160i	−0.145478	+	0.837616i
$281$	9.95495	+	24.0334i	0.593863	+	1.43371i	0.879745	+	0.475447i	$0.157714\pi$
$281$	9.95495	+	24.0334i	0.593863	+	1.43371i	−0.285882	+	0.958265i	$0.592286\pi$
$282$	6.65941	−	2.26057i	0.396562	−	0.134615i
$283$	0.827228	+	12.6211i	0.0491736	+	0.750244i	0.949252	+	0.314516i	$0.101842\pi$
$283$	0.827228	+	12.6211i	0.0491736	+	0.750244i	−0.900079	+	0.435728i	$0.856491\pi$
$284$	7.00040	+	2.37632i	0.415397	+	0.141008i
$285$	−2.14079	+	7.98953i	−0.126809	+	0.473259i
$286$	−2.40474	−	1.60680i	−0.142195	−	0.0950118i
$287$	1.31824	+	14.6346i	0.0778131	+	0.863854i
$288$			5.39017i			0.317619i
$289$	1.88811	−	16.8948i	0.111065	−	0.993813i
$290$	2.28934	+	1.32175i	0.134434	+	0.0776157i
$291$	−3.25876	−	4.24690i	−0.191032	−	0.248958i
$292$	−16.3951	−	1.07459i	−0.959449	−	0.0628856i
$293$	−15.4640	+	15.4640i	−0.903417	+	0.903417i	−0.995730	−	0.0923128i	$-0.970574\pi$
$293$	−15.4640	+	15.4640i	−0.903417	+	0.903417i	0.0923128	+	0.995730i	$0.470574\pi$
$294$	−3.62223	−	1.57167i	−0.211253	−	0.0916614i
$295$	−25.1439	+	16.8006i	−1.46394	+	0.978170i
$296$	−6.19543	−	18.2511i	−0.360102	−	1.06083i
$297$	0.951918	+	0.125322i	0.0552359	+	0.00727194i
$298$	5.77448	+	0.760224i	0.334506	+	0.0440386i
$299$	6.86501	+	20.2237i	0.397014	+	1.16957i
$300$	2.38129	−	1.59113i	0.137484	−	0.0918639i
$301$	−1.59975	−	1.98280i	−0.0922081	−	0.114287i
$302$	3.21888	−	3.21888i	0.185226	−	0.185226i
$303$	−7.23112	−	0.473952i	−0.415417	−	0.0272279i
$304$	−4.26352	−	5.55633i	−0.244530	−	0.318678i
$305$	23.4085	+	13.5149i	1.34037	+	0.773861i
$306$	0.476065	+	2.27648i	0.0272148	+	0.130138i
$307$		−	23.4740i		−	1.33973i	−0.742483	−	0.669865i	$-0.766352\pi$
$307$		−	23.4740i		−	1.33973i	0.742483	−	0.669865i	$-0.233648\pi$
$308$	−3.49335	+	2.45946i	−0.199052	+	0.140141i
$309$	−9.08477	−	6.07025i	−0.516814	−	0.345324i
$310$	3.89013	−	14.5182i	0.220945	−	0.824576i
$311$	32.5369	+	11.0448i	1.84500	+	0.626293i	0.995044	+	0.0994387i	$0.0317047\pi$
$311$	32.5369	+	11.0448i	1.84500	+	0.626293i	0.849956	+	0.526854i	$0.176629\pi$
$312$	−0.725358	−	11.0668i	−0.0410653	−	0.626535i
$313$	−11.6407	+	3.95148i	−0.657970	+	0.223351i	−0.630402	−	0.776269i	$-0.717110\pi$
$313$	−11.6407	+	3.95148i	−0.657970	+	0.223351i	−0.0275685	+	0.999620i	$0.508776\pi$
$314$	0.394929	+	0.953442i	0.0222871	+	0.0538058i
$315$	2.35930	+	6.43070i	0.132932	+	0.362329i
$316$	−4.77100	+	23.9855i	−0.268390	+	1.34929i
$317$	−5.70016	+	11.5588i	−0.320153	+	0.649205i	−0.996147	−	0.0877016i	$-0.972048\pi$
$317$	−5.70016	+	11.5588i	−0.320153	+	0.649205i	0.675994	+	0.736907i	$0.263714\pi$
$318$	0.0333334	−	0.0981971i	0.00186925	−	0.00550662i
$319$	0.449822	+	1.67876i	0.0251852	+	0.0939924i
$320$	−0.227561	+	3.47191i	−0.0127210	+	0.194086i
$321$	−4.05599	+	9.79203i	−0.226383	+	0.546538i
$322$	−5.96352	−	0.245033i	−0.332334	−	0.0136551i
$323$	−9.98833	−	8.58779i	−0.555766	−	0.477838i
$324$	0.840911	+	1.45650i	0.0467173	+	0.0809167i
$325$	−7.21455	+	5.53592i	−0.400191	+	0.307078i
$326$	−2.44220	+	1.20436i	−0.135261	+	0.0667033i
$327$	2.81319	+	0.753792i	0.155570	+	0.0416848i
$328$	−2.25019	−	11.3125i	−0.124246	−	0.624628i
$329$	0.804267	+	32.9764i	0.0443407	+	1.81805i
$330$	−1.37521	−	0.273547i	−0.0757030	−	0.0150583i
$331$	11.5706	+	8.87842i	0.635976	+	0.488002i	0.875710	−	0.482837i	$-0.160394\pi$
$331$	11.5706	+	8.87842i	0.635976	+	0.488002i	−0.239734	+	0.970839i	$0.577060\pi$
$332$	3.48621	−	26.4804i	0.191331	−	1.45330i
$333$	−6.97750	−	6.11911i	−0.382365	−	0.335325i
$334$	−1.23199	−	0.607551i	−0.0674116	−	0.0332437i
$335$	14.7974	−	2.94338i	0.808466	−	0.160814i
$336$	−5.53597	−	1.72987i	−0.302012	−	0.0943721i
$337$	−7.62186	+	11.4069i	−0.415189	+	0.621374i	−0.978837	−	0.204641i	$-0.934397\pi$
$337$	−7.62186	+	11.4069i	−0.415189	+	0.621374i	0.563648	+	0.826015i	$0.309397\pi$
$338$	1.14250	+	8.67816i	0.0621439	+	0.472029i
$339$	6.55071	−	11.3462i	0.355786	−	0.616239i
$340$	2.51769	+	17.7755i	0.136541	+	0.964014i
$341$	8.55783	−	4.94087i	0.463433	−	0.267563i
$342$	1.66493	+	0.689637i	0.0900292	+	0.0372913i
$343$	12.1036	−	14.0179i	0.653535	−	0.756897i
$344$	1.41410	+	1.41410i	0.0762429	+	0.0762429i
$345$	6.82700	+	7.78470i	0.367553	+	0.419114i
$346$	−8.77646	+	0.575239i	−0.471825	+	0.0309251i
$347$	−6.94736	+	7.92194i	−0.372954	+	0.425272i	−0.907621	−	0.419790i	$-0.862104\pi$
$347$	−6.94736	+	7.92194i	−0.372954	+	0.425272i	0.534667	+	0.845063i	$0.320437\pi$
$348$	−1.85328	+	2.41524i	−0.0993462	+	0.129470i
$349$	17.9575	−	7.43826i	0.961245	−	0.398161i	0.153799	−	0.988102i	$-0.450849\pi$
$349$	17.9575	−	7.43826i	0.961245	−	0.398161i	0.807446	+	0.589941i	$0.200849\pi$
$350$	−0.717415	−	2.43802i	−0.0383474	−	0.130318i
$351$	−2.96685	−	4.44020i	−0.158359	−	0.237000i
$352$	3.89098	−	3.41229i	0.207390	−	0.181876i
$353$	−10.8165	+	2.89827i	−0.575704	+	0.154259i	−0.534911	−	0.844908i	$-0.679655\pi$
$353$	−10.8165	+	2.89827i	−0.575704	+	0.154259i	−0.0407925	+	0.999168i	$0.512988\pi$
$354$	2.91404	+	5.90909i	0.154880	+	0.314065i
$355$	−11.2830	+	1.48543i	−0.598839	+	0.0788386i
$356$	−17.2936			−0.916558
$357$	−10.8577	−	1.05337i	−0.574652	−	0.0557502i
$358$	2.80787			0.148400
$359$	12.4910	−	1.64447i	0.659249	−	0.0867918i	0.206524	−	0.978442i	$-0.433785\pi$
$359$	12.4910	−	1.64447i	0.659249	−	0.0867918i	0.452726	+	0.891650i	$0.350452\pi$
$360$	−2.37812	−	4.82236i	−0.125338	−	0.254160i
$361$	8.49350	−	2.27583i	0.447026	−	0.119780i
$362$	0.863962	−	0.757674i	0.0454088	−	0.0398225i
$363$	5.59912	+	8.37967i	0.293878	+	0.439819i
$364$	23.0956	+	5.58864i	1.21054	+	0.292924i
$365$	23.3674	−	9.67909i	1.22310	−	0.506627i
$366$	3.58503	−	4.67211i	0.187393	−	0.244215i
$367$	−5.60280	+	6.38877i	−0.292464	+	0.333491i	−0.879348	−	0.476180i	$-0.842021\pi$
$367$	−5.60280	+	6.38877i	−0.292464	+	0.333491i	0.586884	+	0.809671i	$0.300354\pi$
$368$	−8.74842	+	0.573402i	−0.456043	+	0.0298906i
$369$	−3.66185	−	4.17554i	−0.190628	−	0.217370i
$370$	9.58352	+	9.58352i	0.498224	+	0.498224i
$371$	0.392994	+	0.286606i	0.0204032	+	0.0148798i
$372$	15.9918	+	6.62403i	0.829137	+	0.343440i
$373$	1.25769	−	0.726125i	0.0651205	−	0.0375973i	−0.467086	−	0.884212i	$-0.654696\pi$
$373$	1.25769	−	0.726125i	0.0651205	−	0.0375973i	0.532207	+	0.846614i	$0.321363\pi$
$374$	1.34194	−	1.78480i	0.0693899	−	0.0922899i
$375$	4.26810	−	7.39257i	0.220404	−	0.381750i
$376$	−3.37970	−	25.6714i	−0.174295	−	1.32390i
$377$	5.37043	−	8.03741i	0.276591	−	0.413948i
$378$	1.45618	−	0.326753i	0.0748980	−	0.0168064i
$379$	14.6723	−	2.91851i	0.753668	−	0.149914i	0.196718	−	0.980460i	$-0.436972\pi$
$379$	14.6723	−	2.91851i	0.753668	−	0.149914i	0.556950	+	0.830546i	$0.311972\pi$
$380$	12.4764	+	6.15267i	0.640025	+	0.315625i
$381$	8.91777	+	7.82067i	0.456871	+	0.400665i
$382$	0.0495181	−	0.376127i	0.00253357	−	0.0192444i
$383$	11.0945	+	8.51313i	0.566904	+	0.435000i	0.852033	−	0.523489i	$-0.175370\pi$
$383$	11.0945	+	8.51313i	0.566904	+	0.435000i	−0.285129	+	0.958489i	$0.592036\pi$
$384$	11.3167	+	2.25103i	0.577502	+	0.114872i
$385$	3.14852	−	5.77411i	0.160464	−	0.294276i
$386$	−0.198588	−	0.998371i	−0.0101079	−	0.0508157i
$387$	0.930122	+	0.249226i	0.0472808	+	0.0126688i
$388$	−8.07452	+	3.98191i	−0.409922	+	0.202151i
$389$	4.74045	−	3.63747i	0.240350	−	0.184427i	−0.481562	−	0.876412i	$-0.659930\pi$
$389$	4.74045	−	3.63747i	0.240350	−	0.184427i	0.721912	+	0.691985i	$0.243264\pi$
$390$	3.89935	+	6.75387i	0.197451	+	0.341995i
$391$	−15.8851	+	4.42375i	−0.803346	+	0.223718i
$392$	−8.27721	+	11.9512i	−0.418062	+	0.603629i
$393$	−3.85105	+	9.29726i	−0.194260	+	0.468985i
$394$	−0.227610	+	3.47266i	−0.0114668	+	0.174950i
$395$	−9.74364	−	36.3637i	−0.490256	−	1.82966i
$396$	0.519051	−	1.52908i	0.0260833	−	0.0768390i
$397$	−3.81627	+	7.73863i	−0.191533	+	0.388391i	−0.971363	−	0.237601i	$-0.923639\pi$
$397$	−3.81627	+	7.73863i	−0.191533	+	0.388391i	0.779830	+	0.625992i	$0.215306\pi$
$398$	2.75313	−	13.8409i	0.138002	−	0.693783i
$399$	−5.41665	+	6.48908i	−0.271172	+	0.324860i
$400$	−1.42857	−	3.44887i	−0.0714284	−	0.172443i
$401$	−21.1509	+	7.17975i	−1.05622	+	0.358540i	−0.794918	−	0.606716i	$-0.792486\pi$
$401$	−21.1509	+	7.17975i	−1.05622	+	0.358540i	−0.261306	+	0.965256i	$0.584153\pi$
$402$	−0.214987	−	3.28007i	−0.0107226	−	0.163595i
$403$	−52.0447	−	17.6668i	−2.59253	−	0.880046i
$404$	−3.15437	+	11.7723i	−0.156936	+	0.585692i
$405$	−2.15267	−	1.43837i	−0.106967	−	0.0714731i
$406$	1.55516	+	2.20891i	0.0771815	+	0.109626i
$407$			8.91057i			0.441681i
$408$	8.56251	−	0.0839357i	0.423907	−	0.00415544i
$409$	21.2862	+	12.2896i	1.05253	+	0.607681i	0.923358	−	0.383941i	$-0.125433\pi$
$409$	21.2862	+	12.2896i	1.05253	+	0.607681i	0.129177	+	0.991622i	$0.458767\pi$
$410$	4.93742	+	6.43457i	0.243842	+	0.317781i
$411$	4.51031	+	0.295622i	0.222477	+	0.0145819i
$412$	−12.9937	+	12.9937i	−0.640153	+	0.640153i
$413$	−30.5314	+	4.77952i	−1.50235	+	0.235185i
$414$	1.87571	−	1.25331i	0.0921863	−	0.0615969i
$415$	13.2162	+	38.9336i	0.648756	+	1.91117i
$416$	−28.5383	−	3.75713i	−1.39920	−	0.184209i
$417$	2.13123	+	0.280581i	0.104367	+	0.0137401i
$418$	−0.556175	−	1.63844i	−0.0272034	−	0.0801386i
$419$	−17.0551	+	11.3958i	−0.833196	+	0.556724i	−0.897402	−	0.441213i	$-0.854548\pi$
$419$	−17.0551	+	11.3958i	−0.833196	+	0.556724i	0.0642067	+	0.997937i	$0.479548\pi$
$420$	11.3816	−	1.78172i	0.555365	−	0.0869392i
$421$	−10.3441	+	10.3441i	−0.504141	+	0.504141i	−0.912722	−	0.408581i	$-0.866024\pi$
$421$	−10.3441	+	10.3441i	−0.504141	+	0.504141i	0.408581	+	0.912722i	$0.366024\pi$
$422$	−8.07057	−	0.528973i	−0.392869	−	0.0257500i
$423$	−7.58980	−	9.89122i	−0.369029	−	0.480928i
$424$	−0.330654	−	0.190903i	−0.0160580	−	0.00927109i
$425$	−3.95780	−	5.79939i	−0.191982	−	0.281312i
$426$			2.47947i			0.120131i
$427$	15.9016	+	22.5862i	0.769531	+	1.09302i
$428$	14.8212	+	9.90322i	0.716411	+	0.478690i
$429$	−1.32704	+	4.95258i	−0.0640700	+	0.239113i
$430$	−1.33162	−	0.452024i	−0.0642163	−	0.0217985i
$431$	−1.01662	−	15.5107i	−0.0489690	−	0.747123i	−0.949781	−	0.312914i	$-0.898695\pi$
$431$	−1.01662	−	15.5107i	−0.0489690	−	0.747123i	0.900812	−	0.434208i	$-0.142972\pi$
$432$	2.07584	−	0.704651i	0.0998737	−	0.0339025i
$433$	−6.10014	−	14.7270i	−0.293154	−	0.707736i	−1.00000		0.000368770i	$-0.999883\pi$
$433$	−6.10014	−	14.7270i	−0.293154	−	0.707736i	0.706846	−	0.707367i	$-0.250117\pi$
$434$	9.84285	−	11.7916i	0.472472	−	0.566015i
$435$	0.914282	−	4.59640i	0.0438365	−	0.220381i
$436$	2.16641	−	4.39305i	0.103752	−	0.210389i
$437$	−4.10706	+	12.0990i	−0.196468	+	0.578775i
$438$	−1.42625	−	5.32282i	−0.0681487	−	0.254334i
$439$	0.883317	−	13.4768i	0.0421584	−	0.643213i	−0.923533	−	0.383520i	$-0.874712\pi$
$439$	0.883317	−	13.4768i	0.0421584	−	0.643213i	0.965691	−	0.259693i	$-0.0836215\pi$
$440$	−1.97560	+	4.76952i	−0.0941830	+	0.227378i
$441$	−0.574271	+	6.97640i	−0.0273462	+	0.332210i
$442$	−12.3847	+	0.933738i	−0.589079	+	0.0444134i
$443$	3.22627	+	5.58807i	0.153285	+	0.265497i	0.932433	−	0.361342i	$-0.117681\pi$
$443$	3.22627	+	5.58807i	0.153285	+	0.265497i	−0.779148	+	0.626840i	$0.784348\pi$
$444$	−12.3829	+	9.50172i	−0.587665	+	0.450932i
$445$	23.8763	−	11.7745i	1.13184	−	0.558164i
$446$	−0.704263	−	0.188707i	−0.0333478	−	0.00893552i
$447$	−2.01440	−	10.1271i	−0.0952778	−	0.478994i
$448$	−1.70221	+	3.12170i	−0.0804219	+	0.147487i
$449$	−25.2874	−	5.02997i	−1.19339	−	0.237379i	−0.441860	−	0.897084i	$-0.645681\pi$
$449$	−25.2874	−	5.02997i	−1.19339	−	0.237379i	−0.751525	+	0.659705i	$0.770681\pi$
$450$	0.762057	+	0.584747i	0.0359237	+	0.0275652i
$451$	−0.696010	+	5.28672i	−0.0327738	+	0.248942i
$452$	−16.5662	−	14.5282i	−0.779210	−	0.683349i
$453$	−7.23795	−	3.56936i	−0.340069	−	0.167703i
$454$	0.00884610	−	0.00175960i	0.000415168	−	8.25821e-5i
$455$	−35.6919	+	8.00890i	−1.67326	+	0.375463i
$456$	3.68623	−	5.51684i	0.172624	−	0.258350i
$457$	2.28445	+	17.3521i	0.106862	+	0.811696i	0.958003	+	0.286759i	$0.0925779\pi$
$457$	2.28445	+	17.3521i	0.106862	+	0.811696i	−0.851141	+	0.524937i	$0.824089\pi$
$458$	−1.38609	+	2.40077i	−0.0647676	+	0.112181i
$459$	3.55033	−	2.09645i	0.165715	−	0.0978541i
$460$	15.0809	−	8.70697i	0.703151	−	0.405965i
$461$	29.5926	+	12.2577i	1.37827	+	0.570896i	0.944017	−	0.329897i	$-0.107014\pi$
$461$	29.5926	+	12.2577i	1.37827	+	0.570896i	0.434248	+	0.900793i	$0.357014\pi$
$462$	−1.15772	−	0.844315i	−0.0538621	−	0.0392811i
$463$	−10.4152	−	10.4152i	−0.484035	−	0.484035i	0.422383	−	0.906418i	$-0.361194\pi$
$463$	−10.4152	−	10.4152i	−0.484035	−	0.484035i	−0.906418	+	0.422383i	$0.861194\pi$
$464$	2.61638	+	2.98341i	0.121463	+	0.138502i
$465$	−26.5890	+	1.74274i	−1.23304	+	0.0808175i
$466$	5.78358	−	6.59491i	0.267919	−	0.305503i
$467$	11.2185	−	14.6202i	0.519128	−	0.676541i	−0.458059	−	0.888922i	$-0.651455\pi$
$467$	11.2185	−	14.6202i	0.519128	−	0.676541i	0.977187	+	0.212381i	$0.0681218\pi$
$468$	−8.29759	+	3.43697i	−0.383556	+	0.158874i
$469$	14.9855	+	3.62618i	0.691967	+	0.167441i
$470$	10.1155	+	15.1389i	0.466594	+	0.698307i
$471$	1.37553	−	1.20631i	0.0633810	−	0.0555837i
$472$	23.4313	−	6.27840i	1.07851	−	0.288987i
$473$	−0.408915	−	0.829198i	−0.0188019	−	0.0381265i
$474$	−8.13199	+	1.07060i	−0.373515	+	0.0491741i
$475$	−5.44043			−0.249624
$476$	−5.30004	+	17.5643i	−0.242927	+	0.805058i
$477$	−0.183843			−0.00841758
$478$	−10.0184	+	1.31895i	−0.458231	+	0.0603272i
$479$	5.35277	+	10.8543i	0.244574	+	0.495947i	0.984198	−	0.177074i	$-0.0566630\pi$
$479$	5.35277	+	10.8543i	0.244574	+	0.495947i	−0.739623	+	0.673021i	$0.764996\pi$
$480$	−13.4796	+	3.61185i	−0.615257	+	0.164858i
$481$	37.2612	−	32.6772i	1.69896	−	1.48995i
$482$	−5.85001	−	8.75516i	−0.266461	−	0.398786i
$483$	2.98700	+	10.1508i	0.135913	+	0.461879i
$484$	15.6594	−	6.48635i	0.711793	−	0.294834i
$485$	8.43692	−	10.9952i	0.383101	−	0.499267i
$486$	−0.371918	+	0.424092i	−0.0168706	+	0.0192372i
$487$	−2.55068	+	0.167180i	−0.115582	+	0.00757567i	−0.123085	−	0.992396i	$-0.539279\pi$
$487$	−2.55068	+	0.167180i	−0.115582	+	0.00757567i	0.00750215	+	0.999972i	$0.497612\pi$
$488$	−14.2963	−	16.3018i	−0.647161	−	0.737946i
$489$	3.41351	+	3.41351i	0.154364	+	0.154364i
$490$	1.50320	−	10.1115i	0.0679075	−	0.456792i
$491$	−13.3348	−	5.52347i	−0.601793	−	0.249271i	0.0609223	−	0.998143i	$-0.480596\pi$
$491$	−13.3348	−	5.52347i	−0.601793	−	0.249271i	−0.662715	+	0.748872i	$0.730596\pi$
$492$	−8.08906	+	4.67022i	−0.364683	+	0.210550i
$493$	5.96538	+	4.48518i	0.268667	+	0.202002i
$494$	−4.81180	+	8.33428i	−0.216493	+	0.374977i
$495$	0.324459	+	2.46451i	0.0145833	+	0.110771i
$496$	12.5348	−	18.7596i	0.562828	−	0.842331i
$497$	−11.1005	−	3.46867i	−0.497926	−	0.155591i
$498$	8.78585	−	1.74761i	0.393703	−	0.0783125i
$499$	9.38784	+	4.62957i	0.420257	+	0.207248i	0.640107	−	0.768286i	$-0.278890\pi$
$499$	9.38784	+	4.62957i	0.420257	+	0.207248i	−0.219850	+	0.975534i	$0.570557\pi$
$500$	−10.7937	−	9.46582i	−0.482709	−	0.423324i
$501$	−0.317863	+	2.41441i	−0.0142011	+	0.107868i
$502$	1.55036	+	1.18964i	0.0691961	+	0.0530961i
$503$	−17.5791	−	3.49670i	−0.783813	−	0.155910i	−0.213068	−	0.977037i	$-0.568346\pi$
$503$	−17.5791	−	3.49670i	−0.783813	−	0.155910i	−0.570745	+	0.821127i	$0.693346\pi$
$504$	−0.133972	−	5.49310i	−0.00596759	−	0.244682i
$505$	−3.66018	−	18.4010i	−0.162876	−	0.818833i
$506$	−2.09216	−	0.560593i	−0.0930079	−	0.0249214i
$507$	13.9173	−	6.86326i	0.618089	−	0.304808i
$508$	15.8262	−	12.1439i	0.702176	−	0.538798i
$509$	−17.2110	−	29.8103i	−0.762864	−	1.32132i	−0.941368	−	0.337381i	$-0.890459\pi$
$509$	−17.2110	−	29.8103i	−0.762864	−	1.32132i	0.178504	−	0.983939i	$-0.442874\pi$
$510$	−5.37397	+	2.71596i	−0.237963	+	0.120265i
$511$	25.8254	+	1.06113i	1.14245	+	0.0469415i
$512$	8.00637	−	19.3291i	0.353835	−	0.854233i
$513$	0.208951	−	3.18798i	0.00922543	−	0.140753i
$514$	−3.25699	−	12.1553i	−0.143660	−	0.536145i
$515$	9.09280	−	26.7865i	0.400677	−	1.18036i
$516$	0.716279	−	1.45247i	0.0315324	−	0.0639415i
$517$	−2.33534	+	11.7405i	−0.102708	+	0.516348i
$518$	4.77048	+	13.0028i	0.209603	+	0.571310i
$519$	5.96699	+	14.4056i	0.261922	+	0.632335i
$520$	27.1896	−	9.22962i	1.19234	−	0.404746i
$521$	2.62269	+	40.0145i	0.114902	+	1.75307i	0.534329	+	0.845277i	$0.320564\pi$
$521$	2.62269	+	40.0145i	0.114902	+	1.75307i	−0.419427	+	0.907789i	$0.637769\pi$
$522$	−0.966865	−	0.328206i	−0.0423185	−	0.0143652i
$523$	11.5346	−	43.0478i	0.504374	−	1.88235i	0.0349270	−	0.999390i	$-0.488880\pi$
$523$	11.5346	−	43.0478i	0.504374	−	1.88235i	0.469447	−	0.882960i	$-0.344453\pi$
$524$	14.0723	+	9.40283i	0.614753	+	0.410765i
$525$	−3.68398	+	2.59367i	−0.160782	+	0.113197i
$526$			1.48677i			0.0648263i
$527$	15.8542	−	39.3624i	0.690619	−	1.71465i
$528$	−1.82279	−	1.05239i	−0.0793267	−	0.0457993i
$529$	−4.26466	−	5.55781i	−0.185420	−	0.241644i
$530$	0.267905	+	0.0175594i	0.0116371	+	0.000762733i
$531$	8.25925	−	8.25925i	0.358421	−	0.358421i
$532$	8.92654	+	11.0639i	0.387014	+	0.479682i
$533$	24.6598	−	16.4772i	1.06814	−	0.713705i
$534$	−1.86440	−	5.49234i	−0.0806803	−	0.237677i
$535$	−27.2055	−	3.58167i	−1.17620	−	0.154849i
$536$	−11.9990	−	1.57970i	−0.518278	−	0.0682326i
$537$	−1.60008	−	4.71368i	−0.0690485	−	0.203410i
$538$	2.73374	−	1.82663i	0.117860	−	0.0787515i
$539$	5.39957	−	4.00193i	0.232576	−	0.172375i
$540$	−3.07890	+	3.07890i	−0.132495	+	0.132495i
$541$	−1.19994	−	0.0786481i	−0.0515894	−	0.00338135i	0.0395866	−	0.999216i	$-0.487396\pi$
$541$	−1.19994	−	0.0786481i	−0.0515894	−	0.00338135i	−0.0911760	+	0.995835i	$0.529063\pi$
$542$	−0.257649	−	0.335775i	−0.0110670	−	0.0144228i
$543$	−1.76427	−	1.01860i	−0.0757121	−	0.0437124i
$544$	4.12186	−	21.8387i	0.176723	−	0.936325i
$545$			7.54026i			0.322989i
$546$	0.714986	+	7.93753i	0.0305986	+	0.339695i
$547$	−7.65371	−	5.11404i	−0.327249	−	0.218661i	0.381082	−	0.924541i	$-0.375552\pi$
$547$	−7.65371	−	5.11404i	−0.327249	−	0.218661i	−0.708331	+	0.705880i	$0.750552\pi$
$548$	1.96750	−	7.34280i	0.0840473	−	0.313669i
$549$	−9.88621	−	3.35591i	−0.421933	−	0.143227i
$550$	−0.0603185	−	0.920282i	−0.00257199	−	0.0392410i
$551$	5.47618	−	1.85891i	0.233293	−	0.0791924i
$552$	−3.17850	−	7.67359i	−0.135286	−	0.326610i
$553$	6.58326	−	37.9044i	0.279949	−	1.61186i
$554$	−0.960197	+	4.82724i	−0.0407949	+	0.205090i
$555$	10.6270	−	21.5495i	0.451092	−	0.914724i
$556$	1.16209	−	3.42341i	0.0492837	−	0.145185i
$557$	−10.9699	−	40.9403i	−0.464811	−	1.73470i	−0.657516	−	0.753441i	$-0.728393\pi$
$557$	−10.9699	−	40.9403i	−0.464811	−	1.73470i	0.192705	−	0.981257i	$-0.438274\pi$
$558$	−0.379695	+	5.79303i	−0.0160738	+	0.245239i
$559$	−1.96785	+	4.75081i	−0.0832313	+	0.200938i
$560$	0.616467	−	15.0034i	0.0260505	−	0.634008i
$561$	−3.76093	−	1.23568i	−0.158787	−	0.0521706i
$562$	7.33676	+	12.7076i	0.309482	+	0.536039i
$563$	11.3329	−	8.69605i	0.477625	−	0.366495i	−0.341714	−	0.939804i	$-0.611007\pi$
$563$	11.3329	−	8.69605i	0.477625	−	0.366495i	0.819339	+	0.573309i	$0.194341\pi$
$564$	−18.8059	+	9.27405i	−0.791872	+	0.390508i
$565$	32.7637	+	8.77901i	1.37838	+	0.369336i
$566$	1.39186	+	6.99737i	0.0585044	+	0.294121i
$567$	−1.37835	−	2.25835i	−0.0578852	−	0.0948419i
$568$	8.95356	+	1.78097i	0.375683	+	0.0747280i
$569$	−8.14411	−	6.24920i	−0.341419	−	0.261980i	0.423792	−	0.905759i	$-0.360699\pi$
$569$	−8.14411	−	6.24920i	−0.341419	−	0.261980i	−0.765211	+	0.643780i	$0.777365\pi$
$570$	−0.608990	+	4.62573i	−0.0255078	+	0.193751i
$571$	−0.951907	−	0.834800i	−0.0398361	−	0.0349353i	0.639196	−	0.769044i	$-0.279267\pi$
$571$	−0.951907	−	0.834800i	−0.0398361	−	0.0349353i	−0.679032	+	0.734108i	$0.737600\pi$
$572$	7.73390	+	3.81394i	0.323370	+	0.159469i
$573$	−0.659638	+	0.131210i	−0.0275568	+	0.00548139i
$574$	1.81471	+	8.08730i	0.0757445	+	0.337557i
$575$	−3.78365	+	5.66263i	−0.157789	+	0.236148i
$576$	−0.175415	−	1.33241i	−0.00730894	−	0.0555169i
$577$	−1.52690	+	2.64466i	−0.0635655	+	0.110099i	−0.896057	−	0.443939i	$-0.853581\pi$
$577$	−1.52690	+	2.64466i	−0.0635655	+	0.110099i	0.832491	+	0.554038i	$0.186914\pi$
$578$	−0.187983	−	9.58738i	−0.00781904	−	0.398782i
$579$	−1.56284	+	0.902305i	−0.0649493	+	0.0374985i
$580$	−7.28182	−	3.01623i	−0.302361	−	0.125242i
$581$	−4.46699	+	41.7788i	−0.185322	+	1.73328i
$582$	−2.13513	−	2.13513i	−0.0885042	−	0.0885042i
$583$	0.116383	+	0.132710i	0.00482010	+	0.00549627i
$584$	−20.2456	+	1.32697i	−0.837768	+	0.0549102i
$585$	9.11592	−	10.3947i	0.376897	−	0.429769i
$586$	−7.50964	+	9.78675i	−0.310220	+	0.404287i
$587$	−16.2163	+	6.71703i	−0.669320	+	0.277242i	−0.691355	−	0.722516i	$-0.742986\pi$
$587$	−16.2163	+	6.71703i	−0.669320	+	0.277242i	0.0220343	+	0.999757i	$0.492986\pi$
$588$	11.3192	+	3.23627i	0.466796	+	0.133462i
$589$	−18.2679	−	27.3398i	−0.752714	−	1.12652i
$590$	−12.8247	+	11.2469i	−0.527983	+	0.463029i
$591$	5.95940	−	1.59682i	0.245137	−	0.0656843i
$592$	8.99820	+	18.2465i	0.369824	+	0.749928i
$593$	16.3231	−	2.14898i	0.670311	−	0.0882481i	0.212314	−	0.977202i	$-0.431900\pi$
$593$	16.3231	−	2.14898i	0.670311	−	0.0882481i	0.457998	+	0.888953i	$0.348567\pi$
$594$	0.541583			0.0222214
$595$	−4.64132	−	27.8586i	−0.190276	−	1.14209i
$596$	−17.3656			−0.711323
$597$	−24.8042	+	3.26554i	−1.01517	+	0.133650i
$598$	5.32822	+	10.8046i	0.217887	+	0.441832i
$599$	42.9228	−	11.5011i	1.75378	−	0.469923i	0.768351	−	0.640029i	$-0.221077\pi$
$599$	42.9228	−	11.5011i	1.75378	−	0.469923i	0.985426	+	0.170105i	$0.0544108\pi$
$600$	2.65894	−	2.33183i	0.108551	−	0.0951966i
$601$	3.24051	+	4.84976i	0.132183	+	0.197826i	0.891657	−	0.452712i	$-0.149543\pi$
$601$	3.24051	+	4.84976i	0.132183	+	0.197826i	−0.759474	+	0.650538i	$0.774543\pi$
$602$	−1.04064	−	0.991088i	−0.0424133	−	0.0403937i
$603$	−5.38387	+	2.23007i	−0.219248	+	0.0908156i
$604$	−8.26252	+	10.7679i	−0.336197	+	0.438140i
$605$	−17.2038	+	19.6172i	−0.699435	+	0.797553i
$606$	−4.07887	+	0.267343i	−0.165693	+	0.0108601i
$607$	29.4639	+	33.5971i	1.19590	+	1.36366i	0.914759	+	0.403999i	$0.132380\pi$
$607$	29.4639	+	33.5971i	1.19590	+	1.36366i	0.281143	+	0.959666i	$0.409287\pi$
$608$	−12.1768	−	12.1768i	−0.493835	−	0.493835i
$609$	2.82197	−	3.86948i	0.114352	−	0.156799i
$610$	14.0862	+	5.83468i	0.570332	+	0.236239i
$611$	57.6594	−	33.2897i	2.33265	−	1.34676i
$612$	−2.29323	−	6.54416i	−0.0926982	−	0.264532i
$613$	−15.8887	+	27.5200i	−0.641738	+	1.11152i	0.343306	+	0.939224i	$0.388453\pi$
$613$	−15.8887	+	27.5200i	−0.641738	+	1.11152i	−0.985045	+	0.172300i	$0.944880\pi$
$614$	−1.72830	−	13.1277i	−0.0697485	−	0.529792i
$615$	7.98835	−	11.9554i	0.322121	−	0.482089i
$616$	−3.88046	+	3.57416i	−0.156348	+	0.144007i
$617$	−28.4985	+	5.66871i	−1.14731	+	0.228214i	−0.731894	−	0.681419i	$-0.761363\pi$
$617$	−28.4985	+	5.66871i	−1.14731	+	0.228214i	−0.415414	+	0.909632i	$0.636363\pi$
$618$	−5.52755	−	2.72589i	−0.222351	−	0.109651i
$619$	12.6375	+	11.0828i	0.507944	+	0.445455i	0.874560	−	0.484918i	$-0.161150\pi$
$619$	12.6375	+	11.0828i	0.507944	+	0.445455i	−0.366616	+	0.930372i	$0.619484\pi$
$620$	−5.84940	+	44.4306i	−0.234918	+	1.78438i
$621$	−3.17287	−	2.43463i	−0.127323	−	0.0976983i
$622$	19.0093	+	3.78119i	0.762205	+	0.151612i
$623$	27.1972	−	0.663318i	1.08963	−	0.0265753i
$624$	2.28385	+	11.4817i	0.0914271	+	0.459635i
$625$	29.5714	+	7.92365i	1.18286	+	0.316946i
$626$	−6.21907	+	3.06691i	−0.248564	+	0.122578i
$627$	−2.43357	+	1.86735i	−0.0971875	+	0.0745746i
$628$	−1.53849	−	2.66474i	−0.0613924	−	0.106335i
$629$	23.5906	+	30.1277i	0.940618	+	1.20127i
$630$	1.79290	+	3.42264i	0.0714308	+	0.136361i
$631$	−10.8204	+	26.1228i	−0.430755	+	1.03993i	0.548290	+	0.836288i	$0.315279\pi$
$631$	−10.8204	+	26.1228i	−0.430755	+	1.03993i	−0.979045	+	0.203646i	$0.934721\pi$
$632$	−1.97510	+	30.1342i	−0.0785654	+	1.19868i
$633$	3.71105	+	13.8498i	0.147501	+	0.550482i
$634$	−2.33676	+	6.88388i	−0.0928047	+	0.273394i
$635$	−13.5821	+	27.5418i	−0.538990	+	1.09296i
$636$	−0.0603201	+	0.303250i	−0.00239185	+	0.0120246i
$637$	−36.5363	−	7.90327i	−1.44762	−	0.313139i
$638$	0.375162	+	0.905720i	0.0148528	+	0.0358578i
$639$	4.16239	−	1.41294i	0.164662	−	0.0558951i
$640$	1.95378	+	29.8089i	0.0772298	+	1.17830i
$641$	−31.5986	−	10.7263i	−1.24807	−	0.423662i	−0.382268	−	0.924052i	$-0.624857\pi$
$641$	−31.5986	−	10.7263i	−1.24807	−	0.423662i	−0.865800	+	0.500390i	$0.833190\pi$
$642$	−1.54735	+	5.77478i	−0.0610690	+	0.227912i
$643$	−39.8908	−	26.6542i	−1.57314	−	1.05114i	−0.966668	−	0.256032i	$-0.917585\pi$
$643$	−39.8908	−	26.6542i	−1.57314	−	1.05114i	−0.606470	−	0.795106i	$-0.707415\pi$
$644$	17.7239	−	1.59651i	0.698421	−	0.0629114i
$645$			2.49303i			0.0981629i
$646$	−6.21823	−	4.06729i	−0.244653	−	0.160025i
$647$	−22.2303	−	12.8347i	−0.873963	−	0.504583i	−0.00529975	−	0.999986i	$-0.501687\pi$
$647$	−22.2303	−	12.8347i	−0.873963	−	0.504583i	−0.868663	+	0.495403i	$0.835020\pi$
$648$	1.26428	+	1.64765i	0.0496658	+	0.0647257i
$649$	−11.1907	−	0.733474i	−0.439272	−	0.0287914i
$650$	−3.62712	+	3.62712i	−0.142267	+	0.142267i
$651$	−25.4040	−	9.80407i	−0.995663	−	0.384252i
$652$	6.75060	−	4.51061i	0.264374	−	0.176649i
$653$	5.79848	+	17.0818i	0.226912	+	0.668462i	0.999439	+	0.0334801i	$0.0106590\pi$
$653$	5.79848	+	17.0818i	0.226912	+	0.668462i	−0.772527	+	0.634982i	$0.781008\pi$
$654$	1.62877	+	0.214431i	0.0636898	+	0.00838492i
$655$	−25.8309	−	3.40070i	−1.00930	−	0.132876i
$656$	3.91346	+	11.5287i	0.152795	+	0.450120i
$657$	−8.12288	+	5.42754i	−0.316904	+	0.211748i
$658$	2.87771	+	18.3827i	0.112185	+	0.716633i
$659$	−12.5511	+	12.5511i	−0.488923	+	0.488923i	−0.907966	−	0.419043i	$-0.862366\pi$
$659$	−12.5511	+	12.5511i	−0.488923	+	0.488923i	0.419043	+	0.907966i	$0.362366\pi$
$660$	4.17168	+	0.273427i	0.162383	+	0.0106431i
$661$	−11.7357	−	15.2943i	−0.456467	−	0.594879i	0.507252	−	0.861798i	$-0.330661\pi$
$661$	−11.7357	−	15.2943i	−0.456467	−	0.594879i	−0.963719	+	0.266918i	$0.913995\pi$
$662$	7.12449	+	4.11332i	0.276901	+	0.159869i
$663$	8.62498	+	20.2586i	0.334966	+	0.786777i
$664$		−	32.9817i		−	1.27994i
$665$	−19.8573	−	9.19762i	−0.770034	−	0.356668i
$666$	−4.35267	−	2.90836i	−0.168662	−	0.112697i
$667$	1.87368	−	6.99267i	0.0725491	−	0.270757i
$668$	3.87829	+	1.31650i	0.150056	+	0.0509370i
$669$	0.0845386	+	1.28981i	0.00326845	+	0.0498669i
$670$	8.05866	−	2.73555i	0.311333	−	0.105683i
$671$	3.83603	+	9.26100i	0.148088	+	0.357517i
$672$	−14.0507	−	2.44033i	−0.542018	−	0.0941380i
$673$	3.82921	−	19.2507i	0.147605	−	0.742061i	−0.834094	−	0.551622i	$-0.814009\pi$
$673$	3.82921	−	19.2507i	0.147605	−	0.742061i	0.981699	−	0.190439i	$-0.0609911\pi$
$674$	−3.42265	+	6.94044i	−0.131835	+	0.267336i
$675$	0.547376	−	1.61252i	0.0210685	−	0.0620658i
$676$	−6.75462	−	25.2086i	−0.259793	−	0.969561i
$677$	0.793971	−	12.1137i	0.0305148	−	0.465566i	−0.955070	−	0.296381i	$-0.904220\pi$
$677$	0.793971	−	12.1137i	0.0305148	−	0.465566i	0.985584	−	0.169184i	$-0.0541133\pi$
$678$	2.82808	−	6.82760i	0.108612	−	0.262212i
$679$	12.5459	−	6.57198i	0.481467	−	0.252209i
$680$	5.94748	+	21.3567i	0.228075	+	0.818991i
$681$	−0.00799491	−	0.0138476i	−0.000306366	−	0.000530641i
$682$	4.42216	−	3.39324i	0.169333	−	0.129934i
$683$	5.41443	−	2.67010i	0.207178	−	0.102169i	−0.335740	−	0.941955i	$-0.608986\pi$
$683$	5.41443	−	2.67010i	0.207178	−	0.102169i	0.542917	+	0.839786i	$0.317320\pi$
$684$	−5.19004	−	1.39067i	−0.198446	−	0.0531735i
$685$	2.28299	+	11.4774i	0.0872286	+	0.438528i
$686$	5.73683	−	8.73061i	0.219033	−	0.333336i
$687$	4.82014	+	0.958786i	0.183900	+	0.0365800i
$688$	−1.67470	−	1.28505i	−0.0638475	−	0.0489919i
$689$	0.128145	−	0.973355i	0.00488192	−	0.0370819i
$690$	4.39113	+	3.85092i	0.167168	+	0.146602i
$691$	−24.9597	−	12.3088i	−0.949511	−	0.468247i	−0.0995149	−	0.995036i	$-0.531729\pi$
$691$	−24.9597	−	12.3088i	−0.949511	−	0.468247i	−0.849996	+	0.526789i	$0.823396\pi$
$692$	25.7199	−	5.11601i	0.977725	−	0.194482i
$693$	−0.757651	+	2.42465i	−0.0287808	+	0.0921049i
$694$	−3.30202	+	4.94182i	−0.125343	+	0.187589i
$695$	0.726424	+	5.51773i	0.0275548	+	0.209300i
$696$	−1.87967	+	3.25568i	−0.0712486	+	0.123406i
$697$	11.6432	+	19.7177i	0.441018	+	0.746861i
$698$	9.49504	−	5.48196i	0.359392	−	0.207495i
$699$	−14.3669	−	5.95098i	−0.543408	−	0.225087i
$700$	3.06954	+	6.92775i	0.116018	+	0.261844i
$701$	1.41724	+	1.41724i	0.0535283	+	0.0535283i	0.733364	−	0.679836i	$-0.237949\pi$
$701$	1.41724	+	1.41724i	0.0535283	+	0.0535283i	−0.679836	+	0.733364i	$0.737949\pi$
$702$	−1.98611	−	2.26473i	−0.0749610	−	0.0854767i
$703$	29.5863	−	1.93919i	1.11587	−	0.0731379i
$704$	−0.850770	+	0.970118i	−0.0320646	+	0.0365627i
$705$	19.6500	−	25.6083i	0.740060	−	0.964465i
$706$	−5.83569	+	2.41722i	−0.219629	+	0.0909734i
$707$	4.50927	−	18.6350i	0.169588	−	0.700840i
$708$	−10.9138	−	16.3336i	−0.410164	−	0.613855i
$709$	−7.69108	+	6.74490i	−0.288845	+	0.253310i	−0.791489	−	0.611183i	$-0.790694\pi$
$709$	−7.69108	+	6.74490i	−0.288845	+	0.253310i	0.502644	+	0.864493i	$0.332360\pi$
$710$	−6.20060	+	1.66145i	−0.232704	+	0.0623530i
$711$	6.43131	+	13.0414i	0.241193	+	0.489091i
$712$	−21.1724	+	2.78740i	−0.793470	+	0.104462i
$713$	−41.1612			−1.54150
$714$	−6.14970	+	0.210320i	−0.230147	+	0.00787104i
$715$	−13.2745			−0.496438
$716$	−8.30024	+	1.09275i	−0.310195	+	0.0408379i
$717$	7.92321	+	16.0667i	0.295898	+	0.600021i
$718$	6.86446	−	1.83933i	0.256179	−	0.0686431i
$719$	−1.41456	+	1.24054i	−0.0527542	+	0.0462642i	−0.685317	−	0.728245i	$-0.740336\pi$
$719$	−1.41456	+	1.24054i	−0.0527542	+	0.0462642i	0.632563	+	0.774509i	$0.282003\pi$
$720$	3.15315	+	4.71903i	0.117511	+	0.175868i
$721$	19.9365	−	20.9333i	0.742474	−	0.779596i
$722$	4.58240	−	1.89809i	0.170539	−	0.0706396i
$723$	−11.3640	+	14.8098i	−0.422631	+	0.550783i
$724$	−2.25906	+	2.57597i	−0.0839574	+	0.0957350i
$725$	3.07588	−	0.201604i	0.114235	−	0.00748737i
$726$	3.74825	+	4.27406i	0.139111	+	0.158625i
$727$	27.5414	+	27.5414i	1.02145	+	1.02145i	0.999765	+	0.0216897i	$0.00690460\pi$
$727$	27.5414	+	27.5414i	1.02145	+	1.02145i	0.0216897	+	0.999765i	$0.493095\pi$
$728$	29.1766	+	3.11956i	1.08136	+	0.115619i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	12.3555	−	7.13344i	0.457297	−	0.264021i
$731$	−3.57787	−	1.72102i	−0.132332	−	0.0636542i
$732$	−8.77934	+	15.2063i	−0.324494	+	0.562040i
$733$	3.14145	+	23.8617i	0.116032	+	0.881351i	0.946142	+	0.323751i	$0.104944\pi$
$733$	3.14145	+	23.8617i	0.116032	+	0.881351i	−0.830110	+	0.557599i	$0.811723\pi$
$734$	−2.66297	+	3.98541i	−0.0982919	+	0.147104i
$735$	−17.8312	+	3.23863i	−0.657715	+	0.119459i
$736$	−21.1428	+	4.20556i	−0.779333	+	0.155019i
$737$	5.01812	+	2.47466i	0.184845	+	0.0911554i
$738$	−2.35530	−	2.06555i	−0.0866999	−	0.0760338i
$739$	4.74342	−	36.0299i	0.174490	−	1.32538i	−0.650186	−	0.759775i	$-0.725309\pi$
$739$	4.74342	−	36.0299i	0.174490	−	1.32538i	0.824676	−	0.565605i	$-0.191357\pi$
$740$	−32.0592	−	24.5999i	−1.17852	−	0.904310i
$741$	16.7331	+	3.32842i	0.614707	+	0.122273i
$742$	0.240882	+	0.131349i	0.00884305	+	0.00482196i
$743$	−5.31459	−	26.7183i	−0.194973	−	0.980198i	−0.947041	−	0.321112i	$-0.895943\pi$
$743$	−5.31459	−	26.7183i	−0.194973	−	0.980198i	0.752068	−	0.659086i	$-0.229057\pi$
$744$	20.6464	+	5.53218i	0.756932	+	0.202819i
$745$	23.9757	−	11.8235i	0.878402	−	0.433180i
$746$	0.649894	−	0.498681i	0.0237943	−	0.0182580i
$747$	−7.94046	−	13.7533i	−0.290526	−	0.503206i
$748$	−3.27226	+	5.79824i	−0.119646	+	0.212005i
$749$	−23.6888	−	15.0061i	−0.865572	−	0.548310i
$750$	1.84263	−	4.44851i	0.0672834	−	0.162437i
$751$	−2.90976	+	44.3944i	−0.106179	+	1.61997i	0.529701	+	0.848185i	$0.322304\pi$
$751$	−2.90976	+	44.3944i	−0.106179	+	1.61997i	−0.635879	+	0.771788i	$0.719362\pi$
$752$	7.07383	+	26.3999i	0.257956	+	0.962705i
$753$	1.11361	−	3.28058i	0.0405821	−	0.119551i
$754$	2.41163	−	4.89030i	0.0878263	−	0.178094i
$755$	4.07616	−	20.4923i	0.148347	−	0.745790i
$756$	−4.17741	+	1.53261i	−0.151931	+	0.0557406i
$757$	13.7761	+	33.2584i	0.500700	+	1.20880i	0.949103	+	0.314965i	$0.101993\pi$
$757$	13.7761	+	33.2584i	0.500700	+	1.20880i	−0.448403	+	0.893831i	$0.648007\pi$
$758$	7.99058	−	2.71243i	0.290231	−	0.0985201i
$759$	0.251140	+	3.83165i	0.00911579	+	0.139080i
$760$	16.2665	+	5.52172i	0.590046	+	0.200294i
$761$	−3.56257	+	13.2957i	−0.129143	+	0.481968i	−0.999953	−	0.00965066i	$-0.996928\pi$
$761$	−3.56257	+	13.2957i	−0.129143	+	0.481968i	0.870810	+	0.491619i	$0.163595\pi$
$762$	5.56303	+	3.71710i	0.201527	+	0.134656i
$763$	−3.23857	+	6.99195i	−0.117244	+	0.253126i
$764$			1.13113i			0.0409228i
$765$	7.62178	+	7.47380i	0.275566	+	0.270216i
$766$	6.83136	+	3.94409i	0.246827	+	0.142506i
$767$	37.9716	+	49.4856i	1.37108	+	1.78682i
$768$	3.81250	+	0.249884i	0.137572	+	0.00901692i
$769$	−10.9451	+	10.9451i	−0.394691	+	0.394691i	−0.876356	−	0.481665i	$-0.840032\pi$
$769$	−10.9451	+	10.9451i	−0.394691	+	0.394691i	0.481665	+	0.876356i	$0.340032\pi$
$770$	1.33567	−	3.46096i	0.0481344	−	0.124724i
$771$	−18.5495	+	12.3944i	−0.668044	+	0.446372i
$772$	0.975580	+	2.87397i	0.0351119	+	0.103436i
$773$	−31.2636	−	4.11593i	−1.12447	−	0.148040i	−0.454727	−	0.890631i	$-0.650263\pi$
$773$	−31.2636	−	4.11593i	−1.12447	−	0.148040i	−0.669745	+	0.742591i	$0.733597\pi$
$774$	0.538517	+	0.0708971i	0.0193566	+	0.00254834i
$775$	−5.63362	−	16.5961i	−0.202366	−	0.596150i
$776$	−9.24378	+	6.17650i	−0.331832	+	0.221723i
$777$	19.1098	−	15.4181i	0.685561	−	0.553121i
$778$	2.38327	−	2.38327i	0.0854442	−	0.0854442i
$779$	17.7053	+	1.16047i	0.634357	+	0.0415780i
$780$	−14.1552	−	18.4474i	−0.506836	−	0.660522i
$781$	−3.65499	−	2.11021i	−0.130786	−	0.0755092i
$782$	−8.55800	+	3.64352i	−0.306033	+	0.130292i
$783$			1.81014i			0.0646893i
$784$	7.01564	−	13.6476i	0.250559	−	0.487414i
$785$	3.93842	+	2.63157i	0.140568	+	0.0939246i
$786$	−1.46916	+	5.48299i	−0.0524033	+	0.195572i
$787$	−41.8475	−	14.2053i	−1.49170	−	0.506365i	−0.547806	−	0.836606i	$-0.684537\pi$
$787$	−41.8475	−	14.2053i	−1.49170	−	0.506365i	−0.943897	+	0.330241i	$0.892870\pi$
$788$	−0.678637	−	10.3540i	−0.0241755	−	0.368846i
$789$	2.49590	−	0.847245i	0.0888565	−	0.0301627i
$790$	−8.12641	−	19.6189i	−0.289125	−	0.698009i
$791$	26.6106	+	22.2127i	0.946164	+	0.789794i
$792$	0.389013	−	1.95570i	0.0138230	−	0.0694928i
$793$	24.6589	−	50.0033i	0.875664	−	1.77567i
$794$	−1.56447	+	4.60878i	−0.0555209	+	0.163559i
$795$	−0.123189	−	0.459749i	−0.00436908	−	0.0163056i
$796$	−2.75192	+	41.9862i	−0.0975392	+	1.48816i
$797$	15.5493	−	37.5393i	0.550784	−	1.32971i	−0.366107	−	0.930573i	$-0.619310\pi$
$797$	15.5493	−	37.5393i	0.550784	−	1.32971i	0.916891	−	0.399138i	$-0.130690\pi$
$798$	−2.55147	+	4.02780i	−0.0903212	+	0.142583i
$799$	23.1868	+	45.8789i	0.820290	+	1.62308i
$800$	−4.58943	−	7.94913i	−0.162261	−	0.281044i
$801$	−8.15777	+	6.25968i	−0.288241	+	0.221175i
$802$	−11.2999	+	5.57251i	−0.399014	+	0.196772i
$803$	9.06021	+	2.42768i	0.319728	+	0.0856708i
$804$	1.91203	+	9.61244i	0.0674322	+	0.339005i
$805$	−23.3834	+	14.2717i	−0.824158	+	0.503011i
$806$	−30.4066	−	6.04824i	−1.07103	−	0.213040i
$807$	−4.62427	−	3.54832i	−0.162782	−	0.124907i
$808$	−1.96441	+	14.9211i	−0.0691076	+	0.524924i
$809$	12.8591	+	11.2771i	0.452102	+	0.396483i	0.854889	−	0.518811i	$-0.173625\pi$
$809$	12.8591	+	11.2771i	0.452102	+	0.396483i	−0.402787	+	0.915294i	$0.631958\pi$
$810$	−1.30977	−	0.645909i	−0.0460208	−	0.0226949i
$811$	−33.4977	+	6.66311i	−1.17626	+	0.233973i	−0.744255	−	0.667896i	$-0.767195\pi$
$811$	−33.4977	+	6.66311i	−1.17626	+	0.233973i	−0.432009	+	0.901869i	$0.642195\pi$
$812$	−5.45682	−	5.92446i	−0.191497	−	0.207908i
$813$	−0.416856	+	0.623870i	−0.0146198	+	0.0218801i
$814$	0.656051	+	4.98320i	0.0229946	+	0.174661i
$815$	−6.24909	+	10.8237i	−0.218896	+	0.379139i
$816$	−8.94924	+	1.26755i	−0.313286	+	0.0443732i
$817$	−2.66424	+	1.53820i	−0.0932100	+	0.0538148i
$818$	12.8091	+	5.30568i	0.447858	+	0.185509i
$819$	12.9176	−	5.72352i	0.451378	−	0.199996i
$820$	−17.0995	−	17.0995i	−0.597140	−	0.597140i
$821$	16.8874	+	19.2564i	0.589373	+	0.672052i	0.967256	−	0.253802i	$-0.0816811\pi$
$821$	16.8874	+	19.2564i	0.589373	+	0.672052i	−0.377883	+	0.925853i	$0.623348\pi$
$822$	2.54414	−	0.166752i	0.0887371	−	0.00581614i
$823$	−24.5693	+	28.0159i	−0.856432	+	0.976573i	−0.999914	−	0.0130795i	$-0.995837\pi$
$823$	−24.5693	+	28.0159i	−0.856432	+	0.976573i	0.143483	+	0.989653i	$0.454170\pi$
$824$	−13.8138	+	18.0024i	−0.481225	+	0.627145i
$825$	−1.51054	+	0.625687i	−0.0525903	+	0.0217836i
$826$	−16.7227	+	4.92084i	−0.581857	+	0.171218i
$827$	−11.0441	−	16.5287i	−0.384042	−	0.574760i	0.588206	−	0.808711i	$-0.299834\pi$
$827$	−11.0441	−	16.5287i	−0.384042	−	0.574760i	−0.972248	+	0.233951i	$0.924834\pi$
$828$	−5.05698	+	4.43485i	−0.175742	+	0.154122i
$829$	−28.0681	+	7.52082i	−0.974845	+	0.261209i	−0.710872	−	0.703321i	$-0.751700\pi$
$829$	−28.0681	+	7.52082i	−0.974845	+	0.261209i	−0.263973	+	0.964530i	$0.585033\pi$
$830$	10.2576	+	20.8004i	0.356047	+	0.721993i
$831$	8.65085	−	1.13891i	0.300095	−	0.0395082i
$832$	7.17670			0.248807
$833$	7.66156	−	27.8263i	0.265457	−	0.964123i
$834$	1.21254			0.0419868
$835$	−6.25089	+	0.822945i	−0.216321	+	0.0284792i
$836$	2.28173	+	4.62688i	0.0789152	+	0.160024i
$837$	9.94137	−	2.66378i	0.343624	−	0.0920737i
$838$	−8.69896	+	7.62879i	−0.300501	+	0.263532i
$839$	−1.71714	−	2.56988i	−0.0592822	−	0.0887220i	0.800644	−	0.599140i	$-0.204491\pi$
$839$	−1.71714	−	2.56988i	−0.0592822	−	0.0887220i	−0.859926	+	0.510418i	$0.829491\pi$
$840$	13.6472	−	4.01585i	0.470874	−	0.138560i
$841$	23.7653	−	9.84391i	0.819493	−	0.339445i
$842$	−5.02330	+	6.54650i	−0.173114	+	0.225607i
$843$	17.1519	−	19.5580i	0.590744	−	0.673614i
$844$	24.0630	−	1.57717i	0.828283	−	0.0542886i
$845$	26.4892	+	30.2051i	0.911256	+	1.03909i
$846$	−4.97282	−	4.97282i	−0.170969	−	0.170969i
$847$	−24.3785	+	10.8016i	−0.837654	+	0.371147i
$848$	0.372337	+	0.154227i	0.0127861	+	0.00529618i
$849$	10.9536	−	6.32407i	0.375927	−	0.217041i
$850$	−2.64037	−	2.95189i	−0.0905641	−	0.101249i
$851$	18.5580	−	32.1433i	0.636159	−	1.10186i
$852$	−0.964945	−	7.32948i	−0.0330585	−	0.251104i
$853$	32.0534	−	47.9713i	1.09749	−	1.64250i	0.418796	−	0.908080i	$-0.362452\pi$
$853$	32.0534	−	47.9713i	1.09749	−	1.64250i	0.678690	−	0.734424i	$-0.262548\pi$
$854$	10.5558	+	11.4604i	0.361213	+	0.392168i
$855$	8.11244	−	1.61366i	0.277440	−	0.0551862i
$856$	19.7417	+	9.73555i	0.674759	+	0.332754i
$857$	−23.1965	−	20.3428i	−0.792376	−	0.694895i	0.164184	−	0.986430i	$-0.447501\pi$
$857$	−23.1965	−	20.3428i	−0.792376	−	0.694895i	−0.956560	+	0.291534i	$0.905834\pi$
$858$	−0.377502	+	2.86741i	−0.0128877	+	0.0978919i
$859$	−11.4383	−	8.77692i	−0.390270	−	0.299465i	0.394925	−	0.918713i	$-0.370771\pi$
$859$	−11.4383	−	8.77692i	−0.390270	−	0.299465i	−0.785195	+	0.619249i	$0.787437\pi$
$860$	4.11227	+	0.817981i	0.140227	+	0.0278929i
$861$	12.5423	−	7.65501i	0.427442	−	0.260882i
$862$	−1.71053	−	8.59943i	−0.0582610	−	0.292898i
$863$	−35.6889	−	9.56282i	−1.21486	−	0.325522i	−0.406196	−	0.913786i	$-0.633145\pi$
$863$	−35.6889	−	9.56282i	−1.21486	−	0.325522i	−0.808669	+	0.588264i	$0.799812\pi$
$864$	4.83430	−	2.38401i	0.164466	−	0.0811057i
$865$	−32.0268	+	24.5750i	−1.08894	+	0.835576i
$866$	−4.49577	−	7.78691i	−0.152773	−	0.264610i
$867$	−15.9876	+	5.77899i	−0.542967	+	0.196265i
$868$	−24.5071	+	38.6874i	−0.831827	+	1.31313i
$869$	5.34274	−	12.8985i	0.181240	−	0.437552i
$870$	0.172893	−	2.63784i	0.00586162	−	0.0894311i
$871$	−8.05438	−	30.0593i	−0.272912	−	1.01852i
$872$	1.94425	−	5.72757i	0.0658406	−	0.193960i
$873$	−2.36762	+	4.80105i	−0.0801317	+	0.162491i
$874$	−1.40606	+	7.06872i	−0.0475605	+	0.239103i
$875$	17.3381	+	14.4727i	0.586134	+	0.489265i
$876$	6.28758	+	15.1796i	0.212438	+	0.512870i
$877$	−25.2384	+	8.56730i	−0.852242	+	0.289297i	−0.713175	−	0.700986i	$-0.752744\pi$
$877$	−25.2384	+	8.56730i	−0.852242	+	0.289297i	−0.139067	+	0.990283i	$0.544410\pi$
$878$	−0.498254	−	7.60189i	−0.0168153	−	0.256551i
$879$	20.7088	+	7.02969i	0.698491	+	0.237106i
$880$	1.41037	−	5.26357i	0.0475436	−	0.177435i
$881$	−28.5048	−	19.0463i	−0.960350	−	0.641685i	−0.0266129	−	0.999646i	$-0.508472\pi$
$881$	−28.5048	−	19.0463i	−0.960350	−	0.641685i	−0.933737	+	0.357961i	$0.883472\pi$
$882$	0.192487	+	3.94381i	0.00648138	+	0.132795i
$883$			30.3589i			1.02166i	0.859682	+	0.510829i	$0.170662\pi$
$883$			30.3589i			1.02166i	−0.859682	+	0.510829i	$0.829338\pi$
$884$	36.2465	−	7.57998i	1.21910	−	0.254942i
$885$	26.1889	+	15.1202i	0.880330	+	0.508259i
$886$	2.21571	+	2.88757i	0.0744382	+	0.0970097i
$887$	29.5141	+	1.93445i	0.990985	+	0.0649526i	0.552263	−	0.833670i	$-0.313764\pi$
$887$	29.5141	+	1.93445i	0.990985	+	0.0649526i	0.438722	+	0.898623i	$0.355431\pi$
$888$	−13.6288	+	13.6288i	−0.457352	+	0.457352i
$889$	−24.4238	+	19.7055i	−0.819147	+	0.660900i
$890$	12.4858	−	8.34275i	0.418525	−	0.279650i
$891$	−0.308624	−	0.909178i	−0.0103393	−	0.0304586i
$892$	2.15529	+	0.283749i	0.0721644	+	0.00950062i
$893$	39.4910	+	5.19909i	1.32152	+	0.173981i
$894$	−1.87216	−	5.51521i	−0.0626144	−	0.184456i
$895$	10.7157	−	7.15998i	0.358185	−	0.239332i
$896$	−10.9913	+	28.4804i	−0.367194	+	0.951463i
$897$	15.1017	−	15.1017i	0.504233	−	0.504233i
$898$	−14.5122	−	0.951180i	−0.484279	−	0.0317413i
$899$	11.3413	+	14.7803i	0.378253	+	0.492949i
$900$	−2.48026	−	1.43198i	−0.0826753	−	0.0477326i
$901$	0.744852	+	0.140585i	0.0248146	+	0.00468355i
$902$			3.00782i			0.100150i
$903$	−1.07076	+	2.31174i	−0.0356328	+	0.0769299i
$904$	−22.6236	−	15.1166i	−0.752450	−	0.502771i
$905$	1.36509	−	5.09459i	0.0453772	−	0.169350i
$906$	−4.31060	−	1.46325i	−0.143210	−	0.0486132i
$907$	0.581382	+	8.87017i	0.0193045	+	0.294529i	0.996585	+	0.0825776i	$0.0263152\pi$
$907$	0.581382	+	8.87017i	0.0193045	+	0.294529i	−0.977280	+	0.211952i	$0.932018\pi$
$908$	−0.0254649	+	0.00864416i	−0.000845082	+	0.000286867i
$909$	2.77317	+	6.69502i	0.0919801	+	0.222060i
$910$	−19.3709	+	7.10680i	−0.642138	+	0.235588i
$911$	−2.15595	+	10.8387i	−0.0714297	+	0.359101i	−0.999925	−	0.0122427i	$-0.996103\pi$
$911$	−2.15595	+	10.8387i	−0.0714297	+	0.359101i	0.928495	+	0.371344i	$0.121103\pi$
$912$	−3.09761	+	6.28134i	−0.102572	+	0.207996i
$913$	−4.90124	+	14.4386i	−0.162207	+	0.477847i
$914$	2.55514	+	9.53589i	0.0845164	+	0.315419i
$915$	1.76783	−	26.9719i	0.0584428	−	0.891664i
$916$	3.16305	−	7.63628i	0.104510	−	0.252310i
$917$	−22.4919	−	14.2479i	−0.742748	−	0.470506i
$918$	1.83116	−	1.43383i	0.0604372	−	0.0473235i
$919$	5.39679	+	9.34751i	0.178024	+	0.308346i	0.941203	−	0.337840i	$-0.109696\pi$
$919$	5.39679	+	9.34751i	0.178024	+	0.308346i	−0.763180	+	0.646186i	$0.776363\pi$
$920$	17.0601	−	13.0907i	0.562454	−	0.431586i
$921$	−21.0532	+	10.3823i	−0.693725	+	0.342108i
$922$	17.4520	+	4.67626i	0.574752	+	0.154004i
$923$	4.57949	+	23.0226i	0.150736	+	0.757799i
$924$	3.75089	+	2.04530i	0.123395	+	0.0672853i
$925$	15.5001	+	3.08317i	0.509641	+	0.101374i
$926$	−6.59149	−	5.05783i	−0.216610	−	0.166210i
$927$	−1.42615	+	10.8327i	−0.0468409	+	0.355792i
$928$	7.33569	+	6.43323i	0.240806	+	0.211181i
$929$	−30.5653	−	15.0731i	−1.00282	−	0.494534i	−0.134695	−	0.990887i	$-0.543005\pi$
$929$	−30.5653	−	15.0731i	−1.00282	−	0.494534i	−0.868120	+	0.496354i	$0.834672\pi$
$930$	−14.7415	+	2.93227i	−0.483393	+	0.0961528i
$931$	−14.4629	−	17.0576i	−0.474003	−	0.559040i
$932$	−14.5301	+	21.7458i	−0.475949	+	0.712308i
$933$	−4.48494	−	34.0665i	−0.146830	−	1.11529i
$934$	5.19745	−	9.00225i	0.170066	−	0.294563i
$935$	0.570043	−	10.2332i	0.0186424	−	0.334663i
$936$	−9.60471	+	5.54528i	−0.313940	+	0.181253i
$937$	18.5699	+	7.69191i	0.606652	+	0.251284i	0.664796	−	0.747025i	$-0.268518\pi$
$937$	18.5699	+	7.69191i	0.606652	+	0.251284i	−0.0581441	+	0.998308i	$0.518518\pi$
$938$	8.64758	+	0.924599i	0.282353	+	0.0301892i
$939$	8.69251	+	8.69251i	0.283669	+	0.283669i
$940$	−35.7938	−	40.8150i	−1.16747	−	1.33124i
$941$	60.6618	−	3.97599i	1.97752	−	0.129613i	0.979947	−	0.199259i	$-0.0638534\pi$
$941$	60.6618	−	3.97599i	1.97752	−	0.129613i	0.997572	+	0.0696453i	$0.0221867\pi$
$942$	0.680444	−	0.775897i	0.0221700	−	0.0252801i
$943$	13.5213	−	17.6214i	0.440316	−	0.573830i
$944$	−23.6562	+	9.79874i	−0.769945	+	0.318922i
$945$	4.72403	−	4.96022i	0.153673	−	0.161356i
$946$	−0.289735	−	0.433619i	−0.00942009	−	0.0140982i
$947$	−45.7130	+	40.0892i	−1.48547	+	1.30273i	−0.640445	+	0.768004i	$0.721250\pi$
$947$	−45.7130	+	40.0892i	−1.48547	+	1.30273i	−0.845029	+	0.534721i	$0.820417\pi$
$948$	23.6221	−	6.32951i	0.767209	−	0.205573i
$949$	−23.0742	−	46.7898i	−0.749019	−	1.51886i
$950$	−3.04254	+	0.400558i	−0.0987130	+	0.0129958i
$951$	12.8879			0.417918
$952$	−3.65778	+	22.3581i	−0.118549	+	0.724631i
$953$	−47.5702			−1.54095			−0.770476	−	0.637470i	$-0.779981\pi$
$953$	−47.5702			−1.54095			−0.770476	+	0.637470i	$0.779981\pi$
$954$	−0.102813	+	0.0135356i	−0.00332870	+	0.000438232i
$955$	−0.770139	−	1.56169i	−0.0249211	−	0.0505350i
$956$	29.1018	−	7.79779i	0.941218	−	0.252199i
$957$	1.30668	−	1.14593i	0.0422390	−	0.0370426i
$958$	3.79268	+	5.67614i	0.122536	+	0.183388i
$959$	−2.81259	+	11.6233i	−0.0908234	+	0.375336i
$960$	3.21451	−	1.33149i	0.103748	−	0.0429738i
$961$	45.6124	−	59.4432i	1.47137	−	1.91752i
$962$	18.4323	−	21.0180i	0.594280	−	0.677647i
$963$	10.5761	−	0.693196i	0.340811	−	0.0223379i
$964$	20.7003	+	23.6042i	0.666712	+	0.760239i
$965$	−3.30369	−	3.30369i	−0.106350	−	0.106350i
$966$	2.41784	+	5.45690i	0.0777926	+	0.175573i
$967$	7.30054	+	3.02398i	0.234769	+	0.0972447i	0.496967	−	0.867770i	$-0.334447\pi$
$967$	7.30054	+	3.02398i	0.234769	+	0.0972447i	−0.262197	+	0.965014i	$0.584447\pi$
$968$	18.1263	−	10.4652i	0.582601	−	0.336365i
$969$	−3.28443	+	12.7565i	−0.105511	+	0.409799i
$970$	3.90878	−	6.77021i	0.125503	−	0.217378i
$971$	−5.68905	−	43.2127i	−0.182570	−	1.38676i	−0.799937	−	0.600084i	$-0.795134\pi$
$971$	−5.68905	−	43.2127i	−0.182570	−	1.38676i	0.617366	−	0.786676i	$-0.288200\pi$
$972$	0.934371	−	1.39838i	0.0299700	−	0.0448532i
$973$	−1.69629	+	5.42850i	−0.0543805	+	0.174030i
$974$	−1.41415	+	0.281292i	−0.0453123	+	0.00901317i
$975$	8.15593	+	4.02206i	0.261199	+	0.128809i
$976$	17.2073	+	15.0904i	0.550791	+	0.483031i
$977$	7.75319	−	58.8913i	0.248047	−	1.88410i	−0.185013	−	0.982736i	$-0.559233\pi$
$977$	7.75319	−	58.8913i	0.248047	−	1.88410i	0.433060	−	0.901365i	$-0.357434\pi$
$978$	2.16032	+	1.65767i	0.0690793	+	0.0530064i
$979$	9.68299	+	1.92607i	0.309470	+	0.0615573i
$980$	−0.508411	+	30.4754i	−0.0162406	+	0.973500i
$981$	−0.568187	−	2.85647i	−0.0181408	−	0.0912000i
$982$	−7.86413	−	2.10719i	−0.250954	−	0.0672430i
$983$	−8.22481	+	4.05603i	−0.262331	+	0.129367i	−0.568699	−	0.822546i	$-0.692553\pi$
$983$	−8.22481	+	4.05603i	−0.262331	+	0.129367i	0.306368	+	0.951913i	$0.400886\pi$
$984$	−9.15063	+	7.02153i	−0.291711	+	0.223838i
$985$	7.98656	+	13.8331i	0.254473	+	0.440760i
$986$	3.66634	+	2.06911i	0.116760	+	0.0658940i
$987$	29.2199	−	15.3064i	0.930080	−	0.487209i
$988$	10.9805	−	26.5093i	0.349337	−	0.843374i
$989$	−0.251872	+	3.84283i	−0.00800908	+	0.122195i
$990$	0.362905	+	1.35438i	0.0115339	+	0.0430450i
$991$	1.53268	−	4.51513i	0.0486872	−	0.143428i	−0.919867	−	0.392230i	$-0.871704\pi$
$991$	1.53268	−	4.51513i	0.0486872	−	0.143428i	0.968554	+	0.248802i	$0.0800370\pi$
$992$	24.5364	−	49.7549i	0.779031	−	1.57972i
$993$	2.84527	−	14.3042i	0.0902920	−	0.453929i
$994$	−6.46331	−	1.12255i	−0.205004	−	0.0356052i
$995$	−24.7872	−	59.8416i	−0.785807	−	1.89711i
$996$	−25.2914	+	8.58529i	−0.801390	+	0.272035i
$997$	−1.85524	−	28.3054i	−0.0587559	−	0.896442i	−0.920905	−	0.389787i	$-0.872549\pi$
$997$	−1.85524	−	28.3054i	−0.0587559	−	0.896442i	0.862149	−	0.506655i	$-0.169118\pi$
$998$	5.59097	+	1.89788i	0.176979	+	0.0600763i
$999$	−2.40199	+	8.96434i	−0.0759956	+	0.283619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.15	✓	384
7.5	odd	6	inner	357.2.bl.a.61.10	yes	384
17.12	odd	16	inner	357.2.bl.a.199.10	yes	384
119.12	even	48	inner	357.2.bl.a.250.15	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.15	✓	384	1.1	even	1	trivial
357.2.bl.a.61.10	yes	384	7.5	odd	6	inner
357.2.bl.a.199.10	yes	384	17.12	odd	16	inner
357.2.bl.a.250.15	yes	384	119.12	even	48	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.559246 - 0.0736262i) q^{2} +(-0.442289 - 0.896873i) q^{3} +(-1.62452 + 0.435288i) q^{4} +(1.94651 - 1.70704i) q^{5} +(-0.313382 - 0.469009i) q^{6} +(2.53814 - 0.746878i) q^{7} +(-1.91873 + 0.794762i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(0.962895 - 1.09797i) q^{10} +(0.958076 - 0.0627956i) q^{11} +(1.10890 + 1.26446i) q^{12} +(-3.77608 - 3.77608i) q^{13} +(1.36446 - 0.604562i) q^{14} +(-2.39192 - 0.990765i) q^{15} +(1.89848 - 1.09609i) q^{16} +(3.07312 - 2.74881i) q^{17} +(-0.282036 + 0.488501i) q^{18} +(-0.417008 - 3.16749i) q^{19} +(-2.41908 + 3.62041i) q^{20} +(-1.79245 - 1.94606i) q^{21} +(0.531177 - 0.105658i) q^{22} +(-3.58688 - 1.76885i) q^{23} +(1.56143 + 1.36934i) q^{24} +(0.222272 - 1.68832i) q^{25} +(-2.38978 - 1.83374i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-3.79815 + 2.31814i) q^{28} +(0.353142 + 1.77536i) q^{29} +(-1.41062 - 0.377974i) q^{30} +(9.23067 - 4.55206i) q^{31} +(4.27631 - 3.28133i) q^{32} +(-0.480066 - 0.831499i) q^{33} +(1.51625 - 1.76352i) q^{34} +(3.66557 - 5.78652i) q^{35} +(0.643606 - 1.55380i) q^{36} +(-0.606978 + 9.26070i) q^{37} +(-0.466420 - 1.74070i) q^{38} +(-1.71655 + 5.05678i) q^{39} +(-2.37812 + 4.82236i) q^{40} +(-1.08348 + 5.44704i) q^{41} +(-1.14570 - 0.956354i) q^{42} +(-0.368499 - 0.889635i) q^{43} +(-1.52908 + 0.519051i) q^{44} +(0.169328 + 2.58345i) q^{45} +(-2.13618 - 0.725136i) q^{46} +(-3.22686 + 12.0428i) q^{47} +(-1.82273 - 1.21791i) q^{48} +(5.88435 - 3.79137i) q^{49} -0.960552i q^{50} +(-3.82454 - 1.54043i) q^{51} +(7.77799 + 4.49062i) q^{52} +(0.111916 + 0.145852i) q^{53} +(0.562864 + 0.0368921i) q^{54} +(1.75771 - 1.75771i) q^{55} +(-4.27641 + 3.45027i) q^{56} +(-2.65640 + 1.77495i) q^{57} +(0.328206 + 0.966865i) q^{58} +(-11.5804 - 1.52459i) q^{59} +(4.31698 + 0.568341i) q^{60} +(3.35591 + 9.88621i) q^{61} +(4.82707 - 3.22534i) q^{62} +(-0.952586 + 2.46832i) q^{63} +(-0.950284 + 0.950284i) q^{64} +(-13.7961 - 0.904245i) q^{65} +(-0.329695 - 0.429667i) q^{66} +(5.04673 + 2.91373i) q^{67} +(-3.79581 + 5.80317i) q^{68} +3.99932i q^{69} +(1.62392 - 3.50597i) q^{70} +(-3.65486 - 2.44210i) q^{71} +(0.537519 - 2.00605i) q^{72} +(9.25085 + 3.14024i) q^{73} +(0.342380 + 5.22370i) q^{74} +(-1.61252 + 0.547376i) q^{75} +(2.05621 + 4.96412i) q^{76} +(2.38483 - 0.874950i) q^{77} +(-0.587661 + 2.95437i) q^{78} +(6.43131 - 13.0414i) q^{79} +(1.82434 - 5.37432i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.204890 + 3.12601i) q^{82} +(-6.07736 + 14.6721i) q^{83} +(3.75895 + 2.38117i) q^{84} +(1.28952 - 10.5965i) q^{85} +(-0.271582 - 0.470394i) q^{86} +(1.43608 - 1.10195i) q^{87} +(-1.78838 + 0.881930i) q^{88} +(9.93227 + 2.66134i) q^{89} +(0.284906 + 1.43232i) q^{90} +(-12.4045 - 6.76397i) q^{91} +(6.59690 + 1.31220i) q^{92} +(-8.16524 - 6.26541i) q^{93} +(-0.917943 + 6.97247i) q^{94} +(-6.21875 - 5.45370i) q^{95} +(-4.83430 - 2.38401i) q^{96} +(5.25025 - 1.04434i) q^{97} +(3.01166 - 2.55355i) q^{98} +(-0.533421 + 0.798320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) \) 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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