LMFDB - Embedded newform 384.2.v.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.870630 + 1.11445i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-0.484007 - 1.94055i) q^{4} +(-0.328555 - 3.33588i) q^{5} +(-1.31919 - 0.509633i) q^{6} +(-1.53196 + 2.29274i) q^{7} +(2.58404 + 1.15010i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-0.870630 + 1.11445i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-0.484007 - 1.94055i) q^{4} +(-0.328555 - 3.33588i) q^{5} +(-1.31919 - 0.509633i) q^{6} +(-1.53196 + 2.29274i) q^{7} +(2.58404 + 1.15010i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(4.00372 + 2.53816i) q^{10} +(-2.66601 + 1.42501i) q^{11} +(1.71649 - 1.02648i) q^{12} +(-6.16389 - 0.607091i) q^{13} +(-1.22138 - 3.70343i) q^{14} +(3.09686 - 1.28276i) q^{15} +(-3.53147 + 1.87848i) q^{16} +(1.52921 + 0.633419i) q^{17} +(0.104746 - 1.41033i) q^{18} +(-6.31247 + 5.18051i) q^{19} +(-6.31441 + 2.25216i) q^{20} +(-2.63872 - 0.800448i) q^{21} +(0.733000 - 4.21179i) q^{22} +(-0.448825 + 2.25640i) q^{23} +(-0.350469 + 2.80663i) q^{24} +(-6.11620 + 1.21659i) q^{25} +(6.04304 - 6.34081i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(5.19066 + 1.86315i) q^{28} +(1.20106 - 2.24703i) q^{29} +(-1.26664 + 4.56811i) q^{30} +(0.352623 - 0.352623i) q^{31} +(0.981133 - 5.57112i) q^{32} +(-2.13755 - 2.13755i) q^{33} +(-2.03729 + 1.15276i) q^{34} +(8.15164 + 4.35714i) q^{35} +(1.48055 + 1.34461i) q^{36} +(1.37662 - 1.67741i) q^{37} +(-0.277605 - 11.5453i) q^{38} +(-1.20833 - 6.07471i) q^{39} +(2.98759 - 8.99791i) q^{40} +(0.719462 + 0.143110i) q^{41} +(3.18941 - 2.24384i) q^{42} +(0.498187 - 1.64230i) q^{43} +(4.05567 + 4.48381i) q^{44} +(2.12650 + 2.59114i) q^{45} +(-2.12389 - 2.46468i) q^{46} +(5.00956 - 12.0941i) q^{47} +(-2.82273 - 2.83412i) q^{48} +(-0.230978 - 0.557631i) q^{49} +(3.96912 - 7.87540i) q^{50} +(-0.162238 + 1.64723i) q^{51} +(1.80528 + 12.2552i) q^{52} +(1.75774 + 3.28850i) q^{53} +(1.38001 - 0.309161i) q^{54} +(5.62959 + 8.42528i) q^{55} +(-6.59553 + 4.16263i) q^{56} +(-6.78985 - 4.53684i) q^{57} +(1.45853 + 3.29486i) q^{58} +(-3.13374 + 0.308647i) q^{59} +(-3.98816 - 5.38875i) q^{60} +(-9.72455 + 2.94991i) q^{61} +(0.0859772 + 0.699985i) q^{62} -2.75746i q^{63} +(5.35454 + 5.94381i) q^{64} +20.7614i q^{65} +(4.24321 - 0.521182i) q^{66} +(1.59726 - 0.484525i) q^{67} +(0.489034 - 3.27408i) q^{68} +(-2.28952 + 0.225498i) q^{69} +(-11.9529 + 5.29115i) q^{70} +(-11.9303 - 7.97160i) q^{71} +(-2.78751 + 0.479344i) q^{72} +(-2.78270 - 4.16461i) q^{73} +(0.670872 + 2.99458i) q^{74} +(-2.93964 - 5.49968i) q^{75} +(13.1083 + 9.74227i) q^{76} +(0.817038 - 8.29553i) q^{77} +(7.82198 + 3.94219i) q^{78} +(5.23339 + 12.6345i) q^{79} +(7.42666 + 11.1634i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-0.785875 + 0.677210i) q^{82} +(-0.835860 - 1.01850i) q^{83} +(-0.276150 + 5.50800i) q^{84} +(1.61058 - 5.30936i) q^{85} +(1.39653 + 1.98504i) q^{86} +(2.49893 + 0.497068i) q^{87} +(-8.52798 + 0.616113i) q^{88} +(3.31735 + 16.6774i) q^{89} +(-4.73910 + 0.113951i) q^{90} +(10.8348 - 13.2022i) q^{91} +(4.59589 - 0.221143i) q^{92} +(0.439800 + 0.235078i) q^{93} +(9.11687 + 16.1124i) q^{94} +(19.3555 + 19.3555i) q^{95} +(5.61604 - 0.678325i) q^{96} +(3.58469 - 3.58469i) q^{97} +(0.822550 + 0.228076i) q^{98} +(1.42501 - 2.66601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−0.870630	+	1.11445i	−0.615628	+	0.788037i
$2$	−0.870630	+	1.11445i	−0.615628	+	0.788037i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$4$	−0.484007	−	1.94055i	−0.242003	−	0.970275i
$5$	−0.328555	−	3.33588i	−0.146934	−	1.49185i	−0.732246	−	0.681041i	$-0.761528\pi$
$5$	−0.328555	−	3.33588i	−0.146934	−	1.49185i	0.585311	−	0.810809i	$-0.300972\pi$
$6$	−1.31919	−	0.509633i	−0.538559	−	0.208057i
$7$	−1.53196	+	2.29274i	−0.579027	+	0.866575i	−0.999164	−	0.0408855i	$-0.986982\pi$
$7$	−1.53196	+	2.29274i	−0.579027	+	0.866575i	0.420137	+	0.907461i	$0.361982\pi$
$8$	2.58404	+	1.15010i	0.913597	+	0.406622i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	4.00372	+	2.53816i	1.26609	+	0.802635i
$11$	−2.66601	+	1.42501i	−0.803831	+	0.429657i	−0.821515	−	0.570187i	$-0.806871\pi$
$11$	−2.66601	+	1.42501i	−0.803831	+	0.429657i	0.0176837	+	0.999844i	$0.494371\pi$
$12$	1.71649	−	1.02648i	0.495508	−	0.296319i
$13$	−6.16389	−	0.607091i	−1.70956	−	0.168377i	−0.804582	−	0.593842i	$-0.797610\pi$
$13$	−6.16389	−	0.607091i	−1.70956	−	0.168377i	−0.904975	+	0.425465i	$0.860110\pi$
$14$	−1.22138	−	3.70343i	−0.326428	−	0.989783i
$15$	3.09686	−	1.28276i	0.799606	−	0.331208i
$16$	−3.53147	+	1.87848i	−0.882869	+	0.469620i
$17$	1.52921	+	0.633419i	0.370887	+	0.153627i	0.560339	−	0.828264i	$-0.310671\pi$
$17$	1.52921	+	0.633419i	0.370887	+	0.153627i	−0.189451	+	0.981890i	$0.560671\pi$
$18$	0.104746	−	1.41033i	0.0246889	−	0.332418i
$19$	−6.31247	+	5.18051i	−1.44818	+	1.18849i	−0.501993	+	0.864872i	$0.667400\pi$
$19$	−6.31247	+	5.18051i	−1.44818	+	1.18849i	−0.946187	+	0.323619i	$0.895100\pi$
$20$	−6.31441	+	2.25216i	−1.41195	+	0.503599i
$21$	−2.63872	−	0.800448i	−0.575817	−	0.174672i
$22$	0.733000	−	4.21179i	0.156276	−	0.897957i
$23$	−0.448825	+	2.25640i	−0.0935865	+	0.470491i	0.905362	+	0.424641i	$0.139600\pi$
$23$	−0.448825	+	2.25640i	−0.0935865	+	0.470491i	−0.998948	+	0.0458502i	$0.985400\pi$
$24$	−0.350469	+	2.80663i	−0.0715392	+	0.572901i
$25$	−6.11620	+	1.21659i	−1.22324	+	0.243317i
$26$	6.04304	−	6.34081i	1.18514	−	1.24354i
$27$	−0.773010	−	0.634393i	−0.148766	−	0.122089i
$28$	5.19066	+	1.86315i	0.980943	+	0.352102i
$29$	1.20106	−	2.24703i	0.223032	−	0.417264i	−0.745372	−	0.666648i	$-0.767728\pi$
$29$	1.20106	−	2.24703i	0.223032	−	0.417264i	0.968405	+	0.249385i	$0.0802283\pi$
$30$	−1.26664	+	4.56811i	−0.231256	+	0.834019i
$31$	0.352623	−	0.352623i	0.0633329	−	0.0633329i	−0.674731	−	0.738064i	$-0.735740\pi$
$31$	0.352623	−	0.352623i	0.0633329	−	0.0633329i	0.738064	+	0.674731i	$0.235740\pi$
$32$	0.981133	−	5.57112i	0.173441	−	0.984844i
$33$	−2.13755	−	2.13755i	−0.372100	−	0.372100i
$34$	−2.03729	+	1.15276i	−0.349392	+	0.197696i
$35$	8.15164	+	4.35714i	1.37788	+	0.736491i
$36$	1.48055	+	1.34461i	0.246758	+	0.224102i
$37$	1.37662	−	1.67741i	0.226314	−	0.275765i	−0.647457	−	0.762102i	$-0.724167\pi$
$37$	1.37662	−	1.67741i	0.226314	−	0.275765i	0.873771	+	0.486337i	$0.161667\pi$
$38$	−0.277605	−	11.5453i	−0.0450334	−	1.87289i
$39$	−1.20833	−	6.07471i	−0.193488	−	0.972732i
$40$	2.98759	−	8.99791i	0.472379	−	1.42270i
$41$	0.719462	+	0.143110i	0.112361	+	0.0223500i	0.250951	−	0.968000i	$-0.419257\pi$
$41$	0.719462	+	0.143110i	0.112361	+	0.0223500i	−0.138589	+	0.990350i	$0.544257\pi$
$42$	3.18941	−	2.24384i	0.492137	−	0.346231i
$43$	0.498187	−	1.64230i	0.0759729	−	0.250449i	−0.910725	−	0.413013i	$-0.864476\pi$
$43$	0.498187	−	1.64230i	0.0759729	−	0.250449i	0.986698	+	0.162564i	$0.0519764\pi$
$44$	4.05567	+	4.48381i	0.611415	+	0.675959i
$45$	2.12650	+	2.59114i	0.316999	+	0.386265i
$46$	−2.12389	−	2.46468i	−0.313150	−	0.363397i
$47$	5.00956	−	12.0941i	0.730719	−	1.76411i	0.0905304	−	0.995894i	$-0.471144\pi$
$47$	5.00956	−	12.0941i	0.730719	−	1.76411i	0.640189	−	0.768218i	$-0.278856\pi$
$48$	−2.82273	−	2.83412i	−0.407425	−	0.409070i
$49$	−0.230978	−	0.557631i	−0.0329969	−	0.0796616i
$50$	3.96912	−	7.87540i	0.561318	−	1.11375i
$51$	−0.162238	+	1.64723i	−0.0227179	+	0.230659i
$52$	1.80528	+	12.2552i	0.250347	+	1.69949i
$53$	1.75774	+	3.28850i	0.241444	+	0.451711i	0.973233	−	0.229821i	$-0.0738141\pi$
$53$	1.75774	+	3.28850i	0.241444	+	0.451711i	−0.731788	+	0.681532i	$0.761314\pi$
$54$	1.38001	−	0.309161i	0.187795	−	0.0420715i
$55$	5.62959	+	8.42528i	0.759094	+	1.13606i
$56$	−6.59553	+	4.16263i	−0.881365	+	0.556255i
$57$	−6.78985	−	4.53684i	−0.899338	−	0.600919i
$58$	1.45853	+	3.29486i	0.191514	+	0.432637i
$59$	−3.13374	+	0.308647i	−0.407979	+	0.0401824i	−0.299925	−	0.953963i	$-0.596962\pi$
$59$	−3.13374	+	0.308647i	−0.407979	+	0.0401824i	−0.108053	+	0.994145i	$0.534462\pi$
$60$	−3.98816	−	5.38875i	−0.514870	−	0.695685i
$61$	−9.72455	+	2.94991i	−1.24510	+	0.377697i	−0.843008	−	0.537901i	$-0.819217\pi$
$61$	−9.72455	+	2.94991i	−1.24510	+	0.377697i	−0.402093	+	0.915599i	$0.631717\pi$
$62$	0.0859772	+	0.699985i	0.0109191	+	0.0888982i
$63$		−	2.75746i		−	0.347407i
$64$	5.35454	+	5.94381i	0.669318	+	0.742976i
$65$			20.7614i			2.57514i
$66$	4.24321	−	0.521182i	0.522304	−	0.0641531i
$67$	1.59726	−	0.484525i	0.195137	−	0.0591941i	−0.191203	−	0.981550i	$-0.561239\pi$
$67$	1.59726	−	0.484525i	0.195137	−	0.0591941i	0.386340	+	0.922356i	$0.373739\pi$
$68$	0.489034	−	3.27408i	0.0593041	−	0.397041i
$69$	−2.28952	+	0.225498i	−0.275626	+	0.0271468i
$70$	−11.9529	+	5.29115i	−1.42864	+	0.632414i
$71$	−11.9303	−	7.97160i	−1.41587	−	0.946055i	−0.999317	−	0.0369447i	$-0.988237\pi$
$71$	−11.9303	−	7.97160i	−1.41587	−	0.946055i	−0.416555	−	0.909111i	$-0.636763\pi$
$72$	−2.78751	+	0.479344i	−0.328512	+	0.0564912i
$73$	−2.78270	−	4.16461i	−0.325691	−	0.487431i	0.632104	−	0.774884i	$-0.282192\pi$
$73$	−2.78270	−	4.16461i	−0.325691	−	0.487431i	−0.957795	+	0.287453i	$0.907192\pi$
$74$	0.670872	+	2.99458i	0.0779872	+	0.348113i
$75$	−2.93964	−	5.49968i	−0.339440	−	0.635048i
$76$	13.1083	+	9.74227i	1.50363	+	1.11751i
$77$	0.817038	−	8.29553i	0.0931102	−	0.945363i
$78$	7.82198	+	3.94219i	0.885665	+	0.446365i
$79$	5.23339	+	12.6345i	0.588802	+	1.42149i	0.884649	+	0.466258i	$0.154398\pi$
$79$	5.23339	+	12.6345i	0.588802	+	1.42149i	−0.295847	+	0.955235i	$0.595602\pi$
$80$	7.42666	+	11.1634i	0.830326	+	1.24810i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−0.785875	+	0.677210i	−0.0867853	+	0.0747854i
$83$	−0.835860	−	1.01850i	−0.0917475	−	0.111795i	0.725113	−	0.688630i	$-0.241787\pi$
$83$	−0.835860	−	1.01850i	−0.0917475	−	0.111795i	−0.816861	+	0.576835i	$0.804287\pi$
$84$	−0.276150	+	5.50800i	−0.0301304	+	0.600972i
$85$	1.61058	−	5.30936i	0.174692	−	0.575881i
$86$	1.39653	+	1.98504i	0.150592	+	0.214053i
$87$	2.49893	+	0.497068i	0.267913	+	0.0532913i
$88$	−8.52798	+	0.616113i	−0.909085	+	0.0656779i
$89$	3.31735	+	16.6774i	0.351638	+	1.76781i	0.600855	+	0.799358i	$0.294827\pi$
$89$	3.31735	+	16.6774i	0.351638	+	1.76781i	−0.249217	+	0.968448i	$0.580173\pi$
$90$	−4.73910	+	0.113951i	−0.499545	+	0.0120115i
$91$	10.8348	−	13.2022i	1.13579	−	1.38396i
$92$	4.59589	−	0.221143i	0.479154	−	0.0230558i
$93$	0.439800	+	0.235078i	0.0456052	+	0.0243765i
$94$	9.11687	+	16.1124i	0.940333	+	1.66187i
$95$	19.3555	+	19.3555i	1.98584	+	1.98584i
$96$	5.61604	−	0.678325i	0.573184	−	0.0692313i
$97$	3.58469	−	3.58469i	0.363971	−	0.363971i	−0.501302	−	0.865272i	$-0.667145\pi$
$97$	3.58469	−	3.58469i	0.363971	−	0.363971i	0.865272	+	0.501302i	$0.167145\pi$
$98$	0.822550	+	0.228076i	0.0830901	+	0.0230392i
$99$	1.42501	−	2.66601i	0.143219	−	0.267944i
$100$	5.32113	+	11.2800i	0.532113	+	1.12800i
$101$	−12.7141	−	10.4342i	−1.26510	−	1.03824i	−0.997199	−	0.0747913i	$-0.976171\pi$
$101$	−12.7141	−	10.4342i	−1.26510	−	1.03824i	−0.267898	−	0.963447i	$-0.586329\pi$
$102$	−1.69451	−	1.61494i	−0.167782	−	0.159903i
$103$	7.58160	−	1.50807i	0.747037	−	0.148595i	0.193130	−	0.981173i	$-0.438136\pi$
$103$	7.58160	−	1.50807i	0.747037	−	0.148595i	0.553907	+	0.832578i	$0.313136\pi$
$104$	−15.2295	−	8.65784i	−1.49338	−	0.848971i
$105$	−1.80323	+	9.06544i	−0.175977	+	0.884697i
$106$	−5.19522	−	0.904151i	−0.504605	−	0.0878189i
$107$	1.38489	+	0.420102i	0.133882	+	0.0406128i	0.356515	−	0.934290i	$-0.383965\pi$
$107$	1.38489	+	0.420102i	0.133882	+	0.0406128i	−0.222632	+	0.974902i	$0.571465\pi$
$108$	−0.856930	+	1.80712i	−0.0824581	+	0.173890i
$109$	11.1272	−	9.13186i	1.06579	−	0.874673i	0.0733405	−	0.997307i	$-0.476634\pi$
$109$	11.1272	−	9.13186i	1.06579	−	0.874673i	0.992452	+	0.122634i	$0.0391340\pi$
$110$	−14.2909	−	1.06139i	−1.36258	−	0.101200i
$111$	2.00479	+	0.830413i	0.190287	+	0.0788193i
$112$	1.10321	−	10.9745i	0.104244	−	1.03699i
$113$	−16.3483	+	6.77167i	−1.53791	+	0.637025i	−0.981081	−	0.193599i	$-0.937984\pi$
$113$	−16.3483	+	6.77167i	−1.53791	+	0.637025i	−0.556834	+	0.830624i	$0.687984\pi$
$114$	10.9675	−	3.61706i	1.02720	−	0.338769i
$115$	7.67453	+	0.755875i	0.715653	+	0.0704857i
$116$	−4.94181	−	1.24315i	−0.458835	−	0.115423i
$117$	5.46237	−	2.91970i	0.504996	−	0.269926i
$118$	2.38436	−	3.76112i	0.219498	−	0.346240i
$119$	−3.79495	+	2.53571i	−0.347883	+	0.232448i
$120$	9.47772	+	0.246988i	0.865193	+	0.0225468i
$121$	−1.03433	+	1.54799i	−0.0940303	+	0.140726i
$122$	5.17895	−	13.4058i	0.468880	−	1.21371i
$123$	0.0719012	+	0.730025i	0.00648311	+	0.0658242i
$124$	−0.854955	−	0.513611i	−0.0767772	−	0.0461236i
$125$	1.20270	+	3.96475i	0.107572	+	0.354618i
$126$	3.07305	+	2.40073i	0.273769	+	0.213874i
$127$	3.80678			0.337797			0.168898	−	0.985633i	$-0.445979\pi$
$127$	3.80678			0.337797			0.168898	+	0.985633i	$0.445979\pi$
$128$	−11.2859	+	0.792522i	−0.997544	+	0.0700497i
$129$	1.71620			0.151103
$130$	−23.1376	−	18.0755i	−2.02931	−	1.58533i
$131$	1.94292	+	6.40495i	0.169754	+	0.559603i	0.999998	+	0.00220278i	$0.000701168\pi$
$131$	1.94292	+	6.40495i	0.169754	+	0.559603i	−0.830244	+	0.557400i	$0.811799\pi$
$132$	−3.11344	+	5.18262i	−0.270990	+	0.451089i
$133$	−2.20712	−	22.4092i	−0.191381	−	1.94313i
$134$	−0.850647	+	2.20192i	−0.0734847	+	0.190217i
$135$	−1.86228	+	2.78710i	−0.160280	+	0.239875i
$136$	3.22304	+	3.39552i	0.276374	+	0.291164i
$137$	9.14412	−	6.10991i	0.781235	−	0.522005i	−0.0998271	−	0.995005i	$-0.531829\pi$
$137$	9.14412	−	6.10991i	0.781235	−	0.522005i	0.881062	+	0.473000i	$0.156829\pi$
$138$	1.74202	−	2.74789i	0.148291	−	0.233916i
$139$	−14.3526	+	7.67162i	−1.21737	+	0.650699i	−0.949806	−	0.312841i	$-0.898719\pi$
$139$	−14.3526	+	7.67162i	−1.21737	+	0.650699i	−0.267566	+	0.963540i	$0.586219\pi$
$140$	4.50981	−	17.9276i	0.381148	−	1.51516i
$141$	13.0276	+	1.28310i	1.09712	+	0.108057i
$142$	19.2709	−	6.35548i	1.61718	−	0.533340i
$143$	17.2981	−	7.16510i	1.44654	−	0.599176i
$144$	1.89269	−	3.52388i	0.157724	−	0.293657i
$145$	−7.89045	−	3.26833i	−0.655266	−	0.271420i
$146$	7.06396	+	0.524645i	0.584618	+	0.0434199i
$147$	0.466570	−	0.382904i	0.0384821	−	0.0315814i
$148$	−3.92139	−	1.85952i	−0.322337	−	0.152851i
$149$	10.5467	+	3.19930i	0.864017	+	0.262097i	0.691029	−	0.722827i	$-0.257158\pi$
$149$	10.5467	+	3.19930i	0.864017	+	0.262097i	0.172988	+	0.984924i	$0.444658\pi$
$150$	8.68847	+	1.51210i	0.709410	+	0.123462i
$151$	−3.77518	+	18.9791i	−0.307220	+	1.54450i	0.451016	+	0.892516i	$0.351062\pi$
$151$	−3.77518	+	18.9791i	−0.307220	+	1.54450i	−0.758235	+	0.651981i	$0.773938\pi$
$152$	−22.2698	+	6.12669i	−1.80632	+	0.496940i
$153$	−1.62340	+	0.322914i	−0.131244	+	0.0261061i
$154$	8.53363	+	8.13289i	0.687660	+	0.655367i
$155$	−1.29216	−	1.06045i	−0.103789	−	0.0851774i
$156$	−11.2034	+	5.28503i	−0.896993	+	0.423141i
$157$	−7.55801	+	14.1401i	−0.603195	+	1.12850i	0.376199	+	0.926539i	$0.377231\pi$
$157$	−7.55801	+	14.1401i	−0.603195	+	1.12850i	−0.979394	+	0.201960i	$0.935269\pi$
$158$	−18.6369	−	5.16763i	−1.48267	−	0.411114i
$159$	−2.63666	+	2.63666i	−0.209101	+	0.209101i
$160$	−18.9069	−	1.44252i	−1.49472	−	0.114041i
$161$	−4.48575	−	4.48575i	−0.353527	−	0.353527i
$162$	0.696444	+	1.23084i	0.0547178	+	0.0967039i
$163$	−15.7443	−	8.41548i	−1.23319	−	0.659151i	−0.279554	−	0.960130i	$-0.590187\pi$
$163$	−15.7443	−	8.41548i	−1.23319	−	0.659151i	−0.953631	+	0.300979i	$0.902687\pi$
$164$	−0.0705125	−	1.46542i	−0.00550610	−	0.114430i
$165$	−6.42830	+	7.83291i	−0.500443	+	0.609791i
$166$	1.86279	−	0.0447906i	0.144581	−	0.00347643i
$167$	0.758243	+	3.81194i	0.0586746	+	0.294977i	0.998970	−	0.0453834i	$-0.0144509\pi$
$167$	0.758243	+	3.81194i	0.0586746	+	0.294977i	−0.940295	+	0.340360i	$0.889451\pi$
$168$	−5.89798	−	5.10318i	−0.455039	−	0.393719i
$169$	24.8748	+	4.94791i	1.91345	+	0.380608i
$170$	4.51481	+	6.41740i	0.346270	+	0.492192i
$171$	2.37049	−	7.81446i	0.181276	−	0.597587i
$172$	−3.42810	−	0.171872i	−0.261390	−	0.0131051i
$173$	6.69504	+	8.15792i	0.509014	+	0.620236i	0.962583	−	0.270986i	$-0.0873495\pi$
$173$	6.69504	+	8.15792i	0.509014	+	0.620236i	−0.453569	+	0.891221i	$0.649850\pi$
$174$	−2.72960	+	2.35217i	−0.206930	+	0.178318i
$175$	6.58046	−	15.8866i	0.497436	−	1.20092i
$176$	6.73808	−	10.0404i	0.507902	−	0.756826i
$177$	−1.20503	−	2.90921i	−0.0905759	−	0.218670i
$178$	−21.4744	−	10.8229i	−1.60957	−	0.811207i
$179$	1.84366	−	18.7190i	0.137801	−	1.39912i	−0.638918	−	0.769275i	$-0.720618\pi$
$179$	1.84366	−	18.7190i	0.137801	−	1.39912i	0.776719	−	0.629847i	$-0.216882\pi$
$180$	3.99901	−	5.38071i	0.298068	−	0.401054i
$181$	1.53534	+	2.87241i	0.114121	+	0.213505i	0.932497	−	0.361178i	$-0.117625\pi$
$181$	1.53534	+	2.87241i	0.114121	+	0.213505i	−0.818376	+	0.574683i	$0.805125\pi$
$182$	5.28014	+	23.5690i	0.391390	+	1.74705i
$183$	−5.64578	−	8.44950i	−0.417348	−	0.624605i
$184$	−3.75486	+	5.31443i	−0.276812	+	0.391785i
$185$	−6.04793	−	4.04110i	−0.444653	−	0.297108i
$186$	−0.644886	+	0.285470i	−0.0472854	+	0.0209317i
$187$	−4.97951	+	0.490439i	−0.364138	+	0.0358644i
$188$	−25.8940	−	3.86765i	−1.88851	−	0.282078i
$189$	2.63872	−	0.800448i	0.191939	−	0.0582240i
$190$	−38.4223	+	4.71931i	−2.78745	+	0.342375i
$191$			9.47725i			0.685750i	0.939381	+	0.342875i	$0.111401\pi$
$191$			9.47725i			0.685750i	−0.939381	+	0.342875i	$0.888599\pi$
$192$	−4.13353	+	6.84937i	−0.298312	+	0.494311i
$193$		−	18.2856i		−	1.31623i	−0.752919	−	0.658113i	$-0.771355\pi$
$193$		−	18.2856i		−	1.31623i	0.752919	−	0.658113i	$-0.228645\pi$
$194$	0.874028	+	7.11591i	0.0627515	+	0.510893i
$195$	−19.8675	+	6.02673i	−1.42274	+	0.431583i
$196$	−0.970317	+	0.718123i	−0.0693083	+	0.0512945i
$197$	19.3145	−	1.90231i	1.37610	−	0.135534i	0.617233	−	0.786780i	$-0.288253\pi$
$197$	19.3145	−	1.90231i	1.37610	−	0.135534i	0.758867	+	0.651246i	$0.225753\pi$
$198$	1.73048	+	3.90921i	0.122980	+	0.277816i
$199$	−3.82304	−	2.55448i	−0.271008	−	0.181082i	0.412639	−	0.910895i	$-0.364607\pi$
$199$	−3.82304	−	2.55448i	−0.271008	−	0.181082i	−0.683647	+	0.729813i	$0.739607\pi$
$200$	−17.2037	−	3.89052i	−1.21649	−	0.275101i
$201$	0.927323	+	1.38784i	0.0654083	+	0.0978904i
$202$	22.6976	−	5.08492i	1.59700	−	0.357774i
$203$	3.31189	+	6.19610i	0.232449	+	0.434881i
$204$	3.27506	−	0.482440i	0.229300	−	0.0337776i
$205$	0.241014	−	2.44706i	0.0168332	−	0.170910i
$206$	−4.92009	+	9.76230i	−0.342799	+	0.680172i
$207$	−0.880402	−	2.12548i	−0.0611922	−	0.147731i
$208$	22.9080	−	9.43482i	1.58839	−	0.654187i
$209$	9.44681	−	22.8066i	0.653450	−	1.57757i
$210$	−8.53306	−	9.90226i	−0.588837	−	0.683321i
$211$	12.9802	+	15.8164i	0.893595	+	1.08885i	0.995566	+	0.0940619i	$0.0299851\pi$
$211$	12.9802	+	15.8164i	0.893595	+	1.08885i	−0.101971	+	0.994787i	$0.532515\pi$
$212$	5.53075	−	5.00265i	0.379854	−	0.343583i
$213$	4.16515	−	13.7307i	0.285392	−	0.940810i
$214$	−1.67391	+	1.17764i	−0.114426	+	0.0805018i
$215$	−5.64220	−	1.12230i	−0.384795	−	0.0765405i
$216$	−1.26788	−	2.52834i	−0.0862680	−	0.172032i
$217$	0.268269	+	1.34868i	0.0182113	+	0.0915543i
$218$	0.489343	+	20.3512i	0.0331425	+	1.37836i
$219$	3.17751	−	3.87180i	0.214716	−	0.261632i
$220$	13.6249	−	15.0024i	0.918592	−	1.01146i
$221$	−9.04133	−	4.83269i	−0.608186	−	0.325082i
$222$	−2.67089	+	1.51126i	−0.179258	+	0.101429i
$223$	−8.42798	−	8.42798i	−0.564379	−	0.564379i	0.366169	−	0.930548i	$-0.380669\pi$
$223$	−8.42798	−	8.42798i	−0.564379	−	0.564379i	−0.930548	+	0.366169i	$0.880669\pi$
$224$	11.2701	+	10.7842i	0.753014	+	0.720552i
$225$	4.40953	−	4.40953i	0.293969	−	0.293969i
$226$	6.68658	−	24.1150i	0.444785	−	1.60410i
$227$	4.11408	−	7.69691i	0.273061	−	0.510862i	−0.707590	−	0.706623i	$-0.750218\pi$
$227$	4.11408	−	7.69691i	0.273061	−	0.510862i	0.980652	+	0.195761i	$0.0627178\pi$
$228$	−5.51762	+	15.3719i	−0.365414	+	1.01803i
$229$	−14.6935	−	12.0587i	−0.970974	−	0.796858i	0.00818180	−	0.999967i	$-0.497396\pi$
$229$	−14.6935	−	12.0587i	−0.970974	−	0.796858i	−0.979156	+	0.203108i	$0.934896\pi$
$230$	−7.52406	+	7.89480i	−0.496122	+	0.520568i
$231$	8.17550	−	1.62621i	0.537908	−	0.106997i
$232$	5.68791	−	4.42509i	0.373430	−	0.290521i
$233$	−3.42318	+	17.2095i	−0.224260	+	1.12743i	0.690469	+	0.723362i	$0.257404\pi$
$233$	−3.42318	+	17.2095i	−0.224260	+	1.12743i	−0.914729	+	0.404069i	$0.867596\pi$
$234$	−1.50184	+	8.62953i	−0.0981784	+	0.564130i
$235$	−41.9905	−	12.7377i	−2.73916	−	0.830914i
$236$	2.11570	+	5.93180i	0.137720	+	0.386127i
$237$	−10.5713	+	8.67564i	−0.686680	+	0.563544i
$238$	0.478077	−	6.43696i	0.0309891	−	0.417246i
$239$	−12.4141	−	5.14210i	−0.803003	−	0.332615i	−0.0568446	−	0.998383i	$-0.518104\pi$
$239$	−12.4141	−	5.14210i	−0.803003	−	0.332615i	−0.746159	+	0.665768i	$0.768104\pi$
$240$	−8.52684	+	10.3474i	−0.550405	+	0.667924i
$241$	−17.9906	+	7.45196i	−1.15888	+	0.480023i	−0.877501	−	0.479574i	$-0.840791\pi$
$241$	−17.9906	+	7.45196i	−1.15888	+	0.480023i	−0.281377	+	0.959597i	$0.590791\pi$
$242$	−0.824638	−	2.50044i	−0.0530098	−	0.160734i
$243$	0.995185	+	0.0980171i	0.0638411	+	0.00628780i
$244$	10.4312	+	17.4432i	0.667789	+	1.11669i
$245$	−1.78430	+	0.953728i	−0.113995	+	0.0609314i
$246$	−0.876177	−	0.555451i	−0.0558630	−	0.0354143i
$247$	42.0544	−	28.0999i	2.67586	−	1.78795i
$248$	1.31674	−	0.505641i	0.0836133	−	0.0321082i
$249$	0.732004	−	1.09552i	0.0463889	−	0.0694259i
$250$	−5.46563	−	2.11149i	−0.345677	−	0.133542i
$251$	0.421089	+	4.27539i	0.0265789	+	0.269860i	0.999285	+	0.0378179i	$0.0120407\pi$
$251$	0.421089	+	4.27539i	0.0265789	+	0.269860i	−0.972706	+	0.232042i	$0.925459\pi$
$252$	−5.35099	+	1.33463i	−0.337081	+	0.0840737i
$253$	−2.01882	−	6.65515i	−0.126922	−	0.418406i
$254$	−3.31429	+	4.24247i	−0.207957	+	0.266196i
$255$	5.54827			0.347446
$256$	8.94263	−	13.2676i	0.558914	−	0.829225i
$257$	−22.1092			−1.37913			−0.689567	−	0.724222i	$-0.742199\pi$
$257$	−22.1092			−1.37913			−0.689567	+	0.724222i	$0.742199\pi$
$258$	−1.49418	+	1.91263i	−0.0930234	+	0.119075i
$259$	1.73695	+	5.72596i	0.107929	+	0.355794i
$260$	40.2886	−	10.0487i	2.49860	−	0.623193i
$261$	0.249736	+	2.53562i	0.0154583	+	0.156951i
$262$	−8.82958	−	3.41105i	−0.545493	−	0.210735i
$263$	−4.75646	+	7.11855i	−0.293296	+	0.438949i	−0.948629	−	0.316392i	$-0.897529\pi$
$263$	−4.75646	+	7.11855i	−0.293296	+	0.438949i	0.655332	+	0.755341i	$0.272529\pi$
$264$	−3.06512	−	7.98192i	−0.188645	−	0.491253i
$265$	10.3925	−	6.94407i	0.638408	−	0.426571i
$266$	26.8956	+	17.0504i	1.64907	+	1.04543i
$267$	−14.9963	+	8.01571i	−0.917761	+	0.490554i
$268$	−1.71333	−	2.86506i	−0.104658	−	0.175011i
$269$	−5.69777	−	0.561182i	−0.347399	−	0.0342158i	−0.0771871	−	0.997017i	$-0.524594\pi$
$269$	−5.69777	−	0.561182i	−0.347399	−	0.0342158i	−0.270212	+	0.962801i	$0.587094\pi$
$270$	−1.48473	−	4.50196i	−0.0903579	−	0.273980i
$271$	−17.6558	+	7.31328i	−1.07251	+	0.444250i	−0.847877	−	0.530192i	$-0.822120\pi$
$271$	−17.6558	+	7.31328i	−1.07251	+	0.444250i	−0.224637	+	0.974442i	$0.572120\pi$
$272$	−6.59022	+	0.635684i	−0.399591	+	0.0385440i
$273$	15.7789	+	6.53582i	0.954980	+	0.395566i
$274$	−1.15195	+	15.5102i	−0.0695918	+	0.937003i
$275$	14.5722	−	11.9591i	0.878735	−	0.721159i
$276$	1.54574	+	4.33380i	0.0930424	+	0.260864i
$277$	26.0505	+	7.90234i	1.56522	+	0.474806i	0.949661	−	0.313281i	$-0.101428\pi$
$277$	26.0505	+	7.90234i	1.56522	+	0.474806i	0.615564	+	0.788087i	$0.288928\pi$
$278$	3.94615	−	22.6744i	0.236674	−	1.35992i
$279$	−0.0972885	+	0.489102i	−0.00582451	+	0.0292818i
$280$	16.0530	+	20.6342i	0.959352	+	1.23313i
$281$	20.2298	−	4.02395i	1.20681	−	0.240049i	0.449604	−	0.893228i	$-0.351565\pi$
$281$	20.2298	−	4.02395i	1.20681	−	0.240049i	0.757203	+	0.653179i	$0.226565\pi$
$282$	−12.7721	+	13.4015i	−0.760570	+	0.798047i
$283$	−2.42569	−	1.99071i	−0.144192	−	0.118335i	0.559532	−	0.828809i	$-0.310981\pi$
$283$	−2.42569	−	1.99071i	−0.144192	−	0.118335i	−0.703724	+	0.710473i	$0.748481\pi$
$284$	−9.69493	+	27.0098i	−0.575288	+	1.60273i
$285$	−12.9035	+	24.1407i	−0.764336	+	1.42997i
$286$	−7.07507	+	25.5161i	−0.418358	+	1.50880i
$287$	−1.43030	+	1.43030i	−0.0844281	+	0.0844281i
$288$	2.27937	+	5.17731i	0.134313	+	0.305076i
$289$	−10.0836	−	10.0836i	−0.593150	−	0.593150i
$290$	10.5121	−	5.94802i	0.617289	−	0.349280i
$291$	4.47092	+	2.38976i	0.262090	+	0.140090i
$292$	−6.73479	+	7.41568i	−0.394124	+	0.433970i
$293$	4.50124	−	5.48478i	0.262966	−	0.320424i	−0.624743	−	0.780831i	$-0.714796\pi$
$293$	4.50124	−	5.48478i	0.262966	−	0.320424i	0.887708	+	0.460406i	$0.152296\pi$
$294$	0.0205184	+	0.853338i	0.00119666	+	0.0497677i
$295$	2.05922	+	10.3524i	0.119892	+	0.602738i
$296$	5.48642	−	2.75126i	0.318892	−	0.159914i
$297$	2.96487	+	0.589749i	0.172039	+	0.0342207i
$298$	−12.7477	+	8.96835i	−0.738455	+	0.519523i
$299$	4.13635	−	13.6357i	0.239211	−	0.788574i
$300$	−9.24960	+	8.36640i	−0.534026	+	0.483034i
$301$	3.00218	+	3.65816i	0.173043	+	0.210853i
$302$	−17.8645	−	20.7310i	−1.02799	−	1.19294i
$303$	6.29418	−	15.1955i	0.361591	−	0.872958i
$304$	12.5609	−	30.1527i	0.720414	−	1.72938i
$305$	13.0356	+	31.4707i	0.746416	+	1.80201i
$306$	1.05351	−	2.09034i	0.0602250	−	0.119497i
$307$	−2.35757	+	23.9368i	−0.134554	+	1.36615i	0.656466	+	0.754355i	$0.272050\pi$
$307$	−2.35757	+	23.9368i	−0.134554	+	1.36615i	−0.791020	+	0.611790i	$0.790450\pi$
$308$	−16.4933	+	2.42959i	−0.939796	+	0.138439i
$309$	3.64396	+	6.81737i	0.207298	+	0.387826i
$310$	2.30682	−	0.516793i	0.131018	−	0.0293519i
$311$	−5.30914	−	7.94569i	−0.301054	−	0.450559i	0.649842	−	0.760069i	$-0.274835\pi$
$311$	−5.30914	−	7.94569i	−0.301054	−	0.450559i	−0.950896	+	0.309510i	$0.899835\pi$
$312$	3.86413	−	17.0870i	0.218763	−	0.967361i
$313$	27.2116	+	18.1822i	1.53809	+	1.02772i	0.980247	+	0.197775i	$0.0633715\pi$
$313$	27.2116	+	18.1822i	1.53809	+	1.02772i	0.557845	+	0.829945i	$0.311628\pi$
$314$	−9.17817	−	20.7338i	−0.517954	−	1.17008i
$315$	−9.19854	+	0.905977i	−0.518279	+	0.0510460i
$316$	21.9849	−	16.2708i	1.23675	−	0.915306i
$317$	−11.0760	+	3.35985i	−0.622088	+	0.188708i	−0.585566	−	0.810625i	$-0.699128\pi$
$317$	−11.0760	+	3.35985i	−0.622088	+	0.188708i	−0.0365215	+	0.999333i	$0.511628\pi$
$318$	−0.642875	−	5.23398i	−0.0360506	−	0.293507i
$319$			7.70214i			0.431237i
$320$	18.0686	−	19.8150i	1.01006	−	1.10769i
$321$			1.44721i			0.0807752i
$322$	8.90459	−	1.09373i	0.496233	−	0.0609510i
$323$	−12.9345	+	3.92364i	−0.719696	+	0.218317i
$324$	−1.97806	−	0.295453i	−0.109892	−	0.0164140i
$325$	38.4382	−	3.78583i	2.13217	−	0.210000i
$326$	23.0861	−	10.2194i	1.27862	−	0.566003i
$327$	11.9687	+	7.99723i	0.661871	+	0.442248i
$328$	1.69453	+	1.19726i	0.0935648	+	0.0661074i
$329$	20.0543	+	30.0134i	1.10563	+	1.65469i
$330$	−3.13273	−	13.9836i	−0.172451	−	0.769772i
$331$	2.47669	+	4.63355i	0.136131	+	0.254683i	0.940745	−	0.339115i	$-0.110128\pi$
$331$	2.47669	+	4.63355i	0.136131	+	0.254683i	−0.804614	+	0.593798i	$0.797628\pi$
$332$	−1.57189	+	2.11499i	−0.0862684	+	0.116075i
$333$	−0.212695	+	2.15952i	−0.0116556	+	0.118341i
$334$	−4.90838	−	2.47377i	−0.268574	−	0.135358i
$335$	−2.14110	−	5.16908i	−0.116981	−	0.282417i
$336$	10.8222	−	2.13003i	0.590400	−	0.116202i
$337$	−1.87411	+	4.52450i	−0.102089	+	0.246465i	−0.966669	−	0.256031i	$-0.917585\pi$
$337$	−1.87411	+	4.52450i	−0.102089	+	0.246465i	0.864579	+	0.502497i	$0.167585\pi$
$338$	−27.1710	+	23.4140i	−1.47791	+	1.27355i
$339$	−11.2257	−	13.6786i	−0.609698	−	0.742919i
$340$	−11.0826	−	0.555640i	−0.601039	−	0.0301338i
$341$	−0.437604	+	1.44259i	−0.0236976	+	0.0781204i
$342$	6.64502	+	9.44530i	0.359322	+	0.510743i
$343$	−17.2990	−	3.44098i	−0.934056	−	0.185795i
$344$	3.17615	−	3.67082i	0.171246	−	0.197917i
$345$	1.50447	+	7.56348i	0.0809979	+	0.407204i
$346$	−14.9205	+	0.358762i	−0.802132	+	0.0192872i
$347$	−1.59879	+	1.94813i	−0.0858276	+	0.104581i	−0.814154	−	0.580650i	$-0.802799\pi$
$347$	−1.59879	+	1.94813i	−0.0858276	+	0.104581i	0.728326	+	0.685231i	$0.240299\pi$
$348$	−0.244913	−	5.08988i	−0.0131287	−	0.272846i
$349$	−7.09070	−	3.79006i	−0.379557	−	0.202877i	0.270575	−	0.962699i	$-0.412786\pi$
$349$	−7.09070	−	3.79006i	−0.379557	−	0.202877i	−0.650132	+	0.759822i	$0.725286\pi$
$350$	11.9757	+	21.1650i	0.640130	+	1.13132i
$351$	4.37962	+	4.37962i	0.233767	+	0.233767i
$352$	5.32320	+	16.2508i	0.283727	+	0.866169i
$353$	1.18988	−	1.18988i	0.0633309	−	0.0633309i	−0.674732	−	0.738063i	$-0.735741\pi$
$353$	1.18988	−	1.18988i	0.0633309	−	0.0633309i	0.738063	+	0.674732i	$0.235741\pi$
$354$	4.29131	+	1.18989i	0.228081	+	0.0632421i
$355$	−22.6725	+	42.4173i	−1.20333	+	2.25128i
$356$	30.7578	−	14.5095i	1.63016	−	0.769001i
$357$	−3.52814	−	2.89547i	−0.186729	−	0.153244i
$358$	19.2563	+	18.3520i	1.01772	+	0.969932i
$359$	−26.5730	+	5.28570i	−1.40247	+	0.278968i	−0.837632	−	0.546234i	$-0.816061\pi$
$359$	−26.5730	+	5.28570i	−1.40247	+	0.278968i	−0.564837	+	0.825203i	$0.691061\pi$
$360$	2.51488	+	9.14131i	0.132546	+	0.481789i
$361$	9.30288	−	46.7687i	0.489625	−	2.46151i
$362$	−4.53788	−	0.789750i	−0.238506	−	0.0415083i
$363$	−1.78159	−	0.540438i	−0.0935090	−	0.0283656i
$364$	−30.8636	−	14.6354i	−1.61769	−	0.767105i
$365$	−12.9784	+	10.6511i	−0.679318	+	0.557502i
$366$	14.3319	+	1.06444i	0.749143	+	0.0556393i
$367$	7.51186	+	3.11151i	0.392116	+	0.162420i	0.570025	−	0.821627i	$-0.306933\pi$
$367$	7.51186	+	3.11151i	0.392116	+	0.162420i	−0.177909	+	0.984047i	$0.556933\pi$
$368$	−2.65358	−	8.81152i	−0.138327	−	0.459332i
$369$	−0.677719	+	0.280720i	−0.0352806	+	0.0146137i
$370$	9.76912	−	3.22183i	0.507872	−	0.167495i
$371$	−10.2325	−	1.00781i	−0.531244	−	0.0523230i
$372$	0.243315	−	0.967234i	0.0126153	−	0.0501487i
$373$	−17.9348	+	9.58633i	−0.928627	+	0.496361i	−0.865089	−	0.501618i	$-0.832738\pi$
$373$	−17.9348	+	9.58633i	−0.928627	+	0.496361i	−0.0635377	+	0.997979i	$0.520238\pi$
$374$	3.78874	−	5.97641i	0.195911	−	0.309033i
$375$	−3.44491	+	2.30181i	−0.177894	+	0.118865i
$376$	26.8544	−	25.4903i	1.38491	−	1.31456i
$377$	−8.76739	+	13.1213i	−0.451544	+	0.675783i
$378$	−1.40529	+	3.63762i	−0.0722804	+	0.187099i
$379$	2.41575	+	24.5276i	0.124089	+	1.25990i	0.832472	+	0.554068i	$0.186925\pi$
$379$	2.41575	+	24.5276i	0.124089	+	1.25990i	−0.708383	+	0.705829i	$0.750575\pi$
$380$	28.1922	−	46.9286i	1.44623	−	2.40739i
$381$	1.10505	+	3.64286i	0.0566134	+	0.186629i
$382$	−10.5619	−	8.25118i	−0.540396	−	0.422167i
$383$	−22.1078			−1.12965			−0.564827	−	0.825209i	$-0.691057\pi$
$383$	−22.1078			−1.12965			−0.564827	+	0.825209i	$0.691057\pi$
$384$	−4.03452	−	10.5699i	−0.205886	−	0.539393i
$385$	−27.9413			−1.42402
$386$	20.3784	+	15.9200i	1.03723	+	0.810306i
$387$	0.498187	+	1.64230i	0.0253243	+	0.0834830i
$388$	−8.69130	−	5.22127i	−0.441234	−	0.265070i
$389$	−3.28821	−	33.3858i	−0.166719	−	1.69272i	−0.606870	−	0.794801i	$-0.707575\pi$
$389$	−3.28821	−	33.3858i	−0.166719	−	1.69272i	0.440151	−	0.897924i	$-0.354925\pi$
$390$	10.5807	−	27.3884i	0.535775	−	1.38687i
$391$	−2.11559	+	3.16621i	−0.106990	+	0.160122i
$392$	0.0444735	−	1.70659i	0.00224625	−	0.0861958i
$393$	−5.56516	+	3.71852i	−0.280725	+	0.187574i
$394$	−14.6957	+	23.1813i	−0.740360	+	1.16786i
$395$	40.4277	−	21.6091i	2.03414	−	1.08727i
$396$	−5.86324	−	1.47494i	−0.294639	−	0.0741185i
$397$	−15.1334	−	1.49051i	−0.759524	−	0.0748066i	−0.289162	−	0.957280i	$-0.593377\pi$
$397$	−15.1334	−	1.49051i	−0.759524	−	0.0748066i	−0.470362	+	0.882474i	$0.655877\pi$
$398$	6.17530	−	2.03660i	0.309540	−	0.102085i
$399$	20.8036	−	8.61713i	1.04148	−	0.431396i
$400$	19.3139	−	15.7855i	0.965693	−	0.789275i
$401$	9.26204	+	3.83646i	0.462524	+	0.191584i	0.601762	−	0.798675i	$-0.294465\pi$
$401$	9.26204	+	3.83646i	0.462524	+	0.191584i	−0.139238	+	0.990259i	$0.544465\pi$
$402$	−2.35403	−	0.174835i	−0.117408	−	0.00872000i
$403$	−2.38760	+	1.95946i	−0.118935	+	0.0976075i
$404$	−14.0943	+	29.7225i	−0.701219	+	1.47875i
$405$	−3.20768	−	0.973039i	−0.159391	−	0.0483507i
$406$	−9.78869	−	1.70358i	−0.485804	−	0.0845470i
$407$	−1.27974	+	6.43368i	−0.0634343	+	0.318906i
$408$	−2.31371	+	4.06993i	−0.114546	+	0.201491i
$409$	19.2872	−	3.83646i	0.953690	−	0.189701i	0.306364	−	0.951914i	$-0.400887\pi$
$409$	19.2872	−	3.83646i	0.953690	−	0.189701i	0.647326	+	0.762214i	$0.275887\pi$
$410$	2.51729	+	2.39908i	0.124320	+	0.118482i
$411$	8.50122	+	6.97677i	0.419334	+	0.344139i
$412$	−6.59604	−	13.9826i	−0.324963	−	0.688871i
$413$	4.09313	−	7.65770i	0.201410	−	0.376811i
$414$	3.13525	+	0.869340i	0.154089	+	0.0427257i
$415$	−3.12296	+	3.12296i	−0.153300	+	0.153300i
$416$	−9.42977	+	33.7442i	−0.462333	+	1.65444i
$417$	−11.5076	−	11.5076i	−0.563531	−	0.563531i
$418$	17.1922	+	30.3841i	0.840898	+	1.48614i
$419$	1.65659	+	0.885466i	0.0809297	+	0.0432578i	0.511365	−	0.859364i	$-0.329140\pi$
$419$	1.65659	+	0.885466i	0.0809297	+	0.0432578i	−0.430435	+	0.902621i	$0.641640\pi$
$420$	18.4647	−	0.888479i	0.900987	−	0.0433533i
$421$	−6.42546	+	7.82945i	−0.313158	+	0.381584i	−0.905674	−	0.423975i	$-0.860635\pi$
$421$	−6.42546	+	7.82945i	−0.313158	+	0.381584i	0.592516	+	0.805558i	$0.298135\pi$
$422$	−28.9276	+	0.695562i	−1.40818	+	0.0338594i
$423$	2.55385	+	12.8391i	0.124172	+	0.624257i
$424$	0.759972	+	10.5192i	0.0369075	+	0.510858i
$425$	−10.1235	−	2.01370i	−0.491064	−	0.0976787i
$426$	11.6759	+	16.5962i	0.565697	+	0.804088i
$427$	8.13425	−	26.8150i	0.393644	−	1.29767i
$428$	0.144933	−	2.89078i	0.00700559	−	0.139731i
$429$	11.8779	+	14.4733i	0.573473	+	0.698779i
$430$	6.16303	−	5.31085i	0.297207	−	0.256112i
$431$	−1.82271	+	4.40041i	−0.0877969	+	0.211960i	−0.961679	−	0.274177i	$-0.911595\pi$
$431$	−1.82271	+	4.40041i	−0.0877969	+	0.211960i	0.873882	+	0.486137i	$0.161595\pi$
$432$	3.92156	+	0.788260i	0.188676	+	0.0379252i
$433$	−2.23660	−	5.39962i	−0.107484	−	0.259489i	0.860982	−	0.508636i	$-0.169850\pi$
$433$	−2.23660	−	5.39962i	−0.107484	−	0.259489i	−0.968466	+	0.249146i	$0.919850\pi$
$434$	−1.73660	−	0.875227i	−0.0833595	−	0.0420123i
$435$	0.837121	−	8.49943i	0.0401369	−	0.407517i
$436$	−23.1065	−	17.1730i	−1.10660	−	0.822438i
$437$	−8.85609	−	16.5686i	−0.423644	−	0.792583i
$438$	1.54851	+	6.91209i	0.0739905	+	0.330272i
$439$	6.49893	+	9.72634i	0.310177	+	0.464213i	0.953505	−	0.301378i	$-0.0974467\pi$
$439$	6.49893	+	9.72634i	0.310177	+	0.464213i	−0.643328	+	0.765591i	$0.722447\pi$
$440$	4.85719	+	28.2458i	0.231557	+	1.34657i
$441$	0.501855	+	0.335329i	0.0238978	+	0.0159680i
$442$	13.2575	−	5.86864i	0.630593	−	0.279143i
$443$	−11.8616	+	1.16827i	−0.563563	+	0.0555061i	−0.375788	−	0.926706i	$-0.622628\pi$
$443$	−11.8616	+	1.16827i	−0.563563	+	0.0555061i	−0.187776	+	0.982212i	$0.560128\pi$
$444$	0.641124	−	4.29233i	0.0304264	−	0.203705i
$445$	54.5440	−	16.5457i	2.58563	−	0.784343i
$446$	16.7302	−	2.05493i	0.792199	−	0.0973036i
$447$			11.0212i			0.521287i
$448$	−21.8306	+	3.17090i	−1.03140	+	0.149811i
$449$			18.1664i			0.857324i	0.903465	+	0.428662i	$0.141015\pi$
$449$			18.1664i			0.857324i	−0.903465	+	0.428662i	$0.858985\pi$
$450$	1.07514	+	8.75328i	0.0506826	+	0.412634i
$451$	−2.12202	+	0.643709i	−0.0999223	+	0.0303111i
$452$	21.0534	+	28.4471i	0.990270	+	1.33804i
$453$	−19.2577	+	1.89672i	−0.904807	+	0.0891158i
$454$	4.99599	+	11.2861i	0.234473	+	0.529683i
$455$	−47.6007	−	31.8057i	−2.23155	−	1.49108i
$456$	−12.3275	−	19.5324i	−0.577286	−	0.914688i
$457$	−13.3204	−	19.9354i	−0.623104	−	0.932541i	−0.999980	−	0.00627730i	$-0.998002\pi$
$457$	−13.3204	−	19.9354i	−0.623104	−	0.932541i	0.376876	−	0.926264i	$-0.376998\pi$
$458$	26.2314	−	5.87659i	1.22571	−	0.274595i
$459$	−0.780257	−	1.45976i	−0.0364193	−	0.0681357i
$460$	−2.24771	−	15.2587i	−0.104800	−	0.711438i
$461$	−1.85153	+	18.7989i	−0.0862343	+	0.875551i	0.850608	+	0.525800i	$0.176234\pi$
$461$	−1.85153	+	18.7989i	−0.0862343	+	0.875551i	−0.936843	+	0.349751i	$0.886266\pi$
$462$	−5.30551	+	10.5270i	−0.246834	+	0.489762i
$463$	−12.0608	−	29.1174i	−0.560515	−	1.35320i	−0.909355	−	0.416020i	$-0.863425\pi$
$463$	−12.0608	−	29.1174i	−0.560515	−	1.35320i	0.348841	−	0.937182i	$-0.386575\pi$
$464$	−0.0205227	+	10.1915i	−0.000952742	+	0.473130i
$465$	0.639693	−	1.54436i	0.0296650	−	0.0716177i
$466$	−16.1988	−	18.7981i	−0.750396	−	0.870804i
$467$	19.4433	+	23.6917i	0.899727	+	1.09632i	0.994901	+	0.100860i	$0.0321594\pi$
$467$	19.4433	+	23.6917i	0.899727	+	1.09632i	−0.0951735	+	0.995461i	$0.530341\pi$
$468$	−8.30965	−	9.18686i	−0.384114	−	0.424663i
$469$	−1.33606	+	4.40439i	−0.0616934	+	0.203376i
$470$	50.7537	−	35.7066i	2.34109	−	1.64702i
$471$	−15.7252	−	3.12793i	−0.724577	−	0.144127i
$472$	−8.45270	−	2.80656i	−0.389067	−	0.129182i
$473$	1.01213	+	5.08831i	0.0465377	+	0.233961i
$474$	−0.464896	−	19.3345i	−0.0213534	−	0.888062i
$475$	32.3058	−	39.3647i	1.48229	−	1.80618i
$476$	6.75745	+	6.13700i	0.309727	+	0.281289i
$477$	−3.28850	−	1.75774i	−0.150570	−	0.0804815i
$478$	16.5387	−	9.35808i	0.756464	−	0.428029i
$479$	−12.1606	−	12.1606i	−0.555633	−	0.555633i	0.372428	−	0.928061i	$-0.378525\pi$
$479$	−12.1606	−	12.1606i	−0.555633	−	0.555633i	−0.928061	+	0.372428i	$0.878525\pi$
$480$	−4.10799	−	18.5115i	−0.187503	−	0.844932i
$481$	−9.50366	+	9.50366i	−0.433329	+	0.433329i
$482$	7.35833	−	26.5376i	0.335163	−	1.20875i
$483$	2.99045	−	5.59475i	0.136070	−	0.254570i
$484$	3.50458	+	1.25794i	0.159299	+	0.0571791i
$485$	−13.1359	−	10.7803i	−0.596469	−	0.489509i
$486$	−0.975673	+	1.02375i	−0.0442574	+	0.0464382i
$487$	−19.0198	+	3.78328i	−0.861871	+	0.171437i	−0.606186	−	0.795323i	$-0.707301\pi$
$487$	−19.0198	+	3.78328i	−0.861871	+	0.171437i	−0.255686	+	0.966760i	$0.582301\pi$
$488$	−28.5213	−	3.56151i	−1.29110	−	0.161222i
$489$	3.48280	−	17.5092i	0.157497	−	0.791793i
$490$	0.490581	−	2.81886i	0.0221622	−	0.127343i
$491$	−14.4202	−	4.37433i	−0.650777	−	0.197411i	−0.0524004	−	0.998626i	$-0.516687\pi$
$491$	−14.4202	−	4.37433i	−0.650777	−	0.197411i	−0.598376	+	0.801215i	$0.704187\pi$
$492$	1.38185	−	0.492865i	0.0622986	−	0.0222201i
$493$	3.25999	−	2.67541i	0.146823	−	0.120494i
$494$	−5.29789	+	71.3323i	−0.238363	+	3.20939i
$495$	−9.36166	−	3.87773i	−0.420776	−	0.174291i
$496$	−0.582884	+	1.90767i	−0.0261723	+	0.0856571i
$497$	36.5537	−	15.1410i	1.63966	−	0.679168i
$498$	0.583602	+	1.76958i	0.0261518	+	0.0792967i
$499$	9.73265	+	0.958583i	0.435693	+	0.0429121i	0.313487	−	0.949593i	$-0.398503\pi$
$499$	9.73265	+	0.958583i	0.435693	+	0.0429121i	0.122207	+	0.992505i	$0.461003\pi$
$500$	7.11169	−	4.25286i	0.318045	−	0.190194i
$501$	−3.42770	+	1.83214i	−0.153138	+	0.0818540i
$502$	−5.13132	−	3.25300i	−0.229022	−	0.145188i
$503$	−24.7380	+	16.5294i	−1.10301	+	0.737009i	−0.967273	−	0.253736i	$-0.918341\pi$
$503$	−24.7380	+	16.5294i	−1.10301	+	0.737009i	−0.135738	+	0.990745i	$0.543341\pi$
$504$	3.17135	−	7.12539i	0.141263	−	0.317390i
$505$	−30.6298	+	45.8408i	−1.36301	+	2.03989i
$506$	9.17449	+	3.54430i	0.407856	+	0.157563i
$507$	2.48592	+	25.2400i	0.110404	+	1.12095i
$508$	−1.84251	−	7.38724i	−0.0817480	−	0.327756i
$509$	−11.8641	−	39.1106i	−0.525865	−	1.73355i	−0.668444	−	0.743763i	$-0.733039\pi$
$509$	−11.8641	−	39.1106i	−0.525865	−	1.73355i	0.142578	−	0.989784i	$-0.454461\pi$
$510$	−4.83049	+	6.18328i	−0.213898	+	0.273800i
$511$	13.8114			0.610979
$512$	7.00039	+	21.5173i	0.309376	+	0.950940i
$513$	8.16609			0.360542
$514$	19.2489	−	24.6396i	0.849033	−	1.08681i
$515$	−7.52172	−	24.7958i	−0.331447	−	1.09263i
$516$	−0.830654	−	3.33038i	−0.0365675	−	0.146612i
$517$	3.87876	+	39.3817i	0.170588	+	1.73201i
$518$	−7.89355	−	3.04944i	−0.346822	−	0.133985i
$519$	−5.86318	+	8.77487i	−0.257365	+	0.385174i
$520$	−23.8777	+	53.6484i	−1.04711	+	2.35264i
$521$	16.9859	−	11.3496i	0.744165	−	0.497235i	−0.124755	−	0.992188i	$-0.539815\pi$
$521$	16.9859	−	11.3496i	0.744165	−	0.497235i	0.868920	+	0.494952i	$0.164815\pi$
$522$	−3.04325	−	1.92926i	−0.133199	−	0.0844416i
$523$	6.59925	−	3.52737i	0.288565	−	0.154241i	−0.320763	−	0.947160i	$-0.603939\pi$
$523$	6.59925	−	3.52737i	0.288565	−	0.154241i	0.609328	+	0.792918i	$0.291439\pi$
$524$	11.4887	−	6.87038i	0.501888	−	0.300134i
$525$	17.1128	+	1.68546i	0.746862	+	0.0735595i
$526$	−3.79216	−	11.4985i	−0.165346	−	0.501357i
$527$	0.762592	−	0.315876i	0.0332190	−	0.0137598i
$528$	11.5641	+	3.53336i	0.503261	+	0.153770i
$529$	16.3593	+	6.77626i	0.711276	+	0.294620i
$530$	−1.30922	+	17.6277i	−0.0568689	+	0.765698i
$531$	2.43414	−	1.99764i	0.105633	−	0.0866904i
$532$	−42.4180	+	15.1292i	−1.83905	+	0.655935i
$533$	−4.34781	−	1.31889i	−0.188324	−	0.0571276i
$534$	4.12314	−	23.6914i	0.178426	−	1.02523i
$535$	0.946395	−	4.75785i	0.0409162	−	0.205700i
$536$	4.68465	+	0.584980i	0.202346	+	0.0252673i
$537$	18.4481	−	3.66956i	0.796096	−	0.158353i
$538$	5.58606	−	5.86131i	0.240832	−	0.252699i
$539$	1.41042	+	1.15750i	0.0607511	+	0.0498571i
$540$	6.30987	+	2.26488i	0.271533	+	0.0974647i
$541$	−19.0736	+	35.6842i	−0.820037	+	1.53418i	0.0251326	+	0.999684i	$0.491999\pi$
$541$	−19.0736	+	35.6842i	−0.820037	+	1.53418i	−0.845170	+	0.534498i	$0.820501\pi$
$542$	7.22139	−	26.0437i	0.310185	−	1.11867i
$543$	−2.30304	+	2.30304i	−0.0988330	+	0.0988330i
$544$	5.02921	−	7.89793i	0.215626	−	0.338621i
$545$	−34.1186	−	34.1186i	−1.46148	−	1.46148i
$546$	−21.0214	+	11.8945i	−0.899633	+	0.509038i
$547$	−0.529867	−	0.283220i	−0.0226555	−	0.0121096i	0.460030	−	0.887903i	$-0.347839\pi$
$547$	−0.529867	−	0.283220i	−0.0226555	−	0.0121096i	−0.482686	+	0.875794i	$0.660339\pi$
$548$	−16.2824	−	14.7874i	−0.695550	−	0.631686i
$549$	6.44679	−	7.85543i	0.275142	−	0.335262i
$550$	0.640843	+	26.6519i	0.0273256	+	1.13644i
$551$	4.05910	+	20.4065i	0.172923	+	0.869345i
$552$	−6.17557	−	2.05048i	−0.262850	−	0.0872744i
$553$	−36.9850	−	7.35678i	−1.57276	−	0.312842i
$554$	−31.4872	+	22.1521i	−1.33776	+	0.941151i
$555$	2.11147	−	6.96058i	0.0896269	−	0.295460i
$556$	21.8339	+	24.1388i	0.925965	+	1.02371i
$557$	19.0640	+	23.2296i	0.807769	+	0.984269i	0.999996	+	0.00291890i	$0.000929115\pi$
$557$	19.0640	+	23.2296i	0.807769	+	0.984269i	−0.192227	+	0.981351i	$0.561571\pi$
$558$	−0.460379	−	0.534250i	−0.0194894	−	0.0226166i
$559$	−4.06780	+	9.82054i	−0.172050	+	0.415365i
$560$	−36.9721	−	0.0744508i	−1.56236	−	0.00314612i
$561$	−1.91480	−	4.62272i	−0.0808427	−	0.195172i
$562$	−13.1281	+	26.0485i	−0.553777	+	1.09879i
$563$	3.21199	−	32.6119i	0.135369	−	1.37443i	−0.652128	−	0.758109i	$-0.726123\pi$
$563$	3.21199	−	32.6119i	0.135369	−	1.37443i	0.787497	−	0.616318i	$-0.211377\pi$
$564$	−3.81550	−	25.9017i	−0.160662	−	1.09066i
$565$	27.9608	+	52.3109i	1.17632	+	2.20074i
$566$	4.33043	−	0.970140i	0.182021	−	0.0407780i
$567$	1.53196	+	2.29274i	0.0643363	+	0.0962861i
$568$	−21.6604	−	34.3200i	−0.908849	−	1.44004i
$569$	−2.00649	−	1.34069i	−0.0841163	−	0.0562047i	0.512801	−	0.858508i	$-0.328608\pi$
$569$	−2.00649	−	1.34069i	−0.0841163	−	0.0562047i	−0.596917	+	0.802303i	$0.703608\pi$
$570$	−15.6695	−	35.3979i	−0.656324	−	1.48266i
$571$	13.7718	−	1.35641i	0.576333	−	0.0567638i	0.194348	−	0.980933i	$-0.437741\pi$
$571$	13.7718	−	1.35641i	0.576333	−	0.0567638i	0.381984	+	0.924169i	$0.375241\pi$
$572$	−22.2766	−	30.0999i	−0.931433	−	1.25854i
$573$	−9.06916	+	2.75110i	−0.378870	+	0.114929i
$574$	−0.348739	−	2.83927i	−0.0145561	−	0.118509i
$575$		−	14.3466i		−	0.598295i
$576$	−7.75434	−	1.96727i	−0.323098	−	0.0819697i
$577$			17.6961i			0.736697i	0.929688	+	0.368349i	$0.120077\pi$
$577$			17.6961i			0.736697i	−0.929688	+	0.368349i	$0.879923\pi$
$578$	20.0167	−	2.45859i	0.832584	−	0.102264i
$579$	17.4982	−	5.30803i	0.727201	−	0.220594i
$580$	−2.52333	+	16.8937i	−0.104776	+	0.701473i
$581$	3.61566	−	0.356111i	0.150003	−	0.0147740i
$582$	−6.55579	+	2.90203i	−0.271746	+	0.120293i
$583$	−9.37231	−	6.26238i	−0.388161	−	0.259361i
$584$	−2.40091	−	13.9619i	−0.0993502	−	0.577748i
$585$	−11.5344	−	17.2625i	−0.476891	−	0.713717i
$586$	2.19361	+	9.79164i	0.0906171	+	0.404489i
$587$	3.29025	+	6.15563i	0.135803	+	0.254070i	0.940626	−	0.339446i	$-0.110239\pi$
$587$	3.29025	+	6.15563i	0.135803	+	0.254070i	−0.804822	+	0.593516i	$0.797739\pi$
$588$	−0.968869	−	0.720075i	−0.0399555	−	0.0296954i
$589$	−0.399155	+	4.05269i	−0.0164469	+	0.166988i
$590$	−13.3300	−	6.71819i	−0.548789	−	0.276584i
$591$	7.42710	+	17.9306i	0.305510	+	0.737566i
$592$	−1.71050	+	8.50968i	−0.0703012	+	0.349746i
$593$	11.9144	−	28.7640i	0.489267	−	1.18120i	−0.465823	−	0.884878i	$-0.654242\pi$
$593$	11.9144	−	28.7640i	0.489267	−	1.18120i	0.955090	−	0.296317i	$-0.0957585\pi$
$594$	−3.23855	+	2.79075i	−0.132879	+	0.114506i
$595$	9.70566	+	11.8264i	0.397893	+	0.484834i
$596$	1.10374	−	22.0148i	0.0452109	−	0.901762i
$597$	1.33471	−	4.39995i	0.0546261	−	0.180078i
$598$	11.5951	+	16.4814i	0.474160	+	0.673976i
$599$	19.6942	+	3.91742i	0.804683	+	0.160061i	0.580261	−	0.814431i	$-0.302951\pi$
$599$	19.6942	+	3.91742i	0.804683	+	0.160061i	0.224422	+	0.974492i	$0.427951\pi$
$600$	−1.27097	−	17.5923i	−0.0518873	−	0.718202i
$601$	−7.14508	−	35.9207i	−0.291454	−	1.46524i	−0.797808	−	0.602912i	$-0.794007\pi$
$601$	−7.14508	−	35.9207i	−0.291454	−	1.46524i	0.506354	−	0.862326i	$-0.330993\pi$
$602$	−6.69063	+	0.160876i	−0.272690	+	0.00655680i
$603$	−1.05889	+	1.29026i	−0.0431213	+	0.0525435i
$604$	38.6571	−	1.86009i	1.57294	−	0.0756859i
$605$	5.50374	+	2.94181i	0.223759	+	0.119602i
$606$	11.4547	+	20.2442i	0.465317	+	0.822365i
$607$	−1.85030	−	1.85030i	−0.0751015	−	0.0751015i	0.668558	−	0.743660i	$-0.266912\pi$
$607$	−1.85030	−	1.85030i	−0.0751015	−	0.0751015i	−0.743660	+	0.668558i	$0.766912\pi$
$608$	22.6679	+	40.2503i	0.919304	+	1.63237i
$609$	−4.96791	+	4.96791i	−0.201310	+	0.201310i
$610$	−46.4218	−	12.8718i	−1.87956	−	0.521164i
$611$	−38.2206	+	71.5057i	−1.54624	+	2.89281i
$612$	1.41237	+	2.99399i	0.0570916	+	0.121025i
$613$	11.3769	+	9.33678i	0.459508	+	0.377109i	0.835479	−	0.549523i	$-0.185190\pi$
$613$	11.3769	+	9.33678i	0.459508	+	0.377109i	−0.375970	+	0.926632i	$0.622690\pi$
$614$	−24.6239	−	23.4675i	−0.993738	−	0.947071i
$615$	2.41165	−	0.479707i	0.0972471	−	0.0193437i
$616$	11.6519	−	20.4963i	0.469470	−	0.825820i
$617$	4.26882	−	21.4608i	0.171856	−	0.863980i	−0.794597	−	0.607137i	$-0.792318\pi$
$617$	4.26882	−	21.4608i	0.171856	−	0.863980i	0.966453	−	0.256843i	$-0.0826822\pi$
$618$	−10.7702	−	1.87439i	−0.433240	−	0.0753989i
$619$	25.6478	+	7.78018i	1.03087	+	0.312712i	0.760014	−	0.649907i	$-0.225192\pi$
$619$	25.6478	+	7.78018i	1.03087	+	0.312712i	0.270859	+	0.962619i	$0.412692\pi$
$620$	−1.43244	+	3.02077i	−0.0575283	+	0.121317i
$621$	1.77839	−	1.45949i	0.0713643	−	0.0585672i
$622$	13.4774	+	1.00097i	0.540394	+	0.0401354i
$623$	−43.3191	−	17.9434i	−1.73555	−	0.718886i
$624$	15.6784	+	19.1828i	0.627639	+	0.767928i
$625$	−15.9759	+	6.61742i	−0.639035	+	0.264697i
$626$	−43.9545	+	14.4961i	−1.75677	+	0.579379i
$627$	24.5668	+	2.41962i	0.981105	+	0.0966304i
$628$	31.0976	+	7.82283i	1.24093	+	0.312165i
$629$	3.16764	−	1.69314i	0.126302	−	0.0675098i
$630$	6.99886	−	11.0401i	0.278841	−	0.439848i
$631$	5.00595	−	3.34487i	0.199284	−	0.133157i	−0.451925	−	0.892056i	$-0.649262\pi$
$631$	5.00595	−	3.34487i	0.199284	−	0.133157i	0.651208	+	0.758899i	$0.274262\pi$
$632$	−1.00766	+	38.6670i	−0.0400825	+	1.53809i
$633$	−11.3674	+	17.0126i	−0.451815	+	0.676189i
$634$	5.89866	−	15.2688i	0.234266	−	0.606402i
$635$	−1.25074	−	12.6989i	−0.0496339	−	0.503942i
$636$	6.39273	+	3.84041i	0.253488	+	0.152282i
$637$	1.08519	+	3.57740i	0.0429969	+	0.141742i
$638$	−8.58367	−	6.70571i	−0.339831	−	0.265482i
$639$	14.3485			0.567618
$640$	6.35180	+	37.3880i	0.251077	+	1.47789i
$641$	−8.69663			−0.343496			−0.171748	−	0.985141i	$-0.554942\pi$
$641$	−8.69663			−0.343496			−0.171748	+	0.985141i	$0.554942\pi$
$642$	−1.61284	−	1.25998i	−0.0636538	−	0.0497275i
$643$	3.79019	+	12.4946i	0.149470	+	0.492738i	0.999417	−	0.0341304i	$-0.0108661\pi$
$643$	3.79019	+	12.4946i	0.149470	+	0.492738i	−0.849947	+	0.526868i	$0.823366\pi$
$644$	−6.53370	+	10.8760i	−0.257464	+	0.428573i
$645$	−0.563867	−	5.72504i	−0.0222022	−	0.225423i
$646$	6.88847	−	17.8309i	0.271023	−	0.701549i
$647$	7.85341	−	11.7535i	0.308750	−	0.462076i	−0.644351	−	0.764730i	$-0.722872\pi$
$647$	7.85341	−	11.7535i	0.308750	−	0.462076i	0.953101	+	0.302653i	$0.0978725\pi$
$648$	2.05142	−	1.94722i	0.0805875	−	0.0764940i
$649$	7.91476	−	5.28847i	0.310681	−	0.207591i
$650$	−29.2463	+	46.1335i	−1.14713	+	1.80951i
$651$	−1.21273	+	0.648218i	−0.0475307	+	0.0254057i
$652$	−8.71034	+	34.6257i	−0.341123	+	1.35605i
$653$	19.9405	+	1.96397i	0.780331	+	0.0768559i	0.480336	−	0.877085i	$-0.340515\pi$
$653$	19.9405	+	1.96397i	0.780331	+	0.0768559i	0.299995	+	0.953941i	$0.403015\pi$
$654$	−19.3328	+	6.37591i	−0.755974	+	0.249318i
$655$	20.7278	−	8.58572i	0.809901	−	0.335472i
$656$	−2.80959	+	0.846106i	−0.109696	+	0.0330349i
$657$	4.62747	+	1.91676i	0.180535	+	0.0747799i
$658$	−50.9084	−	3.78099i	−1.98461	−	0.147399i
$659$	11.1451	−	9.14659i	0.434153	−	0.356300i	−0.391789	−	0.920055i	$-0.628144\pi$
$659$	11.1451	−	9.14659i	0.434153	−	0.356300i	0.825942	+	0.563755i	$0.190644\pi$
$660$	18.3115	+	8.68327i	0.712774	+	0.337996i
$661$	−36.7110	−	11.1362i	−1.42789	−	0.433146i	−0.520655	−	0.853767i	$-0.674312\pi$
$661$	−36.7110	−	11.1362i	−1.42789	−	0.433146i	−0.907237	+	0.420621i	$0.861812\pi$
$662$	−7.32015	−	1.27396i	−0.284506	−	0.0495140i
$663$	2.00004	−	10.0549i	0.0776751	−	0.390499i
$664$	−0.988522	−	3.59316i	−0.0383621	−	0.139442i
$665$	−74.0292	+	14.7253i	−2.87073	+	0.571024i
$666$	−2.22151	−	2.11718i	−0.0860817	−	0.0820392i
$667$	4.53113	+	3.71861i	0.175446	+	0.143985i
$668$	7.03027	−	3.31641i	0.272009	−	0.128316i
$669$	5.61856	−	10.5116i	0.217226	−	0.406401i
$670$	7.62481	+	2.11420i	0.294572	+	0.0816787i
$671$	21.7221	−	21.7221i	0.838571	−	0.838571i
$672$	−7.04833	+	13.9153i	−0.271895	+	0.536794i
$673$	6.36340	+	6.36340i	0.245291	+	0.245291i	0.819035	−	0.573744i	$-0.194510\pi$
$673$	6.36340	+	6.36340i	0.245291	+	0.245291i	−0.573744	+	0.819035i	$0.694510\pi$
$674$	−3.41069	−	6.02777i	−0.131375	−	0.232181i
$675$	5.49968	+	2.93964i	0.211683	+	0.113147i
$676$	−2.43791	−	50.6657i	−0.0937658	−	1.94868i
$677$	−12.1660	+	14.8243i	−0.467577	+	0.569745i	−0.952394	−	0.304871i	$-0.901387\pi$
$677$	−12.1660	+	14.8243i	−0.467577	+	0.569745i	0.484816	+	0.874616i	$0.338887\pi$
$678$	25.0176	−	0.601546i	0.960795	−	0.0231022i
$679$	2.72717	+	13.7104i	0.104659	+	0.526157i
$680$	10.2681	−	11.8673i	0.393763	−	0.455090i
$681$	8.55974	+	1.70264i	0.328010	+	0.0652452i
$682$	−1.22670	−	1.74365i	−0.0469729	−	0.0667677i
$683$	2.10434	−	6.93708i	0.0805203	−	0.265440i	−0.907432	−	0.420199i	$-0.861960\pi$
$683$	2.10434	−	6.93708i	0.0805203	−	0.265440i	0.987952	+	0.154759i	$0.0494602\pi$
$684$	−16.3117	−	0.817806i	−0.623693	−	0.0312696i
$685$	−23.3862	−	28.4962i	−0.893543	−	1.08878i
$686$	18.8958	−	16.2830i	0.721445	−	0.621690i
$687$	7.27411	−	17.5613i	0.277525	−	0.670004i
$688$	1.32570	+	6.73559i	0.0505417	+	0.256792i
$689$	−8.83812	−	21.3371i	−0.336705	−	0.812879i
$690$	−9.73897	−	4.90833i	−0.370756	−	0.186857i
$691$	0.542571	−	5.50881i	0.0206404	−	0.209565i	−0.979333	−	0.202255i	$-0.935173\pi$
$691$	0.542571	−	5.50881i	0.0206404	−	0.209565i	0.999973	−	0.00731020i	$-0.00232693\pi$
$692$	12.5904	−	16.9405i	0.478616	−	0.643983i
$693$	3.92941	+	7.35140i	0.149266	+	0.279257i
$694$	−0.779145	−	3.47788i	−0.0295759	−	0.132018i
$695$	30.3072	+	45.3579i	1.14962	+	1.72052i
$696$	5.88566	+	4.15846i	0.223095	+	0.157626i
$697$	1.00956	+	0.674566i	0.0382398	+	0.0255510i
$698$	10.3972	−	4.60251i	0.393541	−	0.174208i
$699$	−17.4622	+	1.71987i	−0.660479	+	0.0650515i
$700$	−34.0138	−	5.08048i	−1.28560	−	0.192024i
$701$	−5.75838	+	1.74678i	−0.217491	+	0.0659752i	−0.397150	−	0.917754i	$-0.630001\pi$
$701$	−5.75838	+	1.74678i	−0.217491	+	0.0659752i	0.179659	+	0.983729i	$0.442501\pi$
$702$	−8.69390	+	1.06785i	−0.328130	+	0.0403033i
$703$			17.7202i			0.668330i
$704$	−22.7452	−	8.21596i	−0.857243	−	0.309651i
$705$		−	43.8799i		−	1.65261i
$706$	0.290119	+	2.36201i	0.0109188	+	0.0888954i
$707$	43.4003	−	13.1653i	1.63224	−	0.495134i
$708$	−5.06223	+	3.74651i	−0.190250	+	0.140802i
$709$	10.6921	−	1.05308i	0.401550	−	0.0395493i	0.104773	−	0.994496i	$-0.466588\pi$
$709$	10.6921	−	1.05308i	0.401550	−	0.0395493i	0.296777	+	0.954947i	$0.404088\pi$
$710$	−27.5327	−	62.1972i	−1.03328	−	2.33422i
$711$	−11.3708	−	7.59770i	−0.426437	−	0.284936i
$712$	−10.6086	+	46.9105i	−0.397572	+	1.75805i
$713$	0.637391	+	0.953923i	0.0238705	+	0.0357247i
$714$	6.29856	−	1.41106i	0.235718	−	0.0528076i
$715$	−29.5853	−	55.3502i	−1.10643	−	2.06998i
$716$	−37.2175	+	5.48240i	−1.39088	+	0.204887i
$717$	1.31705	−	13.3723i	0.0491862	−	0.499396i
$718$	17.2446	−	34.2162i	0.643562	−	1.27694i
$719$	5.30533	+	12.8082i	0.197856	+	0.477666i	0.991403	−	0.130843i	$-0.0417683\pi$
$719$	5.30533	+	12.8082i	0.197856	+	0.477666i	−0.793548	+	0.608508i	$0.791768\pi$
$720$	−12.3771	−	5.15598i	−0.461267	−	0.192152i
$721$	−8.15709	+	19.6930i	−0.303786	+	0.733404i
$722$	44.0222	+	51.0859i	1.63834	+	1.90122i
$723$	−12.3535	−	15.0528i	−0.459431	−	0.559819i
$724$	4.83095	−	4.36967i	0.179541	−	0.162397i
$725$	−4.61224	+	15.2045i	−0.171294	+	0.564681i
$726$	2.15339	−	1.51497i	0.0799199	−	0.0562258i
$727$	18.6884	+	3.71734i	0.693113	+	0.137869i	0.529062	−	0.848583i	$-0.322544\pi$
$727$	18.6884	+	3.71734i	0.693113	+	0.137869i	0.164051	+	0.986452i	$0.447544\pi$
$728$	43.1813	−	21.6539i	1.60040	−	0.802549i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	−0.570751	−	23.7369i	−0.0211244	−	0.878542i
$731$	1.80210	−	2.19586i	0.0666530	−	0.0812169i
$732$	−13.6641	+	15.0455i	−0.505039	+	0.556099i
$733$	−45.4840	−	24.3117i	−1.67999	−	0.897973i	−0.983612	−	0.180297i	$-0.942294\pi$
$733$	−45.4840	−	24.3117i	−1.67999	−	0.897973i	−0.696377	−	0.717676i	$-0.745206\pi$
$734$	−10.0077	+	5.66263i	−0.369390	+	0.209011i
$735$	−1.43062	−	1.43062i	−0.0527691	−	0.0527691i
$736$	12.1303	+	4.71428i	0.447129	+	0.173771i
$737$	−3.56787	+	3.56787i	−0.131424	+	0.131424i
$738$	0.277193	−	0.999689i	0.0102036	−	0.0367990i
$739$	−9.54677	+	17.8608i	−0.351184	+	0.657019i	−0.994046	−	0.108963i	$-0.965247\pi$
$739$	−9.54677	+	17.8608i	−0.351184	+	0.657019i	0.642862	+	0.765982i	$0.277747\pi$
$740$	−4.91472	+	13.6922i	−0.180669	+	0.503337i
$741$	39.0977	+	32.0866i	1.43629	+	1.17873i
$742$	10.0319	−	10.5262i	0.368282	−	0.386428i
$743$	20.0247	−	3.98316i	0.734635	−	0.146128i	0.186425	−	0.982469i	$-0.440310\pi$
$743$	20.0247	−	3.98316i	0.734635	−	0.146128i	0.548209	+	0.836341i	$0.315310\pi$
$744$	0.866099	+	1.11327i	0.0317527	+	0.0408143i
$745$	7.20730	−	36.2335i	0.264055	−	1.32749i
$746$	4.93104	−	28.3336i	0.180538	−	1.03737i
$747$	1.26084	+	0.382471i	0.0461317	+	0.0139939i
$748$	3.36184	+	9.42561i	0.122921	+	0.344635i
$749$	−3.08478	+	2.53162i	−0.112716	+	0.0925032i
$750$	0.433979	−	5.84322i	0.0158467	−	0.213364i
$751$	−8.62476	−	3.57249i	−0.314722	−	0.130362i	0.219731	−	0.975561i	$-0.429482\pi$
$751$	−8.62476	−	3.57249i	−0.314722	−	0.130362i	−0.534453	+	0.845198i	$0.679482\pi$
$752$	5.02747	+	52.1205i	0.183333	+	1.90064i
$753$	−3.96905	+	1.64404i	−0.144640	+	0.0599120i
$754$	−6.98994	−	21.1947i	−0.254558	−	0.771864i
$755$	64.5523	+	6.35784i	2.34930	+	0.231386i
$756$	−2.83047	−	4.73315i	−0.102943	−	0.172143i
$757$	10.2521	−	5.47985i	0.372618	−	0.199169i	−0.274449	−	0.961602i	$-0.588495\pi$
$757$	10.2521	−	5.47985i	0.372618	−	0.199169i	0.647067	+	0.762433i	$0.275995\pi$
$758$	−29.4380	−	18.6622i	−1.06924	−	0.677841i
$759$	5.78255	−	3.86378i	0.209893	−	0.140246i
$760$	27.7547	+	72.2763i	1.00677	+	2.62174i
$761$	3.41603	−	5.11245i	0.123831	−	0.185326i	−0.764375	−	0.644772i	$-0.776952\pi$
$761$	3.41603	−	5.11245i	0.123831	−	0.185326i	0.888206	+	0.459446i	$0.151952\pi$
$762$	−5.02188	−	1.94006i	−0.181923	−	0.0702809i
$763$	3.89055	+	39.5015i	0.140848	+	1.43005i
$764$	18.3911	−	4.58705i	0.665366	−	0.165954i
$765$	1.61058	+	5.30936i	0.0582305	+	0.191960i
$766$	19.2477	−	24.6380i	0.695447	−	0.890208i
$767$	19.5034			0.704228
$768$	15.2922	+	4.70618i	0.551810	+	0.169820i
$769$	19.3705			0.698518			0.349259	−	0.937026i	$-0.386433\pi$
$769$	19.3705			0.698518			0.349259	+	0.937026i	$0.386433\pi$
$770$	24.3265	−	31.1392i	0.876668	−	1.12218i
$771$	−6.41796	−	21.1572i	−0.231137	−	0.761957i
$772$	−35.4841	+	8.85035i	−1.27710	+	0.318531i
$773$	−1.93639	−	19.6605i	−0.0696472	−	0.707139i	−0.965082	−	0.261947i	$-0.915635\pi$
$773$	−1.93639	−	19.6605i	−0.0696472	−	0.707139i	0.895435	−	0.445192i	$-0.146865\pi$
$774$	−2.26401	−	0.874633i	−0.0813780	−	0.0314380i
$775$	−1.72771	+	2.58571i	−0.0620613	+	0.0928814i
$776$	13.3858	−	5.14024i	0.480521	−	0.184524i
$777$	−4.97519	+	3.32432i	−0.178484	+	0.119259i
$778$	40.0696	+	25.4021i	1.43657	+	0.910709i
$779$	−5.28297	+	2.82381i	−0.189282	+	0.101173i
$780$	21.3112	+	35.6369i	0.763062	+	1.27600i
$781$	43.1660	+	4.25148i	1.54460	+	0.152130i
$782$	−1.68669	−	5.11432i	−0.0603158	−	0.182888i
$783$	−2.35394	+	0.975034i	−0.0841229	+	0.0348449i
$784$	1.86319	+	1.53537i	0.0665426	+	0.0548347i
$785$	49.6527	+	20.5668i	1.77218	+	0.734061i
$786$	0.701081	−	9.43955i	0.0250067	−	0.336698i
$787$	13.7127	−	11.2537i	0.488803	−	0.401151i	−0.357449	−	0.933933i	$-0.616353\pi$
$787$	13.7127	−	11.2537i	0.488803	−	0.401151i	0.846252	+	0.532782i	$0.178853\pi$
$788$	−13.0399	−	36.5600i	−0.464526	−	1.30240i
$789$	−8.19276	−	2.48525i	−0.291670	−	0.0884771i
$790$	−11.1153	+	63.8683i	−0.395465	+	2.27233i
$791$	9.51921	−	47.8563i	0.338464	−	1.70157i
$792$	6.74846	−	5.25017i	0.239796	−	0.186557i
$793$	61.7320	−	12.2793i	2.19217	−	0.436049i
$794$	14.8367	−	15.5678i	0.526535	−	0.552480i
$795$	9.66185	+	7.92927i	0.342670	+	0.281222i
$796$	−3.10671	+	8.65520i	−0.110115	+	0.306775i
$797$	8.76043	−	16.3896i	0.310310	−	0.580550i	−0.677627	−	0.735406i	$-0.736991\pi$
$797$	8.76043	−	16.3896i	0.310310	−	0.580550i	0.987937	+	0.154856i	$0.0494915\pi$
$798$	−8.50885	+	30.6869i	−0.301210	+	1.08631i
$799$	15.3213	−	15.3213i	0.542029	−	0.542029i
$800$	0.776952	+	35.2677i	0.0274694	+	1.24690i
$801$	−12.0238	−	12.0238i	−0.424839	−	0.424839i
$802$	−12.3394	+	6.98196i	−0.435718	+	0.246542i
$803$	13.3533	+	7.13750i	0.471229	+	0.251877i
$804$	2.24434	−	2.47124i	0.0791517	−	0.0871539i
$805$	−13.4901	+	16.4377i	−0.475464	+	0.579354i
$806$	−0.105000	−	4.36683i	−0.00369847	−	0.153815i
$807$	−1.11696	−	5.61533i	−0.0393188	−	0.197669i
$808$	−20.8534	−	41.5848i	−0.733619	−	1.46295i
$809$	−4.66719	−	0.928361i	−0.164090	−	0.0326394i	0.112362	−	0.993667i	$-0.464158\pi$
$809$	−4.66719	−	0.928361i	−0.164090	−	0.0326394i	−0.276451	+	0.961028i	$0.589158\pi$
$810$	3.87711	−	2.72765i	0.136228	−	0.0958398i
$811$	6.24686	−	20.5931i	0.219357	−	0.723123i	−0.776328	−	0.630329i	$-0.782920\pi$
$811$	6.24686	−	20.5931i	0.219357	−	0.723123i	0.995685	−	0.0927940i	$-0.0295798\pi$
$812$	10.4209	−	9.42584i	0.365701	−	0.330782i
$813$	−12.1236	−	14.7726i	−0.425193	−	0.518099i
$814$	−6.05585	−	7.02757i	−0.212258	−	0.246316i
$815$	−22.9001	+	55.2858i	−0.802157	+	1.93658i
$816$	−2.52135	−	6.12192i	−0.0882650	−	0.214310i
$817$	5.36318	+	12.9479i	0.187634	+	0.452988i
$818$	−12.5165	+	24.8348i	−0.437627	+	0.868328i
$819$	−1.67403	+	16.9967i	−0.0584952	+	0.593912i
$820$	−4.86529	+	0.716692i	−0.169903	+	0.0250280i
$821$	2.79742	+	5.23361i	0.0976306	+	0.182654i	0.925995	−	0.377535i	$-0.123228\pi$
$821$	2.79742	+	5.23361i	0.0976306	+	0.182654i	−0.828365	+	0.560189i	$0.810728\pi$
$822$	−15.1767	+	3.40001i	−0.529348	+	0.118589i
$823$	−7.64003	−	11.4341i	−0.266315	−	0.398568i	0.674077	−	0.738661i	$-0.264542\pi$
$823$	−7.64003	−	11.4341i	−0.266315	−	0.398568i	−0.940392	+	0.340093i	$0.889542\pi$
$824$	21.3256	+	4.82267i	0.742913	+	0.168006i
$825$	15.6742	+	10.4732i	0.545705	+	0.364629i
$826$	4.97054	+	11.2286i	0.172947	+	0.390694i
$827$	−2.60024	+	0.256102i	−0.0904193	+	0.00890553i	−0.143126	−	0.989705i	$-0.545715\pi$
$827$	−2.60024	+	0.256102i	−0.0904193	+	0.00890553i	0.0527063	+	0.998610i	$0.483215\pi$
$828$	−3.69848	+	2.73721i	−0.128531	+	0.0951247i
$829$	−42.1181	+	12.7764i	−1.46282	+	0.443742i	−0.918596	−	0.395198i	$-0.870676\pi$
$829$	−42.1181	+	12.7764i	−1.46282	+	0.443742i	−0.544225	+	0.838940i	$0.683176\pi$
$830$	−0.761446	−	6.19933i	−0.0264302	−	0.215182i
$831$			27.2227i			0.944346i
$832$	−29.3964	−	39.8877i	−1.01914	−	1.38286i
$833$		−	0.999040i		−	0.0346147i
$834$	22.8436	−	2.80581i	0.791008	−	0.0971573i
$835$	12.4670	−	3.78184i	0.431440	−	0.130876i
$836$	−48.8297	−	7.29346i	−1.68881	−	0.252250i
$837$	−0.496283	+	0.0488796i	−0.0171540	+	0.00168953i
$838$	−2.42909	+	1.07528i	−0.0839114	+	0.0371448i
$839$	−30.0408	−	20.0726i	−1.03712	−	0.692985i	−0.0842799	−	0.996442i	$-0.526859\pi$
$839$	−30.0408	−	20.0726i	−1.03712	−	0.692985i	−0.952845	+	0.303457i	$0.901859\pi$
$840$	−15.0858	+	21.3516i	−0.520509	+	0.736700i
$841$	12.5049	+	18.7150i	0.431204	+	0.645343i
$842$	−3.13134	−	13.9774i	−0.107913	−	0.481694i
$843$	9.72308	+	18.1906i	0.334880	+	0.626517i
$844$	24.4101	−	32.8441i	0.840231	−	1.13054i
$845$	8.33286	−	84.6050i	0.286659	−	2.91050i
$846$	−16.5320	−	8.33194i	−0.568381	−	0.286458i
$847$	−1.96458	−	4.74292i	−0.0675039	−	0.162969i
$848$	−12.3848	−	8.31139i	−0.425296	−	0.285414i
$849$	1.20085	−	2.89911i	0.0412131	−	0.0994972i
$850$	11.0580	−	9.52902i	0.379287	−	0.326843i
$851$	3.16705	+	3.85906i	0.108565	+	0.132287i
$852$	−28.6610	−	1.43695i	−0.981910	−	0.0492292i
$853$	−7.67481	+	25.3005i	−0.262780	+	0.866271i	0.721914	+	0.691983i	$0.243262\pi$
$853$	−7.67481	+	25.3005i	−0.262780	+	0.866271i	−0.984695	+	0.174288i	$0.944238\pi$
$854$	22.8022	+	32.4112i	0.780274	+	1.10909i
$855$	−26.8469	−	5.34018i	−0.918145	−	0.182630i
$856$	3.09545	+	2.67832i	0.105800	+	0.0915431i
$857$	−2.20797	−	11.1002i	−0.0754228	−	0.379176i	0.924576	−	0.380999i	$-0.124420\pi$
$857$	−2.20797	−	11.1002i	−0.0754228	−	0.379176i	−0.999998	+	0.00182270i	$0.999420\pi$
$858$	−26.4711	+	0.636496i	−0.903709	+	0.0217296i
$859$	−20.0793	+	24.4667i	−0.685096	+	0.834791i	−0.993183	−	0.116567i	$-0.962811\pi$
$859$	−20.0793	+	24.4667i	−0.685096	+	0.834791i	0.308087	+	0.951358i	$0.400311\pi$
$860$	0.552977	+	11.4922i	0.0188563	+	0.391880i
$861$	−1.78391	−	0.953520i	−0.0607955	−	0.0324959i
$862$	−3.31714	−	5.86245i	−0.112982	−	0.199676i
$863$	16.4895	+	16.4895i	0.561310	+	0.561310i	0.929679	−	0.368369i	$-0.120084\pi$
$863$	16.4895	+	16.4895i	0.561310	+	0.561310i	−0.368369	+	0.929679i	$0.620084\pi$
$864$	−4.29271	+	3.68411i	−0.146041	+	0.125336i
$865$	25.0141	−	25.0141i	0.850506	−	0.850506i
$866$	7.96486	+	2.20849i	0.270657	+	0.0750476i
$867$	6.72226	−	12.5765i	0.228300	−	0.427119i
$868$	2.48734	−	1.17336i	0.0844257	−	0.0398264i
$869$	−31.9566	−	26.2261i	−1.08405	−	0.889659i
$870$	8.74339	+	8.33279i	0.296429	+	0.282508i
$871$	−10.1395	+	2.01688i	−0.343564	+	0.0683392i
$872$	39.2557	−	10.7997i	1.32937	−	0.365724i
$873$	−0.989015	+	4.97211i	−0.0334731	+	0.168281i
$874$	26.1753	+	4.55542i	0.885392	+	0.154089i
$875$	−10.9326	−	3.31638i	−0.369591	−	0.112114i
$876$	−9.05137	−	4.29214i	−0.305817	−	0.145018i
$877$	−21.7810	+	17.8752i	−0.735492	+	0.603603i	−0.925752	−	0.378131i	$-0.876567\pi$
$877$	−21.7810	+	17.8752i	−0.735492	+	0.603603i	0.190260	+	0.981734i	$0.439067\pi$
$878$	−16.4977	−	1.22529i	−0.556770	−	0.0413517i
$879$	6.55525	+	2.71527i	0.221103	+	0.0915839i
$880$	−35.7075	−	19.1786i	−1.20370	−	0.646510i
$881$	1.68708	−	0.698813i	0.0568393	−	0.0235436i	−0.354083	−	0.935214i	$-0.615207\pi$
$881$	1.68708	−	0.698813i	0.0568393	−	0.0235436i	0.410922	+	0.911671i	$0.365207\pi$
$882$	−0.810638	+	0.267346i	−0.0272956	+	0.00900201i
$883$	18.5113	+	1.82321i	0.622955	+	0.0613557i	0.404570	−	0.914507i	$-0.367421\pi$
$883$	18.5113	+	1.82321i	0.622955	+	0.0613557i	0.218385	+	0.975863i	$0.429921\pi$
$884$	−5.00202	+	19.8842i	−0.168236	+	0.668779i
$885$	−9.30884	+	4.97568i	−0.312913	+	0.167256i
$886$	9.02512	−	14.2364i	0.303205	−	0.478280i
$887$	28.8993	−	19.3099i	0.970343	−	0.648362i	0.0339899	−	0.999422i	$-0.489179\pi$
$887$	28.8993	−	19.3099i	0.970343	−	0.648362i	0.936353	+	0.351060i	$0.114179\pi$
$888$	4.22541	+	4.45153i	0.141796	+	0.149384i
$889$	−5.83184	+	8.72796i	−0.195593	+	0.292726i
$890$	−29.0482	+	75.1918i	−0.973698	+	2.52044i
$891$	0.296301	+	3.00840i	0.00992647	+	0.100785i
$892$	−12.2757	+	20.4341i	−0.411022	+	0.684185i
$893$	31.0311	+	102.296i	1.03842	+	3.42320i
$894$	−12.2826	−	9.59542i	−0.410793	−	0.320919i
$895$	−63.0499			−2.10753
$896$	15.4725	−	27.0898i	0.516901	−	0.905007i
$897$	14.2493			0.475770
$898$	−20.2455	−	15.8162i	−0.675603	−	0.527793i
$899$	−0.368833	−	1.21588i	−0.0123013	−	0.0405518i
$900$	−10.6912	−	6.42268i	−0.356372	−	0.214089i
$901$	0.604953	+	6.14219i	0.0201539	+	0.204626i
$902$	1.13012	−	2.92533i	0.0376287	−	0.0974028i
$903$	−2.62916	+	3.93481i	−0.0874929	+	0.130942i
$904$	−50.0327	−	1.30384i	−1.66406	−	0.0433652i
$905$	9.07757	−	6.06544i	0.301749	−	0.201622i
$906$	14.6526	−	23.1132i	0.486799	−	0.767884i
$907$	8.16286	−	4.36314i	0.271043	−	0.144876i	−0.330276	−	0.943884i	$-0.607142\pi$
$907$	8.16286	−	4.36314i	0.271043	−	0.144876i	0.601320	+	0.799009i	$0.294642\pi$
$908$	−16.9275	−	4.25823i	−0.561758	−	0.141314i
$909$	16.3683	+	1.61213i	0.542901	+	0.0534711i
$910$	76.8885	−	25.3576i	2.54883	−	0.840597i
$911$	4.02038	−	1.66529i	0.133201	−	0.0551737i	−0.315087	−	0.949063i	$-0.602034\pi$
$911$	4.02038	−	1.66529i	0.133201	−	0.0551737i	0.448288	+	0.893889i	$0.352034\pi$
$912$	32.5006	+	3.26712i	1.07620	+	0.108185i
$913$	3.67978	+	1.52421i	0.121783	+	0.0504441i
$914$	33.8143	+	2.51141i	1.11848	+	0.0830700i
$915$	−26.3315	+	21.6097i	−0.870494	+	0.714396i
$916$	−16.2887	+	34.3500i	−0.538193	+	1.13496i
$917$	−17.6614	−	5.35752i	−0.583230	−	0.176921i
$918$	2.30615	+	0.401350i	0.0761142	+	0.0132465i
$919$	−1.22200	+	6.14342i	−0.0403101	+	0.202653i	−0.995692	−	0.0927201i	$-0.970444\pi$
$919$	−1.22200	+	6.14342i	−0.0403101	+	0.202653i	0.955382	+	0.295373i	$0.0954438\pi$
$920$	18.9620	+	10.7797i	0.625157	+	0.355396i
$921$	−23.5905	+	4.69244i	−0.777332	+	0.154621i
$922$	−19.3385	−	18.4303i	−0.636878	−	0.606970i
$923$	68.6979	+	56.3789i	2.26122	+	1.85573i
$924$	−7.11274	−	15.0779i	−0.233992	−	0.496026i
$925$	−6.37894	+	11.9342i	−0.209738	+	0.392392i
$926$	42.9505	+	11.9093i	1.41144	+	0.391364i
$927$	−5.46603	+	5.46603i	−0.179528	+	0.179528i
$928$	−11.3401	−	8.89592i	−0.372257	−	0.292023i
$929$	13.3517	+	13.3517i	0.438054	+	0.438054i	0.891357	−	0.453303i	$-0.149754\pi$
$929$	13.3517	+	13.3517i	0.438054	+	0.438054i	−0.453303	+	0.891357i	$0.649754\pi$
$930$	1.16417	+	2.05747i	0.0381748	+	0.0674671i
$931$	4.34686	+	2.32344i	0.142463	+	0.0761478i
$932$	35.0527	−	1.68665i	1.14819	−	0.0552482i
$933$	6.06239	−	7.38705i	0.198474	−	0.241841i
$934$	−43.3311	+	1.04189i	−1.41784	+	0.0340918i
$935$	3.27209	+	16.4499i	0.107009	+	0.537969i
$936$	17.4729	−	1.26235i	0.571121	−	0.0412613i
$937$	13.5178	+	2.68885i	0.441606	+	0.0878408i	0.410885	−	0.911687i	$-0.365220\pi$
$937$	13.5178	+	2.68885i	0.441606	+	0.0878408i	0.0307207	+	0.999528i	$0.490220\pi$
$938$	−3.74527	−	5.32357i	−0.122287	−	0.173821i
$939$	−9.50019	+	31.3179i	−0.310027	+	1.02202i
$940$	−4.39442	+	87.6498i	−0.143330	+	2.85882i
$941$	7.93399	+	9.66759i	0.258641	+	0.315155i	0.886099	−	0.463495i	$-0.153405\pi$
$941$	7.93399	+	9.66759i	0.258641	+	0.315155i	−0.627459	+	0.778650i	$0.715905\pi$
$942$	17.1767	−	14.8017i	0.559648	−	0.482264i
$943$	−0.645826	+	1.55916i	−0.0210310	+	0.0507733i
$944$	10.4869	−	6.97665i	0.341321	−	0.227071i
$945$	−3.53716	−	8.53946i	−0.115064	−	0.277789i
$946$	−6.55187	−	3.30207i	−0.213020	−	0.107360i
$947$	1.49789	−	15.2083i	0.0486749	−	0.494205i	−0.939682	−	0.342050i	$-0.888879\pi$
$947$	1.49789	−	15.2083i	0.0486749	−	0.494205i	0.988357	−	0.152155i	$-0.0486212\pi$
$948$	21.9521	+	16.3151i	0.712971	+	0.529889i
$949$	14.6240	+	27.3596i	0.474715	+	0.888129i
$950$	15.7437	+	70.2753i	0.510793	+	2.28003i
$951$	−6.43036	−	9.62371i	−0.208519	−	0.312070i
$952$	−12.7226	+	2.18780i	−0.412343	+	0.0709070i
$953$	−38.8543	−	25.9616i	−1.25862	−	0.840980i	−0.266201	−	0.963918i	$-0.585768\pi$
$953$	−38.8543	−	25.9616i	−1.25862	−	0.840980i	−0.992414	+	0.122938i	$0.960768\pi$
$954$	4.82199	−	2.13454i	0.156118	−	0.0691082i
$955$	31.6149	−	3.11380i	1.02304	−	0.100760i
$956$	−3.96999	+	26.5791i	−0.128398	+	0.859628i
$957$	−7.37049	+	2.23581i	−0.238254	+	0.0722736i
$958$	24.1398	−	2.96503i	0.779922	−	0.0957956i
$959$			30.3253i			0.979254i
$960$	24.2068	+	11.5385i	0.781270	+	0.372405i
$961$			30.7513i			0.991978i
$962$	−2.31720	−	18.8655i	−0.0747096	−	0.608249i
$963$	−1.38489	+	0.420102i	−0.0446274	+	0.0135376i
$964$	23.1685	+	31.3049i	0.746207	+	1.00826i
$965$	−60.9985	+	6.00782i	−1.96361	+	0.193399i
$966$	3.63150	+	8.20367i	0.116841	+	0.263949i
$967$	15.5873	+	10.4151i	0.501254	+	0.334927i	0.780357	−	0.625334i	$-0.215037\pi$
$967$	15.5873	+	10.4151i	0.501254	+	0.334927i	−0.279103	+	0.960261i	$0.590037\pi$
$968$	−4.45310	+	2.81048i	−0.143128	+	0.0903324i
$969$	−7.50938	−	11.2386i	−0.241236	−	0.361035i
$970$	23.4506	−	5.25362i	0.752955	−	0.168683i
$971$	22.1348	+	41.4114i	0.710341	+	1.32895i	0.935046	+	0.354527i	$0.115358\pi$
$971$	22.1348	+	41.4114i	0.710341	+	1.32895i	−0.224705	+	0.974427i	$0.572142\pi$
$972$	−0.291469	−	1.97865i	−0.00934887	−	0.0634651i
$973$	4.39857	−	44.6594i	0.141012	−	1.43172i
$974$	12.3430	−	24.4905i	0.395494	−	0.784727i
$975$	14.7808	+	35.6841i	0.473365	+	1.14280i
$976$	28.8007	−	28.6849i	0.921887	−	0.918181i
$977$	8.53411	−	20.6032i	0.273030	−	0.659154i	−0.726579	−	0.687082i	$-0.758891\pi$
$977$	8.53411	−	20.6032i	0.273030	−	0.659154i	0.999610	+	0.0279286i	$0.00889109\pi$
$978$	16.4809	+	19.1254i	0.527002	+	0.611564i
$979$	−32.6096	−	39.7349i	−1.04221	−	1.26993i
$980$	2.71437	+	3.00091i	0.0867074	+	0.0958607i
$981$	−4.17854	+	13.7748i	−0.133411	+	0.439796i
$982$	17.4297	−	12.2622i	0.556204	−	0.391304i
$983$	−5.35316	−	1.06481i	−0.170739	−	0.0339622i	0.108980	−	0.994044i	$-0.465241\pi$
$983$	−5.35316	−	1.06481i	−0.170739	−	0.0339622i	−0.279720	+	0.960082i	$0.590241\pi$
$984$	−0.653806	+	1.96911i	−0.0208426	+	0.0627729i
$985$	−12.6917	−	63.8057i	−0.404393	−	2.03302i
$986$	0.143365	+	5.96239i	0.00456568	+	0.189881i
$987$	−22.8996	+	27.9032i	−0.728901	+	0.888168i
$988$	−74.8839	−	68.0083i	−2.38237	−	2.16363i
$989$	3.48209	+	1.86122i	0.110724	+	0.0591832i
$990$	12.4721	−	7.05706i	0.396389	−	0.224288i
$991$	−11.4300	−	11.4300i	−0.363085	−	0.363085i	0.501862	−	0.864947i	$-0.332648\pi$
$991$	−11.4300	−	11.4300i	−0.363085	−	0.363085i	−0.864947	+	0.501862i	$0.832648\pi$
$992$	−1.61853	−	2.31047i	−0.0513885	−	0.0733576i
$993$	−3.71509	+	3.71509i	−0.117895	+	0.117895i
$994$	−14.9508	+	53.9196i	−0.474210	+	1.71022i
$995$	−7.26534	+	13.5925i	−0.230327	+	0.430911i
$996$	−2.48021	−	0.890252i	−0.0785885	−	0.0282087i
$997$	14.3817	+	11.8027i	0.455472	+	0.373796i	0.833974	−	0.551804i	$-0.186060\pi$
$997$	14.3817	+	11.8027i	0.455472	+	0.373796i	−0.378501	+	0.925601i	$0.623560\pi$
$998$	−9.54184	+	10.0120i	−0.302042	+	0.316925i
$999$	−2.12828	+	0.423341i	−0.0673357	+	0.0133939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.10	✓	512
128.69	even	32	inner	384.2.v.a.325.10	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.10	✓	512	1.1	even	1	trivial
384.2.v.a.325.10	yes	512	128.69	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.870630 + 1.11445i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-0.484007 - 1.94055i) q^{4} +(-0.328555 - 3.33588i) q^{5} +(-1.31919 - 0.509633i) q^{6} +(-1.53196 + 2.29274i) q^{7} +(2.58404 + 1.15010i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-0.870630 + 1.11445i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-0.484007 - 1.94055i) q^{4} +(-0.328555 - 3.33588i) q^{5} +(-1.31919 - 0.509633i) q^{6} +(-1.53196 + 2.29274i) q^{7} +(2.58404 + 1.15010i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(4.00372 + 2.53816i) q^{10} +(-2.66601 + 1.42501i) q^{11} +(1.71649 - 1.02648i) q^{12} +(-6.16389 - 0.607091i) q^{13} +(-1.22138 - 3.70343i) q^{14} +(3.09686 - 1.28276i) q^{15} +(-3.53147 + 1.87848i) q^{16} +(1.52921 + 0.633419i) q^{17} +(0.104746 - 1.41033i) q^{18} +(-6.31247 + 5.18051i) q^{19} +(-6.31441 + 2.25216i) q^{20} +(-2.63872 - 0.800448i) q^{21} +(0.733000 - 4.21179i) q^{22} +(-0.448825 + 2.25640i) q^{23} +(-0.350469 + 2.80663i) q^{24} +(-6.11620 + 1.21659i) q^{25} +(6.04304 - 6.34081i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(5.19066 + 1.86315i) q^{28} +(1.20106 - 2.24703i) q^{29} +(-1.26664 + 4.56811i) q^{30} +(0.352623 - 0.352623i) q^{31} +(0.981133 - 5.57112i) q^{32} +(-2.13755 - 2.13755i) q^{33} +(-2.03729 + 1.15276i) q^{34} +(8.15164 + 4.35714i) q^{35} +(1.48055 + 1.34461i) q^{36} +(1.37662 - 1.67741i) q^{37} +(-0.277605 - 11.5453i) q^{38} +(-1.20833 - 6.07471i) q^{39} +(2.98759 - 8.99791i) q^{40} +(0.719462 + 0.143110i) q^{41} +(3.18941 - 2.24384i) q^{42} +(0.498187 - 1.64230i) q^{43} +(4.05567 + 4.48381i) q^{44} +(2.12650 + 2.59114i) q^{45} +(-2.12389 - 2.46468i) q^{46} +(5.00956 - 12.0941i) q^{47} +(-2.82273 - 2.83412i) q^{48} +(-0.230978 - 0.557631i) q^{49} +(3.96912 - 7.87540i) q^{50} +(-0.162238 + 1.64723i) q^{51} +(1.80528 + 12.2552i) q^{52} +(1.75774 + 3.28850i) q^{53} +(1.38001 - 0.309161i) q^{54} +(5.62959 + 8.42528i) q^{55} +(-6.59553 + 4.16263i) q^{56} +(-6.78985 - 4.53684i) q^{57} +(1.45853 + 3.29486i) q^{58} +(-3.13374 + 0.308647i) q^{59} +(-3.98816 - 5.38875i) q^{60} +(-9.72455 + 2.94991i) q^{61} +(0.0859772 + 0.699985i) q^{62} -2.75746i q^{63} +(5.35454 + 5.94381i) q^{64} +20.7614i q^{65} +(4.24321 - 0.521182i) q^{66} +(1.59726 - 0.484525i) q^{67} +(0.489034 - 3.27408i) q^{68} +(-2.28952 + 0.225498i) q^{69} +(-11.9529 + 5.29115i) q^{70} +(-11.9303 - 7.97160i) q^{71} +(-2.78751 + 0.479344i) q^{72} +(-2.78270 - 4.16461i) q^{73} +(0.670872 + 2.99458i) q^{74} +(-2.93964 - 5.49968i) q^{75} +(13.1083 + 9.74227i) q^{76} +(0.817038 - 8.29553i) q^{77} +(7.82198 + 3.94219i) q^{78} +(5.23339 + 12.6345i) q^{79} +(7.42666 + 11.1634i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-0.785875 + 0.677210i) q^{82} +(-0.835860 - 1.01850i) q^{83} +(-0.276150 + 5.50800i) q^{84} +(1.61058 - 5.30936i) q^{85} +(1.39653 + 1.98504i) q^{86} +(2.49893 + 0.497068i) q^{87} +(-8.52798 + 0.616113i) q^{88} +(3.31735 + 16.6774i) q^{89} +(-4.73910 + 0.113951i) q^{90} +(10.8348 - 13.2022i) q^{91} +(4.59589 - 0.221143i) q^{92} +(0.439800 + 0.235078i) q^{93} +(9.11687 + 16.1124i) q^{94} +(19.3555 + 19.3555i) q^{95} +(5.61604 - 0.678325i) q^{96} +(3.58469 - 3.58469i) q^{97} +(0.822550 + 0.228076i) q^{98} +(1.42501 - 2.66601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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