LMFDB - Embedded newform 384.2.v.a.13.24

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			13.24
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.915950 - 1.07751i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-0.322073 - 1.97390i) q^{4} +(-0.270352 - 2.74493i) q^{5} +(-1.29700 - 0.563723i) q^{6} +(-1.85362 + 2.77413i) q^{7} +(-2.42190 - 1.46095i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(0.915950 - 1.07751i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-0.322073 - 1.97390i) q^{4} +(-0.270352 - 2.74493i) q^{5} +(-1.29700 - 0.563723i) q^{6} +(-1.85362 + 2.77413i) q^{7} +(-2.42190 - 1.46095i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-3.20533 - 2.22291i) q^{10} +(4.99114 - 2.66782i) q^{11} +(-1.79541 + 0.881196i) q^{12} +(-3.79822 - 0.374092i) q^{13} +(1.29135 + 4.53826i) q^{14} +(-2.54826 + 1.05552i) q^{15} +(-3.79254 + 1.27148i) q^{16} +(-0.856052 - 0.354588i) q^{17} +(-0.162950 + 1.40479i) q^{18} +(2.48141 - 2.03644i) q^{19} +(-5.33114 + 1.41772i) q^{20} +(3.19276 + 0.968512i) q^{21} +(1.69702 - 7.82161i) q^{22} +(-1.11391 + 5.59999i) q^{23} +(-0.695003 + 2.74171i) q^{24} +(-2.55765 + 0.508748i) q^{25} +(-3.88206 + 3.74998i) q^{26} +(0.773010 + 0.634393i) q^{27} +(6.07285 + 2.76538i) q^{28} +(2.13322 - 3.99098i) q^{29} +(-1.19674 + 3.71259i) q^{30} +(6.37934 - 6.37934i) q^{31} +(-2.10374 + 5.25112i) q^{32} +(-4.00180 - 4.00180i) q^{33} +(-1.16617 + 0.597623i) q^{34} +(8.11594 + 4.33806i) q^{35} +(1.36443 + 1.46230i) q^{36} +(-5.01961 + 6.11642i) q^{37} +(0.0785535 - 4.53904i) q^{38} +(0.744581 + 3.74326i) q^{39} +(-3.35545 + 7.04294i) q^{40} +(-0.359702 - 0.0715492i) q^{41} +(3.96799 - 2.55313i) q^{42} +(3.25488 - 10.7299i) q^{43} +(-6.87351 - 8.99277i) q^{44} +(1.74979 + 2.13213i) q^{45} +(5.01379 + 6.32956i) q^{46} +(3.33080 - 8.04126i) q^{47} +(2.31764 + 3.26014i) q^{48} +(-1.58114 - 3.81720i) q^{49} +(-1.79449 + 3.22189i) q^{50} +(-0.0908211 + 0.922122i) q^{51} +(0.484883 + 7.61777i) q^{52} +(-0.428920 - 0.802454i) q^{53} +(1.39161 - 0.251857i) q^{54} +(-8.67236 - 12.9791i) q^{55} +(8.54216 - 4.01064i) q^{56} +(-2.66907 - 1.78342i) q^{57} +(-2.34641 - 5.95412i) q^{58} +(0.295840 - 0.0291377i) q^{59} +(2.90422 + 4.69005i) q^{60} +(10.5361 - 3.19610i) q^{61} +(-1.03067 - 12.7170i) q^{62} -3.33642i q^{63} +(3.73124 + 7.07657i) q^{64} +10.5270i q^{65} +(-7.97744 + 0.646548i) q^{66} +(-7.60682 + 2.30750i) q^{67} +(-0.424210 + 1.80396i) q^{68} +(5.68221 - 0.559649i) q^{69} +(12.1081 - 4.77159i) q^{70} +(9.07848 + 6.06605i) q^{71} +(2.82540 - 0.130800i) q^{72} +(-0.960390 - 1.43733i) q^{73} +(1.99281 + 11.0110i) q^{74} +(1.22929 + 2.29983i) q^{75} +(-4.81893 - 4.24217i) q^{76} +(-1.85077 + 18.7912i) q^{77} +(4.71541 + 2.62634i) q^{78} +(3.98665 + 9.62462i) q^{79} +(4.51544 + 10.0665i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-0.406564 + 0.322048i) q^{82} +(9.68419 + 11.8002i) q^{83} +(0.883443 - 6.61410i) q^{84} +(-0.741886 + 2.44567i) q^{85} +(-8.58032 - 13.3352i) q^{86} +(-4.43837 - 0.882848i) q^{87} +(-15.9856 - 0.830615i) q^{88} +(-0.373569 - 1.87806i) q^{89} +(3.90012 + 0.0674963i) q^{90} +(8.07821 - 9.84333i) q^{91} +(11.4126 + 0.395135i) q^{92} +(-7.95647 - 4.25282i) q^{93} +(-5.61372 - 10.9544i) q^{94} +(-6.26076 - 6.26076i) q^{95} +(5.63569 + 0.488834i) q^{96} +(5.88166 - 5.88166i) q^{97} +(-5.56132 - 1.79267i) q^{98} +(-2.66782 + 4.99114i) 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 $

$2$	0.915950	−	1.07751i	0.647674	−	0.761917i
$2$	0.915950	−	1.07751i	0.647674	−	0.761917i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	−0.322073	−	1.97390i	−0.161036	−	0.986948i
$5$	−0.270352	−	2.74493i	−0.120905	−	1.22757i	−0.843817	−	0.536631i	$-0.819697\pi$
$5$	−0.270352	−	2.74493i	−0.120905	−	1.22757i	0.722912	−	0.690941i	$-0.242803\pi$
$6$	−1.29700	−	0.563723i	−0.529499	−	0.230139i
$7$	−1.85362	+	2.77413i	−0.700601	+	1.04852i	0.295061	+	0.955478i	$0.404660\pi$
$7$	−1.85362	+	2.77413i	−0.700601	+	1.04852i	−0.995662	+	0.0930451i	$0.970340\pi$
$8$	−2.42190	−	1.46095i	−0.856272	−	0.516525i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	−3.20533	−	2.22291i	−1.01362	−	0.702947i
$11$	4.99114	−	2.66782i	1.50489	−	0.804378i	0.506559	−	0.862205i	$-0.330917\pi$
$11$	4.99114	−	2.66782i	1.50489	−	0.804378i	0.998327	+	0.0578270i	$0.0184172\pi$
$12$	−1.79541	+	0.881196i	−0.518290	+	0.254379i
$13$	−3.79822	−	0.374092i	−1.05344	−	0.103754i	−0.443555	−	0.896247i	$-0.646283\pi$
$13$	−3.79822	−	0.374092i	−1.05344	−	0.103754i	−0.609881	+	0.792493i	$0.708783\pi$
$14$	1.29135	+	4.53826i	0.345127	+	1.21290i
$15$	−2.54826	+	1.05552i	−0.657958	+	0.272535i
$16$	−3.79254	+	1.27148i	−0.948135	+	0.317869i
$17$	−0.856052	−	0.354588i	−0.207623	−	0.0860003i	0.276448	−	0.961029i	$-0.410843\pi$
$17$	−0.856052	−	0.354588i	−0.207623	−	0.0860003i	−0.484071	+	0.875028i	$0.660843\pi$
$18$	−0.162950	+	1.40479i	−0.0384076	+	0.331113i
$19$	2.48141	−	2.03644i	0.569275	−	0.467192i	−0.305182	−	0.952294i	$-0.598717\pi$
$19$	2.48141	−	2.03644i	0.569275	−	0.467192i	0.874458	+	0.485102i	$0.161217\pi$
$20$	−5.33114	+	1.41772i	−1.19208	+	0.317011i
$21$	3.19276	+	0.968512i	0.696716	+	0.211347i
$22$	1.69702	−	7.82161i	0.361806	−	1.66757i
$23$	−1.11391	+	5.59999i	−0.232266	+	1.16768i	0.671948	+	0.740599i	$0.265458\pi$
$23$	−1.11391	+	5.59999i	−0.232266	+	1.16768i	−0.904214	+	0.427081i	$0.859542\pi$
$24$	−0.695003	+	2.74171i	−0.141867	+	0.559649i
$25$	−2.55765	+	0.508748i	−0.511529	+	0.101750i
$26$	−3.88206	+	3.74998i	−0.761335	+	0.735432i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	6.07285	+	2.76538i	1.14766	+	0.522607i
$29$	2.13322	−	3.99098i	0.396130	−	0.741107i	−0.602232	−	0.798321i	$-0.705722\pi$
$29$	2.13322	−	3.99098i	0.396130	−	0.741107i	0.998362	+	0.0572142i	$0.0182218\pi$
$30$	−1.19674	+	3.71259i	−0.218493	+	0.677823i
$31$	6.37934	−	6.37934i	1.14576	−	1.14576i	0.158386	−	0.987377i	$-0.449371\pi$
$31$	6.37934	−	6.37934i	1.14576	−	1.14576i	0.987377	−	0.158386i	$-0.0506291\pi$
$32$	−2.10374	+	5.25112i	−0.371892	+	0.928276i
$33$	−4.00180	−	4.00180i	−0.696623	−	0.696623i
$34$	−1.16617	+	0.597623i	−0.199997	+	0.102491i
$35$	8.11594	+	4.33806i	1.37184	+	0.733266i
$36$	1.36443	+	1.46230i	0.227405	+	0.243717i
$37$	−5.01961	+	6.11642i	−0.825219	+	1.00553i	0.174563	+	0.984646i	$0.444149\pi$
$37$	−5.01961	+	6.11642i	−0.825219	+	1.00553i	−0.999782	+	0.0208865i	$0.993351\pi$
$38$	0.0785535	−	4.53904i	0.0127431	−	0.736329i
$39$	0.744581	+	3.74326i	0.119228	+	0.599401i
$40$	−3.35545	+	7.04294i	−0.530543	+	1.11359i
$41$	−0.359702	−	0.0715492i	−0.0561760	−	0.0111741i	0.166922	−	0.985970i	$-0.446617\pi$
$41$	−0.359702	−	0.0715492i	−0.0561760	−	0.0111741i	−0.223098	+	0.974796i	$0.571617\pi$
$42$	3.96799	−	2.55313i	0.612274	−	0.393957i
$43$	3.25488	−	10.7299i	0.496365	−	1.63630i	−0.248173	−	0.968716i	$-0.579830\pi$
$43$	3.25488	−	10.7299i	0.496365	−	1.63630i	0.744538	−	0.667580i	$-0.232670\pi$
$44$	−6.87351	−	8.99277i	−1.03622	−	1.35571i
$45$	1.74979	+	2.13213i	0.260844	+	0.317839i
$46$	5.01379	+	6.32956i	0.739242	+	0.933243i
$47$	3.33080	−	8.04126i	0.485847	−	1.17294i	−0.470945	−	0.882163i	$-0.656087\pi$
$47$	3.33080	−	8.04126i	0.485847	−	1.17294i	0.956791	−	0.290775i	$-0.0939132\pi$
$48$	2.31764	+	3.26014i	0.334523	+	0.470561i
$49$	−1.58114	−	3.81720i	−0.225876	−	0.545314i
$50$	−1.79449	+	3.22189i	−0.253780	+	0.455644i
$51$	−0.0908211	+	0.922122i	−0.0127175	+	0.129123i
$52$	0.484883	+	7.61777i	0.0672412	+	1.05639i
$53$	−0.428920	−	0.802454i	−0.0589167	−	0.110225i	0.850739	−	0.525588i	$-0.176155\pi$
$53$	−0.428920	−	0.802454i	−0.0589167	−	0.110225i	−0.909656	+	0.415363i	$0.863655\pi$
$54$	1.39161	−	0.251857i	0.189374	−	0.0342734i
$55$	−8.67236	−	12.9791i	−1.16938	−	1.75010i
$56$	8.54216	−	4.01064i	1.14149	−	0.535944i
$57$	−2.66907	−	1.78342i	−0.353527	−	0.236219i
$58$	−2.34641	−	5.95412i	−0.308099	−	0.781814i
$59$	0.295840	−	0.0291377i	0.0385150	−	0.00379340i	−0.0787413	−	0.996895i	$-0.525090\pi$
$59$	0.295840	−	0.0291377i	0.0385150	−	0.00379340i	0.117256	+	0.993102i	$0.462590\pi$
$60$	2.90422	+	4.69005i	0.374933	+	0.605482i
$61$	10.5361	−	3.19610i	1.34901	−	0.409219i	0.468595	−	0.883413i	$-0.344761\pi$
$61$	10.5361	−	3.19610i	1.34901	−	0.409219i	0.880420	+	0.474194i	$0.157261\pi$
$62$	−1.03067	−	12.7170i	−0.130896	−	1.61506i
$63$		−	3.33642i		−	0.420350i
$64$	3.73124	+	7.07657i	0.466405	+	0.884572i
$65$			10.5270i			1.30571i
$66$	−7.97744	+	0.646548i	−0.981955	+	0.0795845i
$67$	−7.60682	+	2.30750i	−0.929321	+	0.281906i	−0.718427	−	0.695603i	$-0.755137\pi$
$67$	−7.60682	+	2.30750i	−0.929321	+	0.281906i	−0.210894	+	0.977509i	$0.567637\pi$
$68$	−0.424210	+	1.80396i	−0.0514430	+	0.218762i
$69$	5.68221	−	0.559649i	0.684058	−	0.0673738i
$70$	12.1081	−	4.77159i	1.44720	−	0.570315i
$71$	9.07848	+	6.06605i	1.07742	+	0.719907i	0.961901	−	0.273398i	$-0.0881477\pi$
$71$	9.07848	+	6.06605i	1.07742	+	0.719907i	0.115517	+	0.993306i	$0.463148\pi$
$72$	2.82540	−	0.130800i	0.332977	−	0.0154149i
$73$	−0.960390	−	1.43733i	−0.112405	−	0.168226i	0.771002	−	0.636833i	$-0.219756\pi$
$73$	−0.960390	−	1.43733i	−0.112405	−	0.168226i	−0.883407	+	0.468607i	$0.844756\pi$
$74$	1.99281	+	11.0110i	0.231660	+	1.28001i
$75$	1.22929	+	2.29983i	0.141946	+	0.265562i
$76$	−4.81893	−	4.24217i	−0.552769	−	0.486611i
$77$	−1.85077	+	18.7912i	−0.210915	+	2.14146i
$78$	4.71541	+	2.62634i	0.533915	+	0.297375i
$79$	3.98665	+	9.62462i	0.448533	+	1.08285i	0.972872	+	0.231345i	$0.0743126\pi$
$79$	3.98665	+	9.62462i	0.448533	+	1.08285i	−0.524339	+	0.851510i	$0.675687\pi$
$80$	4.51544	+	10.0665i	0.504842	+	1.12547i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−0.406564	+	0.322048i	−0.0448975	+	0.0355643i
$83$	9.68419	+	11.8002i	1.06298	+	1.29524i	0.953546	+	0.301248i	$0.0974032\pi$
$83$	9.68419	+	11.8002i	1.06298	+	1.29524i	0.109432	+	0.993994i	$0.465097\pi$
$84$	0.883443	−	6.61410i	0.0963916	−	0.721658i
$85$	−0.741886	+	2.44567i	−0.0804688	+	0.265270i
$86$	−8.58032	−	13.3352i	−0.925239	−	1.43798i
$87$	−4.43837	−	0.882848i	−0.475844	−	0.0946512i
$88$	−15.9856	−	0.830615i	−1.70407	−	0.0885438i
$89$	−0.373569	−	1.87806i	−0.0395983	−	0.199074i	0.955922	−	0.293620i	$-0.0948600\pi$
$89$	−0.373569	−	1.87806i	−0.0395983	−	0.199074i	−0.995520	+	0.0945461i	$0.969860\pi$
$90$	3.90012	+	0.0674963i	0.411109	+	0.00711474i
$91$	8.07821	−	9.84333i	0.846827	−	1.03186i
$92$	11.4126	+	0.395135i	1.18984	+	0.0411956i
$93$	−7.95647	−	4.25282i	−0.825048	−	0.440997i
$94$	−5.61372	−	10.9544i	−0.579011	−	1.12986i
$95$	−6.26076	−	6.26076i	−0.642340	−	0.642340i
$96$	5.63569	+	0.488834i	0.575191	+	0.0498914i
$97$	5.88166	−	5.88166i	0.597192	−	0.597192i	−0.342372	−	0.939564i	$-0.611230\pi$
$97$	5.88166	−	5.88166i	0.597192	−	0.597192i	0.939564	+	0.342372i	$0.111230\pi$
$98$	−5.56132	−	1.79267i	−0.561779	−	0.181087i
$99$	−2.66782	+	4.99114i	−0.268126	+	0.501629i
$100$	1.82796	+	4.88468i	0.182796	+	0.488468i
$101$	−6.25460	−	5.13302i	−0.622356	−	0.510754i	0.269543	−	0.962988i	$-0.413127\pi$
$101$	−6.25460	−	5.13302i	−0.622356	−	0.510754i	−0.891899	+	0.452234i	$0.850627\pi$
$102$	0.910412	+	0.942478i	0.0901442	+	0.0933193i
$103$	−6.02151	+	1.19775i	−0.593317	+	0.118018i	−0.482611	−	0.875835i	$-0.660311\pi$
$103$	−6.02151	+	1.19775i	−0.593317	+	0.118018i	−0.110706	+	0.993853i	$0.535311\pi$
$104$	8.65238	+	6.45503i	0.848436	+	0.632967i
$105$	1.79533	−	9.02574i	0.175206	−	0.880822i
$106$	−1.25752	−	0.272839i	−0.122142	−	0.0265005i
$107$	11.7202	+	3.55529i	1.13304	+	0.343703i	0.800468	−	0.599376i	$-0.204585\pi$
$107$	11.7202	+	3.55529i	1.13304	+	0.343703i	0.332569	+	0.943079i	$0.392085\pi$
$108$	1.00326	−	1.73016i	0.0965389	−	0.166485i
$109$	−13.3889	+	10.9880i	−1.28243	+	1.05246i	−0.286902	+	0.957960i	$0.592625\pi$
$109$	−13.3889	+	10.9880i	−1.28243	+	1.05246i	−0.995525	+	0.0945000i	$0.969875\pi$
$110$	−21.9286	−	2.54362i	−2.09081	−	0.242524i
$111$	7.31016	+	3.02797i	0.693850	+	0.287402i
$112$	3.50267	−	12.8778i	0.330971	−	1.21684i
$113$	−1.38014	+	0.571672i	−0.129833	+	0.0537784i	−0.446654	−	0.894707i	$-0.647384\pi$
$113$	−1.38014	+	0.571672i	−0.129833	+	0.0537784i	0.316821	+	0.948485i	$0.397384\pi$
$114$	−4.36639	+	1.24244i	−0.408950	+	0.116365i
$115$	15.6728	+	1.54363i	1.46149	+	0.143944i
$116$	−8.56484	−	2.92538i	−0.795226	−	0.271615i
$117$	3.36594	−	1.79913i	0.311181	−	0.166330i
$118$	0.239578	−	0.345460i	0.0220549	−	0.0318022i
$119$	2.57047	−	1.71753i	0.235634	−	0.157446i
$120$	7.71371	+	1.16651i	0.704162	+	0.106487i
$121$	11.6830	−	17.4848i	1.06209	−	1.58953i
$122$	6.20673	−	14.2803i	0.561931	−	1.29288i
$123$	0.0359477	+	0.364983i	0.00324129	+	0.0329094i
$124$	−14.6468	−	10.5376i	−1.31532	−	0.946300i
$125$	−1.91539	−	6.31421i	−0.171318	−	0.564760i
$126$	−3.59504	−	3.05599i	−0.320272	−	0.272250i
$127$	−1.26925			−0.112628			−0.0563138	−	0.998413i	$-0.517935\pi$
$127$	−1.26925			−0.112628			−0.0563138	+	0.998413i	$0.517935\pi$
$128$	11.0427	+	2.46132i	0.976049	+	0.217552i
$129$	−11.2127			−0.987225
$130$	11.3430	+	9.64219i	0.994845	+	0.845676i
$131$	4.47682	+	14.7581i	0.391142	+	1.28942i	0.902736	+	0.430194i	$0.141555\pi$
$131$	4.47682	+	14.7581i	0.391142	+	1.28942i	−0.511595	+	0.859227i	$0.670945\pi$
$132$	−6.61027	+	9.18800i	−0.575350	+	0.799713i
$133$	1.04978	+	10.6586i	0.0910271	+	0.924214i
$134$	−4.48109	+	10.3100i	−0.387108	+	0.890649i
$135$	1.53238	−	2.29337i	0.131886	−	0.197382i
$136$	1.55524	+	2.10943i	0.133361	+	0.180882i
$137$	3.38959	−	2.26485i	0.289592	−	0.193499i	−0.402285	−	0.915515i	$-0.631784\pi$
$137$	3.38959	−	2.26485i	0.289592	−	0.193499i	0.691877	+	0.722015i	$0.256784\pi$
$138$	4.60159	−	6.63527i	0.391713	−	0.564832i
$139$	−11.8870	+	6.35372i	−1.00824	+	0.538916i	−0.890911	−	0.454178i	$-0.849933\pi$
$139$	−11.8870	+	6.35372i	−1.00824	+	0.538916i	−0.117329	+	0.993093i	$0.537433\pi$
$140$	5.94896	−	17.4172i	0.502779	−	1.47202i
$141$	−8.66188	−	0.853121i	−0.729462	−	0.0718458i
$142$	14.8517	−	4.22600i	1.24633	−	0.354638i
$143$	−19.9554	+	8.26582i	−1.66876	+	0.691222i
$144$	2.44699	−	3.16422i	0.203916	−	0.263685i
$145$	−11.5317	−	4.77659i	−0.957656	−	0.396674i
$146$	−2.42841	−	0.281684i	−0.200976	−	0.0233123i
$147$	−3.19385	+	2.62113i	−0.263424	+	0.216187i
$148$	13.6899	+	7.93827i	1.12530	+	0.652522i
$149$	−5.71376	−	1.73325i	−0.468089	−	0.141993i	0.0474240	−	0.998875i	$-0.484899\pi$
$149$	−5.71376	−	1.73325i	−0.468089	−	0.141993i	−0.515513	+	0.856881i	$0.672399\pi$
$150$	3.60407	+	0.781958i	0.294271	+	0.0638466i
$151$	−2.80304	+	14.0918i	−0.228108	+	1.14678i	0.681664	+	0.731666i	$0.261257\pi$
$151$	−2.80304	+	14.0918i	−0.228108	+	1.14678i	−0.909771	+	0.415110i	$0.863743\pi$
$152$	−8.98489	+	1.30684i	−0.728771	+	0.105999i
$153$	0.908780	−	0.180768i	0.0734705	−	0.0146142i
$154$	18.5526	+	19.2060i	1.49501	+	1.54767i
$155$	−19.2355	−	15.7862i	−1.54504	−	1.26798i
$156$	7.14900	−	2.67533i	0.572378	−	0.214198i
$157$	−1.84760	+	3.45661i	−0.147454	+	0.275868i	−0.944795	−	0.327662i	$-0.893739\pi$
$157$	−1.84760	+	3.45661i	−0.147454	+	0.275868i	0.797341	+	0.603529i	$0.206239\pi$
$158$	14.0222	+	4.52000i	1.11555	+	0.359592i
$159$	−0.643391	+	0.643391i	−0.0510242	+	0.0510242i
$160$	14.9827	+	4.35498i	1.18449	+	0.344291i
$161$	−13.4704	−	13.4704i	−1.06161	−	1.06161i
$162$	−0.644974	−	1.25857i	−0.0506740	−	0.0988829i
$163$	−3.74031	−	1.99924i	−0.292964	−	0.156592i	0.318367	−	0.947968i	$-0.396866\pi$
$163$	−3.74031	−	1.99924i	−0.292964	−	0.156592i	−0.611331	+	0.791375i	$0.709366\pi$
$164$	−0.0253805	+	0.733059i	−0.00198189	+	0.0572423i
$165$	−9.90277	+	12.0666i	−0.770930	+	0.939381i
$166$	21.5851	+	0.373557i	1.67533	+	0.0289936i
$167$	2.28230	+	11.4739i	0.176610	+	0.887876i	0.962867	+	0.269977i	$0.0870160\pi$
$167$	2.28230	+	11.4739i	0.176610	+	0.887876i	−0.786257	+	0.617899i	$0.787984\pi$
$168$	−6.31760	−	7.01011i	−0.487413	−	0.540842i
$169$	1.53629	+	0.305588i	0.118176	+	0.0235067i
$170$	1.95571	+	3.03950i	0.149996	+	0.233119i
$171$	−0.931833	+	3.07184i	−0.0712590	+	0.234910i
$172$	−22.2280	−	2.96899i	−1.69487	−	0.226384i
$173$	2.55567	+	3.11410i	0.194304	+	0.236761i	0.861044	−	0.508530i	$-0.169811\pi$
$173$	2.55567	+	3.11410i	0.194304	+	0.236761i	−0.666740	+	0.745290i	$0.732311\pi$
$174$	−5.01661	+	3.97377i	−0.380308	+	0.301250i
$175$	3.32956	−	8.03827i	0.251691	−	0.607636i
$176$	−15.5370	+	16.4639i	−1.17115	+	1.24102i
$177$	−0.113761	−	0.274643i	−0.00855078	−	0.0206434i
$178$	−2.36581	−	1.31768i	−0.177325	−	0.0987644i
$179$	−0.478465	+	4.85794i	−0.0357622	+	0.363099i	0.960604	+	0.277922i	$0.0896457\pi$
$179$	−0.478465	+	4.85794i	−0.0357622	+	0.363099i	−0.996366	+	0.0851773i	$0.972854\pi$
$180$	3.64504	−	4.14061i	0.271685	−	0.308623i
$181$	−3.10387	−	5.80694i	−0.230709	−	0.431626i	0.739754	−	0.672878i	$-0.234942\pi$
$181$	−3.10387	−	5.80694i	−0.230709	−	0.431626i	−0.970463	+	0.241252i	$0.922442\pi$
$182$	−3.20709	−	17.7204i	−0.237725	−	1.31352i
$183$	−6.11696	−	9.15468i	−0.452179	−	0.676733i
$184$	10.8791	−	11.9353i	0.802018	−	0.879880i
$185$	18.1462	+	12.1249i	1.33414	+	0.891442i
$186$	−11.8702	+	4.67784i	−0.870366	+	0.342996i
$187$	−5.21865	+	0.513993i	−0.381626	+	0.0375869i
$188$	−16.9454	−	3.98478i	−1.23587	−	0.290620i
$189$	−3.19276	+	0.968512i	−0.232239	+	0.0704489i
$190$	−12.4806	+	1.01152i	−0.905438	+	0.0733831i
$191$			14.0534i			1.01687i	0.861100	+	0.508435i	$0.169776\pi$
$191$			14.0534i			1.01687i	−0.861100	+	0.508435i	$0.830224\pi$
$192$	5.68874	−	5.62479i	0.410549	−	0.405934i
$193$			16.0653i			1.15640i	0.815894	+	0.578201i	$0.196245\pi$
$193$			16.0653i			1.15640i	−0.815894	+	0.578201i	$0.803755\pi$
$194$	−0.950267	−	11.7249i	−0.0682252	−	0.841797i
$195$	10.0737	−	3.05582i	0.721393	−	0.218832i
$196$	−7.02552	+	4.35041i	−0.501823	+	0.310744i
$197$	19.5636	−	1.92685i	1.39385	−	0.137282i	0.626956	−	0.779055i	$-0.284301\pi$
$197$	19.5636	−	1.92685i	1.39385	−	0.137282i	0.766895	+	0.641773i	$0.221801\pi$
$198$	2.93444	+	7.44625i	0.208541	+	0.529182i
$199$	−14.4757	−	9.67237i	−1.02616	−	0.685656i	−0.0758978	−	0.997116i	$-0.524182\pi$
$199$	−14.4757	−	9.67237i	−1.02616	−	0.685656i	−0.950260	+	0.311459i	$0.899182\pi$
$200$	6.93763	+	2.50446i	0.490564	+	0.177092i
$201$	4.41628	+	6.60944i	0.311501	+	0.466194i
$202$	−11.2598	+	2.03783i	−0.792237	+	0.143381i
$203$	7.11734	+	13.3156i	0.499539	+	0.934572i
$204$	1.84943	−	0.117719i	0.129486	−	0.00824196i
$205$	−0.0991515	+	1.00670i	−0.00692504	+	0.0703111i
$206$	−4.22480	+	7.58534i	−0.294356	+	0.528496i
$207$	−2.18501	−	5.27508i	−0.151869	−	0.366643i
$208$	14.8805	−	3.41059i	1.03178	−	0.236482i
$209$	6.95222	−	16.7841i	0.480895	−	1.16098i
$210$	−8.08093	−	10.2016i	−0.557637	−	0.703979i
$211$	−1.57381	−	1.91769i	−0.108345	−	0.132019i	0.716014	−	0.698086i	$-0.245965\pi$
$211$	−1.57381	−	1.91769i	−0.108345	−	0.132019i	−0.824360	+	0.566067i	$0.808465\pi$
$212$	−1.44582	+	1.10509i	−0.0992991	+	0.0758981i
$213$	3.16950	−	10.4484i	0.217171	−	0.715916i
$214$	14.5660	−	9.37223i	0.995712	−	0.640673i
$215$	−30.3329	−	6.03358i	−2.06868	−	0.411487i
$216$	−0.945339	−	2.66577i	−0.0643221	−	0.181383i
$217$	5.87229	+	29.5220i	0.398637	+	2.00408i
$218$	−0.423850	+	24.4912i	−0.0287067	+	1.65875i
$219$	−1.09665	+	1.33627i	−0.0741046	+	0.0902967i
$220$	−22.8263	+	21.2986i	−1.53895	+	1.43595i
$221$	3.11882	+	1.66704i	0.209795	+	0.112138i
$222$	9.95842	−	5.10333i	0.668365	−	0.342513i
$223$	5.00507	+	5.00507i	0.335164	+	0.335164i	0.854544	−	0.519379i	$-0.173837\pi$
$223$	5.00507	+	5.00507i	0.335164	+	0.335164i	−0.519379	+	0.854544i	$0.673837\pi$
$224$	−10.6678	−	15.5696i	−0.712771	−	1.04029i
$225$	1.84396	−	1.84396i	0.122931	−	0.122931i
$226$	−0.648153	+	2.01074i	−0.0431145	+	0.133753i
$227$	13.4958	−	25.2488i	0.895745	−	1.67582i	0.172751	−	0.984965i	$-0.444734\pi$
$227$	13.4958	−	25.2488i	0.895745	−	1.67582i	0.722993	−	0.690855i	$-0.242766\pi$
$228$	−2.66065	+	5.84286i	−0.176206	+	0.386953i
$229$	6.78600	+	5.56912i	0.448431	+	0.368018i	0.831336	−	0.555770i	$-0.187576\pi$
$229$	6.78600	+	5.56912i	0.448431	+	0.368018i	−0.382905	+	0.923788i	$0.625076\pi$
$230$	16.0187	−	15.4737i	1.05624	−	1.02031i
$231$	18.5193	−	3.68372i	1.21848	−	0.242371i
$232$	−10.9971	+	6.54924i	−0.721995	+	0.429978i
$233$	−0.563245	+	2.83162i	−0.0368994	+	0.185506i	−0.994839	−	0.101463i	$-0.967648\pi$
$233$	−0.563245	+	2.83162i	−0.0368994	+	0.185506i	0.957940	+	0.286969i	$0.0926476\pi$
$234$	1.14444	−	5.27475i	0.0748144	−	0.344822i
$235$	−22.9732	−	6.96885i	−1.49861	−	0.454598i
$236$	−0.152797	−	0.574573i	−0.00994621	−	0.0374015i
$237$	8.05293	−	6.60887i	0.523094	−	0.429292i
$238$	0.503754	−	4.34289i	0.0326535	−	0.281507i
$239$	−14.0612	−	5.82433i	−0.909542	−	0.376745i	−0.121661	−	0.992572i	$-0.538822\pi$
$239$	−14.0612	−	5.82433i	−0.909542	−	0.376745i	−0.787881	+	0.615827i	$0.788822\pi$
$240$	8.32230	−	7.24316i	0.537202	−	0.467544i
$241$	−19.8184	+	8.20906i	−1.27662	+	0.528792i	−0.914969	−	0.403523i	$-0.867785\pi$
$241$	−19.8184	+	8.20906i	−1.27662	+	0.528792i	−0.361647	+	0.932315i	$0.617785\pi$
$242$	−8.13909	−	28.6037i	−0.523201	−	1.83872i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	−9.70218	−	19.7679i	−0.621119	−	1.26551i
$245$	−10.0505	+	5.37210i	−0.642102	+	0.343211i
$246$	0.426200	+	0.295572i	0.0271736	+	0.0188450i
$247$	−10.1868	+	6.80658i	−0.648168	+	0.433092i
$248$	−24.7701	+	6.13024i	−1.57290	+	0.389270i
$249$	8.48093	−	12.6926i	0.537457	−	0.804362i
$250$	−8.55805	−	3.71963i	−0.541259	−	0.235250i
$251$	−0.235613	−	2.39222i	−0.0148718	−	0.150996i	0.984881	−	0.173232i	$-0.0554212\pi$
$251$	−0.235613	−	2.39222i	−0.0148718	−	0.150996i	−0.999753	+	0.0222369i	$0.992921\pi$
$252$	−6.58575	+	1.07457i	−0.414863	+	0.0676915i
$253$	9.38010	+	30.9221i	0.589722	+	1.94405i
$254$	−1.16257	+	1.36763i	−0.0729460	+	0.0858129i
$255$	2.55572			0.160045
$256$	12.7667	−	9.64425i	0.797918	−	0.602765i
$257$	10.0931			0.629588			0.314794	−	0.949160i	$-0.398065\pi$
$257$	10.0931			0.629588			0.314794	+	0.949160i	$0.398065\pi$
$258$	−10.2703	+	12.0819i	−0.639400	+	0.752184i
$259$	−7.66331	−	25.2626i	−0.476175	−	1.56974i
$260$	20.7792	−	3.39046i	1.28867	−	0.210267i
$261$	0.443560	+	4.50354i	0.0274557	+	0.278762i
$262$	20.0026	+	8.69384i	1.23576	+	0.537107i
$263$	5.50093	−	8.23272i	0.339202	−	0.507651i	−0.622178	−	0.782875i	$-0.713752\pi$
$263$	5.50093	−	8.23272i	0.339202	−	0.507651i	0.961380	+	0.275224i	$0.0887522\pi$
$264$	3.84553	+	15.5384i	0.236676	+	0.956323i
$265$	−2.08672	+	1.39430i	−0.128186	+	0.0856514i
$266$	12.4463	+	8.63155i	0.763131	+	0.529234i
$267$	−1.68875	+	0.902655i	−0.103350	+	0.0552416i
$268$	7.00472	+	14.2719i	0.427881	+	0.871794i
$269$	−20.9849	−	2.06683i	−1.27947	−	0.126017i	−0.564653	−	0.825328i	$-0.690990\pi$
$269$	−20.9849	−	2.06683i	−1.27947	−	0.126017i	−0.714817	+	0.699312i	$0.753490\pi$
$270$	−1.06756	−	3.75178i	−0.0649694	−	0.228326i
$271$	21.4754	−	8.89538i	1.30454	−	0.540356i	0.381250	−	0.924472i	$-0.375494\pi$
$271$	21.4754	−	8.89538i	1.30454	−	0.540356i	0.923285	+	0.384116i	$0.125494\pi$
$272$	3.69746	+	0.256340i	0.224191	+	0.0155429i
$273$	−11.7645	−	4.87300i	−0.712018	−	0.294927i
$274$	0.664285	−	5.72683i	0.0401309	−	0.345970i
$275$	−11.4083	+	9.36257i	−0.687948	+	0.564584i
$276$	−2.93477	−	11.0358i	−0.176653	−	0.664280i
$277$	−17.2484	−	5.23226i	−1.03636	−	0.314376i	−0.274136	−	0.961691i	$-0.588392\pi$
$277$	−17.2484	−	5.23226i	−1.03636	−	0.314376i	−0.762222	+	0.647315i	$0.775892\pi$
$278$	−4.04165	+	18.6281i	−0.242402	+	1.11724i
$279$	−1.76006	+	8.84840i	−0.105372	+	0.529740i
$280$	−13.3183	−	22.3634i	−0.795922	−	1.33647i
$281$	8.77904	−	1.74626i	0.523714	−	0.104173i	0.0738482	−	0.997269i	$-0.476472\pi$
$281$	8.77904	−	1.74626i	0.523714	−	0.104173i	0.449865	+	0.893096i	$0.351472\pi$
$282$	−8.85310	+	8.55189i	−0.527194	+	0.509257i
$283$	13.1485	+	10.7907i	0.781598	+	0.641441i	0.938150	−	0.346229i	$-0.112538\pi$
$283$	13.1485	+	10.7907i	0.781598	+	0.641441i	−0.156552	+	0.987670i	$0.550038\pi$
$284$	9.04982	−	19.8737i	0.537008	−	1.17929i
$285$	−4.17377	+	7.80858i	−0.247233	+	0.462540i
$286$	−9.37165	+	29.0733i	−0.554157	+	1.71914i
$287$	0.865236	−	0.865236i	0.0510733	−	0.0510733i
$288$	−1.16817	−	5.53492i	−0.0688351	−	0.326148i
$289$	−11.4137	−	11.4137i	−0.671395	−	0.671395i
$290$	−15.7093	+	8.05046i	−0.922482	+	0.472739i
$291$	−7.33575	−	3.92104i	−0.430029	−	0.229856i
$292$	−2.52782	+	2.35863i	−0.147929	+	0.138029i
$293$	13.1822	−	16.0626i	0.770114	−	0.938387i	−0.229274	−	0.973362i	$-0.573635\pi$
$293$	13.1822	−	16.0626i	0.770114	−	0.938387i	0.999388	+	0.0349751i	$0.0111352\pi$
$294$	−0.101107	+	5.84224i	−0.00589668	+	0.340726i
$295$	−0.159962	−	0.804183i	−0.00931334	−	0.0468213i
$296$	21.0928	−	7.47996i	1.22599	−	0.434764i
$297$	5.55065	+	1.10409i	0.322082	+	0.0640660i
$298$	−7.10112	+	4.56909i	−0.411357	+	0.264680i
$299$	6.32577	−	20.8533i	0.365829	−	1.20598i
$300$	4.14371	−	3.16720i	0.239237	−	0.182858i
$301$	23.7329	+	28.9186i	1.36794	+	1.66684i
$302$	12.6167	+	15.9277i	0.726009	+	0.916536i
$303$	−3.09638	+	7.47532i	−0.177882	+	0.429446i
$304$	−6.82157	+	10.8784i	−0.391244	+	0.623916i
$305$	−11.6216	−	28.0569i	−0.665449	−	1.60654i
$306$	0.637617	−	1.14480i	0.0364501	−	0.0654437i
$307$	−1.87442	+	19.0313i	−0.106979	+	1.08617i	0.780446	+	0.625223i	$0.214992\pi$
$307$	−1.87442	+	19.0313i	−0.106979	+	1.08617i	−0.887425	+	0.460952i	$0.847508\pi$
$308$	37.6880	−	2.39890i	2.14747	−	0.136690i
$309$	2.89413	+	5.41454i	0.164641	+	0.308022i
$310$	−34.6286	+	6.26720i	−1.96677	+	0.355953i
$311$	0.543551	+	0.813481i	0.0308219	+	0.0461283i	0.846561	−	0.532292i	$-0.178669\pi$
$311$	0.543551	+	0.813481i	0.0308219	+	0.0461283i	−0.815739	+	0.578421i	$0.803669\pi$
$312$	3.66542	−	10.1536i	0.207514	−	0.574835i
$313$	−16.7270	−	11.1766i	−0.945465	−	0.631739i	−0.0156934	−	0.999877i	$-0.504996\pi$
$313$	−16.7270	−	11.1766i	−0.945465	−	0.631739i	−0.929771	+	0.368138i	$0.879996\pi$
$314$	2.03224	+	5.15689i	0.114686	+	0.291020i
$315$	−9.15826	+	0.902009i	−0.516009	+	0.0508225i
$316$	17.7140	−	10.9691i	0.996492	−	0.617058i
$317$	10.0869	−	3.05982i	0.566534	−	0.171856i	0.00599200	−	0.999982i	$-0.498093\pi$
$317$	10.0869	−	3.05982i	0.566534	−	0.171856i	0.560542	+	0.828126i	$0.310593\pi$
$318$	0.103949	+	1.28258i	0.00582917	+	0.0719233i
$319$		−	25.6106i		−	1.43392i
$320$	18.4160	−	12.1552i	1.02948	−	0.679494i
$321$		−	12.2476i		−	0.683594i
$322$	−26.8527	+	2.17633i	−1.49644	+	0.121282i
$323$	−2.84632	+	0.863421i	−0.158373	+	0.0480420i
$324$	−1.94689	−	0.457821i	−0.108161	−	0.0254345i
$325$	9.90481	−	0.975539i	0.549420	−	0.0541132i
$326$	−5.58015	+	2.19904i	−0.309056	+	0.121793i
$327$	14.4015	+	9.62275i	0.796403	+	0.532139i
$328$	0.766634	+	0.698793i	0.0423303	+	0.0385844i
$329$	16.1335	+	24.1455i	0.889468	+	1.33118i
$330$	3.93145	+	21.7227i	0.216419	+	1.19580i
$331$	10.9691	+	20.5218i	0.602918	+	1.12798i	0.979471	+	0.201586i	$0.0646095\pi$
$331$	10.9691	+	20.5218i	0.602918	+	1.12798i	−0.376552	+	0.926395i	$0.622891\pi$
$332$	20.1734	−	22.9161i	1.10716	−	1.25769i
$333$	0.775557	−	7.87436i	0.0425003	−	0.431512i
$334$	14.4537	+	8.05029i	0.790874	+	0.440492i
$335$	8.39046	+	20.2564i	0.458420	+	1.10672i
$336$	−13.3401	+	0.386395i	−0.727762	+	0.0210796i
$337$	3.06634	−	7.40280i	0.167034	−	0.403256i	−0.818092	−	0.575087i	$-0.804968\pi$
$337$	3.06634	−	7.40280i	0.167034	−	0.403256i	0.985127	+	0.171831i	$0.0549682\pi$
$338$	1.73644	−	1.37547i	0.0944499	−	0.0748159i
$339$	0.947690	+	1.15476i	0.0514714	+	0.0627181i
$340$	5.06644	+	0.676723i	0.274766	+	0.0367004i
$341$	14.8213	−	48.8591i	0.802616	−	2.64587i
$342$	2.45644	+	3.81771i	0.132829	+	0.206438i
$343$	−9.38596	−	1.86698i	−0.506794	−	0.100808i
$344$	−23.5589	+	21.2316i	−1.27021	+	1.14473i
$345$	−3.07240	−	15.4460i	−0.165412	−	0.831584i
$346$	5.69635	+	0.0985823i	0.306238	+	0.00529982i
$347$	22.3529	−	27.2371i	1.19996	−	1.46216i	0.348853	−	0.937177i	$-0.386571\pi$
$347$	22.3529	−	27.2371i	1.19996	−	1.46216i	0.851112	−	0.524984i	$-0.175929\pi$
$348$	−0.313171	+	9.04524i	−0.0167877	+	0.484876i
$349$	29.4116	+	15.7208i	1.57437	+	0.841516i	0.999733	+	0.0231038i	$0.00735484\pi$
$349$	29.4116	+	15.7208i	1.57437	+	0.841516i	0.574632	+	0.818412i	$0.305145\pi$
$350$	−5.61164	−	10.9503i	−0.299955	−	0.585318i
$351$	−2.69874	−	2.69874i	−0.144048	−	0.144048i
$352$	3.50898	+	31.8215i	0.187029	+	1.69609i
$353$	−14.0477	+	14.0477i	−0.747685	+	0.747685i	−0.974044	−	0.226359i	$-0.927318\pi$
$353$	−14.0477	+	14.0477i	−0.747685	+	0.747685i	0.226359	+	0.974044i	$0.427318\pi$
$354$	−0.400130	−	0.128980i	−0.0212667	−	0.00685521i
$355$	14.1965	−	26.5598i	0.753473	−	1.40965i
$356$	−3.58678	+	1.34226i	−0.190099	+	0.0711396i
$357$	−2.38974	−	1.96121i	−0.126479	−	0.103798i
$358$	4.79625	+	4.96518i	0.253489	+	0.262418i
$359$	−15.8950	+	3.16171i	−0.838906	+	0.166869i	−0.595802	−	0.803131i	$-0.703166\pi$
$359$	−15.8950	+	3.16171i	−0.838906	+	0.166869i	−0.243104	+	0.970000i	$0.578166\pi$
$360$	−1.12289	−	7.72018i	−0.0591816	−	0.406889i
$361$	−1.69640	+	8.52840i	−0.0892844	+	0.448863i
$362$	−9.10004	−	1.97440i	−0.478288	−	0.103772i
$363$	−20.1233	−	6.10433i	−1.05620	−	0.320394i
$364$	−22.0315	−	12.7753i	−1.15476	−	0.669607i
$365$	−3.68572	+	3.02479i	−0.192919	+	0.158325i
$366$	−15.4671	−	1.79411i	−0.808480	−	0.0937798i
$367$	−3.02931	−	1.25478i	−0.158129	−	0.0654991i	0.302215	−	0.953240i	$-0.402274\pi$
$367$	−3.02931	−	1.25478i	−0.158129	−	0.0654991i	−0.460344	+	0.887741i	$0.652274\pi$
$368$	−2.89572	−	22.6545i	−0.150950	−	1.18095i
$369$	0.338832	−	0.140349i	0.0176389	−	0.00730626i
$370$	29.6858	−	8.44699i	1.54329	−	0.439138i
$371$	3.02117	+	0.297559i	0.156851	+	0.0154485i
$372$	−5.83207	+	17.0750i	−0.302379	+	0.885296i
$373$	16.4229	−	8.77821i	0.850345	−	0.454519i	0.0121734	−	0.999926i	$-0.496125\pi$
$373$	16.4229	−	8.77821i	0.850345	−	0.454519i	0.838171	+	0.545407i	$0.183625\pi$
$374$	−4.22619	+	6.09396i	−0.218531	+	0.315111i
$375$	−5.48631	+	3.66584i	−0.283312	+	0.189303i
$376$	−19.8148	+	14.6090i	−1.02187	+	0.753403i
$377$	−9.59544	+	14.3606i	−0.494190	+	0.739608i
$378$	−1.88082	+	4.32735i	−0.0967389	+	0.222575i
$379$	−1.46995	−	14.9247i	−0.0755065	−	0.766630i	−0.956155	−	0.292861i	$-0.905393\pi$
$379$	−1.46995	−	14.9247i	−0.0755065	−	0.766630i	0.880649	−	0.473770i	$-0.157107\pi$
$380$	−10.3417	+	14.3745i	−0.530517	+	0.737397i
$381$	0.368443	+	1.21459i	0.0188759	+	0.0622256i
$382$	15.1428	+	12.8722i	0.774771	+	0.658601i
$383$	−5.61708			−0.287020			−0.143510	−	0.989649i	$-0.545839\pi$
$383$	−5.61708			−0.287020			−0.143510	+	0.989649i	$0.545839\pi$
$384$	−0.850195	−	11.2817i	−0.0433863	−	0.575718i
$385$	52.0810			2.65429
$386$	17.3105	+	14.7150i	0.881083	+	0.748972i
$387$	3.25488	+	10.7299i	0.165455	+	0.545432i
$388$	−13.5041	−	9.71547i	−0.685567	−	0.493228i
$389$	1.34914	+	13.6980i	0.0684039	+	0.694516i	0.966835	+	0.255402i	$0.0822077\pi$
$389$	1.34914	+	13.6980i	0.0684039	+	0.694516i	−0.898431	+	0.439114i	$0.855292\pi$
$390$	5.93431	−	13.6535i	0.300495	−	0.691374i
$391$	2.93925	−	4.39891i	0.148644	−	0.222462i
$392$	−1.74739	+	11.5549i	−0.0882564	+	0.583608i
$393$	12.8231	−	8.56810i	0.646838	−	0.432204i
$394$	15.8431	−	22.8450i	0.798163	−	1.15091i
$395$	25.3412	−	13.5451i	1.27505	−	0.681530i
$396$	10.7112	+	3.65849i	0.538260	+	0.183846i
$397$	−22.1607	−	2.18264i	−1.11222	−	0.109544i	−0.474822	−	0.880082i	$-0.657487\pi$
$397$	−22.1607	−	2.18264i	−1.11222	−	0.109544i	−0.637393	+	0.770538i	$0.719987\pi$
$398$	−23.6812	+	6.73839i	−1.18703	+	0.337765i
$399$	9.89487	−	4.09859i	0.495363	−	0.205186i
$400$	9.05311	−	5.18143i	0.452656	−	0.259072i
$401$	17.6981	+	7.33081i	0.883803	+	0.366083i	0.777970	−	0.628301i	$-0.216249\pi$
$401$	17.6981	+	7.33081i	0.883803	+	0.366083i	0.105832	+	0.994384i	$0.466249\pi$
$402$	11.1669	+	1.29530i	0.556952	+	0.0646038i
$403$	−26.6166	+	21.8437i	−1.32587	+	1.08811i
$404$	−8.11761	+	13.9991i	−0.403866	+	0.696483i
$405$	−2.63945	−	0.800668i	−0.131155	−	0.0397855i
$406$	20.8669	+	4.52739i	1.03561	+	0.224691i
$407$	−8.73610	+	43.9193i	−0.433032	+	2.17700i
$408$	1.56714	−	2.10061i	0.0775848	−	0.103995i
$409$	21.6955	−	4.31551i	1.07277	−	0.213388i	0.373057	−	0.927808i	$-0.378309\pi$
$409$	21.6955	−	4.31551i	1.07277	−	0.213388i	0.699717	+	0.714420i	$0.253309\pi$
$410$	0.993917	+	1.02893i	0.0490861	+	0.0508150i
$411$	−3.15128	−	2.58619i	−0.155441	−	0.127567i
$412$	4.30360	+	11.5001i	0.212023	+	0.566568i
$413$	−0.467541	+	0.874708i	−0.0230062	+	0.0430416i
$414$	−7.68533	−	2.47733i	−0.377713	−	0.121754i
$415$	29.7727	−	29.7727i	1.46148	−	1.46148i
$416$	9.95486	−	19.1579i	0.488077	−	0.939293i
$417$	9.53074	+	9.53074i	0.466722	+	0.466722i
$418$	−11.7173	−	22.8645i	−0.573110	−	1.11834i
$419$	19.1554	+	10.2388i	0.935800	+	0.500196i	0.867482	−	0.497468i	$-0.165737\pi$
$419$	19.1554	+	10.2388i	0.935800	+	0.500196i	0.0683180	+	0.997664i	$0.478237\pi$
$420$	−18.3941	−	0.636855i	−0.897541	−	0.0310754i
$421$	11.0608	−	13.4776i	0.539070	−	0.656859i	−0.430236	−	0.902717i	$-0.641570\pi$
$421$	11.0608	−	13.4776i	0.539070	−	0.656859i	0.969306	+	0.245858i	$0.0790695\pi$
$422$	−3.50786	−	0.0607078i	−0.170760	−	0.00295521i
$423$	1.69803	+	8.53655i	0.0825609	+	0.415061i
$424$	−0.133543	+	2.57010i	−0.00648540	+	0.124815i
$425$	2.36987	+	0.471397i	0.114956	+	0.0228661i
$426$	−8.35524	−	12.9854i	−0.404813	−	0.629146i
$427$	−10.6635	+	35.1530i	−0.516045	+	1.70117i
$428$	3.24301	−	24.2796i	0.156757	−	1.17360i
$429$	13.7027	+	16.6967i	0.661570	+	0.806126i
$430$	−34.2846	+	27.1576i	−1.65335	+	1.30966i
$431$	−1.08407	+	2.61718i	−0.0522178	+	0.126065i	−0.947836	−	0.318759i	$-0.896734\pi$
$431$	−1.08407	+	2.61718i	−0.0522178	+	0.126065i	0.895618	+	0.444824i	$0.146734\pi$
$432$	−3.73829	−	1.42310i	−0.179858	−	0.0684688i
$433$	−1.67653	−	4.04749i	−0.0805687	−	0.194510i	0.878462	−	0.477812i	$-0.158570\pi$
$433$	−1.67653	−	4.04749i	−0.0805687	−	0.194510i	−0.959031	+	0.283302i	$0.908570\pi$
$434$	37.1891	+	20.7132i	1.78513	+	0.994265i
$435$	−1.22343	+	12.4217i	−0.0586591	+	0.595576i
$436$	26.0014	+	22.8894i	1.24524	+	1.09620i
$437$	8.64000	+	16.1643i	0.413307	+	0.773244i
$438$	0.435375	+	2.40561i	0.0208030	+	0.114944i
$439$	1.59577	+	2.38824i	0.0761619	+	0.113984i	0.867595	−	0.497271i	$-0.165665\pi$
$439$	1.59577	+	2.38824i	0.0761619	+	0.113984i	−0.791433	+	0.611256i	$0.790665\pi$
$440$	2.04177	+	44.1040i	0.0973375	+	2.10258i
$441$	3.43539	+	2.29545i	0.163590	+	0.109307i
$442$	4.65295	−	1.83364i	0.221318	−	0.0872176i
$443$	−24.4552	+	2.40862i	−1.16190	+	0.114437i	−0.660532	−	0.750798i	$-0.729669\pi$
$443$	−24.4552	+	2.40862i	−1.16190	+	0.114437i	−0.501367	+	0.865235i	$0.667169\pi$
$444$	3.62249	−	15.4047i	0.171916	−	0.731076i
$445$	−5.05415	+	1.53316i	−0.239590	+	0.0726788i
$446$	9.97743	−	0.808641i	0.472445	−	0.0382903i
$447$			5.97086i			0.282412i
$448$	−26.5476	−	2.76630i	−1.25426	−	0.130696i
$449$			34.6849i			1.63688i	0.574592	+	0.818440i	$0.305161\pi$
$449$			34.6849i			1.63688i	−0.574592	+	0.818440i	$0.694839\pi$
$450$	−0.297918	−	3.67587i	−0.0140440	−	0.173282i
$451$	−1.98620	+	0.602508i	−0.0935267	+	0.0283710i
$452$	1.57293	+	2.54013i	0.0739843	+	0.119478i
$453$	14.2987	−	1.40830i	0.671812	−	0.0661677i
$454$	−14.8445	−	37.6685i	−0.696686	−	1.76787i
$455$	−29.2033	−	19.5130i	−1.36907	−	0.914783i
$456$	3.85875	+	8.21865i	0.180702	+	0.384874i
$457$	10.4150	+	15.5871i	0.487192	+	0.729135i	0.990879	−	0.134751i	$-0.0430236\pi$
$457$	10.4150	+	15.5871i	0.487192	+	0.729135i	−0.503687	+	0.863886i	$0.668024\pi$
$458$	12.2164	−	2.21097i	0.570837	−	0.103312i
$459$	−0.436789	−	0.817174i	−0.0203875	−	0.0381424i
$460$	−2.00080	−	31.4336i	−0.0932876	−	1.46560i
$461$	1.64077	−	16.6590i	0.0764181	−	0.775886i	−0.878248	−	0.478206i	$-0.841287\pi$
$461$	1.64077	−	16.6590i	0.0764181	−	0.775886i	0.954666	−	0.297680i	$-0.0962127\pi$
$462$	12.9935	−	23.3289i	0.604512	−	1.08536i
$463$	1.20652	+	2.91279i	0.0560717	+	0.135369i	0.949433	−	0.313971i	$-0.101659\pi$
$463$	1.20652	+	2.91279i	0.0560717	+	0.135369i	−0.893361	+	0.449340i	$0.851659\pi$
$464$	−3.01590	+	17.8483i	−0.140009	+	0.828587i
$465$	−9.52267	+	22.9898i	−0.441603	+	1.06612i
$466$	2.53521	+	3.20053i	0.117441	+	0.148262i
$467$	−24.0542	−	29.3101i	−1.11309	−	1.35631i	−0.927561	−	0.373671i	$-0.878099\pi$
$467$	−24.0542	−	29.3101i	−1.11309	−	1.35631i	−0.185533	−	0.982638i	$-0.559401\pi$
$468$	−4.63537	−	6.06456i	−0.214270	−	0.280334i
$469$	7.69880	−	25.3795i	0.355498	−	1.17192i
$470$	−28.5513	+	18.3708i	−1.31697	+	0.847384i
$471$	3.84410	+	0.764639i	0.177127	+	0.0352327i
$472$	−0.759064	−	0.361639i	−0.0349387	−	0.0166458i
$473$	−12.3799	−	62.2379i	−0.569228	−	2.86170i
$474$	0.254930	−	14.7305i	0.0117093	−	0.676596i
$475$	−5.31054	+	6.47092i	−0.243664	+	0.296906i
$476$	−4.21811	−	4.52067i	−0.193337	−	0.207204i
$477$	0.802454	+	0.428920i	0.0367418	+	0.0196389i
$478$	−19.1551	+	9.81632i	−0.876135	+	0.448988i
$479$	5.79614	+	5.79614i	0.264832	+	0.264832i	0.827014	−	0.562181i	$-0.190038\pi$
$479$	5.79614	+	5.79614i	0.264832	+	0.264832i	−0.562181	+	0.827014i	$0.690038\pi$
$480$	−0.181806	−	15.6018i	−0.00829827	−	0.712120i
$481$	21.3537	−	21.3537i	0.973644	−	0.973644i
$482$	−9.30730	+	28.8737i	−0.423936	+	1.31516i
$483$	−8.98009	+	16.8006i	−0.408608	+	0.764453i
$484$	−38.2759	−	17.4296i	−1.73981	−	0.792254i
$485$	−17.7349	−	14.5546i	−0.805300	−	0.660892i
$486$	−1.01715	+	0.982547i	−0.0461390	+	0.0445692i
$487$	26.6912	−	5.30922i	1.20950	−	0.240584i	0.451157	−	0.892445i	$-0.351011\pi$
$487$	26.6912	−	5.30922i	1.20950	−	0.240584i	0.758338	+	0.651861i	$0.226011\pi$
$488$	−30.1869	−	7.65215i	−1.36650	−	0.346396i
$489$	−0.827397	+	4.15960i	−0.0374162	+	0.188104i
$490$	−3.41723	+	15.7501i	−0.154375	+	0.711518i
$491$	−3.93252	−	1.19292i	−0.177472	−	0.0538356i	0.200298	−	0.979735i	$-0.435809\pi$
$491$	−3.93252	−	1.19292i	−0.177472	−	0.0538356i	−0.377770	+	0.925899i	$0.623309\pi$
$492$	0.708861	−	0.188508i	0.0319579	−	0.00849860i
$493$	−3.24131	+	2.66007i	−0.145981	+	0.119804i
$494$	−1.99638	+	17.2109i	−0.0898214	+	0.774353i
$495$	14.4216	+	5.97362i	0.648203	+	0.268494i
$496$	−16.0827	+	32.3051i	−0.722135	+	1.45054i
$497$	−33.6560	+	13.9408i	−1.50968	+	0.625330i
$498$	−5.90836	−	20.7641i	−0.264760	−	0.930462i
$499$	−7.21550	−	0.710665i	−0.323010	−	0.0318137i	−0.0647872	−	0.997899i	$-0.520637\pi$
$499$	−7.21550	−	0.710665i	−0.323010	−	0.0318137i	−0.258223	+	0.966085i	$0.583137\pi$
$500$	−11.8467	+	5.81443i	−0.529801	+	0.260029i
$501$	10.3173	−	5.51472i	0.460943	−	0.246379i
$502$	−2.79346	−	1.93728i	−0.124678	−	0.0864649i
$503$	30.5874	−	20.4378i	1.36382	−	0.911278i	0.364026	−	0.931389i	$-0.381402\pi$
$503$	30.5874	−	20.4378i	1.36382	−	0.911278i	0.999798	+	0.0201108i	$0.00640189\pi$
$504$	−4.87435	+	8.08049i	−0.217121	+	0.359934i
$505$	−12.3989	+	18.5562i	−0.551742	+	0.825740i
$506$	41.9107	+	18.2159i	1.86316	+	0.809794i
$507$	−0.153533	−	1.55885i	−0.00681864	−	0.0692308i
$508$	0.408790	+	2.50536i	0.0181371	+	0.111158i
$509$	−3.08105	−	10.1569i	−0.136565	−	0.450195i	0.861807	−	0.507237i	$-0.169333\pi$
$509$	−3.08105	−	10.1569i	−0.136565	−	0.450195i	−0.998372	+	0.0570421i	$0.981833\pi$
$510$	2.34091	−	2.75382i	0.103657	−	0.121941i
$511$	5.76753			0.255140
$512$	1.30184	−	22.5899i	0.0575337	−	0.998344i
$513$	3.21007			0.141728
$514$	9.24474	−	10.8754i	0.407768	−	0.479694i
$515$	4.91568	+	16.2048i	0.216611	+	0.714070i
$516$	3.61131	+	22.1328i	0.158979	+	0.974341i
$517$	−4.82815	−	49.0210i	−0.212342	−	2.15594i
$518$	−34.2400	−	14.8819i	−1.50442	−	0.653873i
$519$	2.23813	−	3.34960i	0.0982432	−	0.147031i
$520$	15.3794	−	25.4954i	0.674433	−	1.11805i
$521$	−7.45955	+	4.98432i	−0.326809	+	0.218367i	−0.708140	−	0.706072i	$-0.750466\pi$
$521$	−7.45955	+	4.98432i	−0.326809	+	0.218367i	0.381331	+	0.924438i	$0.375466\pi$
$522$	5.25890	+	3.64707i	0.230176	+	0.159628i
$523$	0.137896	−	0.0737070i	0.00602978	−	0.00322298i	−0.468379	−	0.883528i	$-0.655162\pi$
$523$	0.137896	−	0.0737070i	0.00602978	−	0.00322298i	0.474409	+	0.880305i	$0.342662\pi$
$524$	27.6891	−	13.5900i	1.20960	−	0.593680i
$525$	−8.65867	−	0.852804i	−0.377895	−	0.0372194i
$526$	−3.83230	−	13.4681i	−0.167096	−	0.587236i
$527$	−7.72309	+	3.19901i	−0.336423	+	0.139351i
$528$	20.2652	+	10.0888i	0.881928	+	0.439058i
$529$	−8.86989	−	3.67403i	−0.385647	−	0.159740i
$530$	−0.408951	+	3.52558i	−0.0177637	+	0.153142i
$531$	−0.229794	+	0.188587i	−0.00997219	+	0.00818397i
$532$	20.7008	−	5.50498i	0.897493	−	0.238671i
$533$	1.33946	+	0.406321i	0.0580184	+	0.0175997i
$534$	−0.574186	+	2.64644i	−0.0248474	+	0.114523i
$535$	6.59045	−	33.1324i	0.284930	−	1.43244i
$536$	21.7941	+	5.52465i	0.941363	+	0.238628i
$537$	4.78765	−	0.952322i	0.206602	−	0.0410957i
$538$	−21.4481	+	20.7184i	−0.924694	+	0.893233i
$539$	−18.0753	−	14.8340i	−0.778557	−	0.638945i
$540$	−5.02042	−	2.28613i	−0.216044	−	0.0983795i
$541$	1.55420	−	2.90771i	0.0668204	−	0.125012i	−0.846293	−	0.532717i	$-0.821171\pi$
$541$	1.55420	−	2.90771i	0.0668204	−	0.125012i	0.913114	+	0.407705i	$0.133671\pi$
$542$	10.0854	−	31.2877i	0.433207	−	1.34392i
$543$	−4.65588	+	4.65588i	−0.199803	+	0.199803i
$544$	3.66290	−	3.74927i	0.157045	−	0.160749i
$545$	33.7811	+	33.7811i	1.44702	+	1.44702i
$546$	−16.0264	+	8.21295i	−0.685866	+	0.351482i
$547$	35.7187	+	19.0920i	1.52722	+	0.816316i	0.999453	−	0.0330736i	$-0.0105296\pi$
$547$	35.7187	+	19.0920i	1.52722	+	0.816316i	0.527767	+	0.849389i	$0.323030\pi$
$548$	−5.56228	−	5.96126i	−0.237609	−	0.254652i
$549$	−6.98482	+	8.51103i	−0.298105	+	0.363242i
$550$	−0.361151	+	20.8683i	−0.0153995	+	0.889826i
$551$	−2.83400	−	14.2475i	−0.120732	−	0.606963i
$552$	−14.5794	−	6.94602i	−0.620540	−	0.295642i
$553$	−34.0897	−	6.78086i	−1.44964	−	0.288352i
$554$	−21.4365	+	13.7929i	−0.910751	+	0.586006i
$555$	6.33525	−	20.8845i	0.268917	−	0.886499i
$556$	16.3701	+	21.4173i	0.694245	+	0.908296i
$557$	−24.6586	−	30.0466i	−1.04482	−	1.27312i	−0.960974	−	0.276638i	$-0.910780\pi$
$557$	−24.6586	−	30.0466i	−1.04482	−	1.27312i	−0.0838454	−	0.996479i	$-0.526720\pi$
$558$	7.92215	+	10.0012i	0.335371	+	0.423383i
$559$	−16.3767	+	39.5369i	−0.692661	+	1.67223i
$560$	−36.2958	−	6.13304i	−1.53378	−	0.259168i
$561$	2.00676	+	4.84474i	0.0847253	+	0.204545i
$562$	6.15954	−	11.0590i	0.259824	−	0.466497i
$563$	−1.93729	+	19.6697i	−0.0816472	+	0.828978i	0.863937	+	0.503600i	$0.167991\pi$
$563$	−1.93729	+	19.6697i	−0.0816472	+	0.828978i	−0.945584	+	0.325378i	$0.894509\pi$
$564$	1.10578	+	17.3724i	0.0465619	+	0.731511i
$565$	1.94233	+	3.63384i	0.0817143	+	0.152877i
$566$	23.6705	−	4.28396i	0.994946	−	0.180068i
$567$	1.85362	+	2.77413i	0.0778446	+	0.116503i
$568$	−13.1250	−	27.9546i	−0.550713	−	1.17295i
$569$	−21.5945	−	14.4290i	−0.905288	−	0.604894i	0.0133859	−	0.999910i	$-0.495739\pi$
$569$	−21.5945	−	14.4290i	−0.905288	−	0.604894i	−0.918674	+	0.395016i	$0.870739\pi$
$570$	4.59089	+	11.6496i	0.192291	+	0.487946i
$571$	−45.8579	+	4.51661i	−1.91909	+	0.189014i	−0.985542	−	0.169432i	$-0.945807\pi$
$571$	−45.8579	+	4.51661i	−1.91909	+	0.189014i	−0.933550	+	0.358447i	$0.883307\pi$
$572$	22.7430	+	36.7278i	0.950931	+	1.53567i
$573$	13.4483	−	4.07950i	0.561811	−	0.170423i
$574$	−0.139791	−	1.72482i	−0.00583478	−	0.0719925i
$575$		−	14.8895i		−	0.620935i
$576$	−7.03394	−	3.81099i	−0.293081	−	0.158791i
$577$		−	15.1695i		−	0.631513i	−0.948840	−	0.315757i	$-0.897742\pi$
$577$		−	15.1695i		−	0.631513i	0.948840	−	0.315757i	$-0.102258\pi$
$578$	−22.7528	+	1.84405i	−0.946393	+	0.0767024i
$579$	15.3735	−	4.66350i	0.638900	−	0.193808i
$580$	−5.71445	+	24.3008i	−0.237280	+	1.00904i
$581$	−50.6861	+	4.99215i	−2.10282	+	0.207109i
$582$	−10.9442	+	4.31290i	−0.453650	+	0.178775i
$583$	−4.28160	−	2.86088i	−0.177326	−	0.118485i
$584$	0.226109	+	4.88415i	0.00935644	+	0.202107i
$585$	−5.84848	−	8.75287i	−0.241805	−	0.361887i
$586$	−5.23341	−	28.9166i	−0.216190	−	1.19453i
$587$	−5.03097	−	9.41229i	−0.207650	−	0.388487i	0.756439	−	0.654064i	$-0.226937\pi$
$587$	−5.03097	−	9.41229i	−0.207650	−	0.388487i	−0.964090	+	0.265578i	$0.914437\pi$
$588$	6.20249	+	5.46014i	0.255786	+	0.225172i
$589$	2.83862	−	28.8210i	0.116963	−	1.18755i
$590$	−1.01304	−	0.564230i	−0.0417060	−	0.0232290i
$591$	−7.52290	−	18.1619i	−0.309451	−	0.747080i
$592$	11.2602	−	29.5791i	0.462791	−	1.21569i
$593$	−3.77599	+	9.11606i	−0.155062	+	0.374352i	−0.982251	−	0.187572i	$-0.939938\pi$
$593$	−3.77599	+	9.11606i	−0.155062	+	0.374352i	0.827189	+	0.561923i	$0.189938\pi$
$594$	6.27379	−	4.96961i	0.257417	−	0.203906i
$595$	−5.40944	−	6.59142i	−0.221765	−	0.270222i
$596$	−1.58101	+	11.8366i	−0.0647608	+	0.484846i
$597$	−5.05380	+	16.6602i	−0.206838	+	0.681855i
$598$	−16.6756	−	25.9167i	−0.681916	−	1.05981i
$599$	−23.0272	−	4.58040i	−0.940867	−	0.187150i	−0.299249	−	0.954175i	$-0.596736\pi$
$599$	−23.0272	−	4.58040i	−0.940867	−	0.187150i	−0.641617	+	0.767025i	$0.721736\pi$
$600$	0.382733	−	7.36590i	0.0156250	−	0.300712i
$601$	4.51625	+	22.7047i	0.184222	+	0.926145i	0.956694	+	0.291096i	$0.0940200\pi$
$601$	4.51625	+	22.7047i	0.184222	+	0.926145i	−0.772472	+	0.635049i	$0.780980\pi$
$602$	52.8983	+	0.915469i	2.15597	+	0.0373117i
$603$	5.04286	−	6.14474i	0.205361	−	0.250233i
$604$	28.7186	+	0.994317i	1.16854	+	0.0404582i
$605$	−51.1531	−	27.3419i	−2.07967	−	1.11161i
$606$	5.21863	+	10.1834i	0.211992	+	0.413673i
$607$	−17.7808	−	17.7808i	−0.721699	−	0.721699i	0.247252	−	0.968951i	$-0.420472\pi$
$607$	−17.7808	−	17.7808i	−0.721699	−	0.721699i	−0.968951	+	0.247252i	$0.920472\pi$
$608$	5.47336	+	17.3144i	0.221974	+	0.702190i
$609$	10.6762	−	10.6762i	0.432621	−	0.432621i
$610$	−40.8765	−	13.1763i	−1.65504	−	0.533495i
$611$	−15.6593	+	29.2964i	−0.633506	+	1.18521i
$612$	−0.649510	−	1.73562i	−0.0262549	−	0.0701582i
$613$	10.4110	+	8.54410i	0.420497	+	0.345093i	0.820726	−	0.571322i	$-0.193569\pi$
$613$	10.4110	+	8.54410i	0.420497	+	0.345093i	−0.400229	+	0.916415i	$0.631069\pi$
$614$	18.7896	+	19.4514i	0.758288	+	0.784996i
$615$	0.992136	−	0.197348i	0.0400068	−	0.00795784i
$616$	31.9354	−	42.8066i	1.28672	−	1.72473i
$617$	−6.95603	+	34.9703i	−0.280039	+	1.40785i	0.542936	+	0.839774i	$0.317313\pi$
$617$	−6.95603	+	34.9703i	−0.280039	+	1.40785i	−0.822975	+	0.568077i	$0.807687\pi$
$618$	8.48512	+	1.84098i	0.341321	+	0.0740550i
$619$	−9.73874	−	2.95421i	−0.391433	−	0.118740i	0.0884321	−	0.996082i	$-0.471814\pi$
$619$	−9.73874	−	2.95421i	−0.391433	−	0.118740i	−0.479865	+	0.877342i	$0.659314\pi$
$620$	−24.9651	+	43.0533i	−1.00262	+	1.72906i
$621$	−4.41366	+	3.62220i	−0.177114	+	0.145354i
$622$	1.37440	+	0.159424i	0.0551085	+	0.00639233i
$623$	5.90244	+	2.44487i	0.236476	+	0.0979517i
$624$	−7.58332	−	13.2497i	−0.303576	−	0.530414i
$625$	−28.8605	+	11.9544i	−1.15442	+	0.478177i
$626$	−27.3640	+	7.78634i	−1.09369	+	0.311205i
$627$	−18.0795	−	1.78068i	−0.722028	−	0.0711135i
$628$	7.41806	+	2.53369i	0.296013	+	0.101105i
$629$	6.46586	−	3.45607i	0.257811	−	0.137803i
$630$	−7.41657	+	10.6943i	−0.295483	+	0.426073i
$631$	−32.1926	+	21.5104i	−1.28157	+	0.856316i	−0.994816	−	0.101689i	$-0.967575\pi$
$631$	−32.1926	+	21.5104i	−1.28157	+	0.856316i	−0.286751	+	0.958005i	$0.592575\pi$
$632$	4.40584	−	29.1342i	0.175255	−	1.15890i
$633$	−1.37826	+	2.06271i	−0.0547810	+	0.0819855i
$634$	5.94206	−	13.6714i	0.235989	−	0.542959i
$635$	0.343144	+	3.48400i	0.0136173	+	0.138258i
$636$	1.47721	+	1.06277i	0.0585751	+	0.0421415i
$637$	4.57751	+	15.0900i	0.181368	+	0.597889i
$638$	−27.5958	−	23.4580i	−1.09253	−	0.928713i
$639$	−10.9186			−0.431933
$640$	3.77075	−	30.9770i	0.149052	−	1.22447i
$641$	11.5175			0.454915			0.227458	−	0.973788i	$-0.426959\pi$
$641$	11.5175			0.454915			0.227458	+	0.973788i	$0.426959\pi$
$642$	−13.1970	−	11.2182i	−0.520842	−	0.442746i
$643$	−7.73065	−	25.4845i	−0.304867	−	1.00501i	−0.966818	−	0.255465i	$-0.917771\pi$
$643$	−7.73065	−	25.4845i	−0.304867	−	1.00501i	0.661951	−	0.749547i	$-0.269729\pi$
$644$	−22.2507	+	30.9275i	−0.876799	+	1.21872i
$645$	3.03139	+	30.7782i	0.119361	+	1.21189i
$646$	−1.67674	+	3.85780i	−0.0659703	+	0.151783i
$647$	5.63912	−	8.43954i	0.221697	−	0.331793i	−0.703903	−	0.710296i	$-0.748561\pi$
$647$	5.63912	−	8.43954i	0.221697	−	0.331793i	0.925600	+	0.378503i	$0.123561\pi$
$648$	−2.27657	+	1.67847i	−0.0894320	+	0.0659363i
$649$	1.39884	−	0.934677i	0.0549094	−	0.0366893i
$650$	8.02115	−	11.5661i	0.314615	−	0.453660i
$651$	26.5461	−	14.1892i	1.04043	−	0.556119i
$652$	−2.74164	+	8.02689i	−0.107371	+	0.314357i
$653$	3.64176	+	0.358682i	0.142513	+	0.0140363i	0.169022	−	0.985612i	$-0.445939\pi$
$653$	3.64176	+	0.358682i	0.142513	+	0.0140363i	−0.0265090	+	0.999649i	$0.508439\pi$
$654$	23.5597	−	6.70382i	0.921256	−	0.262140i
$655$	39.2997	−	16.2785i	1.53557	−	0.636052i
$656$	1.45516	−	0.186000i	0.0568143	−	0.00726206i
$657$	1.59707	+	0.661528i	0.0623077	+	0.0258087i
$658$	40.7946	+	4.73198i	1.59034	+	0.184472i
$659$	−1.79690	+	1.47467i	−0.0699971	+	0.0574452i	−0.668741	−	0.743495i	$-0.733167\pi$
$659$	−1.79690	+	1.47467i	−0.0699971	+	0.0574452i	0.598744	+	0.800940i	$0.295667\pi$
$660$	27.0076	+	15.6607i	1.05127	+	0.609594i
$661$	−25.5559	−	7.75228i	−0.994008	−	0.301529i	−0.248941	−	0.968519i	$-0.580082\pi$
$661$	−25.5559	−	7.75228i	−0.994008	−	0.301529i	−0.745067	+	0.666990i	$0.767582\pi$
$662$	32.1597	+	6.97755i	1.24992	+	0.271190i
$663$	0.689916	−	3.46844i	0.0267941	−	0.134703i
$664$	−6.21462	−	42.7271i	−0.241174	−	1.65813i
$665$	28.9732	−	5.76313i	1.12353	−	0.223485i
$666$	−7.77436	−	8.04819i	−0.301250	−	0.311861i
$667$	19.9733	+	16.3916i	0.773368	+	0.634686i
$668$	21.9132	−	8.20045i	0.847847	−	0.317285i
$669$	3.33666	−	6.24245i	0.129003	−	0.241347i
$670$	29.5118	+	9.51297i	1.14014	+	0.367518i
$671$	44.0607	−	44.0607i	1.70095	−	1.70095i
$672$	−11.8025	+	14.7281i	−0.455291	+	0.568147i
$673$	2.94032	+	2.94032i	0.113341	+	0.113341i	0.761503	−	0.648162i	$-0.224462\pi$
$673$	2.94032	+	2.94032i	0.113341	+	0.113341i	−0.648162	+	0.761503i	$0.724462\pi$
$674$	−5.16801	−	10.0846i	−0.199064	−	0.388445i
$675$	−2.29983	−	1.22929i	−0.0885206	−	0.0473153i
$676$	0.108401	−	3.13090i	0.00416925	−	0.120419i
$677$	−0.531064	+	0.647104i	−0.0204105	+	0.0248702i	−0.783116	−	0.621876i	$-0.786371\pi$
$677$	−0.531064	+	0.647104i	−0.0204105	+	0.0248702i	0.762705	+	0.646746i	$0.223871\pi$
$678$	2.11231	+	0.0365561i	0.0811227	+	0.00140393i
$679$	5.41416	+	27.2188i	0.207777	+	1.04456i
$680$	5.36978	−	4.83932i	0.205922	−	0.185579i
$681$	−28.0792	−	5.58530i	−1.07600	−	0.214029i
$682$	−39.0709	−	60.7226i	−1.49610	−	2.32519i
$683$	−13.3825	+	44.1161i	−0.512066	+	1.68806i	0.194912	+	0.980821i	$0.437558\pi$
$683$	−13.3825	+	44.1161i	−0.512066	+	1.68806i	−0.706978	+	0.707235i	$0.749942\pi$
$684$	6.36361	+	0.849986i	0.243319	+	0.0325000i
$685$	−7.13326	−	8.69190i	−0.272548	−	0.332100i
$686$	−10.6088	+	8.40344i	−0.405044	+	0.320845i
$687$	3.35945	−	8.11042i	0.128171	−	0.309432i
$688$	1.29856	+	44.8321i	0.0495071	+	1.70921i
$689$	1.32894	+	3.20835i	0.0506286	+	0.122228i
$690$	−19.4574	−	10.8372i	−0.740732	−	0.412565i
$691$	3.27198	−	33.2210i	0.124472	−	1.26379i	−0.706596	−	0.707617i	$-0.749770\pi$
$691$	3.27198	−	33.2210i	0.124472	−	1.26379i	0.831069	−	0.556170i	$-0.187730\pi$
$692$	5.32380	−	6.04760i	0.202380	−	0.229895i
$693$	−8.90097	−	16.6525i	−0.338120	−	0.632578i
$694$	−8.87420	−	49.0333i	−0.336860	−	1.86128i
$695$	20.6542	+	30.9112i	0.783459	+	1.17253i
$696$	9.45952	+	8.62243i	0.358562	+	0.326832i
$697$	0.282553	+	0.188796i	0.0107025	+	0.00715115i
$698$	43.8789	−	17.2919i	1.66084	−	0.654508i
$699$	2.87319	−	0.282985i	0.108674	−	0.0107035i
$700$	−16.9391	−	3.98330i	−0.640237	−	0.150555i
$701$	44.7888	−	13.5865i	1.69165	−	0.513156i	0.710058	−	0.704144i	$-0.248669\pi$
$701$	44.7888	−	13.5865i	1.69165	−	0.513156i	0.981593	+	0.190987i	$0.0611689\pi$
$702$	−5.37984	+	0.436020i	−0.203049	+	0.0164565i
$703$			25.3995i			0.957961i
$704$	37.5022	+	25.3659i	1.41342	+	0.956014i
$705$			24.0069i			0.904154i
$706$	2.26961	+	28.0036i	0.0854179	+	1.05393i
$707$	25.8333	−	7.83645i	0.971561	−	0.294720i
$708$	−0.505477	+	0.313007i	−0.0189970	+	0.0117635i
$709$	−13.6157	+	1.34103i	−0.511347	+	0.0503633i	−0.350401	−	0.936600i	$-0.613955\pi$
$709$	−13.6157	+	1.34103i	−0.511347	+	0.0503633i	−0.160946	+	0.986963i	$0.551455\pi$
$710$	−15.6153	−	39.6244i	−0.586031	−	1.48708i
$711$	−8.66193	−	5.78772i	−0.324848	−	0.217056i
$712$	−1.83901	+	5.09425i	−0.0689197	+	0.190915i
$713$	28.6183	+	42.8303i	1.07176	+	1.60401i
$714$	−4.30211	+	0.778610i	−0.161003	+	0.0291388i
$715$	28.0841	+	52.5417i	1.05029	+	1.96495i
$716$	9.74317	−	0.620168i	0.364119	−	0.0231768i
$717$	−1.49179	+	15.1464i	−0.0557120	+	0.565653i
$718$	−11.1522	+	20.0231i	−0.416198	+	0.747254i
$719$	3.28815	+	7.93830i	0.122627	+	0.296049i	0.973258	−	0.229715i	$-0.0737795\pi$
$719$	3.28815	+	7.93830i	0.122627	+	0.296049i	−0.850630	+	0.525764i	$0.823779\pi$
$720$	−9.34711	−	5.86136i	−0.348346	−	0.218440i
$721$	7.83884	−	18.9246i	0.291934	−	0.704790i
$722$	7.63565	+	9.63949i	0.284169	+	0.358745i
$723$	13.6086	+	16.5821i	0.506108	+	0.616694i
$724$	−10.4626	+	7.99698i	−0.388840	+	0.297205i
$725$	−3.42563	+	11.2928i	−0.127225	+	0.419404i
$726$	−25.0094	+	16.0918i	−0.928186	+	0.597224i
$727$	2.59083	+	0.515348i	0.0960886	+	0.0191132i	0.242900	−	0.970051i	$-0.421901\pi$
$727$	2.59083	+	0.515348i	0.0960886	+	0.0191132i	−0.146812	+	0.989164i	$0.546901\pi$
$728$	−33.9453	+	12.0377i	−1.25810	+	0.446148i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	−0.116678	+	6.74197i	−0.00431844	+	0.249532i
$731$	−6.59105	+	8.03121i	−0.243779	+	0.297045i
$732$	−16.1003	+	15.0227i	−0.595084	+	0.555256i
$733$	−20.2574	−	10.8278i	−0.748224	−	0.399934i	0.0527695	−	0.998607i	$-0.483195\pi$
$733$	−20.2574	−	10.8278i	−0.748224	−	0.399934i	−0.800994	+	0.598672i	$0.795695\pi$
$734$	−4.12674	+	2.11481i	−0.152321	+	0.0780590i
$735$	8.05828	+	8.05828i	0.297234	+	0.297234i
$736$	−27.0629	−	17.6302i	−0.997550	−	0.649858i
$737$	−31.8107	+	31.8107i	−1.17176	+	1.17176i
$738$	0.159125	−	0.493648i	0.00585748	−	0.0181714i
$739$	3.51307	−	6.57249i	0.129230	−	0.241773i	−0.808982	−	0.587834i	$-0.799981\pi$
$739$	3.51307	−	6.57249i	0.129230	−	0.241773i	0.938212	+	0.346061i	$0.112481\pi$
$740$	18.0889	−	39.7239i	0.664963	−	1.46028i
$741$	9.47055	+	7.77228i	0.347909	+	0.285522i
$742$	3.08786	−	2.98280i	0.113359	−	0.109502i
$743$	−0.874407	+	0.173930i	−0.0320789	+	0.00638089i	−0.211104	−	0.977464i	$-0.567706\pi$
$743$	−0.874407	+	0.173930i	−0.0320789	+	0.00638089i	0.179025	+	0.983845i	$0.442706\pi$
$744$	13.0566	+	21.9240i	0.478680	+	0.803771i
$745$	−3.21293	+	16.1525i	−0.117713	+	0.591781i
$746$	5.58388	−	25.7363i	0.204441	−	0.942272i
$747$	−14.6080	−	4.43128i	−0.534477	−	0.162132i
$748$	2.69535	+	10.1355i	0.0985519	+	0.370592i
$749$	−31.5876	+	25.9233i	−1.15419	+	0.947217i
$750$	−1.07520	+	9.26930i	−0.0392606	+	0.338467i
$751$	21.1816	+	8.77369i	0.772926	+	0.320156i	0.734057	−	0.679088i	$-0.237624\pi$
$751$	21.1816	+	8.77369i	0.772926	+	0.320156i	0.0388690	+	0.999244i	$0.487624\pi$
$752$	−2.40791	+	34.7318i	−0.0878075	+	1.26654i
$753$	−2.22082	+	0.919892i	−0.0809311	+	0.0335227i
$754$	6.68480	+	23.4928i	0.243446	+	0.855557i
$755$	39.4389	+	3.88439i	1.43533	+	0.141368i
$756$	2.94004	+	5.99024i	0.106928	+	0.217863i
$757$	−32.0171	+	17.1135i	−1.16368	+	0.622000i	−0.936091	−	0.351758i	$-0.885584\pi$
$757$	−32.0171	+	17.1135i	−1.16368	+	0.622000i	−0.227589	+	0.973757i	$0.573084\pi$
$758$	−17.4280	−	12.0864i	−0.633013	−	0.438997i
$759$	26.8677	−	17.9524i	0.975234	−	0.651631i
$760$	6.01629	+	24.3096i	0.218234	+	0.881803i
$761$	−10.8416	+	16.2255i	−0.393006	+	0.588176i	−0.974227	−	0.225571i	$-0.927575\pi$
$761$	−10.8416	+	16.2255i	−0.393006	+	0.588176i	0.581220	+	0.813746i	$0.302575\pi$
$762$	1.64622	+	0.715505i	0.0596362	+	0.0259200i
$763$	−5.66426	−	57.5102i	−0.205060	−	2.08201i
$764$	27.7400	−	4.52623i	1.00360	−	0.163753i
$765$	−0.741886	−	2.44567i	−0.0268229	−	0.0884234i
$766$	−5.14497	+	6.05249i	−0.185895	+	0.218685i
$767$	−1.13456			−0.0409667
$768$	−12.9349	−	9.41739i	−0.466750	−	0.339821i
$769$	−23.7664			−0.857038			−0.428519	−	0.903533i	$-0.640964\pi$
$769$	−23.7664			−0.857038			−0.428519	+	0.903533i	$0.640964\pi$
$770$	47.7036	−	56.1180i	1.71912	−	2.02235i
$771$	−2.92986	−	9.65846i	−0.105516	−	0.347841i
$772$	31.7112	−	5.17418i	1.14131	−	0.186223i
$773$	−0.374875	−	3.80617i	−0.0134833	−	0.136898i	0.986086	−	0.166234i	$-0.0531608\pi$
$773$	−0.374875	−	3.80617i	−0.0134833	−	0.136898i	−0.999570	+	0.0293358i	$0.990661\pi$
$774$	14.5429	+	6.32087i	0.522735	+	0.227199i
$775$	−13.0706	+	19.5616i	−0.469511	+	0.702672i
$776$	−22.8376	+	5.65199i	−0.819823	+	0.202895i
$777$	−21.9502	+	14.6667i	−0.787460	+	0.526164i
$778$	15.9955	+	11.0930i	0.573467	+	0.397702i
$779$	−1.03828	+	0.554970i	−0.0372001	+	0.0198839i
$780$	−9.27634	−	18.9003i	−0.332146	−	0.676738i
$781$	61.4951	+	6.05674i	2.20047	+	0.216727i
$782$	−2.04767	−	7.19626i	−0.0732246	−	0.257338i
$783$	4.18086	−	1.73177i	0.149412	−	0.0618883i
$784$	10.8500	+	12.4665i	0.387500	+	0.445232i
$785$	9.98767	+	4.13703i	0.356475	+	0.147657i
$786$	2.51304	−	21.6650i	0.0896371	−	0.772764i
$787$	−20.5142	+	16.8356i	−0.731254	+	0.600124i	−0.924570	−	0.381012i	$-0.875576\pi$
$787$	−20.5142	+	16.8356i	−0.731254	+	0.600124i	0.193316	+	0.981136i	$0.438076\pi$
$788$	−10.1043	−	37.9960i	−0.359951	−	1.35355i
$789$	−9.47505	−	2.87423i	−0.337321	−	0.102325i
$790$	8.61616	−	39.7121i	0.306549	−	1.41289i
$791$	0.972353	−	4.88835i	0.0345729	−	0.173810i
$792$	13.7530	−	8.19051i	0.488692	−	0.291037i
$793$	−41.2142	+	8.19801i	−1.46356	+	0.291120i
$794$	−22.6499	+	21.8793i	−0.803816	+	0.776467i
$795$	1.94001	+	1.59212i	0.0688050	+	0.0564668i
$796$	−14.4300	+	31.6888i	−0.511459	+	1.12318i
$797$	7.22228	−	13.5119i	0.255826	−	0.478617i	−0.720919	−	0.693019i	$-0.756280\pi$
$797$	7.22228	−	13.5119i	0.255826	−	0.478617i	0.976746	+	0.214402i	$0.0687802\pi$
$798$	4.64691	−	14.4160i	0.164499	−	0.510319i
$799$	−5.70267	+	5.70267i	−0.201746	+	0.201746i
$800$	2.70913	−	14.5008i	0.0957822	−	0.512680i
$801$	1.35401	+	1.35401i	0.0478414	+	0.0478414i
$802$	24.1097	−	12.3553i	0.851341	−	0.436282i
$803$	−8.62797	−	4.61175i	−0.304474	−	0.162745i
$804$	11.6240	−	10.8460i	0.409946	−	0.382509i
$805$	−33.3335	+	40.6170i	−1.17485	+	1.43156i
$806$	−0.842594	+	48.6874i	−0.0296791	+	1.71494i
$807$	4.11375	+	20.6812i	0.144811	+	0.728014i
$808$	7.64895	+	21.5694i	0.269089	+	0.758807i
$809$	32.6335	+	6.49121i	1.14733	+	0.228219i	0.731905	−	0.681407i	$-0.238632\pi$
$809$	32.6335	+	6.49121i	1.14733	+	0.228219i	0.415429	+	0.909626i	$0.363632\pi$
$810$	−3.28033	+	2.11067i	−0.115259	+	0.0741614i
$811$	5.24247	−	17.2821i	0.184088	−	0.606857i	−0.815516	−	0.578734i	$-0.803547\pi$
$811$	5.24247	−	17.2821i	0.184088	−	0.606857i	0.999604	−	0.0281230i	$-0.00895301\pi$
$812$	23.9913	−	18.3375i	0.841930	−	0.643519i
$813$	−14.7463	−	17.9684i	−0.517176	−	0.630181i
$814$	39.3219	+	49.6412i	1.37823	+	1.73992i
$815$	−4.47658	+	10.8074i	−0.156808	+	0.378567i
$816$	−0.828014	−	3.61266i	−0.0289863	−	0.126468i
$817$	−13.7741	−	33.2537i	−0.481896	−	1.16340i
$818$	15.2220	−	27.3300i	0.532224	−	0.955571i
$819$	−1.24813	+	12.6724i	−0.0436131	+	0.442811i
$820$	2.01906	−	0.128516i	0.0705086	−	0.00448798i
$821$	7.05716	+	13.2030i	0.246297	+	0.460789i	0.974444	−	0.224632i	$-0.0721181\pi$
$821$	7.05716	+	13.2030i	0.246297	+	0.460789i	−0.728147	+	0.685421i	$0.759618\pi$
$822$	−5.67306	+	1.02673i	−0.197871	+	0.0358113i
$823$	0.627265	+	0.938769i	0.0218651	+	0.0327234i	0.842241	−	0.539101i	$-0.181236\pi$
$823$	0.627265	+	0.938769i	0.0218651	+	0.0327234i	−0.820376	+	0.571824i	$0.806236\pi$
$824$	16.3334	+	5.89630i	0.569000	+	0.205407i
$825$	12.2711	+	8.19928i	0.427224	+	0.285462i
$826$	0.514266	+	1.30497i	0.0178936	+	0.0454058i
$827$	−9.62629	+	0.948107i	−0.334739	+	0.0329689i	−0.263990	−	0.964525i	$-0.585039\pi$
$827$	−9.62629	+	0.948107i	−0.334739	+	0.0329689i	−0.0707484	+	0.997494i	$0.522539\pi$
$828$	−9.70873	+	6.01194i	−0.337402	+	0.208929i
$829$	7.34433	−	2.22788i	0.255079	−	0.0773774i	−0.160155	−	0.987092i	$-0.551200\pi$
$829$	7.34433	−	2.22788i	0.255079	−	0.0773774i	0.415234	+	0.909714i	$0.363700\pi$
$830$	−4.81020	−	59.3508i	−0.166965	−	2.06009i
$831$			18.0246i			0.625265i
$832$	−11.5248	−	28.2742i	−0.399549	−	0.980231i
$833$			3.82837i			0.132645i
$834$	18.9992	−	1.53983i	0.657888	−	0.0533199i
$835$	30.8780	−	9.36675i	1.06858	−	0.324150i
$836$	−35.3693	−	8.31725i	−1.22327	−	0.287658i
$837$	8.97831	−	0.884286i	0.310336	−	0.0305654i
$838$	28.5777	−	11.2620i	0.987202	−	0.389039i
$839$	4.57749	+	3.05858i	0.158032	+	0.105594i	0.632072	−	0.774910i	$-0.282205\pi$
$839$	4.57749	+	3.05858i	0.158032	+	0.105594i	−0.474040	+	0.880504i	$0.657205\pi$
$840$	−17.5343	+	19.2366i	−0.604991	+	0.663725i
$841$	4.73424	+	7.08529i	0.163250	+	0.244320i
$842$	−4.39119	−	24.2630i	−0.151330	−	0.836158i
$843$	−4.21949	−	7.89410i	−0.145327	−	0.271887i
$844$	−3.27844	+	3.72417i	−0.112849	+	0.128191i
$845$	0.423477	−	4.29964i	0.0145681	−	0.147912i
$846$	10.7536	+	5.98941i	0.369715	+	0.205920i
$847$	26.8494	+	64.8201i	0.922555	+	2.22725i
$848$	2.64700	+	2.49797i	0.0908983	+	0.0857808i
$849$	6.50925	−	15.7147i	0.223397	−	0.539328i
$850$	2.67862	−	2.12180i	0.0918760	−	0.0727770i
$851$	−28.6605	−	34.9229i	−0.982469	−	1.19714i
$852$	−21.6450	−	2.89111i	−0.741544	−	0.0990478i
$853$	8.29598	−	27.3482i	0.284049	−	0.936384i	−0.692560	−	0.721360i	$-0.743517\pi$
$853$	8.29598	−	27.3482i	0.284049	−	0.936384i	0.976609	−	0.215023i	$-0.0689828\pi$
$854$	28.1106	+	43.6885i	0.961924	+	1.49499i
$855$	8.68392	+	1.72734i	0.296984	+	0.0590738i
$856$	−23.1911	−	25.7333i	−0.792657	−	0.879545i
$857$	−9.23063	−	46.4055i	−0.315312	−	1.58518i	−0.735358	−	0.677679i	$-0.762986\pi$
$857$	−9.23063	−	46.4055i	−0.315312	−	1.58518i	0.420046	−	0.907503i	$-0.362014\pi$
$858$	30.5419	+	0.528564i	1.04268	+	0.0180449i
$859$	−29.2118	+	35.5947i	−0.996693	+	1.21447i	−0.0200071	+	0.999800i	$0.506369\pi$
$859$	−29.2118	+	35.5947i	−0.996693	+	1.21447i	−0.976686	+	0.214674i	$0.931131\pi$
$860$	−2.14028	+	61.8172i	−0.0729830	+	2.10795i
$861$	−1.07914	−	0.576815i	−0.0367771	−	0.0196578i
$862$	1.82709	+	3.56530i	0.0622310	+	0.121435i
$863$	−38.1999	−	38.1999i	−1.30034	−	1.30034i	−0.928162	−	0.372176i	$-0.878612\pi$
$863$	−38.1999	−	38.1999i	−1.30034	−	1.30034i	−0.372176	−	0.928162i	$-0.621388\pi$
$864$	−4.95749	+	2.72457i	−0.168657	+	0.0926919i
$865$	7.85706	−	7.85706i	0.267148	−	0.267148i
$866$	−5.89684	−	1.90082i	−0.200383	−	0.0645924i
$867$	−7.60902	+	14.2355i	−0.258416	+	0.483462i
$868$	56.3821	−	21.0995i	1.91373	−	0.716164i
$869$	45.5747	+	37.4022i	1.54602	+	1.26878i
$870$	12.2640	+	12.6959i	0.415788	+	0.430433i
$871$	29.7556	−	5.91875i	1.00823	−	0.200549i
$872$	48.4796	−	7.05131i	1.64173	−	0.238788i
$873$	−1.62275	+	8.15810i	−0.0549216	+	0.276110i
$874$	25.3311	+	5.49597i	0.856836	+	0.185904i
$875$	21.0669	+	6.39056i	0.712190	+	0.216040i
$876$	2.99086	+	1.73429i	0.101052	+	0.0585964i
$877$	−23.4928	+	19.2801i	−0.793297	+	0.651042i	−0.941158	−	0.337966i	$-0.890261\pi$
$877$	−23.4928	+	19.2801i	−0.793297	+	0.651042i	0.147862	+	0.989008i	$0.452761\pi$
$878$	4.03500	+	0.468042i	0.136175	+	0.0157956i
$879$	−19.1975	−	7.95188i	−0.647517	−	0.268210i
$880$	49.3929	+	38.1970i	1.66503	+	1.28762i
$881$	−10.2040	+	4.22663i	−0.343781	+	0.142399i	−0.547892	−	0.836549i	$-0.684570\pi$
$881$	−10.2040	+	4.22663i	−0.343781	+	0.142399i	0.204111	+	0.978948i	$0.434570\pi$
$882$	5.62002	−	1.59916i	0.189236	−	0.0538465i
$883$	−9.47646	−	0.933350i	−0.318908	−	0.0314097i	−0.0627033	−	0.998032i	$-0.519972\pi$
$883$	−9.47646	−	0.933350i	−0.318908	−	0.0314097i	−0.256205	+	0.966622i	$0.582472\pi$
$884$	2.28609	−	6.69314i	0.0768894	−	0.225115i
$885$	−0.723121	+	0.386516i	−0.0243074	+	0.0129926i
$886$	−19.8044	+	28.5569i	−0.665341	+	0.959389i
$887$	2.76734	−	1.84908i	0.0929183	−	0.0620860i	−0.508243	−	0.861214i	$-0.669705\pi$
$887$	2.76734	−	1.84908i	0.0929183	−	0.0620860i	0.601161	+	0.799128i	$0.294705\pi$
$888$	−13.2808	−	18.0132i	−0.445674	−	0.604485i
$889$	2.35270	−	3.52106i	0.0789070	−	0.118093i
$890$	−2.97735	+	6.85022i	−0.0998009	+	0.229620i
$891$	−0.554718	−	5.63214i	−0.0185837	−	0.188684i
$892$	8.26750	−	11.4915i	0.276816	−	0.384764i
$893$	−8.11048	−	26.7367i	−0.271407	−	0.894709i
$894$	6.43369	+	5.46901i	0.215175	+	0.182911i
$895$	13.4641			0.450054
$896$	−27.2970	+	26.0716i	−0.911930	+	0.870993i
$897$	−21.7916			−0.727601
$898$	37.3734	+	31.7696i	1.24717	+	1.06016i
$899$	−11.8513	−	39.0684i	−0.395262	−	1.30300i
$900$	−4.23368	−	3.04590i	−0.141123	−	0.101530i
$901$	0.0826374	+	0.839032i	0.00275305	+	0.0279522i
$902$	−1.17005	+	2.69203i	−0.0389585	+	0.0896348i
$903$	20.7841	−	31.1056i	0.691651	−	1.03513i
$904$	4.17775	+	0.631782i	0.138950	+	0.0210128i
$905$	−15.1005	+	10.0898i	−0.501958	+	0.335398i
$906$	11.5794	−	16.6970i	0.384701	−	0.554720i
$907$	12.7726	−	6.82708i	0.424106	−	0.226689i	−0.245514	−	0.969393i	$-0.578957\pi$
$907$	12.7726	−	6.82708i	0.424106	−	0.226689i	0.669620	+	0.742704i	$0.266457\pi$
$908$	−54.1851	−	18.5073i	−1.79820	−	0.614186i
$909$	8.05226	+	0.793079i	0.267077	+	0.0263048i
$910$	−47.7742	+	13.5940i	−1.58370	+	0.450637i
$911$	12.6506	−	5.24004i	0.419132	−	0.173610i	−0.163142	−	0.986603i	$-0.552163\pi$
$911$	12.6506	−	5.24004i	0.419132	−	0.173610i	0.582274	+	0.812992i	$0.302163\pi$
$912$	12.3901	+	3.37001i	0.410278	+	0.111592i
$913$	79.8160	+	33.0609i	2.64153	+	1.09416i
$914$	26.3349	+	3.05473i	0.871082	+	0.101041i
$915$	−23.4753	+	19.2656i	−0.776068	+	0.636903i
$916$	8.80729	−	15.1885i	0.291001	−	0.501843i
$917$	−49.2392	−	14.9366i	−1.62602	−	0.493249i
$918$	−1.28059	−	0.277844i	−0.0422659	−	0.00917023i
$919$	−0.935412	+	4.70263i	−0.0308564	+	0.155126i	−0.993142	−	0.116917i	$-0.962699\pi$
$919$	−0.935412	+	4.70263i	−0.0308564	+	0.155126i	0.962285	+	0.272042i	$0.0876990\pi$
$920$	−35.7027	−	26.6357i	−1.17708	−	0.878152i
$921$	18.7559	−	3.73079i	0.618030	−	0.122934i
$922$	−16.4474	−	17.0267i	−0.541667	−	0.560745i
$923$	−32.2128	−	26.4363i	−1.06030	−	0.870163i
$924$	−13.2358	−	35.3688i	−0.435427	−	1.16355i
$925$	9.72668	−	18.1973i	0.319811	−	0.598325i
$926$	4.24369	+	1.36793i	0.139456	+	0.0449530i
$927$	4.34127	−	4.34127i	0.142586	−	0.142586i
$928$	16.4694	+	19.5978i	0.540634	+	0.643330i
$929$	−35.6291	−	35.6291i	−1.16895	−	1.16895i	−0.982455	−	0.186498i	$-0.940286\pi$
$929$	−35.6291	−	35.6291i	−1.16895	−	1.16895i	−0.186498	−	0.982455i	$-0.559714\pi$
$930$	16.0495	+	31.3183i	0.526284	+	1.02697i
$931$	−11.6970	−	6.25216i	−0.383352	−	0.204906i
$932$	5.77073	+	0.199799i	0.189027	+	0.00654463i
$933$	0.620668	−	0.756287i	0.0203198	−	0.0247597i
$934$	−53.6144	−	0.927863i	−1.75432	−	0.0303606i
$935$	2.82175	+	14.1859i	0.0922811	+	0.463929i
$936$	−10.7804	−	0.560152i	−0.352369	−	0.0183091i
$937$	−51.7296	−	10.2897i	−1.68993	−	0.336148i	−0.745914	−	0.666043i	$-0.767987\pi$
$937$	−51.7296	−	10.2897i	−1.68993	−	0.336148i	−0.944018	+	0.329895i	$0.892987\pi$
$938$	−20.2951	−	31.5419i	−0.662659	−	1.02988i
$939$	−5.83976	+	19.2511i	−0.190573	+	0.628237i
$940$	−6.35674	+	47.5912i	−0.207334	+	1.55225i
$941$	−22.0684	−	26.8904i	−0.719409	−	0.876603i	0.277035	−	0.960860i	$-0.410648\pi$
$941$	−22.0684	−	26.8904i	−0.719409	−	0.876603i	−0.996444	+	0.0842573i	$0.973148\pi$
$942$	4.34491	−	3.44170i	0.141565	−	0.112137i
$943$	0.801350	−	1.93463i	0.0260955	−	0.0630002i
$944$	−1.08494	+	0.486659i	−0.0353116	+	0.0158394i
$945$	3.52167	+	8.50207i	0.114560	+	0.276572i
$946$	−78.4016	−	43.6673i	−2.54906	−	1.41975i
$947$	3.68880	−	37.4530i	0.119870	−	1.21706i	−0.727520	−	0.686087i	$-0.759327\pi$
$947$	3.68880	−	37.4530i	0.119870	−	1.21706i	0.847390	−	0.530972i	$-0.178173\pi$
$948$	−15.6389	−	13.7671i	−0.507926	−	0.447135i
$949$	3.11008	+	5.81855i	0.100957	+	0.188878i
$950$	2.10831	+	11.6492i	0.0684027	+	0.377951i
$951$	−5.85612	−	8.76430i	−0.189898	−	0.284202i
$952$	−8.73465	+	0.404365i	−0.283092	+	0.0131056i
$953$	32.1411	+	21.4760i	1.04115	+	0.695675i	0.953782	−	0.300500i	$-0.0971537\pi$
$953$	32.1411	+	21.4760i	1.04115	+	0.695675i	0.0873702	+	0.996176i	$0.472154\pi$
$954$	1.19717	−	0.471785i	0.0387600	−	0.0152746i
$955$	38.5757	−	3.79938i	1.24828	−	0.122945i
$956$	−6.96791	+	29.6312i	−0.225358	+	0.958340i
$957$	−24.5078	+	7.43437i	−0.792226	+	0.240319i
$958$	11.5544	−	0.936450i	0.373306	−	0.0302553i
$959$			13.6013i			0.439210i
$960$	−16.9776	−	14.0945i	−0.547951	−	0.454899i
$961$		−	50.3920i		−	1.62555i
$962$	−3.44999	−	42.5678i	−0.111232	−	1.37244i
$963$	−11.7202	+	3.55529i	−0.377679	+	0.114568i
$964$	22.5868	+	36.4756i	0.727472	+	1.17480i
$965$	44.0981	−	4.34328i	1.41957	−	0.139815i
$966$	9.87754	+	25.0647i	0.317805	+	0.806442i
$967$	33.0918	+	22.1112i	1.06416	+	0.711050i	0.959000	−	0.283405i	$-0.0914642\pi$
$967$	33.0918	+	22.1112i	1.06416	+	0.711050i	0.105161	+	0.994455i	$0.466464\pi$
$968$	−53.8394	+	25.2782i	−1.73046	+	0.812472i
$969$	1.65249	+	2.47312i	0.0530855	+	0.0794480i
$970$	−31.9271	+	5.77827i	−1.02512	+	0.185529i
$971$	19.8645	+	37.1638i	0.637481	+	1.19264i	0.968499	+	0.249018i	$0.0801078\pi$
$971$	19.8645	+	37.1638i	0.637481	+	1.19264i	−0.331018	+	0.943624i	$0.607392\pi$
$972$	0.127046	+	1.99596i	0.00407500	+	0.0640205i
$973$	4.40783	−	44.7534i	0.141308	−	1.43473i
$974$	18.7271	−	33.6232i	0.600054	−	1.07736i
$975$	−3.80875	−	9.19513i	−0.121978	−	0.294480i
$976$	−35.8950	+	25.5178i	−1.14897	+	0.816805i
$977$	−14.8624	+	35.8810i	−0.475490	+	1.14793i	0.486214	+	0.873840i	$0.338378\pi$
$977$	−14.8624	+	35.8810i	−0.475490	+	1.14793i	−0.961703	+	0.274093i	$0.911622\pi$
$978$	3.72418	+	4.70152i	0.119086	+	0.150338i
$979$	−6.87486	−	8.37704i	−0.219722	−	0.267731i
$980$	13.8410	+	18.1084i	0.442133	+	0.578453i
$981$	5.02787	−	16.5747i	0.160528	−	0.529189i
$982$	−4.88737	+	3.14469i	−0.155962	+	0.100351i
$983$	49.3182	+	9.81000i	1.57301	+	0.312890i	0.903058	−	0.429518i	$-0.141316\pi$
$983$	49.3182	+	9.81000i	1.57301	+	0.312890i	0.669948	+	0.742408i	$0.266316\pi$
$984$	0.446161	−	0.936471i	0.0142231	−	0.0298536i
$985$	−10.5781	−	53.1799i	−0.337048	−	1.69445i
$986$	−0.102609	+	5.92904i	−0.00326774	+	0.188819i
$987$	18.4225	−	22.4479i	0.586394	−	0.714523i
$988$	16.7164	+	17.9154i	0.531818	+	0.569965i
$989$	56.4618	+	30.1794i	1.79538	+	0.959650i
$990$	19.6461	−	10.0679i	0.624395	−	0.319980i
$991$	16.5761	+	16.5761i	0.526556	+	0.526556i	0.919544	−	0.392988i	$-0.128558\pi$
$991$	16.5761	+	16.5761i	0.526556	+	0.526556i	−0.392988	+	0.919544i	$0.628558\pi$
$992$	20.0782	+	46.9192i	0.637484	+	1.48969i
$993$	16.4540	−	16.4540i	0.522151	−	0.522151i
$994$	−15.8058	+	49.0339i	−0.501331	+	1.55526i
$995$	−22.6365	+	42.3499i	−0.717625	+	1.34258i
$996$	−27.7854	−	12.6525i	−0.880414	−	0.400911i
$997$	−10.0281	−	8.22982i	−0.317592	−	0.260641i	0.462067	−	0.886845i	$-0.347108\pi$
$997$	−10.0281	−	8.22982i	−0.317592	−	0.260641i	−0.779659	+	0.626204i	$0.784608\pi$
$998$	−7.37478	+	7.12387i	−0.233445	+	0.225502i
$999$	−7.76043	+	1.54364i	−0.245529	+	0.0488388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.24	✓	512
128.69	even	32	inner	384.2.v.a.325.24	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.24	✓	512	1.1	even	1	trivial
384.2.v.a.325.24	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)

\(f(q)\)	\(=\)	\(q+(0.915950 - 1.07751i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-0.322073 - 1.97390i) q^{4} +(-0.270352 - 2.74493i) q^{5} +(-1.29700 - 0.563723i) q^{6} +(-1.85362 + 2.77413i) q^{7} +(-2.42190 - 1.46095i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(0.915950 - 1.07751i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-0.322073 - 1.97390i) q^{4} +(-0.270352 - 2.74493i) q^{5} +(-1.29700 - 0.563723i) q^{6} +(-1.85362 + 2.77413i) q^{7} +(-2.42190 - 1.46095i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-3.20533 - 2.22291i) q^{10} +(4.99114 - 2.66782i) q^{11} +(-1.79541 + 0.881196i) q^{12} +(-3.79822 - 0.374092i) q^{13} +(1.29135 + 4.53826i) q^{14} +(-2.54826 + 1.05552i) q^{15} +(-3.79254 + 1.27148i) q^{16} +(-0.856052 - 0.354588i) q^{17} +(-0.162950 + 1.40479i) q^{18} +(2.48141 - 2.03644i) q^{19} +(-5.33114 + 1.41772i) q^{20} +(3.19276 + 0.968512i) q^{21} +(1.69702 - 7.82161i) q^{22} +(-1.11391 + 5.59999i) q^{23} +(-0.695003 + 2.74171i) q^{24} +(-2.55765 + 0.508748i) q^{25} +(-3.88206 + 3.74998i) q^{26} +(0.773010 + 0.634393i) q^{27} +(6.07285 + 2.76538i) q^{28} +(2.13322 - 3.99098i) q^{29} +(-1.19674 + 3.71259i) q^{30} +(6.37934 - 6.37934i) q^{31} +(-2.10374 + 5.25112i) q^{32} +(-4.00180 - 4.00180i) q^{33} +(-1.16617 + 0.597623i) q^{34} +(8.11594 + 4.33806i) q^{35} +(1.36443 + 1.46230i) q^{36} +(-5.01961 + 6.11642i) q^{37} +(0.0785535 - 4.53904i) q^{38} +(0.744581 + 3.74326i) q^{39} +(-3.35545 + 7.04294i) q^{40} +(-0.359702 - 0.0715492i) q^{41} +(3.96799 - 2.55313i) q^{42} +(3.25488 - 10.7299i) q^{43} +(-6.87351 - 8.99277i) q^{44} +(1.74979 + 2.13213i) q^{45} +(5.01379 + 6.32956i) q^{46} +(3.33080 - 8.04126i) q^{47} +(2.31764 + 3.26014i) q^{48} +(-1.58114 - 3.81720i) q^{49} +(-1.79449 + 3.22189i) q^{50} +(-0.0908211 + 0.922122i) q^{51} +(0.484883 + 7.61777i) q^{52} +(-0.428920 - 0.802454i) q^{53} +(1.39161 - 0.251857i) q^{54} +(-8.67236 - 12.9791i) q^{55} +(8.54216 - 4.01064i) q^{56} +(-2.66907 - 1.78342i) q^{57} +(-2.34641 - 5.95412i) q^{58} +(0.295840 - 0.0291377i) q^{59} +(2.90422 + 4.69005i) q^{60} +(10.5361 - 3.19610i) q^{61} +(-1.03067 - 12.7170i) q^{62} -3.33642i q^{63} +(3.73124 + 7.07657i) q^{64} +10.5270i q^{65} +(-7.97744 + 0.646548i) q^{66} +(-7.60682 + 2.30750i) q^{67} +(-0.424210 + 1.80396i) q^{68} +(5.68221 - 0.559649i) q^{69} +(12.1081 - 4.77159i) q^{70} +(9.07848 + 6.06605i) q^{71} +(2.82540 - 0.130800i) q^{72} +(-0.960390 - 1.43733i) q^{73} +(1.99281 + 11.0110i) q^{74} +(1.22929 + 2.29983i) q^{75} +(-4.81893 - 4.24217i) q^{76} +(-1.85077 + 18.7912i) q^{77} +(4.71541 + 2.62634i) q^{78} +(3.98665 + 9.62462i) q^{79} +(4.51544 + 10.0665i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-0.406564 + 0.322048i) q^{82} +(9.68419 + 11.8002i) q^{83} +(0.883443 - 6.61410i) q^{84} +(-0.741886 + 2.44567i) q^{85} +(-8.58032 - 13.3352i) q^{86} +(-4.43837 - 0.882848i) q^{87} +(-15.9856 - 0.830615i) q^{88} +(-0.373569 - 1.87806i) q^{89} +(3.90012 + 0.0674963i) q^{90} +(8.07821 - 9.84333i) q^{91} +(11.4126 + 0.395135i) q^{92} +(-7.95647 - 4.25282i) q^{93} +(-5.61372 - 10.9544i) q^{94} +(-6.26076 - 6.26076i) q^{95} +(5.63569 + 0.488834i) q^{96} +(5.88166 - 5.88166i) q^{97} +(-5.56132 - 1.79267i) q^{98} +(-2.66782 + 4.99114i) 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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