LMFDB - Embedded newform 384.2.v.a.13.5

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			13.5
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26580 + 0.630679i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.20449 - 1.59662i) q^{4} +(-0.0580215 - 0.589102i) q^{5} +(-0.970964 - 1.02822i) q^{6} +(0.672130 - 1.00591i) q^{7} +(-0.517679 + 2.78065i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.26580 + 0.630679i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.20449 - 1.59662i) q^{4} +(-0.0580215 - 0.589102i) q^{5} +(-0.970964 - 1.02822i) q^{6} +(0.672130 - 1.00591i) q^{7} +(-0.517679 + 2.78065i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(0.444978 + 0.709091i) q^{10} +(1.59652 - 0.853357i) q^{11} +(1.87752 + 0.689147i) q^{12} +(1.88694 + 0.185848i) q^{13} +(-0.216372 + 1.69718i) q^{14} +(0.546893 - 0.226531i) q^{15} +(-1.09842 - 3.84623i) q^{16} +(1.21991 + 0.505304i) q^{17} +(0.702086 - 1.22763i) q^{18} +(5.22950 - 4.29174i) q^{19} +(-1.01046 - 0.616928i) q^{20} +(1.15771 + 0.351187i) q^{21} +(-1.48267 + 2.08707i) q^{22} +(-0.631866 + 3.17661i) q^{23} +(-2.81119 + 0.311792i) q^{24} +(4.56025 - 0.907090i) q^{25} +(-2.50570 + 0.954811i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(-0.796494 - 2.28475i) q^{28} +(-2.35464 + 4.40522i) q^{29} +(-0.549388 + 0.631656i) q^{30} +(3.79320 - 3.79320i) q^{31} +(3.81611 + 4.17580i) q^{32} +(1.28006 + 1.28006i) q^{33} +(-1.86284 + 0.129760i) q^{34} +(-0.631584 - 0.337589i) q^{35} +(-0.114458 + 1.99672i) q^{36} +(-6.36386 + 7.75439i) q^{37} +(-3.91278 + 8.73062i) q^{38} +(0.369906 + 1.85964i) q^{39} +(1.66812 + 0.143629i) q^{40} +(7.69774 + 1.53118i) q^{41} +(-1.68691 + 0.285611i) q^{42} +(-0.949767 + 3.13096i) q^{43} +(0.560496 - 3.57690i) q^{44} +(0.375531 + 0.457586i) q^{45} +(-1.20360 - 4.41945i) q^{46} +(2.69276 - 6.50090i) q^{47} +(3.36176 - 2.16762i) q^{48} +(2.11868 + 5.11495i) q^{49} +(-5.20027 + 4.02425i) q^{50} +(-0.129424 + 1.31406i) q^{51} +(2.56953 - 2.78889i) q^{52} +(-0.950734 - 1.77870i) q^{53} +(1.37857 + 0.315492i) q^{54} +(-0.595347 - 0.890999i) q^{55} +(2.44914 + 2.38970i) q^{56} +(5.62499 + 3.75850i) q^{57} +(0.202216 - 7.06114i) q^{58} +(-2.90842 + 0.286454i) q^{59} +(0.297042 - 1.14604i) q^{60} +(1.92274 - 0.583257i) q^{61} +(-2.40913 + 7.19372i) q^{62} +1.20980i q^{63} +(-7.46402 - 2.87897i) q^{64} -1.12239i q^{65} +(-2.42760 - 0.812987i) q^{66} +(-0.992457 + 0.301059i) q^{67} +(2.27615 - 1.33911i) q^{68} +(-3.22324 + 0.317462i) q^{69} +(1.01237 + 0.0289920i) q^{70} +(-5.74744 - 3.84032i) q^{71} +(-1.11441 - 2.59963i) q^{72} +(-1.01384 - 1.51732i) q^{73} +(3.16483 - 13.8290i) q^{74} +(2.19180 + 4.10057i) q^{75} +(-0.553431 - 13.5189i) q^{76} +(0.214664 - 2.17952i) q^{77} +(-1.64106 - 2.12064i) q^{78} +(-5.88979 - 14.2192i) q^{79} +(-2.20209 + 0.870246i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-10.7095 + 2.91665i) q^{82} +(-2.24503 - 2.73558i) q^{83} +(1.95516 - 1.42542i) q^{84} +(0.226894 - 0.747971i) q^{85} +(-0.772420 - 4.56216i) q^{86} +(-4.89905 - 0.974481i) q^{87} +(1.54640 + 4.88112i) q^{88} +(0.0755616 + 0.379874i) q^{89} +(-0.763936 - 0.342371i) q^{90} +(1.45522 - 1.77319i) q^{91} +(4.31077 + 4.83503i) q^{92} +(4.73098 + 2.52876i) q^{93} +(0.691492 + 9.92710i) q^{94} +(-2.83170 - 2.83170i) q^{95} +(-2.88823 + 4.86396i) q^{96} +(-1.53845 + 1.53845i) q^{97} +(-5.90771 - 5.13828i) q^{98} +(-0.853357 + 1.59652i) 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 $

$2$	−1.26580	+	0.630679i	−0.895054	+	0.445958i
$2$	−1.26580	+	0.630679i	−0.895054	+	0.445958i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$4$	1.20449	−	1.59662i	0.602244	−	0.798312i
$5$	−0.0580215	−	0.589102i	−0.0259480	−	0.263455i	−0.999402	−	0.0345726i	$-0.988993\pi$
$5$	−0.0580215	−	0.589102i	−0.0259480	−	0.263455i	0.973454	−	0.228882i	$-0.0735070\pi$
$6$	−0.970964	−	1.02822i	−0.396394	−	0.419768i
$7$	0.672130	−	1.00591i	0.254041	−	0.380199i	−0.682426	−	0.730955i	$-0.739075\pi$
$7$	0.672130	−	1.00591i	0.254041	−	0.380199i	0.936467	+	0.350755i	$0.114075\pi$
$8$	−0.517679	+	2.78065i	−0.183027	+	0.983108i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	0.444978	+	0.709091i	0.140714	+	0.224234i
$11$	1.59652	−	0.853357i	0.481368	−	0.257297i	−0.212818	−	0.977092i	$-0.568264\pi$
$11$	1.59652	−	0.853357i	0.481368	−	0.257297i	0.694187	+	0.719795i	$0.255764\pi$
$12$	1.87752	+	0.689147i	0.541993	+	0.198940i
$13$	1.88694	+	0.185848i	0.523344	+	0.0515449i	0.356240	−	0.934394i	$-0.384058\pi$
$13$	1.88694	+	0.185848i	0.523344	+	0.0515449i	0.167104	+	0.985939i	$0.446558\pi$
$14$	−0.216372	+	1.69718i	−0.0578277	+	0.453591i
$15$	0.546893	−	0.226531i	0.141207	−	0.0584899i
$16$	−1.09842	−	3.84623i	−0.274605	−	0.961557i
$17$	1.21991	+	0.505304i	0.295872	+	0.122554i	0.525682	−	0.850681i	$-0.323810\pi$
$17$	1.21991	+	0.505304i	0.295872	+	0.122554i	−0.229810	+	0.973236i	$0.573810\pi$
$18$	0.702086	−	1.22763i	0.165483	−	0.289355i
$19$	5.22950	−	4.29174i	1.19973	−	0.984593i	0.199742	−	0.979849i	$-0.435990\pi$
$19$	5.22950	−	4.29174i	1.19973	−	0.984593i	0.999989	−	0.00474471i	$-0.00151029\pi$
$20$	−1.01046	−	0.616928i	−0.225946	−	0.137949i
$21$	1.15771	+	0.351187i	0.252633	+	0.0766352i
$22$	−1.48267	+	2.08707i	−0.316107	+	0.444964i
$23$	−0.631866	+	3.17661i	−0.131753	+	0.662368i	0.857301	+	0.514815i	$0.172140\pi$
$23$	−0.631866	+	3.17661i	−0.131753	+	0.662368i	−0.989054	+	0.147553i	$0.952860\pi$
$24$	−2.81119	+	0.311792i	−0.573832	+	0.0636442i
$25$	4.56025	−	0.907090i	0.912050	−	0.181418i
$26$	−2.50570	+	0.954811i	−0.491408	+	0.187254i
$27$	−0.773010	−	0.634393i	−0.148766	−	0.122089i
$28$	−0.796494	−	2.28475i	−0.150523	−	0.431777i
$29$	−2.35464	+	4.40522i	−0.437245	+	0.818029i	−0.999963	−	0.00862064i	$-0.997256\pi$
$29$	−2.35464	+	4.40522i	−0.437245	+	0.818029i	0.562717	+	0.826649i	$0.309756\pi$
$30$	−0.549388	+	0.631656i	−0.100304	+	0.115324i
$31$	3.79320	−	3.79320i	0.681279	−	0.681279i	−0.279009	−	0.960288i	$-0.590006\pi$
$31$	3.79320	−	3.79320i	0.681279	−	0.681279i	0.960288	+	0.279009i	$0.0900060\pi$
$32$	3.81611	+	4.17580i	0.674600	+	0.738183i
$33$	1.28006	+	1.28006i	0.222829	+	0.222829i
$34$	−1.86284	+	0.129760i	−0.319475	+	0.0222537i
$35$	−0.631584	−	0.337589i	−0.106757	−	0.0570629i
$36$	−0.114458	+	1.99672i	−0.0190763	+	0.332787i
$37$	−6.36386	+	7.75439i	−1.04621	+	1.27481i	−0.0857760	+	0.996314i	$0.527337\pi$
$37$	−6.36386	+	7.75439i	−1.04621	+	1.27481i	−0.960436	+	0.278499i	$0.910163\pi$
$38$	−3.91278	+	8.73062i	−0.634737	+	1.41629i
$39$	0.369906	+	1.85964i	0.0592323	+	0.297781i
$40$	1.66812	+	0.143629i	0.263753	+	0.0227097i
$41$	7.69774	+	1.53118i	1.20218	+	0.239129i	0.755250	−	0.655437i	$-0.227516\pi$
$41$	7.69774	+	1.53118i	1.20218	+	0.239129i	0.446935	+	0.894567i	$0.352516\pi$
$42$	−1.68691	+	0.285611i	−0.260296	+	0.0440707i
$43$	−0.949767	+	3.13096i	−0.144838	+	0.477467i	−0.999102	−	0.0423725i	$-0.986508\pi$
$43$	−0.949767	+	3.13096i	−0.144838	+	0.477467i	0.854264	+	0.519840i	$0.174008\pi$
$44$	0.560496	−	3.57690i	0.0844979	−	0.539238i
$45$	0.375531	+	0.457586i	0.0559808	+	0.0682128i
$46$	−1.20360	−	4.41945i	−0.177462	−	0.651612i
$47$	2.69276	−	6.50090i	0.392780	−	0.948254i	−0.596552	−	0.802574i	$-0.703463\pi$
$47$	2.69276	−	6.50090i	0.392780	−	0.948254i	0.989332	−	0.145680i	$-0.0465369\pi$
$48$	3.36176	−	2.16762i	0.485228	−	0.312870i
$49$	2.11868	+	5.11495i	0.302669	+	0.730707i
$50$	−5.20027	+	4.02425i	−0.735430	+	0.569115i
$51$	−0.129424	+	1.31406i	−0.0181230	+	0.184006i
$52$	2.56953	−	2.78889i	0.356330	−	0.386750i
$53$	−0.950734	−	1.77870i	−0.130593	−	0.244323i	0.808123	−	0.589014i	$-0.200484\pi$
$53$	−0.950734	−	1.77870i	−0.130593	−	0.244323i	−0.938716	+	0.344691i	$0.887984\pi$
$54$	1.37857	+	0.315492i	0.187600	+	0.0429330i
$55$	−0.595347	−	0.890999i	−0.0802765	−	0.120142i
$56$	2.44914	+	2.38970i	0.327281	+	0.319337i
$57$	5.62499	+	3.75850i	0.745048	+	0.497825i
$58$	0.202216	−	7.06114i	0.0265522	−	0.927173i
$59$	−2.90842	+	0.286454i	−0.378643	+	0.0372931i	−0.285549	−	0.958364i	$-0.592176\pi$
$59$	−2.90842	+	0.286454i	−0.378643	+	0.0372931i	−0.0930945	+	0.995657i	$0.529676\pi$
$60$	0.297042	−	1.14604i	0.0383479	−	0.147953i
$61$	1.92274	−	0.583257i	0.246182	−	0.0746783i	−0.164782	−	0.986330i	$-0.552692\pi$
$61$	1.92274	−	0.583257i	0.246182	−	0.0746783i	0.410964	+	0.911652i	$0.365192\pi$
$62$	−2.40913	+	7.19372i	−0.305960	+	0.913603i
$63$			1.20980i			0.152421i
$64$	−7.46402	−	2.87897i	−0.933002	−	0.359871i
$65$		−	1.12239i		−	0.139215i
$66$	−2.42760	−	0.812987i	−0.298817	−	0.100072i
$67$	−0.992457	+	0.301059i	−0.121248	+	0.0367802i	−0.350326	−	0.936628i	$-0.613929\pi$
$67$	−0.992457	+	0.301059i	−0.121248	+	0.0367802i	0.229078	+	0.973408i	$0.426429\pi$
$68$	2.27615	−	1.33911i	0.276023	−	0.162391i
$69$	−3.22324	+	0.317462i	−0.388033	+	0.0382179i
$70$	1.01237	+	0.0289920i	0.121001	+	0.00346521i
$71$	−5.74744	−	3.84032i	−0.682096	−	0.455762i	0.165636	−	0.986187i	$-0.447032\pi$
$71$	−5.74744	−	3.84032i	−0.682096	−	0.455762i	−0.847732	+	0.530425i	$0.822032\pi$
$72$	−1.11441	−	2.59963i	−0.131335	−	0.306370i
$73$	−1.01384	−	1.51732i	−0.118661	−	0.177589i	0.767384	−	0.641188i	$-0.221558\pi$
$73$	−1.01384	−	1.51732i	−0.118661	−	0.177589i	−0.886045	+	0.463599i	$0.846558\pi$
$74$	3.16483	−	13.8290i	0.367904	−	1.60759i
$75$	2.19180	+	4.10057i	0.253088	+	0.473494i
$76$	−0.553431	−	13.5189i	−0.0634829	−	1.55072i
$77$	0.214664	−	2.17952i	0.0244633	−	0.248380i
$78$	−1.64106	−	2.12064i	−0.185814	−	0.240115i
$79$	−5.88979	−	14.2192i	−0.662654	−	1.59979i	−0.793629	−	0.608402i	$-0.791811\pi$
$79$	−5.88979	−	14.2192i	−0.662654	−	1.59979i	0.130975	−	0.991386i	$-0.458189\pi$
$80$	−2.20209	+	0.870246i	−0.246201	+	0.0972965i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−10.7095	+	2.91665i	−1.18266	+	0.322090i
$83$	−2.24503	−	2.73558i	−0.246424	−	0.300269i	0.635078	−	0.772448i	$-0.280968\pi$
$83$	−2.24503	−	2.73558i	−0.246424	−	0.300269i	−0.881503	+	0.472179i	$0.843468\pi$
$84$	1.95516	−	1.42542i	0.213325	−	0.155527i
$85$	0.226894	−	0.747971i	0.0246102	−	0.0811288i
$86$	−0.772420	−	4.56216i	−0.0832922	−	0.491951i
$87$	−4.89905	−	0.974481i	−0.525233	−	0.104475i
$88$	1.54640	+	4.88112i	0.164847	+	0.520329i
$89$	0.0755616	+	0.379874i	0.00800952	+	0.0402666i	0.984583	−	0.174916i	$-0.0559654\pi$
$89$	0.0755616	+	0.379874i	0.00800952	+	0.0402666i	−0.976574	+	0.215182i	$0.930965\pi$
$90$	−0.763936	−	0.342371i	−0.0805259	−	0.0360891i
$91$	1.45522	−	1.77319i	0.152548	−	0.185881i
$92$	4.31077	+	4.83503i	0.449429	+	0.504087i
$93$	4.73098	+	2.52876i	0.490579	+	0.262220i
$94$	0.691492	+	9.92710i	0.0713220	+	1.02390i
$95$	−2.83170	−	2.83170i	−0.290526	−	0.290526i
$96$	−2.88823	+	4.86396i	−0.294779	+	0.496426i
$97$	−1.53845	+	1.53845i	−0.156206	+	0.156206i	−0.780883	−	0.624677i	$-0.785231\pi$
$97$	−1.53845	+	1.53845i	−0.156206	+	0.156206i	0.624677	+	0.780883i	$0.285231\pi$
$98$	−5.90771	−	5.13828i	−0.596769	−	0.519045i
$99$	−0.853357	+	1.59652i	−0.0857656	+	0.160456i
$100$	4.04448	−	8.37359i	0.404448	−	0.837359i
$101$	−9.48867	−	7.78715i	−0.944158	−	0.774851i	0.0302719	−	0.999542i	$-0.490363\pi$
$101$	−9.48867	−	7.78715i	−0.944158	−	0.774851i	−0.974430	+	0.224691i	$0.927863\pi$
$102$	−0.664928	−	1.74496i	−0.0658377	−	0.172777i
$103$	0.702244	−	0.139685i	0.0691941	−	0.0137636i	−0.160372	−	0.987057i	$-0.551269\pi$
$103$	0.702244	−	0.139685i	0.0691941	−	0.0137636i	0.229566	+	0.973293i	$0.426269\pi$
$104$	−1.49361	+	5.15072i	−0.146460	+	0.505070i
$105$	0.139713	−	0.702385i	0.0136346	−	0.0685457i
$106$	2.32523	+	1.65186i	0.225846	+	0.160443i
$107$	−9.72088	−	2.94880i	−0.939753	−	0.285071i	−0.216995	−	0.976173i	$-0.569626\pi$
$107$	−9.72088	−	2.94880i	−0.939753	−	0.285071i	−0.722757	+	0.691102i	$0.757126\pi$
$108$	−1.94397	+	0.470089i	−0.187059	+	0.0452343i
$109$	−6.70282	+	5.50086i	−0.642014	+	0.526887i	−0.898114	−	0.439763i	$-0.855062\pi$
$109$	−6.70282	+	5.50086i	−0.642014	+	0.526887i	0.256100	+	0.966650i	$0.417562\pi$
$110$	1.31552	+	0.752352i	0.125430	+	0.0717340i
$111$	−9.26782	−	3.83886i	−0.879662	−	0.364368i
$112$	−4.60725	−	1.48025i	−0.435344	−	0.139870i
$113$	6.35299	−	2.63150i	0.597639	−	0.247550i	−0.0632940	−	0.997995i	$-0.520161\pi$
$113$	6.35299	−	2.63150i	0.597639	−	0.247550i	0.660933	+	0.750445i	$0.270161\pi$
$114$	−9.49050	−	1.20993i	−0.888867	−	0.113321i
$115$	1.90801	+	0.187922i	0.177923	+	0.0175239i
$116$	4.19735	+	9.06551i	0.389714	+	0.841711i
$117$	−1.67219	+	0.893804i	−0.154594	+	0.0826322i
$118$	3.50080	−	2.19687i	0.322275	−	0.202238i
$119$	1.32823	−	0.887495i	0.121759	−	0.0813565i
$120$	0.346787	+	1.63799i	0.0316571	+	0.149527i
$121$	−4.29062	+	6.42137i	−0.390056	+	0.583761i
$122$	−2.06595	+	1.95092i	−0.187042	+	0.176628i
$123$	0.769292	+	7.81075i	0.0693647	+	0.704272i
$124$	−1.48746	−	10.6252i	−0.133577	−	0.954169i
$125$	−1.65814	−	5.46614i	−0.148308	−	0.488907i
$126$	−0.762997	−	1.53136i	−0.0679731	−	0.136425i
$127$	1.00522			0.0891984			0.0445992	−	0.999005i	$-0.485799\pi$
$127$	1.00522			0.0891984			0.0445992	+	0.999005i	$0.485799\pi$
$128$	11.2636	−	1.06321i	0.995575	−	0.0939752i
$129$	−3.27185			−0.288070
$130$	0.707866	+	1.42071i	0.0620840	+	0.124605i
$131$	−1.86185	−	6.13771i	−0.162671	−	0.536254i	0.837274	−	0.546784i	$-0.184148\pi$
$131$	−1.86185	−	6.13771i	−0.162671	−	0.536254i	−0.999945	+	0.0105298i	$0.996648\pi$
$132$	3.58558	−	0.501958i	0.312085	−	0.0436898i
$133$	−0.802216	−	8.14503i	−0.0695609	−	0.706264i
$134$	1.06638	−	1.00700i	0.0921211	−	0.0869917i
$135$	−0.328871	+	0.492191i	−0.0283047	+	0.0423610i
$136$	−2.03659	+	3.13056i	−0.174637	+	0.268443i
$137$	11.7040	−	7.82034i	0.999938	−	0.668137i	0.0560583	−	0.998427i	$-0.482147\pi$
$137$	11.7040	−	7.82034i	0.999938	−	0.668137i	0.943879	+	0.330291i	$0.107147\pi$
$138$	3.87976	−	2.43467i	0.330267	−	0.207253i
$139$	−14.5134	+	7.75759i	−1.23101	+	0.657990i	−0.953111	−	0.302620i	$-0.902139\pi$
$139$	−14.5134	+	7.75759i	−1.23101	+	0.657990i	−0.277901	+	0.960610i	$0.589639\pi$
$140$	−1.29974	+	0.601781i	−0.109848	+	0.0508598i
$141$	7.00264	+	0.689700i	0.589729	+	0.0580832i
$142$	9.69710	+	1.23627i	0.813763	+	0.103746i
$143$	3.17114	−	1.31353i	0.265184	−	0.109843i
$144$	3.05015	+	2.58777i	0.254179	+	0.215648i
$145$	2.73174	+	1.13153i	0.226859	+	0.0939681i
$146$	2.24026	+	1.28121i	0.185405	+	0.106034i
$147$	−4.27968	+	3.51224i	−0.352982	+	0.289685i
$148$	4.71566	+	19.5008i	0.387625	+	1.60295i
$149$	−4.30762	−	1.30670i	−0.352894	−	0.107049i	0.108861	−	0.994057i	$-0.465280\pi$
$149$	−4.30762	−	1.30670i	−0.352894	−	0.107049i	−0.461754	+	0.887008i	$0.652780\pi$
$150$	−5.36053	−	3.80817i	−0.437685	−	0.310936i
$151$	2.00578	−	10.0837i	0.163228	−	0.820603i	−0.809224	−	0.587500i	$-0.800112\pi$
$151$	2.00578	−	10.0837i	0.163228	−	0.820603i	0.972452	−	0.233103i	$-0.0748878\pi$
$152$	9.22662	+	16.7632i	0.748378	+	1.35967i
$153$	−1.29505	+	0.257602i	−0.104699	+	0.0208259i
$154$	1.10286	+	2.89422i	0.0888709	+	0.233223i
$155$	−2.45467	−	2.01450i	−0.197164	−	0.161808i
$156$	3.41470	+	1.64931i	0.273395	+	0.132051i
$157$	−8.77193	+	16.4111i	−0.700076	+	1.30975i	0.240660	+	0.970610i	$0.422636\pi$
$157$	−8.77193	+	16.4111i	−0.700076	+	1.30975i	−0.940736	+	0.339140i	$0.889864\pi$
$158$	16.4231	+	14.2841i	1.30655	+	1.13638i
$159$	1.42613	−	1.42613i	0.113099	−	0.113099i
$160$	2.23855	−	2.49037i	0.176973	−	0.196881i
$161$	2.77069	+	2.77069i	0.218361	+	0.218361i
$162$	0.0982719	+	1.41080i	0.00772097	+	0.110843i
$163$	16.5272	+	8.83397i	1.29451	+	0.691930i	0.967447	−	0.253073i	$-0.0814414\pi$
$163$	16.5272	+	8.83397i	1.29451	+	0.691930i	0.327062	+	0.945003i	$0.393941\pi$
$164$	11.7165	−	10.4461i	0.914908	−	0.815705i
$165$	0.679813	−	0.828355i	0.0529234	−	0.0644873i
$166$	4.56703	+	2.04680i	0.354470	+	0.158862i
$167$	1.85005	+	9.30082i	0.143161	+	0.719719i	0.983962	+	0.178376i	$0.0570842\pi$
$167$	1.85005	+	9.30082i	0.143161	+	0.719719i	−0.840801	+	0.541344i	$0.817916\pi$
$168$	−1.57585	+	3.03738i	−0.121579	+	0.234339i
$169$	−9.22419	−	1.83480i	−0.709553	−	0.141139i
$170$	0.184527	+	1.08988i	0.0141526	+	0.0835898i
$171$	−1.96381	+	6.47381i	−0.150176	+	0.495065i
$172$	3.85499	+	5.28763i	0.293940	+	0.403178i
$173$	7.92733	+	9.65948i	0.602704	+	0.734397i	0.981580	−	0.191051i	$-0.0611894\pi$
$173$	7.92733	+	9.65948i	0.602704	+	0.734397i	−0.378876	+	0.925447i	$0.623689\pi$
$174$	6.81579	−	1.85623i	0.516704	−	0.140721i
$175$	2.15263	−	5.19690i	0.162723	−	0.392849i
$176$	−5.03585	−	5.20323i	−0.379592	−	0.392208i
$177$	−1.11839	−	2.70003i	−0.0840632	−	0.202946i
$178$	−0.335224	−	0.433188i	−0.0251261	−	0.0324688i
$179$	1.44846	−	14.7064i	0.108263	−	1.09921i	−0.775524	−	0.631318i	$-0.782514\pi$
$179$	1.44846	−	14.7064i	0.108263	−	1.09921i	0.883786	−	0.467891i	$-0.154986\pi$
$180$	1.18291	−	0.0484256i	0.0881693	−	0.00360943i
$181$	2.81492	+	5.26634i	0.209231	+	0.391444i	0.964545	−	0.263920i	$-0.0850154\pi$
$181$	2.81492	+	5.26634i	0.209231	+	0.391444i	−0.755314	+	0.655364i	$0.772515\pi$
$182$	−0.723699	+	3.16227i	−0.0536441	+	0.234403i
$183$	1.11628	+	1.67064i	0.0825180	+	0.123497i
$184$	−8.50592	−	3.40146i	−0.627065	−	0.250759i
$185$	4.93737	+	3.29904i	0.363003	+	0.242551i
$186$	−7.58329	−	0.217169i	−0.556034	−	0.0159236i
$187$	2.37881	−	0.234293i	0.173956	−	0.0171332i
$188$	−7.13610	−	12.1296i	−0.520454	−	0.884641i
$189$	−1.15771	+	0.351187i	−0.0842108	+	0.0255451i
$190$	5.37025	+	1.79846i	0.389599	+	0.130474i
$191$		−	6.59932i		−	0.477510i	−0.971080	−	0.238755i	$-0.923261\pi$
$191$		−	6.59932i		−	0.477510i	0.971080	−	0.238755i	$-0.0767393\pi$
$192$	0.588312	−	7.97834i	0.0424577	−	0.575787i
$193$			22.8956i			1.64806i	0.566543	+	0.824032i	$0.308281\pi$
$193$			22.8956i			1.64806i	−0.566543	+	0.824032i	$0.691719\pi$
$194$	0.977100	−	2.91764i	0.0701517	−	0.209474i
$195$	1.07406	−	0.325812i	0.0769148	−	0.0233319i
$196$	10.7186	+	2.77815i	0.765613	+	0.198439i
$197$	−21.1583	+	2.08391i	−1.50747	+	0.148473i	−0.817736	−	0.575593i	$-0.804771\pi$
$197$	−21.1583	+	2.08391i	−1.50747	+	0.148473i	−0.689731	+	0.724066i	$0.742271\pi$
$198$	0.0732861	−	2.55906i	0.00520821	−	0.181865i
$199$	−0.924651	−	0.617832i	−0.0655468	−	0.0437970i	0.522365	−	0.852722i	$-0.325050\pi$
$199$	−0.924651	−	0.617832i	−0.0655468	−	0.0437970i	−0.587912	+	0.808925i	$0.700050\pi$
$200$	0.161552	+	13.1500i	0.0114235	+	0.929848i
$201$	−0.576190	−	0.862330i	−0.0406413	−	0.0608240i
$202$	16.9219	+	3.87265i	1.19062	+	0.272479i
$203$	2.84865	+	5.32944i	0.199936	+	0.374053i
$204$	1.94218	+	1.78941i	0.135980	+	0.125284i
$205$	0.455384	−	4.62360i	0.0318054	−	0.322926i
$206$	−0.800802	+	0.619704i	−0.0557945	+	0.0431768i
$207$	−1.23945	−	2.99230i	−0.0861477	−	0.207979i
$208$	−1.35785	−	7.46176i	−0.0941496	−	0.517380i
$209$	4.68661	−	11.3145i	0.324180	−	0.782639i
$210$	0.266131	+	0.977191i	0.0183648	+	0.0674326i
$211$	15.2811	+	18.6201i	1.05200	+	1.28186i	0.958148	+	0.286275i	$0.0924170\pi$
$211$	15.2811	+	18.6201i	1.05200	+	1.28186i	0.0938486	+	0.995586i	$0.470083\pi$
$212$	−3.98506	−	0.624455i	−0.273695	−	0.0428877i
$213$	2.00656	−	6.61474i	0.137487	−	0.453235i
$214$	14.1644	−	2.39818i	0.968259	−	0.163936i
$215$	1.89956	+	0.377847i	0.129549	+	0.0257689i
$216$	2.16420	−	1.82106i	0.147255	−	0.123907i
$217$	−1.26611	−	6.36515i	−0.0859490	−	0.432095i
$218$	5.01514	−	11.1903i	0.339668	−	0.757904i
$219$	1.15768	−	1.41064i	0.0782289	−	0.0953222i
$220$	−2.13968	−	0.122652i	−0.144257	−	0.00826921i
$221$	2.20800	+	1.18020i	0.148526	+	0.0793887i
$222$	14.1523	−	0.985806i	0.949838	−	0.0661629i
$223$	8.00544	+	8.00544i	0.536084	+	0.536084i	0.922376	−	0.386292i	$-0.126244\pi$
$223$	8.00544	+	8.00544i	0.536084	+	0.536084i	−0.386292	+	0.922376i	$0.626244\pi$
$224$	6.76541	−	1.03200i	0.452033	−	0.0689536i
$225$	−3.28776	+	3.28776i	−0.219184	+	0.219184i
$226$	−6.38197	+	7.33764i	−0.424523	+	0.488093i
$227$	−12.3136	+	23.0371i	−0.817281	+	1.52902i	0.0310252	+	0.999519i	$0.490123\pi$
$227$	−12.3136	+	23.0371i	−0.817281	+	1.52902i	−0.848306	+	0.529506i	$0.822377\pi$
$228$	12.7761	−	4.45393i	0.846120	−	0.294969i
$229$	−11.5411	−	9.47150i	−0.762654	−	0.625894i	0.170505	−	0.985357i	$-0.445460\pi$
$229$	−11.5411	−	9.47150i	−0.762654	−	0.625894i	−0.933159	+	0.359463i	$0.882960\pi$
$230$	−2.53367	+	0.965469i	−0.167065	+	0.0636612i
$231$	2.14799	−	0.427262i	0.141327	−	0.0281117i
$232$	−11.0304	−	8.82791i	−0.724183	−	0.579581i
$233$	5.45128	−	27.4054i	0.357125	−	1.79539i	−0.216511	−	0.976280i	$-0.569468\pi$
$233$	5.45128	−	27.4054i	0.357125	−	1.79539i	0.573636	−	0.819110i	$-0.305532\pi$
$234$	1.55295	−	2.18599i	0.101519	−	0.142903i
$235$	−3.98593	−	1.20912i	−0.260014	−	0.0788743i
$236$	−3.04579	+	4.98868i	−0.198264	+	0.324735i
$237$	11.8972	−	9.76380i	0.772808	−	0.634227i
$238$	−1.12155	+	1.96108i	−0.0726990	+	0.127118i
$239$	−16.0530	−	6.64938i	−1.03838	−	0.430113i	−0.202652	−	0.979251i	$-0.564956\pi$
$239$	−16.0530	−	6.64938i	−1.03838	−	0.430113i	−0.835732	+	0.549138i	$0.814956\pi$
$240$	−1.47201	−	1.85465i	−0.0950176	−	0.119717i
$241$	−21.4995	+	8.90539i	−1.38491	+	0.573647i	−0.945789	−	0.324783i	$-0.894709\pi$
$241$	−21.4995	+	8.90539i	−1.38491	+	0.573647i	−0.439117	+	0.898430i	$0.644709\pi$
$242$	1.38123	−	10.8342i	0.0887891	−	0.696446i
$243$	0.995185	+	0.0980171i	0.0638411	+	0.00628780i
$244$	1.38467	−	3.77242i	0.0886446	−	0.241504i
$245$	2.89030	−	1.54490i	0.184654	−	0.0986999i
$246$	−5.89985	−	9.40165i	−0.376160	−	0.599428i
$247$	10.6654	−	7.12639i	0.678623	−	0.453441i
$248$	8.58390	+	12.5112i	0.545078	+	0.794463i
$249$	1.96609	−	2.94246i	0.124596	−	0.186471i
$250$	5.54625	+	5.87328i	0.350775	+	0.371459i
$251$	0.920371	+	9.34469i	0.0580933	+	0.589831i	0.979529	+	0.201301i	$0.0645170\pi$
$251$	0.920371	+	9.34469i	0.0580933	+	0.589831i	−0.921436	+	0.388530i	$0.872983\pi$
$252$	1.93160	+	1.45719i	0.121679	+	0.0917944i
$253$	1.70199	+	5.61072i	0.107003	+	0.352743i
$254$	−1.27240	+	0.633968i	−0.0798374	+	0.0397787i
$255$	0.781628			0.0489474
$256$	−13.5869	+	8.44955i	−0.849184	+	0.528097i
$257$	−3.40211			−0.212218			−0.106109	−	0.994355i	$-0.533839\pi$
$257$	−3.40211			−0.212218			−0.106109	+	0.994355i	$0.533839\pi$
$258$	4.14150	−	2.06349i	0.257838	−	0.128467i
$259$	3.52290	+	11.6134i	0.218902	+	0.721624i
$260$	−1.79203	−	1.35190i	−0.111137	−	0.0838413i
$261$	−0.489598	−	4.97097i	−0.0303054	−	0.307696i
$262$	6.22766	+	6.59487i	0.384746	+	0.407432i
$263$	−15.3020	+	22.9011i	−0.943562	+	1.41214i	−0.0326830	+	0.999466i	$0.510405\pi$
$263$	−15.3020	+	22.9011i	−0.943562	+	1.41214i	−0.910879	+	0.412674i	$0.864595\pi$
$264$	−4.22205	+	2.89673i	−0.259849	+	0.178281i
$265$	−0.992673	+	0.663283i	−0.0609794	+	0.0407451i
$266$	6.15235	+	9.80402i	0.377225	+	0.601123i
$267$	−0.341582	+	0.182580i	−0.0209045	+	0.0111737i
$268$	−0.714725	+	1.94720i	−0.0436588	+	0.118944i
$269$	−6.35240	−	0.625656i	−0.387312	−	0.0381469i	−0.0975128	−	0.995234i	$-0.531089\pi$
$269$	−6.35240	−	0.625656i	−0.387312	−	0.0381469i	−0.289800	+	0.957087i	$0.593589\pi$
$270$	0.105870	−	0.830426i	0.00644305	−	0.0505381i
$271$	7.17124	−	2.97042i	0.435622	−	0.180440i	−0.154086	−	0.988058i	$-0.549243\pi$
$271$	7.17124	−	2.97042i	0.435622	−	0.180440i	0.589707	+	0.807617i	$0.299243\pi$
$272$	0.603538	−	5.24709i	0.0365949	−	0.318152i
$273$	2.11926	+	0.877828i	0.128264	+	0.0531285i
$274$	−9.88273	+	17.2804i	−0.597038	+	1.04395i
$275$	6.50645	−	5.33971i	0.392354	−	0.321996i
$276$	−3.37549	+	5.52869i	−0.203181	+	0.332788i
$277$	−11.1199	−	3.37319i	−0.668130	−	0.202675i	−0.0620432	−	0.998073i	$-0.519762\pi$
$277$	−11.1199	−	3.37319i	−0.668130	−	0.202675i	−0.606087	+	0.795398i	$0.707262\pi$
$278$	13.4785	−	18.9728i	0.808387	−	1.13792i
$279$	−1.04654	+	5.26132i	−0.0626548	+	0.314987i
$280$	1.26567	−	1.58145i	0.0756384	−	0.0945097i
$281$	15.6124	−	3.10549i	0.931356	−	0.185258i	0.293980	−	0.955812i	$-0.405020\pi$
$281$	15.6124	−	3.10549i	0.931356	−	0.185258i	0.637375	+	0.770553i	$0.280020\pi$
$282$	−9.29891	+	3.54340i	−0.553742	+	0.211006i
$283$	−8.44333	−	6.92926i	−0.501904	−	0.411902i	0.349081	−	0.937093i	$-0.386494\pi$
$283$	−8.44333	−	6.92926i	−0.501904	−	0.411902i	−0.850984	+	0.525191i	$0.823994\pi$
$284$	−13.0543	+	4.55089i	−0.774628	+	0.270046i
$285$	1.88777	−	3.53177i	0.111822	−	0.209204i
$286$	−3.18560	+	3.66263i	−0.188369	+	0.216576i
$287$	6.71411	−	6.71411i	0.396321	−	0.396321i
$288$	−5.49293	−	1.35193i	−0.323674	−	0.0796631i
$289$	−10.7880	−	10.7880i	−0.634586	−	0.634586i
$290$	−4.17147	+	0.290572i	−0.244957	+	0.0170630i
$291$	−1.91880	−	1.02562i	−0.112482	−	0.0601228i
$292$	−3.64375	−	0.208869i	−0.213234	−	0.0122232i
$293$	−19.1236	+	23.3022i	−1.11721	+	1.36133i	−0.192215	+	0.981353i	$0.561567\pi$
$293$	−19.1236	+	23.3022i	−1.11721	+	1.36133i	−0.924997	+	0.379974i	$0.875933\pi$
$294$	3.20211	−	7.14489i	0.186751	−	0.416699i
$295$	0.337501	+	1.69673i	0.0196501	+	0.0987877i
$296$	−18.2678	−	21.7100i	−1.06179	−	1.26187i
$297$	−1.77549	−	0.353167i	−0.103024	−	0.0204928i
$298$	6.27668	−	1.06271i	0.363598	−	0.0615609i
$299$	−1.78266	+	5.87665i	−0.103094	+	0.339855i
$300$	9.18708	+	1.43960i	0.530416	+	0.0831156i
$301$	2.51111	+	3.05980i	0.144738	+	0.176364i
$302$	3.82069	+	14.0290i	0.219856	+	0.807277i
$303$	4.69742	−	11.3406i	0.269860	−	0.651500i
$304$	−22.2512	−	15.3997i	−1.27619	−	0.883235i
$305$	−0.455158	−	1.09885i	−0.0260623	−	0.0629199i
$306$	1.47681	−	1.14283i	0.0844235	−	0.0653314i
$307$	1.19464	−	12.1294i	0.0681819	−	0.692262i	−0.898961	−	0.438029i	$-0.855677\pi$
$307$	1.19464	−	12.1294i	0.0681819	−	0.692262i	0.967143	−	0.254234i	$-0.0818232\pi$
$308$	−3.22132	−	2.96795i	−0.183552	−	0.169115i
$309$	0.337521	+	0.631457i	0.0192009	+	0.0359223i
$310$	4.37762	+	1.00183i	0.248632	+	0.0569004i
$311$	14.1207	+	21.1331i	0.800711	+	1.19835i	0.976838	+	0.213981i	$0.0686431\pi$
$311$	14.1207	+	21.1331i	0.800711	+	1.19835i	−0.176127	+	0.984367i	$0.556357\pi$
$312$	−5.36250	+	0.0658800i	−0.303592	+	0.00372972i
$313$	8.73398	+	5.83586i	0.493674	+	0.329862i	0.777361	−	0.629055i	$-0.216558\pi$
$313$	8.73398	+	5.83586i	0.493674	+	0.329862i	−0.283687	+	0.958917i	$0.591558\pi$
$314$	0.753331	−	26.3054i	0.0425129	−	1.48450i
$315$	0.712697	−	0.0701945i	0.0401559	−	0.00395501i
$316$	−29.7969	−	7.72308i	−1.67621	−	0.434457i
$317$	1.31159	−	0.397866i	0.0736661	−	0.0223464i	−0.253237	−	0.967404i	$-0.581495\pi$
$317$	1.31159	−	0.397866i	0.0736661	−	0.0223464i	0.326903	+	0.945058i	$0.393995\pi$
$318$	−0.905758	+	2.70461i	−0.0507924	+	0.151667i
$319$			9.04236i			0.506275i
$320$	−1.26293	+	4.56411i	−0.0706001	+	0.255142i
$321$		−	10.1583i		−	0.566980i
$322$	−5.25456	−	1.75972i	−0.292825	−	0.0980653i
$323$	8.54816	−	2.59306i	0.475632	−	0.144282i
$324$	−1.01415	−	1.72380i	−0.0563417	−	0.0957668i
$325$	8.77352	−	0.864117i	0.486667	−	0.0479326i
$326$	−26.4915	−	0.758659i	−1.46723	−	0.0420182i
$327$	−7.20973	−	4.81738i	−0.398699	−	0.266402i
$328$	−8.24262	+	20.6120i	−0.455123	+	1.13811i
$329$	−4.72946	−	7.07813i	−0.260743	−	0.390230i
$330$	−0.338080	+	1.47727i	−0.0186107	+	0.0813212i
$331$	−2.87522	−	5.37915i	−0.158036	−	0.295665i	0.790425	−	0.612559i	$-0.209860\pi$
$331$	−2.87522	−	5.37915i	−0.158036	−	0.295665i	−0.948461	+	0.316894i	$0.897360\pi$
$332$	−7.07181	+	0.289503i	−0.388116	+	0.0158885i
$333$	0.983251	−	9.98311i	0.0538818	−	0.547071i
$334$	−8.20762	−	10.6062i	−0.449101	−	0.580344i
$335$	0.234938	+	0.567191i	0.0128360	+	0.0309890i
$336$	0.0790950	−	4.83856i	0.00431498	−	0.263965i
$337$	1.21912	−	2.94321i	0.0664095	−	0.160327i	−0.887190	−	0.461403i	$-0.847346\pi$
$337$	1.21912	−	2.94321i	0.0664095	−	0.160327i	0.953600	+	0.301077i	$0.0973461\pi$
$338$	12.8331	−	3.49501i	0.698030	−	0.190104i
$339$	4.36236	+	5.31555i	0.236931	+	0.288701i
$340$	−0.920937	−	1.26319i	−0.0499448	−	0.0685059i
$341$	2.81896	−	9.29287i	0.152655	−	0.503237i
$342$	−1.59711	−	9.43307i	−0.0863620	−	0.510082i
$343$	14.8751	+	2.95884i	0.803180	+	0.159763i
$344$	−8.21443	−	4.26180i	−0.442893	−	0.229781i
$345$	0.374035	+	1.88040i	0.0201374	+	0.101237i
$346$	−16.1264	−	7.22735i	−0.866962	−	0.388545i
$347$	9.36251	−	11.4083i	0.502606	−	0.612427i	−0.458470	−	0.888710i	$-0.651603\pi$
$347$	9.36251	−	11.4083i	0.502606	−	0.612427i	0.961077	+	0.276282i	$0.0891025\pi$
$348$	−7.45672	+	6.64819i	−0.399722	+	0.356380i
$349$	−8.16611	−	4.36487i	−0.437122	−	0.233646i	0.238131	−	0.971233i	$-0.423465\pi$
$349$	−8.16611	−	4.36487i	−0.437122	−	0.233646i	−0.675252	+	0.737587i	$0.735965\pi$
$350$	0.552787	+	7.93584i	0.0295477	+	0.424188i
$351$	−1.34073	−	1.34073i	−0.0715627	−	0.0715627i
$352$	9.65594	+	3.41023i	0.514663	+	0.181766i
$353$	−2.36347	+	2.36347i	−0.125795	+	0.125795i	−0.767201	−	0.641406i	$-0.778351\pi$
$353$	−2.36347	+	2.36347i	−0.125795	+	0.125795i	0.641406	+	0.767201i	$0.278351\pi$
$354$	3.11850	+	2.71234i	0.165747	+	0.144159i
$355$	−1.92886	+	3.60865i	−0.102373	+	0.191527i
$356$	0.697529	+	0.336910i	0.0369690	+	0.0178562i
$357$	1.23484	+	1.01341i	0.0653549	+	0.0536354i
$358$	7.44158	+	19.5289i	0.393300	+	1.03213i
$359$	14.5931	−	2.90274i	0.770193	−	0.153201i	0.205673	−	0.978621i	$-0.434062\pi$
$359$	14.5931	−	2.90274i	0.770193	−	0.153201i	0.564519	+	0.825420i	$0.309062\pi$
$360$	−1.46679	+	0.807337i	−0.0773066	+	0.0425504i
$361$	5.22194	−	26.2524i	0.274839	−	1.38171i
$362$	−6.88448	−	4.89081i	−0.361840	−	0.257055i
$363$	−7.39037	−	2.24184i	−0.387894	−	0.117666i
$364$	−1.07832	−	4.45922i	−0.0565196	−	0.233727i
$365$	−0.835032	+	0.685293i	−0.0437076	+	0.0358699i
$366$	−2.46662	−	1.41067i	−0.128933	−	0.0737369i
$367$	−33.1507	−	13.7315i	−1.73045	−	0.716777i	−0.999406	−	0.0344488i	$-0.989032\pi$
$367$	−33.1507	−	13.7315i	−1.73045	−	0.716777i	−0.731046	−	0.682328i	$-0.760968\pi$
$368$	12.9120	−	1.05895i	0.673085	−	0.0552014i
$369$	−7.25111	+	3.00351i	−0.377478	+	0.156356i
$370$	−8.33035	−	1.06203i	−0.433074	−	0.0552121i
$371$	−2.42823	−	0.239160i	−0.126068	−	0.0124166i
$372$	9.73588	−	4.50773i	0.504782	−	0.233715i
$373$	20.0625	−	10.7236i	1.03880	−	0.555249i	0.138427	−	0.990373i	$-0.455795\pi$
$373$	20.0625	−	10.7236i	1.03880	−	0.555249i	0.900371	+	0.435124i	$0.143295\pi$
$374$	−2.86333	+	1.79684i	−0.148059	+	0.0929122i
$375$	4.74944	−	3.17347i	0.245260	−	0.163877i
$376$	16.6827	+	10.8530i	0.860347	+	0.559701i
$377$	−5.26177	+	7.87480i	−0.270995	+	0.405573i
$378$	1.24394	−	1.17467i	0.0639812	−	0.0604187i
$379$	1.69661	+	17.2260i	0.0871492	+	0.884841i	0.935010	+	0.354622i	$0.115390\pi$
$379$	1.69661	+	17.2260i	0.0871492	+	0.884841i	−0.847861	+	0.530219i	$0.822110\pi$
$380$	−7.93191	+	1.11041i	−0.406898	+	0.0569631i
$381$	0.291799	+	0.961931i	0.0149493	+	0.0492812i
$382$	4.16205	+	8.35340i	0.212949	+	0.427397i
$383$	18.2232			0.931162			0.465581	−	0.885005i	$-0.345845\pi$
$383$	18.2232			0.931162			0.465581	+	0.885005i	$0.345845\pi$
$384$	4.28709	+	10.4700i	0.218775	+	0.534295i
$385$	−1.29642			−0.0660716
$386$	−14.4398	−	28.9813i	−0.734967	−	1.47511i
$387$	−0.949767	−	3.13096i	−0.0482794	−	0.159156i
$388$	0.603285	+	4.30938i	0.0306271	+	0.218776i
$389$	−3.06441	−	31.1135i	−0.155372	−	1.57752i	−0.684525	−	0.728989i	$-0.739990\pi$
$389$	−3.06441	−	31.1135i	−0.155372	−	1.57752i	0.529153	−	0.848526i	$-0.322510\pi$
$390$	−1.15406	+	1.08980i	−0.0584379	+	0.0551840i
$391$	−2.37597	+	3.55589i	−0.120158	+	0.179829i
$392$	−15.3197	+	3.24341i	−0.773760	+	0.163817i
$393$	5.33296	−	3.56337i	0.269012	−	0.179748i
$394$	25.4679	−	15.9819i	1.28305	−	0.805157i
$395$	−8.03484	+	4.29471i	−0.404277	+	0.216090i
$396$	1.52118	+	3.28548i	0.0764423	+	0.165101i
$397$	15.5747	+	1.53397i	0.781670	+	0.0769878i	0.480977	−	0.876733i	$-0.340282\pi$
$397$	15.5747	+	1.53397i	0.781670	+	0.0769878i	0.300693	+	0.953721i	$0.402782\pi$
$398$	1.56008	+	0.198892i	0.0781995	+	0.00996957i
$399$	7.56144	−	3.13205i	0.378545	−	0.156799i
$400$	−8.49795	−	16.5434i	−0.424897	−	0.827170i
$401$	3.54831	+	1.46976i	0.177194	+	0.0733961i	0.469517	−	0.882924i	$-0.344428\pi$
$401$	3.54831	+	1.46976i	0.177194	+	0.0733961i	−0.292323	+	0.956320i	$0.594428\pi$
$402$	1.27319	+	0.728144i	0.0635011	+	0.0363165i
$403$	7.86252	−	6.45260i	0.391660	−	0.321427i
$404$	−23.8621	+	5.77032i	−1.18719	+	0.287084i
$405$	−0.566463	−	0.171835i	−0.0281478	−	0.00853854i
$406$	−6.96698	−	4.94941i	−0.345765	−	0.245635i
$407$	−3.54276	+	17.8107i	−0.175608	+	0.882842i
$408$	−3.58695	−	1.04015i	−0.177581	−	0.0514949i
$409$	2.19105	−	0.435826i	0.108340	−	0.0215502i	−0.140622	−	0.990063i	$-0.544910\pi$
$409$	2.19105	−	0.435826i	0.108340	−	0.0215502i	0.248963	+	0.968513i	$0.419910\pi$
$410$	2.33958	+	6.13974i	0.115544	+	0.303220i
$411$	10.8811	+	8.92987i	0.536724	+	0.440478i
$412$	0.622819	−	1.28947i	0.0306841	−	0.0635276i
$413$	−1.66668	+	3.11815i	−0.0820122	+	0.153434i
$414$	3.45607	+	3.00595i	0.169857	+	0.147734i
$415$	−1.48128	+	1.48128i	−0.0727130	+	0.0727130i
$416$	6.42473	+	8.58871i	0.314999	+	0.421096i
$417$	−11.6366	−	11.6366i	−0.569845	−	0.569845i
$418$	1.20351	+	17.2776i	0.0588654	+	0.845074i
$419$	28.0517	+	14.9940i	1.37042	+	0.732503i	0.981982	−	0.188973i	$-0.0605160\pi$
$419$	28.0517	+	14.9940i	1.37042	+	0.732503i	0.388434	+	0.921476i	$0.373016\pi$
$420$	−0.953162	−	1.06908i	−0.0465096	−	0.0521659i
$421$	13.1931	−	16.0759i	0.642993	−	0.783489i	−0.344898	−	0.938640i	$-0.612086\pi$
$421$	13.1931	−	16.0759i	0.642993	−	0.783489i	0.987891	+	0.155151i	$0.0495864\pi$
$422$	−31.0861	−	13.9318i	−1.51325	−	0.678189i
$423$	1.37276	+	6.90132i	0.0667458	+	0.335554i
$424$	5.43811	−	1.72286i	0.264098	−	0.0836696i
$425$	6.02146	+	1.19774i	0.292084	+	0.0580990i
$426$	1.63188	+	9.63842i	0.0790649	+	0.466983i
$427$	0.705625	−	2.32613i	0.0341476	−	0.112569i
$428$	−16.4168	+	11.9688i	−0.793536	+	0.578534i
$429$	2.17750	+	2.65329i	0.105131	+	0.128102i
$430$	−2.64276	+	0.719738i	−0.127445	+	0.0347089i
$431$	−14.9948	+	36.2006i	−0.722272	+	1.74372i	−0.0554990	+	0.998459i	$0.517675\pi$
$431$	−14.9948	+	36.2006i	−0.722272	+	1.74372i	−0.666773	+	0.745261i	$0.732325\pi$
$432$	−1.59093	+	3.67001i	−0.0765437	+	0.176573i
$433$	10.3981	+	25.1033i	0.499701	+	1.20639i	0.949645	+	0.313328i	$0.101444\pi$
$433$	10.3981	+	25.1033i	0.499701	+	1.20639i	−0.449944	+	0.893057i	$0.648556\pi$
$434$	5.61701	+	7.25849i	0.269625	+	0.348419i
$435$	−0.289819	+	2.94258i	−0.0138958	+	0.141086i
$436$	0.709350	+	17.3276i	0.0339717	+	0.829842i
$437$	10.3288	+	19.3239i	0.494095	+	0.924386i
$438$	−0.575730	+	2.51571i	−0.0275094	+	0.120205i
$439$	−9.55586	−	14.3014i	−0.456076	−	0.682566i	0.530162	−	0.847896i	$-0.322131\pi$
$439$	−9.55586	−	14.3014i	−0.456076	−	0.682566i	−0.986238	+	0.165330i	$0.947131\pi$
$440$	2.78576	−	1.19420i	0.132806	−	0.0569312i
$441$	−4.60333	−	3.07585i	−0.219206	−	0.146469i
$442$	−3.53920	−	0.101355i	−0.168343	−	0.00482097i
$443$	−1.75723	+	0.173072i	−0.0834884	+	0.00822289i	−0.139675	−	0.990197i	$-0.544606\pi$
$443$	−1.75723	+	0.173072i	−0.0834884	+	0.00822289i	0.0561867	+	0.998420i	$0.482106\pi$
$444$	−17.2922	+	10.1734i	−0.820651	+	0.482807i
$445$	0.219400	−	0.0665544i	0.0104006	−	0.00315498i
$446$	−15.1821	−	5.08440i	−0.718895	−	0.240753i
$447$		−	4.50145i		−	0.212911i
$448$	−7.91278	+	5.57311i	−0.373844	+	0.263305i
$449$			27.2009i			1.28369i	0.766835	+	0.641845i	$0.221831\pi$
$449$			27.2009i			1.28369i	−0.766835	+	0.641845i	$0.778169\pi$
$450$	2.08812	−	6.23516i	0.0984347	−	0.293928i
$451$	13.5962	−	4.12437i	0.640221	−	0.194209i
$452$	3.45059	−	13.3129i	0.162302	−	0.626188i
$453$	10.2318	−	1.00774i	0.480731	−	0.0473479i
$454$	1.05749	−	36.9262i	0.0496303	−	1.73303i
$455$	−1.12902	−	0.754389i	−0.0529294	−	0.0353663i
$456$	−13.3630	+	13.6954i	−0.625780	+	0.641347i
$457$	−20.0373	−	29.9880i	−0.937307	−	1.40278i	−0.915190	−	0.403023i	$-0.867959\pi$
$457$	−20.0373	−	29.9880i	−0.937307	−	1.40278i	−0.0221170	−	0.999755i	$-0.507041\pi$
$458$	20.5821	+	4.71030i	0.961739	+	0.220098i
$459$	−0.622443	−	1.16451i	−0.0290531	−	0.0543546i
$460$	2.59821	−	2.82002i	0.121142	−	0.131484i
$461$	1.64304	−	16.6820i	0.0765238	−	0.776959i	−0.877967	−	0.478720i	$-0.841101\pi$
$461$	1.64304	−	16.6820i	0.0765238	−	0.776959i	0.954491	−	0.298239i	$-0.0963992\pi$
$462$	−2.44945	+	1.89552i	−0.113959	+	0.0881875i
$463$	6.73697	+	16.2645i	0.313094	+	0.755875i	0.999587	+	0.0287388i	$0.00914911\pi$
$463$	6.73697	+	16.2645i	0.313094	+	0.755875i	−0.686493	+	0.727136i	$0.740851\pi$
$464$	19.5299	+	4.21770i	0.906651	+	0.195802i
$465$	1.21520	−	2.93375i	0.0563535	−	0.136049i
$466$	10.3838	+	38.1278i	0.481021	+	1.76623i
$467$	−24.3097	−	29.6214i	−1.12492	−	1.37072i	−0.919992	−	0.391938i	$-0.871805\pi$
$467$	−24.3097	−	29.6214i	−1.12492	−	1.37072i	−0.204926	−	0.978778i	$-0.565695\pi$
$468$	−0.587062	+	3.74643i	−0.0271369	+	0.173179i
$469$	−0.364221	+	1.20068i	−0.0168182	+	0.0554421i
$470$	5.80795	−	0.983345i	0.267901	−	0.0453583i
$471$	−18.2508	−	3.63031i	−0.840953	−	0.167276i
$472$	0.709099	−	8.23557i	0.0326389	−	0.379073i
$473$	1.15551	+	5.80913i	0.0531303	+	0.267104i
$474$	−8.90166	+	19.8623i	−0.408867	+	0.912307i
$475$	19.9549	−	24.3151i	0.915591	−	1.11565i
$476$	0.182840	−	3.18966i	0.00838046	−	0.146198i
$477$	1.77870	+	0.950734i	0.0814410	+	0.0435311i
$478$	24.5135	−	1.70754i	1.12122	−	0.0781010i
$479$	18.1849	+	18.1849i	0.830891	+	0.830891i	0.987639	−	0.156748i	$-0.0501010\pi$
$479$	18.1849	+	18.1849i	0.830891	+	0.830891i	−0.156748	+	0.987639i	$0.550101\pi$
$480$	3.03295	+	1.41925i	0.138435	+	0.0647795i
$481$	−13.4494	+	13.4494i	−0.613239	+	0.613239i
$482$	21.5976	−	24.8317i	0.983744	−	1.13105i
$483$	−1.84710	+	3.45568i	−0.0840459	+	0.157239i
$484$	5.08451	+	14.5850i	0.231114	+	0.662953i
$485$	0.995570	+	0.817043i	0.0452065	+	0.0371000i
$486$	−1.32152	+	0.503572i	−0.0599454	+	0.0228425i
$487$	2.61833	−	0.520818i	0.118648	−	0.0236005i	−0.135409	−	0.990790i	$-0.543235\pi$
$487$	2.61833	−	0.520818i	0.118648	−	0.0236005i	0.254057	+	0.967189i	$0.418235\pi$
$488$	0.626469	+	5.64840i	0.0283589	+	0.255691i
$489$	−3.65599	+	18.3799i	−0.165330	+	0.831168i
$490$	−2.68420	+	3.77838i	−0.121260	+	0.170690i
$491$	−27.0062	−	8.19223i	−1.21877	−	0.369710i	−0.385569	−	0.922679i	$-0.625995\pi$
$491$	−27.0062	−	8.19223i	−1.21877	−	0.369710i	−0.833202	+	0.552969i	$0.813495\pi$
$492$	13.3974	+	8.17968i	0.604003	+	0.368769i
$493$	−5.09842	+	4.18417i	−0.229621	+	0.188445i
$494$	−9.00577	+	15.7470i	−0.405189	+	0.708491i
$495$	0.990026	+	0.410082i	0.0444983	+	0.0184318i
$496$	−18.7560	−	10.4230i	−0.842171	−	0.468006i
$497$	−7.72605	+	3.20023i	−0.346561	+	0.143550i
$498$	−0.632922	+	4.96453i	−0.0283619	+	0.222466i
$499$	40.3587	+	3.97498i	1.80670	+	0.177945i	0.944476	−	0.328580i	$-0.106570\pi$
$499$	40.3587	+	3.97498i	1.80670	+	0.177945i	0.862226	+	0.506524i	$0.169070\pi$
$500$	−10.7246	−	3.93648i	−0.479618	−	0.176045i
$501$	−8.36329	+	4.47027i	−0.373644	+	0.199717i
$502$	−7.05850	−	11.2480i	−0.315036	−	0.502024i
$503$	13.3791	−	8.93960i	0.596543	−	0.398597i	−0.220321	−	0.975427i	$-0.570711\pi$
$503$	13.3791	−	8.93960i	0.596543	−	0.398597i	0.816864	+	0.576830i	$0.195711\pi$
$504$	−3.36403	−	0.626289i	−0.149846	−	0.0278971i
$505$	−4.03688	+	6.04162i	−0.179639	+	0.268849i
$506$	−5.69294	−	6.02862i	−0.253082	−	0.268005i
$507$	−0.921841	−	9.35961i	−0.0409404	−	0.415675i
$508$	1.21077	−	1.60495i	0.0537192	−	0.0712082i
$509$	8.47908	+	27.9518i	0.375828	+	1.23894i	0.917292	+	0.398216i	$0.130371\pi$
$509$	8.47908	+	27.9518i	0.375828	+	1.23894i	−0.541463	+	0.840724i	$0.682129\pi$
$510$	−0.989382	+	0.492956i	−0.0438106	+	0.0218285i
$511$	−2.20772			−0.0976639
$512$	11.8694	−	19.2644i	0.524557	−	0.851375i
$513$	−6.76511			−0.298687
$514$	4.30638	−	2.14564i	0.189946	−	0.0946400i
$515$	−0.123034	−	0.405589i	−0.00542153	−	0.0178724i
$516$	−3.94090	+	5.22391i	−0.173488	+	0.229970i
$517$	−1.24855	−	12.6767i	−0.0549110	−	0.557520i
$518$	−11.7836	−	12.4785i	−0.517743	−	0.548272i
$519$	−6.94236	+	10.3900i	−0.304736	+	0.456070i
$520$	3.12096	+	0.581036i	0.136863	+	0.0254801i
$521$	27.8933	−	18.6377i	1.22203	−	0.816532i	0.234214	−	0.972185i	$-0.424748\pi$
$521$	27.8933	−	18.6377i	1.22203	−	0.816532i	0.987812	+	0.155653i	$0.0497483\pi$
$522$	3.75482	+	5.98347i	0.164344	+	0.261889i
$523$	−18.8158	+	10.0573i	−0.822758	+	0.439773i	−0.828350	−	0.560211i	$-0.810720\pi$
$523$	−18.8158	+	10.0573i	−0.822758	+	0.439773i	0.00559209	+	0.999984i	$0.498220\pi$
$524$	−12.0422	−	4.42011i	−0.526066	−	0.193094i
$525$	5.59800	+	0.551355i	0.244317	+	0.0240631i
$526$	4.92601	−	38.6388i	0.214784	−	1.68473i
$527$	6.54409	−	2.71065i	0.285065	−	0.118078i
$528$	3.51735	−	6.32943i	0.153073	−	0.275453i
$529$	11.5577	+	4.78734i	0.502507	+	0.208145i
$530$	0.838204	−	1.46564i	0.0364093	−	0.0636633i
$531$	2.25911	−	1.85401i	0.0980372	−	0.0804570i
$532$	−13.9708	−	8.52975i	−0.605712	−	0.369812i
$533$	14.2406	+	4.31985i	0.616831	+	0.187113i
$534$	0.317225	−	0.446538i	0.0137277	−	0.0193236i
$535$	−1.17312	+	5.89769i	−0.0507185	+	0.254979i
$536$	−0.323364	−	2.91553i	−0.0139672	−	0.125932i
$537$	14.4936	−	2.88296i	0.625446	−	0.124409i
$538$	8.43544	−	3.21437i	0.363678	−	0.138581i
$539$	7.74739	+	6.35812i	0.333704	+	0.273863i
$540$	0.389722	+	1.11792i	0.0167710	+	0.0481077i
$541$	−10.3779	+	19.4157i	−0.446181	+	0.834746i	0.553817	+	0.832639i	$0.313171\pi$
$541$	−10.3779	+	19.4157i	−0.446181	+	0.834746i	−0.999998	+	0.00210742i	$0.999329\pi$
$542$	−7.20395	+	8.28270i	−0.309436	+	0.355773i
$543$	−4.22244	+	4.22244i	−0.181202	+	0.181202i
$544$	2.54527	+	7.02240i	0.109128	+	0.301083i
$545$	3.62948	+	3.62948i	0.155470	+	0.155470i
$546$	−3.23619	+	0.225423i	−0.138496	+	0.00964722i
$547$	−2.09343	−	1.11896i	−0.0895087	−	0.0478434i	0.426035	−	0.904707i	$-0.359910\pi$
$547$	−2.09343	−	1.11896i	−0.0895087	−	0.0478434i	−0.515544	+	0.856863i	$0.672410\pi$
$548$	1.61113	−	28.1063i	0.0688242	−	1.20064i
$549$	−1.27466	+	1.55318i	−0.0544011	+	0.0662880i
$550$	−4.86821	+	10.8625i	−0.207581	+	0.463177i
$551$	6.59248	+	33.1426i	0.280849	+	1.41192i
$552$	0.785857	−	9.12705i	0.0334483	−	0.388473i
$553$	−18.2620	−	3.63254i	−0.776580	−	0.154471i
$554$	16.2029	−	2.74332i	0.688397	−	0.116553i
$555$	−1.72375	+	5.68243i	−0.0731690	+	0.241206i
$556$	−5.09528	+	32.5164i	−0.216088	+	1.37900i
$557$	−0.951487	−	1.15939i	−0.0403158	−	0.0491249i	0.752462	−	0.658635i	$-0.228866\pi$
$557$	−0.951487	−	1.15939i	−0.0403158	−	0.0491249i	−0.792778	+	0.609510i	$0.791366\pi$
$558$	−1.99350	−	7.31980i	−0.0843914	−	0.309872i
$559$	−2.37404	+	5.73144i	−0.100411	+	0.242414i
$560$	−0.604698	+	2.80003i	−0.0255532	+	0.118323i
$561$	0.914737	+	2.20837i	0.0386202	+	0.0932375i
$562$	−17.8035	+	13.7773i	−0.750996	+	0.581161i
$563$	2.09472	−	21.2680i	0.0882819	−	0.896341i	−0.844417	−	0.535686i	$-0.820053\pi$
$563$	2.09472	−	21.2680i	0.0882819	−	0.896341i	0.932699	−	0.360655i	$-0.117447\pi$
$564$	9.53579	−	10.3499i	0.401529	−	0.435808i
$565$	−1.91883	−	3.58988i	−0.0807258	−	0.151027i
$566$	15.0577	+	3.44601i	0.632922	+	0.144847i
$567$	−0.672130	−	1.00591i	−0.0282268	−	0.0422444i
$568$	13.6539	−	13.9936i	0.572905	−	0.587157i
$569$	8.51360	+	5.68861i	0.356909	+	0.238479i	0.721078	−	0.692854i	$-0.243647\pi$
$569$	8.51360	+	5.68861i	0.356909	+	0.238479i	−0.364169	+	0.931333i	$0.618647\pi$
$570$	−0.162121	+	5.66108i	−0.00679051	+	0.237116i
$571$	−9.33436	+	0.919354i	−0.390631	+	0.0384738i	−0.291426	−	0.956593i	$-0.594130\pi$
$571$	−9.33436	+	0.919354i	−0.390631	+	0.0384738i	−0.0992046	+	0.995067i	$0.531630\pi$
$572$	1.72238	−	6.64524i	0.0720164	−	0.277851i
$573$	6.31515	−	1.91568i	0.263819	−	0.0800287i
$574$	−4.26425	+	12.7331i	−0.177986	+	0.531471i
$575$			15.0593i			0.628015i
$576$	7.80557	−	1.75301i	0.325232	−	0.0730421i
$577$			26.5869i			1.10683i	0.832907	+	0.553413i	$0.186675\pi$
$577$			26.5869i			1.10683i	−0.832907	+	0.553413i	$0.813325\pi$
$578$	20.4591	+	6.85163i	0.850987	+	0.284990i
$579$	−21.9098	+	6.64625i	−0.910539	+	0.276209i
$580$	5.09697	−	2.99866i	0.211640	−	0.124513i
$581$	−4.26071	+	0.419643i	−0.176764	+	0.0174097i
$582$	3.07565	+	0.0880799i	0.127490	+	0.00365103i
$583$	−3.03573	−	2.02841i	−0.125727	−	0.0840081i
$584$	4.74398	−	2.03365i	0.196307	−	0.0841530i
$585$	0.623565	+	0.933230i	0.0257812	+	0.0385843i
$586$	9.51040	−	41.5567i	0.392871	−	1.71669i
$587$	−7.85348	−	14.6928i	−0.324148	−	0.606438i	0.666083	−	0.745878i	$-0.267970\pi$
$587$	−7.85348	−	14.6928i	−0.324148	−	0.606438i	−0.990230	+	0.139440i	$0.955470\pi$
$588$	0.452912	+	11.0635i	0.0186778	+	0.456251i
$589$	3.55712	−	36.1160i	0.146568	−	1.48813i
$590$	−1.49730	−	1.93487i	−0.0616430	−	0.0796572i
$591$	−8.13611	−	19.6423i	−0.334675	−	0.807977i
$592$	36.8153	+	15.9593i	1.51310	+	0.655923i
$593$	17.6410	−	42.5891i	0.724429	−	1.74893i	0.0641085	−	0.997943i	$-0.479580\pi$
$593$	17.6410	−	42.5891i	0.724429	−	1.74893i	0.660321	−	0.750984i	$-0.270420\pi$
$594$	2.47014	−	0.672726i	0.101351	−	0.0276023i
$595$	−0.599891	−	0.730970i	−0.0245931	−	0.0299668i
$596$	−7.27478	+	5.30374i	−0.297987	+	0.217250i
$597$	0.322816	−	1.06418i	0.0132120	−	0.0435541i
$598$	−1.44979	−	8.56294i	−0.0592864	−	0.350164i
$599$	8.94702	+	1.77967i	0.365565	+	0.0727154i	0.374455	−	0.927245i	$-0.377830\pi$
$599$	8.94702	+	1.77967i	0.365565	+	0.0727154i	−0.00888992	+	0.999960i	$0.502830\pi$
$600$	−12.5369	+	3.97185i	−0.511817	+	0.162150i
$601$	−7.11938	−	35.7915i	−0.290406	−	1.45997i	−0.800232	−	0.599690i	$-0.795291\pi$
$601$	−7.11938	−	35.7915i	−0.290406	−	1.45997i	0.509827	−	0.860277i	$-0.329709\pi$
$602$	−5.10831	−	2.28938i	−0.208199	−	0.0933081i
$603$	0.657939	−	0.801701i	0.0267933	−	0.0326478i
$604$	−13.6840	−	15.3482i	−0.556794	−	0.624510i
$605$	4.03179	+	2.15504i	0.163916	+	0.0876147i
$606$	1.20628	+	17.3175i	0.0490019	+	0.703473i
$607$	−22.8447	−	22.8447i	−0.927239	−	0.927239i	0.0702875	−	0.997527i	$-0.477608\pi$
$607$	−22.8447	−	22.8447i	−0.927239	−	0.927239i	−0.997527	+	0.0702875i	$0.977608\pi$
$608$	37.8778	+	5.45956i	1.53615	+	0.221414i
$609$	−4.27304	+	4.27304i	−0.173152	+	0.173152i
$610$	1.26916	+	1.10386i	0.0513867	+	0.0446940i
$611$	6.28927	−	11.7664i	0.254437	−	0.476018i
$612$	−1.14858	+	2.37799i	−0.0464286	+	0.0961244i
$613$	6.25134	+	5.13035i	0.252489	+	0.207213i	0.752121	−	0.659026i	$-0.229031\pi$
$613$	6.25134	+	5.13035i	0.252489	+	0.207213i	−0.499631	+	0.866238i	$0.666531\pi$
$614$	6.13759	+	16.1068i	0.247693	+	0.650019i
$615$	4.55670	−	0.906383i	0.183744	−	0.0365489i
$616$	5.94937	+	1.72520i	0.239707	+	0.0695103i
$617$	−7.84337	+	39.4313i	−0.315762	+	1.58744i	0.418266	+	0.908325i	$0.362638\pi$
$617$	−7.84337	+	39.4313i	−0.315762	+	1.58744i	−0.734028	+	0.679119i	$0.762362\pi$
$618$	−0.825480	−	0.586429i	−0.0332057	−	0.0235897i
$619$	−38.7685	−	11.7603i	−1.55824	−	0.472686i	−0.610574	−	0.791959i	$-0.709061\pi$
$619$	−38.7685	−	11.7603i	−1.55824	−	0.472686i	−0.947663	+	0.319273i	$0.896561\pi$
$620$	−6.17301	+	1.49275i	−0.247914	+	0.0599504i
$621$	2.50366	−	2.05470i	0.100468	−	0.0824522i
$622$	−31.2021	−	17.8446i	−1.25109	−	0.715504i
$623$	0.432907	+	0.179316i	0.0173441	+	0.00718415i
$624$	6.74630	−	3.46541i	0.270068	−	0.138727i
$625$	18.3544	−	7.60264i	0.734176	−	0.304106i
$626$	−14.7360	−	1.87868i	−0.588969	−	0.0750870i
$627$	12.1877	+	1.20039i	0.486731	+	0.0479388i
$628$	15.6367	+	33.7725i	0.623973	+	1.34767i
$629$	−11.6817	+	6.24398i	−0.465779	+	0.248964i
$630$	−0.857860	+	0.538335i	−0.0341780	+	0.0214478i
$631$	28.5770	−	19.0946i	1.13763	−	0.760143i	0.163596	−	0.986527i	$-0.447691\pi$
$631$	28.5770	−	19.0946i	1.13763	−	0.760143i	0.974038	+	0.226385i	$0.0726907\pi$
$632$	42.5877	−	9.01645i	1.69405	−	0.358655i
$633$	−13.3825	+	20.0283i	−0.531905	+	0.796052i
$634$	−1.40928	+	1.33081i	−0.0559696	+	0.0528532i
$635$	−0.0583241	−	0.592175i	−0.00231452	−	0.0234997i
$636$	−0.559237	−	3.99474i	−0.0221752	−	0.158402i
$637$	3.04723	+	10.0454i	0.120736	+	0.398012i
$638$	−5.70283	−	11.4458i	−0.225777	−	0.453143i
$639$	6.91239			0.273450
$640$	−1.27987	−	6.57375i	−0.0505914	−	0.259850i
$641$	−21.0373			−0.830922			−0.415461	−	0.909611i	$-0.636380\pi$
$641$	−21.0373			−0.830922			−0.415461	+	0.909611i	$0.636380\pi$
$642$	6.40662	+	12.8583i	0.252849	+	0.507478i
$643$	−9.36194	−	30.8622i	−0.369199	−	1.21709i	−0.923119	−	0.384515i	$-0.874369\pi$
$643$	−9.36194	−	30.8622i	−0.369199	−	1.21709i	0.553920	−	0.832570i	$-0.313131\pi$
$644$	7.76102	−	1.08649i	0.305827	−	0.0428138i
$645$	0.189838	+	1.92745i	0.00747485	+	0.0758934i
$646$	−9.18486	+	8.67343i	−0.361373	+	0.341252i
$647$	−18.2116	+	27.2556i	−0.715973	+	1.07153i	0.277858	+	0.960622i	$0.410376\pi$
$647$	−18.2116	+	27.2556i	−0.715973	+	1.07153i	−0.993831	+	0.110907i	$0.964624\pi$
$648$	2.37088	+	1.54238i	0.0931369	+	0.0605905i
$649$	−4.39889	+	2.93924i	−0.172672	+	0.115375i
$650$	−10.5605	+	6.62708i	−0.414218	+	0.259935i
$651$	5.72354	−	3.05930i	0.224323	−	0.119903i
$652$	34.0113	−	15.7473i	1.33199	−	0.616712i
$653$	−8.53557	−	0.840680i	−0.334023	−	0.0328984i	−0.0703843	−	0.997520i	$-0.522423\pi$
$653$	−8.53557	−	0.840680i	−0.334023	−	0.0328984i	−0.263638	+	0.964622i	$0.584923\pi$
$654$	12.1643	+	1.55081i	0.475661	+	0.0606415i
$655$	−3.50771	+	1.45294i	−0.137058	+	0.0567712i
$656$	−2.56610	−	31.2891i	−0.100189	−	1.22164i
$657$	1.68595	+	0.698345i	0.0657754	+	0.0272450i
$658$	10.4506	+	5.97671i	0.407406	+	0.232997i
$659$	−15.1682	+	12.4482i	−0.590869	+	0.484914i	−0.881668	−	0.471870i	$-0.843579\pi$
$659$	−15.1682	+	12.4482i	−0.590869	+	0.484914i	0.290799	+	0.956784i	$0.406079\pi$
$660$	−0.503745	−	2.08315i	−0.0196083	−	0.0810865i
$661$	39.1707	+	11.8823i	1.52356	+	0.462168i	0.937467	−	0.348074i	$-0.113164\pi$
$661$	39.1707	+	11.8823i	1.52356	+	0.462168i	0.586096	+	0.810242i	$0.300664\pi$
$662$	7.03196	+	4.99558i	0.273305	+	0.194159i
$663$	−0.488432	+	2.45551i	−0.0189691	+	0.0953642i
$664$	8.76890	−	4.82650i	0.340299	−	0.187304i
$665$	−4.75171	+	0.945174i	−0.184264	+	0.0366523i
$666$	5.05154	+	13.2567i	0.195743	+	0.513687i
$667$	−12.5058	−	10.2633i	−0.484228	−	0.397395i
$668$	17.0783	+	8.24889i	0.660779	+	0.319159i
$669$	−5.33687	+	9.98459i	−0.206335	+	0.386026i
$670$	−0.655100	−	0.569778i	−0.0253087	−	0.0220125i
$671$	2.57196	−	2.57196i	0.0992895	−	0.0992895i
$672$	2.95146	+	6.17452i	0.113855	+	0.238187i
$673$	−16.3921	−	16.3921i	−0.631867	−	0.631867i	0.316669	−	0.948536i	$-0.397436\pi$
$673$	−16.3921	−	16.3921i	−0.631867	−	0.631867i	−0.948536	+	0.316669i	$0.897436\pi$
$674$	0.313065	+	4.49437i	0.0120588	+	0.173117i
$675$	−4.10057	−	2.19180i	−0.157831	−	0.0843625i
$676$	−14.0399	+	12.5176i	−0.539997	+	0.481445i
$677$	−28.4034	+	34.6096i	−1.09163	+	1.33016i	−0.151841	+	0.988405i	$0.548520\pi$
$677$	−28.4034	+	34.6096i	−1.09163	+	1.33016i	−0.939790	+	0.341752i	$0.888980\pi$
$678$	−8.87427	−	3.97716i	−0.340814	−	0.152742i
$679$	0.513510	+	2.58159i	0.0197067	+	0.0990723i
$680$	1.96239	+	1.01812i	0.0752541	+	0.0390432i
$681$	−25.6196	−	5.09605i	−0.981744	−	0.195281i
$682$	2.29259	+	13.5408i	0.0877876	+	0.518502i
$683$	13.2106	−	43.5495i	0.505489	−	1.66637i	−0.217930	−	0.975964i	$-0.569930\pi$
$683$	13.2106	−	43.5495i	0.505489	−	1.66637i	0.723419	−	0.690410i	$-0.242570\pi$
$684$	7.97086	+	10.9331i	0.304774	+	0.418037i
$685$	−5.28606	−	6.44109i	−0.201970	−	0.246101i
$686$	−20.6950	+	5.63613i	−0.790137	+	0.215188i
$687$	5.71347	−	13.7935i	0.217982	−	0.526256i
$688$	13.0856	+	0.213908i	0.498885	+	0.00815518i
$689$	−1.46342	−	3.53300i	−0.0557517	−	0.134597i
$690$	−1.65938	−	2.14431i	−0.0631716	−	0.0816325i
$691$	2.70337	−	27.4477i	0.102841	−	1.04416i	−0.795825	−	0.605527i	$-0.792962\pi$
$691$	2.70337	−	27.4477i	0.102841	−	1.04416i	0.898666	−	0.438634i	$-0.144538\pi$
$692$	24.9709	−	1.02225i	0.949253	−	0.0388601i
$693$	1.03239	+	1.93147i	0.0392173	+	0.0733705i
$694$	−4.65610	+	20.3453i	−0.176743	+	0.772297i
$695$	5.41210	+	8.09978i	0.205293	+	0.307242i
$696$	5.24583	−	13.1181i	0.198843	−	0.497239i
$697$	8.61685	+	5.75759i	0.326386	+	0.218084i
$698$	13.0895	+	0.374854i	0.495444	+	0.0141885i
$699$	27.8078	−	2.73883i	1.05179	−	0.103592i
$700$	−5.70469	−	9.69653i	−0.215617	−	0.366495i
$701$	27.4736	−	8.33402i	1.03766	−	0.314772i	0.274916	−	0.961468i	$-0.411350\pi$
$701$	27.4736	−	8.33402i	1.03766	−	0.314772i	0.762747	+	0.646697i	$0.223850\pi$
$702$	2.54266	+	0.851521i	0.0959665	+	0.0321386i
$703$			67.8637i			2.55953i
$704$	−14.3732	+	1.77314i	−0.541711	+	0.0668278i
$705$		−	4.16529i		−	0.156874i
$706$	1.50109	−	4.48227i	0.0564941	−	0.168693i
$707$	−14.2108	+	4.31080i	−0.534453	+	0.162124i
$708$	−5.65801	−	1.46650i	−0.212641	−	0.0551145i
$709$	12.7053	−	1.25136i	0.477158	−	0.0469960i	0.143420	−	0.989662i	$-0.454190\pi$
$709$	12.7053	−	1.25136i	0.477158	−	0.0469960i	0.333738	+	0.942666i	$0.391690\pi$
$710$	0.165650	−	5.78432i	0.00621675	−	0.217082i
$711$	12.7970	+	8.55066i	0.479924	+	0.320675i
$712$	−1.09541	+	0.0134575i	−0.0410523	+	0.000504340i
$713$	9.65271	+	14.4463i	0.361497	+	0.541018i
$714$	−2.20220	−	0.503982i	−0.0824153	−	0.0188611i
$715$	−0.957796	−	1.79191i	−0.0358195	−	0.0670137i
$716$	−21.7360	−	20.0263i	−0.812312	−	0.748419i
$717$	1.70311	−	17.2920i	0.0636039	−	0.645782i
$718$	−16.6412	+	12.8778i	−0.621043	+	0.480596i
$719$	−2.90394	−	7.01073i	−0.108299	−	0.261456i	0.860435	−	0.509561i	$-0.170192\pi$
$719$	−2.90394	−	7.01073i	−0.108299	−	0.261456i	−0.968733	+	0.248105i	$0.920192\pi$
$720$	1.34749	−	1.94700i	0.0502179	−	0.0725604i
$721$	0.331488	−	0.800283i	0.0123453	−	0.0298041i
$722$	9.94696	+	36.5237i	0.370187	+	1.35927i
$723$	−14.7629	−	17.9887i	−0.549039	−	0.669006i
$724$	11.7989	+	1.84887i	0.438502	+	0.0687128i
$725$	−6.74181	+	22.2248i	−0.250385	+	0.825408i
$726$	10.7686	−	1.82323i	0.399660	−	0.0676664i
$727$	−21.6735	−	4.31112i	−0.803824	−	0.159891i	−0.223954	−	0.974600i	$-0.571897\pi$
$727$	−21.6735	−	4.31112i	−0.803824	−	0.159891i	−0.579870	+	0.814709i	$0.696897\pi$
$728$	4.17728	+	4.96439i	0.154820	+	0.183993i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	0.624781	−	1.39408i	0.0231242	−	0.0515972i
$731$	−2.74072	+	3.33957i	−0.101369	+	0.123519i
$732$	4.01193	+	0.229975i	0.148285	+	0.00850011i
$733$	−4.76971	−	2.54946i	−0.176173	−	0.0941666i	0.380953	−	0.924594i	$-0.375596\pi$
$733$	−4.76971	−	2.54946i	−0.176173	−	0.0941666i	−0.557126	+	0.830428i	$0.688096\pi$
$734$	50.6222	−	3.52620i	1.86850	−	0.130154i
$735$	2.31738	+	2.31738i	0.0854780	+	0.0854780i
$736$	−15.6761	+	9.48375i	−0.577830	+	0.349576i
$737$	−1.32757	+	1.32757i	−0.0489015	+	0.0489015i
$738$	7.28419	−	8.37496i	0.268135	−	0.308286i
$739$	−17.0579	+	31.9131i	−0.627485	+	1.17394i	0.344475	+	0.938796i	$0.388057\pi$
$739$	−17.0579	+	31.9131i	−0.627485	+	1.17394i	−0.971960	+	0.235147i	$0.924443\pi$
$740$	11.2143	−	3.90947i	0.412247	−	0.143715i
$741$	9.91553	+	8.13747i	0.364256	+	0.298937i
$742$	3.22449	−	1.22871i	0.118375	−	0.0451073i
$743$	−35.4306	+	7.04759i	−1.29982	+	0.258551i	−0.796022	−	0.605268i	$-0.793066\pi$
$743$	−35.4306	+	7.04759i	−1.29982	+	0.258551i	−0.503802	+	0.863819i	$0.668066\pi$
$744$	−9.48072	+	11.8461i	−0.347580	+	0.434299i
$745$	−0.519846	+	2.61344i	−0.0190457	+	0.0957492i
$746$	−18.6319	+	26.2270i	−0.682163	+	0.960237i
$747$	3.38648	+	1.02728i	0.123905	+	0.0375862i
$748$	2.49117	−	4.08028i	0.0910863	−	0.149190i
$749$	−9.49992	+	7.79639i	−0.347120	+	0.284874i
$750$	−4.01039	+	7.01235i	−0.146439	+	0.256055i
$751$	−3.24608	−	1.34457i	−0.118451	−	0.0490641i	0.322671	−	0.946511i	$-0.395419\pi$
$751$	−3.24608	−	1.34457i	−0.118451	−	0.0490641i	−0.441122	+	0.897447i	$0.645419\pi$
$752$	−27.9617	−	3.21625i	−1.01966	−	0.117285i
$753$	−8.67514	+	3.59336i	−0.316140	+	0.130949i
$754$	1.69387	−	13.2864i	0.0616870	−	0.483862i
$755$	−6.05673	−	0.596536i	−0.220427	−	0.0217102i
$756$	−0.833731	+	2.27142i	−0.0303225	+	0.0826109i
$757$	30.4332	−	16.2669i	1.10611	−	0.591229i	0.185868	−	0.982575i	$-0.440490\pi$
$757$	30.4332	−	16.2669i	1.10611	−	0.591229i	0.920244	+	0.391345i	$0.127990\pi$
$758$	−13.0117	−	20.7346i	−0.472605	−	0.753116i
$759$	−4.87506	+	3.25741i	−0.176953	+	0.118236i
$760$	9.33987	−	6.40805i	0.338793	−	0.232444i
$761$	−25.2699	+	37.8190i	−0.916032	+	1.37094i	0.0125933	+	0.999921i	$0.495991\pi$
$761$	−25.2699	+	37.8190i	−0.916032	+	1.37094i	−0.928626	+	0.371018i	$0.879009\pi$
$762$	−0.976028	−	1.03358i	−0.0353578	−	0.0374426i
$763$	1.02823	+	10.4398i	0.0372243	+	0.377944i
$764$	−10.5366	−	7.94879i	−0.381202	−	0.287577i
$765$	0.226894	+	0.747971i	0.00820339	+	0.0270429i
$766$	−23.0669	+	11.4930i	−0.833440	+	0.415259i
$767$	−5.54126			−0.200083
$768$	−12.0298	−	10.5491i	−0.434088	−	0.380659i
$769$	−28.7146			−1.03548			−0.517738	−	0.855539i	$-0.673226\pi$
$769$	−28.7146			−1.03548			−0.517738	+	0.855539i	$0.673226\pi$
$770$	1.64100	−	0.817624i	0.0591376	−	0.0294651i
$771$	−0.987579	−	3.25561i	−0.0355668	−	0.117248i
$772$	36.5557	+	27.5775i	1.31567	+	0.992536i
$773$	−2.32678	−	23.6242i	−0.0836885	−	0.849703i	−0.941785	−	0.336215i	$-0.890853\pi$
$773$	−2.32678	−	23.6242i	−0.0836885	−	0.849703i	0.858097	−	0.513488i	$-0.171647\pi$
$774$	3.17685	+	3.36417i	0.114189	+	0.120922i
$775$	13.8572	−	20.7387i	0.497764	−	0.744957i
$776$	−3.48147	−	5.07432i	−0.124978	−	0.182158i
$777$	−10.0907	+	6.74241i	−0.362003	+	0.241883i
$778$	23.5015	+	37.4507i	0.842571	+	1.34267i
$779$	46.8268	−	25.0294i	1.67774	−	0.896772i
$780$	0.773489	−	2.10730i	0.0276954	−	0.0754535i
$781$	−12.4531	−	1.22652i	−0.445605	−	0.0438883i
$782$	0.764871	−	5.99952i	0.0273517	−	0.214542i
$783$	4.61480	−	1.91151i	0.164920	−	0.0683119i
$784$	17.3461	−	13.7673i	0.619502	−	0.491689i
$785$	10.1768	+	4.21536i	0.363225	+	0.150453i
$786$	−4.50310	+	7.87389i	−0.160620	+	0.280852i
$787$	−24.1964	+	19.8575i	−0.862510	+	0.707844i	−0.957747	−	0.287611i	$-0.907139\pi$
$787$	−24.1964	+	19.8575i	−0.862510	+	0.707844i	0.0952374	+	0.995455i	$0.469639\pi$
$788$	−22.1577	+	36.2919i	−0.789335	+	1.29285i
$789$	−26.3569	−	7.99527i	−0.938330	−	0.284639i
$790$	7.46190	−	10.5036i	0.265482	−	0.373703i
$791$	1.62298	−	8.15926i	0.0577065	−	0.290110i
$792$	−3.99759	−	3.19937i	−0.142048	−	0.113685i
$793$	3.73650	−	0.743236i	0.132687	−	0.0263931i
$794$	−20.6818	+	7.88092i	−0.733970	+	0.279683i
$795$	−0.922880	−	0.757388i	−0.0327312	−	0.0268618i
$796$	−2.10018	+	0.732150i	−0.0744388	+	0.0259504i
$797$	−3.72663	+	6.97203i	−0.132004	+	0.246962i	−0.939236	−	0.343272i	$-0.888465\pi$
$797$	−3.72663	+	6.97203i	−0.132004	+	0.246962i	0.807232	+	0.590234i	$0.200965\pi$
$798$	−7.59593	+	8.73339i	−0.268893	+	0.309159i
$799$	6.56986	−	6.56986i	0.232425	−	0.232425i
$800$	21.1903	+	15.5811i	0.749189	+	0.550876i
$801$	−0.273874	−	0.273874i	−0.00967686	−	0.00967686i
$802$	−5.41838	+	0.377429i	−0.191330	+	0.0133275i
$803$	−2.91343	−	1.55726i	−0.102813	−	0.0549545i
$804$	−2.07083	−	0.118706i	−0.0730326	−	0.00418643i
$805$	1.47146	−	1.79298i	0.0518622	−	0.0631943i
$806$	−5.88284	+	13.1264i	−0.207214	+	0.462358i
$807$	−1.24529	−	6.26048i	−0.0438362	−	0.220379i
$808$	26.5654	−	22.3534i	0.934568	−	0.786391i
$809$	−52.8744	−	10.5174i	−1.85896	−	0.369771i	−0.867212	−	0.497939i	$-0.834090\pi$
$809$	−52.8744	−	10.5174i	−1.85896	−	0.369771i	−0.991753	+	0.128168i	$0.959090\pi$
$810$	0.825401	−	0.139749i	0.0290016	−	0.00491027i
$811$	3.06814	−	10.1143i	0.107737	−	0.355161i	−0.886451	−	0.462823i	$-0.846836\pi$
$811$	3.06814	−	10.1143i	0.107737	−	0.355161i	0.994188	+	0.107662i	$0.0343365\pi$
$812$	11.9403	+	1.87103i	0.419021	+	0.0656602i
$813$	4.92422	+	6.00018i	0.172700	+	0.210435i
$814$	−6.74840	−	24.7790i	−0.236531	−	0.868505i
$815$	4.24518	−	10.2488i	0.148702	−	0.358999i
$816$	5.19635	−	0.945600i	0.181909	−	0.0331026i
$817$	8.47048	+	20.4495i	0.296344	+	0.715439i
$818$	−2.49856	+	1.93352i	−0.0873600	+	0.0676038i
$819$	−0.224839	+	2.28283i	−0.00785651	+	0.0797685i
$820$	−6.83364	−	6.29614i	−0.238641	−	0.219871i
$821$	20.7620	+	38.8429i	0.724597	+	1.35563i	0.926528	+	0.376226i	$0.122778\pi$
$821$	20.7620	+	38.8429i	0.724597	+	1.35563i	−0.201931	+	0.979400i	$0.564722\pi$
$822$	−19.4051	−	4.44094i	−0.676832	−	0.154896i
$823$	−20.5674	−	30.7813i	−0.716935	−	1.07297i	−0.993704	−	0.112033i	$-0.964264\pi$
$823$	−20.5674	−	30.7813i	−0.716935	−	1.07297i	0.276769	−	0.960936i	$-0.410736\pi$
$824$	0.0248778	+	2.02501i	0.000866659	+	0.0705444i
$825$	6.99850	+	4.67625i	0.243657	+	0.162806i
$826$	0.143134	−	4.99809i	0.00498029	−	0.173906i
$827$	−8.52258	+	0.839401i	−0.296359	+	0.0291888i	−0.245104	−	0.969497i	$-0.578822\pi$
$827$	−8.52258	+	0.839401i	−0.296359	+	0.0291888i	−0.0512550	+	0.998686i	$0.516322\pi$
$828$	−6.27048	−	1.62525i	−0.217914	−	0.0564813i
$829$	5.44758	−	1.65251i	0.189202	−	0.0573939i	−0.194262	−	0.980950i	$-0.562231\pi$
$829$	5.44758	−	1.65251i	0.189202	−	0.0573939i	0.383464	+	0.923556i	$0.374731\pi$
$830$	0.940786	−	2.80921i	0.0326552	−	0.0975090i
$831$		−	11.6203i		−	0.403103i
$832$	−13.5491	−	6.81963i	−0.469732	−	0.236428i
$833$			7.31036i			0.253289i
$834$	22.0685	+	7.39060i	0.764169	+	0.255916i
$835$	5.37179	−	1.62952i	0.185899	−	0.0563917i
$836$	−12.4200	−	21.1109i	−0.429555	−	0.730136i
$837$	−5.33857	+	0.525803i	−0.184528	+	0.0181744i
$838$	−44.9642	−	1.28768i	−1.55326	−	0.0444821i
$839$	−28.1811	−	18.8300i	−0.972919	−	0.650083i	−0.0358972	−	0.999355i	$-0.511429\pi$
$839$	−28.1811	−	18.8300i	−0.972919	−	0.650083i	−0.937021	+	0.349272i	$0.886429\pi$
$840$	1.88076	+	0.752103i	0.0648923	+	0.0259500i
$841$	2.24990	+	3.36722i	0.0775828	+	0.116111i
$842$	−6.56110	+	28.6694i	−0.226111	+	0.988013i
$843$	7.50380	+	14.0386i	0.258445	+	0.483516i
$844$	48.1352	−	1.97054i	1.65688	−	0.0678288i
$845$	−0.545687	+	5.54045i	−0.0187722	+	0.190597i
$846$	−6.09015	−	7.86991i	−0.209384	−	0.270573i
$847$	3.57548	+	8.63198i	0.122855	+	0.296598i
$848$	−5.79698	+	5.61050i	−0.199069	+	0.192665i
$849$	4.17992	−	10.0912i	0.143454	−	0.346330i
$850$	−8.37734	+	2.28151i	−0.287340	+	0.0782551i
$851$	−20.6115	−	25.1152i	−0.706554	−	0.860939i
$852$	−8.14438	−	11.1711i	−0.279022	−	0.382715i
$853$	2.28072	−	7.51852i	0.0780902	−	0.257429i	−0.909199	−	0.416361i	$-0.863305\pi$
$853$	2.28072	−	7.51852i	0.0780902	−	0.257429i	0.987289	+	0.158932i	$0.0508051\pi$
$854$	0.573866	+	3.38944i	0.0196373	+	0.115984i
$855$	3.92768	+	0.781264i	0.134324	+	0.0267187i
$856$	13.2319	−	25.5038i	0.452256	−	0.871703i
$857$	1.15253	+	5.79414i	0.0393695	+	0.197924i	0.995465	−	0.0951327i	$-0.0303275\pi$
$857$	1.15253	+	5.79414i	0.0393695	+	0.197924i	−0.956095	+	0.293057i	$0.905328\pi$
$858$	−4.42965	−	1.98523i	−0.151226	−	0.0677745i
$859$	19.1086	−	23.2839i	0.651976	−	0.794435i	−0.337159	−	0.941448i	$-0.609466\pi$
$859$	19.1086	−	23.2839i	0.651976	−	0.794435i	0.989135	+	0.147013i	$0.0469658\pi$
$860$	2.89128	−	2.57778i	0.0985919	−	0.0879015i
$861$	8.37400	+	4.47600i	0.285385	+	0.152542i
$862$	−3.85061	−	55.2795i	−0.131152	−	1.88283i
$863$	−20.9486	−	20.9486i	−0.713099	−	0.713099i	0.254083	−	0.967182i	$-0.418226\pi$
$863$	−20.9486	−	20.9486i	−0.713099	−	0.713099i	−0.967182	+	0.254083i	$0.918226\pi$
$864$	−0.300799	−	5.64885i	−0.0102334	−	0.192178i
$865$	5.23047	−	5.23047i	0.177841	−	0.177841i
$866$	−28.9940	−	25.2178i	−0.985256	−	0.856935i
$867$	7.19186	−	13.4550i	0.244248	−	0.456956i
$868$	−11.6878	−	5.64525i	−0.396709	−	0.191612i
$869$	−21.5372	−	17.6751i	−0.730601	−	0.599588i
$870$	−1.48897	−	3.90750i	−0.0504809	−	0.132476i
$871$	−1.92866	+	0.383635i	−0.0653503	+	0.0129990i
$872$	−11.8261	−	21.4859i	−0.400481	−	0.727604i
$873$	0.424458	−	2.13390i	0.0143657	−	0.0722214i
$874$	−25.2614	−	17.9459i	−0.854479	−	0.607031i
$875$	−6.61295	−	2.00602i	−0.223558	−	0.0678157i
$876$	−0.857848	−	3.54748i	−0.0289840	−	0.119858i
$877$	30.7110	−	25.2039i	1.03704	−	0.851075i	0.0480169	−	0.998847i	$-0.484710\pi$
$877$	30.7110	−	25.2039i	1.03704	−	0.851075i	0.989022	+	0.147771i	$0.0472099\pi$
$878$	21.1154	+	12.0759i	0.712609	+	0.407543i
$879$	−27.8501	−	11.5359i	−0.939359	−	0.389095i
$880$	−2.77305	+	3.26853i	−0.0934794	+	0.110182i
$881$	−15.2659	+	6.32334i	−0.514321	+	0.213039i	−0.624720	−	0.780849i	$-0.714787\pi$
$881$	−15.2659	+	6.32334i	−0.514321	+	0.213039i	0.110399	+	0.993887i	$0.464787\pi$
$882$	7.76676	+	0.990175i	0.261520	+	0.0333409i
$883$	−25.2792	−	2.48979i	−0.850714	−	0.0837880i	−0.336744	−	0.941596i	$-0.609326\pi$
$883$	−25.2792	−	2.48979i	−0.850714	−	0.0837880i	−0.513970	+	0.857808i	$0.671826\pi$
$884$	4.54384	−	2.10381i	0.152826	−	0.0707586i
$885$	−1.52570	+	0.815504i	−0.0512859	+	0.0274129i
$886$	2.11514	−	1.32732i	0.0710596	−	0.0445922i
$887$	29.6309	−	19.7987i	0.994908	−	0.664776i	0.0522841	−	0.998632i	$-0.483350\pi$
$887$	29.6309	−	19.7987i	0.994908	−	0.664776i	0.942624	+	0.333856i	$0.108350\pi$
$888$	15.4723	−	23.7833i	0.519215	−	0.798114i
$889$	0.675635	−	1.01116i	0.0226601	−	0.0339132i
$890$	−0.235742	+	0.222616i	−0.00790209	+	0.00746209i
$891$	−0.177438	−	1.80156i	−0.00594439	−	0.0603544i
$892$	22.4241	−	3.13923i	0.750816	−	0.105109i
$893$	−13.8184	−	45.5531i	−0.462415	−	1.52438i
$894$	2.83897	+	5.69792i	0.0949494	+	0.190567i
$895$	−8.74762			−0.292401
$896$	6.50113	−	12.0449i	0.217188	−	0.402390i
$897$	−6.14108			−0.205045
$898$	−17.1550	−	34.4308i	−0.572471	−	1.14897i
$899$	7.77826	+	25.6415i	0.259420	+	0.855192i
$900$	1.28925	+	9.20938i	0.0429751	+	0.306979i
$901$	−0.261028	−	2.65026i	−0.00869611	−	0.0882931i
$902$	−14.6089	+	13.7955i	−0.486423	+	0.459339i
$903$	−2.19911	+	3.29119i	−0.0731817	+	0.109524i
$904$	4.02845	+	19.0277i	0.133984	+	0.632852i
$905$	2.93909	−	1.96383i	0.0976985	−	0.0652801i
$906$	−12.3158	+	7.72857i	−0.409165	+	0.256765i
$907$	−19.8962	+	10.6347i	−0.660643	+	0.353121i	−0.767404	−	0.641164i	$-0.778452\pi$
$907$	−19.8962	+	10.6347i	−0.660643	+	0.353121i	0.106761	+	0.994285i	$0.465952\pi$
$908$	21.9500	+	47.4080i	0.728437	+	1.57329i
$909$	12.2159	+	1.20316i	0.405174	+	0.0399062i
$910$	1.90489	+	0.242853i	0.0631466	+	0.00805049i
$911$	24.1524	−	10.0043i	0.800206	−	0.331456i	0.0551670	−	0.998477i	$-0.482431\pi$
$911$	24.1524	−	10.0043i	0.800206	−	0.331456i	0.745039	+	0.667021i	$0.232431\pi$
$912$	8.27743	−	25.7634i	0.274093	−	0.853111i
$913$	−5.91866	−	2.45159i	−0.195879	−	0.0811358i
$914$	44.2760	+	25.3216i	1.46452	+	0.837564i
$915$	0.919407	−	0.754538i	0.0303947	−	0.0249443i
$916$	−29.0235	+	7.01843i	−0.958963	+	0.231895i
$917$	−7.42541	−	2.25247i	−0.245209	−	0.0743833i
$918$	1.52232	+	1.08147i	0.0502440	+	0.0356938i
$919$	−2.44478	+	12.2908i	−0.0806460	+	0.405435i	0.919284	+	0.393595i	$0.128769\pi$
$919$	−2.44478	+	12.2908i	−0.0806460	+	0.405435i	−0.999930	+	0.0118396i	$0.996231\pi$
$920$	−1.51028	+	5.20822i	−0.0497925	+	0.171710i
$921$	11.9539	−	2.37778i	0.393895	−	0.0783506i
$922$	8.44125	+	22.1523i	0.277998	+	0.729547i
$923$	−10.1314	−	8.31461i	−0.333479	−	0.273679i
$924$	1.90505	−	3.94416i	0.0626715	−	0.129753i
$925$	−21.9869	+	41.1346i	−0.722924	+	1.35250i
$926$	−18.7853	−	16.3387i	−0.617324	−	0.536923i
$927$	−0.506290	+	0.506290i	−0.0166287	+	0.0166287i
$928$	−27.3809	+	6.97833i	−0.898821	+	0.229075i
$929$	−25.3504	−	25.3504i	−0.831719	−	0.831719i	0.156033	−	0.987752i	$-0.450129\pi$
$929$	−25.3504	−	25.3504i	−0.831719	−	0.831719i	−0.987752	+	0.156033i	$0.950129\pi$
$930$	0.312059	+	4.47994i	0.0102328	+	0.146903i
$931$	33.0317	+	17.6558i	1.08257	+	0.578646i
$932$	−37.1902	−	41.7132i	−1.21821	−	1.36636i
$933$	−16.1241	+	19.6473i	−0.527879	+	0.643223i
$934$	49.4527	+	22.1631i	1.61814	+	0.725199i
$935$	−0.276045	−	1.38777i	−0.00902763	−	0.0453850i
$936$	−1.61970	−	5.11247i	−0.0529414	−	0.167106i
$937$	−9.99344	−	1.98782i	−0.326471	−	0.0649392i	0.0291336	−	0.999576i	$-0.490725\pi$
$937$	−9.99344	−	1.98782i	−0.326471	−	0.0649392i	−0.355605	+	0.934636i	$0.615725\pi$
$938$	−0.296211	−	1.74952i	−0.00967164	−	0.0571238i
$939$	−3.04923	+	10.0520i	−0.0995078	+	0.328033i
$940$	−6.73152	+	4.90767i	−0.219558	+	0.160071i
$941$	34.2685	+	41.7563i	1.11712	+	1.36122i	0.925055	+	0.379834i	$0.124019\pi$
$941$	34.2685	+	41.7563i	1.11712	+	1.36122i	0.192066	+	0.981382i	$0.438481\pi$
$942$	25.3914	−	6.91517i	0.827297	−	0.225308i
$943$	−9.72788	+	23.4852i	−0.316783	+	0.764783i
$944$	4.29643	+	10.8718i	0.139837	+	0.353846i
$945$	0.274057	+	0.661632i	0.00891507	+	0.0215229i
$946$	−5.12634	−	6.62443i	−0.166672	−	0.215379i
$947$	4.07736	−	41.3982i	0.132496	−	1.34526i	−0.667211	−	0.744869i	$-0.732512\pi$
$947$	4.07736	−	41.3982i	0.132496	−	1.34526i	0.799707	−	0.600390i	$-0.204988\pi$
$948$	−1.25907	−	30.7558i	−0.0408926	−	0.998902i
$949$	−1.63107	−	3.05152i	−0.0529468	−	0.0990565i
$950$	−9.92380	+	43.3631i	−0.321971	+	1.40688i
$951$	0.761468	+	1.13962i	0.0246923	+	0.0369546i
$952$	1.78021	+	4.15278i	0.0576971	+	0.134592i
$953$	−7.58976	−	5.07132i	−0.245857	−	0.164276i	0.426537	−	0.904470i	$-0.359734\pi$
$953$	−7.58976	−	5.07132i	−0.245857	−	0.164276i	−0.672393	+	0.740194i	$0.734734\pi$
$954$	−2.85108	−	0.0816489i	−0.0923072	−	0.00264348i
$955$	−3.88767	+	0.382902i	−0.125802	+	0.0123904i
$956$	−29.9522	+	17.6216i	−0.968724	+	0.569922i
$957$	−8.65300	+	2.62486i	−0.279712	+	0.0848496i
$958$	−34.4873	−	11.5496i	−1.11423	−	0.373150i
$959$		−	17.0295i		−	0.549910i
$960$	−4.73419	+	0.116340i	−0.152795	+	0.00375484i
$961$			2.22325i			0.0717177i
$962$	8.54196	−	25.5065i	0.275404	−	0.822361i
$963$	9.72088	−	2.94880i	0.313251	−	0.0950236i
$964$	−11.6773	+	45.0531i	−0.376102	+	1.45106i
$965$	13.4879	−	1.32844i	0.434190	−	0.0427640i
$966$	0.158628	−	5.53912i	0.00510378	−	0.178218i
$967$	−25.8312	−	17.2599i	−0.830676	−	0.555040i	0.0659527	−	0.997823i	$-0.478991\pi$
$967$	−25.8312	−	17.2599i	−0.830676	−	0.555040i	−0.896629	+	0.442783i	$0.853991\pi$
$968$	−15.6344	−	15.2549i	−0.502509	−	0.490312i
$969$	4.96280	+	7.42736i	0.159428	+	0.238601i
$970$	−1.77548	−	0.406326i	−0.0570073	−	0.0130463i
$971$	7.59112	+	14.2020i	0.243611	+	0.455764i	0.973777	−	0.227506i	$-0.0730573\pi$
$971$	7.59112	+	14.2020i	0.243611	+	0.455764i	−0.730166	+	0.683270i	$0.760557\pi$
$972$	1.35518	−	1.47088i	0.0434675	−	0.0471784i
$973$	−1.95144	+	19.8133i	−0.0625604	+	0.635187i
$974$	−2.98580	+	2.31058i	−0.0956714	+	0.0740356i
$975$	3.37373	+	8.14490i	0.108046	+	0.260846i
$976$	−4.35531	−	6.75463i	−0.139410	−	0.216211i
$977$	2.80812	−	6.77940i	0.0898397	−	0.216892i	−0.872573	−	0.488484i	$-0.837550\pi$
$977$	2.80812	−	6.77940i	0.0898397	−	0.216892i	0.962413	+	0.271592i	$0.0875500\pi$
$978$	−6.96408	−	25.5710i	−0.222687	−	0.817670i
$979$	0.444803	+	0.541995i	0.0142160	+	0.0173222i
$980$	1.01471	−	6.47553i	0.0324137	−	0.206853i
$981$	2.51708	−	8.29769i	0.0803641	−	0.264925i
$982$	39.3510	−	6.66252i	1.25574	−	0.212610i
$983$	22.5950	+	4.49442i	0.720667	+	0.143350i	0.541780	−	0.840520i	$-0.317750\pi$
$983$	22.5950	+	4.49442i	0.720667	+	0.143350i	0.178887	+	0.983870i	$0.442750\pi$
$984$	−22.1172	−	1.90433i	−0.705071	−	0.0607079i
$985$	2.45527	+	12.3435i	0.0782315	+	0.393296i
$986$	3.81470	−	8.51178i	0.121485	−	0.271070i
$987$	5.40046	−	6.58048i	0.171899	−	0.209459i
$988$	1.46817	−	25.6123i	0.0467086	−	0.814835i
$989$	−9.34571	−	4.99539i	−0.297176	−	0.158844i
$990$	−1.51180	+	0.105308i	−0.0480482	+	0.00334690i
$991$	8.58362	+	8.58362i	0.272668	+	0.272668i	0.830173	−	0.557506i	$-0.188241\pi$
$991$	8.58362	+	8.58362i	0.272668	+	0.272668i	−0.557506	+	0.830173i	$0.688241\pi$
$992$	30.3149	+	1.36435i	0.962500	+	0.0433180i
$993$	4.31290	−	4.31290i	0.136866	−	0.136866i
$994$	7.76129	−	8.92351i	0.246173	−	0.283036i
$995$	−0.310317	+	0.580562i	−0.00983770	+	0.0184050i
$996$	−2.32987	−	6.68326i	−0.0738249	−	0.211767i
$997$	28.4505	+	23.3488i	0.901038	+	0.739463i	0.966032	−	0.258423i	$-0.0832028\pi$
$997$	28.4505	+	23.3488i	0.901038	+	0.739463i	−0.0649940	+	0.997886i	$0.520703\pi$
$998$	−53.5928	+	20.4218i	−1.69645	+	0.646442i
$999$	9.83866	−	1.95703i	0.311282	−	0.0619177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.5	✓	512
128.69	even	32	inner	384.2.v.a.325.5	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.5	✓	512	1.1	even	1	trivial
384.2.v.a.325.5	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)

\(f(q)\)	\(=\)	\(q+(-1.26580 + 0.630679i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.20449 - 1.59662i) q^{4} +(-0.0580215 - 0.589102i) q^{5} +(-0.970964 - 1.02822i) q^{6} +(0.672130 - 1.00591i) q^{7} +(-0.517679 + 2.78065i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.26580 + 0.630679i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.20449 - 1.59662i) q^{4} +(-0.0580215 - 0.589102i) q^{5} +(-0.970964 - 1.02822i) q^{6} +(0.672130 - 1.00591i) q^{7} +(-0.517679 + 2.78065i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(0.444978 + 0.709091i) q^{10} +(1.59652 - 0.853357i) q^{11} +(1.87752 + 0.689147i) q^{12} +(1.88694 + 0.185848i) q^{13} +(-0.216372 + 1.69718i) q^{14} +(0.546893 - 0.226531i) q^{15} +(-1.09842 - 3.84623i) q^{16} +(1.21991 + 0.505304i) q^{17} +(0.702086 - 1.22763i) q^{18} +(5.22950 - 4.29174i) q^{19} +(-1.01046 - 0.616928i) q^{20} +(1.15771 + 0.351187i) q^{21} +(-1.48267 + 2.08707i) q^{22} +(-0.631866 + 3.17661i) q^{23} +(-2.81119 + 0.311792i) q^{24} +(4.56025 - 0.907090i) q^{25} +(-2.50570 + 0.954811i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(-0.796494 - 2.28475i) q^{28} +(-2.35464 + 4.40522i) q^{29} +(-0.549388 + 0.631656i) q^{30} +(3.79320 - 3.79320i) q^{31} +(3.81611 + 4.17580i) q^{32} +(1.28006 + 1.28006i) q^{33} +(-1.86284 + 0.129760i) q^{34} +(-0.631584 - 0.337589i) q^{35} +(-0.114458 + 1.99672i) q^{36} +(-6.36386 + 7.75439i) q^{37} +(-3.91278 + 8.73062i) q^{38} +(0.369906 + 1.85964i) q^{39} +(1.66812 + 0.143629i) q^{40} +(7.69774 + 1.53118i) q^{41} +(-1.68691 + 0.285611i) q^{42} +(-0.949767 + 3.13096i) q^{43} +(0.560496 - 3.57690i) q^{44} +(0.375531 + 0.457586i) q^{45} +(-1.20360 - 4.41945i) q^{46} +(2.69276 - 6.50090i) q^{47} +(3.36176 - 2.16762i) q^{48} +(2.11868 + 5.11495i) q^{49} +(-5.20027 + 4.02425i) q^{50} +(-0.129424 + 1.31406i) q^{51} +(2.56953 - 2.78889i) q^{52} +(-0.950734 - 1.77870i) q^{53} +(1.37857 + 0.315492i) q^{54} +(-0.595347 - 0.890999i) q^{55} +(2.44914 + 2.38970i) q^{56} +(5.62499 + 3.75850i) q^{57} +(0.202216 - 7.06114i) q^{58} +(-2.90842 + 0.286454i) q^{59} +(0.297042 - 1.14604i) q^{60} +(1.92274 - 0.583257i) q^{61} +(-2.40913 + 7.19372i) q^{62} +1.20980i q^{63} +(-7.46402 - 2.87897i) q^{64} -1.12239i q^{65} +(-2.42760 - 0.812987i) q^{66} +(-0.992457 + 0.301059i) q^{67} +(2.27615 - 1.33911i) q^{68} +(-3.22324 + 0.317462i) q^{69} +(1.01237 + 0.0289920i) q^{70} +(-5.74744 - 3.84032i) q^{71} +(-1.11441 - 2.59963i) q^{72} +(-1.01384 - 1.51732i) q^{73} +(3.16483 - 13.8290i) q^{74} +(2.19180 + 4.10057i) q^{75} +(-0.553431 - 13.5189i) q^{76} +(0.214664 - 2.17952i) q^{77} +(-1.64106 - 2.12064i) q^{78} +(-5.88979 - 14.2192i) q^{79} +(-2.20209 + 0.870246i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-10.7095 + 2.91665i) q^{82} +(-2.24503 - 2.73558i) q^{83} +(1.95516 - 1.42542i) q^{84} +(0.226894 - 0.747971i) q^{85} +(-0.772420 - 4.56216i) q^{86} +(-4.89905 - 0.974481i) q^{87} +(1.54640 + 4.88112i) q^{88} +(0.0755616 + 0.379874i) q^{89} +(-0.763936 - 0.342371i) q^{90} +(1.45522 - 1.77319i) q^{91} +(4.31077 + 4.83503i) q^{92} +(4.73098 + 2.52876i) q^{93} +(0.691492 + 9.92710i) q^{94} +(-2.83170 - 2.83170i) q^{95} +(-2.88823 + 4.86396i) q^{96} +(-1.53845 + 1.53845i) q^{97} +(-5.90771 - 5.13828i) q^{98} +(-0.853357 + 1.59652i) 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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