LMFDB - Embedded newform 384.2.v.a.229.1

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			229.1
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40608 + 0.151468i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(1.95411 - 0.425952i) q^{4} +(0.410605 + 0.500324i) q^{5} +(1.16865 - 0.796404i) q^{6} +(3.77588 - 2.52296i) q^{7} +(-2.68312 + 0.894907i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(-1.40608 + 0.151468i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(1.95411 - 0.425952i) q^{4} +(0.410605 + 0.500324i) q^{5} +(1.16865 - 0.796404i) q^{6} +(3.77588 - 2.52296i) q^{7} +(-2.68312 + 0.894907i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-0.653126 - 0.641301i) q^{10} +(-0.820483 + 0.248891i) q^{11} +(-1.52258 + 1.29682i) q^{12} +(-4.17659 - 3.42764i) q^{13} +(-4.92703 + 4.11940i) q^{14} +(-0.597972 - 0.247688i) q^{15} +(3.63713 - 1.66472i) q^{16} +(1.11235 - 0.460750i) q^{17} +(-0.655235 + 1.25326i) q^{18} +(0.204056 + 2.07182i) q^{19} +(1.01548 + 0.802792i) q^{20} +(-2.14071 + 4.00499i) q^{21} +(1.11596 - 0.474237i) q^{22} +(5.13036 - 1.02049i) q^{23} +(1.94445 - 2.05405i) q^{24} +(0.893724 - 4.49306i) q^{25} +(6.39179 + 4.18691i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(6.30384 - 6.53849i) q^{28} +(2.48204 - 8.18218i) q^{29} +(0.878313 + 0.257696i) q^{30} +(2.53778 + 2.53778i) q^{31} +(-4.86194 + 2.89163i) q^{32} +(0.606275 - 0.606275i) q^{33} +(-1.49426 + 0.816335i) q^{34} +(2.81269 + 0.853220i) q^{35} +(0.731482 - 1.86143i) q^{36} +(1.74480 + 0.171848i) q^{37} +(-0.600734 - 2.88223i) q^{38} +(5.29920 + 1.05408i) q^{39} +(-1.54945 - 0.974976i) q^{40} +(1.07035 + 5.38099i) q^{41} +(2.40338 - 5.95558i) q^{42} +(7.39874 + 3.95471i) q^{43} +(-1.49730 + 0.835847i) q^{44} +(0.644124 - 0.0634407i) q^{45} +(-7.05911 + 2.21198i) q^{46} +(-0.0457850 - 0.110535i) q^{47} +(-2.42292 + 3.18268i) q^{48} +(5.21313 - 12.5856i) q^{49} +(-0.576093 + 6.45296i) q^{50} +(-0.763807 + 0.930702i) q^{51} +(-9.62154 - 4.91897i) q^{52} +(-3.07185 - 10.1265i) q^{53} +(-0.0129187 - 1.41415i) q^{54} +(-0.461420 - 0.308311i) q^{55} +(-7.87332 + 10.1485i) q^{56} +(-1.15661 - 1.73099i) q^{57} +(-2.25060 + 11.8807i) q^{58} +(-0.373783 + 0.306755i) q^{59} +(-1.27401 - 0.229304i) q^{60} +(3.11144 + 5.82110i) q^{61} +(-3.95271 - 3.18392i) q^{62} -4.54121i q^{63} +(6.39828 - 4.80229i) q^{64} -3.49705i q^{65} +(-0.760639 + 0.944301i) q^{66} +(-1.96716 - 3.68030i) q^{67} +(1.97740 - 1.37416i) q^{68} +(-4.04351 + 3.31843i) q^{69} +(-4.08410 - 0.773663i) q^{70} +(5.37870 + 8.04979i) q^{71} +(-0.746574 + 2.72812i) q^{72} +(0.580721 + 0.388026i) q^{73} +(-2.47936 + 0.0226497i) q^{74} +(1.32982 + 4.38382i) q^{75} +(1.28124 + 3.96166i) q^{76} +(-2.47010 + 3.00983i) q^{77} +(-7.61075 - 0.679456i) q^{78} +(-4.16297 + 10.0503i) q^{79} +(2.32632 + 1.13620i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-2.32004 - 7.40397i) q^{82} +(-4.25592 + 0.419172i) q^{83} +(-2.47726 + 8.73805i) q^{84} +(0.687260 + 0.367348i) q^{85} +(-11.0022 - 4.43996i) q^{86} +(1.66809 + 8.38606i) q^{87} +(1.97872 - 1.40206i) q^{88} +(-13.0939 - 2.60454i) q^{89} +(-0.896080 + 0.186767i) q^{90} +(-24.4181 - 2.40497i) q^{91} +(9.59063 - 4.17944i) q^{92} +(-3.43442 - 1.04182i) q^{93} +(0.0811198 + 0.148486i) q^{94} +(-0.952794 + 0.952794i) q^{95} +(2.92474 - 4.84209i) q^{96} +(-0.365433 - 0.365433i) q^{97} +(-5.42376 + 18.4860i) q^{98} +(-0.248891 + 0.820483i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−1.40608	+	0.151468i	−0.994248	+	0.107104i
$2$	−1.40608	+	0.151468i	−0.994248	+	0.107104i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$4$	1.95411	−	0.425952i	0.977057	−	0.212976i
$5$	0.410605	+	0.500324i	0.183628	+	0.223752i	0.856686	−	0.515838i	$-0.172519\pi$
$5$	0.410605	+	0.500324i	0.183628	+	0.223752i	−0.673058	+	0.739590i	$0.735019\pi$
$6$	1.16865	−	0.796404i	0.477099	−	0.325130i
$7$	3.77588	−	2.52296i	1.42715	−	0.953589i	0.428398	−	0.903590i	$-0.359078\pi$
$7$	3.77588	−	2.52296i	1.42715	−	0.953589i	0.998749	−	0.0499992i	$-0.0159219\pi$
$8$	−2.68312	+	0.894907i	−0.948627	+	0.316397i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−0.653126	−	0.641301i	−0.206537	−	0.202797i
$11$	−0.820483	+	0.248891i	−0.247385	+	0.0750434i	−0.411542	−	0.911391i	$-0.635010\pi$
$11$	−0.820483	+	0.248891i	−0.247385	+	0.0750434i	0.164157	+	0.986434i	$0.447510\pi$
$12$	−1.52258	+	1.29682i	−0.439532	+	0.374359i
$13$	−4.17659	−	3.42764i	−1.15838	−	0.950655i	−0.159048	−	0.987271i	$-0.550842\pi$
$13$	−4.17659	−	3.42764i	−1.15838	−	0.950655i	−0.999329	+	0.0366154i	$0.988342\pi$
$14$	−4.92703	+	4.11940i	−1.31680	+	1.10096i
$15$	−0.597972	−	0.247688i	−0.154396	−	0.0639528i
$16$	3.63713	−	1.66472i	0.909283	−	0.416179i
$17$	1.11235	−	0.460750i	0.269784	−	0.111748i	−0.243690	−	0.969853i	$-0.578358\pi$
$17$	1.11235	−	0.460750i	0.269784	−	0.111748i	0.513474	+	0.858105i	$0.328358\pi$
$18$	−0.655235	+	1.25326i	−0.154440	+	0.295397i
$19$	0.204056	+	2.07182i	0.0468138	+	0.475308i	0.989799	+	0.142473i	$0.0455053\pi$
$19$	0.204056	+	2.07182i	0.0468138	+	0.475308i	−0.942985	+	0.332835i	$0.891995\pi$
$20$	1.01548	+	0.802792i	0.227069	+	0.179510i
$21$	−2.14071	+	4.00499i	−0.467141	+	0.873960i
$22$	1.11596	−	0.474237i	0.237924	−	0.101108i
$23$	5.13036	−	1.02049i	1.06975	−	0.212787i	0.371351	−	0.928493i	$-0.378895\pi$
$23$	5.13036	−	1.02049i	1.06975	−	0.212787i	0.698402	+	0.715705i	$0.253895\pi$
$24$	1.94445	−	2.05405i	0.396908	−	0.419282i
$25$	0.893724	−	4.49306i	0.178745	−	0.898611i
$26$	6.39179	+	4.18691i	1.25353	+	0.821120i
$27$	−0.0980171	+	0.995185i	−0.0188634	+	0.191523i
$28$	6.30384	−	6.53849i	1.19131	−	1.23566i
$29$	2.48204	−	8.18218i	0.460903	−	1.51939i	−0.351439	−	0.936211i	$-0.614308\pi$
$29$	2.48204	−	8.18218i	0.460903	−	1.51939i	0.812342	−	0.583182i	$-0.198192\pi$
$30$	0.878313	+	0.257696i	0.160357	+	0.0470486i
$31$	2.53778	+	2.53778i	0.455798	+	0.455798i	0.897274	−	0.441475i	$-0.145545\pi$
$31$	2.53778	+	2.53778i	0.455798	+	0.455798i	−0.441475	+	0.897274i	$0.645545\pi$
$32$	−4.86194	+	2.89163i	−0.859478	+	0.511173i
$33$	0.606275	−	0.606275i	0.105539	−	0.105539i
$34$	−1.49426	+	0.816335i	−0.256263	+	0.140000i
$35$	2.81269	+	0.853220i	0.475432	+	0.144221i
$36$	0.731482	−	1.86143i	0.121914	−	0.310239i
$37$	1.74480	+	0.171848i	0.286844	+	0.0282516i	0.240416	−	0.970670i	$-0.422716\pi$
$37$	1.74480	+	0.171848i	0.286844	+	0.0282516i	0.0464279	+	0.998922i	$0.485216\pi$
$38$	−0.600734	−	2.88223i	−0.0974519	−	0.467560i
$39$	5.29920	+	1.05408i	0.848551	+	0.168787i
$40$	−1.54945	−	0.974976i	−0.244989	−	0.154157i
$41$	1.07035	+	5.38099i	0.167160	+	0.840369i	0.969799	+	0.243905i	$0.0784284\pi$
$41$	1.07035	+	5.38099i	0.167160	+	0.840369i	−0.802639	+	0.596465i	$0.796572\pi$
$42$	2.40338	−	5.95558i	0.370850	−	0.918966i
$43$	7.39874	+	3.95471i	1.12830	+	0.603087i	0.926483	−	0.376337i	$-0.122816\pi$
$43$	7.39874	+	3.95471i	1.12830	+	0.603087i	0.201814	+	0.979424i	$0.435316\pi$
$44$	−1.49730	+	0.835847i	−0.225727	+	0.126009i
$45$	0.644124	−	0.0634407i	0.0960203	−	0.00945718i
$46$	−7.05911	+	2.21198i	−1.04081	+	0.326138i
$47$	−0.0457850	−	0.110535i	−0.00667843	−	0.0161231i	0.920505	−	0.390730i	$-0.127778\pi$
$47$	−0.0457850	−	0.110535i	−0.00667843	−	0.0161231i	−0.927184	+	0.374607i	$0.877778\pi$
$48$	−2.42292	+	3.18268i	−0.349718	+	0.459380i
$49$	5.21313	−	12.5856i	0.744733	−	1.79795i
$50$	−0.576093	+	6.45296i	−0.0814719	+	0.912586i
$51$	−0.763807	+	0.930702i	−0.106954	+	0.130324i
$52$	−9.62154	−	4.91897i	−1.33427	−	0.682139i
$53$	−3.07185	−	10.1265i	−0.421951	−	1.39099i	−0.868261	−	0.496108i	$-0.834762\pi$
$53$	−3.07185	−	10.1265i	−0.421951	−	1.39099i	0.446309	−	0.894879i	$-0.352738\pi$
$54$	−0.0129187	−	1.41415i	−0.00175802	−	0.192442i
$55$	−0.461420	−	0.308311i	−0.0622179	−	0.0415727i
$56$	−7.87332	+	10.1485i	−1.05212	+	1.35615i
$57$	−1.15661	−	1.73099i	−0.153197	−	0.229275i
$58$	−2.25060	+	11.8807i	−0.295518	+	1.56002i
$59$	−0.373783	+	0.306755i	−0.0486623	+	0.0399361i	−0.658410	−	0.752659i	$-0.728771\pi$
$59$	−0.373783	+	0.306755i	−0.0486623	+	0.0399361i	0.609748	+	0.792596i	$0.291271\pi$
$60$	−1.27401	−	0.229304i	−0.164474	−	0.0296030i
$61$	3.11144	+	5.82110i	0.398379	+	0.745315i	0.998509	−	0.0545877i	$-0.0173844\pi$
$61$	3.11144	+	5.82110i	0.398379	+	0.745315i	−0.600130	+	0.799903i	$0.704884\pi$
$62$	−3.95271	−	3.18392i	−0.501994	−	0.404359i
$63$		−	4.54121i		−	0.572138i
$64$	6.39828	−	4.80229i	0.799785	−	0.600286i
$65$		−	3.49705i		−	0.433756i
$66$	−0.760639	+	0.944301i	−0.0936282	+	0.116235i
$67$	−1.96716	−	3.68030i	−0.240327	−	0.449620i	0.732624	−	0.680634i	$-0.238296\pi$
$67$	−1.96716	−	3.68030i	−0.240327	−	0.449620i	−0.972950	+	0.231014i	$0.925796\pi$
$68$	1.97740	−	1.37416i	0.239795	−	0.166642i
$69$	−4.04351	+	3.31843i	−0.486782	+	0.399492i
$70$	−4.08410	−	0.773663i	−0.488143	−	0.0924704i
$71$	5.37870	+	8.04979i	0.638334	+	0.955335i	0.999737	+	0.0229250i	$0.00729789\pi$
$71$	5.37870	+	8.04979i	0.638334	+	0.955335i	−0.361403	+	0.932410i	$0.617702\pi$
$72$	−0.746574	+	2.72812i	−0.0879846	+	0.321512i
$73$	0.580721	+	0.388026i	0.0679683	+	0.0454150i	0.589090	−	0.808067i	$-0.299486\pi$
$73$	0.580721	+	0.388026i	0.0679683	+	0.0454150i	−0.521122	+	0.853482i	$0.674486\pi$
$74$	−2.47936	+	0.0226497i	−0.288220	+	0.00263297i
$75$	1.32982	+	4.38382i	0.153554	+	0.506200i
$76$	1.28124	+	3.96166i	0.146969	+	0.454433i
$77$	−2.47010	+	3.00983i	−0.281494	+	0.343002i
$78$	−7.61075	−	0.679456i	−0.861748	−	0.0769332i
$79$	−4.16297	+	10.0503i	−0.468370	+	1.13075i	0.496504	+	0.868035i	$0.334617\pi$
$79$	−4.16297	+	10.0503i	−0.468370	+	1.13075i	−0.964874	+	0.262712i	$0.915383\pi$
$80$	2.32632	+	1.13620i	0.260091	+	0.127031i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−2.32004	−	7.40397i	−0.256205	−	0.817632i
$83$	−4.25592	+	0.419172i	−0.467148	+	0.0460101i	−0.328853	−	0.944381i	$-0.606662\pi$
$83$	−4.25592	+	0.419172i	−0.467148	+	0.0460101i	−0.138295	+	0.990391i	$0.544162\pi$
$84$	−2.47726	+	8.73805i	−0.270292	+	0.953399i
$85$	0.687260	+	0.367348i	0.0745438	+	0.0398445i
$86$	−11.0022	−	4.43996i	−1.18640	−	0.478773i
$87$	1.66809	+	8.38606i	0.178838	+	0.899080i
$88$	1.97872	−	1.40206i	0.210932	−	0.149460i
$89$	−13.0939	−	2.60454i	−1.38795	−	0.276081i	−0.556117	−	0.831104i	$-0.687710\pi$
$89$	−13.0939	−	2.60454i	−1.38795	−	0.276081i	−0.831835	+	0.555023i	$0.812710\pi$
$90$	−0.896080	+	0.186767i	−0.0944551	+	0.0196869i
$91$	−24.4181	−	2.40497i	−2.55971	−	0.252109i
$92$	9.59063	−	4.17944i	0.999892	−	0.435737i
$93$	−3.43442	−	1.04182i	−0.356133	−	0.108032i
$94$	0.0811198	+	0.148486i	0.00836687	+	0.0153151i
$95$	−0.952794	+	0.952794i	−0.0977546	+	0.0977546i
$96$	2.92474	−	4.84209i	0.298505	−	0.494194i
$97$	−0.365433	−	0.365433i	−0.0371041	−	0.0371041i	0.688311	−	0.725415i	$-0.258352\pi$
$97$	−0.365433	−	0.365433i	−0.0371041	−	0.0371041i	−0.725415	+	0.688311i	$0.758352\pi$
$98$	−5.42376	+	18.4860i	−0.547882	+	1.86737i
$99$	−0.248891	+	0.820483i	−0.0250145	+	0.0824616i
$100$	−0.167384	−	9.16063i	−0.0167384	−	0.916063i
$101$	−1.26127	+	12.8059i	−0.125501	+	1.27423i	0.701761	+	0.712413i	$0.252398\pi$
$101$	−1.26127	+	12.8059i	−0.125501	+	1.27423i	−0.827261	+	0.561817i	$0.810102\pi$
$102$	0.933002	−	1.42433i	0.0923809	−	0.141030i
$103$	3.19636	−	16.0692i	0.314947	−	1.58334i	−0.421487	−	0.906834i	$-0.638492\pi$
$103$	3.19636	−	16.0692i	0.314947	−	1.58334i	0.736434	−	0.676510i	$-0.236508\pi$
$104$	14.2737	+	5.45911i	1.39965	+	0.535310i
$105$	−2.88278	+	0.573420i	−0.281330	+	0.0559601i
$106$	5.85311	+	13.7734i	0.568504	+	1.33779i
$107$	4.61675	−	8.63732i	0.446318	−	0.835002i	−0.553680	−	0.832730i	$-0.686777\pi$
$107$	4.61675	−	8.63732i	0.446318	−	0.835002i	0.999997	−	0.00227193i	$-0.000723180\pi$
$108$	0.232364	+	1.98646i	0.0223592	+	0.191147i
$109$	2.00704	+	20.3779i	0.192240	+	1.95184i	0.290974	+	0.956731i	$0.406021\pi$
$109$	2.00704	+	20.3779i	0.192240	+	1.95184i	−0.0987341	+	0.995114i	$0.531479\pi$
$110$	0.695493	+	0.363619i	0.0663126	+	0.0346698i
$111$	−1.61979	+	0.670937i	−0.153743	+	0.0636826i
$112$	9.53334	−	15.4621i	0.900816	−	1.46103i
$113$	−18.9748	−	7.85960i	−1.78499	−	0.739369i	−0.991391	−	0.130934i	$-0.958202\pi$
$113$	−18.9748	−	7.85960i	−1.78499	−	0.739369i	−0.793604	−	0.608435i	$-0.791798\pi$
$114$	1.88848	+	2.25872i	0.176872	+	0.211548i
$115$	2.61713	+	2.14782i	0.244048	+	0.200285i
$116$	1.36497	−	17.0461i	0.126735	−	1.58269i
$117$	−5.17036	+	1.56841i	−0.478000	+	0.145000i
$118$	0.479104	−	0.487938i	0.0441051	−	0.0449184i
$119$	3.03764	−	4.54614i	0.278460	−	0.416744i
$120$	1.82609	+	0.129448i	0.166698	+	0.0118169i
$121$	−8.53492	+	5.70285i	−0.775902	+	0.518441i
$122$	−5.25664	−	7.71364i	−0.475914	−	0.698360i
$123$	−3.48054	−	4.24105i	−0.313830	−	0.382403i
$124$	6.04008	+	3.87814i	0.542415	+	0.348267i
$125$	5.46903	−	2.92326i	0.489165	−	0.261464i
$126$	0.687847	+	6.38530i	0.0612783	+	0.568847i
$127$	1.12673			0.0999812			0.0499906	−	0.998750i	$-0.484081\pi$
$127$	1.12673			0.0999812			0.0499906	+	0.998750i	$0.484081\pi$
$128$	−8.26910	+	7.72153i	−0.730892	+	0.682493i
$129$	−8.38934			−0.738640
$130$	0.529691	+	4.91713i	0.0464570	+	0.431261i
$131$	7.83452	−	4.18764i	0.684505	−	0.365875i	−0.0921998	−	0.995741i	$-0.529390\pi$
$131$	7.83452	−	4.18764i	0.684505	−	0.365875i	0.776705	+	0.629865i	$0.216890\pi$
$132$	0.926487	−	1.44297i	0.0806404	−	0.125595i
$133$	5.99761	+	7.30811i	0.520059	+	0.633694i
$134$	3.32343	+	4.87682i	0.287100	+	0.421293i
$135$	−0.538161	+	0.359588i	−0.0463175	+	0.0309484i
$136$	−2.57224	+	2.23170i	−0.220567	+	0.191366i
$137$	4.00919	−	6.00018i	0.342528	−	0.512630i	−0.619713	−	0.784829i	$-0.712751\pi$
$137$	4.00919	−	6.00018i	0.342528	−	0.512630i	0.962241	+	0.272199i	$0.0877509\pi$
$138$	5.18286	−	5.27843i	0.441195	−	0.449330i
$139$	−16.0914	+	4.88127i	−1.36485	+	0.414024i	−0.885924	−	0.463830i	$-0.846475\pi$
$139$	−16.0914	+	4.88127i	−1.36485	+	0.414024i	−0.478929	+	0.877854i	$0.658975\pi$
$140$	5.85975	+	0.469221i	0.495239	+	0.0396564i
$141$	0.0924845	+	0.0759000i	0.00778860	+	0.00639194i
$142$	−8.78216	−	10.5039i	−0.736983	−	0.881471i
$143$	4.27993	+	1.77280i	0.357905	+	0.148249i
$144$	0.636520	−	3.94903i	0.0530433	−	0.329086i
$145$	5.11287	−	2.11782i	0.424601	−	0.175876i
$146$	−0.875313	−	0.457634i	−0.0724414	−	0.0378740i
$147$	1.33525	+	13.5570i	0.110129	+	1.11816i
$148$	3.48274	−	0.407390i	0.286280	−	0.0334873i
$149$	5.80646	−	10.8631i	0.475684	−	0.889942i	−0.523595	−	0.851967i	$-0.675410\pi$
$149$	5.80646	−	10.8631i	0.475684	−	0.889942i	0.999279	−	0.0379743i	$-0.0120905\pi$
$150$	−2.53384	−	5.96257i	−0.206887	−	0.486842i
$151$	−7.37135	+	1.46625i	−0.599872	+	0.119322i	−0.485680	−	0.874137i	$-0.661428\pi$
$151$	−7.37135	+	1.46625i	−0.599872	+	0.119322i	−0.114192	+	0.993459i	$0.536428\pi$
$152$	−2.40159	−	5.37633i	−0.194795	−	0.436078i
$153$	0.234888	−	1.18086i	0.0189896	−	0.0954670i
$154$	3.01726	−	4.60619i	0.243138	−	0.371178i
$155$	−0.227686	+	2.31174i	−0.0182882	+	0.185683i
$156$	10.8042	−	0.197416i	0.865031	−	0.0158059i
$157$	−5.72913	+	18.8864i	−0.457234	+	1.50730i	0.361083	+	0.932534i	$0.382407\pi$
$157$	−5.72913	+	18.8864i	−0.457234	+	1.50730i	−0.818318	+	0.574766i	$0.805093\pi$
$158$	4.33116	−	14.7621i	0.344569	−	1.17441i
$159$	7.48275	+	7.48275i	0.593421	+	0.593421i
$160$	−3.44309	−	1.24523i	−0.272200	−	0.0984437i
$161$	16.7969	−	16.7969i	1.32378	−	1.32378i
$162$	0.678021	+	1.24108i	0.0532704	+	0.0975087i
$163$	5.03712	+	1.52799i	0.394537	+	0.119682i	0.481318	−	0.876546i	$-0.340158\pi$
$163$	5.03712	+	1.52799i	0.394537	+	0.119682i	−0.0867811	+	0.996227i	$0.527658\pi$
$164$	4.38362	+	10.0592i	0.342303	+	0.785488i
$165$	0.552273	+	0.0543942i	0.0429944	+	0.00423458i
$166$	5.92067	−	1.23402i	0.459533	−	0.0957789i
$167$	17.3677	+	3.45465i	1.34395	+	0.267329i	0.814082	−	0.580750i	$-0.197241\pi$
$167$	17.3677	+	3.45465i	1.34395	+	0.267329i	0.529870	+	0.848079i	$0.322241\pi$
$168$	2.15969	−	12.6616i	0.166624	−	0.976864i
$169$	3.15902	+	15.8814i	0.243001	+	1.22165i
$170$	−1.02198	−	0.412422i	−0.0783825	−	0.0316313i
$171$	1.83602	+	0.981375i	0.140404	+	0.0750476i
$172$	16.1425	+	4.57645i	1.23085	+	0.348951i
$173$	14.6622	−	1.44410i	1.11475	−	0.109793i	0.476173	−	0.879352i	$-0.342024\pi$
$173$	14.6622	−	1.44410i	1.11475	−	0.109793i	0.638576	+	0.769559i	$0.279524\pi$
$174$	−3.61569	−	11.5388i	−0.274104	−	0.874754i
$175$	−7.96121	−	19.2201i	−0.601811	−	1.45290i
$176$	−2.56987	+	2.27112i	−0.193711	+	0.171192i
$177$	0.185043	−	0.446734i	0.0139087	−	0.0335786i
$178$	18.8056	+	1.67888i	1.40954	+	0.125838i
$179$	−4.72194	+	5.75370i	−0.352934	+	0.430052i	−0.918969	−	0.394330i	$-0.870977\pi$
$179$	−4.72194	+	5.75370i	−0.352934	+	0.430052i	0.566035	+	0.824381i	$0.308477\pi$
$180$	1.23167	−	0.398336i	0.0918032	−	0.0296902i
$181$	−5.02243	−	16.5567i	−0.373314	−	1.23065i	−0.919534	−	0.393010i	$-0.871434\pi$
$181$	−5.02243	−	16.5567i	−0.373314	−	1.23065i	0.546220	−	0.837642i	$-0.316066\pi$
$182$	34.6980	−	0.316977i	2.57199	−	0.0234959i
$183$	−5.48809	−	3.66702i	−0.405691	−	0.271074i
$184$	−12.8521	+	7.32930i	−0.947471	+	0.540323i
$185$	0.630445	+	0.943527i	0.0463512	+	0.0693695i
$186$	4.98687	+	0.944677i	0.365655	+	0.0692671i
$187$	−0.797986	+	0.654890i	−0.0583545	+	0.0478903i
$188$	−0.136552	−	0.196495i	−0.00995905	−	0.0143309i
$189$	2.14071	+	4.00499i	0.155714	+	0.291320i
$190$	1.19539	−	1.48402i	0.0867224	−	0.107662i
$191$			2.61143i			0.188956i	0.995527	+	0.0944781i	$0.0301182\pi$
$191$			2.61143i			0.188956i	−0.995527	+	0.0944781i	$0.969882\pi$
$192$	−3.37900	+	7.25137i	−0.243858	+	0.523323i
$193$		−	9.51864i		−	0.685166i	−0.939488	−	0.342583i	$-0.888698\pi$
$193$		−	9.51864i		−	0.685166i	0.939488	−	0.342583i	$-0.111302\pi$
$194$	0.569179	+	0.458476i	0.0408647	+	0.0329167i
$195$	1.64850	+	3.08412i	0.118051	+	0.220859i
$196$	4.82620	−	26.8143i	0.344728	−	1.91531i
$197$	−20.5506	+	16.8654i	−1.46417	+	1.20161i	−0.528402	+	0.848995i	$0.677208\pi$
$197$	−20.5506	+	16.8654i	−1.46417	+	1.20161i	−0.935767	+	0.352618i	$0.885292\pi$
$198$	0.225683	−	1.19136i	0.0160386	−	0.0846664i
$199$	11.2177	+	16.7884i	0.795200	+	1.19010i	0.978338	+	0.207014i	$0.0663745\pi$
$199$	11.2177	+	16.7884i	0.795200	+	1.19010i	−0.183138	+	0.983087i	$0.558625\pi$
$200$	1.62290	+	12.8552i	0.114756	+	0.909001i
$201$	3.46976	+	2.31842i	0.244738	+	0.163529i
$202$	−0.166236	−	18.1971i	−0.0116963	−	1.28034i
$203$	−11.2714	−	37.1570i	−0.791100	−	2.60791i
$204$	−1.09613	+	2.14404i	−0.0767447	+	0.150113i
$205$	−2.25275	+	2.74498i	−0.157339	+	0.191718i
$206$	−2.06037	+	23.0787i	−0.143553	+	1.60797i
$207$	2.00177	−	4.83269i	0.139132	−	0.335895i
$208$	−20.8968	−	5.51393i	−1.44894	−	0.382322i
$209$	−0.683082	−	1.64910i	−0.0472497	−	0.114071i
$210$	3.96656	−	1.24292i	0.273718	−	0.0857698i
$211$	−11.5998	+	1.14248i	−0.798563	+	0.0786516i	−0.489064	−	0.872248i	$-0.662661\pi$
$211$	−11.5998	+	1.14248i	−0.798563	+	0.0786516i	−0.309499	+	0.950900i	$0.600161\pi$
$212$	−10.3162	−	18.4800i	−0.708517	−	1.26921i
$213$	−8.53824	−	4.56378i	−0.585030	−	0.312705i
$214$	−5.18323	+	12.8440i	−0.354318	+	0.878001i
$215$	1.05932	+	5.32559i	0.0722454	+	0.363202i
$216$	−0.627606	−	2.75792i	−0.0427032	−	0.187653i
$217$	15.9851	+	3.17962i	1.08514	+	0.215847i
$218$	−5.90865	−	28.3489i	−0.400184	−	1.92003i
$219$	−0.695064	−	0.0684579i	−0.0469681	−	0.00462595i
$220$	−1.03299	−	0.405933i	−0.0696444	−	0.0273680i
$221$	−6.22510	−	1.88836i	−0.418746	−	0.127025i
$222$	2.17592	−	1.18874i	0.146038	−	0.0797828i
$223$	−13.8314	+	13.8314i	−0.926221	+	0.926221i	−0.997459	−	0.0712387i	$-0.977305\pi$
$223$	−13.8314	+	13.8314i	−0.926221	+	0.926221i	0.0712387	+	0.997459i	$0.477305\pi$
$224$	−11.0626	+	23.1849i	−0.739152	+	1.54911i
$225$	−3.23931	−	3.23931i	−0.215954	−	0.215954i
$226$	27.8705	+	8.17715i	1.85392	+	0.543936i
$227$	−5.73619	+	18.9097i	−0.380725	+	1.25508i	0.532084	+	0.846692i	$0.321409\pi$
$227$	−5.73619	+	18.9097i	−0.380725	+	1.25508i	−0.912808	+	0.408389i	$0.866091\pi$
$228$	−2.99747	−	2.88989i	−0.198512	−	0.191388i
$229$	1.56616	−	15.9015i	0.103495	−	1.05080i	−0.793444	−	0.608643i	$-0.791714\pi$
$229$	1.56616	−	15.9015i	0.103495	−	1.05080i	0.896939	−	0.442155i	$-0.145786\pi$
$230$	−4.00521	−	2.62359i	−0.264096	−	0.172995i
$231$	0.759612	−	3.81883i	0.0499788	−	0.251260i
$232$	0.662684	+	24.1750i	0.0435074	+	1.58716i
$233$	0.820569	−	0.163221i	0.0537572	−	0.0106930i	−0.168138	−	0.985763i	$-0.553776\pi$
$233$	0.820569	−	0.163221i	0.0537572	−	0.0106930i	0.221896	+	0.975070i	$0.428776\pi$
$234$	7.03237	−	2.98846i	0.459721	−	0.195361i
$235$	0.0365036	−	0.0682934i	0.00238123	−	0.00445497i
$236$	−0.599751	+	0.758649i	−0.0390405	+	0.0493838i
$237$	−1.06627	−	10.8260i	−0.0692614	−	0.703223i
$238$	−3.58256	+	6.85234i	−0.232223	+	0.444171i
$239$	13.1214	−	5.43505i	0.848750	−	0.351564i	0.0844527	−	0.996427i	$-0.473086\pi$
$239$	13.1214	−	5.43505i	0.848750	−	0.351564i	0.764298	+	0.644864i	$0.223086\pi$
$240$	−2.58723	+	0.0945801i	−0.167005	+	0.00610512i
$241$	12.4315	+	5.14931i	0.800786	+	0.331696i	0.745271	−	0.666761i	$-0.232320\pi$
$241$	12.4315	+	5.14931i	0.800786	+	0.331696i	0.0555148	+	0.998458i	$0.482320\pi$
$242$	11.1370	−	9.31142i	0.715912	−	0.598561i
$243$	0.773010	+	0.634393i	0.0495886	+	0.0406963i
$244$	8.55962	+	10.0498i	0.547973	+	0.643370i
$245$	8.43742	−	2.55946i	0.539047	−	0.163518i
$246$	5.53630	+	5.43606i	0.352981	+	0.346591i
$247$	6.24919	−	9.35257i	0.397626	−	0.595090i
$248$	−9.08024	−	4.53809i	−0.576596	−	0.288169i
$249$	3.55579	−	2.37591i	0.225339	−	0.150567i
$250$	−7.24710	+	4.93871i	−0.458347	+	0.312351i
$251$	1.67899	+	2.04585i	0.105977	+	0.129133i	0.823298	−	0.567610i	$-0.192132\pi$
$251$	1.67899	+	2.04585i	0.105977	+	0.129133i	−0.717321	+	0.696743i	$0.754632\pi$
$252$	−1.93434	−	8.87404i	−0.121852	−	0.559012i
$253$	−3.95538	+	2.11419i	−0.248673	+	0.132918i
$254$	−1.58427	+	0.170663i	−0.0994060	+	0.0107084i
$255$	−0.779275			−0.0488001
$256$	10.4574	−	12.1096i	0.653590	−	0.756849i
$257$	−29.9558			−1.86859			−0.934295	−	0.356502i	$-0.883969\pi$
$257$	−29.9558			−1.86859			−0.934295	+	0.356502i	$0.883969\pi$
$258$	11.7961	−	1.27072i	0.734391	−	0.0791113i
$259$	7.02172	−	3.75319i	0.436309	−	0.233212i
$260$	−1.48957	−	6.83364i	−0.0923795	−	0.423804i
$261$	−5.42429	−	6.60951i	−0.335755	−	0.409119i
$262$	−10.3817	+	7.07482i	−0.641381	+	0.437084i
$263$	−8.39890	+	5.61196i	−0.517898	+	0.346049i	−0.786889	−	0.617094i	$-0.788310\pi$
$263$	−8.39890	+	5.61196i	−0.517898	+	0.346049i	0.268991	+	0.963143i	$0.413310\pi$
$264$	−1.08415	+	2.16927i	−0.0667248	+	0.133509i
$265$	3.80523	−	5.69493i	0.233753	−	0.349837i
$266$	−9.54006	−	9.36733i	−0.584938	−	0.574348i
$267$	12.7756	−	3.87543i	0.781853	−	0.237172i
$268$	−5.41168	−	6.35381i	−0.330571	−	0.388120i
$269$	13.7064	+	11.2486i	0.835697	+	0.685839i	0.951572	−	0.307425i	$-0.0994673\pi$
$269$	13.7064	+	11.2486i	0.835697	+	0.685839i	−0.115875	+	0.993264i	$0.536967\pi$
$270$	0.702231	−	0.587123i	0.0427364	−	0.0357311i
$271$	−22.2645	−	9.22225i	−1.35247	−	0.560212i	−0.415492	−	0.909597i	$-0.636391\pi$
$271$	−22.2645	−	9.22225i	−1.35247	−	0.560212i	−0.936979	+	0.349385i	$0.886391\pi$
$272$	3.27874	−	3.52755i	0.198803	−	0.213889i
$273$	22.6685	−	9.38961i	1.37196	−	0.568285i
$274$	−4.72840	+	9.04398i	−0.285653	+	0.546367i
$275$	0.384994	+	3.90891i	0.0232160	+	0.235716i
$276$	−6.48800	+	8.20693i	−0.390532	+	0.493999i
$277$	−5.78986	+	10.8321i	−0.347879	+	0.650836i	−0.993627	−	0.112714i	$-0.964045\pi$
$277$	−5.78986	+	10.8321i	−0.347879	+	0.650836i	0.645748	+	0.763550i	$0.276545\pi$
$278$	21.8864	−	9.30077i	1.31266	−	0.557823i
$279$	3.52000	−	0.700171i	0.210737	−	0.0419182i
$280$	−8.31034	+	0.227803i	−0.496638	+	0.0136138i
$281$	−2.72960	+	13.7226i	−0.162834	+	0.818622i	0.809877	+	0.586600i	$0.199534\pi$
$281$	−2.72960	+	13.7226i	−0.162834	+	0.818622i	−0.972711	+	0.232022i	$0.925466\pi$
$282$	−0.141537	−	0.0927130i	−0.00842840	−	0.00552098i
$283$	−0.661765	+	6.71902i	−0.0393379	+	0.399404i	0.955273	+	0.295725i	$0.0955614\pi$
$283$	−0.661765	+	6.71902i	−0.0393379	+	0.399404i	−0.994611	+	0.103679i	$0.966939\pi$
$284$	13.9394	+	13.4392i	0.827152	+	0.797467i
$285$	0.391145	−	1.28943i	0.0231694	−	0.0763794i
$286$	−6.28643	−	1.84443i	−0.371725	−	0.109063i
$287$	17.6175	+	17.6175i	1.03993	+	1.03993i
$288$	−0.296846	+	5.64906i	−0.0174918	+	0.332874i
$289$	−10.9958	+	10.9958i	−0.646811	+	0.646811i
$290$	−6.86832	+	3.75226i	−0.403322	+	0.220340i
$291$	0.494547	+	0.150019i	0.0289909	+	0.00879428i
$292$	1.30008	+	0.510887i	0.0760812	+	0.0298974i
$293$	12.6148	+	1.24245i	0.736964	+	0.0725846i	0.459532	−	0.888161i	$-0.348017\pi$
$293$	12.6148	+	1.24245i	0.736964	+	0.0725846i	0.277431	+	0.960746i	$0.410517\pi$
$294$	−3.93091	−	18.8599i	−0.229255	−	1.09993i
$295$	−0.306954	−	0.0610569i	−0.0178716	−	0.00355487i
$296$	−4.83530	+	1.10035i	−0.281046	+	0.0639564i
$297$	−0.167271	−	0.840927i	−0.00970604	−	0.0487956i
$298$	−6.51892	+	16.1539i	−0.377631	+	0.935770i
$299$	−24.9253	−	13.3228i	−1.44146	−	0.770479i
$300$	4.46591	+	8.00005i	0.257839	+	0.461883i
$301$	37.9143	−	3.73423i	2.18534	−	0.215237i
$302$	10.1426	−	3.17819i	0.583641	−	0.182884i
$303$	−4.92430	−	11.8883i	−0.282894	−	0.682966i
$304$	4.19117	+	7.19578i	0.240380	+	0.412706i
$305$	−1.63486	+	3.94690i	−0.0936117	+	0.225999i
$306$	−0.151408	+	1.69596i	−0.00865544	+	0.0969518i
$307$	0.101098	−	0.123188i	0.00576997	−	0.00703073i	−0.770117	−	0.637902i	$-0.779802\pi$
$307$	0.101098	−	0.123188i	0.00576997	−	0.00703073i	0.775887	+	0.630871i	$0.217302\pi$
$308$	−3.54482	+	6.93369i	−0.201985	+	0.395084i
$309$	4.75602	+	15.6785i	0.270561	+	0.891919i
$310$	−0.0300092	−	3.28497i	−0.00170441	−	0.186574i
$311$	−0.995466	−	0.665149i	−0.0564477	−	0.0377171i	0.527026	−	0.849849i	$-0.323307\pi$
$311$	−0.995466	−	0.665149i	−0.0564477	−	0.0377171i	−0.583474	+	0.812132i	$0.698307\pi$
$312$	−15.1617	+	1.91408i	−0.858362	+	0.108363i
$313$	−0.116001	−	0.173608i	−0.00655677	−	0.00981290i	0.828177	−	0.560467i	$-0.189378\pi$
$313$	−0.116001	−	0.173608i	−0.00655677	−	0.00981290i	−0.834734	+	0.550654i	$0.814378\pi$
$314$	5.19492	−	27.4236i	0.293167	−	1.54760i
$315$	2.27207	−	1.86464i	0.128017	−	0.105061i
$316$	−3.85398	+	21.4127i	−0.216803	+	1.20456i
$317$	5.49604	+	10.2824i	0.308689	+	0.577516i	0.987653	−	0.156655i	$-0.0500711\pi$
$317$	5.49604	+	10.2824i	0.308689	+	0.577516i	−0.678965	+	0.734171i	$0.737571\pi$
$318$	−11.6547	−	9.38794i	−0.653565	−	0.526449i
$319$			7.33109i			0.410462i
$320$	5.02987	+	1.22937i	0.281178	+	0.0687238i
$321$			9.79376i			0.546634i
$322$	−21.0736	+	26.1620i	−1.17439	+	1.45795i
$323$	1.18157	+	2.21057i	0.0657444	+	0.122999i
$324$	−1.14134	−	1.64236i	−0.0634075	−	0.0912423i
$325$	−19.1333	+	15.7023i	−1.06132	+	0.871006i
$326$	−7.31402	−	1.38552i	−0.405086	−	0.0767366i
$327$	−11.3761	−	17.0256i	−0.629100	−	0.941515i
$328$	−7.68735	−	13.4800i	−0.424463	−	0.744308i
$329$	−0.451753	−	0.301852i	−0.0249060	−	0.0166416i
$330$	−0.784779	+	0.00716919i	−0.0432006	+	0.000394651i
$331$	−5.84953	−	19.2833i	−0.321519	−	1.05991i	−0.957556	−	0.288248i	$-0.906927\pi$
$331$	−5.84953	−	19.2833i	−0.321519	−	1.05991i	0.636037	−	0.771659i	$-0.280573\pi$
$332$	−8.13802	+	2.63193i	−0.446632	+	0.144446i
$333$	1.11225	−	1.35528i	0.0609507	−	0.0742687i
$334$	−24.9436	−	2.22686i	−1.36485	−	0.121848i
$335$	1.03361	−	2.49536i	0.0564723	−	0.136336i
$336$	−1.11887	+	18.1303i	−0.0610395	+	0.989091i
$337$	−1.11679	−	2.69616i	−0.0608353	−	0.146869i	0.890539	−	0.454907i	$-0.150328\pi$
$337$	−1.11679	−	2.69616i	−0.0608353	−	0.146869i	−0.951374	+	0.308038i	$0.900328\pi$
$338$	−6.84735	−	21.8521i	−0.372447	−	1.18860i
$339$	20.4392	−	2.01309i	1.11011	−	0.109336i
$340$	1.49946	+	0.425101i	0.0813195	+	0.0230543i
$341$	−2.71383	−	1.45057i	−0.146962	−	0.0785530i
$342$	−2.73024	−	1.10179i	−0.147634	−	0.0595781i
$343$	−5.86724	−	29.4966i	−0.316801	−	1.59267i
$344$	−23.3908	−	3.98978i	−1.26115	−	0.215114i
$345$	−3.32057	−	0.660503i	−0.178774	−	0.0355603i
$346$	−20.3975	+	4.25138i	−1.09658	+	0.228556i
$347$	−4.63748	−	0.456751i	−0.248953	−	0.0245197i	−0.0272290	−	0.999629i	$-0.508668\pi$
$347$	−4.63748	−	0.456751i	−0.248953	−	0.0245197i	−0.221724	+	0.975110i	$0.571168\pi$
$348$	6.83170	+	15.6768i	0.366217	+	0.840365i
$349$	15.4371	+	4.68278i	0.826327	+	0.250664i	0.674998	−	0.737820i	$-0.264145\pi$
$349$	15.4371	+	4.68278i	0.826327	+	0.250664i	0.151329	+	0.988483i	$0.451645\pi$
$350$	14.1053	+	25.8190i	0.753960	+	1.38009i
$351$	3.82051	−	3.82051i	0.203924	−	0.203924i
$352$	3.26944	−	3.58263i	0.174262	−	0.190955i
$353$	8.36360	+	8.36360i	0.445149	+	0.445149i	0.893738	−	0.448589i	$-0.148073\pi$
$353$	8.36360	+	8.36360i	0.445149	+	0.445149i	−0.448589	+	0.893738i	$0.648073\pi$
$354$	−0.192520	+	0.656171i	−0.0102323	+	0.0348751i
$355$	−1.81898	+	5.99638i	−0.0965415	+	0.318255i
$356$	−26.6964	+	0.487801i	−1.41491	+	0.0258534i
$357$	−0.535918	+	5.44127i	−0.0283638	+	0.287983i
$358$	5.76792	−	8.80538i	0.304844	−	0.465379i
$359$	2.88729	−	14.5154i	0.152385	−	0.766092i	−0.826700	−	0.562643i	$-0.809785\pi$
$359$	2.88729	−	14.5154i	0.152385	−	0.766092i	0.979085	−	0.203449i	$-0.0652153\pi$
$360$	−1.67149	+	0.746650i	−0.0880952	+	0.0393519i
$361$	14.3841	−	2.86118i	0.757059	−	0.150588i
$362$	9.56974	+	22.5193i	0.502974	+	1.18359i
$363$	4.83882	−	9.05280i	0.253972	−	0.475149i
$364$	−48.7401	+	5.70133i	−2.55468	+	0.298831i
$365$	0.0443087	+	0.449874i	0.00231922	+	0.0235475i
$366$	8.27212	+	4.32486i	0.432391	+	0.226064i
$367$	−33.7900	+	13.9963i	−1.76382	+	0.730600i	−0.767883	+	0.640590i	$0.778690\pi$
$367$	−33.7900	+	13.9963i	−1.76382	+	0.730600i	−0.995941	+	0.0900098i	$0.971310\pi$
$368$	16.9609	−	12.2523i	0.884151	−	0.638693i
$369$	5.06878	+	2.09956i	0.263870	+	0.109299i
$370$	−1.02937	−	1.23118i	−0.0535144	−	0.0640061i
$371$	−37.1478	−	30.4864i	−1.92862	−	1.58278i
$372$	−7.15502	−	0.572939i	−0.370970	−	0.0297055i
$373$	9.10327	−	2.76145i	0.471349	−	0.142982i	−0.0456689	−	0.998957i	$-0.514542\pi$
$373$	9.10327	−	2.76145i	0.471349	−	0.142982i	0.517018	+	0.855974i	$0.327042\pi$
$374$	1.02284	−	1.04170i	0.0528896	−	0.0538648i
$375$	−3.44524	+	5.15616i	−0.177911	+	0.266263i
$376$	0.221765	+	0.255605i	0.0114367	+	0.0131818i
$377$	−38.4120	+	25.6661i	−1.97832	+	1.32187i
$378$	−3.61664	−	5.30708i	−0.186020	−	0.272967i
$379$	12.4389	+	15.1568i	0.638941	+	0.778552i	0.987310	−	0.158805i	$-0.0507643\pi$
$379$	12.4389	+	15.1568i	0.638941	+	0.778552i	−0.348369	+	0.937358i	$0.613264\pi$
$380$	−1.45602	+	2.26771i	−0.0746925	+	0.116331i
$381$	−0.993688	+	0.531137i	−0.0509082	+	0.0272110i
$382$	−0.395547	−	3.67187i	−0.0202380	−	0.187869i
$383$	−6.38394			−0.326204			−0.163102	−	0.986609i	$-0.552150\pi$
$383$	−6.38394			−0.326204			−0.163102	+	0.986609i	$0.552150\pi$
$384$	3.65279	−	10.7078i	0.186405	−	0.546431i
$385$	−2.52012			−0.128437
$386$	1.44177	+	13.3840i	0.0733840	+	0.681225i
$387$	7.39874	−	3.95471i	0.376099	−	0.201029i
$388$	−0.869755	−	0.558441i	−0.0441551	−	0.0283506i
$389$	−7.54846	−	9.19782i	−0.382722	−	0.466348i	0.545643	−	0.838018i	$-0.316285\pi$
$389$	−7.54846	−	9.19782i	−0.382722	−	0.466348i	−0.928365	+	0.371670i	$0.878785\pi$
$390$	−2.78506	−	4.08683i	−0.141027	−	0.206944i
$391$	5.23655	−	3.49895i	0.264824	−	0.176950i
$392$	−2.72451	+	38.4340i	−0.137609	+	1.94121i
$393$	−4.93539	+	7.38633i	−0.248957	+	0.372591i
$394$	26.3412	−	26.8269i	1.32705	−	1.35152i
$395$	−6.73774	+	2.04387i	−0.339012	+	0.102838i
$396$	−0.136875	+	1.70933i	−0.00687823	+	0.0858972i
$397$	−5.55354	−	4.55767i	−0.278724	−	0.228743i	0.484636	−	0.874716i	$-0.338952\pi$
$397$	−5.55354	−	4.55767i	−0.278724	−	0.228743i	−0.763361	+	0.645973i	$0.776452\pi$
$398$	−18.3158	−	21.9068i	−0.918091	−	1.09809i
$399$	−8.73444	−	3.61792i	−0.437269	−	0.181123i
$400$	−4.22907	−	17.8296i	−0.211454	−	0.891481i
$401$	22.1768	−	9.18593i	1.10746	−	0.458723i	0.247395	−	0.968915i	$-0.420425\pi$
$401$	22.1768	−	9.18593i	1.10746	−	0.458723i	0.860061	+	0.510191i	$0.170425\pi$
$402$	−5.22992	−	2.73432i	−0.260845	−	0.136376i
$403$	−1.90067	−	19.2978i	−0.0946792	−	0.961294i
$404$	2.99001	+	25.5613i	0.148759	+	1.27172i
$405$	0.305107	−	0.570815i	0.0151609	−	0.0283640i
$406$	21.4766	+	50.5384i	1.06587	+	2.50818i
$407$	−1.47435	+	0.293267i	−0.0730809	+	0.0145367i
$408$	1.21650	−	3.18072i	0.0602255	−	0.157469i
$409$	1.69762	−	8.53451i	0.0839419	−	0.422004i	−0.915848	−	0.401524i	$-0.868481\pi$
$409$	1.69762	−	8.53451i	0.0839419	−	0.422004i	0.999790	−	0.0204801i	$-0.00651948\pi$
$410$	2.75176	−	4.20088i	0.135900	−	0.207467i
$411$	−0.707326	+	7.18160i	−0.0348898	+	0.354242i
$412$	−0.598641	−	32.7625i	−0.0294929	−	1.61409i
$413$	−0.637425	+	2.10131i	−0.0313656	+	0.103399i
$414$	−2.08264	+	7.09835i	−0.102356	+	0.348865i
$415$	−1.95723	−	1.95723i	−0.0960764	−	0.0960764i
$416$	30.2178	+	4.58782i	1.48155	+	0.224936i
$417$	11.8903	−	11.8903i	0.582271	−	0.582271i
$418$	1.21025	+	2.21531i	0.0591954	+	0.108354i
$419$	6.59066	+	1.99926i	0.321975	+	0.0976700i	0.447135	−	0.894467i	$-0.352444\pi$
$419$	6.59066	+	1.99926i	0.321975	+	0.0976700i	−0.125160	+	0.992137i	$0.539944\pi$
$420$	−5.38903	+	2.34845i	−0.262958	+	0.114593i
$421$	2.83729	+	0.279448i	0.138281	+	0.0136195i	0.166921	−	0.985970i	$-0.446618\pi$
$421$	2.83729	+	0.279448i	0.138281	+	0.0136195i	−0.0286398	+	0.999590i	$0.509118\pi$
$422$	16.1372	−	3.36341i	0.785545	−	0.163728i
$423$	−0.117343	−	0.0233410i	−0.00570541	−	0.00113488i
$424$	17.3045	+	24.4217i	0.840379	+	1.18602i
$425$	−1.07604	−	5.40962i	−0.0521957	−	0.262405i
$426$	12.6967	+	5.12377i	0.615157	+	0.248247i
$427$	26.4348	+	14.1297i	1.27927	+	0.683784i
$428$	5.34257	−	18.8448i	0.258243	−	0.910899i
$429$	−4.61025	+	0.454070i	−0.222585	+	0.0219227i
$430$	−2.29615	−	7.32774i	−0.110730	−	0.353375i
$431$	14.7150	+	35.5252i	0.708798	+	1.71119i	0.702983	+	0.711207i	$0.251851\pi$
$431$	14.7150	+	35.5252i	0.708798	+	1.71119i	0.00581486	+	0.999983i	$0.498149\pi$
$432$	1.30020	+	3.78279i	0.0625559	+	0.181999i
$433$	7.96552	−	19.2305i	0.382798	−	0.924157i	−0.608624	−	0.793459i	$-0.708278\pi$
$433$	7.96552	−	19.2305i	0.382798	−	0.924157i	0.991422	−	0.130698i	$-0.0417219\pi$
$434$	−22.9579	−	2.04958i	−1.10201	−	0.0983830i
$435$	−3.51082	+	4.27794i	−0.168331	+	0.205112i
$436$	12.6020	+	38.9658i	0.603525	+	1.86612i
$437$	3.16116	+	10.4209i	0.151219	+	0.498501i
$438$	0.987684	−	0.00902279i	0.0471934	−	0.000431126i
$439$	25.8208	+	17.2529i	1.23236	+	0.823437i	0.989203	−	0.146549i	$-0.0468167\pi$
$439$	25.8208	+	17.2529i	1.23236	+	0.823437i	0.243158	+	0.969987i	$0.421817\pi$
$440$	1.51396	+	0.414308i	0.0721751	+	0.0197514i
$441$	−7.56830	−	11.3268i	−0.360395	−	0.539369i
$442$	9.03901	+	1.71229i	0.429942	+	0.0814451i
$443$	4.03268	−	3.30953i	0.191598	−	0.157241i	−0.533704	−	0.845672i	$-0.679200\pi$
$443$	4.03268	−	3.30953i	0.191598	−	0.157241i	0.725302	+	0.688431i	$0.241700\pi$
$444$	−2.87946	+	2.00104i	−0.136653	+	0.0949651i
$445$	−4.07331	−	7.62064i	−0.193094	−	0.361253i
$446$	17.3531	−	21.5431i	0.821691	−	1.02009i
$447$			12.3176i			0.582601i
$448$	12.0431	−	34.2755i	0.568985	−	1.61936i
$449$			21.9796i			1.03728i	0.854992	+	0.518642i	$0.173562\pi$
$449$			21.9796i			1.03728i	−0.854992	+	0.518642i	$0.826438\pi$
$450$	5.04538	+	4.06408i	0.237842	+	0.191582i
$451$	−2.21748	−	4.14861i	−0.104417	−	0.195350i
$452$	−40.4267	−	7.27624i	−1.90151	−	0.342245i
$453$	5.80976	−	4.76795i	0.272966	−	0.224018i
$454$	5.20133	−	27.4574i	0.244110	−	1.28864i
$455$	−8.82292	−	13.2044i	−0.413625	−	0.619033i
$456$	4.65240	+	3.60940i	0.217869	+	0.169026i
$457$	17.4191	+	11.6390i	0.814829	+	0.544451i	0.891720	−	0.452588i	$-0.149499\pi$
$457$	17.4191	+	11.6390i	0.814829	+	0.544451i	−0.0768905	+	0.997040i	$0.524499\pi$
$458$	0.206421	+	22.5959i	0.00964541	+	1.05584i
$459$	0.349502	+	1.15215i	0.0163133	+	0.0537779i
$460$	6.02903	+	3.08232i	0.281105	+	0.143714i
$461$	18.3169	−	22.3192i	0.853101	−	1.03951i	−0.145639	−	0.989338i	$-0.546524\pi$
$461$	18.3169	−	22.3192i	0.853101	−	1.03951i	0.998741	−	0.0501693i	$-0.0159761\pi$
$462$	−0.489644	+	5.48463i	−0.0227803	+	0.255168i
$463$	8.53662	−	20.6092i	0.396730	−	0.957792i	−0.591706	−	0.806154i	$-0.701545\pi$
$463$	8.53662	−	20.6092i	0.396730	−	0.957792i	0.988436	−	0.151638i	$-0.0484547\pi$
$464$	−4.59352	−	33.8915i	−0.213249	−	1.57338i
$465$	−0.888943	−	2.14610i	−0.0412238	−	0.0995230i
$466$	−1.12906	+	0.353792i	−0.0523028	+	0.0163891i
$467$	36.5667	−	3.60151i	1.69211	−	0.166658i	0.794442	−	0.607340i	$-0.207763\pi$
$467$	36.5667	−	3.60151i	1.69211	−	0.166658i	0.897663	+	0.440682i	$0.145263\pi$
$468$	−9.43542	+	5.26718i	−0.436152	+	0.243476i
$469$	−16.7130	−	8.93328i	−0.771734	−	0.412500i
$470$	−0.0409827	+	0.101555i	−0.00189039	+	0.00468439i
$471$	−3.85035	−	19.3570i	−0.177415	−	0.891925i
$472$	0.728386	−	1.15756i	0.0335267	−	0.0532811i
$473$	−7.05482	−	1.40329i	−0.324381	−	0.0645234i
$474$	3.13904	+	15.0607i	0.144181	+	0.691760i
$475$	9.49117	+	0.934799i	0.435485	+	0.0428915i
$476$	3.99945	−	10.1776i	0.183315	−	0.466488i
$477$	−10.1265	−	3.07185i	−0.463662	−	0.140650i
$478$	−17.6264	+	9.62957i	−0.806214	+	0.440446i
$479$	−18.0484	+	18.0484i	−0.824651	+	0.824651i	−0.986771	−	0.162120i	$-0.948167\pi$
$479$	−18.0484	+	18.0484i	−0.824651	+	0.824651i	0.162120	+	0.986771i	$0.448167\pi$
$480$	3.62353	−	0.524870i	0.165391	−	0.0239569i
$481$	−6.69829	−	6.69829i	−0.305416	−	0.305416i
$482$	−18.2597	−	5.35736i	−0.831706	−	0.244021i
$483$	−6.89555	+	22.7316i	−0.313759	+	1.03432i
$484$	−14.2491	+	14.7795i	−0.647685	+	0.671795i
$485$	0.0327862	−	0.332883i	0.00148874	−	0.0151155i
$486$	−1.18300	−	0.774921i	−0.0536621	−	0.0351511i
$487$	6.56276	−	32.9932i	0.297387	−	1.49506i	−0.486236	−	0.873828i	$-0.661630\pi$
$487$	6.56276	−	32.9932i	0.297387	−	1.49506i	0.783623	−	0.621237i	$-0.213370\pi$
$488$	−13.5577	−	12.8343i	−0.613729	−	0.580979i
$489$	−5.16263	+	1.02691i	−0.233462	+	0.0464385i
$490$	−11.4760	+	4.87681i	−0.518433	+	0.220312i
$491$	15.8871	−	29.7227i	0.716974	−	1.34136i	−0.214200	−	0.976790i	$-0.568714\pi$
$491$	15.8871	−	29.7227i	0.716974	−	1.34136i	0.931174	−	0.364575i	$-0.118786\pi$
$492$	−8.60786	−	6.80496i	−0.388072	−	0.306791i
$493$	−1.00905	−	10.2450i	−0.0454452	−	0.461413i
$494$	−7.37024	+	14.0970i	−0.331603	+	0.634254i
$495$	−0.512703	+	0.212368i	−0.0230443	+	0.00954525i
$496$	13.4549	+	5.00555i	0.604143	+	0.224756i
$497$	40.6186	+	16.8248i	1.82199	+	0.754695i
$498$	−4.63985	+	3.87930i	−0.207917	+	0.173836i
$499$	−13.7450	−	11.2802i	−0.615311	−	0.504973i	0.274329	−	0.961636i	$-0.411544\pi$
$499$	−13.7450	−	11.2802i	−0.615311	−	0.504973i	−0.889640	+	0.456663i	$0.849044\pi$
$500$	9.44194	−	8.04192i	0.422256	−	0.359645i
$501$	−16.9454	+	5.14034i	−0.757067	+	0.229654i
$502$	−2.67067	−	2.62232i	−0.119198	−	0.117040i
$503$	−20.0934	+	30.0719i	−0.895920	+	1.34084i	0.0438527	+	0.999038i	$0.486037\pi$
$503$	−20.0934	+	30.0719i	−0.895920	+	1.34084i	−0.939772	+	0.341801i	$0.888963\pi$
$504$	4.06396	+	12.1846i	0.181023	+	0.542746i
$505$	−6.92495	+	4.62711i	−0.308156	+	0.205904i
$506$	5.24134	−	3.57184i	0.233006	−	0.158787i
$507$	−10.2725	−	12.5170i	−0.456216	−	0.555901i
$508$	2.20176	−	0.479933i	0.0976873	−	0.0212936i
$509$	3.11581	−	1.66543i	0.138106	−	0.0738190i	−0.400897	−	0.916123i	$-0.631301\pi$
$509$	3.11581	−	1.66543i	0.138106	−	0.0738190i	0.539002	+	0.842304i	$0.318801\pi$
$510$	1.09572	−	0.118035i	0.0485194	−	0.00522669i
$511$	3.17170			0.140308
$512$	−12.8698	+	18.6110i	−0.568769	+	0.822498i
$513$	−2.08184			−0.0919157
$514$	42.1202	−	4.53734i	1.85784	−	0.200133i
$515$	9.35224	−	4.99887i	0.412109	−	0.220277i
$516$	−16.3937	+	3.57345i	−0.721694	+	0.157312i
$517$	0.0650769	+	0.0792964i	0.00286208	+	0.00348745i
$518$	−9.30461	+	6.34084i	−0.408821	+	0.278601i
$519$	−12.2502	+	8.18531i	−0.537723	+	0.359295i
$520$	3.12954	+	9.38301i	0.137239	+	0.411472i
$521$	−11.0241	+	16.4987i	−0.482975	+	0.722823i	−0.990302	−	0.138931i	$-0.955633\pi$
$521$	−11.0241	+	16.4987i	−0.482975	+	0.722823i	0.507327	+	0.861753i	$0.330633\pi$
$522$	8.62810	+	8.47189i	0.377642	+	0.370805i
$523$	20.0375	−	6.07830i	0.876177	−	0.265785i	0.180009	−	0.983665i	$-0.442387\pi$
$523$	20.0375	−	6.07830i	0.876177	−	0.265785i	0.696167	+	0.717880i	$0.254887\pi$
$524$	13.5258	−	11.5202i	0.590878	−	0.503264i
$525$	16.0814	+	13.1977i	0.701851	+	0.575994i
$526$	10.9595	−	9.16303i	0.477856	−	0.399527i
$527$	3.99217	+	1.65361i	0.173902	+	0.0720325i
$528$	1.19582	−	3.21438i	0.0520416	−	0.139888i
$529$	4.02993	−	1.66925i	0.175214	−	0.0725761i
$530$	−4.48785	+	8.58389i	−0.194940	+	0.372860i
$531$	0.0473953	+	0.481213i	0.00205678	+	0.0208829i
$532$	14.8329	+	11.7262i	0.643089	+	0.508395i
$533$	13.9737	−	26.1429i	0.605267	−	1.13238i
$534$	−17.3765	+	7.38425i	−0.751953	+	0.319548i
$535$	6.21712	−	1.23666i	0.268789	−	0.0534655i
$536$	8.57165	+	8.11426i	0.370239	+	0.350482i
$537$	1.45210	−	7.30022i	0.0626629	−	0.315028i
$538$	−20.9761	−	13.7403i	−0.904346	−	0.592387i
$539$	−1.14484	+	11.6238i	−0.0493119	+	0.500672i
$540$	−0.898461	+	0.931906i	−0.0386636	+	0.0401028i
$541$	9.27001	−	30.5591i	0.398549	−	1.31384i	−0.496564	−	0.868000i	$-0.665405\pi$
$541$	9.27001	−	30.5591i	0.398549	−	1.31384i	0.895113	−	0.445839i	$-0.147095\pi$
$542$	32.7025	+	9.59486i	1.40469	+	0.412134i
$543$	12.2342	+	12.2342i	0.525019	+	0.525019i
$544$	−4.07585	+	5.45664i	−0.174751	+	0.233951i
$545$	−9.37142	+	9.37142i	−0.401428	+	0.401428i
$546$	−30.4515	+	16.6361i	−1.30320	+	0.711958i
$547$	27.9288	+	8.47210i	1.19415	+	0.362241i	0.823923	−	0.566701i	$-0.191781\pi$
$547$	27.9288	+	8.47210i	1.19415	+	0.362241i	0.370225	+	0.928942i	$0.379281\pi$
$548$	5.27863	−	13.4328i	0.225492	−	0.573819i
$549$	6.56869	+	0.646959i	0.280345	+	0.0276115i
$550$	−1.13341	−	5.43793i	−0.0483287	−	0.231874i
$551$	17.4585	+	3.47271i	0.743756	+	0.147942i
$552$	7.87956	−	12.5223i	0.335376	−	0.532985i
$553$	9.63764	+	48.4517i	0.409834	+	2.06037i
$554$	6.50029	−	16.1077i	0.276171	−	0.684351i
$555$	−1.00078	−	0.534927i	−0.0424807	−	0.0227064i
$556$	−29.3652	+	16.3927i	−1.24536	+	0.695206i
$557$	34.3208	−	3.38031i	1.45422	−	0.143228i	0.660187	−	0.751102i	$-0.270477\pi$
$557$	34.3208	−	3.38031i	1.45422	−	0.143228i	0.794034	+	0.607873i	$0.207977\pi$
$558$	−4.84334	+	1.51766i	−0.205035	+	0.0642478i
$559$	−17.3462	−	41.8774i	−0.733665	−	1.77122i
$560$	11.6505	−	1.57906i	0.492323	−	0.0667275i
$561$	0.395048	−	0.953729i	0.0166789	−	0.0402665i
$562$	1.75949	−	19.7085i	0.0742197	−	0.831353i
$563$	−12.1446	+	14.7982i	−0.511832	+	0.623669i	−0.963238	−	0.268649i	$-0.913423\pi$
$563$	−12.1446	+	14.7982i	−0.511832	+	0.623669i	0.451406	+	0.892319i	$0.350923\pi$
$564$	0.213055	+	0.108924i	0.00897124	+	0.00458651i
$565$	−3.85879	−	12.7207i	−0.162340	−	0.535164i
$566$	−0.0872212	−	9.54770i	−0.00366618	−	0.401320i
$567$	−3.77588	−	2.52296i	−0.158572	−	0.105954i
$568$	−21.6355	−	16.7851i	−0.907806	−	0.704289i
$569$	−20.4848	−	30.6577i	−0.858769	−	1.28524i	−0.957004	−	0.290075i	$-0.906320\pi$
$569$	−20.4848	−	30.6577i	−0.858769	−	1.28524i	0.0982353	−	0.995163i	$-0.468680\pi$
$570$	−0.354673	+	1.87229i	−0.0148556	+	0.0784216i
$571$	−17.2162	+	14.1290i	−0.720476	+	0.591279i	−0.921533	−	0.388300i	$-0.873062\pi$
$571$	−17.2162	+	14.1290i	−0.720476	+	0.591279i	0.201057	+	0.979580i	$0.435562\pi$
$572$	9.11859	+	1.64122i	0.381268	+	0.0686229i
$573$	−1.23102	−	2.30307i	−0.0514265	−	0.0962122i
$574$	−27.4401	−	22.1031i	−1.14533	−	0.922566i
$575$		−	23.9630i		−	0.999327i
$576$	−0.438263	−	7.98799i	−0.0182609	−	0.332833i
$577$			7.25988i			0.302233i	0.988516	+	0.151116i	$0.0482868\pi$
$577$			7.25988i			0.302233i	−0.988516	+	0.151116i	$0.951713\pi$
$578$	13.7954	−	17.1265i	0.573814	−	0.712367i
$579$	4.48705	+	8.39469i	0.186476	+	0.348871i
$580$	9.08905	−	6.31630i	0.377402	−	0.262270i
$581$	−15.0123	+	12.3203i	−0.622815	+	0.511131i
$582$	−0.718095	−	0.136031i	−0.0297660	−	0.00563866i
$583$	5.04080	+	7.54410i	0.208769	+	0.312445i
$584$	−1.90539	−	0.521428i	−0.0788457	−	0.0215768i
$585$	−2.90769	−	1.94286i	−0.120218	−	0.0803273i
$586$	−17.9256	+	0.163756i	−0.740499	+	0.00676468i
$587$	9.76925	+	32.2049i	0.403220	+	1.32924i	0.890098	+	0.455769i	$0.150636\pi$
$587$	9.76925	+	32.2049i	0.403220	+	1.32924i	−0.486878	+	0.873470i	$0.661864\pi$
$588$	8.38384	+	25.9231i	0.345744	+	1.06905i
$589$	−4.73997	+	5.77567i	−0.195307	+	0.237982i
$590$	0.440850	+	0.0393572i	0.0181495	+	0.00162031i
$591$	10.1737	−	24.5615i	0.418490	−	1.01032i
$592$	6.63215	−	2.27957i	0.272580	−	0.0936896i
$593$	2.13915	+	5.16436i	0.0878442	+	0.212075i	0.961696	−	0.274117i	$-0.0883856\pi$
$593$	2.13915	+	5.16436i	0.0878442	+	0.212075i	−0.873852	+	0.486192i	$0.838386\pi$
$594$	0.362570	+	1.15707i	0.0148764	+	0.0474753i
$595$	3.52181	−	0.346868i	0.144380	−	0.0142202i
$596$	6.71932	−	23.7011i	0.275234	−	0.970833i
$597$	−17.8071	−	9.51811i	−0.728797	−	0.389550i
$598$	37.0649	+	14.9576i	1.51569	+	0.611661i
$599$	−1.10101	−	5.53513i	−0.0449859	−	0.226159i	0.951752	−	0.306869i	$-0.0992813\pi$
$599$	−1.10101	−	5.53513i	−0.0449859	−	0.226159i	−0.996738	+	0.0807097i	$0.974281\pi$
$600$	−7.49117	−	10.5723i	−0.305826	−	0.431611i
$601$	44.1780	+	8.78756i	1.80206	+	0.358452i	0.978090	−	0.208182i	$-0.0667547\pi$
$601$	44.1780	+	8.78756i	1.80206	+	0.358452i	0.823969	+	0.566634i	$0.191755\pi$
$602$	−52.7449	+	10.9934i	−2.14972	+	0.448058i
$603$	−4.15295	−	0.409030i	−0.169121	−	0.0166570i
$604$	−13.7799	+	6.00506i	−0.560696	+	0.244343i
$605$	−6.35775	−	1.92860i	−0.258479	−	0.0784089i
$606$	8.72465	+	15.9700i	0.354415	+	0.648738i
$607$	−12.4161	+	12.4161i	−0.503953	+	0.503953i	−0.912664	−	0.408711i	$-0.865978\pi$
$607$	−12.4161	+	12.4161i	−0.503953	+	0.503953i	0.408711	+	0.912664i	$0.365978\pi$
$608$	−6.98305	−	9.48301i	−0.283200	−	0.384587i
$609$	27.4562	+	27.4562i	1.11258	+	1.11258i
$610$	1.70091	−	5.79728i	0.0688679	−	0.234725i
$611$	−0.187648	+	0.618592i	−0.00759142	+	0.0250256i
$612$	−0.0439918	−	2.40759i	−0.00177826	−	0.0973211i
$613$	−0.104808	+	1.06413i	−0.00423315	+	0.0429799i	−0.997069	−	0.0765043i	$-0.975624\pi$
$613$	−0.104808	+	1.06413i	−0.00423315	+	0.0429799i	0.992836	+	0.119484i	$0.0381241\pi$
$614$	−0.123493	+	0.188526i	−0.00498376	+	0.00760827i
$615$	0.692771	−	3.48279i	0.0279352	−	0.140440i
$616$	3.93406	−	10.2862i	0.158508	−	0.414444i
$617$	6.41479	−	1.27598i	0.258250	−	0.0513690i	−0.0642674	−	0.997933i	$-0.520471\pi$
$617$	6.41479	−	1.27598i	0.258250	−	0.0513690i	0.322517	+	0.946564i	$0.395471\pi$
$618$	−9.06214	−	21.3248i	−0.364533	−	0.857811i
$619$	6.59408	−	12.3366i	0.265038	−	0.495852i	−0.713837	−	0.700312i	$-0.753044\pi$
$619$	6.59408	−	12.3366i	0.265038	−	0.495852i	0.978875	+	0.204461i	$0.0655440\pi$
$620$	0.539763	+	4.61438i	0.0216774	+	0.185318i
$621$	0.512715	+	5.20568i	0.0205745	+	0.208897i
$622$	1.50045	+	0.784471i	0.0601626	+	0.0314544i
$623$	−56.0122	+	23.2010i	−2.24408	+	0.929529i
$624$	21.0286	−	4.98785i	0.841818	−	0.199674i
$625$	−17.4536	−	7.22954i	−0.698146	−	0.289181i
$626$	0.189403	+	0.226536i	0.00757005	+	0.00905420i
$627$	1.37981	+	1.13238i	0.0551042	+	0.0452228i
$628$	−3.15068	+	39.3466i	−0.125726	+	1.57010i
$629$	2.02001	−	0.612762i	0.0805429	−	0.0244324i
$630$	−2.91228	+	2.96598i	−0.116028	+	0.118168i
$631$	−9.24231	+	13.8321i	−0.367930	+	0.550647i	−0.968528	−	0.248905i	$-0.919929\pi$
$631$	−9.24231	+	13.8321i	−0.367930	+	0.550647i	0.600598	+	0.799551i	$0.294929\pi$
$632$	2.17567	−	30.6916i	0.0865434	−	1.22085i
$633$	9.69154	−	6.47568i	0.385204	−	0.257385i
$634$	−9.28532	−	13.6254i	−0.368767	−	0.541132i
$635$	0.462641	+	0.563730i	0.0183594	+	0.0223709i
$636$	17.8094	+	11.4349i	0.706190	+	0.453422i
$637$	−64.9120	+	34.6962i	−2.57191	+	1.37471i
$638$	−1.11043	−	10.3081i	−0.0439622	−	0.408101i
$639$	9.68140			0.382990
$640$	−7.25860	−	0.966725i	−0.286921	−	0.0382131i
$641$	−20.4930			−0.809426			−0.404713	−	0.914444i	$-0.632629\pi$
$641$	−20.4930			−0.809426			−0.404713	+	0.914444i	$0.632629\pi$
$642$	−1.48344	−	13.7708i	−0.0585467	−	0.543490i
$643$	−33.5517	+	17.9338i	−1.32315	+	0.707239i	−0.973294	−	0.229564i	$-0.926270\pi$
$643$	−33.5517	+	17.9338i	−1.32315	+	0.707239i	−0.349858	+	0.936803i	$0.613770\pi$
$644$	25.6685	−	39.9778i	1.01148	−	1.57535i
$645$	−3.44470	−	4.19738i	−0.135635	−	0.165272i
$646$	−1.99621	−	2.92926i	−0.0785399	−	0.115250i
$647$	15.4776	−	10.3418i	0.608486	−	0.406577i	−0.212799	−	0.977096i	$-0.568258\pi$
$647$	15.4776	−	10.3418i	0.608486	−	0.406577i	0.821284	+	0.570519i	$0.193258\pi$
$648$	1.85357	+	2.13641i	0.0728152	+	0.0839263i
$649$	0.230334	−	0.344718i	0.00904138	−	0.0135314i
$650$	24.5245	−	24.9767i	0.961930	−	0.979667i
$651$	−15.5964	+	4.73112i	−0.611272	+	0.185427i
$652$	10.4940	+	0.840305i	0.410975	+	0.0329089i
$653$	−30.6330	−	25.1399i	−1.19876	−	0.983800i	−0.999993	−	0.00375339i	$-0.998805\pi$
$653$	−30.6330	−	25.1399i	−1.19876	−	0.983800i	−0.198770	−	0.980046i	$-0.563695\pi$
$654$	18.5745	+	22.2162i	0.726322	+	0.868720i
$655$	5.31207	+	2.20033i	0.207560	+	0.0859740i
$656$	12.8508	+	17.7895i	0.501740	+	0.694565i
$657$	0.645263	−	0.267277i	0.0251741	−	0.0104275i
$658$	0.680922	+	0.356001i	0.0265451	+	0.0138784i
$659$	0.487480	+	4.94947i	0.0189895	+	0.192804i	0.999999	−	0.00115418i	$-0.000367387\pi$
$659$	0.487480	+	4.94947i	0.0189895	+	0.192804i	−0.981010	+	0.193958i	$0.937867\pi$
$660$	1.10237	−	0.128949i	0.0429099	−	0.00501934i
$661$	3.38955	−	6.34140i	0.131838	−	0.246652i	−0.807337	−	0.590091i	$-0.799092\pi$
$661$	3.38955	−	6.34140i	0.131838	−	0.246652i	0.939175	+	0.343439i	$0.111592\pi$
$662$	11.1457	+	26.2278i	0.433190	+	1.01937i
$663$	6.38022	−	1.26910i	0.247787	−	0.0492879i
$664$	11.0440	−	4.93335i	0.428592	−	0.191451i
$665$	−1.19377	+	6.00149i	−0.0462925	+	0.232728i
$666$	−1.35863	+	2.07409i	−0.0526457	+	0.0803695i
$667$	4.38389	−	44.5104i	0.169745	−	1.72345i
$668$	35.4100	−	0.647016i	1.37005	−	0.0250338i
$669$	5.67814	−	18.7183i	0.219530	−	0.723692i
$670$	−1.07537	+	3.66524i	−0.0415453	+	0.141600i
$671$	−4.00170	−	4.00170i	−0.154484	−	0.154484i
$672$	−1.17294	−	25.6622i	−0.0452472	−	0.989939i
$673$	−14.0244	+	14.0244i	−0.540600	+	0.540600i	−0.923705	−	0.383105i	$-0.874855\pi$
$673$	−14.0244	+	14.0244i	−0.540600	+	0.540600i	0.383105	+	0.923705i	$0.374855\pi$
$674$	1.97867	+	3.62186i	0.0762156	+	0.139509i
$675$	4.38382	+	1.32982i	0.168733	+	0.0511847i
$676$	12.9378	+	29.6886i	0.497608	+	1.14187i
$677$	−12.3847	−	1.21979i	−0.475984	−	0.0468803i	−0.142819	−	0.989749i	$-0.545617\pi$
$677$	−12.3847	−	1.21979i	−0.475984	−	0.0468803i	−0.333165	+	0.942868i	$0.608117\pi$
$678$	−28.4343	+	5.92645i	−1.09201	+	0.227604i
$679$	−2.30180	−	0.457857i	−0.0883351	−	0.0175709i
$680$	−2.17274	−	0.370605i	−0.0833209	−	0.0142121i
$681$	−3.85510	−	19.3809i	−0.147728	−	0.742677i
$682$	4.03558	+	1.62856i	0.154530	+	0.0623609i
$683$	−4.03299	−	2.15568i	−0.154318	−	0.0824847i	0.392430	−	0.919782i	$-0.371634\pi$
$683$	−4.03299	−	2.15568i	−0.154318	−	0.0824847i	−0.546748	+	0.837297i	$0.684134\pi$
$684$	4.00582	+	1.13566i	0.153166	+	0.0434231i
$685$	4.64822	−	0.457810i	0.177600	−	0.0174920i
$686$	12.7176	+	40.5859i	0.485560	+	1.54958i
$687$	6.11467	+	14.7621i	0.233289	+	0.563210i
$688$	33.4936	+	2.06698i	1.27693	+	0.0788030i
$689$	−21.8802	+	52.8236i	−0.833571	+	2.01242i
$690$	4.76904	+	0.425759i	0.181554	+	0.0162084i
$691$	−14.5439	+	17.7217i	−0.553274	+	0.674167i	−0.972281	−	0.233816i	$-0.924879\pi$
$691$	−14.5439	+	17.7217i	−0.553274	+	0.674167i	0.419006	+	0.907983i	$0.362379\pi$
$692$	28.0366	−	9.06734i	1.06579	−	0.344689i
$693$	1.13026	+	3.72598i	0.0429352	+	0.141538i
$694$	6.58984	−	0.0602002i	0.250147	−	0.00228517i
$695$	−9.04941	−	6.04663i	−0.343264	−	0.229362i
$696$	−11.9804	−	21.0080i	−0.454117	−	0.796307i
$697$	3.66988	+	5.49237i	0.139007	+	0.208038i
$698$	−22.4150	−	4.24614i	−0.848421	−	0.160719i
$699$	−0.646735	+	0.530762i	−0.0244618	+	0.0200753i
$700$	−23.7439	−	34.1671i	−0.897436	−	1.29140i
$701$	3.23923	+	6.06016i	0.122344	+	0.228889i	0.935636	−	0.352966i	$-0.114827\pi$
$701$	3.23923	+	6.06016i	0.122344	+	0.228889i	−0.813292	+	0.581855i	$0.802327\pi$
$702$	−4.79325	+	5.95062i	−0.180910	+	0.224592i
$703$			3.64998i			0.137662i
$704$	−4.05443	+	5.53267i	−0.152807	+	0.208520i
$705$			0.0774371i			0.00291645i
$706$	−13.0267	−	10.4931i	−0.490266	−	0.394912i
$707$	27.5463	+	51.5354i	1.03598	+	1.93819i
$708$	0.171309	−	0.951789i	0.00643818	−	0.0357704i
$709$	20.7723	−	17.0474i	0.780119	−	0.640227i	−0.157647	−	0.987496i	$-0.550391\pi$
$709$	20.7723	−	17.0474i	0.780119	−	0.640227i	0.937766	+	0.347269i	$0.112891\pi$
$710$	1.64937	−	8.70690i	0.0618998	−	0.326764i
$711$	6.04369	+	9.04502i	0.226656	+	0.339215i
$712$	37.4634	−	4.72954i	1.40400	−	0.177247i
$713$	15.6095	+	10.4299i	0.584580	+	0.390604i
$714$	−0.0706344	−	7.73203i	−0.00264343	−	0.289364i
$715$	0.870384	+	2.86927i	0.0325505	+	0.107305i
$716$	−6.77641	+	13.2547i	−0.253246	+	0.495352i
$717$	−9.00995	+	10.9787i	−0.336483	+	0.410005i
$718$	−1.86114	+	20.8471i	−0.0694571	+	0.778006i
$719$	10.5552	−	25.4825i	0.393642	−	0.950337i	−0.595497	−	0.803357i	$-0.703045\pi$
$719$	10.5552	−	25.4825i	0.393642	−	0.950337i	0.989140	−	0.146979i	$-0.0469551\pi$
$720$	2.23715	−	1.30303i	0.0833737	−	0.0485609i
$721$	−28.4729	−	68.7396i	−1.06038	−	2.55999i
$722$	−19.7918	+	6.20178i	−0.736576	+	0.230806i
$723$	−13.3910	+	1.31890i	−0.498017	+	0.0490504i
$724$	−16.8668	−	30.2144i	−0.626848	−	1.12291i
$725$	−34.5447	−	18.4645i	−1.28296	−	0.685756i
$726$	−5.43256	+	13.4619i	−0.201621	+	0.499617i
$727$	0.625319	+	3.14369i	0.0231918	+	0.116593i	0.990647	−	0.136449i	$-0.0435689\pi$
$727$	0.625319	+	3.14369i	0.0231918	+	0.116593i	−0.967455	+	0.253042i	$0.918569\pi$
$728$	67.6689	−	15.3991i	2.50798	−	0.570728i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	−0.130443	−	0.625847i	−0.00482791	−	0.0231636i
$731$	10.0521	+	0.990045i	0.371790	+	0.0366181i
$732$	−12.2863	−	4.82813i	−0.454116	−	0.178453i
$733$	−10.9504	−	3.32177i	−0.404463	−	0.122692i	0.0814971	−	0.996674i	$-0.474030\pi$
$733$	−10.9504	−	3.32177i	−0.404463	−	0.122692i	−0.485960	+	0.873981i	$0.661530\pi$
$734$	45.3914	−	24.7980i	1.67543	−	0.915310i
$735$	−6.23462	+	6.23462i	−0.229967	+	0.229967i
$736$	−21.9926	+	19.7967i	−0.810658	+	0.729715i
$737$	2.53001	+	2.53001i	0.0931942	+	0.0931942i
$738$	−7.44512	−	2.18439i	−0.274059	−	0.0804083i
$739$	11.3566	−	37.4375i	0.417758	−	1.37716i	−0.455644	−	0.890162i	$-0.650591\pi$
$739$	11.3566	−	37.4375i	0.417758	−	1.37716i	0.873402	−	0.487000i	$-0.161909\pi$
$740$	1.63386	+	1.57522i	0.0600618	+	0.0579063i
$741$	−1.10252	+	11.1941i	−0.0405021	+	0.411225i
$742$	56.8504	+	37.2396i	2.08704	+	1.36711i
$743$	−1.55821	+	7.83366i	−0.0571652	+	0.287389i	−0.998784	−	0.0492907i	$-0.984304\pi$
$743$	−1.55821	+	7.83366i	−0.0571652	+	0.287389i	0.941619	+	0.336680i	$0.109304\pi$
$744$	10.1473	−	0.278158i	0.372018	−	0.0101978i
$745$	7.81924	−	1.55534i	0.286475	−	0.0569834i
$746$	−12.3816	+	5.26166i	−0.453324	+	0.192643i
$747$	−2.01594	+	3.77155i	−0.0737593	+	0.137994i
$748$	−1.28040	+	1.61963i	−0.0468162	+	0.0592197i
$749$	−4.35936	−	44.2613i	−0.159288	−	1.61727i
$750$	4.06328	−	7.77181i	0.148370	−	0.283786i
$751$	26.8692	−	11.1296i	0.980470	−	0.406124i	0.165870	−	0.986148i	$-0.446957\pi$
$751$	26.8692	−	11.1296i	0.980470	−	0.406124i	0.814600	+	0.580024i	$0.196957\pi$
$752$	−0.350535	−	0.325810i	−0.0127827	−	0.0118811i
$753$	−2.44514	−	1.01281i	−0.0891060	−	0.0369089i
$754$	50.1227	−	41.9067i	1.82536	−	1.52615i
$755$	−3.76031	−	3.08601i	−0.136852	−	0.112311i
$756$	5.88913	+	6.91437i	0.214185	+	0.251473i
$757$	32.6965	−	9.91837i	1.18837	−	0.360489i	0.366642	−	0.930362i	$-0.380508\pi$
$757$	32.6965	−	9.91837i	1.18837	−	0.360489i	0.821733	+	0.569873i	$0.193008\pi$
$758$	−19.7858	−	19.4276i	−0.718652	−	0.705641i
$759$	2.49171	−	3.72910i	0.0904433	−	0.135358i
$760$	1.70380	−	3.40912i	0.0618033	−	0.123662i
$761$	−20.5636	+	13.7402i	−0.745430	+	0.498080i	−0.869341	−	0.494213i	$-0.835456\pi$
$761$	−20.5636	+	13.7402i	−0.745430	+	0.498080i	0.123911	+	0.992293i	$0.460456\pi$
$762$	1.31675	−	0.897332i	0.0477009	−	0.0325069i
$763$	58.9909	+	71.8806i	2.13561	+	2.60225i
$764$	1.11234	+	5.10303i	0.0402431	+	0.184621i
$765$	0.687260	−	0.367348i	0.0248479	−	0.0132815i
$766$	8.97632	−	0.966962i	0.324328	−	0.0349378i
$767$	2.61258			0.0943349
$768$	−3.51422	+	15.6093i	−0.126808	+	0.563252i

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)

\(f(q)\)	\(=\)	\(q+(-1.40608 + 0.151468i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(1.95411 - 0.425952i) q^{4} +(0.410605 + 0.500324i) q^{5} +(1.16865 - 0.796404i) q^{6} +(3.77588 - 2.52296i) q^{7} +(-2.68312 + 0.894907i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(-1.40608 + 0.151468i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(1.95411 - 0.425952i) q^{4} +(0.410605 + 0.500324i) q^{5} +(1.16865 - 0.796404i) q^{6} +(3.77588 - 2.52296i) q^{7} +(-2.68312 + 0.894907i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-0.653126 - 0.641301i) q^{10} +(-0.820483 + 0.248891i) q^{11} +(-1.52258 + 1.29682i) q^{12} +(-4.17659 - 3.42764i) q^{13} +(-4.92703 + 4.11940i) q^{14} +(-0.597972 - 0.247688i) q^{15} +(3.63713 - 1.66472i) q^{16} +(1.11235 - 0.460750i) q^{17} +(-0.655235 + 1.25326i) q^{18} +(0.204056 + 2.07182i) q^{19} +(1.01548 + 0.802792i) q^{20} +(-2.14071 + 4.00499i) q^{21} +(1.11596 - 0.474237i) q^{22} +(5.13036 - 1.02049i) q^{23} +(1.94445 - 2.05405i) q^{24} +(0.893724 - 4.49306i) q^{25} +(6.39179 + 4.18691i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(6.30384 - 6.53849i) q^{28} +(2.48204 - 8.18218i) q^{29} +(0.878313 + 0.257696i) q^{30} +(2.53778 + 2.53778i) q^{31} +(-4.86194 + 2.89163i) q^{32} +(0.606275 - 0.606275i) q^{33} +(-1.49426 + 0.816335i) q^{34} +(2.81269 + 0.853220i) q^{35} +(0.731482 - 1.86143i) q^{36} +(1.74480 + 0.171848i) q^{37} +(-0.600734 - 2.88223i) q^{38} +(5.29920 + 1.05408i) q^{39} +(-1.54945 - 0.974976i) q^{40} +(1.07035 + 5.38099i) q^{41} +(2.40338 - 5.95558i) q^{42} +(7.39874 + 3.95471i) q^{43} +(-1.49730 + 0.835847i) q^{44} +(0.644124 - 0.0634407i) q^{45} +(-7.05911 + 2.21198i) q^{46} +(-0.0457850 - 0.110535i) q^{47} +(-2.42292 + 3.18268i) q^{48} +(5.21313 - 12.5856i) q^{49} +(-0.576093 + 6.45296i) q^{50} +(-0.763807 + 0.930702i) q^{51} +(-9.62154 - 4.91897i) q^{52} +(-3.07185 - 10.1265i) q^{53} +(-0.0129187 - 1.41415i) q^{54} +(-0.461420 - 0.308311i) q^{55} +(-7.87332 + 10.1485i) q^{56} +(-1.15661 - 1.73099i) q^{57} +(-2.25060 + 11.8807i) q^{58} +(-0.373783 + 0.306755i) q^{59} +(-1.27401 - 0.229304i) q^{60} +(3.11144 + 5.82110i) q^{61} +(-3.95271 - 3.18392i) q^{62} -4.54121i q^{63} +(6.39828 - 4.80229i) q^{64} -3.49705i q^{65} +(-0.760639 + 0.944301i) q^{66} +(-1.96716 - 3.68030i) q^{67} +(1.97740 - 1.37416i) q^{68} +(-4.04351 + 3.31843i) q^{69} +(-4.08410 - 0.773663i) q^{70} +(5.37870 + 8.04979i) q^{71} +(-0.746574 + 2.72812i) q^{72} +(0.580721 + 0.388026i) q^{73} +(-2.47936 + 0.0226497i) q^{74} +(1.32982 + 4.38382i) q^{75} +(1.28124 + 3.96166i) q^{76} +(-2.47010 + 3.00983i) q^{77} +(-7.61075 - 0.679456i) q^{78} +(-4.16297 + 10.0503i) q^{79} +(2.32632 + 1.13620i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-2.32004 - 7.40397i) q^{82} +(-4.25592 + 0.419172i) q^{83} +(-2.47726 + 8.73805i) q^{84} +(0.687260 + 0.367348i) q^{85} +(-11.0022 - 4.43996i) q^{86} +(1.66809 + 8.38606i) q^{87} +(1.97872 - 1.40206i) q^{88} +(-13.0939 - 2.60454i) q^{89} +(-0.896080 + 0.186767i) q^{90} +(-24.4181 - 2.40497i) q^{91} +(9.59063 - 4.17944i) q^{92} +(-3.43442 - 1.04182i) q^{93} +(0.0811198 + 0.148486i) q^{94} +(-0.952794 + 0.952794i) q^{95} +(2.92474 - 4.84209i) q^{96} +(-0.365433 - 0.365433i) q^{97} +(-5.42376 + 18.4860i) q^{98} +(-0.248891 + 0.820483i) 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

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Database

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