LMFDB - Embedded newform 384.2.v.a.349.32

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			349.32
Character	$\chi$	$=$	384.349
Dual form			384.2.v.a.373.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40588 - 0.153334i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(1.95298 - 0.431136i) q^{4} +(-0.589270 - 1.10245i) q^{5} +(-1.41414 + 0.0147953i) q^{6} +(-0.582982 - 2.93085i) q^{7} +(2.67954 - 0.905582i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(1.40588 - 0.153334i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(1.95298 - 0.431136i) q^{4} +(-0.589270 - 1.10245i) q^{5} +(-1.41414 + 0.0147953i) q^{6} +(-0.582982 - 2.93085i) q^{7} +(2.67954 - 0.905582i) q^{8} +(0.980785 + 0.195090i) q^{9} +(-0.997484 - 1.45955i) q^{10} +(0.231083 + 0.189645i) q^{11} +(-1.98583 + 0.237635i) q^{12} +(-0.103529 - 0.0553373i) q^{13} +(-1.26900 - 4.03102i) q^{14} +(0.478374 + 1.15490i) q^{15} +(3.62824 - 1.68400i) q^{16} +(1.89316 - 4.57049i) q^{17} +(1.40878 + 0.123886i) q^{18} +(1.01558 - 0.308074i) q^{19} +(-1.62614 - 1.89900i) q^{20} +(0.292901 + 2.97388i) q^{21} +(0.353954 + 0.231185i) q^{22} +(-7.01912 + 4.69003i) q^{23} +(-2.75540 + 0.638580i) q^{24} +(1.90970 - 2.85807i) q^{25} +(-0.154034 - 0.0619230i) q^{26} +(-0.956940 - 0.290285i) q^{27} +(-2.40215 - 5.47254i) q^{28} +(6.73009 + 8.20064i) q^{29} +(0.849620 + 1.55029i) q^{30} +(2.45339 - 2.45339i) q^{31} +(4.84265 - 2.92383i) q^{32} +(-0.211382 - 0.211382i) q^{33} +(1.96074 - 6.71583i) q^{34} +(-2.88757 + 2.36977i) q^{35} +(1.99956 - 0.0418452i) q^{36} +(-2.39095 + 7.88189i) q^{37} +(1.38055 - 0.588837i) q^{38} +(0.0976063 + 0.0652185i) q^{39} +(-2.57733 - 2.42042i) q^{40} +(3.86309 + 5.78153i) q^{41} +(0.867779 + 4.13599i) q^{42} +(-0.901624 + 0.0888022i) q^{43} +(0.533063 + 0.270744i) q^{44} +(-0.362871 - 1.19622i) q^{45} +(-9.14888 + 7.66987i) q^{46} +(-5.26673 - 2.18155i) q^{47} +(-3.77583 + 1.32026i) q^{48} +(-1.78285 + 0.738480i) q^{49} +(2.24657 - 4.31091i) q^{50} +(-2.33203 + 4.36292i) q^{51} +(-0.226047 - 0.0634375i) q^{52} +(-5.74843 + 7.00448i) q^{53} +(-1.38985 - 0.261373i) q^{54} +(0.0729032 - 0.366509i) q^{55} +(-4.21625 - 7.32538i) q^{56} +(-1.04089 + 0.207046i) q^{57} +(10.7191 + 10.4971i) q^{58} +(-2.09975 + 1.12234i) q^{59} +(1.43217 + 2.04924i) q^{60} +(0.688277 - 6.98819i) q^{61} +(3.07297 - 3.82534i) q^{62} -2.98827i q^{63} +(6.35984 - 4.85308i) q^{64} +0.146744i q^{65} +(-0.329589 - 0.264765i) q^{66} +(-0.178064 + 1.80791i) q^{67} +(1.72679 - 9.74228i) q^{68} +(7.44503 - 3.97945i) q^{69} +(-3.69620 + 3.77436i) q^{70} +(-4.83452 + 0.961647i) q^{71} +(2.80472 - 0.365429i) q^{72} +(-1.07346 + 5.39664i) q^{73} +(-2.15282 + 11.4476i) q^{74} +(-2.18064 + 2.65712i) q^{75} +(1.85059 - 1.03952i) q^{76} +(0.421104 - 0.787830i) q^{77} +(0.147223 + 0.0767228i) q^{78} +(-5.60019 + 2.31968i) q^{79} +(-3.99454 - 3.00762i) q^{80} +(0.923880 + 0.382683i) q^{81} +(6.31754 + 7.53577i) q^{82} +(4.35626 + 14.3607i) q^{83} +(1.85418 + 5.68164i) q^{84} +(-6.15431 + 0.606147i) q^{85} +(-1.25396 + 0.263094i) q^{86} +(-5.89388 - 8.82082i) q^{87} +(0.790935 + 0.298897i) q^{88} +(4.55847 + 3.04587i) q^{89} +(-0.693573 - 1.62610i) q^{90} +(-0.101830 + 0.335688i) q^{91} +(-11.6861 + 12.1857i) q^{92} +(-2.68205 + 2.20110i) q^{93} +(-7.73887 - 2.25942i) q^{94} +(-0.938088 - 0.938088i) q^{95} +(-5.10591 + 2.43509i) q^{96} +(11.4254 - 11.4254i) q^{97} +(-2.39323 + 1.31158i) q^{98} +(0.189645 + 0.231083i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

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 $

$2$	1.40588	−	0.153334i	0.994105	−	0.108423i
$2$	1.40588	−	0.153334i	0.994105	−	0.108423i
$3$	−0.995185	−	0.0980171i	−0.574570	−	0.0565902i
$3$	−0.995185	−	0.0980171i	−0.574570	−	0.0565902i
$4$	1.95298	−	0.431136i	0.976489	−	0.215568i
$5$	−0.589270	−	1.10245i	−0.263530	−	0.493029i	0.715003	−	0.699121i	$-0.246425\pi$
$5$	−0.589270	−	1.10245i	−0.263530	−	0.493029i	−0.978533	+	0.206092i	$0.933925\pi$
$6$	−1.41414	+	0.0147953i	−0.577319	+	0.00604016i
$7$	−0.582982	−	2.93085i	−0.220346	−	1.10776i	−0.919592	−	0.392875i	$-0.871481\pi$
$7$	−0.582982	−	2.93085i	−0.220346	−	1.10776i	0.699245	−	0.714882i	$-0.253519\pi$
$8$	2.67954	−	0.905582i	0.947360	−	0.320171i
$9$	0.980785	+	0.195090i	0.326928	+	0.0650301i
$10$	−0.997484	−	1.45955i	−0.315432	−	0.461550i
$11$	0.231083	+	0.189645i	0.0696742	+	0.0571802i	0.668586	−	0.743635i	$-0.266900\pi$
$11$	0.231083	+	0.189645i	0.0696742	+	0.0571802i	−0.598912	+	0.800815i	$0.704400\pi$
$12$	−1.98583	+	0.237635i	−0.573260	+	0.0685993i
$13$	−0.103529	−	0.0553373i	−0.0287137	−	0.0153478i	0.456977	−	0.889478i	$-0.348932\pi$
$13$	−0.103529	−	0.0553373i	−0.0287137	−	0.0153478i	−0.485691	+	0.874130i	$0.661432\pi$
$14$	−1.26900	−	4.03102i	−0.339154	−	1.07734i
$15$	0.478374	+	1.15490i	0.123516	+	0.298193i
$16$	3.62824	−	1.68400i	0.907061	−	0.421000i
$17$	1.89316	−	4.57049i	0.459159	−	1.10851i	−0.509580	−	0.860423i	$-0.670199\pi$
$17$	1.89316	−	4.57049i	0.459159	−	1.10851i	0.968739	−	0.248084i	$-0.0798008\pi$
$18$	1.40878	+	0.123886i	0.332052	+	0.0292001i
$19$	1.01558	−	0.308074i	0.232991	−	0.0706770i	−0.171630	−	0.985161i	$-0.554903\pi$
$19$	1.01558	−	0.308074i	0.232991	−	0.0706770i	0.404621	+	0.914484i	$0.367403\pi$
$20$	−1.62614	−	1.89900i	−0.363615	−	0.424629i
$21$	0.292901	+	2.97388i	0.0639163	+	0.648953i
$22$	0.353954	+	0.231185i	0.0754631	+	0.0492888i
$23$	−7.01912	+	4.69003i	−1.46359	+	0.977938i	−0.468038	+	0.883708i	$0.655039\pi$
$23$	−7.01912	+	4.69003i	−1.46359	+	0.977938i	−0.995550	+	0.0942301i	$0.969961\pi$
$24$	−2.75540	+	0.638580i	−0.562443	+	0.130350i
$25$	1.90970	−	2.85807i	0.381940	−	0.571614i
$26$	−0.154034	−	0.0619230i	−0.0302085	−	0.0121441i
$27$	−0.956940	−	0.290285i	−0.184163	−	0.0558653i
$28$	−2.40215	−	5.47254i	−0.453963	−	1.03421i
$29$	6.73009	+	8.20064i	1.24975	+	1.52282i	0.758287	+	0.651921i	$0.226037\pi$
$29$	6.73009	+	8.20064i	1.24975	+	1.52282i	0.491460	+	0.870900i	$0.336463\pi$
$30$	0.849620	+	1.55029i	0.155119	+	0.283043i
$31$	2.45339	−	2.45339i	0.440641	−	0.440641i	−0.451586	−	0.892227i	$-0.649142\pi$
$31$	2.45339	−	2.45339i	0.440641	−	0.440641i	0.892227	+	0.451586i	$0.149142\pi$
$32$	4.84265	−	2.92383i	0.856067	−	0.516864i
$33$	−0.211382	−	0.211382i	−0.0367969	−	0.0367969i
$34$	1.96074	−	6.71583i	0.336264	−	1.15176i
$35$	−2.88757	+	2.36977i	−0.488089	+	0.400564i
$36$	1.99956	−	0.0418452i	0.333260	−	0.00697420i
$37$	−2.39095	+	7.88189i	−0.393069	+	1.29578i	0.507721	+	0.861521i	$0.330488\pi$
$37$	−2.39095	+	7.88189i	−0.393069	+	1.29578i	−0.900791	+	0.434254i	$0.857012\pi$
$38$	1.38055	−	0.588837i	0.223954	−	0.0955220i
$39$	0.0976063	+	0.0652185i	0.0156295	+	0.0104433i
$40$	−2.57733	−	2.42042i	−0.407511	−	0.382701i
$41$	3.86309	+	5.78153i	0.603314	+	0.902923i	0.999886	−	0.0150803i	$-0.00480040\pi$
$41$	3.86309	+	5.78153i	0.603314	+	0.902923i	−0.396572	+	0.918003i	$0.629800\pi$
$42$	0.867779	+	4.13599i	0.133901	+	0.638198i
$43$	−0.901624	+	0.0888022i	−0.137496	+	0.0135422i	−0.166531	−	0.986036i	$-0.553257\pi$
$43$	−0.901624	+	0.0888022i	−0.137496	+	0.0135422i	0.0290348	+	0.999578i	$0.490757\pi$
$44$	0.533063	+	0.270744i	0.0803623	+	0.0408162i
$45$	−0.362871	−	1.19622i	−0.0540936	−	0.178323i
$46$	−9.14888	+	7.66987i	−1.34893	+	1.13086i
$47$	−5.26673	−	2.18155i	−0.768231	−	0.318212i	−0.0360755	−	0.999349i	$-0.511486\pi$
$47$	−5.26673	−	2.18155i	−0.768231	−	0.318212i	−0.732156	+	0.681137i	$0.761486\pi$
$48$	−3.77583	+	1.32026i	−0.544995	+	0.190563i
$49$	−1.78285	+	0.738480i	−0.254693	+	0.105497i
$50$	2.24657	−	4.31091i	0.317712	−	0.609655i
$51$	−2.33203	+	4.36292i	−0.326550	+	0.610931i
$52$	−0.226047	−	0.0634375i	−0.0313471	−	0.00879720i
$53$	−5.74843	+	7.00448i	−0.789608	+	0.962140i	−0.999880	−	0.0155030i	$-0.995065\pi$
$53$	−5.74843	+	7.00448i	−0.789608	+	0.962140i	0.210272	+	0.977643i	$0.432565\pi$
$54$	−1.38985	−	0.261373i	−0.189135	−	0.0355684i
$55$	0.0729032	−	0.366509i	0.00983027	−	0.0494201i
$56$	−4.21625	−	7.32538i	−0.563419	−	0.978895i
$57$	−1.04089	+	0.207046i	−0.137869	+	0.0274239i
$58$	10.7191	+	10.4971i	1.40749	+	1.37834i
$59$	−2.09975	+	1.12234i	−0.273364	+	0.146116i	−0.602383	−	0.798207i	$-0.705782\pi$
$59$	−2.09975	+	1.12234i	−0.273364	+	0.146116i	0.329019	+	0.944323i	$0.393282\pi$
$60$	1.43217	+	2.04924i	0.184893	+	0.264556i
$61$	0.688277	−	6.98819i	0.0881248	−	0.894746i	−0.844898	−	0.534928i	$-0.820339\pi$
$61$	0.688277	−	6.98819i	0.0881248	−	0.894746i	0.933022	−	0.359818i	$-0.117161\pi$
$62$	3.07297	−	3.82534i	0.390268	−	0.485819i
$63$		−	2.98827i		−	0.376486i
$64$	6.35984	−	4.85308i	0.794980	−	0.606635i
$65$			0.146744i			0.0182013i
$66$	−0.329589	−	0.264765i	−0.0405696	−	0.0325903i
$67$	−0.178064	+	1.80791i	−0.0217539	+	0.220871i	0.978161	+	0.207847i	$0.0666457\pi$
$67$	−0.178064	+	1.80791i	−0.0217539	+	0.220871i	−0.999915	+	0.0130239i	$0.995854\pi$
$68$	1.72679	−	9.74228i	0.209404	−	1.18142i
$69$	7.44503	−	3.97945i	0.896276	−	0.479069i
$70$	−3.69620	+	3.77436i	−0.441781	+	0.451123i
$71$	−4.83452	+	0.961647i	−0.573752	+	0.114126i	−0.473435	−	0.880829i	$-0.656986\pi$
$71$	−4.83452	+	0.961647i	−0.573752	+	0.114126i	−0.100318	+	0.994955i	$0.531986\pi$
$72$	2.80472	−	0.365429i	0.330540	−	0.0430663i
$73$	−1.07346	+	5.39664i	−0.125639	+	0.631629i	0.865728	+	0.500514i	$0.166856\pi$
$73$	−1.07346	+	5.39664i	−0.125639	+	0.631629i	−0.991367	+	0.131115i	$0.958144\pi$
$74$	−2.15282	+	11.4476i	−0.250260	+	1.33075i
$75$	−2.18064	+	2.65712i	−0.251799	+	0.306818i
$76$	1.85059	−	1.03952i	0.212277	−	0.119241i
$77$	0.421104	−	0.787830i	0.0479892	−	0.0897815i
$78$	0.147223	+	0.0767228i	0.0166697	+	0.00868714i
$79$	−5.60019	+	2.31968i	−0.630071	+	0.260984i	−0.674783	−	0.738016i	$-0.735763\pi$
$79$	−5.60019	+	2.31968i	−0.630071	+	0.260984i	0.0447124	+	0.999000i	$0.485763\pi$
$80$	−3.99454	−	3.00762i	−0.446603	−	0.336262i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	6.31754	+	7.53577i	0.697655	+	0.832187i
$83$	4.35626	+	14.3607i	0.478162	+	1.57629i	0.781818	+	0.623507i	$0.214293\pi$
$83$	4.35626	+	14.3607i	0.478162	+	1.57629i	−0.303656	+	0.952782i	$0.598207\pi$
$84$	1.85418	+	5.68164i	0.202307	+	0.619917i
$85$	−6.15431	+	0.606147i	−0.667529	+	0.0657458i
$86$	−1.25396	+	0.263094i	−0.135218	+	0.0283702i
$87$	−5.89388	−	8.82082i	−0.631891	−	0.945691i
$88$	0.790935	+	0.298897i	0.0843140	+	0.0318625i
$89$	4.55847	+	3.04587i	0.483197	+	0.322862i	0.773198	−	0.634165i	$-0.218656\pi$
$89$	4.55847	+	3.04587i	0.483197	+	0.322862i	−0.290002	+	0.957026i	$0.593656\pi$
$90$	−0.693573	−	1.62610i	−0.0731090	−	0.171406i
$91$	−0.101830	+	0.335688i	−0.0106747	+	0.0351897i
$92$	−11.6861	+	12.1857i	−1.21837	+	1.27045i
$93$	−2.68205	+	2.20110i	−0.278115	+	0.228243i
$94$	−7.73887	−	2.25942i	−0.798204	−	0.233042i
$95$	−0.938088	−	0.938088i	−0.0962458	−	0.0962458i
$96$	−5.10591	+	2.43509i	−0.521120	+	0.248530i
$97$	11.4254	−	11.4254i	1.16007	−	1.16007i	0.175614	−	0.984459i	$-0.443809\pi$
$97$	11.4254	−	11.4254i	1.16007	−	1.16007i	0.984459	−	0.175614i	$-0.0561909\pi$
$98$	−2.39323	+	1.31158i	−0.241753	+	0.132490i
$99$	0.189645	+	0.231083i	0.0190601	+	0.0232247i
$100$	2.49739	−	6.40509i	0.249739	−	0.640509i
$101$	7.01181	+	2.12701i	0.697701	+	0.211645i	0.619159	−	0.785265i	$-0.287474\pi$
$101$	7.01181	+	2.12701i	0.697701	+	0.211645i	0.0785419	+	0.996911i	$0.474974\pi$
$102$	−2.60956	+	6.49131i	−0.258385	+	0.642735i
$103$	1.41972	−	2.12477i	0.139890	−	0.209359i	−0.754909	−	0.655829i	$-0.772319\pi$
$103$	1.41972	−	2.12477i	0.139890	−	0.209359i	0.894799	+	0.446470i	$0.147319\pi$
$104$	−0.327522	−	0.0545246i	−0.0321162	−	0.00534658i
$105$	3.10595	−	2.07533i	0.303109	−	0.202531i
$106$	−7.00756	+	10.7289i	−0.680635	+	1.04208i
$107$	0.0156273	+	0.158666i	0.00151074	+	0.0153388i	0.995911	−	0.0903448i	$-0.0287969\pi$
$107$	0.0156273	+	0.158666i	0.00151074	+	0.0153388i	−0.994400	+	0.105684i	$0.966297\pi$
$108$	−1.99404	−	0.154348i	−0.191876	−	0.0148521i
$109$	5.92641	−	1.79776i	0.567647	−	0.172194i	0.00660082	−	0.999978i	$-0.497899\pi$
$109$	5.92641	−	1.79776i	0.567647	−	0.172194i	0.561047	+	0.827784i	$0.310399\pi$
$110$	0.0462947	−	0.526445i	0.00441403	−	0.0501946i
$111$	3.15199	−	7.60959i	0.299174	−	0.722270i
$112$	−7.05075	−	9.65209i	−0.666233	−	0.912037i
$113$	1.35483	+	3.27085i	0.127452	+	0.307696i	0.974706	−	0.223492i	$-0.0717458\pi$
$113$	1.35483	+	3.27085i	0.127452	+	0.307696i	−0.847254	+	0.531188i	$0.821746\pi$
$114$	−1.43162	+	0.450684i	−0.134083	+	0.0422104i
$115$	9.30667	+	4.97452i	0.867851	+	0.463876i
$116$	16.6793	+	13.1141i	1.54864	+	1.21761i
$117$	−0.0907438	−	0.0744715i	−0.00838927	−	0.00688489i
$118$	−2.77990	+	1.89983i	−0.255910	+	0.174894i
$119$	−14.4991	−	2.88405i	−1.32913	−	0.264380i
$120$	2.32768	+	2.66138i	0.212487	+	0.242950i
$121$	−2.12856	−	10.7010i	−0.193505	−	0.972817i
$122$	−0.103893	−	9.93007i	−0.00940601	−	0.899026i
$123$	−3.27780	−	6.13234i	−0.295550	−	0.552934i
$124$	3.73366	−	5.84915i	0.335293	−	0.525269i
$125$	−10.4964	−	1.03380i	−0.938823	−	0.0924660i
$126$	−0.458202	−	4.20113i	−0.0408199	−	0.374267i
$127$	14.4151			1.27914			0.639569	−	0.768734i	$-0.279113\pi$
$127$	14.4151			1.27914			0.639569	+	0.768734i	$0.279113\pi$
$128$	8.19701	−	7.79801i	0.724521	−	0.689253i
$129$	0.905987			0.0797677
$130$	0.0225007	+	0.206304i	0.00197345	+	0.0180940i
$131$	7.60415	+	0.748943i	0.664377	+	0.0654355i	0.424584	−	0.905389i	$-0.360420\pi$
$131$	7.60415	+	0.748943i	0.664377	+	0.0654355i	0.239793	+	0.970824i	$0.422920\pi$
$132$	−0.503959	−	0.321690i	−0.0438640	−	0.0279995i
$133$	−1.49498	−	2.79692i	−0.129632	−	0.242524i
$134$	0.0268780	+	2.56900i	0.00232191	+	0.221928i
$135$	0.243873	+	1.22603i	0.0209892	+	0.105520i
$136$	0.933839	−	13.9612i	0.0800760	−	1.19716i
$137$	−15.0343	−	2.99050i	−1.28446	−	0.255496i	−0.494784	−	0.869016i	$-0.664753\pi$
$137$	−15.0343	−	2.99050i	−1.28446	−	0.255496i	−0.789679	+	0.613520i	$0.789753\pi$
$138$	9.85661	−	6.73619i	0.839050	−	0.573422i
$139$	−6.08051	−	4.99015i	−0.515742	−	0.423259i	0.340182	−	0.940360i	$-0.389511\pi$
$139$	−6.08051	−	4.99015i	−0.515742	−	0.423259i	−0.855924	+	0.517101i	$0.827011\pi$
$140$	−4.61767	+	5.87304i	−0.390264	+	0.496363i
$141$	5.02754	+	2.68728i	0.423395	+	0.226309i
$142$	−6.64929	+	2.09325i	−0.557996	+	0.175662i
$143$	−0.0134293	−	0.0324213i	−0.00112302	−	0.00271120i
$144$	3.88706	−	0.943807i	0.323922	−	0.0786506i
$145$	5.07493	−	12.2520i	0.421450	−	1.01747i
$146$	−0.681664	+	7.75161i	−0.0564149	+	0.641528i
$147$	1.84665	−	0.560174i	0.152309	−	0.0462024i
$148$	−1.27129	+	16.4240i	−0.104500	+	1.35004i
$149$	−0.0874629	−	0.888026i	−0.00716524	−	0.0727499i	0.990937	−	0.134327i	$-0.0428871\pi$
$149$	−0.0874629	−	0.888026i	−0.00716524	−	0.0727499i	−0.998102	+	0.0615767i	$0.980387\pi$
$150$	−2.65829	+	4.06995i	−0.217049	+	0.332310i
$151$	15.9301	−	10.6441i	1.29637	−	0.866207i	0.300221	−	0.953870i	$-0.402940\pi$
$151$	15.9301	−	10.6441i	1.29637	−	0.866207i	0.996150	+	0.0876623i	$0.0279396\pi$
$152$	2.44231	−	1.74519i	0.198097	−	0.141554i
$153$	2.74844	−	4.11333i	0.222198	−	0.332543i
$154$	0.471219	−	1.17216i	0.0379719	−	0.0944554i
$155$	−4.15043	−	1.25902i	−0.333371	−	0.101127i
$156$	0.218741	+	0.0852885i	0.0175133	+	0.00682855i
$157$	−2.97010	−	3.61907i	−0.237039	−	0.288833i	0.640881	−	0.767640i	$-0.278569\pi$
$157$	−2.97010	−	3.61907i	−0.237039	−	0.288833i	−0.877920	+	0.478807i	$0.841069\pi$
$158$	−7.51749	+	4.11988i	−0.598060	+	0.327760i
$159$	6.40731	−	6.40731i	0.508133	−	0.508133i
$160$	−6.07699	−	3.61584i	−0.480429	−	0.285857i
$161$	17.8378	+	17.8378i	1.40581	+	1.40581i
$162$	1.35754	+	0.396344i	0.106658	+	0.0311397i
$163$	5.67009	−	4.65332i	0.444116	−	0.364476i	−0.385597	−	0.922667i	$-0.626004\pi$
$163$	5.67009	−	4.65332i	0.444116	−	0.364476i	0.829712	+	0.558191i	$0.188504\pi$
$164$	10.0372	+	9.62568i	0.783771	+	0.751639i
$165$	−0.108476	+	0.357599i	−0.00844488	+	0.0278390i
$166$	8.32634	+	19.5214i	0.646249	+	1.51515i
$167$	−10.7640	−	7.19224i	−0.832940	−	0.556552i	0.0643842	−	0.997925i	$-0.479492\pi$
$167$	−10.7640	−	7.19224i	−0.832940	−	0.556552i	−0.897324	+	0.441373i	$0.854492\pi$
$168$	3.47793	+	7.70337i	0.268328	+	0.594328i
$169$	−7.21476	−	10.7976i	−0.554981	−	0.830588i
$170$	−8.55926	+	1.79583i	−0.656465	+	0.137734i
$171$	1.05617	−	0.104024i	0.0807674	−	0.00795490i
$172$	−1.72257	+	0.562152i	−0.131344	+	0.0428637i
$173$	−5.64514	−	18.6095i	−0.429192	−	1.41486i	−0.859018	−	0.511946i	$-0.828925\pi$
$173$	−5.64514	−	18.6095i	−0.429192	−	1.41486i	0.429825	−	0.902912i	$-0.358575\pi$
$174$	−9.63860	−	11.4973i	−0.730700	−	0.871604i
$175$	−9.48989	−	3.93084i	−0.717368	−	0.297144i
$176$	1.15779	+	0.298935i	0.0872716	+	0.0225330i
$177$	2.19965	−	0.911124i	0.165336	−	0.0684842i
$178$	6.87568	+	3.58315i	0.515354	+	0.268569i
$179$	3.52059	−	6.58655i	0.263141	−	0.492302i	−0.715303	−	0.698814i	$-0.753711\pi$
$179$	3.52059	−	6.58655i	0.263141	−	0.492302i	0.978444	+	0.206512i	$0.0662114\pi$
$180$	−1.22441	−	2.17975i	−0.0912625	−	0.162469i
$181$	−14.2228	+	17.3305i	−1.05717	+	1.28817i	−0.101151	+	0.994871i	$0.532253\pi$
$181$	−14.2228	+	17.3305i	−1.05717	+	1.28817i	−0.956021	+	0.293298i	$0.905247\pi$
$182$	−0.0916879	+	0.487550i	−0.00679636	+	0.0361396i
$183$	−1.36992	+	6.88708i	−0.101268	+	0.509107i
$184$	−14.5608	+	18.9235i	−1.07344	+	1.39506i
$185$	10.0983	−	2.00867i	0.742441	−	0.147681i
$186$	−3.43312	+	3.50572i	−0.251729	+	0.257052i
$187$	1.30425	−	0.697136i	0.0953761	−	0.0509796i
$188$	−11.2263	−	1.98984i	−0.818766	−	0.145124i
$189$	−0.292901	+	2.97388i	−0.0213054	+	0.216318i
$190$	−1.46268	−	1.17500i	−0.106114	−	0.0852432i
$191$			11.3344i			0.820130i	0.912056	+	0.410065i	$0.134494\pi$
$191$			11.3344i			0.820130i	−0.912056	+	0.410065i	$0.865506\pi$
$192$	−6.80490	+	4.20634i	−0.491102	+	0.303566i
$193$			18.3442i			1.32045i	0.751070	+	0.660223i	$0.229538\pi$
$193$			18.3442i			1.32045i	−0.751070	+	0.660223i	$0.770462\pi$
$194$	14.3108	−	17.8146i	1.02746	−	1.27901i
$195$	0.0143834	−	0.146037i	0.00103002	−	0.0104579i
$196$	−3.16348	+	2.21089i	−0.225963	+	0.157920i
$197$	−16.2047	+	8.66158i	−1.15454	+	0.617112i	−0.933650	−	0.358188i	$-0.883395\pi$
$197$	−16.2047	+	8.66158i	−1.15454	+	0.617112i	−0.220886	+	0.975300i	$0.570895\pi$
$198$	0.302050	+	0.295796i	0.0214658	+	0.0210213i
$199$	−5.00345	+	0.995248i	−0.354685	+	0.0705512i	−0.369217	−	0.929343i	$-0.620374\pi$
$199$	−5.00345	+	0.995248i	−0.354685	+	0.0705512i	0.0145321	+	0.999894i	$0.495374\pi$
$200$	2.52890	−	9.38769i	0.178820	−	0.663810i
$201$	0.354412	−	1.78175i	0.0249983	−	0.125675i
$202$	10.1839	+	1.91517i	0.716535	+	0.134751i
$203$	20.1113	−	24.5057i	1.41154	−	1.71996i
$204$	−2.67339	+	9.52611i	−0.187175	+	0.666961i
$205$	4.09742	−	7.66574i	0.286176	−	0.535399i
$206$	1.67016	−	3.20485i	0.116365	−	0.223293i
$207$	−7.79923	+	3.23055i	−0.542084	+	0.224539i
$208$	−0.468816	−	0.0264347i	−0.0325065	−	0.00183292i
$209$	0.293109	+	0.121410i	0.0202748	+	0.00839809i
$210$	4.04836	−	3.39390i	0.279363	−	0.234201i
$211$	7.97238	+	26.2814i	0.548841	+	1.80929i	0.586437	+	0.809995i	$0.300530\pi$
$211$	7.97238	+	26.2814i	0.548841	+	1.80929i	−0.0375959	+	0.999293i	$0.511970\pi$
$212$	−8.20667	+	16.1580i	−0.563636	+	1.10973i
$213$	4.90550	−	0.483150i	0.336119	−	0.0331049i
$214$	0.0462989	+	0.220669i	0.00316492	+	0.0150846i
$215$	0.629200	+	0.941664i	0.0429111	+	0.0642210i
$216$	−2.82703	+	0.0887590i	−0.192355	+	0.00603928i
$217$	−8.62078	−	5.76022i	−0.585217	−	0.391029i
$218$	8.05615	−	3.43614i	0.545631	−	0.232725i
$219$	1.59725	−	5.26544i	0.107932	−	0.355805i
$220$	−0.0156371	−	0.747216i	−0.00105425	−	0.0503773i
$221$	−0.448915	+	0.368415i	−0.0301973	+	0.0247823i
$222$	3.26451	−	11.1814i	0.219099	−	0.750449i
$223$	−5.38120	−	5.38120i	−0.360352	−	0.360352i	0.503591	−	0.863942i	$-0.332012\pi$
$223$	−5.38120	−	5.38120i	−0.360352	−	0.360352i	−0.863942	+	0.503591i	$0.832012\pi$
$224$	−11.3925	−	12.4885i	−0.761191	−	0.834425i
$225$	2.43059	−	2.43059i	0.162039	−	0.162039i
$226$	2.40626	+	4.39067i	0.160062	+	0.292063i
$227$	−10.6595	−	12.9886i	−0.707495	−	0.862086i	0.287928	−	0.957652i	$-0.407034\pi$
$227$	−10.6595	−	12.9886i	−0.707495	−	0.862086i	−0.995423	+	0.0955665i	$0.969534\pi$
$228$	−1.94357	+	0.853121i	−0.128716	+	0.0564993i
$229$	−19.6508	−	5.96099i	−1.29856	−	0.393914i	−0.436035	−	0.899930i	$-0.643618\pi$
$229$	−19.6508	−	5.96099i	−1.29856	−	0.393914i	−0.862524	+	0.506016i	$0.831118\pi$
$230$	13.8468	+	5.56653i	0.913030	+	0.367046i
$231$	−0.496297	+	0.742761i	−0.0326539	+	0.0488701i
$232$	25.4599	+	15.8793i	1.67152	+	1.04253i
$233$	4.96457	−	3.31722i	0.325240	−	0.217318i	−0.382221	−	0.924071i	$-0.624841\pi$
$233$	4.96457	−	3.31722i	0.325240	−	0.217318i	0.707461	+	0.706753i	$0.249841\pi$
$234$	−0.138994	−	0.0907837i	−0.00908629	−	0.00593471i
$235$	0.698483	+	7.09181i	0.0455640	+	0.462619i
$236$	−3.61688	+	3.09718i	−0.235439	+	0.201609i
$237$	5.80059	−	1.75959i	0.376789	−	0.114298i
$238$	−20.8262	−	1.83142i	−1.34996	−	0.118713i
$239$	5.92077	−	14.2940i	0.382982	−	0.924602i	−0.608403	−	0.793628i	$-0.708190\pi$
$239$	5.92077	−	14.2940i	0.382982	−	0.924602i	0.991386	−	0.130974i	$-0.0418103\pi$
$240$	3.68050	+	3.38467i	0.237575	+	0.218479i
$241$	−1.60866	−	3.88365i	−0.103623	−	0.250168i	0.863561	−	0.504244i	$-0.168229\pi$
$241$	−1.60866	−	3.88365i	−0.103623	−	0.250168i	−0.967184	+	0.254076i	$0.918229\pi$
$242$	−4.63331	−	14.7179i	−0.297841	−	0.946102i
$243$	−0.881921	−	0.471397i	−0.0565753	−	0.0302401i
$244$	−1.66867	−	13.9445i	−0.106826	−	0.892706i
$245$	1.86472	+	1.53033i	0.119132	+	0.0977693i
$246$	−5.54848	−	8.11871i	−0.353758	−	0.517630i
$247$	−0.122190	−	0.0243051i	−0.00777477	−	0.00154650i
$248$	4.35220	−	8.79568i	0.276365	−	0.558526i
$249$	−2.92769	−	14.7185i	−0.185535	−	0.932748i
$250$	−14.9151	+	0.156048i	−0.943314	+	0.00986937i
$251$	4.75165	+	8.88972i	0.299922	+	0.561114i	0.986067	−	0.166351i	$-0.0531984\pi$
$251$	4.75165	+	8.88972i	0.299922	+	0.561114i	−0.686145	+	0.727465i	$0.740698\pi$
$252$	−1.28835	−	5.83602i	−0.0811585	−	0.367635i
$253$	−2.51144	−	0.247356i	−0.157893	−	0.0155511i
$254$	20.2659	−	2.21033i	1.27160	−	0.138688i
$255$	6.18409			0.387263
$256$	10.3283	−	12.2199i	0.645518	−	0.763745i
$257$	27.0326			1.68625			0.843124	−	0.537720i	$-0.180714\pi$
$257$	27.0326			1.68625			0.843124	+	0.537720i	$0.180714\pi$
$258$	1.27371	−	0.138918i	0.0792974	−	0.00864867i
$259$	24.4945	+	2.41250i	1.52201	+	0.149905i
$260$	0.0632666	+	0.286587i	0.00392362	+	0.0177734i
$261$	5.00091	+	9.35605i	0.309549	+	0.579125i
$262$	10.8053	−	0.113050i	0.667555	−	0.00698426i
$263$	0.978539	+	4.91945i	0.0603393	+	0.303346i	0.999156	−	0.0410703i	$-0.0130768\pi$
$263$	0.978539	+	4.91945i	0.0603393	+	0.303346i	−0.938817	+	0.344417i	$0.888077\pi$
$264$	−0.757830	−	0.374982i	−0.0466412	−	0.0230786i
$265$	11.1095	+	2.20981i	0.682448	+	0.135747i
$266$	−2.53063	−	3.70289i	−0.155163	−	0.227039i
$267$	−4.23797	−	3.47801i	−0.259359	−	0.212851i
$268$	0.431701	+	3.60758i	0.0263704	+	0.220368i
$269$	−10.4411	−	5.58086i	−0.636602	−	0.340271i	0.121322	−	0.992613i	$-0.461287\pi$
$269$	−10.4411	−	5.58086i	−0.636602	−	0.340271i	−0.757925	+	0.652342i	$0.773787\pi$
$270$	0.530847	+	1.68626i	0.0323063	+	0.102622i
$271$	8.60611	+	20.7770i	0.522784	+	1.26211i	0.936167	+	0.351555i	$0.114347\pi$
$271$	8.60611	+	20.7770i	0.522784	+	1.26211i	−0.413384	+	0.910557i	$0.635653\pi$
$272$	−0.827862	−	19.7709i	−0.0501965	−	1.19879i
$273$	0.134243	−	0.324090i	0.00812474	−	0.0196148i
$274$	−21.5948	−	1.89901i	−1.30459	−	0.114724i
$275$	0.983319	−	0.298287i	0.0592964	−	0.0179874i
$276$	12.8243	−	10.9816i	0.771931	−	0.661015i
$277$	1.31040	+	13.3047i	0.0787343	+	0.799403i	0.950757	+	0.309938i	$0.100308\pi$
$277$	1.31040	+	13.3047i	0.0787343	+	0.799403i	−0.872023	+	0.489466i	$0.837192\pi$
$278$	−9.31360	−	6.08318i	−0.558593	−	0.364845i
$279$	2.88488	−	1.92761i	0.172713	−	0.115403i
$280$	−5.59134	+	8.96482i	−0.334146	+	0.535750i
$281$	1.82194	−	2.72673i	0.108688	−	0.162663i	−0.773138	−	0.634238i	$-0.781314\pi$
$281$	1.82194	−	2.72673i	0.108688	−	0.162663i	0.881826	+	0.471574i	$0.156314\pi$
$282$	7.48015	+	3.00709i	0.445436	+	0.179069i
$283$	−21.3617	−	6.48002i	−1.26982	−	0.385197i	−0.417723	−	0.908574i	$-0.637172\pi$
$283$	−21.3617	−	6.48002i	−1.26982	−	0.385197i	−0.852101	+	0.523377i	$0.824672\pi$
$284$	−9.02712	+	3.96241i	−0.535661	+	0.235126i
$285$	0.841622	+	1.02552i	0.0498534	+	0.0607466i
$286$	−0.0238512	−	0.0435211i	−0.00141035	−	0.00257346i
$287$	14.6927	−	14.6927i	0.867281	−	0.867281i
$288$	5.32001	−	1.92289i	0.313484	−	0.113308i
$289$	−5.28453	−	5.28453i	−0.310855	−	0.310855i
$290$	5.25609	−	18.0029i	0.308648	−	1.05717i
$291$	−12.4903	+	10.2505i	−0.732192	+	0.600894i
$292$	0.230248	+	11.0023i	0.0134742	+	0.643863i
$293$	3.73743	−	12.3207i	0.218343	−	0.719780i	−0.777516	−	0.628864i	$-0.783520\pi$
$293$	3.73743	−	12.3207i	0.218343	−	0.719780i	0.995859	−	0.0909166i	$-0.0289797\pi$
$294$	2.51026	−	1.07069i	0.146402	−	0.0624439i
$295$	2.47464	+	1.65350i	0.144079	+	0.0962706i
$296$	0.731068	+	23.2850i	0.0424925	+	1.35341i
$297$	−0.166082	−	0.248559i	−0.00963705	−	0.0144229i
$298$	−0.259126	−	1.23504i	−0.0150108	−	0.0715442i
$299$	0.986215	−	0.0971337i	0.0570343	−	0.00561739i
$300$	−3.11317	+	6.12946i	−0.179739	+	0.353884i
$301$	0.785896	+	2.59075i	0.0452983	+	0.149329i
$302$	20.7636	−	17.4070i	1.19481	−	1.00166i
$303$	−6.76956	−	2.80404i	−0.388901	−	0.161088i
$304$	3.16599	−	2.82801i	0.181582	−	0.162197i
$305$	−8.10969	+	3.35914i	−0.464360	+	0.192344i
$306$	3.23326	−	6.20427i	0.184833	−	0.354674i
$307$	−5.81635	+	10.8816i	−0.331957	+	0.621047i	−0.991424	−	0.130686i	$-0.958282\pi$
$307$	−5.81635	+	10.8816i	−0.331957	+	0.621047i	0.659467	+	0.751733i	$0.270782\pi$
$308$	0.482744	−	1.72017i	0.0275069	−	0.0980156i
$309$	−1.62115	+	1.97538i	−0.0922240	+	0.112375i
$310$	−6.02805	−	1.13363i	−0.342370	−	0.0643856i
$311$	−3.86983	+	19.4549i	−0.219438	+	1.10319i	0.701258	+	0.712908i	$0.252622\pi$
$311$	−3.86983	+	19.4549i	−0.219438	+	1.10319i	−0.920696	+	0.390281i	$0.872378\pi$
$312$	0.320600	+	0.0863648i	0.0181504	+	0.00488944i
$313$	−27.4120	+	5.45259i	−1.54942	+	0.308199i	−0.894349	−	0.447369i	$-0.852361\pi$
$313$	−27.4120	+	5.45259i	−1.54942	+	0.308199i	−0.655070	+	0.755568i	$0.727361\pi$
$314$	−4.73051	−	4.63255i	−0.266958	−	0.261430i
$315$	−3.29441	+	1.76090i	−0.185619	+	0.0992153i
$316$	−9.93695	+	6.94472i	−0.558997	+	0.390671i
$317$	1.85096	−	18.7931i	0.103960	−	1.05552i	−0.791738	−	0.610861i	$-0.790823\pi$
$317$	1.85096	−	18.7931i	0.103960	−	1.05552i	0.895698	−	0.444663i	$-0.146677\pi$
$318$	8.02543	−	9.99034i	0.450044	−	0.560231i
$319$			3.17136i			0.177562i
$320$	−9.09793	−	4.15162i	−0.508590	−	0.232082i
$321$		−	0.159434i		−	0.00889873i
$322$	27.8129	+	22.3426i	1.54995	+	1.24510i
$323$	0.514613	−	5.22495i	0.0286338	−	0.290724i
$324$	1.96930	+	0.349054i	0.109406	+	0.0193919i
$325$	−0.355867	+	0.190215i	−0.0197399	+	0.0105512i
$326$	7.25793	−	7.41141i	0.401980	−	0.410480i
$327$	−6.07409	+	1.20821i	−0.335898	+	0.0668142i
$328$	15.5870	+	11.9935i	0.860646	+	0.662229i
$329$	−3.32339	+	16.7078i	−0.183224	+	0.921130i
$330$	−0.0976725	+	0.519373i	−0.00537669	+	0.0285905i
$331$	17.2137	−	20.9749i	0.946150	−	1.15289i	−0.0419571	−	0.999119i	$-0.513359\pi$
$331$	17.2137	−	20.9749i	0.946150	−	1.15289i	0.988107	−	0.153768i	$-0.0491407\pi$
$332$	14.6991	+	26.1679i	0.806717	+	1.43615i
$333$	−3.88269	+	7.26399i	−0.212770	+	0.398064i
$334$	−16.2356	−	8.46093i	−0.888373	−	0.462961i
$335$	2.09805	−	0.869042i	0.114629	−	0.0474808i
$336$	6.07073	+	10.2967i	0.331185	+	0.561731i
$337$	−15.7159	−	6.50975i	−0.856101	−	0.354609i	−0.0889198	−	0.996039i	$-0.528341\pi$
$337$	−15.7159	−	6.50975i	−0.856101	−	0.354609i	−0.767182	+	0.641430i	$0.778341\pi$
$338$	−11.7987	−	14.0739i	−0.641765	−	0.765519i
$339$	−1.02771	−	3.38790i	−0.0558174	−	0.184005i
$340$	−11.7579	+	3.83714i	−0.637661	+	0.208098i
$341$	1.03221	−	0.101664i	0.0558972	−	0.00550540i
$342$	1.46890	−	0.308191i	0.0794288	−	0.0166651i
$343$	−8.41760	−	12.5978i	−0.454508	−	0.680219i
$344$	−2.33552	+	1.05444i	−0.125923	+	0.0568518i
$345$	−8.77427	−	5.86278i	−0.472391	−	0.315641i
$346$	−10.7898	−	25.2971i	−0.580066	−	1.35998i
$347$	−6.16842	+	20.3346i	−0.331138	+	1.09162i	0.620451	+	0.784245i	$0.286949\pi$
$347$	−6.16842	+	20.3346i	−0.331138	+	1.09162i	−0.951590	+	0.307372i	$0.900551\pi$
$348$	−15.3136	−	14.6858i	−0.820895	−	0.787241i
$349$	−16.4305	+	13.4842i	−0.879506	+	0.721792i	−0.961490	−	0.274841i	$-0.911375\pi$
$349$	−16.4305	+	13.4842i	−0.879506	+	0.721792i	0.0819831	+	0.996634i	$0.473875\pi$
$350$	−13.9443	−	4.07116i	−0.745356	−	0.217613i
$351$	0.0830073	+	0.0830073i	0.00443060	+	0.00443060i
$352$	1.67354	+	0.242737i	0.0892002	+	0.0129379i
$353$	8.43148	−	8.43148i	0.448762	−	0.448762i	−0.446181	−	0.894943i	$-0.647216\pi$
$353$	8.43148	−	8.43148i	0.448762	−	0.448762i	0.894943	+	0.446181i	$0.147216\pi$
$354$	2.95273	−	1.61821i	0.156936	−	0.0860067i
$355$	3.90901	+	4.76314i	0.207468	+	0.252801i
$356$	10.2158	+	3.98320i	0.541435	+	0.211109i
$357$	14.1466	+	4.29132i	0.748717	+	0.227121i
$358$	3.93957	−	9.79970i	0.208213	−	0.517930i
$359$	−16.6522	+	24.9218i	−0.878870	+	1.31532i	0.0693116	+	0.997595i	$0.477920\pi$
$359$	−16.6522	+	24.9218i	−0.878870	+	1.31532i	−0.948182	+	0.317728i	$0.897080\pi$
$360$	−2.05561	−	2.87672i	−0.108340	−	0.151616i
$361$	−14.8614	+	9.93009i	−0.782180	+	0.522636i
$362$	−17.3382	+	26.5454i	−0.911273	+	1.39520i
$363$	1.06943	+	10.8581i	0.0561305	+	0.569902i
$364$	−0.0541441	+	0.699494i	−0.00283792	+	0.0366634i
$365$	6.58207	−	1.99665i	0.344521	−	0.104509i
$366$	−0.869924	+	9.89244i	−0.0454717	+	0.517086i
$367$	−5.29228	+	12.7767i	−0.276255	+	0.666938i	−0.999726	−	0.0234169i	$-0.992545\pi$
$367$	−5.29228	+	12.7767i	−0.276255	+	0.666938i	0.723471	+	0.690355i	$0.242545\pi$
$368$	−17.5691	+	28.8368i	−0.915852	+	1.50322i
$369$	2.66095	+	6.42409i	0.138523	+	0.334425i
$370$	13.8889	−	4.37235i	0.722052	−	0.227308i
$371$	23.8803	+	12.7643i	1.23980	+	0.662689i
$372$	−4.28900	+	5.45502i	−0.222374	+	0.282830i
$373$	10.5547	+	8.66200i	0.546500	+	0.448501i	0.866686	−	0.498853i	$-0.166245\pi$
$373$	10.5547	+	8.66200i	0.546500	+	0.448501i	−0.320186	+	0.947355i	$0.603745\pi$
$374$	1.72672	−	1.18007i	0.0892865	−	0.0610201i
$375$	10.3445	+	2.05765i	0.534187	+	0.106256i
$376$	−16.0880	−	1.07609i	−0.829674	−	0.0554953i
$377$	−0.242957	−	1.22143i	−0.0125129	−	0.0629068i
$378$	0.0442124	+	4.22582i	0.00227404	+	0.217353i
$379$	10.8577	+	20.3134i	0.557724	+	1.04343i	0.989917	+	0.141647i	$0.0452399\pi$
$379$	10.8577	+	20.3134i	0.557724	+	1.04343i	−0.432193	+	0.901781i	$0.642260\pi$
$380$	−2.23651	−	1.42762i	−0.114731	−	0.0732354i
$381$	−14.3457	−	1.41293i	−0.734954	−	0.0723867i
$382$	1.73795	+	15.9348i	0.0889212	+	0.815295i
$383$	3.55257			0.181528			0.0907638	−	0.995872i	$-0.471069\pi$
$383$	3.55257			0.181528			0.0907638	+	0.995872i	$0.471069\pi$
$384$	−8.92188	+	6.95701i	−0.455293	+	0.355024i
$385$	−1.11668			−0.0569115
$386$	2.81279	+	25.7897i	0.143167	+	1.31266i
$387$	−0.901624	−	0.0888022i	−0.0458321	−	0.00451407i
$388$	17.3876	−	27.2394i	0.882723	−	1.38287i
$389$	−12.4715	−	23.3326i	−0.632331	−	1.18301i	−0.970312	−	0.241855i	$-0.922244\pi$
$389$	−12.4715	−	23.3326i	−0.632331	−	1.18301i	0.337982	−	0.941153i	$-0.390256\pi$
$390$	−0.00217112	−	0.207516i	−0.000109939	−	0.0105080i
$391$	8.14741	+	40.9598i	0.412032	+	2.07143i
$392$	−4.10846	+	3.59330i	−0.207508	+	0.181489i
$393$	−7.49412	−	1.49067i	−0.378028	−	0.0751945i
$394$	−21.4537	+	14.6618i	−1.08082	+	0.738652i
$395$	5.85735	+	4.80700i	0.294715	+	0.241866i
$396$	0.470001	+	0.369538i	0.0236184	+	0.0185700i
$397$	12.7911	+	6.83698i	0.641967	+	0.343138i	0.760049	−	0.649865i	$-0.225175\pi$
$397$	12.7911	+	6.83698i	0.641967	+	0.343138i	−0.118083	+	0.993004i	$0.537675\pi$
$398$	−6.88162	+	2.16639i	−0.344945	+	0.108591i
$399$	1.21364	+	2.92999i	0.0607580	+	0.146683i
$400$	2.11587	−	13.5857i	0.105794	−	0.679285i
$401$	−4.46329	+	10.7753i	−0.222886	+	0.538095i	−0.995280	−	0.0970497i	$-0.969059\pi$
$401$	−4.46329	+	10.7753i	−0.222886	+	0.538095i	0.772393	+	0.635144i	$0.219059\pi$
$402$	0.225057	−	2.55926i	0.0112248	−	0.127645i
$403$	−0.389760	+	0.118232i	−0.0194153	+	0.00588957i
$404$	14.6109	+	1.13096i	0.726921	+	0.0562671i
$405$	−0.122526	−	1.24403i	−0.00608839	−	0.0618165i
$406$	24.5165	−	37.5357i	1.21673	−	1.86287i
$407$	−2.04727	+	1.36794i	−0.101479	+	0.0678064i
$408$	−2.29778	+	13.8025i	−0.113757	+	0.683323i
$409$	−12.9115	+	19.3235i	−0.638434	+	0.955485i	0.361300	+	0.932450i	$0.382333\pi$
$409$	−12.9115	+	19.3235i	−0.638434	+	0.955485i	−0.999735	+	0.0230351i	$0.992667\pi$
$410$	4.58506	−	11.4054i	0.226440	−	0.563270i
$411$	14.6687	+	4.44971i	0.723555	+	0.219488i
$412$	1.85662	−	4.76172i	0.0914693	−	0.234593i
$413$	4.51352	+	5.49974i	0.222096	+	0.270625i
$414$	−10.4694	+	5.73764i	−0.514543	+	0.281989i
$415$	13.2649	−	13.2649i	0.651147	−	0.651147i
$416$	−0.663150	+	0.0347213i	−0.0325136	+	0.00170235i
$417$	5.56211	+	5.56211i	0.272378	+	0.272378i
$418$	0.430691	+	0.125744i	0.0210658	+	0.00615032i
$419$	0.828532	−	0.679959i	0.0404765	−	0.0332182i	−0.613938	−	0.789355i	$-0.710415\pi$
$419$	0.828532	−	0.679959i	0.0404765	−	0.0332182i	0.654414	+	0.756136i	$0.272915\pi$
$420$	5.17109	−	5.39215i	0.252323	−	0.263110i
$421$	−6.14103	+	20.2443i	−0.299295	+	0.986645i	0.670333	+	0.742061i	$0.266151\pi$
$421$	−6.14103	+	20.2443i	−0.299295	+	0.986645i	−0.969628	+	0.244584i	$0.921349\pi$
$422$	15.2380	+	35.7260i	0.741775	+	1.73911i
$423$	−4.73993	−	3.16712i	−0.230463	−	0.153991i
$424$	−9.06001	+	23.9745i	−0.439993	+	1.16430i
$425$	−9.44741	−	14.1391i	−0.458267	−	0.685845i
$426$	6.82245	−	1.43143i	0.330549	−	0.0693529i
$427$	−20.8826	+	2.05675i	−1.01058	+	0.0995333i
$428$	0.0989264	+	0.303134i	0.00478179	+	0.0146525i
$429$	0.0101868	+	0.0335815i	0.000491824	+	0.00162133i
$430$	1.02897	+	1.22739i	0.0496212	+	0.0591898i
$431$	−15.0564	−	6.23655i	−0.725240	−	0.300404i	−0.0106454	−	0.999943i	$-0.503389\pi$
$431$	−15.0564	−	6.23655i	−0.725240	−	0.300404i	−0.714594	+	0.699539i	$0.753389\pi$
$432$	−3.96085	+	0.558264i	−0.190567	+	0.0268595i
$433$	−33.4054	+	13.8370i	−1.60536	+	0.664963i	−0.992161	−	0.124965i	$-0.960118\pi$
$433$	−33.4054	+	13.8370i	−1.60536	+	0.664963i	−0.613200	+	0.789927i	$0.710118\pi$
$434$	−13.0030	−	6.77630i	−0.624163	−	0.325273i
$435$	−6.25140	+	11.6955i	−0.299732	+	0.560758i
$436$	10.7991	−	6.06607i	0.517182	−	0.290512i
$437$	−5.68363	+	6.92552i	−0.271885	+	0.331293i
$438$	1.43817	−	7.64747i	0.0687185	−	0.365410i
$439$	6.74231	−	33.8959i	0.321793	−	1.61776i	−0.393767	−	0.919210i	$-0.628828\pi$
$439$	6.74231	−	33.8959i	0.321793	−	1.61776i	0.715560	−	0.698552i	$-0.246172\pi$
$440$	−0.136557	−	1.04810i	−0.00651011	−	0.0499660i
$441$	−1.89266	+	0.376474i	−0.0901268	+	0.0179273i
$442$	−0.574629	+	0.586780i	−0.0273323	+	0.0279103i
$443$	11.8630	−	6.34088i	0.563626	−	0.301264i	−0.164869	−	0.986315i	$-0.552720\pi$
$443$	11.8630	−	6.34088i	0.563626	−	0.301264i	0.728495	+	0.685051i	$0.240220\pi$
$444$	2.87500	−	16.2203i	0.136442	−	0.769781i
$445$	0.671742	−	6.82031i	0.0318436	−	0.323314i
$446$	−8.39042	−	6.74018i	−0.397298	−	0.319157i
$447$			0.892323i			0.0422054i
$448$	−17.9313	−	15.8105i	−0.847175	−	0.746975i
$449$			32.7549i			1.54580i	0.634529	+	0.772899i	$0.281194\pi$
$449$			32.7549i			1.54580i	−0.634529	+	0.772899i	$0.718806\pi$
$450$	3.04442	−	3.78980i	0.143515	−	0.178653i
$451$	−0.203742	+	2.06863i	−0.00959386	+	0.0974081i
$452$	4.05614	+	5.80378i	0.190785	+	0.272987i
$453$	−16.8967	+	9.03146i	−0.793875	+	0.424335i
$454$	−16.9775	−	16.6260i	−0.796795	−	0.780295i
$455$	0.430084	−	0.0855489i	0.0201626	−	0.00401060i
$456$	−2.60161	+	1.49740i	−0.121831	+	0.0701221i
$457$	0.696239	−	3.50023i	0.0325687	−	0.163734i	−0.961078	−	0.276276i	$-0.910899\pi$
$457$	0.696239	−	3.50023i	0.0325687	−	0.163734i	0.993647	+	0.112543i	$0.0358995\pi$
$458$	−28.5406	−	5.36730i	−1.33361	−	0.250797i
$459$	−3.13838	+	3.82413i	−0.146487	+	0.178495i
$460$	20.3204	+	5.70268i	0.947444	+	0.265889i
$461$	1.79069	−	3.35015i	0.0834009	−	0.156032i	−0.836763	−	0.547565i	$-0.815555\pi$
$461$	1.79069	−	3.35015i	0.0834009	−	0.156032i	0.920164	+	0.391533i	$0.128055\pi$
$462$	−0.583842	+	1.12033i	−0.0271628	+	0.0521224i
$463$	34.7647	−	14.4000i	1.61565	−	0.669225i	0.622135	−	0.782910i	$-0.286265\pi$
$463$	34.7647	−	14.4000i	1.61565	−	0.669225i	0.993517	+	0.113685i	$0.0362654\pi$
$464$	38.2283	+	18.4205i	1.77470	+	0.855148i
$465$	4.00704	+	1.65977i	0.185822	+	0.0769701i
$466$	6.47094	−	5.42484i	0.299760	−	0.251301i
$467$	−11.5959	−	38.2267i	−0.536596	−	1.76892i	−0.633627	−	0.773638i	$-0.718435\pi$
$467$	−11.5959	−	38.2267i	−0.536596	−	1.76892i	0.0970313	−	0.995281i	$-0.469065\pi$
$468$	−0.209328	−	0.106318i	−0.00967619	−	0.00491456i
$469$	5.40252	−	0.532101i	0.249465	−	0.0245702i
$470$	2.06939	+	9.86311i	0.0954540	+	0.454951i
$471$	2.60106	+	3.89277i	0.119851	+	0.179369i
$472$	−4.60999	+	4.90884i	−0.212192	+	0.225948i
$473$	−0.225191	−	0.150468i	−0.0103543	−	0.00691852i
$474$	7.88511	−	3.36319i	0.362175	−	0.154477i
$475$	1.05896	−	3.49094i	0.0485886	−	0.160175i
$476$	−29.5598	+	0.618604i	−1.35487	+	0.0283537i
$477$	−7.00448	+	5.74843i	−0.320713	+	0.263203i
$478$	6.13212	−	21.0034i	0.280476	−	0.960675i
$479$	10.1204	+	10.1204i	0.462414	+	0.462414i	0.899446	−	0.437032i	$-0.143970\pi$
$479$	10.1204	+	10.1204i	0.462414	+	0.462414i	−0.437032	+	0.899446i	$0.643970\pi$
$480$	5.69332	+	4.19408i	0.259863	+	0.191433i
$481$	0.683695	−	0.683695i	0.0311738	−	0.0311738i
$482$	−2.85707	−	5.21327i	−0.130136	−	0.237458i
$483$	−16.0035	−	19.5003i	−0.728184	−	0.887294i
$484$	−8.77061	−	19.9811i	−0.398664	−	0.908232i
$485$	−19.3285	−	5.86325i	−0.877664	−	0.266236i
$486$	−1.31215	−	0.527497i	−0.0595205	−	0.0239278i
$487$	2.09293	−	3.13229i	0.0948396	−	0.141938i	−0.781016	−	0.624512i	$-0.785298\pi$
$487$	2.09293	−	3.13229i	0.0948396	−	0.141938i	0.875855	+	0.482574i	$0.160298\pi$
$488$	−4.48411	−	19.3484i	−0.202986	−	0.875861i
$489$	−6.09889	+	4.07515i	−0.275801	+	0.184285i
$490$	2.85621	+	1.86553i	0.129030	+	0.0842763i
$491$	−4.05861	−	41.2077i	−0.183162	−	1.85968i	−0.446253	−	0.894907i	$-0.647242\pi$
$491$	−4.05861	−	41.2077i	−0.183162	−	1.85968i	0.263091	−	0.964771i	$-0.415258\pi$
$492$	−9.04535	−	10.5631i	−0.407796	−	0.476223i
$493$	50.2221	−	15.2347i	2.26189	−	0.686137i
$494$	−0.175511	−	0.0154342i	−0.00789662	−	0.000694415i
$495$	0.143005	−	0.345244i	0.00642759	−	0.0155176i
$496$	4.76998	−	13.0330i	0.214178	−	0.585198i
$497$	5.63688	+	13.6086i	0.252849	+	0.610431i
$498$	−6.37282	−	20.2435i	−0.285573	−	0.907133i
$499$	−2.79266	−	1.49271i	−0.125017	−	0.0668228i	0.407703	−	0.913115i	$-0.366330\pi$
$499$	−2.79266	−	1.49271i	−0.125017	−	0.0668228i	−0.532720	+	0.846292i	$0.678830\pi$
$500$	−20.9449	+	2.50637i	−0.936683	+	0.112088i
$501$	10.0072	+	8.21266i	0.447087	+	0.366915i
$502$	8.04333	+	11.7693i	0.358992	+	0.525288i
$503$	3.12160	+	0.620924i	0.139185	+	0.0276856i	0.264191	−	0.964470i	$-0.414895\pi$
$503$	3.12160	+	0.620924i	0.139185	+	0.0276856i	−0.125006	+	0.992156i	$0.539895\pi$
$504$	−2.70612	−	8.00717i	−0.120540	−	0.356668i
$505$	−1.78694	−	8.98353i	−0.0795176	−	0.399762i
$506$	−3.56871	+	0.0373374i	−0.158648	+	0.00165985i
$507$	6.12166	+	11.4528i	0.271873	+	0.508638i
$508$	28.1525	−	6.21489i	1.24906	−	0.275741i
$509$	−4.56208	−	0.449326i	−0.202211	−	0.0199160i	−0.00359543	−	0.999994i	$-0.501144\pi$
$509$	−4.56208	−	0.449326i	−0.202211	−	0.0199160i	−0.198615	+	0.980078i	$0.563644\pi$
$510$	8.69406	−	0.948229i	0.384980	−	0.0419883i
$511$	16.4425			0.727375
$512$	12.6466	−	18.7634i	0.558905	−	0.829232i
$513$	−1.06128			−0.0468567
$514$	38.0045	−	4.14501i	1.67631	−	0.182828i
$515$	−3.17904	−	0.313108i	−0.140085	−	0.0137972i
$516$	1.76937	−	0.390604i	0.0778922	−	0.0171954i
$517$	−0.803332	−	1.50293i	−0.0353305	−	0.0660988i
$518$	34.8062	−	0.364158i	1.52930	−	0.0160002i
$519$	3.79391	+	19.0733i	0.166534	+	0.837223i
$520$	0.132888	+	0.393205i	0.00582754	+	0.0172432i
$521$	−39.1848	−	7.79434i	−1.71672	−	0.341476i	−0.763972	−	0.645249i	$-0.776753\pi$
$521$	−39.1848	−	7.79434i	−1.71672	−	0.341476i	−0.952744	+	0.303773i	$0.901753\pi$
$522$	8.46526	+	12.3866i	0.370514	+	0.542148i
$523$	5.77552	+	4.73985i	0.252546	+	0.207259i	0.752145	−	0.658998i	$-0.229019\pi$
$523$	5.77552	+	4.73985i	0.252546	+	0.207259i	−0.499599	+	0.866257i	$0.666519\pi$
$524$	15.1736	−	1.81575i	0.662863	−	0.0793216i
$525$	9.05890	+	4.84208i	0.395363	+	0.211326i
$526$	2.13002	+	6.76609i	0.0928734	+	0.295016i
$527$	−6.56853	−	15.8578i	−0.286130	−	0.690778i
$528$	−1.12291	−	0.410978i	−0.0488685	−	0.0178855i
$529$	18.4700	−	44.5905i	0.803044	−	1.93872i
$530$	15.9574	+	1.40326i	0.693143	+	0.0609539i
$531$	−2.27836	+	0.691133i	−0.0988724	+	0.0299926i
$532$	−4.12553	−	4.81778i	−0.178864	−	0.208877i
$533$	−0.0800073	−	0.812328i	−0.00346550	−	0.0351858i
$534$	−6.49136	−	4.23983i	−0.280909	−	0.183475i
$535$	0.165712	−	0.110725i	0.00716437	−	0.00478708i
$536$	1.16008	+	5.00561i	0.0501079	+	0.216210i
$537$	−4.14923	+	6.20976i	−0.179052	+	0.267971i
$538$	−15.5346	−	6.24503i	−0.669743	−	0.269242i
$539$	−0.552036	−	0.167458i	−0.0237779	−	0.00721293i
$540$	1.00487	+	2.28927i	0.0432425	+	0.0985145i
$541$	−4.97796	−	6.06566i	−0.214019	−	0.260783i	0.654924	−	0.755694i	$-0.272700\pi$
$541$	−4.97796	−	6.06566i	−0.214019	−	0.260783i	−0.868943	+	0.494912i	$0.835200\pi$
$542$	15.2849	+	27.8903i	0.656544	+	1.19799i
$543$	15.8530	−	15.8530i	0.680318	−	0.680318i
$544$	−4.19542	−	27.6686i	−0.179877	−	1.18628i
$545$	−5.47419	−	5.47419i	−0.234489	−	0.234489i
$546$	0.139035	−	0.476215i	0.00595013	−	0.0203801i
$547$	−28.7163	+	23.5668i	−1.22782	+	1.00765i	−0.228400	+	0.973567i	$0.573349\pi$
$547$	−28.7163	+	23.5668i	−1.22782	+	1.00765i	−0.999419	+	0.0340780i	$0.989151\pi$
$548$	−30.6509	+	0.641436i	−1.30934	+	0.0274008i
$549$	2.03838	−	6.71964i	0.0869959	−	0.286787i
$550$	1.33669	−	0.570130i	0.0569965	−	0.0243104i
$551$	9.36137	+	6.25507i	0.398808	+	0.266475i
$552$	16.3455	−	17.4052i	0.695711	−	0.740813i
$553$	10.0634	+	15.0610i	0.427941	+	0.640458i
$554$	3.88232	+	18.5039i	0.164944	+	0.786154i
$555$	−10.2465	+	1.00920i	−0.434941	+	0.0428380i
$556$	−14.0265	−	7.12411i	−0.594858	−	0.302130i
$557$	−7.04811	−	23.2345i	−0.298638	−	0.984477i	−0.969950	−	0.243303i	$-0.921769\pi$
$557$	−7.04811	−	23.2345i	−0.298638	−	0.984477i	0.671313	−	0.741174i	$-0.265731\pi$
$558$	3.76021	−	3.15233i	0.159182	−	0.133449i
$559$	0.0982582	+	0.0406999i	0.00415588	+	0.00172142i
$560$	−6.48612	+	13.4608i	−0.274089	+	0.568821i
$561$	−1.36630	+	0.565940i	−0.0576852	+	0.0238940i
$562$	2.14333	−	4.11282i	0.0904109	−	0.173489i
$563$	−21.0987	+	39.4730i	−0.889206	+	1.66359i	−0.151509	+	0.988456i	$0.548413\pi$
$563$	−21.0987	+	39.4730i	−0.889206	+	1.66359i	−0.737697	+	0.675132i	$0.764087\pi$
$564$	10.9773	+	3.08063i	0.462226	+	0.129718i
$565$	2.80758	−	3.42104i	0.118116	−	0.143924i
$566$	−31.0256	−	5.83463i	−1.30410	−	0.245248i
$567$	0.582982	−	2.93085i	0.0244829	−	0.123084i
$568$	−12.0834	+	6.95482i	−0.507010	+	0.291818i
$569$	18.1348	−	3.60724i	0.760252	−	0.151224i	0.200284	−	0.979738i	$-0.435813\pi$
$569$	18.1348	−	3.60724i	0.760252	−	0.151224i	0.559968	+	0.828514i	$0.310813\pi$
$570$	1.34046	+	1.31271i	0.0561459	+	0.0549832i
$571$	0.291644	−	0.155887i	0.0122049	−	0.00652366i	−0.465283	−	0.885162i	$-0.654047\pi$
$571$	0.291644	−	0.155887i	0.0122049	−	0.00652366i	0.477488	+	0.878638i	$0.341547\pi$
$572$	−0.0402052	−	0.0575281i	−0.00168106	−	0.00240537i
$573$	1.11097	−	11.2798i	0.0464113	−	0.471222i
$574$	18.4032	−	22.9090i	0.768135	−	0.956202i
$575$			29.0177i			1.21012i
$576$	7.18443	−	3.51909i	0.299351	−	0.146629i
$577$		−	13.5616i		−	0.564577i	−0.959330	−	0.282289i	$-0.908906\pi$
$577$		−	13.5616i		−	0.564577i	0.959330	−	0.282289i	$-0.0910935\pi$
$578$	−8.23969	−	6.61910i	−0.342726	−	0.275318i
$579$	1.79805	−	18.2559i	0.0747243	−	0.758689i
$580$	4.62896	−	26.1158i	0.192207	−	1.08440i
$581$	39.5493	−	21.1396i	1.64078	−	0.877017i
$582$	−15.9880	+	16.3261i	−0.662725	+	0.676739i
$583$	−2.65673	+	0.528457i	−0.110031	+	0.0218865i
$584$	2.01073	+	15.4326i	0.0832045	+	0.638606i
$585$	−0.0286283	+	0.143924i	−0.00118363	+	0.00595053i
$586$	3.36519	−	17.8944i	0.139015	−	0.739211i
$587$	16.7683	−	20.4323i	0.692103	−	0.843330i	−0.301825	−	0.953363i	$-0.597596\pi$
$587$	16.7683	−	20.4323i	0.692103	−	0.843330i	0.993928	+	0.110033i	$0.0350958\pi$
$588$	3.36495	−	1.89016i	0.138768	−	0.0779491i
$589$	1.73579	−	3.24744i	0.0715221	−	0.133808i
$590$	3.73258	+	1.94517i	0.153668	+	0.0800815i
$591$	16.9756	−	7.03154i	0.698284	−	0.289239i
$592$	4.59817	+	32.6238i	0.188984	+	1.34083i
$593$	−5.59520	−	2.31761i	−0.229768	−	0.0951728i	0.264829	−	0.964295i	$-0.414684\pi$
$593$	−5.59520	−	2.31761i	−0.229768	−	0.0951728i	−0.494597	+	0.869122i	$0.664684\pi$
$594$	−0.271603	−	0.323977i	−0.0111440	−	0.0132930i
$595$	5.36438	+	17.6840i	0.219918	+	0.724972i
$596$	−0.553674	−	1.69659i	−0.0226794	−	0.0694949i
$597$	5.07691	−	0.500032i	0.207784	−	0.0204649i
$598$	1.37160	−	0.287778i	0.0560890	−	0.0117681i
$599$	−13.4899	−	20.1890i	−0.551181	−	0.824901i	0.446369	−	0.894849i	$-0.352717\pi$
$599$	−13.4899	−	20.1890i	−0.551181	−	0.824901i	−0.997551	+	0.0699476i	$0.977717\pi$
$600$	−3.43688	+	9.09461i	−0.140310	+	0.371286i
$601$	34.3599	+	22.9586i	1.40157	+	0.936499i	0.999784	+	0.0207653i	$0.00661028\pi$
$601$	34.3599	+	22.9586i	1.40157	+	0.936499i	0.401786	+	0.915734i	$0.368390\pi$
$602$	1.50212	+	3.52177i	0.0612220	+	0.143537i
$603$	−0.527348	+	1.73843i	−0.0214753	+	0.0707944i
$604$	26.5220	−	27.6558i	1.07917	−	1.12530i
$605$	−10.5430	+	8.65240i	−0.428633	+	0.351770i
$606$	−9.94712	−	2.90414i	−0.404074	−	0.117973i
$607$	11.6252	+	11.6252i	0.471852	+	0.471852i	0.902514	−	0.430661i	$-0.141720\pi$
$607$	11.6252	+	11.6252i	0.471852	+	0.471852i	−0.430661	+	0.902514i	$0.641720\pi$
$608$	4.01736	−	4.46128i	0.162925	−	0.180929i
$609$	−22.4165	+	22.4165i	−0.908361	+	0.908361i
$610$	−10.8862	+	5.96603i	−0.440768	+	0.241558i
$611$	0.424537	+	0.517300i	0.0171749	+	0.0209277i
$612$	3.59424	−	9.21820i	0.145288	−	0.372624i
$613$	−27.7358	−	8.41356i	−1.12024	−	0.339820i	−0.324756	−	0.945798i	$-0.605282\pi$
$613$	−27.7358	−	8.41356i	−1.12024	−	0.339820i	−0.795482	+	0.605978i	$0.792782\pi$
$614$	−6.50855	+	16.1901i	−0.262664	+	0.653378i
$615$	−4.82907	+	7.22721i	−0.194727	+	0.291429i
$616$	0.414919	−	2.49236i	0.0167176	−	0.100420i
$617$	11.1604	−	7.45713i	0.449300	−	0.300213i	−0.310258	−	0.950652i	$-0.600415\pi$
$617$	11.1604	−	7.45713i	0.449300	−	0.300213i	0.759558	+	0.650440i	$0.225415\pi$
$618$	−1.97625	+	3.02571i	−0.0794963	+	0.121712i
$619$	−3.44678	−	34.9957i	−0.138538	−	1.40660i	−0.773374	−	0.633951i	$-0.781432\pi$
$619$	−3.44678	−	34.9957i	−0.138538	−	1.40660i	0.634836	−	0.772647i	$-0.281068\pi$
$620$	−8.64852	−	0.669436i	−0.347333	−	0.0268852i
$621$	8.07833	−	2.45053i	0.324172	−	0.0983365i
$622$	−2.45740	+	27.9446i	−0.0985329	+	1.12048i
$623$	6.26948	−	15.1359i	0.251181	−	0.606406i
$624$	0.463967	+	0.0722594i	0.0185736	+	0.00289269i
$625$	−1.53164	−	3.69771i	−0.0612656	−	0.147908i
$626$	−37.7019	+	11.8689i	−1.50687	+	0.474375i
$627$	−0.279797	−	0.149555i	−0.0111740	−	0.00597264i
$628$	−7.36084	−	5.78745i	−0.293730	−	0.230944i
$629$	31.4977	+	25.8495i	1.25589	+	1.03069i
$630$	−4.36152	+	2.98075i	−0.173767	+	0.118756i
$631$	−1.59159	−	0.316588i	−0.0633603	−	0.0126032i	0.163308	−	0.986575i	$-0.447783\pi$
$631$	−1.59159	−	0.316588i	−0.0633603	−	0.0126032i	−0.226669	+	0.973972i	$0.572783\pi$
$632$	−12.9053	+	11.2871i	−0.513344	+	0.448976i
$633$	−5.35796	−	26.9363i	−0.212960	−	1.07062i
$634$	−0.279395	−	26.7046i	−0.0110962	−	1.06057i
$635$	−8.49442	−	15.8919i	−0.337091	−	0.630652i
$636$	9.75091	−	15.2758i	0.386649	−	0.605723i
$637$	0.225442	+	0.0222041i	0.00893233	+	0.000879757i
$638$	0.486276	+	4.45854i	0.0192519	+	0.176515i
$639$	−4.92924			−0.194998
$640$	−13.4272	−	4.44164i	−0.530755	−	0.175571i
$641$	18.8786			0.745658			0.372829	−	0.927900i	$-0.378388\pi$
$641$	18.8786			0.745658			0.372829	+	0.927900i	$0.378388\pi$
$642$	−0.0244466	−	0.224144i	−0.000964830	−	0.00884627i
$643$	−18.2221	−	1.79472i	−0.718610	−	0.0707769i	−0.267899	−	0.963447i	$-0.586329\pi$
$643$	−18.2221	−	1.79472i	−0.718610	−	0.0707769i	−0.450711	+	0.892670i	$0.648829\pi$
$644$	42.5273	+	27.1463i	1.67581	+	1.06971i
$645$	−0.533871	−	0.998802i	−0.0210211	−	0.0393278i
$646$	−0.0776788	−	7.42454i	−0.00305623	−	0.292115i
$647$	8.91146	+	44.8009i	0.350345	+	1.76131i	0.606902	+	0.794777i	$0.292412\pi$
$647$	8.91146	+	44.8009i	0.350345	+	1.76131i	−0.256557	+	0.966529i	$0.582588\pi$
$648$	2.82212	+	0.188766i	0.110863	+	0.00741544i
$649$	−0.698063	−	0.138853i	−0.0274014	−	0.00545047i
$650$	−0.471139	+	0.321985i	−0.0184796	+	0.0126293i
$651$	8.01467	+	6.57747i	0.314120	+	0.257791i
$652$	9.06734	−	11.5324i	0.355104	−	0.451644i
$653$	2.07743	+	1.11041i	0.0812962	+	0.0434537i	0.511544	−	0.859257i	$-0.329074\pi$
$653$	2.07743	+	1.11041i	0.0812962	+	0.0434537i	−0.430248	+	0.902711i	$0.641574\pi$
$654$	−8.35416	+	2.62996i	−0.326673	+	0.102839i
$655$	−3.65523	−	8.82450i	−0.142822	−	0.344802i
$656$	23.7523	+	14.4713i	0.927373	+	0.565011i
$657$	−2.10567	+	5.08353i	−0.0821498	+	0.198327i
$658$	−2.11040	+	23.9987i	−0.0822721	+	0.935566i
$659$	22.5919	−	6.85317i	0.880055	−	0.266962i	0.182252	−	0.983252i	$-0.441661\pi$
$659$	22.5919	−	6.85317i	0.880055	−	0.266962i	0.697803	+	0.716290i	$0.254161\pi$
$660$	−0.0576781	+	0.745150i	−0.00224512	+	0.0290049i
$661$	−2.48570	−	25.2377i	−0.0966824	−	0.981633i	−0.914073	−	0.405549i	$-0.867080\pi$
$661$	−2.48570	−	25.2377i	−0.0966824	−	0.981633i	0.817391	−	0.576083i	$-0.195420\pi$
$662$	20.9842	−	32.1276i	0.815572	−	1.24868i
$663$	0.482865	−	0.322640i	0.0187529	−	0.0125303i
$664$	24.6775	+	34.5350i	0.957674	+	1.34022i
$665$	−2.20251	+	3.29628i	−0.0854095	+	0.127824i
$666$	−4.34476	+	10.8076i	−0.168356	+	0.418787i
$667$	−85.7006	−	25.9970i	−3.31834	−	1.00661i
$668$	−24.1226	−	9.40556i	−0.933331	−	0.363912i
$669$	4.82783	+	5.88273i	0.186655	+	0.227440i
$670$	2.81635	−	1.54347i	0.108805	−	0.0596293i
$671$	1.48433	−	1.48433i	0.0573017	−	0.0573017i
$672$	10.1135	+	13.5451i	0.390138	+	0.522512i
$673$	−5.46116	−	5.46116i	−0.210512	−	0.210512i	0.593973	−	0.804485i	$-0.297559\pi$
$673$	−5.46116	−	5.46116i	−0.210512	−	0.210512i	−0.804485	+	0.593973i	$0.797559\pi$
$674$	−23.0928	−	6.74213i	−0.889502	−	0.259697i
$675$	−2.65712	+	2.18064i	−0.102273	+	0.0839331i
$676$	−18.7455	−	17.9770i	−0.720981	−	0.691424i
$677$	8.81418	−	29.0565i	0.338757	−	1.11673i	−0.607772	−	0.794111i	$-0.707937\pi$
$677$	8.81418	−	29.0565i	0.338757	−	1.11673i	0.946529	−	0.322619i	$-0.104563\pi$
$678$	−1.96431	−	4.60538i	−0.0754388	−	0.176869i
$679$	−40.1469	−	26.8253i	−1.54070	−	1.02946i
$680$	−15.9418	+	7.19742i	−0.611340	+	0.276009i
$681$	9.33506	+	13.9709i	0.357720	+	0.535366i
$682$	1.43557	−	0.301199i	0.0549708	−	0.0115335i
$683$	21.7619	−	2.14336i	0.832695	−	0.0820133i	0.327320	−	0.944913i	$-0.393854\pi$
$683$	21.7619	−	2.14336i	0.832695	−	0.0820133i	0.505374	+	0.862900i	$0.331354\pi$
$684$	2.01783	−	0.658510i	0.0771537	−	0.0251788i
$685$	5.56237	+	18.3367i	0.212527	+	0.700609i
$686$	−13.7658	−	16.4203i	−0.525580	−	0.626930i
$687$	18.9719	+	7.85840i	0.723822	+	0.299817i
$688$	−3.12177	+	1.84053i	−0.119016	+	0.0701696i
$689$	0.982738	−	0.407063i	0.0374393	−	0.0155079i
$690$	−13.2345	−	6.89695i	−0.503829	−	0.262562i
$691$	13.8015	−	25.8208i	0.525035	−	0.982271i	−0.469993	−	0.882670i	$-0.655743\pi$
$691$	13.8015	−	25.8208i	0.525035	−	0.982271i	0.995027	−	0.0996009i	$-0.0317566\pi$
$692$	−19.0481	−	33.9102i	−0.724100	−	1.28907i
$693$	0.566710	−	0.690539i	0.0215275	−	0.0262314i
$694$	−5.55407	+	29.5337i	−0.210829	+	1.12108i
$695$	−1.91831	+	9.64399i	−0.0727656	+	0.365817i
$696$	−23.7809	−	18.2983i	−0.901411	−	0.693596i
$697$	33.7379	−	6.71088i	1.27791	−	0.254193i
$698$	−21.0317	+	21.4765i	−0.796063	+	0.812896i
$699$	−5.26581	+	2.81464i	−0.199171	+	0.106459i
$700$	−20.2283	−	3.58541i	−0.764557	−	0.135516i
$701$	0.300913	−	3.05522i	0.0113653	−	0.115394i	−0.987828	−	0.155549i	$-0.950285\pi$
$701$	0.300913	−	3.05522i	0.0113653	−	0.115394i	0.999193	+	0.0401552i	$0.0127852\pi$
$702$	0.129426	+	0.103970i	0.00488487	+	0.00392410i
$703$			8.74131i			0.329685i
$704$	2.39002	+	0.0846477i	0.0900771	+	0.00319028i
$705$		−	7.12613i		−	0.268385i
$706$	10.5608	−	13.1464i	0.397461	−	0.494773i
$707$	2.14618	−	21.7906i	0.0807155	−	0.819518i
$708$	3.90304	−	2.72775i	0.146685	−	0.102515i
$709$	38.5483	−	20.6045i	1.44771	−	0.773819i	0.454568	−	0.890712i	$-0.349794\pi$
$709$	38.5483	−	20.6045i	1.44771	−	0.773819i	0.993144	+	0.116893i	$0.0372936\pi$
$710$	6.22593	+	6.09700i	0.233655	+	0.228816i
$711$	−5.94513	+	1.18256i	−0.222960	+	0.0443495i
$712$	14.9729	+	4.03346i	0.561132	+	0.151160i
$713$	−5.71417	+	28.7271i	−0.213997	+	1.07584i
$714$	20.5464	+	3.86392i	0.768929	+	0.144604i
$715$	−0.0278292	+	0.0339100i	−0.00104075	+	0.00126816i
$716$	4.03592	−	14.3812i	0.150829	−	0.537452i
$717$	−7.29331	+	13.6448i	−0.272374	+	0.509575i
$718$	−19.5896	+	37.5903i	−0.731078	+	1.40286i
$719$	−41.3113	+	17.1117i	−1.54065	+	0.638158i	−0.981596	−	0.190972i	$-0.938836\pi$
$719$	−41.3113	+	17.1117i	−1.54065	+	0.638158i	−0.559055	+	0.829130i	$0.688836\pi$
$720$	−3.33103	−	3.72912i	−0.124140	−	0.138976i
$721$	−7.05504	−	2.92229i	−0.262743	−	0.108832i
$722$	−19.3707	+	16.2392i	−0.720903	+	0.604362i
$723$	1.22025	+	4.02262i	0.0453815	+	0.149603i
$724$	−20.3050	+	39.9781i	−0.754629	+	1.48578i
$725$	36.2905	−	3.57430i	1.34779	−	0.132746i
$726$	3.16840	+	15.1012i	0.117590	+	0.560457i
$727$	24.1793	+	36.1869i	0.896761	+	1.34210i	0.939334	+	0.343005i	$0.111445\pi$
$727$	24.1793	+	36.1869i	0.896761	+	1.34210i	−0.0425721	+	0.999093i	$0.513555\pi$
$728$	0.0311360	+	0.991704i	0.00115398	+	0.0367550i
$729$	0.831470	+	0.555570i	0.0307952	+	0.0205767i
$730$	8.94742	−	3.81630i	0.331159	−	0.141247i
$731$	−1.30105	+	4.28898i	−0.0481210	+	0.158634i
$732$	0.293837	+	14.0409i	0.0108605	+	0.518968i
$733$	25.5548	−	20.9723i	0.943889	−	0.774630i	−0.0304913	−	0.999535i	$-0.509707\pi$
$733$	25.5548	−	20.9723i	0.943889	−	0.774630i	0.974381	+	0.224905i	$0.0722072\pi$
$734$	−5.48119	+	18.7739i	−0.202315	+	0.692958i
$735$	−1.70574	−	1.70574i	−0.0629171	−	0.0629171i
$736$	−20.2783	+	43.2349i	−0.747468	+	1.59366i
$737$	−0.384009	+	0.384009i	−0.0141451	+	0.0141451i
$738$	4.72599	+	8.62347i	0.173966	+	0.317434i
$739$	−20.3847	−	24.8388i	−0.749863	−	0.913710i	0.248630	−	0.968599i	$-0.420020\pi$
$739$	−20.3847	−	24.8388i	−0.749863	−	0.913710i	−0.998492	+	0.0548883i	$0.982520\pi$
$740$	18.8557	−	8.27663i	0.693150	−	0.304255i
$741$	0.119219	+	0.0361648i	0.00437964	+	0.00132855i
$742$	35.5300	+	14.2834i	1.30435	+	0.524359i
$743$	19.0594	−	28.5244i	0.699220	−	1.04646i	−0.296589	−	0.955005i	$-0.595849\pi$
$743$	19.0594	−	28.5244i	0.699220	−	1.04646i	0.995809	−	0.0914520i	$-0.0291508\pi$
$744$	−5.19337	+	8.32674i	−0.190398	+	0.305273i
$745$	−0.927463	+	0.619711i	−0.0339796	+	0.0227044i
$746$	16.1667	+	10.5593i	0.591907	+	0.386604i
$747$	1.47093	+	14.9346i	0.0538185	+	0.546429i
$748$	2.24661	−	1.92380i	0.0821442	−	0.0703411i
$749$	0.455916	−	0.138301i	0.0166588	−	0.00505340i
$750$	14.8586	+	1.30664i	0.542559	+	0.0477117i
$751$	−13.2827	+	32.0672i	−0.484691	+	1.17015i	0.472667	+	0.881241i	$0.343291\pi$
$751$	−13.2827	+	32.0672i	−0.484691	+	1.17015i	−0.957357	+	0.288906i	$0.906709\pi$
$752$	−22.7827	+	0.953973i	−0.830800	+	0.0347878i
$753$	−3.85743	−	9.31266i	−0.140573	−	0.339372i
$754$	−0.528854	−	1.67992i	−0.0192597	−	0.0611792i
$755$	−21.1217	−	11.2898i	−0.768698	−	0.410878i
$756$	0.710117	+	5.93420i	0.0258267	+	0.215825i
$757$	14.5785	+	11.9643i	0.529866	+	0.434850i	0.860904	−	0.508768i	$-0.169899\pi$
$757$	14.5785	+	11.9643i	0.529866	+	0.434850i	−0.331038	+	0.943617i	$0.607399\pi$
$758$	18.3794	+	26.8933i	0.667568	+	0.976807i
$759$	2.47510	+	0.492329i	0.0898406	+	0.0178704i
$760$	−3.36316	−	1.66413i	−0.121995	−	0.0603642i
$761$	−6.52767	−	32.8168i	−0.236628	−	1.18961i	−0.898152	−	0.439685i	$-0.855090\pi$
$761$	−6.52767	−	32.8168i	−0.236628	−	1.18961i	0.661524	−	0.749924i	$-0.269910\pi$
$762$	−20.3850	+	0.213277i	−0.738470	+	0.00772620i
$763$	−8.72395	−	16.3214i	−0.315828	−	0.590873i
$764$	4.88668	+	22.1359i	0.176794	+	0.800848i
$765$	−6.15431	−	0.606147i	−0.222510	−	0.0219153i
$766$	4.99447	−	0.544728i	0.180457	−	0.0196818i
$767$	0.279492			0.0100919
$768$	−11.4763	+	11.1487i	−0.414116	+	0.402295i
$769$	27.6208			0.996032			0.498016	−	0.867168i	$-0.334062\pi$
$769$	27.6208			0.996032			0.498016	+	0.867168i	$0.334062\pi$
$770$	−1.56992	+	0.171225i	−0.0565760	+	0.00617053i
$771$	−26.9024	−	2.64966i	−0.968868	−	0.0954251i
$772$	7.90886	+	35.8258i	0.284646	+	1.28940i
$773$	−0.298229	−	0.557947i	−0.0107265	−	0.0200680i	0.876501	−	0.481400i	$-0.159872\pi$
$773$	−0.298229	−	0.557947i	−0.0107265	−	0.0200680i	−0.887227	+	0.461332i	$0.847372\pi$
$774$	−1.28119	+	0.0134044i	−0.0460514	+	0.000481810i
$775$	−2.32671	−	11.6972i	−0.0835780	−	0.420175i
$776$	20.2681	−	40.9614i	0.727584	−	1.47043i
$777$	−24.1401	−	4.80176i	−0.866021	−	0.172262i
$778$	−21.1111	−	30.8904i	−0.756869	−	1.10747i
$779$	5.70443	+	4.68151i	0.204382	+	0.167732i
$780$	−0.0348715	−	0.291408i	−0.00124860	−	0.0104341i
$781$	−1.29955	−	0.694624i	−0.0465015	−	0.0248556i
$782$	17.7348	+	56.3352i	0.634194	+	2.01454i
$783$	−4.05978	−	9.80117i	−0.145085	−	0.350265i
$784$	−5.22501	+	5.68170i	−0.186607	+	0.202918i
$785$	−2.23965	+	5.40699i	−0.0799364	+	0.192984i
$786$	−10.7644	−	0.946602i	−0.383953	−	0.0337642i
$787$	34.1985	−	10.3740i	1.21905	−	0.369794i	0.385741	−	0.922607i	$-0.373946\pi$
$787$	34.1985	−	10.3740i	1.21905	−	0.369794i	0.833305	+	0.552813i	$0.186446\pi$
$788$	−27.9130	+	23.9023i	−0.994361	+	0.851484i
$789$	−0.491637	−	4.99167i	−0.0175027	−	0.177708i
$790$	8.97178	+	5.85992i	0.319202	+	0.208487i
$791$	8.79652	−	5.87765i	0.312768	−	0.208985i
$792$	0.717426	+	0.447457i	0.0254926	+	0.0158997i
$793$	−0.457964	+	0.685392i	−0.0162628	+	0.0243390i
$794$	19.0310	+	7.65065i	0.675386	+	0.271511i
$795$	−10.8394	−	3.28808i	−0.384433	−	0.116616i
$796$	−9.34253	+	4.10086i	−0.331137	+	0.145351i
$797$	−10.4106	−	12.6853i	−0.368761	−	0.449336i	0.555261	−	0.831676i	$-0.312618\pi$
$797$	−10.4106	−	12.6853i	−0.368761	−	0.449336i	−0.924022	+	0.382340i	$0.875118\pi$
$798$	2.15549	+	3.93311i	0.0763036	+	0.139230i
$799$	−19.9415	+	19.9415i	−0.705480	+	0.705480i
$800$	0.891508	−	19.4243i	0.0315196	−	0.686751i
$801$	3.87666	+	3.87666i	0.136975	+	0.136975i
$802$	−4.62261	+	15.8332i	−0.163230	+	0.559089i
$803$	−1.27151	+	1.04350i	−0.0448704	+	0.0368242i
$804$	−0.0760184	−	3.63252i	−0.00268096	−	0.128109i
$805$	9.15394	−	30.1765i	0.322634	−	1.06358i
$806$	−0.529825	+	0.225983i	−0.0186623	+	0.00795993i
$807$	9.84375	+	6.57739i	0.346517	+	0.231535i
$808$	20.7146	−	0.650365i	0.728737	−	0.0228798i
$809$	−10.1518	−	15.1932i	−0.356917	−	0.534164i	0.608948	−	0.793210i	$-0.291592\pi$
$809$	−10.1518	−	15.1932i	−0.356917	−	0.534164i	−0.965865	+	0.259046i	$0.916592\pi$
$810$	−0.363009	−	1.73017i	−0.0127548	−	0.0607919i
$811$	−37.6143	+	3.70468i	−1.32082	+	0.130089i	−0.733733	−	0.679438i	$-0.762224\pi$
$811$	−37.6143	+	3.70468i	−1.32082	+	0.130089i	−0.587082	+	0.809527i	$0.699724\pi$
$812$	28.7117	−	56.5298i	1.00758	−	1.98381i
$813$	−6.52817	−	21.5205i	−0.228953	−	0.754756i
$814$	−2.66846	+	2.23707i	−0.0935294	+	0.0784094i
$815$	−8.47126	−	3.50891i	−0.296735	−	0.122912i
$816$	−1.11401	+	19.7569i	−0.0389983	+	0.691629i
$817$	−0.888317	+	0.367953i	−0.0310783	+	0.0128730i
$818$	−15.1891	+	29.1462i	−0.531074	+	1.01907i
$819$	−0.165363	+	0.309372i	−0.00577824	+	0.0108103i
$820$	4.69720	−	16.7376i	0.164033	−	0.584501i
$821$	−33.8539	+	41.2511i	−1.18151	+	1.43967i	−0.309011	+	0.951058i	$0.599998\pi$
$821$	−33.8539	+	41.2511i	−1.18151	+	1.43967i	−0.872499	+	0.488616i	$0.837502\pi$
$822$	21.3047	+	4.00654i	0.743088	+	0.139744i
$823$	7.42522	−	37.3291i	0.258827	−	1.30121i	−0.604516	−	0.796593i	$-0.706633\pi$
$823$	7.42522	−	37.3291i	0.258827	−	1.30121i	0.863343	−	0.504618i	$-0.168367\pi$
$824$	1.88005	−	6.97907i	0.0654947	−	0.243127i
$825$	−1.00782	+	0.200468i	−0.0350878	+	0.00697940i
$826$	7.18875	+	7.03988i	0.250129	+	0.244949i
$827$	−20.8298	+	11.1338i	−0.724323	+	0.387159i	−0.791978	−	0.610550i	$-0.790948\pi$
$827$	−20.8298	+	11.1338i	−0.724323	+	0.387159i	0.0676544	+	0.997709i	$0.478448\pi$
$828$	−13.8389	+	9.67172i	−0.480936	+	0.336115i
$829$	−1.93702	+	19.6669i	−0.0672754	+	0.683059i	0.901108	+	0.433594i	$0.142755\pi$
$829$	−1.93702	+	19.6669i	−0.0672754	+	0.683059i	−0.968384	+	0.249465i	$0.919745\pi$
$830$	16.6148	−	20.6827i	0.576709	−	0.717908i
$831$		−	13.3691i		−	0.463769i
$832$	−0.926984	+	0.150497i	−0.0321374	+	0.00521755i
$833$			9.54656i			0.330769i
$834$	8.67250	+	6.96678i	0.300304	+	0.241240i
$835$	−1.58619	+	16.1049i	−0.0548924	+	0.557332i
$836$	0.624780	+	0.110741i	0.0216085	+	0.00383004i
$837$	−3.05992	+	1.63556i	−0.105766	+	0.0565333i
$838$	1.06055	−	1.08298i	0.0366362	−	0.0374109i
$839$	32.9421	−	6.55260i	1.13729	−	0.226221i	0.409691	−	0.912224i	$-0.365637\pi$
$839$	32.9421	−	6.55260i	1.13729	−	0.226221i	0.727598	+	0.686003i	$0.240637\pi$
$840$	6.44312	−	8.37360i	0.222309	−	0.288917i
$841$	−16.2988	+	81.9394i	−0.562026	+	2.82550i
$842$	−5.52940	+	29.4026i	−0.190556	+	1.01328i
$843$	−2.08044	+	2.53502i	−0.0716541	+	0.0873108i
$844$	26.9008	+	47.8898i	0.925962	+	1.64844i
$845$	−7.65239	+	14.3166i	−0.263250	+	0.492507i
$846$	−7.14938	−	3.72579i	−0.245801	−	0.128095i
$847$	−30.1221	+	12.4770i	−1.03501	+	0.428714i
$848$	−9.06116	+	35.0943i	−0.311161	+	1.20514i
$849$	20.6237	+	8.54263i	0.707805	+	0.293182i
$850$	−15.4499	−	18.4292i	−0.529927	−	0.632115i
$851$	−20.1840	−	66.5376i	−0.691897	−	2.28088i
$852$	9.37203	−	3.05852i	0.321081	−	0.104783i
$853$	−4.07670	+	0.401520i	−0.139583	+	0.0137478i	−0.167568	−	0.985861i	$-0.553591\pi$
$853$	−4.07670	+	0.401520i	−0.139583	+	0.0137478i	0.0279841	+	0.999608i	$0.491091\pi$
$854$	−29.0430	+	6.09355i	−0.993830	+	0.208517i
$855$	−0.737051	−	1.10308i	−0.0252066	−	0.0377244i
$856$	0.185559	+	0.411000i	0.00634228	+	0.0140477i
$857$	14.1212	+	9.43546i	0.482370	+	0.322309i	0.772869	−	0.634566i	$-0.218821\pi$
$857$	14.1212	+	9.43546i	0.482370	+	0.322309i	−0.290499	+	0.956875i	$0.593821\pi$
$858$	0.0194706	+	0.0456494i	0.000664715	+	0.00155844i
$859$	0.0411455	−	0.135638i	0.00140387	−	0.00462793i	−0.956236	−	0.292598i	$-0.905480\pi$
$859$	0.0411455	−	0.135638i	0.00140387	−	0.00462793i	0.957639	+	0.287970i	$0.0929803\pi$
$860$	1.63480	+	1.56778i	0.0557462	+	0.0534608i
$861$	−16.0621	+	13.1818i	−0.547393	+	0.449234i
$862$	−22.1237	−	6.45917i	−0.753535	−	0.220000i
$863$	5.71487	+	5.71487i	0.194536	+	0.194536i	0.797653	−	0.603117i	$-0.206075\pi$
$863$	5.71487	+	5.71487i	0.194536	+	0.194536i	−0.603117	+	0.797653i	$0.706075\pi$
$864$	−5.48287	+	1.39218i	−0.186531	+	0.0473630i
$865$	−17.1895	+	17.1895i	−0.584461	+	0.584461i
$866$	−44.8422	+	24.5753i	−1.52380	+	0.835101i
$867$	4.74111	+	5.77706i	0.161016	+	0.196199i
$868$	−19.3196	−	7.53285i	−0.655751	−	0.255682i
$869$	−1.73403	−	0.526011i	−0.0588228	−	0.0178437i
$870$	−6.99537	+	17.4010i	−0.237165	+	0.589950i
$871$	0.118480	−	0.177317i	0.00401453	−	0.00600816i
$872$	14.2520	−	10.1840i	0.482635	−	0.344874i
$873$	13.4348	−	8.97687i	0.454700	−	0.303821i
$874$	−6.92857	+	10.6079i	−0.234362	+	0.358818i
$875$	3.08928	+	31.3659i	0.104437	+	1.06036i
$876$	0.849278	−	10.9719i	0.0286944	−	0.370707i
$877$	44.5327	−	13.5089i	1.50376	−	0.456162i	0.572315	−	0.820034i	$-0.306045\pi$
$877$	44.5327	−	13.5089i	1.50376	−	0.456162i	0.931449	+	0.363872i	$0.118545\pi$
$878$	4.28148	−	48.6872i	0.144493	−	1.64312i
$879$	−4.92707	+	11.8950i	−0.166186	+	0.401208i
$880$	−0.352691	−	1.45255i	−0.0118892	−	0.0489656i
$881$	11.1228	+	26.8527i	0.374735	+	0.904690i	0.992934	+	0.118669i	$0.0378626\pi$
$881$	11.1228	+	26.8527i	0.374735	+	0.904690i	−0.618199	+	0.786022i	$0.712137\pi$
$882$	−2.60312	+	0.819485i	−0.0876517	+	0.0275935i
$883$	25.5400	+	13.6514i	0.859490	+	0.459407i	0.841390	−	0.540429i	$-0.181738\pi$
$883$	25.5400	+	13.6514i	0.859490	+	0.459407i	0.0181005	+	0.999836i	$0.494238\pi$
$884$	−0.717884	+	0.913051i	−0.0241451	+	0.0307092i
$885$	−2.30065	−	1.88810i	−0.0773356	−	0.0634677i
$886$	15.7056	−	10.7335i	0.527639	−	0.360599i
$887$	−47.3986	−	9.42817i	−1.59149	−	0.316567i	−0.681699	−	0.731633i	$-0.738759\pi$
$887$	−47.3986	−	9.42817i	−1.59149	−	0.316567i	−0.909791	+	0.415066i	$0.863759\pi$
$888$	1.55478	−	23.2446i	0.0521751	−	0.780036i
$889$	−8.40377	−	42.2486i	−0.281853	−	1.41697i
$890$	−0.101397	−	9.69151i	−0.00339883	−	0.324860i
$891$	0.140919	+	0.263641i	0.00472097	+	0.00883231i
$892$	−12.8294	−	8.18933i	−0.429560	−	0.274199i
$893$	−6.02088	−	0.593005i	−0.201481	−	0.0198442i
$894$	0.136823	+	1.25450i	0.00457605	+	0.0419566i
$895$	−9.33590			−0.312065
$896$	−27.6335	−	19.4781i	−0.923170	−	0.650718i
$897$	−0.990987			−0.0330881
$898$	5.02242	+	46.0493i	0.167600	+	1.53669i
$899$	36.6308	+	3.60782i	1.22171	+	0.120328i
$900$	3.69897	−	5.79480i	0.123299	−	0.193160i
$901$	21.1312	+	39.5338i	0.703984	+	1.31706i
$902$	0.0307542	+	2.93948i	0.00102400	+	0.0978740i
$903$	−0.528174	−	2.65531i	−0.0175765	−	0.0883632i
$904$	6.59234	+	7.53746i	0.219258	+	0.250692i
$905$	27.4871	+	5.46752i	0.913701	+	0.181746i
$906$	−22.3698	+	15.2879i	−0.743187	+	0.507908i
$907$	−9.24231	−	7.58497i	−0.306886	−	0.251855i	0.468326	−	0.883556i	$-0.344857\pi$
$907$	−9.24231	−	7.58497i	−0.306886	−	0.251855i	−0.775212	+	0.631701i	$0.782357\pi$
$908$	−26.4176	−	20.7708i	−0.876700	−	0.689303i
$909$	6.46212	+	3.45408i	0.214335	+	0.114564i
$910$	0.591527	−	0.186218i	0.0196089	−	0.00617305i
$911$	−0.158722	−	0.383188i	−0.00525868	−	0.0126956i	0.921228	−	0.389022i	$-0.127187\pi$
$911$	−0.158722	−	0.383188i	−0.00525868	−	0.0126956i	−0.926487	+	0.376327i	$0.877187\pi$
$912$	−3.42794	+	2.50407i	−0.113510	+	0.0829180i
$913$	−1.71677	+	4.14466i	−0.0568169	+	0.137168i
$914$	0.442123	−	5.02765i	0.0146241	−	0.166300i
$915$	8.39989	−	2.54808i	0.277692	−	0.0842369i
$916$	−40.9475	−	3.16953i	−1.35294	−	0.104724i
$917$	−2.23804	−	22.7232i	−0.0739066	−	0.750387i
$918$	−3.82581	+	5.85748i	−0.126271	+	0.193326i
$919$	33.8353	−	22.6080i	1.11612	−	0.745770i	0.146219	−	0.989252i	$-0.453290\pi$
$919$	33.8353	−	22.6080i	1.11612	−	0.745770i	0.969905	+	0.243482i	$0.0782897\pi$
$920$	29.4424	+	4.90146i	0.970687	+	0.161596i
$921$	6.85493	−	10.2591i	0.225878	−	0.338050i
$922$	2.00380	−	4.98447i	0.0659917	−	0.164155i
$923$	0.553728	+	0.167971i	0.0182262	+	0.00552885i
$924$	−0.649026	+	1.66457i	−0.0213514	+	0.0547602i
$925$	17.9610	+	21.8855i	0.590554	+	0.719592i
$926$	46.6669	−	25.5752i	1.53357	−	0.840454i
$927$	1.80697	−	1.80697i	0.0593485	−	0.0593485i
$928$	56.5687	+	20.0352i	1.85696	+	0.657687i
$929$	−29.5646	−	29.5646i	−0.969983	−	0.969983i	0.0295794	−	0.999562i	$-0.490583\pi$
$929$	−29.5646	−	29.5646i	−0.969983	−	0.969983i	−0.999562	+	0.0295794i	$0.990583\pi$
$930$	5.88791	+	1.71902i	0.193072	+	0.0563689i
$931$	−1.58313	+	1.29924i	−0.0518848	+	0.0425808i
$932$	8.26553	−	8.61887i	0.270746	−	0.282320i
$933$	5.75811	−	18.9820i	0.188512	−	0.621441i
$934$	−22.1639	−	51.9639i	−0.725225	−	1.70031i
$935$	−1.53711	−	1.02706i	−0.0502689	−	0.0335886i
$936$	−0.310591	−	0.117373i	−0.0101520	−	0.00383647i
$937$	16.1548	+	24.1773i	0.527754	+	0.789839i	0.995574	−	0.0939848i	$-0.0299605\pi$
$937$	16.1548	+	24.1773i	0.527754	+	0.789839i	−0.467820	+	0.883824i	$0.654960\pi$
$938$	7.51368	−	1.57646i	0.245330	−	0.0514731i
$939$	27.8145	−	2.73949i	0.907691	−	0.0893998i
$940$	4.42166	+	13.5490i	0.144219	+	0.441920i
$941$	4.03257	+	13.2936i	0.131458	+	0.433359i	0.997815	−	0.0660655i	$-0.0210446\pi$
$941$	4.03257	+	13.2936i	0.131458	+	0.433359i	−0.866357	+	0.499425i	$0.833545\pi$
$942$	4.25366	+	5.07392i	0.138592	+	0.165317i
$943$	−54.2311	−	22.4632i	−1.76601	−	0.731504i
$944$	−5.72838	+	7.60810i	−0.186443	+	0.247622i
$945$	3.45114	−	1.42951i	0.112266	−	0.0465020i
$946$	−0.339663	−	0.177010i	−0.0110434	−	0.00575509i
$947$	−10.7487	+	20.1094i	−0.349286	+	0.653468i	−0.993807	−	0.111118i	$-0.964557\pi$
$947$	−10.7487	+	20.1094i	−0.349286	+	0.653468i	0.644521	+	0.764587i	$0.277057\pi$
$948$	10.5698	−	5.93729i	0.343291	−	0.192834i
$949$	0.409770	−	0.499306i	0.0133017	−	0.0162081i
$950$	0.953495	−	5.07020i	0.0309354	−	0.164499i
$951$	−3.68409	+	18.5212i	−0.119465	+	0.600590i
$952$	−41.4626	+	5.40220i	−1.34381	+	0.175086i
$953$	−11.8169	+	2.35054i	−0.382788	+	0.0761413i	−0.382734	−	0.923859i	$-0.625017\pi$
$953$	−11.8169	+	2.35054i	−0.382788	+	0.0761413i	−5.45595e−5		1.00000i	$0.500017\pi$
$954$	−8.96601	+	9.15561i	−0.290285	+	0.296424i
$955$	12.4956	−	6.67904i	0.404348	−	0.216129i
$956$	5.40046	−	30.4685i	0.174663	−	0.985422i
$957$	0.310848	−	3.15609i	0.0100483	−	0.102022i
$958$	15.7799	+	12.6763i	0.509825	+	0.409552i
$959$			45.8065i			1.47917i
$960$	8.64719	+	5.02338i	0.279087	+	0.162129i
$961$			18.9618i			0.611671i
$962$	0.856357	−	1.06602i	0.0276101	−	0.0343700i
$963$	−0.0156273	+	0.158666i	−0.000503581	+	0.00511295i
$964$	−4.81606	−	6.89112i	−0.155115	−	0.221948i
$965$	20.2235	−	10.8097i	0.651018	−	0.347977i
$966$	−25.4890	−	24.9611i	−0.820094	−	0.803112i
$967$	5.13925	−	1.02226i	0.165267	−	0.0328737i	−0.111763	−	0.993735i	$-0.535650\pi$
$967$	5.13925	−	1.02226i	0.165267	−	0.0328737i	0.277030	+	0.960861i	$0.410650\pi$
$968$	−15.3942	−	26.7461i	−0.494788	−	0.859653i
$969$	−1.02427	+	5.14935i	−0.0329043	+	0.165421i
$970$	−28.0726	−	5.27929i	−0.901356	−	0.169508i
$971$	10.2451	−	12.4836i	0.328780	−	0.400619i	−0.582217	−	0.813034i	$-0.697814\pi$
$971$	10.2451	−	12.4836i	0.328780	−	0.400619i	0.910996	+	0.412415i	$0.135314\pi$
$972$	−1.92561	−	0.540399i	−0.0617639	−	0.0173333i
$973$	−11.0805	+	20.7302i	−0.355226	+	0.664580i
$974$	2.46211	−	4.72453i	0.0788912	−	0.151384i
$975$	0.372798	−	0.154418i	0.0119391	−	0.00494533i
$976$	−9.27087	−	26.5139i	−0.296753	−	0.848689i
$977$	−9.68227	−	4.01053i	−0.309763	−	0.128308i	0.222386	−	0.974959i	$-0.428616\pi$
$977$	−9.68227	−	4.01053i	−0.309763	−	0.128308i	−0.532149	+	0.846651i	$0.678616\pi$
$978$	−7.94943	+	6.66432i	−0.254195	+	0.213101i
$979$	0.475751	+	1.56834i	0.0152051	+	0.0501244i
$980$	4.30153	+	2.18476i	0.137407	+	0.0697895i
$981$	6.16326	−	0.607028i	0.196778	−	0.0193809i
$982$	−12.0244	−	57.3106i	−0.383715	−	1.82886i
$983$	−13.2788	−	19.8731i	−0.423527	−	0.633853i	0.556936	−	0.830555i	$-0.311977\pi$
$983$	−13.2788	−	19.8731i	−0.423527	−	0.633853i	−0.980463	+	0.196702i	$0.936977\pi$
$984$	−14.3363	−	13.4635i	−0.457026	−	0.429201i
$985$	19.0979	+	12.7608i	0.608509	+	0.406592i
$986$	68.2701	−	29.1189i	2.17416	−	0.927334i
$987$	4.94503	−	16.3016i	0.157402	−	0.518885i
$988$	−0.249113	+	0.00521324i	−0.00792535	+	0.000165855i
$989$	5.91212	−	4.85196i	0.187995	−	0.154283i
$990$	0.148110	−	0.507298i	0.00470723	−	0.0161230i
$991$	−13.0512	−	13.0512i	−0.414584	−	0.414584i	0.468748	−	0.883332i	$-0.344705\pi$
$991$	−13.0512	−	13.0512i	−0.414584	−	0.414584i	−0.883332	+	0.468748i	$0.844705\pi$
$992$	4.70761	−	19.0542i	0.149467	−	0.604970i
$993$	−19.1867	+	19.1867i	−0.608872	+	0.608872i
$994$	10.0114	+	18.2677i	0.317543	+	0.579417i
$995$	4.04559	+	4.92957i	0.128254	+	0.156278i
$996$	−12.0634	−	27.4827i	−0.382244	−	0.870822i
$997$	−26.7890	−	8.12636i	−0.848417	−	0.257365i	−0.164005	−	0.986460i	$-0.552441\pi$
$997$	−26.7890	−	8.12636i	−0.848417	−	0.257365i	−0.684412	+	0.729095i	$0.739941\pi$
$998$	−4.15502	−	1.67036i	−0.131525	−	0.0528742i
$999$	4.57599	−	6.84845i	0.144778	−	0.216675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.349.32	✓	512
128.117	even	32	inner	384.2.v.a.373.32	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.349.32	✓	512	1.1	even	1	trivial
384.2.v.a.373.32	yes	512	128.117	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)

\(f(q)\)	\(=\)	\(q+(1.40588 - 0.153334i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(1.95298 - 0.431136i) q^{4} +(-0.589270 - 1.10245i) q^{5} +(-1.41414 + 0.0147953i) q^{6} +(-0.582982 - 2.93085i) q^{7} +(2.67954 - 0.905582i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(1.40588 - 0.153334i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(1.95298 - 0.431136i) q^{4} +(-0.589270 - 1.10245i) q^{5} +(-1.41414 + 0.0147953i) q^{6} +(-0.582982 - 2.93085i) q^{7} +(2.67954 - 0.905582i) q^{8} +(0.980785 + 0.195090i) q^{9} +(-0.997484 - 1.45955i) q^{10} +(0.231083 + 0.189645i) q^{11} +(-1.98583 + 0.237635i) q^{12} +(-0.103529 - 0.0553373i) q^{13} +(-1.26900 - 4.03102i) q^{14} +(0.478374 + 1.15490i) q^{15} +(3.62824 - 1.68400i) q^{16} +(1.89316 - 4.57049i) q^{17} +(1.40878 + 0.123886i) q^{18} +(1.01558 - 0.308074i) q^{19} +(-1.62614 - 1.89900i) q^{20} +(0.292901 + 2.97388i) q^{21} +(0.353954 + 0.231185i) q^{22} +(-7.01912 + 4.69003i) q^{23} +(-2.75540 + 0.638580i) q^{24} +(1.90970 - 2.85807i) q^{25} +(-0.154034 - 0.0619230i) q^{26} +(-0.956940 - 0.290285i) q^{27} +(-2.40215 - 5.47254i) q^{28} +(6.73009 + 8.20064i) q^{29} +(0.849620 + 1.55029i) q^{30} +(2.45339 - 2.45339i) q^{31} +(4.84265 - 2.92383i) q^{32} +(-0.211382 - 0.211382i) q^{33} +(1.96074 - 6.71583i) q^{34} +(-2.88757 + 2.36977i) q^{35} +(1.99956 - 0.0418452i) q^{36} +(-2.39095 + 7.88189i) q^{37} +(1.38055 - 0.588837i) q^{38} +(0.0976063 + 0.0652185i) q^{39} +(-2.57733 - 2.42042i) q^{40} +(3.86309 + 5.78153i) q^{41} +(0.867779 + 4.13599i) q^{42} +(-0.901624 + 0.0888022i) q^{43} +(0.533063 + 0.270744i) q^{44} +(-0.362871 - 1.19622i) q^{45} +(-9.14888 + 7.66987i) q^{46} +(-5.26673 - 2.18155i) q^{47} +(-3.77583 + 1.32026i) q^{48} +(-1.78285 + 0.738480i) q^{49} +(2.24657 - 4.31091i) q^{50} +(-2.33203 + 4.36292i) q^{51} +(-0.226047 - 0.0634375i) q^{52} +(-5.74843 + 7.00448i) q^{53} +(-1.38985 - 0.261373i) q^{54} +(0.0729032 - 0.366509i) q^{55} +(-4.21625 - 7.32538i) q^{56} +(-1.04089 + 0.207046i) q^{57} +(10.7191 + 10.4971i) q^{58} +(-2.09975 + 1.12234i) q^{59} +(1.43217 + 2.04924i) q^{60} +(0.688277 - 6.98819i) q^{61} +(3.07297 - 3.82534i) q^{62} -2.98827i q^{63} +(6.35984 - 4.85308i) q^{64} +0.146744i q^{65} +(-0.329589 - 0.264765i) q^{66} +(-0.178064 + 1.80791i) q^{67} +(1.72679 - 9.74228i) q^{68} +(7.44503 - 3.97945i) q^{69} +(-3.69620 + 3.77436i) q^{70} +(-4.83452 + 0.961647i) q^{71} +(2.80472 - 0.365429i) q^{72} +(-1.07346 + 5.39664i) q^{73} +(-2.15282 + 11.4476i) q^{74} +(-2.18064 + 2.65712i) q^{75} +(1.85059 - 1.03952i) q^{76} +(0.421104 - 0.787830i) q^{77} +(0.147223 + 0.0767228i) q^{78} +(-5.60019 + 2.31968i) q^{79} +(-3.99454 - 3.00762i) q^{80} +(0.923880 + 0.382683i) q^{81} +(6.31754 + 7.53577i) q^{82} +(4.35626 + 14.3607i) q^{83} +(1.85418 + 5.68164i) q^{84} +(-6.15431 + 0.606147i) q^{85} +(-1.25396 + 0.263094i) q^{86} +(-5.89388 - 8.82082i) q^{87} +(0.790935 + 0.298897i) q^{88} +(4.55847 + 3.04587i) q^{89} +(-0.693573 - 1.62610i) q^{90} +(-0.101830 + 0.335688i) q^{91} +(-11.6861 + 12.1857i) q^{92} +(-2.68205 + 2.20110i) q^{93} +(-7.73887 - 2.25942i) q^{94} +(-0.938088 - 0.938088i) q^{95} +(-5.10591 + 2.43509i) q^{96} +(11.4254 - 11.4254i) q^{97} +(-2.39323 + 1.31158i) q^{98} +(0.189645 + 0.231083i) 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

Related objects

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