LMFDB - Embedded newform 230.2.l.a.103.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			103.10
Character	$\chi$	$=$	230.103
Dual form			230.2.l.a.67.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212565 - 0.977147i) q^{2} +(0.521893 - 0.390684i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.172358 - 2.22942i) q^{5} +(-0.270819 - 0.593012i) q^{6} +(0.196919 - 2.75328i) q^{7} +(-0.599278 + 0.800541i) q^{8} +(-0.725460 + 2.47069i) q^{9} +(-2.21510 - 0.305477i) q^{10} +(-0.171272 + 0.266505i) q^{11} +(-0.637026 + 0.138577i) q^{12} +(-0.610881 + 0.0436911i) q^{13} +(-2.64850 - 0.777670i) q^{14} +(-0.960949 - 1.09618i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.930625 - 2.49510i) q^{17} +(2.26002 + 1.23406i) q^{18} +(1.33902 - 2.93205i) q^{19} +(-0.769350 + 2.09955i) q^{20} +(-0.972892 - 1.51385i) q^{21} +(0.224008 + 0.224008i) q^{22} +(4.61891 - 1.29062i) q^{23} +0.651925i q^{24} +(-4.94059 + 0.768515i) q^{25} +(-0.0871595 + 0.606208i) q^{26} +(1.27012 + 3.40532i) q^{27} +(-1.32288 + 2.42267i) q^{28} +(5.55597 - 2.53733i) q^{29} +(-1.27539 + 0.705979i) q^{30} +(1.29230 + 8.98814i) q^{31} +(0.877679 - 0.479249i) q^{32} +(0.0147334 + 0.206000i) q^{33} +(-2.24026 - 1.43973i) q^{34} +(-6.17215 + 0.0355368i) q^{35} +(1.68626 - 1.94605i) q^{36} +(1.15696 + 2.11882i) q^{37} +(-2.58041 - 1.93167i) q^{38} +(-0.301745 + 0.261463i) q^{39} +(1.88803 + 1.19806i) q^{40} +(-7.62326 + 2.23839i) q^{41} +(-1.68606 + 0.628867i) q^{42} +(6.26113 + 8.36389i) q^{43} +(0.266505 - 0.171272i) q^{44} +(5.63323 + 1.19151i) q^{45} +(-0.279308 - 4.78769i) q^{46} +(4.91328 - 4.91328i) q^{47} +(0.637026 + 0.138577i) q^{48} +(-0.613031 - 0.0881405i) q^{49} +(-0.299245 + 4.99104i) q^{50} +(-0.489110 - 1.66576i) q^{51} +(0.573827 + 0.214026i) q^{52} +(5.77904 + 0.413325i) q^{53} +(3.59748 - 0.517240i) q^{54} +(0.623671 + 0.335903i) q^{55} +(2.08611 + 1.80762i) q^{56} +(-0.446679 - 2.05335i) q^{57} +(-1.29834 - 5.96835i) q^{58} +(-3.03630 - 2.63097i) q^{59} +(0.418741 + 1.39631i) q^{60} +(-10.7039 + 1.53899i) q^{61} +(9.05743 + 0.647801i) q^{62} +(6.65964 + 2.48392i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(0.202696 + 1.35438i) q^{65} +(0.204424 + 0.0293918i) q^{66} +(7.50837 + 1.63335i) q^{67} +(-1.88303 + 1.88303i) q^{68} +(1.90635 - 2.47810i) q^{69} +(-1.27726 + 6.03865i) q^{70} +(7.02619 - 4.51545i) q^{71} +(-1.54314 - 2.06139i) q^{72} +(-9.02358 + 3.36562i) q^{73} +(2.31633 - 0.680136i) q^{74} +(-2.27821 + 2.33129i) q^{75} +(-2.43603 + 2.11083i) q^{76} +(0.700037 + 0.524041i) q^{77} +(0.191348 + 0.350427i) q^{78} +(-4.91108 + 5.66768i) q^{79} +(1.57201 - 1.59022i) q^{80} +(-4.50540 - 2.89544i) q^{81} +(0.566796 + 7.92485i) q^{82} +(0.897247 - 0.489934i) q^{83} +(0.256098 + 1.78120i) q^{84} +(-5.72302 - 1.64470i) q^{85} +(9.50365 - 4.34017i) q^{86} +(1.90833 - 3.49484i) q^{87} +(-0.110709 - 0.296821i) q^{88} +(-0.532679 + 3.70486i) q^{89} +(2.36171 - 5.25122i) q^{90} +1.69053i q^{91} +(-4.73765 - 0.744772i) q^{92} +(4.18596 + 4.18596i) q^{93} +(-3.75660 - 5.84539i) q^{94} +(-6.76754 - 2.47987i) q^{95} +(0.270819 - 0.593012i) q^{96} +(-10.5739 - 5.77381i) q^{97} +(-0.216435 + 0.580286i) q^{98} +(-0.534200 - 0.616500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.212565	−	0.977147i	0.150306	−	0.690947i
$2$	0.212565	−	0.977147i	0.150306	−	0.690947i
$3$	0.521893	−	0.390684i	0.301315	−	0.225561i	−0.437912	−	0.899018i	$-0.644282\pi$
$3$	0.521893	−	0.390684i	0.301315	−	0.225561i	0.739227	+	0.673456i	$0.235191\pi$
$4$	−0.909632	−	0.415415i	−0.454816	−	0.207708i
$5$	−0.172358	−	2.22942i	−0.0770808	−	0.997025i
$5$	−0.172358	−	2.22942i	−0.0770808	−	0.997025i
$6$	−0.270819	−	0.593012i	−0.110562	−	0.242096i
$7$	0.196919	−	2.75328i	0.0744282	−	1.04064i	−0.813772	−	0.581185i	$-0.802589\pi$
$7$	0.196919	−	2.75328i	0.0744282	−	1.04064i	0.888200	−	0.459458i	$-0.151956\pi$
$8$	−0.599278	+	0.800541i	−0.211877	+	0.283034i
$9$	−0.725460	+	2.47069i	−0.241820	+	0.823563i
$10$	−2.21510	−	0.305477i	−0.700477	−	0.0966004i
$11$	−0.171272	+	0.266505i	−0.0516406	+	0.0803543i	−0.866114	−	0.499847i	$-0.833390\pi$
$11$	−0.171272	+	0.266505i	−0.0516406	+	0.0803543i	0.814473	+	0.580201i	$0.197026\pi$
$12$	−0.637026	+	0.138577i	−0.183894	+	0.0400036i
$13$	−0.610881	+	0.0436911i	−0.169428	+	0.0121177i	−0.155795	−	0.987789i	$-0.549794\pi$
$13$	−0.610881	+	0.0436911i	−0.169428	+	0.0121177i	−0.0136325	+	0.999907i	$0.504339\pi$
$14$	−2.64850	−	0.777670i	−0.707842	−	0.207841i
$15$	−0.960949	−	1.09618i	−0.248116	−	0.283032i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	0.930625	−	2.49510i	0.225710	−	0.605151i	−0.773894	−	0.633316i	$-0.781693\pi$
$17$	0.930625	−	2.49510i	0.225710	−	0.605151i	0.999603	+	0.0281645i	$0.00896622\pi$
$18$	2.26002	+	1.23406i	0.532691	+	0.290872i
$19$	1.33902	−	2.93205i	0.307193	−	0.672658i	−0.691574	−	0.722305i	$-0.743083\pi$
$19$	1.33902	−	2.93205i	0.307193	−	0.672658i	0.998767	+	0.0496475i	$0.0158098\pi$
$20$	−0.769350	+	2.09955i	−0.172032	+	0.469473i
$21$	−0.972892	−	1.51385i	−0.212303	−	0.330349i
$22$	0.224008	+	0.224008i	0.0477587	+	0.0477587i
$23$	4.61891	−	1.29062i	0.963109	−	0.269113i
$23$	4.61891	−	1.29062i	0.963109	−	0.269113i
$24$			0.651925i			0.133074i
$25$	−4.94059	+	0.768515i	−0.988117	+	0.153703i
$26$	−0.0871595	+	0.606208i	−0.0170934	+	0.118887i
$27$	1.27012	+	3.40532i	0.244435	+	0.655354i
$28$	−1.32288	+	2.42267i	−0.250000	+	0.457842i
$29$	5.55597	−	2.53733i	1.03172	−	0.471170i	0.173705	−	0.984798i	$-0.444426\pi$
$29$	5.55597	−	2.53733i	1.03172	−	0.471170i	0.858013	+	0.513628i	$0.171699\pi$
$30$	−1.27539	+	0.705979i	−0.232854	+	0.128894i
$31$	1.29230	+	8.98814i	0.232104	+	1.61432i	0.688975	+	0.724785i	$0.258061\pi$
$31$	1.29230	+	8.98814i	0.232104	+	1.61432i	−0.456871	+	0.889533i	$0.651030\pi$
$32$	0.877679	−	0.479249i	0.155153	−	0.0847201i
$33$	0.0147334	+	0.206000i	0.00256476	+	0.0358601i
$34$	−2.24026	−	1.43973i	−0.384202	−	0.246912i
$35$	−6.17215	+	0.0355368i	−1.04328	+	0.00600682i
$36$	1.68626	−	1.94605i	0.281044	−	0.324342i
$37$	1.15696	+	2.11882i	0.190204	+	0.348332i	0.955327	−	0.295552i	$-0.0955036\pi$
$37$	1.15696	+	2.11882i	0.190204	+	0.348332i	−0.765123	+	0.643884i	$0.777322\pi$
$38$	−2.58041	−	1.93167i	−0.418598	−	0.313359i
$39$	−0.301745	+	0.261463i	−0.0483178	+	0.0418676i
$40$	1.88803	+	1.19806i	0.298524	+	0.189430i
$41$	−7.62326	+	2.23839i	−1.19055	+	0.349578i	−0.816234	−	0.577722i	$-0.803942\pi$
$41$	−7.62326	+	2.23839i	−1.19055	+	0.349578i	−0.374320	+	0.927300i	$0.622124\pi$
$42$	−1.68606	+	0.628867i	−0.260164	+	0.0970362i
$43$	6.26113	+	8.36389i	0.954814	+	1.27548i	0.961300	+	0.275503i	$0.0888443\pi$
$43$	6.26113	+	8.36389i	0.954814	+	1.27548i	−0.00648654	+	0.999979i	$0.502065\pi$
$44$	0.266505	−	0.171272i	0.0401772	−	0.0258203i
$45$	5.63323	+	1.19151i	0.839752	+	0.177620i
$46$	−0.279308	−	4.78769i	−0.0411818	−	0.705907i
$47$	4.91328	−	4.91328i	0.716675	−	0.716675i	−0.251248	−	0.967923i	$-0.580841\pi$
$47$	4.91328	−	4.91328i	0.716675	−	0.716675i	0.967923	+	0.251248i	$0.0808409\pi$
$48$	0.637026	+	0.138577i	0.0919468	+	0.0200018i
$49$	−0.613031	−	0.0881405i	−0.0875758	−	0.0125915i
$50$	−0.299245	+	4.99104i	−0.0423196	+	0.705839i
$51$	−0.489110	−	1.66576i	−0.0684891	−	0.233252i
$52$	0.573827	+	0.214026i	0.0795755	+	0.0296801i
$53$	5.77904	+	0.413325i	0.793812	+	0.0567746i	0.462354	−	0.886695i	$-0.347005\pi$
$53$	5.77904	+	0.413325i	0.793812	+	0.0567746i	0.331458	+	0.943470i	$0.392459\pi$
$54$	3.59748	−	0.517240i	0.489555	−	0.0703874i
$55$	0.623671	+	0.335903i	0.0840957	+	0.0452932i
$56$	2.08611	+	1.80762i	0.278768	+	0.241554i
$57$	−0.446679	−	2.05335i	−0.0591640	−	0.271973i
$58$	−1.29834	−	5.96835i	−0.170480	−	0.783683i
$59$	−3.03630	−	2.63097i	−0.395292	−	0.342523i	0.434424	−	0.900709i	$-0.356952\pi$
$59$	−3.03630	−	2.63097i	−0.395292	−	0.342523i	−0.829716	+	0.558186i	$0.811498\pi$
$60$	0.418741	+	1.39631i	0.0540593	+	0.180263i
$61$	−10.7039	+	1.53899i	−1.37050	+	0.197048i	−0.787945	−	0.615745i	$-0.788855\pi$
$61$	−10.7039	+	1.53899i	−1.37050	+	0.197048i	−0.582553	+	0.812793i	$0.697946\pi$
$62$	9.05743	+	0.647801i	1.15030	+	0.0822707i
$63$	6.65964	+	2.48392i	0.839036	+	0.312944i
$64$	−0.281733	−	0.959493i	−0.0352166	−	0.119937i
$65$	0.202696	+	1.35438i	0.0251413	+	0.167990i
$66$	0.204424	+	0.0293918i	0.0251629	+	0.00361788i
$67$	7.50837	+	1.63335i	0.917294	+	0.199545i	0.646342	−	0.763048i	$-0.276298\pi$
$67$	7.50837	+	1.63335i	0.917294	+	0.199545i	0.270952	+	0.962593i	$0.412662\pi$
$68$	−1.88303	+	1.88303i	−0.228351	+	0.228351i
$69$	1.90635	−	2.47810i	0.229497	−	0.298328i
$70$	−1.27726	+	6.03865i	−0.152662	+	0.721757i
$71$	7.02619	−	4.51545i	0.833855	−	0.535886i	−0.0526459	−	0.998613i	$-0.516765\pi$
$71$	7.02619	−	4.51545i	0.833855	−	0.535886i	0.886501	+	0.462727i	$0.153129\pi$
$72$	−1.54314	−	2.06139i	−0.181860	−	0.242937i
$73$	−9.02358	+	3.36562i	−1.05613	+	0.393916i	−0.816739	−	0.577007i	$-0.804220\pi$
$73$	−9.02358	+	3.36562i	−1.05613	+	0.393916i	−0.239391	+	0.970923i	$0.576948\pi$
$74$	2.31633	−	0.680136i	0.269268	−	0.0790642i
$75$	−2.27821	+	2.33129i	−0.263065	+	0.269194i
$76$	−2.43603	+	2.11083i	−0.279432	+	0.242129i
$77$	0.700037	+	0.524041i	0.0797766	+	0.0597200i
$78$	0.191348	+	0.350427i	0.0216659	+	0.0396781i
$79$	−4.91108	+	5.66768i	−0.552539	+	0.637664i	−0.961473	−	0.274900i	$-0.911355\pi$
$79$	−4.91108	+	5.66768i	−0.552539	+	0.637664i	0.408934	+	0.912564i	$0.365901\pi$
$80$	1.57201	−	1.59022i	0.175756	−	0.177792i
$81$	−4.50540	−	2.89544i	−0.500600	−	0.321716i
$82$	0.566796	+	7.92485i	0.0625922	+	0.875153i
$83$	0.897247	−	0.489934i	0.0984857	−	0.0537772i	−0.429251	−	0.903185i	$-0.641223\pi$
$83$	0.897247	−	0.489934i	0.0984857	−	0.0537772i	0.527737	+	0.849408i	$0.323041\pi$
$84$	0.256098	+	1.78120i	0.0279426	+	0.194345i
$85$	−5.72302	−	1.64470i	−0.620749	−	0.178393i
$86$	9.50365	−	4.34017i	1.02481	−	0.468013i
$87$	1.90833	−	3.49484i	0.204594	−	0.374686i
$88$	−0.110709	−	0.296821i	−0.0118016	−	0.0316412i
$89$	−0.532679	+	3.70486i	−0.0564638	+	0.392715i	0.941918	+	0.335844i	$0.109021\pi$
$89$	−0.532679	+	3.70486i	−0.0564638	+	0.392715i	−0.998382	+	0.0568709i	$0.981888\pi$
$90$	2.36171	−	5.25122i	0.248946	−	0.553527i
$91$			1.69053i			0.177216i
$92$	−4.73765	−	0.744772i	−0.493934	−	0.0776478i
$93$	4.18596	+	4.18596i	0.434064	+	0.434064i
$94$	−3.75660	−	5.84539i	−0.387464	−	0.602905i
$95$	−6.76754	−	2.47987i	−0.694335	−	0.254430i
$96$	0.270819	−	0.593012i	0.0276404	−	0.0605240i
$97$	−10.5739	−	5.77381i	−1.07362	−	0.586241i	−0.157654	−	0.987494i	$-0.550393\pi$
$97$	−10.5739	−	5.77381i	−1.07362	−	0.586241i	−0.915967	+	0.401253i	$0.868575\pi$
$98$	−0.216435	+	0.580286i	−0.0218633	+	0.0586177i
$99$	−0.534200	−	0.616500i	−0.0536891	−	0.0619605i
$100$	4.81337	+	1.35333i	0.481337	+	0.135333i
$101$	−8.74877	−	2.56887i	−0.870535	−	0.255612i	−0.184192	−	0.982890i	$-0.558967\pi$
$101$	−8.74877	−	2.56887i	−0.870535	−	0.255612i	−0.686343	+	0.727278i	$0.740785\pi$
$102$	−1.73166	+	0.123850i	−0.171459	+	0.0122630i
$103$	4.51246	−	0.981625i	0.444626	−	0.0967224i	0.0153220	−	0.999883i	$-0.495123\pi$
$103$	4.51246	−	0.981625i	0.444626	−	0.0967224i	0.429304	+	0.903160i	$0.358759\pi$
$104$	0.331111	−	0.515218i	0.0324681	−	0.0505213i
$105$	−3.20731	+	2.42991i	−0.313002	+	0.237134i
$106$	1.63230	−	5.55911i	0.158543	−	0.539949i
$107$	2.96493	−	3.96069i	0.286631	−	0.382894i	−0.633997	−	0.773336i	$-0.718587\pi$
$107$	2.96493	−	3.96069i	0.286631	−	0.382894i	0.920628	+	0.390442i	$0.127678\pi$
$108$	0.259281	−	3.62522i	0.0249493	−	0.348837i
$109$	−3.31324	−	7.25499i	−0.317351	−	0.694902i	0.681984	−	0.731367i	$-0.261117\pi$
$109$	−3.31324	−	7.25499i	−0.317351	−	0.694902i	−0.999335	+	0.0364655i	$0.988390\pi$
$110$	0.460797	−	0.538017i	0.0439353	−	0.0512979i
$111$	1.43160	+	0.653790i	0.135882	+	0.0620550i
$112$	2.20975	−	1.65419i	0.208801	−	0.156307i
$113$	−1.30428	+	5.99568i	−0.122696	+	0.564026i	0.874218	+	0.485533i	$0.161374\pi$
$113$	−1.30428	+	5.99568i	−0.122696	+	0.564026i	−0.996915	+	0.0784929i	$0.974989\pi$
$114$	−2.10137			−0.196811
$115$	−3.67344	−	10.0750i	−0.342550	−	0.939500i
$116$	−6.10794			−0.567108
$117$	0.335222	−	1.54099i	0.0309913	−	0.142465i
$118$	−3.21625	+	2.40766i	−0.296080	+	0.221643i
$119$	−6.68646	−	3.05360i	−0.612947	−	0.279923i
$120$	1.45341	−	0.112364i	0.132678	−	0.0102574i
$121$	4.52787	+	9.91466i	0.411625	+	0.901333i
$122$	−0.771462	+	10.7865i	−0.0698449	+	0.976559i
$123$	−3.10402	+	4.14648i	−0.279880	+	0.373876i
$124$	2.55829	−	8.71274i	0.229741	−	0.782428i
$125$	2.56489	+	10.8822i	0.229411	+	0.973330i
$126$	3.84276	−	5.97946i	0.342341	−	0.532692i
$127$	−13.1458	+	2.85969i	−1.16650	+	0.253757i	−0.753796	−	0.657109i	$-0.771779\pi$
$127$	−13.1458	+	2.85969i	−1.16650	+	0.253757i	−0.412704	+	0.910865i	$0.635416\pi$
$128$	−0.997452	+	0.0713392i	−0.0881631	+	0.00630555i
$129$	6.53528	+	1.91893i	0.575399	+	0.168952i
$130$	1.36651	+	0.0898300i	0.119851	+	0.00787861i
$131$	−7.65537	−	8.83477i	−0.668853	−	0.771897i	0.315344	−	0.948978i	$-0.397880\pi$
$131$	−7.65537	−	8.83477i	−0.668853	−	0.771897i	−0.984196	+	0.177080i	$0.943335\pi$
$132$	0.0721737	−	0.193505i	0.00628191	−	0.0168425i
$133$	−7.80907	−	4.26408i	−0.677133	−	0.369742i
$134$	3.19204	−	6.98959i	0.275750	−	0.603809i
$135$	7.37296	−	3.41856i	0.634563	−	0.294223i
$136$	1.43973	+	2.24026i	0.123456	+	0.192101i
$137$	−12.9973	−	12.9973i	−1.11044	−	1.11044i	−0.993091	−	0.117346i	$-0.962561\pi$
$137$	−12.9973	−	12.9973i	−1.11044	−	1.11044i	−0.117346	−	0.993091i	$-0.537439\pi$
$138$	−2.01624	−	2.38954i	−0.171634	−	0.203411i
$139$		−	6.25498i		−	0.530540i	−0.964174	−	0.265270i	$-0.914539\pi$
$139$		−	6.25498i		−	0.530540i	0.964174	−	0.265270i	$-0.0854612\pi$
$140$	5.62915	+	2.53168i	0.475750	+	0.213966i
$141$	0.644665	−	4.48374i	0.0542906	−	0.377599i
$142$	−2.91874	−	7.82544i	−0.244935	−	0.656697i
$143$	0.0929832	−	0.170286i	0.00777564	−	0.0142400i
$144$	−2.34230	+	1.06969i	−0.195191	+	0.0891409i
$145$	−6.61438	−	11.9492i	−0.549294	−	0.992331i
$146$	1.37061	+	9.53277i	0.113432	+	0.788938i
$147$	−0.354371	+	0.193501i	−0.0292281	+	0.0159597i
$148$	−0.172221	−	2.40797i	−0.0141565	−	0.197934i
$149$	16.6602	+	10.7069i	1.36486	+	0.877141i	0.998575	−	0.0533626i	$-0.0169939\pi$
$149$	16.6602	+	10.7069i	1.36486	+	0.877141i	0.366283	+	0.930504i	$0.380630\pi$
$150$	1.79374	+	2.72170i	0.146459	+	0.222226i
$151$	−3.91387	+	4.51685i	−0.318506	+	0.367576i	−0.892315	−	0.451413i	$-0.850920\pi$
$151$	−3.91387	+	4.51685i	−0.318506	+	0.367576i	0.573808	+	0.818990i	$0.305465\pi$
$152$	1.54478	+	2.82905i	0.125298	+	0.229466i
$153$	5.48949	+	4.10938i	0.443799	+	0.332224i
$154$	0.660868	−	0.572646i	0.0532543	−	0.0461451i
$155$	19.8156	−	4.43025i	1.59162	−	0.355846i
$156$	0.383093	−	0.112486i	0.0306720	−	0.00900610i
$157$	−13.3732	+	4.98794i	−1.06730	+	0.398081i	−0.820891	−	0.571085i	$-0.806522\pi$
$157$	−13.3732	+	4.98794i	−1.06730	+	0.398081i	−0.246406	+	0.969167i	$0.579250\pi$
$158$	4.49423	+	6.00359i	0.357542	+	0.477620i
$159$	3.17752	−	2.04207i	0.251994	−	0.161946i
$160$	−1.21972	−	1.87411i	−0.0964273	−	0.148161i
$161$	−2.64390	−	12.9713i	−0.208368	−	1.02228i
$162$	−3.78697	+	3.78697i	−0.297532	+	0.297532i
$163$	11.5926	+	2.52181i	0.908002	+	0.197524i	0.642230	−	0.766512i	$-0.278010\pi$
$163$	11.5926	+	2.52181i	0.908002	+	0.197524i	0.265772	+	0.964036i	$0.414373\pi$
$164$	7.86422	+	1.13070i	0.614093	+	0.0882932i
$165$	0.456721	−	0.0683528i	0.0355557	−	0.00532126i
$166$	−0.288014	−	0.980885i	−0.0223542	−	0.0761314i
$167$	12.5211	+	4.67014i	0.968914	+	0.361386i	0.783581	−	0.621290i	$-0.213391\pi$
$167$	12.5211	+	4.67014i	0.968914	+	0.361386i	0.185333	+	0.982676i	$0.440664\pi$
$168$	1.79493	+	0.128376i	0.138482	+	0.00990443i
$169$	−12.4964	+	1.79671i	−0.961262	+	0.138209i
$170$	−2.82363	+	5.24262i	−0.216562	+	0.402091i
$171$	6.27277	+	5.43539i	0.479691	+	0.415654i
$172$	−2.22084	−	10.2090i	−0.169337	−	0.778432i
$173$	−2.47939	−	11.3976i	−0.188504	−	0.866541i	−0.970091	−	0.242743i	$-0.921953\pi$
$173$	−2.47939	−	11.3976i	−0.188504	−	0.866541i	0.781586	−	0.623797i	$-0.214411\pi$
$174$	−3.00933	−	2.60760i	−0.228137	−	0.197682i
$175$	1.14305	+	13.7542i	0.0864061	+	1.03972i
$176$	−0.313571	+	0.0450847i	−0.0236363	+	0.00339838i
$177$	−2.61250	−	0.186849i	−0.196367	−	0.0140445i
$178$	3.50697	+	1.30803i	0.262858	+	0.0980410i
$179$	2.86500	+	9.75728i	0.214140	+	0.729293i	0.994572	+	0.104053i	$0.0331810\pi$
$179$	2.86500	+	9.75728i	0.214140	+	0.729293i	−0.780432	+	0.625241i	$0.785001\pi$
$180$	−4.62920	−	3.42396i	−0.345040	−	0.255207i
$181$	17.5918	+	2.52932i	1.30759	+	0.188003i	0.760646	−	0.649167i	$-0.224883\pi$
$181$	17.5918	+	2.52932i	1.30759	+	0.188003i	0.546942	+	0.837170i	$0.315792\pi$
$182$	1.65190	+	0.359348i	0.122447	+	0.0266367i
$183$	−4.98504	+	4.98504i	−0.368505	+	0.368505i
$184$	−1.73481	+	4.47107i	−0.127892	+	0.329611i
$185$	4.52432	−	2.94455i	0.332635	−	0.216488i
$186$	4.98009	−	3.20051i	0.365158	−	0.234673i
$187$	0.505567	+	0.675358i	0.0369707	+	0.0493871i
$188$	−6.51032	+	2.42822i	−0.474814	+	0.177097i
$189$	9.62592	−	2.82642i	0.700183	−	0.205592i
$190$	−3.86174	+	6.08575i	−0.280160	+	0.441507i
$191$	−10.0659	+	8.72213i	−0.728341	+	0.631111i	−0.937989	−	0.346666i	$-0.887314\pi$
$191$	−10.0659	+	8.72213i	−0.728341	+	0.631111i	0.209648	+	0.977777i	$0.432768\pi$
$192$	−0.521893	−	0.390684i	−0.0376644	−	0.0281952i
$193$	−11.1731	−	20.4619i	−0.804255	−	1.47288i	−0.879594	−	0.475725i	$-0.842186\pi$
$193$	−11.1731	−	20.4619i	−0.804255	−	1.47288i	0.0753387	−	0.997158i	$-0.475996\pi$
$194$	−7.88951	+	9.10498i	−0.566434	+	0.653699i
$195$	0.634919	+	0.627649i	0.0454675	+	0.0449469i
$196$	0.521018	+	0.334838i	0.0372155	+	0.0239170i
$197$	1.16021	+	16.2218i	0.0826614	+	1.15576i	0.854330	+	0.519732i	$0.173968\pi$
$197$	1.16021	+	16.2218i	0.0826614	+	1.15576i	−0.771668	+	0.636025i	$0.780577\pi$
$198$	−0.715963	+	0.390945i	−0.0508813	+	0.0277833i
$199$	1.06727	+	7.42305i	0.0756570	+	0.526206i	0.992042	+	0.125908i	$0.0401843\pi$
$199$	1.06727	+	7.42305i	0.0756570	+	0.526206i	−0.916385	+	0.400298i	$0.868907\pi$
$200$	2.34555	−	4.41570i	0.165856	−	0.312237i
$201$	4.55669	−	2.08097i	0.321404	−	0.146780i
$202$	−4.36985	+	8.00278i	−0.307461	+	0.563073i
$203$	−5.89190	−	15.7968i	−0.413531	−	1.10872i
$204$	−0.247070	+	1.71841i	−0.0172983	+	0.120313i
$205$	6.30423	+	16.6096i	0.440307	+	1.16007i
$206$		−	4.61799i		−	0.321751i
$207$	−0.162104	+	12.3482i	−0.0112670	+	0.858257i
$208$	−0.433061	−	0.433061i	−0.0300274	−	0.0300274i
$209$	0.552068	+	0.859035i	0.0381874	+	0.0594207i
$210$	1.69261	+	3.65053i	0.116801	+	0.251911i
$211$	−9.66421	+	21.1617i	−0.665312	+	1.45683i	0.212177	+	0.977231i	$0.431945\pi$
$211$	−9.66421	+	21.1617i	−0.665312	+	1.45683i	−0.877488	+	0.479598i	$0.840783\pi$
$212$	−5.08510	−	2.77667i	−0.349246	−	0.190703i
$213$	1.90280	−	5.10160i	0.130378	−	0.349556i
$214$	−3.23993	−	3.73908i	−0.221477	−	0.255598i
$215$	17.5674	−	15.4002i	1.19809	−	1.05029i
$216$	−3.48725	−	1.02395i	−0.237278	−	0.0696710i
$217$	25.0014	−	1.78813i	1.69720	−	0.121386i
$218$	−7.79347	+	1.69536i	−0.527840	+	0.114825i
$219$	−3.39444	+	5.28186i	−0.229375	+	0.356915i
$220$	−0.427772	−	0.564630i	−0.0288404	−	0.0380674i
$221$	−0.459487	+	1.56487i	−0.0309085	+	0.105265i
$222$	0.943158	−	1.25991i	0.0633006	−	0.0845597i
$223$	0.472013	−	6.59961i	0.0316083	−	0.441942i	−0.956864	−	0.290538i	$-0.906166\pi$
$223$	0.472013	−	6.59961i	0.0316083	−	0.441942i	0.988472	−	0.151405i	$-0.0483796\pi$
$224$	−1.14668	−	2.51087i	−0.0766155	−	0.167765i
$225$	1.68543	−	12.7642i	0.112362	−	0.850945i
$226$	5.58141	+	2.54895i	0.371270	+	0.169553i
$227$	11.0560	−	8.27641i	0.733812	−	0.549325i	−0.165724	−	0.986172i	$-0.552996\pi$
$227$	11.0560	−	8.27641i	0.733812	−	0.549325i	0.899536	+	0.436847i	$0.143905\pi$
$228$	−0.446679	+	2.05335i	−0.0295820	+	0.135986i
$229$	22.9134			1.51416			0.757080	−	0.653322i	$-0.226625\pi$
$229$	22.9134			1.51416			0.757080	+	0.653322i	$0.226625\pi$
$230$	−10.6256	+	1.44789i	−0.700632	+	0.0954711i
$231$	0.570078			0.0375084
$232$	−1.29834	+	5.96835i	−0.0852399	+	0.391841i
$233$	1.89415	−	1.41794i	0.124090	−	0.0928926i	−0.535430	−	0.844580i	$-0.679850\pi$
$233$	1.89415	−	1.41794i	0.124090	−	0.0928926i	0.659520	+	0.751687i	$0.270760\pi$
$234$	−1.43452	−	0.655123i	−0.0937775	−	0.0428267i
$235$	−11.8006	−	10.1069i	−0.769785	−	0.659301i
$236$	1.66897	+	3.65453i	0.108641	+	0.237890i
$237$	−0.348781	+	4.87660i	−0.0226558	+	0.316769i
$238$	−4.40513	+	5.88456i	−0.285542	+	0.381440i
$239$	−5.05977	+	17.2320i	−0.327290	+	1.11465i	0.617392	+	0.786656i	$0.288189\pi$
$239$	−5.05977	+	17.2320i	−0.327290	+	1.11465i	−0.944681	+	0.327990i	$0.893629\pi$
$240$	0.199148	−	1.44408i	0.0128550	−	0.0932150i
$241$	−0.312423	+	0.486139i	−0.0201249	+	0.0313150i	−0.851170	−	0.524890i	$-0.824107\pi$
$241$	−0.312423	+	0.486139i	−0.0201249	+	0.0313150i	0.831045	+	0.556205i	$0.187743\pi$
$242$	10.6505	−	2.31689i	0.684643	−	0.148935i
$243$	−14.3582	+	1.02692i	−0.921078	+	0.0658768i
$244$	10.3760	+	3.04666i	0.664253	+	0.195042i
$245$	−0.0908411	+	1.38189i	−0.00580362	+	0.0882859i
$246$	3.39192	+	3.91448i	0.216261	+	0.249578i
$247$	−0.689878	+	1.84964i	−0.0438959	+	0.117689i
$248$	−7.96983	−	4.35185i	−0.506084	−	0.276343i
$249$	0.276857	−	0.606233i	0.0175451	−	0.0384184i
$250$	11.1787	−	0.193104i	0.707001	−	0.0122130i
$251$	3.97999	+	6.19299i	0.251215	+	0.390898i	0.943842	−	0.330398i	$-0.107183\pi$
$251$	3.97999	+	6.19299i	0.251215	+	0.390898i	−0.692627	+	0.721296i	$0.743547\pi$
$252$	−5.02597	−	5.02597i	−0.316606	−	0.316606i
$253$	−0.447134	+	1.45201i	−0.0281111	+	0.0912871i
$254$			13.4532i			0.844131i
$255$	−3.62936	+	1.37754i	−0.227279	+	0.0862646i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	2.46321	+	6.60411i	0.153651	+	0.411953i	0.990854	−	0.134938i	$-0.0430837\pi$
$257$	2.46321	+	6.60411i	0.153651	+	0.411953i	−0.837203	+	0.546892i	$0.815811\pi$
$258$	3.26425	−	5.97803i	0.203223	−	0.372176i
$259$	6.06154	−	2.76821i	0.376646	−	0.172008i
$260$	0.378250	−	1.31619i	0.0234581	−	0.0816265i
$261$	2.23831	+	15.5678i	0.138548	+	0.963624i
$262$	−10.2601	+	5.60246i	−0.633873	+	0.346121i
$263$	−1.27433	−	17.8175i	−0.0785787	−	1.09867i	−0.871839	−	0.489792i	$-0.837073\pi$
$263$	−1.27433	−	17.8175i	−0.0785787	−	1.09867i	0.793261	−	0.608882i	$-0.208382\pi$
$264$	−0.173741	−	0.111657i	−0.0106930	−	0.00687200i
$265$	−0.0745905	−	12.9551i	−0.00458206	−	0.795827i
$266$	−5.82657	+	6.72422i	−0.357250	+	0.412288i
$267$	1.16943	+	2.14165i	0.0715679	+	0.131067i
$268$	−6.15134	−	4.60484i	−0.375753	−	0.281285i
$269$	−13.3924	+	11.6046i	−0.816550	+	0.707545i	−0.959354	−	0.282206i	$-0.908934\pi$
$269$	−13.3924	+	11.6046i	−0.816550	+	0.707545i	0.142803	+	0.989751i	$0.454388\pi$
$270$	−1.77320	−	7.93113i	−0.107913	−	0.482673i
$271$	27.9409	−	8.20418i	1.69729	−	0.498368i	0.717188	−	0.696880i	$-0.245429\pi$
$271$	27.9409	−	8.20418i	1.69729	−	0.498368i	0.980098	+	0.198512i	$0.0636109\pi$
$272$	2.49510	−	0.930625i	0.151288	−	0.0564274i
$273$	0.660463	+	0.882275i	0.0399730	+	0.0533977i
$274$	−15.4631	+	9.93752i	−0.934159	+	0.600348i
$275$	0.641373	−	1.44832i	0.0386762	−	0.0873368i
$276$	−2.76351	+	1.46223i	−0.166344	+	0.0880160i
$277$	−16.6398	+	16.6398i	−0.999786	+	0.999786i	−1.00000		0.000213691i	$-0.999932\pi$
$277$	−16.6398	+	16.6398i	−0.999786	+	0.999786i	0.000213691		1.00000i	$0.499932\pi$
$278$	−6.11203	−	1.32959i	−0.366575	−	0.0797436i
$279$	−23.1444	−	3.32766i	−1.38562	−	0.199222i
$280$	3.67038	−	4.96236i	0.219347	−	0.296557i
$281$	−6.85360	−	23.3412i	−0.408852	−	1.39242i	−0.864666	−	0.502346i	$-0.832470\pi$
$281$	−6.85360	−	23.3412i	−0.408852	−	1.39242i	0.455815	−	0.890075i	$-0.349348\pi$
$282$	−4.24424	−	1.58302i	−0.252741	−	0.0942675i
$283$	−2.22352	−	0.159029i	−0.132175	−	0.00945332i	0.00509507	−	0.999987i	$-0.498378\pi$
$283$	−2.22352	−	0.159029i	−0.132175	−	0.00945332i	−0.137270	+	0.990534i	$0.543833\pi$
$284$	−8.26703	+	1.18862i	−0.490558	+	0.0705316i
$285$	−4.50078	+	1.34974i	−0.266603	+	0.0799519i
$286$	−0.146629	−	0.127055i	−0.00867038	−	0.00751292i
$287$	4.66176	+	21.4298i	0.275175	+	1.26496i
$288$	0.547354	+	2.51615i	0.0322532	+	0.148265i
$289$	7.48827	+	6.48862i	0.440487	+	0.381684i
$290$	−13.0822	+	3.92322i	−0.768211	+	0.230380i
$291$	−7.77419	+	1.11776i	−0.455731	+	0.0655243i
$292$	9.60626	+	0.687054i	0.562164	+	0.0402068i
$293$	23.9931	+	8.94896i	1.40169	+	0.522804i	0.932782	−	0.360442i	$-0.117374\pi$
$293$	23.9931	+	8.94896i	1.40169	+	0.522804i	0.468910	+	0.883246i	$0.344647\pi$
$294$	0.113752	+	0.387405i	0.00663417	+	0.0225939i
$295$	−5.34218	+	7.22263i	−0.311034	+	0.420518i
$296$	−2.38955	−	0.343565i	−0.138890	−	0.0199693i
$297$	−1.12507	−	0.244744i	−0.0652833	−	0.0142015i
$298$	14.0036	−	14.0036i	0.811205	−	0.811205i
$299$	−2.76521	+	0.990222i	−0.159916	+	0.0572660i
$300$	3.04078	−	1.17421i	0.175560	−	0.0677933i
$301$	24.2611	−	15.5917i	1.39839	−	0.898688i
$302$	3.58167	+	4.78455i	0.206102	+	0.275320i
$303$	−5.56953	+	2.07733i	−0.319961	+	0.119339i
$304$	3.09277	−	0.908118i	0.177382	−	0.0520841i
$305$	5.27596	+	23.5983i	0.302101	+	1.35123i
$306$	5.18234	−	4.49053i	0.296255	−	0.256706i
$307$	−9.62496	−	7.20516i	−0.549326	−	0.411220i	0.288239	−	0.957559i	$-0.406930\pi$
$307$	−9.62496	−	7.20516i	−0.549326	−	0.411220i	−0.837564	+	0.546339i	$0.816021\pi$
$308$	−0.419081	−	0.767490i	−0.0238794	−	0.0437318i
$309$	1.97151	−	2.27525i	0.112155	−	0.129434i
$310$	−0.116905	−	20.3044i	−0.00663976	−	1.15321i
$311$	−14.2553	−	9.16132i	−0.808344	−	0.519491i	0.0699851	−	0.997548i	$-0.477705\pi$
$311$	−14.2553	−	9.16132i	−0.808344	−	0.519491i	−0.878329	+	0.478057i	$0.841341\pi$
$312$	−0.0284833	−	0.398248i	−0.00161255	−	0.0225464i
$313$	−15.6324	+	8.53594i	−0.883596	+	0.482480i	−0.855903	−	0.517136i	$-0.826998\pi$
$313$	−15.6324	+	8.53594i	−0.883596	+	0.482480i	−0.0276933	+	0.999616i	$0.508816\pi$
$314$	2.03128	+	14.1278i	0.114632	+	0.797280i
$315$	4.38984	−	15.2752i	0.247340	−	0.860662i
$316$	6.82171	−	3.11537i	0.383751	−	0.175253i
$317$	9.45486	−	17.3153i	0.531038	−	0.972523i	−0.465145	−	0.885234i	$-0.653998\pi$
$317$	9.45486	−	17.3153i	0.531038	−	0.972523i	0.996183	−	0.0872888i	$-0.0278203\pi$
$318$	−1.31997	−	3.53897i	−0.0740202	−	0.198456i
$319$	−0.275374	+	1.91527i	−0.0154180	+	0.107235i
$320$	−2.09055	+	0.793475i	−0.116865	+	0.0443566i
$321$		−	3.22540i		−	0.180024i
$322$	−13.2369	−	0.173770i	−0.737661	−	0.00968385i
$323$	−6.06963	−	6.06963i	−0.337723	−	0.337723i
$324$	2.89544	+	4.50540i	0.160858	+	0.250300i
$325$	2.98453	−	0.685331i	0.165552	−	0.0380153i
$326$	4.92836	−	10.7916i	0.272957	−	0.597692i
$327$	−4.56356	−	2.49189i	−0.252366	−	0.137802i
$328$	2.77653	−	7.44415i	0.153308	−	0.411035i
$329$	−12.5601	−	14.4951i	−0.692462	−	0.799143i
$330$	0.0302923	−	0.460813i	0.00166754	−	0.0253669i
$331$	17.2261	+	5.05804i	0.946831	+	0.278015i	0.718467	−	0.695561i	$-0.244844\pi$
$331$	17.2261	+	5.05804i	0.946831	+	0.278015i	0.228364	+	0.973576i	$0.426662\pi$
$332$	−1.01969	+	0.0729297i	−0.0559628	+	0.00400254i
$333$	−6.07428	+	1.32138i	−0.332869	+	0.0724111i
$334$	7.22497	−	11.2423i	0.395333	−	0.615150i
$335$	2.34728	−	17.0208i	0.128246	−	0.929946i
$336$	0.506983	−	1.72662i	0.0276582	−	0.0941951i
$337$	10.9903	−	14.6813i	0.598680	−	0.799743i	−0.394179	−	0.919034i	$-0.628971\pi$
$337$	10.9903	−	14.6813i	0.598680	−	0.799743i	0.992859	+	0.119291i	$0.0380620\pi$
$338$	−0.900651	+	12.5927i	−0.0489890	+	0.684955i
$339$	1.66172	+	3.63866i	0.0902523	+	0.197625i
$340$	4.52261	+	3.87350i	0.245273	+	0.210070i
$341$	−2.61672	−	1.19502i	−0.141703	−	0.0647138i
$342$	6.64455	−	4.97404i	0.359296	−	0.268966i
$343$	3.74384	−	17.2101i	0.202148	−	0.929260i
$344$	−10.4478			−0.563308
$345$	−5.85329	−	3.82292i	−0.315130	−	0.205819i
$346$	−11.6641			−0.627067
$347$	5.56392	−	25.5769i	0.298687	−	1.37304i	−0.546002	−	0.837784i	$-0.683851\pi$
$347$	5.56392	−	25.5769i	0.298687	−	1.37304i	0.844689	−	0.535258i	$-0.179786\pi$
$348$	−3.18769	+	2.38627i	−0.170878	+	0.127918i
$349$	20.3982	+	9.31555i	1.09189	+	0.498650i	0.878221	−	0.478256i	$-0.158731\pi$
$349$	20.3982	+	9.31555i	1.09189	+	0.498650i	0.213671	+	0.976906i	$0.431458\pi$
$350$	13.6828	+	1.80673i	0.731377	+	0.0965739i
$351$	−0.924674	−	2.02475i	−0.0493554	−	0.108073i
$352$	−0.0225999	+	0.315988i	−0.00120458	+	0.0168422i
$353$	−7.54025	+	10.0726i	−0.401327	+	0.536110i	−0.954993	−	0.296629i	$-0.904138\pi$
$353$	−7.54025	+	10.0726i	−0.401327	+	0.536110i	0.553666	+	0.832739i	$0.313229\pi$
$354$	−0.737905	+	2.51307i	−0.0392192	+	0.133568i
$355$	−11.2778	−	14.8860i	−0.598566	−	0.790067i
$356$	2.02360	−	3.14878i	0.107250	−	0.166885i
$357$	−4.68261	+	1.01864i	−0.247830	+	0.0539121i
$358$	10.1433	−	0.725463i	0.536090	−	0.0383419i
$359$	−20.2928	−	5.95851i	−1.07101	−	0.314478i	−0.301736	−	0.953392i	$-0.597566\pi$
$359$	−20.2928	−	5.95851i	−1.07101	−	0.314478i	−0.769279	+	0.638914i	$0.779384\pi$
$360$	−4.32972	+	3.79559i	−0.228196	+	0.200045i
$361$	5.63843	+	6.50709i	0.296759	+	0.342479i
$362$	6.21092	−	16.6521i	0.326439	−	0.875216i
$363$	6.23656	+	3.40542i	0.327335	+	0.178738i
$364$	0.702272	−	1.53776i	0.0368090	−	0.0806006i
$365$	9.05865	+	19.5372i	0.474151	+	1.02262i
$366$	3.81147	+	5.93077i	0.199229	+	0.310006i
$367$	−13.6323	−	13.6323i	−0.711598	−	0.711598i	0.255271	−	0.966869i	$-0.417835\pi$
$367$	−13.6323	−	13.6323i	−0.711598	−	0.711598i	−0.966869	+	0.255271i	$0.917835\pi$
$368$	4.00013	+	2.64556i	0.208521	+	0.137909i
$369$		−	20.4586i		−	1.06503i
$370$	−1.91554	−	5.04684i	−0.0995844	−	0.262373i
$371$	2.27600	−	15.8299i	0.118164	−	0.821849i
$372$	−2.06877	−	5.54660i	−0.107261	−	0.287578i
$373$	0.0233634	−	0.0427868i	0.00120971	−	0.00221542i	−0.877073	−	0.480356i	$-0.840507\pi$
$373$	0.0233634	−	0.0427868i	0.00120971	−	0.00221542i	0.878283	+	0.478141i	$0.158689\pi$
$374$	0.767390	−	0.350455i	0.0396808	−	0.0181216i
$375$	5.59008	+	4.67726i	0.288670	+	0.241532i
$376$	0.988864	+	6.87770i	0.0509968	+	0.354690i
$377$	−3.28318	+	1.79275i	−0.169092	+	0.0923314i
$378$	−0.715696	−	10.0067i	−0.0368114	−	0.514691i
$379$	−11.0138	−	7.07816i	−0.565742	−	0.363580i	0.226290	−	0.974060i	$-0.427340\pi$
$379$	−11.0138	−	7.07816i	−0.565742	−	0.363580i	−0.792032	+	0.610480i	$0.790977\pi$
$380$	5.12580	+	5.06711i	0.262948	+	0.259937i
$381$	−5.74345	+	6.62830i	−0.294246	+	0.339578i
$382$	6.38315	+	11.6899i	0.326590	+	0.598105i
$383$	−21.6338	−	16.1948i	−1.10543	−	0.827517i	−0.119199	−	0.992870i	$-0.538033\pi$
$383$	−21.6338	−	16.1948i	−1.10543	−	0.827517i	−0.986234	+	0.165353i	$0.947124\pi$
$384$	−0.492692	+	0.426920i	−0.0251426	+	0.0217862i
$385$	1.04765	−	1.65100i	0.0533931	−	0.0841425i
$386$	−22.3693	+	6.56823i	−1.13857	+	0.334314i
$387$	−25.2068	+	9.40164i	−1.28133	+	0.477912i
$388$	7.21987	+	9.64461i	0.366533	+	0.489631i
$389$	−10.3405	+	6.64544i	−0.524285	+	0.336937i	−0.775865	−	0.630899i	$-0.782686\pi$
$389$	−10.3405	+	6.64544i	−0.524285	+	0.336937i	0.251580	+	0.967836i	$0.419050\pi$
$390$	0.748267	−	0.486992i	0.0378900	−	0.0246598i
$391$	1.07823	−	12.7257i	0.0545287	−	0.643568i
$392$	0.437936	−	0.437936i	0.0221191	−	0.0221191i
$393$	−7.44688	−	1.61997i	−0.375646	−	0.0817167i
$394$	16.0977	+	2.31450i	0.810991	+	0.116603i
$395$	13.4821	+	9.97196i	0.678357	+	0.501744i
$396$	0.229822	+	0.782702i	0.0115490	+	0.0393323i
$397$	−7.42520	−	2.76946i	−0.372660	−	0.138995i	0.156154	−	0.987733i	$-0.450090\pi$
$397$	−7.42520	−	2.76946i	−0.372660	−	0.138995i	−0.528814	+	0.848738i	$0.677363\pi$
$398$	7.48027	+	0.535000i	0.374952	+	0.0268171i
$399$	−5.74140	+	0.825489i	−0.287430	+	0.0413262i
$400$	−3.81620	−	3.23057i	−0.190810	−	0.161529i
$401$	10.5343	+	9.12804i	0.526059	+	0.455832i	0.876948	−	0.480584i	$-0.159575\pi$
$401$	10.5343	+	9.12804i	0.526059	+	0.455832i	−0.350890	+	0.936417i	$0.614121\pi$
$402$	−1.06482	−	4.89489i	−0.0531083	−	0.244135i
$403$	−1.18214	−	5.43422i	−0.0588867	−	0.270698i
$404$	6.89101	+	5.97109i	0.342841	+	0.297073i
$405$	−5.67861	+	10.5435i	−0.282172	+	0.523909i
$406$	−16.6882	+	2.39940i	−0.828222	+	0.119080i
$407$	−0.762833	−	0.0545589i	−0.0378122	−	0.00270438i
$408$	1.62662	+	0.606697i	0.0805296	+	0.0300360i
$409$	0.412691	+	1.40550i	0.0204062	+	0.0694973i	0.969067	−	0.246799i	$-0.0793788\pi$
$409$	0.412691	+	1.40550i	0.0204062	+	0.0694973i	−0.948660	+	0.316296i	$0.897561\pi$
$410$	17.5701	−	2.62954i	0.867725	−	0.129864i
$411$	−11.8611	−	1.70536i	−0.585063	−	0.0841193i
$412$	−4.51246	−	0.981625i	−0.222313	−	0.0483612i
$413$	−7.84169	+	7.84169i	−0.385864	+	0.385864i
$414$	12.0315	+	2.78319i	0.591317	+	0.136786i
$415$	−1.24691	−	1.91589i	−0.0612086	−	0.0940474i
$416$	−0.515218	+	0.331111i	−0.0252607	+	0.0162340i
$417$	−2.44372	−	3.26443i	−0.119669	−	0.159860i
$418$	0.956754	−	0.356851i	0.0467964	−	0.0174541i
$419$	−0.132001	+	0.0387591i	−0.00644868	+	0.00189350i	−0.284955	−	0.958541i	$-0.591979\pi$
$419$	−0.132001	+	0.0387591i	−0.00644868	+	0.00189350i	0.278507	+	0.960434i	$0.410161\pi$
$420$	3.92690	−	0.877953i	0.191613	−	0.0428397i
$421$	25.0172	−	21.6775i	1.21926	−	1.05650i	0.222599	−	0.974910i	$-0.428546\pi$
$421$	25.0172	−	21.6775i	1.21926	−	1.05650i	0.996666	−	0.0815888i	$-0.0259994\pi$
$422$	18.6238	+	13.9416i	0.906591	+	0.678666i
$423$	8.57479	+	15.7036i	0.416921	+	0.763533i
$424$	−3.79413	+	4.37866i	−0.184259	+	0.212647i
$425$	−2.68031	+	13.0425i	−0.130014	+	0.632652i
$426$	−4.58054	−	2.94374i	−0.221928	−	0.142625i
$427$	2.12948	+	29.7740i	0.103053	+	1.44086i
$428$	−4.34232	+	2.37109i	−0.209894	+	0.114611i
$429$	−0.0180008	−	0.125198i	−0.000869085	−	0.00604462i
$430$	−11.3141	−	20.4395i	−0.545613	−	0.985681i
$431$	−28.8071	+	13.1558i	−1.38759	+	0.633691i	−0.962456	−	0.271439i	$-0.912501\pi$
$431$	−28.8071	+	13.1558i	−1.38759	+	0.633691i	−0.425135	+	0.905130i	$0.639773\pi$
$432$	−1.74182	+	3.18990i	−0.0838033	+	0.153474i
$433$	12.9645	+	34.7592i	0.623034	+	1.67042i	0.736134	+	0.676836i	$0.236649\pi$
$433$	12.9645	+	34.7592i	0.623034	+	1.67042i	−0.113100	+	0.993584i	$0.536078\pi$
$434$	3.56715	−	24.8101i	0.171229	−	1.19092i
$435$	−8.12037	−	3.65209i	−0.389342	−	0.175104i
$436$			7.97574i			0.381969i
$437$	2.40065	−	15.2710i	0.114839	−	0.730512i
$438$	4.43961	+	4.43961i	0.212133	+	0.212133i
$439$	5.37599	+	8.36521i	0.256582	+	0.399250i	0.945517	−	0.325574i	$-0.105558\pi$
$439$	5.37599	+	8.36521i	0.256582	+	0.399250i	−0.688934	+	0.724824i	$0.741921\pi$
$440$	−0.642656	+	0.297975i	−0.0306374	+	0.0142054i
$441$	0.662497	−	1.45067i	0.0315475	−	0.0690793i
$442$	1.43144	+	0.781624i	0.0680865	+	0.0371781i
$443$	−13.5142	+	36.2330i	−0.642079	+	1.72148i	0.0490953	+	0.998794i	$0.484366\pi$
$443$	−13.5142	+	36.2330i	−0.642079	+	1.72148i	−0.691175	+	0.722688i	$0.742907\pi$
$444$	−1.03064	−	1.18942i	−0.0489118	−	0.0564472i
$445$	8.35149	+	0.549000i	0.395899	+	0.0260251i
$446$	−6.34845	−	1.86407i	−0.300608	−	0.0882664i
$447$	12.8778	−	0.921042i	0.609101	−	0.0435638i
$448$	−2.69723	+	0.586747i	−0.127432	+	0.0277212i
$449$	−10.0638	+	15.6596i	−0.474941	+	0.739022i	−0.993228	−	0.116185i	$-0.962934\pi$
$449$	−10.0638	+	15.6596i	−0.474941	+	0.739022i	0.518287	+	0.855207i	$0.326570\pi$
$450$	−12.1142	−	4.36014i	−0.571069	−	0.205539i
$451$	0.709112	−	2.41501i	0.0333908	−	0.113718i
$452$	3.67711	−	4.91204i	0.172957	−	0.231043i
$453$	−0.277961	+	3.88640i	−0.0130597	+	0.182599i
$454$	−5.73715	−	12.5626i	−0.269258	−	0.589592i
$455$	3.76889	−	0.291376i	0.176689	−	0.0136599i
$456$	1.91147	+	0.872941i	0.0895130	+	0.0408792i
$457$	−3.96387	+	2.96732i	−0.185422	+	0.138805i	−0.687956	−	0.725752i	$-0.741492\pi$
$457$	−3.96387	+	2.96732i	−0.185422	+	0.138805i	0.502534	+	0.864557i	$0.332401\pi$
$458$	4.87059	−	22.3898i	0.227588	−	1.04620i
$459$	9.67863			0.451760
$460$	−0.843833	+	10.6906i	−0.0393439	+	0.498450i
$461$	19.7385			0.919315			0.459658	−	0.888096i	$-0.347972\pi$
$461$	19.7385			0.919315			0.459658	+	0.888096i	$0.347972\pi$
$462$	0.121179	−	0.557050i	0.00563775	−	0.0259163i
$463$	11.3553	−	8.50050i	0.527727	−	0.395052i	−0.301925	−	0.953332i	$-0.597629\pi$
$463$	11.3553	−	8.50050i	0.527727	−	0.395052i	0.829653	+	0.558280i	$0.188538\pi$
$464$	5.55597	+	2.53733i	0.257930	+	0.117793i
$465$	8.61077	−	10.0537i	0.399315	−	0.466231i
$466$	−0.982909	−	2.15227i	−0.0455324	−	0.0997020i
$467$	−1.55348	+	21.7205i	−0.0718864	+	1.00510i	0.825656	+	0.564174i	$0.190805\pi$
$467$	−1.55348	+	21.7205i	−0.0718864	+	1.00510i	−0.897542	+	0.440929i	$0.854649\pi$
$468$	−0.945081	+	1.26248i	−0.0436864	+	0.0583582i
$469$	5.97560	−	20.3510i	0.275928	−	0.939723i
$470$	−12.3843	+	9.38252i	−0.571246	+	0.432784i
$471$	−5.03066	+	7.82786i	−0.231801	+	0.360689i
$472$	3.92578	−	0.854001i	0.180699	−	0.0393086i
$473$	−3.30138	+	0.236119i	−0.151798	+	0.0108568i
$474$	4.69102	+	1.37741i	0.215465	+	0.0632664i
$475$	−4.36223	+	15.5151i	−0.200153	+	0.711881i
$476$	4.81371	+	5.55531i	0.220636	+	0.254627i
$477$	−5.21366	+	13.9784i	−0.238717	+	0.640025i
$478$	15.7627	+	8.60707i	0.720968	+	0.393678i
$479$	12.6195	−	27.6329i	0.576600	−	1.26258i	−0.366608	−	0.930376i	$-0.619481\pi$
$479$	12.6195	−	27.6329i	0.576600	−	1.26258i	0.943208	−	0.332203i	$-0.107792\pi$
$480$	−1.36875	−	0.501558i	−0.0624745	−	0.0228929i
$481$	−0.799341	−	1.24380i	−0.0364468	−	0.0567123i
$482$	0.408619	+	0.408619i	0.0186121	+	0.0186121i
$483$	−6.44751	−	5.73669i	−0.293372	−	0.261029i
$484$		−	10.8996i		−	0.495438i
$485$	−11.0497	+	24.5689i	−0.501742	+	1.11561i
$486$	−2.04860	+	14.2483i	−0.0929265	+	0.646318i
$487$	6.95752	+	18.6538i	0.315275	+	0.845286i	0.993848	+	0.110753i	$0.0353262\pi$
$487$	6.95752	+	18.6538i	0.315275	+	0.845286i	−0.678573	+	0.734533i	$0.737401\pi$
$488$	5.18260	−	9.49122i	0.234605	−	0.429648i
$489$	7.03532	−	3.21292i	0.318148	−	0.145293i
$490$	1.33100	+	0.382507i	0.0601285	+	0.0172799i
$491$	4.55533	+	31.6830i	0.205579	+	1.42984i	0.787362	+	0.616491i	$0.211446\pi$
$491$	4.55533	+	31.6830i	0.205579	+	1.42984i	−0.581782	+	0.813344i	$0.697644\pi$
$492$	4.54603	−	2.48232i	0.204951	−	0.111912i
$493$	−1.16037	−	16.2240i	−0.0522602	−	0.730693i
$494$	1.66072	+	1.06728i	0.0747194	+	0.0480192i
$495$	−1.28236	+	1.29721i	−0.0576378	+	0.0583053i
$496$	−5.94651	+	6.86264i	−0.267006	+	0.308142i
$497$	−11.0487	−	20.2342i	−0.495603	−	0.907630i
$498$	−0.533528	−	0.399394i	−0.0239080	−	0.0178973i
$499$	−25.6825	+	22.2540i	−1.14971	+	0.996227i	−0.149735	+	0.988726i	$0.547842\pi$
$499$	−25.6825	+	22.2540i	−1.14971	+	0.996227i	−0.999972	+	0.00750072i	$0.997612\pi$
$500$	2.18751	−	10.9643i	0.0978283	−	0.490336i
$501$	8.35923	−	2.45449i	0.373463	−	0.109659i
$502$	6.89747	−	2.57262i	0.307849	−	0.114822i
$503$	−11.5785	−	15.4671i	−0.516261	−	0.689645i	0.464340	−	0.885657i	$-0.346292\pi$
$503$	−11.5785	−	15.4671i	−0.516261	−	0.689645i	−0.980601	+	0.196012i	$0.937201\pi$
$504$	−5.97946	+	3.84276i	−0.266346	+	0.171170i
$505$	−4.21916	+	19.9474i	−0.187750	+	0.887647i
$506$	1.32378	+	0.745562i	0.0588493	+	0.0331443i
$507$	−5.81984	+	5.81984i	−0.258468	+	0.258468i
$508$	13.1458	+	2.85969i	0.583250	+	0.126878i
$509$	4.65529	+	0.669329i	0.206342	+	0.0296675i	0.244711	−	0.969596i	$-0.421307\pi$
$509$	4.65529	+	0.669329i	0.206342	+	0.0296675i	−0.0383687	+	0.999264i	$0.512216\pi$
$510$	0.574579	+	3.83923i	0.0254428	+	0.170004i
$511$	7.48959	+	25.5072i	0.331320	+	1.12837i
$512$	0.936950	+	0.349464i	0.0414077	+	0.0154443i
$513$	11.6853	+	0.835748i	0.515918	+	0.0368992i
$514$	6.97678	−	1.00311i	0.307733	−	0.0442453i
$515$	−2.96621	−	9.89095i	−0.130707	−	0.435847i
$516$	−5.14754	−	4.46037i	−0.226608	−	0.196357i
$517$	0.467904	+	2.15092i	0.0205784	+	0.0945974i
$518$	−1.41648	−	6.51144i	−0.0622364	−	0.286096i
$519$	−5.74682	−	4.97965i	−0.252257	−	0.218582i
$520$	−1.20571	−	0.649381i	−0.0528737	−	0.0284773i
$521$	−18.1659	+	2.61186i	−0.795861	+	0.114428i	−0.528238	−	0.849096i	$-0.677147\pi$
$521$	−18.1659	+	2.61186i	−0.795861	+	0.114428i	−0.267623	+	0.963524i	$0.586238\pi$
$522$	15.6878	+	1.12202i	0.686638	+	0.0491093i
$523$	13.2959	+	4.95911i	0.581389	+	0.216847i	0.622914	−	0.782291i	$-0.285949\pi$
$523$	13.2959	+	4.95911i	0.581389	+	0.216847i	−0.0415246	+	0.999137i	$0.513221\pi$
$524$	3.29347	+	11.2165i	0.143876	+	0.489997i
$525$	5.97007	+	6.73162i	0.260555	+	0.293792i
$526$	−17.6812	−	2.54217i	−0.770937	−	0.110844i
$527$	23.6290	+	5.14017i	1.02929	+	0.223909i
$528$	−0.146036	+	0.146036i	−0.00635542	+	0.00635542i
$529$	19.6686	−	11.9225i	0.855156	−	0.518371i
$530$	−12.6749	−	2.68092i	−0.550563	−	0.116452i
$531$	8.70301	−	5.59308i	0.377678	−	0.242719i
$532$	5.33202	+	7.12275i	0.231172	+	0.308810i
$533$	4.55911	−	1.70046i	0.197477	−	0.0736550i
$534$	2.34129	−	0.687464i	0.101317	−	0.0297495i
$535$	−9.34104	−	5.92741i	−0.403848	−	0.256264i
$536$	−5.80716	+	5.03193i	−0.250831	+	0.217346i
$537$	5.30723	+	3.97294i	0.229024	+	0.171445i
$538$	8.49263	+	15.5531i	0.366143	+	0.670542i
$539$	0.128485	−	0.148280i	0.00553425	−	0.00638686i
$540$	−8.12680	+	0.0467909i	−0.349722	+	0.00201356i
$541$	−21.1489	−	13.5916i	−0.909263	−	0.584348i	0.000260505	−	1.00000i	$-0.499917\pi$
$541$	−21.1489	−	13.5916i	−0.909263	−	0.584348i	−0.909524	+	0.415652i	$0.863553\pi$
$542$	−2.07743	−	29.0462i	−0.0892332	−	1.24764i
$543$	10.1692	−	5.55280i	0.436402	−	0.238293i
$544$	−0.378985	−	2.63590i	−0.0162489	−	0.113013i
$545$	−15.6033	+	8.63704i	−0.668372	+	0.369970i
$546$	1.00250	−	0.457828i	0.0429032	−	0.0195932i
$547$	1.42507	−	2.60982i	0.0609315	−	0.111588i	−0.845438	−	0.534074i	$-0.820661\pi$
$547$	1.42507	−	2.60982i	0.0609315	−	0.111588i	0.906370	+	0.422486i	$0.138842\pi$
$548$	6.42350	+	17.2221i	0.274398	+	0.735691i
$549$	3.96290	−	27.5626i	0.169132	−	1.17634i
$550$	−1.27888	−	0.934577i	−0.0545318	−	0.0398505i
$551$		−	19.6879i		−	0.838734i
$552$	0.841389	+	3.01118i	0.0358119	+	0.128164i
$553$	14.6376	+	14.6376i	0.622456	+	0.622456i
$554$	12.7225	+	19.7965i	0.540525	+	0.841074i
$555$	1.21082	−	3.30432i	0.0513965	−	0.140261i
$556$	−2.59841	+	5.68973i	−0.110197	+	0.241298i
$557$	−6.99149	−	3.81764i	−0.296239	−	0.161759i	0.324256	−	0.945970i	$-0.394886\pi$
$557$	−6.99149	−	3.81764i	−0.296239	−	0.161759i	−0.620494	+	0.784211i	$0.713068\pi$
$558$	−8.17132	+	21.9081i	−0.345919	+	0.927446i
$559$	−4.19023	−	4.83579i	−0.177228	−	0.204532i
$560$	−4.06875	−	4.64133i	−0.171936	−	0.196132i
$561$	0.527703	+	0.154948i	0.0222797	+	0.00654190i
$562$	−24.2646	+	1.73544i	−1.02354	+	0.0732052i
$563$	14.8037	−	3.22035i	0.623901	−	0.135721i	0.110509	−	0.993875i	$-0.464752\pi$
$563$	14.8037	−	3.22035i	0.623901	−	0.135721i	0.513393	+	0.858154i	$0.328388\pi$
$564$	−2.44902	+	3.81075i	−0.103122	+	0.160462i
$565$	13.5917	+	1.87438i	0.571805	+	0.0788557i
$566$	−0.628039	+	2.13890i	−0.0263984	+	0.0899049i
$567$	−8.85917	+	11.8345i	−0.372050	+	0.497001i
$568$	−0.595828	+	8.33076i	−0.0250004	+	0.349551i
$569$	−8.90868	−	19.5073i	−0.373471	−	0.817788i	−0.999285	−	0.0378154i	$-0.987960\pi$
$569$	−8.90868	−	19.5073i	−0.373471	−	0.817788i	0.625813	−	0.779973i	$-0.284767\pi$
$570$	0.362188	+	4.68483i	0.0151704	+	0.196226i
$571$	−13.1374	−	5.99965i	−0.549783	−	0.251077i	0.121101	−	0.992640i	$-0.461358\pi$
$571$	−13.1374	−	5.99965i	−0.549783	−	0.251077i	−0.670883	+	0.741563i	$0.734085\pi$
$572$	−0.155320	+	0.116271i	−0.00649425	+	0.00486153i
$573$	−1.84571	+	8.48459i	−0.0771056	+	0.354449i
$574$	21.9310			0.915380
$575$	−21.8282	+	9.92613i	−0.910300	+	0.413948i
$576$	2.57499			0.107291
$577$	8.48076	−	38.9854i	0.353059	−	1.62298i	−0.367802	−	0.929904i	$-0.619889\pi$
$577$	8.48076	−	38.9854i	0.353059	−	1.62298i	0.720860	−	0.693080i	$-0.243747\pi$
$578$	7.93208	−	5.93788i	0.329931	−	0.246983i
$579$	−13.8253	−	6.31380i	−0.574560	−	0.262393i
$580$	1.05275	+	13.6171i	0.0437131	+	0.565420i
$581$	−1.17224	−	2.56685i	−0.0486328	−	0.106491i
$582$	−0.560308	+	7.83413i	−0.0232255	+	0.324735i
$583$	−1.09994	+	1.46935i	−0.0455550	+	0.0608543i
$584$	2.71331	−	9.24069i	0.112278	−	0.382382i
$585$	−3.49329	−	0.481748i	−0.144430	−	0.0199178i
$586$	13.8445	−	21.5425i	0.571913	−	0.889914i
$587$	20.2464	−	4.40434i	0.835659	−	0.181786i	0.225677	−	0.974202i	$-0.427541\pi$
$587$	20.2464	−	4.40434i	0.835659	−	0.181786i	0.609981	+	0.792416i	$0.291177\pi$
$588$	0.402731	−	0.0288039i	0.0166083	−	0.00118785i
$589$	28.0841	+	8.24623i	1.15718	+	0.339780i
$590$	5.92201	+	6.75538i	0.243805	+	0.278115i
$591$	6.94311	+	8.01277i	0.285601	+	0.329601i
$592$	−0.843648	+	2.26191i	−0.0346737	+	0.0929639i
$593$	−31.5118	−	17.2067i	−1.29403	−	0.706596i	−0.323195	−	0.946332i	$-0.604757\pi$
$593$	−31.5118	−	17.2067i	−1.29403	−	0.706596i	−0.970838	+	0.239737i	$0.922939\pi$
$594$	−0.478302	+	1.04734i	−0.0196250	+	0.0429727i
$595$	−5.65529	+	15.4332i	−0.231844	+	0.632700i
$596$	−10.7069	−	16.6602i	−0.438570	−	0.682429i
$597$	3.45707	+	3.45707i	0.141488	+	0.141488i
$598$	0.379804	+	2.91251i	0.0155313	+	0.119101i
$599$		−	45.2263i		−	1.84790i	−0.382517	−	0.923948i	$-0.624943\pi$
$599$		−	45.2263i		−	1.84790i	0.382517	−	0.923948i	$-0.375057\pi$
$600$	−0.501014	−	3.22089i	−0.0204538	−	0.131492i
$601$	5.82478	−	40.5122i	0.237598	−	1.65253i	−0.426209	−	0.904625i	$-0.640151\pi$
$601$	5.82478	−	40.5122i	0.237598	−	1.65253i	0.663807	−	0.747904i	$-0.268940\pi$
$602$	−10.0783	−	27.0209i	−0.410760	−	1.10129i
$603$	−9.48251	+	17.3659i	−0.386158	+	0.707195i
$604$	5.43655	−	2.48279i	0.221210	−	0.101023i
$605$	21.3235	−	11.8034i	0.866923	−	0.479876i
$606$	0.845965	+	5.88382i	0.0343650	+	0.239014i
$607$	0.389892	−	0.212897i	0.0158252	−	0.00864123i	−0.471317	−	0.881964i	$-0.656221\pi$
$607$	0.389892	−	0.212897i	0.0158252	−	0.00864123i	0.487142	+	0.873323i	$0.338039\pi$
$608$	−0.229950	−	3.21512i	−0.00932570	−	0.130390i
$609$	−9.24650	−	5.94236i	−0.374687	−	0.240797i
$610$	24.1804	−	0.139222i	0.979038	−	0.00563692i
$611$	−2.78676	+	3.21609i	−0.112740	+	0.130109i
$612$	−3.28632	−	6.01844i	−0.132842	−	0.243281i
$613$	29.4122	+	22.0177i	1.18795	+	0.889285i	0.995752	−	0.0920719i	$-0.0293490\pi$
$613$	29.4122	+	22.0177i	1.18795	+	0.889285i	0.192193	+	0.981357i	$0.438440\pi$
$614$	−9.08643	+	7.87344i	−0.366698	+	0.317746i
$615$	9.77924	+	6.20547i	0.394337	+	0.250229i
$616$	−0.839033	+	0.246362i	−0.0338056	+	0.00992622i
$617$	−9.62779	+	3.59098i	−0.387600	+	0.144567i	−0.535707	−	0.844404i	$-0.679955\pi$
$617$	−9.62779	+	3.59098i	−0.387600	+	0.144567i	0.148107	+	0.988971i	$0.452682\pi$
$618$	−1.80418	−	2.41010i	−0.0725746	−	0.0969483i
$619$	15.7999	−	10.1540i	0.635053	−	0.408124i	−0.183124	−	0.983090i	$-0.558621\pi$
$619$	15.7999	−	10.1540i	0.635053	−	0.408124i	0.818177	+	0.574966i	$0.194985\pi$
$620$	−19.8653	−	4.20179i	−0.797808	−	0.168748i
$621$	10.2615	+	14.0896i	0.411782	+	0.565397i
$622$	−11.9821	+	11.9821i	−0.480440	+	0.480440i
$623$	10.0956	+	2.19617i	0.404473	+	0.0879877i
$624$	−0.395202	−	0.0568214i	−0.0158207	−	0.00227468i
$625$	23.8188	−	7.59383i	0.952751	−	0.303753i
$626$	5.01796	+	17.0896i	0.200558	+	0.683038i
$627$	0.623731	+	0.232640i	0.0249094	+	0.00929074i
$628$	14.2367	+	1.01823i	0.568108	+	0.0406319i
$629$	6.36338	−	0.914915i	0.253724	−	0.0364801i
$630$	−13.9930	−	7.53651i	−0.557495	−	0.300262i
$631$	3.05021	+	2.64302i	0.121427	+	0.105217i	0.713458	−	0.700698i	$-0.247128\pi$
$631$	3.05021	+	2.64302i	0.121427	+	0.105217i	−0.592031	+	0.805915i	$0.701674\pi$
$632$	−1.59412	−	7.32803i	−0.0634105	−	0.291494i
$633$	3.22384	+	14.8198i	0.128136	+	0.589033i
$634$	−14.9098	−	12.9194i	−0.592144	−	0.513095i
$635$	8.64122	+	28.8145i	0.342916	+	1.14347i
$636$	−3.73868	+	0.537541i	−0.148248	+	0.0213149i
$637$	0.378340	+	0.0270594i	0.0149904	+	0.00107213i
$638$	1.81296	+	0.676201i	0.0717760	+	0.0267711i
$639$	6.05907	+	20.6353i	0.239693	+	0.816320i
$640$	0.330964	+	2.21144i	0.0130825	+	0.0874148i
$641$	−37.1849	−	5.34639i	−1.46872	−	0.211170i	−0.638936	−	0.769260i	$-0.720625\pi$
$641$	−37.1849	−	5.34639i	−1.46872	−	0.211170i	−0.829780	+	0.558090i	$0.811534\pi$
$642$	−3.15169	−	0.685609i	−0.124387	−	0.0270588i
$643$	12.6523	−	12.6523i	0.498957	−	0.498957i	−0.412156	−	0.911113i	$-0.635224\pi$
$643$	12.6523	−	12.6523i	0.498957	−	0.498957i	0.911113	+	0.412156i	$0.135224\pi$
$644$	−2.98350	+	12.8974i	−0.117566	+	0.508230i
$645$	3.15169	−	14.9006i	0.124098	−	0.586710i
$646$	−7.22111	+	4.64073i	−0.284111	+	0.182587i
$647$	−1.81752	−	2.42792i	−0.0714539	−	0.0954512i	0.763390	−	0.645937i	$-0.223533\pi$
$647$	−1.81752	−	2.42792i	−0.0714539	−	0.0954512i	−0.834844	+	0.550486i	$0.814442\pi$
$648$	5.01791	−	1.87158i	0.197122	−	0.0735227i
$649$	1.22120	−	0.358576i	0.0479363	−	0.0140754i
$650$	−0.0352608	−	3.06200i	−0.00138304	−	0.120102i
$651$	12.3494	−	10.7008i	0.484012	−	0.419399i
$652$	−9.49739	−	7.10966i	−0.371947	−	0.278436i
$653$	−7.38259	−	13.5202i	−0.288903	−	0.529087i	0.692410	−	0.721504i	$-0.256549\pi$
$653$	−7.38259	−	13.5202i	−0.288903	−	0.529087i	−0.981313	+	0.192418i	$0.938367\pi$
$654$	−3.40500	+	3.92958i	−0.133146	+	0.153659i
$655$	−18.3769	+	18.5897i	−0.718045	+	0.726361i
$656$	−6.68384	−	4.29544i	−0.260960	−	0.167709i
$657$	−1.76916	−	24.7361i	−0.0690215	−	0.965046i
$658$	−16.8337	+	9.19191i	−0.656247	+	0.358338i
$659$	−4.87682	−	33.9190i	−0.189974	−	1.32130i	−0.832069	−	0.554673i	$-0.812844\pi$
$659$	−4.87682	−	33.9190i	−0.189974	−	1.32130i	0.642095	−	0.766625i	$-0.278066\pi$
$660$	−0.443843	−	0.127553i	−0.0172766	−	0.00496499i
$661$	−34.1974	+	15.6174i	−1.33012	+	0.607447i	−0.948473	−	0.316859i	$-0.897372\pi$
$661$	−34.1974	+	15.6174i	−1.33012	+	0.607447i	−0.381651	+	0.924306i	$0.624645\pi$
$662$	8.60411	−	15.7573i	0.334408	−	0.612423i
$663$	0.371567	+	0.996209i	0.0144304	+	0.0386895i
$664$	−0.145488	+	1.01189i	−0.00564602	+	0.0392689i
$665$	−8.16044	+	18.1446i	−0.316448	+	0.703618i
$666$			6.21634i			0.240878i
$667$	22.3878	−	18.8903i	0.866859	−	0.731437i
$668$	−9.44957	−	9.44957i	−0.365615	−	0.365615i
$669$	−2.33202	−	3.62869i	−0.0901611	−	0.140293i
$670$	−16.1329	−	5.91167i	−0.623267	−	0.228388i
$671$	1.42314	−	3.11624i	0.0549397	−	0.120301i
$672$	−1.57940	−	0.862417i	−0.0609266	−	0.0332684i
$673$	−6.43685	+	17.2579i	−0.248122	+	0.665241i	0.751860	+	0.659322i	$0.229157\pi$
$673$	−6.43685	+	17.2579i	−0.248122	+	0.665241i	−0.999982	+	0.00591883i	$0.998116\pi$
$674$	−12.0097	−	13.8599i	−0.462595	−	0.533863i
$675$	−8.89217	−	15.8482i	−0.342260	−	0.609997i
$676$	12.1135	+	3.55685i	0.465905	+	0.136802i
$677$	6.56309	−	0.469401i	0.252240	−	0.0180406i	0.0553533	−	0.998467i	$-0.482371\pi$
$677$	6.56309	−	0.469401i	0.252240	−	0.0180406i	0.196887	+	0.980426i	$0.436917\pi$
$678$	3.90873	−	0.850292i	0.150114	−	0.0326553i
$679$	−17.9791	+	27.9761i	−0.689975	+	1.07362i
$680$	4.74633	−	3.59588i	0.182013	−	0.137896i
$681$	2.53658	−	8.63880i	0.0972019	−	0.331039i
$682$	−1.72393	+	2.30290i	−0.0660127	+	0.0881827i
$683$	2.40500	−	33.6263i	0.0920248	−	1.28667i	−0.716239	−	0.697855i	$-0.754138\pi$
$683$	2.40500	−	33.6263i	0.0920248	−	1.28667i	0.808264	−	0.588820i	$-0.200407\pi$
$684$	−3.44797	−	7.55001i	−0.131837	−	0.288682i
$685$	−26.7363	+	31.2166i	−1.02154	+	1.19273i
$686$	−16.0210	−	7.31656i	−0.611685	−	0.279347i
$687$	11.9583	−	8.95189i	0.456239	−	0.341536i
$688$	−2.22084	+	10.2090i	−0.0846687	+	0.389216i
$689$	−3.54836			−0.135182
$690$	−4.97976	+	4.90690i	−0.189576	+	0.186802i
$691$	−11.7111			−0.445510			−0.222755	−	0.974874i	$-0.571505\pi$
$691$	−11.7111			−0.445510			−0.222755	+	0.974874i	$0.571505\pi$
$692$	−2.47939	+	11.3976i	−0.0942522	+	0.433270i
$693$	−1.80259	+	1.34940i	−0.0684748	+	0.0512596i
$694$	−23.8097	−	10.8735i	−0.903805	−	0.412754i
$695$	−13.9449	+	1.07810i	−0.528962	+	0.0408945i
$696$	1.65415	+	3.62208i	0.0627003	+	0.137294i
$697$	−1.50938	+	21.1039i	−0.0571719	+	0.799368i
$698$	13.4386	−	17.9519i	0.508659	−	0.679489i
$699$	0.434576	−	1.48003i	0.0164372	−	0.0559799i
$700$	4.67393	−	12.9861i	0.176658	−	0.490827i
$701$	7.90767	−	12.3046i	0.298669	−	0.464737i	−0.659191	−	0.751976i	$-0.729101\pi$
$701$	7.90767	−	12.3046i	0.298669	−	0.464737i	0.957859	+	0.287239i	$0.0927373\pi$
$702$	−2.17503	+	0.473150i	−0.0820914	+	0.0178579i
$703$	7.76169	−	0.555127i	0.292738	−	0.0209370i
$704$	0.303963	+	0.0892515i	0.0114560	+	0.00336379i
$705$	−10.1072	−	0.664417i	−0.380660	−	0.0250234i
$706$	8.23961	+	9.50902i	0.310102	+	0.357877i
$707$	−8.79561	+	23.5820i	−0.330793	+	0.886891i
$708$	2.29879	+	1.25523i	0.0863938	+	0.0471746i
$709$	−0.106146	+	0.232428i	−0.00398641	+	0.00872901i	−0.911615	−	0.411046i	$-0.865164\pi$
$709$	−0.106146	+	0.232428i	−0.00398641	+	0.00872901i	0.907628	+	0.419775i	$0.137891\pi$
$710$	−16.9431	+	7.85586i	−0.635863	+	0.294825i
$711$	−10.4403	−	16.2454i	−0.391542	−	0.609251i
$712$	−2.64667	−	2.64667i	−0.0991883	−	0.0991883i
$713$	17.5693	+	39.8475i	0.657976	+	1.49230i
$714$			4.79212i			0.179341i
$715$	−0.395664	−	0.177948i	−0.0147970	−	0.00665488i
$716$	1.44723	−	10.0657i	0.0540855	−	0.376173i
$717$	4.09161	+	10.9700i	0.152804	+	0.409683i
$718$	−10.1359	+	18.5625i	−0.378268	+	0.692746i
$719$	11.2789	−	5.15090i	0.420632	−	0.192096i	−0.193843	−	0.981033i	$-0.562095\pi$
$719$	11.2789	−	5.15090i	0.420632	−	0.192096i	0.614475	+	0.788936i	$0.289368\pi$
$720$	2.78850	+	5.03758i	0.103921	+	0.187740i
$721$	−1.81410	−	12.6174i	−0.0675607	−	0.469895i
$722$	7.55692	−	4.12639i	0.281239	−	0.153568i
$723$	0.0268757	+	0.375771i	0.000999517	+	0.0139751i
$724$	−14.9513	−	9.60865i	−0.555662	−	0.357103i
$725$	−25.4998	+	16.8057i	−0.947039	+	0.624150i
$726$	4.65327	−	5.37016i	0.172699	−	0.199305i
$727$	−14.7751	−	27.0585i	−0.547977	−	1.00355i	−0.994089	−	0.108568i	$-0.965373\pi$
$727$	−14.7751	−	27.0585i	−0.547977	−	1.00355i	0.446112	−	0.894977i	$-0.352808\pi$
$728$	−1.35334	−	1.01310i	−0.0501581	−	0.0375479i
$729$	5.05020	−	4.37602i	0.187044	−	0.162075i
$730$	21.0163	−	4.69870i	0.777847	−	0.173907i
$731$	26.6955	−	7.83852i	0.987370	−	0.289918i
$732$	6.60542	−	2.46369i	0.244143	−	0.0910607i
$733$	−27.7729	−	37.1002i	−1.02581	−	1.37033i	−0.926932	−	0.375228i	$-0.877564\pi$
$733$	−27.7729	−	37.1002i	−1.02581	−	1.37033i	−0.0988817	−	0.995099i	$-0.531527\pi$
$734$	−16.2185	+	10.4230i	−0.598634	+	0.384719i
$735$	0.492474	+	0.756689i	0.0181652	+	0.0279109i
$736$	3.43539	−	3.34636i	0.126630	−	0.123348i
$737$	−1.72127	+	1.72127i	−0.0634039	+	0.0634039i
$738$	−19.9910	−	4.34878i	−0.735880	−	0.160081i
$739$	11.5958	+	1.66723i	0.426559	+	0.0613300i	0.352251	−	0.935905i	$-0.385416\pi$
$739$	11.5958	+	1.66723i	0.426559	+	0.0613300i	0.0743078	+	0.997235i	$0.476325\pi$
$740$	−5.33868	+	0.798985i	−0.196254	+	0.0293713i
$741$	0.362580	+	1.23484i	0.0133197	+	0.0453628i
$742$	−14.9844	−	5.58888i	−0.550093	−	0.205174i
$743$	19.6035	+	1.40207i	0.719182	+	0.0514369i	0.426133	−	0.904660i	$-0.359875\pi$
$743$	19.6035	+	1.40207i	0.719182	+	0.0514369i	0.293049	+	0.956097i	$0.405330\pi$
$744$	−5.85959	+	0.842482i	−0.214823	+	0.0308869i
$745$	20.9985	−	38.9880i	0.769327	−	1.42841i
$746$	−0.0368427	−	0.0319244i	−0.00134891	−	0.00116884i
$747$	0.559558	+	2.57225i	0.0204731	+	0.0941135i
$748$	−0.179326	−	0.824348i	−0.00655680	−	0.0301411i
$749$	−10.3210	−	8.94322i	−0.377122	−	0.326778i
$750$	5.75862	−	4.46811i	0.210275	−	0.163152i
$751$	40.7610	−	5.86055i	1.48739	−	0.213855i	0.649780	−	0.760122i	$-0.274861\pi$
$751$	40.7610	−	5.86055i	1.48739	−	0.213855i	0.837611	+	0.546267i	$0.183952\pi$
$752$	6.93072	+	0.495695i	0.252737	+	0.0180761i
$753$	4.49663	+	1.67716i	0.163866	+	0.0611190i
$754$	1.05389	+	3.58923i	0.0383805	+	0.130712i
$755$	10.7445	+	7.94713i	0.391033	+	0.289226i
$756$	−9.93018	−	1.42774i	−0.361157	−	0.0519266i
$757$	11.8215	+	2.57161i	0.429660	+	0.0934669i	0.422195	−	0.906505i	$-0.361260\pi$
$757$	11.8215	+	2.57161i	0.429660	+	0.0934669i	0.00746575	+	0.999972i	$0.497624\pi$
$758$	−9.25755	+	9.25755i	−0.336250	+	0.336250i
$759$	0.333921	+	0.932481i	0.0121206	+	0.0338469i
$760$	6.04088	−	3.93156i	0.219126	−	0.142613i
$761$	−24.3584	+	15.6542i	−0.882991	+	0.567464i	−0.901701	−	0.432361i	$-0.857681\pi$
$761$	−24.3584	+	15.6542i	−0.882991	+	0.567464i	0.0187095	+	0.999825i	$0.494044\pi$
$762$	5.25596	+	7.02114i	0.190403	+	0.254349i
$763$	−20.6275	+	7.69364i	−0.746764	+	0.278529i
$764$	12.7795	−	3.75241i	0.462348	−	0.135758i
$765$	8.21536	−	12.9466i	0.297027	−	0.468087i
$766$	−20.4233	+	17.6969i	−0.737924	+	0.639415i
$767$	1.96976	+	1.47455i	0.0711241	+	0.0532428i
$768$	0.312434	+	0.572181i	0.0112740	+	0.0206468i
$769$	−24.3410	+	28.0910i	−0.877757	+	1.01299i	0.122033	+	0.992526i	$0.461058\pi$
$769$	−24.3410	+	28.0910i	−0.877757	+	1.01299i	−0.999791	+	0.0204598i	$0.993487\pi$
$770$	−1.39057	−	1.37465i	−0.0501127	−	0.0495390i
$771$	3.86565	+	2.48430i	0.139218	+	0.0894700i
$772$	1.66318	+	23.2543i	0.0598592	+	0.836941i
$773$	9.46013	−	5.16562i	0.340257	−	0.185794i	−0.300031	−	0.953930i	$-0.596997\pi$
$773$	9.46013	−	5.16562i	0.340257	−	0.185794i	0.640288	+	0.768135i	$0.278815\pi$
$774$	3.82870	+	26.6292i	0.137620	+	0.957166i
$775$	−13.2922	−	43.4135i	−0.477471	−	1.55946i
$776$	10.9589	−	5.00476i	0.393401	−	0.179660i
$777$	2.08198	−	3.81286i	0.0746905	−	0.136785i
$778$	4.29554	+	11.5168i	0.154003	+	0.412897i
$779$	−3.64464	+	25.3490i	−0.130583	+	0.908223i
$780$	−0.316807	−	0.834685i	−0.0113435	−	0.0298865i
$781$			2.64589i			0.0946773i
$782$	−12.2057	−	3.75864i	−0.436475	−	0.134409i
$783$	15.6972	+	15.6972i	0.560971	+	0.560971i
$784$	−0.334838	−	0.521018i	−0.0119585	−	0.0186078i
$785$	13.4252	+	28.9547i	0.479165	+	1.03344i
$786$	−3.16590	+	6.93235i	−0.112924	+	0.247269i
$787$	−21.9909	−	12.0079i	−0.783890	−	0.428036i	0.0368623	−	0.999320i	$-0.488264\pi$
$787$	−21.9909	−	12.0079i	−0.783890	−	0.428036i	−0.820752	+	0.571284i	$0.806446\pi$
$788$	5.68343	−	15.2379i	0.202464	−	0.542826i
$789$	−7.62607	−	8.80096i	−0.271495	−	0.313322i
$790$	12.6099	−	11.0543i	0.448640	−	0.393294i
$791$	16.2509	+	4.77171i	0.577817	+	0.169662i
$792$	0.813667	−	0.0581946i	0.0289124	−	0.00206786i
$793$	6.47159	−	1.40781i	0.229813	−	0.0499927i
$794$	−4.28451	+	6.66682i	−0.152052	+	0.236597i
$795$	−5.10028	−	6.73204i	−0.180888	−	0.238761i
$796$	2.11282	−	7.19560i	0.0748869	−	0.255041i
$797$	29.2439	−	39.0653i	1.03587	−	1.38376i	0.115237	−	0.993338i	$-0.463237\pi$
$797$	29.2439	−	39.0653i	1.03587	−	1.38376i	0.920635	−	0.390425i	$-0.127672\pi$
$798$	−0.413799	+	5.78567i	−0.0146483	+	0.204810i
$799$	−7.68671	−	16.8315i	−0.271936	−	0.595457i
$800$	−3.96794	+	3.04228i	−0.140288	+	0.107561i
$801$	−8.76713	−	4.00381i	−0.309771	−	0.141468i
$802$	11.1587	−	8.35327i	0.394026	−	0.294964i
$803$	0.648535	−	2.98127i	0.0228863	−	0.105207i
$804$	−5.00937			−0.176667
$805$	−28.4627	+	8.13005i	−1.00318	+	0.286547i
$806$	−5.56132			−0.195889
$807$	−2.45568	+	11.2886i	−0.0864439	+	0.397376i
$808$	7.29943	−	5.46428i	0.256793	−	0.192233i
$809$	26.4368	+	12.0733i	0.929468	+	0.424474i	0.821841	−	0.569718i	$-0.192947\pi$
$809$	26.4368	+	12.0733i	0.929468	+	0.424474i	0.107627	+	0.994191i	$0.465675\pi$
$810$	9.09543	+	7.79000i	0.319581	+	0.273713i
$811$	−6.40557	−	14.0262i	−0.224930	−	0.492528i	0.763197	−	0.646166i	$-0.223628\pi$
$811$	−6.40557	−	14.0262i	−0.224930	−	0.492528i	−0.988127	+	0.153637i	$0.950901\pi$
$812$	−1.20277	+	16.8169i	−0.0422088	+	0.590156i
$813$	11.3769	−	15.1977i	0.399005	−	0.533008i
$814$	−0.215464	+	0.733802i	−0.00755200	+	0.0257198i
$815$	3.62409	−	26.2794i	0.126946	−	0.920526i
$816$	0.938595	−	1.46048i	0.0328574	−	0.0511271i
$817$	32.9071	−	7.15851i	1.15127	−	0.250444i
$818$	1.46110	−	0.104500i	0.0510861	−	0.00365375i
$819$	−4.17678	−	1.22641i	−0.145948	−	0.0428543i
$820$	1.16535	−	17.7275i	0.0406957	−	0.619071i
$821$	34.3007	+	39.5851i	1.19710	+	1.38153i	0.905147	+	0.425099i	$0.139761\pi$
$821$	34.3007	+	39.5851i	1.19710	+	1.38153i	0.291956	+	0.956432i	$0.405694\pi$
$822$	−4.18764	+	11.2275i	−0.146061	+	0.391604i
$823$	3.01630	+	1.64702i	0.105142	+	0.0574116i	0.530959	−	0.847397i	$-0.321832\pi$
$823$	3.01630	+	1.64702i	0.105142	+	0.0574116i	−0.425818	+	0.904809i	$0.640014\pi$
$824$	−1.91838	+	4.20067i	−0.0668301	+	0.146337i
$825$	−0.231106	−	1.00644i	−0.00804609	−	0.0350397i
$826$	5.99561	+	9.32935i	0.208614	+	0.324610i
$827$	27.7239	+	27.7239i	0.964054	+	0.964054i	0.999376	−	0.0353224i	$-0.0112458\pi$
$827$	27.7239	+	27.7239i	0.964054	+	0.964054i	−0.0353224	+	0.999376i	$0.511246\pi$
$828$	5.27707	−	11.1650i	0.183391	−	0.388009i
$829$		−	5.54125i		−	0.192455i	−0.995359	−	0.0962277i	$-0.969322\pi$
$829$		−	5.54125i		−	0.192455i	0.995359	−	0.0962277i	$-0.0306777\pi$
$830$	−2.13716	+	0.811166i	−0.0741819	+	0.0281560i
$831$	−2.18328	+	15.1851i	−0.0757372	+	0.526764i
$832$	0.214026	+	0.573827i	0.00742003	+	0.0198939i
$833$	−0.790422	+	1.44755i	−0.0273865	+	0.0501546i
$834$	−3.70927	+	1.69397i	−0.128442	+	0.0586573i
$835$	8.25356	−	28.7197i	0.285626	−	0.993887i
$836$	−0.145323	−	1.01074i	−0.00502610	−	0.0349573i
$837$	−28.9661	+	15.8167i	−1.00122	+	0.546706i
$838$	0.00981441	+	0.137223i	0.000339033	+	0.00474030i
$839$	17.9179	+	11.5151i	0.618595	+	0.397547i	0.812071	−	0.583558i	$-0.198340\pi$
$839$	17.9179	+	11.5151i	0.618595	+	0.397547i	−0.193477	+	0.981105i	$0.561976\pi$
$840$	−0.0231673	−	4.02378i	−0.000799349	−	0.138833i
$841$	5.43986	−	6.27793i	0.187581	−	0.216480i
$842$	−15.8644	−	29.0534i	−0.546722	−	1.00125i
$843$	−12.6959	−	9.50402i	−0.437270	−	0.327336i
$844$	17.5817	−	15.2347i	0.605189	−	0.524399i
$845$	6.15948	+	27.5500i	0.211892	+	0.947749i
$846$	17.1674	−	5.04080i	0.590227	−	0.173306i
$847$	28.1895	−	10.5141i	0.968602	−	0.361270i
$848$	3.47210	+	4.63818i	0.119232	+	0.159276i
$849$	−1.22257	+	0.785698i	−0.0419585	+	0.0269651i
$850$	12.1747	+	5.39143i	0.417587	+	0.184925i
$851$	8.07851	+	8.29344i	0.276928	+	0.284295i
$852$	−3.85013	+	3.85013i	−0.131903	+	0.131903i
$853$	−53.4367	−	11.6244i	−1.82964	−	0.398013i	−0.840116	−	0.542407i	$-0.817513\pi$
$853$	−53.4367	−	11.6244i	−1.82964	−	0.398013i	−0.989520	+	0.144394i	$0.953877\pi$
$854$	29.5462	+	4.24811i	1.01105	+	0.145367i
$855$	11.0366	−	14.9214i	0.377443	−	0.510303i
$856$	1.39387	+	4.74710i	0.0476416	+	0.162253i
$857$	−21.5631	−	8.04263i	−0.736583	−	0.274731i	−0.0469568	−	0.998897i	$-0.514952\pi$
$857$	−21.5631	−	8.04263i	−0.736583	−	0.274731i	−0.689626	+	0.724166i	$0.742225\pi$
$858$	−0.126163	−	0.00902337i	−0.00430714	−	0.000308053i
$859$	−54.0648	+	7.77335i	−1.84467	+	0.265223i	−0.973983	−	0.226619i	$-0.927233\pi$
$859$	−54.0648	+	7.77335i	−1.84467	+	0.265223i	−0.870684	+	0.491842i	$0.836324\pi$
$860$	−22.3774	+	6.71078i	−0.763063	+	0.228836i
$861$	10.8052	+	9.36276i	0.368240	+	0.319082i
$862$	6.73173	+	30.9453i	0.229284	+	1.05400i
$863$	9.96267	+	45.7977i	0.339133	+	1.55897i	0.758819	+	0.651301i	$0.225777\pi$
$863$	9.96267	+	45.7977i	0.339133	+	1.55897i	−0.419686	+	0.907669i	$0.637860\pi$
$864$	2.74675	+	2.38008i	0.0934465	+	0.0809718i
$865$	−24.9826	+	7.49205i	−0.849433	+	0.254737i
$866$	36.7206	−	5.27963i	1.24782	−	0.179409i
$867$	6.44307	+	0.460818i	0.218818	+	0.0156502i
$868$	−23.4849	−	8.75940i	−0.797128	−	0.297313i
$869$	−0.669335	−	2.27954i	−0.0227056	−	0.0773282i
$870$	−5.29474	+	7.15849i	−0.179509	+	0.242695i
$871$	−4.65808	−	0.669731i	−0.157833	−	0.0226930i
$872$	7.79347	+	1.69536i	0.263920	+	0.0574123i
$873$	21.9362	−	21.9362i	0.742429	−	0.742429i
$874$	−14.4117	−	5.59187i	−0.487484	−	0.189148i
$875$	30.4667	−	4.91896i	1.02996	−	0.166291i
$876$	5.28186	−	3.39444i	0.178457	−	0.114688i
$877$	−1.07608	−	1.43747i	−0.0363365	−	0.0485399i	0.782005	−	0.623272i	$-0.214197\pi$
$877$	−1.07608	−	1.43747i	−0.0363365	−	0.0485399i	−0.818342	+	0.574732i	$0.805106\pi$
$878$	9.31678	−	3.47498i	0.314426	−	0.117275i
$879$	16.0180	−	4.70332i	0.540275	−	0.158639i
$880$	0.154559	+	0.691309i	0.00521018	+	0.0233040i
$881$	−36.2934	+	31.4484i	−1.22276	+	1.05952i	−0.226418	+	0.974030i	$0.572702\pi$
$881$	−36.2934	+	31.4484i	−1.22276	+	1.05952i	−0.996339	+	0.0854948i	$0.972753\pi$
$882$	−1.27669	−	0.955718i	−0.0429884	−	0.0321807i
$883$	−2.42340	−	4.43813i	−0.0815540	−	0.149355i	0.833719	−	0.552189i	$-0.186207\pi$
$883$	−2.42340	−	4.43813i	−0.0815540	−	0.149355i	−0.915273	+	0.402834i	$0.868025\pi$
$884$	1.06804	−	1.23258i	0.0359219	−	0.0414561i
$885$	0.0337197	+	5.85654i	0.00113347	+	0.196866i
$886$	32.5323	+	20.9072i	1.09294	+	0.702393i
$887$	1.51833	+	21.2290i	0.0509806	+	0.712802i	0.957096	+	0.289771i	$0.0935792\pi$
$887$	1.51833	+	21.2290i	0.0509806	+	0.712802i	−0.906115	+	0.423031i	$0.860966\pi$
$888$	−1.38131	+	0.754254i	−0.0463538	+	0.0253111i
$889$	5.28488	+	36.7572i	0.177249	+	1.23280i
$890$	2.31169	−	8.04393i	0.0774880	−	0.269633i
$891$	1.54330	−	0.704802i	0.0517025	−	0.0236118i
$892$	−3.17093	+	5.80713i	−0.106171	+	0.194437i
$893$	−7.82698	−	20.9849i	−0.261920	−	0.702234i
$894$	1.83739	−	12.7793i	0.0614515	−	0.427405i
$895$	21.2592	−	8.06901i	0.710618	−	0.269717i
$896$			2.76031i			0.0922156i
$897$	−1.05628	+	1.59711i	−0.0352682	+	0.0533261i
$898$	13.1625	+	13.1625i	0.439239	+	0.439239i
$899$	29.9859	+	46.6589i	1.00008	+	1.55616i
$900$	−6.83555	+	10.9105i	−0.227852	+	0.363685i
$901$	6.40941	−	14.0346i	0.213528	−	0.467562i
$902$	−2.20909	−	1.20625i	−0.0735546	−	0.0401639i
$903$	6.57027	−	17.6156i	0.218645	−	0.586210i
$904$	−4.01816	−	4.63720i	−0.133642	−	0.154231i
$905$	2.60681	−	39.6554i	0.0866535	−	1.31819i
$906$	3.73850	+	1.09772i	0.124203	+	0.0364694i
$907$	28.0297	−	2.00472i	0.930710	−	0.0665657i	0.402256	−	0.915527i	$-0.368226\pi$
$907$	28.0297	−	2.00472i	0.930710	−	0.0665657i	0.528454	+	0.848962i	$0.322772\pi$
$908$	−13.4950	+	2.93566i	−0.447848	+	0.0974234i
$909$	12.6938	−	19.7519i	0.421025	−	0.655128i
$910$	0.516419	−	3.74470i	0.0171191	−	0.124136i
$911$	1.96962	−	6.70790i	0.0652563	−	0.222243i	−0.920408	−	0.390958i	$-0.872144\pi$
$911$	1.96962	−	6.70790i	0.0652563	−	0.222243i	0.985665	+	0.168715i	$0.0539619\pi$
$912$	1.25930	−	1.68223i	0.0416997	−	0.0557043i
$913$	−0.0231038	+	0.323033i	−0.000764624	+	0.0106908i
$914$	2.05692	+	4.50403i	0.0680370	+	0.148980i
$915$	11.9729	+	10.2545i	0.395813	+	0.339004i
$916$	−20.8428	−	9.51857i	−0.688664	−	0.314502i
$917$	−25.8321	+	19.3377i	−0.853051	+	0.638586i
$918$	2.05734	−	9.45744i	0.0679024	−	0.312142i
$919$	7.24774			0.239081			0.119540	−	0.992829i	$-0.461858\pi$
$919$	7.24774			0.239081			0.119540	+	0.992829i	$0.461858\pi$
$920$	10.2669	+	3.09699i	0.338489	+	0.102105i
$921$	−7.83814			−0.258275
$922$	4.19573	−	19.2875i	0.138179	−	0.635198i
$923$	−4.09488	+	3.06539i	−0.134785	+	0.100898i
$924$	−0.518561	−	0.236819i	−0.0170594	−	0.00779078i
$925$	−7.34443	−	9.57908i	−0.241483	−	0.314958i
$926$	−5.89248	−	12.9027i	−0.193639	−	0.424010i
$927$	−0.848316	+	11.8610i	−0.0278624	+	0.389567i
$928$	3.66035	−	4.88966i	0.120157	−	0.160511i
$929$	−13.1265	+	44.7047i	−0.430666	+	1.46671i	0.403388	+	0.915029i	$0.367833\pi$
$929$	−13.1265	+	44.7047i	−0.430666	+	1.46671i	−0.834053	+	0.551684i	$0.813986\pi$
$930$	−7.99363	−	10.5511i	−0.262121	−	0.345983i
$931$	−1.07929	+	1.67941i	−0.0353724	+	0.0550406i
$932$	−2.31202	+	0.502948i	−0.0757326	+	0.0164746i
$933$	−11.0189	+	0.788088i	−0.360743	+	0.0258009i
$934$	20.8939	+	6.13499i	0.683668	+	0.200743i
$935$	1.41852	−	1.24352i	0.0463904	−	0.0406675i
$936$	1.03274	+	1.19184i	0.0337561	+	0.0389566i
$937$	−15.9784	+	42.8398i	−0.521992	+	1.39952i	0.362072	+	0.932150i	$0.382069\pi$
$937$	−15.9784	+	42.8398i	−0.521992	+	1.39952i	−0.884064	+	0.467365i	$0.845203\pi$
$938$	−18.6157	−	10.1650i	−0.607825	−	0.331898i
$939$	−4.82359	+	10.5622i	−0.157412	+	0.344684i
$940$	6.53563	+	14.0957i	0.213169	+	0.459751i
$941$	5.27804	+	8.21278i	0.172059	+	0.267729i	0.916564	−	0.399888i	$-0.130951\pi$
$941$	5.27804	+	8.21278i	0.172059	+	0.267729i	−0.744505	+	0.667617i	$0.767315\pi$
$942$	6.57963	+	6.57963i	0.214376	+	0.214376i
$943$	−32.3222	+	20.1777i	−1.05256	+	0.657075i
$944$		−	4.01760i		−	0.130762i
$945$	−7.96038	−	20.9730i	−0.258951	−	0.682252i
$946$	−0.471035	+	3.27612i	−0.0153147	+	0.106516i
$947$	−18.1408	−	48.6375i	−0.589498	−	1.58051i	−0.798113	−	0.602508i	$-0.794168\pi$
$947$	−18.1408	−	48.6375i	−0.589498	−	1.58051i	0.208615	−	0.977998i	$-0.433105\pi$
$948$	2.34308	−	4.29102i	0.0760996	−	0.139366i
$949$	5.36528	−	2.45024i	0.174164	−	0.0795383i
$950$	14.2333	+	7.56050i	0.461788	+	0.245295i
$951$	−1.83038	−	12.7306i	−0.0593542	−	0.412817i
$952$	6.45158	−	3.52283i	0.209097	−	0.114176i
$953$	−0.0476903	−	0.666798i	−0.00154484	−	0.0215997i	0.996621	−	0.0821349i	$-0.0261738\pi$
$953$	−0.0476903	−	0.666798i	−0.00154484	−	0.0215997i	−0.998166	+	0.0605352i	$0.980719\pi$
$954$	12.5507	+	8.06582i	0.406343	+	0.261141i
$955$	21.1802	+	20.9377i	0.685375	+	0.677528i
$956$	11.7610	−	13.5729i	0.380377	−	0.438978i
$957$	0.604549	+	1.10715i	0.0195423	+	0.0357891i
$958$	−24.3189	−	18.2049i	−0.785708	−	0.588174i
$959$	−38.3447	+	33.2259i	−1.23822	+	1.07292i
$960$	−0.781044	+	1.23085i	−0.0252081	+	0.0397256i
$961$	−49.3724	+	14.4970i	−1.59266	+	0.467647i
$962$	−1.38529	+	0.516685i	−0.0446634	+	0.0166586i
$963$	7.63468	+	10.1987i	0.246024	+	0.328650i
$964$	0.486139	−	0.312423i	0.0156575	−	0.0100625i
$965$	−43.6924	+	28.4362i	−1.40651	+	0.915393i
$966$	−6.97611	+	5.08074i	−0.224453	+	0.163470i
$967$	−18.4956	+	18.4956i	−0.594777	+	0.594777i	−0.938918	−	0.344141i	$-0.888170\pi$
$967$	−18.4956	+	18.4956i	−0.594777	+	0.594777i	0.344141	+	0.938918i	$0.388170\pi$
$968$	−10.6505	−	2.31689i	−0.342322	−	0.0744675i
$969$	−5.53900	−	0.796388i	−0.177938	−	0.0255837i
$970$	21.6586	+	16.0197i	0.695416	+	0.514361i
$971$	7.37991	+	25.1337i	0.236833	+	0.806577i	0.989040	+	0.147651i	$0.0471711\pi$
$971$	7.37991	+	25.1337i	0.236833	+	0.806577i	−0.752207	+	0.658927i	$0.771011\pi$
$972$	13.4873	+	5.03049i	0.432604	+	0.161353i
$973$	−17.2217	−	1.23172i	−0.552103	−	0.0394872i
$974$	19.7065	−	2.83336i	0.631436	−	0.0907868i
$975$	1.28986	−	1.52368i	0.0413085	−	0.0487967i
$976$	−8.17268	−	7.08167i	−0.261601	−	0.226679i
$977$	7.45039	+	34.2489i	0.238359	+	1.09572i	0.928294	+	0.371848i	$0.121276\pi$
$977$	7.45039	+	34.2489i	0.238359	+	1.09572i	−0.689934	+	0.723872i	$0.742361\pi$
$978$	−1.64403	−	7.55750i	−0.0525704	−	0.241662i
$979$	−0.896132	−	0.776502i	−0.0286405	−	0.0248171i
$980$	0.656691	−	1.21928i	0.0209772	−	0.0389484i
$981$	20.3284	−	2.92279i	0.649037	−	0.0933174i
$982$	31.9273	+	2.28349i	1.01884	+	0.0728689i
$983$	−39.8425	−	14.8605i	−1.27078	−	0.473975i	−0.378558	−	0.925578i	$-0.623580\pi$
$983$	−39.8425	−	14.8605i	−1.27078	−	0.473975i	−0.892219	+	0.451602i	$0.850853\pi$
$984$	−1.45926	−	4.96979i	−0.0465196	−	0.158431i
$985$	35.9652	−	5.38255i	1.14595	−	0.171502i
$986$	−16.0999	−	2.31482i	−0.512726	−	0.0737188i
$987$	−12.2181	−	2.65787i	−0.388905	−	0.0846011i
$988$	1.39590	−	1.39590i	0.0444095	−	0.0444095i
$989$	39.7142	+	30.5513i	1.26284	+	0.971474i
$990$	0.994981	+	1.52880i	0.0316226	+	0.0485883i
$991$	−35.2269	+	22.6390i	−1.11902	+	0.719150i	−0.963240	−	0.268642i	$-0.913425\pi$
$991$	−35.2269	+	22.6390i	−1.11902	+	0.719150i	−0.155779	+	0.987792i	$0.549789\pi$
$992$	5.44178	+	7.26937i	0.172777	+	0.230803i
$993$	10.9663	−	4.09020i	0.348004	−	0.129799i
$994$	−22.1204	+	6.49514i	−0.701617	+	0.206013i
$995$	16.3651	−	3.65882i	0.518809	−	0.115992i
$996$	−0.503676	+	0.436438i	−0.0159596	+	0.0138291i
$997$	−33.2259	−	24.8726i	−1.05228	−	0.787724i	−0.0744670	−	0.997223i	$-0.523726\pi$
$997$	−33.2259	−	24.8726i	−1.05228	−	0.787724i	−0.977809	+	0.209500i	$0.932816\pi$
$998$	16.2862	+	29.8260i	0.515532	+	0.944126i
$999$	−5.74579	+	6.63099i	−0.181789	+	0.209795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.103.10	yes	240
5.2	odd	4	inner	230.2.l.a.57.9	✓	240
23.21	odd	22	inner	230.2.l.a.113.9	yes	240
115.67	even	44	inner	230.2.l.a.67.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.9	✓	240	5.2	odd	4	inner
230.2.l.a.67.10	yes	240	115.67	even	44	inner
230.2.l.a.103.10	yes	240	1.1	even	1	trivial
230.2.l.a.113.9	yes	240	23.21	odd	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.212565 - 0.977147i) q^{2} +(0.521893 - 0.390684i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.172358 - 2.22942i) q^{5} +(-0.270819 - 0.593012i) q^{6} +(0.196919 - 2.75328i) q^{7} +(-0.599278 + 0.800541i) q^{8} +(-0.725460 + 2.47069i) q^{9} +(-2.21510 - 0.305477i) q^{10} +(-0.171272 + 0.266505i) q^{11} +(-0.637026 + 0.138577i) q^{12} +(-0.610881 + 0.0436911i) q^{13} +(-2.64850 - 0.777670i) q^{14} +(-0.960949 - 1.09618i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.930625 - 2.49510i) q^{17} +(2.26002 + 1.23406i) q^{18} +(1.33902 - 2.93205i) q^{19} +(-0.769350 + 2.09955i) q^{20} +(-0.972892 - 1.51385i) q^{21} +(0.224008 + 0.224008i) q^{22} +(4.61891 - 1.29062i) q^{23} +0.651925i q^{24} +(-4.94059 + 0.768515i) q^{25} +(-0.0871595 + 0.606208i) q^{26} +(1.27012 + 3.40532i) q^{27} +(-1.32288 + 2.42267i) q^{28} +(5.55597 - 2.53733i) q^{29} +(-1.27539 + 0.705979i) q^{30} +(1.29230 + 8.98814i) q^{31} +(0.877679 - 0.479249i) q^{32} +(0.0147334 + 0.206000i) q^{33} +(-2.24026 - 1.43973i) q^{34} +(-6.17215 + 0.0355368i) q^{35} +(1.68626 - 1.94605i) q^{36} +(1.15696 + 2.11882i) q^{37} +(-2.58041 - 1.93167i) q^{38} +(-0.301745 + 0.261463i) q^{39} +(1.88803 + 1.19806i) q^{40} +(-7.62326 + 2.23839i) q^{41} +(-1.68606 + 0.628867i) q^{42} +(6.26113 + 8.36389i) q^{43} +(0.266505 - 0.171272i) q^{44} +(5.63323 + 1.19151i) q^{45} +(-0.279308 - 4.78769i) q^{46} +(4.91328 - 4.91328i) q^{47} +(0.637026 + 0.138577i) q^{48} +(-0.613031 - 0.0881405i) q^{49} +(-0.299245 + 4.99104i) q^{50} +(-0.489110 - 1.66576i) q^{51} +(0.573827 + 0.214026i) q^{52} +(5.77904 + 0.413325i) q^{53} +(3.59748 - 0.517240i) q^{54} +(0.623671 + 0.335903i) q^{55} +(2.08611 + 1.80762i) q^{56} +(-0.446679 - 2.05335i) q^{57} +(-1.29834 - 5.96835i) q^{58} +(-3.03630 - 2.63097i) q^{59} +(0.418741 + 1.39631i) q^{60} +(-10.7039 + 1.53899i) q^{61} +(9.05743 + 0.647801i) q^{62} +(6.65964 + 2.48392i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(0.202696 + 1.35438i) q^{65} +(0.204424 + 0.0293918i) q^{66} +(7.50837 + 1.63335i) q^{67} +(-1.88303 + 1.88303i) q^{68} +(1.90635 - 2.47810i) q^{69} +(-1.27726 + 6.03865i) q^{70} +(7.02619 - 4.51545i) q^{71} +(-1.54314 - 2.06139i) q^{72} +(-9.02358 + 3.36562i) q^{73} +(2.31633 - 0.680136i) q^{74} +(-2.27821 + 2.33129i) q^{75} +(-2.43603 + 2.11083i) q^{76} +(0.700037 + 0.524041i) q^{77} +(0.191348 + 0.350427i) q^{78} +(-4.91108 + 5.66768i) q^{79} +(1.57201 - 1.59022i) q^{80} +(-4.50540 - 2.89544i) q^{81} +(0.566796 + 7.92485i) q^{82} +(0.897247 - 0.489934i) q^{83} +(0.256098 + 1.78120i) q^{84} +(-5.72302 - 1.64470i) q^{85} +(9.50365 - 4.34017i) q^{86} +(1.90833 - 3.49484i) q^{87} +(-0.110709 - 0.296821i) q^{88} +(-0.532679 + 3.70486i) q^{89} +(2.36171 - 5.25122i) q^{90} +1.69053i q^{91} +(-4.73765 - 0.744772i) q^{92} +(4.18596 + 4.18596i) q^{93} +(-3.75660 - 5.84539i) q^{94} +(-6.76754 - 2.47987i) q^{95} +(0.270819 - 0.593012i) q^{96} +(-10.5739 - 5.77381i) q^{97} +(-0.216435 + 0.580286i) q^{98} +(-0.534200 - 0.616500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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