LMFDB - Embedded newform 925.2.ba.d.99.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(99,925)] 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("925.99"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.ba (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [156,0,0,-6,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.25
Character	$\chi$	$=$	925.99
Dual form			925.2.ba.d.299.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.02455 - 1.69880i) q^{2} +(1.25718 - 1.49825i) q^{3} +(0.865587 - 4.90899i) q^{4} -5.16897i q^{6} +(-0.868717 - 2.38678i) q^{7} +(-3.94409 - 6.83137i) q^{8} +(-0.143302 - 0.812704i) q^{9} +(1.76172 + 3.05138i) q^{11} +(-6.26668 - 7.46833i) q^{12} +(-0.828967 + 4.70130i) q^{13} +(-5.81342 - 3.35638i) q^{14} +(-10.2219 - 3.72048i) q^{16} +(0.397373 + 2.25362i) q^{17} +(-1.67074 - 1.40192i) q^{18} +(4.07971 - 4.86201i) q^{19} +(-4.66812 - 1.69906i) q^{21} +(8.75036 + 3.18487i) q^{22} +(-3.48394 + 6.03437i) q^{23} +(-15.1935 - 2.67903i) q^{24} +(6.30828 + 10.9263i) q^{26} +(3.68359 + 2.12672i) q^{27} +(-12.4686 + 2.19856i) q^{28} +(2.56727 - 1.48222i) q^{29} -7.04104i q^{31} +(-12.1902 + 4.43687i) q^{32} +(6.78651 + 1.19665i) q^{33} +(4.63294 + 3.88750i) q^{34} -4.11359 q^{36} +(3.95288 + 4.62328i) q^{37} -16.7740i q^{38} +(6.00155 + 7.15237i) q^{39} +(0.250970 - 1.42332i) q^{41} +(-12.3372 + 4.49037i) q^{42} -4.36382 q^{43} +(16.5041 - 6.00700i) q^{44} +(3.19776 + 18.1354i) q^{46} +(-8.51267 - 4.91479i) q^{47} +(-18.4250 + 10.6377i) q^{48} +(0.420255 - 0.352636i) q^{49} +(3.87604 + 2.23783i) q^{51} +(22.3611 + 8.13877i) q^{52} +(-4.27534 + 11.7464i) q^{53} +(11.0705 - 1.95202i) q^{54} +(-12.8787 + 15.3482i) q^{56} +(-2.15557 - 12.2248i) q^{57} +(2.67959 - 7.36210i) q^{58} +(-0.273756 + 0.752139i) q^{59} +(-6.93044 - 1.22202i) q^{61} +(-11.9613 - 14.2549i) q^{62} +(-1.81526 + 1.04804i) q^{63} +(-6.26436 + 10.8502i) q^{64} +(15.7725 - 9.10625i) q^{66} +(-2.01910 - 5.54742i) q^{67} +11.4069 q^{68} +(4.66103 + 12.8061i) q^{69} +(-4.93562 - 4.14148i) q^{71} +(-4.98669 + 4.18433i) q^{72} +3.18903i q^{73} +(15.8568 + 2.64490i) q^{74} +(-20.3362 - 24.2358i) q^{76} +(5.75255 - 6.85562i) q^{77} +(24.3009 + 4.28490i) q^{78} +(-5.14320 - 14.1308i) q^{79} +(10.1437 - 3.69201i) q^{81} +(-1.90983 - 3.30793i) q^{82} +(9.56775 - 1.68705i) q^{83} +(-12.3813 + 21.4451i) q^{84} +(-8.83477 + 7.41325i) q^{86} +(1.00680 - 5.70982i) q^{87} +(13.8967 - 24.0699i) q^{88} +(-4.54660 + 12.4917i) q^{89} +(11.9411 - 2.10554i) q^{91} +(26.6070 + 22.3259i) q^{92} +(-10.5492 - 8.85185i) q^{93} +(-25.5836 + 4.51107i) q^{94} +(-8.67773 + 23.8419i) q^{96} +(1.61152 - 2.79124i) q^{97} +(0.251770 - 1.42786i) q^{98} +(2.22741 - 1.86902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{4} + 36 q^{14} + 18 q^{16} + 6 q^{21} - 30 q^{24} + 18 q^{29} + 102 q^{34} - 216 q^{36} + 66 q^{39} - 42 q^{41} + 6 q^{44} + 72 q^{46} - 108 q^{49} + 180 q^{51} + 78 q^{54} - 96 q^{56} - 30 q^{59}+ \cdots + 366 q^{99}+O(q^{100}) $ 156 * q - 6 * q^4 + 36 * q^14 + 18 * q^16 + 6 * q^21 - 30 * q^24 + 18 * q^29 + 102 * q^34 - 216 * q^36 + 66 * q^39 - 42 * q^41 + 6 * q^44 + 72 * q^46 - 108 * q^49 + 180 * q^51 + 78 * q^54 - 96 * q^56 - 30 * q^59 - 36 * q^61 - 132 * q^64 + 252 * q^66 - 90 * q^69 + 96 * q^71 + 24 * q^74 + 162 * q^76 - 168 * q^79 + 96 * q^81 - 114 * q^84 - 132 * q^86 - 78 * q^89 + 114 * q^91 - 156 * q^94 - 156 * q^96 + 366 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	2.02455	−	1.69880i	1.43157	−	1.20123i	0.486796	−	0.873516i	$-0.338165\pi$
$2$	2.02455	−	1.69880i	1.43157	−	1.20123i	0.944776	−	0.327716i	$-0.106279\pi$
$3$	1.25718	−	1.49825i	0.725832	−	0.865013i	−0.269351	−	0.963042i	$-0.586809\pi$
$3$	1.25718	−	1.49825i	0.725832	−	0.865013i	0.995184	+	0.0980287i	$0.0312537\pi$
$4$	0.865587	−	4.90899i	0.432793	−	2.45449i
$5$		0			0
$5$		0			0
$6$		−	5.16897i		−	2.11022i
$7$	−0.868717	−	2.38678i	−0.328344	−	0.902119i	−0.988531	−	0.151017i	$-0.951745\pi$
$7$	−0.868717	−	2.38678i	−0.328344	−	0.902119i	0.660187	−	0.751101i	$-0.270477\pi$
$8$	−3.94409	−	6.83137i	−1.39445	−	2.41525i
$9$	−0.143302	−	0.812704i	−0.0477672	−	0.270901i
$10$		0			0
$11$	1.76172	+	3.05138i	0.531177	+	0.920026i	0.999338	+	0.0363828i	$0.0115836\pi$
$11$	1.76172	+	3.05138i	0.531177	+	0.920026i	−0.468161	+	0.883643i	$0.655083\pi$
$12$	−6.26668	−	7.46833i	−1.80903	−	2.15592i
$13$	−0.828967	+	4.70130i	−0.229914	+	1.30391i	0.623151	+	0.782102i	$0.285852\pi$
$13$	−0.828967	+	4.70130i	−0.229914	+	1.30391i	−0.853065	+	0.521805i	$0.825259\pi$
$14$	−5.81342	−	3.35638i	−1.55370	−	0.897030i
$15$		0			0
$16$	−10.2219	−	3.72048i	−2.55548	−	0.930120i
$17$	0.397373	+	2.25362i	0.0963772	+	0.546582i	0.994317	+	0.106463i	$0.0339526\pi$
$17$	0.397373	+	2.25362i	0.0963772	+	0.546582i	−0.897939	+	0.440119i	$0.854936\pi$
$18$	−1.67074	−	1.40192i	−0.393798	−	0.330436i
$19$	4.07971	−	4.86201i	0.935951	−	1.11542i	−0.0571743	−	0.998364i	$-0.518209\pi$
$19$	4.07971	−	4.86201i	0.935951	−	1.11542i	0.993125	−	0.117058i	$-0.0373465\pi$
$20$		0			0
$21$	−4.66812	−	1.69906i	−1.01867	−	0.370765i
$22$	8.75036	+	3.18487i	1.86558	+	0.679017i
$23$	−3.48394	+	6.03437i	−0.726453	+	1.25825i	0.231921	+	0.972735i	$0.425499\pi$
$23$	−3.48394	+	6.03437i	−0.726453	+	1.25825i	−0.958373	+	0.285518i	$0.907834\pi$
$24$	−15.1935	−	2.67903i	−3.10136	−	0.546854i
$25$		0			0
$26$	6.30828	+	10.9263i	1.23716	+	2.14282i
$27$	3.68359	+	2.12672i	0.708907	+	0.409288i
$28$	−12.4686	+	2.19856i	−2.35635	+	0.415488i
$29$	2.56727	−	1.48222i	0.476731	−	0.275241i	−0.242322	−	0.970196i	$-0.577909\pi$
$29$	2.56727	−	1.48222i	0.476731	−	0.275241i	0.719053	+	0.694955i	$0.244576\pi$
$30$		0			0
$31$		−	7.04104i		−	1.26461i	−0.774720	−	0.632304i	$-0.782109\pi$
$31$		−	7.04104i		−	1.26461i	0.774720	−	0.632304i	$-0.217891\pi$
$32$	−12.1902	+	4.43687i	−2.15494	+	0.784335i
$33$	6.78651	+	1.19665i	1.18138	+	0.208309i
$34$	4.63294	+	3.88750i	0.794543	+	0.666701i
$35$		0			0
$36$	−4.11359			−0.685599
$37$	3.95288	+	4.62328i	0.649850	+	0.760062i
$37$	3.95288	+	4.62328i	0.649850	+	0.760062i
$38$		−	16.7740i		−	2.72110i
$39$	6.00155	+	7.15237i	0.961018	+	1.14530i
$40$		0			0
$41$	0.250970	−	1.42332i	0.0391949	−	0.222285i	−0.958919	−	0.283681i	$-0.908444\pi$
$41$	0.250970	−	1.42332i	0.0391949	−	0.222285i	0.998113	+	0.0613962i	$0.0195553\pi$
$42$	−12.3372	+	4.49037i	−1.90367	+	0.692879i
$43$	−4.36382			−0.665477			−0.332738	−	0.943019i	$-0.607973\pi$
$43$	−4.36382			−0.665477			−0.332738	+	0.943019i	$0.607973\pi$
$44$	16.5041	−	6.00700i	2.48809	−	0.905590i
$45$		0			0
$46$	3.19776	+	18.1354i	0.471484	+	2.67392i
$47$	−8.51267	−	4.91479i	−1.24170	−	0.716897i	−0.272261	−	0.962224i	$-0.587771\pi$
$47$	−8.51267	−	4.91479i	−1.24170	−	0.716897i	−0.969440	+	0.245327i	$0.921105\pi$
$48$	−18.4250	+	10.6377i	−2.65942	+	1.53542i
$49$	0.420255	−	0.352636i	0.0600364	−	0.0503765i
$50$		0			0
$51$	3.87604	+	2.23783i	0.542755	+	0.313360i
$52$	22.3611	+	8.13877i	3.10092	+	1.12864i
$53$	−4.27534	+	11.7464i	−0.587263	+	1.61349i	0.188224	+	0.982126i	$0.439727\pi$
$53$	−4.27534	+	11.7464i	−0.587263	+	1.61349i	−0.775486	+	0.631364i	$0.782495\pi$
$54$	11.0705	−	1.95202i	1.50650	−	0.265637i
$55$		0			0
$56$	−12.8787	+	15.3482i	−1.72099	+	2.05099i
$57$	−2.15557	−	12.2248i	−0.285512	−	1.61922i
$58$	2.67959	−	7.36210i	0.351847	−	0.966691i
$59$	−0.273756	+	0.752139i	−0.0356400	+	0.0979201i	−0.956236	−	0.292596i	$-0.905481\pi$
$59$	−0.273756	+	0.752139i	−0.0356400	+	0.0979201i	0.920596	+	0.390516i	$0.127703\pi$
$60$		0			0
$61$	−6.93044	−	1.22202i	−0.887352	−	0.156464i	−0.288649	−	0.957435i	$-0.593206\pi$
$61$	−6.93044	−	1.22202i	−0.887352	−	0.156464i	−0.598703	+	0.800971i	$0.704317\pi$
$62$	−11.9613	−	14.2549i	−1.51909	−	1.81038i
$63$	−1.81526	+	1.04804i	−0.228701	+	0.132041i
$64$	−6.26436	+	10.8502i	−0.783045	+	1.35627i
$65$		0			0
$66$	15.7725	−	9.10625i	1.94146	−	1.12090i
$67$	−2.01910	−	5.54742i	−0.246672	−	0.677725i	−0.999803	−	0.0198546i	$-0.993680\pi$
$67$	−2.01910	−	5.54742i	−0.246672	−	0.677725i	0.753131	−	0.657870i	$-0.228543\pi$
$68$	11.4069			1.38329
$69$	4.66103	+	12.8061i	0.561123	+	1.54167i
$70$		0			0
$71$	−4.93562	−	4.14148i	−0.585750	−	0.491503i	0.301080	−	0.953599i	$-0.402653\pi$
$71$	−4.93562	−	4.14148i	−0.585750	−	0.491503i	−0.886830	+	0.462096i	$0.847097\pi$
$72$	−4.98669	+	4.18433i	−0.587687	+	0.493128i
$73$			3.18903i			0.373247i	0.982431	+	0.186624i	$0.0597545\pi$
$73$			3.18903i			0.373247i	−0.982431	+	0.186624i	$0.940245\pi$
$74$	15.8568	+	2.64490i	1.84332	+	0.307464i
$75$		0			0
$76$	−20.3362	−	24.2358i	−2.33272	−	2.78003i
$77$	5.75255	−	6.85562i	0.655564	−	0.781270i
$78$	24.3009	+	4.28490i	2.75153	+	0.485169i
$79$	−5.14320	−	14.1308i	−0.578655	−	1.58984i	−0.790449	−	0.612528i	$-0.790153\pi$
$79$	−5.14320	−	14.1308i	−0.578655	−	1.58984i	0.211794	−	0.977314i	$-0.432070\pi$
$80$		0			0
$81$	10.1437	−	3.69201i	1.12708	−	0.410223i
$82$	−1.90983	−	3.30793i	−0.210906	−	0.365300i
$83$	9.56775	−	1.68705i	1.05020	−	0.185178i	0.378194	−	0.925726i	$-0.376545\pi$
$83$	9.56775	−	1.68705i	1.05020	−	0.185178i	0.672003	+	0.740548i	$0.265434\pi$
$84$	−12.3813	+	21.4451i	−1.35091	+	2.33985i
$85$		0			0
$86$	−8.83477	+	7.41325i	−0.952678	+	0.799392i
$87$	1.00680	−	5.70982i	0.107940	−	0.612157i
$88$	13.8967	−	24.0699i	1.48140	−	2.56586i
$89$	−4.54660	+	12.4917i	−0.481939	+	1.32412i	0.425890	+	0.904775i	$0.359961\pi$
$89$	−4.54660	+	12.4917i	−0.481939	+	1.32412i	−0.907829	+	0.419341i	$0.862261\pi$
$90$		0			0
$91$	11.9411	−	2.10554i	1.25177	−	0.220721i
$92$	26.6070	+	22.3259i	2.77397	+	2.32764i
$93$	−10.5492	−	8.85185i	−1.09390	−	0.917894i
$94$	−25.5836	+	4.51107i	−2.63874	+	0.465282i
$95$		0			0
$96$	−8.67773	+	23.8419i	−0.885667	+	2.43335i
$97$	1.61152	−	2.79124i	0.163625	−	0.283407i	−0.772541	−	0.634965i	$-0.781015\pi$
$97$	1.61152	−	2.79124i	0.163625	−	0.283407i	0.936166	+	0.351558i	$0.114348\pi$
$98$	0.251770	−	1.42786i	0.0254326	−	0.144235i
$99$	2.22741	−	1.86902i	0.223864	−	0.187844i
$100$		0			0
$101$	−7.84507	+	13.5881i	−0.780613	+	1.35206i	0.150972	+	0.988538i	$0.451760\pi$
$101$	−7.84507	+	13.5881i	−0.780613	+	1.35206i	−0.931585	+	0.363524i	$0.881574\pi$
$102$	11.6489	−	2.05401i	1.15341	−	0.203377i
$103$	4.26623	+	7.38933i	0.420364	+	0.728092i	0.995975	−	0.0896317i	$-0.0285690\pi$
$103$	4.26623	+	7.38933i	0.420364	+	0.728092i	−0.575611	+	0.817724i	$0.695236\pi$
$104$	35.3859	−	12.8794i	3.46987	−	1.26293i
$105$		0			0
$106$	11.2991	+	31.0441i	1.09747	+	3.01527i
$107$	−15.7538	−	2.77782i	−1.52298	−	0.268542i	−0.651376	−	0.758755i	$-0.725808\pi$
$107$	−15.7538	−	2.77782i	−1.52298	−	0.268542i	−0.871603	+	0.490213i	$0.836919\pi$
$108$	13.6285	−	16.2418i	1.31140	−	1.56287i
$109$	1.67519	+	1.99641i	0.160454	+	0.191221i	0.840281	−	0.542151i	$-0.182390\pi$
$109$	1.67519	+	1.99641i	0.160454	+	0.191221i	−0.679827	+	0.733372i	$0.737945\pi$
$110$		0			0
$111$	11.8963	−	0.110110i	1.12915	−	0.0104512i
$112$			27.6296i			2.61075i
$113$	2.65350	−	2.22655i	0.249620	−	0.209456i	−0.509388	−	0.860537i	$-0.670128\pi$
$113$	2.65350	−	2.22655i	0.249620	−	0.209456i	0.759009	+	0.651080i	$0.225684\pi$
$114$	−25.1316	−	21.0879i	−2.35379	−	1.97506i
$115$		0			0
$116$	−5.05398	−	13.8857i	−0.469250	−	1.28925i
$117$	3.93956			0.364213
$118$	0.723499	+	1.98780i	0.0666035	+	0.182992i
$119$	5.03368	−	2.90620i	0.461437	−	0.266411i
$120$		0			0
$121$	−0.707287	+	1.22506i	−0.0642988	+	0.111369i
$122$	−16.1070	+	9.29938i	−1.45826	+	0.841926i
$123$	−1.81697	−	2.16538i	−0.163831	−	0.195246i
$124$	−34.5644	−	6.09463i	−3.10397	−	0.547314i
$125$		0			0
$126$	−1.89467	+	5.20557i	−0.168791	+	0.463749i
$127$	−4.16376	+	11.4398i	−0.369474	+	1.01512i	0.606088	+	0.795397i	$0.292738\pi$
$127$	−4.16376	+	11.4398i	−0.369474	+	1.01512i	−0.975562	+	0.219724i	$0.929484\pi$
$128$	1.24446	+	7.05771i	0.109996	+	0.623819i
$129$	−5.48610	+	6.53808i	−0.483024	+	0.575646i
$130$		0			0
$131$	12.5975	−	2.22128i	1.10065	−	0.194074i	0.406319	−	0.913731i	$-0.366812\pi$
$131$	12.5975	−	2.22128i	1.10065	−	0.194074i	0.694330	+	0.719657i	$0.255701\pi$
$132$	11.7486	−	32.2791i	1.02259	−	2.80954i
$133$	−15.1487	−	5.51367i	−1.31356	−	0.478096i
$134$	−13.5117	−	7.80098i	−1.16723	−	0.673902i
$135$		0			0
$136$	13.8280	−	11.6031i	1.18574	−	0.994956i
$137$	−3.17406	+	1.83254i	−0.271178	+	0.156565i	−0.629423	−	0.777063i	$-0.716709\pi$
$137$	−3.17406	+	1.83254i	−0.271178	+	0.156565i	0.358245	+	0.933628i	$0.383375\pi$
$138$	31.1915	+	18.0084i	2.65519	+	1.53298i
$139$	3.27722	+	18.5861i	0.277970	+	1.57645i	0.729365	+	0.684125i	$0.239816\pi$
$139$	3.27722	+	18.5861i	0.277970	+	1.57645i	−0.451395	+	0.892324i	$0.649073\pi$
$140$		0			0
$141$	−18.0655	+	6.57531i	−1.52139	+	0.553741i
$142$	−17.0279			−1.42895
$143$	−15.8059	+	5.75287i	−1.32175	+	0.481079i
$144$	−1.55883	+	8.84056i	−0.129902	+	0.736713i
$145$		0			0
$146$	5.41752	+	6.45634i	0.448357	+	0.534331i
$147$		−	1.07297i		−	0.0884972i
$148$	26.1172	−	15.4028i	2.14682	−	1.26610i
$149$	2.38935			0.195743			0.0978714	−	0.995199i	$-0.468797\pi$
$149$	2.38935			0.195743			0.0978714	+	0.995199i	$0.468797\pi$
$150$		0			0
$151$	4.13877	+	3.47284i	0.336808	+	0.282616i	0.795467	−	0.605997i	$-0.207226\pi$
$151$	4.13877	+	3.47284i	0.336808	+	0.282616i	−0.458659	+	0.888612i	$0.651670\pi$
$152$	−49.3050	−	8.69380i	−3.99916	−	0.705160i
$153$	1.77458	−	0.645894i	0.143466	−	0.0522175i
$154$		−	23.6520i		−	1.90593i
$155$		0			0
$156$	40.3058	−	23.2705i	3.22704	−	1.86313i
$157$	17.8252	−	3.14307i	1.42261	−	0.250844i	0.591208	−	0.806519i	$-0.298651\pi$
$157$	17.8252	−	3.14307i	1.42261	−	0.250844i	0.831400	+	0.555675i	$0.187540\pi$
$158$	−34.4181	−	19.8713i	−2.73816	−	1.58088i
$159$	12.2241	+	21.1728i	0.969437	+	1.67911i
$160$		0			0
$161$	17.4293	+	3.07325i	1.37362	+	0.242206i
$162$	14.2644	−	24.7067i	1.12072	−	1.94115i
$163$	19.6736	+	7.16061i	1.54096	+	0.560863i	0.966275	−	0.257514i	$-0.0829033\pi$
$163$	19.6736	+	7.16061i	1.54096	+	0.560863i	0.574683	+	0.818376i	$0.305125\pi$
$164$	−6.76982	−	2.46401i	−0.528634	−	0.192407i
$165$		0			0
$166$	16.5044	−	19.6692i	1.28099	−	1.52663i
$167$	−7.19731	−	6.03926i	−0.556944	−	0.467332i	0.320340	−	0.947303i	$-0.396203\pi$
$167$	−7.19731	−	6.03926i	−0.556944	−	0.467332i	−0.877284	+	0.479971i	$0.840647\pi$
$168$	6.80462	+	38.5909i	0.524988	+	2.97735i
$169$	−9.19906	−	3.34818i	−0.707620	−	0.257553i
$170$		0			0
$171$	−4.53601	−	2.61887i	−0.346877	−	0.200270i
$172$	−3.77727	+	21.4219i	−0.288014	+	1.63341i
$173$	12.7378	+	15.1803i	0.968437	+	1.15414i	0.988019	+	0.154330i	$0.0493220\pi$
$173$	12.7378	+	15.1803i	0.968437	+	1.15414i	−0.0195820	+	0.999808i	$0.506234\pi$
$174$	−7.66153	−	13.2702i	−0.580819	−	1.00601i
$175$		0			0
$176$	−6.65554	−	37.7454i	−0.501680	−	2.84517i
$177$	0.782729	+	1.35573i	0.0588335	+	0.101903i
$178$	12.0160	+	33.0138i	0.900640	+	2.47449i
$179$		−	7.53970i		−	0.563543i	−0.959481	−	0.281772i	$-0.909078\pi$
$179$		−	7.53970i		−	0.563543i	0.959481	−	0.281772i	$-0.0909221\pi$
$180$		0			0
$181$	−1.24809	+	7.07827i	−0.0927698	+	0.526123i	0.902638	+	0.430400i	$0.141628\pi$
$181$	−1.24809	+	7.07827i	−0.0927698	+	0.526123i	−0.995408	+	0.0957233i	$0.969484\pi$
$182$	20.5985	−	24.5483i	1.52686	−	1.81964i
$183$	−10.5437	+	8.84721i	−0.779413	+	0.654005i
$184$	54.9640			4.05200
$185$		0			0
$186$	−36.3949			−2.66861
$187$	−6.17658	+	5.18277i	−0.451677	+	0.379002i
$188$	−31.4951	+	37.5344i	−2.29702	+	2.73748i
$189$	1.87602	−	10.6394i	0.136460	−	0.773905i
$190$		0			0
$191$		−	15.5444i		−	1.12475i	−0.826881	−	0.562376i	$-0.809887\pi$
$191$		−	15.5444i		−	1.12475i	0.826881	−	0.562376i	$-0.190113\pi$
$192$	8.38084	+	23.0262i	0.604835	+	1.66177i
$193$	−11.7838	−	20.4101i	−0.848215	−	1.46915i	−0.882800	−	0.469750i	$-0.844344\pi$
$193$	−11.7838	−	20.4101i	−0.848215	−	1.46915i	0.0345847	−	0.999402i	$-0.488989\pi$
$194$	−1.47914	−	8.38864i	−0.106196	−	0.602269i
$195$		0			0
$196$	−1.36732	−	2.36826i	−0.0976654	−	0.169161i
$197$	−1.85165	−	2.20671i	−0.131925	−	0.157222i	0.696038	−	0.718005i	$-0.254945\pi$
$197$	−1.85165	−	2.20671i	−0.131925	−	0.157222i	−0.827963	+	0.560783i	$0.810500\pi$
$198$	1.33442	−	7.56786i	0.0948329	−	0.537824i
$199$	13.0692	+	7.54550i	0.926451	+	0.534886i	0.885687	−	0.464282i	$-0.153688\pi$
$199$	13.0692	+	7.54550i	0.926451	+	0.534886i	0.0407633	+	0.999169i	$0.487021\pi$
$200$		0			0
$201$	−10.8498	−	3.94899i	−0.765283	−	0.278540i
$202$	7.20064	+	40.8369i	0.506635	+	2.87327i
$203$	−5.76796	−	4.83990i	−0.404832	−	0.339694i
$204$	14.3405	−	17.0904i	1.00404	−	1.19657i
$205$		0			0
$206$	21.1902	+	7.71259i	1.47639	+	0.537362i
$207$	5.40341	+	1.96668i	0.375563	+	0.136694i
$208$	25.9647	−	44.9722i	1.80033	−	3.11826i
$209$	22.0232	+	3.88328i	1.52337	+	0.268612i
$210$		0			0
$211$	−6.02684	−	10.4388i	−0.414904	−	0.718636i	0.580514	−	0.814250i	$-0.302852\pi$
$211$	−6.02684	−	10.4388i	−0.414904	−	0.718636i	−0.995418	+	0.0956147i	$0.969518\pi$
$212$	53.9622	+	31.1551i	3.70614	+	2.13974i
$213$	−12.4099	+	2.18820i	−0.850313	+	0.149933i
$214$	−36.6133	+	21.1387i	−2.50284	+	1.44501i
$215$		0			0
$216$		−	33.5519i		−	2.28292i
$217$	−16.8054	+	6.11668i	−1.14083	+	0.415227i
$218$	6.78300	+	1.19603i	0.459403	+	0.0810051i
$219$	4.77795	+	4.00918i	0.322864	+	0.270915i
$220$		0			0
$221$	−10.9243			−0.734851
$222$	23.8976	−	20.4323i	1.60390	−	1.37133i
$223$		−	20.7126i		−	1.38702i	−0.720448	−	0.693509i	$-0.756064\pi$
$223$		−	20.7126i		−	1.38702i	0.720448	−	0.693509i	$-0.243936\pi$
$224$	21.1797	+	25.2410i	1.41513	+	1.68648i
$225$		0			0
$226$	1.58968	−	9.01552i	0.105744	−	0.599704i
$227$	−9.37125	+	3.41086i	−0.621992	+	0.226387i	−0.633742	−	0.773544i	$-0.718482\pi$
$227$	−9.37125	+	3.41086i	−0.621992	+	0.226387i	0.0117501	+	0.999931i	$0.496260\pi$
$228$	−61.8774			−4.09793
$229$	−9.44345	+	3.43714i	−0.624041	+	0.227132i	−0.634636	−	0.772812i	$-0.718850\pi$
$229$	−9.44345	+	3.43714i	−0.624041	+	0.227132i	0.0105946	+	0.999944i	$0.496628\pi$
$230$		0			0
$231$	−3.03943	−	17.2375i	−0.199980	−	1.13414i
$232$	−20.2511	−	11.6920i	−1.32955	−	0.767617i
$233$	5.76170	−	3.32652i	0.377462	−	0.217928i	−0.299252	−	0.954174i	$-0.596737\pi$
$233$	5.76170	−	3.32652i	0.377462	−	0.217928i	0.676713	+	0.736247i	$0.263404\pi$
$234$	7.97584	−	6.69252i	0.521397	−	0.437504i
$235$		0			0
$236$	3.45528	+	1.99491i	0.224920	+	0.129857i
$237$	−27.6374	−	10.0592i	−1.79524	−	0.653414i
$238$	5.25390	−	14.4350i	0.340559	−	0.935679i
$239$	−17.6102	+	3.10515i	−1.13911	+	0.200855i	−0.711215	−	0.702975i	$-0.751855\pi$
$239$	−17.6102	+	3.10515i	−1.13911	+	0.200855i	−0.427892	+	0.903830i	$0.640744\pi$
$240$		0			0
$241$	−4.61553	+	5.50058i	−0.297313	+	0.354323i	−0.893933	−	0.448200i	$-0.852065\pi$
$241$	−4.61553	+	5.50058i	−0.297313	+	0.354323i	0.596621	+	0.802523i	$0.296510\pi$
$242$	0.649188	+	3.68173i	0.0417314	+	0.236670i
$243$	2.85662	−	7.84850i	0.183252	−	0.503481i
$244$	−11.9978	+	32.9637i	−0.768080	+	2.11028i
$245$		0			0
$246$	−7.35709	−	1.29725i	−0.469071	−	0.0827099i
$247$	19.4759	+	23.2104i	1.23922	+	1.47684i
$248$	−48.1000	+	27.7705i	−3.05435	+	1.76343i
$249$	9.50075	−	16.4558i	0.602086	−	1.04284i
$250$		0			0
$251$	−1.93537	+	1.11739i	−0.122160	+	0.0705289i	−0.559835	−	0.828604i	$-0.689135\pi$
$251$	−1.93537	+	1.11739i	−0.122160	+	0.0705289i	0.437675	+	0.899133i	$0.355802\pi$
$252$	3.57355	+	9.81825i	0.225113	+	0.618492i
$253$	−24.5509			−1.54350
$254$	11.0042	+	30.2339i	0.690467	+	1.89704i
$255$		0			0
$256$	−4.68601	−	3.93203i	−0.292876	−	0.245752i
$257$	5.53602	−	4.64527i	0.345328	−	0.289764i	−0.453583	−	0.891214i	$-0.649854\pi$
$257$	5.53602	−	4.64527i	0.345328	−	0.289764i	0.798911	+	0.601450i	$0.205410\pi$
$258$			22.5564i			1.40430i
$259$	7.60082	−	13.4510i	0.472292	−	0.835804i
$260$		0			0
$261$	−1.57250	−	1.87403i	−0.0973352	−	0.116000i
$262$	21.7307	−	25.8977i	1.34253	−	1.59997i
$263$	16.2296	+	2.86171i	1.00076	+	0.176461i	0.649942	−	0.759984i	$-0.274793\pi$
$263$	16.2296	+	2.86171i	1.00076	+	0.176461i	0.350816	+	0.936444i	$0.385904\pi$
$264$	−18.5919	−	51.0809i	−1.14425	−	3.14381i
$265$		0			0
$266$	−40.0359	+	14.5719i	−2.45476	+	0.893458i
$267$	12.9997	+	22.5162i	0.795571	+	1.37797i
$268$	−28.9799	+	5.10994i	−1.77023	+	0.312139i
$269$	2.19321	−	3.79875i	0.133722	−	0.231614i	−0.791386	−	0.611316i	$-0.790640\pi$
$269$	2.19321	−	3.79875i	0.133722	−	0.231614i	0.925109	+	0.379703i	$0.123974\pi$
$270$		0			0
$271$	6.31192	−	5.29633i	0.383422	−	0.321729i	−0.430622	−	0.902532i	$-0.641706\pi$
$271$	6.31192	−	5.29633i	0.383422	−	0.321729i	0.814044	+	0.580803i	$0.197261\pi$
$272$	4.32261	−	24.5147i	0.262097	−	1.48642i
$273$	11.8575	−	20.5378i	0.717648	−	1.24300i
$274$	−3.31291	+	9.10215i	−0.200140	+	0.549881i
$275$		0			0
$276$	66.8994	−	11.7962i	4.02687	−	0.710046i
$277$	2.55500	+	2.14390i	0.153515	+	0.128814i	0.716310	−	0.697782i	$-0.245830\pi$
$277$	2.55500	+	2.14390i	0.153515	+	0.128814i	−0.562795	+	0.826596i	$0.690274\pi$
$278$	38.2089	+	32.0610i	2.29162	+	1.92289i
$279$	−5.72229	+	1.00899i	−0.342584	+	0.0604069i
$280$		0			0
$281$	−2.71616	+	7.46259i	−0.162033	+	0.445181i	−0.993965	−	0.109696i	$-0.965012\pi$
$281$	−2.71616	+	7.46259i	−0.162033	+	0.445181i	0.831933	+	0.554877i	$0.187235\pi$
$282$	−25.4044	+	44.0017i	−1.51281	+	2.62027i
$283$	−1.90235	+	10.7888i	−0.113083	+	0.641325i	0.874599	+	0.484848i	$0.161125\pi$
$283$	−1.90235	+	10.7888i	−0.113083	+	0.641325i	−0.987682	+	0.156477i	$0.949986\pi$
$284$	−24.6026	+	20.6441i	−1.45990	+	1.22500i
$285$		0			0
$286$	−22.2268	+	38.4980i	−1.31430	+	2.27643i
$287$	−3.61518	+	0.637453i	−0.213397	+	0.0376277i
$288$	5.35274	+	9.27122i	0.315413	+	0.546312i
$289$	11.0539	−	4.02329i	0.650229	−	0.236664i
$290$		0			0
$291$	−2.15599	−	5.92354i	−0.126386	−	0.347244i
$292$	15.6549	+	2.76038i	0.916133	+	0.161539i
$293$	5.80286	−	6.91558i	0.339007	−	0.404012i	−0.569427	−	0.822042i	$-0.692835\pi$
$293$	5.80286	−	6.91558i	0.339007	−	0.404012i	0.908433	+	0.418030i	$0.137279\pi$
$294$	−1.82276	−	2.17228i	−0.106306	−	0.126690i
$295$		0			0
$296$	15.9928	−	45.2383i	0.929562	−	2.62942i
$297$			14.9867i			0.869617i
$298$	4.83735	−	4.05902i	0.280220	−	0.235133i
$299$	−25.4813	−	21.3814i	−1.47362	−	1.23652i
$300$		0			0
$301$	3.79093	+	10.4155i	0.218505	+	0.600339i
$302$	14.2788			0.821652
$303$	10.4956	+	28.8365i	0.602957	+	1.65661i
$304$	−59.7916	+	34.5207i	−3.42928	+	1.97990i
$305$		0			0
$306$	2.49548	−	4.32230i	0.142657	−	0.247089i
$307$	3.07935	−	1.77787i	0.175748	−	0.101468i	−0.409545	−	0.912290i	$-0.634313\pi$
$307$	3.07935	−	1.77787i	0.175748	−	0.101468i	0.585293	+	0.810822i	$0.300979\pi$
$308$	−28.6748	−	34.1733i	−1.63390	−	1.94721i
$309$	16.4344	+	2.89784i	0.934923	+	0.164852i
$310$		0			0
$311$	−5.70682	+	15.6794i	−0.323604	+	0.889095i	0.666087	+	0.745874i	$0.267968\pi$
$311$	−5.70682	+	15.6794i	−0.323604	+	0.889095i	−0.989691	+	0.143220i	$0.954254\pi$
$312$	25.1898	−	69.2085i	1.42609	−	3.91816i
$313$	1.15135	+	6.52963i	0.0650781	+	0.369076i	0.999902	+	0.0139659i	$0.00444564\pi$
$313$	1.15135	+	6.52963i	0.0650781	+	0.369076i	−0.934824	+	0.355110i	$0.884443\pi$
$314$	30.7486	−	36.6448i	1.73524	−	2.06798i
$315$		0			0
$316$	−73.8199	+	13.0164i	−4.15269	+	0.732232i
$317$	−7.06246	+	19.4040i	−0.396667	+	1.08983i	0.567230	+	0.823560i	$0.308015\pi$
$317$	−7.06246	+	19.4040i	−0.396667	+	1.08983i	−0.963897	+	0.266275i	$0.914207\pi$
$318$	60.7167	+	22.0991i	3.40482	+	1.23925i
$319$	9.04562	+	5.22249i	0.506457	+	0.292403i
$320$		0			0
$321$	−23.9672	+	20.1109i	−1.33772	+	1.12248i
$322$	40.5073	−	23.3869i	2.25738	−	1.30330i
$323$	12.5783	+	7.26208i	0.699875	+	0.404073i
$324$	−9.34375	−	52.9910i	−0.519097	−	2.94395i
$325$		0			0
$326$	51.9947	−	18.9245i	2.87972	−	1.04813i
$327$	5.09713			0.281872
$328$	−10.7131	+	3.89924i	−0.591530	+	0.215299i
$329$	−4.33543	+	24.5875i	−0.239020	+	1.35555i
$330$		0			0
$331$	−10.3766	−	12.3663i	−0.570348	−	0.679714i	0.401355	−	0.915923i	$-0.368540\pi$
$331$	−10.3766	−	12.3663i	−0.570348	−	0.679714i	−0.971702	+	0.236209i	$0.924095\pi$
$332$		−	48.4282i		−	2.65785i
$333$	3.19090	−	3.87505i	0.174860	−	0.212351i
$334$	−24.8308			−1.35868
$335$		0			0
$336$	41.3959	+	34.7353i	2.25833	+	1.89497i
$337$	−22.3023	−	3.93249i	−1.21488	−	0.214216i	−0.470761	−	0.882261i	$-0.656020\pi$
$337$	−22.3023	−	3.93249i	−1.21488	−	0.214216i	−0.744121	+	0.668044i	$0.767132\pi$
$338$	−24.3118	+	8.84879i	−1.32239	+	0.481310i
$339$		−	6.77477i		−	0.367955i
$340$		0			0
$341$	21.4849	−	12.4043i	1.16347	−	0.671732i
$342$	−13.6323	+	2.40374i	−0.737151	+	0.129980i
$343$	−16.6044	−	9.58658i	−0.896555	−	0.517626i
$344$	17.2113	+	29.8109i	0.927972	+	1.60729i
$345$		0			0
$346$	51.5766	+	9.09435i	2.77278	+	0.488915i
$347$	5.35808	−	9.28046i	0.287637	−	0.498201i	−0.685608	−	0.727970i	$-0.740464\pi$
$347$	5.35808	−	9.28046i	0.287637	−	0.498201i	0.973245	+	0.229769i	$0.0737971\pi$
$348$	−27.1580	−	9.88469i	−1.45582	−	0.529875i
$349$	−0.866831	−	0.315501i	−0.0464004	−	0.0168884i	0.318716	−	0.947850i	$-0.396748\pi$
$349$	−0.866831	−	0.315501i	−0.0464004	−	0.0168884i	−0.365116	+	0.930962i	$0.618971\pi$
$350$		0			0
$351$	−13.0519	+	15.5547i	−0.696660	+	0.830248i
$352$	−35.0143	−	29.3804i	−1.86627	−	1.56598i
$353$	−4.55689	−	25.8434i	−0.242539	−	1.37551i	−0.826140	−	0.563465i	$-0.809468\pi$
$353$	−4.55689	−	25.8434i	−0.242539	−	1.37551i	0.583601	−	0.812041i	$-0.301643\pi$
$354$	3.88778	+	1.41504i	0.206633	+	0.0752083i
$355$		0			0
$356$	57.3860	+	33.1318i	3.04145	+	1.75598i
$357$	1.97404	−	11.1953i	0.104477	−	0.592519i
$358$	−12.8084	−	15.2645i	−0.676946	−	0.806753i
$359$	−8.57026	−	14.8441i	−0.452321	−	0.783443i	0.546209	−	0.837649i	$-0.316070\pi$
$359$	−8.57026	−	14.8441i	−0.452321	−	0.783443i	−0.998530	+	0.0542064i	$0.982737\pi$
$360$		0			0
$361$	−3.69580	−	20.9599i	−0.194516	−	1.10315i
$362$	9.49773	+	16.4506i	0.499190	+	0.864622i
$363$	0.946252	+	2.59981i	0.0496653	+	0.136454i
$364$		−	60.4413i		−	3.16799i
$365$		0			0
$366$	−6.31660	+	35.8232i	−0.330174	+	1.87251i
$367$	−2.38479	+	2.84209i	−0.124485	+	0.148356i	−0.824687	−	0.565589i	$-0.808649\pi$
$367$	−2.38479	+	2.84209i	−0.124485	+	0.148356i	0.700202	+	0.713945i	$0.253093\pi$
$368$	58.0634	−	48.7210i	3.02676	−	2.53976i
$369$	−1.19270			−0.0620896
$370$		0			0
$371$	31.7501			1.64838
$372$	−52.5849	+	44.1239i	−2.72640	+	2.28772i
$373$	−19.7993	+	23.5959i	−1.02517	+	1.22175i	−0.0503544	+	0.998731i	$0.516035\pi$
$373$	−19.7993	+	23.5959i	−1.02517	+	1.22175i	−0.974814	+	0.223017i	$0.928409\pi$
$374$	−3.70032	+	20.9855i	−0.191339	+	1.08514i
$375$		0			0
$376$			77.5376i			3.99870i
$377$	4.84016	+	13.2982i	0.249281	+	0.684894i
$378$	−14.2762	−	24.7270i	−0.734287	−	1.27182i
$379$	−1.14733	−	6.50683i	−0.0589344	−	0.334233i	0.941058	−	0.338246i	$-0.109834\pi$
$379$	−1.14733	−	6.50683i	−0.0589344	−	0.334233i	−0.999992	+	0.00401302i	$0.998723\pi$
$380$		0			0
$381$	11.9051	+	20.6203i	0.609917	+	1.05641i
$382$	−26.4068	−	31.4704i	−1.35109	−	1.61017i
$383$	3.05957	−	17.3517i	0.156337	−	0.886629i	−0.801217	−	0.598374i	$-0.795814\pi$
$383$	3.05957	−	17.3517i	0.156337	−	0.886629i	0.957554	−	0.288255i	$-0.0930751\pi$
$384$	12.1387	+	7.00828i	0.619450	+	0.357640i
$385$		0			0
$386$	−58.5295	−	21.3030i	−2.97907	−	1.08429i
$387$	0.625343	+	3.54650i	0.0317880	+	0.180279i
$388$	−12.3072	−	10.3270i	−0.624805	−	0.524273i
$389$	9.14062	−	10.8934i	0.463448	−	0.552315i	−0.482812	−	0.875724i	$-0.660384\pi$
$389$	9.14062	−	10.8934i	0.463448	−	0.552315i	0.946259	+	0.323409i	$0.104829\pi$
$390$		0			0
$391$	−14.9836	−	5.45358i	−0.757752	−	0.275799i
$392$	−4.06651	−	1.48009i	−0.205390	−	0.0747557i
$393$	12.5093	−	21.6667i	0.631010	−	1.09294i
$394$	−7.49752	−	1.32201i	−0.377720	−	0.0666021i
$395$		0			0
$396$	−7.24699	−	12.5521i	−0.364175	−	0.630769i
$397$	2.20988	+	1.27587i	0.110911	+	0.0640342i	0.554429	−	0.832231i	$-0.312937\pi$
$397$	2.20988	+	1.27587i	0.110911	+	0.0640342i	−0.443519	+	0.896265i	$0.646270\pi$
$398$	39.2775	−	6.92568i	1.96880	−	0.347153i
$399$	−27.3054	+	15.7648i	−1.36698	+	0.789227i
$400$		0			0
$401$		−	4.83800i		−	0.241598i	−0.992677	−	0.120799i	$-0.961454\pi$
$401$		−	4.83800i		−	0.241598i	0.992677	−	0.120799i	$-0.0385456\pi$
$402$	−28.6744	+	10.4366i	−1.43015	+	0.520532i
$403$	33.1021	+	5.83679i	1.64893	+	0.290751i
$404$	59.9130	+	50.2730i	2.98078	+	2.50117i
$405$		0			0
$406$	−19.8995			−0.987597
$407$	−7.14353	+	20.2067i	−0.354092	+	1.00161i
$408$		−	35.3049i		−	1.74785i
$409$	−13.1076	−	15.6210i	−0.648129	−	0.772410i	0.337502	−	0.941325i	$-0.390418\pi$
$409$	−13.1076	−	15.6210i	−0.648129	−	0.772410i	−0.985631	+	0.168915i	$0.945974\pi$
$410$		0			0
$411$	−1.24475	+	7.05935i	−0.0613992	+	0.348212i
$412$	39.9669	−	14.5468i	1.96903	−	0.716667i
$413$	2.03301			0.100038
$414$	14.2805	−	5.19767i	0.701847	−	0.255451i
$415$		0			0
$416$	−10.7538	−	60.9878i	−0.527248	−	2.99017i
$417$	31.9666	+	18.4559i	1.56541	+	0.903789i
$418$	51.1839	−	29.5510i	2.50349	−	1.44539i
$419$	−21.7690	+	18.2664i	−1.06349	+	0.892371i	−0.994447	−	0.105243i	$-0.966438\pi$
$419$	−21.7690	+	18.2664i	−1.06349	+	0.892371i	−0.0690394	+	0.997614i	$0.521993\pi$
$420$		0			0
$421$	−7.37565	−	4.25833i	−0.359467	−	0.207538i	0.309380	−	0.950939i	$-0.399879\pi$
$421$	−7.37565	−	4.25833i	−0.359467	−	0.207538i	−0.668847	+	0.743400i	$0.733212\pi$
$422$	−29.9350	−	10.8955i	−1.45721	−	0.530382i
$423$	−2.77439	+	7.62259i	−0.134896	+	0.370623i
$424$	97.1062	−	17.1225i	4.71590	−	0.831540i
$425$		0			0
$426$	−21.4071	+	25.5120i	−1.03718	+	1.23606i
$427$	3.10389	+	17.6030i	0.150208	+	0.851871i
$428$	−27.2726	+	74.9308i	−1.31827	+	3.62192i
$429$	−11.2516	+	30.9135i	−0.543232	+	1.49252i
$430$		0			0
$431$	20.5717	+	3.62735i	0.990905	+	0.174723i	0.645525	−	0.763739i	$-0.276639\pi$
$431$	20.5717	+	3.62735i	0.990905	+	0.174723i	0.345381	+	0.938463i	$0.387750\pi$
$432$	−29.7410	−	35.4439i	−1.43091	−	1.70530i
$433$	−10.2732	+	5.93122i	−0.493697	+	0.285036i	−0.726107	−	0.687582i	$-0.758672\pi$
$433$	−10.2732	+	5.93122i	−0.493697	+	0.285036i	0.232410	+	0.972618i	$0.425339\pi$
$434$	−23.6324	+	40.9326i	−1.13439	+	1.96483i
$435$		0			0
$436$	11.2504	−	6.49540i	0.538795	−	0.311073i
$437$	15.1257	+	41.5575i	0.723560	+	1.98796i
$438$	16.4840			0.787635
$439$	−3.94682	−	10.8438i	−0.188371	−	0.517546i	0.809174	−	0.587569i	$-0.199915\pi$
$439$	−3.94682	−	10.8438i	−0.188371	−	0.517546i	−0.997545	+	0.0700232i	$0.977693\pi$
$440$		0			0
$441$	−0.346812	−	0.291010i	−0.0165148	−	0.0138576i
$442$	−22.1169	+	18.5583i	−1.05199	+	0.882726i
$443$			16.9822i			0.806848i	0.915013	+	0.403424i	$0.132180\pi$
$443$			16.9822i			0.806848i	−0.915013	+	0.403424i	$0.867820\pi$
$444$	9.75674	−	58.4940i	0.463035	−	2.77600i
$445$		0			0
$446$	−35.1865	−	41.9337i	−1.66613	−	1.98562i
$447$	3.00383	−	3.57983i	0.142076	−	0.169320i
$448$	31.3390	+	5.52591i	1.48063	+	0.261075i
$449$	5.36509	+	14.7405i	0.253194	+	0.695645i	0.999547	+	0.0300946i	$0.00958087\pi$
$449$	5.36509	+	14.7405i	0.253194	+	0.695645i	−0.746353	+	0.665550i	$0.768197\pi$
$450$		0			0
$451$	4.78523	−	1.74168i	0.225328	−	0.0820126i
$452$	−8.63327	−	14.9533i	−0.406075	−	0.703343i
$453$	10.4063	−	1.83492i	0.488933	−	0.0862120i
$454$	−13.1782	+	22.8253i	−0.618484	+	1.07125i
$455$		0			0
$456$	−75.0106	+	62.9414i	−3.51269	+	2.94750i
$457$	3.20350	−	18.1680i	0.149854	−	0.849862i	−0.813488	−	0.581582i	$-0.802434\pi$
$457$	3.20350	−	18.1680i	0.149854	−	0.849862i	0.963341	−	0.268280i	$-0.0864551\pi$
$458$	−13.2797	+	23.0012i	−0.620521	+	1.07477i
$459$	−3.32905	+	9.14650i	−0.155387	+	0.426922i
$460$		0			0
$461$	−17.9884	+	3.17185i	−0.837805	+	0.147728i	−0.576058	−	0.817409i	$-0.695410\pi$
$461$	−17.9884	+	3.17185i	−0.837805	+	0.147728i	−0.261747	+	0.965136i	$0.584299\pi$
$462$	−35.4365	−	29.7347i	−1.64865	−	1.38338i
$463$	−29.8866	−	25.0778i	−1.38895	−	1.16547i	−0.965764	−	0.259421i	$-0.916468\pi$
$463$	−29.8866	−	25.0778i	−1.38895	−	1.16547i	−0.423183	−	0.906044i	$-0.639087\pi$
$464$	−31.7570	+	5.59962i	−1.47428	+	0.259956i
$465$		0			0
$466$	6.01376	−	16.5227i	0.278582	−	0.765398i
$467$	−2.43403	+	4.21587i	−0.112634	+	0.195087i	−0.916831	−	0.399275i	$-0.869262\pi$
$467$	−2.43403	+	4.21587i	−0.112634	+	0.195087i	0.804198	+	0.594362i	$0.202595\pi$
$468$	3.41003	−	19.3393i	0.157629	−	0.893957i
$469$	−11.4865	+	9.63828i	−0.530395	+	0.445054i
$470$		0			0
$471$	17.7004	−	30.6580i	0.815591	−	1.41265i
$472$	6.21786	−	1.09638i	0.286200	−	0.0504648i
$473$	−7.68781	−	13.3157i	−0.353486	−	0.612256i
$474$	−73.0418	+	26.5850i	−3.35492	+	1.22109i
$475$		0			0
$476$	−9.90940	−	27.2259i	−0.454197	−	1.24789i
$477$	10.1590	+	1.79131i	0.465149	+	0.0820183i
$478$	−30.3776	+	36.2026i	−1.38944	+	1.65587i
$479$	−0.768832	−	0.916258i	−0.0351288	−	0.0418649i	0.748194	−	0.663480i	$-0.230921\pi$
$479$	−0.768832	−	0.916258i	−0.0351288	−	0.0418649i	−0.783323	+	0.621615i	$0.786477\pi$
$480$		0			0
$481$	−25.0122	+	14.7512i	−1.14046	+	0.672595i
$482$			18.9770i			0.864381i
$483$	26.5162	−	22.2497i	1.20653	−	1.01240i
$484$	5.40157	+	4.53245i	0.245526	+	0.206021i
$485$		0			0
$486$	−7.54965	−	20.7425i	−0.342459	−	0.940898i
$487$	−22.8962			−1.03752			−0.518762	−	0.854919i	$-0.673607\pi$
$487$	−22.8962			−1.03752			−0.518762	+	0.854919i	$0.673607\pi$
$488$	18.9862	+	52.1642i	0.859465	+	2.36136i
$489$	35.4616	−	20.4738i	1.60363	−	0.925856i
$490$		0			0
$491$	−12.1475	+	21.0401i	−0.548209	+	0.949526i	0.450188	+	0.892934i	$0.351357\pi$
$491$	−12.1475	+	21.0401i	−0.548209	+	0.949526i	−0.998397	+	0.0565925i	$0.981976\pi$
$492$	−12.2026	+	7.04516i	−0.550135	+	0.317620i
$493$	4.36051	+	5.19666i	0.196388	+	0.234046i
$494$	78.8597	+	13.9051i	3.54806	+	0.625619i
$495$		0			0
$496$	−26.1960	+	71.9731i	−1.17624	+	3.23169i
$497$	−5.59714	+	15.3780i	−0.251066	+	0.689798i
$498$	−8.72032	−	49.4554i	−0.390767	−	2.21615i
$499$	−0.257419	+	0.306780i	−0.0115237	+	0.0137334i	−0.771775	−	0.635895i	$-0.780631\pi$
$499$	−0.257419	+	0.306780i	−0.0115237	+	0.0137334i	0.760252	+	0.649628i	$0.225076\pi$
$500$		0			0
$501$	−18.0966	+	3.19092i	−0.808496	+	0.142560i
$502$	−2.02004	+	5.55001i	−0.0901588	+	0.247709i
$503$	25.9835	+	9.45723i	1.15855	+	0.421677i	0.848578	−	0.529070i	$-0.177459\pi$
$503$	25.9835	+	9.45723i	1.15855	+	0.421677i	0.309969	+	0.950747i	$0.399681\pi$
$504$	14.3191	+	8.26714i	0.637824	+	0.368248i
$505$		0			0
$506$	−49.7045	+	41.7070i	−2.20963	+	1.85410i
$507$	−16.5813	+	9.57320i	−0.736400	+	0.425161i
$508$	52.5539	+	30.3420i	2.33170	+	1.34621i
$509$	3.55827	+	20.1800i	0.157718	+	0.894461i	0.956259	+	0.292521i	$0.0944942\pi$
$509$	3.55827	+	20.1800i	0.157718	+	0.894461i	−0.798541	+	0.601940i	$0.794395\pi$
$510$		0			0
$511$	7.61151	−	2.77036i	0.336714	−	0.122554i
$512$	−30.5000			−1.34792
$513$	25.3681	−	9.23325i	1.12003	−	0.407658i
$514$	3.31656	−	18.8092i	0.146287	−	0.829637i
$515$		0			0
$516$	27.3467	+	32.5905i	1.20387	+	1.43472i
$517$		−	34.6339i		−	1.52320i
$518$	−7.46230	−	40.1445i	−0.327875	−	1.76385i
$519$	38.7576			1.70127
$520$		0			0
$521$	7.49284	+	6.28724i	0.328267	+	0.275449i	0.791993	−	0.610530i	$-0.209043\pi$
$521$	7.49284	+	6.28724i	0.328267	+	0.275449i	−0.463726	+	0.885979i	$0.653488\pi$
$522$	−6.36720	−	1.12271i	−0.278685	−	0.0491397i
$523$	−20.9892	+	7.63944i	−0.917793	+	0.334049i	−0.757360	−	0.652997i	$-0.773511\pi$
$523$	−20.9892	+	7.63944i	−0.917793	+	0.334049i	−0.160433	+	0.987047i	$0.551289\pi$
$524$		−	63.7636i		−	2.78553i
$525$		0			0
$526$	37.7190	−	21.7771i	1.64463	−	0.949527i
$527$	15.8678	−	2.79792i	0.691213	−	0.121879i
$528$	−64.9192	−	37.4811i	−2.82524	−	1.63116i
$529$	−12.7757	−	22.1282i	−0.555467	−	0.962097i
$530$		0			0
$531$	0.650496	+	0.114700i	0.0282291	+	0.00497756i
$532$	−40.1790	+	69.5921i	−1.74198	+	3.01720i
$533$	6.48341	+	2.35977i	0.280828	+	0.102213i
$534$	64.5691	+	23.5012i	2.79418	+	1.01700i
$535$		0			0
$536$	−29.9330	+	35.6727i	−1.29291	+	1.54083i
$537$	−11.2963	−	9.47874i	−0.487473	−	0.409038i
$538$	−2.01305	−	11.4166i	−0.0867887	−	0.492203i
$539$	1.81640	+	0.661114i	0.0782377	+	0.0284762i
$540$		0			0
$541$	−28.5009	−	16.4550i	−1.22535	−	0.707455i	−0.259295	−	0.965798i	$-0.583490\pi$
$541$	−28.5009	−	16.4550i	−1.22535	−	0.707455i	−0.966053	+	0.258343i	$0.916823\pi$
$542$	3.78139	−	21.4454i	0.162425	−	0.921157i
$543$	9.03592	+	10.7686i	0.387768	+	0.462124i
$544$	−14.8431	−	25.7089i	−0.636391	−	1.10226i
$545$		0			0
$546$	−10.8835	−	61.7233i	−0.465770	−	2.64151i
$547$	−4.40299	−	7.62620i	−0.188258	−	0.326073i	0.756411	−	0.654096i	$-0.226951\pi$
$547$	−4.40299	−	7.62620i	−0.188258	−	0.326073i	−0.944670	+	0.328023i	$0.893618\pi$
$548$	6.24850	+	17.1676i	0.266923	+	0.733364i
$549$			5.80752i			0.247859i
$550$		0			0
$551$	3.26719	−	18.5291i	0.139187	−	0.789368i
$552$	69.0996	−	82.3496i	2.94107	−	3.50503i
$553$	−29.2592	+	24.5514i	−1.24423	+	1.04403i
$554$	8.81478			0.374504
$555$		0			0
$556$	94.0754			3.98969
$557$	6.06388	−	5.08820i	0.256935	−	0.215594i	−0.505217	−	0.862992i	$-0.668587\pi$
$557$	6.06388	−	5.08820i	0.256935	−	0.215594i	0.762152	+	0.647399i	$0.224143\pi$
$558$	−9.87097	+	11.7638i	−0.417872	+	0.498000i
$559$	3.61746	−	20.5156i	0.153002	−	0.867719i
$560$		0			0
$561$			15.7697i			0.665798i
$562$	7.17844	+	19.7226i	0.302804	+	0.831947i
$563$	11.9440	+	20.6877i	0.503381	+	0.871882i	0.999992	+	0.00390896i	$0.00124426\pi$
$563$	11.9440	+	20.6877i	0.503381	+	0.871882i	−0.496611	+	0.867973i	$0.665422\pi$
$564$	16.6408	+	94.3749i	0.700706	+	3.97390i
$565$		0			0
$566$	14.4765	+	25.0741i	0.608494	+	1.05394i
$567$	−17.6240	−	21.0035i	−0.740139	−	0.882064i
$568$	−8.82541	+	50.0514i	−0.370306	+	2.10011i
$569$	10.5425	+	6.08672i	0.441965	+	0.255169i	0.704431	−	0.709773i	$-0.251202\pi$
$569$	10.5425	+	6.08672i	0.441965	+	0.255169i	−0.262466	+	0.964941i	$0.584536\pi$
$570$		0			0
$571$	30.0566	+	10.9397i	1.25783	+	0.457812i	0.883039	−	0.469299i	$-0.155493\pi$
$571$	30.0566	+	10.9397i	1.25783	+	0.457812i	0.374788	+	0.927111i	$0.377715\pi$
$572$	14.5594	+	82.5704i	0.608759	+	3.45244i
$573$	−23.2893	−	19.5421i	−0.972926	−	0.816382i
$574$	−6.23620	+	7.43201i	−0.260294	+	0.310206i
$575$		0			0
$576$	9.71569	+	3.53622i	0.404820	+	0.147343i
$577$	−20.2686	−	7.37717i	−0.843794	−	0.307116i	−0.116286	−	0.993216i	$-0.537099\pi$
$577$	−20.2686	−	7.37717i	−0.843794	−	0.307116i	−0.727507	+	0.686100i	$0.759321\pi$
$578$	15.5444	−	26.9237i	0.646562	−	1.11988i
$579$	−45.3937	−	8.00413i	−1.88650	−	0.332640i
$580$		0			0
$581$	−12.3383	−	21.3706i	−0.511879	−	0.886600i
$582$	−14.4278	−	8.32990i	−0.598052	−	0.345285i
$583$	−43.3746	+	7.64812i	−1.79639	+	0.316753i
$584$	21.7854	−	12.5778i	0.901487	−	0.520474i
$585$		0			0
$586$		−	23.8588i		−	0.985598i
$587$	30.8760	−	11.2380i	1.27439	−	0.463840i	0.385817	−	0.922575i	$-0.373920\pi$
$587$	30.8760	−	11.2380i	1.27439	−	0.463840i	0.888573	+	0.458735i	$0.151697\pi$
$588$	−5.26720	−	0.928749i	−0.217216	−	0.0383010i
$589$	−34.2337	−	28.7255i	−1.41057	−	1.18361i
$590$		0			0
$591$	−5.63406			−0.231754
$592$	−23.2053	−	61.9654i	−0.953732	−	2.54676i
$593$		−	7.82707i		−	0.321419i	−0.987002	−	0.160710i	$-0.948622\pi$
$593$		−	7.82707i		−	0.321419i	0.987002	−	0.160710i	$-0.0513783\pi$
$594$	25.4594	+	30.3413i	1.04461	+	1.24492i
$595$		0			0
$596$	2.06819	−	11.7293i	0.0847162	−	0.480449i
$597$	27.7353	−	10.0948i	1.13513	−	0.413154i
$598$	−87.9108			−3.59494
$599$	−31.7845	+	11.5686i	−1.29868	+	0.472681i	−0.896567	−	0.442909i	$-0.853947\pi$
$599$	−31.7845	+	11.5686i	−1.29868	+	0.472681i	−0.402114	+	0.915590i	$0.631724\pi$
$600$		0			0
$601$	−2.71282	−	15.3852i	−0.110658	−	0.627575i	−0.988809	−	0.149190i	$-0.952334\pi$
$601$	−2.71282	−	15.3852i	−0.110658	−	0.627575i	0.878150	−	0.478385i	$-0.158778\pi$
$602$	25.3687	+	14.6466i	1.03395	+	0.596953i
$603$	−4.21907	+	2.43588i	−0.171814	+	0.0991968i
$604$	20.6306	−	17.3111i	0.839446	−	0.704379i
$605$		0			0
$606$	70.2362	+	40.5509i	2.85315	+	1.64727i
$607$	−9.27710	−	3.37659i	−0.376546	−	0.137051i	0.146812	−	0.989164i	$-0.453099\pi$
$607$	−9.27710	−	3.37659i	−0.376546	−	0.137051i	−0.523358	+	0.852113i	$0.675321\pi$
$608$	−28.1604	+	77.3701i	−1.14206	+	3.13777i
$609$	−14.5027	+	2.55722i	−0.587680	+	0.103624i
$610$		0			0
$611$	30.1627	−	35.9465i	1.22025	−	1.45424i
$612$	−1.63463	−	9.27046i	−0.0660761	−	0.374736i
$613$	0.178384	−	0.490106i	0.00720486	−	0.0197952i	−0.936038	−	0.351899i	$-0.885536\pi$
$613$	0.178384	−	0.490106i	0.00720486	−	0.0197952i	0.943243	+	0.332104i	$0.107758\pi$
$614$	3.21407	−	8.83058i	0.129709	−	0.356373i
$615$		0			0
$616$	−69.5219	−	12.2586i	−2.80112	−	0.493912i
$617$	−23.3512	−	27.8289i	−0.940085	−	1.12035i	−0.992563	−	0.121728i	$-0.961156\pi$
$617$	−23.3512	−	27.8289i	−0.940085	−	1.12035i	0.0524782	−	0.998622i	$-0.483288\pi$
$618$	38.1952	−	22.0520i	1.53644	−	0.887062i
$619$	−14.1225	+	24.4609i	−0.567632	+	0.983168i	0.429167	+	0.903225i	$0.358807\pi$
$619$	−14.1225	+	24.4609i	−0.567632	+	0.983168i	−0.996799	+	0.0799427i	$0.974526\pi$
$620$		0			0
$621$	−25.6668	+	14.8188i	−1.02997	+	0.594656i
$622$	15.0823	+	41.4384i	0.604746	+	1.66153i
$623$	33.7646			1.35275
$624$	−34.7372	−	95.4397i	−1.39060	−	3.82065i
$625$		0			0
$626$	13.4235	+	11.2636i	0.536510	+	0.450186i
$627$	33.5052	−	28.1142i	1.33807	−	1.12277i
$628$		−	90.2244i		−	3.60034i
$629$	−8.84833	+	10.7455i	−0.352806	+	0.428449i
$630$		0			0
$631$	5.79199	+	6.90263i	0.230576	+	0.274789i	0.868910	−	0.494970i	$-0.164821\pi$
$631$	5.79199	+	6.90263i	0.230576	+	0.274789i	−0.638335	+	0.769759i	$0.720376\pi$
$632$	−76.2476	+	90.8684i	−3.03297	+	3.61455i
$633$	−23.2167	−	4.09373i	−0.922780	−	0.162711i
$634$	18.6651	+	51.2820i	0.741286	+	2.03667i
$635$		0			0
$636$	114.518	−	41.6812i	4.54094	−	1.65277i
$637$	1.30947	+	2.26807i	0.0518831	+	0.0898641i
$638$	27.1852	−	4.79349i	1.07627	−	0.189776i
$639$	−2.65851	+	4.60468i	−0.105169	+	0.182158i
$640$		0			0
$641$	−22.7157	+	19.0608i	−0.897218	+	0.752855i	−0.969645	−	0.244519i	$-0.921370\pi$
$641$	−22.7157	+	19.0608i	−0.897218	+	0.752855i	0.0724270	+	0.997374i	$0.476926\pi$
$642$	−14.3585	+	81.4310i	−0.566684	+	3.21382i
$643$	−18.5922	+	32.2027i	−0.733206	+	1.26995i	0.222300	+	0.974978i	$0.428644\pi$
$643$	−18.5922	+	32.2027i	−0.733206	+	1.26995i	−0.955506	+	0.294972i	$0.904690\pi$
$644$	30.1731	−	82.8999i	1.18899	−	3.26671i
$645$		0			0
$646$	37.8022	−	6.66554i	1.48731	−	0.262252i
$647$	−1.29198	−	1.08410i	−0.0507928	−	0.0426202i	0.617038	−	0.786933i	$-0.288333\pi$
$647$	−1.29198	−	1.08410i	−0.0507928	−	0.0426202i	−0.667831	+	0.744313i	$0.732777\pi$
$648$	−65.2292	−	54.7338i	−2.56244	−	2.15015i
$649$	−2.77734	+	0.489721i	−0.109020	+	0.0192232i
$650$		0			0
$651$	−11.9631	+	32.8684i	−0.468872	+	1.28822i
$652$	52.1806	−	90.3794i	2.04355	−	3.53953i
$653$	3.97750	−	22.5575i	0.155652	−	0.882744i	−0.802536	−	0.596604i	$-0.796516\pi$
$653$	3.97750	−	22.5575i	0.155652	−	0.882744i	0.958188	−	0.286141i	$-0.0923724\pi$
$654$	10.3194	−	8.65899i	0.403520	−	0.338593i
$655$		0			0
$656$	−7.86083	+	13.6153i	−0.306914	+	0.531590i
$657$	2.59174	−	0.456993i	0.101113	−	0.0178290i
$658$	32.9918	+	57.1435i	1.28616	+	2.22769i
$659$	21.4927	−	7.82272i	0.837238	−	0.304730i	0.112412	−	0.993662i	$-0.464142\pi$
$659$	21.4927	−	7.82272i	0.837238	−	0.304730i	0.724826	+	0.688932i	$0.241920\pi$
$660$		0			0
$661$	8.63104	+	23.7136i	0.335709	+	0.922352i	0.986597	+	0.163178i	$0.0521746\pi$
$661$	8.63104	+	23.7136i	0.335709	+	0.922352i	−0.650888	+	0.759174i	$0.725603\pi$
$662$	−42.0157	−	7.40851i	−1.63299	−	0.287940i
$663$	−13.7338	+	16.3674i	−0.533378	+	0.635656i
$664$	−49.2610	−	58.7070i	−1.91170	−	2.27827i
$665$		0			0
$666$	−0.122788	−	13.2659i	−0.00475792	−	0.514044i
$667$			20.6558i			0.799797i
$668$	−35.8765	+	30.1040i	−1.38810	+	1.16476i
$669$	−31.0326	−	26.0394i	−1.19979	−	1.00674i
$670$		0			0
$671$	−8.48061	−	23.3003i	−0.327390	−	0.899498i
$672$	64.4438			2.48597
$673$	−11.3509	−	31.1865i	−0.437547	−	1.20215i	−0.941083	−	0.338176i	$-0.890190\pi$
$673$	−11.3509	−	31.1865i	−0.437547	−	1.20215i	0.503536	−	0.863974i	$-0.332032\pi$
$674$	−51.8326	+	29.9255i	−1.99652	+	1.15269i
$675$		0			0
$676$	−24.3988	+	42.2599i	−0.938414	+	1.62538i
$677$	13.1625	−	7.59940i	0.505878	−	0.292069i	−0.225260	−	0.974299i	$-0.572323\pi$
$677$	13.1625	−	7.59940i	0.505878	−	0.292069i	0.731138	+	0.682230i	$0.238990\pi$
$678$	−11.5090	−	13.7159i	−0.441999	−	0.526754i
$679$	−8.06202	−	1.42155i	−0.309392	−	0.0545542i
$680$		0			0
$681$	−6.67103	+	18.3285i	−0.255634	+	0.702350i
$682$	22.4248	−	61.6117i	0.858691	−	2.35923i
$683$	−7.50013	−	42.5353i	−0.286984	−	1.62757i	−0.698110	−	0.715991i	$-0.745975\pi$
$683$	−7.50013	−	42.5353i	−0.286984	−	1.62757i	0.411125	−	0.911579i	$-0.365136\pi$
$684$	−16.7823	+	20.0004i	−0.641687	+	0.764733i
$685$		0			0
$686$	−49.9022	+	8.79910i	−1.90527	+	0.335951i
$687$	−6.72243	+	18.4697i	−0.256477	+	0.704664i
$688$	44.6067	+	16.2355i	1.70061	+	0.618973i
$689$	−51.6792	−	29.8370i	−1.96882	−	1.13670i
$690$		0			0
$691$	12.3367	−	10.3517i	0.469310	−	0.393797i	−0.377233	−	0.926118i	$-0.623124\pi$
$691$	12.3367	−	10.3517i	0.469310	−	0.393797i	0.846543	+	0.532321i	$0.178680\pi$
$692$	85.5457	−	49.3898i	3.25196	−	1.87752i
$693$	−6.39594	−	3.69270i	−0.242962	−	0.140274i
$694$	−4.91794	−	27.8910i	−0.186683	−	1.05873i
$695$		0			0
$696$	−42.9768	+	15.6423i	−1.62903	+	0.592919i
$697$	3.30735			0.125275
$698$	−2.29091	+	0.833825i	−0.0867124	+	0.0315607i
$699$	2.25954	−	12.8145i	0.0854636	−	0.484688i
$700$		0			0
$701$	−13.6132	−	16.2236i	−0.514164	−	0.612756i	0.445027	−	0.895517i	$-0.353194\pi$
$701$	−13.6132	−	16.2236i	−0.514164	−	0.612756i	−0.959190	+	0.282761i	$0.908750\pi$
$702$			53.6638i			2.02541i
$703$	38.6051	−	0.357323i	1.45602	−	0.0134767i
$704$	−44.1441			−1.66374
$705$		0			0
$706$	−53.1284	−	44.5800i	−1.99951	−	1.67779i
$707$	39.2469	+	6.92028i	1.47603	+	0.260264i
$708$	7.33276	−	2.66891i	0.275582	−	0.100304i
$709$		−	38.8909i		−	1.46058i	−0.683138	−	0.730289i	$-0.739385\pi$
$709$		−	38.8909i		−	1.46058i	0.683138	−	0.730289i	$-0.260615\pi$
$710$		0			0
$711$	−10.7472	+	6.20487i	−0.403050	+	0.232701i
$712$	103.268	−	18.2089i	3.87011	−	0.682406i
$713$	42.4883	+	24.5306i	1.59120	+	0.918678i
$714$	−15.0220	−	26.0190i	−0.562186	−	0.973735i
$715$		0			0
$716$	−37.0123	−	6.52626i	−1.38321	−	0.243898i
$717$	−17.4868	+	30.2881i	−0.653058	+	1.13113i
$718$	−42.5681	−	15.4935i	−1.58863	−	0.578213i
$719$	−9.46321	−	3.44433i	−0.352918	−	0.128452i	0.159477	−	0.987202i	$-0.449019\pi$
$719$	−9.46321	−	3.44433i	−0.352918	−	0.128452i	−0.512395	+	0.858750i	$0.671242\pi$
$720$		0			0
$721$	13.9306	−	16.6018i	0.518801	−	0.618283i
$722$	−43.0890	−	36.1560i	−1.60361	−	1.34559i
$723$	2.43868	+	13.8304i	0.0906953	+	0.514359i
$724$	33.6668	+	12.2537i	1.25122	+	0.455405i
$725$		0			0
$726$	6.33228	+	3.65594i	0.235013	+	0.135685i
$727$	2.11479	−	11.9936i	0.0784332	−	0.444817i	−0.920148	−	0.391570i	$-0.871932\pi$
$727$	2.11479	−	11.9936i	0.0784332	−	0.444817i	0.998581	−	0.0532466i	$-0.0169569\pi$
$728$	−61.4806	−	73.2698i	−2.27862	−	2.71556i
$729$	8.02435	+	13.8986i	0.297198	+	0.514762i
$730$		0			0
$731$	−1.73407	−	9.83438i	−0.0641368	−	0.363738i
$732$	34.3044	+	59.4169i	1.26793	+	2.19611i
$733$	−6.67122	−	18.3290i	−0.246407	−	0.676998i	−0.999811	−	0.0194399i	$-0.993812\pi$
$733$	−6.67122	−	18.3290i	−0.246407	−	0.676998i	0.753404	−	0.657558i	$-0.228411\pi$
$734$			9.80523i			0.361918i
$735$		0			0
$736$	15.6963	−	89.0180i	0.578572	−	3.28125i
$737$	13.3702	−	15.9340i	0.492498	−	0.586937i
$738$	−2.41469	+	2.02616i	−0.0888858	+	0.0745840i
$739$	31.2931			1.15114			0.575568	−	0.817754i	$-0.304781\pi$
$739$	31.2931			1.15114			0.575568	+	0.817754i	$0.304781\pi$
$740$		0			0
$741$	59.2596			2.17695
$742$	64.2797	−	53.9371i	2.35978	−	1.98009i
$743$	−33.1594	+	39.5179i	−1.21650	+	1.44977i	−0.360530	+	0.932748i	$0.617404\pi$
$743$	−33.1594	+	39.5179i	−1.21650	+	1.44977i	−0.855972	+	0.517023i	$0.827040\pi$
$744$	−18.8631	+	106.978i	−0.691556	+	3.92201i
$745$		0			0
$746$			81.4060i			2.98049i
$747$	−2.74215	−	7.53400i	−0.100330	−	0.275655i
$748$	20.0958	+	34.8069i	0.734774	+	1.27267i
$749$	7.05556	+	40.0141i	0.257804	+	1.46208i
$750$		0			0
$751$	14.2057	+	24.6050i	0.518373	+	0.897848i	0.999772	+	0.0213468i	$0.00679542\pi$
$751$	14.2057	+	24.6050i	0.518373	+	0.897848i	−0.481399	+	0.876501i	$0.659871\pi$
$752$	68.7306	+	81.9099i	2.50635	+	2.98695i
$753$	−0.758985	+	4.30442i	−0.0276590	+	0.156862i
$754$	32.3902	+	18.7005i	1.17958	+	0.681031i
$755$		0			0
$756$	−50.6050	−	18.4187i	−1.84049	−	0.669882i
$757$	−3.98991	−	22.6279i	−0.145016	−	0.822425i	−0.967355	−	0.253427i	$-0.918442\pi$
$757$	−3.98991	−	22.6279i	−0.145016	−	0.822425i	0.822339	−	0.568998i	$-0.192669\pi$
$758$	−13.3766	−	11.2243i	−0.485861	−	0.407685i
$759$	−30.8648	+	36.7833i	−1.12032	+	1.33515i
$760$		0			0
$761$	34.9807	+	12.7319i	1.26805	+	0.461532i	0.886462	−	0.462802i	$-0.153156\pi$
$761$	34.9807	+	12.7319i	1.26805	+	0.461532i	0.381586	+	0.924333i	$0.375378\pi$
$762$	59.1321	+	21.5223i	2.14213	+	0.779672i
$763$	3.30973	−	5.73262i	0.119820	−	0.207535i
$764$	−76.3072	−	13.4550i	−2.76070	−	0.486785i
$765$		0			0
$766$	−23.2827	−	40.3269i	−0.841239	−	1.45707i
$767$	−3.30910	−	1.91051i	−0.119485	−	0.0689845i
$768$	−11.7823	+	2.07754i	−0.425157	+	0.0749667i
$769$	30.4338	−	17.5709i	1.09747	−	0.633624i	0.161914	−	0.986805i	$-0.448233\pi$
$769$	30.4338	−	17.5709i	1.09747	−	0.633624i	0.935555	+	0.353181i	$0.114900\pi$
$770$		0			0
$771$		−	14.1343i		−	0.509033i
$772$	−110.393	+	40.1797i	−3.97312	+	1.44610i
$773$	50.1628	+	8.84505i	1.80423	+	0.318134i	0.971766	−	0.235946i	$-0.0758189\pi$
$773$	50.1628	+	8.84505i	1.80423	+	0.318134i	0.832463	+	0.554080i	$0.186930\pi$
$774$	7.29082	+	6.11773i	0.262063	+	0.219897i
$775$		0			0
$776$	−25.4239			−0.912666
$777$	−10.5973	−	28.2982i	−0.380177	−	1.01519i
$778$		−	37.5822i		−	1.34739i
$779$	−5.89632	−	7.02696i	−0.211258	−	0.251767i
$780$		0			0
$781$	3.94206	−	22.3566i	0.141058	−	0.799981i
$782$	−39.5995	+	14.4130i	−1.41608	+	0.515409i
$783$	12.6090			0.450610
$784$	−5.60779	+	2.04107i	−0.200278	+	0.0728953i
$785$		0			0
$786$	−11.4817	−	65.1161i	−0.409539	−	2.32261i
$787$	−14.3922	−	8.30936i	−0.513027	−	0.296197i	0.221050	−	0.975263i	$-0.429052\pi$
$787$	−14.3922	−	8.30936i	−0.513027	−	0.296197i	−0.734077	+	0.679066i	$0.762385\pi$
$788$	−12.4355	+	7.17963i	−0.442996	+	0.255764i
$789$	24.6910	−	20.7182i	0.879024	−	0.737589i
$790$		0			0
$791$	−7.61943	−	4.39908i	−0.270916	−	0.156413i
$792$	−21.5531	−	7.84469i	−0.765857	−	0.278749i
$793$	11.4902	−	31.5691i	0.408029	−	1.12105i
$794$	6.64145	−	1.17107i	0.235696	−	0.0415596i
$795$		0			0
$796$	48.3533	−	57.6252i	1.71384	−	2.04247i
$797$	−5.90405	−	33.4835i	−0.209132	−	1.18605i	−0.890803	−	0.454389i	$-0.849858\pi$
$797$	−5.90405	−	33.4835i	−0.209132	−	1.18605i	0.681671	−	0.731659i	$-0.261254\pi$
$798$	−28.5000	+	78.3031i	−1.00889	+	2.77190i
$799$	7.69335	−	21.1373i	0.272171	−	0.747784i
$800$		0			0
$801$	10.8036	+	1.90496i	0.381726	+	0.0673086i
$802$	−8.21878	−	9.79476i	−0.290215	−	0.345865i
$803$	−9.73094	+	5.61816i	−0.343397	+	0.198261i
$804$	−28.7770	+	49.8431i	−1.01488	+	1.75783i
$805$		0			0
$806$	76.9323	−	44.4169i	2.70983	−	1.56452i
$807$	−2.93421	−	8.06167i	−0.103289	−	0.283784i
$808$	123.767			4.35410
$809$	−5.96995	−	16.4023i	−0.209892	−	0.576674i	0.789416	−	0.613858i	$-0.210383\pi$
$809$	−5.96995	−	16.4023i	−0.209892	−	0.576674i	−0.999308	+	0.0371842i	$0.988161\pi$
$810$		0			0
$811$	−12.2898	−	10.3124i	−0.431554	−	0.362117i	0.400984	−	0.916085i	$-0.368668\pi$
$811$	−12.2898	−	10.3124i	−0.431554	−	0.362117i	−0.832538	+	0.553968i	$0.813113\pi$
$812$	−28.7516	+	24.1255i	−1.00898	+	0.846639i
$813$		−	16.1152i		−	0.565186i
$814$	19.8646	+	53.0448i	0.696255	+	1.85922i
$815$		0			0
$816$	−31.2948	−	37.2957i	−1.09554	−	1.30561i
$817$	−17.8031	+	21.2170i	−0.622853	+	0.742288i
$818$	−53.0739	−	9.35837i	−1.85569	−	0.327208i
$819$	−3.42237	−	9.40287i	−0.119587	−	0.328563i
$820$		0			0
$821$	23.4887	−	8.54919i	0.819761	−	0.298369i	0.102112	−	0.994773i	$-0.467440\pi$
$821$	23.4887	−	8.54919i	0.819761	−	0.298369i	0.717650	+	0.696404i	$0.245218\pi$
$822$	9.47235	+	16.4066i	0.330386	+	0.572246i
$823$	14.3251	−	2.52591i	0.499343	−	0.0880477i	0.0816967	−	0.996657i	$-0.473966\pi$
$823$	14.3251	−	2.52591i	0.499343	−	0.0880477i	0.417647	+	0.908610i	$0.362855\pi$
$824$	33.6528	−	58.2884i	1.17235	−	2.03057i
$825$		0			0
$826$	4.11592	−	3.45367i	0.143211	−	0.120169i
$827$	−0.497534	+	2.82166i	−0.0173010	+	0.0981186i	−0.992235	−	0.124373i	$-0.960308\pi$
$827$	−0.497534	+	2.82166i	−0.0173010	+	0.0981186i	0.974935	+	0.222492i	$0.0714191\pi$
$828$	14.3315	−	24.8229i	0.498055	−	0.862657i
$829$	1.35407	−	3.72028i	0.0470288	−	0.129211i	−0.913955	−	0.405816i	$-0.866987\pi$
$829$	1.35407	−	3.72028i	0.0470288	−	0.129211i	0.960984	+	0.276606i	$0.0892095\pi$
$830$		0			0
$831$	6.42418	−	1.13276i	0.222852	−	0.0392949i
$832$	−45.8171	−	38.4451i	−1.58842	−	1.33284i
$833$	0.961703	+	0.806965i	0.0333210	+	0.0279597i
$834$	96.0707	−	16.9399i	3.32666	−	0.586579i
$835$		0			0
$836$	38.1259	−	104.750i	1.31861	−	3.62286i
$837$	14.9743	−	25.9363i	0.517589	−	0.896490i
$838$	−13.0416	+	73.9623i	−0.450513	+	2.55499i
$839$	19.2397	−	16.1441i	0.664230	−	0.557355i	−0.247122	−	0.968984i	$-0.579485\pi$
$839$	19.2397	−	16.1441i	0.664230	−	0.557355i	0.911351	+	0.411630i	$0.135040\pi$
$840$		0			0
$841$	−10.1061	+	17.5042i	−0.348485	+	0.603594i
$842$	−22.1664	+	3.90854i	−0.763905	+	0.134697i
$843$	7.76610	+	13.4513i	0.267479	+	0.463287i
$844$	−56.4606	+	20.5500i	−1.94345	+	0.707359i
$845$		0			0
$846$	7.33234	+	20.1454i	0.252091	+	0.692614i
$847$	3.53838	+	0.623911i	0.121580	+	0.0214378i
$848$	87.4044	−	104.164i	3.00148	−	3.57702i
$849$	13.7726	+	16.4136i	0.472675	+	0.563313i
$850$		0			0
$851$	−41.6702	+	7.74592i	−1.42844	+	0.265527i
$852$			62.8141i			2.15198i
$853$	7.29765	−	6.12346i	0.249867	−	0.209663i	−0.509248	−	0.860620i	$-0.670076\pi$
$853$	7.29765	−	6.12346i	0.249867	−	0.209663i	0.759115	+	0.650957i	$0.225632\pi$
$854$	36.1880	+	30.3653i	1.23833	+	1.03908i
$855$		0			0
$856$	43.1582	+	118.576i	1.47512	+	4.05285i
$857$	11.0923			0.378906			0.189453	−	0.981890i	$-0.439329\pi$
$857$	11.0923			0.378906			0.189453	+	0.981890i	$0.439329\pi$
$858$	29.7364	+	81.7000i	1.01518	+	2.78919i
$859$	40.6649	−	23.4779i	1.38747	−	0.801056i	0.394440	−	0.918922i	$-0.370939\pi$
$859$	40.6649	−	23.4779i	1.38747	−	0.801056i	0.993029	+	0.117866i	$0.0376054\pi$
$860$		0			0
$861$	−3.58986	+	6.21782i	−0.122342	+	0.211903i
$862$	47.8106	−	27.6035i	1.62844	−	0.940178i
$863$	12.0857	+	14.4032i	0.411402	+	0.490290i	0.931461	−	0.363840i	$-0.118535\pi$
$863$	12.0857	+	14.4032i	0.411402	+	0.490290i	−0.520059	+	0.854130i	$0.674090\pi$
$864$	−54.3397	−	9.58155i	−1.84867	−	0.325971i
$865$		0			0
$866$	−10.7226	+	29.4601i	−0.364369	+	1.00109i
$867$	7.86884	−	21.6195i	0.267240	−	0.734235i
$868$	15.4801	+	87.7921i	0.525430	+	2.97986i
$869$	34.0577	−	40.5884i	1.15533	−	1.37687i
$870$		0			0
$871$	27.7539	−	4.89375i	0.940404	−	0.165819i
$872$	7.03112	−	19.3179i	0.238104	−	0.654185i
$873$	−2.49938	−	0.909701i	−0.0845913	−	0.0307887i
$874$	101.220	+	58.4397i	3.42383	+	1.97675i
$875$		0			0
$876$	23.8167	−	19.9846i	0.804693	−	0.675217i
$877$	10.4495	−	6.03302i	0.352855	−	0.203721i	−0.313087	−	0.949724i	$-0.601363\pi$
$877$	10.4495	−	6.03302i	0.352855	−	0.203721i	0.665942	+	0.746004i	$0.268030\pi$
$878$	−26.4119	−	15.2489i	−0.891359	−	0.514627i
$879$	−3.06601	−	17.3882i	−0.103414	−	0.586490i
$880$		0			0
$881$	2.13298	−	0.776343i	0.0718620	−	0.0261556i	−0.305839	−	0.952083i	$-0.598937\pi$
$881$	2.13298	−	0.776343i	0.0718620	−	0.0261556i	0.377701	+	0.925928i	$0.376715\pi$
$882$	−1.19650			−0.0402884
$883$	−49.1725	+	17.8973i	−1.65479	+	0.602293i	−0.989531	−	0.144323i	$-0.953900\pi$
$883$	−49.1725	+	17.8973i	−1.65479	+	0.602293i	−0.665256	+	0.746616i	$0.731677\pi$
$884$	−9.45596	+	53.6274i	−0.318039	+	1.80369i
$885$		0			0
$886$	28.8493	+	34.3813i	0.969211	+	1.15506i
$887$			31.2761i			1.05015i	0.851056	+	0.525075i	$0.175963\pi$
$887$			31.2761i			1.05015i	−0.851056	+	0.525075i	$0.824037\pi$
$888$	−47.6723	−	80.8337i	−1.59978	−	2.71260i
$889$	30.9215			1.03707
$890$		0			0
$891$	29.1360	+	24.4480i	0.976094	+	0.819040i
$892$	−101.678	−	17.9286i	−3.40443	−	0.600292i
$893$	−58.6251	+	21.3378i	−1.96181	+	0.714042i
$894$		−	12.3505i		−	0.413061i
$895$		0			0
$896$	15.7641	−	9.10142i	0.526642	−	0.304057i
$897$	−64.0691	+	11.2971i	−2.13921	+	0.377200i
$898$	35.9029	+	20.7286i	1.19810	+	0.691721i
$899$	−10.4364	−	18.0763i	−0.348072	−	0.602878i
$900$		0			0
$901$	−28.1708	−	4.96726i	−0.938504	−	0.165484i
$902$	6.72917	−	11.6553i	0.224057	−	0.388078i
$903$	20.3708	+	7.41438i	0.677899	+	0.246735i
$904$	−25.6760	−	9.34532i	−0.853973	−	0.310821i
$905$		0			0
$906$	17.9510	−	21.3932i	0.596382	−	0.710740i
$907$	33.3775	+	28.0070i	1.10828	+	0.929958i	0.997954	−	0.0639374i	$-0.0203658\pi$
$907$	33.3775	+	28.0070i	1.10828	+	0.929958i	0.110327	+	0.993895i	$0.464810\pi$
$908$	8.63222	+	48.9557i	0.286470	+	1.62465i
$909$	12.1673	+	4.42853i	0.403563	+	0.146885i
$910$		0			0
$911$	36.3275	+	20.9737i	1.20358	+	0.694889i	0.961350	−	0.275329i	$-0.0887869\pi$
$911$	36.3275	+	20.9737i	1.20358	+	0.694889i	0.242233	+	0.970218i	$0.422120\pi$
$912$	−23.4482	+	132.981i	−0.776447	+	4.40345i
$913$	22.0035	+	26.2228i	0.728210	+	0.867847i
$914$	−24.3781	−	42.2241i	−0.806355	−	1.39665i
$915$		0			0
$916$	8.69873	+	49.3329i	0.287414	+	1.63001i
$917$	−16.2454	−	28.1378i	−0.536470	−	0.929193i
$918$	8.79822	+	24.1729i	0.290385	+	0.797825i
$919$			43.9144i			1.44860i	0.689483	+	0.724302i	$0.257838\pi$
$919$			43.9144i			1.44860i	−0.689483	+	0.724302i	$0.742162\pi$
$920$		0			0
$921$	1.20762	−	6.84873i	0.0397923	−	0.225673i
$922$	−31.0302	+	36.9803i	−1.02192	+	1.21788i
$923$	23.5618	−	19.7707i	0.775546	−	0.650760i
$924$	−87.2494			−2.87029
$925$		0			0
$926$	−103.109			−3.38837
$927$	5.39398	−	4.52609i	0.177162	−	0.148656i
$928$	−24.7192	+	29.4592i	−0.811447	+	0.967045i
$929$	−3.89742	+	22.1034i	−0.127870	+	0.725188i	0.851691	+	0.524044i	$0.175577\pi$
$929$	−3.89742	+	22.1034i	−0.127870	+	0.725188i	−0.979562	+	0.201144i	$0.935534\pi$
$930$		0			0
$931$		−	3.48194i		−	0.114116i
$932$	−11.3426	−	31.1635i	−0.371539	−	1.02079i
$933$	16.3171	+	28.2620i	0.534197	+	0.925255i
$934$	2.23409	+	12.6702i	0.0731017	+	0.414580i
$935$		0			0
$936$	−15.5380	−	26.9126i	−0.507875	−	0.879666i
$937$	−15.5470	−	18.5282i	−0.507900	−	0.605291i	0.449776	−	0.893142i	$-0.351504\pi$
$937$	−15.5470	−	18.5282i	−0.507900	−	0.605291i	−0.957675	+	0.287850i	$0.907060\pi$
$938$	−6.88140	+	39.0263i	−0.224686	+	1.27425i
$939$	11.2304	+	6.48390i	0.366492	+	0.211594i
$940$		0			0
$941$	−50.4649	−	18.3677i	−1.64511	−	0.598771i	−0.657188	−	0.753726i	$-0.728254\pi$
$941$	−50.4649	−	18.3677i	−1.64511	−	0.598771i	−0.987921	+	0.154955i	$0.950477\pi$
$942$	−16.2464	−	92.1380i	−0.529337	−	3.00202i
$943$	7.71447	+	6.47321i	0.251218	+	0.210797i
$944$	5.59663	−	6.66981i	0.182155	−	0.217084i
$945$		0			0
$946$	−38.1850	−	13.8982i	−1.24150	−	0.451870i
$947$	−26.3867	−	9.60396i	−0.857452	−	0.312087i	−0.124377	−	0.992235i	$-0.539693\pi$
$947$	−26.3867	−	9.60396i	−0.857452	−	0.312087i	−0.733075	+	0.680148i	$0.761915\pi$
$948$	−73.3030	+	126.964i	−2.38077	+	4.12361i
$949$	−14.9926	−	2.64360i	−0.486680	−	0.0858148i
$950$		0			0
$951$	20.1931	+	34.9755i	0.654808	+	1.13416i
$952$	−39.7066	−	22.9246i	−1.28690	−	0.742992i
$953$	24.8303	−	4.37825i	0.804331	−	0.141825i	0.243657	−	0.969862i	$-0.421653\pi$
$953$	24.8303	−	4.37825i	0.804331	−	0.141825i	0.560675	+	0.828036i	$0.310542\pi$
$954$	23.6105	−	13.6315i	0.764417	−	0.441337i
$955$		0			0
$956$			89.1358i			2.88286i
$957$	19.1965	−	6.98697i	0.620536	−	0.225857i
$958$	−3.11308	−	0.548919i	−0.100579	−	0.0177348i
$959$	7.13123	+	5.98382i	0.230280	+	0.193228i
$960$		0			0
$961$	−18.5763			−0.599235
$962$	−25.5793	+	72.3552i	−0.824708	+	2.33283i
$963$			13.2013i			0.425405i
$964$	23.0071	+	27.4188i	0.741009	+	0.883100i
$965$		0			0
$966$	15.8855	−	90.0914i	0.511109	−	2.89864i
$967$	−13.0601	+	4.75348i	−0.419983	+	0.152861i	−0.543363	−	0.839498i	$-0.682849\pi$
$967$	−13.0601	+	4.75348i	−0.419983	+	0.152861i	0.123379	+	0.992360i	$0.460627\pi$
$968$	11.1584			0.358645
$969$	26.6935	−	9.71565i	0.857520	−	0.312112i
$970$		0			0
$971$	6.65366	+	37.7348i	0.213526	+	1.21097i	0.883446	+	0.468534i	$0.155218\pi$
$971$	6.65366	+	37.7348i	0.213526	+	1.21097i	−0.669919	+	0.742434i	$0.733671\pi$
$972$	−36.0555	−	20.8167i	−1.15648	−	0.667695i
$973$	41.5139	−	23.9681i	1.33087	−	0.768380i
$974$	−46.3544	+	38.8960i	−1.48529	+	1.24631i
$975$		0			0
$976$	66.2960	+	38.2760i	2.12208	+	1.22519i
$977$	−7.53002	−	2.74070i	−0.240907	−	0.0876828i	0.218745	−	0.975782i	$-0.429804\pi$
$977$	−7.53002	−	2.74070i	−0.240907	−	0.0876828i	−0.459652	+	0.888099i	$0.652026\pi$
$978$	37.0130	−	101.692i	1.18354	−	3.25176i
$979$	−46.1267	+	8.13339i	−1.47422	+	0.259944i
$980$		0			0
$981$	1.38243	−	1.64752i	0.0441377	−	0.0526013i
$982$	11.1497	+	63.2329i	0.355800	+	2.01784i
$983$	7.33639	−	20.1566i	0.233995	−	0.642895i	−0.766005	−	0.642834i	$-0.777758\pi$
$983$	7.33639	−	20.1566i	0.233995	−	0.642895i	1.00000		6.07699e-5i	$-1.93437e-5\pi$
$984$	−7.62622	+	20.9529i	−0.243115	+	0.667953i
$985$		0			0
$986$	17.6561	+	3.11325i	0.562286	+	0.0991462i
$987$	31.3877	+	37.4064i	0.999081	+	1.19066i
$988$	130.798	−	75.5161i	4.16123	−	2.40249i
$989$	15.2033	−	26.3329i	0.483437	−	0.837338i
$990$		0			0
$991$	21.8303	−	12.6037i	0.693462	−	0.400371i	−0.111446	−	0.993771i	$-0.535548\pi$
$991$	21.8303	−	12.6037i	0.693462	−	0.400371i	0.804908	+	0.593400i	$0.202215\pi$
$992$	31.2402	+	85.8317i	0.991877	+	2.72516i
$993$	−31.5730			−1.00194
$994$	14.7925	+	40.6420i	0.469188	+	1.28908i
$995$		0			0
$996$	−72.5575	−	60.8829i	−2.29907	−	1.92915i
$997$	33.9416	−	28.4804i	1.07494	−	0.901984i	0.0794515	−	0.996839i	$-0.474683\pi$
$997$	33.9416	−	28.4804i	1.07494	−	0.901984i	0.995491	+	0.0948547i	$0.0302387\pi$
$998$			1.05839i			0.0335029i
$999$	4.72838	+	25.4369i	0.149599	+	0.804789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.ba.d.99.25		156
5.2	odd	4		925.2.bb.c.876.13	yes	78
5.3	odd	4		925.2.bb.d.876.1	yes	78
5.4	even	2	inner	925.2.ba.d.99.2		156
37.3	even	18	inner	925.2.ba.d.299.2		156
185.3	odd	36		925.2.bb.d.151.1	yes	78
185.77	odd	36		925.2.bb.c.151.13	✓	78
185.114	even	18	inner	925.2.ba.d.299.25		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.ba.d.99.2		156	5.4	even	2	inner
925.2.ba.d.99.25		156	1.1	even	1	trivial
925.2.ba.d.299.2		156	37.3	even	18	inner
925.2.ba.d.299.25		156	185.114	even	18	inner
925.2.bb.c.151.13	✓	78	185.77	odd	36
925.2.bb.c.876.13	yes	78	5.2	odd	4
925.2.bb.d.151.1	yes	78	185.3	odd	36
925.2.bb.d.876.1	yes	78	5.3	odd	4

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.02455 - 1.69880i) q^{2} +(1.25718 - 1.49825i) q^{3} +(0.865587 - 4.90899i) q^{4} -5.16897i q^{6} +(-0.868717 - 2.38678i) q^{7} +(-3.94409 - 6.83137i) q^{8} +(-0.143302 - 0.812704i) q^{9} +(1.76172 + 3.05138i) q^{11} +(-6.26668 - 7.46833i) q^{12} +(-0.828967 + 4.70130i) q^{13} +(-5.81342 - 3.35638i) q^{14} +(-10.2219 - 3.72048i) q^{16} +(0.397373 + 2.25362i) q^{17} +(-1.67074 - 1.40192i) q^{18} +(4.07971 - 4.86201i) q^{19} +(-4.66812 - 1.69906i) q^{21} +(8.75036 + 3.18487i) q^{22} +(-3.48394 + 6.03437i) q^{23} +(-15.1935 - 2.67903i) q^{24} +(6.30828 + 10.9263i) q^{26} +(3.68359 + 2.12672i) q^{27} +(-12.4686 + 2.19856i) q^{28} +(2.56727 - 1.48222i) q^{29} -7.04104i q^{31} +(-12.1902 + 4.43687i) q^{32} +(6.78651 + 1.19665i) q^{33} +(4.63294 + 3.88750i) q^{34} -4.11359 q^{36} +(3.95288 + 4.62328i) q^{37} -16.7740i q^{38} +(6.00155 + 7.15237i) q^{39} +(0.250970 - 1.42332i) q^{41} +(-12.3372 + 4.49037i) q^{42} -4.36382 q^{43} +(16.5041 - 6.00700i) q^{44} +(3.19776 + 18.1354i) q^{46} +(-8.51267 - 4.91479i) q^{47} +(-18.4250 + 10.6377i) q^{48} +(0.420255 - 0.352636i) q^{49} +(3.87604 + 2.23783i) q^{51} +(22.3611 + 8.13877i) q^{52} +(-4.27534 + 11.7464i) q^{53} +(11.0705 - 1.95202i) q^{54} +(-12.8787 + 15.3482i) q^{56} +(-2.15557 - 12.2248i) q^{57} +(2.67959 - 7.36210i) q^{58} +(-0.273756 + 0.752139i) q^{59} +(-6.93044 - 1.22202i) q^{61} +(-11.9613 - 14.2549i) q^{62} +(-1.81526 + 1.04804i) q^{63} +(-6.26436 + 10.8502i) q^{64} +(15.7725 - 9.10625i) q^{66} +(-2.01910 - 5.54742i) q^{67} +11.4069 q^{68} +(4.66103 + 12.8061i) q^{69} +(-4.93562 - 4.14148i) q^{71} +(-4.98669 + 4.18433i) q^{72} +3.18903i q^{73} +(15.8568 + 2.64490i) q^{74} +(-20.3362 - 24.2358i) q^{76} +(5.75255 - 6.85562i) q^{77} +(24.3009 + 4.28490i) q^{78} +(-5.14320 - 14.1308i) q^{79} +(10.1437 - 3.69201i) q^{81} +(-1.90983 - 3.30793i) q^{82} +(9.56775 - 1.68705i) q^{83} +(-12.3813 + 21.4451i) q^{84} +(-8.83477 + 7.41325i) q^{86} +(1.00680 - 5.70982i) q^{87} +(13.8967 - 24.0699i) q^{88} +(-4.54660 + 12.4917i) q^{89} +(11.9411 - 2.10554i) q^{91} +(26.6070 + 22.3259i) q^{92} +(-10.5492 - 8.85185i) q^{93} +(-25.5836 + 4.51107i) q^{94} +(-8.67773 + 23.8419i) q^{96} +(1.61152 - 2.79124i) q^{97} +(0.251770 - 1.42786i) q^{98} +(2.22741 - 1.86902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{4} + 36 q^{14} + 18 q^{16} + 6 q^{21} - 30 q^{24} + 18 q^{29} + 102 q^{34} - 216 q^{36} + 66 q^{39} - 42 q^{41} + 6 q^{44} + 72 q^{46} - 108 q^{49} + 180 q^{51} + 78 q^{54} - 96 q^{56} - 30 q^{59}+ \cdots + 366 q^{99}+O(q^{100}) \) 156 * q - 6 * q^4 + 36 * q^14 + 18 * q^16 + 6 * q^21 - 30 * q^24 + 18 * q^29 + 102 * q^34 - 216 * q^36 + 66 * q^39 - 42 * q^41 + 6 * q^44 + 72 * q^46 - 108 * q^49 + 180 * q^51 + 78 * q^54 - 96 * q^56 - 30 * q^59 - 36 * q^61 - 132 * q^64 + 252 * q^66 - 90 * q^69 + 96 * q^71 + 24 * q^74 + 162 * q^76 - 168 * q^79 + 96 * q^81 - 114 * q^84 - 132 * q^86 - 78 * q^89 + 114 * q^91 - 156 * q^94 - 156 * q^96 + 366 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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