LMFDB - Embedded newform 925.2.bb.d.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] 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("925.151"); 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([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [78,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	925.151
Dual form			925.2.bb.d.876.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69880 + 2.02455i) q^{2} +(1.49825 - 1.25718i) q^{3} +(-0.865587 - 4.90899i) q^{4} +5.16897i q^{6} +(-2.38678 - 0.868717i) q^{7} +(6.83137 + 3.94409i) q^{8} +(0.143302 - 0.812704i) q^{9} +(1.76172 - 3.05138i) q^{11} +(-7.46833 - 6.26668i) q^{12} +(-4.70130 + 0.828967i) q^{13} +(5.81342 - 3.35638i) q^{14} +(-10.2219 + 3.72048i) q^{16} +(2.25362 + 0.397373i) q^{17} +(1.40192 + 1.67074i) q^{18} +(-4.07971 - 4.86201i) q^{19} +(-4.66812 + 1.69906i) q^{21} +(3.18487 + 8.75036i) q^{22} +(-6.03437 + 3.48394i) q^{23} +(15.1935 - 2.67903i) q^{24} +(6.30828 - 10.9263i) q^{26} +(2.12672 + 3.68359i) q^{27} +(-2.19856 + 12.4686i) q^{28} +(-2.56727 - 1.48222i) q^{29} +7.04104i q^{31} +(4.43687 - 12.1902i) q^{32} +(-1.19665 - 6.78651i) q^{33} +(-4.63294 + 3.88750i) q^{34} -4.11359 q^{36} +(4.62328 + 3.95288i) q^{37} +16.7740 q^{38} +(-6.00155 + 7.15237i) q^{39} +(0.250970 + 1.42332i) q^{41} +(4.49037 - 12.3372i) q^{42} +4.36382i q^{43} +(-16.5041 - 6.00700i) q^{44} +(3.19776 - 18.1354i) q^{46} +(-4.91479 - 8.51267i) q^{47} +(-10.6377 + 18.4250i) q^{48} +(-0.420255 - 0.352636i) q^{49} +(3.87604 - 2.23783i) q^{51} +(8.13877 + 22.3611i) q^{52} +(-11.7464 + 4.27534i) q^{53} +(-11.0705 - 1.95202i) q^{54} +(-12.8787 - 15.3482i) q^{56} +(-12.2248 - 2.15557i) q^{57} +(7.36210 - 2.67959i) q^{58} +(0.273756 + 0.752139i) q^{59} +(-6.93044 + 1.22202i) q^{61} +(-14.2549 - 11.9613i) q^{62} +(-1.04804 + 1.81526i) q^{63} +(6.26436 + 10.8502i) q^{64} +(15.7725 + 9.10625i) q^{66} +(-5.54742 - 2.01910i) q^{67} -11.4069i q^{68} +(-4.66103 + 12.8061i) q^{69} +(-4.93562 + 4.14148i) q^{71} +(4.18433 - 4.98669i) q^{72} -3.18903 q^{73} +(-15.8568 + 2.64490i) q^{74} +(-20.3362 + 24.2358i) q^{76} +(-6.85562 + 5.75255i) q^{77} +(-4.28490 - 24.3009i) q^{78} +(5.14320 - 14.1308i) q^{79} +(10.1437 + 3.69201i) q^{81} +(-3.30793 - 1.90983i) q^{82} +(1.68705 - 9.56775i) q^{83} +(12.3813 + 21.4451i) q^{84} +(-8.83477 - 7.41325i) q^{86} +(-5.70982 + 1.00680i) q^{87} +(24.0699 - 13.8967i) q^{88} +(4.54660 + 12.4917i) q^{89} +(11.9411 + 2.10554i) q^{91} +(22.3259 + 26.6070i) q^{92} +(8.85185 + 10.5492i) q^{93} +(25.5836 + 4.51107i) q^{94} +(-8.67773 - 23.8419i) q^{96} +(-2.79124 + 1.61152i) q^{97} +(1.42786 - 0.251770i) q^{98} +(-2.22741 - 1.86902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 3 q^{2} + 3 q^{4} - 6 q^{7} + 18 q^{8} + 15 q^{12} - 27 q^{13} - 18 q^{14} + 9 q^{16} - 15 q^{18} + 3 q^{21} - 30 q^{22} + 15 q^{24} + 36 q^{27} + 27 q^{28} - 9 q^{29} - 18 q^{32} - 6 q^{33} - 51 q^{34}+ \cdots - 183 q^{99}+O(q^{100}) $ 78 * q + 3 * q^2 + 3 * q^4 - 6 * q^7 + 18 * q^8 + 15 * q^12 - 27 * q^13 - 18 * q^14 + 9 * q^16 - 15 * q^18 + 3 * q^21 - 30 * q^22 + 15 * q^24 + 36 * q^27 + 27 * q^28 - 9 * q^29 - 18 * q^32 - 6 * q^33 - 51 * q^34 - 108 * q^36 + 6 * q^37 + 84 * q^38 - 33 * q^39 - 21 * q^41 + 42 * q^42 - 3 * q^44 + 36 * q^46 - 57 * q^47 + 54 * q^48 + 54 * q^49 + 90 * q^51 + 75 * q^52 - 24 * q^53 - 39 * q^54 - 48 * q^56 - 9 * q^57 + 9 * q^58 + 15 * q^59 - 18 * q^61 - 120 * q^63 + 66 * q^64 + 126 * q^66 - 24 * q^67 + 45 * q^69 + 48 * q^71 + 132 * q^72 - 60 * q^73 - 12 * q^74 + 81 * q^76 + 21 * q^77 - 258 * q^78 + 84 * q^79 + 48 * q^81 + 234 * q^82 + 42 * q^83 + 57 * q^84 - 66 * q^86 + 24 * q^87 - 90 * q^88 + 39 * q^89 + 57 * q^91 - 87 * q^92 - 12 * q^93 + 78 * q^94 - 78 * q^96 - 36 * q^97 + 126 * q^98 - 183 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	−1.69880	+	2.02455i	−1.20123	+	1.43157i	−0.327716	+	0.944776i	$0.606279\pi$
$2$	−1.69880	+	2.02455i	−1.20123	+	1.43157i	−0.873516	+	0.486796i	$0.838165\pi$
$3$	1.49825	−	1.25718i	0.865013	−	0.725832i	−0.0980287	−	0.995184i	$-0.531254\pi$
$3$	1.49825	−	1.25718i	0.865013	−	0.725832i	0.963042	+	0.269351i	$0.0868093\pi$
$4$	−0.865587	−	4.90899i	−0.432793	−	2.45449i
$5$		0			0
$5$		0			0
$6$			5.16897i			2.11022i
$7$	−2.38678	−	0.868717i	−0.902119	−	0.328344i	−0.151017	−	0.988531i	$-0.548255\pi$
$7$	−2.38678	−	0.868717i	−0.902119	−	0.328344i	−0.751101	+	0.660187i	$0.770477\pi$
$8$	6.83137	+	3.94409i	2.41525	+	1.39445i
$9$	0.143302	−	0.812704i	0.0477672	−	0.270901i
$10$		0			0
$11$	1.76172	−	3.05138i	0.531177	−	0.920026i	−0.468161	−	0.883643i	$-0.655083\pi$
$11$	1.76172	−	3.05138i	0.531177	−	0.920026i	0.999338	−	0.0363828i	$-0.0115836\pi$
$12$	−7.46833	−	6.26668i	−2.15592	−	1.80903i
$13$	−4.70130	+	0.828967i	−1.30391	+	0.229914i	−0.782102	−	0.623151i	$-0.785852\pi$
$13$	−4.70130	+	0.828967i	−1.30391	+	0.229914i	−0.521805	+	0.853065i	$0.674741\pi$
$14$	5.81342	−	3.35638i	1.55370	−	0.897030i
$15$		0			0
$16$	−10.2219	+	3.72048i	−2.55548	+	0.930120i
$17$	2.25362	+	0.397373i	0.546582	+	0.0963772i	0.440119	−	0.897939i	$-0.354936\pi$
$17$	2.25362	+	0.397373i	0.546582	+	0.0963772i	0.106463	+	0.994317i	$0.466047\pi$
$18$	1.40192	+	1.67074i	0.330436	+	0.393798i
$19$	−4.07971	−	4.86201i	−0.935951	−	1.11542i	−0.993125	−	0.117058i	$-0.962654\pi$
$19$	−4.07971	−	4.86201i	−0.935951	−	1.11542i	0.0571743	−	0.998364i	$-0.481791\pi$
$20$		0			0
$21$	−4.66812	+	1.69906i	−1.01867	+	0.370765i
$22$	3.18487	+	8.75036i	0.679017	+	1.86558i
$23$	−6.03437	+	3.48394i	−1.25825	+	0.726453i	−0.972735	−	0.231921i	$-0.925499\pi$
$23$	−6.03437	+	3.48394i	−1.25825	+	0.726453i	−0.285518	+	0.958373i	$0.592166\pi$
$24$	15.1935	−	2.67903i	3.10136	−	0.546854i
$25$		0			0
$26$	6.30828	−	10.9263i	1.23716	−	2.14282i
$27$	2.12672	+	3.68359i	0.409288	+	0.708907i
$28$	−2.19856	+	12.4686i	−0.415488	+	2.35635i
$29$	−2.56727	−	1.48222i	−0.476731	−	0.275241i	0.242322	−	0.970196i	$-0.422091\pi$
$29$	−2.56727	−	1.48222i	−0.476731	−	0.275241i	−0.719053	+	0.694955i	$0.755424\pi$
$30$		0			0
$31$			7.04104i			1.26461i	0.774720	+	0.632304i	$0.217891\pi$
$31$			7.04104i			1.26461i	−0.774720	+	0.632304i	$0.782109\pi$
$32$	4.43687	−	12.1902i	0.784335	−	2.15494i
$33$	−1.19665	−	6.78651i	−0.208309	−	1.18138i
$34$	−4.63294	+	3.88750i	−0.794543	+	0.666701i
$35$		0			0
$36$	−4.11359			−0.685599
$37$	4.62328	+	3.95288i	0.760062	+	0.649850i
$37$	4.62328	+	3.95288i	0.760062	+	0.649850i
$38$	16.7740			2.72110
$39$	−6.00155	+	7.15237i	−0.961018	+	1.14530i
$40$		0			0
$41$	0.250970	+	1.42332i	0.0391949	+	0.222285i	0.998113	−	0.0613962i	$-0.0195553\pi$
$41$	0.250970	+	1.42332i	0.0391949	+	0.222285i	−0.958919	+	0.283681i	$0.908444\pi$
$42$	4.49037	−	12.3372i	0.692879	−	1.90367i
$43$			4.36382i			0.665477i	0.943019	+	0.332738i	$0.107973\pi$
$43$			4.36382i			0.665477i	−0.943019	+	0.332738i	$0.892027\pi$
$44$	−16.5041	−	6.00700i	−2.48809	−	0.905590i
$45$		0			0
$46$	3.19776	−	18.1354i	0.471484	−	2.67392i
$47$	−4.91479	−	8.51267i	−0.716897	−	1.24170i	−0.962224	−	0.272261i	$-0.912229\pi$
$47$	−4.91479	−	8.51267i	−0.716897	−	1.24170i	0.245327	−	0.969440i	$-0.421105\pi$
$48$	−10.6377	+	18.4250i	−1.53542	+	2.65942i
$49$	−0.420255	−	0.352636i	−0.0600364	−	0.0503765i
$50$		0			0
$51$	3.87604	−	2.23783i	0.542755	−	0.313360i
$52$	8.13877	+	22.3611i	1.12864	+	3.10092i
$53$	−11.7464	+	4.27534i	−1.61349	+	0.587263i	−0.982126	−	0.188224i	$-0.939727\pi$
$53$	−11.7464	+	4.27534i	−1.61349	+	0.587263i	−0.631364	+	0.775486i	$0.717505\pi$
$54$	−11.0705	−	1.95202i	−1.50650	−	0.265637i
$55$		0			0
$56$	−12.8787	−	15.3482i	−1.72099	−	2.05099i
$57$	−12.2248	−	2.15557i	−1.61922	−	0.285512i
$58$	7.36210	−	2.67959i	0.966691	−	0.351847i
$59$	0.273756	+	0.752139i	0.0356400	+	0.0979201i	0.956236	−	0.292596i	$-0.0945189\pi$
$59$	0.273756	+	0.752139i	0.0356400	+	0.0979201i	−0.920596	+	0.390516i	$0.872297\pi$
$60$		0			0
$61$	−6.93044	+	1.22202i	−0.887352	+	0.156464i	−0.598703	−	0.800971i	$-0.704317\pi$
$61$	−6.93044	+	1.22202i	−0.887352	+	0.156464i	−0.288649	+	0.957435i	$0.593206\pi$
$62$	−14.2549	−	11.9613i	−1.81038	−	1.51909i
$63$	−1.04804	+	1.81526i	−0.132041	+	0.228701i
$64$	6.26436	+	10.8502i	0.783045	+	1.35627i
$65$		0			0
$66$	15.7725	+	9.10625i	1.94146	+	1.12090i
$67$	−5.54742	−	2.01910i	−0.677725	−	0.246672i	−0.0198546	−	0.999803i	$-0.506320\pi$
$67$	−5.54742	−	2.01910i	−0.677725	−	0.246672i	−0.657870	+	0.753131i	$0.728543\pi$
$68$		−	11.4069i		−	1.38329i
$69$	−4.66103	+	12.8061i	−0.561123	+	1.54167i
$70$		0			0
$71$	−4.93562	+	4.14148i	−0.585750	+	0.491503i	−0.886830	−	0.462096i	$-0.847097\pi$
$71$	−4.93562	+	4.14148i	−0.585750	+	0.491503i	0.301080	+	0.953599i	$0.402653\pi$
$72$	4.18433	−	4.98669i	0.493128	−	0.587687i
$73$	−3.18903			−0.373247			−0.186624	−	0.982431i	$-0.559755\pi$
$73$	−3.18903			−0.373247			−0.186624	+	0.982431i	$0.559755\pi$
$74$	−15.8568	+	2.64490i	−1.84332	+	0.307464i
$75$		0			0
$76$	−20.3362	+	24.2358i	−2.33272	+	2.78003i
$77$	−6.85562	+	5.75255i	−0.781270	+	0.655564i
$78$	−4.28490	−	24.3009i	−0.485169	−	2.75153i
$79$	5.14320	−	14.1308i	0.578655	−	1.58984i	−0.211794	−	0.977314i	$-0.567930\pi$
$79$	5.14320	−	14.1308i	0.578655	−	1.58984i	0.790449	−	0.612528i	$-0.209847\pi$
$80$		0			0
$81$	10.1437	+	3.69201i	1.12708	+	0.410223i
$82$	−3.30793	−	1.90983i	−0.365300	−	0.210906i
$83$	1.68705	−	9.56775i	0.185178	−	1.05020i	−0.740548	−	0.672003i	$-0.765434\pi$
$83$	1.68705	−	9.56775i	0.185178	−	1.05020i	0.925726	−	0.378194i	$-0.123455\pi$
$84$	12.3813	+	21.4451i	1.35091	+	2.33985i
$85$		0			0
$86$	−8.83477	−	7.41325i	−0.952678	−	0.799392i
$87$	−5.70982	+	1.00680i	−0.612157	+	0.107940i
$88$	24.0699	−	13.8967i	2.56586	−	1.48140i
$89$	4.54660	+	12.4917i	0.481939	+	1.32412i	0.907829	+	0.419341i	$0.137739\pi$
$89$	4.54660	+	12.4917i	0.481939	+	1.32412i	−0.425890	+	0.904775i	$0.640039\pi$
$90$		0			0
$91$	11.9411	+	2.10554i	1.25177	+	0.220721i
$92$	22.3259	+	26.6070i	2.32764	+	2.77397i
$93$	8.85185	+	10.5492i	0.917894	+	1.09390i
$94$	25.5836	+	4.51107i	2.63874	+	0.465282i
$95$		0			0
$96$	−8.67773	−	23.8419i	−0.885667	−	2.43335i
$97$	−2.79124	+	1.61152i	−0.283407	+	0.163625i	−0.634965	−	0.772541i	$-0.718985\pi$
$97$	−2.79124	+	1.61152i	−0.283407	+	0.163625i	0.351558	+	0.936166i	$0.385652\pi$
$98$	1.42786	−	0.251770i	0.144235	−	0.0254326i
$99$	−2.22741	−	1.86902i	−0.223864	−	0.187844i
$100$		0			0
$101$	−7.84507	−	13.5881i	−0.780613	−	1.35206i	−0.931585	−	0.363524i	$-0.881574\pi$
$101$	−7.84507	−	13.5881i	−0.780613	−	1.35206i	0.150972	−	0.988538i	$-0.451760\pi$
$102$	−2.05401	+	11.6489i	−0.203377	+	1.15341i
$103$	−7.38933	−	4.26623i	−0.728092	−	0.420364i	0.0896317	−	0.995975i	$-0.471431\pi$
$103$	−7.38933	−	4.26623i	−0.728092	−	0.420364i	−0.817724	+	0.575611i	$0.804764\pi$
$104$	−35.3859	−	12.8794i	−3.46987	−	1.26293i
$105$		0			0
$106$	11.2991	−	31.0441i	1.09747	−	3.01527i
$107$	−2.77782	−	15.7538i	−0.268542	−	1.52298i	−0.758755	−	0.651376i	$-0.774192\pi$
$107$	−2.77782	−	15.7538i	−0.268542	−	1.52298i	0.490213	−	0.871603i	$-0.336919\pi$
$108$	16.2418	−	13.6285i	1.56287	−	1.31140i
$109$	−1.67519	+	1.99641i	−0.160454	+	0.191221i	−0.840281	−	0.542151i	$-0.817610\pi$
$109$	−1.67519	+	1.99641i	−0.160454	+	0.191221i	0.679827	+	0.733372i	$0.262055\pi$
$110$		0			0
$111$	11.8963	+	0.110110i	1.12915	+	0.0104512i
$112$	27.6296			2.61075
$113$	2.22655	−	2.65350i	0.209456	−	0.249620i	−0.651080	−	0.759009i	$-0.725684\pi$
$113$	2.22655	−	2.65350i	0.209456	−	0.249620i	0.860537	+	0.509388i	$0.170128\pi$
$114$	25.1316	−	21.0879i	2.35379	−	1.97506i
$115$		0			0
$116$	−5.05398	+	13.8857i	−0.469250	+	1.28925i
$117$			3.93956i			0.364213i
$118$	−1.98780	−	0.723499i	−0.182992	−	0.0666035i
$119$	−5.03368	−	2.90620i	−0.461437	−	0.266411i
$120$		0			0
$121$	−0.707287	−	1.22506i	−0.0642988	−	0.111369i
$122$	9.29938	−	16.1070i	0.841926	−	1.45826i
$123$	2.16538	+	1.81697i	0.195246	+	0.163831i
$124$	34.5644	−	6.09463i	3.10397	−	0.547314i
$125$		0			0
$126$	−1.89467	−	5.20557i	−0.168791	−	0.463749i
$127$	11.4398	−	4.16376i	1.01512	−	0.369474i	0.219724	−	0.975562i	$-0.429484\pi$
$127$	11.4398	−	4.16376i	1.01512	−	0.369474i	0.795397	+	0.606088i	$0.207262\pi$
$128$	−7.05771	−	1.24446i	−0.623819	−	0.109996i
$129$	5.48610	+	6.53808i	0.483024	+	0.575646i
$130$		0			0
$131$	12.5975	+	2.22128i	1.10065	+	0.194074i	0.694330	−	0.719657i	$-0.255701\pi$
$131$	12.5975	+	2.22128i	1.10065	+	0.194074i	0.406319	+	0.913731i	$0.366812\pi$
$132$	−32.2791	+	11.7486i	−2.80954	+	1.02259i
$133$	5.51367	+	15.1487i	0.478096	+	1.31356i
$134$	13.5117	−	7.80098i	1.16723	−	0.673902i
$135$		0			0
$136$	13.8280	+	11.6031i	1.18574	+	0.994956i
$137$	1.83254	−	3.17406i	0.156565	−	0.271178i	−0.777063	−	0.629423i	$-0.783291\pi$
$137$	1.83254	−	3.17406i	0.156565	−	0.271178i	0.933628	+	0.358245i	$0.116625\pi$
$138$	−18.0084	−	31.1915i	−1.53298	−	2.65519i
$139$	−3.27722	+	18.5861i	−0.277970	+	1.57645i	0.451395	+	0.892324i	$0.350927\pi$
$139$	−3.27722	+	18.5861i	−0.277970	+	1.57645i	−0.729365	+	0.684125i	$0.760184\pi$
$140$		0			0
$141$	−18.0655	−	6.57531i	−1.52139	−	0.553741i
$142$		−	17.0279i		−	1.42895i
$143$	−5.75287	+	15.8059i	−0.481079	+	1.32175i
$144$	1.55883	+	8.84056i	0.129902	+	0.736713i
$145$		0			0
$146$	5.41752	−	6.45634i	0.448357	−	0.534331i
$147$	−1.07297			−0.0884972
$148$	15.4028	−	26.1172i	1.26610	−	2.14682i
$149$	−2.38935			−0.195743			−0.0978714	−	0.995199i	$-0.531203\pi$
$149$	−2.38935			−0.195743			−0.0978714	+	0.995199i	$0.531203\pi$
$150$		0			0
$151$	4.13877	−	3.47284i	0.336808	−	0.282616i	−0.458659	−	0.888612i	$-0.651670\pi$
$151$	4.13877	−	3.47284i	0.336808	−	0.282616i	0.795467	+	0.605997i	$0.207226\pi$
$152$	−8.69380	−	49.3050i	−0.705160	−	3.99916i
$153$	0.645894	−	1.77458i	0.0522175	−	0.143466i
$154$		−	23.6520i		−	1.90593i
$155$		0			0
$156$	40.3058	+	23.2705i	3.22704	+	1.86313i
$157$	−3.14307	+	17.8252i	−0.250844	+	1.42261i	0.555675	+	0.831400i	$0.312460\pi$
$157$	−3.14307	+	17.8252i	−0.250844	+	1.42261i	−0.806519	+	0.591208i	$0.798651\pi$
$158$	19.8713	+	34.4181i	1.58088	+	2.73816i
$159$	−12.2241	+	21.1728i	−0.969437	+	1.67911i
$160$		0			0
$161$	17.4293	−	3.07325i	1.37362	−	0.242206i
$162$	−24.7067	+	14.2644i	−1.94115	+	1.12072i
$163$	−7.16061	−	19.6736i	−0.560863	−	1.54096i	−0.818376	−	0.574683i	$-0.805125\pi$
$163$	−7.16061	−	19.6736i	−0.560863	−	1.54096i	0.257514	−	0.966275i	$-0.417097\pi$
$164$	6.76982	−	2.46401i	0.528634	−	0.192407i
$165$		0			0
$166$	16.5044	+	19.6692i	1.28099	+	1.52663i
$167$	−6.03926	−	7.19731i	−0.467332	−	0.556944i	0.479971	−	0.877284i	$-0.340647\pi$
$167$	−6.03926	−	7.19731i	−0.467332	−	0.556944i	−0.947303	+	0.320340i	$0.896203\pi$
$168$	−38.5909	−	6.80462i	−2.97735	−	0.524988i
$169$	9.19906	−	3.34818i	0.707620	−	0.257553i
$170$		0			0
$171$	−4.53601	+	2.61887i	−0.346877	+	0.200270i
$172$	21.4219	−	3.77727i	1.63341	−	0.288014i
$173$	−15.1803	−	12.7378i	−1.15414	−	0.968437i	−0.154330	−	0.988019i	$-0.549322\pi$
$173$	−15.1803	−	12.7378i	−1.15414	−	0.968437i	−0.999808	+	0.0195820i	$0.993766\pi$
$174$	7.66153	−	13.2702i	0.580819	−	1.00601i
$175$		0			0
$176$	−6.65554	+	37.7454i	−0.501680	+	2.84517i
$177$	1.35573	+	0.782729i	0.101903	+	0.0588335i
$178$	−33.0138	−	12.0160i	−2.47449	−	0.900640i
$179$		−	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	−0.995408	−	0.0957233i	$-0.969484\pi$
$181$	−1.24809	−	7.07827i	−0.0927698	−	0.526123i	0.902638	−	0.430400i	$-0.141628\pi$
$182$	−24.5483	+	20.5985i	−1.81964	+	1.52686i
$183$	−8.84721	+	10.5437i	−0.654005	+	0.779413i
$184$	−54.9640			−4.05200
$185$		0			0
$186$	−36.3949			−2.66861
$187$	5.18277	−	6.17658i	0.379002	−	0.451677i
$188$	−37.5344	+	31.4951i	−2.73748	+	2.29702i
$189$	−1.87602	−	10.6394i	−0.136460	−	0.773905i
$190$		0			0
$191$			15.5444i			1.12475i	0.826881	+	0.562376i	$0.190113\pi$
$191$			15.5444i			1.12475i	−0.826881	+	0.562376i	$0.809887\pi$
$192$	23.0262	+	8.38084i	1.66177	+	0.604835i
$193$	20.4101	+	11.7838i	1.46915	+	0.848215i	0.999402	−	0.0345847i	$-0.0110108\pi$
$193$	20.4101	+	11.7838i	1.46915	+	0.848215i	0.469750	+	0.882800i	$0.344344\pi$
$194$	1.47914	−	8.38864i	0.106196	−	0.602269i
$195$		0			0
$196$	−1.36732	+	2.36826i	−0.0976654	+	0.169161i
$197$	−2.20671	−	1.85165i	−0.157222	−	0.131925i	0.560783	−	0.827963i	$-0.310500\pi$
$197$	−2.20671	−	1.85165i	−0.157222	−	0.131925i	−0.718005	+	0.696038i	$0.754945\pi$
$198$	7.56786	−	1.33442i	0.537824	−	0.0948329i
$199$	−13.0692	+	7.54550i	−0.926451	+	0.534886i	−0.885687	−	0.464282i	$-0.846312\pi$
$199$	−13.0692	+	7.54550i	−0.926451	+	0.534886i	−0.0407633	+	0.999169i	$0.512979\pi$
$200$		0			0
$201$	−10.8498	+	3.94899i	−0.765283	+	0.278540i
$202$	40.8369	+	7.20064i	2.87327	+	0.506635i
$203$	4.83990	+	5.76796i	0.339694	+	0.404832i
$204$	−14.3405	−	17.0904i	−1.00404	−	1.19657i
$205$		0			0
$206$	21.1902	−	7.71259i	1.47639	−	0.537362i
$207$	1.96668	+	5.40341i	0.136694	+	0.375563i
$208$	44.9722	−	25.9647i	3.11826	−	1.80033i
$209$	−22.0232	+	3.88328i	−1.52337	+	0.268612i
$210$		0			0
$211$	−6.02684	+	10.4388i	−0.414904	+	0.718636i	−0.995418	−	0.0956147i	$-0.969518\pi$
$211$	−6.02684	+	10.4388i	−0.414904	+	0.718636i	0.580514	+	0.814250i	$0.302852\pi$
$212$	31.1551	+	53.9622i	2.13974	+	3.70614i
$213$	−2.18820	+	12.4099i	−0.149933	+	0.850313i
$214$	36.6133	+	21.1387i	2.50284	+	1.44501i
$215$		0			0
$216$			33.5519i			2.28292i
$217$	6.11668	−	16.8054i	0.415227	−	1.14083i
$218$	−1.19603	−	6.78300i	−0.0810051	−	0.459403i
$219$	−4.77795	+	4.00918i	−0.322864	+	0.270915i
$220$		0			0
$221$	−10.9243			−0.734851
$222$	−20.4323	+	23.8976i	−1.37133	+	1.60390i
$223$	20.7126			1.38702			0.693509	−	0.720448i	$-0.256064\pi$
$223$	20.7126			1.38702			0.693509	+	0.720448i	$0.256064\pi$
$224$	−21.1797	+	25.2410i	−1.41513	+	1.68648i
$225$		0			0
$226$	1.58968	+	9.01552i	0.105744	+	0.599704i
$227$	3.41086	−	9.37125i	0.226387	−	0.621992i	−0.773544	−	0.633742i	$-0.781518\pi$
$227$	3.41086	−	9.37125i	0.226387	−	0.621992i	0.999931	+	0.0117501i	$0.00374027\pi$
$228$			61.8774i			4.09793i
$229$	9.44345	+	3.43714i	0.624041	+	0.227132i	0.634636	−	0.772812i	$-0.281150\pi$
$229$	9.44345	+	3.43714i	0.624041	+	0.227132i	−0.0105946	+	0.999944i	$0.503372\pi$
$230$		0			0
$231$	−3.03943	+	17.2375i	−0.199980	+	1.13414i
$232$	−11.6920	−	20.2511i	−0.767617	−	1.32955i
$233$	3.32652	−	5.76170i	0.217928	−	0.377462i	−0.736247	−	0.676713i	$-0.763404\pi$
$233$	3.32652	−	5.76170i	0.217928	−	0.377462i	0.954174	+	0.299252i	$0.0967370\pi$
$234$	−7.97584	−	6.69252i	−0.521397	−	0.437504i
$235$		0			0
$236$	3.45528	−	1.99491i	0.224920	−	0.129857i
$237$	−10.0592	−	27.6374i	−0.653414	−	1.79524i
$238$	14.4350	−	5.25390i	0.935679	−	0.340559i
$239$	17.6102	+	3.10515i	1.13911	+	0.200855i	0.711215	−	0.702975i	$-0.248145\pi$
$239$	17.6102	+	3.10515i	1.13911	+	0.200855i	0.427892	+	0.903830i	$0.359256\pi$
$240$		0			0
$241$	−4.61553	−	5.50058i	−0.297313	−	0.354323i	0.596621	−	0.802523i	$-0.296510\pi$
$241$	−4.61553	−	5.50058i	−0.297313	−	0.354323i	−0.893933	+	0.448200i	$0.852065\pi$
$242$	3.68173	+	0.649188i	0.236670	+	0.0417314i
$243$	7.84850	−	2.85662i	0.503481	−	0.183252i
$244$	11.9978	+	32.9637i	0.768080	+	2.11028i
$245$		0			0
$246$	−7.35709	+	1.29725i	−0.469071	+	0.0827099i
$247$	23.2104	+	19.4759i	1.47684	+	1.23922i
$248$	−27.7705	+	48.1000i	−1.76343	+	3.05435i
$249$	−9.50075	−	16.4558i	−0.602086	−	1.04284i
$250$		0			0
$251$	−1.93537	−	1.11739i	−0.122160	−	0.0705289i	0.437675	−	0.899133i	$-0.355802\pi$
$251$	−1.93537	−	1.11739i	−0.122160	−	0.0705289i	−0.559835	+	0.828604i	$0.689135\pi$
$252$	9.81825	+	3.57355i	0.618492	+	0.225113i
$253$			24.5509i			1.54350i
$254$	−11.0042	+	30.2339i	−0.690467	+	1.89704i
$255$		0			0
$256$	−4.68601	+	3.93203i	−0.292876	+	0.245752i
$257$	−4.64527	+	5.53602i	−0.289764	+	0.345328i	−0.891214	−	0.453583i	$-0.850146\pi$
$257$	−4.64527	+	5.53602i	−0.289764	+	0.345328i	0.601450	+	0.798911i	$0.294590\pi$
$258$	−22.5564			−1.40430
$259$	−7.60082	−	13.4510i	−0.472292	−	0.835804i
$260$		0			0
$261$	−1.57250	+	1.87403i	−0.0973352	+	0.116000i
$262$	−25.8977	+	21.7307i	−1.59997	+	1.34253i
$263$	−2.86171	−	16.2296i	−0.176461	−	1.00076i	−0.936444	−	0.350816i	$-0.885904\pi$
$263$	−2.86171	−	16.2296i	−0.176461	−	1.00076i	0.759984	−	0.649942i	$-0.225207\pi$
$264$	18.5919	−	51.0809i	1.14425	−	3.14381i
$265$		0			0
$266$	−40.0359	−	14.5719i	−2.45476	−	0.893458i
$267$	22.5162	+	12.9997i	1.37797	+	0.795571i
$268$	−5.10994	+	28.9799i	−0.312139	+	1.77023i
$269$	−2.19321	−	3.79875i	−0.133722	−	0.231614i	0.791386	−	0.611316i	$-0.209360\pi$
$269$	−2.19321	−	3.79875i	−0.133722	−	0.231614i	−0.925109	+	0.379703i	$0.876026\pi$
$270$		0			0
$271$	6.31192	+	5.29633i	0.383422	+	0.321729i	0.814044	−	0.580803i	$-0.197261\pi$
$271$	6.31192	+	5.29633i	0.383422	+	0.321729i	−0.430622	+	0.902532i	$0.641706\pi$
$272$	−24.5147	+	4.32261i	−1.48642	+	0.262097i
$273$	20.5378	−	11.8575i	1.24300	−	0.717648i
$274$	3.31291	+	9.10215i	0.200140	+	0.549881i
$275$		0			0
$276$	66.8994	+	11.7962i	4.02687	+	0.710046i
$277$	2.14390	+	2.55500i	0.128814	+	0.153515i	0.826596	−	0.562795i	$-0.190274\pi$
$277$	2.14390	+	2.55500i	0.128814	+	0.153515i	−0.697782	+	0.716310i	$0.745830\pi$
$278$	−32.0610	−	38.2089i	−1.92289	−	2.29162i
$279$	5.72229	+	1.00899i	0.342584	+	0.0604069i
$280$		0			0
$281$	−2.71616	−	7.46259i	−0.162033	−	0.445181i	0.831933	−	0.554877i	$-0.187235\pi$
$281$	−2.71616	−	7.46259i	−0.162033	−	0.445181i	−0.993965	+	0.109696i	$0.965012\pi$
$282$	44.0017	−	25.4044i	2.62027	−	1.51281i
$283$	−10.7888	+	1.90235i	−0.641325	+	0.113083i	−0.484848	−	0.874599i	$-0.661125\pi$
$283$	−10.7888	+	1.90235i	−0.641325	+	0.113083i	−0.156477	+	0.987682i	$0.550014\pi$
$284$	24.6026	+	20.6441i	1.45990	+	1.22500i
$285$		0			0
$286$	−22.2268	−	38.4980i	−1.31430	−	2.27643i
$287$	0.637453	−	3.61518i	0.0376277	−	0.213397i
$288$	−9.27122	−	5.35274i	−0.546312	−	0.315413i
$289$	−11.0539	−	4.02329i	−0.650229	−	0.236664i
$290$		0			0
$291$	−2.15599	+	5.92354i	−0.126386	+	0.347244i
$292$	2.76038	+	15.6549i	0.161539	+	0.916133i
$293$	6.91558	−	5.80286i	0.404012	−	0.339007i	−0.418030	−	0.908433i	$-0.637279\pi$
$293$	6.91558	−	5.80286i	0.404012	−	0.339007i	0.822042	+	0.569427i	$0.192835\pi$
$294$	1.82276	−	2.17228i	0.106306	−	0.126690i
$295$		0			0
$296$	15.9928	+	45.2383i	0.929562	+	2.62942i
$297$	14.9867			0.869617
$298$	4.05902	−	4.83735i	0.235133	−	0.280220i
$299$	25.4813	−	21.3814i	1.47362	−	1.23652i
$300$		0			0
$301$	3.79093	−	10.4155i	0.218505	−	0.600339i
$302$			14.2788i			0.821652i
$303$	−28.8365	−	10.4956i	−1.65661	−	0.602957i
$304$	59.7916	+	34.5207i	3.42928	+	1.97990i
$305$		0			0
$306$	2.49548	+	4.32230i	0.142657	+	0.247089i
$307$	−1.77787	+	3.07935i	−0.101468	+	0.175748i	−0.912290	−	0.409545i	$-0.865687\pi$
$307$	−1.77787	+	3.07935i	−0.101468	+	0.175748i	0.810822	+	0.585293i	$0.199021\pi$
$308$	34.1733	+	28.6748i	1.94721	+	1.63390i
$309$	−16.4344	+	2.89784i	−0.934923	+	0.164852i
$310$		0			0
$311$	−5.70682	−	15.6794i	−0.323604	−	0.889095i	−0.989691	−	0.143220i	$-0.954254\pi$
$311$	−5.70682	−	15.6794i	−0.323604	−	0.889095i	0.666087	−	0.745874i	$-0.267968\pi$
$312$	−69.2085	+	25.1898i	−3.91816	+	1.42609i
$313$	−6.52963	−	1.15135i	−0.369076	−	0.0650781i	−0.0139659	−	0.999902i	$-0.504446\pi$
$313$	−6.52963	−	1.15135i	−0.369076	−	0.0650781i	−0.355110	+	0.934824i	$0.615557\pi$
$314$	−30.7486	−	36.6448i	−1.73524	−	2.06798i
$315$		0			0
$316$	−73.8199	−	13.0164i	−4.15269	−	0.732232i
$317$	19.4040	−	7.06246i	1.08983	−	0.396667i	0.266275	−	0.963897i	$-0.414207\pi$
$317$	19.4040	−	7.06246i	1.08983	−	0.396667i	0.823560	+	0.567230i	$0.191985\pi$
$318$	−22.0991	−	60.7167i	−1.23925	−	3.40482i
$319$	−9.04562	+	5.22249i	−0.506457	+	0.292403i
$320$		0			0
$321$	−23.9672	−	20.1109i	−1.33772	−	1.12248i
$322$	−23.3869	+	40.5073i	−1.30330	+	2.25738i
$323$	−7.26208	−	12.5783i	−0.404073	−	0.699875i
$324$	9.34375	−	52.9910i	0.519097	−	2.94395i
$325$		0			0
$326$	51.9947	+	18.9245i	2.87972	+	1.04813i
$327$			5.09713i			0.281872i
$328$	−3.89924	+	10.7131i	−0.215299	+	0.591530i
$329$	4.33543	+	24.5875i	0.239020	+	1.35555i
$330$		0			0
$331$	−10.3766	+	12.3663i	−0.570348	+	0.679714i	−0.971702	−	0.236209i	$-0.924095\pi$
$331$	−10.3766	+	12.3663i	−0.570348	+	0.679714i	0.401355	+	0.915923i	$0.368540\pi$
$332$	−48.4282			−2.65785
$333$	3.87505	−	3.19090i	0.212351	−	0.174860i
$334$	24.8308			1.35868
$335$		0			0
$336$	41.3959	−	34.7353i	2.25833	−	1.89497i
$337$	−3.93249	−	22.3023i	−0.214216	−	1.21488i	−0.882261	−	0.470761i	$-0.843980\pi$
$337$	−3.93249	−	22.3023i	−0.214216	−	1.21488i	0.668044	−	0.744121i	$-0.267132\pi$
$338$	−8.84879	+	24.3118i	−0.481310	+	1.32239i
$339$		−	6.77477i		−	0.367955i
$340$		0			0
$341$	21.4849	+	12.4043i	1.16347	+	0.671732i
$342$	2.40374	−	13.6323i	0.129980	−	0.737151i
$343$	9.58658	+	16.6044i	0.517626	+	0.896555i
$344$	−17.2113	+	29.8109i	−0.927972	+	1.60729i
$345$		0			0
$346$	51.5766	−	9.09435i	2.77278	−	0.488915i
$347$	−9.28046	+	5.35808i	−0.498201	+	0.287637i	−0.727970	−	0.685608i	$-0.759536\pi$
$347$	−9.28046	+	5.35808i	−0.498201	+	0.287637i	0.229769	+	0.973245i	$0.426203\pi$
$348$	9.88469	+	27.1580i	0.529875	+	1.45582i
$349$	0.866831	−	0.315501i	0.0464004	−	0.0168884i	−0.318716	−	0.947850i	$-0.603252\pi$
$349$	0.866831	−	0.315501i	0.0464004	−	0.0168884i	0.365116	+	0.930962i	$0.381029\pi$
$350$		0			0
$351$	−13.0519	−	15.5547i	−0.696660	−	0.830248i
$352$	−29.3804	−	35.0143i	−1.56598	−	1.86627i
$353$	25.8434	+	4.55689i	1.37551	+	0.242539i	0.812041	−	0.583601i	$-0.198357\pi$
$353$	25.8434	+	4.55689i	1.37551	+	0.242539i	0.563465	+	0.826140i	$0.309468\pi$
$354$	−3.88778	+	1.41504i	−0.206633	+	0.0752083i
$355$		0			0
$356$	57.3860	−	33.1318i	3.04145	−	1.75598i
$357$	−11.1953	+	1.97404i	−0.592519	+	0.104477i
$358$	15.2645	+	12.8084i	0.806753	+	0.676946i
$359$	8.57026	−	14.8441i	0.452321	−	0.783443i	−0.546209	−	0.837649i	$-0.683930\pi$
$359$	8.57026	−	14.8441i	0.452321	−	0.783443i	0.998530	+	0.0542064i	$0.0172629\pi$
$360$		0			0
$361$	−3.69580	+	20.9599i	−0.194516	+	1.10315i
$362$	16.4506	+	9.49773i	0.864622	+	0.499190i
$363$	−2.59981	−	0.946252i	−0.136454	−	0.0496653i
$364$		−	60.4413i		−	3.16799i
$365$		0			0
$366$	−6.31660	−	35.8232i	−0.330174	−	1.87251i
$367$	2.84209	−	2.38479i	0.148356	−	0.124485i	−0.565589	−	0.824687i	$-0.691351\pi$
$367$	2.84209	−	2.38479i	0.148356	−	0.124485i	0.713945	+	0.700202i	$0.246907\pi$
$368$	48.7210	−	58.0634i	2.53976	−	3.02676i
$369$	1.19270			0.0620896
$370$		0			0
$371$	31.7501			1.64838
$372$	44.1239	−	52.5849i	2.28772	−	2.72640i
$373$	−23.5959	+	19.7993i	−1.22175	+	1.02517i	−0.223017	+	0.974814i	$0.571591\pi$
$373$	−23.5959	+	19.7993i	−1.22175	+	1.02517i	−0.998731	+	0.0503544i	$0.983965\pi$
$374$	3.70032	+	20.9855i	0.191339	+	1.08514i
$375$		0			0
$376$		−	77.5376i		−	3.99870i
$377$	13.2982	+	4.84016i	0.684894	+	0.249281i
$378$	24.7270	+	14.2762i	1.27182	+	0.734287i
$379$	1.14733	−	6.50683i	0.0589344	−	0.334233i	−0.941058	−	0.338246i	$-0.890166\pi$
$379$	1.14733	−	6.50683i	0.0589344	−	0.334233i	0.999992	+	0.00401302i	$0.00127739\pi$
$380$		0			0
$381$	11.9051	−	20.6203i	0.609917	−	1.05641i
$382$	−31.4704	−	26.4068i	−1.61017	−	1.35109i
$383$	17.3517	−	3.05957i	0.886629	−	0.156337i	0.288255	−	0.957554i	$-0.406925\pi$
$383$	17.3517	−	3.05957i	0.886629	−	0.156337i	0.598374	+	0.801217i	$0.295814\pi$
$384$	−12.1387	+	7.00828i	−0.619450	+	0.357640i
$385$		0			0
$386$	−58.5295	+	21.3030i	−2.97907	+	1.08429i
$387$	3.54650	+	0.625343i	0.180279	+	0.0317880i
$388$	10.3270	+	12.3072i	0.524273	+	0.624805i
$389$	−9.14062	−	10.8934i	−0.463448	−	0.552315i	0.482812	−	0.875724i	$-0.339616\pi$
$389$	−9.14062	−	10.8934i	−0.463448	−	0.552315i	−0.946259	+	0.323409i	$0.895171\pi$
$390$		0			0
$391$	−14.9836	+	5.45358i	−0.757752	+	0.275799i
$392$	−1.48009	−	4.06651i	−0.0747557	−	0.205390i
$393$	21.6667	−	12.5093i	1.09294	−	0.631010i
$394$	7.49752	−	1.32201i	0.377720	−	0.0666021i
$395$		0			0
$396$	−7.24699	+	12.5521i	−0.364175	+	0.630769i
$397$	1.27587	+	2.20988i	0.0640342	+	0.110911i	0.896265	−	0.443519i	$-0.146270\pi$
$397$	1.27587	+	2.20988i	0.0640342	+	0.110911i	−0.832231	+	0.554429i	$0.812937\pi$
$398$	6.92568	−	39.2775i	0.347153	−	1.96880i
$399$	27.3054	+	15.7648i	1.36698	+	0.789227i
$400$		0			0
$401$			4.83800i			0.241598i	0.992677	+	0.120799i	$0.0385456\pi$
$401$			4.83800i			0.241598i	−0.992677	+	0.120799i	$0.961454\pi$
$402$	10.4366	−	28.6744i	0.520532	−	1.43015i
$403$	−5.83679	−	33.1021i	−0.290751	−	1.64893i
$404$	−59.9130	+	50.2730i	−2.98078	+	2.50117i
$405$		0			0
$406$	−19.8995			−0.987597
$407$	20.2067	−	7.14353i	1.00161	−	0.354092i
$408$	35.3049			1.74785
$409$	13.1076	−	15.6210i	0.648129	−	0.772410i	−0.337502	−	0.941325i	$-0.609582\pi$
$409$	13.1076	−	15.6210i	0.648129	−	0.772410i	0.985631	+	0.168915i	$0.0540263\pi$
$410$		0			0
$411$	−1.24475	−	7.05935i	−0.0613992	−	0.348212i
$412$	−14.5468	+	39.9669i	−0.716667	+	1.96903i
$413$		−	2.03301i		−	0.100038i
$414$	−14.2805	−	5.19767i	−0.701847	−	0.255451i
$415$		0			0
$416$	−10.7538	+	60.9878i	−0.527248	+	2.99017i
$417$	18.4559	+	31.9666i	0.903789	+	1.56541i
$418$	29.5510	−	51.1839i	1.44539	−	2.50349i
$419$	21.7690	+	18.2664i	1.06349	+	0.892371i	0.994447	−	0.105243i	$-0.0335621\pi$
$419$	21.7690	+	18.2664i	1.06349	+	0.892371i	0.0690394	+	0.997614i	$0.478007\pi$
$420$		0			0
$421$	−7.37565	+	4.25833i	−0.359467	+	0.207538i	−0.668847	−	0.743400i	$-0.733212\pi$
$421$	−7.37565	+	4.25833i	−0.359467	+	0.207538i	0.309380	+	0.950939i	$0.399879\pi$
$422$	−10.8955	−	29.9350i	−0.530382	−	1.45721i
$423$	−7.62259	+	2.77439i	−0.370623	+	0.134896i
$424$	−97.1062	−	17.1225i	−4.71590	−	0.831540i
$425$		0			0
$426$	−21.4071	−	25.5120i	−1.03718	−	1.23606i
$427$	17.6030	+	3.10389i	0.851871	+	0.150208i
$428$	−74.9308	+	27.2726i	−3.62192	+	1.31827i
$429$	11.2516	+	30.9135i	0.543232	+	1.49252i
$430$		0			0
$431$	20.5717	−	3.62735i	0.990905	−	0.174723i	0.345381	−	0.938463i	$-0.387750\pi$
$431$	20.5717	−	3.62735i	0.990905	−	0.174723i	0.645525	+	0.763739i	$0.276639\pi$
$432$	−35.4439	−	29.7410i	−1.70530	−	1.43091i
$433$	−5.93122	+	10.2732i	−0.285036	+	0.493697i	−0.972618	−	0.232410i	$-0.925339\pi$
$433$	−5.93122	+	10.2732i	−0.285036	+	0.493697i	0.687582	+	0.726107i	$0.258672\pi$
$434$	23.6324	+	40.9326i	1.13439	+	1.96483i
$435$		0			0
$436$	11.2504	+	6.49540i	0.538795	+	0.311073i
$437$	41.5575	+	15.1257i	1.98796	+	0.723560i
$438$		−	16.4840i		−	0.787635i
$439$	3.94682	−	10.8438i	0.188371	−	0.517546i	−0.809174	−	0.587569i	$-0.800085\pi$
$439$	3.94682	−	10.8438i	0.188371	−	0.517546i	0.997545	+	0.0700232i	$0.0223073\pi$
$440$		0			0
$441$	−0.346812	+	0.291010i	−0.0165148	+	0.0138576i
$442$	18.5583	−	22.1169i	0.882726	−	1.05199i
$443$	−16.9822			−0.806848			−0.403424	−	0.915013i	$-0.632180\pi$
$443$	−16.9822			−0.806848			−0.403424	+	0.915013i	$0.632180\pi$
$444$	−9.75674	−	58.4940i	−0.463035	−	2.77600i
$445$		0			0
$446$	−35.1865	+	41.9337i	−1.66613	+	1.98562i
$447$	−3.57983	+	3.00383i	−0.169320	+	0.142076i
$448$	−5.52591	−	31.3390i	−0.261075	−	1.48063i
$449$	−5.36509	+	14.7405i	−0.253194	+	0.695645i	0.746353	+	0.665550i	$0.231803\pi$
$449$	−5.36509	+	14.7405i	−0.253194	+	0.695645i	−0.999547	+	0.0300946i	$0.990419\pi$
$450$		0			0
$451$	4.78523	+	1.74168i	0.225328	+	0.0820126i
$452$	−14.9533	−	8.63327i	−0.703343	−	0.406075i
$453$	1.83492	−	10.4063i	0.0862120	−	0.488933i
$454$	13.1782	+	22.8253i	0.618484	+	1.07125i
$455$		0			0
$456$	−75.0106	−	62.9414i	−3.51269	−	2.94750i
$457$	−18.1680	+	3.20350i	−0.849862	+	0.149854i	−0.581582	−	0.813488i	$-0.697566\pi$
$457$	−18.1680	+	3.20350i	−0.849862	+	0.149854i	−0.268280	+	0.963341i	$0.586455\pi$
$458$	−23.0012	+	13.2797i	−1.07477	+	0.620521i
$459$	3.32905	+	9.14650i	0.155387	+	0.426922i
$460$		0			0
$461$	−17.9884	−	3.17185i	−0.837805	−	0.147728i	−0.261747	−	0.965136i	$-0.584299\pi$
$461$	−17.9884	−	3.17185i	−0.837805	−	0.147728i	−0.576058	+	0.817409i	$0.695410\pi$
$462$	−29.7347	−	35.4365i	−1.38338	−	1.64865i
$463$	25.0778	+	29.8866i	1.16547	+	1.38895i	0.906044	+	0.423183i	$0.139087\pi$
$463$	25.0778	+	29.8866i	1.16547	+	1.38895i	0.259421	+	0.965764i	$0.416468\pi$
$464$	31.7570	+	5.59962i	1.47428	+	0.259956i
$465$		0			0
$466$	6.01376	+	16.5227i	0.278582	+	0.765398i
$467$	4.21587	−	2.43403i	0.195087	−	0.112634i	−0.399275	−	0.916831i	$-0.630738\pi$
$467$	4.21587	−	2.43403i	0.195087	−	0.112634i	0.594362	+	0.804198i	$0.297405\pi$
$468$	19.3393	−	3.41003i	0.893957	−	0.157629i
$469$	11.4865	+	9.63828i	0.530395	+	0.445054i
$470$		0			0
$471$	17.7004	+	30.6580i	0.815591	+	1.41265i
$472$	−1.09638	+	6.21786i	−0.0504648	+	0.286200i
$473$	13.3157	+	7.68781i	0.612256	+	0.353486i
$474$	73.0418	+	26.5850i	3.35492	+	1.22109i
$475$		0			0
$476$	−9.90940	+	27.2259i	−0.454197	+	1.24789i
$477$	1.79131	+	10.1590i	0.0820183	+	0.465149i
$478$	−36.2026	+	30.3776i	−1.65587	+	1.38944i
$479$	0.768832	−	0.916258i	0.0351288	−	0.0418649i	−0.748194	−	0.663480i	$-0.769079\pi$
$479$	0.768832	−	0.916258i	0.0351288	−	0.0418649i	0.783323	+	0.621615i	$0.213523\pi$
$480$		0			0
$481$	−25.0122	−	14.7512i	−1.14046	−	0.672595i
$482$	18.9770			0.864381
$483$	22.2497	−	26.5162i	1.01240	−	1.20653i
$484$	−5.40157	+	4.53245i	−0.245526	+	0.206021i
$485$		0			0
$486$	−7.54965	+	20.7425i	−0.342459	+	0.940898i
$487$		−	22.8962i		−	1.03752i	−0.854919	−	0.518762i	$-0.826393\pi$
$487$		−	22.8962i		−	1.03752i	0.854919	−	0.518762i	$-0.173607\pi$
$488$	−52.1642	−	18.9862i	−2.36136	−	0.859465i
$489$	−35.4616	−	20.4738i	−1.60363	−	0.925856i
$490$		0			0
$491$	−12.1475	−	21.0401i	−0.548209	−	0.949526i	−0.998397	−	0.0565925i	$-0.981976\pi$
$491$	−12.1475	−	21.0401i	−0.548209	−	0.949526i	0.450188	−	0.892934i	$-0.351357\pi$
$492$	7.04516	−	12.2026i	0.317620	−	0.550135i
$493$	−5.19666	−	4.36051i	−0.234046	−	0.196388i
$494$	−78.8597	+	13.9051i	−3.54806	+	0.625619i
$495$		0			0
$496$	−26.1960	−	71.9731i	−1.17624	−	3.23169i
$497$	15.3780	−	5.59714i	0.689798	−	0.251066i
$498$	49.4554	+	8.72032i	2.21615	+	0.390767i
$499$	0.257419	+	0.306780i	0.0115237	+	0.0137334i	0.771775	−	0.635895i	$-0.219369\pi$
$499$	0.257419	+	0.306780i	0.0115237	+	0.0137334i	−0.760252	+	0.649628i	$0.774924\pi$
$500$		0			0
$501$	−18.0966	−	3.19092i	−0.808496	−	0.142560i
$502$	5.55001	−	2.02004i	0.247709	−	0.0901588i
$503$	−9.45723	−	25.9835i	−0.421677	−	1.15855i	−0.950747	−	0.309969i	$-0.899681\pi$
$503$	−9.45723	−	25.9835i	−0.421677	−	1.15855i	0.529070	−	0.848578i	$-0.322541\pi$
$504$	−14.3191	+	8.26714i	−0.637824	+	0.368248i
$505$		0			0
$506$	−49.7045	−	41.7070i	−2.20963	−	1.85410i
$507$	9.57320	−	16.5813i	0.425161	−	0.736400i
$508$	−30.3420	−	52.5539i	−1.34621	−	2.33170i
$509$	−3.55827	+	20.1800i	−0.157718	+	0.894461i	0.798541	+	0.601940i	$0.205605\pi$
$509$	−3.55827	+	20.1800i	−0.157718	+	0.894461i	−0.956259	+	0.292521i	$0.905506\pi$
$510$		0			0
$511$	7.61151	+	2.77036i	0.336714	+	0.122554i
$512$		−	30.5000i		−	1.34792i
$513$	9.23325	−	25.3681i	0.407658	−	1.12003i
$514$	−3.31656	−	18.8092i	−0.146287	−	0.829637i
$515$		0			0
$516$	27.3467	−	32.5905i	1.20387	−	1.43472i
$517$	−34.6339			−1.52320
$518$	40.1445	+	7.46230i	1.76385	+	0.327875i
$519$	−38.7576			−1.70127
$520$		0			0
$521$	7.49284	−	6.28724i	0.328267	−	0.275449i	−0.463726	−	0.885979i	$-0.653488\pi$
$521$	7.49284	−	6.28724i	0.328267	−	0.275449i	0.791993	+	0.610530i	$0.209043\pi$
$522$	−1.12271	−	6.36720i	−0.0491397	−	0.278685i
$523$	−7.63944	+	20.9892i	−0.334049	+	0.917793i	0.652997	+	0.757360i	$0.273511\pi$
$523$	−7.63944	+	20.9892i	−0.334049	+	0.917793i	−0.987047	+	0.160433i	$0.948711\pi$
$524$		−	63.7636i		−	2.78553i
$525$		0			0
$526$	37.7190	+	21.7771i	1.64463	+	0.949527i
$527$	−2.79792	+	15.8678i	−0.121879	+	0.691213i
$528$	37.4811	+	64.9192i	1.63116	+	2.82524i
$529$	12.7757	−	22.1282i	0.555467	−	0.962097i
$530$		0			0
$531$	0.650496	−	0.114700i	0.0282291	−	0.00497756i
$532$	69.5921	−	40.1790i	3.01720	−	1.74198i
$533$	−2.35977	−	6.48341i	−0.102213	−	0.280828i
$534$	−64.5691	+	23.5012i	−2.79418	+	1.01700i
$535$		0			0
$536$	−29.9330	−	35.6727i	−1.29291	−	1.54083i
$537$	−9.47874	−	11.2963i	−0.409038	−	0.487473i
$538$	11.4166	+	2.01305i	0.492203	+	0.0867887i
$539$	−1.81640	+	0.661114i	−0.0782377	+	0.0284762i
$540$		0			0
$541$	−28.5009	+	16.4550i	−1.22535	+	0.707455i	−0.966053	−	0.258343i	$-0.916823\pi$
$541$	−28.5009	+	16.4550i	−1.22535	+	0.707455i	−0.259295	+	0.965798i	$0.583490\pi$
$542$	−21.4454	+	3.78139i	−0.921157	+	0.162425i
$543$	−10.7686	−	9.03592i	−0.462124	−	0.387768i
$544$	14.8431	−	25.7089i	0.636391	−	1.10226i
$545$		0			0
$546$	−10.8835	+	61.7233i	−0.465770	+	2.64151i
$547$	−7.62620	−	4.40299i	−0.326073	−	0.188258i	0.328023	−	0.944670i	$-0.393618\pi$
$547$	−7.62620	−	4.40299i	−0.326073	−	0.188258i	−0.654096	+	0.756411i	$0.726951\pi$
$548$	−17.1676	−	6.24850i	−0.733364	−	0.266923i
$549$			5.80752i			0.247859i
$550$		0			0
$551$	3.26719	+	18.5291i	0.139187	+	0.789368i
$552$	−82.3496	+	69.0996i	−3.50503	+	2.94107i
$553$	−24.5514	+	29.2592i	−1.04403	+	1.24423i
$554$	−8.81478			−0.374504
$555$		0			0
$556$	94.0754			3.98969
$557$	−5.08820	+	6.06388i	−0.215594	+	0.256935i	−0.862992	−	0.505217i	$-0.831413\pi$
$557$	−5.08820	+	6.06388i	−0.215594	+	0.256935i	0.647399	+	0.762152i	$0.275857\pi$
$558$	−11.7638	+	9.87097i	−0.498000	+	0.417872i
$559$	−3.61746	−	20.5156i	−0.153002	−	0.867719i
$560$		0			0
$561$		−	15.7697i		−	0.665798i
$562$	19.7226	+	7.17844i	0.831947	+	0.302804i
$563$	−20.6877	−	11.9440i	−0.871882	−	0.503381i	−0.00390896	−	0.999992i	$-0.501244\pi$
$563$	−20.6877	−	11.9440i	−0.871882	−	0.503381i	−0.867973	+	0.496611i	$0.834578\pi$
$564$	−16.6408	+	94.3749i	−0.700706	+	3.97390i
$565$		0			0
$566$	14.4765	−	25.0741i	0.608494	−	1.05394i
$567$	−21.0035	−	17.6240i	−0.882064	−	0.740139i
$568$	−50.0514	+	8.82541i	−2.10011	+	0.370306i
$569$	−10.5425	+	6.08672i	−0.441965	+	0.255169i	−0.704431	−	0.709773i	$-0.748798\pi$
$569$	−10.5425	+	6.08672i	−0.441965	+	0.255169i	0.262466	+	0.964941i	$0.415464\pi$
$570$		0			0
$571$	30.0566	−	10.9397i	1.25783	−	0.457812i	0.374788	−	0.927111i	$-0.377715\pi$
$571$	30.0566	−	10.9397i	1.25783	−	0.457812i	0.883039	+	0.469299i	$0.155493\pi$
$572$	82.5704	+	14.5594i	3.45244	+	0.608759i
$573$	19.5421	+	23.2893i	0.816382	+	0.972926i
$574$	6.23620	+	7.43201i	0.260294	+	0.310206i
$575$		0			0
$576$	9.71569	−	3.53622i	0.404820	−	0.147343i
$577$	−7.37717	−	20.2686i	−0.307116	−	0.843794i	−0.993216	−	0.116286i	$-0.962901\pi$
$577$	−7.37717	−	20.2686i	−0.307116	−	0.843794i	0.686100	−	0.727507i	$-0.259321\pi$
$578$	26.9237	−	15.5444i	1.11988	−	0.646562i
$579$	45.3937	−	8.00413i	1.88650	−	0.332640i
$580$		0			0
$581$	−12.3383	+	21.3706i	−0.511879	+	0.886600i
$582$	−8.32990	−	14.4278i	−0.345285	−	0.598052i
$583$	−7.64812	+	43.3746i	−0.316753	+	1.79639i
$584$	−21.7854	−	12.5778i	−0.901487	−	0.520474i
$585$		0			0
$586$			23.8588i			0.985598i
$587$	−11.2380	+	30.8760i	−0.463840	+	1.27439i	0.458735	+	0.888573i	$0.348303\pi$
$587$	−11.2380	+	30.8760i	−0.463840	+	1.27439i	−0.922575	+	0.385817i	$0.873920\pi$
$588$	0.928749	+	5.26720i	0.0383010	+	0.217216i
$589$	34.2337	−	28.7255i	1.41057	−	1.18361i
$590$		0			0
$591$	−5.63406			−0.231754
$592$	−61.9654	−	23.2053i	−2.54676	−	0.953732i
$593$	7.82707			0.321419			0.160710	−	0.987002i	$-0.448622\pi$
$593$	7.82707			0.321419			0.160710	+	0.987002i	$0.448622\pi$
$594$	−25.4594	+	30.3413i	−1.04461	+	1.24492i
$595$		0			0
$596$	2.06819	+	11.7293i	0.0847162	+	0.480449i
$597$	−10.0948	+	27.7353i	−0.413154	+	1.13513i
$598$			87.9108i			3.59494i
$599$	31.7845	+	11.5686i	1.29868	+	0.472681i	0.896567	−	0.442909i	$-0.146053\pi$
$599$	31.7845	+	11.5686i	1.29868	+	0.472681i	0.402114	+	0.915590i	$0.368276\pi$
$600$		0			0
$601$	−2.71282	+	15.3852i	−0.110658	+	0.627575i	0.878150	+	0.478385i	$0.158778\pi$
$601$	−2.71282	+	15.3852i	−0.110658	+	0.627575i	−0.988809	+	0.149190i	$0.952334\pi$
$602$	14.6466	+	25.3687i	0.596953	+	1.03395i
$603$	−2.43588	+	4.21907i	−0.0991968	+	0.171814i
$604$	−20.6306	−	17.3111i	−0.839446	−	0.704379i
$605$		0			0
$606$	70.2362	−	40.5509i	2.85315	−	1.64727i
$607$	−3.37659	−	9.27710i	−0.137051	−	0.376546i	0.852113	−	0.523358i	$-0.175321\pi$
$607$	−3.37659	−	9.27710i	−0.137051	−	0.376546i	−0.989164	+	0.146812i	$0.953099\pi$
$608$	−77.3701	+	28.1604i	−3.13777	+	1.14206i
$609$	14.5027	+	2.55722i	0.587680	+	0.103624i
$610$		0			0
$611$	30.1627	+	35.9465i	1.22025	+	1.45424i
$612$	−9.27046	−	1.63463i	−0.374736	−	0.0660761i
$613$	0.490106	−	0.178384i	0.0197952	−	0.00720486i	−0.332104	−	0.943243i	$-0.607758\pi$
$613$	0.490106	−	0.178384i	0.0197952	−	0.00720486i	0.351899	+	0.936038i	$0.385536\pi$
$614$	−3.21407	−	8.83058i	−0.129709	−	0.356373i
$615$		0			0
$616$	−69.5219	+	12.2586i	−2.80112	+	0.493912i
$617$	−27.8289	−	23.3512i	−1.12035	−	0.940085i	−0.121728	−	0.992563i	$-0.538844\pi$
$617$	−27.8289	−	23.3512i	−1.12035	−	0.940085i	−0.998622	+	0.0524782i	$0.983288\pi$
$618$	22.0520	−	38.1952i	0.887062	−	1.53644i
$619$	14.1225	+	24.4609i	0.567632	+	0.983168i	0.996799	+	0.0799427i	$0.0254737\pi$
$619$	14.1225	+	24.4609i	0.567632	+	0.983168i	−0.429167	+	0.903225i	$0.641193\pi$
$620$		0			0
$621$	−25.6668	−	14.8188i	−1.02997	−	0.594656i
$622$	41.4384	+	15.0823i	1.66153	+	0.604746i
$623$		−	33.7646i		−	1.35275i
$624$	34.7372	−	95.4397i	1.39060	−	3.82065i
$625$		0			0
$626$	13.4235	−	11.2636i	0.536510	−	0.450186i
$627$	−28.1142	+	33.5052i	−1.12277	+	1.33807i
$628$	90.2244			3.60034
$629$	8.84833	+	10.7455i	0.352806	+	0.428449i
$630$		0			0
$631$	5.79199	−	6.90263i	0.230576	−	0.274789i	−0.638335	−	0.769759i	$-0.720376\pi$
$631$	5.79199	−	6.90263i	0.230576	−	0.274789i	0.868910	+	0.494970i	$0.164821\pi$
$632$	90.8684	−	76.2476i	3.61455	−	3.03297i
$633$	4.09373	+	23.2167i	0.162711	+	0.922780i
$634$	−18.6651	+	51.2820i	−0.741286	+	2.03667i
$635$		0			0
$636$	114.518	+	41.6812i	4.54094	+	1.65277i
$637$	2.26807	+	1.30947i	0.0898641	+	0.0518831i
$638$	4.79349	−	27.1852i	0.189776	−	1.07627i
$639$	2.65851	+	4.60468i	0.105169	+	0.182158i
$640$		0			0
$641$	−22.7157	−	19.0608i	−0.897218	−	0.752855i	0.0724270	−	0.997374i	$-0.476926\pi$
$641$	−22.7157	−	19.0608i	−0.897218	−	0.752855i	−0.969645	+	0.244519i	$0.921370\pi$
$642$	81.4310	−	14.3585i	3.21382	−	0.566684i
$643$	−32.2027	+	18.5922i	−1.26995	+	0.733206i	−0.974978	−	0.222300i	$-0.928644\pi$
$643$	−32.2027	+	18.5922i	−1.26995	+	0.733206i	−0.294972	+	0.955506i	$0.595310\pi$
$644$	−30.1731	−	82.8999i	−1.18899	−	3.26671i
$645$		0			0
$646$	37.8022	+	6.66554i	1.48731	+	0.262252i
$647$	−1.08410	−	1.29198i	−0.0426202	−	0.0507928i	0.744313	−	0.667831i	$-0.232777\pi$
$647$	−1.08410	−	1.29198i	−0.0426202	−	0.0507928i	−0.786933	+	0.617038i	$0.788333\pi$
$648$	54.7338	+	65.2292i	2.15015	+	2.56244i
$649$	2.77734	+	0.489721i	0.109020	+	0.0192232i
$650$		0			0
$651$	−11.9631	−	32.8684i	−0.468872	−	1.28822i
$652$	−90.3794	+	52.1806i	−3.53953	+	2.04355i
$653$	22.5575	−	3.97750i	0.882744	−	0.155652i	0.286141	−	0.958188i	$-0.407628\pi$
$653$	22.5575	−	3.97750i	0.882744	−	0.155652i	0.596604	+	0.802536i	$0.296516\pi$
$654$	−10.3194	−	8.65899i	−0.403520	−	0.338593i
$655$		0			0
$656$	−7.86083	−	13.6153i	−0.306914	−	0.531590i
$657$	−0.456993	+	2.59174i	−0.0178290	+	0.101113i
$658$	−57.1435	−	32.9918i	−2.22769	−	1.28616i
$659$	−21.4927	−	7.82272i	−0.837238	−	0.304730i	−0.112412	−	0.993662i	$-0.535858\pi$
$659$	−21.4927	−	7.82272i	−0.837238	−	0.304730i	−0.724826	+	0.688932i	$0.758080\pi$
$660$		0			0
$661$	8.63104	−	23.7136i	0.335709	−	0.922352i	−0.650888	−	0.759174i	$-0.725603\pi$
$661$	8.63104	−	23.7136i	0.335709	−	0.922352i	0.986597	−	0.163178i	$-0.0521746\pi$
$662$	−7.40851	−	42.0157i	−0.287940	−	1.63299i
$663$	−16.3674	+	13.7338i	−0.635656	+	0.533378i
$664$	49.2610	−	58.7070i	1.91170	−	2.27827i
$665$		0			0
$666$	−0.122788	+	13.2659i	−0.00475792	+	0.514044i
$667$	20.6558			0.799797
$668$	−30.1040	+	35.8765i	−1.16476	+	1.38810i
$669$	31.0326	−	26.0394i	1.19979	−	1.00674i
$670$		0			0
$671$	−8.48061	+	23.3003i	−0.327390	+	0.899498i
$672$			64.4438i			2.48597i
$673$	31.1865	+	11.3509i	1.20215	+	0.437547i	0.863974	−	0.503536i	$-0.167968\pi$
$673$	31.1865	+	11.3509i	1.20215	+	0.437547i	0.338176	+	0.941083i	$0.390190\pi$
$674$	51.8326	+	29.9255i	1.99652	+	1.15269i
$675$		0			0
$676$	−24.3988	−	42.2599i	−0.938414	−	1.62538i
$677$	−7.59940	+	13.1625i	−0.292069	+	0.505878i	−0.974299	−	0.225260i	$-0.927677\pi$
$677$	−7.59940	+	13.1625i	−0.292069	+	0.505878i	0.682230	+	0.731138i	$0.261010\pi$
$678$	13.7159	+	11.5090i	0.526754	+	0.441999i
$679$	8.06202	−	1.42155i	0.309392	−	0.0545542i
$680$		0			0
$681$	−6.67103	−	18.3285i	−0.255634	−	0.702350i
$682$	−61.6117	+	22.4248i	−2.35923	+	0.858691i
$683$	42.5353	+	7.50013i	1.62757	+	0.286984i	0.911579	−	0.411125i	$-0.134864\pi$
$683$	42.5353	+	7.50013i	1.62757	+	0.286984i	0.715991	+	0.698110i	$0.245975\pi$
$684$	16.7823	+	20.0004i	0.641687	+	0.764733i
$685$		0			0
$686$	−49.9022	−	8.79910i	−1.90527	−	0.335951i
$687$	18.4697	−	6.72243i	0.704664	−	0.256477i
$688$	−16.2355	−	44.6067i	−0.618973	−	1.70061i
$689$	51.6792	−	29.8370i	1.96882	−	1.13670i
$690$		0			0
$691$	12.3367	+	10.3517i	0.469310	+	0.393797i	0.846543	−	0.532321i	$-0.178680\pi$
$691$	12.3367	+	10.3517i	0.469310	+	0.393797i	−0.377233	+	0.926118i	$0.623124\pi$
$692$	−49.3898	+	85.5457i	−1.87752	+	3.25196i
$693$	3.69270	+	6.39594i	0.140274	+	0.242962i
$694$	4.91794	−	27.8910i	0.186683	−	1.05873i
$695$		0			0
$696$	−42.9768	−	15.6423i	−1.62903	−	0.592919i
$697$			3.30735i			0.125275i
$698$	−0.833825	+	2.29091i	−0.0315607	+	0.0867124i
$699$	−2.25954	−	12.8145i	−0.0854636	−	0.484688i
$700$		0			0
$701$	−13.6132	+	16.2236i	−0.514164	+	0.612756i	−0.959190	−	0.282761i	$-0.908750\pi$
$701$	−13.6132	+	16.2236i	−0.514164	+	0.612756i	0.445027	+	0.895517i	$0.353194\pi$
$702$	53.6638			2.02541
$703$	0.357323	−	38.6051i	0.0134767	−	1.45602i
$704$	44.1441			1.66374
$705$		0			0
$706$	−53.1284	+	44.5800i	−1.99951	+	1.67779i
$707$	6.92028	+	39.2469i	0.260264	+	1.47603i
$708$	2.66891	−	7.33276i	0.100304	−	0.275582i
$709$		−	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
$712$	−18.2089	+	103.268i	−0.682406	+	3.87011i
$713$	−24.5306	−	42.4883i	−0.918678	−	1.59120i
$714$	15.0220	−	26.0190i	0.562186	−	0.973735i
$715$		0			0
$716$	−37.0123	+	6.52626i	−1.38321	+	0.243898i
$717$	30.2881	−	17.4868i	1.13113	−	0.653058i
$718$	15.4935	+	42.5681i	0.578213	+	1.58863i
$719$	9.46321	−	3.44433i	0.352918	−	0.128452i	−0.159477	−	0.987202i	$-0.550981\pi$
$719$	9.46321	−	3.44433i	0.352918	−	0.128452i	0.512395	+	0.858750i	$0.328758\pi$
$720$		0			0
$721$	13.9306	+	16.6018i	0.518801	+	0.618283i
$722$	−36.1560	−	43.0890i	−1.34559	−	1.60361i
$723$	−13.8304	−	2.43868i	−0.514359	−	0.0906953i
$724$	−33.6668	+	12.2537i	−1.25122	+	0.455405i
$725$		0			0
$726$	6.33228	−	3.65594i	0.235013	−	0.135685i
$727$	−11.9936	+	2.11479i	−0.444817	+	0.0784332i	−0.391570	−	0.920148i	$-0.628068\pi$
$727$	−11.9936	+	2.11479i	−0.444817	+	0.0784332i	−0.0532466	+	0.998581i	$0.516957\pi$
$728$	73.2698	+	61.4806i	2.71556	+	2.27862i
$729$	−8.02435	+	13.8986i	−0.297198	+	0.514762i
$730$		0			0
$731$	−1.73407	+	9.83438i	−0.0641368	+	0.363738i
$732$	59.4169	+	34.3044i	2.19611	+	1.26793i
$733$	18.3290	+	6.67122i	0.676998	+	0.246407i	0.657558	−	0.753404i	$-0.271589\pi$
$733$	18.3290	+	6.67122i	0.676998	+	0.246407i	0.0194399	+	0.999811i	$0.493812\pi$
$734$			9.80523i			0.361918i
$735$		0			0
$736$	15.6963	+	89.0180i	0.578572	+	3.28125i
$737$	−15.9340	+	13.3702i	−0.586937	+	0.492498i
$738$	−2.02616	+	2.41469i	−0.0745840	+	0.0888858i
$739$	−31.2931			−1.15114			−0.575568	−	0.817754i	$-0.695219\pi$
$739$	−31.2931			−1.15114			−0.575568	+	0.817754i	$0.695219\pi$
$740$		0			0
$741$	59.2596			2.17695
$742$	−53.9371	+	64.2797i	−1.98009	+	2.35978i
$743$	−39.5179	+	33.1594i	−1.44977	+	1.21650i	−0.517023	+	0.855972i	$0.672960\pi$
$743$	−39.5179	+	33.1594i	−1.44977	+	1.21650i	−0.932748	+	0.360530i	$0.882596\pi$
$744$	18.8631	+	106.978i	0.691556	+	3.92201i
$745$		0			0
$746$		−	81.4060i		−	2.98049i
$747$	−7.53400	−	2.74215i	−0.275655	−	0.100330i
$748$	−34.8069	−	20.0958i	−1.27267	−	0.734774i
$749$	−7.05556	+	40.0141i	−0.257804	+	1.46208i
$750$		0			0
$751$	14.2057	−	24.6050i	0.518373	−	0.897848i	−0.481399	−	0.876501i	$-0.659871\pi$
$751$	14.2057	−	24.6050i	0.518373	−	0.897848i	0.999772	−	0.0213468i	$-0.00679542\pi$
$752$	81.9099	+	68.7306i	2.98695	+	2.50635i
$753$	−4.30442	+	0.758985i	−0.156862	+	0.0276590i
$754$	−32.3902	+	18.7005i	−1.17958	+	0.681031i
$755$		0			0
$756$	−50.6050	+	18.4187i	−1.84049	+	0.669882i
$757$	−22.6279	−	3.98991i	−0.822425	−	0.145016i	−0.253427	−	0.967355i	$-0.581558\pi$
$757$	−22.6279	−	3.98991i	−0.822425	−	0.145016i	−0.568998	+	0.822339i	$0.692669\pi$
$758$	11.2243	+	13.3766i	0.407685	+	0.485861i
$759$	30.8648	+	36.7833i	1.12032	+	1.33515i
$760$		0			0
$761$	34.9807	−	12.7319i	1.26805	−	0.461532i	0.381586	−	0.924333i	$-0.375378\pi$
$761$	34.9807	−	12.7319i	1.26805	−	0.461532i	0.886462	+	0.462802i	$0.153156\pi$
$762$	21.5223	+	59.1321i	0.779672	+	2.14213i
$763$	5.73262	−	3.30973i	0.207535	−	0.119820i
$764$	76.3072	−	13.4550i	2.76070	−	0.486785i
$765$		0			0
$766$	−23.2827	+	40.3269i	−0.841239	+	1.45707i
$767$	−1.91051	−	3.30910i	−0.0689845	−	0.119485i
$768$	−2.07754	+	11.7823i	−0.0749667	+	0.425157i
$769$	−30.4338	−	17.5709i	−1.09747	−	0.633624i	−0.161914	−	0.986805i	$-0.551767\pi$
$769$	−30.4338	−	17.5709i	−1.09747	−	0.633624i	−0.935555	+	0.353181i	$0.885100\pi$
$770$		0			0
$771$			14.1343i			0.509033i
$772$	40.1797	−	110.393i	1.44610	−	3.97312i
$773$	−8.84505	−	50.1628i	−0.318134	−	1.80423i	−0.554080	−	0.832463i	$-0.686930\pi$
$773$	−8.84505	−	50.1628i	−0.318134	−	1.80423i	0.235946	−	0.971766i	$-0.424181\pi$
$774$	−7.29082	+	6.11773i	−0.262063	+	0.219897i
$775$		0			0
$776$	−25.4239			−0.912666
$777$	−28.2982	−	10.5973i	−1.01519	−	0.380177i
$778$	37.5822			1.34739
$779$	5.89632	−	7.02696i	0.211258	−	0.251767i
$780$		0			0
$781$	3.94206	+	22.3566i	0.141058	+	0.799981i
$782$	14.4130	−	39.5995i	0.515409	−	1.41608i
$783$		−	12.6090i		−	0.450610i
$784$	5.60779	+	2.04107i	0.200278	+	0.0728953i
$785$		0			0
$786$	−11.4817	+	65.1161i	−0.409539	+	2.32261i
$787$	−8.30936	−	14.3922i	−0.296197	−	0.513027i	0.679066	−	0.734077i	$-0.262385\pi$
$787$	−8.30936	−	14.3922i	−0.296197	−	0.513027i	−0.975263	+	0.221050i	$0.929052\pi$
$788$	−7.17963	+	12.4355i	−0.255764	+	0.442996i
$789$	−24.6910	−	20.7182i	−0.879024	−	0.737589i
$790$		0			0
$791$	−7.61943	+	4.39908i	−0.270916	+	0.156413i
$792$	−7.84469	−	21.5531i	−0.278749	−	0.765857i
$793$	31.5691	−	11.4902i	1.12105	−	0.408029i
$794$	−6.64145	−	1.17107i	−0.235696	−	0.0415596i
$795$		0			0
$796$	48.3533	+	57.6252i	1.71384	+	2.04247i
$797$	−33.4835	−	5.90405i	−1.18605	−	0.209132i	−0.454389	−	0.890803i	$-0.650142\pi$
$797$	−33.4835	−	5.90405i	−1.18605	−	0.209132i	−0.731659	+	0.681671i	$0.761254\pi$
$798$	−78.3031	+	28.5000i	−2.77190	+	1.00889i
$799$	−7.69335	−	21.1373i	−0.272171	−	0.747784i
$800$		0			0
$801$	10.8036	−	1.90496i	0.381726	−	0.0673086i
$802$	−9.79476	−	8.21878i	−0.345865	−	0.290215i
$803$	−5.61816	+	9.73094i	−0.198261	+	0.343397i
$804$	28.7770	+	49.8431i	1.01488	+	1.75783i
$805$		0			0
$806$	76.9323	+	44.4169i	2.70983	+	1.56452i
$807$	−8.06167	−	2.93421i	−0.283784	−	0.103289i
$808$		−	123.767i		−	4.35410i
$809$	5.96995	−	16.4023i	0.209892	−	0.576674i	−0.789416	−	0.613858i	$-0.789617\pi$
$809$	5.96995	−	16.4023i	0.209892	−	0.576674i	0.999308	+	0.0371842i	$0.0118388\pi$
$810$		0			0
$811$	−12.2898	+	10.3124i	−0.431554	+	0.362117i	−0.832538	−	0.553968i	$-0.813113\pi$
$811$	−12.2898	+	10.3124i	−0.431554	+	0.362117i	0.400984	+	0.916085i	$0.368668\pi$
$812$	24.1255	−	28.7516i	0.846639	−	1.00898i
$813$	16.1152			0.565186
$814$	−19.8646	+	53.0448i	−0.696255	+	1.85922i
$815$		0			0
$816$	−31.2948	+	37.2957i	−1.09554	+	1.30561i
$817$	21.2170	−	17.8031i	0.742288	−	0.622853i
$818$	9.35837	+	53.0739i	0.327208	+	1.85569i
$819$	3.42237	−	9.40287i	0.119587	−	0.328563i
$820$		0			0
$821$	23.4887	+	8.54919i	0.819761	+	0.298369i	0.717650	−	0.696404i	$-0.245218\pi$
$821$	23.4887	+	8.54919i	0.819761	+	0.298369i	0.102112	+	0.994773i	$0.467440\pi$
$822$	16.4066	+	9.47235i	0.572246	+	0.330386i
$823$	2.52591	−	14.3251i	0.0880477	−	0.499343i	−0.908610	−	0.417647i	$-0.862855\pi$
$823$	2.52591	−	14.3251i	0.0880477	−	0.499343i	0.996657	−	0.0816967i	$-0.0260339\pi$
$824$	−33.6528	−	58.2884i	−1.17235	−	2.03057i
$825$		0			0
$826$	4.11592	+	3.45367i	0.143211	+	0.120169i
$827$	2.82166	−	0.497534i	0.0981186	−	0.0173010i	−0.124373	−	0.992235i	$-0.539692\pi$
$827$	2.82166	−	0.497534i	0.0981186	−	0.0173010i	0.222492	+	0.974935i	$0.428581\pi$
$828$	24.8229	−	14.3315i	0.862657	−	0.498055i
$829$	−1.35407	−	3.72028i	−0.0470288	−	0.129211i	0.913955	−	0.405816i	$-0.133013\pi$
$829$	−1.35407	−	3.72028i	−0.0470288	−	0.129211i	−0.960984	+	0.276606i	$0.910790\pi$
$830$		0			0
$831$	6.42418	+	1.13276i	0.222852	+	0.0392949i
$832$	−38.4451	−	45.8171i	−1.33284	−	1.58842i
$833$	−0.806965	−	0.961703i	−0.0279597	−	0.0333210i
$834$	−96.0707	−	16.9399i	−3.32666	−	0.586579i
$835$		0			0
$836$	38.1259	+	104.750i	1.31861	+	3.62286i
$837$	−25.9363	+	14.9743i	−0.896490	+	0.517589i
$838$	−73.9623	+	13.0416i	−2.55499	+	0.450513i
$839$	−19.2397	−	16.1441i	−0.664230	−	0.557355i	0.247122	−	0.968984i	$-0.420515\pi$
$839$	−19.2397	−	16.1441i	−0.664230	−	0.557355i	−0.911351	+	0.411630i	$0.864960\pi$
$840$		0			0
$841$	−10.1061	−	17.5042i	−0.348485	−	0.603594i
$842$	3.90854	−	22.1664i	0.134697	−	0.763905i
$843$	−13.4513	−	7.76610i	−0.463287	−	0.267479i
$844$	56.4606	+	20.5500i	1.94345	+	0.707359i
$845$		0			0
$846$	7.33234	−	20.1454i	0.252091	−	0.692614i
$847$	0.623911	+	3.53838i	0.0214378	+	0.121580i
$848$	104.164	−	87.4044i	3.57702	−	3.00148i
$849$	−13.7726	+	16.4136i	−0.472675	+	0.563313i
$850$		0			0
$851$	−41.6702	−	7.74592i	−1.42844	−	0.265527i
$852$	62.8141			2.15198
$853$	6.12346	−	7.29765i	0.209663	−	0.249867i	−0.650957	−	0.759115i	$-0.725632\pi$
$853$	6.12346	−	7.29765i	0.209663	−	0.249867i	0.860620	+	0.509248i	$0.170076\pi$
$854$	−36.1880	+	30.3653i	−1.23833	+	1.03908i
$855$		0			0
$856$	43.1582	−	118.576i	1.47512	−	4.05285i
$857$			11.0923i			0.378906i	0.981890	+	0.189453i	$0.0606714\pi$
$857$			11.0923i			0.378906i	−0.981890	+	0.189453i	$0.939329\pi$
$858$	−81.7000	−	29.7364i	−2.78919	−	1.01518i
$859$	−40.6649	−	23.4779i	−1.38747	−	0.801056i	−0.394440	−	0.918922i	$-0.629061\pi$
$859$	−40.6649	−	23.4779i	−1.38747	−	0.801056i	−0.993029	+	0.117866i	$0.962395\pi$
$860$		0			0
$861$	−3.58986	−	6.21782i	−0.122342	−	0.211903i
$862$	−27.6035	+	47.8106i	−0.940178	+	1.62844i
$863$	−14.4032	−	12.0857i	−0.490290	−	0.411402i	0.363840	−	0.931461i	$-0.381465\pi$
$863$	−14.4032	−	12.0857i	−0.490290	−	0.411402i	−0.854130	+	0.520059i	$0.825910\pi$
$864$	54.3397	−	9.58155i	1.84867	−	0.325971i
$865$		0			0
$866$	−10.7226	−	29.4601i	−0.364369	−	1.00109i
$867$	−21.6195	+	7.86884i	−0.734235	+	0.267240i
$868$	−87.7921	−	15.4801i	−2.97986	−	0.525430i
$869$	−34.0577	−	40.5884i	−1.15533	−	1.37687i
$870$		0			0
$871$	27.7539	+	4.89375i	0.940404	+	0.165819i
$872$	−19.3179	+	7.03112i	−0.654185	+	0.238104i
$873$	0.909701	+	2.49938i	0.0307887	+	0.0845913i
$874$	−101.220	+	58.4397i	−3.42383	+	1.97675i
$875$		0			0
$876$	23.8167	+	19.9846i	0.804693	+	0.675217i
$877$	−6.03302	+	10.4495i	−0.203721	+	0.352855i	−0.949724	−	0.313087i	$-0.898637\pi$
$877$	−6.03302	+	10.4495i	−0.203721	+	0.352855i	0.746004	+	0.665942i	$0.231970\pi$
$878$	15.2489	+	26.4119i	0.514627	+	0.891359i
$879$	3.06601	−	17.3882i	0.103414	−	0.586490i
$880$		0			0
$881$	2.13298	+	0.776343i	0.0718620	+	0.0261556i	0.377701	−	0.925928i	$-0.376715\pi$
$881$	2.13298	+	0.776343i	0.0718620	+	0.0261556i	−0.305839	+	0.952083i	$0.598937\pi$
$882$		−	1.19650i		−	0.0402884i
$883$	−17.8973	+	49.1725i	−0.602293	+	1.65479i	0.144323	+	0.989531i	$0.453900\pi$
$883$	−17.8973	+	49.1725i	−0.602293	+	1.65479i	−0.746616	+	0.665256i	$0.768323\pi$
$884$	9.45596	+	53.6274i	0.318039	+	1.80369i
$885$		0			0
$886$	28.8493	−	34.3813i	0.969211	−	1.15506i
$887$	31.2761			1.05015			0.525075	−	0.851056i	$-0.324037\pi$
$887$	31.2761			1.05015			0.525075	+	0.851056i	$0.324037\pi$
$888$	80.8337	+	47.6723i	2.71260	+	1.59978i
$889$	−30.9215			−1.03707
$890$		0			0
$891$	29.1360	−	24.4480i	0.976094	−	0.819040i
$892$	−17.9286	−	101.678i	−0.600292	−	3.40443i
$893$	−21.3378	+	58.6251i	−0.714042	+	1.96181i
$894$		−	12.3505i		−	0.413061i
$895$		0			0
$896$	15.7641	+	9.10142i	0.526642	+	0.304057i
$897$	11.2971	−	64.0691i	0.377200	−	2.13921i
$898$	−20.7286	−	35.9029i	−0.691721	−	1.19810i
$899$	10.4364	−	18.0763i	0.348072	−	0.602878i
$900$		0			0
$901$	−28.1708	+	4.96726i	−0.938504	+	0.165484i
$902$	−11.6553	+	6.72917i	−0.388078	+	0.224057i
$903$	−7.41438	−	20.3708i	−0.246735	−	0.677899i
$904$	25.6760	−	9.34532i	0.853973	−	0.310821i
$905$		0			0
$906$	17.9510	+	21.3932i	0.596382	+	0.710740i
$907$	28.0070	+	33.3775i	0.929958	+	1.10828i	0.993895	+	0.110327i	$0.0351897\pi$
$907$	28.0070	+	33.3775i	0.929958	+	1.10828i	−0.0639374	+	0.997954i	$0.520366\pi$
$908$	−48.9557	−	8.63222i	−1.62465	−	0.286470i
$909$	−12.1673	+	4.42853i	−0.403563	+	0.146885i
$910$		0			0
$911$	36.3275	−	20.9737i	1.20358	−	0.694889i	0.242233	−	0.970218i	$-0.422120\pi$
$911$	36.3275	−	20.9737i	1.20358	−	0.694889i	0.961350	+	0.275329i	$0.0887869\pi$
$912$	132.981	−	23.4482i	4.40345	−	0.776447i
$913$	−26.2228	−	22.0035i	−0.867847	−	0.728210i
$914$	24.3781	−	42.2241i	0.806355	−	1.39665i
$915$		0			0
$916$	8.69873	−	49.3329i	0.287414	−	1.63001i
$917$	−28.1378	−	16.2454i	−0.929193	−	0.536470i
$918$	−24.1729	−	8.79822i	−0.797825	−	0.290385i
$919$			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
$922$	36.9803	−	31.0302i	1.21788	−	1.02192i
$923$	19.7707	−	23.5618i	0.650760	−	0.775546i
$924$	87.2494			2.87029
$925$		0			0
$926$	−103.109			−3.38837
$927$	−4.52609	+	5.39398i	−0.148656	+	0.177162i
$928$	−29.4592	+	24.7192i	−0.967045	+	0.811447i
$929$	3.89742	+	22.1034i	0.127870	+	0.725188i	0.979562	+	0.201144i	$0.0644660\pi$
$929$	3.89742	+	22.1034i	0.127870	+	0.725188i	−0.851691	+	0.524044i	$0.824423\pi$
$930$		0			0
$931$			3.48194i			0.114116i
$932$	−31.1635	−	11.3426i	−1.02079	−	0.371539i
$933$	−28.2620	−	16.3171i	−0.925255	−	0.534197i
$934$	−2.23409	+	12.6702i	−0.0731017	+	0.414580i
$935$		0			0
$936$	−15.5380	+	26.9126i	−0.507875	+	0.879666i
$937$	−18.5282	−	15.5470i	−0.605291	−	0.507900i	0.287850	−	0.957675i	$-0.407060\pi$
$937$	−18.5282	−	15.5470i	−0.605291	−	0.507900i	−0.893142	+	0.449776i	$0.851504\pi$
$938$	−39.0263	+	6.88140i	−1.27425	+	0.224686i
$939$	−11.2304	+	6.48390i	−0.366492	+	0.211594i
$940$		0			0
$941$	−50.4649	+	18.3677i	−1.64511	+	0.598771i	−0.987921	−	0.154955i	$-0.950477\pi$
$941$	−50.4649	+	18.3677i	−1.64511	+	0.598771i	−0.657188	+	0.753726i	$0.728254\pi$
$942$	−92.1380	−	16.2464i	−3.00202	−	0.529337i
$943$	−6.47321	−	7.71447i	−0.210797	−	0.251218i
$944$	−5.59663	−	6.66981i	−0.182155	−	0.217084i
$945$		0			0
$946$	−38.1850	+	13.8982i	−1.24150	+	0.451870i
$947$	−9.60396	−	26.3867i	−0.312087	−	0.857452i	−0.992235	−	0.124377i	$-0.960307\pi$
$947$	−9.60396	−	26.3867i	−0.312087	−	0.857452i	0.680148	−	0.733075i	$-0.261915\pi$
$948$	−126.964	+	73.3030i	−4.12361	+	2.38077i
$949$	14.9926	−	2.64360i	0.486680	−	0.0858148i
$950$		0			0
$951$	20.1931	−	34.9755i	0.654808	−	1.13416i
$952$	−22.9246	−	39.7066i	−0.742992	−	1.28690i
$953$	4.37825	−	24.8303i	0.141825	−	0.804331i	−0.828036	−	0.560675i	$-0.810542\pi$
$953$	4.37825	−	24.8303i	0.141825	−	0.804331i	0.969862	−	0.243657i	$-0.0783470\pi$
$954$	−23.6105	−	13.6315i	−0.764417	−	0.441337i
$955$		0			0
$956$		−	89.1358i		−	2.88286i
$957$	−6.98697	+	19.1965i	−0.225857	+	0.620536i
$958$	0.548919	+	3.11308i	0.0177348	+	0.100579i
$959$	−7.13123	+	5.98382i	−0.230280	+	0.193228i
$960$		0			0
$961$	−18.5763			−0.599235
$962$	72.3552	−	25.5793i	2.33283	−	0.824708i
$963$	−13.2013			−0.425405
$964$	−23.0071	+	27.4188i	−0.741009	+	0.883100i
$965$		0			0
$966$	15.8855	+	90.0914i	0.511109	+	2.89864i
$967$	4.75348	−	13.0601i	0.152861	−	0.419983i	−0.839498	−	0.543363i	$-0.817151\pi$
$967$	4.75348	−	13.0601i	0.152861	−	0.419983i	0.992360	+	0.123379i	$0.0393731\pi$
$968$		−	11.1584i		−	0.358645i
$969$	−26.6935	−	9.71565i	−0.857520	−	0.312112i
$970$		0			0
$971$	6.65366	−	37.7348i	0.213526	−	1.21097i	−0.669919	−	0.742434i	$-0.733671\pi$
$971$	6.65366	−	37.7348i	0.213526	−	1.21097i	0.883446	−	0.468534i	$-0.155218\pi$
$972$	−20.8167	−	36.0555i	−0.667695	−	1.15648i
$973$	23.9681	−	41.5139i	0.768380	−	1.33087i
$974$	46.3544	+	38.8960i	1.48529	+	1.24631i
$975$		0			0
$976$	66.2960	−	38.2760i	2.12208	−	1.22519i
$977$	−2.74070	−	7.53002i	−0.0876828	−	0.240907i	0.888099	−	0.459652i	$-0.152026\pi$
$977$	−2.74070	−	7.53002i	−0.0876828	−	0.240907i	−0.975782	+	0.218745i	$0.929804\pi$
$978$	101.692	−	37.0130i	3.25176	−	1.18354i
$979$	46.1267	+	8.13339i	1.47422	+	0.259944i
$980$		0			0
$981$	1.38243	+	1.64752i	0.0441377	+	0.0526013i
$982$	63.2329	+	11.1497i	2.01784	+	0.355800i
$983$	20.1566	−	7.33639i	0.642895	−	0.233995i	6.07699e−5	−	1.00000i	$-0.499981\pi$
$983$	20.1566	−	7.33639i	0.642895	−	0.233995i	0.642834	+	0.766005i	$0.277758\pi$
$984$	7.62622	+	20.9529i	0.243115	+	0.667953i
$985$		0			0
$986$	17.6561	−	3.11325i	0.562286	−	0.0991462i
$987$	37.4064	+	31.3877i	1.19066	+	0.999081i
$988$	75.5161	−	130.798i	2.40249	−	4.16123i
$989$	−15.2033	−	26.3329i	−0.483437	−	0.837338i
$990$		0			0
$991$	21.8303	+	12.6037i	0.693462	+	0.400371i	0.804908	−	0.593400i	$-0.202215\pi$
$991$	21.8303	+	12.6037i	0.693462	+	0.400371i	−0.111446	+	0.993771i	$0.535548\pi$
$992$	85.8317	+	31.2402i	2.72516	+	0.991877i
$993$			31.5730i			1.00194i
$994$	−14.7925	+	40.6420i	−0.469188	+	1.28908i
$995$		0			0
$996$	−72.5575	+	60.8829i	−2.29907	+	1.92915i
$997$	−28.4804	+	33.9416i	−0.901984	+	1.07494i	0.0948547	+	0.995491i	$0.469761\pi$
$997$	−28.4804	+	33.9416i	−0.901984	+	1.07494i	−0.996839	+	0.0794515i	$0.974683\pi$
$998$	−1.05839			−0.0335029
$999$	−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.bb.d.151.1	yes	78
5.2	odd	4		925.2.ba.d.299.2		156
5.3	odd	4		925.2.ba.d.299.25		156
5.4	even	2		925.2.bb.c.151.13	✓	78
37.25	even	18	inner	925.2.bb.d.876.1	yes	78
185.62	odd	36		925.2.ba.d.99.25		156
185.99	even	18		925.2.bb.c.876.13	yes	78
185.173	odd	36		925.2.ba.d.99.2		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.ba.d.99.2		156	185.173	odd	36
925.2.ba.d.99.25		156	185.62	odd	36
925.2.ba.d.299.2		156	5.2	odd	4
925.2.ba.d.299.25		156	5.3	odd	4
925.2.bb.c.151.13	✓	78	5.4	even	2
925.2.bb.c.876.13	yes	78	185.99	even	18
925.2.bb.d.151.1	yes	78	1.1	even	1	trivial
925.2.bb.d.876.1	yes	78	37.25	even	18	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69880 + 2.02455i) q^{2} +(1.49825 - 1.25718i) q^{3} +(-0.865587 - 4.90899i) q^{4} +5.16897i q^{6} +(-2.38678 - 0.868717i) q^{7} +(6.83137 + 3.94409i) q^{8} +(0.143302 - 0.812704i) q^{9} +(1.76172 - 3.05138i) q^{11} +(-7.46833 - 6.26668i) q^{12} +(-4.70130 + 0.828967i) q^{13} +(5.81342 - 3.35638i) q^{14} +(-10.2219 + 3.72048i) q^{16} +(2.25362 + 0.397373i) q^{17} +(1.40192 + 1.67074i) q^{18} +(-4.07971 - 4.86201i) q^{19} +(-4.66812 + 1.69906i) q^{21} +(3.18487 + 8.75036i) q^{22} +(-6.03437 + 3.48394i) q^{23} +(15.1935 - 2.67903i) q^{24} +(6.30828 - 10.9263i) q^{26} +(2.12672 + 3.68359i) q^{27} +(-2.19856 + 12.4686i) q^{28} +(-2.56727 - 1.48222i) q^{29} +7.04104i q^{31} +(4.43687 - 12.1902i) q^{32} +(-1.19665 - 6.78651i) q^{33} +(-4.63294 + 3.88750i) q^{34} -4.11359 q^{36} +(4.62328 + 3.95288i) q^{37} +16.7740 q^{38} +(-6.00155 + 7.15237i) q^{39} +(0.250970 + 1.42332i) q^{41} +(4.49037 - 12.3372i) q^{42} +4.36382i q^{43} +(-16.5041 - 6.00700i) q^{44} +(3.19776 - 18.1354i) q^{46} +(-4.91479 - 8.51267i) q^{47} +(-10.6377 + 18.4250i) q^{48} +(-0.420255 - 0.352636i) q^{49} +(3.87604 - 2.23783i) q^{51} +(8.13877 + 22.3611i) q^{52} +(-11.7464 + 4.27534i) q^{53} +(-11.0705 - 1.95202i) q^{54} +(-12.8787 - 15.3482i) q^{56} +(-12.2248 - 2.15557i) q^{57} +(7.36210 - 2.67959i) q^{58} +(0.273756 + 0.752139i) q^{59} +(-6.93044 + 1.22202i) q^{61} +(-14.2549 - 11.9613i) q^{62} +(-1.04804 + 1.81526i) q^{63} +(6.26436 + 10.8502i) q^{64} +(15.7725 + 9.10625i) q^{66} +(-5.54742 - 2.01910i) q^{67} -11.4069i q^{68} +(-4.66103 + 12.8061i) q^{69} +(-4.93562 + 4.14148i) q^{71} +(4.18433 - 4.98669i) q^{72} -3.18903 q^{73} +(-15.8568 + 2.64490i) q^{74} +(-20.3362 + 24.2358i) q^{76} +(-6.85562 + 5.75255i) q^{77} +(-4.28490 - 24.3009i) q^{78} +(5.14320 - 14.1308i) q^{79} +(10.1437 + 3.69201i) q^{81} +(-3.30793 - 1.90983i) q^{82} +(1.68705 - 9.56775i) q^{83} +(12.3813 + 21.4451i) q^{84} +(-8.83477 - 7.41325i) q^{86} +(-5.70982 + 1.00680i) q^{87} +(24.0699 - 13.8967i) q^{88} +(4.54660 + 12.4917i) q^{89} +(11.9411 + 2.10554i) q^{91} +(22.3259 + 26.6070i) q^{92} +(8.85185 + 10.5492i) q^{93} +(25.5836 + 4.51107i) q^{94} +(-8.67773 - 23.8419i) q^{96} +(-2.79124 + 1.61152i) q^{97} +(1.42786 - 0.251770i) q^{98} +(-2.22741 - 1.86902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 3 q^{2} + 3 q^{4} - 6 q^{7} + 18 q^{8} + 15 q^{12} - 27 q^{13} - 18 q^{14} + 9 q^{16} - 15 q^{18} + 3 q^{21} - 30 q^{22} + 15 q^{24} + 36 q^{27} + 27 q^{28} - 9 q^{29} - 18 q^{32} - 6 q^{33} - 51 q^{34}+ \cdots - 183 q^{99}+O(q^{100}) \) 78 * q + 3 * q^2 + 3 * q^4 - 6 * q^7 + 18 * q^8 + 15 * q^12 - 27 * q^13 - 18 * q^14 + 9 * q^16 - 15 * q^18 + 3 * q^21 - 30 * q^22 + 15 * q^24 + 36 * q^27 + 27 * q^28 - 9 * q^29 - 18 * q^32 - 6 * q^33 - 51 * q^34 - 108 * q^36 + 6 * q^37 + 84 * q^38 - 33 * q^39 - 21 * q^41 + 42 * q^42 - 3 * q^44 + 36 * q^46 - 57 * q^47 + 54 * q^48 + 54 * q^49 + 90 * q^51 + 75 * q^52 - 24 * q^53 - 39 * q^54 - 48 * q^56 - 9 * q^57 + 9 * q^58 + 15 * q^59 - 18 * q^61 - 120 * q^63 + 66 * q^64 + 126 * q^66 - 24 * q^67 + 45 * q^69 + 48 * q^71 + 132 * q^72 - 60 * q^73 - 12 * q^74 + 81 * q^76 + 21 * q^77 - 258 * q^78 + 84 * q^79 + 48 * q^81 + 234 * q^82 + 42 * q^83 + 57 * q^84 - 66 * q^86 + 24 * q^87 - 90 * q^88 + 39 * q^89 + 57 * q^91 - 87 * q^92 - 12 * q^93 + 78 * q^94 - 78 * q^96 - 36 * q^97 + 126 * q^98 - 183 * q^99

Introduction

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