LMFDB - Embedded newform 1148.2.ba.a.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.2
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81622i q^{3} +(1.10836 + 3.41119i) q^{5} +(0.587785 + 0.809017i) q^{7} -4.93108 q^{9} +O(q^{10})$	\(q-2.81622i q^{3} +(1.10836 + 3.41119i) q^{5} +(0.587785 + 0.809017i) q^{7} -4.93108 q^{9} +(-0.213839 - 0.0694806i) q^{11} +(-3.07430 + 4.23140i) q^{13} +(9.60667 - 3.12140i) q^{15} +(-3.00515 - 0.976434i) q^{17} +(2.68046 + 3.68934i) q^{19} +(2.27837 - 1.65533i) q^{21} +(3.82515 + 2.77914i) q^{23} +(-6.36269 + 4.62277i) q^{25} +5.43835i q^{27} +(-0.396882 + 0.128955i) q^{29} +(-1.43283 + 4.40979i) q^{31} +(-0.195673 + 0.602218i) q^{33} +(-2.10823 + 2.90174i) q^{35} +(0.846662 + 2.60576i) q^{37} +(11.9166 + 8.65788i) q^{39} +(4.14062 + 4.88418i) q^{41} +(0.388402 + 0.282190i) q^{43} +(-5.46544 - 16.8209i) q^{45} +(-4.40935 + 6.06894i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-2.74985 + 8.46317i) q^{51} +(-1.20312 + 0.390916i) q^{53} -0.806457i q^{55} +(10.3900 - 7.54877i) q^{57} +(-8.96171 - 6.51107i) q^{59} +(9.89239 - 7.18725i) q^{61} +(-2.89842 - 3.98933i) q^{63} +(-17.8416 - 5.79708i) q^{65} +(-6.70062 + 2.17716i) q^{67} +(7.82666 - 10.7725i) q^{69} +(11.1052 + 3.60829i) q^{71} -3.44830 q^{73} +(13.0187 + 17.9187i) q^{75} +(-0.0694806 - 0.213839i) q^{77} -12.1848i q^{79} +0.522330 q^{81} +15.1285 q^{83} -11.3334i q^{85} +(0.363165 + 1.11771i) q^{87} +(4.68737 + 6.45161i) q^{89} -5.23030 q^{91} +(12.4189 + 4.03515i) q^{93} +(-9.61413 + 13.2327i) q^{95} +(7.28078 - 2.36567i) q^{97} +(1.05446 + 0.342615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	2.81622i		−	1.62594i	−0.582303	−	0.812972i	$-0.697848\pi$
$3$		−	2.81622i		−	1.62594i	0.582303	−	0.812972i	$-0.302152\pi$
$4$		0			0
$5$	1.10836	+	3.41119i	0.495676	+	1.52553i	0.815901	+	0.578191i	$0.196241\pi$
$5$	1.10836	+	3.41119i	0.495676	+	1.52553i	−0.320226	+	0.947341i	$0.603759\pi$
$6$		0			0
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$8$		0			0
$9$	−4.93108			−1.64369
$10$		0			0
$11$	−0.213839	−	0.0694806i	−0.0644750	−	0.0209492i	0.276602	−	0.960985i	$-0.410792\pi$
$11$	−0.213839	−	0.0694806i	−0.0644750	−	0.0209492i	−0.341077	+	0.940035i	$0.610792\pi$
$12$		0			0
$13$	−3.07430	+	4.23140i	−0.852656	+	1.17358i	0.130615	+	0.991433i	$0.458305\pi$
$13$	−3.07430	+	4.23140i	−0.852656	+	1.17358i	−0.983271	+	0.182147i	$0.941695\pi$
$14$		0			0
$15$	9.60667	−	3.12140i	2.48043	−	0.805941i
$16$		0			0
$17$	−3.00515	−	0.976434i	−0.728857	−	0.236820i	−0.0789980	−	0.996875i	$-0.525172\pi$
$17$	−3.00515	−	0.976434i	−0.728857	−	0.236820i	−0.649859	+	0.760055i	$0.725172\pi$
$18$		0			0
$19$	2.68046	+	3.68934i	0.614941	+	0.846393i	0.996972	−	0.0777561i	$-0.0247755\pi$
$19$	2.68046	+	3.68934i	0.614941	+	0.846393i	−0.382032	+	0.924149i	$0.624776\pi$
$20$		0			0
$21$	2.27837	−	1.65533i	0.497181	−	0.361223i
$22$		0			0
$23$	3.82515	+	2.77914i	0.797600	+	0.579490i	0.910209	−	0.414149i	$-0.135921\pi$
$23$	3.82515	+	2.77914i	0.797600	+	0.579490i	−0.112609	+	0.993639i	$0.535921\pi$
$24$		0			0
$25$	−6.36269	+	4.62277i	−1.27254	+	0.924553i
$26$		0			0
$27$			5.43835i			1.04661i
$28$		0			0
$29$	−0.396882	+	0.128955i	−0.0736991	+	0.0239463i	−0.345635	−	0.938369i	$-0.612336\pi$
$29$	−0.396882	+	0.128955i	−0.0736991	+	0.0239463i	0.271935	+	0.962316i	$0.412336\pi$
$30$		0			0
$31$	−1.43283	+	4.40979i	−0.257343	+	0.792021i	0.736016	+	0.676964i	$0.236705\pi$
$31$	−1.43283	+	4.40979i	−0.257343	+	0.792021i	−0.993359	+	0.115057i	$0.963295\pi$
$32$		0			0
$33$	−0.195673	+	0.602218i	−0.0340622	+	0.104833i
$34$		0			0
$35$	−2.10823	+	2.90174i	−0.356357	+	0.490483i
$36$		0			0
$37$	0.846662	+	2.60576i	0.139190	+	0.428384i	0.996218	−	0.0868860i	$-0.0276916\pi$
$37$	0.846662	+	2.60576i	0.139190	+	0.428384i	−0.857028	+	0.515270i	$0.827692\pi$
$38$		0			0
$39$	11.9166	+	8.65788i	1.90818	+	1.38637i
$40$		0			0
$41$	4.14062	+	4.88418i	0.646657	+	0.762781i
$41$	4.14062	+	4.88418i	0.646657	+	0.762781i
$42$		0			0
$43$	0.388402	+	0.282190i	0.0592307	+	0.0430336i	0.617007	−	0.786958i	$-0.288345\pi$
$43$	0.388402	+	0.282190i	0.0592307	+	0.0430336i	−0.557776	+	0.829992i	$0.688345\pi$
$44$		0			0
$45$	−5.46544	−	16.8209i	−0.814739	−	2.50751i
$46$		0			0
$47$	−4.40935	+	6.06894i	−0.643169	+	0.885247i	−0.998780	−	0.0493877i	$-0.984273\pi$
$47$	−4.40935	+	6.06894i	−0.643169	+	0.885247i	0.355610	+	0.934634i	$0.384273\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	−2.74985	+	8.46317i	−0.385056	+	1.18508i
$52$		0			0
$53$	−1.20312	+	0.390916i	−0.165261	+	0.0536964i	−0.390479	−	0.920612i	$-0.627691\pi$
$53$	−1.20312	+	0.390916i	−0.165261	+	0.0536964i	0.225218	+	0.974308i	$0.427691\pi$
$54$		0			0
$55$		−	0.806457i		−	0.108743i
$56$		0			0
$57$	10.3900	−	7.54877i	1.37619	−	0.999859i
$58$		0			0
$59$	−8.96171	−	6.51107i	−1.16672	−	0.847668i	−0.176104	−	0.984372i	$-0.556349\pi$
$59$	−8.96171	−	6.51107i	−1.16672	−	0.847668i	−0.990612	+	0.136703i	$0.956349\pi$
$60$		0			0
$61$	9.89239	−	7.18725i	1.26659	−	0.920232i	0.267530	−	0.963550i	$-0.413793\pi$
$61$	9.89239	−	7.18725i	1.26659	−	0.920232i	0.999061	+	0.0433171i	$0.0137926\pi$
$62$		0			0
$63$	−2.89842	−	3.98933i	−0.365166	−	0.502608i
$64$		0			0
$65$	−17.8416	−	5.79708i	−2.21298	−	0.719039i
$66$		0			0
$67$	−6.70062	+	2.17716i	−0.818612	+	0.265983i	−0.688241	−	0.725482i	$-0.741617\pi$
$67$	−6.70062	+	2.17716i	−0.818612	+	0.265983i	−0.130371	+	0.991465i	$0.541617\pi$
$68$		0			0
$69$	7.82666	−	10.7725i	0.942219	−	1.29685i
$70$		0			0
$71$	11.1052	+	3.60829i	1.31794	+	0.428226i	0.881788	−	0.471646i	$-0.156340\pi$
$71$	11.1052	+	3.60829i	1.31794	+	0.428226i	0.436155	+	0.899871i	$0.356340\pi$
$72$		0			0
$73$	−3.44830			−0.403593			−0.201796	−	0.979428i	$-0.564678\pi$
$73$	−3.44830			−0.403593			−0.201796	+	0.979428i	$0.564678\pi$
$74$		0			0
$75$	13.0187	+	17.9187i	1.50327	+	2.06908i
$76$		0			0
$77$	−0.0694806	−	0.213839i	−0.00791805	−	0.0243693i
$78$		0			0
$79$		−	12.1848i		−	1.37090i	−0.728119	−	0.685450i	$-0.759605\pi$
$79$		−	12.1848i		−	1.37090i	0.728119	−	0.685450i	$-0.240395\pi$
$80$		0			0
$81$	0.522330			0.0580367
$82$		0			0
$83$	15.1285			1.66057			0.830284	−	0.557341i	$-0.188178\pi$
$83$	15.1285			1.66057			0.830284	+	0.557341i	$0.188178\pi$
$84$		0			0
$85$		−	11.3334i		−	1.22928i
$86$		0			0
$87$	0.363165	+	1.11771i	0.0389353	+	0.119831i
$88$		0			0
$89$	4.68737	+	6.45161i	0.496860	+	0.683870i	0.981635	−	0.190769i	$-0.0610983\pi$
$89$	4.68737	+	6.45161i	0.496860	+	0.683870i	−0.484774	+	0.874639i	$0.661098\pi$
$90$		0			0
$91$	−5.23030			−0.548285
$92$		0			0
$93$	12.4189	+	4.03515i	1.28778	+	0.418426i
$94$		0			0
$95$	−9.61413	+	13.2327i	−0.986389	+	1.35765i
$96$		0			0
$97$	7.28078	−	2.36567i	0.739252	−	0.240197i	0.0849018	−	0.996389i	$-0.472942\pi$
$97$	7.28078	−	2.36567i	0.739252	−	0.240197i	0.654350	+	0.756192i	$0.272942\pi$
$98$		0			0
$99$	1.05446	+	0.342615i	0.105977	+	0.0344341i
$100$		0			0
$101$	5.70889	+	7.85762i	0.568056	+	0.781862i	0.992323	−	0.123675i	$-0.0394681\pi$
$101$	5.70889	+	7.85762i	0.568056	+	0.781862i	−0.424267	+	0.905537i	$0.639468\pi$
$102$		0			0
$103$	7.78404	−	5.65544i	0.766984	−	0.557247i	−0.134060	−	0.990973i	$-0.542802\pi$
$103$	7.78404	−	5.65544i	0.766984	−	0.557247i	0.901045	+	0.433727i	$0.142802\pi$
$104$		0			0
$105$	8.17192	+	5.93725i	0.797498	+	0.579416i
$106$		0			0
$107$	4.43447	−	3.22183i	0.428696	−	0.311466i	−0.352431	−	0.935838i	$-0.614645\pi$
$107$	4.43447	−	3.22183i	0.428696	−	0.311466i	0.781127	+	0.624372i	$0.214645\pi$
$108$		0			0
$109$		−	14.3127i		−	1.37091i	−0.728115	−	0.685455i	$-0.759603\pi$
$109$		−	14.3127i		−	1.37091i	0.728115	−	0.685455i	$-0.240397\pi$
$110$		0			0
$111$	7.33838	−	2.38439i	0.696529	−	0.226316i
$112$		0			0
$113$	−3.56698	+	10.9780i	−0.335554	+	1.03273i	0.630895	+	0.775868i	$0.282688\pi$
$113$	−3.56698	+	10.9780i	−0.335554	+	1.03273i	−0.966449	+	0.256860i	$0.917312\pi$
$114$		0			0
$115$	−5.24051	+	16.1286i	−0.488680	+	1.50400i
$116$		0			0
$117$	15.1596	−	20.8654i	1.40151	−	1.92901i
$118$		0			0
$119$	−0.976434	−	3.00515i	−0.0895095	−	0.275482i
$120$		0			0
$121$	−8.85829	−	6.43592i	−0.805299	−	0.585084i
$122$		0			0
$123$	13.7549	−	11.6609i	1.24024	−	1.05143i
$124$		0			0
$125$	−8.31266	−	6.03950i	−0.743507	−	0.540189i
$126$		0			0
$127$	2.64540	+	8.14171i	0.234742	+	0.722460i	0.997156	+	0.0753706i	$0.0240140\pi$
$127$	2.64540	+	8.14171i	0.234742	+	0.722460i	−0.762414	+	0.647089i	$0.775986\pi$
$128$		0			0
$129$	0.794709	−	1.09382i	0.0699702	−	0.0963058i
$130$		0			0
$131$	0.682712	−	2.10117i	0.0596489	−	0.183580i	−0.916792	−	0.399365i	$-0.869231\pi$
$131$	0.682712	−	2.10117i	0.0596489	−	0.183580i	0.976441	+	0.215784i	$0.0692308\pi$
$132$		0			0
$133$	−1.40920	+	4.33708i	−0.122193	+	0.376073i
$134$		0			0
$135$	−18.5513	+	6.02767i	−1.59664	+	0.518780i
$136$		0			0
$137$		−	5.43989i		−	0.464761i	−0.972625	−	0.232381i	$-0.925349\pi$
$137$		−	5.43989i		−	0.464761i	0.972625	−	0.232381i	$-0.0746515\pi$
$138$		0			0
$139$	−7.07087	+	5.13729i	−0.599743	+	0.435739i	−0.845788	−	0.533520i	$-0.820869\pi$
$139$	−7.07087	+	5.13729i	−0.599743	+	0.435739i	0.246045	+	0.969259i	$0.420869\pi$
$140$		0			0
$141$	17.0915	+	12.4177i	1.43936	+	1.04576i
$142$		0			0
$143$	0.951406	−	0.691237i	0.0795606	−	0.0578041i
$144$		0			0
$145$	−0.879779	−	1.21091i	−0.0730617	−	0.100561i
$146$		0			0
$147$	2.67838	+	0.870259i	0.220909	+	0.0717778i
$148$		0			0
$149$	−10.5188	+	3.41778i	−0.861737	+	0.279995i	−0.706354	−	0.707859i	$-0.749661\pi$
$149$	−10.5188	+	3.41778i	−0.861737	+	0.279995i	−0.155383	+	0.987854i	$0.549661\pi$
$150$		0			0
$151$	12.0773	−	16.6229i	0.982834	−	1.35275i	0.0475449	−	0.998869i	$-0.484860\pi$
$151$	12.0773	−	16.6229i	0.982834	−	1.35275i	0.935289	−	0.353885i	$-0.115140\pi$
$152$		0			0
$153$	14.8187	+	4.81488i	1.19802	+	0.389260i
$154$		0			0
$155$	−16.6307			−1.33581
$156$		0			0
$157$	−9.77240	−	13.4506i	−0.779922	−	1.07347i	−0.995290	−	0.0969381i	$-0.969095\pi$
$157$	−9.77240	−	13.4506i	−0.779922	−	1.07347i	0.215368	−	0.976533i	$-0.430905\pi$
$158$		0			0
$159$	1.10090	+	3.38824i	0.0873074	+	0.268705i
$160$		0			0
$161$			4.72815i			0.372630i
$162$		0			0
$163$	16.7104			1.30886			0.654428	−	0.756124i	$-0.272909\pi$
$163$	16.7104			1.30886			0.654428	+	0.756124i	$0.272909\pi$
$164$		0			0
$165$	−2.27116			−0.176810
$166$		0			0
$167$			5.98742i			0.463321i	0.972797	+	0.231660i	$0.0744158\pi$
$167$			5.98742i			0.463321i	−0.972797	+	0.231660i	$0.925584\pi$
$168$		0			0
$169$	−4.43627	−	13.6534i	−0.341252	−	1.05026i
$170$		0			0
$171$	−13.2176	−	18.1925i	−1.01077	−	1.39121i
$172$		0			0
$173$	−20.3113			−1.54424			−0.772120	−	0.635477i	$-0.780804\pi$
$173$	−20.3113			−1.54424			−0.772120	+	0.635477i	$0.780804\pi$
$174$		0			0
$175$	−7.47979	−	2.43033i	−0.565419	−	0.183716i
$176$		0			0
$177$	−18.3366	+	25.2381i	−1.37826	+	1.89701i
$178$		0			0
$179$	−22.4093	+	7.28123i	−1.67495	+	0.544225i	−0.983921	−	0.178602i	$-0.942843\pi$
$179$	−22.4093	+	7.28123i	−1.67495	+	0.544225i	−0.691029	+	0.722827i	$0.742843\pi$
$180$		0			0
$181$	−12.8254	−	4.16721i	−0.953302	−	0.309747i	−0.209245	−	0.977863i	$-0.567101\pi$
$181$	−12.8254	−	4.16721i	−0.953302	−	0.309747i	−0.744057	+	0.668117i	$0.767101\pi$
$182$		0			0
$183$	−20.2408	−	27.8591i	−1.49625	−	2.05941i
$184$		0			0
$185$	−7.95034	+	5.77626i	−0.584521	+	0.424679i
$186$		0			0
$187$	0.574777	+	0.417600i	0.0420319	+	0.0305379i
$188$		0			0
$189$	−4.39972	+	3.19658i	−0.320032	+	0.232517i
$190$		0			0
$191$		−	24.7883i		−	1.79362i	−0.442416	−	0.896810i	$-0.645879\pi$
$191$		−	24.7883i		−	1.79362i	0.442416	−	0.896810i	$-0.354121\pi$
$192$		0			0
$193$	−8.55539	+	2.77982i	−0.615831	+	0.200095i	−0.600288	−	0.799784i	$-0.704947\pi$
$193$	−8.55539	+	2.77982i	−0.615831	+	0.200095i	−0.0155423	+	0.999879i	$0.504947\pi$
$194$		0			0
$195$	−16.3258	+	50.2458i	−1.16912	+	3.59818i
$196$		0			0
$197$	−4.18408	+	12.8773i	−0.298103	+	0.917468i	0.684058	+	0.729428i	$0.260214\pi$
$197$	−4.18408	+	12.8773i	−0.298103	+	0.917468i	−0.982161	+	0.188040i	$0.939786\pi$
$198$		0			0
$199$	2.74535	−	3.77865i	0.194613	−	0.267861i	−0.700548	−	0.713606i	$-0.747061\pi$
$199$	2.74535	−	3.77865i	0.194613	−	0.267861i	0.895160	+	0.445744i	$0.147061\pi$
$200$		0			0
$201$	6.13137	+	18.8704i	0.432474	+	1.33102i
$202$		0			0
$203$	−0.337608	−	0.245286i	−0.0236954	−	0.0172157i
$204$		0			0
$205$	−12.0716	+	19.5379i	−0.843115	+	1.36459i
$206$		0			0
$207$	−18.8622	−	13.7042i	−1.31101	−	0.952505i
$208$		0			0
$209$	−0.316851	−	0.975167i	−0.0219170	−	0.0674537i
$210$		0			0
$211$	−5.81663	+	8.00590i	−0.400433	+	0.551149i	−0.960853	−	0.277060i	$-0.910640\pi$
$211$	−5.81663	+	8.00590i	−0.400433	+	0.551149i	0.560420	+	0.828209i	$0.310640\pi$
$212$		0			0
$213$	10.1617	−	31.2746i	0.696271	−	2.14290i
$214$		0			0
$215$	−0.532115	+	1.63768i	−0.0362900	+	0.111689i
$216$		0			0
$217$	−4.40979	+	1.43283i	−0.299356	+	0.0972666i
$218$		0			0
$219$			9.71116i			0.656219i
$220$		0			0
$221$	13.3704	−	9.71418i	0.899392	−	0.653446i
$222$		0			0
$223$	15.2615	+	11.0881i	1.02198	+	0.742515i	0.966689	−	0.255955i	$-0.0823900\pi$
$223$	15.2615	+	11.0881i	1.02198	+	0.742515i	0.0552953	+	0.998470i	$0.482390\pi$
$224$		0			0
$225$	31.3750	−	22.7952i	2.09166	−	1.51968i
$226$		0			0
$227$	11.2478	+	15.4812i	0.746542	+	1.02753i	0.998215	+	0.0597145i	$0.0190190\pi$
$227$	11.2478	+	15.4812i	0.746542	+	1.02753i	−0.251674	+	0.967812i	$0.580981\pi$
$228$		0			0
$229$	−11.8359	−	3.84572i	−0.782139	−	0.254132i	−0.109386	−	0.993999i	$-0.534888\pi$
$229$	−11.8359	−	3.84572i	−0.782139	−	0.254132i	−0.672753	+	0.739867i	$0.734888\pi$
$230$		0			0
$231$	−0.602218	+	0.195673i	−0.0396230	+	0.0128743i
$232$		0			0
$233$	6.79638	−	9.35441i	0.445246	−	0.612828i	−0.526122	−	0.850409i	$-0.676355\pi$
$233$	6.79638	−	9.35441i	0.445246	−	0.612828i	0.971368	+	0.237581i	$0.0763545\pi$
$234$		0			0
$235$	−25.5895	−	8.31454i	−1.66928	−	0.542381i
$236$		0			0
$237$	−34.3151			−2.22901
$238$		0			0
$239$	−3.84320	−	5.28971i	−0.248596	−	0.342163i	0.666423	−	0.745574i	$-0.267824\pi$
$239$	−3.84320	−	5.28971i	−0.248596	−	0.342163i	−0.915019	+	0.403411i	$0.867824\pi$
$240$		0			0
$241$	8.15022	+	25.0838i	0.525002	+	1.61579i	0.764312	+	0.644847i	$0.223079\pi$
$241$	8.15022	+	25.0838i	0.525002	+	1.61579i	−0.239310	+	0.970943i	$0.576921\pi$
$242$		0			0
$243$			14.8441i			0.952247i
$244$		0			0
$245$	−3.58674			−0.229149
$246$		0			0
$247$	−23.8516			−1.51764
$248$		0			0
$249$		−	42.6051i		−	2.69999i
$250$		0			0
$251$	7.18170	+	22.1030i	0.453305	+	1.39513i	0.873114	+	0.487516i	$0.162097\pi$
$251$	7.18170	+	22.1030i	0.453305	+	1.39513i	−0.419810	+	0.907612i	$0.637903\pi$
$252$		0			0
$253$	−0.624872	−	0.860063i	−0.0392854	−	0.0540717i
$254$		0			0
$255$	−31.9174			−1.99874
$256$		0			0
$257$	13.3030	+	4.32241i	0.829819	+	0.269625i	0.692969	−	0.720967i	$-0.256302\pi$
$257$	13.3030	+	4.32241i	0.829819	+	0.269625i	0.136850	+	0.990592i	$0.456302\pi$
$258$		0			0
$259$	−1.61045	+	2.21659i	−0.100068	+	0.137732i
$260$		0			0
$261$	1.95706	−	0.635887i	0.121139	−	0.0393604i
$262$		0			0
$263$	−5.95221	−	1.93399i	−0.367029	−	0.119255i	0.119695	−	0.992811i	$-0.461808\pi$
$263$	−5.95221	−	1.93399i	−0.367029	−	0.119255i	−0.486724	+	0.873556i	$0.661808\pi$
$264$		0			0
$265$	−2.66698	−	3.67078i	−0.163831	−	0.225495i
$266$		0			0
$267$	18.1692	−	13.2007i	1.11193	−	0.807867i
$268$		0			0
$269$	17.4003	+	12.6421i	1.06092	+	0.770800i	0.974258	−	0.225438i	$-0.0723812\pi$
$269$	17.4003	+	12.6421i	1.06092	+	0.770800i	0.0866582	+	0.996238i	$0.472381\pi$
$270$		0			0
$271$	−7.50412	+	5.45207i	−0.455843	+	0.331189i	−0.791898	−	0.610653i	$-0.790907\pi$
$271$	−7.50412	+	5.45207i	−0.455843	+	0.331189i	0.336055	+	0.941842i	$0.390907\pi$
$272$		0			0
$273$			14.7297i			0.891480i
$274$		0			0
$275$	1.68179	−	0.546446i	0.101416	−	0.0329519i
$276$		0			0
$277$	−6.06768	+	18.6744i	−0.364572	+	1.12204i	0.585677	+	0.810545i	$0.300829\pi$
$277$	−6.06768	+	18.6744i	−0.364572	+	1.12204i	−0.950249	+	0.311492i	$0.899171\pi$
$278$		0			0
$279$	7.06539	−	21.7450i	0.422994	−	1.30184i
$280$		0			0
$281$	17.6892	−	24.3470i	1.05525	−	1.45242i	0.171076	−	0.985258i	$-0.445276\pi$
$281$	17.6892	−	24.3470i	1.05525	−	1.45242i	0.884170	−	0.467164i	$-0.154724\pi$
$282$		0			0
$283$	−7.18655	−	22.1179i	−0.427196	−	1.31477i	−0.900876	−	0.434077i	$-0.857074\pi$
$283$	−7.18655	−	22.1179i	−0.427196	−	1.31477i	0.473679	−	0.880697i	$-0.342926\pi$
$284$		0			0
$285$	37.2662	+	27.0755i	2.20746	+	1.60381i
$286$		0			0
$287$	−1.51759	+	6.22069i	−0.0895804	+	0.367195i
$288$		0			0
$289$	−5.67576	−	4.12368i	−0.333868	−	0.242569i
$290$		0			0
$291$	−6.66224	−	20.5043i	−0.390548	−	1.20198i
$292$		0			0
$293$	−2.62647	+	3.61503i	−0.153440	+	0.211192i	−0.878816	−	0.477161i	$-0.841666\pi$
$293$	−2.62647	+	3.61503i	−0.153440	+	0.211192i	0.725376	+	0.688353i	$0.241666\pi$
$294$		0			0
$295$	12.2777	−	37.7868i	0.714833	−	2.20003i
$296$		0			0
$297$	0.377860	−	1.16293i	0.0219257	−	0.0674802i
$298$		0			0
$299$	−23.5193	+	7.64189i	−1.36016	+	0.441942i
$300$		0			0
$301$			0.480091i			0.0276720i
$302$		0			0
$303$	22.1288	−	16.0775i	1.27126	−	0.923628i
$304$		0			0
$305$	35.4815	+	25.7788i	2.03166	+	1.47609i
$306$		0			0
$307$	−12.4056	+	9.01318i	−0.708023	+	0.514409i	−0.882535	−	0.470246i	$-0.844165\pi$
$307$	−12.4056	+	9.01318i	−0.708023	+	0.514409i	0.174512	+	0.984655i	$0.444165\pi$
$308$		0			0
$309$	−15.9269	−	21.9215i	−0.906052	−	1.24707i
$310$		0			0
$311$	9.99483	+	3.24752i	0.566755	+	0.184150i	0.578358	−	0.815783i	$-0.303694\pi$
$311$	9.99483	+	3.24752i	0.566755	+	0.184150i	−0.0116035	+	0.999933i	$0.503694\pi$
$312$		0			0
$313$	27.2840	−	8.86510i	1.54218	−	0.501085i	0.590204	−	0.807254i	$-0.299047\pi$
$313$	27.2840	−	8.86510i	1.54218	−	0.501085i	0.951977	+	0.306169i	$0.0990473\pi$
$314$		0			0
$315$	10.3959	−	14.3087i	0.585741	−	0.806204i
$316$		0			0
$317$	14.2729	+	4.63755i	0.801647	+	0.260471i	0.681056	−	0.732231i	$-0.261521\pi$
$317$	14.2729	+	4.63755i	0.801647	+	0.260471i	0.120591	+	0.992702i	$0.461521\pi$
$318$		0			0
$319$	0.0938288			0.00525341
$320$		0			0
$321$	−9.07338	−	12.4884i	−0.506426	−	0.697036i
$322$		0			0
$323$	−4.45281	−	13.7043i	−0.247761	−	0.762530i
$324$		0			0
$325$		−	41.1349i		−	2.28175i
$326$		0			0
$327$	−40.3077			−2.22902
$328$		0			0
$329$	−7.50163			−0.413578
$330$		0			0
$331$		−	26.5738i		−	1.46063i	−0.683112	−	0.730313i	$-0.739374\pi$
$331$		−	26.5738i		−	1.46063i	0.683112	−	0.730313i	$-0.260626\pi$
$332$		0			0
$333$	−4.17496	−	12.8492i	−0.228787	−	0.704132i
$334$		0			0
$335$	−14.8535	−	20.4440i	−0.811532	−	1.11698i
$336$		0			0
$337$	−26.3291			−1.43424			−0.717119	−	0.696951i	$-0.754540\pi$
$337$	−26.3291			−1.43424			−0.717119	+	0.696951i	$0.754540\pi$
$338$		0			0
$339$	30.9166	+	10.0454i	1.67916	+	0.545591i
$340$		0			0
$341$	0.612789	−	0.843432i	0.0331844	−	0.0456744i
$342$		0			0
$343$	−0.951057	+	0.309017i	−0.0513522	+	0.0166853i
$344$		0			0
$345$	45.4218	+	14.7584i	2.44543	+	0.794567i
$346$		0			0
$347$	11.3889	+	15.6755i	0.611388	+	0.841503i	0.996691	−	0.0812871i	$-0.0259031\pi$
$347$	11.3889	+	15.6755i	0.611388	+	0.841503i	−0.385303	+	0.922790i	$0.625903\pi$
$348$		0			0
$349$	9.87461	−	7.17432i	0.528576	−	0.384033i	−0.291249	−	0.956647i	$-0.594071\pi$
$349$	9.87461	−	7.17432i	0.528576	−	0.384033i	0.819825	+	0.572615i	$0.194071\pi$
$350$		0			0
$351$	−23.0119	−	16.7191i	−1.22828	−	0.892399i
$352$		0			0
$353$	2.11741	−	1.53839i	0.112698	−	0.0818801i	−0.530009	−	0.847992i	$-0.677811\pi$
$353$	2.11741	−	1.53839i	0.112698	−	0.0818801i	0.642707	+	0.766112i	$0.277811\pi$
$354$		0			0
$355$			41.8813i			2.22283i
$356$		0			0
$357$	−8.46317	+	2.74985i	−0.447918	+	0.145538i
$358$		0			0
$359$	1.03472	−	3.18454i	0.0546104	−	0.168074i	−0.920031	−	0.391845i	$-0.871837\pi$
$359$	1.03472	−	3.18454i	0.0546104	−	0.168074i	0.974642	+	0.223771i	$0.0718369\pi$
$360$		0			0
$361$	−0.555034	+	1.70822i	−0.0292123	+	0.0899063i
$362$		0			0
$363$	−18.1250	+	24.9469i	−0.951314	+	1.30937i
$364$		0			0
$365$	−3.82197	−	11.7628i	−0.200051	−	0.615694i
$366$		0			0
$367$	21.6390	+	15.7217i	1.12955	+	0.820665i	0.985629	−	0.168925i	$-0.0540294\pi$
$367$	21.6390	+	15.7217i	1.12955	+	0.820665i	0.143919	+	0.989589i	$0.454029\pi$
$368$		0			0
$369$	−20.4178	−	24.0843i	−1.06291	−	1.25378i
$370$		0			0
$371$	−1.02343	−	0.743566i	−0.0531339	−	0.0386040i
$372$		0			0
$373$	11.0333	+	33.9570i	0.571282	+	1.75823i	0.648504	+	0.761211i	$0.275395\pi$
$373$	11.0333	+	33.9570i	0.571282	+	1.75823i	−0.0772217	+	0.997014i	$0.524605\pi$
$374$		0			0
$375$	−17.0085	+	23.4103i	−0.878318	+	1.20890i
$376$		0			0
$377$	0.674472	−	2.07581i	0.0347371	−	0.106910i
$378$		0			0
$379$	6.83014	−	21.0210i	0.350841	−	1.07978i	−0.607541	−	0.794288i	$-0.707844\pi$
$379$	6.83014	−	21.0210i	0.350841	−	1.07978i	0.958382	−	0.285489i	$-0.0921560\pi$
$380$		0			0
$381$	22.9288	−	7.45003i	1.17468	−	0.381677i
$382$		0			0
$383$		−	1.35520i		−	0.0692474i	−0.999400	−	0.0346237i	$-0.988977\pi$
$383$		−	1.35520i		−	0.0692474i	0.999400	−	0.0346237i	$-0.0110233\pi$
$384$		0			0
$385$	0.652438	−	0.474024i	0.0332513	−	0.0241585i
$386$		0			0
$387$	−1.91524	−	1.39150i	−0.0973571	−	0.0707341i
$388$		0			0
$389$	19.7815	−	14.3721i	1.00296	−	0.728693i	0.0402387	−	0.999190i	$-0.487188\pi$
$389$	19.7815	−	14.3721i	1.00296	−	0.728693i	0.962721	+	0.270497i	$0.0871882\pi$
$390$		0			0
$391$	−8.78153	−	12.0867i	−0.444101	−	0.611253i
$392$		0			0
$393$	−5.91736	−	1.92267i	−0.298491	−	0.0969857i
$394$		0			0
$395$	41.5648	−	13.5052i	2.09135	−	0.679522i
$396$		0			0
$397$	3.70117	−	5.09423i	0.185756	−	0.255672i	−0.705975	−	0.708237i	$-0.749491\pi$
$397$	3.70117	−	5.09423i	0.185756	−	0.255672i	0.891731	+	0.452565i	$0.149491\pi$
$398$		0			0
$399$	12.2142	+	3.96862i	0.611473	+	0.198680i
$400$		0			0
$401$	24.2022			1.20860			0.604301	−	0.796756i	$-0.293453\pi$
$401$	24.2022			1.20860			0.604301	+	0.796756i	$0.293453\pi$
$402$		0			0
$403$	−14.2547	−	19.6199i	−0.710075	−	0.977334i
$404$		0			0
$405$	0.578932	+	1.78177i	0.0287674	+	0.0885369i
$406$		0			0
$407$		−	0.616040i		−	0.0305360i
$408$		0			0
$409$	−14.7138			−0.727549			−0.363774	−	0.931487i	$-0.618512\pi$
$409$	−14.7138			−0.727549			−0.363774	+	0.931487i	$0.618512\pi$
$410$		0			0
$411$	−15.3199			−0.755676
$412$		0			0
$413$		−	11.0773i		−	0.545078i
$414$		0			0
$415$	16.7679	+	51.6062i	0.823103	+	2.53325i
$416$		0			0
$417$	14.4677	+	19.9131i	0.708487	+	0.975149i
$418$		0			0
$419$	13.8648			0.677342			0.338671	−	0.940905i	$-0.390023\pi$
$419$	13.8648			0.677342			0.338671	+	0.940905i	$0.390023\pi$
$420$		0			0
$421$	−5.75433	−	1.86970i	−0.280449	−	0.0911234i	0.165415	−	0.986224i	$-0.447104\pi$
$421$	−5.75433	−	1.86970i	−0.280449	−	0.0911234i	−0.445864	+	0.895101i	$0.647104\pi$
$422$		0			0
$423$	21.7429	−	29.9265i	1.05717	−	1.45507i
$424$		0			0
$425$	23.6347	−	7.67938i	1.14645	−	0.372505i
$426$		0			0
$427$	11.6292	+	3.77856i	0.562777	+	0.182857i
$428$		0			0
$429$	−1.94667	−	2.67937i	−0.0939863	−	0.129361i
$430$		0			0
$431$	−5.11074	+	3.71317i	−0.246176	+	0.178857i	−0.704030	−	0.710170i	$-0.748618\pi$
$431$	−5.11074	+	3.71317i	−0.246176	+	0.178857i	0.457855	+	0.889027i	$0.348618\pi$
$432$		0			0
$433$	−28.8183	−	20.9377i	−1.38492	−	1.00620i	−0.996401	−	0.0847597i	$-0.972988\pi$
$433$	−28.8183	−	20.9377i	−1.38492	−	1.00620i	−0.388516	−	0.921442i	$-0.627012\pi$
$434$		0			0
$435$	−3.41019	+	2.47765i	−0.163506	+	0.118794i
$436$		0			0
$437$			21.5617i			1.03143i
$438$		0			0
$439$	9.11777	−	2.96254i	0.435168	−	0.141395i	−0.0832374	−	0.996530i	$-0.526526\pi$
$439$	9.11777	−	2.96254i	0.435168	−	0.141395i	0.518405	+	0.855135i	$0.326526\pi$
$440$		0			0
$441$	1.52379	−	4.68974i	0.0725614	−	0.223321i
$442$		0			0
$443$	0.0918636	−	0.282727i	0.00436457	−	0.0134328i	−0.948851	−	0.315726i	$-0.897752\pi$
$443$	0.0918636	−	0.282727i	0.00436457	−	0.0134328i	0.953215	+	0.302293i	$0.0977521\pi$
$444$		0			0
$445$	−16.8124	+	23.1403i	−0.796984	+	1.09695i
$446$		0			0
$447$	9.62521	+	29.6233i	0.455257	+	1.40114i
$448$		0			0
$449$	−18.8419	−	13.6894i	−0.889203	−	0.646044i	0.0464672	−	0.998920i	$-0.485204\pi$
$449$	−18.8419	−	13.6894i	−0.889203	−	0.646044i	−0.935670	+	0.352876i	$0.885204\pi$
$450$		0			0
$451$	−0.546072	−	1.33212i	−0.0257135	−	0.0627272i
$452$		0			0
$453$	−46.8138	−	34.0122i	−2.19950	−	1.59803i
$454$		0			0
$455$	−5.79708	−	17.8416i	−0.271771	−	0.836426i
$456$		0			0
$457$	14.9801	−	20.6184i	0.700741	−	0.964487i	−0.299206	−	0.954189i	$-0.596722\pi$
$457$	14.9801	−	20.6184i	0.700741	−	0.964487i	0.999947	−	0.0102988i	$-0.00327828\pi$
$458$		0			0
$459$	5.31019	−	16.3431i	0.247858	−	0.762830i
$460$		0			0
$461$	−6.53726	+	20.1196i	−0.304471	+	0.937064i	0.675404	+	0.737448i	$0.263969\pi$
$461$	−6.53726	+	20.1196i	−0.304471	+	0.937064i	−0.979874	+	0.199616i	$0.936031\pi$
$462$		0			0
$463$	9.94406	−	3.23102i	0.462140	−	0.150158i	−0.0686878	−	0.997638i	$-0.521881\pi$
$463$	9.94406	−	3.23102i	0.462140	−	0.150158i	0.530827	+	0.847480i	$0.321881\pi$
$464$		0			0
$465$			46.8358i			2.17196i
$466$		0			0
$467$	−24.4593	+	17.7707i	−1.13184	+	0.822330i	−0.985962	−	0.166972i	$-0.946601\pi$
$467$	−24.4593	+	17.7707i	−1.13184	+	0.822330i	−0.145879	+	0.989302i	$0.546601\pi$
$468$		0			0
$469$	−5.69989	−	4.14121i	−0.263197	−	0.191223i
$470$		0			0
$471$	−37.8797	+	27.5212i	−1.74540	+	1.26811i
$472$		0			0
$473$	−0.0634488	−	0.0873298i	−0.00291738	−	0.00401543i
$474$		0			0
$475$	−34.1099	−	11.0830i	−1.56507	−	0.508522i
$476$		0			0
$477$	5.93266	−	1.92764i	0.271638	−	0.0882605i
$478$		0			0
$479$	19.5030	−	26.8435i	0.891114	−	1.22651i	−0.0821029	−	0.996624i	$-0.526164\pi$
$479$	19.5030	−	26.8435i	0.891114	−	1.22651i	0.973217	−	0.229889i	$-0.0738364\pi$
$480$		0			0
$481$	−13.6289	−	4.42830i	−0.621425	−	0.201913i
$482$		0			0
$483$	13.3155			0.605876
$484$		0			0
$485$	16.1395	+	22.2141i	0.732858	+	1.00869i
$486$		0			0
$487$	−2.89232	−	8.90163i	−0.131063	−	0.403371i	0.863894	−	0.503674i	$-0.168019\pi$
$487$	−2.89232	−	8.90163i	−0.131063	−	0.403371i	−0.994957	+	0.100303i	$0.968019\pi$
$488$		0			0
$489$		−	47.0600i		−	2.12813i
$490$		0			0
$491$	12.9066			0.582466			0.291233	−	0.956652i	$-0.405935\pi$
$491$	12.9066			0.582466			0.291233	+	0.956652i	$0.405935\pi$
$492$		0			0
$493$	1.31861			0.0593871
$494$		0			0
$495$			3.97671i			0.178740i
$496$		0			0
$497$	3.60829	+	11.1052i	0.161854	+	0.498136i
$498$		0			0
$499$	−4.10437	−	5.64918i	−0.183737	−	0.252892i	0.707206	−	0.707008i	$-0.249955\pi$
$499$	−4.10437	−	5.64918i	−0.183737	−	0.252892i	−0.890943	+	0.454115i	$0.849955\pi$
$500$		0			0
$501$	16.8619			0.753334
$502$		0			0
$503$	41.0672	+	13.3435i	1.83110	+	0.594959i	0.999198	+	0.0400303i	$0.0127454\pi$
$503$	41.0672	+	13.3435i	1.83110	+	0.594959i	0.831898	+	0.554929i	$0.187255\pi$
$504$		0			0
$505$	−20.4763	+	28.1832i	−0.911185	+	1.25414i
$506$		0			0
$507$	−38.4511	+	12.4935i	−1.70767	+	0.554856i
$508$		0			0
$509$	16.8407	+	5.47188i	0.746452	+	0.242537i	0.657454	−	0.753495i	$-0.271633\pi$
$509$	16.8407	+	5.47188i	0.746452	+	0.242537i	0.0889982	+	0.996032i	$0.471633\pi$
$510$		0			0
$511$	−2.02686	−	2.78973i	−0.0896629	−	0.123410i
$512$		0			0
$513$	−20.0639	+	14.5773i	−0.885844	+	0.643604i
$514$		0			0
$515$	27.9193	+	20.2846i	1.23027	+	0.893846i
$516$		0			0
$517$	1.36457	−	0.991415i	0.0600135	−	0.0436024i
$518$		0			0
$519$			57.2011i			2.51085i
$520$		0			0
$521$	1.13142	−	0.367619i	0.0495682	−	0.0161057i	−0.284128	−	0.958786i	$-0.591704\pi$
$521$	1.13142	−	0.367619i	0.0495682	−	0.0161057i	0.333696	+	0.942681i	$0.391704\pi$
$522$		0			0
$523$	3.72967	−	11.4787i	0.163087	−	0.501930i	−0.835803	−	0.549029i	$-0.814998\pi$
$523$	3.72967	−	11.4787i	0.163087	−	0.501930i	0.998890	+	0.0470989i	$0.0149976\pi$
$524$		0			0
$525$	−6.84434	+	21.0647i	−0.298712	+	0.919340i
$526$		0			0
$527$	8.61173	−	11.8530i	0.375133	−	0.516326i
$528$		0			0
$529$	−0.199190	−	0.613043i	−0.00866043	−	0.0266541i
$530$		0			0
$531$	44.1909	+	32.1066i	1.91772	+	1.39331i
$532$		0			0
$533$	−33.3964	+	2.50524i	−1.44656	+	0.108514i
$534$		0			0
$535$	15.9053	+	11.5559i	0.687646	+	0.499604i
$536$		0			0
$537$	20.5055	+	63.1095i	0.884879	+	2.72338i
$538$		0			0
$539$	0.132160	−	0.181903i	0.00569253	−	0.00783510i
$540$		0			0
$541$	−3.68004	+	11.3260i	−0.158217	+	0.486943i	−0.998473	−	0.0552481i	$-0.982405\pi$
$541$	−3.68004	+	11.3260i	−0.158217	+	0.486943i	0.840255	+	0.542191i	$0.182405\pi$
$542$		0			0
$543$	−11.7358	+	36.1190i	−0.503631	+	1.55002i
$544$		0			0
$545$	48.8235	−	15.8637i	2.09137	−	0.679527i
$546$		0			0
$547$			24.3251i			1.04007i	0.854146	+	0.520033i	$0.174080\pi$
$547$			24.3251i			1.04007i	−0.854146	+	0.520033i	$0.825920\pi$
$548$		0			0
$549$	−48.7802	+	35.4409i	−2.08189	+	1.51258i
$550$		0			0
$551$	−1.53959	−	1.11857i	−0.0655885	−	0.0476529i
$552$		0			0
$553$	9.85774	−	7.16207i	0.419194	−	0.304562i
$554$		0			0
$555$	16.2672	+	22.3899i	0.690504	+	0.950398i
$556$		0			0
$557$	−37.6344	−	12.2282i	−1.59462	−	0.518124i	−0.628852	−	0.777525i	$-0.716475\pi$
$557$	−37.6344	−	12.2282i	−1.59462	−	0.518124i	−0.965770	+	0.259401i	$0.916475\pi$
$558$		0			0
$559$	−2.38812	+	0.775948i	−0.101007	+	0.0328191i
$560$		0			0
$561$	1.17605	−	1.61870i	0.0496530	−	0.0683415i
$562$		0			0
$563$	−29.1783	−	9.48062i	−1.22972	−	0.399560i	−0.379107	−	0.925353i	$-0.623769\pi$
$563$	−29.1783	−	9.48062i	−1.22972	−	0.399560i	−0.850613	+	0.525792i	$0.823769\pi$
$564$		0			0
$565$	−41.4018			−1.74179
$566$		0			0
$567$	0.307018	+	0.422574i	0.0128935	+	0.0177464i
$568$		0			0
$569$	8.12477	+	25.0055i	0.340608	+	1.04828i	0.963893	+	0.266290i	$0.0857977\pi$
$569$	8.12477	+	25.0055i	0.340608	+	1.04828i	−0.623285	+	0.781995i	$0.714202\pi$
$570$		0			0
$571$			34.5365i			1.44531i	0.691211	+	0.722653i	$0.257078\pi$
$571$			34.5365i			1.44531i	−0.691211	+	0.722653i	$0.742922\pi$
$572$		0			0
$573$	−69.8093			−2.91633
$574$		0			0
$575$	−37.1856			−1.55075
$576$		0			0
$577$		−	24.1300i		−	1.00455i	−0.864709	−	0.502273i	$-0.832497\pi$
$577$		−	24.1300i		−	1.00455i	0.864709	−	0.502273i	$-0.167503\pi$
$578$		0			0
$579$	7.82856	+	24.0938i	0.325344	+	1.00131i
$580$		0			0
$581$	8.89230	+	12.2392i	0.368915	+	0.507768i
$582$		0			0
$583$	0.284435			0.0117801
$584$		0			0
$585$	87.9783	+	28.5859i	3.63746	+	1.18188i
$586$		0			0
$587$	−13.0777	+	18.0000i	−0.539776	+	0.742938i	−0.988581	−	0.150692i	$-0.951850\pi$
$587$	−13.0777	+	18.0000i	−0.539776	+	0.742938i	0.448804	+	0.893630i	$0.351850\pi$
$588$		0			0
$589$	−20.1098	+	6.53409i	−0.828612	+	0.269232i
$590$		0			0
$591$	36.2652	+	11.7833i	1.49175	+	0.484700i
$592$		0			0
$593$	−11.8651	−	16.3309i	−0.487241	−	0.670630i	0.492635	−	0.870236i	$-0.336034\pi$
$593$	−11.8651	−	16.3309i	−0.487241	−	0.670630i	−0.979876	+	0.199606i	$0.936034\pi$
$594$		0			0
$595$	9.16892	−	6.66161i	0.375889	−	0.273099i
$596$		0			0
$597$	−10.6415	−	7.73150i	−0.435527	−	0.316429i
$598$		0			0
$599$	11.7519	−	8.53827i	0.480170	−	0.348864i	−0.321221	−	0.947004i	$-0.604093\pi$
$599$	11.7519	−	8.53827i	0.480170	−	0.348864i	0.801392	+	0.598140i	$0.204093\pi$
$600$		0			0
$601$		−	32.6497i		−	1.33181i	−0.746037	−	0.665905i	$-0.768046\pi$
$601$		−	32.6497i		−	1.33181i	0.746037	−	0.665905i	$-0.231954\pi$
$602$		0			0
$603$	33.0413	−	10.7358i	1.34555	−	0.437195i
$604$		0			0
$605$	12.1360	−	37.3507i	0.493398	−	1.51852i
$606$		0			0
$607$	5.36027	−	16.4972i	0.217566	−	0.669601i	−0.781395	−	0.624037i	$-0.785492\pi$
$607$	5.36027	−	16.4972i	0.217566	−	0.669601i	0.998961	−	0.0455639i	$-0.0145085\pi$
$608$		0			0
$609$	−0.690780	+	0.950777i	−0.0279918	+	0.0385274i
$610$		0			0
$611$	−12.1245	−	37.3155i	−0.490506	−	1.50962i
$612$		0			0
$613$	−9.33601	−	6.78301i	−0.377078	−	0.273963i	0.383062	−	0.923723i	$-0.374870\pi$
$613$	−9.33601	−	6.78301i	−0.377078	−	0.273963i	−0.760140	+	0.649760i	$0.774870\pi$
$614$		0			0
$615$	55.0231	+	33.9962i	2.21874	+	1.37086i
$616$		0			0
$617$	−20.8528	−	15.1504i	−0.839501	−	0.609933i	0.0827305	−	0.996572i	$-0.473636\pi$
$617$	−20.8528	−	15.1504i	−0.839501	−	0.609933i	−0.922231	+	0.386639i	$0.873636\pi$
$618$		0			0
$619$	1.35463	+	4.16914i	0.0544474	+	0.167572i	0.974582	−	0.224030i	$-0.0719212\pi$
$619$	1.35463	+	4.16914i	0.0544474	+	0.167572i	−0.920135	+	0.391601i	$0.871921\pi$
$620$		0			0
$621$	−15.1139	+	20.8025i	−0.606501	+	0.834777i
$622$		0			0
$623$	−2.46430	+	7.58433i	−0.0987300	+	0.303860i
$624$		0			0
$625$	−0.763206	+	2.34891i	−0.0305282	+	0.0939563i
$626$		0			0
$627$	−2.74628	+	0.892321i	−0.109676	+	0.0356359i
$628$		0			0
$629$		−	8.65742i		−	0.345194i
$630$		0			0
$631$	35.8654	−	26.0577i	1.42778	−	1.03734i	0.437354	−	0.899289i	$-0.355916\pi$
$631$	35.8654	−	26.0577i	1.42778	−	1.03734i	0.990425	−	0.138053i	$-0.0440843\pi$
$632$		0			0
$633$	22.5464	+	16.3809i	0.896137	+	0.651082i
$634$		0			0
$635$	−24.8409	+	18.0480i	−0.985781	+	0.716212i
$636$		0			0
$637$	−3.07430	−	4.23140i	−0.121808	−	0.167654i
$638$		0			0
$639$	−54.7606	−	17.7928i	−2.16630	−	0.703872i
$640$		0			0
$641$	15.5795	−	5.06209i	0.615353	−	0.199940i	0.0152771	−	0.999883i	$-0.495137\pi$
$641$	15.5795	−	5.06209i	0.615353	−	0.199940i	0.600076	+	0.799943i	$0.295137\pi$
$642$		0			0
$643$	1.76286	−	2.42637i	0.0695205	−	0.0956867i	−0.772841	−	0.634600i	$-0.781165\pi$
$643$	1.76286	−	2.42637i	0.0695205	−	0.0956867i	0.842361	+	0.538913i	$0.181165\pi$
$644$		0			0
$645$	4.61207	+	1.49855i	0.181600	+	0.0590055i
$646$		0			0
$647$	46.5087			1.82845			0.914223	−	0.405211i	$-0.132802\pi$
$647$	46.5087			1.82845			0.914223	+	0.405211i	$0.132802\pi$
$648$		0			0
$649$	1.46397	+	2.01499i	0.0574660	+	0.0790952i
$650$		0			0
$651$	4.03515	+	12.4189i	0.158150	+	0.486736i
$652$		0			0
$653$			9.17878i			0.359193i	0.983740	+	0.179597i	$0.0574792\pi$
$653$			9.17878i			0.359193i	−0.983740	+	0.179597i	$0.942521\pi$
$654$		0			0
$655$	7.92420			0.309624
$656$		0			0
$657$	17.0038			0.663383
$658$		0			0
$659$		−	37.4362i		−	1.45831i	−0.684349	−	0.729154i	$-0.739914\pi$
$659$		−	37.4362i		−	1.45831i	0.684349	−	0.729154i	$-0.260086\pi$
$660$		0			0
$661$	−3.78564	−	11.6510i	−0.147244	−	0.453172i	0.850048	−	0.526705i	$-0.176573\pi$
$661$	−3.78564	−	11.6510i	−0.147244	−	0.453172i	−0.997293	+	0.0735330i	$0.976573\pi$
$662$		0			0
$663$	−27.3572	−	37.6540i	−1.06247	−	1.46236i
$664$		0			0
$665$	−16.3565			−0.634279
$666$		0			0
$667$	−1.87652	−	0.609717i	−0.0726590	−	0.0236084i
$668$		0			0
$669$	31.2265	−	42.9796i	1.20729	−	1.66169i
$670$		0			0
$671$	−2.61476	+	0.849586i	−0.100942	+	0.0327979i
$672$		0			0
$673$	−1.86293	−	0.605304i	−0.0718108	−	0.0233328i	0.272891	−	0.962045i	$-0.412020\pi$
$673$	−1.86293	−	0.605304i	−0.0718108	−	0.0233328i	−0.344702	+	0.938712i	$0.612020\pi$
$674$		0			0
$675$	−25.1402	−	34.6025i	−0.967648	−	1.33185i
$676$		0			0
$677$	−13.8596	+	10.0696i	−0.532668	+	0.387006i	−0.821355	−	0.570418i	$-0.806781\pi$
$677$	−13.8596	+	10.0696i	−0.532668	+	0.387006i	0.288687	+	0.957424i	$0.406781\pi$
$678$		0			0
$679$	6.19341	+	4.49977i	0.237681	+	0.172685i
$680$		0			0
$681$	43.5986	−	31.6762i	1.67070	−	1.21384i
$682$		0			0
$683$		−	15.3586i		−	0.587680i	−0.955855	−	0.293840i	$-0.905067\pi$
$683$		−	15.3586i		−	0.587680i	0.955855	−	0.293840i	$-0.0949333\pi$
$684$		0			0
$685$	18.5565	−	6.02938i	0.709008	−	0.230371i
$686$		0			0
$687$	−10.8304	+	33.3325i	−0.413205	+	1.27171i
$688$		0			0
$689$	2.04461	−	6.29266i	0.0778934	−	0.239731i
$690$		0			0
$691$	12.1798	−	16.7641i	0.463342	−	0.637735i	−0.511856	−	0.859071i	$-0.671042\pi$
$691$	12.1798	−	16.7641i	0.463342	−	0.637735i	0.975198	+	0.221336i	$0.0710418\pi$
$692$		0			0
$693$	0.342615	+	1.05446i	0.0130149	+	0.0400556i
$694$		0			0
$695$	−25.3614	−	18.4261i	−0.962012	−	0.698943i
$696$		0			0
$697$	−7.67413	−	18.7208i	−0.290679	−	0.709100i
$698$		0			0
$699$	−26.3441	−	19.1401i	−0.996424	−	0.723945i
$700$		0			0
$701$	−2.35289	−	7.24147i	−0.0888676	−	0.273506i	0.896739	−	0.442559i	$-0.145929\pi$
$701$	−2.35289	−	7.24147i	−0.0888676	−	0.273506i	−0.985607	+	0.169053i	$0.945929\pi$
$702$		0			0
$703$	−7.34409	+	10.1083i	−0.276987	+	0.381241i
$704$		0			0
$705$	−23.4155	+	72.0656i	−0.881881	+	2.71415i
$706$		0			0
$707$	−3.00134	+	9.23718i	−0.112877	+	0.347400i
$708$		0			0
$709$	45.4560	−	14.7696i	1.70714	−	0.554682i	0.717284	−	0.696780i	$-0.245385\pi$
$709$	45.4560	−	14.7696i	1.70714	−	0.554682i	0.989853	+	0.142098i	$0.0453848\pi$
$710$		0			0
$711$			60.0844i			2.25334i
$712$		0			0
$713$	−17.7362	+	12.8861i	−0.664225	+	0.482588i
$714$		0			0
$715$	3.41245	+	2.47929i	0.127618	+	0.0927201i
$716$		0			0
$717$	−14.8970	+	10.8233i	−0.556337	+	0.404203i
$718$		0			0
$719$	−7.56657	−	10.4145i	−0.282185	−	0.388395i	0.644271	−	0.764797i	$-0.277161\pi$
$719$	−7.56657	−	10.4145i	−0.282185	−	0.388395i	−0.926456	+	0.376403i	$0.877161\pi$
$720$		0			0
$721$	9.15069	+	2.97324i	0.340789	+	0.110729i
$722$		0			0
$723$	70.6415	−	22.9528i	2.62718	−	0.853624i
$724$		0			0
$725$	1.92911	−	2.65519i	0.0716453	−	0.0986113i
$726$		0			0
$727$	−34.9096	−	11.3428i	−1.29472	−	0.420681i	−0.420981	−	0.907069i	$-0.638314\pi$
$727$	−34.9096	−	11.3428i	−1.29472	−	0.420681i	−0.873743	+	0.486388i	$0.838314\pi$
$728$		0			0
$729$	43.3711			1.60634
$730$		0			0
$731$	−0.891666	−	1.22727i	−0.0329795	−	0.0453924i
$732$		0			0
$733$	−6.00841	−	18.4920i	−0.221926	−	0.683017i	−0.998589	−	0.0531013i	$-0.983089\pi$
$733$	−6.00841	−	18.4920i	−0.221926	−	0.683017i	0.776663	−	0.629916i	$-0.216911\pi$
$734$		0			0
$735$			10.1010i			0.372583i
$736$		0			0
$737$	1.58413			0.0583521
$738$		0			0
$739$	19.9961			0.735569			0.367784	−	0.929911i	$-0.380116\pi$
$739$	19.9961			0.735569			0.367784	+	0.929911i	$0.380116\pi$
$740$		0			0
$741$			67.1714i			2.46760i
$742$		0			0
$743$	15.4902	+	47.6740i	0.568281	+	1.74899i	0.657996	+	0.753021i	$0.271404\pi$
$743$	15.4902	+	47.6740i	0.568281	+	1.74899i	−0.0897153	+	0.995967i	$0.528596\pi$
$744$		0			0
$745$	−23.3174	−	32.0937i	−0.854284	−	1.17582i
$746$		0			0
$747$	−74.5999			−2.72947
$748$		0			0
$749$	5.21303	+	1.69382i	0.190480	+	0.0618907i
$750$		0			0
$751$	12.5232	−	17.2368i	0.456980	−	0.628979i	−0.516899	−	0.856046i	$-0.672914\pi$
$751$	12.5232	−	17.2368i	0.456980	−	0.628979i	0.973879	+	0.227068i	$0.0729138\pi$
$752$		0			0
$753$	62.2468	−	20.2252i	2.26840	−	0.737048i
$754$		0			0
$755$	70.0900	+	22.7736i	2.55084	+	0.828817i
$756$		0			0
$757$	−3.08626	−	4.24787i	−0.112172	−	0.154391i	0.749240	−	0.662299i	$-0.230419\pi$
$757$	−3.08626	−	4.24787i	−0.112172	−	0.154391i	−0.861412	+	0.507908i	$0.830419\pi$
$758$		0			0
$759$	−2.42212	+	1.75978i	−0.0879176	+	0.0638758i
$760$		0			0
$761$	21.4646	+	15.5949i	0.778090	+	0.565315i	0.904405	−	0.426675i	$-0.140315\pi$
$761$	21.4646	+	15.5949i	0.778090	+	0.565315i	−0.126315	+	0.991990i	$0.540315\pi$
$762$		0			0
$763$	11.5792	−	8.41281i	0.419196	−	0.304564i
$764$		0			0
$765$			55.8860i			2.02056i
$766$		0			0
$767$	55.1019	−	17.9037i	1.98961	−	0.646465i
$768$		0			0
$769$	−10.4719	+	32.2292i	−0.377626	+	1.16221i	0.564063	+	0.825731i	$0.309237\pi$
$769$	−10.4719	+	32.2292i	−0.377626	+	1.16221i	−0.941690	+	0.336483i	$0.890763\pi$
$770$		0			0
$771$	12.1729	−	37.4642i	0.438395	−	1.34924i
$772$		0			0
$773$	−13.8034	+	18.9987i	−0.496473	+	0.683337i	−0.981565	−	0.191126i	$-0.938786\pi$
$773$	−13.8034	+	18.9987i	−0.496473	+	0.683337i	0.485092	+	0.874463i	$0.338786\pi$
$774$		0			0
$775$	−11.2688	−	34.6817i	−0.404786	−	1.24580i
$776$		0			0
$777$	6.24240	+	4.53537i	0.223945	+	0.162706i
$778$		0			0
$779$	−6.92062	+	28.3680i	−0.247957	+	1.01639i
$780$		0			0
$781$	−2.12402	−	1.54319i	−0.0760034	−	0.0552197i
$782$		0			0
$783$	−0.701301	−	2.15838i	−0.0250625	−	0.0771343i
$784$		0			0
$785$	35.0511	−	48.2437i	1.25103	−	1.72189i
$786$		0			0
$787$	6.24017	−	19.2053i	0.222438	−	0.684594i	−0.776104	−	0.630606i	$-0.782807\pi$
$787$	6.24017	−	19.2053i	0.222438	−	0.684594i	0.998542	−	0.0539884i	$-0.0171934\pi$
$788$		0			0
$789$	−5.44654	+	16.7627i	−0.193902	+	0.596769i
$790$		0			0
$791$	−10.9780	+	3.56698i	−0.390334	+	0.126827i
$792$		0			0
$793$			63.9544i			2.27109i
$794$		0			0
$795$	−10.3377	+	7.51080i	−0.366641	+	0.266381i
$796$		0			0
$797$	−2.41203	−	1.75244i	−0.0854385	−	0.0620747i	0.544246	−	0.838926i	$-0.316816\pi$
$797$	−2.41203	−	1.75244i	−0.0854385	−	0.0620747i	−0.629684	+	0.776851i	$0.716816\pi$
$798$		0			0
$799$	19.1767	−	13.9327i	0.678422	−	0.492903i
$800$		0			0
$801$	−23.1138	−	31.8134i	−0.816687	−	1.12407i
$802$		0			0
$803$	0.737382	+	0.239590i	0.0260216	+	0.00845494i
$804$		0			0
$805$	−16.1286	+	5.24051i	−0.568460	+	0.184704i
$806$		0			0
$807$	35.6028	−	49.0031i	1.25328	−	1.72499i
$808$		0			0
$809$	2.85232	+	0.926774i	0.100282	+	0.0325836i	0.358728	−	0.933442i	$-0.383210\pi$
$809$	2.85232	+	0.926774i	0.100282	+	0.0325836i	−0.258446	+	0.966026i	$0.583210\pi$
$810$		0			0
$811$	12.6202			0.443156			0.221578	−	0.975143i	$-0.428879\pi$
$811$	12.6202			0.443156			0.221578	+	0.975143i	$0.428879\pi$
$812$		0			0
$813$	15.3542	+	21.1332i	0.538495	+	0.741175i
$814$		0			0
$815$	18.5212	+	57.0023i	0.648768	+	1.99670i
$816$		0			0
$817$			2.18935i			0.0765955i
$818$		0			0
$819$	25.7911			0.901213
$820$		0			0
$821$	−35.3732			−1.23453			−0.617267	−	0.786754i	$-0.711760\pi$
$821$	−35.3732			−1.23453			−0.617267	+	0.786754i	$0.711760\pi$
$822$		0			0
$823$		−	21.0341i		−	0.733203i	−0.930378	−	0.366602i	$-0.880521\pi$
$823$		−	21.0341i		−	0.733203i	0.930378	−	0.366602i	$-0.119479\pi$
$824$		0			0
$825$	−1.53891	−	4.73628i	−0.0535780	−	0.164896i
$826$		0			0
$827$	−11.8384	−	16.2941i	−0.411661	−	0.566603i	0.551962	−	0.833870i	$-0.313879\pi$
$827$	−11.8384	−	16.2941i	−0.411661	−	0.566603i	−0.963623	+	0.267267i	$0.913879\pi$
$828$		0			0
$829$	42.6755			1.48218			0.741091	−	0.671405i	$-0.234309\pi$
$829$	42.6755			1.48218			0.741091	+	0.671405i	$0.234309\pi$
$830$		0			0
$831$	52.5912	+	17.0879i	1.82437	+	0.592773i
$832$		0			0
$833$	1.85729	−	2.55634i	0.0643512	−	0.0885718i
$834$		0			0
$835$	−20.4243	+	6.63625i	−0.706811	+	0.229657i
$836$		0			0
$837$	−23.9820	−	7.79221i	−0.828938	−	0.269338i
$838$		0			0
$839$	28.4428	+	39.1482i	0.981955	+	1.35155i	0.935769	+	0.352612i	$0.114707\pi$
$839$	28.4428	+	39.1482i	0.981955	+	1.35155i	0.0461856	+	0.998933i	$0.485293\pi$
$840$		0			0
$841$	−23.3206	+	16.9434i	−0.804159	+	0.584256i
$842$		0			0
$843$	−68.5666	−	49.8165i	−2.36156	−	1.71577i
$844$		0			0
$845$	41.6575	−	30.2660i	1.43306	−	1.04118i
$846$		0			0
$847$		−	10.9494i		−	0.376227i
$848$		0			0
$849$	−62.2889	+	20.2389i	−2.13775	+	0.694597i
$850$		0			0
$851$	−4.00315	+	12.3204i	−0.137226	+	0.422339i
$852$		0			0
$853$	−15.2637	+	46.9769i	−0.522620	+	1.60846i	0.246355	+	0.969180i	$0.420767\pi$
$853$	−15.2637	+	46.9769i	−0.522620	+	1.60846i	−0.768975	+	0.639279i	$0.779233\pi$
$854$		0			0
$855$	47.4081	−	65.2516i	1.62132	−	2.23156i
$856$		0			0
$857$	15.2874	+	47.0498i	0.522208	+	1.60719i	0.769773	+	0.638318i	$0.220370\pi$
$857$	15.2874	+	47.0498i	0.522208	+	1.60719i	−0.247565	+	0.968871i	$0.579630\pi$
$858$		0			0
$859$	−19.7120	−	14.3216i	−0.672564	−	0.488647i	0.198318	−	0.980138i	$-0.436452\pi$
$859$	−19.7120	−	14.3216i	−0.672564	−	0.488647i	−0.870883	+	0.491491i	$0.836452\pi$
$860$		0			0
$861$	17.5188	+	4.27386i	0.597039	+	0.145653i
$862$		0			0
$863$	−7.33000	−	5.32556i	−0.249516	−	0.181284i	0.455996	−	0.889982i	$-0.349283\pi$
$863$	−7.33000	−	5.32556i	−0.249516	−	0.181284i	−0.705512	+	0.708698i	$0.749283\pi$
$864$		0			0
$865$	−22.5123	−	69.2858i	−0.765442	−	2.35579i
$866$		0			0
$867$	−11.6132	+	15.9842i	−0.394404	+	0.542851i
$868$		0			0
$869$	−0.846610	+	2.60560i	−0.0287193	+	0.0883888i
$870$		0			0
$871$	11.3872	−	35.0463i	0.385842	−	1.18750i
$872$		0			0
$873$	−35.9022	+	11.6653i	−1.21510	+	0.394811i
$874$		0			0
$875$		−	10.2750i		−	0.347359i
$876$		0			0
$877$	14.1004	−	10.2445i	0.476136	−	0.345933i	−0.323692	−	0.946163i	$-0.604924\pi$
$877$	14.1004	−	10.2445i	0.476136	−	0.345933i	0.799828	+	0.600230i	$0.204924\pi$
$878$		0			0
$879$	10.1807	+	7.39671i	0.343386	+	0.249485i
$880$		0			0
$881$	26.8614	−	19.5160i	0.904984	−	0.657510i	−0.0347569	−	0.999396i	$-0.511066\pi$
$881$	26.8614	−	19.5160i	0.904984	−	0.657510i	0.939741	+	0.341886i	$0.111066\pi$
$882$		0			0
$883$	15.7369	+	21.6599i	0.529588	+	0.728915i	0.987068	−	0.160305i	$-0.0512477\pi$
$883$	15.7369	+	21.6599i	0.529588	+	0.728915i	−0.457480	+	0.889220i	$0.651248\pi$
$884$		0			0
$885$	−106.416	−	34.5766i	−3.57713	−	1.16228i
$886$		0			0
$887$	11.6502	−	3.78538i	0.391176	−	0.127101i	−0.106824	−	0.994278i	$-0.534068\pi$
$887$	11.6502	−	3.78538i	0.391176	−	0.127101i	0.498000	+	0.867177i	$0.334068\pi$
$888$		0			0
$889$	−5.03185	+	6.92575i	−0.168763	+	0.232282i
$890$		0			0
$891$	−0.111695	−	0.0362918i	−0.00374192	−	0.00121582i
$892$		0			0
$893$	−34.2095			−1.14478
$894$		0			0
$895$	−49.6754	−	68.3723i	−1.66046	−	2.28543i
$896$		0			0
$897$	21.5212	+	66.2355i	0.718572	+	2.21154i
$898$		0			0
$899$		−	1.93493i		−	0.0645337i
$900$		0			0
$901$	3.99725			0.133168
$902$		0			0
$903$	1.35204			0.0449931
$904$		0			0
$905$		−	48.3686i		−	1.60783i
$906$		0			0
$907$	−15.4776	−	47.6352i	−0.513926	−	1.58170i	−0.785227	−	0.619207i	$-0.787454\pi$
$907$	−15.4776	−	47.6352i	−0.513926	−	1.58170i	0.271301	−	0.962494i	$-0.412546\pi$
$908$		0			0
$909$	−28.1510	−	38.7466i	−0.933711	−	1.28514i
$910$		0			0
$911$	−42.3036			−1.40158			−0.700790	−	0.713367i	$-0.747169\pi$
$911$	−42.3036			−1.40158			−0.700790	+	0.713367i	$0.747169\pi$
$912$		0			0
$913$	−3.23507	−	1.05114i	−0.107065	−	0.0347876i
$914$		0			0
$915$	72.5987	−	99.9235i	2.40004	−	3.30337i
$916$		0			0
$917$	2.10117	−	0.682712i	0.0693868	−	0.0225451i
$918$		0			0
$919$	14.7521	+	4.79326i	0.486628	+	0.158115i	0.542047	−	0.840348i	$-0.317650\pi$
$919$	14.7521	+	4.79326i	0.486628	+	0.158115i	−0.0554192	+	0.998463i	$0.517650\pi$
$920$		0			0
$921$	25.3831	+	34.9368i	0.836400	+	1.15121i
$922$		0			0
$923$	−49.4088	+	35.8976i	−1.62631	+	1.18158i
$924$		0			0
$925$	−17.4329	−	12.6657i	−0.573189	−	0.416446i
$926$		0			0
$927$	−38.3837	+	27.8874i	−1.26069	+	0.915943i
$928$		0			0
$929$			0.644184i			0.0211350i	0.999944	+	0.0105675i	$0.00336380\pi$
$929$			0.644184i			0.0211350i	−0.999944	+	0.0105675i	$0.996636\pi$
$930$		0			0
$931$	−4.33708	+	1.40920i	−0.142142	+	0.0461848i
$932$		0			0
$933$	9.14571	−	28.1476i	0.299417	−	0.921512i
$934$		0			0
$935$	−0.787452	+	2.42353i	−0.0257524	+	0.0792579i
$936$		0			0
$937$	−34.5107	+	47.4998i	−1.12741	+	1.55175i	−0.334525	+	0.942387i	$0.608576\pi$
$937$	−34.5107	+	47.4998i	−1.12741	+	1.55175i	−0.792889	+	0.609365i	$0.791424\pi$
$938$		0			0
$939$	−24.9660	−	76.8376i	−0.814736	−	2.50750i
$940$		0			0
$941$	15.3822	+	11.1758i	0.501446	+	0.364322i	0.809569	−	0.587025i	$-0.199701\pi$
$941$	15.3822	+	11.1758i	0.501446	+	0.364322i	−0.308123	+	0.951347i	$0.599701\pi$
$942$		0			0
$943$	2.26471	+	30.1901i	0.0737492	+	0.983125i
$944$		0			0
$945$	−15.7807	−	11.4653i	−0.513345	−	0.372967i
$946$		0			0
$947$	−1.36525	−	4.20181i	−0.0443647	−	0.136540i	0.926421	−	0.376490i	$-0.122869\pi$
$947$	−1.36525	−	4.20181i	−0.0443647	−	0.136540i	−0.970785	+	0.239950i	$0.922869\pi$
$948$		0			0
$949$	10.6011	−	14.5911i	0.344126	−	0.473648i
$950$		0			0
$951$	13.0604	−	40.1957i	0.423511	−	1.30343i
$952$		0			0
$953$	−5.67452	+	17.4644i	−0.183816	+	0.565727i	−0.999926	−	0.0121696i	$-0.996126\pi$
$953$	−5.67452	+	17.4644i	−0.183816	+	0.565727i	0.816110	+	0.577896i	$0.196126\pi$
$954$		0			0
$955$	84.5578	−	27.4745i	2.73623	−	0.889054i
$956$		0			0
$957$		−	0.264242i		−	0.00854174i
$958$		0			0
$959$	4.40096	−	3.19749i	0.142114	−	0.103252i
$960$		0			0
$961$	7.68630	+	5.58443i	0.247945	+	0.180143i
$962$		0			0
$963$	−21.8667	+	15.8871i	−0.704646	+	0.511955i
$964$		0			0
$965$	−18.9650	−	26.1031i	−0.610504	−	0.840287i
$966$		0			0
$967$	10.6199	+	3.45061i	0.341512	+	0.110964i	0.474752	−	0.880120i	$-0.342538\pi$
$967$	10.6199	+	3.45061i	0.341512	+	0.110964i	−0.133239	+	0.991084i	$0.542538\pi$
$968$		0			0
$969$	−38.5944	+	12.5401i	−1.23983	+	0.402845i
$970$		0			0
$971$	19.5001	−	26.8395i	0.625787	−	0.861322i	−0.371971	−	0.928244i	$-0.621318\pi$
$971$	19.5001	−	26.8395i	0.625787	−	0.861322i	0.997758	+	0.0669224i	$0.0213180\pi$
$972$		0			0
$973$	−8.31230	−	2.70083i	−0.266480	−	0.0865847i
$974$		0			0
$975$	−115.845			−3.71000
$976$		0			0
$977$	−16.6750	−	22.9512i	−0.533482	−	0.734275i	0.454174	−	0.890913i	$-0.349934\pi$
$977$	−16.6750	−	22.9512i	−0.533482	−	0.734275i	−0.987656	+	0.156638i	$0.949934\pi$
$978$		0			0
$979$	−0.554082	−	1.70529i	−0.0177086	−	0.0545013i
$980$		0			0
$981$			70.5772i			2.25336i
$982$		0			0
$983$	18.4078			0.587119			0.293559	−	0.955941i	$-0.405160\pi$
$983$	18.4078			0.587119			0.293559	+	0.955941i	$0.405160\pi$
$984$		0			0
$985$	−48.5644			−1.54739
$986$		0			0
$987$			21.1262i			0.672455i
$988$		0			0
$989$	0.701450	+	2.15884i	0.0223048	+	0.0686472i
$990$		0			0
$991$	−21.1531	−	29.1147i	−0.671950	−	0.924860i	0.327852	−	0.944729i	$-0.393675\pi$
$991$	−21.1531	−	29.1147i	−0.671950	−	0.924860i	−0.999803	+	0.0198687i	$0.993675\pi$
$992$		0			0
$993$	−74.8375			−2.37490
$994$		0			0
$995$	15.9325	+	5.17680i	0.505096	+	0.164116i
$996$		0			0
$997$	24.4321	−	33.6280i	0.773774	−	1.06501i	−0.222168	−	0.975008i	$-0.571313\pi$
$997$	24.4321	−	33.6280i	0.773774	−	1.06501i	0.995942	−	0.0899996i	$-0.0286866\pi$
$998$		0			0
$999$	−14.1710	+	4.60445i	−0.448352	+	0.145678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.2	✓	80
41.4	even	10	inner	1148.2.ba.a.701.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.2	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.19	yes	80	41.4	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.81622i q^{3} +(1.10836 + 3.41119i) q^{5} +(0.587785 + 0.809017i) q^{7} -4.93108 q^{9} +O(q^{10})\)	\(q-2.81622i q^{3} +(1.10836 + 3.41119i) q^{5} +(0.587785 + 0.809017i) q^{7} -4.93108 q^{9} +(-0.213839 - 0.0694806i) q^{11} +(-3.07430 + 4.23140i) q^{13} +(9.60667 - 3.12140i) q^{15} +(-3.00515 - 0.976434i) q^{17} +(2.68046 + 3.68934i) q^{19} +(2.27837 - 1.65533i) q^{21} +(3.82515 + 2.77914i) q^{23} +(-6.36269 + 4.62277i) q^{25} +5.43835i q^{27} +(-0.396882 + 0.128955i) q^{29} +(-1.43283 + 4.40979i) q^{31} +(-0.195673 + 0.602218i) q^{33} +(-2.10823 + 2.90174i) q^{35} +(0.846662 + 2.60576i) q^{37} +(11.9166 + 8.65788i) q^{39} +(4.14062 + 4.88418i) q^{41} +(0.388402 + 0.282190i) q^{43} +(-5.46544 - 16.8209i) q^{45} +(-4.40935 + 6.06894i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-2.74985 + 8.46317i) q^{51} +(-1.20312 + 0.390916i) q^{53} -0.806457i q^{55} +(10.3900 - 7.54877i) q^{57} +(-8.96171 - 6.51107i) q^{59} +(9.89239 - 7.18725i) q^{61} +(-2.89842 - 3.98933i) q^{63} +(-17.8416 - 5.79708i) q^{65} +(-6.70062 + 2.17716i) q^{67} +(7.82666 - 10.7725i) q^{69} +(11.1052 + 3.60829i) q^{71} -3.44830 q^{73} +(13.0187 + 17.9187i) q^{75} +(-0.0694806 - 0.213839i) q^{77} -12.1848i q^{79} +0.522330 q^{81} +15.1285 q^{83} -11.3334i q^{85} +(0.363165 + 1.11771i) q^{87} +(4.68737 + 6.45161i) q^{89} -5.23030 q^{91} +(12.4189 + 4.03515i) q^{93} +(-9.61413 + 13.2327i) q^{95} +(7.28078 - 2.36567i) q^{97} +(1.05446 + 0.342615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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