LMFDB - Embedded newform 1100.2.n.e.801.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(201,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1100.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.n (of order $5$, 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:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 13 x^{14} - 15 x^{13} + 59 x^{12} + 4 x^{11} + 369 x^{10} + 618 x^{9} + 1481 x^{8} + \cdots + 400 $ x^16 - 3x^15 + 13x^14 - 15x^13 + 59x^12 + 4x^11 + 369x^10 + 618x^9 + 1481x^8 + 1013x^7 + 1564x^6 + 276x^5 + 1041x^4 + 220x^3 + 240x^2 + 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			801.4
Root			$0.927142 + 2.85345i$ of defining polynomial
Character	$\chi$	$=$	1100.801
Dual form			1100.2.n.e.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.42729 - 1.76353i) q^{3} +(-1.36631 - 0.992679i) q^{7} +(1.85465 - 5.70802i) q^{9} +(2.77267 + 1.81998i) q^{11} +(1.14660 - 3.52887i) q^{13} +(1.19594 + 3.68071i) q^{17} +(5.21062 - 3.78574i) q^{19} -5.06704 q^{21} -7.43878 q^{23} +(-2.78307 - 8.56540i) q^{27} +(2.55959 + 1.85965i) q^{29} +(0.787699 - 2.42429i) q^{31} +(9.93965 - 0.472068i) q^{33} +(-5.29843 - 3.84954i) q^{37} +(-3.44014 - 10.5877i) q^{39} +(-6.93840 + 5.04104i) q^{41} -3.49875 q^{43} +(3.44003 - 2.49933i) q^{47} +(-1.28174 - 3.94479i) q^{49} +(9.39392 + 6.82509i) q^{51} +(3.00470 - 9.24750i) q^{53} +(5.97143 - 18.3782i) q^{57} +(2.33853 + 1.69904i) q^{59} +(1.93043 + 5.94126i) q^{61} +(-8.20025 + 5.95783i) q^{63} +10.5387 q^{67} +(-18.0561 + 13.1185i) q^{69} +(2.85383 + 8.78318i) q^{71} +(2.96007 + 2.15062i) q^{73} +(-1.98166 - 5.23901i) q^{77} +(-5.23846 + 16.1223i) q^{79} +(-7.29404 - 5.29943i) q^{81} +(3.71779 + 11.4422i) q^{83} +9.49240 q^{87} -15.5881 q^{89} +(-5.06965 + 3.68331i) q^{91} +(-2.36333 - 7.27358i) q^{93} +(-2.07343 + 6.38135i) q^{97} +(15.5308 - 12.4510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - 5 q^{11} - q^{13} - 8 q^{17} + 13 q^{19} - 6 q^{21} - 16 q^{23} - 37 q^{27} - 7 q^{29} + 2 q^{31} + 14 q^{33} - 8 q^{37} - 17 q^{39} - 15 q^{41} - 18 q^{47} - 24 q^{49} + 13 q^{51} - 6 q^{53}+ \cdots + 40 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - 5 * q^11 - q^13 - 8 * q^17 + 13 * q^19 - 6 * q^21 - 16 * q^23 - 37 * q^27 - 7 * q^29 + 2 * q^31 + 14 * q^33 - 8 * q^37 - 17 * q^39 - 15 * q^41 - 18 * q^47 - 24 * q^49 + 13 * q^51 - 6 * q^53 - 31 * q^57 + 6 * q^59 + 24 * q^61 + 5 * q^63 + 18 * q^67 - 53 * q^69 + 36 * q^71 - 9 * q^73 + 45 * q^77 - 45 * q^79 + 17 * q^81 - 14 * q^83 + 18 * q^87 + 18 * q^89 + 38 * q^91 - 29 * q^93 + 49 * q^97 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	2.42729	−	1.76353i	1.40140	−	1.01817i	0.406892	−	0.913476i	$-0.366612\pi$
$3$	2.42729	−	1.76353i	1.40140	−	1.01817i	0.994504	−	0.104698i	$-0.0333875\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.36631	−	0.992679i	−0.516415	−	0.375197i	0.298837	−	0.954304i	$-0.403401\pi$
$7$	−1.36631	−	0.992679i	−0.516415	−	0.375197i	−0.815252	+	0.579107i	$0.803401\pi$
$8$		0			0
$9$	1.85465	−	5.70802i	0.618216	−	1.90267i
$10$		0			0
$11$	2.77267	+	1.81998i	0.835991	+	0.548744i
$11$	2.77267	+	1.81998i	0.835991	+	0.548744i
$12$		0			0
$13$	1.14660	−	3.52887i	0.318010	−	0.978733i	−0.656488	−	0.754336i	$-0.727959\pi$
$13$	1.14660	−	3.52887i	0.318010	−	0.978733i	0.974498	−	0.224397i	$-0.0720412\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.19594	+	3.68071i	0.290057	+	0.892704i	0.984837	+	0.173481i	$0.0555017\pi$
$17$	1.19594	+	3.68071i	0.290057	+	0.892704i	−0.694780	+	0.719222i	$0.744498\pi$
$18$		0			0
$19$	5.21062	−	3.78574i	1.19540	−	0.868508i	0.201575	−	0.979473i	$-0.435394\pi$
$19$	5.21062	−	3.78574i	1.19540	−	0.868508i	0.993824	+	0.110965i	$0.0353941\pi$
$20$		0			0
$21$	−5.06704			−1.10572
$22$		0			0
$23$	−7.43878			−1.55109			−0.775546	−	0.631291i	$-0.782525\pi$
$23$	−7.43878			−1.55109			−0.775546	+	0.631291i	$0.782525\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.78307	−	8.56540i	−0.535601	−	1.64841i
$28$		0			0
$29$	2.55959	+	1.85965i	0.475303	+	0.345328i	0.799505	−	0.600660i	$-0.205095\pi$
$29$	2.55959	+	1.85965i	0.475303	+	0.345328i	−0.324201	+	0.945988i	$0.605095\pi$
$30$		0			0
$31$	0.787699	−	2.42429i	0.141475	−	0.435415i	−0.855066	−	0.518519i	$-0.826483\pi$
$31$	0.787699	−	2.42429i	0.141475	−	0.435415i	0.996541	+	0.0831043i	$0.0264835\pi$
$32$		0			0
$33$	9.93965	−	0.472068i	1.73027	−	0.0821764i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.29843	−	3.84954i	−0.871057	−	0.632860i	0.0598135	−	0.998210i	$-0.480949\pi$
$37$	−5.29843	−	3.84954i	−0.871057	−	0.632860i	−0.930870	+	0.365350i	$0.880949\pi$
$38$		0			0
$39$	−3.44014	−	10.5877i	−0.550863	−	1.69538i
$40$		0			0
$41$	−6.93840	+	5.04104i	−1.08360	+	0.787279i	−0.978306	−	0.207163i	$-0.933577\pi$
$41$	−6.93840	+	5.04104i	−1.08360	+	0.787279i	−0.105290	+	0.994442i	$0.533577\pi$
$42$		0			0
$43$	−3.49875			−0.533554			−0.266777	−	0.963758i	$-0.585959\pi$
$43$	−3.49875			−0.533554			−0.266777	+	0.963758i	$0.585959\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.44003	−	2.49933i	0.501781	−	0.364565i	−0.307916	−	0.951414i	$-0.599632\pi$
$47$	3.44003	−	2.49933i	0.501781	−	0.364565i	0.809697	+	0.586849i	$0.199632\pi$
$48$		0			0
$49$	−1.28174	−	3.94479i	−0.183106	−	0.563541i
$50$		0			0
$51$	9.39392	+	6.82509i	1.31541	+	0.955703i
$52$		0			0
$53$	3.00470	−	9.24750i	0.412727	−	1.27024i	−0.501542	−	0.865133i	$-0.667234\pi$
$53$	3.00470	−	9.24750i	0.412727	−	1.27024i	0.914269	−	0.405109i	$-0.132766\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.97143	−	18.3782i	0.790935	−	2.43425i
$58$		0			0
$59$	2.33853	+	1.69904i	0.304450	+	0.221196i	0.729512	−	0.683968i	$-0.239747\pi$
$59$	2.33853	+	1.69904i	0.304450	+	0.221196i	−0.425061	+	0.905165i	$0.639747\pi$
$60$		0			0
$61$	1.93043	+	5.94126i	0.247167	+	0.760700i	0.995273	+	0.0971212i	$0.0309634\pi$
$61$	1.93043	+	5.94126i	0.247167	+	0.760700i	−0.748106	+	0.663579i	$0.769037\pi$
$62$		0			0
$63$	−8.20025	+	5.95783i	−1.03313	+	0.750616i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	10.5387			1.28750			0.643751	−	0.765235i	$-0.277377\pi$
$67$	10.5387			1.28750			0.643751	+	0.765235i	$0.277377\pi$
$68$		0			0
$69$	−18.0561	+	13.1185i	−2.17369	+	1.57928i
$70$		0			0
$71$	2.85383	+	8.78318i	0.338687	+	1.04237i	0.964877	+	0.262701i	$0.0846133\pi$
$71$	2.85383	+	8.78318i	0.338687	+	1.04237i	−0.626190	+	0.779670i	$0.715387\pi$
$72$		0			0
$73$	2.96007	+	2.15062i	0.346450	+	0.251711i	0.747378	−	0.664399i	$-0.231312\pi$
$73$	2.96007	+	2.15062i	0.346450	+	0.251711i	−0.400928	+	0.916110i	$0.631312\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.98166	−	5.23901i	−0.225831	−	0.597041i
$78$		0			0
$79$	−5.23846	+	16.1223i	−0.589373	+	1.81390i	−0.00842422	+	0.999965i	$0.502682\pi$
$79$	−5.23846	+	16.1223i	−0.589373	+	1.81390i	−0.580949	+	0.813940i	$0.697318\pi$
$80$		0			0
$81$	−7.29404	−	5.29943i	−0.810449	−	0.588825i
$82$		0			0
$83$	3.71779	+	11.4422i	0.408080	+	1.25594i	0.918296	+	0.395896i	$0.129566\pi$
$83$	3.71779	+	11.4422i	0.408080	+	1.25594i	−0.510215	+	0.860047i	$0.670434\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	9.49240			1.01769
$88$		0			0
$89$	−15.5881			−1.65233			−0.826166	−	0.563426i	$-0.809483\pi$
$89$	−15.5881			−1.65233			−0.826166	+	0.563426i	$0.809483\pi$
$90$		0			0
$91$	−5.06965	+	3.68331i	−0.531443	+	0.386116i
$92$		0			0
$93$	−2.36333	−	7.27358i	−0.245066	−	0.754235i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.07343	+	6.38135i	−0.210525	+	0.647928i	0.788916	+	0.614500i	$0.210642\pi$
$97$	−2.07343	+	6.38135i	−0.210525	+	0.647928i	−0.999441	+	0.0334279i	$0.989358\pi$
$98$		0			0
$99$	15.5308	−	12.4510i	1.56090	−	1.25138i
$100$		0			0
$101$	1.51211	−	4.65380i	0.150461	−	0.463071i	−0.847212	−	0.531255i	$-0.821721\pi$
$101$	1.51211	−	4.65380i	0.150461	−	0.463071i	0.997673	+	0.0681843i	$0.0217206\pi$
$102$		0			0
$103$	−13.4922	−	9.80269i	−1.32943	−	0.965888i	−0.999763	−	0.0217908i	$-0.993063\pi$
$103$	−13.4922	−	9.80269i	−1.32943	−	0.965888i	−0.329668	−	0.944097i	$-0.606937\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.92664	−	1.39979i	0.186256	−	0.135323i	−0.490750	−	0.871300i	$-0.663277\pi$
$107$	1.92664	−	1.39979i	0.186256	−	0.135323i	0.677006	+	0.735978i	$0.263277\pi$
$108$		0			0
$109$	15.3246			1.46783			0.733916	−	0.679240i	$-0.237691\pi$
$109$	15.3246			1.46783			0.733916	+	0.679240i	$0.237691\pi$
$110$		0			0
$111$	−19.6496			−1.86506
$112$		0			0
$113$	−1.41763	+	1.02997i	−0.133359	+	0.0968910i	−0.652465	−	0.757819i	$-0.726265\pi$
$113$	−1.41763	+	1.02997i	−0.133359	+	0.0968910i	0.519106	+	0.854710i	$0.326265\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−18.0163	−	13.0896i	−1.66561	−	1.21014i
$118$		0			0
$119$	2.01975	−	6.21616i	0.185150	−	0.569834i
$120$		0			0
$121$	4.37537	+	10.0924i	0.397761	+	0.917489i
$122$		0			0
$123$	−7.95148	+	24.4721i	−0.716961	+	2.20658i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	2.89048	+	8.89597i	0.256488	+	0.789390i	0.993533	+	0.113546i	$0.0362208\pi$
$127$	2.89048	+	8.89597i	0.256488	+	0.789390i	−0.737045	+	0.675844i	$0.763779\pi$
$128$		0			0
$129$	−8.49247	+	6.17014i	−0.747720	+	0.543251i
$130$		0			0
$131$	10.3843			0.907282			0.453641	−	0.891185i	$-0.350125\pi$
$131$	10.3843			0.907282			0.453641	+	0.891185i	$0.350125\pi$
$132$		0			0
$133$	−10.8773			−0.943184
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.79131	+	14.7461i	0.409349	+	1.25985i	0.917208	+	0.398408i	$0.130437\pi$
$137$	4.79131	+	14.7461i	0.409349	+	1.25985i	−0.507859	+	0.861440i	$0.669563\pi$
$138$		0			0
$139$	16.9807	+	12.3372i	1.44029	+	1.04643i	0.987982	+	0.154567i	$0.0493983\pi$
$139$	16.9807	+	12.3372i	1.44029	+	1.04643i	0.452305	+	0.891863i	$0.350602\pi$
$140$		0			0
$141$	3.94232	−	12.1332i	0.332003	−	1.02180i
$142$		0			0
$143$	9.60161	−	7.69760i	0.802927	−	0.643706i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−10.0679	−	7.31476i	−0.830387	−	0.603311i
$148$		0			0
$149$	−0.899897	−	2.76960i	−0.0737224	−	0.226894i	0.907405	−	0.420258i	$-0.138060\pi$
$149$	−0.899897	−	2.76960i	−0.0737224	−	0.226894i	−0.981127	+	0.193363i	$0.938060\pi$
$150$		0			0
$151$	3.65731	−	2.65719i	0.297628	−	0.216239i	−0.428942	−	0.903332i	$-0.641113\pi$
$151$	3.65731	−	2.65719i	0.297628	−	0.216239i	0.726570	+	0.687093i	$0.241113\pi$
$152$		0			0
$153$	23.2276			1.87784
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.52962	+	5.47059i	−0.600929	+	0.436601i	−0.846209	−	0.532852i	$-0.821120\pi$
$157$	−7.52962	+	5.47059i	−0.600929	+	0.436601i	0.245279	+	0.969452i	$0.421120\pi$
$158$		0			0
$159$	−9.01497	−	27.7452i	−0.714934	−	2.20034i
$160$		0			0
$161$	10.1636	+	7.38432i	0.801007	+	0.581966i
$162$		0			0
$163$	3.90948	−	12.0321i	0.306214	−	0.942429i	−0.673008	−	0.739635i	$-0.734998\pi$
$163$	3.90948	−	12.0321i	0.306214	−	0.942429i	0.979221	−	0.202794i	$-0.0650021\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.25303	+	16.1672i	−0.406492	+	1.25105i	0.513152	+	0.858298i	$0.328478\pi$
$167$	−5.25303	+	16.1672i	−0.406492	+	1.25105i	−0.919643	+	0.392754i	$0.871522\pi$
$168$		0			0
$169$	−0.621033	−	0.451207i	−0.0477718	−	0.0347082i
$170$		0			0
$171$	−11.9452	−	36.7636i	−0.913473	−	2.81138i
$172$		0			0
$173$	10.1067	−	7.34298i	0.768401	−	0.558276i	−0.133074	−	0.991106i	$-0.542485\pi$
$173$	10.1067	−	7.34298i	0.768401	−	0.558276i	0.901476	+	0.432830i	$0.142485\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.67259			0.651872
$178$		0			0
$179$	−1.03046	+	0.748673i	−0.0770202	+	0.0559584i	−0.625629	−	0.780121i	$-0.715158\pi$
$179$	−1.03046	+	0.748673i	−0.0770202	+	0.0559584i	0.548609	+	0.836079i	$0.315158\pi$
$180$		0			0
$181$	−5.34282	−	16.4435i	−0.397129	−	1.22224i	−0.927291	−	0.374341i	$-0.877869\pi$
$181$	−5.34282	−	16.4435i	−0.397129	−	1.22224i	0.530162	−	0.847896i	$-0.322131\pi$
$182$		0			0
$183$	15.1633	+	11.0168i	1.12090	+	0.814384i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.38288	+	12.3820i	−0.247381	+	0.905459i
$188$		0			0
$189$	−4.70017	+	14.4656i	−0.341887	+	1.05222i
$190$		0			0
$191$	12.2106	+	8.87154i	0.883530	+	0.641922i	0.934183	−	0.356794i	$-0.116130\pi$
$191$	12.2106	+	8.87154i	0.883530	+	0.641922i	−0.0506530	+	0.998716i	$0.516130\pi$
$192$		0			0
$193$	−6.77546	−	20.8527i	−0.487708	−	1.50101i	−0.828020	−	0.560699i	$-0.810533\pi$
$193$	−6.77546	−	20.8527i	−0.487708	−	1.50101i	0.340312	−	0.940313i	$-0.389467\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	19.4874			1.38842			0.694210	−	0.719772i	$-0.255754\pi$
$197$	19.4874			1.38842			0.694210	+	0.719772i	$0.255754\pi$
$198$		0			0
$199$	−4.59408			−0.325666			−0.162833	−	0.986654i	$-0.552063\pi$
$199$	−4.59408			−0.325666			−0.162833	+	0.986654i	$0.552063\pi$
$200$		0			0
$201$	25.5804	−	18.5852i	1.80430	−	1.31090i
$202$		0			0
$203$	−1.65114	−	5.08170i	−0.115888	−	0.356665i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−13.7963	+	42.4607i	−0.958910	+	2.95122i
$208$		0			0
$209$	21.3373	−	1.01338i	1.47593	−	0.0700970i
$210$		0			0
$211$	−7.77574	+	23.9313i	−0.535304	+	1.64750i	0.207687	+	0.978195i	$0.433406\pi$
$211$	−7.77574	+	23.9313i	−0.535304	+	1.64750i	−0.742991	+	0.669301i	$0.766594\pi$
$212$		0			0
$213$	22.4165	+	16.2865i	1.53595	+	1.11593i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.48278	+	2.53039i	−0.236426	+	0.171774i
$218$		0			0
$219$	10.9776			0.741800
$220$		0			0
$221$	14.3600			0.965960
$222$		0			0
$223$	−20.9426	+	15.2157i	−1.40242	+	1.01892i	−0.408051	+	0.912959i	$0.633792\pi$
$223$	−20.9426	+	15.2157i	−1.40242	+	1.01892i	−0.994370	+	0.105960i	$0.966208\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.8810	−	14.4444i	−1.31955	−	0.958710i	−0.999938	−	0.0111621i	$-0.996447\pi$
$227$	−19.8810	−	14.4444i	−1.31955	−	0.958710i	−0.319614	−	0.947548i	$-0.603553\pi$
$228$		0			0
$229$	3.90485	−	12.0179i	0.258040	−	0.794165i	−0.735175	−	0.677877i	$-0.762900\pi$
$229$	3.90485	−	12.0179i	0.258040	−	0.794165i	0.993215	−	0.116289i	$-0.0370997\pi$
$230$		0			0
$231$	−14.0492	−	9.22189i	−0.924370	−	0.606756i
$232$		0			0
$233$	−1.97304	+	6.07238i	−0.129258	+	0.397815i	−0.994653	−	0.103276i	$-0.967068\pi$
$233$	−1.97304	+	6.07238i	−0.129258	+	0.397815i	0.865395	+	0.501090i	$0.167068\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	15.7169	+	48.3718i	1.02092	+	3.14208i
$238$		0			0
$239$	−10.9264	+	7.93851i	−0.706771	+	0.513499i	−0.882130	−	0.471005i	$-0.843891\pi$
$239$	−10.9264	+	7.93851i	−0.706771	+	0.513499i	0.175359	+	0.984505i	$0.443891\pi$
$240$		0			0
$241$	−26.7883			−1.72559			−0.862793	−	0.505557i	$-0.831287\pi$
$241$	−26.7883			−1.72559			−0.862793	+	0.505557i	$0.831287\pi$
$242$		0			0
$243$	−0.0318587			−0.00204373
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.38489	−	22.7284i	−0.469889	−	1.44617i
$248$		0			0
$249$	29.2028	+	21.2171i	1.85065	+	1.34458i
$250$		0			0
$251$	2.03249	−	6.25535i	0.128289	−	0.394834i	−0.866197	−	0.499703i	$-0.833442\pi$
$251$	2.03249	−	6.25535i	0.128289	−	0.394834i	0.994486	+	0.104869i	$0.0334424\pi$
$252$		0			0
$253$	−20.6253	−	13.5384i	−1.29670	−	0.851152i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.5647	+	11.3084i	0.970898	+	0.705399i	0.955656	−	0.294485i	$-0.0951482\pi$
$257$	15.5647	+	11.3084i	0.970898	+	0.705399i	0.0152419	+	0.999884i	$0.495148\pi$
$258$		0			0
$259$	3.41792	+	10.5193i	0.212379	+	0.653637i
$260$		0			0
$261$	15.3621	−	11.1612i	0.950887	−	0.690860i
$262$		0			0
$263$	−4.89929			−0.302103			−0.151052	−	0.988526i	$-0.548266\pi$
$263$	−4.89929			−0.302103			−0.151052	+	0.988526i	$0.548266\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−37.8368	+	27.4900i	−2.31557	+	1.68236i
$268$		0			0
$269$	1.13958	+	3.50727i	0.0694814	+	0.213842i	0.979768	−	0.200137i	$-0.0641387\pi$
$269$	1.13958	+	3.50727i	0.0694814	+	0.213842i	−0.910286	+	0.413979i	$0.864139\pi$
$270$		0			0
$271$	−3.28380	−	2.38582i	−0.199477	−	0.144928i	0.483563	−	0.875310i	$-0.339342\pi$
$271$	−3.28380	−	2.38582i	−0.199477	−	0.144928i	−0.683040	+	0.730381i	$0.739342\pi$
$272$		0			0
$273$	−5.80987	+	17.8809i	−0.351629	+	1.08220i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.32631	−	10.2373i	0.199859	−	0.615101i	−0.800027	−	0.599964i	$-0.795181\pi$
$277$	3.32631	−	10.2373i	0.199859	−	0.615101i	0.999885	−	0.0151373i	$-0.00481852\pi$
$278$		0			0
$279$	−12.3770	−	8.99240i	−0.740991	−	0.538361i
$280$		0			0
$281$	−4.18268	−	12.8730i	−0.249518	−	0.767936i	−0.994860	−	0.101255i	$-0.967714\pi$
$281$	−4.18268	−	12.8730i	−0.249518	−	0.767936i	0.745343	−	0.666681i	$-0.232286\pi$
$282$		0			0
$283$	−9.04814	+	6.57386i	−0.537856	+	0.390775i	−0.823288	−	0.567624i	$-0.807863\pi$
$283$	−9.04814	+	6.57386i	−0.537856	+	0.390775i	0.285432	+	0.958399i	$0.407863\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.4841			0.854970
$288$		0			0
$289$	1.63591	−	1.18856i	0.0962302	−	0.0699154i
$290$		0			0
$291$	6.22089	+	19.1459i	0.364675	+	1.12236i
$292$		0			0
$293$	7.81212	+	5.67584i	0.456389	+	0.331586i	0.792113	−	0.610374i	$-0.208981\pi$
$293$	7.81212	+	5.67584i	0.456389	+	0.331586i	−0.335724	+	0.941960i	$0.608981\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	7.87231	−	28.8141i	0.456798	−	1.67196i
$298$		0			0
$299$	−8.52931	+	26.2505i	−0.493262	+	1.51811i
$300$		0			0
$301$	4.78036	+	3.47313i	0.275535	+	0.200188i
$302$		0			0
$303$	−4.53678	−	13.9628i	−0.260631	−	0.802141i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−5.20959			−0.297327			−0.148664	−	0.988888i	$-0.547497\pi$
$307$	−5.20959			−0.297327			−0.148664	+	0.988888i	$0.547497\pi$
$308$		0			0
$309$	−50.0369			−2.84650
$310$		0			0
$311$	−19.5453	+	14.2005i	−1.10831	+	0.805237i	−0.982397	−	0.186803i	$-0.940187\pi$
$311$	−19.5453	+	14.2005i	−1.10831	+	0.805237i	−0.125917	+	0.992041i	$0.540187\pi$
$312$		0			0
$313$	−4.04956	−	12.4633i	−0.228895	−	0.704465i	−0.997873	−	0.0651903i	$-0.979235\pi$
$313$	−4.04956	−	12.4633i	−0.228895	−	0.704465i	0.768978	−	0.639275i	$-0.220765\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.18818	+	6.73454i	−0.122901	+	0.378249i	−0.993513	−	0.113721i	$-0.963723\pi$
$317$	−2.18818	+	6.73454i	−0.122901	+	0.378249i	0.870612	+	0.491970i	$0.163723\pi$
$318$		0			0
$319$	3.71236	+	9.81458i	0.207853	+	0.549511i
$320$		0			0
$321$	2.20795	−	6.79538i	0.123236	−	0.379281i
$322$		0			0
$323$	20.1658	+	14.6513i	1.12205	+	0.815220i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	37.1973	−	27.0254i	2.05701	−	1.49451i
$328$		0			0
$329$	−7.18117			−0.395911
$330$		0			0
$331$	−1.76299			−0.0969025			−0.0484513	−	0.998826i	$-0.515429\pi$
$331$	−1.76299			−0.0969025			−0.0484513	+	0.998826i	$0.515429\pi$
$332$		0			0
$333$	−31.8000	+	23.1040i	−1.74263	+	1.26609i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−9.59687	−	6.97253i	−0.522775	−	0.379818i	0.294874	−	0.955536i	$-0.404722\pi$
$337$	−9.59687	−	6.97253i	−0.522775	−	0.379818i	−0.817648	+	0.575718i	$0.804722\pi$
$338$		0			0
$339$	−1.62461	+	5.00005i	−0.0882369	+	0.271565i
$340$		0			0
$341$	6.59617	−	5.28815i	0.357203	−	0.286369i
$342$		0			0
$343$	−5.81784	+	17.9055i	−0.314134	+	0.966804i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.51731	+	7.74747i	0.135136	+	0.415906i	0.995611	−	0.0935864i	$-0.0298331\pi$
$347$	2.51731	+	7.74747i	0.135136	+	0.415906i	−0.860475	+	0.509493i	$0.829833\pi$
$348$		0			0
$349$	−13.8784	+	10.0832i	−0.742893	+	0.539743i	−0.893616	−	0.448833i	$-0.851840\pi$
$349$	−13.8784	+	10.0832i	−0.742893	+	0.539743i	0.150723	+	0.988576i	$0.451840\pi$
$350$		0			0
$351$	−33.4173			−1.78368
$352$		0			0
$353$	9.89553			0.526686			0.263343	−	0.964702i	$-0.415175\pi$
$353$	9.89553			0.526686			0.263343	+	0.964702i	$0.415175\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.05985	−	18.6503i	−0.320721	−	0.987079i
$358$		0			0
$359$	−30.2411	−	21.9715i	−1.59607	−	1.15961i	−0.894561	−	0.446946i	$-0.852512\pi$
$359$	−30.2411	−	21.9715i	−1.59607	−	1.15961i	−0.701506	−	0.712664i	$-0.747488\pi$
$360$		0			0
$361$	6.94745	−	21.3821i	0.365655	−	1.12537i
$362$		0			0
$363$	28.4185	+	16.7810i	1.49158	+	0.880777i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	15.6840	+	11.3951i	0.818698	+	0.594819i	0.916339	−	0.400403i	$-0.131130\pi$
$367$	15.6840	+	11.3951i	0.818698	+	0.594819i	−0.0976415	+	0.995222i	$0.531130\pi$
$368$		0			0
$369$	15.9061	+	48.9539i	0.828038	+	2.54844i
$370$		0			0
$371$	−13.2851	+	9.65221i	−0.689730	+	0.501118i
$372$		0			0
$373$	−1.02733			−0.0531933			−0.0265967	−	0.999646i	$-0.508467\pi$
$373$	−1.02733			−0.0531933			−0.0265967	+	0.999646i	$0.508467\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.49729	−	6.90018i	0.489135	−	0.355378i
$378$		0			0
$379$	2.32646	+	7.16010i	0.119502	+	0.367790i	0.992859	−	0.119290i	$-0.0380620\pi$
$379$	2.32646	+	7.16010i	0.119502	+	0.367790i	−0.873357	+	0.487080i	$0.838062\pi$
$380$		0			0
$381$	22.7043	+	16.4957i	1.16318	+	0.845098i
$382$		0			0
$383$	−4.67756	+	14.3960i	−0.239012	+	0.735603i	0.757552	+	0.652775i	$0.226395\pi$
$383$	−4.67756	+	14.3960i	−0.239012	+	0.735603i	−0.996564	+	0.0828281i	$0.973605\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.48895	+	19.9709i	−0.329852	+	1.01518i
$388$		0			0
$389$	−4.11088	−	2.98673i	−0.208430	−	0.151433i	0.478673	−	0.877993i	$-0.341118\pi$
$389$	−4.11088	−	2.98673i	−0.208430	−	0.151433i	−0.687103	+	0.726560i	$0.741118\pi$
$390$		0			0
$391$	−8.89630	−	27.3800i	−0.449905	−	1.38467i
$392$		0			0
$393$	25.2057	−	18.3130i	1.27146	−	0.923771i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.78023			−0.290101			−0.145051	−	0.989424i	$-0.546335\pi$
$397$	−5.78023			−0.290101			−0.145051	+	0.989424i	$0.546335\pi$
$398$		0			0
$399$	−26.4024	+	19.1825i	−1.32177	+	0.960326i
$400$		0			0
$401$	7.23049	+	22.2532i	0.361074	+	1.11127i	0.952403	+	0.304841i	$0.0986032\pi$
$401$	7.23049	+	22.2532i	0.361074	+	1.11127i	−0.591330	+	0.806430i	$0.701397\pi$
$402$		0			0
$403$	−7.65183	−	5.55938i	−0.381165	−	0.276932i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.68472	−	20.3165i	−0.380917	−	1.00705i
$408$		0			0
$409$	2.63551	−	8.11126i	0.130318	−	0.401076i	−0.864515	−	0.502607i	$-0.832374\pi$
$409$	2.63551	−	8.11126i	0.130318	−	0.401076i	0.994832	+	0.101531i	$0.0323742\pi$
$410$		0			0
$411$	37.6352	+	27.3435i	1.85641	+	1.34876i
$412$		0			0
$413$	−1.50854	−	4.64282i	−0.0742305	−	0.228458i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	62.9742			3.08386
$418$		0			0
$419$	26.9789			1.31801			0.659003	−	0.752141i	$-0.270979\pi$
$419$	26.9789			1.31801			0.659003	+	0.752141i	$0.270979\pi$
$420$		0			0
$421$	18.6021	−	13.5152i	0.906612	−	0.658692i	−0.0335437	−	0.999437i	$-0.510679\pi$
$421$	18.6021	−	13.5152i	0.906612	−	0.658692i	0.940156	+	0.340745i	$0.110679\pi$
$422$		0			0
$423$	−7.88618	−	24.2712i	−0.383439	−	1.18010i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.26020	−	10.0339i	0.157772	−	0.485573i
$428$		0			0
$429$	9.73094	−	35.6170i	0.469814	−	1.71961i
$430$		0			0
$431$	0.655391	−	2.01708i	0.0315691	−	0.0971596i	−0.934030	−	0.357193i	$-0.883734\pi$
$431$	0.655391	−	2.01708i	0.0315691	−	0.0971596i	0.965600	+	0.260034i	$0.0837337\pi$
$432$		0			0
$433$	−22.1563	−	16.0975i	−1.06476	−	0.773597i	−0.0898005	−	0.995960i	$-0.528623\pi$
$433$	−22.1563	−	16.0975i	−1.06476	−	0.773597i	−0.974964	+	0.222363i	$0.928623\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−38.7607	+	28.1613i	−1.85417	+	1.34714i
$438$		0			0
$439$	31.5257			1.50464			0.752319	−	0.658799i	$-0.228935\pi$
$439$	31.5257			1.50464			0.752319	+	0.658799i	$0.228935\pi$
$440$		0			0
$441$	−24.8941			−1.18543
$442$		0			0
$443$	−5.43740	+	3.95050i	−0.258339	+	0.187694i	−0.709414	−	0.704792i	$-0.751040\pi$
$443$	−5.43740	+	3.95050i	−0.258339	+	0.187694i	0.451076	+	0.892486i	$0.351040\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.06858	−	5.13562i	−0.334332	−	0.242907i
$448$		0			0
$449$	3.99069	−	12.2821i	0.188332	−	0.579627i	−0.811658	−	0.584133i	$-0.801435\pi$
$449$	3.99069	−	12.2821i	0.188332	−	0.579627i	0.999990	+	0.00450672i	$0.00143454\pi$
$450$		0			0
$451$	−28.4125	+	1.34940i	−1.33789	+	0.0635409i
$452$		0			0
$453$	4.19132	−	12.8996i	0.196925	−	0.606074i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.44706	−	10.6090i	−0.161247	−	0.496267i	0.837493	−	0.546448i	$-0.184020\pi$
$457$	−3.44706	−	10.6090i	−0.161247	−	0.496267i	−0.998740	+	0.0501808i	$0.984020\pi$
$458$		0			0
$459$	28.1984	−	20.4873i	1.31619	−	0.956267i
$460$		0			0
$461$	11.7060			0.545205			0.272602	−	0.962127i	$-0.412116\pi$
$461$	11.7060			0.545205			0.272602	+	0.962127i	$0.412116\pi$
$462$		0			0
$463$	−10.7840			−0.501173			−0.250586	−	0.968094i	$-0.580623\pi$
$463$	−10.7840			−0.501173			−0.250586	+	0.968094i	$0.580623\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.46289	−	19.8907i	−0.299067	−	0.920433i	−0.981825	−	0.189789i	$-0.939220\pi$
$467$	−6.46289	−	19.8907i	−0.299067	−	0.920433i	0.682758	−	0.730644i	$-0.260780\pi$
$468$		0			0
$469$	−14.3990	−	10.4615i	−0.664885	−	0.483067i
$470$		0			0
$471$	−8.62903	+	26.5574i	−0.397605	+	1.22370i
$472$		0			0
$473$	−9.70086	−	6.36764i	−0.446046	−	0.292784i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−47.2123	−	34.3017i	−2.16170	−	1.57057i
$478$		0			0
$479$	−3.47943	−	10.7086i	−0.158979	−	0.489288i	0.839563	−	0.543262i	$-0.182811\pi$
$479$	−3.47943	−	10.7086i	−0.158979	−	0.489288i	−0.998542	+	0.0539745i	$0.982811\pi$
$480$		0			0
$481$	−19.6597	+	14.2836i	−0.896406	+	0.651277i
$482$		0			0
$483$	37.6926			1.71507
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−6.88160	+	4.99978i	−0.311835	+	0.226562i	−0.732684	−	0.680569i	$-0.761732\pi$
$487$	−6.88160	+	4.99978i	−0.311835	+	0.226562i	0.420848	+	0.907131i	$0.361732\pi$
$488$		0			0
$489$	−11.7296	−	36.0999i	−0.530430	−	1.63250i
$490$		0			0
$491$	−11.2974	−	8.20808i	−0.509847	−	0.370425i	0.302919	−	0.953016i	$-0.402039\pi$
$491$	−11.2974	−	8.20808i	−0.509847	−	0.370425i	−0.812765	+	0.582591i	$0.802039\pi$
$492$		0			0
$493$	−3.78373	+	11.6451i	−0.170411	+	0.524470i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.81968	−	14.8334i	0.216192	−	0.665371i
$498$		0			0
$499$	4.47304	+	3.24985i	0.200241	+	0.145483i	0.683387	−	0.730056i	$-0.260506\pi$
$499$	4.47304	+	3.24985i	0.200241	+	0.145483i	−0.483146	+	0.875540i	$0.660506\pi$
$500$		0			0
$501$	15.7606	+	48.5062i	0.704133	+	2.16710i
$502$		0			0
$503$	7.43868	−	5.40452i	0.331674	−	0.240976i	−0.409466	−	0.912325i	$-0.634285\pi$
$503$	7.43868	−	5.40452i	0.331674	−	0.240976i	0.741141	+	0.671350i	$0.234285\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.30314			−0.102286
$508$		0			0
$509$	−8.96759	+	6.51534i	−0.397482	+	0.288787i	−0.768514	−	0.639832i	$-0.779004\pi$
$509$	−8.96759	+	6.51534i	−0.397482	+	0.288787i	0.371033	+	0.928620i	$0.379004\pi$
$510$		0			0
$511$	−1.90949	−	5.87681i	−0.0844709	−	0.259975i
$512$		0			0
$513$	−46.9279	−	34.0951i	−2.07192	−	1.50534i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	14.0868	−	0.669030i	0.619537	−	0.0294239i
$518$		0			0
$519$	11.5824	−	35.6471i	0.508413	−	1.56473i
$520$		0			0
$521$	−14.8879	−	10.8167i	−0.652252	−	0.473889i	0.211786	−	0.977316i	$-0.432072\pi$
$521$	−14.8879	−	10.8167i	−0.652252	−	0.473889i	−0.864038	+	0.503427i	$0.832072\pi$
$522$		0			0
$523$	7.61361	+	23.4323i	0.332920	+	1.02462i	0.967738	+	0.251960i	$0.0810751\pi$
$523$	7.61361	+	23.4323i	0.332920	+	1.02462i	−0.634818	+	0.772662i	$0.718925\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.86514			0.429732
$528$		0			0
$529$	32.3354			1.40589
$530$		0			0
$531$	14.0353	−	10.1972i	0.609080	−	0.442523i
$532$		0			0
$533$	9.83363	+	30.2648i	0.425942	+	1.31091i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.18092	+	3.63449i	−0.0509604	+	0.156840i
$538$		0			0
$539$	3.62559	−	13.2703i	0.156165	−	0.571593i
$540$		0			0
$541$	2.02811	−	6.24188i	0.0871953	−	0.268360i	−0.897946	−	0.440106i	$-0.854941\pi$
$541$	2.02811	−	6.24188i	0.0871953	−	0.268360i	0.985141	+	0.171746i	$0.0549409\pi$
$542$		0			0
$543$	−41.9672	−	30.4910i	−1.80098	−	1.30849i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.527878	+	0.383526i	−0.0225704	+	0.0163984i	−0.599013	−	0.800739i	$-0.704440\pi$
$547$	−0.527878	+	0.383526i	−0.0225704	+	0.0163984i	0.576443	+	0.817137i	$0.304440\pi$
$548$		0			0
$549$	37.4931			1.60017
$550$		0			0
$551$	20.3772			0.868098
$552$		0			0
$553$	23.1617	−	16.8279i	0.984934	−	0.715596i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.37704	+	1.00048i	0.0583469	+	0.0423915i	0.616576	−	0.787295i	$-0.288519\pi$
$557$	1.37704	+	1.00048i	0.0583469	+	0.0423915i	−0.558230	+	0.829687i	$0.688519\pi$
$558$		0			0
$559$	−4.01166	+	12.3466i	−0.169675	+	0.522207i
$560$		0			0
$561$	13.6247	+	36.0204i	0.575236	+	1.52078i
$562$		0			0
$563$	13.5063	−	41.5681i	0.569222	−	1.75189i	−0.0858390	−	0.996309i	$-0.527357\pi$
$563$	13.5063	−	41.5681i	0.569222	−	1.75189i	0.655061	−	0.755576i	$-0.272643\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	4.70525	+	14.4813i	0.197602	+	0.608157i
$568$		0			0
$569$	25.3587	−	18.4242i	1.06309	−	0.772382i	0.0884349	−	0.996082i	$-0.471813\pi$
$569$	25.3587	−	18.4242i	1.06309	−	0.772382i	0.974658	+	0.223700i	$0.0718135\pi$
$570$		0			0
$571$	9.86361			0.412779			0.206390	−	0.978470i	$-0.433829\pi$
$571$	9.86361			0.412779			0.206390	+	0.978470i	$0.433829\pi$
$572$		0			0
$573$	45.2840			1.89176
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−7.96943	−	24.5274i	−0.331772	−	1.02109i	−0.968290	−	0.249827i	$-0.919626\pi$
$577$	−7.96943	−	24.5274i	−0.331772	−	1.02109i	0.636519	−	0.771261i	$-0.280374\pi$
$578$		0			0
$579$	−53.2204	−	38.6669i	−2.21176	−	1.60694i
$580$		0			0
$581$	6.27878	−	19.3241i	0.260488	−	0.801698i
$582$		0			0
$583$	25.1613	−	20.1718i	1.04207	−	0.835429i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.860653	−	0.625301i	−0.0355229	−	0.0258089i	0.569882	−	0.821726i	$-0.306989\pi$
$587$	−0.860653	−	0.625301i	−0.0355229	−	0.0258089i	−0.605405	+	0.795918i	$0.706989\pi$
$588$		0			0
$589$	−5.07332	−	15.6141i	−0.209043	−	0.643367i
$590$		0			0
$591$	47.3016	−	34.3666i	1.94573	−	1.41365i
$592$		0			0
$593$	19.7906			0.812702			0.406351	−	0.913717i	$-0.366801\pi$
$593$	19.7906			0.812702			0.406351	+	0.913717i	$0.366801\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−11.1512	+	8.10180i	−0.456387	+	0.331585i
$598$		0			0
$599$	−1.40163	−	4.31378i	−0.0572692	−	0.176256i	0.918330	−	0.395816i	$-0.129538\pi$
$599$	−1.40163	−	4.31378i	−0.0572692	−	0.176256i	−0.975599	+	0.219559i	$0.929538\pi$
$600$		0			0
$601$	−38.2474	−	27.7883i	−1.56014	−	1.13351i	−0.935892	−	0.352286i	$-0.885404\pi$
$601$	−38.2474	−	27.7883i	−1.56014	−	1.13351i	−0.624251	−	0.781224i	$-0.714596\pi$
$602$		0			0
$603$	19.5455	−	60.1549i	0.795954	−	2.44970i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−3.91282	+	12.0424i	−0.158817	+	0.488787i	−0.998528	−	0.0542464i	$-0.982724\pi$
$607$	−3.91282	+	12.0424i	−0.158817	+	0.488787i	0.839711	+	0.543033i	$0.182724\pi$
$608$		0			0
$609$	−12.9695	−	9.42291i	−0.525552	−	0.381836i
$610$		0			0
$611$	−4.87548	−	15.0052i	−0.197241	−	0.607045i
$612$		0			0
$613$	−9.33212	+	6.78018i	−0.376921	+	0.273849i	−0.760075	−	0.649835i	$-0.774838\pi$
$613$	−9.33212	+	6.78018i	−0.376921	+	0.273849i	0.383154	+	0.923684i	$0.374838\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.58142			−0.385733			−0.192867	−	0.981225i	$-0.561779\pi$
$617$	−9.58142			−0.385733			−0.192867	+	0.981225i	$0.561779\pi$
$618$		0			0
$619$	0.972177	−	0.706328i	0.0390751	−	0.0283897i	−0.568076	−	0.822976i	$-0.692312\pi$
$619$	0.972177	−	0.706328i	0.0390751	−	0.0283897i	0.607151	+	0.794586i	$0.292312\pi$
$620$		0			0
$621$	20.7026	+	63.7161i	0.830767	+	2.55684i
$622$		0			0
$623$	21.2981	+	15.4740i	0.853289	+	0.619951i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	50.0046	−	40.0887i	1.99699	−	1.60099i
$628$		0			0
$629$	7.83245	−	24.1058i	0.312300	−	0.961161i
$630$		0			0
$631$	−11.5819	−	8.41474i	−0.461068	−	0.334985i	0.332882	−	0.942968i	$-0.391979\pi$
$631$	−11.5819	−	8.41474i	−0.461068	−	0.334985i	−0.793950	+	0.607983i	$0.791979\pi$
$632$		0			0
$633$	23.3295	+	71.8009i	0.927265	+	2.85383i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−15.3903			−0.609786
$638$		0			0
$639$	55.4274			2.19267
$640$		0			0
$641$	29.9553	−	21.7638i	1.18316	−	0.859618i	0.190637	−	0.981661i	$-0.438945\pi$
$641$	29.9553	−	21.7638i	1.18316	−	0.859618i	0.992525	+	0.122043i	$0.0389445\pi$
$642$		0			0
$643$	−1.38308	−	4.25667i	−0.0545432	−	0.167867i	0.920074	−	0.391745i	$-0.128128\pi$
$643$	−1.38308	−	4.25667i	−0.0545432	−	0.167867i	−0.974617	+	0.223878i	$0.928128\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.82850	−	27.1713i	0.347084	−	1.06822i	−0.613374	−	0.789792i	$-0.710188\pi$
$647$	8.82850	−	27.1713i	0.347084	−	1.06822i	0.960458	−	0.278423i	$-0.0898118\pi$
$648$		0			0
$649$	3.39175	+	8.96694i	0.133138	+	0.351983i
$650$		0			0
$651$	−3.99130	+	12.2840i	−0.156431	+	0.481446i
$652$		0			0
$653$	0.545672	+	0.396454i	0.0213538	+	0.0155144i	0.598411	−	0.801189i	$-0.295799\pi$
$653$	0.545672	+	0.396454i	0.0213538	+	0.0155144i	−0.577057	+	0.816704i	$0.695799\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	17.7657	−	12.9075i	0.693105	−	0.503570i
$658$		0			0
$659$	−30.4518			−1.18623			−0.593117	−	0.805116i	$-0.702103\pi$
$659$	−30.4518			−1.18623			−0.593117	+	0.805116i	$0.702103\pi$
$660$		0			0
$661$	−29.2772			−1.13875			−0.569375	−	0.822078i	$-0.692815\pi$
$661$	−29.2772			−1.13875			−0.569375	+	0.822078i	$0.692815\pi$
$662$		0			0
$663$	34.8559	−	25.3243i	1.35369	−	0.983515i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−19.0402	−	13.8335i	−0.737239	−	0.535636i
$668$		0			0
$669$	−24.0005	+	73.8658i	−0.927912	+	2.85582i
$670$		0			0
$671$	−5.46051	+	19.9865i	−0.210801	+	0.771569i
$672$		0			0
$673$	0.494242	−	1.52112i	0.0190516	−	0.0586349i	−0.941079	−	0.338188i	$-0.890186\pi$
$673$	0.494242	−	1.52112i	0.0190516	−	0.0586349i	0.960130	+	0.279553i	$0.0901862\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.22089	+	9.91287i	0.123789	+	0.380982i	0.993678	−	0.112264i	$-0.0358102\pi$
$677$	3.22089	+	9.91287i	0.123789	+	0.380982i	−0.869890	+	0.493246i	$0.835810\pi$
$678$		0			0
$679$	9.16757	−	6.66063i	0.351819	−	0.255612i
$680$		0			0
$681$	−73.7302			−2.82535
$682$		0			0
$683$	−38.4144			−1.46988			−0.734942	−	0.678130i	$-0.762791\pi$
$683$	−38.4144			−1.46988			−0.734942	+	0.678130i	$0.762791\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−11.7157	−	36.0573i	−0.446982	−	1.37567i
$688$		0			0
$689$	−29.1881	−	21.2064i	−1.11198	−	0.807899i
$690$		0			0
$691$	5.37655	−	16.5473i	0.204534	−	0.629490i	−0.795199	−	0.606349i	$-0.792633\pi$
$691$	5.37655	−	16.5473i	0.204534	−	0.629490i	0.999732	−	0.0231407i	$-0.00736657\pi$
$692$		0			0
$693$	−33.5797	+	1.59481i	−1.27559	+	0.0605819i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−26.8525	−	19.5095i	−1.01711	−	0.738974i
$698$		0			0
$699$	5.91969	+	18.2189i	0.223903	+	0.689103i
$700$		0			0
$701$	−41.3290	+	30.0273i	−1.56098	+	1.13412i	−0.625771	+	0.780007i	$0.715216\pi$
$701$	−41.3290	+	30.0273i	−1.56098	+	1.13412i	−0.935204	+	0.354109i	$0.884784\pi$
$702$		0			0
$703$	−42.1815			−1.59090
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.68574	+	4.85748i	−0.251443	+	0.182684i
$708$		0			0
$709$	−3.11182	−	9.57719i	−0.116867	−	0.359679i	0.875465	−	0.483281i	$-0.160555\pi$
$709$	−3.11182	−	9.57719i	−0.116867	−	0.359679i	−0.992332	+	0.123603i	$0.960555\pi$
$710$		0			0
$711$	82.3111	+	59.8025i	3.08691	+	2.24277i
$712$		0			0
$713$	−5.85952	+	18.0337i	−0.219441	+	0.675369i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−12.5218	+	38.5381i	−0.467635	+	1.43923i
$718$		0			0
$719$	17.8912	+	12.9987i	0.667230	+	0.484771i	0.869097	−	0.494642i	$-0.164701\pi$
$719$	17.8912	+	12.9987i	0.667230	+	0.484771i	−0.201867	+	0.979413i	$0.564701\pi$
$720$		0			0
$721$	8.70361	+	26.7869i	0.324139	+	0.997598i
$722$		0			0
$723$	−65.0230	+	47.2420i	−2.41823	+	1.75695i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−25.8714			−0.959517			−0.479758	−	0.877401i	$-0.659276\pi$
$727$	−25.8714			−0.959517			−0.479758	+	0.877401i	$0.659276\pi$
$728$		0			0
$729$	21.8048	−	15.8421i	0.807585	−	0.586745i
$730$		0			0
$731$	−4.18428	−	12.8779i	−0.154761	−	0.476306i
$732$		0			0
$733$	−29.5324	−	21.4566i	−1.09080	−	0.792516i	−0.111270	−	0.993790i	$-0.535492\pi$
$733$	−29.5324	−	21.4566i	−1.09080	−	0.792516i	−0.979535	+	0.201274i	$0.935492\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	29.2202	+	19.1801i	1.07634	+	0.706508i
$738$		0			0
$739$	5.51149	−	16.9626i	0.202743	−	0.623980i	−0.797055	−	0.603907i	$-0.793610\pi$
$739$	5.51149	−	16.9626i	0.202743	−	0.623980i	0.999799	−	0.0200734i	$-0.00639000\pi$
$740$		0			0
$741$	−58.0074	−	42.1448i	−2.13096	−	1.54823i
$742$		0			0
$743$	12.2316	+	37.6450i	0.448733	+	1.38106i	0.878337	+	0.478042i	$0.158653\pi$
$743$	12.2316	+	37.6450i	0.448733	+	1.38106i	−0.429604	+	0.903018i	$0.641347\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	72.2074			2.64193
$748$		0			0
$749$	−4.02192			−0.146958
$750$		0			0
$751$	5.73271	−	4.16506i	0.209190	−	0.151985i	−0.478257	−	0.878220i	$-0.658731\pi$
$751$	5.73271	−	4.16506i	0.209190	−	0.151985i	0.687447	+	0.726235i	$0.258731\pi$
$752$		0			0
$753$	−6.09806	−	18.7679i	−0.222226	−	0.683940i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	2.44983	−	7.53982i	0.0890407	−	0.274039i	−0.896614	−	0.442813i	$-0.853981\pi$
$757$	2.44983	−	7.53982i	0.0890407	−	0.274039i	0.985655	+	0.168774i	$0.0539806\pi$
$758$		0			0
$759$	−73.9388	+	3.51161i	−2.68381	+	0.127463i
$760$		0			0
$761$	9.04626	−	27.8415i	0.327927	−	1.00925i	−0.642175	−	0.766558i	$-0.721968\pi$
$761$	9.04626	−	27.8415i	0.327927	−	1.00925i	0.970102	−	0.242697i	$-0.0780321\pi$
$762$		0			0
$763$	−20.9381	−	15.2124i	−0.758010	−	0.550727i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.67705	−	6.30425i	0.313310	−	0.227633i
$768$		0			0
$769$	−3.78340			−0.136433			−0.0682165	−	0.997671i	$-0.521731\pi$
$769$	−3.78340			−0.136433			−0.0682165	+	0.997671i	$0.521731\pi$
$770$		0			0
$771$	57.7227			2.07883
$772$		0			0
$773$	−2.08683	+	1.51617i	−0.0750581	+	0.0545329i	−0.624682	−	0.780880i	$-0.714771\pi$
$773$	−2.08683	+	1.51617i	−0.0750581	+	0.0545329i	0.549623	+	0.835413i	$0.314771\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	26.8474	+	19.5057i	0.963143	+	0.699765i
$778$		0			0
$779$	−17.0693	+	52.5340i	−0.611572	+	1.88222i
$780$		0			0
$781$	−8.07247	+	29.5467i	−0.288856	+	1.05726i
$782$		0			0
$783$	8.80513	−	27.0994i	0.314670	−	0.968454i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−4.23200	−	13.0248i	−0.150854	−	0.464282i	0.846863	−	0.531811i	$-0.178488\pi$
$787$	−4.23200	−	13.0248i	−0.150854	−	0.464282i	−0.997717	+	0.0675291i	$0.978488\pi$
$788$		0			0
$789$	−11.8920	+	8.64005i	−0.423367	+	0.307594i
$790$		0			0
$791$	2.95933			0.105222
$792$		0			0
$793$	23.1794			0.823124
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.3218	−	44.0779i	−0.507303	−	1.56132i	−0.796864	−	0.604159i	$-0.793509\pi$
$797$	−14.3218	−	44.0779i	−0.507303	−	1.56132i	0.289561	−	0.957160i	$-0.406491\pi$
$798$		0			0
$799$	13.3134	+	9.67274i	0.470993	+	0.342197i
$800$		0			0
$801$	−28.9104	+	88.9771i	−1.02150	+	3.14385i
$802$		0			0
$803$	4.29322	+	11.3502i	0.151504	+	0.400541i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	8.95126	+	6.50347i	0.315099	+	0.228933i
$808$		0			0
$809$	2.35528	+	7.24879i	0.0828071	+	0.254854i	0.983885	−	0.178804i	$-0.0572227\pi$
$809$	2.35528	+	7.24879i	0.0828071	+	0.254854i	−0.901078	+	0.433658i	$0.857223\pi$
$810$		0			0
$811$	−23.5550	+	17.1137i	−0.827127	+	0.600943i	−0.918745	−	0.394851i	$-0.870796\pi$
$811$	−23.5550	+	17.1137i	−0.827127	+	0.600943i	0.0916180	+	0.995794i	$0.470796\pi$
$812$		0			0
$813$	−12.1782			−0.427108
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−18.2307	+	13.2453i	−0.637810	+	0.463396i
$818$		0			0
$819$	11.6220	+	35.7689i	0.406106	+	1.24987i
$820$		0			0
$821$	−39.7129	−	28.8531i	−1.38599	−	1.00698i	−0.996292	−	0.0860379i	$-0.972579\pi$
$821$	−39.7129	−	28.8531i	−1.38599	−	1.00698i	−0.389698	−	0.920943i	$-0.627421\pi$
$822$		0			0
$823$	−17.2838	+	53.1942i	−0.602476	+	1.85423i	−0.0891893	+	0.996015i	$0.528428\pi$
$823$	−17.2838	+	53.1942i	−0.602476	+	1.85423i	−0.513287	+	0.858217i	$0.671572\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	5.95965	−	18.3419i	0.207237	−	0.637811i	−0.792377	−	0.610032i	$-0.791156\pi$
$827$	5.95965	−	18.3419i	0.207237	−	0.637811i	0.999614	−	0.0277792i	$-0.00884352\pi$
$828$		0			0
$829$	13.8870	+	10.0895i	0.482316	+	0.350423i	0.802222	−	0.597026i	$-0.203651\pi$
$829$	13.8870	+	10.0895i	0.482316	+	0.350423i	−0.319906	+	0.947449i	$0.603651\pi$
$830$		0			0
$831$	−9.97991	−	30.7150i	−0.346199	−	1.06549i
$832$		0			0
$833$	12.9868	−	9.43543i	0.449964	−	0.326918i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−22.9572			−0.793517
$838$		0			0
$839$	−30.5653	+	22.2070i	−1.05523	+	0.766671i	−0.973200	−	0.229959i	$-0.926141\pi$
$839$	−30.5653	+	22.2070i	−1.05523	+	0.766671i	−0.0820317	+	0.996630i	$0.526141\pi$
$840$		0			0
$841$	−5.86830	−	18.0608i	−0.202355	−	0.622785i
$842$		0			0
$843$	−32.8544	−	23.8701i	−1.13157	−	0.822131i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	4.04041	−	18.1326i	0.138830	−	0.623044i
$848$		0			0
$849$	−10.3693	+	31.9133i	−0.355872	+	1.09526i
$850$		0			0
$851$	39.4139	+	28.6358i	1.35109	+	0.981624i
$852$		0			0
$853$	3.26607	+	10.0519i	0.111828	+	0.344171i	0.991272	−	0.131831i	$-0.0420855\pi$
$853$	3.26607	+	10.0519i	0.111828	+	0.344171i	−0.879444	+	0.476002i	$0.842086\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.6489			0.500395			0.250198	−	0.968195i	$-0.419504\pi$
$857$	14.6489			0.500395			0.250198	+	0.968195i	$0.419504\pi$
$858$		0			0
$859$	−1.44844			−0.0494202			−0.0247101	−	0.999695i	$-0.507866\pi$
$859$	−1.44844			−0.0494202			−0.0247101	+	0.999695i	$0.507866\pi$
$860$		0			0
$861$	35.1571	−	25.5432i	1.19815	−	0.870508i
$862$		0			0
$863$	14.9448	+	45.9954i	0.508727	+	1.56570i	0.794414	+	0.607377i	$0.207778\pi$
$863$	14.9448	+	45.9954i	0.508727	+	1.56570i	−0.285687	+	0.958323i	$0.592222\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.87477	−	5.76996i	0.0636707	−	0.195958i
$868$		0			0
$869$	−43.8668	+	35.1680i	−1.48808	+	1.19299i
$870$		0			0
$871$	12.0836	−	37.1896i	0.409438	−	1.26012i
$872$		0			0
$873$	32.5794	+	23.6703i	1.10265	+	0.801120i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.16586	+	4.47976i	−0.208206	+	0.151271i	−0.687002	−	0.726656i	$-0.741074\pi$
$877$	−6.16586	+	4.47976i	−0.208206	+	0.151271i	0.478795	+	0.877926i	$0.341074\pi$
$878$		0			0
$879$	28.9718			0.977194
$880$		0			0
$881$	−14.1585			−0.477013			−0.238506	−	0.971141i	$-0.576658\pi$
$881$	−14.1585			−0.477013			−0.238506	+	0.971141i	$0.576658\pi$
$882$		0			0
$883$	24.6162	−	17.8847i	0.828400	−	0.601868i	−0.0907061	−	0.995878i	$-0.528912\pi$
$883$	24.6162	−	17.8847i	0.828400	−	0.601868i	0.919106	+	0.394010i	$0.128912\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	40.5308	+	29.4474i	1.36089	+	0.988746i	0.998388	+	0.0567640i	$0.0180782\pi$
$887$	40.5308	+	29.4474i	1.36089	+	0.988746i	0.362504	+	0.931982i	$0.381922\pi$
$888$		0			0
$889$	4.88157	−	15.0239i	0.163723	−	0.503886i
$890$		0			0
$891$	−10.5791	−	27.9685i	−0.354413	−	0.936981i
$892$		0			0
$893$	8.46291	−	26.0462i	0.283200	−	0.871601i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	25.5904	+	78.7592i	0.854440	+	2.62969i
$898$		0			0
$899$	6.52451	−	4.74033i	0.217605	−	0.158099i
$900$		0			0
$901$	37.6308			1.25366
$902$		0			0
$903$	17.7283			0.589960
$904$		0			0
$905$		0			0
$906$		0			0
$907$	11.0004	+	33.8559i	0.365264	+	1.12417i	0.949816	+	0.312810i	$0.101270\pi$
$907$	11.0004	+	33.8559i	0.365264	+	1.12417i	−0.584552	+	0.811356i	$0.698730\pi$
$908$		0			0
$909$	−23.7596	−	17.2623i	−0.788055	−	0.572556i
$910$		0			0
$911$	14.7216	−	45.3086i	0.487750	−	1.50114i	−0.340208	−	0.940350i	$-0.610498\pi$
$911$	14.7216	−	45.3086i	0.487750	−	1.50114i	0.827958	−	0.560790i	$-0.189502\pi$
$912$		0			0
$913$	−10.5163	+	38.4917i	−0.348039	+	1.27389i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.1881	−	10.3083i	−0.468534	−	0.340410i
$918$		0			0
$919$	17.3383	+	53.3617i	0.571937	+	1.76024i	0.646380	+	0.763016i	$0.276282\pi$
$919$	17.3383	+	53.3617i	0.571937	+	1.76024i	−0.0744426	+	0.997225i	$0.523718\pi$
$920$		0			0
$921$	−12.6452	+	9.18726i	−0.416673	+	0.302731i
$922$		0			0
$923$	34.2669			1.12791
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−80.9773	+	58.8335i	−2.65965	+	1.93235i
$928$		0			0
$929$	−8.31625	−	25.5948i	−0.272847	−	0.839737i	−0.989781	−	0.142596i	$-0.954455\pi$
$929$	−8.31625	−	25.5948i	−0.272847	−	0.839737i	0.716934	−	0.697141i	$-0.245545\pi$
$930$		0			0
$931$	−21.6126	−	15.7025i	−0.708325	−	0.514628i
$932$		0			0
$933$	−22.3992	+	68.9375i	−0.733316	+	2.25691i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	2.18459	−	6.72349i	0.0713676	−	0.219647i	−0.909010	−	0.416773i	$-0.863161\pi$
$937$	2.18459	−	6.72349i	0.0713676	−	0.219647i	0.980378	+	0.197126i	$0.0631609\pi$
$938$		0			0
$939$	−31.8088	−	23.1104i	−1.03804	−	0.754180i
$940$		0			0
$941$	−4.39849	−	13.5372i	−0.143387	−	0.441298i	0.853413	−	0.521235i	$-0.174528\pi$
$941$	−4.39849	−	13.5372i	−0.143387	−	0.441298i	−0.996800	+	0.0799361i	$0.974528\pi$
$942$		0			0
$943$	51.6132	−	37.4992i	1.68076	−	1.22114i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.1617			−0.460194			−0.230097	−	0.973168i	$-0.573904\pi$
$947$	−14.1617			−0.460194			−0.230097	+	0.973168i	$0.573904\pi$
$948$		0			0
$949$	10.9833	−	7.97982i	0.356533	−	0.259036i
$950$		0			0
$951$	6.56520	+	20.2056i	0.212891	+	0.655211i
$952$		0			0
$953$	0.256983	+	0.186709i	0.00832448	+	0.00604809i	0.591940	−	0.805982i	$-0.298362\pi$
$953$	0.256983	+	0.186709i	0.00832448	+	0.00604809i	−0.583615	+	0.812030i	$0.698362\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	26.3193	+	17.2760i	0.850781	+	0.558452i
$958$		0			0
$959$	8.09179	−	24.9040i	0.261298	−	0.804191i
$960$		0			0
$961$	19.8228	+	14.4021i	0.639446	+	0.464585i
$962$		0			0
$963$	−4.41678	−	13.5934i	−0.142329	−	0.438042i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	37.3690			1.20171			0.600853	−	0.799359i	$-0.294828\pi$
$967$	37.3690			1.20171			0.600853	+	0.799359i	$0.294828\pi$
$968$		0			0
$969$	74.7862			2.40248
$970$		0			0
$971$	−24.6036	+	17.8756i	−0.789568	+	0.573655i	−0.907835	−	0.419327i	$-0.862266\pi$
$971$	−24.6036	+	17.8756i	−0.789568	+	0.573655i	0.118267	+	0.992982i	$0.462266\pi$
$972$		0			0
$973$	−10.9540	−	33.7129i	−0.351168	−	1.08078i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.66642	+	20.5171i	−0.213278	+	0.656401i	0.785994	+	0.618235i	$0.212152\pi$
$977$	−6.66642	+	20.5171i	−0.213278	+	0.656401i	−0.999271	+	0.0381668i	$0.987848\pi$
$978$		0			0
$979$	−43.2205	−	28.3699i	−1.38133	−	0.906707i
$980$		0			0
$981$	28.4218	−	87.4732i	0.907437	−	2.79281i
$982$		0			0
$983$	−9.34171	−	6.78715i	−0.297954	−	0.216477i	0.428756	−	0.903420i	$-0.358952\pi$
$983$	−9.34171	−	6.78715i	−0.297954	−	0.216477i	−0.726711	+	0.686944i	$0.758952\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−17.4308	+	12.6642i	−0.554828	+	0.403106i
$988$		0			0
$989$	26.0264			0.827591
$990$		0			0
$991$	10.6881			0.339518			0.169759	−	0.985486i	$-0.445701\pi$
$991$	10.6881			0.339518			0.169759	+	0.985486i	$0.445701\pi$
$992$		0			0
$993$	−4.27928	+	3.10908i	−0.135799	+	0.0986636i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−27.6093	−	20.0593i	−0.874394	−	0.635285i	0.0573683	−	0.998353i	$-0.481729\pi$
$997$	−27.6093	−	20.0593i	−0.874394	−	0.635285i	−0.931762	+	0.363069i	$0.881729\pi$
$998$		0			0
$999$	−18.2269	+	56.0967i	−0.576674	+	1.77482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.n.e.801.4	yes	16
5.2	odd	4		1100.2.cb.d.449.1		32
5.3	odd	4		1100.2.cb.d.449.8		32
5.4	even	2		1100.2.n.d.801.1	yes	16
11.5	even	5	inner	1100.2.n.e.401.4	yes	16
55.27	odd	20		1100.2.cb.d.49.8		32
55.38	odd	20		1100.2.cb.d.49.1		32
55.49	even	10		1100.2.n.d.401.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.n.d.401.1	✓	16	55.49	even	10
1100.2.n.d.801.1	yes	16	5.4	even	2
1100.2.n.e.401.4	yes	16	11.5	even	5	inner
1100.2.n.e.801.4	yes	16	1.1	even	1	trivial
1100.2.cb.d.49.1		32	55.38	odd	20
1100.2.cb.d.49.8		32	55.27	odd	20
1100.2.cb.d.449.1		32	5.2	odd	4
1100.2.cb.d.449.8		32	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.42729 - 1.76353i) q^{3} +(-1.36631 - 0.992679i) q^{7} +(1.85465 - 5.70802i) q^{9} +(2.77267 + 1.81998i) q^{11} +(1.14660 - 3.52887i) q^{13} +(1.19594 + 3.68071i) q^{17} +(5.21062 - 3.78574i) q^{19} -5.06704 q^{21} -7.43878 q^{23} +(-2.78307 - 8.56540i) q^{27} +(2.55959 + 1.85965i) q^{29} +(0.787699 - 2.42429i) q^{31} +(9.93965 - 0.472068i) q^{33} +(-5.29843 - 3.84954i) q^{37} +(-3.44014 - 10.5877i) q^{39} +(-6.93840 + 5.04104i) q^{41} -3.49875 q^{43} +(3.44003 - 2.49933i) q^{47} +(-1.28174 - 3.94479i) q^{49} +(9.39392 + 6.82509i) q^{51} +(3.00470 - 9.24750i) q^{53} +(5.97143 - 18.3782i) q^{57} +(2.33853 + 1.69904i) q^{59} +(1.93043 + 5.94126i) q^{61} +(-8.20025 + 5.95783i) q^{63} +10.5387 q^{67} +(-18.0561 + 13.1185i) q^{69} +(2.85383 + 8.78318i) q^{71} +(2.96007 + 2.15062i) q^{73} +(-1.98166 - 5.23901i) q^{77} +(-5.23846 + 16.1223i) q^{79} +(-7.29404 - 5.29943i) q^{81} +(3.71779 + 11.4422i) q^{83} +9.49240 q^{87} -15.5881 q^{89} +(-5.06965 + 3.68331i) q^{91} +(-2.36333 - 7.27358i) q^{93} +(-2.07343 + 6.38135i) q^{97} +(15.5308 - 12.4510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 5 q^{11} - q^{13} - 8 q^{17} + 13 q^{19} - 6 q^{21} - 16 q^{23} - 37 q^{27} - 7 q^{29} + 2 q^{31} + 14 q^{33} - 8 q^{37} - 17 q^{39} - 15 q^{41} - 18 q^{47} - 24 q^{49} + 13 q^{51} - 6 q^{53}+ \cdots + 40 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - 5 * q^11 - q^13 - 8 * q^17 + 13 * q^19 - 6 * q^21 - 16 * q^23 - 37 * q^27 - 7 * q^29 + 2 * q^31 + 14 * q^33 - 8 * q^37 - 17 * q^39 - 15 * q^41 - 18 * q^47 - 24 * q^49 + 13 * q^51 - 6 * q^53 - 31 * q^57 + 6 * q^59 + 24 * q^61 + 5 * q^63 + 18 * q^67 - 53 * q^69 + 36 * q^71 - 9 * q^73 + 45 * q^77 - 45 * q^79 + 17 * q^81 - 14 * q^83 + 18 * q^87 + 18 * q^89 + 38 * q^91 - 29 * q^93 + 49 * q^97 + 40 * q^99

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