LMFDB - Embedded newform 768.2.o.b.287.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (of order $8$, degree $4$, not 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			287.4
Character	$\chi$	$=$	768.287
Dual form			768.2.o.b.479.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14895 - 1.29612i) q^{3} +(0.970873 - 2.34389i) q^{5} +(-1.60572 + 1.60572i) q^{7} +(-0.359830 + 2.97834i) q^{9} +O(q^{10})$	\(q+(-1.14895 - 1.29612i) q^{3} +(0.970873 - 2.34389i) q^{5} +(-1.60572 + 1.60572i) q^{7} +(-0.359830 + 2.97834i) q^{9} +(-1.85010 + 4.46654i) q^{11} +(-3.76813 + 1.56081i) q^{13} +(-4.15344 + 1.43465i) q^{15} +3.52935 q^{17} +(1.87141 + 4.51799i) q^{19} +(3.92609 + 0.236307i) q^{21} +(-2.48603 + 2.48603i) q^{23} +(-1.01571 - 1.01571i) q^{25} +(4.27370 - 2.95558i) q^{27} +(0.681149 - 0.282141i) q^{29} -4.63882i q^{31} +(7.91483 - 2.73389i) q^{33} +(2.20469 + 5.32259i) q^{35} +(-4.35102 - 1.80225i) q^{37} +(6.35238 + 3.09064i) q^{39} +(0.606628 + 0.606628i) q^{41} +(-0.565994 - 0.234442i) q^{43} +(6.63157 + 3.73499i) q^{45} -1.04074i q^{47} +1.84333i q^{49} +(-4.05505 - 4.57445i) q^{51} +(5.29738 + 2.19425i) q^{53} +(8.67289 + 8.67289i) q^{55} +(3.70568 - 7.61652i) q^{57} +(2.26739 + 0.939185i) q^{59} +(5.63874 + 13.6131i) q^{61} +(-4.20460 - 5.36017i) q^{63} +10.3474i q^{65} +(-10.1483 + 4.20357i) q^{67} +(6.07851 + 0.365859i) q^{69} +(-1.52242 - 1.52242i) q^{71} +(-10.0596 + 10.0596i) q^{73} +(-0.149478 + 2.48349i) q^{75} +(-4.20127 - 10.1428i) q^{77} -5.48744 q^{79} +(-8.74105 - 2.14339i) q^{81} +(-3.39246 + 1.40520i) q^{83} +(3.42655 - 8.27243i) q^{85} +(-1.14829 - 0.558681i) q^{87} +(-0.460940 + 0.460940i) q^{89} +(3.54433 - 8.55678i) q^{91} +(-6.01245 + 5.32977i) q^{93} +12.4066 q^{95} -3.50976 q^{97} +(-12.6372 - 7.11743i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

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
$3$	−1.14895	−	1.29612i	−0.663346	−	0.748312i
$3$	−1.14895	−	1.29612i	−0.663346	−	0.748312i
$4$		0			0
$5$	0.970873	−	2.34389i	0.434188	−	1.04822i	−0.543736	−	0.839257i	$-0.682991\pi$
$5$	0.970873	−	2.34389i	0.434188	−	1.04822i	0.977923	−	0.208965i	$-0.0670095\pi$
$6$		0			0
$7$	−1.60572	+	1.60572i	−0.606905	+	0.606905i	−0.942136	−	0.335231i	$-0.891186\pi$
$7$	−1.60572	+	1.60572i	−0.606905	+	0.606905i	0.335231	+	0.942136i	$0.391186\pi$
$8$		0			0
$9$	−0.359830	+	2.97834i	−0.119943	+	0.992781i
$10$		0			0
$11$	−1.85010	+	4.46654i	−0.557827	+	1.34671i	0.353657	+	0.935375i	$0.384938\pi$
$11$	−1.85010	+	4.46654i	−0.557827	+	1.34671i	−0.911483	+	0.411337i	$0.865062\pi$
$12$		0			0
$13$	−3.76813	+	1.56081i	−1.04509	+	0.432891i	−0.838137	−	0.545460i	$-0.816355\pi$
$13$	−3.76813	+	1.56081i	−1.04509	+	0.432891i	−0.206954	+	0.978351i	$0.566355\pi$
$14$		0			0
$15$	−4.15344	+	1.43465i	−1.07241	+	0.370426i
$16$		0			0
$17$	3.52935			0.855994			0.427997	−	0.903780i	$-0.359219\pi$
$17$	3.52935			0.855994			0.427997	+	0.903780i	$0.359219\pi$
$18$		0			0
$19$	1.87141	+	4.51799i	0.429332	+	1.03650i	0.979500	+	0.201445i	$0.0645637\pi$
$19$	1.87141	+	4.51799i	0.429332	+	1.03650i	−0.550168	+	0.835054i	$0.685436\pi$
$20$		0			0
$21$	3.92609	+	0.236307i	0.856743	+	0.0515663i
$22$		0			0
$23$	−2.48603	+	2.48603i	−0.518374	+	0.518374i	−0.917079	−	0.398705i	$-0.869460\pi$
$23$	−2.48603	+	2.48603i	−0.518374	+	0.518374i	0.398705	+	0.917079i	$0.369460\pi$
$24$		0			0
$25$	−1.01571	−	1.01571i	−0.203143	−	0.203143i
$26$		0			0
$27$	4.27370	−	2.95558i	0.822474	−	0.568803i
$28$		0			0
$29$	0.681149	−	0.282141i	0.126486	−	0.0523923i	−0.318543	−	0.947909i	$-0.603193\pi$
$29$	0.681149	−	0.282141i	0.126486	−	0.0523923i	0.445029	+	0.895516i	$0.353193\pi$
$30$		0			0
$31$		−	4.63882i		−	0.833157i	−0.909100	−	0.416578i	$-0.863229\pi$
$31$		−	4.63882i		−	0.833157i	0.909100	−	0.416578i	$-0.136771\pi$
$32$		0			0
$33$	7.91483	−	2.73389i	1.37779	−	0.475908i
$34$		0			0
$35$	2.20469	+	5.32259i	0.372660	+	0.899681i
$36$		0			0
$37$	−4.35102	−	1.80225i	−0.715304	−	0.296289i	−0.00480655	−	0.999988i	$-0.501530\pi$
$37$	−4.35102	−	1.80225i	−0.715304	−	0.296289i	−0.710497	+	0.703700i	$0.751530\pi$
$38$		0			0
$39$	6.35238	+	3.09064i	1.01719	+	0.494898i
$40$		0			0
$41$	0.606628	+	0.606628i	0.0947393	+	0.0947393i	0.752888	−	0.658149i	$-0.228660\pi$
$41$	0.606628	+	0.606628i	0.0947393	+	0.0947393i	−0.658149	+	0.752888i	$0.728660\pi$
$42$		0			0
$43$	−0.565994	−	0.234442i	−0.0863133	−	0.0357521i	0.339109	−	0.940747i	$-0.389874\pi$
$43$	−0.565994	−	0.234442i	−0.0863133	−	0.0357521i	−0.425422	+	0.904995i	$0.639874\pi$
$44$		0			0
$45$	6.63157	+	3.73499i	0.988576	+	0.556780i
$46$		0			0
$47$		−	1.04074i		−	0.151808i	−0.997115	−	0.0759039i	$-0.975816\pi$
$47$		−	1.04074i		−	0.151808i	0.997115	−	0.0759039i	$-0.0241842\pi$
$48$		0			0
$49$			1.84333i			0.263333i
$50$		0			0
$51$	−4.05505	−	4.57445i	−0.567820	−	0.640551i
$52$		0			0
$53$	5.29738	+	2.19425i	0.727651	+	0.301403i	0.715586	−	0.698524i	$-0.246160\pi$
$53$	5.29738	+	2.19425i	0.727651	+	0.301403i	0.0120644	+	0.999927i	$0.496160\pi$
$54$		0			0
$55$	8.67289	+	8.67289i	1.16945	+	1.16945i
$56$		0			0
$57$	3.70568	−	7.61652i	0.490829	−	1.00883i
$58$		0			0
$59$	2.26739	+	0.939185i	0.295189	+	0.122271i	0.525363	−	0.850878i	$-0.323929\pi$
$59$	2.26739	+	0.939185i	0.295189	+	0.122271i	−0.230174	+	0.973150i	$0.573929\pi$
$60$		0			0
$61$	5.63874	+	13.6131i	0.721967	+	1.74298i	0.667670	+	0.744457i	$0.267292\pi$
$61$	5.63874	+	13.6131i	0.721967	+	1.74298i	0.0542969	+	0.998525i	$0.482708\pi$
$62$		0			0
$63$	−4.20460	−	5.36017i	−0.529729	−	0.675318i
$64$		0			0
$65$			10.3474i			1.28344i
$66$		0			0
$67$	−10.1483	+	4.20357i	−1.23981	+	0.513548i	−0.903656	−	0.428258i	$-0.859127\pi$
$67$	−10.1483	+	4.20357i	−1.23981	+	0.513548i	−0.336157	+	0.941806i	$0.609127\pi$
$68$		0			0
$69$	6.07851	+	0.365859i	0.731767	+	0.0440442i
$70$		0			0
$71$	−1.52242	−	1.52242i	−0.180678	−	0.180678i	0.610973	−	0.791651i	$-0.290778\pi$
$71$	−1.52242	−	1.52242i	−0.180678	−	0.180678i	−0.791651	+	0.610973i	$0.790778\pi$
$72$		0			0
$73$	−10.0596	+	10.0596i	−1.17739	+	1.17739i	−0.196979	+	0.980408i	$0.563113\pi$
$73$	−10.0596	+	10.0596i	−1.17739	+	1.17739i	−0.980408	+	0.196979i	$0.936887\pi$
$74$		0			0
$75$	−0.149478	+	2.48349i	−0.0172603	+	0.286769i
$76$		0			0
$77$	−4.20127	−	10.1428i	−0.478779	−	1.15587i
$78$		0			0
$79$	−5.48744			−0.617385			−0.308693	−	0.951162i	$-0.599891\pi$
$79$	−5.48744			−0.617385			−0.308693	+	0.951162i	$0.599891\pi$
$80$		0			0
$81$	−8.74105	−	2.14339i	−0.971227	−	0.238155i
$82$		0			0
$83$	−3.39246	+	1.40520i	−0.372371	+	0.154241i	−0.561018	−	0.827804i	$-0.689590\pi$
$83$	−3.39246	+	1.40520i	−0.372371	+	0.154241i	0.188646	+	0.982045i	$0.439590\pi$
$84$		0			0
$85$	3.42655	−	8.27243i	0.371662	−	0.897271i
$86$		0			0
$87$	−1.14829	−	0.558681i	−0.123110	−	0.0598969i
$88$		0			0
$89$	−0.460940	+	0.460940i	−0.0488596	+	0.0488596i	−0.731114	−	0.682255i	$-0.760999\pi$
$89$	−0.460940	+	0.460940i	−0.0488596	+	0.0488596i	0.682255	+	0.731114i	$0.260999\pi$
$90$		0			0
$91$	3.54433	−	8.55678i	0.371547	−	0.896994i
$92$		0			0
$93$	−6.01245	+	5.32977i	−0.623462	+	0.552672i
$94$		0			0
$95$	12.4066			1.27289
$96$		0			0
$97$	−3.50976			−0.356362			−0.178181	−	0.983998i	$-0.557021\pi$
$97$	−3.50976			−0.356362			−0.178181	+	0.983998i	$0.557021\pi$
$98$		0			0
$99$	−12.6372	−	7.11743i	−1.27008	−	0.715329i
$100$		0			0
$101$	−4.59506	+	11.0935i	−0.457225	+	1.10384i	0.512291	+	0.858812i	$0.328797\pi$
$101$	−4.59506	+	11.0935i	−0.457225	+	1.10384i	−0.969516	+	0.245028i	$0.921203\pi$
$102$		0			0
$103$	0.531901	−	0.531901i	0.0524097	−	0.0524097i	−0.680416	−	0.732826i	$-0.738201\pi$
$103$	0.531901	−	0.531901i	0.0524097	−	0.0524097i	0.732826	+	0.680416i	$0.238201\pi$
$104$		0			0
$105$	4.36561	−	8.97291i	0.426040	−	0.875667i
$106$		0			0
$107$	6.91982	−	16.7059i	0.668964	−	1.61502i	−0.114382	−	0.993437i	$-0.536489\pi$
$107$	6.91982	−	16.7059i	0.668964	−	1.61502i	0.783346	−	0.621586i	$-0.213511\pi$
$108$		0			0
$109$	−4.18161	+	1.73208i	−0.400526	+	0.165903i	−0.573848	−	0.818962i	$-0.694550\pi$
$109$	−4.18161	+	1.73208i	−0.400526	+	0.165903i	0.173322	+	0.984865i	$0.444550\pi$
$110$		0			0
$111$	2.66318	+	7.71013i	0.252778	+	0.731813i
$112$		0			0
$113$	11.4007			1.07248			0.536242	−	0.844064i	$-0.319844\pi$
$113$	11.4007			1.07248			0.536242	+	0.844064i	$0.319844\pi$
$114$		0			0
$115$	3.41338	+	8.24062i	0.318299	+	0.768442i
$116$		0			0
$117$	−3.29274	−	11.7844i	−0.304414	−	1.08947i
$118$		0			0
$119$	−5.66715	+	5.66715i	−0.519507	+	0.519507i
$120$		0			0
$121$	−8.74893	−	8.74893i	−0.795358	−	0.795358i
$122$		0			0
$123$	0.0892747	−	1.48324i	0.00804963	−	0.133740i
$124$		0			0
$125$	8.35262	−	3.45977i	0.747081	−	0.309451i
$126$		0			0
$127$			17.0225i			1.51051i	0.655434	+	0.755253i	$0.272486\pi$
$127$			17.0225i			1.51051i	−0.655434	+	0.755253i	$0.727514\pi$
$128$		0			0
$129$	0.346434	+	1.00296i	0.0305018	+	0.0883053i
$130$		0			0
$131$	1.01086	+	2.44044i	0.0883195	+	0.213222i	0.961867	−	0.273516i	$-0.0881866\pi$
$131$	1.01086	+	2.44044i	0.0883195	+	0.213222i	−0.873548	+	0.486738i	$0.838187\pi$
$132$		0			0
$133$	−10.2596	−	4.24966i	−0.889620	−	0.368493i
$134$		0			0
$135$	−2.77836	−	12.8866i	−0.239123	−	1.10910i
$136$		0			0
$137$	−14.5134	−	14.5134i	−1.23997	−	1.23997i	−0.960014	−	0.279953i	$-0.909681\pi$
$137$	−14.5134	−	14.5134i	−1.23997	−	1.23997i	−0.279953	−	0.960014i	$-0.590319\pi$
$138$		0			0
$139$	15.9809	+	6.61950i	1.35548	+	0.561459i	0.937813	−	0.347141i	$-0.112847\pi$
$139$	15.9809	+	6.61950i	1.35548	+	0.561459i	0.417669	+	0.908599i	$0.362847\pi$
$140$		0			0
$141$	−1.34892	+	1.19576i	−0.113600	+	0.100701i
$142$		0			0
$143$		−	19.7182i		−	1.64891i
$144$		0			0
$145$		−	1.87046i		−	0.155334i
$146$		0			0
$147$	2.38917	−	2.11790i	0.197055	−	0.174681i
$148$		0			0
$149$	−12.5382	−	5.19348i	−1.02717	−	0.425466i	−0.195477	−	0.980708i	$-0.562626\pi$
$149$	−12.5382	−	5.19348i	−1.02717	−	0.425466i	−0.831689	+	0.555242i	$0.812626\pi$
$150$		0			0
$151$	3.63118	+	3.63118i	0.295501	+	0.295501i	0.839249	−	0.543748i	$-0.182995\pi$
$151$	3.63118	+	3.63118i	0.295501	+	0.295501i	−0.543748	+	0.839249i	$0.682995\pi$
$152$		0			0
$153$	−1.26997	+	10.5116i	−0.102671	+	0.849814i
$154$		0			0
$155$	−10.8729	−	4.50371i	−0.873333	−	0.361746i
$156$		0			0
$157$	−6.88058	−	16.6112i	−0.549130	−	1.32572i	−0.918127	−	0.396286i	$-0.870299\pi$
$157$	−6.88058	−	16.6112i	−0.549130	−	1.32572i	0.368997	−	0.929431i	$-0.379701\pi$
$158$		0			0
$159$	−3.24242	−	9.38709i	−0.257141	−	0.744444i
$160$		0			0
$161$		−	7.98374i		−	0.629207i
$162$		0			0
$163$	9.77028	−	4.04698i	0.765268	−	0.316984i	0.0343138	−	0.999411i	$-0.489075\pi$
$163$	9.77028	−	4.04698i	0.765268	−	0.316984i	0.730954	+	0.682427i	$0.239075\pi$
$164$		0			0
$165$	1.27635	−	21.2058i	0.0993638	−	1.65087i
$166$		0			0
$167$	−9.39415	−	9.39415i	−0.726941	−	0.726941i	0.243068	−	0.970009i	$-0.421846\pi$
$167$	−9.39415	−	9.39415i	−0.726941	−	0.726941i	−0.970009	+	0.243068i	$0.921846\pi$
$168$		0			0
$169$	2.57027	−	2.57027i	0.197713	−	0.197713i
$170$		0			0
$171$	−14.1295	+	3.94800i	−1.08051	+	0.301911i
$172$		0			0
$173$	2.32375	+	5.61003i	0.176671	+	0.426522i	0.987265	−	0.159087i	$-0.0508551\pi$
$173$	2.32375	+	5.61003i	0.176671	+	0.426522i	−0.810593	+	0.585610i	$0.800855\pi$
$174$		0			0
$175$	3.26190			0.246577
$176$		0			0
$177$	−1.38783	−	4.01788i	−0.104316	−	0.302002i
$178$		0			0
$179$	6.06280	−	2.51129i	0.453155	−	0.187703i	−0.144419	−	0.989517i	$-0.546131\pi$
$179$	6.06280	−	2.51129i	0.453155	−	0.187703i	0.597574	+	0.801814i	$0.296131\pi$
$180$		0			0
$181$	−4.36208	+	10.5310i	−0.324231	+	0.782763i	0.674768	+	0.738030i	$0.264244\pi$
$181$	−4.36208	+	10.5310i	−0.324231	+	0.782763i	−0.998999	+	0.0447329i	$0.985756\pi$
$182$		0			0
$183$	11.1656	−	22.9493i	0.825381	−	1.69646i
$184$		0			0
$185$	−8.44858	+	8.44858i	−0.621152	+	0.621152i
$186$		0			0
$187$	−6.52966	+	15.7640i	−0.477496	+	1.15278i
$188$		0			0
$189$	−2.11652	+	11.6082i	−0.153954	+	0.844372i
$190$		0			0
$191$	3.01629			0.218251			0.109126	−	0.994028i	$-0.465195\pi$
$191$	3.01629			0.218251			0.109126	+	0.994028i	$0.465195\pi$
$192$		0			0
$193$	4.88422			0.351574			0.175787	−	0.984428i	$-0.443753\pi$
$193$	4.88422			0.351574			0.175787	+	0.984428i	$0.443753\pi$
$194$		0			0
$195$	13.4115	−	11.8887i	0.960416	−	0.851367i
$196$		0			0
$197$	−5.02958	+	12.1425i	−0.358343	+	0.865116i	0.637191	+	0.770706i	$0.280096\pi$
$197$	−5.02958	+	12.1425i	−0.358343	+	0.865116i	−0.995533	+	0.0944095i	$0.969904\pi$
$198$		0			0
$199$	0.383062	−	0.383062i	0.0271545	−	0.0271545i	−0.693399	−	0.720554i	$-0.743888\pi$
$199$	0.383062	−	0.383062i	0.0271545	−	0.0271545i	0.720554	+	0.693399i	$0.243888\pi$
$200$		0			0
$201$	17.1082	+	8.32370i	1.20672	+	0.587108i
$202$		0			0
$203$	−0.640694	+	1.54677i	−0.0449679	+	0.108562i
$204$		0			0
$205$	2.01083	−	0.832913i	0.140442	−	0.0581732i
$206$		0			0
$207$	−6.50971	−	8.29880i	−0.452456	−	0.576807i
$208$		0			0
$209$	−23.6421			−1.63536
$210$		0			0
$211$	−4.15639	−	10.0344i	−0.286138	−	0.690798i	0.713817	−	0.700332i	$-0.246965\pi$
$211$	−4.15639	−	10.0344i	−0.286138	−	0.690798i	−0.999955	+	0.00953483i	$0.996965\pi$
$212$		0			0
$213$	−0.224048	+	3.72242i	−0.0153515	+	0.255056i
$214$		0			0
$215$	−1.09902	+	1.09902i	−0.0749523	+	0.0749523i
$216$		0			0
$217$	7.44864	+	7.44864i	0.505647	+	0.505647i
$218$		0			0
$219$	24.5964	+	1.48043i	1.66207	+	0.100038i
$220$		0			0
$221$	−13.2991	+	5.50865i	−0.894591	+	0.370552i
$222$		0			0
$223$		−	8.46207i		−	0.566662i	−0.959022	−	0.283331i	$-0.908560\pi$
$223$		−	8.46207i		−	0.566662i	0.959022	−	0.283331i	$-0.0914395\pi$
$224$		0			0
$225$	3.39063	−	2.65966i	0.226042	−	0.177311i
$226$		0			0
$227$	−1.09044	−	2.63257i	−0.0723754	−	0.174730i	0.883552	−	0.468333i	$-0.155145\pi$
$227$	−1.09044	−	2.63257i	−0.0723754	−	0.174730i	−0.955927	+	0.293604i	$0.905145\pi$
$228$		0			0
$229$	19.1182	+	7.91903i	1.26337	+	0.523305i	0.910942	−	0.412535i	$-0.135356\pi$
$229$	19.1182	+	7.91903i	1.26337	+	0.523305i	0.352427	+	0.935839i	$0.385356\pi$
$230$		0			0
$231$	−8.31913	+	17.0988i	−0.547359	+	1.12502i
$232$		0			0
$233$	−0.892522	−	0.892522i	−0.0584710	−	0.0584710i	0.677267	−	0.735738i	$-0.263164\pi$
$233$	−0.892522	−	0.892522i	−0.0584710	−	0.0584710i	−0.735738	+	0.677267i	$0.763164\pi$
$234$		0			0
$235$	−2.43939	−	1.01043i	−0.159128	−	0.0659131i
$236$		0			0
$237$	6.30479	+	7.11236i	0.409540	+	0.461997i
$238$		0			0
$239$			11.6414i			0.753017i	0.926413	+	0.376509i	$0.122876\pi$
$239$			11.6414i			0.753017i	−0.926413	+	0.376509i	$0.877124\pi$
$240$		0			0
$241$			10.7911i			0.695116i	0.937659	+	0.347558i	$0.112989\pi$
$241$			10.7911i			0.695116i	−0.937659	+	0.347558i	$0.887011\pi$
$242$		0			0
$243$	7.26494	+	13.7921i	0.466046	+	0.884760i
$244$		0			0
$245$	4.32058	+	1.78964i	0.276031	+	0.114336i
$246$		0			0
$247$	−14.1035	−	14.1035i	−0.897381	−	0.897381i
$248$		0			0
$249$	5.71908	+	2.78252i	0.362432	+	0.176335i
$250$		0			0
$251$	−16.4676	−	6.82109i	−1.03942	−	0.430543i	−0.203318	−	0.979113i	$-0.565173\pi$
$251$	−16.4676	−	6.82109i	−1.03942	−	0.430543i	−0.836105	+	0.548570i	$0.815173\pi$
$252$		0			0
$253$	−6.50455	−	15.7034i	−0.408938	−	0.987263i
$254$		0			0
$255$	−14.6590	+	5.06340i	−0.917980	+	0.317082i
$256$		0			0
$257$			1.65839i			0.103448i	0.998661	+	0.0517239i	$0.0164716\pi$
$257$			1.65839i			0.103448i	−0.998661	+	0.0517239i	$0.983528\pi$
$258$		0			0
$259$	9.88043	−	4.09261i	0.613940	−	0.254302i
$260$		0			0
$261$	0.595215	+	2.13022i	0.0368429	+	0.131857i
$262$		0			0
$263$	19.0749	+	19.0749i	1.17621	+	1.17621i	0.980703	+	0.195503i	$0.0626339\pi$
$263$	19.0749	+	19.0749i	1.17621	+	1.17621i	0.195503	+	0.980703i	$0.437366\pi$
$264$		0			0
$265$	10.2862	−	10.2862i	0.631874	−	0.631874i
$266$		0			0
$267$	1.12703	+	0.0678346i	0.0689731	+	0.00415141i
$268$		0			0
$269$	−10.0864	−	24.3507i	−0.614979	−	1.48469i	−0.857469	−	0.514536i	$-0.827964\pi$
$269$	−10.0864	−	24.3507i	−0.614979	−	1.48469i	0.242490	−	0.970154i	$-0.422036\pi$
$270$		0			0
$271$	10.5104			0.638463			0.319231	−	0.947677i	$-0.396575\pi$
$271$	10.5104			0.638463			0.319231	+	0.947677i	$0.396575\pi$
$272$		0			0
$273$	−15.1628	+	5.23744i	−0.917696	+	0.316984i
$274$		0			0
$275$	6.41591	−	2.65756i	0.386894	−	0.160257i
$276$		0			0
$277$	−8.45233	+	20.4057i	−0.507851	+	1.22606i	0.437267	+	0.899332i	$0.355947\pi$
$277$	−8.45233	+	20.4057i	−0.507851	+	1.22606i	−0.945118	+	0.326729i	$0.894053\pi$
$278$		0			0
$279$	13.8160	+	1.66918i	0.827142	+	0.0999315i
$280$		0			0
$281$	3.13790	−	3.13790i	0.187191	−	0.187191i	−0.607289	−	0.794481i	$-0.707743\pi$
$281$	3.13790	−	3.13790i	0.187191	−	0.187191i	0.794481	+	0.607289i	$0.207743\pi$
$282$		0			0
$283$	−3.61311	+	8.72283i	−0.214777	+	0.518518i	−0.994146	−	0.108048i	$-0.965540\pi$
$283$	−3.61311	+	8.72283i	−0.214777	+	0.518518i	0.779368	+	0.626566i	$0.215540\pi$
$284$		0			0
$285$	−14.2546	−	16.0804i	−0.844368	−	0.952520i
$286$		0			0
$287$	−1.94815			−0.114995
$288$		0			0
$289$	−4.54367			−0.267275
$290$		0			0
$291$	4.03254	+	4.54905i	0.236392	+	0.266670i
$292$		0			0
$293$	−1.40313	+	3.38745i	−0.0819716	+	0.197897i	−0.959551	−	0.281534i	$-0.909157\pi$
$293$	−1.40313	+	3.38745i	−0.0819716	+	0.197897i	0.877580	+	0.479431i	$0.159157\pi$
$294$		0			0
$295$	4.40270	−	4.40270i	0.256335	−	0.256335i
$296$		0			0
$297$	5.29446	+	24.5568i	0.307216	+	1.42493i
$298$		0			0
$299$	5.48746	−	13.2479i	0.317348	−	0.766146i
$300$		0			0
$301$	1.28528	−	0.532379i	0.0740821	−	0.0306858i
$302$		0			0
$303$	19.6579	−	6.79009i	1.12932	−	0.390081i
$304$		0			0
$305$	37.3822			2.14050
$306$		0			0
$307$	−6.27230	−	15.1427i	−0.357979	−	0.864238i	−0.995584	−	0.0938743i	$-0.970075\pi$
$307$	−6.27230	−	15.1427i	−0.357979	−	0.864238i	0.637605	−	0.770363i	$-0.279925\pi$
$308$		0			0
$309$	−1.30053	−	0.0782775i	−0.0739847	−	0.00445305i
$310$		0			0
$311$	−11.1566	+	11.1566i	−0.632635	+	0.632635i	−0.948728	−	0.316094i	$-0.897629\pi$
$311$	−11.1566	+	11.1566i	−0.632635	+	0.632635i	0.316094	+	0.948728i	$0.397629\pi$
$312$		0			0
$313$	7.05760	+	7.05760i	0.398919	+	0.398919i	0.877852	−	0.478933i	$-0.158976\pi$
$313$	7.05760	+	7.05760i	0.398919	+	0.398919i	−0.478933	+	0.877852i	$0.658976\pi$
$314$		0			0
$315$	−16.6458	+	4.65109i	−0.937884	+	0.262059i
$316$		0			0
$317$	26.1796	−	10.8440i	1.47039	−	0.609057i	0.503446	−	0.864027i	$-0.332065\pi$
$317$	26.1796	−	10.8440i	1.47039	−	0.609057i	0.966949	+	0.254969i	$0.0820654\pi$
$318$		0			0
$319$			3.56437i			0.199566i
$320$		0			0
$321$	−29.6033	+	10.2254i	−1.65230	+	0.570725i
$322$		0			0
$323$	6.60488	+	15.9456i	0.367505	+	0.887237i
$324$		0			0
$325$	5.41268	+	2.24201i	0.300241	+	0.124364i
$326$		0			0
$327$	7.04944	+	3.42978i	0.389835	+	0.189667i
$328$		0			0
$329$	1.67114	+	1.67114i	0.0921329	+	0.0921329i
$330$		0			0
$331$	−20.9565	−	8.68047i	−1.15187	−	0.477122i	−0.276713	−	0.960953i	$-0.589245\pi$
$331$	−20.9565	−	8.68047i	−1.15187	−	0.477122i	−0.875162	+	0.483831i	$0.839245\pi$
$332$		0			0
$333$	6.93335	−	12.3103i	0.379945	−	0.674602i
$334$		0			0
$335$			27.8677i			1.52258i
$336$		0			0
$337$		−	31.4720i		−	1.71439i	−0.514992	−	0.857195i	$-0.672205\pi$
$337$		−	31.4720i		−	1.71439i	0.514992	−	0.857195i	$-0.327795\pi$
$338$		0			0
$339$	−13.0988	−	14.7766i	−0.711428	−	0.802553i
$340$		0			0
$341$	20.7195	+	8.58229i	1.12202	+	0.464757i
$342$		0			0
$343$	−14.1999	−	14.1999i	−0.766723	−	0.766723i
$344$		0			0
$345$	6.75900	−	13.8922i	0.363892	−	0.747930i
$346$		0			0
$347$	1.28308	+	0.531467i	0.0688791	+	0.0285307i	0.416857	−	0.908972i	$-0.363132\pi$
$347$	1.28308	+	0.531467i	0.0688791	+	0.0285307i	−0.347978	+	0.937503i	$0.613132\pi$
$348$		0			0
$349$	3.87192	+	9.34765i	0.207259	+	0.500368i	0.992990	−	0.118201i	$-0.0377127\pi$
$349$	3.87192	+	9.34765i	0.207259	+	0.500368i	−0.785730	+	0.618569i	$0.787713\pi$
$350$		0			0
$351$	−11.4907	+	17.8075i	−0.613331	+	0.950492i
$352$		0			0
$353$		−	30.0966i		−	1.60188i	−0.598744	−	0.800941i	$-0.704333\pi$
$353$		−	30.0966i		−	1.60188i	0.598744	−	0.800941i	$-0.295667\pi$
$354$		0			0
$355$	−5.04648	+	2.09032i	−0.267839	+	0.110943i
$356$		0			0
$357$	13.8565	+	0.834010i	0.733366	+	0.0441405i
$358$		0			0
$359$	−6.32903	−	6.32903i	−0.334034	−	0.334034i	0.520082	−	0.854116i	$-0.325901\pi$
$359$	−6.32903	−	6.32903i	−0.334034	−	0.334034i	−0.854116	+	0.520082i	$0.825901\pi$
$360$		0			0
$361$	−3.47505	+	3.47505i	−0.182897	+	0.182897i
$362$		0			0
$363$	−1.28754	+	21.3917i	−0.0675785	+	1.12277i
$364$		0			0
$365$	13.8120	+	33.3452i	0.722956	+	1.74537i
$366$		0			0
$367$	14.6156			0.762928			0.381464	−	0.924384i	$-0.375420\pi$
$367$	14.6156			0.762928			0.381464	+	0.924384i	$0.375420\pi$
$368$		0			0
$369$	−2.02503	+	1.58846i	−0.105419	+	0.0826920i
$370$		0			0
$371$	−12.0294	+	4.98276i	−0.624537	+	0.258692i
$372$		0			0
$373$	−0.624034	+	1.50655i	−0.0323113	+	0.0780063i	−0.939212	−	0.343339i	$-0.888442\pi$
$373$	−0.624034	+	1.50655i	−0.0323113	+	0.0780063i	0.906900	+	0.421345i	$0.138442\pi$
$374$		0			0
$375$	−14.0810	−	6.85086i	−0.727139	−	0.353777i
$376$		0			0
$377$	−2.12629	+	2.12629i	−0.109509	+	0.109509i
$378$		0			0
$379$	−0.943771	+	2.27846i	−0.0484782	+	0.117037i	−0.946264	−	0.323397i	$-0.895175\pi$
$379$	−0.943771	+	2.27846i	−0.0484782	+	0.117037i	0.897785	+	0.440433i	$0.145175\pi$
$380$		0			0
$381$	22.0632	−	19.5580i	1.13033	−	1.00199i
$382$		0			0
$383$	−4.75455			−0.242946			−0.121473	−	0.992595i	$-0.538762\pi$
$383$	−4.75455			−0.242946			−0.121473	+	0.992595i	$0.538762\pi$
$384$		0			0
$385$	−27.8524			−1.41949
$386$		0			0
$387$	0.901911	−	1.60136i	0.0458467	−	0.0814019i
$388$		0			0
$389$	1.83890	−	4.43949i	0.0932357	−	0.225091i	−0.870381	−	0.492379i	$-0.836127\pi$
$389$	1.83890	−	4.43949i	0.0932357	−	0.225091i	0.963617	+	0.267288i	$0.0861275\pi$
$390$		0			0
$391$	−8.77409	+	8.77409i	−0.443725	+	0.443725i
$392$		0			0
$393$	2.00166	−	4.11413i	0.100970	−	0.207531i
$394$		0			0
$395$	−5.32761	+	12.8620i	−0.268061	+	0.647157i
$396$		0			0
$397$	18.6101	−	7.70855i	0.934014	−	0.386881i	0.136814	−	0.990597i	$-0.456314\pi$
$397$	18.6101	−	7.70855i	0.934014	−	0.386881i	0.797200	+	0.603716i	$0.206314\pi$
$398$		0			0
$399$	6.27970	+	18.1803i	0.314378	+	0.910152i
$400$		0			0
$401$	12.1070			0.604595			0.302297	−	0.953214i	$-0.402246\pi$
$401$	12.1070			0.604595			0.302297	+	0.953214i	$0.402246\pi$
$402$		0			0
$403$	7.24032	+	17.4797i	0.360666	+	0.870724i
$404$		0			0
$405$	−13.5103	+	18.4071i	−0.671334	+	0.914658i
$406$		0			0
$407$	16.0997	−	16.0997i	0.798031	−	0.798031i
$408$		0			0
$409$	0.903424	+	0.903424i	0.0446714	+	0.0446714i	0.729090	−	0.684418i	$-0.239944\pi$
$409$	0.903424	+	0.903424i	0.0446714	+	0.0446714i	−0.684418	+	0.729090i	$0.739944\pi$
$410$		0			0
$411$	−2.13588	+	35.4863i	−0.105355	+	1.75041i
$412$		0			0
$413$	−5.14886	+	2.13273i	−0.253359	+	0.104945i
$414$		0			0
$415$			9.31585i			0.457297i
$416$		0			0
$417$	−9.78160	−	28.3186i	−0.479007	−	1.38677i
$418$		0			0
$419$	6.08627	+	14.6935i	0.297334	+	0.717827i	0.999980	+	0.00628784i	$0.00200150\pi$
$419$	6.08627	+	14.6935i	0.297334	+	0.717827i	−0.702647	+	0.711539i	$0.747999\pi$
$420$		0			0
$421$	−1.96867	−	0.815452i	−0.0959473	−	0.0397427i	0.334194	−	0.942504i	$-0.391536\pi$
$421$	−1.96867	−	0.815452i	−0.0959473	−	0.0397427i	−0.430141	+	0.902762i	$0.641536\pi$
$422$		0			0
$423$	3.09969	+	0.374490i	0.150712	+	0.0182083i
$424$		0			0
$425$	−3.58482	−	3.58482i	−0.173889	−	0.173889i
$426$		0			0
$427$	−30.9131	−	12.8046i	−1.49599	−	0.619659i
$428$		0			0
$429$	−25.5570	+	22.6552i	−1.23390	+	1.09380i
$430$		0			0
$431$		−	10.3316i		−	0.497658i	−0.968547	−	0.248829i	$-0.919954\pi$
$431$		−	10.3316i		−	0.497658i	0.968547	−	0.248829i	$-0.0800457\pi$
$432$		0			0
$433$			28.8197i			1.38499i	0.721423	+	0.692494i	$0.243488\pi$
$433$			28.8197i			1.38499i	−0.721423	+	0.692494i	$0.756512\pi$
$434$		0			0
$435$	−2.42434	+	2.14907i	−0.116238	+	0.103040i
$436$		0			0
$437$	−15.8843	−	6.57948i	−0.759848	−	0.314739i
$438$		0			0
$439$	8.85668	+	8.85668i	0.422706	+	0.422706i	0.886135	−	0.463428i	$-0.153381\pi$
$439$	8.85668	+	8.85668i	0.422706	+	0.422706i	−0.463428	+	0.886135i	$0.653381\pi$
$440$		0			0
$441$	−5.49007	−	0.663285i	−0.261432	−	0.0315850i
$442$		0			0
$443$	5.89186	+	2.44049i	0.279931	+	0.115951i	0.518232	−	0.855240i	$-0.326590\pi$
$443$	5.89186	+	2.44049i	0.279931	+	0.115951i	−0.238301	+	0.971191i	$0.576590\pi$
$444$		0			0
$445$	0.632881	+	1.52791i	0.0300014	+	0.0724299i
$446$		0			0
$447$	7.67437	+	22.2179i	0.362985	+	1.05087i
$448$		0			0
$449$			36.3009i			1.71315i	0.516025	+	0.856574i	$0.327411\pi$
$449$			36.3009i			1.71315i	−0.516025	+	0.856574i	$0.672589\pi$
$450$		0			0
$451$	−3.83185	+	1.58720i	−0.180435	+	0.0747385i
$452$		0			0
$453$	0.534384	−	8.87846i	0.0251076	−	0.417147i
$454$		0			0
$455$	−16.6151	−	16.6151i	−0.778927	−	0.778927i
$456$		0			0
$457$	23.9408	−	23.9408i	1.11990	−	1.11990i	0.128149	−	0.991755i	$-0.459096\pi$
$457$	23.9408	−	23.9408i	1.11990	−	1.11990i	0.991755	−	0.128149i	$-0.0409037\pi$
$458$		0			0
$459$	15.0834	−	10.4313i	0.704033	−	0.486891i
$460$		0			0
$461$	3.52528	+	8.51078i	0.164189	+	0.396387i	0.984465	−	0.175581i	$-0.0561804\pi$
$461$	3.52528	+	8.51078i	0.164189	+	0.396387i	−0.820276	+	0.571967i	$0.806180\pi$
$462$		0			0
$463$	−23.3090			−1.08326			−0.541630	−	0.840617i	$-0.682193\pi$
$463$	−23.3090			−1.08326			−0.541630	+	0.840617i	$0.682193\pi$
$464$		0			0
$465$	6.65510	+	19.2671i	0.308623	+	0.893489i
$466$		0			0
$467$	13.7618	−	5.70032i	0.636819	−	0.263779i	−0.0408280	−	0.999166i	$-0.513000\pi$
$467$	13.7618	−	5.70032i	0.636819	−	0.263779i	0.677647	+	0.735387i	$0.263000\pi$
$468$		0			0
$469$	9.54559	−	23.0451i	0.440774	−	1.06412i
$470$		0			0
$471$	−13.6246	+	28.0034i	−0.627787	+	1.29033i
$472$		0			0
$473$	2.09429	−	2.09429i	0.0962957	−	0.0962957i
$474$		0			0
$475$	2.68817	−	6.48982i	0.123342	−	0.297773i
$476$		0			0
$477$	−8.44137	+	14.9878i	−0.386504	+	0.686246i
$478$		0			0
$479$	27.5679			1.25961			0.629805	−	0.776753i	$-0.283135\pi$
$479$	27.5679			1.25961			0.629805	+	0.776753i	$0.283135\pi$
$480$		0			0
$481$	19.2082			0.875818
$482$		0			0
$483$	−10.3478	+	9.17291i	−0.470843	+	0.417382i
$484$		0			0
$485$	−3.40753	+	8.22651i	−0.154728	+	0.373547i
$486$		0			0
$487$	14.7280	−	14.7280i	0.667392	−	0.667392i	−0.289720	−	0.957111i	$-0.593562\pi$
$487$	14.7280	−	14.7280i	0.667392	−	0.667392i	0.957111	+	0.289720i	$0.0935622\pi$
$488$		0			0
$489$	−16.4709	−	8.01363i	−0.744841	−	0.362389i
$490$		0			0
$491$	−5.50514	+	13.2906i	−0.248444	+	0.599796i	−0.998072	−	0.0620627i	$-0.980232\pi$
$491$	−5.50514	+	13.2906i	−0.248444	+	0.599796i	0.749629	+	0.661859i	$0.230232\pi$
$492$		0			0
$493$	2.40401	−	0.995775i	0.108271	−	0.0448475i
$494$		0			0
$495$	−28.9516	+	22.7101i	−1.30128	+	1.02074i
$496$		0			0
$497$	4.88917			0.219309
$498$		0			0
$499$	−14.9661	−	36.1315i	−0.669977	−	1.61747i	−0.781647	−	0.623721i	$-0.785620\pi$
$499$	−14.9661	−	36.1315i	−0.669977	−	1.61747i	0.111670	−	0.993745i	$-0.464380\pi$
$500$		0			0
$501$	−1.38250	+	22.9693i	−0.0617654	+	1.02619i
$502$		0			0
$503$	−24.0188	+	24.0188i	−1.07095	+	1.07095i	−0.0736641	+	0.997283i	$0.523469\pi$
$503$	−24.0188	+	24.0188i	−1.07095	+	1.07095i	−0.997283	+	0.0736641i	$0.976531\pi$
$504$		0			0
$505$	21.5407	+	21.5407i	0.958547	+	0.958547i
$506$		0			0
$507$	−6.28448	−	0.378256i	−0.279104	−	0.0167989i
$508$		0			0
$509$	34.0535	−	14.1054i	1.50940	−	0.625213i	0.533963	−	0.845508i	$-0.320702\pi$
$509$	34.0535	−	14.1054i	1.50940	−	0.625213i	0.975433	+	0.220295i	$0.0707020\pi$
$510$		0			0
$511$		−	32.3058i		−	1.42912i
$512$		0			0
$513$	21.3512	+	13.7774i	0.942678	+	0.608288i
$514$		0			0
$515$	−0.730311	−	1.76313i	−0.0321814	−	0.0776927i
$516$		0			0
$517$	4.64852	+	1.92548i	0.204442	+	0.0846824i
$518$		0			0
$519$	4.60137	−	9.45748i	0.201978	−	0.415137i
$520$		0			0
$521$	16.9782	+	16.9782i	0.743826	+	0.743826i	0.973312	−	0.229486i	$-0.0737044\pi$
$521$	16.9782	+	16.9782i	0.743826	+	0.743826i	−0.229486	+	0.973312i	$0.573704\pi$
$522$		0			0
$523$	25.0460	+	10.3744i	1.09519	+	0.453641i	0.855812	−	0.517286i	$-0.173058\pi$
$523$	25.0460	+	10.3744i	1.09519	+	0.453641i	0.239374	+	0.970927i	$0.423058\pi$
$524$		0			0
$525$	−3.74776	−	4.22780i	−0.163566	−	0.184517i
$526$		0			0
$527$		−	16.3720i		−	0.713177i
$528$		0			0
$529$			10.6393i			0.462578i
$530$		0			0
$531$	−3.61309	+	6.41513i	−0.156795	+	0.278393i
$532$		0			0
$533$	−3.23268	−	1.33902i	−0.140023	−	0.0579994i
$534$		0			0
$535$	−32.4387	−	32.4387i	−1.40245	−	1.40245i
$536$		0			0
$537$	−10.2208	−	4.97273i	−0.441059	−	0.214589i
$538$		0			0
$539$	−8.23332	−	3.41035i	−0.354634	−	0.146894i
$540$		0			0
$541$	6.82494	+	16.4769i	0.293427	+	0.708396i	1.00000		0.000755337i	$0.000240431\pi$
$541$	6.82494	+	16.4769i	0.293427	+	0.708396i	−0.706572	+	0.707641i	$0.749760\pi$
$542$		0			0
$543$	18.6612	−	6.44582i	0.800829	−	0.276617i
$544$		0			0
$545$			11.4829i			0.491873i
$546$		0			0
$547$	41.1024	−	17.0252i	1.75741	−	0.727943i	0.760505	−	0.649332i	$-0.224952\pi$
$547$	41.1024	−	17.0252i	1.75741	−	0.727943i	0.996905	−	0.0786106i	$-0.0250484\pi$
$548$		0			0
$549$	−42.5735	+	11.8957i	−1.81699	+	0.507696i
$550$		0			0
$551$	2.54942	+	2.54942i	0.108609	+	0.108609i
$552$		0			0
$553$	8.81129	−	8.81129i	0.374694	−	0.374694i
$554$		0			0
$555$	20.6573	+	1.24334i	0.876855	+	0.0527769i
$556$		0			0
$557$	−12.0200	−	29.0188i	−0.509303	−	1.22957i	−0.944286	−	0.329127i	$-0.893246\pi$
$557$	−12.0200	−	29.0188i	−0.509303	−	1.22957i	0.434983	−	0.900439i	$-0.356754\pi$
$558$		0			0
$559$	2.49866			0.105682
$560$		0			0
$561$	27.9342	−	9.64885i	1.17938	−	0.407375i
$562$		0			0
$563$	−1.38276	+	0.572760i	−0.0582766	+	0.0241389i	−0.411631	−	0.911350i	$-0.635041\pi$
$563$	−1.38276	+	0.572760i	−0.0582766	+	0.0241389i	0.353355	+	0.935489i	$0.385041\pi$
$564$		0			0
$565$	11.0686	−	26.7219i	0.465659	−	1.12420i
$566$		0			0
$567$	17.4773	−	10.5940i	0.733980	−	0.444905i
$568$		0			0
$569$	7.17341	−	7.17341i	0.300725	−	0.300725i	−0.540573	−	0.841297i	$-0.681792\pi$
$569$	7.17341	−	7.17341i	0.300725	−	0.300725i	0.841297	+	0.540573i	$0.181792\pi$
$570$		0			0
$571$	14.0237	−	33.8562i	0.586874	−	1.41684i	−0.299602	−	0.954064i	$-0.596854\pi$
$571$	14.0237	−	33.8562i	0.586874	−	1.41684i	0.886476	−	0.462775i	$-0.153146\pi$
$572$		0			0
$573$	−3.46556	−	3.90946i	−0.144776	−	0.163320i
$574$		0			0
$575$	5.05020			0.210608
$576$		0			0
$577$	0.998741			0.0415781			0.0207891	−	0.999784i	$-0.493382\pi$
$577$	0.998741			0.0415781			0.0207891	+	0.999784i	$0.493382\pi$
$578$		0			0
$579$	−5.61173	−	6.33052i	−0.233215	−	0.263087i
$580$		0			0
$581$	3.19098	−	7.70371i	0.132384	−	0.319604i
$582$		0			0
$583$	−19.6014	+	19.6014i	−0.811806	+	0.811806i
$584$		0			0
$585$	−30.8182	−	3.72332i	−1.27418	−	0.153940i
$586$		0			0
$587$	6.37457	−	15.3896i	0.263106	−	0.635195i	−0.736021	−	0.676959i	$-0.763298\pi$
$587$	6.37457	−	15.3896i	0.263106	−	0.635195i	0.999128	+	0.0417634i	$0.0132976\pi$
$588$		0			0
$589$	20.9582	−	8.68116i	0.863566	−	0.357701i
$590$		0			0
$591$	21.5168	−	7.43218i	0.885082	−	0.305719i
$592$		0			0
$593$	−35.6688			−1.46474			−0.732371	−	0.680906i	$-0.761586\pi$
$593$	−35.6688			−1.46474			−0.732371	+	0.680906i	$0.761586\pi$
$594$		0			0
$595$	7.78112	+	18.7853i	0.318995	+	0.770122i
$596$		0			0
$597$	−0.936611	−	0.0563736i	−0.0383329	−	0.00230722i
$598$		0			0
$599$	18.1105	−	18.1105i	0.739973	−	0.739973i	−0.232600	−	0.972573i	$-0.574723\pi$
$599$	18.1105	−	18.1105i	0.739973	−	0.739973i	0.972573	+	0.232600i	$0.0747232\pi$
$600$		0			0
$601$	−10.0737	−	10.0737i	−0.410916	−	0.410916i	0.471141	−	0.882058i	$-0.343842\pi$
$601$	−10.0737	−	10.0737i	−0.410916	−	0.410916i	−0.882058	+	0.471141i	$0.843842\pi$
$602$		0			0
$603$	−8.86801	−	31.7377i	−0.361133	−	1.29246i
$604$		0			0
$605$	−29.0007	+	12.0125i	−1.17905	+	0.488377i
$606$		0			0
$607$			7.28221i			0.295576i	0.989019	+	0.147788i	$0.0472153\pi$
$607$			7.28221i			0.295576i	−0.989019	+	0.147788i	$0.952785\pi$
$608$		0			0
$609$	2.74092	−	0.946750i	0.111068	−	0.0383643i
$610$		0			0
$611$	1.62440	+	3.92165i	0.0657162	+	0.158653i
$612$		0			0
$613$	−0.372820	−	0.154427i	−0.0150581	−	0.00623725i	0.375142	−	0.926967i	$-0.377594\pi$
$613$	−0.372820	−	0.154427i	−0.0150581	−	0.00623725i	−0.390200	+	0.920730i	$0.627594\pi$
$614$		0			0
$615$	−3.38989	−	1.64929i	−0.136694	−	0.0665059i
$616$		0			0
$617$	0.952724	+	0.952724i	0.0383552	+	0.0383552i	0.726024	−	0.687669i	$-0.241366\pi$
$617$	0.952724	+	0.952724i	0.0383552	+	0.0383552i	−0.687669	+	0.726024i	$0.741366\pi$
$618$		0			0
$619$	29.7961	+	12.3419i	1.19761	+	0.496065i	0.890225	−	0.455522i	$-0.150547\pi$
$619$	29.7961	+	12.3419i	1.19761	+	0.496065i	0.307381	+	0.951586i	$0.400547\pi$
$620$		0			0
$621$	−3.27688	+	17.9722i	−0.131497	+	0.721201i
$622$		0			0
$623$		−	1.48028i		−	0.0593062i
$624$		0			0
$625$		−	30.1188i		−	1.20475i
$626$		0			0
$627$	27.1636	+	30.6429i	1.08481	+	1.22376i
$628$		0			0
$629$	−15.3563	−	6.36079i	−0.612296	−	0.253621i
$630$		0			0
$631$	20.1478	+	20.1478i	0.802070	+	0.802070i	0.983419	−	0.181349i	$-0.0580463\pi$
$631$	20.1478	+	20.1478i	0.802070	+	0.802070i	−0.181349	+	0.983419i	$0.558046\pi$
$632$		0			0
$633$	−8.23028	+	16.9162i	−0.327124	+	0.672359i
$634$		0			0
$635$	39.8990	+	16.5267i	1.58334	+	0.655843i
$636$		0			0
$637$	−2.87709	−	6.94591i	−0.113994	−	0.275207i
$638$		0			0
$639$	5.08211	−	3.98649i	0.201045	−	0.157703i
$640$		0			0
$641$			14.0316i			0.554215i	0.960839	+	0.277108i	$0.0893758\pi$
$641$			14.0316i			0.554215i	−0.960839	+	0.277108i	$0.910624\pi$
$642$		0			0
$643$	−29.2893	+	12.1320i	−1.15506	+	0.478441i	−0.876227	−	0.481899i	$-0.839947\pi$
$643$	−29.2893	+	12.1320i	−1.15506	+	0.478441i	−0.278832	+	0.960340i	$0.589947\pi$
$644$		0			0
$645$	2.68717	+	0.161737i	0.105807	+	0.00636841i
$646$		0			0
$647$	22.8248	+	22.8248i	0.897334	+	0.897334i	0.995200	−	0.0978653i	$-0.0312014\pi$
$647$	22.8248	+	22.8248i	0.897334	+	0.897334i	−0.0978653	+	0.995200i	$0.531201\pi$
$648$		0			0
$649$	−8.38982	+	8.38982i	−0.329329	+	0.329329i
$650$		0			0
$651$	1.09618	−	18.2124i	0.0429629	−	0.713801i
$652$		0			0
$653$	−15.1160	−	36.4932i	−0.591534	−	1.42809i	−0.882021	−	0.471211i	$-0.843817\pi$
$653$	−15.1160	−	36.4932i	−0.591534	−	1.42809i	0.290486	−	0.956879i	$-0.406183\pi$
$654$		0			0
$655$	6.70155			0.261851
$656$		0			0
$657$	−26.3412	−	33.5807i	−1.02767	−	1.31011i
$658$		0			0
$659$	−35.1778	+	14.5711i	−1.37033	+	0.567611i	−0.941879	−	0.335952i	$-0.890942\pi$
$659$	−35.1778	+	14.5711i	−1.37033	+	0.567611i	−0.428455	+	0.903563i	$0.640942\pi$
$660$		0			0
$661$	4.52621	−	10.9272i	0.176049	−	0.425021i	−0.811082	−	0.584932i	$-0.801121\pi$
$661$	4.52621	−	10.9272i	0.176049	−	0.425021i	0.987131	+	0.159912i	$0.0511210\pi$
$662$		0			0
$663$	22.4198	+	10.9079i	0.870712	+	0.423630i
$664$		0			0
$665$	−19.9215	+	19.9215i	−0.772524	+	0.772524i
$666$		0			0
$667$	−0.991946	+	2.39477i	−0.0384083	+	0.0927258i
$668$		0			0
$669$	−10.9678	+	9.72249i	−0.424040	+	0.375893i
$670$		0			0
$671$	−71.2358			−2.75003
$672$		0			0
$673$	24.6062			0.948499			0.474249	−	0.880391i	$-0.342719\pi$
$673$	24.6062			0.948499			0.474249	+	0.880391i	$0.342719\pi$
$674$		0			0
$675$	−7.34289	−	1.33883i	−0.282628	−	0.0515316i
$676$		0			0
$677$	15.9784	−	38.5753i	0.614100	−	1.48257i	−0.244359	−	0.969685i	$-0.578577\pi$
$677$	15.9784	−	38.5753i	0.614100	−	1.48257i	0.858458	−	0.512883i	$-0.171423\pi$
$678$		0			0
$679$	5.63569	−	5.63569i	0.216278	−	0.216278i
$680$		0			0
$681$	−2.15924	+	4.43803i	−0.0827424	+	0.170066i
$682$		0			0
$683$	−3.00142	+	7.24607i	−0.114846	+	0.277263i	−0.970842	−	0.239719i	$-0.922945\pi$
$683$	−3.00142	+	7.24607i	−0.114846	+	0.277263i	0.855996	+	0.516982i	$0.172945\pi$
$684$		0			0
$685$	−48.1087	+	19.9273i	−1.83814	+	0.761382i
$686$		0			0
$687$	−11.7019	−	33.8780i	−0.446456	−	1.29253i
$688$		0			0
$689$	−23.3860			−0.890935
$690$		0			0
$691$	−6.64017	−	16.0308i	−0.252604	−	0.609840i	0.745809	−	0.666160i	$-0.232063\pi$
$691$	−6.64017	−	16.0308i	−0.252604	−	0.609840i	−0.998413	+	0.0563199i	$0.982063\pi$
$692$		0			0
$693$	31.7203	−	8.86315i	1.20496	−	0.336683i
$694$		0			0
$695$	31.0308	−	31.0308i	1.17707	−	1.17707i
$696$		0			0
$697$	2.14100	+	2.14100i	0.0810963	+	0.0810963i
$698$		0			0
$699$	−0.131349	+	2.18227i	−0.00496806	+	0.0825412i
$700$		0			0
$701$	−30.4348	+	12.6065i	−1.14951	+	0.476142i	−0.874369	−	0.485262i	$-0.838724\pi$
$701$	−30.4348	+	12.6065i	−1.14951	+	0.476142i	−0.275140	+	0.961404i	$0.588724\pi$
$702$		0			0
$703$		−	23.0307i		−	0.868618i
$704$		0			0
$705$	1.49310	+	4.32266i	0.0562336	+	0.162801i
$706$		0			0
$707$	−10.4346	−	25.1913i	−0.392433	−	0.947418i
$708$		0			0
$709$	1.50725	+	0.624323i	0.0566059	+	0.0234469i	0.410807	−	0.911722i	$-0.365247\pi$
$709$	1.50725	+	0.624323i	0.0566059	+	0.0234469i	−0.354201	+	0.935169i	$0.615247\pi$
$710$		0			0
$711$	1.97454	−	16.3435i	0.0740512	−	0.612928i
$712$		0			0
$713$	11.5323	+	11.5323i	0.431887	+	0.431887i
$714$		0			0
$715$	−46.2173	−	19.1438i	−1.72843	−	0.715938i
$716$		0			0
$717$	15.0886	−	13.3753i	0.563492	−	0.499511i
$718$		0			0
$719$		−	23.0397i		−	0.859235i	−0.903011	−	0.429617i	$-0.858648\pi$
$719$		−	23.0397i		−	0.859235i	0.903011	−	0.429617i	$-0.141352\pi$
$720$		0			0
$721$			1.70817i			0.0636154i
$722$		0			0
$723$	13.9865	−	12.3984i	0.520164	−	0.461102i
$724$		0			0
$725$	−0.978427	−	0.405278i	−0.0363379	−	0.0150516i
$726$		0			0
$727$	14.9321	+	14.9321i	0.553800	+	0.553800i	0.927535	−	0.373735i	$-0.121923\pi$
$727$	14.9321	+	14.9321i	0.553800	+	0.553800i	−0.373735	+	0.927535i	$0.621923\pi$
$728$		0			0
$729$	9.52904	−	25.2626i	0.352927	−	0.935651i
$730$		0			0
$731$	−1.99759	−	0.827430i	−0.0738836	−	0.0306036i
$732$		0			0
$733$	−9.10293	−	21.9764i	−0.336224	−	0.811717i	−0.998071	−	0.0620784i	$-0.980227\pi$
$733$	−9.10293	−	21.9764i	−0.336224	−	0.811717i	0.661847	−	0.749639i	$-0.269773\pi$
$734$		0			0
$735$	−2.64454	−	7.65617i	−0.0975454	−	0.282402i
$736$		0			0
$737$		−	53.1049i		−	1.95614i
$738$		0			0
$739$	−20.9490	+	8.67734i	−0.770620	+	0.319201i	−0.733123	−	0.680096i	$-0.761938\pi$
$739$	−20.9490	+	8.67734i	−0.770620	+	0.319201i	−0.0374963	+	0.999297i	$0.511938\pi$
$740$		0			0
$741$	−2.07554	+	34.4839i	−0.0762470	+	1.26680i
$742$		0			0
$743$	−6.18457	−	6.18457i	−0.226890	−	0.226890i	0.584502	−	0.811392i	$-0.301290\pi$
$743$	−6.18457	−	6.18457i	−0.226890	−	0.226890i	−0.811392	+	0.584502i	$0.801290\pi$
$744$		0			0
$745$	−24.3459	+	24.3459i	−0.891966	+	0.891966i
$746$		0			0
$747$	−2.96447	−	10.6096i	−0.108464	−	0.388183i
$748$		0			0
$749$	15.7137	+	37.9363i	0.574167	+	1.38616i
$750$		0			0
$751$	−45.6086			−1.66428			−0.832140	−	0.554565i	$-0.812885\pi$
$751$	−45.6086			−1.66428			−0.832140	+	0.554565i	$0.812885\pi$
$752$		0			0
$753$	10.0795	+	29.1809i	0.367317	+	1.06341i
$754$		0			0
$755$	12.0365	−	4.98569i	0.438053	−	0.181448i
$756$		0			0
$757$	−15.2177	+	36.7389i	−0.553098	+	1.33530i	0.362042	+	0.932162i	$0.382080\pi$
$757$	−15.2177	+	36.7389i	−0.553098	+	1.33530i	−0.915140	+	0.403135i	$0.867920\pi$
$758$		0			0
$759$	−12.8800	+	26.4730i	−0.467514	+	0.960910i
$760$		0			0
$761$	22.7252	−	22.7252i	0.823790	−	0.823790i	−0.162860	−	0.986649i	$-0.552072\pi$
$761$	22.7252	−	22.7252i	0.823790	−	0.823790i	0.986649	+	0.162860i	$0.0520718\pi$
$762$		0			0
$763$	3.93326	−	9.49573i	0.142394	−	0.343769i
$764$		0			0
$765$	23.4052	+	13.1821i	0.846215	+	0.476600i
$766$		0			0
$767$	−10.0097			−0.361430
$768$		0			0
$769$	31.6105			1.13990			0.569951	−	0.821679i	$-0.306962\pi$
$769$	31.6105			1.13990			0.569951	+	0.821679i	$0.306962\pi$
$770$		0			0
$771$	2.14947	−	1.90541i	0.0774112	−	0.0686217i
$772$		0			0
$773$	−6.78635	+	16.3837i	−0.244088	+	0.589280i	−0.997681	−	0.0680606i	$-0.978319\pi$
$773$	−6.78635	+	16.3837i	−0.244088	+	0.589280i	0.753593	+	0.657341i	$0.228319\pi$
$774$		0			0
$775$	−4.71172	+	4.71172i	−0.169250	+	0.169250i
$776$		0			0
$777$	−16.6566	−	8.10398i	−0.597553	−	0.290729i
$778$		0			0
$779$	−1.60549	+	3.87599i	−0.0575226	+	0.138872i
$780$		0			0
$781$	9.61661	−	3.98333i	0.344109	−	0.142535i
$782$		0			0
$783$	2.07713	−	3.21898i	0.0742307	−	0.115037i
$784$		0			0
$785$	−45.6150			−1.62807
$786$		0			0
$787$	11.9194	+	28.7761i	0.424882	+	1.02576i	0.980887	+	0.194578i	$0.0623336\pi$
$787$	11.9194	+	28.7761i	0.424882	+	1.02576i	−0.556005	+	0.831179i	$0.687666\pi$
$788$		0			0
$789$	2.80716	−	46.6393i	0.0999377	−	1.66040i
$790$		0			0
$791$	−18.3063	+	18.3063i	−0.650895	+	0.650895i
$792$		0			0
$793$	−42.4950	−	42.4950i	−1.50904	−	1.50904i
$794$		0			0
$795$	−25.1503	−	1.51377i	−0.891990	−	0.0536879i
$796$		0			0
$797$	−44.5158	+	18.4390i	−1.57683	+	0.653144i	−0.987907	−	0.155045i	$-0.950448\pi$
$797$	−44.5158	+	18.4390i	−1.57683	+	0.653144i	−0.588922	+	0.808190i	$0.700448\pi$
$798$		0			0
$799$		−	3.67315i		−	0.129947i
$800$		0			0
$801$	−1.20698	−	1.53870i	−0.0426465	−	0.0543672i
$802$		0			0
$803$	−26.3203	−	63.5429i	−0.928824	−	2.24238i
$804$		0			0
$805$	−18.7130	−	7.75120i	−0.659548	−	0.273194i
$806$		0			0
$807$	−19.9726	+	41.0509i	−0.703068	+	1.44506i
$808$		0			0
$809$	−30.9024	−	30.9024i	−1.08647	−	1.08647i	−0.995889	−	0.0905826i	$-0.971127\pi$
$809$	−30.9024	−	30.9024i	−1.08647	−	1.08647i	−0.0905826	−	0.995889i	$-0.528873\pi$
$810$		0			0
$811$	32.4986	+	13.4614i	1.14118	+	0.472692i	0.871567	−	0.490277i	$-0.163104\pi$
$811$	32.4986	+	13.4614i	1.14118	+	0.472692i	0.269613	+	0.962969i	$0.413104\pi$
$812$		0			0
$813$	−12.0759	−	13.6227i	−0.423522	−	0.477770i
$814$		0			0
$815$		−	26.8296i		−	0.939801i
$816$		0			0
$817$		−	2.99590i		−	0.104813i
$818$		0			0
$819$	24.2097	+	13.6352i	0.845954	+	0.476453i
$820$		0			0
$821$	24.0620	+	9.96681i	0.839770	+	0.347844i	0.760763	−	0.649030i	$-0.224825\pi$
$821$	24.0620	+	9.96681i	0.839770	+	0.347844i	0.0790070	+	0.996874i	$0.474825\pi$
$822$		0			0
$823$	25.5395	+	25.5395i	0.890250	+	0.890250i	0.994546	−	0.104296i	$-0.0332591\pi$
$823$	25.5395	+	25.5395i	0.890250	+	0.890250i	−0.104296	+	0.994546i	$0.533259\pi$
$824$		0			0
$825$	−10.8161	−	5.26236i	−0.376567	−	0.183212i
$826$		0			0
$827$	−0.240161	−	0.0994780i	−0.00835122	−	0.00345919i	0.378504	−	0.925600i	$-0.376439\pi$
$827$	−0.240161	−	0.0994780i	−0.00835122	−	0.00345919i	−0.386855	+	0.922141i	$0.626439\pi$
$828$		0			0
$829$	19.0464	+	45.9821i	0.661509	+	1.59702i	0.795440	+	0.606032i	$0.207240\pi$
$829$	19.0464	+	45.9821i	0.661509	+	1.59702i	−0.133931	+	0.990991i	$0.542760\pi$
$830$		0			0
$831$	36.1595	−	12.4900i	1.25436	−	0.433272i
$832$		0			0
$833$			6.50577i			0.225412i
$834$		0			0
$835$	−31.1394	+	12.8984i	−1.07762	+	0.446367i
$836$		0			0
$837$	−13.7104	−	19.8249i	−0.473902	−	0.685250i
$838$		0			0
$839$	−40.2356	−	40.2356i	−1.38909	−	1.38909i	−0.827245	−	0.561841i	$-0.810093\pi$
$839$	−40.2356	−	40.2356i	−1.38909	−	1.38909i	−0.561841	−	0.827245i	$-0.689907\pi$
$840$		0			0
$841$	−20.1217	+	20.1217i	−0.693853	+	0.693853i
$842$		0			0
$843$	−7.67237	−	0.461791i	−0.264250	−	0.0159049i
$844$		0			0
$845$	−3.52904	−	8.51986i	−0.121403	−	0.293092i
$846$		0			0
$847$	28.0967			0.965413
$848$		0			0
$849$	15.4571	−	5.33908i	0.530486	−	0.183237i
$850$		0			0
$851$	15.2972	−	6.33633i	0.524383	−	0.217206i
$852$		0			0
$853$	4.53620	−	10.9514i	0.155317	−	0.374967i	−0.826998	−	0.562205i	$-0.809953\pi$
$853$	4.53620	−	10.9514i	0.155317	−	0.374967i	0.982315	+	0.187237i	$0.0599533\pi$
$854$		0			0
$855$	−4.46426	+	36.9511i	−0.152675	+	1.26370i
$856$		0			0
$857$	−5.00592	+	5.00592i	−0.170999	+	0.170999i	−0.787418	−	0.616419i	$-0.788583\pi$
$857$	−5.00592	+	5.00592i	−0.170999	+	0.170999i	0.616419	+	0.787418i	$0.288583\pi$
$858$		0			0
$859$	−2.35702	+	5.69036i	−0.0804206	+	0.194153i	−0.958976	−	0.283489i	$-0.908508\pi$
$859$	−2.35702	+	5.69036i	−0.0804206	+	0.194153i	0.878555	+	0.477641i	$0.158508\pi$
$860$		0			0
$861$	2.23832	+	2.52502i	0.0762818	+	0.0860526i
$862$		0			0
$863$	19.1654			0.652398			0.326199	−	0.945301i	$-0.394232\pi$
$863$	19.1654			0.652398			0.326199	+	0.945301i	$0.394232\pi$
$864$		0			0
$865$	15.4054			0.523798
$866$		0			0
$867$	5.22045	+	5.88912i	0.177296	+	0.200005i
$868$		0			0
$869$	10.1523	−	24.5099i	0.344394	−	0.831441i
$870$		0			0
$871$	31.6792	−	31.6792i	1.07341	−	1.07341i
$872$		0			0
$873$	1.26292	−	10.4533i	0.0427432	−	0.353790i
$874$		0			0
$875$	−7.85654	+	18.9674i	−0.265600	+	0.641214i
$876$		0			0
$877$	44.9885	−	18.6348i	1.51915	−	0.629254i	0.541731	−	0.840552i	$-0.317769\pi$
$877$	44.9885	−	18.6348i	1.51915	−	0.629254i	0.977422	+	0.211298i	$0.0677691\pi$
$878$		0			0
$879$	6.00265	−	2.07339i	0.202464	−	0.0699338i
$880$		0			0
$881$	44.2055			1.48932			0.744660	−	0.667444i	$-0.232612\pi$
$881$	44.2055			1.48932			0.744660	+	0.667444i	$0.232612\pi$
$882$		0			0
$883$	5.33610	+	12.8825i	0.179574	+	0.433530i	0.987877	−	0.155236i	$-0.0496138\pi$
$883$	5.33610	+	12.8825i	0.179574	+	0.433530i	−0.808303	+	0.588766i	$0.799614\pi$
$884$		0			0
$885$	−10.7649	−	0.647927i	−0.361858	−	0.0217798i
$886$		0			0
$887$	20.9210	−	20.9210i	0.702460	−	0.702460i	−0.262478	−	0.964938i	$-0.584540\pi$
$887$	20.9210	−	20.9210i	0.702460	−	0.702460i	0.964938	+	0.262478i	$0.0845398\pi$
$888$		0			0
$889$	−27.3334	−	27.3334i	−0.916733	−	0.916733i
$890$		0			0
$891$	25.7454	−	35.0767i	0.862502	−	1.17512i
$892$		0			0
$893$	4.70207	−	1.94766i	0.157349	−	0.0651759i
$894$		0			0
$895$		−	16.6487i		−	0.556505i
$896$		0			0
$897$	−23.4756	+	8.10880i	−0.783829	+	0.270745i
$898$		0			0
$899$	−1.30880	−	3.15973i	−0.0436510	−	0.105383i
$900$		0			0
$901$	18.6963	+	7.74427i	0.622864	+	0.257999i
$902$		0			0
$903$	−2.16674	−	1.05419i	−0.0721046	−	0.0350812i
$904$		0			0
$905$	20.4485	+	20.4485i	0.679732	+	0.679732i
$906$		0			0
$907$	−5.30447	−	2.19718i	−0.176132	−	0.0729562i	0.292875	−	0.956151i	$-0.405388\pi$
$907$	−5.30447	−	2.19718i	−0.176132	−	0.0729562i	−0.469007	+	0.883195i	$0.655388\pi$
$908$		0			0
$909$	−31.3867	−	17.6774i	−1.04103	−	0.586323i
$910$		0			0
$911$			55.3232i			1.83294i	0.400106	+	0.916469i	$0.368973\pi$
$911$			55.3232i			1.83294i	−0.400106	+	0.916469i	$0.631027\pi$
$912$		0			0
$913$		−	17.7524i		−	0.587517i
$914$		0			0
$915$	−42.9503	−	48.4517i	−1.41989	−	1.60176i
$916$		0			0
$917$	−5.54182	−	2.29550i	−0.183007	−	0.0758040i
$918$		0			0
$919$	21.3662	+	21.3662i	0.704805	+	0.704805i	0.965438	−	0.260633i	$-0.0839313\pi$
$919$	21.3662	+	21.3662i	0.704805	+	0.704805i	−0.260633	+	0.965438i	$0.583931\pi$
$920$		0			0
$921$	−12.4201	+	25.5278i	−0.409256	+	0.841169i
$922$		0			0
$923$	8.11290	+	3.36047i	0.267039	+	0.110611i
$924$		0			0
$925$	2.58882	+	6.24997i	0.0851200	+	0.205498i
$926$		0			0
$927$	1.39279	+	1.77558i	0.0457452	+	0.0583176i
$928$		0			0
$929$			11.2935i			0.370528i	0.982689	+	0.185264i	$0.0593140\pi$
$929$			11.2935i			0.370528i	−0.982689	+	0.185264i	$0.940686\pi$
$930$		0			0
$931$	−8.32816	+	3.44964i	−0.272944	+	0.113057i
$932$		0			0
$933$	27.2787	+	1.64187i	0.893064	+	0.0537525i
$934$		0			0
$935$	30.6097	+	30.6097i	1.00104	+	1.00104i
$936$		0			0
$937$	−3.21838	+	3.21838i	−0.105140	+	0.105140i	−0.757720	−	0.652580i	$-0.773687\pi$
$937$	−3.21838	+	3.21838i	−0.105140	+	0.105140i	0.652580	+	0.757720i	$0.273687\pi$
$938$		0			0
$939$	1.03864	−	17.2563i	0.0338946	−	0.563138i
$940$		0			0
$941$	19.9995	+	48.2830i	0.651964	+	1.57398i	0.809925	+	0.586534i	$0.199508\pi$
$941$	19.9995	+	48.2830i	0.651964	+	1.57398i	−0.157961	+	0.987445i	$0.550492\pi$
$942$		0			0
$943$	−3.01619			−0.0982207
$944$		0			0
$945$	25.1535	+	16.2310i	0.818244	+	0.527995i
$946$		0			0
$947$	8.42901	−	3.49141i	0.273906	−	0.113456i	−0.241503	−	0.970400i	$-0.577640\pi$
$947$	8.42901	−	3.49141i	0.273906	−	0.113456i	0.515408	+	0.856945i	$0.327640\pi$
$948$		0			0
$949$	22.2047	−	53.6070i	0.720796	−	1.74016i
$950$		0			0
$951$	−44.1341	−	21.4727i	−1.43115	−	0.696299i
$952$		0			0
$953$	−14.3540	+	14.3540i	−0.464972	+	0.464972i	−0.900281	−	0.435309i	$-0.856639\pi$
$953$	−14.3540	+	14.3540i	−0.464972	+	0.464972i	0.435309	+	0.900281i	$0.356639\pi$
$954$		0			0
$955$	2.92843	−	7.06986i	0.0947619	−	0.228775i
$956$		0			0
$957$	4.61983	−	4.09528i	0.149338	−	0.132382i
$958$		0			0
$959$	46.6090			1.50508
$960$		0			0
$961$	9.48134			0.305850
$962$		0			0
$963$	47.2660	+	26.6209i	1.52313	+	0.857846i
$964$		0			0
$965$	4.74196	−	11.4481i	0.152649	−	0.368528i
$966$		0			0
$967$	26.5434	−	26.5434i	0.853577	−	0.853577i	−0.136995	−	0.990572i	$-0.543744\pi$
$967$	26.5434	−	26.5434i	0.853577	−	0.853577i	0.990572	+	0.136995i	$0.0437443\pi$
$968$		0			0
$969$	13.0787	−	26.8814i	0.420147	−	0.863554i
$970$		0			0
$971$	−10.9641	+	26.4696i	−0.351853	+	0.849449i	0.644538	+	0.764572i	$0.277050\pi$
$971$	−10.9641	+	26.4696i	−0.351853	+	0.849449i	−0.996391	+	0.0848771i	$0.972950\pi$
$972$		0			0
$973$	−36.2899	+	15.0318i	−1.16340	+	0.481896i
$974$		0			0
$975$	−3.31300	−	9.59141i	−0.106101	−	0.307171i
$976$		0			0
$977$	−10.8538			−0.347243			−0.173622	−	0.984812i	$-0.555547\pi$
$977$	−10.8538			−0.347243			−0.173622	+	0.984812i	$0.555547\pi$
$978$		0			0
$979$	−1.20602	−	2.91160i	−0.0385446	−	0.0930550i
$980$		0			0
$981$	−3.65406	−	13.0775i	−0.116665	−	0.417533i
$982$		0			0
$983$	−12.9191	+	12.9191i	−0.412054	+	0.412054i	−0.882454	−	0.470400i	$-0.844110\pi$
$983$	−12.9191	+	12.9191i	−0.412054	+	0.412054i	0.470400	+	0.882454i	$0.344110\pi$
$984$		0			0
$985$	23.5776	+	23.5776i	0.751245	+	0.751245i
$986$		0			0
$987$	0.245934	−	4.08604i	0.00782817	−	0.130060i
$988$		0			0
$989$	1.98991	−	0.824248i	0.0632755	−	0.0262096i
$990$		0			0
$991$			22.7469i			0.722581i	0.932453	+	0.361290i	$0.117664\pi$
$991$			22.7469i			0.722581i	−0.932453	+	0.361290i	$0.882336\pi$
$992$		0			0
$993$	12.8271	+	37.1355i	0.407055	+	1.17846i
$994$		0			0
$995$	−0.525952	−	1.26976i	−0.0166738	−	0.0402541i
$996$		0			0
$997$	−19.7372	−	8.17540i	−0.625082	−	0.258917i	0.0475799	−	0.998867i	$-0.484849\pi$
$997$	−19.7372	−	8.17540i	−0.625082	−	0.258917i	−0.672662	+	0.739950i	$0.734849\pi$
$998$		0			0
$999$	−23.9217	+	5.15753i	−0.756849	+	0.163177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.b.287.4		56
3.2	odd	2	inner	768.2.o.b.287.7		56
4.3	odd	2		768.2.o.a.287.11		56
8.3	odd	2		384.2.o.a.143.4		56
8.5	even	2		96.2.o.a.59.3	✓	56
12.11	even	2		768.2.o.a.287.8		56
24.5	odd	2		96.2.o.a.59.12	yes	56
24.11	even	2		384.2.o.a.143.7		56
32.3	odd	8		96.2.o.a.83.12	yes	56
32.13	even	8		768.2.o.a.479.8		56
32.19	odd	8	inner	768.2.o.b.479.7		56
32.29	even	8		384.2.o.a.239.7		56
96.29	odd	8		384.2.o.a.239.4		56
96.35	even	8		96.2.o.a.83.3	yes	56
96.77	odd	8		768.2.o.a.479.11		56
96.83	even	8	inner	768.2.o.b.479.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.59.3	✓	56	8.5	even	2
96.2.o.a.59.12	yes	56	24.5	odd	2
96.2.o.a.83.3	yes	56	96.35	even	8
96.2.o.a.83.12	yes	56	32.3	odd	8
384.2.o.a.143.4		56	8.3	odd	2
384.2.o.a.143.7		56	24.11	even	2
384.2.o.a.239.4		56	96.29	odd	8
384.2.o.a.239.7		56	32.29	even	8
768.2.o.a.287.8		56	12.11	even	2
768.2.o.a.287.11		56	4.3	odd	2
768.2.o.a.479.8		56	32.13	even	8
768.2.o.a.479.11		56	96.77	odd	8
768.2.o.b.287.4		56	1.1	even	1	trivial
768.2.o.b.287.7		56	3.2	odd	2	inner
768.2.o.b.479.4		56	96.83	even	8	inner
768.2.o.b.479.7		56	32.19	odd	8	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.14895 - 1.29612i) q^{3} +(0.970873 - 2.34389i) q^{5} +(-1.60572 + 1.60572i) q^{7} +(-0.359830 + 2.97834i) q^{9} +O(q^{10})\)	\(q+(-1.14895 - 1.29612i) q^{3} +(0.970873 - 2.34389i) q^{5} +(-1.60572 + 1.60572i) q^{7} +(-0.359830 + 2.97834i) q^{9} +(-1.85010 + 4.46654i) q^{11} +(-3.76813 + 1.56081i) q^{13} +(-4.15344 + 1.43465i) q^{15} +3.52935 q^{17} +(1.87141 + 4.51799i) q^{19} +(3.92609 + 0.236307i) q^{21} +(-2.48603 + 2.48603i) q^{23} +(-1.01571 - 1.01571i) q^{25} +(4.27370 - 2.95558i) q^{27} +(0.681149 - 0.282141i) q^{29} -4.63882i q^{31} +(7.91483 - 2.73389i) q^{33} +(2.20469 + 5.32259i) q^{35} +(-4.35102 - 1.80225i) q^{37} +(6.35238 + 3.09064i) q^{39} +(0.606628 + 0.606628i) q^{41} +(-0.565994 - 0.234442i) q^{43} +(6.63157 + 3.73499i) q^{45} -1.04074i q^{47} +1.84333i q^{49} +(-4.05505 - 4.57445i) q^{51} +(5.29738 + 2.19425i) q^{53} +(8.67289 + 8.67289i) q^{55} +(3.70568 - 7.61652i) q^{57} +(2.26739 + 0.939185i) q^{59} +(5.63874 + 13.6131i) q^{61} +(-4.20460 - 5.36017i) q^{63} +10.3474i q^{65} +(-10.1483 + 4.20357i) q^{67} +(6.07851 + 0.365859i) q^{69} +(-1.52242 - 1.52242i) q^{71} +(-10.0596 + 10.0596i) q^{73} +(-0.149478 + 2.48349i) q^{75} +(-4.20127 - 10.1428i) q^{77} -5.48744 q^{79} +(-8.74105 - 2.14339i) q^{81} +(-3.39246 + 1.40520i) q^{83} +(3.42655 - 8.27243i) q^{85} +(-1.14829 - 0.558681i) q^{87} +(-0.460940 + 0.460940i) q^{89} +(3.54433 - 8.55678i) q^{91} +(-6.01245 + 5.32977i) q^{93} +12.4066 q^{95} -3.50976 q^{97} +(-12.6372 - 7.11743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

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