LMFDB - Embedded newform 1344.2.u.a.1231.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(559,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 2]))

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

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

chi := DirichletCharacter("1344.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.u (of order $4$, degree $2$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1231.9
Character	$\chi$	$=$	1344.1231
Dual form			1344.2.u.a.559.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-0.308965 + 0.308965i) q^{5} +(-1.19726 - 2.35936i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.308965 + 0.308965i) q^{5} +(-1.19726 - 2.35936i) q^{7} -1.00000i q^{9} +(-2.04703 + 2.04703i) q^{11} +(3.42060 + 3.42060i) q^{13} -0.436943i q^{15} -1.82932i q^{17} +(3.59065 - 3.59065i) q^{19} +(2.51491 + 0.821727i) q^{21} -8.35220 q^{23} +4.80908i q^{25} +(0.707107 + 0.707107i) q^{27} +(-0.297070 + 0.297070i) q^{29} -5.96943 q^{31} -2.89494i q^{33} +(1.09887 + 0.359048i) q^{35} +(-4.17272 - 4.17272i) q^{37} -4.83747 q^{39} -6.03833 q^{41} +(-3.98189 + 3.98189i) q^{43} +(0.308965 + 0.308965i) q^{45} +4.18122 q^{47} +(-4.13314 + 5.64953i) q^{49} +(1.29352 + 1.29352i) q^{51} +(-7.54994 - 7.54994i) q^{53} -1.26492i q^{55} +5.07794i q^{57} +(0.385926 + 0.385926i) q^{59} +(-6.18244 - 6.18244i) q^{61} +(-2.35936 + 1.19726i) q^{63} -2.11370 q^{65} +(2.13532 + 2.13532i) q^{67} +(5.90590 - 5.90590i) q^{69} -6.57589 q^{71} +3.68918 q^{73} +(-3.40053 - 3.40053i) q^{75} +(7.28051 + 2.37885i) q^{77} +6.40389i q^{79} -1.00000 q^{81} +(-7.68714 + 7.68714i) q^{83} +(0.565195 + 0.565195i) q^{85} -0.420120i q^{87} -10.9636 q^{89} +(3.97508 - 12.1658i) q^{91} +(4.22102 - 4.22102i) q^{93} +2.21877i q^{95} -15.3999i q^{97} +(2.04703 + 2.04703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−0.308965	+	0.308965i	−0.138173	+	0.138173i	−0.772810	−	0.634637i	$-0.781150\pi$
$5$	−0.308965	+	0.308965i	−0.138173	+	0.138173i	0.634637	+	0.772810i	$0.281150\pi$
$6$		0			0
$7$	−1.19726	−	2.35936i	−0.452522	−	0.891753i
$7$	−1.19726	−	2.35936i	−0.452522	−	0.891753i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−2.04703	+	2.04703i	−0.617203	+	0.617203i	−0.944813	−	0.327610i	$-0.893757\pi$
$11$	−2.04703	+	2.04703i	−0.617203	+	0.617203i	0.327610	+	0.944813i	$0.393757\pi$
$12$		0			0
$13$	3.42060	+	3.42060i	0.948705	+	0.948705i	0.998747	−	0.0500421i	$-0.0159355\pi$
$13$	3.42060	+	3.42060i	0.948705	+	0.948705i	−0.0500421	+	0.998747i	$0.515936\pi$
$14$		0			0
$15$		−	0.436943i		−	0.112818i
$16$		0			0
$17$		−	1.82932i		−	0.443674i	−0.975084	−	0.221837i	$-0.928795\pi$
$17$		−	1.82932i		−	0.443674i	0.975084	−	0.221837i	$-0.0712053\pi$
$18$		0			0
$19$	3.59065	−	3.59065i	0.823751	−	0.823751i	−0.162893	−	0.986644i	$-0.552082\pi$
$19$	3.59065	−	3.59065i	0.823751	−	0.823751i	0.986644	+	0.162893i	$0.0520824\pi$
$20$		0			0
$21$	2.51491	+	0.821727i	0.548798	+	0.179316i
$22$		0			0
$23$	−8.35220			−1.74155			−0.870777	−	0.491678i	$-0.836384\pi$
$23$	−8.35220			−1.74155			−0.870777	+	0.491678i	$0.836384\pi$
$24$		0			0
$25$			4.80908i			0.961816i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−0.297070	+	0.297070i	−0.0551644	+	0.0551644i	−0.734151	−	0.678986i	$-0.762420\pi$
$29$	−0.297070	+	0.297070i	−0.0551644	+	0.0551644i	0.678986	+	0.734151i	$0.262420\pi$
$30$		0			0
$31$	−5.96943			−1.07214			−0.536070	−	0.844173i	$-0.680092\pi$
$31$	−5.96943			−1.07214			−0.536070	+	0.844173i	$0.680092\pi$
$32$		0			0
$33$		−	2.89494i		−	0.503944i
$34$		0			0
$35$	1.09887	+	0.359048i	0.185743	+	0.0606902i
$36$		0			0
$37$	−4.17272	−	4.17272i	−0.685990	−	0.685990i	0.275353	−	0.961343i	$-0.411205\pi$
$37$	−4.17272	−	4.17272i	−0.685990	−	0.685990i	−0.961343	+	0.275353i	$0.911205\pi$
$38$		0			0
$39$	−4.83747			−0.774614
$40$		0			0
$41$	−6.03833			−0.943029			−0.471515	−	0.881858i	$-0.656293\pi$
$41$	−6.03833			−0.943029			−0.471515	+	0.881858i	$0.656293\pi$
$42$		0			0
$43$	−3.98189	+	3.98189i	−0.607232	+	0.607232i	−0.942222	−	0.334990i	$-0.891267\pi$
$43$	−3.98189	+	3.98189i	−0.607232	+	0.607232i	0.334990	+	0.942222i	$0.391267\pi$
$44$		0			0
$45$	0.308965	+	0.308965i	0.0460578	+	0.0460578i
$46$		0			0
$47$	4.18122			0.609893			0.304947	−	0.952369i	$-0.401361\pi$
$47$	4.18122			0.609893			0.304947	+	0.952369i	$0.401361\pi$
$48$		0			0
$49$	−4.13314	+	5.64953i	−0.590448	+	0.807075i
$50$		0			0
$51$	1.29352	+	1.29352i	0.181129	+	0.181129i
$52$		0			0
$53$	−7.54994	−	7.54994i	−1.03706	−	1.03706i	−0.999286	−	0.0377784i	$-0.987972\pi$
$53$	−7.54994	−	7.54994i	−1.03706	−	1.03706i	−0.0377784	−	0.999286i	$-0.512028\pi$
$54$		0			0
$55$		−	1.26492i		−	0.170562i
$56$		0			0
$57$			5.07794i			0.672590i
$58$		0			0
$59$	0.385926	+	0.385926i	0.0502432	+	0.0502432i	0.731782	−	0.681539i	$-0.238689\pi$
$59$	0.385926	+	0.385926i	0.0502432	+	0.0502432i	−0.681539	+	0.731782i	$0.738689\pi$
$60$		0			0
$61$	−6.18244	−	6.18244i	−0.791581	−	0.791581i	0.190170	−	0.981751i	$-0.439096\pi$
$61$	−6.18244	−	6.18244i	−0.791581	−	0.791581i	−0.981751	+	0.190170i	$0.939096\pi$
$62$		0			0
$63$	−2.35936	+	1.19726i	−0.297251	+	0.150841i
$64$		0			0
$65$	−2.11370			−0.262172
$66$		0			0
$67$	2.13532	+	2.13532i	0.260870	+	0.260870i	0.825408	−	0.564537i	$-0.190945\pi$
$67$	2.13532	+	2.13532i	0.260870	+	0.260870i	−0.564537	+	0.825408i	$0.690945\pi$
$68$		0			0
$69$	5.90590	−	5.90590i	0.710987	−	0.710987i
$70$		0			0
$71$	−6.57589			−0.780415			−0.390207	−	0.920727i	$-0.627597\pi$
$71$	−6.57589			−0.780415			−0.390207	+	0.920727i	$0.627597\pi$
$72$		0			0
$73$	3.68918			0.431786			0.215893	−	0.976417i	$-0.430734\pi$
$73$	3.68918			0.431786			0.215893	+	0.976417i	$0.430734\pi$
$74$		0			0
$75$	−3.40053	−	3.40053i	−0.392660	−	0.392660i
$76$		0			0
$77$	7.28051	+	2.37885i	0.829691	+	0.271095i
$78$		0			0
$79$			6.40389i			0.720494i	0.932857	+	0.360247i	$0.117308\pi$
$79$			6.40389i			0.720494i	−0.932857	+	0.360247i	$0.882692\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−7.68714	+	7.68714i	−0.843774	+	0.843774i	−0.989347	−	0.145574i	$-0.953497\pi$
$83$	−7.68714	+	7.68714i	−0.843774	+	0.843774i	0.145574	+	0.989347i	$0.453497\pi$
$84$		0			0
$85$	0.565195	+	0.565195i	0.0613040	+	0.0613040i
$86$		0			0
$87$		−	0.420120i		−	0.0450416i
$88$		0			0
$89$	−10.9636			−1.16214			−0.581070	−	0.813854i	$-0.697366\pi$
$89$	−10.9636			−1.16214			−0.581070	+	0.813854i	$0.697366\pi$
$90$		0			0
$91$	3.97508	−	12.1658i	0.416701	−	1.27532i
$92$		0			0
$93$	4.22102	−	4.22102i	0.437700	−	0.437700i
$94$		0			0
$95$			2.21877i			0.227641i
$96$		0			0
$97$		−	15.3999i		−	1.56363i	−0.623513	−	0.781813i	$-0.714295\pi$
$97$		−	15.3999i		−	1.56363i	0.623513	−	0.781813i	$-0.285705\pi$
$98$		0			0
$99$	2.04703	+	2.04703i	0.205734	+	0.205734i
$100$		0			0
$101$	1.81331	−	1.81331i	0.180431	−	0.180431i	−0.611112	−	0.791544i	$-0.709278\pi$
$101$	1.81331	−	1.81331i	0.180431	−	0.180431i	0.791544	+	0.611112i	$0.209278\pi$
$102$		0			0
$103$		−	19.9614i		−	1.96685i	−0.181306	−	0.983427i	$-0.558033\pi$
$103$		−	19.9614i		−	1.96685i	0.181306	−	0.983427i	$-0.441967\pi$
$104$		0			0
$105$	−1.03090	+	0.523134i	−0.100606	+	0.0510526i
$106$		0			0
$107$	6.45274	−	6.45274i	0.623810	−	0.623810i	−0.322693	−	0.946504i	$-0.604588\pi$
$107$	6.45274	−	6.45274i	0.623810	−	0.623810i	0.946504	+	0.322693i	$0.104588\pi$
$108$		0			0
$109$	−1.65121	+	1.65121i	−0.158157	+	0.158157i	−0.781750	−	0.623592i	$-0.785673\pi$
$109$	−1.65121	+	1.65121i	−0.158157	+	0.158157i	0.623592	+	0.781750i	$0.285673\pi$
$110$		0			0
$111$	5.90111			0.560109
$112$		0			0
$113$	−15.9340			−1.49894			−0.749471	−	0.662037i	$-0.769692\pi$
$113$	−15.9340			−1.49894			−0.749471	+	0.662037i	$0.769692\pi$
$114$		0			0
$115$	2.58054	−	2.58054i	0.240637	−	0.240637i
$116$		0			0
$117$	3.42060	−	3.42060i	0.316235	−	0.316235i
$118$		0			0
$119$	−4.31601	+	2.19017i	−0.395648	+	0.200772i
$120$		0			0
$121$			2.61933i			0.238121i
$122$		0			0
$123$	4.26975	−	4.26975i	0.384990	−	0.384990i
$124$		0			0
$125$	−3.03066	−	3.03066i	−0.271071	−	0.271071i
$126$		0			0
$127$		−	8.14654i		−	0.722889i	−0.932394	−	0.361444i	$-0.882284\pi$
$127$		−	8.14654i		−	0.722889i	0.932394	−	0.361444i	$-0.117716\pi$
$128$		0			0
$129$		−	5.63124i		−	0.495803i
$130$		0			0
$131$	−8.53792	+	8.53792i	−0.745962	+	0.745962i	−0.973718	−	0.227757i	$-0.926861\pi$
$131$	−8.53792	+	8.53792i	−0.745962	+	0.745962i	0.227757	+	0.973718i	$0.426861\pi$
$132$		0			0
$133$	−12.7706	−	4.17269i	−1.10735	−	0.361818i
$134$		0			0
$135$	−0.436943			−0.0376060
$136$		0			0
$137$			18.1170i			1.54784i	0.633285	+	0.773919i	$0.281706\pi$
$137$			18.1170i			1.54784i	−0.633285	+	0.773919i	$0.718294\pi$
$138$		0			0
$139$	14.5066	+	14.5066i	1.23043	+	1.23043i	0.963798	+	0.266635i	$0.0859118\pi$
$139$	14.5066	+	14.5066i	1.23043	+	1.23043i	0.266635	+	0.963798i	$0.414088\pi$
$140$		0			0
$141$	−2.95657	+	2.95657i	−0.248988	+	0.248988i
$142$		0			0
$143$	−14.0042			−1.17109
$144$		0			0
$145$		−	0.183568i		−	0.0152445i
$146$		0			0
$147$	−1.07225	−	6.91739i	−0.0884377	−	0.570537i
$148$		0			0
$149$	6.18057	+	6.18057i	0.506332	+	0.506332i	0.913399	−	0.407066i	$-0.133448\pi$
$149$	6.18057	+	6.18057i	0.506332	+	0.506332i	−0.407066	+	0.913399i	$0.633448\pi$
$150$		0			0
$151$	−10.5139			−0.855606			−0.427803	−	0.903872i	$-0.640712\pi$
$151$	−10.5139			−0.855606			−0.427803	+	0.903872i	$0.640712\pi$
$152$		0			0
$153$	−1.82932			−0.147891
$154$		0			0
$155$	1.84434	−	1.84434i	0.148141	−	0.148141i
$156$		0			0
$157$	6.30605	+	6.30605i	0.503277	+	0.503277i	0.912455	−	0.409177i	$-0.134184\pi$
$157$	6.30605	+	6.30605i	0.503277	+	0.503277i	−0.409177	+	0.912455i	$0.634184\pi$
$158$		0			0
$159$	10.6772			0.846760
$160$		0			0
$161$	9.99976	+	19.7058i	0.788091	+	1.55304i
$162$		0			0
$163$	9.33622	+	9.33622i	0.731270	+	0.731270i	0.970871	−	0.239602i	$-0.0770169\pi$
$163$	9.33622	+	9.33622i	0.731270	+	0.731270i	−0.239602	+	0.970871i	$0.577017\pi$
$164$		0			0
$165$	0.894435	+	0.894435i	0.0696317	+	0.0696317i
$166$		0			0
$167$			24.2089i			1.87334i	0.350210	+	0.936671i	$0.386110\pi$
$167$			24.2089i			1.87334i	−0.350210	+	0.936671i	$0.613890\pi$
$168$		0			0
$169$			10.4011i			0.800083i
$170$		0			0
$171$	−3.59065	−	3.59065i	−0.274584	−	0.274584i
$172$		0			0
$173$	−4.78406	−	4.78406i	−0.363725	−	0.363725i	0.501457	−	0.865182i	$-0.332797\pi$
$173$	−4.78406	−	4.78406i	−0.363725	−	0.363725i	−0.865182	+	0.501457i	$0.832797\pi$
$174$		0			0
$175$	11.3463	−	5.75772i	0.857703	−	0.435243i
$176$		0			0
$177$	−0.545781			−0.0410234
$178$		0			0
$179$	2.64090	+	2.64090i	0.197390	+	0.197390i	0.798880	−	0.601490i	$-0.205426\pi$
$179$	2.64090	+	2.64090i	0.197390	+	0.197390i	−0.601490	+	0.798880i	$0.705426\pi$
$180$		0			0
$181$	−12.0446	+	12.0446i	−0.895269	+	0.895269i	−0.995013	−	0.0997445i	$-0.968197\pi$
$181$	−12.0446	+	12.0446i	−0.895269	+	0.895269i	0.0997445	+	0.995013i	$0.468197\pi$
$182$		0			0
$183$	8.74330			0.646323
$184$		0			0
$185$	2.57845			0.189571
$186$		0			0
$187$	3.74466	+	3.74466i	0.273837	+	0.273837i
$188$		0			0
$189$	0.821727	−	2.51491i	0.0597719	−	0.182933i
$190$		0			0
$191$		−	23.1824i		−	1.67742i	−0.544581	−	0.838708i	$-0.683311\pi$
$191$		−	23.1824i		−	1.67742i	0.544581	−	0.838708i	$-0.316689\pi$
$192$		0			0
$193$	4.91878			0.354062			0.177031	−	0.984205i	$-0.443351\pi$
$193$	4.91878			0.354062			0.177031	+	0.984205i	$0.443351\pi$
$194$		0			0
$195$	1.49461	−	1.49461i	0.107031	−	0.107031i
$196$		0			0
$197$	−4.92703	−	4.92703i	−0.351036	−	0.351036i	0.509459	−	0.860495i	$-0.329846\pi$
$197$	−4.92703	−	4.92703i	−0.351036	−	0.351036i	−0.860495	+	0.509459i	$0.829846\pi$
$198$		0			0
$199$		−	20.8397i		−	1.47729i	−0.674095	−	0.738645i	$-0.735466\pi$
$199$		−	20.8397i		−	1.47729i	0.674095	−	0.738645i	$-0.264534\pi$
$200$		0			0
$201$	−3.01979			−0.213000
$202$		0			0
$203$	1.05656	+	0.345224i	0.0741562	+	0.0242300i
$204$		0			0
$205$	1.86563	−	1.86563i	0.130302	−	0.130302i
$206$		0			0
$207$			8.35220i			0.580518i
$208$		0			0
$209$			14.7003i			1.01684i
$210$		0			0
$211$	2.60100	+	2.60100i	0.179061	+	0.179061i	0.790946	−	0.611886i	$-0.209589\pi$
$211$	2.60100	+	2.60100i	0.179061	+	0.179061i	−0.611886	+	0.790946i	$0.709589\pi$
$212$		0			0
$213$	4.64986	−	4.64986i	0.318603	−	0.318603i
$214$		0			0
$215$		−	2.46053i		−	0.167807i
$216$		0			0
$217$	7.14695	+	14.0840i	0.485167	+	0.956085i
$218$		0			0
$219$	−2.60865	+	2.60865i	−0.176276	+	0.176276i
$220$		0			0
$221$	6.25736	−	6.25736i	0.420916	−	0.420916i
$222$		0			0
$223$	6.59099			0.441365			0.220683	−	0.975346i	$-0.429171\pi$
$223$	6.59099			0.441365			0.220683	+	0.975346i	$0.429171\pi$
$224$		0			0
$225$	4.80908			0.320605
$226$		0			0
$227$	−0.205430	+	0.205430i	−0.0136348	+	0.0136348i	−0.713891	−	0.700256i	$-0.753069\pi$
$227$	−0.205430	+	0.205430i	−0.0136348	+	0.0136348i	0.700256	+	0.713891i	$0.253069\pi$
$228$		0			0
$229$	10.2378	−	10.2378i	0.676531	−	0.676531i	−0.282683	−	0.959213i	$-0.591224\pi$
$229$	10.2378	−	10.2378i	0.676531	−	0.676531i	0.959213	+	0.282683i	$0.0912243\pi$
$230$		0			0
$231$	−6.83020	+	3.46599i	−0.449394	+	0.228046i
$232$		0			0
$233$		−	1.59881i		−	0.104742i	−0.998628	−	0.0523708i	$-0.983322\pi$
$233$		−	1.59881i		−	0.104742i	0.998628	−	0.0523708i	$-0.0166778\pi$
$234$		0			0
$235$	−1.29185	+	1.29185i	−0.0842711	+	0.0842711i
$236$		0			0
$237$	−4.52823	−	4.52823i	−0.294140	−	0.294140i
$238$		0			0
$239$			10.2177i			0.660928i	0.943819	+	0.330464i	$0.107205\pi$
$239$			10.2177i			0.660928i	−0.943819	+	0.330464i	$0.892795\pi$
$240$		0			0
$241$		−	15.8232i		−	1.01926i	−0.860392	−	0.509632i	$-0.829781\pi$
$241$		−	15.8232i		−	1.01926i	0.860392	−	0.509632i	$-0.170219\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−0.468512	−	3.02250i	−0.0299321	−	0.193101i
$246$		0			0
$247$	24.5644			1.56299
$248$		0			0
$249$		−	10.8713i		−	0.688938i
$250$		0			0
$251$	15.3043	+	15.3043i	0.965997	+	0.965997i	0.999441	−	0.0334433i	$-0.0106473\pi$
$251$	15.3043	+	15.3043i	0.965997	+	0.965997i	−0.0334433	+	0.999441i	$0.510647\pi$
$252$		0			0
$253$	17.0972	−	17.0972i	1.07489	−	1.07489i
$254$		0			0
$255$	−0.799306			−0.0500545
$256$		0			0
$257$		−	1.64593i		−	0.102670i	−0.998681	−	0.0513351i	$-0.983652\pi$
$257$		−	1.64593i		−	0.102670i	0.998681	−	0.0513351i	$-0.0163477\pi$
$258$		0			0
$259$	−4.84911	+	14.8408i	−0.301309	+	0.922160i
$260$		0			0
$261$	0.297070	+	0.297070i	0.0183881	+	0.0183881i
$262$		0			0
$263$	1.81577			0.111965			0.0559827	−	0.998432i	$-0.482171\pi$
$263$	1.81577			0.111965			0.0559827	+	0.998432i	$0.482171\pi$
$264$		0			0
$265$	4.66534			0.286590
$266$		0			0
$267$	7.75244	−	7.75244i	0.474442	−	0.474442i
$268$		0			0
$269$	16.1538	+	16.1538i	0.984917	+	0.984917i	0.999888	−	0.0149705i	$-0.00476543\pi$
$269$	16.1538	+	16.1538i	0.984917	+	0.984917i	−0.0149705	+	0.999888i	$0.504765\pi$
$270$		0			0
$271$	−16.1518			−0.981149			−0.490575	−	0.871399i	$-0.663213\pi$
$271$	−16.1518			−0.981149			−0.490575	+	0.871399i	$0.663213\pi$
$272$		0			0
$273$	5.79170	+	11.4133i	0.350530	+	0.690765i
$274$		0			0
$275$	−9.84434	−	9.84434i	−0.593636	−	0.593636i
$276$		0			0
$277$	0.313279	+	0.313279i	0.0188231	+	0.0188231i	0.716456	−	0.697633i	$-0.245763\pi$
$277$	0.313279	+	0.313279i	0.0188231	+	0.0188231i	−0.697633	+	0.716456i	$0.745763\pi$
$278$		0			0
$279$			5.96943i			0.357380i
$280$		0			0
$281$		−	26.0125i		−	1.55177i	−0.630872	−	0.775887i	$-0.717303\pi$
$281$		−	26.0125i		−	1.55177i	0.630872	−	0.775887i	$-0.282697\pi$
$282$		0			0
$283$	11.6918	+	11.6918i	0.695006	+	0.695006i	0.963329	−	0.268323i	$-0.0864695\pi$
$283$	11.6918	+	11.6918i	0.695006	+	0.695006i	−0.268323	+	0.963329i	$0.586470\pi$
$284$		0			0
$285$	−1.56891	−	1.56891i	−0.0929341	−	0.0929341i
$286$		0			0
$287$	7.22945	+	14.2466i	0.426741	+	0.840950i
$288$		0			0
$289$	13.6536			0.803153
$290$		0			0
$291$	10.8894	+	10.8894i	0.638347	+	0.638347i
$292$		0			0
$293$	−2.40354	+	2.40354i	−0.140416	+	0.140416i	−0.773821	−	0.633405i	$-0.781657\pi$
$293$	−2.40354	+	2.40354i	−0.140416	+	0.140416i	0.633405	+	0.773821i	$0.281657\pi$
$294$		0			0
$295$	−0.238475			−0.0138846
$296$		0			0
$297$	−2.89494			−0.167981
$298$		0			0
$299$	−28.5696	−	28.5696i	−1.65222	−	1.65222i
$300$		0			0
$301$	14.1620	+	4.62734i	0.816287	+	0.266716i
$302$		0			0
$303$			2.56441i			0.147322i
$304$		0			0
$305$	3.82032			0.218751
$306$		0			0
$307$	−5.88593	+	5.88593i	−0.335928	+	0.335928i	−0.854832	−	0.518904i	$-0.826340\pi$
$307$	−5.88593	+	5.88593i	−0.335928	+	0.335928i	0.518904	+	0.854832i	$0.326340\pi$
$308$		0			0
$309$	14.1148	+	14.1148i	0.802965	+	0.802965i
$310$		0			0
$311$			2.12428i			0.120457i	0.998185	+	0.0602283i	$0.0191829\pi$
$311$			2.12428i			0.120457i	−0.998185	+	0.0602283i	$0.980817\pi$
$312$		0			0
$313$	4.63421			0.261941			0.130970	−	0.991386i	$-0.458191\pi$
$313$	4.63421			0.261941			0.130970	+	0.991386i	$0.458191\pi$
$314$		0			0
$315$	0.359048	−	1.09887i	0.0202301	−	0.0619144i
$316$		0			0
$317$	−3.49936	+	3.49936i	−0.196544	+	0.196544i	−0.798517	−	0.601973i	$-0.794382\pi$
$317$	−3.49936	+	3.49936i	−0.196544	+	0.196544i	0.601973	+	0.798517i	$0.294382\pi$
$318$		0			0
$319$		−	1.21622i		−	0.0680953i
$320$		0			0
$321$			9.12556i			0.509339i
$322$		0			0
$323$	−6.56843	−	6.56843i	−0.365477	−	0.365477i
$324$		0			0
$325$	−16.4500	+	16.4500i	−0.912480	+	0.912480i
$326$		0			0
$327$		−	2.33516i		−	0.129135i
$328$		0			0
$329$	−5.00600	−	9.86499i	−0.275990	−	0.543875i
$330$		0			0
$331$	−5.95146	+	5.95146i	−0.327122	+	0.327122i	−0.851491	−	0.524369i	$-0.824301\pi$
$331$	−5.95146	+	5.95146i	−0.327122	+	0.327122i	0.524369	+	0.851491i	$0.324301\pi$
$332$		0			0
$333$	−4.17272	+	4.17272i	−0.228663	+	0.228663i
$334$		0			0
$335$	−1.31948			−0.0720907
$336$		0			0
$337$	15.3988			0.838824			0.419412	−	0.907796i	$-0.362236\pi$
$337$	15.3988			0.838824			0.419412	+	0.907796i	$0.362236\pi$
$338$		0			0
$339$	11.2670	−	11.2670i	0.611941	−	0.611941i
$340$		0			0
$341$	12.2196	−	12.2196i	0.661729	−	0.661729i
$342$		0			0
$343$	18.2777	+	2.98760i	0.986903	+	0.161315i
$344$		0			0
$345$			3.64943i			0.196479i
$346$		0			0
$347$	18.9321	−	18.9321i	1.01633	−	1.01633i	0.0164659	−	0.999864i	$-0.494759\pi$
$347$	18.9321	−	18.9321i	1.01633	−	1.01633i	0.999864	−	0.0164659i	$-0.00524149\pi$
$348$		0			0
$349$	1.33215	+	1.33215i	0.0713086	+	0.0713086i	0.741862	−	0.670553i	$-0.233943\pi$
$349$	1.33215	+	1.33215i	0.0713086	+	0.0713086i	−0.670553	+	0.741862i	$0.733943\pi$
$350$		0			0
$351$			4.83747i			0.258205i
$352$		0			0
$353$		−	0.733019i		−	0.0390147i	−0.999810	−	0.0195073i	$-0.993790\pi$
$353$		−	0.733019i		−	0.0390147i	0.999810	−	0.0195073i	$-0.00620977\pi$
$354$		0			0
$355$	2.03172	−	2.03172i	0.107833	−	0.107833i
$356$		0			0
$357$	1.50320	−	4.60056i	0.0795577	−	0.243487i
$358$		0			0
$359$	−11.3175			−0.597317			−0.298659	−	0.954360i	$-0.596539\pi$
$359$	−11.3175			−0.597317			−0.298659	+	0.954360i	$0.596539\pi$
$360$		0			0
$361$		−	6.78552i		−	0.357132i
$362$		0			0
$363$	−1.85214	−	1.85214i	−0.0972124	−	0.0972124i
$364$		0			0
$365$	−1.13983	+	1.13983i	−0.0596614	+	0.0596614i
$366$		0			0
$367$	−26.4924			−1.38289			−0.691447	−	0.722427i	$-0.743026\pi$
$367$	−26.4924			−1.38289			−0.691447	+	0.722427i	$0.743026\pi$
$368$		0			0
$369$			6.03833i			0.314343i
$370$		0			0
$371$	−8.77377	+	26.8523i	−0.455512	+	1.39410i
$372$		0			0
$373$	−8.60941	−	8.60941i	−0.445778	−	0.445778i	0.448170	−	0.893948i	$-0.352076\pi$
$373$	−8.60941	−	8.60941i	−0.445778	−	0.445778i	−0.893948	+	0.448170i	$0.852076\pi$
$374$		0			0
$375$	4.28601			0.221328
$376$		0			0
$377$	−2.03232			−0.104670
$378$		0			0
$379$	−6.82854	+	6.82854i	−0.350759	+	0.350759i	−0.860392	−	0.509633i	$-0.829781\pi$
$379$	−6.82854	+	6.82854i	−0.350759	+	0.350759i	0.509633	+	0.860392i	$0.329781\pi$
$380$		0			0
$381$	5.76048	+	5.76048i	0.295118	+	0.295118i
$382$		0			0
$383$	19.3483			0.988653			0.494327	−	0.869276i	$-0.335415\pi$
$383$	19.3483			0.988653			0.494327	+	0.869276i	$0.335415\pi$
$384$		0			0
$385$	−2.98440	+	1.51444i	−0.152099	+	0.0771831i
$386$		0			0
$387$	3.98189	+	3.98189i	0.202411	+	0.202411i
$388$		0			0
$389$	20.3447	+	20.3447i	1.03152	+	1.03152i	0.999487	+	0.0320321i	$0.0101979\pi$
$389$	20.3447	+	20.3447i	1.03152	+	1.03152i	0.0320321	+	0.999487i	$0.489802\pi$
$390$		0			0
$391$			15.2788i			0.772683i
$392$		0			0
$393$		−	12.0744i		−	0.609075i
$394$		0			0
$395$	−1.97858	−	1.97858i	−0.0995531	−	0.0995531i
$396$		0			0
$397$	−23.2141	−	23.2141i	−1.16508	−	1.16508i	−0.983348	−	0.181733i	$-0.941829\pi$
$397$	−23.2141	−	23.2141i	−1.16508	−	1.16508i	−0.181733	−	0.983348i	$-0.558171\pi$
$398$		0			0
$399$	11.9807	−	6.07962i	0.599785	−	0.304362i
$400$		0			0
$401$	−3.02266			−0.150945			−0.0754723	−	0.997148i	$-0.524046\pi$
$401$	−3.02266			−0.150945			−0.0754723	+	0.997148i	$0.524046\pi$
$402$		0			0
$403$	−20.4190	−	20.4190i	−1.01715	−	1.01715i
$404$		0			0
$405$	0.308965	−	0.308965i	0.0153526	−	0.0153526i
$406$		0			0
$407$	17.0834			0.846791
$408$		0			0
$409$	20.2826			1.00291			0.501456	−	0.865183i	$-0.332798\pi$
$409$	20.2826			1.00291			0.501456	+	0.865183i	$0.332798\pi$
$410$		0			0
$411$	−12.8106	−	12.8106i	−0.631902	−	0.631902i
$412$		0			0
$413$	0.448483	−	1.37259i	0.0220684	−	0.0675407i
$414$		0			0
$415$		−	4.75012i		−	0.233174i
$416$		0			0
$417$	−20.5154			−1.00464
$418$		0			0
$419$	17.0057	−	17.0057i	0.830784	−	0.830784i	−0.156840	−	0.987624i	$-0.550131\pi$
$419$	17.0057	−	17.0057i	0.830784	−	0.830784i	0.987624	+	0.156840i	$0.0501307\pi$
$420$		0			0
$421$	24.1058	+	24.1058i	1.17484	+	1.17484i	0.981041	+	0.193803i	$0.0620821\pi$
$421$	24.1058	+	24.1058i	1.17484	+	1.17484i	0.193803	+	0.981041i	$0.437918\pi$
$422$		0			0
$423$		−	4.18122i		−	0.203298i
$424$		0			0
$425$	8.79732			0.426733
$426$		0			0
$427$	−7.18461	+	21.9886i	−0.347687	+	1.06410i
$428$		0			0
$429$	9.90244	−	9.90244i	0.478094	−	0.478094i
$430$		0			0
$431$			11.7153i			0.564305i	0.959370	+	0.282152i	$0.0910484\pi$
$431$			11.7153i			0.564305i	−0.959370	+	0.282152i	$0.908952\pi$
$432$		0			0
$433$		−	2.22307i		−	0.106834i	−0.998572	−	0.0534170i	$-0.982989\pi$
$433$		−	2.22307i		−	0.106834i	0.998572	−	0.0534170i	$-0.0170113\pi$
$434$		0			0
$435$	0.129802	+	0.129802i	0.00622355	+	0.00622355i
$436$		0			0
$437$	−29.9898	+	29.9898i	−1.43461	+	1.43461i
$438$		0			0
$439$			7.97837i			0.380787i	0.981708	+	0.190393i	$0.0609764\pi$
$439$			7.97837i			0.380787i	−0.981708	+	0.190393i	$0.939024\pi$
$440$		0			0
$441$	5.64953	+	4.13314i	0.269025	+	0.196816i
$442$		0			0
$443$	−1.28683	+	1.28683i	−0.0611393	+	0.0611393i	−0.737015	−	0.675876i	$-0.763765\pi$
$443$	−1.28683	+	1.28683i	−0.0611393	+	0.0611393i	0.675876	+	0.737015i	$0.263765\pi$
$444$		0			0
$445$	3.38737	−	3.38737i	0.160577	−	0.160577i
$446$		0			0
$447$	−8.74065			−0.413418
$448$		0			0
$449$	−6.31177			−0.297871			−0.148936	−	0.988847i	$-0.547585\pi$
$449$	−6.31177			−0.297871			−0.148936	+	0.988847i	$0.547585\pi$
$450$		0			0
$451$	12.3607	−	12.3607i	0.582041	−	0.582041i
$452$		0			0
$453$	7.43442	−	7.43442i	0.349299	−	0.349299i
$454$		0			0
$455$	2.53064	+	4.98696i	0.118638	+	0.233792i
$456$		0			0
$457$		−	22.0436i		−	1.03115i	−0.856843	−	0.515577i	$-0.827578\pi$
$457$		−	22.0436i		−	1.03115i	0.856843	−	0.515577i	$-0.172422\pi$
$458$		0			0
$459$	1.29352	−	1.29352i	0.0603764	−	0.0603764i
$460$		0			0
$461$	12.8409	+	12.8409i	0.598061	+	0.598061i	0.939796	−	0.341735i	$-0.111015\pi$
$461$	12.8409	+	12.8409i	0.598061	+	0.598061i	−0.341735	+	0.939796i	$0.611015\pi$
$462$		0			0
$463$		−	7.82977i		−	0.363880i	−0.983310	−	0.181940i	$-0.941762\pi$
$463$		−	7.82977i		−	0.363880i	0.983310	−	0.181940i	$-0.0582377\pi$
$464$		0			0
$465$			2.60830i			0.120957i
$466$		0			0
$467$	14.7200	−	14.7200i	0.681159	−	0.681159i	−0.279102	−	0.960261i	$-0.590037\pi$
$467$	14.7200	−	14.7200i	0.681159	−	0.681159i	0.960261	+	0.279102i	$0.0900369\pi$
$468$		0			0
$469$	2.48145	−	7.59450i	0.114583	−	0.350681i
$470$		0			0
$471$	−8.91810			−0.410924
$472$		0			0
$473$		−	16.3021i		−	0.749571i
$474$		0			0
$475$	17.2677	+	17.2677i	0.792297	+	0.792297i
$476$		0			0
$477$	−7.54994	+	7.54994i	−0.345688	+	0.345688i
$478$		0			0
$479$	−10.1353			−0.463092			−0.231546	−	0.972824i	$-0.574378\pi$
$479$	−10.1353			−0.463092			−0.231546	+	0.972824i	$0.574378\pi$
$480$		0			0
$481$		−	28.5464i		−	1.30161i
$482$		0			0
$483$	−21.0050	−	6.86323i	−0.955762	−	0.312288i
$484$		0			0
$485$	4.75804	+	4.75804i	0.216051	+	0.216051i
$486$		0			0
$487$	−19.3524			−0.876940			−0.438470	−	0.898746i	$-0.644479\pi$
$487$	−19.3524			−0.876940			−0.438470	+	0.898746i	$0.644479\pi$
$488$		0			0
$489$	−13.2034			−0.597079
$490$		0			0
$491$	−30.4054	+	30.4054i	−1.37218	+	1.37218i	−0.514964	+	0.857212i	$0.672195\pi$
$491$	−30.4054	+	30.4054i	−1.37218	+	1.37218i	−0.857212	+	0.514964i	$0.827805\pi$
$492$		0			0
$493$	0.543434	+	0.543434i	0.0244750	+	0.0244750i
$494$		0			0
$495$	−1.26492			−0.0568540
$496$		0			0
$497$	7.87305	+	15.5149i	0.353155	+	0.695938i
$498$		0			0
$499$	−23.9216	−	23.9216i	−1.07088	−	1.07088i	−0.997289	−	0.0735874i	$-0.976555\pi$
$499$	−23.9216	−	23.9216i	−1.07088	−	1.07088i	−0.0735874	−	0.997289i	$-0.523445\pi$
$500$		0			0
$501$	−17.1183	−	17.1183i	−0.764789	−	0.764789i
$502$		0			0
$503$			9.76228i			0.435278i	0.976029	+	0.217639i	$0.0698356\pi$
$503$			9.76228i			0.435278i	−0.976029	+	0.217639i	$0.930164\pi$
$504$		0			0
$505$			1.12050i			0.0498617i
$506$		0			0
$507$	−7.35467	−	7.35467i	−0.326632	−	0.326632i
$508$		0			0
$509$	−25.6672	−	25.6672i	−1.13768	−	1.13768i	−0.988865	−	0.148813i	$-0.952455\pi$
$509$	−25.6672	−	25.6672i	−1.13768	−	1.13768i	−0.148813	−	0.988865i	$-0.547545\pi$
$510$		0			0
$511$	−4.41691	−	8.70410i	−0.195393	−	0.385047i
$512$		0			0
$513$	5.07794			0.224197
$514$		0			0
$515$	6.16737	+	6.16737i	0.271767	+	0.271767i
$516$		0			0
$517$	−8.55908	+	8.55908i	−0.376428	+	0.376428i
$518$		0			0
$519$	6.76568			0.296980
$520$		0			0
$521$	−37.1252			−1.62648			−0.813242	−	0.581926i	$-0.802299\pi$
$521$	−37.1252			−1.62648			−0.813242	+	0.581926i	$0.802299\pi$
$522$		0			0
$523$	−17.1825	−	17.1825i	−0.751339	−	0.751339i	0.223390	−	0.974729i	$-0.428288\pi$
$523$	−17.1825	−	17.1825i	−0.751339	−	0.751339i	−0.974729	+	0.223390i	$0.928288\pi$
$524$		0			0
$525$	−3.95175	+	12.0944i	−0.172469	+	0.527843i
$526$		0			0
$527$			10.9200i			0.475681i
$528$		0			0
$529$	46.7593			2.03301
$530$		0			0
$531$	0.385926	−	0.385926i	0.0167477	−	0.0167477i
$532$		0			0
$533$	−20.6548	−	20.6548i	−0.894657	−	0.894657i
$534$		0			0
$535$			3.98735i			0.172388i
$536$		0			0
$537$	−3.73480			−0.161168
$538$		0			0
$539$	−3.10410	−	20.0254i	−0.133703	−	0.862556i
$540$		0			0
$541$	−32.0353	+	32.0353i	−1.37730	+	1.37730i	−0.528160	+	0.849145i	$0.677118\pi$
$541$	−32.0353	+	32.0353i	−1.37730	+	1.37730i	−0.849145	+	0.528160i	$0.822882\pi$
$542$		0			0
$543$		−	17.0336i		−	0.730984i
$544$		0			0
$545$		−	1.02033i		−	0.0437063i
$546$		0			0
$547$	14.8377	+	14.8377i	0.634413	+	0.634413i	0.949172	−	0.314759i	$-0.101924\pi$
$547$	14.8377	+	14.8377i	0.634413	+	0.634413i	−0.314759	+	0.949172i	$0.601924\pi$
$548$		0			0
$549$	−6.18244	+	6.18244i	−0.263860	+	0.263860i
$550$		0			0
$551$			2.13335i			0.0908836i
$552$		0			0
$553$	15.1091	−	7.66712i	0.642503	−	0.326039i
$554$		0			0
$555$	−1.82324	+	1.82324i	−0.0773922	+	0.0773922i
$556$		0			0
$557$	−16.9357	+	16.9357i	−0.717591	+	0.717591i	−0.968111	−	0.250521i	$-0.919398\pi$
$557$	−16.9357	+	16.9357i	−0.717591	+	0.717591i	0.250521	+	0.968111i	$0.419398\pi$
$558$		0			0
$559$	−27.2409			−1.15217
$560$		0			0
$561$	−5.29576			−0.223587
$562$		0			0
$563$	29.1837	−	29.1837i	1.22995	−	1.22995i	0.265964	−	0.963983i	$-0.414310\pi$
$563$	29.1837	−	29.1837i	1.22995	−	1.22995i	0.963983	−	0.265964i	$-0.0856902\pi$
$564$		0			0
$565$	4.92304	−	4.92304i	0.207114	−	0.207114i
$566$		0			0
$567$	1.19726	+	2.35936i	0.0502802	+	0.0990837i
$568$		0			0
$569$			26.0759i			1.09316i	0.837407	+	0.546579i	$0.184070\pi$
$569$			26.0759i			1.09316i	−0.837407	+	0.546579i	$0.815930\pi$
$570$		0			0
$571$	−13.0888	+	13.0888i	−0.547749	+	0.547749i	−0.925789	−	0.378040i	$-0.876598\pi$
$571$	−13.0888	+	13.0888i	−0.547749	+	0.547749i	0.378040	+	0.925789i	$0.376598\pi$
$572$		0			0
$573$	16.3924	+	16.3924i	0.684802	+	0.684802i
$574$		0			0
$575$		−	40.1664i		−	1.67506i
$576$		0			0
$577$		−	37.0472i		−	1.54229i	−0.636658	−	0.771147i	$-0.719683\pi$
$577$		−	37.0472i		−	1.54229i	0.636658	−	0.771147i	$-0.280317\pi$
$578$		0			0
$579$	−3.47810	+	3.47810i	−0.144545	+	0.144545i
$580$		0			0
$581$	27.3402	+	8.93321i	1.13426	+	0.370612i
$582$		0			0
$583$	30.9099			1.28016
$584$		0			0
$585$			2.11370i			0.0873905i
$586$		0			0
$587$	−6.53953	−	6.53953i	−0.269915	−	0.269915i	0.559151	−	0.829066i	$-0.311127\pi$
$587$	−6.53953	−	6.53953i	−0.269915	−	0.269915i	−0.829066	+	0.559151i	$0.811127\pi$
$588$		0			0
$589$	−21.4341	+	21.4341i	−0.883177	+	0.883177i
$590$		0			0
$591$	6.96787			0.286620
$592$		0			0
$593$			1.63788i			0.0672598i	0.999434	+	0.0336299i	$0.0107068\pi$
$593$			1.63788i			0.0672598i	−0.999434	+	0.0336299i	$0.989293\pi$
$594$		0			0
$595$	0.656812	−	2.01018i	0.0269266	−	0.0824094i
$596$		0			0
$597$	14.7359	+	14.7359i	0.603101	+	0.603101i
$598$		0			0
$599$	45.9685			1.87822			0.939112	−	0.343612i	$-0.111651\pi$
$599$	45.9685			1.87822			0.939112	+	0.343612i	$0.111651\pi$
$600$		0			0
$601$	28.5842			1.16598			0.582988	−	0.812481i	$-0.301883\pi$
$601$	28.5842			1.16598			0.582988	+	0.812481i	$0.301883\pi$
$602$		0			0
$603$	2.13532	−	2.13532i	0.0869568	−	0.0869568i
$604$		0			0
$605$	−0.809281	−	0.809281i	−0.0329020	−	0.0329020i
$606$		0			0
$607$	23.1827			0.940955			0.470477	−	0.882412i	$-0.344082\pi$
$607$	23.1827			0.940955			0.470477	+	0.882412i	$0.344082\pi$
$608$		0			0
$609$	−0.991213	+	0.502993i	−0.0401660	+	0.0203823i
$610$		0			0
$611$	14.3023	+	14.3023i	0.578609	+	0.578609i
$612$		0			0
$613$	−7.71960	−	7.71960i	−0.311792	−	0.311792i	0.533812	−	0.845603i	$-0.320759\pi$
$613$	−7.71960	−	7.71960i	−0.311792	−	0.311792i	−0.845603	+	0.533812i	$0.820759\pi$
$614$		0			0
$615$			2.63841i			0.106391i
$616$		0			0
$617$		−	23.2689i		−	0.936769i	−0.883525	−	0.468385i	$-0.844836\pi$
$617$		−	23.2689i		−	0.936769i	0.883525	−	0.468385i	$-0.155164\pi$
$618$		0			0
$619$	21.2386	+	21.2386i	0.853652	+	0.853652i	0.990581	−	0.136928i	$-0.0437231\pi$
$619$	21.2386	+	21.2386i	0.853652	+	0.853652i	−0.136928	+	0.990581i	$0.543723\pi$
$620$		0			0
$621$	−5.90590	−	5.90590i	−0.236996	−	0.236996i
$622$		0			0
$623$	13.1263	+	25.8671i	0.525893	+	1.03634i
$624$		0			0
$625$	−22.1727			−0.886907
$626$		0			0
$627$	−10.3947	−	10.3947i	−0.415125	−	0.415125i
$628$		0			0
$629$	−7.63321	+	7.63321i	−0.304356	+	0.304356i
$630$		0			0
$631$	17.6160			0.701281			0.350640	−	0.936510i	$-0.385964\pi$
$631$	17.6160			0.701281			0.350640	+	0.936510i	$0.385964\pi$
$632$		0			0
$633$	−3.67838			−0.146202
$634$		0			0
$635$	2.51700	+	2.51700i	0.0998840	+	0.0998840i
$636$		0			0
$637$	−33.4626	+	5.18697i	−1.32584	+	0.205515i
$638$		0			0
$639$			6.57589i			0.260138i
$640$		0			0
$641$	−23.9948			−0.947739			−0.473870	−	0.880595i	$-0.657143\pi$
$641$	−23.9948			−0.947739			−0.473870	+	0.880595i	$0.657143\pi$
$642$		0			0
$643$	−7.03418	+	7.03418i	−0.277401	+	0.277401i	−0.832071	−	0.554670i	$-0.812845\pi$
$643$	−7.03418	+	7.03418i	−0.277401	+	0.277401i	0.554670	+	0.832071i	$0.312845\pi$
$644$		0			0
$645$	1.73986	+	1.73986i	0.0685068	+	0.0685068i
$646$		0			0
$647$		−	26.3201i		−	1.03475i	−0.855759	−	0.517374i	$-0.826909\pi$
$647$		−	26.3201i		−	1.03475i	0.855759	−	0.517374i	$-0.173091\pi$
$648$		0			0
$649$	−1.58000			−0.0620206
$650$		0			0
$651$	−15.0126	−	4.90524i	−0.588389	−	0.192252i
$652$		0			0
$653$	−1.54617	+	1.54617i	−0.0605064	+	0.0605064i	−0.736712	−	0.676206i	$-0.763623\pi$
$653$	−1.54617	+	1.54617i	−0.0605064	+	0.0605064i	0.676206	+	0.736712i	$0.263623\pi$
$654$		0			0
$655$		−	5.27584i		−	0.206144i
$656$		0			0
$657$		−	3.68918i		−	0.143929i
$658$		0			0
$659$	−34.9606	−	34.9606i	−1.36187	−	1.36187i	−0.871528	−	0.490345i	$-0.836871\pi$
$659$	−34.9606	−	34.9606i	−1.36187	−	1.36187i	−0.490345	−	0.871528i	$-0.663129\pi$
$660$		0			0
$661$	−25.3606	+	25.3606i	−0.986413	+	0.986413i	−0.999909	−	0.0134957i	$-0.995704\pi$
$661$	−25.3606	+	25.3606i	−0.986413	+	0.986413i	0.0134957	+	0.999909i	$0.495704\pi$
$662$		0			0
$663$			8.84925i			0.343676i
$664$		0			0
$665$	5.23487	−	2.65644i	0.203000	−	0.103013i
$666$		0			0
$667$	2.48119	−	2.48119i	0.0960719	−	0.0960719i
$668$		0			0
$669$	−4.66053	+	4.66053i	−0.180187	+	0.180187i
$670$		0			0
$671$	25.3113			0.977132
$672$		0			0
$673$	−27.3585			−1.05459			−0.527295	−	0.849682i	$-0.676794\pi$
$673$	−27.3585			−1.05459			−0.527295	+	0.849682i	$0.676794\pi$
$674$		0			0
$675$	−3.40053	+	3.40053i	−0.130887	+	0.130887i
$676$		0			0
$677$	30.5718	−	30.5718i	1.17497	−	1.17497i	0.193961	−	0.981009i	$-0.437867\pi$
$677$	30.5718	−	30.5718i	1.17497	−	1.17497i	0.981009	−	0.193961i	$-0.0621335\pi$
$678$		0			0
$679$	−36.3339	+	18.4377i	−1.39437	+	0.707574i
$680$		0			0
$681$		−	0.290521i		−	0.0111328i
$682$		0			0
$683$	−9.46926	+	9.46926i	−0.362331	+	0.362331i	−0.864671	−	0.502339i	$-0.832473\pi$
$683$	−9.46926	+	9.46926i	−0.362331	+	0.362331i	0.502339	+	0.864671i	$0.332473\pi$
$684$		0			0
$685$	−5.59751	−	5.59751i	−0.213870	−	0.213870i
$686$		0			0
$687$			14.4784i			0.552385i
$688$		0			0
$689$		−	51.6507i		−	1.96774i
$690$		0			0
$691$	−17.7078	+	17.7078i	−0.673638	+	0.673638i	−0.958553	−	0.284915i	$-0.908035\pi$
$691$	−17.7078	+	17.7078i	−0.673638	+	0.673638i	0.284915	+	0.958553i	$0.408035\pi$
$692$		0			0
$693$	2.37885	−	7.28051i	0.0903651	−	0.276564i
$694$		0			0
$695$	−8.96406			−0.340026
$696$		0			0
$697$			11.0460i			0.418398i
$698$		0			0
$699$	1.13053	+	1.13053i	0.0427606	+	0.0427606i
$700$		0			0
$701$	−16.5609	+	16.5609i	−0.625498	+	0.625498i	−0.946932	−	0.321434i	$-0.895835\pi$
$701$	−16.5609	+	16.5609i	−0.625498	+	0.625498i	0.321434	+	0.946932i	$0.395835\pi$
$702$		0			0
$703$	−29.9655			−1.13017
$704$		0			0
$705$		−	1.82695i		−	0.0688070i
$706$		0			0
$707$	−6.44926	−	2.10725i	−0.242549	−	0.0792512i
$708$		0			0
$709$	−7.14462	−	7.14462i	−0.268322	−	0.268322i	0.560102	−	0.828424i	$-0.310762\pi$
$709$	−7.14462	−	7.14462i	−0.268322	−	0.268322i	−0.828424	+	0.560102i	$0.810762\pi$
$710$		0			0
$711$	6.40389			0.240165
$712$		0			0
$713$	49.8579			1.86719
$714$		0			0
$715$	4.32680	−	4.32680i	0.161813	−	0.161813i
$716$		0			0
$717$	−7.22500	−	7.22500i	−0.269823	−	0.269823i
$718$		0			0
$719$	−3.38226			−0.126137			−0.0630684	−	0.998009i	$-0.520089\pi$
$719$	−3.38226			−0.126137			−0.0630684	+	0.998009i	$0.520089\pi$
$720$		0			0
$721$	−47.0960	+	23.8990i	−1.75395	+	0.890044i
$722$		0			0
$723$	11.1887	+	11.1887i	0.416113	+	0.416113i
$724$		0			0
$725$	−1.42863	−	1.42863i	−0.0530580	−	0.0530580i
$726$		0			0
$727$		−	10.4037i		−	0.385851i	−0.981213	−	0.192925i	$-0.938202\pi$
$727$		−	10.4037i		−	0.385851i	0.981213	−	0.192925i	$-0.0617975\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	7.28413	+	7.28413i	0.269413	+	0.269413i
$732$		0			0
$733$	−8.20541	−	8.20541i	−0.303074	−	0.303074i	0.539141	−	0.842215i	$-0.318749\pi$
$733$	−8.20541	−	8.20541i	−0.303074	−	0.303074i	−0.842215	+	0.539141i	$0.818749\pi$
$734$		0			0
$735$	2.46852	+	1.80594i	0.0910527	+	0.0666133i
$736$		0			0
$737$	−8.74211			−0.322020
$738$		0			0
$739$	−29.2394	−	29.2394i	−1.07559	−	1.07559i	−0.996899	−	0.0786901i	$-0.974926\pi$
$739$	−29.2394	−	29.2394i	−1.07559	−	1.07559i	−0.0786901	−	0.996899i	$-0.525074\pi$
$740$		0			0
$741$	−17.3696	+	17.3696i	−0.638090	+	0.638090i
$742$		0			0
$743$	−22.2251			−0.815361			−0.407680	−	0.913125i	$-0.633662\pi$
$743$	−22.2251			−0.815361			−0.407680	+	0.913125i	$0.633662\pi$
$744$		0			0
$745$	−3.81916			−0.139923
$746$		0			0
$747$	7.68714	+	7.68714i	0.281258	+	0.281258i
$748$		0			0
$749$	−22.9499	−	7.49872i	−0.838573	−	0.273997i
$750$		0			0
$751$			50.4433i			1.84070i	0.391091	+	0.920352i	$0.372098\pi$
$751$			50.4433i			1.84070i	−0.391091	+	0.920352i	$0.627902\pi$
$752$		0			0
$753$	−21.6435			−0.788734
$754$		0			0
$755$	3.24842	−	3.24842i	0.118222	−	0.118222i
$756$		0			0
$757$	−3.04992	−	3.04992i	−0.110851	−	0.110851i	0.649506	−	0.760357i	$-0.274976\pi$
$757$	−3.04992	−	3.04992i	−0.110851	−	0.110851i	−0.760357	+	0.649506i	$0.774976\pi$
$758$		0			0
$759$			24.1791i			0.877646i
$760$		0			0
$761$	−20.2949			−0.735689			−0.367844	−	0.929887i	$-0.619904\pi$
$761$	−20.2949			−0.735689			−0.367844	+	0.929887i	$0.619904\pi$
$762$		0			0
$763$	5.87272	+	1.91887i	0.212607	+	0.0694677i
$764$		0			0
$765$	0.565195	−	0.565195i	0.0204347	−	0.0204347i
$766$		0			0
$767$			2.64020i			0.0953320i
$768$		0			0
$769$			52.1827i			1.88176i	0.338746	+	0.940878i	$0.389997\pi$
$769$			52.1827i			1.88176i	−0.338746	+	0.940878i	$0.610003\pi$
$770$		0			0
$771$	1.16385	+	1.16385i	0.0419149	+	0.0419149i
$772$		0			0
$773$	35.1095	−	35.1095i	1.26280	−	1.26280i	0.313070	−	0.949730i	$-0.398643\pi$
$773$	35.1095	−	35.1095i	1.26280	−	1.26280i	0.949730	−	0.313070i	$-0.101357\pi$
$774$		0			0
$775$		−	28.7075i		−	1.03120i
$776$		0			0
$777$	−7.06517	−	13.9228i	−0.253461	−	0.499479i
$778$		0			0
$779$	−21.6815	+	21.6815i	−0.776822	+	0.776822i
$780$		0			0
$781$	13.4611	−	13.4611i	0.481674	−	0.481674i
$782$		0			0
$783$	−0.420120			−0.0150139
$784$		0			0
$785$	−3.89670			−0.139079
$786$		0			0
$787$	26.8397	−	26.8397i	0.956731	−	0.956731i	−0.0423708	−	0.999102i	$-0.513491\pi$
$787$	26.8397	−	26.8397i	0.956731	−	0.956731i	0.999102	+	0.0423708i	$0.0134911\pi$
$788$		0			0
$789$	−1.28395	+	1.28395i	−0.0457097	+	0.0457097i
$790$		0			0
$791$	19.0771	+	37.5939i	0.678304	+	1.33669i
$792$		0			0
$793$		−	42.2954i		−	1.50195i
$794$		0			0
$795$	−3.29889	+	3.29889i	−0.117000	+	0.117000i
$796$		0			0
$797$	0.966881	+	0.966881i	0.0342487	+	0.0342487i	0.724024	−	0.689775i	$-0.242291\pi$
$797$	0.966881	+	0.966881i	0.0342487	+	0.0342487i	−0.689775	+	0.724024i	$0.742291\pi$
$798$		0			0
$799$		−	7.64877i		−	0.270594i
$800$		0			0
$801$			10.9636i			0.387380i
$802$		0			0
$803$	−7.55187	+	7.55187i	−0.266500	+	0.266500i
$804$		0			0
$805$	−9.17799	−	2.99884i	−0.323482	−	0.105695i
$806$		0			0
$807$	−22.8450			−0.804182
$808$		0			0
$809$		−	1.55218i		−	0.0545717i	−0.999628	−	0.0272858i	$-0.991314\pi$
$809$		−	1.55218i		−	0.0545717i	0.999628	−	0.0272858i	$-0.00868643\pi$
$810$		0			0
$811$	−24.8712	−	24.8712i	−0.873347	−	0.873347i	0.119488	−	0.992836i	$-0.461875\pi$
$811$	−24.8712	−	24.8712i	−0.873347	−	0.873347i	−0.992836	+	0.119488i	$0.961875\pi$
$812$		0			0
$813$	11.4210	−	11.4210i	0.400553	−	0.400553i
$814$		0			0
$815$	−5.76914			−0.202084
$816$		0			0
$817$			28.5951i			1.00042i
$818$		0			0
$819$	−12.1658	−	3.97508i	−0.425107	−	0.138900i
$820$		0			0
$821$	20.3922	+	20.3922i	0.711693	+	0.711693i	0.966889	−	0.255196i	$-0.0821401\pi$
$821$	20.3922	+	20.3922i	0.711693	+	0.711693i	−0.255196	+	0.966889i	$0.582140\pi$
$822$		0			0
$823$	9.69427			0.337921			0.168961	−	0.985623i	$-0.445959\pi$
$823$	9.69427			0.337921			0.168961	+	0.985623i	$0.445959\pi$
$824$		0			0
$825$	13.9220			0.484702
$826$		0			0
$827$	16.1394	−	16.1394i	0.561222	−	0.561222i	−0.368433	−	0.929654i	$-0.620106\pi$
$827$	16.1394	−	16.1394i	0.561222	−	0.561222i	0.929654	+	0.368433i	$0.120106\pi$
$828$		0			0
$829$	13.4926	+	13.4926i	0.468618	+	0.468618i	0.901467	−	0.432848i	$-0.142491\pi$
$829$	13.4926	+	13.4926i	0.468618	+	0.468618i	−0.432848	+	0.901467i	$0.642491\pi$
$830$		0			0
$831$	−0.443043			−0.0153690
$832$		0			0
$833$	10.3348	+	7.56081i	0.358078	+	0.261967i
$834$		0			0
$835$	−7.47971	−	7.47971i	−0.258846	−	0.258846i
$836$		0			0
$837$	−4.22102	−	4.22102i	−0.145900	−	0.145900i
$838$		0			0
$839$		−	40.3880i		−	1.39435i	−0.716902	−	0.697173i	$-0.754441\pi$
$839$		−	40.3880i		−	1.39435i	0.716902	−	0.697173i	$-0.245559\pi$
$840$		0			0
$841$			28.8235i			0.993914i
$842$		0			0
$843$	18.3936	+	18.3936i	0.633509	+	0.633509i
$844$		0			0
$845$	−3.21357	−	3.21357i	−0.110550	−	0.110550i
$846$		0			0
$847$	6.17993	−	3.13602i	0.212345	−	0.107755i
$848$		0			0
$849$	−16.5347			−0.567470
$850$		0			0
$851$	34.8514	+	34.8514i	1.19469	+	1.19469i
$852$		0			0
$853$	2.58804	−	2.58804i	0.0886129	−	0.0886129i	−0.661411	−	0.750024i	$-0.730042\pi$
$853$	2.58804	−	2.58804i	0.0886129	−	0.0886129i	0.750024	+	0.661411i	$0.230042\pi$
$854$		0			0
$855$	2.21877			0.0758804
$856$		0			0
$857$	41.2958			1.41064			0.705318	−	0.708891i	$-0.250804\pi$
$857$	41.2958			1.41064			0.705318	+	0.708891i	$0.250804\pi$
$858$		0			0
$859$	−28.3119	−	28.3119i	−0.965989	−	0.965989i	0.0334509	−	0.999440i	$-0.489350\pi$
$859$	−28.3119	−	28.3119i	−0.965989	−	0.965989i	−0.999440	+	0.0334509i	$0.989350\pi$
$860$		0			0
$861$	−15.1859	−	4.96186i	−0.517533	−	0.169100i
$862$		0			0
$863$		−	10.9831i		−	0.373867i	−0.982373	−	0.186934i	$-0.940145\pi$
$863$		−	10.9831i		−	0.373867i	0.982373	−	0.186934i	$-0.0598550\pi$
$864$		0			0
$865$	2.95622			0.100514
$866$		0			0
$867$	−9.65456	+	9.65456i	−0.327886	+	0.327886i
$868$		0			0
$869$	−13.1090	−	13.1090i	−0.444691	−	0.444691i
$870$		0			0
$871$			14.6081i			0.494978i
$872$		0			0
$873$	−15.3999			−0.521208
$874$		0			0
$875$	−3.52193	+	10.7789i	−0.119063	+	0.364394i
$876$		0			0
$877$	−11.3081	+	11.3081i	−0.381848	+	0.381848i	−0.871767	−	0.489920i	$-0.837026\pi$
$877$	−11.3081	+	11.3081i	−0.381848	+	0.381848i	0.489920	+	0.871767i	$0.337026\pi$
$878$		0			0
$879$		−	3.39912i		−	0.114649i
$880$		0			0
$881$		−	38.7274i		−	1.30476i	−0.757892	−	0.652380i	$-0.773771\pi$
$881$		−	38.7274i		−	1.30476i	0.757892	−	0.652380i	$-0.226229\pi$
$882$		0			0
$883$	0.0518282	+	0.0518282i	0.00174416	+	0.00174416i	0.707978	−	0.706234i	$-0.249607\pi$
$883$	0.0518282	+	0.0518282i	0.00174416	+	0.00174416i	−0.706234	+	0.707978i	$0.749607\pi$
$884$		0			0
$885$	0.168627	−	0.168627i	0.00566835	−	0.00566835i
$886$		0			0
$887$		−	46.0125i		−	1.54495i	−0.635046	−	0.772474i	$-0.719019\pi$
$887$		−	46.0125i		−	1.54495i	0.635046	−	0.772474i	$-0.280981\pi$
$888$		0			0
$889$	−19.2206	+	9.75353i	−0.644638	+	0.327123i
$890$		0			0
$891$	2.04703	−	2.04703i	0.0685781	−	0.0685781i
$892$		0			0
$893$	15.0133	−	15.0133i	0.502400	−	0.502400i
$894$		0			0
$895$	−1.63189			−0.0545481
$896$		0			0
$897$	40.4035			1.34903
$898$		0			0
$899$	1.77334	−	1.77334i	0.0591440	−	0.0591440i
$900$		0			0
$901$	−13.8112	+	13.8112i	−0.460119	+	0.460119i
$902$		0			0
$903$	−13.2861	+	6.74205i	−0.442134	+	0.224362i
$904$		0			0
$905$		−	7.44273i		−	0.247405i
$906$		0			0
$907$	−34.9149	+	34.9149i	−1.15933	+	1.15933i	−0.174712	+	0.984620i	$0.555899\pi$
$907$	−34.9149	+	34.9149i	−1.15933	+	1.15933i	−0.984620	+	0.174712i	$0.944101\pi$
$908$		0			0
$909$	−1.81331	−	1.81331i	−0.0601438	−	0.0601438i
$910$		0			0
$911$			40.9075i			1.35533i	0.735372	+	0.677664i	$0.237007\pi$
$911$			40.9075i			1.35533i	−0.735372	+	0.677664i	$0.762993\pi$
$912$		0			0
$913$		−	31.4716i		−	1.04156i
$914$		0			0
$915$	−2.70137	+	2.70137i	−0.0893047	+	0.0893047i
$916$		0			0
$917$	30.3661	+	9.92190i	1.00278	+	0.327650i
$918$		0			0
$919$	19.6759			0.649049			0.324525	−	0.945877i	$-0.394796\pi$
$919$	19.6759			0.649049			0.324525	+	0.945877i	$0.394796\pi$
$920$		0			0
$921$		−	8.32396i		−	0.274284i
$922$		0			0
$923$	−22.4935	−	22.4935i	−0.740383	−	0.740383i
$924$		0			0
$925$	20.0669	−	20.0669i	0.659797	−	0.659797i
$926$		0			0
$927$	−19.9614			−0.655618
$928$		0			0
$929$			31.8408i			1.04466i	0.852743	+	0.522331i	$0.174938\pi$
$929$			31.8408i			1.04466i	−0.852743	+	0.522331i	$0.825062\pi$
$930$		0			0
$931$	5.44482	+	35.1261i	0.178447	+	1.15121i
$932$		0			0
$933$	−1.50209	−	1.50209i	−0.0491762	−	0.0491762i
$934$		0			0
$935$	−2.31394			−0.0756740
$936$		0			0
$937$	−42.9199			−1.40213			−0.701067	−	0.713096i	$-0.747292\pi$
$937$	−42.9199			−1.40213			−0.701067	+	0.713096i	$0.747292\pi$
$938$		0			0
$939$	−3.27688	+	3.27688i	−0.106937	+	0.106937i
$940$		0			0
$941$	−20.3485	−	20.3485i	−0.663342	−	0.663342i	0.292825	−	0.956166i	$-0.405405\pi$
$941$	−20.3485	−	20.3485i	−0.663342	−	0.663342i	−0.956166	+	0.292825i	$0.905405\pi$
$942$		0			0
$943$	50.4334			1.64234
$944$		0			0
$945$	0.523134	+	1.03090i	0.0170175	+	0.0335353i
$946$		0			0
$947$	−30.8398	−	30.8398i	−1.00216	−	1.00216i	−0.999998	−	0.00216162i	$-0.999312\pi$
$947$	−30.8398	−	30.8398i	−1.00216	−	1.00216i	−0.00216162	−	0.999998i	$-0.500688\pi$
$948$		0			0
$949$	12.6192	+	12.6192i	0.409638	+	0.409638i
$950$		0			0
$951$		−	4.94884i		−	0.160477i
$952$		0			0
$953$			17.1584i			0.555816i	0.960608	+	0.277908i	$0.0896410\pi$
$953$			17.1584i			0.555816i	−0.960608	+	0.277908i	$0.910359\pi$
$954$		0			0
$955$	7.16254	+	7.16254i	0.231774	+	0.231774i
$956$		0			0
$957$	0.859998	+	0.859998i	0.0277998	+	0.0277998i
$958$		0			0
$959$	42.7444	−	21.6907i	1.38029	−	0.700430i
$960$		0			0
$961$	4.63406			0.149486
$962$		0			0
$963$	−6.45274	−	6.45274i	−0.207937	−	0.207937i
$964$		0			0
$965$	−1.51973	+	1.51973i	−0.0489219	+	0.0489219i
$966$		0			0
$967$	−4.63922			−0.149187			−0.0745937	−	0.997214i	$-0.523766\pi$
$967$	−4.63922			−0.149187			−0.0745937	+	0.997214i	$0.523766\pi$
$968$		0			0
$969$	9.28916			0.298411
$970$		0			0
$971$	−25.7650	−	25.7650i	−0.826839	−	0.826839i	0.160239	−	0.987078i	$-0.448773\pi$
$971$	−25.7650	−	25.7650i	−0.826839	−	0.826839i	−0.987078	+	0.160239i	$0.948773\pi$
$972$		0			0
$973$	16.8581	−	51.5944i	0.540445	−	1.65404i
$974$		0			0
$975$		−	23.2638i		−	0.745037i
$976$		0			0
$977$	51.2641			1.64008			0.820042	−	0.572304i	$-0.193950\pi$
$977$	51.2641			1.64008			0.820042	+	0.572304i	$0.193950\pi$
$978$		0			0
$979$	22.4428	−	22.4428i	0.717276	−	0.717276i
$980$		0			0
$981$	1.65121	+	1.65121i	0.0527191	+	0.0527191i
$982$		0			0
$983$			7.11266i			0.226859i	0.993546	+	0.113429i	$0.0361836\pi$
$983$			7.11266i			0.226859i	−0.993546	+	0.113429i	$0.963816\pi$
$984$		0			0
$985$	3.04456			0.0970078
$986$		0			0
$987$	10.5154	+	3.43582i	0.334708	+	0.109363i
$988$		0			0
$989$	33.2575	−	33.2575i	1.05753	−	1.05753i
$990$		0			0
$991$		−	28.4966i		−	0.905225i	−0.891707	−	0.452613i	$-0.850492\pi$
$991$		−	28.4966i		−	0.905225i	0.891707	−	0.452613i	$-0.149508\pi$
$992$		0			0
$993$		−	8.41663i		−	0.267094i
$994$		0			0
$995$	6.43875	+	6.43875i	0.204122	+	0.204122i
$996$		0			0
$997$	−15.6831	+	15.6831i	−0.496687	+	0.496687i	−0.910405	−	0.413718i	$-0.864230\pi$
$997$	−15.6831	+	15.6831i	−0.496687	+	0.496687i	0.413718	+	0.910405i	$0.364230\pi$
$998$		0			0
$999$		−	5.90111i		−	0.186703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.u.a.1231.9		64
4.3	odd	2		336.2.u.a.139.14	yes	64
7.6	odd	2	inner	1344.2.u.a.1231.24		64
16.3	odd	4	inner	1344.2.u.a.559.24		64
16.13	even	4		336.2.u.a.307.13	yes	64
28.27	even	2		336.2.u.a.139.13	✓	64
112.13	odd	4		336.2.u.a.307.14	yes	64
112.83	even	4	inner	1344.2.u.a.559.9		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.13	✓	64	28.27	even	2
336.2.u.a.139.14	yes	64	4.3	odd	2
336.2.u.a.307.13	yes	64	16.13	even	4
336.2.u.a.307.14	yes	64	112.13	odd	4
1344.2.u.a.559.9		64	112.83	even	4	inner
1344.2.u.a.559.24		64	16.3	odd	4	inner
1344.2.u.a.1231.9		64	1.1	even	1	trivial
1344.2.u.a.1231.24		64	7.6	odd	2	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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.308965 + 0.308965i) q^{5} +(-1.19726 - 2.35936i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.308965 + 0.308965i) q^{5} +(-1.19726 - 2.35936i) q^{7} -1.00000i q^{9} +(-2.04703 + 2.04703i) q^{11} +(3.42060 + 3.42060i) q^{13} -0.436943i q^{15} -1.82932i q^{17} +(3.59065 - 3.59065i) q^{19} +(2.51491 + 0.821727i) q^{21} -8.35220 q^{23} +4.80908i q^{25} +(0.707107 + 0.707107i) q^{27} +(-0.297070 + 0.297070i) q^{29} -5.96943 q^{31} -2.89494i q^{33} +(1.09887 + 0.359048i) q^{35} +(-4.17272 - 4.17272i) q^{37} -4.83747 q^{39} -6.03833 q^{41} +(-3.98189 + 3.98189i) q^{43} +(0.308965 + 0.308965i) q^{45} +4.18122 q^{47} +(-4.13314 + 5.64953i) q^{49} +(1.29352 + 1.29352i) q^{51} +(-7.54994 - 7.54994i) q^{53} -1.26492i q^{55} +5.07794i q^{57} +(0.385926 + 0.385926i) q^{59} +(-6.18244 - 6.18244i) q^{61} +(-2.35936 + 1.19726i) q^{63} -2.11370 q^{65} +(2.13532 + 2.13532i) q^{67} +(5.90590 - 5.90590i) q^{69} -6.57589 q^{71} +3.68918 q^{73} +(-3.40053 - 3.40053i) q^{75} +(7.28051 + 2.37885i) q^{77} +6.40389i q^{79} -1.00000 q^{81} +(-7.68714 + 7.68714i) q^{83} +(0.565195 + 0.565195i) q^{85} -0.420120i q^{87} -10.9636 q^{89} +(3.97508 - 12.1658i) q^{91} +(4.22102 - 4.22102i) q^{93} +2.21877i q^{95} -15.3999i q^{97} +(2.04703 + 2.04703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Introduction

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