LMFDB - Embedded newform 1920.2.w.i.1663.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(127,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("1920.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.w (of order $4$, degree $2$, 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 71x^{8} + 158x^{6} + 149x^{4} + 52x^{2} + 4 $ x^12 + 14x^10 + 71x^8 + 158x^6 + 149x^4 + 52*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1663.6
Root			$1.72303i$ of defining polynomial
Character	$\chi$	$=$	1920.1663
Dual form			1920.2.w.i.127.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(1.25633 - 1.84977i) q^{5} +(0.660026 + 0.660026i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(1.25633 - 1.84977i) q^{5} +(0.660026 + 0.660026i) q^{7} -1.00000i q^{9} +1.06658i q^{11} +(1.61597 + 1.61597i) q^{13} +(-0.419628 - 2.19634i) q^{15} +(3.06204 - 3.06204i) q^{17} -3.08761 q^{19} +0.933418 q^{21} +(4.94939 - 4.94939i) q^{23} +(-1.84329 - 4.64782i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.36083i q^{29} +1.95301i q^{31} +(0.754187 + 0.754187i) q^{33} +(2.05010 - 0.391689i) q^{35} +(4.38209 - 4.38209i) q^{37} +2.28533 q^{39} +2.99857 q^{41} +(-1.44607 + 1.44607i) q^{43} +(-1.84977 - 1.25633i) q^{45} +(8.81622 + 8.81622i) q^{47} -6.12873i q^{49} -4.33037i q^{51} +(-5.15114 - 5.15114i) q^{53} +(1.97293 + 1.33997i) q^{55} +(-2.18327 + 2.18327i) q^{57} -3.59218 q^{59} +8.24869 q^{61} +(0.660026 - 0.660026i) q^{63} +(5.01935 - 0.958988i) q^{65} +(-6.57065 - 6.57065i) q^{67} -6.99949i q^{69} +7.24725i q^{71} +(-7.31955 - 7.31955i) q^{73} +(-4.58991 - 1.98310i) q^{75} +(-0.703972 + 0.703972i) q^{77} +3.45462 q^{79} -1.00000 q^{81} +(-1.74653 + 1.74653i) q^{83} +(-1.81715 - 9.51098i) q^{85} +(1.66936 + 1.66936i) q^{87} -15.1307i q^{89} +2.13316i q^{91} +(1.38099 + 1.38099i) q^{93} +(-3.87904 + 5.71136i) q^{95} +(-11.0604 + 11.0604i) q^{97} +1.06658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) $ 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$5$	1.25633	−	1.84977i	0.561846	−	0.827242i
$5$	1.25633	−	1.84977i	0.561846	−	0.827242i
$6$		0			0
$7$	0.660026	+	0.660026i	0.249466	+	0.249466i	0.820752	−	0.571285i	$-0.193555\pi$
$7$	0.660026	+	0.660026i	0.249466	+	0.249466i	−0.571285	+	0.820752i	$0.693555\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			1.06658i			0.321587i	0.986988	+	0.160793i	$0.0514052\pi$
$11$			1.06658i			0.321587i	−0.986988	+	0.160793i	$0.948595\pi$
$12$		0			0
$13$	1.61597	+	1.61597i	0.448189	+	0.448189i	0.894752	−	0.446563i	$-0.147352\pi$
$13$	1.61597	+	1.61597i	0.448189	+	0.448189i	−0.446563	+	0.894752i	$0.647352\pi$
$14$		0			0
$15$	−0.419628	−	2.19634i	−0.108348	−	0.567093i
$16$		0			0
$17$	3.06204	−	3.06204i	0.742653	−	0.742653i	−0.230435	−	0.973088i	$-0.574015\pi$
$17$	3.06204	−	3.06204i	0.742653	−	0.742653i	0.973088	+	0.230435i	$0.0740148\pi$
$18$		0			0
$19$	−3.08761			−0.708346			−0.354173	−	0.935180i	$-0.615238\pi$
$19$	−3.08761			−0.708346			−0.354173	+	0.935180i	$0.615238\pi$
$20$		0			0
$21$	0.933418			0.203689
$22$		0			0
$23$	4.94939	−	4.94939i	1.03202	−	1.03202i	0.0325487	−	0.999470i	$-0.489638\pi$
$23$	4.94939	−	4.94939i	1.03202	−	1.03202i	0.999470	−	0.0325487i	$-0.0103624\pi$
$24$		0			0
$25$	−1.84329	−	4.64782i	−0.368659	−	0.929565i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			2.36083i			0.438394i	0.975681	+	0.219197i	$0.0703438\pi$
$29$			2.36083i			0.438394i	−0.975681	+	0.219197i	$0.929656\pi$
$30$		0			0
$31$			1.95301i			0.350771i	0.984500	+	0.175385i	$0.0561172\pi$
$31$			1.95301i			0.350771i	−0.984500	+	0.175385i	$0.943883\pi$
$32$		0			0
$33$	0.754187	+	0.754187i	0.131287	+	0.131287i
$34$		0			0
$35$	2.05010	−	0.391689i	0.346531	−	0.0662075i
$36$		0			0
$37$	4.38209	−	4.38209i	0.720411	−	0.720411i	−0.248278	−	0.968689i	$-0.579865\pi$
$37$	4.38209	−	4.38209i	0.720411	−	0.720411i	0.968689	+	0.248278i	$0.0798646\pi$
$38$		0			0
$39$	2.28533			0.365945
$40$		0			0
$41$	2.99857			0.468297			0.234149	−	0.972201i	$-0.424770\pi$
$41$	2.99857			0.468297			0.234149	+	0.972201i	$0.424770\pi$
$42$		0			0
$43$	−1.44607	+	1.44607i	−0.220523	+	0.220523i	−0.808719	−	0.588195i	$-0.799839\pi$
$43$	−1.44607	+	1.44607i	−0.220523	+	0.220523i	0.588195	+	0.808719i	$0.299839\pi$
$44$		0			0
$45$	−1.84977	−	1.25633i	−0.275747	−	0.187282i
$46$		0			0
$47$	8.81622	+	8.81622i	1.28598	+	1.28598i	0.937208	+	0.348770i	$0.113401\pi$
$47$	8.81622	+	8.81622i	1.28598	+	1.28598i	0.348770	+	0.937208i	$0.386599\pi$
$48$		0			0
$49$		−	6.12873i		−	0.875533i
$50$		0			0
$51$		−	4.33037i		−	0.606374i
$52$		0			0
$53$	−5.15114	−	5.15114i	−0.707564	−	0.707564i	0.258458	−	0.966022i	$-0.416786\pi$
$53$	−5.15114	−	5.15114i	−0.707564	−	0.707564i	−0.966022	+	0.258458i	$0.916786\pi$
$54$		0			0
$55$	1.97293	+	1.33997i	0.266030	+	0.180682i
$56$		0			0
$57$	−2.18327	+	2.18327i	−0.289181	+	0.289181i
$58$		0			0
$59$	−3.59218			−0.467662			−0.233831	−	0.972277i	$-0.575126\pi$
$59$	−3.59218			−0.467662			−0.233831	+	0.972277i	$0.575126\pi$
$60$		0			0
$61$	8.24869			1.05614			0.528068	−	0.849202i	$-0.322917\pi$
$61$	8.24869			1.05614			0.528068	+	0.849202i	$0.322917\pi$
$62$		0			0
$63$	0.660026	−	0.660026i	0.0831555	−	0.0831555i
$64$		0			0
$65$	5.01935	−	0.958988i	0.622574	−	0.118948i
$66$		0			0
$67$	−6.57065	−	6.57065i	−0.802733	−	0.802733i	0.180789	−	0.983522i	$-0.442135\pi$
$67$	−6.57065	−	6.57065i	−0.802733	−	0.802733i	−0.983522	+	0.180789i	$0.942135\pi$
$68$		0			0
$69$		−	6.99949i		−	0.842640i
$70$		0			0
$71$			7.24725i			0.860091i	0.902807	+	0.430045i	$0.141502\pi$
$71$			7.24725i			0.860091i	−0.902807	+	0.430045i	$0.858498\pi$
$72$		0			0
$73$	−7.31955	−	7.31955i	−0.856688	−	0.856688i	0.134258	−	0.990946i	$-0.457135\pi$
$73$	−7.31955	−	7.31955i	−0.856688	−	0.856688i	−0.990946	+	0.134258i	$0.957135\pi$
$74$		0			0
$75$	−4.58991	−	1.98310i	−0.529998	−	0.228989i
$76$		0			0
$77$	−0.703972	+	0.703972i	−0.0802251	+	0.0802251i
$78$		0			0
$79$	3.45462			0.388675			0.194338	−	0.980935i	$-0.437744\pi$
$79$	3.45462			0.388675			0.194338	+	0.980935i	$0.437744\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−1.74653	+	1.74653i	−0.191707	+	0.191707i	−0.796433	−	0.604727i	$-0.793282\pi$
$83$	−1.74653	+	1.74653i	−0.191707	+	0.191707i	0.604727	+	0.796433i	$0.293282\pi$
$84$		0			0
$85$	−1.81715	−	9.51098i	−0.197097	−	1.03161i
$86$		0			0
$87$	1.66936	+	1.66936i	0.178974	+	0.178974i
$88$		0			0
$89$		−	15.1307i		−	1.60385i	−0.597423	−	0.801926i	$-0.703809\pi$
$89$		−	15.1307i		−	1.60385i	0.597423	−	0.801926i	$-0.296191\pi$
$90$		0			0
$91$			2.13316i			0.223616i
$92$		0			0
$93$	1.38099	+	1.38099i	0.143202	+	0.143202i
$94$		0			0
$95$	−3.87904	+	5.71136i	−0.397981	+	0.585973i
$96$		0			0
$97$	−11.0604	+	11.0604i	−1.12301	+	1.12301i	−0.131723	+	0.991287i	$0.542051\pi$
$97$	−11.0604	+	11.0604i	−1.12301	+	1.12301i	−0.991287	+	0.131723i	$0.957949\pi$
$98$		0			0
$99$	1.06658			0.107196
$100$		0			0
$101$	−3.40731			−0.339040			−0.169520	−	0.985527i	$-0.554222\pi$
$101$	−3.40731			−0.339040			−0.169520	+	0.985527i	$0.554222\pi$
$102$		0			0
$103$	−1.65952	+	1.65952i	−0.163517	+	0.163517i	−0.784123	−	0.620606i	$-0.786887\pi$
$103$	−1.65952	+	1.65952i	−0.163517	+	0.163517i	0.620606	+	0.784123i	$0.286887\pi$
$104$		0			0
$105$	1.17268	−	1.72661i	0.114442	−	0.168500i
$106$		0			0
$107$	−9.63723	−	9.63723i	−0.931666	−	0.931666i	0.0661437	−	0.997810i	$-0.478930\pi$
$107$	−9.63723	−	9.63723i	−0.931666	−	0.931666i	−0.997810	+	0.0661437i	$0.978930\pi$
$108$		0			0
$109$			2.63155i			0.252057i	0.992027	+	0.126029i	$0.0402231\pi$
$109$			2.63155i			0.252057i	−0.992027	+	0.126029i	$0.959777\pi$
$110$		0			0
$111$		−	6.19721i		−	0.588213i
$112$		0			0
$113$	10.0971	+	10.0971i	0.949855	+	0.949855i	0.998801	−	0.0489460i	$-0.0155862\pi$
$113$	10.0971	+	10.0971i	0.949855	+	0.949855i	−0.0489460	+	0.998801i	$0.515586\pi$
$114$		0			0
$115$	−2.93719	−	15.3733i	−0.273894	−	1.43356i
$116$		0			0
$117$	1.61597	−	1.61597i	0.149396	−	0.149396i
$118$		0			0
$119$	4.04205			0.370534
$120$		0			0
$121$	9.86240			0.896582
$122$		0			0
$123$	2.12031	−	2.12031i	0.191182	−	0.191182i
$124$		0			0
$125$	−10.9132	−	2.42951i	−0.976104	−	0.217302i
$126$		0			0
$127$	6.88947	+	6.88947i	0.611342	+	0.611342i	0.943296	−	0.331954i	$-0.107708\pi$
$127$	6.88947	+	6.88947i	0.611342	+	0.611342i	−0.331954	+	0.943296i	$0.607708\pi$
$128$		0			0
$129$			2.04505i			0.180057i
$130$		0			0
$131$			18.2708i			1.59632i	0.602442	+	0.798162i	$0.294194\pi$
$131$			18.2708i			1.59632i	−0.602442	+	0.798162i	$0.705806\pi$
$132$		0			0
$133$	−2.03790	−	2.03790i	−0.176708	−	0.176708i
$134$		0			0
$135$	−2.19634	+	0.419628i	−0.189031	+	0.0361159i
$136$		0			0
$137$	7.80235	−	7.80235i	0.666600	−	0.666600i	−0.290328	−	0.956927i	$-0.593764\pi$
$137$	7.80235	−	7.80235i	0.666600	−	0.666600i	0.956927	+	0.290328i	$0.0937643\pi$
$138$		0			0
$139$	−7.80926			−0.662373			−0.331186	−	0.943565i	$-0.607449\pi$
$139$	−7.80926			−0.662373			−0.331186	+	0.943565i	$0.607449\pi$
$140$		0			0
$141$	12.4680			1.05000
$142$		0			0
$143$	−1.72356	+	1.72356i	−0.144132	+	0.144132i
$144$		0			0
$145$	4.36698	+	2.96597i	0.362658	+	0.246310i
$146$		0			0
$147$	−4.33367	−	4.33367i	−0.357435	−	0.357435i
$148$		0			0
$149$		−	15.9300i		−	1.30504i	−0.757772	−	0.652520i	$-0.773712\pi$
$149$		−	15.9300i		−	1.30504i	0.757772	−	0.652520i	$-0.226288\pi$
$150$		0			0
$151$		−	14.3799i		−	1.17022i	−0.810954	−	0.585110i	$-0.801051\pi$
$151$		−	14.3799i		−	1.17022i	0.810954	−	0.585110i	$-0.198949\pi$
$152$		0			0
$153$	−3.06204	−	3.06204i	−0.247551	−	0.247551i
$154$		0			0
$155$	3.61262	+	2.45361i	0.290172	+	0.197079i
$156$		0			0
$157$	3.53200	−	3.53200i	0.281885	−	0.281885i	−0.551976	−	0.833860i	$-0.686126\pi$
$157$	3.53200	−	3.53200i	0.281885	−	0.281885i	0.833860	+	0.551976i	$0.186126\pi$
$158$		0			0
$159$	−7.28482			−0.577724
$160$		0			0
$161$	6.53345			0.514908
$162$		0			0
$163$	−11.4461	+	11.4461i	−0.896525	+	0.896525i	−0.995127	−	0.0986017i	$-0.968563\pi$
$163$	−11.4461	+	11.4461i	−0.896525	+	0.896525i	0.0986017	+	0.995127i	$0.468563\pi$
$164$		0			0
$165$	2.34258	−	0.447568i	0.182369	−	0.0348431i
$166$		0			0
$167$	11.0098	+	11.0098i	0.851960	+	0.851960i	0.990374	−	0.138414i	$-0.0442005\pi$
$167$	11.0098	+	11.0098i	0.851960	+	0.851960i	−0.138414	+	0.990374i	$0.544200\pi$
$168$		0			0
$169$		−	7.77729i		−	0.598253i
$170$		0			0
$171$			3.08761i			0.236115i
$172$		0			0
$173$	5.63993	+	5.63993i	0.428796	+	0.428796i	0.888218	−	0.459422i	$-0.151944\pi$
$173$	5.63993	+	5.63993i	0.428796	+	0.428796i	−0.459422	+	0.888218i	$0.651944\pi$
$174$		0			0
$175$	1.85106	−	4.28431i	0.139927	−	0.323863i
$176$		0			0
$177$	−2.54006	+	2.54006i	−0.190922	+	0.190922i
$178$		0			0
$179$	−0.313836			−0.0234572			−0.0117286	−	0.999931i	$-0.503733\pi$
$179$	−0.313836			−0.0234572			−0.0117286	+	0.999931i	$0.503733\pi$
$180$		0			0
$181$	3.19323			0.237351			0.118676	−	0.992933i	$-0.462135\pi$
$181$	3.19323			0.237351			0.118676	+	0.992933i	$0.462135\pi$
$182$		0			0
$183$	5.83270	−	5.83270i	0.431166	−	0.431166i
$184$		0			0
$185$	−2.60053	−	13.6112i	−0.191194	−	1.00071i
$186$		0			0
$187$	3.26591	+	3.26591i	0.238827	+	0.238827i
$188$		0			0
$189$		−	0.933418i		−	0.0678962i
$190$		0			0
$191$			6.89687i			0.499040i	0.968370	+	0.249520i	$0.0802728\pi$
$191$			6.89687i			0.499040i	−0.968370	+	0.249520i	$0.919727\pi$
$192$		0			0
$193$	13.0061	+	13.0061i	0.936202	+	0.936202i	0.998084	−	0.0618815i	$-0.0197101\pi$
$193$	13.0061	+	13.0061i	0.936202	+	0.936202i	−0.0618815	+	0.998084i	$0.519710\pi$
$194$		0			0
$195$	2.87111	−	4.22733i	0.205605	−	0.302725i
$196$		0			0
$197$	−15.1745	+	15.1745i	−1.08114	+	1.08114i	−0.0847375	+	0.996403i	$0.527005\pi$
$197$	−15.1745	+	15.1745i	−1.08114	+	1.08114i	−0.996403	+	0.0847375i	$0.972995\pi$
$198$		0			0
$199$	−24.4650			−1.73428			−0.867140	−	0.498065i	$-0.834044\pi$
$199$	−24.4650			−1.73428			−0.867140	+	0.498065i	$0.834044\pi$
$200$		0			0
$201$	−9.29230			−0.655429
$202$		0			0
$203$	−1.55821	+	1.55821i	−0.109365	+	0.109365i
$204$		0			0
$205$	3.76717	−	5.54666i	0.263111	−	0.387395i
$206$		0			0
$207$	−4.94939	−	4.94939i	−0.344006	−	0.344006i
$208$		0			0
$209$		−	3.29319i		−	0.227794i
$210$		0			0
$211$		−	9.54006i		−	0.656765i	−0.944545	−	0.328383i	$-0.893496\pi$
$211$		−	9.54006i		−	0.656765i	0.944545	−	0.328383i	$-0.106504\pi$
$212$		0			0
$213$	5.12458	+	5.12458i	0.351131	+	0.351131i
$214$		0			0
$215$	0.858161	+	4.49163i	0.0585261	+	0.306326i
$216$		0			0
$217$	−1.28904	+	1.28904i	−0.0875056	+	0.0875056i
$218$		0			0
$219$	−10.3514			−0.699483
$220$		0			0
$221$	9.89632			0.665698
$222$		0			0
$223$	14.9552	−	14.9552i	1.00147	−	1.00147i	0.00147312	−	0.999999i	$-0.499531\pi$
$223$	14.9552	−	14.9552i	1.00147	−	1.00147i	0.999999	−	0.00147312i	$-0.000468908\pi$
$224$		0			0
$225$	−4.64782	+	1.84329i	−0.309855	+	0.122886i
$226$		0			0
$227$	19.7829	+	19.7829i	1.31304	+	1.31304i	0.919165	+	0.393873i	$0.128865\pi$
$227$	19.7829	+	19.7829i	1.31304	+	1.31304i	0.393873	+	0.919165i	$0.371135\pi$
$228$		0			0
$229$		−	18.4720i		−	1.22066i	−0.792147	−	0.610330i	$-0.791037\pi$
$229$		−	18.4720i		−	1.22066i	0.792147	−	0.610330i	$-0.208963\pi$
$230$		0			0
$231$			0.995567i			0.0655035i
$232$		0			0
$233$	4.14351	+	4.14351i	0.271450	+	0.271450i	0.829684	−	0.558233i	$-0.188521\pi$
$233$	4.14351	+	4.14351i	0.271450	+	0.271450i	−0.558233	+	0.829684i	$0.688521\pi$
$234$		0			0
$235$	27.3840	−	5.23194i	1.78634	−	0.341294i
$236$		0			0
$237$	2.44279	−	2.44279i	0.158676	−	0.158676i
$238$		0			0
$239$	−0.834994			−0.0540113			−0.0270056	−	0.999635i	$-0.508597\pi$
$239$	−0.834994			−0.0540113			−0.0270056	+	0.999635i	$0.508597\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−11.3367	−	7.69968i	−0.724278	−	0.491914i
$246$		0			0
$247$	−4.98948	−	4.98948i	−0.317473	−	0.317473i
$248$		0			0
$249$			2.46997i			0.156528i
$250$		0			0
$251$			19.6551i			1.24062i	0.784358	+	0.620309i	$0.212993\pi$
$251$			19.6551i			1.24062i	−0.784358	+	0.620309i	$0.787007\pi$
$252$		0			0
$253$	5.27893	+	5.27893i	0.331883	+	0.331883i
$254$		0			0
$255$	−8.01020	−	5.44036i	−0.501618	−	0.340688i
$256$		0			0
$257$	−14.4161	+	14.4161i	−0.899249	+	0.899249i	−0.995370	−	0.0961203i	$-0.969357\pi$
$257$	−14.4161	+	14.4161i	−0.899249	+	0.899249i	0.0961203	+	0.995370i	$0.469357\pi$
$258$		0			0
$259$	5.78459			0.359437
$260$		0			0
$261$	2.36083			0.146131
$262$		0			0
$263$	−0.986364	+	0.986364i	−0.0608218	+	0.0608218i	−0.736863	−	0.676042i	$-0.763694\pi$
$263$	−0.986364	+	0.986364i	−0.0608218	+	0.0608218i	0.676042	+	0.736863i	$0.263694\pi$
$264$		0			0
$265$	−15.9999	+	3.05692i	−0.982869	+	0.187785i
$266$		0			0
$267$	−10.6990	−	10.6990i	−0.654770	−	0.654770i
$268$		0			0
$269$			24.7358i			1.50817i	0.656778	+	0.754084i	$0.271919\pi$
$269$			24.7358i			1.50817i	−0.656778	+	0.754084i	$0.728081\pi$
$270$		0			0
$271$		−	17.3209i		−	1.05217i	−0.850433	−	0.526084i	$-0.823660\pi$
$271$		−	17.3209i		−	1.05217i	0.850433	−	0.526084i	$-0.176340\pi$
$272$		0			0
$273$	1.50837	+	1.50837i	0.0912910	+	0.0912910i
$274$		0			0
$275$	4.95729	−	1.96602i	0.298936	−	0.118556i
$276$		0			0
$277$	−12.4702	+	12.4702i	−0.749262	+	0.749262i	−0.974341	−	0.225079i	$-0.927736\pi$
$277$	−12.4702	+	12.4702i	−0.749262	+	0.749262i	0.225079	+	0.974341i	$0.427736\pi$
$278$		0			0
$279$	1.95301			0.116924
$280$		0			0
$281$	10.3398			0.616821			0.308410	−	0.951253i	$-0.400203\pi$
$281$	10.3398			0.616821			0.308410	+	0.951253i	$0.400203\pi$
$282$		0			0
$283$	5.22217	−	5.22217i	0.310426	−	0.310426i	−0.534648	−	0.845075i	$-0.679556\pi$
$283$	5.22217	−	5.22217i	0.310426	−	0.310426i	0.845075	+	0.534648i	$0.179556\pi$
$284$		0			0
$285$	1.29565	+	6.78144i	0.0767476	+	0.401698i
$286$		0			0
$287$	1.97913	+	1.97913i	0.116824	+	0.116824i
$288$		0			0
$289$		−	1.75215i		−	0.103067i
$290$		0			0
$291$			15.6417i			0.916934i
$292$		0			0
$293$	4.52970	+	4.52970i	0.264628	+	0.264628i	0.826931	−	0.562303i	$-0.190085\pi$
$293$	4.52970	+	4.52970i	0.264628	+	0.264628i	−0.562303	+	0.826931i	$0.690085\pi$
$294$		0			0
$295$	−4.51295	+	6.64471i	−0.262754	+	0.386870i
$296$		0			0
$297$	0.754187	−	0.754187i	0.0437624	−	0.0437624i
$298$		0			0
$299$	15.9961			0.925079
$300$		0			0
$301$	−1.90889			−0.110026
$302$		0			0
$303$	−2.40933	+	2.40933i	−0.138412	+	0.138412i
$304$		0			0
$305$	10.3630	−	15.2582i	0.593386	−	0.873680i
$306$		0			0
$307$	−21.8299	−	21.8299i	−1.24590	−	1.24590i	−0.957515	−	0.288383i	$-0.906882\pi$
$307$	−21.8299	−	21.8299i	−1.24590	−	1.24590i	−0.288383	−	0.957515i	$-0.593118\pi$
$308$		0			0
$309$			2.34691i			0.133511i
$310$		0			0
$311$			21.2462i			1.20476i	0.798208	+	0.602382i	$0.205782\pi$
$311$			21.2462i			1.20476i	−0.798208	+	0.602382i	$0.794218\pi$
$312$		0			0
$313$	−2.28569	−	2.28569i	−0.129195	−	0.129195i	0.639552	−	0.768747i	$-0.279120\pi$
$313$	−2.28569	−	2.28569i	−0.129195	−	0.129195i	−0.768747	+	0.639552i	$0.779120\pi$
$314$		0			0
$315$	−0.391689	−	2.05010i	−0.0220692	−	0.115510i
$316$		0			0
$317$	−18.7175	+	18.7175i	−1.05128	+	1.05128i	−0.0526686	+	0.998612i	$0.516773\pi$
$317$	−18.7175	+	18.7175i	−1.05128	+	1.05128i	−0.998612	+	0.0526686i	$0.983227\pi$
$318$		0			0
$319$	−2.51801			−0.140982
$320$		0			0
$321$	−13.6291			−0.760702
$322$		0			0
$323$	−9.45437	+	9.45437i	−0.526055	+	0.526055i
$324$		0			0
$325$	4.53203	−	10.4894i	0.251392	−	0.581850i
$326$		0			0
$327$	1.86079	+	1.86079i	0.102902	+	0.102902i
$328$		0			0
$329$			11.6379i			0.641617i
$330$		0			0
$331$		−	16.2077i		−	0.890858i	−0.895317	−	0.445429i	$-0.853051\pi$
$331$		−	16.2077i		−	0.890858i	0.895317	−	0.445429i	$-0.146949\pi$
$332$		0			0
$333$	−4.38209	−	4.38209i	−0.240137	−	0.240137i
$334$		0			0
$335$	−20.4091	+	3.89932i	−1.11507	+	0.213042i
$336$		0			0
$337$	−19.5561	+	19.5561i	−1.06529	+	1.06529i	−0.0675767	+	0.997714i	$0.521527\pi$
$337$	−19.5561	+	19.5561i	−1.06529	+	1.06529i	−0.997714	+	0.0675767i	$0.978473\pi$
$338$		0			0
$339$	14.2795			0.775554
$340$		0			0
$341$	−2.08304			−0.112803
$342$		0			0
$343$	8.66531	−	8.66531i	0.467883	−	0.467883i
$344$		0			0
$345$	−12.9474	−	8.79364i	−0.697067	−	0.473434i
$346$		0			0
$347$	5.04260	+	5.04260i	0.270701	+	0.270701i	0.829382	−	0.558681i	$-0.188693\pi$
$347$	5.04260	+	5.04260i	0.270701	+	0.270701i	−0.558681	+	0.829382i	$0.688693\pi$
$348$		0			0
$349$			34.3260i			1.83743i	0.394920	+	0.918715i	$0.370772\pi$
$349$			34.3260i			1.83743i	−0.394920	+	0.918715i	$0.629228\pi$
$350$		0			0
$351$		−	2.28533i		−	0.121982i
$352$		0			0
$353$	11.4318	+	11.4318i	0.608453	+	0.608453i	0.942542	−	0.334089i	$-0.108428\pi$
$353$	11.4318	+	11.4318i	0.608453	+	0.608453i	−0.334089	+	0.942542i	$0.608428\pi$
$354$		0			0
$355$	13.4057	+	9.10491i	0.711503	+	0.483238i
$356$		0			0
$357$	2.85816	−	2.85816i	0.151270	−	0.151270i
$358$		0			0
$359$	−5.29032			−0.279212			−0.139606	−	0.990207i	$-0.544584\pi$
$359$	−5.29032			−0.279212			−0.139606	+	0.990207i	$0.544584\pi$
$360$		0			0
$361$	−9.46668			−0.498246
$362$		0			0
$363$	6.97377	−	6.97377i	0.366028	−	0.366028i
$364$		0			0
$365$	−22.7352	+	4.34374i	−1.19001	+	0.227362i
$366$		0			0
$367$	17.9158	+	17.9158i	0.935199	+	0.935199i	0.998025	−	0.0628257i	$-0.0200112\pi$
$367$	17.9158	+	17.9158i	0.935199	+	0.935199i	−0.0628257	+	0.998025i	$0.520011\pi$
$368$		0			0
$369$		−	2.99857i		−	0.156099i
$370$		0			0
$371$		−	6.79978i		−	0.353027i
$372$		0			0
$373$	19.6991	+	19.6991i	1.01998	+	1.01998i	0.999796	+	0.0201867i	$0.00642607\pi$
$373$	19.6991	+	19.6991i	1.01998	+	1.01998i	0.0201867	+	0.999796i	$0.493574\pi$
$374$		0			0
$375$	−9.43471	+	5.99886i	−0.487206	+	0.309780i
$376$		0			0
$377$	−3.81502	+	3.81502i	−0.196484	+	0.196484i
$378$		0			0
$379$	28.6274			1.47049			0.735245	−	0.677801i	$-0.237067\pi$
$379$	28.6274			1.47049			0.735245	+	0.677801i	$0.237067\pi$
$380$		0			0
$381$	9.74319			0.499158
$382$		0			0
$383$	−0.864619	+	0.864619i	−0.0441800	+	0.0441800i	−0.728852	−	0.684672i	$-0.759946\pi$
$383$	−0.864619	+	0.864619i	−0.0441800	+	0.0441800i	0.684672	+	0.728852i	$0.259946\pi$
$384$		0			0
$385$	0.417768	+	2.18660i	0.0212914	+	0.111440i
$386$		0			0
$387$	1.44607	+	1.44607i	0.0735078	+	0.0735078i
$388$		0			0
$389$		−	2.79573i		−	0.141749i	−0.997485	−	0.0708745i	$-0.977421\pi$
$389$		−	2.79573i		−	0.141749i	0.997485	−	0.0708745i	$-0.0225790\pi$
$390$		0			0
$391$		−	30.3104i		−	1.53286i
$392$		0			0
$393$	12.9194	+	12.9194i	0.651697	+	0.651697i
$394$		0			0
$395$	4.34013	−	6.39025i	0.218375	−	0.321528i
$396$		0			0
$397$	−7.78036	+	7.78036i	−0.390485	+	0.390485i	−0.874860	−	0.484375i	$-0.839047\pi$
$397$	−7.78036	+	7.78036i	−0.390485	+	0.390485i	0.484375	+	0.874860i	$0.339047\pi$
$398$		0			0
$399$	−2.88203			−0.144282
$400$		0			0
$401$	3.81180			0.190352			0.0951761	−	0.995460i	$-0.469659\pi$
$401$	3.81180			0.190352			0.0951761	+	0.995460i	$0.469659\pi$
$402$		0			0
$403$	−3.15600	+	3.15600i	−0.157212	+	0.157212i
$404$		0			0
$405$	−1.25633	+	1.84977i	−0.0624273	+	0.0919158i
$406$		0			0
$407$	4.67386	+	4.67386i	0.231675	+	0.231675i
$408$		0			0
$409$			19.3569i			0.957138i	0.878050	+	0.478569i	$0.158844\pi$
$409$			19.3569i			0.957138i	−0.878050	+	0.478569i	$0.841156\pi$
$410$		0			0
$411$		−	11.0342i		−	0.544276i
$412$		0			0
$413$	−2.37094	−	2.37094i	−0.116666	−	0.116666i
$414$		0			0
$415$	1.03647	+	5.42489i	0.0508782	+	0.266297i
$416$		0			0
$417$	−5.52198	+	5.52198i	−0.270413	+	0.270413i
$418$		0			0
$419$	36.0437			1.76085			0.880424	−	0.474187i	$-0.157258\pi$
$419$	36.0437			1.76085			0.880424	+	0.474187i	$0.157258\pi$
$420$		0			0
$421$	−13.2288			−0.644733			−0.322367	−	0.946615i	$-0.604478\pi$
$421$	−13.2288			−0.644733			−0.322367	+	0.946615i	$0.604478\pi$
$422$		0			0
$423$	8.81622	−	8.81622i	0.428660	−	0.428660i
$424$		0			0
$425$	−19.8760	−	8.58758i	−0.964130	−	0.416559i
$426$		0			0
$427$	5.44435	+	5.44435i	0.263471	+	0.263471i
$428$		0			0
$429$			2.43749i			0.117683i
$430$		0			0
$431$		−	37.4645i		−	1.80460i	−0.431106	−	0.902301i	$-0.641877\pi$
$431$		−	37.4645i		−	1.80460i	0.431106	−	0.902301i	$-0.358123\pi$
$432$		0			0
$433$	−9.82455	−	9.82455i	−0.472138	−	0.472138i	0.430468	−	0.902606i	$-0.358348\pi$
$433$	−9.82455	−	9.82455i	−0.472138	−	0.472138i	−0.902606	+	0.430468i	$0.858348\pi$
$434$		0			0
$435$	5.18518	−	0.990670i	0.248610	−	0.0474990i
$436$		0			0
$437$	−15.2818	+	15.2818i	−0.731026	+	0.731026i
$438$		0			0
$439$	−38.9317			−1.85811			−0.929055	−	0.369943i	$-0.879377\pi$
$439$	−38.9317			−1.85811			−0.929055	+	0.369943i	$0.879377\pi$
$440$		0			0
$441$	−6.12873			−0.291844
$442$		0			0
$443$	−15.0192	+	15.0192i	−0.713584	+	0.713584i	−0.967283	−	0.253699i	$-0.918353\pi$
$443$	−15.0192	+	15.0192i	−0.713584	+	0.713584i	0.253699	+	0.967283i	$0.418353\pi$
$444$		0			0
$445$	−27.9883	−	19.0091i	−1.32677	−	0.901118i
$446$		0			0
$447$	−11.2642	−	11.2642i	−0.532780	−	0.532780i
$448$		0			0
$449$		−	11.3953i		−	0.537775i	−0.963172	−	0.268888i	$-0.913344\pi$
$449$		−	11.3953i		−	0.537775i	0.963172	−	0.268888i	$-0.0866560\pi$
$450$		0			0
$451$			3.19822i			0.150598i
$452$		0			0
$453$	−10.1681	−	10.1681i	−0.477741	−	0.477741i
$454$		0			0
$455$	3.94586	+	2.67995i	0.184985	+	0.125638i
$456$		0			0
$457$	−19.1407	+	19.1407i	−0.895364	+	0.895364i	−0.995022	−	0.0996576i	$-0.968225\pi$
$457$	−19.1407	+	19.1407i	−0.895364	+	0.895364i	0.0996576	+	0.995022i	$0.468225\pi$
$458$		0			0
$459$	−4.33037			−0.202125
$460$		0			0
$461$	1.84281			0.0858283			0.0429141	−	0.999079i	$-0.486336\pi$
$461$	1.84281			0.0858283			0.0429141	+	0.999079i	$0.486336\pi$
$462$		0			0
$463$	−24.5008	+	24.5008i	−1.13865	+	1.13865i	−0.149958	+	0.988692i	$0.547914\pi$
$463$	−24.5008	+	24.5008i	−1.13865	+	1.13865i	−0.988692	+	0.149958i	$0.952086\pi$
$464$		0			0
$465$	4.28947	−	0.819538i	0.198920	−	0.0380052i
$466$		0			0
$467$	−6.56839	−	6.56839i	−0.303949	−	0.303949i	0.538608	−	0.842557i	$-0.318950\pi$
$467$	−6.56839	−	6.56839i	−0.303949	−	0.303949i	−0.842557	+	0.538608i	$0.818950\pi$
$468$		0			0
$469$		−	8.67360i		−	0.400510i
$470$		0			0
$471$		−	4.99501i		−	0.230158i
$472$		0			0
$473$	−1.54235	−	1.54235i	−0.0709174	−	0.0709174i
$474$		0			0
$475$	5.69137	+	14.3507i	0.261138	+	0.658453i
$476$		0			0
$477$	−5.15114	+	5.15114i	−0.235855	+	0.235855i
$478$		0			0
$479$	−0.954116			−0.0435947			−0.0217973	−	0.999762i	$-0.506939\pi$
$479$	−0.954116			−0.0435947			−0.0217973	+	0.999762i	$0.506939\pi$
$480$		0			0
$481$	14.1626			0.645761
$482$		0			0
$483$	4.61985	−	4.61985i	0.210210	−	0.210210i
$484$		0			0
$485$	6.56371	+	34.3545i	0.298043	+	1.55996i
$486$		0			0
$487$	−7.06715	−	7.06715i	−0.320243	−	0.320243i	0.528617	−	0.848860i	$-0.322711\pi$
$487$	−7.06715	−	7.06715i	−0.320243	−	0.320243i	−0.848860	+	0.528617i	$0.822711\pi$
$488$		0			0
$489$			16.1872i			0.732010i
$490$		0			0
$491$			37.6332i			1.69836i	0.528101	+	0.849182i	$0.322904\pi$
$491$			37.6332i			1.69836i	−0.528101	+	0.849182i	$0.677096\pi$
$492$		0			0
$493$	7.22894	+	7.22894i	0.325575	+	0.325575i
$494$		0			0
$495$	1.33997	−	1.97293i	0.0602273	−	0.0886766i
$496$		0			0
$497$	−4.78338	+	4.78338i	−0.214564	+	0.214564i
$498$		0			0
$499$	−29.6741			−1.32839			−0.664197	−	0.747558i	$-0.731226\pi$
$499$	−29.6741			−1.32839			−0.664197	+	0.747558i	$0.731226\pi$
$500$		0			0
$501$	15.5701			0.695623
$502$		0			0
$503$	−4.90632	+	4.90632i	−0.218762	+	0.218762i	−0.807977	−	0.589214i	$-0.799437\pi$
$503$	−4.90632	+	4.90632i	−0.218762	+	0.218762i	0.589214	+	0.807977i	$0.299437\pi$
$504$		0			0
$505$	−4.28069	+	6.30274i	−0.190488	+	0.280468i
$506$		0			0
$507$	−5.49937	−	5.49937i	−0.244236	−	0.244236i
$508$		0			0
$509$		−	15.9024i		−	0.704862i	−0.935838	−	0.352431i	$-0.885355\pi$
$509$		−	15.9024i		−	0.704862i	0.935838	−	0.352431i	$-0.114645\pi$
$510$		0			0
$511$		−	9.66218i		−	0.427430i
$512$		0			0
$513$	2.18327	+	2.18327i	0.0963936	+	0.0963936i
$514$		0			0
$515$	0.984832	+	5.15462i	0.0433969	+	0.227140i
$516$		0			0
$517$	−9.40323	+	9.40323i	−0.413553	+	0.413553i
$518$		0			0
$519$	7.97606			0.350110
$520$		0			0
$521$	40.5698			1.77740			0.888698	−	0.458493i	$-0.151611\pi$
$521$	40.5698			1.77740			0.888698	+	0.458493i	$0.151611\pi$
$522$		0			0
$523$	−3.79678	+	3.79678i	−0.166022	+	0.166022i	−0.785228	−	0.619206i	$-0.787454\pi$
$523$	−3.79678	+	3.79678i	−0.166022	+	0.166022i	0.619206	+	0.785228i	$0.287454\pi$
$524$		0			0
$525$	−1.72056	−	4.33836i	−0.0750916	−	0.189342i
$526$		0			0
$527$	5.98019	+	5.98019i	0.260501	+	0.260501i
$528$		0			0
$529$		−	25.9929i		−	1.13013i
$530$		0			0
$531$			3.59218i			0.155887i
$532$		0			0
$533$	4.84559	+	4.84559i	0.209886	+	0.209886i
$534$		0			0
$535$	−29.9342	+	5.71916i	−1.29417	+	0.247261i
$536$		0			0
$537$	−0.221915	+	0.221915i	−0.00957635	+	0.00957635i
$538$		0			0
$539$	6.53679			0.281560
$540$		0			0
$541$	18.5998			0.799670			0.399835	−	0.916587i	$-0.369067\pi$
$541$	18.5998			0.799670			0.399835	+	0.916587i	$0.369067\pi$
$542$		0			0
$543$	2.25796	−	2.25796i	0.0968982	−	0.0968982i
$544$		0			0
$545$	4.86777	+	3.30609i	0.208512	+	0.141617i
$546$		0			0
$547$	16.9737	+	16.9737i	0.725744	+	0.725744i	0.969769	−	0.244025i	$-0.0784678\pi$
$547$	16.9737	+	16.9737i	0.725744	+	0.725744i	−0.244025	+	0.969769i	$0.578468\pi$
$548$		0			0
$549$		−	8.24869i		−	0.352045i
$550$		0			0
$551$		−	7.28930i		−	0.310535i
$552$		0			0
$553$	2.28014	+	2.28014i	0.0969614	+	0.0969614i
$554$		0			0
$555$	−11.4634	−	7.78571i	−0.486595	−	0.330485i
$556$		0			0
$557$	3.26768	−	3.26768i	0.138456	−	0.138456i	−0.634482	−	0.772938i	$-0.718786\pi$
$557$	3.26768	−	3.26768i	0.138456	−	0.138456i	0.772938	+	0.634482i	$0.218786\pi$
$558$		0			0
$559$	−4.67360			−0.197672
$560$		0			0
$561$	4.61870			0.195002
$562$		0			0
$563$	21.8418	−	21.8418i	0.920521	−	0.920521i	−0.0765452	−	0.997066i	$-0.524389\pi$
$563$	21.8418	−	21.8418i	0.920521	−	0.920521i	0.997066	+	0.0765452i	$0.0243889\pi$
$564$		0			0
$565$	31.3626	−	5.99207i	1.31943	−	0.252088i
$566$		0			0
$567$	−0.660026	−	0.660026i	−0.0277185	−	0.0277185i
$568$		0			0
$569$			44.8598i			1.88062i	0.340320	+	0.940310i	$0.389465\pi$
$569$			44.8598i			1.88062i	−0.340320	+	0.940310i	$0.610535\pi$
$570$		0			0
$571$			27.9666i			1.17036i	0.810902	+	0.585182i	$0.198977\pi$
$571$			27.9666i			1.17036i	−0.810902	+	0.585182i	$0.801023\pi$
$572$		0			0
$573$	4.87682	+	4.87682i	0.203732	+	0.203732i
$574$		0			0
$575$	−32.1271	−	13.8807i	−1.33979	−	0.578866i
$576$		0			0
$577$	−6.94720	+	6.94720i	−0.289216	+	0.289216i	−0.836770	−	0.547554i	$-0.815559\pi$
$577$	−6.94720	+	6.94720i	−0.289216	+	0.289216i	0.547554	+	0.836770i	$0.315559\pi$
$578$		0			0
$579$	18.3935			0.764406
$580$		0			0
$581$	−2.30551			−0.0956487
$582$		0			0
$583$	5.49412	−	5.49412i	0.227543	−	0.227543i
$584$		0			0
$585$	−0.958988	−	5.01935i	−0.0396493	−	0.207525i
$586$		0			0
$587$	−33.6726	−	33.6726i	−1.38982	−	1.38982i	−0.825684	−	0.564132i	$-0.809211\pi$
$587$	−33.6726	−	33.6726i	−1.38982	−	1.38982i	−0.564132	−	0.825684i	$-0.690789\pi$
$588$		0			0
$589$		−	6.03013i		−	0.248467i
$590$		0			0
$591$			21.4600i			0.882748i
$592$		0			0
$593$	12.3392	+	12.3392i	0.506712	+	0.506712i	0.913516	−	0.406804i	$-0.133357\pi$
$593$	12.3392	+	12.3392i	0.506712	+	0.506712i	−0.406804	+	0.913516i	$0.633357\pi$
$594$		0			0
$595$	5.07813	−	7.47686i	0.208183	−	0.306521i
$596$		0			0
$597$	−17.2994	+	17.2994i	−0.708017	+	0.708017i
$598$		0			0
$599$	20.0512			0.819268			0.409634	−	0.912250i	$-0.365656\pi$
$599$	20.0512			0.819268			0.409634	+	0.912250i	$0.365656\pi$
$600$		0			0
$601$	41.9737			1.71214			0.856071	−	0.516859i	$-0.172899\pi$
$601$	41.9737			1.71214			0.856071	+	0.516859i	$0.172899\pi$
$602$		0			0
$603$	−6.57065	+	6.57065i	−0.267578	+	0.267578i
$604$		0			0
$605$	12.3904	−	18.2432i	0.503741	−	0.741690i
$606$		0			0
$607$	6.44430	+	6.44430i	0.261566	+	0.261566i	0.825690	−	0.564124i	$-0.190786\pi$
$607$	6.44430	+	6.44430i	0.261566	+	0.261566i	−0.564124	+	0.825690i	$0.690786\pi$
$608$		0			0
$609$			2.20364i			0.0892959i
$610$		0			0
$611$			28.4935i			1.15272i
$612$		0			0
$613$	23.7304	+	23.7304i	0.958460	+	0.958460i	0.999171	−	0.0407109i	$-0.0129623\pi$
$613$	23.7304	+	23.7304i	0.958460	+	0.958460i	−0.0407109	+	0.999171i	$0.512962\pi$
$614$		0			0
$615$	−1.25828	−	6.58587i	−0.0507389	−	0.265568i
$616$		0			0
$617$	−2.52562	+	2.52562i	−0.101678	+	0.101678i	−0.756116	−	0.654438i	$-0.772905\pi$
$617$	−2.52562	+	2.52562i	−0.101678	+	0.101678i	0.654438	+	0.756116i	$0.272905\pi$
$618$		0			0
$619$	0.186858			0.00751047			0.00375523	−	0.999993i	$-0.498805\pi$
$619$	0.186858			0.00751047			0.00375523	+	0.999993i	$0.498805\pi$
$620$		0			0
$621$	−6.99949			−0.280880
$622$		0			0
$623$	9.98667	−	9.98667i	0.400107	−	0.400107i
$624$		0			0
$625$	−18.2045	+	17.1346i	−0.728181	+	0.685384i
$626$		0			0
$627$	−2.32863	−	2.32863i	−0.0929967	−	0.0929967i
$628$		0			0
$629$		−	26.8362i		−	1.07003i
$630$		0			0
$631$		−	17.7728i		−	0.707524i	−0.935335	−	0.353762i	$-0.884902\pi$
$631$		−	17.7728i		−	0.707524i	0.935335	−	0.353762i	$-0.115098\pi$
$632$		0			0
$633$	−6.74584	−	6.74584i	−0.268123	−	0.268123i
$634$		0			0
$635$	21.3994	−	4.08852i	0.849207	−	0.162248i
$636$		0			0
$637$	9.90384	−	9.90384i	0.392404	−	0.392404i
$638$		0			0
$639$	7.24725			0.286697
$640$		0			0
$641$	−26.8224			−1.05942			−0.529710	−	0.848179i	$-0.677699\pi$
$641$	−26.8224			−1.05942			−0.529710	+	0.848179i	$0.677699\pi$
$642$		0			0
$643$	−31.3223	+	31.3223i	−1.23523	+	1.23523i	−0.273303	+	0.961928i	$0.588116\pi$
$643$	−31.3223	+	31.3223i	−1.23523	+	1.23523i	−0.961928	+	0.273303i	$0.911884\pi$
$644$		0			0
$645$	3.78287	+	2.56925i	0.148950	+	0.101164i
$646$		0			0
$647$	2.60438	+	2.60438i	0.102389	+	0.102389i	0.756445	−	0.654057i	$-0.226934\pi$
$647$	2.60438	+	2.60438i	0.102389	+	0.102389i	−0.654057	+	0.756445i	$0.726934\pi$
$648$		0			0
$649$		−	3.83136i		−	0.150394i
$650$		0			0
$651$			1.82297i			0.0714480i
$652$		0			0
$653$	−10.8736	−	10.8736i	−0.425517	−	0.425517i	0.461581	−	0.887098i	$-0.347282\pi$
$653$	−10.8736	−	10.8736i	−0.425517	−	0.425517i	−0.887098	+	0.461581i	$0.847282\pi$
$654$		0			0
$655$	33.7967	+	22.9540i	1.32055	+	0.896888i
$656$		0			0
$657$	−7.31955	+	7.31955i	−0.285563	+	0.285563i
$658$		0			0
$659$	8.30598			0.323555			0.161778	−	0.986827i	$-0.448277\pi$
$659$	8.30598			0.323555			0.161778	+	0.986827i	$0.448277\pi$
$660$		0			0
$661$	−19.8594			−0.772439			−0.386220	−	0.922407i	$-0.626219\pi$
$661$	−19.8594			−0.772439			−0.386220	+	0.922407i	$0.626219\pi$
$662$		0			0
$663$	6.99775	−	6.99775i	0.271770	−	0.271770i
$664$		0			0
$665$	−6.32992	+	1.20938i	−0.245464	+	0.0468978i
$666$		0			0
$667$	11.6846	+	11.6846i	0.452431	+	0.452431i
$668$		0			0
$669$		−	21.1498i		−	0.817698i
$670$		0			0
$671$			8.79790i			0.339639i
$672$		0			0
$673$	−17.9049	−	17.9049i	−0.690185	−	0.690185i	0.272088	−	0.962272i	$-0.412286\pi$
$673$	−17.9049	−	17.9049i	−0.690185	−	0.690185i	−0.962272	+	0.272088i	$0.912286\pi$
$674$		0			0
$675$	−1.98310	+	4.58991i	−0.0763296	+	0.176666i
$676$		0			0
$677$	−11.2642	+	11.2642i	−0.432918	+	0.432918i	−0.889620	−	0.456702i	$-0.849031\pi$
$677$	−11.2642	+	11.2642i	−0.432918	+	0.432918i	0.456702	+	0.889620i	$0.349031\pi$
$678$		0			0
$679$	−14.6003			−0.560307
$680$		0			0
$681$	27.9773			1.07209
$682$		0			0
$683$	1.76705	−	1.76705i	0.0676144	−	0.0676144i	−0.672491	−	0.740105i	$-0.734776\pi$
$683$	1.76705	−	1.76705i	0.0676144	−	0.0676144i	0.740105	+	0.672491i	$0.234776\pi$
$684$		0			0
$685$	−4.63026	−	24.2348i	−0.176913	−	0.925966i
$686$		0			0
$687$	−13.0616	−	13.0616i	−0.498333	−	0.498333i
$688$		0			0
$689$		−	16.6482i		−	0.634245i
$690$		0			0
$691$		−	43.0446i		−	1.63749i	−0.574156	−	0.818746i	$-0.694670\pi$
$691$		−	43.0446i		−	1.63749i	0.574156	−	0.818746i	$-0.305330\pi$
$692$		0			0
$693$	0.703972	+	0.703972i	0.0267417	+	0.0267417i
$694$		0			0
$695$	−9.81097	+	14.4453i	−0.372151	+	0.547943i
$696$		0			0
$697$	9.18172	−	9.18172i	0.347783	−	0.347783i
$698$		0			0
$699$	5.85981			0.221638
$700$		0			0
$701$	4.28658			0.161902			0.0809510	−	0.996718i	$-0.474204\pi$
$701$	4.28658			0.161902			0.0809510	+	0.996718i	$0.474204\pi$
$702$		0			0
$703$	−13.5302	+	13.5302i	−0.510300	+	0.510300i
$704$		0			0
$705$	15.6639	−	23.0630i	0.589936	−	0.868602i
$706$		0			0
$707$	−2.24891	−	2.24891i	−0.0845791	−	0.0845791i
$708$		0			0
$709$			23.6211i			0.887109i	0.896247	+	0.443555i	$0.146283\pi$
$709$			23.6211i			0.887109i	−0.896247	+	0.443555i	$0.853717\pi$
$710$		0			0
$711$		−	3.45462i		−	0.129558i
$712$		0			0
$713$	9.66620	+	9.66620i	0.362002	+	0.362002i
$714$		0			0
$715$	1.02284	+	5.35355i	0.0382520	+	0.200211i
$716$		0			0
$717$	−0.590430	+	0.590430i	−0.0220500	+	0.0220500i
$718$		0			0
$719$	−38.8528			−1.44896			−0.724482	−	0.689293i	$-0.757921\pi$
$719$	−38.8528			−1.44896			−0.724482	+	0.689293i	$0.757921\pi$
$720$		0			0
$721$	−2.19065			−0.0815841
$722$		0			0
$723$	2.82843	−	2.82843i	0.105190	−	0.105190i
$724$		0			0
$725$	10.9727	−	4.35170i	0.407516	−	0.161618i
$726$		0			0
$727$	12.1614	+	12.1614i	0.451041	+	0.451041i	0.895700	−	0.444659i	$-0.146675\pi$
$727$	12.1614	+	12.1614i	0.451041	+	0.451041i	−0.444659	+	0.895700i	$0.646675\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			8.85583i			0.327545i
$732$		0			0
$733$	−2.72674	−	2.72674i	−0.100715	−	0.100715i	0.654954	−	0.755669i	$-0.272688\pi$
$733$	−2.72674	−	2.72674i	−0.100715	−	0.100715i	−0.755669	+	0.654954i	$0.772688\pi$
$734$		0			0
$735$	−13.4608	+	2.57179i	−0.496508	+	0.0948619i
$736$		0			0
$737$	7.00814	−	7.00814i	0.258148	−	0.258148i
$738$		0			0
$739$	−21.5464			−0.792599			−0.396299	−	0.918121i	$-0.629706\pi$
$739$	−21.5464			−0.792599			−0.396299	+	0.918121i	$0.629706\pi$
$740$		0			0
$741$	−7.05619			−0.259215
$742$		0			0
$743$	17.0432	−	17.0432i	0.625254	−	0.625254i	−0.321616	−	0.946870i	$-0.604226\pi$
$743$	17.0432	−	17.0432i	0.625254	−	0.625254i	0.946870	+	0.321616i	$0.104226\pi$
$744$		0			0
$745$	−29.4669	−	20.0133i	−1.07958	−	0.733231i
$746$		0			0
$747$	1.74653	+	1.74653i	0.0639022	+	0.0639022i
$748$		0			0
$749$		−	12.7217i		−	0.464839i
$750$		0			0
$751$		−	2.33514i		−	0.0852106i	−0.999092	−	0.0426053i	$-0.986434\pi$
$751$		−	2.33514i		−	0.0852106i	0.999092	−	0.0426053i	$-0.0135658\pi$
$752$		0			0
$753$	13.8982	+	13.8982i	0.506480	+	0.506480i
$754$		0			0
$755$	−26.5995	−	18.0658i	−0.968056	−	0.657483i
$756$		0			0
$757$	−29.2677	+	29.2677i	−1.06375	+	1.06375i	−0.0659267	+	0.997824i	$0.521000\pi$
$757$	−29.2677	+	29.2677i	−1.06375	+	1.06375i	−0.997824	+	0.0659267i	$0.979000\pi$
$758$		0			0
$759$	7.46553			0.270982
$760$		0			0
$761$	−18.9563			−0.687164			−0.343582	−	0.939123i	$-0.611640\pi$
$761$	−18.9563			−0.687164			−0.343582	+	0.939123i	$0.611640\pi$
$762$		0			0
$763$	−1.73689	+	1.73689i	−0.0628798	+	0.0628798i
$764$		0			0
$765$	−9.51098	+	1.81715i	−0.343870	+	0.0656991i
$766$		0			0
$767$	−5.80486	−	5.80486i	−0.209601	−	0.209601i
$768$		0			0
$769$		−	23.7084i		−	0.854945i	−0.904028	−	0.427473i	$-0.859404\pi$
$769$		−	23.7084i		−	0.854945i	0.904028	−	0.427473i	$-0.140596\pi$
$770$		0			0
$771$			20.3874i			0.734234i
$772$		0			0
$773$	−1.00639	−	1.00639i	−0.0361973	−	0.0361973i	0.688776	−	0.724974i	$-0.258148\pi$
$773$	−1.00639	−	1.00639i	−0.0361973	−	0.0361973i	−0.724974	+	0.688776i	$0.758148\pi$
$774$		0			0
$775$	9.07724	−	3.59997i	0.326064	−	0.129315i
$776$		0			0
$777$	4.09032	−	4.09032i	0.146739	−	0.146739i
$778$		0			0
$779$	−9.25839			−0.331716
$780$		0			0
$781$	−7.72979			−0.276594
$782$		0			0
$783$	1.66936	−	1.66936i	0.0596579	−	0.0596579i
$784$		0			0
$785$	−2.09605	−	10.9707i	−0.0748111	−	0.391562i
$786$		0			0
$787$	−36.0200	−	36.0200i	−1.28397	−	1.28397i	−0.938387	−	0.345587i	$-0.887680\pi$
$787$	−36.0200	−	36.0200i	−1.28397	−	1.28397i	−0.345587	−	0.938387i	$-0.612320\pi$
$788$		0			0
$789$			1.39493i			0.0496608i
$790$		0			0
$791$			13.3287i			0.473914i
$792$		0			0
$793$	13.3296	+	13.3296i	0.473349	+	0.473349i
$794$		0			0
$795$	−9.15210	+	13.4752i	−0.324592	+	0.477917i
$796$		0			0
$797$	12.0130	−	12.0130i	0.425524	−	0.425524i	−0.461577	−	0.887100i	$-0.652716\pi$
$797$	12.0130	−	12.0130i	0.425524	−	0.425524i	0.887100	+	0.461577i	$0.152716\pi$
$798$		0			0
$799$	53.9912			1.91007
$800$		0			0
$801$	−15.1307			−0.534618
$802$		0			0
$803$	7.80689	−	7.80689i	0.275499	−	0.275499i
$804$		0			0
$805$	8.20814	−	12.0854i	0.289299	−	0.425954i
$806$		0			0
$807$	17.4908	+	17.4908i	0.615707	+	0.615707i
$808$		0			0
$809$			7.37863i			0.259419i	0.991552	+	0.129709i	$0.0414045\pi$
$809$			7.37863i			0.259419i	−0.991552	+	0.129709i	$0.958596\pi$
$810$		0			0
$811$		−	28.2165i		−	0.990817i	−0.868660	−	0.495408i	$-0.835018\pi$
$811$		−	28.2165i		−	0.990817i	0.868660	−	0.495408i	$-0.164982\pi$
$812$		0			0
$813$	−12.2477	−	12.2477i	−0.429545	−	0.429545i
$814$		0			0
$815$	6.79260	+	35.5526i	0.237935	+	1.24535i
$816$		0			0
$817$	4.46489	−	4.46489i	0.156207	−	0.156207i
$818$		0			0
$819$	2.13316			0.0745388
$820$		0			0
$821$	23.0596			0.804785			0.402392	−	0.915467i	$-0.368179\pi$
$821$	23.0596			0.804785			0.402392	+	0.915467i	$0.368179\pi$
$822$		0			0
$823$	−34.3615	+	34.3615i	−1.19777	+	1.19777i	−0.222933	+	0.974834i	$0.571563\pi$
$823$	−34.3615	+	34.3615i	−1.19777	+	1.19777i	−0.974834	+	0.222933i	$0.928437\pi$
$824$		0			0
$825$	2.11514	−	4.89552i	0.0736398	−	0.170440i
$826$		0			0
$827$	−28.8647	−	28.8647i	−1.00373	−	1.00373i	−0.999993	−	0.00373206i	$-0.998812\pi$
$827$	−28.8647	−	28.8647i	−1.00373	−	1.00373i	−0.00373206	−	0.999993i	$-0.501188\pi$
$828$		0			0
$829$		−	12.4285i		−	0.431660i	−0.976431	−	0.215830i	$-0.930754\pi$
$829$		−	12.4285i		−	0.431660i	0.976431	−	0.215830i	$-0.0692457\pi$
$830$		0			0
$831$			17.6355i			0.611770i
$832$		0			0
$833$	−18.7664	−	18.7664i	−0.650217	−	0.650217i
$834$		0			0
$835$	34.1973	−	6.53368i	1.18345	−	0.226107i
$836$		0			0
$837$	1.38099	−	1.38099i	0.0477339	−	0.0477339i
$838$		0			0
$839$	36.7792			1.26976			0.634879	−	0.772611i	$-0.281050\pi$
$839$	36.7792			1.26976			0.634879	+	0.772611i	$0.281050\pi$
$840$		0			0
$841$	23.4265			0.807810
$842$		0			0
$843$	7.31134	−	7.31134i	0.251816	−	0.251816i
$844$		0			0
$845$	−14.3862	−	9.77080i	−0.494900	−	0.336126i
$846$		0			0
$847$	6.50944	+	6.50944i	0.223667	+	0.223667i
$848$		0			0
$849$		−	7.38527i		−	0.253462i
$850$		0			0
$851$		−	43.3773i		−	1.48696i
$852$		0			0
$853$	25.2629	+	25.2629i	0.864986	+	0.864986i	0.991912	−	0.126926i	$-0.0405112\pi$
$853$	25.2629	+	25.2629i	0.864986	+	0.864986i	−0.126926	+	0.991912i	$0.540511\pi$
$854$		0			0
$855$	5.71136	+	3.87904i	0.195324	+	0.132660i
$856$		0			0
$857$	8.12706	−	8.12706i	0.277615	−	0.277615i	−0.554541	−	0.832156i	$-0.687106\pi$
$857$	8.12706	−	8.12706i	0.277615	−	0.277615i	0.832156	+	0.554541i	$0.187106\pi$
$858$		0			0
$859$	−11.4528			−0.390766			−0.195383	−	0.980727i	$-0.562595\pi$
$859$	−11.4528			−0.390766			−0.195383	+	0.980727i	$0.562595\pi$
$860$		0			0
$861$	2.79892			0.0953868
$862$		0			0
$863$	37.6662	−	37.6662i	1.28217	−	1.28217i	0.342743	−	0.939429i	$-0.388644\pi$
$863$	37.6662	−	37.6662i	1.28217	−	1.28217i	0.939429	−	0.342743i	$-0.111356\pi$
$864$		0			0
$865$	17.5181	−	3.34698i	0.595635	−	0.113801i
$866$		0			0
$867$	−1.23895	−	1.23895i	−0.0420771	−	0.0420771i
$868$		0			0
$869$			3.68464i			0.124993i
$870$		0			0
$871$		−	21.2359i		−	0.719552i
$872$		0			0
$873$	11.0604	+	11.0604i	0.374337	+	0.374337i
$874$		0			0
$875$	−5.59944	−	8.80652i	−0.189296	−	0.297715i
$876$		0			0
$877$	35.7207	−	35.7207i	1.20620	−	1.20620i	0.233954	−	0.972248i	$-0.424833\pi$
$877$	35.7207	−	35.7207i	1.20620	−	1.20620i	0.972248	−	0.233954i	$-0.0751666\pi$
$878$		0			0
$879$	6.40596			0.216068
$880$		0			0
$881$	−42.2127			−1.42218			−0.711091	−	0.703100i	$-0.751799\pi$
$881$	−42.2127			−1.42218			−0.711091	+	0.703100i	$0.751799\pi$
$882$		0			0
$883$	−9.49667	+	9.49667i	−0.319588	+	0.319588i	−0.848609	−	0.529021i	$-0.822559\pi$
$883$	−9.49667	+	9.49667i	−0.319588	+	0.319588i	0.529021	+	0.848609i	$0.322559\pi$
$884$		0			0
$885$	1.50738	+	7.88966i	0.0506701	+	0.265208i
$886$		0			0
$887$	−26.3510	−	26.3510i	−0.884780	−	0.884780i	0.109236	−	0.994016i	$-0.465160\pi$
$887$	−26.3510	−	26.3510i	−0.884780	−	0.884780i	−0.994016	+	0.109236i	$0.965160\pi$
$888$		0			0
$889$			9.09446i			0.305019i
$890$		0			0
$891$		−	1.06658i		−	0.0357318i
$892$		0			0
$893$	−27.2210	−	27.2210i	−0.910917	−	0.910917i
$894$		0			0
$895$	−0.394280	+	0.580524i	−0.0131793	+	0.0194048i
$896$		0			0
$897$	11.3110	−	11.3110i	0.377662	−	0.377662i
$898$		0			0
$899$	−4.61072			−0.153776
$900$		0			0
$901$	−31.5460			−1.05095
$902$		0			0
$903$	−1.34979	+	1.34979i	−0.0449181	+	0.0449181i
$904$		0			0
$905$	4.01174	−	5.90674i	0.133355	−	0.196347i
$906$		0			0
$907$	5.47488	+	5.47488i	0.181790	+	0.181790i	0.792136	−	0.610345i	$-0.208969\pi$
$907$	5.47488	+	5.47488i	0.181790	+	0.181790i	−0.610345	+	0.792136i	$0.708969\pi$
$908$		0			0
$909$			3.40731i			0.113013i
$910$		0			0
$911$		−	0.141166i		−	0.00467702i	−0.999997	−	0.00233851i	$-0.999256\pi$
$911$		−	0.141166i		−	0.00467702i	0.999997	−	0.00233851i	$-0.000744372\pi$
$912$		0			0
$913$	−1.86282	−	1.86282i	−0.0616502	−	0.0616502i
$914$		0			0
$915$	−3.46138	−	18.1169i	−0.114430	−	0.598927i
$916$		0			0
$917$	−12.0592	+	12.0592i	−0.398229	+	0.398229i
$918$		0			0
$919$	53.3636			1.76030			0.880151	−	0.474693i	$-0.157441\pi$
$919$	53.3636			1.76030			0.880151	+	0.474693i	$0.157441\pi$
$920$		0			0
$921$	−30.8721			−1.01727
$922$		0			0
$923$	−11.7113	+	11.7113i	−0.385483	+	0.385483i
$924$		0			0
$925$	−28.4447	−	12.2897i	−0.935255	−	0.404083i
$926$		0			0
$927$	1.65952	+	1.65952i	0.0545058	+	0.0545058i
$928$		0			0
$929$		−	50.5020i		−	1.65692i	−0.560051	−	0.828458i	$-0.689218\pi$
$929$		−	50.5020i		−	1.65692i	0.560051	−	0.828458i	$-0.310782\pi$
$930$		0			0
$931$			18.9231i			0.620180i
$932$		0			0
$933$	15.0234	+	15.0234i	0.491843	+	0.491843i
$934$		0			0
$935$	10.1442	−	1.93814i	0.331752	−	0.0633839i
$936$		0			0
$937$	15.6317	−	15.6317i	0.510665	−	0.510665i	−0.404065	−	0.914730i	$-0.632403\pi$
$937$	15.6317	−	15.6317i	0.510665	−	0.510665i	0.914730	+	0.404065i	$0.132403\pi$
$938$		0			0
$939$	−3.23246			−0.105487
$940$		0			0
$941$	38.1985			1.24523			0.622617	−	0.782527i	$-0.286069\pi$
$941$	38.1985			1.24523			0.622617	+	0.782527i	$0.286069\pi$
$942$		0			0
$943$	14.8411	−	14.8411i	0.483292	−	0.483292i
$944$		0			0
$945$	−1.72661	−	1.17268i	−0.0561666	−	0.0381472i
$946$		0			0
$947$	−15.4058	−	15.4058i	−0.500621	−	0.500621i	0.411010	−	0.911631i	$-0.365176\pi$
$947$	−15.4058	−	15.4058i	−0.500621	−	0.500621i	−0.911631	+	0.411010i	$0.865176\pi$
$948$		0			0
$949$		−	23.6563i		−	0.767917i
$950$		0			0
$951$			26.4706i			0.858367i
$952$		0			0
$953$	−19.2632	−	19.2632i	−0.623995	−	0.623995i	0.322556	−	0.946550i	$-0.395458\pi$
$953$	−19.2632	−	19.2632i	−0.623995	−	0.623995i	−0.946550	+	0.322556i	$0.895458\pi$
$954$		0			0
$955$	12.7576	+	8.66471i	0.412827	+	0.280383i
$956$		0			0
$957$	−1.78051	+	1.78051i	−0.0575556	+	0.0575556i
$958$		0			0
$959$	10.2995			0.332589
$960$		0			0
$961$	27.1858			0.876960
$962$		0			0
$963$	−9.63723	+	9.63723i	−0.310555	+	0.310555i
$964$		0			0
$965$	40.3983	−	7.71842i	1.30047	−	0.248465i
$966$		0			0
$967$	20.7366	+	20.7366i	0.666845	+	0.666845i	0.956984	−	0.290139i	$-0.0937016\pi$
$967$	20.7366	+	20.7366i	0.666845	+	0.666845i	−0.290139	+	0.956984i	$0.593702\pi$
$968$		0			0
$969$			13.3705i			0.429522i
$970$		0			0
$971$		−	48.1991i		−	1.54678i	−0.633929	−	0.773391i	$-0.718559\pi$
$971$		−	48.1991i		−	1.54678i	0.633929	−	0.773391i	$-0.281441\pi$
$972$		0			0
$973$	−5.15432	−	5.15432i	−0.165240	−	0.165240i
$974$		0			0
$975$	−4.21253	−	10.6218i	−0.134909	−	0.340170i
$976$		0			0
$977$	−10.5699	+	10.5699i	−0.338162	+	0.338162i	−0.855675	−	0.517513i	$-0.826858\pi$
$977$	−10.5699	+	10.5699i	−0.338162	+	0.338162i	0.517513	+	0.855675i	$0.326858\pi$
$978$		0			0
$979$	16.1381			0.515777
$980$		0			0
$981$	2.63155			0.0840190
$982$		0			0
$983$	6.59866	−	6.59866i	0.210464	−	0.210464i	−0.594000	−	0.804465i	$-0.702452\pi$
$983$	6.59866	−	6.59866i	0.210464	−	0.210464i	0.804465	+	0.594000i	$0.202452\pi$
$984$		0			0
$985$	9.00524	+	47.1335i	0.286931	+	1.50180i
$986$		0			0
$987$	8.22922	+	8.22922i	0.261939	+	0.261939i
$988$		0			0
$989$			14.3143i			0.455169i
$990$		0			0
$991$			16.0245i			0.509035i	0.967068	+	0.254517i	$0.0819166\pi$
$991$			16.0245i			0.509035i	−0.967068	+	0.254517i	$0.918083\pi$
$992$		0			0
$993$	−11.4606	−	11.4606i	−0.363691	−	0.363691i
$994$		0			0
$995$	−30.7360	+	45.2547i	−0.974398	+	1.43467i
$996$		0			0
$997$	26.1819	−	26.1819i	0.829190	−	0.829190i	−0.158215	−	0.987405i	$-0.550574\pi$
$997$	26.1819	−	26.1819i	0.829190	−	0.829190i	0.987405	+	0.158215i	$0.0505738\pi$
$998$		0			0
$999$	−6.19721			−0.196071

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.w.i.1663.6	yes	12
4.3	odd	2		1920.2.w.j.1663.3	yes	12
5.2	odd	4		1920.2.w.j.127.3	yes	12
8.3	odd	2		1920.2.w.l.1663.4	yes	12
8.5	even	2		1920.2.w.k.1663.1	yes	12
20.7	even	4	inner	1920.2.w.i.127.6	✓	12
40.27	even	4		1920.2.w.k.127.1	yes	12
40.37	odd	4		1920.2.w.l.127.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.w.i.127.6	✓	12	20.7	even	4	inner
1920.2.w.i.1663.6	yes	12	1.1	even	1	trivial
1920.2.w.j.127.3	yes	12	5.2	odd	4
1920.2.w.j.1663.3	yes	12	4.3	odd	2
1920.2.w.k.127.1	yes	12	40.27	even	4
1920.2.w.k.1663.1	yes	12	8.5	even	2
1920.2.w.l.127.4	yes	12	40.37	odd	4
1920.2.w.l.1663.4	yes	12	8.3	odd	2

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.25633 - 1.84977i) q^{5} +(0.660026 + 0.660026i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.25633 - 1.84977i) q^{5} +(0.660026 + 0.660026i) q^{7} -1.00000i q^{9} +1.06658i q^{11} +(1.61597 + 1.61597i) q^{13} +(-0.419628 - 2.19634i) q^{15} +(3.06204 - 3.06204i) q^{17} -3.08761 q^{19} +0.933418 q^{21} +(4.94939 - 4.94939i) q^{23} +(-1.84329 - 4.64782i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.36083i q^{29} +1.95301i q^{31} +(0.754187 + 0.754187i) q^{33} +(2.05010 - 0.391689i) q^{35} +(4.38209 - 4.38209i) q^{37} +2.28533 q^{39} +2.99857 q^{41} +(-1.44607 + 1.44607i) q^{43} +(-1.84977 - 1.25633i) q^{45} +(8.81622 + 8.81622i) q^{47} -6.12873i q^{49} -4.33037i q^{51} +(-5.15114 - 5.15114i) q^{53} +(1.97293 + 1.33997i) q^{55} +(-2.18327 + 2.18327i) q^{57} -3.59218 q^{59} +8.24869 q^{61} +(0.660026 - 0.660026i) q^{63} +(5.01935 - 0.958988i) q^{65} +(-6.57065 - 6.57065i) q^{67} -6.99949i q^{69} +7.24725i q^{71} +(-7.31955 - 7.31955i) q^{73} +(-4.58991 - 1.98310i) q^{75} +(-0.703972 + 0.703972i) q^{77} +3.45462 q^{79} -1.00000 q^{81} +(-1.74653 + 1.74653i) q^{83} +(-1.81715 - 9.51098i) q^{85} +(1.66936 + 1.66936i) q^{87} -15.1307i q^{89} +2.13316i q^{91} +(1.38099 + 1.38099i) q^{93} +(-3.87904 + 5.71136i) q^{95} +(-11.0604 + 11.0604i) q^{97} +1.06658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) \) 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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