LMFDB - Embedded newform 2100.2.ce.a.1657.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1657.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2100.1657
Dual form			2100.2.ce.a.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{3} +(-1.15539 - 2.38014i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{3} +(-1.15539 - 2.38014i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(0.366025 + 0.633975i) q^{11} +(0.707107 + 0.707107i) q^{13} +(-3.15660 - 0.845807i) q^{17} +(-0.767949 + 1.33013i) q^{19} +(2.59808 - 0.500000i) q^{21} +(0.138701 + 0.517638i) q^{23} +(0.707107 - 0.707107i) q^{27} +6.92820i q^{29} +(1.73205 - 1.00000i) q^{31} +(-0.707107 + 0.189469i) q^{33} +(-0.776457 + 0.208051i) q^{37} +(-0.866025 + 0.500000i) q^{39} +6.19615i q^{41} +(-5.27792 + 5.27792i) q^{43} +(-0.0507680 - 0.189469i) q^{47} +(-4.33013 + 5.50000i) q^{49} +(1.63397 - 2.83013i) q^{51} +(-5.08845 - 1.36345i) q^{53} +(-1.08604 - 1.08604i) q^{57} +(6.36603 + 11.0263i) q^{59} +(5.42820 + 3.13397i) q^{61} +(-0.189469 + 2.63896i) q^{63} +(1.81173 - 6.76148i) q^{67} -0.535898 q^{69} -8.00000 q^{71} +(-1.39563 + 5.20857i) q^{73} +(1.08604 - 1.60368i) q^{77} +(4.96410 + 2.86603i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.896575 + 0.896575i) q^{83} +(-6.69213 - 1.79315i) q^{87} +(-5.36603 + 9.29423i) q^{89} +(0.866025 - 2.50000i) q^{91} +(0.517638 + 1.93185i) q^{93} +(-7.39924 + 7.39924i) q^{97} -0.732051i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{11} - 20 q^{19} + 20 q^{51} + 44 q^{59} - 12 q^{61} - 32 q^{69} - 64 q^{71} + 12 q^{79} + 4 q^{81} - 36 q^{89}+O(q^{100}) $ 8 * q - 4 * q^11 - 20 * q^19 + 20 * q^51 + 44 * q^59 - 12 * q^61 - 32 * q^69 - 64 * q^71 + 12 * q^79 + 4 * q^81 - 36 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.15539	−	2.38014i	−0.436698	−	0.899608i
$7$	−1.15539	−	2.38014i	−0.436698	−	0.899608i
$8$		0			0
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	0.915916	−	0.401371i	$-0.131466\pi$
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	−0.805555	+	0.592521i	$0.798133\pi$
$12$		0			0
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i	0.798333	−	0.602217i	$-0.205716\pi$
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i	−0.602217	+	0.798333i	$0.705716\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.15660	−	0.845807i	−0.765587	−	0.205138i	−0.145166	−	0.989407i	$-0.546372\pi$
$17$	−3.15660	−	0.845807i	−0.765587	−	0.205138i	−0.620421	+	0.784269i	$0.713038\pi$
$18$		0			0
$19$	−0.767949	+	1.33013i	−0.176180	+	0.305152i	−0.940569	−	0.339603i	$-0.889707\pi$
$19$	−0.767949	+	1.33013i	−0.176180	+	0.305152i	0.764389	+	0.644755i	$0.223041\pi$
$20$		0			0
$21$	2.59808	−	0.500000i	0.566947	−	0.109109i
$22$		0			0
$23$	0.138701	+	0.517638i	0.0289211	+	0.107935i	0.978878	−	0.204447i	$-0.0655397\pi$
$23$	0.138701	+	0.517638i	0.0289211	+	0.107935i	−0.949956	+	0.312382i	$0.898873\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			6.92820i			1.28654i	0.765641	+	0.643268i	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$		0			0
$31$	1.73205	−	1.00000i	0.311086	−	0.179605i	−0.336327	−	0.941745i	$-0.609185\pi$
$31$	1.73205	−	1.00000i	0.311086	−	0.179605i	0.647412	+	0.762140i	$0.275851\pi$
$32$		0			0
$33$	−0.707107	+	0.189469i	−0.123091	+	0.0329823i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.776457	+	0.208051i	−0.127649	+	0.0342034i	−0.322078	−	0.946713i	$-0.604381\pi$
$37$	−0.776457	+	0.208051i	−0.127649	+	0.0342034i	0.194429	+	0.980917i	$0.437715\pi$
$38$		0			0
$39$	−0.866025	+	0.500000i	−0.138675	+	0.0800641i
$40$		0			0
$41$			6.19615i			0.967676i	0.875157	+	0.483838i	$0.160758\pi$
$41$			6.19615i			0.967676i	−0.875157	+	0.483838i	$0.839242\pi$
$42$		0			0
$43$	−5.27792	+	5.27792i	−0.804875	+	0.804875i	−0.983853	−	0.178978i	$-0.942721\pi$
$43$	−5.27792	+	5.27792i	−0.804875	+	0.804875i	0.178978	+	0.983853i	$0.442721\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.0507680	−	0.189469i	−0.00740527	−	0.0276368i	0.962124	−	0.272611i	$-0.0878872\pi$
$47$	−0.0507680	−	0.189469i	−0.00740527	−	0.0276368i	−0.969530	+	0.244974i	$0.921221\pi$
$48$		0			0
$49$	−4.33013	+	5.50000i	−0.618590	+	0.785714i
$50$		0			0
$51$	1.63397	−	2.83013i	0.228802	−	0.396297i
$52$		0			0
$53$	−5.08845	−	1.36345i	−0.698952	−	0.187284i	−0.108191	−	0.994130i	$-0.534506\pi$
$53$	−5.08845	−	1.36345i	−0.698952	−	0.187284i	−0.590761	+	0.806846i	$0.701172\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.08604	−	1.08604i	−0.143850	−	0.143850i
$58$		0			0
$59$	6.36603	+	11.0263i	0.828786	+	1.43550i	0.898991	+	0.437967i	$0.144301\pi$
$59$	6.36603	+	11.0263i	0.828786	+	1.43550i	−0.0702053	+	0.997533i	$0.522365\pi$
$60$		0			0
$61$	5.42820	+	3.13397i	0.695010	+	0.401264i	0.805486	−	0.592614i	$-0.201904\pi$
$61$	5.42820	+	3.13397i	0.695010	+	0.401264i	−0.110476	+	0.993879i	$0.535238\pi$
$62$		0			0
$63$	−0.189469	+	2.63896i	−0.0238708	+	0.332478i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.81173	−	6.76148i	0.221338	−	0.826046i	−0.762500	−	0.646988i	$-0.776028\pi$
$67$	1.81173	−	6.76148i	0.221338	−	0.826046i	0.983838	−	0.179058i	$-0.0573050\pi$
$68$		0			0
$69$	−0.535898			−0.0645146
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−1.39563	+	5.20857i	−0.163346	+	0.609617i	0.834899	+	0.550403i	$0.185526\pi$
$73$	−1.39563	+	5.20857i	−0.163346	+	0.609617i	−0.998245	+	0.0592135i	$0.981141\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.08604	−	1.60368i	0.123766	−	0.182757i
$78$		0			0
$79$	4.96410	+	2.86603i	0.558505	+	0.322453i	0.752545	−	0.658541i	$-0.228826\pi$
$79$	4.96410	+	2.86603i	0.558505	+	0.322453i	−0.194040	+	0.980994i	$0.562159\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	0.896575	+	0.896575i	0.0984119	+	0.0984119i	0.754599	−	0.656187i	$-0.227832\pi$
$83$	0.896575	+	0.896575i	0.0984119	+	0.0984119i	−0.656187	+	0.754599i	$0.727832\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.69213	−	1.79315i	−0.717472	−	0.192246i
$88$		0			0
$89$	−5.36603	+	9.29423i	−0.568798	+	0.985186i	0.427888	+	0.903832i	$0.359258\pi$
$89$	−5.36603	+	9.29423i	−0.568798	+	0.985186i	−0.996685	+	0.0813544i	$0.974075\pi$
$90$		0			0
$91$	0.866025	−	2.50000i	0.0907841	−	0.262071i
$92$		0			0
$93$	0.517638	+	1.93185i	0.0536766	+	0.200324i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.39924	+	7.39924i	−0.751279	+	0.751279i	−0.974718	−	0.223439i	$-0.928272\pi$
$97$	−7.39924	+	7.39924i	−0.751279	+	0.751279i	0.223439	+	0.974718i	$0.428272\pi$
$98$		0			0
$99$		−	0.732051i		−	0.0735739i
$100$		0			0
$101$	−2.83013	+	1.63397i	−0.281608	+	0.162587i	−0.634151	−	0.773209i	$-0.718650\pi$
$101$	−2.83013	+	1.63397i	−0.281608	+	0.162587i	0.352543	+	0.935796i	$0.385317\pi$
$102$		0			0
$103$	−12.2289	+	3.27671i	−1.20495	+	0.322864i	−0.804777	−	0.593577i	$-0.797715\pi$
$103$	−12.2289	+	3.27671i	−1.20495	+	0.322864i	−0.400169	+	0.916441i	$0.631049\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.8840	−	2.91636i	1.05220	−	0.281935i	0.309037	−	0.951050i	$-0.399993\pi$
$107$	10.8840	−	2.91636i	1.05220	−	0.281935i	0.743159	+	0.669115i	$0.233327\pi$
$108$		0			0
$109$	0.0621778	−	0.0358984i	0.00595556	−	0.00343844i	−0.497019	−	0.867740i	$-0.665572\pi$
$109$	0.0621778	−	0.0358984i	0.00595556	−	0.00343844i	0.502975	+	0.864301i	$0.332239\pi$
$110$		0			0
$111$		−	0.803848i		−	0.0762978i
$112$		0			0
$113$	−10.9348	+	10.9348i	−1.02866	+	1.02866i	−0.0290796	+	0.999577i	$0.509258\pi$
$113$	−10.9348	+	10.9348i	−1.02866	+	1.02866i	−0.999577	+	0.0290796i	$0.990742\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.258819	−	0.965926i	−0.0239278	−	0.0892999i
$118$		0			0
$119$	1.63397	+	8.49038i	0.149786	+	0.778312i
$120$		0			0
$121$	5.23205	−	9.06218i	0.475641	−	0.823834i
$122$		0			0
$123$	−5.98502	−	1.60368i	−0.539651	−	0.144599i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.84873	−	9.84873i	−0.873933	−	0.873933i	0.118965	−	0.992898i	$-0.462042\pi$
$127$	−9.84873	−	9.84873i	−0.873933	−	0.873933i	−0.992898	+	0.118965i	$0.962042\pi$
$128$		0			0
$129$	−3.73205	−	6.46410i	−0.328589	−	0.569132i
$130$		0			0
$131$	−2.66025	−	1.53590i	−0.232427	−	0.134192i	0.379264	−	0.925289i	$-0.376177\pi$
$131$	−2.66025	−	1.53590i	−0.232427	−	0.134192i	−0.611691	+	0.791096i	$0.709511\pi$
$132$		0			0
$133$	4.05317	+	0.291005i	0.351455	+	0.0252333i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.55291	+	5.79555i	−0.132674	+	0.495148i	−0.999997	−	0.00259945i	$-0.999173\pi$
$137$	−1.55291	+	5.79555i	−0.132674	+	0.495148i	0.867322	+	0.497747i	$0.165839\pi$
$138$		0			0
$139$	−10.8564			−0.920828			−0.460414	−	0.887704i	$-0.652299\pi$
$139$	−10.8564			−0.920828			−0.460414	+	0.887704i	$0.652299\pi$
$140$		0			0
$141$	0.196152			0.0165190
$142$		0			0
$143$	−0.189469	+	0.707107i	−0.0158442	+	0.0591312i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.19187	−	5.60609i	−0.345740	−	0.462382i
$148$		0			0
$149$	13.0981	+	7.56218i	1.07304	+	0.619518i	0.929009	−	0.370056i	$-0.120662\pi$
$149$	13.0981	+	7.56218i	1.07304	+	0.619518i	0.144027	+	0.989574i	$0.453995\pi$
$150$		0			0
$151$	−3.33013	−	5.76795i	−0.271002	−	0.469389i	0.698117	−	0.715984i	$-0.254022\pi$
$151$	−3.33013	−	5.76795i	−0.271002	−	0.469389i	−0.969119	+	0.246595i	$0.920688\pi$
$152$		0			0
$153$	2.31079	+	2.31079i	0.186816	+	0.186816i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−14.3502	−	3.84512i	−1.14527	−	0.306874i	−0.364202	−	0.931320i	$-0.618658\pi$
$157$	−14.3502	−	3.84512i	−1.14527	−	0.306874i	−0.781068	+	0.624446i	$0.785325\pi$
$158$		0			0
$159$	2.63397	−	4.56218i	0.208888	−	0.361804i
$160$		0			0
$161$	1.07180	−	0.928203i	0.0844694	−	0.0731527i
$162$		0			0
$163$	0.776457	+	2.89778i	0.0608168	+	0.226971i	0.989644	−	0.143541i	$-0.0458488\pi$
$163$	0.776457	+	2.89778i	0.0608168	+	0.226971i	−0.928828	+	0.370512i	$0.879182\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.4877	−	12.4877i	0.966326	−	0.966326i	−0.0331251	−	0.999451i	$-0.510546\pi$
$167$	12.4877	−	12.4877i	0.966326	−	0.966326i	0.999451	+	0.0331251i	$0.0105460\pi$
$168$		0			0
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	1.33013	−	0.767949i	0.101717	−	0.0587265i
$172$		0			0
$173$	−18.8009	+	5.03768i	−1.42940	+	0.383008i	−0.888810	−	0.458276i	$-0.848467\pi$
$173$	−18.8009	+	5.03768i	−1.42940	+	0.383008i	−0.540594	+	0.841283i	$0.681801\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.2982	+	3.29530i	−0.924391	+	0.247690i
$178$		0			0
$179$	2.19615	−	1.26795i	0.164148	−	0.0947710i	−0.415675	−	0.909513i	$-0.636455\pi$
$179$	2.19615	−	1.26795i	0.164148	−	0.0947710i	0.579824	+	0.814742i	$0.303121\pi$
$180$		0			0
$181$			14.3923i			1.06977i	0.844924	+	0.534886i	$0.179645\pi$
$181$			14.3923i			1.06977i	−0.844924	+	0.534886i	$0.820355\pi$
$182$		0			0
$183$	−4.43211	+	4.43211i	−0.327631	+	0.327631i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.619174	−	2.31079i	−0.0452785	−	0.168982i
$188$		0			0
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$	6.90192	−	11.9545i	0.499406	−	0.864996i	−0.500594	−	0.865682i	$-0.666885\pi$
$191$	6.90192	−	11.9545i	0.499406	−	0.864996i	1.00000		0.000686128i	$0.000218401\pi$
$192$		0			0
$193$	−20.5940	−	5.51815i	−1.48239	−	0.397205i	−0.575231	−	0.817991i	$-0.695088\pi$
$193$	−20.5940	−	5.51815i	−1.48239	−	0.397205i	−0.907160	+	0.420786i	$0.861754\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.3843	+	13.3843i	0.953589	+	0.953589i	0.998970	−	0.0453807i	$-0.0144501\pi$
$197$	13.3843	+	13.3843i	0.953589	+	0.953589i	−0.0453807	+	0.998970i	$0.514450\pi$
$198$		0			0
$199$	−0.767949	−	1.33013i	−0.0544385	−	0.0942902i	0.837522	−	0.546404i	$-0.184004\pi$
$199$	−0.767949	−	1.33013i	−0.0544385	−	0.0942902i	−0.891960	+	0.452113i	$0.850670\pi$
$200$		0			0
$201$	6.06218	+	3.50000i	0.427593	+	0.246871i
$202$		0			0
$203$	16.4901	−	8.00481i	1.15738	−	0.561827i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.138701	−	0.517638i	0.00964037	−	0.0359783i
$208$		0			0
$209$	−1.12436			−0.0777733
$210$		0			0
$211$	−12.2679			−0.844560			−0.422280	−	0.906465i	$-0.638770\pi$
$211$	−12.2679			−0.844560			−0.422280	+	0.906465i	$0.638770\pi$
$212$		0			0
$213$	2.07055	−	7.72741i	0.141872	−	0.529473i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.38134	−	2.96713i	−0.297425	−	0.201422i
$218$		0			0
$219$	−4.66987	−	2.69615i	−0.315561	−	0.182189i
$220$		0			0
$221$	−1.63397	−	2.83013i	−0.109913	−	0.190375i
$222$		0			0
$223$	13.1948	+	13.1948i	0.883589	+	0.883589i	0.993897	−	0.110309i	$-0.0351840\pi$
$223$	13.1948	+	13.1948i	0.883589	+	0.883589i	−0.110309	+	0.993897i	$0.535184\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.3843	+	3.58630i	0.888345	+	0.238031i	0.674004	−	0.738728i	$-0.264573\pi$
$227$	13.3843	+	3.58630i	0.888345	+	0.238031i	0.214341	+	0.976759i	$0.431240\pi$
$228$		0			0
$229$	4.13397	−	7.16025i	0.273181	−	0.473163i	−0.696494	−	0.717563i	$-0.745258\pi$
$229$	4.13397	−	7.16025i	0.273181	−	0.473163i	0.969675	+	0.244400i	$0.0785910\pi$
$230$		0			0
$231$	1.26795	+	1.46410i	0.0834249	+	0.0963308i
$232$		0			0
$233$	−1.88108	−	7.02030i	−0.123234	−	0.459915i	0.876537	−	0.481335i	$-0.159848\pi$
$233$	−1.88108	−	7.02030i	−0.123234	−	0.459915i	−0.999771	+	0.0214199i	$0.993181\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.05317	+	4.05317i	−0.263282	+	0.263282i
$238$		0			0
$239$			11.3205i			0.732263i	0.930563	+	0.366131i	$0.119318\pi$
$239$			11.3205i			0.732263i	−0.930563	+	0.366131i	$0.880682\pi$
$240$		0			0
$241$	0.696152	−	0.401924i	0.0448431	−	0.0258902i	−0.477411	−	0.878680i	$-0.658425\pi$
$241$	0.696152	−	0.401924i	0.0448431	−	0.0258902i	0.522254	+	0.852790i	$0.325091\pi$
$242$		0			0
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.48356	+	0.397520i	−0.0943969	+	0.0252936i
$248$		0			0
$249$	−1.09808	+	0.633975i	−0.0695878	+	0.0401765i
$250$		0			0
$251$			20.5885i			1.29953i	0.760134	+	0.649766i	$0.225133\pi$
$251$			20.5885i			1.29953i	−0.760134	+	0.649766i	$0.774867\pi$
$252$		0			0
$253$	−0.277401	+	0.277401i	−0.0174401	+	0.0174401i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.08656	+	22.7153i	0.379669	+	1.41694i	0.846401	+	0.532546i	$0.178765\pi$
$257$	6.08656	+	22.7153i	0.379669	+	1.41694i	−0.466732	+	0.884399i	$0.654569\pi$
$258$		0			0
$259$	1.39230	+	1.60770i	0.0865136	+	0.0998973i
$260$		0			0
$261$	3.46410	−	6.00000i	0.214423	−	0.371391i
$262$		0			0
$263$	22.1469	+	5.93426i	1.36564	+	0.365922i	0.865884	−	0.500245i	$-0.166757\pi$
$263$	22.1469	+	5.93426i	1.36564	+	0.365922i	0.499755	+	0.866167i	$0.333423\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−7.58871	−	7.58871i	−0.464421	−	0.464421i
$268$		0			0
$269$	11.2942	+	19.5622i	0.688621	+	1.19273i	0.972284	+	0.233803i	$0.0751171\pi$
$269$	11.2942	+	19.5622i	0.688621	+	1.19273i	−0.283663	+	0.958924i	$0.591550\pi$
$270$		0			0
$271$	−0.928203	−	0.535898i	−0.0563843	−	0.0325535i	0.471543	−	0.881843i	$-0.343697\pi$
$271$	−0.928203	−	0.535898i	−0.0563843	−	0.0325535i	−0.527927	+	0.849290i	$0.677031\pi$
$272$		0			0
$273$	2.19067	+	1.48356i	0.132585	+	0.0897894i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.79624	+	10.4357i	−0.168010	+	0.627021i	0.829627	+	0.558318i	$0.188553\pi$
$277$	−2.79624	+	10.4357i	−0.168010	+	0.627021i	−0.997637	+	0.0687037i	$0.978114\pi$
$278$		0			0
$279$	−2.00000			−0.119737
$280$		0			0
$281$	−33.1244			−1.97603			−0.988017	−	0.154347i	$-0.950673\pi$
$281$	−33.1244			−1.97603			−0.988017	+	0.154347i	$0.950673\pi$
$282$		0			0
$283$	6.38254	−	23.8200i	0.379403	−	1.41595i	−0.467401	−	0.884045i	$-0.654810\pi$
$283$	6.38254	−	23.8200i	0.379403	−	1.41595i	0.846804	−	0.531905i	$-0.178524\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.7477	−	7.15900i	0.870530	−	0.422582i
$288$		0			0
$289$	−5.47372	−	3.16025i	−0.321984	−	0.185897i
$290$		0			0
$291$	−5.23205	−	9.06218i	−0.306708	−	0.531234i
$292$		0			0
$293$	−3.10583	−	3.10583i	−0.181444	−	0.181444i	0.610541	−	0.791985i	$-0.290952\pi$
$293$	−3.10583	−	3.10583i	−0.181444	−	0.181444i	−0.791985	+	0.610541i	$0.790952\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.707107	+	0.189469i	0.0410305	+	0.0109941i
$298$		0			0
$299$	−0.267949	+	0.464102i	−0.0154959	+	0.0268397i
$300$		0			0
$301$	18.6603	+	6.46410i	1.07556	+	0.372585i
$302$		0			0
$303$	−0.845807	−	3.15660i	−0.0485904	−	0.181342i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	6.69213	−	6.69213i	0.381940	−	0.381940i	−0.489861	−	0.871801i	$-0.662952\pi$
$307$	6.69213	−	6.69213i	0.381940	−	0.381940i	0.871801	+	0.489861i	$0.162952\pi$
$308$		0			0
$309$		−	12.6603i		−	0.720217i
$310$		0			0
$311$	−5.19615	+	3.00000i	−0.294647	+	0.170114i	−0.640036	−	0.768345i	$-0.721080\pi$
$311$	−5.19615	+	3.00000i	−0.294647	+	0.170114i	0.345389	+	0.938460i	$0.387747\pi$
$312$		0			0
$313$	9.14162	−	2.44949i	0.516715	−	0.138453i	0.00896828	−	0.999960i	$-0.497145\pi$
$313$	9.14162	−	2.44949i	0.516715	−	0.138453i	0.507747	+	0.861506i	$0.330479\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.7656	−	4.76028i	0.997816	−	0.267364i	0.277286	−	0.960788i	$-0.410565\pi$
$317$	17.7656	−	4.76028i	0.997816	−	0.267364i	0.720530	+	0.693424i	$0.243899\pi$
$318$		0			0
$319$	−4.39230	+	2.53590i	−0.245922	+	0.141983i
$320$		0			0
$321$			11.2679i			0.628916i
$322$		0			0
$323$	3.54914	−	3.54914i	0.197479	−	0.197479i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.0185824	+	0.0693504i	0.00102761	+	0.00383508i
$328$		0			0
$329$	−0.392305	+	0.339746i	−0.0216285	+	0.0187308i
$330$		0			0
$331$	15.3301	−	26.5526i	0.842620	−	1.45946i	−0.0450522	−	0.998985i	$-0.514345\pi$
$331$	15.3301	−	26.5526i	0.842620	−	1.45946i	0.887672	−	0.460476i	$-0.152321\pi$
$332$		0			0
$333$	0.776457	+	0.208051i	0.0425496	+	0.0114011i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.14162	+	9.14162i	0.497976	+	0.497976i	0.910807	−	0.412832i	$-0.135460\pi$
$337$	9.14162	+	9.14162i	0.497976	+	0.497976i	−0.412832	+	0.910807i	$0.635460\pi$
$338$		0			0
$339$	−7.73205	−	13.3923i	−0.419947	−	0.727370i
$340$		0			0
$341$	1.26795	+	0.732051i	0.0686633	+	0.0396428i
$342$		0			0
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.46309	+	9.19239i	−0.132226	+	0.493473i	−0.999994	−	0.00349604i	$-0.998887\pi$
$347$	−2.46309	+	9.19239i	−0.132226	+	0.493473i	0.867768	+	0.496969i	$0.165554\pi$
$348$		0			0
$349$	0.928203			0.0496856			0.0248428	−	0.999691i	$-0.492091\pi$
$349$	0.928203			0.0496856			0.0248428	+	0.999691i	$0.492091\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$		0			0
$353$	1.46498	−	5.46739i	0.0779731	−	0.291000i	−0.915918	−	0.401366i	$-0.868536\pi$
$353$	1.46498	−	5.46739i	0.0779731	−	0.291000i	0.993891	+	0.110366i	$0.0352023\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−8.62398	−	0.619174i	−0.456430	−	0.0327702i
$358$		0			0
$359$	8.70577	+	5.02628i	0.459473	+	0.265277i	0.711823	−	0.702359i	$-0.247870\pi$
$359$	8.70577	+	5.02628i	0.459473	+	0.265277i	−0.252350	+	0.967636i	$0.581203\pi$
$360$		0			0
$361$	8.32051	+	14.4115i	0.437921	+	0.758502i
$362$		0			0
$363$	7.39924	+	7.39924i	0.388359	+	0.388359i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.517638	−	0.138701i	−0.0270205	−	0.00724012i	0.245283	−	0.969451i	$-0.421119\pi$
$367$	−0.517638	−	0.138701i	−0.0270205	−	0.00724012i	−0.272304	+	0.962211i	$0.587786\pi$
$368$		0			0
$369$	3.09808	−	5.36603i	0.161279	−	0.279344i
$370$		0			0
$371$	2.63397	+	13.6865i	0.136749	+	0.710569i
$372$		0			0
$373$	−5.96644	−	22.2671i	−0.308931	−	1.15294i	−0.929509	−	0.368800i	$-0.879769\pi$
$373$	−5.96644	−	22.2671i	−0.308931	−	1.15294i	0.620578	−	0.784145i	$-0.286898\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.89898	+	4.89898i	−0.252310	+	0.252310i
$378$		0			0
$379$		−	35.4449i		−	1.82068i	−0.413861	−	0.910340i	$-0.635820\pi$
$379$		−	35.4449i		−	1.82068i	0.413861	−	0.910340i	$-0.364180\pi$
$380$		0			0
$381$	12.0622	−	6.96410i	0.617964	−	0.356782i
$382$		0			0
$383$	24.8367	−	6.65497i	1.26909	−	0.340053i	0.439411	−	0.898286i	$-0.355187\pi$
$383$	24.8367	−	6.65497i	1.26909	−	0.340053i	0.829684	+	0.558233i	$0.188521\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.20977	−	1.93185i	0.366493	−	0.0982015i
$388$		0			0
$389$	24.4186	−	14.0981i	1.23807	−	0.714801i	0.269372	−	0.963036i	$-0.413184\pi$
$389$	24.4186	−	14.0981i	1.23807	−	0.714801i	0.968700	+	0.248235i	$0.0798507\pi$
$390$		0			0
$391$		−	1.75129i		−	0.0885665i
$392$		0			0
$393$	2.17209	−	2.17209i	0.109567	−	0.109567i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	3.48477	+	13.0053i	0.174895	+	0.652718i	0.996569	+	0.0827608i	$0.0263737\pi$
$397$	3.48477	+	13.0053i	0.174895	+	0.652718i	−0.821674	+	0.569958i	$0.806960\pi$
$398$		0			0
$399$	−1.33013	+	3.83975i	−0.0665896	+	0.192228i
$400$		0			0
$401$	−2.29423	+	3.97372i	−0.114568	+	0.198438i	−0.917607	−	0.397489i	$-0.869882\pi$
$401$	−2.29423	+	3.97372i	−0.114568	+	0.198438i	0.803039	+	0.595927i	$0.203215\pi$
$402$		0			0
$403$	1.93185	+	0.517638i	0.0962324	+	0.0257854i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.416102	−	0.416102i	−0.0206254	−	0.0206254i
$408$		0			0
$409$	−9.79423	−	16.9641i	−0.484293	−	0.838821i	0.515544	−	0.856863i	$-0.327590\pi$
$409$	−9.79423	−	16.9641i	−0.484293	−	0.838821i	−0.999837	+	0.0180424i	$0.994257\pi$
$410$		0			0
$411$	−5.19615	−	3.00000i	−0.256307	−	0.147979i
$412$		0			0
$413$	18.8888	−	27.8917i	0.929458	−	1.37246i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.80984	−	10.4865i	0.137599	−	0.513525i
$418$		0			0
$419$	−38.0526			−1.85899			−0.929495	−	0.368836i	$-0.879756\pi$
$419$	−38.0526			−1.85899			−0.929495	+	0.368836i	$0.879756\pi$
$420$		0			0
$421$	−10.6077			−0.516987			−0.258494	−	0.966013i	$-0.583226\pi$
$421$	−10.6077			−0.516987			−0.258494	+	0.966013i	$0.583226\pi$
$422$		0			0
$423$	−0.0507680	+	0.189469i	−0.00246842	+	0.00921228i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.18758	−	16.5409i	0.0574710	−	0.800468i
$428$		0			0
$429$	−0.633975	−	0.366025i	−0.0306086	−	0.0176719i
$430$		0			0
$431$	−12.4641	−	21.5885i	−0.600375	−	1.03988i	−0.992764	−	0.120080i	$-0.961685\pi$
$431$	−12.4641	−	21.5885i	−0.600375	−	1.03988i	0.392390	−	0.919799i	$-0.371649\pi$
$432$		0			0
$433$	26.4911	+	26.4911i	1.27308	+	1.27308i	0.944462	+	0.328620i	$0.106583\pi$
$433$	26.4911	+	26.4911i	1.27308	+	1.27308i	0.328620	+	0.944462i	$0.393417\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.795040	−	0.213030i	−0.0380319	−	0.0101906i
$438$		0			0
$439$	13.8923	−	24.0622i	0.663044	−	1.14843i	−0.316768	−	0.948503i	$-0.602598\pi$
$439$	13.8923	−	24.0622i	0.663044	−	1.14843i	0.979812	−	0.199922i	$-0.0640689\pi$
$440$		0			0
$441$	6.50000	−	2.59808i	0.309524	−	0.123718i
$442$		0			0
$443$	−10.1397	−	37.8420i	−0.481753	−	1.79793i	−0.594256	−	0.804276i	$-0.702553\pi$
$443$	−10.1397	−	37.8420i	−0.481753	−	1.79793i	0.112503	−	0.993651i	$-0.464113\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−10.6945	+	10.6945i	−0.505834	+	0.505834i
$448$		0			0
$449$		−	27.6603i		−	1.30537i	−0.757630	−	0.652684i	$-0.773643\pi$
$449$		−	27.6603i		−	1.30537i	0.757630	−	0.652684i	$-0.226357\pi$
$450$		0			0
$451$	−3.92820	+	2.26795i	−0.184972	+	0.106794i
$452$		0			0
$453$	6.43331	−	1.72380i	0.302263	−	0.0809912i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.84752	+	2.10274i	−0.367092	+	0.0983619i	−0.437649	−	0.899146i	$-0.644189\pi$
$457$	−7.84752	+	2.10274i	−0.367092	+	0.0983619i	0.0705575	+	0.997508i	$0.477522\pi$
$458$		0			0
$459$	−2.83013	+	1.63397i	−0.132099	+	0.0762674i
$460$		0			0
$461$			37.7128i			1.75646i	0.478238	+	0.878230i	$0.341276\pi$
$461$			37.7128i			1.75646i	−0.478238	+	0.878230i	$0.658724\pi$
$462$		0			0
$463$	−12.1967	+	12.1967i	−0.566828	+	0.566828i	−0.931238	−	0.364411i	$-0.881270\pi$
$463$	−12.1967	+	12.1967i	−0.566828	+	0.566828i	0.364411	+	0.931238i	$0.381270\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.0371647	−	0.138701i	−0.00171978	−	0.00641830i	0.965061	−	0.262027i	$-0.0843909\pi$
$467$	−0.0371647	−	0.138701i	−0.00171978	−	0.00641830i	−0.966780	+	0.255608i	$0.917724\pi$
$468$		0			0
$469$	−18.1865	+	3.50000i	−0.839776	+	0.161615i
$470$		0			0
$471$	7.42820	−	12.8660i	0.342274	−	0.592835i
$472$		0			0
$473$	−5.27792	−	1.41421i	−0.242679	−	0.0650256i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.72500	+	3.72500i	0.170556	+	0.170556i
$478$		0			0
$479$	16.2224	+	28.0981i	0.741222	+	1.28383i	0.951939	+	0.306287i	$0.0990867\pi$
$479$	16.2224	+	28.0981i	0.741222	+	1.28383i	−0.210717	+	0.977547i	$0.567580\pi$
$480$		0			0
$481$	−0.696152	−	0.401924i	−0.0317418	−	0.0183261i
$482$		0			0
$483$	0.619174	+	1.27551i	0.0281734	+	0.0580378i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.41233	+	9.00292i	−0.109313	+	0.407961i	−0.998799	−	0.0490015i	$-0.984396\pi$
$487$	−2.41233	+	9.00292i	−0.109313	+	0.407961i	0.889486	+	0.456963i	$0.151063\pi$
$488$		0			0
$489$	−3.00000			−0.135665
$490$		0			0
$491$	−6.39230			−0.288481			−0.144240	−	0.989543i	$-0.546074\pi$
$491$	−6.39230			−0.288481			−0.144240	+	0.989543i	$0.546074\pi$
$492$		0			0
$493$	5.85993	−	21.8695i	0.263918	−	0.984955i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.24316	+	19.0411i	0.414612	+	0.854111i
$498$		0			0
$499$	−7.96410	−	4.59808i	−0.356522	−	0.205838i	0.311032	−	0.950399i	$-0.399325\pi$
$499$	−7.96410	−	4.59808i	−0.356522	−	0.205838i	−0.667554	+	0.744561i	$0.732659\pi$
$500$		0			0
$501$	8.83013	+	15.2942i	0.394501	+	0.683296i
$502$		0			0
$503$	14.6969	+	14.6969i	0.655304	+	0.655304i	0.954265	−	0.298961i	$-0.0966401\pi$
$503$	14.6969	+	14.6969i	0.655304	+	0.655304i	−0.298961	+	0.954265i	$0.596640\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	11.5911	+	3.10583i	0.514779	+	0.137935i
$508$		0			0
$509$	7.26795	−	12.5885i	0.322146	−	0.557974i	−0.658784	−	0.752332i	$-0.728929\pi$
$509$	7.26795	−	12.5885i	0.322146	−	0.557974i	0.980931	+	0.194358i	$0.0622624\pi$
$510$		0			0
$511$	14.0096	−	2.69615i	0.619749	−	0.119271i
$512$		0			0
$513$	0.397520	+	1.48356i	0.0175509	+	0.0655009i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.101536	−	0.101536i	0.00446555	−	0.00446555i
$518$		0			0
$519$		−	19.4641i		−	0.854379i
$520$		0			0
$521$	−2.32051	+	1.33975i	−0.101663	+	0.0586953i	−0.549970	−	0.835185i	$-0.685361\pi$
$521$	−2.32051	+	1.33975i	−0.101663	+	0.0586953i	0.448306	+	0.893880i	$0.352027\pi$
$522$		0			0
$523$	14.7985	−	3.96524i	0.647092	−	0.173388i	0.0796783	−	0.996821i	$-0.474611\pi$
$523$	14.7985	−	3.96524i	0.647092	−	0.173388i	0.567414	+	0.823433i	$0.307944\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.31319	+	1.69161i	−0.275007	+	0.0736879i
$528$		0			0
$529$	19.6699	−	11.3564i	0.855212	−	0.493757i
$530$		0			0
$531$		−	12.7321i		−	0.552524i
$532$		0			0
$533$	−4.38134	+	4.38134i	−0.189777	+	0.189777i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.656339	+	2.44949i	0.0283231	+	0.105703i
$538$		0			0
$539$	−5.07180	−	0.732051i	−0.218458	−	0.0315317i
$540$		0			0
$541$	1.83975	−	3.18653i	0.0790969	−	0.137000i	−0.823764	−	0.566933i	$-0.808130\pi$
$541$	1.83975	−	3.18653i	0.0790969	−	0.137000i	0.902861	+	0.429934i	$0.141463\pi$
$542$		0			0
$543$	−13.9019	−	3.72500i	−0.596588	−	0.159855i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	9.04008	+	9.04008i	0.386526	+	0.386526i	0.873446	−	0.486920i	$-0.161880\pi$
$547$	9.04008	+	9.04008i	0.386526	+	0.386526i	−0.486920	+	0.873446i	$0.661880\pi$
$548$		0			0
$549$	−3.13397	−	5.42820i	−0.133755	−	0.231670i
$550$		0			0
$551$	−9.21539	−	5.32051i	−0.392589	−	0.226661i
$552$		0			0
$553$	1.08604	−	15.1266i	0.0461833	−	0.643250i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.24264	+	15.8338i	−0.179766	+	0.670898i	0.815924	+	0.578159i	$0.196229\pi$
$557$	−4.24264	+	15.8338i	−0.179766	+	0.670898i	−0.995691	+	0.0927384i	$0.970438\pi$
$558$		0			0
$559$	−7.46410			−0.315698
$560$		0			0
$561$	2.39230			0.101003
$562$		0			0
$563$	1.42782	−	5.32868i	0.0601753	−	0.224577i	−0.929289	−	0.369353i	$-0.879579\pi$
$563$	1.42782	−	5.32868i	0.0601753	−	0.224577i	0.989465	+	0.144776i	$0.0462460\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.48356	−	2.19067i	0.0623038	−	0.0919995i
$568$		0			0
$569$	6.41858	+	3.70577i	0.269081	+	0.155354i	0.628470	−	0.777834i	$-0.283682\pi$
$569$	6.41858	+	3.70577i	0.269081	+	0.155354i	−0.359389	+	0.933188i	$0.617015\pi$
$570$		0			0
$571$	−19.4545	−	33.6962i	−0.814145	−	1.41014i	−0.909940	−	0.414739i	$-0.863873\pi$
$571$	−19.4545	−	33.6962i	−0.814145	−	1.41014i	0.0957956	−	0.995401i	$-0.469460\pi$
$572$		0			0
$573$	9.76079	+	9.76079i	0.407763	+	0.407763i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.65926	+	2.58819i	0.402120	+	0.107748i	0.454210	−	0.890895i	$-0.349922\pi$
$577$	9.65926	+	2.58819i	0.402120	+	0.107748i	−0.0520899	+	0.998642i	$0.516588\pi$
$578$		0			0
$579$	10.6603	−	18.4641i	0.443025	−	0.767342i
$580$		0			0
$581$	1.09808	−	3.16987i	0.0455559	−	0.131508i
$582$		0			0
$583$	−0.998111	−	3.72500i	−0.0413376	−	0.154274i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.1817	−	18.1817i	0.750439	−	0.750439i	−0.224122	−	0.974561i	$-0.571951\pi$
$587$	18.1817	−	18.1817i	0.750439	−	0.750439i	0.974561	+	0.224122i	$0.0719514\pi$
$588$		0			0
$589$			3.07180i			0.126571i
$590$		0			0
$591$	−16.3923	+	9.46410i	−0.674289	+	0.389301i
$592$		0			0
$593$	−26.2509	+	7.03390i	−1.07799	+	0.288848i	−0.753774	−	0.657134i	$-0.771769\pi$
$593$	−26.2509	+	7.03390i	−1.07799	+	0.288848i	−0.324221	+	0.945982i	$0.605102\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.48356	−	0.397520i	0.0607182	−	0.0162694i
$598$		0			0
$599$	20.9545	−	12.0981i	0.856177	−	0.494314i	−0.00655324	−	0.999979i	$-0.502086\pi$
$599$	20.9545	−	12.0981i	0.856177	−	0.494314i	0.862730	+	0.505665i	$0.168753\pi$
$600$		0			0
$601$			32.5167i			1.32638i	0.748450	+	0.663191i	$0.230798\pi$
$601$			32.5167i			1.32638i	−0.748450	+	0.663191i	$0.769202\pi$
$602$		0			0
$603$	−4.94975	+	4.94975i	−0.201569	+	0.201569i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	0.688524	+	2.56961i	0.0279463	+	0.104297i	0.978490	−	0.206293i	$-0.0661400\pi$
$607$	0.688524	+	2.56961i	0.0279463	+	0.104297i	−0.950544	+	0.310590i	$0.899473\pi$
$608$		0			0
$609$	3.46410	+	18.0000i	0.140372	+	0.729397i
$610$		0			0
$611$	0.0980762	−	0.169873i	0.00396774	−	0.00687233i
$612$		0			0
$613$	0.138701	+	0.0371647i	0.00560207	+	0.00150107i	0.261619	−	0.965171i	$-0.415744\pi$
$613$	0.138701	+	0.0371647i	0.00560207	+	0.00150107i	−0.256017	+	0.966672i	$0.582410\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.4548	+	15.4548i	0.622187	+	0.622187i	0.946090	−	0.323903i	$-0.104995\pi$
$617$	15.4548	+	15.4548i	0.622187	+	0.622187i	−0.323903	+	0.946090i	$0.604995\pi$
$618$		0			0
$619$	−8.80385	−	15.2487i	−0.353857	−	0.612897i	0.633065	−	0.774099i	$-0.281797\pi$
$619$	−8.80385	−	15.2487i	−0.353857	−	0.612897i	−0.986922	+	0.161201i	$0.948463\pi$
$620$		0			0
$621$	0.464102	+	0.267949i	0.0186238	+	0.0107524i
$622$		0			0
$623$	28.3214	+	2.03339i	1.13467	+	0.0814660i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.291005	−	1.08604i	0.0116216	−	0.0433724i
$628$		0			0
$629$	2.62693			0.104743
$630$		0			0
$631$	−37.1962			−1.48076			−0.740378	−	0.672191i	$-0.765353\pi$
$631$	−37.1962			−1.48076			−0.740378	+	0.672191i	$0.765353\pi$
$632$		0			0
$633$	3.17518	−	11.8499i	0.126202	−	0.470992i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−6.95095	+	0.827225i	−0.275407	+	0.0327759i
$638$		0			0
$639$	6.92820	+	4.00000i	0.274075	+	0.158238i
$640$		0			0
$641$	−8.58846	−	14.8756i	−0.339224	−	0.587553i	0.645063	−	0.764129i	$-0.276831\pi$
$641$	−8.58846	−	14.8756i	−0.339224	−	0.587553i	−0.984287	+	0.176577i	$0.943498\pi$
$642$		0			0
$643$	−8.09274	−	8.09274i	−0.319147	−	0.319147i	0.529293	−	0.848439i	$-0.322457\pi$
$643$	−8.09274	−	8.09274i	−0.319147	−	0.319147i	−0.848439	+	0.529293i	$0.822457\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.19239	−	2.46309i	−0.361390	−	0.0968342i	0.0735550	−	0.997291i	$-0.476566\pi$
$647$	−9.19239	−	2.46309i	−0.361390	−	0.0968342i	−0.434945	+	0.900457i	$0.643232\pi$
$648$		0			0
$649$	−4.66025	+	8.07180i	−0.182931	+	0.316846i
$650$		0			0
$651$	4.00000	−	3.46410i	0.156772	−	0.135769i
$652$		0			0
$653$	−7.91688	−	29.5462i	−0.309811	−	1.15623i	−0.928724	−	0.370772i	$-0.879093\pi$
$653$	−7.91688	−	29.5462i	−0.309811	−	1.15623i	0.618913	−	0.785460i	$-0.287573\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.81294	−	3.81294i	0.148757	−	0.148757i
$658$		0			0
$659$		−	11.6603i		−	0.454219i	−0.973869	−	0.227110i	$-0.927072\pi$
$659$		−	11.6603i		−	0.454219i	0.973869	−	0.227110i	$-0.0729275\pi$
$660$		0			0
$661$	25.6244	−	14.7942i	0.996672	−	0.575429i	0.0894100	−	0.995995i	$-0.471502\pi$
$661$	25.6244	−	14.7942i	0.996672	−	0.575429i	0.907262	+	0.420566i	$0.138169\pi$
$662$		0			0
$663$	3.15660	−	0.845807i	0.122592	−	0.0328484i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.58630	+	0.960947i	−0.138862	+	0.0372080i
$668$		0			0
$669$	−16.1603	+	9.33013i	−0.624792	+	0.360724i
$670$		0			0
$671$			4.58846i			0.177135i
$672$		0			0
$673$	−5.84632	+	5.84632i	−0.225359	+	0.225359i	−0.810751	−	0.585392i	$-0.800941\pi$
$673$	−5.84632	+	5.84632i	−0.225359	+	0.225359i	0.585392	+	0.810751i	$0.300941\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−0.896575	−	3.34607i	−0.0344582	−	0.128600i	0.946554	−	0.322545i	$-0.104538\pi$
$677$	−0.896575	−	3.34607i	−0.0344582	−	0.128600i	−0.981012	+	0.193945i	$0.937872\pi$
$678$		0			0
$679$	26.1603	+	9.06218i	1.00394	+	0.347774i
$680$		0			0
$681$	−6.92820	+	12.0000i	−0.265489	+	0.459841i
$682$		0			0
$683$	14.2301	+	3.81294i	0.544498	+	0.145898i	0.520575	−	0.853816i	$-0.325718\pi$
$683$	14.2301	+	3.81294i	0.544498	+	0.145898i	0.0239233	+	0.999714i	$0.492384\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.84632	+	5.84632i	0.223051	+	0.223051i
$688$		0			0
$689$	−2.63397	−	4.56218i	−0.100346	−	0.173805i
$690$		0			0
$691$	−30.5263	−	17.6244i	−1.16127	−	0.670462i	−0.209665	−	0.977773i	$-0.567237\pi$
$691$	−30.5263	−	17.6244i	−1.16127	−	0.670462i	−0.951609	+	0.307311i	$0.900571\pi$
$692$		0			0
$693$	−1.74238	+	0.845807i	−0.0661877	+	0.0321296i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	5.24075	−	19.5588i	0.198508	−	0.740841i
$698$		0			0
$699$	7.26795			0.274899
$700$		0			0
$701$	−35.6603			−1.34687			−0.673435	−	0.739247i	$-0.735182\pi$
$701$	−35.6603			−1.34687			−0.673435	+	0.739247i	$0.735182\pi$
$702$		0			0
$703$	0.319545	−	1.19256i	0.0120519	−	0.0449782i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.15900	+	4.84821i	0.269242	+	0.182336i
$708$		0			0
$709$	28.4545	+	16.4282i	1.06863	+	0.616974i	0.927807	−	0.373061i	$-0.121692\pi$
$709$	28.4545	+	16.4282i	1.06863	+	0.616974i	0.140824	+	0.990035i	$0.455025\pi$
$710$		0			0
$711$	−2.86603	−	4.96410i	−0.107484	−	0.186168i
$712$		0			0
$713$	0.757875	+	0.757875i	0.0283826	+	0.0283826i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−10.9348	−	2.92996i	−0.408367	−	0.109421i
$718$		0			0
$719$	−17.7583	+	30.7583i	−0.662274	+	1.14709i	0.317743	+	0.948177i	$0.397075\pi$
$719$	−17.7583	+	30.7583i	−0.662274	+	1.14709i	−0.980017	+	0.198915i	$0.936258\pi$
$720$		0			0
$721$	21.9282	+	25.3205i	0.816649	+	0.942985i
$722$		0			0
$723$	0.208051	+	0.776457i	0.00773750	+	0.0288768i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−7.91688	+	7.91688i	−0.293621	+	0.293621i	−0.838509	−	0.544888i	$-0.816572\pi$
$727$	−7.91688	+	7.91688i	−0.293621	+	0.293621i	0.544888	+	0.838509i	$0.316572\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	21.1244	−	12.1962i	0.781313	−	0.451091i
$732$		0			0
$733$	−9.21097	+	2.46807i	−0.340215	+	0.0911603i	−0.424881	−	0.905249i	$-0.639684\pi$
$733$	−9.21097	+	2.46807i	−0.340215	+	0.0911603i	0.0846664	+	0.996409i	$0.473018\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.94975	−	1.32628i	0.182326	−	0.0488542i
$738$		0			0
$739$	−31.9641	+	18.4545i	−1.17582	+	0.678859i	−0.955044	−	0.296466i	$-0.904192\pi$
$739$	−31.9641	+	18.4545i	−1.17582	+	0.678859i	−0.220775	+	0.975325i	$0.570859\pi$
$740$		0			0
$741$		−	1.53590i		−	0.0564226i
$742$		0			0
$743$	−29.7728	+	29.7728i	−1.09226	+	1.09226i	−0.0969715	+	0.995287i	$0.530916\pi$
$743$	−29.7728	+	29.7728i	−1.09226	+	1.09226i	−0.995287	+	0.0969715i	$0.969084\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.328169	−	1.22474i	−0.0120071	−	0.0448111i
$748$		0			0
$749$	−19.5167	−	22.5359i	−0.713123	−	0.823444i
$750$		0			0
$751$	12.0622	−	20.8923i	0.440155	−	0.762371i	−0.557545	−	0.830146i	$-0.688257\pi$
$751$	12.0622	−	20.8923i	0.440155	−	0.762371i	0.997701	+	0.0677754i	$0.0215901\pi$
$752$		0			0
$753$	−19.8869	−	5.32868i	−0.724720	−	0.194188i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	11.4016	+	11.4016i	0.414400	+	0.414400i	0.883268	−	0.468868i	$-0.155338\pi$
$757$	11.4016	+	11.4016i	0.414400	+	0.414400i	−0.468868	+	0.883268i	$0.655338\pi$
$758$		0			0
$759$	−0.196152	−	0.339746i	−0.00711988	−	0.0123320i
$760$		0			0
$761$	−5.49038	−	3.16987i	−0.199026	−	0.114908i	0.397175	−	0.917743i	$-0.369991\pi$
$761$	−5.49038	−	3.16987i	−0.199026	−	0.114908i	−0.596201	+	0.802835i	$0.703324\pi$
$762$		0			0
$763$	−0.157283	−	0.106515i	−0.00569403	−	0.00385611i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.29530	+	12.2982i	−0.118986	+	0.444063i
$768$		0			0
$769$	13.3205			0.480350			0.240175	−	0.970730i	$-0.422795\pi$
$769$	13.3205			0.480350			0.240175	+	0.970730i	$0.422795\pi$
$770$		0			0
$771$	−23.5167			−0.846932
$772$		0			0
$773$	−11.5911	+	43.2586i	−0.416903	+	1.55590i	0.364089	+	0.931364i	$0.381380\pi$
$773$	−11.5911	+	43.2586i	−0.416903	+	1.55590i	−0.780993	+	0.624540i	$0.785286\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.91327	+	0.928761i	−0.0686382	+	0.0333191i
$778$		0			0
$779$	−8.24167	−	4.75833i	−0.295288	−	0.170485i
$780$		0			0
$781$	−2.92820	−	5.07180i	−0.104779	−	0.181483i
$782$		0			0
$783$	4.89898	+	4.89898i	0.175075	+	0.175075i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	30.5121	+	8.17569i	1.08764	+	0.291432i	0.757722	−	0.652578i	$-0.226312\pi$
$787$	30.5121	+	8.17569i	1.08764	+	0.291432i	0.329917	+	0.944010i	$0.392979\pi$
$788$		0			0
$789$	−11.4641	+	19.8564i	−0.408133	+	0.706907i
$790$		0			0
$791$	38.6603	+	13.3923i	1.37460	+	0.476176i
$792$		0			0
$793$	1.62226	+	6.05437i	0.0576083	+	0.214997i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.2789	−	15.2789i	0.541208	−	0.541208i	−0.382675	−	0.923883i	$-0.624997\pi$
$797$	15.2789	−	15.2789i	0.541208	−	0.541208i	0.923883	+	0.382675i	$0.124997\pi$
$798$		0			0
$799$			0.641016i			0.0226775i
$800$		0			0
$801$	9.29423	−	5.36603i	0.328395	−	0.189599i
$802$		0			0
$803$	−3.81294	+	1.02167i	−0.134556	+	0.0360541i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−21.8188	+	5.84632i	−0.768057	+	0.205800i
$808$		0			0
$809$	38.5692	−	22.2679i	1.35602	−	0.782899i	0.366937	−	0.930246i	$-0.380407\pi$
$809$	38.5692	−	22.2679i	1.35602	−	0.782899i	0.989085	+	0.147347i	$0.0470733\pi$
$810$		0			0
$811$			54.8564i			1.92627i	0.269020	+	0.963134i	$0.413300\pi$
$811$			54.8564i			1.92627i	−0.269020	+	0.963134i	$0.586700\pi$
$812$		0			0
$813$	0.757875	−	0.757875i	0.0265798	−	0.0265798i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.96713	−	11.0735i	−0.103807	−	0.387412i
$818$		0			0
$819$	−2.00000	+	1.73205i	−0.0698857	+	0.0605228i
$820$		0			0
$821$	17.1699	−	29.7391i	0.599233	−	1.03790i	−0.393702	−	0.919238i	$-0.628806\pi$
$821$	17.1699	−	29.7391i	0.599233	−	1.03790i	0.992935	−	0.118663i	$-0.0378609\pi$
$822$		0			0
$823$	−33.1511	−	8.88280i	−1.15557	−	0.309635i	−0.370377	−	0.928882i	$-0.620771\pi$
$823$	−33.1511	−	8.88280i	−1.15557	−	0.309635i	−0.785197	+	0.619247i	$0.787438\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.1774	−	15.1774i	−0.527770	−	0.527770i	0.392137	−	0.919907i	$-0.371736\pi$
$827$	−15.1774	−	15.1774i	−0.527770	−	0.527770i	−0.919907	+	0.392137i	$0.871736\pi$
$828$		0			0
$829$	−6.72243	−	11.6436i	−0.233480	−	0.404399i	0.725350	−	0.688380i	$-0.241678\pi$
$829$	−6.72243	−	11.6436i	−0.233480	−	0.404399i	−0.958830	+	0.283981i	$0.908345\pi$
$830$		0			0
$831$	−9.35641	−	5.40192i	−0.324570	−	0.187391i
$832$		0			0
$833$	18.3204	−	13.6988i	0.634764	−	0.474636i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.517638	−	1.93185i	0.0178922	−	0.0667746i
$838$		0			0
$839$	−51.9615			−1.79391			−0.896956	−	0.442121i	$-0.854226\pi$
$839$	−51.9615			−1.79391			−0.896956	+	0.442121i	$0.854226\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$		0			0
$843$	8.57321	−	31.9957i	0.295277	−	1.10199i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−27.6143	−	1.98262i	−0.948840	−	0.0681236i
$848$		0			0
$849$	21.3564	+	12.3301i	0.732950	+	0.423169i
$850$		0			0
$851$	−0.215390	−	0.373067i	−0.00738348	−	0.0127886i
$852$		0			0
$853$	15.5563	+	15.5563i	0.532639	+	0.532639i	0.921357	−	0.388718i	$-0.127082\pi$
$853$	15.5563	+	15.5563i	0.532639	+	0.532639i	−0.388718	+	0.921357i	$0.627082\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−43.1199	−	11.5539i	−1.47295	−	0.394675i	−0.569007	−	0.822333i	$-0.692672\pi$
$857$	−43.1199	−	11.5539i	−1.47295	−	0.394675i	−0.903941	+	0.427657i	$0.859339\pi$
$858$		0			0
$859$	6.46410	−	11.1962i	0.220552	−	0.382008i	−0.734424	−	0.678691i	$-0.762547\pi$
$859$	6.46410	−	11.1962i	0.220552	−	0.382008i	0.954976	+	0.296684i	$0.0958807\pi$
$860$		0			0
$861$	3.09808	+	16.0981i	0.105582	+	0.548621i
$862$		0			0
$863$	3.47116	+	12.9546i	0.118160	+	0.440978i	0.999504	−	0.0314967i	$-0.0100274\pi$
$863$	3.47116	+	12.9546i	0.118160	+	0.440978i	−0.881344	+	0.472475i	$0.843361\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	4.46927	−	4.46927i	0.151785	−	0.151785i
$868$		0			0
$869$			4.19615i			0.142345i
$870$		0			0
$871$	6.06218	−	3.50000i	0.205409	−	0.118593i
$872$		0			0
$873$	10.1075	−	2.70831i	0.342089	−	0.0916624i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−33.3405	+	8.93357i	−1.12583	+	0.301665i	−0.773240	−	0.634113i	$-0.781365\pi$
$877$	−33.3405	+	8.93357i	−1.12583	+	0.301665i	−0.352589	+	0.935778i	$0.614699\pi$
$878$		0			0
$879$	3.80385	−	2.19615i	0.128301	−	0.0740744i
$880$		0			0
$881$		−	20.0000i		−	0.673817i	−0.941537	−	0.336909i	$-0.890619\pi$
$881$		−	20.0000i		−	0.673817i	0.941537	−	0.336909i	$-0.109381\pi$
$882$		0			0
$883$	−24.2683	+	24.2683i	−0.816692	+	0.816692i	−0.985627	−	0.168935i	$-0.945967\pi$
$883$	−24.2683	+	24.2683i	−0.816692	+	0.816692i	0.168935	+	0.985627i	$0.445967\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.6245	−	50.8473i	−0.457466	−	1.70729i	−0.680736	−	0.732529i	$-0.738340\pi$
$887$	−13.6245	−	50.8473i	−0.457466	−	1.70729i	0.223270	−	0.974757i	$-0.428327\pi$
$888$		0			0
$889$	−12.0622	+	34.8205i	−0.404552	+	1.16784i
$890$		0			0
$891$	−0.366025	+	0.633975i	−0.0122623	+	0.0212389i
$892$		0			0
$893$	0.291005	+	0.0779745i	0.00973810	+	0.00260932i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.378937	−	0.378937i	−0.0126524	−	0.0126524i
$898$		0			0
$899$	6.92820	+	12.0000i	0.231069	+	0.400222i
$900$		0			0
$901$	14.9090	+	8.60770i	0.496690	+	0.286764i
$902$		0			0
$903$	−11.0735	+	16.3514i	−0.368502	+	0.544140i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4.74170	−	17.6963i	0.157445	−	0.587594i	−0.841438	−	0.540354i	$-0.818291\pi$
$907$	4.74170	−	17.6963i	0.157445	−	0.587594i	0.998884	−	0.0472409i	$-0.0150428\pi$
$908$		0			0
$909$	3.26795			0.108391
$910$		0			0
$911$	45.7128			1.51453			0.757267	−	0.653106i	$-0.226534\pi$
$911$	45.7128			1.51453			0.757267	+	0.653106i	$0.226534\pi$
$912$		0			0
$913$	−0.240237	+	0.896575i	−0.00795067	+	0.0296723i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.582009	+	8.10634i	−0.0192196	+	0.267695i
$918$		0			0
$919$	10.3923	+	6.00000i	0.342811	+	0.197922i	0.661514	−	0.749933i	$-0.269914\pi$
$919$	10.3923	+	6.00000i	0.342811	+	0.197922i	−0.318704	+	0.947854i	$0.603247\pi$
$920$		0			0
$921$	4.73205	+	8.19615i	0.155926	+	0.270072i
$922$		0			0
$923$	−5.65685	−	5.65685i	−0.186198	−	0.186198i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	12.2289	+	3.27671i	0.401649	+	0.107621i
$928$		0			0
$929$	0.901924	−	1.56218i	0.0295912	−	0.0512534i	−0.850851	−	0.525408i	$-0.823913\pi$
$929$	0.901924	−	1.56218i	0.0295912	−	0.0512534i	0.880442	+	0.474154i	$0.157246\pi$
$930$		0			0
$931$	−3.99038	−	9.98334i	−0.130779	−	0.327191i
$932$		0			0
$933$	−1.55291	−	5.79555i	−0.0508401	−	0.189738i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	17.5254	−	17.5254i	0.572529	−	0.572529i	−0.360306	−	0.932834i	$-0.617328\pi$
$937$	17.5254	−	17.5254i	0.572529	−	0.572529i	0.932834	+	0.360306i	$0.117328\pi$
$938$		0			0
$939$			9.46410i			0.308849i
$940$		0			0
$941$	24.1244	−	13.9282i	0.786432	−	0.454046i	−0.0522732	−	0.998633i	$-0.516647\pi$
$941$	24.1244	−	13.9282i	0.786432	−	0.454046i	0.838705	+	0.544586i	$0.183313\pi$
$942$		0			0
$943$	−3.20736	+	0.859411i	−0.104446	+	0.0279863i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−35.3925	+	9.48339i	−1.15010	+	0.308169i	−0.783006	−	0.622014i	$-0.786315\pi$
$947$	−35.3925	+	9.48339i	−1.15010	+	0.308169i	−0.367096	+	0.930183i	$0.619648\pi$
$948$		0			0
$949$	−4.66987	+	2.69615i	−0.151590	+	0.0875208i
$950$		0			0
$951$			18.3923i			0.596411i
$952$		0			0
$953$	−24.4577	+	24.4577i	−0.792264	+	0.792264i	−0.981862	−	0.189598i	$-0.939281\pi$
$953$	−24.4577	+	24.4577i	−0.792264	+	0.792264i	0.189598	+	0.981862i	$0.439281\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.31268	−	4.89898i	−0.0424328	−	0.158362i
$958$		0			0
$959$	15.5885	−	3.00000i	0.503378	−	0.0968751i
$960$		0			0
$961$	−13.5000	+	23.3827i	−0.435484	+	0.754280i
$962$		0			0
$963$	−10.8840	−	2.91636i	−0.350732	−	0.0939784i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−7.39924	−	7.39924i	−0.237943	−	0.237943i	0.578055	−	0.815998i	$-0.303812\pi$
$967$	−7.39924	−	7.39924i	−0.237943	−	0.237943i	−0.815998	+	0.578055i	$0.803812\pi$
$968$		0			0
$969$	2.50962	+	4.34679i	0.0806206	+	0.139639i
$970$		0			0
$971$	28.2224	+	16.2942i	0.905701	+	0.522907i	0.879045	−	0.476738i	$-0.158181\pi$
$971$	28.2224	+	16.2942i	0.905701	+	0.522907i	0.0266555	+	0.999645i	$0.491514\pi$
$972$		0			0
$973$	12.5434	+	25.8398i	0.402124	+	0.828385i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.70522	+	6.36396i	−0.0545548	+	0.203601i	−0.987824	−	0.155577i	$-0.950276\pi$
$977$	−1.70522	+	6.36396i	−0.0545548	+	0.203601i	0.933269	+	0.359178i	$0.116943\pi$
$978$		0			0
$979$	−7.85641			−0.251092
$980$		0			0
$981$	−0.0717968			−0.00229229
$982$		0			0
$983$	−12.2982	+	45.8976i	−0.392252	+	1.46391i	0.434158	+	0.900837i	$0.357046\pi$
$983$	−12.2982	+	45.8976i	−0.392252	+	1.46391i	−0.826410	+	0.563068i	$0.809621\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.226633	−	0.466870i	−0.00721382	−	0.0148606i
$988$		0			0
$989$	−3.46410	−	2.00000i	−0.110152	−	0.0635963i
$990$		0			0
$991$	6.66025	+	11.5359i	0.211570	+	0.366450i	0.952206	−	0.305456i	$-0.0988091\pi$
$991$	6.66025	+	11.5359i	0.211570	+	0.366450i	−0.740636	+	0.671906i	$0.765476\pi$
$992$		0			0
$993$	21.6801	+	21.6801i	0.687996	+	0.687996i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−6.90018	−	1.84890i	−0.218531	−	0.0585552i	0.147892	−	0.989003i	$-0.452751\pi$
$997$	−6.90018	−	1.84890i	−0.218531	−	0.0585552i	−0.366423	+	0.930448i	$0.619418\pi$
$998$		0			0
$999$	−0.401924	+	0.696152i	−0.0127163	+	0.0220253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.a.1657.1	yes	8
5.2	odd	4		2100.2.ce.b.1993.2	yes	8
5.3	odd	4		2100.2.ce.b.1993.1	yes	8
5.4	even	2	inner	2100.2.ce.a.1657.2	yes	8
7.3	odd	6		2100.2.ce.b.157.1	yes	8
35.3	even	12	inner	2100.2.ce.a.493.1	✓	8
35.17	even	12	inner	2100.2.ce.a.493.2	yes	8
35.24	odd	6		2100.2.ce.b.157.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.a.493.1	✓	8	35.3	even	12	inner
2100.2.ce.a.493.2	yes	8	35.17	even	12	inner
2100.2.ce.a.1657.1	yes	8	1.1	even	1	trivial
2100.2.ce.a.1657.2	yes	8	5.4	even	2	inner
2100.2.ce.b.157.1	yes	8	7.3	odd	6
2100.2.ce.b.157.2	yes	8	35.24	odd	6
2100.2.ce.b.1993.1	yes	8	5.3	odd	4
2100.2.ce.b.1993.2	yes	8	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{3} +(-1.15539 - 2.38014i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{3} +(-1.15539 - 2.38014i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(0.366025 + 0.633975i) q^{11} +(0.707107 + 0.707107i) q^{13} +(-3.15660 - 0.845807i) q^{17} +(-0.767949 + 1.33013i) q^{19} +(2.59808 - 0.500000i) q^{21} +(0.138701 + 0.517638i) q^{23} +(0.707107 - 0.707107i) q^{27} +6.92820i q^{29} +(1.73205 - 1.00000i) q^{31} +(-0.707107 + 0.189469i) q^{33} +(-0.776457 + 0.208051i) q^{37} +(-0.866025 + 0.500000i) q^{39} +6.19615i q^{41} +(-5.27792 + 5.27792i) q^{43} +(-0.0507680 - 0.189469i) q^{47} +(-4.33013 + 5.50000i) q^{49} +(1.63397 - 2.83013i) q^{51} +(-5.08845 - 1.36345i) q^{53} +(-1.08604 - 1.08604i) q^{57} +(6.36603 + 11.0263i) q^{59} +(5.42820 + 3.13397i) q^{61} +(-0.189469 + 2.63896i) q^{63} +(1.81173 - 6.76148i) q^{67} -0.535898 q^{69} -8.00000 q^{71} +(-1.39563 + 5.20857i) q^{73} +(1.08604 - 1.60368i) q^{77} +(4.96410 + 2.86603i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.896575 + 0.896575i) q^{83} +(-6.69213 - 1.79315i) q^{87} +(-5.36603 + 9.29423i) q^{89} +(0.866025 - 2.50000i) q^{91} +(0.517638 + 1.93185i) q^{93} +(-7.39924 + 7.39924i) q^{97} -0.732051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{11} - 20 q^{19} + 20 q^{51} + 44 q^{59} - 12 q^{61} - 32 q^{69} - 64 q^{71} + 12 q^{79} + 4 q^{81} - 36 q^{89}+O(q^{100}) \) 8 * q - 4 * q^11 - 20 * q^19 + 20 * q^51 + 44 * q^59 - 12 * q^61 - 32 * q^69 - 64 * q^71 + 12 * q^79 + 4 * q^81 - 36 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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