LMFDB - Embedded newform 2100.2.ce.b.157.1

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			157.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.b.1993.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{3} +(-2.38014 - 1.15539i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{3} +(-2.38014 - 1.15539i) q^{7} +(0.866025 - 0.500000i) q^{9} +(0.366025 - 0.633975i) q^{11} +(-0.707107 - 0.707107i) q^{13} +(-0.845807 - 3.15660i) q^{17} +(0.767949 + 1.33013i) q^{19} +(2.59808 + 0.500000i) q^{21} +(-0.517638 - 0.138701i) q^{23} +(-0.707107 + 0.707107i) q^{27} +6.92820i q^{29} +(1.73205 + 1.00000i) q^{31} +(-0.189469 + 0.707107i) q^{33} +(0.208051 - 0.776457i) q^{37} +(0.866025 + 0.500000i) q^{39} -6.19615i q^{41} +(-5.27792 + 5.27792i) q^{43} +(-0.189469 - 0.0507680i) q^{47} +(4.33013 + 5.50000i) q^{49} +(1.63397 + 2.83013i) q^{51} +(1.36345 + 5.08845i) q^{53} +(-1.08604 - 1.08604i) q^{57} +(-6.36603 + 11.0263i) q^{59} +(5.42820 - 3.13397i) q^{61} +(-2.63896 + 0.189469i) q^{63} +(-6.76148 + 1.81173i) q^{67} +0.535898 q^{69} -8.00000 q^{71} +(-5.20857 + 1.39563i) q^{73} +(-1.60368 + 1.08604i) q^{77} +(-4.96410 + 2.86603i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.896575 - 0.896575i) q^{83} +(-1.79315 - 6.69213i) q^{87} +(5.36603 + 9.29423i) q^{89} +(0.866025 + 2.50000i) q^{91} +(-1.93185 - 0.517638i) q^{93} +(7.39924 - 7.39924i) q^{97} -0.732051i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.38014	−	1.15539i	−0.899608	−	0.436698i
$7$	−2.38014	−	1.15539i	−0.899608	−	0.436698i
$8$		0			0
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	0.366025	−	0.633975i	0.110361	−	0.191151i	−0.805555	−	0.592521i	$-0.798133\pi$
$11$	0.366025	−	0.633975i	0.110361	−	0.191151i	0.915916	+	0.401371i	$0.131466\pi$
$12$		0			0
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	0.602217	−	0.798333i	$-0.294284\pi$
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	−0.798333	+	0.602217i	$0.794284\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.845807	−	3.15660i	−0.205138	−	0.765587i	−0.989407	−	0.145166i	$-0.953628\pi$
$17$	−0.845807	−	3.15660i	−0.205138	−	0.765587i	0.784269	−	0.620421i	$-0.213038\pi$
$18$		0			0
$19$	0.767949	+	1.33013i	0.176180	+	0.305152i	0.940569	−	0.339603i	$-0.110293\pi$
$19$	0.767949	+	1.33013i	0.176180	+	0.305152i	−0.764389	+	0.644755i	$0.776959\pi$
$20$		0			0
$21$	2.59808	+	0.500000i	0.566947	+	0.109109i
$22$		0			0
$23$	−0.517638	−	0.138701i	−0.107935	−	0.0289211i	0.204447	−	0.978878i	$-0.434460\pi$
$23$	−0.517638	−	0.138701i	−0.107935	−	0.0289211i	−0.312382	+	0.949956i	$0.601127\pi$
$24$		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	0.647412	−	0.762140i	$-0.275851\pi$
$31$	1.73205	+	1.00000i	0.311086	+	0.179605i	−0.336327	+	0.941745i	$0.609185\pi$
$32$		0			0
$33$	−0.189469	+	0.707107i	−0.0329823	+	0.123091i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.208051	−	0.776457i	0.0342034	−	0.127649i	−0.946713	−	0.322078i	$-0.895619\pi$
$37$	0.208051	−	0.776457i	0.0342034	−	0.127649i	0.980917	+	0.194429i	$0.0622854\pi$
$38$		0			0
$39$	0.866025	+	0.500000i	0.138675	+	0.0800641i
$40$		0			0
$41$		−	6.19615i		−	0.967676i	−0.875157	−	0.483838i	$-0.839242\pi$
$41$		−	6.19615i		−	0.967676i	0.875157	−	0.483838i	$-0.160758\pi$
$42$		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
$47$	−0.189469	−	0.0507680i	−0.0276368	−	0.00740527i	0.244974	−	0.969530i	$-0.421221\pi$
$47$	−0.189469	−	0.0507680i	−0.0276368	−	0.00740527i	−0.272611	+	0.962124i	$0.587887\pi$
$48$		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
$53$	1.36345	+	5.08845i	0.187284	+	0.698952i	0.994130	+	0.108191i	$0.0345058\pi$
$53$	1.36345	+	5.08845i	0.187284	+	0.698952i	−0.806846	+	0.590761i	$0.798828\pi$
$54$		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	0.0702053	+	0.997533i	$0.477635\pi$
$59$	−6.36603	+	11.0263i	−0.828786	+	1.43550i	−0.898991	+	0.437967i	$0.855699\pi$
$60$		0			0
$61$	5.42820	−	3.13397i	0.695010	−	0.401264i	−0.110476	−	0.993879i	$-0.535238\pi$
$61$	5.42820	−	3.13397i	0.695010	−	0.401264i	0.805486	+	0.592614i	$0.201904\pi$
$62$		0			0
$63$	−2.63896	+	0.189469i	−0.332478	+	0.0238708i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.76148	+	1.81173i	−0.826046	+	0.221338i	−0.646988	−	0.762500i	$-0.723972\pi$
$67$	−6.76148	+	1.81173i	−0.826046	+	0.221338i	−0.179058	+	0.983838i	$0.557305\pi$
$68$		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
$73$	−5.20857	+	1.39563i	−0.609617	+	0.163346i	−0.550403	−	0.834899i	$-0.685526\pi$
$73$	−5.20857	+	1.39563i	−0.609617	+	0.163346i	−0.0592135	+	0.998245i	$0.518859\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.60368	+	1.08604i	−0.182757	+	0.123766i
$78$		0			0
$79$	−4.96410	+	2.86603i	−0.558505	+	0.322453i	−0.752545	−	0.658541i	$-0.771174\pi$
$79$	−4.96410	+	2.86603i	−0.558505	+	0.322453i	0.194040	+	0.980994i	$0.437841\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	−0.896575	−	0.896575i	−0.0984119	−	0.0984119i	0.656187	−	0.754599i	$-0.272168\pi$
$83$	−0.896575	−	0.896575i	−0.0984119	−	0.0984119i	−0.754599	+	0.656187i	$0.772168\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.79315	−	6.69213i	−0.192246	−	0.717472i
$88$		0			0
$89$	5.36603	+	9.29423i	0.568798	+	0.985186i	0.996685	+	0.0813544i	$0.0259245\pi$
$89$	5.36603	+	9.29423i	0.568798	+	0.985186i	−0.427888	+	0.903832i	$0.640742\pi$
$90$		0			0
$91$	0.866025	+	2.50000i	0.0907841	+	0.262071i
$92$		0			0
$93$	−1.93185	−	0.517638i	−0.200324	−	0.0536766i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.39924	−	7.39924i	0.751279	−	0.751279i	−0.223439	−	0.974718i	$-0.571728\pi$
$97$	7.39924	−	7.39924i	0.751279	−	0.751279i	0.974718	+	0.223439i	$0.0717284\pi$
$98$		0			0
$99$		−	0.732051i		−	0.0735739i
$100$		0			0
$101$	−2.83013	−	1.63397i	−0.281608	−	0.162587i	0.352543	−	0.935796i	$-0.385317\pi$
$101$	−2.83013	−	1.63397i	−0.281608	−	0.162587i	−0.634151	+	0.773209i	$0.718650\pi$
$102$		0			0
$103$	−3.27671	+	12.2289i	−0.322864	+	1.20495i	0.593577	+	0.804777i	$0.297715\pi$
$103$	−3.27671	+	12.2289i	−0.322864	+	1.20495i	−0.916441	+	0.400169i	$0.868951\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.91636	+	10.8840i	−0.281935	+	1.05220i	0.669115	+	0.743159i	$0.266673\pi$
$107$	−2.91636	+	10.8840i	−0.281935	+	1.05220i	−0.951050	+	0.309037i	$0.899993\pi$
$108$		0			0
$109$	−0.0621778	−	0.0358984i	−0.00595556	−	0.00343844i	0.497019	−	0.867740i	$-0.334428\pi$
$109$	−0.0621778	−	0.0358984i	−0.00595556	−	0.00343844i	−0.502975	+	0.864301i	$0.667761\pi$
$110$		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
$117$	−0.965926	−	0.258819i	−0.0892999	−	0.0239278i
$118$		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
$123$	1.60368	+	5.98502i	0.144599	+	0.539651i
$124$		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	−0.611691	−	0.791096i	$-0.709511\pi$
$131$	−2.66025	+	1.53590i	−0.232427	+	0.134192i	0.379264	+	0.925289i	$0.376177\pi$
$132$		0			0
$133$	−0.291005	−	4.05317i	−0.0252333	−	0.351455i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.79555	−	1.55291i	0.495148	−	0.132674i	−0.00259945	−	0.999997i	$-0.500827\pi$
$137$	5.79555	−	1.55291i	0.495148	−	0.132674i	0.497747	+	0.867322i	$0.334161\pi$
$138$		0			0
$139$	10.8564			0.920828			0.460414	−	0.887704i	$-0.347701\pi$
$139$	10.8564			0.920828			0.460414	+	0.887704i	$0.347701\pi$
$140$		0			0
$141$	0.196152			0.0165190
$142$		0			0
$143$	−0.707107	+	0.189469i	−0.0591312	+	0.0158442i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.60609	−	4.19187i	−0.462382	−	0.345740i
$148$		0			0
$149$	−13.0981	+	7.56218i	−1.07304	+	0.619518i	−0.929009	−	0.370056i	$-0.879338\pi$
$149$	−13.0981	+	7.56218i	−1.07304	+	0.619518i	−0.144027	+	0.989574i	$0.546005\pi$
$150$		0			0
$151$	−3.33013	+	5.76795i	−0.271002	+	0.469389i	−0.969119	−	0.246595i	$-0.920688\pi$
$151$	−3.33013	+	5.76795i	−0.271002	+	0.469389i	0.698117	+	0.715984i	$0.254022\pi$
$152$		0			0
$153$	−2.31079	−	2.31079i	−0.186816	−	0.186816i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.84512	−	14.3502i	−0.306874	−	1.14527i	−0.931320	−	0.364202i	$-0.881342\pi$
$157$	−3.84512	−	14.3502i	−0.306874	−	1.14527i	0.624446	−	0.781068i	$-0.285325\pi$
$158$		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
$163$	−2.89778	−	0.776457i	−0.226971	−	0.0608168i	0.143541	−	0.989644i	$-0.454151\pi$
$163$	−2.89778	−	0.776457i	−0.226971	−	0.0608168i	−0.370512	+	0.928828i	$0.620818\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.4877	+	12.4877i	−0.966326	+	0.966326i	−0.999451	−	0.0331251i	$-0.989454\pi$
$167$	−12.4877	+	12.4877i	−0.966326	+	0.966326i	0.0331251	+	0.999451i	$0.489454\pi$
$168$		0			0
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	1.33013	+	0.767949i	0.101717	+	0.0587265i
$172$		0			0
$173$	−5.03768	+	18.8009i	−0.383008	+	1.42940i	0.458276	+	0.888810i	$0.348467\pi$
$173$	−5.03768	+	18.8009i	−0.383008	+	1.42940i	−0.841283	+	0.540594i	$0.818199\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.29530	−	12.2982i	0.247690	−	0.924391i
$178$		0			0
$179$	−2.19615	−	1.26795i	−0.164148	−	0.0947710i	0.415675	−	0.909513i	$-0.363545\pi$
$179$	−2.19615	−	1.26795i	−0.164148	−	0.0947710i	−0.579824	+	0.814742i	$0.696879\pi$
$180$		0			0
$181$		−	14.3923i		−	1.06977i	−0.844924	−	0.534886i	$-0.820355\pi$
$181$		−	14.3923i		−	1.06977i	0.844924	−	0.534886i	$-0.179645\pi$
$182$		0			0
$183$	−4.43211	+	4.43211i	−0.327631	+	0.327631i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.31079	−	0.619174i	−0.168982	−	0.0452785i
$188$		0			0
$189$	2.50000	−	0.866025i	0.181848	−	0.0629941i
$190$		0			0
$191$	6.90192	+	11.9545i	0.499406	+	0.864996i	1.00000		0.000686128i	$-0.000218401\pi$
$191$	6.90192	+	11.9545i	0.499406	+	0.864996i	−0.500594	+	0.865682i	$0.666885\pi$
$192$		0			0
$193$	5.51815	+	20.5940i	0.397205	+	1.48239i	0.817991	+	0.575231i	$0.195088\pi$
$193$	5.51815	+	20.5940i	0.397205	+	1.48239i	−0.420786	+	0.907160i	$0.638246\pi$
$194$		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	$-0.815996\pi$
$199$	0.767949	−	1.33013i	0.0544385	−	0.0942902i	0.891960	+	0.452113i	$0.149330\pi$
$200$		0			0
$201$	6.06218	−	3.50000i	0.427593	−	0.246871i
$202$		0			0
$203$	8.00481	−	16.4901i	0.561827	−	1.15738i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.517638	+	0.138701i	−0.0359783	+	0.00964037i
$208$		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
$213$	7.72741	−	2.07055i	0.529473	−	0.141872i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.96713	−	4.38134i	−0.201422	−	0.297425i
$218$		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	0.110309	−	0.993897i	$-0.464816\pi$
$223$	−13.1948	−	13.1948i	−0.883589	−	0.883589i	−0.993897	+	0.110309i	$0.964816\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.58630	+	13.3843i	0.238031	+	0.888345i	0.976759	+	0.214341i	$0.0687603\pi$
$227$	3.58630	+	13.3843i	0.238031	+	0.888345i	−0.738728	+	0.674004i	$0.764573\pi$
$228$		0			0
$229$	−4.13397	−	7.16025i	−0.273181	−	0.473163i	0.696494	−	0.717563i	$-0.254742\pi$
$229$	−4.13397	−	7.16025i	−0.273181	−	0.473163i	−0.969675	+	0.244400i	$0.921409\pi$
$230$		0			0
$231$	1.26795	−	1.46410i	0.0834249	−	0.0963308i
$232$		0			0
$233$	7.02030	+	1.88108i	0.459915	+	0.123234i	0.481335	−	0.876537i	$-0.340152\pi$
$233$	7.02030	+	1.88108i	0.459915	+	0.123234i	−0.0214199	+	0.999771i	$0.506819\pi$
$234$		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	0.522254	−	0.852790i	$-0.325091\pi$
$241$	0.696152	+	0.401924i	0.0448431	+	0.0258902i	−0.477411	+	0.878680i	$0.658425\pi$
$242$		0			0
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.397520	−	1.48356i	0.0252936	−	0.0943969i
$248$		0			0
$249$	1.09808	+	0.633975i	0.0695878	+	0.0401765i
$250$		0			0
$251$		−	20.5885i		−	1.29953i	−0.760134	−	0.649766i	$-0.774867\pi$
$251$		−	20.5885i		−	1.29953i	0.760134	−	0.649766i	$-0.225133\pi$
$252$		0			0
$253$	−0.277401	+	0.277401i	−0.0174401	+	0.0174401i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	22.7153	+	6.08656i	1.41694	+	0.379669i	0.884399	−	0.466732i	$-0.154569\pi$
$257$	22.7153	+	6.08656i	1.41694	+	0.379669i	0.532546	+	0.846401i	$0.321235\pi$
$258$		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
$263$	−5.93426	−	22.1469i	−0.365922	−	1.36564i	−0.866167	−	0.499755i	$-0.833423\pi$
$263$	−5.93426	−	22.1469i	−0.365922	−	1.36564i	0.500245	−	0.865884i	$-0.333243\pi$
$264$		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	0.283663	+	0.958924i	$0.408450\pi$
$269$	−11.2942	+	19.5622i	−0.688621	+	1.19273i	−0.972284	+	0.233803i	$0.924883\pi$
$270$		0			0
$271$	−0.928203	+	0.535898i	−0.0563843	+	0.0325535i	−0.527927	−	0.849290i	$-0.677031\pi$
$271$	−0.928203	+	0.535898i	−0.0563843	+	0.0325535i	0.471543	+	0.881843i	$0.343697\pi$
$272$		0			0
$273$	−1.48356	−	2.19067i	−0.0897894	−	0.132585i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.4357	−	2.79624i	0.627021	−	0.168010i	0.0687037	−	0.997637i	$-0.478114\pi$
$277$	10.4357	−	2.79624i	0.627021	−	0.168010i	0.558318	+	0.829627i	$0.311447\pi$
$278$		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
$283$	23.8200	−	6.38254i	1.41595	−	0.379403i	0.531905	−	0.846804i	$-0.321476\pi$
$283$	23.8200	−	6.38254i	1.41595	−	0.379403i	0.884045	+	0.467401i	$0.154810\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.15900	+	14.7477i	−0.422582	+	0.870530i
$288$		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	0.791985	−	0.610541i	$-0.209048\pi$
$293$	3.10583	+	3.10583i	0.181444	+	0.181444i	−0.610541	+	0.791985i	$0.709048\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.189469	+	0.707107i	0.0109941	+	0.0410305i
$298$		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
$303$	3.15660	+	0.845807i	0.181342	+	0.0485904i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−6.69213	+	6.69213i	−0.381940	+	0.381940i	−0.871801	−	0.489861i	$-0.837048\pi$
$307$	−6.69213	+	6.69213i	−0.381940	+	0.381940i	0.489861	+	0.871801i	$0.337048\pi$
$308$		0			0
$309$		−	12.6603i		−	0.720217i
$310$		0			0
$311$	−5.19615	−	3.00000i	−0.294647	−	0.170114i	0.345389	−	0.938460i	$-0.387747\pi$
$311$	−5.19615	−	3.00000i	−0.294647	−	0.170114i	−0.640036	+	0.768345i	$0.721080\pi$
$312$		0			0
$313$	2.44949	−	9.14162i	0.138453	−	0.516715i	−0.861506	−	0.507747i	$-0.830479\pi$
$313$	2.44949	−	9.14162i	0.138453	−	0.516715i	0.999960	−	0.00896828i	$-0.00285473\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.76028	+	17.7656i	−0.267364	+	0.997816i	0.693424	+	0.720530i	$0.256101\pi$
$317$	−4.76028	+	17.7656i	−0.267364	+	0.997816i	−0.960788	+	0.277286i	$0.910565\pi$
$318$		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
$327$	0.0693504	+	0.0185824i	0.00383508	+	0.00102761i
$328$		0			0
$329$	0.392305	+	0.339746i	0.0216285	+	0.0187308i
$330$		0			0
$331$	15.3301	+	26.5526i	0.842620	+	1.45946i	0.887672	+	0.460476i	$0.152321\pi$
$331$	15.3301	+	26.5526i	0.842620	+	1.45946i	−0.0450522	+	0.998985i	$0.514345\pi$
$332$		0			0
$333$	−0.208051	−	0.776457i	−0.0114011	−	0.0425496i
$334$		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
$343$	−3.95164	−	18.0938i	−0.213368	−	0.976972i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.19239	−	2.46309i	0.493473	−	0.132226i	−0.00349604	−	0.999994i	$-0.501113\pi$
$347$	9.19239	−	2.46309i	0.493473	−	0.132226i	0.496969	+	0.867768i	$0.334446\pi$
$348$		0			0
$349$	−0.928203			−0.0496856			−0.0248428	−	0.999691i	$-0.507909\pi$
$349$	−0.928203			−0.0496856			−0.0248428	+	0.999691i	$0.507909\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$		0			0
$353$	5.46739	−	1.46498i	0.291000	−	0.0779731i	−0.110366	−	0.993891i	$-0.535202\pi$
$353$	5.46739	−	1.46498i	0.291000	−	0.0779731i	0.401366	+	0.915918i	$0.368536\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.619174	−	8.62398i	−0.0327702	−	0.456430i
$358$		0			0
$359$	−8.70577	+	5.02628i	−0.459473	+	0.265277i	−0.711823	−	0.702359i	$-0.752130\pi$
$359$	−8.70577	+	5.02628i	−0.459473	+	0.265277i	0.252350	+	0.967636i	$0.418797\pi$
$360$		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
$367$	−0.138701	−	0.517638i	−0.00724012	−	0.0270205i	0.962211	−	0.272304i	$-0.0877856\pi$
$367$	−0.138701	−	0.517638i	−0.00724012	−	0.0270205i	−0.969451	+	0.245283i	$0.921119\pi$
$368$		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
$373$	22.2671	+	5.96644i	1.15294	+	0.308931i	0.784145	−	0.620578i	$-0.213102\pi$
$373$	22.2671	+	5.96644i	1.15294	+	0.308931i	0.368800	+	0.929509i	$0.379769\pi$
$374$		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
$383$	6.65497	−	24.8367i	0.340053	−	1.26909i	−0.558233	−	0.829684i	$-0.688521\pi$
$383$	6.65497	−	24.8367i	0.340053	−	1.26909i	0.898286	−	0.439411i	$-0.144813\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.93185	+	7.20977i	−0.0982015	+	0.366493i
$388$		0			0
$389$	−24.4186	−	14.0981i	−1.23807	−	0.714801i	−0.269372	−	0.963036i	$-0.586816\pi$
$389$	−24.4186	−	14.0981i	−1.23807	−	0.714801i	−0.968700	+	0.248235i	$0.920149\pi$
$390$		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
$397$	13.0053	+	3.48477i	0.652718	+	0.174895i	0.569958	−	0.821674i	$-0.306960\pi$
$397$	13.0053	+	3.48477i	0.652718	+	0.174895i	0.0827608	+	0.996569i	$0.473626\pi$
$398$		0			0
$399$	1.33013	+	3.83975i	0.0665896	+	0.192228i
$400$		0			0
$401$	−2.29423	−	3.97372i	−0.114568	−	0.198438i	0.803039	−	0.595927i	$-0.203215\pi$
$401$	−2.29423	−	3.97372i	−0.114568	−	0.198438i	−0.917607	+	0.397489i	$0.869882\pi$
$402$		0			0
$403$	−0.517638	−	1.93185i	−0.0257854	−	0.0962324i
$404$		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	$-0.672410\pi$
$409$	9.79423	−	16.9641i	0.484293	−	0.838821i	0.999837	+	0.0180424i	$0.00574338\pi$
$410$		0			0
$411$	−5.19615	+	3.00000i	−0.256307	+	0.147979i
$412$		0			0
$413$	27.8917	−	18.8888i	1.37246	−	0.929458i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−10.4865	+	2.80984i	−0.513525	+	0.137599i
$418$		0			0
$419$	38.0526			1.85899			0.929495	−	0.368836i	$-0.120244\pi$
$419$	38.0526			1.85899			0.929495	+	0.368836i	$0.120244\pi$
$420$		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
$423$	−0.189469	+	0.0507680i	−0.00921228	+	0.00246842i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−16.5409	+	1.18758i	−0.800468	+	0.0574710i
$428$		0			0
$429$	0.633975	−	0.366025i	0.0306086	−	0.0176719i
$430$		0			0
$431$	−12.4641	+	21.5885i	−0.600375	+	1.03988i	0.392390	+	0.919799i	$0.371649\pi$
$431$	−12.4641	+	21.5885i	−0.600375	+	1.03988i	−0.992764	+	0.120080i	$0.961685\pi$
$432$		0			0
$433$	−26.4911	−	26.4911i	−1.27308	−	1.27308i	−0.944462	−	0.328620i	$-0.893417\pi$
$433$	−26.4911	−	26.4911i	−1.27308	−	1.27308i	−0.328620	−	0.944462i	$-0.606583\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.213030	−	0.795040i	−0.0101906	−	0.0380319i
$438$		0			0
$439$	−13.8923	−	24.0622i	−0.663044	−	1.14843i	−0.979812	−	0.199922i	$-0.935931\pi$
$439$	−13.8923	−	24.0622i	−0.663044	−	1.14843i	0.316768	−	0.948503i	$-0.397402\pi$
$440$		0			0
$441$	6.50000	+	2.59808i	0.309524	+	0.123718i
$442$		0			0
$443$	37.8420	+	10.1397i	1.79793	+	0.481753i	0.993651	−	0.112503i	$-0.0358867\pi$
$443$	37.8420	+	10.1397i	1.79793	+	0.481753i	0.804276	+	0.594256i	$0.202553\pi$
$444$		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
$453$	1.72380	−	6.43331i	0.0809912	−	0.302263i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.10274	−	7.84752i	0.0983619	−	0.367092i	−0.899146	−	0.437649i	$-0.855811\pi$
$457$	2.10274	−	7.84752i	0.0983619	−	0.367092i	0.997508	+	0.0705575i	$0.0224778\pi$
$458$		0			0
$459$	2.83013	+	1.63397i	0.132099	+	0.0762674i
$460$		0			0
$461$		−	37.7128i		−	1.75646i	−0.478238	−	0.878230i	$-0.658724\pi$
$461$		−	37.7128i		−	1.75646i	0.478238	−	0.878230i	$-0.341276\pi$
$462$		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
$467$	−0.138701	−	0.0371647i	−0.00641830	−	0.00171978i	0.255608	−	0.966780i	$-0.417724\pi$
$467$	−0.138701	−	0.0371647i	−0.00641830	−	0.00171978i	−0.262027	+	0.965061i	$0.584391\pi$
$468$		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
$473$	1.41421	+	5.27792i	0.0650256	+	0.242679i
$474$		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	0.210717	+	0.977547i	$0.432420\pi$
$479$	−16.2224	+	28.0981i	−0.741222	+	1.28383i	−0.951939	+	0.306287i	$0.900913\pi$
$480$		0			0
$481$	−0.696152	+	0.401924i	−0.0317418	+	0.0183261i
$482$		0			0
$483$	−1.27551	−	0.619174i	−0.0580378	−	0.0281734i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	9.00292	−	2.41233i	0.407961	−	0.109313i	−0.0490015	−	0.998799i	$-0.515604\pi$
$487$	9.00292	−	2.41233i	0.407961	−	0.109313i	0.456963	+	0.889486i	$0.348937\pi$
$488$		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
$493$	21.8695	−	5.85993i	0.984955	−	0.263918i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	19.0411	+	9.24316i	0.854111	+	0.414612i
$498$		0			0
$499$	7.96410	−	4.59808i	0.356522	−	0.205838i	−0.311032	−	0.950399i	$-0.600675\pi$
$499$	7.96410	−	4.59808i	0.356522	−	0.205838i	0.667554	+	0.744561i	$0.267341\pi$
$500$		0			0
$501$	8.83013	−	15.2942i	0.394501	−	0.683296i
$502$		0			0
$503$	−14.6969	−	14.6969i	−0.655304	−	0.655304i	0.298961	−	0.954265i	$-0.403360\pi$
$503$	−14.6969	−	14.6969i	−0.655304	−	0.655304i	−0.954265	+	0.298961i	$0.903360\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.10583	+	11.5911i	0.137935	+	0.514779i
$508$		0			0
$509$	−7.26795	−	12.5885i	−0.322146	−	0.557974i	0.658784	−	0.752332i	$-0.271071\pi$
$509$	−7.26795	−	12.5885i	−0.322146	−	0.557974i	−0.980931	+	0.194358i	$0.937738\pi$
$510$		0			0
$511$	14.0096	+	2.69615i	0.619749	+	0.119271i
$512$		0			0
$513$	−1.48356	−	0.397520i	−0.0655009	−	0.0175509i
$514$		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	0.448306	−	0.893880i	$-0.352027\pi$
$521$	−2.32051	−	1.33975i	−0.101663	−	0.0586953i	−0.549970	+	0.835185i	$0.685361\pi$
$522$		0			0
$523$	3.96524	−	14.7985i	0.173388	−	0.647092i	−0.823433	−	0.567414i	$-0.807944\pi$
$523$	3.96524	−	14.7985i	0.173388	−	0.647092i	0.996821	−	0.0796783i	$-0.0253893\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.69161	−	6.31319i	0.0736879	−	0.275007i
$528$		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
$537$	2.44949	+	0.656339i	0.105703	+	0.0283231i
$538$		0			0
$539$	5.07180	−	0.732051i	0.218458	−	0.0315317i
$540$		0			0
$541$	1.83975	+	3.18653i	0.0790969	+	0.137000i	0.902861	−	0.429934i	$-0.141463\pi$
$541$	1.83975	+	3.18653i	0.0790969	+	0.137000i	−0.823764	+	0.566933i	$0.808130\pi$
$542$		0			0
$543$	3.72500	+	13.9019i	0.159855	+	0.596588i
$544$		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
$553$	15.1266	−	1.08604i	0.643250	−	0.0461833i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15.8338	−	4.24264i	0.670898	−	0.179766i	0.0927384	−	0.995691i	$-0.470438\pi$
$557$	15.8338	−	4.24264i	0.670898	−	0.179766i	0.578159	+	0.815924i	$0.303771\pi$
$558$		0			0
$559$	7.46410			0.315698
$560$		0			0
$561$	2.39230			0.101003
$562$		0			0
$563$	5.32868	−	1.42782i	0.224577	−	0.0601753i	−0.144776	−	0.989465i	$-0.546246\pi$
$563$	5.32868	−	1.42782i	0.224577	−	0.0601753i	0.369353	+	0.929289i	$0.379579\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.19067	+	1.48356i	−0.0919995	+	0.0623038i
$568$		0			0
$569$	−6.41858	+	3.70577i	−0.269081	+	0.155354i	−0.628470	−	0.777834i	$-0.716318\pi$
$569$	−6.41858	+	3.70577i	−0.269081	+	0.155354i	0.359389	+	0.933188i	$0.382985\pi$
$570$		0			0
$571$	−19.4545	+	33.6962i	−0.814145	+	1.41014i	0.0957956	+	0.995401i	$0.469460\pi$
$571$	−19.4545	+	33.6962i	−0.814145	+	1.41014i	−0.909940	+	0.414739i	$0.863873\pi$
$572$		0			0
$573$	−9.76079	−	9.76079i	−0.407763	−	0.407763i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	2.58819	+	9.65926i	0.107748	+	0.402120i	0.998642	−	0.0520899i	$-0.0165882\pi$
$577$	2.58819	+	9.65926i	0.107748	+	0.402120i	−0.890895	+	0.454210i	$0.849922\pi$
$578$		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
$583$	3.72500	+	0.998111i	0.154274	+	0.0413376i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.1817	+	18.1817i	−0.750439	+	0.750439i	−0.974561	−	0.224122i	$-0.928049\pi$
$587$	−18.1817	+	18.1817i	−0.750439	+	0.750439i	0.224122	+	0.974561i	$0.428049\pi$
$588$		0			0
$589$			3.07180i			0.126571i
$590$		0			0
$591$	−16.3923	−	9.46410i	−0.674289	−	0.389301i
$592$		0			0
$593$	−7.03390	+	26.2509i	−0.288848	+	1.07799i	0.657134	+	0.753774i	$0.271769\pi$
$593$	−7.03390	+	26.2509i	−0.288848	+	1.07799i	−0.945982	+	0.324221i	$0.894898\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.397520	+	1.48356i	−0.0162694	+	0.0607182i
$598$		0			0
$599$	−20.9545	−	12.0981i	−0.856177	−	0.494314i	0.00655324	−	0.999979i	$-0.497914\pi$
$599$	−20.9545	−	12.0981i	−0.856177	−	0.494314i	−0.862730	+	0.505665i	$0.831247\pi$
$600$		0			0
$601$		−	32.5167i		−	1.32638i	−0.748450	−	0.663191i	$-0.769202\pi$
$601$		−	32.5167i		−	1.32638i	0.748450	−	0.663191i	$-0.230798\pi$
$602$		0			0
$603$	−4.94975	+	4.94975i	−0.201569	+	0.201569i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	2.56961	+	0.688524i	0.104297	+	0.0279463i	0.310590	−	0.950544i	$-0.399473\pi$
$607$	2.56961	+	0.688524i	0.104297	+	0.0279463i	−0.206293	+	0.978490i	$0.566140\pi$
$608$		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
$613$	−0.0371647	−	0.138701i	−0.00150107	−	0.00560207i	0.965171	−	0.261619i	$-0.0842564\pi$
$613$	−0.0371647	−	0.138701i	−0.00150107	−	0.00560207i	−0.966672	+	0.256017i	$0.917590\pi$
$614$		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	$-0.718203\pi$
$619$	8.80385	−	15.2487i	0.353857	−	0.612897i	0.986922	+	0.161201i	$0.0515368\pi$
$620$		0			0
$621$	0.464102	−	0.267949i	0.0186238	−	0.0107524i
$622$		0			0
$623$	−2.03339	−	28.3214i	−0.0814660	−	1.13467i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.08604	+	0.291005i	−0.0433724	+	0.0116216i
$628$		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
$633$	11.8499	−	3.17518i	0.470992	−	0.126202i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.827225	−	6.95095i	0.0327759	−	0.275407i
$638$		0			0
$639$	−6.92820	+	4.00000i	−0.274075	+	0.158238i
$640$		0			0
$641$	−8.58846	+	14.8756i	−0.339224	+	0.587553i	−0.984287	−	0.176577i	$-0.943498\pi$
$641$	−8.58846	+	14.8756i	−0.339224	+	0.587553i	0.645063	+	0.764129i	$0.276831\pi$
$642$		0			0
$643$	8.09274	+	8.09274i	0.319147	+	0.319147i	0.848439	−	0.529293i	$-0.177543\pi$
$643$	8.09274	+	8.09274i	0.319147	+	0.319147i	−0.529293	+	0.848439i	$0.677543\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.46309	−	9.19239i	−0.0968342	−	0.361390i	0.900457	−	0.434945i	$-0.143232\pi$
$647$	−2.46309	−	9.19239i	−0.0968342	−	0.361390i	−0.997291	+	0.0735550i	$0.976566\pi$
$648$		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
$653$	29.5462	+	7.91688i	1.15623	+	0.309811i	0.785460	−	0.618913i	$-0.212427\pi$
$653$	29.5462	+	7.91688i	1.15623	+	0.309811i	0.370772	+	0.928724i	$0.379093\pi$
$654$		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	0.907262	−	0.420566i	$-0.138169\pi$
$661$	25.6244	+	14.7942i	0.996672	+	0.575429i	0.0894100	+	0.995995i	$0.471502\pi$
$662$		0			0
$663$	0.845807	−	3.15660i	0.0328484	−	0.122592i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.960947	−	3.58630i	0.0372080	−	0.138862i
$668$		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
$677$	−3.34607	−	0.896575i	−0.128600	−	0.0344582i	0.193945	−	0.981012i	$-0.437872\pi$
$677$	−3.34607	−	0.896575i	−0.128600	−	0.0344582i	−0.322545	+	0.946554i	$0.604538\pi$
$678$		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
$683$	−3.81294	−	14.2301i	−0.145898	−	0.544498i	−0.999714	−	0.0239233i	$-0.992384\pi$
$683$	−3.81294	−	14.2301i	−0.145898	−	0.544498i	0.853816	−	0.520575i	$-0.174282\pi$
$684$		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	−0.951609	−	0.307311i	$-0.900571\pi$
$691$	−30.5263	+	17.6244i	−1.16127	+	0.670462i	−0.209665	+	0.977773i	$0.567237\pi$
$692$		0			0
$693$	−0.845807	+	1.74238i	−0.0321296	+	0.0661877i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−19.5588	+	5.24075i	−0.740841	+	0.198508i
$698$		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
$703$	1.19256	−	0.319545i	0.0449782	−	0.0120519i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.84821	+	7.15900i	0.182336	+	0.269242i
$708$		0			0
$709$	−28.4545	+	16.4282i	−1.06863	+	0.616974i	−0.927807	−	0.373061i	$-0.878308\pi$
$709$	−28.4545	+	16.4282i	−1.06863	+	0.616974i	−0.140824	+	0.990035i	$0.544975\pi$
$710$		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
$717$	−2.92996	−	10.9348i	−0.109421	−	0.408367i
$718$		0			0
$719$	17.7583	+	30.7583i	0.662274	+	1.14709i	0.980017	+	0.198915i	$0.0637418\pi$
$719$	17.7583	+	30.7583i	0.662274	+	1.14709i	−0.317743	+	0.948177i	$0.602925\pi$
$720$		0			0
$721$	21.9282	−	25.3205i	0.816649	−	0.942985i
$722$		0			0
$723$	−0.776457	−	0.208051i	−0.0288768	−	0.00773750i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	7.91688	−	7.91688i	0.293621	−	0.293621i	−0.544888	−	0.838509i	$-0.683428\pi$
$727$	7.91688	−	7.91688i	0.293621	−	0.293621i	0.838509	+	0.544888i	$0.183428\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	21.1244	+	12.1962i	0.781313	+	0.451091i
$732$		0			0
$733$	−2.46807	+	9.21097i	−0.0911603	+	0.340215i	−0.996409	−	0.0846664i	$-0.973018\pi$
$733$	−2.46807	+	9.21097i	−0.0911603	+	0.340215i	0.905249	+	0.424881i	$0.139684\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.32628	+	4.94975i	−0.0488542	+	0.182326i
$738$		0			0
$739$	31.9641	+	18.4545i	1.17582	+	0.678859i	0.955044	−	0.296466i	$-0.0958080\pi$
$739$	31.9641	+	18.4545i	1.17582	+	0.678859i	0.220775	+	0.975325i	$0.429141\pi$
$740$		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
$747$	−1.22474	−	0.328169i	−0.0448111	−	0.0120071i
$748$		0			0
$749$	19.5167	−	22.5359i	0.713123	−	0.823444i
$750$		0			0
$751$	12.0622	+	20.8923i	0.440155	+	0.762371i	0.997701	−	0.0677754i	$-0.0215901\pi$
$751$	12.0622	+	20.8923i	0.440155	+	0.762371i	−0.557545	+	0.830146i	$0.688257\pi$
$752$		0			0
$753$	5.32868	+	19.8869i	0.194188	+	0.724720i
$754$		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	−0.596201	−	0.802835i	$-0.703324\pi$
$761$	−5.49038	+	3.16987i	−0.199026	+	0.114908i	0.397175	+	0.917743i	$0.369991\pi$
$762$		0			0
$763$	0.106515	+	0.157283i	0.00385611	+	0.00569403i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.2982	−	3.29530i	0.444063	−	0.118986i
$768$		0			0
$769$	−13.3205			−0.480350			−0.240175	−	0.970730i	$-0.577205\pi$
$769$	−13.3205			−0.480350			−0.240175	+	0.970730i	$0.577205\pi$
$770$		0			0
$771$	−23.5167			−0.846932
$772$		0			0
$773$	−43.2586	+	11.5911i	−1.55590	+	0.416903i	−0.931364	−	0.364089i	$-0.881380\pi$
$773$	−43.2586	+	11.5911i	−1.55590	+	0.416903i	−0.624540	+	0.780993i	$0.714714\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.928761	−	1.91327i	0.0333191	−	0.0686382i
$778$		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
$787$	8.17569	+	30.5121i	0.291432	+	1.08764i	0.944010	+	0.329917i	$0.107021\pi$
$787$	8.17569	+	30.5121i	0.291432	+	1.08764i	−0.652578	+	0.757722i	$0.726312\pi$
$788$		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
$793$	−6.05437	−	1.62226i	−0.214997	−	0.0576083i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.2789	+	15.2789i	−0.541208	+	0.541208i	−0.923883	−	0.382675i	$-0.875003\pi$
$797$	−15.2789	+	15.2789i	−0.541208	+	0.541208i	0.382675	+	0.923883i	$0.375003\pi$
$798$		0			0
$799$			0.641016i			0.0226775i
$800$		0			0
$801$	9.29423	+	5.36603i	0.328395	+	0.189599i
$802$		0			0
$803$	−1.02167	+	3.81294i	−0.0360541	+	0.134556i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.84632	−	21.8188i	0.205800	−	0.768057i
$808$		0			0
$809$	−38.5692	−	22.2679i	−1.35602	−	0.782899i	−0.366937	−	0.930246i	$-0.619593\pi$
$809$	−38.5692	−	22.2679i	−1.35602	−	0.782899i	−0.989085	+	0.147347i	$0.952927\pi$
$810$		0			0
$811$		−	54.8564i		−	1.92627i	−0.269020	−	0.963134i	$-0.586700\pi$
$811$		−	54.8564i		−	1.92627i	0.269020	−	0.963134i	$-0.413300\pi$
$812$		0			0
$813$	0.757875	−	0.757875i	0.0265798	−	0.0265798i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−11.0735	−	2.96713i	−0.387412	−	0.103807i
$818$		0			0
$819$	2.00000	+	1.73205i	0.0698857	+	0.0605228i
$820$		0			0
$821$	17.1699	+	29.7391i	0.599233	+	1.03790i	0.992935	+	0.118663i	$0.0378609\pi$
$821$	17.1699	+	29.7391i	0.599233	+	1.03790i	−0.393702	+	0.919238i	$0.628806\pi$
$822$		0			0
$823$	8.88280	+	33.1511i	0.309635	+	1.15557i	0.928882	+	0.370377i	$0.120771\pi$
$823$	8.88280	+	33.1511i	0.309635	+	1.15557i	−0.619247	+	0.785197i	$0.712562\pi$
$824$		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	$-0.758322\pi$
$829$	6.72243	−	11.6436i	0.233480	−	0.404399i	0.958830	+	0.283981i	$0.0916554\pi$
$830$		0			0
$831$	−9.35641	+	5.40192i	−0.324570	+	0.187391i
$832$		0			0
$833$	13.6988	−	18.3204i	0.474636	−	0.634764i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.93185	+	0.517638i	−0.0667746	+	0.0178922i
$838$		0			0
$839$	51.9615			1.79391			0.896956	−	0.442121i	$-0.145774\pi$
$839$	51.9615			1.79391			0.896956	+	0.442121i	$0.145774\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$		0			0
$843$	31.9957	−	8.57321i	1.10199	−	0.295277i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.98262	−	27.6143i	−0.0681236	−	0.948840i
$848$		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	0.388718	−	0.921357i	$-0.372918\pi$
$853$	−15.5563	−	15.5563i	−0.532639	−	0.532639i	−0.921357	+	0.388718i	$0.872918\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.5539	−	43.1199i	−0.394675	−	1.47295i	−0.822333	−	0.569007i	$-0.807328\pi$
$857$	−11.5539	−	43.1199i	−0.394675	−	1.47295i	0.427657	−	0.903941i	$-0.359339\pi$
$858$		0			0
$859$	−6.46410	−	11.1962i	−0.220552	−	0.382008i	0.734424	−	0.678691i	$-0.237453\pi$
$859$	−6.46410	−	11.1962i	−0.220552	−	0.382008i	−0.954976	+	0.296684i	$0.904119\pi$
$860$		0			0
$861$	3.09808	−	16.0981i	0.105582	−	0.548621i
$862$		0			0
$863$	−12.9546	−	3.47116i	−0.440978	−	0.118160i	0.0314967	−	0.999504i	$-0.489973\pi$
$863$	−12.9546	−	3.47116i	−0.440978	−	0.118160i	−0.472475	+	0.881344i	$0.656639\pi$
$864$		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
$873$	2.70831	−	10.1075i	0.0916624	−	0.342089i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.93357	−	33.3405i	0.301665	−	1.12583i	−0.634113	−	0.773240i	$-0.718635\pi$
$877$	8.93357	−	33.3405i	0.301665	−	1.12583i	0.935778	−	0.352589i	$-0.114699\pi$
$878$		0			0
$879$	−3.80385	−	2.19615i	−0.128301	−	0.0740744i
$880$		0			0
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$		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
$887$	−50.8473	−	13.6245i	−1.70729	−	0.457466i	−0.732529	−	0.680736i	$-0.761660\pi$
$887$	−50.8473	−	13.6245i	−1.70729	−	0.457466i	−0.974757	+	0.223270i	$0.928327\pi$
$888$		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
$893$	−0.0779745	−	0.291005i	−0.00260932	−	0.00973810i
$894$		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
$903$	−16.3514	+	11.0735i	−0.544140	+	0.368502i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−17.6963	+	4.74170i	−0.587594	+	0.157445i	−0.540354	−	0.841438i	$-0.681709\pi$
$907$	−17.6963	+	4.74170i	−0.587594	+	0.157445i	−0.0472409	+	0.998884i	$0.515043\pi$
$908$		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
$913$	−0.896575	+	0.240237i	−0.0296723	+	0.00795067i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.10634	−	0.582009i	0.267695	−	0.0192196i
$918$		0			0
$919$	−10.3923	+	6.00000i	−0.342811	+	0.197922i	−0.661514	−	0.749933i	$-0.730086\pi$
$919$	−10.3923	+	6.00000i	−0.342811	+	0.197922i	0.318704	+	0.947854i	$0.396753\pi$
$920$		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
$927$	3.27671	+	12.2289i	0.107621	+	0.401649i
$928$		0			0
$929$	−0.901924	−	1.56218i	−0.0295912	−	0.0512534i	0.850851	−	0.525408i	$-0.176087\pi$
$929$	−0.901924	−	1.56218i	−0.0295912	−	0.0512534i	−0.880442	+	0.474154i	$0.842754\pi$
$930$		0			0
$931$	−3.99038	+	9.98334i	−0.130779	+	0.327191i
$932$		0			0
$933$	5.79555	+	1.55291i	0.189738	+	0.0508401i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−17.5254	+	17.5254i	−0.572529	+	0.572529i	−0.932834	−	0.360306i	$-0.882672\pi$
$937$	−17.5254	+	17.5254i	−0.572529	+	0.572529i	0.360306	+	0.932834i	$0.382672\pi$
$938$		0			0
$939$			9.46410i			0.308849i
$940$		0			0
$941$	24.1244	+	13.9282i	0.786432	+	0.454046i	0.838705	−	0.544586i	$-0.183313\pi$
$941$	24.1244	+	13.9282i	0.786432	+	0.454046i	−0.0522732	+	0.998633i	$0.516647\pi$
$942$		0			0
$943$	−0.859411	+	3.20736i	−0.0279863	+	0.104446i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.48339	−	35.3925i	0.308169	−	1.15010i	−0.622014	−	0.783006i	$-0.713685\pi$
$947$	9.48339	−	35.3925i	0.308169	−	1.15010i	0.930183	−	0.367096i	$-0.119648\pi$
$948$		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
$957$	−4.89898	−	1.31268i	−0.158362	−	0.0424328i
$958$		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
$963$	2.91636	+	10.8840i	0.0939784	+	0.350732i
$964$		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	0.0266555	−	0.999645i	$-0.491514\pi$
$971$	28.2224	−	16.2942i	0.905701	−	0.522907i	0.879045	+	0.476738i	$0.158181\pi$
$972$		0			0
$973$	−25.8398	−	12.5434i	−0.828385	−	0.402124i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.36396	−	1.70522i	0.203601	−	0.0545548i	−0.155577	−	0.987824i	$-0.549724\pi$
$977$	6.36396	−	1.70522i	0.203601	−	0.0545548i	0.359178	+	0.933269i	$0.383057\pi$
$978$		0			0
$979$	7.85641			0.251092
$980$		0			0
$981$	−0.0717968			−0.00229229
$982$		0			0
$983$	−45.8976	+	12.2982i	−1.46391	+	0.392252i	−0.900837	−	0.434158i	$-0.857046\pi$
$983$	−45.8976	+	12.2982i	−1.46391	+	0.392252i	−0.563068	+	0.826410i	$0.690379\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.466870	−	0.226633i	−0.0148606	−	0.00721382i
$988$		0			0
$989$	3.46410	−	2.00000i	0.110152	−	0.0635963i
$990$		0			0
$991$	6.66025	−	11.5359i	0.211570	−	0.366450i	−0.740636	−	0.671906i	$-0.765476\pi$
$991$	6.66025	−	11.5359i	0.211570	−	0.366450i	0.952206	+	0.305456i	$0.0988091\pi$
$992$		0			0
$993$	−21.6801	−	21.6801i	−0.687996	−	0.687996i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.84890	−	6.90018i	−0.0585552	−	0.218531i	0.930448	−	0.366423i	$-0.119418\pi$
$997$	−1.84890	−	6.90018i	−0.0585552	−	0.218531i	−0.989003	+	0.147892i	$0.952751\pi$
$998$		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.b.157.1	yes	8
5.2	odd	4		2100.2.ce.a.493.2	yes	8
5.3	odd	4		2100.2.ce.a.493.1	✓	8
5.4	even	2	inner	2100.2.ce.b.157.2	yes	8
7.5	odd	6		2100.2.ce.a.1657.1	yes	8
35.12	even	12	inner	2100.2.ce.b.1993.2	yes	8
35.19	odd	6		2100.2.ce.a.1657.2	yes	8
35.33	even	12	inner	2100.2.ce.b.1993.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.a.493.1	✓	8	5.3	odd	4
2100.2.ce.a.493.2	yes	8	5.2	odd	4
2100.2.ce.a.1657.1	yes	8	7.5	odd	6
2100.2.ce.a.1657.2	yes	8	35.19	odd	6
2100.2.ce.b.157.1	yes	8	1.1	even	1	trivial
2100.2.ce.b.157.2	yes	8	5.4	even	2	inner
2100.2.ce.b.1993.1	yes	8	35.33	even	12	inner
2100.2.ce.b.1993.2	yes	8	35.12	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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