LMFDB - Embedded newform 1040.2.bp.a.287.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(287,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1040.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.bp (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.1
Character	$\chi$	$=$	1040.287
Dual form			1040.2.bp.a.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25777 - 2.25777i) q^{3} +(-0.545687 - 2.16846i) q^{5} +(-0.195046 + 0.195046i) q^{7} +7.19503i q^{9} +O(q^{10})$	\(q+(-2.25777 - 2.25777i) q^{3} +(-0.545687 - 2.16846i) q^{5} +(-0.195046 + 0.195046i) q^{7} +7.19503i q^{9} -5.47322i q^{11} +(-0.707107 + 0.707107i) q^{13} +(-3.66385 + 6.12792i) q^{15} +(-2.48587 - 2.48587i) q^{17} -3.40583 q^{19} +0.880736 q^{21} +(-5.13037 - 5.13037i) q^{23} +(-4.40445 + 2.36660i) q^{25} +(9.47140 - 9.47140i) q^{27} +3.80458i q^{29} +2.80013i q^{31} +(-12.3573 + 12.3573i) q^{33} +(0.529383 + 0.316515i) q^{35} +(0.638509 + 0.638509i) q^{37} +3.19297 q^{39} +11.0701 q^{41} +(3.08275 + 3.08275i) q^{43} +(15.6021 - 3.92623i) q^{45} +(-1.80937 + 1.80937i) q^{47} +6.92391i q^{49} +11.2250i q^{51} +(6.15718 - 6.15718i) q^{53} +(-11.8685 + 2.98666i) q^{55} +(7.68958 + 7.68958i) q^{57} +3.37019 q^{59} -4.49292 q^{61} +(-1.40336 - 1.40336i) q^{63} +(1.91919 + 1.14747i) q^{65} +(-0.0139756 + 0.0139756i) q^{67} +23.1664i q^{69} +14.3127i q^{71} +(5.21396 - 5.21396i) q^{73} +(15.2875 + 4.60099i) q^{75} +(1.06753 + 1.06753i) q^{77} +13.8383 q^{79} -21.1834 q^{81} +(-7.90629 - 7.90629i) q^{83} +(-4.03400 + 6.74701i) q^{85} +(8.58986 - 8.58986i) q^{87} -16.2093i q^{89} -0.275836i q^{91} +(6.32204 - 6.32204i) q^{93} +(1.85852 + 7.38542i) q^{95} +(-8.79518 - 8.79518i) q^{97} +39.3800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{5}+O(q^{10}) $ 24 * q - 8 * q^5	$ 24 q - 8 q^{5} + 16 q^{17} + 16 q^{21} - 16 q^{25} - 24 q^{33} - 24 q^{37} + 16 q^{41} + 48 q^{45} + 8 q^{53} + 8 q^{57} + 16 q^{61} + 8 q^{73} + 24 q^{77} + 40 q^{81} + 16 q^{85} + 56 q^{93} + 32 q^{97}+O(q^{100}) $ 24 * q - 8 * q^5 + 16 * q^17 + 16 * q^21 - 16 * q^25 - 24 * q^33 - 24 * q^37 + 16 * q^41 + 48 * q^45 + 8 * q^53 + 8 * q^57 + 16 * q^61 + 8 * q^73 + 24 * q^77 + 40 * q^81 + 16 * q^85 + 56 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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
$3$	−2.25777	−	2.25777i	−1.30352	−	1.30352i	−0.926000	−	0.377522i	$-0.876776\pi$
$3$	−2.25777	−	2.25777i	−1.30352	−	1.30352i	−0.377522	−	0.926000i	$-0.623224\pi$
$4$		0			0
$5$	−0.545687	−	2.16846i	−0.244039	−	0.969766i
$5$	−0.545687	−	2.16846i	−0.244039	−	0.969766i
$6$		0			0
$7$	−0.195046	+	0.195046i	−0.0737204	+	0.0737204i	−0.743006	−	0.669285i	$-0.766600\pi$
$7$	−0.195046	+	0.195046i	−0.0737204	+	0.0737204i	0.669285	+	0.743006i	$0.266600\pi$
$8$		0			0
$9$			7.19503i			2.39834i
$10$		0			0
$11$		−	5.47322i		−	1.65024i	−0.564960	−	0.825119i	$-0.691108\pi$
$11$		−	5.47322i		−	1.65024i	0.564960	−	0.825119i	$-0.308892\pi$
$12$		0			0
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$		0			0
$15$	−3.66385	+	6.12792i	−0.946001	+	1.58222i
$16$		0			0
$17$	−2.48587	−	2.48587i	−0.602911	−	0.602911i	0.338173	−	0.941084i	$-0.390191\pi$
$17$	−2.48587	−	2.48587i	−0.602911	−	0.602911i	−0.941084	+	0.338173i	$0.890191\pi$
$18$		0			0
$19$	−3.40583			−0.781352			−0.390676	−	0.920528i	$-0.627759\pi$
$19$	−3.40583			−0.781352			−0.390676	+	0.920528i	$0.627759\pi$
$20$		0			0
$21$	0.880736			0.192192
$22$		0			0
$23$	−5.13037	−	5.13037i	−1.06976	−	1.06976i	−0.997377	−	0.0723792i	$-0.976941\pi$
$23$	−5.13037	−	5.13037i	−1.06976	−	1.06976i	−0.0723792	−	0.997377i	$-0.523059\pi$
$24$		0			0
$25$	−4.40445	+	2.36660i	−0.880890	+	0.473321i
$26$		0			0
$27$	9.47140	−	9.47140i	1.82277	−	1.82277i
$28$		0			0
$29$			3.80458i			0.706493i	0.935530	+	0.353246i	$0.114922\pi$
$29$			3.80458i			0.706493i	−0.935530	+	0.353246i	$0.885078\pi$
$30$		0			0
$31$			2.80013i			0.502918i	0.967868	+	0.251459i	$0.0809103\pi$
$31$			2.80013i			0.502918i	−0.967868	+	0.251459i	$0.919090\pi$
$32$		0			0
$33$	−12.3573	+	12.3573i	−2.15112	+	2.15112i
$34$		0			0
$35$	0.529383	+	0.316515i	0.0894821	+	0.0535009i
$36$		0			0
$37$	0.638509	+	0.638509i	0.104970	+	0.104970i	0.757641	−	0.652671i	$-0.226352\pi$
$37$	0.638509	+	0.638509i	0.104970	+	0.104970i	−0.652671	+	0.757641i	$0.726352\pi$
$38$		0			0
$39$	3.19297			0.511284
$40$		0			0
$41$	11.0701			1.72886			0.864432	−	0.502750i	$-0.167678\pi$
$41$	11.0701			1.72886			0.864432	+	0.502750i	$0.167678\pi$
$42$		0			0
$43$	3.08275	+	3.08275i	0.470115	+	0.470115i	0.901952	−	0.431837i	$-0.142134\pi$
$43$	3.08275	+	3.08275i	0.470115	+	0.470115i	−0.431837	+	0.901952i	$0.642134\pi$
$44$		0			0
$45$	15.6021	−	3.92623i	2.32583	−	0.585289i
$46$		0			0
$47$	−1.80937	+	1.80937i	−0.263924	+	0.263924i	−0.826646	−	0.562722i	$-0.809754\pi$
$47$	−1.80937	+	1.80937i	−0.263924	+	0.263924i	0.562722	+	0.826646i	$0.309754\pi$
$48$		0			0
$49$			6.92391i			0.989131i
$50$		0			0
$51$			11.2250i			1.57182i
$52$		0			0
$53$	6.15718	−	6.15718i	0.845754	−	0.845754i	−0.143846	−	0.989600i	$-0.545947\pi$
$53$	6.15718	−	6.15718i	0.845754	−	0.845754i	0.989600	+	0.143846i	$0.0459470\pi$
$54$		0			0
$55$	−11.8685	+	2.98666i	−1.60034	+	0.402722i
$56$		0			0
$57$	7.68958	+	7.68958i	1.01851	+	1.01851i
$58$		0			0
$59$	3.37019			0.438761			0.219381	−	0.975639i	$-0.429596\pi$
$59$	3.37019			0.438761			0.219381	+	0.975639i	$0.429596\pi$
$60$		0			0
$61$	−4.49292			−0.575259			−0.287630	−	0.957742i	$-0.592867\pi$
$61$	−4.49292			−0.575259			−0.287630	+	0.957742i	$0.592867\pi$
$62$		0			0
$63$	−1.40336	−	1.40336i	−0.176807	−	0.176807i
$64$		0			0
$65$	1.91919	+	1.14747i	0.238047	+	0.142327i
$66$		0			0
$67$	−0.0139756	+	0.0139756i	−0.00170740	+	0.00170740i	−0.707960	−	0.706253i	$-0.750384\pi$
$67$	−0.0139756	+	0.0139756i	−0.00170740	+	0.00170740i	0.706253	+	0.707960i	$0.250384\pi$
$68$		0			0
$69$			23.1664i			2.78890i
$70$		0			0
$71$			14.3127i			1.69861i	0.527903	+	0.849305i	$0.322979\pi$
$71$			14.3127i			1.69861i	−0.527903	+	0.849305i	$0.677021\pi$
$72$		0			0
$73$	5.21396	−	5.21396i	0.610248	−	0.610248i	−0.332763	−	0.943011i	$-0.607981\pi$
$73$	5.21396	−	5.21396i	0.610248	−	0.610248i	0.943011	+	0.332763i	$0.107981\pi$
$74$		0			0
$75$	15.2875	+	4.60099i	1.76524	+	0.531276i
$76$		0			0
$77$	1.06753	+	1.06753i	0.121656	+	0.121656i
$78$		0			0
$79$	13.8383			1.55693			0.778466	−	0.627686i	$-0.215998\pi$
$79$	13.8383			1.55693			0.778466	+	0.627686i	$0.215998\pi$
$80$		0			0
$81$	−21.1834			−2.35371
$82$		0			0
$83$	−7.90629	−	7.90629i	−0.867828	−	0.867828i	0.124403	−	0.992232i	$-0.460298\pi$
$83$	−7.90629	−	7.90629i	−0.867828	−	0.867828i	−0.992232	+	0.124403i	$0.960298\pi$
$84$		0			0
$85$	−4.03400	+	6.74701i	−0.437549	+	0.731816i
$86$		0			0
$87$	8.58986	−	8.58986i	0.920930	−	0.920930i
$88$		0			0
$89$		−	16.2093i		−	1.71818i	−0.511822	−	0.859092i	$-0.671029\pi$
$89$		−	16.2093i		−	1.71818i	0.511822	−	0.859092i	$-0.328971\pi$
$90$		0			0
$91$		−	0.275836i		−	0.0289155i
$92$		0			0
$93$	6.32204	−	6.32204i	0.655565	−	0.655565i
$94$		0			0
$95$	1.85852	+	7.38542i	0.190680	+	0.757728i
$96$		0			0
$97$	−8.79518	−	8.79518i	−0.893015	−	0.893015i	0.101791	−	0.994806i	$-0.467543\pi$
$97$	−8.79518	−	8.79518i	−0.893015	−	0.893015i	−0.994806	+	0.101791i	$0.967543\pi$
$98$		0			0
$99$	39.3800			3.95784
$100$		0			0
$101$	−12.1031			−1.20430			−0.602151	−	0.798382i	$-0.705689\pi$
$101$	−12.1031			−1.20430			−0.602151	+	0.798382i	$0.705689\pi$
$102$		0			0
$103$	1.91896	+	1.91896i	0.189081	+	0.189081i	0.795299	−	0.606218i	$-0.207314\pi$
$103$	1.91896	+	1.91896i	0.189081	+	0.189081i	−0.606218	+	0.795299i	$0.707314\pi$
$104$		0			0
$105$	−0.480606	−	1.90984i	−0.0469024	−	0.186382i
$106$		0			0
$107$	−11.1393	+	11.1393i	−1.07688	+	1.07688i	−0.0800937	+	0.996787i	$0.525522\pi$
$107$	−11.1393	+	11.1393i	−1.07688	+	1.07688i	−0.996787	+	0.0800937i	$0.974478\pi$
$108$		0			0
$109$			10.1287i			0.970155i	0.874471	+	0.485078i	$0.161209\pi$
$109$			10.1287i			0.970155i	−0.874471	+	0.485078i	$0.838791\pi$
$110$		0			0
$111$		−	2.88321i		−	0.273662i
$112$		0			0
$113$	−7.89191	+	7.89191i	−0.742409	+	0.742409i	−0.973041	−	0.230632i	$-0.925921\pi$
$113$	−7.89191	+	7.89191i	−0.742409	+	0.742409i	0.230632	+	0.973041i	$0.425921\pi$
$114$		0			0
$115$	−8.32544	+	13.9246i	−0.776351	+	1.29847i
$116$		0			0
$117$	−5.08765	−	5.08765i	−0.470354	−	0.470354i
$118$		0			0
$119$	0.969716			0.0888937
$120$		0			0
$121$	−18.9561			−1.72328
$122$		0			0
$123$	−24.9938	−	24.9938i	−2.25361	−	2.25361i
$124$		0			0
$125$	7.53534	+	8.25946i	0.673981	+	0.738748i
$126$		0			0
$127$	−5.28668	+	5.28668i	−0.469117	+	0.469117i	−0.901628	−	0.432511i	$-0.857628\pi$
$127$	−5.28668	+	5.28668i	−0.469117	+	0.469117i	0.432511	+	0.901628i	$0.357628\pi$
$128$		0			0
$129$		−	13.9203i		−	1.22561i
$130$		0			0
$131$			10.1294i			0.885007i	0.896767	+	0.442503i	$0.145910\pi$
$131$			10.1294i			0.885007i	−0.896767	+	0.442503i	$0.854090\pi$
$132$		0			0
$133$	0.664294	−	0.664294i	0.0576016	−	0.0576016i
$134$		0			0
$135$	−25.7068	−	15.3700i	−2.21249	−	1.32283i
$136$		0			0
$137$	−2.21475	−	2.21475i	−0.189219	−	0.189219i	0.606139	−	0.795358i	$-0.292717\pi$
$137$	−2.21475	−	2.21475i	−0.189219	−	0.189219i	−0.795358	+	0.606139i	$0.792717\pi$
$138$		0			0
$139$	−12.2783			−1.04143			−0.520716	−	0.853730i	$-0.674335\pi$
$139$	−12.2783			−1.04143			−0.520716	+	0.853730i	$0.674335\pi$
$140$		0			0
$141$	8.17027			0.688061
$142$		0			0
$143$	3.87015	+	3.87015i	0.323638	+	0.323638i
$144$		0			0
$145$	8.25009	−	2.07611i	0.685133	−	0.172412i
$146$		0			0
$147$	15.6326	−	15.6326i	1.28935	−	1.28935i
$148$		0			0
$149$		−	3.33730i		−	0.273402i	−0.990612	−	0.136701i	$-0.956350\pi$
$149$		−	3.33730i		−	0.273402i	0.990612	−	0.136701i	$-0.0436500\pi$
$150$		0			0
$151$		−	6.77899i		−	0.551666i	−0.961206	−	0.275833i	$-0.911046\pi$
$151$		−	6.77899i		−	0.551666i	0.961206	−	0.275833i	$-0.0889538\pi$
$152$		0			0
$153$	17.8859	−	17.8859i	1.44599	−	1.44599i
$154$		0			0
$155$	6.07197	−	1.52799i	0.487712	−	0.122731i
$156$		0			0
$157$	−8.47026	−	8.47026i	−0.676000	−	0.676000i	0.283092	−	0.959093i	$-0.408640\pi$
$157$	−8.47026	−	8.47026i	−0.676000	−	0.676000i	−0.959093	+	0.283092i	$0.908640\pi$
$158$		0			0
$159$	−27.8030			−2.20492
$160$		0			0
$161$	2.00131			0.157726
$162$		0			0
$163$	−5.99778	−	5.99778i	−0.469783	−	0.469783i	0.432062	−	0.901844i	$-0.357786\pi$
$163$	−5.99778	−	5.99778i	−0.469783	−	0.469783i	−0.901844	+	0.432062i	$0.857786\pi$
$164$		0			0
$165$	33.5394	+	20.0530i	2.61104	+	1.56113i
$166$		0			0
$167$	−2.73522	+	2.73522i	−0.211657	+	0.211657i	−0.804971	−	0.593314i	$-0.797819\pi$
$167$	−2.73522	+	2.73522i	−0.211657	+	0.211657i	0.593314	+	0.804971i	$0.297819\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$		0			0
$171$		−	24.5051i		−	1.87395i
$172$		0			0
$173$	17.6186	−	17.6186i	1.33952	−	1.33952i	0.442994	−	0.896525i	$-0.353916\pi$
$173$	17.6186	−	17.6186i	1.33952	−	1.33952i	0.896525	−	0.442994i	$-0.146084\pi$
$174$		0			0
$175$	0.397474	−	1.32067i	0.0300462	−	0.0998329i
$176$		0			0
$177$	−7.60910	−	7.60910i	−0.571935	−	0.571935i
$178$		0			0
$179$	−2.92916			−0.218936			−0.109468	−	0.993990i	$-0.534915\pi$
$179$	−2.92916			−0.218936			−0.109468	+	0.993990i	$0.534915\pi$
$180$		0			0
$181$	−8.45851			−0.628716			−0.314358	−	0.949304i	$-0.601789\pi$
$181$	−8.45851			−0.628716			−0.314358	+	0.949304i	$0.601789\pi$
$182$		0			0
$183$	10.1440	+	10.1440i	0.749863	+	0.749863i
$184$		0			0
$185$	1.03616	−	1.73301i	0.0761798	−	0.127413i
$186$		0			0
$187$	−13.6057	+	13.6057i	−0.994947	+	0.994947i
$188$		0			0
$189$			3.69471i			0.268751i
$190$		0			0
$191$			18.1126i			1.31058i	0.755378	+	0.655289i	$0.227453\pi$
$191$			18.1126i			1.31058i	−0.755378	+	0.655289i	$0.772547\pi$
$192$		0			0
$193$	−4.82549	+	4.82549i	−0.347346	+	0.347346i	−0.859120	−	0.511774i	$-0.828989\pi$
$193$	−4.82549	+	4.82549i	−0.347346	+	0.347346i	0.511774	+	0.859120i	$0.328989\pi$
$194$		0			0
$195$	−1.74236	−	6.92382i	−0.124773	−	0.495825i
$196$		0			0
$197$	6.31156	+	6.31156i	0.449680	+	0.449680i	0.895248	−	0.445568i	$-0.146998\pi$
$197$	6.31156	+	6.31156i	0.449680	+	0.449680i	−0.445568	+	0.895248i	$0.646998\pi$
$198$		0			0
$199$	5.25674			0.372640			0.186320	−	0.982489i	$-0.440344\pi$
$199$	5.25674			0.372640			0.186320	+	0.982489i	$0.440344\pi$
$200$		0			0
$201$	0.0631075			0.00445126
$202$		0			0
$203$	−0.742068	−	0.742068i	−0.0520829	−	0.0520829i
$204$		0			0
$205$	−6.04083	−	24.0051i	−0.421910	−	1.67659i
$206$		0			0
$207$	36.9132	−	36.9132i	2.56564	−	2.56564i
$208$		0			0
$209$			18.6409i			1.28942i
$210$		0			0
$211$		−	22.5336i		−	1.55128i	−0.631175	−	0.775640i	$-0.717427\pi$
$211$		−	22.5336i		−	1.55128i	0.631175	−	0.775640i	$-0.282573\pi$
$212$		0			0
$213$	32.3148	−	32.3148i	2.21418	−	2.21418i
$214$		0			0
$215$	5.00261	−	8.36705i	0.341175	−	0.570628i
$216$		0			0
$217$	−0.546153	−	0.546153i	−0.0370753	−	0.0370753i
$218$		0			0
$219$	−23.5438			−1.59094
$220$		0			0
$221$	3.51555			0.236481
$222$		0			0
$223$	9.28909	+	9.28909i	0.622043	+	0.622043i	0.946054	−	0.324010i	$-0.105031\pi$
$223$	9.28909	+	9.28909i	0.622043	+	0.622043i	−0.324010	+	0.946054i	$0.605031\pi$
$224$		0			0
$225$	−17.0278	−	31.6902i	−1.13519	−	2.11268i
$226$		0			0
$227$	−10.1127	+	10.1127i	−0.671207	+	0.671207i	−0.957994	−	0.286788i	$-0.907413\pi$
$227$	−10.1127	+	10.1127i	−0.671207	+	0.671207i	0.286788	+	0.957994i	$0.407413\pi$
$228$		0			0
$229$			0.637314i			0.0421149i	0.999778	+	0.0210574i	$0.00670329\pi$
$229$			0.637314i			0.0421149i	−0.999778	+	0.0210574i	$0.993297\pi$
$230$		0			0
$231$		−	4.82046i		−	0.317163i
$232$		0			0
$233$	−3.26818	+	3.26818i	−0.214105	+	0.214105i	−0.806009	−	0.591903i	$-0.798377\pi$
$233$	−3.26818	+	3.26818i	−0.214105	+	0.214105i	0.591903	+	0.806009i	$0.298377\pi$
$234$		0			0
$235$	4.91090	+	2.93620i	0.320352	+	0.191537i
$236$		0			0
$237$	−31.2437	−	31.2437i	−2.02950	−	2.02950i
$238$		0			0
$239$	−19.4120			−1.25566			−0.627830	−	0.778351i	$-0.716057\pi$
$239$	−19.4120			−1.25566			−0.627830	+	0.778351i	$0.716057\pi$
$240$		0			0
$241$	14.7648			0.951087			0.475544	−	0.879692i	$-0.342251\pi$
$241$	14.7648			0.951087			0.475544	+	0.879692i	$0.342251\pi$
$242$		0			0
$243$	19.4129	+	19.4129i	1.24534	+	1.24534i
$244$		0			0
$245$	15.0142	−	3.77829i	0.959225	−	0.241386i
$246$		0			0
$247$	2.40829	−	2.40829i	0.153236	−	0.153236i
$248$		0			0
$249$			35.7011i			2.26247i
$250$		0			0
$251$		−	15.0545i		−	0.950230i	−0.879924	−	0.475115i	$-0.842406\pi$
$251$		−	15.0545i		−	0.950230i	0.879924	−	0.475115i	$-0.157594\pi$
$252$		0			0
$253$	−28.0796	+	28.0796i	−1.76535	+	1.76535i
$254$		0			0
$255$	24.3410	−	6.12535i	1.52429	−	0.383584i
$256$		0			0
$257$	3.27000	+	3.27000i	0.203977	+	0.203977i	0.801701	−	0.597725i	$-0.203928\pi$
$257$	3.27000	+	3.27000i	0.203977	+	0.203977i	−0.597725	+	0.801701i	$0.703928\pi$
$258$		0			0
$259$	−0.249077			−0.0154769
$260$		0			0
$261$	−27.3741			−1.69441
$262$		0			0
$263$	−10.8008	−	10.8008i	−0.666003	−	0.666003i	0.290785	−	0.956788i	$-0.406084\pi$
$263$	−10.8008	−	10.8008i	−0.666003	−	0.666003i	−0.956788	+	0.290785i	$0.906084\pi$
$264$		0			0
$265$	−16.7115	−	9.99172i	−1.02658	−	0.613786i
$266$		0			0
$267$	−36.5969	+	36.5969i	−2.23969	+	2.23969i
$268$		0			0
$269$		−	24.8167i		−	1.51310i	−0.653934	−	0.756552i	$-0.726883\pi$
$269$		−	24.8167i		−	1.51310i	0.653934	−	0.756552i	$-0.273117\pi$
$270$		0			0
$271$			0.536069i			0.0325639i	0.999867	+	0.0162819i	$0.00518293\pi$
$271$			0.536069i			0.0325639i	−0.999867	+	0.0162819i	$0.994817\pi$
$272$		0			0
$273$	−0.622775	+	0.622775i	−0.0376920	+	0.0376920i
$274$		0			0
$275$	12.9529	+	24.1065i	0.781091	+	1.45368i
$276$		0			0
$277$	16.9382	+	16.9382i	1.01772	+	1.01772i	0.999840	+	0.0178773i	$0.00569082\pi$
$277$	16.9382	+	16.9382i	1.01772	+	1.01772i	0.0178773	+	0.999840i	$0.494309\pi$
$278$		0			0
$279$	−20.1470			−1.20617
$280$		0			0
$281$	−13.7103			−0.817886			−0.408943	−	0.912560i	$-0.634103\pi$
$281$	−13.7103			−0.817886			−0.408943	+	0.912560i	$0.634103\pi$
$282$		0			0
$283$	−4.67456	−	4.67456i	−0.277874	−	0.277874i	0.554386	−	0.832260i	$-0.312953\pi$
$283$	−4.67456	−	4.67456i	−0.277874	−	0.277874i	−0.832260	+	0.554386i	$0.812953\pi$
$284$		0			0
$285$	12.4785	−	20.8707i	0.739160	−	1.23627i
$286$		0			0
$287$	−2.15918	+	2.15918i	−0.127452	+	0.127452i
$288$		0			0
$289$		−	4.64093i		−	0.272996i
$290$		0			0
$291$			39.7149i			2.32813i
$292$		0			0
$293$	8.53679	−	8.53679i	0.498724	−	0.498724i	−0.412316	−	0.911041i	$-0.635280\pi$
$293$	8.53679	−	8.53679i	0.498724	−	0.498724i	0.911041	+	0.412316i	$0.135280\pi$
$294$		0			0
$295$	−1.83907	−	7.30813i	−0.107075	−	0.425496i
$296$		0			0
$297$	−51.8391	−	51.8391i	−3.00801	−	3.00801i
$298$		0			0
$299$	7.25544			0.419593
$300$		0			0
$301$	−1.20256			−0.0693142
$302$		0			0
$303$	27.3259	+	27.3259i	1.56983	+	1.56983i
$304$		0			0
$305$	2.45173	+	9.74272i	0.140385	+	0.557866i
$306$		0			0
$307$	−17.6954	+	17.6954i	−1.00993	+	1.00993i	−0.00997675	+	0.999950i	$0.503176\pi$
$307$	−17.6954	+	17.6954i	−1.00993	+	1.00993i	−0.999950	+	0.00997675i	$0.996824\pi$
$308$		0			0
$309$		−	8.66514i		−	0.492943i
$310$		0			0
$311$		−	27.3589i		−	1.55138i	−0.631113	−	0.775691i	$-0.717402\pi$
$311$		−	27.3589i		−	1.55138i	0.631113	−	0.775691i	$-0.282598\pi$
$312$		0			0
$313$	−16.1656	+	16.1656i	−0.913735	+	0.913735i	−0.996564	−	0.0828291i	$-0.973604\pi$
$313$	−16.1656	+	16.1656i	−0.913735	+	0.913735i	0.0828291	+	0.996564i	$0.473604\pi$
$314$		0			0
$315$	−2.27734	+	3.80893i	−0.128313	+	0.214609i
$316$		0			0
$317$	22.6081	+	22.6081i	1.26980	+	1.26980i	0.946191	+	0.323609i	$0.104896\pi$
$317$	22.6081	+	22.6081i	1.26980	+	1.26980i	0.323609	+	0.946191i	$0.395104\pi$
$318$		0			0
$319$	20.8233			1.16588
$320$		0			0
$321$	50.3001			2.80748
$322$		0			0
$323$	8.46645	+	8.46645i	0.471086	+	0.471086i
$324$		0			0
$325$	1.44098	−	4.78786i	0.0799310	−	0.265583i
$326$		0			0
$327$	22.8683	−	22.8683i	1.26462	−	1.26462i
$328$		0			0
$329$		−	0.705820i		−	0.0389131i
$330$		0			0
$331$		−	11.9906i		−	0.659062i	−0.944145	−	0.329531i	$-0.893109\pi$
$331$		−	11.9906i		−	0.659062i	0.944145	−	0.329531i	$-0.106891\pi$
$332$		0			0
$333$	−4.59409	+	4.59409i	−0.251755	+	0.251755i
$334$		0			0
$335$	0.0379320	+	0.0226793i	0.00207244	+	0.00123910i
$336$		0			0
$337$	−18.1693	−	18.1693i	−0.989744	−	0.989744i	0.0102040	−	0.999948i	$-0.496752\pi$
$337$	−18.1693	−	18.1693i	−0.989744	−	0.989744i	−0.999948	+	0.0102040i	$0.996752\pi$
$338$		0			0
$339$	35.6362			1.93549
$340$		0			0
$341$	15.3257			0.829934
$342$		0			0
$343$	−2.71580	−	2.71580i	−0.146639	−	0.146639i
$344$		0			0
$345$	50.2354	−	12.6416i	2.70458	−	0.680600i
$346$		0			0
$347$	6.88819	−	6.88819i	0.369777	−	0.369777i	−0.497619	−	0.867396i	$-0.665792\pi$
$347$	6.88819	−	6.88819i	0.369777	−	0.369777i	0.867396	+	0.497619i	$0.165792\pi$
$348$		0			0
$349$			1.31300i			0.0702831i	0.999382	+	0.0351415i	$0.0111882\pi$
$349$			1.31300i			0.0702831i	−0.999382	+	0.0351415i	$0.988812\pi$
$350$		0			0
$351$			13.3946i			0.714950i
$352$		0			0
$353$	−10.8238	+	10.8238i	−0.576093	+	0.576093i	−0.933825	−	0.357731i	$-0.883550\pi$
$353$	−10.8238	+	10.8238i	−0.576093	+	0.576093i	0.357731	+	0.933825i	$0.383550\pi$
$354$		0			0
$355$	31.0366	−	7.81028i	1.64725	−	0.414526i
$356$		0			0
$357$	−2.18939	−	2.18939i	−0.115875	−	0.115875i
$358$		0			0
$359$	−1.34420			−0.0709443			−0.0354722	−	0.999371i	$-0.511294\pi$
$359$	−1.34420			−0.0709443			−0.0354722	+	0.999371i	$0.511294\pi$
$360$		0			0
$361$	−7.40030			−0.389489
$362$		0			0
$363$	42.7985	+	42.7985i	2.24634	+	2.24634i
$364$		0			0
$365$	−14.1515	−	8.46108i	−0.740721	−	0.442873i
$366$		0			0
$367$	−1.20993	+	1.20993i	−0.0631581	+	0.0631581i	−0.737980	−	0.674822i	$-0.764220\pi$
$367$	−1.20993	+	1.20993i	−0.0631581	+	0.0631581i	0.674822	+	0.737980i	$0.264220\pi$
$368$		0			0
$369$			79.6499i			4.14641i
$370$		0			0
$371$			2.40186i			0.124699i
$372$		0			0
$373$	−1.37292	+	1.37292i	−0.0710873	+	0.0710873i	−0.741757	−	0.670669i	$-0.766007\pi$
$373$	−1.37292	+	1.37292i	−0.0710873	+	0.0710873i	0.670669	+	0.741757i	$0.266007\pi$
$374$		0			0
$375$	1.63489	−	35.6610i	0.0844255	−	1.84153i
$376$		0			0
$377$	−2.69025	−	2.69025i	−0.138555	−	0.138555i
$378$		0			0
$379$	−32.3429			−1.66134			−0.830671	−	0.556764i	$-0.812043\pi$
$379$	−32.3429			−1.66134			−0.830671	+	0.556764i	$0.812043\pi$
$380$		0			0
$381$	23.8722			1.22301
$382$		0			0
$383$	26.2250	+	26.2250i	1.34004	+	1.34004i	0.896019	+	0.444017i	$0.146447\pi$
$383$	26.2250	+	26.2250i	1.34004	+	1.34004i	0.444017	+	0.896019i	$0.353553\pi$
$384$		0			0
$385$	1.73236	−	2.89743i	0.0882891	−	0.147667i
$386$		0			0
$387$	−22.1805	+	22.1805i	−1.12750	+	1.12750i
$388$		0			0
$389$			18.8399i			0.955219i	0.878572	+	0.477610i	$0.158497\pi$
$389$			18.8399i			0.955219i	−0.878572	+	0.477610i	$0.841503\pi$
$390$		0			0
$391$			25.5068i			1.28994i
$392$		0			0
$393$	22.8698	−	22.8698i	1.15363	−	1.15363i
$394$		0			0
$395$	−7.55139	−	30.0079i	−0.379952	−	1.50986i
$396$		0			0
$397$	−19.2065	−	19.2065i	−0.963949	−	0.963949i	0.0354239	−	0.999372i	$-0.488722\pi$
$397$	−19.2065	−	19.2065i	−0.963949	−	0.963949i	−0.999372	+	0.0354239i	$0.988722\pi$
$398$		0			0
$399$	−2.99964			−0.150170
$400$		0			0
$401$	−26.3262			−1.31467			−0.657333	−	0.753600i	$-0.728316\pi$
$401$	−26.3262			−1.31467			−0.657333	+	0.753600i	$0.728316\pi$
$402$		0			0
$403$	−1.97999	−	1.97999i	−0.0986303	−	0.0986303i
$404$		0			0
$405$	11.5595	+	45.9353i	0.574396	+	2.28254i
$406$		0			0
$407$	3.49470	−	3.49470i	0.173226	−	0.173226i
$408$		0			0
$409$		−	27.7880i		−	1.37403i	−0.726645	−	0.687013i	$-0.758921\pi$
$409$		−	27.7880i		−	1.37403i	0.726645	−	0.687013i	$-0.241079\pi$
$410$		0			0
$411$			10.0008i			0.493302i
$412$		0			0
$413$	−0.657341	+	0.657341i	−0.0323456	+	0.0323456i
$414$		0			0
$415$	−12.8301	+	21.4589i	−0.629806	+	1.05337i
$416$		0			0
$417$	27.7215	+	27.7215i	1.35753	+	1.35753i
$418$		0			0
$419$	−31.7037			−1.54883			−0.774414	−	0.632679i	$-0.781955\pi$
$419$	−31.7037			−1.54883			−0.774414	+	0.632679i	$0.781955\pi$
$420$		0			0
$421$	−25.3910			−1.23748			−0.618742	−	0.785595i	$-0.712357\pi$
$421$	−25.3910			−1.23748			−0.618742	+	0.785595i	$0.712357\pi$
$422$		0			0
$423$	−13.0185	−	13.0185i	−0.632980	−	0.632980i
$424$		0			0
$425$	16.8319	+	5.06582i	0.816469	+	0.245728i
$426$		0			0
$427$	0.876325	−	0.876325i	0.0424083	−	0.0424083i
$428$		0			0
$429$		−	17.4758i		−	0.843739i
$430$		0			0
$431$		−	12.5292i		−	0.603511i	−0.953385	−	0.301755i	$-0.902427\pi$
$431$		−	12.5292i		−	0.603511i	0.953385	−	0.301755i	$-0.0975726\pi$
$432$		0			0
$433$	15.5520	−	15.5520i	0.747379	−	0.747379i	−0.226607	−	0.973986i	$-0.572763\pi$
$433$	15.5520	−	15.5520i	0.747379	−	0.747379i	0.973986	+	0.226607i	$0.0727633\pi$
$434$		0			0
$435$	−23.3142	−	13.9394i	−1.11783	−	0.668343i
$436$		0			0
$437$	17.4732	+	17.4732i	0.835856	+	0.835856i
$438$		0			0
$439$	27.7381			1.32387			0.661933	−	0.749563i	$-0.269736\pi$
$439$	27.7381			1.32387			0.661933	+	0.749563i	$0.269736\pi$
$440$		0			0
$441$	−49.8178			−2.37227
$442$		0			0
$443$	−8.86045	−	8.86045i	−0.420973	−	0.420973i	0.464566	−	0.885539i	$-0.346210\pi$
$443$	−8.86045	−	8.86045i	−0.420973	−	0.420973i	−0.885539	+	0.464566i	$0.846210\pi$
$444$		0			0
$445$	−35.1493	+	8.84521i	−1.66624	+	0.419303i
$446$		0			0
$447$	−7.53485	+	7.53485i	−0.356386	+	0.356386i
$448$		0			0
$449$			4.09458i			0.193235i	0.995322	+	0.0966175i	$0.0308024\pi$
$449$			4.09458i			0.193235i	−0.995322	+	0.0966175i	$0.969198\pi$
$450$		0			0
$451$		−	60.5892i		−	2.85304i
$452$		0			0
$453$	−15.3054	+	15.3054i	−0.719110	+	0.719110i
$454$		0			0
$455$	−0.598141	+	0.150520i	−0.0280413	+	0.00705650i
$456$		0			0
$457$	−13.0454	−	13.0454i	−0.610237	−	0.610237i	0.332771	−	0.943008i	$-0.392016\pi$
$457$	−13.0454	−	13.0454i	−0.610237	−	0.610237i	−0.943008	+	0.332771i	$0.892016\pi$
$458$		0			0
$459$	−47.0893			−2.19794
$460$		0			0
$461$	0.999049			0.0465304			0.0232652	−	0.999729i	$-0.492594\pi$
$461$	0.999049			0.0465304			0.0232652	+	0.999729i	$0.492594\pi$
$462$		0			0
$463$	−1.63846	−	1.63846i	−0.0761459	−	0.0761459i	0.668008	−	0.744154i	$-0.267147\pi$
$463$	−1.63846	−	1.63846i	−0.0761459	−	0.0761459i	−0.744154	+	0.668008i	$0.767147\pi$
$464$		0			0
$465$	−17.1589	−	10.2592i	−0.795727	−	0.475761i
$466$		0			0
$467$	−10.8850	+	10.8850i	−0.503700	+	0.503700i	−0.912586	−	0.408886i	$-0.865917\pi$
$467$	−10.8850	+	10.8850i	−0.503700	+	0.503700i	0.408886	+	0.912586i	$0.365917\pi$
$468$		0			0
$469$		−	0.00545178i		−	0.000251740i
$470$		0			0
$471$			38.2478i			1.76236i
$472$		0			0
$473$	16.8726	−	16.8726i	0.775802	−	0.775802i
$474$		0			0
$475$	15.0008	−	8.06026i	0.688285	−	0.369830i
$476$		0			0
$477$	44.3011	+	44.3011i	2.02841	+	2.02841i
$478$		0			0
$479$	21.3979			0.977697			0.488848	−	0.872369i	$-0.337417\pi$
$479$	21.3979			0.977697			0.488848	+	0.872369i	$0.337417\pi$
$480$		0			0
$481$	−0.902989			−0.0411727
$482$		0			0
$483$	−4.51850	−	4.51850i	−0.205599	−	0.205599i
$484$		0			0
$485$	−14.2726	+	23.8714i	−0.648085	+	1.08395i
$486$		0			0
$487$	−23.4905	+	23.4905i	−1.06446	+	1.06446i	−0.0666813	+	0.997774i	$0.521241\pi$
$487$	−23.4905	+	23.4905i	−1.06446	+	1.06446i	−0.997774	+	0.0666813i	$0.978759\pi$
$488$		0			0
$489$			27.0832i			1.22474i
$490$		0			0
$491$		−	42.7324i		−	1.92849i	−0.265020	−	0.964243i	$-0.585379\pi$
$491$		−	42.7324i		−	1.92849i	0.265020	−	0.964243i	$-0.414621\pi$
$492$		0			0
$493$	9.45768	−	9.45768i	0.425953	−	0.425953i
$494$		0			0
$495$	−21.4891	−	85.3939i	−0.965865	−	3.83817i
$496$		0			0
$497$	−2.79164	−	2.79164i	−0.125222	−	0.125222i
$498$		0			0
$499$	22.8754			1.02404			0.512021	−	0.858973i	$-0.328897\pi$
$499$	22.8754			1.02404			0.512021	+	0.858973i	$0.328897\pi$
$500$		0			0
$501$	12.3510			0.551800
$502$		0			0
$503$	−15.5026	−	15.5026i	−0.691228	−	0.691228i	0.271274	−	0.962502i	$-0.412555\pi$
$503$	−15.5026	−	15.5026i	−0.691228	−	0.691228i	−0.962502	+	0.271274i	$0.912555\pi$
$504$		0			0
$505$	6.60450	+	26.2451i	0.293896	+	1.16789i
$506$		0			0
$507$	−2.25777	+	2.25777i	−0.100271	+	0.100271i
$508$		0			0
$509$			11.3604i			0.503542i	0.967787	+	0.251771i	$0.0810129\pi$
$509$			11.3604i			0.503542i	−0.967787	+	0.251771i	$0.918987\pi$
$510$		0			0
$511$			2.03392i			0.0899754i
$512$		0			0
$513$	−32.2580	+	32.2580i	−1.42423	+	1.42423i
$514$		0			0
$515$	3.11404	−	5.20835i	0.137221	−	0.229507i
$516$		0			0
$517$	9.90308	+	9.90308i	0.435537	+	0.435537i
$518$		0			0
$519$	−79.5575			−3.49219
$520$		0			0
$521$	−9.79291			−0.429035			−0.214518	−	0.976720i	$-0.568818\pi$
$521$	−9.79291			−0.429035			−0.214518	+	0.976720i	$0.568818\pi$
$522$		0			0
$523$	4.79528	+	4.79528i	0.209683	+	0.209683i	0.804133	−	0.594450i	$-0.202630\pi$
$523$	4.79528	+	4.79528i	0.209683	+	0.209683i	−0.594450	+	0.804133i	$0.702630\pi$
$524$		0			0
$525$	−3.87916	+	2.08435i	−0.169300	+	0.0909686i
$526$		0			0
$527$	6.96074	−	6.96074i	0.303215	−	0.303215i
$528$		0			0
$529$			29.6414i			1.28876i
$530$		0			0
$531$			24.2486i			1.05230i
$532$		0			0
$533$	−7.82776	+	7.82776i	−0.339058	+	0.339058i
$534$		0			0
$535$	30.2338	+	18.0766i	1.30712	+	0.781521i
$536$		0			0
$537$	6.61337	+	6.61337i	0.285388	+	0.285388i
$538$		0			0
$539$	37.8961			1.63230
$540$		0			0
$541$	−3.62908			−0.156026			−0.0780132	−	0.996952i	$-0.524858\pi$
$541$	−3.62908			−0.156026			−0.0780132	+	0.996952i	$0.524858\pi$
$542$		0			0
$543$	19.0974	+	19.0974i	0.819546	+	0.819546i
$544$		0			0
$545$	21.9637	−	5.52711i	0.940823	−	0.236755i
$546$		0			0
$547$	−14.5143	+	14.5143i	−0.620585	+	0.620585i	−0.945681	−	0.325096i	$-0.894603\pi$
$547$	−14.5143	+	14.5143i	−0.620585	+	0.620585i	0.325096	+	0.945681i	$0.394603\pi$
$548$		0			0
$549$		−	32.3267i		−	1.37967i
$550$		0			0
$551$		−	12.9578i		−	0.552020i
$552$		0			0
$553$	−2.69911	+	2.69911i	−0.114778	+	0.114778i
$554$		0			0
$555$	−6.25213	+	1.57333i	−0.265388	+	0.0667842i
$556$		0			0
$557$	−9.17686	−	9.17686i	−0.388836	−	0.388836i	0.485436	−	0.874272i	$-0.338661\pi$
$557$	−9.17686	−	9.17686i	−0.388836	−	0.388836i	−0.874272	+	0.485436i	$0.838661\pi$
$558$		0			0
$559$	−4.35967			−0.184394
$560$		0			0
$561$	61.4370			2.59387
$562$		0			0
$563$	−24.9043	−	24.9043i	−1.04959	−	1.04959i	−0.998705	−	0.0508848i	$-0.983796\pi$
$563$	−24.9043	−	24.9043i	−1.04959	−	1.04959i	−0.0508848	−	0.998705i	$-0.516204\pi$
$564$		0			0
$565$	21.4198	+	12.8068i	0.901139	+	0.538786i
$566$		0			0
$567$	4.13173	−	4.13173i	0.173516	−	0.173516i
$568$		0			0
$569$		−	0.125174i		−	0.00524756i	−0.999997	−	0.00262378i	$-0.999165\pi$
$569$		−	0.125174i		−	0.00524756i	0.999997	−	0.00262378i	$-0.000835176\pi$
$570$		0			0
$571$		−	11.8334i		−	0.495214i	−0.968861	−	0.247607i	$-0.920356\pi$
$571$		−	11.8334i		−	0.495214i	0.968861	−	0.247607i	$-0.0796441\pi$
$572$		0			0
$573$	40.8939	−	40.8939i	1.70837	−	1.70837i
$574$		0			0
$575$	34.7380	+	10.4549i	1.44868	+	0.436000i
$576$		0			0
$577$	7.08284	+	7.08284i	0.294862	+	0.294862i	0.838998	−	0.544135i	$-0.183142\pi$
$577$	7.08284	+	7.08284i	0.294862	+	0.294862i	−0.544135	+	0.838998i	$0.683142\pi$
$578$		0			0
$579$	21.7897			0.905548
$580$		0			0
$581$	3.08418			0.127953
$582$		0			0
$583$	−33.6996	−	33.6996i	−1.39569	−	1.39569i
$584$		0			0
$585$	−8.25612	+	13.8087i	−0.341348	+	0.570917i
$586$		0			0
$587$	3.96938	−	3.96938i	0.163834	−	0.163834i	−0.620429	−	0.784263i	$-0.713041\pi$
$587$	3.96938	−	3.96938i	0.163834	−	0.163834i	0.784263	+	0.620429i	$0.213041\pi$
$588$		0			0
$589$		−	9.53677i		−	0.392956i
$590$		0			0
$591$		−	28.5001i		−	1.17234i
$592$		0			0
$593$	15.0637	−	15.0637i	0.618590	−	0.618590i	−0.326579	−	0.945170i	$-0.605896\pi$
$593$	15.0637	−	15.0637i	0.618590	−	0.618590i	0.945170	+	0.326579i	$0.105896\pi$
$594$		0			0
$595$	−0.529161	−	2.10279i	−0.0216935	−	0.0862060i
$596$		0			0
$597$	−11.8685	−	11.8685i	−0.485745	−	0.485745i
$598$		0			0
$599$	22.1252			0.904012			0.452006	−	0.892015i	$-0.350708\pi$
$599$	22.1252			0.904012			0.452006	+	0.892015i	$0.350708\pi$
$600$		0			0
$601$	−4.30608			−0.175649			−0.0878243	−	0.996136i	$-0.527991\pi$
$601$	−4.30608			−0.175649			−0.0878243	+	0.996136i	$0.527991\pi$
$602$		0			0
$603$	−0.100555	−	0.100555i	−0.00409492	−	0.00409492i
$604$		0			0
$605$	10.3441	+	41.1056i	0.420548	+	1.67118i
$606$		0			0
$607$	−15.0142	+	15.0142i	−0.609406	+	0.609406i	−0.942791	−	0.333385i	$-0.891809\pi$
$607$	−15.0142	+	15.0142i	−0.609406	+	0.609406i	0.333385	+	0.942791i	$0.391809\pi$
$608$		0			0
$609$			3.35083i			0.135783i
$610$		0			0
$611$		−	2.55884i		−	0.103519i
$612$		0			0
$613$	−16.6118	+	16.6118i	−0.670944	+	0.670944i	−0.957934	−	0.286990i	$-0.907345\pi$
$613$	−16.6118	+	16.6118i	−0.670944	+	0.670944i	0.286990	+	0.957934i	$0.407345\pi$
$614$		0			0
$615$	−40.5593	+	67.8368i	−1.63551	+	2.73545i
$616$		0			0
$617$	25.1687	+	25.1687i	1.01325	+	1.01325i	0.999911	+	0.0133419i	$0.00424699\pi$
$617$	25.1687	+	25.1687i	1.01325	+	1.01325i	0.0133419	+	0.999911i	$0.495753\pi$
$618$		0			0
$619$	7.85622			0.315768			0.157884	−	0.987458i	$-0.449533\pi$
$619$	7.85622			0.315768			0.157884	+	0.987458i	$0.449533\pi$
$620$		0			0
$621$	−97.1836			−3.89984
$622$		0			0
$623$	3.16156	+	3.16156i	0.126665	+	0.126665i
$624$		0			0
$625$	13.7984	−	20.8472i	0.551935	−	0.833887i
$626$		0			0
$627$	42.0868	−	42.0868i	1.68078	−	1.68078i
$628$		0			0
$629$		−	3.17450i		−	0.126576i
$630$		0			0
$631$		−	13.9525i		−	0.555442i	−0.960662	−	0.277721i	$-0.910421\pi$
$631$		−	13.9525i		−	0.555442i	0.960662	−	0.277721i	$-0.0895790\pi$
$632$		0			0
$633$	−50.8757	+	50.8757i	−2.02213	+	2.02213i
$634$		0			0
$635$	14.3488	+	8.57909i	0.569416	+	0.340451i
$636$		0			0
$637$	−4.89595	−	4.89595i	−0.193984	−	0.193984i
$638$		0			0
$639$	−102.981			−4.07385
$640$		0			0
$641$	−21.1143			−0.833964			−0.416982	−	0.908915i	$-0.636912\pi$
$641$	−21.1143			−0.833964			−0.416982	+	0.908915i	$0.636912\pi$
$642$		0			0
$643$	12.0614	+	12.0614i	0.475656	+	0.475656i	0.903739	−	0.428083i	$-0.140811\pi$
$643$	12.0614	+	12.0614i	0.475656	+	0.475656i	−0.428083	+	0.903739i	$0.640811\pi$
$644$		0			0
$645$	−30.1856	+	7.59611i	−1.18856	+	0.299097i
$646$		0			0
$647$	−6.74997	+	6.74997i	−0.265369	+	0.265369i	−0.827231	−	0.561862i	$-0.810085\pi$
$647$	−6.74997	+	6.74997i	−0.265369	+	0.265369i	0.561862	+	0.827231i	$0.310085\pi$
$648$		0			0
$649$		−	18.4458i		−	0.724060i
$650$		0			0
$651$			2.46617i			0.0966570i
$652$		0			0
$653$	5.64046	−	5.64046i	0.220728	−	0.220728i	−0.588077	−	0.808805i	$-0.700115\pi$
$653$	5.64046	−	5.64046i	0.220728	−	0.220728i	0.808805	+	0.588077i	$0.200115\pi$
$654$		0			0
$655$	21.9651	−	5.52746i	0.858249	−	0.215976i
$656$		0			0
$657$	37.5146	+	37.5146i	1.46358	+	1.46358i
$658$		0			0
$659$	28.1394			1.09616			0.548078	−	0.836427i	$-0.315360\pi$
$659$	28.1394			1.09616			0.548078	+	0.836427i	$0.315360\pi$
$660$		0			0
$661$	−40.5686			−1.57794			−0.788968	−	0.614435i	$-0.789384\pi$
$661$	−40.5686			−1.57794			−0.788968	+	0.614435i	$0.789384\pi$
$662$		0			0
$663$	−7.93729	−	7.93729i	−0.308259	−	0.308259i
$664$		0			0
$665$	−1.80299	−	1.07800i	−0.0699170	−	0.0418030i
$666$		0			0
$667$	19.5189	−	19.5189i	0.755775	−	0.755775i
$668$		0			0
$669$		−	41.9452i		−	1.62169i
$670$		0			0
$671$			24.5907i			0.949314i
$672$		0			0
$673$	−5.80450	+	5.80450i	−0.223747	+	0.223747i	−0.810074	−	0.586327i	$-0.800573\pi$
$673$	−5.80450	+	5.80450i	−0.223747	+	0.223747i	0.586327	+	0.810074i	$0.300573\pi$
$674$		0			0
$675$	−19.3013	+	64.1314i	−0.742907	+	2.46842i
$676$		0			0
$677$	−21.5023	−	21.5023i	−0.826400	−	0.826400i	0.160617	−	0.987017i	$-0.448652\pi$
$677$	−21.5023	−	21.5023i	−0.826400	−	0.826400i	−0.987017	+	0.160617i	$0.948652\pi$
$678$		0			0
$679$	3.43092			0.131667
$680$		0			0
$681$	45.6645			1.74987
$682$		0			0
$683$	14.8407	+	14.8407i	0.567862	+	0.567862i	0.931529	−	0.363667i	$-0.118475\pi$
$683$	14.8407	+	14.8407i	0.567862	+	0.567862i	−0.363667	+	0.931529i	$0.618475\pi$
$684$		0			0
$685$	−3.59404	+	6.01116i	−0.137321	+	0.229675i
$686$		0			0
$687$	1.43891	−	1.43891i	0.0548977	−	0.0548977i
$688$		0			0
$689$			8.70757i			0.331732i
$690$		0			0
$691$			19.4005i			0.738031i	0.929423	+	0.369015i	$0.120305\pi$
$691$			19.4005i			0.738031i	−0.929423	+	0.369015i	$0.879695\pi$
$692$		0			0
$693$	−7.68090	+	7.68090i	−0.291773	+	0.291773i
$694$		0			0
$695$	6.70010	+	26.6250i	0.254149	+	1.00994i
$696$		0			0
$697$	−27.5189	−	27.5189i	−1.04235	−	1.04235i
$698$		0			0
$699$	14.7576			0.558183
$700$		0			0
$701$	9.04240			0.341527			0.170763	−	0.985312i	$-0.445377\pi$
$701$	9.04240			0.341527			0.170763	+	0.985312i	$0.445377\pi$
$702$		0			0
$703$	−2.17466	−	2.17466i	−0.0820187	−	0.0820187i
$704$		0			0
$705$	−4.45841	−	17.7169i	−0.167914	−	0.667258i
$706$		0			0
$707$	2.36066	−	2.36066i	0.0887816	−	0.0887816i
$708$		0			0
$709$			15.2034i			0.570976i	0.958382	+	0.285488i	$0.0921557\pi$
$709$			15.2034i			0.570976i	−0.958382	+	0.285488i	$0.907844\pi$
$710$		0			0
$711$			99.5671i			3.73406i
$712$		0			0
$713$	14.3657	−	14.3657i	0.537999	−	0.537999i
$714$		0			0
$715$	6.28038	−	10.5042i	0.234873	−	0.392833i
$716$		0			0
$717$	43.8278	+	43.8278i	1.63678	+	1.63678i
$718$		0			0
$719$	−15.8869			−0.592480			−0.296240	−	0.955113i	$-0.595733\pi$
$719$	−15.8869			−0.592480			−0.296240	+	0.955113i	$0.595733\pi$
$720$		0			0
$721$	−0.748571			−0.0278782
$722$		0			0
$723$	−33.3356	−	33.3356i	−1.23976	−	1.23976i
$724$		0			0
$725$	−9.00393	−	16.7571i	−0.334398	−	0.622343i
$726$		0			0
$727$	32.0845	−	32.0845i	1.18995	−	1.18995i	0.212868	−	0.977081i	$-0.431720\pi$
$727$	32.0845	−	32.0845i	1.18995	−	1.18995i	0.977081	−	0.212868i	$-0.0682803\pi$
$728$		0			0
$729$		−	24.1096i		−	0.892948i
$730$		0			0
$731$		−	15.3266i		−	0.566876i
$732$		0			0
$733$	−22.7444	+	22.7444i	−0.840082	+	0.840082i	−0.988869	−	0.148787i	$-0.952463\pi$
$733$	−22.7444	+	22.7444i	−0.840082	+	0.840082i	0.148787	+	0.988869i	$0.452463\pi$
$734$		0			0
$735$	−42.4292	−	25.3682i	−1.56502	−	0.935719i
$736$		0			0
$737$	0.0764917	+	0.0764917i	0.00281761	+	0.00281761i
$738$		0			0
$739$	31.9494			1.17528			0.587639	−	0.809123i	$-0.300058\pi$
$739$	31.9494			1.17528			0.587639	+	0.809123i	$0.300058\pi$
$740$		0			0
$741$	−10.8747			−0.399492
$742$		0			0
$743$	28.7073	+	28.7073i	1.05317	+	1.05317i	0.998505	+	0.0546647i	$0.0174090\pi$
$743$	28.7073	+	28.7073i	1.05317	+	1.05317i	0.0546647	+	0.998505i	$0.482591\pi$
$744$		0			0
$745$	−7.23681	+	1.82112i	−0.265136	+	0.0667207i
$746$		0			0
$747$	56.8860	−	56.8860i	2.08135	−	2.08135i
$748$		0			0
$749$		−	4.34536i		−	0.158776i
$750$		0			0
$751$			19.9042i			0.726316i	0.931728	+	0.363158i	$0.118301\pi$
$751$			19.9042i			0.726316i	−0.931728	+	0.363158i	$0.881699\pi$
$752$		0			0
$753$	−33.9895	+	33.9895i	−1.23865	+	1.23865i
$754$		0			0
$755$	−14.7000	+	3.69921i	−0.534987	+	0.134628i
$756$		0			0
$757$	−15.3723	−	15.3723i	−0.558714	−	0.558714i	0.370227	−	0.928941i	$-0.379280\pi$
$757$	−15.3723	−	15.3723i	−0.558714	−	0.558714i	−0.928941	+	0.370227i	$0.879280\pi$
$758$		0			0
$759$	126.795			4.60235
$760$		0			0
$761$	−2.20482			−0.0799247			−0.0399624	−	0.999201i	$-0.512724\pi$
$761$	−2.20482			−0.0799247			−0.0399624	+	0.999201i	$0.512724\pi$
$762$		0			0
$763$	−1.97556	−	1.97556i	−0.0715202	−	0.0715202i
$764$		0			0
$765$	−48.5450	−	29.0248i	−1.75515	−	1.04939i
$766$		0			0
$767$	−2.38308	+	2.38308i	−0.0860482	+	0.0860482i
$768$		0			0
$769$		−	1.03317i		−	0.0372569i	−0.999826	−	0.0186285i	$-0.994070\pi$
$769$		−	1.03317i		−	0.0372569i	0.999826	−	0.0186285i	$-0.00592997\pi$
$770$		0			0
$771$		−	14.7658i		−	0.531777i
$772$		0			0
$773$	31.8292	−	31.8292i	1.14482	−	1.14482i	0.157259	−	0.987557i	$-0.449734\pi$
$773$	31.8292	−	31.8292i	1.14482	−	1.14482i	0.987557	−	0.157259i	$-0.0502656\pi$
$774$		0			0
$775$	−6.62679	−	12.3330i	−0.238041	−	0.443015i
$776$		0			0
$777$	0.562358	+	0.562358i	0.0201745	+	0.0201745i
$778$		0			0
$779$	−37.7030			−1.35085
$780$		0			0
$781$	78.3367			2.80311
$782$		0			0
$783$	36.0347	+	36.0347i	1.28778	+	1.28778i
$784$		0			0
$785$	−13.7453	+	22.9895i	−0.490592	+	0.820532i
$786$		0			0
$787$	16.3916	−	16.3916i	0.584298	−	0.584298i	−0.351783	−	0.936082i	$-0.614425\pi$
$787$	16.3916	−	16.3916i	0.584298	−	0.584298i	0.936082	+	0.351783i	$0.114425\pi$
$788$		0			0
$789$			48.7712i			1.73630i
$790$		0			0
$791$		−	3.07857i		−	0.109461i
$792$		0			0
$793$	3.17697	−	3.17697i	0.112818	−	0.112818i
$794$		0			0
$795$	15.1717	+	60.2897i	0.538086	+	2.13825i
$796$		0			0
$797$	−11.5032	−	11.5032i	−0.407465	−	0.407465i	0.473389	−	0.880854i	$-0.343031\pi$
$797$	−11.5032	−	11.5032i	−0.407465	−	0.407465i	−0.880854	+	0.473389i	$0.843031\pi$
$798$		0			0
$799$	8.99570			0.318245
$800$		0			0
$801$	116.626			4.12079
$802$		0			0
$803$	−28.5371	−	28.5371i	−1.00705	−	1.00705i
$804$		0			0
$805$	−1.09209	−	4.33977i	−0.0384912	−	0.152957i
$806$		0			0
$807$	−56.0304	+	56.0304i	−1.97236	+	1.97236i
$808$		0			0
$809$		−	25.1242i		−	0.883321i	−0.897182	−	0.441661i	$-0.854390\pi$
$809$		−	25.1242i		−	0.883321i	0.897182	−	0.441661i	$-0.145610\pi$
$810$		0			0
$811$			24.4081i			0.857086i	0.903521	+	0.428543i	$0.140973\pi$
$811$			24.4081i			0.857086i	−0.903521	+	0.428543i	$0.859027\pi$
$812$		0			0
$813$	1.21032	−	1.21032i	0.0424477	−	0.0424477i
$814$		0			0
$815$	−9.73305	+	16.2789i	−0.340934	+	0.570224i
$816$		0			0
$817$	−10.4993	−	10.4993i	−0.367325	−	0.367325i
$818$		0			0
$819$	1.98465			0.0693493
$820$		0			0
$821$	5.40062			0.188483			0.0942414	−	0.995549i	$-0.469957\pi$
$821$	5.40062			0.188483			0.0942414	+	0.995549i	$0.469957\pi$
$822$		0			0
$823$	1.21602	+	1.21602i	0.0423877	+	0.0423877i	0.727983	−	0.685595i	$-0.240458\pi$
$823$	1.21602	+	1.21602i	0.0423877	+	0.0423877i	−0.685595	+	0.727983i	$0.740458\pi$
$824$		0			0
$825$	25.1822	−	83.6716i	0.876732	−	2.91307i
$826$		0			0
$827$	−14.3851	+	14.3851i	−0.500218	+	0.500218i	−0.911506	−	0.411287i	$-0.865079\pi$
$827$	−14.3851	+	14.3851i	−0.500218	+	0.500218i	0.411287	+	0.911506i	$0.365079\pi$
$828$		0			0
$829$			30.2650i			1.05115i	0.850748	+	0.525574i	$0.176150\pi$
$829$			30.2650i			1.05115i	−0.850748	+	0.525574i	$0.823850\pi$
$830$		0			0
$831$		−	76.4850i		−	2.65324i
$832$		0			0
$833$	17.2119	−	17.2119i	0.596358	−	0.596358i
$834$		0			0
$835$	7.42378	+	4.43864i	0.256911	+	0.153605i
$836$		0			0
$837$	26.5211	+	26.5211i	0.916704	+	0.916704i
$838$		0			0
$839$	36.6914			1.26673			0.633364	−	0.773854i	$-0.281674\pi$
$839$	36.6914			1.26673			0.633364	+	0.773854i	$0.281674\pi$
$840$		0			0
$841$	14.5252			0.500868
$842$		0			0
$843$	30.9546	+	30.9546i	1.06613	+	1.06613i
$844$		0			0
$845$	−2.16846	+	0.545687i	−0.0745973	+	0.0187722i
$846$		0			0
$847$	3.69731	−	3.69731i	0.127041	−	0.127041i
$848$		0			0
$849$			21.1082i			0.724430i
$850$		0			0
$851$		−	6.55158i		−	0.224585i
$852$		0			0
$853$	−10.6528	+	10.6528i	−0.364744	+	0.364744i	−0.865556	−	0.500812i	$-0.833035\pi$
$853$	−10.6528	+	10.6528i	−0.364744	+	0.364744i	0.500812	+	0.865556i	$0.333035\pi$
$854$		0			0
$855$	−53.1383	+	13.3721i	−1.81729	+	0.457316i
$856$		0			0
$857$	22.4034	+	22.4034i	0.765286	+	0.765286i	0.977273	−	0.211987i	$-0.0679934\pi$
$857$	22.4034	+	22.4034i	0.765286	+	0.765286i	−0.211987	+	0.977273i	$0.567993\pi$
$858$		0			0
$859$	−1.87126			−0.0638466			−0.0319233	−	0.999490i	$-0.510163\pi$
$859$	−1.87126			−0.0638466			−0.0319233	+	0.999490i	$0.510163\pi$
$860$		0			0
$861$	9.74986			0.332274
$862$		0			0
$863$	−5.56404	−	5.56404i	−0.189402	−	0.189402i	0.606035	−	0.795438i	$-0.292759\pi$
$863$	−5.56404	−	5.56404i	−0.189402	−	0.189402i	−0.795438	+	0.606035i	$0.792759\pi$
$864$		0			0
$865$	−47.8195	−	28.5910i	−1.62591	−	0.972125i
$866$		0			0
$867$	−10.4782	+	10.4782i	−0.355857	+	0.355857i
$868$		0			0
$869$		−	75.7402i		−	2.56931i
$870$		0			0
$871$		−	0.0197645i		−	0.000669696i
$872$		0			0
$873$	63.2815	−	63.2815i	2.14176	−	2.14176i
$874$		0			0
$875$	−3.08071	−	0.141236i	−0.104147	−	0.00477466i
$876$		0			0
$877$	−2.22717	−	2.22717i	−0.0752061	−	0.0752061i	0.668503	−	0.743709i	$-0.266935\pi$
$877$	−2.22717	−	2.22717i	−0.0752061	−	0.0752061i	−0.743709	+	0.668503i	$0.766935\pi$
$878$		0			0
$879$	−38.5482			−1.30020
$880$		0			0
$881$	37.0003			1.24657			0.623286	−	0.781994i	$-0.285797\pi$
$881$	37.0003			1.24657			0.623286	+	0.781994i	$0.285797\pi$
$882$		0			0
$883$	−22.9203	−	22.9203i	−0.771330	−	0.771330i	0.207009	−	0.978339i	$-0.433627\pi$
$883$	−22.9203	−	22.9203i	−0.771330	−	0.771330i	−0.978339	+	0.207009i	$0.933627\pi$
$884$		0			0
$885$	−12.3479	+	20.6522i	−0.415069	+	0.694217i
$886$		0			0
$887$	32.1138	−	32.1138i	1.07828	−	1.07828i	0.0816116	−	0.996664i	$-0.473993\pi$
$887$	32.1138	−	32.1138i	1.07828	−	1.07828i	0.996664	−	0.0816116i	$-0.0260067\pi$
$888$		0			0
$889$		−	2.06229i		−	0.0691670i
$890$		0			0
$891$			115.941i			3.88418i
$892$		0			0
$893$	6.16241	−	6.16241i	0.206217	−	0.206217i
$894$		0			0
$895$	1.59841	+	6.35178i	0.0534288	+	0.212316i
$896$		0			0
$897$	−16.3811	−	16.3811i	−0.546949	−	0.546949i
$898$		0			0
$899$	−10.6533			−0.355308
$900$		0			0
$901$	−30.6119			−1.01983
$902$		0			0
$903$	2.71509	+	2.71509i	0.0903526	+	0.0903526i
$904$		0			0
$905$	4.61570	+	18.3420i	0.153431	+	0.609707i
$906$		0			0
$907$	28.8450	−	28.8450i	0.957783	−	0.957783i	−0.0413615	−	0.999144i	$-0.513170\pi$
$907$	28.8450	−	28.8450i	0.957783	−	0.957783i	0.999144	+	0.0413615i	$0.0131695\pi$
$908$		0			0
$909$		−	87.0820i		−	2.88833i
$910$		0			0
$911$			39.1426i			1.29685i	0.761278	+	0.648426i	$0.224572\pi$
$911$			39.1426i			1.29685i	−0.761278	+	0.648426i	$0.775428\pi$
$912$		0			0
$913$	−43.2729	+	43.2729i	−1.43212	+	1.43212i
$914$		0			0
$915$	16.4614	−	27.5322i	0.544196	−	0.910187i
$916$		0			0
$917$	−1.97569	−	1.97569i	−0.0652430	−	0.0652430i
$918$		0			0
$919$	21.4598			0.707892			0.353946	−	0.935266i	$-0.384840\pi$
$919$	21.4598			0.707892			0.353946	+	0.935266i	$0.384840\pi$
$920$		0			0
$921$	79.9040			2.63293
$922$		0			0
$923$	−10.1206	−	10.1206i	−0.333125	−	0.333125i
$924$		0			0
$925$	−4.32338	−	1.30119i	−0.142152	−	0.0427827i
$926$		0			0
$927$	−13.8070	+	13.8070i	−0.453481	+	0.453481i
$928$		0			0
$929$		−	2.76417i		−	0.0906896i	−0.998971	−	0.0453448i	$-0.985561\pi$
$929$		−	2.76417i		−	0.0906896i	0.998971	−	0.0453448i	$-0.0144386\pi$
$930$		0			0
$931$		−	23.5817i		−	0.772859i
$932$		0			0
$933$	−61.7701	+	61.7701i	−2.02226	+	2.02226i
$934$		0			0
$935$	36.9279	+	22.0790i	1.20767	+	0.722059i
$936$		0			0
$937$	−1.64905	−	1.64905i	−0.0538720	−	0.0538720i	0.679658	−	0.733530i	$-0.262128\pi$
$937$	−1.64905	−	1.64905i	−0.0538720	−	0.0538720i	−0.733530	+	0.679658i	$0.762128\pi$
$938$		0			0
$939$	72.9964			2.38215
$940$		0			0
$941$	4.99721			0.162905			0.0814523	−	0.996677i	$-0.474044\pi$
$941$	4.99721			0.162905			0.0814523	+	0.996677i	$0.474044\pi$
$942$		0			0
$943$	−56.7939	−	56.7939i	−1.84946	−	1.84946i
$944$		0			0
$945$	8.01185	−	2.01616i	0.260625	−	0.0655856i
$946$		0			0
$947$	−25.0443	+	25.0443i	−0.813829	+	0.813829i	−0.985206	−	0.171376i	$-0.945179\pi$
$947$	−25.0443	+	25.0443i	−0.813829	+	0.813829i	0.171376	+	0.985206i	$0.445179\pi$
$948$		0			0
$949$			7.37365i			0.239359i
$950$		0			0
$951$		−	102.088i		−	3.31043i
$952$		0			0
$953$	−3.74548	+	3.74548i	−0.121328	+	0.121328i	−0.765164	−	0.643836i	$-0.777342\pi$
$953$	−3.74548	+	3.74548i	−0.121328	+	0.121328i	0.643836	+	0.765164i	$0.277342\pi$
$954$		0			0
$955$	39.2764	−	9.88378i	1.27095	−	0.319832i
$956$		0			0
$957$	−47.0142	−	47.0142i	−1.51975	−	1.51975i
$958$		0			0
$959$	0.863956			0.0278986
$960$		0			0
$961$	23.1593			0.747074
$962$		0			0
$963$	−80.1479	−	80.1479i	−2.58273	−	2.58273i
$964$		0			0
$965$	13.0971	+	7.83068i	0.421610	+	0.252079i
$966$		0			0
$967$	15.3197	−	15.3197i	0.492647	−	0.492647i	−0.416492	−	0.909139i	$-0.636741\pi$
$967$	15.3197	−	15.3197i	0.492647	−	0.492647i	0.909139	+	0.416492i	$0.136741\pi$
$968$		0			0
$969$		−	38.2305i		−	1.22814i
$970$		0			0
$971$		−	50.9086i		−	1.63374i	−0.576825	−	0.816868i	$-0.695708\pi$
$971$		−	50.9086i		−	1.63374i	0.576825	−	0.816868i	$-0.304292\pi$
$972$		0			0
$973$	2.39483	−	2.39483i	0.0767747	−	0.0767747i
$974$		0			0
$975$	−14.0633	+	7.55648i	−0.450385	+	0.242001i
$976$		0			0
$977$	−21.0348	−	21.0348i	−0.672963	−	0.672963i	0.285435	−	0.958398i	$-0.407862\pi$
$977$	−21.0348	−	21.0348i	−0.672963	−	0.672963i	−0.958398	+	0.285435i	$0.907862\pi$
$978$		0			0
$979$	−88.7171			−2.83541
$980$		0			0
$981$	−72.8764			−2.32677
$982$		0			0
$983$	−23.1754	−	23.1754i	−0.739180	−	0.739180i	0.233240	−	0.972419i	$-0.425067\pi$
$983$	−23.1754	−	23.1754i	−0.739180	−	0.739180i	−0.972419	+	0.233240i	$0.925067\pi$
$984$		0			0
$985$	10.2422	−	17.1305i	0.326345	−	0.545824i
$986$		0			0
$987$	−1.59358	+	1.59358i	−0.0507241	+	0.0507241i
$988$		0			0
$989$		−	31.6313i		−	1.00582i
$990$		0			0
$991$		−	3.92478i		−	0.124675i	−0.998055	−	0.0623373i	$-0.980145\pi$
$991$		−	3.92478i		−	0.124675i	0.998055	−	0.0623373i	$-0.0198555\pi$
$992$		0			0
$993$	−27.0719	+	27.0719i	−0.859102	+	0.859102i
$994$		0			0
$995$	−2.86854	−	11.3990i	−0.0909387	−	0.361374i
$996$		0			0
$997$	6.79800	+	6.79800i	0.215295	+	0.215295i	0.806512	−	0.591217i	$-0.201352\pi$
$997$	6.79800	+	6.79800i	0.215295	+	0.215295i	−0.591217	+	0.806512i	$0.701352\pi$
$998$		0			0
$999$	12.0952			0.382674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.bp.a.287.1	✓	24
4.3	odd	2	inner	1040.2.bp.a.287.12	yes	24
5.3	odd	4	inner	1040.2.bp.a.703.12	yes	24
20.3	even	4	inner	1040.2.bp.a.703.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1040.2.bp.a.287.1	✓	24	1.1	even	1	trivial
1040.2.bp.a.287.12	yes	24	4.3	odd	2	inner
1040.2.bp.a.703.1	yes	24	20.3	even	4	inner
1040.2.bp.a.703.12	yes	24	5.3	odd	4	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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.bp (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25777 - 2.25777i) q^{3} +(-0.545687 - 2.16846i) q^{5} +(-0.195046 + 0.195046i) q^{7} +7.19503i q^{9} +O(q^{10})\)	\(q+(-2.25777 - 2.25777i) q^{3} +(-0.545687 - 2.16846i) q^{5} +(-0.195046 + 0.195046i) q^{7} +7.19503i q^{9} -5.47322i q^{11} +(-0.707107 + 0.707107i) q^{13} +(-3.66385 + 6.12792i) q^{15} +(-2.48587 - 2.48587i) q^{17} -3.40583 q^{19} +0.880736 q^{21} +(-5.13037 - 5.13037i) q^{23} +(-4.40445 + 2.36660i) q^{25} +(9.47140 - 9.47140i) q^{27} +3.80458i q^{29} +2.80013i q^{31} +(-12.3573 + 12.3573i) q^{33} +(0.529383 + 0.316515i) q^{35} +(0.638509 + 0.638509i) q^{37} +3.19297 q^{39} +11.0701 q^{41} +(3.08275 + 3.08275i) q^{43} +(15.6021 - 3.92623i) q^{45} +(-1.80937 + 1.80937i) q^{47} +6.92391i q^{49} +11.2250i q^{51} +(6.15718 - 6.15718i) q^{53} +(-11.8685 + 2.98666i) q^{55} +(7.68958 + 7.68958i) q^{57} +3.37019 q^{59} -4.49292 q^{61} +(-1.40336 - 1.40336i) q^{63} +(1.91919 + 1.14747i) q^{65} +(-0.0139756 + 0.0139756i) q^{67} +23.1664i q^{69} +14.3127i q^{71} +(5.21396 - 5.21396i) q^{73} +(15.2875 + 4.60099i) q^{75} +(1.06753 + 1.06753i) q^{77} +13.8383 q^{79} -21.1834 q^{81} +(-7.90629 - 7.90629i) q^{83} +(-4.03400 + 6.74701i) q^{85} +(8.58986 - 8.58986i) q^{87} -16.2093i q^{89} -0.275836i q^{91} +(6.32204 - 6.32204i) q^{93} +(1.85852 + 7.38542i) q^{95} +(-8.79518 - 8.79518i) q^{97} +39.3800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{5}+O(q^{10}) \) 24 * q - 8 * q^5	\( 24 q - 8 q^{5} + 16 q^{17} + 16 q^{21} - 16 q^{25} - 24 q^{33} - 24 q^{37} + 16 q^{41} + 48 q^{45} + 8 q^{53} + 8 q^{57} + 16 q^{61} + 8 q^{73} + 24 q^{77} + 40 q^{81} + 16 q^{85} + 56 q^{93} + 32 q^{97}+O(q^{100}) \) 24 * q - 8 * q^5 + 16 * q^17 + 16 * q^21 - 16 * q^25 - 24 * q^33 - 24 * q^37 + 16 * q^41 + 48 * q^45 + 8 * q^53 + 8 * q^57 + 16 * q^61 + 8 * q^73 + 24 * q^77 + 40 * q^81 + 16 * q^85 + 56 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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