LMFDB - Embedded newform 80.7.p.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,7,Mod(17,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("80.17"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	80.p (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,46] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$18.4043266896$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.17
Dual form			80.7.p.a.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(23.0000 - 23.0000i) q^{3} +(-75.0000 + 100.000i) q^{5} +(247.000 + 247.000i) q^{7} -329.000i q^{9} -1402.00 q^{11} +(-2703.00 + 2703.00i) q^{13} +(575.000 + 4025.00i) q^{15} +(2593.00 + 2593.00i) q^{17} -1720.00i q^{19} +11362.0 q^{21} +(-2137.00 + 2137.00i) q^{23} +(-4375.00 - 15000.0i) q^{25} +(9200.00 + 9200.00i) q^{27} +30520.0i q^{29} +37838.0 q^{31} +(-32246.0 + 32246.0i) q^{33} +(-43225.0 + 6175.00i) q^{35} +(37113.0 + 37113.0i) q^{37} +124338. i q^{39} -35438.0 q^{41} +(-39177.0 + 39177.0i) q^{43} +(32900.0 + 24675.0i) q^{45} +(-95193.0 - 95193.0i) q^{47} +4369.00i q^{49} +119278. q^{51} +(36017.0 - 36017.0i) q^{53} +(105150. - 140200. i) q^{55} +(-39560.0 - 39560.0i) q^{57} +35960.0i q^{59} +83322.0 q^{61} +(81263.0 - 81263.0i) q^{63} +(-67575.0 - 473025. i) q^{65} +(-60833.0 - 60833.0i) q^{67} +98302.0i q^{69} +40318.0 q^{71} +(-129023. + 129023. i) q^{73} +(-445625. - 244375. i) q^{75} +(-346294. - 346294. i) q^{77} -524640. i q^{79} +663041. q^{81} +(114423. - 114423. i) q^{83} +(-453775. + 64825.0i) q^{85} +(701960. + 701960. i) q^{87} +187280. i q^{89} -1.33528e6 q^{91} +(870274. - 870274. i) q^{93} +(172000. + 129000. i) q^{95} +(532833. + 532833. i) q^{97} +461258. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 46 q^{3} - 150 q^{5} + 494 q^{7} - 2804 q^{11} - 5406 q^{13} + 1150 q^{15} + 5186 q^{17} + 22724 q^{21} - 4274 q^{23} - 8750 q^{25} + 18400 q^{27} + 75676 q^{31} - 64492 q^{33} - 86450 q^{35} + 74226 q^{37}+ \cdots + 1065666 q^{97}+O(q^{100}) $ 2 * q + 46 * q^3 - 150 * q^5 + 494 * q^7 - 2804 * q^11 - 5406 * q^13 + 1150 * q^15 + 5186 * q^17 + 22724 * q^21 - 4274 * q^23 - 8750 * q^25 + 18400 * q^27 + 75676 * q^31 - 64492 * q^33 - 86450 * q^35 + 74226 * q^37 - 70876 * q^41 - 78354 * q^43 + 65800 * q^45 - 190386 * q^47 + 238556 * q^51 + 72034 * q^53 + 210300 * q^55 - 79120 * q^57 + 166644 * q^61 + 162526 * q^63 - 135150 * q^65 - 121666 * q^67 + 80636 * q^71 - 258046 * q^73 - 891250 * q^75 - 692588 * q^77 + 1326082 * q^81 + 228846 * q^83 - 907550 * q^85 + 1403920 * q^87 - 2670564 * q^91 + 1740548 * q^93 + 344000 * q^95 + 1065666 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	23.0000	−	23.0000i	0.851852	−	0.851852i	−0.138509	−	0.990361i	$-0.544231\pi$
$3$	23.0000	−	23.0000i	0.851852	−	0.851852i	0.990361	+	0.138509i	$0.0442311\pi$
$4$		0			0
$5$	−75.0000	+	100.000i	−0.600000	+	0.800000i
$5$	−75.0000	+	100.000i	−0.600000	+	0.800000i
$6$		0			0
$7$	247.000	+	247.000i	0.720117	+	0.720117i	0.968629	−	0.248512i	$-0.0799416\pi$
$7$	247.000	+	247.000i	0.720117	+	0.720117i	−0.248512	+	0.968629i	$0.579942\pi$
$8$		0			0
$9$		−	329.000i		−	0.451303i
$10$		0			0
$11$	−1402.00			−1.05334			−0.526672	−	0.850069i	$-0.676560\pi$
$11$	−1402.00			−1.05334			−0.526672	+	0.850069i	$0.676560\pi$
$12$		0			0
$13$	−2703.00	+	2703.00i	−1.23031	+	1.23031i	−0.266471	+	0.963843i	$0.585858\pi$
$13$	−2703.00	+	2703.00i	−1.23031	+	1.23031i	−0.963843	+	0.266471i	$0.914142\pi$
$14$		0			0
$15$	575.000	+	4025.00i	0.170370	+	1.19259i
$16$		0			0
$17$	2593.00	+	2593.00i	0.527783	+	0.527783i	0.919911	−	0.392127i	$-0.128261\pi$
$17$	2593.00	+	2593.00i	0.527783	+	0.527783i	−0.392127	+	0.919911i	$0.628261\pi$
$18$		0			0
$19$		−	1720.00i		−	0.250765i	−0.992108	−	0.125383i	$-0.959984\pi$
$19$		−	1720.00i		−	0.250765i	0.992108	−	0.125383i	$-0.0400159\pi$
$20$		0			0
$21$	11362.0			1.22687
$22$		0			0
$23$	−2137.00	+	2137.00i	−0.175639	+	0.175639i	−0.789452	−	0.613813i	$-0.789635\pi$
$23$	−2137.00	+	2137.00i	−0.175639	+	0.175639i	0.613813	+	0.789452i	$0.289635\pi$
$24$		0			0
$25$	−4375.00	−	15000.0i	−0.280000	−	0.960000i
$26$		0			0
$27$	9200.00	+	9200.00i	0.467408	+	0.467408i
$28$		0			0
$29$			30520.0i			1.25138i	0.780070	+	0.625692i	$0.215183\pi$
$29$			30520.0i			1.25138i	−0.780070	+	0.625692i	$0.784817\pi$
$30$		0			0
$31$	37838.0			1.27012			0.635058	−	0.772465i	$-0.280976\pi$
$31$	37838.0			1.27012			0.635058	+	0.772465i	$0.280976\pi$
$32$		0			0
$33$	−32246.0	+	32246.0i	−0.897292	+	0.897292i
$34$		0			0
$35$	−43225.0	+	6175.00i	−1.00816	+	0.144023i
$36$		0			0
$37$	37113.0	+	37113.0i	0.732691	+	0.732691i	0.971152	−	0.238461i	$-0.0766429\pi$
$37$	37113.0	+	37113.0i	0.732691	+	0.732691i	−0.238461	+	0.971152i	$0.576643\pi$
$38$		0			0
$39$			124338.i			2.09609i
$40$		0			0
$41$	−35438.0			−0.514183			−0.257091	−	0.966387i	$-0.582764\pi$
$41$	−35438.0			−0.514183			−0.257091	+	0.966387i	$0.582764\pi$
$42$		0			0
$43$	−39177.0	+	39177.0i	−0.492749	+	0.492749i	−0.909171	−	0.416422i	$-0.863284\pi$
$43$	−39177.0	+	39177.0i	−0.492749	+	0.492749i	0.416422	+	0.909171i	$0.363284\pi$
$44$		0			0
$45$	32900.0	+	24675.0i	0.361043	+	0.270782i
$46$		0			0
$47$	−95193.0	−	95193.0i	−0.916878	−	0.916878i	0.0799233	−	0.996801i	$-0.474532\pi$
$47$	−95193.0	−	95193.0i	−0.916878	−	0.916878i	−0.996801	+	0.0799233i	$0.974532\pi$
$48$		0			0
$49$			4369.00i			0.0371359i
$50$		0			0
$51$	119278.			0.899187
$52$		0			0
$53$	36017.0	−	36017.0i	0.241925	−	0.241925i	−0.575721	−	0.817646i	$-0.695279\pi$
$53$	36017.0	−	36017.0i	0.241925	−	0.241925i	0.817646	+	0.575721i	$0.195279\pi$
$54$		0			0
$55$	105150.	−	140200.i	0.632006	−	0.842675i
$56$		0			0
$57$	−39560.0	−	39560.0i	−0.213615	−	0.213615i
$58$		0			0
$59$			35960.0i			0.175091i	0.996161	+	0.0875455i	$0.0279023\pi$
$59$			35960.0i			0.175091i	−0.996161	+	0.0875455i	$0.972098\pi$
$60$		0			0
$61$	83322.0			0.367088			0.183544	−	0.983011i	$-0.441243\pi$
$61$	83322.0			0.367088			0.183544	+	0.983011i	$0.441243\pi$
$62$		0			0
$63$	81263.0	−	81263.0i	0.324991	−	0.324991i
$64$		0			0
$65$	−67575.0	−	473025.i	−0.246063	−	1.72244i
$66$		0			0
$67$	−60833.0	−	60833.0i	−0.202262	−	0.202262i	0.598706	−	0.800969i	$-0.295682\pi$
$67$	−60833.0	−	60833.0i	−0.202262	−	0.202262i	−0.800969	+	0.598706i	$0.795682\pi$
$68$		0			0
$69$			98302.0i			0.299237i
$70$		0			0
$71$	40318.0			0.112648			0.0563241	−	0.998413i	$-0.482062\pi$
$71$	40318.0			0.112648			0.0563241	+	0.998413i	$0.482062\pi$
$72$		0			0
$73$	−129023.	+	129023.i	−0.331664	+	0.331664i	−0.853218	−	0.521554i	$-0.825352\pi$
$73$	−129023.	+	129023.i	−0.331664	+	0.331664i	0.521554	+	0.853218i	$0.325352\pi$
$74$		0			0
$75$	−445625.	−	244375.i	−1.05630	−	0.579259i
$76$		0			0
$77$	−346294.	−	346294.i	−0.758530	−	0.758530i
$78$		0			0
$79$		−	524640.i		−	1.06409i	−0.846715	−	0.532047i	$-0.821423\pi$
$79$		−	524640.i		−	1.06409i	0.846715	−	0.532047i	$-0.178577\pi$
$80$		0			0
$81$	663041.			1.24763
$82$		0			0
$83$	114423.	−	114423.i	0.200115	−	0.200115i	−0.599934	−	0.800049i	$-0.704807\pi$
$83$	114423.	−	114423.i	0.200115	−	0.200115i	0.800049	+	0.599934i	$0.204807\pi$
$84$		0			0
$85$	−453775.	+	64825.0i	−0.738897	+	0.105557i
$86$		0			0
$87$	701960.	+	701960.i	1.06599	+	1.06599i
$88$		0			0
$89$			187280.i			0.265657i	0.991139	+	0.132829i	$0.0424060\pi$
$89$			187280.i			0.265657i	−0.991139	+	0.132829i	$0.957594\pi$
$90$		0			0
$91$	−1.33528e6			−1.77194
$92$		0			0
$93$	870274.	−	870274.i	1.08195	−	1.08195i
$94$		0			0
$95$	172000.	+	129000.i	0.200612	+	0.150459i
$96$		0			0
$97$	532833.	+	532833.i	0.583816	+	0.583816i	0.935950	−	0.352134i	$-0.114544\pi$
$97$	532833.	+	532833.i	0.583816	+	0.583816i	−0.352134	+	0.935950i	$0.614544\pi$
$98$		0			0
$99$			461258.i			0.475377i
$100$		0			0
$101$	−1.70508e6			−1.65493			−0.827466	−	0.561516i	$-0.810218\pi$
$101$	−1.70508e6			−1.65493			−0.827466	+	0.561516i	$0.810218\pi$
$102$		0			0
$103$	665063.	−	665063.i	0.608627	−	0.608627i	−0.333960	−	0.942587i	$-0.608385\pi$
$103$	665063.	−	665063.i	0.608627	−	0.608627i	0.942587	+	0.333960i	$0.108385\pi$
$104$		0			0
$105$	−852150.	+	1.13620e6i	−0.736119	+	0.981492i
$106$		0			0
$107$	−309073.	−	309073.i	−0.252296	−	0.252296i	0.569616	−	0.821911i	$-0.307092\pi$
$107$	−309073.	−	309073.i	−0.252296	−	0.252296i	−0.821911	+	0.569616i	$0.807092\pi$
$108$		0			0
$109$		−	362440.i		−	0.279870i	−0.990161	−	0.139935i	$-0.955311\pi$
$109$		−	362440.i		−	0.279870i	0.990161	−	0.139935i	$-0.0446894\pi$
$110$		0			0
$111$	1.70720e6			1.24829
$112$		0			0
$113$	722657.	−	722657.i	0.500838	−	0.500838i	−0.410861	−	0.911698i	$-0.634772\pi$
$113$	722657.	−	722657.i	0.500838	−	0.500838i	0.911698	+	0.410861i	$0.134772\pi$
$114$		0			0
$115$	−53425.0	−	373975.i	−0.0351278	−	0.245895i
$116$		0			0
$117$	889287.	+	889287.i	0.555245	+	0.555245i
$118$		0			0
$119$			1.28094e6i			0.760131i
$120$		0			0
$121$	194043.			0.109532
$122$		0			0
$123$	−815074.	+	815074.i	−0.438008	+	0.438008i
$124$		0			0
$125$	1.82812e6	+	687500.i	0.936000	+	0.352000i
$126$		0			0
$127$	1.94641e6	+	1.94641e6i	0.950216	+	0.950216i	0.998818	−	0.0486019i	$-0.0154766\pi$
$127$	1.94641e6	+	1.94641e6i	0.950216	+	0.950216i	−0.0486019	+	0.998818i	$0.515477\pi$
$128$		0			0
$129$			1.80214e6i			0.839498i
$130$		0			0
$131$	−3.75620e6			−1.67084			−0.835420	−	0.549612i	$-0.814776\pi$
$131$	−3.75620e6			−1.67084			−0.835420	+	0.549612i	$0.814776\pi$
$132$		0			0
$133$	424840.	−	424840.i	0.180580	−	0.180580i
$134$		0			0
$135$	−1.61000e6	+	230000.i	−0.654372	+	0.0934817i
$136$		0			0
$137$	1.04283e6	+	1.04283e6i	0.405558	+	0.405558i	0.880186	−	0.474628i	$-0.157417\pi$
$137$	1.04283e6	+	1.04283e6i	0.405558	+	0.405558i	−0.474628	+	0.880186i	$0.657417\pi$
$138$		0			0
$139$			3.24700e6i			1.20903i	0.796593	+	0.604516i	$0.206634\pi$
$139$			3.24700e6i			1.20903i	−0.796593	+	0.604516i	$0.793366\pi$
$140$		0			0
$141$	−4.37888e6			−1.56209
$142$		0			0
$143$	3.78961e6	−	3.78961e6i	1.29594	−	1.29594i
$144$		0			0
$145$	−3.05200e6	−	2.28900e6i	−1.00111	−	0.750830i
$146$		0			0
$147$	100487.	+	100487.i	0.0316343	+	0.0316343i
$148$		0			0
$149$			5.76420e6i			1.74253i	0.490813	+	0.871265i	$0.336700\pi$
$149$			5.76420e6i			1.74253i	−0.490813	+	0.871265i	$0.663300\pi$
$150$		0			0
$151$	−1.03280e6			−0.299976			−0.149988	−	0.988688i	$-0.547923\pi$
$151$	−1.03280e6			−0.299976			−0.149988	+	0.988688i	$0.547923\pi$
$152$		0			0
$153$	853097.	−	853097.i	0.238190	−	0.238190i
$154$		0			0
$155$	−2.83785e6	+	3.78380e6i	−0.762069	+	1.01609i
$156$		0			0
$157$	2.30055e6	+	2.30055e6i	0.594475	+	0.594475i	0.938837	−	0.344362i	$-0.111905\pi$
$157$	2.30055e6	+	2.30055e6i	0.594475	+	0.594475i	−0.344362	+	0.938837i	$0.611905\pi$
$158$		0			0
$159$		−	1.65678e6i		−	0.412168i
$160$		0			0
$161$	−1.05568e6			−0.252961
$162$		0			0
$163$	4.02178e6	−	4.02178e6i	0.928658	−	0.928658i	−0.0689613	−	0.997619i	$-0.521968\pi$
$163$	4.02178e6	−	4.02178e6i	0.928658	−	0.928658i	0.997619	+	0.0689613i	$0.0219685\pi$
$164$		0			0
$165$	−806150.	−	5.64305e6i	−0.179458	−	1.25621i
$166$		0			0
$167$	710167.	+	710167.i	0.152479	+	0.152479i	0.779224	−	0.626745i	$-0.215613\pi$
$167$	710167.	+	710167.i	0.152479	+	0.152479i	−0.626745	+	0.779224i	$0.715613\pi$
$168$		0			0
$169$		−	9.78561e6i		−	2.02735i
$170$		0			0
$171$	−565880.			−0.113171
$172$		0			0
$173$	3.77650e6	−	3.77650e6i	0.729375	−	0.729375i	−0.241120	−	0.970495i	$-0.577515\pi$
$173$	3.77650e6	−	3.77650e6i	0.729375	−	0.729375i	0.970495	+	0.241120i	$0.0775148\pi$
$174$		0			0
$175$	2.62438e6	−	4.78562e6i	0.489679	−	0.892945i
$176$		0			0
$177$	827080.	+	827080.i	0.149152	+	0.149152i
$178$		0			0
$179$		−	5.46380e6i		−	0.952655i	−0.879268	−	0.476328i	$-0.841968\pi$
$179$		−	5.46380e6i		−	0.952655i	0.879268	−	0.476328i	$-0.158032\pi$
$180$		0			0
$181$	9.02436e6			1.52188			0.760941	−	0.648821i	$-0.224738\pi$
$181$	9.02436e6			1.52188			0.760941	+	0.648821i	$0.224738\pi$
$182$		0			0
$183$	1.91641e6	−	1.91641e6i	0.312705	−	0.312705i
$184$		0			0
$185$	−6.49478e6	+	927825.i	−1.02577	+	0.146538i
$186$		0			0
$187$	−3.63539e6	−	3.63539e6i	−0.555937	−	0.555937i
$188$		0			0
$189$			4.54480e6i			0.673177i
$190$		0			0
$191$	4.02120e6			0.577106			0.288553	−	0.957464i	$-0.406826\pi$
$191$	4.02120e6			0.577106			0.288553	+	0.957464i	$0.406826\pi$
$192$		0			0
$193$	−1.05414e6	+	1.05414e6i	−0.146632	+	0.146632i	−0.776611	−	0.629980i	$-0.783063\pi$
$193$	−1.05414e6	+	1.05414e6i	−0.146632	+	0.146632i	0.629980	+	0.776611i	$0.283063\pi$
$194$		0			0
$195$	−1.24338e7	−	9.32535e6i	−1.67687	−	1.25765i
$196$		0			0
$197$	−7.29489e6	−	7.29489e6i	−0.954157	−	0.954157i	0.0448372	−	0.998994i	$-0.485723\pi$
$197$	−7.29489e6	−	7.29489e6i	−0.954157	−	0.954157i	−0.998994	+	0.0448372i	$0.985723\pi$
$198$		0			0
$199$			1.41170e7i			1.79137i	0.444693	+	0.895683i	$0.353313\pi$
$199$			1.41170e7i			1.79137i	−0.444693	+	0.895683i	$0.646687\pi$
$200$		0			0
$201$	−2.79832e6			−0.344595
$202$		0			0
$203$	−7.53844e6	+	7.53844e6i	−0.901142	+	0.901142i
$204$		0			0
$205$	2.65785e6	−	3.54380e6i	0.308510	−	0.411346i
$206$		0			0
$207$	703073.	+	703073.i	0.0792664	+	0.0792664i
$208$		0			0
$209$			2.41144e6i			0.264142i
$210$		0			0
$211$	1.23188e7			1.31136			0.655681	−	0.755038i	$-0.272382\pi$
$211$	1.23188e7			1.31136			0.655681	+	0.755038i	$0.272382\pi$
$212$		0			0
$213$	927314.	−	927314.i	0.0959595	−	0.0959595i
$214$		0			0
$215$	−979425.	−	6.85598e6i	−0.0985498	−	0.689849i
$216$		0			0
$217$	9.34599e6	+	9.34599e6i	0.914631	+	0.914631i
$218$		0			0
$219$			5.93506e6i			0.565057i
$220$		0			0
$221$	−1.40178e7			−1.29868
$222$		0			0
$223$	−328857.	+	328857.i	−0.0296546	+	0.0296546i	−0.721779	−	0.692124i	$-0.756675\pi$
$223$	−328857.	+	328857.i	−0.0296546	+	0.0296546i	0.692124	+	0.721779i	$0.256675\pi$
$224$		0			0
$225$	−4.93500e6	+	1.43938e6i	−0.433251	+	0.126365i
$226$		0			0
$227$	7.95085e6	+	7.95085e6i	0.679729	+	0.679729i	0.959939	−	0.280210i	$-0.0904040\pi$
$227$	7.95085e6	+	7.95085e6i	0.679729	+	0.679729i	−0.280210	+	0.959939i	$0.590404\pi$
$228$		0			0
$229$			2.28695e7i			1.90436i	0.305532	+	0.952182i	$0.401166\pi$
$229$			2.28695e7i			1.90436i	−0.305532	+	0.952182i	$0.598834\pi$
$230$		0			0
$231$	−1.59295e7			−1.29231
$232$		0			0
$233$	8.59050e6	−	8.59050e6i	0.679126	−	0.679126i	−0.280676	−	0.959803i	$-0.590559\pi$
$233$	8.59050e6	−	8.59050e6i	0.679126	−	0.679126i	0.959803	+	0.280676i	$0.0905587\pi$
$234$		0			0
$235$	1.66588e7	−	2.37982e6i	1.28363	−	0.183376i
$236$		0			0
$237$	−1.20667e7	−	1.20667e7i	−0.906451	−	0.906451i
$238$		0			0
$239$		−	9.66576e6i		−	0.708015i	−0.935243	−	0.354007i	$-0.884819\pi$
$239$		−	9.66576e6i		−	0.708015i	0.935243	−	0.354007i	$-0.115181\pi$
$240$		0			0
$241$	1.85926e7			1.32828			0.664141	−	0.747608i	$-0.268798\pi$
$241$	1.85926e7			1.32828			0.664141	+	0.747608i	$0.268798\pi$
$242$		0			0
$243$	8.54314e6	−	8.54314e6i	0.595386	−	0.595386i
$244$		0			0
$245$	−436900.	−	327675.i	−0.0297087	−	0.0222815i
$246$		0			0
$247$	4.64916e6	+	4.64916e6i	0.308520	+	0.308520i
$248$		0			0
$249$		−	5.26346e6i		−	0.340936i
$250$		0			0
$251$	−1.19350e7			−0.754747			−0.377373	−	0.926061i	$-0.623173\pi$
$251$	−1.19350e7			−0.754747			−0.377373	+	0.926061i	$0.623173\pi$
$252$		0			0
$253$	2.99607e6	−	2.99607e6i	0.185008	−	0.185008i
$254$		0			0
$255$	−8.94585e6	+	1.19278e7i	−0.539512	+	0.719349i
$256$		0			0
$257$	1.54304e7	+	1.54304e7i	0.909031	+	0.909031i	0.996194	−	0.0871630i	$-0.0277801\pi$
$257$	1.54304e7	+	1.54304e7i	0.909031	+	0.909031i	−0.0871630	+	0.996194i	$0.527780\pi$
$258$		0			0
$259$			1.83338e7i			1.05525i
$260$		0			0
$261$	1.00411e7			0.564753
$262$		0			0
$263$	−1.27108e7	+	1.27108e7i	−0.698723	+	0.698723i	−0.964135	−	0.265412i	$-0.914492\pi$
$263$	−1.27108e7	+	1.27108e7i	−0.698723	+	0.698723i	0.265412	+	0.964135i	$0.414492\pi$
$264$		0			0
$265$	900425.	+	6.30298e6i	0.0483849	+	0.338694i
$266$		0			0
$267$	4.30744e6	+	4.30744e6i	0.226300	+	0.226300i
$268$		0			0
$269$			2.54188e6i			0.130586i	0.997866	+	0.0652932i	$0.0207983\pi$
$269$			2.54188e6i			0.130586i	−0.997866	+	0.0652932i	$0.979202\pi$
$270$		0			0
$271$	−6.13384e6			−0.308194			−0.154097	−	0.988056i	$-0.549247\pi$
$271$	−6.13384e6			−0.308194			−0.154097	+	0.988056i	$0.549247\pi$
$272$		0			0
$273$	−3.07115e7	+	3.07115e7i	−1.50943	+	1.50943i
$274$		0			0
$275$	6.13375e6	+	2.10300e7i	0.294936	+	1.01121i
$276$		0			0
$277$	−3.00513e6	−	3.00513e6i	−0.141392	−	0.141392i	0.632868	−	0.774260i	$-0.281878\pi$
$277$	−3.00513e6	−	3.00513e6i	−0.141392	−	0.141392i	−0.774260	+	0.632868i	$0.781878\pi$
$278$		0			0
$279$		−	1.24487e7i		−	0.573207i
$280$		0			0
$281$	−6.49352e6			−0.292658			−0.146329	−	0.989236i	$-0.546746\pi$
$281$	−6.49352e6			−0.292658			−0.146329	+	0.989236i	$0.546746\pi$
$282$		0			0
$283$	2.71607e7	−	2.71607e7i	1.19834	−	1.19834i	0.223680	−	0.974663i	$-0.428193\pi$
$283$	2.71607e7	−	2.71607e7i	1.19834	−	1.19834i	0.974663	−	0.223680i	$-0.0718071\pi$
$284$		0			0
$285$	6.92300e6	−	989000.i	0.299061	−	0.0427230i
$286$		0			0
$287$	−8.75319e6	−	8.75319e6i	−0.370272	−	0.370272i
$288$		0			0
$289$		−	1.06903e7i		−	0.442889i
$290$		0			0
$291$	2.45103e7			0.994649
$292$		0			0
$293$	−4.78734e6	+	4.78734e6i	−0.190323	+	0.190323i	−0.795836	−	0.605513i	$-0.792968\pi$
$293$	−4.78734e6	+	4.78734e6i	−0.190323	+	0.190323i	0.605513	+	0.795836i	$0.292968\pi$
$294$		0			0
$295$	−3.59600e6	−	2.69700e6i	−0.140073	−	0.105055i
$296$		0			0
$297$	−1.28984e7	−	1.28984e7i	−0.492342	−	0.492342i
$298$		0			0
$299$		−	1.15526e7i		−	0.432182i
$300$		0			0
$301$	−1.93534e7			−0.709674
$302$		0			0
$303$	−3.92168e7	+	3.92168e7i	−1.40976	+	1.40976i
$304$		0			0
$305$	−6.24915e6	+	8.33220e6i	−0.220253	+	0.293670i
$306$		0			0
$307$	−9.72339e6	−	9.72339e6i	−0.336049	−	0.336049i	0.518829	−	0.854878i	$-0.326368\pi$
$307$	−9.72339e6	−	9.72339e6i	−0.336049	−	0.336049i	−0.854878	+	0.518829i	$0.826368\pi$
$308$		0			0
$309$		−	3.05929e7i		−	1.03692i
$310$		0			0
$311$	−7.03344e6			−0.233823			−0.116911	−	0.993142i	$-0.537299\pi$
$311$	−7.03344e6			−0.233823			−0.116911	+	0.993142i	$0.537299\pi$
$312$		0			0
$313$	2.98895e7	−	2.98895e7i	0.974734	−	0.974734i	−0.0249545	−	0.999689i	$-0.507944\pi$
$313$	2.98895e7	−	2.98895e7i	0.974734	−	0.974734i	0.999689	+	0.0249545i	$0.00794407\pi$
$314$		0			0
$315$	2.03158e6	+	1.42210e7i	0.0649982	+	0.454987i
$316$		0			0
$317$	2.11266e7	+	2.11266e7i	0.663212	+	0.663212i	0.956136	−	0.292924i	$-0.0946282\pi$
$317$	2.11266e7	+	2.11266e7i	0.663212	+	0.663212i	−0.292924	+	0.956136i	$0.594628\pi$
$318$		0			0
$319$		−	4.27890e7i		−	1.31814i
$320$		0			0
$321$	−1.42174e7			−0.429837
$322$		0			0
$323$	4.45996e6	−	4.45996e6i	0.132350	−	0.132350i
$324$		0			0
$325$	5.23706e7	+	2.87194e7i	1.52559	+	0.836614i
$326$		0			0
$327$	−8.33612e6	−	8.33612e6i	−0.238408	−	0.238408i
$328$		0			0
$329$		−	4.70253e7i		−	1.32052i
$330$		0			0
$331$	4.23279e7			1.16719			0.583596	−	0.812044i	$-0.301645\pi$
$331$	4.23279e7			1.16719			0.583596	+	0.812044i	$0.301645\pi$
$332$		0			0
$333$	1.22102e7	−	1.22102e7i	0.330666	−	0.330666i
$334$		0			0
$335$	1.06458e7	−	1.52082e6i	0.283167	−	0.0404524i
$336$		0			0
$337$	−1.46217e7	−	1.46217e7i	−0.382040	−	0.382040i	0.489797	−	0.871837i	$-0.337071\pi$
$337$	−1.46217e7	−	1.46217e7i	−0.382040	−	0.382040i	−0.871837	+	0.489797i	$0.837071\pi$
$338$		0			0
$339$		−	3.32422e7i		−	0.853279i
$340$		0			0
$341$	−5.30489e7			−1.33787
$342$		0			0
$343$	2.79802e7	−	2.79802e7i	0.693374	−	0.693374i
$344$		0			0
$345$	−9.83020e6	−	7.37265e6i	−0.239389	−	0.179542i
$346$		0			0
$347$	−4.59792e7	−	4.59792e7i	−1.10046	−	1.10046i	−0.994355	−	0.106100i	$-0.966164\pi$
$347$	−4.59792e7	−	4.59792e7i	−1.10046	−	1.10046i	−0.106100	−	0.994355i	$-0.533836\pi$
$348$		0			0
$349$		−	5.03359e7i		−	1.18414i	−0.805888	−	0.592068i	$-0.798312\pi$
$349$		−	5.03359e7i		−	1.18414i	0.805888	−	0.592068i	$-0.201688\pi$
$350$		0			0
$351$	−4.97352e7			−1.15012
$352$		0			0
$353$	−1.59140e7	+	1.59140e7i	−0.361789	+	0.361789i	−0.864471	−	0.502683i	$-0.832346\pi$
$353$	−1.59140e7	+	1.59140e7i	−0.361789	+	0.361789i	0.502683	+	0.864471i	$0.332346\pi$
$354$		0			0
$355$	−3.02385e6	+	4.03180e6i	−0.0675889	+	0.0901185i
$356$		0			0
$357$	2.94617e7	+	2.94617e7i	0.647519	+	0.647519i
$358$		0			0
$359$			4.47023e7i			0.966155i	0.875578	+	0.483077i	$0.160481\pi$
$359$			4.47023e7i			0.966155i	−0.875578	+	0.483077i	$0.839519\pi$
$360$		0			0
$361$	4.40875e7			0.937117
$362$		0			0
$363$	4.46299e6	−	4.46299e6i	0.0933052	−	0.0933052i
$364$		0			0
$365$	−3.22558e6	−	2.25790e7i	−0.0663328	−	0.464330i
$366$		0			0
$367$	2.70624e7	+	2.70624e7i	0.547480	+	0.547480i	0.925711	−	0.378231i	$-0.123468\pi$
$367$	2.70624e7	+	2.70624e7i	0.547480	+	0.547480i	−0.378231	+	0.925711i	$0.623468\pi$
$368$		0			0
$369$			1.16591e7i			0.232052i
$370$		0			0
$371$	1.77924e7			0.348428
$372$		0			0
$373$	−3.82355e7	+	3.82355e7i	−0.736784	+	0.736784i	−0.971954	−	0.235170i	$-0.924435\pi$
$373$	−3.82355e7	+	3.82355e7i	−0.736784	+	0.736784i	0.235170	+	0.971954i	$0.424435\pi$
$374$		0			0
$375$	5.78594e7	−	2.62344e7i	1.09719	−	0.497481i
$376$		0			0
$377$	−8.24956e7	−	8.24956e7i	−1.53960	−	1.53960i
$378$		0			0
$379$		−	2.50612e6i		−	0.0460346i	−0.999735	−	0.0230173i	$-0.992673\pi$
$379$		−	2.50612e6i		−	0.0460346i	0.999735	−	0.0230173i	$-0.00732728\pi$
$380$		0			0
$381$	8.95347e7			1.61889
$382$		0			0
$383$	−4.72095e7	+	4.72095e7i	−0.840297	+	0.840297i	−0.988897	−	0.148600i	$-0.952523\pi$
$383$	−4.72095e7	+	4.72095e7i	−0.840297	+	0.840297i	0.148600	+	0.988897i	$0.452523\pi$
$384$		0			0
$385$	6.06014e7	−	8.65735e6i	1.06194	−	0.151706i
$386$		0			0
$387$	1.28892e7	+	1.28892e7i	0.222379	+	0.222379i
$388$		0			0
$389$			1.00159e8i			1.70153i	0.525547	+	0.850765i	$0.323861\pi$
$389$			1.00159e8i			1.70153i	−0.525547	+	0.850765i	$0.676139\pi$
$390$		0			0
$391$	−1.10825e7			−0.185399
$392$		0			0
$393$	−8.63926e7	+	8.63926e7i	−1.42331	+	1.42331i
$394$		0			0
$395$	5.24640e7	+	3.93480e7i	0.851275	+	0.638457i
$396$		0			0
$397$	−7.26282e7	−	7.26282e7i	−1.16074	−	1.16074i	−0.984314	−	0.176423i	$-0.943547\pi$
$397$	−7.26282e7	−	7.26282e7i	−1.16074	−	1.16074i	−0.176423	−	0.984314i	$-0.556453\pi$
$398$		0			0
$399$		−	1.95426e7i		−	0.307655i
$400$		0			0
$401$	5.26293e7			0.816196			0.408098	−	0.912938i	$-0.366192\pi$
$401$	5.26293e7			0.816196			0.408098	+	0.912938i	$0.366192\pi$
$402$		0			0
$403$	−1.02276e8	+	1.02276e8i	−1.56264	+	1.56264i
$404$		0			0
$405$	−4.97281e7	+	6.63041e7i	−0.748577	+	0.998103i
$406$		0			0
$407$	−5.20324e7	−	5.20324e7i	−0.771775	−	0.771775i
$408$		0			0
$409$			1.10687e8i			1.61781i	0.587939	+	0.808906i	$0.299940\pi$
$409$			1.10687e8i			1.61781i	−0.587939	+	0.808906i	$0.700060\pi$
$410$		0			0
$411$	4.79703e7			0.690951
$412$		0			0
$413$	−8.88212e6	+	8.88212e6i	−0.126086	+	0.126086i
$414$		0			0
$415$	2.86058e6	+	2.00240e7i	0.0400229	+	0.280161i
$416$		0			0
$417$	7.46810e7	+	7.46810e7i	1.02992	+	1.02992i
$418$		0			0
$419$			9.92484e6i			0.134922i	0.997722	+	0.0674608i	$0.0214898\pi$
$419$			9.92484e6i			0.134922i	−0.997722	+	0.0674608i	$0.978510\pi$
$420$		0			0
$421$	3.46957e7			0.464975			0.232488	−	0.972599i	$-0.425314\pi$
$421$	3.46957e7			0.464975			0.232488	+	0.972599i	$0.425314\pi$
$422$		0			0
$423$	−3.13185e7	+	3.13185e7i	−0.413790	+	0.413790i
$424$		0			0
$425$	2.75506e7	−	5.02394e7i	0.358893	−	0.654451i
$426$		0			0
$427$	2.05805e7	+	2.05805e7i	0.264346	+	0.264346i
$428$		0			0
$429$		−	1.74322e8i		−	2.20790i
$430$		0			0
$431$	2.72975e7			0.340951			0.170475	−	0.985362i	$-0.445470\pi$
$431$	2.72975e7			0.340951			0.170475	+	0.985362i	$0.445470\pi$
$432$		0			0
$433$	4.50017e7	−	4.50017e7i	0.554326	−	0.554326i	−0.373360	−	0.927686i	$-0.621795\pi$
$433$	4.50017e7	−	4.50017e7i	0.554326	−	0.554326i	0.927686	+	0.373360i	$0.121795\pi$
$434$		0			0
$435$	−1.22843e8	+	1.75490e7i	−1.49239	+	0.213199i
$436$		0			0
$437$	3.67564e6	+	3.67564e6i	0.0440442	+	0.0440442i
$438$		0			0
$439$		−	4.79986e7i		−	0.567330i	−0.958924	−	0.283665i	$-0.908450\pi$
$439$		−	4.79986e7i		−	0.567330i	0.958924	−	0.283665i	$-0.0915503\pi$
$440$		0			0
$441$	1.43740e6			0.0167595
$442$		0			0
$443$	3.36631e7	−	3.36631e7i	0.387206	−	0.387206i	−0.486483	−	0.873690i	$-0.661721\pi$
$443$	3.36631e7	−	3.36631e7i	0.387206	−	0.387206i	0.873690	+	0.486483i	$0.161721\pi$
$444$		0			0
$445$	−1.87280e7	−	1.40460e7i	−0.212526	−	0.159394i
$446$		0			0
$447$	1.32577e8	+	1.32577e8i	1.48438	+	1.48438i
$448$		0			0
$449$			8.64789e7i			0.955369i	0.878532	+	0.477684i	$0.158524\pi$
$449$			8.64789e7i			0.955369i	−0.878532	+	0.477684i	$0.841476\pi$
$450$		0			0
$451$	4.96841e7			0.541611
$452$		0			0
$453$	−2.37544e7	+	2.37544e7i	−0.255535	+	0.255535i
$454$		0			0
$455$	1.00146e8	−	1.33528e8i	1.06316	−	1.41755i
$456$		0			0
$457$	−3.72501e6	−	3.72501e6i	−0.0390282	−	0.0390282i	0.687323	−	0.726352i	$-0.258786\pi$
$457$	−3.72501e6	−	3.72501e6i	−0.0390282	−	0.0390282i	−0.726352	+	0.687323i	$0.758786\pi$
$458$		0			0
$459$			4.77112e7i			0.493381i
$460$		0			0
$461$	4.07112e7			0.415538			0.207769	−	0.978178i	$-0.433380\pi$
$461$	4.07112e7			0.415538			0.207769	+	0.978178i	$0.433380\pi$
$462$		0			0
$463$	2.69113e7	−	2.69113e7i	0.271139	−	0.271139i	−0.558420	−	0.829559i	$-0.688592\pi$
$463$	2.69113e7	−	2.69113e7i	0.271139	−	0.271139i	0.829559	+	0.558420i	$0.188592\pi$
$464$		0			0
$465$	2.17568e7	+	1.52298e8i	0.216390	+	1.51473i
$466$		0			0
$467$	−1.38966e8	−	1.38966e8i	−1.36446	−	1.36446i	−0.868146	−	0.496310i	$-0.834688\pi$
$467$	−1.38966e8	−	1.38966e8i	−1.36446	−	1.36446i	−0.496310	−	0.868146i	$-0.665312\pi$
$468$		0			0
$469$		−	3.00515e7i		−	0.291305i
$470$		0			0
$471$	1.05825e8			1.01281
$472$		0			0
$473$	5.49262e7	−	5.49262e7i	0.519034	−	0.519034i
$474$		0			0
$475$	−2.58000e7	+	7.52500e6i	−0.240735	+	0.0702143i
$476$		0			0
$477$	−1.18496e7	−	1.18496e7i	−0.109181	−	0.109181i
$478$		0			0
$479$			3.19942e7i			0.291115i	0.989350	+	0.145558i	$0.0464977\pi$
$479$			3.19942e7i			0.291115i	−0.989350	+	0.145558i	$0.953502\pi$
$480$		0			0
$481$	−2.00633e8			−1.80288
$482$		0			0
$483$	−2.42806e7	+	2.42806e7i	−0.215485	+	0.215485i
$484$		0			0
$485$	−9.32458e7	+	1.33208e7i	−0.817342	+	0.116763i
$486$		0			0
$487$	7.96441e7	+	7.96441e7i	0.689551	+	0.689551i	0.962133	−	0.272581i	$-0.0878774\pi$
$487$	7.96441e7	+	7.96441e7i	0.689551	+	0.689551i	−0.272581	+	0.962133i	$0.587877\pi$
$488$		0			0
$489$		−	1.85002e8i		−	1.58216i
$490$		0			0
$491$	−1.53965e8			−1.30070			−0.650350	−	0.759634i	$-0.725378\pi$
$491$	−1.53965e8			−1.30070			−0.650350	+	0.759634i	$0.725378\pi$
$492$		0			0
$493$	−7.91384e7	+	7.91384e7i	−0.660460	+	0.660460i
$494$		0			0
$495$	−4.61258e7	−	3.45944e7i	−0.380302	−	0.285226i
$496$		0			0
$497$	9.95855e6	+	9.95855e6i	0.0811198	+	0.0811198i
$498$		0			0
$499$			1.02698e8i			0.826537i	0.910609	+	0.413268i	$0.135613\pi$
$499$			1.02698e8i			0.826537i	−0.910609	+	0.413268i	$0.864387\pi$
$500$		0			0
$501$	3.26677e7			0.259780
$502$		0			0
$503$	−8.43625e7	+	8.43625e7i	−0.662896	+	0.662896i	−0.956062	−	0.293166i	$-0.905291\pi$
$503$	−8.43625e7	+	8.43625e7i	−0.662896	+	0.662896i	0.293166	+	0.956062i	$0.405291\pi$
$504$		0			0
$505$	1.27881e8	−	1.70508e8i	0.992959	−	1.32395i
$506$		0			0
$507$	−2.25069e8	−	2.25069e8i	−1.72700	−	1.72700i
$508$		0			0
$509$			4.03774e7i			0.306186i	0.988212	+	0.153093i	$0.0489234\pi$
$509$			4.03774e7i			0.306186i	−0.988212	+	0.153093i	$0.951077\pi$
$510$		0			0
$511$	−6.37374e7			−0.477674
$512$		0			0
$513$	1.58240e7	−	1.58240e7i	0.117210	−	0.117210i
$514$		0			0
$515$	1.66266e7	+	1.16386e8i	0.121725	+	0.852078i
$516$		0			0
$517$	1.33461e8	+	1.33461e8i	0.965787	+	0.965787i
$518$		0			0
$519$		−	1.73719e8i		−	1.24264i
$520$		0			0
$521$	−3.68161e7			−0.260330			−0.130165	−	0.991492i	$-0.541551\pi$
$521$	−3.68161e7			−0.260330			−0.130165	+	0.991492i	$0.541551\pi$
$522$		0			0
$523$	1.60054e8	−	1.60054e8i	1.11882	−	1.11882i	0.126907	−	0.991915i	$-0.459495\pi$
$523$	1.60054e8	−	1.60054e8i	1.11882	−	1.11882i	0.991915	−	0.126907i	$-0.0405050\pi$
$524$		0			0
$525$	−4.97088e7	−	1.70430e8i	−0.343522	−	1.17779i
$526$		0			0
$527$	9.81139e7	+	9.81139e7i	0.670346	+	0.670346i
$528$		0			0
$529$			1.38902e8i			0.938302i
$530$		0			0
$531$	1.18308e7			0.0790191
$532$		0			0
$533$	9.57889e7	−	9.57889e7i	0.632606	−	0.632606i
$534$		0			0
$535$	5.40878e7	−	7.72682e6i	0.353214	−	0.0504591i
$536$		0			0
$537$	−1.25667e8	−	1.25667e8i	−0.811521	−	0.811521i
$538$		0			0
$539$		−	6.12534e6i		−	0.0391168i
$540$		0			0
$541$	1.30022e7			0.0821155			0.0410577	−	0.999157i	$-0.486927\pi$
$541$	1.30022e7			0.0821155			0.0410577	+	0.999157i	$0.486927\pi$
$542$		0			0
$543$	2.07560e8	−	2.07560e8i	1.29642	−	1.29642i
$544$		0			0
$545$	3.62440e7	+	2.71830e7i	0.223896	+	0.167922i
$546$		0			0
$547$	−7.28319e7	−	7.28319e7i	−0.444999	−	0.444999i	0.448689	−	0.893688i	$-0.351891\pi$
$547$	−7.28319e7	−	7.28319e7i	−0.444999	−	0.444999i	−0.893688	+	0.448689i	$0.851891\pi$
$548$		0			0
$549$		−	2.74129e7i		−	0.165668i
$550$		0			0
$551$	5.24944e7			0.313804
$552$		0			0
$553$	1.29586e8	−	1.29586e8i	0.766272	−	0.766272i
$554$		0			0
$555$	−1.28040e8	+	1.70720e8i	−0.748973	+	0.998631i
$556$		0			0
$557$	−4.55401e7	−	4.55401e7i	−0.263529	−	0.263529i	0.562957	−	0.826486i	$-0.309664\pi$
$557$	−4.55401e7	−	4.55401e7i	−0.263529	−	0.263529i	−0.826486	+	0.562957i	$0.809664\pi$
$558$		0			0
$559$		−	2.11791e8i		−	1.21247i
$560$		0			0
$561$	−1.67228e8			−0.947152
$562$		0			0
$563$	1.85012e8	−	1.85012e8i	1.03675	−	1.03675i	0.0374524	−	0.999298i	$-0.488076\pi$
$563$	1.85012e8	−	1.85012e8i	1.03675	−	1.03675i	0.999298	−	0.0374524i	$-0.0119243\pi$
$564$		0			0
$565$	1.80664e7	+	1.26465e8i	0.100168	+	0.701173i
$566$		0			0
$567$	1.63771e8	+	1.63771e8i	0.898438	+	0.898438i
$568$		0			0
$569$		−	7.17210e7i		−	0.389323i	−0.980871	−	0.194661i	$-0.937639\pi$
$569$		−	7.17210e7i		−	0.389323i	0.980871	−	0.194661i	$-0.0623608\pi$
$570$		0			0
$571$	−3.09478e8			−1.66234			−0.831172	−	0.556015i	$-0.812330\pi$
$571$	−3.09478e8			−1.66234			−0.831172	+	0.556015i	$0.812330\pi$
$572$		0			0
$573$	9.24876e7	−	9.24876e7i	0.491609	−	0.491609i
$574$		0			0
$575$	4.14044e7	+	2.27056e7i	0.217792	+	0.119435i
$576$		0			0
$577$	−2.15868e7	−	2.15868e7i	−0.112373	−	0.112373i	0.648684	−	0.761057i	$-0.275319\pi$
$577$	−2.15868e7	−	2.15868e7i	−0.112373	−	0.112373i	−0.761057	+	0.648684i	$0.775319\pi$
$578$		0			0
$579$			4.84906e7i			0.249817i
$580$		0			0
$581$	5.65250e7			0.288212
$582$		0			0
$583$	−5.04958e7	+	5.04958e7i	−0.254830	+	0.254830i
$584$		0			0
$585$	−1.55625e8	+	2.22322e7i	−0.777342	+	0.111049i
$586$		0			0
$587$	2.30927e8	+	2.30927e8i	1.14172	+	1.14172i	0.988135	+	0.153588i	$0.0490830\pi$
$587$	2.30927e8	+	2.30927e8i	1.14172	+	1.14172i	0.153588	+	0.988135i	$0.450917\pi$
$588$		0			0
$589$		−	6.50814e7i		−	0.318501i
$590$		0			0
$591$	−3.35565e8			−1.62560
$592$		0			0
$593$	−2.66433e7	+	2.66433e7i	−0.127768	+	0.127768i	−0.768099	−	0.640331i	$-0.778797\pi$
$593$	−2.66433e7	+	2.66433e7i	−0.127768	+	0.127768i	0.640331	+	0.768099i	$0.278797\pi$
$594$		0			0
$595$	−1.28094e8	−	9.60706e7i	−0.608105	−	0.456079i
$596$		0			0
$597$	3.24692e8	+	3.24692e8i	1.52598	+	1.52598i
$598$		0			0
$599$			3.14489e8i			1.46327i	0.681695	+	0.731637i	$0.261243\pi$
$599$			3.14489e8i			1.46327i	−0.681695	+	0.731637i	$0.738757\pi$
$600$		0			0
$601$	−2.50382e8			−1.15340			−0.576700	−	0.816956i	$-0.695660\pi$
$601$	−2.50382e8			−1.15340			−0.576700	+	0.816956i	$0.695660\pi$
$602$		0			0
$603$	−2.00141e7	+	2.00141e7i	−0.0912816	+	0.0912816i
$604$		0			0
$605$	−1.45532e7	+	1.94043e7i	−0.0657193	+	0.0876258i
$606$		0			0
$607$	−9.40326e7	−	9.40326e7i	−0.420448	−	0.420448i	0.464910	−	0.885358i	$-0.346087\pi$
$607$	−9.40326e7	−	9.40326e7i	−0.420448	−	0.420448i	−0.885358	+	0.464910i	$0.846087\pi$
$608$		0			0
$609$			3.46768e8i			1.53528i
$610$		0			0
$611$	5.14613e8			2.25610
$612$		0			0
$613$	−1.72963e8	+	1.72963e8i	−0.750880	+	0.750880i	−0.974644	−	0.223763i	$-0.928166\pi$
$613$	−1.72963e8	+	1.72963e8i	−0.750880	+	0.750880i	0.223763	+	0.974644i	$0.428166\pi$
$614$		0			0
$615$	−2.03768e7	−	1.42638e8i	−0.0876015	−	0.613211i
$616$		0			0
$617$	1.31974e8	+	1.31974e8i	0.561868	+	0.561868i	0.929838	−	0.367970i	$-0.119947\pi$
$617$	1.31974e8	+	1.31974e8i	0.561868	+	0.561868i	−0.367970	+	0.929838i	$0.619947\pi$
$618$		0			0
$619$			4.22584e8i			1.78173i	0.454271	+	0.890863i	$0.349900\pi$
$619$			4.22584e8i			1.78173i	−0.454271	+	0.890863i	$0.650100\pi$
$620$		0			0
$621$	−3.93208e7			−0.164190
$622$		0			0
$623$	−4.62582e7	+	4.62582e7i	−0.191304	+	0.191304i
$624$		0			0
$625$	−2.05859e8	+	1.31250e8i	−0.843200	+	0.537600i
$626$		0			0
$627$	5.54631e7	+	5.54631e7i	0.225010	+	0.225010i
$628$		0			0
$629$			1.92468e8i			0.773404i
$630$		0			0
$631$	−2.95144e8			−1.17475			−0.587376	−	0.809314i	$-0.699839\pi$
$631$	−2.95144e8			−1.17475			−0.587376	+	0.809314i	$0.699839\pi$
$632$		0			0
$633$	2.83333e8	−	2.83333e8i	1.11709	−	1.11709i
$634$		0			0
$635$	−3.40621e8	+	4.86602e7i	−1.33030	+	0.190043i
$636$		0			0
$637$	−1.18094e7	−	1.18094e7i	−0.0456888	−	0.0456888i
$638$		0			0
$639$		−	1.32646e7i		−	0.0508385i
$640$		0			0
$641$	3.85293e8			1.46291			0.731453	−	0.681891i	$-0.238842\pi$
$641$	3.85293e8			1.46291			0.731453	+	0.681891i	$0.238842\pi$
$642$		0			0
$643$	−1.75998e8	+	1.75998e8i	−0.662024	+	0.662024i	−0.955857	−	0.293833i	$-0.905069\pi$
$643$	−1.75998e8	+	1.75998e8i	−0.662024	+	0.662024i	0.293833	+	0.955857i	$0.405069\pi$
$644$		0			0
$645$	−1.80214e8	−	1.35161e8i	−0.671599	−	0.503699i
$646$		0			0
$647$	1.00835e8	+	1.00835e8i	0.372304	+	0.372304i	0.868316	−	0.496012i	$-0.165203\pi$
$647$	1.00835e8	+	1.00835e8i	0.372304	+	0.372304i	−0.496012	+	0.868316i	$0.665203\pi$
$648$		0			0
$649$		−	5.04159e7i		−	0.184431i
$650$		0			0
$651$	4.29915e8			1.55826
$652$		0			0
$653$	1.92563e8	−	1.92563e8i	0.691566	−	0.691566i	−0.271010	−	0.962576i	$-0.587358\pi$
$653$	1.92563e8	−	1.92563e8i	0.691566	−	0.691566i	0.962576	+	0.271010i	$0.0873577\pi$
$654$		0			0
$655$	2.81715e8	−	3.75620e8i	1.00250	−	1.33667i
$656$		0			0
$657$	4.24486e7	+	4.24486e7i	0.149681	+	0.149681i
$658$		0			0
$659$		−	1.31172e8i		−	0.458337i	−0.973387	−	0.229168i	$-0.926399\pi$
$659$		−	1.31172e8i		−	0.458337i	0.973387	−	0.229168i	$-0.0736007\pi$
$660$		0			0
$661$	−1.97154e8			−0.682656			−0.341328	−	0.939944i	$-0.610877\pi$
$661$	−1.97154e8			−0.682656			−0.341328	+	0.939944i	$0.610877\pi$
$662$		0			0
$663$	−3.22408e8	+	3.22408e8i	−1.10628	+	1.10628i
$664$		0			0
$665$	1.06210e7	+	7.43470e7i	0.0361161	+	0.252812i
$666$		0			0
$667$	−6.52212e7	−	6.52212e7i	−0.219792	−	0.219792i
$668$		0			0
$669$			1.51274e7i			0.0505227i
$670$		0			0
$671$	−1.16817e8			−0.386670
$672$		0			0
$673$	−1.93253e8	+	1.93253e8i	−0.633987	+	0.633987i	−0.949066	−	0.315079i	$-0.897969\pi$
$673$	−1.93253e8	+	1.93253e8i	−0.633987	+	0.633987i	0.315079	+	0.949066i	$0.397969\pi$
$674$		0			0
$675$	9.77500e7	−	1.78250e8i	0.317838	−	0.579586i
$676$		0			0
$677$	−2.07906e8	−	2.07906e8i	−0.670042	−	0.670042i	0.287684	−	0.957725i	$-0.407115\pi$
$677$	−2.07906e8	−	2.07906e8i	−0.670042	−	0.670042i	−0.957725	+	0.287684i	$0.907115\pi$
$678$		0			0
$679$			2.63220e8i			0.840831i
$680$		0			0
$681$	3.65739e8			1.15806
$682$		0			0
$683$	3.57632e8	−	3.57632e8i	1.12247	−	1.12247i	0.131099	−	0.991369i	$-0.458149\pi$
$683$	3.57632e8	−	3.57632e8i	1.12247	−	1.12247i	0.991369	−	0.131099i	$-0.0418506\pi$
$684$		0			0
$685$	−1.82496e8	+	2.60708e7i	−0.567781	+	0.0811116i
$686$		0			0
$687$	5.25998e8	+	5.25998e8i	1.62224	+	1.62224i
$688$		0			0
$689$			1.94708e8i			0.595286i
$690$		0			0
$691$	1.76748e8			0.535698			0.267849	−	0.963461i	$-0.413687\pi$
$691$	1.76748e8			0.535698			0.267849	+	0.963461i	$0.413687\pi$
$692$		0			0
$693$	−1.13931e8	+	1.13931e8i	−0.342327	+	0.342327i
$694$		0			0
$695$	−3.24700e8	−	2.43525e8i	−0.967226	−	0.725419i
$696$		0			0
$697$	−9.18907e7	−	9.18907e7i	−0.271377	−	0.271377i
$698$		0			0
$699$		−	3.95163e8i		−	1.15703i
$700$		0			0
$701$	−3.12897e8			−0.908338			−0.454169	−	0.890916i	$-0.650064\pi$
$701$	−3.12897e8			−0.908338			−0.454169	+	0.890916i	$0.650064\pi$
$702$		0			0
$703$	6.38344e7	−	6.38344e7i	0.183734	−	0.183734i
$704$		0			0
$705$	3.28416e8	−	4.37888e8i	0.937253	−	1.24967i
$706$		0			0
$707$	−4.21154e8	−	4.21154e8i	−1.19174	−	1.19174i
$708$		0			0
$709$			1.07924e8i			0.302817i	0.988471	+	0.151408i	$0.0483809\pi$
$709$			1.07924e8i			0.302817i	−0.988471	+	0.151408i	$0.951619\pi$
$710$		0			0
$711$	−1.72607e8			−0.480229
$712$		0			0
$713$	−8.08598e7	+	8.08598e7i	−0.223082	+	0.223082i
$714$		0			0
$715$	9.47402e7	+	6.63181e8i	0.259189	+	1.81432i
$716$		0			0
$717$	−2.22312e8	−	2.22312e8i	−0.603124	−	0.603124i
$718$		0			0
$719$		−	1.83233e8i		−	0.492967i	−0.969147	−	0.246484i	$-0.920725\pi$
$719$		−	1.83233e8i		−	0.492967i	0.969147	−	0.246484i	$-0.0792752\pi$
$720$		0			0
$721$	3.28541e8			0.876565
$722$		0			0
$723$	4.27631e8	−	4.27631e8i	1.13150	−	1.13150i
$724$		0			0
$725$	4.57800e8	−	1.33525e8i	1.20133	−	0.350387i
$726$		0			0
$727$	−2.98719e8	−	2.98719e8i	−0.777428	−	0.777428i	0.201965	−	0.979393i	$-0.435267\pi$
$727$	−2.98719e8	−	2.98719e8i	−0.777428	−	0.777428i	−0.979393	+	0.201965i	$0.935267\pi$
$728$		0			0
$729$			9.03723e7i			0.233267i
$730$		0			0
$731$	−2.03172e8			−0.520130
$732$		0			0
$733$	4.34598e8	−	4.34598e8i	1.10351	−	1.10351i	0.109524	−	0.993984i	$-0.465067\pi$
$733$	4.34598e8	−	4.34598e8i	1.10351	−	1.10351i	0.993984	−	0.109524i	$-0.0349325\pi$
$734$		0			0
$735$	−1.75852e7	+	2.51218e6i	−0.0442880	+	0.00632685i
$736$		0			0
$737$	8.52879e7	+	8.52879e7i	0.213052	+	0.213052i
$738$		0			0
$739$			5.77645e8i			1.43129i	0.698463	+	0.715646i	$0.253867\pi$
$739$			5.77645e8i			1.43129i	−0.698463	+	0.715646i	$0.746133\pi$
$740$		0			0
$741$	2.13861e8			0.525627
$742$		0			0
$743$	−9.71697e7	+	9.71697e7i	−0.236900	+	0.236900i	−0.815565	−	0.578665i	$-0.803574\pi$
$743$	−9.71697e7	+	9.71697e7i	−0.236900	+	0.236900i	0.578665	+	0.815565i	$0.303574\pi$
$744$		0			0
$745$	−5.76420e8	−	4.32315e8i	−1.39402	−	1.04552i
$746$		0			0
$747$	−3.76452e7	−	3.76452e7i	−0.0903124	−	0.0903124i
$748$		0			0
$749$		−	1.52682e8i		−	0.363365i
$750$		0			0
$751$	−6.96310e8			−1.64393			−0.821963	−	0.569540i	$-0.807121\pi$
$751$	−6.96310e8			−1.64393			−0.821963	+	0.569540i	$0.807121\pi$
$752$		0			0
$753$	−2.74505e8	+	2.74505e8i	−0.642933	+	0.642933i
$754$		0			0
$755$	7.74602e7	−	1.03280e8i	0.179985	−	0.239981i
$756$		0			0
$757$	−2.26996e8	−	2.26996e8i	−0.523276	−	0.523276i	0.395283	−	0.918559i	$-0.370646\pi$
$757$	−2.26996e8	−	2.26996e8i	−0.523276	−	0.523276i	−0.918559	+	0.395283i	$0.870646\pi$
$758$		0			0
$759$		−	1.37819e8i		−	0.315199i
$760$		0			0
$761$	−3.36900e8			−0.764447			−0.382224	−	0.924070i	$-0.624842\pi$
$761$	−3.36900e8			−0.764447			−0.382224	+	0.924070i	$0.624842\pi$
$762$		0			0
$763$	8.95227e7	−	8.95227e7i	0.201539	−	0.201539i
$764$		0			0
$765$	2.13274e7	+	1.49292e8i	0.0476381	+	0.333466i
$766$		0			0
$767$	−9.71999e7	−	9.71999e7i	−0.215417	−	0.215417i
$768$		0			0
$769$		−	2.53257e8i		−	0.556907i	−0.960450	−	0.278454i	$-0.910178\pi$
$769$		−	2.53257e8i		−	0.556907i	0.960450	−	0.278454i	$-0.0898219\pi$
$770$		0			0
$771$	7.09800e8			1.54872
$772$		0			0
$773$	9.22029e7	−	9.22029e7i	0.199621	−	0.199621i	−0.600217	−	0.799838i	$-0.704919\pi$
$773$	9.22029e7	−	9.22029e7i	0.199621	−	0.199621i	0.799838	+	0.600217i	$0.204919\pi$
$774$		0			0
$775$	−1.65541e8	−	5.67570e8i	−0.355632	−	1.21931i
$776$		0			0
$777$	4.21678e8	+	4.21678e8i	0.898913	+	0.898913i
$778$		0			0
$779$			6.09534e7i			0.128939i
$780$		0			0
$781$	−5.65258e7			−0.118657
$782$		0			0
$783$	−2.80784e8	+	2.80784e8i	−0.584907	+	0.584907i
$784$		0			0
$785$	−4.02597e8	+	5.75138e7i	−0.832264	+	0.118895i
$786$		0			0
$787$	−1.88154e8	−	1.88154e8i	−0.386003	−	0.386003i	0.487256	−	0.873259i	$-0.337998\pi$
$787$	−1.88154e8	−	1.88154e8i	−0.386003	−	0.386003i	−0.873259	+	0.487256i	$0.837998\pi$
$788$		0			0
$789$			5.84696e8i			1.19042i
$790$		0			0
$791$	3.56993e8			0.721323
$792$		0			0
$793$	−2.25219e8	+	2.25219e8i	−0.451634	+	0.451634i
$794$		0			0
$795$	1.65678e8	+	1.24259e8i	0.329734	+	0.247301i
$796$		0			0
$797$	−4.42167e7	−	4.42167e7i	−0.0873397	−	0.0873397i	0.662087	−	0.749427i	$-0.269671\pi$
$797$	−4.42167e7	−	4.42167e7i	−0.0873397	−	0.0873397i	−0.749427	+	0.662087i	$0.769671\pi$
$798$		0			0
$799$		−	4.93671e8i		−	0.967826i
$800$		0			0
$801$	6.16151e7			0.119892
$802$		0			0
$803$	1.80890e8	−	1.80890e8i	0.349356	−	0.349356i
$804$		0			0
$805$	7.91758e7	−	1.05568e8i	0.151777	−	0.202369i
$806$		0			0
$807$	5.84632e7	+	5.84632e7i	0.111240	+	0.111240i
$808$		0			0
$809$		−	1.04607e9i		−	1.97568i	−0.155470	−	0.987841i	$-0.549689\pi$
$809$		−	1.04607e9i		−	1.97568i	0.155470	−	0.987841i	$-0.450311\pi$
$810$		0			0
$811$	6.48376e8			1.21553			0.607763	−	0.794118i	$-0.292067\pi$
$811$	6.48376e8			1.21553			0.607763	+	0.794118i	$0.292067\pi$
$812$		0			0
$813$	−1.41078e8	+	1.41078e8i	−0.262536	+	0.262536i
$814$		0			0
$815$	1.00545e8	+	7.03812e8i	0.185732	+	1.30012i
$816$		0			0
$817$	6.73844e7	+	6.73844e7i	0.123564	+	0.123564i
$818$		0			0
$819$			4.39308e8i			0.799682i
$820$		0			0
$821$	−2.19206e8			−0.396117			−0.198058	−	0.980190i	$-0.563464\pi$
$821$	−2.19206e8			−0.396117			−0.198058	+	0.980190i	$0.563464\pi$
$822$		0			0
$823$	−5.40313e8	+	5.40313e8i	−0.969272	+	0.969272i	−0.999542	−	0.0302695i	$-0.990363\pi$
$823$	−5.40313e8	+	5.40313e8i	−0.969272	+	0.969272i	0.0302695	+	0.999542i	$0.490363\pi$
$824$		0			0
$825$	6.24766e8	+	3.42614e8i	1.11264	+	0.610159i
$826$		0			0
$827$	2.57157e6	+	2.57157e6i	0.00454654	+	0.00454654i	0.709376	−	0.704830i	$-0.248977\pi$
$827$	2.57157e6	+	2.57157e6i	0.00454654	+	0.00454654i	−0.704830	+	0.709376i	$0.748977\pi$
$828$		0			0
$829$		−	4.66597e8i		−	0.818989i	−0.912313	−	0.409494i	$-0.865705\pi$
$829$		−	4.66597e8i		−	0.818989i	0.912313	−	0.409494i	$-0.134295\pi$
$830$		0			0
$831$	−1.38236e8			−0.240889
$832$		0			0
$833$	−1.13288e7	+	1.13288e7i	−0.0195997	+	0.0195997i
$834$		0			0
$835$	−1.24279e8	+	1.77542e7i	−0.213471	+	0.0304959i
$836$		0			0
$837$	3.48110e8	+	3.48110e8i	0.593663	+	0.593663i
$838$		0			0
$839$		−	5.23913e8i		−	0.887102i	−0.896249	−	0.443551i	$-0.853718\pi$
$839$		−	5.23913e8i		−	0.887102i	0.896249	−	0.443551i	$-0.146282\pi$
$840$		0			0
$841$	−3.36647e8			−0.565961
$842$		0			0
$843$	−1.49351e8	+	1.49351e8i	−0.249302	+	0.249302i
$844$		0			0
$845$	9.78561e8	+	7.33921e8i	1.62188	+	1.21641i
$846$		0			0
$847$	4.79286e7	+	4.79286e7i	0.0788760	+	0.0788760i
$848$		0			0
$849$		−	1.24939e9i		−	2.04162i
$850$		0			0
$851$	−1.58621e8			−0.257378
$852$		0			0
$853$	−1.57695e8	+	1.57695e8i	−0.254080	+	0.254080i	−0.822641	−	0.568561i	$-0.807500\pi$
$853$	−1.57695e8	+	1.57695e8i	−0.254080	+	0.254080i	0.568561	+	0.822641i	$0.307500\pi$
$854$		0			0
$855$	4.24410e7	−	5.65880e7i	0.0679027	−	0.0905370i
$856$		0			0
$857$	−3.71033e8	−	3.71033e8i	−0.589481	−	0.589481i	0.348010	−	0.937491i	$-0.386857\pi$
$857$	−3.71033e8	−	3.71033e8i	−0.589481	−	0.589481i	−0.937491	+	0.348010i	$0.886857\pi$
$858$		0			0
$859$		−	9.20945e8i		−	1.45296i	−0.687186	−	0.726481i	$-0.741154\pi$
$859$		−	9.20945e8i		−	1.45296i	0.687186	−	0.726481i	$-0.258846\pi$
$860$		0			0
$861$	−4.02647e8			−0.630833
$862$		0			0
$863$	3.54269e8	−	3.54269e8i	0.551189	−	0.551189i	−0.375595	−	0.926784i	$-0.622562\pi$
$863$	3.54269e8	−	3.54269e8i	0.551189	−	0.551189i	0.926784	+	0.375595i	$0.122562\pi$
$864$		0			0
$865$	9.44124e7	+	6.60887e8i	0.145875	+	1.02112i
$866$		0			0
$867$	−2.45876e8	−	2.45876e8i	−0.377276	−	0.377276i
$868$		0			0
$869$			7.35545e8i			1.12086i
$870$		0			0
$871$	3.28863e8			0.497692
$872$		0			0
$873$	1.75302e8	−	1.75302e8i	0.263478	−	0.263478i
$874$		0			0
$875$	2.81734e8	+	6.21359e8i	0.420548	+	0.927510i
$876$		0			0
$877$	5.40230e8	+	5.40230e8i	0.800903	+	0.800903i	0.983237	−	0.182333i	$-0.0583650\pi$
$877$	5.40230e8	+	5.40230e8i	0.800903	+	0.800903i	−0.182333	+	0.983237i	$0.558365\pi$
$878$		0			0
$879$			2.20218e8i			0.324254i
$880$		0			0
$881$	5.18142e8			0.757742			0.378871	−	0.925450i	$-0.376312\pi$
$881$	5.18142e8			0.757742			0.378871	+	0.925450i	$0.376312\pi$
$882$		0			0
$883$	−4.34467e8	+	4.34467e8i	−0.631066	+	0.631066i	−0.948335	−	0.317269i	$-0.897234\pi$
$883$	−4.34467e8	+	4.34467e8i	−0.631066	+	0.631066i	0.317269	+	0.948335i	$0.397234\pi$
$884$		0			0
$885$	−1.44739e8	+	2.06770e7i	−0.208812	+	0.0298303i
$886$		0			0
$887$	8.33860e8	+	8.33860e8i	1.19487	+	1.19487i	0.975682	+	0.219193i	$0.0703424\pi$
$887$	8.33860e8	+	8.33860e8i	1.19487	+	1.19487i	0.219193	+	0.975682i	$0.429658\pi$
$888$		0			0
$889$			9.61525e8i			1.36853i
$890$		0			0
$891$	−9.29583e8			−1.31418
$892$		0			0
$893$	−1.63732e8	+	1.63732e8i	−0.229921	+	0.229921i
$894$		0			0
$895$	5.46380e8	+	4.09785e8i	0.762124	+	0.571593i
$896$		0			0
$897$	−2.65710e8	−	2.65710e8i	−0.368155	−	0.368155i
$898$		0			0
$899$			1.15482e9i			1.58940i
$900$		0			0
$901$	1.86784e8			0.255368
$902$		0			0
$903$	−4.45129e8	+	4.45129e8i	−0.604537	+	0.604537i
$904$		0			0
$905$	−6.76827e8	+	9.02436e8i	−0.913129	+	1.21751i
$906$		0			0
$907$	4.28686e8	+	4.28686e8i	0.574536	+	0.574536i	0.933393	−	0.358856i	$-0.116833\pi$
$907$	4.28686e8	+	4.28686e8i	0.574536	+	0.574536i	−0.358856	+	0.933393i	$0.616833\pi$
$908$		0			0
$909$			5.60971e8i			0.746876i
$910$		0			0
$911$	−1.25314e9			−1.65746			−0.828730	−	0.559649i	$-0.810936\pi$
$911$	−1.25314e9			−1.65746			−0.828730	+	0.559649i	$0.810936\pi$
$912$		0			0
$913$	−1.60421e8	+	1.60421e8i	−0.210790	+	0.210790i
$914$		0			0
$915$	4.79102e7	+	3.35371e8i	0.0625409	+	0.437786i
$916$		0			0
$917$	−9.27782e8	−	9.27782e8i	−1.20320	−	1.20320i
$918$		0			0
$919$		−	5.35804e8i		−	0.690335i	−0.938541	−	0.345167i	$-0.887822\pi$
$919$		−	5.35804e8i		−	0.690335i	0.938541	−	0.345167i	$-0.112178\pi$
$920$		0			0
$921$	−4.47276e8			−0.572528
$922$		0			0
$923$	−1.08980e8	+	1.08980e8i	−0.138593	+	0.138593i
$924$		0			0
$925$	3.94326e8	−	7.19064e8i	0.498230	−	0.908537i
$926$		0			0
$927$	−2.18806e8	−	2.18806e8i	−0.274675	−	0.274675i
$928$		0			0
$929$			6.63938e7i			0.0828095i	0.999142	+	0.0414047i	$0.0131833\pi$
$929$			6.63938e7i			0.0828095i	−0.999142	+	0.0414047i	$0.986817\pi$
$930$		0			0
$931$	7.51468e6			0.00931240
$932$		0			0
$933$	−1.61769e8	+	1.61769e8i	−0.199182	+	0.199182i
$934$		0			0
$935$	6.36193e8	−	9.08846e7i	0.778312	−	0.111187i
$936$		0			0
$937$	5.38039e8	+	5.38039e8i	0.654026	+	0.654026i	0.953960	−	0.299934i	$-0.0969648\pi$
$937$	5.38039e8	+	5.38039e8i	0.654026	+	0.654026i	−0.299934	+	0.953960i	$0.596965\pi$
$938$		0			0
$939$		−	1.37492e9i		−	1.66066i
$940$		0			0
$941$	1.17829e9			1.41411			0.707053	−	0.707160i	$-0.250024\pi$
$941$	1.17829e9			1.41411			0.707053	+	0.707160i	$0.250024\pi$
$942$		0			0
$943$	7.57310e7	−	7.57310e7i	0.0903106	−	0.0903106i
$944$		0			0
$945$	−4.54480e8	−	3.40860e8i	−0.538542	−	0.403906i
$946$		0			0
$947$	−9.34402e8	−	9.34402e8i	−1.10023	−	1.10023i	−0.994382	−	0.105849i	$-0.966244\pi$
$947$	−9.34402e8	−	9.34402e8i	−1.10023	−	1.10023i	−0.105849	−	0.994382i	$-0.533756\pi$
$948$		0			0
$949$		−	6.97498e8i		−	0.816102i
$950$		0			0
$951$	9.71825e8			1.12992
$952$		0			0
$953$	−5.18005e8	+	5.18005e8i	−0.598487	+	0.598487i	−0.939910	−	0.341423i	$-0.889091\pi$
$953$	−5.18005e8	+	5.18005e8i	−0.598487	+	0.598487i	0.341423	+	0.939910i	$0.389091\pi$
$954$		0			0
$955$	−3.01590e8	+	4.02120e8i	−0.346263	+	0.461685i
$956$		0			0
$957$	−9.84148e8	−	9.84148e8i	−1.12286	−	1.12286i
$958$		0			0
$959$			5.15160e8i			0.584098i
$960$		0			0
$961$	5.44211e8			0.613192
$962$		0			0
$963$	−1.01685e8	+	1.01685e8i	−0.113862	+	0.113862i
$964$		0			0
$965$	−2.63536e7	−	1.84475e8i	−0.0293263	−	0.205284i
$966$		0			0
$967$	2.61561e8	+	2.61561e8i	0.289264	+	0.289264i	0.836789	−	0.547525i	$-0.184430\pi$
$967$	2.61561e8	+	2.61561e8i	0.289264	+	0.289264i	−0.547525	+	0.836789i	$0.684430\pi$
$968$		0			0
$969$		−	2.05158e8i		−	0.225485i
$970$		0			0
$971$	4.59360e8			0.501759			0.250880	−	0.968018i	$-0.419280\pi$
$971$	4.59360e8			0.501759			0.250880	+	0.968018i	$0.419280\pi$
$972$		0			0
$973$	−8.02009e8	+	8.02009e8i	−0.870644	+	0.870644i
$974$		0			0
$975$	1.86507e9	−	5.43979e8i	2.01225	−	0.586905i
$976$		0			0
$977$	−8.60529e7	−	8.60529e7i	−0.0922746	−	0.0922746i	0.659463	−	0.751737i	$-0.270784\pi$
$977$	−8.60529e7	−	8.60529e7i	−0.0922746	−	0.0922746i	−0.751737	+	0.659463i	$0.770784\pi$
$978$		0			0
$979$		−	2.62567e8i		−	0.279828i
$980$		0			0
$981$	−1.19243e8			−0.126306
$982$		0			0
$983$	9.00900e8	−	9.00900e8i	0.948454	−	0.948454i	−0.0502815	−	0.998735i	$-0.516012\pi$
$983$	9.00900e8	−	9.00900e8i	0.948454	−	0.948454i	0.998735	+	0.0502815i	$0.0160119\pi$
$984$		0			0
$985$	1.27661e9	−	1.82372e8i	1.33582	−	0.190831i
$986$		0			0
$987$	−1.08158e9	−	1.08158e9i	−1.12489	−	1.12489i
$988$		0			0
$989$		−	1.67442e8i		−	0.173092i
$990$		0			0
$991$	2.71537e8			0.279003			0.139501	−	0.990222i	$-0.455450\pi$
$991$	2.71537e8			0.279003			0.139501	+	0.990222i	$0.455450\pi$
$992$		0			0
$993$	9.73541e8	−	9.73541e8i	0.994275	−	0.994275i
$994$		0			0
$995$	−1.41170e9	−	1.05878e9i	−1.43309	−	1.07482i
$996$		0			0
$997$	−3.63500e8	−	3.63500e8i	−0.366791	−	0.366791i	0.499514	−	0.866306i	$-0.333512\pi$
$997$	−3.63500e8	−	3.63500e8i	−0.366791	−	0.366791i	−0.866306	+	0.499514i	$0.833512\pi$
$998$		0			0
$999$			6.82879e8i			0.684932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.7.p.a.17.1		2
4.3	odd	2		10.7.c.a.7.1	yes	2
5.3	odd	4	inner	80.7.p.a.33.1		2
12.11	even	2		90.7.g.a.37.1		2
20.3	even	4		10.7.c.a.3.1	✓	2
20.7	even	4		50.7.c.c.43.1		2
20.19	odd	2		50.7.c.c.7.1		2
60.23	odd	4		90.7.g.a.73.1		2
60.47	odd	4		450.7.g.b.343.1		2
60.59	even	2		450.7.g.b.307.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.7.c.a.3.1	✓	2	20.3	even	4
10.7.c.a.7.1	yes	2	4.3	odd	2
50.7.c.c.7.1		2	20.19	odd	2
50.7.c.c.43.1		2	20.7	even	4
80.7.p.a.17.1		2	1.1	even	1	trivial
80.7.p.a.33.1		2	5.3	odd	4	inner
90.7.g.a.37.1		2	12.11	even	2
90.7.g.a.73.1		2	60.23	odd	4
450.7.g.b.307.1		2	60.59	even	2
450.7.g.b.343.1		2	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(23.0000 - 23.0000i) q^{3} +(-75.0000 + 100.000i) q^{5} +(247.000 + 247.000i) q^{7} -329.000i q^{9} -1402.00 q^{11} +(-2703.00 + 2703.00i) q^{13} +(575.000 + 4025.00i) q^{15} +(2593.00 + 2593.00i) q^{17} -1720.00i q^{19} +11362.0 q^{21} +(-2137.00 + 2137.00i) q^{23} +(-4375.00 - 15000.0i) q^{25} +(9200.00 + 9200.00i) q^{27} +30520.0i q^{29} +37838.0 q^{31} +(-32246.0 + 32246.0i) q^{33} +(-43225.0 + 6175.00i) q^{35} +(37113.0 + 37113.0i) q^{37} +124338. i q^{39} -35438.0 q^{41} +(-39177.0 + 39177.0i) q^{43} +(32900.0 + 24675.0i) q^{45} +(-95193.0 - 95193.0i) q^{47} +4369.00i q^{49} +119278. q^{51} +(36017.0 - 36017.0i) q^{53} +(105150. - 140200. i) q^{55} +(-39560.0 - 39560.0i) q^{57} +35960.0i q^{59} +83322.0 q^{61} +(81263.0 - 81263.0i) q^{63} +(-67575.0 - 473025. i) q^{65} +(-60833.0 - 60833.0i) q^{67} +98302.0i q^{69} +40318.0 q^{71} +(-129023. + 129023. i) q^{73} +(-445625. - 244375. i) q^{75} +(-346294. - 346294. i) q^{77} -524640. i q^{79} +663041. q^{81} +(114423. - 114423. i) q^{83} +(-453775. + 64825.0i) q^{85} +(701960. + 701960. i) q^{87} +187280. i q^{89} -1.33528e6 q^{91} +(870274. - 870274. i) q^{93} +(172000. + 129000. i) q^{95} +(532833. + 532833. i) q^{97} +461258. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 46 q^{3} - 150 q^{5} + 494 q^{7} - 2804 q^{11} - 5406 q^{13} + 1150 q^{15} + 5186 q^{17} + 22724 q^{21} - 4274 q^{23} - 8750 q^{25} + 18400 q^{27} + 75676 q^{31} - 64492 q^{33} - 86450 q^{35} + 74226 q^{37}+ \cdots + 1065666 q^{97}+O(q^{100}) \) 2 * q + 46 * q^3 - 150 * q^5 + 494 * q^7 - 2804 * q^11 - 5406 * q^13 + 1150 * q^15 + 5186 * q^17 + 22724 * q^21 - 4274 * q^23 - 8750 * q^25 + 18400 * q^27 + 75676 * q^31 - 64492 * q^33 - 86450 * q^35 + 74226 * q^37 - 70876 * q^41 - 78354 * q^43 + 65800 * q^45 - 190386 * q^47 + 238556 * q^51 + 72034 * q^53 + 210300 * q^55 - 79120 * q^57 + 166644 * q^61 + 162526 * q^63 - 135150 * q^65 - 121666 * q^67 + 80636 * q^71 - 258046 * q^73 - 891250 * q^75 - 692588 * q^77 + 1326082 * q^81 + 228846 * q^83 - 907550 * q^85 + 1403920 * q^87 - 2670564 * q^91 + 1740548 * q^93 + 344000 * q^95 + 1065666 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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