LMFDB - Embedded newform 160.6.n.a.63.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(63,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.n (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:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} + \cdots + 69451154208 $ x^14 - 4x^13 + 8x^12 - 4626x^11 + 149441x^10 - 2113414x^9 + 17958066x^8 - 97717112x^7 + 355171384x^6 - 910571904x^5 + 2428303248x^4 - 9166992192x^3 + 32237484304x^2 - 66916821408*x + 69451154208
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{31}\cdot 5^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.5
Root			$2.04998 + 2.04998i$ of defining polynomial
Character	$\chi$	$=$	160.63
Dual form			160.6.n.a.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65790 - 5.65790i) q^{3} +(-54.5514 + 12.2124i) q^{5} +(-23.8754 - 23.8754i) q^{7} +178.976i q^{9} +O(q^{10})$	\(q+(5.65790 - 5.65790i) q^{3} +(-54.5514 + 12.2124i) q^{5} +(-23.8754 - 23.8754i) q^{7} +178.976i q^{9} -218.294i q^{11} +(152.629 + 152.629i) q^{13} +(-239.550 + 377.743i) q^{15} +(318.212 - 318.212i) q^{17} +2458.73 q^{19} -270.169 q^{21} +(512.053 - 512.053i) q^{23} +(2826.71 - 1332.41i) q^{25} +(2387.50 + 2387.50i) q^{27} -5946.31i q^{29} +3065.42i q^{31} +(-1235.09 - 1235.09i) q^{33} +(1594.01 + 1010.86i) q^{35} +(1314.27 - 1314.27i) q^{37} +1727.12 q^{39} +6094.04 q^{41} +(1906.24 - 1906.24i) q^{43} +(-2185.74 - 9763.41i) q^{45} +(8043.61 + 8043.61i) q^{47} -15666.9i q^{49} -3600.83i q^{51} +(-8094.04 - 8094.04i) q^{53} +(2665.90 + 11908.2i) q^{55} +(13911.3 - 13911.3i) q^{57} +41644.1 q^{59} +43094.2 q^{61} +(4273.13 - 4273.13i) q^{63} +(-10190.1 - 6462.16i) q^{65} +(41625.7 + 41625.7i) q^{67} -5794.29i q^{69} +23788.6i q^{71} +(9336.77 + 9336.77i) q^{73} +(8454.62 - 23531.9i) q^{75} +(-5211.86 + 5211.86i) q^{77} -86090.7 q^{79} -16474.8 q^{81} +(75841.2 - 75841.2i) q^{83} +(-13472.8 + 21245.1i) q^{85} +(-33643.6 - 33643.6i) q^{87} -18677.4i q^{89} -7288.16i q^{91} +(17343.8 + 17343.8i) q^{93} +(-134127. + 30027.1i) q^{95} +(-97740.2 + 97740.2i) q^{97} +39069.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7}+O(q^{10}) $ 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7	$ 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7} - 414 q^{13} - 278 q^{15} + 1222 q^{17} - 5672 q^{19} + 5924 q^{21} - 2902 q^{23} - 4466 q^{25} + 2168 q^{27} - 2444 q^{33} + 2618 q^{35} - 1790 q^{37} + 11076 q^{39} + 11644 q^{41} + 3982 q^{43} + 14704 q^{45} + 1278 q^{47} + 5882 q^{53} - 65608 q^{55} - 14552 q^{57} + 8504 q^{59} + 20564 q^{61} - 19422 q^{63} + 40798 q^{65} - 107926 q^{67} - 16418 q^{73} - 66586 q^{75} - 13348 q^{77} + 146544 q^{79} + 173806 q^{81} + 36398 q^{83} - 66262 q^{85} - 124384 q^{87} - 306620 q^{93} - 173768 q^{95} - 60314 q^{97} + 388628 q^{99}+O(q^{100}) $ 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7 - 414 * q^13 - 278 * q^15 + 1222 * q^17 - 5672 * q^19 + 5924 * q^21 - 2902 * q^23 - 4466 * q^25 + 2168 * q^27 - 2444 * q^33 + 2618 * q^35 - 1790 * q^37 + 11076 * q^39 + 11644 * q^41 + 3982 * q^43 + 14704 * q^45 + 1278 * q^47 + 5882 * q^53 - 65608 * q^55 - 14552 * q^57 + 8504 * q^59 + 20564 * q^61 - 19422 * q^63 + 40798 * q^65 - 107926 * q^67 - 16418 * q^73 - 66586 * q^75 - 13348 * q^77 + 146544 * q^79 + 173806 * q^81 + 36398 * q^83 - 66262 * q^85 - 124384 * q^87 - 306620 * q^93 - 173768 * q^95 - 60314 * q^97 + 388628 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	5.65790	−	5.65790i	0.362954	−	0.362954i	−0.501945	−	0.864900i	$-0.667382\pi$
$3$	5.65790	−	5.65790i	0.362954	−	0.362954i	0.864900	+	0.501945i	$0.167382\pi$
$4$		0			0
$5$	−54.5514	+	12.2124i	−0.975845	+	0.218463i
$5$	−54.5514	+	12.2124i	−0.975845	+	0.218463i
$6$		0			0
$7$	−23.8754	−	23.8754i	−0.184164	−	0.184164i	0.609003	−	0.793168i	$-0.291570\pi$
$7$	−23.8754	−	23.8754i	−0.184164	−	0.184164i	−0.793168	+	0.609003i	$0.791570\pi$
$8$		0			0
$9$			178.976i			0.736528i
$10$		0			0
$11$		−	218.294i		−	0.543951i	−0.962304	−	0.271976i	$-0.912323\pi$
$11$		−	218.294i		−	0.543951i	0.962304	−	0.271976i	$-0.0876770\pi$
$12$		0			0
$13$	152.629	+	152.629i	0.250483	+	0.250483i	0.821169	−	0.570685i	$-0.193322\pi$
$13$	152.629	+	152.629i	0.250483	+	0.250483i	−0.570685	+	0.821169i	$0.693322\pi$
$14$		0			0
$15$	−239.550	+	377.743i	−0.274895	+	0.433479i
$16$		0			0
$17$	318.212	−	318.212i	0.267051	−	0.267051i	−0.560860	−	0.827911i	$-0.689529\pi$
$17$	318.212	−	318.212i	0.267051	−	0.267051i	0.827911	+	0.560860i	$0.189529\pi$
$18$		0			0
$19$	2458.73			1.56253			0.781264	−	0.624201i	$-0.214575\pi$
$19$	2458.73			1.56253			0.781264	+	0.624201i	$0.214575\pi$
$20$		0			0
$21$	−270.169			−0.133687
$22$		0			0
$23$	512.053	−	512.053i	0.201834	−	0.201834i	−0.598951	−	0.800786i	$-0.704416\pi$
$23$	512.053	−	512.053i	0.201834	−	0.201834i	0.800786	+	0.598951i	$0.204416\pi$
$24$		0			0
$25$	2826.71	−	1332.41i	0.904548	−	0.426371i
$26$		0			0
$27$	2387.50	+	2387.50i	0.630281	+	0.630281i
$28$		0			0
$29$		−	5946.31i		−	1.31296i	−0.754342	−	0.656482i	$-0.772044\pi$
$29$		−	5946.31i		−	1.31296i	0.754342	−	0.656482i	$-0.227956\pi$
$30$		0			0
$31$			3065.42i			0.572909i	0.958094	+	0.286454i	$0.0924767\pi$
$31$			3065.42i			0.572909i	−0.958094	+	0.286454i	$0.907523\pi$
$32$		0			0
$33$	−1235.09	−	1235.09i	−0.197430	−	0.197430i
$34$		0			0
$35$	1594.01	+	1010.86i	0.219949	+	0.139483i
$36$		0			0
$37$	1314.27	−	1314.27i	0.157827	−	0.157827i	−0.623776	−	0.781603i	$-0.714402\pi$
$37$	1314.27	−	1314.27i	0.157827	−	0.157827i	0.781603	+	0.623776i	$0.214402\pi$
$38$		0			0
$39$	1727.12			0.181828
$40$		0			0
$41$	6094.04			0.566168			0.283084	−	0.959095i	$-0.408642\pi$
$41$	6094.04			0.566168			0.283084	+	0.959095i	$0.408642\pi$
$42$		0			0
$43$	1906.24	−	1906.24i	0.157220	−	0.157220i	−0.624114	−	0.781334i	$-0.714540\pi$
$43$	1906.24	−	1906.24i	0.157220	−	0.157220i	0.781334	+	0.624114i	$0.214540\pi$
$44$		0			0
$45$	−2185.74	−	9763.41i	−0.160904	−	0.718737i
$46$		0			0
$47$	8043.61	+	8043.61i	0.531137	+	0.531137i	0.920911	−	0.389774i	$-0.127447\pi$
$47$	8043.61	+	8043.61i	0.531137	+	0.531137i	−0.389774	+	0.920911i	$0.627447\pi$
$48$		0			0
$49$		−	15666.9i		−	0.932167i
$50$		0			0
$51$		−	3600.83i		−	0.193855i
$52$		0			0
$53$	−8094.04	−	8094.04i	−0.395800	−	0.395800i	0.480949	−	0.876749i	$-0.340292\pi$
$53$	−8094.04	−	8094.04i	−0.395800	−	0.395800i	−0.876749	+	0.480949i	$0.840292\pi$
$54$		0			0
$55$	2665.90	+	11908.2i	0.118833	+	0.530812i
$56$		0			0
$57$	13911.3	−	13911.3i	0.567126	−	0.567126i
$58$		0			0
$59$	41644.1			1.55748			0.778742	−	0.627344i	$-0.215858\pi$
$59$	41644.1			1.55748			0.778742	+	0.627344i	$0.215858\pi$
$60$		0			0
$61$	43094.2			1.48284			0.741420	−	0.671041i	$-0.234153\pi$
$61$	43094.2			1.48284			0.741420	+	0.671041i	$0.234153\pi$
$62$		0			0
$63$	4273.13	−	4273.13i	0.135642	−	0.135642i
$64$		0			0
$65$	−10190.1	−	6462.16i	−0.299154	−	0.189712i
$66$		0			0
$67$	41625.7	+	41625.7i	1.13285	+	1.13285i	0.989700	+	0.143154i	$0.0457244\pi$
$67$	41625.7	+	41625.7i	1.13285	+	1.13285i	0.143154	+	0.989700i	$0.454276\pi$
$68$		0			0
$69$		−	5794.29i		−	0.146513i
$70$		0			0
$71$			23788.6i			0.560045i	0.959993	+	0.280023i	$0.0903419\pi$
$71$			23788.6i			0.560045i	−0.959993	+	0.280023i	$0.909658\pi$
$72$		0			0
$73$	9336.77	+	9336.77i	0.205064	+	0.205064i	0.802166	−	0.597102i	$-0.203681\pi$
$73$	9336.77	+	9336.77i	0.205064	+	0.205064i	−0.597102	+	0.802166i	$0.703681\pi$
$74$		0			0
$75$	8454.62	−	23531.9i	0.173556	−	0.483063i
$76$		0			0
$77$	−5211.86	+	5211.86i	−0.100177	+	0.100177i
$78$		0			0
$79$	−86090.7			−1.55199			−0.775994	−	0.630740i	$-0.782751\pi$
$79$	−86090.7			−1.55199			−0.775994	+	0.630740i	$0.782751\pi$
$80$		0			0
$81$	−16474.8			−0.279002
$82$		0			0
$83$	75841.2	−	75841.2i	1.20840	−	1.20840i	0.236852	−	0.971546i	$-0.423884\pi$
$83$	75841.2	−	75841.2i	1.20840	−	1.20840i	0.971546	−	0.236852i	$-0.0761156\pi$
$84$		0			0
$85$	−13472.8	+	21245.1i	−0.202260	+	0.318942i
$86$		0			0
$87$	−33643.6	−	33643.6i	−0.476546	−	0.476546i
$88$		0			0
$89$		−	18677.4i		−	0.249943i	−0.992160	−	0.124971i	$-0.960116\pi$
$89$		−	18677.4i		−	0.249943i	0.992160	−	0.124971i	$-0.0398839\pi$
$90$		0			0
$91$		−	7288.16i		−	0.0922602i
$92$		0			0
$93$	17343.8	+	17343.8i	0.207940	+	0.207940i
$94$		0			0
$95$	−134127.	+	30027.1i	−1.52479	+	0.341354i
$96$		0			0
$97$	−97740.2	+	97740.2i	−1.05474	+	1.05474i	−0.0563240	+	0.998413i	$0.517938\pi$
$97$	−97740.2	+	97740.2i	−1.05474	+	1.05474i	−0.998413	+	0.0563240i	$0.982062\pi$
$98$		0			0
$99$	39069.5			0.400635
$100$		0			0
$101$	−14938.3			−0.145713			−0.0728565	−	0.997342i	$-0.523211\pi$
$101$	−14938.3			−0.145713			−0.0728565	+	0.997342i	$0.523211\pi$
$102$		0			0
$103$	−85212.1	+	85212.1i	−0.791422	+	0.791422i	−0.981725	−	0.190303i	$-0.939053\pi$
$103$	−85212.1	+	85212.1i	−0.791422	+	0.791422i	0.190303	+	0.981725i	$0.439053\pi$
$104$		0			0
$105$	14738.1	−	3299.42i	0.130457	−	0.0292055i
$106$		0			0
$107$	−78160.1	−	78160.1i	−0.659972	−	0.659972i	0.295401	−	0.955373i	$-0.404547\pi$
$107$	−78160.1	−	78160.1i	−0.659972	−	0.659972i	−0.955373	+	0.295401i	$0.904547\pi$
$108$		0			0
$109$			36099.2i			0.291026i	0.989356	+	0.145513i	$0.0464832\pi$
$109$			36099.2i			0.291026i	−0.989356	+	0.145513i	$0.953517\pi$
$110$		0			0
$111$		−	14872.0i		−	0.114568i
$112$		0			0
$113$	−10180.6	−	10180.6i	−0.0750028	−	0.0750028i	0.668610	−	0.743613i	$-0.266889\pi$
$113$	−10180.6	−	10180.6i	−0.0750028	−	0.0750028i	−0.743613	+	0.668610i	$0.766889\pi$
$114$		0			0
$115$	−21679.8	+	34186.6i	−0.152866	+	0.241052i
$116$		0			0
$117$	−27317.0	+	27317.0i	−0.184488	+	0.184488i
$118$		0			0
$119$	−15194.9			−0.0983627
$120$		0			0
$121$	113399.			0.704117
$122$		0			0
$123$	34479.5	−	34479.5i	0.205493	−	0.205493i
$124$		0			0
$125$	−137929.	+	107206.i	−0.789553	+	0.613682i
$126$		0			0
$127$	−88663.6	−	88663.6i	−0.487794	−	0.487794i	0.419816	−	0.907609i	$-0.362095\pi$
$127$	−88663.6	−	88663.6i	−0.487794	−	0.487794i	−0.907609	+	0.419816i	$0.862095\pi$
$128$		0			0
$129$		−	21570.7i		−	0.114127i
$130$		0			0
$131$		−	4797.45i		−	0.0244249i	−0.999925	−	0.0122124i	$-0.996113\pi$
$131$		−	4797.45i		−	0.0244249i	0.999925	−	0.0122124i	$-0.00388744\pi$
$132$		0			0
$133$	−58703.3	−	58703.3i	−0.287762	−	0.287762i
$134$		0			0
$135$	−159399.	−	101084.i	−0.752749	−	0.477364i
$136$		0			0
$137$	−149951.	+	149951.i	−0.682569	+	0.682569i	−0.960578	−	0.278009i	$-0.910325\pi$
$137$	−149951.	+	149951.i	−0.682569	+	0.682569i	0.278009	+	0.960578i	$0.410325\pi$
$138$		0			0
$139$	22452.1			0.0985642			0.0492821	−	0.998785i	$-0.484307\pi$
$139$	22452.1			0.0985642			0.0492821	+	0.998785i	$0.484307\pi$
$140$		0			0
$141$	91019.9			0.385557
$142$		0			0
$143$	33318.0	−	33318.0i	0.136251	−	0.136251i
$144$		0			0
$145$	72618.9	+	324380.i	0.286833	+	1.28125i
$146$		0			0
$147$	−88641.9	−	88641.9i	−0.338334	−	0.338334i
$148$		0			0
$149$			107764.i			0.397656i	0.980034	+	0.198828i	$0.0637135\pi$
$149$			107764.i			0.397656i	−0.980034	+	0.198828i	$0.936286\pi$
$150$		0			0
$151$			140313.i			0.500789i	0.968144	+	0.250394i	$0.0805603\pi$
$151$			140313.i			0.500789i	−0.968144	+	0.250394i	$0.919440\pi$
$152$		0			0
$153$	56952.5	+	56952.5i	0.196691	+	0.196691i
$154$		0			0
$155$	−37436.2	−	167223.i	−0.125159	−	0.559070i
$156$		0			0
$157$	−151141.	+	151141.i	−0.489366	+	0.489366i	−0.908106	−	0.418740i	$-0.862472\pi$
$157$	−151141.	+	151141.i	−0.489366	+	0.489366i	0.418740	+	0.908106i	$0.362472\pi$
$158$		0			0
$159$	−91590.5			−0.287315
$160$		0			0
$161$	−24451.0			−0.0743415
$162$		0			0
$163$	126439.	−	126439.i	0.372746	−	0.372746i	−0.495730	−	0.868476i	$-0.665100\pi$
$163$	126439.	−	126439.i	0.372746	−	0.372746i	0.868476	+	0.495730i	$0.165100\pi$
$164$		0			0
$165$	82459.1	+	52292.3i	0.235792	+	0.149530i
$166$		0			0
$167$	125948.	+	125948.i	0.349463	+	0.349463i	0.859909	−	0.510447i	$-0.170520\pi$
$167$	125948.	+	125948.i	0.349463	+	0.349463i	−0.510447	+	0.859909i	$0.670520\pi$
$168$		0			0
$169$		−	324702.i		−	0.874516i
$170$		0			0
$171$			440055.i			1.15085i
$172$		0			0
$173$	−399318.	−	399318.i	−1.01439	−	1.01439i	−0.999895	−	0.0144914i	$-0.995387\pi$
$173$	−399318.	−	399318.i	−1.01439	−	1.01439i	−0.0144914	−	0.999895i	$-0.504613\pi$
$174$		0			0
$175$	−99300.8	−	35677.1i	−0.245108	−	0.0880632i
$176$		0			0
$177$	235618.	−	235618.i	0.565296	−	0.565296i
$178$		0			0
$179$	457843.			1.06803			0.534016	−	0.845474i	$-0.320682\pi$
$179$	457843.			1.06803			0.534016	+	0.845474i	$0.320682\pi$
$180$		0			0
$181$	625293.			1.41869			0.709344	−	0.704863i	$-0.248991\pi$
$181$	625293.			1.41869			0.709344	+	0.704863i	$0.248991\pi$
$182$		0			0
$183$	243823.	−	243823.i	0.538204	−	0.538204i
$184$		0			0
$185$	−55644.8	+	87745.7i	−0.119535	+	0.188494i
$186$		0			0
$187$	−69463.9	−	69463.9i	−0.145263	−	0.145263i
$188$		0			0
$189$		−	114005.i		−	0.232151i
$190$		0			0
$191$			426964.i			0.846853i	0.905930	+	0.423426i	$0.139173\pi$
$191$			426964.i			0.846853i	−0.905930	+	0.423426i	$0.860827\pi$
$192$		0			0
$193$	−519101.	−	519101.i	−1.00313	−	1.00313i	−0.999995	−	0.00313800i	$-0.999001\pi$
$193$	−519101.	−	519101.i	−1.00313	−	1.00313i	−0.00313800	−	0.999995i	$-0.500999\pi$
$194$		0			0
$195$	−94216.8	+	21092.3i	−0.177436	+	0.0397226i
$196$		0			0
$197$	645637.	−	645637.i	1.18529	−	1.18529i	0.206930	−	0.978356i	$-0.433653\pi$
$197$	645637.	−	645637.i	1.18529	−	1.18529i	0.978356	−	0.206930i	$-0.0663472\pi$
$198$		0			0
$199$	824647.			1.47617			0.738083	−	0.674710i	$-0.235731\pi$
$199$	824647.			1.47617			0.738083	+	0.674710i	$0.235731\pi$
$200$		0			0
$201$	471028.			0.822349
$202$		0			0
$203$	−141971.	+	141971.i	−0.241801	+	0.241801i
$204$		0			0
$205$	−332438.	+	74423.0i	−0.552492	+	0.123687i
$206$		0			0
$207$	91645.4	+	91645.4i	0.148657	+	0.148657i
$208$		0			0
$209$		−	536727.i		−	0.849939i
$210$		0			0
$211$			1.27068e6i			1.96485i	0.186670	+	0.982423i	$0.440231\pi$
$211$			1.27068e6i			1.96485i	−0.186670	+	0.982423i	$0.559769\pi$
$212$		0			0
$213$	134594.	+	134594.i	0.203271	+	0.203271i
$214$		0			0
$215$	−80708.4	+	127268.i	−0.119076	+	0.187769i
$216$		0			0
$217$	73188.1	−	73188.1i	0.105509	−	0.105509i
$218$		0			0
$219$	105653.			0.148858
$220$		0			0
$221$	97136.9			0.133784
$222$		0			0
$223$	946335.	−	946335.i	1.27433	−	1.27433i	0.330540	−	0.943792i	$-0.392769\pi$
$223$	946335.	−	946335.i	1.27433	−	1.27433i	0.943792	−	0.330540i	$-0.107231\pi$
$224$		0			0
$225$	238470.	+	505915.i	0.314034	+	0.666225i
$226$		0			0
$227$	−751480.	−	751480.i	−0.967950	−	0.967950i	0.0315523	−	0.999502i	$-0.489955\pi$
$227$	−751480.	−	751480.i	−0.967950	−	0.967950i	−0.999502	+	0.0315523i	$0.989955\pi$
$228$		0			0
$229$		−	792900.i		−	0.999147i	−0.866271	−	0.499574i	$-0.833490\pi$
$229$		−	792900.i		−	0.999147i	0.866271	−	0.499574i	$-0.166510\pi$
$230$		0			0
$231$			58976.4i			0.0727190i
$232$		0			0
$233$	−310134.	−	310134.i	−0.374248	−	0.374248i	0.494774	−	0.869022i	$-0.335251\pi$
$233$	−310134.	−	310134.i	−0.374248	−	0.374248i	−0.869022	+	0.494774i	$0.835251\pi$
$234$		0			0
$235$	−537022.	−	340558.i	−0.634341	−	0.402274i
$236$		0			0
$237$	−487092.	+	487092.i	−0.563301	+	0.563301i
$238$		0			0
$239$	1.36178e6			1.54210			0.771048	−	0.636777i	$-0.219733\pi$
$239$	1.36178e6			1.54210			0.771048	+	0.636777i	$0.219733\pi$
$240$		0			0
$241$	77351.9			0.0857883			0.0428942	−	0.999080i	$-0.486342\pi$
$241$	77351.9			0.0857883			0.0428942	+	0.999080i	$0.486342\pi$
$242$		0			0
$243$	−673375.	+	673375.i	−0.731546	+	0.731546i
$244$		0			0
$245$	191331.	+	854653.i	0.203644	+	0.909651i
$246$		0			0
$247$	375274.	+	375274.i	0.391387	+	0.391387i
$248$		0			0
$249$		−	858204.i		−	0.877187i
$250$		0			0
$251$			312063.i			0.312649i	0.987706	+	0.156325i	$0.0499646\pi$
$251$			312063.i			0.312649i	−0.987706	+	0.156325i	$0.950035\pi$
$252$		0			0
$253$	−111778.	−	111778.i	−0.109788	−	0.109788i
$254$		0			0
$255$	43974.9	+	196430.i	0.0423501	+	0.189173i
$256$		0			0
$257$	−981036.	+	981036.i	−0.926514	+	0.926514i	−0.997479	−	0.0709649i	$-0.977392\pi$
$257$	−981036.	+	981036.i	−0.926514	+	0.926514i	0.0709649	+	0.997479i	$0.477392\pi$
$258$		0			0
$259$	−62757.5			−0.0581321
$260$		0			0
$261$	1.06425e6			0.967035
$262$		0			0
$263$	1.26719e6	−	1.26719e6i	1.12968	−	1.12968i	0.139446	−	0.990230i	$-0.455468\pi$
$263$	1.26719e6	−	1.26719e6i	1.12968	−	1.12968i	0.990230	−	0.139446i	$-0.0445321\pi$
$264$		0			0
$265$	540389.	+	342693.i	0.472707	+	0.299772i
$266$		0			0
$267$	−105675.	−	105675.i	−0.0907178	−	0.0907178i
$268$		0			0
$269$		−	396279.i		−	0.333903i	−0.985965	−	0.166951i	$-0.946608\pi$
$269$		−	396279.i		−	0.333903i	0.985965	−	0.166951i	$-0.0533923\pi$
$270$		0			0
$271$			490416.i			0.405640i	0.979216	+	0.202820i	$0.0650107\pi$
$271$			490416.i			0.405640i	−0.979216	+	0.202820i	$0.934989\pi$
$272$		0			0
$273$	−41235.7	−	41235.7i	−0.0334863	−	0.0334863i
$274$		0			0
$275$	−290857.	−	617055.i	−0.231925	−	0.492030i
$276$		0			0
$277$	130834.	−	130834.i	0.102452	−	0.102452i	−0.654023	−	0.756475i	$-0.726920\pi$
$277$	130834.	−	130834.i	0.102452	−	0.102452i	0.756475	+	0.654023i	$0.226920\pi$
$278$		0			0
$279$	−548637.			−0.421963
$280$		0			0
$281$	1.58558e6			1.19790			0.598952	−	0.800785i	$-0.295584\pi$
$281$	1.58558e6			1.19790			0.598952	+	0.800785i	$0.295584\pi$
$282$		0			0
$283$	−269779.	+	269779.i	−0.200236	+	0.200236i	−0.800101	−	0.599865i	$-0.795221\pi$
$283$	−269779.	+	269779.i	−0.200236	+	0.200236i	0.599865	+	0.800101i	$0.295221\pi$
$284$		0			0
$285$	−588989.	+	928770.i	−0.429532	+	0.677323i
$286$		0			0
$287$	−145498.	−	145498.i	−0.104268	−	0.104268i
$288$		0			0
$289$			1.21734e6i			0.857367i
$290$		0			0
$291$			1.10601e6i			0.765643i
$292$		0			0
$293$	−1.67347e6	−	1.67347e6i	−1.13880	−	1.13880i	−0.988665	−	0.150135i	$-0.952029\pi$
$293$	−1.67347e6	−	1.67347e6i	−1.13880	−	1.13880i	−0.150135	−	0.988665i	$-0.547971\pi$
$294$		0			0
$295$	−2.27175e6	+	508576.i	−1.51986	+	0.340252i
$296$		0			0
$297$	521177.	−	521177.i	0.342842	−	0.342842i
$298$		0			0
$299$	156308.			0.101112
$300$		0			0
$301$	−91024.7			−0.0579086
$302$		0			0
$303$	−84519.5	+	84519.5i	−0.0528872	+	0.0528872i
$304$		0			0
$305$	−2.35085e6	+	526285.i	−1.44702	+	0.323945i
$306$		0			0
$307$	−1.87184e6	−	1.87184e6i	−1.13350	−	1.13350i	−0.989590	−	0.143914i	$-0.954031\pi$
$307$	−1.87184e6	−	1.87184e6i	−1.13350	−	1.13350i	−0.143914	−	0.989590i	$-0.545969\pi$
$308$		0			0
$309$			964243.i			0.574500i
$310$		0			0
$311$		−	2.01273e6i		−	1.18001i	−0.807400	−	0.590005i	$-0.799126\pi$
$311$		−	2.01273e6i		−	1.18001i	0.807400	−	0.590005i	$-0.200874\pi$
$312$		0			0
$313$	1.09008e6	+	1.09008e6i	0.628921	+	0.628921i	0.947797	−	0.318876i	$-0.103305\pi$
$313$	1.09008e6	+	1.09008e6i	0.628921	+	0.628921i	−0.318876	+	0.947797i	$0.603305\pi$
$314$		0			0
$315$	−180920.	+	285291.i	−0.102733	+	0.161999i
$316$		0			0
$317$	−2.18740e6	+	2.18740e6i	−1.22259	+	1.22259i	−0.255877	+	0.966709i	$0.582364\pi$
$317$	−2.18740e6	+	2.18740e6i	−1.22259	+	1.22259i	−0.966709	+	0.255877i	$0.917636\pi$
$318$		0			0
$319$	−1.29804e6			−0.714188
$320$		0			0
$321$	−884444.			−0.479080
$322$		0			0
$323$	782400.	−	782400.i	0.417275	−	0.417275i
$324$		0			0
$325$	634803.	+	228074.i	0.333373	+	0.119775i
$326$		0			0
$327$	204246.	+	204246.i	0.105629	+	0.105629i
$328$		0			0
$329$		−	384089.i		−	0.195633i
$330$		0			0
$331$			1.45657e6i			0.730738i	0.930863	+	0.365369i	$0.119057\pi$
$331$			1.45657e6i			0.730738i	−0.930863	+	0.365369i	$0.880943\pi$
$332$		0			0
$333$	235223.	+	235223.i	0.116244	+	0.116244i
$334$		0			0
$335$	−2.77909e6	−	1.76239e6i	−1.35298	−	0.858004i
$336$		0			0
$337$	−1.63889e6	+	1.63889e6i	−0.786096	+	0.786096i	−0.980852	−	0.194756i	$-0.937609\pi$
$337$	−1.63889e6	+	1.63889e6i	−0.786096	+	0.786096i	0.194756	+	0.980852i	$0.437609\pi$
$338$		0			0
$339$	−115202.			−0.0544452
$340$		0			0
$341$	669162.			0.311634
$342$		0			0
$343$	−775328.	+	775328.i	−0.355836	+	0.355836i
$344$		0			0
$345$	70762.3	+	316087.i	0.0320077	+	0.142974i
$346$		0			0
$347$	−1.26972e6	−	1.26972e6i	−0.566087	−	0.566087i	0.364943	−	0.931030i	$-0.381088\pi$
$347$	−1.26972e6	−	1.26972e6i	−0.566087	−	0.566087i	−0.931030	+	0.364943i	$0.881088\pi$
$348$		0			0
$349$		−	26961.5i		−	0.0118490i	−0.999982	−	0.00592449i	$-0.998114\pi$
$349$		−	26961.5i		−	0.0118490i	0.999982	−	0.00592449i	$-0.00188584\pi$
$350$		0			0
$351$			728804.i			0.315750i
$352$		0			0
$353$	−1.76514e6	−	1.76514e6i	−0.753949	−	0.753949i	0.221265	−	0.975214i	$-0.428981\pi$
$353$	−1.76514e6	−	1.76514e6i	−0.753949	−	0.753949i	−0.975214	+	0.221265i	$0.928981\pi$
$354$		0			0
$355$	−290516.	−	1.29770e6i	−0.122349	−	0.546517i
$356$		0			0
$357$	−85971.3	+	85971.3i	−0.0357012	+	0.0357012i
$358$		0			0
$359$	−1.46738e6			−0.600905			−0.300453	−	0.953797i	$-0.597138\pi$
$359$	−1.46738e6			−0.600905			−0.300453	+	0.953797i	$0.597138\pi$
$360$		0			0
$361$	3.56928e6			1.44149
$362$		0			0
$363$	641599.	−	641599.i	0.255562	−	0.255562i
$364$		0			0
$365$	−623359.	−	395310.i	−0.244910	−	0.155312i
$366$		0			0
$367$	3.11806e6	+	3.11806e6i	1.20842	+	1.20842i	0.971537	+	0.236886i	$0.0761268\pi$
$367$	3.11806e6	+	3.11806e6i	1.20842	+	1.20842i	0.236886	+	0.971537i	$0.423873\pi$
$368$		0			0
$369$			1.09069e6i			0.416999i
$370$		0			0
$371$			386497.i			0.145785i
$372$		0			0
$373$	2.88408e6	+	2.88408e6i	1.07333	+	1.07333i	0.997089	+	0.0762441i	$0.0242928\pi$
$373$	2.88408e6	+	2.88408e6i	1.07333	+	1.07333i	0.0762441	+	0.997089i	$0.475707\pi$
$374$		0			0
$375$	−173830.	+	1.38695e6i	−0.0638331	+	0.509311i
$376$		0			0
$377$	907580.	−	907580.i	0.328875	−	0.328875i
$378$		0			0
$379$	2.02320e6			0.723505			0.361753	−	0.932274i	$-0.382179\pi$
$379$	2.02320e6			0.723505			0.361753	+	0.932274i	$0.382179\pi$
$380$		0			0
$381$	−1.00330e6			−0.354094
$382$		0			0
$383$	2.69527e6	−	2.69527e6i	0.938871	−	0.938871i	−0.0593656	−	0.998236i	$-0.518908\pi$
$383$	2.69527e6	−	2.69527e6i	0.938871	−	0.938871i	0.998236	+	0.0593656i	$0.0189078\pi$
$384$		0			0
$385$	220665.	−	347964.i	0.0758720	−	0.119642i
$386$		0			0
$387$	341172.	+	341172.i	0.115797	+	0.115797i
$388$		0			0
$389$		−	4.00903e6i		−	1.34328i	−0.740880	−	0.671638i	$-0.765591\pi$
$389$		−	4.00903e6i		−	1.34328i	0.740880	−	0.671638i	$-0.234409\pi$
$390$		0			0
$391$		−	325883.i		−	0.107800i
$392$		0			0
$393$	−27143.5	−	27143.5i	−0.00886512	−	0.00886512i
$394$		0			0
$395$	4.69637e6	−	1.05138e6i	1.51450	−	0.339051i
$396$		0			0
$397$	107569.	−	107569.i	0.0342541	−	0.0342541i	−0.689772	−	0.724026i	$-0.742289\pi$
$397$	107569.	−	107569.i	0.0342541	−	0.0342541i	0.724026	+	0.689772i	$0.242289\pi$
$398$		0			0
$399$	−664275.			−0.208889
$400$		0			0
$401$	−3.65913e6			−1.13636			−0.568182	−	0.822903i	$-0.692353\pi$
$401$	−3.65913e6			−1.13636			−0.568182	+	0.822903i	$0.692353\pi$
$402$		0			0
$403$	−467872.	+	467872.i	−0.143504	+	0.143504i
$404$		0			0
$405$	898722.	−	201197.i	0.272262	−	0.0609514i
$406$		0			0
$407$	−286897.	−	286897.i	−0.0858500	−	0.0858500i
$408$		0			0
$409$		−	297521.i		−	0.0879445i	−0.999033	−	0.0439723i	$-0.985999\pi$
$409$		−	297521.i		−	0.0879445i	0.999033	−	0.0439723i	$-0.0140013\pi$
$410$		0			0
$411$			1.69681e6i			0.495483i
$412$		0			0
$413$	−994270.	−	994270.i	−0.286833	−	0.286833i
$414$		0			0
$415$	−3.21104e6	+	5.06345e6i	−0.915220	+	1.44320i
$416$		0			0
$417$	127032.	−	127032.i	0.0357743	−	0.0357743i
$418$		0			0
$419$	6.52109e6			1.81462			0.907309	−	0.420464i	$-0.138133\pi$
$419$	6.52109e6			1.81462			0.907309	+	0.420464i	$0.138133\pi$
$420$		0			0
$421$	4.57043e6			1.25676			0.628379	−	0.777907i	$-0.283719\pi$
$421$	4.57043e6			1.25676			0.628379	+	0.777907i	$0.283719\pi$
$422$		0			0
$423$	−1.43962e6	+	1.43962e6i	−0.391197	+	0.391197i
$424$		0			0
$425$	475506.	−	1.32348e6i	0.127698	−	0.355424i
$426$		0			0
$427$	−1.02889e6	−	1.02889e6i	−0.273087	−	0.273087i
$428$		0			0
$429$		−	377020.i		−	0.0989056i
$430$		0			0
$431$		−	4.64706e6i		−	1.20499i	−0.798121	−	0.602497i	$-0.794173\pi$
$431$		−	4.64706e6i		−	1.20499i	0.798121	−	0.602497i	$-0.205827\pi$
$432$		0			0
$433$	−1.28765e6	−	1.28765e6i	−0.330049	−	0.330049i	0.522556	−	0.852605i	$-0.324979\pi$
$433$	−1.28765e6	−	1.28765e6i	−0.330049	−	0.330049i	−0.852605	+	0.522556i	$0.824979\pi$
$434$		0			0
$435$	2.24618e6	+	1.42444e6i	0.569143	+	0.360928i
$436$		0			0
$437$	1.25900e6	−	1.25900e6i	0.315372	−	0.315372i
$438$		0			0
$439$	−2.49221e6			−0.617196			−0.308598	−	0.951193i	$-0.599860\pi$
$439$	−2.49221e6			−0.617196			−0.308598	+	0.951193i	$0.599860\pi$
$440$		0			0
$441$	2.80401e6			0.686567
$442$		0			0
$443$	108531.	−	108531.i	0.0262751	−	0.0262751i	−0.693847	−	0.720122i	$-0.744086\pi$
$443$	108531.	−	108531.i	0.0262751	−	0.0262751i	0.720122	+	0.693847i	$0.244086\pi$
$444$		0			0
$445$	228096.	+	1.01888e6i	0.0546031	+	0.243905i
$446$		0			0
$447$	609717.	+	609717.i	0.144331	+	0.144331i
$448$		0			0
$449$		−	1.27740e6i		−	0.299029i	−0.988760	−	0.149514i	$-0.952229\pi$
$449$		−	1.27740e6i		−	0.299029i	0.988760	−	0.149514i	$-0.0477710\pi$
$450$		0			0
$451$		−	1.33029e6i		−	0.307968i
$452$		0			0
$453$	793875.	+	793875.i	0.181764	+	0.181764i
$454$		0			0
$455$	89006.2	+	397580.i	0.0201554	+	0.0900317i
$456$		0			0
$457$	4.12352e6	−	4.12352e6i	0.923586	−	0.923586i	−0.0736949	−	0.997281i	$-0.523479\pi$
$457$	4.12352e6	−	4.12352e6i	0.923586	−	0.923586i	0.997281	+	0.0736949i	$0.0234791\pi$
$458$		0			0
$459$	1.51946e6			0.336635
$460$		0			0
$461$	−8.86506e6			−1.94280			−0.971402	−	0.237439i	$-0.923692\pi$
$461$	−8.86506e6			−1.94280			−0.971402	+	0.237439i	$0.923692\pi$
$462$		0			0
$463$	−3.00796e6	+	3.00796e6i	−0.652108	+	0.652108i	−0.953500	−	0.301392i	$-0.902549\pi$
$463$	−3.00796e6	+	3.00796e6i	−0.652108	+	0.652108i	0.301392	+	0.953500i	$0.402549\pi$
$464$		0			0
$465$	−1.15794e6	−	734320.i	−0.248344	−	0.157490i
$466$		0			0
$467$	2.19836e6	+	2.19836e6i	0.466452	+	0.466452i	0.900763	−	0.434311i	$-0.143008\pi$
$467$	2.19836e6	+	2.19836e6i	0.466452	+	0.466452i	−0.434311	+	0.900763i	$0.643008\pi$
$468$		0			0
$469$		−	1.98766e6i		−	0.417263i
$470$		0			0
$471$			1.71028e6i			0.355235i
$472$		0			0
$473$	−416122.	−	416122.i	−0.0855199	−	0.0855199i
$474$		0			0
$475$	6.95014e6	−	3.27604e6i	1.41338	−	0.666217i
$476$		0			0
$477$	1.44864e6	−	1.44864e6i	0.291518	−	0.291518i
$478$		0			0
$479$	−3.12528e6			−0.622372			−0.311186	−	0.950349i	$-0.600726\pi$
$479$	−3.12528e6			−0.622372			−0.311186	+	0.950349i	$0.600726\pi$
$480$		0			0
$481$	401191.			0.0790659
$482$		0			0
$483$	−138341.	+	138341.i	−0.0269826	+	0.0269826i
$484$		0			0
$485$	4.13822e6	−	6.52551e6i	0.798839	−	1.25968i
$486$		0			0
$487$	5.74900e6	+	5.74900e6i	1.09842	+	1.09842i	0.994595	+	0.103828i	$0.0331091\pi$
$487$	5.74900e6	+	5.74900e6i	1.09842	+	1.09842i	0.103828	+	0.994595i	$0.466891\pi$
$488$		0			0
$489$		−	1.43076e6i		−	0.270580i
$490$		0			0
$491$			1.06215e6i			0.198830i	0.995046	+	0.0994149i	$0.0316971\pi$
$491$			1.06215e6i			0.198830i	−0.995046	+	0.0994149i	$0.968303\pi$
$492$		0			0
$493$	−1.89219e6	−	1.89219e6i	−0.350629	−	0.350629i
$494$		0			0
$495$	−2.13129e6	+	477133.i	−0.390958	+	0.0875238i
$496$		0			0
$497$	567963.	−	567963.i	0.103140	−	0.103140i
$498$		0			0
$499$	1.96563e6			0.353386			0.176693	−	0.984266i	$-0.443460\pi$
$499$	1.96563e6			0.353386			0.176693	+	0.984266i	$0.443460\pi$
$500$		0			0
$501$	1.42520e6			0.253678
$502$		0			0
$503$	4.00724e6	−	4.00724e6i	0.706196	−	0.706196i	−0.259537	−	0.965733i	$-0.583570\pi$
$503$	4.00724e6	−	4.00724e6i	0.706196	−	0.706196i	0.965733	+	0.259537i	$0.0835700\pi$
$504$		0			0
$505$	814906.	−	182433.i	0.142193	−	0.0318328i
$506$		0			0
$507$	−1.83713e6	−	1.83713e6i	−0.317410	−	0.317410i
$508$		0			0
$509$			4.63858e6i			0.793580i	0.917909	+	0.396790i	$0.129876\pi$
$509$			4.63858e6i			0.793580i	−0.917909	+	0.396790i	$0.870124\pi$
$510$		0			0
$511$		−	445839.i		−	0.0755310i
$512$		0			0
$513$	5.87023e6	+	5.87023e6i	0.984831	+	0.984831i
$514$		0			0
$515$	3.60779e6	−	5.68909e6i	0.599409	−	0.945201i
$516$		0			0
$517$	1.75587e6	−	1.75587e6i	0.288913	−	0.288913i
$518$		0			0
$519$	−4.51860e6			−0.736352
$520$		0			0
$521$	−6.43145e6			−1.03804			−0.519021	−	0.854762i	$-0.673703\pi$
$521$	−6.43145e6			−1.03804			−0.519021	+	0.854762i	$0.673703\pi$
$522$		0			0
$523$	−7.62526e6	+	7.62526e6i	−1.21899	+	1.21899i	−0.251006	+	0.967986i	$0.580761\pi$
$523$	−7.62526e6	+	7.62526e6i	−1.21899	+	1.21899i	−0.967986	+	0.251006i	$0.919239\pi$
$524$		0			0
$525$	−763691.	+	359976.i	−0.120926	+	0.0570001i
$526$		0			0
$527$	975454.	+	975454.i	0.152996	+	0.152996i
$528$		0			0
$529$			5.91195e6i			0.918526i
$530$		0			0
$531$			7.45331e6i			1.14713i
$532$		0			0
$533$	930127.	+	930127.i	0.141816	+	0.141816i
$534$		0			0
$535$	5.21827e6	+	3.30922e6i	0.788210	+	0.499852i
$536$		0			0
$537$	2.59043e6	−	2.59043e6i	0.387647	−	0.387647i
$538$		0			0
$539$	−3.42000e6			−0.507053
$540$		0			0
$541$	−7.69592e6			−1.13049			−0.565246	−	0.824923i	$-0.691219\pi$
$541$	−7.69592e6			−1.13049			−0.565246	+	0.824923i	$0.691219\pi$
$542$		0			0
$543$	3.53784e6	−	3.53784e6i	0.514919	−	0.514919i
$544$		0			0
$545$	−440859.	−	1.96926e6i	−0.0635782	−	0.283996i
$546$		0			0
$547$	−8.31090e6	−	8.31090e6i	−1.18763	−	1.18763i	−0.977722	−	0.209904i	$-0.932685\pi$
$547$	−8.31090e6	−	8.31090e6i	−1.18763	−	1.18763i	−0.209904	−	0.977722i	$-0.567315\pi$
$548$		0			0
$549$			7.71285e6i			1.09215i
$550$		0			0
$551$		−	1.46204e7i		−	2.05154i
$552$		0			0
$553$	2.05545e6	+	2.05545e6i	0.285821	+	0.285821i
$554$		0			0
$555$	181623.	+	811289.i	0.0250288	+	0.111800i
$556$		0			0
$557$	−2.90207e6	+	2.90207e6i	−0.396341	+	0.396341i	−0.876940	−	0.480599i	$-0.840419\pi$
$557$	−2.90207e6	+	2.90207e6i	−0.396341	+	0.396341i	0.480599	+	0.876940i	$0.340419\pi$
$558$		0			0
$559$	581896.			0.0787619
$560$		0			0
$561$	−786039.			−0.105448
$562$		0			0
$563$	−7.08912e6	+	7.08912e6i	−0.942586	+	0.942586i	−0.998439	−	0.0558525i	$-0.982212\pi$
$563$	−7.08912e6	+	7.08912e6i	−0.942586	+	0.942586i	0.0558525	+	0.998439i	$0.482212\pi$
$564$		0			0
$565$	679697.	+	431037.i	0.0895765	+	0.0568059i
$566$		0			0
$567$	393342.	+	393342.i	0.0513822	+	0.0513822i
$568$		0			0
$569$			1.02793e7i			1.33102i	0.746389	+	0.665509i	$0.231786\pi$
$569$			1.02793e7i			1.33102i	−0.746389	+	0.665509i	$0.768214\pi$
$570$		0			0
$571$		−	9.92423e6i		−	1.27382i	−0.770940	−	0.636908i	$-0.780213\pi$
$571$		−	9.92423e6i		−	1.27382i	0.770940	−	0.636908i	$-0.219787\pi$
$572$		0			0
$573$	2.41572e6	+	2.41572e6i	0.307369	+	0.307369i
$574$		0			0
$575$	765162.	−	2.12969e6i	0.0965126	−	0.268625i
$576$		0			0
$577$	−7.82091e6	+	7.82091e6i	−0.977953	+	0.977953i	−0.999762	−	0.0218096i	$-0.993057\pi$
$577$	−7.82091e6	+	7.82091e6i	−0.977953	+	0.977953i	0.0218096	+	0.999762i	$0.493057\pi$
$578$		0			0
$579$	−5.87404e6			−0.728183
$580$		0			0
$581$	−3.62148e6			−0.445088
$582$		0			0
$583$	−1.76688e6	+	1.76688e6i	−0.215296	+	0.215296i
$584$		0			0
$585$	1.15657e6	−	1.82379e6i	0.139728	−	0.220335i
$586$		0			0
$587$	−4.94337e6	−	4.94337e6i	−0.592144	−	0.592144i	0.346066	−	0.938210i	$-0.387517\pi$
$587$	−4.94337e6	−	4.94337e6i	−0.592144	−	0.592144i	−0.938210	+	0.346066i	$0.887517\pi$
$588$		0			0
$589$			7.53705e6i			0.895185i
$590$		0			0
$591$		−	7.30590e6i		−	0.860409i
$592$		0			0
$593$	−5.40438e6	−	5.40438e6i	−0.631116	−	0.631116i	0.317232	−	0.948348i	$-0.397247\pi$
$593$	−5.40438e6	−	5.40438e6i	−0.631116	−	0.631116i	−0.948348	+	0.317232i	$0.897247\pi$
$594$		0			0
$595$	828904.	−	185567.i	0.0959868	−	0.0214886i
$596$		0			0
$597$	4.66577e6	−	4.66577e6i	0.535781	−	0.535781i
$598$		0			0
$599$	−3.02994e6			−0.345039			−0.172519	−	0.985006i	$-0.555191\pi$
$599$	−3.02994e6			−0.345039			−0.172519	+	0.985006i	$0.555191\pi$
$600$		0			0
$601$	−8.33982e6			−0.941825			−0.470913	−	0.882180i	$-0.656075\pi$
$601$	−8.33982e6			−0.941825			−0.470913	+	0.882180i	$0.656075\pi$
$602$		0			0
$603$	−7.45001e6	+	7.45001e6i	−0.834379	+	0.834379i
$604$		0			0
$605$	−6.18606e6	+	1.38487e6i	−0.687109	+	0.153823i
$606$		0			0
$607$	4.99673e6	+	4.99673e6i	0.550445	+	0.550445i	0.926569	−	0.376124i	$-0.122743\pi$
$607$	4.99673e6	+	4.99673e6i	0.550445	+	0.550445i	−0.376124	+	0.926569i	$0.622743\pi$
$608$		0			0
$609$			1.60651e6i			0.175526i
$610$		0			0
$611$			2.45538e6i			0.266082i
$612$		0			0
$613$	3.24993e6	+	3.24993e6i	0.349320	+	0.349320i	0.859856	−	0.510536i	$-0.170553\pi$
$613$	3.24993e6	+	3.24993e6i	0.349320	+	0.349320i	−0.510536	+	0.859856i	$0.670553\pi$
$614$		0			0
$615$	−1.45982e6	+	2.30198e6i	−0.155637	+	0.245422i
$616$		0			0
$617$	1.74236e6	−	1.74236e6i	0.184258	−	0.184258i	−0.608951	−	0.793208i	$-0.708409\pi$
$617$	1.74236e6	−	1.74236e6i	0.184258	−	0.184258i	0.793208	+	0.608951i	$0.208409\pi$
$618$		0			0
$619$	−1.08664e7			−1.13988			−0.569941	−	0.821686i	$-0.693034\pi$
$619$	−1.08664e7			−1.13988			−0.569941	+	0.821686i	$0.693034\pi$
$620$		0			0
$621$	2.44505e6			0.254425
$622$		0			0
$623$	−445929.	+	445929.i	−0.0460305	+	0.0460305i
$624$		0			0
$625$	6.21499e6	−	7.53268e6i	0.636415	−	0.771347i
$626$		0			0
$627$	−3.03675e6	−	3.03675e6i	−0.308489	−	0.308489i
$628$		0			0
$629$		−	836434.i		−	0.0842956i
$630$		0			0
$631$		−	6.31541e6i		−	0.631434i	−0.948853	−	0.315717i	$-0.897755\pi$
$631$		−	6.31541e6i		−	0.631434i	0.948853	−	0.315717i	$-0.102245\pi$
$632$		0			0
$633$	7.18935e6	+	7.18935e6i	0.713149	+	0.713149i
$634$		0			0
$635$	5.91952e6	+	3.75393e6i	0.582576	+	0.369447i
$636$		0			0
$637$	2.39123e6	−	2.39123e6i	0.233492	−	0.233492i
$638$		0			0
$639$	−4.25760e6			−0.412489
$640$		0			0
$641$	−1.01885e7			−0.979408			−0.489704	−	0.871889i	$-0.662895\pi$
$641$	−1.01885e7			−0.979408			−0.489704	+	0.871889i	$0.662895\pi$
$642$		0			0
$643$	−1.11631e6	+	1.11631e6i	−0.106478	+	0.106478i	−0.758339	−	0.651861i	$-0.773989\pi$
$643$	−1.11631e6	+	1.11631e6i	−0.106478	+	0.106478i	0.651861	+	0.758339i	$0.273989\pi$
$644$		0			0
$645$	263430.	+	1.17671e6i	0.0249325	+	0.111371i
$646$		0			0
$647$	1.08225e7	+	1.08225e7i	1.01640	+	1.01640i	0.999863	+	0.0165382i	$0.00526451\pi$
$647$	1.08225e7	+	1.08225e7i	1.01640	+	1.01640i	0.0165382	+	0.999863i	$0.494735\pi$
$648$		0			0
$649$		−	9.09066e6i		−	0.847196i
$650$		0			0
$651$		−	828182.i		−	0.0765902i
$652$		0			0
$653$	5.19640e6	+	5.19640e6i	0.476892	+	0.476892i	0.904136	−	0.427244i	$-0.140516\pi$
$653$	5.19640e6	+	5.19640e6i	0.476892	+	0.476892i	−0.427244	+	0.904136i	$0.640516\pi$
$654$		0			0
$655$	58588.5	+	261708.i	0.00533592	+	0.0238349i
$656$		0			0
$657$	−1.67106e6	+	1.67106e6i	−0.151035	+	0.151035i
$658$		0			0
$659$	−5.17149e6			−0.463876			−0.231938	−	0.972731i	$-0.574507\pi$
$659$	−5.17149e6			−0.463876			−0.231938	+	0.972731i	$0.574507\pi$
$660$		0			0
$661$	−8.28147e6			−0.737231			−0.368616	−	0.929582i	$-0.620168\pi$
$661$	−8.28147e6			−0.737231			−0.368616	+	0.929582i	$0.620168\pi$
$662$		0			0
$663$	549591.	−	549591.i	0.0485574	−	0.0485574i
$664$		0			0
$665$	3.91926e6	+	2.48544e6i	0.343676	+	0.217946i
$666$		0			0
$667$	−3.04483e6	−	3.04483e6i	−0.265001	−	0.265001i
$668$		0			0
$669$		−	1.07085e7i		−	0.925049i
$670$		0			0
$671$		−	9.40721e6i		−	0.806593i
$672$		0			0
$673$	3.42754e6	+	3.42754e6i	0.291706	+	0.291706i	0.837754	−	0.546048i	$-0.183868\pi$
$673$	3.42754e6	+	3.42754e6i	0.291706	+	0.291706i	−0.546048	+	0.837754i	$0.683868\pi$
$674$		0			0
$675$	9.92991e6	+	3.56765e6i	0.838853	+	0.301386i
$676$		0			0
$677$	−8.26736e6	+	8.26736e6i	−0.693258	+	0.693258i	−0.962947	−	0.269689i	$-0.913079\pi$
$677$	−8.26736e6	+	8.26736e6i	−0.693258	+	0.693258i	0.269689	+	0.962947i	$0.413079\pi$
$678$		0			0
$679$	4.66718e6			0.388490
$680$		0			0
$681$	−8.50360e6			−0.702643
$682$		0			0
$683$	−3.18611e6	+	3.18611e6i	−0.261342	+	0.261342i	−0.825599	−	0.564257i	$-0.809163\pi$
$683$	−3.18611e6	+	3.18611e6i	−0.261342	+	0.261342i	0.564257	+	0.825599i	$0.309163\pi$
$684$		0			0
$685$	6.34876e6	−	1.00113e7i	0.516966	−	0.815198i
$686$		0			0
$687$	−4.48615e6	−	4.48615e6i	−0.362645	−	0.362645i
$688$		0			0
$689$		−	2.47077e6i		−	0.198283i
$690$		0			0
$691$			1.80913e6i			0.144137i	0.997400	+	0.0720685i	$0.0229600\pi$
$691$			1.80913e6i			0.144137i	−0.997400	+	0.0720685i	$0.977040\pi$
$692$		0			0
$693$	−932799.	−	932799.i	−0.0737828	−	0.0737828i
$694$		0			0
$695$	−1.22479e6	+	274194.i	−0.0961834	+	0.0215326i
$696$		0			0
$697$	1.93920e6	−	1.93920e6i	0.151196	−	0.151196i
$698$		0			0
$699$	−3.50941e6			−0.271670
$700$		0			0
$701$	8.47023e6			0.651029			0.325514	−	0.945537i	$-0.394463\pi$
$701$	8.47023e6			0.651029			0.325514	+	0.945537i	$0.394463\pi$
$702$		0			0
$703$	3.23144e6	−	3.23144e6i	0.246608	−	0.246608i
$704$		0			0
$705$	−4.96526e6	+	1.11157e6i	−0.376244	+	0.0842297i
$706$		0			0
$707$	356658.	+	356658.i	0.0268351	+	0.0268351i
$708$		0			0
$709$			1.88589e7i			1.40896i	0.709722	+	0.704482i	$0.248821\pi$
$709$			1.88589e7i			1.40896i	−0.709722	+	0.704482i	$0.751179\pi$
$710$		0			0
$711$		−	1.54082e7i		−	1.14308i
$712$		0			0
$713$	1.56966e6	+	1.56966e6i	0.115633	+	0.115633i
$714$		0			0
$715$	−1.41065e6	+	2.22444e6i	−0.103194	+	0.162725i
$716$		0			0
$717$	7.70480e6	−	7.70480e6i	0.559711	−	0.559711i
$718$		0			0
$719$	1.02992e7			0.742989			0.371495	−	0.928435i	$-0.378845\pi$
$719$	1.02992e7			0.742989			0.371495	+	0.928435i	$0.378845\pi$
$720$		0			0
$721$	4.06895e6			0.291504
$722$		0			0
$723$	437649.	−	437649.i	0.0311373	−	0.0311373i
$724$		0			0
$725$	−7.92293e6	−	1.68085e7i	−0.559810	−	1.18764i
$726$		0			0
$727$	1.33721e7	+	1.33721e7i	0.938346	+	0.938346i	0.998207	−	0.0598611i	$-0.0190658\pi$
$727$	1.33721e7	+	1.33721e7i	0.938346	+	0.938346i	−0.0598611	+	0.998207i	$0.519066\pi$
$728$		0			0
$729$			3.61641e6i			0.252034i
$730$		0			0
$731$		−	1.21318e6i		−	0.0839715i
$732$		0			0
$733$	1.34325e6	+	1.34325e6i	0.0923418	+	0.0923418i	0.751769	−	0.659427i	$-0.229201\pi$
$733$	1.34325e6	+	1.34325e6i	0.0923418	+	0.0923418i	−0.659427	+	0.751769i	$0.729201\pi$
$734$		0			0
$735$	5.91808e6	+	3.75301e6i	0.404075	+	0.256248i
$736$		0			0
$737$	9.08663e6	−	9.08663e6i	0.616218	−	0.616218i
$738$		0			0
$739$	3.77236e6			0.254099			0.127049	−	0.991896i	$-0.459449\pi$
$739$	3.77236e6			0.254099			0.127049	+	0.991896i	$0.459449\pi$
$740$		0			0
$741$	4.24653e6			0.284111
$742$		0			0
$743$	4.63047e6	−	4.63047e6i	0.307718	−	0.307718i	−0.536306	−	0.844024i	$-0.680181\pi$
$743$	4.63047e6	−	4.63047e6i	0.307718	−	0.307718i	0.844024	+	0.536306i	$0.180181\pi$
$744$		0			0
$745$	−1.31606e6	−	5.87867e6i	−0.0868729	−	0.388051i
$746$		0			0
$747$	1.35738e7	+	1.35738e7i	0.890019	+	0.890019i
$748$		0			0
$749$			3.73221e6i			0.243087i
$750$		0			0
$751$			2.08661e7i			1.35002i	0.737807	+	0.675012i	$0.235862\pi$
$751$			2.08661e7i			1.35002i	−0.737807	+	0.675012i	$0.764138\pi$
$752$		0			0
$753$	1.76562e6	+	1.76562e6i	0.113477	+	0.113477i
$754$		0			0
$755$	−1.71356e6	−	7.65426e6i	−0.109404	−	0.488692i
$756$		0			0
$757$	−964426.	+	964426.i	−0.0611687	+	0.0611687i	−0.737029	−	0.675861i	$-0.763772\pi$
$757$	−964426.	+	964426.i	−0.0611687	+	0.0611687i	0.675861	+	0.737029i	$0.263772\pi$
$758$		0			0
$759$	−1.26486e6			−0.0796962
$760$		0			0
$761$	1.49933e7			0.938505			0.469252	−	0.883064i	$-0.344523\pi$
$761$	1.49933e7			0.938505			0.469252	+	0.883064i	$0.344523\pi$
$762$		0			0
$763$	861883.	−	861883.i	0.0535966	−	0.0535966i
$764$		0			0
$765$	−3.80237e6	−	2.41131e6i	−0.234909	−	0.148970i
$766$		0			0
$767$	6.35610e6	+	6.35610e6i	0.390124	+	0.390124i
$768$		0			0
$769$		−	4.51581e6i		−	0.275372i	−0.990476	−	0.137686i	$-0.956034\pi$
$769$		−	4.51581e6i		−	0.275372i	0.990476	−	0.137686i	$-0.0439664\pi$
$770$		0			0
$771$			1.11012e7i			0.672565i
$772$		0			0
$773$	−1.29303e7	−	1.29303e7i	−0.778320	−	0.778320i	0.201225	−	0.979545i	$-0.435508\pi$
$773$	−1.29303e7	−	1.29303e7i	−0.778320	−	0.778320i	−0.979545	+	0.201225i	$0.935508\pi$
$774$		0			0
$775$	4.08439e6	+	8.66505e6i	0.244272	+	0.518223i
$776$		0			0
$777$	−355075.	+	355075.i	−0.0210993	+	0.0210993i
$778$		0			0
$779$	1.49836e7			0.884653
$780$		0			0
$781$	5.19291e6			0.304637
$782$		0			0
$783$	1.41968e7	−	1.41968e7i	0.827536	−	0.827536i
$784$		0			0
$785$	6.39917e6	−	1.00908e7i	0.370637	−	0.584454i
$786$		0			0
$787$	−3.11176e6	−	3.11176e6i	−0.179089	−	0.179089i	0.611869	−	0.790959i	$-0.290418\pi$
$787$	−3.11176e6	−	3.11176e6i	−0.179089	−	0.179089i	−0.790959	+	0.611869i	$0.790418\pi$
$788$		0			0
$789$		−	1.43393e7i		−	0.820042i
$790$		0			0
$791$			486132.i			0.0276257i
$792$		0			0
$793$	6.57743e6	+	6.57743e6i	0.371427	+	0.371427i
$794$		0			0
$795$	4.99639e6	−	1.11854e6i	0.280375	−	0.0627675i
$796$		0			0
$797$	1.47157e7	−	1.47157e7i	0.820607	−	0.820607i	−0.165588	−	0.986195i	$-0.552952\pi$
$797$	1.47157e7	−	1.47157e7i	0.820607	−	0.820607i	0.986195	+	0.165588i	$0.0529521\pi$
$798$		0			0
$799$	5.11915e6			0.283682
$800$		0			0
$801$	3.34280e6			0.184090
$802$		0			0
$803$	2.03816e6	−	2.03816e6i	0.111545	−	0.111545i
$804$		0			0
$805$	1.33383e6	−	298605.i	0.0725458	−	0.0162408i
$806$		0			0
$807$	−2.24211e6	−	2.24211e6i	−0.121192	−	0.121192i
$808$		0			0
$809$		−	1.92301e7i		−	1.03303i	−0.856280	−	0.516513i	$-0.827230\pi$
$809$		−	1.92301e7i		−	1.03303i	0.856280	−	0.516513i	$-0.172770\pi$
$810$		0			0
$811$		−	1.25439e7i		−	0.669701i	−0.942271	−	0.334850i	$-0.891314\pi$
$811$		−	1.25439e7i		−	0.669701i	0.942271	−	0.334850i	$-0.108686\pi$
$812$		0			0
$813$	2.77472e6	+	2.77472e6i	0.147229	+	0.147229i
$814$		0			0
$815$	−5.35331e6	+	8.44158e6i	−0.282312	+	0.445174i
$816$		0			0
$817$	4.68695e6	−	4.68695e6i	0.245660	−	0.245660i
$818$		0			0
$819$	1.30441e6			0.0679523
$820$		0			0
$821$	−5.56071e6			−0.287920			−0.143960	−	0.989583i	$-0.545984\pi$
$821$	−5.56071e6			−0.287920			−0.143960	+	0.989583i	$0.545984\pi$
$822$		0			0
$823$	−1.87493e7	+	1.87493e7i	−0.964909	+	0.964909i	−0.999405	−	0.0344961i	$-0.989017\pi$
$823$	−1.87493e7	+	1.87493e7i	−0.964909	+	0.964909i	0.0344961	+	0.999405i	$0.489017\pi$
$824$		0			0
$825$	−5.13687e6	−	1.84559e6i	−0.262763	−	0.0944063i
$826$		0			0
$827$	1.46263e7	+	1.46263e7i	0.743652	+	0.743652i	0.973279	−	0.229627i	$-0.0737505\pi$
$827$	1.46263e7	+	1.46263e7i	0.743652	+	0.743652i	−0.229627	+	0.973279i	$0.573750\pi$
$828$		0			0
$829$		−	1.77285e7i		−	0.895954i	−0.894045	−	0.447977i	$-0.852145\pi$
$829$		−	1.77285e7i		−	0.895954i	0.894045	−	0.447977i	$-0.147855\pi$
$830$		0			0
$831$		−	1.48049e6i		−	0.0743707i
$832$		0			0
$833$	−4.98541e6	−	4.98541e6i	−0.248936	−	0.248936i
$834$		0			0
$835$	−8.40878e6	−	5.33252e6i	−0.417366	−	0.264677i
$836$		0			0
$837$	−7.31868e6	+	7.31868e6i	−0.361093	+	0.361093i
$838$		0			0
$839$	−3.43040e7			−1.68244			−0.841221	−	0.540692i	$-0.818163\pi$
$839$	−3.43040e7			−1.68244			−0.841221	+	0.540692i	$0.818163\pi$
$840$		0			0
$841$	−1.48475e7			−0.723874
$842$		0			0
$843$	8.97105e6	−	8.97105e6i	0.434785	−	0.434785i
$844$		0			0
$845$	3.96540e6	+	1.77129e7i	0.191049	+	0.853393i
$846$		0			0
$847$	−2.70744e6	−	2.70744e6i	−0.129673	−	0.129673i
$848$		0			0
$849$			3.05277e6i			0.145353i
$850$		0			0
$851$		−	1.34595e6i		−	0.0637097i
$852$		0			0
$853$	−5.28231e6	−	5.28231e6i	−0.248572	−	0.248572i	0.571813	−	0.820384i	$-0.306240\pi$
$853$	−5.28231e6	−	5.28231e6i	−0.248572	−	0.248572i	−0.820384	+	0.571813i	$0.806240\pi$
$854$		0			0
$855$	−5.37414e6	−	2.40056e7i	−0.251417	−	1.12305i
$856$		0			0
$857$	−2.66196e7	+	2.66196e7i	−1.23808	+	1.23808i	−0.277296	+	0.960785i	$0.589438\pi$
$857$	−2.66196e7	+	2.66196e7i	−1.23808	+	1.23808i	−0.960785	+	0.277296i	$0.910562\pi$
$858$		0			0
$859$	1.67064e7			0.772503			0.386252	−	0.922393i	$-0.373770\pi$
$859$	1.67064e7			0.772503			0.386252	+	0.922393i	$0.373770\pi$
$860$		0			0
$861$	−1.64642e6			−0.0756891
$862$		0			0
$863$	−1.80862e7	+	1.80862e7i	−0.826646	+	0.826646i	−0.987051	−	0.160406i	$-0.948720\pi$
$863$	−1.80862e7	+	1.80862e7i	−0.826646	+	0.826646i	0.160406	+	0.987051i	$0.448720\pi$
$864$		0			0
$865$	2.66600e7	+	1.69067e7i	1.21149	+	0.768279i
$866$		0			0
$867$	6.88758e6	+	6.88758e6i	0.311185	+	0.311185i
$868$		0			0
$869$			1.87931e7i			0.844206i
$870$		0			0
$871$			1.27066e7i			0.567522i
$872$		0			0
$873$	−1.74932e7	−	1.74932e7i	−0.776843	−	0.776843i
$874$		0			0
$875$	5.85270e6	+	733533.i	0.258426	+	0.0323891i
$876$		0			0
$877$	−4.69228e6	+	4.69228e6i	−0.206008	+	0.206008i	−0.802568	−	0.596560i	$-0.796534\pi$
$877$	−4.69228e6	+	4.69228e6i	−0.206008	+	0.206008i	0.596560	+	0.802568i	$0.296534\pi$
$878$		0			0
$879$	−1.89366e7			−0.826666
$880$		0			0
$881$	3.72179e7			1.61552			0.807760	−	0.589511i	$-0.200680\pi$
$881$	3.72179e7			1.61552			0.807760	+	0.589511i	$0.200680\pi$
$882$		0			0
$883$	1.77903e7	−	1.77903e7i	0.767859	−	0.767859i	−0.209871	−	0.977729i	$-0.567304\pi$
$883$	1.77903e7	−	1.77903e7i	0.767859	−	0.767859i	0.977729	+	0.209871i	$0.0673043\pi$
$884$		0			0
$885$	−9.97584e6	+	1.57308e7i	−0.428145	+	0.675137i
$886$		0			0
$887$	−3.08604e7	−	3.08604e7i	−1.31702	−	1.31702i	−0.916122	−	0.400899i	$-0.868698\pi$
$887$	−3.08604e7	−	3.08604e7i	−1.31702	−	1.31702i	−0.400899	−	0.916122i	$-0.631302\pi$
$888$		0			0
$889$			4.23376e6i			0.179669i
$890$		0			0
$891$			3.59634e6i			0.151763i
$892$		0			0
$893$	1.97771e7	+	1.97771e7i	0.829916	+	0.829916i
$894$		0			0
$895$	−2.49760e7	+	5.59138e6i	−1.04223	+	0.233325i
$896$		0			0
$897$	884377.	−	884377.i	0.0366992	−	0.0366992i
$898$		0			0
$899$	1.82279e7			0.752208
$900$		0			0
$901$	−5.15125e6			−0.211398
$902$		0			0
$903$	−515009.	+	515009.i	−0.0210182	+	0.0210182i
$904$		0			0
$905$	−3.41106e7	+	7.63634e6i	−1.38442	+	0.309930i
$906$		0			0
$907$	−2.23972e7	−	2.23972e7i	−0.904016	−	0.904016i	0.0917650	−	0.995781i	$-0.470749\pi$
$907$	−2.23972e7	−	2.23972e7i	−0.904016	−	0.904016i	−0.995781	+	0.0917650i	$0.970749\pi$
$908$		0			0
$909$		−	2.67360e6i		−	0.107322i
$910$		0			0
$911$			1.43417e7i			0.572538i	0.958149	+	0.286269i	$0.0924151\pi$
$911$			1.43417e7i			0.572538i	−0.958149	+	0.286269i	$0.907585\pi$
$912$		0			0
$913$	−1.65557e7	−	1.65557e7i	−0.657310	−	0.657310i
$914$		0			0
$915$	−1.03232e7	+	1.62785e7i	−0.407626	+	0.642781i
$916$		0			0
$917$	−114541.	+	114541.i	−0.00449819	+	0.00449819i
$918$		0			0
$919$	1.70726e7			0.666823			0.333411	−	0.942781i	$-0.391800\pi$
$919$	1.70726e7			0.666823			0.333411	+	0.942781i	$0.391800\pi$
$920$		0			0
$921$	−2.11814e7			−0.822821
$922$		0			0
$923$	−3.63083e6	+	3.63083e6i	−0.140282	+	0.140282i
$924$		0			0
$925$	1.96392e6	−	5.46621e6i	0.0754690	−	0.210054i
$926$		0			0
$927$	−1.52509e7	−	1.52509e7i	−0.582905	−	0.582905i
$928$		0			0
$929$			2.41131e7i			0.916672i	0.888779	+	0.458336i	$0.151554\pi$
$929$			2.41131e7i			0.916672i	−0.888779	+	0.458336i	$0.848446\pi$
$930$		0			0
$931$		−	3.85208e7i		−	1.45654i
$932$		0			0
$933$	−1.13879e7	−	1.13879e7i	−0.428290	−	0.428290i
$934$		0			0
$935$	4.63767e6	+	2.94103e6i	0.173489	+	0.110020i
$936$		0			0
$937$	−1.17497e7	+	1.17497e7i	−0.437198	+	0.437198i	−0.891068	−	0.453870i	$-0.850043\pi$
$937$	−1.17497e7	+	1.17497e7i	−0.437198	+	0.437198i	0.453870	+	0.891068i	$0.350043\pi$
$938$		0			0
$939$	1.23351e7			0.456539
$940$		0			0
$941$	2.10237e7			0.773988			0.386994	−	0.922082i	$-0.373513\pi$
$941$	2.10237e7			0.773988			0.386994	+	0.922082i	$0.373513\pi$
$942$		0			0
$943$	3.12047e6	−	3.12047e6i	0.114272	−	0.114272i
$944$		0			0
$945$	1.39228e6	+	6.21914e6i	0.0507162	+	0.226543i
$946$		0			0
$947$	6.44103e6	+	6.44103e6i	0.233389	+	0.233389i	0.814106	−	0.580717i	$-0.197228\pi$
$947$	6.44103e6	+	6.44103e6i	0.233389	+	0.233389i	−0.580717	+	0.814106i	$0.697228\pi$
$948$		0			0
$949$			2.85013e6i			0.102730i
$950$		0			0
$951$			2.47522e7i			0.887486i
$952$		0			0
$953$	1.92602e7	+	1.92602e7i	0.686957	+	0.686957i	0.961558	−	0.274601i	$-0.0885458\pi$
$953$	1.92602e7	+	1.92602e7i	0.686957	+	0.686957i	−0.274601	+	0.961558i	$0.588546\pi$
$954$		0			0
$955$	−5.21427e6	−	2.32915e7i	−0.185006	−	0.826397i
$956$		0			0
$957$	−7.34421e6	+	7.34421e6i	−0.259218	+	0.259218i
$958$		0			0
$959$	7.16027e6			0.251410
$960$		0			0
$961$	1.92324e7			0.671776
$962$		0			0
$963$	1.39888e7	−	1.39888e7i	0.486088	−	0.486088i
$964$		0			0
$965$	3.46572e7	+	2.19782e7i	1.19805	+	0.759756i
$966$		0			0
$967$	−2.31321e7	−	2.31321e7i	−0.795515	−	0.795515i	0.186870	−	0.982385i	$-0.440166\pi$
$967$	−2.31321e7	−	2.31321e7i	−0.795515	−	0.795515i	−0.982385	+	0.186870i	$0.940166\pi$
$968$		0			0
$969$		−	8.85348e6i		−	0.302904i
$970$		0			0
$971$			3.13091e7i			1.06567i	0.846219	+	0.532835i	$0.178873\pi$
$971$			3.13091e7i			1.06567i	−0.846219	+	0.532835i	$0.821127\pi$
$972$		0			0
$973$	−536052.	−	536052.i	−0.0181520	−	0.0181520i
$974$		0			0
$975$	4.88207e6	−	2.30123e6i	0.164472	−	0.0775263i
$976$		0			0
$977$	1.59117e7	−	1.59117e7i	0.533310	−	0.533310i	−0.388246	−	0.921556i	$-0.626919\pi$
$977$	1.59117e7	−	1.59117e7i	0.533310	−	0.533310i	0.921556	+	0.388246i	$0.126919\pi$
$978$		0			0
$979$	−4.07715e6			−0.135957
$980$		0			0
$981$	−6.46090e6			−0.214349
$982$		0			0
$983$	−5.17343e6	+	5.17343e6i	−0.170763	+	0.170763i	−0.787315	−	0.616551i	$-0.788529\pi$
$983$	−5.17343e6	+	5.17343e6i	−0.170763	+	0.170763i	0.616551	+	0.787315i	$0.288529\pi$
$984$		0			0
$985$	−2.73356e7	+	4.31052e7i	−0.897715	+	1.41560i
$986$		0			0
$987$	−2.17314e6	−	2.17314e6i	−0.0710059	−	0.0710059i
$988$		0			0
$989$		−	1.95220e6i		−	0.0634647i
$990$		0			0
$991$			1.98249e7i			0.641250i	0.947206	+	0.320625i	$0.103893\pi$
$991$			1.98249e7i			0.641250i	−0.947206	+	0.320625i	$0.896107\pi$
$992$		0			0
$993$	8.24113e6	+	8.24113e6i	0.265225	+	0.265225i
$994$		0			0
$995$	−4.49856e7	+	1.00709e7i	−1.44051	+	0.322487i
$996$		0			0
$997$	−3.59461e7	+	3.59461e7i	−1.14529	+	1.14529i	−0.157818	+	0.987468i	$0.550446\pi$
$997$	−3.59461e7	+	3.59461e7i	−1.14529	+	1.14529i	−0.987468	+	0.157818i	$0.949554\pi$
$998$		0			0
$999$	6.27564e6			0.198950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.a.63.5	✓	14
4.3	odd	2		160.6.n.b.63.3	yes	14
5.2	odd	4		160.6.n.b.127.3	yes	14
20.7	even	4	inner	160.6.n.a.127.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.a.63.5	✓	14	1.1	even	1	trivial
160.6.n.a.127.5	yes	14	20.7	even	4	inner
160.6.n.b.63.3	yes	14	4.3	odd	2
160.6.n.b.127.3	yes	14	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.65790 - 5.65790i) q^{3} +(-54.5514 + 12.2124i) q^{5} +(-23.8754 - 23.8754i) q^{7} +178.976i q^{9} +O(q^{10})\)	\(q+(5.65790 - 5.65790i) q^{3} +(-54.5514 + 12.2124i) q^{5} +(-23.8754 - 23.8754i) q^{7} +178.976i q^{9} -218.294i q^{11} +(152.629 + 152.629i) q^{13} +(-239.550 + 377.743i) q^{15} +(318.212 - 318.212i) q^{17} +2458.73 q^{19} -270.169 q^{21} +(512.053 - 512.053i) q^{23} +(2826.71 - 1332.41i) q^{25} +(2387.50 + 2387.50i) q^{27} -5946.31i q^{29} +3065.42i q^{31} +(-1235.09 - 1235.09i) q^{33} +(1594.01 + 1010.86i) q^{35} +(1314.27 - 1314.27i) q^{37} +1727.12 q^{39} +6094.04 q^{41} +(1906.24 - 1906.24i) q^{43} +(-2185.74 - 9763.41i) q^{45} +(8043.61 + 8043.61i) q^{47} -15666.9i q^{49} -3600.83i q^{51} +(-8094.04 - 8094.04i) q^{53} +(2665.90 + 11908.2i) q^{55} +(13911.3 - 13911.3i) q^{57} +41644.1 q^{59} +43094.2 q^{61} +(4273.13 - 4273.13i) q^{63} +(-10190.1 - 6462.16i) q^{65} +(41625.7 + 41625.7i) q^{67} -5794.29i q^{69} +23788.6i q^{71} +(9336.77 + 9336.77i) q^{73} +(8454.62 - 23531.9i) q^{75} +(-5211.86 + 5211.86i) q^{77} -86090.7 q^{79} -16474.8 q^{81} +(75841.2 - 75841.2i) q^{83} +(-13472.8 + 21245.1i) q^{85} +(-33643.6 - 33643.6i) q^{87} -18677.4i q^{89} -7288.16i q^{91} +(17343.8 + 17343.8i) q^{93} +(-134127. + 30027.1i) q^{95} +(-97740.2 + 97740.2i) q^{97} +39069.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7}+O(q^{10}) \) 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7	\( 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7} - 414 q^{13} - 278 q^{15} + 1222 q^{17} - 5672 q^{19} + 5924 q^{21} - 2902 q^{23} - 4466 q^{25} + 2168 q^{27} - 2444 q^{33} + 2618 q^{35} - 1790 q^{37} + 11076 q^{39} + 11644 q^{41} + 3982 q^{43} + 14704 q^{45} + 1278 q^{47} + 5882 q^{53} - 65608 q^{55} - 14552 q^{57} + 8504 q^{59} + 20564 q^{61} - 19422 q^{63} + 40798 q^{65} - 107926 q^{67} - 16418 q^{73} - 66586 q^{75} - 13348 q^{77} + 146544 q^{79} + 173806 q^{81} + 36398 q^{83} - 66262 q^{85} - 124384 q^{87} - 306620 q^{93} - 173768 q^{95} - 60314 q^{97} + 388628 q^{99}+O(q^{100}) \) 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7 - 414 * q^13 - 278 * q^15 + 1222 * q^17 - 5672 * q^19 + 5924 * q^21 - 2902 * q^23 - 4466 * q^25 + 2168 * q^27 - 2444 * q^33 + 2618 * q^35 - 1790 * q^37 + 11076 * q^39 + 11644 * q^41 + 3982 * q^43 + 14704 * q^45 + 1278 * q^47 + 5882 * q^53 - 65608 * q^55 - 14552 * q^57 + 8504 * q^59 + 20564 * q^61 - 19422 * q^63 + 40798 * q^65 - 107926 * q^67 - 16418 * q^73 - 66586 * q^75 - 13348 * q^77 + 146544 * q^79 + 173806 * q^81 + 36398 * q^83 - 66262 * q^85 - 124384 * q^87 - 306620 * q^93 - 173768 * q^95 - 60314 * q^97 + 388628 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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