LMFDB - Embedded newform 2070.2.j.a.737.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.a.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.707107 + 2.12132i) q^{10} -0.828427i q^{11} +(1.41421 - 1.41421i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-5.41421 + 5.41421i) q^{17} +3.41421i q^{19} +(1.00000 + 2.00000i) q^{20} +(-0.585786 - 0.585786i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(3.00000 - 4.00000i) q^{25} -2.00000i q^{26} +(2.00000 - 2.00000i) q^{28} -4.82843 q^{29} -4.82843 q^{31} +(-0.707107 + 0.707107i) q^{32} +7.65685i q^{34} +(-6.00000 - 2.00000i) q^{35} +(1.41421 + 1.41421i) q^{37} +(2.41421 + 2.41421i) q^{38} +(2.12132 + 0.707107i) q^{40} +2.58579i q^{41} +(-6.24264 + 6.24264i) q^{43} -0.828427 q^{44} -1.00000 q^{46} +1.00000i q^{49} +(-0.707107 - 4.94975i) q^{50} +(-1.41421 - 1.41421i) q^{52} +(2.65685 + 2.65685i) q^{53} +(0.828427 + 1.65685i) q^{55} -2.82843i q^{56} +(-3.41421 + 3.41421i) q^{58} -2.82843 q^{59} +2.58579 q^{61} +(-3.41421 + 3.41421i) q^{62} +1.00000i q^{64} +(-1.41421 + 4.24264i) q^{65} +(1.17157 + 1.17157i) q^{67} +(5.41421 + 5.41421i) q^{68} +(-5.65685 + 2.82843i) q^{70} +4.58579i q^{71} +(-4.17157 + 4.17157i) q^{73} +2.00000 q^{74} +3.41421 q^{76} +(1.65685 - 1.65685i) q^{77} +6.82843i q^{79} +(2.00000 - 1.00000i) q^{80} +(1.82843 + 1.82843i) q^{82} +(9.24264 + 9.24264i) q^{83} +(5.41421 - 16.2426i) q^{85} +8.82843i q^{86} +(-0.585786 + 0.585786i) q^{88} -14.0000 q^{89} +5.65685 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-3.41421 - 6.82843i) q^{95} +(5.07107 + 5.07107i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{5} + 8 q^{7}+O(q^{10}) $ 4 * q - 8 * q^5 + 8 * q^7	$ 4 q - 8 q^{5} + 8 q^{7} - 4 q^{16} - 16 q^{17} + 4 q^{20} - 8 q^{22} + 12 q^{25} + 8 q^{28} - 8 q^{29} - 8 q^{31} - 24 q^{35} + 4 q^{38} - 8 q^{43} + 8 q^{44} - 4 q^{46} - 12 q^{53} - 8 q^{55} - 8 q^{58} + 16 q^{61} - 8 q^{62} + 16 q^{67} + 16 q^{68} - 28 q^{73} + 8 q^{74} + 8 q^{76} - 16 q^{77} + 8 q^{80} - 4 q^{82} + 20 q^{83} + 16 q^{85} - 8 q^{88} - 56 q^{89} - 8 q^{95} - 8 q^{97}+O(q^{100}) $ 4 * q - 8 * q^5 + 8 * q^7 - 4 * q^16 - 16 * q^17 + 4 * q^20 - 8 * q^22 + 12 * q^25 + 8 * q^28 - 8 * q^29 - 8 * q^31 - 24 * q^35 + 4 * q^38 - 8 * q^43 + 8 * q^44 - 4 * q^46 - 12 * q^53 - 8 * q^55 - 8 * q^58 + 16 * q^61 - 8 * q^62 + 16 * q^67 + 16 * q^68 - 28 * q^73 + 8 * q^74 + 8 * q^76 - 16 * q^77 + 8 * q^80 - 4 * q^82 + 20 * q^83 + 16 * q^85 - 8 * q^88 - 56 * q^89 - 8 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$		0			0
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	0.975579	−	0.219650i	$-0.0704915\pi$
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	−0.219650	+	0.975579i	$0.570491\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.707107	+	2.12132i	−0.223607	+	0.670820i
$11$		−	0.828427i		−	0.249780i	−0.992171	−	0.124890i	$-0.960142\pi$
$11$		−	0.828427i		−	0.249780i	0.992171	−	0.124890i	$-0.0398578\pi$
$12$		0			0
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	−0.483250	−	0.875482i	$-0.660544\pi$
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	0.875482	+	0.483250i	$0.160544\pi$
$14$	2.82843			0.755929
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−5.41421	+	5.41421i	−1.31314	+	1.31314i	−0.394051	+	0.919089i	$0.628927\pi$
$17$	−5.41421	+	5.41421i	−1.31314	+	1.31314i	−0.919089	+	0.394051i	$0.871073\pi$
$18$		0			0
$19$			3.41421i			0.783274i	0.920120	+	0.391637i	$0.128091\pi$
$19$			3.41421i			0.783274i	−0.920120	+	0.391637i	$0.871909\pi$
$20$	1.00000	+	2.00000i	0.223607	+	0.447214i
$21$		0			0
$22$	−0.585786	−	0.585786i	−0.124890	−	0.124890i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		−	2.00000i		−	0.392232i
$27$		0			0
$28$	2.00000	−	2.00000i	0.377964	−	0.377964i
$29$	−4.82843			−0.896616			−0.448308	−	0.893879i	$-0.647973\pi$
$29$	−4.82843			−0.896616			−0.448308	+	0.893879i	$0.647973\pi$
$30$		0			0
$31$	−4.82843			−0.867211			−0.433606	−	0.901103i	$-0.642759\pi$
$31$	−4.82843			−0.867211			−0.433606	+	0.901103i	$0.642759\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			7.65685i			1.31314i
$35$	−6.00000	−	2.00000i	−1.01419	−	0.338062i
$36$		0			0
$37$	1.41421	+	1.41421i	0.232495	+	0.232495i	0.813733	−	0.581238i	$-0.197432\pi$
$37$	1.41421	+	1.41421i	0.232495	+	0.232495i	−0.581238	+	0.813733i	$0.697432\pi$
$38$	2.41421	+	2.41421i	0.391637	+	0.391637i
$39$		0			0
$40$	2.12132	+	0.707107i	0.335410	+	0.111803i
$41$			2.58579i			0.403832i	0.979403	+	0.201916i	$0.0647168\pi$
$41$			2.58579i			0.403832i	−0.979403	+	0.201916i	$0.935283\pi$
$42$		0			0
$43$	−6.24264	+	6.24264i	−0.951994	+	0.951994i	−0.998899	−	0.0469055i	$-0.985064\pi$
$43$	−6.24264	+	6.24264i	−0.951994	+	0.951994i	0.0469055	+	0.998899i	$0.485064\pi$
$44$	−0.828427			−0.124890
$45$		0			0
$46$	−1.00000			−0.147442
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	−0.707107	−	4.94975i	−0.100000	−	0.700000i
$51$		0			0
$52$	−1.41421	−	1.41421i	−0.196116	−	0.196116i
$53$	2.65685	+	2.65685i	0.364947	+	0.364947i	0.865630	−	0.500683i	$-0.166918\pi$
$53$	2.65685	+	2.65685i	0.364947	+	0.364947i	−0.500683	+	0.865630i	$0.666918\pi$
$54$		0			0
$55$	0.828427	+	1.65685i	0.111705	+	0.223410i
$56$		−	2.82843i		−	0.377964i
$57$		0			0
$58$	−3.41421	+	3.41421i	−0.448308	+	0.448308i
$59$	−2.82843			−0.368230			−0.184115	−	0.982905i	$-0.558942\pi$
$59$	−2.82843			−0.368230			−0.184115	+	0.982905i	$0.558942\pi$
$60$		0			0
$61$	2.58579			0.331076			0.165538	−	0.986203i	$-0.447064\pi$
$61$	2.58579			0.331076			0.165538	+	0.986203i	$0.447064\pi$
$62$	−3.41421	+	3.41421i	−0.433606	+	0.433606i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−1.41421	+	4.24264i	−0.175412	+	0.526235i
$66$		0			0
$67$	1.17157	+	1.17157i	0.143130	+	0.143130i	0.775041	−	0.631911i	$-0.217729\pi$
$67$	1.17157	+	1.17157i	0.143130	+	0.143130i	−0.631911	+	0.775041i	$0.717729\pi$
$68$	5.41421	+	5.41421i	0.656570	+	0.656570i
$69$		0			0
$70$	−5.65685	+	2.82843i	−0.676123	+	0.338062i
$71$			4.58579i			0.544233i	0.962264	+	0.272116i	$0.0877236\pi$
$71$			4.58579i			0.544233i	−0.962264	+	0.272116i	$0.912276\pi$
$72$		0			0
$73$	−4.17157	+	4.17157i	−0.488246	+	0.488246i	−0.907752	−	0.419507i	$-0.862203\pi$
$73$	−4.17157	+	4.17157i	−0.488246	+	0.488246i	0.419507	+	0.907752i	$0.362203\pi$
$74$	2.00000			0.232495
$75$		0			0
$76$	3.41421			0.391637
$77$	1.65685	−	1.65685i	0.188816	−	0.188816i
$78$		0			0
$79$			6.82843i			0.768258i	0.923279	+	0.384129i	$0.125498\pi$
$79$			6.82843i			0.768258i	−0.923279	+	0.384129i	$0.874502\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$		0			0
$82$	1.82843	+	1.82843i	0.201916	+	0.201916i
$83$	9.24264	+	9.24264i	1.01451	+	1.01451i	0.999893	+	0.0146185i	$0.00465337\pi$
$83$	9.24264	+	9.24264i	1.01451	+	1.01451i	0.0146185	+	0.999893i	$0.495347\pi$
$84$		0			0
$85$	5.41421	−	16.2426i	0.587254	−	1.76176i
$86$			8.82843i			0.951994i
$87$		0			0
$88$	−0.585786	+	0.585786i	−0.0624450	+	0.0624450i
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$		0			0
$91$	5.65685			0.592999
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$		0			0
$94$		0			0
$95$	−3.41421	−	6.82843i	−0.350291	−	0.700582i
$96$		0			0
$97$	5.07107	+	5.07107i	0.514889	+	0.514889i	0.916020	−	0.401132i	$-0.131383\pi$
$97$	5.07107	+	5.07107i	0.514889	+	0.514889i	−0.401132	+	0.916020i	$0.631383\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	−4.00000	−	3.00000i	−0.400000	−	0.300000i
$101$			7.65685i			0.761885i	0.924599	+	0.380943i	$0.124401\pi$
$101$			7.65685i			0.761885i	−0.924599	+	0.380943i	$0.875599\pi$
$102$		0			0
$103$	−10.8284	+	10.8284i	−1.06696	+	1.06696i	−0.0693653	+	0.997591i	$0.522097\pi$
$103$	−10.8284	+	10.8284i	−1.06696	+	1.06696i	−0.997591	+	0.0693653i	$0.977903\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	3.75736			0.364947
$107$	−10.0711	+	10.0711i	−0.973607	+	0.973607i	−0.999661	−	0.0260537i	$-0.991706\pi$
$107$	−10.0711	+	10.0711i	−0.973607	+	0.973607i	0.0260537	+	0.999661i	$0.491706\pi$
$108$		0			0
$109$		−	4.92893i		−	0.472106i	−0.971740	−	0.236053i	$-0.924146\pi$
$109$		−	4.92893i		−	0.472106i	0.971740	−	0.236053i	$-0.0758539\pi$
$110$	1.75736	+	0.585786i	0.167558	+	0.0558525i
$111$		0			0
$112$	−2.00000	−	2.00000i	−0.188982	−	0.188982i
$113$	−3.75736	−	3.75736i	−0.353463	−	0.353463i	0.507934	−	0.861396i	$-0.330410\pi$
$113$	−3.75736	−	3.75736i	−0.353463	−	0.353463i	−0.861396	+	0.507934i	$0.830410\pi$
$114$		0			0
$115$	2.12132	+	0.707107i	0.197814	+	0.0659380i
$116$			4.82843i			0.448308i
$117$		0			0
$118$	−2.00000	+	2.00000i	−0.184115	+	0.184115i
$119$	−21.6569			−1.98528
$120$		0			0
$121$	10.3137			0.937610
$122$	1.82843	−	1.82843i	0.165538	−	0.165538i
$123$		0			0
$124$			4.82843i			0.433606i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$	−4.41421	−	4.41421i	−0.391698	−	0.391698i	0.483594	−	0.875292i	$-0.339331\pi$
$127$	−4.41421	−	4.41421i	−0.391698	−	0.391698i	−0.875292	+	0.483594i	$0.839331\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	2.00000	+	4.00000i	0.175412	+	0.350823i
$131$			5.65685i			0.494242i	0.968985	+	0.247121i	$0.0794845\pi$
$131$			5.65685i			0.494242i	−0.968985	+	0.247121i	$0.920516\pi$
$132$		0			0
$133$	−6.82843	+	6.82843i	−0.592100	+	0.592100i
$134$	1.65685			0.143130
$135$		0			0
$136$	7.65685			0.656570
$137$	13.0711	−	13.0711i	1.11674	−	1.11674i	0.124520	−	0.992217i	$-0.460261\pi$
$137$	13.0711	−	13.0711i	1.11674	−	1.11674i	0.992217	−	0.124520i	$-0.0397389\pi$
$138$		0			0
$139$			1.17157i			0.0993715i	0.998765	+	0.0496858i	$0.0158220\pi$
$139$			1.17157i			0.0993715i	−0.998765	+	0.0496858i	$0.984178\pi$
$140$	−2.00000	+	6.00000i	−0.169031	+	0.507093i
$141$		0			0
$142$	3.24264	+	3.24264i	0.272116	+	0.272116i
$143$	−1.17157	−	1.17157i	−0.0979718	−	0.0979718i
$144$		0			0
$145$	9.65685	−	4.82843i	0.801958	−	0.400979i
$146$			5.89949i			0.488246i
$147$		0			0
$148$	1.41421	−	1.41421i	0.116248	−	0.116248i
$149$	0.343146			0.0281116			0.0140558	−	0.999901i	$-0.495526\pi$
$149$	0.343146			0.0281116			0.0140558	+	0.999901i	$0.495526\pi$
$150$		0			0
$151$	16.9706			1.38104			0.690522	−	0.723311i	$-0.257381\pi$
$151$	16.9706			1.38104			0.690522	+	0.723311i	$0.257381\pi$
$152$	2.41421	−	2.41421i	0.195819	−	0.195819i
$153$		0			0
$154$		−	2.34315i		−	0.188816i
$155$	9.65685	−	4.82843i	0.775657	−	0.387829i
$156$		0			0
$157$	4.24264	+	4.24264i	0.338600	+	0.338600i	0.855840	−	0.517241i	$-0.173041\pi$
$157$	4.24264	+	4.24264i	0.338600	+	0.338600i	−0.517241	+	0.855840i	$0.673041\pi$
$158$	4.82843	+	4.82843i	0.384129	+	0.384129i
$159$		0			0
$160$	0.707107	−	2.12132i	0.0559017	−	0.167705i
$161$		−	2.82843i		−	0.222911i
$162$		0			0
$163$	10.4853	−	10.4853i	0.821271	−	0.821271i	−0.165020	−	0.986290i	$-0.552769\pi$
$163$	10.4853	−	10.4853i	0.821271	−	0.821271i	0.986290	+	0.165020i	$0.0527688\pi$
$164$	2.58579			0.201916
$165$		0			0
$166$	13.0711			1.01451
$167$	3.89949	−	3.89949i	0.301752	−	0.301752i	−0.539947	−	0.841699i	$-0.681556\pi$
$167$	3.89949	−	3.89949i	0.301752	−	0.301752i	0.841699	+	0.539947i	$0.181556\pi$
$168$		0			0
$169$			9.00000i			0.692308i
$170$	−7.65685	−	15.3137i	−0.587254	−	1.17451i
$171$		0			0
$172$	6.24264	+	6.24264i	0.475997	+	0.475997i
$173$	−9.89949	−	9.89949i	−0.752645	−	0.752645i	0.222327	−	0.974972i	$-0.428635\pi$
$173$	−9.89949	−	9.89949i	−0.752645	−	0.752645i	−0.974972	+	0.222327i	$0.928635\pi$
$174$		0			0
$175$	14.0000	−	2.00000i	1.05830	−	0.151186i
$176$			0.828427i			0.0624450i
$177$		0			0
$178$	−9.89949	+	9.89949i	−0.741999	+	0.741999i
$179$	0.686292			0.0512958			0.0256479	−	0.999671i	$-0.491835\pi$
$179$	0.686292			0.0512958			0.0256479	+	0.999671i	$0.491835\pi$
$180$		0			0
$181$	10.5858			0.786835			0.393418	−	0.919360i	$-0.371293\pi$
$181$	10.5858			0.786835			0.393418	+	0.919360i	$0.371293\pi$
$182$	4.00000	−	4.00000i	0.296500	−	0.296500i
$183$		0			0
$184$			1.00000i			0.0737210i
$185$	−4.24264	−	1.41421i	−0.311925	−	0.103975i
$186$		0			0
$187$	4.48528	+	4.48528i	0.327996	+	0.327996i
$188$		0			0
$189$		0			0
$190$	−7.24264	−	2.41421i	−0.525436	−	0.175145i
$191$		−	14.8284i		−	1.07295i	−0.843917	−	0.536474i	$-0.819756\pi$
$191$		−	14.8284i		−	1.07295i	0.843917	−	0.536474i	$-0.180244\pi$
$192$		0			0
$193$	−5.00000	+	5.00000i	−0.359908	+	0.359908i	−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−5.00000	+	5.00000i	−0.359908	+	0.359908i	0.503871	+	0.863779i	$0.331909\pi$
$194$	7.17157			0.514889
$195$		0			0
$196$	1.00000			0.0714286
$197$	7.07107	−	7.07107i	0.503793	−	0.503793i	−0.408822	−	0.912614i	$-0.634060\pi$
$197$	7.07107	−	7.07107i	0.503793	−	0.503793i	0.912614	+	0.408822i	$0.134060\pi$
$198$		0			0
$199$		−	17.6569i		−	1.25166i	−0.779959	−	0.625831i	$-0.784760\pi$
$199$		−	17.6569i		−	1.25166i	0.779959	−	0.625831i	$-0.215240\pi$
$200$	−4.94975	+	0.707107i	−0.350000	+	0.0500000i
$201$		0			0
$202$	5.41421	+	5.41421i	0.380943	+	0.380943i
$203$	−9.65685	−	9.65685i	−0.677778	−	0.677778i
$204$		0			0
$205$	−2.58579	−	5.17157i	−0.180599	−	0.361198i
$206$			15.3137i			1.06696i
$207$		0			0
$208$	−1.41421	+	1.41421i	−0.0980581	+	0.0980581i
$209$	2.82843			0.195646
$210$		0			0
$211$	−9.17157			−0.631397			−0.315699	−	0.948860i	$-0.602239\pi$
$211$	−9.17157			−0.631397			−0.315699	+	0.948860i	$0.602239\pi$
$212$	2.65685	−	2.65685i	0.182473	−	0.182473i
$213$		0			0
$214$			14.2426i			0.973607i
$215$	6.24264	−	18.7279i	0.425745	−	1.27723i
$216$		0			0
$217$	−9.65685	−	9.65685i	−0.655550	−	0.655550i
$218$	−3.48528	−	3.48528i	−0.236053	−	0.236053i
$219$		0			0
$220$	1.65685	−	0.828427i	0.111705	−	0.0558525i
$221$			15.3137i			1.03011i
$222$		0			0
$223$	5.24264	−	5.24264i	0.351073	−	0.351073i	−0.509436	−	0.860509i	$-0.670146\pi$
$223$	5.24264	−	5.24264i	0.351073	−	0.351073i	0.860509	+	0.509436i	$0.170146\pi$
$224$	−2.82843			−0.188982
$225$		0			0
$226$	−5.31371			−0.353463
$227$	14.8995	−	14.8995i	0.988914	−	0.988914i	−0.0110250	−	0.999939i	$-0.503509\pi$
$227$	14.8995	−	14.8995i	0.988914	−	0.988914i	0.999939	+	0.0110250i	$0.00350944\pi$
$228$		0			0
$229$			10.5858i			0.699528i	0.936838	+	0.349764i	$0.113738\pi$
$229$			10.5858i			0.699528i	−0.936838	+	0.349764i	$0.886262\pi$
$230$	2.00000	−	1.00000i	0.131876	−	0.0659380i
$231$		0			0
$232$	3.41421	+	3.41421i	0.224154	+	0.224154i
$233$	−18.8284	−	18.8284i	−1.23349	−	1.23349i	−0.962614	−	0.270877i	$-0.912686\pi$
$233$	−18.8284	−	18.8284i	−1.23349	−	1.23349i	−0.270877	−	0.962614i	$-0.587314\pi$
$234$		0			0
$235$		0			0
$236$			2.82843i			0.184115i
$237$		0			0
$238$	−15.3137	+	15.3137i	−0.992640	+	0.992640i
$239$	−21.5563			−1.39436			−0.697182	−	0.716894i	$-0.745563\pi$
$239$	−21.5563			−1.39436			−0.697182	+	0.716894i	$0.745563\pi$
$240$		0			0
$241$	−25.7990			−1.66186			−0.830930	−	0.556378i	$-0.812191\pi$
$241$	−25.7990			−1.66186			−0.830930	+	0.556378i	$0.812191\pi$
$242$	7.29289	−	7.29289i	0.468805	−	0.468805i
$243$		0			0
$244$		−	2.58579i		−	0.165538i
$245$	−1.00000	−	2.00000i	−0.0638877	−	0.127775i
$246$		0			0
$247$	4.82843	+	4.82843i	0.307225	+	0.307225i
$248$	3.41421	+	3.41421i	0.216803	+	0.216803i
$249$		0			0
$250$	6.36396	+	9.19239i	0.402492	+	0.581378i
$251$		−	23.1716i		−	1.46258i	−0.682068	−	0.731288i	$-0.738919\pi$
$251$		−	23.1716i		−	1.46258i	0.682068	−	0.731288i	$-0.261081\pi$
$252$		0			0
$253$	−0.585786	+	0.585786i	−0.0368281	+	0.0368281i
$254$	−6.24264			−0.391698
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.17157	+	5.17157i	−0.322594	+	0.322594i	−0.849761	−	0.527168i	$-0.823254\pi$
$257$	−5.17157	+	5.17157i	−0.322594	+	0.322594i	0.527168	+	0.849761i	$0.323254\pi$
$258$		0			0
$259$			5.65685i			0.351500i
$260$	4.24264	+	1.41421i	0.263117	+	0.0877058i
$261$		0			0
$262$	4.00000	+	4.00000i	0.247121	+	0.247121i
$263$	16.1421	+	16.1421i	0.995367	+	0.995367i	0.999989	−	0.00462259i	$-0.00147142\pi$
$263$	16.1421	+	16.1421i	0.995367	+	0.995367i	−0.00462259	+	0.999989i	$0.501471\pi$
$264$		0			0
$265$	−7.97056	−	2.65685i	−0.489628	−	0.163209i
$266$			9.65685i			0.592100i
$267$		0			0
$268$	1.17157	−	1.17157i	0.0715652	−	0.0715652i
$269$	−2.00000			−0.121942			−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000			−0.121942			−0.0609711	+	0.998140i	$0.519420\pi$
$270$		0			0
$271$	−24.9706			−1.51685			−0.758427	−	0.651758i	$-0.774032\pi$
$271$	−24.9706			−1.51685			−0.758427	+	0.651758i	$0.774032\pi$
$272$	5.41421	−	5.41421i	0.328285	−	0.328285i
$273$		0			0
$274$		−	18.4853i		−	1.11674i
$275$	−3.31371	−	2.48528i	−0.199824	−	0.149868i
$276$		0			0
$277$	−2.72792	−	2.72792i	−0.163905	−	0.163905i	0.620389	−	0.784294i	$-0.286975\pi$
$277$	−2.72792	−	2.72792i	−0.163905	−	0.163905i	−0.784294	+	0.620389i	$0.786975\pi$
$278$	0.828427	+	0.828427i	0.0496858	+	0.0496858i
$279$		0			0
$280$	2.82843	+	5.65685i	0.169031	+	0.338062i
$281$			2.97056i			0.177209i	0.996067	+	0.0886045i	$0.0282407\pi$
$281$			2.97056i			0.177209i	−0.996067	+	0.0886045i	$0.971759\pi$
$282$		0			0
$283$	2.82843	−	2.82843i	0.168133	−	0.168133i	−0.618026	−	0.786158i	$-0.712067\pi$
$283$	2.82843	−	2.82843i	0.168133	−	0.168133i	0.786158	+	0.618026i	$0.212067\pi$
$284$	4.58579			0.272116
$285$		0			0
$286$	−1.65685			−0.0979718
$287$	−5.17157	+	5.17157i	−0.305268	+	0.305268i
$288$		0			0
$289$		−	41.6274i		−	2.44867i
$290$	3.41421	−	10.2426i	0.200490	−	0.601469i
$291$		0			0
$292$	4.17157	+	4.17157i	0.244123	+	0.244123i
$293$	18.6569	+	18.6569i	1.08995	+	1.08995i	0.995533	+	0.0944118i	$0.0300970\pi$
$293$	18.6569	+	18.6569i	1.08995	+	1.08995i	0.0944118	+	0.995533i	$0.469903\pi$
$294$		0			0
$295$	5.65685	−	2.82843i	0.329355	−	0.164677i
$296$		−	2.00000i		−	0.116248i
$297$		0			0
$298$	0.242641	−	0.242641i	0.0140558	−	0.0140558i
$299$	−2.00000			−0.115663
$300$		0			0
$301$	−24.9706			−1.43928
$302$	12.0000	−	12.0000i	0.690522	−	0.690522i
$303$		0			0
$304$		−	3.41421i		−	0.195819i
$305$	−5.17157	+	2.58579i	−0.296123	+	0.148062i
$306$		0			0
$307$	5.17157	+	5.17157i	0.295157	+	0.295157i	0.839114	−	0.543956i	$-0.183074\pi$
$307$	5.17157	+	5.17157i	0.295157	+	0.295157i	−0.543956	+	0.839114i	$0.683074\pi$
$308$	−1.65685	−	1.65685i	−0.0944080	−	0.0944080i
$309$		0			0
$310$	3.41421	−	10.2426i	0.193914	−	0.581743i
$311$			11.2132i			0.635842i	0.948117	+	0.317921i	$0.102985\pi$
$311$			11.2132i			0.635842i	−0.948117	+	0.317921i	$0.897015\pi$
$312$		0			0
$313$	15.0711	−	15.0711i	0.851867	−	0.851867i	−0.138496	−	0.990363i	$-0.544227\pi$
$313$	15.0711	−	15.0711i	0.851867	−	0.851867i	0.990363	+	0.138496i	$0.0442268\pi$
$314$	6.00000			0.338600
$315$		0			0
$316$	6.82843			0.384129
$317$	14.7279	−	14.7279i	0.827203	−	0.827203i	−0.159926	−	0.987129i	$-0.551126\pi$
$317$	14.7279	−	14.7279i	0.827203	−	0.827203i	0.987129	+	0.159926i	$0.0511257\pi$
$318$		0			0
$319$			4.00000i			0.223957i
$320$	−1.00000	−	2.00000i	−0.0559017	−	0.111803i
$321$		0			0
$322$	−2.00000	−	2.00000i	−0.111456	−	0.111456i
$323$	−18.4853	−	18.4853i	−1.02855	−	1.02855i
$324$		0			0
$325$	−1.41421	−	9.89949i	−0.0784465	−	0.549125i
$326$		−	14.8284i		−	0.821271i
$327$		0			0
$328$	1.82843	−	1.82843i	0.100958	−	0.100958i
$329$		0			0
$330$		0			0
$331$	7.79899			0.428671			0.214336	−	0.976760i	$-0.431241\pi$
$331$	7.79899			0.428671			0.214336	+	0.976760i	$0.431241\pi$
$332$	9.24264	−	9.24264i	0.507256	−	0.507256i
$333$		0			0
$334$		−	5.51472i		−	0.301752i
$335$	−3.51472	−	1.17157i	−0.192030	−	0.0640099i
$336$		0			0
$337$	−6.24264	−	6.24264i	−0.340058	−	0.340058i	0.516331	−	0.856389i	$-0.327297\pi$
$337$	−6.24264	−	6.24264i	−0.340058	−	0.340058i	−0.856389	+	0.516331i	$0.827297\pi$
$338$	6.36396	+	6.36396i	0.346154	+	0.346154i
$339$		0			0
$340$	−16.2426	−	5.41421i	−0.880881	−	0.293627i
$341$			4.00000i			0.216612i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	8.82843			0.475997
$345$		0			0
$346$	−14.0000			−0.752645
$347$	10.0000	−	10.0000i	0.536828	−	0.536828i	−0.385768	−	0.922596i	$-0.626063\pi$
$347$	10.0000	−	10.0000i	0.536828	−	0.536828i	0.922596	+	0.385768i	$0.126063\pi$
$348$		0			0
$349$			12.3431i			0.660713i	0.943856	+	0.330357i	$0.107169\pi$
$349$			12.3431i			0.660713i	−0.943856	+	0.330357i	$0.892831\pi$
$350$	8.48528	−	11.3137i	0.453557	−	0.604743i
$351$		0			0
$352$	0.585786	+	0.585786i	0.0312225	+	0.0312225i
$353$	13.8995	+	13.8995i	0.739795	+	0.739795i	0.972538	−	0.232743i	$-0.0747700\pi$
$353$	13.8995	+	13.8995i	0.739795	+	0.739795i	−0.232743	+	0.972538i	$0.574770\pi$
$354$		0			0
$355$	−4.58579	−	9.17157i	−0.243388	−	0.486777i
$356$			14.0000i			0.741999i
$357$		0			0
$358$	0.485281	−	0.485281i	0.0256479	−	0.0256479i
$359$	−1.17157			−0.0618333			−0.0309166	−	0.999522i	$-0.509843\pi$
$359$	−1.17157			−0.0618333			−0.0309166	+	0.999522i	$0.509843\pi$
$360$		0			0
$361$	7.34315			0.386481
$362$	7.48528	−	7.48528i	0.393418	−	0.393418i
$363$		0			0
$364$		−	5.65685i		−	0.296500i
$365$	4.17157	−	12.5147i	0.218350	−	0.655050i
$366$		0			0
$367$	6.00000	+	6.00000i	0.313197	+	0.313197i	0.846147	−	0.532950i	$-0.178916\pi$
$367$	6.00000	+	6.00000i	0.313197	+	0.313197i	−0.532950	+	0.846147i	$0.678916\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$		0			0
$370$	−4.00000	+	2.00000i	−0.207950	+	0.103975i
$371$			10.6274i			0.551748i
$372$		0			0
$373$	−4.24264	+	4.24264i	−0.219676	+	0.219676i	−0.808362	−	0.588686i	$-0.799645\pi$
$373$	−4.24264	+	4.24264i	−0.219676	+	0.219676i	0.588686	+	0.808362i	$0.299645\pi$
$374$	6.34315			0.327996
$375$		0			0
$376$		0			0
$377$	−6.82843	+	6.82843i	−0.351682	+	0.351682i
$378$		0			0
$379$		−	18.0416i		−	0.926736i	−0.886166	−	0.463368i	$-0.846641\pi$
$379$		−	18.0416i		−	0.926736i	0.886166	−	0.463368i	$-0.153359\pi$
$380$	−6.82843	+	3.41421i	−0.350291	+	0.175145i
$381$		0			0
$382$	−10.4853	−	10.4853i	−0.536474	−	0.536474i
$383$	11.1716	+	11.1716i	0.570841	+	0.570841i	0.932363	−	0.361523i	$-0.117743\pi$
$383$	11.1716	+	11.1716i	0.570841	+	0.570841i	−0.361523	+	0.932363i	$0.617743\pi$
$384$		0			0
$385$	−1.65685	+	4.97056i	−0.0844411	+	0.253323i
$386$			7.07107i			0.359908i
$387$		0			0
$388$	5.07107	−	5.07107i	0.257444	−	0.257444i
$389$	−36.2843			−1.83969			−0.919843	−	0.392287i	$-0.871684\pi$
$389$	−36.2843			−1.83969			−0.919843	+	0.392287i	$0.871684\pi$
$390$		0			0
$391$	7.65685			0.387224
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	10.0000i		−	0.503793i
$395$	−6.82843	−	13.6569i	−0.343575	−	0.687151i
$396$		0			0
$397$	2.58579	+	2.58579i	0.129777	+	0.129777i	0.769012	−	0.639235i	$-0.220749\pi$
$397$	2.58579	+	2.58579i	0.129777	+	0.129777i	−0.639235	+	0.769012i	$0.720749\pi$
$398$	−12.4853	−	12.4853i	−0.625831	−	0.625831i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$			34.0000i			1.69788i	0.528490	+	0.848939i	$0.322758\pi$
$401$			34.0000i			1.69788i	−0.528490	+	0.848939i	$0.677242\pi$
$402$		0			0
$403$	−6.82843	+	6.82843i	−0.340148	+	0.340148i
$404$	7.65685			0.380943
$405$		0			0
$406$	−13.6569			−0.677778
$407$	1.17157	−	1.17157i	0.0580727	−	0.0580727i
$408$		0			0
$409$			17.3137i			0.856108i	0.903753	+	0.428054i	$0.140801\pi$
$409$			17.3137i			0.856108i	−0.903753	+	0.428054i	$0.859199\pi$
$410$	−5.48528	−	1.82843i	−0.270899	−	0.0902996i
$411$		0			0
$412$	10.8284	+	10.8284i	0.533478	+	0.533478i
$413$	−5.65685	−	5.65685i	−0.278356	−	0.278356i
$414$		0			0
$415$	−27.7279	−	9.24264i	−1.36111	−	0.453703i
$416$			2.00000i			0.0980581i
$417$		0			0
$418$	2.00000	−	2.00000i	0.0978232	−	0.0978232i
$419$	22.3431			1.09153			0.545767	−	0.837937i	$-0.316238\pi$
$419$	22.3431			1.09153			0.545767	+	0.837937i	$0.316238\pi$
$420$		0			0
$421$	−28.7279			−1.40011			−0.700057	−	0.714087i	$-0.746842\pi$
$421$	−28.7279			−1.40011			−0.700057	+	0.714087i	$0.746842\pi$
$422$	−6.48528	+	6.48528i	−0.315699	+	0.315699i
$423$		0			0
$424$		−	3.75736i		−	0.182473i
$425$	5.41421	+	37.8995i	0.262628	+	1.83840i
$426$		0			0
$427$	5.17157	+	5.17157i	0.250270	+	0.250270i
$428$	10.0711	+	10.0711i	0.486803	+	0.486803i
$429$		0			0
$430$	−8.82843	−	17.6569i	−0.425745	−	0.851489i
$431$		−	5.17157i		−	0.249106i	−0.992213	−	0.124553i	$-0.960250\pi$
$431$		−	5.17157i		−	0.249106i	0.992213	−	0.124553i	$-0.0397497\pi$
$432$		0			0
$433$	−23.4142	+	23.4142i	−1.12522	+	1.12522i	−0.134271	+	0.990945i	$0.542869\pi$
$433$	−23.4142	+	23.4142i	−1.12522	+	1.12522i	−0.990945	+	0.134271i	$0.957131\pi$
$434$	−13.6569			−0.655550
$435$		0			0
$436$	−4.92893			−0.236053
$437$	2.41421	−	2.41421i	0.115487	−	0.115487i
$438$		0			0
$439$			24.1421i			1.15224i	0.817365	+	0.576121i	$0.195434\pi$
$439$			24.1421i			1.15224i	−0.817365	+	0.576121i	$0.804566\pi$
$440$	0.585786	−	1.75736i	0.0279263	−	0.0837788i
$441$		0			0
$442$	10.8284	+	10.8284i	0.515056	+	0.515056i
$443$	0.828427	+	0.828427i	0.0393598	+	0.0393598i	0.726513	−	0.687153i	$-0.241140\pi$
$443$	0.828427	+	0.828427i	0.0393598	+	0.0393598i	−0.687153	+	0.726513i	$0.741140\pi$
$444$		0			0
$445$	28.0000	−	14.0000i	1.32733	−	0.663664i
$446$		−	7.41421i		−	0.351073i
$447$		0			0
$448$	−2.00000	+	2.00000i	−0.0944911	+	0.0944911i
$449$	19.0711			0.900019			0.450010	−	0.893024i	$-0.351421\pi$
$449$	19.0711			0.900019			0.450010	+	0.893024i	$0.351421\pi$
$450$		0			0
$451$	2.14214			0.100869
$452$	−3.75736	+	3.75736i	−0.176731	+	0.176731i
$453$		0			0
$454$		−	21.0711i		−	0.988914i
$455$	−11.3137	+	5.65685i	−0.530395	+	0.265197i
$456$		0			0
$457$	−26.7279	−	26.7279i	−1.25028	−	1.25028i	−0.955594	−	0.294685i	$-0.904785\pi$
$457$	−26.7279	−	26.7279i	−1.25028	−	1.25028i	−0.294685	−	0.955594i	$-0.595215\pi$
$458$	7.48528	+	7.48528i	0.349764	+	0.349764i
$459$		0			0
$460$	0.707107	−	2.12132i	0.0329690	−	0.0989071i
$461$			30.4853i			1.41984i	0.704282	+	0.709921i	$0.251269\pi$
$461$			30.4853i			1.41984i	−0.704282	+	0.709921i	$0.748731\pi$
$462$		0			0
$463$	27.8701	−	27.8701i	1.29523	−	1.29523i	0.363725	−	0.931506i	$-0.381505\pi$
$463$	27.8701	−	27.8701i	1.29523	−	1.29523i	0.931506	−	0.363725i	$-0.118495\pi$
$464$	4.82843			0.224154
$465$		0			0
$466$	−26.6274			−1.23349
$467$	22.0711	−	22.0711i	1.02133	−	1.02133i	0.0215597	−	0.999768i	$-0.493137\pi$
$467$	22.0711	−	22.0711i	1.02133	−	1.02133i	0.999768	−	0.0215597i	$-0.00686318\pi$
$468$		0			0
$469$			4.68629i			0.216393i
$470$		0			0
$471$		0			0
$472$	2.00000	+	2.00000i	0.0920575	+	0.0920575i
$473$	5.17157	+	5.17157i	0.237789	+	0.237789i
$474$		0			0
$475$	13.6569	+	10.2426i	0.626619	+	0.469965i
$476$			21.6569i			0.992640i
$477$		0			0
$478$	−15.2426	+	15.2426i	−0.697182	+	0.697182i
$479$	−26.6274			−1.21664			−0.608319	−	0.793693i	$-0.708156\pi$
$479$	−26.6274			−1.21664			−0.608319	+	0.793693i	$0.708156\pi$
$480$		0			0
$481$	4.00000			0.182384
$482$	−18.2426	+	18.2426i	−0.830930	+	0.830930i
$483$		0			0
$484$		−	10.3137i		−	0.468805i
$485$	−15.2132	−	5.07107i	−0.690796	−	0.230265i
$486$		0			0
$487$	−14.2132	−	14.2132i	−0.644062	−	0.644062i	0.307490	−	0.951551i	$-0.400511\pi$
$487$	−14.2132	−	14.2132i	−0.644062	−	0.644062i	−0.951551	+	0.307490i	$0.900511\pi$
$488$	−1.82843	−	1.82843i	−0.0827690	−	0.0827690i
$489$		0			0
$490$	−2.12132	−	0.707107i	−0.0958315	−	0.0319438i
$491$			14.8284i			0.669198i	0.942361	+	0.334599i	$0.108601\pi$
$491$			14.8284i			0.669198i	−0.942361	+	0.334599i	$0.891399\pi$
$492$		0			0
$493$	26.1421	−	26.1421i	1.17738	−	1.17738i
$494$	6.82843			0.307225
$495$		0			0
$496$	4.82843			0.216803
$497$	−9.17157	+	9.17157i	−0.411401	+	0.411401i
$498$		0			0
$499$		−	20.9706i		−	0.938771i	−0.882993	−	0.469386i	$-0.844475\pi$
$499$		−	20.9706i		−	0.938771i	0.882993	−	0.469386i	$-0.155525\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$		0			0
$502$	−16.3848	−	16.3848i	−0.731288	−	0.731288i
$503$	13.7990	+	13.7990i	0.615267	+	0.615267i	0.944314	−	0.329047i	$-0.106727\pi$
$503$	13.7990	+	13.7990i	0.615267	+	0.615267i	−0.329047	+	0.944314i	$0.606727\pi$
$504$		0			0
$505$	−7.65685	−	15.3137i	−0.340726	−	0.681451i
$506$			0.828427i			0.0368281i
$507$		0			0
$508$	−4.41421	+	4.41421i	−0.195849	+	0.195849i
$509$	39.4558			1.74885			0.874425	−	0.485161i	$-0.161239\pi$
$509$	39.4558			1.74885			0.874425	+	0.485161i	$0.161239\pi$
$510$		0			0
$511$	−16.6863			−0.738158
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			7.31371i			0.322594i
$515$	10.8284	−	32.4853i	0.477158	−	1.43147i
$516$		0			0
$517$		0			0
$518$	4.00000	+	4.00000i	0.175750	+	0.175750i
$519$		0			0
$520$	4.00000	−	2.00000i	0.175412	−	0.0877058i
$521$		−	16.1421i		−	0.707200i	−0.935397	−	0.353600i	$-0.884957\pi$
$521$		−	16.1421i		−	0.707200i	0.935397	−	0.353600i	$-0.115043\pi$
$522$		0			0
$523$	−27.2132	+	27.2132i	−1.18995	+	1.18995i	−0.212870	+	0.977081i	$0.568281\pi$
$523$	−27.2132	+	27.2132i	−1.18995	+	1.18995i	−0.977081	+	0.212870i	$0.931719\pi$
$524$	5.65685			0.247121
$525$		0			0
$526$	22.8284			0.995367
$527$	26.1421	−	26.1421i	1.13877	−	1.13877i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−7.51472	+	3.75736i	−0.326419	+	0.163209i
$531$		0			0
$532$	6.82843	+	6.82843i	0.296050	+	0.296050i
$533$	3.65685	+	3.65685i	0.158396	+	0.158396i
$534$		0			0
$535$	10.0711	−	30.2132i	0.435410	−	1.30623i
$536$		−	1.65685i		−	0.0715652i
$537$		0			0
$538$	−1.41421	+	1.41421i	−0.0609711	+	0.0609711i
$539$	0.828427			0.0356829
$540$		0			0
$541$	−1.31371			−0.0564807			−0.0282404	−	0.999601i	$-0.508990\pi$
$541$	−1.31371			−0.0564807			−0.0282404	+	0.999601i	$0.508990\pi$
$542$	−17.6569	+	17.6569i	−0.758427	+	0.758427i
$543$		0			0
$544$		−	7.65685i		−	0.328285i
$545$	4.92893	+	9.85786i	0.211132	+	0.422265i
$546$		0			0
$547$	28.1421	+	28.1421i	1.20327	+	1.20327i	0.973166	+	0.230105i	$0.0739070\pi$
$547$	28.1421	+	28.1421i	1.20327	+	1.20327i	0.230105	+	0.973166i	$0.426093\pi$
$548$	−13.0711	−	13.0711i	−0.558368	−	0.558368i
$549$		0			0
$550$	−4.10051	+	0.585786i	−0.174846	+	0.0249780i
$551$		−	16.4853i		−	0.702297i
$552$		0			0
$553$	−13.6569	+	13.6569i	−0.580749	+	0.580749i
$554$	−3.85786			−0.163905
$555$		0			0
$556$	1.17157			0.0496858
$557$	19.8284	−	19.8284i	0.840157	−	0.840157i	−0.148722	−	0.988879i	$-0.547516\pi$
$557$	19.8284	−	19.8284i	0.840157	−	0.840157i	0.988879	+	0.148722i	$0.0475158\pi$
$558$		0			0
$559$			17.6569i			0.746805i
$560$	6.00000	+	2.00000i	0.253546	+	0.0845154i
$561$		0			0
$562$	2.10051	+	2.10051i	0.0886045	+	0.0886045i
$563$	13.9289	+	13.9289i	0.587035	+	0.587035i	0.936827	−	0.349793i	$-0.113748\pi$
$563$	13.9289	+	13.9289i	0.587035	+	0.587035i	−0.349793	+	0.936827i	$0.613748\pi$
$564$		0			0
$565$	11.2721	+	3.75736i	0.474220	+	0.158073i
$566$		−	4.00000i		−	0.168133i
$567$		0			0
$568$	3.24264	−	3.24264i	0.136058	−	0.136058i
$569$	−17.3137			−0.725828			−0.362914	−	0.931823i	$-0.618218\pi$
$569$	−17.3137			−0.725828			−0.362914	+	0.931823i	$0.618218\pi$
$570$		0			0
$571$	−26.2426			−1.09822			−0.549110	−	0.835750i	$-0.685033\pi$
$571$	−26.2426			−1.09822			−0.549110	+	0.835750i	$0.685033\pi$
$572$	−1.17157	+	1.17157i	−0.0489859	+	0.0489859i
$573$		0			0
$574$			7.31371i			0.305268i
$575$	−4.94975	+	0.707107i	−0.206419	+	0.0294884i
$576$		0			0
$577$	−27.1421	−	27.1421i	−1.12994	−	1.12994i	−0.990186	−	0.139756i	$-0.955368\pi$
$577$	−27.1421	−	27.1421i	−1.12994	−	1.12994i	−0.139756	−	0.990186i	$-0.544632\pi$
$578$	−29.4350	−	29.4350i	−1.22434	−	1.22434i
$579$		0			0
$580$	−4.82843	−	9.65685i	−0.200490	−	0.400979i
$581$			36.9706i			1.53380i
$582$		0			0
$583$	2.20101	−	2.20101i	0.0911565	−	0.0911565i
$584$	5.89949			0.244123
$585$		0			0
$586$	26.3848			1.08995
$587$	26.6274	−	26.6274i	1.09903	−	1.09903i	0.104507	−	0.994524i	$-0.466674\pi$
$587$	26.6274	−	26.6274i	1.09903	−	1.09903i	0.994524	−	0.104507i	$-0.0333265\pi$
$588$		0			0
$589$		−	16.4853i		−	0.679264i
$590$	2.00000	−	6.00000i	0.0823387	−	0.247016i
$591$		0			0
$592$	−1.41421	−	1.41421i	−0.0581238	−	0.0581238i
$593$	−0.485281	−	0.485281i	−0.0199281	−	0.0199281i	0.697073	−	0.717001i	$-0.254486\pi$
$593$	−0.485281	−	0.485281i	−0.0199281	−	0.0199281i	−0.717001	+	0.697073i	$0.754486\pi$
$594$		0			0
$595$	43.3137	−	21.6569i	1.77569	−	0.887844i
$596$		−	0.343146i		−	0.0140558i
$597$		0			0
$598$	−1.41421	+	1.41421i	−0.0578315	+	0.0578315i
$599$	−13.5563			−0.553897			−0.276949	−	0.960885i	$-0.589323\pi$
$599$	−13.5563			−0.553897			−0.276949	+	0.960885i	$0.589323\pi$
$600$		0			0
$601$	25.6569			1.04656			0.523282	−	0.852159i	$-0.324707\pi$
$601$	25.6569			1.04656			0.523282	+	0.852159i	$0.324707\pi$
$602$	−17.6569	+	17.6569i	−0.719640	+	0.719640i
$603$		0			0
$604$		−	16.9706i		−	0.690522i
$605$	−20.6274	+	10.3137i	−0.838624	+	0.419312i
$606$		0			0
$607$	−14.0711	−	14.0711i	−0.571127	−	0.571127i	0.361316	−	0.932443i	$-0.382327\pi$
$607$	−14.0711	−	14.0711i	−0.571127	−	0.571127i	−0.932443	+	0.361316i	$0.882327\pi$
$608$	−2.41421	−	2.41421i	−0.0979093	−	0.0979093i
$609$		0			0
$610$	−1.82843	+	5.48528i	−0.0740309	+	0.222093i
$611$		0			0
$612$		0			0
$613$	−33.4558	+	33.4558i	−1.35127	+	1.35127i	−0.467024	+	0.884244i	$0.654674\pi$
$613$	−33.4558	+	33.4558i	−1.35127	+	1.35127i	−0.884244	+	0.467024i	$0.845326\pi$
$614$	7.31371			0.295157
$615$		0			0
$616$	−2.34315			−0.0944080
$617$	19.2132	−	19.2132i	0.773494	−	0.773494i	−0.205221	−	0.978716i	$-0.565791\pi$
$617$	19.2132	−	19.2132i	0.773494	−	0.773494i	0.978716	+	0.205221i	$0.0657914\pi$
$618$		0			0
$619$			4.58579i			0.184318i	0.995744	+	0.0921592i	$0.0293769\pi$
$619$			4.58579i			0.184318i	−0.995744	+	0.0921592i	$0.970623\pi$
$620$	−4.82843	−	9.65685i	−0.193914	−	0.387829i
$621$		0			0
$622$	7.92893	+	7.92893i	0.317921	+	0.317921i
$623$	−28.0000	−	28.0000i	−1.12180	−	1.12180i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		−	21.3137i		−	0.851867i
$627$		0			0
$628$	4.24264	−	4.24264i	0.169300	−	0.169300i
$629$	−15.3137			−0.610598
$630$		0			0
$631$	18.3431			0.730229			0.365115	−	0.930963i	$-0.381030\pi$
$631$	18.3431			0.730229			0.365115	+	0.930963i	$0.381030\pi$
$632$	4.82843	−	4.82843i	0.192065	−	0.192065i
$633$		0			0
$634$		−	20.8284i		−	0.827203i
$635$	13.2426	+	4.41421i	0.525518	+	0.175173i
$636$		0			0
$637$	1.41421	+	1.41421i	0.0560332	+	0.0560332i
$638$	2.82843	+	2.82843i	0.111979	+	0.111979i
$639$		0			0
$640$	−2.12132	−	0.707107i	−0.0838525	−	0.0279508i
$641$		−	5.51472i		−	0.217818i	−0.994052	−	0.108909i	$-0.965264\pi$
$641$		−	5.51472i		−	0.217818i	0.994052	−	0.108909i	$-0.0347358\pi$
$642$		0			0
$643$	31.7990	−	31.7990i	1.25403	−	1.25403i	0.300132	−	0.953898i	$-0.402969\pi$
$643$	31.7990	−	31.7990i	1.25403	−	1.25403i	0.953898	−	0.300132i	$-0.0970308\pi$
$644$	−2.82843			−0.111456
$645$		0			0
$646$	−26.1421			−1.02855
$647$	22.7279	−	22.7279i	0.893527	−	0.893527i	−0.101326	−	0.994853i	$-0.532309\pi$
$647$	22.7279	−	22.7279i	0.893527	−	0.893527i	0.994853	+	0.101326i	$0.0323086\pi$
$648$		0			0
$649$			2.34315i			0.0919765i
$650$	−8.00000	−	6.00000i	−0.313786	−	0.235339i
$651$		0			0
$652$	−10.4853	−	10.4853i	−0.410635	−	0.410635i
$653$	19.7574	+	19.7574i	0.773165	+	0.773165i	0.978659	−	0.205493i	$-0.0658799\pi$
$653$	19.7574	+	19.7574i	0.773165	+	0.773165i	−0.205493	+	0.978659i	$0.565880\pi$
$654$		0			0
$655$	−5.65685	−	11.3137i	−0.221032	−	0.442063i
$656$		−	2.58579i		−	0.100958i
$657$		0			0
$658$		0			0
$659$	29.9411			1.16634			0.583170	−	0.812350i	$-0.301812\pi$
$659$	29.9411			1.16634			0.583170	+	0.812350i	$0.301812\pi$
$660$		0			0
$661$	−20.5269			−0.798404			−0.399202	−	0.916863i	$-0.630713\pi$
$661$	−20.5269			−0.798404			−0.399202	+	0.916863i	$0.630713\pi$
$662$	5.51472	−	5.51472i	0.214336	−	0.214336i
$663$		0			0
$664$		−	13.0711i		−	0.507256i
$665$	6.82843	−	20.4853i	0.264795	−	0.794385i
$666$		0			0
$667$	3.41421	+	3.41421i	0.132199	+	0.132199i
$668$	−3.89949	−	3.89949i	−0.150876	−	0.150876i
$669$		0			0
$670$	−3.31371	+	1.65685i	−0.128020	+	0.0640099i
$671$		−	2.14214i		−	0.0826962i
$672$		0			0
$673$	−15.4853	+	15.4853i	−0.596914	+	0.596914i	−0.939490	−	0.342576i	$-0.888700\pi$
$673$	−15.4853	+	15.4853i	−0.596914	+	0.596914i	0.342576	+	0.939490i	$0.388700\pi$
$674$	−8.82843			−0.340058
$675$		0			0
$676$	9.00000			0.346154
$677$	22.6569	−	22.6569i	0.870774	−	0.870774i	−0.121783	−	0.992557i	$-0.538861\pi$
$677$	22.6569	−	22.6569i	0.870774	−	0.870774i	0.992557	+	0.121783i	$0.0388612\pi$
$678$		0			0
$679$			20.2843i			0.778439i
$680$	−15.3137	+	7.65685i	−0.587254	+	0.293627i
$681$		0			0
$682$	2.82843	+	2.82843i	0.108306	+	0.108306i
$683$	28.2843	+	28.2843i	1.08227	+	1.08227i	0.996298	+	0.0859698i	$0.0273989\pi$
$683$	28.2843	+	28.2843i	1.08227	+	1.08227i	0.0859698	+	0.996298i	$0.472601\pi$
$684$		0			0
$685$	−13.0711	+	39.2132i	−0.499420	+	1.49826i
$686$		−	16.9706i		−	0.647939i
$687$		0			0
$688$	6.24264	−	6.24264i	0.237998	−	0.237998i
$689$	7.51472			0.286288
$690$		0			0
$691$	−35.3137			−1.34340			−0.671698	−	0.740825i	$-0.734435\pi$
$691$	−35.3137			−1.34340			−0.671698	+	0.740825i	$0.734435\pi$
$692$	−9.89949	+	9.89949i	−0.376322	+	0.376322i
$693$		0			0
$694$		−	14.1421i		−	0.536828i
$695$	−1.17157	−	2.34315i	−0.0444403	−	0.0888806i
$696$		0			0
$697$	−14.0000	−	14.0000i	−0.530288	−	0.530288i
$698$	8.72792	+	8.72792i	0.330357	+	0.330357i
$699$		0			0
$700$	−2.00000	−	14.0000i	−0.0755929	−	0.529150i
$701$			47.9411i			1.81071i	0.424654	+	0.905356i	$0.360396\pi$
$701$			47.9411i			1.81071i	−0.424654	+	0.905356i	$0.639604\pi$
$702$		0			0
$703$	−4.82843	+	4.82843i	−0.182108	+	0.182108i
$704$	0.828427			0.0312225
$705$		0			0
$706$	19.6569			0.739795
$707$	−15.3137	+	15.3137i	−0.575931	+	0.575931i
$708$		0			0
$709$			25.8995i			0.972676i	0.873771	+	0.486338i	$0.161668\pi$
$709$			25.8995i			0.972676i	−0.873771	+	0.486338i	$0.838332\pi$
$710$	−9.72792	−	3.24264i	−0.365082	−	0.121694i
$711$		0			0
$712$	9.89949	+	9.89949i	0.370999	+	0.370999i
$713$	3.41421	+	3.41421i	0.127863	+	0.127863i
$714$		0			0
$715$	3.51472	+	1.17157i	0.131443	+	0.0438143i
$716$		−	0.686292i		−	0.0256479i
$717$		0			0
$718$	−0.828427	+	0.828427i	−0.0309166	+	0.0309166i
$719$	−30.5269			−1.13846			−0.569231	−	0.822178i	$-0.692759\pi$
$719$	−30.5269			−1.13846			−0.569231	+	0.822178i	$0.692759\pi$
$720$		0			0
$721$	−43.3137			−1.61309
$722$	5.19239	−	5.19239i	0.193241	−	0.193241i
$723$		0			0
$724$		−	10.5858i		−	0.393418i
$725$	−14.4853	+	19.3137i	−0.537970	+	0.717293i
$726$		0			0
$727$	−2.34315	−	2.34315i	−0.0869025	−	0.0869025i	0.662319	−	0.749222i	$-0.269572\pi$
$727$	−2.34315	−	2.34315i	−0.0869025	−	0.0869025i	−0.749222	+	0.662319i	$0.769572\pi$
$728$	−4.00000	−	4.00000i	−0.148250	−	0.148250i
$729$		0			0
$730$	−5.89949	−	11.7990i	−0.218350	−	0.436700i
$731$		−	67.5980i		−	2.50020i
$732$		0			0
$733$	−32.0000	+	32.0000i	−1.18195	+	1.18195i	−0.202708	+	0.979239i	$0.564974\pi$
$733$	−32.0000	+	32.0000i	−1.18195	+	1.18195i	−0.979239	+	0.202708i	$0.935026\pi$
$734$	8.48528			0.313197
$735$		0			0
$736$	1.00000			0.0368605
$737$	0.970563	−	0.970563i	0.0357511	−	0.0357511i
$738$		0			0
$739$			10.1421i			0.373084i	0.982447	+	0.186542i	$0.0597281\pi$
$739$			10.1421i			0.373084i	−0.982447	+	0.186542i	$0.940272\pi$
$740$	−1.41421	+	4.24264i	−0.0519875	+	0.155963i
$741$		0			0
$742$	7.51472	+	7.51472i	0.275874	+	0.275874i
$743$	30.4853	+	30.4853i	1.11840	+	1.11840i	0.991977	+	0.126420i	$0.0403486\pi$
$743$	30.4853	+	30.4853i	1.11840	+	1.11840i	0.126420	+	0.991977i	$0.459651\pi$
$744$		0			0
$745$	−0.686292	+	0.343146i	−0.0251438	+	0.0125719i
$746$			6.00000i			0.219676i
$747$		0			0
$748$	4.48528	−	4.48528i	0.163998	−	0.163998i
$749$	−40.2843			−1.47196
$750$		0			0
$751$	18.1421			0.662016			0.331008	−	0.943628i	$-0.392611\pi$
$751$	18.1421			0.662016			0.331008	+	0.943628i	$0.392611\pi$
$752$		0			0
$753$		0			0
$754$			9.65685i			0.351682i
$755$	−33.9411	+	16.9706i	−1.23524	+	0.617622i
$756$		0			0
$757$	35.1127	+	35.1127i	1.27619	+	1.27619i	0.942781	+	0.333411i	$0.108200\pi$
$757$	35.1127	+	35.1127i	1.27619	+	1.27619i	0.333411	+	0.942781i	$0.391800\pi$
$758$	−12.7574	−	12.7574i	−0.463368	−	0.463368i
$759$		0			0
$760$	−2.41421	+	7.24264i	−0.0875727	+	0.262718i
$761$		−	23.5563i		−	0.853917i	−0.904271	−	0.426958i	$-0.859585\pi$
$761$		−	23.5563i		−	0.853917i	0.904271	−	0.426958i	$-0.140415\pi$
$762$		0			0
$763$	9.85786	−	9.85786i	0.356879	−	0.356879i
$764$	−14.8284			−0.536474
$765$		0			0
$766$	15.7990			0.570841
$767$	−4.00000	+	4.00000i	−0.144432	+	0.144432i
$768$		0			0
$769$		−	5.31371i		−	0.191617i	−0.995400	−	0.0958086i	$-0.969456\pi$
$769$		−	5.31371i		−	0.191617i	0.995400	−	0.0958086i	$-0.0305437\pi$
$770$	2.34315	+	4.68629i	0.0844411	+	0.168882i
$771$		0			0
$772$	5.00000	+	5.00000i	0.179954	+	0.179954i
$773$	25.8284	+	25.8284i	0.928984	+	0.928984i	0.997640	−	0.0686564i	$-0.0218712\pi$
$773$	25.8284	+	25.8284i	0.928984	+	0.928984i	−0.0686564	+	0.997640i	$0.521871\pi$
$774$		0			0
$775$	−14.4853	+	19.3137i	−0.520327	+	0.693769i
$776$		−	7.17157i		−	0.257444i
$777$		0			0
$778$	−25.6569	+	25.6569i	−0.919843	+	0.919843i
$779$	−8.82843			−0.316311
$780$		0			0
$781$	3.79899			0.135939
$782$	5.41421	−	5.41421i	0.193612	−	0.193612i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	−12.7279	−	4.24264i	−0.454279	−	0.151426i
$786$		0			0
$787$	2.82843	+	2.82843i	0.100823	+	0.100823i	0.755719	−	0.654896i	$-0.227288\pi$
$787$	2.82843	+	2.82843i	0.100823	+	0.100823i	−0.654896	+	0.755719i	$0.727288\pi$
$788$	−7.07107	−	7.07107i	−0.251896	−	0.251896i
$789$		0			0
$790$	−14.4853	−	4.82843i	−0.515363	−	0.171788i
$791$		−	15.0294i		−	0.534385i
$792$		0			0
$793$	3.65685	−	3.65685i	0.129859	−	0.129859i
$794$	3.65685			0.129777
$795$		0			0
$796$	−17.6569			−0.625831
$797$	−12.5147	+	12.5147i	−0.443294	+	0.443294i	−0.893118	−	0.449823i	$-0.851487\pi$
$797$	−12.5147	+	12.5147i	−0.443294	+	0.443294i	0.449823	+	0.893118i	$0.351487\pi$
$798$		0			0
$799$		0			0
$800$	0.707107	+	4.94975i	0.0250000	+	0.175000i
$801$		0			0
$802$	24.0416	+	24.0416i	0.848939	+	0.848939i
$803$	3.45584	+	3.45584i	0.121954	+	0.121954i
$804$		0			0
$805$	2.82843	+	5.65685i	0.0996890	+	0.199378i
$806$			9.65685i			0.340148i
$807$		0			0
$808$	5.41421	−	5.41421i	0.190471	−	0.190471i
$809$	−11.7574			−0.413367			−0.206683	−	0.978408i	$-0.566267\pi$
$809$	−11.7574			−0.413367			−0.206683	+	0.978408i	$0.566267\pi$
$810$		0			0
$811$	16.9706			0.595917			0.297959	−	0.954579i	$-0.403694\pi$
$811$	16.9706			0.595917			0.297959	+	0.954579i	$0.403694\pi$
$812$	−9.65685	+	9.65685i	−0.338889	+	0.338889i
$813$		0			0
$814$		−	1.65685i		−	0.0580727i
$815$	−10.4853	+	31.4558i	−0.367283	+	1.10185i
$816$		0			0
$817$	−21.3137	−	21.3137i	−0.745672	−	0.745672i
$818$	12.2426	+	12.2426i	0.428054	+	0.428054i
$819$		0			0
$820$	−5.17157	+	2.58579i	−0.180599	+	0.0902996i
$821$			33.5147i			1.16967i	0.811152	+	0.584836i	$0.198841\pi$
$821$			33.5147i			1.16967i	−0.811152	+	0.584836i	$0.801159\pi$
$822$		0			0
$823$	28.4142	−	28.4142i	0.990457	−	0.990457i	−0.00949767	−	0.999955i	$-0.503023\pi$
$823$	28.4142	−	28.4142i	0.990457	−	0.990457i	0.999955	+	0.00949767i	$0.00302325\pi$
$824$	15.3137			0.533478
$825$		0			0
$826$	−8.00000			−0.278356
$827$	30.7574	−	30.7574i	1.06954	−	1.06954i	0.0721439	−	0.997394i	$-0.477016\pi$
$827$	30.7574	−	30.7574i	1.06954	−	1.06954i	0.997394	−	0.0721439i	$-0.0229841\pi$
$828$		0			0
$829$			46.2843i			1.60752i	0.594954	+	0.803760i	$0.297170\pi$
$829$			46.2843i			1.60752i	−0.594954	+	0.803760i	$0.702830\pi$
$830$	−26.1421	+	13.0711i	−0.907407	+	0.453703i
$831$		0			0
$832$	1.41421	+	1.41421i	0.0490290	+	0.0490290i
$833$	−5.41421	−	5.41421i	−0.187591	−	0.187591i
$834$		0			0
$835$	−3.89949	+	11.6985i	−0.134948	+	0.404843i
$836$		−	2.82843i		−	0.0978232i
$837$		0			0
$838$	15.7990	−	15.7990i	0.545767	−	0.545767i
$839$	28.4853			0.983421			0.491711	−	0.870759i	$-0.336372\pi$
$839$	28.4853			0.983421			0.491711	+	0.870759i	$0.336372\pi$
$840$		0			0
$841$	−5.68629			−0.196079
$842$	−20.3137	+	20.3137i	−0.700057	+	0.700057i
$843$		0			0
$844$			9.17157i			0.315699i
$845$	−9.00000	−	18.0000i	−0.309609	−	0.619219i
$846$		0			0
$847$	20.6274	+	20.6274i	0.708766	+	0.708766i
$848$	−2.65685	−	2.65685i	−0.0912367	−	0.0912367i
$849$		0			0
$850$	30.6274	+	22.9706i	1.05051	+	0.787884i
$851$		−	2.00000i		−	0.0685591i
$852$		0			0
$853$	−5.21320	+	5.21320i	−0.178497	+	0.178497i	−0.790700	−	0.612204i	$-0.790283\pi$
$853$	−5.21320	+	5.21320i	−0.178497	+	0.178497i	0.612204	+	0.790700i	$0.290283\pi$
$854$	7.31371			0.250270
$855$		0			0
$856$	14.2426			0.486803
$857$	−11.7574	+	11.7574i	−0.401624	+	0.401624i	−0.878805	−	0.477181i	$-0.841659\pi$
$857$	−11.7574	+	11.7574i	−0.401624	+	0.401624i	0.477181	+	0.878805i	$0.341659\pi$
$858$		0			0
$859$		−	6.82843i		−	0.232983i	−0.993192	−	0.116491i	$-0.962835\pi$
$859$		−	6.82843i		−	0.232983i	0.993192	−	0.116491i	$-0.0371648\pi$
$860$	−18.7279	−	6.24264i	−0.638617	−	0.212872i
$861$		0			0
$862$	−3.65685	−	3.65685i	−0.124553	−	0.124553i
$863$	−38.2426	−	38.2426i	−1.30179	−	1.30179i	−0.927181	−	0.374614i	$-0.877775\pi$
$863$	−38.2426	−	38.2426i	−1.30179	−	1.30179i	−0.374614	−	0.927181i	$-0.622225\pi$
$864$		0			0
$865$	29.6985	+	9.89949i	1.00978	+	0.336593i
$866$			33.1127i			1.12522i
$867$		0			0
$868$	−9.65685	+	9.65685i	−0.327775	+	0.327775i
$869$	5.65685			0.191896
$870$		0			0
$871$	3.31371			0.112281
$872$	−3.48528	+	3.48528i	−0.118027	+	0.118027i
$873$		0			0
$874$		−	3.41421i		−	0.115487i
$875$	−26.0000	+	18.0000i	−0.878960	+	0.608511i
$876$		0			0
$877$	18.0416	+	18.0416i	0.609223	+	0.609223i	0.942743	−	0.333520i	$-0.108237\pi$
$877$	18.0416	+	18.0416i	0.609223	+	0.609223i	−0.333520	+	0.942743i	$0.608237\pi$
$878$	17.0711	+	17.0711i	0.576121	+	0.576121i
$879$		0			0
$880$	−0.828427	−	1.65685i	−0.0279263	−	0.0558525i
$881$		−	18.9706i		−	0.639134i	−0.947564	−	0.319567i	$-0.896462\pi$
$881$		−	18.9706i		−	0.639134i	0.947564	−	0.319567i	$-0.103538\pi$
$882$		0			0
$883$	12.9706	−	12.9706i	0.436494	−	0.436494i	−0.454336	−	0.890830i	$-0.650123\pi$
$883$	12.9706	−	12.9706i	0.436494	−	0.436494i	0.890830	+	0.454336i	$0.150123\pi$
$884$	15.3137			0.515056
$885$		0			0
$886$	1.17157			0.0393598
$887$	20.2843	−	20.2843i	0.681079	−	0.681079i	−0.279164	−	0.960243i	$-0.590057\pi$
$887$	20.2843	−	20.2843i	0.681079	−	0.681079i	0.960243	+	0.279164i	$0.0900574\pi$
$888$		0			0
$889$		−	17.6569i		−	0.592192i
$890$	9.89949	−	29.6985i	0.331832	−	0.995495i
$891$		0			0
$892$	−5.24264	−	5.24264i	−0.175537	−	0.175537i
$893$		0			0
$894$		0			0
$895$	−1.37258	+	0.686292i	−0.0458804	+	0.0229402i
$896$			2.82843i			0.0944911i
$897$		0			0
$898$	13.4853	−	13.4853i	0.450010	−	0.450010i
$899$	23.3137			0.777556
$900$		0			0
$901$	−28.7696			−0.958453
$902$	1.51472	−	1.51472i	0.0504346	−	0.0504346i
$903$		0			0
$904$			5.31371i			0.176731i
$905$	−21.1716	+	10.5858i	−0.703767	+	0.351883i
$906$		0			0
$907$	37.3553	+	37.3553i	1.24036	+	1.24036i	0.959850	+	0.280514i	$0.0905048\pi$
$907$	37.3553	+	37.3553i	1.24036	+	1.24036i	0.280514	+	0.959850i	$0.409495\pi$
$908$	−14.8995	−	14.8995i	−0.494457	−	0.494457i
$909$		0			0
$910$	−4.00000	+	12.0000i	−0.132599	+	0.397796i
$911$		−	8.28427i		−	0.274470i	−0.990539	−	0.137235i	$-0.956178\pi$
$911$		−	8.28427i		−	0.274470i	0.990539	−	0.137235i	$-0.0438216\pi$
$912$		0			0
$913$	7.65685	−	7.65685i	0.253405	−	0.253405i
$914$	−37.7990			−1.25028
$915$		0			0
$916$	10.5858			0.349764
$917$	−11.3137	+	11.3137i	−0.373612	+	0.373612i
$918$		0			0
$919$		−	4.97056i		−	0.163964i	−0.996634	−	0.0819819i	$-0.973875\pi$
$919$		−	4.97056i		−	0.163964i	0.996634	−	0.0819819i	$-0.0261250\pi$
$920$	−1.00000	−	2.00000i	−0.0329690	−	0.0659380i
$921$		0			0
$922$	21.5563	+	21.5563i	0.709921	+	0.709921i
$923$	6.48528	+	6.48528i	0.213466	+	0.213466i
$924$		0			0
$925$	9.89949	−	1.41421i	0.325493	−	0.0464991i
$926$		−	39.4142i		−	1.29523i
$927$		0			0
$928$	3.41421	−	3.41421i	0.112077	−	0.112077i
$929$	49.6985			1.63055			0.815277	−	0.579071i	$-0.196585\pi$
$929$	49.6985			1.63055			0.815277	+	0.579071i	$0.196585\pi$
$930$		0			0
$931$	−3.41421			−0.111896
$932$	−18.8284	+	18.8284i	−0.616746	+	0.616746i
$933$		0			0
$934$		−	31.2132i		−	1.02133i
$935$	−13.4558	−	4.48528i	−0.440053	−	0.146684i
$936$		0			0
$937$	−28.5269	−	28.5269i	−0.931934	−	0.931934i	0.0658931	−	0.997827i	$-0.479010\pi$
$937$	−28.5269	−	28.5269i	−0.931934	−	0.931934i	−0.997827	+	0.0658931i	$0.979010\pi$
$938$	3.31371	+	3.31371i	0.108196	+	0.108196i
$939$		0			0
$940$		0			0
$941$		−	21.9411i		−	0.715260i	−0.933863	−	0.357630i	$-0.883585\pi$
$941$		−	21.9411i		−	0.715260i	0.933863	−	0.357630i	$-0.116415\pi$
$942$		0			0
$943$	1.82843	−	1.82843i	0.0595418	−	0.0595418i
$944$	2.82843			0.0920575
$945$		0			0
$946$	7.31371			0.237789
$947$	−25.4558	+	25.4558i	−0.827204	+	0.827204i	−0.987129	−	0.159925i	$-0.948875\pi$
$947$	−25.4558	+	25.4558i	−0.827204	+	0.827204i	0.159925	+	0.987129i	$0.448875\pi$
$948$		0			0
$949$			11.7990i			0.383011i
$950$	16.8995	−	2.41421i	0.548292	−	0.0783274i
$951$		0			0
$952$	15.3137	+	15.3137i	0.496320	+	0.496320i
$953$	−14.9289	−	14.9289i	−0.483596	−	0.483596i	0.422682	−	0.906278i	$-0.361089\pi$
$953$	−14.9289	−	14.9289i	−0.483596	−	0.483596i	−0.906278	+	0.422682i	$0.861089\pi$
$954$		0			0
$955$	14.8284	+	29.6569i	0.479837	+	0.959673i
$956$			21.5563i			0.697182i
$957$		0			0
$958$	−18.8284	+	18.8284i	−0.608319	+	0.608319i
$959$	52.2843			1.68835
$960$		0			0
$961$	−7.68629			−0.247945
$962$	2.82843	−	2.82843i	0.0911922	−	0.0911922i
$963$		0			0
$964$			25.7990i			0.830930i
$965$	5.00000	−	15.0000i	0.160956	−	0.482867i
$966$		0			0
$967$	0.414214	+	0.414214i	0.0133202	+	0.0133202i	0.713736	−	0.700415i	$-0.247002\pi$
$967$	0.414214	+	0.414214i	0.0133202	+	0.0133202i	−0.700415	+	0.713736i	$0.747002\pi$
$968$	−7.29289	−	7.29289i	−0.234402	−	0.234402i
$969$		0			0
$970$	−14.3431	+	7.17157i	−0.460531	+	0.230265i
$971$		−	5.37258i		−	0.172414i	−0.996277	−	0.0862072i	$-0.972525\pi$
$971$		−	5.37258i		−	0.172414i	0.996277	−	0.0862072i	$-0.0274747\pi$
$972$		0			0
$973$	−2.34315	+	2.34315i	−0.0751178	+	0.0751178i
$974$	−20.1005			−0.644062
$975$		0			0
$976$	−2.58579			−0.0827690
$977$	−4.44365	+	4.44365i	−0.142165	+	0.142165i	−0.774607	−	0.632442i	$-0.782053\pi$
$977$	−4.44365	+	4.44365i	−0.142165	+	0.142165i	0.632442	+	0.774607i	$0.282053\pi$
$978$		0			0
$979$			11.5980i			0.370673i
$980$	−2.00000	+	1.00000i	−0.0638877	+	0.0319438i
$981$		0			0
$982$	10.4853	+	10.4853i	0.334599	+	0.334599i
$983$	37.9411	+	37.9411i	1.21013	+	1.21013i	0.970982	+	0.239152i	$0.0768693\pi$
$983$	37.9411	+	37.9411i	1.21013	+	1.21013i	0.239152	+	0.970982i	$0.423131\pi$
$984$		0			0
$985$	−7.07107	+	21.2132i	−0.225303	+	0.675909i
$986$		−	36.9706i		−	1.17738i
$987$		0			0
$988$	4.82843	−	4.82843i	0.153613	−	0.153613i
$989$	8.82843			0.280728
$990$		0			0
$991$	−25.9411			−0.824047			−0.412024	−	0.911173i	$-0.635178\pi$
$991$	−25.9411			−0.824047			−0.412024	+	0.911173i	$0.635178\pi$
$992$	3.41421	−	3.41421i	0.108401	−	0.108401i
$993$		0			0
$994$			12.9706i			0.411401i
$995$	17.6569	+	35.3137i	0.559760	+	1.11952i
$996$		0			0
$997$	−9.07107	−	9.07107i	−0.287284	−	0.287284i	0.548722	−	0.836005i	$-0.315115\pi$
$997$	−9.07107	−	9.07107i	−0.287284	−	0.287284i	−0.836005	+	0.548722i	$0.815115\pi$
$998$	−14.8284	−	14.8284i	−0.469386	−	0.469386i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.a.737.2	yes	4
3.2	odd	2		2070.2.j.f.737.1	yes	4
5.3	odd	4		2070.2.j.f.323.1	yes	4
15.8	even	4	inner	2070.2.j.a.323.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.a.323.2	✓	4	15.8	even	4	inner
2070.2.j.a.737.2	yes	4	1.1	even	1	trivial
2070.2.j.f.323.1	yes	4	5.3	odd	4
2070.2.j.f.737.1	yes	4	3.2	odd	2

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.707107 + 2.12132i) q^{10} -0.828427i q^{11} +(1.41421 - 1.41421i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-5.41421 + 5.41421i) q^{17} +3.41421i q^{19} +(1.00000 + 2.00000i) q^{20} +(-0.585786 - 0.585786i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(3.00000 - 4.00000i) q^{25} -2.00000i q^{26} +(2.00000 - 2.00000i) q^{28} -4.82843 q^{29} -4.82843 q^{31} +(-0.707107 + 0.707107i) q^{32} +7.65685i q^{34} +(-6.00000 - 2.00000i) q^{35} +(1.41421 + 1.41421i) q^{37} +(2.41421 + 2.41421i) q^{38} +(2.12132 + 0.707107i) q^{40} +2.58579i q^{41} +(-6.24264 + 6.24264i) q^{43} -0.828427 q^{44} -1.00000 q^{46} +1.00000i q^{49} +(-0.707107 - 4.94975i) q^{50} +(-1.41421 - 1.41421i) q^{52} +(2.65685 + 2.65685i) q^{53} +(0.828427 + 1.65685i) q^{55} -2.82843i q^{56} +(-3.41421 + 3.41421i) q^{58} -2.82843 q^{59} +2.58579 q^{61} +(-3.41421 + 3.41421i) q^{62} +1.00000i q^{64} +(-1.41421 + 4.24264i) q^{65} +(1.17157 + 1.17157i) q^{67} +(5.41421 + 5.41421i) q^{68} +(-5.65685 + 2.82843i) q^{70} +4.58579i q^{71} +(-4.17157 + 4.17157i) q^{73} +2.00000 q^{74} +3.41421 q^{76} +(1.65685 - 1.65685i) q^{77} +6.82843i q^{79} +(2.00000 - 1.00000i) q^{80} +(1.82843 + 1.82843i) q^{82} +(9.24264 + 9.24264i) q^{83} +(5.41421 - 16.2426i) q^{85} +8.82843i q^{86} +(-0.585786 + 0.585786i) q^{88} -14.0000 q^{89} +5.65685 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-3.41421 - 6.82843i) q^{95} +(5.07107 + 5.07107i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{5} + 8 q^{7}+O(q^{10}) \) 4 * q - 8 * q^5 + 8 * q^7	\( 4 q - 8 q^{5} + 8 q^{7} - 4 q^{16} - 16 q^{17} + 4 q^{20} - 8 q^{22} + 12 q^{25} + 8 q^{28} - 8 q^{29} - 8 q^{31} - 24 q^{35} + 4 q^{38} - 8 q^{43} + 8 q^{44} - 4 q^{46} - 12 q^{53} - 8 q^{55} - 8 q^{58} + 16 q^{61} - 8 q^{62} + 16 q^{67} + 16 q^{68} - 28 q^{73} + 8 q^{74} + 8 q^{76} - 16 q^{77} + 8 q^{80} - 4 q^{82} + 20 q^{83} + 16 q^{85} - 8 q^{88} - 56 q^{89} - 8 q^{95} - 8 q^{97}+O(q^{100}) \) 4 * q - 8 * q^5 + 8 * q^7 - 4 * q^16 - 16 * q^17 + 4 * q^20 - 8 * q^22 + 12 * q^25 + 8 * q^28 - 8 * q^29 - 8 * q^31 - 24 * q^35 + 4 * q^38 - 8 * q^43 + 8 * q^44 - 4 * q^46 - 12 * q^53 - 8 * q^55 - 8 * q^58 + 16 * q^61 - 8 * q^62 + 16 * q^67 + 16 * q^68 - 28 * q^73 + 8 * q^74 + 8 * q^76 - 16 * q^77 + 8 * q^80 - 4 * q^82 + 20 * q^83 + 16 * q^85 - 8 * q^88 - 56 * q^89 - 8 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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