LMFDB - Embedded newform 425.2.m.a.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(26,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,4,0,0,4,4,-4,8,0,-4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	425.151
Dual form			425.2.m.a.76.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70711 + 1.70711i) q^{2} +(-0.414214 - 1.00000i) q^{3} +3.82843i q^{4} +(1.00000 - 2.41421i) q^{6} +(2.41421 + 1.00000i) q^{7} +(-3.12132 + 3.12132i) q^{8} +(1.29289 - 1.29289i) q^{9} +(-1.00000 + 2.41421i) q^{11} +(3.82843 - 1.58579i) q^{12} +1.41421i q^{13} +(2.41421 + 5.82843i) q^{14} -3.00000 q^{16} +(-2.82843 + 3.00000i) q^{17} +4.41421 q^{18} +(0.585786 + 0.585786i) q^{19} -2.82843i q^{21} +(-5.82843 + 2.41421i) q^{22} +(1.82843 - 4.41421i) q^{23} +(4.41421 + 1.82843i) q^{24} +(-2.41421 + 2.41421i) q^{26} +(-4.82843 - 2.00000i) q^{27} +(-3.82843 + 9.24264i) q^{28} +(-0.292893 + 0.121320i) q^{29} +(-3.00000 - 7.24264i) q^{31} +(1.12132 + 1.12132i) q^{32} +2.82843 q^{33} +(-9.94975 + 0.292893i) q^{34} +(4.94975 + 4.94975i) q^{36} +(-3.53553 - 8.53553i) q^{37} +2.00000i q^{38} +(1.41421 - 0.585786i) q^{39} +(1.12132 + 0.464466i) q^{41} +(4.82843 - 4.82843i) q^{42} +(0.585786 - 0.585786i) q^{43} +(-9.24264 - 3.82843i) q^{44} +(10.6569 - 4.41421i) q^{46} +5.17157i q^{47} +(1.24264 + 3.00000i) q^{48} +(-0.121320 - 0.121320i) q^{49} +(4.17157 + 1.58579i) q^{51} -5.41421 q^{52} +(1.00000 + 1.00000i) q^{53} +(-4.82843 - 11.6569i) q^{54} +(-10.6569 + 4.41421i) q^{56} +(0.343146 - 0.828427i) q^{57} +(-0.707107 - 0.292893i) q^{58} +(4.24264 - 4.24264i) q^{59} +(-3.53553 - 1.46447i) q^{61} +(7.24264 - 17.4853i) q^{62} +(4.41421 - 1.82843i) q^{63} +9.82843i q^{64} +(4.82843 + 4.82843i) q^{66} -1.17157 q^{67} +(-11.4853 - 10.8284i) q^{68} -5.17157 q^{69} +(-2.07107 - 5.00000i) q^{71} +8.07107i q^{72} +(11.9497 - 4.94975i) q^{73} +(8.53553 - 20.6066i) q^{74} +(-2.24264 + 2.24264i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(3.41421 + 1.41421i) q^{78} +(1.82843 - 4.41421i) q^{79} +0.171573i q^{81} +(1.12132 + 2.70711i) q^{82} +(-8.24264 - 8.24264i) q^{83} +10.8284 q^{84} +2.00000 q^{86} +(0.242641 + 0.242641i) q^{87} +(-4.41421 - 10.6569i) q^{88} +6.58579i q^{89} +(-1.41421 + 3.41421i) q^{91} +(16.8995 + 7.00000i) q^{92} +(-6.00000 + 6.00000i) q^{93} +(-8.82843 + 8.82843i) q^{94} +(0.656854 - 1.58579i) q^{96} +(-9.53553 + 3.94975i) q^{97} -0.414214i q^{98} +(1.82843 + 4.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 4 q^{11} + 4 q^{12} + 4 q^{14} - 12 q^{16} + 12 q^{18} + 8 q^{19} - 12 q^{22} - 4 q^{23} + 12 q^{24} - 4 q^{26} - 8 q^{27} - 4 q^{28} - 4 q^{29}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 4 * q^11 + 4 * q^12 + 4 * q^14 - 12 * q^16 + 12 * q^18 + 8 * q^19 - 12 * q^22 - 4 * q^23 + 12 * q^24 - 4 * q^26 - 8 * q^27 - 4 * q^28 - 4 * q^29 - 12 * q^31 - 4 * q^32 - 20 * q^34 - 4 * q^41 + 8 * q^42 + 8 * q^43 - 20 * q^44 + 20 * q^46 - 12 * q^48 + 8 * q^49 + 28 * q^51 - 16 * q^52 + 4 * q^53 - 8 * q^54 - 20 * q^56 + 24 * q^57 + 12 * q^62 + 12 * q^63 + 8 * q^66 - 16 * q^67 - 12 * q^68 - 32 * q^69 + 20 * q^71 + 28 * q^73 + 20 * q^74 + 8 * q^76 - 8 * q^77 + 8 * q^78 - 4 * q^79 - 4 * q^82 - 16 * q^83 + 32 * q^84 + 8 * q^86 - 16 * q^87 - 12 * q^88 + 28 * q^92 - 24 * q^93 - 24 * q^94 - 20 * q^96 - 24 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.70711	+	1.70711i	1.20711	+	1.20711i	0.971960	+	0.235147i	$0.0755571\pi$
$2$	1.70711	+	1.70711i	1.20711	+	1.20711i	0.235147	+	0.971960i	$0.424443\pi$
$3$	−0.414214	−	1.00000i	−0.239146	−	0.577350i	0.758049	−	0.652198i	$-0.226153\pi$
$3$	−0.414214	−	1.00000i	−0.239146	−	0.577350i	−0.997195	+	0.0748477i	$0.976153\pi$
$4$			3.82843i			1.91421i
$5$		0			0
$5$		0			0
$6$	1.00000	−	2.41421i	0.408248	−	0.985599i
$7$	2.41421	+	1.00000i	0.912487	+	0.377964i	0.789008	−	0.614383i	$-0.210595\pi$
$7$	2.41421	+	1.00000i	0.912487	+	0.377964i	0.123479	+	0.992347i	$0.460595\pi$
$8$	−3.12132	+	3.12132i	−1.10355	+	1.10355i
$9$	1.29289	−	1.29289i	0.430964	−	0.430964i
$10$		0			0
$11$	−1.00000	+	2.41421i	−0.301511	+	0.727913i	0.698414	+	0.715694i	$0.253889\pi$
$11$	−1.00000	+	2.41421i	−0.301511	+	0.727913i	−0.999925	+	0.0122188i	$0.996111\pi$
$12$	3.82843	−	1.58579i	1.10517	−	0.457777i
$13$			1.41421i			0.392232i	0.980581	+	0.196116i	$0.0628330\pi$
$13$			1.41421i			0.392232i	−0.980581	+	0.196116i	$0.937167\pi$
$14$	2.41421	+	5.82843i	0.645226	+	1.55771i
$15$		0			0
$16$	−3.00000			−0.750000
$17$	−2.82843	+	3.00000i	−0.685994	+	0.727607i
$17$	−2.82843	+	3.00000i	−0.685994	+	0.727607i
$18$	4.41421			1.04044
$19$	0.585786	+	0.585786i	0.134389	+	0.134389i	0.771101	−	0.636713i	$-0.219706\pi$
$19$	0.585786	+	0.585786i	0.134389	+	0.134389i	−0.636713	+	0.771101i	$0.719706\pi$
$20$		0			0
$21$		−	2.82843i		−	0.617213i
$22$	−5.82843	+	2.41421i	−1.24262	+	0.514712i
$23$	1.82843	−	4.41421i	0.381253	−	0.920427i	−0.610471	−	0.792039i	$-0.709020\pi$
$23$	1.82843	−	4.41421i	0.381253	−	0.920427i	0.991724	−	0.128388i	$-0.0409804\pi$
$24$	4.41421	+	1.82843i	0.901048	+	0.373226i
$25$		0			0
$26$	−2.41421	+	2.41421i	−0.473466	+	0.473466i
$27$	−4.82843	−	2.00000i	−0.929231	−	0.384900i
$28$	−3.82843	+	9.24264i	−0.723505	+	1.74669i
$29$	−0.292893	+	0.121320i	−0.0543889	+	0.0225286i	−0.409712	−	0.912215i	$-0.634371\pi$
$29$	−0.292893	+	0.121320i	−0.0543889	+	0.0225286i	0.355323	+	0.934744i	$0.384371\pi$
$30$		0			0
$31$	−3.00000	−	7.24264i	−0.538816	−	1.30082i	−0.925550	−	0.378625i	$-0.876397\pi$
$31$	−3.00000	−	7.24264i	−0.538816	−	1.30082i	0.386734	−	0.922191i	$-0.373603\pi$
$32$	1.12132	+	1.12132i	0.198223	+	0.198223i
$33$	2.82843			0.492366
$34$	−9.94975	+	0.292893i	−1.70637	+	0.0502308i
$35$		0			0
$36$	4.94975	+	4.94975i	0.824958	+	0.824958i
$37$	−3.53553	−	8.53553i	−0.581238	−	1.40323i	−0.891691	−	0.452644i	$-0.850481\pi$
$37$	−3.53553	−	8.53553i	−0.581238	−	1.40323i	0.310453	−	0.950589i	$-0.399519\pi$
$38$			2.00000i			0.324443i
$39$	1.41421	−	0.585786i	0.226455	−	0.0938009i
$40$		0			0
$41$	1.12132	+	0.464466i	0.175121	+	0.0725374i	0.468521	−	0.883452i	$-0.344787\pi$
$41$	1.12132	+	0.464466i	0.175121	+	0.0725374i	−0.293400	+	0.955990i	$0.594787\pi$
$42$	4.82843	−	4.82843i	0.745042	−	0.745042i
$43$	0.585786	−	0.585786i	0.0893316	−	0.0893316i	−0.661029	−	0.750360i	$-0.729880\pi$
$43$	0.585786	−	0.585786i	0.0893316	−	0.0893316i	0.750360	+	0.661029i	$0.229880\pi$
$44$	−9.24264	−	3.82843i	−1.39338	−	0.577157i
$45$		0			0
$46$	10.6569	−	4.41421i	1.57127	−	0.650840i
$47$			5.17157i			0.754351i	0.926142	+	0.377176i	$0.123105\pi$
$47$			5.17157i			0.754351i	−0.926142	+	0.377176i	$0.876895\pi$
$48$	1.24264	+	3.00000i	0.179360	+	0.433013i
$49$	−0.121320	−	0.121320i	−0.0173315	−	0.0173315i
$50$		0			0
$51$	4.17157	+	1.58579i	0.584137	+	0.222055i
$52$	−5.41421			−0.750816
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$	−4.82843	−	11.6569i	−0.657066	−	1.58630i
$55$		0			0
$56$	−10.6569	+	4.41421i	−1.42408	+	0.589874i
$57$	0.343146	−	0.828427i	0.0454508	−	0.109728i
$58$	−0.707107	−	0.292893i	−0.0928477	−	0.0384588i
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	−0.374772	−	0.927117i	$-0.622279\pi$
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	0.927117	+	0.374772i	$0.122279\pi$
$60$		0			0
$61$	−3.53553	−	1.46447i	−0.452679	−	0.187506i	0.144682	−	0.989478i	$-0.453784\pi$
$61$	−3.53553	−	1.46447i	−0.452679	−	0.187506i	−0.597361	+	0.801973i	$0.703784\pi$
$62$	7.24264	−	17.4853i	0.919816	−	2.22063i
$63$	4.41421	−	1.82843i	0.556139	−	0.230360i
$64$			9.82843i			1.22855i
$65$		0			0
$66$	4.82843	+	4.82843i	0.594338	+	0.594338i
$67$	−1.17157			−0.143130			−0.0715652	−	0.997436i	$-0.522799\pi$
$67$	−1.17157			−0.143130			−0.0715652	+	0.997436i	$0.522799\pi$
$68$	−11.4853	−	10.8284i	−1.39279	−	1.31314i
$69$	−5.17157			−0.622584
$70$		0			0
$71$	−2.07107	−	5.00000i	−0.245791	−	0.593391i	0.752048	−	0.659109i	$-0.229066\pi$
$71$	−2.07107	−	5.00000i	−0.245791	−	0.593391i	−0.997838	+	0.0657178i	$0.979066\pi$
$72$			8.07107i			0.951184i
$73$	11.9497	−	4.94975i	1.39861	−	0.579324i	0.449221	−	0.893421i	$-0.351702\pi$
$73$	11.9497	−	4.94975i	1.39861	−	0.579324i	0.949391	+	0.314097i	$0.101702\pi$
$74$	8.53553	−	20.6066i	0.992236	−	2.39547i
$75$		0			0
$76$	−2.24264	+	2.24264i	−0.257249	+	0.257249i
$77$	−4.82843	+	4.82843i	−0.550250	+	0.550250i
$78$	3.41421	+	1.41421i	0.386584	+	0.160128i
$79$	1.82843	−	4.41421i	0.205714	−	0.496638i	−0.787026	−	0.616920i	$-0.788380\pi$
$79$	1.82843	−	4.41421i	0.205714	−	0.496638i	0.992740	+	0.120283i	$0.0383801\pi$
$80$		0			0
$81$			0.171573i			0.0190637i
$82$	1.12132	+	2.70711i	0.123829	+	0.298950i
$83$	−8.24264	−	8.24264i	−0.904747	−	0.904747i	0.0910949	−	0.995842i	$-0.470963\pi$
$83$	−8.24264	−	8.24264i	−0.904747	−	0.904747i	−0.995842	+	0.0910949i	$0.970963\pi$
$84$	10.8284			1.18148
$85$		0			0
$86$	2.00000			0.215666
$87$	0.242641	+	0.242641i	0.0260138	+	0.0260138i
$88$	−4.41421	−	10.6569i	−0.470557	−	1.13602i
$89$			6.58579i			0.698092i	0.937106	+	0.349046i	$0.113494\pi$
$89$			6.58579i			0.698092i	−0.937106	+	0.349046i	$0.886506\pi$
$90$		0			0
$91$	−1.41421	+	3.41421i	−0.148250	+	0.357907i
$92$	16.8995	+	7.00000i	1.76189	+	0.729800i
$93$	−6.00000	+	6.00000i	−0.622171	+	0.622171i
$94$	−8.82843	+	8.82843i	−0.910583	+	0.910583i
$95$		0			0
$96$	0.656854	−	1.58579i	0.0670399	−	0.161849i
$97$	−9.53553	+	3.94975i	−0.968187	+	0.401036i	−0.810037	−	0.586379i	$-0.800553\pi$
$97$	−9.53553	+	3.94975i	−0.968187	+	0.401036i	−0.158150	+	0.987415i	$0.550553\pi$
$98$		−	0.414214i		−	0.0418419i
$99$	1.82843	+	4.41421i	0.183764	+	0.443645i
$100$		0			0
$101$	−10.5858			−1.05333			−0.526663	−	0.850074i	$-0.676557\pi$
$101$	−10.5858			−1.05333			−0.526663	+	0.850074i	$0.676557\pi$
$102$	4.41421	+	9.82843i	0.437072	+	0.973159i
$103$	−12.4853			−1.23021			−0.615106	−	0.788445i	$-0.710887\pi$
$103$	−12.4853			−1.23021			−0.615106	+	0.788445i	$0.710887\pi$
$104$	−4.41421	−	4.41421i	−0.432849	−	0.432849i
$105$		0			0
$106$			3.41421i			0.331618i
$107$	−0.414214	+	0.171573i	−0.0400435	+	0.0165866i	−0.402615	−	0.915369i	$-0.631899\pi$
$107$	−0.414214	+	0.171573i	−0.0400435	+	0.0165866i	0.362572	+	0.931956i	$0.381899\pi$
$108$	7.65685	−	18.4853i	0.736781	−	1.77875i
$109$	14.3640	+	5.94975i	1.37582	+	0.569882i	0.943360	−	0.331772i	$-0.107646\pi$
$109$	14.3640	+	5.94975i	1.37582	+	0.569882i	0.432458	+	0.901654i	$0.357646\pi$
$110$		0			0
$111$	−7.07107	+	7.07107i	−0.671156	+	0.671156i
$112$	−7.24264	−	3.00000i	−0.684365	−	0.283473i
$113$	−5.05025	+	12.1924i	−0.475088	+	1.14696i	0.486799	+	0.873514i	$0.338165\pi$
$113$	−5.05025	+	12.1924i	−0.475088	+	1.14696i	−0.961886	+	0.273449i	$0.911835\pi$
$114$	2.00000	−	0.828427i	0.187317	−	0.0775893i
$115$		0			0
$116$	−0.464466	−	1.12132i	−0.0431246	−	0.104112i
$117$	1.82843	+	1.82843i	0.169038	+	0.169038i
$118$	14.4853			1.33348
$119$	−9.82843	+	4.41421i	−0.900970	+	0.404650i
$120$		0			0
$121$	2.94975	+	2.94975i	0.268159	+	0.268159i
$122$	−3.53553	−	8.53553i	−0.320092	−	0.772771i
$123$		−	1.31371i		−	0.118453i
$124$	27.7279	−	11.4853i	2.49004	−	1.03141i
$125$		0			0
$126$	10.6569	+	4.41421i	0.949388	+	0.393249i
$127$	3.75736	−	3.75736i	0.333412	−	0.333412i	−0.520469	−	0.853881i	$-0.674243\pi$
$127$	3.75736	−	3.75736i	0.333412	−	0.333412i	0.853881	+	0.520469i	$0.174243\pi$
$128$	−14.5355	+	14.5355i	−1.28477	+	1.28477i
$129$	−0.828427	−	0.343146i	−0.0729389	−	0.0302123i
$130$		0			0
$131$	−14.0711	+	5.82843i	−1.22939	+	0.509232i	−0.900385	−	0.435094i	$-0.856715\pi$
$131$	−14.0711	+	5.82843i	−1.22939	+	0.509232i	−0.329010	+	0.944326i	$0.606715\pi$
$132$			10.8284i			0.942494i
$133$	0.828427	+	2.00000i	0.0718337	+	0.173422i
$134$	−2.00000	−	2.00000i	−0.172774	−	0.172774i
$135$		0			0
$136$	−0.535534	−	18.1924i	−0.0459217	−	1.55998i
$137$	16.7279			1.42916			0.714581	−	0.699552i	$-0.246617\pi$
$137$	16.7279			1.42916			0.714581	+	0.699552i	$0.246617\pi$
$138$	−8.82843	−	8.82843i	−0.751526	−	0.751526i
$139$	−8.17157	−	19.7279i	−0.693104	−	1.67330i	−0.738432	−	0.674328i	$-0.764433\pi$
$139$	−8.17157	−	19.7279i	−0.693104	−	1.67330i	0.0453279	−	0.998972i	$-0.485567\pi$
$140$		0			0
$141$	5.17157	−	2.14214i	0.435525	−	0.180400i
$142$	5.00000	−	12.0711i	0.419591	−	1.01298i
$143$	−3.41421	−	1.41421i	−0.285511	−	0.118262i
$144$	−3.87868	+	3.87868i	−0.323223	+	0.323223i
$145$		0			0
$146$	28.8492	+	11.9497i	2.38758	+	0.988968i
$147$	−0.0710678	+	0.171573i	−0.00586157	+	0.0141511i
$148$	32.6777	−	13.5355i	2.68609	−	1.11261i
$149$			16.9706i			1.39028i	0.718873	+	0.695141i	$0.244658\pi$
$149$			16.9706i			1.39028i	−0.718873	+	0.695141i	$0.755342\pi$
$150$		0			0
$151$	5.07107	+	5.07107i	0.412678	+	0.412678i	0.882670	−	0.469993i	$-0.155743\pi$
$151$	5.07107	+	5.07107i	0.412678	+	0.412678i	−0.469993	+	0.882670i	$0.655743\pi$
$152$	−3.65685			−0.296610
$153$	0.221825	+	7.53553i	0.0179335	+	0.609212i
$154$	−16.4853			−1.32842
$155$		0			0
$156$	2.24264	+	5.41421i	0.179555	+	0.433484i
$157$			9.65685i			0.770701i	0.922770	+	0.385350i	$0.125919\pi$
$157$			9.65685i			0.770701i	−0.922770	+	0.385350i	$0.874081\pi$
$158$	10.6569	−	4.41421i	0.847814	−	0.351176i
$159$	0.585786	−	1.41421i	0.0464559	−	0.112154i
$160$		0			0
$161$	8.82843	−	8.82843i	0.695778	−	0.695778i
$162$	−0.292893	+	0.292893i	−0.0230119	+	0.0230119i
$163$	7.82843	+	3.24264i	0.613170	+	0.253983i	0.667583	−	0.744535i	$-0.267329\pi$
$163$	7.82843	+	3.24264i	0.613170	+	0.253983i	−0.0544134	+	0.998518i	$0.517329\pi$
$164$	−1.77817	+	4.29289i	−0.138852	+	0.335219i
$165$		0			0
$166$		−	28.1421i		−	2.18425i
$167$	−0.757359	−	1.82843i	−0.0586062	−	0.141488i	0.891864	−	0.452304i	$-0.149398\pi$
$167$	−0.757359	−	1.82843i	−0.0586062	−	0.141488i	−0.950470	+	0.310816i	$0.899398\pi$
$168$	8.82843	+	8.82843i	0.681128	+	0.681128i
$169$	11.0000			0.846154
$170$		0			0
$171$	1.51472			0.115833
$172$	2.24264	+	2.24264i	0.171000	+	0.171000i
$173$	−1.12132	−	2.70711i	−0.0852524	−	0.205818i	0.875504	−	0.483211i	$-0.160530\pi$
$173$	−1.12132	−	2.70711i	−0.0852524	−	0.205818i	−0.960756	+	0.277393i	$0.910530\pi$
$174$			0.828427i			0.0628029i
$175$		0			0
$176$	3.00000	−	7.24264i	0.226134	−	0.545935i
$177$	−6.00000	−	2.48528i	−0.450988	−	0.186805i
$178$	−11.2426	+	11.2426i	−0.842672	+	0.842672i
$179$	−4.24264	+	4.24264i	−0.317110	+	0.317110i	−0.847656	−	0.530546i	$-0.821987\pi$
$179$	−4.24264	+	4.24264i	−0.317110	+	0.317110i	0.530546	+	0.847656i	$0.321987\pi$
$180$		0			0
$181$	−4.46447	+	10.7782i	−0.331841	+	0.801135i	0.666605	+	0.745411i	$0.267747\pi$
$181$	−4.46447	+	10.7782i	−0.331841	+	0.801135i	−0.998446	+	0.0557243i	$0.982253\pi$
$182$	−8.24264	+	3.41421i	−0.610985	+	0.253078i
$183$			4.14214i			0.306195i
$184$	8.07107	+	19.4853i	0.595007	+	1.43647i
$185$		0			0
$186$	−20.4853			−1.50205
$187$	−4.41421	−	9.82843i	−0.322799	−	0.718726i
$188$	−19.7990			−1.44399
$189$	−9.65685	−	9.65685i	−0.702433	−	0.702433i
$190$		0			0
$191$			20.0000i			1.44715i	0.690246	+	0.723575i	$0.257502\pi$
$191$			20.0000i			1.44715i	−0.690246	+	0.723575i	$0.742498\pi$
$192$	9.82843	−	4.07107i	0.709306	−	0.293804i
$193$	−0.878680	+	2.12132i	−0.0632487	+	0.152696i	−0.952344	−	0.305027i	$-0.901335\pi$
$193$	−0.878680	+	2.12132i	−0.0632487	+	0.152696i	0.889095	+	0.457722i	$0.151335\pi$
$194$	−23.0208	−	9.53553i	−1.65280	−	0.684611i
$195$		0			0
$196$	0.464466	−	0.464466i	0.0331761	−	0.0331761i
$197$	4.29289	+	1.77817i	0.305856	+	0.126690i	0.530332	−	0.847790i	$-0.322067\pi$
$197$	4.29289	+	1.77817i	0.305856	+	0.126690i	−0.224476	+	0.974480i	$0.572067\pi$
$198$	−4.41421	+	10.6569i	−0.313704	+	0.757350i
$199$	10.6569	−	4.41421i	0.755444	−	0.312915i	0.0284836	−	0.999594i	$-0.490932\pi$
$199$	10.6569	−	4.41421i	0.755444	−	0.312915i	0.726961	+	0.686679i	$0.240932\pi$
$200$		0			0
$201$	0.485281	+	1.17157i	0.0342291	+	0.0826364i
$202$	−18.0711	−	18.0711i	−1.27148	−	1.27148i
$203$	−0.828427			−0.0581442
$204$	−6.07107	+	15.9706i	−0.425060	+	1.11816i
$205$		0			0
$206$	−21.3137	−	21.3137i	−1.48500	−	1.48500i
$207$	−3.34315	−	8.07107i	−0.232365	−	0.560978i
$208$		−	4.24264i		−	0.294174i
$209$	−2.00000	+	0.828427i	−0.138343	+	0.0573035i
$210$		0			0
$211$	−19.7279	−	8.17157i	−1.35813	−	0.562554i	−0.419583	−	0.907717i	$-0.637824\pi$
$211$	−19.7279	−	8.17157i	−1.35813	−	0.562554i	−0.938543	+	0.345163i	$0.887824\pi$
$212$	−3.82843	+	3.82843i	−0.262937	+	0.262937i
$213$	−4.14214	+	4.14214i	−0.283814	+	0.283814i
$214$	−1.00000	−	0.414214i	−0.0683586	−	0.0283151i
$215$		0			0
$216$	21.3137	−	8.82843i	1.45021	−	0.600698i
$217$		−	20.4853i		−	1.39063i
$218$	14.3640	+	34.6777i	0.972850	+	2.34867i
$219$	−9.89949	−	9.89949i	−0.668946	−	0.668946i
$220$		0			0
$221$	−4.24264	−	4.00000i	−0.285391	−	0.269069i
$222$	−24.1421			−1.62031
$223$	−3.41421	−	3.41421i	−0.228633	−	0.228633i	0.583489	−	0.812121i	$-0.301687\pi$
$223$	−3.41421	−	3.41421i	−0.228633	−	0.228633i	−0.812121	+	0.583489i	$0.801687\pi$
$224$	1.58579	+	3.82843i	0.105955	+	0.255798i
$225$		0			0
$226$	−29.4350	+	12.1924i	−1.95799	+	0.811026i
$227$	−6.65685	+	16.0711i	−0.441831	+	1.06667i	0.533475	+	0.845816i	$0.320886\pi$
$227$	−6.65685	+	16.0711i	−0.441831	+	1.06667i	−0.975306	+	0.220858i	$0.929114\pi$
$228$	3.17157	+	1.31371i	0.210043	+	0.0870025i
$229$	−12.1421	+	12.1421i	−0.802375	+	0.802375i	−0.983466	−	0.181091i	$-0.942037\pi$
$229$	−12.1421	+	12.1421i	−0.802375	+	0.802375i	0.181091	+	0.983466i	$0.442037\pi$
$230$		0			0
$231$	6.82843	+	2.82843i	0.449278	+	0.186097i
$232$	0.535534	−	1.29289i	0.0351595	−	0.0848826i
$233$	−8.12132	+	3.36396i	−0.532045	+	0.220380i	−0.632499	−	0.774561i	$-0.717971\pi$
$233$	−8.12132	+	3.36396i	−0.532045	+	0.220380i	0.100453	+	0.994942i	$0.467971\pi$
$234$			6.24264i			0.408094i
$235$		0			0
$236$	16.2426	+	16.2426i	1.05731	+	1.05731i
$237$	−5.17157			−0.335930
$238$	−24.3137	−	9.24264i	−1.57602	−	0.599111i
$239$	14.8284			0.959171			0.479586	−	0.877495i	$-0.340787\pi$
$239$	14.8284			0.959171			0.479586	+	0.877495i	$0.340787\pi$
$240$		0			0
$241$	−1.36396	−	3.29289i	−0.0878605	−	0.212114i	0.873842	−	0.486211i	$-0.161621\pi$
$241$	−1.36396	−	3.29289i	−0.0878605	−	0.212114i	−0.961702	+	0.274097i	$0.911621\pi$
$242$			10.0711i			0.647393i
$243$	−14.3137	+	5.92893i	−0.918225	+	0.380341i
$244$	5.60660	−	13.5355i	0.358926	−	0.866524i
$245$		0			0
$246$	2.24264	−	2.24264i	0.142986	−	0.142986i
$247$	−0.828427	+	0.828427i	−0.0527116	+	0.0527116i
$248$	31.9706	+	13.2426i	2.03013	+	0.840909i
$249$	−4.82843	+	11.6569i	−0.305989	+	0.738723i
$250$		0			0
$251$		−	20.4853i		−	1.29302i	−0.762906	−	0.646510i	$-0.776228\pi$
$251$		−	20.4853i		−	1.29302i	0.762906	−	0.646510i	$-0.223772\pi$
$252$	7.00000	+	16.8995i	0.440959	+	1.06457i
$253$	8.82843	+	8.82843i	0.555038	+	0.555038i
$254$	12.8284			0.804927
$255$		0			0
$256$	−29.9706			−1.87316
$257$	4.34315	+	4.34315i	0.270918	+	0.270918i	0.829470	−	0.558552i	$-0.188643\pi$
$257$	4.34315	+	4.34315i	0.270918	+	0.270918i	−0.558552	+	0.829470i	$0.688643\pi$
$258$	−0.828427	−	2.00000i	−0.0515756	−	0.124515i
$259$		−	24.1421i		−	1.50012i
$260$		0			0
$261$	−0.221825	+	0.535534i	−0.0137306	+	0.0331487i
$262$	−33.9706	−	14.0711i	−2.09871	−	0.869313i
$263$	7.41421	−	7.41421i	0.457180	−	0.457180i	−0.440549	−	0.897729i	$-0.645216\pi$
$263$	7.41421	−	7.41421i	0.457180	−	0.457180i	0.897729	+	0.440549i	$0.145216\pi$
$264$	−8.82843	+	8.82843i	−0.543352	+	0.543352i
$265$		0			0
$266$	−2.00000	+	4.82843i	−0.122628	+	0.296050i
$267$	6.58579	−	2.72792i	0.403044	−	0.166946i
$268$		−	4.48528i		−	0.273982i
$269$	10.1213	+	24.4350i	0.617108	+	1.48983i	0.855047	+	0.518550i	$0.173528\pi$
$269$	10.1213	+	24.4350i	0.617108	+	1.48983i	−0.237939	+	0.971280i	$0.576472\pi$
$270$		0			0
$271$	22.1421			1.34504			0.672519	−	0.740079i	$-0.265212\pi$
$271$	22.1421			1.34504			0.672519	+	0.740079i	$0.265212\pi$
$272$	8.48528	−	9.00000i	0.514496	−	0.545705i
$273$	4.00000			0.242091
$274$	28.5563	+	28.5563i	1.72515	+	1.72515i
$275$		0			0
$276$		−	19.7990i		−	1.19176i
$277$	18.4350	−	7.63604i	1.10765	−	0.458805i	0.247525	−	0.968882i	$-0.420383\pi$
$277$	18.4350	−	7.63604i	1.10765	−	0.458805i	0.860129	+	0.510077i	$0.170383\pi$
$278$	19.7279	−	47.6274i	1.18320	−	2.85650i
$279$	−13.2426	−	5.48528i	−0.792816	−	0.328395i
$280$		0			0
$281$	−1.34315	+	1.34315i	−0.0801254	+	0.0801254i	−0.746034	−	0.665908i	$-0.768044\pi$
$281$	−1.34315	+	1.34315i	−0.0801254	+	0.0801254i	0.665908	+	0.746034i	$0.268044\pi$
$282$	12.4853	+	5.17157i	0.743488	+	0.307963i
$283$	7.14214	−	17.2426i	0.424556	−	1.02497i	−0.556431	−	0.830894i	$-0.687830\pi$
$283$	7.14214	−	17.2426i	0.424556	−	1.02497i	0.980987	−	0.194075i	$-0.0621704\pi$
$284$	19.1421	−	7.92893i	1.13588	−	0.470496i
$285$		0			0
$286$	−3.41421	−	8.24264i	−0.201887	−	0.487398i
$287$	2.24264	+	2.24264i	0.132379	+	0.132379i
$288$	2.89949			0.170854
$289$	−1.00000	−	16.9706i	−0.0588235	−	0.998268i
$290$		0			0
$291$	7.89949	+	7.89949i	0.463077	+	0.463077i
$292$	18.9497	+	45.7487i	1.10895	+	2.67724i
$293$			12.3431i			0.721094i	0.932741	+	0.360547i	$0.117410\pi$
$293$			12.3431i			0.721094i	−0.932741	+	0.360547i	$0.882590\pi$
$294$	−0.414214	+	0.171573i	−0.0241574	+	0.0100063i
$295$		0			0
$296$	37.6777	+	15.6066i	2.18997	+	0.907115i
$297$	9.65685	−	9.65685i	0.560348	−	0.560348i
$298$	−28.9706	+	28.9706i	−1.67822	+	1.67822i
$299$	6.24264	+	2.58579i	0.361021	+	0.149540i
$300$		0			0
$301$	2.00000	−	0.828427i	0.115278	−	0.0477497i
$302$			17.3137i			0.996292i
$303$	4.38478	+	10.5858i	0.251899	+	0.608138i
$304$	−1.75736	−	1.75736i	−0.100791	−	0.100791i
$305$		0			0
$306$	−12.4853	+	13.2426i	−0.713736	+	0.757031i
$307$	26.1421			1.49201			0.746005	−	0.665940i	$-0.231969\pi$
$307$	26.1421			1.49201			0.746005	+	0.665940i	$0.231969\pi$
$308$	−18.4853	−	18.4853i	−1.05330	−	1.05330i
$309$	5.17157	+	12.4853i	0.294201	+	0.710263i
$310$		0			0
$311$	23.7279	−	9.82843i	1.34549	−	0.557319i	0.410455	−	0.911881i	$-0.365370\pi$
$311$	23.7279	−	9.82843i	1.34549	−	0.557319i	0.935032	+	0.354562i	$0.115370\pi$
$312$	−2.58579	+	6.24264i	−0.146391	+	0.353420i
$313$	9.12132	+	3.77817i	0.515568	+	0.213555i	0.625269	−	0.780410i	$-0.284989\pi$
$313$	9.12132	+	3.77817i	0.515568	+	0.213555i	−0.109701	+	0.993965i	$0.534989\pi$
$314$	−16.4853	+	16.4853i	−0.930318	+	0.930318i
$315$		0			0
$316$	16.8995	+	7.00000i	0.950671	+	0.393781i
$317$	−7.36396	+	17.7782i	−0.413601	+	0.998522i	0.570562	+	0.821255i	$0.306726\pi$
$317$	−7.36396	+	17.7782i	−0.413601	+	0.998522i	−0.984163	+	0.177267i	$0.943274\pi$
$318$	3.41421	−	1.41421i	0.191460	−	0.0793052i
$319$		−	0.828427i		−	0.0463830i
$320$		0			0
$321$	0.343146	+	0.343146i	0.0191525	+	0.0191525i
$322$	30.1421			1.67976
$323$	−3.41421	+	0.100505i	−0.189972	+	0.00559225i
$324$	−0.656854			−0.0364919
$325$		0			0
$326$	7.82843	+	18.8995i	0.433576	+	1.04675i
$327$		−	16.8284i		−	0.930614i
$328$	−4.94975	+	2.05025i	−0.273304	+	0.113206i
$329$	−5.17157	+	12.4853i	−0.285118	+	0.688336i
$330$		0			0
$331$	−15.4142	+	15.4142i	−0.847242	+	0.847242i	−0.989788	−	0.142546i	$-0.954471\pi$
$331$	−15.4142	+	15.4142i	−0.847242	+	0.847242i	0.142546	+	0.989788i	$0.454471\pi$
$332$	31.5563	−	31.5563i	1.73188	−	1.73188i
$333$	−15.6066	−	6.46447i	−0.855237	−	0.354251i
$334$	1.82843	−	4.41421i	0.100047	−	0.241535i
$335$		0			0
$336$			8.48528i			0.462910i
$337$	2.15076	+	5.19239i	0.117159	+	0.282847i	0.971571	−	0.236750i	$-0.0760821\pi$
$337$	2.15076	+	5.19239i	0.117159	+	0.282847i	−0.854411	+	0.519597i	$0.826082\pi$
$338$	18.7782	+	18.7782i	1.02140	+	1.02140i
$339$	14.2843			0.775815
$340$		0			0
$341$	20.4853			1.10934
$342$	2.58579	+	2.58579i	0.139823	+	0.139823i
$343$	−7.17157	−	17.3137i	−0.387229	−	0.934852i
$344$			3.65685i			0.197164i
$345$		0			0
$346$	2.70711	−	6.53553i	0.145535	−	0.351352i
$347$	−15.4853	−	6.41421i	−0.831293	−	0.344333i	−0.0738788	−	0.997267i	$-0.523538\pi$
$347$	−15.4853	−	6.41421i	−0.831293	−	0.344333i	−0.757415	+	0.652934i	$0.773538\pi$
$348$	−0.928932	+	0.928932i	−0.0497960	+	0.0497960i
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$		0			0
$351$	2.82843	−	6.82843i	0.150970	−	0.364474i
$352$	−3.82843	+	1.58579i	−0.204056	+	0.0845227i
$353$		−	14.0000i		−	0.745145i	−0.928003	−	0.372572i	$-0.878476\pi$
$353$		−	14.0000i		−	0.745145i	0.928003	−	0.372572i	$-0.121524\pi$
$354$	−6.00000	−	14.4853i	−0.318896	−	0.769884i
$355$		0			0
$356$	−25.2132			−1.33630
$357$	8.48528	+	8.00000i	0.449089	+	0.423405i
$358$	−14.4853			−0.765571
$359$	−20.3848	−	20.3848i	−1.07587	−	1.07587i	−0.996875	−	0.0789921i	$-0.974830\pi$
$359$	−20.3848	−	20.3848i	−1.07587	−	1.07587i	−0.0789921	−	0.996875i	$-0.525170\pi$
$360$		0			0
$361$		−	18.3137i		−	0.963879i
$362$	−26.0208	+	10.7782i	−1.36762	+	0.566488i
$363$	1.72792	−	4.17157i	0.0906924	−	0.218951i
$364$	−13.0711	−	5.41421i	−0.685110	−	0.283782i
$365$		0			0
$366$	−7.07107	+	7.07107i	−0.369611	+	0.369611i
$367$	4.07107	+	1.68629i	0.212508	+	0.0880237i	0.486398	−	0.873737i	$-0.338310\pi$
$367$	4.07107	+	1.68629i	0.212508	+	0.0880237i	−0.273890	+	0.961761i	$0.588310\pi$
$368$	−5.48528	+	13.2426i	−0.285940	+	0.690320i
$369$	2.05025	−	0.849242i	0.106732	−	0.0442098i
$370$		0			0
$371$	1.41421	+	3.41421i	0.0734223	+	0.177257i
$372$	−22.9706	−	22.9706i	−1.19097	−	1.19097i
$373$	−11.5563			−0.598365			−0.299183	−	0.954196i	$-0.596714\pi$
$373$	−11.5563			−0.598365			−0.299183	+	0.954196i	$0.596714\pi$
$374$	9.24264	−	24.3137i	0.477926	−	1.25723i
$375$		0			0
$376$	−16.1421	−	16.1421i	−0.832467	−	0.832467i
$377$	−0.171573	−	0.414214i	−0.00883645	−	0.0213331i
$378$		−	32.9706i		−	1.69582i
$379$	−2.41421	+	1.00000i	−0.124010	+	0.0513665i	−0.443826	−	0.896113i	$-0.646379\pi$
$379$	−2.41421	+	1.00000i	−0.124010	+	0.0513665i	0.319816	+	0.947480i	$0.396379\pi$
$380$		0			0
$381$	−5.31371	−	2.20101i	−0.272230	−	0.112761i
$382$	−34.1421	+	34.1421i	−1.74686	+	1.74686i
$383$	15.8995	−	15.8995i	0.812426	−	0.812426i	−0.172571	−	0.984997i	$-0.555207\pi$
$383$	15.8995	−	15.8995i	0.812426	−	0.812426i	0.984997	+	0.172571i	$0.0552074\pi$
$384$	20.5563	+	8.51472i	1.04901	+	0.434515i
$385$		0			0
$386$	−5.12132	+	2.12132i	−0.260668	+	0.107972i
$387$		−	1.51472i		−	0.0769975i
$388$	−15.1213	−	36.5061i	−0.767669	−	1.85332i
$389$	−8.58579	−	8.58579i	−0.435317	−	0.435317i	0.455116	−	0.890432i	$-0.349598\pi$
$389$	−8.58579	−	8.58579i	−0.435317	−	0.435317i	−0.890432	+	0.455116i	$0.849598\pi$
$390$		0			0
$391$	8.07107	+	17.9706i	0.408171	+	0.908810i
$392$	0.757359			0.0382524
$393$	11.6569	+	11.6569i	0.588011	+	0.588011i
$394$	4.29289	+	10.3640i	0.216273	+	0.522129i
$395$		0			0
$396$	−16.8995	+	7.00000i	−0.849232	+	0.351763i
$397$	−6.80761	+	16.4350i	−0.341664	+	0.824850i	0.655884	+	0.754862i	$0.272296\pi$
$397$	−6.80761	+	16.4350i	−0.341664	+	0.824850i	−0.997548	+	0.0699884i	$0.977704\pi$
$398$	25.7279	+	10.6569i	1.28962	+	0.534180i
$399$	1.65685	−	1.65685i	0.0829465	−	0.0829465i
$400$		0			0
$401$	−0.535534	−	0.221825i	−0.0267433	−	0.0110774i	0.369272	−	0.929321i	$-0.379607\pi$
$401$	−0.535534	−	0.221825i	−0.0267433	−	0.0110774i	−0.396015	+	0.918244i	$0.629607\pi$
$402$	−1.17157	+	2.82843i	−0.0584327	+	0.141069i
$403$	10.2426	−	4.24264i	0.510222	−	0.211341i
$404$		−	40.5269i		−	2.01629i
$405$		0			0
$406$	−1.41421	−	1.41421i	−0.0701862	−	0.0701862i
$407$	24.1421			1.19668
$408$	−17.9706	+	8.07107i	−0.889675	+	0.399577i
$409$	−3.31371			−0.163852			−0.0819262	−	0.996638i	$-0.526107\pi$
$409$	−3.31371			−0.163852			−0.0819262	+	0.996638i	$0.526107\pi$
$410$		0			0
$411$	−6.92893	−	16.7279i	−0.341779	−	0.825128i
$412$		−	47.7990i		−	2.35489i
$413$	14.4853	−	6.00000i	0.712774	−	0.295241i
$414$	8.07107	−	19.4853i	0.396671	−	0.957649i
$415$		0			0
$416$	−1.58579	+	1.58579i	−0.0777496	+	0.0777496i
$417$	−16.3431	+	16.3431i	−0.800327	+	0.800327i
$418$	−4.82843	−	2.00000i	−0.236166	−	0.0978232i
$419$	−5.10051	+	12.3137i	−0.249176	+	0.601564i	−0.998135	−	0.0610528i	$-0.980554\pi$
$419$	−5.10051	+	12.3137i	−0.249176	+	0.601564i	0.748959	+	0.662617i	$0.230554\pi$
$420$		0			0
$421$		−	14.5858i		−	0.710868i	−0.934701	−	0.355434i	$-0.884333\pi$
$421$		−	14.5858i		−	0.710868i	0.934701	−	0.355434i	$-0.115667\pi$
$422$	−19.7279	−	47.6274i	−0.960340	−	2.31847i
$423$	6.68629	+	6.68629i	0.325099	+	0.325099i
$424$	−6.24264			−0.303169
$425$		0			0
$426$	−14.1421			−0.685189
$427$	−7.07107	−	7.07107i	−0.342193	−	0.342193i
$428$	−0.656854	−	1.58579i	−0.0317502	−	0.0766519i
$429$			4.00000i			0.193122i
$430$		0			0
$431$	2.79899	−	6.75736i	0.134823	−	0.325491i	−0.842021	−	0.539445i	$-0.818634\pi$
$431$	2.79899	−	6.75736i	0.134823	−	0.325491i	0.976844	+	0.213954i	$0.0686343\pi$
$432$	14.4853	+	6.00000i	0.696923	+	0.288675i
$433$	−14.7279	+	14.7279i	−0.707779	+	0.707779i	−0.966068	−	0.258289i	$-0.916841\pi$
$433$	−14.7279	+	14.7279i	−0.707779	+	0.707779i	0.258289	+	0.966068i	$0.416841\pi$
$434$	34.9706	−	34.9706i	1.67864	−	1.67864i
$435$		0			0
$436$	−22.7782	+	54.9914i	−1.09088	+	2.63361i
$437$	3.65685	−	1.51472i	0.174931	−	0.0724588i
$438$		−	33.7990i		−	1.61498i
$439$	−4.07107	−	9.82843i	−0.194301	−	0.469085i	0.796462	−	0.604689i	$-0.206703\pi$
$439$	−4.07107	−	9.82843i	−0.194301	−	0.469085i	−0.990763	+	0.135604i	$0.956703\pi$
$440$		0			0
$441$	−0.313708			−0.0149385
$442$	−0.414214	−	14.0711i	−0.0197021	−	0.669292i
$443$	23.7990			1.13072			0.565362	−	0.824843i	$-0.308736\pi$
$443$	23.7990			1.13072			0.565362	+	0.824843i	$0.308736\pi$
$444$	−27.0711	−	27.0711i	−1.28474	−	1.28474i
$445$		0			0
$446$		−	11.6569i		−	0.551968i
$447$	16.9706	−	7.02944i	0.802680	−	0.332481i
$448$	−9.82843	+	23.7279i	−0.464350	+	1.12104i
$449$	11.1924	+	4.63604i	0.528201	+	0.218788i	0.630815	−	0.775933i	$-0.282721\pi$
$449$	11.1924	+	4.63604i	0.528201	+	0.218788i	−0.102614	+	0.994721i	$0.532721\pi$
$450$		0			0
$451$	−2.24264	+	2.24264i	−0.105602	+	0.105602i
$452$	−46.6777	−	19.3345i	−2.19553	−	0.909419i
$453$	2.97056	−	7.17157i	0.139569	−	0.336950i
$454$	−38.7990	+	16.0711i	−1.82093	+	0.754253i
$455$		0			0
$456$	1.51472	+	3.65685i	0.0709332	+	0.171248i
$457$	−9.31371	−	9.31371i	−0.435677	−	0.435677i	0.454877	−	0.890554i	$-0.349683\pi$
$457$	−9.31371	−	9.31371i	−0.435677	−	0.435677i	−0.890554	+	0.454877i	$0.849683\pi$
$458$	−41.4558			−1.93710
$459$	19.6569	−	8.82843i	0.917503	−	0.412076i
$460$		0			0
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	0.981782	−	0.190013i	$-0.0608529\pi$
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	−0.190013	+	0.981782i	$0.560853\pi$
$462$	6.82843	+	16.4853i	0.317687	+	0.766965i
$463$		−	14.6274i		−	0.679794i	−0.940463	−	0.339897i	$-0.889608\pi$
$463$		−	14.6274i		−	0.679794i	0.940463	−	0.339897i	$-0.110392\pi$
$464$	0.878680	−	0.363961i	0.0407917	−	0.0168965i
$465$		0			0
$466$	−19.6066	−	8.12132i	−0.908258	−	0.376213i
$467$	−23.0711	+	23.0711i	−1.06760	+	1.06760i	−0.0700588	+	0.997543i	$0.522319\pi$
$467$	−23.0711	+	23.0711i	−1.06760	+	1.06760i	−0.997543	+	0.0700588i	$0.977681\pi$
$468$	−7.00000	+	7.00000i	−0.323575	+	0.323575i
$469$	−2.82843	−	1.17157i	−0.130605	−	0.0540982i
$470$		0			0
$471$	9.65685	−	4.00000i	0.444964	−	0.184310i
$472$			26.4853i			1.21908i
$473$	0.828427	+	2.00000i	0.0380911	+	0.0919601i
$474$	−8.82843	−	8.82843i	−0.405503	−	0.405503i
$475$		0			0
$476$	−16.8995	−	37.6274i	−0.774587	−	1.72465i
$477$	2.58579			0.118395
$478$	25.3137	+	25.3137i	1.15782	+	1.15782i
$479$	1.97056	+	4.75736i	0.0900373	+	0.217369i	0.962483	−	0.271342i	$-0.0874673\pi$
$479$	1.97056	+	4.75736i	0.0900373	+	0.217369i	−0.872446	+	0.488711i	$0.837467\pi$
$480$		0			0
$481$	12.0711	−	5.00000i	0.550393	−	0.227980i
$482$	3.29289	−	7.94975i	0.149987	−	0.362101i
$483$	−12.4853	−	5.17157i	−0.568100	−	0.235315i
$484$	−11.2929	+	11.2929i	−0.513313	+	0.513313i
$485$		0			0
$486$	−34.5563	−	14.3137i	−1.56751	−	0.649283i
$487$	−10.0711	+	24.3137i	−0.456364	+	1.10176i	0.513495	+	0.858092i	$0.328350\pi$
$487$	−10.0711	+	24.3137i	−0.456364	+	1.10176i	−0.969859	+	0.243667i	$0.921650\pi$
$488$	15.6066	−	6.46447i	0.706478	−	0.292633i
$489$		−	9.17157i		−	0.414753i
$490$		0			0
$491$	26.2426	+	26.2426i	1.18431	+	1.18431i	0.978615	+	0.205698i	$0.0659466\pi$
$491$	26.2426	+	26.2426i	1.18431	+	1.18431i	0.205698	+	0.978615i	$0.434053\pi$
$492$	5.02944			0.226745
$493$	0.464466	−	1.22183i	0.0209185	−	0.0550282i
$494$	−2.82843			−0.127257
$495$		0			0
$496$	9.00000	+	21.7279i	0.404112	+	0.975613i
$497$		−	14.1421i		−	0.634361i
$498$	−28.1421	+	11.6569i	−1.26108	+	0.522356i
$499$	−8.21320	+	19.8284i	−0.367673	+	0.887642i	0.626457	+	0.779456i	$0.284504\pi$
$499$	−8.21320	+	19.8284i	−0.367673	+	0.887642i	−0.994131	+	0.108186i	$0.965496\pi$
$500$		0			0
$501$	−1.51472	+	1.51472i	−0.0676726	+	0.0676726i
$502$	34.9706	−	34.9706i	1.56081	−	1.56081i
$503$	19.7279	+	8.17157i	0.879625	+	0.364352i	0.776351	−	0.630301i	$-0.217068\pi$
$503$	19.7279	+	8.17157i	0.879625	+	0.364352i	0.103273	+	0.994653i	$0.467068\pi$
$504$	−8.07107	+	19.4853i	−0.359514	+	0.867943i
$505$		0			0
$506$			30.1421i			1.33998i
$507$	−4.55635	−	11.0000i	−0.202355	−	0.488527i
$508$	14.3848	+	14.3848i	0.638221	+	0.638221i
$509$	−36.9706			−1.63869			−0.819346	−	0.573300i	$-0.805663\pi$
$509$	−36.9706			−1.63869			−0.819346	+	0.573300i	$0.805663\pi$
$510$		0			0
$511$	33.7990			1.49518
$512$	−22.0919	−	22.0919i	−0.976333	−	0.976333i
$513$	−1.65685	−	4.00000i	−0.0731519	−	0.176604i
$514$			14.8284i			0.654054i
$515$		0			0
$516$	1.31371	−	3.17157i	0.0578328	−	0.139621i
$517$	−12.4853	−	5.17157i	−0.549102	−	0.227446i
$518$	41.2132	−	41.2132i	1.81080	−	1.81080i
$519$	−2.24264	+	2.24264i	−0.0984410	+	0.0984410i
$520$		0			0
$521$	7.12132	−	17.1924i	0.311991	−	0.753212i	−0.687640	−	0.726051i	$-0.741353\pi$
$521$	7.12132	−	17.1924i	0.311991	−	0.753212i	0.999631	−	0.0271607i	$-0.00864660\pi$
$522$	−1.29289	+	0.535534i	−0.0565884	+	0.0234397i
$523$			1.17157i			0.0512293i	0.999672	+	0.0256147i	$0.00815429\pi$
$523$			1.17157i			0.0512293i	−0.999672	+	0.0256147i	$0.991846\pi$
$524$	−22.3137	−	53.8701i	−0.974779	−	2.35332i
$525$		0			0
$526$	25.3137			1.10373
$527$	30.2132	+	11.4853i	1.31611	+	0.500307i
$528$	−8.48528			−0.369274
$529$	0.121320	+	0.121320i	0.00527480	+	0.00527480i
$530$		0			0
$531$		−	10.9706i		−	0.476082i
$532$	−7.65685	+	3.17157i	−0.331967	+	0.137505i
$533$	−0.656854	+	1.58579i	−0.0284515	+	0.0686880i
$534$	15.8995	+	6.58579i	0.688038	+	0.284995i
$535$		0			0
$536$	3.65685	−	3.65685i	0.157952	−	0.157952i
$537$	6.00000	+	2.48528i	0.258919	+	0.107248i
$538$	−24.4350	+	58.9914i	−1.05347	+	2.54330i
$539$	0.414214	−	0.171573i	0.0178414	−	0.00739017i
$540$		0			0
$541$	−7.05025	−	17.0208i	−0.303114	−	0.731782i	−0.999895	−	0.0144979i	$-0.995385\pi$
$541$	−7.05025	−	17.0208i	−0.303114	−	0.731782i	0.696781	−	0.717284i	$-0.254615\pi$
$542$	37.7990	+	37.7990i	1.62361	+	1.62361i
$543$	12.6274			0.541894
$544$	−6.53553	+	0.192388i	−0.280209	+	0.00824857i
$545$		0			0
$546$	6.82843	+	6.82843i	0.292230	+	0.292230i
$547$	−3.10051	−	7.48528i	−0.132568	−	0.320048i	0.843631	−	0.536923i	$-0.180413\pi$
$547$	−3.10051	−	7.48528i	−0.132568	−	0.320048i	−0.976199	+	0.216875i	$0.930413\pi$
$548$			64.0416i			2.73572i
$549$	−6.46447	+	2.67767i	−0.275897	+	0.114280i
$550$		0			0
$551$	−0.242641	−	0.100505i	−0.0103368	−	0.00428166i
$552$	16.1421	−	16.1421i	0.687055	−	0.687055i
$553$	8.82843	−	8.82843i	0.375423	−	0.375423i
$554$	44.5061	+	18.4350i	1.89088	+	0.783229i
$555$		0			0
$556$	75.5269	−	31.2843i	3.20305	−	1.32675i
$557$		−	19.7574i		−	0.837146i	−0.908183	−	0.418573i	$-0.862530\pi$
$557$		−	19.7574i		−	0.837146i	0.908183	−	0.418573i	$-0.137470\pi$
$558$	−13.2426	−	31.9706i	−0.560606	−	1.35342i
$559$	0.828427	+	0.828427i	0.0350387	+	0.0350387i
$560$		0			0
$561$	−8.00000	+	8.48528i	−0.337760	+	0.358249i
$562$	−4.58579			−0.193440
$563$	−24.5858	−	24.5858i	−1.03617	−	1.03617i	−0.999321	−	0.0368464i	$-0.988269\pi$
$563$	−24.5858	−	24.5858i	−1.03617	−	1.03617i	−0.0368464	−	0.999321i	$-0.511731\pi$
$564$	8.20101	+	19.7990i	0.345325	+	0.833688i
$565$		0			0
$566$	41.6274	−	17.2426i	1.74973	−	0.724762i
$567$	−0.171573	+	0.414214i	−0.00720538	+	0.0173953i
$568$	22.0711	+	9.14214i	0.926081	+	0.383595i
$569$	8.51472	−	8.51472i	0.356956	−	0.356956i	−0.505734	−	0.862690i	$-0.668778\pi$
$569$	8.51472	−	8.51472i	0.356956	−	0.356956i	0.862690	+	0.505734i	$0.168778\pi$
$570$		0			0
$571$	−3.92893	−	1.62742i	−0.164421	−	0.0681053i	0.298955	−	0.954267i	$-0.403362\pi$
$571$	−3.92893	−	1.62742i	−0.164421	−	0.0681053i	−0.463376	+	0.886162i	$0.653362\pi$
$572$	5.41421	−	13.0711i	0.226380	−	0.546529i
$573$	20.0000	−	8.28427i	0.835512	−	0.346080i
$574$			7.65685i			0.319591i
$575$		0			0
$576$	12.7071	+	12.7071i	0.529463	+	0.529463i
$577$	27.0711			1.12698			0.563492	−	0.826122i	$-0.309458\pi$
$577$	27.0711			1.12698			0.563492	+	0.826122i	$0.309458\pi$
$578$	27.2635	−	30.6777i	1.13401	−	1.27602i
$579$	2.48528			0.103285
$580$		0			0
$581$	−11.6569	−	28.1421i	−0.483608	−	1.16753i
$582$			26.9706i			1.11797i
$583$	−3.41421	+	1.41421i	−0.141402	+	0.0585707i
$584$	−21.8492	+	52.7487i	−0.904128	+	2.18276i
$585$		0			0
$586$	−21.0711	+	21.0711i	−0.870438	+	0.870438i
$587$	−32.0416	+	32.0416i	−1.32250	+	1.32250i	−0.410753	+	0.911747i	$0.634734\pi$
$587$	−32.0416	+	32.0416i	−1.32250	+	1.32250i	−0.911747	+	0.410753i	$0.865266\pi$
$588$	−0.656854	−	0.272078i	−0.0270882	−	0.0112203i
$589$	2.48528	−	6.00000i	0.102404	−	0.247226i
$590$		0			0
$591$		−	5.02944i		−	0.206883i
$592$	10.6066	+	25.6066i	0.435929	+	1.05242i
$593$	−9.14214	−	9.14214i	−0.375423	−	0.375423i	0.494025	−	0.869448i	$-0.335525\pi$
$593$	−9.14214	−	9.14214i	−0.375423	−	0.375423i	−0.869448	+	0.494025i	$0.835525\pi$
$594$	32.9706			1.35280
$595$		0			0
$596$	−64.9706			−2.66130
$597$	−8.82843	−	8.82843i	−0.361323	−	0.361323i
$598$	6.24264	+	15.0711i	0.255281	+	0.616302i
$599$		−	10.6274i		−	0.434224i	−0.976147	−	0.217112i	$-0.930336\pi$
$599$		−	10.6274i		−	0.434224i	0.976147	−	0.217112i	$-0.0696638\pi$
$600$		0			0
$601$	−3.22183	+	7.77817i	−0.131421	+	0.317278i	−0.975868	−	0.218360i	$-0.929929\pi$
$601$	−3.22183	+	7.77817i	−0.131421	+	0.317278i	0.844447	+	0.535639i	$0.179929\pi$
$602$	4.82843	+	2.00000i	0.196792	+	0.0815139i
$603$	−1.51472	+	1.51472i	−0.0616841	+	0.0616841i
$604$	−19.4142	+	19.4142i	−0.789953	+	0.789953i
$605$		0			0
$606$	−10.5858	+	25.5563i	−0.430018	+	1.03816i
$607$	−15.1421	+	6.27208i	−0.614600	+	0.254576i	−0.668194	−	0.743987i	$-0.732932\pi$
$607$	−15.1421	+	6.27208i	−0.614600	+	0.254576i	0.0535937	+	0.998563i	$0.482932\pi$
$608$			1.31371i			0.0532779i
$609$	0.343146	+	0.828427i	0.0139050	+	0.0335696i
$610$		0			0
$611$	−7.31371			−0.295881
$612$	−28.8492	+	0.849242i	−1.16616	+	0.0343286i
$613$	−5.31371			−0.214619			−0.107309	−	0.994226i	$-0.534224\pi$
$613$	−5.31371			−0.214619			−0.107309	+	0.994226i	$0.534224\pi$
$614$	44.6274	+	44.6274i	1.80102	+	1.80102i
$615$		0			0
$616$		−	30.1421i		−	1.21446i
$617$	2.70711	−	1.12132i	0.108984	−	0.0451427i	−0.327525	−	0.944842i	$-0.606215\pi$
$617$	2.70711	−	1.12132i	0.108984	−	0.0451427i	0.436509	+	0.899700i	$0.356215\pi$
$618$	−12.4853	+	30.1421i	−0.502232	+	1.21249i
$619$	26.3137	+	10.8995i	1.05764	+	0.438088i	0.842612	−	0.538521i	$-0.181017\pi$
$619$	26.3137	+	10.8995i	1.05764	+	0.438088i	0.215025	+	0.976609i	$0.431017\pi$
$620$		0			0
$621$	−17.6569	+	17.6569i	−0.708545	+	0.708545i
$622$	57.2843	+	23.7279i	2.29689	+	0.951403i
$623$	−6.58579	+	15.8995i	−0.263854	+	0.637000i
$624$	−4.24264	+	1.75736i	−0.169842	+	0.0703507i
$625$		0			0
$626$	9.12132	+	22.0208i	0.364561	+	0.880129i
$627$	1.65685	+	1.65685i	0.0661684	+	0.0661684i
$628$	−36.9706			−1.47529
$629$	35.6066	+	13.5355i	1.41973	+	0.539697i
$630$		0			0
$631$	−20.7279	−	20.7279i	−0.825166	−	0.825166i	0.161678	−	0.986844i	$-0.448309\pi$
$631$	−20.7279	−	20.7279i	−0.825166	−	0.825166i	−0.986844	+	0.161678i	$0.948309\pi$
$632$	8.07107	+	19.4853i	0.321050	+	0.775083i
$633$			23.1127i			0.918647i
$634$	−42.9203	+	17.7782i	−1.70458	+	0.706062i
$635$		0			0
$636$	5.41421	+	2.24264i	0.214688	+	0.0889265i
$637$	0.171573	−	0.171573i	0.00679796	−	0.00679796i
$638$	1.41421	−	1.41421i	0.0559893	−	0.0559893i
$639$	−9.14214	−	3.78680i	−0.361657	−	0.149803i
$640$		0			0
$641$	−38.2635	+	15.8492i	−1.51132	+	0.626007i	−0.975829	−	0.218536i	$-0.929872\pi$
$641$	−38.2635	+	15.8492i	−1.51132	+	0.626007i	−0.535487	+	0.844544i	$0.679872\pi$
$642$			1.17157i			0.0462383i
$643$	−11.0416	−	26.6569i	−0.435439	−	1.05124i	−0.977506	−	0.210908i	$-0.932358\pi$
$643$	−11.0416	−	26.6569i	−0.435439	−	1.05124i	0.542066	−	0.840336i	$-0.317642\pi$
$644$	33.7990	+	33.7990i	1.33187	+	1.33187i
$645$		0			0
$646$	−6.00000	−	5.65685i	−0.236067	−	0.222566i
$647$	2.82843			0.111197			0.0555985	−	0.998453i	$-0.482293\pi$
$647$	2.82843			0.111197			0.0555985	+	0.998453i	$0.482293\pi$
$648$	−0.535534	−	0.535534i	−0.0210378	−	0.0210378i
$649$	6.00000	+	14.4853i	0.235521	+	0.568597i
$650$		0			0
$651$	−20.4853	+	8.48528i	−0.802881	+	0.332564i
$652$	−12.4142	+	29.9706i	−0.486178	+	1.17374i
$653$	−8.77817	−	3.63604i	−0.343517	−	0.142289i	0.204254	−	0.978918i	$-0.434523\pi$
$653$	−8.77817	−	3.63604i	−0.343517	−	0.142289i	−0.547770	+	0.836629i	$0.684523\pi$
$654$	28.7279	−	28.7279i	1.12335	−	1.12335i
$655$		0			0
$656$	−3.36396	−	1.39340i	−0.131341	−	0.0544031i
$657$	9.05025	−	21.8492i	0.353084	−	0.852420i
$658$	−30.1421	+	12.4853i	−1.17506	+	0.486727i
$659$			8.48528i			0.330540i	0.986248	+	0.165270i	$0.0528495\pi$
$659$			8.48528i			0.330540i	−0.986248	+	0.165270i	$0.947151\pi$
$660$		0			0
$661$	0.857864	+	0.857864i	0.0333671	+	0.0333671i	0.723593	−	0.690226i	$-0.242489\pi$
$661$	0.857864	+	0.857864i	0.0333671	+	0.0333671i	−0.690226	+	0.723593i	$0.742489\pi$
$662$	−52.6274			−2.04542
$663$	−2.24264	+	5.89949i	−0.0870969	+	0.229117i
$664$	51.4558			1.99687
$665$		0			0
$666$	−15.6066	−	37.6777i	−0.604744	−	1.45998i
$667$			1.51472i			0.0586501i
$668$	7.00000	−	2.89949i	0.270838	−	0.112185i
$669$	−2.00000	+	4.82843i	−0.0773245	+	0.186678i
$670$		0			0
$671$	7.07107	−	7.07107i	0.272976	−	0.272976i
$672$	3.17157	−	3.17157i	0.122346	−	0.122346i
$673$	−4.12132	−	1.70711i	−0.158865	−	0.0658041i	0.301834	−	0.953361i	$-0.402401\pi$
$673$	−4.12132	−	1.70711i	−0.158865	−	0.0658041i	−0.460699	+	0.887556i	$0.652401\pi$
$674$	−5.19239	+	12.5355i	−0.200003	+	0.482851i
$675$		0			0
$676$			42.1127i			1.61972i
$677$	14.5772	+	35.1924i	0.560246	+	1.35255i	0.909570	+	0.415551i	$0.136411\pi$
$677$	14.5772	+	35.1924i	0.560246	+	1.35255i	−0.349324	+	0.937002i	$0.613589\pi$
$678$	24.3848	+	24.3848i	0.936492	+	0.936492i
$679$	−26.9706			−1.03504
$680$		0			0
$681$	18.8284			0.721507
$682$	34.9706	+	34.9706i	1.33909	+	1.33909i
$683$	9.10051	+	21.9706i	0.348221	+	0.840680i	0.996830	+	0.0795585i	$0.0253510\pi$
$683$	9.10051	+	21.9706i	0.348221	+	0.840680i	−0.648609	+	0.761122i	$0.724649\pi$
$684$			5.79899i			0.221730i
$685$		0			0
$686$	17.3137	−	41.7990i	0.661040	−	1.59589i
$687$	17.1716	+	7.11270i	0.655136	+	0.271366i
$688$	−1.75736	+	1.75736i	−0.0669987	+	0.0669987i
$689$	−1.41421	+	1.41421i	−0.0538772	+	0.0538772i
$690$		0			0
$691$	−7.62742	+	18.4142i	−0.290161	+	0.700510i	−0.999993	−	0.00386139i	$-0.998771\pi$
$691$	−7.62742	+	18.4142i	−0.290161	+	0.700510i	0.709832	+	0.704371i	$0.248771\pi$
$692$	10.3640	−	4.29289i	0.393979	−	0.163191i
$693$			12.4853i			0.474277i
$694$	−15.4853	−	37.3848i	−0.587813	−	1.41911i
$695$		0			0
$696$	−1.51472			−0.0574153
$697$	−4.56497	+	2.05025i	−0.172911	+	0.0776589i
$698$	10.2426			0.387690
$699$	6.72792	+	6.72792i	0.254473	+	0.254473i
$700$		0			0
$701$			37.6985i			1.42385i	0.702254	+	0.711926i	$0.252177\pi$
$701$			37.6985i			1.42385i	−0.702254	+	0.711926i	$0.747823\pi$
$702$	16.4853	−	6.82843i	0.622197	−	0.257722i
$703$	2.92893	−	7.07107i	0.110467	−	0.266690i
$704$	−23.7279	−	9.82843i	−0.894280	−	0.370423i
$705$		0			0
$706$	23.8995	−	23.8995i	0.899469	−	0.899469i
$707$	−25.5563	−	10.5858i	−0.961145	−	0.398119i
$708$	9.51472	−	22.9706i	0.357585	−	0.863287i
$709$	22.4350	−	9.29289i	0.842565	−	0.349002i	0.0807007	−	0.996738i	$-0.474284\pi$
$709$	22.4350	−	9.29289i	0.842565	−	0.349002i	0.761864	+	0.647736i	$0.224284\pi$
$710$		0			0
$711$	−3.34315	−	8.07107i	−0.125378	−	0.302689i
$712$	−20.5563	−	20.5563i	−0.770382	−	0.770382i
$713$	−37.4558			−1.40273
$714$	0.828427	+	28.1421i	0.0310031	+	1.05319i
$715$		0			0
$716$	−16.2426	−	16.2426i	−0.607016	−	0.607016i
$717$	−6.14214	−	14.8284i	−0.229382	−	0.553778i
$718$		−	69.5980i		−	2.59737i
$719$	−31.3848	+	13.0000i	−1.17045	+	0.484818i	−0.881343	−	0.472477i	$-0.843360\pi$
$719$	−31.3848	+	13.0000i	−1.17045	+	0.484818i	−0.289112	+	0.957295i	$0.593360\pi$
$720$		0			0
$721$	−30.1421	−	12.4853i	−1.12255	−	0.464976i
$722$	31.2635	−	31.2635i	1.16351	−	1.16351i
$723$	−2.72792	+	2.72792i	−0.101453	+	0.101453i
$724$	−41.2635	−	17.0919i	−1.53354	−	0.635215i
$725$		0			0
$726$	10.0711	−	4.17157i	0.373772	−	0.154822i
$727$		−	43.1127i		−	1.59896i	−0.600692	−	0.799481i	$-0.705108\pi$
$727$		−	43.1127i		−	1.59896i	0.600692	−	0.799481i	$-0.294892\pi$
$728$	−6.24264	−	15.0711i	−0.231368	−	0.558571i
$729$	12.2218	+	12.2218i	0.452660	+	0.452660i
$730$		0			0
$731$	0.100505	+	3.41421i	0.00371731	+	0.126279i
$732$	−15.8579			−0.586124
$733$	25.4853	+	25.4853i	0.941320	+	0.941320i	0.998371	−	0.0570509i	$-0.0181697\pi$
$733$	25.4853	+	25.4853i	0.941320	+	0.941320i	−0.0570509	+	0.998371i	$0.518170\pi$
$734$	4.07107	+	9.82843i	0.150266	+	0.362774i
$735$		0			0
$736$	7.00000	−	2.89949i	0.258023	−	0.106877i
$737$	1.17157	−	2.82843i	0.0431554	−	0.104186i
$738$	4.94975	+	2.05025i	0.182203	+	0.0754708i
$739$	15.7574	−	15.7574i	0.579644	−	0.579644i	−0.355161	−	0.934805i	$-0.615574\pi$
$739$	15.7574	−	15.7574i	0.579644	−	0.579644i	0.934805	+	0.355161i	$0.115574\pi$
$740$		0			0
$741$	1.17157	+	0.485281i	0.0430388	+	0.0178273i
$742$	−3.41421	+	8.24264i	−0.125340	+	0.302597i
$743$	−47.1421	+	19.5269i	−1.72948	+	0.716373i	−0.730020	+	0.683426i	$0.760489\pi$
$743$	−47.1421	+	19.5269i	−1.72948	+	0.716373i	−0.999457	+	0.0329473i	$0.989511\pi$
$744$		−	37.4558i		−	1.37320i
$745$		0			0
$746$	−19.7279	−	19.7279i	−0.722291	−	0.722291i
$747$	−21.3137			−0.779828
$748$	37.6274	−	16.8995i	1.37579	−	0.617907i
$749$	−1.17157			−0.0428083
$750$		0			0
$751$	18.2132	+	43.9706i	0.664609	+	1.60451i	0.790498	+	0.612464i	$0.209822\pi$
$751$	18.2132	+	43.9706i	0.664609	+	1.60451i	−0.125889	+	0.992044i	$0.540178\pi$
$752$		−	15.5147i		−	0.565764i
$753$	−20.4853	+	8.48528i	−0.746525	+	0.309221i
$754$	0.414214	−	1.00000i	0.0150848	−	0.0364179i
$755$		0			0
$756$	36.9706	−	36.9706i	1.34461	−	1.34461i
$757$	1.79899	−	1.79899i	0.0653854	−	0.0653854i	−0.673658	−	0.739043i	$-0.735278\pi$
$757$	1.79899	−	1.79899i	0.0653854	−	0.0653854i	0.739043	+	0.673658i	$0.235278\pi$
$758$	−5.82843	−	2.41421i	−0.211698	−	0.0876882i
$759$	5.17157	−	12.4853i	0.187716	−	0.453187i
$760$		0			0
$761$		−	37.6985i		−	1.36657i	−0.730152	−	0.683285i	$-0.760551\pi$
$761$		−	37.6985i		−	1.36657i	0.730152	−	0.683285i	$-0.239449\pi$
$762$	−5.31371	−	12.8284i	−0.192495	−	0.464725i
$763$	28.7279	+	28.7279i	1.04002	+	1.04002i
$764$	−76.5685			−2.77015
$765$		0			0
$766$	54.2843			1.96137
$767$	6.00000	+	6.00000i	0.216647	+	0.216647i
$768$	12.4142	+	29.9706i	0.447959	+	1.08147i
$769$			12.7279i			0.458981i	0.973311	+	0.229490i	$0.0737059\pi$
$769$			12.7279i			0.458981i	−0.973311	+	0.229490i	$0.926294\pi$
$770$		0			0
$771$	2.54416	−	6.14214i	0.0916255	−	0.221204i
$772$	−8.12132	−	3.36396i	−0.292293	−	0.121072i
$773$	0.585786	−	0.585786i	0.0210693	−	0.0210693i	−0.696494	−	0.717563i	$-0.745258\pi$
$773$	0.585786	−	0.585786i	0.0210693	−	0.0210693i	0.717563	+	0.696494i	$0.245258\pi$
$774$	2.58579	−	2.58579i	0.0929442	−	0.0929442i
$775$		0			0
$776$	17.4350	−	42.0919i	0.625881	−	1.51101i
$777$	−24.1421	+	10.0000i	−0.866094	+	0.358748i
$778$		−	29.3137i		−	1.05095i
$779$	0.384776	+	0.928932i	0.0137860	+	0.0332824i
$780$		0			0
$781$	14.1421			0.506045
$782$	−16.8995	+	44.4558i	−0.604325	+	1.58974i
$783$	1.65685			0.0592111
$784$	0.363961	+	0.363961i	0.0129986	+	0.0129986i
$785$		0			0
$786$			39.7990i			1.41958i
$787$	19.0000	−	7.87006i	0.677277	−	0.280537i	−0.0174112	−	0.999848i	$-0.505542\pi$
$787$	19.0000	−	7.87006i	0.677277	−	0.280537i	0.694688	+	0.719311i	$0.255542\pi$
$788$	−6.80761	+	16.4350i	−0.242511	+	0.585474i
$789$	−10.4853	−	4.34315i	−0.373286	−	0.154620i
$790$		0			0
$791$	−24.3848	+	24.3848i	−0.867023	+	0.867023i
$792$	−19.4853	−	8.07107i	−0.692379	−	0.286793i
$793$	2.07107	−	5.00000i	0.0735458	−	0.177555i
$794$	−39.6777	+	16.4350i	−1.40811	+	0.583257i
$795$		0			0
$796$	16.8995	+	40.7990i	0.598987	+	1.44608i
$797$	17.8284	+	17.8284i	0.631515	+	0.631515i	0.948448	−	0.316933i	$-0.102653\pi$
$797$	17.8284	+	17.8284i	0.631515	+	0.631515i	−0.316933	+	0.948448i	$0.602653\pi$
$798$	5.65685			0.200250
$799$	−15.5147	−	14.6274i	−0.548871	−	0.517481i
$800$		0			0
$801$	8.51472	+	8.51472i	0.300853	+	0.300853i
$802$	−0.535534	−	1.29289i	−0.0189104	−	0.0456536i
$803$			33.7990i			1.19274i
$804$	−4.48528	+	1.85786i	−0.158184	+	0.0655218i
$805$		0			0
$806$	24.7279	+	10.2426i	0.871004	+	0.360782i
$807$	20.2426	−	20.2426i	0.712575	−	0.712575i
$808$	33.0416	−	33.0416i	1.16240	−	1.16240i
$809$	−32.6066	−	13.5061i	−1.14639	−	0.474849i	−0.273067	−	0.961995i	$-0.588038\pi$
$809$	−32.6066	−	13.5061i	−1.14639	−	0.474849i	−0.873321	+	0.487146i	$0.838038\pi$
$810$		0			0
$811$	−50.9411	+	21.1005i	−1.78878	+	0.740939i	−0.798481	+	0.602020i	$0.794363\pi$
$811$	−50.9411	+	21.1005i	−1.78878	+	0.740939i	−0.990304	+	0.138919i	$0.955637\pi$
$812$		−	3.17157i		−	0.111300i
$813$	−9.17157	−	22.1421i	−0.321661	−	0.776559i
$814$	41.2132	+	41.2132i	1.44452	+	1.44452i
$815$		0			0
$816$	−12.5147	−	4.75736i	−0.438103	−	0.166541i
$817$	0.686292			0.0240103
$818$	−5.65685	−	5.65685i	−0.197787	−	0.197787i
$819$	2.58579	+	6.24264i	0.0903547	+	0.218136i
$820$		0			0
$821$	35.5061	−	14.7071i	1.23917	−	0.513282i	0.335716	−	0.941963i	$-0.391022\pi$
$821$	35.5061	−	14.7071i	1.23917	−	0.513282i	0.903456	+	0.428682i	$0.141022\pi$
$822$	16.7279	−	40.3848i	0.583453	−	1.40858i
$823$	−9.00000	−	3.72792i	−0.313720	−	0.129947i	0.220267	−	0.975440i	$-0.429307\pi$
$823$	−9.00000	−	3.72792i	−0.313720	−	0.129947i	−0.533987	+	0.845492i	$0.679307\pi$
$824$	38.9706	−	38.9706i	1.35760	−	1.35760i
$825$		0			0
$826$	34.9706	+	14.4853i	1.21678	+	0.504007i
$827$	17.9289	−	43.2843i	0.623450	−	1.50514i	−0.224177	−	0.974549i	$-0.571969\pi$
$827$	17.9289	−	43.2843i	0.623450	−	1.50514i	0.847627	−	0.530593i	$-0.178031\pi$
$828$	30.8995	−	12.7990i	1.07383	−	0.444796i
$829$		−	53.9411i		−	1.87345i	−0.350062	−	0.936726i	$-0.613840\pi$
$829$		−	53.9411i		−	1.87345i	0.350062	−	0.936726i	$-0.386160\pi$
$830$		0			0
$831$	−15.2721	−	15.2721i	−0.529783	−	0.529783i
$832$	−13.8995			−0.481878
$833$	0.707107	−	0.0208153i	0.0244998	−	0.000721207i
$834$	−55.7990			−1.93216
$835$		0			0
$836$	−3.17157	−	7.65685i	−0.109691	−	0.264818i
$837$			40.9706i			1.41615i
$838$	−29.7279	+	12.3137i	−1.02693	+	0.425370i
$839$	−6.41421	+	15.4853i	−0.221443	+	0.534611i	−0.995086	−	0.0990102i	$-0.968432\pi$
$839$	−6.41421	+	15.4853i	−0.221443	+	0.534611i	0.773643	+	0.633622i	$0.218432\pi$
$840$		0			0
$841$	−20.4350	+	20.4350i	−0.704656	+	0.704656i
$842$	24.8995	−	24.8995i	0.858093	−	0.858093i
$843$	1.89949	+	0.786797i	0.0654221	+	0.0270987i
$844$	31.2843	−	75.5269i	1.07685	−	2.59974i
$845$		0			0
$846$			22.8284i			0.784857i
$847$	4.17157	+	10.0711i	0.143337	+	0.346046i
$848$	−3.00000	−	3.00000i	−0.103020	−	0.103020i
$849$	−20.2010			−0.693297
$850$		0			0
$851$	−44.1421			−1.51317
$852$	−15.8579	−	15.8579i	−0.543281	−	0.543281i
$853$	7.33452	+	17.7071i	0.251129	+	0.606280i	0.998296	−	0.0583572i	$-0.0185862\pi$
$853$	7.33452	+	17.7071i	0.251129	+	0.606280i	−0.747166	+	0.664637i	$0.768586\pi$
$854$		−	24.1421i		−	0.826127i
$855$		0			0
$856$	0.757359	−	1.82843i	0.0258860	−	0.0624944i
$857$	8.53553	+	3.53553i	0.291568	+	0.120772i	0.523673	−	0.851919i	$-0.324561\pi$
$857$	8.53553	+	3.53553i	0.291568	+	0.120772i	−0.232105	+	0.972691i	$0.574561\pi$
$858$	−6.82843	+	6.82843i	−0.233119	+	0.233119i
$859$	24.7279	−	24.7279i	0.843706	−	0.843706i	−0.145633	−	0.989339i	$-0.546522\pi$
$859$	24.7279	−	24.7279i	0.843706	−	0.843706i	0.989339	+	0.145633i	$0.0465218\pi$
$860$		0			0
$861$	1.31371	−	3.17157i	0.0447711	−	0.108087i
$862$	16.3137	−	6.75736i	0.555647	−	0.230157i
$863$		−	10.6274i		−	0.361761i	−0.983505	−	0.180881i	$-0.942105\pi$
$863$		−	10.6274i		−	0.361761i	0.983505	−	0.180881i	$-0.0578948\pi$
$864$	−3.17157	−	7.65685i	−0.107899	−	0.260491i
$865$		0			0
$866$	−50.2843			−1.70873
$867$	−16.5563	+	8.02944i	−0.562283	+	0.272694i
$868$	78.4264			2.66197
$869$	8.82843	+	8.82843i	0.299484	+	0.299484i
$870$		0			0
$871$		−	1.65685i		−	0.0561404i
$872$	−63.4056	+	26.2635i	−2.14718	+	0.889393i
$873$	−7.22183	+	17.4350i	−0.244422	+	0.590086i
$874$	8.82843	+	3.65685i	0.298626	+	0.123695i
$875$		0			0
$876$	37.8995	−	37.8995i	1.28051	−	1.28051i
$877$	−46.4056	−	19.2218i	−1.56701	−	0.649075i	−0.580717	−	0.814105i	$-0.697228\pi$
$877$	−46.4056	−	19.2218i	−1.56701	−	0.649075i	−0.986288	+	0.165031i	$0.947228\pi$
$878$	9.82843	−	23.7279i	0.331693	−	0.800779i
$879$	12.3431	−	5.11270i	0.416324	−	0.172447i
$880$		0			0
$881$	12.8787	+	31.0919i	0.433894	+	1.04751i	0.978020	+	0.208509i	$0.0668611\pi$
$881$	12.8787	+	31.0919i	0.433894	+	1.04751i	−0.544127	+	0.839003i	$0.683139\pi$
$882$	−0.535534	−	0.535534i	−0.0180324	−	0.0180324i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	15.3137	−	16.2426i	0.515056	−	0.546299i
$885$		0			0
$886$	40.6274	+	40.6274i	1.36490	+	1.36490i
$887$	−16.8579	−	40.6985i	−0.566032	−	1.36652i	−0.904875	−	0.425678i	$-0.860035\pi$
$887$	−16.8579	−	40.6985i	−0.566032	−	1.36652i	0.338843	−	0.940843i	$-0.389965\pi$
$888$		−	44.1421i		−	1.48131i
$889$	12.8284	−	5.31371i	0.430252	−	0.178216i
$890$		0			0
$891$	−0.414214	−	0.171573i	−0.0138767	−	0.00574791i
$892$	13.0711	−	13.0711i	0.437652	−	0.437652i
$893$	−3.02944	+	3.02944i	−0.101376	+	0.101376i
$894$	40.9706	+	16.9706i	1.37026	+	0.567581i
$895$		0			0
$896$	−49.6274	+	20.5563i	−1.65794	+	0.686739i
$897$		−	7.31371i		−	0.244198i
$898$	11.1924	+	27.0208i	0.373495	+	0.901696i
$899$	1.75736	+	1.75736i	0.0586112	+	0.0586112i
$900$		0			0
$901$	−5.82843	+	0.171573i	−0.194173	+	0.00571592i
$902$	−7.65685			−0.254945
$903$	−1.65685	−	1.65685i	−0.0551367	−	0.0551367i
$904$	−22.2929	−	53.8198i	−0.741451	−	1.79002i
$905$		0			0
$906$	17.3137	−	7.17157i	0.575209	−	0.238260i
$907$	−5.14214	+	12.4142i	−0.170742	+	0.412207i	−0.985968	−	0.166936i	$-0.946613\pi$
$907$	−5.14214	+	12.4142i	−0.170742	+	0.412207i	0.815226	+	0.579143i	$0.196613\pi$
$908$	−61.5269	−	25.4853i	−2.04184	−	0.845759i
$909$	−13.6863	+	13.6863i	−0.453946	+	0.453946i
$910$		0			0
$911$	5.24264	+	2.17157i	0.173696	+	0.0719474i	0.467837	−	0.883815i	$-0.345033\pi$
$911$	5.24264	+	2.17157i	0.173696	+	0.0719474i	−0.294141	+	0.955762i	$0.595033\pi$
$912$	−1.02944	+	2.48528i	−0.0340881	+	0.0822959i
$913$	28.1421	−	11.6569i	0.931369	−	0.385786i
$914$		−	31.7990i		−	1.05182i
$915$		0			0
$916$	−46.4853	−	46.4853i	−1.53592	−	1.53592i
$917$	−39.7990			−1.31428
$918$	48.6274	+	18.4853i	1.60494	+	0.610105i
$919$	19.3137			0.637100			0.318550	−	0.947906i	$-0.396804\pi$
$919$	19.3137			0.637100			0.318550	+	0.947906i	$0.396804\pi$
$920$		0			0
$921$	−10.8284	−	26.1421i	−0.356809	−	0.861413i
$922$			58.0416i			1.91150i
$923$	7.07107	−	2.92893i	0.232747	−	0.0964070i
$924$	−10.8284	+	26.1421i	−0.356229	+	0.860013i
$925$		0			0
$926$	24.9706	−	24.9706i	0.820584	−	0.820584i
$927$	−16.1421	+	16.1421i	−0.530177	+	0.530177i
$928$	−0.464466	−	0.192388i	−0.0152468	−	0.00631545i
$929$	6.63604	−	16.0208i	0.217721	−	0.525626i	−0.776850	−	0.629686i	$-0.783183\pi$
$929$	6.63604	−	16.0208i	0.217721	−	0.525626i	0.994571	+	0.104060i	$0.0331835\pi$
$930$		0			0
$931$		−	0.142136i		−	0.00465831i
$932$	−12.8787	−	31.0919i	−0.421855	−	1.01845i
$933$	−19.6569	−	19.6569i	−0.643537	−	0.643537i
$934$	−78.7696			−2.57742
$935$		0			0
$936$	−11.4142			−0.373085
$937$	−19.4853	−	19.4853i	−0.636556	−	0.636556i	0.313148	−	0.949704i	$-0.398616\pi$
$937$	−19.4853	−	19.4853i	−0.636556	−	0.636556i	−0.949704	+	0.313148i	$0.898616\pi$
$938$	−2.82843	−	6.82843i	−0.0923514	−	0.222956i
$939$		−	10.6863i		−	0.348734i
$940$		0			0
$941$	−15.2635	+	36.8492i	−0.497574	+	1.20125i	0.453212	+	0.891403i	$0.350278\pi$
$941$	−15.2635	+	36.8492i	−0.497574	+	1.20125i	−0.950786	+	0.309848i	$0.899722\pi$
$942$	23.3137	+	9.65685i	0.759602	+	0.314637i
$943$	4.10051	−	4.10051i	0.133531	−	0.133531i
$944$	−12.7279	+	12.7279i	−0.414259	+	0.414259i
$945$		0			0
$946$	−2.00000	+	4.82843i	−0.0650256	+	0.156986i
$947$	−28.3137	+	11.7279i	−0.920072	+	0.381106i	−0.791904	−	0.610646i	$-0.790910\pi$
$947$	−28.3137	+	11.7279i	−0.920072	+	0.381106i	−0.128168	+	0.991752i	$0.540910\pi$
$948$		−	19.7990i		−	0.643041i
$949$	7.00000	+	16.8995i	0.227230	+	0.548581i
$950$		0			0
$951$	20.8284			0.675408
$952$	16.8995	−	44.4558i	0.547716	−	1.44082i
$953$	−49.6985			−1.60989			−0.804946	−	0.593348i	$-0.797806\pi$
$953$	−49.6985			−1.60989			−0.804946	+	0.593348i	$0.797806\pi$
$954$	4.41421	+	4.41421i	0.142915	+	0.142915i
$955$		0			0
$956$			56.7696i			1.83606i
$957$	−0.828427	+	0.343146i	−0.0267792	+	0.0110923i
$958$	−4.75736	+	11.4853i	−0.153703	+	0.371073i
$959$	40.3848	+	16.7279i	1.30409	+	0.540173i
$960$		0			0
$961$	−21.5355	+	21.5355i	−0.694695	+	0.694695i
$962$	29.1421	+	12.0711i	0.939580	+	0.389187i
$963$	−0.313708	+	0.757359i	−0.0101091	+	0.0244056i
$964$	12.6066	−	5.22183i	0.406031	−	0.168184i
$965$		0			0
$966$	−12.4853	−	30.1421i	−0.401707	−	0.969807i
$967$	30.8701	+	30.8701i	0.992714	+	0.992714i	0.999974	−	0.00725952i	$-0.00231080\pi$
$967$	30.8701	+	30.8701i	0.992714	+	0.992714i	−0.00725952	+	0.999974i	$0.502311\pi$
$968$	−18.4142			−0.591855
$969$	1.51472	+	3.37258i	0.0486598	+	0.108343i
$970$		0			0
$971$	−36.5858	−	36.5858i	−1.17409	−	1.17409i	−0.981224	−	0.192869i	$-0.938221\pi$
$971$	−36.5858	−	36.5858i	−1.17409	−	1.17409i	−0.192869	−	0.981224i	$-0.561779\pi$
$972$	−22.6985	−	54.7990i	−0.728054	−	1.75768i
$973$		−	55.7990i		−	1.78883i
$974$	−58.6985	+	24.3137i	−1.88082	+	0.779061i
$975$		0			0
$976$	10.6066	+	4.39340i	0.339509	+	0.140629i
$977$	27.1421	−	27.1421i	0.868354	−	0.868354i	−0.123936	−	0.992290i	$-0.539552\pi$
$977$	27.1421	−	27.1421i	0.868354	−	0.868354i	0.992290	+	0.123936i	$0.0395519\pi$
$978$	15.6569	−	15.6569i	0.500651	−	0.500651i
$979$	−15.8995	−	6.58579i	−0.508150	−	0.210483i
$980$		0			0
$981$	26.2635	−	10.8787i	0.838528	−	0.347330i
$982$			89.5980i			2.85919i
$983$	−3.72792	−	9.00000i	−0.118902	−	0.287055i	0.853212	−	0.521565i	$-0.174652\pi$
$983$	−3.72792	−	9.00000i	−0.118902	−	0.287055i	−0.972114	+	0.234510i	$0.924652\pi$
$984$	4.10051	+	4.10051i	0.130719	+	0.130719i
$985$		0			0
$986$	2.87868	−	1.29289i	0.0916758	−	0.0411741i
$987$	14.6274			0.465596
$988$	−3.17157	−	3.17157i	−0.100901	−	0.100901i
$989$	−1.51472	−	3.65685i	−0.0481653	−	0.116281i
$990$		0			0
$991$	37.7279	−	15.6274i	1.19847	−	0.496421i	0.307964	−	0.951398i	$-0.400352\pi$
$991$	37.7279	−	15.6274i	1.19847	−	0.496421i	0.890503	+	0.454977i	$0.150352\pi$
$992$	4.75736	−	11.4853i	0.151046	−	0.364658i
$993$	21.7990	+	9.02944i	0.691770	+	0.286541i
$994$	24.1421	−	24.1421i	0.765742	−	0.765742i
$995$		0			0
$996$	−44.6274	−	18.4853i	−1.41407	−	0.585729i
$997$	2.87868	−	6.94975i	0.0911687	−	0.220101i	−0.871717	−	0.490009i	$-0.836993\pi$
$997$	2.87868	−	6.94975i	0.0911687	−	0.220101i	0.962886	+	0.269908i	$0.0869934\pi$
$998$	−47.8701	+	19.8284i	−1.51530	+	0.627658i
$999$			48.2843i			1.52765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.a.151.1		4
5.2	odd	4		425.2.n.a.49.1		4
5.3	odd	4		425.2.n.b.49.1		4
5.4	even	2		17.2.d.a.15.1	yes	4
15.14	odd	2		153.2.l.c.100.1		4
17.5	odd	16		7225.2.a.u.1.2		4
17.8	even	8	inner	425.2.m.a.76.1		4
17.12	odd	16		7225.2.a.u.1.1		4
20.19	odd	2		272.2.v.d.49.1		4
35.4	even	6		833.2.v.b.814.1		8
35.9	even	6		833.2.v.b.508.1		8
35.19	odd	6		833.2.v.a.508.1		8
35.24	odd	6		833.2.v.a.814.1		8
35.34	odd	2		833.2.l.a.491.1		4
85.4	even	4		289.2.d.c.155.1		4
85.8	odd	8		425.2.n.a.399.1		4
85.9	even	8		289.2.d.a.110.1		4
85.14	odd	16		289.2.b.b.288.1		4
85.19	even	8		289.2.d.c.179.1		4
85.24	odd	16		289.2.c.c.38.4		8
85.29	odd	16		289.2.a.f.1.4		4
85.39	odd	16		289.2.a.f.1.3		4
85.42	odd	8		425.2.n.b.399.1		4
85.44	odd	16		289.2.c.c.38.3		8
85.49	even	8		289.2.d.b.179.1		4
85.54	odd	16		289.2.b.b.288.2		4
85.59	even	8		17.2.d.a.8.1	✓	4
85.64	even	4		289.2.d.b.155.1		4
85.74	odd	16		289.2.c.c.251.2		8
85.79	odd	16		289.2.c.c.251.1		8
85.84	even	2		289.2.d.a.134.1		4
255.29	even	16		2601.2.a.bb.1.2		4
255.59	odd	8		153.2.l.c.127.1		4
255.209	even	16		2601.2.a.bb.1.1		4
340.39	even	16		4624.2.a.bp.1.3		4
340.59	odd	8		272.2.v.d.161.1		4
340.199	even	16		4624.2.a.bp.1.2		4
595.59	odd	24		833.2.v.a.569.1		8
595.144	even	24		833.2.v.b.569.1		8
595.229	odd	24		833.2.v.a.263.1		8
595.314	odd	8		833.2.l.a.246.1		4
595.569	even	24		833.2.v.b.263.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	85.59	even	8
17.2.d.a.15.1	yes	4	5.4	even	2
153.2.l.c.100.1		4	15.14	odd	2
153.2.l.c.127.1		4	255.59	odd	8
272.2.v.d.49.1		4	20.19	odd	2
272.2.v.d.161.1		4	340.59	odd	8
289.2.a.f.1.3		4	85.39	odd	16
289.2.a.f.1.4		4	85.29	odd	16
289.2.b.b.288.1		4	85.14	odd	16
289.2.b.b.288.2		4	85.54	odd	16
289.2.c.c.38.3		8	85.44	odd	16
289.2.c.c.38.4		8	85.24	odd	16
289.2.c.c.251.1		8	85.79	odd	16
289.2.c.c.251.2		8	85.74	odd	16
289.2.d.a.110.1		4	85.9	even	8
289.2.d.a.134.1		4	85.84	even	2
289.2.d.b.155.1		4	85.64	even	4
289.2.d.b.179.1		4	85.49	even	8
289.2.d.c.155.1		4	85.4	even	4
289.2.d.c.179.1		4	85.19	even	8
425.2.m.a.76.1		4	17.8	even	8	inner
425.2.m.a.151.1		4	1.1	even	1	trivial
425.2.n.a.49.1		4	5.2	odd	4
425.2.n.a.399.1		4	85.8	odd	8
425.2.n.b.49.1		4	5.3	odd	4
425.2.n.b.399.1		4	85.42	odd	8
833.2.l.a.246.1		4	595.314	odd	8
833.2.l.a.491.1		4	35.34	odd	2
833.2.v.a.263.1		8	595.229	odd	24
833.2.v.a.508.1		8	35.19	odd	6
833.2.v.a.569.1		8	595.59	odd	24
833.2.v.a.814.1		8	35.24	odd	6
833.2.v.b.263.1		8	595.569	even	24
833.2.v.b.508.1		8	35.9	even	6
833.2.v.b.569.1		8	595.144	even	24
833.2.v.b.814.1		8	35.4	even	6
2601.2.a.bb.1.1		4	255.209	even	16
2601.2.a.bb.1.2		4	255.29	even	16
4624.2.a.bp.1.2		4	340.199	even	16
4624.2.a.bp.1.3		4	340.39	even	16
7225.2.a.u.1.1		4	17.12	odd	16
7225.2.a.u.1.2		4	17.5	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70711 + 1.70711i) q^{2} +(-0.414214 - 1.00000i) q^{3} +3.82843i q^{4} +(1.00000 - 2.41421i) q^{6} +(2.41421 + 1.00000i) q^{7} +(-3.12132 + 3.12132i) q^{8} +(1.29289 - 1.29289i) q^{9} +(-1.00000 + 2.41421i) q^{11} +(3.82843 - 1.58579i) q^{12} +1.41421i q^{13} +(2.41421 + 5.82843i) q^{14} -3.00000 q^{16} +(-2.82843 + 3.00000i) q^{17} +4.41421 q^{18} +(0.585786 + 0.585786i) q^{19} -2.82843i q^{21} +(-5.82843 + 2.41421i) q^{22} +(1.82843 - 4.41421i) q^{23} +(4.41421 + 1.82843i) q^{24} +(-2.41421 + 2.41421i) q^{26} +(-4.82843 - 2.00000i) q^{27} +(-3.82843 + 9.24264i) q^{28} +(-0.292893 + 0.121320i) q^{29} +(-3.00000 - 7.24264i) q^{31} +(1.12132 + 1.12132i) q^{32} +2.82843 q^{33} +(-9.94975 + 0.292893i) q^{34} +(4.94975 + 4.94975i) q^{36} +(-3.53553 - 8.53553i) q^{37} +2.00000i q^{38} +(1.41421 - 0.585786i) q^{39} +(1.12132 + 0.464466i) q^{41} +(4.82843 - 4.82843i) q^{42} +(0.585786 - 0.585786i) q^{43} +(-9.24264 - 3.82843i) q^{44} +(10.6569 - 4.41421i) q^{46} +5.17157i q^{47} +(1.24264 + 3.00000i) q^{48} +(-0.121320 - 0.121320i) q^{49} +(4.17157 + 1.58579i) q^{51} -5.41421 q^{52} +(1.00000 + 1.00000i) q^{53} +(-4.82843 - 11.6569i) q^{54} +(-10.6569 + 4.41421i) q^{56} +(0.343146 - 0.828427i) q^{57} +(-0.707107 - 0.292893i) q^{58} +(4.24264 - 4.24264i) q^{59} +(-3.53553 - 1.46447i) q^{61} +(7.24264 - 17.4853i) q^{62} +(4.41421 - 1.82843i) q^{63} +9.82843i q^{64} +(4.82843 + 4.82843i) q^{66} -1.17157 q^{67} +(-11.4853 - 10.8284i) q^{68} -5.17157 q^{69} +(-2.07107 - 5.00000i) q^{71} +8.07107i q^{72} +(11.9497 - 4.94975i) q^{73} +(8.53553 - 20.6066i) q^{74} +(-2.24264 + 2.24264i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(3.41421 + 1.41421i) q^{78} +(1.82843 - 4.41421i) q^{79} +0.171573i q^{81} +(1.12132 + 2.70711i) q^{82} +(-8.24264 - 8.24264i) q^{83} +10.8284 q^{84} +2.00000 q^{86} +(0.242641 + 0.242641i) q^{87} +(-4.41421 - 10.6569i) q^{88} +6.58579i q^{89} +(-1.41421 + 3.41421i) q^{91} +(16.8995 + 7.00000i) q^{92} +(-6.00000 + 6.00000i) q^{93} +(-8.82843 + 8.82843i) q^{94} +(0.656854 - 1.58579i) q^{96} +(-9.53553 + 3.94975i) q^{97} -0.414214i q^{98} +(1.82843 + 4.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 4 q^{11} + 4 q^{12} + 4 q^{14} - 12 q^{16} + 12 q^{18} + 8 q^{19} - 12 q^{22} - 4 q^{23} + 12 q^{24} - 4 q^{26} - 8 q^{27} - 4 q^{28} - 4 q^{29}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 4 * q^11 + 4 * q^12 + 4 * q^14 - 12 * q^16 + 12 * q^18 + 8 * q^19 - 12 * q^22 - 4 * q^23 + 12 * q^24 - 4 * q^26 - 8 * q^27 - 4 * q^28 - 4 * q^29 - 12 * q^31 - 4 * q^32 - 20 * q^34 - 4 * q^41 + 8 * q^42 + 8 * q^43 - 20 * q^44 + 20 * q^46 - 12 * q^48 + 8 * q^49 + 28 * q^51 - 16 * q^52 + 4 * q^53 - 8 * q^54 - 20 * q^56 + 24 * q^57 + 12 * q^62 + 12 * q^63 + 8 * q^66 - 16 * q^67 - 12 * q^68 - 32 * q^69 + 20 * q^71 + 28 * q^73 + 20 * q^74 + 8 * q^76 - 8 * q^77 + 8 * q^78 - 4 * q^79 - 4 * q^82 - 16 * q^83 + 32 * q^84 + 8 * q^86 - 16 * q^87 - 12 * q^88 + 28 * q^92 - 24 * q^93 - 24 * q^94 - 20 * q^96 - 24 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more