LMFDB - Embedded newform 425.2.m.a.76.1

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			76.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	425.76
Dual form			425.2.m.a.151.1

$q$-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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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	0.235147	−	0.971960i	$-0.424443\pi$
$2$	1.70711	−	1.70711i	1.20711	−	1.20711i	0.971960	−	0.235147i	$-0.0755571\pi$
$3$	−0.414214	+	1.00000i	−0.239146	+	0.577350i	−0.997195	−	0.0748477i	$-0.976153\pi$
$3$	−0.414214	+	1.00000i	−0.239146	+	0.577350i	0.758049	+	0.652198i	$0.226153\pi$
$4$		−	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	0.123479	−	0.992347i	$-0.460595\pi$
$7$	2.41421	−	1.00000i	0.912487	−	0.377964i	0.789008	+	0.614383i	$0.210595\pi$
$8$	−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	−0.999925	−	0.0122188i	$-0.996111\pi$
$11$	−1.00000	−	2.41421i	−0.301511	−	0.727913i	0.698414	−	0.715694i	$-0.253889\pi$
$12$	3.82843	+	1.58579i	1.10517	+	0.457777i
$13$		−	1.41421i		−	0.392232i	−0.980581	−	0.196116i	$-0.937167\pi$
$13$		−	1.41421i		−	0.392232i	0.980581	−	0.196116i	$-0.0628330\pi$
$14$	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	−0.636713	−	0.771101i	$-0.719706\pi$
$19$	0.585786	−	0.585786i	0.134389	−	0.134389i	0.771101	+	0.636713i	$0.219706\pi$
$20$		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	0.991724	+	0.128388i	$0.0409804\pi$
$23$	1.82843	+	4.41421i	0.381253	+	0.920427i	−0.610471	+	0.792039i	$0.709020\pi$
$24$	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	0.355323	−	0.934744i	$-0.384371\pi$
$29$	−0.292893	−	0.121320i	−0.0543889	−	0.0225286i	−0.409712	+	0.912215i	$0.634371\pi$
$30$		0			0
$31$	−3.00000	+	7.24264i	−0.538816	+	1.30082i	0.386734	+	0.922191i	$0.373603\pi$
$31$	−3.00000	+	7.24264i	−0.538816	+	1.30082i	−0.925550	+	0.378625i	$0.876397\pi$
$32$	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	0.310453	+	0.950589i	$0.399519\pi$
$37$	−3.53553	+	8.53553i	−0.581238	+	1.40323i	−0.891691	+	0.452644i	$0.850481\pi$
$38$		−	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	−0.293400	−	0.955990i	$-0.594787\pi$
$41$	1.12132	−	0.464466i	0.175121	−	0.0725374i	0.468521	+	0.883452i	$0.344787\pi$
$42$	4.82843	+	4.82843i	0.745042	+	0.745042i
$43$	0.585786	+	0.585786i	0.0893316	+	0.0893316i	0.750360	−	0.661029i	$-0.229880\pi$
$43$	0.585786	+	0.585786i	0.0893316	+	0.0893316i	−0.661029	+	0.750360i	$0.729880\pi$
$44$	−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	$-0.876895\pi$
$47$		−	5.17157i		−	0.754351i	0.926142	−	0.377176i	$-0.123105\pi$
$48$	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	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$	−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	0.927117	−	0.374772i	$-0.122279\pi$
$59$	4.24264	+	4.24264i	0.552345	+	0.552345i	−0.374772	+	0.927117i	$0.622279\pi$
$60$		0			0
$61$	−3.53553	+	1.46447i	−0.452679	+	0.187506i	−0.597361	−	0.801973i	$-0.703784\pi$
$61$	−3.53553	+	1.46447i	−0.452679	+	0.187506i	0.144682	+	0.989478i	$0.453784\pi$
$62$	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	−0.997838	−	0.0657178i	$-0.979066\pi$
$71$	−2.07107	+	5.00000i	−0.245791	+	0.593391i	0.752048	+	0.659109i	$0.229066\pi$
$72$		−	8.07107i		−	0.951184i
$73$	11.9497	+	4.94975i	1.39861	+	0.579324i	0.949391	−	0.314097i	$-0.101702\pi$
$73$	11.9497	+	4.94975i	1.39861	+	0.579324i	0.449221	+	0.893421i	$0.351702\pi$
$74$	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	0.992740	−	0.120283i	$-0.0383801\pi$
$79$	1.82843	+	4.41421i	0.205714	+	0.496638i	−0.787026	+	0.616920i	$0.788380\pi$
$80$		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	−0.995842	−	0.0910949i	$-0.970963\pi$
$83$	−8.24264	+	8.24264i	−0.904747	+	0.904747i	0.0910949	+	0.995842i	$0.470963\pi$
$84$	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	$-0.886506\pi$
$89$		−	6.58579i		−	0.698092i	0.937106	−	0.349046i	$-0.113494\pi$
$90$		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	−0.158150	−	0.987415i	$-0.550553\pi$
$97$	−9.53553	−	3.94975i	−0.968187	−	0.401036i	−0.810037	+	0.586379i	$0.800553\pi$
$98$			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	0.362572	−	0.931956i	$-0.381899\pi$
$107$	−0.414214	−	0.171573i	−0.0400435	−	0.0165866i	−0.402615	+	0.915369i	$0.631899\pi$
$108$	7.65685	+	18.4853i	0.736781	+	1.77875i
$109$	14.3640	−	5.94975i	1.37582	−	0.569882i	0.432458	−	0.901654i	$-0.357646\pi$
$109$	14.3640	−	5.94975i	1.37582	−	0.569882i	0.943360	+	0.331772i	$0.107646\pi$
$110$		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	−0.961886	−	0.273449i	$-0.911835\pi$
$113$	−5.05025	−	12.1924i	−0.475088	−	1.14696i	0.486799	−	0.873514i	$-0.338165\pi$
$114$	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	0.853881	−	0.520469i	$-0.174243\pi$
$127$	3.75736	+	3.75736i	0.333412	+	0.333412i	−0.520469	+	0.853881i	$0.674243\pi$
$128$	−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	−0.329010	−	0.944326i	$-0.606715\pi$
$131$	−14.0711	−	5.82843i	−1.22939	−	0.509232i	−0.900385	+	0.435094i	$0.856715\pi$
$132$		−	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	0.0453279	+	0.998972i	$0.485567\pi$
$139$	−8.17157	+	19.7279i	−0.693104	+	1.67330i	−0.738432	+	0.674328i	$0.764433\pi$
$140$		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	$-0.755342\pi$
$149$		−	16.9706i		−	1.39028i	0.718873	−	0.695141i	$-0.244658\pi$
$150$		0			0
$151$	5.07107	−	5.07107i	0.412678	−	0.412678i	−0.469993	−	0.882670i	$-0.655743\pi$
$151$	5.07107	−	5.07107i	0.412678	−	0.412678i	0.882670	+	0.469993i	$0.155743\pi$
$152$	−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	$-0.874081\pi$
$157$		−	9.65685i		−	0.770701i	0.922770	−	0.385350i	$-0.125919\pi$
$158$	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	−0.0544134	−	0.998518i	$-0.517329\pi$
$163$	7.82843	−	3.24264i	0.613170	−	0.253983i	0.667583	+	0.744535i	$0.267329\pi$
$164$	−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	−0.950470	−	0.310816i	$-0.899398\pi$
$167$	−0.757359	+	1.82843i	−0.0586062	+	0.141488i	0.891864	+	0.452304i	$0.149398\pi$
$168$	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	−0.960756	−	0.277393i	$-0.910530\pi$
$173$	−1.12132	+	2.70711i	−0.0852524	+	0.205818i	0.875504	+	0.483211i	$0.160530\pi$
$174$		−	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	0.530546	−	0.847656i	$-0.321987\pi$
$179$	−4.24264	−	4.24264i	−0.317110	−	0.317110i	−0.847656	+	0.530546i	$0.821987\pi$
$180$		0			0
$181$	−4.46447	−	10.7782i	−0.331841	−	0.801135i	−0.998446	−	0.0557243i	$-0.982253\pi$
$181$	−4.46447	−	10.7782i	−0.331841	−	0.801135i	0.666605	−	0.745411i	$-0.267747\pi$
$182$	−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	$-0.742498\pi$
$191$		−	20.0000i		−	1.44715i	0.690246	−	0.723575i	$-0.257502\pi$
$192$	9.82843	+	4.07107i	0.709306	+	0.293804i
$193$	−0.878680	−	2.12132i	−0.0632487	−	0.152696i	0.889095	−	0.457722i	$-0.151335\pi$
$193$	−0.878680	−	2.12132i	−0.0632487	−	0.152696i	−0.952344	+	0.305027i	$0.901335\pi$
$194$	−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	−0.224476	−	0.974480i	$-0.572067\pi$
$197$	4.29289	−	1.77817i	0.305856	−	0.126690i	0.530332	+	0.847790i	$0.322067\pi$
$198$	−4.41421	−	10.6569i	−0.313704	−	0.757350i
$199$	10.6569	+	4.41421i	0.755444	+	0.312915i	0.726961	−	0.686679i	$-0.240932\pi$
$199$	10.6569	+	4.41421i	0.755444	+	0.312915i	0.0284836	+	0.999594i	$0.490932\pi$
$200$		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	−0.938543	−	0.345163i	$-0.887824\pi$
$211$	−19.7279	+	8.17157i	−1.35813	+	0.562554i	−0.419583	+	0.907717i	$0.637824\pi$
$212$	−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	−0.812121	−	0.583489i	$-0.801687\pi$
$223$	−3.41421	+	3.41421i	−0.228633	+	0.228633i	0.583489	+	0.812121i	$0.301687\pi$
$224$	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	−0.975306	−	0.220858i	$-0.929114\pi$
$227$	−6.65685	−	16.0711i	−0.441831	−	1.06667i	0.533475	−	0.845816i	$-0.320886\pi$
$228$	3.17157	−	1.31371i	0.210043	−	0.0870025i
$229$	−12.1421	−	12.1421i	−0.802375	−	0.802375i	0.181091	−	0.983466i	$-0.442037\pi$
$229$	−12.1421	−	12.1421i	−0.802375	−	0.802375i	−0.983466	+	0.181091i	$0.942037\pi$
$230$		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	0.100453	−	0.994942i	$-0.467971\pi$
$233$	−8.12132	−	3.36396i	−0.532045	−	0.220380i	−0.632499	+	0.774561i	$0.717971\pi$
$234$		−	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	−0.961702	−	0.274097i	$-0.911621\pi$
$241$	−1.36396	+	3.29289i	−0.0878605	+	0.212114i	0.873842	+	0.486211i	$0.161621\pi$
$242$		−	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	$0.223772\pi$
$251$			20.4853i			1.29302i	−0.762906	+	0.646510i	$0.776228\pi$
$252$	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	−0.558552	−	0.829470i	$-0.688643\pi$
$257$	4.34315	−	4.34315i	0.270918	−	0.270918i	0.829470	+	0.558552i	$0.188643\pi$
$258$	−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	0.897729	−	0.440549i	$-0.145216\pi$
$263$	7.41421	+	7.41421i	0.457180	+	0.457180i	−0.440549	+	0.897729i	$0.645216\pi$
$264$	−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	−0.237939	−	0.971280i	$-0.576472\pi$
$269$	10.1213	−	24.4350i	0.617108	−	1.48983i	0.855047	−	0.518550i	$-0.173528\pi$
$270$		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	0.860129	−	0.510077i	$-0.170383\pi$
$277$	18.4350	+	7.63604i	1.10765	+	0.458805i	0.247525	+	0.968882i	$0.420383\pi$
$278$	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	0.665908	−	0.746034i	$-0.268044\pi$
$281$	−1.34315	−	1.34315i	−0.0801254	−	0.0801254i	−0.746034	+	0.665908i	$0.768044\pi$
$282$	12.4853	−	5.17157i	0.743488	−	0.307963i
$283$	7.14214	+	17.2426i	0.424556	+	1.02497i	0.980987	+	0.194075i	$0.0621704\pi$
$283$	7.14214	+	17.2426i	0.424556	+	1.02497i	−0.556431	+	0.830894i	$0.687830\pi$
$284$	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	$-0.882590\pi$
$293$		−	12.3431i		−	0.721094i	0.932741	−	0.360547i	$-0.117410\pi$
$294$	−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	0.935032	−	0.354562i	$-0.115370\pi$
$311$	23.7279	+	9.82843i	1.34549	+	0.557319i	0.410455	+	0.911881i	$0.365370\pi$
$312$	−2.58579	−	6.24264i	−0.146391	−	0.353420i
$313$	9.12132	−	3.77817i	0.515568	−	0.213555i	−0.109701	−	0.993965i	$-0.534989\pi$
$313$	9.12132	−	3.77817i	0.515568	−	0.213555i	0.625269	+	0.780410i	$0.284989\pi$
$314$	−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	−0.984163	−	0.177267i	$-0.943274\pi$
$317$	−7.36396	−	17.7782i	−0.413601	−	0.998522i	0.570562	−	0.821255i	$-0.306726\pi$
$318$	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	0.142546	−	0.989788i	$-0.454471\pi$
$331$	−15.4142	−	15.4142i	−0.847242	−	0.847242i	−0.989788	+	0.142546i	$0.954471\pi$
$332$	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	−0.854411	−	0.519597i	$-0.826082\pi$
$337$	2.15076	−	5.19239i	0.117159	−	0.282847i	0.971571	+	0.236750i	$0.0760821\pi$
$338$	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	−0.757415	−	0.652934i	$-0.773538\pi$
$347$	−15.4853	+	6.41421i	−0.831293	+	0.344333i	−0.0738788	+	0.997267i	$0.523538\pi$
$348$	−0.928932	−	0.928932i	−0.0497960	−	0.0497960i
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	0.782826	−	0.622240i	$-0.213777\pi$
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	−0.622240	+	0.782826i	$0.713777\pi$
$350$		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	$0.121524\pi$
$353$			14.0000i			0.745145i	−0.928003	+	0.372572i	$0.878476\pi$
$354$	−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	−0.0789921	+	0.996875i	$0.525170\pi$
$359$	−20.3848	+	20.3848i	−1.07587	+	1.07587i	−0.996875	+	0.0789921i	$0.974830\pi$
$360$		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	−0.273890	−	0.961761i	$-0.588310\pi$
$367$	4.07107	−	1.68629i	0.212508	−	0.0880237i	0.486398	+	0.873737i	$0.338310\pi$
$368$	−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	0.319816	−	0.947480i	$-0.396379\pi$
$379$	−2.41421	−	1.00000i	−0.124010	−	0.0513665i	−0.443826	+	0.896113i	$0.646379\pi$
$380$		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	0.984997	−	0.172571i	$-0.0552074\pi$
$383$	15.8995	+	15.8995i	0.812426	+	0.812426i	−0.172571	+	0.984997i	$0.555207\pi$
$384$	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	−0.890432	−	0.455116i	$-0.849598\pi$
$389$	−8.58579	+	8.58579i	−0.435317	+	0.435317i	0.455116	+	0.890432i	$0.349598\pi$
$390$		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	−0.997548	−	0.0699884i	$-0.977704\pi$
$397$	−6.80761	−	16.4350i	−0.341664	−	0.824850i	0.655884	−	0.754862i	$-0.272296\pi$
$398$	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	−0.396015	−	0.918244i	$-0.629607\pi$
$401$	−0.535534	+	0.221825i	−0.0267433	+	0.0110774i	0.369272	+	0.929321i	$0.379607\pi$
$402$	−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	0.748959	−	0.662617i	$-0.230554\pi$
$419$	−5.10051	−	12.3137i	−0.249176	−	0.601564i	−0.998135	+	0.0610528i	$0.980554\pi$
$420$		0			0
$421$			14.5858i			0.710868i	0.934701	+	0.355434i	$0.115667\pi$
$421$			14.5858i			0.710868i	−0.934701	+	0.355434i	$0.884333\pi$
$422$	−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	0.976844	−	0.213954i	$-0.0686343\pi$
$431$	2.79899	+	6.75736i	0.134823	+	0.325491i	−0.842021	+	0.539445i	$0.818634\pi$
$432$	14.4853	−	6.00000i	0.696923	−	0.288675i
$433$	−14.7279	−	14.7279i	−0.707779	−	0.707779i	0.258289	−	0.966068i	$-0.416841\pi$
$433$	−14.7279	−	14.7279i	−0.707779	−	0.707779i	−0.966068	+	0.258289i	$0.916841\pi$
$434$	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	−0.990763	−	0.135604i	$-0.956703\pi$
$439$	−4.07107	+	9.82843i	−0.194301	+	0.469085i	0.796462	+	0.604689i	$0.206703\pi$
$440$		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	−0.102614	−	0.994721i	$-0.532721\pi$
$449$	11.1924	−	4.63604i	0.528201	−	0.218788i	0.630815	+	0.775933i	$0.282721\pi$
$450$		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	−0.890554	−	0.454877i	$-0.849683\pi$
$457$	−9.31371	+	9.31371i	−0.435677	+	0.435677i	0.454877	+	0.890554i	$0.349683\pi$
$458$	−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	−0.190013	−	0.981782i	$-0.560853\pi$
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	0.981782	+	0.190013i	$0.0608529\pi$
$462$	6.82843	−	16.4853i	0.317687	−	0.766965i
$463$			14.6274i			0.679794i	0.940463	+	0.339897i	$0.110392\pi$
$463$			14.6274i			0.679794i	−0.940463	+	0.339897i	$0.889608\pi$
$464$	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	−0.997543	−	0.0700588i	$-0.977681\pi$
$467$	−23.0711	−	23.0711i	−1.06760	−	1.06760i	−0.0700588	−	0.997543i	$-0.522319\pi$
$468$	−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	−0.872446	−	0.488711i	$-0.837467\pi$
$479$	1.97056	−	4.75736i	0.0900373	−	0.217369i	0.962483	+	0.271342i	$0.0874673\pi$
$480$		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	−0.969859	−	0.243667i	$-0.921650\pi$
$487$	−10.0711	−	24.3137i	−0.456364	−	1.10176i	0.513495	−	0.858092i	$-0.328350\pi$
$488$	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	0.205698	−	0.978615i	$-0.434053\pi$
$491$	26.2426	−	26.2426i	1.18431	−	1.18431i	0.978615	−	0.205698i	$-0.0659466\pi$
$492$	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	−0.994131	−	0.108186i	$-0.965496\pi$
$499$	−8.21320	−	19.8284i	−0.367673	−	0.887642i	0.626457	−	0.779456i	$-0.284504\pi$
$500$		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	0.103273	−	0.994653i	$-0.467068\pi$
$503$	19.7279	−	8.17157i	0.879625	−	0.364352i	0.776351	+	0.630301i	$0.217068\pi$
$504$	−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	0.999631	+	0.0271607i	$0.00864660\pi$
$521$	7.12132	+	17.1924i	0.311991	+	0.753212i	−0.687640	+	0.726051i	$0.741353\pi$
$522$	−1.29289	−	0.535534i	−0.0565884	−	0.0234397i
$523$		−	1.17157i		−	0.0512293i	−0.999672	−	0.0256147i	$-0.991846\pi$
$523$		−	1.17157i		−	0.0512293i	0.999672	−	0.0256147i	$-0.00815429\pi$
$524$	−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	0.696781	+	0.717284i	$0.254615\pi$
$541$	−7.05025	+	17.0208i	−0.303114	+	0.731782i	−0.999895	+	0.0144979i	$0.995385\pi$
$542$	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	−0.976199	−	0.216875i	$-0.930413\pi$
$547$	−3.10051	+	7.48528i	−0.132568	+	0.320048i	0.843631	+	0.536923i	$0.180413\pi$
$548$		−	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	$0.137470\pi$
$557$			19.7574i			0.837146i	−0.908183	+	0.418573i	$0.862530\pi$
$558$	−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	−0.0368464	+	0.999321i	$0.511731\pi$
$563$	−24.5858	+	24.5858i	−1.03617	+	1.03617i	−0.999321	+	0.0368464i	$0.988269\pi$
$564$	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	0.862690	−	0.505734i	$-0.168778\pi$
$569$	8.51472	+	8.51472i	0.356956	+	0.356956i	−0.505734	+	0.862690i	$0.668778\pi$
$570$		0			0
$571$	−3.92893	+	1.62742i	−0.164421	+	0.0681053i	−0.463376	−	0.886162i	$-0.653362\pi$
$571$	−3.92893	+	1.62742i	−0.164421	+	0.0681053i	0.298955	+	0.954267i	$0.403362\pi$
$572$	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	−0.911747	−	0.410753i	$-0.865266\pi$
$587$	−32.0416	−	32.0416i	−1.32250	−	1.32250i	−0.410753	−	0.911747i	$-0.634734\pi$
$588$	−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	−0.869448	−	0.494025i	$-0.835525\pi$
$593$	−9.14214	+	9.14214i	−0.375423	+	0.375423i	0.494025	+	0.869448i	$0.335525\pi$
$594$	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	$0.0696638\pi$
$599$			10.6274i			0.434224i	−0.976147	+	0.217112i	$0.930336\pi$
$600$		0			0
$601$	−3.22183	−	7.77817i	−0.131421	−	0.317278i	0.844447	−	0.535639i	$-0.179929\pi$
$601$	−3.22183	−	7.77817i	−0.131421	−	0.317278i	−0.975868	+	0.218360i	$0.929929\pi$
$602$	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	0.0535937	−	0.998563i	$-0.482932\pi$
$607$	−15.1421	−	6.27208i	−0.614600	−	0.254576i	−0.668194	+	0.743987i	$0.732932\pi$
$608$		−	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	0.436509	−	0.899700i	$-0.356215\pi$
$617$	2.70711	+	1.12132i	0.108984	+	0.0451427i	−0.327525	+	0.944842i	$0.606215\pi$
$618$	−12.4853	−	30.1421i	−0.502232	−	1.21249i
$619$	26.3137	−	10.8995i	1.05764	−	0.438088i	0.215025	−	0.976609i	$-0.431017\pi$
$619$	26.3137	−	10.8995i	1.05764	−	0.438088i	0.842612	+	0.538521i	$0.181017\pi$
$620$		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	−0.986844	−	0.161678i	$-0.948309\pi$
$631$	−20.7279	+	20.7279i	−0.825166	+	0.825166i	0.161678	+	0.986844i	$0.448309\pi$
$632$	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	−0.535487	−	0.844544i	$-0.679872\pi$
$641$	−38.2635	−	15.8492i	−1.51132	−	0.626007i	−0.975829	+	0.218536i	$0.929872\pi$
$642$		−	1.17157i		−	0.0462383i
$643$	−11.0416	+	26.6569i	−0.435439	+	1.05124i	0.542066	+	0.840336i	$0.317642\pi$
$643$	−11.0416	+	26.6569i	−0.435439	+	1.05124i	−0.977506	+	0.210908i	$0.932358\pi$
$644$	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	−0.547770	−	0.836629i	$-0.684523\pi$
$653$	−8.77817	+	3.63604i	−0.343517	+	0.142289i	0.204254	+	0.978918i	$0.434523\pi$
$654$	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	$-0.947151\pi$
$659$		−	8.48528i		−	0.330540i	0.986248	−	0.165270i	$-0.0528495\pi$
$660$		0			0
$661$	0.857864	−	0.857864i	0.0333671	−	0.0333671i	−0.690226	−	0.723593i	$-0.742489\pi$
$661$	0.857864	−	0.857864i	0.0333671	−	0.0333671i	0.723593	+	0.690226i	$0.242489\pi$
$662$	−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	−0.460699	−	0.887556i	$-0.652401\pi$
$673$	−4.12132	+	1.70711i	−0.158865	+	0.0658041i	0.301834	+	0.953361i	$0.402401\pi$
$674$	−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	−0.349324	−	0.937002i	$-0.613589\pi$
$677$	14.5772	−	35.1924i	0.560246	−	1.35255i	0.909570	−	0.415551i	$-0.136411\pi$
$678$	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	−0.648609	−	0.761122i	$-0.724649\pi$
$683$	9.10051	−	21.9706i	0.348221	−	0.840680i	0.996830	−	0.0795585i	$-0.0253510\pi$
$684$		−	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	0.709832	−	0.704371i	$-0.248771\pi$
$691$	−7.62742	−	18.4142i	−0.290161	−	0.700510i	−0.999993	+	0.00386139i	$0.998771\pi$
$692$	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	$-0.747823\pi$
$701$		−	37.6985i		−	1.42385i	0.702254	−	0.711926i	$-0.252177\pi$
$702$	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	0.761864	−	0.647736i	$-0.224284\pi$
$709$	22.4350	+	9.29289i	0.842565	+	0.349002i	0.0807007	+	0.996738i	$0.474284\pi$
$710$		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	−0.289112	−	0.957295i	$-0.593360\pi$
$719$	−31.3848	−	13.0000i	−1.17045	−	0.484818i	−0.881343	+	0.472477i	$0.843360\pi$
$720$		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	$0.294892\pi$
$727$			43.1127i			1.59896i	−0.600692	+	0.799481i	$0.705108\pi$
$728$	−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	−0.0570509	−	0.998371i	$-0.518170\pi$
$733$	25.4853	−	25.4853i	0.941320	−	0.941320i	0.998371	+	0.0570509i	$0.0181697\pi$
$734$	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	0.934805	−	0.355161i	$-0.115574\pi$
$739$	15.7574	+	15.7574i	0.579644	+	0.579644i	−0.355161	+	0.934805i	$0.615574\pi$
$740$		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	−0.999457	−	0.0329473i	$-0.989511\pi$
$743$	−47.1421	−	19.5269i	−1.72948	−	0.716373i	−0.730020	−	0.683426i	$-0.760489\pi$
$744$			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	−0.125889	−	0.992044i	$-0.540178\pi$
$751$	18.2132	−	43.9706i	0.664609	−	1.60451i	0.790498	−	0.612464i	$-0.209822\pi$
$752$			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	0.739043	−	0.673658i	$-0.235278\pi$
$757$	1.79899	+	1.79899i	0.0653854	+	0.0653854i	−0.673658	+	0.739043i	$0.735278\pi$
$758$	−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	$0.239449\pi$
$761$			37.6985i			1.36657i	−0.730152	+	0.683285i	$0.760551\pi$
$762$	−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	$-0.926294\pi$
$769$		−	12.7279i		−	0.458981i	0.973311	−	0.229490i	$-0.0737059\pi$
$770$		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	0.717563	−	0.696494i	$-0.245258\pi$
$773$	0.585786	+	0.585786i	0.0210693	+	0.0210693i	−0.696494	+	0.717563i	$0.745258\pi$
$774$	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	0.694688	−	0.719311i	$-0.255542\pi$
$787$	19.0000	+	7.87006i	0.677277	+	0.280537i	−0.0174112	+	0.999848i	$0.505542\pi$
$788$	−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	−0.316933	−	0.948448i	$-0.602653\pi$
$797$	17.8284	−	17.8284i	0.631515	−	0.631515i	0.948448	+	0.316933i	$0.102653\pi$
$798$	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	−0.873321	−	0.487146i	$-0.838038\pi$
$809$	−32.6066	+	13.5061i	−1.14639	+	0.474849i	−0.273067	+	0.961995i	$0.588038\pi$
$810$		0			0
$811$	−50.9411	−	21.1005i	−1.78878	−	0.740939i	−0.990304	−	0.138919i	$-0.955637\pi$
$811$	−50.9411	−	21.1005i	−1.78878	−	0.740939i	−0.798481	−	0.602020i	$-0.794363\pi$
$812$			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	0.903456	−	0.428682i	$-0.141022\pi$
$821$	35.5061	+	14.7071i	1.23917	+	0.513282i	0.335716	+	0.941963i	$0.391022\pi$
$822$	16.7279	+	40.3848i	0.583453	+	1.40858i
$823$	−9.00000	+	3.72792i	−0.313720	+	0.129947i	−0.533987	−	0.845492i	$-0.679307\pi$
$823$	−9.00000	+	3.72792i	−0.313720	+	0.129947i	0.220267	+	0.975440i	$0.429307\pi$
$824$	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	0.847627	+	0.530593i	$0.178031\pi$
$827$	17.9289	+	43.2843i	0.623450	+	1.50514i	−0.224177	+	0.974549i	$0.571969\pi$
$828$	30.8995	+	12.7990i	1.07383	+	0.444796i
$829$			53.9411i			1.87345i	0.350062	+	0.936726i	$0.386160\pi$
$829$			53.9411i			1.87345i	−0.350062	+	0.936726i	$0.613840\pi$
$830$		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	0.773643	−	0.633622i	$-0.218432\pi$
$839$	−6.41421	−	15.4853i	−0.221443	−	0.534611i	−0.995086	+	0.0990102i	$0.968432\pi$
$840$		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	−0.747166	−	0.664637i	$-0.768586\pi$
$853$	7.33452	−	17.7071i	0.251129	−	0.606280i	0.998296	+	0.0583572i	$0.0185862\pi$
$854$			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	−0.232105	−	0.972691i	$-0.574561\pi$
$857$	8.53553	−	3.53553i	0.291568	−	0.120772i	0.523673	+	0.851919i	$0.324561\pi$
$858$	−6.82843	−	6.82843i	−0.233119	−	0.233119i
$859$	24.7279	+	24.7279i	0.843706	+	0.843706i	0.989339	−	0.145633i	$-0.0465218\pi$
$859$	24.7279	+	24.7279i	0.843706	+	0.843706i	−0.145633	+	0.989339i	$0.546522\pi$
$860$		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	$0.0578948\pi$
$863$			10.6274i			0.361761i	−0.983505	+	0.180881i	$0.942105\pi$
$864$	−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	−0.986288	−	0.165031i	$-0.947228\pi$
$877$	−46.4056	+	19.2218i	−1.56701	+	0.649075i	−0.580717	+	0.814105i	$0.697228\pi$
$878$	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	−0.544127	−	0.839003i	$-0.683139\pi$
$881$	12.8787	−	31.0919i	0.433894	−	1.04751i	0.978020	−	0.208509i	$-0.0668611\pi$
$882$	−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	0.338843	+	0.940843i	$0.389965\pi$
$887$	−16.8579	+	40.6985i	−0.566032	+	1.36652i	−0.904875	+	0.425678i	$0.860035\pi$
$888$			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	0.815226	−	0.579143i	$-0.196613\pi$
$907$	−5.14214	−	12.4142i	−0.170742	−	0.412207i	−0.985968	+	0.166936i	$0.946613\pi$
$908$	−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	−0.294141	−	0.955762i	$-0.595033\pi$
$911$	5.24264	−	2.17157i	0.173696	−	0.0719474i	0.467837	+	0.883815i	$0.345033\pi$
$912$	−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	0.994571	−	0.104060i	$-0.0331835\pi$
$929$	6.63604	+	16.0208i	0.217721	+	0.525626i	−0.776850	+	0.629686i	$0.783183\pi$
$930$		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	−0.949704	−	0.313148i	$-0.898616\pi$
$937$	−19.4853	+	19.4853i	−0.636556	+	0.636556i	0.313148	+	0.949704i	$0.398616\pi$
$938$	−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	−0.950786	−	0.309848i	$-0.899722\pi$
$941$	−15.2635	−	36.8492i	−0.497574	−	1.20125i	0.453212	−	0.891403i	$-0.350278\pi$
$942$	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	−0.128168	−	0.991752i	$-0.540910\pi$
$947$	−28.3137	−	11.7279i	−0.920072	−	0.381106i	−0.791904	+	0.610646i	$0.790910\pi$
$948$			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	−0.00725952	−	0.999974i	$-0.502311\pi$
$967$	30.8701	−	30.8701i	0.992714	−	0.992714i	0.999974	+	0.00725952i	$0.00231080\pi$
$968$	−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	−0.192869	+	0.981224i	$0.561779\pi$
$971$	−36.5858	+	36.5858i	−1.17409	+	1.17409i	−0.981224	+	0.192869i	$0.938221\pi$
$972$	−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	0.992290	−	0.123936i	$-0.0395519\pi$
$977$	27.1421	+	27.1421i	0.868354	+	0.868354i	−0.123936	+	0.992290i	$0.539552\pi$
$978$	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	−0.972114	−	0.234510i	$-0.924652\pi$
$983$	−3.72792	+	9.00000i	−0.118902	+	0.287055i	0.853212	+	0.521565i	$0.174652\pi$
$984$	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	0.890503	−	0.454977i	$-0.150352\pi$
$991$	37.7279	+	15.6274i	1.19847	+	0.496421i	0.307964	+	0.951398i	$0.400352\pi$
$992$	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	0.962886	−	0.269908i	$-0.0869934\pi$
$997$	2.87868	+	6.94975i	0.0911687	+	0.220101i	−0.871717	+	0.490009i	$0.836993\pi$
$998$	−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.76.1		4
5.2	odd	4		425.2.n.b.399.1		4
5.3	odd	4		425.2.n.a.399.1		4
5.4	even	2		17.2.d.a.8.1	✓	4
15.14	odd	2		153.2.l.c.127.1		4
17.7	odd	16		7225.2.a.u.1.2		4
17.10	odd	16		7225.2.a.u.1.1		4
17.15	even	8	inner	425.2.m.a.151.1		4
20.19	odd	2		272.2.v.d.161.1		4
35.4	even	6		833.2.v.b.569.1		8
35.9	even	6		833.2.v.b.263.1		8
35.19	odd	6		833.2.v.a.263.1		8
35.24	odd	6		833.2.v.a.569.1		8
35.34	odd	2		833.2.l.a.246.1		4
85.4	even	4		289.2.d.b.179.1		4
85.9	even	8		289.2.d.c.155.1		4
85.14	odd	16		289.2.c.c.38.3		8
85.19	even	8		289.2.d.a.134.1		4
85.24	odd	16		289.2.a.f.1.3		4
85.29	odd	16		289.2.c.c.251.1		8
85.32	odd	8		425.2.n.a.49.1		4
85.39	odd	16		289.2.c.c.251.2		8
85.44	odd	16		289.2.a.f.1.4		4
85.49	even	8		17.2.d.a.15.1	yes	4
85.54	odd	16		289.2.c.c.38.4		8
85.59	even	8		289.2.d.b.155.1		4
85.64	even	4		289.2.d.c.179.1		4
85.74	odd	16		289.2.b.b.288.1		4
85.79	odd	16		289.2.b.b.288.2		4
85.83	odd	8		425.2.n.b.49.1		4
85.84	even	2		289.2.d.a.110.1		4
255.44	even	16		2601.2.a.bb.1.2		4
255.134	odd	8		153.2.l.c.100.1		4
255.194	even	16		2601.2.a.bb.1.1		4
340.219	odd	8		272.2.v.d.49.1		4
340.279	even	16		4624.2.a.bp.1.3		4
340.299	even	16		4624.2.a.bp.1.2		4
595.219	even	24		833.2.v.b.508.1		8
595.304	odd	24		833.2.v.a.814.1		8
595.389	even	24		833.2.v.b.814.1		8
595.474	odd	24		833.2.v.a.508.1		8
595.559	odd	8		833.2.l.a.491.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	5.4	even	2
17.2.d.a.15.1	yes	4	85.49	even	8
153.2.l.c.100.1		4	255.134	odd	8
153.2.l.c.127.1		4	15.14	odd	2
272.2.v.d.49.1		4	340.219	odd	8
272.2.v.d.161.1		4	20.19	odd	2
289.2.a.f.1.3		4	85.24	odd	16
289.2.a.f.1.4		4	85.44	odd	16
289.2.b.b.288.1		4	85.74	odd	16
289.2.b.b.288.2		4	85.79	odd	16
289.2.c.c.38.3		8	85.14	odd	16
289.2.c.c.38.4		8	85.54	odd	16
289.2.c.c.251.1		8	85.29	odd	16
289.2.c.c.251.2		8	85.39	odd	16
289.2.d.a.110.1		4	85.84	even	2
289.2.d.a.134.1		4	85.19	even	8
289.2.d.b.155.1		4	85.59	even	8
289.2.d.b.179.1		4	85.4	even	4
289.2.d.c.155.1		4	85.9	even	8
289.2.d.c.179.1		4	85.64	even	4
425.2.m.a.76.1		4	1.1	even	1	trivial
425.2.m.a.151.1		4	17.15	even	8	inner
425.2.n.a.49.1		4	85.32	odd	8
425.2.n.a.399.1		4	5.3	odd	4
425.2.n.b.49.1		4	85.83	odd	8
425.2.n.b.399.1		4	5.2	odd	4
833.2.l.a.246.1		4	35.34	odd	2
833.2.l.a.491.1		4	595.559	odd	8
833.2.v.a.263.1		8	35.19	odd	6
833.2.v.a.508.1		8	595.474	odd	24
833.2.v.a.569.1		8	35.24	odd	6
833.2.v.a.814.1		8	595.304	odd	24
833.2.v.b.263.1		8	35.9	even	6
833.2.v.b.508.1		8	595.219	even	24
833.2.v.b.569.1		8	35.4	even	6
833.2.v.b.814.1		8	595.389	even	24
2601.2.a.bb.1.1		4	255.194	even	16
2601.2.a.bb.1.2		4	255.44	even	16
4624.2.a.bp.1.2		4	340.299	even	16
4624.2.a.bp.1.3		4	340.279	even	16
7225.2.a.u.1.1		4	17.10	odd	16
7225.2.a.u.1.2		4	17.7	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

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