LMFDB - Embedded newform 425.2.m.d.26.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			26.4
Character	$\chi$	$=$	425.26
Dual form			425.2.m.d.376.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.982785 - 0.982785i) q^{2} +(-0.102388 - 0.0424107i) q^{3} +0.0682683i q^{4} +(-0.142306 + 0.0589452i) q^{6} +(0.656642 + 1.58527i) q^{7} +(2.03266 + 2.03266i) q^{8} +(-2.11264 - 2.11264i) q^{9} +O(q^{10})$	\(q+(0.982785 - 0.982785i) q^{2} +(-0.102388 - 0.0424107i) q^{3} +0.0682683i q^{4} +(-0.142306 + 0.0589452i) q^{6} +(0.656642 + 1.58527i) q^{7} +(2.03266 + 2.03266i) q^{8} +(-2.11264 - 2.11264i) q^{9} +(5.35924 - 2.21987i) q^{11} +(0.00289530 - 0.00698988i) q^{12} +1.25411i q^{13} +(2.20332 + 0.912645i) q^{14} +3.85880 q^{16} +(3.68474 + 1.85005i) q^{17} -4.15253 q^{18} +(1.99782 - 1.99782i) q^{19} -0.190162i q^{21} +(3.08532 - 7.44863i) q^{22} +(-1.89620 + 0.785431i) q^{23} +(-0.121915 - 0.294328i) q^{24} +(1.23252 + 1.23252i) q^{26} +(0.253943 + 0.613073i) q^{27} +(-0.108224 + 0.0448278i) q^{28} +(-1.99220 + 4.80961i) q^{29} +(-2.64434 - 1.09532i) q^{31} +(-0.272952 + 0.272952i) q^{32} -0.642871 q^{33} +(5.43951 - 1.80310i) q^{34} +(0.144226 - 0.144226i) q^{36} +(-5.82896 - 2.41443i) q^{37} -3.92685i q^{38} +(0.0531875 - 0.128406i) q^{39} +(-3.61688 - 8.73191i) q^{41} +(-0.186889 - 0.186889i) q^{42} +(-5.25643 - 5.25643i) q^{43} +(0.151547 + 0.365866i) q^{44} +(-1.09165 + 2.63546i) q^{46} +7.63491i q^{47} +(-0.395097 - 0.163655i) q^{48} +(2.86784 - 2.86784i) q^{49} +(-0.298813 - 0.345696i) q^{51} -0.0856157 q^{52} +(-5.09637 + 5.09637i) q^{53} +(0.852091 + 0.352948i) q^{54} +(-1.88759 + 4.55706i) q^{56} +(-0.289282 + 0.119825i) q^{57} +(2.76890 + 6.68472i) q^{58} +(-1.54321 - 1.54321i) q^{59} +(2.19586 + 5.30128i) q^{61} +(-3.67528 + 1.52235i) q^{62} +(1.96186 - 4.73635i) q^{63} +8.25411i q^{64} +(-0.631803 + 0.631803i) q^{66} -2.46660 q^{67} +(-0.126300 + 0.251551i) q^{68} +0.227460 q^{69} +(-12.4522 - 5.15787i) q^{71} -8.58855i q^{72} +(2.23393 - 5.39319i) q^{73} +(-8.10148 + 3.35574i) q^{74} +(0.136388 + 0.136388i) q^{76} +(7.03820 + 7.03820i) q^{77} +(-0.0739236 - 0.178467i) q^{78} +(-3.62361 + 1.50095i) q^{79} +8.88961i q^{81} +(-12.1362 - 5.02698i) q^{82} +(6.29967 - 6.29967i) q^{83} +0.0129821 q^{84} -10.3319 q^{86} +(0.407958 - 0.407958i) q^{87} +(15.4058 + 6.38128i) q^{88} -14.3079i q^{89} +(-1.98810 + 0.823498i) q^{91} +(-0.0536200 - 0.129450i) q^{92} +(0.224296 + 0.224296i) q^{93} +(7.50348 + 7.50348i) q^{94} +(0.0395233 - 0.0163711i) q^{96} +(-3.25033 + 7.84699i) q^{97} -5.63693i q^{98} +(-16.0119 - 6.63234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^6 + 12 * q^9	$ 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31} + 60 q^{32} - 48 q^{33} + 16 q^{34} + 60 q^{36} + 12 q^{37} + 8 q^{39} - 20 q^{41} - 12 q^{42} - 32 q^{43} + 64 q^{44} - 40 q^{46} + 40 q^{48} + 24 q^{49} + 16 q^{51} + 48 q^{52} + 12 q^{53} - 20 q^{54} - 32 q^{56} - 68 q^{57} + 16 q^{58} - 16 q^{59} - 64 q^{61} - 100 q^{62} + 44 q^{63} - 72 q^{66} - 40 q^{67} - 20 q^{68} - 48 q^{69} - 24 q^{71} + 32 q^{74} + 52 q^{76} - 24 q^{77} + 16 q^{78} - 48 q^{79} - 100 q^{82} - 12 q^{83} - 40 q^{84} - 16 q^{86} - 24 q^{87} - 4 q^{88} + 24 q^{91} + 88 q^{92} + 32 q^{93} - 40 q^{94} + 132 q^{96} + 88 q^{97} - 80 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.982785	−	0.982785i	0.694934	−	0.694934i	−0.268380	−	0.963313i	$-0.586488\pi$
$2$	0.982785	−	0.982785i	0.694934	−	0.694934i	0.963313	+	0.268380i	$0.0864881\pi$
$3$	−0.102388	−	0.0424107i	−0.0591140	−	0.0244858i	0.352931	−	0.935650i	$-0.385185\pi$
$3$	−0.102388	−	0.0424107i	−0.0591140	−	0.0244858i	−0.412045	+	0.911164i	$0.635185\pi$
$4$			0.0682683i			0.0341341i
$5$		0			0
$5$		0			0
$6$	−0.142306	+	0.0589452i	−0.0580964	+	0.0240643i
$7$	0.656642	+	1.58527i	0.248187	+	0.599177i	0.998050	−	0.0624163i	$-0.0198806\pi$
$7$	0.656642	+	1.58527i	0.248187	+	0.599177i	−0.749863	+	0.661593i	$0.769881\pi$
$8$	2.03266	+	2.03266i	0.718655	+	0.718655i
$9$	−2.11264	−	2.11264i	−0.704212	−	0.704212i
$10$		0			0
$11$	5.35924	−	2.21987i	1.61587	−	0.669316i	0.622327	−	0.782758i	$-0.286188\pi$
$11$	5.35924	−	2.21987i	1.61587	−	0.669316i	0.993545	+	0.113442i	$0.0361876\pi$
$12$	0.00289530	−	0.00698988i	0.000835803	−	0.00201781i
$13$			1.25411i			0.347827i	0.984761	+	0.173913i	$0.0556412\pi$
$13$			1.25411i			0.347827i	−0.984761	+	0.173913i	$0.944359\pi$
$14$	2.20332	+	0.912645i	0.588862	+	0.243915i
$15$		0			0
$16$	3.85880			0.964701
$17$	3.68474	+	1.85005i	0.893681	+	0.448703i
$17$	3.68474	+	1.85005i	0.893681	+	0.448703i
$18$	−4.15253			−0.978761
$19$	1.99782	−	1.99782i	0.458331	−	0.458331i	−0.439776	−	0.898107i	$-0.644942\pi$
$19$	1.99782	−	1.99782i	0.458331	−	0.458331i	0.898107	+	0.439776i	$0.144942\pi$
$20$		0			0
$21$		−	0.190162i		−	0.0414968i
$22$	3.08532	−	7.44863i	0.657793	−	1.58805i
$23$	−1.89620	+	0.785431i	−0.395385	+	0.163774i	−0.571512	−	0.820594i	$-0.693643\pi$
$23$	−1.89620	+	0.785431i	−0.395385	+	0.163774i	0.176127	+	0.984367i	$0.443643\pi$
$24$	−0.121915	−	0.294328i	−0.0248857	−	0.0600794i
$25$		0			0
$26$	1.23252	+	1.23252i	0.241716	+	0.241716i
$27$	0.253943	+	0.613073i	0.0488714	+	0.117986i
$28$	−0.108224	+	0.0448278i	−0.0204524	+	0.00847165i
$29$	−1.99220	+	4.80961i	−0.369943	+	0.893122i	0.623816	+	0.781572i	$0.285582\pi$
$29$	−1.99220	+	4.80961i	−0.369943	+	0.893122i	−0.993759	+	0.111550i	$0.964418\pi$
$30$		0			0
$31$	−2.64434	−	1.09532i	−0.474937	−	0.196725i	0.132358	−	0.991202i	$-0.457745\pi$
$31$	−2.64434	−	1.09532i	−0.474937	−	0.196725i	−0.607295	+	0.794477i	$0.707745\pi$
$32$	−0.272952	+	0.272952i	−0.0482516	+	0.0482516i
$33$	−0.642871			−0.111909
$34$	5.43951	−	1.80310i	0.932868	−	0.309230i
$35$		0			0
$36$	0.144226	−	0.144226i	0.0240377	−	0.0240377i
$37$	−5.82896	−	2.41443i	−0.958275	−	0.396931i	−0.151940	−	0.988390i	$-0.548552\pi$
$37$	−5.82896	−	2.41443i	−0.958275	−	0.396931i	−0.806335	+	0.591459i	$0.798552\pi$
$38$		−	3.92685i		−	0.637019i
$39$	0.0531875	−	0.128406i	0.00851682	−	0.0205614i
$40$		0			0
$41$	−3.61688	−	8.73191i	−0.564861	−	1.36370i	−0.905838	−	0.423624i	$-0.860758\pi$
$41$	−3.61688	−	8.73191i	−0.564861	−	1.36370i	0.340977	−	0.940072i	$-0.389242\pi$
$42$	−0.186889	−	0.186889i	−0.0288375	−	0.0288375i
$43$	−5.25643	−	5.25643i	−0.801597	−	0.801597i	0.181748	−	0.983345i	$-0.441825\pi$
$43$	−5.25643	−	5.25643i	−0.801597	−	0.801597i	−0.983345	+	0.181748i	$0.941825\pi$
$44$	0.151547	+	0.365866i	0.0228465	+	0.0551564i
$45$		0			0
$46$	−1.09165	+	2.63546i	−0.160954	+	0.388578i
$47$			7.63491i			1.11367i	0.830624	+	0.556833i	$0.187984\pi$
$47$			7.63491i			1.11367i	−0.830624	+	0.556833i	$0.812016\pi$
$48$	−0.395097	−	0.163655i	−0.0570273	−	0.0236215i
$49$	2.86784	−	2.86784i	0.409691	−	0.409691i
$50$		0			0
$51$	−0.298813	−	0.345696i	−0.0418422	−	0.0484072i
$52$	−0.0856157			−0.0118728
$53$	−5.09637	+	5.09637i	−0.700040	+	0.700040i	−0.964419	−	0.264379i	$-0.914833\pi$
$53$	−5.09637	+	5.09637i	−0.700040	+	0.700040i	0.264379	+	0.964419i	$0.414833\pi$
$54$	0.852091	+	0.352948i	0.115955	+	0.0480301i
$55$		0			0
$56$	−1.88759	+	4.55706i	−0.252240	+	0.608962i
$57$	−0.289282	+	0.119825i	−0.0383164	+	0.0158712i
$58$	2.76890	+	6.68472i	0.363574	+	0.877746i
$59$	−1.54321	−	1.54321i	−0.200908	−	0.200908i	0.599481	−	0.800389i	$-0.295374\pi$
$59$	−1.54321	−	1.54321i	−0.200908	−	0.200908i	−0.800389	+	0.599481i	$0.795374\pi$
$60$		0			0
$61$	2.19586	+	5.30128i	0.281152	+	0.678760i	0.999863	−	0.0165485i	$-0.00526780\pi$
$61$	2.19586	+	5.30128i	0.281152	+	0.678760i	−0.718712	+	0.695308i	$0.755268\pi$
$62$	−3.67528	+	1.52235i	−0.466761	+	0.193339i
$63$	1.96186	−	4.73635i	0.247171	−	0.596724i
$64$			8.25411i			1.03176i
$65$		0			0
$66$	−0.631803	+	0.631803i	−0.0777696	+	0.0777696i
$67$	−2.46660			−0.301343			−0.150672	−	0.988584i	$-0.548144\pi$
$67$	−2.46660			−0.301343			−0.150672	+	0.988584i	$0.548144\pi$
$68$	−0.126300	+	0.251551i	−0.0153161	+	0.0305050i
$69$	0.227460			0.0273829
$70$		0			0
$71$	−12.4522	−	5.15787i	−1.47780	−	0.612126i	−0.509180	−	0.860660i	$-0.670051\pi$
$71$	−12.4522	−	5.15787i	−1.47780	−	0.612126i	−0.968623	+	0.248534i	$0.920051\pi$
$72$		−	8.58855i		−	1.01217i
$73$	2.23393	−	5.39319i	0.261462	−	0.631225i	−0.737567	−	0.675273i	$-0.764026\pi$
$73$	2.23393	−	5.39319i	0.261462	−	0.631225i	0.999029	+	0.0440485i	$0.0140256\pi$
$74$	−8.10148	+	3.35574i	−0.941778	+	0.390097i
$75$		0			0
$76$	0.136388	+	0.136388i	0.0156447	+	0.0156447i
$77$	7.03820	+	7.03820i	0.802077	+	0.802077i
$78$	−0.0739236	−	0.178467i	−0.00837020	−	0.0202075i
$79$	−3.62361	+	1.50095i	−0.407688	+	0.168870i	−0.577096	−	0.816676i	$-0.695814\pi$
$79$	−3.62361	+	1.50095i	−0.407688	+	0.168870i	0.169408	+	0.985546i	$0.445814\pi$
$80$		0			0
$81$			8.88961i			0.987735i
$82$	−12.1362	−	5.02698i	−1.34022	−	0.555137i
$83$	6.29967	−	6.29967i	0.691478	−	0.691478i	−0.271079	−	0.962557i	$-0.587380\pi$
$83$	6.29967	−	6.29967i	0.691478	−	0.691478i	0.962557	+	0.271079i	$0.0873804\pi$
$84$	0.0129821			0.00141646
$85$		0			0
$86$	−10.3319			−1.11411
$87$	0.407958	−	0.407958i	0.0437376	−	0.0437376i
$88$	15.4058	+	6.38128i	1.64226	+	0.680247i
$89$		−	14.3079i		−	1.51664i	−0.651885	−	0.758318i	$-0.726022\pi$
$89$		−	14.3079i		−	1.51664i	0.651885	−	0.758318i	$-0.273978\pi$
$90$		0			0
$91$	−1.98810	+	0.823498i	−0.208410	+	0.0863261i
$92$	−0.0536200	−	0.129450i	−0.00559027	−	0.0134961i
$93$	0.224296	+	0.224296i	0.0232584	+	0.0232584i
$94$	7.50348	+	7.50348i	0.773925	+	0.773925i
$95$		0			0
$96$	0.0395233	−	0.0163711i	0.00403383	−	0.00167087i
$97$	−3.25033	+	7.84699i	−0.330021	+	0.796741i	0.668569	+	0.743650i	$0.266907\pi$
$97$	−3.25033	+	7.84699i	−0.330021	+	0.796741i	−0.998590	+	0.0530907i	$0.983093\pi$
$98$		−	5.63693i		−	0.569416i
$99$	−16.0119	−	6.63234i	−1.60926	−	0.666576i
$100$		0			0
$101$	2.53832			0.252572			0.126286	−	0.991994i	$-0.459694\pi$
$101$	2.53832			0.252572			0.126286	+	0.991994i	$0.459694\pi$
$102$	−0.633414	−	0.0460763i	−0.0627173	−	0.00456224i
$103$	16.6715			1.64269			0.821347	−	0.570429i	$-0.193223\pi$
$103$	16.6715			1.64269			0.821347	+	0.570429i	$0.193223\pi$
$104$	−2.54918	+	2.54918i	−0.249967	+	0.249967i
$105$		0			0
$106$			10.0173i			0.972962i
$107$	−3.48078	+	8.40335i	−0.336500	+	0.812382i	0.661546	+	0.749904i	$0.269900\pi$
$107$	−3.48078	+	8.40335i	−0.336500	+	0.812382i	−0.998046	+	0.0624783i	$0.980100\pi$
$108$	−0.0418535	+	0.0173363i	−0.00402735	+	0.00166818i
$109$	0.284608	+	0.687106i	0.0272605	+	0.0658128i	0.936924	−	0.349534i	$-0.113660\pi$
$109$	0.284608	+	0.687106i	0.0272605	+	0.0658128i	−0.909663	+	0.415347i	$0.863660\pi$
$110$		0			0
$111$	0.494421	+	0.494421i	0.0469283	+	0.0469283i
$112$	2.53385	+	6.11726i	0.239426	+	0.578026i
$113$	−8.34896	+	3.45825i	−0.785404	+	0.325325i	−0.739094	−	0.673602i	$-0.764746\pi$
$113$	−8.34896	+	3.45825i	−0.785404	+	0.325325i	−0.0463099	+	0.998927i	$0.514746\pi$
$114$	−0.166540	+	0.402064i	−0.0155979	+	0.0376568i
$115$		0			0
$116$	−0.328344	−	0.136004i	−0.0304859	−	0.0126277i
$117$	2.64947	−	2.64947i	0.244944	−	0.244944i
$118$	−3.03328			−0.279236
$119$	−0.513284	+	7.05614i	−0.0470526	+	0.646835i
$120$		0			0
$121$	16.0154	−	16.0154i	1.45595	−	1.45595i
$122$	7.36808	+	3.05196i	0.667075	+	0.276311i
$123$			1.04744i			0.0944446i
$124$	0.0747756	−	0.180524i	0.00671505	−	0.0162116i
$125$		0			0
$126$	−2.72673	−	6.58290i	−0.242916	−	0.586451i
$127$	−10.2527	−	10.2527i	−0.909779	−	0.909779i	0.0864752	−	0.996254i	$-0.472440\pi$
$127$	−10.2527	−	10.2527i	−0.909779	−	0.909779i	−0.996254	+	0.0864752i	$0.972440\pi$
$128$	7.56611	+	7.56611i	0.668756	+	0.668756i
$129$	0.315269	+	0.761126i	0.0277579	+	0.0670134i
$130$		0			0
$131$	−6.44750	+	15.5656i	−0.563321	+	1.35998i	0.343775	+	0.939052i	$0.388294\pi$
$131$	−6.44750	+	15.5656i	−0.563321	+	1.35998i	−0.907096	+	0.420924i	$0.861706\pi$
$132$		−	0.0438877i		−	0.00381993i
$133$	4.47894	+	1.85524i	0.388373	+	0.160869i
$134$	−2.42414	+	2.42414i	−0.209414	+	0.209414i
$135$		0			0
$136$	3.72930	+	11.2504i	0.319785	+	0.964711i
$137$	20.2283			1.72822			0.864111	−	0.503300i	$-0.167881\pi$
$137$	20.2283			1.72822			0.864111	+	0.503300i	$0.167881\pi$
$138$	0.223544	−	0.223544i	0.0190293	−	0.0190293i
$139$	−3.93292	−	1.62907i	−0.333586	−	0.138176i	0.209603	−	0.977787i	$-0.432783\pi$
$139$	−3.93292	−	1.62907i	−0.333586	−	0.138176i	−0.543188	+	0.839611i	$0.682783\pi$
$140$		0			0
$141$	0.323802	−	0.781727i	0.0272690	−	0.0658333i
$142$	−17.3069	+	7.16875i	−1.45236	+	0.601588i
$143$	2.78395	+	6.72106i	0.232806	+	0.562043i
$144$	−8.15224	−	8.15224i	−0.679354	−	0.679354i
$145$		0			0
$146$	−3.10487	−	7.49582i	−0.256961	−	0.620358i
$147$	−0.415260	+	0.172006i	−0.0342501	+	0.0141868i
$148$	0.164829	−	0.397933i	0.0135489	−	0.0327099i
$149$		−	4.32633i		−	0.354427i	−0.984172	−	0.177213i	$-0.943292\pi$
$149$		−	4.32633i		−	0.354427i	0.984172	−	0.177213i	$-0.0567083\pi$
$150$		0			0
$151$	−14.1854	+	14.1854i	−1.15439	+	1.15439i	−0.168725	+	0.985663i	$0.553965\pi$
$151$	−14.1854	+	14.1854i	−1.15439	+	1.15439i	−0.985663	+	0.168725i	$0.946035\pi$
$152$	8.12178			0.658763
$153$	−3.87603	−	11.6930i	−0.313358	−	0.945323i
$154$	13.8341			1.11478
$155$		0			0
$156$	0.00876606	+	0.00363102i	0.000701846	+	0.000290714i
$157$		−	21.7028i		−	1.73207i	−0.499983	−	0.866035i	$-0.666661\pi$
$157$		−	21.7028i		−	1.73207i	0.499983	−	0.866035i	$-0.333339\pi$
$158$	−2.08612	+	5.03634i	−0.165963	+	0.400669i
$159$	0.737950	−	0.305669i	0.0585232	−	0.0242411i
$160$		0			0
$161$	−2.49025	−	2.49025i	−0.196259	−	0.196259i
$162$	8.73658	+	8.73658i	0.686410	+	0.686410i
$163$	−0.507480	−	1.22517i	−0.0397489	−	0.0959623i	0.902758	−	0.430148i	$-0.141539\pi$
$163$	−0.507480	−	1.22517i	−0.0397489	−	0.0959623i	−0.942507	+	0.334186i	$0.891539\pi$
$164$	0.596112	−	0.246918i	0.0465486	−	0.0192810i
$165$		0			0
$166$		−	12.3824i		−	0.961063i
$167$	−23.0887	−	9.56366i	−1.78666	−	0.740058i	−0.990926	−	0.134411i	$-0.957086\pi$
$167$	−23.0887	−	9.56366i	−1.78666	−	0.740058i	−0.795733	−	0.605647i	$-0.792914\pi$
$168$	0.386536	−	0.386536i	0.0298219	−	0.0298219i
$169$	11.4272			0.879017
$170$		0			0
$171$	−8.44132			−0.645524
$172$	0.358847	−	0.358847i	0.0273618	−	0.0273618i
$173$	−14.7454	−	6.10776i	−1.12108	−	0.464364i	−0.256337	−	0.966587i	$-0.582516\pi$
$173$	−14.7454	−	6.10776i	−1.12108	−	0.464364i	−0.864738	+	0.502223i	$0.832516\pi$
$174$		−	0.801869i		−	0.0607895i
$175$		0			0
$176$	20.6802	−	8.56604i	1.55883	−	0.645689i
$177$	0.0925582	+	0.223455i	0.00695710	+	0.0167959i
$178$	−14.0616	−	14.0616i	−1.05396	−	1.05396i
$179$	10.5747	+	10.5747i	0.790389	+	0.790389i	0.981557	−	0.191168i	$-0.0612276\pi$
$179$	10.5747	+	10.5747i	0.790389	+	0.790389i	−0.191168	+	0.981557i	$0.561228\pi$
$180$		0			0
$181$	22.6278	−	9.37275i	1.68191	−	0.696671i	0.682499	−	0.730887i	$-0.260893\pi$
$181$	22.6278	−	9.37275i	1.68191	−	0.696671i	0.999414	+	0.0342158i	$0.0108933\pi$
$182$	−1.14455	+	2.76320i	−0.0848400	+	0.204822i
$183$		−	0.635918i		−	0.0470084i
$184$	−5.45085	−	2.25782i	−0.401842	−	0.166448i
$185$		0			0
$186$	0.440870			0.0323262
$187$	23.8543	+	1.73523i	1.74440	+	0.126892i
$188$	−0.521222			−0.0380140
$189$	−0.805139	+	0.805139i	−0.0585652	+	0.0585652i
$190$		0			0
$191$			0.254656i			0.0184263i	0.999958	+	0.00921313i	$0.00293267\pi$
$191$			0.254656i			0.0184263i	−0.999958	+	0.00921313i	$0.997067\pi$
$192$	0.350063	−	0.845126i	0.0252636	−	0.0609917i
$193$	−2.74301	+	1.13619i	−0.197446	+	0.0817848i	−0.479215	−	0.877697i	$-0.659079\pi$
$193$	−2.74301	+	1.13619i	−0.197446	+	0.0817848i	0.281769	+	0.959482i	$0.409079\pi$
$194$	4.51753	+	10.9063i	0.324340	+	0.783025i
$195$		0			0
$196$	0.195782	+	0.195782i	0.0139844	+	0.0139844i
$197$	2.32716	+	5.61826i	0.165803	+	0.400284i	0.984842	−	0.173454i	$-0.0554927\pi$
$197$	2.32716	+	5.61826i	0.165803	+	0.400284i	−0.819039	+	0.573738i	$0.805493\pi$
$198$	−22.2544	+	9.21808i	−1.58155	+	0.655100i
$199$	4.80772	−	11.6069i	0.340810	−	0.822789i	−0.656824	−	0.754044i	$-0.728100\pi$
$199$	4.80772	−	11.6069i	0.340810	−	0.822789i	0.997634	−	0.0687451i	$-0.0218995\pi$
$200$		0			0
$201$	0.252552	+	0.104610i	0.0178136	+	0.00737864i
$202$	2.49462	−	2.49462i	0.175521	−	0.175521i
$203$	−8.93271			−0.626953
$204$	0.0236001	−	0.0203994i	0.00165234	−	0.00142825i
$205$		0			0
$206$	16.3845	−	16.3845i	1.14156	−	1.14156i
$207$	5.66531	+	2.34665i	0.393766	+	0.163103i
$208$			4.83935i			0.335549i
$209$	6.27189	−	15.1417i	0.433836	−	1.04737i
$210$		0			0
$211$	−4.60978	−	11.1290i	−0.317351	−	0.766152i	−0.999393	−	0.0348394i	$-0.988908\pi$
$211$	−4.60978	−	11.1290i	−0.317351	−	0.766152i	0.682042	−	0.731313i	$-0.261092\pi$
$212$	−0.347920	−	0.347920i	−0.0238953	−	0.0238953i
$213$	1.05621	+	1.05621i	0.0723705	+	0.0723705i
$214$	4.83783	+	11.6795i	0.330707	+	0.798397i
$215$		0			0
$216$	−0.729990	+	1.76235i	−0.0496695	+	0.119913i
$217$		−	4.91123i		−	0.333396i
$218$	0.954986	+	0.395568i	0.0646798	+	0.0267912i
$219$	−0.457458	+	0.457458i	−0.0309121	+	0.0309121i
$220$		0			0
$221$	−2.32016	+	4.62106i	−0.156071	+	0.310846i
$222$	0.971818			0.0652242
$223$	−12.5656	+	12.5656i	−0.841453	+	0.841453i	−0.989048	−	0.147595i	$-0.952847\pi$
$223$	−12.5656	+	12.5656i	−0.841453	+	0.841453i	0.147595	+	0.989048i	$0.452847\pi$
$224$	−0.611936	−	0.253472i	−0.0408867	−	0.0169358i
$225$		0			0
$226$	−4.80651	+	11.6039i	−0.319724	+	0.771883i
$227$	−10.3226	+	4.27575i	−0.685133	+	0.283791i	−0.697971	−	0.716126i	$-0.745914\pi$
$227$	−10.3226	+	4.27575i	−0.685133	+	0.283791i	0.0128377	+	0.999918i	$0.495914\pi$
$228$	−0.00818022	−	0.0197488i	−0.000541749	−	0.00130790i
$229$	15.0941	+	15.0941i	0.997445	+	0.997445i	0.999997	−	0.00255174i	$-0.000812246\pi$
$229$	15.0941	+	15.0941i	0.997445	+	0.997445i	−0.00255174	+	0.999997i	$0.500812\pi$
$230$		0			0
$231$	−0.422135	−	1.01913i	−0.0277745	−	0.0670535i
$232$	−13.8258	+	5.72683i	−0.907708	+	0.375985i
$233$	3.17839	−	7.67330i	0.208223	−	0.502695i	−0.784920	−	0.619597i	$-0.787296\pi$
$233$	3.17839	−	7.67330i	0.208223	−	0.502695i	0.993143	+	0.116902i	$0.0372963\pi$
$234$		−	5.20772i		−	0.340439i
$235$		0			0
$236$	0.105352	−	0.105352i	0.00685784	−	0.00685784i
$237$	0.434672			0.0282350
$238$	6.43022	+	7.43911i	0.416809	+	0.482206i
$239$	−3.42382			−0.221468			−0.110734	−	0.993850i	$-0.535320\pi$
$239$	−3.42382			−0.221468			−0.110734	+	0.993850i	$0.535320\pi$
$240$		0			0
$241$	−5.86504	−	2.42938i	−0.377800	−	0.156490i	0.185699	−	0.982607i	$-0.440545\pi$
$241$	−5.86504	−	2.42938i	−0.377800	−	0.156490i	−0.563499	+	0.826117i	$0.690545\pi$
$242$		−	31.4795i		−	2.02358i
$243$	1.13884	−	2.74941i	0.0730569	−	0.176375i
$244$	−0.361909	+	0.149908i	−0.0231689	+	0.00959686i
$245$		0			0
$246$	1.02941	+	1.02941i	0.0656327	+	0.0656327i
$247$	2.50548	+	2.50548i	0.159420	+	0.159420i
$248$	−3.14863	−	7.60146i	−0.199938	−	0.482693i
$249$	−0.912187	+	0.377840i	−0.0578075	+	0.0239446i
$250$		0			0
$251$			5.06308i			0.319579i	0.987151	+	0.159789i	$0.0510815\pi$
$251$			5.06308i			0.319579i	−0.987151	+	0.159789i	$0.948919\pi$
$252$	0.323342	+	0.133933i	0.0203687	+	0.00843697i
$253$	−8.41863	+	8.41863i	−0.529275	+	0.529275i
$254$	−20.1524			−1.26447
$255$		0			0
$256$	−1.63651			−0.102282
$257$	12.6054	−	12.6054i	0.786305	−	0.786305i	−0.194582	−	0.980886i	$-0.562335\pi$
$257$	12.6054	−	12.6054i	0.786305	−	0.786305i	0.980886	+	0.194582i	$0.0623349\pi$
$258$	1.05786	+	0.438182i	0.0658598	+	0.0272800i
$259$		−	10.8259i		−	0.672689i
$260$		0			0
$261$	14.3698	−	5.95215i	0.889465	−	0.368429i
$262$	8.96117	+	21.6342i	0.553623	+	1.33656i
$263$	6.44016	+	6.44016i	0.397117	+	0.397117i	0.877215	−	0.480098i	$-0.159399\pi$
$263$	6.44016	+	6.44016i	0.397117	+	0.397117i	−0.480098	+	0.877215i	$0.659399\pi$
$264$	−1.30674	−	1.30674i	−0.0804242	−	0.0804242i
$265$		0			0
$266$	6.22513	−	2.57853i	0.381687	−	0.158100i
$267$	−0.606808	+	1.46496i	−0.0371361	+	0.0896544i
$268$		−	0.168391i		−	0.0102861i
$269$	−11.7926	−	4.88466i	−0.719008	−	0.297823i	−0.00698191	−	0.999976i	$-0.502222\pi$
$269$	−11.7926	−	4.88466i	−0.719008	−	0.297823i	−0.712027	+	0.702153i	$0.752222\pi$
$270$		0			0
$271$	16.4128			0.997004			0.498502	−	0.866889i	$-0.333884\pi$
$271$	16.4128			0.997004			0.498502	+	0.866889i	$0.333884\pi$
$272$	14.2187	+	7.13899i	0.862134	+	0.432865i
$273$	0.238484			0.0144337
$274$	19.8801	−	19.8801i	1.20100	−	1.20100i
$275$		0			0
$276$			0.0155283i			0.000934692i
$277$	7.05850	−	17.0407i	0.424104	−	1.02388i	−0.557020	−	0.830499i	$-0.688055\pi$
$277$	7.05850	−	17.0407i	0.424104	−	1.02388i	0.981124	−	0.193379i	$-0.0619447\pi$
$278$	−5.46623	+	2.26419i	−0.327843	+	0.135797i
$279$	3.27251	+	7.90053i	0.195920	+	0.472992i
$280$		0			0
$281$	13.2557	+	13.2557i	0.790767	+	0.790767i	0.981619	−	0.190852i	$-0.0611251\pi$
$281$	13.2557	+	13.2557i	0.790767	+	0.790767i	−0.190852	+	0.981619i	$0.561125\pi$
$282$	−0.450042	−	1.08650i	−0.0267996	−	0.0647000i
$283$	18.2837	−	7.57337i	1.08686	−	0.450190i	0.233946	−	0.972250i	$-0.424836\pi$
$283$	18.2837	−	7.57337i	1.08686	−	0.450190i	0.852909	+	0.522059i	$0.174836\pi$
$284$	0.352119	−	0.850090i	0.0208944	−	0.0504435i
$285$		0			0
$286$	9.34138	+	3.86933i	0.552367	+	0.228798i
$287$	11.4675	−	11.4675i	0.676903	−	0.676903i
$288$	1.15330			0.0679587
$289$	10.1546	+	13.6339i	0.597330	+	0.801995i
$290$		0			0
$291$	0.665592	−	0.665592i	0.0390177	−	0.0390177i
$292$	0.368184	+	0.152507i	0.0215463	+	0.00892478i
$293$		−	14.0051i		−	0.818189i	−0.912492	−	0.409094i	$-0.865845\pi$
$293$		−	14.0051i		−	0.818189i	0.912492	−	0.409094i	$-0.134155\pi$
$294$	−0.239066	+	0.577157i	−0.0139426	+	0.0336605i
$295$		0			0
$296$	−6.94058	−	16.7560i	−0.403413	−	0.973925i
$297$	2.72189	+	2.72189i	0.157940	+	0.157940i
$298$	−4.25185	−	4.25185i	−0.246303	−	0.246303i
$299$	−0.985014	−	2.37803i	−0.0569648	−	0.137525i
$300$		0			0
$301$	4.88128	−	11.7845i	0.281352	−	0.679245i
$302$			27.8823i			1.60445i
$303$	−0.259895	−	0.107652i	−0.0149306	−	0.00618444i
$304$	7.70919	−	7.70919i	0.442152	−	0.442152i
$305$		0			0
$306$	−15.3010	−	7.68240i	−0.874700	−	0.439174i
$307$	−13.2813			−0.758001			−0.379001	−	0.925396i	$-0.623732\pi$
$307$	−13.2813			−0.758001			−0.379001	+	0.925396i	$0.623732\pi$
$308$	−0.480486	+	0.480486i	−0.0273782	+	0.0273782i
$309$	−1.70697	−	0.707051i	−0.0971062	−	0.0402227i
$310$		0			0
$311$	−9.01417	+	21.7621i	−0.511147	+	1.23402i	0.432070	+	0.901840i	$0.357783\pi$
$311$	−9.01417	+	21.7621i	−0.511147	+	1.23402i	−0.943217	+	0.332178i	$0.892217\pi$
$312$	0.369118	−	0.152894i	0.0208972	−	0.00865591i
$313$	12.4974	+	30.1714i	0.706394	+	1.70539i	0.708821	+	0.705389i	$0.249228\pi$
$313$	12.4974	+	30.1714i	0.706394	+	1.70539i	−0.00242660	+	0.999997i	$0.500772\pi$
$314$	−21.3292	−	21.3292i	−1.20367	−	1.20367i
$315$		0			0
$316$	−0.102467	−	0.247378i	−0.00576423	−	0.0139161i
$317$	−23.4674	+	9.72053i	−1.31806	+	0.545960i	−0.927227	−	0.374501i	$-0.877814\pi$
$317$	−23.4674	+	9.72053i	−1.31806	+	0.545960i	−0.390836	+	0.920460i	$0.627814\pi$
$318$	0.424839	−	1.02565i	0.0238238	−	0.0575157i
$319$			30.1983i			1.69078i
$320$		0			0
$321$	0.712784	−	0.712784i	0.0397837	−	0.0397837i
$322$	−4.89475			−0.272774
$323$	11.0575	−	3.66537i	0.615256	−	0.203947i
$324$	−0.606878			−0.0337155
$325$		0			0
$326$	−1.70282	−	0.705330i	−0.0943103	−	0.0390646i
$327$		−	0.0824221i		−	0.00455795i
$328$	10.3971	−	25.1009i	0.574086	−	1.38597i
$329$	−12.1034	+	5.01340i	−0.667283	+	0.276398i
$330$		0			0
$331$	13.0376	+	13.0376i	0.716613	+	0.716613i	0.967910	−	0.251297i	$-0.0808570\pi$
$331$	13.0376	+	13.0376i	0.716613	+	0.716613i	−0.251297	+	0.967910i	$0.580857\pi$
$332$	0.430067	+	0.430067i	0.0236030	+	0.0236030i
$333$	7.21365	+	17.4153i	0.395306	+	0.954352i
$334$	−32.0903	+	13.2922i	−1.75590	+	0.727318i
$335$		0			0
$336$		−	0.733799i		−	0.0400320i
$337$	−6.10439	−	2.52852i	−0.332527	−	0.137737i	0.210172	−	0.977664i	$-0.432598\pi$
$337$	−6.10439	−	2.52852i	−0.332527	−	0.137737i	−0.542699	+	0.839927i	$0.682598\pi$
$338$	11.2305	−	11.2305i	0.610858	−	0.610858i
$339$	1.00150			0.0543942
$340$		0			0
$341$	−16.6031			−0.899108
$342$	−8.29600	+	8.29600i	−0.448596	+	0.448596i
$343$	17.5264	+	7.25965i	0.946334	+	0.391984i
$344$		−	21.3691i		−	1.15214i
$345$		0			0
$346$	−20.4942	+	8.48898i	−1.10178	+	0.456370i
$347$	3.67954	+	8.88319i	0.197528	+	0.476875i	0.991345	−	0.131282i	$-0.0419093\pi$
$347$	3.67954	+	8.88319i	0.197528	+	0.476875i	−0.793817	+	0.608157i	$0.791909\pi$
$348$	0.0278506	+	0.0278506i	0.00149295	+	0.00149295i
$349$	−0.486525	−	0.486525i	−0.0260431	−	0.0260431i	0.693965	−	0.720008i	$-0.255862\pi$
$349$	−0.486525	−	0.486525i	−0.0260431	−	0.0260431i	−0.720008	+	0.693965i	$0.755862\pi$
$350$		0			0
$351$	−0.768859	+	0.318472i	−0.0410387	+	0.0169988i
$352$	−0.856898	+	2.06874i	−0.0456728	+	0.110264i
$353$			15.3590i			0.817475i	0.912652	+	0.408737i	$0.134031\pi$
$353$			15.3590i			0.817475i	−0.912652	+	0.408737i	$0.865969\pi$
$354$	0.310573	+	0.128644i	0.0165068	+	0.00683733i
$355$		0			0
$356$	0.976776			0.0517690
$357$	0.351810	−	0.700699i	0.0186198	−	0.0370849i
$358$	20.7853			1.09854
$359$	−18.0696	+	18.0696i	−0.953676	+	0.953676i	−0.998974	−	0.0452975i	$-0.985576\pi$
$359$	−18.0696	+	18.0696i	−0.953676	+	0.953676i	0.0452975	+	0.998974i	$0.485576\pi$
$360$		0			0
$361$			11.0174i			0.579866i
$362$	13.0269	−	31.4497i	0.684678	−	1.65296i
$363$	−2.31902	+	0.960571i	−0.121717	+	0.0504169i
$364$	−0.0562188	−	0.135724i	−0.00294667	−	0.00711388i
$365$		0			0
$366$	−0.624971	−	0.624971i	−0.0326678	−	0.0326678i
$367$	−0.442844	−	1.06912i	−0.0231163	−	0.0558076i	0.911900	−	0.410413i	$-0.134615\pi$
$367$	−0.442844	−	1.06912i	−0.0231163	−	0.0558076i	−0.935016	+	0.354605i	$0.884615\pi$
$368$	−7.31706	+	3.03082i	−0.381428	+	0.157993i
$369$	−10.8062	+	26.0885i	−0.562549	+	1.35811i
$370$		0			0
$371$	−11.4256	−	4.73265i	−0.593188	−	0.245707i
$372$	−0.0153123	+	0.0153123i	−0.000793907	+	0.000793907i
$373$	−15.1464			−0.784251			−0.392126	−	0.919912i	$-0.628260\pi$
$373$	−15.1464			−0.784251			−0.392126	+	0.919912i	$0.628260\pi$
$374$	25.1490	−	21.7383i	1.30042	−	1.12406i
$375$		0			0
$376$	−15.5192	+	15.5192i	−0.800342	+	0.800342i
$377$	−6.03176	−	2.49844i	−0.310651	−	0.128676i
$378$			1.58256i			0.0813979i
$379$	5.98525	−	14.4497i	0.307442	−	0.742230i	−0.692345	−	0.721567i	$-0.743422\pi$
$379$	5.98525	−	14.4497i	0.307442	−	0.742230i	0.999786	−	0.0206630i	$-0.00657770\pi$
$380$		0			0
$381$	0.614933	+	1.48458i	0.0315040	+	0.0760574i
$382$	0.250272	+	0.250272i	0.0128050	+	0.0128050i
$383$	−3.26890	−	3.26890i	−0.167033	−	0.167033i	0.618641	−	0.785674i	$-0.287684\pi$
$383$	−3.26890	−	3.26890i	−0.167033	−	0.167033i	−0.785674	+	0.618641i	$0.787684\pi$
$384$	−0.453799	−	1.09557i	−0.0231578	−	0.0559079i
$385$		0			0
$386$	−1.57915	+	3.81242i	−0.0803769	+	0.194047i
$387$			22.2098i			1.12899i
$388$	−0.535700	−	0.221894i	−0.0271961	−	0.0112650i
$389$	4.48189	−	4.48189i	0.227241	−	0.227241i	−0.584298	−	0.811539i	$-0.698630\pi$
$389$	4.48189	−	4.48189i	0.227241	−	0.227241i	0.811539	+	0.584298i	$0.198630\pi$
$390$		0			0
$391$	−8.44009	−	0.613956i	−0.426834	−	0.0310491i
$392$	11.6587			0.588852
$393$	1.32030	−	1.32030i	0.0666003	−	0.0666003i
$394$	7.80864	+	3.23444i	0.393393	+	0.162949i
$395$		0			0
$396$	0.452779	−	1.09310i	0.0227530	−	0.0549306i
$397$	−2.99848	+	1.24201i	−0.150490	+	0.0623348i	−0.456657	−	0.889643i	$-0.650953\pi$
$397$	−2.99848	+	1.24201i	−0.150490	+	0.0623348i	0.306167	+	0.951978i	$0.400953\pi$
$398$	−6.68210	−	16.1320i	−0.334943	−	0.808625i
$399$	−0.379910	−	0.379910i	−0.0190193	−	0.0190193i
$400$		0			0
$401$	4.78153	+	11.5436i	0.238778	+	0.576462i	0.997157	−	0.0753522i	$-0.0240081\pi$
$401$	4.78153	+	11.5436i	0.238778	+	0.576462i	−0.758379	+	0.651814i	$0.774008\pi$
$402$	0.351013	−	0.145394i	0.0175069	−	0.00725161i
$403$	1.37365	−	3.31628i	0.0684263	−	0.165196i
$404$			0.173287i			0.00862133i
$405$		0			0
$406$	−8.77893	+	8.77893i	−0.435691	+	0.435691i
$407$	−36.5985			−1.81412
$408$	0.0952982	−	1.31007i	0.00471797	−	0.0648581i
$409$	11.7076			0.578904			0.289452	−	0.957192i	$-0.406527\pi$
$409$	11.7076			0.578904			0.289452	+	0.957192i	$0.406527\pi$
$410$		0			0
$411$	−2.07115	−	0.857898i	−0.102162	−	0.0423170i
$412$			1.13814i			0.0560719i
$413$	1.43307	−	3.45974i	0.0705168	−	0.170243i
$414$	7.87403	−	3.26153i	0.386987	−	0.160295i
$415$		0			0
$416$	−0.342311	−	0.342311i	−0.0167832	−	0.0167832i
$417$	0.333596	+	0.333596i	0.0163362	+	0.0163362i
$418$	−8.71709	−	21.0449i	−0.426367	−	1.02934i
$419$	0.503085	−	0.208385i	0.0245773	−	0.0101803i	−0.370361	−	0.928888i	$-0.620766\pi$
$419$	0.503085	−	0.208385i	0.0245773	−	0.0101803i	0.394938	+	0.918708i	$0.370766\pi$
$420$		0			0
$421$		−	24.3097i		−	1.18478i	−0.805651	−	0.592391i	$-0.798184\pi$
$421$		−	24.3097i		−	1.18478i	0.805651	−	0.592391i	$-0.201816\pi$
$422$	−15.4678	−	6.40699i	−0.752963	−	0.311887i
$423$	16.1298	−	16.1298i	0.784257	−	0.784257i
$424$	−20.7184			−1.00617
$425$		0			0
$426$	2.07606			0.100585
$427$	−6.96209	+	6.96209i	−0.336919	+	0.336919i
$428$	−0.573682	−	0.237627i	−0.0277300	−	0.0114861i
$429$		−	0.806228i		−	0.0389251i
$430$		0			0
$431$	−3.92135	+	1.62428i	−0.188885	+	0.0782387i	−0.475121	−	0.879920i	$-0.657596\pi$
$431$	−3.92135	+	1.62428i	−0.188885	+	0.0782387i	0.286236	+	0.958159i	$0.407596\pi$
$432$	0.979917	+	2.36573i	0.0471463	+	0.113821i
$433$	18.1756	+	18.1756i	0.873464	+	0.873464i	0.992848	−	0.119384i	$-0.0380919\pi$
$433$	18.1756	+	18.1756i	0.873464	+	0.873464i	−0.119384	+	0.992848i	$0.538092\pi$
$434$	−4.82668	−	4.82668i	−0.231688	−	0.231688i
$435$		0			0
$436$	−0.0469075	+	0.0194297i	−0.00224646	+	0.000930515i
$437$	−2.21911	+	5.35741i	−0.106154	+	0.256280i
$438$			0.899165i			0.0429638i
$439$	2.86412	+	1.18636i	0.136697	+	0.0566217i	0.449983	−	0.893037i	$-0.351430\pi$
$439$	2.86412	+	1.18636i	0.136697	+	0.0566217i	−0.313286	+	0.949659i	$0.601430\pi$
$440$		0			0
$441$	−12.1174			−0.577018
$442$	2.26128	+	6.82172i	0.107558	+	0.324476i
$443$	−26.3141			−1.25022			−0.625109	−	0.780537i	$-0.714946\pi$
$443$	−26.3141			−1.25022			−0.625109	+	0.780537i	$0.714946\pi$
$444$	−0.0337532	+	0.0337532i	−0.00160186	+	0.00160186i
$445$		0			0
$446$			24.6985i			1.16951i
$447$	−0.183483	+	0.442967i	−0.00867844	+	0.0209516i
$448$	−13.0850	+	5.41999i	−0.618209	+	0.256071i
$449$	5.62744	+	13.5858i	0.265575	+	0.641156i	0.999265	−	0.0383289i	$-0.0122035\pi$
$449$	5.62744	+	13.5858i	0.265575	+	0.641156i	−0.733690	+	0.679485i	$0.762203\pi$
$450$		0			0
$451$	−38.7674	−	38.7674i	−1.82549	−	1.82549i
$452$	−0.236089	−	0.569969i	−0.0111047	−	0.0268091i
$453$	2.05403	−	0.850807i	0.0965067	−	0.0399744i
$454$	−5.94272	+	14.3470i	−0.278906	+	0.673338i
$455$		0			0
$456$	−0.831577	−	0.344450i	−0.0389421	−	0.0161304i
$457$	−7.48280	+	7.48280i	−0.350030	+	0.350030i	−0.860121	−	0.510090i	$-0.829612\pi$
$457$	−7.48280	+	7.48280i	−0.350030	+	0.350030i	0.510090	+	0.860121i	$0.329612\pi$
$458$	29.6685			1.38632
$459$	−0.198502	+	2.72882i	−0.00926530	+	0.127371i
$460$		0			0
$461$	−13.0851	+	13.0851i	−0.609433	+	0.609433i	−0.942798	−	0.333365i	$-0.891816\pi$
$461$	−13.0851	+	13.0851i	−0.609433	+	0.609433i	0.333365	+	0.942798i	$0.391816\pi$
$462$	−1.41645	−	0.586712i	−0.0658992	−	0.0272963i
$463$		−	37.7389i		−	1.75387i	−0.480605	−	0.876937i	$-0.659583\pi$
$463$		−	37.7389i		−	1.75387i	0.480605	−	0.876937i	$-0.340417\pi$
$464$	−7.68753	+	18.5593i	−0.356884	+	0.861595i
$465$		0			0
$466$	−4.41754	−	10.6649i	−0.204638	−	0.494041i
$467$	−21.3821	−	21.3821i	−0.989444	−	0.989444i	0.0105009	−	0.999945i	$-0.496657\pi$
$467$	−21.3821	−	21.3821i	−0.989444	−	0.989444i	−0.999945	+	0.0105009i	$0.996657\pi$
$468$	0.180875	+	0.180875i	0.00836094	+	0.00836094i
$469$	−1.61967	−	3.91024i	−0.0747895	−	0.180558i
$470$		0			0
$471$	−0.920430	+	2.22211i	−0.0424112	+	0.102390i
$472$		−	6.27364i		−	0.288768i
$473$	−39.8390	−	16.5019i	−1.83180	−	0.758756i
$474$	0.427189	−	0.427189i	0.0196214	−	0.0196214i
$475$		0			0
$476$	−0.481710	−	0.0350410i	−0.0220792	−	0.00160610i
$477$	21.5335			0.985953
$478$	−3.36487	+	3.36487i	−0.153906	+	0.153906i
$479$	24.9054	+	10.3162i	1.13796	+	0.471358i	0.870479	−	0.492206i	$-0.163809\pi$
$479$	24.9054	+	10.3162i	1.13796	+	0.471358i	0.267480	+	0.963563i	$0.413809\pi$
$480$		0			0
$481$	3.02796	−	7.31014i	0.138063	−	0.333314i
$482$	−8.15163	+	3.37651i	−0.371296	+	0.153796i
$483$	0.149359	+	0.360585i	0.00679609	+	0.0164072i
$484$	1.09335	+	1.09335i	0.0496976	+	0.0496976i
$485$		0			0
$486$	−1.58284	−	3.82132i	−0.0717992	−	0.173339i
$487$	−3.54069	+	1.46660i	−0.160444	+	0.0664581i	−0.461460	−	0.887161i	$-0.652674\pi$
$487$	−3.54069	+	1.46660i	−0.160444	+	0.0664581i	0.301016	+	0.953619i	$0.402674\pi$
$488$	−6.31227	+	15.2392i	−0.285743	+	0.689845i
$489$			0.146965i			0.00664600i
$490$		0			0
$491$	−4.17285	+	4.17285i	−0.188318	+	0.188318i	−0.794969	−	0.606651i	$-0.792513\pi$
$491$	−4.17285	+	4.17285i	−0.188318	+	0.188318i	0.606651	+	0.794969i	$0.292513\pi$
$492$	−0.0715070			−0.00322378
$493$	−16.2388	+	14.0365i	−0.731358	+	0.632171i
$494$	4.92469			0.221572
$495$		0			0
$496$	−10.2040	−	4.22662i	−0.458172	−	0.189781i
$497$		−	23.1270i		−	1.03739i
$498$	−0.525148	+	1.26782i	−0.0235324	+	0.0568123i
$499$	−40.7345	+	16.8728i	−1.82352	+	0.755329i	−0.849986	+	0.526805i	$0.823390\pi$
$499$	−40.7345	+	16.8728i	−1.82352	+	0.755329i	−0.973538	+	0.228524i	$0.926610\pi$
$500$		0			0
$501$	1.95842	+	1.95842i	0.0874956	+	0.0874956i
$502$	4.97592	+	4.97592i	0.222086	+	0.222086i
$503$	13.5984	+	32.8295i	0.606324	+	1.46380i	0.866969	+	0.498362i	$0.166065\pi$
$503$	13.5984	+	32.8295i	0.606324	+	1.46380i	−0.260645	+	0.965435i	$0.583935\pi$
$504$	13.6152	−	5.63960i	0.606469	−	0.251208i
$505$		0			0
$506$			16.5474i			0.735621i
$507$	−1.17002	−	0.484636i	−0.0519622	−	0.0215235i
$508$	0.699933	−	0.699933i	0.0310545	−	0.0310545i
$509$	32.9351			1.45982			0.729911	−	0.683542i	$-0.239562\pi$
$509$	32.9351			1.45982			0.729911	+	0.683542i	$0.239562\pi$
$510$		0			0
$511$	10.0166			0.443107
$512$	−16.7406	+	16.7406i	−0.739835	+	0.739835i
$513$	1.73214	+	0.717476i	0.0764759	+	0.0316774i
$514$		−	24.7768i		−	1.09286i
$515$		0			0
$516$	−0.0519608	+	0.0215229i	−0.00228744	+	0.000947491i
$517$	16.9485	+	40.9173i	0.745395	+	1.79954i
$518$	−10.6395	−	10.6395i	−0.467475	−	0.467475i
$519$	1.25073	+	1.25073i	0.0549009	+	0.0549009i
$520$		0			0
$521$	22.6197	−	9.36938i	0.990986	−	0.410480i	0.172502	−	0.985009i	$-0.444815\pi$
$521$	22.6197	−	9.36938i	0.990986	−	0.410480i	0.818484	+	0.574529i	$0.194815\pi$
$522$	8.27269	−	19.9721i	0.362086	−	0.874153i
$523$			9.59229i			0.419442i	0.977761	+	0.209721i	$0.0672555\pi$
$523$			9.59229i			0.419442i	−0.977761	+	0.209721i	$0.932744\pi$
$524$	−1.06264	−	0.440160i	−0.0464216	−	0.0192285i
$525$		0			0
$526$	12.6586			0.551940
$527$	−7.71729	−	8.92813i	−0.336171	−	0.388915i
$528$	−2.48071			−0.107959
$529$	−13.2848	+	13.2848i	−0.577600	+	0.577600i
$530$		0			0
$531$			6.52047i			0.282964i
$532$	−0.126654	+	0.305769i	−0.00549114	+	0.0132568i
$533$	10.9507	−	4.53595i	0.474329	−	0.196474i
$534$	0.843383	+	2.03611i	0.0364968	+	0.0881110i
$535$		0			0
$536$	−5.01377	−	5.01377i	−0.216562	−	0.216562i
$537$	−0.634246	−	1.53121i	−0.0273697	−	0.0660764i
$538$	−16.3902	+	6.78903i	−0.706631	+	0.292696i
$539$	9.00320	−	21.7356i	0.387795	−	0.936220i
$540$		0			0
$541$	34.9482	+	14.4760i	1.50254	+	0.622373i	0.974003	−	0.226536i	$-0.0727402\pi$
$541$	34.9482	+	14.4760i	1.50254	+	0.622373i	0.528539	+	0.848909i	$0.322740\pi$
$542$	16.1302	−	16.1302i	0.692852	−	0.692852i
$543$	−2.71433			−0.116483
$544$	−1.51073	+	0.500782i	−0.0647722	+	0.0214709i
$545$		0			0
$546$	0.234378	−	0.234378i	0.0100305	−	0.0100305i
$547$	22.4642	+	9.30496i	0.960498	+	0.397851i	0.807167	−	0.590323i	$-0.201000\pi$
$547$	22.4642	+	9.30496i	0.960498	+	0.397851i	0.153332	+	0.988175i	$0.451000\pi$
$548$			1.38095i			0.0589914i
$549$	6.56062	−	15.8387i	0.280000	−	0.675981i
$550$		0			0
$551$	5.62866	+	13.5888i	0.239789	+	0.578902i
$552$	0.462349	+	0.462349i	0.0196789	+	0.0196789i
$553$	−4.75882	−	4.75882i	−0.202366	−	0.202366i
$554$	−9.81038	−	23.6844i	−0.416803	−	1.00625i
$555$		0			0
$556$	0.111214	−	0.268493i	0.00471651	−	0.0113867i
$557$		−	26.8276i		−	1.13672i	−0.822780	−	0.568360i	$-0.807578\pi$
$557$		−	26.8276i		−	1.13672i	0.822780	−	0.568360i	$-0.192422\pi$
$558$	10.9807	+	4.54835i	0.464850	+	0.192547i
$559$	6.59212	−	6.59212i	0.278817	−	0.278817i
$560$		0			0
$561$	−2.36881	−	1.18934i	−0.100011	−	0.0502141i
$562$	26.0549			1.09906
$563$	27.7735	−	27.7735i	1.17051	−	1.17051i	0.188426	−	0.982087i	$-0.439662\pi$
$563$	27.7735	−	27.7735i	1.17051	−	1.17051i	0.982087	−	0.188426i	$-0.0603384\pi$
$564$	0.0533672	+	0.0221054i	0.00224716	+	0.000930805i
$565$		0			0
$566$	10.5260	−	25.4120i	0.442440	−	1.06814i
$567$	−14.0925	+	5.83729i	−0.591828	+	0.245143i
$568$	−14.8269	−	35.7953i	−0.622123	−	1.50194i
$569$	7.03027	+	7.03027i	0.294724	+	0.294724i	0.838943	−	0.544219i	$-0.183174\pi$
$569$	7.03027	+	7.03027i	0.294724	+	0.294724i	−0.544219	+	0.838943i	$0.683174\pi$
$570$		0			0
$571$	0.173542	+	0.418968i	0.00726251	+	0.0175333i	0.927469	−	0.373900i	$-0.121980\pi$
$571$	0.173542	+	0.418968i	0.00726251	+	0.0175333i	−0.920207	+	0.391433i	$0.871980\pi$
$572$	−0.458835	+	0.190056i	−0.0191848	+	0.00794662i
$573$	0.0108001	−	0.0260738i	0.000451182	−	0.00108925i
$574$		−	22.5401i		−	0.940806i
$575$		0			0
$576$	17.4379	−	17.4379i	0.726581	−	0.726581i
$577$	28.8048			1.19916			0.599579	−	0.800316i	$-0.295335\pi$
$577$	28.8048			1.19916			0.599579	+	0.800316i	$0.295335\pi$
$578$	23.3790	+	3.41941i	0.972439	+	0.142229i
$579$	0.329039			0.0136744
$580$		0			0
$581$	14.1233	+	5.85007i	0.585934	+	0.242702i
$582$		−	1.30827i		−	0.0542295i
$583$	−15.9994	+	38.6259i	−0.662626	+	1.59972i
$584$	15.5034	−	6.42170i	0.641534	−	0.265732i
$585$		0			0
$586$	−13.7640	−	13.7640i	−0.568587	−	0.568587i
$587$	14.9214	+	14.9214i	0.615871	+	0.615871i	0.944470	−	0.328599i	$-0.106576\pi$
$587$	14.9214	+	14.9214i	0.615871	+	0.615871i	−0.328599	+	0.944470i	$0.606576\pi$
$588$	−0.0117426	−	0.0283491i	−0.000484256	−	0.00116910i
$589$	−7.47115	+	3.09465i	−0.307843	+	0.127513i
$590$		0			0
$591$		−	0.673942i		−	0.0277223i
$592$	−22.4928	−	9.31683i	−0.924449	−	0.382919i
$593$	−26.9570	+	26.9570i	−1.10699	+	1.10699i	−0.113445	+	0.993544i	$0.536189\pi$
$593$	−26.9570	+	26.9570i	−1.10699	+	1.10699i	−0.993544	+	0.113445i	$0.963811\pi$
$594$	5.35005			0.219515
$595$		0			0
$596$	0.295351			0.0120981
$597$	−0.984511	+	0.984511i	−0.0402933	+	0.0402933i
$598$	−3.30515	−	1.36904i	−0.135158	−	0.0559842i
$599$			35.4595i			1.44884i	0.689360	+	0.724418i	$0.257892\pi$
$599$			35.4595i			1.44884i	−0.689360	+	0.724418i	$0.742108\pi$
$600$		0			0
$601$	24.4610	−	10.1321i	0.997784	−	0.413296i	0.176800	−	0.984247i	$-0.443425\pi$
$601$	24.4610	−	10.1321i	0.997784	−	0.413296i	0.820984	+	0.570951i	$0.193425\pi$
$602$	−6.78433	−	16.3788i	−0.276509	−	0.667551i
$603$	5.21103	+	5.21103i	0.212210	+	0.212210i
$604$	−0.968410	−	0.968410i	−0.0394041	−	0.0394041i
$605$		0			0
$606$	−0.361219	+	0.149622i	−0.0146735	+	0.00607797i
$607$	9.36932	−	22.6195i	0.380289	−	0.918099i	−0.611620	−	0.791151i	$-0.709482\pi$
$607$	9.36932	−	22.6195i	0.380289	−	0.918099i	0.991909	−	0.126948i	$-0.0405180\pi$
$608$			1.09062i			0.0442304i
$609$	0.914606	+	0.378842i	0.0370617	+	0.0153515i
$610$		0			0
$611$	−9.57499			−0.387363
$612$	0.798261	−	0.264610i	0.0322678	−	0.0106962i
$613$	13.6998			0.553329			0.276665	−	0.960967i	$-0.410771\pi$
$613$	13.6998			0.553329			0.276665	+	0.960967i	$0.410771\pi$
$614$	−13.0526	+	13.0526i	−0.526761	+	0.526761i
$615$		0			0
$616$			28.6126i			1.15283i
$617$	−2.94554	+	7.11117i	−0.118583	+	0.286285i	−0.972015	−	0.234920i	$-0.924517\pi$
$617$	−2.94554	+	7.11117i	−0.118583	+	0.286285i	0.853432	+	0.521205i	$0.174517\pi$
$618$	−2.37247	+	0.982707i	−0.0954345	+	0.0395303i
$619$	−16.5857	−	40.0413i	−0.666634	−	1.60940i	−0.787204	−	0.616692i	$-0.788472\pi$
$619$	−16.5857	−	40.0413i	−0.666634	−	1.60940i	0.120570	−	0.992705i	$-0.461528\pi$
$620$		0			0
$621$	−0.963054	−	0.963054i	−0.0386460	−	0.0386460i
$622$	12.5285	+	30.2465i	0.502347	+	1.21277i
$623$	22.6819	−	9.39517i	0.908733	−	0.376409i
$624$	0.205240	−	0.495494i	0.00821618	−	0.0198356i
$625$		0			0
$626$	41.9342	+	17.3697i	1.67603	+	0.694233i
$627$	−1.28434	+	1.28434i	−0.0512915	+	0.0512915i
$628$	1.48161			0.0591227
$629$	−17.0114	−	19.6804i	−0.678288	−	0.784711i
$630$		0			0
$631$	0.518808	−	0.518808i	0.0206534	−	0.0206534i	−0.696705	−	0.717358i	$-0.745351\pi$
$631$	0.518808	−	0.518808i	0.0206534	−	0.0206534i	0.717358	+	0.696705i	$0.245351\pi$
$632$	−10.4165	−	4.31465i	−0.414346	−	0.171628i
$633$			1.33499i			0.0530609i
$634$	−13.5103	+	32.6166i	−0.536561	+	1.29537i
$635$		0			0
$636$	0.0208675	+	0.0503785i	0.000827449	+	0.00199764i
$637$	3.59657	+	3.59657i	0.142501	+	0.142501i
$638$	29.6784	+	29.6784i	1.17498	+	1.17498i
$639$	15.4103	+	37.2036i	0.609620	+	1.47175i
$640$		0			0
$641$	10.7822	−	26.0306i	0.425872	−	1.02815i	−0.554711	−	0.832043i	$-0.687171\pi$
$641$	10.7822	−	26.0306i	0.425872	−	1.02815i	0.980583	−	0.196103i	$-0.0628287\pi$
$642$		−	1.40103i		−	0.0552941i
$643$	−8.75122	−	3.62487i	−0.345114	−	0.142951i	0.203392	−	0.979097i	$-0.434803\pi$
$643$	−8.75122	−	3.62487i	−0.345114	−	0.142951i	−0.548506	+	0.836146i	$0.684803\pi$
$644$	0.170005	−	0.170005i	0.00669913	−	0.00669913i
$645$		0			0
$646$	7.26488	−	14.4694i	0.285833	−	0.569292i
$647$	24.3690			0.958044			0.479022	−	0.877803i	$-0.340991\pi$
$647$	24.3690			0.958044			0.479022	+	0.877803i	$0.340991\pi$
$648$	−18.0696	+	18.0696i	−0.709840	+	0.709840i
$649$	−11.6961	−	4.84470i	−0.459114	−	0.190171i
$650$		0			0
$651$	−0.208289	+	0.502853i	−0.00816347	+	0.0197084i
$652$	0.0836399	−	0.0346448i	0.00327559	−	0.00135679i
$653$	1.93076	+	4.66127i	0.0755565	+	0.182410i	0.957145	−	0.289609i	$-0.0935254\pi$
$653$	1.93076	+	4.66127i	0.0755565	+	0.182410i	−0.881588	+	0.472019i	$0.843525\pi$
$654$	−0.0810032	−	0.0810032i	−0.00316748	−	0.00316748i
$655$		0			0
$656$	−13.9568	−	33.6947i	−0.544922	−	1.31556i
$657$	−16.1133	+	6.67436i	−0.628641	+	0.260392i
$658$	−6.96796	+	16.8222i	−0.271640	+	0.655796i
$659$		−	8.17372i		−	0.318403i	−0.987246	−	0.159201i	$-0.949108\pi$
$659$		−	8.17372i		−	0.318403i	0.987246	−	0.159201i	$-0.0508919\pi$
$660$		0			0
$661$	21.6693	−	21.6693i	0.842839	−	0.842839i	−0.146388	−	0.989227i	$-0.546765\pi$
$661$	21.6693	−	21.6693i	0.842839	−	0.842839i	0.989227	+	0.146388i	$0.0467649\pi$
$662$	25.6264			0.995998
$663$	0.433540	−	0.374743i	0.0168373	−	0.0145538i
$664$	25.6102			0.993869
$665$		0			0
$666$	24.2049	+	10.0260i	0.937923	+	0.388500i
$667$		−	10.6847i		−	0.413714i
$668$	0.652895	−	1.57623i	0.0252613	−	0.0609861i
$669$	1.81948	−	0.753655i	0.0703453	−	0.0291380i
$670$		0			0
$671$	23.5363	+	23.5363i	0.908609	+	0.908609i
$672$	0.0519053	+	0.0519053i	0.00200229	+	0.00200229i
$673$	−2.53266	−	6.11439i	−0.0976270	−	0.235692i	0.867519	−	0.497404i	$-0.165713\pi$
$673$	−2.53266	−	6.11439i	−0.0976270	−	0.235692i	−0.965146	+	0.261711i	$0.915713\pi$
$674$	−8.48430	+	3.51431i	−0.326803	+	0.135366i
$675$		0			0
$676$			0.780116i			0.0300045i
$677$	38.1352	+	15.7961i	1.46565	+	0.607094i	0.965863	−	0.259052i	$-0.0834100\pi$
$677$	38.1352	+	15.7961i	1.46565	+	0.607094i	0.499791	+	0.866146i	$0.333410\pi$
$678$	0.984263	−	0.984263i	0.0378004	−	0.0378004i
$679$	−14.5739			−0.559296
$680$		0			0
$681$	1.23825			0.0474498
$682$	−16.3173	+	16.3173i	−0.624821	+	0.624821i
$683$	−12.2219	−	5.06249i	−0.467659	−	0.193711i	0.136394	−	0.990655i	$-0.456449\pi$
$683$	−12.2219	−	5.06249i	−0.467659	−	0.193711i	−0.604054	+	0.796944i	$0.706449\pi$
$684$		−	0.576275i		−	0.0220344i
$685$		0			0
$686$	24.3593	−	10.0900i	0.930043	−	0.385236i
$687$	−0.905310	−	2.18561i	−0.0345397	−	0.0833862i
$688$	−20.2835	−	20.2835i	−0.773302	−	0.773302i
$689$	−6.39139	−	6.39139i	−0.243492	−	0.243492i
$690$		0			0
$691$	−31.9758	+	13.2448i	−1.21642	+	0.503856i	−0.896269	−	0.443512i	$-0.853732\pi$
$691$	−31.9758	+	13.2448i	−1.21642	+	0.503856i	−0.320147	+	0.947368i	$0.603732\pi$
$692$	0.416966	−	1.00665i	0.0158507	−	0.0382669i
$693$		−	29.7383i		−	1.12966i
$694$	12.3465	+	5.11407i	0.468665	+	0.194127i
$695$		0			0
$696$	1.65848			0.0628645
$697$	2.82724	−	38.8662i	0.107089	−	1.47216i
$698$	−0.956299			−0.0361965
$699$	−0.650860	+	0.650860i	−0.0246178	+	0.0246178i
$700$		0			0
$701$		−	15.6045i		−	0.589373i	−0.955594	−	0.294687i	$-0.904785\pi$
$701$		−	15.6045i		−	0.589373i	0.955594	−	0.294687i	$-0.0952152\pi$
$702$	−0.442634	+	1.06861i	−0.0167061	+	0.0403322i
$703$	−16.4688	+	6.82160i	−0.621133	+	0.257282i
$704$	18.3231	+	44.2358i	0.690576	+	1.66720i
$705$		0			0
$706$	15.0945	+	15.0945i	0.568091	+	0.568091i
$707$	1.66677	+	4.02393i	0.0626852	+	0.151335i
$708$	−0.0152549	+	0.00631879i	−0.000573314	+	0.000237475i
$709$	17.9860	−	43.4221i	0.675480	−	1.63075i	−0.0966730	−	0.995316i	$-0.530820\pi$
$709$	17.9860	−	43.4221i	0.675480	−	1.63075i	0.772153	−	0.635437i	$-0.219180\pi$
$710$		0			0
$711$	10.8263	+	4.48441i	0.406019	+	0.168179i
$712$	29.0831	−	29.0831i	1.08994	−	1.08994i
$713$	5.87449			0.220001
$714$	−0.342882	−	1.03439i	−0.0128320	−	0.0387111i
$715$		0			0
$716$	−0.721916	+	0.721916i	−0.0269793	+	0.0269793i
$717$	0.350559	+	0.145206i	0.0130919	+	0.00542283i
$718$			35.5170i			1.32548i
$719$	14.5015	−	35.0097i	0.540815	−	1.30564i	−0.383334	−	0.923610i	$-0.625224\pi$
$719$	14.5015	−	35.0097i	0.540815	−	1.30564i	0.924149	−	0.382033i	$-0.124776\pi$
$720$		0			0
$721$	10.9472	+	26.4289i	0.407696	+	0.984264i
$722$	10.8278	+	10.8278i	0.402968	+	0.402968i
$723$	0.497481	+	0.497481i	0.0185015	+	0.0185015i
$724$	0.639862	+	1.54476i	0.0237803	+	0.0574106i
$725$		0			0
$726$	−1.33507	+	3.22314i	−0.0495490	+	0.119622i
$727$		−	20.6445i		−	0.765664i	−0.923818	−	0.382832i	$-0.874949\pi$
$727$		−	20.6445i		−	0.765664i	0.923818	−	0.382832i	$-0.125051\pi$
$728$	−5.71503	−	2.36724i	−0.211813	−	0.0877359i
$729$	18.6245	−	18.6245i	0.689797	−	0.689797i
$730$		0			0
$731$	−9.64390	−	29.0932i	−0.356693	−	1.07605i
$732$	0.0434131			0.00160459
$733$	24.3066	−	24.3066i	0.897786	−	0.897786i	−0.0974544	−	0.995240i	$-0.531070\pi$
$733$	24.3066	−	24.3066i	0.897786	−	0.897786i	0.995240	+	0.0974544i	$0.0310700\pi$
$734$	−1.48594	−	0.615494i	−0.0548469	−	0.0227183i
$735$		0			0
$736$	0.303187	−	0.731957i	0.0111756	−	0.0269803i
$737$	−13.2191	+	5.47553i	−0.486932	+	0.201694i
$738$	15.0192	+	36.2595i	0.552864	+	1.33473i
$739$	−12.3512	−	12.3512i	−0.454347	−	0.454347i	0.442448	−	0.896794i	$-0.354110\pi$
$739$	−12.3512	−	12.3512i	−0.454347	−	0.454347i	−0.896794	+	0.442448i	$0.854110\pi$
$740$		0			0
$741$	−0.150273	−	0.362791i	−0.00552041	−	0.0133275i
$742$	−15.8801	+	6.57775i	−0.582977	+	0.241477i
$743$	−7.04274	+	17.0027i	−0.258373	+	0.623768i	−0.998831	−	0.0483348i	$-0.984609\pi$
$743$	−7.04274	+	17.0027i	−0.258373	+	0.623768i	0.740458	+	0.672102i	$0.234609\pi$
$744$			0.911837i			0.0334296i
$745$		0			0
$746$	−14.8857	+	14.8857i	−0.545003	+	0.545003i
$747$	−26.6178			−0.973895
$748$	−0.118461	+	1.62849i	−0.00433136	+	0.0595435i
$749$	−15.6072			−0.570276
$750$		0			0
$751$	2.79602	+	1.15815i	0.102028	+	0.0422615i	0.433114	−	0.901339i	$-0.357415\pi$
$751$	2.79602	+	1.15815i	0.102028	+	0.0422615i	−0.331085	+	0.943601i	$0.607415\pi$
$752$			29.4616i			1.07436i
$753$	0.214729	−	0.518401i	0.00782515	−	0.0188916i
$754$	−8.38335	+	3.47250i	−0.305304	+	0.126461i
$755$		0			0
$756$	−0.0549654	−	0.0549654i	−0.00199907	−	0.00199907i
$757$	−8.25327	−	8.25327i	−0.299970	−	0.299970i	0.541032	−	0.841002i	$-0.318034\pi$
$757$	−8.25327	−	8.25327i	−0.299970	−	0.299970i	−0.841002	+	0.541032i	$0.818034\pi$
$758$	−8.31870	−	20.0831i	−0.302149	−	0.729452i
$759$	1.21901	−	0.504931i	0.0442473	−	0.0183278i
$760$		0			0
$761$		−	1.13354i		−	0.0410908i	−0.999789	−	0.0205454i	$-0.993460\pi$
$761$		−	1.13354i		−	0.0410908i	0.999789	−	0.0205454i	$-0.00654027\pi$
$762$	2.06337	+	0.854676i	0.0747480	+	0.0309616i
$763$	−0.902364	+	0.902364i	−0.0326678	+	0.0326678i
$764$	−0.0173849			−0.000628964
$765$		0			0
$766$	−6.42526			−0.232154
$767$	1.93535	−	1.93535i	0.0698813	−	0.0698813i
$768$	0.167560	+	0.0694054i	0.00604628	+	0.00250445i
$769$		−	14.6207i		−	0.527235i	−0.964627	−	0.263617i	$-0.915084\pi$
$769$		−	14.6207i		−	0.527235i	0.964627	−	0.263617i	$-0.0849156\pi$
$770$		0			0
$771$	−1.82526	+	0.756045i	−0.0657350	+	0.0272283i
$772$	−0.0775658	−	0.187260i	−0.00279165	−	0.00673965i
$773$	−17.5891	−	17.5891i	−0.632636	−	0.632636i	0.316092	−	0.948729i	$-0.397629\pi$
$773$	−17.5891	−	17.5891i	−0.632636	−	0.632636i	−0.948729	+	0.316092i	$0.897629\pi$
$774$	21.8275	+	21.8275i	0.784572	+	0.784572i
$775$		0			0
$776$	−22.5571	+	9.34346i	−0.809753	+	0.335411i
$777$	−0.459134	+	1.10845i	−0.0164714	+	0.0397654i
$778$		−	8.80946i		−	0.315834i
$779$	−24.6706	−	10.2189i	−0.883917	−	0.366130i
$780$		0			0
$781$	−78.1841			−2.79765
$782$	−8.89818	+	7.69140i	−0.318198	+	0.275044i
$783$	−3.45455			−0.123456
$784$	11.0664	−	11.0664i	0.395229	−	0.395229i
$785$		0			0
$786$		−	2.59514i		−	0.0925656i
$787$	−9.01386	+	21.7614i	−0.321309	+	0.775709i	0.677869	+	0.735183i	$0.262904\pi$
$787$	−9.01386	+	21.7614i	−0.321309	+	0.775709i	−0.999178	+	0.0405267i	$0.987096\pi$
$788$	−0.383549	+	0.158871i	−0.0136634	+	0.00565955i
$789$	−0.386267	−	0.932530i	−0.0137515	−	0.0331989i
$790$		0			0
$791$	−10.9645	−	10.9645i	−0.389854	−	0.389854i
$792$	−19.0655	−	46.0281i	−0.677462	−	1.63554i
$793$	−6.64837	+	2.75385i	−0.236091	+	0.0977920i
$794$	−1.72623	+	4.16749i	−0.0612617	+	0.147899i
$795$		0			0
$796$	0.792381	+	0.328215i	0.0280852	+	0.0116333i
$797$	−22.4878	+	22.4878i	−0.796558	+	0.796558i	−0.982551	−	0.185993i	$-0.940450\pi$
$797$	−22.4878	+	22.4878i	−0.796558	+	0.796558i	0.185993	+	0.982551i	$0.440450\pi$
$798$	−0.746739			−0.0264343
$799$	−14.1250	+	28.1327i	−0.499706	+	0.995262i
$800$		0			0
$801$	−30.2274	+	30.2274i	−1.06803	+	1.06803i
$802$	16.0441	+	6.64570i	0.566538	+	0.234668i
$803$		−	33.8624i		−	1.19498i
$804$	−0.00714156	+	0.0172413i	−0.000251863	+	0.000608052i
$805$		0			0
$806$	−1.90919	−	4.60919i	−0.0672483	−	0.162352i
$807$	1.00027	+	1.00027i	0.0352110	+	0.0352110i
$808$	5.15954	+	5.15954i	0.181512	+	0.181512i
$809$	6.40172	+	15.4551i	0.225072	+	0.543373i	0.995565	−	0.0940762i	$-0.0299897\pi$
$809$	6.40172	+	15.4551i	0.225072	+	0.543373i	−0.770493	+	0.637449i	$0.779990\pi$
$810$		0			0
$811$	19.0514	−	45.9940i	0.668983	−	1.61507i	−0.114331	−	0.993443i	$-0.536472\pi$
$811$	19.0514	−	45.9940i	0.668983	−	1.61507i	0.783314	−	0.621626i	$-0.213528\pi$
$812$		−	0.609820i		−	0.0214005i
$813$	−1.68048	−	0.696076i	−0.0589369	−	0.0244125i
$814$	−35.9685	+	35.9685i	−1.26069	+	1.26069i
$815$		0			0
$816$	−1.15306	−	1.33397i	−0.0403652	−	0.0466984i
$817$	−21.0028			−0.734794
$818$	11.5061	−	11.5061i	0.402300	−	0.402300i
$819$	5.93988	+	2.46038i	0.207556	+	0.0859727i
$820$		0			0
$821$	−6.13317	+	14.8068i	−0.214049	+	0.516760i	−0.994038	−	0.109033i	$-0.965225\pi$
$821$	−6.13317	+	14.8068i	−0.214049	+	0.516760i	0.779989	+	0.625793i	$0.215225\pi$
$822$	−2.87862	+	1.19236i	−0.100403	+	0.0415885i
$823$	−12.2758	−	29.6365i	−0.427909	−	1.03306i	−0.979949	−	0.199247i	$-0.936151\pi$
$823$	−12.2758	−	29.6365i	−0.427909	−	1.03306i	0.552040	−	0.833817i	$-0.313849\pi$
$824$	33.8876	+	33.8876i	1.18053	+	1.18053i
$825$		0			0
$826$	−1.99178	−	4.80858i	−0.0693028	−	0.167312i
$827$	3.53653	−	1.46488i	0.122977	−	0.0509389i	−0.320346	−	0.947301i	$-0.603799\pi$
$827$	3.53653	−	1.46488i	0.122977	−	0.0509389i	0.443324	+	0.896362i	$0.353799\pi$
$828$	−0.160202	+	0.386761i	−0.00556739	+	0.0134409i
$829$			4.09989i			0.142395i	0.997462	+	0.0711976i	$0.0226821\pi$
$829$			4.09989i			0.142395i	−0.997462	+	0.0711976i	$0.977318\pi$
$830$		0			0
$831$	−1.44542	+	1.44542i	−0.0501410	+	0.0501410i
$832$	−10.3515			−0.358875
$833$	15.8729	−	5.26158i	0.549962	−	0.182303i
$834$	0.655705			0.0227052
$835$		0			0
$836$	1.03370	+	0.428171i	0.0357511	+	0.0148086i
$837$		−	1.89932i		−	0.0656501i
$838$	0.289627	−	0.699221i	0.0100050	−	0.0241542i
$839$	43.0380	−	17.8269i	1.48584	−	0.615453i	0.515430	−	0.856932i	$-0.327632\pi$
$839$	43.0380	−	17.8269i	1.48584	−	0.615453i	0.970406	+	0.241479i	$0.0776324\pi$
$840$		0			0
$841$	1.34265	+	1.34265i	0.0462982	+	0.0462982i
$842$	−23.8912	−	23.8912i	−0.823345	−	0.823345i
$843$	−0.795045	−	1.91941i	−0.0273828	−	0.0661080i
$844$	0.759758	−	0.314702i	0.0261519	−	0.0108325i
$845$		0			0
$846$		−	31.7042i		−	1.09001i
$847$	35.9053	+	14.8724i	1.23372	+	0.511023i
$848$	−19.6659	+	19.6659i	−0.675329	+	0.675329i
$849$	−2.19324			−0.0752717
$850$		0			0
$851$	12.9492			0.443894
$852$	−0.0721058	+	0.0721058i	−0.00247030	+	0.00247030i
$853$	−32.6885	−	13.5400i	−1.11923	−	0.463602i	−0.255125	−	0.966908i	$-0.582117\pi$
$853$	−32.6885	−	13.5400i	−1.11923	−	0.463602i	−0.864108	+	0.503306i	$0.832117\pi$
$854$			13.6845i			0.468273i
$855$		0			0
$856$	−24.1564	+	10.0059i	−0.825650	+	0.341995i
$857$	3.52531	+	8.51086i	0.120422	+	0.290725i	0.972583	−	0.232554i	$-0.0747083\pi$
$857$	3.52531	+	8.51086i	0.120422	+	0.290725i	−0.852161	+	0.523280i	$0.824708\pi$
$858$	−0.792349	−	0.792349i	−0.0270503	−	0.0270503i
$859$	−11.8621	−	11.8621i	−0.404730	−	0.404730i	0.475166	−	0.879896i	$-0.342388\pi$
$859$	−11.8621	−	11.8621i	−0.404730	−	0.404730i	−0.879896	+	0.475166i	$0.842388\pi$
$860$		0			0
$861$	−1.66048	+	0.687793i	−0.0565890	+	0.0234399i
$862$	−2.25753	+	5.45016i	−0.0768918	+	0.185633i
$863$			34.1729i			1.16326i	0.813454	+	0.581630i	$0.197585\pi$
$863$			34.1729i			1.16326i	−0.813454	+	0.581630i	$0.802415\pi$
$864$	−0.236654	−	0.0980254i	−0.00805114	−	0.00333489i
$865$		0			0
$866$	35.7254			1.21400
$867$	−0.461492	−	1.82662i	−0.0156731	−	0.0620353i
$868$	0.335281			0.0113802
$869$	−16.0879	+	16.0879i	−0.545744	+	0.545744i
$870$		0			0
$871$		−	3.09338i		−	0.104815i
$872$	−0.818141	+	1.97517i	−0.0277057	+	0.0668876i
$873$	23.4446	−	9.71107i	0.793479	−	0.328670i
$874$	3.08427	+	7.44609i	0.104327	+	0.251868i
$875$		0			0
$876$	−0.0312299	−	0.0312299i	−0.00105516	−	0.00105516i
$877$	−5.04652	−	12.1834i	−0.170409	−	0.411404i	0.815484	−	0.578779i	$-0.196471\pi$
$877$	−5.04652	−	12.1834i	−0.170409	−	0.411404i	−0.985893	+	0.167376i	$0.946471\pi$
$878$	3.98075	−	1.64888i	0.134344	−	0.0556470i
$879$	−0.593968	+	1.43396i	−0.0200340	+	0.0483664i
$880$		0			0
$881$	−29.5578	−	12.2433i	−0.995829	−	0.412486i	−0.175563	−	0.984468i	$-0.556175\pi$
$881$	−29.5578	−	12.2433i	−0.995829	−	0.412486i	−0.820266	+	0.571982i	$0.806175\pi$
$882$	−11.9088	+	11.9088i	−0.400989	+	0.400989i
$883$	−48.1807			−1.62141			−0.810704	−	0.585456i	$-0.800915\pi$
$883$	−48.1807			−1.62141			−0.810704	+	0.585456i	$0.800915\pi$
$884$	−0.315472	−	0.158393i	−0.0106105	−	0.00532735i
$885$		0			0
$886$	−25.8611	+	25.8611i	−0.868819	+	0.868819i
$887$	37.8812	+	15.6909i	1.27193	+	0.526850i	0.913550	−	0.406727i	$-0.133330\pi$
$887$	37.8812	+	15.6909i	1.27193	+	0.526850i	0.358378	+	0.933577i	$0.383330\pi$
$888$			2.00998i			0.0674505i
$889$	9.52097	−	22.9856i	0.319323	−	0.770914i
$890$		0			0
$891$	19.7338	+	47.6416i	0.661106	+	1.59605i
$892$	−0.857830	−	0.857830i	−0.0287223	−	0.0287223i
$893$	15.2532	+	15.2532i	0.510428	+	0.510428i
$894$	0.255017	+	0.615665i	0.00852904	+	0.0205909i
$895$		0			0
$896$	−7.02613	+	16.9626i	−0.234726	+	0.566680i
$897$			0.285259i			0.00952450i
$898$	18.8825	+	7.82140i	0.630118	+	0.261003i
$899$	10.5361	−	10.5361i	0.351399	−	0.351399i
$900$		0			0
$901$	−28.2073	+	9.35024i	−0.939722	+	0.311502i
$902$	−76.2000			−2.53718
$903$	−0.999574	+	0.999574i	−0.0332637	+	0.0332637i
$904$	−24.0001	−	9.94116i	−0.798231	−	0.330638i
$905$		0			0
$906$	1.18251	−	2.85483i	0.0392862	−	0.0948453i
$907$	51.4191	−	21.2985i	1.70734	−	0.707205i	0.707344	−	0.706869i	$-0.249893\pi$
$907$	51.4191	−	21.2985i	1.70734	−	0.707205i	1.00000		0.000335808i	$-0.000106891\pi$
$908$	−0.291898	−	0.704704i	−0.00968698	−	0.0233864i
$909$	−5.36254	−	5.36254i	−0.177864	−	0.177864i
$910$		0			0
$911$	5.61087	+	13.5458i	0.185897	+	0.448794i	0.989162	−	0.146827i	$-0.0469061\pi$
$911$	5.61087	+	13.5458i	0.185897	+	0.448794i	−0.803266	+	0.595621i	$0.796906\pi$
$912$	−1.11628	+	0.462380i	−0.0369638	+	0.0153109i
$913$	19.7770	−	47.7459i	0.654523	−	1.58016i
$914$			14.7080i			0.486496i
$915$		0			0
$916$	−1.03045	+	1.03045i	−0.0340469	+	0.0340469i
$917$	−28.9095			−0.954675
$918$	2.48676	+	2.87693i	0.0820754	+	0.0949529i
$919$	1.54175			0.0508578			0.0254289	−	0.999677i	$-0.491905\pi$
$919$	1.54175			0.0508578			0.0254289	+	0.999677i	$0.491905\pi$
$920$		0			0
$921$	1.35985	+	0.563267i	0.0448085	+	0.0185603i
$922$			25.7196i			0.847031i
$923$	6.46851	−	15.6164i	0.212914	−	0.514019i
$924$	0.0695739	−	0.0288185i	0.00228881	−	0.000948058i
$925$		0			0
$926$	−37.0892	−	37.0892i	−1.21883	−	1.21883i
$927$	−35.2209	−	35.2209i	−1.15680	−	1.15680i
$928$	−0.769017	−	1.85657i	−0.0252442	−	0.0609449i
$929$	−12.5602	+	5.20262i	−0.412088	+	0.170692i	−0.579089	−	0.815264i	$-0.696592\pi$
$929$	−12.5602	+	5.20262i	−0.412088	+	0.170692i	0.167001	+	0.985957i	$0.446592\pi$
$930$		0			0
$931$		−	11.4588i		−	0.375548i
$932$	0.523843	+	0.216983i	0.0171591	+	0.00710751i
$933$	1.84589	−	1.84589i	0.0604319	−	0.0604319i
$934$	−42.0279			−1.37520
$935$		0			0
$936$	10.7710			0.352060
$937$	−11.1059	+	11.1059i	−0.362815	+	0.362815i	−0.864848	−	0.502033i	$-0.832586\pi$
$937$	−11.1059	+	11.1059i	−0.362815	+	0.362815i	0.502033	+	0.864848i	$0.332586\pi$
$938$	−5.43471	−	2.25113i	−0.177450	−	0.0735020i
$939$		−	3.61922i		−	0.118109i
$940$		0			0
$941$	−39.9824	+	16.5613i	−1.30339	+	0.539882i	−0.922948	−	0.384924i	$-0.874228\pi$
$941$	−39.9824	+	16.5613i	−1.30339	+	0.539882i	−0.380441	+	0.924805i	$0.624228\pi$
$942$	1.27928	+	3.08844i	0.0416810	+	0.100627i
$943$	13.7166	+	13.7166i	0.446675	+	0.446675i
$944$	−5.95493	−	5.95493i	−0.193817	−	0.193817i
$945$		0			0
$946$	−55.3710	+	22.9354i	−1.80027	+	0.745694i
$947$	−7.84765	+	18.9459i	−0.255014	+	0.615659i	−0.998595	−	0.0529869i	$-0.983126\pi$
$947$	−7.84765	+	18.9459i	−0.255014	+	0.615659i	0.743581	+	0.668646i	$0.233126\pi$
$948$			0.0296743i			0.000963777i
$949$	6.76363	+	2.80159i	0.219557	+	0.0909434i
$950$		0			0
$951$	2.81505			0.0912843
$952$	−15.3861	+	13.2994i	−0.498666	+	0.431037i
$953$	5.27570			0.170897			0.0854483	−	0.996343i	$-0.472768\pi$
$953$	5.27570			0.170897			0.0854483	+	0.996343i	$0.472768\pi$
$954$	21.1628	−	21.1628i	0.685172	−	0.685172i
$955$		0			0
$956$		−	0.233738i		−	0.00755963i
$957$	1.28073	−	3.09196i	0.0414001	−	0.0999487i
$958$	34.6153	−	14.3381i	1.11837	−	0.463243i
$959$	13.2828	+	32.0674i	0.428923	+	1.03551i
$960$		0			0
$961$	−16.1275	−	16.1275i	−0.520243	−	0.520243i
$962$	−4.20846	−	10.1601i	−0.135686	−	0.327575i
$963$	25.1068	−	10.3996i	0.809057	−	0.335122i
$964$	0.165849	−	0.400396i	0.00534165	−	0.0128959i
$965$		0			0
$966$	0.501166	+	0.207590i	0.0161248	+	0.00667909i
$967$	4.17382	−	4.17382i	0.134221	−	0.134221i	−0.636804	−	0.771025i	$-0.719744\pi$
$967$	4.17382	−	4.17382i	0.134221	−	0.134221i	0.771025	+	0.636804i	$0.219744\pi$
$968$	65.1080			2.09265
$969$	−1.28761	−	0.0936646i	−0.0413641	−	0.00300894i
$970$		0			0
$971$	1.27662	−	1.27662i	0.0409687	−	0.0409687i	−0.686326	−	0.727294i	$-0.740778\pi$
$971$	1.27662	−	1.27662i	0.0409687	−	0.0409687i	0.727294	+	0.686326i	$0.240778\pi$
$972$	0.187698	+	0.0777469i	0.00602041	+	0.00249373i
$973$		−	7.30446i		−	0.234170i
$974$	−2.03838	+	4.92109i	−0.0653140	+	0.157682i
$975$		0			0
$976$	8.47341	+	20.4566i	0.271227	+	0.654800i
$977$	6.89768	+	6.89768i	0.220676	+	0.220676i	0.808783	−	0.588107i	$-0.200127\pi$
$977$	6.89768	+	6.89768i	0.220676	+	0.220676i	−0.588107	+	0.808783i	$0.700127\pi$
$978$	0.144435	+	0.144435i	0.00461853	+	0.00461853i
$979$	−31.7617	−	76.6795i	−1.01511	−	2.45069i
$980$		0			0
$981$	0.850330	−	2.05288i	0.0271489	−	0.0655433i
$982$			8.20202i			0.261737i
$983$	3.71298	+	1.53797i	0.118426	+	0.0490535i	0.441110	−	0.897453i	$-0.354585\pi$
$983$	3.71298	+	1.53797i	0.118426	+	0.0490535i	−0.322684	+	0.946507i	$0.604585\pi$
$984$	−2.12909	+	2.12909i	−0.0678731	+	0.0678731i
$985$		0			0
$986$	−2.16440	+	29.7541i	−0.0689284	+	0.947562i
$987$	1.45187			0.0462136
$988$	−0.171045	+	0.171045i	−0.00544165	+	0.00544165i
$989$	14.0958	+	5.83867i	0.448220	+	0.185659i
$990$		0			0
$991$	−5.31652	+	12.8352i	−0.168885	+	0.407724i	−0.985549	−	0.169389i	$-0.945821\pi$
$991$	−5.31652	+	12.8352i	−0.168885	+	0.407724i	0.816665	+	0.577113i	$0.195821\pi$
$992$	1.02075	−	0.422808i	0.0324088	−	0.0134242i
$993$	−0.781969	−	1.88784i	−0.0248150	−	0.0599088i
$994$	−22.7289	−	22.7289i	−0.720915	−	0.720915i
$995$		0			0
$996$	−0.0257945	−	0.0622734i	−0.000817330	−	0.00197321i
$997$	14.8458	−	6.14934i	0.470172	−	0.194751i	−0.135001	−	0.990845i	$-0.543104\pi$
$997$	14.8458	−	6.14934i	0.470172	−	0.194751i	0.605173	+	0.796094i	$0.293104\pi$
$998$	−23.4509	+	56.6155i	−0.742325	+	1.79213i
$999$		−	4.18671i		−	0.132462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.d.26.4	yes	24
5.2	odd	4		425.2.n.e.349.4		24
5.3	odd	4		425.2.n.d.349.3		24
5.4	even	2		425.2.m.c.26.3	✓	24
17.2	even	8	inner	425.2.m.d.376.4	yes	24
17.6	odd	16		7225.2.a.cb.1.17		24
17.11	odd	16		7225.2.a.cb.1.18		24
85.2	odd	8		425.2.n.d.274.3		24
85.19	even	8		425.2.m.c.376.3	yes	24
85.53	odd	8		425.2.n.e.274.4		24
85.74	odd	16		7225.2.a.bx.1.8		24
85.79	odd	16		7225.2.a.bx.1.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.26.3	✓	24	5.4	even	2
425.2.m.c.376.3	yes	24	85.19	even	8
425.2.m.d.26.4	yes	24	1.1	even	1	trivial
425.2.m.d.376.4	yes	24	17.2	even	8	inner
425.2.n.d.274.3		24	85.2	odd	8
425.2.n.d.349.3		24	5.3	odd	4
425.2.n.e.274.4		24	85.53	odd	8
425.2.n.e.349.4		24	5.2	odd	4
7225.2.a.bx.1.7		24	85.79	odd	16
7225.2.a.bx.1.8		24	85.74	odd	16
7225.2.a.cb.1.17		24	17.6	odd	16
7225.2.a.cb.1.18		24	17.11	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.982785 - 0.982785i) q^{2} +(-0.102388 - 0.0424107i) q^{3} +0.0682683i q^{4} +(-0.142306 + 0.0589452i) q^{6} +(0.656642 + 1.58527i) q^{7} +(2.03266 + 2.03266i) q^{8} +(-2.11264 - 2.11264i) q^{9} +O(q^{10})\)	\(q+(0.982785 - 0.982785i) q^{2} +(-0.102388 - 0.0424107i) q^{3} +0.0682683i q^{4} +(-0.142306 + 0.0589452i) q^{6} +(0.656642 + 1.58527i) q^{7} +(2.03266 + 2.03266i) q^{8} +(-2.11264 - 2.11264i) q^{9} +(5.35924 - 2.21987i) q^{11} +(0.00289530 - 0.00698988i) q^{12} +1.25411i q^{13} +(2.20332 + 0.912645i) q^{14} +3.85880 q^{16} +(3.68474 + 1.85005i) q^{17} -4.15253 q^{18} +(1.99782 - 1.99782i) q^{19} -0.190162i q^{21} +(3.08532 - 7.44863i) q^{22} +(-1.89620 + 0.785431i) q^{23} +(-0.121915 - 0.294328i) q^{24} +(1.23252 + 1.23252i) q^{26} +(0.253943 + 0.613073i) q^{27} +(-0.108224 + 0.0448278i) q^{28} +(-1.99220 + 4.80961i) q^{29} +(-2.64434 - 1.09532i) q^{31} +(-0.272952 + 0.272952i) q^{32} -0.642871 q^{33} +(5.43951 - 1.80310i) q^{34} +(0.144226 - 0.144226i) q^{36} +(-5.82896 - 2.41443i) q^{37} -3.92685i q^{38} +(0.0531875 - 0.128406i) q^{39} +(-3.61688 - 8.73191i) q^{41} +(-0.186889 - 0.186889i) q^{42} +(-5.25643 - 5.25643i) q^{43} +(0.151547 + 0.365866i) q^{44} +(-1.09165 + 2.63546i) q^{46} +7.63491i q^{47} +(-0.395097 - 0.163655i) q^{48} +(2.86784 - 2.86784i) q^{49} +(-0.298813 - 0.345696i) q^{51} -0.0856157 q^{52} +(-5.09637 + 5.09637i) q^{53} +(0.852091 + 0.352948i) q^{54} +(-1.88759 + 4.55706i) q^{56} +(-0.289282 + 0.119825i) q^{57} +(2.76890 + 6.68472i) q^{58} +(-1.54321 - 1.54321i) q^{59} +(2.19586 + 5.30128i) q^{61} +(-3.67528 + 1.52235i) q^{62} +(1.96186 - 4.73635i) q^{63} +8.25411i q^{64} +(-0.631803 + 0.631803i) q^{66} -2.46660 q^{67} +(-0.126300 + 0.251551i) q^{68} +0.227460 q^{69} +(-12.4522 - 5.15787i) q^{71} -8.58855i q^{72} +(2.23393 - 5.39319i) q^{73} +(-8.10148 + 3.35574i) q^{74} +(0.136388 + 0.136388i) q^{76} +(7.03820 + 7.03820i) q^{77} +(-0.0739236 - 0.178467i) q^{78} +(-3.62361 + 1.50095i) q^{79} +8.88961i q^{81} +(-12.1362 - 5.02698i) q^{82} +(6.29967 - 6.29967i) q^{83} +0.0129821 q^{84} -10.3319 q^{86} +(0.407958 - 0.407958i) q^{87} +(15.4058 + 6.38128i) q^{88} -14.3079i q^{89} +(-1.98810 + 0.823498i) q^{91} +(-0.0536200 - 0.129450i) q^{92} +(0.224296 + 0.224296i) q^{93} +(7.50348 + 7.50348i) q^{94} +(0.0395233 - 0.0163711i) q^{96} +(-3.25033 + 7.84699i) q^{97} -5.63693i q^{98} +(-16.0119 - 6.63234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^6 + 12 * q^9	\( 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31} + 60 q^{32} - 48 q^{33} + 16 q^{34} + 60 q^{36} + 12 q^{37} + 8 q^{39} - 20 q^{41} - 12 q^{42} - 32 q^{43} + 64 q^{44} - 40 q^{46} + 40 q^{48} + 24 q^{49} + 16 q^{51} + 48 q^{52} + 12 q^{53} - 20 q^{54} - 32 q^{56} - 68 q^{57} + 16 q^{58} - 16 q^{59} - 64 q^{61} - 100 q^{62} + 44 q^{63} - 72 q^{66} - 40 q^{67} - 20 q^{68} - 48 q^{69} - 24 q^{71} + 32 q^{74} + 52 q^{76} - 24 q^{77} + 16 q^{78} - 48 q^{79} - 100 q^{82} - 12 q^{83} - 40 q^{84} - 16 q^{86} - 24 q^{87} - 4 q^{88} + 24 q^{91} + 88 q^{92} + 32 q^{93} - 40 q^{94} + 132 q^{96} + 88 q^{97} - 80 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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