LMFDB - Embedded newform 625.2.d.h.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	625.251
Dual form			625.2.d.h.376.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034 q^{7} +(0.690983 + 2.12663i) q^{8} +(1.61803 + 1.17557i) q^{9} +O(q^{10})$	\(q+(1.30902 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034 q^{7} +(0.690983 + 2.12663i) q^{8} +(1.61803 + 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(-0.500000 - 0.363271i) q^{12} +(-1.50000 - 1.08981i) q^{13} +(0.809017 - 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(-1.61803 - 4.97980i) q^{17} +3.23607 q^{18} +(0.263932 + 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(2.61803 - 8.05748i) q^{22} +(-3.04508 + 2.21238i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(4.04508 - 2.93893i) q^{27} +(0.118034 - 0.363271i) q^{28} +(-1.11803 + 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} +3.38197 q^{32} +(-1.61803 - 4.97980i) q^{33} +(-6.85410 - 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(0.190983 + 0.138757i) q^{37} +(1.11803 + 0.812299i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(-0.309017 - 0.951057i) q^{42} -4.85410 q^{43} +(-1.00000 - 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(0.190983 - 0.587785i) q^{47} +(3.92705 - 2.85317i) q^{48} -6.61803 q^{49} -5.23607 q^{51} +(-0.927051 + 0.673542i) q^{52} +(-1.07295 + 3.30220i) q^{53} +(2.50000 - 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} +0.854102 q^{57} +(1.80902 + 5.56758i) q^{58} +(8.78115 + 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-3.92705 - 2.85317i) q^{62} +(1.00000 + 0.726543i) q^{63} +(-3.42705 + 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(1.47214 + 4.53077i) q^{67} -3.23607 q^{68} +(1.16312 + 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(-1.38197 + 4.25325i) q^{72} +(7.28115 - 5.29007i) q^{73} +0.381966 q^{74} +0.527864 q^{76} +(2.61803 - 1.90211i) q^{77} +(-0.927051 + 2.85317i) q^{78} +(-2.50000 + 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} +1.23607 q^{82} +(-1.92705 - 5.93085i) q^{83} +(-0.309017 - 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(2.92705 + 2.12663i) q^{87} +(9.47214 + 6.88191i) q^{88} +(7.23607 - 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(0.718847 + 2.21238i) q^{92} -3.00000 q^{93} +(-0.309017 - 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(-1.19098 + 3.66547i) q^{97} +(-8.66312 + 6.29412i) q^{98} +10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 - 2 * q^7 + 5 * q^8 + 2 * q^9	$ 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9} + 8 q^{11} - 2 q^{12} - 6 q^{13} + q^{14} + 9 q^{16} - 2 q^{17} + 4 q^{18} + 10 q^{19} + 3 q^{21} + 6 q^{22} - q^{23} - 12 q^{26} + 5 q^{27} - 4 q^{28} + 3 q^{31} + 18 q^{32} - 2 q^{33} - 14 q^{34} + 4 q^{36} + 3 q^{37} - 6 q^{39} - 2 q^{41} + q^{42} - 6 q^{43} - 4 q^{44} - 12 q^{46} + 3 q^{47} + 9 q^{48} - 22 q^{49} - 12 q^{51} + 3 q^{52} - 11 q^{53} + 10 q^{54} - 5 q^{56} - 10 q^{57} + 5 q^{58} + 15 q^{59} - 17 q^{61} - 9 q^{62} + 4 q^{63} - 7 q^{64} - 14 q^{66} - 12 q^{67} - 4 q^{68} - 11 q^{69} + 3 q^{71} - 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{76} + 6 q^{77} + 3 q^{78} - 10 q^{79} - q^{81} - 4 q^{82} - q^{83} + q^{84} - 12 q^{86} + 5 q^{87} + 20 q^{88} + 20 q^{89} + 3 q^{91} + 23 q^{92} - 12 q^{93} + q^{94} - 7 q^{96} - 7 q^{97} - 19 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 - 2 * q^7 + 5 * q^8 + 2 * q^9 + 8 * q^11 - 2 * q^12 - 6 * q^13 + q^14 + 9 * q^16 - 2 * q^17 + 4 * q^18 + 10 * q^19 + 3 * q^21 + 6 * q^22 - q^23 - 12 * q^26 + 5 * q^27 - 4 * q^28 + 3 * q^31 + 18 * q^32 - 2 * q^33 - 14 * q^34 + 4 * q^36 + 3 * q^37 - 6 * q^39 - 2 * q^41 + q^42 - 6 * q^43 - 4 * q^44 - 12 * q^46 + 3 * q^47 + 9 * q^48 - 22 * q^49 - 12 * q^51 + 3 * q^52 - 11 * q^53 + 10 * q^54 - 5 * q^56 - 10 * q^57 + 5 * q^58 + 15 * q^59 - 17 * q^61 - 9 * q^62 + 4 * q^63 - 7 * q^64 - 14 * q^66 - 12 * q^67 - 4 * q^68 - 11 * q^69 + 3 * q^71 - 10 * q^72 + 9 * q^73 + 6 * q^74 + 20 * q^76 + 6 * q^77 + 3 * q^78 - 10 * q^79 - q^81 - 4 * q^82 - q^83 + q^84 - 12 * q^86 + 5 * q^87 + 20 * q^88 + 20 * q^89 + 3 * q^91 + 23 * q^92 - 12 * q^93 + q^94 - 7 * q^96 - 7 * q^97 - 19 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.30902	−	0.951057i	0.925615	−	0.672499i	−0.0193004	−	0.999814i	$-0.506144\pi$
$2$	1.30902	−	0.951057i	0.925615	−	0.672499i	0.944915	+	0.327315i	$0.106144\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i	−0.821362	−	0.570408i	$-0.806785\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i	0.999773	+	0.0213149i	$0.00678525\pi$
$4$	0.190983	−	0.587785i	0.0954915	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	1.53884i	−0.204124	−	0.628230i
$7$	0.618034			0.233595			0.116797	−	0.993156i	$-0.462737\pi$
$7$	0.618034			0.233595			0.116797	+	0.993156i	$0.462737\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	1.61803	+	1.17557i	0.539345	+	0.391857i
$10$		0			0
$11$	4.23607	−	3.07768i	1.27722	−	0.927957i	0.277757	−	0.960651i	$-0.410409\pi$
$11$	4.23607	−	3.07768i	1.27722	−	0.927957i	0.999465	+	0.0326948i	$0.0104089\pi$
$12$	−0.500000	−	0.363271i	−0.144338	−	0.104867i
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	0.360011	−	0.932948i	$-0.382773\pi$
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	−0.776037	+	0.630688i	$0.782773\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$		0			0
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	−1.61803	−	4.97980i	−0.392431	−	1.20778i	−0.930944	−	0.365161i	$-0.881014\pi$
$17$	−1.61803	−	4.97980i	−0.392431	−	1.20778i	0.538513	−	0.842617i	$-0.318986\pi$
$18$	3.23607			0.762749
$19$	0.263932	+	0.812299i	0.0605502	+	0.186354i	0.976756	−	0.214353i	$-0.0687644\pi$
$19$	0.263932	+	0.812299i	0.0605502	+	0.186354i	−0.916206	+	0.400707i	$0.868764\pi$
$20$		0			0
$21$	0.190983	−	0.587785i	0.0416759	−	0.128265i
$22$	2.61803	−	8.05748i	0.558167	−	1.71786i
$23$	−3.04508	+	2.21238i	−0.634944	+	0.461314i	−0.858110	−	0.513467i	$-0.828361\pi$
$23$	−3.04508	+	2.21238i	−0.634944	+	0.461314i	0.223165	+	0.974781i	$0.428361\pi$
$24$	2.23607			0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	4.04508	−	2.93893i	0.778477	−	0.565597i
$28$	0.118034	−	0.363271i	0.0223063	−	0.0686518i
$29$	−1.11803	+	3.44095i	−0.207614	+	0.638969i	0.791982	+	0.610544i	$0.209049\pi$
$29$	−1.11803	+	3.44095i	−0.207614	+	0.638969i	−0.999596	+	0.0284251i	$0.990951\pi$
$30$		0			0
$31$	−0.927051	−	2.85317i	−0.166503	−	0.512444i	0.832641	−	0.553814i	$-0.186828\pi$
$31$	−0.927051	−	2.85317i	−0.166503	−	0.512444i	−0.999144	+	0.0413693i	$0.986828\pi$
$32$	3.38197			0.597853
$33$	−1.61803	−	4.97980i	−0.281664	−	0.866871i
$34$	−6.85410	−	4.97980i	−1.17547	−	0.854028i
$35$		0			0
$36$	1.00000	−	0.726543i	0.166667	−	0.121090i
$37$	0.190983	+	0.138757i	0.0313974	+	0.0228116i	0.603373	−	0.797459i	$-0.293823\pi$
$37$	0.190983	+	0.138757i	0.0313974	+	0.0228116i	−0.571976	+	0.820270i	$0.693823\pi$
$38$	1.11803	+	0.812299i	0.181369	+	0.131772i
$39$	−1.50000	+	1.08981i	−0.240192	+	0.174510i
$40$		0			0
$41$	0.618034	+	0.449028i	0.0965207	+	0.0701264i	0.634999	−	0.772513i	$-0.281001\pi$
$41$	0.618034	+	0.449028i	0.0965207	+	0.0701264i	−0.538478	+	0.842639i	$0.681001\pi$
$42$	−0.309017	−	0.951057i	−0.0476824	−	0.146751i
$43$	−4.85410			−0.740244			−0.370122	−	0.928983i	$-0.620684\pi$
$43$	−4.85410			−0.740244			−0.370122	+	0.928983i	$0.620684\pi$
$44$	−1.00000	−	3.07768i	−0.150756	−	0.463978i
$45$		0			0
$46$	−1.88197	+	5.79210i	−0.277481	+	0.853998i
$47$	0.190983	−	0.587785i	0.0278577	−	0.0857373i	−0.936161	−	0.351572i	$-0.885647\pi$
$47$	0.190983	−	0.587785i	0.0278577	−	0.0857373i	0.964019	+	0.265834i	$0.0856474\pi$
$48$	3.92705	−	2.85317i	0.566821	−	0.411820i
$49$	−6.61803			−0.945433
$50$		0			0
$51$	−5.23607			−0.733196
$52$	−0.927051	+	0.673542i	−0.128559	+	0.0934035i
$53$	−1.07295	+	3.30220i	−0.147381	+	0.453592i	−0.997309	−	0.0733062i	$-0.976645\pi$
$53$	−1.07295	+	3.30220i	−0.147381	+	0.453592i	0.849929	+	0.526898i	$0.176645\pi$
$54$	2.50000	−	7.69421i	0.340207	−	1.04705i
$55$		0			0
$56$	0.427051	+	1.31433i	0.0570671	+	0.175634i
$57$	0.854102			0.113129
$58$	1.80902	+	5.56758i	0.237536	+	0.731059i
$59$	8.78115	+	6.37988i	1.14321	+	0.830590i	0.987563	−	0.157223i	$-0.0502542\pi$
$59$	8.78115	+	6.37988i	1.14321	+	0.830590i	0.155646	+	0.987813i	$0.450254\pi$
$60$		0			0
$61$	−7.04508	+	5.11855i	−0.902031	+	0.655364i	−0.938987	−	0.343953i	$-0.888234\pi$
$61$	−7.04508	+	5.11855i	−0.902031	+	0.655364i	0.0369561	+	0.999317i	$0.488234\pi$
$62$	−3.92705	−	2.85317i	−0.498736	−	0.362353i
$63$	1.00000	+	0.726543i	0.125988	+	0.0915358i
$64$	−3.42705	+	2.48990i	−0.428381	+	0.311237i
$65$		0			0
$66$	−6.85410	−	4.97980i	−0.843682	−	0.612971i
$67$	1.47214	+	4.53077i	0.179850	+	0.553521i	0.999822	−	0.0188826i	$-0.00601088\pi$
$67$	1.47214	+	4.53077i	0.179850	+	0.553521i	−0.819972	+	0.572404i	$0.806011\pi$
$68$	−3.23607			−0.392431
$69$	1.16312	+	3.57971i	0.140023	+	0.430947i
$70$		0			0
$71$	−2.04508	+	6.29412i	−0.242707	+	0.746975i	0.753298	+	0.657679i	$0.228462\pi$
$71$	−2.04508	+	6.29412i	−0.242707	+	0.746975i	−0.996005	+	0.0892960i	$0.971538\pi$
$72$	−1.38197	+	4.25325i	−0.162866	+	0.501251i
$73$	7.28115	−	5.29007i	0.852194	−	0.619156i	−0.0735557	−	0.997291i	$-0.523435\pi$
$73$	7.28115	−	5.29007i	0.852194	−	0.619156i	0.925750	+	0.378136i	$0.123435\pi$
$74$	0.381966			0.0444026
$75$		0			0
$76$	0.527864			0.0605502
$77$	2.61803	−	1.90211i	0.298353	−	0.216766i
$78$	−0.927051	+	2.85317i	−0.104968	+	0.323058i
$79$	−2.50000	+	7.69421i	−0.281272	+	0.865666i	0.706219	+	0.707993i	$0.250399\pi$
$79$	−2.50000	+	7.69421i	−0.281272	+	0.865666i	−0.987491	+	0.157673i	$0.949601\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.23607			0.136501
$83$	−1.92705	−	5.93085i	−0.211521	−	0.650996i	−0.999382	−	0.0351426i	$-0.988811\pi$
$83$	−1.92705	−	5.93085i	−0.211521	−	0.650996i	0.787861	−	0.615853i	$-0.211189\pi$
$84$	−0.309017	−	0.224514i	−0.0337165	−	0.0244965i
$85$		0			0
$86$	−6.35410	+	4.61653i	−0.685180	+	0.497813i
$87$	2.92705	+	2.12663i	0.313813	+	0.227998i
$88$	9.47214	+	6.88191i	1.00973	+	0.733614i
$89$	7.23607	−	5.25731i	0.767022	−	0.557274i	−0.134034	−	0.990977i	$-0.542793\pi$
$89$	7.23607	−	5.25731i	0.767022	−	0.557274i	0.901056	+	0.433703i	$0.142793\pi$
$90$		0			0
$91$	−0.927051	−	0.673542i	−0.0971813	−	0.0706064i
$92$	0.718847	+	2.21238i	0.0749450	+	0.230657i
$93$	−3.00000			−0.311086
$94$	−0.309017	−	0.951057i	−0.0318727	−	0.0980940i
$95$		0			0
$96$	1.04508	−	3.21644i	0.106664	−	0.328277i
$97$	−1.19098	+	3.66547i	−0.120926	+	0.372172i	−0.993137	−	0.116958i	$-0.962686\pi$
$97$	−1.19098	+	3.66547i	−0.120926	+	0.372172i	0.872211	+	0.489130i	$0.162686\pi$
$98$	−8.66312	+	6.29412i	−0.875107	+	0.635803i
$99$	10.4721			1.05249
$100$		0			0
$101$	1.47214			0.146483			0.0732415	−	0.997314i	$-0.476666\pi$
$101$	1.47214			0.146483			0.0732415	+	0.997314i	$0.476666\pi$
$102$	−6.85410	+	4.97980i	−0.678657	+	0.493073i
$103$	2.64590	−	8.14324i	0.260708	−	0.802377i	−0.731943	−	0.681366i	$-0.761386\pi$
$103$	2.64590	−	8.14324i	0.260708	−	0.802377i	0.992651	−	0.121011i	$-0.0386137\pi$
$104$	1.28115	−	3.94298i	0.125627	−	0.386641i
$105$		0			0
$106$	1.73607	+	5.34307i	0.168622	+	0.518965i
$107$	−16.4164			−1.58703			−0.793517	−	0.608548i	$-0.791752\pi$
$107$	−16.4164			−1.58703			−0.793517	+	0.608548i	$0.791752\pi$
$108$	−0.954915	−	2.93893i	−0.0918867	−	0.282798i
$109$	−8.09017	−	5.87785i	−0.774898	−	0.562996i	0.128546	−	0.991704i	$-0.458969\pi$
$109$	−8.09017	−	5.87785i	−0.774898	−	0.562996i	−0.903443	+	0.428707i	$0.858969\pi$
$110$		0			0
$111$	0.190983	−	0.138757i	0.0181273	−	0.0131703i
$112$	2.42705	+	1.76336i	0.229335	+	0.166621i
$113$	−13.6353	−	9.90659i	−1.28270	−	0.931934i	−0.283066	−	0.959100i	$-0.591352\pi$
$113$	−13.6353	−	9.90659i	−1.28270	−	0.931934i	−0.999631	+	0.0271666i	$0.991352\pi$
$114$	1.11803	−	0.812299i	0.104713	−	0.0760788i
$115$		0			0
$116$	1.80902	+	1.31433i	0.167963	+	0.122032i
$117$	−1.14590	−	3.52671i	−0.105938	−	0.326045i
$118$	17.5623			1.61674
$119$	−1.00000	−	3.07768i	−0.0916698	−	0.282131i
$120$		0			0
$121$	5.07295	−	15.6129i	0.461177	−	1.41936i
$122$	−4.35410	+	13.4005i	−0.394202	+	1.21323i
$123$	0.618034	−	0.449028i	0.0557262	−	0.0404875i
$124$	−1.85410			−0.166503
$125$		0			0
$126$	2.00000			0.178174
$127$	−16.0902	+	11.6902i	−1.42777	+	1.03734i	−0.437346	+	0.899294i	$0.644081\pi$
$127$	−16.0902	+	11.6902i	−1.42777	+	1.03734i	−0.990426	+	0.138043i	$0.955919\pi$
$128$	−4.20820	+	12.9515i	−0.371956	+	1.14476i
$129$	−1.50000	+	4.61653i	−0.132068	+	0.406462i
$130$		0			0
$131$	2.10081	+	6.46564i	0.183549	+	0.564905i	0.999920	−	0.0126218i	$-0.00401775\pi$
$131$	2.10081	+	6.46564i	0.183549	+	0.564905i	−0.816371	+	0.577527i	$0.804018\pi$
$132$	−3.23607			−0.281664
$133$	0.163119	+	0.502029i	0.0141442	+	0.0435314i
$134$	6.23607	+	4.53077i	0.538714	+	0.391399i
$135$		0			0
$136$	9.47214	−	6.88191i	0.812229	−	0.590119i
$137$	9.66312	+	7.02067i	0.825576	+	0.599816i	0.918304	−	0.395875i	$-0.129559\pi$
$137$	9.66312	+	7.02067i	0.825576	+	0.599816i	−0.0927283	+	0.995691i	$0.529559\pi$
$138$	4.92705	+	3.57971i	0.419418	+	0.304725i
$139$	−4.04508	+	2.93893i	−0.343100	+	0.249276i	−0.745968	−	0.665981i	$-0.768013\pi$
$139$	−4.04508	+	2.93893i	−0.343100	+	0.249276i	0.402869	+	0.915258i	$0.368013\pi$
$140$		0			0
$141$	−0.500000	−	0.363271i	−0.0421076	−	0.0305930i
$142$	3.30902	+	10.1841i	0.277687	+	0.854631i
$143$	−9.70820			−0.811841
$144$	3.00000	+	9.23305i	0.250000	+	0.769421i
$145$		0			0
$146$	4.50000	−	13.8496i	0.372423	−	1.14620i
$147$	−2.04508	+	6.29412i	−0.168676	+	0.519131i
$148$	0.118034	−	0.0857567i	0.00970233	−	0.00704916i
$149$	−3.94427			−0.323127			−0.161564	−	0.986862i	$-0.551654\pi$
$149$	−3.94427			−0.323127			−0.161564	+	0.986862i	$0.551654\pi$
$150$		0			0
$151$	14.5623			1.18506			0.592532	−	0.805547i	$-0.298128\pi$
$151$	14.5623			1.18506			0.592532	+	0.805547i	$0.298128\pi$
$152$	−1.54508	+	1.12257i	−0.125323	+	0.0910524i
$153$	3.23607	−	9.95959i	0.261621	−	0.805185i
$154$	1.61803	−	4.97980i	0.130385	−	0.401283i
$155$		0			0
$156$	0.354102	+	1.08981i	0.0283508	+	0.0872549i
$157$	13.1803			1.05191			0.525953	−	0.850514i	$-0.323709\pi$
$157$	13.1803			1.05191			0.525953	+	0.850514i	$0.323709\pi$
$158$	4.04508	+	12.4495i	0.321810	+	0.990428i
$159$	2.80902	+	2.04087i	0.222770	+	0.161852i
$160$		0			0
$161$	−1.88197	+	1.36733i	−0.148320	+	0.107761i
$162$	1.30902	+	0.951057i	0.102846	+	0.0747221i
$163$	−8.89919	−	6.46564i	−0.697038	−	0.506428i	0.181928	−	0.983312i	$-0.441766\pi$
$163$	−8.89919	−	6.46564i	−0.697038	−	0.506428i	−0.878966	+	0.476884i	$0.841766\pi$
$164$	0.381966	−	0.277515i	0.0298265	−	0.0216702i
$165$		0			0
$166$	−8.16312	−	5.93085i	−0.633581	−	0.460323i
$167$	4.50000	+	13.8496i	0.348220	+	1.07171i	0.959837	+	0.280558i	$0.0905195\pi$
$167$	4.50000	+	13.8496i	0.348220	+	1.07171i	−0.611617	+	0.791154i	$0.709480\pi$
$168$	1.38197			0.106621
$169$	−2.95492	−	9.09429i	−0.227301	−	0.699561i
$170$		0			0
$171$	−0.527864	+	1.62460i	−0.0403668	+	0.124236i
$172$	−0.927051	+	2.85317i	−0.0706870	+	0.217552i
$173$	−15.2812	+	11.1024i	−1.16180	+	0.844100i	−0.990005	−	0.141032i	$-0.954958\pi$
$173$	−15.2812	+	11.1024i	−1.16180	+	0.844100i	−0.171799	+	0.985132i	$0.554958\pi$
$174$	5.85410			0.443798
$175$		0			0
$176$	25.4164			1.91583
$177$	8.78115	−	6.37988i	0.660032	−	0.479541i
$178$	4.47214	−	13.7638i	0.335201	−	1.03164i
$179$	−0.163119	+	0.502029i	−0.0121921	+	0.0375234i	−0.956967	−	0.290195i	$-0.906280\pi$
$179$	−0.163119	+	0.502029i	−0.0121921	+	0.0375234i	0.944775	+	0.327719i	$0.106280\pi$
$180$		0			0
$181$	0.0901699	+	0.277515i	0.00670228	+	0.0206275i	0.954352	−	0.298685i	$-0.0965480\pi$
$181$	0.0901699	+	0.277515i	0.00670228	+	0.0206275i	−0.947649	+	0.319313i	$0.896548\pi$
$182$	−1.85410			−0.137435
$183$	2.69098	+	8.28199i	0.198923	+	0.612223i
$184$	−6.80902	−	4.94704i	−0.501967	−	0.364701i
$185$		0			0
$186$	−3.92705	+	2.85317i	−0.287945	+	0.209205i
$187$	−22.1803	−	16.1150i	−1.62199	−	1.17844i
$188$	−0.309017	−	0.224514i	−0.0225374	−	0.0163744i
$189$	2.50000	−	1.81636i	0.181848	−	0.132120i
$190$		0			0
$191$	1.47214	+	1.06957i	0.106520	+	0.0773913i	0.639770	−	0.768566i	$-0.279030\pi$
$191$	1.47214	+	1.06957i	0.106520	+	0.0773913i	−0.533250	+	0.845958i	$0.679030\pi$
$192$	1.30902	+	4.02874i	0.0944702	+	0.290749i
$193$	7.70820			0.554849			0.277424	−	0.960747i	$-0.410519\pi$
$193$	7.70820			0.554849			0.277424	+	0.960747i	$0.410519\pi$
$194$	1.92705	+	5.93085i	0.138354	+	0.425810i
$195$		0			0
$196$	−1.26393	+	3.88998i	−0.0902809	+	0.277856i
$197$	1.14590	−	3.52671i	0.0816419	−	0.251268i	−0.901901	−	0.431943i	$-0.857828\pi$
$197$	1.14590	−	3.52671i	0.0816419	−	0.251268i	0.983543	+	0.180675i	$0.0578282\pi$
$198$	13.7082	−	9.95959i	0.974200	−	0.707797i
$199$	−17.5623			−1.24496			−0.622479	−	0.782636i	$-0.713875\pi$
$199$	−17.5623			−1.24496			−0.622479	+	0.782636i	$0.713875\pi$
$200$		0			0
$201$	4.76393			0.336022
$202$	1.92705	−	1.40008i	0.135587	−	0.0985096i
$203$	−0.690983	+	2.12663i	−0.0484975	+	0.149260i
$204$	−1.00000	+	3.07768i	−0.0700140	+	0.215481i
$205$		0			0
$206$	−4.28115	−	13.1760i	−0.298282	−	0.918018i
$207$	−7.52786			−0.523223
$208$	−2.78115	−	8.55951i	−0.192838	−	0.593495i
$209$	3.61803	+	2.62866i	0.250265	+	0.181828i
$210$		0			0
$211$	7.42705	−	5.39607i	0.511299	−	0.371481i	−0.302017	−	0.953303i	$-0.597660\pi$
$211$	7.42705	−	5.39607i	0.511299	−	0.371481i	0.813316	+	0.581822i	$0.197660\pi$
$212$	1.73607	+	1.26133i	0.119234	+	0.0866283i
$213$	5.35410	+	3.88998i	0.366857	+	0.266537i
$214$	−21.4894	+	15.6129i	−1.46898	+	1.06728i
$215$		0			0
$216$	9.04508	+	6.57164i	0.615440	+	0.447143i
$217$	−0.572949	−	1.76336i	−0.0388943	−	0.119704i
$218$	−16.1803			−1.09587
$219$	−2.78115	−	8.55951i	−0.187933	−	0.578398i
$220$		0			0
$221$	−3.00000	+	9.23305i	−0.201802	+	0.621082i
$222$	0.118034	−	0.363271i	0.00792192	−	0.0243812i
$223$	0.145898	−	0.106001i	0.00977005	−	0.00709836i	−0.582890	−	0.812551i	$-0.698078\pi$
$223$	0.145898	−	0.106001i	0.00977005	−	0.00709836i	0.592660	+	0.805453i	$0.298078\pi$
$224$	2.09017			0.139655
$225$		0			0
$226$	−27.2705			−1.81401
$227$	−11.9443	+	8.67802i	−0.792769	+	0.575981i	−0.908784	−	0.417267i	$-0.862988\pi$
$227$	−11.9443	+	8.67802i	−0.792769	+	0.575981i	0.116015	+	0.993247i	$0.462988\pi$
$228$	0.163119	−	0.502029i	0.0108028	−	0.0332477i
$229$	6.70820	−	20.6457i	0.443291	−	1.36431i	−0.441057	−	0.897479i	$-0.645396\pi$
$229$	6.70820	−	20.6457i	0.443291	−	1.36431i	0.884348	−	0.466829i	$-0.154604\pi$
$230$		0			0
$231$	−1.00000	−	3.07768i	−0.0657952	−	0.202497i
$232$	−8.09017			−0.531146
$233$	−0.909830	−	2.80017i	−0.0596049	−	0.183445i	0.916821	−	0.399299i	$-0.130746\pi$
$233$	−0.909830	−	2.80017i	−0.0596049	−	0.183445i	−0.976426	+	0.215854i	$0.930746\pi$
$234$	−4.85410	−	3.52671i	−0.317323	−	0.230548i
$235$		0			0
$236$	5.42705	−	3.94298i	0.353271	−	0.256666i
$237$	6.54508	+	4.75528i	0.425149	+	0.308889i
$238$	−4.23607	−	3.07768i	−0.274584	−	0.199497i
$239$	16.6074	−	12.0660i	1.07424	−	0.780483i	0.0975727	−	0.995228i	$-0.468892\pi$
$239$	16.6074	−	12.0660i	1.07424	−	0.780483i	0.976670	+	0.214745i	$0.0688921\pi$
$240$		0			0
$241$	−2.04508	−	1.48584i	−0.131736	−	0.0957114i	0.519966	−	0.854187i	$-0.325945\pi$
$241$	−2.04508	−	1.48584i	−0.131736	−	0.0957114i	−0.651702	+	0.758475i	$0.725945\pi$
$242$	−8.20820	−	25.2623i	−0.527643	−	1.62392i
$243$	16.0000			1.02640
$244$	1.66312	+	5.11855i	0.106470	+	0.327682i
$245$		0			0
$246$	0.381966	−	1.17557i	0.0243533	−	0.0749516i
$247$	0.489357	−	1.50609i	0.0311370	−	0.0958299i
$248$	5.42705	−	3.94298i	0.344618	−	0.250380i
$249$	−6.23607			−0.395195
$250$		0			0
$251$	−29.1803			−1.84185			−0.920923	−	0.389744i	$-0.872564\pi$
$251$	−29.1803			−1.84185			−0.920923	+	0.389744i	$0.872564\pi$
$252$	0.618034	−	0.449028i	0.0389325	−	0.0282861i
$253$	−6.09017	+	18.7436i	−0.382886	+	1.17840i
$254$	−9.94427	+	30.6053i	−0.623959	+	1.92035i
$255$		0			0
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$	22.8541			1.42560			0.712800	−	0.701367i	$-0.247427\pi$
$257$	22.8541			1.42560			0.712800	+	0.701367i	$0.247427\pi$
$258$	2.42705	+	7.46969i	0.151102	+	0.465043i
$259$	0.118034	+	0.0857567i	0.00733428	+	0.00532866i
$260$		0			0
$261$	−5.85410	+	4.25325i	−0.362360	+	0.263270i
$262$	8.89919	+	6.46564i	0.549794	+	0.399448i
$263$	8.82624	+	6.41264i	0.544249	+	0.395420i	0.825661	−	0.564167i	$-0.190803\pi$
$263$	8.82624	+	6.41264i	0.544249	+	0.395420i	−0.281412	+	0.959587i	$0.590803\pi$
$264$	9.47214	−	6.88191i	0.582970	−	0.423552i
$265$		0			0
$266$	0.690983	+	0.502029i	0.0423669	+	0.0307813i
$267$	−2.76393	−	8.50651i	−0.169150	−	0.520590i
$268$	2.94427			0.179850
$269$	−3.94427	−	12.1392i	−0.240487	−	0.740141i	−0.996346	−	0.0854076i	$-0.972781\pi$
$269$	−3.94427	−	12.1392i	−0.240487	−	0.740141i	0.755860	−	0.654734i	$-0.227219\pi$
$270$		0			0
$271$	−2.47214	+	7.60845i	−0.150172	+	0.462181i	−0.997640	−	0.0686657i	$-0.978126\pi$
$271$	−2.47214	+	7.60845i	−0.150172	+	0.462181i	0.847468	+	0.530846i	$0.178126\pi$
$272$	7.85410	−	24.1724i	0.476225	−	1.46567i
$273$	−0.927051	+	0.673542i	−0.0561077	+	0.0407646i
$274$	19.3262			1.16754
$275$		0			0
$276$	2.32624			0.140023
$277$	19.9894	−	14.5231i	1.20104	−	0.872610i	0.206657	−	0.978413i	$-0.433742\pi$
$277$	19.9894	−	14.5231i	1.20104	−	0.872610i	0.994387	+	0.105804i	$0.0337416\pi$
$278$	−2.50000	+	7.69421i	−0.149940	+	0.461468i
$279$	1.85410	−	5.70634i	0.111002	−	0.341630i
$280$		0			0
$281$	3.11803	+	9.59632i	0.186006	+	0.572469i	0.999964	−	0.00845524i	$-0.00269142\pi$
$281$	3.11803	+	9.59632i	0.186006	+	0.572469i	−0.813958	+	0.580924i	$0.802691\pi$
$282$	−1.00000			−0.0595491
$283$	−9.22542	−	28.3929i	−0.548395	−	1.68778i	−0.712779	−	0.701389i	$-0.752564\pi$
$283$	−9.22542	−	28.3929i	−0.548395	−	1.68778i	0.164384	−	0.986396i	$-0.447436\pi$
$284$	3.30902	+	2.40414i	0.196354	+	0.142660i
$285$		0			0
$286$	−12.7082	+	9.23305i	−0.751452	+	0.545962i
$287$	0.381966	+	0.277515i	0.0225467	+	0.0163812i
$288$	5.47214	+	3.97574i	0.322449	+	0.234273i
$289$	−8.42705	+	6.12261i	−0.495709	+	0.360154i
$290$		0			0
$291$	3.11803	+	2.26538i	0.182782	+	0.132799i
$292$	−1.71885	−	5.29007i	−0.100588	−	0.309578i
$293$	−19.5279			−1.14083			−0.570415	−	0.821357i	$-0.693218\pi$
$293$	−19.5279			−1.14083			−0.570415	+	0.821357i	$0.693218\pi$
$294$	3.30902	+	10.1841i	0.192986	+	0.593949i
$295$		0			0
$296$	−0.163119	+	0.502029i	−0.00948110	+	0.0291798i
$297$	8.09017	−	24.8990i	0.469439	−	1.44479i
$298$	−5.16312	+	3.75123i	−0.299091	+	0.217303i
$299$	6.97871			0.403589
$300$		0			0
$301$	−3.00000			−0.172917
$302$	19.0623	−	13.8496i	1.09691	−	0.796954i
$303$	0.454915	−	1.40008i	0.0261342	−	0.0804328i
$304$	−1.28115	+	3.94298i	−0.0734792	+	0.226146i
$305$		0			0
$306$	−5.23607	−	16.1150i	−0.299326	−	0.921231i
$307$	9.23607			0.527130			0.263565	−	0.964642i	$-0.415102\pi$
$307$	9.23607			0.527130			0.263565	+	0.964642i	$0.415102\pi$
$308$	−0.618034	−	1.90211i	−0.0352158	−	0.108383i
$309$	−6.92705	−	5.03280i	−0.394066	−	0.286306i
$310$		0			0
$311$	−6.88197	+	5.00004i	−0.390240	+	0.283526i	−0.765554	−	0.643372i	$-0.777535\pi$
$311$	−6.88197	+	5.00004i	−0.390240	+	0.283526i	0.375314	+	0.926898i	$0.377535\pi$
$312$	−3.35410	−	2.43690i	−0.189889	−	0.137962i
$313$	13.5623	+	9.85359i	0.766587	+	0.556958i	0.900924	−	0.433978i	$-0.142890\pi$
$313$	13.5623	+	9.85359i	0.766587	+	0.556958i	−0.134337	+	0.990936i	$0.542890\pi$
$314$	17.2533	−	12.5352i	0.973659	−	0.707405i
$315$		0			0
$316$	4.04508	+	2.93893i	0.227554	+	0.165328i
$317$	2.36475	+	7.27794i	0.132817	+	0.408770i	0.995244	−	0.0974121i	$-0.0310565\pi$
$317$	2.36475	+	7.27794i	0.132817	+	0.408770i	−0.862427	+	0.506182i	$0.831056\pi$
$318$	5.61803			0.315044
$319$	5.85410	+	18.0171i	0.327767	+	1.00876i
$320$		0			0
$321$	−5.07295	+	15.6129i	−0.283144	+	0.871429i
$322$	−1.16312	+	3.57971i	−0.0648181	+	0.199490i
$323$	3.61803	−	2.62866i	0.201313	−	0.146262i
$324$	0.618034			0.0343352
$325$		0			0
$326$	−17.7984			−0.985761
$327$	−8.09017	+	5.87785i	−0.447387	+	0.325046i
$328$	−0.527864	+	1.62460i	−0.0291464	+	0.0897034i
$329$	0.118034	−	0.363271i	0.00650742	−	0.0200278i
$330$		0			0
$331$	−7.14590	−	21.9928i	−0.392774	−	1.20883i	−0.930682	−	0.365830i	$-0.880785\pi$
$331$	−7.14590	−	21.9928i	−0.392774	−	1.20883i	0.537907	−	0.843004i	$-0.319215\pi$
$332$	−3.85410			−0.211521
$333$	0.145898	+	0.449028i	0.00799516	+	0.0246066i
$334$	19.0623	+	13.8496i	1.04304	+	0.757815i
$335$		0			0
$336$	2.42705	−	1.76336i	0.132406	−	0.0961989i
$337$	−6.35410	−	4.61653i	−0.346130	−	0.251478i	0.401114	−	0.916028i	$-0.368623\pi$
$337$	−6.35410	−	4.61653i	−0.346130	−	0.251478i	−0.747244	+	0.664550i	$0.768623\pi$
$338$	−12.5172	−	9.09429i	−0.680847	−	0.494664i
$339$	−13.6353	+	9.90659i	−0.740565	+	0.538052i
$340$		0			0
$341$	−12.7082	−	9.23305i	−0.688188	−	0.499998i
$342$	0.854102	+	2.62866i	0.0461845	+	0.142141i
$343$	−8.41641			−0.454443
$344$	−3.35410	−	10.3229i	−0.180841	−	0.556572i
$345$		0			0
$346$	−9.44427	+	29.0665i	−0.507727	+	1.56262i
$347$	−6.15248	+	18.9354i	−0.330282	+	1.01650i	0.638717	+	0.769441i	$0.279465\pi$
$347$	−6.15248	+	18.9354i	−0.330282	+	1.01650i	−0.969000	+	0.247063i	$0.920535\pi$
$348$	1.80902	−	1.31433i	0.0969735	−	0.0704554i
$349$	21.7082			1.16201			0.581007	−	0.813899i	$-0.302659\pi$
$349$	21.7082			1.16201			0.581007	+	0.813899i	$0.302659\pi$
$350$		0			0
$351$	−9.27051			−0.494823
$352$	14.3262	−	10.4086i	0.763591	−	0.554781i
$353$	3.98936	−	12.2780i	0.212332	−	0.653491i	−0.787000	−	0.616953i	$-0.788367\pi$
$353$	3.98936	−	12.2780i	0.212332	−	0.653491i	0.999332	−	0.0365381i	$-0.0116330\pi$
$354$	5.42705	−	16.7027i	0.288445	−	0.887741i
$355$		0			0
$356$	−1.70820	−	5.25731i	−0.0905346	−	0.278637i
$357$	−3.23607			−0.171271
$358$	0.263932	+	0.812299i	0.0139492	+	0.0429313i
$359$	−11.1180	−	8.07772i	−0.586787	−	0.426326i	0.254377	−	0.967105i	$-0.418130\pi$
$359$	−11.1180	−	8.07772i	−0.586787	−	0.426326i	−0.841165	+	0.540779i	$0.818130\pi$
$360$		0			0
$361$	14.7812	−	10.7391i	0.777955	−	0.565218i
$362$	0.381966	+	0.277515i	0.0200757	+	0.0145858i
$363$	−13.2812	−	9.64932i	−0.697080	−	0.506458i
$364$	−0.572949	+	0.416272i	−0.0300307	+	0.0218186i
$365$		0			0
$366$	11.3992	+	8.28199i	0.595845	+	0.432907i
$367$	−7.89919	−	24.3112i	−0.412334	−	1.26903i	−0.914614	−	0.404329i	$-0.867505\pi$
$367$	−7.89919	−	24.3112i	−0.412334	−	1.26903i	0.502279	−	0.864705i	$-0.332495\pi$
$368$	−18.2705			−0.952416
$369$	0.472136	+	1.45309i	0.0245784	+	0.0756446i
$370$		0			0
$371$	−0.663119	+	2.04087i	−0.0344274	+	0.105957i
$372$	−0.572949	+	1.76336i	−0.0297060	+	0.0914257i
$373$	22.8713	−	16.6170i	1.18423	−	0.860395i	0.191589	−	0.981475i	$-0.438636\pi$
$373$	22.8713	−	16.6170i	1.18423	−	0.860395i	0.992643	+	0.121080i	$0.0386358\pi$
$374$	−44.3607			−2.29384
$375$		0			0
$376$	1.38197			0.0712695
$377$	5.42705	−	3.94298i	0.279507	−	0.203074i
$378$	1.54508	−	4.75528i	0.0794706	−	0.244585i
$379$	4.51064	−	13.8823i	0.231696	−	0.713087i	−0.765846	−	0.643024i	$-0.777680\pi$
$379$	4.51064	−	13.8823i	0.231696	−	0.713087i	0.997543	−	0.0700639i	$-0.0223203\pi$
$380$		0			0
$381$	6.14590	+	18.9151i	0.314864	+	0.969051i
$382$	2.94427			0.150642
$383$	10.3090	+	31.7279i	0.526766	+	1.62122i	0.760797	+	0.648990i	$0.224808\pi$
$383$	10.3090	+	31.7279i	0.526766	+	1.62122i	−0.234031	+	0.972229i	$0.575192\pi$
$384$	11.0172	+	8.00448i	0.562220	+	0.408477i
$385$		0			0
$386$	10.0902	−	7.33094i	0.513576	−	0.373135i
$387$	−7.85410	−	5.70634i	−0.399246	−	0.290070i
$388$	1.92705	+	1.40008i	0.0978312	+	0.0710785i
$389$	−12.1353	+	8.81678i	−0.615282	+	0.447028i	−0.851270	−	0.524727i	$-0.824167\pi$
$389$	−12.1353	+	8.81678i	−0.615282	+	0.447028i	0.235988	+	0.971756i	$0.424167\pi$
$390$		0			0
$391$	15.9443	+	11.5842i	0.806336	+	0.585838i
$392$	−4.57295	−	14.0741i	−0.230969	−	0.710849i
$393$	6.79837			0.342933
$394$	−1.85410	−	5.70634i	−0.0934083	−	0.287481i
$395$		0			0
$396$	2.00000	−	6.15537i	0.100504	−	0.309319i
$397$	8.97214	−	27.6134i	0.450299	−	1.38588i	−0.426268	−	0.904597i	$-0.640172\pi$
$397$	8.97214	−	27.6134i	0.450299	−	1.38588i	0.876567	−	0.481280i	$-0.159828\pi$
$398$	−22.9894	+	16.7027i	−1.15235	+	0.837233i
$399$	0.527864			0.0264263
$400$		0			0
$401$	26.5967			1.32818			0.664089	−	0.747653i	$-0.268820\pi$
$401$	26.5967			1.32818			0.664089	+	0.747653i	$0.268820\pi$
$402$	6.23607	−	4.53077i	0.311027	−	0.225974i
$403$	−1.71885	+	5.29007i	−0.0856219	+	0.263517i
$404$	0.281153	−	0.865300i	0.0139879	−	0.0430503i
$405$		0			0
$406$	1.11803	+	3.44095i	0.0554871	+	0.170772i
$407$	1.23607			0.0612696
$408$	−3.61803	−	11.1352i	−0.179119	−	0.551273i
$409$	−1.28115	−	0.930812i	−0.0633489	−	0.0460257i	0.555660	−	0.831410i	$-0.312466\pi$
$409$	−1.28115	−	0.930812i	−0.0633489	−	0.0460257i	−0.619009	+	0.785384i	$0.712466\pi$
$410$		0			0
$411$	9.66312	−	7.02067i	0.476647	−	0.346304i
$412$	−4.28115	−	3.11044i	−0.210917	−	0.153240i
$413$	5.42705	+	3.94298i	0.267048	+	0.194022i
$414$	−9.85410	+	7.15942i	−0.484303	+	0.351867i
$415$		0			0
$416$	−5.07295	−	3.68571i	−0.248722	−	0.180707i
$417$	1.54508	+	4.75528i	0.0756631	+	0.232867i
$418$	7.23607			0.353928
$419$	−2.92705	−	9.00854i	−0.142996	−	0.440096i	0.853752	−	0.520680i	$-0.174321\pi$
$419$	−2.92705	−	9.00854i	−0.142996	−	0.440096i	−0.996748	+	0.0805840i	$0.974321\pi$
$420$		0			0
$421$	9.88854	−	30.4338i	0.481938	−	1.48325i	−0.354429	−	0.935083i	$-0.615325\pi$
$421$	9.88854	−	30.4338i	0.481938	−	1.48325i	0.836367	−	0.548170i	$-0.184675\pi$
$422$	4.59017	−	14.1271i	0.223446	−	0.687696i
$423$	1.00000	−	0.726543i	0.0486217	−	0.0353257i
$424$	−7.76393			−0.377050
$425$		0			0
$426$	10.7082			0.518814
$427$	−4.35410	+	3.16344i	−0.210710	+	0.153090i
$428$	−3.13525	+	9.64932i	−0.151548	+	0.466418i
$429$	−3.00000	+	9.23305i	−0.144841	+	0.445776i
$430$		0			0
$431$	−9.21885	−	28.3727i	−0.444056	−	1.36666i	−0.883515	−	0.468402i	$-0.844830\pi$
$431$	−9.21885	−	28.3727i	−0.444056	−	1.36666i	0.439459	−	0.898263i	$-0.355170\pi$
$432$	24.2705			1.16772
$433$	8.29837	+	25.5398i	0.398794	+	1.22736i	0.925967	+	0.377605i	$0.123252\pi$
$433$	8.29837	+	25.5398i	0.398794	+	1.22736i	−0.527173	+	0.849758i	$0.676748\pi$
$434$	−2.42705	−	1.76336i	−0.116502	−	0.0846438i
$435$		0			0
$436$	−5.00000	+	3.63271i	−0.239457	+	0.173975i
$437$	−2.60081	−	1.88960i	−0.124414	−	0.0903919i
$438$	−11.7812	−	8.55951i	−0.562925	−	0.408989i
$439$	33.1525	−	24.0867i	1.58228	−	1.14959i	0.668261	−	0.743927i	$-0.267039\pi$
$439$	33.1525	−	24.0867i	1.58228	−	1.14959i	0.914021	−	0.405667i	$-0.132961\pi$
$440$		0			0
$441$	−10.7082	−	7.77997i	−0.509914	−	0.370475i
$442$	4.85410	+	14.9394i	0.230886	+	0.710594i
$443$	29.9443			1.42270			0.711348	−	0.702840i	$-0.248085\pi$
$443$	29.9443			1.42270			0.711348	+	0.702840i	$0.248085\pi$
$444$	−0.0450850	−	0.138757i	−0.00213964	−	0.00658513i
$445$		0			0
$446$	0.0901699	−	0.277515i	0.00426967	−	0.0131407i
$447$	−1.21885	+	3.75123i	−0.0576495	+	0.177427i
$448$	−2.11803	+	1.53884i	−0.100068	+	0.0727034i
$449$	4.67376			0.220568			0.110284	−	0.993900i	$-0.464824\pi$
$449$	4.67376			0.220568			0.110284	+	0.993900i	$0.464824\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−8.42705	+	6.12261i	−0.396375	+	0.287983i
$453$	4.50000	−	13.8496i	0.211428	−	0.650710i
$454$	−7.38197	+	22.7194i	−0.346453	+	1.06627i
$455$		0			0
$456$	0.590170	+	1.81636i	0.0276372	+	0.0850587i
$457$	−21.4164			−1.00182			−0.500909	−	0.865500i	$-0.667001\pi$
$457$	−21.4164			−1.00182			−0.500909	+	0.865500i	$0.667001\pi$
$458$	−10.8541	−	33.4055i	−0.507179	−	1.56094i
$459$	−21.1803	−	15.3884i	−0.988614	−	0.718270i
$460$		0			0
$461$	−0.663119	+	0.481784i	−0.0308845	+	0.0224389i	−0.603120	−	0.797650i	$-0.706076\pi$
$461$	−0.663119	+	0.481784i	−0.0308845	+	0.0224389i	0.572236	+	0.820089i	$0.306076\pi$
$462$	−4.23607	−	3.07768i	−0.197080	−	0.143187i
$463$	19.5172	+	14.1801i	0.907042	+	0.659005i	0.940265	−	0.340443i	$-0.110577\pi$
$463$	19.5172	+	14.1801i	0.907042	+	0.659005i	−0.0332229	+	0.999448i	$0.510577\pi$
$464$	−14.2082	+	10.3229i	−0.659599	+	0.479227i
$465$		0			0
$466$	−3.85410	−	2.80017i	−0.178538	−	0.129715i
$467$	8.48278	+	26.1073i	0.392536	+	1.20810i	0.930864	+	0.365367i	$0.119056\pi$
$467$	8.48278	+	26.1073i	0.392536	+	1.20810i	−0.538328	+	0.842736i	$0.680944\pi$
$468$	−2.29180			−0.105938
$469$	0.909830	+	2.80017i	0.0420120	+	0.129300i
$470$		0			0
$471$	4.07295	−	12.5352i	0.187672	−	0.577594i
$472$	−7.50000	+	23.0826i	−0.345215	+	1.06246i
$473$	−20.5623	+	14.9394i	−0.945456	+	0.686914i
$474$	13.0902			0.601251
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	−5.61803	+	4.08174i	−0.257232	+	0.186890i
$478$	10.2639	−	31.5891i	0.469461	−	1.44485i
$479$	−3.35410	+	10.3229i	−0.153253	+	0.471664i	−0.997980	−	0.0635340i	$-0.979763\pi$
$479$	−3.35410	+	10.3229i	−0.153253	+	0.471664i	0.844727	+	0.535198i	$0.179763\pi$
$480$		0			0
$481$	−0.135255	−	0.416272i	−0.00616709	−	0.0189804i
$482$	−4.09017			−0.186302
$483$	0.718847	+	2.21238i	0.0327087	+	0.100667i
$484$	−8.20820	−	5.96361i	−0.373100	−	0.271073i
$485$		0			0
$486$	20.9443	−	15.2169i	0.950051	−	0.690253i
$487$	29.4615	+	21.4050i	1.33503	+	0.969954i	0.999611	+	0.0278844i	$0.00887705\pi$
$487$	29.4615	+	21.4050i	1.33503	+	0.969954i	0.335417	+	0.942070i	$0.391123\pi$
$488$	−15.7533	−	11.4454i	−0.713118	−	0.518110i
$489$	−8.89919	+	6.46564i	−0.402435	+	0.292386i
$490$		0			0
$491$	34.9894	+	25.4213i	1.57905	+	1.14725i	0.917776	+	0.397099i	$0.129983\pi$
$491$	34.9894	+	25.4213i	1.57905	+	1.14725i	0.661272	+	0.750147i	$0.270017\pi$
$492$	−0.145898	−	0.449028i	−0.00657759	−	0.0202437i
$493$	18.9443			0.853207
$494$	−0.791796	−	2.43690i	−0.0356246	−	0.109641i
$495$		0			0
$496$	4.50000	−	13.8496i	0.202056	−	0.621864i
$497$	−1.26393	+	3.88998i	−0.0566951	+	0.174490i
$498$	−8.16312	+	5.93085i	−0.365798	+	0.265768i
$499$	7.56231			0.338535			0.169268	−	0.985570i	$-0.445860\pi$
$499$	7.56231			0.338535			0.169268	+	0.985570i	$0.445860\pi$
$500$		0			0
$501$	14.5623			0.650596
$502$	−38.1976	+	27.7522i	−1.70484	+	1.23864i
$503$	−11.5623	+	35.5851i	−0.515538	+	1.58666i	0.266764	+	0.963762i	$0.414046\pi$
$503$	−11.5623	+	35.5851i	−0.515538	+	1.58666i	−0.782301	+	0.622900i	$0.785954\pi$
$504$	−0.854102	+	2.62866i	−0.0380447	+	0.117090i
$505$		0			0
$506$	9.85410	+	30.3278i	0.438068	+	1.34824i
$507$	−9.56231			−0.424677
$508$	3.79837	+	11.6902i	0.168526	+	0.518668i
$509$	16.4443	+	11.9475i	0.728880	+	0.529562i	0.889209	−	0.457502i	$-0.151256\pi$
$509$	16.4443	+	11.9475i	0.728880	+	0.529562i	−0.160329	+	0.987064i	$0.551256\pi$
$510$		0			0
$511$	4.50000	−	3.26944i	0.199068	−	0.144632i
$512$	−4.28115	−	3.11044i	−0.189202	−	0.137463i
$513$	3.45492	+	2.51014i	0.152538	+	0.110826i
$514$	29.9164	−	21.7355i	1.31956	−	0.958714i
$515$		0			0
$516$	2.42705	+	1.76336i	0.106845	+	0.0776274i
$517$	−1.00000	−	3.07768i	−0.0439799	−	0.135356i
$518$	0.236068			0.0103722
$519$	5.83688	+	17.9641i	0.256211	+	0.788535i
$520$		0			0
$521$	9.07295	−	27.9237i	0.397493	−	1.22336i	−0.529510	−	0.848304i	$-0.677624\pi$
$521$	9.07295	−	27.9237i	0.397493	−	1.22336i	0.927003	−	0.375054i	$-0.122376\pi$
$522$	−3.61803	+	11.1352i	−0.158357	+	0.487373i
$523$	10.6353	−	7.72696i	0.465047	−	0.337877i	−0.330461	−	0.943820i	$-0.607204\pi$
$523$	10.6353	−	7.72696i	0.465047	−	0.337877i	0.795508	+	0.605943i	$0.207204\pi$
$524$	4.20163			0.183549
$525$		0			0
$526$	17.6525			0.769685
$527$	−12.7082	+	9.23305i	−0.553578	+	0.402198i
$528$	7.85410	−	24.1724i	0.341806	−	1.05197i
$529$	−2.72949	+	8.40051i	−0.118673	+	0.365239i
$530$		0			0
$531$	6.70820	+	20.6457i	0.291111	+	0.895948i
$532$	0.326238			0.0141442
$533$	−0.437694	−	1.34708i	−0.0189586	−	0.0583487i
$534$	−11.7082	−	8.50651i	−0.506664	−	0.368113i
$535$		0			0
$536$	−8.61803	+	6.26137i	−0.372242	+	0.270450i
$537$	0.427051	+	0.310271i	0.0184286	+	0.0133892i
$538$	−16.7082	−	12.1392i	−0.720342	−	0.523359i
$539$	−28.0344	+	20.3682i	−1.20753	+	0.877321i
$540$		0			0
$541$	−21.9443	−	15.9434i	−0.943458	−	0.685462i	0.00579261	−	0.999983i	$-0.498156\pi$
$541$	−21.9443	−	15.9434i	−0.943458	−	0.685462i	−0.949251	+	0.314521i	$0.898156\pi$
$542$	4.00000	+	12.3107i	0.171815	+	0.528791i
$543$	0.291796			0.0125222
$544$	−5.47214	−	16.8415i	−0.234616	−	0.722073i
$545$		0			0
$546$	−0.572949	+	1.76336i	−0.0245200	+	0.0754647i
$547$	−6.57953	+	20.2497i	−0.281320	+	0.865815i	0.706157	+	0.708055i	$0.250427\pi$
$547$	−6.57953	+	20.2497i	−0.281320	+	0.865815i	−0.987478	+	0.157760i	$0.949573\pi$
$548$	5.97214	−	4.33901i	0.255117	−	0.185353i
$549$	−17.4164			−0.743314
$550$		0			0
$551$	−3.09017			−0.131646
$552$	−6.80902	+	4.94704i	−0.289811	+	0.210560i
$553$	−1.54508	+	4.75528i	−0.0657037	+	0.202215i
$554$	12.3541	−	38.0220i	0.524875	−	1.61540i
$555$		0			0
$556$	0.954915	+	2.93893i	0.0404974	+	0.124638i
$557$	4.76393			0.201854			0.100927	−	0.994894i	$-0.467819\pi$
$557$	4.76393			0.201854			0.100927	+	0.994894i	$0.467819\pi$
$558$	−3.00000	−	9.23305i	−0.127000	−	0.390866i
$559$	7.28115	+	5.29007i	0.307960	+	0.223746i
$560$		0			0
$561$	−22.1803	+	16.1150i	−0.936455	+	0.680374i
$562$	13.2082	+	9.59632i	0.557154	+	0.404796i
$563$	−5.97214	−	4.33901i	−0.251696	−	0.182868i	0.454782	−	0.890603i	$-0.349717\pi$
$563$	−5.97214	−	4.33901i	−0.251696	−	0.182868i	−0.706478	+	0.707735i	$0.749717\pi$
$564$	−0.309017	+	0.224514i	−0.0130120	+	0.00945374i
$565$		0			0
$566$	−39.0795	−	28.3929i	−1.64264	−	1.19344i
$567$	0.190983	+	0.587785i	0.00802053	+	0.0246847i
$568$	−14.7984			−0.620926
$569$	6.34346	+	19.5232i	0.265932	+	0.818453i	0.991477	+	0.130279i	$0.0415874\pi$
$569$	6.34346	+	19.5232i	0.265932	+	0.818453i	−0.725546	+	0.688174i	$0.758413\pi$
$570$		0			0
$571$	−2.51064	+	7.72696i	−0.105067	+	0.323363i	−0.989746	−	0.142837i	$-0.954377\pi$
$571$	−2.51064	+	7.72696i	−0.105067	+	0.323363i	0.884679	+	0.466201i	$0.154377\pi$
$572$	−1.85410	+	5.70634i	−0.0775239	+	0.238594i
$573$	1.47214	−	1.06957i	0.0614994	−	0.0446819i
$574$	0.763932			0.0318859
$575$		0			0
$576$	−8.47214			−0.353006
$577$	27.3262	−	19.8537i	1.13761	−	0.826519i	0.150822	−	0.988561i	$-0.451808\pi$
$577$	27.3262	−	19.8537i	1.13761	−	0.826519i	0.986784	+	0.162042i	$0.0518079\pi$
$578$	−5.20820	+	16.0292i	−0.216633	+	0.666727i
$579$	2.38197	−	7.33094i	0.0989911	−	0.304663i
$580$		0			0
$581$	−1.19098	−	3.66547i	−0.0494103	−	0.152069i
$582$	6.23607			0.258493
$583$	5.61803	+	17.2905i	0.232675	+	0.716101i
$584$	16.2812	+	11.8290i	0.673719	+	0.489485i
$585$		0			0
$586$	−25.5623	+	18.5721i	−1.05597	+	0.767206i
$587$	−4.28115	−	3.11044i	−0.176702	−	0.128382i	0.495919	−	0.868369i	$-0.334831\pi$
$587$	−4.28115	−	3.11044i	−0.176702	−	0.128382i	−0.672621	+	0.739987i	$0.734831\pi$
$588$	3.30902	+	2.40414i	0.136462	+	0.0991451i
$589$	2.07295	−	1.50609i	0.0854144	−	0.0620572i
$590$		0			0
$591$	−3.00000	−	2.17963i	−0.123404	−	0.0896579i
$592$	0.354102	+	1.08981i	0.0145535	+	0.0447911i
$593$	−10.9098			−0.448013			−0.224007	−	0.974588i	$-0.571914\pi$
$593$	−10.9098			−0.448013			−0.224007	+	0.974588i	$0.571914\pi$
$594$	−13.0902	−	40.2874i	−0.537096	−	1.65301i
$595$		0			0
$596$	−0.753289	+	2.31838i	−0.0308559	+	0.0949647i
$597$	−5.42705	+	16.7027i	−0.222114	+	0.683598i
$598$	9.13525	−	6.63715i	0.373568	−	0.271413i
$599$	−9.47214			−0.387021			−0.193510	−	0.981098i	$-0.561987\pi$
$599$	−9.47214			−0.387021			−0.193510	+	0.981098i	$0.561987\pi$
$600$		0			0
$601$	2.72949			0.111338			0.0556691	−	0.998449i	$-0.482271\pi$
$601$	2.72949			0.111338			0.0556691	+	0.998449i	$0.482271\pi$
$602$	−3.92705	+	2.85317i	−0.160055	+	0.116287i
$603$	−2.94427	+	9.06154i	−0.119900	+	0.369014i
$604$	2.78115	−	8.55951i	0.113164	−	0.348281i
$605$		0			0
$606$	−0.736068	−	2.26538i	−0.0299007	−	0.0920249i
$607$	−35.5623			−1.44343			−0.721715	−	0.692191i	$-0.756646\pi$
$607$	−35.5623			−1.44343			−0.721715	+	0.692191i	$0.756646\pi$
$608$	0.892609	+	2.74717i	0.0362001	+	0.111412i
$609$	1.80902	+	1.31433i	0.0733051	+	0.0532592i
$610$		0			0
$611$	−0.927051	+	0.673542i	−0.0375045	+	0.0272486i
$612$	−5.23607	−	3.80423i	−0.211656	−	0.153777i
$613$	12.1180	+	8.80427i	0.489443	+	0.355601i	0.804970	−	0.593316i	$-0.202181\pi$
$613$	12.1180	+	8.80427i	0.489443	+	0.355601i	−0.315527	+	0.948917i	$0.602181\pi$
$614$	12.0902	−	8.78402i	0.487920	−	0.354494i
$615$		0			0
$616$	5.85410	+	4.25325i	0.235868	+	0.171368i
$617$	4.39919	+	13.5393i	0.177105	+	0.545072i	0.999723	−	0.0235215i	$-0.00748780\pi$
$617$	4.39919	+	13.5393i	0.177105	+	0.545072i	−0.822619	+	0.568593i	$0.807488\pi$
$618$	−13.8541			−0.557294
$619$	9.43363	+	29.0337i	0.379170	+	1.16696i	0.940622	+	0.339455i	$0.110243\pi$
$619$	9.43363	+	29.0337i	0.379170	+	1.16696i	−0.561453	+	0.827509i	$0.689757\pi$
$620$		0			0
$621$	−5.81559	+	17.8986i	−0.233372	+	0.718244i
$622$	−4.25329	+	13.0903i	−0.170541	+	0.524872i
$623$	4.47214	−	3.24920i	0.179172	−	0.130176i
$624$	−9.00000			−0.360288
$625$		0			0
$626$	27.1246			1.08412
$627$	3.61803	−	2.62866i	0.144490	−	0.104978i
$628$	2.51722	−	7.74721i	0.100448	−	0.309147i
$629$	0.381966	−	1.17557i	0.0152300	−	0.0468731i
$630$		0			0
$631$	−3.16312	−	9.73508i	−0.125922	−	0.387547i	0.868146	−	0.496309i	$-0.165312\pi$
$631$	−3.16312	−	9.73508i	−0.125922	−	0.387547i	−0.994068	+	0.108761i	$0.965312\pi$
$632$	−18.0902			−0.719588
$633$	−2.83688	−	8.73102i	−0.112756	−	0.347027i
$634$	10.0172	+	7.27794i	0.397835	+	0.289044i
$635$		0			0
$636$	1.73607	−	1.26133i	0.0688396	−	0.0500149i
$637$	9.92705	+	7.21242i	0.393324	+	0.285767i
$638$	24.7984	+	18.0171i	0.981777	+	0.713303i
$639$	−10.7082	+	7.77997i	−0.423610	+	0.307771i
$640$		0			0
$641$	0.881966	+	0.640786i	0.0348356	+	0.0253095i	0.605067	−	0.796175i	$-0.293146\pi$
$641$	0.881966	+	0.640786i	0.0348356	+	0.0253095i	−0.570231	+	0.821484i	$0.693146\pi$
$642$	8.20820	+	25.2623i	0.323952	+	0.997022i
$643$	−30.8328			−1.21593			−0.607964	−	0.793965i	$-0.708013\pi$
$643$	−30.8328			−1.21593			−0.607964	+	0.793965i	$0.708013\pi$
$644$	0.444272	+	1.36733i	0.0175068	+	0.0538803i
$645$		0			0
$646$	2.23607	−	6.88191i	0.0879769	−	0.270765i
$647$	−11.2918	+	34.7526i	−0.443926	+	1.36626i	0.439731	+	0.898130i	$0.355074\pi$
$647$	−11.2918	+	34.7526i	−0.443926	+	1.36626i	−0.883657	+	0.468135i	$0.844926\pi$
$648$	−1.80902	+	1.31433i	−0.0710649	+	0.0516317i
$649$	56.8328			2.23088
$650$		0			0
$651$	−1.85410			−0.0726680
$652$	−5.50000	+	3.99598i	−0.215397	+	0.156495i
$653$	5.89919	−	18.1558i	0.230853	−	0.710493i	−0.766791	−	0.641896i	$-0.778148\pi$
$653$	5.89919	−	18.1558i	0.230853	−	0.710493i	0.997645	−	0.0685963i	$-0.0218520\pi$
$654$	−5.00000	+	15.3884i	−0.195515	+	0.601735i
$655$		0			0
$656$	1.14590	+	3.52671i	0.0447398	+	0.137695i
$657$	18.0000			0.702247
$658$	−0.190983	−	0.587785i	−0.00744529	−	0.0229143i
$659$	−12.5623	−	9.12705i	−0.489358	−	0.355539i	0.315579	−	0.948899i	$-0.397801\pi$
$659$	−12.5623	−	9.12705i	−0.489358	−	0.355539i	−0.804937	+	0.593360i	$0.797801\pi$
$660$		0			0
$661$	−15.9271	+	11.5717i	−0.619490	+	0.450086i	−0.852744	−	0.522330i	$-0.825063\pi$
$661$	−15.9271	+	11.5717i	−0.619490	+	0.450086i	0.233253	+	0.972416i	$0.425063\pi$
$662$	−30.2705	−	21.9928i	−1.17650	−	0.854775i
$663$	7.85410	+	5.70634i	0.305028	+	0.221616i
$664$	11.2812	−	8.19624i	0.437794	−	0.318076i
$665$		0			0
$666$	0.618034	+	0.449028i	0.0239483	+	0.0173995i
$667$	−4.20820	−	12.9515i	−0.162942	−	0.501485i
$668$	9.00000			0.348220
$669$	−0.0557281	−	0.171513i	−0.00215457	−	0.00663109i
$670$		0			0
$671$	−14.0902	+	43.3651i	−0.543945	+	1.67409i
$672$	0.645898	−	1.98787i	0.0249161	−	0.0766837i
$673$	−9.85410	+	7.15942i	−0.379848	+	0.275976i	−0.761283	−	0.648420i	$-0.775430\pi$
$673$	−9.85410	+	7.15942i	−0.379848	+	0.275976i	0.381435	+	0.924396i	$0.375430\pi$
$674$	−12.7082			−0.489502
$675$		0			0
$676$	−5.90983			−0.227301
$677$	−8.59017	+	6.24112i	−0.330147	+	0.239866i	−0.740493	−	0.672064i	$-0.765408\pi$
$677$	−8.59017	+	6.24112i	−0.330147	+	0.239866i	0.410346	+	0.911930i	$0.365408\pi$
$678$	−8.42705	+	25.9358i	−0.323639	+	0.996058i
$679$	−0.736068	+	2.26538i	−0.0282477	+	0.0869375i
$680$		0			0
$681$	4.56231	+	14.0413i	0.174828	+	0.538065i
$682$	−25.4164			−0.973245
$683$	−4.16312	−	12.8128i	−0.159297	−	0.490267i	0.839274	−	0.543709i	$-0.182981\pi$
$683$	−4.16312	−	12.8128i	−0.159297	−	0.490267i	−0.998571	+	0.0534426i	$0.982981\pi$
$684$	0.854102	+	0.620541i	0.0326574	+	0.0237270i
$685$		0			0
$686$	−11.0172	+	8.00448i	−0.420639	+	0.305612i
$687$	−17.5623	−	12.7598i	−0.670044	−	0.486815i
$688$	−19.0623	−	13.8496i	−0.726744	−	0.528010i
$689$	5.20820	−	3.78398i	0.198417	−	0.144158i
$690$		0			0
$691$	−29.3435	−	21.3193i	−1.11628	−	0.811023i	−0.132637	−	0.991165i	$-0.542344\pi$
$691$	−29.3435	−	21.3193i	−1.11628	−	0.811023i	−0.983641	+	0.180141i	$0.942344\pi$
$692$	3.60739	+	11.1024i	0.137132	+	0.422050i
$693$	6.47214			0.245856
$694$	9.95492	+	30.6381i	0.377883	+	1.16301i
$695$		0			0
$696$	−2.50000	+	7.69421i	−0.0947623	+	0.291648i
$697$	1.23607	−	3.80423i	0.0468194	−	0.144095i
$698$	28.4164	−	20.6457i	1.07558	−	0.781452i
$699$	−2.94427			−0.111363
$700$		0			0
$701$	−41.0132			−1.54905			−0.774523	−	0.632546i	$-0.782010\pi$
$701$	−41.0132			−1.54905			−0.774523	+	0.632546i	$0.782010\pi$
$702$	−12.1353	+	8.81678i	−0.458016	+	0.332768i
$703$	−0.0623059	+	0.191758i	−0.00234991	+	0.00723228i
$704$	−6.85410	+	21.0948i	−0.258324	+	0.795039i
$705$		0			0
$706$	−6.45492	−	19.8662i	−0.242934	−	0.747674i
$707$	0.909830			0.0342177
$708$	−2.07295	−	6.37988i	−0.0779062	−	0.239771i
$709$	27.1353	+	19.7149i	1.01909	+	0.740409i	0.966095	−	0.258186i	$-0.0831247\pi$
$709$	27.1353	+	19.7149i	1.01909	+	0.740409i	0.0529906	+	0.998595i	$0.483125\pi$
$710$		0			0
$711$	−13.0902	+	9.51057i	−0.490920	+	0.356674i
$712$	16.1803	+	11.7557i	0.606384	+	0.440564i
$713$	9.13525	+	6.63715i	0.342118	+	0.248563i
$714$	−4.23607	+	3.07768i	−0.158531	+	0.115179i
$715$		0			0
$716$	0.263932	+	0.191758i	0.00986360	+	0.00716633i
$717$	−6.34346	−	19.5232i	−0.236901	−	0.729106i
$718$	−22.2361			−0.829843
$719$	−7.19756	−	22.1518i	−0.268424	−	0.826123i	−0.990885	−	0.134712i	$-0.956989\pi$
$719$	−7.19756	−	22.1518i	−0.268424	−	0.826123i	0.722461	−	0.691412i	$-0.243011\pi$
$720$		0			0
$721$	1.63525	−	5.03280i	0.0609001	−	0.187431i
$722$	9.13525	−	28.1154i	0.339979	−	1.04635i
$723$	−2.04508	+	1.48584i	−0.0760575	+	0.0552590i
$724$	0.180340			0.00670228
$725$		0			0
$726$	−26.5623			−0.985820
$727$	−19.8713	+	14.4374i	−0.736987	+	0.535452i	−0.891766	−	0.452497i	$-0.850533\pi$
$727$	−19.8713	+	14.4374i	−0.736987	+	0.535452i	0.154779	+	0.987949i	$0.450533\pi$
$728$	0.791796	−	2.43690i	0.0293459	−	0.0903174i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$		0			0
$731$	7.85410	+	24.1724i	0.290494	+	0.894050i
$732$	5.38197			0.198923
$733$	−6.17376	−	19.0009i	−0.228033	−	0.701814i	−0.997970	−	0.0636931i	$-0.979712\pi$
$733$	−6.17376	−	19.0009i	−0.228033	−	0.701814i	0.769936	−	0.638121i	$-0.220288\pi$
$734$	−33.4615	−	24.3112i	−1.23509	−	0.897343i
$735$		0			0
$736$	−10.2984	+	7.48221i	−0.379603	+	0.275798i
$737$	20.1803	+	14.6619i	0.743352	+	0.540077i
$738$	2.00000	+	1.45309i	0.0736210	+	0.0534888i
$739$	−12.9271	+	9.39205i	−0.475529	+	0.345492i	−0.799592	−	0.600543i	$-0.794951\pi$
$739$	−12.9271	+	9.39205i	−0.475529	+	0.345492i	0.324063	+	0.946036i	$0.394951\pi$
$740$		0			0
$741$	−1.28115	−	0.930812i	−0.0470643	−	0.0341942i
$742$	1.07295	+	3.30220i	0.0393892	+	0.121227i
$743$	28.3607			1.04045			0.520226	−	0.854029i	$-0.325848\pi$
$743$	28.3607			1.04045			0.520226	+	0.854029i	$0.325848\pi$
$744$	−2.07295	−	6.37988i	−0.0759980	−	0.233898i
$745$		0			0
$746$	14.1353	−	43.5038i	0.517528	−	1.59279i
$747$	3.85410	−	11.8617i	0.141014	−	0.433997i
$748$	−13.7082	+	9.95959i	−0.501222	+	0.364159i
$749$	−10.1459			−0.370723
$750$		0			0
$751$	−5.11146			−0.186520			−0.0932598	−	0.995642i	$-0.529729\pi$
$751$	−5.11146			−0.186520			−0.0932598	+	0.995642i	$0.529729\pi$
$752$	2.42705	−	1.76336i	0.0885054	−	0.0643030i
$753$	−9.01722	+	27.7522i	−0.328606	+	1.01134i
$754$	3.35410	−	10.3229i	0.122149	−	0.375937i
$755$		0			0
$756$	−0.590170	−	1.81636i	−0.0214643	−	0.0660602i
$757$	30.4164			1.10550			0.552752	−	0.833346i	$-0.313578\pi$
$757$	30.4164			1.10550			0.552752	+	0.833346i	$0.313578\pi$
$758$	−7.29837	−	22.4621i	−0.265089	−	0.815860i
$759$	15.9443	+	11.5842i	0.578740	+	0.420480i
$760$		0			0
$761$	14.9271	−	10.8451i	0.541105	−	0.393136i	−0.283390	−	0.959005i	$-0.591459\pi$
$761$	14.9271	−	10.8451i	0.541105	−	0.393136i	0.824495	+	0.565869i	$0.191459\pi$
$762$	26.0344	+	18.9151i	0.943128	+	0.685223i
$763$	−5.00000	−	3.63271i	−0.181012	−	0.131513i
$764$	0.909830	−	0.661030i	0.0329165	−	0.0239152i
$765$		0			0
$766$	43.6697	+	31.7279i	1.57785	+	1.14638i
$767$	−6.21885	−	19.1396i	−0.224550	−	0.691092i
$768$	13.5623			0.489388
$769$	4.14590	+	12.7598i	0.149505	+	0.460129i	0.997563	−	0.0697749i	$-0.0222281\pi$
$769$	4.14590	+	12.7598i	0.149505	+	0.460129i	−0.848058	+	0.529904i	$0.822228\pi$
$770$		0			0
$771$	7.06231	−	21.7355i	0.254343	−	0.782786i
$772$	1.47214	−	4.53077i	0.0529833	−	0.163066i
$773$	29.2533	−	21.2538i	1.05217	−	0.764445i	0.0795442	−	0.996831i	$-0.474654\pi$
$773$	29.2533	−	21.2538i	1.05217	−	0.764445i	0.972623	+	0.232387i	$0.0746535\pi$
$774$	−15.7082			−0.564620
$775$		0			0
$776$	−8.61803			−0.309369
$777$	0.118034	−	0.0857567i	0.00423445	−	0.00307650i
$778$	−7.50000	+	23.0826i	−0.268888	+	0.827552i
$779$	−0.201626	+	0.620541i	−0.00722401	+	0.0222332i
$780$		0			0
$781$	10.7082	+	32.9565i	0.383170	+	1.17927i
$782$	31.8885			1.14033
$783$	5.59017	+	17.2048i	0.199776	+	0.614848i
$784$	−25.9894	−	18.8824i	−0.928191	−	0.674370i
$785$		0			0
$786$	8.89919	−	6.46564i	0.317423	−	0.230622i
$787$	9.56231	+	6.94742i	0.340859	+	0.247649i	0.745024	−	0.667037i	$-0.232438\pi$
$787$	9.56231	+	6.94742i	0.340859	+	0.247649i	−0.404165	+	0.914686i	$0.632438\pi$
$788$	−1.85410	−	1.34708i	−0.0660496	−	0.0479879i
$789$	8.82624	−	6.41264i	0.314222	−	0.228296i
$790$		0			0
$791$	−8.42705	−	6.12261i	−0.299631	−	0.217695i
$792$	7.23607	+	22.2703i	0.257122	+	0.791342i
$793$	16.1459			0.573358
$794$	−14.5172	−	44.6794i	−0.515197	−	1.58561i
$795$		0			0
$796$	−3.35410	+	10.3229i	−0.118883	+	0.365884i
$797$	3.01722	−	9.28605i	0.106875	−	0.328929i	−0.883291	−	0.468826i	$-0.844677\pi$
$797$	3.01722	−	9.28605i	0.106875	−	0.328929i	0.990166	+	0.139897i	$0.0446772\pi$
$798$	0.690983	−	0.502029i	0.0244605	−	0.0177716i
$799$	−3.23607			−0.114484
$800$		0			0
$801$	17.8885			0.632061
$802$	34.8156	−	25.2950i	1.22938	−	0.893198i
$803$	14.5623	−	44.8182i	0.513893	−	1.58160i
$804$	0.909830	−	2.80017i	0.0320872	−	0.0987543i
$805$		0			0
$806$	2.78115	+	8.55951i	0.0979619	+	0.301496i
$807$	−12.7639			−0.449312
$808$	1.01722	+	3.13068i	0.0357857	+	0.110137i
$809$	−25.0623	−	18.2088i	−0.881144	−	0.640188i	0.0524101	−	0.998626i	$-0.483310\pi$
$809$	−25.0623	−	18.2088i	−0.881144	−	0.640188i	−0.933554	+	0.358437i	$0.883310\pi$
$810$		0			0
$811$	11.8992	−	8.64527i	0.417837	−	0.303576i	−0.358930	−	0.933364i	$-0.616858\pi$
$811$	11.8992	−	8.64527i	0.417837	−	0.303576i	0.776767	+	0.629788i	$0.216858\pi$
$812$	1.11803	+	0.812299i	0.0392353	+	0.0285061i
$813$	6.47214	+	4.70228i	0.226988	+	0.164916i
$814$	1.61803	−	1.17557i	0.0567121	−	0.0412037i
$815$		0			0
$816$	−20.5623	−	14.9394i	−0.719825	−	0.522983i
$817$	−1.28115	−	3.94298i	−0.0448219	−	0.137948i
$818$	−2.56231			−0.0895889
$819$	−0.708204	−	2.17963i	−0.0247466	−	0.0761624i
$820$		0			0
$821$	−12.5729	+	38.6956i	−0.438799	+	1.35048i	0.450344	+	0.892855i	$0.351301\pi$
$821$	−12.5729	+	38.6956i	−0.438799	+	1.35048i	−0.889143	+	0.457629i	$0.848699\pi$
$822$	5.97214	−	18.3803i	0.208302	−	0.641088i
$823$	−38.5967	+	28.0422i	−1.34540	+	0.977489i	−0.346171	+	0.938171i	$0.612518\pi$
$823$	−38.5967	+	28.0422i	−1.34540	+	0.977489i	−0.999227	+	0.0393176i	$0.987482\pi$
$824$	19.1459			0.666979
$825$		0			0
$826$	10.8541			0.377663
$827$	0.781153	−	0.567541i	0.0271633	−	0.0197353i	−0.574121	−	0.818771i	$-0.694656\pi$
$827$	0.781153	−	0.567541i	0.0271633	−	0.0197353i	0.601284	+	0.799035i	$0.294656\pi$
$828$	−1.43769	+	4.42477i	−0.0499633	+	0.153771i
$829$	−11.0795	+	34.0993i	−0.384808	+	1.18432i	0.551812	+	0.833969i	$0.313937\pi$
$829$	−11.0795	+	34.0993i	−0.384808	+	1.18432i	−0.936620	+	0.350348i	$0.886063\pi$
$830$		0			0
$831$	−7.63525	−	23.4989i	−0.264864	−	0.815168i
$832$	7.85410			0.272292
$833$	10.7082	+	32.9565i	0.371017	+	1.14187i
$834$	6.54508	+	4.75528i	0.226638	+	0.164662i
$835$		0			0
$836$	2.23607	−	1.62460i	0.0773360	−	0.0561879i
$837$	−12.1353	−	8.81678i	−0.419456	−	0.304752i
$838$	−12.3992	−	9.00854i	−0.428323	−	0.311195i
$839$	−8.78115	+	6.37988i	−0.303159	+	0.220258i	−0.728956	−	0.684561i	$-0.759994\pi$
$839$	−8.78115	+	6.37988i	−0.303159	+	0.220258i	0.425797	+	0.904819i	$0.359994\pi$
$840$		0			0
$841$	12.8713	+	9.35156i	0.443839	+	0.322468i
$842$	−16.0000	−	49.2429i	−0.551396	−	1.69702i
$843$	10.0902			0.347524
$844$	−1.75329	−	5.39607i	−0.0603507	−	0.185740i
$845$		0			0
$846$	0.618034	−	1.90211i	0.0212484	−	0.0653960i
$847$	3.13525	−	9.64932i	0.107729	−	0.331555i
$848$	−13.6353	+	9.90659i	−0.468237	+	0.340194i
$849$	−29.8541			−1.02459
$850$		0			0
$851$	−0.888544			−0.0304589
$852$	3.30902	−	2.40414i	0.113365	−	0.0823645i
$853$	−4.72949	+	14.5559i	−0.161935	+	0.498384i	−0.998797	−	0.0490292i	$-0.984387\pi$
$853$	−4.72949	+	14.5559i	−0.161935	+	0.498384i	0.836863	+	0.547413i	$0.184387\pi$
$854$	−2.69098	+	8.28199i	−0.0920835	+	0.283404i
$855$		0			0
$856$	−11.3435	−	34.9116i	−0.387711	−	1.19325i
$857$	19.6869			0.672492			0.336246	−	0.941774i	$-0.390843\pi$
$857$	19.6869			0.672492			0.336246	+	0.941774i	$0.390843\pi$
$858$	4.85410	+	14.9394i	0.165716	+	0.510022i
$859$	1.28115	+	0.930812i	0.0437124	+	0.0317589i	0.609427	−	0.792842i	$-0.291400\pi$
$859$	1.28115	+	0.930812i	0.0437124	+	0.0317589i	−0.565715	+	0.824601i	$0.691400\pi$
$860$		0			0
$861$	0.381966	−	0.277515i	0.0130174	−	0.00945767i
$862$	−39.0517	−	28.3727i	−1.33010	−	0.966378i
$863$	17.3435	+	12.6008i	0.590378	+	0.428935i	0.842451	−	0.538773i	$-0.181112\pi$
$863$	17.3435	+	12.6008i	0.590378	+	0.428935i	−0.252072	+	0.967708i	$0.581112\pi$
$864$	13.6803	−	9.93935i	0.465415	−	0.338144i
$865$		0			0
$866$	35.1525	+	25.5398i	1.19453	+	0.867877i
$867$	3.21885	+	9.90659i	0.109318	+	0.336446i
$868$	−1.14590			−0.0388943
$869$	13.0902	+	40.2874i	0.444054	+	1.36666i
$870$		0			0
$871$	2.72949	−	8.40051i	0.0924852	−	0.284640i
$872$	6.90983	−	21.2663i	0.233996	−	0.720167i
$873$	−6.23607	+	4.53077i	−0.211059	+	0.153343i
$874$	−5.20163			−0.175948
$875$		0			0
$876$	−5.56231			−0.187933
$877$	29.5623	−	21.4783i	0.998248	−	0.725270i	0.0365363	−	0.999332i	$-0.488368\pi$
$877$	29.5623	−	21.4783i	0.998248	−	0.725270i	0.961712	+	0.274063i	$0.0883676\pi$
$878$	20.4894	−	63.0598i	0.691482	−	2.12816i
$879$	−6.03444	+	18.5721i	−0.203537	+	0.626421i
$880$		0			0
$881$	−12.4721	−	38.3853i	−0.420197	−	1.29323i	−0.907519	−	0.420011i	$-0.862026\pi$
$881$	−12.4721	−	38.3853i	−0.420197	−	1.29323i	0.487322	−	0.873222i	$-0.337974\pi$
$882$	−21.4164			−0.721128
$883$	−6.36068	−	19.5762i	−0.214054	−	0.658790i	−0.999219	−	0.0395042i	$-0.987422\pi$
$883$	−6.36068	−	19.5762i	−0.214054	−	0.658790i	0.785165	−	0.619286i	$-0.212578\pi$
$884$	4.85410	+	3.52671i	0.163261	+	0.118616i
$885$		0			0
$886$	39.1976	−	28.4787i	1.31687	−	0.956760i
$887$	−24.1803	−	17.5680i	−0.811896	−	0.589877i	0.102483	−	0.994735i	$-0.467321\pi$
$887$	−24.1803	−	17.5680i	−0.811896	−	0.589877i	−0.914380	+	0.404857i	$0.867321\pi$
$888$	0.427051	+	0.310271i	0.0143309	+	0.0104120i
$889$	−9.94427	+	7.22494i	−0.333520	+	0.242317i
$890$		0			0
$891$	4.23607	+	3.07768i	0.141914	+	0.103106i
$892$	−0.0344419	−	0.106001i	−0.00115320	−	0.00354918i
$893$	0.527864			0.0176643
$894$	1.97214	+	6.06961i	0.0659581	+	0.202998i
$895$		0			0
$896$	−2.60081	+	8.00448i	−0.0868871	+	0.267411i
$897$	2.15654	−	6.63715i	0.0720048	−	0.221608i
$898$	6.11803	−	4.44501i	0.204161	−	0.148332i
$899$	10.8541			0.362005
$900$		0			0
$901$	18.1803			0.605675
$902$	5.23607	−	3.80423i	0.174342	−	0.126667i
$903$	−0.927051	+	2.85317i	−0.0308503	+	0.0949475i
$904$	11.6459	−	35.8424i	0.387337	−	1.19210i
$905$		0			0
$906$	−7.28115	−	22.4091i	−0.241900	−	0.744492i
$907$	−33.2492			−1.10402			−0.552011	−	0.833837i	$-0.686139\pi$
$907$	−33.2492			−1.10402			−0.552011	+	0.833837i	$0.686139\pi$
$908$	2.81966	+	8.67802i	0.0935737	+	0.287990i
$909$	2.38197	+	1.73060i	0.0790048	+	0.0574004i
$910$		0			0
$911$	32.5517	−	23.6502i	1.07848	−	0.783565i	0.101067	−	0.994880i	$-0.467774\pi$
$911$	32.5517	−	23.6502i	1.07848	−	0.783565i	0.977418	+	0.211315i	$0.0677745\pi$
$912$	3.35410	+	2.43690i	0.111065	+	0.0806937i
$913$	−26.4164	−	19.1926i	−0.874255	−	0.635184i
$914$	−28.0344	+	20.3682i	−0.927297	+	0.673721i
$915$		0			0
$916$	−10.8541	−	7.88597i	−0.358630	−	0.260560i
$917$	1.29837	+	3.99598i	0.0428761	+	0.131959i
$918$	−42.3607			−1.39811
$919$	−16.4443	−	50.6103i	−0.542446	−	1.66948i	−0.726985	−	0.686653i	$-0.759079\pi$
$919$	−16.4443	−	50.6103i	−0.542446	−	1.66948i	0.184539	−	0.982825i	$-0.440921\pi$
$920$		0			0
$921$	2.85410	−	8.78402i	0.0940459	−	0.289443i
$922$	−0.409830	+	1.26133i	−0.0134970	+	0.0415396i
$923$	9.92705	−	7.21242i	0.326753	−	0.237400i
$924$	−2.00000			−0.0657952
$925$		0			0
$926$	39.0344			1.28275
$927$	13.8541	−	10.0656i	0.455028	−	0.330597i
$928$	−3.78115	+	11.6372i	−0.124122	+	0.382010i
$929$	12.8647	−	39.5936i	0.422079	−	1.29902i	−0.483685	−	0.875242i	$-0.660702\pi$
$929$	12.8647	−	39.5936i	0.422079	−	1.29902i	0.905764	−	0.423782i	$-0.139298\pi$
$930$		0			0
$931$	−1.74671	−	5.37582i	−0.0572461	−	0.176186i
$932$	−1.81966			−0.0596049
$933$	2.62868	+	8.09024i	0.0860590	+	0.264862i
$934$	35.9336	+	26.1073i	1.17578	+	0.854257i
$935$		0			0
$936$	6.70820	−	4.87380i	0.219265	−	0.159305i
$937$	−14.3435	−	10.4211i	−0.468580	−	0.340444i	0.328307	−	0.944571i	$-0.393522\pi$
$937$	−14.3435	−	10.4211i	−0.468580	−	0.340444i	−0.796888	+	0.604127i	$0.793522\pi$
$938$	3.85410	+	2.80017i	0.125841	+	0.0914288i
$939$	13.5623	−	9.85359i	0.442589	−	0.321560i
$940$		0			0
$941$	37.5517	+	27.2829i	1.22415	+	0.889396i	0.996438	−	0.0843322i	$-0.0268757\pi$
$941$	37.5517	+	27.2829i	1.22415	+	0.889396i	0.227712	+	0.973729i	$0.426876\pi$
$942$	−6.59017	−	20.2825i	−0.214719	−	0.660838i
$943$	−2.87539			−0.0936355
$944$	16.2812	+	50.1082i	0.529906	+	1.63088i
$945$		0			0
$946$	−12.7082	+	39.1118i	−0.413179	+	1.27164i
$947$	0.819660	−	2.52265i	0.0266354	−	0.0819753i	−0.936855	−	0.349718i	$-0.886278\pi$
$947$	0.819660	−	2.52265i	0.0266354	−	0.0819753i	0.963491	+	0.267742i	$0.0862776\pi$
$948$	4.04508	−	2.93893i	0.131378	−	0.0954519i
$949$	−16.6869			−0.541680
$950$		0			0
$951$	7.65248			0.248149
$952$	5.85410	−	4.25325i	0.189733	−	0.137849i
$953$	−2.39261	+	7.36369i	−0.0775042	+	0.238533i	−0.982301	−	0.187311i	$-0.940023\pi$
$953$	−2.39261	+	7.36369i	−0.0775042	+	0.238533i	0.904796	+	0.425844i	$0.140023\pi$
$954$	−3.47214	+	10.6861i	−0.112415	+	0.345976i
$955$		0			0
$956$	−3.92047	−	12.0660i	−0.126797	−	0.390242i
$957$	18.9443			0.612381
$958$	5.42705	+	16.7027i	0.175340	+	0.539641i
$959$	5.97214	+	4.33901i	0.192850	+	0.140114i
$960$		0			0
$961$	17.7984	−	12.9313i	0.574141	−	0.417138i
$962$	−0.572949	−	0.416272i	−0.0184726	−	0.0134211i
$963$	−26.5623	−	19.2986i	−0.855958	−	0.621890i
$964$	−1.26393	+	0.918300i	−0.0407085	+	0.0295765i
$965$		0			0
$966$	3.04508	+	2.21238i	0.0979740	+	0.0711823i
$967$	1.27051	+	3.91023i	0.0408568	+	0.125744i	0.969404	−	0.245469i	$-0.0789419\pi$
$967$	1.27051	+	3.91023i	0.0408568	+	0.125744i	−0.928548	+	0.371213i	$0.878942\pi$
$968$	36.7082			1.17985
$969$	−1.38197	−	4.25325i	−0.0443951	−	0.136634i
$970$		0			0
$971$	1.73607	−	5.34307i	0.0557131	−	0.171467i	−0.919328	−	0.393492i	$-0.871267\pi$
$971$	1.73607	−	5.34307i	0.0557131	−	0.171467i	0.975041	+	0.222025i	$0.0712667\pi$
$972$	3.05573	−	9.40456i	0.0980125	−	0.301652i
$973$	−2.50000	+	1.81636i	−0.0801463	+	0.0582297i
$974$	58.9230			1.88801
$975$		0			0
$976$	−42.2705			−1.35305
$977$	1.89919	−	1.37984i	0.0607604	−	0.0441450i	−0.556990	−	0.830519i	$-0.688044\pi$
$977$	1.89919	−	1.37984i	0.0607604	−	0.0441450i	0.617751	+	0.786374i	$0.288044\pi$
$978$	−5.50000	+	16.9273i	−0.175871	+	0.541274i
$979$	14.4721	−	44.5407i	0.462531	−	1.42353i
$980$		0			0
$981$	−6.18034	−	19.0211i	−0.197323	−	0.607298i
$982$	69.9787			2.23311
$983$	2.97214	+	9.14729i	0.0947964	+	0.291753i	0.987201	−	0.159484i	$-0.0509829\pi$
$983$	2.97214	+	9.14729i	0.0947964	+	0.291753i	−0.892404	+	0.451237i	$0.850983\pi$
$984$	1.38197	+	1.00406i	0.0440555	+	0.0320082i
$985$		0			0
$986$	24.7984	−	18.0171i	0.789741	−	0.573781i
$987$	−0.309017	−	0.224514i	−0.00983612	−	0.00714636i
$988$	−0.791796	−	0.575274i	−0.0251904	−	0.0183019i
$989$	14.7812	−	10.7391i	0.470013	−	0.341485i
$990$		0			0
$991$	12.4271	+	9.02878i	0.394758	+	0.286809i	0.767403	−	0.641166i	$-0.221549\pi$
$991$	12.4271	+	9.02878i	0.394758	+	0.286809i	−0.372644	+	0.927974i	$0.621549\pi$
$992$	−3.13525	−	9.64932i	−0.0995444	−	0.306366i
$993$	−23.1246			−0.733837
$994$	2.04508	+	6.29412i	0.0648662	+	0.199638i
$995$		0			0
$996$	−1.19098	+	3.66547i	−0.0377377	+	0.116145i
$997$	7.69098	−	23.6704i	0.243576	−	0.749649i	−0.752292	−	0.658830i	$-0.771051\pi$
$997$	7.69098	−	23.6704i	0.243576	−	0.749649i	0.995867	−	0.0908191i	$-0.0289485\pi$
$998$	9.89919	−	7.19218i	0.313353	−	0.227664i
$999$	1.18034			0.0373443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.h.251.1		4
5.2	odd	4		625.2.e.c.374.2		8
5.3	odd	4		625.2.e.c.374.1		8
5.4	even	2		625.2.d.b.251.1		4
25.2	odd	20		125.2.e.a.99.2		8
25.3	odd	20		625.2.b.a.624.4		4
25.4	even	10		625.2.a.c.1.2		2
25.6	even	5		25.2.d.a.21.1	yes	4
25.8	odd	20		125.2.e.a.24.2		8
25.9	even	10		625.2.d.b.376.1		4
25.11	even	5		25.2.d.a.6.1	✓	4
25.12	odd	20		625.2.e.c.249.1		8
25.13	odd	20		625.2.e.c.249.2		8
25.14	even	10		125.2.d.a.26.1		4
25.16	even	5	inner	625.2.d.h.376.1		4
25.17	odd	20		125.2.e.a.24.1		8
25.19	even	10		125.2.d.a.101.1		4
25.21	even	5		625.2.a.b.1.1		2
25.22	odd	20		625.2.b.a.624.1		4
25.23	odd	20		125.2.e.a.99.1		8
75.11	odd	10		225.2.h.b.181.1		4
75.29	odd	10		5625.2.a.d.1.1		2
75.56	odd	10		225.2.h.b.46.1		4
75.71	odd	10		5625.2.a.f.1.2		2
100.11	odd	10		400.2.u.b.81.1		4
100.31	odd	10		400.2.u.b.321.1		4
100.71	odd	10		10000.2.a.c.1.1		2
100.79	odd	10		10000.2.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.6.1	✓	4	25.11	even	5
25.2.d.a.21.1	yes	4	25.6	even	5
125.2.d.a.26.1		4	25.14	even	10
125.2.d.a.101.1		4	25.19	even	10
125.2.e.a.24.1		8	25.17	odd	20
125.2.e.a.24.2		8	25.8	odd	20
125.2.e.a.99.1		8	25.23	odd	20
125.2.e.a.99.2		8	25.2	odd	20
225.2.h.b.46.1		4	75.56	odd	10
225.2.h.b.181.1		4	75.11	odd	10
400.2.u.b.81.1		4	100.11	odd	10
400.2.u.b.321.1		4	100.31	odd	10
625.2.a.b.1.1		2	25.21	even	5
625.2.a.c.1.2		2	25.4	even	10
625.2.b.a.624.1		4	25.22	odd	20
625.2.b.a.624.4		4	25.3	odd	20
625.2.d.b.251.1		4	5.4	even	2
625.2.d.b.376.1		4	25.9	even	10
625.2.d.h.251.1		4	1.1	even	1	trivial
625.2.d.h.376.1		4	25.16	even	5	inner
625.2.e.c.249.1		8	25.12	odd	20
625.2.e.c.249.2		8	25.13	odd	20
625.2.e.c.374.1		8	5.3	odd	4
625.2.e.c.374.2		8	5.2	odd	4
5625.2.a.d.1.1		2	75.29	odd	10
5625.2.a.f.1.2		2	75.71	odd	10
10000.2.a.c.1.1		2	100.71	odd	10
10000.2.a.l.1.2		2	100.79	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034 q^{7} +(0.690983 + 2.12663i) q^{8} +(1.61803 + 1.17557i) q^{9} +O(q^{10})\)	\(q+(1.30902 - 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034 q^{7} +(0.690983 + 2.12663i) q^{8} +(1.61803 + 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(-0.500000 - 0.363271i) q^{12} +(-1.50000 - 1.08981i) q^{13} +(0.809017 - 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(-1.61803 - 4.97980i) q^{17} +3.23607 q^{18} +(0.263932 + 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(2.61803 - 8.05748i) q^{22} +(-3.04508 + 2.21238i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(4.04508 - 2.93893i) q^{27} +(0.118034 - 0.363271i) q^{28} +(-1.11803 + 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} +3.38197 q^{32} +(-1.61803 - 4.97980i) q^{33} +(-6.85410 - 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(0.190983 + 0.138757i) q^{37} +(1.11803 + 0.812299i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(-0.309017 - 0.951057i) q^{42} -4.85410 q^{43} +(-1.00000 - 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(0.190983 - 0.587785i) q^{47} +(3.92705 - 2.85317i) q^{48} -6.61803 q^{49} -5.23607 q^{51} +(-0.927051 + 0.673542i) q^{52} +(-1.07295 + 3.30220i) q^{53} +(2.50000 - 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} +0.854102 q^{57} +(1.80902 + 5.56758i) q^{58} +(8.78115 + 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-3.92705 - 2.85317i) q^{62} +(1.00000 + 0.726543i) q^{63} +(-3.42705 + 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(1.47214 + 4.53077i) q^{67} -3.23607 q^{68} +(1.16312 + 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(-1.38197 + 4.25325i) q^{72} +(7.28115 - 5.29007i) q^{73} +0.381966 q^{74} +0.527864 q^{76} +(2.61803 - 1.90211i) q^{77} +(-0.927051 + 2.85317i) q^{78} +(-2.50000 + 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} +1.23607 q^{82} +(-1.92705 - 5.93085i) q^{83} +(-0.309017 - 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(2.92705 + 2.12663i) q^{87} +(9.47214 + 6.88191i) q^{88} +(7.23607 - 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(0.718847 + 2.21238i) q^{92} -3.00000 q^{93} +(-0.309017 - 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(-1.19098 + 3.66547i) q^{97} +(-8.66312 + 6.29412i) q^{98} +10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 - 2 * q^7 + 5 * q^8 + 2 * q^9	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9} + 8 q^{11} - 2 q^{12} - 6 q^{13} + q^{14} + 9 q^{16} - 2 q^{17} + 4 q^{18} + 10 q^{19} + 3 q^{21} + 6 q^{22} - q^{23} - 12 q^{26} + 5 q^{27} - 4 q^{28} + 3 q^{31} + 18 q^{32} - 2 q^{33} - 14 q^{34} + 4 q^{36} + 3 q^{37} - 6 q^{39} - 2 q^{41} + q^{42} - 6 q^{43} - 4 q^{44} - 12 q^{46} + 3 q^{47} + 9 q^{48} - 22 q^{49} - 12 q^{51} + 3 q^{52} - 11 q^{53} + 10 q^{54} - 5 q^{56} - 10 q^{57} + 5 q^{58} + 15 q^{59} - 17 q^{61} - 9 q^{62} + 4 q^{63} - 7 q^{64} - 14 q^{66} - 12 q^{67} - 4 q^{68} - 11 q^{69} + 3 q^{71} - 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{76} + 6 q^{77} + 3 q^{78} - 10 q^{79} - q^{81} - 4 q^{82} - q^{83} + q^{84} - 12 q^{86} + 5 q^{87} + 20 q^{88} + 20 q^{89} + 3 q^{91} + 23 q^{92} - 12 q^{93} + q^{94} - 7 q^{96} - 7 q^{97} - 19 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 - 2 * q^7 + 5 * q^8 + 2 * q^9 + 8 * q^11 - 2 * q^12 - 6 * q^13 + q^14 + 9 * q^16 - 2 * q^17 + 4 * q^18 + 10 * q^19 + 3 * q^21 + 6 * q^22 - q^23 - 12 * q^26 + 5 * q^27 - 4 * q^28 + 3 * q^31 + 18 * q^32 - 2 * q^33 - 14 * q^34 + 4 * q^36 + 3 * q^37 - 6 * q^39 - 2 * q^41 + q^42 - 6 * q^43 - 4 * q^44 - 12 * q^46 + 3 * q^47 + 9 * q^48 - 22 * q^49 - 12 * q^51 + 3 * q^52 - 11 * q^53 + 10 * q^54 - 5 * q^56 - 10 * q^57 + 5 * q^58 + 15 * q^59 - 17 * q^61 - 9 * q^62 + 4 * q^63 - 7 * q^64 - 14 * q^66 - 12 * q^67 - 4 * q^68 - 11 * q^69 + 3 * q^71 - 10 * q^72 + 9 * q^73 + 6 * q^74 + 20 * q^76 + 6 * q^77 + 3 * q^78 - 10 * q^79 - q^81 - 4 * q^82 - q^83 + q^84 - 12 * q^86 + 5 * q^87 + 20 * q^88 + 20 * q^89 + 3 * q^91 + 23 * q^92 - 12 * q^93 + q^94 - 7 * q^96 - 7 * q^97 - 19 * q^98 + 24 * q^99

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