LMFDB - Embedded newform 625.2.d.b.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.b.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} +(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} + 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}+ \cdots + 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

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	−0.944915	−	0.327315i	$-0.893856\pi$
$2$	−1.30902	+	0.951057i	−0.925615	+	0.672499i	0.0193004	+	0.999814i	$0.493856\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	−0.999773	−	0.0213149i	$-0.993215\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	0.821362	+	0.570408i	$0.193215\pi$
$4$	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	$-0.537263\pi$
$7$	−0.618034			−0.233595			−0.116797	+	0.993156i	$0.537263\pi$
$8$	−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	0.776037	−	0.630688i	$-0.217227\pi$
$13$	1.50000	+	1.08981i	0.416025	+	0.302260i	−0.360011	+	0.932948i	$0.617227\pi$
$14$	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	$0.118986\pi$
$17$	1.61803	+	4.97980i	0.392431	+	1.20778i	−0.538513	+	0.842617i	$0.681014\pi$
$18$	−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	−0.223165	−	0.974781i	$-0.571639\pi$
$23$	3.04508	−	2.21238i	0.634944	−	0.461314i	0.858110	+	0.513467i	$0.171639\pi$
$24$	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	0.571976	−	0.820270i	$-0.306177\pi$
$37$	−0.190983	−	0.138757i	−0.0313974	−	0.0228116i	−0.603373	+	0.797459i	$0.706177\pi$
$38$	−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	$-0.379316\pi$
$43$	4.85410			0.740244			0.370122	+	0.928983i	$0.379316\pi$
$44$	−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	−0.964019	−	0.265834i	$-0.914353\pi$
$47$	−0.190983	+	0.587785i	−0.0278577	+	0.0857373i	0.936161	+	0.351572i	$0.114353\pi$
$48$	−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	−0.849929	−	0.526898i	$-0.823355\pi$
$53$	1.07295	−	3.30220i	0.147381	−	0.453592i	0.997309	+	0.0733062i	$0.0233550\pi$
$54$	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	0.819972	−	0.572404i	$-0.193989\pi$
$67$	−1.47214	−	4.53077i	−0.179850	−	0.553521i	−0.999822	+	0.0188826i	$0.993989\pi$
$68$	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	−0.925750	−	0.378136i	$-0.876565\pi$
$73$	−7.28115	+	5.29007i	−0.852194	+	0.619156i	0.0735557	+	0.997291i	$0.476565\pi$
$74$	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	$0.0111885\pi$
$83$	1.92705	+	5.93085i	0.211521	+	0.650996i	−0.787861	+	0.615853i	$0.788811\pi$
$84$	−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	−0.872211	−	0.489130i	$-0.837314\pi$
$97$	1.19098	−	3.66547i	0.120926	−	0.372172i	0.993137	+	0.116958i	$0.0373143\pi$
$98$	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	$0.238614\pi$
$103$	−2.64590	+	8.14324i	−0.260708	+	0.802377i	−0.992651	+	0.121011i	$0.961386\pi$
$104$	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	$-0.208248\pi$
$107$	16.4164			1.58703			0.793517	+	0.608548i	$0.208248\pi$
$108$	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	0.999631	−	0.0271666i	$-0.00864846\pi$
$113$	13.6353	+	9.90659i	1.28270	+	0.931934i	0.283066	+	0.959100i	$0.408648\pi$
$114$	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	$-0.355919\pi$
$127$	16.0902	−	11.6902i	1.42777	−	1.03734i	0.990426	−	0.138043i	$-0.0440813\pi$
$128$	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	0.0927283	−	0.995691i	$-0.470441\pi$
$137$	−9.66312	−	7.02067i	−0.825576	−	0.599816i	−0.918304	+	0.395875i	$0.870441\pi$
$138$	−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	$-0.676291\pi$
$157$	−13.1803			−1.05191			−0.525953	+	0.850514i	$0.676291\pi$
$158$	−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	0.878966	−	0.476884i	$-0.158234\pi$
$163$	8.89919	+	6.46564i	0.697038	+	0.506428i	−0.181928	+	0.983312i	$0.558234\pi$
$164$	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	$-0.909480\pi$
$167$	−4.50000	−	13.8496i	−0.348220	−	1.07171i	0.611617	−	0.791154i	$-0.290520\pi$
$168$	−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	0.171799	−	0.985132i	$-0.445042\pi$
$173$	15.2812	−	11.1024i	1.16180	−	0.844100i	0.990005	+	0.141032i	$0.0450419\pi$
$174$	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	$-0.589481\pi$
$193$	−7.70820			−0.554849			−0.277424	+	0.960747i	$0.589481\pi$
$194$	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	−0.983543	−	0.180675i	$-0.942172\pi$
$197$	−1.14590	+	3.52671i	−0.0816419	+	0.251268i	0.901901	+	0.431943i	$0.142172\pi$
$198$	−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	−0.592660	−	0.805453i	$-0.701922\pi$
$223$	−0.145898	+	0.106001i	−0.00977005	+	0.00709836i	0.582890	+	0.812551i	$0.301922\pi$
$224$	2.09017			0.139655
$225$		0			0
$226$	−27.2705			−1.81401
$227$	11.9443	−	8.67802i	0.792769	−	0.575981i	−0.116015	−	0.993247i	$-0.537012\pi$
$227$	11.9443	−	8.67802i	0.792769	−	0.575981i	0.908784	+	0.417267i	$0.137012\pi$
$228$	−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	0.976426	−	0.215854i	$-0.0692535\pi$
$233$	0.909830	+	2.80017i	0.0596049	+	0.183445i	−0.916821	+	0.399299i	$0.869254\pi$
$234$	−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	$-0.752573\pi$
$257$	−22.8541			−1.42560			−0.712800	+	0.701367i	$0.752573\pi$
$258$	−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	0.281412	−	0.959587i	$-0.409197\pi$
$263$	−8.82624	−	6.41264i	−0.544249	−	0.395420i	−0.825661	+	0.564167i	$0.809197\pi$
$264$	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	−0.994387	−	0.105804i	$-0.966258\pi$
$277$	−19.9894	+	14.5231i	−1.20104	+	0.872610i	−0.206657	+	0.978413i	$0.566258\pi$
$278$	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	$0.247436\pi$
$283$	9.22542	+	28.3929i	0.548395	+	1.68778i	−0.164384	+	0.986396i	$0.552564\pi$
$284$	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	$-0.306782\pi$
$293$	19.5279			1.14083			0.570415	+	0.821357i	$0.306782\pi$
$294$	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	$-0.584898\pi$
$307$	−9.23607			−0.527130			−0.263565	+	0.964642i	$0.584898\pi$
$308$	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	0.134337	−	0.990936i	$-0.457110\pi$
$313$	−13.5623	−	9.85359i	−0.766587	−	0.556958i	−0.900924	+	0.433978i	$0.857110\pi$
$314$	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	0.862427	−	0.506182i	$-0.168944\pi$
$317$	−2.36475	−	7.27794i	−0.132817	−	0.408770i	−0.995244	+	0.0974121i	$0.968944\pi$
$318$	−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	0.747244	−	0.664550i	$-0.231377\pi$
$337$	6.35410	+	4.61653i	0.346130	+	0.251478i	−0.401114	+	0.916028i	$0.631377\pi$
$338$	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	$-0.720535\pi$
$347$	6.15248	−	18.9354i	0.330282	−	1.01650i	0.969000	−	0.247063i	$-0.0794653\pi$
$348$	−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	$0.211633\pi$
$353$	−3.98936	+	12.2780i	−0.212332	+	0.653491i	−0.999332	+	0.0365381i	$0.988367\pi$
$354$	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	$0.132495\pi$
$367$	7.89919	+	24.3112i	0.412334	+	1.26903i	−0.502279	+	0.864705i	$0.667505\pi$
$368$	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	−0.992643	−	0.121080i	$-0.961364\pi$
$373$	−22.8713	+	16.6170i	−1.18423	+	0.860395i	−0.191589	+	0.981475i	$0.561364\pi$
$374$	−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	$-0.775192\pi$
$383$	−10.3090	−	31.7279i	−0.526766	−	1.62122i	0.234031	−	0.972229i	$-0.424808\pi$
$384$	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	$0.359828\pi$
$397$	−8.97214	+	27.6134i	−0.450299	+	1.38588i	−0.876567	+	0.481280i	$0.840172\pi$
$398$	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	$-0.876748\pi$
$433$	−8.29837	−	25.5398i	−0.398794	−	1.22736i	0.527173	−	0.849758i	$-0.323252\pi$
$434$	−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	$-0.751915\pi$
$443$	−29.9443			−1.42270			−0.711348	+	0.702840i	$0.751915\pi$
$444$	−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	$-0.332999\pi$
$457$	21.4164			1.00182			0.500909	+	0.865500i	$0.332999\pi$
$458$	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	0.0332229	−	0.999448i	$-0.489423\pi$
$463$	−19.5172	−	14.1801i	−0.907042	−	0.659005i	−0.940265	+	0.340443i	$0.889423\pi$
$464$	−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	$-0.880944\pi$
$467$	−8.48278	−	26.1073i	−0.392536	−	1.20810i	0.538328	−	0.842736i	$-0.319056\pi$
$468$	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	$-0.991123\pi$
$487$	−29.4615	−	21.4050i	−1.33503	−	0.969954i	−0.335417	−	0.942070i	$-0.608877\pi$
$488$	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	$-0.585954\pi$
$503$	11.5623	−	35.5851i	0.515538	−	1.58666i	0.782301	−	0.622900i	$-0.214046\pi$
$504$	−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	−0.795508	−	0.605943i	$-0.792796\pi$
$523$	−10.6353	+	7.72696i	−0.465047	+	0.337877i	0.330461	+	0.943820i	$0.392796\pi$
$524$	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	$-0.749573\pi$
$547$	6.57953	−	20.2497i	0.281320	−	0.865815i	0.987478	−	0.157760i	$-0.0504271\pi$
$548$	−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	$-0.532181\pi$
$557$	−4.76393			−0.201854			−0.100927	+	0.994894i	$0.532181\pi$
$558$	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	0.706478	−	0.707735i	$-0.250283\pi$
$563$	5.97214	+	4.33901i	0.251696	+	0.182868i	−0.454782	+	0.890603i	$0.650283\pi$
$564$	−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	−0.986784	−	0.162042i	$-0.948192\pi$
$577$	−27.3262	+	19.8537i	−1.13761	+	0.826519i	−0.150822	+	0.988561i	$0.548192\pi$
$578$	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	0.672621	−	0.739987i	$-0.265169\pi$
$587$	4.28115	+	3.11044i	0.176702	+	0.128382i	−0.495919	+	0.868369i	$0.665169\pi$
$588$	−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	$-0.428086\pi$
$593$	10.9098			0.448013			0.224007	+	0.974588i	$0.428086\pi$
$594$	−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	$-0.243354\pi$
$607$	35.5623			1.44343			0.721715	+	0.692191i	$0.243354\pi$
$608$	−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	0.315527	−	0.948917i	$-0.397819\pi$
$613$	−12.1180	−	8.80427i	−0.489443	−	0.355601i	−0.804970	+	0.593316i	$0.797819\pi$
$614$	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	0.822619	−	0.568593i	$-0.192512\pi$
$617$	−4.39919	−	13.5393i	−0.177105	−	0.545072i	−0.999723	+	0.0235215i	$0.992512\pi$
$618$	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	$-0.291987\pi$
$643$	30.8328			1.21593			0.607964	+	0.793965i	$0.291987\pi$
$644$	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	$-0.644926\pi$
$647$	11.2918	−	34.7526i	0.443926	−	1.36626i	0.883657	−	0.468135i	$-0.155074\pi$
$648$	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	$0.221852\pi$
$653$	−5.89919	+	18.1558i	−0.230853	+	0.710493i	−0.997645	+	0.0685963i	$0.978148\pi$
$654$	−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	−0.381435	−	0.924396i	$-0.624570\pi$
$673$	9.85410	−	7.15942i	0.379848	−	0.275976i	0.761283	+	0.648420i	$0.224570\pi$
$674$	−12.7082			−0.489502
$675$		0			0
$676$	−5.90983			−0.227301
$677$	8.59017	−	6.24112i	0.330147	−	0.239866i	−0.410346	−	0.911930i	$-0.634592\pi$
$677$	8.59017	−	6.24112i	0.330147	−	0.239866i	0.740493	+	0.672064i	$0.234592\pi$
$678$	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	0.998571	−	0.0534426i	$-0.0170194\pi$
$683$	4.16312	+	12.8128i	0.159297	+	0.490267i	−0.839274	+	0.543709i	$0.817019\pi$
$684$	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	−0.154779	−	0.987949i	$-0.549467\pi$
$727$	19.8713	−	14.4374i	0.736987	−	0.535452i	0.891766	+	0.452497i	$0.149467\pi$
$728$	−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	$0.0202879\pi$
$733$	6.17376	+	19.0009i	0.228033	+	0.701814i	−0.769936	+	0.638121i	$0.779712\pi$
$734$	−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	$-0.674152\pi$
$743$	−28.3607			−1.04045			−0.520226	+	0.854029i	$0.674152\pi$
$744$	−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	$-0.686422\pi$
$757$	−30.4164			−1.10550			−0.552752	+	0.833346i	$0.686422\pi$
$758$	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	−0.972623	−	0.232387i	$-0.925346\pi$
$773$	−29.2533	+	21.2538i	−1.05217	+	0.764445i	−0.0795442	+	0.996831i	$0.525346\pi$
$774$	−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	0.404165	−	0.914686i	$-0.367562\pi$
$787$	−9.56231	−	6.94742i	−0.340859	−	0.247649i	−0.745024	+	0.667037i	$0.767562\pi$
$788$	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	−0.990166	−	0.139897i	$-0.955323\pi$
$797$	−3.01722	+	9.28605i	−0.106875	+	0.328929i	0.883291	+	0.468826i	$0.155323\pi$
$798$	−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	$-0.387482\pi$
$823$	38.5967	−	28.0422i	1.34540	−	0.977489i	0.999227	−	0.0393176i	$-0.0125184\pi$
$824$	19.1459			0.666979
$825$		0			0
$826$	10.8541			0.377663
$827$	−0.781153	+	0.567541i	−0.0271633	+	0.0197353i	−0.601284	−	0.799035i	$-0.705344\pi$
$827$	−0.781153	+	0.567541i	−0.0271633	+	0.0197353i	0.574121	+	0.818771i	$0.305344\pi$
$828$	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	−0.836863	−	0.547413i	$-0.815613\pi$
$853$	4.72949	−	14.5559i	0.161935	−	0.498384i	0.998797	+	0.0490292i	$0.0156127\pi$
$854$	−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	$-0.609157\pi$
$857$	−19.6869			−0.672492			−0.336246	+	0.941774i	$0.609157\pi$
$858$	−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	0.252072	−	0.967708i	$-0.418888\pi$
$863$	−17.3435	−	12.6008i	−0.590378	−	0.428935i	−0.842451	+	0.538773i	$0.818888\pi$
$864$	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	−0.961712	−	0.274063i	$-0.911632\pi$
$877$	−29.5623	+	21.4783i	−0.998248	+	0.725270i	−0.0365363	+	0.999332i	$0.511632\pi$
$878$	−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	$0.0125779\pi$
$883$	6.36068	+	19.5762i	0.214054	+	0.658790i	−0.785165	+	0.619286i	$0.787422\pi$
$884$	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	0.914380	−	0.404857i	$-0.132679\pi$
$887$	24.1803	+	17.5680i	0.811896	+	0.589877i	−0.102483	+	0.994735i	$0.532679\pi$
$888$	−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	$-0.313861\pi$
$907$	33.2492			1.10402			0.552011	+	0.833837i	$0.313861\pi$
$908$	−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	0.796888	−	0.604127i	$-0.206478\pi$
$937$	14.3435	+	10.4211i	0.468580	+	0.340444i	−0.328307	+	0.944571i	$0.606478\pi$
$938$	−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	−0.963491	−	0.267742i	$-0.913722\pi$
$947$	−0.819660	+	2.52265i	−0.0266354	+	0.0819753i	0.936855	+	0.349718i	$0.113722\pi$
$948$	−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	−0.904796	−	0.425844i	$-0.859977\pi$
$953$	2.39261	−	7.36369i	0.0775042	−	0.238533i	0.982301	+	0.187311i	$0.0599772\pi$
$954$	−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	0.928548	−	0.371213i	$-0.121058\pi$
$967$	−1.27051	−	3.91023i	−0.0408568	−	0.125744i	−0.969404	+	0.245469i	$0.921058\pi$
$968$	−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	−0.617751	−	0.786374i	$-0.711956\pi$
$977$	−1.89919	+	1.37984i	−0.0607604	+	0.0441450i	0.556990	+	0.830519i	$0.311956\pi$
$978$	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	0.892404	−	0.451237i	$-0.149017\pi$
$983$	−2.97214	−	9.14729i	−0.0947964	−	0.291753i	−0.987201	+	0.159484i	$0.949017\pi$
$984$	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	$0.228949\pi$
$997$	−7.69098	+	23.6704i	−0.243576	+	0.749649i	−0.995867	+	0.0908191i	$0.971051\pi$
$998$	−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.b.251.1		4
5.2	odd	4		625.2.e.c.374.1		8
5.3	odd	4		625.2.e.c.374.2		8
5.4	even	2		625.2.d.h.251.1		4
25.2	odd	20		125.2.e.a.99.1		8
25.3	odd	20		625.2.b.a.624.1		4
25.4	even	10		625.2.a.b.1.1		2
25.6	even	5		125.2.d.a.101.1		4
25.8	odd	20		125.2.e.a.24.1		8
25.9	even	10		625.2.d.h.376.1		4
25.11	even	5		125.2.d.a.26.1		4
25.12	odd	20		625.2.e.c.249.2		8
25.13	odd	20		625.2.e.c.249.1		8
25.14	even	10		25.2.d.a.6.1	✓	4
25.16	even	5	inner	625.2.d.b.376.1		4
25.17	odd	20		125.2.e.a.24.2		8
25.19	even	10		25.2.d.a.21.1	yes	4
25.21	even	5		625.2.a.c.1.2		2
25.22	odd	20		625.2.b.a.624.4		4
25.23	odd	20		125.2.e.a.99.2		8
75.14	odd	10		225.2.h.b.181.1		4
75.29	odd	10		5625.2.a.f.1.2		2
75.44	odd	10		225.2.h.b.46.1		4
75.71	odd	10		5625.2.a.d.1.1		2
100.19	odd	10		400.2.u.b.321.1		4
100.39	odd	10		400.2.u.b.81.1		4
100.71	odd	10		10000.2.a.l.1.2		2
100.79	odd	10		10000.2.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.6.1	✓	4	25.14	even	10
25.2.d.a.21.1	yes	4	25.19	even	10
125.2.d.a.26.1		4	25.11	even	5
125.2.d.a.101.1		4	25.6	even	5
125.2.e.a.24.1		8	25.8	odd	20
125.2.e.a.24.2		8	25.17	odd	20
125.2.e.a.99.1		8	25.2	odd	20
125.2.e.a.99.2		8	25.23	odd	20
225.2.h.b.46.1		4	75.44	odd	10
225.2.h.b.181.1		4	75.14	odd	10
400.2.u.b.81.1		4	100.39	odd	10
400.2.u.b.321.1		4	100.19	odd	10
625.2.a.b.1.1		2	25.4	even	10
625.2.a.c.1.2		2	25.21	even	5
625.2.b.a.624.1		4	25.3	odd	20
625.2.b.a.624.4		4	25.22	odd	20
625.2.d.b.251.1		4	1.1	even	1	trivial
625.2.d.b.376.1		4	25.16	even	5	inner
625.2.d.h.251.1		4	5.4	even	2
625.2.d.h.376.1		4	25.9	even	10
625.2.e.c.249.1		8	25.13	odd	20
625.2.e.c.249.2		8	25.12	odd	20
625.2.e.c.374.1		8	5.2	odd	4
625.2.e.c.374.2		8	5.3	odd	4
5625.2.a.d.1.1		2	75.71	odd	10
5625.2.a.f.1.2		2	75.29	odd	10
10000.2.a.c.1.1		2	100.79	odd	10
10000.2.a.l.1.2		2	100.71	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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{6} + 2 q^{7} - 5 q^{8} + 2 q^{9} + 8 q^{11} + 2 q^{12} + 6 q^{13} + q^{14} + 9 q^{16} + 2 q^{17} - 4 q^{18} + 10 q^{19} + 3 q^{21} - 6 q^{22} + q^{23} - 12 q^{26}+ \cdots + 24 q^{99}+O(q^{100}) \) 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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