LMFDB - Embedded newform 625.2.e.c.374.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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([1]))

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

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

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			374.2
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	625.374
Dual form			625.2.e.c.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 1.30902i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034i q^{7} +(2.12663 - 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(0.951057 + 1.30902i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034i q^{7} +(2.12663 - 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(0.363271 - 0.500000i) q^{12} +(-1.08981 + 1.50000i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(4.97980 - 1.61803i) q^{17} -3.23607i q^{18} +(-0.263932 - 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(8.05748 + 2.61803i) q^{22} +(2.21238 + 3.04508i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(2.93893 + 4.04508i) q^{27} +(-0.363271 - 0.118034i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} +3.38197i q^{32} +(-4.97980 + 1.61803i) q^{33} +(6.85410 + 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(-0.138757 + 0.190983i) q^{37} +(0.812299 - 1.11803i) q^{38} +(1.50000 - 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(0.951057 - 0.309017i) q^{42} +4.85410i q^{43} +(1.00000 + 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(0.587785 + 0.190983i) q^{47} +(-2.85317 - 3.92705i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(-0.673542 - 0.927051i) q^{52} +(3.30220 + 1.07295i) q^{53} +(-2.50000 + 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} +0.854102i q^{57} +(5.56758 - 1.80902i) q^{58} +(-8.78115 - 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(2.85317 - 3.92705i) q^{62} +(0.726543 - 1.00000i) q^{63} +(3.42705 - 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(-4.53077 + 1.47214i) q^{67} +3.23607i q^{68} +(-1.16312 - 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(-4.25325 - 1.38197i) q^{72} +(-5.29007 - 7.28115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(1.90211 + 2.61803i) q^{77} +(2.85317 + 0.927051i) q^{78} +(2.50000 - 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} +1.23607i q^{82} +(-5.93085 + 1.92705i) q^{83} +(0.309017 + 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(-2.12663 + 2.92705i) q^{87} +(6.88191 - 9.47214i) q^{88} +(-7.23607 + 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(-2.21238 + 0.718847i) q^{92} +3.00000i q^{93} +(0.309017 + 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(-3.66547 - 1.19098i) q^{97} +(6.29412 + 8.66312i) q^{98} -10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^4 - 4 * q^6 - 4 * q^9	$ 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + 16 q^{11} - 2 q^{14} + 18 q^{16} - 20 q^{19} + 6 q^{21} - 24 q^{26} + 6 q^{31} + 28 q^{34} + 8 q^{36} + 12 q^{39} - 4 q^{41} + 8 q^{44} - 24 q^{46} + 44 q^{49} - 24 q^{51} - 20 q^{54} - 10 q^{56} - 30 q^{59} - 34 q^{61} + 14 q^{64} - 28 q^{66} + 22 q^{69} + 6 q^{71} - 12 q^{74} + 40 q^{76} + 20 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} - 40 q^{89} + 6 q^{91} - 2 q^{94} - 14 q^{96} - 48 q^{99}+O(q^{100}) $ 8 * q - 6 * q^4 - 4 * q^6 - 4 * q^9 + 16 * q^11 - 2 * q^14 + 18 * q^16 - 20 * q^19 + 6 * q^21 - 24 * q^26 + 6 * q^31 + 28 * q^34 + 8 * q^36 + 12 * q^39 - 4 * q^41 + 8 * q^44 - 24 * q^46 + 44 * q^49 - 24 * q^51 - 20 * q^54 - 10 * q^56 - 30 * q^59 - 34 * q^61 + 14 * q^64 - 28 * q^66 + 22 * q^69 + 6 * q^71 - 12 * q^74 + 40 * q^76 + 20 * q^79 - 2 * q^81 - 2 * q^84 - 24 * q^86 - 40 * q^89 + 6 * q^91 - 2 * q^94 - 14 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.951057	+	1.30902i	0.672499	+	0.925615i	0.999814	−	0.0193004i	$-0.00614389\pi$
$2$	0.951057	+	1.30902i	0.672499	+	0.925615i	−0.327315	+	0.944915i	$0.606144\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i	0.0213149	−	0.999773i	$-0.493215\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i	−0.570408	+	0.821362i	$0.693215\pi$
$4$	−0.190983	+	0.587785i	−0.0954915	+	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	1.53884i	−0.204124	−	0.628230i
$7$			0.618034i			0.233595i	0.993156	+	0.116797i	$0.0372628\pi$
$7$			0.618034i			0.233595i	−0.993156	+	0.116797i	$0.962737\pi$
$8$	2.12663	−	0.690983i	0.751876	−	0.244299i
$9$	−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	$0.0104089\pi$
$12$	0.363271	−	0.500000i	0.104867	−	0.144338i
$13$	−1.08981	+	1.50000i	−0.302260	+	0.416025i	−0.932948	−	0.360011i	$-0.882773\pi$
$13$	−1.08981	+	1.50000i	−0.302260	+	0.416025i	0.630688	+	0.776037i	$0.282773\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$		0			0
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	4.97980	−	1.61803i	1.20778	−	0.392431i	0.365161	−	0.930944i	$-0.381014\pi$
$17$	4.97980	−	1.61803i	1.20778	−	0.392431i	0.842617	+	0.538513i	$0.181014\pi$
$18$		−	3.23607i		−	0.762749i
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	0.916206	−	0.400707i	$-0.131236\pi$
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	−0.976756	+	0.214353i	$0.931236\pi$
$20$		0			0
$21$	0.190983	−	0.587785i	0.0416759	−	0.128265i
$22$	8.05748	+	2.61803i	1.71786	+	0.558167i
$23$	2.21238	+	3.04508i	0.461314	+	0.634944i	0.974781	−	0.223165i	$-0.0716390\pi$
$23$	2.21238	+	3.04508i	0.461314	+	0.634944i	−0.513467	+	0.858110i	$0.671639\pi$
$24$	−2.23607			−0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	2.93893	+	4.04508i	0.565597	+	0.778477i
$28$	−0.363271	−	0.118034i	−0.0686518	−	0.0223063i
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	−0.791982	−	0.610544i	$-0.790951\pi$
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	0.999596	−	0.0284251i	$-0.00904922\pi$
$30$		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	$0.986828\pi$
$32$			3.38197i			0.597853i
$33$	−4.97980	+	1.61803i	−0.866871	+	0.281664i
$34$	6.85410	+	4.97980i	1.17547	+	0.854028i
$35$		0			0
$36$	1.00000	−	0.726543i	0.166667	−	0.121090i
$37$	−0.138757	+	0.190983i	−0.0228116	+	0.0313974i	−0.820270	−	0.571976i	$-0.806177\pi$
$37$	−0.138757	+	0.190983i	−0.0228116	+	0.0313974i	0.797459	+	0.603373i	$0.206177\pi$
$38$	0.812299	−	1.11803i	0.131772	−	0.181369i
$39$	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	$0.681001\pi$
$42$	0.951057	−	0.309017i	0.146751	−	0.0476824i
$43$			4.85410i			0.740244i	0.928983	+	0.370122i	$0.120684\pi$
$43$			4.85410i			0.740244i	−0.928983	+	0.370122i	$0.879316\pi$
$44$	1.00000	+	3.07768i	0.150756	+	0.463978i
$45$		0			0
$46$	−1.88197	+	5.79210i	−0.277481	+	0.853998i
$47$	0.587785	+	0.190983i	0.0857373	+	0.0278577i	0.351572	−	0.936161i	$-0.385647\pi$
$47$	0.587785	+	0.190983i	0.0857373	+	0.0278577i	−0.265834	+	0.964019i	$0.585647\pi$
$48$	−2.85317	−	3.92705i	−0.411820	−	0.566821i
$49$	6.61803			0.945433
$50$		0			0
$51$	−5.23607			−0.733196
$52$	−0.673542	−	0.927051i	−0.0934035	−	0.128559i
$53$	3.30220	+	1.07295i	0.453592	+	0.147381i	0.526898	−	0.849929i	$-0.323355\pi$
$53$	3.30220	+	1.07295i	0.453592	+	0.147381i	−0.0733062	+	0.997309i	$0.523355\pi$
$54$	−2.50000	+	7.69421i	−0.340207	+	1.04705i
$55$		0			0
$56$	0.427051	+	1.31433i	0.0570671	+	0.175634i
$57$			0.854102i			0.113129i
$58$	5.56758	−	1.80902i	0.731059	−	0.237536i
$59$	−8.78115	−	6.37988i	−1.14321	−	0.830590i	−0.155646	−	0.987813i	$-0.549746\pi$
$59$	−8.78115	−	6.37988i	−1.14321	−	0.830590i	−0.987563	+	0.157223i	$0.949746\pi$
$60$		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	$0.488234\pi$
$62$	2.85317	−	3.92705i	0.362353	−	0.498736i
$63$	0.726543	−	1.00000i	0.0915358	−	0.125988i
$64$	3.42705	−	2.48990i	0.428381	−	0.311237i
$65$		0			0
$66$	−6.85410	−	4.97980i	−0.843682	−	0.612971i
$67$	−4.53077	+	1.47214i	−0.553521	+	0.179850i	−0.572404	−	0.819972i	$-0.693989\pi$
$67$	−4.53077	+	1.47214i	−0.553521	+	0.179850i	0.0188826	+	0.999822i	$0.493989\pi$
$68$			3.23607i			0.392431i
$69$	−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	$0.971538\pi$
$72$	−4.25325	−	1.38197i	−0.501251	−	0.162866i
$73$	−5.29007	−	7.28115i	−0.619156	−	0.852194i	0.378136	−	0.925750i	$-0.376565\pi$
$73$	−5.29007	−	7.28115i	−0.619156	−	0.852194i	−0.997291	+	0.0735557i	$0.976565\pi$
$74$	−0.381966			−0.0444026
$75$		0			0
$76$	0.527864			0.0605502
$77$	1.90211	+	2.61803i	0.216766	+	0.298353i
$78$	2.85317	+	0.927051i	0.323058	+	0.104968i
$79$	2.50000	−	7.69421i	0.281272	−	0.865666i	−0.706219	−	0.707993i	$-0.749601\pi$
$79$	2.50000	−	7.69421i	0.281272	−	0.865666i	0.987491	−	0.157673i	$-0.0503992\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			1.23607i			0.136501i
$83$	−5.93085	+	1.92705i	−0.650996	+	0.211521i	−0.615853	−	0.787861i	$-0.711189\pi$
$83$	−5.93085	+	1.92705i	−0.650996	+	0.211521i	−0.0351426	+	0.999382i	$0.511189\pi$
$84$	0.309017	+	0.224514i	0.0337165	+	0.0244965i
$85$		0			0
$86$	−6.35410	+	4.61653i	−0.685180	+	0.497813i
$87$	−2.12663	+	2.92705i	−0.227998	+	0.313813i
$88$	6.88191	−	9.47214i	0.733614	−	1.00973i
$89$	−7.23607	+	5.25731i	−0.767022	+	0.557274i	−0.901056	−	0.433703i	$-0.857207\pi$
$89$	−7.23607	+	5.25731i	−0.767022	+	0.557274i	0.134034	+	0.990977i	$0.457207\pi$
$90$		0			0
$91$	−0.927051	−	0.673542i	−0.0971813	−	0.0706064i
$92$	−2.21238	+	0.718847i	−0.230657	+	0.0749450i
$93$			3.00000i			0.311086i
$94$	0.309017	+	0.951057i	0.0318727	+	0.0980940i
$95$		0			0
$96$	1.04508	−	3.21644i	0.106664	−	0.328277i
$97$	−3.66547	−	1.19098i	−0.372172	−	0.120926i	0.116958	−	0.993137i	$-0.462686\pi$
$97$	−3.66547	−	1.19098i	−0.372172	−	0.120926i	−0.489130	+	0.872211i	$0.662686\pi$
$98$	6.29412	+	8.66312i	0.635803	+	0.875107i
$99$	−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	$0.476666\pi$
$102$	−4.97980	−	6.85410i	−0.493073	−	0.678657i
$103$	−8.14324	−	2.64590i	−0.802377	−	0.260708i	−0.121011	−	0.992651i	$-0.538614\pi$
$103$	−8.14324	−	2.64590i	−0.802377	−	0.260708i	−0.681366	+	0.731943i	$0.738614\pi$
$104$	−1.28115	+	3.94298i	−0.125627	+	0.386641i
$105$		0			0
$106$	1.73607	+	5.34307i	0.168622	+	0.518965i
$107$		−	16.4164i		−	1.58703i	−0.608548	−	0.793517i	$-0.708248\pi$
$107$		−	16.4164i		−	1.58703i	0.608548	−	0.793517i	$-0.291752\pi$
$108$	−2.93893	+	0.954915i	−0.282798	+	0.0918867i
$109$	8.09017	+	5.87785i	0.774898	+	0.562996i	0.903443	−	0.428707i	$-0.141031\pi$
$109$	8.09017	+	5.87785i	0.774898	+	0.562996i	−0.128546	+	0.991704i	$0.541031\pi$
$110$		0			0
$111$	0.190983	−	0.138757i	0.0181273	−	0.0131703i
$112$	−1.76336	+	2.42705i	−0.166621	+	0.229335i
$113$	−9.90659	+	13.6353i	−0.931934	+	1.28270i	0.0271666	+	0.999631i	$0.491352\pi$
$113$	−9.90659	+	13.6353i	−0.931934	+	1.28270i	−0.959100	+	0.283066i	$0.908648\pi$
$114$	−1.11803	+	0.812299i	−0.104713	+	0.0760788i
$115$		0			0
$116$	1.80902	+	1.31433i	0.167963	+	0.122032i
$117$	3.52671	−	1.14590i	0.326045	−	0.105938i
$118$		−	17.5623i		−	1.61674i
$119$	1.00000	+	3.07768i	0.0916698	+	0.282131i
$120$		0			0
$121$	5.07295	−	15.6129i	0.461177	−	1.41936i
$122$	−13.4005	−	4.35410i	−1.21323	−	0.394202i
$123$	−0.449028	−	0.618034i	−0.0404875	−	0.0557262i
$124$	1.85410			0.166503
$125$		0			0
$126$	2.00000			0.178174
$127$	−11.6902	−	16.0902i	−1.03734	−	1.42777i	−0.899294	−	0.437346i	$-0.855919\pi$
$127$	−11.6902	−	16.0902i	−1.03734	−	1.42777i	−0.138043	−	0.990426i	$-0.544081\pi$
$128$	12.9515	+	4.20820i	1.14476	+	0.371956i
$129$	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	$0.804018\pi$
$132$		−	3.23607i		−	0.281664i
$133$	0.502029	−	0.163119i	0.0435314	−	0.0141442i
$134$	−6.23607	−	4.53077i	−0.538714	−	0.391399i
$135$		0			0
$136$	9.47214	−	6.88191i	0.812229	−	0.590119i
$137$	−7.02067	+	9.66312i	−0.599816	+	0.825576i	−0.995691	−	0.0927283i	$-0.970441\pi$
$137$	−7.02067	+	9.66312i	−0.599816	+	0.825576i	0.395875	+	0.918304i	$0.370441\pi$
$138$	3.57971	−	4.92705i	0.304725	−	0.419418i
$139$	4.04508	−	2.93893i	0.343100	−	0.249276i	−0.402869	−	0.915258i	$-0.631987\pi$
$139$	4.04508	−	2.93893i	0.343100	−	0.249276i	0.745968	+	0.665981i	$0.231987\pi$
$140$		0			0
$141$	−0.500000	−	0.363271i	−0.0421076	−	0.0305930i
$142$	−10.1841	+	3.30902i	−0.854631	+	0.277687i
$143$			9.70820i			0.811841i
$144$	−3.00000	−	9.23305i	−0.250000	−	0.769421i
$145$		0			0
$146$	4.50000	−	13.8496i	0.372423	−	1.14620i
$147$	−6.29412	−	2.04508i	−0.519131	−	0.168676i
$148$	−0.0857567	−	0.118034i	−0.00704916	−	0.00970233i
$149$	3.94427			0.323127			0.161564	−	0.986862i	$-0.448346\pi$
$149$	3.94427			0.323127			0.161564	+	0.986862i	$0.448346\pi$
$150$		0			0
$151$	14.5623			1.18506			0.592532	−	0.805547i	$-0.298128\pi$
$151$	14.5623			1.18506			0.592532	+	0.805547i	$0.298128\pi$
$152$	−1.12257	−	1.54508i	−0.0910524	−	0.125323i
$153$	−9.95959	−	3.23607i	−0.805185	−	0.261621i
$154$	−1.61803	+	4.97980i	−0.130385	+	0.401283i
$155$		0			0
$156$	0.354102	+	1.08981i	0.0283508	+	0.0872549i
$157$			13.1803i			1.05191i	0.850514	+	0.525953i	$0.176291\pi$
$157$			13.1803i			1.05191i	−0.850514	+	0.525953i	$0.823709\pi$
$158$	12.4495	−	4.04508i	0.990428	−	0.321810i
$159$	−2.80902	−	2.04087i	−0.222770	−	0.161852i
$160$		0			0
$161$	−1.88197	+	1.36733i	−0.148320	+	0.107761i
$162$	−0.951057	+	1.30902i	−0.0747221	+	0.102846i
$163$	−6.46564	+	8.89919i	−0.506428	+	0.697038i	−0.983312	−	0.181928i	$-0.941766\pi$
$163$	−6.46564	+	8.89919i	−0.506428	+	0.697038i	0.476884	+	0.878966i	$0.341766\pi$
$164$	−0.381966	+	0.277515i	−0.0298265	+	0.0216702i
$165$		0			0
$166$	−8.16312	−	5.93085i	−0.633581	−	0.460323i
$167$	−13.8496	+	4.50000i	−1.07171	+	0.348220i	−0.791154	−	0.611617i	$-0.790520\pi$
$167$	−13.8496	+	4.50000i	−1.07171	+	0.348220i	−0.280558	+	0.959837i	$0.590520\pi$
$168$		−	1.38197i		−	0.106621i
$169$	2.95492	+	9.09429i	0.227301	+	0.699561i
$170$		0			0
$171$	−0.527864	+	1.62460i	−0.0403668	+	0.124236i
$172$	−2.85317	−	0.927051i	−0.217552	−	0.0706870i
$173$	11.1024	+	15.2812i	0.844100	+	1.16180i	0.985132	+	0.171799i	$0.0549581\pi$
$173$	11.1024	+	15.2812i	0.844100	+	1.16180i	−0.141032	+	0.990005i	$0.545042\pi$
$174$	−5.85410			−0.443798
$175$		0			0
$176$	25.4164			1.91583
$177$	6.37988	+	8.78115i	0.479541	+	0.660032i
$178$	−13.7638	−	4.47214i	−1.03164	−	0.335201i
$179$	0.163119	−	0.502029i	0.0121921	−	0.0375234i	−0.944775	−	0.327719i	$-0.893720\pi$
$179$	0.163119	−	0.502029i	0.0121921	−	0.0375234i	0.956967	+	0.290195i	$0.0937202\pi$
$180$		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	$0.896548\pi$
$182$		−	1.85410i		−	0.137435i
$183$	8.28199	−	2.69098i	0.612223	−	0.198923i
$184$	6.80902	+	4.94704i	0.501967	+	0.364701i
$185$		0			0
$186$	−3.92705	+	2.85317i	−0.287945	+	0.209205i
$187$	16.1150	−	22.1803i	1.17844	−	1.62199i
$188$	−0.224514	+	0.309017i	−0.0163744	+	0.0225374i
$189$	−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	$0.679030\pi$
$192$	−4.02874	+	1.30902i	−0.290749	+	0.0944702i
$193$		−	7.70820i		−	0.554849i	−0.960747	−	0.277424i	$-0.910519\pi$
$193$		−	7.70820i		−	0.554849i	0.960747	−	0.277424i	$-0.0894808\pi$
$194$	−1.92705	−	5.93085i	−0.138354	−	0.425810i
$195$		0			0
$196$	−1.26393	+	3.88998i	−0.0902809	+	0.277856i
$197$	3.52671	+	1.14590i	0.251268	+	0.0816419i	0.431943	−	0.901901i	$-0.357828\pi$
$197$	3.52671	+	1.14590i	0.251268	+	0.0816419i	−0.180675	+	0.983543i	$0.557828\pi$
$198$	−9.95959	−	13.7082i	−0.707797	−	0.974200i
$199$	17.5623			1.24496			0.622479	−	0.782636i	$-0.286125\pi$
$199$	17.5623			1.24496			0.622479	+	0.782636i	$0.286125\pi$
$200$		0			0
$201$	4.76393			0.336022
$202$	1.40008	+	1.92705i	0.0985096	+	0.135587i
$203$	2.12663	+	0.690983i	0.149260	+	0.0484975i
$204$	1.00000	−	3.07768i	0.0700140	−	0.215481i
$205$		0			0
$206$	−4.28115	−	13.1760i	−0.298282	−	0.918018i
$207$		−	7.52786i		−	0.523223i
$208$	−8.55951	+	2.78115i	−0.593495	+	0.192838i
$209$	−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	$0.197660\pi$
$212$	−1.26133	+	1.73607i	−0.0866283	+	0.119234i
$213$	3.88998	−	5.35410i	0.266537	−	0.366857i
$214$	21.4894	−	15.6129i	1.46898	−	1.06728i
$215$		0			0
$216$	9.04508	+	6.57164i	0.615440	+	0.447143i
$217$	1.76336	−	0.572949i	0.119704	−	0.0388943i
$218$			16.1803i			1.09587i
$219$	2.78115	+	8.55951i	0.187933	+	0.578398i
$220$		0			0
$221$	−3.00000	+	9.23305i	−0.201802	+	0.621082i
$222$	0.363271	+	0.118034i	0.0243812	+	0.00792192i
$223$	−0.106001	−	0.145898i	−0.00709836	−	0.00977005i	0.805453	−	0.592660i	$-0.201922\pi$
$223$	−0.106001	−	0.145898i	−0.00709836	−	0.00977005i	−0.812551	+	0.582890i	$0.801922\pi$
$224$	−2.09017			−0.139655
$225$		0			0
$226$	−27.2705			−1.81401
$227$	−8.67802	−	11.9443i	−0.575981	−	0.792769i	0.417267	−	0.908784i	$-0.362988\pi$
$227$	−8.67802	−	11.9443i	−0.575981	−	0.792769i	−0.993247	+	0.116015i	$0.962988\pi$
$228$	−0.502029	−	0.163119i	−0.0332477	−	0.0108028i
$229$	−6.70820	+	20.6457i	−0.443291	+	1.36431i	0.441057	+	0.897479i	$0.354604\pi$
$229$	−6.70820	+	20.6457i	−0.443291	+	1.36431i	−0.884348	+	0.466829i	$0.845396\pi$
$230$		0			0
$231$	−1.00000	−	3.07768i	−0.0657952	−	0.202497i
$232$		−	8.09017i		−	0.531146i
$233$	−2.80017	+	0.909830i	−0.183445	+	0.0596049i	−0.399299	−	0.916821i	$-0.630746\pi$
$233$	−2.80017	+	0.909830i	−0.183445	+	0.0596049i	0.215854	+	0.976426i	$0.430746\pi$
$234$	4.85410	+	3.52671i	0.317323	+	0.230548i
$235$		0			0
$236$	5.42705	−	3.94298i	0.353271	−	0.256666i
$237$	−4.75528	+	6.54508i	−0.308889	+	0.425149i
$238$	−3.07768	+	4.23607i	−0.199497	+	0.274584i
$239$	−16.6074	+	12.0660i	−1.07424	+	0.780483i	−0.976670	−	0.214745i	$-0.931108\pi$
$239$	−16.6074	+	12.0660i	−1.07424	+	0.780483i	−0.0975727	+	0.995228i	$0.531108\pi$
$240$		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	$0.725945\pi$
$242$	25.2623	−	8.20820i	1.62392	−	0.527643i
$243$		−	16.0000i		−	1.02640i
$244$	−1.66312	−	5.11855i	−0.106470	−	0.327682i
$245$		0			0
$246$	0.381966	−	1.17557i	0.0243533	−	0.0749516i
$247$	1.50609	+	0.489357i	0.0958299	+	0.0311370i
$248$	−3.94298	−	5.42705i	−0.250380	−	0.344618i
$249$	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	$0.872564\pi$
$252$	0.449028	+	0.618034i	0.0282861	+	0.0389325i
$253$	18.7436	+	6.09017i	1.17840	+	0.382886i
$254$	9.94427	−	30.6053i	0.623959	−	1.92035i
$255$		0			0
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$			22.8541i			1.42560i	0.701367	+	0.712800i	$0.252573\pi$
$257$			22.8541i			1.42560i	−0.701367	+	0.712800i	$0.747427\pi$
$258$	7.46969	−	2.42705i	0.465043	−	0.151102i
$259$	−0.118034	−	0.0857567i	−0.00733428	−	0.00532866i
$260$		0			0
$261$	−5.85410	+	4.25325i	−0.362360	+	0.263270i
$262$	−6.46564	+	8.89919i	−0.399448	+	0.549794i
$263$	6.41264	−	8.82624i	0.395420	−	0.544249i	−0.564167	−	0.825661i	$-0.690803\pi$
$263$	6.41264	−	8.82624i	0.395420	−	0.544249i	0.959587	+	0.281412i	$0.0908026\pi$
$264$	−9.47214	+	6.88191i	−0.582970	+	0.423552i
$265$		0			0
$266$	0.690983	+	0.502029i	0.0423669	+	0.0307813i
$267$	8.50651	−	2.76393i	0.520590	−	0.169150i
$268$		−	2.94427i		−	0.179850i
$269$	3.94427	+	12.1392i	0.240487	+	0.740141i	0.996346	+	0.0854076i	$0.0272192\pi$
$269$	3.94427	+	12.1392i	0.240487	+	0.740141i	−0.755860	+	0.654734i	$0.772781\pi$
$270$		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	$0.178126\pi$
$272$	24.1724	+	7.85410i	1.46567	+	0.476225i
$273$	0.673542	+	0.927051i	0.0407646	+	0.0561077i
$274$	−19.3262			−1.16754
$275$		0			0
$276$	2.32624			0.140023
$277$	14.5231	+	19.9894i	0.872610	+	1.20104i	0.978413	+	0.206657i	$0.0662584\pi$
$277$	14.5231	+	19.9894i	0.872610	+	1.20104i	−0.105804	+	0.994387i	$0.533742\pi$
$278$	7.69421	+	2.50000i	0.461468	+	0.149940i
$279$	−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	$0.802691\pi$
$282$		−	1.00000i		−	0.0595491i
$283$	−28.3929	+	9.22542i	−1.68778	+	0.548395i	−0.986396	−	0.164384i	$-0.947436\pi$
$283$	−28.3929	+	9.22542i	−1.68778	+	0.548395i	−0.701389	+	0.712779i	$0.747436\pi$
$284$	−3.30902	−	2.40414i	−0.196354	−	0.142660i
$285$		0			0
$286$	−12.7082	+	9.23305i	−0.751452	+	0.545962i
$287$	−0.277515	+	0.381966i	−0.0163812	+	0.0225467i
$288$	3.97574	−	5.47214i	0.234273	−	0.322449i
$289$	8.42705	−	6.12261i	0.495709	−	0.360154i
$290$		0			0
$291$	3.11803	+	2.26538i	0.182782	+	0.132799i
$292$	5.29007	−	1.71885i	0.309578	−	0.100588i
$293$			19.5279i			1.14083i	0.821357	+	0.570415i	$0.193218\pi$
$293$			19.5279i			1.14083i	−0.821357	+	0.570415i	$0.806782\pi$
$294$	−3.30902	−	10.1841i	−0.192986	−	0.593949i
$295$		0			0
$296$	−0.163119	+	0.502029i	−0.00948110	+	0.0291798i
$297$	24.8990	+	8.09017i	1.44479	+	0.469439i
$298$	3.75123	+	5.16312i	0.217303	+	0.299091i
$299$	−6.97871			−0.403589
$300$		0			0
$301$	−3.00000			−0.172917
$302$	13.8496	+	19.0623i	0.796954	+	1.09691i
$303$	−1.40008	−	0.454915i	−0.0804328	−	0.0261342i
$304$	1.28115	−	3.94298i	0.0734792	−	0.226146i
$305$		0			0
$306$	−5.23607	−	16.1150i	−0.299326	−	0.921231i
$307$			9.23607i			0.527130i	0.964642	+	0.263565i	$0.0848984\pi$
$307$			9.23607i			0.527130i	−0.964642	+	0.263565i	$0.915102\pi$
$308$	−1.90211	+	0.618034i	−0.108383	+	0.0352158i
$309$	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	$0.377535\pi$
$312$	2.43690	−	3.35410i	0.137962	−	0.189889i
$313$	9.85359	−	13.5623i	0.556958	−	0.766587i	−0.433978	−	0.900924i	$-0.642890\pi$
$313$	9.85359	−	13.5623i	0.556958	−	0.766587i	0.990936	+	0.134337i	$0.0428904\pi$
$314$	−17.2533	+	12.5352i	−0.973659	+	0.707405i
$315$		0			0
$316$	4.04508	+	2.93893i	0.227554	+	0.165328i
$317$	−7.27794	+	2.36475i	−0.408770	+	0.132817i	−0.506182	−	0.862427i	$-0.668944\pi$
$317$	−7.27794	+	2.36475i	−0.408770	+	0.132817i	0.0974121	+	0.995244i	$0.468944\pi$
$318$		−	5.61803i		−	0.315044i
$319$	−5.85410	−	18.0171i	−0.327767	−	1.00876i
$320$		0			0
$321$	−5.07295	+	15.6129i	−0.283144	+	0.871429i
$322$	−3.57971	−	1.16312i	−0.199490	−	0.0648181i
$323$	−2.62866	−	3.61803i	−0.146262	−	0.201313i
$324$	−0.618034			−0.0343352
$325$		0			0
$326$	−17.7984			−0.985761
$327$	−5.87785	−	8.09017i	−0.325046	−	0.447387i
$328$	1.62460	+	0.527864i	0.0897034	+	0.0291464i
$329$	−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	$-0.319215\pi$
$332$		−	3.85410i		−	0.211521i
$333$	0.449028	−	0.145898i	0.0246066	−	0.00799516i
$334$	−19.0623	−	13.8496i	−1.04304	−	0.757815i
$335$		0			0
$336$	2.42705	−	1.76336i	0.132406	−	0.0961989i
$337$	4.61653	−	6.35410i	0.251478	−	0.346130i	−0.664550	−	0.747244i	$-0.731377\pi$
$337$	4.61653	−	6.35410i	0.251478	−	0.346130i	0.916028	+	0.401114i	$0.131377\pi$
$338$	−9.09429	+	12.5172i	−0.494664	+	0.680847i
$339$	13.6353	−	9.90659i	0.740565	−	0.538052i
$340$		0			0
$341$	−12.7082	−	9.23305i	−0.688188	−	0.499998i
$342$	−2.62866	+	0.854102i	−0.142141	+	0.0461845i
$343$			8.41641i			0.454443i
$344$	3.35410	+	10.3229i	0.180841	+	0.556572i
$345$		0			0
$346$	−9.44427	+	29.0665i	−0.507727	+	1.56262i
$347$	−18.9354	−	6.15248i	−1.01650	−	0.330282i	−0.247063	−	0.969000i	$-0.579465\pi$
$347$	−18.9354	−	6.15248i	−1.01650	−	0.330282i	−0.769441	+	0.638717i	$0.779465\pi$
$348$	−1.31433	−	1.80902i	−0.0704554	−	0.0969735i
$349$	−21.7082			−1.16201			−0.581007	−	0.813899i	$-0.697341\pi$
$349$	−21.7082			−1.16201			−0.581007	+	0.813899i	$0.697341\pi$
$350$		0			0
$351$	−9.27051			−0.494823
$352$	10.4086	+	14.3262i	0.554781	+	0.763591i
$353$	−12.2780	−	3.98936i	−0.653491	−	0.212332i	−0.0365381	−	0.999332i	$-0.511633\pi$
$353$	−12.2780	−	3.98936i	−0.653491	−	0.212332i	−0.616953	+	0.787000i	$0.711633\pi$
$354$	−5.42705	+	16.7027i	−0.288445	+	0.887741i
$355$		0			0
$356$	−1.70820	−	5.25731i	−0.0905346	−	0.278637i
$357$		−	3.23607i		−	0.171271i
$358$	0.812299	−	0.263932i	0.0429313	−	0.0139492i
$359$	11.1180	+	8.07772i	0.586787	+	0.426326i	0.841165	−	0.540779i	$-0.181870\pi$
$359$	11.1180	+	8.07772i	0.586787	+	0.426326i	−0.254377	+	0.967105i	$0.581870\pi$
$360$		0			0
$361$	14.7812	−	10.7391i	0.777955	−	0.565218i
$362$	−0.277515	+	0.381966i	−0.0145858	+	0.0200757i
$363$	−9.64932	+	13.2812i	−0.506458	+	0.697080i
$364$	0.572949	−	0.416272i	0.0300307	−	0.0218186i
$365$		0			0
$366$	11.3992	+	8.28199i	0.595845	+	0.432907i
$367$	24.3112	−	7.89919i	1.26903	−	0.412334i	0.404329	−	0.914614i	$-0.367505\pi$
$367$	24.3112	−	7.89919i	1.26903	−	0.412334i	0.864705	+	0.502279i	$0.167505\pi$
$368$			18.2705i			0.952416i
$369$	−0.472136	−	1.45309i	−0.0245784	−	0.0756446i
$370$		0			0
$371$	−0.663119	+	2.04087i	−0.0344274	+	0.105957i
$372$	−1.76336	−	0.572949i	−0.0914257	−	0.0297060i
$373$	−16.6170	−	22.8713i	−0.860395	−	1.18423i	−0.981475	−	0.191589i	$-0.938636\pi$
$373$	−16.6170	−	22.8713i	−0.860395	−	1.18423i	0.121080	−	0.992643i	$-0.461364\pi$
$374$	44.3607			2.29384
$375$		0			0
$376$	1.38197			0.0712695
$377$	3.94298	+	5.42705i	0.203074	+	0.279507i
$378$	−4.75528	−	1.54508i	−0.244585	−	0.0794706i
$379$	−4.51064	+	13.8823i	−0.231696	+	0.713087i	0.765846	+	0.643024i	$0.222320\pi$
$379$	−4.51064	+	13.8823i	−0.231696	+	0.713087i	−0.997543	+	0.0700639i	$0.977680\pi$
$380$		0			0
$381$	6.14590	+	18.9151i	0.314864	+	0.969051i
$382$			2.94427i			0.150642i
$383$	31.7279	−	10.3090i	1.62122	−	0.526766i	0.648990	−	0.760797i	$-0.275192\pi$
$383$	31.7279	−	10.3090i	1.62122	−	0.526766i	0.972229	+	0.234031i	$0.0751916\pi$
$384$	−11.0172	−	8.00448i	−0.562220	−	0.408477i
$385$		0			0
$386$	10.0902	−	7.33094i	0.513576	−	0.373135i
$387$	5.70634	−	7.85410i	0.290070	−	0.399246i
$388$	1.40008	−	1.92705i	0.0710785	−	0.0978312i
$389$	12.1353	−	8.81678i	0.615282	−	0.447028i	−0.235988	−	0.971756i	$-0.575833\pi$
$389$	12.1353	−	8.81678i	0.615282	−	0.447028i	0.851270	+	0.524727i	$0.175833\pi$
$390$		0			0
$391$	15.9443	+	11.5842i	0.806336	+	0.585838i
$392$	14.0741	−	4.57295i	0.710849	−	0.230969i
$393$		−	6.79837i		−	0.342933i
$394$	1.85410	+	5.70634i	0.0934083	+	0.287481i
$395$		0			0
$396$	2.00000	−	6.15537i	0.100504	−	0.309319i
$397$	27.6134	+	8.97214i	1.38588	+	0.450299i	0.904597	−	0.426268i	$-0.140172\pi$
$397$	27.6134	+	8.97214i	1.38588	+	0.450299i	0.481280	+	0.876567i	$0.340172\pi$
$398$	16.7027	+	22.9894i	0.837233	+	1.15235i
$399$	−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	$0.268820\pi$
$402$	4.53077	+	6.23607i	0.225974	+	0.311027i
$403$	5.29007	+	1.71885i	0.263517	+	0.0856219i
$404$	−0.281153	+	0.865300i	−0.0139879	+	0.0430503i
$405$		0			0
$406$	1.11803	+	3.44095i	0.0554871	+	0.170772i
$407$			1.23607i			0.0612696i
$408$	−11.1352	+	3.61803i	−0.551273	+	0.179119i
$409$	1.28115	+	0.930812i	0.0633489	+	0.0460257i	0.619009	−	0.785384i	$-0.287534\pi$
$409$	1.28115	+	0.930812i	0.0633489	+	0.0460257i	−0.555660	+	0.831410i	$0.687534\pi$
$410$		0			0
$411$	9.66312	−	7.02067i	0.476647	−	0.346304i
$412$	3.11044	−	4.28115i	0.153240	−	0.210917i
$413$	3.94298	−	5.42705i	0.194022	−	0.267048i
$414$	9.85410	−	7.15942i	0.484303	−	0.351867i
$415$		0			0
$416$	−5.07295	−	3.68571i	−0.248722	−	0.180707i
$417$	−4.75528	+	1.54508i	−0.232867	+	0.0756631i
$418$		−	7.23607i		−	0.353928i
$419$	2.92705	+	9.00854i	0.142996	+	0.440096i	0.996748	−	0.0805840i	$-0.0256785\pi$
$419$	2.92705	+	9.00854i	0.142996	+	0.440096i	−0.853752	+	0.520680i	$0.825679\pi$
$420$		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	$-0.184675\pi$
$422$	14.1271	+	4.59017i	0.687696	+	0.223446i
$423$	−0.726543	−	1.00000i	−0.0353257	−	0.0486217i
$424$	7.76393			0.377050
$425$		0			0
$426$	10.7082			0.518814
$427$	−3.16344	−	4.35410i	−0.153090	−	0.210710i
$428$	9.64932	+	3.13525i	0.466418	+	0.151548i
$429$	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	$-0.355170\pi$
$432$			24.2705i			1.16772i
$433$	25.5398	−	8.29837i	1.22736	−	0.398794i	0.377605	−	0.925967i	$-0.376748\pi$
$433$	25.5398	−	8.29837i	1.22736	−	0.398794i	0.849758	+	0.527173i	$0.176748\pi$
$434$	2.42705	+	1.76336i	0.116502	+	0.0846438i
$435$		0			0
$436$	−5.00000	+	3.63271i	−0.239457	+	0.173975i
$437$	1.88960	−	2.60081i	0.0903919	−	0.124414i
$438$	−8.55951	+	11.7812i	−0.408989	+	0.562925i
$439$	−33.1525	+	24.0867i	−1.58228	+	1.14959i	−0.668261	+	0.743927i	$0.732961\pi$
$439$	−33.1525	+	24.0867i	−1.58228	+	1.14959i	−0.914021	+	0.405667i	$0.867039\pi$
$440$		0			0
$441$	−10.7082	−	7.77997i	−0.509914	−	0.370475i
$442$	−14.9394	+	4.85410i	−0.710594	+	0.230886i
$443$		−	29.9443i		−	1.42270i	−0.702840	−	0.711348i	$-0.748085\pi$
$443$		−	29.9443i		−	1.42270i	0.702840	−	0.711348i	$-0.251915\pi$
$444$	0.0450850	+	0.138757i	0.00213964	+	0.00658513i
$445$		0			0
$446$	0.0901699	−	0.277515i	0.00426967	−	0.0131407i
$447$	−3.75123	−	1.21885i	−0.177427	−	0.0576495i
$448$	1.53884	+	2.11803i	0.0727034	+	0.100068i
$449$	−4.67376			−0.220568			−0.110284	−	0.993900i	$-0.535176\pi$
$449$	−4.67376			−0.220568			−0.110284	+	0.993900i	$0.535176\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−6.12261	−	8.42705i	−0.287983	−	0.396375i
$453$	−13.8496	−	4.50000i	−0.650710	−	0.211428i
$454$	7.38197	−	22.7194i	0.346453	−	1.06627i
$455$		0			0
$456$	0.590170	+	1.81636i	0.0276372	+	0.0850587i
$457$		−	21.4164i		−	1.00182i	−0.865500	−	0.500909i	$-0.832999\pi$
$457$		−	21.4164i		−	1.00182i	0.865500	−	0.500909i	$-0.167001\pi$
$458$	−33.4055	+	10.8541i	−1.56094	+	0.507179i
$459$	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	$0.306076\pi$
$462$	3.07768	−	4.23607i	0.143187	−	0.197080i
$463$	14.1801	−	19.5172i	0.659005	−	0.907042i	−0.340443	−	0.940265i	$-0.610577\pi$
$463$	14.1801	−	19.5172i	0.659005	−	0.907042i	0.999448	+	0.0332229i	$0.0105771\pi$
$464$	14.2082	−	10.3229i	0.659599	−	0.479227i
$465$		0			0
$466$	−3.85410	−	2.80017i	−0.178538	−	0.129715i
$467$	−26.1073	+	8.48278i	−1.20810	+	0.392536i	−0.842736	−	0.538328i	$-0.819056\pi$
$467$	−26.1073	+	8.48278i	−1.20810	+	0.392536i	−0.365367	+	0.930864i	$0.619056\pi$
$468$			2.29180i			0.105938i
$469$	−0.909830	−	2.80017i	−0.0420120	−	0.129300i
$470$		0			0
$471$	4.07295	−	12.5352i	0.187672	−	0.577594i
$472$	−23.0826	−	7.50000i	−1.06246	−	0.345215i
$473$	14.9394	+	20.5623i	0.686914	+	0.945456i
$474$	−13.0902			−0.601251
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	−4.08174	−	5.61803i	−0.186890	−	0.257232i
$478$	−31.5891	−	10.2639i	−1.44485	−	0.469461i
$479$	3.35410	−	10.3229i	0.153253	−	0.471664i	−0.844727	−	0.535198i	$-0.820237\pi$
$479$	3.35410	−	10.3229i	0.153253	−	0.471664i	0.997980	+	0.0635340i	$0.0202371\pi$
$480$		0			0
$481$	−0.135255	−	0.416272i	−0.00616709	−	0.0189804i
$482$		−	4.09017i		−	0.186302i
$483$	2.21238	−	0.718847i	0.100667	−	0.0327087i
$484$	8.20820	+	5.96361i	0.373100	+	0.271073i
$485$		0			0
$486$	20.9443	−	15.2169i	0.950051	−	0.690253i
$487$	−21.4050	+	29.4615i	−0.969954	+	1.33503i	−0.0278844	+	0.999611i	$0.508877\pi$
$487$	−21.4050	+	29.4615i	−0.969954	+	1.33503i	−0.942070	+	0.335417i	$0.891123\pi$
$488$	−11.4454	+	15.7533i	−0.518110	+	0.713118i
$489$	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	$0.270017\pi$
$492$	0.449028	−	0.145898i	0.0202437	−	0.00657759i
$493$		−	18.9443i		−	0.853207i
$494$	0.791796	+	2.43690i	0.0356246	+	0.109641i
$495$		0			0
$496$	4.50000	−	13.8496i	0.202056	−	0.621864i
$497$	−3.88998	−	1.26393i	−0.174490	−	0.0566951i
$498$	5.93085	+	8.16312i	0.265768	+	0.365798i
$499$	−7.56231			−0.338535			−0.169268	−	0.985570i	$-0.554140\pi$
$499$	−7.56231			−0.338535			−0.169268	+	0.985570i	$0.554140\pi$
$500$		0			0
$501$	14.5623			0.650596
$502$	−27.7522	−	38.1976i	−1.23864	−	1.70484i
$503$	35.5851	+	11.5623i	1.58666	+	0.515538i	0.963762	−	0.266764i	$-0.0859543\pi$
$503$	35.5851	+	11.5623i	1.58666	+	0.515538i	0.622900	+	0.782301i	$0.285954\pi$
$504$	0.854102	−	2.62866i	0.0380447	−	0.117090i
$505$		0			0
$506$	9.85410	+	30.3278i	0.438068	+	1.34824i
$507$		−	9.56231i		−	0.424677i
$508$	11.6902	−	3.79837i	0.518668	−	0.168526i
$509$	−16.4443	−	11.9475i	−0.728880	−	0.529562i	0.160329	−	0.987064i	$-0.448744\pi$
$509$	−16.4443	−	11.9475i	−0.728880	−	0.529562i	−0.889209	+	0.457502i	$0.848744\pi$
$510$		0			0
$511$	4.50000	−	3.26944i	0.199068	−	0.144632i
$512$	3.11044	−	4.28115i	0.137463	−	0.189202i
$513$	2.51014	−	3.45492i	0.110826	−	0.152538i
$514$	−29.9164	+	21.7355i	−1.31956	+	0.958714i
$515$		0			0
$516$	2.42705	+	1.76336i	0.106845	+	0.0776274i
$517$	3.07768	−	1.00000i	0.135356	−	0.0439799i
$518$		−	0.236068i		−	0.0103722i
$519$	−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	$-0.122376\pi$
$522$	−11.1352	−	3.61803i	−0.487373	−	0.158357i
$523$	−7.72696	−	10.6353i	−0.337877	−	0.465047i	0.605943	−	0.795508i	$-0.292796\pi$
$523$	−7.72696	−	10.6353i	−0.337877	−	0.465047i	−0.943820	+	0.330461i	$0.892796\pi$
$524$	−4.20163			−0.183549
$525$		0			0
$526$	17.6525			0.769685
$527$	−9.23305	−	12.7082i	−0.402198	−	0.553578i
$528$	−24.1724	−	7.85410i	−1.05197	−	0.341806i
$529$	2.72949	−	8.40051i	0.118673	−	0.365239i
$530$		0			0
$531$	6.70820	+	20.6457i	0.291111	+	0.895948i
$532$			0.326238i			0.0141442i
$533$	−1.34708	+	0.437694i	−0.0583487	+	0.0189586i
$534$	11.7082	+	8.50651i	0.506664	+	0.368113i
$535$		0			0
$536$	−8.61803	+	6.26137i	−0.372242	+	0.270450i
$537$	−0.310271	+	0.427051i	−0.0133892	+	0.0184286i
$538$	−12.1392	+	16.7082i	−0.523359	+	0.720342i
$539$	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	$0.898156\pi$
$542$	−12.3107	+	4.00000i	−0.528791	+	0.171815i
$543$		−	0.291796i		−	0.0125222i
$544$	5.47214	+	16.8415i	0.234616	+	0.722073i
$545$		0			0
$546$	−0.572949	+	1.76336i	−0.0245200	+	0.0754647i
$547$	−20.2497	−	6.57953i	−0.865815	−	0.281320i	−0.157760	−	0.987478i	$-0.550427\pi$
$547$	−20.2497	−	6.57953i	−0.865815	−	0.281320i	−0.708055	+	0.706157i	$0.750427\pi$
$548$	−4.33901	−	5.97214i	−0.185353	−	0.255117i
$549$	17.4164			0.743314
$550$		0			0
$551$	−3.09017			−0.131646
$552$	−4.94704	−	6.80902i	−0.210560	−	0.289811i
$553$	4.75528	+	1.54508i	0.202215	+	0.0657037i
$554$	−12.3541	+	38.0220i	−0.524875	+	1.61540i
$555$		0			0
$556$	0.954915	+	2.93893i	0.0404974	+	0.124638i
$557$			4.76393i			0.201854i	0.994894	+	0.100927i	$0.0321809\pi$
$557$			4.76393i			0.201854i	−0.994894	+	0.100927i	$0.967819\pi$
$558$	−9.23305	+	3.00000i	−0.390866	+	0.127000i
$559$	−7.28115	−	5.29007i	−0.307960	−	0.223746i
$560$		0			0
$561$	−22.1803	+	16.1150i	−0.936455	+	0.680374i
$562$	−9.59632	+	13.2082i	−0.404796	+	0.557154i
$563$	−4.33901	+	5.97214i	−0.182868	+	0.251696i	−0.890603	−	0.454782i	$-0.849717\pi$
$563$	−4.33901	+	5.97214i	−0.182868	+	0.251696i	0.707735	+	0.706478i	$0.249717\pi$
$564$	0.309017	−	0.224514i	0.0130120	−	0.00945374i
$565$		0			0
$566$	−39.0795	−	28.3929i	−1.64264	−	1.19344i
$567$	−0.587785	+	0.190983i	−0.0246847	+	0.00802053i
$568$			14.7984i			0.620926i
$569$	−6.34346	−	19.5232i	−0.265932	−	0.818453i	−0.991477	−	0.130279i	$-0.958413\pi$
$569$	−6.34346	−	19.5232i	−0.265932	−	0.818453i	0.725546	−	0.688174i	$-0.241587\pi$
$570$		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	$0.154377\pi$
$572$	−5.70634	−	1.85410i	−0.238594	−	0.0775239i
$573$	−1.06957	−	1.47214i	−0.0446819	−	0.0614994i
$574$	−0.763932			−0.0318859
$575$		0			0
$576$	−8.47214			−0.353006
$577$	19.8537	+	27.3262i	0.826519	+	1.13761i	0.988561	+	0.150822i	$0.0481921\pi$
$577$	19.8537	+	27.3262i	0.826519	+	1.13761i	−0.162042	+	0.986784i	$0.551808\pi$
$578$	16.0292	+	5.20820i	0.666727	+	0.216633i
$579$	−2.38197	+	7.33094i	−0.0989911	+	0.304663i
$580$		0			0
$581$	−1.19098	−	3.66547i	−0.0494103	−	0.152069i
$582$			6.23607i			0.258493i
$583$	17.2905	−	5.61803i	0.716101	−	0.232675i
$584$	−16.2812	−	11.8290i	−0.673719	−	0.489485i
$585$		0			0
$586$	−25.5623	+	18.5721i	−1.05597	+	0.767206i
$587$	3.11044	−	4.28115i	0.128382	−	0.176702i	−0.739987	−	0.672621i	$-0.765169\pi$
$587$	3.11044	−	4.28115i	0.128382	−	0.176702i	0.868369	+	0.495919i	$0.165169\pi$
$588$	2.40414	−	3.30902i	0.0991451	−	0.136462i
$589$	−2.07295	+	1.50609i	−0.0854144	+	0.0620572i
$590$		0			0
$591$	−3.00000	−	2.17963i	−0.123404	−	0.0896579i
$592$	−1.08981	+	0.354102i	−0.0447911	+	0.0145535i
$593$			10.9098i			0.448013i	0.974588	+	0.224007i	$0.0719137\pi$
$593$			10.9098i			0.448013i	−0.974588	+	0.224007i	$0.928086\pi$
$594$	13.0902	+	40.2874i	0.537096	+	1.65301i
$595$		0			0
$596$	−0.753289	+	2.31838i	−0.0308559	+	0.0949647i
$597$	−16.7027	−	5.42705i	−0.683598	−	0.222114i
$598$	−6.63715	−	9.13525i	−0.271413	−	0.373568i
$599$	9.47214			0.387021			0.193510	−	0.981098i	$-0.438013\pi$
$599$	9.47214			0.387021			0.193510	+	0.981098i	$0.438013\pi$
$600$		0			0
$601$	2.72949			0.111338			0.0556691	−	0.998449i	$-0.482271\pi$
$601$	2.72949			0.111338			0.0556691	+	0.998449i	$0.482271\pi$
$602$	−2.85317	−	3.92705i	−0.116287	−	0.160055i
$603$	9.06154	+	2.94427i	0.369014	+	0.119900i
$604$	−2.78115	+	8.55951i	−0.113164	+	0.348281i
$605$		0			0
$606$	−0.736068	−	2.26538i	−0.0299007	−	0.0920249i
$607$		−	35.5623i		−	1.44343i	−0.692191	−	0.721715i	$-0.743354\pi$
$607$		−	35.5623i		−	1.44343i	0.692191	−	0.721715i	$-0.256646\pi$
$608$	2.74717	−	0.892609i	0.111412	−	0.0362001i
$609$	−1.80902	−	1.31433i	−0.0733051	−	0.0532592i
$610$		0			0
$611$	−0.927051	+	0.673542i	−0.0375045	+	0.0272486i
$612$	3.80423	−	5.23607i	0.153777	−	0.211656i
$613$	8.80427	−	12.1180i	0.355601	−	0.489443i	−0.593316	−	0.804970i	$-0.702181\pi$
$613$	8.80427	−	12.1180i	0.355601	−	0.489443i	0.948917	+	0.315527i	$0.102181\pi$
$614$	−12.0902	+	8.78402i	−0.487920	+	0.354494i
$615$		0			0
$616$	5.85410	+	4.25325i	0.235868	+	0.171368i
$617$	−13.5393	+	4.39919i	−0.545072	+	0.177105i	−0.568593	−	0.822619i	$-0.692512\pi$
$617$	−13.5393	+	4.39919i	−0.545072	+	0.177105i	0.0235215	+	0.999723i	$0.492512\pi$
$618$			13.8541i			0.557294i
$619$	−9.43363	−	29.0337i	−0.379170	−	1.16696i	−0.940622	−	0.339455i	$-0.889757\pi$
$619$	−9.43363	−	29.0337i	−0.379170	−	1.16696i	0.561453	−	0.827509i	$-0.310243\pi$
$620$		0			0
$621$	−5.81559	+	17.8986i	−0.233372	+	0.718244i
$622$	−13.0903	−	4.25329i	−0.524872	−	0.170541i
$623$	−3.24920	−	4.47214i	−0.130176	−	0.179172i
$624$	9.00000			0.360288
$625$		0			0
$626$	27.1246			1.08412
$627$	2.62866	+	3.61803i	0.104978	+	0.144490i
$628$	−7.74721	−	2.51722i	−0.309147	−	0.100448i
$629$	−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	$0.965312\pi$
$632$		−	18.0902i		−	0.719588i
$633$	−8.73102	+	2.83688i	−0.347027	+	0.112756i
$634$	−10.0172	−	7.27794i	−0.397835	−	0.289044i
$635$		0			0
$636$	1.73607	−	1.26133i	0.0688396	−	0.0500149i
$637$	−7.21242	+	9.92705i	−0.285767	+	0.393324i
$638$	18.0171	−	24.7984i	0.713303	−	0.981777i
$639$	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	$0.693146\pi$
$642$	−25.2623	+	8.20820i	−0.997022	+	0.323952i
$643$			30.8328i			1.21593i	0.793965	+	0.607964i	$0.208013\pi$
$643$			30.8328i			1.21593i	−0.793965	+	0.607964i	$0.791987\pi$
$644$	−0.444272	−	1.36733i	−0.0175068	−	0.0538803i
$645$		0			0
$646$	2.23607	−	6.88191i	0.0879769	−	0.270765i
$647$	−34.7526	−	11.2918i	−1.36626	−	0.443926i	−0.468135	−	0.883657i	$-0.655074\pi$
$647$	−34.7526	−	11.2918i	−1.36626	−	0.443926i	−0.898130	+	0.439731i	$0.855074\pi$
$648$	1.31433	+	1.80902i	0.0516317	+	0.0710649i
$649$	−56.8328			−2.23088
$650$		0			0
$651$	−1.85410			−0.0726680
$652$	−3.99598	−	5.50000i	−0.156495	−	0.215397i
$653$	−18.1558	−	5.89919i	−0.710493	−	0.230853i	−0.0685963	−	0.997645i	$-0.521852\pi$
$653$	−18.1558	−	5.89919i	−0.710493	−	0.230853i	−0.641896	+	0.766791i	$0.721852\pi$
$654$	5.00000	−	15.3884i	0.195515	−	0.601735i
$655$		0			0
$656$	1.14590	+	3.52671i	0.0447398	+	0.137695i
$657$			18.0000i			0.702247i
$658$	−0.587785	+	0.190983i	−0.0229143	+	0.00744529i
$659$	12.5623	+	9.12705i	0.489358	+	0.355539i	0.804937	−	0.593360i	$-0.202199\pi$
$659$	12.5623	+	9.12705i	0.489358	+	0.355539i	−0.315579	+	0.948899i	$0.602199\pi$
$660$		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	$0.425063\pi$
$662$	21.9928	−	30.2705i	0.854775	−	1.17650i
$663$	5.70634	−	7.85410i	0.221616	−	0.305028i
$664$	−11.2812	+	8.19624i	−0.437794	+	0.318076i
$665$		0			0
$666$	0.618034	+	0.449028i	0.0239483	+	0.0173995i
$667$	12.9515	−	4.20820i	0.501485	−	0.162942i
$668$		−	9.00000i		−	0.348220i
$669$	0.0557281	+	0.171513i	0.00215457	+	0.00663109i
$670$		0			0
$671$	−14.0902	+	43.3651i	−0.543945	+	1.67409i
$672$	1.98787	+	0.645898i	0.0766837	+	0.0249161i
$673$	7.15942	+	9.85410i	0.275976	+	0.379848i	0.924396	−	0.381435i	$-0.124570\pi$
$673$	7.15942	+	9.85410i	0.275976	+	0.379848i	−0.648420	+	0.761283i	$0.724570\pi$
$674$	12.7082			0.489502
$675$		0			0
$676$	−5.90983			−0.227301
$677$	−6.24112	−	8.59017i	−0.239866	−	0.330147i	0.672064	−	0.740493i	$-0.265408\pi$
$677$	−6.24112	−	8.59017i	−0.239866	−	0.330147i	−0.911930	+	0.410346i	$0.865408\pi$
$678$	25.9358	+	8.42705i	0.996058	+	0.323639i
$679$	0.736068	−	2.26538i	0.0282477	−	0.0869375i
$680$		0			0
$681$	4.56231	+	14.0413i	0.174828	+	0.538065i
$682$		−	25.4164i		−	0.973245i
$683$	−12.8128	+	4.16312i	−0.490267	+	0.159297i	−0.543709	−	0.839274i	$-0.682981\pi$
$683$	−12.8128	+	4.16312i	−0.490267	+	0.159297i	0.0534426	+	0.998571i	$0.482981\pi$
$684$	−0.854102	−	0.620541i	−0.0326574	−	0.0237270i
$685$		0			0
$686$	−11.0172	+	8.00448i	−0.420639	+	0.305612i
$687$	12.7598	−	17.5623i	0.486815	−	0.670044i
$688$	−13.8496	+	19.0623i	−0.528010	+	0.726744i
$689$	−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	$0.942344\pi$
$692$	−11.1024	+	3.60739i	−0.422050	+	0.137132i
$693$		−	6.47214i		−	0.245856i
$694$	−9.95492	−	30.6381i	−0.377883	−	1.16301i
$695$		0			0
$696$	−2.50000	+	7.69421i	−0.0947623	+	0.291648i
$697$	3.80423	+	1.23607i	0.144095	+	0.0468194i
$698$	−20.6457	−	28.4164i	−0.781452	−	1.07558i
$699$	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	$0.782010\pi$
$702$	−8.81678	−	12.1353i	−0.332768	−	0.458016i
$703$	0.191758	+	0.0623059i	0.00723228	+	0.00234991i
$704$	6.85410	−	21.0948i	0.258324	−	0.795039i
$705$		0			0
$706$	−6.45492	−	19.8662i	−0.242934	−	0.747674i
$707$			0.909830i			0.0342177i
$708$	−6.37988	+	2.07295i	−0.239771	+	0.0779062i
$709$	−27.1353	−	19.7149i	−1.01909	−	0.740409i	−0.0529906	−	0.998595i	$-0.516875\pi$
$709$	−27.1353	−	19.7149i	−1.01909	−	0.740409i	−0.966095	+	0.258186i	$0.916875\pi$
$710$		0			0
$711$	−13.0902	+	9.51057i	−0.490920	+	0.356674i
$712$	−11.7557	+	16.1803i	−0.440564	+	0.606384i
$713$	6.63715	−	9.13525i	0.248563	−	0.342118i
$714$	4.23607	−	3.07768i	0.158531	−	0.115179i
$715$		0			0
$716$	0.263932	+	0.191758i	0.00986360	+	0.00716633i
$717$	19.5232	−	6.34346i	0.729106	−	0.236901i
$718$			22.2361i			0.829843i
$719$	7.19756	+	22.1518i	0.268424	+	0.826123i	0.990885	+	0.134712i	$0.0430108\pi$
$719$	7.19756	+	22.1518i	0.268424	+	0.826123i	−0.722461	+	0.691412i	$0.756989\pi$
$720$		0			0
$721$	1.63525	−	5.03280i	0.0609001	−	0.187431i
$722$	28.1154	+	9.13525i	1.04635	+	0.339979i
$723$	1.48584	+	2.04508i	0.0552590	+	0.0760575i
$724$	−0.180340			−0.00670228
$725$		0			0
$726$	−26.5623			−0.985820
$727$	−14.4374	−	19.8713i	−0.535452	−	0.736987i	0.452497	−	0.891766i	$-0.350533\pi$
$727$	−14.4374	−	19.8713i	−0.535452	−	0.736987i	−0.987949	+	0.154779i	$0.950533\pi$
$728$	−2.43690	−	0.791796i	−0.0903174	−	0.0293459i
$729$	−4.01722	+	12.3637i	−0.148786	+	0.457916i
$730$		0			0
$731$	7.85410	+	24.1724i	0.290494	+	0.894050i
$732$			5.38197i			0.198923i
$733$	−19.0009	+	6.17376i	−0.701814	+	0.228033i	−0.638121	−	0.769936i	$-0.720288\pi$
$733$	−19.0009	+	6.17376i	−0.701814	+	0.228033i	−0.0636931	+	0.997970i	$0.520288\pi$
$734$	33.4615	+	24.3112i	1.23509	+	0.897343i
$735$		0			0
$736$	−10.2984	+	7.48221i	−0.379603	+	0.275798i
$737$	−14.6619	+	20.1803i	−0.540077	+	0.743352i
$738$	1.45309	−	2.00000i	0.0534888	−	0.0736210i
$739$	12.9271	−	9.39205i	0.475529	−	0.345492i	−0.324063	−	0.946036i	$-0.605049\pi$
$739$	12.9271	−	9.39205i	0.475529	−	0.345492i	0.799592	+	0.600543i	$0.205049\pi$
$740$		0			0
$741$	−1.28115	−	0.930812i	−0.0470643	−	0.0341942i
$742$	−3.30220	+	1.07295i	−0.121227	+	0.0393892i
$743$		−	28.3607i		−	1.04045i	−0.854029	−	0.520226i	$-0.825848\pi$
$743$		−	28.3607i		−	1.04045i	0.854029	−	0.520226i	$-0.174152\pi$
$744$	2.07295	+	6.37988i	0.0759980	+	0.233898i
$745$		0			0
$746$	14.1353	−	43.5038i	0.517528	−	1.59279i
$747$	11.8617	+	3.85410i	0.433997	+	0.141014i
$748$	9.95959	+	13.7082i	0.364159	+	0.501222i
$749$	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	$0.529729\pi$
$752$	1.76336	+	2.42705i	0.0643030	+	0.0885054i
$753$	27.7522	+	9.01722i	1.01134	+	0.328606i
$754$	−3.35410	+	10.3229i	−0.122149	+	0.375937i
$755$		0			0
$756$	−0.590170	−	1.81636i	−0.0214643	−	0.0660602i
$757$			30.4164i			1.10550i	0.833346	+	0.552752i	$0.186422\pi$
$757$			30.4164i			1.10550i	−0.833346	+	0.552752i	$0.813578\pi$
$758$	−22.4621	+	7.29837i	−0.815860	+	0.265089i
$759$	−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	$0.191459\pi$
$762$	−18.9151	+	26.0344i	−0.685223	+	0.943128i
$763$	−3.63271	+	5.00000i	−0.131513	+	0.181012i
$764$	−0.909830	+	0.661030i	−0.0329165	+	0.0239152i
$765$		0			0
$766$	43.6697	+	31.7279i	1.57785	+	1.14638i
$767$	19.1396	−	6.21885i	0.691092	−	0.224550i
$768$		−	13.5623i		−	0.489388i
$769$	−4.14590	−	12.7598i	−0.149505	−	0.460129i	0.848058	−	0.529904i	$-0.177772\pi$
$769$	−4.14590	−	12.7598i	−0.149505	−	0.460129i	−0.997563	+	0.0697749i	$0.977772\pi$
$770$		0			0
$771$	7.06231	−	21.7355i	0.254343	−	0.782786i
$772$	4.53077	+	1.47214i	0.163066	+	0.0529833i
$773$	−21.2538	−	29.2533i	−0.764445	−	1.05217i	−0.996831	−	0.0795442i	$-0.974654\pi$
$773$	−21.2538	−	29.2533i	−0.764445	−	1.05217i	0.232387	−	0.972623i	$-0.425346\pi$
$774$	15.7082			0.564620
$775$		0			0
$776$	−8.61803			−0.309369
$777$	0.0857567	+	0.118034i	0.00307650	+	0.00423445i
$778$	23.0826	+	7.50000i	0.827552	+	0.268888i
$779$	0.201626	−	0.620541i	0.00722401	−	0.0222332i
$780$		0			0
$781$	10.7082	+	32.9565i	0.383170	+	1.17927i
$782$			31.8885i			1.14033i
$783$	17.2048	−	5.59017i	0.614848	−	0.199776i
$784$	25.9894	+	18.8824i	0.928191	+	0.674370i
$785$		0			0
$786$	8.89919	−	6.46564i	0.317423	−	0.230622i
$787$	−6.94742	+	9.56231i	−0.247649	+	0.340859i	−0.914686	−	0.404165i	$-0.867562\pi$
$787$	−6.94742	+	9.56231i	−0.247649	+	0.340859i	0.667037	+	0.745024i	$0.267562\pi$
$788$	−1.34708	+	1.85410i	−0.0479879	+	0.0660496i
$789$	−8.82624	+	6.41264i	−0.314222	+	0.228296i
$790$		0			0
$791$	−8.42705	−	6.12261i	−0.299631	−	0.217695i
$792$	−22.2703	+	7.23607i	−0.791342	+	0.257122i
$793$		−	16.1459i		−	0.573358i
$794$	14.5172	+	44.6794i	0.515197	+	1.58561i
$795$		0			0
$796$	−3.35410	+	10.3229i	−0.118883	+	0.365884i
$797$	9.28605	+	3.01722i	0.328929	+	0.106875i	0.468826	−	0.883291i	$-0.344677\pi$
$797$	9.28605	+	3.01722i	0.328929	+	0.106875i	−0.139897	+	0.990166i	$0.544677\pi$
$798$	−0.502029	−	0.690983i	−0.0177716	−	0.0244605i
$799$	3.23607			0.114484
$800$		0			0
$801$	17.8885			0.632061
$802$	25.2950	+	34.8156i	0.893198	+	1.22938i
$803$	−44.8182	−	14.5623i	−1.58160	−	0.513893i
$804$	−0.909830	+	2.80017i	−0.0320872	+	0.0987543i
$805$		0			0
$806$	2.78115	+	8.55951i	0.0979619	+	0.301496i
$807$		−	12.7639i		−	0.449312i
$808$	3.13068	−	1.01722i	0.110137	−	0.0357857i
$809$	25.0623	+	18.2088i	0.881144	+	0.640188i	0.933554	−	0.358437i	$-0.116690\pi$
$809$	25.0623	+	18.2088i	0.881144	+	0.640188i	−0.0524101	+	0.998626i	$0.516690\pi$
$810$		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	$0.216858\pi$
$812$	−0.812299	+	1.11803i	−0.0285061	+	0.0392353i
$813$	4.70228	−	6.47214i	0.164916	−	0.226988i
$814$	−1.61803	+	1.17557i	−0.0567121	+	0.0412037i
$815$		0			0
$816$	−20.5623	−	14.9394i	−0.719825	−	0.522983i
$817$	3.94298	−	1.28115i	0.137948	−	0.0448219i
$818$			2.56231i			0.0895889i
$819$	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	$0.848699\pi$
$822$	18.3803	+	5.97214i	0.641088	+	0.208302i
$823$	28.0422	+	38.5967i	0.977489	+	1.34540i	0.938171	+	0.346171i	$0.112518\pi$
$823$	28.0422	+	38.5967i	0.977489	+	1.34540i	0.0393176	+	0.999227i	$0.487482\pi$
$824$	−19.1459			−0.666979
$825$		0			0
$826$	10.8541			0.377663
$827$	0.567541	+	0.781153i	0.0197353	+	0.0271633i	0.818771	−	0.574121i	$-0.194656\pi$
$827$	0.567541	+	0.781153i	0.0197353	+	0.0271633i	−0.799035	+	0.601284i	$0.794656\pi$
$828$	4.42477	+	1.43769i	0.153771	+	0.0499633i
$829$	11.0795	−	34.0993i	0.384808	−	1.18432i	−0.551812	−	0.833969i	$-0.686063\pi$
$829$	11.0795	−	34.0993i	0.384808	−	1.18432i	0.936620	−	0.350348i	$-0.113937\pi$
$830$		0			0
$831$	−7.63525	−	23.4989i	−0.264864	−	0.815168i
$832$			7.85410i			0.272292i
$833$	32.9565	−	10.7082i	1.14187	−	0.371017i
$834$	−6.54508	−	4.75528i	−0.226638	−	0.164662i
$835$		0			0
$836$	2.23607	−	1.62460i	0.0773360	−	0.0561879i
$837$	8.81678	−	12.1353i	0.304752	−	0.419456i
$838$	−9.00854	+	12.3992i	−0.311195	+	0.428323i
$839$	8.78115	−	6.37988i	0.303159	−	0.220258i	−0.425797	−	0.904819i	$-0.640006\pi$
$839$	8.78115	−	6.37988i	0.303159	−	0.220258i	0.728956	+	0.684561i	$0.240006\pi$
$840$		0			0
$841$	12.8713	+	9.35156i	0.443839	+	0.322468i
$842$	49.2429	−	16.0000i	1.69702	−	0.551396i
$843$		−	10.0902i		−	0.347524i
$844$	1.75329	+	5.39607i	0.0603507	+	0.185740i
$845$		0			0
$846$	0.618034	−	1.90211i	0.0212484	−	0.0653960i
$847$	9.64932	+	3.13525i	0.331555	+	0.107729i
$848$	9.90659	+	13.6353i	0.340194	+	0.468237i
$849$	29.8541			1.02459
$850$		0			0
$851$	−0.888544			−0.0304589
$852$	2.40414	+	3.30902i	0.0823645	+	0.113365i
$853$	14.5559	+	4.72949i	0.498384	+	0.161935i	0.547413	−	0.836863i	$-0.315613\pi$
$853$	14.5559	+	4.72949i	0.498384	+	0.161935i	−0.0490292	+	0.998797i	$0.515613\pi$
$854$	2.69098	−	8.28199i	0.0920835	−	0.283404i
$855$		0			0
$856$	−11.3435	−	34.9116i	−0.387711	−	1.19325i
$857$			19.6869i			0.672492i	0.941774	+	0.336246i	$0.109157\pi$
$857$			19.6869i			0.672492i	−0.941774	+	0.336246i	$0.890843\pi$
$858$	14.9394	−	4.85410i	0.510022	−	0.165716i
$859$	−1.28115	−	0.930812i	−0.0437124	−	0.0317589i	0.565715	−	0.824601i	$-0.308600\pi$
$859$	−1.28115	−	0.930812i	−0.0437124	−	0.0317589i	−0.609427	+	0.792842i	$0.708600\pi$
$860$		0			0
$861$	0.381966	−	0.277515i	0.0130174	−	0.00945767i
$862$	28.3727	−	39.0517i	0.966378	−	1.33010i
$863$	12.6008	−	17.3435i	0.428935	−	0.590378i	−0.538773	−	0.842451i	$-0.681112\pi$
$863$	12.6008	−	17.3435i	0.428935	−	0.590378i	0.967708	+	0.252072i	$0.0811121\pi$
$864$	−13.6803	+	9.93935i	−0.465415	+	0.338144i
$865$		0			0
$866$	35.1525	+	25.5398i	1.19453	+	0.867877i
$867$	−9.90659	+	3.21885i	−0.336446	+	0.109318i
$868$			1.14590i			0.0388943i
$869$	−13.0902	−	40.2874i	−0.444054	−	1.36666i
$870$		0			0
$871$	2.72949	−	8.40051i	0.0924852	−	0.284640i
$872$	21.2663	+	6.90983i	0.720167	+	0.233996i
$873$	4.53077	+	6.23607i	0.153343	+	0.211059i
$874$	5.20163			0.175948
$875$		0			0
$876$	−5.56231			−0.187933
$877$	21.4783	+	29.5623i	0.725270	+	0.998248i	0.999332	+	0.0365363i	$0.0116324\pi$
$877$	21.4783	+	29.5623i	0.725270	+	0.998248i	−0.274063	+	0.961712i	$0.588368\pi$
$878$	−63.0598	−	20.4894i	−2.12816	−	0.691482i
$879$	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	$-0.337974\pi$
$882$		−	21.4164i		−	0.721128i
$883$	−19.5762	+	6.36068i	−0.658790	+	0.214054i	−0.619286	−	0.785165i	$-0.712578\pi$
$883$	−19.5762	+	6.36068i	−0.658790	+	0.214054i	−0.0395042	+	0.999219i	$0.512578\pi$
$884$	−4.85410	−	3.52671i	−0.163261	−	0.118616i
$885$		0			0
$886$	39.1976	−	28.4787i	1.31687	−	0.956760i
$887$	17.5680	−	24.1803i	0.589877	−	0.811896i	−0.404857	−	0.914380i	$-0.632679\pi$
$887$	17.5680	−	24.1803i	0.589877	−	0.811896i	0.994735	+	0.102483i	$0.0326789\pi$
$888$	0.310271	−	0.427051i	0.0104120	−	0.0143309i
$889$	9.94427	−	7.22494i	0.333520	−	0.242317i
$890$		0			0
$891$	4.23607	+	3.07768i	0.141914	+	0.103106i
$892$	0.106001	−	0.0344419i	0.00354918	−	0.00115320i
$893$		−	0.527864i		−	0.0176643i
$894$	−1.97214	−	6.06961i	−0.0659581	−	0.202998i
$895$		0			0
$896$	−2.60081	+	8.00448i	−0.0868871	+	0.267411i
$897$	6.63715	+	2.15654i	0.221608	+	0.0720048i
$898$	−4.44501	−	6.11803i	−0.148332	−	0.204161i
$899$	−10.8541			−0.362005
$900$		0			0
$901$	18.1803			0.605675
$902$	3.80423	+	5.23607i	0.126667	+	0.174342i
$903$	2.85317	+	0.927051i	0.0949475	+	0.0308503i
$904$	−11.6459	+	35.8424i	−0.387337	+	1.19210i
$905$		0			0
$906$	−7.28115	−	22.4091i	−0.241900	−	0.744492i
$907$		−	33.2492i		−	1.10402i	−0.833837	−	0.552011i	$-0.813861\pi$
$907$		−	33.2492i		−	1.10402i	0.833837	−	0.552011i	$-0.186139\pi$
$908$	8.67802	−	2.81966i	0.287990	−	0.0935737i
$909$	−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	$0.0677745\pi$
$912$	−2.43690	+	3.35410i	−0.0806937	+	0.111065i
$913$	−19.1926	+	26.4164i	−0.635184	+	0.874255i
$914$	28.0344	−	20.3682i	0.927297	−	0.673721i
$915$		0			0
$916$	−10.8541	−	7.88597i	−0.358630	−	0.260560i
$917$	−3.99598	+	1.29837i	−0.131959	+	0.0428761i
$918$			42.3607i			1.39811i
$919$	16.4443	+	50.6103i	0.542446	+	1.66948i	0.726985	+	0.686653i	$0.240921\pi$
$919$	16.4443	+	50.6103i	0.542446	+	1.66948i	−0.184539	+	0.982825i	$0.559079\pi$
$920$		0			0
$921$	2.85410	−	8.78402i	0.0940459	−	0.289443i
$922$	−1.26133	−	0.409830i	−0.0415396	−	0.0134970i
$923$	−7.21242	−	9.92705i	−0.237400	−	0.326753i
$924$	2.00000			0.0657952
$925$		0			0
$926$	39.0344			1.28275
$927$	10.0656	+	13.8541i	0.330597	+	0.455028i
$928$	11.6372	+	3.78115i	0.382010	+	0.124122i
$929$	−12.8647	+	39.5936i	−0.422079	+	1.29902i	0.483685	+	0.875242i	$0.339298\pi$
$929$	−12.8647	+	39.5936i	−0.422079	+	1.29902i	−0.905764	+	0.423782i	$0.860702\pi$
$930$		0			0
$931$	−1.74671	−	5.37582i	−0.0572461	−	0.176186i
$932$		−	1.81966i		−	0.0596049i
$933$	8.09024	−	2.62868i	0.264862	−	0.0860590i
$934$	−35.9336	−	26.1073i	−1.17578	−	0.854257i
$935$		0			0
$936$	6.70820	−	4.87380i	0.219265	−	0.159305i
$937$	10.4211	−	14.3435i	0.340444	−	0.468580i	−0.604127	−	0.796888i	$-0.706478\pi$
$937$	10.4211	−	14.3435i	0.340444	−	0.468580i	0.944571	+	0.328307i	$0.106478\pi$
$938$	2.80017	−	3.85410i	0.0914288	−	0.125841i
$939$	−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	$0.426876\pi$
$942$	20.2825	−	6.59017i	0.660838	−	0.214719i
$943$			2.87539i			0.0936355i
$944$	−16.2812	−	50.1082i	−0.529906	−	1.63088i
$945$		0			0
$946$	−12.7082	+	39.1118i	−0.413179	+	1.27164i
$947$	2.52265	+	0.819660i	0.0819753	+	0.0266354i	0.349718	−	0.936855i	$-0.386278\pi$
$947$	2.52265	+	0.819660i	0.0819753	+	0.0266354i	−0.267742	+	0.963491i	$0.586278\pi$
$948$	−2.93893	−	4.04508i	−0.0954519	−	0.131378i
$949$	16.6869			0.541680
$950$		0			0
$951$	7.65248			0.248149
$952$	4.25325	+	5.85410i	0.137849	+	0.189733i
$953$	7.36369	+	2.39261i	0.238533	+	0.0775042i	0.425844	−	0.904796i	$-0.359977\pi$
$953$	7.36369	+	2.39261i	0.238533	+	0.0775042i	−0.187311	+	0.982301i	$0.559977\pi$
$954$	3.47214	−	10.6861i	0.112415	−	0.345976i
$955$		0			0
$956$	−3.92047	−	12.0660i	−0.126797	−	0.390242i
$957$			18.9443i			0.612381i
$958$	16.7027	−	5.42705i	0.539641	−	0.175340i
$959$	−5.97214	−	4.33901i	−0.192850	−	0.140114i
$960$		0			0
$961$	17.7984	−	12.9313i	0.574141	−	0.417138i
$962$	0.416272	−	0.572949i	0.0134211	−	0.0184726i
$963$	−19.2986	+	26.5623i	−0.621890	+	0.855958i
$964$	1.26393	−	0.918300i	0.0407085	−	0.0295765i
$965$		0			0
$966$	3.04508	+	2.21238i	0.0979740	+	0.0711823i
$967$	−3.91023	+	1.27051i	−0.125744	+	0.0408568i	−0.371213	−	0.928548i	$-0.621058\pi$
$967$	−3.91023	+	1.27051i	−0.125744	+	0.0408568i	0.245469	+	0.969404i	$0.421058\pi$
$968$		−	36.7082i		−	1.17985i
$969$	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	$0.0712667\pi$
$972$	9.40456	+	3.05573i	0.301652	+	0.0980125i
$973$	1.81636	+	2.50000i	0.0582297	+	0.0801463i
$974$	−58.9230			−1.88801
$975$		0			0
$976$	−42.2705			−1.35305
$977$	1.37984	+	1.89919i	0.0441450	+	0.0607604i	0.830519	−	0.556990i	$-0.188044\pi$
$977$	1.37984	+	1.89919i	0.0441450	+	0.0607604i	−0.786374	+	0.617751i	$0.788044\pi$
$978$	16.9273	+	5.50000i	0.541274	+	0.175871i
$979$	−14.4721	+	44.5407i	−0.462531	+	1.42353i
$980$		0			0
$981$	−6.18034	−	19.0211i	−0.197323	−	0.607298i
$982$			69.9787i			2.23311i
$983$	9.14729	−	2.97214i	0.291753	−	0.0947964i	−0.159484	−	0.987201i	$-0.550983\pi$
$983$	9.14729	−	2.97214i	0.291753	−	0.0947964i	0.451237	+	0.892404i	$0.350983\pi$
$984$	−1.38197	−	1.00406i	−0.0440555	−	0.0320082i
$985$		0			0
$986$	24.7984	−	18.0171i	0.789741	−	0.573781i
$987$	0.224514	−	0.309017i	0.00714636	−	0.00983612i
$988$	−0.575274	+	0.791796i	−0.0183019	+	0.0251904i
$989$	−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	$0.621549\pi$
$992$	9.64932	−	3.13525i	0.306366	−	0.0995444i
$993$			23.1246i			0.733837i
$994$	−2.04508	−	6.29412i	−0.0648662	−	0.199638i
$995$		0			0
$996$	−1.19098	+	3.66547i	−0.0377377	+	0.116145i
$997$	23.6704	+	7.69098i	0.749649	+	0.243576i	0.658830	−	0.752292i	$-0.271051\pi$
$997$	23.6704	+	7.69098i	0.749649	+	0.243576i	0.0908191	+	0.995867i	$0.471051\pi$
$998$	−7.19218	−	9.89919i	−0.227664	−	0.313353i
$999$	−1.18034			−0.0373443

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.6.1	✓	4	25.23	odd	20
25.2.d.a.21.1	yes	4	25.8	odd	20
125.2.d.a.26.1		4	25.2	odd	20
125.2.d.a.101.1		4	25.17	odd	20
125.2.e.a.24.1		8	25.6	even	5
125.2.e.a.24.2		8	25.19	even	10
125.2.e.a.99.1		8	25.14	even	10
125.2.e.a.99.2		8	25.11	even	5
225.2.h.b.46.1		4	75.8	even	20
225.2.h.b.181.1		4	75.23	even	20
400.2.u.b.81.1		4	100.23	even	20
400.2.u.b.321.1		4	100.83	even	20
625.2.a.b.1.1		2	25.3	odd	20
625.2.a.c.1.2		2	25.22	odd	20
625.2.b.a.624.1		4	25.21	even	5
625.2.b.a.624.4		4	25.4	even	10
625.2.d.b.251.1		4	5.2	odd	4
625.2.d.b.376.1		4	25.12	odd	20
625.2.d.h.251.1		4	5.3	odd	4
625.2.d.h.376.1		4	25.13	odd	20
625.2.e.c.249.1		8	25.16	even	5	inner
625.2.e.c.249.2		8	25.9	even	10	inner
625.2.e.c.374.1		8	5.4	even	2	inner
625.2.e.c.374.2		8	1.1	even	1	trivial
5625.2.a.d.1.1		2	75.47	even	20
5625.2.a.f.1.2		2	75.53	even	20
10000.2.a.c.1.1		2	100.3	even	20
10000.2.a.l.1.2		2	100.47	even	20

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.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 1.30902i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034i q^{7} +(2.12663 - 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 1.30902i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} +0.618034i q^{7} +(2.12663 - 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(0.363271 - 0.500000i) q^{12} +(-1.08981 + 1.50000i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(4.97980 - 1.61803i) q^{17} -3.23607i q^{18} +(-0.263932 - 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(8.05748 + 2.61803i) q^{22} +(2.21238 + 3.04508i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(2.93893 + 4.04508i) q^{27} +(-0.363271 - 0.118034i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} +3.38197i q^{32} +(-4.97980 + 1.61803i) q^{33} +(6.85410 + 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(-0.138757 + 0.190983i) q^{37} +(0.812299 - 1.11803i) q^{38} +(1.50000 - 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(0.951057 - 0.309017i) q^{42} +4.85410i q^{43} +(1.00000 + 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(0.587785 + 0.190983i) q^{47} +(-2.85317 - 3.92705i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(-0.673542 - 0.927051i) q^{52} +(3.30220 + 1.07295i) q^{53} +(-2.50000 + 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} +0.854102i q^{57} +(5.56758 - 1.80902i) q^{58} +(-8.78115 - 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(2.85317 - 3.92705i) q^{62} +(0.726543 - 1.00000i) q^{63} +(3.42705 - 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(-4.53077 + 1.47214i) q^{67} +3.23607i q^{68} +(-1.16312 - 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(-4.25325 - 1.38197i) q^{72} +(-5.29007 - 7.28115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(1.90211 + 2.61803i) q^{77} +(2.85317 + 0.927051i) q^{78} +(2.50000 - 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} +1.23607i q^{82} +(-5.93085 + 1.92705i) q^{83} +(0.309017 + 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(-2.12663 + 2.92705i) q^{87} +(6.88191 - 9.47214i) q^{88} +(-7.23607 + 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(-2.21238 + 0.718847i) q^{92} +3.00000i q^{93} +(0.309017 + 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(-3.66547 - 1.19098i) q^{97} +(6.29412 + 8.66312i) q^{98} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^4 - 4 * q^6 - 4 * q^9	\( 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + 16 q^{11} - 2 q^{14} + 18 q^{16} - 20 q^{19} + 6 q^{21} - 24 q^{26} + 6 q^{31} + 28 q^{34} + 8 q^{36} + 12 q^{39} - 4 q^{41} + 8 q^{44} - 24 q^{46} + 44 q^{49} - 24 q^{51} - 20 q^{54} - 10 q^{56} - 30 q^{59} - 34 q^{61} + 14 q^{64} - 28 q^{66} + 22 q^{69} + 6 q^{71} - 12 q^{74} + 40 q^{76} + 20 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} - 40 q^{89} + 6 q^{91} - 2 q^{94} - 14 q^{96} - 48 q^{99}+O(q^{100}) \) 8 * q - 6 * q^4 - 4 * q^6 - 4 * q^9 + 16 * q^11 - 2 * q^14 + 18 * q^16 - 20 * q^19 + 6 * q^21 - 24 * q^26 + 6 * q^31 + 28 * q^34 + 8 * q^36 + 12 * q^39 - 4 * q^41 + 8 * q^44 - 24 * q^46 + 44 * q^49 - 24 * q^51 - 20 * q^54 - 10 * q^56 - 30 * q^59 - 34 * q^61 + 14 * q^64 - 28 * q^66 + 22 * q^69 + 6 * q^71 - 12 * q^74 + 40 * q^76 + 20 * q^79 - 2 * q^81 - 2 * q^84 - 24 * q^86 - 40 * q^89 + 6 * q^91 - 2 * q^94 - 14 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

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