LMFDB - Embedded newform 625.2.d.h.501.1

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			501.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	625.501
Dual form			625.2.d.h.126.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.500000 + 0.363271i) q^{6} -1.61803 q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.618034 - 1.90211i) q^{9} +O(q^{10})$	\(q+(0.190983 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.500000 + 0.363271i) q^{6} -1.61803 q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.618034 - 1.90211i) q^{9} +(-0.236068 + 0.726543i) q^{11} +(-0.500000 - 1.53884i) q^{12} +(-1.50000 - 4.61653i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.572949 + 1.76336i) q^{16} +(0.618034 - 0.449028i) q^{17} -1.23607 q^{18} +(4.73607 - 3.44095i) q^{19} +(1.30902 + 0.951057i) q^{21} +(0.381966 + 0.277515i) q^{22} +(2.54508 - 7.83297i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-1.54508 + 4.75528i) q^{27} +(-2.11803 - 1.53884i) q^{28} +(1.11803 + 0.812299i) q^{29} +(2.42705 - 1.76336i) q^{31} +5.61803 q^{32} +(0.618034 - 0.449028i) q^{33} +(-0.145898 - 0.449028i) q^{34} +(1.00000 - 3.07768i) q^{36} +(1.30902 + 4.02874i) q^{37} +(-1.11803 - 3.44095i) q^{38} +(-1.50000 + 4.61653i) q^{39} +(-1.61803 - 4.97980i) q^{41} +(0.809017 - 0.587785i) q^{42} +1.85410 q^{43} +(-1.00000 + 0.726543i) q^{44} +(-4.11803 - 2.99193i) q^{46} +(1.30902 + 0.951057i) q^{47} +(0.572949 - 1.76336i) q^{48} -4.38197 q^{49} -0.763932 q^{51} +(2.42705 - 7.46969i) q^{52} +(-4.42705 - 3.21644i) q^{53} +(2.50000 + 1.81636i) q^{54} +(-2.92705 + 2.12663i) q^{56} -5.85410 q^{57} +(0.690983 - 0.502029i) q^{58} +(-1.28115 - 3.94298i) q^{59} +(-1.45492 + 4.47777i) q^{61} +(-0.572949 - 1.76336i) q^{62} +(1.00000 + 3.07768i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +(-0.145898 - 0.449028i) q^{66} +(-7.47214 + 5.42882i) q^{67} +1.23607 q^{68} +(-6.66312 + 4.84104i) q^{69} +(3.54508 + 2.57565i) q^{71} +(-3.61803 - 2.62866i) q^{72} +(-2.78115 + 8.55951i) q^{73} +2.61803 q^{74} +9.47214 q^{76} +(0.381966 - 1.17557i) q^{77} +(2.42705 + 1.76336i) q^{78} +(-2.50000 - 1.81636i) q^{79} +(-0.809017 + 0.587785i) q^{81} -3.23607 q^{82} +(1.42705 - 1.03681i) q^{83} +(0.809017 + 2.48990i) q^{84} +(0.354102 - 1.08981i) q^{86} +(-0.427051 - 1.31433i) q^{87} +(0.527864 + 1.62460i) q^{88} +(2.76393 - 8.50651i) q^{89} +(2.42705 + 7.46969i) q^{91} +(10.7812 - 7.83297i) q^{92} -3.00000 q^{93} +(0.809017 - 0.587785i) q^{94} +(-4.54508 - 3.30220i) q^{96} +(-2.30902 - 1.67760i) q^{97} +(-0.836881 + 2.57565i) q^{98} +1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 - 2 * q^7 + 5 * q^8 + 2 * q^9	$ 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9} + 8 q^{11} - 2 q^{12} - 6 q^{13} + q^{14} + 9 q^{16} - 2 q^{17} + 4 q^{18} + 10 q^{19} + 3 q^{21} + 6 q^{22} - q^{23} - 12 q^{26} + 5 q^{27} - 4 q^{28} + 3 q^{31} + 18 q^{32} - 2 q^{33} - 14 q^{34} + 4 q^{36} + 3 q^{37} - 6 q^{39} - 2 q^{41} + q^{42} - 6 q^{43} - 4 q^{44} - 12 q^{46} + 3 q^{47} + 9 q^{48} - 22 q^{49} - 12 q^{51} + 3 q^{52} - 11 q^{53} + 10 q^{54} - 5 q^{56} - 10 q^{57} + 5 q^{58} + 15 q^{59} - 17 q^{61} - 9 q^{62} + 4 q^{63} - 7 q^{64} - 14 q^{66} - 12 q^{67} - 4 q^{68} - 11 q^{69} + 3 q^{71} - 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{76} + 6 q^{77} + 3 q^{78} - 10 q^{79} - q^{81} - 4 q^{82} - q^{83} + q^{84} - 12 q^{86} + 5 q^{87} + 20 q^{88} + 20 q^{89} + 3 q^{91} + 23 q^{92} - 12 q^{93} + q^{94} - 7 q^{96} - 7 q^{97} - 19 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 - 2 * q^7 + 5 * q^8 + 2 * q^9 + 8 * q^11 - 2 * q^12 - 6 * q^13 + q^14 + 9 * q^16 - 2 * q^17 + 4 * q^18 + 10 * q^19 + 3 * q^21 + 6 * q^22 - q^23 - 12 * q^26 + 5 * q^27 - 4 * q^28 + 3 * q^31 + 18 * q^32 - 2 * q^33 - 14 * q^34 + 4 * q^36 + 3 * q^37 - 6 * q^39 - 2 * q^41 + q^42 - 6 * q^43 - 4 * q^44 - 12 * q^46 + 3 * q^47 + 9 * q^48 - 22 * q^49 - 12 * q^51 + 3 * q^52 - 11 * q^53 + 10 * q^54 - 5 * q^56 - 10 * q^57 + 5 * q^58 + 15 * q^59 - 17 * q^61 - 9 * q^62 + 4 * q^63 - 7 * q^64 - 14 * q^66 - 12 * q^67 - 4 * q^68 - 11 * q^69 + 3 * q^71 - 10 * q^72 + 9 * q^73 + 6 * q^74 + 20 * q^76 + 6 * q^77 + 3 * q^78 - 10 * q^79 - q^81 - 4 * q^82 - q^83 + q^84 - 12 * q^86 + 5 * q^87 + 20 * q^88 + 20 * q^89 + 3 * q^91 + 23 * q^92 - 12 * q^93 + q^94 - 7 * q^96 - 7 * q^97 - 19 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	−0.860552	−	0.509363i	$-0.829881\pi$
$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	0.995597	+	0.0937362i	$0.0298810\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i	0.329218	−	0.944254i	$-0.393215\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i	−0.796305	+	0.604896i	$0.793215\pi$
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.363271i	−0.204124	+	0.148305i
$7$	−1.61803			−0.611559			−0.305780	−	0.952102i	$-0.598917\pi$
$7$	−1.61803			−0.611559			−0.305780	+	0.952102i	$0.598917\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	−0.618034	−	1.90211i	−0.206011	−	0.634038i
$10$		0			0
$11$	−0.236068	+	0.726543i	−0.0711772	+	0.219061i	−0.980317	−	0.197430i	$-0.936740\pi$
$11$	−0.236068	+	0.726543i	−0.0711772	+	0.219061i	0.909140	+	0.416491i	$0.136740\pi$
$12$	−0.500000	−	1.53884i	−0.144338	−	0.444225i
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	−0.911331	−	0.411675i	$-0.864944\pi$
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	0.495306	−	0.868719i	$-0.335056\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$		0			0
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	0.618034	−	0.449028i	0.149895	−	0.108905i	−0.510310	−	0.859991i	$-0.670469\pi$
$17$	0.618034	−	0.449028i	0.149895	−	0.108905i	0.660205	+	0.751085i	$0.270469\pi$
$18$	−1.23607			−0.291344
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.107719	−	0.994181i	$-0.465645\pi$
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.978810	+	0.204772i	$0.0656454\pi$
$20$		0			0
$21$	1.30902	+	0.951057i	0.285651	+	0.207538i
$22$	0.381966	+	0.277515i	0.0814354	+	0.0591663i
$23$	2.54508	−	7.83297i	0.530687	−	1.63329i	−0.222101	−	0.975024i	$-0.571292\pi$
$23$	2.54508	−	7.83297i	0.530687	−	1.63329i	0.752788	−	0.658263i	$-0.228708\pi$
$24$	−2.23607			−0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	−1.54508	+	4.75528i	−0.297352	+	0.915155i
$28$	−2.11803	−	1.53884i	−0.400271	−	0.290814i
$29$	1.11803	+	0.812299i	0.207614	+	0.150840i	0.686733	−	0.726909i	$-0.259044\pi$
$29$	1.11803	+	0.812299i	0.207614	+	0.150840i	−0.479120	+	0.877750i	$0.659044\pi$
$30$		0			0
$31$	2.42705	−	1.76336i	0.435911	−	0.316708i	−0.348097	−	0.937459i	$-0.613172\pi$
$31$	2.42705	−	1.76336i	0.435911	−	0.316708i	0.784008	+	0.620750i	$0.213172\pi$
$32$	5.61803			0.993137
$33$	0.618034	−	0.449028i	0.107586	−	0.0781657i
$34$	−0.145898	−	0.449028i	−0.0250213	−	0.0770077i
$35$		0			0
$36$	1.00000	−	3.07768i	0.166667	−	0.512947i
$37$	1.30902	+	4.02874i	0.215201	+	0.662321i	0.999139	+	0.0414819i	$0.0132079\pi$
$37$	1.30902	+	4.02874i	0.215201	+	0.662321i	−0.783938	+	0.620839i	$0.786792\pi$
$38$	−1.11803	−	3.44095i	−0.181369	−	0.558197i
$39$	−1.50000	+	4.61653i	−0.240192	+	0.739236i
$40$		0			0
$41$	−1.61803	−	4.97980i	−0.252694	−	0.777714i	−0.994275	−	0.106850i	$-0.965924\pi$
$41$	−1.61803	−	4.97980i	−0.252694	−	0.777714i	0.741581	−	0.670864i	$-0.234076\pi$
$42$	0.809017	−	0.587785i	0.124834	−	0.0906972i
$43$	1.85410			0.282748			0.141374	−	0.989956i	$-0.454848\pi$
$43$	1.85410			0.282748			0.141374	+	0.989956i	$0.454848\pi$
$44$	−1.00000	+	0.726543i	−0.150756	+	0.109530i
$45$		0			0
$46$	−4.11803	−	2.99193i	−0.607171	−	0.441136i
$47$	1.30902	+	0.951057i	0.190940	+	0.138726i	0.679148	−	0.734001i	$-0.262349\pi$
$47$	1.30902	+	0.951057i	0.190940	+	0.138726i	−0.488208	+	0.872727i	$0.662349\pi$
$48$	0.572949	−	1.76336i	0.0826981	−	0.254518i
$49$	−4.38197			−0.625995
$50$		0			0
$51$	−0.763932			−0.106972
$52$	2.42705	−	7.46969i	0.336571	−	1.03586i
$53$	−4.42705	−	3.21644i	−0.608102	−	0.441812i	0.240643	−	0.970614i	$-0.422642\pi$
$53$	−4.42705	−	3.21644i	−0.608102	−	0.441812i	−0.848746	+	0.528801i	$0.822642\pi$
$54$	2.50000	+	1.81636i	0.340207	+	0.247175i
$55$		0			0
$56$	−2.92705	+	2.12663i	−0.391144	+	0.284182i
$57$	−5.85410			−0.775395
$58$	0.690983	−	0.502029i	0.0907305	−	0.0659196i
$59$	−1.28115	−	3.94298i	−0.166792	−	0.513333i	0.832372	−	0.554217i	$-0.186982\pi$
$59$	−1.28115	−	3.94298i	−0.166792	−	0.513333i	−0.999164	+	0.0408847i	$0.986982\pi$
$60$		0			0
$61$	−1.45492	+	4.47777i	−0.186283	+	0.573319i	−0.999968	−	0.00798614i	$-0.997458\pi$
$61$	−1.45492	+	4.47777i	−0.186283	+	0.573319i	0.813685	+	0.581306i	$0.197458\pi$
$62$	−0.572949	−	1.76336i	−0.0727646	−	0.223946i
$63$	1.00000	+	3.07768i	0.125988	+	0.387752i
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$		0			0
$66$	−0.145898	−	0.449028i	−0.0179588	−	0.0552715i
$67$	−7.47214	+	5.42882i	−0.912867	+	0.663236i	−0.941738	−	0.336347i	$-0.890809\pi$
$67$	−7.47214	+	5.42882i	−0.912867	+	0.663236i	0.0288716	+	0.999583i	$0.490809\pi$
$68$	1.23607			0.149895
$69$	−6.66312	+	4.84104i	−0.802145	+	0.582793i
$70$		0			0
$71$	3.54508	+	2.57565i	0.420724	+	0.305674i	0.777929	−	0.628352i	$-0.216270\pi$
$71$	3.54508	+	2.57565i	0.420724	+	0.305674i	−0.357205	+	0.934026i	$0.616270\pi$
$72$	−3.61803	−	2.62866i	−0.426389	−	0.309790i
$73$	−2.78115	+	8.55951i	−0.325509	+	1.00181i	0.645701	+	0.763590i	$0.276565\pi$
$73$	−2.78115	+	8.55951i	−0.325509	+	1.00181i	−0.971210	+	0.238224i	$0.923435\pi$
$74$	2.61803			0.304340
$75$		0			0
$76$	9.47214			1.08653
$77$	0.381966	−	1.17557i	0.0435291	−	0.133969i
$78$	2.42705	+	1.76336i	0.274809	+	0.199661i
$79$	−2.50000	−	1.81636i	−0.281272	−	0.204356i	0.438200	−	0.898877i	$-0.355616\pi$
$79$	−2.50000	−	1.81636i	−0.281272	−	0.204356i	−0.719472	+	0.694521i	$0.755616\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−3.23607			−0.357364
$83$	1.42705	−	1.03681i	0.156639	−	0.113805i	−0.506705	−	0.862120i	$-0.669137\pi$
$83$	1.42705	−	1.03681i	0.156639	−	0.113805i	0.663344	+	0.748315i	$0.269137\pi$
$84$	0.809017	+	2.48990i	0.0882710	+	0.271670i
$85$		0			0
$86$	0.354102	−	1.08981i	0.0381838	−	0.117518i
$87$	−0.427051	−	1.31433i	−0.0457847	−	0.140911i
$88$	0.527864	+	1.62460i	0.0562705	+	0.173183i
$89$	2.76393	−	8.50651i	0.292976	−	0.901688i	−0.690918	−	0.722934i	$-0.742793\pi$
$89$	2.76393	−	8.50651i	0.292976	−	0.901688i	0.983894	−	0.178754i	$-0.0572068\pi$
$90$		0			0
$91$	2.42705	+	7.46969i	0.254424	+	0.783037i
$92$	10.7812	−	7.83297i	1.12401	−	0.816643i
$93$	−3.00000			−0.311086
$94$	0.809017	−	0.587785i	0.0834437	−	0.0606254i
$95$		0			0
$96$	−4.54508	−	3.30220i	−0.463881	−	0.337029i
$97$	−2.30902	−	1.67760i	−0.234445	−	0.170334i	0.464360	−	0.885647i	$-0.346284\pi$
$97$	−2.30902	−	1.67760i	−0.234445	−	0.170334i	−0.698805	+	0.715312i	$0.746284\pi$
$98$	−0.836881	+	2.57565i	−0.0845378	+	0.260180i
$99$	1.52786			0.153556
$100$		0			0
$101$	−7.47214			−0.743505			−0.371753	−	0.928332i	$-0.621243\pi$
$101$	−7.47214			−0.743505			−0.371753	+	0.928332i	$0.621243\pi$
$102$	−0.145898	+	0.449028i	−0.0144461	+	0.0444604i
$103$	9.35410	+	6.79615i	0.921687	+	0.669645i	0.943943	−	0.330107i	$-0.107085\pi$
$103$	9.35410	+	6.79615i	0.921687	+	0.669645i	−0.0222563	+	0.999752i	$0.507085\pi$
$104$	−8.78115	−	6.37988i	−0.861063	−	0.625599i
$105$		0			0
$106$	−2.73607	+	1.98787i	−0.265750	+	0.193079i
$107$	10.4164			1.00699			0.503496	−	0.863998i	$-0.332047\pi$
$107$	10.4164			1.00699			0.503496	+	0.863998i	$0.332047\pi$
$108$	−6.54508	+	4.75528i	−0.629801	+	0.457577i
$109$	3.09017	+	9.51057i	0.295985	+	0.910947i	0.982889	+	0.184199i	$0.0589691\pi$
$109$	3.09017	+	9.51057i	0.295985	+	0.910947i	−0.686904	+	0.726748i	$0.741031\pi$
$110$		0			0
$111$	1.30902	−	4.02874i	0.124246	−	0.382391i
$112$	−0.927051	−	2.85317i	−0.0875981	−	0.269599i
$113$	3.13525	+	9.64932i	0.294940	+	0.907732i	0.983242	+	0.182307i	$0.0583566\pi$
$113$	3.13525	+	9.64932i	0.294940	+	0.907732i	−0.688302	+	0.725425i	$0.741643\pi$
$114$	−1.11803	+	3.44095i	−0.104713	+	0.322275i
$115$		0			0
$116$	0.690983	+	2.12663i	0.0641562	+	0.197452i
$117$	−7.85410	+	5.70634i	−0.726112	+	0.527551i
$118$	−2.56231			−0.235879
$119$	−1.00000	+	0.726543i	−0.0916698	+	0.0666020i
$120$		0			0
$121$	8.42705	+	6.12261i	0.766096	+	0.556601i
$122$	2.35410	+	1.71036i	0.213130	+	0.154848i
$123$	−1.61803	+	4.97980i	−0.145893	+	0.449013i
$124$	4.85410			0.435911
$125$		0			0
$126$	2.00000			0.178174
$127$	−4.90983	+	15.1109i	−0.435677	+	1.34088i	0.456714	+	0.889613i	$0.349026\pi$
$127$	−4.90983	+	15.1109i	−0.435677	+	1.34088i	−0.892391	+	0.451262i	$0.850974\pi$
$128$	9.20820	+	6.69015i	0.813898	+	0.591331i
$129$	−1.50000	−	1.08981i	−0.132068	−	0.0959528i
$130$		0			0
$131$	14.3992	−	10.4616i	1.25806	−	0.914036i	0.259402	−	0.965769i	$-0.416475\pi$
$131$	14.3992	−	10.4616i	1.25806	−	0.914036i	0.998661	+	0.0517333i	$0.0164746\pi$
$132$	1.23607			0.107586
$133$	−7.66312	+	5.56758i	−0.664477	+	0.482771i
$134$	1.76393	+	5.42882i	0.152381	+	0.468979i
$135$		0			0
$136$	0.527864	−	1.62460i	0.0452640	−	0.139308i
$137$	1.83688	+	5.65334i	0.156935	+	0.482997i	0.998352	−	0.0573898i	$-0.0182778\pi$
$137$	1.83688	+	5.65334i	0.156935	+	0.482997i	−0.841417	+	0.540387i	$0.818278\pi$
$138$	1.57295	+	4.84104i	0.133898	+	0.412097i
$139$	1.54508	−	4.75528i	0.131052	−	0.403338i	−0.863903	−	0.503659i	$-0.831987\pi$
$139$	1.54508	−	4.75528i	0.131052	−	0.403338i	0.994955	+	0.100321i	$0.0319869\pi$
$140$		0			0
$141$	−0.500000	−	1.53884i	−0.0421076	−	0.129594i
$142$	2.19098	−	1.59184i	0.183863	−	0.133584i
$143$	3.70820			0.310096
$144$	3.00000	−	2.17963i	0.250000	−	0.181636i
$145$		0			0
$146$	4.50000	+	3.26944i	0.372423	+	0.270581i
$147$	3.54508	+	2.57565i	0.292394	+	0.212436i
$148$	−2.11803	+	6.51864i	−0.174101	+	0.535829i
$149$	13.9443			1.14236			0.571180	−	0.820825i	$-0.306486\pi$
$149$	13.9443			1.14236			0.571180	+	0.820825i	$0.306486\pi$
$150$		0			0
$151$	−5.56231			−0.452654			−0.226327	−	0.974051i	$-0.572672\pi$
$151$	−5.56231			−0.452654			−0.226327	+	0.974051i	$0.572672\pi$
$152$	4.04508	−	12.4495i	0.328100	−	1.00979i
$153$	−1.23607	−	0.898056i	−0.0999302	−	0.0726035i
$154$	−0.618034	−	0.449028i	−0.0498026	−	0.0361837i
$155$		0			0
$156$	−6.35410	+	4.61653i	−0.508735	+	0.369618i
$157$	−9.18034			−0.732671			−0.366335	−	0.930483i	$-0.619388\pi$
$157$	−9.18034			−0.732671			−0.366335	+	0.930483i	$0.619388\pi$
$158$	−1.54508	+	1.12257i	−0.122920	+	0.0893069i
$159$	1.69098	+	5.20431i	0.134104	+	0.412729i
$160$		0			0
$161$	−4.11803	+	12.6740i	−0.324547	+	0.998852i
$162$	0.190983	+	0.587785i	0.0150050	+	0.0461808i
$163$	3.39919	+	10.4616i	0.266245	+	0.819417i	0.991404	+	0.130836i	$0.0417662\pi$
$163$	3.39919	+	10.4616i	0.266245	+	0.819417i	−0.725159	+	0.688581i	$0.758234\pi$
$164$	2.61803	−	8.05748i	0.204434	−	0.629183i
$165$		0			0
$166$	−0.336881	−	1.03681i	−0.0261470	−	0.0804723i
$167$	4.50000	−	3.26944i	0.348220	−	0.252997i	−0.399902	−	0.916558i	$-0.630956\pi$
$167$	4.50000	−	3.26944i	0.348220	−	0.252997i	0.748122	+	0.663561i	$0.230956\pi$
$168$	3.61803			0.279137
$169$	−8.54508	+	6.20837i	−0.657314	+	0.477567i
$170$		0			0
$171$	−9.47214	−	6.88191i	−0.724352	−	0.526273i
$172$	2.42705	+	1.76336i	0.185061	+	0.134455i
$173$	−5.21885	+	16.0620i	−0.396782	+	1.22117i	0.530784	+	0.847507i	$0.321898\pi$
$173$	−5.21885	+	16.0620i	−0.396782	+	1.22117i	−0.927565	+	0.373661i	$0.878102\pi$
$174$	−0.854102			−0.0647493
$175$		0			0
$176$	−1.41641			−0.106766
$177$	−1.28115	+	3.94298i	−0.0962974	+	0.296373i
$178$	−4.47214	−	3.24920i	−0.335201	−	0.243538i
$179$	7.66312	+	5.56758i	0.572768	+	0.416141i	0.836110	−	0.548562i	$-0.184825\pi$
$179$	7.66312	+	5.56758i	0.572768	+	0.416141i	−0.263341	+	0.964703i	$0.584825\pi$
$180$		0			0
$181$	−11.0902	+	8.05748i	−0.824326	+	0.598908i	−0.917948	−	0.396700i	$-0.870155\pi$
$181$	−11.0902	+	8.05748i	−0.824326	+	0.598908i	0.0936225	+	0.995608i	$0.470155\pi$
$182$	4.85410			0.359810
$183$	3.80902	−	2.76741i	0.281571	−	0.204573i
$184$	−5.69098	−	17.5150i	−0.419545	−	1.29123i
$185$		0			0
$186$	−0.572949	+	1.76336i	−0.0420107	+	0.129296i
$187$	0.180340	+	0.555029i	0.0131878	+	0.0405877i
$188$	0.809017	+	2.48990i	0.0590036	+	0.181594i
$189$	2.50000	−	7.69421i	0.181848	−	0.559671i
$190$		0			0
$191$	−7.47214	−	22.9969i	−0.540665	−	1.66400i	−0.731080	−	0.682292i	$-0.760984\pi$
$191$	−7.47214	−	22.9969i	−0.540665	−	1.66400i	0.190415	−	0.981704i	$-0.439016\pi$
$192$	0.190983	−	0.138757i	0.0137830	−	0.0100139i
$193$	−5.70820			−0.410886			−0.205443	−	0.978669i	$-0.565863\pi$
$193$	−5.70820			−0.410886			−0.205443	+	0.978669i	$0.565863\pi$
$194$	−1.42705	+	1.03681i	−0.102456	+	0.0744389i
$195$		0			0
$196$	−5.73607	−	4.16750i	−0.409719	−	0.297678i
$197$	7.85410	+	5.70634i	0.559582	+	0.406560i	0.831306	−	0.555815i	$-0.187594\pi$
$197$	7.85410	+	5.70634i	0.559582	+	0.406560i	−0.271724	+	0.962375i	$0.587594\pi$
$198$	0.291796	−	0.898056i	0.0207370	−	0.0638221i
$199$	2.56231			0.181637			0.0908185	−	0.995867i	$-0.471052\pi$
$199$	2.56231			0.181637			0.0908185	+	0.995867i	$0.471052\pi$
$200$		0			0
$201$	9.23607			0.651462
$202$	−1.42705	+	4.39201i	−0.100407	+	0.309021i
$203$	−1.80902	−	1.31433i	−0.126968	−	0.0922477i
$204$	−1.00000	−	0.726543i	−0.0700140	−	0.0508682i
$205$		0			0
$206$	5.78115	−	4.20025i	0.402792	−	0.292646i
$207$	−16.4721			−1.14489
$208$	7.28115	−	5.29007i	0.504857	−	0.366800i
$209$	1.38197	+	4.25325i	0.0955926	+	0.294204i
$210$		0			0
$211$	4.07295	−	12.5352i	0.280393	−	0.862962i	−0.707348	−	0.706865i	$-0.750109\pi$
$211$	4.07295	−	12.5352i	0.280393	−	0.862962i	0.987742	−	0.156097i	$-0.0498912\pi$
$212$	−2.73607	−	8.42075i	−0.187914	−	0.578340i
$213$	−1.35410	−	4.16750i	−0.0927815	−	0.285552i
$214$	1.98936	−	6.12261i	0.135990	−	0.418533i
$215$		0			0
$216$	3.45492	+	10.6331i	0.235077	+	0.723493i
$217$	−3.92705	+	2.85317i	−0.266586	+	0.193686i
$218$	6.18034			0.418585
$219$	7.28115	−	5.29007i	0.492015	−	0.357470i
$220$		0			0
$221$	−3.00000	−	2.17963i	−0.201802	−	0.146618i
$222$	−2.11803	−	1.53884i	−0.142153	−	0.103280i
$223$	6.85410	−	21.0948i	0.458985	−	1.41261i	−0.407408	−	0.913246i	$-0.633567\pi$
$223$	6.85410	−	21.0948i	0.458985	−	1.41261i	0.866393	−	0.499363i	$-0.166433\pi$
$224$	−9.09017			−0.607363
$225$		0			0
$226$	6.27051			0.417108
$227$	5.94427	−	18.2946i	0.394535	−	1.21425i	−0.534788	−	0.844986i	$-0.679608\pi$
$227$	5.94427	−	18.2946i	0.394535	−	1.21425i	0.929323	−	0.369268i	$-0.120392\pi$
$228$	−7.66312	−	5.56758i	−0.507502	−	0.368722i
$229$	−6.70820	−	4.87380i	−0.443291	−	0.322069i	0.343650	−	0.939098i	$-0.388336\pi$
$229$	−6.70820	−	4.87380i	−0.443291	−	0.322069i	−0.786941	+	0.617028i	$0.788336\pi$
$230$		0			0
$231$	−1.00000	+	0.726543i	−0.0657952	+	0.0478030i
$232$	3.09017			0.202880
$233$	−12.0902	+	8.78402i	−0.792053	+	0.575460i	−0.908572	−	0.417728i	$-0.862826\pi$
$233$	−12.0902	+	8.78402i	−0.792053	+	0.575460i	0.116519	+	0.993188i	$0.462826\pi$
$234$	1.85410	+	5.70634i	0.121206	+	0.373035i
$235$		0			0
$236$	2.07295	−	6.37988i	0.134937	−	0.415295i
$237$	0.954915	+	2.93893i	0.0620284	+	0.190904i
$238$	0.236068	+	0.726543i	0.0153020	+	0.0470948i
$239$	−9.10739	+	28.0297i	−0.589108	+	1.81309i	−0.00700219	+	0.999975i	$0.502229\pi$
$239$	−9.10739	+	28.0297i	−0.589108	+	1.81309i	−0.582106	+	0.813113i	$0.697771\pi$
$240$		0			0
$241$	3.54508	+	10.9106i	0.228359	+	0.702817i	0.997933	+	0.0642594i	$0.0204685\pi$
$241$	3.54508	+	10.9106i	0.228359	+	0.702817i	−0.769574	+	0.638557i	$0.779532\pi$
$242$	5.20820	−	3.78398i	0.334796	−	0.243244i
$243$	16.0000			1.02640
$244$	−6.16312	+	4.47777i	−0.394553	+	0.286660i
$245$		0			0
$246$	2.61803	+	1.90211i	0.166920	+	0.121274i
$247$	−22.9894	−	16.7027i	−1.46278	−	1.06277i
$248$	2.07295	−	6.37988i	0.131632	−	0.405123i
$249$	−1.76393			−0.111785
$250$		0			0
$251$	−6.81966			−0.430453			−0.215227	−	0.976564i	$-0.569049\pi$
$251$	−6.81966			−0.430453			−0.215227	+	0.976564i	$0.569049\pi$
$252$	−1.61803	+	4.97980i	−0.101927	+	0.313698i
$253$	5.09017	+	3.69822i	0.320016	+	0.232505i
$254$	7.94427	+	5.77185i	0.498468	+	0.362158i
$255$		0			0
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	16.1459			1.00715			0.503577	−	0.863951i	$-0.332017\pi$
$257$	16.1459			1.00715			0.503577	+	0.863951i	$0.332017\pi$
$258$	−0.927051	+	0.673542i	−0.0577157	+	0.0419329i
$259$	−2.11803	−	6.51864i	−0.131608	−	0.405048i
$260$		0			0
$261$	0.854102	−	2.62866i	0.0528676	−	0.162710i
$262$	−3.39919	−	10.4616i	−0.210002	−	0.646321i
$263$	−6.82624	−	21.0090i	−0.420924	−	1.29547i	−0.906844	−	0.421467i	$-0.861515\pi$
$263$	−6.82624	−	21.0090i	−0.420924	−	1.29547i	0.485920	−	0.874003i	$-0.338485\pi$
$264$	0.527864	−	1.62460i	0.0324878	−	0.0999871i
$265$		0			0
$266$	1.80902	+	5.56758i	0.110918	+	0.341370i
$267$	−7.23607	+	5.25731i	−0.442840	+	0.321742i
$268$	−14.9443			−0.912867
$269$	13.9443	−	10.1311i	0.850197	−	0.617704i	−0.0750032	−	0.997183i	$-0.523897\pi$
$269$	13.9443	−	10.1311i	0.850197	−	0.617704i	0.925200	+	0.379479i	$0.123897\pi$
$270$		0			0
$271$	6.47214	+	4.70228i	0.393154	+	0.285643i	0.766747	−	0.641950i	$-0.221874\pi$
$271$	6.47214	+	4.70228i	0.393154	+	0.285643i	−0.373593	+	0.927593i	$0.621874\pi$
$272$	1.14590	+	0.832544i	0.0694803	+	0.0504804i
$273$	2.42705	−	7.46969i	0.146892	−	0.452086i
$274$	3.67376			0.221940
$275$		0			0
$276$	−13.3262			−0.802145
$277$	−3.48936	+	10.7391i	−0.209655	+	0.645252i	0.789835	+	0.613320i	$0.210166\pi$
$277$	−3.48936	+	10.7391i	−0.209655	+	0.645252i	−0.999490	+	0.0319326i	$0.989834\pi$
$278$	−2.50000	−	1.81636i	−0.149940	−	0.108938i
$279$	−4.85410	−	3.52671i	−0.290607	−	0.211139i
$280$		0			0
$281$	0.881966	−	0.640786i	0.0526137	−	0.0382261i	−0.561168	−	0.827702i	$-0.689648\pi$
$281$	0.881966	−	0.640786i	0.0526137	−	0.0382261i	0.613781	+	0.789476i	$0.289648\pi$
$282$	−1.00000			−0.0595491
$283$	18.7254	−	13.6048i	1.11311	−	0.808722i	0.129960	−	0.991519i	$-0.458515\pi$
$283$	18.7254	−	13.6048i	1.11311	−	0.808722i	0.983151	+	0.182797i	$0.0585150\pi$
$284$	2.19098	+	6.74315i	0.130011	+	0.400132i
$285$		0			0
$286$	0.708204	−	2.17963i	0.0418770	−	0.128884i
$287$	2.61803	+	8.05748i	0.154538	+	0.475618i
$288$	−3.47214	−	10.6861i	−0.204598	−	0.629687i
$289$	−5.07295	+	15.6129i	−0.298409	+	0.918408i
$290$		0			0
$291$	0.881966	+	2.71441i	0.0517018	+	0.159122i
$292$	−11.7812	+	8.55951i	−0.689440	+	0.500907i
$293$	−28.4721			−1.66336			−0.831680	−	0.555255i	$-0.812621\pi$
$293$	−28.4721			−1.66336			−0.831680	+	0.555255i	$0.812621\pi$
$294$	2.19098	−	1.59184i	0.127781	−	0.0928381i
$295$		0			0
$296$	7.66312	+	5.56758i	0.445410	+	0.323609i
$297$	−3.09017	−	2.24514i	−0.179310	−	0.130276i
$298$	2.66312	−	8.19624i	0.154270	−	0.474795i
$299$	−39.9787			−2.31203
$300$		0			0
$301$	−3.00000			−0.172917
$302$	−1.06231	+	3.26944i	−0.0611288	+	0.188135i
$303$	6.04508	+	4.39201i	0.347281	+	0.252314i
$304$	8.78115	+	6.37988i	0.503634	+	0.365911i
$305$		0			0
$306$	−0.763932	+	0.555029i	−0.0436711	+	0.0317289i
$307$	4.76393			0.271892			0.135946	−	0.990716i	$-0.456593\pi$
$307$	4.76393			0.271892			0.135946	+	0.990716i	$0.456593\pi$
$308$	1.61803	−	1.17557i	0.0921960	−	0.0669843i
$309$	−3.57295	−	10.9964i	−0.203258	−	0.625564i
$310$		0			0
$311$	−9.11803	+	28.0624i	−0.517036	+	1.59127i	0.262510	+	0.964929i	$0.415450\pi$
$311$	−9.11803	+	28.0624i	−0.517036	+	1.59127i	−0.779546	+	0.626345i	$0.784550\pi$
$312$	3.35410	+	10.3229i	0.189889	+	0.584417i
$313$	−6.56231	−	20.1967i	−0.370923	−	1.14159i	−0.946188	−	0.323618i	$-0.895101\pi$
$313$	−6.56231	−	20.1967i	−0.370923	−	1.14159i	0.575265	−	0.817967i	$-0.304899\pi$
$314$	−1.75329	+	5.39607i	−0.0989438	+	0.304518i
$315$		0			0
$316$	−1.54508	−	4.75528i	−0.0869178	−	0.267506i
$317$	19.1353	−	13.9026i	1.07474	−	0.780846i	0.0979842	−	0.995188i	$-0.468761\pi$
$317$	19.1353	−	13.9026i	1.07474	−	0.780846i	0.976759	+	0.214341i	$0.0687605\pi$
$318$	3.38197			0.189651
$319$	−0.854102	+	0.620541i	−0.0478205	+	0.0347436i
$320$		0			0
$321$	−8.42705	−	6.12261i	−0.470352	−	0.341731i
$322$	6.66312	+	4.84104i	0.371321	+	0.269781i
$323$	1.38197	−	4.25325i	0.0768946	−	0.236657i
$324$	−1.61803			−0.0898908
$325$		0			0
$326$	6.79837			0.376527
$327$	3.09017	−	9.51057i	0.170887	−	0.525935i
$328$	−9.47214	−	6.88191i	−0.523011	−	0.379990i
$329$	−2.11803	−	1.53884i	−0.116771	−	0.0848391i
$330$		0			0
$331$	−13.8541	+	10.0656i	−0.761490	+	0.553255i	−0.899367	−	0.437194i	$-0.855972\pi$
$331$	−13.8541	+	10.0656i	−0.761490	+	0.553255i	0.137877	+	0.990449i	$0.455972\pi$
$332$	2.85410			0.156639
$333$	6.85410	−	4.97980i	0.375602	−	0.272891i
$334$	−1.06231	−	3.26944i	−0.0581268	−	0.178896i
$335$		0			0
$336$	−0.927051	+	2.85317i	−0.0505748	+	0.155653i
$337$	0.354102	+	1.08981i	0.0192892	+	0.0593659i	0.960238	−	0.279183i	$-0.0900638\pi$
$337$	0.354102	+	1.08981i	0.0192892	+	0.0593659i	−0.940949	+	0.338549i	$0.890064\pi$
$338$	2.01722	+	6.20837i	0.109722	+	0.337691i
$339$	3.13525	−	9.64932i	0.170284	−	0.524079i
$340$		0			0
$341$	0.708204	+	2.17963i	0.0383514	+	0.118033i
$342$	−5.85410	+	4.25325i	−0.316554	+	0.229990i
$343$	18.4164			0.994393
$344$	3.35410	−	2.43690i	0.180841	−	0.131389i
$345$		0			0
$346$	8.44427	+	6.13512i	0.453967	+	0.329826i
$347$	25.1525	+	18.2743i	1.35026	+	0.981018i	0.998999	+	0.0447390i	$0.0142456\pi$
$347$	25.1525	+	18.2743i	1.35026	+	0.981018i	0.351257	+	0.936279i	$0.385754\pi$
$348$	0.690983	−	2.12663i	0.0370406	−	0.113999i
$349$	8.29180			0.443850			0.221925	−	0.975064i	$-0.428766\pi$
$349$	8.29180			0.443850			0.221925	+	0.975064i	$0.428766\pi$
$350$		0			0
$351$	24.2705			1.29546
$352$	−1.32624	+	4.08174i	−0.0706887	+	0.217558i
$353$	−19.4894	−	14.1598i	−1.03731	−	0.753653i	−0.0675544	−	0.997716i	$-0.521520\pi$
$353$	−19.4894	−	14.1598i	−1.03731	−	0.753653i	−0.969759	+	0.244063i	$0.921520\pi$
$354$	2.07295	+	1.50609i	0.110176	+	0.0800475i
$355$		0			0
$356$	11.7082	−	8.50651i	0.620534	−	0.450844i
$357$	1.23607			0.0654197
$358$	4.73607	−	3.44095i	0.250309	−	0.181860i
$359$	−8.88197	−	27.3359i	−0.468772	−	1.44273i	−0.854176	−	0.519984i	$-0.825938\pi$
$359$	−8.88197	−	27.3359i	−0.468772	−	1.44273i	0.385403	−	0.922748i	$-0.374062\pi$
$360$		0			0
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$	2.61803	+	8.05748i	0.137601	+	0.423492i
$363$	−3.21885	−	9.90659i	−0.168946	−	0.519961i
$364$	−3.92705	+	12.0862i	−0.205833	+	0.633490i
$365$		0			0
$366$	−0.899187	−	2.76741i	−0.0470013	−	0.144655i
$367$	4.39919	−	3.19620i	0.229636	−	0.166840i	−0.467018	−	0.884248i	$-0.654672\pi$
$367$	4.39919	−	3.19620i	0.229636	−	0.166840i	0.696653	+	0.717408i	$0.254672\pi$
$368$	15.2705			0.796030
$369$	−8.47214	+	6.15537i	−0.441042	+	0.320436i
$370$		0			0
$371$	7.16312	+	5.20431i	0.371891	+	0.270194i
$372$	−3.92705	−	2.85317i	−0.203608	−	0.147930i
$373$	1.62868	−	5.01255i	0.0843297	−	0.259540i	−0.899997	−	0.435897i	$-0.856431\pi$
$373$	1.62868	−	5.01255i	0.0843297	−	0.259540i	0.984326	+	0.176357i	$0.0564312\pi$
$374$	0.360680			0.0186503
$375$		0			0
$376$	3.61803			0.186586
$377$	2.07295	−	6.37988i	0.106762	−	0.328581i
$378$	−4.04508	−	2.93893i	−0.208057	−	0.151162i
$379$	27.9894	+	20.3355i	1.43772	+	1.04456i	0.988513	+	0.151133i	$0.0482921\pi$
$379$	27.9894	+	20.3355i	1.43772	+	1.04456i	0.449203	+	0.893430i	$0.351708\pi$
$380$		0			0
$381$	12.8541	−	9.33905i	0.658536	−	0.478454i
$382$	−14.9443			−0.764615
$383$	9.19098	−	6.67764i	0.469637	−	0.341211i	−0.327663	−	0.944795i	$-0.606261\pi$
$383$	9.19098	−	6.67764i	0.469637	−	0.341211i	0.797300	+	0.603583i	$0.206261\pi$
$384$	−3.51722	−	10.8249i	−0.179487	−	0.552406i
$385$		0			0
$386$	−1.09017	+	3.35520i	−0.0554882	+	0.170775i
$387$	−1.14590	−	3.52671i	−0.0582493	−	0.179273i
$388$	−1.42705	−	4.39201i	−0.0724475	−	0.222971i
$389$	4.63525	−	14.2658i	0.235017	−	0.723307i	−0.762102	−	0.647456i	$-0.775833\pi$
$389$	4.63525	−	14.2658i	0.235017	−	0.723307i	0.997119	−	0.0758507i	$-0.0241672\pi$
$390$		0			0
$391$	−1.94427	−	5.98385i	−0.0983261	−	0.302616i
$392$	−7.92705	+	5.75934i	−0.400377	+	0.290891i
$393$	−17.7984			−0.897809
$394$	4.85410	−	3.52671i	0.244546	−	0.177673i
$395$		0			0
$396$	2.00000	+	1.45309i	0.100504	+	0.0730203i
$397$	0.0278640	+	0.0202444i	0.00139846	+	0.00101604i	0.588484	−	0.808509i	$-0.299725\pi$
$397$	0.0278640	+	0.0202444i	0.00139846	+	0.00101604i	−0.587086	+	0.809525i	$0.699725\pi$
$398$	0.489357	−	1.50609i	0.0245292	−	0.0754933i
$399$	9.47214			0.474200
$400$		0			0
$401$	−22.5967			−1.12843			−0.564214	−	0.825629i	$-0.690821\pi$
$401$	−22.5967			−1.12843			−0.564214	+	0.825629i	$0.690821\pi$
$402$	1.76393	−	5.42882i	0.0879769	−	0.270765i
$403$	−11.7812	−	8.55951i	−0.586861	−	0.426379i
$404$	−9.78115	−	7.10642i	−0.486631	−	0.353558i
$405$		0			0
$406$	−1.11803	+	0.812299i	−0.0554871	+	0.0403137i
$407$	−3.23607			−0.160406
$408$	−1.38197	+	1.00406i	−0.0684175	+	0.0497082i
$409$	8.78115	+	27.0256i	0.434200	+	1.33633i	0.893904	+	0.448258i	$0.147955\pi$
$409$	8.78115	+	27.0256i	0.434200	+	1.33633i	−0.459704	+	0.888072i	$0.652045\pi$
$410$		0			0
$411$	1.83688	−	5.65334i	0.0906067	−	0.278859i
$412$	5.78115	+	17.7926i	0.284817	+	0.876576i
$413$	2.07295	+	6.37988i	0.102003	+	0.313933i
$414$	−3.14590	+	9.68208i	−0.154612	+	0.475848i
$415$		0			0
$416$	−8.42705	−	25.9358i	−0.413170	−	1.27161i
$417$	−4.04508	+	2.93893i	−0.198089	+	0.143920i
$418$	2.76393			0.135188
$419$	0.427051	−	0.310271i	0.0208628	−	0.0151577i	−0.577305	−	0.816529i	$-0.695896\pi$
$419$	0.427051	−	0.310271i	0.0208628	−	0.0151577i	0.598168	+	0.801371i	$0.295896\pi$
$420$		0			0
$421$	−25.8885	−	18.8091i	−1.26173	−	0.916701i	−0.262889	−	0.964826i	$-0.584675\pi$
$421$	−25.8885	−	18.8091i	−1.26173	−	0.916701i	−0.998841	+	0.0481252i	$0.984675\pi$
$422$	−6.59017	−	4.78804i	−0.320804	−	0.233078i
$423$	1.00000	−	3.07768i	0.0486217	−	0.149642i
$424$	−12.2361			−0.594236
$425$		0			0
$426$	−2.70820			−0.131213
$427$	2.35410	−	7.24518i	0.113923	−	0.350619i
$428$	13.6353	+	9.90659i	0.659085	+	0.478853i
$429$	−3.00000	−	2.17963i	−0.144841	−	0.105233i
$430$		0			0
$431$	−19.2812	+	14.0086i	−0.928740	+	0.674769i	−0.945684	−	0.325087i	$-0.894606\pi$
$431$	−19.2812	+	14.0086i	−0.928740	+	0.674769i	0.0169437	+	0.999856i	$0.494606\pi$
$432$	−9.27051			−0.446028
$433$	−16.2984	+	11.8415i	−0.783250	+	0.569064i	−0.905953	−	0.423379i	$-0.860844\pi$
$433$	−16.2984	+	11.8415i	−0.783250	+	0.569064i	0.122703	+	0.992443i	$0.460844\pi$
$434$	0.927051	+	2.85317i	0.0444999	+	0.136957i
$435$		0			0
$436$	−5.00000	+	15.3884i	−0.239457	+	0.736972i
$437$	−14.8992	−	45.8550i	−0.712725	−	2.19354i
$438$	−1.71885	−	5.29007i	−0.0821297	−	0.252769i
$439$	1.84752	−	5.68609i	0.0881775	−	0.271382i	−0.897238	−	0.441547i	$-0.854430\pi$
$439$	1.84752	−	5.68609i	0.0881775	−	0.271382i	0.985416	+	0.170164i	$0.0544299\pi$
$440$		0			0
$441$	2.70820	+	8.33499i	0.128962	+	0.396905i
$442$	−1.85410	+	1.34708i	−0.0881906	+	0.0640742i
$443$	12.0557			0.572785			0.286392	−	0.958112i	$-0.407544\pi$
$443$	12.0557			0.572785			0.286392	+	0.958112i	$0.407544\pi$
$444$	5.54508	−	4.02874i	0.263158	−	0.191196i
$445$		0			0
$446$	−11.0902	−	8.05748i	−0.525135	−	0.381533i
$447$	−11.2812	−	8.19624i	−0.533580	−	0.387669i
$448$	0.118034	−	0.363271i	0.00557658	−	0.0171630i
$449$	20.3262			0.959254			0.479627	−	0.877472i	$-0.340772\pi$
$449$	20.3262			0.959254			0.479627	+	0.877472i	$0.340772\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−5.07295	+	15.6129i	−0.238611	+	0.734371i
$453$	4.50000	+	3.26944i	0.211428	+	0.153612i
$454$	−9.61803	−	6.98791i	−0.451397	−	0.327959i
$455$		0			0
$456$	−10.5902	+	7.69421i	−0.495930	+	0.360314i
$457$	5.41641			0.253369			0.126684	−	0.991943i	$-0.459566\pi$
$457$	5.41641			0.253369			0.126684	+	0.991943i	$0.459566\pi$
$458$	−4.14590	+	3.01217i	−0.193725	+	0.140750i
$459$	1.18034	+	3.63271i	0.0550935	+	0.169561i
$460$		0			0
$461$	7.16312	−	22.0458i	0.333620	−	1.02678i	−0.633778	−	0.773515i	$-0.718497\pi$
$461$	7.16312	−	22.0458i	0.333620	−	1.02678i	0.967398	−	0.253261i	$-0.0815032\pi$
$462$	0.236068	+	0.726543i	0.0109829	+	0.0338018i
$463$	4.98278	+	15.3354i	0.231569	+	0.712697i	0.997558	+	0.0698431i	$0.0222499\pi$
$463$	4.98278	+	15.3354i	0.231569	+	0.712697i	−0.765989	+	0.642854i	$0.777750\pi$
$464$	−0.791796	+	2.43690i	−0.0367582	+	0.113130i
$465$		0			0
$466$	2.85410	+	8.78402i	0.132214	+	0.406912i
$467$	23.0172	−	16.7230i	1.06511	−	0.773848i	0.0900830	−	0.995934i	$-0.471287\pi$
$467$	23.0172	−	16.7230i	1.06511	−	0.773848i	0.975027	+	0.222087i	$0.0712868\pi$
$468$	−15.7082			−0.726112
$469$	12.0902	−	8.78402i	0.558272	−	0.405608i
$470$		0			0
$471$	7.42705	+	5.39607i	0.342220	+	0.248638i
$472$	−7.50000	−	5.44907i	−0.345215	−	0.250814i
$473$	−0.437694	+	1.34708i	−0.0201252	+	0.0619390i
$474$	1.90983			0.0877214
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	−3.38197	+	10.4086i	−0.154850	+	0.476578i
$478$	14.7361	+	10.7064i	0.674012	+	0.489698i
$479$	3.35410	+	2.43690i	0.153253	+	0.111345i	0.661769	−	0.749708i	$-0.269806\pi$
$479$	3.35410	+	2.43690i	0.153253	+	0.111345i	−0.508516	+	0.861052i	$0.669806\pi$
$480$		0			0
$481$	16.6353	−	12.0862i	0.758502	−	0.551084i
$482$	7.09017			0.322948
$483$	10.7812	−	7.83297i	0.490559	−	0.356412i
$484$	5.20820	+	16.0292i	0.236737	+	0.728600i
$485$		0			0
$486$	3.05573	−	9.40456i	0.138611	−	0.426600i
$487$	−2.96149	−	9.11454i	−0.134198	−	0.413019i	0.861266	−	0.508154i	$-0.169672\pi$
$487$	−2.96149	−	9.11454i	−0.134198	−	0.413019i	−0.995464	+	0.0951346i	$0.969672\pi$
$488$	3.25329	+	10.0126i	0.147269	+	0.453249i
$489$	3.39919	−	10.4616i	0.153717	−	0.473091i
$490$		0			0
$491$	11.5106	+	35.4261i	0.519468	+	1.59876i	0.775002	+	0.631958i	$0.217749\pi$
$491$	11.5106	+	35.4261i	0.519468	+	1.59876i	−0.255534	+	0.966800i	$0.582251\pi$
$492$	−6.85410	+	4.97980i	−0.309007	+	0.224507i
$493$	1.05573			0.0475476
$494$	−14.2082	+	10.3229i	−0.639257	+	0.464448i
$495$		0			0
$496$	4.50000	+	3.26944i	0.202056	+	0.146802i
$497$	−5.73607	−	4.16750i	−0.257298	−	0.186938i
$498$	−0.336881	+	1.03681i	−0.0150960	+	0.0464607i
$499$	−12.5623			−0.562366			−0.281183	−	0.959654i	$-0.590727\pi$
$499$	−12.5623			−0.562366			−0.281183	+	0.959654i	$0.590727\pi$
$500$		0			0
$501$	−5.56231			−0.248506
$502$	−1.30244	+	4.00850i	−0.0581307	+	0.178908i
$503$	8.56231	+	6.22088i	0.381774	+	0.277375i	0.762076	−	0.647487i	$-0.224180\pi$
$503$	8.56231	+	6.22088i	0.381774	+	0.277375i	−0.380302	+	0.924862i	$0.624180\pi$
$504$	5.85410	+	4.25325i	0.260762	+	0.189455i
$505$		0			0
$506$	3.14590	−	2.28563i	0.139852	−	0.101609i
$507$	10.5623			0.469088
$508$	−20.7984	+	15.1109i	−0.922779	+	0.670438i
$509$	−1.44427	−	4.44501i	−0.0640162	−	0.197022i	0.913933	−	0.405866i	$-0.133030\pi$
$509$	−1.44427	−	4.44501i	−0.0640162	−	0.197022i	−0.977949	+	0.208844i	$0.933030\pi$
$510$		0			0
$511$	4.50000	−	13.8496i	0.199068	−	0.612669i
$512$	5.78115	+	17.7926i	0.255493	+	0.786327i
$513$	9.04508	+	27.8379i	0.399350	+	1.22907i
$514$	3.08359	−	9.49032i	0.136011	−	0.418600i
$515$		0			0
$516$	−0.927051	−	2.85317i	−0.0408111	−	0.125604i
$517$	−1.00000	+	0.726543i	−0.0439799	+	0.0319533i
$518$	−4.23607			−0.186122
$519$	13.6631	−	9.92684i	0.599744	−	0.435740i
$520$		0			0
$521$	12.4271	+	9.02878i	0.544439	+	0.395558i	0.825731	−	0.564064i	$-0.190763\pi$
$521$	12.4271	+	9.02878i	0.544439	+	0.395558i	−0.281292	+	0.959622i	$0.590763\pi$
$522$	−1.38197	−	1.00406i	−0.0604870	−	0.0439464i
$523$	−6.13525	+	18.8824i	−0.268276	+	0.825669i	0.722645	+	0.691220i	$0.242926\pi$
$523$	−6.13525	+	18.8824i	−0.268276	+	0.825669i	−0.990921	+	0.134449i	$0.957074\pi$
$524$	28.7984			1.25806
$525$		0			0
$526$	−13.6525			−0.595276
$527$	0.708204	−	2.17963i	0.0308498	−	0.0949461i
$528$	1.14590	+	0.832544i	0.0498688	+	0.0362318i
$529$	−36.2705	−	26.3521i	−1.57698	−	1.14574i
$530$		0			0
$531$	−6.70820	+	4.87380i	−0.291111	+	0.211505i
$532$	−15.3262			−0.664477
$533$	−20.5623	+	14.9394i	−0.890652	+	0.647097i
$534$	1.70820	+	5.25731i	0.0739212	+	0.227506i
$535$		0			0
$536$	−6.38197	+	19.6417i	−0.275659	+	0.848391i
$537$	−2.92705	−	9.00854i	−0.126312	−	0.388747i
$538$	−3.29180	−	10.1311i	−0.141919	−	0.436783i
$539$	1.03444	−	3.18368i	0.0445566	−	0.137131i
$540$		0			0
$541$	−4.05573	−	12.4822i	−0.174369	−	0.536654i	0.825235	−	0.564790i	$-0.191043\pi$
$541$	−4.05573	−	12.4822i	−0.174369	−	0.536654i	−0.999604	+	0.0281362i	$0.991043\pi$
$542$	4.00000	−	2.90617i	0.171815	−	0.124831i
$543$	13.7082			0.588275
$544$	3.47214	−	2.52265i	0.148867	−	0.108158i
$545$		0			0
$546$	−3.92705	−	2.85317i	−0.168062	−	0.122104i
$547$	28.0795	+	20.4010i	1.20059	+	0.872283i	0.994343	−	0.106217i	$-0.0338737\pi$
$547$	28.0795	+	20.4010i	1.20059	+	0.872283i	0.206251	+	0.978499i	$0.433874\pi$
$548$	−2.97214	+	9.14729i	−0.126963	+	0.390753i
$549$	9.41641			0.401882
$550$		0			0
$551$	8.09017			0.344653
$552$	−5.69098	+	17.5150i	−0.242224	+	0.745490i
$553$	4.04508	+	2.93893i	0.172015	+	0.124976i
$554$	5.64590	+	4.10199i	0.239871	+	0.174277i
$555$		0			0
$556$	6.54508	−	4.75528i	0.277573	−	0.201669i
$557$	9.23607			0.391345			0.195672	−	0.980669i	$-0.437311\pi$
$557$	9.23607			0.391345			0.195672	+	0.980669i	$0.437311\pi$
$558$	−3.00000	+	2.17963i	−0.127000	+	0.0922710i
$559$	−2.78115	−	8.55951i	−0.117630	−	0.362029i
$560$		0			0
$561$	0.180340	−	0.555029i	0.00761396	−	0.0234333i
$562$	−0.208204	−	0.640786i	−0.00878255	−	0.0270299i
$563$	2.97214	+	9.14729i	0.125261	+	0.385512i	0.993948	−	0.109847i	$-0.0350362\pi$
$563$	2.97214	+	9.14729i	0.125261	+	0.385512i	−0.868688	+	0.495360i	$0.835036\pi$
$564$	0.809017	−	2.48990i	0.0340658	−	0.104844i
$565$		0			0
$566$	−4.42047	−	13.6048i	−0.185806	−	0.571853i
$567$	1.30902	−	0.951057i	0.0549735	−	0.0399406i
$568$	9.79837			0.411131
$569$	−23.8435	+	17.3233i	−0.999570	+	0.726230i	−0.961996	−	0.273064i	$-0.911963\pi$
$569$	−23.8435	+	17.3233i	−0.999570	+	0.726230i	−0.0375739	+	0.999294i	$0.511963\pi$
$570$		0			0
$571$	−25.9894	−	18.8824i	−1.08762	−	0.790203i	−0.108625	−	0.994083i	$-0.534645\pi$
$571$	−25.9894	−	18.8824i	−1.08762	−	0.790203i	−0.978996	+	0.203880i	$0.934645\pi$
$572$	4.85410	+	3.52671i	0.202960	+	0.147459i
$573$	−7.47214	+	22.9969i	−0.312153	+	0.960708i
$574$	5.23607			0.218549
$575$		0			0
$576$	0.472136			0.0196723
$577$	11.6738	−	35.9281i	0.485985	−	1.49571i	−0.344564	−	0.938763i	$-0.611973\pi$
$577$	11.6738	−	35.9281i	0.485985	−	1.49571i	0.830549	−	0.556945i	$-0.188027\pi$
$578$	8.20820	+	5.96361i	0.341416	+	0.248053i
$579$	4.61803	+	3.35520i	0.191919	+	0.139437i
$580$		0			0
$581$	−2.30902	+	1.67760i	−0.0957942	+	0.0695985i
$582$	1.76393			0.0731173
$583$	3.38197	−	2.45714i	0.140067	−	0.101764i
$584$	6.21885	+	19.1396i	0.257338	+	0.792004i
$585$		0			0
$586$	−5.43769	+	16.7355i	−0.224629	+	0.691337i
$587$	5.78115	+	17.7926i	0.238614	+	0.734378i	0.996621	+	0.0821320i	$0.0261729\pi$
$587$	5.78115	+	17.7926i	0.238614	+	0.734378i	−0.758008	+	0.652246i	$0.773827\pi$
$588$	2.19098	+	6.74315i	0.0903546	+	0.278083i
$589$	5.42705	−	16.7027i	0.223618	−	0.688225i
$590$		0			0
$591$	−3.00000	−	9.23305i	−0.123404	−	0.379797i
$592$	−6.35410	+	4.61653i	−0.261152	+	0.189738i
$593$	−22.0902			−0.907135			−0.453567	−	0.891222i	$-0.649849\pi$
$593$	−22.0902			−0.907135			−0.453567	+	0.891222i	$0.649849\pi$
$594$	−1.90983	+	1.38757i	−0.0783613	+	0.0569328i
$595$		0			0
$596$	18.2533	+	13.2618i	0.747684	+	0.543224i
$597$	−2.07295	−	1.50609i	−0.0848402	−	0.0616400i
$598$	−7.63525	+	23.4989i	−0.312229	+	0.960941i
$599$	−0.527864			−0.0215679			−0.0107840	−	0.999942i	$-0.503433\pi$
$599$	−0.527864			−0.0215679			−0.0107840	+	0.999942i	$0.503433\pi$
$600$		0			0
$601$	36.2705			1.47950			0.739752	−	0.672879i	$-0.234943\pi$
$601$	36.2705			1.47950			0.739752	+	0.672879i	$0.234943\pi$
$602$	−0.572949	+	1.76336i	−0.0233517	+	0.0718690i
$603$	14.9443	+	10.8576i	0.608578	+	0.442158i
$604$	−7.28115	−	5.29007i	−0.296266	−	0.215250i
$605$		0			0
$606$	3.73607	−	2.71441i	0.151767	−	0.110265i
$607$	−15.4377			−0.626597			−0.313298	−	0.949655i	$-0.601434\pi$
$607$	−15.4377			−0.626597			−0.313298	+	0.949655i	$0.601434\pi$
$608$	26.6074	−	19.3314i	1.07907	−	0.783992i
$609$	0.690983	+	2.12663i	0.0280000	+	0.0861753i
$610$		0			0
$611$	2.42705	−	7.46969i	0.0981880	−	0.302192i
$612$	−0.763932	−	2.35114i	−0.0308801	−	0.0950392i
$613$	9.88197	+	30.4136i	0.399129	+	1.22839i	0.925699	+	0.378261i	$0.123478\pi$
$613$	9.88197	+	30.4136i	0.399129	+	1.22839i	−0.526570	+	0.850132i	$0.676522\pi$
$614$	0.909830	−	2.80017i	0.0367178	−	0.113006i
$615$		0			0
$616$	−0.854102	−	2.62866i	−0.0344127	−	0.105912i
$617$	−7.89919	+	5.73910i	−0.318009	+	0.231047i	−0.735326	−	0.677714i	$-0.762971\pi$
$617$	−7.89919	+	5.73910i	−0.318009	+	0.231047i	0.417316	+	0.908761i	$0.362971\pi$
$618$	−7.14590			−0.287450
$619$	−31.9336	+	23.2011i	−1.28352	+	0.932533i	−0.999653	−	0.0263310i	$-0.991618\pi$
$619$	−31.9336	+	23.2011i	−1.28352	+	0.932533i	−0.283868	+	0.958863i	$0.591618\pi$
$620$		0			0
$621$	33.3156	+	24.2052i	1.33691	+	0.971321i
$622$	14.7533	+	10.7189i	0.591553	+	0.429788i
$623$	−4.47214	+	13.7638i	−0.179172	+	0.551436i
$624$	−9.00000			−0.360288
$625$		0			0
$626$	−13.1246			−0.524565
$627$	1.38197	−	4.25325i	0.0551904	−	0.169859i
$628$	−12.0172	−	8.73102i	−0.479539	−	0.348406i
$629$	2.61803	+	1.90211i	0.104388	+	0.0758422i
$630$		0			0
$631$	4.66312	−	3.38795i	0.185636	−	0.134872i	−0.491086	−	0.871111i	$-0.663400\pi$
$631$	4.66312	−	3.38795i	0.185636	−	0.134872i	0.676722	+	0.736239i	$0.263400\pi$
$632$	−6.90983			−0.274858
$633$	−10.6631	+	7.74721i	−0.423821	+	0.307924i
$634$	−4.51722	−	13.9026i	−0.179402	−	0.552142i
$635$		0			0
$636$	−2.73607	+	8.42075i	−0.108492	+	0.333905i
$637$	6.57295	+	20.2295i	0.260430	+	0.801520i
$638$	0.201626	+	0.620541i	0.00798245	+	0.0245675i
$639$	2.70820	−	8.33499i	0.107135	−	0.329727i
$640$		0			0
$641$	3.11803	+	9.59632i	0.123155	+	0.379032i	0.993560	−	0.113304i	$-0.0361433\pi$
$641$	3.11803	+	9.59632i	0.123155	+	0.379032i	−0.870405	+	0.492336i	$0.836143\pi$
$642$	−5.20820	+	3.78398i	−0.205551	+	0.149342i
$643$	22.8328			0.900438			0.450219	−	0.892918i	$-0.351346\pi$
$643$	22.8328			0.900438			0.450219	+	0.892918i	$0.351346\pi$
$644$	−17.4443	+	12.6740i	−0.687401	+	0.499426i
$645$		0			0
$646$	−2.23607	−	1.62460i	−0.0879769	−	0.0639190i
$647$	−24.7082	−	17.9516i	−0.971380	−	0.705749i	−0.0156141	−	0.999878i	$-0.504970\pi$
$647$	−24.7082	−	17.9516i	−0.971380	−	0.705749i	−0.955766	+	0.294129i	$0.904970\pi$
$648$	−0.690983	+	2.12663i	−0.0271444	+	0.0835418i
$649$	3.16718			0.124323
$650$		0			0
$651$	4.85410			0.190247
$652$	−5.50000	+	16.9273i	−0.215397	+	0.662923i
$653$	−6.39919	−	4.64928i	−0.250420	−	0.181940i	0.455493	−	0.890239i	$-0.349463\pi$
$653$	−6.39919	−	4.64928i	−0.250420	−	0.181940i	−0.705913	+	0.708299i	$0.749463\pi$
$654$	−5.00000	−	3.63271i	−0.195515	−	0.142050i
$655$		0			0
$656$	7.85410	−	5.70634i	0.306651	−	0.222795i
$657$	18.0000			0.702247
$658$	−1.30902	+	0.951057i	−0.0510308	+	0.0370760i
$659$	7.56231	+	23.2744i	0.294586	+	0.906641i	0.983360	+	0.181666i	$0.0581489\pi$
$659$	7.56231	+	23.2744i	0.294586	+	0.906641i	−0.688775	+	0.724975i	$0.741851\pi$
$660$		0			0
$661$	−12.5729	+	38.6956i	−0.489031	+	1.50508i	0.337025	+	0.941496i	$0.390579\pi$
$661$	−12.5729	+	38.6956i	−0.489031	+	1.50508i	−0.826057	+	0.563587i	$0.809421\pi$
$662$	3.27051	+	10.0656i	0.127112	+	0.391210i
$663$	1.14590	+	3.52671i	0.0445030	+	0.136966i
$664$	1.21885	−	3.75123i	0.0473004	−	0.145576i
$665$		0			0
$666$	−1.61803	−	4.97980i	−0.0626975	−	0.192963i
$667$	9.20820	−	6.69015i	0.356543	−	0.259044i
$668$	9.00000			0.348220
$669$	−17.9443	+	13.0373i	−0.693766	+	0.504050i
$670$		0			0
$671$	−2.90983	−	2.11412i	−0.112333	−	0.0816145i
$672$	7.35410	+	5.34307i	0.283691	+	0.206113i
$673$	−3.14590	+	9.68208i	−0.121265	+	0.373217i	−0.993202	−	0.116402i	$-0.962864\pi$
$673$	−3.14590	+	9.68208i	−0.121265	+	0.373217i	0.871937	+	0.489619i	$0.162864\pi$
$674$	0.708204			0.0272790
$675$		0			0
$676$	−17.0902			−0.657314
$677$	2.59017	−	7.97172i	0.0995483	−	0.306378i	−0.888864	−	0.458171i	$-0.848505\pi$
$677$	2.59017	−	7.97172i	0.0995483	−	0.306378i	0.988412	+	0.151793i	$0.0485047\pi$
$678$	−5.07295	−	3.68571i	−0.194825	−	0.141549i
$679$	3.73607	+	2.71441i	0.143377	+	0.104170i
$680$		0			0
$681$	−15.5623	+	11.3067i	−0.596349	+	0.433273i
$682$	1.41641			0.0542371
$683$	3.66312	−	2.66141i	0.140165	−	0.101836i	−0.515493	−	0.856894i	$-0.672391\pi$
$683$	3.66312	−	2.66141i	0.140165	−	0.101836i	0.655658	+	0.755058i	$0.272391\pi$
$684$	−5.85410	−	18.0171i	−0.223837	−	0.688900i
$685$		0			0
$686$	3.51722	−	10.8249i	0.134288	−	0.413296i
$687$	2.56231	+	7.88597i	0.0977581	+	0.300868i
$688$	1.06231	+	3.26944i	0.0405000	+	0.124646i
$689$	−8.20820	+	25.2623i	−0.312708	+	0.962415i
$690$		0			0
$691$	0.843459	+	2.59590i	0.0320867	+	0.0987527i	0.965817	−	0.259224i	$-0.0834668\pi$
$691$	0.843459	+	2.59590i	0.0320867	+	0.0987527i	−0.933731	+	0.357977i	$0.883467\pi$
$692$	−22.1074	+	16.0620i	−0.840397	+	0.610584i
$693$	−2.47214			−0.0939087
$694$	15.5451	−	11.2942i	0.590083	−	0.428721i
$695$		0			0
$696$	−2.50000	−	1.81636i	−0.0947623	−	0.0688488i
$697$	−3.23607	−	2.35114i	−0.122575	−	0.0890558i
$698$	1.58359	−	4.87380i	0.0599398	−	0.184476i
$699$	14.9443			0.565244
$700$		0			0
$701$	35.0132			1.32243			0.661214	−	0.750197i	$-0.270041\pi$
$701$	35.0132			1.32243			0.661214	+	0.750197i	$0.270041\pi$
$702$	4.63525	−	14.2658i	0.174946	−	0.538430i
$703$	20.0623	+	14.5761i	0.756664	+	0.549749i
$704$	−0.145898	−	0.106001i	−0.00549874	−	0.00399507i
$705$		0			0
$706$	−12.0451	+	8.75127i	−0.453323	+	0.329358i
$707$	12.0902			0.454698
$708$	−5.42705	+	3.94298i	−0.203961	+	0.148186i
$709$	10.3647	+	31.8994i	0.389256	+	1.19801i	0.933345	+	0.358980i	$0.116875\pi$
$709$	10.3647	+	31.8994i	0.389256	+	1.19801i	−0.544089	+	0.839027i	$0.683125\pi$
$710$		0			0
$711$	−1.90983	+	5.87785i	−0.0716242	+	0.220437i
$712$	−6.18034	−	19.0211i	−0.231618	−	0.712847i
$713$	−7.63525	−	23.4989i	−0.285943	−	0.880041i
$714$	0.236068	−	0.726543i	0.00883462	−	0.0271902i
$715$		0			0
$716$	4.73607	+	14.5761i	0.176995	+	0.544735i
$717$	23.8435	−	17.3233i	0.890450	−	0.646950i
$718$	−17.7639			−0.662944
$719$	29.6976	−	21.5765i	1.10753	−	0.804669i	0.125259	−	0.992124i	$-0.460024\pi$
$719$	29.6976	−	21.5765i	1.10753	−	0.804669i	0.982273	+	0.187455i	$0.0600238\pi$
$720$		0			0
$721$	−15.1353	−	10.9964i	−0.563666	−	0.409528i
$722$	−7.63525	−	5.54734i	−0.284155	−	0.206451i
$723$	3.54508	−	10.9106i	0.131843	−	0.405771i
$724$	−22.1803			−0.824326
$725$		0			0
$726$	−6.43769			−0.238925
$727$	1.37132	−	4.22050i	0.0508596	−	0.156530i	−0.922401	−	0.386234i	$-0.873776\pi$
$727$	1.37132	−	4.22050i	0.0508596	−	0.156530i	0.973261	+	0.229704i	$0.0737758\pi$
$728$	14.2082	+	10.3229i	0.526591	+	0.382591i
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$		0			0
$731$	1.14590	−	0.832544i	0.0423826	−	0.0307927i
$732$	7.61803			0.281571
$733$	−21.8262	+	15.8577i	−0.806170	+	0.585717i	−0.912718	−	0.408590i	$-0.866020\pi$
$733$	−21.8262	+	15.8577i	−0.806170	+	0.585717i	0.106547	+	0.994308i	$0.466020\pi$
$734$	−1.03851	−	3.19620i	−0.0383320	−	0.117974i
$735$		0			0
$736$	14.2984	−	44.0059i	0.527045	−	1.62208i
$737$	−2.18034	−	6.71040i	−0.0803139	−	0.247181i
$738$	2.00000	+	6.15537i	0.0736210	+	0.226582i
$739$	−9.57295	+	29.4625i	−0.352147	+	1.08380i	0.605499	+	0.795846i	$0.292974\pi$
$739$	−9.57295	+	29.4625i	−0.352147	+	1.08380i	−0.957646	+	0.287950i	$0.907026\pi$
$740$		0			0
$741$	8.78115	+	27.0256i	0.322584	+	0.992811i
$742$	4.42705	−	3.21644i	0.162522	−	0.118079i
$743$	−16.3607			−0.600215			−0.300108	−	0.953905i	$-0.597023\pi$
$743$	−16.3607			−0.600215			−0.300108	+	0.953905i	$0.597023\pi$
$744$	−5.42705	+	3.94298i	−0.198965	+	0.144557i
$745$		0			0
$746$	−2.63525	−	1.91462i	−0.0964835	−	0.0700994i
$747$	−2.85410	−	2.07363i	−0.104426	−	0.0758700i
$748$	−0.291796	+	0.898056i	−0.0106691	+	0.0328362i
$749$	−16.8541			−0.615835
$750$		0			0
$751$	−40.8885			−1.49204			−0.746022	−	0.665921i	$-0.768039\pi$
$751$	−40.8885			−1.49204			−0.746022	+	0.665921i	$0.768039\pi$
$752$	−0.927051	+	2.85317i	−0.0338061	+	0.104044i
$753$	5.51722	+	4.00850i	0.201059	+	0.146078i
$754$	−3.35410	−	2.43690i	−0.122149	−	0.0887466i
$755$		0			0
$756$	10.5902	−	7.69421i	0.385161	−	0.279836i
$757$	3.58359			0.130248			0.0651239	−	0.997877i	$-0.479256\pi$
$757$	3.58359			0.130248			0.0651239	+	0.997877i	$0.479256\pi$
$758$	17.2984	−	12.5680i	0.628305	−	0.456490i
$759$	−1.94427	−	5.98385i	−0.0705726	−	0.217200i
$760$		0			0
$761$	11.5729	−	35.6179i	0.419519	−	1.29115i	−0.488627	−	0.872493i	$-0.662502\pi$
$761$	11.5729	−	35.6179i	0.419519	−	1.29115i	0.908146	−	0.418654i	$-0.137498\pi$
$762$	−3.03444	−	9.33905i	−0.109926	−	0.338318i
$763$	−5.00000	−	15.3884i	−0.181012	−	0.557098i
$764$	12.0902	−	37.2097i	0.437407	−	1.34620i
$765$		0			0
$766$	−2.16970	−	6.67764i	−0.0783943	−	0.241273i
$767$	−16.2812	+	11.8290i	−0.587878	+	0.427119i
$768$	−6.56231			−0.236797
$769$	10.8541	−	7.88597i	0.391409	−	0.284375i	−0.374624	−	0.927177i	$-0.622228\pi$
$769$	10.8541	−	7.88597i	0.391409	−	0.284375i	0.766033	+	0.642802i	$0.222228\pi$
$770$		0			0
$771$	−13.0623	−	9.49032i	−0.470427	−	0.341786i
$772$	−7.47214	−	5.42882i	−0.268928	−	0.195388i
$773$	10.2467	−	31.5361i	0.368549	−	1.13428i	−0.579180	−	0.815199i	$-0.696627\pi$
$773$	10.2467	−	31.5361i	0.368549	−	1.13428i	0.947729	−	0.319076i	$-0.103373\pi$
$774$	−2.29180			−0.0823769
$775$		0			0
$776$	−6.38197			−0.229099
$777$	−2.11803	+	6.51864i	−0.0759840	+	0.233855i
$778$	−7.50000	−	5.44907i	−0.268888	−	0.195359i
$779$	−24.7984	−	18.0171i	−0.888494	−	0.645529i
$780$		0			0
$781$	−2.70820	+	1.96763i	−0.0969072	+	0.0704072i
$782$	−3.88854			−0.139054
$783$	−5.59017	+	4.06150i	−0.199776	+	0.145146i
$784$	−2.51064	−	7.72696i	−0.0896658	−	0.275963i
$785$		0			0
$786$	−3.39919	+	10.4616i	−0.121245	+	0.373154i
$787$	−10.5623	−	32.5074i	−0.376506	−	1.15876i	−0.942457	−	0.334327i	$-0.891491\pi$
$787$	−10.5623	−	32.5074i	−0.376506	−	1.15876i	0.565952	−	0.824438i	$-0.308509\pi$
$788$	4.85410	+	14.9394i	0.172920	+	0.532194i
$789$	−6.82624	+	21.0090i	−0.243021	+	0.747940i
$790$		0			0
$791$	−5.07295	−	15.6129i	−0.180373	−	0.555132i
$792$	2.76393	−	2.00811i	0.0982120	−	0.0713552i
$793$	22.8541			0.811573
$794$	0.0172209	−	0.0125117i	0.000611148	−	0.000444025i
$795$		0			0
$796$	3.35410	+	2.43690i	0.118883	+	0.0863735i
$797$	−11.5172	−	8.36775i	−0.407961	−	0.296401i	0.364815	−	0.931080i	$-0.381132\pi$
$797$	−11.5172	−	8.36775i	−0.407961	−	0.296401i	−0.772776	+	0.634679i	$0.781132\pi$
$798$	1.80902	−	5.56758i	0.0640385	−	0.197090i
$799$	1.23607			0.0437289
$800$		0			0
$801$	−17.8885			−0.632061
$802$	−4.31559	+	13.2820i	−0.152389	+	0.469005i
$803$	−5.56231	−	4.04125i	−0.196290	−	0.142613i
$804$	12.0902	+	8.78402i	0.426387	+	0.309789i
$805$		0			0
$806$	−7.28115	+	5.29007i	−0.256468	+	0.186335i
$807$	−17.2361			−0.606738
$808$	−13.5172	+	9.82084i	−0.475534	+	0.345496i
$809$	−4.93769	−	15.1967i	−0.173600	−	0.534286i	0.825967	−	0.563719i	$-0.190630\pi$
$809$	−4.93769	−	15.1967i	−0.173600	−	0.534286i	−0.999567	+	0.0294328i	$0.990630\pi$
$810$		0			0
$811$	−0.399187	+	1.22857i	−0.0140173	+	0.0431410i	−0.957821	−	0.287367i	$-0.907220\pi$
$811$	−0.399187	+	1.22857i	−0.0140173	+	0.0431410i	0.943803	+	0.330508i	$0.107220\pi$
$812$	−1.11803	−	3.44095i	−0.0392353	−	0.120754i
$813$	−2.47214	−	7.60845i	−0.0867016	−	0.266840i
$814$	−0.618034	+	1.90211i	−0.0216621	+	0.0666690i
$815$		0			0
$816$	−0.437694	−	1.34708i	−0.0153224	−	0.0471574i
$817$	8.78115	−	6.37988i	0.307214	−	0.223204i
$818$	17.5623			0.614052
$819$	12.7082	−	9.23305i	0.444061	−	0.322629i
$820$		0			0
$821$	−15.9271	−	11.5717i	−0.555858	−	0.403854i	0.274083	−	0.961706i	$-0.411626\pi$
$821$	−15.9271	−	11.5717i	−0.555858	−	0.403854i	−0.829941	+	0.557852i	$0.811626\pi$
$822$	−2.97214	−	2.15938i	−0.103665	−	0.0753171i
$823$	10.5967	−	32.6134i	0.369379	−	1.13683i	−0.577814	−	0.816169i	$-0.696094\pi$
$823$	10.5967	−	32.6134i	0.369379	−	1.13683i	0.947193	−	0.320664i	$-0.103906\pi$
$824$	25.8541			0.900670
$825$		0			0
$826$	4.14590			0.144254
$827$	−9.28115	+	28.5645i	−0.322737	+	0.993283i	0.649714	+	0.760178i	$0.274889\pi$
$827$	−9.28115	+	28.5645i	−0.322737	+	0.993283i	−0.972452	+	0.233105i	$0.925111\pi$
$828$	−21.5623	−	15.6659i	−0.749342	−	0.544429i
$829$	23.5795	+	17.1315i	0.818951	+	0.595003i	0.916412	−	0.400237i	$-0.131072\pi$
$829$	23.5795	+	17.1315i	0.818951	+	0.595003i	−0.0974610	+	0.995239i	$0.531072\pi$
$830$		0			0
$831$	9.13525	−	6.63715i	0.316898	−	0.230240i
$832$	1.14590			0.0397269
$833$	−2.70820	+	1.96763i	−0.0938337	+	0.0681742i
$834$	0.954915	+	2.93893i	0.0330660	+	0.101767i
$835$		0			0
$836$	−2.23607	+	6.88191i	−0.0773360	+	0.238016i
$837$	4.63525	+	14.2658i	0.160218	+	0.493100i
$838$	−0.100813	−	0.310271i	−0.00348253	−	0.0107181i
$839$	1.28115	−	3.94298i	0.0442303	−	0.136127i	−0.926503	−	0.376288i	$-0.877200\pi$
$839$	1.28115	−	3.94298i	0.0442303	−	0.136127i	0.970733	+	0.240161i	$0.0772003\pi$
$840$		0			0
$841$	−8.37132	−	25.7643i	−0.288666	−	0.888424i
$842$	−16.0000	+	11.6247i	−0.551396	+	0.400613i
$843$	−1.09017			−0.0375474
$844$	17.2533	−	12.5352i	0.593883	−	0.431481i
$845$		0			0
$846$	−1.61803	−	1.17557i	−0.0556292	−	0.0404169i
$847$	−13.6353	−	9.90659i	−0.468513	−	0.340395i
$848$	3.13525	−	9.64932i	0.107665	−	0.331359i
$849$	−23.1459			−0.794365
$850$		0			0
$851$	34.8885			1.19596
$852$	2.19098	−	6.74315i	0.0750618	−	0.231017i
$853$	−38.2705	−	27.8052i	−1.31036	−	0.952030i	−0.999999	−	0.00141065i	$-0.999551\pi$
$853$	−38.2705	−	27.8052i	−1.31036	−	0.952030i	−0.310358	−	0.950620i	$-0.600449\pi$
$854$	−3.80902	−	2.76741i	−0.130342	−	0.0946989i
$855$		0			0
$856$	18.8435	−	13.6906i	0.644056	−	0.467934i
$857$	−40.6869			−1.38984			−0.694919	−	0.719088i	$-0.744560\pi$
$857$	−40.6869			−1.38984			−0.694919	+	0.719088i	$0.744560\pi$
$858$	−1.85410	+	1.34708i	−0.0632980	+	0.0459887i
$859$	−8.78115	−	27.0256i	−0.299609	−	0.922102i	−0.981634	−	0.190773i	$-0.938901\pi$
$859$	−8.78115	−	27.0256i	−0.299609	−	0.922102i	0.682025	−	0.731329i	$-0.261099\pi$
$860$		0			0
$861$	2.61803	−	8.05748i	0.0892224	−	0.274598i
$862$	4.55166	+	14.0086i	0.155030	+	0.477134i
$863$	−12.8435	−	39.5281i	−0.437196	−	1.34555i	−0.890819	−	0.454358i	$-0.849869\pi$
$863$	−12.8435	−	39.5281i	−0.437196	−	1.34555i	0.453623	−	0.891194i	$-0.350131\pi$
$864$	−8.68034	+	26.7153i	−0.295311	+	0.908874i
$865$		0			0
$866$	3.84752	+	11.8415i	0.130744	+	0.402389i
$867$	13.2812	−	9.64932i	0.451052	−	0.327708i
$868$	−7.85410			−0.266586
$869$	1.90983	−	1.38757i	0.0647865	−	0.0470702i
$870$		0			0
$871$	36.2705	+	26.3521i	1.22898	+	0.892906i
$872$	18.0902	+	13.1433i	0.612610	+	0.445088i
$873$	−1.76393	+	5.42882i	−0.0597001	+	0.183738i
$874$	−29.7984			−1.00795
$875$		0			0
$876$	14.5623			0.492015
$877$	9.43769	−	29.0462i	0.318688	−	0.980822i	−0.655521	−	0.755177i	$-0.727551\pi$
$877$	9.43769	−	29.0462i	0.318688	−	0.980822i	0.974210	−	0.225645i	$-0.0724489\pi$
$878$	−2.98936	−	2.17189i	−0.100886	−	0.0732979i
$879$	23.0344	+	16.7355i	0.776932	+	0.564474i
$880$		0			0
$881$	−3.52786	+	2.56314i	−0.118857	+	0.0863545i	−0.645626	−	0.763654i	$-0.723403\pi$
$881$	−3.52786	+	2.56314i	−0.118857	+	0.0863545i	0.526769	+	0.850009i	$0.323403\pi$
$882$	5.41641			0.182380
$883$	38.3607	−	27.8707i	1.29094	−	0.937923i	0.291116	−	0.956688i	$-0.405974\pi$
$883$	38.3607	−	27.8707i	1.29094	−	0.937923i	0.999824	+	0.0187653i	$0.00597352\pi$
$884$	−1.85410	−	5.70634i	−0.0623602	−	0.191925i
$885$		0			0
$886$	2.30244	−	7.08618i	0.0773520	−	0.238065i
$887$	−1.81966	−	5.60034i	−0.0610982	−	0.188041i	0.915849	−	0.401524i	$-0.131519\pi$
$887$	−1.81966	−	5.60034i	−0.0610982	−	0.188041i	−0.976947	+	0.213483i	$0.931519\pi$
$888$	−2.92705	−	9.00854i	−0.0982254	−	0.302307i
$889$	7.94427	−	24.4500i	0.266442	−	0.820025i
$890$		0			0
$891$	−0.236068	−	0.726543i	−0.00790857	−	0.0243401i
$892$	29.0344	−	21.0948i	0.972145	−	0.706305i
$893$	9.47214			0.316973
$894$	−6.97214	+	5.06555i	−0.233183	+	0.169417i
$895$		0			0
$896$	−14.8992	−	10.8249i	−0.497747	−	0.361634i
$897$	32.3435	+	23.4989i	1.07992	+	0.784605i
$898$	3.88197	−	11.9475i	0.129543	−	0.398692i
$899$	4.14590			0.138273
$900$		0			0
$901$	−4.18034			−0.139267
$902$	0.763932	−	2.35114i	0.0254362	−	0.0782844i
$903$	2.42705	+	1.76336i	0.0807672	+	0.0586808i
$904$	18.3541	+	13.3350i	0.610448	+	0.443517i
$905$		0			0
$906$	2.78115	−	2.02063i	0.0923976	−	0.0671308i
$907$	47.2492			1.56888			0.784442	−	0.620202i	$-0.212949\pi$
$907$	47.2492			1.56888			0.784442	+	0.620202i	$0.212949\pi$
$908$	25.1803	−	18.2946i	0.835639	−	0.607127i
$909$	4.61803	+	14.2128i	0.153171	+	0.471410i
$910$		0			0
$911$	−11.0517	+	34.0135i	−0.366158	+	1.12692i	0.583095	+	0.812404i	$0.301842\pi$
$911$	−11.0517	+	34.0135i	−0.366158	+	1.12692i	−0.949253	+	0.314514i	$0.898158\pi$
$912$	−3.35410	−	10.3229i	−0.111065	−	0.341824i
$913$	0.416408	+	1.28157i	0.0137811	+	0.0424138i
$914$	1.03444	−	3.18368i	0.0342163	−	0.105307i
$915$		0			0
$916$	−4.14590	−	12.7598i	−0.136984	−	0.421594i
$917$	−23.2984	+	16.9273i	−0.769380	+	0.558987i
$918$	2.36068			0.0779140
$919$	1.44427	−	1.04932i	0.0476421	−	0.0346140i	−0.563709	−	0.825973i	$-0.690626\pi$
$919$	1.44427	−	1.04932i	0.0476421	−	0.0346140i	0.611351	+	0.791359i	$0.290626\pi$
$920$		0			0
$921$	−3.85410	−	2.80017i	−0.126997	−	0.0922687i
$922$	−11.5902	−	8.42075i	−0.381702	−	0.277323i
$923$	6.57295	−	20.2295i	0.216351	−	0.665861i
$924$	−2.00000			−0.0657952
$925$		0			0
$926$	9.96556			0.327489
$927$	7.14590	−	21.9928i	0.234702	−	0.722339i
$928$	6.28115	+	4.56352i	0.206189	+	0.149805i
$929$	29.6353	+	21.5313i	0.972301	+	0.706418i	0.955975	−	0.293449i	$-0.0948029\pi$
$929$	29.6353	+	21.5313i	0.972301	+	0.706418i	0.0163263	+	0.999867i	$0.494803\pi$
$930$		0			0
$931$	−20.7533	+	15.0781i	−0.680162	+	0.494166i
$932$	−24.1803			−0.792053
$933$	23.8713	−	17.3435i	0.781512	−	0.567802i
$934$	−5.43363	−	16.7230i	−0.177794	−	0.547193i
$935$		0			0
$936$	−6.70820	+	20.6457i	−0.219265	+	0.674827i
$937$	15.8435	+	48.7612i	0.517583	+	1.59296i	0.778532	+	0.627605i	$0.215965\pi$
$937$	15.8435	+	48.7612i	0.517583	+	1.59296i	−0.260949	+	0.965353i	$0.584035\pi$
$938$	−2.85410	−	8.78402i	−0.0931897	−	0.286809i
$939$	−6.56231	+	20.1967i	−0.214153	+	0.659094i
$940$		0			0
$941$	−6.05166	−	18.6251i	−0.197279	−	0.607161i	−0.999942	−	0.0107294i	$-0.996585\pi$
$941$	−6.05166	−	18.6251i	−0.197279	−	0.607161i	0.802664	−	0.596432i	$-0.203415\pi$
$942$	4.59017	−	3.33495i	0.149556	−	0.108659i
$943$	−43.1246			−1.40433
$944$	6.21885	−	4.51826i	0.202406	−	0.147057i
$945$		0			0
$946$	0.708204	+	0.514540i	0.0230257	+	0.0167291i
$947$	23.1803	+	16.8415i	0.753260	+	0.547275i	0.896836	−	0.442364i	$-0.145860\pi$
$947$	23.1803	+	16.8415i	0.753260	+	0.547275i	−0.143576	+	0.989639i	$0.545860\pi$
$948$	−1.54508	+	4.75528i	−0.0501820	+	0.154444i
$949$	43.6869			1.41814
$950$		0			0
$951$	−23.6525			−0.766984
$952$	−0.854102	+	2.62866i	−0.0276816	+	0.0851952i
$953$	−28.1074	−	20.4212i	−0.910488	−	0.661508i	0.0306505	−	0.999530i	$-0.490242\pi$
$953$	−28.1074	−	20.4212i	−0.910488	−	0.661508i	−0.941138	+	0.338022i	$0.890242\pi$
$954$	5.47214	+	3.97574i	0.177167	+	0.128719i
$955$		0			0
$956$	−38.5795	+	28.0297i	−1.24775	+	0.906544i
$957$	1.05573			0.0341268
$958$	2.07295	−	1.50609i	0.0669739	−	0.0486594i
$959$	−2.97214	−	9.14729i	−0.0959753	−	0.295382i
$960$		0			0
$961$	−6.79837	+	20.9232i	−0.219302	+	0.674943i
$962$	−3.92705	−	12.0862i	−0.126613	−	0.389675i
$963$	−6.43769	−	19.8132i	−0.207452	−	0.638471i
$964$	−5.73607	+	17.6538i	−0.184746	+	0.568591i
$965$		0			0
$966$	−2.54508	−	7.83297i	−0.0818868	−	0.252022i
$967$	−32.2705	+	23.4459i	−1.03775	+	0.753969i	−0.969845	−	0.243723i	$-0.921631\pi$
$967$	−32.2705	+	23.4459i	−1.03775	+	0.753969i	−0.0679046	+	0.997692i	$0.521631\pi$
$968$	23.2918			0.748627
$969$	−3.61803	+	2.62866i	−0.116228	+	0.0844446i
$970$		0			0
$971$	−2.73607	−	1.98787i	−0.0878046	−	0.0637938i	0.543017	−	0.839722i	$-0.317282\pi$
$971$	−2.73607	−	1.98787i	−0.0878046	−	0.0637938i	−0.630821	+	0.775928i	$0.717282\pi$
$972$	20.9443	+	15.2169i	0.671788	+	0.488082i
$973$	−2.50000	+	7.69421i	−0.0801463	+	0.246665i
$974$	−5.92299			−0.189785
$975$		0			0
$976$	−8.72949			−0.279424
$977$	−10.3992	+	32.0054i	−0.332699	+	1.02394i	0.635145	+	0.772393i	$0.280940\pi$
$977$	−10.3992	+	32.0054i	−0.332699	+	1.02394i	−0.967844	+	0.251551i	$0.919060\pi$
$978$	−5.50000	−	3.99598i	−0.175871	−	0.127777i
$979$	5.52786	+	4.01623i	0.176671	+	0.128359i
$980$		0			0
$981$	16.1803	−	11.7557i	0.516598	−	0.375331i
$982$	23.0213			0.734639
$983$	−5.97214	+	4.33901i	−0.190482	+	0.138393i	−0.678939	−	0.734195i	$-0.737560\pi$
$983$	−5.97214	+	4.33901i	−0.190482	+	0.138393i	0.488457	+	0.872588i	$0.337560\pi$
$984$	3.61803	+	11.1352i	0.115339	+	0.354976i
$985$		0			0
$986$	0.201626	−	0.620541i	0.00642108	−	0.0197621i
$987$	0.809017	+	2.48990i	0.0257513	+	0.0792543i
$988$	−14.2082	−	43.7284i	−0.452023	−	1.39118i
$989$	4.71885	−	14.5231i	0.150051	−	0.461808i
$990$		0			0
$991$	9.07295	+	27.9237i	0.288212	+	0.887024i	0.985418	+	0.170153i	$0.0544264\pi$
$991$	9.07295	+	27.9237i	0.288212	+	0.887024i	−0.697206	+	0.716871i	$0.745574\pi$
$992$	13.6353	−	9.90659i	0.432920	−	0.314535i
$993$	17.1246			0.543433
$994$	−3.54508	+	2.57565i	−0.112443	+	0.0816948i
$995$		0			0
$996$	−2.30902	−	1.67760i	−0.0731640	−	0.0531568i
$997$	8.80902	+	6.40013i	0.278984	+	0.202694i	0.718474	−	0.695554i	$-0.244841\pi$
$997$	8.80902	+	6.40013i	0.278984	+	0.202694i	−0.439490	+	0.898248i	$0.644841\pi$
$998$	−2.39919	+	7.38394i	−0.0759449	+	0.233734i
$999$	−21.1803			−0.670116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.h.501.1		4
5.2	odd	4		625.2.e.c.124.2		8
5.3	odd	4		625.2.e.c.124.1		8
5.4	even	2		625.2.d.b.501.1		4
25.2	odd	20		125.2.e.a.49.2		8
25.3	odd	20		125.2.e.a.74.2		8
25.4	even	10		125.2.d.a.51.1		4
25.6	even	5	inner	625.2.d.h.126.1		4
25.8	odd	20		625.2.e.c.499.2		8
25.9	even	10		625.2.a.c.1.1		2
25.11	even	5		25.2.d.a.16.1	yes	4
25.12	odd	20		625.2.b.a.624.3		4
25.13	odd	20		625.2.b.a.624.2		4
25.14	even	10		125.2.d.a.76.1		4
25.16	even	5		625.2.a.b.1.2		2
25.17	odd	20		625.2.e.c.499.1		8
25.19	even	10		625.2.d.b.126.1		4
25.21	even	5		25.2.d.a.11.1	✓	4
25.22	odd	20		125.2.e.a.74.1		8
25.23	odd	20		125.2.e.a.49.1		8
75.11	odd	10		225.2.h.b.91.1		4
75.41	odd	10		5625.2.a.f.1.1		2
75.59	odd	10		5625.2.a.d.1.2		2
75.71	odd	10		225.2.h.b.136.1		4
100.11	odd	10		400.2.u.b.241.1		4
100.59	odd	10		10000.2.a.l.1.1		2
100.71	odd	10		400.2.u.b.161.1		4
100.91	odd	10		10000.2.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.11.1	✓	4	25.21	even	5
25.2.d.a.16.1	yes	4	25.11	even	5
125.2.d.a.51.1		4	25.4	even	10
125.2.d.a.76.1		4	25.14	even	10
125.2.e.a.49.1		8	25.23	odd	20
125.2.e.a.49.2		8	25.2	odd	20
125.2.e.a.74.1		8	25.22	odd	20
125.2.e.a.74.2		8	25.3	odd	20
225.2.h.b.91.1		4	75.11	odd	10
225.2.h.b.136.1		4	75.71	odd	10
400.2.u.b.161.1		4	100.71	odd	10
400.2.u.b.241.1		4	100.11	odd	10
625.2.a.b.1.2		2	25.16	even	5
625.2.a.c.1.1		2	25.9	even	10
625.2.b.a.624.2		4	25.13	odd	20
625.2.b.a.624.3		4	25.12	odd	20
625.2.d.b.126.1		4	25.19	even	10
625.2.d.b.501.1		4	5.4	even	2
625.2.d.h.126.1		4	25.6	even	5	inner
625.2.d.h.501.1		4	1.1	even	1	trivial
625.2.e.c.124.1		8	5.3	odd	4
625.2.e.c.124.2		8	5.2	odd	4
625.2.e.c.499.1		8	25.17	odd	20
625.2.e.c.499.2		8	25.8	odd	20
5625.2.a.d.1.2		2	75.59	odd	10
5625.2.a.f.1.1		2	75.41	odd	10
10000.2.a.c.1.2		2	100.91	odd	10
10000.2.a.l.1.1		2	100.59	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)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.500000 + 0.363271i) q^{6} -1.61803 q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.618034 - 1.90211i) q^{9} +O(q^{10})\)	\(q+(0.190983 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.500000 + 0.363271i) q^{6} -1.61803 q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.618034 - 1.90211i) q^{9} +(-0.236068 + 0.726543i) q^{11} +(-0.500000 - 1.53884i) q^{12} +(-1.50000 - 4.61653i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.572949 + 1.76336i) q^{16} +(0.618034 - 0.449028i) q^{17} -1.23607 q^{18} +(4.73607 - 3.44095i) q^{19} +(1.30902 + 0.951057i) q^{21} +(0.381966 + 0.277515i) q^{22} +(2.54508 - 7.83297i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-1.54508 + 4.75528i) q^{27} +(-2.11803 - 1.53884i) q^{28} +(1.11803 + 0.812299i) q^{29} +(2.42705 - 1.76336i) q^{31} +5.61803 q^{32} +(0.618034 - 0.449028i) q^{33} +(-0.145898 - 0.449028i) q^{34} +(1.00000 - 3.07768i) q^{36} +(1.30902 + 4.02874i) q^{37} +(-1.11803 - 3.44095i) q^{38} +(-1.50000 + 4.61653i) q^{39} +(-1.61803 - 4.97980i) q^{41} +(0.809017 - 0.587785i) q^{42} +1.85410 q^{43} +(-1.00000 + 0.726543i) q^{44} +(-4.11803 - 2.99193i) q^{46} +(1.30902 + 0.951057i) q^{47} +(0.572949 - 1.76336i) q^{48} -4.38197 q^{49} -0.763932 q^{51} +(2.42705 - 7.46969i) q^{52} +(-4.42705 - 3.21644i) q^{53} +(2.50000 + 1.81636i) q^{54} +(-2.92705 + 2.12663i) q^{56} -5.85410 q^{57} +(0.690983 - 0.502029i) q^{58} +(-1.28115 - 3.94298i) q^{59} +(-1.45492 + 4.47777i) q^{61} +(-0.572949 - 1.76336i) q^{62} +(1.00000 + 3.07768i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +(-0.145898 - 0.449028i) q^{66} +(-7.47214 + 5.42882i) q^{67} +1.23607 q^{68} +(-6.66312 + 4.84104i) q^{69} +(3.54508 + 2.57565i) q^{71} +(-3.61803 - 2.62866i) q^{72} +(-2.78115 + 8.55951i) q^{73} +2.61803 q^{74} +9.47214 q^{76} +(0.381966 - 1.17557i) q^{77} +(2.42705 + 1.76336i) q^{78} +(-2.50000 - 1.81636i) q^{79} +(-0.809017 + 0.587785i) q^{81} -3.23607 q^{82} +(1.42705 - 1.03681i) q^{83} +(0.809017 + 2.48990i) q^{84} +(0.354102 - 1.08981i) q^{86} +(-0.427051 - 1.31433i) q^{87} +(0.527864 + 1.62460i) q^{88} +(2.76393 - 8.50651i) q^{89} +(2.42705 + 7.46969i) q^{91} +(10.7812 - 7.83297i) q^{92} -3.00000 q^{93} +(0.809017 - 0.587785i) q^{94} +(-4.54508 - 3.30220i) q^{96} +(-2.30902 - 1.67760i) q^{97} +(-0.836881 + 2.57565i) q^{98} +1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 - 2 * q^7 + 5 * q^8 + 2 * q^9	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} - 2 q^{7} + 5 q^{8} + 2 q^{9} + 8 q^{11} - 2 q^{12} - 6 q^{13} + q^{14} + 9 q^{16} - 2 q^{17} + 4 q^{18} + 10 q^{19} + 3 q^{21} + 6 q^{22} - q^{23} - 12 q^{26} + 5 q^{27} - 4 q^{28} + 3 q^{31} + 18 q^{32} - 2 q^{33} - 14 q^{34} + 4 q^{36} + 3 q^{37} - 6 q^{39} - 2 q^{41} + q^{42} - 6 q^{43} - 4 q^{44} - 12 q^{46} + 3 q^{47} + 9 q^{48} - 22 q^{49} - 12 q^{51} + 3 q^{52} - 11 q^{53} + 10 q^{54} - 5 q^{56} - 10 q^{57} + 5 q^{58} + 15 q^{59} - 17 q^{61} - 9 q^{62} + 4 q^{63} - 7 q^{64} - 14 q^{66} - 12 q^{67} - 4 q^{68} - 11 q^{69} + 3 q^{71} - 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{76} + 6 q^{77} + 3 q^{78} - 10 q^{79} - q^{81} - 4 q^{82} - q^{83} + q^{84} - 12 q^{86} + 5 q^{87} + 20 q^{88} + 20 q^{89} + 3 q^{91} + 23 q^{92} - 12 q^{93} + q^{94} - 7 q^{96} - 7 q^{97} - 19 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 - 2 * q^7 + 5 * q^8 + 2 * q^9 + 8 * q^11 - 2 * q^12 - 6 * q^13 + q^14 + 9 * q^16 - 2 * q^17 + 4 * q^18 + 10 * q^19 + 3 * q^21 + 6 * q^22 - q^23 - 12 * q^26 + 5 * q^27 - 4 * q^28 + 3 * q^31 + 18 * q^32 - 2 * q^33 - 14 * q^34 + 4 * q^36 + 3 * q^37 - 6 * q^39 - 2 * q^41 + q^42 - 6 * q^43 - 4 * q^44 - 12 * q^46 + 3 * q^47 + 9 * q^48 - 22 * q^49 - 12 * q^51 + 3 * q^52 - 11 * q^53 + 10 * q^54 - 5 * q^56 - 10 * q^57 + 5 * q^58 + 15 * q^59 - 17 * q^61 - 9 * q^62 + 4 * q^63 - 7 * q^64 - 14 * q^66 - 12 * q^67 - 4 * q^68 - 11 * q^69 + 3 * q^71 - 10 * q^72 + 9 * q^73 + 6 * q^74 + 20 * q^76 + 6 * q^77 + 3 * q^78 - 10 * q^79 - q^81 - 4 * q^82 - q^83 + q^84 - 12 * q^86 + 5 * q^87 + 20 * q^88 + 20 * q^89 + 3 * q^91 + 23 * q^92 - 12 * q^93 + q^94 - 7 * q^96 - 7 * q^97 - 19 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more