LMFDB - Embedded newform 575.2.k.g.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	575.101
Dual form			575.2.k.g.501.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.601743 + 0.176688i) q^{2} +(0.488459 + 0.563711i) q^{3} +(-1.35163 + 0.868641i) q^{4} +(-0.393527 - 0.252905i) q^{6} +(0.283387 - 0.620531i) q^{7} +(1.48124 - 1.70945i) q^{8} +(0.347766 - 2.41877i) q^{9} +O(q^{10})$	\(q+(-0.601743 + 0.176688i) q^{2} +(0.488459 + 0.563711i) q^{3} +(-1.35163 + 0.868641i) q^{4} +(-0.393527 - 0.252905i) q^{6} +(0.283387 - 0.620531i) q^{7} +(1.48124 - 1.70945i) q^{8} +(0.347766 - 2.41877i) q^{9} +(0.318051 + 0.0933881i) q^{11} +(-1.14988 - 0.337635i) q^{12} +(2.04767 + 4.48376i) q^{13} +(-0.0608859 + 0.423471i) q^{14} +(0.745594 - 1.63262i) q^{16} +(4.37052 + 2.80876i) q^{17} +(0.218100 + 1.51692i) q^{18} +(3.00018 - 1.92810i) q^{19} +(0.488223 - 0.143355i) q^{21} -0.207885 q^{22} +(-0.683074 + 4.74694i) q^{23} +1.68716 q^{24} +(-2.02439 - 2.33628i) q^{26} +(3.41582 - 2.19521i) q^{27} +(0.155984 + 1.08489i) q^{28} +(-1.41248 - 0.907743i) q^{29} +(-5.48185 + 6.32639i) q^{31} +(-0.804002 + 5.59195i) q^{32} +(0.102711 + 0.224905i) q^{33} +(-3.12620 - 0.917936i) q^{34} +(1.63099 + 3.57136i) q^{36} +(-0.733242 + 5.09981i) q^{37} +(-1.46467 + 1.69032i) q^{38} +(-1.52735 + 3.34442i) q^{39} +(-0.445398 - 3.09781i) q^{41} +(-0.268456 + 0.172526i) q^{42} +(4.84184 + 5.58778i) q^{43} +(-0.511008 + 0.150045i) q^{44} +(-0.427690 - 2.97713i) q^{46} -0.330027 q^{47} +(1.28452 - 0.377169i) q^{48} +(4.27927 + 4.93855i) q^{49} +(0.551487 + 3.83567i) q^{51} +(-6.66247 - 4.28171i) q^{52} +(3.75505 - 8.22242i) q^{53} +(-1.66758 + 1.92449i) q^{54} +(-0.640999 - 1.40359i) q^{56} +(2.55236 + 0.749439i) q^{57} +(1.01033 + 0.296661i) q^{58} +(0.559864 + 1.22593i) q^{59} +(3.65863 - 4.22228i) q^{61} +(2.18087 - 4.77543i) q^{62} +(-1.40237 - 0.901246i) q^{63} +(0.00663133 + 0.0461219i) q^{64} +(-0.101543 - 0.117187i) q^{66} +(0.468400 - 0.137535i) q^{67} -8.34713 q^{68} +(-3.00955 + 1.93363i) q^{69} +(13.9609 - 4.09929i) q^{71} +(-3.61962 - 4.17727i) q^{72} +(6.37754 - 4.09859i) q^{73} +(-0.459850 - 3.19833i) q^{74} +(-2.38031 + 5.21216i) q^{76} +(0.148082 - 0.170895i) q^{77} +(0.328152 - 2.28235i) q^{78} +(-4.48603 - 9.82303i) q^{79} +(-4.12801 - 1.21209i) q^{81} +(0.815360 + 1.78539i) q^{82} +(0.537881 - 3.74104i) q^{83} +(-0.535373 + 0.617854i) q^{84} +(-3.90083 - 2.50691i) q^{86} +(-0.178231 - 1.23962i) q^{87} +(0.630752 - 0.405360i) q^{88} +(9.39014 + 10.8368i) q^{89} +3.36260 q^{91} +(-3.20012 - 7.00945i) q^{92} -6.24391 q^{93} +(0.198592 - 0.0583118i) q^{94} +(-3.54497 + 2.27821i) q^{96} +(1.14089 + 7.93510i) q^{97} +(-3.44760 - 2.21564i) q^{98} +(0.336491 - 0.736813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	−0.601743	+	0.176688i	−0.425496	+	0.124937i	−0.487468	−	0.873141i	$-0.662079\pi$
$2$	−0.601743	+	0.176688i	−0.425496	+	0.124937i	0.0619715	+	0.998078i	$0.480261\pi$
$3$	0.488459	+	0.563711i	0.282012	+	0.325459i	0.879028	−	0.476770i	$-0.158193\pi$
$3$	0.488459	+	0.563711i	0.282012	+	0.325459i	−0.597016	+	0.802229i	$0.703647\pi$
$4$	−1.35163	+	0.868641i	−0.675816	+	0.434320i
$5$		0			0
$5$		0			0
$6$	−0.393527	−	0.252905i	−0.160657	−	0.103248i
$7$	0.283387	−	0.620531i	0.107110	−	0.234539i	−0.848486	−	0.529218i	$-0.822485\pi$
$7$	0.283387	−	0.620531i	0.107110	−	0.234539i	0.955596	+	0.294679i	$0.0952127\pi$
$8$	1.48124	−	1.70945i	0.523699	−	0.604381i
$9$	0.347766	−	2.41877i	0.115922	−	0.806255i
$10$		0			0
$11$	0.318051	+	0.0933881i	0.0958959	+	0.0281576i	0.329328	−	0.944215i	$-0.393178\pi$
$11$	0.318051	+	0.0933881i	0.0958959	+	0.0281576i	−0.233433	+	0.972373i	$0.574996\pi$
$12$	−1.14988	−	0.337635i	−0.331941	−	0.0974667i
$13$	2.04767	+	4.48376i	0.567920	+	1.24357i	0.947897	+	0.318576i	$0.103205\pi$
$13$	2.04767	+	4.48376i	0.567920	+	1.24357i	−0.379977	+	0.924996i	$0.624068\pi$
$14$	−0.0608859	+	0.423471i	−0.0162725	+	0.113177i
$15$		0			0
$16$	0.745594	−	1.63262i	0.186399	−	0.408156i
$17$	4.37052	+	2.80876i	1.06001	+	0.681225i	0.949855	−	0.312690i	$-0.101230\pi$
$17$	4.37052	+	2.80876i	1.06001	+	0.681225i	0.110151	+	0.993915i	$0.464866\pi$
$18$	0.218100	+	1.51692i	0.0514067	+	0.357542i
$19$	3.00018	−	1.92810i	0.688289	−	0.442337i	−0.149188	−	0.988809i	$-0.547666\pi$
$19$	3.00018	−	1.92810i	0.688289	−	0.442337i	0.837477	+	0.546472i	$0.184030\pi$
$20$		0			0
$21$	0.488223	−	0.143355i	0.106539	−	0.0312827i
$22$	−0.207885			−0.0443213
$23$	−0.683074	+	4.74694i	−0.142431	+	0.989805i
$23$	−0.683074	+	4.74694i	−0.142431	+	0.989805i
$24$	1.68716			0.344390
$25$		0			0
$26$	−2.02439	−	2.33628i	−0.397016	−	0.458181i
$27$	3.41582	−	2.19521i	0.657375	−	0.422469i
$28$	0.155984	+	1.08489i	0.0294781	+	0.205025i
$29$	−1.41248	−	0.907743i	−0.262290	−	0.168564i	0.402886	−	0.915250i	$-0.368007\pi$
$29$	−1.41248	−	0.907743i	−0.262290	−	0.168564i	−0.665176	+	0.746687i	$0.731643\pi$
$30$		0			0
$31$	−5.48185	+	6.32639i	−0.984569	+	1.13625i	0.00610251	+	0.999981i	$0.498057\pi$
$31$	−5.48185	+	6.32639i	−0.984569	+	1.13625i	−0.990671	+	0.136272i	$0.956488\pi$
$32$	−0.804002	+	5.59195i	−0.142129	+	0.988527i
$33$	0.102711	+	0.224905i	0.0178796	+	0.0391509i
$34$	−3.12620	−	0.917936i	−0.536139	−	0.157425i
$35$		0			0
$36$	1.63099	+	3.57136i	0.271831	+	0.595227i
$37$	−0.733242	+	5.09981i	−0.120544	+	0.838404i	0.836397	+	0.548124i	$0.184658\pi$
$37$	−0.733242	+	5.09981i	−0.120544	+	0.838404i	−0.956942	+	0.290280i	$0.906251\pi$
$38$	−1.46467	+	1.69032i	−0.237600	+	0.274205i
$39$	−1.52735	+	3.34442i	−0.244571	+	0.535537i
$40$		0			0
$41$	−0.445398	−	3.09781i	−0.0695595	−	0.483797i	−0.994588	−	0.103899i	$-0.966868\pi$
$41$	−0.445398	−	3.09781i	−0.0695595	−	0.483797i	0.925028	−	0.379898i	$-0.124041\pi$
$42$	−0.268456	+	0.172526i	−0.0414236	+	0.0266213i
$43$	4.84184	+	5.58778i	0.738374	+	0.852129i	0.993388	−	0.114809i	$-0.0366255\pi$
$43$	4.84184	+	5.58778i	0.738374	+	0.852129i	−0.255014	+	0.966937i	$0.582080\pi$
$44$	−0.511008	+	0.150045i	−0.0770373	+	0.0226202i
$45$		0			0
$46$	−0.427690	−	2.97713i	−0.0630595	−	0.438953i
$47$	−0.330027			−0.0481395			−0.0240697	−	0.999710i	$-0.507662\pi$
$47$	−0.330027			−0.0481395			−0.0240697	+	0.999710i	$0.507662\pi$
$48$	1.28452	−	0.377169i	0.185404	−	0.0544397i
$49$	4.27927	+	4.93855i	0.611325	+	0.705507i
$50$		0			0
$51$	0.551487	+	3.83567i	0.0772236	+	0.537102i
$52$	−6.66247	−	4.28171i	−0.923918	−	0.593766i
$53$	3.75505	−	8.22242i	0.515796	−	1.12944i	−0.455211	−	0.890384i	$-0.650436\pi$
$53$	3.75505	−	8.22242i	0.515796	−	1.12944i	0.971007	−	0.239052i	$-0.0768367\pi$
$54$	−1.66758	+	1.92449i	−0.226929	+	0.261890i
$55$		0			0
$56$	−0.640999	−	1.40359i	−0.0856571	−	0.187563i
$57$	2.55236	+	0.749439i	0.338068	+	0.0992657i
$58$	1.01033	+	0.296661i	0.132663	+	0.0389535i
$59$	0.559864	+	1.22593i	0.0728881	+	0.159603i	0.942569	−	0.334012i	$-0.108403\pi$
$59$	0.559864	+	1.22593i	0.0728881	+	0.159603i	−0.869681	+	0.493615i	$0.835675\pi$
$60$		0			0
$61$	3.65863	−	4.22228i	0.468440	−	0.540608i	−0.471537	−	0.881846i	$-0.656301\pi$
$61$	3.65863	−	4.22228i	0.468440	−	0.540608i	0.939977	+	0.341238i	$0.110846\pi$
$62$	2.18087	−	4.77543i	0.276971	−	0.606481i
$63$	−1.40237	−	0.901246i	−0.176682	−	0.113546i
$64$	0.00663133	+	0.0461219i	0.000828917	+	0.00576524i
$65$		0			0
$66$	−0.101543	−	0.117187i	−0.0124991	−	0.0144247i
$67$	0.468400	−	0.137535i	0.0572242	−	0.0168025i	−0.252995	−	0.967468i	$-0.581416\pi$
$67$	0.468400	−	0.137535i	0.0572242	−	0.0168025i	0.310219	+	0.950665i	$0.399597\pi$
$68$	−8.34713			−1.01224
$69$	−3.00955	+	1.93363i	−0.362308	+	0.232781i
$70$		0			0
$71$	13.9609	−	4.09929i	1.65685	−	0.486496i	0.686287	−	0.727331i	$-0.259240\pi$
$71$	13.9609	−	4.09929i	1.65685	−	0.486496i	0.970566	+	0.240835i	$0.0774214\pi$
$72$	−3.61962	−	4.17727i	−0.426577	−	0.492296i
$73$	6.37754	−	4.09859i	0.746434	−	0.479704i	−0.111307	−	0.993786i	$-0.535504\pi$
$73$	6.37754	−	4.09859i	0.746434	−	0.479704i	0.857741	+	0.514082i	$0.171867\pi$
$74$	−0.459850	−	3.19833i	−0.0534565	−	0.371798i
$75$		0			0
$76$	−2.38031	+	5.21216i	−0.273041	+	0.597876i
$77$	0.148082	−	0.170895i	0.0168755	−	0.0194753i
$78$	0.328152	−	2.28235i	0.0371559	−	0.258425i
$79$	−4.48603	−	9.82303i	−0.504717	−	1.10518i	−0.974907	−	0.222612i	$-0.928542\pi$
$79$	−4.48603	−	9.82303i	−0.504717	−	1.10518i	0.470190	−	0.882565i	$-0.344185\pi$
$80$		0			0
$81$	−4.12801	−	1.21209i	−0.458668	−	0.134677i
$82$	0.815360	+	1.78539i	0.0900415	+	0.197163i
$83$	0.537881	−	3.74104i	0.0590401	−	0.410633i	−0.938773	−	0.344536i	$-0.888036\pi$
$83$	0.537881	−	3.74104i	0.0590401	−	0.410633i	0.997813	−	0.0660968i	$-0.0210546\pi$
$84$	−0.535373	+	0.617854i	−0.0584140	+	0.0674134i
$85$		0			0
$86$	−3.90083	−	2.50691i	−0.420638	−	0.270328i
$87$	−0.178231	−	1.23962i	−0.0191084	−	0.132902i
$88$	0.630752	−	0.405360i	0.0672384	−	0.0432115i
$89$	9.39014	+	10.8368i	0.995353	+	1.14870i	0.988879	+	0.148720i	$0.0475152\pi$
$89$	9.39014	+	10.8368i	0.995353	+	1.14870i	0.00647382	+	0.999979i	$0.497939\pi$
$90$		0			0
$91$	3.36260			0.352496
$92$	−3.20012	−	7.00945i	−0.333635	−	0.730786i
$93$	−6.24391			−0.647464
$94$	0.198592	−	0.0583118i	0.0204832	−	0.00601440i
$95$		0			0
$96$	−3.54497	+	2.27821i	−0.361807	+	0.232519i
$97$	1.14089	+	7.93510i	0.115840	+	0.805687i	0.962057	+	0.272848i	$0.0879657\pi$
$97$	1.14089	+	7.93510i	0.115840	+	0.805687i	−0.846217	+	0.532839i	$0.821125\pi$
$98$	−3.44760	−	2.21564i	−0.348260	−	0.223813i
$99$	0.336491	−	0.736813i	0.0338186	−	0.0740525i
$100$		0			0
$101$	−1.33265	+	9.26880i	−0.132604	+	0.922281i	0.809538	+	0.587067i	$0.199718\pi$
$101$	−1.33265	+	9.26880i	−0.132604	+	0.922281i	−0.942142	+	0.335213i	$0.891192\pi$
$102$	−1.00957	−	2.21065i	−0.0999623	−	0.218887i
$103$	−18.4500	−	5.41741i	−1.81793	−	0.533794i	−0.818749	−	0.574151i	$-0.805332\pi$
$103$	−18.4500	−	5.41741i	−1.81793	−	0.533794i	−0.999185	+	0.0403576i	$0.987150\pi$
$104$	10.6978	+	3.14117i	1.04901	+	0.308017i
$105$		0			0
$106$	−0.806776	+	5.61125i	−0.0783610	+	0.545013i
$107$	2.62441	−	3.02873i	0.253712	−	0.292799i	−0.614578	−	0.788856i	$-0.710674\pi$
$107$	2.62441	−	3.02873i	0.253712	−	0.292799i	0.868290	+	0.496057i	$0.165219\pi$
$108$	−2.71008	+	5.93424i	−0.260777	+	0.571022i
$109$	−4.33801	−	2.78787i	−0.415506	−	0.267030i	0.316142	−	0.948712i	$-0.397612\pi$
$109$	−4.33801	−	2.78787i	−0.415506	−	0.267030i	−0.731648	+	0.681682i	$0.761249\pi$
$110$		0			0
$111$	−3.23298	+	2.07771i	−0.306861	+	0.197207i
$112$	−0.801802	−	0.925328i	−0.0757631	−	0.0874353i
$113$	4.23590	−	1.24377i	0.398480	−	0.117004i	−0.0763517	−	0.997081i	$-0.524327\pi$
$113$	4.23590	−	1.24377i	0.398480	−	0.117004i	0.474832	+	0.880077i	$0.342509\pi$
$114$	−1.66828			−0.156249
$115$		0			0
$116$	2.69765			0.250470
$117$	11.5573	−	3.39352i	1.06847	−	0.313731i
$118$	−0.553501	−	0.638774i	−0.0509539	−	0.0588039i
$119$	2.98147	−	1.91608i	0.273311	−	0.175646i
$120$		0			0
$121$	−9.16135	−	5.88764i	−0.832850	−	0.535240i
$122$	−1.45553	+	3.18716i	−0.131777	+	0.288552i
$123$	1.52871	−	1.76423i	0.137839	−	0.159075i
$124$	1.91408	−	13.3127i	0.171889	−	1.19552i
$125$		0			0
$126$	1.00310	+	0.294538i	0.0893635	+	0.0262395i
$127$	−13.3585	−	3.92240i	−1.18537	−	0.348056i	−0.371129	−	0.928581i	$-0.621029\pi$
$127$	−13.3585	−	3.92240i	−1.18537	−	0.348056i	−0.814243	+	0.580525i	$0.802847\pi$
$128$	−4.70588	−	10.3044i	−0.415945	−	0.910792i
$129$	−0.784857	+	5.45880i	−0.0691028	+	0.480620i
$130$		0			0
$131$	3.15052	−	6.89868i	0.275263	−	0.602741i	−0.720626	−	0.693324i	$-0.756146\pi$
$131$	3.15052	−	6.89868i	0.275263	−	0.602741i	0.995889	+	0.0905827i	$0.0288730\pi$
$132$	−0.334188	−	0.214770i	−0.0290874	−	0.0186933i
$133$	−0.346233	−	2.40810i	−0.0300222	−	0.208809i
$134$	−0.257556	+	0.165521i	−0.0222494	+	0.0142988i
$135$		0			0
$136$	11.2752	−	3.31071i	0.966843	−	0.283891i
$137$	10.7067			0.914738			0.457369	−	0.889277i	$-0.348792\pi$
$137$	10.7067			0.914738			0.457369	+	0.889277i	$0.348792\pi$
$138$	1.46933	−	1.69530i	0.125078	−	0.144313i
$139$	2.70899			0.229774			0.114887	−	0.993379i	$-0.463349\pi$
$139$	2.70899			0.229774			0.114887	+	0.993379i	$0.463349\pi$
$140$		0			0
$141$	−0.161205	−	0.186040i	−0.0135759	−	0.0156674i
$142$	−7.67657	+	4.93343i	−0.644204	+	0.414004i
$143$	0.232531	+	1.61729i	0.0194453	+	0.135245i
$144$	−3.68964	−	2.37119i	−0.307470	−	0.197599i
$145$		0			0
$146$	−3.11347	+	3.59313i	−0.257672	+	0.297370i
$147$	−0.693666	+	4.82455i	−0.0572126	+	0.397922i
$148$	−3.43883	−	7.52999i	−0.282670	−	0.618961i
$149$	−20.8446	−	6.12051i	−1.70765	−	0.501412i	−0.725297	−	0.688436i	$-0.758298\pi$
$149$	−20.8446	−	6.12051i	−1.70765	−	0.501412i	−0.982355	+	0.187024i	$0.940116\pi$
$150$		0			0
$151$	−1.55851	−	3.41266i	−0.126830	−	0.277718i	0.835556	−	0.549405i	$-0.185146\pi$
$151$	−1.55851	−	3.41266i	−0.126830	−	0.277718i	−0.962386	+	0.271687i	$0.912418\pi$
$152$	1.14802	−	7.98464i	0.0931165	−	0.647640i
$153$	8.31365	−	9.59447i	0.672119	−	0.775667i
$154$	−0.0589120	+	0.128999i	−0.00474726	+	0.0103951i
$155$		0			0
$156$	−0.840692	−	5.84714i	−0.0673093	−	0.468146i
$157$	−11.1375	+	7.15764i	−0.888869	+	0.571242i	−0.903470	−	0.428652i	$-0.858989\pi$
$157$	−11.1375	+	7.15764i	−0.888869	+	0.571242i	0.0146006	+	0.999893i	$0.495352\pi$
$158$	4.43504	+	5.11831i	0.352833	+	0.407191i
$159$	6.46926	−	1.89954i	0.513045	−	0.150644i
$160$		0			0
$161$	2.75205	+	1.76909i	0.216892	+	0.139424i
$162$	2.69816			0.211988
$163$	−15.3156	+	4.49707i	−1.19961	+	0.352238i	−0.819704	−	0.572787i	$-0.805862\pi$
$163$	−15.3156	+	4.49707i	−1.19961	+	0.352238i	−0.379907	+	0.925024i	$0.624044\pi$
$164$	3.29290	+	3.80021i	0.257132	+	0.296746i
$165$		0			0
$166$	0.337330	+	2.34618i	0.0261819	+	0.182099i
$167$	8.85605	+	5.69144i	0.685302	+	0.440417i	0.836413	−	0.548100i	$-0.184649\pi$
$167$	8.85605	+	5.69144i	0.685302	+	0.440417i	−0.151111	+	0.988517i	$0.548285\pi$
$168$	0.478119	−	1.04694i	0.0368877	−	0.0807728i
$169$	−7.39801	+	8.53776i	−0.569077	+	0.656750i
$170$		0			0
$171$	−3.62026	−	7.92726i	−0.276848	−	0.606213i
$172$	−11.3982	−	3.34680i	−0.869101	−	0.255191i
$173$	7.11798	+	2.09003i	0.541170	+	0.158902i	0.540883	−	0.841098i	$-0.318090\pi$
$173$	7.11798	+	2.09003i	0.541170	+	0.158902i	0.000287607		1.00000i	$0.499908\pi$
$174$	0.326275	+	0.714443i	0.0247349	+	0.0541618i
$175$		0			0
$176$	0.389604	−	0.449627i	0.0293675	−	0.0338919i
$177$	−0.417601	+	0.914418i	−0.0313888	+	0.0687319i
$178$	−7.56518	−	4.86185i	−0.567034	−	0.364411i
$179$	−2.25969	−	15.7165i	−0.168897	−	1.17471i	−0.881169	−	0.472802i	$-0.843243\pi$
$179$	−2.25969	−	15.7165i	−0.168897	−	1.17471i	0.712272	−	0.701904i	$-0.247666\pi$
$180$		0			0
$181$	0.777285	+	0.897034i	0.0577751	+	0.0666760i	0.783901	−	0.620885i	$-0.213227\pi$
$181$	0.777285	+	0.897034i	0.0577751	+	0.0666760i	−0.726126	+	0.687561i	$0.758681\pi$
$182$	−2.02342	+	0.594129i	−0.149986	+	0.0440398i
$183$	4.16724			0.308051
$184$	7.10283	+	8.19905i	0.523628	+	0.604442i
$185$		0			0
$186$	3.75723	−	1.10322i	0.275493	−	0.0808922i
$187$	1.12774	+	1.30148i	0.0824686	+	0.0951738i
$188$	0.446075	−	0.286675i	0.0325334	−	0.0209079i
$189$	−0.394199	−	2.74172i	−0.0286738	−	0.199431i
$190$		0			0
$191$	0.0820154	−	0.179589i	0.00593443	−	0.0129946i	−0.906642	−	0.421902i	$-0.861363\pi$
$191$	0.0820154	−	0.179589i	0.00593443	−	0.0129946i	0.912576	+	0.408907i	$0.134090\pi$
$192$	−0.0227603	+	0.0262668i	−0.00164258	+	0.00189564i
$193$	0.489915	−	3.40744i	0.0352649	−	0.245273i	−0.964562	−	0.263855i	$-0.915006\pi$
$193$	0.489915	−	3.40744i	0.0352649	−	0.245273i	0.999827	+	0.0185820i	$0.00591517\pi$
$194$	−2.08856	−	4.57331i	−0.149950	−	0.328344i
$195$		0			0
$196$	−10.0738	−	2.95794i	−0.719559	−	0.211282i
$197$	−9.74780	−	21.3447i	−0.694502	−	1.52075i	−0.846513	−	0.532368i	$-0.821302\pi$
$197$	−9.74780	−	21.3447i	−0.694502	−	1.52075i	0.152011	−	0.988379i	$-0.451425\pi$
$198$	−0.0722954	+	0.502825i	−0.00513781	+	0.0357343i
$199$	−13.4152	+	15.4820i	−0.950981	+	1.09749i	0.0441598	+	0.999024i	$0.485939\pi$
$199$	−13.4152	+	15.4820i	−0.950981	+	1.09749i	−0.995140	+	0.0984657i	$0.968607\pi$
$200$		0			0
$201$	0.306324	+	0.196862i	0.0216064	+	0.0138856i
$202$	−0.835769	−	5.81290i	−0.0588045	−	0.408994i
$203$	−0.963559	+	0.619242i	−0.0676286	+	0.0434623i
$204$	−4.07723	−	4.70537i	−0.285463	−	0.329442i
$205$		0			0
$206$	12.0594			0.840215
$207$	11.2442	+	3.30302i	0.781524	+	0.229576i
$208$	8.84702			0.613431
$209$	1.13427	−	0.333052i	0.0784592	−	0.0230377i
$210$		0			0
$211$	−8.87705	+	5.70494i	−0.611122	+	0.392744i	−0.809278	−	0.587427i	$-0.800141\pi$
$211$	−8.87705	+	5.70494i	−0.611122	+	0.392744i	0.198156	+	0.980171i	$0.436505\pi$
$212$	2.06688	+	14.3755i	0.141954	+	0.987311i
$213$	9.13013	+	5.86758i	0.625586	+	0.402040i
$214$	−1.04408	+	2.28622i	−0.0713720	+	0.156283i
$215$		0			0
$216$	1.30706	−	9.09081i	0.0889342	−	0.618551i
$217$	2.37224	+	5.19447i	0.161038	+	0.352624i
$218$	3.10295	+	0.911108i	0.210158	+	0.0617080i
$219$	5.42559	+	1.59310i	0.366627	+	0.107651i
$220$		0			0
$221$	−3.64446	+	25.3478i	−0.245153	+	1.70508i
$222$	1.57832	−	1.82147i	0.105930	−	0.122249i
$223$	−3.25608	+	7.12981i	−0.218043	+	0.477447i	−0.986769	−	0.162130i	$-0.948164\pi$
$223$	−3.25608	+	7.12981i	−0.218043	+	0.477447i	0.768726	+	0.639578i	$0.220891\pi$
$224$	3.24214	+	2.08359i	0.216624	+	0.139216i
$225$		0			0
$226$	−2.32916	+	1.49686i	−0.154934	+	0.0995698i
$227$	−10.4949	−	12.1118i	−0.696573	−	0.803888i	0.291712	−	0.956506i	$-0.405775\pi$
$227$	−10.4949	−	12.1118i	−0.696573	−	0.803888i	−0.988285	+	0.152618i	$0.951230\pi$
$228$	−4.10084	+	1.20411i	−0.271585	+	0.0797444i
$229$	23.6597			1.56348			0.781738	−	0.623607i	$-0.214334\pi$
$229$	23.6597			1.56348			0.781738	+	0.623607i	$0.214334\pi$
$230$		0			0
$231$	0.168667			0.0110975
$232$	−3.64396	+	1.06996i	−0.239238	+	0.0702465i
$233$	4.62051	+	5.33235i	0.302699	+	0.349334i	0.886638	−	0.462464i	$-0.153035\pi$
$233$	4.62051	+	5.33235i	0.302699	+	0.349334i	−0.583939	+	0.811798i	$0.698489\pi$
$234$	−6.35492	+	4.08406i	−0.415434	+	0.266983i
$235$		0			0
$236$	−1.82162	−	1.17069i	−0.118578	−	0.0762052i
$237$	3.34611	−	7.32697i	0.217353	−	0.475938i
$238$	−1.45553	+	1.67977i	−0.0943481	+	0.108884i
$239$	2.20794	−	15.3566i	0.142820	−	0.993334i	−0.784784	−	0.619769i	$-0.787226\pi$
$239$	2.20794	−	15.3566i	0.142820	−	0.993334i	0.927604	−	0.373565i	$-0.121865\pi$
$240$		0			0
$241$	5.22796	+	1.53507i	0.336762	+	0.0988824i	0.445742	−	0.895162i	$-0.352940\pi$
$241$	5.22796	+	1.53507i	0.336762	+	0.0988824i	−0.108979	+	0.994044i	$0.534758\pi$
$242$	6.55305	+	1.92415i	0.421246	+	0.123689i
$243$	−6.39333	−	13.9994i	−0.410133	−	0.898065i
$244$	−1.27747	+	8.88501i	−0.0817817	+	0.568804i
$245$		0			0
$246$	−0.608175	+	1.33172i	−0.0387758	+	0.0849071i
$247$	14.7885	+	9.50400i	0.940971	+	0.604725i
$248$	2.69467	+	18.7419i	0.171112	+	1.19011i
$249$	2.37160	−	1.52413i	0.150294	−	0.0965881i
$250$		0			0
$251$	−10.0309	+	2.94534i	−0.633145	+	0.185908i	−0.582529	−	0.812810i	$-0.697937\pi$
$251$	−10.0309	+	2.94534i	−0.633145	+	0.185908i	−0.0506162	+	0.998718i	$0.516119\pi$
$252$	2.67834			0.168720
$253$	−0.660560	+	1.44598i	−0.0415290	+	0.0909077i
$254$	8.73140			0.547856
$255$		0			0
$256$	4.59137	+	5.29872i	0.286960	+	0.331170i
$257$	23.0424	−	14.8085i	1.43735	−	0.923726i	0.437649	−	0.899146i	$-0.355811\pi$
$257$	23.0424	−	14.8085i	1.43735	−	0.923726i	0.999698	−	0.0245804i	$-0.00782497\pi$
$258$	−0.492220	−	3.42347i	−0.0306443	−	0.213136i
$259$	2.95680	+	1.90022i	0.183727	+	0.118074i
$260$		0			0
$261$	−2.68683	+	3.10076i	−0.166310	+	0.191932i
$262$	−0.676893	+	4.70789i	−0.0418186	+	0.290855i
$263$	5.36587	+	11.7496i	0.330874	+	0.724513i	0.999823	−	0.0187952i	$-0.00598306\pi$
$263$	5.36587	+	11.7496i	0.330874	+	0.724513i	−0.668950	+	0.743308i	$0.733256\pi$
$264$	0.536602	+	0.157561i	0.0330256	+	0.00969719i
$265$		0			0
$266$	0.633826	+	1.38788i	0.0388623	+	0.0850967i
$267$	−1.52213	+	10.5867i	−0.0931529	+	0.647893i
$268$	−0.513636	+	0.592768i	−0.0313753	+	0.0362090i
$269$	7.21770	−	15.8046i	0.440071	−	0.963621i	−0.551514	−	0.834166i	$-0.685950\pi$
$269$	7.21770	−	15.8046i	0.440071	−	0.963621i	0.991585	−	0.129456i	$-0.0413230\pi$
$270$		0			0
$271$	−2.26606	−	15.7608i	−0.137653	−	0.957401i	−0.935194	−	0.354135i	$-0.884775\pi$
$271$	−2.26606	−	15.7608i	−0.137653	−	0.957401i	0.797541	−	0.603265i	$-0.206134\pi$
$272$	7.84428	−	5.04121i	0.475629	−	0.305669i
$273$	1.64249	+	1.89553i	0.0994079	+	0.114723i
$274$	−6.44270	+	1.89175i	−0.389218	+	0.114285i
$275$		0			0
$276$	2.38818	−	5.22777i	0.143752	−	0.314675i
$277$	−11.2072			−0.673373			−0.336686	−	0.941617i	$-0.609306\pi$
$277$	−11.2072			−0.673373			−0.336686	+	0.941617i	$0.609306\pi$
$278$	−1.63012	+	0.478646i	−0.0977679	+	0.0287073i
$279$	13.3957	+	15.4594i	0.801977	+	0.925530i
$280$		0			0
$281$	−2.18825	−	15.2196i	−0.130540	−	0.907927i	−0.944852	−	0.327499i	$-0.893794\pi$
$281$	−2.18825	−	15.2196i	−0.130540	−	0.907927i	0.814311	−	0.580428i	$-0.197115\pi$
$282$	0.129875	+	0.0834655i	0.00773393	+	0.00497030i
$283$	−12.4197	+	27.1954i	−0.738276	+	1.61660i	0.0480939	+	0.998843i	$0.484685\pi$
$283$	−12.4197	+	27.1954i	−0.738276	+	1.61660i	−0.786370	+	0.617756i	$0.788042\pi$
$284$	−15.3092	+	17.6677i	−0.908432	+	1.04839i
$285$		0			0
$286$	−0.425679	−	0.932108i	−0.0251710	−	0.0551167i
$287$	−2.04851	−	0.601496i	−0.120920	−	0.0355052i
$288$	13.2460	+	3.88938i	0.780529	+	0.229184i
$289$	4.15024	+	9.08775i	0.244131	+	0.534573i
$290$		0			0
$291$	−3.91582	+	4.51910i	−0.229550	+	0.264914i
$292$	−5.05987	+	11.0796i	−0.296107	+	0.648383i
$293$	7.04095	+	4.52495i	0.411337	+	0.264350i	0.729903	−	0.683550i	$-0.239565\pi$
$293$	7.04095	+	4.52495i	0.411337	+	0.264350i	−0.318566	+	0.947901i	$0.603201\pi$
$294$	−0.435030	−	3.02570i	−0.0253715	−	0.176462i
$295$		0			0
$296$	7.63174	+	8.80750i	0.443586	+	0.511926i
$297$	1.29141	−	0.379192i	0.0749352	−	0.0220030i
$298$	13.6245			0.789245
$299$	−22.6828	+	6.65740i	−1.31178	+	0.385007i
$300$		0			0
$301$	4.83951	−	1.42101i	0.278944	−	0.0819055i
$302$	1.54080	+	1.77817i	0.0886629	+	0.102322i
$303$	−5.87587	+	3.77620i	−0.337560	+	0.216937i
$304$	−0.910943	−	6.33575i	−0.0522462	−	0.363380i
$305$		0			0
$306$	−3.30746	+	7.24232i	−0.189075	+	0.414016i
$307$	−18.6958	+	21.5761i	−1.06703	+	1.23141i	−0.0952648	+	0.995452i	$0.530370\pi$
$307$	−18.6958	+	21.5761i	−1.06703	+	1.23141i	−0.971762	+	0.235963i	$0.924176\pi$
$308$	−0.0517051	+	0.359617i	−0.00294617	+	0.0204911i
$309$	−5.95821	−	13.0467i	−0.338951	−	0.742199i
$310$		0			0
$311$	16.0356	+	4.70847i	0.909293	+	0.266993i	0.702743	−	0.711443i	$-0.251958\pi$
$311$	16.0356	+	4.70847i	0.909293	+	0.266993i	0.206550	+	0.978436i	$0.433776\pi$
$312$	3.45474	+	7.56483i	0.195586	+	0.428274i
$313$	−0.508914	+	3.53958i	−0.0287655	+	0.200069i	−0.999136	−	0.0415519i	$-0.986770\pi$
$313$	−0.508914	+	3.53958i	−0.0287655	+	0.200069i	0.970371	+	0.241621i	$0.0776789\pi$
$314$	5.43724	−	6.27491i	0.306841	−	0.354114i
$315$		0			0
$316$	14.5961	+	9.38037i	0.821097	+	0.527687i
$317$	2.71307	+	18.8698i	0.152381	+	1.05984i	0.912213	+	0.409716i	$0.134372\pi$
$317$	2.71307	+	18.8698i	0.152381	+	1.05984i	−0.759832	+	0.650120i	$0.774719\pi$
$318$	−3.55720	+	2.28607i	−0.199478	+	0.128197i
$319$	−0.364466	−	0.420616i	−0.0204062	−	0.0235500i
$320$		0			0
$321$	2.98925			0.166844
$322$	−1.96860	−	0.578284i	−0.109706	−	0.0322265i
$323$	18.5279			1.03092
$324$	6.63242	−	1.94745i	0.368468	−	0.108192i
$325$		0			0
$326$	8.42149	−	5.41216i	0.466423	−	0.299752i
$327$	−0.547385	−	3.80715i	−0.0302705	−	0.210536i
$328$	−5.95529	−	3.82723i	−0.328826	−	0.211323i
$329$	−0.0935255	+	0.204792i	−0.00515623	+	0.0112906i
$330$		0			0
$331$	2.89685	−	20.1481i	0.159226	−	1.10744i	−0.740839	−	0.671682i	$-0.765572\pi$
$331$	2.89685	−	20.1481i	0.159226	−	1.10744i	0.900065	−	0.435756i	$-0.143519\pi$
$332$	2.52260	+	5.52373i	0.138446	+	0.303154i
$333$	12.0803	+	3.54708i	0.661994	+	0.194379i
$334$	−6.33467	−	1.86003i	−0.346618	−	0.101776i
$335$		0			0
$336$	0.129971	−	0.903969i	0.00709051	−	0.0493156i
$337$	4.07049	−	4.69760i	0.221734	−	0.255894i	−0.633973	−	0.773355i	$-0.718577\pi$
$337$	4.07049	−	4.69760i	0.221734	−	0.255894i	0.855707	+	0.517461i	$0.173123\pi$
$338$	2.94318	−	6.44467i	0.160088	−	0.350544i
$339$	2.77019	+	1.78029i	0.150456	+	0.0966922i
$340$		0			0
$341$	−2.33431	+	1.50017i	−0.126410	+	0.0812389i
$342$	3.57912	+	4.13052i	0.193536	+	0.223353i
$343$	8.85903	−	2.60124i	0.478342	−	0.140454i
$344$	16.7240			0.901696
$345$		0			0
$346$	−4.65248			−0.250119
$347$	−17.7190	+	5.20278i	−0.951207	+	0.279300i	−0.720290	−	0.693674i	$-0.755991\pi$
$347$	−17.7190	+	5.20278i	−0.951207	+	0.279300i	−0.230918	+	0.972973i	$0.574173\pi$
$348$	1.31769	+	1.52069i	0.0706355	+	0.0815178i
$349$	11.2395	−	7.22316i	0.601634	−	0.386647i	−0.204077	−	0.978955i	$-0.565419\pi$
$349$	11.2395	−	7.22316i	0.601634	−	0.386647i	0.805712	+	0.592308i	$0.201783\pi$
$350$		0			0
$351$	16.8373	+	10.8207i	0.898707	+	0.577564i
$352$	−0.777935	+	1.70344i	−0.0414641	+	0.0907937i
$353$	2.03751	−	2.35141i	0.108446	−	0.125153i	−0.698932	−	0.715188i	$-0.746341\pi$
$353$	2.03751	−	2.35141i	0.108446	−	0.125153i	0.807377	+	0.590036i	$0.200886\pi$
$354$	0.0897219	−	0.624029i	0.00476866	−	0.0331668i
$355$		0			0
$356$	−22.1053	−	6.49070i	−1.17158	−	0.344006i
$357$	2.53644	+	0.744766i	0.134243	+	0.0394172i
$358$	4.13666	+	9.05802i	0.218629	+	0.478731i
$359$	−4.58962	+	31.9215i	−0.242231	+	1.68475i	0.398642	+	0.917107i	$0.369482\pi$
$359$	−4.58962	+	31.9215i	−0.242231	+	1.68475i	−0.640873	+	0.767647i	$0.721427\pi$
$360$		0			0
$361$	−2.60936	+	5.71370i	−0.137335	+	0.300721i
$362$	−0.626220	−	0.402447i	−0.0329134	−	0.0211522i
$363$	−1.15601	−	8.04023i	−0.0606748	−	0.422003i
$364$	−4.54499	+	2.92089i	−0.238222	+	0.153096i
$365$		0			0
$366$	−2.50761	+	0.736299i	−0.131075	+	0.0384870i
$367$	−16.6172			−0.867410			−0.433705	−	0.901055i	$-0.642794\pi$
$367$	−16.6172			−0.867410			−0.433705	+	0.901055i	$0.642794\pi$
$368$	7.24066	+	4.65449i	0.377446	+	0.242632i
$369$	−7.64777			−0.398127
$370$		0			0
$371$	−4.03813	−	4.66025i	−0.209649	−	0.241948i
$372$	8.43947	−	5.42372i	0.437566	−	0.281207i
$373$	3.39980	+	23.6461i	0.176035	+	1.22435i	0.865828	+	0.500342i	$0.166792\pi$
$373$	3.39980	+	23.6461i	0.176035	+	1.22435i	−0.689793	+	0.724007i	$0.742298\pi$
$374$	−0.908566	−	0.583900i	−0.0469808	−	0.0301928i
$375$		0			0
$376$	−0.488851	+	0.564164i	−0.0252106	+	0.0290946i
$377$	1.17783	−	8.19196i	0.0606611	−	0.421907i
$378$	0.721634	+	1.58016i	0.0371168	+	0.0812746i
$379$	−29.7006	−	8.72087i	−1.52561	−	0.447961i	−0.591910	−	0.806004i	$-0.701626\pi$
$379$	−29.7006	−	8.72087i	−1.52561	−	0.447961i	−0.933705	+	0.358043i	$0.883444\pi$
$380$		0			0
$381$	−4.31395	−	9.44624i	−0.221011	−	0.483946i
$382$	−0.0176211	+	0.122557i	−0.000901573	+	0.00627058i
$383$	1.57563	−	1.81837i	0.0805109	−	0.0929146i	−0.714065	−	0.700080i	$-0.753148\pi$
$383$	1.57563	−	1.81837i	0.0805109	−	0.0929146i	0.794576	+	0.607165i	$0.207693\pi$
$384$	3.51010	−	7.68605i	0.179124	−	0.392227i
$385$		0			0
$386$	0.307249	+	2.13696i	0.0156386	+	0.108769i
$387$	15.1994	−	9.76804i	0.772627	−	0.496537i
$388$	−8.43482	−	9.73430i	−0.428213	−	0.494184i
$389$	−9.99300	+	2.93421i	−0.506665	+	0.148770i	−0.525068	−	0.851060i	$-0.675960\pi$
$389$	−9.99300	+	2.93421i	−0.506665	+	0.148770i	0.0184026	+	0.999831i	$0.494142\pi$
$390$		0			0
$391$	−16.3184	+	18.8280i	−0.825257	+	0.952172i
$392$	14.7808			0.746545
$393$	5.42777	−	1.59374i	0.273795	−	0.0803933i
$394$	9.63701	+	11.1217i	0.485506	+	0.560303i
$395$		0			0
$396$	0.185214	+	1.28819i	0.00930733	+	0.0647339i
$397$	−27.6246	−	17.7532i	−1.38644	−	0.891009i	−0.386921	−	0.922113i	$-0.626461\pi$
$397$	−27.6246	−	17.7532i	−1.38644	−	0.891009i	−0.999516	+	0.0311036i	$0.990098\pi$
$398$	5.33704	−	11.6865i	0.267522	−	0.585791i
$399$	1.18835	−	1.37143i	0.0594922	−	0.0686576i
$400$		0			0
$401$	−3.76143	−	8.23638i	−0.187837	−	0.411305i	0.792161	−	0.610312i	$-0.208956\pi$
$401$	−3.76143	−	8.23638i	−0.187837	−	0.411305i	−0.979998	+	0.199007i	$0.936229\pi$
$402$	−0.219111	−	0.0643369i	−0.0109283	−	0.00320883i
$403$	−39.5910	−	11.6250i	−1.97217	−	0.579081i
$404$	−6.25000	−	13.6856i	−0.310949	−	0.680884i
$405$		0			0
$406$	0.470403	−	0.542874i	0.0233457	−	0.0269424i
$407$	−0.709470	+	1.55352i	−0.0351671	+	0.0770052i
$408$	7.37377	+	4.73883i	0.365056	+	0.234607i
$409$	−2.84706	−	19.8018i	−0.140778	−	0.979135i	−0.930663	−	0.365879i	$-0.880769\pi$
$409$	−2.84706	−	19.8018i	−0.140778	−	0.979135i	0.789884	−	0.613256i	$-0.210141\pi$
$410$		0			0
$411$	5.22980	+	6.03551i	0.257967	+	0.297710i
$412$	29.6434	−	8.70409i	1.46043	−	0.428820i
$413$	0.919386			0.0452400
$414$	−7.34970		0.000861232i	−0.361218		4.23273e-5i
$415$		0			0
$416$	−26.7193	+	7.84550i	−1.31002	+	0.384657i
$417$	1.32323	+	1.52709i	0.0647989	+	0.0747819i
$418$	−0.623694	+	0.400823i	−0.0305058	+	0.0196049i
$419$	1.15949	+	8.06441i	0.0566447	+	0.393972i	0.998344	+	0.0575181i	$0.0183187\pi$
$419$	1.15949	+	8.06441i	0.0566447	+	0.393972i	−0.941700	+	0.336454i	$0.890772\pi$
$420$		0			0
$421$	7.93751	−	17.3807i	0.386851	−	0.847085i	−0.611585	−	0.791178i	$-0.709468\pi$
$421$	7.93751	−	17.3807i	0.386851	−	0.847085i	0.998436	−	0.0559063i	$-0.0178048\pi$
$422$	4.33371	−	5.00137i	0.210962	−	0.243463i
$423$	−0.114772	+	0.798259i	−0.00558042	+	0.0388127i
$424$	−8.49363	−	18.5985i	−0.412487	−	0.903221i
$425$		0			0
$426$	−6.53072	−	1.91759i	−0.316414	−	0.0929076i
$427$	−1.58325	−	3.46683i	−0.0766188	−	0.167772i
$428$	−0.916357	+	6.37340i	−0.0442938	+	0.308070i
$429$	−0.798103	+	0.921060i	−0.0385328	+	0.0444692i
$430$		0			0
$431$	−6.57609	−	4.22620i	−0.316759	−	0.203569i	0.372593	−	0.927995i	$-0.378469\pi$
$431$	−6.57609	−	4.22620i	−0.316759	−	0.203569i	−0.689353	+	0.724426i	$0.742105\pi$
$432$	−1.03714	−	7.21348i	−0.0498995	−	0.347059i
$433$	14.2006	−	9.12617i	0.682437	−	0.438576i	−0.152953	−	0.988233i	$-0.548878\pi$
$433$	14.2006	−	9.12617i	0.682437	−	0.438576i	0.835390	+	0.549658i	$0.185242\pi$
$434$	−2.34528	−	2.70659i	−0.112577	−	0.129921i
$435$		0			0
$436$	8.28505			0.396782
$437$	7.10322	+	15.5587i	0.339793	+	0.744274i
$438$	−3.54629			−0.169448
$439$	30.7525	−	9.02974i	1.46773	−	0.430966i	0.552373	−	0.833597i	$-0.313723\pi$
$439$	30.7525	−	9.02974i	1.46773	−	0.430966i	0.915362	+	0.402631i	$0.131904\pi$
$440$		0			0
$441$	13.4334	−	8.63310i	0.639684	−	0.411100i
$442$	−2.28561	−	15.8968i	−0.108715	−	0.756132i
$443$	−26.2725	−	16.8843i	−1.24824	−	0.802198i	−0.261614	−	0.965172i	$-0.584255\pi$
$443$	−26.2725	−	16.8843i	−1.24824	−	0.802198i	−0.986630	+	0.162974i	$0.947891\pi$
$444$	2.56501	−	5.61659i	0.121730	−	0.266552i
$445$		0			0
$446$	0.699571	−	4.86562i	0.0331256	−	0.230394i
$447$	−6.73150	−	14.7399i	−0.318389	−	0.697174i
$448$	0.0304993	+	0.00895541i	0.00144096	+	0.000423103i
$449$	13.2496	+	3.89045i	0.625289	+	0.183601i	0.579001	−	0.815327i	$-0.303443\pi$
$449$	13.2496	+	3.89045i	0.625289	+	0.183601i	0.0462880	+	0.998928i	$0.485261\pi$
$450$		0			0
$451$	0.147640	−	1.02686i	0.00695208	−	0.0483528i
$452$	−4.64498	+	5.36060i	−0.218482	+	0.252141i
$453$	1.16249	−	2.54549i	0.0546184	−	0.119598i
$454$	8.45525	+	5.43386i	0.396825	+	0.255024i
$455$		0			0
$456$	5.06179	−	3.25301i	0.237040	−	0.152336i
$457$	10.4402	+	12.0486i	0.488370	+	0.563609i	0.945429	−	0.325827i	$-0.105643\pi$
$457$	10.4402	+	12.0486i	0.488370	+	0.563609i	−0.457060	+	0.889436i	$0.651097\pi$
$458$	−14.2370	+	4.18037i	−0.665253	+	0.195336i
$459$	21.0947			0.984618
$460$		0			0
$461$	11.5522			0.538040			0.269020	−	0.963135i	$-0.413300\pi$
$461$	11.5522			0.538040			0.269020	+	0.963135i	$0.413300\pi$
$462$	−0.101494	+	0.0298014i	−0.00472194	+	0.00138649i
$463$	−24.1695	−	27.8930i	−1.12325	−	1.29630i	−0.950288	−	0.311371i	$-0.899212\pi$
$463$	−24.1695	−	27.8930i	−1.12325	−	1.29630i	−0.172961	−	0.984929i	$-0.555334\pi$
$464$	−2.53513	+	1.62923i	−0.117691	+	0.0756352i
$465$		0			0
$466$	−3.72252	−	2.39232i	−0.172442	−	0.110822i
$467$	7.56068	−	16.5556i	0.349867	−	0.766101i	−0.650114	−	0.759837i	$-0.725279\pi$
$467$	7.56068	−	16.5556i	0.349867	−	0.766101i	0.999980	−	0.00626403i	$-0.00199392\pi$
$468$	−12.6734	+	14.6259i	−0.585829	+	0.676083i
$469$	0.0473940	−	0.329632i	0.00218845	−	0.0152210i
$470$		0			0
$471$	−9.47505	−	2.78212i	−0.436587	−	0.128194i
$472$	2.92496	+	0.858845i	0.134632	+	0.0395316i
$473$	1.01812	+	2.22937i	0.0468131	+	0.102506i
$474$	−0.718915	+	5.00017i	−0.0330209	+	0.229665i
$475$		0			0
$476$	−2.36547	+	5.17965i	−0.108421	+	0.237409i
$477$	−18.5822	−	11.9421i	−0.850821	−	0.546790i
$478$	1.38470	+	9.63082i	0.0633348	+	0.440504i
$479$	−18.1099	+	11.6385i	−0.827463	+	0.531778i	−0.884471	−	0.466596i	$-0.845480\pi$
$479$	−18.1099	+	11.6385i	−0.827463	+	0.531778i	0.0570081	+	0.998374i	$0.481844\pi$
$480$		0			0
$481$	−24.3678	+	7.15503i	−1.11108	+	0.326241i
$482$	−3.41711			−0.155645
$483$	0.347006	+	2.41549i	0.0157893	+	0.109908i
$484$	17.4970			0.795319
$485$		0			0
$486$	6.32067	+	7.29444i	0.286712	+	0.330883i
$487$	−24.9345	+	16.0245i	−1.12989	+	0.726137i	−0.965538	−	0.260264i	$-0.916190\pi$
$487$	−24.9345	+	16.0245i	−1.12989	+	0.726137i	−0.164354	+	0.986401i	$0.552554\pi$
$488$	−1.79845	−	12.5085i	−0.0814118	−	0.566232i
$489$	−10.0161	−	6.43695i	−0.452943	−	0.291089i
$490$		0			0
$491$	5.36441	−	6.19086i	0.242093	−	0.279390i	−0.621680	−	0.783271i	$-0.713550\pi$
$491$	5.36441	−	6.19086i	0.242093	−	0.279390i	0.863773	+	0.503881i	$0.168095\pi$
$492$	−0.533775	+	3.71249i	−0.0240644	+	0.167372i
$493$	−3.62362	−	7.93461i	−0.163199	−	0.357357i
$494$	−10.5781	−	3.10602i	−0.475932	−	0.139746i
$495$		0			0
$496$	6.24138	+	13.6667i	0.280246	+	0.613653i
$497$	1.41260	−	9.82485i	0.0633638	−	0.440705i
$498$	−1.15780	+	1.33617i	−0.0518821	+	0.0598752i
$499$	17.6070	−	38.5539i	0.788197	−	1.72591i	0.106456	−	0.994317i	$-0.466050\pi$
$499$	17.6070	−	38.5539i	0.788197	−	1.72591i	0.681741	−	0.731593i	$-0.261223\pi$
$500$		0			0
$501$	1.11749	+	7.77229i	0.0499256	+	0.347240i
$502$	5.51562	−	3.54467i	0.246174	−	0.158207i
$503$	−25.9914	−	29.9957i	−1.15890	−	1.33744i	−0.931543	−	0.363630i	$-0.881537\pi$
$503$	−25.9914	−	29.9957i	−1.15890	−	1.33744i	−0.227356	−	0.973812i	$-0.573008\pi$
$504$	−3.61788	+	1.06230i	−0.161153	+	0.0473188i
$505$		0			0
$506$	0.142001	−	0.986818i	0.00631272	−	0.0438694i
$507$	−8.42645			−0.374232
$508$	21.4629	−	6.30206i	0.952260	−	0.279609i
$509$	−1.56358	−	1.80446i	−0.0693043	−	0.0799815i	0.720039	−	0.693934i	$-0.244124\pi$
$509$	−1.56358	−	1.80446i	−0.0693043	−	0.0799815i	−0.789343	+	0.613953i	$0.789579\pi$
$510$		0			0
$511$	−0.735993	−	5.11895i	−0.0325584	−	0.226449i
$512$	15.3606	+	9.87168i	0.678850	+	0.436271i
$513$	6.01549	−	13.1721i	0.265590	−	0.581562i
$514$	−11.2491	+	12.9822i	−0.496178	+	0.572620i
$515$		0			0
$516$	−3.68090	−	8.06004i	−0.162042	−	0.354824i
$517$	−0.104965	−	0.0308206i	−0.00461637	−	0.00135549i
$518$	−2.11498	−	0.621014i	−0.0929268	−	0.0272858i
$519$	2.29867	+	5.03338i	0.100900	+	0.220941i
$520$		0			0
$521$	−16.7682	+	19.3515i	−0.734627	+	0.847804i	−0.992984	−	0.118245i	$-0.962273\pi$
$521$	−16.7682	+	19.3515i	−0.734627	+	0.847804i	0.258358	+	0.966049i	$0.416819\pi$
$522$	1.06891	−	2.34059i	0.0467850	−	0.102445i
$523$	20.9263	+	13.4485i	0.915045	+	0.588063i	0.911216	−	0.411929i	$-0.135145\pi$
$523$	20.9263	+	13.4485i	0.915045	+	0.588063i	0.00382875	+	0.999993i	$0.498781\pi$
$524$	1.73413	+	12.0611i	0.0757559	+	0.526894i
$525$		0			0
$526$	−5.30489	−	6.12217i	−0.231304	−	0.266939i
$527$	−41.7278	+	12.2524i	−1.81769	+	0.533723i
$528$	0.443765			0.0193124
$529$	−22.0668	−	6.48502i	−0.959427	−	0.281957i
$530$		0			0
$531$	3.15994	−	0.927842i	0.137130	−	0.0402649i
$532$	2.55976	+	2.95412i	0.110980	+	0.128077i
$533$	12.9778	−	8.34034i	0.562132	−	0.361260i
$534$	−0.954600	−	6.63939i	−0.0413096	−	0.287314i
$535$		0			0
$536$	0.458707	−	1.00443i	0.0198131	−	0.0433847i
$537$	7.75579	−	8.95066i	0.334687	−	0.386250i
$538$	−1.55073	+	10.7856i	−0.0668567	+	0.464999i
$539$	0.899825	+	1.97034i	0.0387582	+	0.0848686i
$540$		0			0
$541$	39.2602	+	11.5278i	1.68793	+	0.495621i	0.977992	−	0.208643i	$-0.0669047\pi$
$541$	39.2602	+	11.5278i	1.68793	+	0.495621i	0.709938	+	0.704264i	$0.248723\pi$
$542$	4.14833	+	9.08357i	0.178186	+	0.390173i
$543$	−0.125997	+	0.876328i	−0.00540705	+	0.0376068i
$544$	−19.2204	+	22.1815i	−0.824067	+	0.951024i
$545$		0			0
$546$	−1.32327	−	0.850416i	−0.0566309	−	0.0363944i
$547$	−0.613851	−	4.26943i	−0.0262464	−	0.182547i	0.972481	−	0.232982i	$-0.0748484\pi$
$547$	−0.613851	−	4.26943i	−0.0262464	−	0.182547i	−0.998727	+	0.0504348i	$0.983939\pi$
$548$	−14.4716	+	9.30031i	−0.618194	+	0.397289i
$549$	−8.94037	−	10.3177i	−0.381566	−	0.440350i
$550$		0			0
$551$	−5.98790			−0.255093
$552$	−1.15246	+	8.00884i	−0.0490518	+	0.340879i
$553$	−7.36677			−0.313267
$554$	6.74383	−	1.98017i	0.286518	−	0.0841292i
$555$		0			0
$556$	−3.66156	+	2.35314i	−0.155285	+	0.0997954i
$557$	−1.03732	−	7.21472i	−0.0439527	−	0.305697i	−0.999925	−	0.0122409i	$-0.996103\pi$
$557$	−1.03732	−	7.21472i	−0.0439527	−	0.305697i	0.955972	−	0.293457i	$-0.0948056\pi$
$558$	−10.7922	−	6.93574i	−0.456871	−	0.293613i
$559$	−15.1398	+	33.1516i	−0.640346	+	1.40216i
$560$		0			0
$561$	−0.182806	+	1.27144i	−0.00771806	+	0.0536803i
$562$	4.00589	+	8.77167i	0.168978	+	0.370010i
$563$	−5.98146	−	1.75632i	−0.252089	−	0.0740199i	0.153247	−	0.988188i	$-0.451027\pi$
$563$	−5.98146	−	1.75632i	−0.252089	−	0.0740199i	−0.405335	+	0.914168i	$0.632845\pi$
$564$	0.379491	+	0.111429i	0.0159795	+	0.00469200i
$565$		0			0
$566$	2.66839	−	18.5590i	0.112161	−	0.780095i
$567$	−1.92196	+	2.21807i	−0.0807149	+	0.0931500i
$568$	13.6720	−	29.9374i	0.573663	−	1.25615i
$569$	27.0577	+	17.3890i	1.13432	+	0.728983i	0.966457	−	0.256828i	$-0.0826773\pi$
$569$	27.0577	+	17.3890i	1.13432	+	0.728983i	0.167862	+	0.985810i	$0.446314\pi$
$570$		0			0
$571$	13.4126	−	8.61978i	0.561302	−	0.360727i	−0.229017	−	0.973422i	$-0.573551\pi$
$571$	13.4126	−	8.61978i	0.561302	−	0.360727i	0.790319	+	0.612696i	$0.209915\pi$
$572$	−1.71914	−	1.98400i	−0.0718809	−	0.0829550i
$573$	0.141297	−	0.0414886i	0.00590278	−	0.00173321i
$574$	1.33895			0.0558868
$575$		0			0
$576$	0.113864			0.00474434
$577$	1.25386	−	0.368166i	0.0521989	−	0.0153270i	−0.255529	−	0.966801i	$-0.582250\pi$
$577$	1.25386	−	0.368166i	0.0521989	−	0.0153270i	0.307728	+	0.951474i	$0.400431\pi$
$578$	−4.10307	−	4.73519i	−0.170665	−	0.196958i
$579$	2.16011	−	1.38822i	0.0897712	−	0.0576925i
$580$		0			0
$581$	−2.16900	−	1.39393i	−0.0899854	−	0.0578301i
$582$	1.55785	−	3.41121i	0.0645749	−	0.141399i
$583$	1.96217	−	2.26447i	0.0812649	−	0.0937847i
$584$	2.44036	−	16.9731i	0.100983	−	0.702351i
$585$		0			0
$586$	−5.03635	−	1.47880i	−0.208049	−	0.0610888i
$587$	10.5950	+	3.11097i	0.437302	+	0.128403i	0.492971	−	0.870046i	$-0.335911\pi$
$587$	10.5950	+	3.11097i	0.437302	+	0.128403i	−0.0556688	+	0.998449i	$0.517729\pi$
$588$	−3.25322	−	7.12356i	−0.134161	−	0.293771i
$589$	−4.24863	+	29.5499i	−0.175062	+	1.21758i
$590$		0			0
$591$	7.27085	−	15.9209i	0.299083	−	0.654900i
$592$	7.77937	+	4.99950i	0.319730	+	0.205478i
$593$	−5.42480	−	37.7303i	−0.222770	−	1.54940i	−0.727492	−	0.686116i	$-0.759314\pi$
$593$	−5.42480	−	37.7303i	−0.222770	−	1.54940i	0.504723	−	0.863282i	$-0.331595\pi$
$594$	−0.710098	+	0.456352i	−0.0291357	+	0.0187244i
$595$		0			0
$596$	33.4907	−	9.83375i	1.37183	−	0.402806i
$597$	−15.2802			−0.625375
$598$	12.4730	−	8.01382i	0.510057	−	0.327710i
$599$	32.5001			1.32792			0.663959	−	0.747769i	$-0.268875\pi$
$599$	32.5001			1.32792			0.663959	+	0.747769i	$0.268875\pi$
$600$		0			0
$601$	29.3475	+	33.8688i	1.19711	+	1.38154i	0.905141	+	0.425110i	$0.139765\pi$
$601$	29.3475	+	33.8688i	1.19711	+	1.38154i	0.291968	+	0.956428i	$0.405690\pi$
$602$	−2.66106	+	1.71016i	−0.108457	+	0.0697010i
$603$	−0.169771	−	1.18078i	−0.00691359	−	0.0480851i
$604$	5.07091	+	3.25887i	0.206332	+	0.132602i
$605$		0			0
$606$	2.86856	−	3.31049i	0.116527	−	0.134480i
$607$	4.94501	−	34.3933i	0.200712	−	1.39598i	−0.601467	−	0.798898i	$-0.705417\pi$
$607$	4.94501	−	34.3933i	0.200712	−	1.39598i	0.802179	−	0.597084i	$-0.203674\pi$
$608$	8.36970	+	18.3271i	0.339436	+	0.743261i
$609$	−0.819732	−	0.240695i	−0.0332172	−	0.00975346i
$610$		0			0
$611$	−0.675786	−	1.47977i	−0.0273394	−	0.0598649i
$612$	−2.90285	+	20.1898i	−0.117341	+	0.816123i
$613$	−18.3577	+	21.1859i	−0.741461	+	0.855691i	−0.993712	−	0.111970i	$-0.964284\pi$
$613$	−18.3577	+	21.1859i	−0.741461	+	0.855691i	0.252251	+	0.967662i	$0.418829\pi$
$614$	7.43784	−	16.2866i	0.300167	−	0.657274i
$615$		0			0
$616$	−0.0727914	−	0.506275i	−0.00293285	−	0.0203984i
$617$	11.1312	−	7.15357i	0.448124	−	0.287992i	−0.297050	−	0.954862i	$-0.596003\pi$
$617$	11.1312	−	7.15357i	0.448124	−	0.287992i	0.745174	+	0.666870i	$0.232366\pi$
$618$	5.89050	+	6.79799i	0.236951	+	0.273455i
$619$	−9.59908	+	2.81854i	−0.385820	+	0.113287i	−0.468889	−	0.883257i	$-0.655346\pi$
$619$	−9.59908	+	2.81854i	−0.385820	+	0.113287i	0.0830698	+	0.996544i	$0.473528\pi$
$620$		0			0
$621$	8.08728	+	17.7142i	0.324531	+	0.710845i
$622$	−10.4812			−0.420258
$623$	9.38562	−	2.75587i	0.376027	−	0.110411i
$624$	4.32140	+	4.98717i	0.172995	+	0.199646i
$625$		0			0
$626$	−0.319164	−	2.21983i	−0.0127564	−	0.0887224i
$627$	0.741790	+	0.476719i	0.0296242	+	0.0190383i
$628$	8.83638	−	19.3490i	0.352610	−	0.772108i
$629$	−17.5288	+	20.2293i	−0.698919	+	0.806596i
$630$		0			0
$631$	7.02551	+	15.3837i	0.279681	+	0.612416i	0.996384	−	0.0849623i	$-0.0270770\pi$
$631$	7.02551	+	15.3837i	0.279681	+	0.612416i	−0.716703	+	0.697378i	$0.754350\pi$
$632$	−23.4368	−	6.88168i	−0.932267	−	0.273738i
$633$	−7.55201	−	2.21747i	−0.300165	−	0.0881365i
$634$	−4.96664	−	10.8754i	−0.197250	−	0.431918i
$635$		0			0
$636$	−7.09403	+	8.18694i	−0.281296	+	0.324633i
$637$	−13.3807	+	29.2997i	−0.530164	+	1.16090i
$638$	0.293633	+	0.188706i	0.0116250	+	0.00747095i
$639$	−5.06009	−	35.1937i	−0.200174	−	1.39224i
$640$		0			0
$641$	−19.5982	−	22.6175i	−0.774081	−	0.893338i	0.222586	−	0.974913i	$-0.428550\pi$
$641$	−19.5982	−	22.6175i	−0.774081	−	0.893338i	−0.996667	+	0.0815755i	$0.974005\pi$
$642$	−1.79876	+	0.528163i	−0.0709914	+	0.0208449i
$643$	−24.1238			−0.951351			−0.475675	−	0.879621i	$-0.657796\pi$
$643$	−24.1238			−0.951351			−0.475675	+	0.879621i	$0.657796\pi$
$644$	−5.25645		0.000615947i	−0.207133		2.42717e-5i
$645$		0			0
$646$	−11.1490	+	3.27366i	−0.438653	+	0.128800i
$647$	5.39457	+	6.22567i	0.212082	+	0.244756i	0.851817	−	0.523840i	$-0.175501\pi$
$647$	5.39457	+	6.22567i	0.212082	+	0.244756i	−0.639734	+	0.768596i	$0.720956\pi$
$648$	−8.18659	+	5.26120i	−0.321600	+	0.206680i
$649$	0.0635777	+	0.442193i	0.00249564	+	0.0173576i
$650$		0			0
$651$	−1.76944	+	3.87454i	−0.0693500	+	0.151855i
$652$	16.7947	−	19.3822i	0.657732	−	0.759064i
$653$	−1.44418	+	10.0445i	−0.0565150	+	0.393070i	0.941856	+	0.336016i	$0.109080\pi$
$653$	−1.44418	+	10.0445i	−0.0565150	+	0.393070i	−0.998371	+	0.0570539i	$0.981829\pi$
$654$	1.00206	+	2.19421i	0.0391837	+	0.0858003i
$655$		0			0
$656$	−5.38965	−	1.58254i	−0.210430	−	0.0617879i
$657$	−7.69565	−	16.8511i	−0.300236	−	0.657425i
$658$	0.0200940	−	0.139757i	0.000783347	−	0.00544830i
$659$	−14.7008	+	16.9656i	−0.572661	+	0.660885i	−0.966010	−	0.258503i	$-0.916771\pi$
$659$	−14.7008	+	16.9656i	−0.572661	+	0.660885i	0.393350	+	0.919389i	$0.371316\pi$
$660$		0			0
$661$	−9.98338	−	6.41593i	−0.388309	−	0.249551i	0.331891	−	0.943318i	$-0.392313\pi$
$661$	−9.98338	−	6.41593i	−0.388309	−	0.249551i	−0.720200	+	0.693767i	$0.755950\pi$
$662$	1.81675	+	12.6358i	0.0706101	+	0.491104i
$663$	−16.0690	+	10.3269i	−0.624068	+	0.401064i
$664$	−5.59838	−	6.46087i	−0.217259	−	0.250730i
$665$		0			0
$666$	−7.89593			−0.305961
$667$	5.27382	−	6.08487i	0.204203	−	0.235607i
$668$	−16.9139			−0.654420
$669$	−5.60961	+	1.64713i	−0.216880	+	0.0636818i
$670$		0			0
$671$	1.55794	−	1.00123i	0.0601436	−	0.0386520i
$672$	0.409104	+	2.84538i	0.0157815	+	0.109763i
$673$	29.2690	+	18.8100i	1.12824	+	0.725074i	0.965191	−	0.261545i	$-0.0842320\pi$
$673$	29.2690	+	18.8100i	1.12824	+	0.725074i	0.163045	+	0.986619i	$0.447868\pi$
$674$	−1.61938	+	3.54595i	−0.0623762	+	0.136585i
$675$		0			0
$676$	2.58314	−	17.9661i	0.0993514	−	0.691004i
$677$	−3.77751	−	8.27158i	−0.145181	−	0.317903i	0.823046	−	0.567975i	$-0.192273\pi$
$677$	−3.77751	−	8.27158i	−0.145181	−	0.317903i	−0.968227	+	0.250072i	$0.919546\pi$
$678$	−1.98150	−	0.581820i	−0.0760989	−	0.0223447i
$679$	5.24729	+	1.54074i	0.201372	+	0.0591283i
$680$		0			0
$681$	1.70122	−	11.8322i	0.0651907	−	0.453412i
$682$	1.13960	−	1.31516i	0.0436374	−	0.0503602i
$683$	0.398412	−	0.872401i	0.0152448	−	0.0333815i	−0.901856	−	0.432036i	$-0.857795\pi$
$683$	0.398412	−	0.872401i	0.0152448	−	0.0333815i	0.917101	+	0.398654i	$0.130523\pi$
$684$	11.7792	+	7.57003i	0.450389	+	0.289447i
$685$		0			0
$686$	−4.87125	+	3.13056i	−0.185985	+	0.119525i
$687$	11.5568	+	13.3372i	0.440918	+	0.508847i
$688$	12.7328	−	3.73868i	0.485433	−	0.142536i
$689$	44.5565			1.69747
$690$		0			0
$691$	−1.18099			−0.0449269			−0.0224634	−	0.999748i	$-0.507151\pi$
$691$	−1.18099			−0.0449269			−0.0224634	+	0.999748i	$0.507151\pi$
$692$	−11.4364	+	3.35802i	−0.434746	+	0.127653i
$693$	−0.361858	−	0.417606i	−0.0137458	−	0.0158635i
$694$	9.74303	−	6.26147i	0.369840	−	0.237682i
$695$		0			0
$696$	−2.38307	−	1.53151i	−0.0903301	−	0.0580516i
$697$	6.75439	−	14.7901i	0.255841	−	0.560214i
$698$	−5.48702	+	6.33236i	−0.207687	+	0.239683i
$699$	−0.748979	+	5.20926i	−0.0283290	+	0.197032i
$700$		0			0
$701$	−50.2799	−	14.7635i	−1.89905	−	0.557610i	−0.990032	−	0.140846i	$-0.955018\pi$
$701$	−50.2799	−	14.7635i	−1.89905	−	0.557610i	−0.909015	−	0.416764i	$-0.863164\pi$
$702$	−12.0436	−	3.53632i	−0.454556	−	0.133470i
$703$	7.63309	+	16.7141i	0.287887	+	0.630385i
$704$	−0.00219814	+	0.0152884i	−8.28455e−5	+	0.000576203i
$705$		0			0
$706$	−0.810590	+	1.77494i	−0.0305070	+	0.0668009i
$707$	5.37392	+	3.45361i	0.202107	+	0.129886i
$708$	−0.229858	−	1.59870i	−0.00863861	−	0.0600828i
$709$	23.0765	−	14.8304i	0.866658	−	0.556967i	−0.0300710	−	0.999548i	$-0.509573\pi$
$709$	23.0765	−	14.8304i	0.866658	−	0.556967i	0.896729	+	0.442581i	$0.145937\pi$
$710$		0			0
$711$	−25.3197	+	7.43453i	−0.949562	+	0.278817i
$712$	32.4340			1.21552
$713$	−26.2865	−	30.3434i	−0.984436	−	1.13637i
$714$	−1.65787			−0.0620444
$715$		0			0
$716$	16.7062	+	19.2800i	0.624342	+	0.720529i
$717$	9.73516	−	6.25641i	0.363566	−	0.233650i
$718$	−2.87837	−	20.0195i	−0.107420	−	0.747120i
$719$	−30.4388	−	19.5618i	−1.13518	−	0.729533i	−0.168542	−	0.985695i	$-0.553906\pi$
$719$	−30.4388	−	19.5618i	−1.13518	−	0.729533i	−0.966634	+	0.256161i	$0.917542\pi$
$720$		0			0
$721$	−8.59017	+	9.91358i	−0.319915	+	0.369201i
$722$	0.560623	−	3.89922i	0.0208642	−	0.145114i
$723$	1.68831	+	3.69688i	0.0627888	+	0.137488i
$724$	−1.82980	−	0.537279i	−0.0680041	−	0.0199678i
$725$		0			0
$726$	2.11623	+	4.63390i	0.0785407	+	0.171980i
$727$	6.88269	−	47.8701i	0.255265	−	1.77541i	−0.310238	−	0.950659i	$-0.600409\pi$
$727$	6.88269	−	47.8701i	0.255265	−	1.77541i	0.565503	−	0.824746i	$-0.308682\pi$
$728$	4.98082	−	5.74818i	0.184602	−	0.213042i
$729$	−0.592928	+	1.29833i	−0.0219603	+	0.0480864i
$730$		0			0
$731$	5.46661	+	38.0211i	0.202190	+	1.40626i
$732$	−5.63257	+	3.61983i	−0.208186	+	0.133793i
$733$	19.5409	+	22.5514i	0.721759	+	0.832954i	0.991517	−	0.129974i	$-0.0414894\pi$
$733$	19.5409	+	22.5514i	0.721759	+	0.832954i	−0.269759	+	0.962928i	$0.586944\pi$
$734$	9.99927	−	2.93605i	0.369080	−	0.108372i
$735$		0			0
$736$	−25.9955	−	7.63626i	−0.958205	−	0.281476i
$737$	0.161819			0.00596068
$738$	4.60199	−	1.35127i	0.169402	−	0.0497408i
$739$	16.9295	+	19.5377i	0.622763	+	0.718707i	0.976229	−	0.216740i	$-0.0695424\pi$
$739$	16.9295	+	19.5377i	0.622763	+	0.718707i	−0.353466	+	0.935447i	$0.614997\pi$
$740$		0			0
$741$	1.86606	+	12.9788i	0.0685516	+	0.476787i
$742$	3.25333	+	2.09079i	0.119433	+	0.0767551i
$743$	−15.4483	+	33.8272i	−0.566745	+	1.24100i	0.381768	+	0.924258i	$0.375315\pi$
$743$	−15.4483	+	33.8272i	−0.566745	+	1.24100i	−0.948512	+	0.316740i	$0.897412\pi$
$744$	−9.24876	+	10.6736i	−0.339076	+	0.391314i
$745$		0			0
$746$	−6.22378	−	13.6282i	−0.227869	−	0.498963i
$747$	−8.86164	−	2.60201i	−0.324231	−	0.0952027i
$748$	−2.65481	−	0.779523i	−0.0970695	−	0.0285022i
$749$	−1.13570	−	2.48683i	−0.0414975	−	0.0908669i
$750$		0			0
$751$	−6.11771	+	7.06022i	−0.223239	+	0.257631i	−0.856310	−	0.516463i	$-0.827249\pi$
$751$	−6.11771	+	7.06022i	−0.223239	+	0.257631i	0.633071	+	0.774094i	$0.281794\pi$
$752$	−0.246067	+	0.538811i	−0.00897312	+	0.0196484i
$753$	−6.56000	−	4.21586i	−0.239060	−	0.153634i
$754$	0.738670	+	5.13756i	0.0269008	+	0.187099i
$755$		0			0
$756$	2.91438	+	3.36337i	0.105995	+	0.122325i
$757$	15.0052	−	4.40593i	0.545374	−	0.160136i	0.00257145	−	0.999997i	$-0.499181\pi$
$757$	15.0052	−	4.40593i	0.545374	−	0.160136i	0.542802	+	0.839861i	$0.317363\pi$
$758$	19.4130			0.705111
$759$	−1.13777	+	0.333934i	−0.0412984	+	0.0121210i
$760$		0			0
$761$	5.35844	−	1.57338i	0.194243	−	0.0570350i	−0.183164	−	0.983082i	$-0.558634\pi$
$761$	5.35844	−	1.57338i	0.194243	−	0.0570350i	0.377407	+	0.926047i	$0.376816\pi$
$762$	4.26492	+	4.92199i	0.154502	+	0.178305i
$763$	−2.95930	+	1.90182i	−0.107134	+	0.0688507i
$764$	0.0451435	+	0.313980i	0.00163323	+	0.0113594i
$765$		0			0
$766$	−0.626840	+	1.37259i	−0.0226486	+	0.0495936i
$767$	−4.35037	+	5.02059i	−0.157083	+	0.181283i
$768$	−0.744255	+	5.17641i	−0.0268560	+	0.186788i
$769$	−19.5148	−	42.7314i	−0.703720	−	1.54093i	−0.835401	−	0.549640i	$-0.814765\pi$
$769$	−19.5148	−	42.7314i	−0.703720	−	1.54093i	0.131681	−	0.991292i	$-0.457963\pi$
$770$		0			0
$771$	19.6030	+	5.75595i	0.705983	+	0.207295i
$772$	2.29765	+	5.03116i	0.0826943	+	0.181075i
$773$	0.318064	−	2.21219i	0.0114400	−	0.0795668i	−0.983302	−	0.181983i	$-0.941748\pi$
$773$	0.318064	−	2.21219i	0.0114400	−	0.0795668i	0.994742	+	0.102416i	$0.0326574\pi$
$774$	−7.42021	+	8.56338i	−0.266714	+	0.307804i
$775$		0			0
$776$	15.2546	+	9.80352i	0.547607	+	0.351926i
$777$	0.373099	+	2.59496i	0.0133848	+	0.0930937i
$778$	5.49478	−	3.53128i	0.196997	−	0.126603i
$779$	−7.30917	−	8.43523i	−0.261878	−	0.302223i
$780$		0			0
$781$	4.82309			0.172584
$782$	6.49281	−	14.2129i	0.232182	−	0.508251i
$783$	−6.81745			−0.243636
$784$	11.2534	−	3.30429i	0.401907	−	0.118010i
$785$		0			0
$786$	−2.98453	+	1.91804i	−0.106454	+	0.0684142i
$787$	3.76607	+	26.1936i	0.134246	+	0.933700i	0.939933	+	0.341359i	$0.110887\pi$
$787$	3.76607	+	26.1936i	0.134246	+	0.933700i	−0.805687	+	0.592341i	$0.798204\pi$
$788$	31.7163	+	20.3828i	1.12985	+	0.726108i
$789$	−4.00239	+	8.76400i	−0.142489	+	0.312007i
$790$		0			0
$791$	0.428600	−	2.98098i	0.0152392	−	0.105991i
$792$	−0.761116	−	1.66661i	−0.0270451	−	0.0592205i
$793$	26.4234	+	7.75860i	0.938322	+	0.275516i
$794$	19.7597	+	5.80196i	0.701244	+	0.205904i
$795$		0			0
$796$	4.68415	−	32.5790i	0.166025	−	1.15473i
$797$	−26.1347	+	30.1610i	−0.925737	+	1.06836i	0.0717435	+	0.997423i	$0.477144\pi$
$797$	−26.1347	+	30.1610i	−0.925737	+	1.06836i	−0.997481	+	0.0709348i	$0.977402\pi$
$798$	−0.472768	+	1.03522i	−0.0167358	+	0.0366463i
$799$	−1.44239	−	0.926969i	−0.0510281	−	0.0327938i
$800$		0			0
$801$	29.4773	−	18.9439i	1.04153	−	0.669349i
$802$	3.71868	+	4.29158i	0.131311	+	0.151541i
$803$	2.41114	−	0.707974i	0.0850873	−	0.0249839i
$804$	−0.585040			−0.0206328
$805$		0			0
$806$	25.8776			0.911500
$807$	12.4348	−	3.65117i	0.437724	−	0.128527i
$808$	13.8705	+	16.0075i	0.487964	+	0.563140i
$809$	0.752013	−	0.483289i	0.0264394	−	0.0169915i	−0.527354	−	0.849645i	$-0.676816\pi$
$809$	0.752013	−	0.483289i	0.0264394	−	0.0169915i	0.553794	+	0.832654i	$0.313180\pi$
$810$		0			0
$811$	−6.28784	−	4.04095i	−0.220796	−	0.141897i	0.425567	−	0.904927i	$-0.360075\pi$
$811$	−6.28784	−	4.04095i	−0.220796	−	0.141897i	−0.646363	+	0.763030i	$0.723711\pi$
$812$	0.764478	−	1.67397i	0.0268279	−	0.0587450i
$813$	7.77766	−	8.97590i	0.272775	−	0.314799i
$814$	0.152430	−	1.06018i	0.00534268	−	0.0371591i
$815$		0			0
$816$	6.67340	+	1.95949i	0.233616	+	0.0685957i
$817$	25.3002	+	7.42881i	0.885142	+	0.259901i
$818$	5.21193	+	11.4125i	0.182231	+	0.399030i
$819$	1.16940	−	8.13333i	0.0408620	−	0.284202i
$820$		0			0
$821$	6.02859	−	13.2008i	0.210399	−	0.460710i	−0.774782	−	0.632229i	$-0.782140\pi$
$821$	6.02859	−	13.2008i	0.210399	−	0.460710i	0.985181	+	0.171519i	$0.0548675\pi$
$822$	−4.21339	−	2.70778i	−0.146959	−	0.0944448i
$823$	3.47250	+	24.1518i	0.121044	+	0.841877i	0.956377	+	0.292134i	$0.0943654\pi$
$823$	3.47250	+	24.1518i	0.121044	+	0.841877i	−0.835334	+	0.549743i	$0.814726\pi$
$824$	−36.5898	+	23.5148i	−1.27466	+	0.819177i
$825$		0			0
$826$	−0.553234	+	0.162444i	−0.0192495	+	0.00565216i
$827$	−18.2026			−0.632965			−0.316483	−	0.948598i	$-0.602502\pi$
$827$	−18.2026			−0.632965			−0.316483	+	0.948598i	$0.602502\pi$
$828$	−18.0671	+	5.30268i	−0.627876	+	0.184281i
$829$	1.17628			0.0408540			0.0204270	−	0.999791i	$-0.493497\pi$
$829$	1.17628			0.0408540			0.0204270	+	0.999791i	$0.493497\pi$
$830$		0			0
$831$	−5.47423	−	6.31760i	−0.189899	−	0.219155i
$832$	−0.193221	+	0.124176i	−0.00669874	+	0.00430502i
$833$	4.83145	+	33.6035i	0.167400	+	1.16429i
$834$	−1.06606	−	0.685117i	−0.0369147	−	0.0237237i
$835$		0			0
$836$	−1.24381	+	1.43544i	−0.0430182	+	0.0496457i
$837$	−4.83722	+	33.6436i	−0.167199	+	1.16289i
$838$	−2.12260	−	4.64784i	−0.0733239	−	0.160557i
$839$	−40.4730	−	11.8840i	−1.39728	−	0.410280i	−0.505534	−	0.862807i	$-0.668704\pi$
$839$	−40.4730	−	11.8840i	−1.39728	−	0.410280i	−0.891751	+	0.452527i	$0.850523\pi$
$840$		0			0
$841$	−10.8759	−	23.8150i	−0.375033	−	0.821207i
$842$	−1.70538	+	11.8612i	−0.0587713	+	0.408764i
$843$	7.51060	−	8.66770i	0.258679	−	0.298531i
$844$	7.04296	−	15.4219i	0.242429	−	0.530845i
$845$		0			0
$846$	−0.0719791	−	0.500625i	−0.00247469	−	0.0172119i
$847$	−6.24967	+	4.01642i	−0.214741	+	0.138006i
$848$	−10.6244	−	12.2612i	−0.364842	−	0.421050i
$849$	−21.3969	+	6.28269i	−0.734339	+	0.215621i
$850$		0			0
$851$	−23.7076	−	6.96420i	−0.812687	−	0.238730i
$852$	−17.4374			−0.597395
$853$	15.2919	−	4.49011i	0.523585	−	0.153738i	−0.00925078	−	0.999957i	$-0.502945\pi$
$853$	15.2919	−	4.49011i	0.523585	−	0.153738i	0.532835	+	0.846219i	$0.321126\pi$
$854$	1.56526	+	1.80640i	0.0535620	+	0.0618138i
$855$		0			0
$856$	−1.29006	−	8.97259i	−0.0440935	−	0.306677i
$857$	5.68973	+	3.65657i	0.194358	+	0.124906i	0.634200	−	0.773169i	$-0.281329\pi$
$857$	5.68973	+	3.65657i	0.194358	+	0.124906i	−0.439843	+	0.898075i	$0.644966\pi$
$858$	0.317513	−	0.695256i	0.0108397	−	0.0237357i
$859$	−2.18077	+	2.51674i	−0.0744068	+	0.0858700i	−0.791732	−	0.610868i	$-0.790821\pi$
$859$	−2.18077	+	2.51674i	−0.0744068	+	0.0858700i	0.717326	+	0.696738i	$0.245366\pi$
$860$		0			0
$861$	−0.661541	−	1.44857i	−0.0225453	−	0.0493672i
$862$	4.70383	+	1.38117i	0.160213	+	0.0470428i
$863$	37.3315	+	10.9615i	1.27078	+	0.373135i	0.846496	−	0.532394i	$-0.178708\pi$
$863$	37.3315	+	10.9615i	1.27078	+	0.373135i	0.424284	+	0.905529i	$0.360526\pi$
$864$	9.52921	+	20.8661i	0.324190	+	0.709878i
$865$		0			0
$866$	−6.93263	+	8.00068i	−0.235580	+	0.271874i
$867$	−3.09565	+	6.77852i	−0.105134	+	0.230211i
$868$	−7.71852	−	4.96039i	−0.261984	−	0.168367i
$869$	−0.509430	−	3.54316i	−0.0172812	−	0.120194i
$870$		0			0
$871$	1.57580	+	1.81857i	0.0533939	+	0.0616199i
$872$	−11.1914	+	3.28608i	−0.378988	+	0.111281i
$873$	19.5899			0.663018
$874$	−7.02335	−	8.10729i	−0.237568	−	0.274233i
$875$		0			0
$876$	−8.71722	+	2.55961i	−0.294528	+	0.0864811i
$877$	21.2088	+	24.4763i	0.716171	+	0.826505i	0.990841	−	0.135034i	$-0.0431142\pi$
$877$	21.2088	+	24.4763i	0.716171	+	0.826505i	−0.274670	+	0.961538i	$0.588569\pi$
$878$	−16.9096	+	10.8672i	−0.570672	+	0.366749i
$879$	0.888451	+	6.17931i	0.0299667	+	0.208423i
$880$		0			0
$881$	1.57762	−	3.45451i	0.0531515	−	0.116385i	−0.881193	−	0.472757i	$-0.843259\pi$
$881$	1.57762	−	3.45451i	0.0531515	−	0.116385i	0.934344	+	0.356371i	$0.115986\pi$
$882$	−6.55807	+	7.56842i	−0.220822	+	0.254842i
$883$	−1.18666	+	8.25337i	−0.0399342	+	0.277748i	−0.999998	−	0.00203308i	$-0.999353\pi$
$883$	−1.18666	+	8.25337i	−0.0399342	+	0.277748i	0.960064	+	0.279781i	$0.0902619\pi$
$884$	−17.0921	−	37.4266i	−0.574871	−	1.25879i
$885$		0			0
$886$	18.7925	+	5.51799i	0.631348	+	0.185380i
$887$	5.08398	+	11.1324i	0.170703	+	0.373788i	0.975577	−	0.219658i	$-0.0704942\pi$
$887$	5.08398	+	11.1324i	0.170703	+	0.373788i	−0.804874	+	0.593446i	$0.797767\pi$
$888$	−1.23710	+	8.60420i	−0.0415143	+	0.288738i
$889$	−6.21958	+	7.17778i	−0.208598	+	0.240735i
$890$		0			0
$891$	−1.19972	−	0.771013i	−0.0401921	−	0.0258299i
$892$	−1.79223	−	12.4652i	−0.0600083	−	0.417367i
$893$	−0.990143	+	0.636326i	−0.0331339	+	0.0212938i
$894$	6.65499	+	7.68027i	0.222576	+	0.256867i
$895$		0			0
$896$	−7.72781			−0.258168
$897$	−14.8325	−	9.53471i	−0.495242	−	0.318355i
$898$	−8.66027			−0.288997
$899$	13.4857	−	3.95976i	0.449774	−	0.132065i
$900$		0			0
$901$	39.5063	−	25.3892i	1.31615	−	0.845836i
$902$	0.0925917	+	0.643989i	0.00308297	+	0.0214425i
$903$	3.16494	+	2.03398i	0.105322	+	0.0676866i
$904$	4.14824	−	9.08337i	0.137968	−	0.302108i
$905$		0			0
$906$	−0.249761	+	1.73713i	−0.00829777	+	0.0577122i
$907$	2.56409	+	5.61456i	0.0851391	+	0.186429i	0.947413	−	0.320014i	$-0.103688\pi$
$907$	2.56409	+	5.61456i	0.0851391	+	0.186429i	−0.862274	+	0.506442i	$0.830960\pi$
$908$	24.7061	+	7.25436i	0.819900	+	0.240744i
$909$	21.9556	+	6.44675i	0.728222	+	0.213825i
$910$		0			0
$911$	−3.96194	+	27.5559i	−0.131265	+	0.912967i	0.812644	+	0.582761i	$0.198028\pi$
$911$	−3.96194	+	27.5559i	−0.131265	+	0.912967i	−0.943909	+	0.330207i	$0.892882\pi$
$912$	3.12657	−	3.60826i	0.103531	−	0.119481i
$913$	0.520442	−	1.13961i	0.0172241	−	0.0377155i
$914$	−8.41112	−	5.40550i	−0.278215	−	0.178798i
$915$		0			0
$916$	−31.9792	+	20.5518i	−1.05662	+	0.679049i
$917$	−3.38803	−	3.90999i	−0.111883	−	0.129119i
$918$	−12.6936	+	3.72718i	−0.418951	+	0.123015i
$919$	10.1186			0.333783			0.166892	−	0.985975i	$-0.446627\pi$
$919$	10.1186			0.333783			0.166892	+	0.985975i	$0.446627\pi$
$920$		0			0
$921$	−21.2948			−0.701689
$922$	−6.95146	+	2.04113i	−0.228934	+	0.0672211i
$923$	46.9675	+	54.2033i	1.54595	+	1.78412i
$924$	−0.227976	+	0.146511i	−0.00749986	+	0.00481987i
$925$		0			0
$926$	19.4722	+	12.5140i	0.639895	+	0.411235i
$927$	−19.5197	+	42.7423i	−0.641112	+	1.40384i
$928$	6.21169	−	7.16867i	0.203909	−	0.235323i
$929$	3.82221	−	26.5841i	0.125403	−	0.872195i	−0.825874	−	0.563855i	$-0.809318\pi$
$929$	3.82221	−	26.5841i	0.125403	−	0.872195i	0.951276	−	0.308340i	$-0.0997734\pi$
$930$		0			0
$931$	22.3606	+	6.56567i	0.732840	+	0.215181i
$932$	−10.8771	−	3.19381i	−0.356292	−	0.104617i
$933$	5.17849	+	11.3393i	0.169536	+	0.371233i
$934$	−1.62442	+	11.2981i	−0.0531526	+	0.369684i
$935$		0			0
$936$	11.3181	−	24.7832i	0.369944	−	0.810064i
$937$	−7.04765	−	4.52925i	−0.230237	−	0.147964i	0.420437	−	0.907322i	$-0.361877\pi$
$937$	−7.04765	−	4.52925i	−0.230237	−	0.147964i	−0.650673	+	0.759358i	$0.725513\pi$
$938$	0.0297230	+	0.206728i	0.000970489	+	0.00674990i
$939$	−2.24388	+	1.44206i	−0.0732263	+	0.0470597i
$940$		0			0
$941$	17.3245	−	5.08692i	0.564761	−	0.165829i	0.0131254	−	0.999914i	$-0.495822\pi$
$941$	17.3245	−	5.08692i	0.564761	−	0.165829i	0.551636	+	0.834085i	$0.314004\pi$
$942$	6.19311			0.201782
$943$	15.0094	+	0.00175878i	0.488772	+	5.72739e-5i
$944$	2.41891			0.0787290
$945$		0			0
$946$	−1.00655	−	1.16162i	−0.0327257	−	0.0377674i
$947$	2.24700	−	1.44406i	0.0730177	−	0.0469256i	−0.503623	−	0.863924i	$-0.668000\pi$
$947$	2.24700	−	1.44406i	0.0730177	−	0.0469256i	0.576640	+	0.816998i	$0.304363\pi$
$948$	1.84179	+	12.8099i	0.0598185	+	0.416047i
$949$	31.4362	+	20.2028i	1.02046	+	0.655811i
$950$		0			0
$951$	−9.31191	+	10.7465i	−0.301959	+	0.348480i
$952$	1.14086	−	7.93484i	0.0369754	−	0.257170i
$953$	−19.7829	−	43.3185i	−0.640831	−	1.40322i	−0.899355	−	0.437219i	$-0.855963\pi$
$953$	−19.7829	−	43.3185i	−0.640831	−	1.40322i	0.258524	−	0.966005i	$-0.416764\pi$
$954$	13.2917	+	3.90280i	0.430336	+	0.126358i
$955$		0			0
$956$	10.3550	+	22.6743i	0.334905	+	0.733340i
$957$	0.0590796	−	0.410907i	0.00190977	−	0.0132827i
$958$	8.84112	−	10.2032i	0.285644	−	0.329650i
$959$	3.03415	−	6.64386i	0.0979778	−	0.214541i
$960$		0			0
$961$	−5.56079	−	38.6762i	−0.179380	−	1.24762i
$962$	13.3989	−	8.61097i	0.431999	−	0.277629i
$963$	−6.41312	−	7.40113i	−0.206660	−	0.238498i
$964$	−8.39969	+	2.46637i	−0.270536	+	0.0794365i
$965$		0			0
$966$	−0.635595	−	1.39219i	−0.0204499	−	0.0447930i
$967$	45.2970			1.45665			0.728327	−	0.685230i	$-0.240298\pi$
$967$	45.2970			1.45665			0.728327	+	0.685230i	$0.240298\pi$
$968$	−23.6348	+	6.93981i	−0.759652	+	0.223054i
$969$	9.05012	+	10.4444i	0.290732	+	0.335522i
$970$		0			0
$971$	1.61600	+	11.2395i	0.0518600	+	0.360694i	0.999183	+	0.0404143i	$0.0128678\pi$
$971$	1.61600	+	11.2395i	0.0518600	+	0.360694i	−0.947323	+	0.320280i	$0.896223\pi$
$972$	20.8019	+	13.3686i	0.667222	+	0.428797i
$973$	0.767693	−	1.68101i	0.0246111	−	0.0538908i
$974$	12.1729	−	14.0482i	0.390044	−	0.450134i
$975$		0			0
$976$	−4.16555	−	9.12128i	−0.133336	−	0.291965i
$977$	29.8860	+	8.77534i	0.956139	+	0.280748i	0.722341	−	0.691537i	$-0.243066\pi$
$977$	29.8860	+	8.77534i	0.956139	+	0.280748i	0.233799	+	0.972285i	$0.424884\pi$
$978$	7.16444	+	2.10367i	0.229094	+	0.0672680i
$979$	1.97451	+	4.32358i	0.0631057	+	0.138182i
$980$		0			0
$981$	−8.25182	+	9.52311i	−0.263460	+	0.304049i
$982$	−2.13415	+	4.67313i	−0.0681034	+	0.149126i
$983$	−29.5490	−	18.9900i	−0.942467	−	0.605687i	−0.0233737	−	0.999727i	$-0.507441\pi$
$983$	−29.5490	−	18.9900i	−0.942467	−	0.605687i	−0.919093	+	0.394040i	$0.871077\pi$
$984$	−0.751458	−	5.22650i	−0.0239556	−	0.166615i
$985$		0			0
$986$	3.58243	+	4.13435i	0.114088	+	0.131664i
$987$	−0.161127	+	0.0473112i	−0.00512873	+	0.00150593i
$988$	−28.2442			−0.898567
$989$	−29.8322	+	19.1670i	−0.948608	+	0.609476i
$990$		0			0
$991$	1.91867	−	0.563371i	0.0609484	−	0.0178961i	−0.251116	−	0.967957i	$-0.580798\pi$
$991$	1.91867	−	0.563371i	0.0609484	−	0.0178961i	0.312065	+	0.950061i	$0.398979\pi$
$992$	−30.9695	−	35.7407i	−0.983282	−	1.13477i
$993$	12.7727	−	8.20850i	0.405329	−	0.260489i
$994$	0.885907	+	6.16162i	0.0280993	+	0.195435i
$995$		0			0
$996$	−1.88160	+	4.12013i	−0.0596209	+	0.130551i
$997$	−6.38647	+	7.37038i	−0.202262	+	0.233422i	−0.847814	−	0.530294i	$-0.822082\pi$
$997$	−6.38647	+	7.37038i	−0.202262	+	0.233422i	0.645553	+	0.763716i	$0.276627\pi$
$998$	−3.78288	+	26.3105i	−0.119745	+	0.832844i
$999$	8.69055	+	19.0297i	0.274957	+	0.602072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.k.g.101.5		100
5.2	odd	4		115.2.j.a.9.5	✓	100
5.3	odd	4		115.2.j.a.9.6	yes	100
5.4	even	2	inner	575.2.k.g.101.6		100
23.18	even	11	inner	575.2.k.g.501.5		100
115.18	odd	44		115.2.j.a.64.5	yes	100
115.64	even	22	inner	575.2.k.g.501.6		100
115.87	odd	44		115.2.j.a.64.6	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.9.5	✓	100	5.2	odd	4
115.2.j.a.9.6	yes	100	5.3	odd	4
115.2.j.a.64.5	yes	100	115.18	odd	44
115.2.j.a.64.6	yes	100	115.87	odd	44
575.2.k.g.101.5		100	1.1	even	1	trivial
575.2.k.g.101.6		100	5.4	even	2	inner
575.2.k.g.501.5		100	23.18	even	11	inner
575.2.k.g.501.6		100	115.64	even	22	inner

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.601743 + 0.176688i) q^{2} +(0.488459 + 0.563711i) q^{3} +(-1.35163 + 0.868641i) q^{4} +(-0.393527 - 0.252905i) q^{6} +(0.283387 - 0.620531i) q^{7} +(1.48124 - 1.70945i) q^{8} +(0.347766 - 2.41877i) q^{9} +O(q^{10})\)	\(q+(-0.601743 + 0.176688i) q^{2} +(0.488459 + 0.563711i) q^{3} +(-1.35163 + 0.868641i) q^{4} +(-0.393527 - 0.252905i) q^{6} +(0.283387 - 0.620531i) q^{7} +(1.48124 - 1.70945i) q^{8} +(0.347766 - 2.41877i) q^{9} +(0.318051 + 0.0933881i) q^{11} +(-1.14988 - 0.337635i) q^{12} +(2.04767 + 4.48376i) q^{13} +(-0.0608859 + 0.423471i) q^{14} +(0.745594 - 1.63262i) q^{16} +(4.37052 + 2.80876i) q^{17} +(0.218100 + 1.51692i) q^{18} +(3.00018 - 1.92810i) q^{19} +(0.488223 - 0.143355i) q^{21} -0.207885 q^{22} +(-0.683074 + 4.74694i) q^{23} +1.68716 q^{24} +(-2.02439 - 2.33628i) q^{26} +(3.41582 - 2.19521i) q^{27} +(0.155984 + 1.08489i) q^{28} +(-1.41248 - 0.907743i) q^{29} +(-5.48185 + 6.32639i) q^{31} +(-0.804002 + 5.59195i) q^{32} +(0.102711 + 0.224905i) q^{33} +(-3.12620 - 0.917936i) q^{34} +(1.63099 + 3.57136i) q^{36} +(-0.733242 + 5.09981i) q^{37} +(-1.46467 + 1.69032i) q^{38} +(-1.52735 + 3.34442i) q^{39} +(-0.445398 - 3.09781i) q^{41} +(-0.268456 + 0.172526i) q^{42} +(4.84184 + 5.58778i) q^{43} +(-0.511008 + 0.150045i) q^{44} +(-0.427690 - 2.97713i) q^{46} -0.330027 q^{47} +(1.28452 - 0.377169i) q^{48} +(4.27927 + 4.93855i) q^{49} +(0.551487 + 3.83567i) q^{51} +(-6.66247 - 4.28171i) q^{52} +(3.75505 - 8.22242i) q^{53} +(-1.66758 + 1.92449i) q^{54} +(-0.640999 - 1.40359i) q^{56} +(2.55236 + 0.749439i) q^{57} +(1.01033 + 0.296661i) q^{58} +(0.559864 + 1.22593i) q^{59} +(3.65863 - 4.22228i) q^{61} +(2.18087 - 4.77543i) q^{62} +(-1.40237 - 0.901246i) q^{63} +(0.00663133 + 0.0461219i) q^{64} +(-0.101543 - 0.117187i) q^{66} +(0.468400 - 0.137535i) q^{67} -8.34713 q^{68} +(-3.00955 + 1.93363i) q^{69} +(13.9609 - 4.09929i) q^{71} +(-3.61962 - 4.17727i) q^{72} +(6.37754 - 4.09859i) q^{73} +(-0.459850 - 3.19833i) q^{74} +(-2.38031 + 5.21216i) q^{76} +(0.148082 - 0.170895i) q^{77} +(0.328152 - 2.28235i) q^{78} +(-4.48603 - 9.82303i) q^{79} +(-4.12801 - 1.21209i) q^{81} +(0.815360 + 1.78539i) q^{82} +(0.537881 - 3.74104i) q^{83} +(-0.535373 + 0.617854i) q^{84} +(-3.90083 - 2.50691i) q^{86} +(-0.178231 - 1.23962i) q^{87} +(0.630752 - 0.405360i) q^{88} +(9.39014 + 10.8368i) q^{89} +3.36260 q^{91} +(-3.20012 - 7.00945i) q^{92} -6.24391 q^{93} +(0.198592 - 0.0583118i) q^{94} +(-3.54497 + 2.27821i) q^{96} +(1.14089 + 7.93510i) q^{97} +(-3.44760 - 2.21564i) q^{98} +(0.336491 - 0.736813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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