LMFDB - Embedded newform 605.2.g.p.366.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 6 x^{10} - 12 x^{9} + 43 x^{8} + 72 x^{7} + 155 x^{6} + 162 x^{5} + 541 x^{4} + \cdots + 1 $ x^12 - x^11 + 6x^10 - 12x^9 + 43x^8 + 72x^7 + 155x^6 + 162x^5 + 541x^4 + 114x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.2
Root			$0.511560 + 1.57442i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.p.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12933 - 0.820508i) q^{2} +(-0.511560 - 1.57442i) q^{3} +(-0.0158755 + 0.0488598i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-1.86955 - 1.35830i) q^{6} +(-1.45449 + 4.47645i) q^{7} +(0.884894 + 2.72343i) q^{8} +(0.209948 - 0.152536i) q^{9} +O(q^{10})$	\(q+(1.12933 - 0.820508i) q^{2} +(-0.511560 - 1.57442i) q^{3} +(-0.0158755 + 0.0488598i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-1.86955 - 1.35830i) q^{6} +(-1.45449 + 4.47645i) q^{7} +(0.884894 + 2.72343i) q^{8} +(0.209948 - 0.152536i) q^{9} +1.39593 q^{10} +0.0850471 q^{12} +(4.08665 - 2.96912i) q^{13} +(2.03036 + 6.24882i) q^{14} +(0.511560 - 1.57442i) q^{15} +(3.15081 + 2.28920i) q^{16} +(4.29660 + 3.12166i) q^{17} +(0.111944 - 0.344529i) q^{18} +(-0.698227 - 2.14892i) q^{19} +(-0.0415626 + 0.0301970i) q^{20} +7.79186 q^{21} +1.05137 q^{23} +(3.83514 - 2.78639i) q^{24} +(0.309017 + 0.951057i) q^{25} +(2.17899 - 6.70626i) q^{26} +(-4.36540 - 3.17165i) q^{27} +(-0.195628 - 0.142132i) q^{28} +(-0.862733 + 2.65522i) q^{29} +(-0.714103 - 2.19778i) q^{30} +(-3.02612 + 2.19860i) q^{31} -0.290544 q^{32} +7.41363 q^{34} +(-3.80789 + 2.76660i) q^{35} +(0.00411986 + 0.0126796i) q^{36} +(-0.244699 + 0.753107i) q^{37} +(-2.55174 - 1.85395i) q^{38} +(-6.76521 - 4.91521i) q^{39} +(-0.884894 + 2.72343i) q^{40} +(1.90173 + 5.85292i) q^{41} +(8.79961 - 6.39329i) q^{42} +2.70682 q^{43} +0.259511 q^{45} +(1.18735 - 0.862661i) q^{46} +(-3.47309 - 10.6891i) q^{47} +(1.99233 - 6.13175i) q^{48} +(-12.2599 - 8.90737i) q^{49} +(1.12933 + 0.820508i) q^{50} +(2.71684 - 8.36156i) q^{51} +(0.0801932 + 0.246809i) q^{52} +(-0.850580 + 0.617982i) q^{53} -7.53235 q^{54} -13.4783 q^{56} +(-3.02612 + 2.19860i) q^{57} +(1.20432 + 3.70651i) q^{58} +(1.40057 - 4.31052i) q^{59} +(0.0688045 + 0.0499894i) q^{60} +(7.99412 + 5.80807i) q^{61} +(-1.61352 + 4.96591i) q^{62} +(0.377455 + 1.16169i) q^{63} +(-6.62974 + 4.81679i) q^{64} +5.05137 q^{65} +10.4473 q^{67} +(-0.220734 + 0.160373i) q^{68} +(-0.537841 - 1.65530i) q^{69} +(-2.03036 + 6.24882i) q^{70} +(0.850580 + 0.617982i) q^{71} +(0.601204 + 0.436800i) q^{72} +(3.12192 - 9.60828i) q^{73} +(0.341584 + 1.05129i) q^{74} +(1.33928 - 0.973045i) q^{75} +0.116081 q^{76} -11.6731 q^{78} +(-7.61579 + 5.53319i) q^{79} +(1.20350 + 3.70400i) q^{80} +(-2.51976 + 7.75503i) q^{81} +(6.95005 + 5.04951i) q^{82} +(-2.55174 - 1.85395i) q^{83} +(-0.123700 + 0.380709i) q^{84} +(1.64115 + 5.05095i) q^{85} +(3.05690 - 2.22097i) q^{86} +4.62177 q^{87} -12.5164 q^{89} +(0.293074 - 0.212931i) q^{90} +(7.34715 + 22.6122i) q^{91} +(-0.0166911 + 0.0513699i) q^{92} +(5.00957 + 3.63966i) q^{93} +(-12.6928 - 9.22183i) q^{94} +(0.698227 - 2.14892i) q^{95} +(0.148631 + 0.457438i) q^{96} +(14.3810 - 10.4484i) q^{97} -21.1541 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - q^{3} - 9 q^{4} + 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 12 * q + q^2 - q^3 - 9 * q^4 + 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 - 2 * q^9	$ 12 q + q^{2} - q^{3} - 9 q^{4} + 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 36 q^{12} + 6 q^{13} - 5 q^{14} + q^{15} - 13 q^{16} + 4 q^{17} + 20 q^{18} + 4 q^{19} + 9 q^{20} + 68 q^{21} - 24 q^{23} + 17 q^{24} - 3 q^{25} - 12 q^{26} - 13 q^{27} - 25 q^{28} + 2 q^{29} - 5 q^{30} - 14 q^{31} + 108 q^{32} - 32 q^{34} + q^{35} - 2 q^{36} - 4 q^{37} + 18 q^{38} - 4 q^{39} + 9 q^{40} + 9 q^{41} + 35 q^{42} - 28 q^{43} - 8 q^{45} + 8 q^{46} + 15 q^{47} - 7 q^{48} - 18 q^{49} + q^{50} - 20 q^{51} + 2 q^{52} + 6 q^{53} - 76 q^{54} - 12 q^{56} - 14 q^{57} - 30 q^{58} - 10 q^{59} + 9 q^{60} + 3 q^{61} + 24 q^{62} - 12 q^{63} - 29 q^{64} + 24 q^{65} + 76 q^{67} + 8 q^{69} + 5 q^{70} - 6 q^{71} + 48 q^{72} - 12 q^{73} - 28 q^{74} - q^{75} - 64 q^{76} - 8 q^{78} + 2 q^{79} + 13 q^{80} - 3 q^{81} + 27 q^{82} + 18 q^{83} - 31 q^{84} - 4 q^{85} + 3 q^{86} - 40 q^{87} + 44 q^{89} - 20 q^{90} - 20 q^{91} + 34 q^{92} - 20 q^{93} - 59 q^{94} - 4 q^{95} - 7 q^{96} + 2 q^{97} - 144 q^{98}+O(q^{100}) $ 12 * q + q^2 - q^3 - 9 * q^4 + 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 36 * q^12 + 6 * q^13 - 5 * q^14 + q^15 - 13 * q^16 + 4 * q^17 + 20 * q^18 + 4 * q^19 + 9 * q^20 + 68 * q^21 - 24 * q^23 + 17 * q^24 - 3 * q^25 - 12 * q^26 - 13 * q^27 - 25 * q^28 + 2 * q^29 - 5 * q^30 - 14 * q^31 + 108 * q^32 - 32 * q^34 + q^35 - 2 * q^36 - 4 * q^37 + 18 * q^38 - 4 * q^39 + 9 * q^40 + 9 * q^41 + 35 * q^42 - 28 * q^43 - 8 * q^45 + 8 * q^46 + 15 * q^47 - 7 * q^48 - 18 * q^49 + q^50 - 20 * q^51 + 2 * q^52 + 6 * q^53 - 76 * q^54 - 12 * q^56 - 14 * q^57 - 30 * q^58 - 10 * q^59 + 9 * q^60 + 3 * q^61 + 24 * q^62 - 12 * q^63 - 29 * q^64 + 24 * q^65 + 76 * q^67 + 8 * q^69 + 5 * q^70 - 6 * q^71 + 48 * q^72 - 12 * q^73 - 28 * q^74 - q^75 - 64 * q^76 - 8 * q^78 + 2 * q^79 + 13 * q^80 - 3 * q^81 + 27 * q^82 + 18 * q^83 - 31 * q^84 - 4 * q^85 + 3 * q^86 - 40 * q^87 + 44 * q^89 - 20 * q^90 - 20 * q^91 + 34 * q^92 - 20 * q^93 - 59 * q^94 - 4 * q^95 - 7 * q^96 + 2 * q^97 - 144 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	1.12933	−	0.820508i	0.798559	−	0.580187i	−0.111932	−	0.993716i	$-0.535704\pi$
$2$	1.12933	−	0.820508i	0.798559	−	0.580187i	0.910491	+	0.413529i	$0.135704\pi$
$3$	−0.511560	−	1.57442i	−0.295349	−	0.908991i	−0.983104	−	0.183048i	$-0.941404\pi$
$3$	−0.511560	−	1.57442i	−0.295349	−	0.908991i	0.687755	−	0.725943i	$-0.258596\pi$
$4$	−0.0158755	+	0.0488598i	−0.00793776	+	0.0244299i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−1.86955	−	1.35830i	−0.763239	−	0.554525i
$7$	−1.45449	+	4.47645i	−0.549744	+	1.69194i	0.159690	+	0.987167i	$0.448950\pi$
$7$	−1.45449	+	4.47645i	−0.549744	+	1.69194i	−0.709434	+	0.704771i	$0.751050\pi$
$8$	0.884894	+	2.72343i	0.312857	+	0.962876i
$9$	0.209948	−	0.152536i	0.0699828	−	0.0508455i
$10$	1.39593			0.441432
$11$		0			0
$11$		0			0
$12$	0.0850471			0.0245510
$13$	4.08665	−	2.96912i	1.13343	−	0.823487i	0.147241	−	0.989101i	$-0.452961\pi$
$13$	4.08665	−	2.96912i	1.13343	−	0.823487i	0.986191	+	0.165614i	$0.0529606\pi$
$14$	2.03036	+	6.24882i	0.542638	+	1.67007i
$15$	0.511560	−	1.57442i	0.132084	−	0.406513i
$16$	3.15081	+	2.28920i	0.787702	+	0.572299i
$17$	4.29660	+	3.12166i	1.04208	+	0.757114i	0.970690	−	0.240335i	$-0.0772573\pi$
$17$	4.29660	+	3.12166i	1.04208	+	0.757114i	0.0713876	+	0.997449i	$0.477257\pi$
$18$	0.111944	−	0.344529i	0.0263855	−	0.0812062i
$19$	−0.698227	−	2.14892i	−0.160184	−	0.492997i	0.838465	−	0.544956i	$-0.183453\pi$
$19$	−0.698227	−	2.14892i	−0.160184	−	0.492997i	−0.998649	+	0.0519590i	$0.983453\pi$
$20$	−0.0415626	+	0.0301970i	−0.00929369	+	0.00675226i
$21$	7.79186			1.70032
$22$		0			0
$23$	1.05137			0.219227			0.109613	−	0.993974i	$-0.465039\pi$
$23$	1.05137			0.219227			0.109613	+	0.993974i	$0.465039\pi$
$24$	3.83514	−	2.78639i	0.782844	−	0.568769i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	2.17899	−	6.70626i	0.427336	−	1.31520i
$27$	−4.36540	−	3.17165i	−0.840122	−	0.610384i
$28$	−0.195628	−	0.142132i	−0.0369702	−	0.0268604i
$29$	−0.862733	+	2.65522i	−0.160206	+	0.493062i	−0.998651	−	0.0519234i	$-0.983465\pi$
$29$	−0.862733	+	2.65522i	−0.160206	+	0.493062i	0.838446	+	0.544985i	$0.183465\pi$
$30$	−0.714103	−	2.19778i	−0.130377	−	0.401258i
$31$	−3.02612	+	2.19860i	−0.543507	+	0.394881i	−0.825386	−	0.564569i	$-0.809042\pi$
$31$	−3.02612	+	2.19860i	−0.543507	+	0.394881i	0.281879	+	0.959450i	$0.409042\pi$
$32$	−0.290544			−0.0513614
$33$		0			0
$34$	7.41363			1.27143
$35$	−3.80789	+	2.76660i	−0.643652	+	0.467640i
$36$	0.00411986	+	0.0126796i	0.000686644	+	0.00211327i
$37$	−0.244699	+	0.753107i	−0.0402283	+	0.123810i	−0.969154	−	0.246457i	$-0.920734\pi$
$37$	−0.244699	+	0.753107i	−0.0402283	+	0.123810i	0.928925	+	0.370267i	$0.120734\pi$
$38$	−2.55174	−	1.85395i	−0.413947	−	0.300750i
$39$	−6.76521	−	4.91521i	−1.08330	−	0.787064i
$40$	−0.884894	+	2.72343i	−0.139914	+	0.430611i
$41$	1.90173	+	5.85292i	0.297000	+	0.914072i	0.982542	+	0.186039i	$0.0595652\pi$
$41$	1.90173	+	5.85292i	0.297000	+	0.914072i	−0.685542	+	0.728033i	$0.740435\pi$
$42$	8.79961	−	6.39329i	1.35781	−	0.986506i
$43$	2.70682			0.412786			0.206393	−	0.978469i	$-0.433828\pi$
$43$	2.70682			0.412786			0.206393	+	0.978469i	$0.433828\pi$
$44$		0			0
$45$	0.259511			0.0386855
$46$	1.18735	−	0.862661i	0.175065	−	0.127192i
$47$	−3.47309	−	10.6891i	−0.506603	−	1.55916i	−0.798059	−	0.602579i	$-0.794140\pi$
$47$	−3.47309	−	10.6891i	−0.506603	−	1.55916i	0.291456	−	0.956584i	$-0.405860\pi$
$48$	1.99233	−	6.13175i	0.287568	−	0.885042i
$49$	−12.2599	−	8.90737i	−1.75142	−	1.27248i
$50$	1.12933	+	0.820508i	0.159712	+	0.116037i
$51$	2.71684	−	8.36156i	0.380433	−	1.17085i
$52$	0.0801932	+	0.246809i	0.0111208	+	0.0342263i
$53$	−0.850580	+	0.617982i	−0.116836	+	0.0848864i	−0.644669	−	0.764462i	$-0.723005\pi$
$53$	−0.850580	+	0.617982i	−0.116836	+	0.0848864i	0.527833	+	0.849348i	$0.323005\pi$
$54$	−7.53235			−1.02502
$55$		0			0
$56$	−13.4783			−1.80112
$57$	−3.02612	+	2.19860i	−0.400819	+	0.291212i
$58$	1.20432	+	3.70651i	0.158135	+	0.486688i
$59$	1.40057	−	4.31052i	0.182339	−	0.561182i	−0.817553	−	0.575853i	$-0.804670\pi$
$59$	1.40057	−	4.31052i	0.182339	−	0.561182i	0.999892	+	0.0146707i	$0.00467000\pi$
$60$	0.0688045	+	0.0499894i	0.00888263	+	0.00645361i
$61$	7.99412	+	5.80807i	1.02354	+	0.743647i	0.967006	−	0.254753i	$-0.0819943\pi$
$61$	7.99412	+	5.80807i	1.02354	+	0.743647i	0.0565365	+	0.998401i	$0.481994\pi$
$62$	−1.61352	+	4.96591i	−0.204918	+	0.630671i
$63$	0.377455	+	1.16169i	0.0475548	+	0.146359i
$64$	−6.62974	+	4.81679i	−0.828717	+	0.602098i
$65$	5.05137			0.626546
$66$		0			0
$67$	10.4473			1.27634			0.638171	−	0.769895i	$-0.279691\pi$
$67$	10.4473			1.27634			0.638171	+	0.769895i	$0.279691\pi$
$68$	−0.220734	+	0.160373i	−0.0267680	+	0.0194481i
$69$	−0.537841	−	1.65530i	−0.0647484	−	0.199275i
$70$	−2.03036	+	6.24882i	−0.242675	+	0.746877i
$71$	0.850580	+	0.617982i	0.100945	+	0.0733410i	0.637113	−	0.770771i	$-0.280129\pi$
$71$	0.850580	+	0.617982i	0.100945	+	0.0733410i	−0.536168	+	0.844112i	$0.680129\pi$
$72$	0.601204	+	0.436800i	0.0708525	+	0.0514774i
$73$	3.12192	−	9.60828i	0.365393	−	1.12456i	−0.584341	−	0.811508i	$-0.698647\pi$
$73$	3.12192	−	9.60828i	0.365393	−	1.12456i	0.949734	−	0.313057i	$-0.101353\pi$
$74$	0.341584	+	1.05129i	0.0397083	+	0.122210i
$75$	1.33928	−	0.973045i	0.154647	−	0.112358i
$76$	0.116081			0.0133154
$77$		0			0
$78$	−11.6731			−1.32172
$79$	−7.61579	+	5.53319i	−0.856843	+	0.622533i	−0.927024	−	0.375001i	$-0.877642\pi$
$79$	−7.61579	+	5.53319i	−0.856843	+	0.622533i	0.0701811	+	0.997534i	$0.477642\pi$
$80$	1.20350	+	3.70400i	0.134556	+	0.414119i
$81$	−2.51976	+	7.75503i	−0.279974	+	0.861670i
$82$	6.95005	+	5.04951i	0.767505	+	0.557625i
$83$	−2.55174	−	1.85395i	−0.280090	−	0.203497i	0.438867	−	0.898552i	$-0.355380\pi$
$83$	−2.55174	−	1.85395i	−0.280090	−	0.203497i	−0.718957	+	0.695055i	$0.755380\pi$
$84$	−0.123700	+	0.380709i	−0.0134968	+	0.0415388i
$85$	1.64115	+	5.05095i	0.178008	+	0.547853i
$86$	3.05690	−	2.22097i	0.329634	−	0.239493i
$87$	4.62177			0.495506
$88$		0			0
$89$	−12.5164			−1.32673			−0.663367	−	0.748294i	$-0.730873\pi$
$89$	−12.5164			−1.32673			−0.663367	+	0.748294i	$0.730873\pi$
$90$	0.293074	−	0.212931i	0.0308927	−	0.0224448i
$91$	7.34715	+	22.6122i	0.770191	+	2.37040i
$92$	−0.0166911	+	0.0513699i	−0.00174017	+	0.00535569i
$93$	5.00957	+	3.63966i	0.519468	+	0.377415i
$94$	−12.6928	−	9.22183i	−1.30916	−	0.951159i
$95$	0.698227	−	2.14892i	0.0716366	−	0.220475i
$96$	0.148631	+	0.457438i	0.0151696	+	0.0466871i
$97$	14.3810	−	10.4484i	1.46017	−	1.06088i	0.476850	−	0.878984i	$-0.341778\pi$
$97$	14.3810	−	10.4484i	1.46017	−	1.06088i	0.983319	−	0.181891i	$-0.0582217\pi$
$98$	−21.1541			−2.13689
$99$		0			0
$100$	−0.0513742			−0.00513742
$101$	−2.98456	+	2.16841i	−0.296975	+	0.215765i	−0.726287	−	0.687391i	$-0.758756\pi$
$101$	−2.98456	+	2.16841i	−0.296975	+	0.215765i	0.429313	+	0.903156i	$0.358756\pi$
$102$	−3.79252	−	11.6722i	−0.375515	−	1.15572i
$103$	−0.00411986	+	0.0126796i	−0.000405942	+	0.00124936i	−0.951259	−	0.308392i	$-0.900209\pi$
$103$	−0.00411986	+	0.0126796i	−0.000405942	+	0.00124936i	0.950853	+	0.309642i	$0.100209\pi$
$104$	11.7024	+	8.50232i	1.14752	+	0.833721i
$105$	6.30375	+	4.57994i	0.615183	+	0.446957i
$106$	−0.453528	+	1.39582i	−0.0440505	+	0.135574i
$107$	−3.60173	−	11.0850i	−0.348192	−	1.07163i	−0.959852	−	0.280505i	$-0.909498\pi$
$107$	−3.60173	−	11.0850i	−0.348192	−	1.07163i	0.611660	−	0.791121i	$-0.290502\pi$
$108$	0.224269	−	0.162941i	0.0215803	−	0.0156790i
$109$	−12.9460			−1.24000			−0.620000	−	0.784602i	$-0.712868\pi$
$109$	−12.9460			−1.24000			−0.620000	+	0.784602i	$0.712868\pi$
$110$		0			0
$111$	1.31088			0.124424
$112$	−14.8303	+	10.7748i	−1.40133	+	1.01813i
$113$	−5.13641	−	15.8082i	−0.483193	−	1.48711i	−0.834581	−	0.550885i	$-0.814290\pi$
$113$	−5.13641	−	15.8082i	−0.483193	−	1.48711i	0.351389	−	0.936230i	$-0.385710\pi$
$114$	−1.61352	+	4.96591i	−0.151120	+	0.465100i
$115$	0.850580	+	0.617982i	0.0793170	+	0.0576271i
$116$	−0.116037	−	0.0843060i	−0.0107738	−	0.00782761i
$117$	0.405086	−	1.24673i	0.0374502	−	0.115260i
$118$	−1.95511	−	6.01720i	−0.179982	−	0.553928i
$119$	−20.2233	+	14.6931i	−1.85387	+	1.34691i
$120$	4.74049			0.432746
$121$		0			0
$122$	13.7936			1.24881
$123$	8.24210	−	5.98824i	0.743165	−	0.539941i
$124$	−0.0593822	−	0.182760i	−0.00533268	−	0.0164123i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	1.37944	+	1.00222i	0.122891	+	0.0892853i
$127$	−3.37721	−	2.45369i	−0.299679	−	0.217730i	0.427776	−	0.903885i	$-0.359297\pi$
$127$	−3.37721	−	2.45369i	−0.299679	−	0.217730i	−0.727455	+	0.686155i	$0.759297\pi$
$128$	−3.35540	+	10.3269i	−0.296578	+	0.912774i
$129$	−1.38470	−	4.26166i	−0.121916	−	0.375219i
$130$	5.70468	−	4.14469i	0.500334	−	0.363514i
$131$	−8.88128			−0.775961			−0.387981	−	0.921668i	$-0.626827\pi$
$131$	−8.88128			−0.775961			−0.387981	+	0.921668i	$0.626827\pi$
$132$		0			0
$133$	10.6351			0.922180
$134$	11.7985	−	8.57210i	1.01923	−	0.740517i
$135$	−1.66743	−	5.13184i	−0.143510	−	0.441678i
$136$	−4.69957	+	14.4638i	−0.402985	+	1.24026i
$137$	−0.629845	−	0.457609i	−0.0538113	−	0.0390962i	0.560554	−	0.828118i	$-0.310588\pi$
$137$	−0.629845	−	0.457609i	−0.0538113	−	0.0390962i	−0.614366	+	0.789021i	$0.710588\pi$
$138$	−1.96559	−	1.42809i	−0.167322	−	0.121567i
$139$	2.71272	−	8.34888i	0.230090	−	0.708143i	−0.767645	−	0.640875i	$-0.778572\pi$
$139$	2.71272	−	8.34888i	0.230090	−	0.708143i	0.997735	−	0.0672679i	$-0.0214282\pi$
$140$	−0.0747231	−	0.229974i	−0.00631526	−	0.0194364i
$141$	−15.0524	+	10.9362i	−1.26764	+	0.920995i
$142$	1.46765			0.123162
$143$		0			0
$144$	1.01069			0.0842244
$145$	−2.25867	+	1.64102i	−0.187572	+	0.136279i
$146$	−4.35799	−	13.4125i	−0.360670	−	1.11003i
$147$	−7.75224	+	23.8589i	−0.639394	+	1.96785i
$148$	−0.0329119	−	0.0239119i	−0.00270535	−	0.00196555i
$149$	8.13173	+	5.90805i	0.666177	+	0.484006i	0.868743	−	0.495262i	$-0.164928\pi$
$149$	8.13173	+	5.90805i	0.666177	+	0.484006i	−0.202566	+	0.979269i	$0.564928\pi$
$150$	0.714103	−	2.19778i	0.0583062	−	0.179448i
$151$	−3.28643	−	10.1146i	−0.267446	−	0.823113i	−0.991120	−	0.132971i	$-0.957548\pi$
$151$	−3.28643	−	10.1146i	−0.267446	−	0.823113i	0.723674	−	0.690142i	$-0.242452\pi$
$152$	5.23457	−	3.80314i	0.424580	−	0.308475i
$153$	1.37823			0.111423
$154$		0			0
$155$	−3.74049			−0.300443
$156$	0.347558	−	0.252515i	0.0278269	−	0.0202174i
$157$	−0.160386	−	0.493618i	−0.0128002	−	0.0393950i	0.944452	−	0.328648i	$-0.106593\pi$
$157$	−0.160386	−	0.493618i	−0.0128002	−	0.0393950i	−0.957253	+	0.289253i	$0.906593\pi$
$158$	−4.06073	+	12.4976i	−0.323054	+	0.994258i
$159$	1.40809	+	1.02303i	0.111668	+	0.0811319i
$160$	−0.235055	−	0.170778i	−0.0185827	−	0.0135011i
$161$	−1.52921	+	4.70642i	−0.120519	+	0.370918i
$162$	3.51742	+	10.8255i	0.276354	+	0.850531i
$163$	−15.9739	+	11.6057i	−1.25117	+	0.909031i	−0.998289	−	0.0584649i	$-0.981379\pi$
$163$	−15.9739	+	11.6057i	−1.25117	+	0.909031i	−0.252885	+	0.967496i	$0.581379\pi$
$164$	−0.316163			−0.0246882
$165$		0			0
$166$	−4.40294			−0.341734
$167$	1.46610	−	1.06519i	0.113451	−	0.0824266i	−0.529613	−	0.848239i	$-0.677663\pi$
$167$	1.46610	−	1.06519i	0.113451	−	0.0824266i	0.643064	+	0.765813i	$0.277663\pi$
$168$	6.89498	+	21.2206i	0.531959	+	1.63720i
$169$	3.86777	−	11.9038i	0.297521	−	0.915676i
$170$	5.99776	+	4.35762i	0.460007	+	0.334215i
$171$	−0.474381	−	0.344658i	−0.0362768	−	0.0263566i
$172$	−0.0429721	+	0.132255i	−0.00327659	+	0.0100843i
$173$	−1.40057	−	4.31052i	−0.106484	−	0.327723i	0.883592	−	0.468257i	$-0.155118\pi$
$173$	−1.40057	−	4.31052i	−0.106484	−	0.327723i	−0.990076	+	0.140534i	$0.955118\pi$
$174$	5.21951	−	3.79220i	0.395690	−	0.287486i
$175$	−4.70682			−0.355802
$176$		0			0
$177$	−7.50305			−0.563964
$178$	−14.1352	+	10.2698i	−1.05947	+	0.769754i
$179$	0.128635	+	0.395899i	0.00961465	+	0.0295909i	0.955749	−	0.294184i	$-0.0950479\pi$
$179$	0.128635	+	0.395899i	0.00961465	+	0.0295909i	−0.946134	+	0.323775i	$0.895048\pi$
$180$	−0.00411986	+	0.0126796i	−0.000307076	+	0.000945084i
$181$	3.06768	+	2.22880i	0.228019	+	0.165666i	0.695929	−	0.718111i	$-0.254993\pi$
$181$	3.06768	+	2.22880i	0.228019	+	0.165666i	−0.467910	+	0.883776i	$0.654993\pi$
$182$	26.8509	+	19.5083i	1.99032	+	1.44605i
$183$	5.05487	−	15.5573i	0.373666	−	1.15003i
$184$	0.930355	+	2.86334i	0.0685867	+	0.211088i
$185$	−0.640631	+	0.465446i	−0.0471001	+	0.0342203i
$186$	8.64384			0.633797
$187$		0			0
$188$	0.577404			0.0421115
$189$	20.5471	−	14.9284i	1.49458	−	1.08588i
$190$	−0.974678	−	2.99975i	−0.0707105	−	0.217625i
$191$	6.11109	−	18.8080i	0.442183	−	1.36090i	−0.443361	−	0.896343i	$-0.646214\pi$
$191$	6.11109	−	18.8080i	0.442183	−	1.36090i	0.885544	−	0.464555i	$-0.153786\pi$
$192$	10.9751	+	7.97391i	0.792063	+	0.575467i
$193$	−6.50078	−	4.72309i	−0.467936	−	0.339976i	0.328700	−	0.944434i	$-0.393389\pi$
$193$	−6.50078	−	4.72309i	−0.467936	−	0.339976i	−0.796636	+	0.604459i	$0.793389\pi$
$194$	7.66793	−	23.5995i	0.550525	−	1.69434i
$195$	−2.58408	−	7.95298i	−0.185050	−	0.569525i
$196$	0.629845	−	0.457609i	0.0449889	−	0.0326864i
$197$	14.7919			1.05388			0.526938	−	0.849904i	$-0.323340\pi$
$197$	14.7919			1.05388			0.526938	+	0.849904i	$0.323340\pi$
$198$		0			0
$199$	−9.16745			−0.649864			−0.324932	−	0.945737i	$-0.605341\pi$
$199$	−9.16745			−0.649864			−0.324932	+	0.945737i	$0.605341\pi$
$200$	−2.31668	+	1.68317i	−0.163814	+	0.119018i
$201$	−5.34442	−	16.4484i	−0.376966	−	1.16018i
$202$	−1.59136	+	4.89771i	−0.111968	+	0.344601i
$203$	−10.6311	−	7.72396i	−0.746159	−	0.542116i
$204$	0.365413	+	0.265488i	0.0255840	+	0.0185879i
$205$	−1.90173	+	5.85292i	−0.132822	+	0.408786i
$206$	0.00575105	+	0.0176999i	0.000400694	+	0.00123321i
$207$	0.220734	−	0.160373i	0.0153421	−	0.0111467i
$208$	19.6731			1.36409
$209$		0			0
$210$	10.8769			0.750578
$211$	−7.10198	+	5.15989i	−0.488921	+	0.355222i	−0.804769	−	0.593588i	$-0.797711\pi$
$211$	−7.10198	+	5.15989i	−0.488921	+	0.355222i	0.315848	+	0.948810i	$0.397711\pi$
$212$	−0.0166911	−	0.0513699i	−0.00114635	−	0.00352810i
$213$	0.537841	−	1.65530i	0.0368522	−	0.113420i
$214$	−13.1629	−	9.56339i	−0.899795	−	0.653740i
$215$	2.18986	+	1.59103i	0.149347	+	0.108507i
$216$	4.77483	−	14.6954i	0.324886	−	0.999896i
$217$	−5.44049	−	16.7441i	−0.369325	−	1.13666i
$218$	−14.6203	+	10.6223i	−0.990213	+	0.719432i
$219$	−16.7245			−1.13014
$220$		0			0
$221$	26.8273			1.80460
$222$	1.48042	−	1.07559i	0.0993596	−	0.0721890i
$223$	7.35674	+	22.6417i	0.492644	+	1.51620i	0.820596	+	0.571508i	$0.193641\pi$
$223$	7.35674	+	22.6417i	0.492644	+	1.51620i	−0.327952	+	0.944694i	$0.606359\pi$
$224$	0.422592	−	1.30061i	0.0282356	−	0.0869004i
$225$	0.209948	+	0.152536i	0.0139966	+	0.0101691i
$226$	−18.7715	−	13.6383i	−1.24866	−	0.907206i
$227$	−2.63799	+	8.11891i	−0.175090	+	0.538871i	−0.999638	−	0.0269215i	$-0.991430\pi$
$227$	−2.63799	+	8.11891i	−0.175090	+	0.538871i	0.824548	+	0.565792i	$0.191430\pi$
$228$	−0.0593822	−	0.182760i	−0.00393268	−	0.0121035i
$229$	11.9976	−	8.71680i	0.792827	−	0.576022i	−0.115974	−	0.993252i	$-0.536999\pi$
$229$	11.9976	−	8.71680i	0.792827	−	0.576022i	0.908801	+	0.417230i	$0.136999\pi$
$230$	1.46765			0.0967738
$231$		0			0
$232$	−7.99472			−0.524879
$233$	−5.14718	+	3.73964i	−0.337203	+	0.244992i	−0.743481	−	0.668757i	$-0.766826\pi$
$233$	−5.14718	+	3.73964i	−0.337203	+	0.244992i	0.406278	+	0.913750i	$0.366826\pi$
$234$	−0.565472	−	1.74034i	−0.0369661	−	0.113770i
$235$	3.47309	−	10.6891i	0.226560	−	0.697279i
$236$	0.188377	+	0.136864i	0.0122623	+	0.00890906i
$237$	12.6075	+	9.15989i	0.818945	+	0.594998i
$238$	−10.7830	+	33.1867i	−0.698960	+	2.15118i
$239$	1.44490	+	4.44693i	0.0934626	+	0.287648i	0.986850	−	0.161639i	$-0.0516780\pi$
$239$	1.44490	+	4.44693i	0.0934626	+	0.287648i	−0.893387	+	0.449287i	$0.851678\pi$
$240$	5.21598	−	3.78963i	0.336690	−	0.244620i
$241$	−7.63510			−0.491820			−0.245910	−	0.969293i	$-0.579087\pi$
$241$	−7.63510			−0.491820			−0.245910	+	0.969293i	$0.579087\pi$
$242$		0			0
$243$	−2.68912			−0.172507
$244$	−0.410692	+	0.298385i	−0.0262919	+	0.0191022i
$245$	−4.68288	−	14.4124i	−0.299178	−	0.920776i
$246$	4.39468	−	13.5254i	0.280194	−	0.862349i
$247$	−9.23382	−	6.70877i	−0.587534	−	0.426869i
$248$	−8.66553	−	6.29588i	−0.550262	−	0.399789i
$249$	−1.61352	+	4.96591i	−0.102253	+	0.314702i
$250$	0.431367	+	1.32761i	0.0272820	+	0.0839654i
$251$	17.3634	−	12.6153i	1.09597	−	0.796268i	0.115572	−	0.993299i	$-0.463130\pi$
$251$	17.3634	−	12.6153i	1.09597	−	0.796268i	0.980397	+	0.197031i	$0.0631299\pi$
$252$	−0.0627520			−0.00395301
$253$		0			0
$254$	−5.82727			−0.365635
$255$	7.11277	−	5.16773i	0.445419	−	0.323616i
$256$	−0.380759	−	1.17186i	−0.0237974	−	0.0732409i
$257$	5.20403	−	16.0164i	0.324619	−	0.999073i	−0.646994	−	0.762495i	$-0.723974\pi$
$257$	5.20403	−	16.0164i	0.324619	−	0.999073i	0.971612	−	0.236578i	$-0.0760259\pi$
$258$	−5.06052	−	3.67668i	−0.315054	−	0.228900i
$259$	−3.01533	−	2.19077i	−0.187364	−	0.136128i
$260$	−0.0801932	+	0.246809i	−0.00497337	+	0.0153065i
$261$	0.223888	+	0.689058i	0.0138583	+	0.0426516i
$262$	−10.0299	+	7.28716i	−0.619650	+	0.450202i
$263$	−11.2215			−0.691945			−0.345973	−	0.938245i	$-0.612451\pi$
$263$	−11.2215			−0.691945			−0.345973	+	0.938245i	$0.612451\pi$
$264$		0			0
$265$	−1.05137			−0.0645854
$266$	12.0106	−	8.72619i	0.736415	−	0.535037i
$267$	6.40288	+	19.7060i	0.391850	+	1.20599i
$268$	−0.165856	+	0.510453i	−0.0101313	+	0.0311809i
$269$	10.0536	+	7.30439i	0.612980	+	0.445356i	0.850463	−	0.526036i	$-0.176322\pi$
$269$	10.0536	+	7.30439i	0.612980	+	0.445356i	−0.237482	+	0.971392i	$0.576322\pi$
$270$	−6.09380	−	4.42741i	−0.370857	−	0.269443i
$271$	−5.50974	+	16.9572i	−0.334693	+	1.03008i	0.632180	+	0.774822i	$0.282160\pi$
$271$	−5.50974	+	16.9572i	−0.334693	+	1.03008i	−0.966873	+	0.255258i	$0.917840\pi$
$272$	6.39166	+	19.6715i	0.387551	+	1.19276i
$273$	31.8426	−	23.1350i	1.92720	−	1.40019i
$274$	−1.08678			−0.0656546
$275$		0			0
$276$	0.0894163			0.00538223
$277$	−13.9217	+	10.1147i	−0.836472	+	0.607733i	−0.921383	−	0.388656i	$-0.872940\pi$
$277$	−13.9217	+	10.1147i	−0.836472	+	0.607733i	0.0849106	+	0.996389i	$0.472940\pi$
$278$	−3.78677	−	11.6545i	−0.227115	−	0.698988i
$279$	−0.299962	+	0.923187i	−0.0179582	+	0.0552698i
$280$	−10.9042	−	7.92237i	−0.651651	−	0.473452i
$281$	−21.3669	−	15.5240i	−1.27464	−	0.926084i	−0.275268	−	0.961368i	$-0.588766\pi$
$281$	−21.3669	−	15.5240i	−1.27464	−	0.926084i	−0.999377	+	0.0352839i	$0.988766\pi$
$282$	−8.02592	+	24.7012i	−0.477937	+	1.47094i
$283$	5.64797	+	17.3827i	0.335737	+	1.03329i	0.966358	+	0.257201i	$0.0828003\pi$
$283$	5.64797	+	17.3827i	0.335737	+	1.03329i	−0.630621	+	0.776091i	$0.717200\pi$
$284$	−0.0436979	+	0.0317484i	−0.00259299	+	0.00188392i
$285$	−3.74049			−0.221567
$286$		0			0
$287$	−28.9663			−1.70983
$288$	−0.0609993	+	0.0443186i	−0.00359442	+	0.00261150i
$289$	3.46269	+	10.6571i	0.203688	+	0.626886i
$290$	−1.20432	+	3.70651i	−0.0707199	+	0.217654i
$291$	−23.8069	−	17.2967i	−1.39559	−	1.01395i
$292$	0.419897	+	0.305073i	0.0245726	+	0.0178530i
$293$	7.92087	−	24.3779i	0.462742	−	1.42417i	−0.399058	−	0.916926i	$-0.630663\pi$
$293$	7.92087	−	24.3779i	0.462742	−	1.42417i	0.861800	−	0.507248i	$-0.169337\pi$
$294$	10.8216	+	33.3055i	0.631128	+	1.94241i
$295$	3.66675	−	2.66405i	0.213486	−	0.155107i
$296$	−2.26756			−0.131799
$297$		0			0
$298$	14.0310			0.812796
$299$	4.29660	−	3.12166i	0.248479	−	0.180530i
$300$	0.0262810	+	0.0808846i	0.00151733	+	0.00466987i
$301$	−3.93703	+	12.1169i	−0.226927	+	0.698408i
$302$	−12.0106	−	8.72619i	−0.691130	−	0.502136i
$303$	4.94076	+	3.58967i	0.283839	+	0.206221i
$304$	2.71932	−	8.36922i	0.155964	−	0.480008i
$305$	3.05348	+	9.39766i	0.174842	+	0.538108i
$306$	1.55648	−	1.13085i	0.0889781	−	0.0646464i
$307$	27.3596			1.56150			0.780748	−	0.624846i	$-0.214838\pi$
$307$	27.3596			1.56150			0.780748	+	0.624846i	$0.214838\pi$
$308$		0			0
$309$	0.0220706			0.00125555
$310$	−4.22426	+	3.06910i	−0.239922	+	0.174313i
$311$	6.02677	+	18.5485i	0.341747	+	1.05179i	0.963302	+	0.268419i	$0.0865011\pi$
$311$	6.02677	+	18.5485i	0.341747	+	1.05179i	−0.621555	+	0.783370i	$0.713499\pi$
$312$	7.39972	−	22.7740i	0.418926	−	1.28932i
$313$	6.09594	+	4.42896i	0.344563	+	0.250339i	0.746584	−	0.665291i	$-0.231692\pi$
$313$	6.09594	+	4.42896i	0.344563	+	0.250339i	−0.402022	+	0.915630i	$0.631692\pi$
$314$	−0.586147	−	0.425861i	−0.0330782	−	0.0240327i
$315$	−0.377455	+	1.16169i	−0.0212672	+	0.0654536i
$316$	−0.149446	−	0.459948i	−0.00840701	−	0.0258741i
$317$	9.37143	−	6.80874i	0.526352	−	0.382417i	−0.292639	−	0.956223i	$-0.594534\pi$
$317$	9.37143	−	6.80874i	0.526352	−	0.382417i	0.818991	+	0.573806i	$0.194534\pi$
$318$	2.42960			0.136245
$319$		0			0
$320$	−8.19480			−0.458103
$321$	−15.6099	+	11.3413i	−0.871260	+	0.633008i
$322$	2.13467	+	6.56985i	0.118961	+	0.366123i
$323$	3.70820	−	11.4127i	0.206330	−	0.635018i
$324$	−0.338907	−	0.246230i	−0.0188282	−	0.0136795i
$325$	4.08665	+	2.96912i	0.226686	+	0.164697i
$326$	−8.51727	+	26.2135i	−0.471728	+	1.45183i
$327$	6.62265	+	20.3824i	0.366233	+	1.12715i
$328$	−14.2572	+	10.3584i	−0.787220	+	0.571949i
$329$	52.9007			2.91651
$330$		0			0
$331$	18.5324			1.01863			0.509315	−	0.860580i	$-0.329899\pi$
$331$	18.5324			1.01863			0.509315	+	0.860580i	$0.329899\pi$
$332$	0.131094	−	0.0952451i	0.00719470	−	0.00522725i
$333$	0.0635021	+	0.195439i	0.00347989	+	0.0107100i
$334$	0.781725	−	2.40590i	0.0427741	−	0.131645i
$335$	8.45205	+	6.14077i	0.461785	+	0.335506i
$336$	24.5507	+	17.8371i	1.33935	+	0.973094i
$337$	2.37113	−	7.29759i	0.129164	−	0.397525i	−0.865473	−	0.500956i	$-0.832982\pi$
$337$	2.37113	−	7.29759i	0.129164	−	0.397525i	0.994637	+	0.103430i	$0.0329819\pi$
$338$	−5.39915	−	16.6169i	−0.293675	−	0.903839i
$339$	−22.2612	+	16.1737i	−1.20906	+	0.878436i
$340$	−0.272843			−0.0147970
$341$		0			0
$342$	−0.818528			−0.0442609
$343$	31.0500	−	22.5592i	1.67654	−	1.21808i
$344$	2.39525	+	7.37181i	0.129143	+	0.397461i
$345$	0.537841	−	1.65530i	0.0289564	−	0.0891186i
$346$	−5.11853	−	3.71883i	−0.275174	−	0.199926i
$347$	−22.8044	−	16.5684i	−1.22420	−	0.889437i	−0.227763	−	0.973717i	$-0.573141\pi$
$347$	−22.8044	−	16.5684i	−1.22420	−	0.889437i	−0.996442	+	0.0842800i	$0.973141\pi$
$348$	−0.0733730	+	0.225819i	−0.00393320	+	0.0121052i
$349$	−2.74859	−	8.45928i	−0.147128	−	0.452815i	0.850150	−	0.526540i	$-0.176511\pi$
$349$	−2.74859	−	8.45928i	−0.147128	−	0.452815i	−0.997279	+	0.0737256i	$0.976511\pi$
$350$	−5.31556	+	3.86198i	−0.284129	+	0.206432i
$351$	−27.2569			−1.45486
$352$		0			0
$353$	−28.0221			−1.49146			−0.745732	−	0.666246i	$-0.767900\pi$
$353$	−28.0221			−1.49146			−0.745732	+	0.666246i	$0.767900\pi$
$354$	−8.47344	+	6.15631i	−0.450358	+	0.327204i
$355$	0.324893	+	0.999916i	0.0172435	+	0.0530700i
$356$	0.198704	−	0.611548i	0.0105313	−	0.0324120i
$357$	33.4785	+	24.3235i	1.77187	+	1.28734i
$358$	0.470110	+	0.341555i	0.0248461	+	0.0180517i
$359$	−3.47856	+	10.7059i	−0.183592	+	0.565037i	−0.999921	−	0.0125494i	$-0.996005\pi$
$359$	−3.47856	+	10.7059i	−0.183592	+	0.565037i	0.816330	+	0.577586i	$0.196005\pi$
$360$	0.229639	+	0.706757i	0.0121031	+	0.0372494i
$361$	11.2410	−	8.16705i	0.591630	−	0.429845i
$362$	5.29318			0.278204
$363$		0			0
$364$	−1.22147			−0.0640223
$365$	8.17330	−	5.93825i	0.427810	−	0.310822i
$366$	−7.05625	−	21.7169i	−0.368836	−	1.13516i
$367$	1.71588	−	5.28093i	0.0895680	−	0.275662i	−0.896232	−	0.443586i	$-0.853706\pi$
$367$	1.71588	−	5.28093i	0.0895680	−	0.275662i	0.985800	+	0.167924i	$0.0537062\pi$
$368$	3.31268	+	2.40680i	0.172685	+	0.125463i
$369$	1.29205	+	0.938728i	0.0672614	+	0.0488682i
$370$	−0.341584	+	1.05129i	−0.0177581	+	0.0546538i
$371$	−1.52921	−	4.70642i	−0.0793926	−	0.244345i
$372$	−0.257363	+	0.186985i	−0.0133436	+	0.00969472i
$373$	6.80520			0.352360			0.176180	−	0.984358i	$-0.443626\pi$
$373$	6.80520			0.352360			0.176180	+	0.984358i	$0.443626\pi$
$374$		0			0
$375$	1.65544			0.0854867
$376$	26.0376	−	18.9174i	1.34279	−	0.975592i
$377$	4.35799	+	13.4125i	0.224448	+	0.690779i
$378$	10.9557	−	33.7182i	0.563501	−	1.73428i
$379$	10.1567	+	7.37931i	0.521717	+	0.379049i	0.817250	−	0.576283i	$-0.195497\pi$
$379$	10.1567	+	7.37931i	0.521717	+	0.379049i	−0.295533	+	0.955332i	$0.595497\pi$
$380$	0.0939112	+	0.0682305i	0.00481754	+	0.00350015i
$381$	−2.13549	+	6.57236i	−0.109404	+	0.336712i
$382$	−8.53066	−	26.2547i	−0.436467	−	1.34331i
$383$	29.6671	−	21.5544i	1.51592	−	1.10138i	0.552450	−	0.833546i	$-0.313693\pi$
$383$	29.6671	−	21.5544i	1.51592	−	1.10138i	0.963466	−	0.267832i	$-0.0863071\pi$
$384$	17.9753			0.917298
$385$		0			0
$386$	−11.2169			−0.570924
$387$	0.568292	−	0.412888i	0.0288879	−	0.0209883i
$388$	0.282201	+	0.868527i	0.0143266	+	0.0440928i
$389$	2.12562	−	6.54198i	0.107773	−	0.331691i	−0.882598	−	0.470128i	$-0.844208\pi$
$389$	2.12562	−	6.54198i	0.107773	−	0.331691i	0.990371	+	0.138437i	$0.0442077\pi$
$390$	−9.44377	−	6.86130i	−0.478204	−	0.347436i
$391$	4.51733	+	3.28203i	0.228451	+	0.165980i
$392$	13.4098	−	41.2711i	0.677297	−	2.08451i
$393$	4.54331	+	13.9829i	0.229179	+	0.705342i
$394$	16.7049	−	12.1368i	0.841582	−	0.611445i
$395$	−9.41363			−0.473651
$396$		0			0
$397$	37.7626			1.89525			0.947624	−	0.319387i	$-0.103477\pi$
$397$	37.7626			1.89525			0.947624	+	0.319387i	$0.103477\pi$
$398$	−10.3531	+	7.52197i	−0.518954	+	0.377042i
$399$	−5.44049	−	16.7441i	−0.272365	−	0.838254i
$400$	−1.20350	+	3.70400i	−0.0601751	+	0.185200i
$401$	−15.5376	−	11.2887i	−0.775909	−	0.563731i	0.127839	−	0.991795i	$-0.459196\pi$
$401$	−15.5376	−	11.2887i	−0.775909	−	0.563731i	−0.903749	+	0.428064i	$0.859196\pi$
$402$	−19.5317	−	14.1906i	−0.974153	−	0.707764i
$403$	−5.83876	+	17.9698i	−0.290849	+	0.895142i
$404$	−0.0585666	−	0.180249i	−0.00291380	−	0.00896775i
$405$	−6.59682	+	4.79287i	−0.327799	+	0.238160i
$406$	−18.3436			−0.910380
$407$		0			0
$408$	25.1762			1.24641
$409$	−21.9374	+	15.9384i	−1.08473	+	0.788105i	−0.978502	−	0.206237i	$-0.933878\pi$
$409$	−21.9374	+	15.9384i	−1.08473	+	0.788105i	−0.106231	+	0.994341i	$0.533878\pi$
$410$	2.65468	+	8.17028i	0.131105	+	0.403501i
$411$	−0.398265	+	1.22574i	−0.0196450	+	0.0604611i
$412$	−0.000554120	0	0.000402591i	−2.72995e−5	0	1.98343e-5i
$413$	17.2587	+	12.5392i	0.849246	+	0.617014i
$414$	0.117695	−	0.362229i	0.00578441	−	0.0178026i
$415$	−0.974678	−	2.99975i	−0.0478450	−	0.147252i
$416$	−1.18735	+	0.862661i	−0.0582147	+	0.0422954i
$417$	−14.5324			−0.711652
$418$		0			0
$419$	11.9106			0.581870			0.290935	−	0.956743i	$-0.406034\pi$
$419$	11.9106			0.581870			0.290935	+	0.956743i	$0.406034\pi$
$420$	−0.323850	+	0.235291i	−0.0158023	+	0.0114810i
$421$	−0.986433	−	3.03593i	−0.0480758	−	0.147962i	0.924137	−	0.382062i	$-0.124786\pi$
$421$	−0.986433	−	3.03593i	−0.0480758	−	0.147962i	−0.972213	+	0.234100i	$0.924786\pi$
$422$	−3.78677	+	11.6545i	−0.184337	+	0.567331i
$423$	−2.35965	−	1.71438i	−0.114730	−	0.0833562i
$424$	−2.43570	−	1.76964i	−0.118288	−	0.0859414i
$425$	−1.64115	+	5.05095i	−0.0796076	+	0.245007i
$426$	−0.750789	−	2.31069i	−0.0363759	−	0.111953i
$427$	−37.6269	+	27.3375i	−1.82089	+	1.32296i
$428$	0.598790			0.0289436
$429$		0			0
$430$	3.77853			0.182217
$431$	29.1533	−	21.1811i	1.40426	−	1.02026i	0.410137	−	0.912024i	$-0.365481\pi$
$431$	29.1533	−	21.1811i	1.40426	−	1.02026i	0.994126	−	0.108233i	$-0.0345192\pi$
$432$	−6.49401	−	19.9865i	−0.312443	−	0.961601i
$433$	−7.99694	+	24.6120i	−0.384308	+	1.18278i	0.552672	+	0.833399i	$0.313608\pi$
$433$	−7.99694	+	24.6120i	−0.384308	+	1.18278i	−0.936981	+	0.349381i	$0.886392\pi$
$434$	−19.8828	−	14.4457i	−0.954405	−	0.693416i
$435$	3.73909	+	2.71661i	0.179276	+	0.130251i
$436$	0.205524	−	0.632538i	0.00984282	−	0.0302931i
$437$	−0.734098	−	2.25932i	−0.0351167	−	0.108078i
$438$	−18.8875	+	13.7226i	−0.902482	+	0.655691i
$439$	−12.0673			−0.575943			−0.287971	−	0.957639i	$-0.592981\pi$
$439$	−12.0673			−0.575943			−0.287971	+	0.957639i	$0.592981\pi$
$440$		0			0
$441$	−3.93265			−0.187269
$442$	30.2969	−	22.0120i	1.44108	−	1.04700i
$443$	−5.65209	−	17.3953i	−0.268539	−	0.826478i	−0.990857	−	0.134917i	$-0.956923\pi$
$443$	−5.65209	−	17.3953i	−0.268539	−	0.826478i	0.722318	−	0.691561i	$-0.243077\pi$
$444$	−0.0208110	+	0.0640496i	−0.000987645	+	0.00303966i
$445$	−10.1260	−	7.35694i	−0.480017	−	0.348753i
$446$	26.8859	+	19.5338i	1.27309	+	0.924951i
$447$	5.14188	−	15.8251i	0.243203	−	0.748500i
$448$	−11.9192	−	36.6836i	−0.563131	−	1.73314i
$449$	−0.345422	+	0.250964i	−0.0163015	+	0.0118437i	−0.595906	−	0.803054i	$-0.703207\pi$
$449$	−0.345422	+	0.250964i	−0.0163015	+	0.0118437i	0.579605	+	0.814898i	$0.303207\pi$
$450$	0.362259			0.0170771
$451$		0			0
$452$	0.853931			0.0401655
$453$	−14.2434	+	10.3484i	−0.669213	+	0.486212i
$454$	3.68246	+	11.3334i	0.172826	+	0.531905i
$455$	−7.34715	+	22.6122i	−0.344440	+	1.06008i
$456$	−8.66553	−	6.29588i	−0.405801	−	0.294831i
$457$	12.4305	+	9.03126i	0.581473	+	0.422465i	0.839255	−	0.543739i	$-0.182992\pi$
$457$	12.4305	+	9.03126i	0.581473	+	0.422465i	−0.257782	+	0.966203i	$0.582992\pi$
$458$	6.39713	−	19.6883i	0.298918	−	0.919975i
$459$	−8.85555	−	27.2546i	−0.413342	−	1.27214i
$460$	−0.0436979	+	0.0317484i	−0.00203742	+	0.00148028i
$461$	20.6191			0.960329			0.480164	−	0.877179i	$-0.340577\pi$
$461$	20.6191			0.960329			0.480164	+	0.877179i	$0.340577\pi$
$462$		0			0
$463$	−1.64211			−0.0763153			−0.0381577	−	0.999272i	$-0.512149\pi$
$463$	−1.64211			−0.0763153			−0.0381577	+	0.999272i	$0.512149\pi$
$464$	−8.79663	+	6.39112i	−0.408373	+	0.296700i
$465$	1.91348	+	5.88910i	0.0887357	+	0.273100i
$466$	−2.74447	+	8.44660i	−0.127135	+	0.391281i
$467$	2.53742	+	1.84354i	0.117418	+	0.0853090i	0.644944	−	0.764230i	$-0.276881\pi$
$467$	2.53742	+	1.84354i	0.117418	+	0.0853090i	−0.527527	+	0.849538i	$0.676881\pi$
$468$	0.0544838	+	0.0395848i	0.00251852	+	0.00182981i
$469$	−15.1955	+	46.7668i	−0.701661	+	2.15949i
$470$	−4.84820	−	14.9212i	−0.223631	−	0.688265i
$471$	−0.695115	+	0.505031i	−0.0320292	+	0.0232706i
$472$	12.9787			0.597395
$473$		0			0
$474$	21.7538			0.999186
$475$	1.82798	−	1.32811i	0.0838736	−	0.0609377i
$476$	−0.396846	−	1.22137i	−0.0181894	−	0.0559812i
$477$	−0.0843130	+	0.259489i	−0.00386043	+	0.0118812i
$478$	5.28051	+	3.83652i	0.241525	+	0.175478i
$479$	8.03569	+	5.83827i	0.367160	+	0.266757i	0.756032	−	0.654534i	$-0.227135\pi$
$479$	8.03569	+	5.83827i	0.367160	+	0.266757i	−0.388872	+	0.921292i	$0.627135\pi$
$480$	−0.148631	+	0.457438i	−0.00678403	+	0.0208791i
$481$	1.23607	+	3.80423i	0.0563598	+	0.173458i
$482$	−8.62257	+	6.26466i	−0.392747	+	0.285348i
$483$	8.19216			0.372756
$484$		0			0
$485$	17.7759			0.807162
$486$	−3.03691	+	2.20644i	−0.137757	+	0.100086i
$487$	1.49746	+	4.60870i	0.0678563	+	0.208840i	0.979235	−	0.202729i	$-0.0649809\pi$
$487$	1.49746	+	4.60870i	0.0678563	+	0.208840i	−0.911379	+	0.411569i	$0.864981\pi$
$488$	−8.74389	+	26.9109i	−0.395817	+	1.21820i
$489$	26.4439	+	19.2126i	1.19584	+	0.868825i
$490$	−17.1140	−	12.4341i	−0.773134	−	0.561715i
$491$	3.23799	−	9.96549i	0.146128	−	0.449736i	−0.851026	−	0.525123i	$-0.824019\pi$
$491$	3.23799	−	9.96549i	0.146128	−	0.449736i	0.997154	+	0.0753869i	$0.0240192\pi$
$492$	0.161736	+	0.497774i	0.00729164	+	0.0224414i
$493$	−11.9955	+	8.71525i	−0.540251	+	0.392515i
$494$	−15.9327			−0.716844
$495$		0			0
$496$	−14.5678			−0.654112
$497$	−4.00352	+	2.90873i	−0.179583	+	0.130474i
$498$	2.25237	+	6.93207i	0.100931	+	0.310634i
$499$	−4.61363	+	14.1993i	−0.206534	+	0.635647i	0.793113	+	0.609075i	$0.208459\pi$
$499$	−4.61363	+	14.1993i	−0.206534	+	0.635647i	−0.999647	+	0.0265723i	$0.991541\pi$
$500$	−0.0415626	−	0.0301970i	−0.00185874	−	0.00135045i
$501$	−2.42705	−	1.76336i	−0.108433	−	0.0787809i
$502$	9.25815	−	28.4937i	0.413211	−	1.27173i
$503$	12.1048	+	37.2546i	0.539725	+	1.66110i	0.733213	+	0.679999i	$0.238020\pi$
$503$	12.1048	+	37.2546i	0.539725	+	1.66110i	−0.193489	+	0.981103i	$0.561980\pi$
$504$	−2.82976	+	2.05594i	−0.126047	+	0.0915788i
$505$	−3.68912			−0.164163
$506$		0			0
$507$	−20.7201			−0.920214
$508$	0.173502	−	0.126056i	0.00769789	−	0.00559285i
$509$	−5.24072	−	16.1293i	−0.232291	−	0.714917i	−0.997469	−	0.0710992i	$-0.977349\pi$
$509$	−5.24072	−	16.1293i	−0.232291	−	0.714917i	0.765179	−	0.643818i	$-0.222651\pi$
$510$	3.79252	−	11.6722i	0.167935	−	0.516852i
$511$	38.4702	+	27.9502i	1.70182	+	1.23645i
$512$	−18.9606	−	13.7757i	−0.837949	−	0.608805i
$513$	−3.76759	+	11.5954i	−0.166343	+	0.511951i
$514$	−7.26447	−	22.3577i	−0.320422	−	0.986158i
$515$	−0.0107859	+	0.00783644i	−0.000475285	+	0.000345315i
$516$	0.230207			0.0101343
$517$		0			0
$518$	−5.20286			−0.228600
$519$	−6.07009	+	4.41018i	−0.266448	+	0.193585i
$520$	4.46993	+	13.7570i	0.196020	+	0.603286i
$521$	−7.92850	+	24.4014i	−0.347354	+	1.06905i	0.612958	+	0.790116i	$0.289980\pi$
$521$	−7.92850	+	24.4014i	−0.347354	+	1.06905i	−0.960311	+	0.278930i	$0.910020\pi$
$522$	0.818222	+	0.594473i	0.0358126	+	0.0260194i
$523$	3.19237	+	2.31939i	0.139593	+	0.101420i	0.655390	−	0.755291i	$-0.272504\pi$
$523$	3.19237	+	2.31939i	0.139593	+	0.101420i	−0.515797	+	0.856711i	$0.672504\pi$
$524$	0.140995	−	0.433938i	0.00615939	−	0.0189567i
$525$	2.40782	+	7.41050i	0.105086	+	0.323421i
$526$	−12.6728	+	9.20731i	−0.552559	+	0.401458i
$527$	−19.8653			−0.865346
$528$		0			0
$529$	−21.8946			−0.951940
$530$	−1.18735	+	0.862661i	−0.0515752	+	0.0374716i
$531$	−0.363464	−	1.11863i	−0.0157730	−	0.0485442i
$532$	−0.168838	+	0.519629i	−0.00732004	+	0.0225288i
$533$	25.1497	+	18.2723i	1.08936	+	0.791463i
$534$	23.3999	+	17.0011i	1.01261	+	0.735707i
$535$	3.60173	−	11.0850i	0.155716	−	0.479246i
$536$	9.24476	+	28.4525i	0.399313	+	1.22896i
$537$	0.557506	−	0.405052i	0.0240582	−	0.0174793i
$538$	17.3472			0.747891
$539$		0			0
$540$	0.277212			0.0119293
$541$	−36.7167	+	26.6762i	−1.57857	+	1.14690i	−0.660268	+	0.751030i	$0.729557\pi$
$541$	−36.7167	+	26.6762i	−1.57857	+	1.14690i	−0.918306	+	0.395871i	$0.870443\pi$
$542$	7.69123	+	23.6712i	0.330366	+	1.01676i
$543$	1.93977	−	5.96998i	0.0832433	−	0.256197i
$544$	−1.24835	−	0.906980i	−0.0535226	−	0.0388864i
$545$	−10.4735	−	7.60946i	−0.448636	−	0.325953i
$546$	16.9784	−	52.2542i	0.726610	−	2.23627i
$547$	5.39617	+	16.6077i	0.230724	+	0.710094i	0.997660	+	0.0683709i	$0.0217801\pi$
$547$	5.39617	+	16.6077i	0.230724	+	0.710094i	−0.766936	+	0.641723i	$0.778220\pi$
$548$	0.0323578	−	0.0235093i	0.00138226	−	0.00100427i
$549$	2.56430			0.109441
$550$		0			0
$551$	6.30825			0.268740
$552$	4.03216	−	2.92954i	0.171620	−	0.124689i
$553$	−13.6920	−	42.1396i	−0.582243	−	1.79196i
$554$	−7.42302	+	22.8457i	−0.315374	+	0.970621i
$555$	1.06053	+	0.770519i	0.0450169	+	0.0327067i
$556$	0.364859	+	0.265086i	0.0154735	+	0.0112421i
$557$	−7.98188	+	24.5657i	−0.338203	+	1.04088i	0.626920	+	0.779084i	$0.284315\pi$
$557$	−7.98188	+	24.5657i	−0.338203	+	1.04088i	−0.965123	+	0.261798i	$0.915685\pi$
$558$	0.418726	+	1.28871i	0.0177261	+	0.0545553i
$559$	11.0618	−	8.03687i	0.467865	−	0.339923i
$560$	−18.3312			−0.774636
$561$		0			0
$562$	−36.8679			−1.55518
$563$	−8.68357	+	6.30898i	−0.365969	+	0.265892i	−0.755537	−	0.655106i	$-0.772624\pi$
$563$	−8.68357	+	6.30898i	−0.365969	+	0.265892i	0.389569	+	0.920997i	$0.372624\pi$
$564$	−0.295377	−	0.909076i	−0.0124376	−	0.0382790i
$565$	5.13641	−	15.8082i	0.216090	−	0.665058i
$566$	20.6411	+	14.9966i	0.867608	+	0.630354i
$567$	−31.0500	−	22.5592i	−1.30398	−	0.947396i
$568$	−0.930355	+	2.86334i	−0.0390368	+	0.120143i
$569$	−8.15814	−	25.1082i	−0.342007	−	1.05259i	−0.963167	−	0.268905i	$-0.913338\pi$
$569$	−8.15814	−	25.1082i	−0.342007	−	1.05259i	0.621159	−	0.783684i	$-0.286662\pi$
$570$	−4.22426	+	3.06910i	−0.176935	+	0.128551i
$571$	2.45168			0.102599			0.0512997	−	0.998683i	$-0.483664\pi$
$571$	2.45168			0.102599			0.0512997	+	0.998683i	$0.483664\pi$
$572$		0			0
$573$	−32.7379			−1.36764
$574$	−32.7126	+	23.7671i	−1.36540	+	0.992020i
$575$	0.324893	+	0.999916i	0.0135490	+	0.0416994i
$576$	−0.657167	+	2.02255i	−0.0273820	+	0.0842730i
$577$	−22.1630	−	16.1024i	−0.922659	−	0.670351i	0.0215252	−	0.999768i	$-0.493148\pi$
$577$	−22.1630	−	16.1024i	−0.922659	−	0.670351i	−0.944185	+	0.329417i	$0.893148\pi$
$578$	12.6547	+	9.19420i	0.526368	+	0.382428i
$579$	−4.11059	+	12.6511i	−0.170830	+	0.525761i
$580$	−0.0443223	−	0.136410i	−0.00184038	−	0.00566411i
$581$	12.0106	−	8.72619i	0.498282	−	0.362023i
$582$	−41.0780			−1.70274
$583$		0			0
$584$	28.9300			1.19713
$585$	1.06053	−	0.770519i	0.0438474	−	0.0318570i
$586$	−11.0570	−	34.0299i	−0.456760	−	1.40576i
$587$	4.37440	−	13.4630i	0.180551	−	0.555678i	−0.819293	−	0.573376i	$-0.805634\pi$
$587$	4.37440	−	13.4630i	0.180551	−	0.555678i	0.999843	+	0.0176975i	$0.00563358\pi$
$588$	−1.04267	−	0.757546i	−0.0429991	−	0.0312407i
$589$	6.83755	+	4.96777i	0.281736	+	0.204693i
$590$	1.95511	−	6.01720i	0.0804904	−	0.247724i
$591$	−7.56692	−	23.2886i	−0.311262	−	0.957965i
$592$	−2.49501	+	1.81273i	−0.102544	+	0.0745028i
$593$	−23.0194			−0.945295			−0.472647	−	0.881252i	$-0.656702\pi$
$593$	−23.0194			−0.945295			−0.472647	+	0.881252i	$0.656702\pi$
$594$		0			0
$595$	−24.9974			−1.02479
$596$	−0.417762	+	0.303522i	−0.0171122	+	0.0124327i
$597$	4.68970	+	14.4334i	0.191937	+	0.590720i
$598$	2.29094	−	7.05078i	0.0936834	−	0.288328i
$599$	−5.92542	−	4.30507i	−0.242106	−	0.175900i	0.460115	−	0.887859i	$-0.347808\pi$
$599$	−5.92542	−	4.30507i	−0.242106	−	0.175900i	−0.702221	+	0.711959i	$0.747808\pi$
$600$	3.83514	+	2.78639i	0.156569	+	0.113754i
$601$	−4.30543	+	13.2507i	−0.175622	+	0.540509i	−0.999661	−	0.0260236i	$-0.991715\pi$
$601$	−4.30543	+	13.2507i	−0.175622	+	0.540509i	0.824039	+	0.566533i	$0.191715\pi$
$602$	5.49582	+	16.9144i	0.223993	+	0.689380i
$603$	2.19340	−	1.59360i	0.0893220	−	0.0648962i
$604$	0.546370			0.0222315
$605$		0			0
$606$	8.52512			0.346309
$607$	9.05679	−	6.58014i	0.367604	−	0.267080i	−0.388613	−	0.921401i	$-0.627046\pi$
$607$	9.05679	−	6.58014i	0.367604	−	0.267080i	0.756217	+	0.654321i	$0.227046\pi$
$608$	0.202866	+	0.624357i	0.00822729	+	0.0253210i
$609$	−6.72230	+	20.6891i	−0.272401	+	0.838365i
$610$	11.1593	+	8.10767i	0.451825	+	0.328270i
$611$	−45.9305	−	33.3705i	−1.85815	−	1.35003i
$612$	−0.0218801	+	0.0673401i	−0.000884451	+	0.00272206i
$613$	3.98465	+	12.2635i	0.160939	+	0.495318i	0.998714	−	0.0506967i	$-0.0161442\pi$
$613$	3.98465	+	12.2635i	0.160939	+	0.495318i	−0.837775	+	0.546015i	$0.816144\pi$
$614$	30.8981	−	22.4488i	1.24695	−	0.905959i
$615$	10.1878			0.410812
$616$		0			0
$617$	20.8813			0.840649			0.420324	−	0.907374i	$-0.361916\pi$
$617$	20.8813			0.840649			0.420324	+	0.907374i	$0.361916\pi$
$618$	0.0249251	−	0.0181091i	0.00100263	−	0.000728456i
$619$	7.08740	+	21.8128i	0.284866	+	0.876729i	0.986439	+	0.164130i	$0.0524818\pi$
$619$	7.08740	+	21.8128i	0.284866	+	0.876729i	−0.701572	+	0.712598i	$0.747518\pi$
$620$	0.0593822	−	0.182760i	0.00238485	−	0.00733980i
$621$	−4.58967	−	3.33459i	−0.184177	−	0.133812i
$622$	22.0254	+	16.0024i	0.883139	+	0.641638i
$623$	18.2049	−	56.0289i	0.729364	−	2.24475i
$624$	−10.0640	−	30.9738i	−0.402882	−	1.23994i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	10.5183			0.420397
$627$		0			0
$628$	0.0266643			0.00106402
$629$	−3.40232	+	2.47193i	−0.135659	+	0.0985623i
$630$	0.526901	+	1.62163i	0.0209922	+	0.0646074i
$631$	5.10466	−	15.7105i	0.203213	−	0.625426i	−0.796569	−	0.604548i	$-0.793354\pi$
$631$	5.10466	−	15.7105i	0.203213	−	0.625426i	0.999782	−	0.0208781i	$-0.00664620\pi$
$632$	−21.8084	−	15.8447i	−0.867492	−	0.630270i
$633$	11.7569	+	8.54190i	0.467296	+	0.339510i
$634$	4.99683	−	15.3787i	0.198450	−	0.610765i
$635$	−1.28998	−	3.97015i	−0.0511913	−	0.157551i
$636$	−0.0723393	+	0.0525576i	−0.00286844	+	0.00208404i
$637$	−76.5491			−3.03299
$638$		0			0
$639$	0.272843			0.0107935
$640$	−8.78455	+	6.38235i	−0.347240	+	0.252284i
$641$	6.04346	+	18.5999i	0.238703	+	0.734651i	0.996609	+	0.0822872i	$0.0262225\pi$
$641$	6.04346	+	18.5999i	0.238703	+	0.734651i	−0.757906	+	0.652364i	$0.773778\pi$
$642$	−8.32318	+	25.6161i	−0.328490	+	1.01099i
$643$	0.991724	+	0.720529i	0.0391098	+	0.0284149i	0.607168	−	0.794573i	$-0.292305\pi$
$643$	0.991724	+	0.720529i	0.0391098	+	0.0284149i	−0.568059	+	0.822988i	$0.692305\pi$
$644$	−0.205678	−	0.149434i	−0.00810485	−	0.00588852i
$645$	1.38470	−	4.26166i	0.0545225	−	0.167803i
$646$	−5.17640	−	15.9313i	−0.203663	−	0.626809i
$647$	−6.01208	+	4.36803i	−0.236359	+	0.171725i	−0.699660	−	0.714476i	$-0.746665\pi$
$647$	−6.01208	+	4.36803i	−0.236359	+	0.171725i	0.463301	+	0.886201i	$0.346665\pi$
$648$	−23.3500			−0.917274
$649$		0			0
$650$	7.05137			0.276578
$651$	−23.5791	+	17.1312i	−0.924138	+	0.671426i
$652$	−0.313460	−	0.964730i	−0.0122760	−	0.0377817i
$653$	−13.0849	+	40.2712i	−0.512052	+	1.57593i	0.276531	+	0.961005i	$0.410815\pi$
$653$	−13.0849	+	40.2712i	−0.512052	+	1.57593i	−0.788583	+	0.614929i	$0.789185\pi$
$654$	24.2031	+	17.5846i	0.946416	+	0.687612i
$655$	−7.18511	−	5.22029i	−0.280745	−	0.203973i
$656$	−7.40650	+	22.7948i	−0.289175	+	0.889989i
$657$	−0.810171	−	2.49345i	−0.0316078	−	0.0972788i
$658$	59.7425	−	43.4055i	2.32901	−	1.69212i
$659$	−35.4897			−1.38248			−0.691242	−	0.722624i	$-0.742936\pi$
$659$	−35.4897			−1.38248			−0.691242	+	0.722624i	$0.742936\pi$
$660$		0			0
$661$	−19.2188			−0.747526			−0.373763	−	0.927524i	$-0.621933\pi$
$661$	−19.2188			−0.747526			−0.373763	+	0.927524i	$0.621933\pi$
$662$	20.9292	−	15.2059i	0.813436	−	0.590996i
$663$	−13.7238	−	42.2374i	−0.532986	−	1.64036i
$664$	2.79107	−	8.59002i	0.108314	−	0.333357i
$665$	8.60398	+	6.25116i	0.333648	+	0.242409i
$666$	0.232074	+	0.168612i	0.00899270	+	0.00653358i
$667$	−0.907056	+	2.79163i	−0.0351213	+	0.108092i
$668$	0.0287697	+	0.0885440i	0.00111313	+	0.00342587i
$669$	31.8842	−	23.1652i	1.23271	−	0.895618i
$670$	14.5837			0.563419
$671$		0			0
$672$	−2.26388			−0.0873311
$673$	35.1618	−	25.5465i	1.35539	−	0.984747i	0.356664	−	0.934233i	$-0.383914\pi$
$673$	35.1618	−	25.5465i	1.35539	−	0.984747i	0.998723	−	0.0505141i	$-0.0160860\pi$
$674$	−3.30994	−	10.1869i	−0.127494	−	0.392386i
$675$	1.66743	−	5.13184i	0.0641796	−	0.197524i
$676$	0.520214	+	0.377957i	0.0200082	+	0.0145368i
$677$	−14.2255	−	10.3355i	−0.546732	−	0.397224i	0.279847	−	0.960045i	$-0.409716\pi$
$677$	−14.2255	−	10.3355i	−0.546732	−	0.397224i	−0.826579	+	0.562821i	$0.809716\pi$
$678$	−11.8696	+	36.5310i	−0.455851	+	1.40297i
$679$	25.8548	+	79.5729i	0.992216	+	3.05373i
$680$	−12.3036	+	8.93912i	−0.471823	+	0.342800i
$681$	14.1321			0.541541
$682$		0			0
$683$	12.0177			0.459845			0.229922	−	0.973209i	$-0.426153\pi$
$683$	12.0177			0.459845			0.229922	+	0.973209i	$0.426153\pi$
$684$	0.0243709	−	0.0177065i	0.000931846	−	0.000677026i
$685$	−0.240579	−	0.740428i	−0.00919207	−	0.0282903i
$686$	16.5558	−	50.9536i	0.632105	−	1.94542i
$687$	−19.8614	−	14.4302i	−0.757760	−	0.550545i
$688$	8.52866	+	6.19643i	0.325152	+	0.236237i
$689$	−1.64115	+	5.05095i	−0.0625230	+	0.192426i
$690$	−0.750789	−	2.31069i	−0.0285821	−	0.0879665i
$691$	−28.2482	+	20.5235i	−1.07461	+	0.780751i	−0.976736	−	0.214447i	$-0.931205\pi$
$691$	−28.2482	+	20.5235i	−1.07461	+	0.780751i	−0.0978763	+	0.995199i	$0.531205\pi$
$692$	0.232846			0.00885148
$693$		0			0
$694$	−39.3482			−1.49364
$695$	7.10198	−	5.15989i	0.269394	−	0.195726i
$696$	4.08978	+	12.5870i	0.155023	+	0.477111i
$697$	−10.0999	+	31.0842i	−0.382560	+	1.17740i
$698$	−10.0450	−	7.29810i	−0.380208	−	0.276237i
$699$	8.52085	+	6.19076i	0.322288	+	0.234156i
$700$	0.0747231	−	0.229974i	0.00282427	−	0.00869221i
$701$	5.38935	+	16.5867i	0.203553	+	0.626471i	0.999770	+	0.0214600i	$0.00683144\pi$
$701$	5.38935	+	16.5867i	0.203553	+	0.626471i	−0.796217	+	0.605011i	$0.793169\pi$
$702$	−30.7821	+	22.3645i	−1.16179	+	0.844093i
$703$	1.78922			0.0674819
$704$		0			0
$705$	−18.6058			−0.700735
$706$	−31.6462	+	22.9923i	−1.19102	+	0.865328i
$707$	−5.36577	−	16.5141i	−0.201800	−	0.621078i
$708$	0.119115	−	0.366598i	0.00447661	−	0.0137776i
$709$	−41.9249	−	30.4602i	−1.57452	−	1.14396i	−0.922657	−	0.385621i	$-0.873987\pi$
$709$	−41.9249	−	30.4602i	−1.57452	−	1.14396i	−0.651864	−	0.758336i	$-0.726013\pi$
$710$	1.18735	+	0.862661i	0.0445605	+	0.0323751i
$711$	−0.754909	+	2.32337i	−0.0283113	+	0.0871332i
$712$	−11.0757	−	34.0874i	−0.415079	−	1.27748i
$713$	−3.18158	+	2.31156i	−0.119151	+	0.0865685i
$714$	57.7660			2.16184
$715$		0			0
$716$	−0.0213857			−0.000799221
$717$	6.26219	−	4.54975i	0.233866	−	0.169913i
$718$	4.85584	+	14.9447i	0.181218	+	0.557733i
$719$	−8.31771	+	25.5993i	−0.310198	+	0.954692i	0.667488	+	0.744621i	$0.267370\pi$
$719$	−8.31771	+	25.5993i	−0.310198	+	0.954692i	−0.977686	+	0.210071i	$0.932630\pi$
$720$	0.817668	+	0.594070i	0.0304727	+	0.0221397i
$721$	−0.0507674	−	0.0368847i	−0.00189068	−	0.00137366i
$722$	5.99367	−	18.4466i	0.223061	−	0.686512i
$723$	3.90581	+	12.0209i	0.145259	+	0.447060i
$724$	−0.157600	+	0.114503i	−0.00585715	+	0.00425547i
$725$	−2.79186			−0.103687
$726$		0			0
$727$	−21.7449			−0.806472			−0.403236	−	0.915096i	$-0.632115\pi$
$727$	−21.7449			−0.806472			−0.403236	+	0.915096i	$0.632115\pi$
$728$	−55.0812	+	40.0189i	−2.04145	+	1.48320i
$729$	8.93493	+	27.4989i	0.330923	+	1.01848i
$730$	4.35799	−	13.4125i	0.161296	−	0.496419i
$731$	11.6301	+	8.44976i	0.430155	+	0.312526i
$732$	0.679877	+	0.493960i	0.0251290	+	0.0182573i
$733$	−1.48901	+	4.58269i	−0.0549977	+	0.169266i	−0.974782	−	0.223158i	$-0.928363\pi$
$733$	−1.48901	+	4.58269i	−0.0549977	+	0.169266i	0.919785	+	0.392424i	$0.128363\pi$
$734$	−2.39525	−	7.37181i	−0.0884102	−	0.272099i
$735$	−20.2956	+	14.7456i	−0.748616	+	0.543901i
$736$	−0.305471			−0.0112598
$737$		0			0
$738$	2.22939			0.0820648
$739$	−39.0277	+	28.3553i	−1.43566	+	1.04307i	−0.446730	+	0.894669i	$0.647411\pi$
$739$	−39.0277	+	28.3553i	−1.43566	+	1.04307i	−0.988928	+	0.148397i	$0.952589\pi$
$740$	−0.0125712	−	0.0386903i	−0.000462128	−	0.00142228i
$741$	−5.83876	+	17.9698i	−0.214492	+	0.660139i
$742$	−5.58864	−	4.06039i	−0.205166	−	0.149062i
$743$	−21.6743	−	15.7473i	−0.795154	−	0.577713i	0.114334	−	0.993442i	$-0.463527\pi$
$743$	−21.6743	−	15.7473i	−0.795154	−	0.577713i	−0.909489	+	0.415729i	$0.863527\pi$
$744$	−5.47941	+	16.8639i	−0.200885	+	0.618260i
$745$	3.10605	+	9.55942i	0.113797	+	0.350230i
$746$	7.68533	−	5.58372i	0.281380	−	0.204434i
$747$	−0.818528			−0.0299484
$748$		0			0
$749$	54.8600			2.00454
$750$	1.86955	−	1.35830i	0.0682661	−	0.0495982i
$751$	0.136875	+	0.421258i	0.00499464	+	0.0153719i	0.953523	−	0.301321i	$-0.0974276\pi$
$751$	0.136875	+	0.421258i	0.00499464	+	0.0153719i	−0.948528	+	0.316693i	$0.897428\pi$
$752$	13.5264	−	41.6298i	0.493255	−	1.51808i
$753$	−28.7441	−	20.8838i	−1.04749	−	0.761050i
$754$	15.9267	+	11.5714i	0.580016	+	0.421406i
$755$	3.28643	−	10.1146i	0.119605	−	0.368107i
$756$	0.403201	+	1.24092i	0.0146643	+	0.0451320i
$757$	−22.3551	+	16.2420i	−0.812511	+	0.590324i	−0.914558	−	0.404456i	$-0.867461\pi$
$757$	−22.3551	+	16.2420i	−0.812511	+	0.590324i	0.102046	+	0.994780i	$0.467461\pi$
$758$	17.5251			0.636541
$759$		0			0
$760$	6.47029			0.234702
$761$	1.50907	−	1.09640i	0.0547036	−	0.0397445i	−0.560097	−	0.828427i	$-0.689236\pi$
$761$	1.50907	−	1.09640i	0.0547036	−	0.0397445i	0.614801	+	0.788682i	$0.289236\pi$
$762$	2.98100	+	9.17456i	0.107990	+	0.332359i
$763$	18.8298	−	57.9520i	0.681683	−	2.09800i
$764$	0.821938	+	0.597173i	0.0297367	+	0.0216050i
$765$	1.11501	+	0.810104i	0.0403133	+	0.0292894i
$766$	15.8184	−	48.6841i	0.571543	−	1.75903i
$767$	−7.07482	−	21.7741i	−0.255457	−	0.786216i
$768$	−1.65021	+	1.19895i	−0.0595468	+	0.0432633i
$769$	47.5872			1.71604			0.858019	−	0.513618i	$-0.171695\pi$
$769$	47.5872			1.71604			0.858019	+	0.513618i	$0.171695\pi$
$770$		0			0
$771$	−27.8786			−1.00402
$772$	0.333973	−	0.242645i	0.0120199	−	0.00873299i
$773$	12.9839	+	39.9603i	0.466999	+	1.43727i	0.856452	+	0.516227i	$0.172664\pi$
$773$	12.9839	+	39.9603i	0.466999	+	1.43727i	−0.389453	+	0.921046i	$0.627336\pi$
$774$	0.303012	−	0.932576i	0.0108916	−	0.0335208i
$775$	−3.02612	−	2.19860i	−0.108701	−	0.0789762i
$776$	41.1811	+	29.9198i	1.47832	+	1.07406i
$777$	−1.90666	+	5.86811i	−0.0684012	+	0.210517i
$778$	−2.96722	−	9.13215i	−0.106380	−	0.327404i
$779$	11.2496	−	8.17333i	0.403060	−	0.292840i
$780$	0.429605			0.0153823
$781$		0			0
$782$	7.79450			0.278731
$783$	12.1876	−	8.85481i	0.435549	−	0.316445i
$784$	−18.2380	−	56.1308i	−0.651357	−	2.00467i
$785$	0.160386	−	0.493618i	0.00572443	−	0.0176180i
$786$	16.6040	+	12.0635i	0.592243	+	0.430290i
$787$	−14.0844	−	10.2329i	−0.502054	−	0.364764i	0.307747	−	0.951468i	$-0.400425\pi$
$787$	−14.0844	−	10.2329i	−0.502054	−	0.364764i	−0.809801	+	0.586704i	$0.800425\pi$
$788$	−0.234828	+	0.722728i	−0.00836542	+	0.0257461i
$789$	5.74045	+	17.6673i	0.204366	+	0.628972i
$790$	−10.6311	+	7.72396i	−0.378238	+	0.274806i
$791$	78.2356			2.78174
$792$		0			0
$793$	49.9140			1.77250
$794$	42.6465	−	30.9845i	1.51347	−	1.09960i
$795$	0.537841	+	1.65530i	0.0190752	+	0.0587076i
$796$	0.145538	−	0.447920i	0.00515846	−	0.0158761i
$797$	−4.81040	−	3.49496i	−0.170393	−	0.123798i	0.499320	−	0.866417i	$-0.333583\pi$
$797$	−4.81040	−	3.49496i	−0.170393	−	0.123798i	−0.669714	+	0.742620i	$0.733583\pi$
$798$	−19.8828	−	14.4457i	−0.703844	−	0.511372i
$799$	18.4452	−	56.7685i	0.652544	−	2.00833i
$800$	−0.0897831	−	0.276324i	−0.00317431	−	0.00976952i
$801$	−2.62779	+	1.90920i	−0.0928486	+	0.0674584i
$802$	−26.8096			−0.946679
$803$		0			0
$804$	0.888513			0.0313354
$805$	−4.00352	+	2.90873i	−0.141106	+	0.102519i
$806$	8.15051	+	25.0847i	0.287089	+	0.883570i
$807$	6.35714	−	19.5653i	0.223782	−	0.688730i
$808$	−8.54651	−	6.20941i	−0.300665	−	0.218446i
$809$	−16.4842	−	11.9765i	−0.579554	−	0.421070i	0.259010	−	0.965875i	$-0.416604\pi$
$809$	−16.4842	−	11.9765i	−0.579554	−	0.421070i	−0.838563	+	0.544804i	$0.816604\pi$
$810$	−3.51742	+	10.8255i	−0.123589	+	0.380369i
$811$	−0.995488	−	3.06380i	−0.0349563	−	0.107585i	0.932056	−	0.362315i	$-0.118013\pi$
$811$	−0.995488	−	3.06380i	−0.0349563	−	0.107585i	−0.967012	+	0.254730i	$0.918013\pi$
$812$	0.546166	−	0.396813i	0.0191667	−	0.0139254i
$813$	29.5164			1.03518
$814$		0			0
$815$	−19.7449			−0.691632
$816$	27.7015	−	20.1263i	0.969745	−	0.704561i
$817$	−1.88997	−	5.81674i	−0.0661218	−	0.203502i
$818$	−11.6970	+	35.9996i	−0.408975	+	1.25870i
$819$	4.99171	+	3.62669i	0.174425	+	0.126727i
$820$	−0.255782	−	0.185836i	−0.00893228	−	0.00648968i
$821$	1.82836	−	5.62710i	0.0638100	−	0.196387i	−0.914069	−	0.405559i	$-0.867077\pi$
$821$	1.82836	−	5.62710i	0.0638100	−	0.196387i	0.977879	+	0.209172i	$0.0670768\pi$
$822$	0.555951	+	1.71104i	0.0193910	+	0.0596795i
$823$	−10.3739	+	7.53711i	−0.361613	+	0.262727i	−0.753725	−	0.657191i	$-0.771745\pi$
$823$	−10.3739	+	7.53711i	−0.361613	+	0.262727i	0.392112	+	0.919918i	$0.371745\pi$
$824$	−0.0381777			−0.00132998
$825$		0			0
$826$	29.7794			1.03616
$827$	31.9400	−	23.2058i	1.11066	−	0.806945i	0.127896	−	0.991788i	$-0.459178\pi$
$827$	31.9400	−	23.2058i	1.11066	−	0.806945i	0.982768	+	0.184843i	$0.0591776\pi$
$828$	0.00433152	+	0.0133310i	0.000150531	+	0.000463286i
$829$	7.00639	−	21.5634i	0.243342	−	0.748929i	−0.752563	−	0.658520i	$-0.771183\pi$
$829$	7.00639	−	21.5634i	0.243342	−	0.748929i	0.995905	−	0.0904089i	$-0.0288174\pi$
$830$	−3.56205	−	2.58798i	−0.123641	−	0.0898302i
$831$	23.0465	+	16.7443i	0.799475	+	0.580853i
$832$	−12.7918	+	39.3690i	−0.443475	+	1.36487i
$833$	−24.8702	−	76.5427i	−0.861703	−	2.65205i
$834$	−16.4119	+	11.9239i	−0.568296	+	0.412891i
$835$	1.81220			0.0627139
$836$		0			0
$837$	20.1834			0.697641
$838$	13.4510	−	9.77273i	0.464657	−	0.337593i
$839$	−13.6838	−	42.1143i	−0.472416	−	1.45395i	−0.849411	−	0.527731i	$-0.823043\pi$
$839$	−13.6838	−	42.1143i	−0.472416	−	1.45395i	0.376995	−	0.926215i	$-0.376957\pi$
$840$	−6.89498	+	21.2206i	−0.237899	+	0.732179i
$841$	17.1556	+	12.4643i	0.591573	+	0.429803i
$842$	−3.60502	−	2.61920i	−0.124237	−	0.0902635i
$843$	−13.5108	+	41.5820i	−0.465337	+	1.43216i
$844$	−0.139364	−	0.428917i	−0.00479710	−	0.0147639i
$845$	10.1260	−	7.35694i	0.348344	−	0.253087i
$846$	−4.07149			−0.139981
$847$		0			0
$848$	−4.09469			−0.140612
$849$	24.4783	−	17.7845i	0.840094	−	0.610364i
$850$	2.29094	+	7.05078i	0.0785785	+	0.241840i
$851$	−0.257271	+	0.791797i	−0.00881912	+	0.0271425i
$852$	0.0723393	+	0.0525576i	0.00247830	+	0.00180059i
$853$	30.5721	+	22.2119i	1.04677	+	0.760523i	0.971596	−	0.236648i	$-0.0760487\pi$
$853$	30.5721	+	22.2119i	1.04677	+	0.760523i	0.0751741	+	0.997170i	$0.476049\pi$
$854$	−20.0626	+	61.7463i	−0.686528	+	2.11292i
$855$	−0.181197	−	0.557668i	−0.00619682	−	0.0190718i
$856$	27.0020	−	19.6181i	0.922908	−	0.670532i
$857$	12.0354			0.411122			0.205561	−	0.978644i	$-0.434098\pi$
$857$	12.0354			0.411122			0.205561	+	0.978644i	$0.434098\pi$
$858$		0			0
$859$	24.9486			0.851236			0.425618	−	0.904903i	$-0.360057\pi$
$859$	24.9486			0.851236			0.425618	+	0.904903i	$0.360057\pi$
$860$	−0.112502	+	0.0817378i	−0.00383630	+	0.00278724i
$861$	14.8180	+	45.6051i	0.504996	+	1.55422i
$862$	15.5445	−	47.8410i	0.529447	−	1.62947i
$863$	46.0895	+	33.4860i	1.56891	+	1.13988i	0.928195	+	0.372094i	$0.121360\pi$
$863$	46.0895	+	33.4860i	1.56891	+	1.13988i	0.640711	+	0.767782i	$0.278640\pi$
$864$	1.26834	+	0.921504i	0.0431498	+	0.0313502i
$865$	1.40057	−	4.31052i	0.0476210	−	0.146562i
$866$	11.1632	+	34.3567i	0.379340	+	1.16749i
$867$	15.0073	−	10.9034i	0.509675	−	0.370301i
$868$	0.904485			0.0307002
$869$		0			0
$870$	6.45168			0.218732
$871$	42.6945	−	31.0193i	1.44665	−	1.05105i
$872$	−11.4558	−	35.2574i	−0.387943	−	1.19397i
$873$	1.42550	−	4.38725i	0.0482460	−	0.148486i
$874$	−2.68283	−	1.94919i	−0.0907482	−	0.0659324i
$875$	−3.80789	−	2.76660i	−0.128730	−	0.0935281i
$876$	0.265510	−	0.817157i	0.00897076	−	0.0276092i
$877$	18.0333	+	55.5008i	0.608941	+	1.87413i	0.467010	+	0.884252i	$0.345331\pi$
$877$	18.0333	+	55.5008i	0.608941	+	1.87413i	0.141931	+	0.989877i	$0.454669\pi$
$878$	−13.6280	+	9.90136i	−0.459924	+	0.334155i
$879$	−42.4331			−1.43123
$880$		0			0
$881$	−31.7466			−1.06957			−0.534785	−	0.844988i	$-0.679607\pi$
$881$	−31.7466			−1.06957			−0.534785	+	0.844988i	$0.679607\pi$
$882$	−4.44127	+	3.22677i	−0.149545	+	0.108651i
$883$	8.06207	+	24.8125i	0.271310	+	0.835007i	0.990172	+	0.139854i	$0.0446634\pi$
$883$	8.06207	+	24.8125i	0.271310	+	0.835007i	−0.718862	+	0.695153i	$0.755337\pi$
$884$	−0.425897	+	1.31078i	−0.0143245	+	0.0440861i
$885$	−6.07009	−	4.41018i	−0.204044	−	0.148247i
$886$	−20.6561	−	15.0075i	−0.693956	−	0.504188i
$887$	−3.66935	+	11.2931i	−0.123205	+	0.379185i	−0.993570	−	0.113222i	$-0.963883\pi$
$887$	−3.66935	+	11.2931i	−0.123205	+	0.379185i	0.870365	+	0.492407i	$0.163883\pi$
$888$	1.15999	+	3.57010i	0.0389269	+	0.119805i
$889$	15.8959	−	11.5491i	0.533132	−	0.387343i
$890$	−17.4720			−0.585663
$891$		0			0
$892$	−1.22306			−0.0409512
$893$	−20.5450	+	14.9268i	−0.687512	+	0.499507i
$894$	−7.17771	−	22.0907i	−0.240059	−	0.738825i
$895$	−0.128635	+	0.395899i	−0.00429980	+	0.0132334i
$896$	−41.3473	−	30.0405i	−1.38132	−	1.00358i
$897$	−7.11277	−	5.16773i	−0.237488	−	0.172545i
$898$	−0.184179	+	0.566844i	−0.00614612	+	0.0189158i
$899$	−3.22704	−	9.93182i	−0.107628	−	0.331245i
$900$	−0.0107859	+	0.00783644i	−0.000359531	+	0.000261215i
$901$	−5.58373			−0.186021
$902$		0			0
$903$	21.0911			0.701869
$904$	38.5074	−	27.9773i	1.28074	−	0.930510i
$905$	1.17175	+	3.60628i	0.0389503	+	0.119877i
$906$	−7.59455	+	23.3736i	−0.252312	+	0.776537i
$907$	1.24110	+	0.901711i	0.0412100	+	0.0299408i	0.608200	−	0.793784i	$-0.291892\pi$
$907$	1.24110	+	0.901711i	0.0412100	+	0.0299408i	−0.566990	+	0.823725i	$0.691892\pi$
$908$	−0.354809	−	0.257784i	−0.0117747	−	0.00855485i
$909$	−0.295842	+	0.910507i	−0.00981245	+	0.0301996i
$910$	10.2561	+	31.5651i	0.339987	+	1.04637i
$911$	−26.1924	+	19.0299i	−0.867793	+	0.630489i	−0.929994	−	0.367575i	$-0.880188\pi$
$911$	−26.1924	+	19.0299i	−0.867793	+	0.630489i	0.0622008	+	0.998064i	$0.480188\pi$
$912$	−14.5678			−0.482387
$913$		0			0
$914$	21.4484			0.709448
$915$	13.2338	−	9.61493i	0.437496	−	0.317860i
$916$	0.235432	+	0.724586i	0.00777890	+	0.0239410i
$917$	12.9177	−	39.7566i	0.426580	−	1.31288i
$918$	−32.3635	−	23.5134i	−1.06815	−	0.776059i
$919$	28.5018	+	20.7078i	0.940189	+	0.683087i	0.948466	−	0.316879i	$-0.102635\pi$
$919$	28.5018	+	20.7078i	0.940189	+	0.683087i	−0.00827729	+	0.999966i	$0.502635\pi$
$920$	−0.930355	+	2.86334i	−0.0306729	+	0.0944015i
$921$	−13.9961	−	43.0755i	−0.461187	−	1.41939i
$922$	23.2859	−	16.9182i	0.766879	−	0.557170i
$923$	5.31088			0.174810
$924$		0			0
$925$	−0.791864			−0.0260363
$926$	−1.85449	+	1.34736i	−0.0609423	+	0.0442772i
$927$	0.00106915	+	0.00329050i	3.51154e−5	+	0.000108074i
$928$	0.250662	−	0.771458i	0.00822838	−	0.0253244i
$929$	3.65169	+	2.65311i	0.119808	+	0.0870458i	0.646076	−	0.763273i	$-0.276409\pi$
$929$	3.65169	+	2.65311i	0.119808	+	0.0870458i	−0.526268	+	0.850319i	$0.676409\pi$
$930$	6.99301	+	5.08072i	0.229310	+	0.166603i
$931$	−10.5810	+	32.5650i	−0.346779	+	1.06728i
$932$	−0.101004	−	0.310859i	−0.00330850	−	0.0101825i
$933$	26.1201	−	18.9773i	0.855133	−	0.621290i
$934$	4.37823			0.143260
$935$		0			0
$936$	3.75382			0.122697
$937$	9.48320	−	6.88995i	0.309803	−	0.225085i	−0.422009	−	0.906592i	$-0.638675\pi$
$937$	9.48320	−	6.88995i	0.309803	−	0.225085i	0.731812	+	0.681507i	$0.238675\pi$
$938$	21.2118	+	65.2833i	0.692591	+	2.13158i
$939$	3.85460	−	11.8632i	0.125790	−	0.387142i
$940$	0.467130	+	0.339389i	0.0152361	+	0.0110697i
$941$	31.6089	+	22.9652i	1.03042	+	0.748646i	0.968393	−	0.249429i	$-0.0802429\pi$
$941$	31.6089	+	22.9652i	1.03042	+	0.748646i	0.0620290	+	0.998074i	$0.480243\pi$
$942$	−0.370634	+	1.14070i	−0.0120759	+	0.0371659i
$943$	1.99943	+	6.15361i	0.0651103	+	0.200389i
$944$	14.2806	−	10.3754i	0.464793	−	0.337692i
$945$	25.3977			0.826186
$946$		0			0
$947$	26.7733			0.870014			0.435007	−	0.900427i	$-0.356746\pi$
$947$	26.7733			0.870014			0.435007	+	0.900427i	$0.356746\pi$
$948$	−0.647701	+	0.470582i	−0.0210363	+	0.0152838i
$949$	−15.7700	−	48.5350i	−0.511916	−	1.57551i
$950$	0.974678	−	2.99975i	0.0316227	−	0.0973247i
$951$	−15.5139	−	11.2715i	−0.503072	−	0.365503i
$952$	−57.9110	−	42.0748i	−1.87691	−	1.36365i
$953$	−3.53525	+	10.8804i	−0.114518	+	0.352450i	−0.991846	−	0.127441i	$-0.959324\pi$
$953$	−3.53525	+	10.8804i	−0.114518	+	0.352450i	0.877328	+	0.479891i	$0.159324\pi$
$954$	0.117695	+	0.362229i	0.00381052	+	0.0117276i
$955$	15.9990	−	11.6240i	0.517717	−	0.376143i
$956$	−0.240215			−0.00776910
$957$		0			0
$958$	13.8653			0.447968
$959$	2.96457	−	2.15388i	0.0957308	−	0.0695525i
$960$	4.19213	+	12.9021i	0.135300	+	0.416412i
$961$	−5.25599	+	16.1763i	−0.169548	+	0.521815i
$962$	4.51733	+	3.28203i	0.145645	+	0.105817i
$963$	−2.44704	−	1.77788i	−0.0788548	−	0.0572914i
$964$	0.121211	−	0.373050i	0.00390395	−	0.0120151i
$965$	−2.48308	−	7.64212i	−0.0799330	−	0.246009i
$966$	9.25168	−	6.72174i	0.297668	−	0.216268i
$967$	3.28881			0.105761			0.0528806	−	0.998601i	$-0.483160\pi$
$967$	3.28881			0.105761			0.0528806	+	0.998601i	$0.483160\pi$
$968$		0			0
$969$	−19.8653			−0.638166
$970$	20.0749	−	14.5853i	0.644566	−	0.468305i
$971$	11.9140	+	36.6674i	0.382338	+	1.17671i	0.938393	+	0.345569i	$0.112314\pi$
$971$	11.9140	+	36.6674i	0.382338	+	1.17671i	−0.556056	+	0.831145i	$0.687686\pi$
$972$	0.0426911	−	0.131390i	0.00136932	−	0.00421433i
$973$	33.4277	+	24.2867i	1.07164	+	0.778595i
$974$	5.47261	+	3.97608i	0.175354	+	0.127402i
$975$	2.58408	−	7.95298i	0.0827568	−	0.254699i
$976$	11.8921	+	36.6002i	0.380658	+	1.17154i
$977$	−43.1867	+	31.3770i	−1.38166	+	1.00384i	−0.384942	+	0.922941i	$0.625779\pi$
$977$	−43.1867	+	31.3770i	−1.38166	+	1.00384i	−0.996722	+	0.0808976i	$0.974221\pi$
$978$	45.6281			1.45903
$979$		0			0
$980$	0.778532			0.0248693
$981$	−2.71799	+	1.97473i	−0.0867787	+	0.0630484i
$982$	−4.52001	−	13.9111i	−0.144239	−	0.443923i
$983$	6.63771	−	20.4288i	0.211710	−	0.651576i	−0.787661	−	0.616109i	$-0.788708\pi$
$983$	6.63771	−	20.4288i	0.211710	−	0.651576i	0.999371	−	0.0354672i	$-0.0112919\pi$
$984$	23.6019	+	17.1478i	0.752401	+	0.546651i
$985$	11.9669	+	8.69444i	0.381296	+	0.277028i
$986$	−6.39599	+	19.6848i	−0.203690	+	0.626893i
$987$	−27.0619	−	83.2879i	−0.861389	−	2.65108i
$988$	0.474381	−	0.344658i	0.0150921	−	0.0109650i
$989$	2.84588			0.0904936
$990$		0			0
$991$	−2.87600			−0.0913592			−0.0456796	−	0.998956i	$-0.514545\pi$
$991$	−2.87600			−0.0913592			−0.0456796	+	0.998956i	$0.514545\pi$
$992$	0.879221	−	0.638792i	0.0279153	−	0.0202817i
$993$	−9.48041	−	29.1777i	−0.300852	−	0.925926i
$994$	−2.13467	+	6.56985i	−0.0677077	+	0.208383i
$995$	−7.41663	−	5.38849i	−0.235123	−	0.170827i
$996$	−0.217018	−	0.157673i	−0.00687648	−	0.00499605i
$997$	3.99041	−	12.2812i	0.126377	−	0.388950i	−0.867772	−	0.496962i	$-0.834449\pi$
$997$	3.99041	−	12.2812i	0.126377	−	0.388950i	0.994150	+	0.108013i	$0.0344487\pi$
$998$	6.44031	+	19.8212i	0.203864	+	0.627430i
$999$	3.45680	−	2.51151i	0.109368	−	0.0794608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.p.366.2		12
11.2	odd	10		605.2.a.h.1.2	yes	3
11.3	even	5	inner	605.2.g.p.511.2		12
11.4	even	5	inner	605.2.g.p.81.2		12
11.5	even	5	inner	605.2.g.p.251.2		12
11.6	odd	10		605.2.g.o.251.2		12
11.7	odd	10		605.2.g.o.81.2		12
11.8	odd	10		605.2.g.o.511.2		12
11.9	even	5		605.2.a.g.1.2	✓	3
11.10	odd	2		605.2.g.o.366.2		12
33.2	even	10		5445.2.a.bb.1.2		3
33.20	odd	10		5445.2.a.bd.1.2		3
44.31	odd	10		9680.2.a.bz.1.3		3
44.35	even	10		9680.2.a.cb.1.3		3
55.9	even	10		3025.2.a.u.1.2		3
55.24	odd	10		3025.2.a.p.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.2	✓	3	11.9	even	5
605.2.a.h.1.2	yes	3	11.2	odd	10
605.2.g.o.81.2		12	11.7	odd	10
605.2.g.o.251.2		12	11.6	odd	10
605.2.g.o.366.2		12	11.10	odd	2
605.2.g.o.511.2		12	11.8	odd	10
605.2.g.p.81.2		12	11.4	even	5	inner
605.2.g.p.251.2		12	11.5	even	5	inner
605.2.g.p.366.2		12	1.1	even	1	trivial
605.2.g.p.511.2		12	11.3	even	5	inner
3025.2.a.p.1.2		3	55.24	odd	10
3025.2.a.u.1.2		3	55.9	even	10
5445.2.a.bb.1.2		3	33.2	even	10
5445.2.a.bd.1.2		3	33.20	odd	10
9680.2.a.bz.1.3		3	44.31	odd	10
9680.2.a.cb.1.3		3	44.35	even	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.12933 - 0.820508i) q^{2} +(-0.511560 - 1.57442i) q^{3} +(-0.0158755 + 0.0488598i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-1.86955 - 1.35830i) q^{6} +(-1.45449 + 4.47645i) q^{7} +(0.884894 + 2.72343i) q^{8} +(0.209948 - 0.152536i) q^{9} +O(q^{10})\)	\(q+(1.12933 - 0.820508i) q^{2} +(-0.511560 - 1.57442i) q^{3} +(-0.0158755 + 0.0488598i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-1.86955 - 1.35830i) q^{6} +(-1.45449 + 4.47645i) q^{7} +(0.884894 + 2.72343i) q^{8} +(0.209948 - 0.152536i) q^{9} +1.39593 q^{10} +0.0850471 q^{12} +(4.08665 - 2.96912i) q^{13} +(2.03036 + 6.24882i) q^{14} +(0.511560 - 1.57442i) q^{15} +(3.15081 + 2.28920i) q^{16} +(4.29660 + 3.12166i) q^{17} +(0.111944 - 0.344529i) q^{18} +(-0.698227 - 2.14892i) q^{19} +(-0.0415626 + 0.0301970i) q^{20} +7.79186 q^{21} +1.05137 q^{23} +(3.83514 - 2.78639i) q^{24} +(0.309017 + 0.951057i) q^{25} +(2.17899 - 6.70626i) q^{26} +(-4.36540 - 3.17165i) q^{27} +(-0.195628 - 0.142132i) q^{28} +(-0.862733 + 2.65522i) q^{29} +(-0.714103 - 2.19778i) q^{30} +(-3.02612 + 2.19860i) q^{31} -0.290544 q^{32} +7.41363 q^{34} +(-3.80789 + 2.76660i) q^{35} +(0.00411986 + 0.0126796i) q^{36} +(-0.244699 + 0.753107i) q^{37} +(-2.55174 - 1.85395i) q^{38} +(-6.76521 - 4.91521i) q^{39} +(-0.884894 + 2.72343i) q^{40} +(1.90173 + 5.85292i) q^{41} +(8.79961 - 6.39329i) q^{42} +2.70682 q^{43} +0.259511 q^{45} +(1.18735 - 0.862661i) q^{46} +(-3.47309 - 10.6891i) q^{47} +(1.99233 - 6.13175i) q^{48} +(-12.2599 - 8.90737i) q^{49} +(1.12933 + 0.820508i) q^{50} +(2.71684 - 8.36156i) q^{51} +(0.0801932 + 0.246809i) q^{52} +(-0.850580 + 0.617982i) q^{53} -7.53235 q^{54} -13.4783 q^{56} +(-3.02612 + 2.19860i) q^{57} +(1.20432 + 3.70651i) q^{58} +(1.40057 - 4.31052i) q^{59} +(0.0688045 + 0.0499894i) q^{60} +(7.99412 + 5.80807i) q^{61} +(-1.61352 + 4.96591i) q^{62} +(0.377455 + 1.16169i) q^{63} +(-6.62974 + 4.81679i) q^{64} +5.05137 q^{65} +10.4473 q^{67} +(-0.220734 + 0.160373i) q^{68} +(-0.537841 - 1.65530i) q^{69} +(-2.03036 + 6.24882i) q^{70} +(0.850580 + 0.617982i) q^{71} +(0.601204 + 0.436800i) q^{72} +(3.12192 - 9.60828i) q^{73} +(0.341584 + 1.05129i) q^{74} +(1.33928 - 0.973045i) q^{75} +0.116081 q^{76} -11.6731 q^{78} +(-7.61579 + 5.53319i) q^{79} +(1.20350 + 3.70400i) q^{80} +(-2.51976 + 7.75503i) q^{81} +(6.95005 + 5.04951i) q^{82} +(-2.55174 - 1.85395i) q^{83} +(-0.123700 + 0.380709i) q^{84} +(1.64115 + 5.05095i) q^{85} +(3.05690 - 2.22097i) q^{86} +4.62177 q^{87} -12.5164 q^{89} +(0.293074 - 0.212931i) q^{90} +(7.34715 + 22.6122i) q^{91} +(-0.0166911 + 0.0513699i) q^{92} +(5.00957 + 3.63966i) q^{93} +(-12.6928 - 9.22183i) q^{94} +(0.698227 - 2.14892i) q^{95} +(0.148631 + 0.457438i) q^{96} +(14.3810 - 10.4484i) q^{97} -21.1541 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - q^{3} - 9 q^{4} + 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 12 * q + q^2 - q^3 - 9 * q^4 + 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 - 2 * q^9	\( 12 q + q^{2} - q^{3} - 9 q^{4} + 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 36 q^{12} + 6 q^{13} - 5 q^{14} + q^{15} - 13 q^{16} + 4 q^{17} + 20 q^{18} + 4 q^{19} + 9 q^{20} + 68 q^{21} - 24 q^{23} + 17 q^{24} - 3 q^{25} - 12 q^{26} - 13 q^{27} - 25 q^{28} + 2 q^{29} - 5 q^{30} - 14 q^{31} + 108 q^{32} - 32 q^{34} + q^{35} - 2 q^{36} - 4 q^{37} + 18 q^{38} - 4 q^{39} + 9 q^{40} + 9 q^{41} + 35 q^{42} - 28 q^{43} - 8 q^{45} + 8 q^{46} + 15 q^{47} - 7 q^{48} - 18 q^{49} + q^{50} - 20 q^{51} + 2 q^{52} + 6 q^{53} - 76 q^{54} - 12 q^{56} - 14 q^{57} - 30 q^{58} - 10 q^{59} + 9 q^{60} + 3 q^{61} + 24 q^{62} - 12 q^{63} - 29 q^{64} + 24 q^{65} + 76 q^{67} + 8 q^{69} + 5 q^{70} - 6 q^{71} + 48 q^{72} - 12 q^{73} - 28 q^{74} - q^{75} - 64 q^{76} - 8 q^{78} + 2 q^{79} + 13 q^{80} - 3 q^{81} + 27 q^{82} + 18 q^{83} - 31 q^{84} - 4 q^{85} + 3 q^{86} - 40 q^{87} + 44 q^{89} - 20 q^{90} - 20 q^{91} + 34 q^{92} - 20 q^{93} - 59 q^{94} - 4 q^{95} - 7 q^{96} + 2 q^{97} - 144 q^{98}+O(q^{100}) \) 12 * q + q^2 - q^3 - 9 * q^4 + 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 36 * q^12 + 6 * q^13 - 5 * q^14 + q^15 - 13 * q^16 + 4 * q^17 + 20 * q^18 + 4 * q^19 + 9 * q^20 + 68 * q^21 - 24 * q^23 + 17 * q^24 - 3 * q^25 - 12 * q^26 - 13 * q^27 - 25 * q^28 + 2 * q^29 - 5 * q^30 - 14 * q^31 + 108 * q^32 - 32 * q^34 + q^35 - 2 * q^36 - 4 * q^37 + 18 * q^38 - 4 * q^39 + 9 * q^40 + 9 * q^41 + 35 * q^42 - 28 * q^43 - 8 * q^45 + 8 * q^46 + 15 * q^47 - 7 * q^48 - 18 * q^49 + q^50 - 20 * q^51 + 2 * q^52 + 6 * q^53 - 76 * q^54 - 12 * q^56 - 14 * q^57 - 30 * q^58 - 10 * q^59 + 9 * q^60 + 3 * q^61 + 24 * q^62 - 12 * q^63 - 29 * q^64 + 24 * q^65 + 76 * q^67 + 8 * q^69 + 5 * q^70 - 6 * q^71 + 48 * q^72 - 12 * q^73 - 28 * q^74 - q^75 - 64 * q^76 - 8 * q^78 + 2 * q^79 + 13 * q^80 - 3 * q^81 + 27 * q^82 + 18 * q^83 - 31 * q^84 - 4 * q^85 + 3 * q^86 - 40 * q^87 + 44 * q^89 - 20 * q^90 - 20 * q^91 + 34 * q^92 - 20 * q^93 - 59 * q^94 - 4 * q^95 - 7 * q^96 + 2 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more