LMFDB - Embedded newform 605.2.g.p.511.3

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			511.3
Root			$-0.170505 - 0.123879i$ of defining polynomial
Character	$\chi$	$=$	605.511
Dual form			605.2.g.p.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.848198 + 2.61048i) q^{2} +(0.170505 + 0.123879i) q^{3} +(-4.47716 + 3.25284i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.178763 + 0.550175i) q^{6} +(-1.87960 + 1.36561i) q^{7} +(-7.84779 - 5.70176i) q^{8} +(-0.913325 - 2.81093i) q^{9} +O(q^{10})$	\(q+(0.848198 + 2.61048i) q^{2} +(0.170505 + 0.123879i) q^{3} +(-4.47716 + 3.25284i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.178763 + 0.550175i) q^{6} +(-1.87960 + 1.36561i) q^{7} +(-7.84779 - 5.70176i) q^{8} +(-0.913325 - 2.81093i) q^{9} -2.74483 q^{10} -1.16634 q^{12} +(0.165037 + 0.507931i) q^{13} +(-5.15918 - 3.74836i) q^{14} +(-0.170505 + 0.123879i) q^{15} +(4.80762 - 14.7963i) q^{16} +(-0.748288 + 2.30299i) q^{17} +(6.56320 - 4.76844i) q^{18} +(4.00915 + 2.91282i) q^{19} +(-1.71012 - 5.26321i) q^{20} -0.489652 q^{21} -4.53407 q^{23} +(-0.631760 - 1.94436i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-1.18596 + 0.861652i) q^{26} +(0.387870 - 1.19374i) q^{27} +(3.97315 - 12.2281i) q^{28} +(-4.44122 + 3.22674i) q^{29} +(-0.468007 - 0.340027i) q^{30} +(0.322743 + 0.993301i) q^{31} +23.3026 q^{32} -6.64663 q^{34} +(-0.717944 - 2.20960i) q^{35} +(13.2326 + 9.61405i) q^{36} +(-6.05926 + 4.40231i) q^{37} +(-4.20331 + 12.9365i) q^{38} +(-0.0347825 + 0.107049i) q^{39} +(7.84779 - 5.70176i) q^{40} +(8.57737 + 6.23182i) q^{41} +(-0.415322 - 1.27823i) q^{42} -4.32331 q^{43} +2.95558 q^{45} +(-3.84579 - 11.8361i) q^{46} +(-5.47587 - 3.97845i) q^{47} +(2.65268 - 1.92729i) q^{48} +(-0.495110 + 1.52379i) q^{49} +(0.848198 - 2.61048i) q^{50} +(-0.412880 + 0.299975i) q^{51} +(-2.39112 - 1.73725i) q^{52} +(-1.40110 - 4.31216i) q^{53} +3.44523 q^{54} +22.5371 q^{56} +(0.322743 + 0.993301i) q^{57} +(-12.1904 - 8.85683i) q^{58} +(5.21430 - 3.78841i) q^{59} +(0.360418 - 1.10925i) q^{60} +(-2.10088 + 6.46586i) q^{61} +(-2.31925 + 1.68503i) q^{62} +(5.55531 + 4.03617i) q^{63} +(10.1500 + 31.2385i) q^{64} -0.534070 q^{65} +0.721104 q^{67} +(-4.14108 - 12.7449i) q^{68} +(-0.773082 - 0.561677i) q^{69} +(5.15918 - 3.74836i) q^{70} +(1.40110 - 4.31216i) q^{71} +(-8.85963 + 27.2671i) q^{72} +(0.864144 - 0.627837i) q^{73} +(-16.6316 - 12.0836i) q^{74} +(-0.0651271 - 0.200441i) q^{75} -27.4245 q^{76} -0.308953 q^{78} +(-1.43589 - 4.41921i) q^{79} +(12.5865 + 9.14464i) q^{80} +(-6.95933 + 5.05625i) q^{81} +(-8.99277 + 27.6769i) q^{82} +(-4.20331 + 12.9365i) q^{83} +(2.19225 - 1.59276i) q^{84} +(-1.95904 - 1.42333i) q^{85} +(-3.66703 - 11.2859i) q^{86} -1.15698 q^{87} +12.7148 q^{89} +(2.50692 + 7.71550i) q^{90} +(-1.00384 - 0.729332i) q^{91} +(20.2997 - 14.7486i) q^{92} +(-0.0680200 + 0.209344i) q^{93} +(5.74107 - 17.6692i) q^{94} +(-4.00915 + 2.91282i) q^{95} +(3.97322 + 2.88671i) q^{96} +(1.47067 + 4.52626i) q^{97} -4.39779 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.848198	+	2.61048i	0.599766	+	1.84589i	0.529404	+	0.848370i	$0.322416\pi$
$2$	0.848198	+	2.61048i	0.599766	+	1.84589i	0.0703627	+	0.997521i	$0.477584\pi$
$3$	0.170505	+	0.123879i	0.0984412	+	0.0715217i	0.635917	−	0.771757i	$-0.280622\pi$
$3$	0.170505	+	0.123879i	0.0984412	+	0.0715217i	−0.537476	+	0.843279i	$0.680622\pi$
$4$	−4.47716	+	3.25284i	−2.23858	+	1.62642i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	−0.178763	+	0.550175i	−0.0729796	+	0.224608i
$7$	−1.87960	+	1.36561i	−0.710422	+	0.516152i	−0.883310	−	0.468790i	$-0.844690\pi$
$7$	−1.87960	+	1.36561i	−0.710422	+	0.516152i	0.172888	+	0.984942i	$0.444690\pi$
$8$	−7.84779	−	5.70176i	−2.77461	−	2.01588i
$9$	−0.913325	−	2.81093i	−0.304442	−	0.936975i
$10$	−2.74483			−0.867990
$11$		0			0
$11$		0			0
$12$	−1.16634			−0.336693
$13$	0.165037	+	0.507931i	0.0457730	+	0.140875i	0.971331	−	0.237731i	$-0.0764037\pi$
$13$	0.165037	+	0.507931i	0.0457730	+	0.140875i	−0.925558	+	0.378606i	$0.876404\pi$
$14$	−5.15918	−	3.74836i	−1.37885	−	1.00179i
$15$	−0.170505	+	0.123879i	−0.0440242	+	0.0319855i
$16$	4.80762	−	14.7963i	1.20191	−	3.69908i
$17$	−0.748288	+	2.30299i	−0.181487	+	0.558558i	−0.999870	−	0.0161141i	$-0.994870\pi$
$17$	−0.748288	+	2.30299i	−0.181487	+	0.558558i	0.818384	+	0.574672i	$0.194870\pi$
$18$	6.56320	−	4.76844i	1.54696	−	1.12393i
$19$	4.00915	+	2.91282i	0.919762	+	0.668246i	0.943465	−	0.331473i	$-0.107546\pi$
$19$	4.00915	+	2.91282i	0.919762	+	0.668246i	−0.0237027	+	0.999719i	$0.507546\pi$
$20$	−1.71012	−	5.26321i	−0.382395	−	1.17689i
$21$	−0.489652			−0.106851
$22$		0			0
$23$	−4.53407			−0.945419			−0.472709	−	0.881218i	$-0.656724\pi$
$23$	−4.53407			−0.945419			−0.472709	+	0.881218i	$0.656724\pi$
$24$	−0.631760	−	1.94436i	−0.128957	−	0.396890i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−1.18596	+	0.861652i	−0.232586	+	0.168984i
$27$	0.387870	−	1.19374i	0.0746456	−	0.229736i
$28$	3.97315	−	12.2281i	0.750855	−	2.31089i
$29$	−4.44122	+	3.22674i	−0.824714	+	0.599190i	−0.918059	−	0.396444i	$-0.870244\pi$
$29$	−4.44122	+	3.22674i	−0.824714	+	0.599190i	0.0933447	+	0.995634i	$0.470244\pi$
$30$	−0.468007	−	0.340027i	−0.0854460	−	0.0620801i
$31$	0.322743	+	0.993301i	0.0579663	+	0.178402i	0.975847	−	0.218454i	$-0.0701013\pi$
$31$	0.322743	+	0.993301i	0.0579663	+	0.178402i	−0.917881	+	0.396856i	$0.870101\pi$
$32$	23.3026			4.11936
$33$		0			0
$34$	−6.64663			−1.13989
$35$	−0.717944	−	2.20960i	−0.121355	−	0.373491i
$36$	13.2326	+	9.61405i	2.20543	+	1.60234i
$37$	−6.05926	+	4.40231i	−0.996136	+	0.723735i	−0.961256	−	0.275657i	$-0.911105\pi$
$37$	−6.05926	+	4.40231i	−0.996136	+	0.723735i	−0.0348794	+	0.999392i	$0.511105\pi$
$38$	−4.20331	+	12.9365i	−0.681868	+	2.09857i
$39$	−0.0347825	+	0.107049i	−0.00556965	+	0.0171416i
$40$	7.84779	−	5.70176i	1.24085	−	0.901527i
$41$	8.57737	+	6.23182i	1.33956	+	0.973247i	0.999460	+	0.0328579i	$0.0104609\pi$
$41$	8.57737	+	6.23182i	1.33956	+	0.973247i	0.340100	+	0.940389i	$0.389539\pi$
$42$	−0.415322	−	1.27823i	−0.0640856	−	0.197235i
$43$	−4.32331			−0.659299			−0.329650	−	0.944103i	$-0.606931\pi$
$43$	−4.32331			−0.659299			−0.329650	+	0.944103i	$0.606931\pi$
$44$		0			0
$45$	2.95558			0.440592
$46$	−3.84579	−	11.8361i	−0.567031	−	1.74514i
$47$	−5.47587	−	3.97845i	−0.798738	−	0.580317i	0.111806	−	0.993730i	$-0.464337\pi$
$47$	−5.47587	−	3.97845i	−0.798738	−	0.580317i	−0.910544	+	0.413413i	$0.864337\pi$
$48$	2.65268	−	1.92729i	0.382882	−	0.278180i
$49$	−0.495110	+	1.52379i	−0.0707300	+	0.217685i
$50$	0.848198	−	2.61048i	0.119953	−	0.369178i
$51$	−0.412880	+	0.299975i	−0.0578148	+	0.0420049i
$52$	−2.39112	−	1.73725i	−0.331588	−	0.240913i
$53$	−1.40110	−	4.31216i	−0.192457	−	0.592320i	−0.999997	−	0.00250794i	$-0.999202\pi$
$53$	−1.40110	−	4.31216i	−0.192457	−	0.592320i	0.807540	−	0.589812i	$-0.200798\pi$
$54$	3.44523			0.468837
$55$		0			0
$56$	22.5371			3.01165
$57$	0.322743	+	0.993301i	0.0427483	+	0.131566i
$58$	−12.1904	−	8.85683i	−1.60068	−	1.16296i
$59$	5.21430	−	3.78841i	0.678845	−	0.493209i	−0.194130	−	0.980976i	$-0.562188\pi$
$59$	5.21430	−	3.78841i	0.678845	−	0.493209i	0.872974	+	0.487766i	$0.162188\pi$
$60$	0.360418	−	1.10925i	0.0465298	−	0.143204i
$61$	−2.10088	+	6.46586i	−0.268991	+	0.827868i	0.721756	+	0.692147i	$0.243335\pi$
$61$	−2.10088	+	6.46586i	−0.268991	+	0.827868i	−0.990747	+	0.135721i	$0.956665\pi$
$62$	−2.31925	+	1.68503i	−0.294545	+	0.213999i
$63$	5.55531	+	4.03617i	0.699904	+	0.508510i
$64$	10.1500	+	31.2385i	1.26875	+	3.90481i
$65$	−0.534070			−0.0662433
$66$		0			0
$67$	0.721104			0.0880968			0.0440484	−	0.999029i	$-0.485974\pi$
$67$	0.721104			0.0880968			0.0440484	+	0.999029i	$0.485974\pi$
$68$	−4.14108	−	12.7449i	−0.502180	−	1.54555i
$69$	−0.773082	−	0.561677i	−0.0930681	−	0.0676180i
$70$	5.15918	−	3.74836i	0.616640	−	0.448015i
$71$	1.40110	−	4.31216i	0.166281	−	0.511759i	−0.832848	−	0.553502i	$-0.813291\pi$
$71$	1.40110	−	4.31216i	0.166281	−	0.511759i	0.999128	+	0.0417431i	$0.0132911\pi$
$72$	−8.85963	+	27.2671i	−1.04412	+	3.21346i
$73$	0.864144	−	0.627837i	0.101140	−	0.0734828i	−0.536066	−	0.844176i	$-0.680090\pi$
$73$	0.864144	−	0.627837i	0.101140	−	0.0734828i	0.637206	+	0.770694i	$0.280090\pi$
$74$	−16.6316	−	12.0836i	−1.93338	−	1.40469i
$75$	−0.0651271	−	0.200441i	−0.00752024	−	0.0231449i
$76$	−27.4245			−3.14581
$77$		0			0
$78$	−0.308953			−0.0349821
$79$	−1.43589	−	4.41921i	−0.161550	−	0.497200i	0.837216	−	0.546873i	$-0.184182\pi$
$79$	−1.43589	−	4.41921i	−0.161550	−	0.497200i	−0.998766	+	0.0496734i	$0.984182\pi$
$80$	12.5865	+	9.14464i	1.40722	+	1.02240i
$81$	−6.95933	+	5.05625i	−0.773259	+	0.561806i
$82$	−8.99277	+	27.6769i	−0.993086	+	3.05640i
$83$	−4.20331	+	12.9365i	−0.461374	+	1.41996i	0.402113	+	0.915590i	$0.368276\pi$
$83$	−4.20331	+	12.9365i	−0.461374	+	1.41996i	−0.863486	+	0.504372i	$0.831724\pi$
$84$	2.19225	−	1.59276i	0.239194	−	0.173785i
$85$	−1.95904	−	1.42333i	−0.212488	−	0.154382i
$86$	−3.66703	−	11.2859i	−0.395426	−	1.21699i
$87$	−1.15698			−0.124041
$88$		0			0
$89$	12.7148			1.34776			0.673881	−	0.738840i	$-0.264626\pi$
$89$	12.7148			1.34776			0.673881	+	0.738840i	$0.264626\pi$
$90$	2.50692	+	7.71550i	0.264252	+	0.813285i
$91$	−1.00384	−	0.729332i	−0.105231	−	0.0764547i
$92$	20.2997	−	14.7486i	2.11639	−	1.53765i
$93$	−0.0680200	+	0.209344i	−0.00705334	+	0.0217080i
$94$	5.74107	−	17.6692i	0.592146	−	1.82244i
$95$	−4.00915	+	2.91282i	−0.411330	+	0.298849i
$96$	3.97322	+	2.88671i	0.405515	+	0.294624i
$97$	1.47067	+	4.52626i	0.149324	+	0.459572i	0.997542	−	0.0700760i	$-0.0223242\pi$
$97$	1.47067	+	4.52626i	0.149324	+	0.459572i	−0.848218	+	0.529648i	$0.822324\pi$
$98$	−4.39779			−0.444244
$99$		0			0
$100$	5.53407			0.553407
$101$	2.03286	+	6.25651i	0.202278	+	0.622546i	0.999814	+	0.0192759i	$0.00613608\pi$
$101$	2.03286	+	6.25651i	0.202278	+	0.622546i	−0.797537	+	0.603271i	$0.793864\pi$
$102$	−1.13328	−	0.823379i	−0.112212	−	0.0815267i
$103$	−13.2326	+	9.61405i	−1.30385	+	0.947300i	−0.999985	−	0.00541565i	$-0.998276\pi$
$103$	−13.2326	+	9.61405i	−1.30385	+	0.947300i	−0.303862	+	0.952716i	$0.598276\pi$
$104$	1.60092	−	4.92714i	0.156984	−	0.483146i
$105$	0.151311	−	0.465687i	0.0147664	−	0.0454464i
$106$	10.0684	−	7.31513i	0.977930	−	0.710508i
$107$	8.26068	+	6.00173i	0.798590	+	0.580209i	0.910500	−	0.413509i	$-0.135697\pi$
$107$	8.26068	+	6.00173i	0.798590	+	0.580209i	−0.111910	+	0.993718i	$0.535697\pi$
$108$	2.14650	+	6.60625i	0.206547	+	0.635687i
$109$	12.0919			1.15819			0.579095	−	0.815260i	$-0.303406\pi$
$109$	12.0919			1.15819			0.579095	+	0.815260i	$0.303406\pi$
$110$		0			0
$111$	−1.57849			−0.149823
$112$	11.1696	+	34.3765i	1.05543	+	3.24828i
$113$	8.77219	+	6.37337i	0.825218	+	0.599556i	0.918202	−	0.396111i	$-0.129641\pi$
$113$	8.77219	+	6.37337i	0.825218	+	0.599556i	−0.0929842	+	0.995668i	$0.529641\pi$
$114$	−2.31925	+	1.68503i	−0.217217	+	0.157818i
$115$	1.40110	−	4.31216i	0.130654	−	0.402111i
$116$	9.38797	−	28.8932i	0.871651	−	2.68267i
$117$	1.27702	−	0.927812i	0.118061	−	0.0857763i
$118$	14.3124	+	10.3985i	1.31756	+	0.957263i
$119$	−1.73851	−	5.35058i	−0.159369	−	0.490487i
$120$	2.04442			0.186629
$121$		0			0
$122$	−18.6610			−1.68949
$123$	0.690492	+	2.12512i	0.0622595	+	0.191615i
$124$	−4.67602	−	3.39733i	−0.419919	−	0.305089i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	−5.82436	+	17.9255i	−0.518875	+	1.59693i
$127$	2.50981	−	7.72440i	0.222710	−	0.685430i	−0.775806	−	0.630971i	$-0.782657\pi$
$127$	2.50981	−	7.72440i	0.222710	−	0.685430i	0.998516	−	0.0544589i	$-0.0173434\pi$
$128$	−35.2339	+	25.5989i	−3.11426	+	2.26264i
$129$	−0.737147	−	0.535569i	−0.0649022	−	0.0471542i
$130$	−0.452997	−	1.39418i	−0.0397305	−	0.122278i
$131$	−5.79861			−0.506627			−0.253313	−	0.967384i	$-0.581520\pi$
$131$	−5.79861			−0.506627			−0.253313	+	0.967384i	$0.581520\pi$
$132$		0			0
$133$	−11.5134			−0.998336
$134$	0.611639	+	1.88243i	0.0528375	+	0.162617i
$135$	1.01546	+	0.737773i	0.0873966	+	0.0634974i
$136$	19.0035	−	13.8069i	1.62954	−	1.18393i
$137$	2.73998	−	8.43278i	0.234092	−	0.720461i	−0.763149	−	0.646223i	$-0.776348\pi$
$137$	2.73998	−	8.43278i	0.234092	−	0.720461i	0.997241	−	0.0742378i	$-0.0236524\pi$
$138$	0.810523	−	2.49453i	0.0689963	−	0.212349i
$139$	−13.6455	+	9.91402i	−1.15739	+	0.840897i	−0.989446	−	0.144899i	$-0.953714\pi$
$139$	−13.6455	+	9.91402i	−1.15739	+	0.840897i	−0.167948	+	0.985796i	$0.553714\pi$
$140$	10.4018	+	7.55738i	0.879116	+	0.638715i
$141$	−0.440816	−	1.35669i	−0.0371234	−	0.114254i
$142$	12.4452			1.04438
$143$		0			0
$144$	−45.9823			−3.83186
$145$	−1.69640	−	5.22097i	−0.140878	−	0.433578i
$146$	2.37192	+	1.72330i	0.196302	+	0.142622i
$147$	−0.273185	+	0.198481i	−0.0225319	+	0.0163704i
$148$	12.8082	−	39.4196i	1.05283	−	3.24027i
$149$	−1.38005	+	4.24735i	−0.113058	+	0.347957i	−0.991537	−	0.129824i	$-0.958559\pi$
$149$	−1.38005	+	4.24735i	−0.113058	+	0.347957i	0.878479	+	0.477781i	$0.158559\pi$
$150$	0.468007	−	0.340027i	0.0382126	−	0.0277631i
$151$	−9.31452	−	6.76739i	−0.758005	−	0.550723i	0.140293	−	0.990110i	$-0.455196\pi$
$151$	−9.31452	−	6.76739i	−0.758005	−	0.550723i	−0.898298	+	0.439387i	$0.855196\pi$
$152$	−14.8548	−	45.7184i	−1.20488	−	3.70825i
$153$	7.15698			0.578607
$154$		0			0
$155$	−1.04442			−0.0838897
$156$	−0.192489	−	0.592419i	−0.0154114	−	0.0474315i
$157$	4.78223	+	3.47449i	0.381664	+	0.277295i	0.762031	−	0.647541i	$-0.224202\pi$
$157$	4.78223	+	3.47449i	0.381664	+	0.277295i	−0.380367	+	0.924836i	$0.624202\pi$
$158$	10.3184	−	7.49672i	0.820884	−	0.596407i
$159$	0.295291	−	0.908812i	0.0234181	−	0.0720735i
$160$	−7.20091	+	22.1621i	−0.569282	+	1.75207i
$161$	8.52224	−	6.19177i	0.671647	−	0.487980i
$162$	−19.1022	−	13.8785i	−1.50081	−	1.09040i
$163$	7.26159	+	22.3489i	0.568772	+	1.75050i	0.656469	+	0.754353i	$0.272049\pi$
$163$	7.26159	+	22.3489i	0.568772	+	1.75050i	−0.0876971	+	0.996147i	$0.527951\pi$
$164$	−58.6734			−4.58162
$165$		0			0
$166$	−37.3357			−2.89781
$167$	−4.39870	−	13.5378i	−0.340381	−	1.04759i	−0.964010	−	0.265865i	$-0.914342\pi$
$167$	−4.39870	−	13.5378i	−0.340381	−	1.04759i	0.623629	−	0.781721i	$-0.285658\pi$
$168$	3.84269	+	2.79188i	0.296470	+	0.215398i
$169$	10.2865	−	7.47355i	0.791266	−	0.574889i
$170$	2.05392	−	6.32132i	0.157529	−	0.484823i
$171$	4.52606	−	13.9298i	0.346116	−	1.06524i
$172$	19.3562	−	14.0631i	1.47589	−	1.07230i
$173$	−5.21430	−	3.78841i	−0.396436	−	0.288028i	0.371652	−	0.928372i	$-0.378792\pi$
$173$	−5.21430	−	3.78841i	−0.396436	−	0.288028i	−0.768088	+	0.640345i	$0.778792\pi$
$174$	−0.981345	−	3.02027i	−0.0743956	−	0.228966i
$175$	2.32331			0.175626
$176$		0			0
$177$	1.35837			0.102101
$178$	10.7846	+	33.1917i	0.808343	+	2.48782i
$179$	−13.7365	−	9.98018i	−1.02672	−	0.745954i	−0.0590685	−	0.998254i	$-0.518813\pi$
$179$	−13.7365	−	9.98018i	−1.02672	−	0.745954i	−0.967649	+	0.252300i	$0.918813\pi$
$180$	−13.2326	+	9.61405i	−0.986300	+	0.716589i
$181$	1.38738	−	4.26991i	0.103123	−	0.317380i	−0.886162	−	0.463375i	$-0.846638\pi$
$181$	1.38738	−	4.26991i	0.103123	−	0.317380i	0.989285	+	0.145995i	$0.0466383\pi$
$182$	1.05245	−	3.23912i	0.0780131	−	0.240100i
$183$	−1.15920	+	0.842206i	−0.0856903	+	0.0622576i
$184$	35.5825	+	25.8522i	2.62317	+	1.90585i
$185$	−2.31443	−	7.12308i	−0.170160	−	0.523699i
$186$	−0.604184			−0.0443009
$187$		0			0
$188$	37.4576			2.73188
$189$	0.901144	+	2.77344i	0.0655486	+	0.201738i
$190$	−11.0044	−	7.99518i	−0.798345	−	0.580031i
$191$	2.23223	−	1.62181i	0.161518	−	0.117350i	−0.504090	−	0.863651i	$-0.668172\pi$
$191$	2.23223	−	1.62181i	0.161518	−	0.117350i	0.665609	+	0.746301i	$0.268172\pi$
$192$	−2.13917	+	6.58369i	−0.154381	+	0.475137i
$193$	−3.64751	+	11.2259i	−0.262554	+	0.808058i	0.729693	+	0.683775i	$0.239663\pi$
$193$	−3.64751	+	11.2259i	−0.262554	+	0.808058i	−0.992247	+	0.124283i	$0.960337\pi$
$194$	−10.5683	+	7.67832i	−0.758760	+	0.551271i
$195$	−0.0910617	−	0.0661602i	−0.00652106	−	0.00473783i
$196$	−2.73998	−	8.43278i	−0.195713	−	0.602341i
$197$	6.51035			0.463843			0.231922	−	0.972734i	$-0.425499\pi$
$197$	6.51035			0.463843			0.231922	+	0.972734i	$0.425499\pi$
$198$		0			0
$199$	23.9586			1.69838			0.849190	−	0.528087i	$-0.177090\pi$
$199$	23.9586			1.69838			0.849190	+	0.528087i	$0.177090\pi$
$200$	2.99759	+	9.22564i	0.211962	+	0.652351i
$201$	0.122952	+	0.0893298i	0.00867236	+	0.00630083i
$202$	−14.6083	+	10.6135i	−1.02783	+	0.746765i
$203$	3.94126	−	12.1300i	0.276622	−	0.851356i
$204$	0.872757	−	2.68607i	0.0611052	−	0.188062i
$205$	−8.57737	+	6.23182i	−0.599069	+	0.435249i
$206$	−36.3212	−	26.3889i	−2.53062	−	1.83860i
$207$	4.14108	+	12.7449i	0.287825	+	0.885834i
$208$	8.30895			0.576122
$209$		0			0
$210$	1.34401			0.0927455
$211$	5.21211	+	16.0412i	0.358817	+	1.10432i	0.953763	+	0.300559i	$0.0971731\pi$
$211$	5.21211	+	16.0412i	0.358817	+	1.10432i	−0.594947	+	0.803765i	$0.702827\pi$
$212$	20.2997	+	14.7486i	1.39419	+	1.01294i
$213$	0.773082	−	0.561677i	0.0529707	−	0.0384855i
$214$	−8.66074	+	26.6550i	−0.592036	+	1.82210i
$215$	1.33598	−	4.11172i	0.0911129	−	0.280417i
$216$	−9.85035	+	7.15670i	−0.670231	+	0.486952i
$217$	−1.96309	−	1.42627i	−0.133263	−	0.0968214i
$218$	10.2563	+	31.5656i	0.694644	+	2.13789i
$219$	0.225117			0.0152120
$220$		0			0
$221$	−1.29326			−0.0869939
$222$	−1.33887	−	4.12062i	−0.0898591	−	0.276558i
$223$	20.2395	+	14.7049i	1.35534	+	0.984710i	0.998726	+	0.0504565i	$0.0160676\pi$
$223$	20.2395	+	14.7049i	1.35534	+	0.984710i	0.356610	+	0.934253i	$0.383932\pi$
$224$	−43.7996	+	31.8223i	−2.92649	+	2.12622i
$225$	−0.913325	+	2.81093i	−0.0608883	+	0.187395i
$226$	−9.19703	+	28.3055i	−0.611777	+	1.88286i
$227$	3.24364	−	2.35664i	0.215288	−	0.156416i	−0.474915	−	0.880032i	$-0.657521\pi$
$227$	3.24364	−	2.35664i	0.215288	−	0.156416i	0.690203	+	0.723616i	$0.257521\pi$
$228$	−4.67602	−	3.39733i	−0.309677	−	0.224994i
$229$	−5.35609	−	16.4844i	−0.353940	−	1.08932i	−0.956621	−	0.291334i	$-0.905901\pi$
$229$	−5.35609	−	16.4844i	−0.353940	−	1.08932i	0.602681	−	0.797982i	$-0.294099\pi$
$230$	12.4452			0.820614
$231$		0			0
$232$	53.2519			3.49616
$233$	−0.652816	−	2.00916i	−0.0427674	−	0.131625i	0.927393	−	0.374089i	$-0.122044\pi$
$233$	−0.652816	−	2.00916i	−0.0427674	−	0.131625i	−0.970160	+	0.242464i	$0.922044\pi$
$234$	3.50521	+	2.54668i	0.229143	+	0.166482i
$235$	5.47587	−	3.97845i	0.357206	−	0.259526i
$236$	−11.0221	+	33.9226i	−0.717480	+	2.20818i
$237$	0.302622	−	0.931374i	0.0196574	−	0.0604992i
$238$	12.4930	−	9.07670i	0.809801	−	0.588355i
$239$	−19.3637	−	14.0686i	−1.25254	−	0.910020i	−0.254169	−	0.967160i	$-0.581802\pi$
$239$	−19.3637	−	14.0686i	−1.25254	−	0.910020i	−0.998366	+	0.0571394i	$0.981802\pi$
$240$	1.01323	+	3.11842i	0.0654040	+	0.201293i
$241$	14.5134			0.934889			0.467444	−	0.884023i	$-0.345175\pi$
$241$	14.5134			0.934889			0.467444	+	0.884023i	$0.345175\pi$
$242$		0			0
$243$	−5.57849			−0.357860
$244$	−11.6264	−	35.7825i	−0.744307	−	2.29074i
$245$	−1.29622	−	0.941756i	−0.0828122	−	0.0601666i
$246$	−4.96191	+	3.60504i	−0.316360	+	0.229849i
$247$	−0.817853	+	2.51709i	−0.0520388	+	0.160159i
$248$	3.13074	−	9.63542i	0.198802	−	0.611850i
$249$	−2.31925	+	1.68503i	−0.146976	+	0.106784i
$250$	2.22061	+	1.61337i	0.140444	+	0.102038i
$251$	8.90174	+	27.3967i	0.561873	+	1.72927i	0.677065	+	0.735923i	$0.263252\pi$
$251$	8.90174	+	27.3967i	0.561873	+	1.72927i	−0.115192	+	0.993343i	$0.536748\pi$
$252$	−38.0011			−2.39384
$253$		0			0
$254$	22.2933			1.39880
$255$	−0.157706	−	0.485370i	−0.00987594	−	0.0303950i
$256$	−43.5648	−	31.6517i	−2.72280	−	1.97823i
$257$	22.3690	−	16.2521i	1.39534	−	1.01378i	0.400087	−	0.916477i	$-0.368980\pi$
$257$	22.3690	−	16.2521i	1.39534	−	1.01378i	0.995255	−	0.0972985i	$-0.0310202\pi$
$258$	0.772847	−	2.37858i	0.0481154	−	0.148084i
$259$	5.37715	−	16.5492i	0.334120	−	1.02831i
$260$	2.39112	−	1.73725i	0.148291	−	0.107740i
$261$	13.1264	+	9.53688i	0.812503	+	0.590318i
$262$	−4.91837	−	15.1372i	−0.303858	−	0.935178i
$263$	−3.13325			−0.193205			−0.0966024	−	0.995323i	$-0.530798\pi$
$263$	−3.13325			−0.193205			−0.0966024	+	0.995323i	$0.530798\pi$
$264$		0			0
$265$	4.53407			0.278526
$266$	−9.76562	−	30.0555i	−0.598769	−	1.84282i
$267$	2.16793	+	1.57510i	0.132675	+	0.0963943i
$268$	−3.22849	+	2.34564i	−0.197212	+	0.143283i
$269$	5.56324	−	17.1219i	0.339197	−	1.04394i	−0.625421	−	0.780288i	$-0.715073\pi$
$269$	5.56324	−	17.1219i	0.339197	−	1.04394i	0.964618	−	0.263653i	$-0.0849273\pi$
$270$	−1.06464	+	3.27661i	−0.0647917	+	0.199408i
$271$	16.4495	−	11.9512i	0.999235	−	0.725987i	0.0373108	−	0.999304i	$-0.488121\pi$
$271$	16.4495	−	11.9512i	0.999235	−	0.725987i	0.961924	+	0.273317i	$0.0881209\pi$
$272$	30.4784	+	22.1439i	1.84802	+	1.34267i
$273$	−0.0808106	−	0.248709i	−0.00489088	−	0.0150526i
$274$	24.3377			1.47029
$275$		0			0
$276$	5.28826			0.318316
$277$	7.87674	+	24.2421i	0.473267	+	1.45657i	0.848280	+	0.529547i	$0.177638\pi$
$277$	7.87674	+	24.2421i	0.473267	+	1.45657i	−0.375013	+	0.927019i	$0.622362\pi$
$278$	−37.4545	−	27.2123i	−2.24637	−	1.63208i
$279$	2.49732	−	1.81441i	0.149511	−	0.108626i
$280$	−6.96435	+	21.4341i	−0.416199	+	1.28093i
$281$	−5.64653	+	17.3782i	−0.336844	+	1.03670i	0.628963	+	0.777435i	$0.283480\pi$
$281$	−5.64653	+	17.3782i	−0.336844	+	1.03670i	−0.965807	+	0.259263i	$0.916520\pi$
$282$	3.16773	−	2.30149i	0.188635	−	0.137052i
$283$	−8.94270	−	6.49725i	−0.531588	−	0.386221i	0.289363	−	0.957219i	$-0.406556\pi$
$283$	−8.94270	−	6.49725i	−0.531588	−	0.386221i	−0.820951	+	0.570998i	$0.806556\pi$
$284$	7.75381	+	23.8638i	0.460104	+	1.41605i
$285$	−1.04442			−0.0618660
$286$		0			0
$287$	−24.6323			−1.45400
$288$	−21.2829	−	65.5019i	−1.25410	−	3.85974i
$289$	9.00944	+	6.54574i	0.529967	+	0.385044i
$290$	12.1904	−	8.85683i	0.715844	−	0.520091i
$291$	−0.309952	+	0.953935i	−0.0181697	+	0.0559207i
$292$	−1.82665	+	5.62185i	−0.106897	+	0.328994i
$293$	21.9562	−	15.9521i	1.28269	−	0.931931i	0.283062	−	0.959102i	$-0.408650\pi$
$293$	21.9562	−	15.9521i	1.28269	−	0.931931i	0.999631	+	0.0271709i	$0.00864984\pi$
$294$	−0.749845	−	0.544795i	−0.0437319	−	0.0317731i
$295$	1.99169	+	6.12978i	0.115960	+	0.356890i
$296$	72.6527			4.22285
$297$		0			0
$298$	−12.2582			−0.710098
$299$	−0.748288	−	2.30299i	−0.0432746	−	0.133186i
$300$	0.943587	+	0.685556i	0.0544780	+	0.0395806i
$301$	8.12610	−	5.90396i	0.468381	−	0.340299i
$302$	9.76562	−	30.0555i	0.561948	−	1.72950i
$303$	−0.428438	+	1.31860i	−0.0246131	+	0.0757514i
$304$	62.3735	−	45.3170i	3.57737	−	2.59911i
$305$	−5.50019	−	3.99612i	−0.314940	−	0.228817i
$306$	6.07053	+	18.6832i	0.347029	+	1.06805i
$307$	−11.7385			−0.669951			−0.334976	−	0.942227i	$-0.608728\pi$
$307$	−11.7385			−0.669951			−0.334976	+	0.942227i	$0.608728\pi$
$308$		0			0
$309$	−3.44721			−0.196105
$310$	−0.885873	−	2.72644i	−0.0503142	−	0.154851i
$311$	−8.60926	−	6.25499i	−0.488186	−	0.354688i	0.316300	−	0.948659i	$-0.397559\pi$
$311$	−8.60926	−	6.25499i	−0.488186	−	0.354688i	−0.804486	+	0.593971i	$0.797559\pi$
$312$	0.883336	−	0.641781i	0.0500090	−	0.0363337i
$313$	−8.39930	+	25.8504i	−0.474756	+	1.46115i	0.371530	+	0.928421i	$0.378833\pi$
$313$	−8.39930	+	25.8504i	−0.474756	+	1.46115i	−0.846286	+	0.532729i	$0.821167\pi$
$314$	−5.01384	+	15.4310i	−0.282947	+	0.870822i
$315$	−5.55531	+	4.03617i	−0.313006	+	0.227413i
$316$	20.8037	+	15.1148i	1.17030	+	0.850272i
$317$	1.53869	+	4.73560i	0.0864214	+	0.265978i	0.984923	−	0.172992i	$-0.0553435\pi$
$317$	1.53869	+	4.73560i	0.0864214	+	0.265978i	−0.898502	+	0.438970i	$0.855343\pi$
$318$	2.62291			0.147085
$319$		0			0
$320$	−32.8461			−1.83615
$321$	0.664997	+	2.04665i	0.0371165	+	0.114233i
$322$	23.3921	+	16.9953i	1.30359	+	0.947113i
$323$	−9.70820	+	7.05342i	−0.540179	+	0.392463i
$324$	14.7108	−	45.2753i	0.817268	−	2.51529i
$325$	0.165037	−	0.507931i	0.00915459	−	0.0281749i
$326$	−52.1822	+	37.9126i	−2.89010	+	2.09978i
$327$	2.06172	+	1.49793i	0.114014	+	0.0828357i
$328$	−31.7811	−	97.8121i	−1.75482	−	5.40077i
$329$	15.7255			0.866973
$330$		0			0
$331$	7.55477			0.415247			0.207624	−	0.978209i	$-0.433427\pi$
$331$	7.55477			0.415247			0.207624	+	0.978209i	$0.433427\pi$
$332$	−23.2614	−	71.5913i	−1.27664	−	3.92909i
$333$	17.9086	+	13.0114i	0.981387	+	0.713019i
$334$	31.6092	−	22.9655i	1.72958	−	1.25661i
$335$	−0.222833	+	0.685810i	−0.0121747	+	0.0374698i
$336$	−2.35406	+	7.24506i	−0.128425	+	0.395250i
$337$	2.98612	−	2.16954i	0.162664	−	0.118183i	−0.503475	−	0.864010i	$-0.667946\pi$
$337$	2.98612	−	2.16954i	0.162664	−	0.118183i	0.666140	+	0.745827i	$0.267946\pi$
$338$	28.2346	+	20.5136i	1.53576	+	1.11579i
$339$	0.706175	+	2.17338i	0.0383542	+	0.118042i
$340$	13.4008			0.726761
$341$		0			0
$342$	40.2024			2.17390
$343$	−6.17590	−	19.0075i	−0.333467	−	1.02631i
$344$	33.9285	+	24.6505i	1.82930	+	1.32907i
$345$	0.773082	−	0.561677i	0.0416213	−	0.0302397i
$346$	5.46683	−	16.8252i	0.293899	−	0.904528i
$347$	4.87181	−	14.9939i	0.261533	−	0.804915i	−0.730939	−	0.682443i	$-0.760918\pi$
$347$	4.87181	−	14.9939i	0.261533	−	0.804915i	0.992472	−	0.122472i	$-0.0390823\pi$
$348$	5.17997	−	3.76346i	0.277675	−	0.201743i
$349$	−8.54143	−	6.20571i	−0.457212	−	0.332184i	0.335224	−	0.942138i	$-0.391188\pi$
$349$	−8.54143	−	6.20571i	−0.457212	−	0.332184i	−0.792437	+	0.609954i	$0.791188\pi$
$350$	1.97063	+	6.06498i	0.105335	+	0.324187i
$351$	0.670351			0.0357807
$352$		0			0
$353$	−24.5528			−1.30681			−0.653407	−	0.757007i	$-0.726661\pi$
$353$	−24.5528			−1.30681			−0.653407	+	0.757007i	$0.726661\pi$
$354$	1.15217	+	3.54601i	0.0612370	+	0.188468i
$355$	3.66814	+	2.66506i	0.194685	+	0.141447i
$356$	−56.9260	+	41.3592i	−3.01707	+	2.19203i
$357$	0.366401	−	1.12767i	0.0193920	−	0.0596824i
$358$	14.4018	−	44.3242i	0.761159	−	2.34261i
$359$	−13.4866	+	9.79859i	−0.711795	+	0.517150i	−0.883752	−	0.467955i	$-0.844991\pi$
$359$	−13.4866	+	9.79859i	−0.711795	+	0.517150i	0.171957	+	0.985104i	$0.444991\pi$
$360$	−23.1948	−	16.8520i	−1.22247	−	0.888179i
$361$	1.71745	+	5.28577i	0.0903922	+	0.278199i
$362$	12.3233			0.647699
$363$		0			0
$364$	6.86675			0.359915
$365$	0.330074	+	1.01586i	0.0172768	+	0.0531726i
$366$	−3.18179	−	2.31171i	−0.166315	−	0.120835i
$367$	−12.3609	+	8.98071i	−0.645233	+	0.468789i	−0.861644	−	0.507513i	$-0.830565\pi$
$367$	−12.3609	+	8.98071i	−0.645233	+	0.468789i	0.216411	+	0.976302i	$0.430565\pi$
$368$	−21.7981	+	67.0876i	−1.13630	+	3.49719i
$369$	9.68326	−	29.8020i	0.504091	−	1.55143i
$370$	16.6316	−	12.0836i	0.864636	−	0.628195i
$371$	8.52224	+	6.19177i	0.442453	+	0.321461i
$372$	−0.376427	−	1.15852i	−0.0195168	−	0.0600667i
$373$	−17.8461			−0.924033			−0.462017	−	0.886871i	$-0.652874\pi$
$373$	−17.8461			−0.924033			−0.462017	+	0.886871i	$0.652874\pi$
$374$		0			0
$375$	0.210756			0.0108834
$376$	20.2893	+	62.4442i	1.04634	+	3.22031i
$377$	−2.37192	−	1.72330i	−0.122160	−	0.0887547i
$378$	−6.47566	+	4.70485i	−0.333072	+	0.241991i
$379$	0.584796	−	1.79982i	0.0300390	−	0.0924505i	−0.934913	−	0.354877i	$-0.884523\pi$
$379$	0.584796	−	1.79982i	0.0300390	−	0.0924505i	0.964952	+	0.262427i	$0.0845227\pi$
$380$	8.47465	−	26.0823i	0.434740	−	1.33799i
$381$	1.38483	−	1.00614i	0.0709469	−	0.0515460i
$382$	6.12708	+	4.45158i	0.313489	+	0.227763i
$383$	1.64304	+	5.05675i	0.0839553	+	0.258388i	0.984218	−	0.176959i	$-0.0566259\pi$
$383$	1.64304	+	5.05675i	0.0839553	+	0.258388i	−0.900263	+	0.435346i	$0.856626\pi$
$384$	−9.17873			−0.468400
$385$		0			0
$386$	−32.3988			−1.64906
$387$	3.94859	+	12.1525i	0.200718	+	0.617747i
$388$	−21.3076	−	15.4809i	−1.08173	−	0.785923i
$389$	21.7038	−	15.7687i	1.10042	−	0.799505i	0.119295	−	0.992859i	$-0.461936\pi$
$389$	21.7038	−	15.7687i	1.10042	−	0.799505i	0.981129	+	0.193354i	$0.0619365\pi$
$390$	0.0954718	−	0.293832i	0.00483440	−	0.0148788i
$391$	3.39279	−	10.4419i	0.171581	−	0.528072i
$392$	12.5738	−	9.13542i	0.635074	−	0.461408i
$393$	−0.988692	−	0.718327i	−0.0498729	−	0.0362348i
$394$	5.52206	+	16.9952i	0.278198	+	0.856204i
$395$	4.64663			0.233797
$396$		0			0
$397$	31.5972			1.58582			0.792909	−	0.609340i	$-0.208565\pi$
$397$	31.5972			1.58582			0.792909	+	0.609340i	$0.208565\pi$
$398$	20.3216	+	62.5436i	1.01863	+	3.13503i
$399$	−1.96309	−	1.42627i	−0.0982774	−	0.0714027i
$400$	−12.5865	+	9.14464i	−0.629326	+	0.457232i
$401$	−0.969164	+	2.98278i	−0.0483977	+	0.148953i	−0.972335	−	0.233592i	$-0.924952\pi$
$401$	−0.969164	+	2.98278i	−0.0483977	+	0.148953i	0.923937	+	0.382545i	$0.124952\pi$
$402$	−0.128906	+	0.396733i	−0.00642927	+	0.0197873i
$403$	−0.451264	+	0.327862i	−0.0224790	+	0.0163320i
$404$	−29.4529	−	21.3988i	−1.46534	−	1.06463i
$405$	−2.65823	−	8.18119i	−0.132088	−	0.406527i
$406$	35.0080			1.73742
$407$		0			0
$408$	4.95058			0.245090
$409$	−0.131190	−	0.403760i	−0.00648691	−	0.0199646i	0.947761	−	0.318982i	$-0.103341\pi$
$409$	−0.131190	−	0.403760i	−0.00648691	−	0.0199646i	−0.954248	+	0.299018i	$0.903341\pi$
$410$	−23.5434	−	17.1053i	−1.16272	−	0.844769i
$411$	1.51183	−	1.09841i	0.0745728	−	0.0541803i
$412$	27.9714	−	86.0872i	1.37805	−	4.24121i
$413$	−4.62731	+	14.2414i	−0.227695	+	0.700774i
$414$	−29.7580	+	21.6205i	−1.46253	+	1.06259i
$415$	−11.0044	−	7.99518i	−0.540186	−	0.392468i
$416$	3.84579	+	11.8361i	0.188555	+	0.580314i
$417$	−3.55477			−0.174078
$418$		0			0
$419$	6.71174			0.327890			0.163945	−	0.986469i	$-0.447578\pi$
$419$	6.71174			0.327890			0.163945	+	0.986469i	$0.447578\pi$
$420$	0.837365	+	2.57714i	0.0408592	+	0.125752i
$421$	−2.24897	−	1.63397i	−0.109608	−	0.0796350i	0.531631	−	0.846976i	$-0.321579\pi$
$421$	−2.24897	−	1.63397i	−0.109608	−	0.0796350i	−0.641239	+	0.767341i	$0.721579\pi$
$422$	−37.4545	+	27.2123i	−1.82326	+	1.32467i
$423$	−6.18188	+	19.0259i	−0.300574	+	0.925070i
$424$	−13.5913	+	41.8297i	−0.660051	+	2.03143i
$425$	1.95904	−	1.42333i	0.0950276	−	0.0690416i
$426$	2.12198	+	1.54171i	0.102810	+	0.0746959i
$427$	−4.88102	−	15.0222i	−0.236209	−	0.726976i
$428$	−56.5070			−2.73137
$429$		0			0
$430$	11.8667			0.572265
$431$	−5.00496	−	15.4037i	−0.241081	−	0.741969i	−0.996256	−	0.0864473i	$-0.972449\pi$
$431$	−5.00496	−	15.4037i	−0.241081	−	0.741969i	0.755176	−	0.655522i	$-0.227551\pi$
$432$	−15.7983	−	11.4781i	−0.760095	−	0.552241i
$433$	−6.33244	+	4.60079i	−0.304318	+	0.221100i	−0.729454	−	0.684029i	$-0.760226\pi$
$433$	−6.33244	+	4.60079i	−0.304318	+	0.221100i	0.425137	+	0.905129i	$0.360226\pi$
$434$	2.05816	−	6.33437i	0.0987949	−	0.304060i
$435$	0.357525	−	1.10035i	0.0171420	−	0.0527577i
$436$	−54.1372	+	39.3330i	−2.59270	+	1.88371i
$437$	−18.1778	−	13.2069i	−0.869561	−	0.631773i
$438$	0.190944	+	0.587664i	0.00912364	+	0.0280797i
$439$	−20.7355			−0.989650			−0.494825	−	0.868993i	$-0.664768\pi$
$439$	−20.7355			−0.989650			−0.494825	+	0.868993i	$0.664768\pi$
$440$		0			0
$441$	4.73546			0.225498
$442$	−1.09694	−	3.37603i	−0.0521760	−	0.160581i
$443$	−4.28991	−	3.11680i	−0.203820	−	0.148084i	0.481193	−	0.876615i	$-0.340204\pi$
$443$	−4.28991	−	3.11680i	−0.203820	−	0.148084i	−0.685013	+	0.728531i	$0.740204\pi$
$444$	7.06714	−	5.13458i	0.335392	−	0.243676i
$445$	−3.92908	+	12.0925i	−0.186256	+	0.573238i
$446$	−21.2197	+	65.3075i	−1.00478	+	3.09240i
$447$	−0.761464	+	0.553236i	−0.0360160	+	0.0261672i
$448$	−61.7375	−	44.8549i	−2.91682	−	2.11919i
$449$	−9.27145	−	28.5346i	−0.437547	−	1.34663i	−0.890454	−	0.455072i	$-0.849613\pi$
$449$	−9.27145	−	28.5346i	−0.437547	−	1.34663i	0.452908	−	0.891557i	$-0.350387\pi$
$450$	−8.11256			−0.382430
$451$		0			0
$452$	−60.0061			−2.82245
$453$	−0.749833	−	2.30775i	−0.0352302	−	0.108428i
$454$	8.90323	+	6.46858i	0.417849	+	0.303585i
$455$	1.00384	−	0.729332i	0.0470607	−	0.0341916i
$456$	3.13074	−	9.63542i	0.146610	−	0.451220i
$457$	−11.5923	+	35.6773i	−0.542264	+	1.66892i	0.185145	+	0.982711i	$0.440724\pi$
$457$	−11.5923	+	35.6773i	−0.542264	+	1.66892i	−0.727409	+	0.686204i	$0.759276\pi$
$458$	38.4891	−	27.9640i	1.79848	−	1.30667i
$459$	2.45894	+	1.78653i	0.114774	+	0.0833879i
$460$	7.75381	+	23.8638i	0.361523	+	1.11265i
$461$	−15.7829			−0.735083			−0.367542	−	0.930007i	$-0.619800\pi$
$461$	−15.7829			−0.735083			−0.367542	+	0.930007i	$0.619800\pi$
$462$		0			0
$463$	−16.5672			−0.769941			−0.384970	−	0.922929i	$-0.625788\pi$
$463$	−16.5672			−0.769941			−0.384970	+	0.922929i	$0.625788\pi$
$464$	26.3922	+	81.2268i	1.22523	+	3.77086i
$465$	−0.178079	−	0.129382i	−0.00825820	−	0.00599993i
$466$	4.69117	−	3.40833i	0.217314	−	0.157888i
$467$	1.14349	−	3.51930i	0.0529144	−	0.162854i	−0.921107	−	0.389309i	$-0.872714\pi$
$467$	1.14349	−	3.51930i	0.0529144	−	0.162854i	0.974022	+	0.226455i	$0.0727138\pi$
$468$	−2.69941	+	8.30792i	−0.124780	+	0.384034i
$469$	−1.35539	+	0.984746i	−0.0625860	+	0.0454714i
$470$	15.0303	+	10.9202i	0.693297	+	0.503709i
$471$	0.384977	+	1.18484i	0.0177388	+	0.0545945i
$472$	−62.5214			−2.87778
$473$		0			0
$474$	2.68802			0.123465
$475$	−1.53136	−	4.71304i	−0.0702636	−	0.216249i
$476$	25.1882	+	18.3003i	1.15450	+	0.838792i
$477$	−10.8415	+	7.87680i	−0.496398	+	0.360654i
$478$	20.3015	−	62.4817i	0.928570	−	2.85784i
$479$	−0.390763	+	1.20264i	−0.0178544	+	0.0549502i	−0.959587	−	0.281413i	$-0.909197\pi$
$479$	−0.390763	+	1.20264i	−0.0178544	+	0.0549502i	0.941732	+	0.336363i	$0.109197\pi$
$480$	−3.97322	+	2.88671i	−0.181352	+	0.131760i
$481$	−3.23607	−	2.35114i	−0.147552	−	0.107203i
$482$	12.3102	+	37.8869i	0.560715	+	1.72570i
$483$	2.22012			0.101019
$484$		0			0
$485$	−4.75919			−0.216104
$486$	−4.73166	−	14.5626i	−0.214633	−	0.660571i
$487$	−17.4766	−	12.6975i	−0.791938	−	0.575377i	0.116600	−	0.993179i	$-0.462801\pi$
$487$	−17.4766	−	12.6975i	−0.791938	−	0.575377i	−0.908538	+	0.417802i	$0.862801\pi$
$488$	53.3541	−	38.7640i	2.41522	−	1.75476i
$489$	−1.53042	+	4.71016i	−0.0692082	+	0.213001i
$490$	1.35899	−	4.18255i	0.0613930	−	0.188948i
$491$	20.6599	−	15.0103i	0.932370	−	0.677407i	−0.0142017	−	0.999899i	$-0.504521\pi$
$491$	20.6599	−	15.0103i	0.932370	−	0.677407i	0.946572	+	0.322492i	$0.104521\pi$
$492$	−10.0041	−	7.26841i	−0.451020	−	0.327685i
$493$	−4.10784	−	12.6426i	−0.185008	−	0.569396i
$494$	−7.26454			−0.326847
$495$		0			0
$496$	16.2488			0.729594
$497$	3.25521	+	10.0185i	0.146016	+	0.449391i
$498$	−6.36593	−	4.62512i	−0.285264	−	0.207256i
$499$	−19.7088	+	14.3193i	−0.882286	+	0.641019i	−0.933855	−	0.357651i	$-0.883578\pi$
$499$	−19.7088	+	14.3193i	−0.882286	+	0.641019i	0.0515690	+	0.998669i	$0.483578\pi$
$500$	−1.71012	+	5.26321i	−0.0764790	+	0.235378i
$501$	0.927051	−	2.85317i	0.0414176	−	0.127470i
$502$	−63.9683	+	46.4757i	−2.85505	+	2.07431i
$503$	−10.1095	−	7.34496i	−0.450759	−	0.327495i	0.339136	−	0.940737i	$-0.389865\pi$
$503$	−10.1095	−	7.34496i	−0.450759	−	0.327495i	−0.789895	+	0.613242i	$0.789865\pi$
$504$	−20.5837	−	63.3501i	−0.916871	−	2.82184i
$505$	−6.57849			−0.292739
$506$		0			0
$507$	2.67971			0.119010
$508$	13.8895	+	42.7474i	0.616246	+	1.89661i
$509$	−19.7791	−	14.3703i	−0.876691	−	0.636954i	0.0556827	−	0.998449i	$-0.482266\pi$
$509$	−19.7791	−	14.3703i	−0.876691	−	0.636954i	−0.932374	+	0.361495i	$0.882266\pi$
$510$	1.13328	−	0.823379i	0.0501827	−	0.0364598i
$511$	−0.766865	+	2.36017i	−0.0339241	+	0.104408i
$512$	18.7584	−	57.7324i	0.829012	−	2.55144i
$513$	5.03218	−	3.65609i	0.222176	−	0.161420i
$514$	61.3991	+	44.6091i	2.70820	+	1.96762i
$515$	−5.05440	−	15.5559i	−0.222724	−	0.685473i
$516$	5.04245			0.221981
$517$		0			0
$518$	47.7622			2.09855
$519$	−0.419760	−	1.29189i	−0.0184254	−	0.0567076i
$520$	4.19127	+	3.04514i	0.183799	+	0.133538i
$521$	0.0318902	−	0.0231696i	0.00139713	−	0.00101508i	−0.587086	−	0.809524i	$-0.699725\pi$
$521$	0.0318902	−	0.0231696i	0.00139713	−	0.00101508i	0.588484	+	0.808509i	$0.299725\pi$
$522$	−13.7621	+	42.3554i	−0.602351	+	1.85385i
$523$	6.51774	−	20.0596i	0.285001	−	0.877143i	−0.701397	−	0.712771i	$-0.747440\pi$
$523$	6.51774	−	20.0596i	0.285001	−	0.877143i	0.986398	−	0.164372i	$-0.0525599\pi$
$524$	25.9613	−	18.8620i	1.13412	−	0.823989i
$525$	0.396137	+	0.287810i	0.0172888	+	0.0125611i
$526$	−2.65762	−	8.17931i	−0.115878	−	0.356635i
$527$	−2.52907			−0.110168
$528$		0			0
$529$	−2.44221			−0.106183
$530$	3.84579	+	11.8361i	0.167050	+	0.514128i
$531$	−15.4113	−	11.1970i	−0.668794	−	0.485907i
$532$	51.5472	−	37.4512i	2.23485	−	1.62372i
$533$	−1.74975	+	5.38519i	−0.0757903	+	0.233259i
$534$	−2.27293	+	6.99535i	−0.0983591	+	0.302718i
$535$	−8.26068	+	6.00173i	−0.357140	+	0.259477i
$536$	−5.65907	−	4.11156i	−0.244435	−	0.177592i
$537$	−1.10581	−	3.40334i	−0.0477194	−	0.146865i
$538$	49.4152			2.13044
$539$		0			0
$540$	−6.94622			−0.298918
$541$	10.3336	+	31.8036i	0.444276	+	1.36734i	0.883276	+	0.468854i	$0.155333\pi$
$541$	10.3336	+	31.8036i	0.444276	+	1.36734i	−0.438999	+	0.898487i	$0.644667\pi$
$542$	45.1510	+	32.8041i	1.93940	+	1.40906i
$543$	0.765509	−	0.556175i	0.0328511	−	0.0238677i
$544$	−17.4371	+	53.6658i	−0.747608	+	2.30090i
$545$	−3.73659	+	11.5000i	−0.160058	+	0.492608i
$546$	0.580709	−	0.421910i	0.0248520	−	0.0180561i
$547$	26.5411	+	19.2833i	1.13482	+	0.824492i	0.986389	−	0.164431i	$-0.0525787\pi$
$547$	26.5411	+	19.2833i	1.13482	+	0.824492i	0.148428	+	0.988923i	$0.452579\pi$
$548$	15.1632	+	46.6676i	0.647740	+	1.99354i
$549$	20.0938			0.857584
$550$		0			0
$551$	−27.2044			−1.15895
$552$	2.86444	+	8.81585i	0.121919	+	0.375228i
$553$	8.73381	+	6.34548i	0.371399	+	0.269837i
$554$	−56.6026	+	41.1242i	−2.40481	+	1.74720i
$555$	0.487780	−	1.50123i	0.0207051	−	0.0637237i
$556$	28.8442	−	88.7733i	1.22327	−	3.76483i
$557$	22.9216	−	16.6535i	0.971220	−	0.705633i	0.0154907	−	0.999880i	$-0.495069\pi$
$557$	22.9216	−	16.6535i	0.971220	−	0.705633i	0.955729	+	0.294247i	$0.0950689\pi$
$558$	6.85472	+	4.98025i	0.290184	+	0.210831i
$559$	−0.713506	−	2.19595i	−0.0301781	−	0.0928786i
$560$	−36.1456			−1.52743
$561$		0			0
$562$	−50.1550			−2.11566
$563$	−8.97265	−	27.6150i	−0.378152	−	1.16383i	−0.941327	−	0.337495i	$-0.890420\pi$
$563$	−8.97265	−	27.6150i	−0.378152	−	1.16383i	0.563175	−	0.826338i	$-0.309580\pi$
$564$	6.38672	+	4.64022i	0.268929	+	0.195389i
$565$	−8.77219	+	6.37337i	−0.369049	+	0.268130i
$566$	9.37579	−	28.8557i	0.394094	−	1.21290i
$567$	6.17590	−	19.0075i	0.259364	−	0.798239i
$568$	−35.5825	+	25.8522i	−1.49301	+	1.08473i
$569$	23.2267	+	16.8752i	0.973714	+	0.707444i	0.956295	−	0.292404i	$-0.0944552\pi$
$569$	23.2267	+	16.8752i	0.973714	+	0.707444i	0.0174187	+	0.999848i	$0.494455\pi$
$570$	−0.885873	−	2.72644i	−0.0371051	−	0.114198i
$571$	−0.824301			−0.0344959			−0.0172480	−	0.999851i	$-0.505490\pi$
$571$	−0.824301			−0.0344959			−0.0172480	+	0.999851i	$0.505490\pi$
$572$		0			0
$573$	0.581515			0.0242931
$574$	−20.8930	−	64.3022i	−0.872059	−	2.68392i
$575$	3.66814	+	2.66506i	0.152972	+	0.111141i
$576$	78.5387	−	57.0617i	3.27245	−	2.37757i
$577$	−9.74704	+	29.9983i	−0.405775	+	1.24885i	0.514472	+	0.857507i	$0.327988\pi$
$577$	−9.74704	+	29.9983i	−0.405775	+	1.24885i	−0.920247	+	0.391339i	$0.872012\pi$
$578$	−9.44577	+	29.0711i	−0.392892	+	1.20920i
$579$	−2.01257	+	1.46222i	−0.0836398	+	0.0607678i
$580$	24.5780	+	17.8570i	1.02055	+	0.741471i
$581$	−9.76562	−	30.0555i	−0.405146	−	1.24691i
$582$	−2.75313			−0.114121
$583$		0			0
$584$	−10.3614			−0.428758
$585$	0.487780	+	1.50123i	0.0201672	+	0.0620683i
$586$	60.2658	+	43.7857i	2.48956	+	1.80877i
$587$	21.6603	−	15.7371i	0.894014	−	0.649539i	−0.0429072	−	0.999079i	$-0.513662\pi$
$587$	21.6603	−	15.7371i	0.894014	−	0.649539i	0.936922	+	0.349540i	$0.113662\pi$
$588$	0.577466	−	1.77726i	0.0238143	−	0.0732929i
$589$	−1.59938	+	4.92238i	−0.0659013	+	0.202823i
$590$	−14.3124	+	10.3985i	−0.589230	+	0.428101i
$591$	1.11005	+	0.806497i	0.0456613	+	0.0331748i
$592$	36.0074	+	110.819i	1.47990	+	4.55465i
$593$	11.0731			0.454719			0.227360	−	0.973811i	$-0.426991\pi$
$593$	11.0731			0.454719			0.227360	+	0.973811i	$0.426991\pi$
$594$		0			0
$595$	5.62593			0.230641
$596$	−7.63728	−	23.5051i	−0.312835	−	0.962808i
$597$	4.08506	+	2.96797i	0.167191	+	0.121471i
$598$	5.37724	−	3.90679i	0.219892	−	0.159761i
$599$	−3.68808	+	11.3508i	−0.150691	+	0.463779i	−0.997699	−	0.0678012i	$-0.978402\pi$
$599$	−3.68808	+	11.3508i	−0.150691	+	0.463779i	0.847008	+	0.531580i	$0.178402\pi$
$600$	−0.631760	+	1.94436i	−0.0257915	+	0.0793780i
$601$	4.25910	−	3.09442i	0.173732	−	0.126224i	−0.497521	−	0.867452i	$-0.665756\pi$
$601$	4.25910	−	3.09442i	0.173732	−	0.126224i	0.671253	+	0.741228i	$0.265756\pi$
$602$	22.3047	+	16.2053i	0.909074	+	0.660481i
$603$	−0.658602	−	2.02697i	−0.0268204	−	0.0825446i
$604$	63.7158			2.59256
$605$		0			0
$606$	−3.80558			−0.154591
$607$	−11.0770	−	34.0916i	−0.449603	−	1.38374i	−0.877356	−	0.479840i	$-0.840695\pi$
$607$	−11.0770	−	34.0916i	−0.449603	−	1.38374i	0.427753	−	0.903896i	$-0.359305\pi$
$608$	93.4237	+	67.8763i	3.78883	+	2.75275i
$609$	2.17465	−	1.57998i	0.0881214	−	0.0640240i
$610$	5.76656	−	17.7477i	0.233481	−	0.718582i
$611$	1.11706	−	3.43796i	0.0451914	−	0.139085i
$612$	−32.0429	+	23.2805i	−1.29526	+	0.941060i
$613$	5.30537	+	3.85457i	0.214282	+	0.155685i	0.689749	−	0.724049i	$-0.257721\pi$
$613$	5.30537	+	3.85457i	0.214282	+	0.155685i	−0.475467	+	0.879733i	$0.657721\pi$
$614$	−9.95656	−	30.6432i	−0.401814	−	1.23666i
$615$	−2.23448			−0.0901029
$616$		0			0
$617$	17.7986			0.716545			0.358272	−	0.933617i	$-0.383366\pi$
$617$	17.7986			0.716545			0.358272	+	0.933617i	$0.383366\pi$
$618$	−2.92391	−	8.99888i	−0.117617	−	0.361988i
$619$	−36.3172	−	26.3860i	−1.45971	−	1.06054i	−0.983438	−	0.181243i	$-0.941988\pi$
$619$	−36.3172	−	26.3860i	−1.45971	−	1.06054i	−0.476271	−	0.879298i	$-0.658012\pi$
$620$	4.67602	−	3.39733i	0.187794	−	0.136440i
$621$	−1.75863	+	5.41251i	−0.0705714	+	0.217196i
$622$	9.02621	−	27.7798i	0.361918	−	1.11387i
$623$	−23.8987	+	17.3634i	−0.957481	+	0.695651i
$624$	1.41672	+	1.02931i	0.0567141	+	0.0412052i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−74.6063			−2.98187
$627$		0			0
$628$	−32.7128			−1.30538
$629$	−5.60442	−	17.2486i	−0.223463	−	0.687748i
$630$	−15.2484	−	11.0786i	−0.607510	−	0.441382i
$631$	−17.7265	+	12.8791i	−0.705681	+	0.512707i	−0.881777	−	0.471666i	$-0.843653\pi$
$631$	−17.7265	+	12.8791i	−0.705681	+	0.512707i	0.176096	+	0.984373i	$0.443653\pi$
$632$	−13.9287	+	42.8681i	−0.554054	+	1.70520i
$633$	−1.09848	+	3.38078i	−0.0436608	+	0.134374i
$634$	−11.0571	+	8.03345i	−0.439133	+	0.319049i
$635$	6.57077	+	4.77394i	0.260753	+	0.189448i
$636$	1.63416	+	5.02943i	0.0647987	+	0.199430i
$637$	−0.855693			−0.0339038
$638$		0			0
$639$	−13.4008			−0.530128
$640$	−13.4581	−	41.4199i	−0.531980	−	1.63727i
$641$	−28.9090	−	21.0036i	−1.14184	−	0.829593i	−0.154463	−	0.987999i	$-0.549365\pi$
$641$	−28.9090	−	21.0036i	−1.14184	−	0.829593i	−0.987374	+	0.158406i	$0.949365\pi$
$642$	−4.77870	+	3.47193i	−0.188600	+	0.137026i
$643$	0.127361	−	0.391978i	0.00502265	−	0.0154581i	−0.948514	−	0.316736i	$-0.897413\pi$
$643$	0.127361	−	0.391978i	0.00502265	−	0.0154581i	0.953536	+	0.301278i	$0.0974131\pi$
$644$	−18.0145	+	55.4431i	−0.709872	+	2.18476i
$645$	0.737147	−	0.535569i	0.0290251	−	0.0210880i
$646$	−26.6473	−	19.3604i	−1.04843	−	0.761726i
$647$	−5.11375	−	15.7385i	−0.201042	−	0.618744i	−0.999853	−	0.0171614i	$-0.994537\pi$
$647$	−5.11375	−	15.7385i	−0.201042	−	0.618744i	0.798811	−	0.601583i	$-0.205463\pi$
$648$	83.4450			3.27803
$649$		0			0
$650$	1.46593			0.0574985
$651$	−0.158032	−	0.486372i	−0.00619375	−	0.0190624i
$652$	−105.209	−	76.4386i	−4.12029	−	2.99357i
$653$	−8.90568	+	6.47036i	−0.348506	+	0.253205i	−0.748242	−	0.663426i	$-0.769102\pi$
$653$	−8.90568	+	6.47036i	−0.348506	+	0.253205i	0.399736	+	0.916630i	$0.369102\pi$
$654$	−2.16157	+	6.65264i	−0.0845242	+	0.260139i
$655$	1.79187	−	5.51480i	0.0700141	−	0.215481i
$656$	133.445	−	96.9534i	5.21015	−	3.78539i
$657$	−2.55405	−	1.85562i	−0.0996429	−	0.0723948i
$658$	13.3383	+	41.0511i	0.519981	+	1.60034i
$659$	−42.9980			−1.67497			−0.837483	−	0.546464i	$-0.815974\pi$
$659$	−42.9980			−1.67497			−0.837483	+	0.546464i	$0.815974\pi$
$660$		0			0
$661$	19.4927			0.758177			0.379089	−	0.925360i	$-0.376238\pi$
$661$	19.4927			0.758177			0.379089	+	0.925360i	$0.376238\pi$
$662$	6.40794	+	19.7216i	0.249052	+	0.766502i
$663$	−0.220507	−	0.160208i	−0.00856378	−	0.00622195i
$664$	106.747	−	77.5565i	4.14260	−	3.00978i
$665$	3.55783	−	10.9499i	0.137967	−	0.424618i
$666$	−18.7759	+	57.7864i	−0.727553	+	2.23918i
$667$	20.1368	−	14.6303i	0.779700	−	0.566486i
$668$	63.7300	+	46.3025i	2.46579	+	1.79150i
$669$	1.62931	+	5.01450i	0.0629928	+	0.193872i
$670$	−1.97930			−0.0764672
$671$		0			0
$672$	−11.4102			−0.440157
$673$	2.10336	+	6.47349i	0.0810788	+	0.249535i	0.983376	−	0.181579i	$-0.0581208\pi$
$673$	2.10336	+	6.47349i	0.0810788	+	0.249535i	−0.902298	+	0.431114i	$0.858121\pi$
$674$	8.19638	+	5.95502i	0.315713	+	0.229379i
$675$	−1.01546	+	0.737773i	−0.0390850	+	0.0283969i
$676$	−21.7438	+	66.9205i	−0.836300	+	2.57387i
$677$	0.315412	−	0.970739i	0.0121223	−	0.0373085i	−0.944812	−	0.327612i	$-0.893756\pi$
$677$	0.315412	−	0.970739i	0.0121223	−	0.0373085i	0.956935	+	0.290303i	$0.0937562\pi$
$678$	−5.07461	+	3.68692i	−0.194889	+	0.141595i
$679$	−8.94537	−	6.49919i	−0.343292	−	0.249416i
$680$	7.25870	+	22.3400i	0.278359	+	0.856699i
$681$	0.844996			0.0323803
$682$		0			0
$683$	2.09820			0.0802853			0.0401426	−	0.999194i	$-0.487219\pi$
$683$	2.09820			0.0802853			0.0401426	+	0.999194i	$0.487219\pi$
$684$	25.0475	+	77.0883i	0.957716	+	2.94755i
$685$	7.17335	+	5.21174i	0.274080	+	0.199130i
$686$	44.3803	−	32.2442i	1.69445	−	1.23109i
$687$	1.12883	−	3.47417i	0.0430675	−	0.132548i
$688$	−20.7849	+	63.9692i	−0.792415	+	2.43880i
$689$	1.95904	−	1.42333i	0.0746336	−	0.0542245i
$690$	2.12198	+	1.54171i	0.0807822	+	0.0586917i
$691$	3.70666	+	11.4079i	0.141008	+	0.433978i	0.996476	−	0.0838776i	$-0.0267305\pi$
$691$	3.70666	+	11.4079i	0.141008	+	0.433978i	−0.855468	+	0.517855i	$0.826730\pi$
$692$	35.6684			1.35591
$693$		0			0
$694$	43.2736			1.64264
$695$	−5.21211	−	16.0412i	−0.197707	−	0.608478i
$696$	9.07971	+	6.59680i	0.344166	+	0.250051i
$697$	−20.7702	+	15.0904i	−0.786727	+	0.571591i
$698$	8.95510	−	27.5610i	0.338955	−	1.04320i
$699$	0.137585	−	0.423443i	0.00520394	−	0.0160161i
$700$	−10.4018	+	7.55738i	−0.393153	+	0.285642i
$701$	23.7523	+	17.2570i	0.897111	+	0.651789i	0.937722	−	0.347386i	$-0.112931\pi$
$701$	23.7523	+	17.2570i	0.897111	+	0.651789i	−0.0406113	+	0.999175i	$0.512931\pi$
$702$	0.568590	+	1.74994i	0.0214601	+	0.0660473i
$703$	−37.1156			−1.39984
$704$		0			0
$705$	1.42651			0.0537255
$706$	−20.8256	−	64.0947i	−0.783783	−	2.41224i
$707$	−12.3649	−	8.98365i	−0.465031	−	0.337865i
$708$	−6.08164	+	4.41857i	−0.228562	+	0.166060i
$709$	−11.6021	+	35.7075i	−0.435725	+	1.34102i	0.456616	+	0.889664i	$0.349061\pi$
$709$	−11.6021	+	35.7075i	−0.435725	+	1.34102i	−0.892342	+	0.451361i	$0.850939\pi$
$710$	−3.84579	+	11.8361i	−0.144330	+	0.444202i
$711$	−11.1106	+	8.07234i	−0.416681	+	0.302737i
$712$	−99.7829	−	72.4965i	−3.73952	−	2.71692i
$713$	−1.46334	−	4.50369i	−0.0548025	−	0.168665i
$714$	3.25454			0.121798
$715$		0			0
$716$	93.9647			3.51162
$717$	−1.55881	−	4.79753i	−0.0582149	−	0.179167i
$718$	−37.0184	−	26.8954i	−1.38151	−	1.00373i
$719$	3.23202	−	2.34820i	0.120534	−	0.0875732i	−0.525885	−	0.850556i	$-0.676266\pi$
$719$	3.23202	−	2.34820i	0.120534	−	0.0875732i	0.646419	+	0.762983i	$0.276266\pi$
$720$	14.2093	−	43.7318i	0.529550	−	1.62979i
$721$	11.7430	−	36.1411i	0.437331	−	1.34597i
$722$	−12.3417	+	8.96677i	−0.459310	+	0.333708i
$723$	2.47460	+	1.79791i	0.0920315	+	0.0668648i
$724$	7.67785	+	23.6300i	0.285345	+	0.878202i
$725$	5.48965			0.203881
$726$		0			0
$727$	−25.4990			−0.945706			−0.472853	−	0.881141i	$-0.656776\pi$
$727$	−25.4990			−0.945706			−0.472853	+	0.881141i	$0.656776\pi$
$728$	3.71945	+	11.4473i	0.137852	+	0.424265i
$729$	19.9268	+	14.4777i	0.738031	+	0.536211i
$730$	−2.37192	+	1.72330i	−0.0877889	+	0.0637823i
$731$	3.23509	−	9.95657i	0.119654	−	0.368257i
$732$	2.45034	−	7.54137i	0.0905672	−	0.278737i
$733$	−29.2884	+	21.2793i	−1.08179	+	0.785968i	−0.977994	−	0.208631i	$-0.933099\pi$
$733$	−29.2884	+	21.2793i	−1.08179	+	0.785968i	−0.103797	+	0.994598i	$0.533099\pi$
$734$	−33.9285	−	24.6505i	−1.25232	−	0.909866i
$735$	−0.104347	−	0.321148i	−0.00384891	−	0.0118457i
$736$	−105.656			−3.89452
$737$		0			0
$738$	86.0111			3.16611
$739$	1.87268	+	5.76351i	0.0688876	+	0.212014i	0.979574	−	0.201084i	$-0.0644465\pi$
$739$	1.87268	+	5.76351i	0.0688876	+	0.212014i	−0.910686	+	0.413098i	$0.864447\pi$
$740$	33.5323	+	24.3627i	1.23267	+	0.895590i
$741$	−0.451264	+	0.327862i	−0.0165776	+	0.0120443i
$742$	−8.93498	+	27.4990i	−0.328013	+	1.00952i
$743$	−11.2133	+	34.5109i	−0.411375	+	1.26608i	0.504078	+	0.863658i	$0.331832\pi$
$743$	−11.2133	+	34.5109i	−0.411375	+	1.26608i	−0.915453	+	0.402425i	$0.868168\pi$
$744$	1.72743	−	1.25505i	0.0633308	−	0.0460125i
$745$	−3.61301	−	2.62501i	−0.132371	−	0.0961728i
$746$	−15.1370	−	46.5868i	−0.554204	−	1.70567i
$747$	40.2024			1.47093
$748$		0			0
$749$	−23.7228			−0.866812
$750$	0.178763	+	0.550175i	0.00652749	+	0.0200896i
$751$	12.7287	+	9.24791i	0.464475	+	0.337461i	0.795284	−	0.606237i	$-0.207322\pi$
$751$	12.7287	+	9.24791i	0.464475	+	0.337461i	−0.330809	+	0.943698i	$0.607322\pi$
$752$	−85.1925	+	61.8959i	−3.10665	+	2.25711i
$753$	−1.87609	+	5.77402i	−0.0683687	+	0.210417i
$754$	2.48680	−	7.65357i	0.0905638	−	0.278727i
$755$	9.31452	−	6.76739i	0.338990	−	0.246291i
$756$	−13.0561	−	9.48583i	−0.474847	−	0.344996i
$757$	−7.76847	−	23.9089i	−0.282350	−	0.868984i	−0.987180	−	0.159608i	$-0.948977\pi$
$757$	−7.76847	−	23.9089i	−0.282350	−	0.868984i	0.704830	−	0.709376i	$-0.251023\pi$
$758$	5.19442			0.188670
$759$		0			0
$760$	48.0712			1.74372
$761$	4.78078	+	14.7137i	0.173303	+	0.533372i	0.999552	−	0.0299332i	$-0.00952945\pi$
$761$	4.78078	+	14.7137i	0.173303	+	0.533372i	−0.826249	+	0.563305i	$0.809529\pi$
$762$	3.80111	+	2.76167i	0.137700	+	0.100045i
$763$	−22.7279	+	16.5128i	−0.822804	+	0.597802i
$764$	−4.71855	+	14.5222i	−0.170711	+	0.525394i
$765$	−2.21163	+	6.80669i	−0.0799616	+	0.246096i
$766$	−11.8069	+	8.57825i	−0.426602	+	0.309945i
$767$	2.78480	+	2.02328i	0.100553	+	0.0730564i
$768$	−3.50704	−	10.7935i	−0.126549	−	0.389479i
$769$	−17.3220			−0.624647			−0.312323	−	0.949976i	$-0.601107\pi$
$769$	−17.3220			−0.624647			−0.312323	+	0.949976i	$0.601107\pi$
$770$		0			0
$771$	5.82733			0.209866
$772$	−20.1856	−	62.1249i	−0.726496	−	2.23592i
$773$	18.3639	+	13.3422i	0.660505	+	0.479885i	0.866833	−	0.498598i	$-0.166152\pi$
$773$	18.3639	+	13.3422i	0.660505	+	0.479885i	−0.206329	+	0.978483i	$0.566152\pi$
$774$	−28.3748	+	20.6155i	−1.01991	+	0.741008i
$775$	0.322743	−	0.993301i	0.0115933	−	0.0356804i
$776$	14.2661	−	43.9065i	0.512123	−	1.57615i
$777$	2.96693	−	2.15560i	0.106438	−	0.0773317i
$778$	59.5731	+	43.2824i	2.13580	+	1.55175i
$779$	16.2358	+	49.9686i	0.581708	+	1.79031i
$780$	0.622906			0.0223036
$781$		0			0
$782$	30.1363			1.07767
$783$	2.12927	+	6.55322i	0.0760940	+	0.234193i
$784$	20.1663	+	14.6516i	0.720223	+	0.523273i
$785$	−4.78223	+	3.47449i	−0.170685	+	0.124010i
$786$	1.03657	−	3.19025i	0.0369734	−	0.113792i
$787$	−0.958331	+	2.94944i	−0.0341608	+	0.105136i	−0.966683	−	0.255977i	$-0.917603\pi$
$787$	−0.958331	+	2.94944i	−0.0341608	+	0.105136i	0.932522	+	0.361113i	$0.117603\pi$
$788$	−29.1478	+	21.1772i	−1.03835	+	0.754405i
$789$	−0.534236	−	0.388145i	−0.0190193	−	0.0138183i
$790$	3.94126	+	12.1300i	0.140224	+	0.431564i
$791$	−25.1918			−0.895716
$792$		0			0
$793$	−3.63093			−0.128938
$794$	26.8007	+	82.4840i	0.951121	+	2.92725i
$795$	0.773082	+	0.561677i	0.0274184	+	0.0199206i
$796$	−107.266	+	77.9336i	−3.80196	+	2.76228i
$797$	−5.89971	+	18.1574i	−0.208978	+	0.643170i	0.790548	+	0.612400i	$0.209796\pi$
$797$	−5.89971	+	18.1574i	−0.208978	+	0.643170i	−0.999527	+	0.0307695i	$0.990204\pi$
$798$	2.05816	−	6.33437i	0.0728581	−	0.224234i
$799$	13.2599	−	9.63387i	0.469101	−	0.340822i
$800$	−18.8522	−	13.6969i	−0.666526	−	0.484260i
$801$	−11.6127	−	35.7403i	−0.410315	−	1.26282i
$802$	−8.60855			−0.303978
$803$		0			0
$804$	−0.841051			−0.0296616
$805$	3.25521	+	10.0185i	0.114731	+	0.353106i
$806$	−1.23864	−	0.899925i	−0.0436292	−	0.0316985i
$807$	3.06961	−	2.23020i	0.108055	−	0.0785068i
$808$	19.7196	−	60.6907i	0.693734	−	2.13509i
$809$	−1.38098	+	4.25023i	−0.0485528	+	0.149430i	−0.972394	−	0.233347i	$-0.925032\pi$
$809$	−1.38098	+	4.25023i	−0.0485528	+	0.149430i	0.923841	+	0.382777i	$0.125032\pi$
$810$	19.1022	−	13.8785i	0.671182	−	0.487642i
$811$	−3.93728	−	2.86060i	−0.138257	−	0.100449i	0.516507	−	0.856283i	$-0.327232\pi$
$811$	−3.93728	−	2.86060i	−0.138257	−	0.100449i	−0.654764	+	0.755834i	$0.727232\pi$
$812$	21.8112	+	67.1280i	0.765424	+	2.35573i
$813$	4.28523			0.150290
$814$		0			0
$815$	−23.4990			−0.823135
$816$	2.45356	+	7.55128i	0.0858918	+	0.264348i
$817$	−17.3328	−	12.5930i	−0.606398	−	0.440574i
$818$	0.942735	−	0.684937i	0.0329619	−	0.0239483i
$819$	−1.13327	+	3.48783i	−0.0395995	+	0.121875i
$820$	18.1311	−	55.8017i	0.633164	−	1.94868i
$821$	13.7573	−	9.99529i	0.480134	−	0.348838i	−0.321243	−	0.946997i	$-0.604101\pi$
$821$	13.7573	−	9.99529i	0.480134	−	0.348838i	0.801378	+	0.598159i	$0.204101\pi$
$822$	4.14970	+	3.01493i	0.144737	+	0.105158i
$823$	−6.72046	−	20.6834i	−0.234260	−	0.720979i	−0.997219	−	0.0745316i	$-0.976254\pi$
$823$	−6.72046	−	20.6834i	−0.234260	−	0.720979i	0.762958	−	0.646448i	$-0.223746\pi$
$824$	158.664			5.52731
$825$		0			0
$826$	−41.1019			−1.43012
$827$	6.39926	+	19.6949i	0.222524	+	0.684858i	0.998534	+	0.0541373i	$0.0172409\pi$
$827$	6.39926	+	19.6949i	0.222524	+	0.684858i	−0.776009	+	0.630721i	$0.782759\pi$
$828$	−59.9976	−	43.5908i	−2.08506	−	1.51488i
$829$	−9.14914	+	6.64724i	−0.317763	+	0.230868i	−0.735220	−	0.677828i	$-0.762921\pi$
$829$	−9.14914	+	6.64724i	−0.317763	+	0.230868i	0.417458	+	0.908696i	$0.362921\pi$
$830$	11.5374	−	35.5084i	0.400468	−	1.23251i
$831$	−1.66007	+	5.10917i	−0.0575871	+	0.177235i
$832$	−14.1919	+	10.3110i	−0.492014	+	0.357469i
$833$	−3.13880	−	2.28047i	−0.108753	−	0.0790137i
$834$	−3.01514	−	9.27966i	−0.104406	−	0.321328i
$835$	14.2345			0.492604
$836$		0			0
$837$	1.31093			0.0453122
$838$	5.69289	+	17.5209i	0.196657	+	0.605249i
$839$	35.1990	+	25.5736i	1.21520	+	0.882898i	0.995693	−	0.0927117i	$-0.0295535\pi$
$839$	35.1990	+	25.5736i	1.21520	+	0.882898i	0.219512	+	0.975610i	$0.429554\pi$
$840$	−3.84269	+	2.79188i	−0.132585	+	0.0963289i
$841$	0.351130	−	1.08067i	0.0121079	−	0.0372644i
$842$	2.35789	−	7.25684i	0.0812583	−	0.250087i
$843$	−3.11556	+	2.26359i	−0.107306	+	0.0779622i
$844$	−75.5151	−	54.8649i	−2.59934	−	1.88853i
$845$	3.92908	+	12.0925i	0.135164	+	0.415993i
$846$	−54.9102			−1.88785
$847$		0			0
$848$	−70.5401			−2.42236
$849$	−0.719901	−	2.21563i	−0.0247069	−	0.0760402i
$850$	5.37724	+	3.90679i	0.184438	+	0.134002i
$851$	27.4731	−	19.9604i	0.941765	−	0.684233i
$852$	−1.63416	+	5.02943i	−0.0559854	+	0.172305i
$853$	0.344735	−	1.06098i	0.0118035	−	0.0363274i	−0.944981	−	0.327124i	$-0.893920\pi$
$853$	0.344735	−	1.06098i	0.0118035	−	0.0363274i	0.956785	+	0.290797i	$0.0939204\pi$
$854$	35.0752	−	25.4836i	1.20025	−	0.872032i
$855$	11.8494	+	8.60907i	0.405240	+	0.294424i
$856$	−30.6077	−	94.2007i	−1.04615	−	3.21971i
$857$	−7.80361			−0.266566			−0.133283	−	0.991078i	$-0.542552\pi$
$857$	−7.80361			−0.266566			−0.133283	+	0.991078i	$0.542552\pi$
$858$		0			0
$859$	30.5341			1.04181			0.520905	−	0.853615i	$-0.325595\pi$
$859$	30.5341			1.04181			0.520905	+	0.853615i	$0.325595\pi$
$860$	7.39339	+	22.7545i	0.252113	+	0.775923i
$861$	−4.19993	−	3.05143i	−0.143133	−	0.103992i
$862$	35.9659	−	26.1307i	1.22500	−	0.890017i
$863$	−1.32556	+	4.07965i	−0.0451225	+	0.138873i	−0.971080	−	0.238756i	$-0.923260\pi$
$863$	−1.32556	+	4.07965i	−0.0451225	+	0.138873i	0.925957	+	0.377629i	$0.123260\pi$
$864$	9.03839	−	27.8173i	0.307492	−	0.946364i
$865$	5.21430	−	3.78841i	0.177292	−	0.128810i
$866$	−17.3814	−	12.6284i	−0.590646	−	0.429129i
$867$	0.725274	+	2.23216i	0.0246316	+	0.0758083i
$868$	13.4285			0.455792
$869$		0			0
$870$	3.17570			0.107666
$871$	0.119009	+	0.366271i	0.00403245	+	0.0124106i
$872$	−94.8945	−	68.9449i	−3.21353	−	2.33477i
$873$	11.3798	−	8.26789i	0.385147	−	0.279826i
$874$	19.0581	−	58.6549i	0.644651	−	1.98403i
$875$	−0.717944	+	2.20960i	−0.0242709	+	0.0746982i
$876$	−1.00788	+	0.732270i	−0.0340532	+	0.0247411i
$877$	9.19401	+	6.67984i	0.310460	+	0.225562i	0.732094	−	0.681204i	$-0.238543\pi$
$877$	9.19401	+	6.67984i	0.310460	+	0.225562i	−0.421634	+	0.906766i	$0.638543\pi$
$878$	−17.5878	−	54.1296i	−0.593559	−	1.82679i
$879$	5.71977			0.192923
$880$		0			0
$881$	−11.3277			−0.381639			−0.190820	−	0.981625i	$-0.561115\pi$
$881$	−11.3277			−0.381639			−0.190820	+	0.981625i	$0.561115\pi$
$882$	4.01661	+	12.3619i	0.135246	+	0.416245i
$883$	−25.3127	−	18.3908i	−0.851841	−	0.618899i	0.0738118	−	0.997272i	$-0.476484\pi$
$883$	−25.3127	−	18.3908i	−0.851841	−	0.618899i	−0.925653	+	0.378373i	$0.876484\pi$
$884$	5.79012	−	4.20677i	0.194743	−	0.141489i
$885$	−0.419760	+	1.29189i	−0.0141101	+	0.0434263i
$886$	4.49767	−	13.8424i	0.151102	−	0.465045i
$887$	−22.8806	+	16.6237i	−0.768254	+	0.558169i	−0.901431	−	0.432923i	$-0.857482\pi$
$887$	−22.8806	+	16.6237i	−0.768254	+	0.558169i	0.133177	+	0.991092i	$0.457482\pi$
$888$	12.3877	+	9.00016i	0.415702	+	0.302025i
$889$	5.83108	+	17.9462i	0.195568	+	0.601897i
$890$	−34.8998			−1.16984
$891$		0			0
$892$	−138.448			−4.63558
$893$	−10.3651	−	31.9004i	−0.346854	−	1.06751i
$894$	−2.09009	−	1.51854i	−0.0699029	−	0.0507874i
$895$	13.7365	−	9.98018i	0.459162	−	0.333601i
$896$	31.2675	−	96.2314i	1.04457	−	3.21487i
$897$	0.157706	−	0.485370i	0.00526566	−	0.0162060i
$898$	66.6250	−	48.4059i	2.22331	−	1.61533i
$899$	−4.63849	−	3.37006i	−0.154702	−	0.112398i
$900$	−5.05440	−	15.5559i	−0.168480	−	0.518529i
$901$	10.9793			0.365774
$902$		0			0
$903$	2.11692			0.0704467
$904$	−32.5029	−	100.034i	−1.08103	−	3.32707i
$905$	3.63220	+	2.63895i	0.120739	+	0.0877217i
$906$	5.38834	−	3.91486i	0.179016	−	0.130062i
$907$	10.3881	−	31.9713i	0.344931	−	1.06159i	−0.616690	−	0.787206i	$-0.711527\pi$
$907$	10.3881	−	31.9713i	0.344931	−	1.06159i	0.961621	−	0.274382i	$-0.0884733\pi$
$908$	−6.85650	+	21.1021i	−0.227541	+	0.700299i
$909$	15.7299	−	11.4285i	0.521729	−	0.379058i
$910$	2.75536	+	2.00189i	0.0913394	+	0.0663619i
$911$	2.32722	+	7.16245i	0.0771043	+	0.237302i	0.982178	−	0.187951i	$-0.0601848\pi$
$911$	2.32722	+	7.16245i	0.0771043	+	0.237302i	−0.905074	+	0.425254i	$0.860185\pi$
$912$	16.2488			0.538053
$913$		0			0
$914$	−102.968			−3.40587
$915$	−0.442774	−	1.36272i	−0.0146377	−	0.0450501i
$916$	77.6011	+	56.3805i	2.56401	+	1.86286i
$917$	10.8991	−	7.91863i	0.359919	−	0.261496i
$918$	−2.57803	+	7.93436i	−0.0850876	+	0.261873i
$919$	−12.3738	+	38.0826i	−0.408174	+	1.25623i	0.510042	+	0.860150i	$0.329630\pi$
$919$	−12.3738	+	38.0826i	−0.408174	+	1.25623i	−0.918216	+	0.396080i	$0.870370\pi$
$920$	−35.5825	+	25.8522i	−1.17312	+	0.852321i
$921$	−2.00147	−	1.45415i	−0.0659508	−	0.0479160i
$922$	−13.3870	−	41.2010i	−0.440878	−	1.35688i
$923$	2.42151			0.0797050
$924$		0			0
$925$	7.48965			0.246258
$926$	−14.0522	−	43.2483i	−0.461785	−	1.42123i
$927$	39.1100	+	28.4151i	1.28454	+	0.933275i
$928$	−103.492	+	75.1914i	−3.39729	+	2.46828i
$929$	15.8651	−	48.8279i	0.520519	−	1.60199i	−0.252492	−	0.967599i	$-0.581250\pi$
$929$	15.8651	−	48.8279i	0.520519	−	1.60199i	0.773011	−	0.634393i	$-0.218750\pi$
$930$	0.186703	−	0.574613i	0.00612223	−	0.0188423i
$931$	−6.42350	+	4.66695i	−0.210522	+	0.152953i
$932$	9.45826	+	6.87182i	0.309815	+	0.225094i
$933$	−0.693059	−	2.13302i	−0.0226897	−	0.0698318i
$934$	10.1570			0.332346
$935$		0			0
$936$	−15.3120			−0.500488
$937$	11.0786	+	34.0964i	0.361922	+	1.11388i	0.951886	+	0.306451i	$0.0991416\pi$
$937$	11.0786	+	34.0964i	0.361922	+	1.11388i	−0.589965	+	0.807429i	$0.700858\pi$
$938$	−3.72030	−	2.70296i	−0.121472	−	0.0882547i
$939$	−4.63445	+	3.36712i	−0.151239	+	0.109882i
$940$	−11.5750	+	35.6243i	−0.377536	+	1.16194i
$941$	0.187638	−	0.577491i	0.00611683	−	0.0188257i	−0.947952	−	0.318415i	$-0.896850\pi$
$941$	0.187638	−	0.577491i	0.00611683	−	0.0188257i	0.954068	+	0.299589i	$0.0968496\pi$
$942$	−2.76647	+	2.00995i	−0.0901363	+	0.0654879i
$943$	−38.8904	−	28.2555i	−1.26645	−	0.920126i
$944$	−30.9863	−	95.3659i	−1.00852	−	3.10389i
$945$	−2.91616			−0.0948628
$946$		0			0
$947$	−26.3851			−0.857401			−0.428701	−	0.903447i	$-0.641028\pi$
$947$	−26.3851			−0.857401			−0.428701	+	0.903447i	$0.641028\pi$
$948$	1.67473	+	5.15429i	0.0543927	+	0.167403i
$949$	0.461513	+	0.335309i	0.0149814	+	0.0108846i
$950$	11.0044	−	7.99518i	0.357031	−	0.259398i
$951$	−0.324288	+	0.998056i	−0.0105158	+	0.0323642i
$952$	−16.8642	+	51.9028i	−0.546573	+	1.68218i
$953$	−28.6064	+	20.7837i	−0.926651	+	0.673252i	−0.945171	−	0.326577i	$-0.894105\pi$
$953$	−28.6064	+	20.7837i	−0.926651	+	0.673252i	0.0185193	+	0.999829i	$0.494105\pi$
$954$	−29.7580	−	21.6205i	−0.963451	−	0.699988i
$955$	0.852636	+	2.62414i	0.0275906	+	0.0849153i
$956$	132.457			4.28398
$957$		0			0
$958$	−3.47093			−0.112141
$959$	6.36582	+	19.5920i	0.205563	+	0.632658i
$960$	−5.60042	−	4.06894i	−0.180753	−	0.131325i
$961$	24.1970	−	17.5802i	0.780550	−	0.567103i
$962$	3.39279	−	10.4419i	0.109388	−	0.336662i
$963$	9.32574	−	28.7017i	0.300518	−	0.924899i
$964$	−64.9787	+	47.2098i	−2.09282	+	1.52052i
$965$	−9.54932	−	6.93799i	−0.307403	−	0.223342i
$966$	1.88310	+	5.79558i	0.0605877	+	0.186470i
$967$	3.86872			0.124410			0.0622048	−	0.998063i	$-0.480187\pi$
$967$	3.86872			0.124410			0.0622048	+	0.998063i	$0.480187\pi$
$968$		0			0
$969$	−2.52907			−0.0812455
$970$	−4.03673	−	12.4238i	−0.129612	−	0.398904i
$971$	−19.5034	−	14.1701i	−0.625895	−	0.454739i	0.229081	−	0.973407i	$-0.426428\pi$
$971$	−19.5034	−	14.1701i	−0.625895	−	0.454739i	−0.854976	+	0.518668i	$0.826428\pi$
$972$	24.9758	−	18.1460i	0.801098	−	0.582032i
$973$	12.1094	−	37.2688i	0.388209	−	1.19478i
$974$	18.3229	−	56.3922i	0.587105	−	1.80692i
$975$	0.0910617	−	0.0661602i	0.00291631	−	0.00211882i
$976$	85.5708	+	62.1708i	2.73905	+	1.99004i
$977$	3.34180	+	10.2850i	0.106914	+	0.329047i	0.990175	−	0.139835i	$-0.0446571\pi$
$977$	3.34180	+	10.2850i	0.106914	+	0.329047i	−0.883261	+	0.468881i	$0.844657\pi$
$978$	−13.5939			−0.434685
$979$		0			0
$980$	8.86675			0.283238
$981$	−11.0438	−	33.9893i	−0.352601	−	1.08520i
$982$	56.7080	+	41.2007i	1.80962	+	1.31477i
$983$	31.3158	−	22.7522i	0.998818	−	0.725684i	0.0369838	−	0.999316i	$-0.488225\pi$
$983$	31.3158	−	22.7522i	0.998818	−	0.725684i	0.961834	+	0.273632i	$0.0882250\pi$
$984$	6.69805	−	20.6145i	0.213526	−	0.657166i
$985$	−2.01181	+	6.19171i	−0.0641015	+	0.197284i
$986$	29.5192	−	21.4469i	0.940081	−	0.683009i
$987$	2.68127	+	1.94806i	0.0853458	+	0.0620074i
$988$	−4.52606	−	13.9298i	−0.143993	−	0.443165i
$989$	19.6022			0.623314
$990$		0			0
$991$	61.4533			1.95213			0.976064	−	0.217485i	$-0.0697854\pi$
$991$	61.4533			1.95213			0.976064	+	0.217485i	$0.0697854\pi$
$992$	7.52076	+	23.1465i	0.238784	+	0.734902i
$993$	1.28813	+	0.935878i	0.0408774	+	0.0296992i
$994$	−23.3921	+	16.9953i	−0.741951	+	0.539059i
$995$	−7.40362	+	22.7860i	−0.234710	+	0.722364i
$996$	4.90248	−	15.0883i	0.155341	−	0.478091i
$997$	−31.0158	+	22.5343i	−0.982281	+	0.713669i	−0.958217	−	0.286041i	$-0.907661\pi$
$997$	−31.0158	+	22.5343i	−0.982281	+	0.713669i	−0.0240639	+	0.999710i	$0.507661\pi$
$998$	−54.0972	−	39.3039i	−1.71242	−	1.24414i
$999$	2.90501	+	8.94071i	0.0919105	+	0.282871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.p.511.3		12
11.2	odd	10		605.2.g.o.251.1		12
11.3	even	5		605.2.a.g.1.3	✓	3
11.4	even	5	inner	605.2.g.p.366.1		12
11.5	even	5	inner	605.2.g.p.81.1		12
11.6	odd	10		605.2.g.o.81.3		12
11.7	odd	10		605.2.g.o.366.3		12
11.8	odd	10		605.2.a.h.1.1	yes	3
11.9	even	5	inner	605.2.g.p.251.3		12
11.10	odd	2		605.2.g.o.511.1		12
33.8	even	10		5445.2.a.bb.1.3		3
33.14	odd	10		5445.2.a.bd.1.1		3
44.3	odd	10		9680.2.a.bz.1.2		3
44.19	even	10		9680.2.a.cb.1.2		3
55.14	even	10		3025.2.a.u.1.1		3
55.19	odd	10		3025.2.a.p.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.3	✓	3	11.3	even	5
605.2.a.h.1.1	yes	3	11.8	odd	10
605.2.g.o.81.3		12	11.6	odd	10
605.2.g.o.251.1		12	11.2	odd	10
605.2.g.o.366.3		12	11.7	odd	10
605.2.g.o.511.1		12	11.10	odd	2
605.2.g.p.81.1		12	11.5	even	5	inner
605.2.g.p.251.3		12	11.9	even	5	inner
605.2.g.p.366.1		12	11.4	even	5	inner
605.2.g.p.511.3		12	1.1	even	1	trivial
3025.2.a.p.1.3		3	55.19	odd	10
3025.2.a.u.1.1		3	55.14	even	10
5445.2.a.bb.1.3		3	33.8	even	10
5445.2.a.bd.1.1		3	33.14	odd	10
9680.2.a.bz.1.2		3	44.3	odd	10
9680.2.a.cb.1.2		3	44.19	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)

\(f(q)\)	\(=\)	\(q+(0.848198 + 2.61048i) q^{2} +(0.170505 + 0.123879i) q^{3} +(-4.47716 + 3.25284i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.178763 + 0.550175i) q^{6} +(-1.87960 + 1.36561i) q^{7} +(-7.84779 - 5.70176i) q^{8} +(-0.913325 - 2.81093i) q^{9} +O(q^{10})\)	\(q+(0.848198 + 2.61048i) q^{2} +(0.170505 + 0.123879i) q^{3} +(-4.47716 + 3.25284i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.178763 + 0.550175i) q^{6} +(-1.87960 + 1.36561i) q^{7} +(-7.84779 - 5.70176i) q^{8} +(-0.913325 - 2.81093i) q^{9} -2.74483 q^{10} -1.16634 q^{12} +(0.165037 + 0.507931i) q^{13} +(-5.15918 - 3.74836i) q^{14} +(-0.170505 + 0.123879i) q^{15} +(4.80762 - 14.7963i) q^{16} +(-0.748288 + 2.30299i) q^{17} +(6.56320 - 4.76844i) q^{18} +(4.00915 + 2.91282i) q^{19} +(-1.71012 - 5.26321i) q^{20} -0.489652 q^{21} -4.53407 q^{23} +(-0.631760 - 1.94436i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-1.18596 + 0.861652i) q^{26} +(0.387870 - 1.19374i) q^{27} +(3.97315 - 12.2281i) q^{28} +(-4.44122 + 3.22674i) q^{29} +(-0.468007 - 0.340027i) q^{30} +(0.322743 + 0.993301i) q^{31} +23.3026 q^{32} -6.64663 q^{34} +(-0.717944 - 2.20960i) q^{35} +(13.2326 + 9.61405i) q^{36} +(-6.05926 + 4.40231i) q^{37} +(-4.20331 + 12.9365i) q^{38} +(-0.0347825 + 0.107049i) q^{39} +(7.84779 - 5.70176i) q^{40} +(8.57737 + 6.23182i) q^{41} +(-0.415322 - 1.27823i) q^{42} -4.32331 q^{43} +2.95558 q^{45} +(-3.84579 - 11.8361i) q^{46} +(-5.47587 - 3.97845i) q^{47} +(2.65268 - 1.92729i) q^{48} +(-0.495110 + 1.52379i) q^{49} +(0.848198 - 2.61048i) q^{50} +(-0.412880 + 0.299975i) q^{51} +(-2.39112 - 1.73725i) q^{52} +(-1.40110 - 4.31216i) q^{53} +3.44523 q^{54} +22.5371 q^{56} +(0.322743 + 0.993301i) q^{57} +(-12.1904 - 8.85683i) q^{58} +(5.21430 - 3.78841i) q^{59} +(0.360418 - 1.10925i) q^{60} +(-2.10088 + 6.46586i) q^{61} +(-2.31925 + 1.68503i) q^{62} +(5.55531 + 4.03617i) q^{63} +(10.1500 + 31.2385i) q^{64} -0.534070 q^{65} +0.721104 q^{67} +(-4.14108 - 12.7449i) q^{68} +(-0.773082 - 0.561677i) q^{69} +(5.15918 - 3.74836i) q^{70} +(1.40110 - 4.31216i) q^{71} +(-8.85963 + 27.2671i) q^{72} +(0.864144 - 0.627837i) q^{73} +(-16.6316 - 12.0836i) q^{74} +(-0.0651271 - 0.200441i) q^{75} -27.4245 q^{76} -0.308953 q^{78} +(-1.43589 - 4.41921i) q^{79} +(12.5865 + 9.14464i) q^{80} +(-6.95933 + 5.05625i) q^{81} +(-8.99277 + 27.6769i) q^{82} +(-4.20331 + 12.9365i) q^{83} +(2.19225 - 1.59276i) q^{84} +(-1.95904 - 1.42333i) q^{85} +(-3.66703 - 11.2859i) q^{86} -1.15698 q^{87} +12.7148 q^{89} +(2.50692 + 7.71550i) q^{90} +(-1.00384 - 0.729332i) q^{91} +(20.2997 - 14.7486i) q^{92} +(-0.0680200 + 0.209344i) q^{93} +(5.74107 - 17.6692i) q^{94} +(-4.00915 + 2.91282i) q^{95} +(3.97322 + 2.88671i) q^{96} +(1.47067 + 4.52626i) q^{97} -4.39779 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

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