LMFDB - Embedded newform 210.3.e.a.71.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(71,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.e (of order $2$, degree $1$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 34 x^{14} - 80 x^{13} + 97 x^{12} - 80 x^{11} + 498 x^{10} - 3288 x^{9} + \cdots + 43046721 $ x^16 - 8x^15 + 34x^14 - 80x^13 + 97x^12 - 80x^11 + 498x^10 - 3288x^9 + 11844x^8 - 29592x^7 + 40338x^6 - 58320x^5 + 636417x^4 - 4723920x^3 + 18068994x^2 - 38263752*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.6
Root			$-0.650833 - 2.92855i$ of defining polynomial
Character	$\chi$	$=$	210.71
Dual form			210.3.e.a.71.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(0.650833 + 2.92855i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(4.14160 - 0.920417i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(-8.15283 + 3.81200i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(0.650833 + 2.92855i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(4.14160 - 0.920417i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(-8.15283 + 3.81200i) q^{9} +3.16228 q^{10} +7.97556i q^{11} +(-1.30167 - 5.85710i) q^{12} -5.79363 q^{13} +3.74166i q^{14} +(-6.54844 + 1.45531i) q^{15} +4.00000 q^{16} +9.35782i q^{17} +(5.39098 + 11.5298i) q^{18} -22.7979 q^{19} -4.47214i q^{20} +(-1.72194 - 7.74822i) q^{21} +11.2792 q^{22} +34.9882i q^{23} +(-8.28320 + 1.84083i) q^{24} -5.00000 q^{25} +8.19343i q^{26} +(-16.4698 - 21.3950i) q^{27} +5.29150 q^{28} +15.5858i q^{29} +(2.05811 + 9.26089i) q^{30} +25.5869 q^{31} -5.65685i q^{32} +(-23.3569 + 5.19076i) q^{33} +13.2340 q^{34} -5.91608i q^{35} +(16.3057 - 7.62399i) q^{36} +38.4908 q^{37} +32.2412i q^{38} +(-3.77068 - 16.9669i) q^{39} -6.32456 q^{40} -35.1062i q^{41} +(-10.9576 + 2.43519i) q^{42} +59.0951 q^{43} -15.9511i q^{44} +(-8.52388 - 18.2303i) q^{45} +49.4808 q^{46} -1.03517i q^{47} +(2.60333 + 11.7142i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(-27.4049 + 6.09038i) q^{51} +11.5873 q^{52} -41.5179i q^{53} +(-30.2571 + 23.2918i) q^{54} -17.8339 q^{55} -7.48331i q^{56} +(-14.8377 - 66.7650i) q^{57} +22.0417 q^{58} +55.1602i q^{59} +(13.0969 - 2.91061i) q^{60} -94.7726 q^{61} -36.1853i q^{62} +(21.5704 - 10.0856i) q^{63} -8.00000 q^{64} -12.9549i q^{65} +(7.34084 + 33.0316i) q^{66} +77.1064 q^{67} -18.7156i q^{68} +(-102.465 + 22.7715i) q^{69} -8.36660 q^{70} +18.0046i q^{71} +(-10.7820 - 23.0597i) q^{72} +33.2022 q^{73} -54.4342i q^{74} +(-3.25416 - 14.6428i) q^{75} +45.5959 q^{76} -21.1014i q^{77} +(-23.9949 + 5.33255i) q^{78} -54.9427 q^{79} +8.94427i q^{80} +(51.9374 - 62.1571i) q^{81} -49.6477 q^{82} -78.6593i q^{83} +(3.44388 + 15.4964i) q^{84} -20.9247 q^{85} -83.5731i q^{86} +(-45.6439 + 10.1438i) q^{87} -22.5583 q^{88} -120.028i q^{89} +(-25.7815 + 12.0546i) q^{90} +15.3285 q^{91} -69.9764i q^{92} +(16.6528 + 74.9326i) q^{93} -1.46395 q^{94} -50.9777i q^{95} +(16.5664 - 3.68167i) q^{96} +24.5127 q^{97} -9.89949i q^{98} +(-30.4028 - 65.0234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9	$ 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9 + 16 * q^12 - 20 * q^15 + 64 * q^16 - 32 * q^18 + 48 * q^19 + 28 * q^21 - 96 * q^22 - 32 * q^24 - 80 * q^25 + 64 * q^27 - 88 * q^33 + 160 * q^34 + 8 * q^36 + 80 * q^37 + 156 * q^39 - 336 * q^43 - 80 * q^45 + 32 * q^46 - 32 * q^48 + 112 * q^49 + 84 * q^51 - 32 * q^54 - 80 * q^55 - 264 * q^57 + 96 * q^58 + 40 * q^60 + 112 * q^61 + 112 * q^63 - 128 * q^64 + 240 * q^67 + 8 * q^69 + 64 * q^72 + 48 * q^73 + 40 * q^75 - 96 * q^76 + 208 * q^78 + 8 * q^79 - 124 * q^81 - 608 * q^82 - 56 * q^84 + 120 * q^85 - 120 * q^87 + 192 * q^88 + 160 * q^90 - 56 * q^91 + 104 * q^93 + 32 * q^94 + 64 * q^96 - 192 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	0.650833	+	2.92855i	0.216944	+	0.976184i
$3$	0.650833	+	2.92855i	0.216944	+	0.976184i
$4$	−2.00000			−0.500000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	4.14160	−	0.920417i	0.690266	−	0.153403i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$			2.82843i			0.353553i
$9$	−8.15283	+	3.81200i	−0.905870	+	0.423555i
$10$	3.16228			0.316228
$11$			7.97556i			0.725051i	0.931974	+	0.362526i	$0.118085\pi$
$11$			7.97556i			0.725051i	−0.931974	+	0.362526i	$0.881915\pi$
$12$	−1.30167	−	5.85710i	−0.108472	−	0.488092i
$13$	−5.79363			−0.445664			−0.222832	−	0.974857i	$-0.571530\pi$
$13$	−5.79363			−0.445664			−0.222832	+	0.974857i	$0.571530\pi$
$14$			3.74166i			0.267261i
$15$	−6.54844	+	1.45531i	−0.436563	+	0.0970204i
$16$	4.00000			0.250000
$17$			9.35782i			0.550460i	0.961378	+	0.275230i	$0.0887541\pi$
$17$			9.35782i			0.550460i	−0.961378	+	0.275230i	$0.911246\pi$
$18$	5.39098	+	11.5298i	0.299499	+	0.640547i
$19$	−22.7979			−1.19989			−0.599946	−	0.800041i	$-0.704811\pi$
$19$	−22.7979			−1.19989			−0.599946	+	0.800041i	$0.704811\pi$
$20$		−	4.47214i		−	0.223607i
$21$	−1.72194	−	7.74822i	−0.0819972	−	0.368963i
$22$	11.2792			0.512689
$23$			34.9882i			1.52123i	0.649205	+	0.760613i	$0.275102\pi$
$23$			34.9882i			1.52123i	−0.649205	+	0.760613i	$0.724898\pi$
$24$	−8.28320	+	1.84083i	−0.345133	+	0.0767014i
$25$	−5.00000			−0.200000
$26$			8.19343i			0.315132i
$27$	−16.4698	−	21.3950i	−0.609991	−	0.792408i
$28$	5.29150			0.188982
$29$			15.5858i			0.537442i	0.963218	+	0.268721i	$0.0866010\pi$
$29$			15.5858i			0.537442i	−0.963218	+	0.268721i	$0.913399\pi$
$30$	2.05811	+	9.26089i	0.0686038	+	0.308696i
$31$	25.5869			0.825384			0.412692	−	0.910871i	$-0.364589\pi$
$31$	25.5869			0.825384			0.412692	+	0.910871i	$0.364589\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−23.3569	+	5.19076i	−0.707783	+	0.157296i
$34$	13.2340			0.389234
$35$		−	5.91608i		−	0.169031i
$36$	16.3057	−	7.62399i	0.452935	−	0.211778i
$37$	38.4908			1.04029			0.520145	−	0.854078i	$-0.325878\pi$
$37$	38.4908			1.04029			0.520145	+	0.854078i	$0.325878\pi$
$38$			32.2412i			0.848451i
$39$	−3.77068	−	16.9669i	−0.0966842	−	0.435050i
$40$	−6.32456			−0.158114
$41$		−	35.1062i		−	0.856249i	−0.903720	−	0.428125i	$-0.859174\pi$
$41$		−	35.1062i		−	0.856249i	0.903720	−	0.428125i	$-0.140826\pi$
$42$	−10.9576	+	2.43519i	−0.260896	+	0.0579808i
$43$	59.0951			1.37431			0.687153	−	0.726513i	$-0.258860\pi$
$43$	59.0951			1.37431			0.687153	+	0.726513i	$0.258860\pi$
$44$		−	15.9511i		−	0.362526i
$45$	−8.52388	−	18.2303i	−0.189420	−	0.405118i
$46$	49.4808			1.07567
$47$		−	1.03517i		−	0.0220249i	−0.999939	−	0.0110124i	$-0.996495\pi$
$47$		−	1.03517i		−	0.0220249i	0.999939	−	0.0110124i	$-0.00350544\pi$
$48$	2.60333	+	11.7142i	0.0542361	+	0.244046i
$49$	7.00000			0.142857
$50$			7.07107i			0.141421i
$51$	−27.4049	+	6.09038i	−0.537351	+	0.119419i
$52$	11.5873			0.222832
$53$		−	41.5179i		−	0.783357i	−0.920102	−	0.391679i	$-0.871895\pi$
$53$		−	41.5179i		−	0.783357i	0.920102	−	0.391679i	$-0.128105\pi$
$54$	−30.2571	+	23.2918i	−0.560317	+	0.431329i
$55$	−17.8339			−0.324253
$56$		−	7.48331i		−	0.133631i
$57$	−14.8377	−	66.7650i	−0.260310	−	1.17131i
$58$	22.0417			0.380029
$59$			55.1602i			0.934919i	0.884014	+	0.467460i	$0.154831\pi$
$59$			55.1602i			0.934919i	−0.884014	+	0.467460i	$0.845169\pi$
$60$	13.0969	−	2.91061i	0.218281	−	0.0485102i
$61$	−94.7726			−1.55365			−0.776824	−	0.629717i	$-0.783171\pi$
$61$	−94.7726			−1.55365			−0.776824	+	0.629717i	$0.783171\pi$
$62$		−	36.1853i		−	0.583635i
$63$	21.5704	−	10.0856i	0.342387	−	0.160089i
$64$	−8.00000			−0.125000
$65$		−	12.9549i		−	0.199307i
$66$	7.34084	+	33.0316i	0.111225	+	0.500478i
$67$	77.1064			1.15084			0.575421	−	0.817857i	$-0.304838\pi$
$67$	77.1064			1.15084			0.575421	+	0.817857i	$0.304838\pi$
$68$		−	18.7156i		−	0.275230i
$69$	−102.465	+	22.7715i	−1.48500	+	0.330021i
$70$	−8.36660			−0.119523
$71$			18.0046i			0.253586i	0.991929	+	0.126793i	$0.0404684\pi$
$71$			18.0046i			0.253586i	−0.991929	+	0.126793i	$0.959532\pi$
$72$	−10.7820	−	23.0597i	−0.149749	−	0.320274i
$73$	33.2022			0.454825			0.227412	−	0.973799i	$-0.426973\pi$
$73$	33.2022			0.454825			0.227412	+	0.973799i	$0.426973\pi$
$74$		−	54.4342i		−	0.735597i
$75$	−3.25416	−	14.6428i	−0.0433889	−	0.195237i
$76$	45.5959			0.599946
$77$		−	21.1014i		−	0.274044i
$78$	−23.9949	+	5.33255i	−0.307627	+	0.0683660i
$79$	−54.9427			−0.695478			−0.347739	−	0.937591i	$-0.613050\pi$
$79$	−54.9427			−0.695478			−0.347739	+	0.937591i	$0.613050\pi$
$80$			8.94427i			0.111803i
$81$	51.9374	−	62.1571i	0.641202	−	0.767372i
$82$	−49.6477			−0.605460
$83$		−	78.6593i		−	0.947703i	−0.880605	−	0.473851i	$-0.842863\pi$
$83$		−	78.6593i		−	0.947703i	0.880605	−	0.473851i	$-0.157137\pi$
$84$	3.44388	+	15.4964i	0.0409986	+	0.184481i
$85$	−20.9247			−0.246173
$86$		−	83.5731i		−	0.971781i
$87$	−45.6439	+	10.1438i	−0.524643	+	0.116595i
$88$	−22.5583			−0.256344
$89$		−	120.028i		−	1.34863i	−0.738442	−	0.674317i	$-0.764438\pi$
$89$		−	120.028i		−	1.34863i	0.738442	−	0.674317i	$-0.235562\pi$
$90$	−25.7815	+	12.0546i	−0.286461	+	0.133940i
$91$	15.3285			0.168445
$92$		−	69.9764i		−	0.760613i
$93$	16.6528	+	74.9326i	0.179062	+	0.805727i
$94$	−1.46395			−0.0155739
$95$		−	50.9777i		−	0.536608i
$96$	16.5664	−	3.68167i	0.172567	−	0.0383507i
$97$	24.5127			0.252708			0.126354	−	0.991985i	$-0.459672\pi$
$97$	24.5127			0.252708			0.126354	+	0.991985i	$0.459672\pi$
$98$		−	9.89949i		−	0.101015i
$99$	−30.4028	−	65.0234i	−0.307099	−	0.656802i
$100$	10.0000			0.100000
$101$			158.695i			1.57124i	0.618709	+	0.785620i	$0.287656\pi$
$101$			158.695i			1.57124i	−0.618709	+	0.785620i	$0.712344\pi$
$102$	8.61310	+	38.7563i	0.0844421	+	0.379964i
$103$	177.505			1.72335			0.861674	−	0.507461i	$-0.169416\pi$
$103$	177.505			1.72335			0.861674	+	0.507461i	$0.169416\pi$
$104$		−	16.3869i		−	0.157566i
$105$	17.3255	−	3.85038i	0.165005	−	0.0366703i
$106$	−58.7152			−0.553917
$107$			210.992i			1.97189i	0.167064	+	0.985946i	$0.446571\pi$
$107$			210.992i			1.97189i	−0.167064	+	0.985946i	$0.553429\pi$
$108$	32.9395	+	42.7900i	0.304996	+	0.396204i
$109$	−98.5237			−0.903887			−0.451943	−	0.892047i	$-0.649269\pi$
$109$	−98.5237			−0.903887			−0.451943	+	0.892047i	$0.649269\pi$
$110$			25.2209i			0.229281i
$111$	25.0511	+	112.722i	0.225685	+	1.01552i
$112$	−10.5830			−0.0944911
$113$		−	102.830i		−	0.910000i	−0.890492	−	0.455000i	$-0.849639\pi$
$113$		−	102.830i		−	0.910000i	0.890492	−	0.455000i	$-0.150361\pi$
$114$	−94.4199	+	20.9836i	−0.828245	+	0.184067i
$115$	−78.2360			−0.680313
$116$		−	31.1717i		−	0.268721i
$117$	47.2345	−	22.0853i	0.403713	−	0.188763i
$118$	78.0084			0.661088
$119$		−	24.7585i		−	0.208054i
$120$	−4.11623	−	18.5218i	−0.0343019	−	0.154348i
$121$	57.3904			0.474301
$122$			134.029i			1.09860i
$123$	102.810	−	22.8483i	0.835857	−	0.185758i
$124$	−51.1738			−0.412692
$125$		−	11.1803i		−	0.0894427i
$126$	−14.2632	−	30.5051i	−0.113200	−	0.242104i
$127$	157.688			1.24164			0.620819	−	0.783954i	$-0.286800\pi$
$127$	157.688			1.24164			0.620819	+	0.783954i	$0.286800\pi$
$128$			11.3137i			0.0883883i
$129$	38.4611	+	173.063i	0.298148	+	1.34158i
$130$	−18.3211			−0.140931
$131$			250.120i			1.90932i	0.297705	+	0.954658i	$0.403779\pi$
$131$			250.120i			1.90932i	−0.297705	+	0.954658i	$0.596221\pi$
$132$	46.7137	−	10.3815i	0.353892	−	0.0786479i
$133$	60.3177			0.453516
$134$		−	109.045i		−	0.813768i
$135$	47.8407	−	36.8275i	0.354376	−	0.272796i
$136$	−26.4679			−0.194617
$137$			191.896i			1.40070i	0.713800	+	0.700350i	$0.246973\pi$
$137$			191.896i			1.40070i	−0.713800	+	0.700350i	$0.753027\pi$
$138$	32.2037	+	144.907i	0.233360	+	1.05005i
$139$	21.4645			0.154421			0.0772103	−	0.997015i	$-0.475399\pi$
$139$	21.4645			0.154421			0.0772103	+	0.997015i	$0.475399\pi$
$140$			11.8322i			0.0845154i
$141$	3.03155	−	0.673722i	0.0215003	−	0.00477817i
$142$	25.4624			0.179313
$143$		−	46.2074i		−	0.323129i
$144$	−32.6113	+	15.2480i	−0.226468	+	0.105889i
$145$	−34.8510			−0.240352
$146$		−	46.9550i		−	0.321610i
$147$	4.55583	+	20.4999i	0.0309920	+	0.139455i
$148$	−76.9815			−0.520145
$149$			66.8671i			0.448772i	0.974500	+	0.224386i	$0.0720377\pi$
$149$			66.8671i			0.448772i	−0.974500	+	0.224386i	$0.927962\pi$
$150$	−20.7080	+	4.60208i	−0.138053	+	0.0306806i
$151$	−64.4712			−0.426962			−0.213481	−	0.976947i	$-0.568480\pi$
$151$	−64.4712			−0.426962			−0.213481	+	0.976947i	$0.568480\pi$
$152$		−	64.4823i		−	0.424226i
$153$	−35.6720	−	76.2928i	−0.233150	−	0.498646i
$154$	−29.8418			−0.193778
$155$			57.2141i			0.369123i
$156$	7.54137	+	33.9339i	0.0483421	+	0.217525i
$157$	−207.257			−1.32011			−0.660056	−	0.751217i	$-0.729467\pi$
$157$	−207.257			−1.32011			−0.660056	+	0.751217i	$0.729467\pi$
$158$			77.7008i			0.491777i
$159$	121.587	−	27.0212i	0.764701	−	0.169945i
$160$	12.6491			0.0790569
$161$		−	92.5701i		−	0.574970i
$162$	−87.9035	−	73.4505i	−0.542614	−	0.453398i
$163$	236.067			1.44826			0.724132	−	0.689662i	$-0.242241\pi$
$163$	236.067			1.44826			0.724132	+	0.689662i	$0.242241\pi$
$164$			70.2124i			0.428125i
$165$	−11.6069	−	52.2275i	−0.0703448	−	0.316530i
$166$	−111.241			−0.670127
$167$			109.647i			0.656568i	0.944579	+	0.328284i	$0.106470\pi$
$167$			109.647i			0.656568i	−0.944579	+	0.328284i	$0.893530\pi$
$168$	21.9153	−	4.87039i	0.130448	−	0.0289904i
$169$	−135.434			−0.801384
$170$			29.5920i			0.174071i
$171$	185.868	−	86.9057i	1.08695	−	0.508220i
$172$	−118.190			−0.687153
$173$			46.7105i			0.270003i	0.990845	+	0.135001i	$0.0431039\pi$
$173$			46.7105i			0.270003i	−0.990845	+	0.135001i	$0.956896\pi$
$174$	14.3455	+	64.5502i	0.0824452	+	0.370978i
$175$	13.2288			0.0755929
$176$			31.9023i			0.181263i
$177$	−161.540	+	35.9001i	−0.912653	+	0.202825i
$178$	−169.746			−0.953629
$179$		−	293.828i		−	1.64150i	−0.571289	−	0.820749i	$-0.693556\pi$
$179$		−	293.828i		−	1.64150i	0.571289	−	0.820749i	$-0.306444\pi$
$180$	17.0478	+	36.4606i	0.0947098	+	0.202559i
$181$	−129.626			−0.716168			−0.358084	−	0.933689i	$-0.616570\pi$
$181$	−129.626			−0.716168			−0.358084	+	0.933689i	$0.616570\pi$
$182$		−	21.6778i		−	0.119109i
$183$	−61.6811	−	277.546i	−0.337055	−	1.51665i
$184$	−98.9616			−0.537835
$185$			86.0680i			0.465232i
$186$	105.971	−	23.5506i	0.569735	−	0.126616i
$187$	−74.6339			−0.399112
$188$			2.07034i			0.0110124i
$189$	43.5749	+	56.6059i	0.230555	+	0.299502i
$190$	−72.0934			−0.379439
$191$			7.24400i			0.0379267i	0.999820	+	0.0189633i	$0.00603658\pi$
$191$			7.24400i			0.0379267i	−0.999820	+	0.0189633i	$0.993963\pi$
$192$	−5.20666	−	23.4284i	−0.0271180	−	0.122023i
$193$	−313.671			−1.62524			−0.812620	−	0.582793i	$-0.801960\pi$
$193$	−313.671			−1.62524			−0.812620	+	0.582793i	$0.801960\pi$
$194$		−	34.6662i		−	0.178692i
$195$	37.9392	−	8.43150i	0.194560	−	0.0432385i
$196$	−14.0000			−0.0714286
$197$			94.5137i			0.479765i	0.970802	+	0.239882i	$0.0771089\pi$
$197$			94.5137i			0.479765i	−0.970802	+	0.239882i	$0.922891\pi$
$198$	−91.9570	+	42.9961i	−0.464429	+	0.217152i
$199$	−185.816			−0.933747			−0.466874	−	0.884324i	$-0.654620\pi$
$199$	−185.816			−0.933747			−0.466874	+	0.884324i	$0.654620\pi$
$200$		−	14.1421i		−	0.0707107i
$201$	50.1834	+	225.810i	0.249669	+	1.12343i
$202$	224.429			1.11104
$203$		−	41.2362i		−	0.203134i
$204$	54.8098	−	12.1808i	0.268675	−	0.0597096i
$205$	78.4999			0.382926
$206$		−	251.030i		−	1.21859i
$207$	−133.375	−	285.253i	−0.644323	−	1.37803i
$208$	−23.1745			−0.111416
$209$		−	181.826i		−	0.869983i
$210$	−5.44526	−	24.5020i	−0.0259298	−	0.116676i
$211$	375.709			1.78061			0.890306	−	0.455363i	$-0.150491\pi$
$211$	375.709			1.78061			0.890306	+	0.455363i	$0.150491\pi$
$212$			83.0359i			0.391679i
$213$	−52.7275	+	11.7180i	−0.247547	+	0.0550141i
$214$	298.388			1.39434
$215$			132.141i			0.614608i
$216$	60.5143	−	46.5835i	0.280159	−	0.215664i
$217$	−67.6966			−0.311966
$218$			139.334i			0.639145i
$219$	21.6091	+	97.2344i	0.0986717	+	0.443993i
$220$	35.6678			0.162126
$221$		−	54.2158i		−	0.245320i
$222$	159.413	−	35.4275i	0.718078	−	0.159584i
$223$	−19.6107			−0.0879404			−0.0439702	−	0.999033i	$-0.514001\pi$
$223$	−19.6107			−0.0879404			−0.0439702	+	0.999033i	$0.514001\pi$
$224$			14.9666i			0.0668153i
$225$	40.7642	−	19.0600i	0.181174	−	0.0847110i
$226$	−145.424			−0.643467
$227$			250.934i			1.10543i	0.833369	+	0.552717i	$0.186409\pi$
$227$			250.934i			1.10543i	−0.833369	+	0.552717i	$0.813591\pi$
$228$	29.6753	+	133.530i	0.130155	+	0.585657i
$229$	296.680			1.29555			0.647773	−	0.761833i	$-0.275701\pi$
$229$	296.680			1.29555			0.647773	+	0.761833i	$0.275701\pi$
$230$			110.642i			0.481054i
$231$	61.7964	−	13.7335i	0.267517	−	0.0594522i
$232$	−44.0834			−0.190015
$233$		−	157.483i		−	0.675891i	−0.941166	−	0.337946i	$-0.890268\pi$
$233$		−	157.483i		−	0.675891i	0.941166	−	0.337946i	$-0.109732\pi$
$234$	−31.2333	−	66.7996i	−0.133476	−	0.285469i
$235$	2.31471			0.00984983
$236$		−	110.320i		−	0.467460i
$237$	−35.7586	−	160.903i	−0.150880	−	0.678914i
$238$	−35.0138			−0.147117
$239$		−	78.7765i		−	0.329609i	−0.986326	−	0.164804i	$-0.947301\pi$
$239$		−	78.7765i		−	0.329609i	0.986326	−	0.164804i	$-0.0526993\pi$
$240$	−26.1938	+	5.82123i	−0.109141	+	0.0242551i
$241$	−148.348			−0.615553			−0.307777	−	0.951459i	$-0.599585\pi$
$241$	−148.348			−0.615553			−0.307777	+	0.951459i	$0.599585\pi$
$242$		−	81.1623i		−	0.335381i
$243$	215.833	+	111.647i	0.888201	+	0.459454i
$244$	189.545			0.776824
$245$			15.6525i			0.0638877i
$246$	−32.3124	−	145.396i	−0.131351	−	0.591040i
$247$	132.083			0.534748
$248$			72.3707i			0.291817i
$249$	230.358	−	51.1941i	0.925132	−	0.205599i
$250$	−15.8114			−0.0632456
$251$		−	223.217i		−	0.889310i	−0.895702	−	0.444655i	$-0.853326\pi$
$251$		−	223.217i		−	0.889310i	0.895702	−	0.444655i	$-0.146674\pi$
$252$	−43.1407	+	20.1712i	−0.171193	+	0.0800444i
$253$	−279.051			−1.10297
$254$		−	223.004i		−	0.877970i
$255$	−13.6185	−	61.2792i	−0.0534059	−	0.240310i
$256$	16.0000			0.0625000
$257$		−	359.930i		−	1.40051i	−0.713894	−	0.700254i	$-0.753070\pi$
$257$		−	359.930i		−	1.40051i	0.713894	−	0.700254i	$-0.246930\pi$
$258$	244.748	−	54.3922i	0.948637	−	0.210822i
$259$	−101.837			−0.393193
$260$			25.9099i			0.0996534i
$261$	−59.4131	−	127.069i	−0.227637	−	0.486853i
$262$	353.724			1.35009
$263$			228.402i			0.868447i	0.900805	+	0.434224i	$0.142977\pi$
$263$			228.402i			0.868447i	−0.900805	+	0.434224i	$0.857023\pi$
$264$	−14.6817	−	66.0632i	−0.0556124	−	0.250239i
$265$	92.8369			0.350328
$266$		−	85.3021i		−	0.320685i
$267$	351.510	−	78.1185i	1.31652	−	0.292579i
$268$	−154.213			−0.575421
$269$			283.528i			1.05401i	0.849863	+	0.527003i	$0.176684\pi$
$269$			283.528i			1.05401i	−0.849863	+	0.527003i	$0.823316\pi$
$270$	−52.0820	−	67.6570i	−0.192896	−	0.250581i
$271$	−290.789			−1.07302			−0.536512	−	0.843893i	$-0.680258\pi$
$271$	−290.789			−1.07302			−0.536512	+	0.843893i	$0.680258\pi$
$272$			37.4313i			0.137615i
$273$	9.97629	+	44.8903i	0.0365432	+	0.164433i
$274$	271.382			0.990444
$275$		−	39.8778i		−	0.145010i
$276$	204.930	−	45.5430i	0.742498	−	0.165011i
$277$	−267.470			−0.965596			−0.482798	−	0.875732i	$-0.660379\pi$
$277$	−267.470			−0.965596			−0.482798	+	0.875732i	$0.660379\pi$
$278$		−	30.3553i		−	0.109192i
$279$	−208.606	+	97.5372i	−0.747691	+	0.349596i
$280$	16.7332			0.0597614
$281$			212.689i			0.756900i	0.925622	+	0.378450i	$0.123543\pi$
$281$			212.689i			0.756900i	−0.925622	+	0.378450i	$0.876457\pi$
$282$	−0.952787	−	4.28725i	−0.00337868	−	0.0152030i
$283$	−249.746			−0.882496			−0.441248	−	0.897385i	$-0.645464\pi$
$283$	−249.746			−0.882496			−0.441248	+	0.897385i	$0.645464\pi$
$284$		−	36.0092i		−	0.126793i
$285$	149.291	−	33.1780i	0.523828	−	0.116414i
$286$	−65.3472			−0.228487
$287$			92.8823i			0.323632i
$288$	21.5639	+	46.1194i	0.0748747	+	0.160137i
$289$	201.431			0.696993
$290$			49.2867i			0.169954i
$291$	15.9537	+	71.7868i	0.0548237	+	0.246690i
$292$	−66.4044			−0.227412
$293$		−	312.196i		−	1.06552i	−0.846268	−	0.532758i	$-0.821156\pi$
$293$		−	312.196i		−	1.06552i	0.846268	−	0.532758i	$-0.178844\pi$
$294$	28.9912	−	6.44292i	0.0986095	−	0.0219147i
$295$	−123.342			−0.418109
$296$			108.868i			0.367798i
$297$	170.637	−	131.356i	0.574537	−	0.442275i
$298$	94.5643			0.317330
$299$		−	202.709i		−	0.677955i
$300$	6.50833	+	29.2855i	0.0216944	+	0.0976184i
$301$	−156.351			−0.519439
$302$			91.1760i			0.301907i
$303$	−464.748	+	103.284i	−1.53382	+	0.340872i
$304$	−91.1918			−0.299973
$305$		−	211.918i		−	0.694813i
$306$	−107.894	+	50.4478i	−0.352596	+	0.164862i
$307$	−155.259			−0.505729			−0.252864	−	0.967502i	$-0.581373\pi$
$307$	−155.259			−0.505729			−0.252864	+	0.967502i	$0.581373\pi$
$308$			42.2027i			0.137022i
$309$	115.526	+	519.832i	0.373871	+	1.68231i
$310$	80.9129			0.261009
$311$		−	338.149i		−	1.08730i	−0.839313	−	0.543649i	$-0.817042\pi$
$311$		−	338.149i		−	1.08730i	0.839313	−	0.543649i	$-0.182958\pi$
$312$	47.9897	−	10.6651i	0.153813	−	0.0341830i
$313$	32.5551			0.104010			0.0520050	−	0.998647i	$-0.483439\pi$
$313$	32.5551			0.104010			0.0520050	+	0.998647i	$0.483439\pi$
$314$			293.106i			0.933460i
$315$	22.5521	+	48.2328i	0.0715939	+	0.153120i
$316$	109.885			0.347739
$317$		−	156.813i		−	0.494679i	−0.968929	−	0.247340i	$-0.920444\pi$
$317$		−	156.813i		−	0.494679i	0.968929	−	0.247340i	$-0.0795563\pi$
$318$	−38.2138	−	171.951i	−0.120169	−	0.540725i
$319$	−124.306			−0.389673
$320$		−	17.8885i		−	0.0559017i
$321$	−617.902	+	137.321i	−1.92493	+	0.427791i
$322$	−130.914			−0.406565
$323$		−	213.339i		−	0.660493i
$324$	−103.875	+	124.314i	−0.320601	+	0.383686i
$325$	28.9681			0.0891327
$326$		−	333.849i		−	1.02408i
$327$	−64.1225	−	288.532i	−0.196093	−	0.882360i
$328$	99.2954			0.302730
$329$			2.73880i			0.00832462i
$330$	−73.8609	+	16.4146i	−0.223821	+	0.0497413i
$331$	62.7666			0.189627			0.0948136	−	0.995495i	$-0.469775\pi$
$331$	62.7666			0.189627			0.0948136	+	0.995495i	$0.469775\pi$
$332$			157.319i			0.473851i
$333$	−313.809	+	146.727i	−0.942369	+	0.440620i
$334$	155.064			0.464263
$335$			172.415i			0.514672i
$336$	−6.88777	−	30.9929i	−0.0204993	−	0.0922407i
$337$	429.763			1.27526			0.637631	−	0.770342i	$-0.279914\pi$
$337$	429.763			1.27526			0.637631	+	0.770342i	$0.279914\pi$
$338$			191.532i			0.566664i
$339$	301.143	−	66.9251i	0.888327	−	0.197419i
$340$	41.8495			0.123087
$341$			204.070i			0.598446i
$342$	−122.903	−	262.857i	−0.359366	−	0.768587i
$343$	−18.5203			−0.0539949
$344$			167.146i			0.485890i
$345$	−50.9186	−	229.118i	−0.147590	−	0.664111i
$346$	66.0586			0.190921
$347$			611.203i			1.76139i	0.473683	+	0.880695i	$0.342924\pi$
$347$			611.203i			1.76139i	−0.473683	+	0.880695i	$0.657076\pi$
$348$	91.2878	−	20.2875i	0.262321	−	0.0582975i
$349$	−229.756			−0.658327			−0.329163	−	0.944273i	$-0.606767\pi$
$349$	−229.756			−0.658327			−0.329163	+	0.944273i	$0.606767\pi$
$350$		−	18.7083i		−	0.0534522i
$351$	95.4197	+	123.955i	0.271851	+	0.353148i
$352$	45.1166			0.128172
$353$		−	434.601i		−	1.23117i	−0.788072	−	0.615583i	$-0.788921\pi$
$353$		−	434.601i		−	1.23117i	0.788072	−	0.615583i	$-0.211079\pi$
$354$	50.7704	+	228.452i	0.143419	+	0.645343i
$355$	−40.2596			−0.113407
$356$			240.057i			0.674317i
$357$	72.5065	−	16.1136i	0.203099	−	0.0451362i
$358$	−415.536			−1.16071
$359$		−	185.884i		−	0.517782i	−0.965907	−	0.258891i	$-0.916643\pi$
$359$		−	185.884i		−	0.517782i	0.965907	−	0.258891i	$-0.0833570\pi$
$360$	51.5630	−	24.1092i	0.143231	−	0.0669699i
$361$	158.746			0.439740
$362$			183.320i			0.506408i
$363$	37.3516	+	168.071i	0.102897	+	0.463005i
$364$	−30.6570			−0.0842225
$365$			74.2424i			0.203404i
$366$	−392.510	+	87.2303i	−1.07243	+	0.238334i
$367$	−418.446			−1.14018			−0.570090	−	0.821582i	$-0.693092\pi$
$367$	−418.446			−1.14018			−0.570090	+	0.821582i	$0.693092\pi$
$368$			139.953i			0.380307i
$369$	133.825	+	286.215i	0.362669	+	0.775651i
$370$	121.718			0.328969
$371$			109.846i			0.296081i
$372$	−33.3056	−	149.865i	−0.0895312	−	0.402863i
$373$	597.593			1.60213			0.801063	−	0.598581i	$-0.204268\pi$
$373$	597.593			1.60213			0.801063	+	0.598581i	$0.204268\pi$
$374$			105.548i			0.282215i
$375$	32.7422	−	7.27653i	0.0873125	−	0.0194041i
$376$	2.92790			0.00778697
$377$		−	90.2985i		−	0.239519i
$378$	80.0528	−	61.6242i	0.211780	−	0.163027i
$379$	563.466			1.48672			0.743358	−	0.668894i	$-0.233232\pi$
$379$	563.466			1.48672			0.743358	+	0.668894i	$0.233232\pi$
$380$			101.955i			0.268304i
$381$	102.629	+	461.797i	0.269366	+	1.21207i
$382$	10.2446			0.0268182
$383$			108.726i			0.283881i	0.989875	+	0.141940i	$0.0453341\pi$
$383$			108.726i			0.283881i	−0.989875	+	0.141940i	$0.954666\pi$
$384$	−33.1328	+	7.36333i	−0.0862833	+	0.0191753i
$385$	47.1841			0.122556
$386$			443.598i			1.14922i
$387$	−481.793	+	225.270i	−1.24494	+	0.582094i
$388$	−49.0254			−0.126354
$389$			128.348i			0.329944i	0.986298	+	0.164972i	$0.0527534\pi$
$389$			128.348i			0.329944i	−0.986298	+	0.164972i	$0.947247\pi$
$390$	−11.9239	−	53.6542i	−0.0305742	−	0.137575i
$391$	−327.414			−0.837375
$392$			19.7990i			0.0505076i
$393$	−732.490	+	162.787i	−1.86384	+	0.414215i
$394$	133.663			0.339245
$395$		−	122.856i		−	0.311027i
$396$	60.8056	+	130.047i	0.153550	+	0.328401i
$397$	−165.453			−0.416758			−0.208379	−	0.978048i	$-0.566819\pi$
$397$	−165.453			−0.416758			−0.208379	+	0.978048i	$0.566819\pi$
$398$			262.783i			0.660259i
$399$	39.2567	+	176.643i	0.0983878	+	0.442715i
$400$	−20.0000			−0.0500000
$401$		−	397.048i		−	0.990144i	−0.868852	−	0.495072i	$-0.835142\pi$
$401$		−	397.048i		−	0.990144i	0.868852	−	0.495072i	$-0.164858\pi$
$402$	319.344	−	70.9700i	0.794387	−	0.176542i
$403$	−148.241			−0.367844
$404$		−	317.391i		−	0.785620i
$405$	138.988	+	116.135i	0.343179	+	0.286754i
$406$	−58.3168			−0.143638
$407$			306.985i			0.754264i
$408$	−17.2262	−	77.5127i	−0.0422211	−	0.189982i
$409$	590.813			1.44453			0.722265	−	0.691616i	$-0.243101\pi$
$409$	590.813			1.44453			0.722265	+	0.691616i	$0.243101\pi$
$410$		−	111.016i		−	0.270770i
$411$	−561.977	+	124.892i	−1.36734	+	0.303874i
$412$	−355.010			−0.861674
$413$		−	145.940i		−	0.353366i
$414$	−403.409	+	188.621i	−0.974417	+	0.455605i
$415$	175.888			0.423826
$416$			32.7737i			0.0787829i
$417$	13.9698	+	62.8598i	0.0335007	+	0.150743i
$418$	−257.141			−0.615171
$419$			275.411i			0.657305i	0.944451	+	0.328653i	$0.106595\pi$
$419$			275.411i			0.657305i	−0.944451	+	0.328653i	$0.893405\pi$
$420$	−34.6511	+	7.70076i	−0.0825026	+	0.0183351i
$421$	570.120			1.35420			0.677102	−	0.735890i	$-0.263236\pi$
$421$	570.120			1.35420			0.677102	+	0.735890i	$0.263236\pi$
$422$		−	531.333i		−	1.25908i
$423$	3.94606	+	8.43956i	0.00932875	+	0.0199517i
$424$	117.430			0.276959
$425$		−	46.7891i		−	0.110092i
$426$	16.5718	+	74.5679i	0.0389008	+	0.175042i
$427$	250.745			0.587224
$428$		−	421.985i		−	0.985946i
$429$	135.321	−	30.0733i	0.315433	−	0.0701010i
$430$	186.875			0.434594
$431$			650.331i			1.50889i	0.656365	+	0.754444i	$0.272093\pi$
$431$			650.331i			1.50889i	−0.656365	+	0.754444i	$0.727907\pi$
$432$	−65.8790	−	85.5801i	−0.152498	−	0.198102i
$433$	635.503			1.46767			0.733837	−	0.679325i	$-0.237727\pi$
$433$	635.503			1.46767			0.733837	+	0.679325i	$0.237727\pi$
$434$			95.7374i			0.220593i
$435$	−22.6822	−	102.063i	−0.0521429	−	0.234627i
$436$	197.047			0.451943
$437$		−	797.659i		−	1.82531i
$438$	137.510	−	30.5599i	0.313950	−	0.0697714i
$439$	−341.898			−0.778810			−0.389405	−	0.921067i	$-0.627319\pi$
$439$	−341.898			−0.778810			−0.389405	+	0.921067i	$0.627319\pi$
$440$		−	50.4419i		−	0.114641i
$441$	−57.0698	+	26.6840i	−0.129410	+	0.0605079i
$442$	−76.6726			−0.173468
$443$		−	254.231i		−	0.573884i	−0.957948	−	0.286942i	$-0.907361\pi$
$443$		−	254.231i		−	0.573884i	0.957948	−	0.286942i	$-0.0926387\pi$
$444$	−50.1021	−	225.444i	−0.112843	−	0.507758i
$445$	268.392			0.603128
$446$			27.7337i			0.0621833i
$447$	−195.824	+	43.5193i	−0.438084	+	0.0973586i
$448$	21.1660			0.0472456
$449$		−	73.2691i		−	0.163183i	−0.996666	−	0.0815915i	$-0.974000\pi$
$449$		−	73.2691i		−	0.163183i	0.996666	−	0.0815915i	$-0.0260003\pi$
$450$	−26.9549	−	57.6492i	−0.0598997	−	0.128109i
$451$	279.992			0.620825
$452$			205.660i			0.455000i
$453$	−41.9600	−	188.807i	−0.0926269	−	0.416793i
$454$	354.874			0.781660
$455$			34.2756i			0.0753309i
$456$	188.840	−	41.9672i	0.414122	−	0.0920334i
$457$	201.124			0.440097			0.220049	−	0.975489i	$-0.429378\pi$
$457$	201.124			0.440097			0.220049	+	0.975489i	$0.429378\pi$
$458$		−	419.569i		−	0.916089i
$459$	200.211	−	154.121i	0.436189	−	0.335776i
$460$	156.472			0.340157
$461$		−	500.367i		−	1.08539i	−0.839929	−	0.542697i	$-0.817403\pi$
$461$		−	500.367i		−	1.08539i	0.839929	−	0.542697i	$-0.182597\pi$
$462$	−19.4220	−	87.3933i	−0.0420391	−	0.189163i
$463$	−601.585			−1.29932			−0.649660	−	0.760225i	$-0.725089\pi$
$463$	−601.585			−1.29932			−0.649660	+	0.760225i	$0.725089\pi$
$464$			62.3433i			0.134361i
$465$	−167.554	+	37.2368i	−0.360332	+	0.0800791i
$466$	−222.714			−0.477927
$467$			271.025i			0.580353i	0.956973	+	0.290176i	$0.0937140\pi$
$467$			271.025i			0.580353i	−0.956973	+	0.290176i	$0.906286\pi$
$468$	−94.4690	+	44.1706i	−0.201857	+	0.0943816i
$469$	−204.004			−0.434977
$470$		−	3.27349i		−	0.00696488i
$471$	−134.890	−	606.964i	−0.286391	−	1.28867i
$472$	−156.017			−0.330544
$473$			471.317i			0.996442i
$474$	−227.551	+	50.5702i	−0.480065	+	0.106688i
$475$	113.990			0.239978
$476$			49.5170i			0.104027i
$477$	158.266	+	338.489i	0.331795	+	0.709620i
$478$	−111.407			−0.233069
$479$		−	203.003i		−	0.423807i	−0.977291	−	0.211903i	$-0.932034\pi$
$479$		−	203.003i		−	0.423807i	0.977291	−	0.211903i	$-0.0679662\pi$
$480$	8.23246	+	37.0436i	0.0171510	+	0.0771741i
$481$	−223.001			−0.463620
$482$			209.796i			0.435262i
$483$	271.096	−	60.2477i	0.561276	−	0.124736i
$484$	−114.781			−0.237150
$485$			54.8121i			0.113015i
$486$	157.893	−	305.234i	0.324883	−	0.628053i
$487$	795.875			1.63424			0.817120	−	0.576468i	$-0.195569\pi$
$487$	795.875			1.63424			0.817120	+	0.576468i	$0.195569\pi$
$488$		−	268.057i		−	0.549298i
$489$	153.640	+	691.334i	0.314193	+	1.41377i
$490$	22.1359			0.0451754
$491$		−	41.1374i		−	0.0837830i	−0.999122	−	0.0418915i	$-0.986662\pi$
$491$		−	41.1374i		−	0.0837830i	0.999122	−	0.0418915i	$-0.0133384\pi$
$492$	−205.621	+	45.6966i	−0.417928	+	0.0928792i
$493$	−145.849			−0.295841
$494$		−	186.793i		−	0.378124i
$495$	145.397	−	67.9828i	0.293731	−	0.137339i
$496$	102.348			0.206346
$497$		−	47.6357i		−	0.0958466i
$498$	−72.3994	−	325.775i	−0.145380	−	0.654167i
$499$	590.508			1.18338			0.591692	−	0.806164i	$-0.298460\pi$
$499$	590.508			1.18338			0.591692	+	0.806164i	$0.298460\pi$
$500$			22.3607i			0.0447214i
$501$	−321.106	+	71.3618i	−0.640931	+	0.142439i
$502$	−315.676			−0.628837
$503$			276.575i			0.549850i	0.961466	+	0.274925i	$0.0886531\pi$
$503$			276.575i			0.549850i	−0.961466	+	0.274925i	$0.911347\pi$
$504$	28.5264	+	61.0102i	0.0565999	+	0.121052i
$505$	−354.854			−0.702680
$506$			394.637i			0.779916i
$507$	−88.1448	−	396.625i	−0.173856	−	0.782298i
$508$	−315.376			−0.620819
$509$		−	311.610i		−	0.612201i	−0.951999	−	0.306100i	$-0.900976\pi$
$509$		−	311.610i		−	0.612201i	0.951999	−	0.306100i	$-0.0990243\pi$
$510$	−86.6618	+	19.2595i	−0.169925	+	0.0377637i
$511$	−87.8448			−0.171908
$512$		−	22.6274i		−	0.0441942i
$513$	375.477	+	487.762i	0.731923	+	0.950804i
$514$	−509.019			−0.990309
$515$			396.913i			0.770705i
$516$	−76.9221	−	346.126i	−0.149074	−	0.670788i
$517$	8.25606			0.0159692
$518$			144.019i			0.278029i
$519$	−136.794	+	30.4007i	−0.263572	+	0.0585756i
$520$	36.6421			0.0704656
$521$		−	435.399i		−	0.835698i	−0.908516	−	0.417849i	$-0.862784\pi$
$521$		−	435.399i		−	0.835698i	0.908516	−	0.417849i	$-0.137216\pi$
$522$	−179.702	+	84.0229i	−0.344257	+	0.160963i
$523$	619.746			1.18498			0.592491	−	0.805577i	$-0.298144\pi$
$523$	619.746			1.18498			0.592491	+	0.805577i	$0.298144\pi$
$524$		−	500.241i		−	0.954658i
$525$	8.60971	+	38.7411i	0.0163994	+	0.0737926i
$526$	323.009			0.614085
$527$			239.438i			0.454341i
$528$	−93.4274	+	20.7630i	−0.176946	+	0.0393239i
$529$	−695.175			−1.31413
$530$		−	131.291i		−	0.247719i
$531$	−210.271	−	449.712i	−0.395990	−	0.846916i
$532$	−120.635			−0.226758
$533$			203.392i			0.381599i
$534$	−110.476	−	497.110i	−0.206884	−	0.930917i
$535$	−471.793			−0.881857
$536$			218.090i			0.406884i
$537$	860.491	−	191.233i	1.60240	−	0.356114i
$538$	400.969			0.745295
$539$			55.8289i			0.103579i
$540$	−95.6814	+	73.6550i	−0.177188	+	0.136398i
$541$	709.366			1.31121			0.655606	−	0.755103i	$-0.272413\pi$
$541$	709.366			1.31121			0.655606	+	0.755103i	$0.272413\pi$
$542$			411.238i			0.758742i
$543$	−84.3652	−	379.618i	−0.155369	−	0.699112i
$544$	52.9359			0.0973086
$545$		−	220.306i		−	0.404231i
$546$	63.4845	−	14.1086i	0.116272	−	0.0258399i
$547$	−306.448			−0.560234			−0.280117	−	0.959966i	$-0.590373\pi$
$547$	−306.448			−0.560234			−0.280117	+	0.959966i	$0.590373\pi$
$548$		−	383.792i		−	0.700350i
$549$	772.665	−	361.273i	1.40740	−	0.658056i
$550$	−56.3958			−0.102538
$551$		−	355.325i		−	0.644873i
$552$	−64.4075	−	289.814i	−0.116680	−	0.525026i
$553$	145.365			0.262866
$554$			378.260i			0.682780i
$555$	−252.054	+	56.0159i	−0.454152	+	0.100929i
$556$	−42.9289			−0.0772103
$557$		−	259.701i		−	0.466250i	−0.972447	−	0.233125i	$-0.925105\pi$
$557$		−	259.701i		−	0.466250i	0.972447	−	0.233125i	$-0.0748951\pi$
$558$	137.938	+	295.013i	0.247201	+	0.528697i
$559$	−342.375			−0.612478
$560$		−	23.6643i		−	0.0422577i
$561$	−48.5742	−	218.569i	−0.0865851	−	0.389607i
$562$	300.787			0.535209
$563$		−	1066.78i		−	1.89481i	−0.320032	−	0.947407i	$-0.603694\pi$
$563$		−	1066.78i		−	1.89481i	0.320032	−	0.947407i	$-0.396306\pi$
$564$	−6.06309	+	1.34744i	−0.0107502	+	0.00238909i
$565$	229.935			0.406964
$566$			353.195i			0.624019i
$567$	−137.413	+	164.452i	−0.242352	+	0.290039i
$568$	−50.9248			−0.0896563
$569$			294.913i			0.518301i	0.965837	+	0.259150i	$0.0834425\pi$
$569$			294.913i			0.518301i	−0.965837	+	0.259150i	$0.916557\pi$
$570$	−46.9208	−	211.129i	−0.0823171	−	0.370402i
$571$	183.465			0.321304			0.160652	−	0.987011i	$-0.448640\pi$
$571$	183.465			0.321304			0.160652	+	0.987011i	$0.448640\pi$
$572$			92.4149i			0.161564i
$573$	−21.2144	+	4.71463i	−0.0370234	+	0.00822798i
$574$	131.355			0.228842
$575$		−	174.941i		−	0.304245i
$576$	65.2227	−	30.4960i	0.113234	−	0.0529444i
$577$	740.634			1.28359			0.641797	−	0.766874i	$-0.278189\pi$
$577$	740.634			1.28359			0.641797	+	0.766874i	$0.278189\pi$
$578$		−	284.867i		−	0.492849i
$579$	−204.148	−	918.603i	−0.352587	−	1.58653i
$580$	69.7020			0.120176
$581$			208.113i			0.358198i
$582$	101.522	−	22.5619i	0.174436	−	0.0387662i
$583$	331.129			0.567974
$584$			93.9101i			0.160805i
$585$	49.3842	+	105.619i	0.0844174	+	0.180546i
$586$	−441.512			−0.753433
$587$			694.040i			1.18235i	0.806543	+	0.591175i	$0.201336\pi$
$587$			694.040i			1.18235i	−0.806543	+	0.591175i	$0.798664\pi$
$588$	−9.11166	−	40.9997i	−0.0154960	−	0.0697274i
$589$	−583.329			−0.990371
$590$			174.432i			0.295647i
$591$	−276.788	+	61.5126i	−0.468339	+	0.104082i
$592$	153.963			0.260073
$593$			428.653i			0.722855i	0.932400	+	0.361427i	$0.117710\pi$
$593$			428.653i			0.722855i	−0.932400	+	0.361427i	$0.882290\pi$
$594$	−185.765	−	241.318i	−0.312736	−	0.406259i
$595$	55.3616			0.0930448
$596$		−	133.734i		−	0.224386i
$597$	−120.935	−	544.171i	−0.202571	−	0.911509i
$598$	−286.673			−0.479387
$599$		−	1068.82i		−	1.78433i	−0.451705	−	0.892167i	$-0.649184\pi$
$599$		−	1068.82i		−	1.78433i	0.451705	−	0.892167i	$-0.350816\pi$
$600$	41.4160	−	9.20417i	0.0690266	−	0.0153403i
$601$	259.767			0.432224			0.216112	−	0.976369i	$-0.430662\pi$
$601$	259.767			0.432224			0.216112	+	0.976369i	$0.430662\pi$
$602$			221.114i			0.367299i
$603$	−628.636	+	293.929i	−1.04251	+	0.487445i
$604$	128.942			0.213481
$605$			128.329i			0.212114i
$606$	146.066	+	657.252i	0.241033	+	1.08457i
$607$	−1147.06			−1.88972			−0.944858	−	0.327479i	$-0.893801\pi$
$607$	−1147.06			−1.88972			−0.944858	+	0.327479i	$0.893801\pi$
$608$			128.965i			0.212113i
$609$	120.762	−	26.8379i	0.198296	−	0.0440688i
$610$	−299.697			−0.491307
$611$			5.99739i			0.00981569i
$612$	71.3440	+	152.586i	0.116575	+	0.249323i
$613$	−166.678			−0.271905			−0.135952	−	0.990715i	$-0.543409\pi$
$613$	−166.678			−0.271905			−0.135952	+	0.990715i	$0.543409\pi$
$614$			219.569i			0.357604i
$615$	51.0903	+	229.891i	0.0830737	+	0.373807i
$616$	59.6837			0.0968890
$617$		−	319.900i		−	0.518477i	−0.965813	−	0.259238i	$-0.916528\pi$
$617$		−	319.900i		−	0.518477i	0.965813	−	0.259238i	$-0.0834716\pi$
$618$	735.154	−	163.379i	1.18957	−	0.264367i
$619$	−917.131			−1.48163			−0.740817	−	0.671707i	$-0.765561\pi$
$619$	−917.131			−1.48163			−0.740817	+	0.671707i	$0.765561\pi$
$620$		−	114.428i		−	0.184561i
$621$	748.574	−	576.247i	1.20543	−	0.927935i
$622$	−478.216			−0.768835
$623$			317.565i			0.509736i
$624$	−15.0827	−	67.8678i	−0.0241710	−	0.108762i
$625$	25.0000			0.0400000
$626$		−	46.0399i		−	0.0735461i
$627$	532.488	−	118.339i	0.849263	−	0.188738i
$628$	414.515			0.660056
$629$			360.190i			0.572639i
$630$	68.2115	−	31.8934i	0.108272	−	0.0506245i
$631$	695.889			1.10283			0.551417	−	0.834229i	$-0.314087\pi$
$631$	695.889			1.10283			0.551417	+	0.834229i	$0.314087\pi$
$632$		−	155.402i		−	0.245889i
$633$	244.524	+	1100.28i	0.386294	+	1.73820i
$634$	−221.767			−0.349791
$635$			352.601i			0.555277i
$636$	−243.175	+	54.0425i	−0.382350	+	0.0849725i
$637$	−40.5554			−0.0636662
$638$			175.795i			0.275541i
$639$	−68.6335	−	146.789i	−0.107408	−	0.229716i
$640$	−25.2982			−0.0395285
$641$			75.7558i			0.118184i	0.998253	+	0.0590919i	$0.0188205\pi$
$641$			75.7558i			0.118184i	−0.998253	+	0.0590919i	$0.981180\pi$
$642$	194.201	+	873.846i	0.302494	+	1.36113i
$643$	1173.40			1.82488			0.912438	−	0.409215i	$-0.134197\pi$
$643$	1173.40			1.82488			0.912438	+	0.409215i	$0.134197\pi$
$644$			185.140i			0.287485i
$645$	−386.981	+	86.0016i	−0.599971	+	0.133336i
$646$	−301.707			−0.467039
$647$		−	322.830i		−	0.498964i	−0.968379	−	0.249482i	$-0.919740\pi$
$647$		−	322.830i		−	0.498964i	0.968379	−	0.249482i	$-0.0802603\pi$
$648$	175.807	+	146.901i	0.271307	+	0.226699i
$649$	−439.934			−0.677864
$650$		−	40.9671i		−	0.0630264i
$651$	−44.0592	−	198.253i	−0.0676792	−	0.304536i
$652$	−472.134			−0.724132
$653$			1056.82i			1.61841i	0.587526	+	0.809206i	$0.300102\pi$
$653$			1056.82i			1.61841i	−0.587526	+	0.809206i	$0.699898\pi$
$654$	−408.045	+	90.6828i	−0.623923	+	0.138659i
$655$	−559.286			−0.853872
$656$		−	140.425i		−	0.214062i
$657$	−270.692	+	126.567i	−0.412012	+	0.192643i
$658$	3.87325			0.00588640
$659$		−	808.670i		−	1.22712i	−0.789649	−	0.613559i	$-0.789737\pi$
$659$		−	808.670i		−	1.22712i	0.789649	−	0.613559i	$-0.210263\pi$
$660$	23.2138	+	104.455i	0.0351724	+	0.158265i
$661$	1068.86			1.61703			0.808515	−	0.588476i	$-0.200272\pi$
$661$	1068.86			1.61703			0.808515	+	0.588476i	$0.200272\pi$
$662$		−	88.7654i		−	0.134087i
$663$	158.774	−	35.2854i	0.239478	−	0.0532208i
$664$	222.482			0.335064
$665$			134.874i			0.202819i
$666$	207.503	+	443.793i	0.311566	+	0.666355i
$667$	−545.320			−0.817572
$668$		−	219.294i		−	0.328284i
$669$	−12.7633	−	57.4310i	−0.0190782	−	0.0858460i
$670$	243.832			0.363928
$671$		−	755.865i		−	1.12647i
$672$	−43.8306	+	9.74078i	−0.0652240	+	0.0144952i
$673$	−1159.59			−1.72302			−0.861508	−	0.507744i	$-0.830479\pi$
$673$	−1159.59			−1.72302			−0.861508	+	0.507744i	$0.830479\pi$
$674$		−	607.777i		−	0.901747i
$675$	82.3488	+	106.975i	0.121998	+	0.158482i
$676$	270.868			0.400692
$677$			202.423i			0.298999i	0.988762	+	0.149500i	$0.0477663\pi$
$677$			202.423i			0.298999i	−0.988762	+	0.149500i	$0.952234\pi$
$678$	−94.6464	−	425.880i	−0.139596	−	0.628142i
$679$	−64.8546			−0.0955148
$680$		−	59.1841i		−	0.0870354i
$681$	−734.872	+	163.316i	−1.07911	+	0.239818i
$682$	288.599			0.423165
$683$			432.740i			0.633587i	0.948494	+	0.316794i	$0.102606\pi$
$683$			432.740i			0.633587i	−0.948494	+	0.316794i	$0.897394\pi$
$684$	−371.736	+	173.811i	−0.543473	+	0.254110i
$685$	−429.092			−0.626412
$686$			26.1916i			0.0381802i
$687$	193.089	+	868.843i	0.281061	+	1.26469i
$688$	236.381			0.343576
$689$			240.539i			0.349114i
$690$	−324.022	+	72.0097i	−0.469597	+	0.104362i
$691$	−507.481			−0.734415			−0.367208	−	0.930139i	$-0.619686\pi$
$691$	−507.481			−0.734415			−0.367208	+	0.930139i	$0.619686\pi$
$692$		−	93.4210i		−	0.135001i
$693$	80.4383	+	172.036i	0.116073	+	0.248248i
$694$	864.371			1.24549
$695$			47.9960i			0.0690590i
$696$	−28.6909	−	129.100i	−0.0412226	−	0.185489i
$697$	328.518			0.471331
$698$			324.924i			0.465507i
$699$	461.196	−	102.495i	0.659794	−	0.146631i
$700$	−26.4575			−0.0377964
$701$			465.228i			0.663663i	0.943339	+	0.331831i	$0.107667\pi$
$701$			465.228i			0.663663i	−0.943339	+	0.331831i	$0.892333\pi$
$702$	175.299	−	134.944i	0.249713	−	0.192228i
$703$	−877.510			−1.24824
$704$		−	63.8045i		−	0.0906314i
$705$	1.50649	+	6.77875i	0.00213686	+	0.00961524i
$706$	−614.619			−0.870566
$707$		−	419.868i		−	0.593873i
$708$	323.079	−	71.8002i	0.456327	−	0.101413i
$709$	−902.795			−1.27334			−0.636668	−	0.771138i	$-0.719688\pi$
$709$	−902.795			−1.27334			−0.636668	+	0.771138i	$0.719688\pi$
$710$			56.9356i			0.0801910i
$711$	447.939	−	209.442i	0.630013	−	0.294573i
$712$	339.492			0.476814
$713$			895.240i			1.25560i
$714$	−22.7881	−	102.540i	−0.0319161	−	0.143613i
$715$	103.323			0.144508
$716$			587.656i			0.820749i
$717$	230.701	−	51.2703i	0.321759	−	0.0715067i
$718$	−262.879			−0.366127
$719$			1105.81i			1.53798i	0.639262	+	0.768989i	$0.279240\pi$
$719$			1105.81i			1.53798i	−0.639262	+	0.768989i	$0.720760\pi$
$720$	−34.0955	−	72.9212i	−0.0473549	−	0.101279i
$721$	−469.634			−0.651365
$722$		−	224.501i		−	0.310943i
$723$	−96.5500	−	434.446i	−0.133541	−	0.600893i
$724$	259.253			0.358084
$725$		−	77.9292i		−	0.107488i
$726$	237.688	−	52.8231i	0.327394	−	0.0727591i
$727$	−215.564			−0.296512			−0.148256	−	0.988949i	$-0.547366\pi$
$727$	−215.564			−0.296512			−0.148256	+	0.988949i	$0.547366\pi$
$728$			43.3555i			0.0595543i
$729$	−186.494	+	704.742i	−0.255822	+	0.966724i
$730$	104.995			0.143828
$731$			553.002i			0.756501i
$732$	123.362	+	555.093i	0.168528	+	0.758323i
$733$	1068.10			1.45716			0.728578	−	0.684963i	$-0.240181\pi$
$733$	1068.10			1.45716			0.728578	+	0.684963i	$0.240181\pi$
$734$			591.772i			0.806229i
$735$	−45.8391	+	10.1871i	−0.0623661	+	0.0138601i
$736$	197.923			0.268917
$737$			614.967i			0.834419i
$738$	404.769	−	189.257i	0.548468	−	0.256446i
$739$	−156.720			−0.212071			−0.106035	−	0.994362i	$-0.533816\pi$
$739$	−156.720			−0.212071			−0.106035	+	0.994362i	$0.533816\pi$
$740$		−	172.136i		−	0.232616i
$741$	85.9638	+	386.811i	0.116011	+	0.522012i
$742$	155.346			0.209361
$743$			423.464i			0.569938i	0.958537	+	0.284969i	$0.0919834\pi$
$743$			423.464i			0.569938i	−0.958537	+	0.284969i	$0.908017\pi$
$744$	−211.941	+	47.1012i	−0.284867	+	0.0633081i
$745$	−149.519			−0.200697
$746$		−	845.124i		−	1.13287i
$747$	299.849	+	641.296i	0.401404	+	0.858496i
$748$	149.268			0.199556
$749$		−	558.234i		−	0.745305i
$750$	−10.2906	−	46.3045i	−0.0137208	−	0.0617393i
$751$	−1305.05			−1.73776			−0.868878	−	0.495026i	$-0.835158\pi$
$751$	−1305.05			−1.73776			−0.868878	+	0.495026i	$0.835158\pi$
$752$		−	4.14068i		−	0.00550622i
$753$	653.702	−	145.277i	0.868130	−	0.192931i
$754$	−127.701			−0.169365
$755$		−	144.162i		−	0.190943i
$756$	−87.1498	−	113.212i	−0.115277	−	0.149751i
$757$	59.6912			0.0788523			0.0394261	−	0.999222i	$-0.487447\pi$
$757$	59.6912			0.0788523			0.0394261	+	0.999222i	$0.487447\pi$
$758$		−	796.861i		−	1.05127i
$759$	−181.615	−	817.214i	−0.239282	−	1.07670i
$760$	144.187			0.189720
$761$		−	899.617i		−	1.18215i	−0.806616	−	0.591075i	$-0.798704\pi$
$761$		−	899.617i		−	1.18215i	0.806616	−	0.591075i	$-0.201296\pi$
$762$	653.080	−	145.139i	0.857060	−	0.190471i
$763$	260.669			0.341637
$764$		−	14.4880i		−	0.0189633i
$765$	170.596	−	79.7650i	0.223001	−	0.104268i
$766$	153.762			0.200734
$767$		−	319.578i		−	0.416660i
$768$	10.4133	+	46.8568i	0.0135590	+	0.0610115i
$769$	−268.385			−0.349005			−0.174503	−	0.984657i	$-0.555832\pi$
$769$	−268.385			−0.349005			−0.174503	+	0.984657i	$0.555832\pi$
$770$		−	66.7284i		−	0.0866602i
$771$	1054.08	−	234.255i	1.36715	−	0.303832i
$772$	627.343			0.812620
$773$		−	80.8488i		−	0.104591i	−0.998632	−	0.0522955i	$-0.983346\pi$
$773$		−	80.8488i		−	0.104591i	0.998632	−	0.0522955i	$-0.0166538\pi$
$774$	318.581	+	681.358i	0.411603	+	0.880307i
$775$	−127.935			−0.165077
$776$			69.3324i			0.0893459i
$777$	−66.2789	−	298.235i	−0.0853010	−	0.383829i
$778$	181.512			0.233306
$779$			800.350i			1.02741i
$780$	−75.8785	+	16.8630i	−0.0972801	+	0.0216192i
$781$	−143.597			−0.183863
$782$			463.033i			0.592113i
$783$	333.459	−	256.695i	0.425874	−	0.327835i
$784$	28.0000			0.0357143
$785$		−	463.442i		−	0.590372i
$786$	230.215	+	1035.90i	0.292894	+	1.31794i
$787$	592.703			0.753117			0.376559	−	0.926393i	$-0.377107\pi$
$787$	592.703			0.753117			0.376559	+	0.926393i	$0.377107\pi$
$788$		−	189.027i		−	0.239882i
$789$	−668.886	+	148.651i	−0.847764	+	0.188405i
$790$	−173.744			−0.219929
$791$			272.062i			0.343948i
$792$	183.914	−	85.9922i	0.232215	−	0.108576i
$793$	549.077			0.692405
$794$			233.986i			0.294693i
$795$	60.4213	+	271.878i	0.0760017	+	0.341985i
$796$	371.632			0.466874
$797$		−	463.874i		−	0.582025i	−0.956719	−	0.291012i	$-0.906008\pi$
$797$		−	463.874i		−	0.582025i	0.956719	−	0.291012i	$-0.0939921\pi$
$798$	249.812	−	55.5174i	0.313047	−	0.0695707i
$799$	9.68693			0.0121238
$800$			28.2843i			0.0353553i
$801$	457.548	+	978.572i	0.571221	+	1.22169i
$802$	−561.510			−0.700138
$803$			264.806i			0.329771i
$804$	−100.367	−	451.620i	−0.124834	−	0.561717i
$805$	206.993			0.257134
$806$			209.644i			0.260105i
$807$	−830.326	+	184.529i	−1.02890	+	0.228661i
$808$	−448.858			−0.555518
$809$			454.905i			0.562305i	0.959663	+	0.281152i	$0.0907166\pi$
$809$			454.905i			0.562305i	−0.959663	+	0.281152i	$0.909283\pi$
$810$	164.240	−	196.558i	0.202766	−	0.242664i
$811$	349.822			0.431346			0.215673	−	0.976466i	$-0.430805\pi$
$811$	349.822			0.431346			0.215673	+	0.976466i	$0.430805\pi$
$812$			82.4725i			0.101567i
$813$	−189.255	−	851.591i	−0.232786	−	1.04747i
$814$	434.143			0.533345
$815$			527.862i			0.647683i
$816$	−109.620	+	24.3615i	−0.134338	+	0.0298548i
$817$	−1347.25			−1.64902
$818$		−	835.536i		−	1.02144i
$819$	−124.971	+	58.4322i	−0.152589	+	0.0713458i
$820$	−157.000			−0.191463
$821$		−	779.459i		−	0.949402i	−0.880147	−	0.474701i	$-0.842556\pi$
$821$		−	779.459i		−	0.949402i	0.880147	−	0.474701i	$-0.157444\pi$
$822$	176.624	+	794.755i	0.214871	+	0.966856i
$823$	−931.372			−1.13168			−0.565839	−	0.824516i	$-0.691448\pi$
$823$	−931.372			−1.13168			−0.565839	+	0.824516i	$0.691448\pi$
$824$			502.060i			0.609296i
$825$	116.784	−	25.9538i	0.141557	−	0.0314591i
$826$	−206.391			−0.249868
$827$			197.854i			0.239243i	0.992820	+	0.119621i	$0.0381681\pi$
$827$			197.854i			0.239243i	−0.992820	+	0.119621i	$0.961832\pi$
$828$	266.750	+	570.506i	0.322162	+	0.689017i
$829$	−767.502			−0.925816			−0.462908	−	0.886406i	$-0.653194\pi$
$829$	−767.502			−0.925816			−0.462908	+	0.886406i	$0.653194\pi$
$830$		−	248.743i		−	0.299690i
$831$	−174.078	−	783.300i	−0.209481	−	0.942599i
$832$	46.3490			0.0557080
$833$			65.5048i			0.0786372i
$834$	88.8972	−	19.7563i	0.106591	−	0.0236886i
$835$	−245.178			−0.293626
$836$			363.653i			0.434991i
$837$	−421.410	−	547.432i	−0.503477	−	0.654041i
$838$	389.490			0.464785
$839$		−	789.441i		−	0.940931i	−0.882418	−	0.470466i	$-0.844086\pi$
$839$		−	789.441i		−	0.940931i	0.882418	−	0.470466i	$-0.155914\pi$
$840$	10.8905	+	49.0040i	0.0129649	+	0.0583382i
$841$	598.082			0.711156
$842$		−	806.271i		−	0.957566i
$843$	−622.870	+	138.425i	−0.738874	+	0.164205i
$844$	−751.418			−0.890306
$845$		−	302.839i		−	0.358390i
$846$	11.9353	−	5.58057i	0.0141080	−	0.00659642i
$847$	−151.841			−0.179269
$848$		−	166.072i		−	0.195839i
$849$	−162.543	−	731.395i	−0.191452	−	0.861478i
$850$	−66.1698			−0.0778468
$851$			1346.72i			1.58252i
$852$	105.455	−	23.4360i	0.123773	−	0.0275070i
$853$	−167.784			−0.196699			−0.0983493	−	0.995152i	$-0.531356\pi$
$853$	−167.784			−0.196699			−0.0983493	+	0.995152i	$0.531356\pi$
$854$		−	354.606i		−	0.415230i
$855$	194.327	+	415.613i	0.227283	+	0.486097i
$856$	−596.777			−0.697169
$857$		−	873.473i		−	1.01922i	−0.860405	−	0.509611i	$-0.829789\pi$
$857$		−	873.473i		−	1.01922i	0.860405	−	0.509611i	$-0.170211\pi$
$858$	−42.5301	−	191.373i	−0.0495689	−	0.223045i
$859$	480.534			0.559411			0.279705	−	0.960086i	$-0.409763\pi$
$859$	480.534			0.559411			0.279705	+	0.960086i	$0.409763\pi$
$860$		−	264.282i		−	0.307304i
$861$	−272.011	+	60.4509i	−0.315924	+	0.0702101i
$862$	919.706			1.06694
$863$		−	263.159i		−	0.304936i	−0.988308	−	0.152468i	$-0.951278\pi$
$863$		−	263.159i		−	0.304936i	0.988308	−	0.152468i	$-0.0487220\pi$
$864$	−121.029	+	93.1670i	−0.140079	+	0.107832i
$865$	−104.448			−0.120749
$866$		−	898.737i		−	1.03780i
$867$	131.098	+	589.901i	0.151209	+	0.680394i
$868$	135.393			0.155983
$869$		−	438.199i		−	0.504257i
$870$	−144.339	+	32.0774i	−0.165907	+	0.0368706i
$871$	−446.726			−0.512888
$872$		−	278.667i		−	0.319572i
$873$	−199.848	+	93.4424i	−0.228921	+	0.107036i
$874$	−1128.06			−1.29069
$875$			29.5804i			0.0338062i
$876$	−43.2182	−	194.469i	−0.0493358	−	0.221996i
$877$	−982.305			−1.12007			−0.560037	−	0.828468i	$-0.689213\pi$
$877$	−982.305			−1.12007			−0.560037	+	0.828468i	$0.689213\pi$
$878$			483.517i			0.550702i
$879$	914.282	−	203.187i	1.04014	−	0.231158i
$880$	−71.3356			−0.0810632
$881$			651.840i			0.739886i	0.929054	+	0.369943i	$0.120623\pi$
$881$			651.840i			0.739886i	−0.929054	+	0.369943i	$0.879377\pi$
$882$	37.7368	+	80.7089i	0.0427855	+	0.0915067i
$883$	811.043			0.918509			0.459254	−	0.888305i	$-0.348117\pi$
$883$	811.043			0.918509			0.459254	+	0.888305i	$0.348117\pi$
$884$			108.432i			0.122660i
$885$	−80.2751	−	361.214i	−0.0907063	−	0.408151i
$886$	−359.536			−0.405797
$887$		−	795.521i		−	0.896867i	−0.893816	−	0.448433i	$-0.851982\pi$
$887$		−	795.521i		−	0.896867i	0.893816	−	0.448433i	$-0.148018\pi$
$888$	−318.826	+	70.8551i	−0.359039	+	0.0797918i
$889$	−417.203			−0.469295
$890$		−	379.563i		−	0.426476i
$891$	495.738	+	414.230i	0.556384	+	0.464904i
$892$	39.2214			0.0439702
$893$			23.5997i			0.0264275i
$894$	61.5456	+	276.937i	0.0688429	+	0.309772i
$895$	657.020			0.734100
$896$		−	29.9333i		−	0.0334077i
$897$	593.643	−	131.929i	0.661809	−	0.147079i
$898$	−103.618			−0.115388
$899$			398.793i			0.443596i
$900$	−81.5283	+	38.1200i	−0.0905870	+	0.0423555i
$901$	388.518			0.431207
$902$		−	395.968i		−	0.438989i
$903$	−101.758	−	457.882i	−0.112689	−	0.507068i
$904$	290.847			0.321733
$905$		−	289.854i		−	0.320280i
$906$	−267.014	+	59.3404i	−0.294717	+	0.0654971i
$907$	855.003			0.942672			0.471336	−	0.881954i	$-0.343772\pi$
$907$	855.003			0.942672			0.471336	+	0.881954i	$0.343772\pi$
$908$		−	501.867i		−	0.552717i
$909$	−604.946	−	1293.82i	−0.665507	−	1.42334i
$910$	48.4730			0.0532670
$911$		−	1234.06i		−	1.35462i	−0.735696	−	0.677312i	$-0.763145\pi$
$911$		−	1234.06i		−	1.35462i	0.735696	−	0.677312i	$-0.236855\pi$
$912$	−59.3506	−	267.060i	−0.0650774	−	0.292829i
$913$	627.352			0.687133
$914$		−	284.433i		−	0.311196i
$915$	620.613	−	137.923i	0.678265	−	0.150736i
$916$	−593.360			−0.647773
$917$		−	661.756i		−	0.721653i
$918$	−217.960	−	283.141i	−0.237429	−	0.308432i
$919$	−1390.69			−1.51326			−0.756632	−	0.653842i	$-0.773156\pi$
$919$	−1390.69			−1.51326			−0.756632	+	0.653842i	$0.773156\pi$
$920$		−	221.285i		−	0.240527i
$921$	−101.048	−	454.683i	−0.109715	−	0.493684i
$922$	−707.625			−0.767490
$923$		−	104.312i		−	0.113014i
$924$	−123.593	+	27.4669i	−0.133758	+	0.0297261i
$925$	−192.454			−0.208058
$926$			850.770i			0.918758i
$927$	−1447.17	+	676.648i	−1.56113	+	0.729933i
$928$	88.1668			0.0950073
$929$			934.368i			1.00578i	0.864351	+	0.502889i	$0.167730\pi$
$929$			934.368i			1.00578i	−0.864351	+	0.502889i	$0.832270\pi$
$930$	52.6608	+	236.958i	0.0566245	+	0.254793i
$931$	−159.586			−0.171413
$932$			314.965i			0.337946i
$933$	990.288	−	220.079i	1.06140	−	0.235883i
$934$	383.287			0.410372
$935$		−	166.887i		−	0.178488i
$936$	62.4666	+	133.599i	0.0667378	+	0.142734i
$937$	229.679			0.245122			0.122561	−	0.992461i	$-0.460889\pi$
$937$	229.679			0.245122			0.122561	+	0.992461i	$0.460889\pi$
$938$			288.506i			0.307575i
$939$	21.1879	+	95.3393i	0.0225644	+	0.101533i
$940$	−4.62942			−0.00492491
$941$			688.683i			0.731863i	0.930642	+	0.365932i	$0.119250\pi$
$941$			688.683i			0.731863i	−0.930642	+	0.365932i	$0.880750\pi$
$942$	−858.377	+	190.763i	−0.911228	+	0.202509i
$943$	1228.30			1.30255
$944$			220.641i			0.233730i
$945$	−126.575	+	97.4364i	−0.133941	+	0.103107i
$946$	666.543			0.704591
$947$		−	897.803i		−	0.948049i	−0.880512	−	0.474025i	$-0.842801\pi$
$947$		−	897.803i		−	0.948049i	0.880512	−	0.474025i	$-0.157199\pi$
$948$	71.5171	+	321.805i	0.0754400	+	0.339457i
$949$	−192.361			−0.202699
$950$		−	161.206i		−	0.169690i
$951$	459.236	−	102.059i	0.482898	−	0.107318i
$952$	70.0275			0.0735584
$953$		−	809.558i		−	0.849483i	−0.905315	−	0.424742i	$-0.860365\pi$
$953$		−	809.558i		−	0.849483i	0.905315	−	0.424742i	$-0.139635\pi$
$954$	478.695	−	223.822i	0.501777	−	0.234614i
$955$	−16.1981			−0.0169613
$956$			157.553i			0.164804i
$957$	−80.9023	−	364.036i	−0.0845374	−	0.380393i
$958$	−287.090			−0.299677
$959$		−	507.709i		−	0.529415i
$960$	52.3875	−	11.6425i	0.0545703	−	0.0121276i
$961$	−306.310			−0.318741
$962$			315.371i			0.327829i
$963$	−804.302	−	1720.19i	−0.835205	−	1.78628i
$964$	296.697			0.307777
$965$		−	701.391i		−	0.726830i
$966$	−85.2031	−	383.388i	−0.0882019	−	0.396882i
$967$	952.817			0.985333			0.492667	−	0.870218i	$-0.336022\pi$
$967$	952.817			0.985333			0.492667	+	0.870218i	$0.336022\pi$
$968$			162.325i			0.167691i
$969$	624.775	−	138.848i	0.644762	−	0.143290i
$970$	77.5160			0.0799134
$971$			755.094i			0.777646i	0.921313	+	0.388823i	$0.127118\pi$
$971$			755.094i			0.777646i	−0.921313	+	0.388823i	$0.872882\pi$
$972$	−431.666	−	223.295i	−0.444101	−	0.229727i
$973$	−56.7897			−0.0583655
$974$		−	1125.54i		−	1.15558i
$975$	18.8534	+	84.8347i	0.0193368	+	0.0870099i
$976$	−379.090			−0.388412
$977$		−	1865.83i		−	1.90975i	−0.297006	−	0.954876i	$-0.595988\pi$
$977$		−	1865.83i		−	1.90975i	0.297006	−	0.954876i	$-0.404012\pi$
$978$	977.694	−	217.280i	0.999687	−	0.222168i
$979$	957.295			0.977829
$980$		−	31.3050i		−	0.0319438i
$981$	803.247	−	375.572i	0.818804	−	0.382846i
$982$	−58.1771			−0.0592435
$983$			1469.42i			1.49483i	0.664356	+	0.747417i	$0.268706\pi$
$983$			1469.42i			1.49483i	−0.664356	+	0.747417i	$0.731294\pi$
$984$	64.6247	+	290.792i	0.0656755	+	0.295520i
$985$	−211.339			−0.214557
$986$			206.262i			0.209191i
$987$	−8.02072	+	1.78250i	−0.00812636	+	0.00180598i
$988$	−264.166			−0.267374
$989$			2067.63i			2.09063i
$990$	−96.1422	−	205.622i	−0.0971133	−	0.207699i
$991$	1075.76			1.08553			0.542764	−	0.839885i	$-0.317378\pi$
$991$	1075.76			1.08553			0.542764	+	0.839885i	$0.317378\pi$
$992$		−	144.741i		−	0.145909i
$993$	40.8506	+	183.815i	0.0411385	+	0.185111i
$994$	−67.3671			−0.0677738
$995$		−	415.497i		−	0.417585i
$996$	−460.716	+	102.388i	−0.462566	+	0.102799i
$997$	1114.55			1.11791			0.558953	−	0.829199i	$-0.311203\pi$
$997$	1114.55			1.11791			0.558953	+	0.829199i	$0.311203\pi$
$998$		−	835.105i		−	0.836779i
$999$	−633.934	−	823.511i	−0.634568	−	0.824335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.e.a.71.6	✓	16
3.2	odd	2	inner	210.3.e.a.71.14	yes	16
4.3	odd	2		1680.3.l.c.1121.5		16
5.2	odd	4		1050.3.c.c.449.31		32
5.3	odd	4		1050.3.c.c.449.2		32
5.4	even	2		1050.3.e.d.701.11		16
12.11	even	2		1680.3.l.c.1121.6		16
15.2	even	4		1050.3.c.c.449.1		32
15.8	even	4		1050.3.c.c.449.32		32
15.14	odd	2		1050.3.e.d.701.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.6	✓	16	1.1	even	1	trivial
210.3.e.a.71.14	yes	16	3.2	odd	2	inner
1050.3.c.c.449.1		32	15.2	even	4
1050.3.c.c.449.2		32	5.3	odd	4
1050.3.c.c.449.31		32	5.2	odd	4
1050.3.c.c.449.32		32	15.8	even	4
1050.3.e.d.701.3		16	15.14	odd	2
1050.3.e.d.701.11		16	5.4	even	2
1680.3.l.c.1121.5		16	4.3	odd	2
1680.3.l.c.1121.6		16	12.11	even	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(0.650833 + 2.92855i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(4.14160 - 0.920417i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(-8.15283 + 3.81200i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(0.650833 + 2.92855i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(4.14160 - 0.920417i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(-8.15283 + 3.81200i) q^{9} +3.16228 q^{10} +7.97556i q^{11} +(-1.30167 - 5.85710i) q^{12} -5.79363 q^{13} +3.74166i q^{14} +(-6.54844 + 1.45531i) q^{15} +4.00000 q^{16} +9.35782i q^{17} +(5.39098 + 11.5298i) q^{18} -22.7979 q^{19} -4.47214i q^{20} +(-1.72194 - 7.74822i) q^{21} +11.2792 q^{22} +34.9882i q^{23} +(-8.28320 + 1.84083i) q^{24} -5.00000 q^{25} +8.19343i q^{26} +(-16.4698 - 21.3950i) q^{27} +5.29150 q^{28} +15.5858i q^{29} +(2.05811 + 9.26089i) q^{30} +25.5869 q^{31} -5.65685i q^{32} +(-23.3569 + 5.19076i) q^{33} +13.2340 q^{34} -5.91608i q^{35} +(16.3057 - 7.62399i) q^{36} +38.4908 q^{37} +32.2412i q^{38} +(-3.77068 - 16.9669i) q^{39} -6.32456 q^{40} -35.1062i q^{41} +(-10.9576 + 2.43519i) q^{42} +59.0951 q^{43} -15.9511i q^{44} +(-8.52388 - 18.2303i) q^{45} +49.4808 q^{46} -1.03517i q^{47} +(2.60333 + 11.7142i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(-27.4049 + 6.09038i) q^{51} +11.5873 q^{52} -41.5179i q^{53} +(-30.2571 + 23.2918i) q^{54} -17.8339 q^{55} -7.48331i q^{56} +(-14.8377 - 66.7650i) q^{57} +22.0417 q^{58} +55.1602i q^{59} +(13.0969 - 2.91061i) q^{60} -94.7726 q^{61} -36.1853i q^{62} +(21.5704 - 10.0856i) q^{63} -8.00000 q^{64} -12.9549i q^{65} +(7.34084 + 33.0316i) q^{66} +77.1064 q^{67} -18.7156i q^{68} +(-102.465 + 22.7715i) q^{69} -8.36660 q^{70} +18.0046i q^{71} +(-10.7820 - 23.0597i) q^{72} +33.2022 q^{73} -54.4342i q^{74} +(-3.25416 - 14.6428i) q^{75} +45.5959 q^{76} -21.1014i q^{77} +(-23.9949 + 5.33255i) q^{78} -54.9427 q^{79} +8.94427i q^{80} +(51.9374 - 62.1571i) q^{81} -49.6477 q^{82} -78.6593i q^{83} +(3.44388 + 15.4964i) q^{84} -20.9247 q^{85} -83.5731i q^{86} +(-45.6439 + 10.1438i) q^{87} -22.5583 q^{88} -120.028i q^{89} +(-25.7815 + 12.0546i) q^{90} +15.3285 q^{91} -69.9764i q^{92} +(16.6528 + 74.9326i) q^{93} -1.46395 q^{94} -50.9777i q^{95} +(16.5664 - 3.68167i) q^{96} +24.5127 q^{97} -9.89949i q^{98} +(-30.4028 - 65.0234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9	\( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9 + 16 * q^12 - 20 * q^15 + 64 * q^16 - 32 * q^18 + 48 * q^19 + 28 * q^21 - 96 * q^22 - 32 * q^24 - 80 * q^25 + 64 * q^27 - 88 * q^33 + 160 * q^34 + 8 * q^36 + 80 * q^37 + 156 * q^39 - 336 * q^43 - 80 * q^45 + 32 * q^46 - 32 * q^48 + 112 * q^49 + 84 * q^51 - 32 * q^54 - 80 * q^55 - 264 * q^57 + 96 * q^58 + 40 * q^60 + 112 * q^61 + 112 * q^63 - 128 * q^64 + 240 * q^67 + 8 * q^69 + 64 * q^72 + 48 * q^73 + 40 * q^75 - 96 * q^76 + 208 * q^78 + 8 * q^79 - 124 * q^81 - 608 * q^82 - 56 * q^84 + 120 * q^85 - 120 * q^87 + 192 * q^88 + 160 * q^90 - 56 * q^91 + 104 * q^93 + 32 * q^94 + 64 * q^96 - 192 * q^97 - 52 * q^99

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