LMFDB - Embedded newform 42.4.e.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,4,Mod(25,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("42.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	42.e (of order $3$, degree $2$, 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:	$2.47808022024$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	42.25
Dual form			42.4.e.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(7.50000 + 12.9904i) q^{5} +6.00000 q^{6} +(17.5000 - 6.06218i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(7.50000 + 12.9904i) q^{5} +6.00000 q^{6} +(17.5000 - 6.06218i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-15.0000 + 25.9808i) q^{10} +(4.50000 - 7.79423i) q^{11} +(6.00000 + 10.3923i) q^{12} -88.0000 q^{13} +(28.0000 + 24.2487i) q^{14} +45.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(42.0000 - 72.7461i) q^{17} +(9.00000 - 15.5885i) q^{18} +(-52.0000 - 90.0666i) q^{19} -60.0000 q^{20} +(10.5000 - 54.5596i) q^{21} +18.0000 q^{22} +(42.0000 + 72.7461i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-50.0000 + 86.6025i) q^{25} +(-88.0000 - 152.420i) q^{26} -27.0000 q^{27} +(-14.0000 + 72.7461i) q^{28} +51.0000 q^{29} +(45.0000 + 77.9423i) q^{30} +(-92.5000 + 160.215i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-13.5000 - 23.3827i) q^{33} +168.000 q^{34} +(210.000 + 181.865i) q^{35} +36.0000 q^{36} +(-22.0000 - 38.1051i) q^{37} +(104.000 - 180.133i) q^{38} +(-132.000 + 228.631i) q^{39} +(-60.0000 - 103.923i) q^{40} -168.000 q^{41} +(105.000 - 36.3731i) q^{42} +326.000 q^{43} +(18.0000 + 31.1769i) q^{44} +(67.5000 - 116.913i) q^{45} +(-84.0000 + 145.492i) q^{46} +(69.0000 + 119.512i) q^{47} -48.0000 q^{48} +(269.500 - 212.176i) q^{49} -200.000 q^{50} +(-126.000 - 218.238i) q^{51} +(176.000 - 304.841i) q^{52} +(-319.500 + 553.390i) q^{53} +(-27.0000 - 46.7654i) q^{54} +135.000 q^{55} +(-140.000 + 48.4974i) q^{56} -312.000 q^{57} +(51.0000 + 88.3346i) q^{58} +(-79.5000 + 137.698i) q^{59} +(-90.0000 + 155.885i) q^{60} +(-361.000 - 625.270i) q^{61} -370.000 q^{62} +(-126.000 - 109.119i) q^{63} +64.0000 q^{64} +(-660.000 - 1143.15i) q^{65} +(27.0000 - 46.7654i) q^{66} +(83.0000 - 143.760i) q^{67} +(168.000 + 290.985i) q^{68} +252.000 q^{69} +(-105.000 + 545.596i) q^{70} +1086.00 q^{71} +(36.0000 + 62.3538i) q^{72} +(-109.000 + 188.794i) q^{73} +(44.0000 - 76.2102i) q^{74} +(150.000 + 259.808i) q^{75} +416.000 q^{76} +(31.5000 - 163.679i) q^{77} -528.000 q^{78} +(291.500 + 504.893i) q^{79} +(120.000 - 207.846i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-168.000 - 290.985i) q^{82} -597.000 q^{83} +(168.000 + 145.492i) q^{84} +1260.00 q^{85} +(326.000 + 564.649i) q^{86} +(76.5000 - 132.502i) q^{87} +(-36.0000 + 62.3538i) q^{88} +(519.000 + 898.934i) q^{89} +270.000 q^{90} +(-1540.00 + 533.472i) q^{91} -336.000 q^{92} +(277.500 + 480.644i) q^{93} +(-138.000 + 239.023i) q^{94} +(780.000 - 1351.00i) q^{95} +(-48.0000 - 83.1384i) q^{96} -169.000 q^{97} +(637.000 + 254.611i) q^{98} -81.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 15 q^{5} + 12 q^{6} + 35 q^{7} - 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 15 * q^5 + 12 * q^6 + 35 * q^7 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 15 q^{5} + 12 q^{6} + 35 q^{7} - 16 q^{8} - 9 q^{9} - 30 q^{10} + 9 q^{11} + 12 q^{12} - 176 q^{13} + 56 q^{14} + 90 q^{15} - 16 q^{16} + 84 q^{17} + 18 q^{18} - 104 q^{19} - 120 q^{20} + 21 q^{21} + 36 q^{22} + 84 q^{23} - 24 q^{24} - 100 q^{25} - 176 q^{26} - 54 q^{27} - 28 q^{28} + 102 q^{29} + 90 q^{30} - 185 q^{31} + 32 q^{32} - 27 q^{33} + 336 q^{34} + 420 q^{35} + 72 q^{36} - 44 q^{37} + 208 q^{38} - 264 q^{39} - 120 q^{40} - 336 q^{41} + 210 q^{42} + 652 q^{43} + 36 q^{44} + 135 q^{45} - 168 q^{46} + 138 q^{47} - 96 q^{48} + 539 q^{49} - 400 q^{50} - 252 q^{51} + 352 q^{52} - 639 q^{53} - 54 q^{54} + 270 q^{55} - 280 q^{56} - 624 q^{57} + 102 q^{58} - 159 q^{59} - 180 q^{60} - 722 q^{61} - 740 q^{62} - 252 q^{63} + 128 q^{64} - 1320 q^{65} + 54 q^{66} + 166 q^{67} + 336 q^{68} + 504 q^{69} - 210 q^{70} + 2172 q^{71} + 72 q^{72} - 218 q^{73} + 88 q^{74} + 300 q^{75} + 832 q^{76} + 63 q^{77} - 1056 q^{78} + 583 q^{79} + 240 q^{80} - 81 q^{81} - 336 q^{82} - 1194 q^{83} + 336 q^{84} + 2520 q^{85} + 652 q^{86} + 153 q^{87} - 72 q^{88} + 1038 q^{89} + 540 q^{90} - 3080 q^{91} - 672 q^{92} + 555 q^{93} - 276 q^{94} + 1560 q^{95} - 96 q^{96} - 338 q^{97} + 1274 q^{98} - 162 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 15 * q^5 + 12 * q^6 + 35 * q^7 - 16 * q^8 - 9 * q^9 - 30 * q^10 + 9 * q^11 + 12 * q^12 - 176 * q^13 + 56 * q^14 + 90 * q^15 - 16 * q^16 + 84 * q^17 + 18 * q^18 - 104 * q^19 - 120 * q^20 + 21 * q^21 + 36 * q^22 + 84 * q^23 - 24 * q^24 - 100 * q^25 - 176 * q^26 - 54 * q^27 - 28 * q^28 + 102 * q^29 + 90 * q^30 - 185 * q^31 + 32 * q^32 - 27 * q^33 + 336 * q^34 + 420 * q^35 + 72 * q^36 - 44 * q^37 + 208 * q^38 - 264 * q^39 - 120 * q^40 - 336 * q^41 + 210 * q^42 + 652 * q^43 + 36 * q^44 + 135 * q^45 - 168 * q^46 + 138 * q^47 - 96 * q^48 + 539 * q^49 - 400 * q^50 - 252 * q^51 + 352 * q^52 - 639 * q^53 - 54 * q^54 + 270 * q^55 - 280 * q^56 - 624 * q^57 + 102 * q^58 - 159 * q^59 - 180 * q^60 - 722 * q^61 - 740 * q^62 - 252 * q^63 + 128 * q^64 - 1320 * q^65 + 54 * q^66 + 166 * q^67 + 336 * q^68 + 504 * q^69 - 210 * q^70 + 2172 * q^71 + 72 * q^72 - 218 * q^73 + 88 * q^74 + 300 * q^75 + 832 * q^76 + 63 * q^77 - 1056 * q^78 + 583 * q^79 + 240 * q^80 - 81 * q^81 - 336 * q^82 - 1194 * q^83 + 336 * q^84 + 2520 * q^85 + 652 * q^86 + 153 * q^87 - 72 * q^88 + 1038 * q^89 + 540 * q^90 - 3080 * q^91 - 672 * q^92 + 555 * q^93 - 276 * q^94 + 1560 * q^95 - 96 * q^96 - 338 * q^97 + 1274 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	7.50000	+	12.9904i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	7.50000	+	12.9904i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$	6.00000			0.408248
$7$	17.5000	−	6.06218i	0.944911	−	0.327327i
$7$	17.5000	−	6.06218i	0.944911	−	0.327327i
$8$	−8.00000			−0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−15.0000	+	25.9808i	−0.474342	+	0.821584i
$11$	4.50000	−	7.79423i	0.123346	−	0.213641i	−0.797739	−	0.603002i	$-0.793971\pi$
$11$	4.50000	−	7.79423i	0.123346	−	0.213641i	0.921085	+	0.389362i	$0.127304\pi$
$12$	6.00000	+	10.3923i	0.144338	+	0.250000i
$13$	−88.0000			−1.87745			−0.938723	−	0.344671i	$-0.887990\pi$
$13$	−88.0000			−1.87745			−0.938723	+	0.344671i	$0.887990\pi$
$14$	28.0000	+	24.2487i	0.534522	+	0.462910i
$15$	45.0000			0.774597
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	42.0000	−	72.7461i	0.599206	−	1.03785i	−0.393733	−	0.919225i	$-0.628817\pi$
$17$	42.0000	−	72.7461i	0.599206	−	1.03785i	0.992939	−	0.118630i	$-0.0378502\pi$
$18$	9.00000	−	15.5885i	0.117851	−	0.204124i
$19$	−52.0000	−	90.0666i	−0.627875	−	1.08751i	−0.987977	−	0.154598i	$-0.950592\pi$
$19$	−52.0000	−	90.0666i	−0.627875	−	1.08751i	0.360103	−	0.932913i	$-0.382742\pi$
$20$	−60.0000			−0.670820
$21$	10.5000	−	54.5596i	0.109109	−	0.566947i
$22$	18.0000			0.174437
$23$	42.0000	+	72.7461i	0.380765	+	0.659505i	0.991172	−	0.132583i	$-0.0423272\pi$
$23$	42.0000	+	72.7461i	0.380765	+	0.659505i	−0.610406	+	0.792088i	$0.708994\pi$
$24$	−12.0000	+	20.7846i	−0.102062	+	0.176777i
$25$	−50.0000	+	86.6025i	−0.400000	+	0.692820i
$26$	−88.0000	−	152.420i	−0.663778	−	1.14970i
$27$	−27.0000			−0.192450
$28$	−14.0000	+	72.7461i	−0.0944911	+	0.490990i
$29$	51.0000			0.326568			0.163284	−	0.986579i	$-0.447791\pi$
$29$	51.0000			0.326568			0.163284	+	0.986579i	$0.447791\pi$
$30$	45.0000	+	77.9423i	0.273861	+	0.474342i
$31$	−92.5000	+	160.215i	−0.535919	+	0.928239i	0.463199	+	0.886254i	$0.346701\pi$
$31$	−92.5000	+	160.215i	−0.535919	+	0.928239i	−0.999118	+	0.0419848i	$0.986632\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−13.5000	−	23.3827i	−0.0712136	−	0.123346i
$34$	168.000			0.847405
$35$	210.000	+	181.865i	1.01419	+	0.878310i
$36$	36.0000			0.166667
$37$	−22.0000	−	38.1051i	−0.0977507	−	0.169309i	0.813003	−	0.582260i	$-0.197831\pi$
$37$	−22.0000	−	38.1051i	−0.0977507	−	0.169309i	−0.910753	+	0.412951i	$0.864498\pi$
$38$	104.000	−	180.133i	0.443974	−	0.768986i
$39$	−132.000	+	228.631i	−0.541972	+	0.938723i
$40$	−60.0000	−	103.923i	−0.237171	−	0.410792i
$41$	−168.000			−0.639932			−0.319966	−	0.947429i	$-0.603671\pi$
$41$	−168.000			−0.639932			−0.319966	+	0.947429i	$0.603671\pi$
$42$	105.000	−	36.3731i	0.385758	−	0.133631i
$43$	326.000			1.15615			0.578076	−	0.815983i	$-0.303804\pi$
$43$	326.000			1.15615			0.578076	+	0.815983i	$0.303804\pi$
$44$	18.0000	+	31.1769i	0.0616728	+	0.106820i
$45$	67.5000	−	116.913i	0.223607	−	0.387298i
$46$	−84.0000	+	145.492i	−0.269242	+	0.466341i
$47$	69.0000	+	119.512i	0.214142	+	0.370905i	0.953007	−	0.302949i	$-0.0979711\pi$
$47$	69.0000	+	119.512i	0.214142	+	0.370905i	−0.738865	+	0.673854i	$0.764638\pi$
$48$	−48.0000			−0.144338
$49$	269.500	−	212.176i	0.785714	−	0.618590i
$50$	−200.000			−0.565685
$51$	−126.000	−	218.238i	−0.345952	−	0.599206i
$52$	176.000	−	304.841i	0.469362	−	0.812958i
$53$	−319.500	+	553.390i	−0.828051	+	1.43423i	0.0715141	+	0.997440i	$0.477217\pi$
$53$	−319.500	+	553.390i	−0.828051	+	1.43423i	−0.899565	+	0.436787i	$0.856116\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	135.000			0.330971
$56$	−140.000	+	48.4974i	−0.334077	+	0.115728i
$57$	−312.000			−0.725007
$58$	51.0000	+	88.3346i	0.115459	+	0.199981i
$59$	−79.5000	+	137.698i	−0.175424	+	0.303843i	−0.940308	−	0.340325i	$-0.889463\pi$
$59$	−79.5000	+	137.698i	−0.175424	+	0.303843i	0.764884	+	0.644168i	$0.222796\pi$
$60$	−90.0000	+	155.885i	−0.193649	+	0.335410i
$61$	−361.000	−	625.270i	−0.757726	−	1.31242i	−0.944007	−	0.329924i	$-0.892977\pi$
$61$	−361.000	−	625.270i	−0.757726	−	1.31242i	0.186281	−	0.982497i	$-0.440357\pi$
$62$	−370.000			−0.757904
$63$	−126.000	−	109.119i	−0.251976	−	0.218218i
$64$	64.0000			0.125000
$65$	−660.000	−	1143.15i	−1.25943	−	2.18140i
$66$	27.0000	−	46.7654i	0.0503556	−	0.0872185i
$67$	83.0000	−	143.760i	0.151344	−	0.262136i	−0.780378	−	0.625309i	$-0.784973\pi$
$67$	83.0000	−	143.760i	0.151344	−	0.262136i	0.931722	+	0.363173i	$0.118306\pi$
$68$	168.000	+	290.985i	0.299603	+	0.518927i
$69$	252.000			0.439670
$70$	−105.000	+	545.596i	−0.179284	+	0.931589i
$71$	1086.00			1.81527			0.907637	−	0.419755i	$-0.137884\pi$
$71$	1086.00			1.81527			0.907637	+	0.419755i	$0.137884\pi$
$72$	36.0000	+	62.3538i	0.0589256	+	0.102062i
$73$	−109.000	+	188.794i	−0.174760	+	0.302693i	−0.940078	−	0.340959i	$-0.889248\pi$
$73$	−109.000	+	188.794i	−0.174760	+	0.302693i	0.765318	+	0.643652i	$0.222582\pi$
$74$	44.0000	−	76.2102i	0.0691202	−	0.119720i
$75$	150.000	+	259.808i	0.230940	+	0.400000i
$76$	416.000			0.627875
$77$	31.5000	−	163.679i	0.0466202	−	0.242246i
$78$	−528.000			−0.766464
$79$	291.500	+	504.893i	0.415143	+	0.719049i	0.995443	−	0.0953535i	$-0.0303981\pi$
$79$	291.500	+	504.893i	0.415143	+	0.719049i	−0.580300	+	0.814403i	$0.697065\pi$
$80$	120.000	−	207.846i	0.167705	−	0.290474i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−168.000	−	290.985i	−0.226250	−	0.391876i
$83$	−597.000			−0.789509			−0.394755	−	0.918787i	$-0.629170\pi$
$83$	−597.000			−0.789509			−0.394755	+	0.918787i	$0.629170\pi$
$84$	168.000	+	145.492i	0.218218	+	0.188982i
$85$	1260.00			1.60784
$86$	326.000	+	564.649i	0.408761	+	0.707996i
$87$	76.5000	−	132.502i	0.0942720	−	0.163284i
$88$	−36.0000	+	62.3538i	−0.0436092	+	0.0755334i
$89$	519.000	+	898.934i	0.618134	+	1.07064i	0.989826	+	0.142283i	$0.0454443\pi$
$89$	519.000	+	898.934i	0.618134	+	1.07064i	−0.371692	+	0.928356i	$0.621222\pi$
$90$	270.000			0.316228
$91$	−1540.00	+	533.472i	−1.77402	+	0.614539i
$92$	−336.000			−0.380765
$93$	277.500	+	480.644i	0.309413	+	0.535919i
$94$	−138.000	+	239.023i	−0.151421	+	0.262270i
$95$	780.000	−	1351.00i	0.842382	−	1.45905i
$96$	−48.0000	−	83.1384i	−0.0510310	−	0.0883883i
$97$	−169.000			−0.176901			−0.0884503	−	0.996081i	$-0.528191\pi$
$97$	−169.000			−0.176901			−0.0884503	+	0.996081i	$0.528191\pi$
$98$	637.000	+	254.611i	0.656599	+	0.262445i
$99$	−81.0000			−0.0822304
$100$	−200.000	−	346.410i	−0.200000	−	0.346410i
$101$	−321.000	+	555.988i	−0.316244	+	0.547752i	−0.979701	−	0.200463i	$-0.935755\pi$
$101$	−321.000	+	555.988i	−0.316244	+	0.547752i	0.663457	+	0.748215i	$0.269089\pi$
$102$	252.000	−	436.477i	0.244625	−	0.423702i
$103$	−232.000	−	401.836i	−0.221938	−	0.384408i	0.733458	−	0.679735i	$-0.237905\pi$
$103$	−232.000	−	401.836i	−0.221938	−	0.384408i	−0.955396	+	0.295326i	$0.904572\pi$
$104$	704.000			0.663778
$105$	787.500	−	272.798i	0.731925	−	0.253546i
$106$	−1278.00			−1.17104
$107$	−196.500	−	340.348i	−0.177536	−	0.307502i	0.763500	−	0.645808i	$-0.223479\pi$
$107$	−196.500	−	340.348i	−0.177536	−	0.307502i	−0.941036	+	0.338306i	$0.890146\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	−7.00000	+	12.1244i	−0.00615118	+	0.0106542i	−0.869085	−	0.494663i	$-0.835291\pi$
$109$	−7.00000	+	12.1244i	−0.00615118	+	0.0106542i	0.862933	+	0.505318i	$0.168625\pi$
$110$	135.000	+	233.827i	0.117016	+	0.202677i
$111$	−132.000			−0.112873
$112$	−224.000	−	193.990i	−0.188982	−	0.163663i
$113$	−2184.00			−1.81817			−0.909086	−	0.416608i	$-0.863219\pi$
$113$	−2184.00			−1.81817			−0.909086	+	0.416608i	$0.863219\pi$
$114$	−312.000	−	540.400i	−0.256329	−	0.443974i
$115$	−630.000	+	1091.19i	−0.510850	+	0.884819i
$116$	−102.000	+	176.669i	−0.0816419	+	0.141408i
$117$	396.000	+	685.892i	0.312908	+	0.541972i
$118$	−318.000			−0.248087
$119$	294.000	−	1527.67i	0.226478	−	1.17682i
$120$	−360.000			−0.273861
$121$	625.000	+	1082.53i	0.469572	+	0.813322i
$122$	722.000	−	1250.54i	0.535794	−	0.928022i
$123$	−252.000	+	436.477i	−0.184732	+	0.319966i
$124$	−370.000	−	640.859i	−0.267960	−	0.464120i
$125$	375.000			0.268328
$126$	63.0000	−	327.358i	0.0445435	−	0.231455i
$127$	−373.000			−0.260617			−0.130309	−	0.991473i	$-0.541597\pi$
$127$	−373.000			−0.260617			−0.130309	+	0.991473i	$0.541597\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	489.000	−	846.973i	0.333752	−	0.578076i
$130$	1320.00	−	2286.31i	0.890551	−	1.54248i
$131$	586.500	+	1015.85i	0.391166	+	0.677519i	0.992604	−	0.121400i	$-0.0387385\pi$
$131$	586.500	+	1015.85i	0.391166	+	0.677519i	−0.601438	+	0.798920i	$0.705405\pi$
$132$	108.000			0.0712136
$133$	−1456.00	−	1260.93i	−0.949257	−	0.822081i
$134$	332.000			0.214033
$135$	−202.500	−	350.740i	−0.129099	−	0.223607i
$136$	−336.000	+	581.969i	−0.211851	+	0.366937i
$137$	−15.0000	+	25.9808i	−0.00935428	+	0.0162021i	−0.870665	−	0.491877i	$-0.836311\pi$
$137$	−15.0000	+	25.9808i	−0.00935428	+	0.0162021i	0.861310	+	0.508079i	$0.169644\pi$
$138$	252.000	+	436.477i	0.155447	+	0.269242i
$139$	−82.0000			−0.0500370			−0.0250185	−	0.999687i	$-0.507964\pi$
$139$	−82.0000			−0.0500370			−0.0250185	+	0.999687i	$0.507964\pi$
$140$	−1050.00	+	363.731i	−0.633866	+	0.219578i
$141$	414.000			0.247270
$142$	1086.00	+	1881.01i	0.641796	+	1.11162i
$143$	−396.000	+	685.892i	−0.231575	+	0.401099i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	382.500	+	662.509i	0.219068	+	0.379437i
$146$	−436.000			−0.247148
$147$	−147.000	−	1018.45i	−0.0824786	−	0.571429i
$148$	176.000			0.0977507
$149$	717.000	+	1241.88i	0.394221	+	0.682811i	0.993001	−	0.118102i	$-0.0376811\pi$
$149$	717.000	+	1241.88i	0.394221	+	0.682811i	−0.598780	+	0.800913i	$0.704348\pi$
$150$	−300.000	+	519.615i	−0.163299	+	0.282843i
$151$	1335.50	−	2313.15i	0.719745	−	1.24663i	−0.241356	−	0.970437i	$-0.577592\pi$
$151$	1335.50	−	2313.15i	0.719745	−	1.24663i	0.961101	−	0.276198i	$-0.0890745\pi$
$152$	416.000	+	720.533i	0.221987	+	0.384493i
$153$	−756.000			−0.399470
$154$	315.000	−	109.119i	0.164827	−	0.0570979i
$155$	−2775.00			−1.43802
$156$	−528.000	−	914.523i	−0.270986	−	0.469362i
$157$	−1126.00	+	1950.29i	−0.572386	+	0.991401i	0.423934	+	0.905693i	$0.360649\pi$
$157$	−1126.00	+	1950.29i	−0.572386	+	0.991401i	−0.996320	+	0.0857085i	$0.972685\pi$
$158$	−583.000	+	1009.79i	−0.293551	+	0.508444i
$159$	958.500	+	1660.17i	0.478075	+	0.828051i
$160$	480.000			0.237171
$161$	1176.00	+	1018.45i	0.575663	+	0.498539i
$162$	−162.000			−0.0785674
$163$	−838.000	−	1451.46i	−0.402682	−	0.697466i	0.591366	−	0.806403i	$-0.298589\pi$
$163$	−838.000	−	1451.46i	−0.402682	−	0.697466i	−0.994049	+	0.108937i	$0.965255\pi$
$164$	336.000	−	581.969i	0.159983	−	0.277098i
$165$	202.500	−	350.740i	0.0955431	−	0.165485i
$166$	−597.000	−	1034.03i	−0.279134	−	0.483474i
$167$	3030.00			1.40400			0.702001	−	0.712176i	$-0.252290\pi$
$167$	3030.00			1.40400			0.702001	+	0.712176i	$0.252290\pi$
$168$	−84.0000	+	436.477i	−0.0385758	+	0.200446i
$169$	5547.00			2.52481
$170$	1260.00	+	2182.38i	0.568456	+	0.984595i
$171$	−468.000	+	810.600i	−0.209292	+	0.362504i
$172$	−652.000	+	1129.30i	−0.289038	+	0.500628i
$173$	−1719.00	−	2977.40i	−0.755452	−	1.30848i	−0.945149	−	0.326638i	$-0.894084\pi$
$173$	−1719.00	−	2977.40i	−0.755452	−	1.30848i	0.189698	−	0.981843i	$-0.439249\pi$
$174$	306.000			0.133321
$175$	−350.000	+	1818.65i	−0.151186	+	0.785584i
$176$	−144.000			−0.0616728
$177$	238.500	+	413.094i	0.101281	+	0.175424i
$178$	−1038.00	+	1797.87i	−0.437086	+	0.757056i
$179$	606.000	−	1049.62i	0.253042	−	0.438282i	−0.711320	−	0.702869i	$-0.751902\pi$
$179$	606.000	−	1049.62i	0.253042	−	0.438282i	0.964362	+	0.264587i	$0.0852355\pi$
$180$	270.000	+	467.654i	0.111803	+	0.193649i
$181$	3032.00			1.24512			0.622560	−	0.782572i	$-0.286093\pi$
$181$	3032.00			1.24512			0.622560	+	0.782572i	$0.286093\pi$
$182$	−2464.00	−	2133.89i	−1.00354	−	0.869089i
$183$	−2166.00			−0.874947
$184$	−336.000	−	581.969i	−0.134621	−	0.233170i
$185$	330.000	−	571.577i	0.131146	−	0.227152i
$186$	−555.000	+	961.288i	−0.218788	+	0.378952i
$187$	−378.000	−	654.715i	−0.147819	−	0.256030i
$188$	−552.000			−0.214142
$189$	−472.500	+	163.679i	−0.181848	+	0.0629941i
$190$	3120.00			1.19131
$191$	−1260.00	−	2182.38i	−0.477332	−	0.826763i	0.522331	−	0.852743i	$-0.325063\pi$
$191$	−1260.00	−	2182.38i	−0.477332	−	0.826763i	−0.999662	+	0.0259799i	$0.991729\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	−182.500	+	316.099i	−0.0680655	+	0.117893i	−0.898050	−	0.439894i	$-0.855016\pi$
$193$	−182.500	+	316.099i	−0.0680655	+	0.117893i	0.829984	+	0.557787i	$0.188349\pi$
$194$	−169.000	−	292.717i	−0.0625438	−	0.108329i
$195$	−3960.00			−1.45426
$196$	196.000	+	1357.93i	0.0714286	+	0.494872i
$197$	−1590.00			−0.575040			−0.287520	−	0.957775i	$-0.592831\pi$
$197$	−1590.00			−0.575040			−0.287520	+	0.957775i	$0.592831\pi$
$198$	−81.0000	−	140.296i	−0.0290728	−	0.0503556i
$199$	2690.00	−	4659.22i	0.958236	−	1.65971i	0.231455	−	0.972846i	$-0.425652\pi$
$199$	2690.00	−	4659.22i	0.958236	−	1.65971i	0.726782	−	0.686868i	$-0.241015\pi$
$200$	400.000	−	692.820i	0.141421	−	0.244949i
$201$	−249.000	−	431.281i	−0.0873786	−	0.151344i
$202$	−1284.00			−0.447237
$203$	892.500	−	309.171i	0.308577	−	0.106894i
$204$	1008.00			0.345952
$205$	−1260.00	−	2182.38i	−0.429279	−	0.743533i
$206$	464.000	−	803.672i	0.156934	−	0.271818i
$207$	378.000	−	654.715i	0.126922	−	0.219835i
$208$	704.000	+	1219.36i	0.234681	+	0.406479i
$209$	−936.000			−0.309782
$210$	1260.00	+	1091.19i	0.414039	+	0.358569i
$211$	−5362.00			−1.74946			−0.874728	−	0.484614i	$-0.838960\pi$
$211$	−5362.00			−1.74946			−0.874728	+	0.484614i	$0.838960\pi$
$212$	−1278.00	−	2213.56i	−0.414025	−	0.717113i
$213$	1629.00	−	2821.51i	0.524025	−	0.907637i
$214$	393.000	−	680.696i	0.125537	−	0.217437i
$215$	2445.00	+	4234.86i	0.775570	+	1.34333i
$216$	216.000			0.0680414
$217$	−647.500	+	3364.51i	−0.202558	+	1.05252i
$218$	−28.0000			−0.00869908
$219$	327.000	+	566.381i	0.100898	+	0.174760i
$220$	−270.000	+	467.654i	−0.0827427	+	0.143315i
$221$	−3696.00	+	6401.66i	−1.12498	+	1.94852i
$222$	−132.000	−	228.631i	−0.0399066	−	0.0691202i
$223$	−1573.00			−0.472358			−0.236179	−	0.971710i	$-0.575895\pi$
$223$	−1573.00			−0.472358			−0.236179	+	0.971710i	$0.575895\pi$
$224$	112.000	−	581.969i	0.0334077	−	0.173591i
$225$	900.000			0.266667
$226$	−2184.00	−	3782.80i	−0.642821	−	1.11340i
$227$	−460.500	+	797.609i	−0.134645	+	0.233212i	−0.925462	−	0.378841i	$-0.876323\pi$
$227$	−460.500	+	797.609i	−0.134645	+	0.233212i	0.790817	+	0.612053i	$0.209656\pi$
$228$	624.000	−	1080.80i	0.181252	−	0.313937i
$229$	−2026.00	−	3509.13i	−0.584637	−	1.01262i	−0.994921	−	0.100663i	$-0.967904\pi$
$229$	−2026.00	−	3509.13i	−0.584637	−	1.01262i	0.410284	−	0.911958i	$-0.365430\pi$
$230$	−2520.00			−0.722452
$231$	−378.000	−	327.358i	−0.107665	−	0.0932405i
$232$	−408.000			−0.115459
$233$	234.000	+	405.300i	0.0657933	+	0.113957i	0.897046	−	0.441938i	$-0.145709\pi$
$233$	234.000	+	405.300i	0.0657933	+	0.113957i	−0.831252	+	0.555895i	$0.812376\pi$
$234$	−792.000	+	1371.78i	−0.221259	+	0.383232i
$235$	−1035.00	+	1792.67i	−0.287302	+	0.497622i
$236$	−318.000	−	550.792i	−0.0877120	−	0.151922i
$237$	1749.00			0.479366
$238$	2940.00	−	1018.45i	0.800722	−	0.277378i
$239$	4932.00			1.33483			0.667415	−	0.744686i	$-0.267401\pi$
$239$	4932.00			1.33483			0.667415	+	0.744686i	$0.267401\pi$
$240$	−360.000	−	623.538i	−0.0968246	−	0.167705i
$241$	768.500	−	1331.08i	0.205408	−	0.355778i	−0.744854	−	0.667227i	$-0.767481\pi$
$241$	768.500	−	1331.08i	0.205408	−	0.355778i	0.950263	+	0.311449i	$0.100814\pi$
$242$	−1250.00	+	2165.06i	−0.332037	+	0.575106i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	2888.00			0.757726
$245$	4777.50	+	1909.59i	1.24581	+	0.497955i
$246$	−1008.00			−0.261251
$247$	4576.00	+	7925.86i	1.17880	+	2.04174i
$248$	740.000	−	1281.72i	0.189476	−	0.328182i
$249$	−895.500	+	1551.05i	−0.227912	+	0.394755i
$250$	375.000	+	649.519i	0.0948683	+	0.164317i
$251$	5319.00			1.33758			0.668789	−	0.743452i	$-0.266813\pi$
$251$	5319.00			1.33758			0.668789	+	0.743452i	$0.266813\pi$
$252$	630.000	−	218.238i	0.157485	−	0.0545545i
$253$	756.000			0.187863
$254$	−373.000	−	646.055i	−0.0921421	−	0.159595i
$255$	1890.00	−	3273.58i	0.464143	−	0.803919i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2673.00	−	4629.77i	−0.648783	−	1.12372i	−0.983414	−	0.181375i	$-0.941945\pi$
$257$	−2673.00	−	4629.77i	−0.648783	−	1.12372i	0.334631	−	0.942349i	$-0.391388\pi$
$258$	1956.00			0.471997
$259$	−616.000	−	533.472i	−0.147785	−	0.127986i
$260$	5280.00			1.25943
$261$	−229.500	−	397.506i	−0.0544279	−	0.0942720i
$262$	−1173.00	+	2031.70i	−0.276596	+	0.479079i
$263$	−387.000	+	670.304i	−0.0907355	+	0.157159i	−0.907821	−	0.419358i	$-0.862255\pi$
$263$	−387.000	+	670.304i	−0.0907355	+	0.157159i	0.817085	+	0.576517i	$0.195588\pi$
$264$	108.000	+	187.061i	0.0251778	+	0.0436092i
$265$	−9585.00			−2.22189
$266$	728.000	−	3782.80i	0.167807	−	0.871948i
$267$	3114.00			0.713759
$268$	332.000	+	575.041i	0.0756721	+	0.131068i
$269$	−1207.50	+	2091.45i	−0.273690	+	0.474045i	−0.969804	−	0.243887i	$-0.921578\pi$
$269$	−1207.50	+	2091.45i	−0.273690	+	0.474045i	0.696114	+	0.717931i	$0.254911\pi$
$270$	405.000	−	701.481i	0.0912871	−	0.158114i
$271$	237.500	+	411.362i	0.0532365	+	0.0922084i	0.891416	−	0.453187i	$-0.149713\pi$
$271$	237.500	+	411.362i	0.0532365	+	0.0922084i	−0.838179	+	0.545395i	$0.816380\pi$
$272$	−1344.00			−0.299603
$273$	−924.000	+	4801.24i	−0.204846	+	1.06441i
$274$	−60.0000			−0.0132290
$275$	450.000	+	779.423i	0.0986764	+	0.170913i
$276$	−504.000	+	872.954i	−0.109918	+	0.190383i
$277$	−1864.00	+	3228.54i	−0.404321	+	0.700304i	−0.994242	−	0.107156i	$-0.965825\pi$
$277$	−1864.00	+	3228.54i	−0.404321	+	0.700304i	0.589921	+	0.807461i	$0.299159\pi$
$278$	−82.0000	−	142.028i	−0.0176908	−	0.0306413i
$279$	1665.00			0.357279
$280$	−1680.00	−	1454.92i	−0.358569	−	0.310530i
$281$	1602.00			0.340097			0.170049	−	0.985436i	$-0.445608\pi$
$281$	1602.00			0.340097			0.170049	+	0.985436i	$0.445608\pi$
$282$	414.000	+	717.069i	0.0874232	+	0.151421i
$283$	−343.000	+	594.093i	−0.0720468	+	0.124789i	−0.899798	−	0.436306i	$-0.856286\pi$
$283$	−343.000	+	594.093i	−0.0720468	+	0.124789i	0.827751	+	0.561095i	$0.189620\pi$
$284$	−2172.00	+	3762.01i	−0.453819	+	0.786037i
$285$	−2340.00	−	4053.00i	−0.486350	−	0.842382i
$286$	−1584.00			−0.327496
$287$	−2940.00	+	1018.45i	−0.604678	+	0.209467i
$288$	−288.000			−0.0589256
$289$	−1071.50	−	1855.89i	−0.218095	−	0.377751i
$290$	−765.000	+	1325.02i	−0.154905	+	0.268303i
$291$	−253.500	+	439.075i	−0.0510668	+	0.0884503i
$292$	−436.000	−	755.174i	−0.0873800	−	0.151347i
$293$	−1101.00			−0.219526			−0.109763	−	0.993958i	$-0.535009\pi$
$293$	−1101.00			−0.219526			−0.109763	+	0.993958i	$0.535009\pi$
$294$	1617.00	−	1273.06i	0.320767	−	0.252538i
$295$	−2385.00			−0.470712
$296$	176.000	+	304.841i	0.0345601	+	0.0598599i
$297$	−121.500	+	210.444i	−0.0237379	+	0.0411152i
$298$	−1434.00	+	2483.76i	−0.278756	+	0.482820i
$299$	−3696.00	−	6401.66i	−0.714867	−	1.23819i
$300$	−1200.00			−0.230940
$301$	5705.00	−	1976.27i	1.09246	−	0.378440i
$302$	5342.00			1.01787
$303$	963.000	+	1667.96i	0.182584	+	0.316244i
$304$	−832.000	+	1441.07i	−0.156969	+	0.271878i
$305$	5415.00	−	9379.06i	1.01660	−	1.76080i
$306$	−756.000	−	1309.43i	−0.141234	−	0.244625i
$307$	2780.00			0.516818			0.258409	−	0.966036i	$-0.416802\pi$
$307$	2780.00			0.516818			0.258409	+	0.966036i	$0.416802\pi$
$308$	504.000	+	436.477i	0.0932405	+	0.0807486i
$309$	−1392.00			−0.256272
$310$	−2775.00	−	4806.44i	−0.508417	−	0.880605i
$311$	−2148.00	+	3720.45i	−0.391646	+	0.678351i	−0.992667	−	0.120883i	$-0.961428\pi$
$311$	−2148.00	+	3720.45i	−0.391646	+	0.678351i	0.601021	+	0.799233i	$0.294761\pi$
$312$	1056.00	−	1829.05i	0.191616	−	0.331889i
$313$	−2744.50	−	4753.61i	−0.495618	−	0.858435i	0.504370	−	0.863488i	$-0.331725\pi$
$313$	−2744.50	−	4753.61i	−0.495618	−	0.858435i	−0.999987	+	0.00505298i	$0.998392\pi$
$314$	−4504.00			−0.809476
$315$	472.500	−	2455.18i	0.0845154	−	0.439155i
$316$	−2332.00			−0.415143
$317$	−2245.50	−	3889.32i	−0.397854	−	0.689104i	0.595607	−	0.803276i	$-0.296912\pi$
$317$	−2245.50	−	3889.32i	−0.397854	−	0.689104i	−0.993461	+	0.114172i	$0.963578\pi$
$318$	−1917.00	+	3320.34i	−0.338050	+	0.585520i
$319$	229.500	−	397.506i	0.0402807	−	0.0697682i
$320$	480.000	+	831.384i	0.0838525	+	0.145237i
$321$	−1179.00			−0.205001
$322$	−588.000	+	3055.34i	−0.101764	+	0.528780i
$323$	−8736.00			−1.50490
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	4400.00	−	7621.02i	0.750979	−	1.30073i
$326$	1676.00	−	2902.92i	0.284739	−	0.493183i
$327$	21.0000	+	36.3731i	0.00355138	+	0.00615118i
$328$	1344.00			0.226250
$329$	1932.00	+	1673.16i	0.323753	+	0.280378i
$330$	810.000			0.135118
$331$	1982.00	+	3432.92i	0.329126	+	0.570062i	0.982339	−	0.187112i	$-0.0599127\pi$
$331$	1982.00	+	3432.92i	0.329126	+	0.570062i	−0.653213	+	0.757174i	$0.726579\pi$
$332$	1194.00	−	2068.07i	0.197377	−	0.341868i
$333$	−198.000	+	342.946i	−0.0325836	+	0.0564364i
$334$	3030.00	+	5248.11i	0.496390	+	0.859773i
$335$	2490.00			0.406099
$336$	−840.000	+	290.985i	−0.136386	+	0.0472456i
$337$	161.000			0.0260244			0.0130122	−	0.999915i	$-0.495858\pi$
$337$	161.000			0.0260244			0.0130122	+	0.999915i	$0.495858\pi$
$338$	5547.00	+	9607.69i	0.892654	+	1.54612i
$339$	−3276.00	+	5674.20i	−0.524861	+	0.909086i
$340$	−2520.00	+	4364.77i	−0.401959	+	0.696214i
$341$	832.500	+	1441.93i	0.132206	+	0.228988i
$342$	−1872.00			−0.295983
$343$	3430.00	−	5346.84i	0.539949	−	0.841698i
$344$	−2608.00			−0.408761
$345$	1890.00	+	3273.58i	0.294940	+	0.510850i
$346$	3438.00	−	5954.79i	0.534185	−	0.925236i
$347$	2958.00	−	5123.41i	0.457619	−	0.792619i	−0.541216	−	0.840884i	$-0.682036\pi$
$347$	2958.00	−	5123.41i	0.457619	−	0.792619i	0.998835	+	0.0482646i	$0.0153691\pi$
$348$	306.000	+	530.008i	0.0471360	+	0.0816419i
$349$	−142.000			−0.0217796			−0.0108898	−	0.999941i	$-0.503466\pi$
$349$	−142.000			−0.0217796			−0.0108898	+	0.999941i	$0.503466\pi$
$350$	−3500.00	+	1212.44i	−0.534522	+	0.185164i
$351$	2376.00			0.361315
$352$	−144.000	−	249.415i	−0.0218046	−	0.0377667i
$353$	2220.00	−	3845.15i	0.334727	−	0.579764i	−0.648705	−	0.761040i	$-0.724689\pi$
$353$	2220.00	−	3845.15i	0.334727	−	0.579764i	0.983432	+	0.181275i	$0.0580225\pi$
$354$	−477.000	+	826.188i	−0.0716166	+	0.124044i
$355$	8145.00	+	14107.6i	1.21772	+	2.10916i
$356$	−4152.00			−0.618134
$357$	−3528.00	−	3055.34i	−0.523030	−	0.452957i
$358$	2424.00			0.357856
$359$	−1143.00	−	1979.73i	−0.168037	−	0.291048i	0.769693	−	0.638415i	$-0.220409\pi$
$359$	−1143.00	−	1979.73i	−0.168037	−	0.291048i	−0.937730	+	0.347366i	$0.887076\pi$
$360$	−540.000	+	935.307i	−0.0790569	+	0.136931i
$361$	−1978.50	+	3426.86i	−0.288453	+	0.499615i
$362$	3032.00	+	5251.58i	0.440217	+	0.762477i
$363$	3750.00			0.542215
$364$	1232.00	−	6401.66i	0.177402	−	0.921808i
$365$	−3270.00			−0.468930
$366$	−2166.00	−	3751.62i	−0.309341	−	0.535794i
$367$	1434.50	−	2484.63i	0.204033	−	0.353396i	−0.745791	−	0.666180i	$-0.767928\pi$
$367$	1434.50	−	2484.63i	0.204033	−	0.353396i	0.949824	+	0.312784i	$0.101262\pi$
$368$	672.000	−	1163.94i	0.0951914	−	0.164876i
$369$	756.000	+	1309.43i	0.106655	+	0.184732i
$370$	1320.00			0.185469
$371$	−2236.50	+	11621.2i	−0.312974	+	1.62626i
$372$	−2220.00			−0.309413
$373$	1532.00	+	2653.50i	0.212665	+	0.368346i	0.952548	−	0.304390i	$-0.0984524\pi$
$373$	1532.00	+	2653.50i	0.212665	+	0.368346i	−0.739883	+	0.672736i	$0.765119\pi$
$374$	756.000	−	1309.43i	0.104524	−	0.181040i
$375$	562.500	−	974.279i	0.0774597	−	0.134164i
$376$	−552.000	−	956.092i	−0.0757107	−	0.131135i
$377$	−4488.00			−0.613113
$378$	−756.000	−	654.715i	−0.102869	−	0.0890871i
$379$	−6040.00			−0.818612			−0.409306	−	0.912397i	$-0.634229\pi$
$379$	−6040.00			−0.818612			−0.409306	+	0.912397i	$0.634229\pi$
$380$	3120.00	+	5404.00i	0.421191	+	0.729524i
$381$	−559.500	+	969.082i	−0.0752337	+	0.130309i
$382$	2520.00	−	4364.77i	0.337525	−	0.584610i
$383$	−921.000	−	1595.22i	−0.122874	−	0.212825i	0.798026	−	0.602623i	$-0.205878\pi$
$383$	−921.000	−	1595.22i	−0.122874	−	0.212825i	−0.920900	+	0.389799i	$0.872545\pi$
$384$	384.000			0.0510310
$385$	2362.50	−	818.394i	0.312738	−	0.108336i
$386$	−730.000			−0.0962591
$387$	−1467.00	−	2540.92i	−0.192692	−	0.333752i
$388$	338.000	−	585.433i	0.0442251	−	0.0766002i
$389$	−3915.00	+	6780.98i	−0.510279	+	0.883828i	0.489650	+	0.871919i	$0.337124\pi$
$389$	−3915.00	+	6780.98i	−0.510279	+	0.883828i	−0.999929	+	0.0119097i	$0.996209\pi$
$390$	−3960.00	−	6858.92i	−0.514160	−	0.890551i
$391$	7056.00			0.912627
$392$	−2156.00	+	1697.41i	−0.277792	+	0.218704i
$393$	3519.00			0.451680
$394$	−1590.00	−	2753.96i	−0.203307	−	0.352138i
$395$	−4372.50	+	7573.39i	−0.556973	+	0.964706i
$396$	162.000	−	280.592i	0.0205576	−	0.0356068i
$397$	7382.00	+	12786.0i	0.933229	+	1.61640i	0.777762	+	0.628559i	$0.216355\pi$
$397$	7382.00	+	12786.0i	0.933229	+	1.61640i	0.155467	+	0.987841i	$0.450312\pi$
$398$	10760.0			1.35515
$399$	−5460.00	+	1891.40i	−0.685067	+	0.237314i
$400$	1600.00			0.200000
$401$	−3132.00	−	5424.78i	−0.390036	−	0.675563i	0.602417	−	0.798181i	$-0.294204\pi$
$401$	−3132.00	−	5424.78i	−0.390036	−	0.675563i	−0.992454	+	0.122618i	$0.960871\pi$
$402$	498.000	−	862.561i	0.0617860	−	0.107017i
$403$	8140.00	−	14098.9i	1.00616	−	1.74272i
$404$	−1284.00	−	2223.95i	−0.158122	−	0.273876i
$405$	−1215.00			−0.149071
$406$	1428.00	+	1236.68i	0.174558	+	0.151171i
$407$	−396.000			−0.0482285
$408$	1008.00	+	1745.91i	0.122312	+	0.211851i
$409$	−2375.50	+	4114.49i	−0.287191	+	0.497429i	−0.973138	−	0.230222i	$-0.926055\pi$
$409$	−2375.50	+	4114.49i	−0.287191	+	0.497429i	0.685948	+	0.727651i	$0.259388\pi$
$410$	2520.00	−	4364.77i	0.303546	−	0.525757i
$411$	45.0000	+	77.9423i	0.00540070	+	0.00935428i
$412$	1856.00			0.221938
$413$	−556.500	+	2891.66i	−0.0663041	+	0.344526i
$414$	1512.00			0.179495
$415$	−4477.50	−	7755.26i	−0.529619	−	0.917327i
$416$	−1408.00	+	2438.73i	−0.165944	+	0.287424i
$417$	−123.000	+	213.042i	−0.0144445	+	0.0250185i
$418$	−936.000	−	1621.20i	−0.109525	−	0.189702i
$419$	−4704.00			−0.548462			−0.274231	−	0.961664i	$-0.588423\pi$
$419$	−4704.00			−0.548462			−0.274231	+	0.961664i	$0.588423\pi$
$420$	−630.000	+	3273.58i	−0.0731925	+	0.380319i
$421$	−4474.00			−0.517932			−0.258966	−	0.965886i	$-0.583382\pi$
$421$	−4474.00			−0.517932			−0.258966	+	0.965886i	$0.583382\pi$
$422$	−5362.00	−	9287.26i	−0.618526	−	1.07132i
$423$	621.000	−	1075.60i	0.0713807	−	0.123635i
$424$	2556.00	−	4427.12i	0.292760	−	0.507076i
$425$	4200.00	+	7274.61i	0.479365	+	0.830284i
$426$	6516.00			0.741083
$427$	−10108.0	−	8753.78i	−1.14557	−	0.992097i
$428$	1572.00			0.177536
$429$	1188.00	+	2057.68i	0.133700	+	0.231575i
$430$	−4890.00	+	8469.73i	−0.548411	+	0.949876i
$431$	6402.00	−	11088.6i	0.715484	−	1.23925i	−0.247289	−	0.968942i	$-0.579540\pi$
$431$	6402.00	−	11088.6i	0.715484	−	1.23925i	0.962773	−	0.270312i	$-0.0871270\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−5074.00			−0.563143			−0.281571	−	0.959540i	$-0.590856\pi$
$433$	−5074.00			−0.563143			−0.281571	+	0.959540i	$0.590856\pi$
$434$	−6475.00	+	2243.01i	−0.716152	+	0.248082i
$435$	2295.00			0.252958
$436$	−28.0000	−	48.4974i	−0.00307559	−	0.00532708i
$437$	4368.00	−	7565.60i	0.478146	−	0.828173i
$438$	−654.000	+	1132.76i	−0.0713455	+	0.123574i
$439$	633.500	+	1097.25i	0.0688731	+	0.119292i	0.898406	−	0.439167i	$-0.144726\pi$
$439$	633.500	+	1097.25i	0.0688731	+	0.119292i	−0.829532	+	0.558459i	$0.811393\pi$
$440$	−1080.00			−0.117016
$441$	−2866.50	−	1145.75i	−0.309524	−	0.123718i
$442$	−14784.0			−1.59096
$443$	3466.50	+	6004.15i	0.371780	+	0.643941i	0.989839	−	0.142190i	$-0.0454144\pi$
$443$	3466.50	+	6004.15i	0.371780	+	0.643941i	−0.618060	+	0.786131i	$0.712081\pi$
$444$	264.000	−	457.261i	0.0282182	−	0.0488754i
$445$	−7785.00	+	13484.0i	−0.829313	+	1.43641i
$446$	−1573.00	−	2724.52i	−0.167004	−	0.289259i
$447$	4302.00			0.455207
$448$	1120.00	−	387.979i	0.118114	−	0.0409159i
$449$	11688.0			1.22849			0.614244	−	0.789116i	$-0.289461\pi$
$449$	11688.0			1.22849			0.614244	+	0.789116i	$0.289461\pi$
$450$	900.000	+	1558.85i	0.0942809	+	0.163299i
$451$	−756.000	+	1309.43i	−0.0789327	+	0.136715i
$452$	4368.00	−	7565.60i	0.454543	−	0.787292i
$453$	−4006.50	−	6939.46i	−0.415545	−	0.719745i
$454$	−1842.00			−0.190417
$455$	−18480.0	−	16004.1i	−1.90408	−	1.64898i
$456$	2496.00			0.256329
$457$	−275.500	−	477.180i	−0.0281999	−	0.0488436i	0.851581	−	0.524223i	$-0.175644\pi$
$457$	−275.500	−	477.180i	−0.0281999	−	0.0488436i	−0.879781	+	0.475379i	$0.842311\pi$
$458$	4052.00	−	7018.27i	0.413401	−	0.716031i
$459$	−1134.00	+	1964.15i	−0.115317	+	0.199735i
$460$	−2520.00	−	4364.77i	−0.255425	−	0.442409i
$461$	13386.0			1.35238			0.676191	−	0.736726i	$-0.263629\pi$
$461$	13386.0			1.35238			0.676191	+	0.736726i	$0.263629\pi$
$462$	189.000	−	982.073i	0.0190326	−	0.0988965i
$463$	−6376.00			−0.639995			−0.319998	−	0.947418i	$-0.603682\pi$
$463$	−6376.00			−0.639995			−0.319998	+	0.947418i	$0.603682\pi$
$464$	−408.000	−	706.677i	−0.0408210	−	0.0707040i
$465$	−4162.50	+	7209.66i	−0.415121	+	0.719011i
$466$	−468.000	+	810.600i	−0.0465229	+	0.0805801i
$467$	−2850.00	−	4936.34i	−0.282403	−	0.489137i	0.689573	−	0.724216i	$-0.257798\pi$
$467$	−2850.00	−	4936.34i	−0.282403	−	0.489137i	−0.971976	+	0.235080i	$0.924465\pi$
$468$	−3168.00			−0.312908
$469$	581.000	−	3018.96i	0.0572027	−	0.297234i
$470$	−4140.00			−0.406306
$471$	3378.00	+	5850.87i	0.330467	+	0.572386i
$472$	636.000	−	1101.58i	0.0620218	−	0.107425i
$473$	1467.00	−	2540.92i	0.142606	−	0.247001i
$474$	1749.00	+	3029.36i	0.169481	+	0.293551i
$475$	10400.0			1.00460
$476$	4704.00	+	4073.78i	0.452957	+	0.392272i
$477$	5751.00			0.552034
$478$	4932.00	+	8542.47i	0.471934	+	0.817414i
$479$	−9897.00	+	17142.1i	−0.944062	+	1.63516i	−0.186442	+	0.982466i	$0.559696\pi$
$479$	−9897.00	+	17142.1i	−0.944062	+	1.63516i	−0.757619	+	0.652697i	$0.773638\pi$
$480$	720.000	−	1247.08i	0.0684653	−	0.118585i
$481$	1936.00	+	3353.25i	0.183522	+	0.317869i
$482$	3074.00			0.290491
$483$	4410.00	−	1527.67i	0.415449	−	0.143916i
$484$	−5000.00			−0.469572
$485$	−1267.50	−	2195.37i	−0.118668	−	0.205540i
$486$	−243.000	+	420.888i	−0.0226805	+	0.0392837i
$487$	−7967.50	+	13800.1i	−0.741359	+	1.28407i	0.210517	+	0.977590i	$0.432485\pi$
$487$	−7967.50	+	13800.1i	−0.741359	+	1.28407i	−0.951877	+	0.306482i	$0.900848\pi$
$488$	2888.00	+	5002.16i	0.267897	+	0.464011i
$489$	−5028.00			−0.464978
$490$	1470.00	+	10184.5i	0.135526	+	0.938953i
$491$	9963.00			0.915731			0.457865	−	0.889021i	$-0.348614\pi$
$491$	9963.00			0.915731			0.457865	+	0.889021i	$0.348614\pi$
$492$	−1008.00	−	1745.91i	−0.0923662	−	0.159983i
$493$	2142.00	−	3710.05i	0.195681	−	0.338930i
$494$	−9152.00	+	15851.7i	−0.833538	+	1.44373i
$495$	−607.500	−	1052.22i	−0.0551618	−	0.0955431i
$496$	2960.00			0.267960
$497$	19005.0	−	6583.53i	1.71527	−	0.594188i
$498$	−3582.00			−0.322316
$499$	−9571.00	−	16577.5i	−0.858631	−	1.48719i	−0.873235	−	0.487299i	$-0.837982\pi$
$499$	−9571.00	−	16577.5i	−0.858631	−	1.48719i	0.0146043	−	0.999893i	$-0.495351\pi$
$500$	−750.000	+	1299.04i	−0.0670820	+	0.116190i
$501$	4545.00	−	7872.17i	0.405301	−	0.702001i
$502$	5319.00	+	9212.78i	0.472906	+	0.819096i
$503$	−12192.0			−1.08074			−0.540372	−	0.841426i	$-0.681717\pi$
$503$	−12192.0			−1.08074			−0.540372	+	0.841426i	$0.681717\pi$
$504$	1008.00	+	872.954i	0.0890871	+	0.0771517i
$505$	−9630.00			−0.848573
$506$	756.000	+	1309.43i	0.0664196	+	0.115042i
$507$	8320.50	−	14411.5i	0.728849	−	1.26240i
$508$	746.000	−	1292.11i	0.0651543	−	0.112851i
$509$	9904.50	+	17155.1i	0.862494	+	1.49388i	0.869515	+	0.493907i	$0.164432\pi$
$509$	9904.50	+	17155.1i	0.862494	+	1.49388i	−0.00702091	+	0.999975i	$0.502235\pi$
$510$	7560.00			0.656397
$511$	−763.000	+	3964.66i	−0.0660531	+	0.343222i
$512$	−512.000			−0.0441942
$513$	1404.00	+	2431.80i	0.120835	+	0.209292i
$514$	5346.00	−	9259.54i	0.458759	−	0.794593i
$515$	3480.00	−	6027.54i	0.297761	−	0.515738i
$516$	1956.00	+	3387.89i	0.166876	+	0.289038i
$517$	1242.00			0.105654
$518$	308.000	−	1600.41i	0.0261250	−	0.135749i
$519$	−10314.0			−0.872321
$520$	5280.00	+	9145.23i	0.445276	+	0.771240i
$521$	897.000	−	1553.65i	0.0754286	−	0.130646i	−0.825844	−	0.563899i	$-0.809301\pi$
$521$	897.000	−	1553.65i	0.0754286	−	0.130646i	0.901273	+	0.433253i	$0.142634\pi$
$522$	459.000	−	795.011i	0.0384864	−	0.0666603i
$523$	3224.00	+	5584.13i	0.269552	+	0.466878i	0.968746	−	0.248054i	$-0.0797911\pi$
$523$	3224.00	+	5584.13i	0.269552	+	0.466878i	−0.699194	+	0.714932i	$0.746458\pi$
$524$	−4692.00			−0.391166
$525$	4200.00	+	3637.31i	0.349149	+	0.302372i
$526$	−1548.00			−0.128319
$527$	7770.00	+	13458.0i	0.642251	+	1.11241i
$528$	−216.000	+	374.123i	−0.0178034	+	0.0308364i
$529$	2555.50	−	4426.26i	0.210035	−	0.363792i
$530$	−9585.00	−	16601.7i	−0.785558	−	1.36063i
$531$	1431.00			0.116949
$532$	7280.00	−	2521.87i	0.593286	−	0.205520i
$533$	14784.0			1.20144
$534$	3114.00	+	5393.61i	0.252352	+	0.437086i
$535$	2947.50	−	5105.22i	0.238190	−	0.412557i
$536$	−664.000	+	1150.08i	−0.0535083	+	0.0926790i
$537$	−1818.00	−	3148.87i	−0.146094	−	0.253042i
$538$	−4830.00			−0.387056
$539$	−441.000	−	3055.34i	−0.0352416	−	0.244161i
$540$	1620.00			0.129099
$541$	−3631.00	−	6289.08i	−0.288556	−	0.499794i	0.684909	−	0.728628i	$-0.259842\pi$
$541$	−3631.00	−	6289.08i	−0.288556	−	0.499794i	−0.973465	+	0.228835i	$0.926509\pi$
$542$	−475.000	+	822.724i	−0.0376439	+	0.0652012i
$543$	4548.00	−	7877.37i	0.359435	−	0.622560i
$544$	−1344.00	−	2327.88i	−0.105926	−	0.183469i
$545$	−210.000			−0.0165053
$546$	−9240.00	+	3200.83i	−0.724241	+	0.250884i
$547$	14204.0			1.11027			0.555136	−	0.831759i	$-0.312666\pi$
$547$	14204.0			1.11027			0.555136	+	0.831759i	$0.312666\pi$
$548$	−60.0000	−	103.923i	−0.00467714	−	0.00810104i
$549$	−3249.00	+	5627.43i	−0.252575	+	0.437474i
$550$	−900.000	+	1558.85i	−0.0697748	+	0.120853i
$551$	−2652.00	−	4593.40i	−0.205044	−	0.355146i
$552$	−2016.00			−0.155447
$553$	8162.00	+	7068.50i	0.627638	+	0.543550i
$554$	−7456.00			−0.571796
$555$	−990.000	−	1714.73i	−0.0757174	−	0.131146i
$556$	164.000	−	284.056i	0.0125093	−	0.0216667i
$557$	−7912.50	+	13704.9i	−0.601909	+	1.04254i	0.390623	+	0.920551i	$0.372260\pi$
$557$	−7912.50	+	13704.9i	−0.601909	+	1.04254i	−0.992532	+	0.121986i	$0.961074\pi$
$558$	1665.00	+	2883.86i	0.126317	+	0.218788i
$559$	−28688.0			−2.17061
$560$	840.000	−	4364.77i	0.0633866	−	0.329366i
$561$	−2268.00			−0.170686
$562$	1602.00	+	2774.75i	0.120243	+	0.208266i
$563$	−529.500	+	917.121i	−0.0396372	+	0.0686537i	−0.885163	−	0.465280i	$-0.845954\pi$
$563$	−529.500	+	917.121i	−0.0396372	+	0.0686537i	0.845526	+	0.533934i	$0.179287\pi$
$564$	−828.000	+	1434.14i	−0.0618175	+	0.107071i
$565$	−16380.0	−	28371.0i	−1.21967	−	2.11252i
$566$	−1372.00			−0.101890
$567$	−283.500	+	1473.11i	−0.0209980	+	0.109109i
$568$	−8688.00			−0.641796
$569$	−1980.00	−	3429.46i	−0.145880	−	0.252672i	0.783821	−	0.620987i	$-0.213268\pi$
$569$	−1980.00	−	3429.46i	−0.145880	−	0.252672i	−0.929701	+	0.368315i	$0.879935\pi$
$570$	4680.00	−	8106.00i	0.343901	−	0.595654i
$571$	1265.00	−	2191.04i	0.0927121	−	0.160582i	−0.815939	−	0.578138i	$-0.803780\pi$
$571$	1265.00	−	2191.04i	0.0927121	−	0.160582i	0.908651	+	0.417555i	$0.137113\pi$
$572$	−1584.00	−	2743.57i	−0.115787	−	0.200550i
$573$	−7560.00			−0.551175
$574$	−4704.00	−	4073.78i	−0.342058	−	0.296231i
$575$	−8400.00			−0.609225
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−5915.50	+	10245.9i	−0.426803	+	0.739245i	−0.996587	−	0.0825498i	$-0.973694\pi$
$577$	−5915.50	+	10245.9i	−0.426803	+	0.739245i	0.569784	+	0.821795i	$0.307027\pi$
$578$	2143.00	−	3711.78i	0.154216	−	0.267111i
$579$	547.500	+	948.298i	0.0392976	+	0.0680655i
$580$	−3060.00			−0.219068
$581$	−10447.5	+	3619.12i	−0.746016	+	0.258428i
$582$	−1014.00			−0.0722193
$583$	2875.50	+	4980.51i	0.204273	+	0.353811i
$584$	872.000	−	1510.35i	0.0617870	−	0.107018i
$585$	−5940.00	+	10288.4i	−0.419810	+	0.727132i
$586$	−1101.00	−	1906.99i	−0.0776141	−	0.134432i
$587$	4809.00			0.338141			0.169070	−	0.985604i	$-0.445923\pi$
$587$	4809.00			0.338141			0.169070	+	0.985604i	$0.445923\pi$
$588$	3822.00	+	1527.67i	0.268055	+	0.107143i
$589$	19240.0			1.34596
$590$	−2385.00	−	4130.94i	−0.166422	−	0.288251i
$591$	−2385.00	+	4130.94i	−0.166000	+	0.287520i
$592$	−352.000	+	609.682i	−0.0244377	+	0.0423273i
$593$	−10902.0	−	18882.8i	−0.754960	−	1.30763i	−0.945394	−	0.325930i	$-0.894323\pi$
$593$	−10902.0	−	18882.8i	−0.754960	−	1.30763i	0.190434	−	0.981700i	$-0.439011\pi$
$594$	−486.000			−0.0335704
$595$	22050.0	−	7638.34i	1.51926	−	0.526288i
$596$	−5736.00			−0.394221
$597$	−8070.00	−	13977.7i	−0.553238	−	0.958236i
$598$	7392.00	−	12803.3i	0.505487	−	0.875530i
$599$	−7083.00	+	12268.1i	−0.483144	+	0.836831i	−0.999813	−	0.0193549i	$-0.993839\pi$
$599$	−7083.00	+	12268.1i	−0.483144	+	0.836831i	0.516668	+	0.856186i	$0.327172\pi$
$600$	−1200.00	−	2078.46i	−0.0816497	−	0.141421i
$601$	5891.00			0.399832			0.199916	−	0.979813i	$-0.435933\pi$
$601$	5891.00			0.399832			0.199916	+	0.979813i	$0.435933\pi$
$602$	9128.00	+	7905.08i	0.617989	+	0.535194i
$603$	−1494.00			−0.100896
$604$	5342.00	+	9252.62i	0.359872	+	0.623317i
$605$	−9375.00	+	16238.0i	−0.629997	+	1.09119i
$606$	−1926.00	+	3335.93i	−0.129106	+	0.223619i
$607$	1368.50	+	2370.31i	0.0915086	+	0.158497i	0.908146	−	0.418653i	$-0.137498\pi$
$607$	1368.50	+	2370.31i	0.0915086	+	0.158497i	−0.816638	+	0.577151i	$0.804164\pi$
$608$	−3328.00			−0.221987
$609$	535.500	−	2782.54i	0.0356315	−	0.185146i
$610$	21660.0			1.43768
$611$	−6072.00	−	10517.0i	−0.402041	−	0.696355i
$612$	1512.00	−	2618.86i	0.0998676	−	0.172976i
$613$	13094.0	−	22679.5i	0.862743	−	1.49432i	−0.00652719	−	0.999979i	$-0.502078\pi$
$613$	13094.0	−	22679.5i	0.862743	−	1.49432i	0.869271	−	0.494337i	$-0.164589\pi$
$614$	2780.00	+	4815.10i	0.182723	+	0.316485i
$615$	−7560.00			−0.495689
$616$	−252.000	+	1309.43i	−0.0164827	+	0.0856468i
$617$	−2358.00			−0.153857			−0.0769283	−	0.997037i	$-0.524511\pi$
$617$	−2358.00			−0.153857			−0.0769283	+	0.997037i	$0.524511\pi$
$618$	−1392.00	−	2411.01i	−0.0906059	−	0.156934i
$619$	−6883.00	+	11921.7i	−0.446932	+	0.774110i	−0.998185	−	0.0602291i	$-0.980817\pi$
$619$	−6883.00	+	11921.7i	−0.446932	+	0.774110i	0.551252	+	0.834339i	$0.314150\pi$
$620$	5550.00	−	9612.88i	0.359505	−	0.622682i
$621$	−1134.00	−	1964.15i	−0.0732783	−	0.126922i
$622$	−8592.00			−0.553871
$623$	14532.0	+	12585.1i	0.934530	+	0.809327i
$624$	4224.00			0.270986
$625$	9062.50	+	15696.7i	0.580000	+	1.00459i
$626$	5489.00	−	9507.23i	0.350455	−	0.607005i
$627$	−1404.00	+	2431.80i	−0.0894264	+	0.154891i
$628$	−4504.00	−	7801.16i	−0.286193	−	0.495701i
$629$	−3696.00			−0.234291
$630$	4725.00	−	1636.79i	0.298807	−	0.103510i
$631$	21287.0			1.34298			0.671491	−	0.741012i	$-0.265654\pi$
$631$	21287.0			1.34298			0.671491	+	0.741012i	$0.265654\pi$
$632$	−2332.00	−	4039.14i	−0.146775	−	0.254222i
$633$	−8043.00	+	13930.9i	−0.505025	+	0.874728i
$634$	4491.00	−	7778.64i	0.281326	−	0.487270i
$635$	−2797.50	−	4845.41i	−0.174827	−	0.302810i
$636$	−7668.00			−0.478075
$637$	−23716.0	+	18671.5i	−1.47514	+	1.16137i
$638$	918.000			0.0569655
$639$	−4887.00	−	8464.53i	−0.302546	−	0.524025i
$640$	−960.000	+	1662.77i	−0.0592927	+	0.102698i
$641$	−10713.0	+	18555.5i	−0.660122	+	1.14336i	0.320462	+	0.947262i	$0.396162\pi$
$641$	−10713.0	+	18555.5i	−0.660122	+	1.14336i	−0.980583	+	0.196103i	$0.937171\pi$
$642$	−1179.00	−	2042.09i	−0.0724788	−	0.125537i
$643$	9962.00			0.610984			0.305492	−	0.952195i	$-0.401179\pi$
$643$	9962.00			0.610984			0.305492	+	0.952195i	$0.401179\pi$
$644$	−5880.00	+	2036.89i	−0.359790	+	0.124635i
$645$	14670.0			0.895551
$646$	−8736.00	−	15131.2i	−0.532064	−	0.921562i
$647$	9087.00	−	15739.1i	0.552159	−	0.956367i	−0.445960	−	0.895053i	$-0.647137\pi$
$647$	9087.00	−	15739.1i	0.552159	−	0.956367i	0.998119	−	0.0613142i	$-0.0195292\pi$
$648$	324.000	−	561.184i	0.0196419	−	0.0340207i
$649$	715.500	+	1239.28i	0.0432755	+	0.0749555i
$650$	17600.0			1.06204
$651$	7770.00	+	6729.02i	0.467788	+	0.405117i
$652$	6704.00			0.402682
$653$	9583.50	+	16599.1i	0.574321	+	0.994752i	0.996115	+	0.0880610i	$0.0280670\pi$
$653$	9583.50	+	16599.1i	0.574321	+	0.994752i	−0.421795	+	0.906691i	$0.638600\pi$
$654$	−42.0000	+	72.7461i	−0.00251121	+	0.00434954i
$655$	−8797.50	+	15237.7i	−0.524804	+	0.908988i
$656$	1344.00	+	2327.88i	0.0799914	+	0.138549i
$657$	1962.00			0.116507
$658$	−966.000	+	5019.48i	−0.0572319	+	0.297386i
$659$	13080.0			0.773178			0.386589	−	0.922252i	$-0.373653\pi$
$659$	13080.0			0.773178			0.386589	+	0.922252i	$0.373653\pi$
$660$	810.000	+	1402.96i	0.0477715	+	0.0827427i
$661$	7595.00	−	13154.9i	0.446916	−	0.774081i	−0.551268	−	0.834328i	$-0.685856\pi$
$661$	7595.00	−	13154.9i	0.446916	−	0.774081i	0.998183	+	0.0602477i	$0.0191891\pi$
$662$	−3964.00	+	6865.85i	−0.232727	+	0.403095i
$663$	11088.0	+	19205.0i	0.649506	+	1.12498i
$664$	4776.00			0.279134
$665$	5460.00	−	28371.0i	0.318391	−	1.65441i
$666$	−792.000			−0.0460801
$667$	2142.00	+	3710.05i	0.124346	+	0.215373i
$668$	−6060.00	+	10496.2i	−0.351001	+	0.607951i
$669$	−2359.50	+	4086.77i	−0.136358	+	0.236179i
$670$	2490.00	+	4312.81i	0.143578	+	0.248684i
$671$	−6498.00			−0.373849
$672$	−1344.00	−	1163.94i	−0.0771517	−	0.0668153i
$673$	4397.00			0.251845			0.125923	−	0.992040i	$-0.459811\pi$
$673$	4397.00			0.251845			0.125923	+	0.992040i	$0.459811\pi$
$674$	161.000	+	278.860i	0.00920102	+	0.0159366i
$675$	1350.00	−	2338.27i	0.0769800	−	0.133333i
$676$	−11094.0	+	19215.4i	−0.631202	+	1.09327i
$677$	−2014.50	−	3489.22i	−0.114363	−	0.198082i	0.803162	−	0.595761i	$-0.203149\pi$
$677$	−2014.50	−	3489.22i	−0.114363	−	0.198082i	−0.917525	+	0.397679i	$0.869816\pi$
$678$	−13104.0			−0.742266
$679$	−2957.50	+	1024.51i	−0.167155	+	0.0579043i
$680$	−10080.0			−0.568456
$681$	1381.50	+	2392.83i	0.0777374	+	0.134645i
$682$	−1665.00	+	2883.86i	−0.0934841	+	0.161919i
$683$	−7510.50	+	13008.6i	−0.420763	+	0.728783i	−0.996014	−	0.0891936i	$-0.971571\pi$
$683$	−7510.50	+	13008.6i	−0.420763	+	0.728783i	0.575251	+	0.817977i	$0.304904\pi$
$684$	−1872.00	−	3242.40i	−0.104646	−	0.181252i
$685$	−450.000			−0.0251002
$686$	12691.0	+	594.093i	0.706333	+	0.0330650i
$687$	−12156.0			−0.675081
$688$	−2608.00	−	4517.19i	−0.144519	−	0.250314i
$689$	28116.0	−	48698.3i	1.55462	−	2.69268i
$690$	−3780.00	+	6547.15i	−0.208554	+	0.361226i
$691$	6992.00	+	12110.5i	0.384932	+	0.666722i	0.991760	−	0.128111i	$-0.0408915\pi$
$691$	6992.00	+	12110.5i	0.384932	+	0.666722i	−0.606828	+	0.794834i	$0.707558\pi$
$692$	13752.0			0.755452
$693$	−1417.50	+	491.036i	−0.0777004	+	0.0269162i
$694$	11832.0			0.647171
$695$	−615.000	−	1065.21i	−0.0335659	−	0.0581378i
$696$	−612.000	+	1060.02i	−0.0333302	+	0.0577296i
$697$	−7056.00	+	12221.4i	−0.383451	+	0.664156i
$698$	−142.000	−	245.951i	−0.00770026	−	0.0133372i
$699$	1404.00			0.0759716
$700$	−5600.00	−	4849.74i	−0.302372	−	0.261861i
$701$	−31053.0			−1.67312			−0.836559	−	0.547877i	$-0.815436\pi$
$701$	−31053.0			−1.67312			−0.836559	+	0.547877i	$0.815436\pi$
$702$	2376.00	+	4115.35i	0.127744	+	0.221259i
$703$	−2288.00	+	3962.93i	−0.122750	+	0.212610i
$704$	288.000	−	498.831i	0.0154182	−	0.0267051i
$705$	3105.00	+	5378.02i	0.165874	+	0.287302i
$706$	8880.00			0.473376
$707$	−2247.00	+	11675.8i	−0.119529	+	0.621092i
$708$	−1908.00			−0.101281
$709$	−7543.00	−	13064.9i	−0.399553	−	0.692047i	0.594117	−	0.804378i	$-0.297501\pi$
$709$	−7543.00	−	13064.9i	−0.399553	−	0.692047i	−0.993671	+	0.112332i	$0.964168\pi$
$710$	−16290.0	+	28215.1i	−0.861060	+	1.49140i
$711$	2623.50	−	4544.04i	0.138381	−	0.239683i
$712$	−4152.00	−	7191.47i	−0.218543	−	0.378528i
$713$	−15540.0			−0.816238
$714$	1764.00	−	9166.01i	0.0924594	−	0.480433i
$715$	−11880.0			−0.621380
$716$	2424.00	+	4198.49i	0.126521	+	0.219141i
$717$	7398.00	−	12813.7i	0.385332	−	0.667415i
$718$	2286.00	−	3959.47i	0.118820	−	0.205802i
$719$	3189.00	+	5523.51i	0.165410	+	0.286498i	0.936801	−	0.349863i	$-0.113772\pi$
$719$	3189.00	+	5523.51i	0.165410	+	0.286498i	−0.771391	+	0.636362i	$0.780439\pi$
$720$	−2160.00			−0.111803
$721$	−6496.00	−	5625.70i	−0.335539	−	0.290585i
$722$	−7914.00			−0.407934
$723$	−2305.50	−	3993.24i	−0.118593	−	0.205408i
$724$	−6064.00	+	10503.2i	−0.311280	+	0.539153i
$725$	−2550.00	+	4416.73i	−0.130627	+	0.226253i
$726$	3750.00	+	6495.19i	0.191702	+	0.332037i
$727$	−7363.00			−0.375624			−0.187812	−	0.982205i	$-0.560140\pi$
$727$	−7363.00			−0.375624			−0.187812	+	0.982205i	$0.560140\pi$
$728$	12320.0	−	4267.77i	0.627211	−	0.217272i
$729$	729.000			0.0370370
$730$	−3270.00	−	5663.81i	−0.165792	−	0.287160i
$731$	13692.0	−	23715.2i	0.692773	−	1.19992i
$732$	4332.00	−	7503.24i	0.218737	−	0.378863i
$733$	−16405.0	−	28414.3i	−0.826647	−	1.43180i	−0.900654	−	0.434537i	$-0.856912\pi$
$733$	−16405.0	−	28414.3i	−0.826647	−	1.43180i	0.0740064	−	0.997258i	$-0.476421\pi$
$734$	5738.00			0.288547
$735$	12127.5	−	9547.93i	0.608612	−	0.479157i
$736$	2688.00			0.134621
$737$	−747.000	−	1293.84i	−0.0373353	−	0.0646666i
$738$	−1512.00	+	2618.86i	−0.0754167	+	0.130625i
$739$	12017.0	−	20814.1i	0.598177	−	1.03607i	−0.394914	−	0.918718i	$-0.629225\pi$
$739$	12017.0	−	20814.1i	0.598177	−	1.03607i	0.993090	−	0.117354i	$-0.0374412\pi$
$740$	1320.00	+	2286.31i	0.0655732	+	0.113576i
$741$	27456.0			1.36116
$742$	−22365.0	+	7747.46i	−1.10653	+	0.383313i
$743$	−8022.00			−0.396095			−0.198048	−	0.980192i	$-0.563460\pi$
$743$	−8022.00			−0.396095			−0.198048	+	0.980192i	$0.563460\pi$
$744$	−2220.00	−	3845.15i	−0.109394	−	0.189476i
$745$	−10755.0	+	18628.2i	−0.528903	+	0.916087i
$746$	−3064.00	+	5307.00i	−0.150377	+	0.260460i
$747$	2686.50	+	4653.15i	0.131585	+	0.227912i
$748$	3024.00			0.147819
$749$	−5502.00	−	4764.87i	−0.268409	−	0.232449i
$750$	2250.00			0.109545
$751$	−14759.5	−	25564.2i	−0.717153	−	1.24215i	−0.962123	−	0.272615i	$-0.912112\pi$
$751$	−14759.5	−	25564.2i	−0.717153	−	1.24215i	0.244970	−	0.969531i	$-0.421222\pi$
$752$	1104.00	−	1912.18i	0.0535356	−	0.0927263i
$753$	7978.50	−	13819.2i	0.386126	−	0.668789i
$754$	−4488.00	−	7773.44i	−0.216768	−	0.375454i
$755$	40065.0			1.93128
$756$	378.000	−	1964.15i	0.0181848	−	0.0944911i
$757$	−3742.00			−0.179664			−0.0898318	−	0.995957i	$-0.528633\pi$
$757$	−3742.00			−0.179664			−0.0898318	+	0.995957i	$0.528633\pi$
$758$	−6040.00	−	10461.6i	−0.289423	−	0.501295i
$759$	1134.00	−	1964.15i	0.0542313	−	0.0939314i
$760$	−6240.00	+	10808.0i	−0.297827	+	0.515852i
$761$	5448.00	+	9436.21i	0.259514	+	0.449491i	0.966112	−	0.258124i	$-0.0831044\pi$
$761$	5448.00	+	9436.21i	0.259514	+	0.449491i	−0.706598	+	0.707615i	$0.749771\pi$
$762$	−2238.00			−0.106397
$763$	−49.0000	+	254.611i	−0.00232493	+	0.0120807i
$764$	10080.0			0.477332
$765$	−5670.00	−	9820.73i	−0.267973	−	0.464143i
$766$	1842.00	−	3190.44i	0.0868853	−	0.150490i
$767$	6996.00	−	12117.4i	0.329349	−	0.570450i

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	42.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(7.50000 + 12.9904i) q^{5} +6.00000 q^{6} +(17.5000 - 6.06218i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(7.50000 + 12.9904i) q^{5} +6.00000 q^{6} +(17.5000 - 6.06218i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-15.0000 + 25.9808i) q^{10} +(4.50000 - 7.79423i) q^{11} +(6.00000 + 10.3923i) q^{12} -88.0000 q^{13} +(28.0000 + 24.2487i) q^{14} +45.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(42.0000 - 72.7461i) q^{17} +(9.00000 - 15.5885i) q^{18} +(-52.0000 - 90.0666i) q^{19} -60.0000 q^{20} +(10.5000 - 54.5596i) q^{21} +18.0000 q^{22} +(42.0000 + 72.7461i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-50.0000 + 86.6025i) q^{25} +(-88.0000 - 152.420i) q^{26} -27.0000 q^{27} +(-14.0000 + 72.7461i) q^{28} +51.0000 q^{29} +(45.0000 + 77.9423i) q^{30} +(-92.5000 + 160.215i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-13.5000 - 23.3827i) q^{33} +168.000 q^{34} +(210.000 + 181.865i) q^{35} +36.0000 q^{36} +(-22.0000 - 38.1051i) q^{37} +(104.000 - 180.133i) q^{38} +(-132.000 + 228.631i) q^{39} +(-60.0000 - 103.923i) q^{40} -168.000 q^{41} +(105.000 - 36.3731i) q^{42} +326.000 q^{43} +(18.0000 + 31.1769i) q^{44} +(67.5000 - 116.913i) q^{45} +(-84.0000 + 145.492i) q^{46} +(69.0000 + 119.512i) q^{47} -48.0000 q^{48} +(269.500 - 212.176i) q^{49} -200.000 q^{50} +(-126.000 - 218.238i) q^{51} +(176.000 - 304.841i) q^{52} +(-319.500 + 553.390i) q^{53} +(-27.0000 - 46.7654i) q^{54} +135.000 q^{55} +(-140.000 + 48.4974i) q^{56} -312.000 q^{57} +(51.0000 + 88.3346i) q^{58} +(-79.5000 + 137.698i) q^{59} +(-90.0000 + 155.885i) q^{60} +(-361.000 - 625.270i) q^{61} -370.000 q^{62} +(-126.000 - 109.119i) q^{63} +64.0000 q^{64} +(-660.000 - 1143.15i) q^{65} +(27.0000 - 46.7654i) q^{66} +(83.0000 - 143.760i) q^{67} +(168.000 + 290.985i) q^{68} +252.000 q^{69} +(-105.000 + 545.596i) q^{70} +1086.00 q^{71} +(36.0000 + 62.3538i) q^{72} +(-109.000 + 188.794i) q^{73} +(44.0000 - 76.2102i) q^{74} +(150.000 + 259.808i) q^{75} +416.000 q^{76} +(31.5000 - 163.679i) q^{77} -528.000 q^{78} +(291.500 + 504.893i) q^{79} +(120.000 - 207.846i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-168.000 - 290.985i) q^{82} -597.000 q^{83} +(168.000 + 145.492i) q^{84} +1260.00 q^{85} +(326.000 + 564.649i) q^{86} +(76.5000 - 132.502i) q^{87} +(-36.0000 + 62.3538i) q^{88} +(519.000 + 898.934i) q^{89} +270.000 q^{90} +(-1540.00 + 533.472i) q^{91} -336.000 q^{92} +(277.500 + 480.644i) q^{93} +(-138.000 + 239.023i) q^{94} +(780.000 - 1351.00i) q^{95} +(-48.0000 - 83.1384i) q^{96} -169.000 q^{97} +(637.000 + 254.611i) q^{98} -81.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 15 q^{5} + 12 q^{6} + 35 q^{7} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 15 * q^5 + 12 * q^6 + 35 * q^7 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 15 q^{5} + 12 q^{6} + 35 q^{7} - 16 q^{8} - 9 q^{9} - 30 q^{10} + 9 q^{11} + 12 q^{12} - 176 q^{13} + 56 q^{14} + 90 q^{15} - 16 q^{16} + 84 q^{17} + 18 q^{18} - 104 q^{19} - 120 q^{20} + 21 q^{21} + 36 q^{22} + 84 q^{23} - 24 q^{24} - 100 q^{25} - 176 q^{26} - 54 q^{27} - 28 q^{28} + 102 q^{29} + 90 q^{30} - 185 q^{31} + 32 q^{32} - 27 q^{33} + 336 q^{34} + 420 q^{35} + 72 q^{36} - 44 q^{37} + 208 q^{38} - 264 q^{39} - 120 q^{40} - 336 q^{41} + 210 q^{42} + 652 q^{43} + 36 q^{44} + 135 q^{45} - 168 q^{46} + 138 q^{47} - 96 q^{48} + 539 q^{49} - 400 q^{50} - 252 q^{51} + 352 q^{52} - 639 q^{53} - 54 q^{54} + 270 q^{55} - 280 q^{56} - 624 q^{57} + 102 q^{58} - 159 q^{59} - 180 q^{60} - 722 q^{61} - 740 q^{62} - 252 q^{63} + 128 q^{64} - 1320 q^{65} + 54 q^{66} + 166 q^{67} + 336 q^{68} + 504 q^{69} - 210 q^{70} + 2172 q^{71} + 72 q^{72} - 218 q^{73} + 88 q^{74} + 300 q^{75} + 832 q^{76} + 63 q^{77} - 1056 q^{78} + 583 q^{79} + 240 q^{80} - 81 q^{81} - 336 q^{82} - 1194 q^{83} + 336 q^{84} + 2520 q^{85} + 652 q^{86} + 153 q^{87} - 72 q^{88} + 1038 q^{89} + 540 q^{90} - 3080 q^{91} - 672 q^{92} + 555 q^{93} - 276 q^{94} + 1560 q^{95} - 96 q^{96} - 338 q^{97} + 1274 q^{98} - 162 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 15 * q^5 + 12 * q^6 + 35 * q^7 - 16 * q^8 - 9 * q^9 - 30 * q^10 + 9 * q^11 + 12 * q^12 - 176 * q^13 + 56 * q^14 + 90 * q^15 - 16 * q^16 + 84 * q^17 + 18 * q^18 - 104 * q^19 - 120 * q^20 + 21 * q^21 + 36 * q^22 + 84 * q^23 - 24 * q^24 - 100 * q^25 - 176 * q^26 - 54 * q^27 - 28 * q^28 + 102 * q^29 + 90 * q^30 - 185 * q^31 + 32 * q^32 - 27 * q^33 + 336 * q^34 + 420 * q^35 + 72 * q^36 - 44 * q^37 + 208 * q^38 - 264 * q^39 - 120 * q^40 - 336 * q^41 + 210 * q^42 + 652 * q^43 + 36 * q^44 + 135 * q^45 - 168 * q^46 + 138 * q^47 - 96 * q^48 + 539 * q^49 - 400 * q^50 - 252 * q^51 + 352 * q^52 - 639 * q^53 - 54 * q^54 + 270 * q^55 - 280 * q^56 - 624 * q^57 + 102 * q^58 - 159 * q^59 - 180 * q^60 - 722 * q^61 - 740 * q^62 - 252 * q^63 + 128 * q^64 - 1320 * q^65 + 54 * q^66 + 166 * q^67 + 336 * q^68 + 504 * q^69 - 210 * q^70 + 2172 * q^71 + 72 * q^72 - 218 * q^73 + 88 * q^74 + 300 * q^75 + 832 * q^76 + 63 * q^77 - 1056 * q^78 + 583 * q^79 + 240 * q^80 - 81 * q^81 - 336 * q^82 - 1194 * q^83 + 336 * q^84 + 2520 * q^85 + 652 * q^86 + 153 * q^87 - 72 * q^88 + 1038 * q^89 + 540 * q^90 - 3080 * q^91 - 672 * q^92 + 555 * q^93 - 276 * q^94 + 1560 * q^95 - 96 * q^96 - 338 * q^97 + 1274 * q^98 - 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more