LMFDB - Embedded newform 48.3.i.b.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, 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:	$1.30790526893$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.4
Root			$-1.21144 + 1.59136i$ of defining polynomial
Character	$\chi$	$=$	48.29
Dual form			48.3.i.b.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21144 - 1.59136i) q^{2} +(1.14944 + 2.77106i) q^{3} +(-1.06484 + 3.85566i) q^{4} +(4.80434 + 4.80434i) q^{5} +(3.01728 - 5.18614i) q^{6} -7.36187i q^{7} +(7.42573 - 2.97634i) q^{8} +(-6.35757 + 6.37035i) q^{9} +O(q^{10})$	\(q+(-1.21144 - 1.59136i) q^{2} +(1.14944 + 2.77106i) q^{3} +(-1.06484 + 3.85566i) q^{4} +(4.80434 + 4.80434i) q^{5} +(3.01728 - 5.18614i) q^{6} -7.36187i q^{7} +(7.42573 - 2.97634i) q^{8} +(-6.35757 + 6.37035i) q^{9} +(1.82527 - 13.4656i) q^{10} +(-0.514693 - 0.514693i) q^{11} +(-11.9082 + 1.48110i) q^{12} +(7.12969 + 7.12969i) q^{13} +(-11.7154 + 8.91843i) q^{14} +(-7.79081 + 18.8354i) q^{15} +(-13.7322 - 8.21135i) q^{16} -11.1126i q^{17} +(17.8393 + 2.39991i) q^{18} +(-21.1403 - 21.1403i) q^{19} +(-23.6398 + 13.4080i) q^{20} +(20.4002 - 8.46203i) q^{21} +(-0.195543 + 1.44258i) q^{22} -7.80231 q^{23} +(16.7830 + 17.1560i) q^{24} +21.1633i q^{25} +(2.70873 - 19.9831i) q^{26} +(-24.9603 - 10.2949i) q^{27} +(28.3849 + 7.83924i) q^{28} +(34.6058 - 34.6058i) q^{29} +(39.4120 - 10.4199i) q^{30} +24.8644 q^{31} +(3.56850 + 31.8004i) q^{32} +(0.834637 - 2.01786i) q^{33} +(-17.6842 + 13.4623i) q^{34} +(35.3689 - 35.3689i) q^{35} +(-17.7921 - 31.2960i) q^{36} +(-18.2760 + 18.2760i) q^{37} +(-8.03168 + 59.2520i) q^{38} +(-11.5617 + 27.9520i) q^{39} +(49.9750 + 21.3764i) q^{40} -64.2448 q^{41} +(-38.1797 - 22.2128i) q^{42} +(7.24058 - 7.24058i) q^{43} +(2.53255 - 1.43641i) q^{44} +(-61.1492 + 0.0613789i) q^{45} +(9.45200 + 12.4163i) q^{46} +23.0508i q^{47} +(6.96979 - 47.4913i) q^{48} -5.19710 q^{49} +(33.6784 - 25.6380i) q^{50} +(30.7938 - 12.7733i) q^{51} +(-35.0817 + 19.8976i) q^{52} +(31.9199 + 31.9199i) q^{53} +(13.8549 + 52.1923i) q^{54} -4.94552i q^{55} +(-21.9114 - 54.6672i) q^{56} +(34.2816 - 82.8807i) q^{57} +(-96.9929 - 13.1475i) q^{58} +(17.6272 + 17.6272i) q^{59} +(-64.3270 - 50.0955i) q^{60} +(-12.3933 - 12.3933i) q^{61} +(-30.1216 - 39.5682i) q^{62} +(46.8976 + 46.8036i) q^{63} +(46.2828 - 44.2029i) q^{64} +68.5069i q^{65} +(-4.22224 + 1.11630i) q^{66} +(41.1425 + 41.1425i) q^{67} +(42.8465 + 11.8332i) q^{68} +(-8.96830 - 21.6207i) q^{69} +(-99.1318 - 13.4374i) q^{70} -25.6785 q^{71} +(-28.2493 + 66.2267i) q^{72} +56.1845i q^{73} +(51.2239 + 6.94346i) q^{74} +(-58.6449 + 24.3260i) q^{75} +(104.021 - 58.9988i) q^{76} +(-3.78910 + 3.78910i) q^{77} +(58.4878 - 15.4633i) q^{78} -35.7013 q^{79} +(-26.5241 - 105.424i) q^{80} +(-0.162608 - 80.9998i) q^{81} +(77.8285 + 102.236i) q^{82} +(-94.9424 + 94.9424i) q^{83} +(10.9037 + 87.6669i) q^{84} +(53.3889 - 53.3889i) q^{85} +(-20.2939 - 2.75086i) q^{86} +(135.672 + 56.1175i) q^{87} +(-5.35387 - 2.29007i) q^{88} -44.8713 q^{89} +(74.1760 + 97.2360i) q^{90} +(52.4878 - 52.4878i) q^{91} +(8.30824 - 30.0830i) q^{92} +(28.5802 + 68.9008i) q^{93} +(36.6821 - 27.9246i) q^{94} -203.131i q^{95} +(-84.0191 + 46.4412i) q^{96} -82.3636 q^{97} +(6.29596 + 8.27045i) q^{98} +(6.55097 - 0.00657558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6}+O(q^{10}) $ 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6	$ 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6 + 32 * q^10 - 88 * q^12 + 92 * q^13 - 116 * q^15 - 16 * q^16 + 4 * q^18 - 52 * q^19 + 48 * q^21 + 24 * q^22 - 8 * q^24 + 18 * q^27 + 56 * q^28 + 28 * q^30 - 80 * q^31 + 60 * q^33 + 104 * q^34 + 92 * q^36 - 116 * q^37 + 88 * q^40 + 304 * q^42 + 172 * q^43 + 60 * q^45 - 424 * q^46 + 176 * q^48 - 364 * q^49 + 128 * q^51 - 208 * q^52 + 40 * q^54 - 512 * q^58 - 240 * q^60 - 244 * q^61 + 296 * q^63 + 88 * q^64 - 492 * q^66 + 356 * q^67 - 20 * q^69 + 200 * q^70 - 472 * q^72 - 146 * q^75 + 328 * q^76 + 84 * q^78 + 384 * q^79 - 188 * q^81 + 560 * q^82 + 816 * q^84 + 48 * q^85 + 416 * q^88 + 616 * q^90 + 136 * q^91 - 132 * q^93 + 32 * q^94 - 24 * q^96 + 472 * q^97 - 452 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.21144	−	1.59136i	−0.605718	−	0.795679i
$2$	−1.21144	−	1.59136i	−0.605718	−	0.795679i
$3$	1.14944	+	2.77106i	0.383147	+	0.923687i
$3$	1.14944	+	2.77106i	0.383147	+	0.923687i
$4$	−1.06484	+	3.85566i	−0.266211	+	0.963915i
$5$	4.80434	+	4.80434i	0.960868	+	0.960868i	0.999263	−	0.0383950i	$-0.0122245\pi$
$5$	4.80434	+	4.80434i	0.960868	+	0.960868i	−0.0383950	+	0.999263i	$0.512225\pi$
$6$	3.01728	−	5.18614i	0.502880	−	0.864356i
$7$		−	7.36187i		−	1.05170i	−0.850579	−	0.525848i	$-0.823748\pi$
$7$		−	7.36187i		−	1.05170i	0.850579	−	0.525848i	$-0.176252\pi$
$8$	7.42573	−	2.97634i	0.928216	−	0.372042i
$9$	−6.35757	+	6.37035i	−0.706397	+	0.707816i
$10$	1.82527	−	13.4656i	0.182527	−	1.34656i
$11$	−0.514693	−	0.514693i	−0.0467903	−	0.0467903i	0.683325	−	0.730115i	$-0.260533\pi$
$11$	−0.514693	−	0.514693i	−0.0467903	−	0.0467903i	−0.730115	+	0.683325i	$0.760533\pi$
$12$	−11.9082	+	1.48110i	−0.992354	+	0.123425i
$13$	7.12969	+	7.12969i	0.548438	+	0.548438i	0.925989	−	0.377551i	$-0.123234\pi$
$13$	7.12969	+	7.12969i	0.548438	+	0.548438i	−0.377551	+	0.925989i	$0.623234\pi$
$14$	−11.7154	+	8.91843i	−0.836812	+	0.637031i
$15$	−7.79081	+	18.8354i	−0.519388	+	1.25569i
$16$	−13.7322	−	8.21135i	−0.858263	−	0.513210i
$17$		−	11.1126i		−	0.653684i	−0.945079	−	0.326842i	$-0.894015\pi$
$17$		−	11.1126i		−	0.653684i	0.945079	−	0.326842i	$-0.105985\pi$
$18$	17.8393	+	2.39991i	0.991072	+	0.133328i
$19$	−21.1403	−	21.1403i	−1.11265	−	1.11265i	−0.992791	−	0.119858i	$-0.961756\pi$
$19$	−21.1403	−	21.1403i	−1.11265	−	1.11265i	−0.119858	−	0.992791i	$-0.538244\pi$
$20$	−23.6398	+	13.4080i	−1.18199	+	0.670401i
$21$	20.4002	−	8.46203i	0.971438	−	0.402954i
$22$	−0.195543	+	1.44258i	−0.00888834	+	0.0655718i
$23$	−7.80231			−0.339231			−0.169615	−	0.985510i	$-0.554253\pi$
$23$	−7.80231			−0.339231			−0.169615	+	0.985510i	$0.554253\pi$
$24$	16.7830	+	17.1560i	0.699294	+	0.714834i
$25$			21.1633i			0.846533i
$26$	2.70873	−	19.9831i	0.104182	−	0.768579i
$27$	−24.9603	−	10.2949i	−0.924455	−	0.381292i
$28$	28.3849	+	7.83924i	1.01374	+	0.279973i
$29$	34.6058	−	34.6058i	1.19330	−	1.19330i	0.217169	−	0.976134i	$-0.430318\pi$
$29$	34.6058	−	34.6058i	1.19330	−	1.19330i	0.976134	−	0.217169i	$-0.0696823\pi$
$30$	39.4120	−	10.4199i	1.31373	−	0.347331i
$31$	24.8644			0.802078			0.401039	−	0.916061i	$-0.368649\pi$
$31$	24.8644			0.802078			0.401039	+	0.916061i	$0.368649\pi$
$32$	3.56850	+	31.8004i	0.111516	+	0.993763i
$33$	0.834637	−	2.01786i	0.0252920	−	0.0611472i
$34$	−17.6842	+	13.4623i	−0.520123	+	0.395949i
$35$	35.3689	−	35.3689i	1.01054	−	1.01054i
$36$	−17.7921	−	31.2960i	−0.494224	−	0.869335i
$37$	−18.2760	+	18.2760i	−0.493946	+	0.493946i	−0.909547	−	0.415601i	$-0.863571\pi$
$37$	−18.2760	+	18.2760i	−0.493946	+	0.493946i	0.415601	+	0.909547i	$0.363571\pi$
$38$	−8.03168	+	59.2520i	−0.211360	+	1.55926i
$39$	−11.5617	+	27.9520i	−0.296453	+	0.716717i
$40$	49.9750	+	21.3764i	1.24938	+	0.534409i
$41$	−64.2448			−1.56695			−0.783473	−	0.621426i	$-0.786554\pi$
$41$	−64.2448			−1.56695			−0.783473	+	0.621426i	$0.786554\pi$
$42$	−38.1797	−	22.2128i	−0.909040	−	0.528876i
$43$	7.24058	−	7.24058i	0.168386	−	0.168386i	−0.617884	−	0.786269i	$-0.712010\pi$
$43$	7.24058	−	7.24058i	0.168386	−	0.168386i	0.786269	+	0.617884i	$0.212010\pi$
$44$	2.53255	−	1.43641i	0.0575579	−	0.0326458i
$45$	−61.1492	+	0.0613789i	−1.35887	+	0.00136398i
$46$	9.45200	+	12.4163i	0.205478	+	0.269919i
$47$			23.0508i			0.490442i	0.969467	+	0.245221i	$0.0788606\pi$
$47$			23.0508i			0.490442i	−0.969467	+	0.245221i	$0.921139\pi$
$48$	6.96979	−	47.4913i	0.145204	−	0.989402i
$49$	−5.19710			−0.106063
$50$	33.6784	−	25.6380i	0.673569	−	0.512760i
$51$	30.7938	−	12.7733i	0.603800	−	0.250457i
$52$	−35.0817	+	19.8976i	−0.674647	+	0.382647i
$53$	31.9199	+	31.9199i	0.602263	+	0.602263i	0.940913	−	0.338650i	$-0.109970\pi$
$53$	31.9199	+	31.9199i	0.602263	+	0.602263i	−0.338650	+	0.940913i	$0.609970\pi$
$54$	13.8549	+	52.1923i	0.256573	+	0.966525i
$55$		−	4.94552i		−	0.0899185i
$56$	−21.9114	−	54.6672i	−0.391275	−	0.976200i
$57$	34.2816	−	82.8807i	0.601432	−	1.45405i
$58$	−96.9929	−	13.1475i	−1.67229	−	0.226681i
$59$	17.6272	+	17.6272i	0.298766	+	0.298766i	0.840530	−	0.541764i	$-0.182244\pi$
$59$	17.6272	+	17.6272i	0.298766	+	0.298766i	−0.541764	+	0.840530i	$0.682244\pi$
$60$	−64.3270	−	50.0955i	−1.07212	−	0.834925i
$61$	−12.3933	−	12.3933i	−0.203170	−	0.203170i	0.598187	−	0.801357i	$-0.295888\pi$
$61$	−12.3933	−	12.3933i	−0.203170	−	0.203170i	−0.801357	+	0.598187i	$0.795888\pi$
$62$	−30.1216	−	39.5682i	−0.485833	−	0.638196i
$63$	46.8976	+	46.8036i	0.744407	+	0.742914i
$64$	46.2828	−	44.2029i	0.723169	−	0.690671i
$65$			68.5069i			1.05395i
$66$	−4.22224	+	1.11630i	−0.0639734	+	0.0169136i
$67$	41.1425	+	41.1425i	0.614067	+	0.614067i	0.944003	−	0.329936i	$-0.107027\pi$
$67$	41.1425	+	41.1425i	0.614067	+	0.614067i	−0.329936	+	0.944003i	$0.607027\pi$
$68$	42.8465	+	11.8332i	0.630096	+	0.174018i
$69$	−8.96830	−	21.6207i	−0.129975	−	0.313343i
$70$	−99.1318	−	13.4374i	−1.41617	−	0.191963i
$71$	−25.6785			−0.361669			−0.180834	−	0.983514i	$-0.557880\pi$
$71$	−25.6785			−0.361669			−0.180834	+	0.983514i	$0.557880\pi$
$72$	−28.2493	+	66.2267i	−0.392351	+	0.919815i
$73$			56.1845i			0.769650i	0.922990	+	0.384825i	$0.125738\pi$
$73$			56.1845i			0.769650i	−0.922990	+	0.384825i	$0.874262\pi$
$74$	51.2239	+	6.94346i	0.692214	+	0.0938305i
$75$	−58.6449	+	24.3260i	−0.781932	+	0.324347i
$76$	104.021	−	58.9988i	1.36870	−	0.776299i
$77$	−3.78910	+	3.78910i	−0.0492091	+	0.0492091i
$78$	58.4878	−	15.4633i	0.749844	−	0.198247i
$79$	−35.7013			−0.451915			−0.225957	−	0.974137i	$-0.572551\pi$
$79$	−35.7013			−0.451915			−0.225957	+	0.974137i	$0.572551\pi$
$80$	−26.5241	−	105.424i	−0.331551	−	1.31780i
$81$	−0.162608	−	80.9998i	−0.00200751	−	0.999998i
$82$	77.8285	+	102.236i	0.949128	+	1.24679i
$83$	−94.9424	+	94.9424i	−1.14388	+	1.14388i	−0.156151	+	0.987733i	$0.549909\pi$
$83$	−94.9424	+	94.9424i	−1.14388	+	1.14388i	−0.987733	+	0.156151i	$0.950091\pi$
$84$	10.9037	+	87.6669i	0.129806	+	1.04365i
$85$	53.3889	−	53.3889i	0.628104	−	0.628104i
$86$	−20.2939	−	2.75086i	−0.235975	−	0.0319867i
$87$	135.672	+	56.1175i	1.55945	+	0.645028i
$88$	−5.35387	−	2.29007i	−0.0608394	−	0.0260235i
$89$	−44.8713			−0.504172			−0.252086	−	0.967705i	$-0.581117\pi$
$89$	−44.8713			−0.504172			−0.252086	+	0.967705i	$0.581117\pi$
$90$	74.1760	+	97.2360i	0.824178	+	1.08040i
$91$	52.4878	−	52.4878i	0.576789	−	0.576789i
$92$	8.30824	−	30.0830i	0.0903070	−	0.326990i
$93$	28.5802	+	68.9008i	0.307314	+	0.740869i
$94$	36.6821	−	27.9246i	0.390235	−	0.297070i
$95$		−	203.131i		−	2.13822i
$96$	−84.0191	+	46.4412i	−0.875199	+	0.483763i
$97$	−82.3636			−0.849109			−0.424554	−	0.905402i	$-0.639569\pi$
$97$	−82.3636			−0.849109			−0.424554	+	0.905402i	$0.639569\pi$
$98$	6.29596	+	8.27045i	0.0642445	+	0.0843924i
$99$	6.55097	−	0.00657558i	0.0661714	−	6.64200e-5i
$100$	−81.5986	−	22.5356i	−0.815986	−	0.225356i
$101$	−36.3420	−	36.3420i	−0.359822	−	0.359822i	0.503925	−	0.863747i	$-0.331889\pi$
$101$	−36.3420	−	36.3420i	−0.359822	−	0.359822i	−0.863747	+	0.503925i	$0.831889\pi$
$102$	−57.6317	−	33.5299i	−0.565016	−	0.328725i
$103$		−	87.5176i		−	0.849685i	−0.905267	−	0.424843i	$-0.860329\pi$
$103$		−	87.5176i		−	0.849685i	0.905267	−	0.424843i	$-0.139671\pi$
$104$	74.1635	+	31.7228i	0.713110	+	0.305027i
$105$	138.664	+	57.3550i	1.32061	+	0.546238i
$106$	12.1271	−	89.4650i	0.114407	−	0.844010i
$107$	104.866	+	104.866i	0.980058	+	0.980058i	0.999805	−	0.0197471i	$-0.00628610\pi$
$107$	104.866	+	104.866i	0.980058	+	0.980058i	−0.0197471	+	0.999805i	$0.506286\pi$
$108$	66.2724	−	85.2759i	0.613633	−	0.789591i
$109$	7.64006	+	7.64006i	0.0700923	+	0.0700923i	0.741284	−	0.671192i	$-0.234217\pi$
$109$	7.64006	+	7.64006i	0.0700923	+	0.0700923i	−0.671192	+	0.741284i	$0.734217\pi$
$110$	−7.87010	+	5.99118i	−0.0715463	+	0.0544653i
$111$	−71.6511	−	29.6367i	−0.645505	−	0.266998i
$112$	−60.4509	+	101.095i	−0.539740	+	0.902632i
$113$			13.1273i			0.116171i	0.998312	+	0.0580853i	$0.0184995\pi$
$113$			13.1273i			0.116171i	−0.998312	+	0.0580853i	$0.981500\pi$
$114$	−173.423	+	45.8504i	−1.52125	+	0.402197i
$115$	−37.4849	−	37.4849i	−0.325956	−	0.325956i
$116$	96.5784	+	170.278i	0.832572	+	1.46791i
$117$	−90.7461	+	0.0910869i	−0.775607	+	0.000778521i
$118$	6.69696	−	49.4054i	0.0567539	−	0.418690i
$119$	−81.8098			−0.687477
$120$	−1.79191	+	163.055i	−0.0149326	+	1.35879i
$121$		−	120.470i		−	0.995621i
$122$	−4.70851	+	34.7360i	−0.0385943	+	0.284721i
$123$	−73.8456	−	178.026i	−0.600371	−	1.44737i
$124$	−26.4767	+	95.8687i	−0.213522	+	0.773134i
$125$	18.4327	−	18.4327i	0.147461	−	0.147461i
$126$	17.6678	−	131.331i	0.140221	−	1.04231i
$127$	−88.2707			−0.695045			−0.347523	−	0.937672i	$-0.612977\pi$
$127$	−88.2707			−0.695045			−0.347523	+	0.937672i	$0.612977\pi$
$128$	−126.411	−	20.1036i	−0.987589	−	0.157059i
$129$	28.3867	+	11.7415i	0.220052	+	0.0910192i
$130$	109.019	−	82.9917i	0.838608	−	0.638398i
$131$	−57.0518	+	57.0518i	−0.435510	+	0.435510i	−0.890498	−	0.454988i	$-0.849644\pi$
$131$	−57.0518	+	57.0518i	−0.435510	+	0.435510i	0.454988	+	0.890498i	$0.349644\pi$
$132$	6.89141	+	5.36678i	0.0522076	+	0.0406574i
$133$	−155.632	+	155.632i	−1.17017	+	1.17017i
$134$	15.6310	−	115.314i	0.116649	−	0.860552i
$135$	−70.4575	−	169.378i	−0.521907	−	1.25465i
$136$	−33.0749	−	82.5194i	−0.243198	−	0.606760i
$137$	165.112			1.20520			0.602599	−	0.798045i	$-0.294132\pi$
$137$	165.112			1.20520			0.602599	+	0.798045i	$0.294132\pi$
$138$	−23.5417	+	40.4639i	−0.170592	+	0.293216i
$139$	−95.0802	+	95.0802i	−0.684030	+	0.684030i	−0.960906	−	0.276875i	$-0.910701\pi$
$139$	−95.0802	+	95.0802i	−0.684030	+	0.684030i	0.276875	+	0.960906i	$0.410701\pi$
$140$	98.7081	+	174.033i	0.705058	+	1.24309i
$141$	−63.8752	+	26.4955i	−0.453015	+	0.187912i
$142$	31.1078	+	40.8637i	0.219069	+	0.287772i
$143$		−	7.33920i		−	0.0513231i
$144$	139.613	−	35.2747i	0.969532	−	0.244963i
$145$	332.516			2.29321
$146$	89.4096	−	68.0639i	0.612395	−	0.466191i
$147$	−5.97376	−	14.4015i	−0.0406378	−	0.0979693i
$148$	−51.0049	−	89.9271i	−0.344628	−	0.607615i
$149$	−131.077	−	131.077i	−0.879709	−	0.879709i	0.113795	−	0.993504i	$-0.463699\pi$
$149$	−131.077	−	131.077i	−0.879709	−	0.879709i	−0.993504	+	0.113795i	$0.963699\pi$
$150$	109.756	+	63.8557i	0.731706	+	0.425704i
$151$			123.070i			0.815031i	0.913198	+	0.407515i	$0.133605\pi$
$151$			123.070i			0.815031i	−0.913198	+	0.407515i	$0.866395\pi$
$152$	−219.903	−	94.0616i	−1.44673	−	0.618826i
$153$	70.7913	+	70.6494i	0.462688	+	0.461761i
$154$	10.6201	+	1.43956i	0.0689615	+	0.00934782i
$155$	119.457	+	119.457i	0.770690	+	0.770690i
$156$	−95.4619	−	74.3423i	−0.611935	−	0.476553i
$157$	139.181	+	139.181i	0.886503	+	0.886503i	0.994185	−	0.107683i	$-0.0343430\pi$
$157$	139.181	+	139.181i	0.886503	+	0.886503i	−0.107683	+	0.994185i	$0.534343\pi$
$158$	43.2498	+	56.8135i	0.273733	+	0.359579i
$159$	−51.7620	+	125.142i	−0.325547	+	0.787058i
$160$	−135.636	+	169.924i	−0.847723	+	1.06203i
$161$			57.4396i			0.356768i
$162$	−128.703	+	98.3849i	−0.794462	+	0.607314i
$163$	−19.9311	−	19.9311i	−0.122277	−	0.122277i	0.643320	−	0.765597i	$-0.277556\pi$
$163$	−19.9311	−	19.9311i	−0.122277	−	0.122277i	−0.765597	+	0.643320i	$0.777556\pi$
$164$	68.4107	−	247.706i	0.417138	−	1.51040i
$165$	13.7043	−	5.68458i	0.0830566	−	0.0344520i
$166$	266.104	+	36.0707i	1.60304	+	0.217294i
$167$	60.3220			0.361210			0.180605	−	0.983556i	$-0.442194\pi$
$167$	60.3220			0.361210			0.180605	+	0.983556i	$0.442194\pi$
$168$	126.300	−	123.555i	0.751788	−	0.735444i
$169$		−	67.3351i		−	0.398432i
$170$	−149.638	−	20.2836i	−0.880224	−	0.119315i
$171$	269.072	−	0.270083i	1.57352	−	0.00157943i
$172$	20.2071	+	35.6273i	0.117483	+	0.207135i
$173$	74.8292	−	74.8292i	0.432539	−	0.432539i	−0.456952	−	0.889491i	$-0.651059\pi$
$173$	74.8292	−	74.8292i	0.432539	−	0.432539i	0.889491	+	0.456952i	$0.151059\pi$
$174$	−75.0551	−	283.886i	−0.431351	−	1.63153i
$175$	155.802			0.890295
$176$	2.84155	+	11.2942i	0.0161452	+	0.0641716i
$177$	−28.5846	+	69.1074i	−0.161495	+	0.390438i
$178$	54.3587	+	71.4063i	0.305386	+	0.401159i
$179$	3.96558	−	3.96558i	0.0221541	−	0.0221541i	−0.695943	−	0.718097i	$-0.745013\pi$
$179$	3.96558	−	3.96558i	0.0221541	−	0.0221541i	0.718097	+	0.695943i	$0.245013\pi$
$180$	64.8777	−	235.836i	0.360432	−	1.31020i
$181$	158.820	−	158.820i	0.877457	−	0.877457i	−0.115814	−	0.993271i	$-0.536948\pi$
$181$	158.820	−	158.820i	0.877457	−	0.877457i	0.993271	+	0.115814i	$0.0369475\pi$
$182$	−147.113	−	19.9413i	−0.808311	−	0.109568i
$183$	20.0973	−	48.5882i	0.109821	−	0.265509i
$184$	−57.9378	+	23.2223i	−0.314879	+	0.126208i
$185$	−175.608			−0.949233
$186$	75.0228	−	128.950i	0.403349	−	0.693281i
$187$	−5.71960	+	5.71960i	−0.0305861	+	0.0305861i
$188$	−88.8760	−	24.5455i	−0.472745	−	0.130561i
$189$	−75.7896	+	183.754i	−0.401003	+	0.972245i
$190$	−323.254	+	246.080i	−1.70133	+	1.29516i
$191$		−	68.8639i		−	0.360544i	−0.983617	−	0.180272i	$-0.942302\pi$
$191$		−	68.8639i		−	0.360544i	0.983617	−	0.180272i	$-0.0576978\pi$
$192$	175.688	+	77.4440i	0.915044	+	0.403354i
$193$	−366.645			−1.89971			−0.949856	−	0.312686i	$-0.898771\pi$
$193$	−366.645			−1.89971			−0.949856	+	0.312686i	$0.898771\pi$
$194$	99.7782	+	131.070i	0.514321	+	0.675618i
$195$	−189.837	+	78.7446i	−0.973522	+	0.403819i
$196$	5.53410	−	20.0383i	0.0282352	−	0.102236i
$197$	246.744	+	246.744i	1.25251	+	1.25251i	0.954593	+	0.297912i	$0.0962901\pi$
$197$	246.744	+	246.744i	1.25251	+	1.25251i	0.297912	+	0.954593i	$0.403710\pi$
$198$	−7.94655	−	10.4170i	−0.0401341	−	0.0526110i
$199$			287.802i			1.44624i	0.690722	+	0.723120i	$0.257293\pi$
$199$			287.802i			1.44624i	−0.690722	+	0.723120i	$0.742707\pi$
$200$	62.9892	+	157.153i	0.314946	+	0.785765i
$201$	−66.7176	+	161.299i	−0.331928	+	0.802484i
$202$	−13.8071	+	101.859i	−0.0683521	+	0.504253i
$203$	−254.763	−	254.763i	−1.25499	−	1.25499i
$204$	16.4590	+	132.332i	0.0806812	+	0.648686i
$205$	−308.654	−	308.654i	−1.50563	−	1.50563i
$206$	−139.272	+	106.022i	−0.676077	+	0.514670i
$207$	49.6037	−	49.7034i	0.239632	−	0.240113i
$208$	−39.3620	−	156.451i	−0.189240	−	0.752167i
$209$			21.7616i			0.104122i
$210$	−76.7102	−	290.146i	−0.365287	−	1.38165i
$211$	156.146	+	156.146i	0.740027	+	0.740027i	0.972583	−	0.232556i	$-0.0747089\pi$
$211$	156.146	+	156.146i	0.740027	+	0.740027i	−0.232556	+	0.972583i	$0.574709\pi$
$212$	−157.062	+	89.0826i	−0.740859	+	0.420201i
$213$	−29.5159	−	71.1567i	−0.138572	−	0.334069i
$214$	39.8410	−	293.918i	0.186173	−	1.37345i
$215$	69.5724			0.323593
$216$	−215.989	−	2.15681i	−0.999950	−	0.00998524i
$217$		−	183.048i		−	0.843541i
$218$	2.90263	−	21.4135i	0.0133148	−	0.0982271i
$219$	−155.691	+	64.5807i	−0.710916	+	0.294889i
$220$	19.0682	+	5.26621i	0.0866738	+	0.0239373i
$221$	79.2296	−	79.2296i	0.358505	−	0.358505i
$222$	39.6381	+	149.926i	0.178550	+	0.675340i
$223$	45.2998			0.203138			0.101569	−	0.994828i	$-0.467614\pi$
$223$	45.2998			0.203138			0.101569	+	0.994828i	$0.467614\pi$
$224$	234.110	−	26.2708i	1.04514	−	0.117280i
$225$	−134.818	−	134.547i	−0.599190	−	0.597988i
$226$	20.8902	−	15.9029i	0.0924345	−	0.0703666i
$227$	300.757	−	300.757i	1.32492	−	1.32492i	0.415186	−	0.909737i	$-0.363717\pi$
$227$	300.757	−	300.757i	1.32492	−	1.32492i	0.909737	−	0.415186i	$-0.136283\pi$
$228$	283.055	+	220.433i	1.24147	+	0.966813i
$229$	65.7088	−	65.7088i	0.286938	−	0.286938i	−0.548930	−	0.835868i	$-0.684965\pi$
$229$	65.7088	−	65.7088i	0.286938	−	0.286938i	0.835868	+	0.548930i	$0.184965\pi$
$230$	−14.2414	+	105.063i	−0.0619190	+	0.456794i
$231$	−14.8552	−	6.14449i	−0.0643082	−	0.0265995i
$232$	153.975	−	359.972i	0.663684	−	1.55160i
$233$	−42.8218			−0.183785			−0.0918923	−	0.995769i	$-0.529292\pi$
$233$	−42.8218			−0.183785			−0.0918923	+	0.995769i	$0.529292\pi$
$234$	110.078	+	144.299i	0.470419	+	0.616663i
$235$	−110.744	+	110.744i	−0.471250	+	0.471250i
$236$	−86.7346	+	49.1942i	−0.367520	+	0.208450i
$237$	−41.0365	−	98.9305i	−0.173150	−	0.417428i
$238$	99.1073	+	130.189i	0.416417	+	0.547011i
$239$			100.598i			0.420913i	0.977603	+	0.210456i	$0.0674950\pi$
$239$			100.598i			0.420913i	−0.977603	+	0.210456i	$0.932505\pi$
$240$	261.649	−	194.679i	1.09021	−	0.811162i
$241$	−5.23162			−0.0217080			−0.0108540	−	0.999941i	$-0.503455\pi$
$241$	−5.23162			−0.0217080			−0.0108540	+	0.999941i	$0.503455\pi$
$242$	−191.711	+	145.942i	−0.792195	+	0.603066i
$243$	224.269	−	93.5551i	0.922916	−	0.385001i
$244$	60.9815	−	34.5875i	0.249924	−	0.141752i
$245$	−24.9686	−	24.9686i	−0.101913	−	0.101913i
$246$	−193.844	+	333.182i	−0.787985	+	1.35440i
$247$		−	301.448i		−	1.22044i
$248$	184.636	−	74.0048i	0.744501	−	0.298407i
$249$	−372.222	−	153.961i	−1.49487	−	0.618315i
$250$	−51.6630	−	7.00298i	−0.206652	−	0.0280119i
$251$	17.4381	+	17.4381i	0.0694747	+	0.0694747i	0.740990	−	0.671516i	$-0.234356\pi$
$251$	17.4381	+	17.4381i	0.0694747	+	0.0694747i	−0.671516	+	0.740990i	$0.734356\pi$
$252$	−230.397	+	130.983i	−0.914275	+	0.519773i
$253$	4.01579	+	4.01579i	0.0158727	+	0.0158727i
$254$	106.934	+	140.470i	0.421001	+	0.553033i
$255$	209.311	+	86.5765i	0.820828	+	0.339516i
$256$	121.147	+	225.520i	0.473232	+	0.880938i
$257$		−	343.676i		−	1.33726i	−0.743595	−	0.668630i	$-0.766881\pi$
$257$		−	343.676i		−	1.33726i	0.743595	−	0.668630i	$-0.233119\pi$
$258$	−15.7038	−	59.3975i	−0.0608674	−	0.230223i
$259$	134.545	+	134.545i	0.519480	+	0.519480i
$260$	−264.139	−	72.9491i	−1.01592	−	0.280574i
$261$	0.442114	+	440.460i	0.00169392	+	1.68758i
$262$	159.904	+	21.6752i	0.610322	+	0.0827299i
$263$	98.0863			0.372952			0.186476	−	0.982460i	$-0.440293\pi$
$263$	98.0863			0.372952			0.186476	+	0.982460i	$0.440293\pi$
$264$	0.191969	−	17.4682i	0.000727155	−	0.0661675i
$265$			306.708i			1.15739i
$266$	436.206	+	59.1282i	1.63987	+	0.222286i
$267$	−51.5769	−	124.341i	−0.193172	−	0.465697i
$268$	−202.442	+	114.821i	−0.755380	+	0.428437i
$269$	−126.560	+	126.560i	−0.470482	+	0.470482i	−0.902070	−	0.431589i	$-0.857953\pi$
$269$	−126.560	+	126.560i	−0.470482	+	0.470482i	0.431589	+	0.902070i	$0.357953\pi$
$270$	−184.186	+	317.313i	−0.682170	+	1.17523i
$271$	−206.487			−0.761945			−0.380972	−	0.924586i	$-0.624411\pi$
$271$	−206.487			−0.761945			−0.380972	+	0.924586i	$0.624411\pi$
$272$	−91.2498	+	152.601i	−0.335477	+	0.561033i
$273$	205.779	+	85.1154i	0.753768	+	0.311778i
$274$	−200.023	−	262.752i	−0.730010	−	0.958950i
$275$	10.8926	−	10.8926i	0.0396095	−	0.0396095i
$276$	92.9118	−	11.5560i	0.336637	−	0.0418697i
$277$	183.416	−	183.416i	0.662153	−	0.662153i	−0.293734	−	0.955887i	$-0.594898\pi$
$277$	183.416	−	183.416i	0.662153	−	0.662153i	0.955887	+	0.293734i	$0.0948980\pi$
$278$	266.490	+	36.1231i	0.958598	+	0.129939i
$279$	−158.077	+	158.395i	−0.566585	+	0.567723i
$280$	157.370	−	367.910i	0.562036	−	1.31396i
$281$	−109.143			−0.388409			−0.194204	−	0.980961i	$-0.562213\pi$
$281$	−109.143			−0.388409			−0.194204	+	0.980961i	$0.562213\pi$
$282$	119.545	+	69.5507i	0.423917	+	0.246634i
$283$	60.4623	−	60.4623i	0.213648	−	0.213648i	−0.592167	−	0.805815i	$-0.701728\pi$
$283$	60.4623	−	60.4623i	0.213648	−	0.213648i	0.805815	+	0.592167i	$0.201728\pi$
$284$	27.3436	−	99.0075i	0.0962802	−	0.348618i
$285$	562.888	−	233.487i	1.97504	−	0.819252i
$286$	−11.6793	+	8.89098i	−0.0408367	+	0.0310873i
$287$			472.962i			1.64795i
$288$	−225.267	−	179.441i	−0.782176	−	0.623058i
$289$	165.509			0.572697
$290$	−402.822	−	529.152i	−1.38904	−	1.82466i
$291$	−94.6721	−	228.235i	−0.325334	−	0.784311i
$292$	−216.628	−	59.8277i	−0.741877	−	0.204889i
$293$	19.4639	+	19.4639i	0.0664296	+	0.0664296i	0.739541	−	0.673111i	$-0.235043\pi$
$293$	19.4639	+	19.4639i	0.0664296	+	0.0664296i	−0.673111	+	0.739541i	$0.735043\pi$
$294$	−15.6811	+	26.9529i	−0.0533371	+	0.0916765i
$295$			169.374i			0.574149i
$296$	−81.3170	+	190.108i	−0.274720	+	0.642257i
$297$	7.54818	+	18.1456i	0.0254147	+	0.0610963i
$298$	−49.7990	+	367.381i	−0.167111	+	1.23282i
$299$	−55.6280	−	55.6280i	−0.186047	−	0.186047i
$300$	−31.3451	−	252.018i	−0.104484	−	0.840060i
$301$	−53.3042	−	53.3042i	−0.177090	−	0.177090i
$302$	195.848	−	149.091i	0.648503	−	0.493679i
$303$	58.9329	−	142.479i	0.194498	−	0.470227i
$304$	116.713	+	463.894i	0.383924	+	1.52597i
$305$		−	119.084i		−	0.390438i
$306$	26.6693	−	198.242i	0.0871545	−	0.647848i
$307$	−408.201	−	408.201i	−1.32964	−	1.32964i	−0.905677	−	0.423967i	$-0.860637\pi$
$307$	−408.201	−	408.201i	−1.32964	−	1.32964i	−0.423967	−	0.905677i	$-0.639363\pi$
$308$	−10.5747	−	18.6443i	−0.0343334	−	0.0605334i
$309$	242.517	−	100.596i	0.784844	−	0.325554i
$310$	45.3844	−	334.813i	0.146401	−	1.08004i
$311$	−360.965			−1.16066			−0.580330	−	0.814381i	$-0.697076\pi$
$311$	−360.965			−1.16066			−0.580330	+	0.814381i	$0.697076\pi$
$312$	−2.65921	+	241.975i	−0.00852311	+	0.775561i
$313$			73.9217i			0.236172i	0.993003	+	0.118086i	$0.0376758\pi$
$313$			73.9217i			0.236172i	−0.993003	+	0.118086i	$0.962324\pi$
$314$	52.8779	−	390.096i	0.168401	−	1.24234i
$315$	0.451863	+	450.172i	0.00143449	+	1.42912i
$316$	38.0163	−	137.652i	0.120305	−	0.435607i
$317$	−172.709	+	172.709i	−0.544825	+	0.544825i	−0.924939	−	0.380115i	$-0.875884\pi$
$317$	−172.709	+	172.709i	−0.544825	+	0.544825i	0.380115	+	0.924939i	$0.375884\pi$
$318$	261.853	−	69.2299i	0.823436	−	0.217704i
$319$	−35.6227			−0.111670
$320$	434.724	+	9.99263i	1.35851	+	0.0312270i
$321$	−170.053	+	411.128i	−0.529761	+	1.28077i
$322$	91.4070	−	69.5844i	0.283873	−	0.216101i
$323$	−234.925	+	234.925i	−0.727321	+	0.727321i
$324$	312.481	+	85.6252i	0.964447	+	0.264275i
$325$	−150.888	+	150.888i	−0.464271	+	0.464271i
$326$	−7.57226	+	55.8627i	−0.0232278	+	0.171358i
$327$	−12.3893	+	29.9529i	−0.0378877	+	0.0915990i
$328$	−477.064	+	191.214i	−1.45446	+	0.582970i
$329$	169.697			0.515796
$330$	−25.6481	−	14.9220i	−0.0777217	−	0.0452182i
$331$	261.507	−	261.507i	0.790051	−	0.790051i	−0.191451	−	0.981502i	$-0.561319\pi$
$331$	261.507	−	261.507i	0.790051	−	0.790051i	0.981502	+	0.191451i	$0.0613194\pi$
$332$	−264.967	−	467.164i	−0.798092	−	1.40712i
$333$	−0.233489	−	232.615i	−0.000701168	−	0.698544i
$334$	−73.0763	−	95.9940i	−0.218791	−	0.287407i
$335$			395.325i			1.18007i
$336$	−349.625	−	51.3107i	−1.04055	−	0.152710i
$337$	18.2211			0.0540684			0.0270342	−	0.999635i	$-0.491394\pi$
$337$	18.2211			0.0540684			0.0270342	+	0.999635i	$0.491394\pi$
$338$	−107.154	+	81.5722i	−0.317024	+	0.241338i
$339$	−36.3765	+	15.0890i	−0.107305	+	0.0445104i
$340$	148.998	+	262.700i	0.438231	+	0.772647i
$341$	−12.7975	−	12.7975i	−0.0375294	−	0.0375294i
$342$	−326.394	−	427.863i	−0.954368	−	1.25106i
$343$		−	322.471i		−	0.940149i
$344$	32.2162	−	75.3170i	0.0936517	−	0.218945i
$345$	60.7863	−	146.960i	0.176192	−	0.425970i
$346$	−209.731	−	28.4293i	−0.606159	−	0.0821656i
$347$	−173.710	−	173.710i	−0.500605	−	0.500605i	0.411021	−	0.911626i	$-0.365172\pi$
$347$	−173.710	−	173.710i	−0.500605	−	0.500605i	−0.911626	+	0.411021i	$0.865172\pi$
$348$	−360.839	+	463.349i	−1.03690	+	1.33146i
$349$	387.899	+	387.899i	1.11146	+	1.11146i	0.992953	+	0.118506i	$0.0378106\pi$
$349$	387.899	+	387.899i	1.11146	+	1.11146i	0.118506	+	0.992953i	$0.462189\pi$
$350$	−188.744	−	247.936i	−0.539268	−	0.708389i
$351$	−104.560	−	251.358i	−0.297891	−	0.716121i
$352$	14.5308	−	18.2041i	0.0412806	−	0.0517163i
$353$			676.812i			1.91732i	0.284561	+	0.958658i	$0.408152\pi$
$353$			676.812i			1.91732i	−0.284561	+	0.958658i	$0.591848\pi$
$354$	144.603	−	38.2309i	0.408484	−	0.107997i
$355$	−123.368	−	123.368i	−0.347516	−	0.347516i
$356$	47.7809	−	173.008i	0.134216	−	0.485979i
$357$	−94.0355	−	226.700i	−0.263405	−	0.635014i
$358$	−11.1147	−	1.50661i	−0.0310467	−	0.00420842i
$359$	240.896			0.671020			0.335510	−	0.942037i	$-0.391091\pi$
$359$	240.896			0.671020			0.335510	+	0.942037i	$0.391091\pi$
$360$	−453.895	+	182.456i	−1.26082	+	0.506823i
$361$			532.827i			1.47598i
$362$	−445.139	−	60.3392i	−1.22967	−	0.166683i
$363$	333.830	−	138.473i	0.919643	−	0.381469i
$364$	146.484	+	258.267i	0.402428	+	0.709523i
$365$	−269.929	+	269.929i	−0.739532	+	0.739532i
$366$	−101.668	+	26.8794i	−0.277781	+	0.0734411i
$367$	666.702			1.81663			0.908313	−	0.418291i	$-0.137371\pi$
$367$	666.702			1.81663			0.908313	+	0.418291i	$0.137371\pi$
$368$	107.143	+	64.0675i	0.291149	+	0.174096i
$369$	408.441	−	409.261i	1.10689	−	1.10911i
$370$	212.738	+	279.455i	0.574968	+	0.755285i
$371$	234.990	−	234.990i	0.633397	−	0.633397i
$372$	−296.091	+	36.8268i	−0.795945	+	0.0989967i
$373$	−358.513	+	358.513i	−0.961160	+	0.961160i	−0.999273	−	0.0381137i	$-0.987865\pi$
$373$	−358.513	+	358.513i	−0.961160	+	0.961160i	0.0381137	+	0.999273i	$0.487865\pi$
$374$	16.0309	+	2.17300i	0.0428633	+	0.00581017i
$375$	72.2653	+	29.8908i	0.192708	+	0.0797088i
$376$	68.6069	+	171.169i	0.182465	+	0.455236i
$377$	493.457			1.30890
$378$	384.233	−	101.998i	1.01649	−	0.269836i
$379$	−140.959	+	140.959i	−0.371925	+	0.371925i	−0.868178	−	0.496253i	$-0.834709\pi$
$379$	−140.959	+	140.959i	−0.371925	+	0.371925i	0.496253	+	0.868178i	$0.334709\pi$
$380$	783.202	+	216.302i	2.06106	+	0.569217i
$381$	−101.462	−	244.604i	−0.266305	−	0.642004i
$382$	−109.587	+	83.4242i	−0.286877	+	0.218388i
$383$		−	69.4683i		−	0.181379i	−0.995879	−	0.0906897i	$-0.971093\pi$
$383$		−	69.4683i		−	0.181379i	0.995879	−	0.0906897i	$-0.0289071\pi$
$384$	−89.5942	−	373.402i	−0.233318	−	0.972400i
$385$	−36.4083			−0.0945669
$386$	444.167	+	583.463i	1.15069	+	1.51156i
$387$	0.0925037	+	92.1575i	0.000239028	+	0.238133i
$388$	87.7043	−	317.566i	0.226042	−	0.818468i
$389$	−265.362	−	265.362i	−0.682165	−	0.682165i	0.278322	−	0.960488i	$-0.410222\pi$
$389$	−265.362	−	265.362i	−0.682165	−	0.682165i	−0.960488	+	0.278322i	$0.910222\pi$
$390$	355.286	+	206.704i	0.910990	+	0.530011i
$391$			86.7042i			0.221750i
$392$	−38.5923	+	15.4683i	−0.0984496	+	0.0394600i
$393$	−223.672	−	92.5164i	−0.569139	−	0.235411i
$394$	93.7434	−	691.571i	0.237927	−	1.75526i
$395$	−171.521	−	171.521i	−0.434230	−	0.434230i
$396$	−6.95041	+	25.2653i	−0.0175515	+	0.0638013i
$397$	259.123	+	259.123i	0.652703	+	0.652703i	0.953643	−	0.300940i	$-0.0973004\pi$
$397$	259.123	+	259.123i	0.652703	+	0.652703i	−0.300940	+	0.953643i	$0.597300\pi$
$398$	457.996	−	348.654i	1.15074	−	0.876014i
$399$	−610.157	−	252.377i	−1.52922	−	0.632523i
$400$	173.780	−	290.619i	0.434449	−	0.726548i
$401$		−	664.163i		−	1.65627i	−0.560531	−	0.828133i	$-0.689403\pi$
$401$		−	664.163i		−	1.65627i	0.560531	−	0.828133i	$-0.310597\pi$
$402$	337.509	−	89.2323i	0.839575	−	0.221971i
$403$	177.275	+	177.275i	0.439889	+	0.439889i
$404$	178.821	−	101.424i	0.442626	−	0.251049i
$405$	388.369	−	389.932i	0.958937	−	0.962795i
$406$	−96.7902	+	714.049i	−0.238400	+	1.75874i
$407$	18.8131			0.0462237
$408$	190.649	−	186.504i	0.467276	−	0.457117i
$409$		−	530.421i		−	1.29687i	−0.761269	−	0.648437i	$-0.775423\pi$
$409$		−	530.421i		−	1.29687i	0.761269	−	0.648437i	$-0.224577\pi$
$410$	−117.264	+	865.093i	−0.286011	+	2.10998i
$411$	189.787	+	457.536i	0.461768	+	1.11323i
$412$	337.438	+	93.1926i	0.819024	+	0.226196i
$413$	129.769	−	129.769i	0.314211	−	0.314211i
$414$	−139.188	−	18.7248i	−0.336202	−	0.0452290i
$415$	−912.271			−2.19824
$416$	−201.285	+	252.169i	−0.483857	+	0.606176i
$417$	−372.762	−	154.184i	−0.893914	−	0.369746i
$418$	34.6305	−	26.3628i	0.0828480	−	0.0630688i
$419$	−404.149	+	404.149i	−0.964556	+	0.964556i	−0.999393	−	0.0348367i	$-0.988909\pi$
$419$	−404.149	+	404.149i	−0.964556	+	0.964556i	0.0348367	+	0.999393i	$0.488909\pi$
$420$	−368.797	+	473.567i	−0.878087	+	1.12754i
$421$	−264.630	+	264.630i	−0.628575	+	0.628575i	−0.947710	−	0.319134i	$-0.896608\pi$
$421$	−264.630	+	264.630i	−0.628575	+	0.628575i	0.319134	+	0.947710i	$0.396608\pi$
$422$	59.3232	−	437.644i	0.140576	−	1.03707i
$423$	−146.842	−	146.547i	−0.347143	−	0.346447i
$424$	332.033	+	142.024i	0.783097	+	0.334963i
$425$	235.180			0.553366
$426$	−77.4791	+	133.172i	−0.181876	+	0.312611i
$427$	−91.2382	+	91.2382i	−0.213673	+	0.213673i
$428$	−515.994	+	292.662i	−1.20559	+	0.683790i
$429$	20.3374	−	8.43598i	0.0474065	−	0.0196643i
$430$	−84.2825	−	110.715i	−0.196006	−	0.257476i
$431$		−	766.652i		−	1.77877i	−0.457155	−	0.889387i	$-0.651132\pi$
$431$		−	766.652i		−	1.77877i	0.457155	−	0.889387i	$-0.348868\pi$
$432$	258.225	+	346.329i	0.597743	+	0.801688i
$433$	151.222			0.349243			0.174622	−	0.984636i	$-0.444130\pi$
$433$	151.222			0.349243			0.174622	+	0.984636i	$0.444130\pi$
$434$	−291.296	+	221.752i	−0.671188	+	0.510948i
$435$	382.207	+	921.422i	0.878638	+	2.11821i
$436$	−37.5929	+	21.3220i	−0.0862223	+	0.0489036i
$437$	164.943	+	164.943i	0.377445	+	0.377445i
$438$	291.380	+	169.524i	0.665252	+	0.387041i
$439$		−	565.007i		−	1.28703i	−0.765433	−	0.643516i	$-0.777475\pi$
$439$		−	565.007i		−	1.28703i	0.765433	−	0.643516i	$-0.222525\pi$
$440$	−14.7195	−	36.7241i	−0.0334535	−	0.0834638i
$441$	33.0409	−	33.1073i	0.0749228	−	0.0750733i
$442$	−222.064	−	30.1011i	−0.502408	−	0.0681020i
$443$	−100.963	−	100.963i	−0.227907	−	0.227907i	0.583911	−	0.811818i	$-0.301522\pi$
$443$	−100.963	−	100.963i	−0.227907	−	0.227907i	−0.811818	+	0.583911i	$0.801522\pi$
$444$	190.566	−	244.704i	0.429204	−	0.551134i
$445$	−215.577	−	215.577i	−0.484442	−	0.484442i
$446$	−54.8779	−	72.0883i	−0.123045	−	0.161633i
$447$	212.557	−	513.887i	0.475518	−	1.14963i
$448$	−325.416	−	340.728i	−0.726375	−	0.760554i
$449$		−	131.725i		−	0.293375i	−0.989183	−	0.146687i	$-0.953139\pi$
$449$		−	131.725i		−	0.293375i	0.989183	−	0.146687i	$-0.0468611\pi$
$450$	−50.7900	+	377.539i	−0.112867	+	0.838975i
$451$	33.0663	+	33.0663i	0.0733178	+	0.0733178i
$452$	−50.6143	−	13.9785i	−0.111979	−	0.0309259i
$453$	−341.034	+	141.461i	−0.752833	+	0.312277i
$454$	−842.961	−	114.264i	−1.85674	−	0.251684i
$455$	504.339			1.10844
$456$	7.88486	−	717.483i	0.0172914	−	1.57343i
$457$		−	137.963i		−	0.301888i	−0.988542	−	0.150944i	$-0.951769\pi$
$457$		−	137.963i		−	0.301888i	0.988542	−	0.150944i	$-0.0482313\pi$
$458$	−184.168	−	24.9642i	−0.402114	−	0.0545071i
$459$	−114.403	+	277.374i	−0.249245	+	0.604302i
$460$	184.445	−	104.613i	0.400967	−	0.227421i
$461$	−303.536	+	303.536i	−0.658430	+	0.658430i	−0.955008	−	0.296579i	$-0.904154\pi$
$461$	−303.536	+	303.536i	−0.658430	+	0.658430i	0.296579	+	0.955008i	$0.404154\pi$
$462$	8.21803	+	31.0836i	0.0177879	+	0.0672805i
$463$	280.379			0.605570			0.302785	−	0.953059i	$-0.402084\pi$
$463$	280.379			0.605570			0.302785	+	0.953059i	$0.402084\pi$
$464$	−759.374	+	191.054i	−1.63658	+	0.411754i
$465$	−193.714	+	468.332i	−0.416589	+	1.00716i
$466$	51.8759	+	68.1449i	0.111322	+	0.146234i
$467$	−65.6355	+	65.6355i	−0.140547	+	0.140547i	−0.773880	−	0.633333i	$-0.781687\pi$
$467$	−65.6355	+	65.6355i	−0.140547	+	0.140547i	0.633333	+	0.773880i	$0.281687\pi$
$468$	96.2792	−	349.983i	0.205725	−	0.747827i
$469$	302.886	−	302.886i	0.645812	−	0.645812i
$470$	310.392	+	42.0740i	0.660409	+	0.0895192i
$471$	−225.699	+	545.659i	−0.479190	+	1.15851i
$472$	183.359	+	78.4302i	0.388473	+	0.166166i
$473$	−7.45335			−0.0157576
$474$	−107.721	+	185.152i	−0.227259	+	0.390616i
$475$	447.400	−	447.400i	0.941894	−	0.941894i
$476$	87.1147	−	315.431i	0.183014	−	0.662669i
$477$	−406.274	+	0.407800i	−0.851728	+	0.000854927i
$478$	160.088	−	121.868i	0.334912	−	0.254955i
$479$			373.272i			0.779273i	0.920969	+	0.389636i	$0.127399\pi$
$479$			373.272i			0.779273i	−0.920969	+	0.389636i	$0.872601\pi$
$480$	−626.776	−	180.537i	−1.30578	−	0.376119i
$481$	−260.604			−0.541797
$482$	6.33778	+	8.32539i	0.0131489	+	0.0172726i
$483$	−159.169	+	66.0234i	−0.329542	+	0.136694i
$484$	464.492	+	128.282i	0.959694	+	0.265045i
$485$	−395.702	−	395.702i	−0.815881	−	0.815881i
$486$	−420.567	−	243.556i	−0.865364	−	0.501144i
$487$		−	0.0470526i		−	9.66171e-5i	−1.00000		4.83086e-5i	$-0.999985\pi$
$487$		−	0.0470526i		−	9.66171e-5i	1.00000		4.83086e-5i	$-1.53771e-5\pi$
$488$	−128.916	−	55.1429i	−0.264173	−	0.112998i
$489$	32.3206	−	78.1398i	0.0660954	−	0.159795i
$490$	−9.48614	+	69.9820i	−0.0193595	+	0.142820i
$491$	273.442	+	273.442i	0.556908	+	0.556908i	0.928426	−	0.371518i	$-0.121163\pi$
$491$	273.442	+	273.442i	0.556908	+	0.556908i	−0.371518	+	0.928426i	$0.621163\pi$
$492$	765.043	−	95.1532i	1.55496	−	0.193401i
$493$	−384.562	−	384.562i	−0.780044	−	0.780044i
$494$	−479.712	+	365.185i	−0.971077	+	0.739241i
$495$	31.5047	+	31.4415i	0.0636458	+	0.0635182i
$496$	−341.443	−	204.170i	−0.688394	−	0.411634i
$497$			189.042i			0.380365i
$498$	205.917	+	778.852i	0.413487	+	1.56396i
$499$	−46.2637	−	46.2637i	−0.0927129	−	0.0927129i	0.659229	−	0.751942i	$-0.270883\pi$
$499$	−46.2637	−	46.2637i	−0.0927129	−	0.0927129i	−0.751942	+	0.659229i	$0.770883\pi$
$500$	51.4422	+	90.6980i	0.102884	+	0.181396i
$501$	69.3366	+	167.156i	0.138396	+	0.333645i
$502$	6.62514	−	48.8755i	0.0131975	−	0.0973616i
$503$	864.426			1.71854			0.859270	−	0.511522i	$-0.170918\pi$
$503$	864.426			1.71854			0.859270	+	0.511522i	$0.170918\pi$
$504$	487.552	+	207.968i	0.967366	+	0.412634i
$505$		−	349.198i		−	0.691482i
$506$	1.52569	−	11.2554i	0.00301520	−	0.0222440i
$507$	186.590	−	77.3977i	0.368027	−	0.152658i
$508$	93.9946	−	340.342i	0.185029	−	0.669964i
$509$	−171.041	+	171.041i	−0.336033	+	0.336033i	−0.854872	−	0.518839i	$-0.826365\pi$
$509$	−171.041	+	171.041i	−0.336033	+	0.336033i	0.518839	+	0.854872i	$0.326365\pi$
$510$	−115.793	−	437.971i	−0.227045	−	0.858767i
$511$	413.623			0.809438
$512$	212.121	−	465.992i	0.414299	−	0.910141i
$513$	310.031	+	745.306i	0.604349	+	1.45284i
$514$	−546.911	+	416.341i	−1.06403	+	0.810002i
$515$	420.464	−	420.464i	0.816435	−	0.816435i
$516$	−75.4986	+	96.9467i	−0.146315	+	0.187881i
$517$	11.8641	−	11.8641i	0.0229479	−	0.0229479i
$518$	51.1168	−	377.103i	0.0986811	−	0.727999i
$519$	293.368	+	121.345i	0.565257	+	0.233805i
$520$	203.899	+	508.713i	0.392114	+	0.978295i
$521$	351.572			0.674802			0.337401	−	0.941361i	$-0.390452\pi$
$521$	351.572			0.674802			0.337401	+	0.941361i	$0.390452\pi$
$522$	700.394	−	534.292i	1.34175	−	1.02355i
$523$	−287.638	+	287.638i	−0.549977	+	0.549977i	−0.926434	−	0.376457i	$-0.877142\pi$
$523$	−287.638	+	287.638i	−0.549977	+	0.549977i	0.376457	+	0.926434i	$0.377142\pi$
$524$	−159.221	−	280.724i	−0.303857	−	0.535732i
$525$	179.085	+	431.736i	0.341114	+	0.822354i
$526$	−118.825	−	156.090i	−0.225904	−	0.296750i
$527$		−	276.309i		−	0.524306i
$528$	−28.0307	+	20.8561i	−0.0530885	+	0.0395003i
$529$	−468.124			−0.884922
$530$	488.083	−	371.558i	0.920911	−	0.701052i
$531$	−224.357	+	0.225200i	−0.422519	+	0.000424106i
$532$	−434.341	−	765.789i	−0.816431	−	1.43945i
$533$	−458.045	−	458.045i	−0.859372	−	0.859372i
$534$	−135.389	+	232.709i	−0.253538	+	0.435784i
$535$			1007.63i			1.88341i
$536$	427.967	+	183.059i	0.798446	+	0.341528i
$537$	15.5471	+	6.43067i	0.0289517	+	0.0119752i
$538$	354.721	+	48.0828i	0.659332	+	0.0893732i
$539$	2.67491	+	2.67491i	0.00496273	+	0.00496273i
$540$	728.089	−	91.2993i	1.34831	−	0.169073i
$541$	419.846	+	419.846i	0.776056	+	0.776056i	0.979158	−	0.203102i	$-0.0651021\pi$
$541$	419.846	+	419.846i	0.776056	+	0.776056i	−0.203102	+	0.979158i	$0.565102\pi$
$542$	250.146	+	328.595i	0.461524	+	0.606264i
$543$	622.654	+	257.545i	1.14669	+	0.474301i
$544$	353.386	−	39.6554i	0.649607	−	0.0728960i
$545$			73.4108i			0.134699i
$546$	−113.839	−	430.580i	−0.208496	−	0.788607i
$547$	517.346	+	517.346i	0.945789	+	0.945789i	0.998604	−	0.0528155i	$-0.0168195\pi$
$547$	517.346	+	517.346i	0.945789	+	0.945789i	−0.0528155	+	0.998604i	$0.516820\pi$
$548$	−175.819	+	636.616i	−0.320837	+	1.16171i
$549$	157.742	−	0.158334i	0.287325	−	0.000288404i
$550$	−30.5298	−	4.13835i	−0.0555087	−	0.00752427i
$551$	−1463.16			−2.65546
$552$	−130.947	−	133.857i	−0.237222	−	0.242494i
$553$			262.828i			0.475277i
$554$	−514.079	−	69.6840i	−0.927940	−	0.125783i
$555$	−201.851	−	486.621i	−0.363696	−	0.876794i
$556$	−265.351	−	467.843i	−0.477251	−	0.841443i
$557$	31.8976	−	31.8976i	0.0572667	−	0.0572667i	−0.677893	−	0.735160i	$-0.737107\pi$
$557$	31.8976	−	31.8976i	0.0572667	−	0.0572667i	0.735160	+	0.677893i	$0.237107\pi$
$558$	443.563	+	59.6722i	0.794917	+	0.106939i
$559$	103.246			0.184698
$560$	−776.120	+	195.267i	−1.38593	+	0.348691i
$561$	−22.4237	−	9.27502i	−0.0399709	−	0.0165330i
$562$	132.220	+	173.685i	0.235266	+	0.309049i
$563$	−32.9214	+	32.9214i	−0.0584750	+	0.0584750i	−0.735740	−	0.677265i	$-0.763165\pi$
$563$	−32.9214	+	32.9214i	−0.0584750	+	0.0584750i	0.677265	+	0.735740i	$0.263165\pi$
$564$	−34.1406	−	274.495i	−0.0605330	−	0.486692i
$565$	−63.0679	+	63.0679i	−0.111625	+	0.111625i
$566$	−169.464	−	22.9710i	−0.299406	−	0.0405848i
$567$	−596.310	+	1.19710i	−1.05169	+	0.00211129i
$568$	−190.681	+	76.4278i	−0.335707	+	0.134556i
$569$	647.095			1.13725			0.568624	−	0.822597i	$-0.307476\pi$
$569$	647.095			1.13725			0.568624	+	0.822597i	$0.307476\pi$
$570$	−1053.46	−	612.902i	−1.84818	−	1.07527i
$571$	451.861	−	451.861i	0.791350	−	0.791350i	−0.190363	−	0.981714i	$-0.560967\pi$
$571$	451.861	−	451.861i	0.791350	−	0.791350i	0.981714	+	0.190363i	$0.0609666\pi$
$572$	28.2975	+	7.81511i	0.0494711	+	0.0136628i
$573$	190.826	−	79.1550i	0.333030	−	0.138141i
$574$	752.652	−	572.963i	1.31124	−	0.998193i
$575$		−	165.123i		−	0.287170i
$576$	−12.6585	+	575.861i	−0.0219766	+	0.999758i
$577$	532.176			0.922315			0.461157	−	0.887318i	$-0.347434\pi$
$577$	532.176			0.922315			0.461157	+	0.887318i	$0.347434\pi$
$578$	−200.504	−	263.385i	−0.346893	−	0.455683i
$579$	−421.436	−	1015.99i	−0.727869	−	1.75474i
$580$	−354.078	+	1282.07i	−0.610478	+	2.21046i
$581$	698.953	+	698.953i	1.20302	+	1.20302i
$582$	−248.514	+	427.149i	−0.427000	+	0.733933i
$583$		−	32.8579i		−	0.0563601i
$584$	167.224	+	417.210i	0.286342	+	0.714402i
$585$	−436.412	−	435.537i	−0.746004	−	0.744508i
$586$	7.39475	−	54.5532i	0.0126190	−	0.0930942i
$587$	532.393	+	532.393i	0.906973	+	0.906973i	0.996027	−	0.0890534i	$-0.0283842\pi$
$587$	532.393	+	532.393i	0.906973	+	0.906973i	−0.0890534	+	0.996027i	$0.528384\pi$
$588$	61.8884	−	7.69745i	0.105252	−	0.0130909i
$589$	−525.642	−	525.642i	−0.892431	−	0.892431i
$590$	269.535	−	205.186i	0.456838	−	0.347772i
$591$	−400.124	+	967.359i	−0.677029	+	1.63682i
$592$	401.040	−	100.899i	0.677433	−	0.170438i
$593$			254.750i			0.429595i	0.976659	+	0.214798i	$0.0689092\pi$
$593$			254.750i			0.429595i	−0.976659	+	0.214798i	$0.931091\pi$
$594$	19.7320	−	33.9941i	0.0332189	−	0.0572291i
$595$	−393.042	−	393.042i	−0.660574	−	0.660574i
$596$	644.963	−	365.811i	1.08215	−	0.613777i
$597$	−797.517	+	330.811i	−1.33587	+	0.554123i
$598$	−21.1343	+	155.914i	−0.0353417	+	0.260726i
$599$	624.772			1.04303			0.521513	−	0.853244i	$-0.325368\pi$
$599$	624.772			1.04303			0.521513	+	0.853244i	$0.325368\pi$
$600$	−363.079	+	355.185i	−0.605131	+	0.591975i
$601$			386.910i			0.643777i	0.946778	+	0.321889i	$0.104318\pi$
$601$			386.910i			0.643777i	−0.946778	+	0.321889i	$0.895682\pi$
$602$	−20.2515	+	149.401i	−0.0336403	+	0.248174i
$603$	−523.658	+	0.525625i	−0.868422	+	0.000871684i
$604$	−474.514	−	131.050i	−0.785620	−	0.216970i
$605$	578.779	−	578.779i	0.956660	−	0.956660i
$606$	−298.128	+	78.8207i	−0.491961	+	0.130067i
$607$	−951.141			−1.56695			−0.783477	−	0.621421i	$-0.786556\pi$
$607$	−951.141			−1.56695			−0.783477	+	0.621421i	$0.786556\pi$
$608$	596.832	−	747.710i	0.981632	−	1.22979i
$609$	413.129	−	998.800i	0.678373	−	1.64007i
$610$	−189.505	+	144.262i	−0.310664	+	0.236496i
$611$	−164.345	+	164.345i	−0.268977	+	0.268977i
$612$	−347.782	+	197.717i	−0.568271	+	0.323066i
$613$	387.896	−	387.896i	0.632783	−	0.632783i	−0.315982	−	0.948765i	$-0.602334\pi$
$613$	387.896	−	387.896i	0.632783	−	0.632783i	0.948765	+	0.315982i	$0.102334\pi$
$614$	−155.085	+	1144.10i	−0.252581	+	1.86336i
$615$	500.519	−	1210.08i	0.813852	−	1.96761i
$616$	−16.8592	+	39.4145i	−0.0273688	+	0.0639846i
$617$	−882.945			−1.43103			−0.715514	−	0.698598i	$-0.753808\pi$
$617$	−882.945			−1.43103			−0.715514	+	0.698598i	$0.753808\pi$
$618$	−453.878	−	264.065i	−0.734431	−	0.427290i
$619$	−694.731	+	694.731i	−1.12234	+	1.12234i	−0.130955	+	0.991388i	$0.541804\pi$
$619$	−694.731	+	694.731i	−1.12234	+	1.12234i	−0.991388	+	0.130955i	$0.958196\pi$
$620$	−587.789	+	333.382i	−0.948046	+	0.537714i
$621$	194.748	+	80.3239i	0.313604	+	0.129346i
$622$	437.286	+	574.425i	0.703033	+	0.923513i
$623$			330.337i			0.530235i
$624$	388.291	−	288.906i	0.622260	−	0.462990i
$625$	706.197			1.12991
$626$	117.636	−	89.5515i	0.187917	−	0.143053i
$627$	−60.3027	+	25.0136i	−0.0961765	+	0.0398942i
$628$	−684.840	+	388.428i	−1.09051	+	0.618516i
$629$	203.094	+	203.094i	0.322885	+	0.322885i
$630$	715.838	−	546.074i	1.13625	−	0.866785i
$631$		−	927.845i		−	1.47044i	−0.677831	−	0.735218i	$-0.737080\pi$
$631$		−	927.845i		−	1.47044i	0.677831	−	0.735218i	$-0.262920\pi$
$632$	−265.108	+	106.259i	−0.419475	+	0.168131i
$633$	−253.209	+	612.170i	−0.400014	+	0.967093i
$634$	484.069	+	65.6161i	0.763516	+	0.103495i
$635$	−424.082	−	424.082i	−0.667846	−	0.667846i
$636$	−427.387	−	332.834i	−0.671992	−	0.523323i
$637$	−37.0537	−	37.0537i	−0.0581691	−	0.0581691i
$638$	43.1547	+	56.6885i	0.0676405	+	0.0888535i
$639$	163.253	−	163.581i	0.255482	−	0.255995i
$640$	−510.739	−	703.908i	−0.798029	−	1.09986i
$641$		−	759.287i		−	1.18453i	−0.805741	−	0.592267i	$-0.798233\pi$
$641$		−	759.287i		−	1.18453i	0.805741	−	0.592267i	$-0.201767\pi$
$642$	860.261	−	227.440i	1.33997	−	0.354268i
$643$	274.424	+	274.424i	0.426787	+	0.426787i	0.887532	−	0.460746i	$-0.152418\pi$
$643$	274.424	+	274.424i	0.426787	+	0.426787i	−0.460746	+	0.887532i	$0.652418\pi$
$644$	−221.467	−	61.1642i	−0.343893	−	0.0949755i
$645$	79.9694	+	192.789i	0.123984	+	0.298898i
$646$	658.446	+	89.2532i	1.01927	+	0.138163i
$647$	−747.683			−1.15561			−0.577807	−	0.816173i	$-0.696092\pi$
$647$	−747.683			−1.15561			−0.577807	+	0.816173i	$0.696092\pi$
$648$	−242.290	−	600.999i	−0.373905	−	0.927467i
$649$		−	18.1452i		−	0.0279587i
$650$	422.908	+	57.3257i	0.650628	+	0.0881934i
$651$	507.239	−	210.403i	0.779168	−	0.323200i
$652$	98.0709	−	55.6239i	0.150416	−	0.0853128i
$653$	605.127	−	605.127i	0.926688	−	0.926688i	−0.0708022	−	0.997490i	$-0.522556\pi$
$653$	605.127	−	605.127i	0.926688	−	0.926688i	0.997490	+	0.0708022i	$0.0225559\pi$
$654$	62.6746	−	16.5702i	0.0958327	−	0.0253367i
$655$	−548.192			−0.836935
$656$	882.223	+	527.537i	1.34485	+	0.804172i
$657$	−357.914	−	357.197i	−0.544771	−	0.543678i
$658$	−205.577	−	270.049i	−0.312427	−	0.410408i
$659$	588.767	−	588.767i	0.893425	−	0.893425i	−0.101418	−	0.994844i	$-0.532338\pi$
$659$	588.767	−	588.767i	0.893425	−	0.893425i	0.994844	+	0.101418i	$0.0323381\pi$
$660$	7.32483	+	58.8925i	0.0110982	+	0.0892310i
$661$	3.60334	−	3.60334i	0.00545135	−	0.00545135i	−0.704376	−	0.709827i	$-0.748773\pi$
$661$	3.60334	−	3.60334i	0.00545135	−	0.00545135i	0.709827	+	0.704376i	$0.248773\pi$
$662$	−732.950	−	99.3523i	−1.10718	−	0.150079i
$663$	310.620	+	128.480i	0.468507	+	0.193786i
$664$	−422.436	+	987.597i	−0.636198	+	1.48734i
$665$	−1495.42			−2.24875
$666$	−369.891	+	282.170i	−0.555393	+	0.423679i
$667$	−270.005	+	270.005i	−0.404805	+	0.404805i
$668$	−64.2336	+	232.581i	−0.0961581	+	0.348176i
$669$	52.0695	+	125.529i	0.0778319	+	0.187636i
$670$	629.104	−	478.911i	0.938961	−	0.714793i
$671$			12.7575i			0.0190127i
$672$	341.894	+	618.538i	0.508771	+	0.920443i
$673$	−460.445			−0.684167			−0.342084	−	0.939670i	$-0.611133\pi$
$673$	−460.445			−0.684167			−0.342084	+	0.939670i	$0.611133\pi$
$674$	−22.0737	−	28.9963i	−0.0327502	−	0.0430211i
$675$	217.874	−	528.242i	0.322776	−	0.782581i
$676$	259.621	+	71.7014i	0.384055	+	0.106067i
$677$	150.713	+	150.713i	0.222618	+	0.222618i	0.809600	−	0.586982i	$-0.199684\pi$
$677$	150.713	+	150.713i	0.222618	+	0.222618i	−0.586982	+	0.809600i	$0.699684\pi$
$678$	68.0799	+	39.6086i	0.100413	+	0.0584198i
$679$			606.350i			0.893004i
$680$	237.548	−	555.354i	0.349335	−	0.816698i
$681$	1179.12	+	487.714i	1.73145	+	0.716174i
$682$	−4.86207	+	35.8689i	−0.00712913	+	0.0525937i
$683$	−577.893	−	577.893i	−0.846109	−	0.846109i	0.143536	−	0.989645i	$-0.454153\pi$
$683$	−577.893	−	577.893i	−0.846109	−	0.846109i	−0.989645	+	0.143536i	$0.954153\pi$
$684$	−285.479	+	1037.74i	−0.417367	+	1.51716i
$685$	793.254	+	793.254i	1.15803	+	1.15803i
$686$	−513.167	+	390.653i	−0.748057	+	0.569465i
$687$	257.612	+	106.555i	0.374981	+	0.155102i
$688$	−158.884	+	39.9742i	−0.230936	+	0.0581021i
$689$			455.158i			0.660607i
$690$	−307.505	+	81.2996i	−0.445659	+	0.117825i
$691$	−545.023	−	545.023i	−0.788745	−	0.788745i	0.192544	−	0.981288i	$-0.438326\pi$
$691$	−545.023	−	545.023i	−0.788745	−	0.788745i	−0.981288	+	0.192544i	$0.938326\pi$
$692$	208.834	+	368.197i	0.301784	+	0.532077i
$693$	−0.0484085	−	48.2274i	−6.98536e−5	−	0.0695922i
$694$	−65.9963	+	486.874i	−0.0950956	+	0.701547i
$695$	−913.595			−1.31453
$696$	1174.49	+	12.9072i	1.68748	+	0.0185448i
$697$			713.929i			1.02429i
$698$	147.372	−	1087.20i	0.211134	−	1.55760i
$699$	−49.2212	−	118.662i	−0.0704165	−	0.169760i
$700$	−165.904	+	600.718i	−0.237006	+	0.858169i
$701$	−413.745	+	413.745i	−0.590221	+	0.590221i	−0.937691	−	0.347470i	$-0.887041\pi$
$701$	−413.745	+	413.745i	−0.590221	+	0.590221i	0.347470	+	0.937691i	$0.387041\pi$
$702$	−273.334	+	470.897i	−0.389364	+	0.670793i
$703$	772.721			1.09918
$704$	−46.5724	−	1.07052i	−0.0661540	−	0.00152062i
$705$	−434.171	−	179.584i	−0.615846	−	0.254730i
$706$	1077.05	−	819.915i	1.52557	−	1.16135i
$707$	−267.545	+	267.545i	−0.378423	+	0.378423i
$708$	−236.017	−	183.801i	−0.333357	−	0.259606i
$709$	521.959	−	521.959i	0.736191	−	0.736191i	−0.235648	−	0.971839i	$-0.575721\pi$
$709$	521.959	−	521.959i	0.736191	−	0.736191i	0.971839	+	0.235648i	$0.0757212\pi$
$710$	−46.8703	+	345.776i	−0.0660145	+	0.487008i
$711$	226.973	−	227.429i	0.319231	−	0.319873i
$712$	−333.202	+	133.552i	−0.467980	+	0.187573i
$713$	−194.000			−0.272089
$714$	−246.843	+	424.277i	−0.345718	+	0.594225i
$715$	35.2600	−	35.2600i	0.0493147	−	0.0493147i
$716$	11.0672	+	19.5127i	0.0154570	+	0.0272523i
$717$	−278.764	+	115.632i	−0.388792	+	0.161272i
$718$	−291.830	−	383.352i	−0.406449	−	0.533917i
$719$			567.983i			0.789963i	0.918689	+	0.394981i	$0.129249\pi$
$719$			567.983i			0.789963i	−0.918689	+	0.394981i	$0.870751\pi$
$720$	840.218	+	501.275i	1.16697	+	0.696215i
$721$	−644.293			−0.893610
$722$	847.919	−	645.486i	1.17440	−	0.894025i
$723$	−6.01344	−	14.4972i	−0.00831735	−	0.0200514i
$724$	443.237	+	781.473i	0.612205	+	1.07938i
$725$	732.374	+	732.374i	1.01017	+	1.01017i
$726$	−624.775	−	363.492i	−0.860572	−	0.500678i
$727$			635.396i			0.873998i	0.899462	+	0.436999i	$0.143959\pi$
$727$			635.396i			0.873998i	−0.899462	+	0.436999i	$0.856041\pi$
$728$	233.539	−	545.982i	0.320795	−	0.749975i
$729$	517.031	+	513.926i	0.709233	+	0.704974i
$730$	756.556	+	102.552i	1.03638	+	0.140482i
$731$	−80.4619	−	80.4619i	−0.110071	−	0.110071i
$732$	165.939	+	129.227i	0.226692	+	0.176540i
$733$	−637.378	−	637.378i	−0.869547	−	0.869547i	0.122875	−	0.992422i	$-0.460788\pi$
$733$	−637.378	−	637.378i	−0.869547	−	0.869547i	−0.992422	+	0.122875i	$0.960788\pi$
$734$	−807.667	−	1060.96i	−1.10036	−	1.44545i
$735$	40.4897	−	97.8896i	0.0550880	−	0.133183i
$736$	−27.8425	−	248.117i	−0.0378295	−	0.337115i
$737$		−	42.3515i		−	0.0574648i
$738$	−1146.08	−	154.181i	−1.55296	−	0.208918i
$739$	397.296	+	397.296i	0.537613	+	0.537613i	0.922827	−	0.385214i	$-0.125872\pi$
$739$	397.296	+	397.296i	0.537613	+	0.537613i	−0.385214	+	0.922827i	$0.625872\pi$
$740$	186.995	−	677.085i	0.252696	−	0.914980i
$741$	835.331	−	346.497i	1.12730	−	0.467607i
$742$	−658.630	−	89.2781i	−0.887641	−	0.120321i
$743$	1160.78			1.56229			0.781145	−	0.624349i	$-0.214636\pi$
$743$	1160.78			1.56229			0.781145	+	0.624349i	$0.214636\pi$
$744$	417.301	+	426.574i	0.560888	+	0.573353i
$745$		−	1259.47i		−	1.69057i
$746$	1004.84	+	136.207i	1.34697	+	0.182583i
$747$	−1.21296	−	1208.42i	−0.00162377	−	1.61770i
$748$	−15.9623	−	28.1433i	−0.0213400	−	0.0376247i
$749$	772.011	−	772.011i	1.03072	−	1.03072i
$750$	−39.9779	−	151.211i	−0.0533038	−	0.201615i
$751$	1220.14			1.62469			0.812343	−	0.583181i	$-0.198192\pi$
$751$	1220.14			1.62469			0.812343	+	0.583181i	$0.198192\pi$
$752$	189.278	−	316.538i	0.251700	−	0.420929i
$753$	−28.2781	+	68.3663i	−0.0375539	+	0.0907919i
$754$	−597.792	−	785.267i	−0.792827	−	1.04147i
$755$	−591.268	+	591.268i	−0.783136	+	0.783136i
$756$	−627.790	−	487.888i	−0.830410	−	0.645355i
$757$	202.623	−	202.623i	0.267666	−	0.267666i	−0.560493	−	0.828159i	$-0.689388\pi$
$757$	202.623	−	202.623i	0.267666	−	0.267666i	0.828159	+	0.560493i	$0.189388\pi$
$758$	395.080	+	53.5536i	0.521214	+	0.0706512i
$759$	−6.51210	+	15.7439i	−0.00857984	+	0.0207430i
$760$	−604.585	−	1508.39i	−0.795507	−	1.98473i
$761$	−694.461			−0.912563			−0.456282	−	0.889835i	$-0.650819\pi$
$761$	−694.461			−0.912563			−0.456282	+	0.889835i	$0.650819\pi$
$762$	−266.337	+	457.784i	−0.349524	+	0.600767i
$763$	56.2451	−	56.2451i	0.0737157	−	0.0737157i
$764$	265.516	+	73.3293i	0.347534	+	0.0959808i
$765$	0.682081	+	679.529i	0.000891610	+	0.888273i
$766$	−110.549	+	84.1564i	−0.144320	+	0.109865i
$767$			251.353i			0.327709i
$768$	−485.678	+	594.929i	−0.632394	+	0.774647i
$769$	405.268			0.527007			0.263503	−	0.964658i	$-0.415122\pi$
$769$	405.268			0.527007			0.263503	+	0.964658i	$0.415122\pi$
$770$	44.1063	+	57.9386i	0.0572809	+	0.0752449i
$771$	952.347	−	395.035i	1.23521	−	0.512367i
$772$	390.419	−	1413.66i	0.505725	−	1.83116i
$773$	142.479	+	142.479i	0.184320	+	0.184320i	0.793235	−	0.608916i	$-0.208395\pi$
$773$	142.479	+	142.479i	0.184320	+	0.184320i	−0.608916	+	0.793235i	$0.708395\pi$
$774$	146.544	−	111.790i	0.189333	−	0.144432i
$775$			526.214i			0.678985i
$776$	−611.609	+	245.142i	−0.788156	+	0.315904i
$777$	−218.182	+	527.486i	−0.280800	+	0.678875i
$778$	−100.817	+	743.756i	−0.129585	+	0.955985i
$779$	1358.16	+	1358.16i	1.74346	+	1.74346i
$780$	−101.466	−	815.797i	−0.130084	−	1.04589i
$781$	13.2165	+	13.2165i	0.0169226	+	0.0169226i
$782$	137.978	−	105.037i	0.176442	−	0.134318i
$783$	−1220.03	+	507.507i	−1.55815	+	0.648158i
$784$	71.3677	+	42.6752i	0.0910302	+	0.0544327i
$785$			1337.34i			1.70362i
$786$	123.737	+	468.020i	0.157427	+	0.595445i
$787$	−482.883	−	482.883i	−0.613574	−	0.613574i	0.330301	−	0.943876i	$-0.392850\pi$
$787$	−482.883	−	482.883i	−0.613574	−	0.613574i	−0.943876	+	0.330301i	$0.892850\pi$
$788$	−1214.10	+	688.615i	−1.54074	+	0.873877i
$789$	112.744	+	271.803i	0.142895	+	0.344491i
$790$	−65.1647	+	480.738i	−0.0824869	+	0.608529i
$791$	96.6413			0.122176
$792$	48.6262	−	19.5467i	0.0613967	−	0.0246802i
$793$		−	176.721i		−	0.222852i
$794$	98.4466	−	726.269i	0.123988	−	0.914696i
$795$	−849.908	+	352.543i	−1.06907	+	0.443451i
$796$	−1109.67	−	306.464i	−1.39405	−	0.385005i
$797$	−552.965	+	552.965i	−0.693808	+	0.693808i	−0.963068	−	0.269260i	$-0.913221\pi$
$797$	−552.965	+	552.965i	−0.693808	+	0.693808i	0.269260	+	0.963068i	$0.413221\pi$
$798$	337.545	+	1276.72i	0.422988	+	1.59990i
$799$	256.155			0.320595
$800$	−673.002	+	75.5213i	−0.841253	+	0.0944016i
$801$	285.272	−	285.846i	0.356145	−	0.356861i
$802$	−1056.92	+	804.591i	−1.31786	+	1.00323i
$803$	28.9178	−	28.9178i	0.0360122	−	0.0360122i
$804$	−550.871	−	428.999i	−0.685164	−	0.533581i
$805$	−275.959	+	275.959i	−0.342806	+	0.342806i
$806$	67.3509	−	496.867i	0.0835619	−	0.616460i
$807$	−496.177	−	205.232i	−0.614842	−	0.254314i
$808$	−378.032	−	161.700i	−0.467861	−	0.200123i
$809$	−930.240			−1.14986			−0.574932	−	0.818201i	$-0.694972\pi$
$809$	−930.240			−1.14986			−0.574932	+	0.818201i	$0.694972\pi$
$810$	−1091.01	−	145.657i	−1.34692	−	0.179824i
$811$	−611.506	+	611.506i	−0.754015	+	0.754015i	−0.975226	−	0.221211i	$-0.928999\pi$
$811$	−611.506	+	611.506i	−0.754015	+	0.754015i	0.221211	+	0.975226i	$0.428999\pi$
$812$	1253.56	−	710.997i	1.54380	−	0.875612i
$813$	−237.345	−	572.188i	−0.291937	−	0.703799i
$814$	−22.7908	−	29.9383i	−0.0279985	−	0.0367793i
$815$		−	191.511i		−	0.234983i
$816$	−527.753	−	77.4528i	−0.646757	−	0.0949176i
$817$	−306.137			−0.374708
$818$	−844.090	+	642.571i	−1.03190	+	0.785540i
$819$	0.670570	+	668.061i	0.000818767	+	0.815703i
$820$	1518.73	−	861.395i	1.85211	−	1.05048i
$821$	−963.577	−	963.577i	−1.17366	−	1.17366i	−0.981330	−	0.192334i	$-0.938394\pi$
$821$	−963.577	−	963.577i	−1.17366	−	1.17366i	−0.192334	−	0.981330i	$-0.561606\pi$
$822$	498.189	−	856.294i	0.606069	−	1.04172i
$823$		−	1112.81i		−	1.35214i	−0.736836	−	0.676071i	$-0.763681\pi$
$823$		−	1112.81i		−	1.35214i	0.736836	−	0.676071i	$-0.236319\pi$
$824$	−260.482	−	649.882i	−0.316119	−	0.788691i
$825$	42.7046	+	17.6637i	0.0517631	+	0.0214105i
$826$	−363.716	−	49.3021i	−0.440334	−	0.0596878i
$827$	600.156	+	600.156i	0.725703	+	0.725703i	0.969761	−	0.244058i	$-0.0784786\pi$
$827$	600.156	+	600.156i	0.725703	+	0.725703i	−0.244058	+	0.969761i	$0.578479\pi$
$828$	138.819	+	244.181i	0.167656	+	0.294905i
$829$	−921.578	−	921.578i	−1.11167	−	1.11167i	−0.992924	−	0.118750i	$-0.962111\pi$
$829$	−921.578	−	921.578i	−1.11167	−	1.11167i	−0.118750	−	0.992924i	$-0.537889\pi$
$830$	1105.16	+	1451.75i	1.33152	+	1.74910i
$831$	719.085	+	297.432i	0.865324	+	0.357920i
$832$	645.135	+	14.8292i	0.775403	+	0.0178235i
$833$			57.7535i			0.0693319i
$834$	206.216	+	779.983i	0.247261	+	0.935231i
$835$	289.807	+	289.807i	0.347075	+	0.347075i
$836$	−83.9052	−	23.1727i	−0.100365	−	0.0277185i
$837$	−620.622	−	255.976i	−0.741484	−	0.305826i
$838$	1132.75	+	153.545i	1.35173	+	0.183228i
$839$	−1230.19			−1.46625			−0.733127	−	0.680091i	$-0.761940\pi$
$839$	−1230.19			−1.46625			−0.733127	+	0.680091i	$0.761940\pi$
$840$	1200.39	+	13.1918i	1.42903	+	0.0157045i
$841$		−	1554.12i		−	1.84794i
$842$	741.704	+	100.539i	0.880884	+	0.119405i
$843$	−125.453	−	302.442i	−0.148818	−	0.358768i
$844$	−768.315	+	435.774i	−0.910326	+	0.516320i
$845$	323.501	−	323.501i	0.382841	−	0.382841i
$846$	−55.3197	+	411.210i	−0.0653898	+	0.486064i
$847$	−886.886			−1.04709
$848$	−176.226	−	700.437i	−0.207813	−	0.825987i
$849$	237.043	+	98.0470i	0.279202	+	0.115485i
$850$	−284.906	−	374.256i	−0.335184	−	0.440302i
$851$	142.595	−	142.595i	0.167562	−	0.167562i
$852$	305.786	−	38.0325i	0.358903	−	0.0446391i
$853$	−1032.73	+	1032.73i	−1.21070	+	1.21070i	−0.239902	+	0.970797i	$0.577115\pi$
$853$	−1032.73	+	1032.73i	−1.21070	+	1.21070i	−0.970797	+	0.239902i	$0.922885\pi$
$854$	255.722	+	34.6634i	0.299440	+	0.0405895i
$855$	1294.01	+	1291.42i	1.51346	+	1.51043i
$856$	1090.82	+	466.591i	1.27433	+	0.545083i
$857$	609.799			0.711550			0.355775	−	0.934572i	$-0.384217\pi$
$857$	609.799			0.711550			0.355775	+	0.934572i	$0.384217\pi$
$858$	−38.0621	−	22.1444i	−0.0443614	−	0.0258093i
$859$	889.225	−	889.225i	1.03519	−	1.03519i	0.0358288	−	0.999358i	$-0.488593\pi$
$859$	889.225	−	889.225i	1.03519	−	1.03519i	0.999358	−	0.0358288i	$-0.0114071\pi$
$860$	−74.0838	+	268.247i	−0.0861439	+	0.311916i
$861$	−1310.61	+	543.642i	−1.52219	+	0.631407i
$862$	−1220.02	+	928.750i	−1.41533	+	1.07744i
$863$		−	1322.86i		−	1.53286i	−0.642329	−	0.766429i	$-0.722032\pi$
$863$		−	1322.86i		−	1.53286i	0.642329	−	0.766429i	$-0.277968\pi$
$864$	238.311	−	830.484i	0.275823	−	0.961209i
$865$	719.010			0.831225
$866$	−183.196	−	240.649i	−0.211543	−	0.277886i
$867$	190.243	+	458.637i	0.219427	+	0.528993i
$868$	705.772	+	194.918i	0.813102	+	0.224560i
$869$	18.3752	+	18.3752i	0.0211452	+	0.0211452i
$870$	1003.29	−	1724.47i	1.15321	−	1.98215i
$871$			586.667i			0.673555i
$872$	79.4723	+	33.9936i	0.0911380	+	0.0389835i
$873$	523.632	−	524.684i	0.599808	−	0.601013i
$874$	62.6657	−	462.303i	0.0716999	−	0.528950i
$875$	−135.699	−	135.699i	−0.155084	−	0.155084i
$876$	−83.2150	−	669.058i	−0.0949943	−	0.763765i
$877$	853.500	+	853.500i	0.973204	+	0.973204i	0.999650	−	0.0264461i	$-0.00841905\pi$
$877$	853.500	+	853.500i	0.973204	+	0.973204i	−0.0264461	+	0.999650i	$0.508419\pi$
$878$	−899.128	+	684.470i	−1.02406	+	0.779578i
$879$	−31.5630	+	76.3081i	−0.0359078	+	0.0868124i
$880$	−40.6094	+	67.9129i	−0.0461470	+	0.0771738i
$881$		−	1075.39i		−	1.22064i	−0.792153	−	0.610322i	$-0.791040\pi$
$881$		−	1075.39i		−	1.22064i	0.792153	−	0.610322i	$-0.208960\pi$
$882$	−92.7126	−	12.4726i	−0.105116	−	0.0141412i
$883$	283.702	+	283.702i	0.321294	+	0.321294i	0.849263	−	0.527970i	$-0.177046\pi$
$883$	283.702	+	283.702i	0.321294	+	0.321294i	−0.527970	+	0.849263i	$0.677046\pi$
$884$	221.115	+	389.850i	0.250130	+	0.441006i
$885$	−469.346	+	194.685i	−0.530334	+	0.219983i
$886$	−38.3580	+	282.978i	−0.0432934	+	0.319388i
$887$	−282.642			−0.318650			−0.159325	−	0.987226i	$-0.550932\pi$
$887$	−282.642			−0.318650			−0.159325	+	0.987226i	$0.550932\pi$
$888$	−620.270	−	6.81653i	−0.698503	−	0.00767627i
$889$			649.838i			0.730976i
$890$	−81.9024	+	604.218i	−0.0920252	+	0.678896i
$891$	−41.6064	+	41.7738i	−0.0466963	+	0.0468841i
$892$	−48.2373	+	174.661i	−0.0540777	+	0.195808i
$893$	487.301	−	487.301i	0.545690	−	0.545690i
$894$	−1075.28	+	284.287i	−1.20277	+	0.317994i
$895$	38.1040			0.0425743
$896$	−148.000	+	930.624i	−0.165178	+	1.03864i
$897$	90.2076	−	218.090i	0.100566	−	0.243133i
$898$	−209.622	+	159.577i	−0.233432	+	0.177702i
$899$	860.452	−	860.452i	0.957122	−	0.957122i
$900$	662.329	−	376.539i	0.735921	−	0.418377i
$901$	354.715	−	354.715i	0.393690	−	0.393690i
$902$	12.5626	−	92.6782i	0.0139275	−	0.102747i
$903$	86.4392	−	208.979i	0.0957245	−	0.231428i
$904$	39.0712	+	97.4796i	0.0432203	+	0.107831i
$905$	1526.05			1.68624
$906$	638.256	+	371.335i	0.704477	+	0.409862i
$907$	−216.816	+	216.816i	−0.239047	+	0.239047i	−0.816456	−	0.577408i	$-0.804064\pi$
$907$	−216.816	+	216.816i	−0.239047	+	0.239047i	0.577408	+	0.816456i	$0.304064\pi$
$908$	839.358	+	1479.88i	0.924403	+	1.62982i
$909$	462.558	−	0.464295i	0.508864	−	0.000510776i
$910$	−610.974	−	802.583i	−0.671400	−	0.881960i
$911$		−	1193.35i		−	1.30994i	−0.755657	−	0.654968i	$-0.772682\pi$
$911$		−	1193.35i		−	1.30994i	0.755657	−	0.654968i	$-0.227318\pi$
$912$	−1151.33	+	856.638i	−1.26242	+	0.939296i
$913$	97.7324			0.107045
$914$	−219.548	+	167.133i	−0.240206	+	0.182859i
$915$	329.988	−	136.880i	0.360643	−	0.149595i
$916$	183.381	+	323.321i	0.200198	+	0.352970i
$917$	420.008	+	420.008i	0.458024	+	0.458024i
$918$	579.995	−	153.965i	0.631802	−	0.167718i
$919$			345.202i			0.375628i	0.982205	+	0.187814i	$0.0601402\pi$
$919$			345.202i			0.375628i	−0.982205	+	0.187814i	$0.939860\pi$
$920$	−389.921	−	166.785i	−0.423827	−	0.181288i
$921$	661.947	−	1600.35i	0.718727	−	1.73763i
$922$	850.749	+	115.320i	0.922722	+	0.125076i
$923$	−183.080	−	183.080i	−0.198353	−	0.198353i
$924$	39.5095	−	50.7336i	0.0427592	−	0.0549065i
$925$	−386.781	−	386.781i	−0.418141	−	0.418141i
$926$	−339.661	−	446.183i	−0.366805	−	0.481839i
$927$	557.517	+	556.399i	0.601421	+	0.600215i
$928$	1223.97	+	976.988i	1.31893	+	1.05279i
$929$			1417.53i			1.52587i	0.646475	+	0.762935i	$0.276242\pi$
$929$			1417.53i			1.52587i	−0.646475	+	0.762935i	$0.723758\pi$
$930$	979.956	−	259.085i	1.05372	−	0.278587i
$931$	109.868	+	109.868i	0.118011	+	0.118011i
$932$	45.5986	−	165.106i	0.0489255	−	0.177153i
$933$	−414.908	−	1000.26i	−0.444704	−	1.07209i
$934$	183.963	+	24.9364i	0.196962	+	0.0266985i
$935$	−54.9578			−0.0587784
$936$	−673.584	+	270.767i	−0.719642	+	0.289281i
$937$			182.650i			0.194931i	0.995239	+	0.0974656i	$0.0310736\pi$
$937$			182.650i			0.194931i	−0.995239	+	0.0974656i	$0.968926\pi$
$938$	−848.927	−	115.073i	−0.905039	−	0.122679i
$939$	−204.842	+	84.9687i	−0.218149	+	0.0904885i
$940$	−309.065	−	544.915i	−0.328793	−	0.579697i
$941$	−524.733	+	524.733i	−0.557634	+	0.557634i	−0.928633	−	0.371000i	$-0.879015\pi$
$941$	−524.733	+	524.733i	−0.557634	+	0.557634i	0.371000	+	0.928633i	$0.379015\pi$
$942$	1141.76	−	301.864i	1.21206	−	0.320450i
$943$	501.258			0.531556
$944$	−97.3173	−	386.803i	−0.103090	−	0.409749i
$945$	−1246.94	+	518.699i	−1.31951	+	0.548888i
$946$	9.02926	+	11.8610i	0.00954468	+	0.0125380i
$947$	−278.292	+	278.292i	−0.293867	+	0.293867i	−0.838606	−	0.544739i	$-0.816629\pi$
$947$	−278.292	+	278.292i	−0.293867	+	0.293867i	0.544739	+	0.838606i	$0.316629\pi$
$948$	425.140	−	52.8773i	0.448460	−	0.0557778i
$949$	−400.578	+	400.578i	−0.422105	+	0.422105i
$950$	−1253.97	−	169.977i	−1.31997	−	0.178923i
$951$	−677.108	−	280.069i	−0.711996	−	0.294500i
$952$	−607.497	+	243.493i	−0.638127	+	0.255770i
$953$	545.447			0.572348			0.286174	−	0.958178i	$-0.407617\pi$
$953$	545.447			0.572348			0.286174	+	0.958178i	$0.407617\pi$
$954$	492.824	+	646.034i	0.516587	+	0.677184i
$955$	330.845	−	330.845i	0.346435	−	0.346435i
$956$	−387.872	−	107.121i	−0.405724	−	0.112052i
$957$	−40.9462	−	98.7128i	−0.0427860	−	0.103148i
$958$	594.009	−	452.195i	0.620051	−	0.472020i
$959$		−	1215.53i		−	1.26750i
$960$	472.000	+	1216.13i	0.491666	+	1.26681i
$961$	−342.761			−0.356672
$962$	315.705	+	414.715i	0.328176	+	0.431096i
$963$	−1334.73	+	1.33974i	−1.38601	+	0.00139122i
$964$	5.57086	−	20.1714i	0.00577890	−	0.0209246i
$965$	−1761.48	−	1761.48i	−1.82537	−	1.82537i
$966$	297.890	+	173.311i	0.308374	+	0.179411i
$967$			216.237i			0.223616i	0.993730	+	0.111808i	$0.0356642\pi$
$967$			216.237i			0.223616i	−0.993730	+	0.111808i	$0.964336\pi$
$968$	−358.560	−	894.579i	−0.370413	−	0.924152i
$969$	−921.024	−	380.959i	−0.950489	−	0.393147i
$970$	−150.336	+	1109.07i	−0.154986	+	1.14337i
$971$	−147.926	−	147.926i	−0.152344	−	0.152344i	0.626820	−	0.779164i	$-0.284356\pi$
$971$	−147.926	−	147.926i	−0.152344	−	0.152344i	−0.779164	+	0.626820i	$0.784356\pi$
$972$	121.906	+	964.325i	0.125417	+	0.992104i
$973$	699.968	+	699.968i	0.719392	+	0.719392i
$974$	−0.0748775	+	0.0570012i	−7.68763e−5	+	5.85228e-5i
$975$	−591.557	−	244.683i	−0.606725	−	0.250957i
$976$	68.4220	+	271.954i	0.0701045	+	0.278642i
$977$		−	553.321i		−	0.566347i	−0.959069	−	0.283174i	$-0.908613\pi$
$977$		−	553.321i		−	0.566347i	0.959069	−	0.283174i	$-0.0913873\pi$
$978$	−163.503	+	43.2277i	−0.167181	+	0.0442001i
$979$	23.0949	+	23.0949i	0.0235903	+	0.0235903i
$980$	122.858	−	69.6828i	0.125366	−	0.0711049i
$981$	−97.2420	+	0.0976072i	−0.0991254	+	9.94977e-5i
$982$	103.887	−	766.401i	0.105791	−	0.780449i
$983$	1107.13			1.12628			0.563139	−	0.826362i	$-0.309594\pi$
$983$	1107.13			1.12628			0.563139	+	0.826362i	$0.309594\pi$
$984$	−1078.22	−	1102.19i	−1.09576	−	1.12011i
$985$			2370.88i			2.40698i
$986$	−146.103	+	1077.85i	−0.148178	+	1.09315i
$987$	195.057	+	470.241i	0.197626	+	0.476434i
$988$	1162.28	+	320.995i	1.17640	+	0.324894i
$989$	−56.4932	+	56.4932i	−0.0571216	+	0.0571216i
$990$	11.8688	−	88.2246i	0.0119887	−	0.0891157i
$991$	−1635.60			−1.65046			−0.825228	−	0.564800i	$-0.808953\pi$
$991$	−1635.60			−1.65046			−0.825228	+	0.564800i	$0.808953\pi$
$992$	88.7285	+	790.698i	0.0894441	+	0.797075i
$993$	1025.24	+	424.065i	1.03247	+	0.427054i
$994$	300.833	−	229.012i	0.302649	−	0.230394i
$995$	−1382.70	+	1382.70i	−1.38965	+	1.38965i
$996$	989.978	−	1271.22i	0.993954	−	1.27632i
$997$	152.140	−	152.140i	0.152598	−	0.152598i	−0.626679	−	0.779277i	$-0.715586\pi$
$997$	152.140	−	152.140i	0.152598	−	0.152598i	0.779277	+	0.626679i	$0.215586\pi$
$998$	−17.5766	+	129.668i	−0.0176118	+	0.129928i
$999$	644.323	−	268.025i	0.644968	−	0.268293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.i.b.29.4	yes	20
3.2	odd	2	inner	48.3.i.b.29.7	yes	20
4.3	odd	2		192.3.i.b.17.4		20
8.3	odd	2		384.3.i.c.161.7		20
8.5	even	2		384.3.i.d.161.4		20
12.11	even	2		192.3.i.b.17.1		20
16.3	odd	4		384.3.i.c.353.10		20
16.5	even	4	inner	48.3.i.b.5.7	yes	20
16.11	odd	4		192.3.i.b.113.1		20
16.13	even	4		384.3.i.d.353.1		20
24.5	odd	2		384.3.i.d.161.1		20
24.11	even	2		384.3.i.c.161.10		20
48.5	odd	4	inner	48.3.i.b.5.4	✓	20
48.11	even	4		192.3.i.b.113.4		20
48.29	odd	4		384.3.i.d.353.4		20
48.35	even	4		384.3.i.c.353.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.4	✓	20	48.5	odd	4	inner
48.3.i.b.5.7	yes	20	16.5	even	4	inner
48.3.i.b.29.4	yes	20	1.1	even	1	trivial
48.3.i.b.29.7	yes	20	3.2	odd	2	inner
192.3.i.b.17.1		20	12.11	even	2
192.3.i.b.17.4		20	4.3	odd	2
192.3.i.b.113.1		20	16.11	odd	4
192.3.i.b.113.4		20	48.11	even	4
384.3.i.c.161.7		20	8.3	odd	2
384.3.i.c.161.10		20	24.11	even	2
384.3.i.c.353.7		20	48.35	even	4
384.3.i.c.353.10		20	16.3	odd	4
384.3.i.d.161.1		20	24.5	odd	2
384.3.i.d.161.4		20	8.5	even	2
384.3.i.d.353.1		20	16.13	even	4
384.3.i.d.353.4		20	48.29	odd	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21144 - 1.59136i) q^{2} +(1.14944 + 2.77106i) q^{3} +(-1.06484 + 3.85566i) q^{4} +(4.80434 + 4.80434i) q^{5} +(3.01728 - 5.18614i) q^{6} -7.36187i q^{7} +(7.42573 - 2.97634i) q^{8} +(-6.35757 + 6.37035i) q^{9} +O(q^{10})\)	\(q+(-1.21144 - 1.59136i) q^{2} +(1.14944 + 2.77106i) q^{3} +(-1.06484 + 3.85566i) q^{4} +(4.80434 + 4.80434i) q^{5} +(3.01728 - 5.18614i) q^{6} -7.36187i q^{7} +(7.42573 - 2.97634i) q^{8} +(-6.35757 + 6.37035i) q^{9} +(1.82527 - 13.4656i) q^{10} +(-0.514693 - 0.514693i) q^{11} +(-11.9082 + 1.48110i) q^{12} +(7.12969 + 7.12969i) q^{13} +(-11.7154 + 8.91843i) q^{14} +(-7.79081 + 18.8354i) q^{15} +(-13.7322 - 8.21135i) q^{16} -11.1126i q^{17} +(17.8393 + 2.39991i) q^{18} +(-21.1403 - 21.1403i) q^{19} +(-23.6398 + 13.4080i) q^{20} +(20.4002 - 8.46203i) q^{21} +(-0.195543 + 1.44258i) q^{22} -7.80231 q^{23} +(16.7830 + 17.1560i) q^{24} +21.1633i q^{25} +(2.70873 - 19.9831i) q^{26} +(-24.9603 - 10.2949i) q^{27} +(28.3849 + 7.83924i) q^{28} +(34.6058 - 34.6058i) q^{29} +(39.4120 - 10.4199i) q^{30} +24.8644 q^{31} +(3.56850 + 31.8004i) q^{32} +(0.834637 - 2.01786i) q^{33} +(-17.6842 + 13.4623i) q^{34} +(35.3689 - 35.3689i) q^{35} +(-17.7921 - 31.2960i) q^{36} +(-18.2760 + 18.2760i) q^{37} +(-8.03168 + 59.2520i) q^{38} +(-11.5617 + 27.9520i) q^{39} +(49.9750 + 21.3764i) q^{40} -64.2448 q^{41} +(-38.1797 - 22.2128i) q^{42} +(7.24058 - 7.24058i) q^{43} +(2.53255 - 1.43641i) q^{44} +(-61.1492 + 0.0613789i) q^{45} +(9.45200 + 12.4163i) q^{46} +23.0508i q^{47} +(6.96979 - 47.4913i) q^{48} -5.19710 q^{49} +(33.6784 - 25.6380i) q^{50} +(30.7938 - 12.7733i) q^{51} +(-35.0817 + 19.8976i) q^{52} +(31.9199 + 31.9199i) q^{53} +(13.8549 + 52.1923i) q^{54} -4.94552i q^{55} +(-21.9114 - 54.6672i) q^{56} +(34.2816 - 82.8807i) q^{57} +(-96.9929 - 13.1475i) q^{58} +(17.6272 + 17.6272i) q^{59} +(-64.3270 - 50.0955i) q^{60} +(-12.3933 - 12.3933i) q^{61} +(-30.1216 - 39.5682i) q^{62} +(46.8976 + 46.8036i) q^{63} +(46.2828 - 44.2029i) q^{64} +68.5069i q^{65} +(-4.22224 + 1.11630i) q^{66} +(41.1425 + 41.1425i) q^{67} +(42.8465 + 11.8332i) q^{68} +(-8.96830 - 21.6207i) q^{69} +(-99.1318 - 13.4374i) q^{70} -25.6785 q^{71} +(-28.2493 + 66.2267i) q^{72} +56.1845i q^{73} +(51.2239 + 6.94346i) q^{74} +(-58.6449 + 24.3260i) q^{75} +(104.021 - 58.9988i) q^{76} +(-3.78910 + 3.78910i) q^{77} +(58.4878 - 15.4633i) q^{78} -35.7013 q^{79} +(-26.5241 - 105.424i) q^{80} +(-0.162608 - 80.9998i) q^{81} +(77.8285 + 102.236i) q^{82} +(-94.9424 + 94.9424i) q^{83} +(10.9037 + 87.6669i) q^{84} +(53.3889 - 53.3889i) q^{85} +(-20.2939 - 2.75086i) q^{86} +(135.672 + 56.1175i) q^{87} +(-5.35387 - 2.29007i) q^{88} -44.8713 q^{89} +(74.1760 + 97.2360i) q^{90} +(52.4878 - 52.4878i) q^{91} +(8.30824 - 30.0830i) q^{92} +(28.5802 + 68.9008i) q^{93} +(36.6821 - 27.9246i) q^{94} -203.131i q^{95} +(-84.0191 + 46.4412i) q^{96} -82.3636 q^{97} +(6.29596 + 8.27045i) q^{98} +(6.55097 - 0.00657558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6}+O(q^{10}) \) 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6	\( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6 + 32 * q^10 - 88 * q^12 + 92 * q^13 - 116 * q^15 - 16 * q^16 + 4 * q^18 - 52 * q^19 + 48 * q^21 + 24 * q^22 - 8 * q^24 + 18 * q^27 + 56 * q^28 + 28 * q^30 - 80 * q^31 + 60 * q^33 + 104 * q^34 + 92 * q^36 - 116 * q^37 + 88 * q^40 + 304 * q^42 + 172 * q^43 + 60 * q^45 - 424 * q^46 + 176 * q^48 - 364 * q^49 + 128 * q^51 - 208 * q^52 + 40 * q^54 - 512 * q^58 - 240 * q^60 - 244 * q^61 + 296 * q^63 + 88 * q^64 - 492 * q^66 + 356 * q^67 - 20 * q^69 + 200 * q^70 - 472 * q^72 - 146 * q^75 + 328 * q^76 + 84 * q^78 + 384 * q^79 - 188 * q^81 + 560 * q^82 + 816 * q^84 + 48 * q^85 + 416 * q^88 + 616 * q^90 + 136 * q^91 - 132 * q^93 + 32 * q^94 - 24 * q^96 + 472 * q^97 - 452 * q^99

Introduction

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