LMFDB - Embedded newform 48.3.i.b.29.7

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			29.7
Root			$1.21144 - 1.59136i$ of defining polynomial
Character	$\chi$	$=$	48.29
Dual form			48.3.i.b.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21144 + 1.59136i) q^{2} +(2.77106 + 1.14944i) q^{3} +(-1.06484 + 3.85566i) q^{4} +(-4.80434 - 4.80434i) q^{5} +(1.52779 + 5.80223i) q^{6} -7.36187i q^{7} +(-7.42573 + 2.97634i) q^{8} +(6.35757 + 6.37035i) q^{9} +O(q^{10})$	\(q+(1.21144 + 1.59136i) q^{2} +(2.77106 + 1.14944i) q^{3} +(-1.06484 + 3.85566i) q^{4} +(-4.80434 - 4.80434i) q^{5} +(1.52779 + 5.80223i) 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} +(-7.38260 + 9.46029i) 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} +(-2.43571 + 17.8344i) q^{18} +(-21.1403 - 21.1403i) q^{19} +(23.6398 - 13.4080i) q^{20} +(8.46203 - 20.4002i) q^{21} +(-0.195543 + 1.44258i) q^{22} +7.80231 q^{23} +(-23.9983 - 0.287823i) q^{24} +21.1633i q^{25} +(-2.70873 + 19.9831i) q^{26} +(10.2949 + 24.9603i) q^{27} +(28.3849 + 7.83924i) q^{28} +(-34.6058 + 34.6058i) q^{29} +(20.5358 - 35.2159i) 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} +(-31.3317 + 17.7292i) 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} +(42.7152 - 11.2474i) q^{42} +(7.24058 - 7.24058i) q^{43} +(-2.53255 + 1.43641i) q^{44} +(0.0613789 - 61.1492i) q^{45} +(9.45200 + 12.4163i) q^{46} -23.0508i q^{47} +(-28.6144 - 38.5385i) q^{48} -5.19710 q^{49} +(-33.6784 + 25.6380i) q^{50} +(-12.7733 + 30.7938i) q^{51} +(-35.0817 + 19.8976i) q^{52} +(-31.9199 - 31.9199i) q^{53} +(-27.2492 + 46.6206i) 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} +(80.9190 - 9.98194i) 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} +(-2.20002 + 3.77271i) q^{66} +(41.1425 + 41.1425i) q^{67} +(-42.8465 - 11.8332i) q^{68} +(21.6207 + 8.96830i) q^{69} +(-99.1318 - 13.4374i) q^{70} +25.6785 q^{71} +(-66.1699 - 28.3822i) q^{72} +56.1845i q^{73} +(-51.2239 - 6.94346i) q^{74} +(-24.3260 + 58.6449i) q^{75} +(104.021 - 58.9988i) q^{76} +(3.78910 - 3.78910i) q^{77} +(-30.4754 + 52.2608i) 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} +(69.6454 + 54.3497i) 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} +(97.3847 - 73.9807i) q^{90} +(52.4878 - 52.4878i) q^{91} +(-8.30824 + 30.0830i) q^{92} +(68.9008 + 28.5802i) q^{93} +(36.6821 - 27.9246i) q^{94} +203.131i q^{95} +(26.6642 - 92.2227i) q^{96} -82.3636 q^{97} +(-6.29596 - 8.27045i) q^{98} +(-0.00657558 + 6.55097i) 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
$3$	2.77106	+	1.14944i	0.923687	+	0.383147i
$3$	2.77106	+	1.14944i	0.923687	+	0.383147i
$4$	−1.06484	+	3.85566i	−0.266211	+	0.963915i
$5$	−4.80434	−	4.80434i	−0.960868	−	0.960868i	0.0383950	−	0.999263i	$-0.487775\pi$
$5$	−4.80434	−	4.80434i	−0.960868	−	0.960868i	−0.999263	+	0.0383950i	$0.987775\pi$
$6$	1.52779	+	5.80223i	0.254632	+	0.967038i
$7$		−	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	0.730115	−	0.683325i	$-0.239467\pi$
$11$	0.514693	+	0.514693i	0.0467903	+	0.0467903i	−0.683325	+	0.730115i	$0.739467\pi$
$12$	−7.38260	+	9.46029i	−0.615217	+	0.788358i
$13$	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	$0.105985\pi$
$17$			11.1126i			0.653684i	−0.945079	+	0.326842i	$0.894015\pi$
$18$	−2.43571	+	17.8344i	−0.135317	+	0.990802i
$19$	−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
$21$	8.46203	−	20.4002i	0.402954	−	0.971438i
$22$	−0.195543	+	1.44258i	−0.00888834	+	0.0655718i
$23$	7.80231			0.339231			0.169615	−	0.985510i	$-0.445747\pi$
$23$	7.80231			0.339231			0.169615	+	0.985510i	$0.445747\pi$
$24$	−23.9983	−	0.287823i	−0.999928	−	0.0119926i
$25$			21.1633i			0.846533i
$26$	−2.70873	+	19.9831i	−0.104182	+	0.768579i
$27$	10.2949	+	24.9603i	0.381292	+	0.924455i
$28$	28.3849	+	7.83924i	1.01374	+	0.279973i
$29$	−34.6058	+	34.6058i	−1.19330	+	1.19330i	−0.217169	+	0.976134i	$0.569682\pi$
$29$	−34.6058	+	34.6058i	−1.19330	+	1.19330i	−0.976134	+	0.217169i	$0.930318\pi$
$30$	20.5358	−	35.2159i	0.684528	−	1.17386i
$31$	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
$36$	−31.3317	+	17.7292i	−0.870325	+	0.492478i
$37$	−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	$-0.213446\pi$
$41$	64.2448			1.56695			0.783473	+	0.621426i	$0.213446\pi$
$42$	42.7152	−	11.2474i	1.01703	−	0.267795i
$43$	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
$45$	0.0613789	−	61.1492i	0.00136398	−	1.35887i
$46$	9.45200	+	12.4163i	0.205478	+	0.269919i
$47$		−	23.0508i		−	0.490442i	−0.969467	−	0.245221i	$-0.921139\pi$
$47$		−	23.0508i		−	0.490442i	0.969467	−	0.245221i	$-0.0788606\pi$
$48$	−28.6144	−	38.5385i	−0.596132	−	0.802886i
$49$	−5.19710			−0.106063
$50$	−33.6784	+	25.6380i	−0.673569	+	0.512760i
$51$	−12.7733	+	30.7938i	−0.250457	+	0.603800i
$52$	−35.0817	+	19.8976i	−0.674647	+	0.382647i
$53$	−31.9199	−	31.9199i	−0.602263	−	0.602263i	0.338650	−	0.940913i	$-0.390030\pi$
$53$	−31.9199	−	31.9199i	−0.602263	−	0.602263i	−0.940913	+	0.338650i	$0.890030\pi$
$54$	−27.2492	+	46.6206i	−0.504614	+	0.863345i
$55$		−	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	0.541764	−	0.840530i	$-0.317756\pi$
$59$	−17.6272	−	17.6272i	−0.298766	−	0.298766i	−0.840530	+	0.541764i	$0.817756\pi$
$60$	80.9190	−	9.98194i	1.34865	−	0.166366i
$61$	−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
$66$	−2.20002	+	3.77271i	−0.0333337	+	0.0571623i
$67$	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
$69$	21.6207	+	8.96830i	0.313343	+	0.129975i
$70$	−99.1318	−	13.4374i	−1.41617	−	0.191963i
$71$	25.6785			0.361669			0.180834	−	0.983514i	$-0.442120\pi$
$71$	25.6785			0.361669			0.180834	+	0.983514i	$0.442120\pi$
$72$	−66.1699	−	28.3822i	−0.919026	−	0.394197i
$73$			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
$75$	−24.3260	+	58.6449i	−0.324347	+	0.781932i
$76$	104.021	−	58.9988i	1.36870	−	0.776299i
$77$	3.78910	−	3.78910i	0.0492091	−	0.0492091i
$78$	−30.4754	+	52.2608i	−0.390710	+	0.670010i
$79$	−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	$-0.450091\pi$
$83$	94.9424	−	94.9424i	1.14388	−	1.14388i	0.987733	−	0.156151i	$-0.0499086\pi$
$84$	69.6454	+	54.3497i	0.829112	+	0.647021i
$85$	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	$-0.418883\pi$
$89$	44.8713			0.504172			0.252086	+	0.967705i	$0.418883\pi$
$90$	97.3847	−	73.9807i	1.08205	−	0.822008i
$91$	52.4878	−	52.4878i	0.576789	−	0.576789i
$92$	−8.30824	+	30.0830i	−0.0903070	+	0.326990i
$93$	68.9008	+	28.5802i	0.740869	+	0.307314i
$94$	36.6821	−	27.9246i	0.390235	−	0.297070i
$95$			203.131i			2.13822i
$96$	26.6642	−	92.2227i	0.277752	−	0.960653i
$97$	−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
$99$	−0.00657558	+	6.55097i	−6.64200e−5	+	0.0661714i
$100$	−81.5986	−	22.5356i	−0.815986	−	0.225356i
$101$	36.3420	+	36.3420i	0.359822	+	0.359822i	0.863747	−	0.503925i	$-0.168111\pi$
$101$	36.3420	+	36.3420i	0.359822	+	0.359822i	−0.503925	+	0.863747i	$0.668111\pi$
$102$	−64.4781	+	16.9778i	−0.632138	+	0.166449i
$103$		−	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	0.0197471	−	0.999805i	$-0.493714\pi$
$107$	−104.866	−	104.866i	−0.980058	−	0.980058i	−0.999805	+	0.0197471i	$0.993714\pi$
$108$	−107.201	+	13.1148i	−0.992600	+	0.121433i
$109$	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	$-0.981500\pi$
$113$		−	13.1273i		−	0.116171i	0.998312	−	0.0580853i	$-0.0184995\pi$
$114$	90.3630	−	154.959i	0.792658	−	1.35929i
$115$	−37.4849	−	37.4849i	−0.325956	−	0.325956i
$116$	−96.5784	−	170.278i	−0.832572	−	1.46791i
$117$	−0.0910869	+	90.7461i	−0.000778521	+	0.775607i
$118$	6.69696	−	49.4054i	0.0567539	−	0.418690i
$119$	81.8098			0.687477
$120$	113.913	+	116.679i	0.949275	+	0.972322i
$121$		−	120.470i		−	0.995621i
$122$	4.70851	−	34.7360i	0.0385943	−	0.284721i
$123$	178.026	+	73.8456i	1.44737	+	0.600371i
$124$	−26.4767	+	95.8687i	−0.213522	+	0.773134i
$125$	−18.4327	+	18.4327i	−0.147461	+	0.147461i
$126$	131.295	+	17.9314i	1.04202	+	0.142313i
$127$	−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	−0.454988	−	0.890498i	$-0.650356\pi$
$131$	57.0518	−	57.0518i	0.435510	−	0.435510i	0.890498	+	0.454988i	$0.150356\pi$
$132$	−8.66892	+	1.06937i	−0.0656737	+	0.00810132i
$133$	−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	$-0.705868\pi$
$137$	−165.112			−1.20520			−0.602599	+	0.798045i	$0.705868\pi$
$138$	11.9203	+	45.2708i	0.0863790	+	0.328049i
$139$	−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
$141$	26.4955	−	63.8752i	0.187912	−	0.453015i
$142$	31.1078	+	40.8637i	0.219069	+	0.287772i
$143$			7.33920i			0.0513231i
$144$	−34.9944	−	139.683i	−0.243016	−	0.970022i
$145$	332.516			2.29321
$146$	−89.4096	+	68.0639i	−0.612395	+	0.466191i
$147$	−14.4015	−	5.97376i	−0.0979693	−	0.0406378i
$148$	−51.0049	−	89.9271i	−0.344628	−	0.607615i
$149$	131.077	+	131.077i	0.879709	+	0.879709i	0.993504	−	0.113795i	$-0.0363006\pi$
$149$	131.077	+	131.077i	0.879709	+	0.879709i	−0.113795	+	0.993504i	$0.536301\pi$
$150$	−122.794	+	32.3332i	−0.818630	+	0.215554i
$151$			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
$156$	−120.085	+	14.8133i	−0.769773	+	0.0949570i
$157$	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
$162$	−129.097	+	97.8674i	−0.796894	+	0.604120i
$163$	−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
$165$	5.68458	−	13.7043i	0.0344520	−	0.0830566i
$166$	266.104	+	36.0707i	1.60304	+	0.217294i
$167$	−60.3220			−0.361210			−0.180605	−	0.983556i	$-0.557806\pi$
$167$	−60.3220			−0.361210			−0.180605	+	0.983556i	$0.557806\pi$
$168$	−2.11892	+	176.672i	−0.0126126	+	1.05162i
$169$		−	67.3351i		−	0.398432i
$170$	149.638	+	20.2836i	0.880224	+	0.119315i
$171$	0.270083	−	269.072i	0.00157943	−	1.57352i
$172$	20.2071	+	35.6273i	0.117483	+	0.207135i
$173$	−74.8292	+	74.8292i	−0.432539	+	0.432539i	−0.889491	−	0.456952i	$-0.848941\pi$
$173$	−74.8292	+	74.8292i	−0.432539	+	0.432539i	0.456952	+	0.889491i	$0.348941\pi$
$174$	−253.661	−	147.920i	−1.45782	−	0.850116i
$175$	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	−0.718097	−	0.695943i	$-0.754987\pi$
$179$	−3.96558	+	3.96558i	−0.0221541	+	0.0221541i	0.695943	+	0.718097i	$0.254987\pi$
$180$	235.705	+	65.3510i	1.30947	+	0.363061i
$181$	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
$186$	37.9876	+	144.269i	0.204235	+	0.775639i
$187$	−5.71960	+	5.71960i	−0.0305861	+	0.0305861i
$188$	88.8760	+	24.5455i	0.472745	+	0.130561i
$189$	183.754	−	75.7896i	0.972245	−	0.401003i
$190$	−323.254	+	246.080i	−1.70133	+	1.29516i
$191$			68.8639i			0.360544i	0.983617	+	0.180272i	$0.0576978\pi$
$191$			68.8639i			0.360544i	−0.983617	+	0.180272i	$0.942302\pi$
$192$	179.061	−	69.2896i	0.932611	−	0.360884i
$193$	−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
$195$	78.7446	−	189.837i	0.403819	−	0.973522i
$196$	5.53410	−	20.0383i	0.0282352	−	0.102236i
$197$	−246.744	−	246.744i	−1.25251	−	1.25251i	−0.954593	−	0.297912i	$-0.903710\pi$
$197$	−246.744	−	246.744i	−1.25251	−	1.25251i	−0.297912	−	0.954593i	$-0.596290\pi$
$198$	−10.4329	+	7.92562i	−0.0526915	+	0.0400284i
$199$			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
$204$	−105.129	−	82.0402i	−0.515337	−	0.402158i
$205$	−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
$210$	−259.255	−	151.182i	−1.23455	−	0.719915i
$211$	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
$213$	71.1567	+	29.5159i	0.334069	+	0.138572i
$214$	39.8410	−	293.918i	0.186173	−	1.37345i
$215$	−69.5724			−0.323593
$216$	−150.737	−	154.707i	−0.697857	−	0.716237i
$217$		−	183.048i		−	0.843541i
$218$	−2.90263	+	21.4135i	−0.0133148	+	0.0982271i
$219$	−64.5807	+	155.691i	−0.294889	+	0.710916i
$220$	19.0682	+	5.26621i	0.0866738	+	0.0239373i
$221$	−79.2296	+	79.2296i	−0.358505	+	0.358505i
$222$	−133.963	−	78.1196i	−0.603439	−	0.351890i
$223$	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	$0.636283\pi$
$227$	−300.757	+	300.757i	−1.32492	+	1.32492i	−0.909737	+	0.415186i	$0.863717\pi$
$228$	356.064	−	43.9231i	1.56169	−	0.192645i
$229$	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	$-0.470708\pi$
$233$	42.8218			0.183785			0.0918923	+	0.995769i	$0.470708\pi$
$234$	−144.520	+	109.788i	−0.617606	+	0.469180i
$235$	−110.744	+	110.744i	−0.471250	+	0.471250i
$236$	86.7346	−	49.1942i	0.367520	−	0.208450i
$237$	−98.9305	−	41.0365i	−0.417428	−	0.173150i
$238$	99.1073	+	130.189i	0.416417	+	0.547011i
$239$		−	100.598i		−	0.420913i	−0.977603	−	0.210456i	$-0.932505\pi$
$239$		−	100.598i		−	0.420913i	0.977603	−	0.210456i	$-0.0674950\pi$
$240$	−47.6792	+	322.625i	−0.198663	+	1.34427i
$241$	−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
$243$	−93.5551	+	224.269i	−0.385001	+	0.922916i
$244$	60.9815	−	34.5875i	0.249924	−	0.141752i
$245$	24.9686	+	24.9686i	0.101913	+	0.101913i
$246$	98.1527	+	372.763i	0.398995	+	1.51530i
$247$		−	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	0.671516	−	0.740990i	$-0.265644\pi$
$251$	−17.4381	−	17.4381i	−0.0694747	−	0.0694747i	−0.740990	+	0.671516i	$0.765644\pi$
$252$	130.520	+	230.660i	0.517937	+	0.915317i
$253$	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	$0.233119\pi$
$257$			343.676i			1.33726i	−0.743595	+	0.668630i	$0.766881\pi$
$258$	53.0736	+	30.9494i	0.205712	+	0.119959i
$259$	134.545	+	134.545i	0.519480	+	0.519480i
$260$	264.139	+	72.9491i	1.01592	+	0.280574i
$261$	−440.460	−	0.442114i	−1.68758	−	0.00169392i
$262$	159.904	+	21.6752i	0.610322	+	0.0827299i
$263$	−98.0863			−0.372952			−0.186476	−	0.982460i	$-0.559707\pi$
$263$	−98.0863			−0.372952			−0.186476	+	0.982460i	$0.559707\pi$
$264$	−12.2036	−	12.4999i	−0.0462258	−	0.0473481i
$265$			306.708i			1.15739i
$266$	−436.206	−	59.1282i	−1.63987	−	0.222286i
$267$	124.341	+	51.5769i	0.465697	+	0.193172i
$268$	−202.442	+	114.821i	−0.755380	+	0.428437i
$269$	126.560	−	126.560i	0.470482	−	0.470482i	−0.431589	−	0.902070i	$-0.642047\pi$
$269$	126.560	−	126.560i	0.470482	−	0.470482i	0.902070	+	0.431589i	$0.142047\pi$
$270$	354.895	−	93.0671i	1.31443	−	0.344693i
$271$	−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
$276$	−57.6013	+	73.8121i	−0.208701	+	0.267435i
$277$	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	$-0.437787\pi$
$281$	109.143			0.388409			0.194204	+	0.980961i	$0.437787\pi$
$282$	133.746	−	35.2168i	0.474277	−	0.124882i
$283$	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
$285$	−233.487	+	562.888i	−0.819252	+	1.97504i
$286$	−11.6793	+	8.89098i	−0.0408367	+	0.0310873i
$287$		−	472.962i		−	1.64795i
$288$	179.893	−	224.906i	0.624627	−	0.780923i
$289$	165.509			0.572697
$290$	402.822	+	529.152i	1.38904	+	1.82466i
$291$	−228.235	−	94.6721i	−0.784311	−	0.325334i
$292$	−216.628	−	59.8277i	−0.741877	−	0.204889i
$293$	−19.4639	−	19.4639i	−0.0664296	−	0.0664296i	0.673111	−	0.739541i	$-0.264957\pi$
$293$	−19.4639	−	19.4639i	−0.0664296	−	0.0664296i	−0.739541	+	0.673111i	$0.764957\pi$
$294$	−7.94009	−	30.1548i	−0.0270071	−	0.102567i
$295$			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
$300$	−200.211	−	156.240i	−0.667371	−	0.520801i
$301$	−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
$306$	−198.188	−	27.0672i	−0.647672	−	0.0884549i
$307$	−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
$309$	100.596	−	242.517i	0.325554	−	0.784844i
$310$	45.3844	−	334.813i	0.146401	−	1.08004i
$311$	360.965			1.16066			0.580330	−	0.814381i	$-0.302924\pi$
$311$	360.965			1.16066			0.580330	+	0.814381i	$0.302924\pi$
$312$	−169.048	−	173.152i	−0.541821	−	0.554975i
$313$			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
$315$	−450.172	−	0.451863i	−1.42912	−	0.00143449i
$316$	38.0163	−	137.652i	0.120305	−	0.435607i
$317$	172.709	−	172.709i	0.544825	−	0.544825i	−0.380115	−	0.924939i	$-0.624116\pi$
$317$	172.709	−	172.709i	0.544825	−	0.544825i	0.924939	+	0.380115i	$0.124116\pi$
$318$	136.440	−	233.974i	0.429056	−	0.735767i
$319$	−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
$324$	−312.135	−	86.8792i	−0.963378	−	0.268146i
$325$	−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
$330$	28.6950	−	7.55573i	0.0869546	−	0.0228961i
$331$	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
$333$	−232.615	−	0.233489i	−0.698544	−	0.000701168i
$334$	−73.0763	−	95.9940i	−0.218791	−	0.287407i
$335$		−	395.325i		−	1.18007i
$336$	−283.716	+	210.655i	−0.844392	+	0.626950i
$337$	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
$339$	15.0890	−	36.3765i	0.0445104	−	0.107305i
$340$	148.998	+	262.700i	0.438231	+	0.772647i
$341$	12.7975	+	12.7975i	0.0375294	+	0.0375294i
$342$	428.518	−	325.534i	1.25298	−	0.951855i
$343$		−	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	0.911626	−	0.411021i	$-0.134828\pi$
$347$	173.710	+	173.710i	0.500605	+	0.500605i	−0.411021	+	0.911626i	$0.634828\pi$
$348$	−71.9002	−	582.862i	−0.206610	−	1.67489i
$349$	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	$-0.591848\pi$
$353$		−	676.812i		−	1.91732i	0.284561	−	0.958658i	$-0.408152\pi$
$354$	75.3463	−	129.208i	0.212843	−	0.364993i
$355$	−123.368	−	123.368i	−0.347516	−	0.347516i
$356$	−47.7809	+	173.008i	−0.134216	+	0.485979i
$357$	226.700	+	94.0355i	0.635014	+	0.263405i
$358$	−11.1147	−	1.50661i	−0.0310467	−	0.00420842i
$359$	−240.896			−0.671020			−0.335510	−	0.942037i	$-0.608909\pi$
$359$	−240.896			−0.671020			−0.335510	+	0.942037i	$0.608909\pi$
$360$	181.545	+	454.260i	0.504291	+	1.26183i
$361$			532.827i			1.47598i
$362$	445.139	+	60.3392i	1.22967	+	0.166683i
$363$	138.473	−	333.830i	0.381469	−	0.919643i
$364$	146.484	+	258.267i	0.402428	+	0.709523i
$365$	269.929	−	269.929i	0.739532	−	0.739532i
$366$	52.9746	−	90.8435i	0.144739	−	0.248206i
$367$	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
$372$	−183.564	+	235.225i	−0.493452	+	0.632324i
$373$	−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
$378$	343.215	+	200.605i	0.907976	+	0.530700i
$379$	−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
$381$	−244.604	−	101.462i	−0.642004	−	0.266305i
$382$	−109.587	+	83.4242i	−0.286877	+	0.218388i
$383$			69.4683i			0.181379i	0.995879	+	0.0906897i	$0.0289071\pi$
$383$			69.4683i			0.181379i	−0.995879	+	0.0906897i	$0.971093\pi$
$384$	327.186	+	201.011i	0.852047	+	0.523465i
$385$	−36.4083			−0.0945669
$386$	−444.167	−	583.463i	−1.15069	−	1.51156i
$387$	92.1575	+	0.0925037i	0.238133	+	0.000239028i
$388$	87.7043	−	317.566i	0.226042	−	0.818468i
$389$	265.362	+	265.362i	0.682165	+	0.682165i	0.960488	−	0.278322i	$-0.0897783\pi$
$389$	265.362	+	265.362i	0.682165	+	0.682165i	−0.278322	+	0.960488i	$0.589778\pi$
$390$	397.492	−	104.664i	1.01921	−	0.268370i
$391$			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
$396$	−25.2513	−	7.00112i	−0.0637659	−	0.0176796i
$397$	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	$0.310597\pi$
$401$			664.163i			1.65627i	−0.560531	+	0.828133i	$0.689403\pi$
$402$	−175.861	+	301.575i	−0.437465	+	0.750188i
$403$	177.275	+	177.275i	0.439889	+	0.439889i
$404$	−178.821	+	101.424i	−0.442626	+	0.251049i
$405$	389.932	−	388.369i	0.962795	−	0.958937i
$406$	−96.7902	+	714.049i	−0.238400	+	1.75874i
$407$	−18.8131			−0.0462237
$408$	3.19847	−	266.684i	0.00783940	−	0.653637i
$409$		−	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
$411$	−457.536	−	189.787i	−1.11323	−	0.461768i
$412$	337.438	+	93.1926i	0.819024	+	0.226196i
$413$	−129.769	+	129.769i	−0.314211	+	0.314211i
$414$	−19.0042	+	139.150i	−0.0459038	+	0.336111i
$415$	−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	−0.0348367	−	0.999393i	$-0.511091\pi$
$419$	404.149	−	404.149i	0.964556	−	0.964556i	0.999393	+	0.0348367i	$0.0110911\pi$
$420$	−73.4857	−	595.715i	−0.174966	−	1.41837i
$421$	−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
$426$	39.2314	+	148.992i	0.0920925	+	0.349747i
$427$	−91.2382	+	91.2382i	−0.213673	+	0.213673i
$428$	515.994	−	292.662i	1.20559	−	0.683790i
$429$	−8.43598	+	20.3374i	−0.0196643	+	0.0474065i
$430$	−84.2825	−	110.715i	−0.196006	−	0.257476i
$431$			766.652i			1.77877i	0.457155	+	0.889387i	$0.348868\pi$
$431$			766.652i			1.77877i	−0.457155	+	0.889387i	$0.651132\pi$
$432$	63.5861	−	427.295i	0.147190	−	0.989108i
$433$	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
$435$	921.422	+	382.207i	2.11821	+	0.878638i
$436$	−37.5929	+	21.3220i	−0.0862223	+	0.0489036i
$437$	−164.943	−	164.943i	−0.377445	−	0.377445i
$438$	−325.995	+	85.8382i	−0.744281	+	0.195978i
$439$		−	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	0.811818	−	0.583911i	$-0.198478\pi$
$443$	100.963	+	100.963i	0.227907	+	0.227907i	−0.583911	+	0.811818i	$0.698478\pi$
$444$	−37.9719	−	307.821i	−0.0855223	−	0.693290i
$445$	−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	$0.0468611\pi$
$449$			131.725i			0.293375i	−0.989183	+	0.146687i	$0.953139\pi$
$450$	−377.436	−	51.5478i	−0.838747	−	0.114551i
$451$	33.0663	+	33.0663i	0.0733178	+	0.0733178i
$452$	50.6143	+	13.9785i	0.111979	+	0.0309259i
$453$	−141.461	+	341.034i	−0.312277	+	0.752833i
$454$	−842.961	−	114.264i	−1.85674	−	0.251684i
$455$	−504.339			−1.10844
$456$	501.247	+	513.416i	1.09923	+	1.12591i
$457$		−	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
$459$	−277.374	+	114.403i	−0.604302	+	0.249245i
$460$	184.445	−	104.613i	0.400967	−	0.227421i
$461$	303.536	−	303.536i	0.658430	−	0.658430i	−0.296579	−	0.955008i	$-0.595846\pi$
$461$	303.536	−	303.536i	0.658430	−	0.658430i	0.955008	+	0.296579i	$0.0958457\pi$
$462$	27.7742	+	16.1963i	0.0601173	+	0.0350569i
$463$	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	−0.633333	−	0.773880i	$-0.718313\pi$
$467$	65.6355	−	65.6355i	0.140547	−	0.140547i	0.773880	+	0.633333i	$0.218313\pi$
$468$	−349.789	−	96.9816i	−0.747412	−	0.207226i
$469$	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
$474$	−54.5441	−	207.147i	−0.115072	−	0.437019i
$475$	447.400	−	447.400i	0.941894	−	0.941894i
$476$	−87.1147	+	315.431i	−0.183014	+	0.662669i
$477$	0.407800	−	406.274i	0.000854927	−	0.851728i
$478$	160.088	−	121.868i	0.334912	−	0.254955i
$479$		−	373.272i		−	0.779273i	−0.920969	−	0.389636i	$-0.872601\pi$
$479$		−	373.272i		−	0.779273i	0.920969	−	0.389636i	$-0.127399\pi$
$480$	−571.173	+	314.965i	−1.18994	+	0.656178i
$481$	−260.604			−0.541797
$482$	−6.33778	−	8.32539i	−0.0131489	−	0.0172726i
$483$	66.0234	−	159.169i	0.136694	−	0.329542i
$484$	464.492	+	128.282i	0.959694	+	0.265045i
$485$	395.702	+	395.702i	0.815881	+	0.815881i
$486$	−470.228	+	122.807i	−0.967547	+	0.252690i
$487$		−	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	0.371518	−	0.928426i	$-0.378837\pi$
$491$	−273.442	−	273.442i	−0.556908	−	0.556908i	−0.928426	+	0.371518i	$0.878837\pi$
$492$	−474.294	+	607.775i	−0.964012	+	1.23531i
$493$	−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
$498$	695.930	+	405.825i	1.39745	+	0.814910i
$499$	−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
$501$	−167.156	−	69.3366i	−0.333645	−	0.138396i
$502$	6.62514	−	48.8755i	0.0131975	−	0.0973616i
$503$	−864.426			−1.71854			−0.859270	−	0.511522i	$-0.829082\pi$
$503$	−864.426			−1.71854			−0.859270	+	0.511522i	$0.829082\pi$
$504$	−208.946	+	487.134i	−0.414575	+	0.966535i
$505$		−	349.198i		−	0.691482i
$506$	−1.52569	+	11.2554i	−0.00301520	+	0.0222440i
$507$	77.3977	−	186.590i	0.152658	−	0.368027i
$508$	93.9946	−	340.342i	0.185029	−	0.669964i
$509$	171.041	−	171.041i	0.336033	−	0.336033i	−0.518839	−	0.854872i	$-0.673635\pi$
$509$	171.041	−	171.041i	0.336033	−	0.336033i	0.854872	+	0.518839i	$0.173635\pi$
$510$	391.341	+	228.207i	0.767336	+	0.447465i
$511$	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
$516$	15.0437	+	121.952i	0.0291545	+	0.236342i
$517$	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	$-0.609548\pi$
$521$	−351.572			−0.674802			−0.337401	+	0.941361i	$0.609548\pi$
$522$	−532.885	−	701.465i	−1.02085	−	1.34380i
$523$	−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
$525$	431.736	+	179.085i	0.822354	+	0.341114i
$526$	−118.825	−	156.090i	−0.225904	−	0.296750i
$527$			276.309i			0.524306i
$528$	5.10791	−	34.5631i	0.00967407	−	0.0654605i
$529$	−468.124			−0.884922
$530$	−488.083	+	371.558i	−0.920911	+	0.701052i
$531$	0.225200	−	224.357i	0.000424106	−	0.422519i
$532$	−434.341	−	765.789i	−0.816431	−	1.43945i
$533$	458.045	+	458.045i	0.859372	+	0.859372i
$534$	68.5540	+	260.353i	0.128378	+	0.487553i
$535$			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
$540$	578.036	+	452.021i	1.07044	+	0.837076i
$541$	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
$546$	384.737	+	224.356i	0.704646	+	0.410908i
$547$	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
$549$	0.158334	−	157.742i	0.000288404	−	0.287325i
$550$	−30.5298	−	4.13835i	−0.0555087	−	0.00752427i
$551$	1463.16			2.65546
$552$	−187.242	−	2.24569i	−0.339206	−	0.00406827i
$553$			262.828i			0.475277i
$554$	514.079	+	69.6840i	0.927940	+	0.125783i
$555$	486.621	+	201.851i	0.876794	+	0.363696i
$556$	−265.351	−	467.843i	−0.477251	−	0.841443i
$557$	−31.8976	+	31.8976i	−0.0572667	+	0.0572667i	−0.735160	−	0.677893i	$-0.762893\pi$
$557$	−31.8976	+	31.8976i	−0.0572667	+	0.0572667i	0.677893	+	0.735160i	$0.262893\pi$
$558$	−60.5626	+	443.443i	−0.108535	+	0.794700i
$559$	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	−0.677265	−	0.735740i	$-0.736835\pi$
$563$	32.9214	−	32.9214i	0.0584750	−	0.0584750i	0.735740	+	0.677265i	$0.236835\pi$
$564$	218.067	+	170.175i	0.386644	+	0.301728i
$565$	−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	$-0.692524\pi$
$569$	−647.095			−1.13725			−0.568624	+	0.822597i	$0.692524\pi$
$570$	−1178.61	+	310.341i	−2.06774	+	0.544459i
$571$	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
$573$	−79.1550	+	190.826i	−0.138141	+	0.333030i
$574$	752.652	−	572.963i	1.31124	−	0.998193i
$575$			165.123i			0.287170i
$576$	575.834	+	13.8145i	0.999712	+	0.0239835i
$577$	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
$579$	−1015.99	−	421.436i	−1.75474	−	0.727869i
$580$	−354.078	+	1282.07i	−0.610478	+	2.21046i
$581$	−698.953	−	698.953i	−1.20302	−	1.20302i
$582$	−125.834	−	477.892i	−0.216210	−	0.821120i
$583$		−	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	0.0890534	−	0.996027i	$-0.471616\pi$
$587$	−532.393	−	532.393i	−0.906973	−	0.906973i	−0.996027	+	0.0890534i	$0.971616\pi$
$588$	38.3681	−	49.1661i	0.0652519	−	0.0836158i
$589$	−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	$-0.931091\pi$
$593$		−	254.750i		−	0.429595i	0.976659	−	0.214798i	$-0.0689092\pi$
$594$	−38.0203	+	9.97037i	−0.0640072	+	0.0167851i
$595$	−393.042	−	393.042i	−0.660574	−	0.660574i
$596$	−644.963	+	365.811i	−1.08215	+	0.613777i
$597$	−330.811	+	797.517i	−0.554123	+	1.33587i
$598$	−21.1343	+	155.914i	−0.0353417	+	0.260726i
$599$	−624.772			−1.04303			−0.521513	−	0.853244i	$-0.674632\pi$
$599$	−624.772			−1.04303			−0.521513	+	0.853244i	$0.674632\pi$
$600$	6.09130	−	507.883i	0.0101522	−	0.846472i
$601$			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
$603$	−0.525625	+	523.658i	−0.000871684	+	0.868422i
$604$	−474.514	−	131.050i	−0.785620	−	0.216970i
$605$	−578.779	+	578.779i	−0.956660	+	0.956660i
$606$	−155.341	+	266.387i	−0.256339	+	0.439583i
$607$	−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
$612$	−197.018	−	348.178i	−0.321925	−	0.568918i
$613$	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	$-0.246192\pi$
$617$	882.945			1.43103			0.715514	+	0.698598i	$0.246192\pi$
$618$	507.797	−	133.709i	0.821678	−	0.216357i
$619$	−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
$621$	80.3239	+	194.748i	0.129346	+	0.313604i
$622$	437.286	+	574.425i	0.703033	+	0.923513i
$623$		−	330.337i		−	0.530235i
$624$	70.7564	−	478.779i	0.113392	−	0.767274i
$625$	706.197			1.12991
$626$	−117.636	+	89.5515i	−0.187917	+	0.143053i
$627$	25.0136	−	60.3027i	0.0398942	−	0.0961765i
$628$	−684.840	+	388.428i	−1.09051	+	0.618516i
$629$	−203.094	−	203.094i	−0.322885	−	0.322885i
$630$	−544.636	−	716.933i	−0.864502	−	1.13799i
$631$		−	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
$636$	537.624	−	66.3198i	0.845321	−	0.104276i
$637$	−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	$0.201767\pi$
$641$			759.287i			1.18453i	−0.805741	+	0.592267i	$0.798233\pi$
$642$	448.244	−	768.671i	0.698199	−	1.19731i
$643$	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
$645$	−192.789	−	79.9694i	−0.298898	−	0.123984i
$646$	658.446	+	89.2532i	1.01927	+	0.138163i
$647$	747.683			1.15561			0.577807	−	0.816173i	$-0.303908\pi$
$647$	747.683			1.15561			0.577807	+	0.816173i	$0.303908\pi$
$648$	−239.875	−	601.967i	−0.370178	−	0.928961i
$649$		−	18.1452i		−	0.0279587i
$650$	−422.908	−	57.3257i	−0.650628	−	0.0881934i
$651$	210.403	−	507.239i	0.323200	−	0.779168i
$652$	98.0709	−	55.6239i	0.150416	−	0.0853128i
$653$	−605.127	+	605.127i	−0.926688	+	0.926688i	−0.997490	−	0.0708022i	$-0.977444\pi$
$653$	−605.127	+	605.127i	−0.926688	+	0.926688i	0.0708022	+	0.997490i	$0.477444\pi$
$654$	−32.6569	+	56.0018i	−0.0499341	+	0.0856296i
$655$	−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	−0.994844	−	0.101418i	$-0.967662\pi$
$659$	−588.767	+	588.767i	−0.893425	+	0.893425i	0.101418	+	0.994844i	$0.467662\pi$
$660$	46.7861	+	36.5108i	0.0708880	+	0.0553194i
$661$	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
$666$	−281.427	−	370.457i	−0.422563	−	0.556242i
$667$	−270.005	+	270.005i	−0.404805	+	0.404805i
$668$	64.2336	−	232.581i	0.0961581	−	0.348176i
$669$	125.529	+	52.0695i	0.187636	+	0.0778319i
$670$	629.104	−	478.911i	0.938961	−	0.714793i
$671$		−	12.7575i		−	0.0190127i
$672$	−678.931	−	196.298i	−1.01031	−	0.292110i
$673$	−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
$675$	−528.242	+	217.874i	−0.782581	+	0.322776i
$676$	259.621	+	71.7014i	0.384055	+	0.106067i
$677$	−150.713	−	150.713i	−0.222618	−	0.222618i	0.586982	−	0.809600i	$-0.300316\pi$
$677$	−150.713	−	150.713i	−0.222618	−	0.222618i	−0.809600	+	0.586982i	$0.800316\pi$
$678$	76.1674	−	20.0557i	0.112341	−	0.0295807i
$679$			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	0.989645	−	0.143536i	$-0.0458473\pi$
$683$	577.893	+	577.893i	0.846109	+	0.846109i	−0.143536	+	0.989645i	$0.545847\pi$
$684$	1037.16	+	287.561i	1.51632	+	0.420412i
$685$	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
$690$	160.227	−	274.765i	0.232213	−	0.398211i
$691$	−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
$693$	48.2274	+	0.0484085i	0.0695922	+	6.98536e-5i
$694$	−65.9963	+	486.874i	−0.0950956	+	0.701547i
$695$	913.595			1.31453
$696$	840.440	−	820.519i	1.20753	−	1.17891i
$697$			713.929i			1.02429i
$698$	−147.372	+	1087.20i	−0.211134	+	1.55760i
$699$	118.662	+	49.2212i	0.169760	+	0.0704165i
$700$	−165.904	+	600.718i	−0.237006	+	0.858169i
$701$	413.745	−	413.745i	0.590221	−	0.590221i	−0.347470	−	0.937691i	$-0.612959\pi$
$701$	413.745	−	413.745i	0.590221	−	0.590221i	0.937691	+	0.347470i	$0.112959\pi$
$702$	−526.669	+	138.113i	−0.750240	+	0.196742i
$703$	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
$708$	296.893	−	36.6239i	0.419340	−	0.0517286i
$709$	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
$714$	124.988	+	474.679i	0.175054	+	0.664816i
$715$	35.2600	−	35.2600i	0.0493147	−	0.0493147i
$716$	−11.0672	−	19.5127i	−0.0154570	−	0.0272523i
$717$	115.632	−	278.764i	0.161272	−	0.388792i
$718$	−291.830	−	383.352i	−0.406449	−	0.533917i
$719$		−	567.983i		−	0.789963i	−0.918689	−	0.394981i	$-0.870751\pi$
$719$		−	567.983i		−	0.789963i	0.918689	−	0.394981i	$-0.129249\pi$
$720$	−502.961	+	839.210i	−0.698556	+	1.16557i
$721$	−644.293			−0.893610
$722$	−847.919	+	645.486i	−1.17440	+	0.894025i
$723$	−14.4972	−	6.01344i	−0.0200514	−	0.00831735i
$724$	443.237	+	781.473i	0.612205	+	1.07938i
$725$	−732.374	−	732.374i	−1.01017	−	1.01017i
$726$	698.995	−	184.053i	0.962804	−	0.253517i
$727$			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
$732$	208.740	−	25.7496i	0.285164	−	0.0351770i
$733$	−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
$738$	−156.482	+	1145.77i	−0.212035	+	1.55253i
$739$	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
$741$	346.497	−	835.331i	0.467607	−	1.12730i
$742$	−658.630	−	89.2781i	−0.887641	−	0.120321i
$743$	−1160.78			−1.56229			−0.781145	−	0.624349i	$-0.785364\pi$
$743$	−1160.78			−1.56229			−0.781145	+	0.624349i	$0.785364\pi$
$744$	−596.703	−	7.15655i	−0.802020	−	0.00961902i
$745$		−	1259.47i		−	1.69057i
$746$	−1004.84	−	136.207i	−1.34697	−	0.182583i
$747$	1208.42	+	1.21296i	1.61770	+	0.00162377i
$748$	−15.9623	−	28.1433i	−0.0213400	−	0.0376247i
$749$	−772.011	+	772.011i	−1.03072	+	1.03072i
$750$	−135.112	−	78.7893i	−0.180149	−	0.105052i
$751$	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
$756$	96.5491	+	789.198i	0.127710	+	1.04391i
$757$	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	$-0.349181\pi$
$761$	694.461			0.912563			0.456282	+	0.889835i	$0.349181\pi$
$762$	−134.859	−	512.167i	−0.176981	−	0.672135i
$763$	56.2451	−	56.2451i	0.0737157	−	0.0737157i
$764$	−265.516	−	73.3293i	−0.347534	−	0.0959808i
$765$	679.529	+	0.682081i	0.888273	+	0.000891610i
$766$	−110.549	+	84.1564i	−0.144320	+	0.109865i
$767$		−	251.353i		−	0.327709i
$768$	76.4849	+	764.182i	0.0995897	+	0.995029i
$769$	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
$771$	−395.035	+	952.347i	−0.512367	+	1.23521i
$772$	390.419	−	1413.66i	0.505725	−	1.83116i
$773$	−142.479	−	142.479i	−0.184320	−	0.184320i	0.608916	−	0.793235i	$-0.291605\pi$
$773$	−142.479	−	142.479i	−0.184320	−	0.184320i	−0.793235	+	0.608916i	$0.791605\pi$
$774$	111.496	+	146.768i	0.144051	+	0.189622i
$775$			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
$780$	648.095	+	505.759i	0.830891	+	0.648409i
$781$	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
$786$	418.191	+	243.864i	0.532049	+	0.310260i
$787$	−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
$789$	−271.803	−	112.744i	−0.344491	−	0.142895i
$790$	−65.1647	+	480.738i	−0.0824869	+	0.608529i
$791$	−96.6413			−0.122176
$792$	−19.4491	−	48.6653i	−0.0245569	−	0.0614461i
$793$		−	176.721i		−	0.222852i
$794$	−98.4466	+	726.269i	−0.123988	+	0.914696i
$795$	−352.543	+	849.908i	−0.443451	+	1.06907i
$796$	−1109.67	−	306.464i	−1.39405	−	0.385005i
$797$	552.965	−	552.965i	0.693808	−	0.693808i	−0.269260	−	0.963068i	$-0.586779\pi$
$797$	552.965	−	552.965i	0.693808	−	0.693808i	0.963068	+	0.269260i	$0.0867791\pi$
$798$	−1140.79	−	665.240i	−1.42956	−	0.833635i
$799$	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
$804$	−692.959	+	85.4815i	−0.861889	+	0.106320i
$805$	−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	$-0.305028\pi$
$809$	930.240			1.14986			0.574932	+	0.818201i	$0.305028\pi$
$810$	1090.41	+	150.037i	1.34619	+	0.185230i
$811$	−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
$813$	−572.188	−	237.345i	−0.703799	−	0.291937i
$814$	−22.7908	−	29.9383i	−0.0279985	−	0.0367793i
$815$			191.511i			0.234983i
$816$	428.265	−	317.981i	0.524834	−	0.389682i
$817$	−306.137			−0.374708
$818$	844.090	−	642.571i	1.03190	−	0.785540i
$819$	668.061	+	0.670570i	0.815703	+	0.000818767i
$820$	1518.73	−	861.395i	1.85211	−	1.05048i
$821$	963.577	+	963.577i	1.17366	+	1.17366i	0.981330	+	0.192334i	$0.0616056\pi$
$821$	963.577	+	963.577i	1.17366	+	1.17366i	0.192334	+	0.981330i	$0.438394\pi$
$822$	−252.257	−	958.017i	−0.306882	−	1.16547i
$823$		−	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	0.244058	−	0.969761i	$-0.421521\pi$
$827$	−600.156	−	600.156i	−0.725703	−	0.725703i	−0.969761	+	0.244058i	$0.921521\pi$
$828$	−244.460	+	138.329i	−0.295241	+	0.167064i
$829$	−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
$834$	−696.940	−	406.414i	−0.835659	−	0.487307i
$835$	289.807	+	289.807i	0.347075	+	0.347075i
$836$	83.9052	+	23.1727i	0.100365	+	0.0277185i
$837$	255.976	+	620.622i	0.305826	+	0.741484i
$838$	1132.75	+	153.545i	1.35173	+	0.183228i
$839$	1230.19			1.46625			0.733127	−	0.680091i	$-0.238060\pi$
$839$	1230.19			1.46625			0.733127	+	0.680091i	$0.238060\pi$
$840$	858.973	−	838.613i	1.02259	−	0.998348i
$841$		−	1554.12i		−	1.84794i
$842$	−741.704	−	100.539i	−0.880884	−	0.119405i
$843$	302.442	+	125.453i	0.358768	+	0.148818i
$844$	−768.315	+	435.774i	−0.910326	+	0.516320i
$845$	−323.501	+	323.501i	−0.382841	+	0.382841i
$846$	411.098	+	56.1451i	0.485932	+	0.0663654i
$847$	−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
$852$	−189.574	+	242.926i	−0.222505	+	0.285124i
$853$	−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	$-0.615783\pi$
$857$	−609.799			−0.711550			−0.355775	+	0.934572i	$0.615783\pi$
$858$	−42.5837	+	11.2128i	−0.0496314	+	0.0130685i
$859$	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
$861$	543.642	−	1310.61i	0.631407	−	1.52219i
$862$	−1220.02	+	928.750i	−1.41533	+	1.07744i
$863$			1322.86i			1.53286i	0.642329	+	0.766429i	$0.277968\pi$
$863$			1322.86i			1.53286i	−0.642329	+	0.766429i	$0.722032\pi$
$864$	757.010	−	416.452i	0.876169	−	0.482005i
$865$	719.010			0.831225
$866$	183.196	+	240.649i	0.211543	+	0.277886i
$867$	458.637	+	190.243i	0.528993	+	0.219427i
$868$	705.772	+	194.918i	0.813102	+	0.224560i
$869$	−18.3752	−	18.3752i	−0.0211452	−	0.0211452i
$870$	508.015	+	1929.33i	0.583925	+	2.21762i
$871$			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
$876$	−531.522	−	414.788i	−0.606760	−	0.473502i
$877$	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	$0.208960\pi$
$881$			1075.39i			1.22064i	−0.792153	+	0.610322i	$0.791040\pi$
$882$	12.6586	−	92.6874i	0.0143522	−	0.105088i
$883$	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
$885$	−194.685	+	469.346i	−0.219983	+	0.530334i
$886$	−38.3580	+	282.978i	−0.0432934	+	0.319388i
$887$	282.642			0.318650			0.159325	−	0.987226i	$-0.449068\pi$
$887$	282.642			0.318650			0.159325	+	0.987226i	$0.449068\pi$
$888$	443.853	−	433.332i	0.499834	−	0.487987i
$889$			649.838i			0.730976i
$890$	81.9024	−	604.218i	0.0920252	−	0.678896i
$891$	−41.7738	+	41.6064i	−0.0468841	+	0.0466963i
$892$	−48.2373	+	174.661i	−0.0540777	+	0.195808i
$893$	−487.301	+	487.301i	−0.545690	+	0.545690i
$894$	−560.279	+	960.795i	−0.626710	+	1.07471i
$895$	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
$900$	−375.209	−	663.083i	−0.416899	−	0.736759i
$901$	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
$906$	−714.078	+	188.025i	−0.788166	+	0.207533i
$907$	−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
$909$	−0.464295	+	462.558i	−0.000510776	+	0.508864i
$910$	−610.974	−	802.583i	−0.671400	−	0.881960i
$911$			1193.35i			1.30994i	0.755657	+	0.654968i	$0.227318\pi$
$911$			1193.35i			1.30994i	−0.755657	+	0.654968i	$0.772682\pi$
$912$	−209.801	+	1419.63i	−0.230045	+	1.55662i
$913$	97.7324			0.107045
$914$	219.548	−	167.133i	0.240206	−	0.182859i
$915$	−136.880	+	329.988i	−0.149595	+	0.360643i
$916$	183.381	+	323.321i	0.200198	+	0.352970i
$917$	−420.008	−	420.008i	−0.458024	−	0.458024i
$918$	−518.078	−	302.810i	−0.564355	−	0.329858i
$919$			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
$924$	7.87259	+	63.8195i	0.00852012	+	0.0690687i
$925$	−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	$-0.723758\pi$
$929$		−	1417.53i		−	1.52587i	0.646475	−	0.762935i	$-0.276242\pi$
$930$	510.611	−	875.622i	0.549044	−	0.941529i
$931$	109.868	+	109.868i	0.118011	+	0.118011i
$932$	−45.5986	+	165.106i	−0.0489255	+	0.177153i
$933$	1000.26	+	414.908i	1.07209	+	0.444704i
$934$	183.963	+	24.9364i	0.196962	+	0.0266985i
$935$	54.9578			0.0587784
$936$	−269.414	−	674.127i	−0.287836	−	0.720221i
$937$			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
$939$	−84.9687	+	204.842i	−0.0904885	+	0.218149i
$940$	−309.065	−	544.915i	−0.328793	−	0.579697i
$941$	524.733	−	524.733i	0.557634	−	0.557634i	−0.371000	−	0.928633i	$-0.620985\pi$
$941$	524.733	−	524.733i	0.557634	−	0.557634i	0.928633	+	0.371000i	$0.120985\pi$
$942$	−594.920	+	1020.20i	−0.631550	+	1.08301i
$943$	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	−0.544739	−	0.838606i	$-0.683371\pi$
$947$	278.292	−	278.292i	0.293867	−	0.293867i	0.838606	+	0.544739i	$0.183371\pi$
$948$	263.568	−	337.745i	0.278026	−	0.356271i
$949$	−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	$-0.592383\pi$
$953$	−545.447			−0.572348			−0.286174	+	0.958178i	$0.592383\pi$
$954$	647.022	−	491.526i	0.678220	−	0.515227i
$955$	330.845	−	330.845i	0.346435	−	0.346435i
$956$	387.872	+	107.121i	0.405724	+	0.112052i
$957$	−98.7128	−	40.9462i	−0.103148	−	0.0427860i
$958$	594.009	−	452.195i	0.620051	−	0.472020i
$959$			1215.53i			1.26750i
$960$	−1193.16	−	527.380i	−1.24288	−	0.549354i
$961$	−342.761			−0.356672
$962$	−315.705	−	414.715i	−0.328176	−	0.431096i
$963$	1.33974	−	1334.73i	0.00139122	−	1.38601i
$964$	5.57086	−	20.1714i	0.00577890	−	0.0209246i
$965$	1761.48	+	1761.48i	1.82537	+	1.82537i
$966$	333.277	−	87.7557i	0.345008	−	0.0908444i
$967$			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	0.779164	−	0.626820i	$-0.215644\pi$
$971$	147.926	+	147.926i	0.152344	+	0.152344i	−0.626820	+	0.779164i	$0.715644\pi$
$972$	−765.082	−	599.528i	−0.787121	−	0.616798i
$973$	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	$0.0913873\pi$
$977$			553.321i			0.566347i	−0.959069	+	0.283174i	$0.908613\pi$
$978$	85.1941	−	146.095i	0.0871105	−	0.149382i
$979$	23.0949	+	23.0949i	0.0235903	+	0.0235903i
$980$	−122.858	+	69.6828i	−0.125366	+	0.0711049i
$981$	−0.0976072	+	97.2420i	−9.94977e−5	+	0.0991254i
$982$	103.887	−	766.401i	0.105791	−	0.780449i
$983$	−1107.13			−1.12628			−0.563139	−	0.826362i	$-0.690406\pi$
$983$	−1107.13			−1.12628			−0.563139	+	0.826362i	$0.690406\pi$
$984$	−1541.76	−	18.4911i	−1.56683	−	0.0187918i
$985$			2370.88i			2.40698i
$986$	146.103	−	1077.85i	0.148178	−	1.09315i
$987$	−470.241	−	195.057i	−0.476434	−	0.197626i
$988$	1162.28	+	320.995i	1.17640	+	0.324894i
$989$	56.4932	−	56.4932i	0.0571216	−	0.0571216i
$990$	88.2006	+	12.0459i	0.0890915	+	0.0121675i
$991$	−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
$996$	197.261	+	1599.10i	0.198053	+	1.60553i
$997$	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.29.7	yes	20
3.2	odd	2	inner	48.3.i.b.29.4	yes	20
4.3	odd	2		192.3.i.b.17.1		20
8.3	odd	2		384.3.i.c.161.10		20
8.5	even	2		384.3.i.d.161.1		20
12.11	even	2		192.3.i.b.17.4		20
16.3	odd	4		384.3.i.c.353.7		20
16.5	even	4	inner	48.3.i.b.5.4	✓	20
16.11	odd	4		192.3.i.b.113.4		20
16.13	even	4		384.3.i.d.353.4		20
24.5	odd	2		384.3.i.d.161.4		20
24.11	even	2		384.3.i.c.161.7		20
48.5	odd	4	inner	48.3.i.b.5.7	yes	20
48.11	even	4		192.3.i.b.113.1		20
48.29	odd	4		384.3.i.d.353.1		20
48.35	even	4		384.3.i.c.353.10		20

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

\(f(q)\)	\(=\)	\(q+(1.21144 + 1.59136i) q^{2} +(2.77106 + 1.14944i) q^{3} +(-1.06484 + 3.85566i) q^{4} +(-4.80434 - 4.80434i) q^{5} +(1.52779 + 5.80223i) q^{6} -7.36187i q^{7} +(-7.42573 + 2.97634i) q^{8} +(6.35757 + 6.37035i) q^{9} +O(q^{10})\)	\(q+(1.21144 + 1.59136i) q^{2} +(2.77106 + 1.14944i) q^{3} +(-1.06484 + 3.85566i) q^{4} +(-4.80434 - 4.80434i) q^{5} +(1.52779 + 5.80223i) 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} +(-7.38260 + 9.46029i) 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} +(-2.43571 + 17.8344i) q^{18} +(-21.1403 - 21.1403i) q^{19} +(23.6398 - 13.4080i) q^{20} +(8.46203 - 20.4002i) q^{21} +(-0.195543 + 1.44258i) q^{22} +7.80231 q^{23} +(-23.9983 - 0.287823i) q^{24} +21.1633i q^{25} +(-2.70873 + 19.9831i) q^{26} +(10.2949 + 24.9603i) q^{27} +(28.3849 + 7.83924i) q^{28} +(-34.6058 + 34.6058i) q^{29} +(20.5358 - 35.2159i) 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} +(-31.3317 + 17.7292i) 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} +(42.7152 - 11.2474i) q^{42} +(7.24058 - 7.24058i) q^{43} +(-2.53255 + 1.43641i) q^{44} +(0.0613789 - 61.1492i) q^{45} +(9.45200 + 12.4163i) q^{46} -23.0508i q^{47} +(-28.6144 - 38.5385i) q^{48} -5.19710 q^{49} +(-33.6784 + 25.6380i) q^{50} +(-12.7733 + 30.7938i) q^{51} +(-35.0817 + 19.8976i) q^{52} +(-31.9199 - 31.9199i) q^{53} +(-27.2492 + 46.6206i) 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} +(80.9190 - 9.98194i) 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} +(-2.20002 + 3.77271i) q^{66} +(41.1425 + 41.1425i) q^{67} +(-42.8465 - 11.8332i) q^{68} +(21.6207 + 8.96830i) q^{69} +(-99.1318 - 13.4374i) q^{70} +25.6785 q^{71} +(-66.1699 - 28.3822i) q^{72} +56.1845i q^{73} +(-51.2239 - 6.94346i) q^{74} +(-24.3260 + 58.6449i) q^{75} +(104.021 - 58.9988i) q^{76} +(3.78910 - 3.78910i) q^{77} +(-30.4754 + 52.2608i) 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} +(69.6454 + 54.3497i) 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} +(97.3847 - 73.9807i) q^{90} +(52.4878 - 52.4878i) q^{91} +(-8.30824 + 30.0830i) q^{92} +(68.9008 + 28.5802i) q^{93} +(36.6821 - 27.9246i) q^{94} +203.131i q^{95} +(26.6642 - 92.2227i) q^{96} -82.3636 q^{97} +(-6.29596 - 8.27045i) q^{98} +(-0.00657558 + 6.55097i) 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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