LMFDB - Embedded newform 63.4.f.b.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 $ x^16 - 3x^15 + 58x^14 - 129x^13 + 2107x^12 - 4455x^11 + 42901x^10 - 76404x^9 + 599392x^8 - 1089732x^7 + 4808401x^6 - 7939134x^5 + 26225236x^4 - 39450864x^3 + 62254768x^2 - 39660672*x + 21307456
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.7
Root			$-1.96709 + 3.40709i$ of defining polynomial
Character	$\chi$	$=$	63.43
Dual form			63.4.f.b.22.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.96709 - 3.40709i) q^{2} +(1.35403 - 5.01663i) q^{3} +(-3.73885 - 6.47588i) q^{4} +(1.21571 + 2.10567i) q^{5} +(-14.4286 - 14.4814i) q^{6} +(3.50000 - 6.06218i) q^{7} +2.05480 q^{8} +(-23.3332 - 13.5853i) q^{9} +O(q^{10})$	\(q+(1.96709 - 3.40709i) q^{2} +(1.35403 - 5.01663i) q^{3} +(-3.73885 - 6.47588i) q^{4} +(1.21571 + 2.10567i) q^{5} +(-14.4286 - 14.4814i) q^{6} +(3.50000 - 6.06218i) q^{7} +2.05480 q^{8} +(-23.3332 - 13.5853i) q^{9} +9.56561 q^{10} +(-21.0862 + 36.5223i) q^{11} +(-37.5496 + 9.98793i) q^{12} +(19.7866 + 34.2714i) q^{13} +(-13.7696 - 23.8496i) q^{14} +(12.2095 - 3.24763i) q^{15} +(33.9528 - 58.8079i) q^{16} -2.07697 q^{17} +(-92.1849 + 52.7750i) q^{18} +96.1013 q^{19} +(9.09070 - 15.7456i) q^{20} +(-25.6726 - 25.7666i) q^{21} +(82.9566 + 143.685i) q^{22} +(-36.8754 - 63.8701i) q^{23} +(2.78225 - 10.3082i) q^{24} +(59.5441 - 103.133i) q^{25} +155.688 q^{26} +(-99.7463 + 98.6594i) q^{27} -52.3439 q^{28} +(-9.60379 + 16.6342i) q^{29} +(12.9521 - 47.9871i) q^{30} +(119.748 + 207.410i) q^{31} +(-125.357 - 217.124i) q^{32} +(154.668 + 155.234i) q^{33} +(-4.08557 + 7.07642i) q^{34} +17.0199 q^{35} +(-0.737407 + 201.897i) q^{36} -144.310 q^{37} +(189.039 - 327.426i) q^{38} +(198.718 - 52.8577i) q^{39} +(2.49803 + 4.32672i) q^{40} +(36.1409 + 62.5979i) q^{41} +(-138.289 + 36.7840i) q^{42} +(-240.274 + 416.167i) q^{43} +315.352 q^{44} +(0.239772 - 65.6478i) q^{45} -290.148 q^{46} +(-147.354 + 255.224i) q^{47} +(-249.045 - 249.956i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-234.257 - 405.745i) q^{50} +(-2.81227 + 10.4194i) q^{51} +(147.958 - 256.271i) q^{52} -627.210 q^{53} +(139.932 + 533.916i) q^{54} -102.538 q^{55} +(7.19179 - 12.4565i) q^{56} +(130.124 - 482.105i) q^{57} +(37.7829 + 65.4420i) q^{58} +(-74.8093 - 129.573i) q^{59} +(-66.6807 - 66.9246i) q^{60} +(315.358 - 546.216i) q^{61} +942.221 q^{62} +(-164.023 + 93.9016i) q^{63} -443.106 q^{64} +(-48.1094 + 83.3279i) q^{65} +(833.141 - 221.610i) q^{66} +(-2.02124 - 3.50089i) q^{67} +(7.76547 + 13.4502i) q^{68} +(-370.343 + 98.5087i) q^{69} +(33.4796 - 57.9884i) q^{70} -798.373 q^{71} +(-47.9450 - 27.9150i) q^{72} +444.022 q^{73} +(-283.871 + 491.679i) q^{74} +(-436.758 - 438.356i) q^{75} +(-359.309 - 622.341i) q^{76} +(147.603 + 255.656i) q^{77} +(210.805 - 781.027i) q^{78} +(287.769 - 498.431i) q^{79} +165.107 q^{80} +(359.879 + 633.978i) q^{81} +284.369 q^{82} +(-645.117 + 1117.38i) q^{83} +(-70.8751 + 262.590i) q^{84} +(-2.52498 - 4.37340i) q^{85} +(945.280 + 1637.27i) q^{86} +(70.4441 + 70.7019i) q^{87} +(-43.3278 + 75.0459i) q^{88} +750.701 q^{89} +(-223.196 - 129.952i) q^{90} +277.012 q^{91} +(-275.744 + 477.602i) q^{92} +(1202.64 - 319.895i) q^{93} +(579.714 + 1004.09i) q^{94} +(116.831 + 202.357i) q^{95} +(-1258.97 + 334.877i) q^{96} +(-209.774 + 363.339i) q^{97} -192.774 q^{98} +(988.175 - 565.721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.96709	−	3.40709i	0.695470	−	1.20459i	−0.274552	−	0.961572i	$-0.588530\pi$
$2$	1.96709	−	3.40709i	0.695470	−	1.20459i	0.970022	−	0.243017i	$-0.0781371\pi$
$3$	1.35403	−	5.01663i	0.260583	−	0.965452i
$3$	1.35403	−	5.01663i	0.260583	−	0.965452i
$4$	−3.73885	−	6.47588i	−0.467357	−	0.809485i
$5$	1.21571	+	2.10567i	0.108736	+	0.188337i	0.915259	−	0.402867i	$-0.131986\pi$
$5$	1.21571	+	2.10567i	0.108736	+	0.188337i	−0.806522	+	0.591204i	$0.798653\pi$
$6$	−14.4286	−	14.4814i	−0.981745	−	0.985337i
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i
$8$	2.05480			0.0908100
$9$	−23.3332	−	13.5853i	−0.864193	−	0.503160i
$10$	9.56561			0.302491
$11$	−21.0862	+	36.5223i	−0.577975	+	1.00108i	0.417737	+	0.908568i	$0.362823\pi$
$11$	−21.0862	+	36.5223i	−0.577975	+	1.00108i	−0.995711	+	0.0925133i	$0.970510\pi$
$12$	−37.5496	+	9.98793i	−0.903304	+	0.240272i
$13$	19.7866	+	34.2714i	0.422139	+	0.731166i	0.996148	−	0.0876824i	$-0.0279460\pi$
$13$	19.7866	+	34.2714i	0.422139	+	0.731166i	−0.574009	+	0.818849i	$0.694613\pi$
$14$	−13.7696	−	23.8496i	−0.262863	−	0.455292i
$15$	12.2095	−	3.24763i	0.210165	−	0.0559023i
$16$	33.9528	−	58.8079i	0.530512	−	0.918874i
$17$	−2.07697			−0.0296317			−0.0148158	−	0.999890i	$-0.504716\pi$
$17$	−2.07697			−0.0296317			−0.0148158	+	0.999890i	$0.504716\pi$
$18$	−92.1849	+	52.7750i	−1.20712	+	0.691066i
$19$	96.1013			1.16038			0.580188	−	0.814483i	$-0.302979\pi$
$19$	96.1013			1.16038			0.580188	+	0.814483i	$0.302979\pi$
$20$	9.09070	−	15.7456i	0.101637	−	0.176041i
$21$	−25.6726	−	25.7666i	−0.266773	−	0.267749i
$22$	82.9566	+	143.685i	0.803928	+	1.39244i
$23$	−36.8754	−	63.8701i	−0.334307	−	0.579036i	0.649045	−	0.760750i	$-0.275169\pi$
$23$	−36.8754	−	63.8701i	−0.334307	−	0.579036i	−0.983351	+	0.181714i	$0.941836\pi$
$24$	2.78225	−	10.3082i	0.0236635	−	0.0876727i
$25$	59.5441	−	103.133i	0.476353	−	0.825067i
$26$	155.688			1.17434
$27$	−99.7463	+	98.6594i	−0.710970	+	0.703222i
$28$	−52.3439			−0.353288
$29$	−9.60379	+	16.6342i	−0.0614958	+	0.106514i	−0.895134	−	0.445797i	$-0.852920\pi$
$29$	−9.60379	+	16.6342i	−0.0614958	+	0.106514i	0.833638	+	0.552311i	$0.186254\pi$
$30$	12.9521	−	47.9871i	0.0788239	−	0.292040i
$31$	119.748	+	207.410i	0.693788	+	1.20168i	0.970587	+	0.240749i	$0.0773930\pi$
$31$	119.748	+	207.410i	0.693788	+	1.20168i	−0.276799	+	0.960928i	$0.589274\pi$
$32$	−125.357	−	217.124i	−0.692505	−	1.19945i
$33$	154.668	+	155.234i	0.815885	+	0.818871i
$34$	−4.08557	+	7.07642i	−0.0206079	+	0.0356940i
$35$	17.0199			0.0821968
$36$	−0.737407	+	201.897i	−0.00341392	+	0.934707i
$37$	−144.310			−0.641202			−0.320601	−	0.947214i	$-0.603885\pi$
$37$	−144.310			−0.641202			−0.320601	+	0.947214i	$0.603885\pi$
$38$	189.039	−	327.426i	0.807007	−	1.39778i
$39$	198.718	−	52.8577i	0.815908	−	0.217026i
$40$	2.49803	+	4.32672i	0.00987434	+	0.0171029i
$41$	36.1409	+	62.5979i	0.137665	+	0.238443i	0.926612	−	0.376018i	$-0.122707\pi$
$41$	36.1409	+	62.5979i	0.137665	+	0.238443i	−0.788947	+	0.614461i	$0.789374\pi$
$42$	−138.289	+	36.7840i	−0.508060	+	0.135140i
$43$	−240.274	+	416.167i	−0.852128	+	1.47593i	0.0271568	+	0.999631i	$0.491355\pi$
$43$	−240.274	+	416.167i	−0.852128	+	1.47593i	−0.879284	+	0.476297i	$0.841979\pi$
$44$	315.352			1.08048
$45$	0.239772	−	65.6478i	0.000794291	−	0.217471i
$46$	−290.148			−0.930001
$47$	−147.354	+	255.224i	−0.457313	+	0.792090i	−0.998818	−	0.0486079i	$-0.984522\pi$
$47$	−147.354	+	255.224i	−0.457313	+	0.792090i	0.541505	+	0.840698i	$0.317855\pi$
$48$	−249.045	−	249.956i	−0.748886	−	0.751626i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	−234.257	−	405.745i	−0.662578	−	1.14762i
$51$	−2.81227	+	10.4194i	−0.00772150	+	0.0286079i
$52$	147.958	−	256.271i	0.394579	−	0.683431i
$53$	−627.210			−1.62555			−0.812773	−	0.582580i	$-0.802043\pi$
$53$	−627.210			−1.62555			−0.812773	+	0.582580i	$0.802043\pi$
$54$	139.932	+	533.916i	0.352636	+	1.34550i
$55$	−102.538			−0.251387
$56$	7.19179	−	12.4565i	0.0171615	−	0.0297246i
$57$	130.124	−	482.105i	0.302374	−	1.12029i
$58$	37.7829	+	65.4420i	0.0855370	+	0.148154i
$59$	−74.8093	−	129.573i	−0.165074	−	0.285916i	0.771608	−	0.636098i	$-0.219453\pi$
$59$	−74.8093	−	129.573i	−0.165074	−	0.285916i	−0.936681	+	0.350183i	$0.886119\pi$
$60$	−66.6807	−	66.9246i	−0.143474	−	0.143999i
$61$	315.358	−	546.216i	0.661926	−	1.14649i	−0.318183	−	0.948029i	$-0.603073\pi$
$61$	315.358	−	546.216i	0.661926	−	1.14649i	0.980109	−	0.198460i	$-0.0635939\pi$
$62$	942.221			1.93004
$63$	−164.023	+	93.9016i	−0.328015	+	0.187785i
$64$	−443.106			−0.865442
$65$	−48.1094	+	83.3279i	−0.0918036	+	0.159009i
$66$	833.141	−	221.610i	1.55383	−	0.413307i
$67$	−2.02124	−	3.50089i	−0.00368558	−	0.00638361i	0.864177	−	0.503188i	$-0.167840\pi$
$67$	−2.02124	−	3.50089i	−0.00368558	−	0.00638361i	−0.867862	+	0.496805i	$0.834506\pi$
$68$	7.76547	+	13.4502i	0.0138486	+	0.0239864i
$69$	−370.343	+	98.5087i	−0.646146	+	0.171870i
$70$	33.4796	−	57.9884i	0.0571654	−	0.0990134i
$71$	−798.373			−1.33450			−0.667249	−	0.744835i	$-0.732528\pi$
$71$	−798.373			−1.33450			−0.667249	+	0.744835i	$0.732528\pi$
$72$	−47.9450	−	27.9150i	−0.0784774	−	0.0456919i
$73$	444.022			0.711902			0.355951	−	0.934505i	$-0.384157\pi$
$73$	444.022			0.711902			0.355951	+	0.934505i	$0.384157\pi$
$74$	−283.871	+	491.679i	−0.445937	+	0.772386i
$75$	−436.758	−	438.356i	−0.672433	−	0.674894i
$76$	−359.309	−	622.341i	−0.542309	−	0.939308i
$77$	147.603	+	255.656i	0.218454	+	0.378373i
$78$	210.805	−	781.027i	0.306013	−	1.13377i
$79$	287.769	−	498.431i	0.409830	−	0.709847i	−0.585040	−	0.811004i	$-0.698921\pi$
$79$	287.769	−	498.431i	0.409830	−	0.709847i	0.994870	+	0.101158i	$0.0322547\pi$
$80$	165.107			0.230744
$81$	359.879	+	633.978i	0.493661	+	0.869655i
$82$	284.369			0.382967
$83$	−645.117	+	1117.38i	−0.853143	+	1.47769i	0.0252150	+	0.999682i	$0.491973\pi$
$83$	−645.117	+	1117.38i	−0.853143	+	1.47769i	−0.878358	+	0.478004i	$0.841360\pi$
$84$	−70.8751	+	262.590i	−0.0920608	+	0.341083i
$85$	−2.52498	−	4.37340i	−0.00322204	−	0.00558073i
$86$	945.280	+	1637.27i	1.18526	+	2.05293i
$87$	70.4441	+	70.7019i	0.0868092	+	0.0871269i
$88$	−43.3278	+	75.0459i	−0.0524859	+	0.0909082i
$89$	750.701			0.894091			0.447046	−	0.894511i	$-0.352476\pi$
$89$	750.701			0.894091			0.447046	+	0.894511i	$0.352476\pi$
$90$	−223.196	−	129.952i	−0.261411	−	0.152201i
$91$	277.012			0.319107
$92$	−275.744	+	477.602i	−0.312481	+	0.541233i
$93$	1202.64	−	319.895i	1.34095	−	0.356683i
$94$	579.714	+	1004.09i	0.636095	+	1.10175i
$95$	116.831	+	202.357i	0.126175	+	0.218541i
$96$	−1258.97	+	334.877i	−1.33847	+	0.356024i
$97$	−209.774	+	363.339i	−0.219581	+	0.380325i	−0.954680	−	0.297635i	$-0.903802\pi$
$97$	−209.774	+	363.339i	−0.219581	+	0.380325i	0.735099	+	0.677960i	$0.237136\pi$
$98$	−192.774			−0.198706
$99$	988.175	−	565.721i	1.00319	−	0.574314i
$100$	−890.507			−0.890507
$101$	−452.812	+	784.293i	−0.446103	+	0.772674i	−0.998128	−	0.0611539i	$-0.980522\pi$
$101$	−452.812	+	784.293i	−0.446103	+	0.772674i	0.552025	+	0.833828i	$0.313855\pi$
$102$	29.9678	+	30.0775i	0.0290907	+	0.0291972i
$103$	−1033.87	−	1790.71i	−0.989030	−	1.71305i	−0.622439	−	0.782668i	$-0.713858\pi$
$103$	−1033.87	−	1790.71i	−0.989030	−	1.71305i	−0.366591	−	0.930382i	$-0.619475\pi$
$104$	40.6574	+	70.4206i	0.0383345	+	0.0663972i
$105$	23.0454	−	85.3826i	0.0214191	−	0.0793571i
$106$	−1233.78	+	2136.96i	−1.13052	+	1.95812i
$107$	1728.25			1.56146			0.780730	−	0.624869i	$-0.214848\pi$
$107$	1728.25			1.56146			0.780730	+	0.624869i	$0.214848\pi$
$108$	1011.84	+	277.073i	0.901525	+	0.246864i
$109$	925.211			0.813020			0.406510	−	0.913646i	$-0.366746\pi$
$109$	925.211			0.813020			0.406510	+	0.913646i	$0.366746\pi$
$110$	−201.702	+	349.358i	−0.174832	+	0.302818i
$111$	−195.400	+	723.953i	−0.167086	+	0.619050i
$112$	−237.669	−	411.656i	−0.200515	−	0.347302i
$113$	−1093.61	−	1894.18i	−0.910424	−	1.57690i	−0.813467	−	0.581612i	$-0.802422\pi$
$113$	−1093.61	−	1894.18i	−0.910424	−	1.57690i	−0.0969571	−	0.995289i	$-0.530911\pi$
$114$	−1386.61	−	1391.69i	−1.13919	−	1.14336i
$115$	89.6595	−	155.295i	0.0727025	−	0.125924i
$116$	143.629			0.114962
$117$	3.90247	−	1068.47i	0.00308362	−	0.844273i
$118$	−588.625			−0.459215
$119$	−7.26938	+	12.5909i	−0.00559986	+	0.00969924i
$120$	25.0880	−	6.67322i	0.0190851	−	0.00507649i
$121$	−223.753	−	387.552i	−0.168109	−	0.291174i
$122$	−1240.67	−	2148.91i	−0.920699	−	1.59470i
$123$	362.967	−	96.5465i	0.266078	−	0.0707748i
$124$	895.443	−	1550.95i	0.648493	−	1.12322i
$125$	593.480			0.424660
$126$	−2.71575	+	743.553i	−0.00192015	+	0.525722i
$127$	898.130			0.627529			0.313764	−	0.949501i	$-0.398410\pi$
$127$	898.130			0.627529			0.313764	+	0.949501i	$0.398410\pi$
$128$	131.227	−	227.291i	0.0906165	−	0.156952i
$129$	1762.42	+	1768.87i	1.20289	+	1.20729i
$130$	189.271	+	327.826i	0.127693	+	0.221171i
$131$	−1067.26	−	1848.56i	−0.711812	−	1.23289i	−0.964176	−	0.265262i	$-0.914541\pi$
$131$	−1067.26	−	1848.56i	−0.711812	−	1.23289i	0.252364	−	0.967632i	$-0.418792\pi$
$132$	426.996	−	1582.01i	0.281554	−	1.04315i
$133$	336.355	−	582.583i	0.219290	−	0.379822i
$134$	−15.9038			−0.0102528
$135$	−329.006	−	90.0917i	−0.209751	−	0.0574360i
$136$	−4.26774			−0.00269085
$137$	1080.63	−	1871.71i	0.673901	−	1.16723i	−0.302888	−	0.953026i	$-0.597951\pi$
$137$	1080.63	−	1871.71i	0.673901	−	1.16723i	0.976789	−	0.214205i	$-0.0687160\pi$
$138$	−392.869	+	1455.57i	−0.242342	+	0.897871i
$139$	−1150.08	−	1992.00i	−0.701789	−	1.21553i	−0.967838	−	0.251575i	$-0.919052\pi$
$139$	−1150.08	−	1992.00i	−0.701789	−	1.21553i	0.266049	−	0.963960i	$-0.414282\pi$
$140$	−63.6349	−	110.219i	−0.0384152	−	0.0665371i
$141$	1080.84	+	1084.80i	0.645557	+	0.647919i
$142$	−1570.47	+	2720.13i	−0.928103	+	1.60752i
$143$	−1668.89			−0.975943
$144$	−1591.15	+	910.920i	−0.920806	+	0.527153i
$145$	−46.7016			−0.0267473
$146$	873.430	−	1512.82i	0.495107	−	0.857550i
$147$	−246.056	+	65.4491i	−0.138057	+	0.0367221i
$148$	539.556	+	934.538i	0.299670	+	0.519044i
$149$	591.768	+	1024.97i	0.325366	+	0.563551i	0.981586	−	0.191019i	$-0.0611791\pi$
$149$	591.768	+	1024.97i	0.325366	+	0.563551i	−0.656220	+	0.754569i	$0.727846\pi$
$150$	−2352.66	+	625.791i	−1.28063	+	0.340638i
$151$	−1718.81	+	2977.06i	−0.926322	+	1.60444i	−0.136901	+	0.990585i	$0.543714\pi$
$151$	−1718.81	+	2977.06i	−0.926322	+	1.60444i	−0.789421	+	0.613852i	$0.789619\pi$
$152$	197.469			0.105374
$153$	48.4623	+	28.2162i	0.0256075	+	0.0149095i
$154$	1161.39			0.607712
$155$	−291.158	+	504.300i	−0.150880	+	0.261331i
$156$	−1085.28	−	1089.25i	−0.556999	−	0.559037i
$157$	10.4307	+	18.0665i	0.00530229	+	0.00918383i	0.868664	−	0.495401i	$-0.164979\pi$
$157$	10.4307	+	18.0665i	0.00530229	+	0.00918383i	−0.863362	+	0.504585i	$0.831646\pi$
$158$	−1132.13	−	1960.91i	−0.570049	−	0.987354i
$159$	−849.260	+	3146.49i	−0.423589	+	1.56939i
$160$	304.795	−	527.920i	0.150601	−	0.260848i
$161$	−516.256			−0.252712
$162$	2867.93	+	20.9500i	1.39090	+	0.0101604i
$163$	−1654.46			−0.795015			−0.397507	−	0.917599i	$-0.630125\pi$
$163$	−1654.46			−0.795015			−0.397507	+	0.917599i	$0.630125\pi$
$164$	270.251	−	468.089i	0.128677	−	0.222876i
$165$	−138.840	+	514.398i	−0.0655071	+	0.242702i
$166$	2538.00	+	4395.95i	1.18667	+	2.05537i
$167$	980.611	+	1698.47i	0.454383	+	0.787014i	0.998652	−	0.0518963i	$-0.0165265\pi$
$167$	980.611	+	1698.47i	0.454383	+	0.787014i	−0.544270	+	0.838910i	$0.683193\pi$
$168$	−52.7520	−	52.9450i	−0.0242256	−	0.0243143i
$169$	315.483	−	546.433i	0.143597	−	0.248718i
$170$	−19.8674			−0.00896331
$171$	−2242.35	−	1305.57i	−1.00279	−	0.583855i
$172$	3593.40			1.59299
$173$	13.6713	−	23.6794i	0.00600816	−	0.0104064i	−0.863006	−	0.505194i	$-0.831421\pi$
$173$	13.6713	−	23.6794i	0.00600816	−	0.0104064i	0.869014	+	0.494788i	$0.164754\pi$
$174$	379.458	−	100.933i	0.165325	−	0.0439754i
$175$	−416.809	−	721.934i	−0.180044	−	0.311846i
$176$	1431.87	+	2480.07i	0.613245	+	1.06217i
$177$	−751.316	+	199.845i	−0.319053	+	0.0848658i
$178$	1476.69	−	2557.71i	0.621813	−	1.07701i
$179$	130.832			0.0546302			0.0273151	−	0.999627i	$-0.491304\pi$
$179$	130.832			0.0546302			0.0273151	+	0.999627i	$0.491304\pi$
$180$	−426.024	+	243.895i	−0.176411	+	0.100994i
$181$	2460.11			1.01027			0.505134	−	0.863041i	$-0.331443\pi$
$181$	2460.11			1.01027			0.505134	+	0.863041i	$0.331443\pi$
$182$	544.906	−	943.806i	0.221929	−	0.384393i
$183$	−2313.16	−	2321.63i	−0.934393	−	0.937812i
$184$	−75.7715	−	131.240i	−0.0303584	−	0.0525823i
$185$	−175.439	−	303.870i	−0.0697219	−	0.120762i
$186$	1275.79	−	4726.78i	0.502934	−	1.86336i
$187$	43.7953	−	75.8556i	0.0171264	−	0.0296637i
$188$	2203.73			0.854914
$189$	248.978	+	949.988i	0.0958228	+	0.365616i
$190$	919.267			0.351003
$191$	654.703	−	1133.98i	0.248024	−	0.429591i	−0.714953	−	0.699172i	$-0.753552\pi$
$191$	654.703	−	1133.98i	0.248024	−	0.429591i	0.962978	+	0.269581i	$0.0868853\pi$
$192$	−599.978	+	2222.90i	−0.225519	+	0.835543i
$193$	−431.867	−	748.016i	−0.161070	−	0.278981i	0.774183	−	0.632962i	$-0.218161\pi$
$193$	−431.867	−	748.016i	−0.161070	−	0.278981i	−0.935253	+	0.353981i	$0.884828\pi$
$194$	825.287	+	1429.44i	0.305424	+	0.529009i
$195$	352.884	+	354.175i	0.129593	+	0.130067i
$196$	−183.204	+	317.318i	−0.0667652	+	0.115641i
$197$	2958.90			1.07012			0.535058	−	0.844815i	$-0.320290\pi$
$197$	2958.90			1.07012			0.535058	+	0.844815i	$0.320290\pi$
$198$	16.3614	−	4479.63i	0.00587249	−	1.60784i
$199$	−1559.83			−0.555646			−0.277823	−	0.960632i	$-0.589613\pi$
$199$	−1559.83			−0.555646			−0.277823	+	0.960632i	$0.589613\pi$
$200$	122.351	−	211.918i	0.0432576	−	0.0749244i
$201$	−20.2995	+	5.39952i	−0.00712346	+	0.00189479i
$202$	1781.44	+	3085.54i	0.620503	+	1.07474i
$203$	67.2265	+	116.440i	0.0232432	+	0.0402585i
$204$	77.9893	−	20.7446i	0.0267664	−	0.00711967i
$205$	−87.8736	+	152.202i	−0.0299383	+	0.0518547i
$206$	−8134.83			−2.75136
$207$	−7.27288	+	1991.26i	−0.00244203	+	0.668609i
$208$	2687.24			0.895800
$209$	−2026.41	+	3509.84i	−0.670668	+	1.16163i
$210$	−245.574	−	246.473i	−0.0806964	−	0.0809916i
$211$	−1253.20	−	2170.60i	−0.408880	−	0.708201i	0.585885	−	0.810394i	$-0.300747\pi$
$211$	−1253.20	−	2170.60i	−0.408880	−	0.708201i	−0.994765	+	0.102194i	$0.967414\pi$
$212$	2345.05	+	4061.74i	0.759710	+	1.31586i
$213$	−1081.02	+	4005.14i	−0.347747	+	1.28839i
$214$	3399.61	−	5888.31i	1.08595	−	1.88092i
$215$	−1168.41			−0.370628
$216$	−204.958	+	202.725i	−0.0645632	+	0.0638596i
$217$	1676.48			0.524455
$218$	1819.97	−	3152.28i	0.565431	−	0.979355i
$219$	601.218	−	2227.50i	0.185509	−	0.687307i
$220$	383.376	+	664.027i	0.117487	+	0.203494i
$221$	−41.0961	−	71.1805i	−0.0125087	−	0.0216657i
$222$	2082.20	+	2089.82i	0.629497	+	0.631801i
$223$	−2024.21	+	3506.03i	−0.607851	+	1.05283i	0.383743	+	0.923440i	$0.374635\pi$
$223$	−2024.21	+	3506.03i	−0.607851	+	1.05283i	−0.991594	+	0.129389i	$0.958698\pi$
$224$	−1755.00			−0.523485
$225$	−2790.46	+	1597.51i	−0.826802	+	0.473336i
$226$	−8604.87			−2.53269
$227$	313.734	−	543.404i	0.0917325	−	0.158885i	−0.816508	−	0.577335i	$-0.804093\pi$
$227$	313.734	−	543.404i	0.0917325	−	0.158885i	0.908240	+	0.418449i	$0.137426\pi$
$228$	−3608.57	+	959.853i	−1.04817	+	0.278806i
$229$	494.563	+	856.608i	0.142715	+	0.247189i	0.928518	−	0.371288i	$-0.121084\pi$
$229$	494.563	+	856.608i	0.142715	+	0.247189i	−0.785803	+	0.618476i	$0.787750\pi$
$230$	−352.736	−	610.956i	−0.101125	−	0.175153i
$231$	1482.39	−	394.306i	0.422226	−	0.112309i
$232$	−19.7338	+	34.1800i	−0.00558444	+	0.00967253i
$233$	−3125.53			−0.878799			−0.439399	−	0.898292i	$-0.644809\pi$
$233$	−3125.53			−0.878799			−0.439399	+	0.898292i	$0.644809\pi$
$234$	−3632.69	−	2115.06i	−1.01486	−	0.590881i
$235$	−716.555			−0.198906
$236$	−559.402	+	968.912i	−0.154296	+	0.267249i
$237$	−2110.80	−	2118.52i	−0.578528	−	0.580645i
$238$	28.5990	+	49.5349i	0.00778907	+	0.0134911i
$239$	1512.51	+	2619.75i	0.409357	+	0.709027i	0.994818	−	0.101674i	$-0.0324197\pi$
$239$	1512.51	+	2619.75i	0.409357	+	0.709027i	−0.585461	+	0.810701i	$0.699086\pi$
$240$	223.559	−	828.279i	0.0601277	−	0.222772i
$241$	2799.43	−	4848.75i	0.748245	−	1.29600i	−0.200419	−	0.979710i	$-0.564230\pi$
$241$	2799.43	−	4848.75i	0.748245	−	1.29600i	0.948663	−	0.316288i	$-0.102436\pi$
$242$	−1760.57			−0.467659
$243$	3667.72	−	946.955i	0.968249	−	0.249989i
$244$	−4716.31			−1.23742
$245$	59.5697	−	103.178i	0.0155337	−	0.0269052i
$246$	385.043	−	1426.58i	0.0997946	−	0.369736i
$247$	1901.52	+	3293.52i	0.489840	+	0.848428i
$248$	246.058	+	426.186i	0.0630029	+	0.109124i
$249$	4731.96	+	4749.27i	1.20432	+	1.20873i
$250$	1167.43	−	2022.04i	0.295338	−	0.511540i
$251$	2960.32			0.744438			0.372219	−	0.928145i	$-0.378597\pi$
$251$	2960.32			0.744438			0.372219	+	0.928145i	$0.378597\pi$
$252$	1221.35	+	711.109i	0.305310	+	0.177760i
$253$	3110.25			0.772883
$254$	1766.70	−	3060.01i	0.436427	−	0.755915i
$255$	−25.3586	+	6.74522i	−0.00622753	+	0.00165648i
$256$	−2288.69	−	3964.13i	−0.558763	−	0.967806i
$257$	−2997.84	−	5192.41i	−0.727627	−	1.26029i	−0.957884	−	0.287157i	$-0.907290\pi$
$257$	−2997.84	−	5192.41i	−0.727627	−	1.26029i	0.230256	−	0.973130i	$-0.426044\pi$
$258$	9493.54	−	2525.21i	2.29086	−	0.609352i
$259$	−505.087	+	874.836i	−0.121176	+	0.209883i
$260$	719.496			0.171620
$261$	450.069	−	257.660i	0.106738	−	0.0611064i
$262$	−8397.61			−1.98017
$263$	−891.843	+	1544.72i	−0.209100	+	0.362172i	−0.951431	−	0.307861i	$-0.900387\pi$
$263$	−891.843	+	1544.72i	−0.209100	+	0.362172i	0.742331	+	0.670033i	$0.233720\pi$
$264$	317.811	+	318.974i	0.0740906	+	0.0743617i
$265$	−762.505	−	1320.70i	−0.176756	−	0.306150i
$266$	−1323.28	−	2291.98i	−0.305020	−	0.528310i
$267$	1016.47	−	3765.99i	0.232985	−	0.863202i
$268$	−15.1142	+	26.1786i	−0.00344496	+	0.00596684i
$269$	6348.32			1.43890			0.719450	−	0.694545i	$-0.244394\pi$
$269$	6348.32			1.43890			0.719450	+	0.694545i	$0.244394\pi$
$270$	−954.134	+	943.736i	−0.215062	+	0.212718i
$271$	−6712.35			−1.50460			−0.752299	−	0.658822i	$-0.771055\pi$
$271$	−6712.35			−1.50460			−0.752299	+	0.658822i	$0.771055\pi$
$272$	−70.5188	+	122.142i	−0.0157200	+	0.0272278i
$273$	375.082	−	1389.67i	0.0831538	−	0.308083i
$274$	−4251.38	−	7363.61i	−0.937356	−	1.62355i
$275$	2511.11	+	4349.38i	0.550640	+	0.953736i
$276$	2022.59	+	2029.99i	0.441107	+	0.442721i
$277$	−1138.28	+	1971.56i	−0.246905	+	0.427653i	−0.962666	−	0.270693i	$-0.912747\pi$
$277$	−1138.28	+	1971.56i	−0.246905	+	0.427653i	0.715760	+	0.698346i	$0.246080\pi$
$278$	−9049.24			−1.95229
$279$	23.6178	−	6466.37i	0.00506795	−	1.38757i
$280$	34.9724			0.00746430
$281$	742.994	−	1286.90i	0.157734	−	0.273203i	−0.776317	−	0.630343i	$-0.782914\pi$
$281$	742.994	−	1286.90i	0.157734	−	0.273203i	0.934051	+	0.357139i	$0.116248\pi$
$282$	5822.12	−	1548.64i	1.22944	−	0.327022i
$283$	4505.10	+	7803.06i	0.946291	+	1.63902i	0.753146	+	0.657853i	$0.228535\pi$
$283$	4505.10	+	7803.06i	0.946291	+	1.63902i	0.193144	+	0.981170i	$0.438132\pi$
$284$	2985.00	+	5170.17i	0.623687	+	1.08026i
$285$	1173.35	−	312.101i	0.243870	−	0.0648677i
$286$	−3282.85	+	5686.07i	−0.678739	+	1.17561i
$287$	505.973			0.104065
$288$	−24.7239	+	6769.23i	−0.00505858	+	1.38500i
$289$	−4908.69			−0.999122
$290$	−91.8660	+	159.117i	−0.0186019	+	0.0322195i
$291$	1538.70	+	1544.33i	0.309966	+	0.311101i
$292$	−1660.13	−	2875.44i	−0.332712	−	0.576274i
$293$	−3767.56	−	6525.60i	−0.751205	−	1.30113i	−0.947239	−	0.320528i	$-0.896140\pi$
$293$	−3767.56	−	6525.60i	−0.751205	−	1.30113i	0.196034	−	0.980597i	$-0.437194\pi$
$294$	−261.022	+	967.079i	−0.0517792	+	0.191841i
$295$	181.892	−	315.047i	0.0358989	−	0.0621788i
$296$	−296.529			−0.0582276
$297$	−1500.00	−	5723.32i	−0.293060	−	1.11818i
$298$	4656.24			0.905129
$299$	1459.28	−	2527.54i	0.282248	−	0.488868i
$300$	−1205.77	+	4467.35i	−0.232051	+	0.859741i
$301$	1681.92	+	2913.17i	0.322074	+	0.557848i
$302$	6762.09	+	11712.3i	1.28846	+	2.23167i
$303$	3321.39	+	3333.54i	0.629732	+	0.632036i
$304$	3262.91	−	5651.52i	0.615594	−	1.06624i
$305$	1533.53			0.287901
$306$	191.465	−	109.612i	0.0357690	−	0.0204774i
$307$	2765.48			0.514119			0.257059	−	0.966396i	$-0.417246\pi$
$307$	2765.48			0.514119			0.257059	+	0.966396i	$0.417246\pi$
$308$	1103.73	−	1911.72i	0.204192	−	0.353670i
$309$	−10383.2	+	2761.87i	−1.91159	+	0.508470i
$310$	1145.47	+	1984.00i	0.209865	+	0.363496i
$311$	1507.11	+	2610.39i	0.274792	+	0.475953i	0.970083	−	0.242775i	$-0.0780578\pi$
$311$	1507.11	+	2610.39i	0.274792	+	0.475953i	−0.695291	+	0.718728i	$0.744724\pi$
$312$	408.326	−	108.612i	0.0740926	−	0.0197081i
$313$	−1374.07	+	2379.96i	−0.248138	+	0.429787i	−0.963009	−	0.269469i	$-0.913152\pi$
$313$	−1374.07	+	2379.96i	−0.248138	+	0.429787i	0.714871	+	0.699256i	$0.246485\pi$
$314$	82.0722			0.0147503
$315$	−397.129	−	231.221i	−0.0710340	−	0.0413581i
$316$	−4303.71			−0.766147
$317$	−1966.70	+	3406.42i	−0.348457	+	0.603545i	−0.985976	−	0.166890i	$-0.946627\pi$
$317$	−1966.70	+	3406.42i	−0.348457	+	0.603545i	0.637519	+	0.770435i	$0.279961\pi$
$318$	9049.80	+	9082.91i	1.59587	+	1.60171i
$319$	−405.014	−	701.505i	−0.0710860	−	0.123125i
$320$	−538.688	−	933.035i	−0.0941049	−	0.162994i
$321$	2340.10	−	8669.99i	0.406889	−	1.50751i
$322$	−1015.52	+	1758.93i	−0.175754	+	0.304414i
$323$	−199.599			−0.0343839
$324$	2760.04	−	4700.88i	0.473257	−	0.806050i
$325$	4712.70			0.804349
$326$	−3254.47	+	5636.90i	−0.552909	+	0.957666i
$327$	1252.76	−	4641.45i	0.211859	−	0.784931i
$328$	74.2622	+	128.626i	0.0125014	+	0.0216530i
$329$	1031.47	+	1786.57i	0.172848	+	0.299382i
$330$	1479.49	+	1484.91i	0.246798	+	0.247701i
$331$	−2302.21	+	3987.55i	−0.382299	+	0.662161i	−0.991390	−	0.130939i	$-0.958201\pi$
$331$	−2302.21	+	3987.55i	−0.382299	+	0.662161i	0.609092	+	0.793100i	$0.291534\pi$
$332$	9648.00			1.59489
$333$	3367.23	+	1960.50i	0.554123	+	0.322627i
$334$	7715.78			1.26404
$335$	4.91447	−	8.51211i	0.000801511	−	0.00138826i
$336$	−2386.94	+	634.908i	−0.387554	+	0.103087i
$337$	−1386.37	−	2401.26i	−0.224096	−	0.388146i	0.731952	−	0.681356i	$-0.238610\pi$
$337$	−1386.37	−	2401.26i	−0.224096	−	0.388146i	−0.956048	+	0.293211i	$0.905276\pi$
$338$	−1241.16	−	2149.76i	−0.199735	−	0.345951i
$339$	−10983.2	+	2921.45i	−1.75966	+	0.468057i
$340$	−18.8811	+	32.7030i	−0.00301168	+	0.00521638i
$341$	−10100.1			−1.60397
$342$	−8859.08	+	5071.74i	−1.40071	+	0.801896i
$343$	−343.000			−0.0539949
$344$	−493.715	+	855.139i	−0.0773817	+	0.134029i
$345$	−657.656	−	660.062i	−0.102629	−	0.103004i
$346$	−53.7854	−	93.1590i	−0.00835699	−	0.0144747i
$347$	−4211.45	−	7294.44i	−0.651534	−	1.12849i	−0.982751	−	0.184935i	$-0.940792\pi$
$347$	−4211.45	−	7294.44i	−0.651534	−	1.12849i	0.331217	−	0.943555i	$-0.392541\pi$
$348$	194.477	−	720.532i	0.0299571	−	0.110990i
$349$	1939.99	−	3360.15i	0.297550	−	0.515372i	−0.678025	−	0.735039i	$-0.737164\pi$
$349$	1939.99	−	3360.15i	0.297550	−	0.515372i	0.975575	+	0.219667i	$0.0704971\pi$
$350$	−3279.59			−0.500862
$351$	−5354.83	−	1466.31i	−0.814301	−	0.222980i
$352$	10573.2			1.60100
$353$	−1962.36	+	3398.91i	−0.295881	+	0.512481i	−0.975190	−	0.221372i	$-0.928947\pi$
$353$	−1962.36	+	3398.91i	−0.295881	+	0.512481i	0.679308	+	0.733853i	$0.262280\pi$
$354$	−797.014	+	2952.92i	−0.119663	+	0.443349i
$355$	−970.588	−	1681.11i	−0.145108	−	0.251335i
$356$	−2806.76	−	4861.45i	−0.417859	−	0.723754i
$357$	53.3212	+	53.5163i	0.00790492	+	0.00793385i
$358$	257.357	−	445.755i	0.0379937	−	0.0658069i
$359$	6623.52			0.973749			0.486874	−	0.873472i	$-0.338137\pi$
$359$	6623.52			0.973749			0.486874	+	0.873472i	$0.338137\pi$
$360$	0.492682	−	134.893i	7.21296e−5	−	0.0197485i
$361$	2376.46			0.346473
$362$	4839.24	−	8381.82i	0.702611	−	1.21696i
$363$	−2247.17	+	597.732i	−0.324920	+	0.0864265i
$364$	−1035.71	−	1793.90i	−0.149137	−	0.258313i
$365$	539.801	+	934.963i	0.0774095	+	0.134077i
$366$	−12460.2	+	3314.32i	−1.77952	+	0.473340i
$367$	4605.97	−	7977.77i	0.655122	−	1.13470i	−0.326742	−	0.945114i	$-0.605951\pi$
$367$	4605.97	−	7977.77i	0.655122	−	1.13470i	0.981863	−	0.189590i	$-0.0607159\pi$
$368$	−5008.09			−0.709415
$369$	7.12801	−	1951.60i	0.00100561	−	0.275328i
$370$	−1380.42			−0.193958
$371$	−2195.24	+	3802.26i	−0.307199	+	0.532085i
$372$	−6568.11	−	6592.14i	−0.915431	−	0.918781i
$373$	3763.16	+	6517.99i	0.522384	+	0.904796i	0.999661	+	0.0260427i	$0.00829058\pi$
$373$	3763.16	+	6517.99i	0.522384	+	0.904796i	−0.477277	+	0.878753i	$0.658376\pi$
$374$	−172.298	−	298.429i	−0.0238217	−	0.0412604i
$375$	803.588	−	2977.27i	0.110659	−	0.409988i
$376$	−302.781	+	524.433i	−0.0415286	+	0.0719297i
$377$	−760.104			−0.103839
$378$	3726.46	+	1020.42i	0.507059	+	0.138848i
$379$	9542.86			1.29336			0.646681	−	0.762761i	$-0.276157\pi$
$379$	9542.86			1.29336			0.646681	+	0.762761i	$0.276157\pi$
$380$	873.628	−	1513.17i	0.117937	−	0.204273i
$381$	1216.09	−	4505.59i	0.163523	−	0.605849i
$382$	−2575.71	−	4461.27i	−0.344987	−	0.597535i
$383$	1896.64	+	3285.08i	0.253039	+	0.438276i	0.964361	−	0.264590i	$-0.0852366\pi$
$383$	1896.64	+	3285.08i	0.253039	+	0.438276i	−0.711322	+	0.702866i	$0.751903\pi$
$384$	−962.553	−	966.075i	−0.127917	−	0.128385i
$385$	−358.885	+	621.607i	−0.0475077	+	0.0822857i
$386$	−3398.08			−0.448077
$387$	11260.1	−	6446.32i	1.47903	−	0.846731i
$388$	3137.26			0.410490
$389$	3089.58	−	5351.31i	0.402694	−	0.697486i	−0.591356	−	0.806411i	$-0.701407\pi$
$389$	3089.58	−	5351.31i	0.402694	−	0.697486i	0.994050	+	0.108924i	$0.0347406\pi$
$390$	1900.86	−	505.616i	0.246805	−	0.0656483i
$391$	76.5890	+	132.656i	0.00990607	+	0.0171578i
$392$	−50.3425	−	87.1958i	−0.00648643	−	0.0112348i
$393$	−10718.6	+	2851.08i	−1.37579	+	0.365949i
$394$	5820.41	−	10081.2i	0.744233	−	1.28905i
$395$	1399.37			0.178253
$396$	−7358.19	−	4284.16i	−0.933744	−	0.543654i
$397$	179.912			0.0227444			0.0113722	−	0.999935i	$-0.496380\pi$
$397$	179.912			0.0227444			0.0113722	+	0.999935i	$0.496380\pi$
$398$	−3068.32	+	5314.49i	−0.386435	+	0.669325i
$399$	−2467.17	−	2476.20i	−0.309557	−	0.310689i
$400$	−4043.38	−	7003.33i	−0.505422	−	0.875417i
$401$	−3651.73	−	6324.98i	−0.454760	−	0.787667i	0.543915	−	0.839140i	$-0.316941\pi$
$401$	−3651.73	−	6324.98i	−0.454760	−	0.787667i	−0.998674	+	0.0514737i	$0.983608\pi$
$402$	−21.5342	+	79.7835i	−0.00267171	+	0.00989861i
$403$	−4738.82	+	8207.87i	−0.585750	+	1.01455i
$404$	6771.98			0.833957
$405$	−897.440	+	1528.52i	−0.110109	+	0.187537i
$406$	528.961			0.0646599
$407$	3042.95	−	5270.55i	0.370599	−	0.641896i
$408$	−5.77864	+	21.4097i	−0.000701189	+	0.00259789i
$409$	1055.98	+	1829.01i	0.127664	+	0.221121i	0.922771	−	0.385348i	$-0.125919\pi$
$409$	1055.98	+	1829.01i	0.127664	+	0.221121i	−0.795107	+	0.606469i	$0.792585\pi$
$410$	345.710	+	598.787i	0.0416424	+	0.0721268i
$411$	−7926.46	−	7955.47i	−0.951298	−	0.954779i
$412$	−7730.96	+	13390.4i	−0.924459	+	1.60121i
$413$	−1047.33			−0.124784
$414$	6770.10	+	3941.76i	0.803701	+	0.467939i
$415$	−3137.10			−0.371070
$416$	4960.77	−	8592.30i	0.584667	−	1.01267i
$417$	−11550.4	+	3072.32i	−1.35641	+	0.360796i
$418$	7972.24	+	13808.3i	0.932859	+	1.61576i
$419$	2862.87	+	4958.63i	0.333795	+	0.578151i	0.983253	−	0.182247i	$-0.0583372\pi$
$419$	2862.87	+	4958.63i	0.333795	+	0.578151i	−0.649457	+	0.760398i	$0.725004\pi$
$420$	−639.091	+	169.994i	−0.0742487	+	0.0197496i
$421$	−2633.26	+	4560.94i	−0.304839	+	0.527997i	−0.977225	−	0.212204i	$-0.931936\pi$
$421$	−2633.26	+	4560.94i	−0.304839	+	0.527997i	0.672386	+	0.740200i	$0.265269\pi$
$422$	−9860.59			−1.13745
$423$	6905.53	−	3953.35i	0.793755	−	0.454417i
$424$	−1288.79			−0.147616
$425$	−123.671	+	214.205i	−0.0141151	+	0.0244481i
$426$	11519.4	+	11561.6i	1.31014	+	1.31493i
$427$	−2207.51	−	3823.51i	−0.250184	−	0.433332i
$428$	−6461.67	−	11191.9i	−0.729758	−	1.26398i
$429$	−2259.73	+	8372.22i	−0.254314	+	0.942225i
$430$	−2298.37	+	3980.89i	−0.257761	+	0.446455i
$431$	15827.4			1.76886			0.884430	−	0.466672i	$-0.154547\pi$
$431$	15827.4			1.76886			0.884430	+	0.466672i	$0.154547\pi$
$432$	2415.29	+	9215.64i	0.268994	+	1.02636i
$433$	4537.27			0.503574			0.251787	−	0.967783i	$-0.418982\pi$
$433$	4537.27			0.503574			0.251787	+	0.967783i	$0.418982\pi$
$434$	3297.77	−	5711.91i	0.364742	−	0.631752i
$435$	−63.2352	+	234.285i	−0.00696988	+	0.0258232i
$436$	−3459.23	−	5991.56i	−0.379970	−	0.658128i
$437$	−3543.78	−	6138.00i	−0.387922	−	0.671900i
$438$	−6406.64	−	6430.08i	−0.698907	−	0.701464i
$439$	−4463.41	+	7730.85i	−0.485255	+	0.840486i	−0.999856	−	0.0169432i	$-0.994607\pi$
$439$	−4463.41	+	7730.85i	−0.485255	+	0.840486i	0.514601	+	0.857429i	$0.327940\pi$
$440$	−210.696			−0.0228285
$441$	−4.83209	+	1322.99i	−0.000521768	+	0.142856i
$442$	−323.358			−0.0347977
$443$	3222.48	−	5581.50i	0.345609	−	0.598612i	−0.639856	−	0.768495i	$-0.721006\pi$
$443$	3222.48	−	5581.50i	0.345609	−	0.598612i	0.985464	+	0.169884i	$0.0543392\pi$
$444$	5418.81	−	1441.36i	0.579201	−	0.154063i
$445$	912.632	+	1580.73i	0.0972201	+	0.168390i
$446$	7963.57	+	13793.3i	0.845484	+	1.46442i
$447$	5943.18	−	1580.84i	0.628866	−	0.167274i
$448$	−1550.87	+	2686.19i	−0.163553	+	0.283282i
$449$	−6202.27			−0.651901			−0.325950	−	0.945387i	$-0.605684\pi$
$449$	−6202.27			−0.651901			−0.325950	+	0.945387i	$0.605684\pi$
$450$	−46.2021	+	12649.8i	−0.00483997	+	1.32515i
$451$	−3048.29			−0.318267
$452$	−8177.67	+	14164.1i	−0.850985	+	1.47395i
$453$	12607.5	+	12653.7i	1.30762	+	1.31241i
$454$	−1234.28	−	2137.84i	−0.127594	−	0.221000i
$455$	336.766	+	583.295i	0.0346985	+	0.0600996i
$456$	267.378	−	990.627i	0.0274586	−	0.101733i
$457$	1550.46	−	2685.48i	0.158704	−	0.274883i	−0.775698	−	0.631105i	$-0.782602\pi$
$457$	1550.46	−	2685.48i	0.158704	−	0.274883i	0.934402	+	0.356222i	$0.115935\pi$
$458$	3891.39			0.397015
$459$	207.170	−	204.912i	0.0210672	−	0.0208376i
$460$	−1340.89			−0.135912
$461$	−2174.51	+	3766.36i	−0.219690	+	0.380514i	−0.954713	−	0.297528i	$-0.903838\pi$
$461$	−2174.51	+	3766.36i	−0.219690	+	0.380514i	0.735023	+	0.678042i	$0.237171\pi$
$462$	1572.56	−	5826.28i	0.158359	−	0.586717i
$463$	3722.76	+	6448.00i	0.373674	+	0.647223i	0.990128	−	0.140169i	$-0.0447645\pi$
$463$	3722.76	+	6448.00i	0.373674	+	0.647223i	−0.616453	+	0.787391i	$0.711431\pi$
$464$	652.151	+	1129.56i	0.0652486	+	0.113014i
$465$	2135.65	+	2143.47i	0.212986	+	0.213766i
$466$	−6148.18	+	10649.0i	−0.611178	+	1.05859i
$467$	15424.1			1.52836			0.764178	−	0.645006i	$-0.223145\pi$
$467$	15424.1			1.52836			0.764178	+	0.645006i	$0.223145\pi$
$468$	−6933.86	+	3969.57i	−0.684867	+	0.392080i
$469$	−28.2973			−0.00278603
$470$	−1409.53	+	2441.37i	−0.138333	+	0.239600i
$471$	104.756	−	27.8644i	0.0102482	−	0.00272596i
$472$	−153.718	−	266.247i	−0.0149903	−	0.0259640i
$473$	−10132.9	−	17550.8i	−0.985016	−	1.70610i
$474$	−11370.1	+	3024.37i	−1.10179	+	0.293067i
$475$	5722.27	−	9911.25i	0.552749	−	0.957389i
$476$	108.717			0.0104685
$477$	14634.8	+	8520.85i	1.40479	+	0.817910i
$478$	11901.0			1.13878
$479$	−4325.21	+	7491.49i	−0.412576	+	0.714603i	−0.995171	−	0.0981602i	$-0.968704\pi$
$479$	−4325.21	+	7491.49i	−0.412576	+	0.714603i	0.582595	+	0.812763i	$0.302038\pi$
$480$	−2235.68	−	2243.86i	−0.212592	−	0.213370i
$481$	−2855.41	−	4945.71i	−0.270677	−	0.468826i
$482$	−11013.4	−	19075.8i	−1.04076	−	1.80265i
$483$	−699.024	+	2589.87i	−0.0658524	+	0.243981i
$484$	−1673.16	+	2898.00i	−0.157134	+	0.272164i
$485$	−1020.10			−0.0955055
$486$	3988.36	−	14359.0i	0.372254	−	1.34020i
$487$	−13668.2			−1.27179			−0.635897	−	0.771774i	$-0.719370\pi$
$487$	−13668.2			−1.27179			−0.635897	+	0.771774i	$0.719370\pi$
$488$	647.997	−	1122.36i	0.0601095	−	0.104113i
$489$	−2240.18	+	8299.83i	−0.207167	+	0.767548i
$490$	−234.357	−	405.919i	−0.0216065	−	0.0374236i
$491$	589.304	+	1020.70i	0.0541648	+	0.0938162i	0.891836	−	0.452358i	$-0.149417\pi$
$491$	589.304	+	1020.70i	0.0541648	+	0.0938162i	−0.837672	+	0.546174i	$0.816084\pi$
$492$	−1982.30	−	1989.56i	−0.181644	−	0.182309i
$493$	19.9467	−	34.5488i	0.00182222	−	0.00315618i
$494$	14961.8			1.36268
$495$	2392.55	+	1393.02i	0.217247	+	0.126488i
$496$	16263.2			1.47225
$497$	−2794.30	+	4839.88i	−0.252196	+	0.436817i
$498$	25489.4	−	6780.00i	2.29359	−	0.610078i
$499$	19.2536	+	33.3482i	0.00172727	+	0.00299173i	0.866888	−	0.498503i	$-0.166117\pi$
$499$	19.2536	+	33.3482i	0.00172727	+	0.00299173i	−0.865160	+	0.501495i	$0.832784\pi$
$500$	−2218.93	−	3843.31i	−0.198467	−	0.343756i
$501$	9848.36	−	2619.59i	0.878228	−	0.233602i
$502$	5823.21	−	10086.1i	0.517734	−	0.896742i
$503$	4489.37			0.397954			0.198977	−	0.980004i	$-0.436238\pi$
$503$	4489.37			0.397954			0.198977	+	0.980004i	$0.436238\pi$
$504$	−337.033	+	192.949i	−0.0297870	+	0.0170528i
$505$	−2201.95			−0.194030
$506$	6118.12	−	10596.9i	0.537517	−	0.931007i
$507$	−2314.08	−	2322.55i	−0.202706	−	0.203448i
$508$	−3357.98	−	5816.19i	−0.293280	−	0.507976i
$509$	6578.27	+	11393.9i	0.572842	+	0.992192i	0.996272	+	0.0862632i	$0.0274926\pi$
$509$	6578.27	+	11393.9i	0.572842	+	0.992192i	−0.423430	+	0.905929i	$0.639174\pi$
$510$	−26.9010	+	99.6677i	−0.00233568	+	0.00865365i
$511$	1554.08	−	2691.74i	0.134537	−	0.233025i
$512$	−15908.6			−1.37318
$513$	−9585.75	+	9481.29i	−0.824993	+	0.816002i
$514$	−23588.0			−2.02417
$515$	2513.76	−	4353.97i	0.215087	−	0.372541i
$516$	4865.56	−	18026.8i	0.415105	−	1.53795i
$517$	−6214.24	−	10763.4i	−0.528631	−	0.915616i
$518$	1987.10	+	3441.75i	0.168548	+	0.291934i
$519$	−100.280	−	100.647i	−0.00848130	−	0.00851233i
$520$	−98.8550	+	171.222i	−0.00833669	+	0.0144396i
$521$	2198.40			0.184863			0.0924317	−	0.995719i	$-0.470536\pi$
$521$	2198.40			0.184863			0.0924317	+	0.995719i	$0.470536\pi$
$522$	7.45187	−	2040.27i	0.000624826	−	0.171073i
$523$	−7784.24			−0.650824			−0.325412	−	0.945572i	$-0.605503\pi$
$523$	−7784.24			−0.650824			−0.325412	+	0.945572i	$0.605503\pi$
$524$	−7980.69	+	13823.0i	−0.665340	+	1.15240i
$525$	−4186.05	+	1113.46i	−0.347989	+	0.0925625i
$526$	3508.66	+	6077.18i	0.290846	+	0.503760i
$527$	−248.713	−	430.784i	−0.0205581	−	0.0356077i
$528$	14380.4	−	3825.08i	1.18528	−	0.315275i
$529$	3363.91	−	5826.46i	0.276478	−	0.478874i
$530$	−5999.65			−0.491713
$531$	−14.7545	+	4039.67i	−0.00120582	+	0.330145i
$532$	−5030.32			−0.409947
$533$	−1430.21	+	2477.20i	−0.116228	+	0.201312i
$534$	−10831.6	−	10871.2i	−0.877769	−	0.880981i
$535$	2101.05	+	3639.12i	0.169787	+	0.294080i
$536$	−4.15323	−	7.19361i	−0.000334687	−	0.000579695i
$537$	177.149	−	656.334i	0.0142357	−	0.0527428i
$538$	12487.7	−	21629.3i	1.00071	−	1.73328i
$539$	2066.44			0.165136
$540$	646.682	+	2467.45i	0.0515348	+	0.196633i
$541$	−8493.26			−0.674961			−0.337480	−	0.941333i	$-0.609575\pi$
$541$	−8493.26			−0.674961			−0.337480	+	0.941333i	$0.609575\pi$
$542$	−13203.8	+	22869.6i	−1.04640	+	1.81242i
$543$	3331.05	−	12341.5i	0.263258	−	0.975364i
$544$	260.362	+	450.960i	0.0205201	+	0.0355418i
$545$	1124.79	+	1948.19i	0.0884047	+	0.153121i
$546$	−3996.91	−	4011.53i	−0.313282	−	0.314428i
$547$	−3663.38	+	6345.16i	−0.286352	+	0.495977i	−0.972936	−	0.231074i	$-0.925776\pi$
$547$	−3663.38	+	6345.16i	−0.286352	+	0.495977i	0.686584	+	0.727051i	$0.259109\pi$
$548$	−16161.3			−1.25981
$549$	−14778.8	+	8460.75i	−1.14890	+	0.657734i
$550$	19758.3			1.53181
$551$	−922.936	+	1598.57i	−0.0713583	+	0.123596i
$552$	−760.980	+	202.415i	−0.0586765	+	0.0156075i
$553$	−2014.39	−	3489.02i	−0.154901	−	0.268297i
$554$	4478.20	+	7756.47i	0.343431	+	0.594839i
$555$	−1761.95	+	468.667i	−0.134758	+	0.0358447i
$556$	−8599.97	+	14895.6i	−0.655971	+	1.13618i
$557$	7394.34			0.562492			0.281246	−	0.959636i	$-0.409252\pi$
$557$	7394.34			0.562492			0.281246	+	0.959636i	$0.409252\pi$
$558$	−21985.1	−	12800.4i	−1.66792	−	0.971116i
$559$	−19016.8			−1.43887
$560$	577.873	−	1000.91i	0.0436064	−	0.0755286i
$561$	−321.240	−	322.415i	−0.0241760	−	0.0242645i
$562$	−2923.06	−	5062.90i	−0.219399	−	0.380010i
$563$	1437.18	+	2489.27i	0.107584	+	0.186341i	0.914791	−	0.403927i	$-0.132355\pi$
$563$	1437.18	+	2489.27i	0.107584	+	0.186341i	−0.807207	+	0.590269i	$0.799022\pi$
$564$	2983.91	−	11055.3i	0.222776	−	0.825378i
$565$	2659.01	−	4605.55i	0.197992	−	0.342932i
$566$	35447.6			2.63247
$567$	5102.86	+	37.2759i	0.377954	+	0.00276092i
$568$	−1640.49			−0.121186
$569$	−7864.92	+	13622.4i	−0.579463	+	1.00366i	0.416078	+	0.909329i	$0.363404\pi$
$569$	−7864.92	+	13622.4i	−0.579463	+	1.00366i	−0.995541	+	0.0943307i	$0.969929\pi$
$570$	1244.71	−	4611.63i	0.0914654	−	0.338877i
$571$	5659.53	+	9802.59i	0.414788	+	0.718434i	0.995406	−	0.0957422i	$-0.0305224\pi$
$571$	5659.53	+	9802.59i	0.414788	+	0.718434i	−0.580618	+	0.814176i	$0.697189\pi$
$572$	6239.74	+	10807.6i	0.456113	+	0.790011i
$573$	−4802.27	−	4819.84i	−0.350118	−	0.351399i
$574$	995.292	−	1723.90i	0.0723740	−	0.125355i
$575$	−8782.86			−0.636992
$576$	10339.1	+	6019.74i	0.747910	+	0.435456i
$577$	1090.45			0.0786758			0.0393379	−	0.999226i	$-0.487475\pi$
$577$	1090.45			0.0786758			0.0393379	+	0.999226i	$0.487475\pi$
$578$	−9655.81	+	16724.3i	−0.694859	+	1.20353i
$579$	−4337.28	+	1153.69i	−0.311315	+	0.0828076i
$580$	174.610	+	302.434i	0.0125005	+	0.0216515i
$581$	4515.82	+	7821.63i	0.322458	+	0.558513i
$582$	8288.43	−	2204.66i	0.590321	−	0.157021i
$583$	13225.5	−	22907.2i	0.939525	−	1.62730i
$584$	912.375			0.0646478
$585$	2254.58	−	1290.73i	0.159343	−	0.0912222i
$586$	−29644.4			−2.08976
$587$	−13048.0	+	22599.8i	−0.917458	+	1.58908i	−0.114197	+	0.993458i	$0.536429\pi$
$587$	−13048.0	+	22599.8i	−0.917458	+	1.58908i	−0.803262	+	0.595626i	$0.796904\pi$
$588$	1343.81	+	1348.72i	0.0942477	+	0.0945926i
$589$	11508.0	+	19932.4i	0.805055	+	1.39440i
$590$	−715.596	−	1239.45i	−0.0499333	−	0.0864869i
$591$	4006.43	−	14843.7i	0.278853	−	1.03314i
$592$	−4899.74	+	8486.60i	−0.340166	+	0.589184i
$593$	−2675.40			−0.185271			−0.0926354	−	0.995700i	$-0.529529\pi$
$593$	−2675.40			−0.185271			−0.0926354	+	0.995700i	$0.529529\pi$
$594$	−22450.5	−	6147.61i	−1.55077	−	0.424646i
$595$	−35.3498			−0.00243563
$596$	4425.07	−	7664.45i	0.304124	−	0.526758i
$597$	−2112.05	+	7825.10i	−0.144792	+	0.536449i
$598$	−5741.04	−	9943.78i	−0.392590	−	0.679986i
$599$	2483.86	+	4302.18i	0.169429	+	0.293459i	0.938219	−	0.346042i	$-0.112474\pi$
$599$	2483.86	+	4302.18i	0.169429	+	0.293459i	−0.768790	+	0.639501i	$0.779141\pi$
$600$	−897.449	−	900.733i	−0.0610637	−	0.0612871i
$601$	9440.30	−	16351.1i	0.640728	−	1.10977i	−0.344542	−	0.938771i	$-0.611966\pi$
$601$	9440.30	−	16351.1i	0.640728	−	1.10977i	0.985270	−	0.171003i	$-0.0547009\pi$
$602$	13233.9			0.895971
$603$	−0.398645	+	109.146i	−2.69222e−5	+	0.00737110i
$604$	25705.5			1.73169
$605$	544.037	−	942.300i	0.0365591	−	0.0633222i
$606$	17891.1	−	4758.92i	1.19930	−	0.319006i
$607$	−11401.1	−	19747.2i	−0.762364	−	1.32045i	−0.941629	−	0.336653i	$-0.890705\pi$
$607$	−11401.1	−	19747.2i	−0.762364	−	1.32045i	0.179265	−	0.983801i	$-0.442628\pi$
$608$	−12047.0	−	20865.9i	−0.803567	−	1.39182i
$609$	675.162	−	179.588i	0.0449244	−	0.0119496i
$610$	3016.59	−	5224.89i	0.200227	−	0.346803i
$611$	−11662.5			−0.772199
$612$	1.53157	−	419.333i	0.000101160	−	0.0276969i
$613$	−16589.5			−1.09306			−0.546529	−	0.837440i	$-0.684051\pi$
$613$	−16589.5			−1.09306			−0.546529	+	0.837440i	$0.684051\pi$
$614$	5439.94	−	9422.26i	0.357554	−	0.619302i
$615$	644.556	+	646.914i	0.0422618	+	0.0424164i
$616$	303.294	+	525.321i	0.0198378	+	0.0343601i
$617$	−12595.3	−	21815.7i	−0.821827	−	1.42345i	−0.904320	−	0.426855i	$-0.859622\pi$
$617$	−12595.3	−	21815.7i	−0.821827	−	1.42345i	0.0824929	−	0.996592i	$-0.473712\pi$
$618$	−11014.8	+	40809.5i	−0.716957	+	2.65631i
$619$	−6076.11	+	10524.1i	−0.394538	+	0.683361i	−0.993042	−	0.117759i	$-0.962429\pi$
$619$	−6076.11	+	10524.1i	−0.394538	+	0.683361i	0.598504	+	0.801120i	$0.295762\pi$
$620$	4354.39			0.282059
$621$	9979.57	+	2732.70i	0.644873	+	0.176586i
$622$	11858.4			0.764437
$623$	2627.45	−	4550.88i	0.168967	−	0.292660i
$624$	3638.59	−	13480.9i	0.233430	−	0.864851i
$625$	−6721.52	−	11642.0i	−0.430177	−	0.745088i
$626$	5405.83	+	9363.17i	0.345144	+	0.597808i
$627$	14863.8	+	14918.2i	0.946734	+	0.950198i
$628$	77.9976	−	135.096i	0.00495612	−	0.00858425i
$629$	299.728			0.0189999
$630$	−1568.98	+	898.225i	−0.0992216	+	0.0568034i
$631$	13761.8			0.868224			0.434112	−	0.900859i	$-0.357062\pi$
$631$	13761.8			0.868224			0.434112	+	0.900859i	$0.357062\pi$
$632$	591.307	−	1024.17i	0.0372167	−	0.0644612i
$633$	−12586.0	+	3347.78i	−0.790281	+	0.210209i
$634$	7737.33	+	13401.4i	0.484682	+	0.839494i
$635$	1091.86	+	1891.16i	0.0682351	+	0.118187i
$636$	23551.5	−	6264.54i	1.46836	−	0.390574i
$637$	969.542	−	1679.30i	0.0603056	−	0.104452i
$638$	−3186.79			−0.197753
$639$	18628.6	+	10846.1i	1.15326	+	0.671466i
$640$	638.133			0.0394132
$641$	191.189	−	331.149i	0.0117808	−	0.0204050i	−0.860075	−	0.510168i	$-0.829583\pi$
$641$	191.189	−	331.149i	0.0117808	−	0.0204050i	0.871856	+	0.489763i	$0.162917\pi$
$642$	−24936.3	−	25027.5i	−1.53296	−	1.53856i
$643$	4008.98	+	6943.76i	0.245877	+	0.425871i	0.962378	−	0.271715i	$-0.0875908\pi$
$643$	4008.98	+	6943.76i	0.245877	+	0.425871i	−0.716501	+	0.697586i	$0.754257\pi$
$644$	1930.20	+	3343.21i	0.118107	+	0.204567i
$645$	−1582.06	+	5861.50i	−0.0965793	+	0.357824i
$646$	−392.629	+	680.053i	−0.0239130	+	0.0414185i
$647$	−548.646			−0.0333377			−0.0166689	−	0.999861i	$-0.505306\pi$
$647$	−548.646			−0.0333377			−0.0166689	+	0.999861i	$0.505306\pi$
$648$	739.477	+	1302.70i	0.0448293	+	0.0789733i
$649$	6309.76			0.381633
$650$	9270.28	−	16056.6i	0.559400	−	0.968910i
$651$	2269.99	−	8410.27i	0.136664	−	0.506336i
$652$	6185.79	+	10714.1i	0.371555	+	0.643553i
$653$	−3408.56	−	5903.80i	−0.204268	−	0.353803i	0.745631	−	0.666359i	$-0.232148\pi$
$653$	−3408.56	−	5903.80i	−0.204268	−	0.353803i	−0.949899	+	0.312556i	$0.898815\pi$
$654$	−13349.5	−	13398.4i	−0.798178	−	0.801099i
$655$	2594.96	−	4494.61i	0.154799	−	0.268121i
$656$	4908.34			0.292132
$657$	−10360.5	−	6032.18i	−0.615221	−	0.358201i
$658$	8116.00			0.480843
$659$	15876.6	−	27499.0i	0.938487	−	1.62551i	0.170193	−	0.985411i	$-0.445561\pi$
$659$	15876.6	−	27499.0i	0.938487	−	1.62551i	0.768294	−	0.640097i	$-0.221106\pi$
$660$	3850.28	−	1024.15i	0.227079	−	0.0604014i
$661$	9540.80	+	16525.1i	0.561413	+	0.972396i	0.997374	+	0.0724299i	$0.0230754\pi$
$661$	9540.80	+	16525.1i	0.561413	+	0.972396i	−0.435961	+	0.899966i	$0.643591\pi$
$662$	9057.29	+	15687.7i	0.531755	+	0.921026i
$663$	−412.731	+	109.784i	−0.0241767	+	0.00643083i
$664$	−1325.58	+	2295.98i	−0.0774739	+	0.134189i
$665$	1635.64			0.0953793
$666$	13303.2	−	7615.98i	0.774009	−	0.443113i
$667$	1416.58			0.0822339
$668$	7332.72	−	12700.6i	0.424718	−	0.735632i
$669$	14847.6	+	14902.0i	0.858060	+	0.861200i
$670$	−19.3344	−	33.4881i	−0.00111485	−	0.00193098i
$671$	13299.4	+	23035.2i	0.765152	+	1.32528i
$672$	−2376.31	+	8804.17i	−0.136411	+	0.505399i
$673$	6635.90	−	11493.7i	0.380082	−	0.658321i	−0.610992	−	0.791637i	$-0.709229\pi$
$673$	6635.90	−	11493.7i	0.380082	−	0.658321i	0.991074	+	0.133316i	$0.0425625\pi$
$674$	−10908.4			−0.623408
$675$	4235.77	+	16161.8i	0.241533	+	0.921580i
$676$	−4718.18			−0.268444
$677$	−2667.73	+	4620.64i	−0.151446	+	0.262312i	−0.931759	−	0.363077i	$-0.881726\pi$
$677$	−2667.73	+	4620.64i	−0.151446	+	0.262312i	0.780313	+	0.625389i	$0.215060\pi$
$678$	−11651.2	+	43167.5i	−0.659975	+	2.44519i
$679$	1468.42	+	2543.38i	0.0829937	+	0.143749i
$680$	−5.18833	−	8.98645i	−0.000292593	−	0.000506786i
$681$	−2301.25	−	2309.67i	−0.129492	−	0.129966i
$682$	−19867.8	+	34412.1i	−1.11551	+	1.93212i
$683$	−26921.0			−1.50820			−0.754101	−	0.656758i	$-0.771927\pi$
$683$	−26921.0			−1.50820			−0.754101	+	0.656758i	$0.771927\pi$
$684$	−70.8658	+	19402.5i	−0.00396144	+	1.08461i
$685$	5254.92			0.293110
$686$	−674.710	+	1168.63i	−0.0375518	+	0.0650417i
$687$	4966.94	−	1321.17i	0.275838	−	0.0733709i
$688$	16316.0	+	28260.1i	0.904128	+	1.56600i
$689$	−12410.3	−	21495.4i	−0.686207	−	1.18855i
$690$	−3542.56	+	942.295i	−0.195453	+	0.0519892i
$691$	−2308.65	+	3998.69i	−0.127099	+	0.220141i	−0.922551	−	0.385875i	$-0.873900\pi$
$691$	−2308.65	+	3998.69i	−0.127099	+	0.220141i	0.795453	+	0.606016i	$0.207233\pi$
$692$	−204.460			−0.0112318
$693$	29.1115	−	7970.52i	0.00159575	−	0.436905i
$694$	−33137.1			−1.81249
$695$	2796.33	−	4843.38i	0.152620	−	0.264345i
$696$	144.748	+	145.278i	0.00788315	+	0.00791199i
$697$	−75.0635	−	130.014i	−0.00407924	−	0.00706546i
$698$	−7632.24	−	13219.4i	−0.413874	−	0.716852i
$699$	−4232.05	+	15679.6i	−0.229000	+	0.848438i
$700$	−3116.77	+	5398.41i	−0.168290	+	0.291487i
$701$	−15895.3			−0.856430			−0.428215	−	0.903677i	$-0.640857\pi$
$701$	−15895.3			−0.856430			−0.428215	+	0.903677i	$0.640857\pi$
$702$	−15529.3	+	15360.0i	−0.834921	+	0.825822i
$703$	−13868.4			−0.744036
$704$	9343.42	−	16183.3i	0.500204	−	0.866378i
$705$	−970.235	+	3594.70i	−0.0518315	+	0.192034i
$706$	7720.27	+	13371.9i	0.411553	+	0.712831i
$707$	3169.68	+	5490.05i	0.168611	+	0.292043i
$708$	4103.23	+	4118.25i	0.217809	+	0.218606i
$709$	1794.91	−	3108.88i	0.0950766	−	0.164677i	−0.814564	−	0.580074i	$-0.803024\pi$
$709$	1794.91	−	3108.88i	0.0950766	−	0.164677i	0.909641	+	0.415396i	$0.136357\pi$
$710$	−7636.92			−0.403674
$711$	−13485.9	+	7720.57i	−0.711339	+	0.407235i
$712$	1542.54			0.0811924
$713$	8831.54	−	15296.7i	0.463876	−	0.803457i
$714$	287.222	−	76.3991i	0.0150547	−	0.00400443i
$715$	−2028.89	−	3514.13i	−0.106120	−	0.183806i
$716$	−489.160	−	847.250i	−0.0255318	−	0.0442223i
$717$	15190.3	−	4040.51i	0.791203	−	0.210454i
$718$	13029.0	−	22566.9i	0.677213	−	1.17297i
$719$	3759.41			0.194996			0.0974981	−	0.995236i	$-0.468916\pi$
$719$	3759.41			0.194996			0.0974981	+	0.995236i	$0.468916\pi$
$720$	−3852.47	−	2243.03i	−0.199407	−	0.116101i
$721$	−14474.2			−0.747636
$722$	4674.70	−	8096.81i	0.240961	−	0.417358i
$723$	−20533.9	−	20609.0i	−1.05624	−	1.06011i
$724$	−9197.98	−	15931.4i	−0.472155	−	0.817797i
$725$	1143.70	+	1980.94i	0.0585874	+	0.101476i
$726$	−2383.86	+	8832.12i	−0.121864	+	0.451503i
$727$	−12693.7	+	21986.2i	−0.647572	+	1.12163i	0.336129	+	0.941816i	$0.390882\pi$
$727$	−12693.7	+	21986.2i	−0.647572	+	1.12163i	−0.983701	+	0.179811i	$0.942451\pi$
$728$	569.203			0.0289781
$729$	215.665	−	19681.8i	0.0109569	−	0.999940i
$730$	4247.34			0.215344
$731$	499.042	−	864.366i	0.0252500	−	0.0437342i
$732$	−6386.01	+	23660.0i	−0.322450	+	1.19467i
$733$	−10097.6	−	17489.5i	−0.508815	−	0.881294i	−0.999948	−	0.0102093i	$-0.996750\pi$
$733$	−10097.6	−	17489.5i	−0.508815	−	0.881294i	0.491132	−	0.871085i	$-0.336583\pi$
$734$	−18120.7	−	31385.9i	−0.911235	−	1.57830i
$735$	−436.946	−	438.545i	−0.0219279	−	0.0220081i
$736$	−9245.18	+	16013.1i	−0.463019	+	0.801972i
$737$	170.481			0.00852068
$738$	−6635.25	−	3863.24i	−0.330958	−	0.192694i
$739$	−2153.33			−0.107187			−0.0535936	−	0.998563i	$-0.517068\pi$
$739$	−2153.33			−0.107187			−0.0535936	+	0.998563i	$0.517068\pi$
$740$	−1311.88	+	2272.25i	−0.0651700	+	0.112878i
$741$	19097.1	−	5079.69i	0.946760	−	0.251831i
$742$	8636.44	+	14958.7i	0.427296	+	0.740098i
$743$	−494.183	−	855.949i	−0.0244008	−	0.0422634i	0.853567	−	0.520983i	$-0.174434\pi$
$743$	−494.183	−	855.949i	−0.0244008	−	0.0422634i	−0.877968	+	0.478719i	$0.841101\pi$
$744$	2471.19	−	657.318i	0.121772	−	0.0323904i
$745$	−1438.83	+	2492.14i	−0.0707582	+	0.122557i
$746$	29609.9			1.45321
$747$	30232.6	−	17307.9i	1.48079	−	0.847740i
$748$	−654.976			−0.0320165
$749$	6048.87	−	10477.0i	0.295088	−	0.511108i
$750$	−8563.11	−	8594.44i	−0.416908	−	0.418433i
$751$	−8964.88	−	15527.6i	−0.435597	−	0.754476i	0.561747	−	0.827309i	$-0.310129\pi$
$751$	−8964.88	−	15527.6i	−0.435597	−	0.754476i	−0.997344	+	0.0728330i	$0.976796\pi$
$752$	10006.1	+	17331.1i	0.485221	+	0.840427i
$753$	4008.36	−	14850.9i	0.193988	−	0.718719i
$754$	−1495.19	+	2589.75i	−0.0722170	+	0.125084i
$755$	−8358.27			−0.402899
$756$	5221.12	−	5164.22i	0.251177	−	0.248440i
$757$	34271.4			1.64546			0.822732	−	0.568429i	$-0.192449\pi$
$757$	34271.4			1.64546			0.822732	+	0.568429i	$0.192449\pi$
$758$	18771.6	−	32513.4i	0.899494	−	1.55797i
$759$	4211.36	−	15603.0i	0.201400	−	0.746182i
$760$	240.064	+	415.803i	0.0114579	+	0.0198457i
$761$	8679.95	+	15034.1i	0.413466	+	0.716145i	0.995266	−	0.0971873i	$-0.0309846\pi$
$761$	8679.95	+	15034.1i	0.413466	+	0.716145i	−0.581800	+	0.813332i	$0.697651\pi$
$762$	−12958.8	−	13006.2i	−0.616073	−	0.618328i
$763$	3238.24	−	5608.80i	0.153646	−	0.266123i
$764$	−9791.36			−0.463663
$765$	−0.497998	+	136.348i	−2.35362e−5	+	0.00644403i
$766$	14923.4			0.703923
$767$	2960.44	−	5127.63i	0.139368	−	0.241392i
$768$	−22985.6	+	6114.00i	−1.07997	+	0.287265i
$769$	2411.70	+	4177.19i	0.113093	+	0.195882i	0.917016	−	0.398851i	$-0.130591\pi$
$769$	2411.70	+	4177.19i	0.113093	+	0.195882i	−0.803923	+	0.594733i	$0.797258\pi$
$770$	1411.91	+	2445.51i	0.0660803	+	0.114454i
$771$	−30107.6	+	8008.40i	−1.40635	+	0.374080i
$772$	−3229.38	+	5593.45i	−0.150554	+	0.260768i
$773$	4103.77			0.190947			0.0954736	−	0.995432i	$-0.469563\pi$
$773$	4103.77			0.190947			0.0954736	+	0.995432i	$0.469563\pi$
$774$	186.436	−	51044.8i	0.00865801	−	2.37050i
$775$	28521.2			1.32195
$776$	−431.043	+	746.588i	−0.0199401	+	0.0345373i
$777$	3704.83	+	3718.39i	0.171055	+	0.171681i
$778$	−12154.9	−	21053.0i	−0.560123	−	0.970162i
$779$	3473.19	+	6015.74i	0.159743	+	0.276683i
$780$	974.216	−	3609.45i	0.0447212	−	0.165691i
$781$	16834.6	−	29158.4i	0.771306	−	1.33594i
$782$	602.629			0.0275575
$783$	−683.181	−	2606.71i	−0.0311812	−	0.118973i
$784$	−3327.37			−0.151575
$785$	−25.3613	+	43.9271i	−0.00115310	+	0.00199723i
$786$	−11370.6	+	42127.7i	−0.515999	+	1.91176i
$787$	−12340.2	−	21373.9i	−0.558934	−	0.968102i	−0.997586	−	0.0694447i	$-0.977877\pi$
$787$	−12340.2	−	21373.9i	−0.558934	−	0.968102i	0.438652	−	0.898657i	$-0.355456\pi$
$788$	−11062.9	−	19161.5i	−0.500126	−	0.866243i
$789$	6541.70	+	6565.64i	0.295172	+	0.296252i
$790$	2752.69	−	4767.79i	0.123970	−	0.214722i
$791$	−15310.5			−0.688216
$792$	2030.50	−	1162.44i	0.0910993	−	0.0521535i
$793$	24959.4			1.11770
$794$	353.902	−	612.976i	0.0158180	−	0.0273976i
$795$	−7657.90	+	2036.95i	−0.341632	+	0.0908718i
$796$	5831.98	+	10101.3i	0.259685	+	0.449787i
$797$	−5069.67	−	8780.93i	−0.225316	−	0.390259i	0.731098	−	0.682272i	$-0.239008\pi$
$797$	−5069.67	−	8780.93i	−0.225316	−	0.390259i	−0.956414	+	0.292013i	$0.905675\pi$
$798$	−13289.8	+	3534.99i	−0.589540	+	0.156814i
$799$	306.048	−	530.091i	0.0135510	−	0.0234709i
$800$	−29857.1			−1.31951
$801$	−17516.3	−	10198.5i	−0.772668	−	0.449871i
$802$	−28733.1			−1.26509
$803$	−9362.73	+	16216.7i	−0.411461	+	0.712672i
$804$	110.863	+	111.269i	0.00486300	+	0.00488079i
$805$	−627.616	−	1087.06i	−0.0274790	−	0.0475950i
$806$	18643.3	+	32291.2i	0.814743	+	1.41118i
$807$	8595.79	−	31847.2i	0.374952	−	1.38919i
$808$	−930.435	+	1611.56i	−0.0405106	+	0.0701665i
$809$	−25446.0			−1.10585			−0.552926	−	0.833230i	$-0.686489\pi$
$809$	−25446.0			−1.10585			−0.552926	+	0.833230i	$0.686489\pi$
$810$	3442.46	+	6064.39i	0.149328	+	0.263063i
$811$	22279.3			0.964652			0.482326	−	0.875992i	$-0.339792\pi$
$811$	22279.3			0.964652			0.482326	+	0.875992i	$0.339792\pi$
$812$	502.700	−	870.702i	0.0217258	−	0.0376301i
$813$	−9088.70	+	33673.4i	−0.392072	+	1.45262i
$814$	−11971.5	−	20735.3i	−0.515480	−	0.892838i
$815$	−2011.34	−	3483.75i	−0.0864469	−	0.149730i
$816$	517.258	+	519.151i	0.0221907	+	0.0222719i
$817$	−23090.7	+	39994.2i	−0.988789	+	1.71263i
$818$	8308.80			0.355147
$819$	−6463.58	−	3763.29i	−0.275770	−	0.160562i
$820$	1314.19			0.0559675
$821$	−4403.40	+	7626.91i	−0.187186	+	0.324216i	−0.944311	−	0.329054i	$-0.893270\pi$
$821$	−4403.40	+	7626.91i	−0.187186	+	0.324216i	0.757125	+	0.653270i	$0.226603\pi$
$822$	−42697.0	+	11357.1i	−1.81172	+	0.481903i
$823$	5036.16	+	8722.89i	0.213304	+	0.369454i	0.952747	−	0.303766i	$-0.0982441\pi$
$823$	5036.16	+	8722.89i	0.213304	+	0.369454i	−0.739442	+	0.673220i	$0.764911\pi$
$824$	−2124.39	−	3679.55i	−0.0898138	−	0.155562i
$825$	25219.4	−	6708.17i	1.06427	−	0.283089i
$826$	−2060.19	+	3568.35i	−0.0867834	+	0.150313i
$827$	24609.0			1.03475			0.517375	−	0.855759i	$-0.326909\pi$
$827$	24609.0			1.03475			0.517375	+	0.855759i	$0.326909\pi$
$828$	12922.4	−	7397.93i	0.542371	−	0.310502i
$829$	40946.1			1.71546			0.857730	−	0.514101i	$-0.171874\pi$
$829$	40946.1			1.71546			0.857730	+	0.514101i	$0.171874\pi$
$830$	−6170.94	+	10688.4i	−0.258068	+	0.446987i
$831$	8349.35	+	8379.90i	0.348539	+	0.349814i
$832$	−8767.56	−	15185.9i	−0.365337	−	0.632782i
$833$	50.8857	+	88.1366i	0.00211655	+	0.00366597i
$834$	−12252.9	+	45396.7i	−0.508733	+	1.88484i
$835$	−2384.27	+	4129.68i	−0.0988157	+	0.171154i
$836$	30305.8			1.25376
$837$	−32407.4	−	8874.12i	−1.33831	−	0.366469i
$838$	22526.0			0.928579
$839$	−20439.4	+	35402.2i	−0.841058	+	1.45676i	0.0479423	+	0.998850i	$0.484734\pi$
$839$	−20439.4	+	35402.2i	−0.841058	+	1.45676i	−0.889001	+	0.457906i	$0.848600\pi$
$840$	47.3536	−	175.444i	0.00194507	−	0.00720642i
$841$	12010.0	+	20802.0i	0.492437	+	0.852925i
$842$	10359.7	+	17943.5i	0.424013	+	0.734412i
$843$	−5449.89	−	5469.83i	−0.222662	−	0.223477i
$844$	−9371.04	+	16231.1i	−0.382185	+	0.661965i
$845$	1534.14			0.0624568
$846$	114.336	−	31304.4i	0.00464652	−	1.27218i
$847$	−3132.55			−0.127079
$848$	−21295.5	+	36885.0i	−0.862372	+	1.49367i
$849$	45245.1	−	12034.9i	1.82898	−	0.486497i
$850$	486.543	+	842.718i	0.0196333	+	0.0340059i
$851$	5321.51	+	9217.12i	0.214358	+	0.371280i
$852$	29978.6	−	7974.09i	1.20546	−	0.320643i
$853$	1184.06	−	2050.85i	0.0475279	−	0.0823208i	−0.841283	−	0.540595i	$-0.818199\pi$
$853$	1184.06	−	2050.85i	0.0475279	−	0.0823208i	0.888811	+	0.458275i	$0.151532\pi$
$854$	−17369.4			−0.695983
$855$	23.0424	−	6308.84i	0.000921676	−	0.252348i
$856$	3551.20			0.141796
$857$	6095.19	−	10557.2i	0.242949	−	0.420801i	−0.718604	−	0.695420i	$-0.755218\pi$
$857$	6095.19	−	10557.2i	0.242949	−	0.420801i	0.961553	+	0.274619i	$0.0885517\pi$
$858$	24079.9	+	24168.0i	0.958127	+	0.961633i
$859$	9118.19	+	15793.2i	0.362175	+	0.627306i	0.988319	−	0.152402i	$-0.0487008\pi$
$859$	9118.19	+	15793.2i	0.362175	+	0.627306i	−0.626143	+	0.779708i	$0.715367\pi$
$860$	4368.53	+	7566.51i	0.173216	+	0.300018i
$861$	685.101	−	2538.28i	0.0271175	−	0.100470i
$862$	31133.8	−	53925.4i	1.23019	−	2.13075i
$863$	−35518.1			−1.40099			−0.700493	−	0.713659i	$-0.747036\pi$
$863$	−35518.1			−1.40099			−0.700493	+	0.713659i	$0.747036\pi$
$864$	33925.3	+	9289.75i	1.33583	+	0.365791i
$865$	66.4814			0.00261322
$866$	8925.20	−	15458.9i	0.350220	−	0.606599i
$867$	−6646.49	+	24625.1i	−0.260354	+	0.964604i
$868$	−6268.10	−	10856.7i	−0.245107	−	0.424538i
$869$	12135.9	+	21020.0i	0.473743	+	0.820546i
$870$	673.841	+	676.307i	0.0262590	+	0.0263551i
$871$	79.9868	−	138.541i	0.00311165	−	0.00538954i
$872$	1901.12			0.0738303
$873$	9830.78	−	5628.03i	0.381124	−	0.218190i
$874$	−27883.6			−1.07915
$875$	2077.18	−	3597.78i	0.0802531	−	0.139002i
$876$	−16672.9	+	4434.86i	−0.643064	+	0.171050i
$877$	−92.2388	−	159.762i	−0.00355152	−	0.00615141i	0.864244	−	0.503073i	$-0.167797\pi$
$877$	−92.2388	−	159.762i	−0.00355152	−	0.00615141i	−0.867796	+	0.496921i	$0.834464\pi$
$878$	17559.8	+	30414.5i	0.674960	+	1.16907i
$879$	−37837.9	+	10064.6i	−1.45192	+	0.386201i
$880$	−3481.47	+	6030.08i	−0.133364	+	0.230993i
$881$	16067.4			0.614444			0.307222	−	0.951638i	$-0.400601\pi$
$881$	16067.4			0.614444			0.307222	+	0.951638i	$0.400601\pi$
$882$	4498.05	+	2618.90i	0.171720	+	0.0999807i
$883$	−591.975			−0.0225612			−0.0112806	−	0.999936i	$-0.503591\pi$
$883$	−591.975			−0.0225612			−0.0112806	+	0.999936i	$0.503591\pi$
$884$	−307.304	+	532.266i	−0.0116920	+	0.0202512i
$885$	−1334.19	−	1339.07i	−0.0506760	−	0.0508614i
$886$	−12677.8	−	21958.6i	−0.480721	−	0.832633i
$887$	8427.50	+	14596.9i	0.319017	+	0.552553i	0.980283	−	0.197598i	$-0.0633140\pi$
$887$	8427.50	+	14596.9i	0.319017	+	0.552553i	−0.661266	+	0.750151i	$0.729981\pi$
$888$	−401.508	+	1487.57i	−0.0151731	+	0.0562159i
$889$	3143.46	−	5444.63i	0.118592	−	0.205407i
$890$	7180.91			0.270454
$891$	−30742.8	−	224.573i	−1.15592	−	0.00844386i
$892$	30272.8			1.13633
$893$	−14160.9	+	24527.3i	−0.530655	+	0.919122i
$894$	6304.67	−	23358.6i	0.235861	−	0.873859i
$895$	159.053	+	275.488i	0.00594028	+	0.0102889i
$896$	−918.587	−	1591.04i	−0.0342498	−	0.0593224i
$897$	−10703.8	−	10743.0i	−0.398429	−	0.399887i
$898$	−12200.4	+	21131.7i	−0.453377	+	0.785273i
$899$	−4600.15			−0.170660
$900$	20778.4	+	12097.8i	0.769570	+	0.448067i
$901$	1302.70			0.0481677
$902$	−5996.26	+	10385.8i	−0.221345	+	0.383381i
$903$	16891.7	−	4493.06i	0.622503	−	0.165581i
$904$	−2247.14	−	3892.16i	−0.0826756	−	0.143198i
$905$	2990.77	+	5180.17i	0.109853	+	0.190270i
$906$	67912.2	−	18064.2i	2.49032	−	0.662408i
$907$	−19344.8	+	33506.2i	−0.708195	+	1.22663i	0.257331	+	0.966323i	$0.417157\pi$
$907$	−19344.8	+	33506.2i	−0.708195	+	1.22663i	−0.965526	+	0.260307i	$0.916176\pi$
$908$	−4692.03			−0.171487
$909$	21220.4	−	12148.5i	0.774298	−	0.443278i
$910$	2649.79			0.0965270
$911$	11808.0	−	20452.0i	0.429436	−	0.743804i	−0.567388	−	0.823451i	$-0.692046\pi$
$911$	11808.0	−	20452.0i	0.429436	−	0.743804i	0.996823	+	0.0796467i	$0.0253792\pi$
$912$	−23933.5	−	24021.1i	−0.868990	−	0.872169i
$913$	−27206.1	−	47122.4i	−0.986189	−	1.70813i
$914$	−6099.79	−	10565.2i	−0.220747	−	0.382346i
$915$	2076.44	−	7693.17i	0.0750220	−	0.277955i
$916$	3698.20	−	6405.46i	0.133397	−	0.231051i
$917$	−14941.7			−0.538079
$918$	−290.634	−	1108.93i	−0.0104492	−	0.0398693i
$919$	−30560.7			−1.09696			−0.548478	−	0.836165i	$-0.684793\pi$
$919$	−30560.7			−1.09696			−0.548478	+	0.836165i	$0.684793\pi$
$920$	184.232	−	319.099i	0.00660212	−	0.0114352i
$921$	3744.54	−	13873.4i	0.133970	−	0.496357i
$922$	8554.89	+	14817.5i	0.305575	+	0.529272i
$923$	−15797.1	−	27361.3i	−0.563344	−	0.975740i
$924$	−8095.92	−	8125.55i	−0.288243	−	0.289298i
$925$	−8592.84	+	14883.2i	−0.305439	+	0.529035i
$926$	29291.9			1.03952
$927$	−203.908	+	55828.5i	−0.00722462	+	1.97805i
$928$	4815.60			0.170345
$929$	−5842.24	+	10119.1i	−0.206327	+	0.357369i	−0.950555	−	0.310557i	$-0.899484\pi$
$929$	−5842.24	+	10119.1i	−0.206327	+	0.357369i	0.744228	+	0.667926i	$0.232818\pi$
$930$	11504.0	−	3059.98i	0.405625	−	0.107893i
$931$	−2354.48	−	4078.08i	−0.0828840	−	0.143559i
$932$	11685.9	+	20240.6i	0.410712	+	0.711375i
$933$	15136.0	−	4026.07i	0.531116	−	0.141273i
$934$	30340.5	−	52551.3i	1.06293	−	1.84104i
$935$	212.969			0.00744902
$936$	8.01878	−	2195.48i	0.000280024	−	0.0766684i
$937$	−49115.3			−1.71241			−0.856204	−	0.516638i	$-0.827183\pi$
$937$	−49115.3			−1.71241			−0.856204	+	0.516638i	$0.827183\pi$
$938$	−55.6633	+	96.4117i	−0.00193760	+	0.00335603i
$939$	10078.9	+	10115.7i	0.350278	+	0.351560i
$940$	2679.10	+	4640.33i	0.0929601	+	0.161012i
$941$	11827.1	+	20485.1i	0.409725	+	0.709665i	0.994859	−	0.101272i	$-0.0322912\pi$
$941$	11827.1	+	20485.1i	0.409725	+	0.709665i	−0.585133	+	0.810937i	$0.698958\pi$
$942$	111.128	−	411.726i	0.00384368	−	0.0142407i
$943$	2665.42	−	4616.65i	0.0920447	−	0.159426i
$944$	−10159.9			−0.350294
$945$	−1697.67	+	1679.17i	−0.0584395	+	0.0578027i
$946$	−79729.4			−2.74020
$947$	22791.8	−	39476.6i	0.782086	−	1.35461i	−0.148639	−	0.988892i	$-0.547489\pi$
$947$	22791.8	−	39476.6i	0.782086	−	1.35461i	0.930725	−	0.365721i	$-0.119177\pi$
$948$	−5827.34	+	21590.1i	−0.199645	+	0.739678i
$949$	8785.68	+	15217.2i	0.300522	+	0.520519i
$950$	−22512.4	−	38992.6i	−0.768840	−	1.33167i
$951$	14425.8	+	14478.6i	0.491891	+	0.493691i
$952$	−14.9371	+	25.8718i	−0.000508523	+	0.000880788i
$953$	44104.9			1.49916			0.749579	−	0.661915i	$-0.230256\pi$
$953$	44104.9			1.49916			0.749579	+	0.661915i	$0.230256\pi$
$954$	57819.3	−	33101.0i	1.96223	−	1.12336i
$955$	3183.71			0.107877
$956$	11310.1	−	19589.7i	0.382631	−	0.662737i
$957$	−4067.59	+	1081.95i	−0.137395	+	0.0365460i
$958$	17016.1	+	29472.8i	0.573868	+	0.993969i
$959$	−7564.41	−	13101.9i	−0.254711	−	0.441172i
$960$	−5410.09	+	1439.05i	−0.181885	+	0.0483802i
$961$	−13783.8	+	23874.3i	−0.462684	+	0.801393i
$962$	−22467.3			−0.752990
$963$	−40325.6	−	23478.8i	−1.34940	−	0.785664i
$964$	−41866.6			−1.39879
$965$	1050.05	−	1818.74i	0.0350283	−	0.0606707i
$966$	7448.87	+	7476.13i	0.248099	+	0.249007i
$967$	−20951.9	−	36289.7i	−0.696760	−	1.20682i	−0.969584	−	0.244760i	$-0.921291\pi$
$967$	−20951.9	−	36289.7i	−0.696760	−	1.20682i	0.272824	−	0.962064i	$-0.412042\pi$
$968$	−459.767	−	796.340i	−0.0152660	−	0.0264415i
$969$	−270.263	+	1001.32i	−0.00895984	+	0.0331960i
$970$	−2006.62	+	3475.56i	−0.0664212	+	0.115045i
$971$	−21924.5			−0.724606			−0.362303	−	0.932060i	$-0.618009\pi$
$971$	−21924.5			−0.724606			−0.362303	+	0.932060i	$0.618009\pi$
$972$	−19845.4	−	20211.2i	−0.654880	−	0.666949i
$973$	−16101.1			−0.530503
$974$	−26886.5	+	46568.7i	−0.884495	+	1.53199i
$975$	6381.12	−	23641.9i	0.209599	−	0.776560i
$976$	−21414.6	−	37091.1i	−0.702319	−	1.21645i
$977$	6888.95	+	11932.0i	0.225586	+	0.390726i	0.956495	−	0.291749i	$-0.0942372\pi$
$977$	6888.95	+	11932.0i	0.225586	+	0.390726i	−0.730909	+	0.682474i	$0.760904\pi$
$978$	23871.6	+	23959.0i	0.780502	+	0.783358i
$979$	−15829.4	+	27417.3i	−0.516762	+	0.895058i
$980$	−890.889			−0.0290392
$981$	−21588.2	−	12569.3i	−0.702606	−	0.409079i
$982$	4636.85			0.150680
$983$	6554.20	−	11352.2i	0.212662	−	0.368341i	−0.739885	−	0.672733i	$-0.765120\pi$
$983$	6554.20	−	11352.2i	0.212662	−	0.368341i	0.952547	+	0.304393i	$0.0984534\pi$
$984$	745.822	−	198.383i	0.0241625	−	0.00642706i
$985$	3597.16	+	6230.46i	0.116360	+	0.201542i
$986$	−78.4739	−	135.921i	−0.00253460	−	0.00439006i
$987$	10359.2	−	2755.47i	0.334080	−	0.0888629i
$988$	14219.0	−	24628.0i	0.457860	−	0.793037i
$989$	35440.9			1.13949
$990$	9452.50	−	5411.47i	0.303455	−	0.173725i
$991$	−12950.1			−0.415109			−0.207555	−	0.978223i	$-0.566550\pi$
$991$	−12950.1			−0.415109			−0.207555	+	0.978223i	$0.566550\pi$
$992$	30022.6	−	52000.6i	0.960904	−	1.66434i
$993$	16886.8	+	16948.6i	0.539664	+	0.541639i
$994$	10993.3	+	19040.9i	0.350790	+	0.607586i
$995$	−1896.30	−	3284.49i	−0.0604188	−	0.104648i
$996$	13063.6	−	48400.5i	0.415600	−	1.53979i
$997$	−18059.8	+	31280.5i	−0.573682	+	0.993646i	0.422502	+	0.906362i	$0.361152\pi$
$997$	−18059.8	+	31280.5i	−0.573682	+	0.993646i	−0.996184	+	0.0872835i	$0.972181\pi$
$998$	151.494			0.00480507
$999$	14394.4	−	14237.6i	0.455876	−	0.450908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.b.43.7	yes	16
3.2	odd	2		189.4.f.b.127.2		16
9.2	odd	6		567.4.a.g.1.7		8
9.4	even	3	inner	63.4.f.b.22.7	✓	16
9.5	odd	6		189.4.f.b.64.2		16
9.7	even	3		567.4.a.i.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.b.22.7	✓	16	9.4	even	3	inner
63.4.f.b.43.7	yes	16	1.1	even	1	trivial
189.4.f.b.64.2		16	9.5	odd	6
189.4.f.b.127.2		16	3.2	odd	2
567.4.a.g.1.7		8	9.2	odd	6
567.4.a.i.1.2		8	9.7	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.96709 - 3.40709i) q^{2} +(1.35403 - 5.01663i) q^{3} +(-3.73885 - 6.47588i) q^{4} +(1.21571 + 2.10567i) q^{5} +(-14.4286 - 14.4814i) q^{6} +(3.50000 - 6.06218i) q^{7} +2.05480 q^{8} +(-23.3332 - 13.5853i) q^{9} +O(q^{10})\)	\(q+(1.96709 - 3.40709i) q^{2} +(1.35403 - 5.01663i) q^{3} +(-3.73885 - 6.47588i) q^{4} +(1.21571 + 2.10567i) q^{5} +(-14.4286 - 14.4814i) q^{6} +(3.50000 - 6.06218i) q^{7} +2.05480 q^{8} +(-23.3332 - 13.5853i) q^{9} +9.56561 q^{10} +(-21.0862 + 36.5223i) q^{11} +(-37.5496 + 9.98793i) q^{12} +(19.7866 + 34.2714i) q^{13} +(-13.7696 - 23.8496i) q^{14} +(12.2095 - 3.24763i) q^{15} +(33.9528 - 58.8079i) q^{16} -2.07697 q^{17} +(-92.1849 + 52.7750i) q^{18} +96.1013 q^{19} +(9.09070 - 15.7456i) q^{20} +(-25.6726 - 25.7666i) q^{21} +(82.9566 + 143.685i) q^{22} +(-36.8754 - 63.8701i) q^{23} +(2.78225 - 10.3082i) q^{24} +(59.5441 - 103.133i) q^{25} +155.688 q^{26} +(-99.7463 + 98.6594i) q^{27} -52.3439 q^{28} +(-9.60379 + 16.6342i) q^{29} +(12.9521 - 47.9871i) q^{30} +(119.748 + 207.410i) q^{31} +(-125.357 - 217.124i) q^{32} +(154.668 + 155.234i) q^{33} +(-4.08557 + 7.07642i) q^{34} +17.0199 q^{35} +(-0.737407 + 201.897i) q^{36} -144.310 q^{37} +(189.039 - 327.426i) q^{38} +(198.718 - 52.8577i) q^{39} +(2.49803 + 4.32672i) q^{40} +(36.1409 + 62.5979i) q^{41} +(-138.289 + 36.7840i) q^{42} +(-240.274 + 416.167i) q^{43} +315.352 q^{44} +(0.239772 - 65.6478i) q^{45} -290.148 q^{46} +(-147.354 + 255.224i) q^{47} +(-249.045 - 249.956i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-234.257 - 405.745i) q^{50} +(-2.81227 + 10.4194i) q^{51} +(147.958 - 256.271i) q^{52} -627.210 q^{53} +(139.932 + 533.916i) q^{54} -102.538 q^{55} +(7.19179 - 12.4565i) q^{56} +(130.124 - 482.105i) q^{57} +(37.7829 + 65.4420i) q^{58} +(-74.8093 - 129.573i) q^{59} +(-66.6807 - 66.9246i) q^{60} +(315.358 - 546.216i) q^{61} +942.221 q^{62} +(-164.023 + 93.9016i) q^{63} -443.106 q^{64} +(-48.1094 + 83.3279i) q^{65} +(833.141 - 221.610i) q^{66} +(-2.02124 - 3.50089i) q^{67} +(7.76547 + 13.4502i) q^{68} +(-370.343 + 98.5087i) q^{69} +(33.4796 - 57.9884i) q^{70} -798.373 q^{71} +(-47.9450 - 27.9150i) q^{72} +444.022 q^{73} +(-283.871 + 491.679i) q^{74} +(-436.758 - 438.356i) q^{75} +(-359.309 - 622.341i) q^{76} +(147.603 + 255.656i) q^{77} +(210.805 - 781.027i) q^{78} +(287.769 - 498.431i) q^{79} +165.107 q^{80} +(359.879 + 633.978i) q^{81} +284.369 q^{82} +(-645.117 + 1117.38i) q^{83} +(-70.8751 + 262.590i) q^{84} +(-2.52498 - 4.37340i) q^{85} +(945.280 + 1637.27i) q^{86} +(70.4441 + 70.7019i) q^{87} +(-43.3278 + 75.0459i) q^{88} +750.701 q^{89} +(-223.196 - 129.952i) q^{90} +277.012 q^{91} +(-275.744 + 477.602i) q^{92} +(1202.64 - 319.895i) q^{93} +(579.714 + 1004.09i) q^{94} +(116.831 + 202.357i) q^{95} +(-1258.97 + 334.877i) q^{96} +(-209.774 + 363.339i) q^{97} -192.774 q^{98} +(988.175 - 565.721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * q^99

Introduction

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