LMFDB - Embedded newform 105.3.o.a.74.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(44,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("105.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 4 x^{15} - 4 x^{14} + 12 x^{13} + 162 x^{12} - 524 x^{11} - 88 x^{10} + 1492 x^{9} + \cdots + 1521 $ x^16 - 4x^15 - 4x^14 + 12x^13 + 162x^12 - 524x^11 - 88x^10 + 1492x^9 + 6266x^8 - 41348x^7 + 103092x^6 - 152724x^5 + 148342x^4 - 96348x^3 + 41016x^2 - 10764*x + 1521
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			74.5
Root			$0.752308 + 0.673492i$ of defining polynomial
Character	$\chi$	$=$	105.74
Dual form			105.3.o.a.44.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.530805 + 0.919382i) q^{2} +(-2.96077 - 0.483560i) q^{3} +(1.43649 - 2.48808i) q^{4} +(0.901243 + 4.91811i) q^{5} +(-1.12702 - 2.97876i) q^{6} +(3.04726 + 6.30192i) q^{7} +7.29643 q^{8} +(8.53234 + 2.86342i) q^{9} +O(q^{10})$	\(q+(0.530805 + 0.919382i) q^{2} +(-2.96077 - 0.483560i) q^{3} +(1.43649 - 2.48808i) q^{4} +(0.901243 + 4.91811i) q^{5} +(-1.12702 - 2.97876i) q^{6} +(3.04726 + 6.30192i) q^{7} +7.29643 q^{8} +(8.53234 + 2.86342i) q^{9} +(-4.04323 + 3.43914i) q^{10} +(9.99105 + 5.76833i) q^{11} +(-5.45626 + 6.67200i) q^{12} -5.56650i q^{13} +(-4.17637 + 6.14669i) q^{14} +(-0.290174 - 14.9972i) q^{15} +(-1.87298 - 3.24410i) q^{16} +(-7.82724 + 13.5572i) q^{17} +(1.89643 + 9.36440i) q^{18} +(1.06351 + 1.84205i) q^{19} +(13.5313 + 4.82246i) q^{20} +(-5.97488 - 20.1321i) q^{21} +12.2474i q^{22} +(-13.0004 - 22.5174i) q^{23} +(-21.6031 - 3.52826i) q^{24} +(-23.3755 + 8.86482i) q^{25} +(5.11774 - 2.95473i) q^{26} +(-23.8777 - 12.6038i) q^{27} +(20.0570 + 1.47084i) q^{28} +13.3804i q^{29} +(13.6341 - 8.22737i) q^{30} +(25.3730 - 43.9473i) q^{31} +(16.5812 - 28.7195i) q^{32} +(-26.7919 - 21.9100i) q^{33} -16.6190 q^{34} +(-28.2472 + 20.6663i) q^{35} +(19.3810 - 17.1158i) q^{36} +(19.8268 - 11.4470i) q^{37} +(-1.12903 + 1.95554i) q^{38} +(-2.69174 + 16.4811i) q^{39} +(6.57586 + 35.8846i) q^{40} +53.9959i q^{41} +(15.3376 - 16.1794i) q^{42} -38.8354i q^{43} +(28.7041 - 16.5723i) q^{44} +(-6.39291 + 44.5436i) q^{45} +(13.8014 - 23.9047i) q^{46} +(-2.72145 - 4.71368i) q^{47} +(3.97676 + 10.5107i) q^{48} +(-30.4284 + 38.4072i) q^{49} +(-20.5580 - 16.7855i) q^{50} +(29.7304 - 36.3547i) q^{51} +(-13.8499 - 7.99623i) q^{52} +(-15.5196 + 26.8808i) q^{53} +(-1.08665 - 28.6429i) q^{54} +(-19.3649 + 54.3357i) q^{55} +(22.2341 + 45.9815i) q^{56} +(-2.25806 - 5.96816i) q^{57} +(-12.3017 + 7.10237i) q^{58} +(-97.9861 - 56.5723i) q^{59} +(-37.7310 - 20.8214i) q^{60} +(-14.8175 - 25.6647i) q^{61} +53.8724 q^{62} +(7.95518 + 62.4957i) q^{63} +20.2218 q^{64} +(27.3766 - 5.01677i) q^{65} +(5.92238 - 36.2619i) q^{66} +(-23.5648 - 13.6051i) q^{67} +(22.4875 + 38.9495i) q^{68} +(27.6028 + 72.9555i) q^{69} +(-33.9940 - 15.0002i) q^{70} -79.6697i q^{71} +(62.2556 + 20.8928i) q^{72} +(-1.70004 - 0.981521i) q^{73} +(21.0483 + 12.1523i) q^{74} +(73.4963 - 14.9432i) q^{75} +6.11088 q^{76} +(-5.90628 + 80.5404i) q^{77} +(-16.5812 + 6.27354i) q^{78} +(43.8095 + 75.8802i) q^{79} +(14.2668 - 12.1353i) q^{80} +(64.6016 + 48.8634i) q^{81} +(-49.6429 + 28.6613i) q^{82} +71.3633 q^{83} +(-58.6730 - 14.0536i) q^{84} +(-73.7298 - 26.2769i) q^{85} +(35.7046 - 20.6141i) q^{86} +(6.47022 - 39.6162i) q^{87} +(72.8990 + 42.0883i) q^{88} +(106.791 - 61.6560i) q^{89} +(-44.3459 + 17.7664i) q^{90} +(35.0796 - 16.9626i) q^{91} -74.7001 q^{92} +(-96.3748 + 117.849i) q^{93} +(2.88912 - 5.00410i) q^{94} +(-8.10092 + 6.89058i) q^{95} +(-62.9809 + 77.0140i) q^{96} -1.02391i q^{97} +(-51.4624 - 7.58861i) q^{98} +(68.7298 + 77.8260i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} - 80 q^{6} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^4 - 80 * q^6 - 8 * q^9	$ 16 q - 8 q^{4} - 80 q^{6} - 8 q^{9} - 40 q^{10} - 80 q^{15} + 32 q^{16} + 48 q^{19} - 8 q^{21} + 40 q^{30} + 344 q^{31} - 80 q^{34} + 496 q^{36} - 32 q^{39} + 120 q^{40} - 80 q^{45} - 120 q^{46} - 208 q^{49} - 40 q^{51} + 200 q^{54} + 40 q^{60} - 392 q^{61} - 544 q^{64} + 120 q^{66} - 240 q^{69} - 760 q^{70} + 200 q^{75} - 336 q^{76} + 608 q^{79} - 328 q^{81} - 344 q^{84} - 560 q^{85} + 80 q^{90} + 1088 q^{91} + 480 q^{94} - 400 q^{96} + 480 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 - 80 * q^6 - 8 * q^9 - 40 * q^10 - 80 * q^15 + 32 * q^16 + 48 * q^19 - 8 * q^21 + 40 * q^30 + 344 * q^31 - 80 * q^34 + 496 * q^36 - 32 * q^39 + 120 * q^40 - 80 * q^45 - 120 * q^46 - 208 * q^49 - 40 * q^51 + 200 * q^54 + 40 * q^60 - 392 * q^61 - 544 * q^64 + 120 * q^66 - 240 * q^69 - 760 * q^70 + 200 * q^75 - 336 * q^76 + 608 * q^79 - 328 * q^81 - 344 * q^84 - 560 * q^85 + 80 * q^90 + 1088 * q^91 + 480 * q^94 - 400 * q^96 + 480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.530805	+	0.919382i	0.265403	+	0.459691i	0.967669	−	0.252223i	$-0.0811618\pi$
$2$	0.530805	+	0.919382i	0.265403	+	0.459691i	−0.702266	+	0.711914i	$0.747828\pi$
$3$	−2.96077	−	0.483560i	−0.986924	−	0.161187i
$3$	−2.96077	−	0.483560i	−0.986924	−	0.161187i
$4$	1.43649	−	2.48808i	0.359123	−	0.622019i
$5$	0.901243	+	4.91811i	0.180249	+	0.983621i
$5$	0.901243	+	4.91811i	0.180249	+	0.983621i
$6$	−1.12702	−	2.97876i	−0.187836	−	0.496459i
$7$	3.04726	+	6.30192i	0.435323	+	0.900274i
$7$	3.04726	+	6.30192i	0.435323	+	0.900274i
$8$	7.29643			0.912054
$9$	8.53234	+	2.86342i	0.948038	+	0.318158i
$10$	−4.04323	+	3.43914i	−0.404323	+	0.343914i
$11$	9.99105	+	5.76833i	0.908277	+	0.524394i	0.879876	−	0.475203i	$-0.157625\pi$
$11$	9.99105	+	5.76833i	0.908277	+	0.524394i	0.0284008	+	0.999597i	$0.490959\pi$
$12$	−5.45626	+	6.67200i	−0.454688	+	0.556000i
$13$		−	5.56650i		−	0.428192i	−0.976813	−	0.214096i	$-0.931319\pi$
$13$		−	5.56650i		−	0.428192i	0.976813	−	0.214096i	$-0.0686806\pi$
$14$	−4.17637	+	6.14669i	−0.298312	+	0.439049i
$15$	−0.290174	−	14.9972i	−0.0193450	−	0.999813i
$16$	−1.87298	−	3.24410i	−0.117061	−	0.202756i
$17$	−7.82724	+	13.5572i	−0.460426	+	0.797481i	−0.998982	−	0.0451088i	$-0.985637\pi$
$17$	−7.82724	+	13.5572i	−0.460426	+	0.797481i	0.538556	+	0.842589i	$0.318970\pi$
$18$	1.89643	+	9.36440i	0.105357	+	0.520244i
$19$	1.06351	+	1.84205i	0.0559741	+	0.0969500i	0.892655	−	0.450741i	$-0.148840\pi$
$19$	1.06351	+	1.84205i	0.0559741	+	0.0969500i	−0.836681	+	0.547691i	$0.815507\pi$
$20$	13.5313	+	4.82246i	0.676563	+	0.241123i
$21$	−5.97488	−	20.1321i	−0.284518	−	0.958671i
$22$			12.2474i			0.556702i
$23$	−13.0004	−	22.5174i	−0.565237	−	0.979019i	−0.997028	−	0.0770450i	$-0.975451\pi$
$23$	−13.0004	−	22.5174i	−0.565237	−	0.979019i	0.431791	−	0.901974i	$-0.357882\pi$
$24$	−21.6031	−	3.52826i	−0.900128	−	0.147011i
$25$	−23.3755	+	8.86482i	−0.935021	+	0.354593i
$26$	5.11774	−	2.95473i	0.196836	−	0.113643i
$27$	−23.8777	−	12.6038i	−0.884358	−	0.466809i
$28$	20.0570	+	1.47084i	0.716322	+	0.0525301i
$29$			13.3804i			0.461392i	0.973026	+	0.230696i	$0.0741003\pi$
$29$			13.3804i			0.461392i	−0.973026	+	0.230696i	$0.925900\pi$
$30$	13.6341	−	8.22737i	0.454471	−	0.274246i
$31$	25.3730	−	43.9473i	0.818483	−	1.41765i	−0.0883161	−	0.996092i	$-0.528149\pi$
$31$	25.3730	−	43.9473i	0.818483	−	1.41765i	0.906799	−	0.421562i	$-0.138518\pi$
$32$	16.5812	−	28.7195i	0.518164	−	0.897486i
$33$	−26.7919	−	21.9100i	−0.811875	−	0.663939i
$34$	−16.6190			−0.488793
$35$	−28.2472	+	20.6663i	−0.807063	+	0.590466i
$36$	19.3810	−	17.1158i	0.538362	−	0.475440i
$37$	19.8268	−	11.4470i	0.535859	−	0.309378i	−0.207540	−	0.978227i	$-0.566546\pi$
$37$	19.8268	−	11.4470i	0.535859	−	0.309378i	0.743399	+	0.668848i	$0.233212\pi$
$38$	−1.12903	+	1.95554i	−0.0297114	+	0.0514616i
$39$	−2.69174	+	16.4811i	−0.0690189	+	0.422593i
$40$	6.57586	+	35.8846i	0.164396	+	0.897115i
$41$			53.9959i			1.31697i	0.752592	+	0.658487i	$0.228803\pi$
$41$			53.9959i			1.31697i	−0.752592	+	0.658487i	$0.771197\pi$
$42$	15.3376	−	16.1794i	0.365180	−	0.385224i
$43$		−	38.8354i		−	0.903150i	−0.892233	−	0.451575i	$-0.850862\pi$
$43$		−	38.8354i		−	0.903150i	0.892233	−	0.451575i	$-0.149138\pi$
$44$	28.7041	−	16.5723i	0.652366	−	0.376644i
$45$	−6.39291	+	44.5436i	−0.142065	+	0.989857i
$46$	13.8014	−	23.9047i	0.300031	−	0.519668i
$47$	−2.72145	−	4.71368i	−0.0579031	−	0.100291i	0.835621	−	0.549307i	$-0.185108\pi$
$47$	−2.72145	−	4.71368i	−0.0579031	−	0.100291i	−0.893524	+	0.449016i	$0.851775\pi$
$48$	3.97676	+	10.5107i	0.0828491	+	0.218974i
$49$	−30.4284	+	38.4072i	−0.620988	+	0.783820i
$50$	−20.5580	−	16.7855i	−0.411160	−	0.335711i
$51$	29.7304	−	36.3547i	0.582948	−	0.712838i
$52$	−13.8499	−	7.99623i	−0.266344	−	0.153774i
$53$	−15.5196	+	26.8808i	−0.292823	+	0.507185i	−0.974476	−	0.224491i	$-0.927928\pi$
$53$	−15.5196	+	26.8808i	−0.292823	+	0.507185i	0.681653	+	0.731676i	$0.261261\pi$
$54$	−1.08665	−	28.6429i	−0.0201232	−	0.530424i
$55$	−19.3649	+	54.3357i	−0.352089	+	0.987922i
$56$	22.2341	+	45.9815i	0.397038	+	0.821099i
$57$	−2.25806	−	5.96816i	−0.0396151	−	0.104705i
$58$	−12.3017	+	7.10237i	−0.212098	+	0.122455i
$59$	−97.9861	−	56.5723i	−1.66078	−	0.958853i	−0.972343	−	0.233559i	$-0.924963\pi$
$59$	−97.9861	−	56.5723i	−1.66078	−	0.958853i	−0.688439	−	0.725294i	$-0.741704\pi$
$60$	−37.7310	−	20.8214i	−0.628850	−	0.347023i
$61$	−14.8175	−	25.6647i	−0.242911	−	0.420733i	0.718632	−	0.695391i	$-0.244769\pi$
$61$	−14.8175	−	25.6647i	−0.242911	−	0.420733i	−0.961542	+	0.274658i	$0.911435\pi$
$62$	53.8724			0.868910
$63$	7.95518	+	62.4957i	0.126273	+	0.991996i
$64$	20.2218			0.315965
$65$	27.3766	−	5.01677i	0.421179	−	0.0771811i
$66$	5.92238	−	36.2619i	0.0897330	−	0.549423i
$67$	−23.5648	−	13.6051i	−0.351713	−	0.203062i	0.313727	−	0.949513i	$-0.398422\pi$
$67$	−23.5648	−	13.6051i	−0.351713	−	0.203062i	−0.665439	+	0.746452i	$0.731756\pi$
$68$	22.4875	+	38.9495i	0.330699	+	0.572787i
$69$	27.6028	+	72.9555i	0.400041	+	1.05733i
$70$	−33.9940	−	15.0002i	−0.485628	−	0.214288i
$71$		−	79.6697i		−	1.12211i	−0.827779	−	0.561054i	$-0.810396\pi$
$71$		−	79.6697i		−	1.12211i	0.827779	−	0.561054i	$-0.189604\pi$
$72$	62.2556	+	20.8928i	0.864661	+	0.290177i
$73$	−1.70004	−	0.981521i	−0.0232883	−	0.0134455i	0.488311	−	0.872670i	$-0.337613\pi$
$73$	−1.70004	−	0.981521i	−0.0232883	−	0.0134455i	−0.511599	+	0.859224i	$0.670947\pi$
$74$	21.0483	+	12.1523i	0.284437	+	0.164220i
$75$	73.4963	−	14.9432i	0.979950	−	0.199243i
$76$	6.11088			0.0804064
$77$	−5.90628	+	80.5404i	−0.0767049	+	1.04598i
$78$	−16.5812	+	6.27354i	−0.212580	+	0.0804300i
$79$	43.8095	+	75.8802i	0.554550	+	0.960509i	0.997938	+	0.0641796i	$0.0204430\pi$
$79$	43.8095	+	75.8802i	0.554550	+	0.960509i	−0.443388	+	0.896330i	$0.646224\pi$
$80$	14.2668	−	12.1353i	0.178335	−	0.151691i
$81$	64.6016	+	48.8634i	0.797551	+	0.603252i
$82$	−49.6429	+	28.6613i	−0.605401	+	0.349528i
$83$	71.3633			0.859799			0.429900	−	0.902877i	$-0.358549\pi$
$83$	71.3633			0.859799			0.429900	+	0.902877i	$0.358549\pi$
$84$	−58.6730	−	14.0536i	−0.698488	−	0.167305i
$85$	−73.7298	−	26.2769i	−0.867410	−	0.309140i
$86$	35.7046	−	20.6141i	0.415170	−	0.239698i
$87$	6.47022	−	39.6162i	0.0743703	−	0.455359i
$88$	72.8990	+	42.0883i	0.828398	+	0.478276i
$89$	106.791	−	61.6560i	1.19990	−	0.692764i	0.239370	−	0.970928i	$-0.423059\pi$
$89$	106.791	−	61.6560i	1.19990	−	0.692764i	0.960534	+	0.278164i	$0.0897259\pi$
$90$	−44.3459	+	17.7664i	−0.492733	+	0.197405i
$91$	35.0796	−	16.9626i	0.385491	−	0.186402i
$92$	−74.7001			−0.811958
$93$	−96.3748	+	117.849i	−1.03629	+	1.26719i
$94$	2.88912	−	5.00410i	0.0307353	−	0.0532351i
$95$	−8.10092	+	6.89058i	−0.0852728	+	0.0725324i
$96$	−62.9809	+	77.0140i	−0.656051	+	0.802229i
$97$		−	1.02391i		−	0.0105558i	−0.999986	−	0.00527791i	$-0.998320\pi$
$97$		−	1.02391i		−	0.0105558i	0.999986	−	0.00527791i	$-0.00168002\pi$
$98$	−51.4624	−	7.58861i	−0.525127	−	0.0774348i
$99$	68.7298	+	77.8260i	0.694241	+	0.786121i
$100$	−11.5224	+	70.8943i	−0.115224	+	0.708943i
$101$	−102.573	−	59.2208i	−1.01558	−	0.586344i	−0.102758	−	0.994706i	$-0.532767\pi$
$101$	−102.573	−	59.2208i	−1.01558	−	0.586344i	−0.912820	+	0.408362i	$0.866100\pi$
$102$	49.2049	+	8.03626i	0.482401	+	0.0787869i
$103$	148.497	−	85.7350i	1.44172	−	0.832379i	0.443758	−	0.896147i	$-0.353645\pi$
$103$	148.497	−	85.7350i	1.44172	−	0.832379i	0.997965	+	0.0637681i	$0.0203118\pi$
$104$		−	40.6156i		−	0.390534i
$105$	93.6269	−	47.5290i	0.891685	−	0.452657i
$106$	−32.9516			−0.310864
$107$	−83.5130	−	144.649i	−0.780495	−	1.35186i	−0.931654	−	0.363348i	$-0.881634\pi$
$107$	−83.5130	−	144.649i	−0.780495	−	1.35186i	0.151158	−	0.988510i	$-0.451700\pi$
$108$	−65.6594	+	41.3042i	−0.607957	+	0.382446i
$109$	38.1744	−	66.1200i	0.350224	−	0.606605i	−0.636065	−	0.771636i	$-0.719439\pi$
$109$	38.1744	−	66.1200i	0.350224	−	0.606605i	0.986288	+	0.165030i	$0.0527722\pi$
$110$	−60.2342	+	11.0379i	−0.547584	+	0.100345i
$111$	−64.2379	+	24.3045i	−0.578720	+	0.218960i
$112$	14.7366	−	21.6890i	0.131577	−	0.193652i
$113$	−6.36966			−0.0563687			−0.0281843	−	0.999603i	$-0.508973\pi$
$113$	−6.36966			−0.0563687			−0.0281843	+	0.999603i	$0.508973\pi$
$114$	4.28843	−	5.24395i	0.0376178	−	0.0459996i
$115$	99.0265	−	84.2312i	0.861100	−	0.732446i
$116$	33.2914	+	19.2208i	0.286995	+	0.165696i
$117$	15.9392	−	47.4953i	0.136233	−	0.405942i
$118$		−	120.116i		−	1.01793i
$119$	−109.288	−	8.01442i	−0.918385	−	0.0673480i
$120$	−2.11724	−	109.426i	−0.0176436	−	0.911883i
$121$	6.04738	+	10.4744i	0.0499783	+	0.0865650i
$122$	15.7305	−	27.2459i	0.128938	−	0.223327i
$123$	26.1103	−	159.870i	0.212279	−	1.29975i
$124$	−72.8962	−	126.260i	−0.587872	−	1.01822i
$125$	−64.6651	−	106.974i	−0.517321	−	0.855791i
$126$	−53.2348	+	40.4869i	−0.422498	+	0.321325i
$127$			244.202i			1.92285i	0.275061	+	0.961427i	$0.411302\pi$
$127$			244.202i			1.92285i	−0.275061	+	0.961427i	$0.588698\pi$
$128$	−55.5911	−	96.2867i	−0.434306	−	0.752240i
$129$	−18.7793	+	114.983i	−0.145576	+	0.891340i
$130$	19.1440	+	22.5066i	0.147261	+	0.173128i
$131$	−44.6710	+	25.7908i	−0.341000	+	0.196877i	−0.660714	−	0.750637i	$-0.729746\pi$
$131$	−44.6710	+	25.7908i	−0.341000	+	0.196877i	0.319714	+	0.947514i	$0.396413\pi$
$132$	−93.0001	+	35.1867i	−0.704546	+	0.266566i
$133$	−8.36767	+	12.3154i	−0.0629148	+	0.0925966i
$134$		−	28.8867i		−	0.215572i
$135$	40.4674	−	128.792i	0.299759	−	0.954015i
$136$	−57.1109	+	98.9190i	−0.419933	+	0.727345i
$137$	−71.8353	+	124.422i	−0.524345	+	0.908192i	0.475253	+	0.879849i	$0.342356\pi$
$137$	−71.8353	+	124.422i	−0.524345	+	0.908192i	−0.999598	+	0.0283432i	$0.990977\pi$
$138$	−52.4222	+	64.1027i	−0.379871	+	0.464512i
$139$	−1.84072			−0.0132426			−0.00662128	−	0.999978i	$-0.502108\pi$
$139$	−1.84072			−0.0132426			−0.00662128	+	0.999978i	$0.502108\pi$
$140$	10.8425	+	99.9682i	0.0774463	+	0.714058i
$141$	5.77823	+	15.2721i	0.0409804	+	0.108313i
$142$	73.2468	−	42.2891i	0.515823	−	0.297810i
$143$	32.1094	−	55.6152i	0.224541	−	0.388917i
$144$	−6.69169	−	33.0429i	−0.0464701	−	0.229465i
$145$	−65.8061	+	12.0590i	−0.453835	+	0.0831653i
$146$		−	2.08399i		−	0.0142739i
$147$	108.664	−	99.0009i	0.739210	−	0.673475i
$148$		−	65.7741i		−	0.444419i
$149$	−101.674	+	58.7013i	−0.682374	+	0.393969i	−0.800749	−	0.599000i	$-0.795565\pi$
$149$	−101.674	+	58.7013i	−0.682374	+	0.393969i	0.118375	+	0.992969i	$0.462231\pi$
$150$	52.7507	+	59.6392i	0.351671	+	0.397594i
$151$	−125.801	+	217.894i	−0.833122	+	1.44301i	0.0624285	+	0.998049i	$0.480115\pi$
$151$	−125.801	+	217.894i	−0.833122	+	1.44301i	−0.895550	+	0.444960i	$0.853218\pi$
$152$	7.75981	+	13.4404i	0.0510514	+	0.0884236i
$153$	−105.605	+	93.2617i	−0.690226	+	0.609553i
$154$	−77.1825	+	37.3211i	−0.501185	+	0.242345i
$155$	239.005	+	85.1798i	1.54197	+	0.549547i
$156$	37.1397	+	30.3723i	0.238075	+	0.194694i
$157$	−229.808	−	132.680i	−1.46375	−	0.845095i	−0.464565	−	0.885539i	$-0.653789\pi$
$157$	−229.808	−	132.680i	−1.46375	−	0.845095i	−0.999182	+	0.0404444i	$0.987123\pi$
$158$	−46.5086	+	80.5552i	−0.294358	+	0.509843i
$159$	58.9486	−	72.0832i	0.370746	−	0.453353i
$160$	156.190	+	55.6650i	0.976184	+	0.347906i
$161$	102.287	−	150.544i	0.635325	−	0.935057i
$162$	−10.6332	+	85.3305i	−0.0656372	+	0.526731i
$163$	132.913	−	76.7375i	0.815419	−	0.470782i	−0.0334153	−	0.999442i	$-0.510638\pi$
$163$	132.913	−	76.7375i	0.815419	−	0.470782i	0.848834	+	0.528659i	$0.177305\pi$
$164$	134.346	+	77.5647i	0.819183	+	0.472956i
$165$	83.6097	−	151.512i	0.506725	−	0.918252i
$166$	37.8800	+	65.6101i	0.228193	+	0.395242i
$167$	179.226			1.07321			0.536605	−	0.843834i	$-0.319707\pi$
$167$	179.226			1.07321			0.536605	+	0.843834i	$0.319707\pi$
$168$	−43.5953	−	146.892i	−0.259496	−	0.874359i
$169$	138.014			0.816651
$170$	−14.9777	−	81.7337i	−0.0881042	−	0.480787i
$171$	3.79964	+	18.7623i	0.0222201	+	0.109721i
$172$	−96.6256	−	55.7868i	−0.561776	−	0.324342i
$173$	52.3475	+	90.6684i	0.302586	+	0.524095i	0.976721	−	0.214513i	$-0.0688166\pi$
$173$	52.3475	+	90.6684i	0.302586	+	0.524095i	−0.674135	+	0.738609i	$0.735483\pi$
$174$	39.8569	−	15.0799i	0.229062	−	0.0866661i
$175$	−127.097	−	120.297i	−0.726267	−	0.687413i
$176$		−	43.2160i		−	0.245545i
$177$	262.758	+	214.880i	1.48451	+	1.21401i
$178$	113.371	+	65.4547i	0.636915	+	0.367723i
$179$	70.7539	+	40.8498i	0.395273	+	0.228211i	0.684442	−	0.729067i	$-0.260046\pi$
$179$	70.7539	+	40.8498i	0.395273	+	0.228211i	−0.289169	+	0.957278i	$0.593379\pi$
$180$	101.644	+	79.8925i	0.564692	+	0.443847i
$181$	80.7923			0.446366			0.223183	−	0.974777i	$-0.428355\pi$
$181$	80.7923			0.446366			0.223183	+	0.974777i	$0.428355\pi$
$182$	34.2155	+	23.2478i	0.187997	+	0.127735i
$183$	31.4609	+	83.1526i	0.171918	+	0.454386i
$184$	−94.8569	−	164.297i	−0.515526	−	0.892918i
$185$	74.1663	+	87.1937i	0.400899	+	0.471317i
$186$	−159.504	−	26.0506i	−0.857548	−	0.140057i
$187$	−156.405	+	90.3002i	−0.836388	+	0.482889i
$188$	−15.6373			−0.0831774
$189$	6.66698	−	188.882i	0.0352750	−	0.999378i
$190$	−10.6351	−	3.79028i	−0.0559741	−	0.0199488i
$191$	−290.723	+	167.849i	−1.52211	+	0.878792i	−0.522453	+	0.852668i	$0.674983\pi$
$191$	−290.723	+	167.849i	−1.52211	+	0.878792i	−0.999659	+	0.0261240i	$0.991684\pi$
$192$	−59.8720	−	9.77844i	−0.311834	−	0.0509294i
$193$	11.1162	+	6.41797i	0.0575971	+	0.0332537i	0.528522	−	0.848920i	$-0.322746\pi$
$193$	11.1162	+	6.41797i	0.0575971	+	0.0332537i	−0.470925	+	0.882173i	$0.656080\pi$
$194$	0.941368	−	0.543499i	0.00485241	−	0.00280154i
$195$	−83.4819	+	1.61525i	−0.428112	+	0.00828336i
$196$	51.8498	+	130.880i	0.264540	+	0.667754i
$197$	79.1991			0.402026			0.201013	−	0.979589i	$-0.435577\pi$
$197$	79.1991			0.402026			0.201013	+	0.979589i	$0.435577\pi$
$198$	−35.0696	+	104.499i	−0.177119	+	0.527775i
$199$	−2.70666	+	4.68807i	−0.0136013	+	0.0235581i	−0.872746	−	0.488175i	$-0.837663\pi$
$199$	−2.70666	+	4.68807i	−0.0136013	+	0.0235581i	0.859145	+	0.511733i	$0.170996\pi$
$200$	−170.558	+	64.6815i	−0.852789	+	0.323408i
$201$	63.1910	+	51.6766i	0.314383	+	0.257098i
$202$		−	125.739i		−	0.622469i
$203$	−84.3220	+	40.7735i	−0.415380	+	0.200854i
$204$	−47.7460	−	126.195i	−0.234049	−	0.618602i
$205$	−265.558	+	48.6635i	−1.29540	+	0.237383i
$206$	157.646	+	91.0172i	0.765274	+	0.441831i
$207$	−46.4473	−	229.352i	−0.224383	−	1.10798i
$208$	−18.0583	+	10.4260i	−0.0868187	+	0.0501248i
$209$			24.5387i			0.117410i
$210$	93.3949	+	60.8502i	0.444738	+	0.289763i
$211$	−206.268			−0.977574			−0.488787	−	0.872403i	$-0.662560\pi$
$211$	−206.268			−0.977574			−0.488787	+	0.872403i	$0.662560\pi$
$212$	44.5876	+	77.2281i	0.210319	+	0.364283i
$213$	−38.5251	+	235.884i	−0.180869	+	1.10744i
$214$	88.6583	−	153.561i	0.414291	−	0.717573i
$215$	190.997	−	35.0002i	0.888357	−	0.162791i
$216$	−174.222	−	91.9631i	−0.806582	−	0.425755i
$217$	354.270	+	25.9798i	1.63258	+	0.119722i
$218$	81.0527			0.371801
$219$	4.55882	+	3.72813i	0.0208165	+	0.0170234i
$220$	107.374	+	126.234i	0.488063	+	0.573792i
$221$	75.4660	+	43.5703i	0.341475	+	0.197151i
$222$	−56.4429	−	46.1582i	−0.254247	−	0.207920i
$223$			75.6231i			0.339117i	0.985520	+	0.169558i	$0.0542341\pi$
$223$			75.6231i			0.339117i	−0.985520	+	0.169558i	$0.945766\pi$
$224$	231.516	+	16.9778i	1.03355	+	0.0757936i
$225$	−224.832	+	8.70360i	−0.999252	+	0.0386827i
$226$	−3.38105	−	5.85615i	−0.0149604	−	0.0259122i
$227$	76.2166	−	132.011i	0.335756	−	0.581546i	−0.647874	−	0.761748i	$-0.724342\pi$
$227$	76.2166	−	132.011i	0.335756	−	0.581546i	0.983630	+	0.180202i	$0.0576750\pi$
$228$	−18.0929	−	2.95498i	−0.0793550	−	0.0129604i
$229$	151.690	+	262.734i	0.662400	+	1.14731i	0.979983	+	0.199079i	$0.0637952\pi$
$229$	151.690	+	262.734i	0.662400	+	1.14731i	−0.317584	+	0.948230i	$0.602871\pi$
$230$	130.004	+	46.3328i	0.565237	+	0.201447i
$231$	56.4333	−	235.606i	0.244300	−	1.01994i
$232$			97.6289i			0.420814i
$233$	−68.9287	−	119.388i	−0.295831	−	0.512395i	0.679347	−	0.733818i	$-0.262263\pi$
$233$	−68.9287	−	119.388i	−0.295831	−	0.512395i	−0.975178	+	0.221423i	$0.928930\pi$
$234$	52.1269	−	10.5565i	0.222765	−	0.0451132i
$235$	20.7297	−	17.6325i	0.0882115	−	0.0750321i
$236$	−281.513	+	162.531i	−1.19285	+	0.688692i
$237$	−93.0172	−	245.849i	−0.392478	−	1.03734i
$238$	−50.6422	−	104.731i	−0.212783	−	0.440048i
$239$			355.222i			1.48629i	0.669132	+	0.743143i	$0.266666\pi$
$239$			355.222i			1.48629i	−0.669132	+	0.743143i	$0.733334\pi$
$240$	−48.1089	+	29.0308i	−0.200454	+	0.120962i
$241$	−61.7853	+	107.015i	−0.256370	+	0.444047i	−0.965267	−	0.261266i	$-0.915860\pi$
$241$	−61.7853	+	107.015i	−0.256370	+	0.444047i	0.708896	+	0.705313i	$0.249193\pi$
$242$	−6.41996	+	11.1197i	−0.0265287	+	0.0459491i
$243$	−167.642	−	175.912i	−0.689886	−	0.723918i
$244$	−85.1411			−0.348939
$245$	−216.314	−	115.036i	−0.882914	−	0.469535i
$246$	160.841	−	60.8543i	0.653824	−	0.247375i
$247$	10.2538	−	5.92002i	0.0415133	−	0.0239677i
$248$	185.132	−	320.658i	0.746501	−	1.29298i
$249$	−211.291	−	34.5085i	−0.848556	−	0.138588i
$250$	64.0253	−	116.234i	0.256101	−	0.464937i
$251$		−	190.923i		−	0.760648i	−0.924853	−	0.380324i	$-0.875813\pi$
$251$		−	190.923i		−	0.760648i	0.924853	−	0.380324i	$-0.124187\pi$
$252$	166.922	+	69.9815i	0.662388	+	0.277704i
$253$		−	299.964i		−	1.18563i
$254$	−224.515	+	129.624i	−0.883918	+	0.510330i
$255$	205.591	+	113.453i	0.806238	+	0.444912i
$256$	99.4597	−	172.269i	0.388514	−	0.672927i
$257$	−90.2872	−	156.382i	−0.351312	−	0.608490i	0.635168	−	0.772374i	$-0.280931\pi$
$257$	−90.2872	−	156.382i	−0.351312	−	0.608490i	−0.986480	+	0.163884i	$0.947598\pi$
$258$	−115.681	+	43.7682i	−0.448377	+	0.169644i
$259$	132.555	+	90.0649i	0.511797	+	0.347741i
$260$	26.8442	−	75.3217i	0.103247	−	0.289699i
$261$	−38.3137	+	114.166i	−0.146796	+	0.437417i
$262$	−47.4232	−	27.3798i	−0.181005	−	0.104503i
$263$	−86.9761	+	150.647i	−0.330707	+	0.572802i	−0.982651	−	0.185466i	$-0.940621\pi$
$263$	−86.9761	+	150.647i	−0.330707	+	0.572802i	0.651943	+	0.758268i	$0.273954\pi$
$264$	−195.485	−	159.865i	−0.740474	−	0.605548i
$265$	−146.190	−	52.1011i	−0.551658	−	0.196608i
$266$	−15.7641	−	1.15603i	−0.0592636	−	0.00434598i
$267$	−345.999	+	130.909i	−1.29588	+	0.490297i
$268$	−67.7012	+	39.0873i	−0.252616	+	0.145848i
$269$	149.824	+	86.5010i	0.556967	+	0.321565i	0.751927	−	0.659246i	$-0.229124\pi$
$269$	149.824	+	86.5010i	0.556967	+	0.321565i	−0.194960	+	0.980811i	$0.562458\pi$
$270$	139.889	−	31.1585i	0.518109	−	0.115402i
$271$	−124.515	−	215.666i	−0.459465	−	0.795817i	0.539467	−	0.842007i	$-0.318626\pi$
$271$	−124.515	−	215.666i	−0.459465	−	0.795817i	−0.998933	+	0.0461892i	$0.985292\pi$
$272$	58.6411			0.215592
$273$	−112.065	+	33.2592i	−0.410495	+	0.121828i
$274$	−152.522			−0.556650
$275$	−284.681	−	46.2690i	−1.03520	−	0.168251i
$276$	221.170	+	36.1220i	0.801341	+	0.130877i
$277$	145.097	+	83.7720i	0.523817	+	0.302426i	0.738495	−	0.674259i	$-0.235537\pi$
$277$	145.097	+	83.7720i	0.523817	+	0.302426i	−0.214678	+	0.976685i	$0.568870\pi$
$278$	−0.977062	−	1.69232i	−0.00351461	−	0.00608749i
$279$	342.331	−	302.320i	1.22699	−	1.08358i
$280$	−206.104	+	150.790i	−0.736085	+	0.538537i
$281$			117.775i			0.419128i	0.977795	+	0.209564i	$0.0672044\pi$
$281$			117.775i			0.419128i	−0.977795	+	0.209564i	$0.932796\pi$
$282$	−10.9738	+	13.4189i	−0.0389142	+	0.0475848i
$283$	230.342	+	132.988i	0.813930	+	0.469923i	0.848319	−	0.529486i	$-0.177615\pi$
$283$	230.342	+	132.988i	0.813930	+	0.469923i	−0.0343889	+	0.999409i	$0.510948\pi$
$284$	−198.224	−	114.445i	−0.697973	−	0.402975i
$285$	27.3170	−	16.4842i	0.0958491	−	0.0578391i
$286$	68.1754			0.238376
$287$	−340.278	+	164.540i	−1.18564	+	0.573309i
$288$	223.713	−	197.566i	0.776781	−	0.685992i
$289$	21.9688	+	38.0510i	0.0760165	+	0.131664i
$290$	−46.0170	−	54.0999i	−0.158679	−	0.186551i
$291$	−0.495124	+	3.03158i	−0.00170146	+	0.0104178i
$292$	−4.88420	+	2.81989i	−0.0167267	+	0.00965717i
$293$	−0.117715			−0.000401758			−0.000200879	−	1.00000i	$-0.500064\pi$
$293$	−0.117715			−0.000401758			−0.000200879		1.00000i	$0.500064\pi$
$294$	148.699	+	47.3533i	0.505779	+	0.161066i
$295$	189.919	−	532.892i	0.643794	−	1.80641i
$296$	144.665	−	83.5222i	0.488732	−	0.282170i
$297$	−165.860	−	263.660i	−0.558450	−	0.887744i
$298$	−107.938	−	62.3179i	−0.362207	−	0.209121i
$299$	−125.343	+	72.3670i	−0.419208	+	0.242030i
$300$	68.3969	−	204.330i	0.227990	−	0.681100i
$301$	244.738	−	118.342i	0.813083	−	0.393162i
$302$	−267.104			−0.884451
$303$	275.060	+	224.940i	0.907788	+	0.742375i
$304$	3.98387	−	6.90026i	0.0131048	−	0.0226982i
$305$	112.868	−	96.0044i	0.370058	−	0.314769i
$306$	−141.799	−	47.5871i	−0.463394	−	0.155513i
$307$			35.5036i			0.115647i	0.998327	+	0.0578234i	$0.0184160\pi$
$307$			35.5036i			0.115647i	−0.998327	+	0.0578234i	$0.981584\pi$
$308$	191.906	+	130.391i	0.623073	+	0.423347i
$309$	−481.125	+	182.034i	−1.55704	+	0.589108i
$310$	48.5522	+	264.950i	0.156620	+	0.854679i
$311$	38.9449	+	22.4848i	0.125225	+	0.0722985i	0.561304	−	0.827610i	$-0.310300\pi$
$311$	38.9449	+	22.4848i	0.125225	+	0.0722985i	−0.436079	+	0.899908i	$0.643633\pi$
$312$	−19.6401	+	120.253i	−0.0629490	+	0.385428i
$313$	−11.6352	+	6.71759i	−0.0371732	+	0.0214620i	−0.518471	−	0.855095i	$-0.673499\pi$
$313$	−11.6352	+	6.71759i	−0.0371732	+	0.0214620i	0.481298	+	0.876557i	$0.340165\pi$
$314$		−	281.709i		−	0.897161i
$315$	−300.191	+	95.4482i	−0.952987	+	0.303010i
$316$	251.728			0.796607
$317$	72.1809	+	125.021i	0.227700	+	0.394388i	0.957126	−	0.289672i	$-0.0935461\pi$
$317$	72.1809	+	125.021i	0.227700	+	0.394388i	−0.729426	+	0.684060i	$0.760213\pi$
$318$	97.5622	+	15.9341i	0.306799	+	0.0501072i
$319$	−77.1825	+	133.684i	−0.241951	+	0.419072i
$320$	18.2247	+	99.4528i	0.0569523	+	0.310790i
$321$	177.317	+	468.655i	0.552388	+	1.45999i
$322$	192.702	+	14.1315i	0.598454	+	0.0438865i
$323$	−33.2973			−0.103088
$324$	214.376	−	90.5419i	0.661653	−	0.279450i
$325$	49.3460	+	130.120i	0.151834	+	0.400369i
$326$	141.102	+	81.4653i	0.432829	+	0.249894i
$327$	−144.999	+	177.307i	−0.443421	+	0.542222i
$328$			393.978i			1.20115i
$329$	21.4123	−	31.5142i	0.0650830	−	0.0957877i
$330$	183.677	−	3.55389i	0.556598	−	0.0107694i
$331$	−256.119	−	443.611i	−0.773773	−	1.34021i	−0.935481	−	0.353376i	$-0.885034\pi$
$331$	−256.119	−	443.611i	−0.773773	−	1.34021i	0.161708	−	0.986839i	$-0.448300\pi$
$332$	102.513	−	177.557i	0.308774	−	0.534812i
$333$	201.946	−	40.8972i	0.606446	−	0.122814i
$334$	95.1341	+	164.777i	0.284833	+	0.493344i
$335$	45.6739	−	128.156i	0.136340	−	0.382554i
$336$	−54.1197	+	57.0902i	−0.161071	+	0.169911i
$337$			513.556i			1.52390i	0.647633	+	0.761952i	$0.275759\pi$
$337$			513.556i			1.52390i	−0.647633	+	0.761952i	$0.724241\pi$
$338$	73.2586	+	126.888i	0.216741	+	0.375407i
$339$	18.8591	+	3.08012i	0.0556316	+	0.00908589i
$340$	−171.291	+	145.699i	−0.503797	+	0.428526i
$341$	507.005	−	292.720i	1.48682	−	0.858416i
$342$	−15.2328	+	13.4524i	−0.0445404	+	0.0393346i
$343$	−334.762	−	74.7209i	−0.975983	−	0.217845i
$344$		−	283.360i		−	0.823721i
$345$	−333.926	+	201.504i	−0.967901	+	0.584070i
$346$	−55.5726	+	96.2546i	−0.160614	+	0.278192i
$347$	73.4865	−	127.282i	0.211777	−	0.366808i	−0.740494	−	0.672063i	$-0.765408\pi$
$347$	73.4865	−	127.282i	0.211777	−	0.366808i	0.952271	+	0.305255i	$0.0987417\pi$
$348$	−89.2738	−	73.0068i	−0.256534	−	0.209790i
$349$	−507.141			−1.45313			−0.726563	−	0.687100i	$-0.758884\pi$
$349$	−507.141			−1.45313			−0.726563	+	0.687100i	$0.758884\pi$
$350$	43.1356	−	180.705i	0.123245	−	0.516299i
$351$	−70.1593	+	132.915i	−0.199884	+	0.378675i
$352$	331.328	−	191.292i	0.941273	−	0.543444i
$353$	−181.265	+	313.960i	−0.513497	+	0.889404i	0.486380	+	0.873747i	$0.338317\pi$
$353$	−181.265	+	313.960i	−0.513497	+	0.889404i	−0.999877	+	0.0156563i	$0.995016\pi$
$354$	−58.0831	+	355.635i	−0.164077	+	1.00462i
$355$	391.824	−	71.8017i	1.10373	−	0.202258i
$356$		−	354.274i		−	0.995150i
$357$	319.701	+	76.5761i	0.895521	+	0.214499i
$358$			86.7331i			0.242271i
$359$	325.653	−	188.016i	0.907112	−	0.523721i	0.0276110	−	0.999619i	$-0.491210\pi$
$359$	325.653	−	188.016i	0.907112	−	0.523721i	0.879501	+	0.475898i	$0.157877\pi$
$360$	−46.6454	+	325.009i	−0.129571	+	0.902803i
$361$	178.238	−	308.717i	0.493734	−	0.855172i
$362$	42.8850	+	74.2790i	0.118467	+	0.205191i
$363$	−12.8399	−	33.9365i	−0.0353717	−	0.0934889i
$364$	8.18745	−	111.647i	0.0224930	−	0.306724i
$365$	3.29507	−	9.24558i	0.00902759	−	0.0253304i
$366$	−59.7493	+	73.0624i	−0.163250	+	0.199624i
$367$	−258.008	−	148.961i	−0.703018	−	0.405888i	0.105452	−	0.994424i	$-0.466371\pi$
$367$	−258.008	−	148.961i	−0.703018	−	0.405888i	−0.808471	+	0.588537i	$0.799704\pi$
$368$	−48.6992	+	84.3496i	−0.132335	+	0.229211i
$369$	−154.613	+	460.712i	−0.419006	+	1.24854i
$370$	−40.7964	+	114.470i	−0.110261	+	0.309378i
$371$	−216.693	−	15.8908i	−0.584078	−	0.0428322i
$372$	154.775	+	409.076i	0.416061	+	1.09967i
$373$	−205.783	+	118.809i	−0.551697	+	0.318522i	−0.749806	−	0.661658i	$-0.769853\pi$
$373$	−205.783	+	118.809i	−0.551697	+	0.318522i	0.198109	+	0.980180i	$0.436520\pi$
$374$	−166.041	−	95.8637i	−0.443959	−	0.256320i
$375$	139.730	+	347.995i	0.372614	+	0.927986i
$376$	−19.8569	−	34.3931i	−0.0528108	−	0.0914709i
$377$	74.4818			0.197565
$378$	177.194	−	94.1302i	0.468767	−	0.249022i
$379$	37.3186			0.0984659			0.0492329	−	0.998787i	$-0.484322\pi$
$379$	37.3186			0.0984659			0.0492329	+	0.998787i	$0.484322\pi$
$380$	5.50739	+	30.0540i	0.0144931	+	0.0790894i
$381$	118.087	−	723.028i	0.309939	−	1.89771i
$382$	−308.635	−	178.190i	−0.807945	−	0.466467i
$383$	263.110	+	455.720i	0.686972	+	1.18987i	0.972813	+	0.231593i	$0.0743939\pi$
$383$	263.110	+	455.720i	0.686972	+	1.18987i	−0.285841	+	0.958277i	$0.592273\pi$
$384$	118.032	+	311.965i	0.307376	+	0.812408i
$385$	−401.429	+	43.5388i	−1.04267	+	0.113088i
$386$			13.6268i			0.0353025i
$387$	111.202	−	331.357i	0.287344	−	0.856220i
$388$	−2.54758	−	1.47084i	−0.00656592	−	0.00379083i
$389$	−78.2432	−	45.1737i	−0.201139	−	0.116128i	0.396048	−	0.918230i	$-0.370382\pi$
$389$	−78.2432	−	45.1737i	−0.201139	−	0.116128i	−0.597187	+	0.802102i	$0.703715\pi$
$390$	−45.7976	−	75.8943i	−0.117430	−	0.194601i
$391$	407.030			1.04100
$392$	−222.019	+	280.235i	−0.566375	+	0.714886i
$393$	144.732	−	54.7596i	0.368275	−	0.139337i
$394$	42.0393	+	72.8142i	0.106699	+	0.184808i
$395$	−333.704	+	283.846i	−0.844820	+	0.718598i
$396$	292.367	−	59.2087i	0.738300	−	0.149517i
$397$	−220.946	+	127.563i	−0.556539	+	0.321318i	−0.751755	−	0.659442i	$-0.770792\pi$
$397$	−220.946	+	127.563i	−0.556539	+	0.321318i	0.195216	+	0.980760i	$0.437459\pi$
$398$	−5.74683			−0.0144393
$399$	30.7300	−	32.4167i	0.0770175	−	0.0812448i
$400$	72.5403	+	59.2289i	0.181351	+	0.148072i
$401$	102.199	−	59.0045i	0.254860	−	0.147143i	−0.367128	−	0.930171i	$-0.619659\pi$
$401$	102.199	−	59.0045i	0.254860	−	0.147143i	0.621988	+	0.783027i	$0.286325\pi$
$402$	−13.9685	+	85.5269i	−0.0347474	+	0.212753i
$403$	−244.633	−	141.239i	−0.607029	−	0.350468i
$404$	−294.692	+	170.140i	−0.729435	+	0.421139i
$405$	−182.094	+	361.755i	−0.449614	+	0.893223i
$406$	−82.2449	−	55.8814i	−0.202574	−	0.137639i
$407$	264.121			0.648945
$408$	216.926	−	265.260i	0.531680	−	0.650147i
$409$	202.038	−	349.941i	0.493981	−	0.855600i	−0.505995	−	0.862537i	$-0.668875\pi$
$409$	202.038	−	349.941i	0.493981	−	0.855600i	0.999976	+	0.00693610i	$0.00220785\pi$
$410$	−185.700	−	218.318i	−0.452926	−	0.532483i
$411$	272.854	−	333.649i	0.663877	−	0.811799i
$412$		−	492.631i		−	1.19571i
$413$	57.9252	−	789.891i	0.140255	−	1.91257i
$414$	186.208	−	164.444i	0.449777	−	0.397208i
$415$	64.3157	+	350.972i	0.154978	+	0.845717i
$416$	−159.867	−	92.2995i	−0.384297	−	0.221874i
$417$	5.44994	+	0.890098i	0.0130694	+	0.00213453i
$418$	−22.5604	+	13.0253i	−0.0539723	+	0.0311609i
$419$			309.034i			0.737551i	0.929519	+	0.368775i	$0.120223\pi$
$419$			309.034i			0.737551i	−0.929519	+	0.368775i	$0.879777\pi$
$420$	16.2385	−	301.226i	0.0386631	−	0.717204i
$421$	173.079			0.411113			0.205557	−	0.978645i	$-0.434100\pi$
$421$	173.079			0.411113			0.205557	+	0.978645i	$0.434100\pi$
$422$	−109.488	−	189.639i	−0.259451	−	0.449382i
$423$	−9.72304	−	48.0114i	−0.0229859	−	0.113502i
$424$	−113.238	+	196.134i	−0.267071	+	0.462580i
$425$	62.7839	−	386.293i	0.147727	−	0.908925i
$426$	−237.317	+	89.7891i	−0.557081	+	0.210772i
$427$	116.584	−	171.586i	0.273031	−	0.401841i
$428$	−479.863			−1.12117
$429$	−121.962	+	149.137i	−0.284294	+	0.347639i
$430$	133.561	+	157.021i	0.310606	+	0.365164i
$431$	10.2824	+	5.93653i	0.0238570	+	0.0137739i	0.511881	−	0.859056i	$-0.328949\pi$
$431$	10.2824	+	5.93653i	0.0238570	+	0.0137739i	−0.488024	+	0.872830i	$0.662282\pi$
$432$	3.83432	+	101.068i	0.00887575	+	0.233955i
$433$		−	46.2629i		−	0.106843i	−0.998572	−	0.0534214i	$-0.982987\pi$
$433$		−	46.2629i		−	0.106843i	0.998572	−	0.0534214i	$-0.0170127\pi$
$434$	164.163	+	339.500i	0.378256	+	0.782258i
$435$	200.668	−	3.88264i	0.461306	−	0.00892561i
$436$	−109.674	−	189.962i	−0.251547	−	0.435692i
$437$	27.6522	−	47.8950i	0.0632773	−	0.109599i
$438$	−1.00773	+	6.17021i	−0.00230076	+	0.0140872i
$439$	82.7046	+	143.249i	0.188393	+	0.326307i	0.944715	−	0.327894i	$-0.106339\pi$
$439$	82.7046	+	143.249i	0.188393	+	0.326307i	−0.756321	+	0.654200i	$0.773005\pi$
$440$	−141.295	+	396.457i	−0.321124	+	0.901038i
$441$	−369.602	+	240.574i	−0.838099	+	0.545518i
$442$			92.5094i			0.209297i
$443$	−340.885	−	590.430i	−0.769492	−	1.33280i	−0.937839	−	0.347072i	$-0.887176\pi$
$443$	−340.885	−	590.430i	−0.769492	−	1.33280i	0.168347	−	0.985728i	$-0.446157\pi$
$444$	−31.8057	+	194.742i	−0.0716345	+	0.438608i
$445$	399.476	+	469.644i	0.897699	+	1.05538i
$446$	−69.5264	+	40.1411i	−0.155889	+	0.0900025i
$447$	329.418	−	124.636i	0.736953	−	0.278827i
$448$	61.6210	+	127.436i	0.137547	+	0.284455i
$449$		−	715.742i		−	1.59408i	−0.603927	−	0.797040i	$-0.706398\pi$
$449$		−	715.742i		−	1.59408i	0.603927	−	0.797040i	$-0.293602\pi$
$450$	−127.344	−	202.086i	−0.282986	−	0.449080i
$451$	−311.467	+	539.476i	−0.690614	+	1.19618i
$452$	−9.14997	+	15.8482i	−0.0202433	+	0.0350624i
$453$	477.834	−	584.303i	1.05482	−	1.28985i
$454$	161.825			0.356442
$455$	115.039	+	157.238i	0.252833	+	0.345578i
$456$	−16.4758	−	43.5463i	−0.0361311	−	0.0954962i
$457$	399.925	−	230.897i	0.875110	−	0.505245i	0.00606692	−	0.999982i	$-0.498069\pi$
$457$	399.925	−	230.897i	0.875110	−	0.505245i	0.869043	+	0.494737i	$0.164735\pi$
$458$	−161.035	+	278.921i	−0.351605	+	0.608998i
$459$	357.769	−	225.060i	0.779452	−	0.490328i
$460$	−67.3230	−	367.383i	−0.146354	−	0.798659i
$461$			659.572i			1.43074i	0.698745	+	0.715371i	$0.253742\pi$
$461$			659.572i			1.43074i	−0.698745	+	0.715371i	$0.746258\pi$
$462$	246.567	−	73.1770i	0.533694	−	0.158392i
$463$			370.241i			0.799656i	0.916590	+	0.399828i	$0.130930\pi$
$463$			370.241i			0.799656i	−0.916590	+	0.399828i	$0.869070\pi$
$464$	43.4073	−	25.0612i	0.0935502	−	0.0540112i
$465$	−666.449	−	367.771i	−1.43322	−	0.790906i
$466$	73.1754	−	126.744i	0.157029	−	0.271982i
$467$	7.00962	+	12.1410i	0.0150099	+	0.0259979i	0.873433	−	0.486945i	$-0.161889\pi$
$467$	7.00962	+	12.1410i	0.0150099	+	0.0259979i	−0.858423	+	0.512943i	$0.828555\pi$
$468$	−95.2753	−	107.885i	−0.203580	−	0.230523i
$469$	13.9305	−	189.962i	0.0297025	−	0.405035i
$470$	27.2145	+	9.69907i	0.0579031	+	0.0206363i
$471$	616.251	+	503.961i	1.30839	+	1.06998i
$472$	−714.949	−	412.776i	−1.51472	−	0.874525i
$473$	224.016	−	388.007i	0.473606	−	0.820310i
$474$	176.655	−	216.016i	0.372689	−	0.455730i
$475$	−41.1895	−	33.6311i	−0.0867147	−	0.0708023i
$476$	−176.932	+	260.404i	−0.371705	+	0.547067i
$477$	−209.390	+	184.917i	−0.438972	+	0.387666i
$478$	−326.585	+	188.554i	−0.683232	+	0.394464i
$479$	−145.809	−	84.1828i	−0.304403	−	0.175747i	0.340016	−	0.940420i	$-0.389567\pi$
$479$	−145.809	−	84.1828i	−0.304403	−	0.175747i	−0.644419	+	0.764673i	$0.722901\pi$
$480$	−435.524	−	240.338i	−0.907342	−	0.500705i
$481$	−63.7197	−	110.366i	−0.132473	−	0.229451i
$482$	−131.184			−0.272166
$483$	−375.647	+	396.265i	−0.777737	+	0.820424i
$484$	34.7480			0.0717934
$485$	5.03572	−	0.922795i	0.0103829	−	0.00190267i
$486$	72.7450	−	247.502i	0.149681	−	0.509264i
$487$	378.350	+	218.440i	0.776899	+	0.448543i	0.835330	−	0.549749i	$-0.185276\pi$
$487$	378.350	+	218.440i	0.776899	+	0.448543i	−0.0584311	+	0.998291i	$0.518610\pi$
$488$	−108.115	−	187.261i	−0.221547	−	0.383731i
$489$	−430.633	+	162.931i	−0.880640	+	0.333192i
$490$	−9.05857	−	259.937i	−0.0184869	−	0.530483i
$491$			103.782i			0.211369i	0.994400	+	0.105684i	$0.0337033\pi$
$491$			103.782i			0.211369i	−0.994400	+	0.105684i	$0.966297\pi$
$492$	−360.261	−	294.616i	−0.732237	−	0.598813i
$493$	−181.400	−	104.731i	−0.367951	−	0.212437i
$494$	10.8855	+	6.28475i	0.0220354	+	0.0127222i
$495$	−320.814	+	408.161i	−0.648109	+	0.824567i
$496$	−190.093			−0.383251
$497$	502.072	−	242.774i	1.01021	−	0.488479i
$498$	−80.4277	−	212.574i	−0.161501	−	0.426855i
$499$	−132.720	−	229.877i	−0.265971	−	0.460676i	0.701846	−	0.712328i	$-0.252359\pi$
$499$	−132.720	−	229.877i	−0.265971	−	0.460676i	−0.967818	+	0.251652i	$0.919026\pi$
$500$	−359.050	+	7.22462i	−0.718100	+	0.0144492i
$501$	−530.647	−	86.6665i	−1.05918	−	0.172987i
$502$	175.531	−	101.343i	0.349663	−	0.201878i
$503$	34.9818			0.0695462			0.0347731	−	0.999395i	$-0.488929\pi$
$503$	34.9818			0.0695462			0.0347731	+	0.999395i	$0.488929\pi$
$504$	58.0444	+	455.996i	0.115167	+	0.904753i
$505$	198.810	−	557.839i	0.393684	−	1.10463i
$506$	275.781	−	159.222i	0.545022	−	0.314669i
$507$	−408.628	−	66.7381i	−0.805973	−	0.131633i
$508$	607.594	+	350.795i	1.19605	+	0.690541i
$509$	310.955	−	179.530i	0.610914	−	0.352711i	−0.162409	−	0.986724i	$-0.551926\pi$
$509$	310.955	−	179.530i	0.610914	−	0.352711i	0.773323	+	0.634012i	$0.218593\pi$
$510$	4.82239	+	249.238i	0.00945567	+	0.488701i
$511$	1.00499	−	13.7045i	0.00196672	−	0.0268190i
$512$	−233.554			−0.456161
$513$	−2.17719	−	57.3882i	−0.00424403	−	0.111868i
$514$	95.8498	−	166.017i	0.186478	−	0.322990i
$515$	555.486	+	653.058i	1.07861	+	1.26807i
$516$	259.110	+	211.896i	0.502151	+	0.410652i
$517$		−	62.7929i		−	0.121456i
$518$	−12.4429	+	169.676i	−0.0240210	+	0.327560i
$519$	−111.145	−	293.762i	−0.214153	−	0.566015i
$520$	199.752	−	36.6045i	0.384138	−	0.0703933i
$521$	−254.036	−	146.668i	−0.487593	−	0.281512i	0.235982	−	0.971757i	$-0.424169\pi$
$521$	−254.036	−	146.668i	−0.487593	−	0.281512i	−0.723575	+	0.690245i	$0.757503\pi$
$522$	−125.299	+	25.3750i	−0.240037	+	0.0486110i
$523$	−62.1505	+	35.8826i	−0.118835	+	0.0686092i	−0.558239	−	0.829680i	$-0.688523\pi$
$523$	−62.1505	+	35.8826i	−0.118835	+	0.0686092i	0.439404	+	0.898289i	$0.355189\pi$
$524$			148.193i			0.282812i
$525$	318.133	+	417.632i	0.605968	+	0.795489i
$526$	−184.669			−0.351083
$527$	397.201	+	687.972i	0.753701	+	1.30545i
$528$	−20.8975	+	127.953i	−0.0395787	+	0.242335i
$529$	−73.5232	+	127.346i	−0.138985	+	0.240729i
$530$	−29.6974	−	162.059i	−0.0560328	−	0.305773i
$531$	−674.060	−	763.270i	−1.26942	−	1.43742i
$532$	18.6214	+	38.5103i	0.0350027	+	0.0723878i
$533$	300.568			0.563918
$534$	−304.014	−	248.618i	−0.569314	−	0.465577i
$535$	636.132	−	541.089i	1.18903	−	1.01138i
$536$	−171.939	−	99.2688i	−0.320781	−	0.185203i
$537$	−189.733	−	155.161i	−0.353320	−	0.288940i
$538$			183.661i			0.341377i
$539$	−525.557	+	208.207i	−0.975060	+	0.386283i
$540$	−262.313	−	285.695i	−0.485765	−	0.529064i
$541$	200.706	+	347.632i	0.370990	+	0.642574i	0.989718	−	0.143032i	$-0.0456850\pi$
$541$	200.706	+	347.632i	0.370990	+	0.642574i	−0.618728	+	0.785605i	$0.712352\pi$
$542$	132.187	−	228.954i	0.243887	−	0.422424i
$543$	−239.208	−	39.0680i	−0.440530	−	0.0719484i
$544$	259.571	+	449.589i	0.477152	+	0.826451i
$545$	359.589	+	128.156i	0.659797	+	0.235148i
$546$	−90.0627	−	85.3766i	−0.164950	−	0.156367i
$547$			377.855i			0.690777i	0.938460	+	0.345389i	$0.112253\pi$
$547$			377.855i			0.690777i	−0.938460	+	0.345389i	$0.887747\pi$
$548$	206.382	+	357.463i	0.376609	+	0.652305i
$549$	−52.9393	−	261.409i	−0.0964286	−	0.476155i
$550$	−108.571	−	286.291i	−0.197403	−	0.520528i
$551$	−24.6473	+	14.2301i	−0.0447320	+	0.0258260i
$552$	201.402	+	532.315i	0.364859	+	0.964338i
$553$	−344.692	+	507.311i	−0.623314	+	0.917379i
$554$			177.866i			0.321058i
$555$	−177.426	−	294.024i	−0.319687	−	0.529774i
$556$	−2.64417	+	4.57984i	−0.00475571	+	0.00823713i
$557$	73.2928	−	126.947i	0.131585	−	0.227912i	−0.792703	−	0.609608i	$-0.791327\pi$
$557$	73.2928	−	126.947i	0.131585	−	0.227912i	0.924288	+	0.381696i	$0.124660\pi$
$558$	459.658	+	154.260i	0.823760	+	0.276451i
$559$	−216.177			−0.386722
$560$	119.950	+	52.9291i	0.214197	+	0.0945163i
$561$	506.744	−	191.727i	0.903287	−	0.341760i
$562$	−108.280	+	62.5155i	−0.192669	+	0.111238i
$563$	24.5005	−	42.4361i	0.0435178	−	0.0753750i	−0.843446	−	0.537214i	$-0.819477\pi$
$563$	24.5005	−	42.4361i	0.0435178	−	0.0753750i	0.886964	+	0.461839i	$0.152810\pi$
$564$	46.2986	+	7.56160i	0.0820897	+	0.0134071i
$565$	−5.74061	−	31.3267i	−0.0101604	−	0.0554454i
$566$			282.363i			0.498875i
$567$	−111.075	+	556.014i	−0.195900	+	0.980624i
$568$		−	581.304i		−	1.02342i
$569$	531.169	−	306.671i	0.933514	−	0.538964i	0.0455925	−	0.998960i	$-0.485482\pi$
$569$	531.169	−	306.671i	0.933514	−	0.538964i	0.887921	+	0.459996i	$0.152149\pi$
$570$	29.6552	+	16.3649i	0.0520267	+	0.0287103i
$571$	−312.648	+	541.522i	−0.547545	+	0.948376i	0.450897	+	0.892576i	$0.351104\pi$
$571$	−312.648	+	541.522i	−0.547545	+	0.948376i	−0.998442	+	0.0557997i	$0.982229\pi$
$572$	−92.2499	−	159.781i	−0.161276	−	0.279338i
$573$	941.931	−	356.381i	1.64386	−	0.621956i
$574$	−331.896	−	225.507i	−0.578216	−	0.392869i
$575$	503.505	+	411.110i	0.875661	+	0.714974i
$576$	172.539	+	57.9035i	0.299547	+	0.100527i
$577$	641.687	+	370.478i	1.11211	+	0.642077i	0.939375	−	0.342892i	$-0.111406\pi$
$577$	641.687	+	370.478i	1.11211	+	0.642077i	0.172735	+	0.984968i	$0.444740\pi$
$578$	−23.3223	+	40.3953i	−0.0403499	+	0.0698881i
$579$	−29.8092	−	24.3775i	−0.0514839	−	0.0421028i
$580$	−64.5262	+	181.053i	−0.111252	+	0.312161i
$581$	217.463	+	449.726i	0.374290	+	0.774055i
$582$	−3.04999	+	1.15397i	−0.00524053	+	0.00198276i
$583$	−310.115	+	179.045i	−0.531929	+	0.307110i
$584$	−12.4043	−	7.16160i	−0.0212402	−	0.0122630i
$585$	247.952	+	35.5861i	0.423849	+	0.0608310i
$586$	−0.0624837	−	0.108225i	−0.000106628	−	0.000184684i
$587$	−779.387			−1.32775			−0.663873	−	0.747845i	$-0.731088\pi$
$587$	−779.387			−1.32775			−0.663873	+	0.747845i	$0.731088\pi$
$588$	−90.2272	−	412.578i	−0.153448	−	0.701663i
$589$	107.938			0.183256
$590$	590.741	−	108.253i	1.00126	−	0.183480i
$591$	−234.491	−	38.2976i	−0.396769	−	0.0648013i
$592$	−74.2705	−	42.8801i	−0.125457	−	0.0724326i
$593$	195.369	+	338.390i	0.329459	+	0.570641i	0.982405	−	0.186765i	$-0.0598002\pi$
$593$	195.369	+	338.390i	0.329459	+	0.570641i	−0.652945	+	0.757405i	$0.726467\pi$
$594$	154.365	−	292.441i	0.259874	−	0.492324i
$595$	−59.0791	−	544.712i	−0.0992927	−	0.915482i
$596$			337.296i			0.565933i
$597$	10.2808	−	12.5715i	0.0172207	−	0.0210577i
$598$	−133.066	−	76.8255i	−0.222518	−	0.128471i
$599$	564.372	+	325.840i	0.942190	+	0.543974i	0.890646	−	0.454697i	$-0.150252\pi$
$599$	564.372	+	325.840i	0.942190	+	0.543974i	0.0515441	+	0.998671i	$0.483586\pi$
$600$	536.260	−	109.032i	0.893767	−	0.181720i
$601$	807.425			1.34347			0.671735	−	0.740792i	$-0.265549\pi$
$601$	807.425			1.34347			0.671735	+	0.740792i	$0.265549\pi$
$602$	238.709	+	162.191i	0.396527	+	0.269421i
$603$	−162.105	−	183.559i	−0.268831	−	0.304410i
$604$	361.425	+	626.007i	0.598386	+	1.03644i
$605$	−46.0639	+	39.1816i	−0.0761386	+	0.0647629i
$606$	−60.8023	+	372.284i	−0.100334	+	0.614330i
$607$	−359.361	+	207.477i	−0.592027	+	0.341807i	−0.765899	−	0.642961i	$-0.777706\pi$
$607$	−359.361	+	207.477i	−0.592027	+	0.341807i	0.173871	+	0.984768i	$0.444372\pi$
$608$	70.5371			0.116015
$609$	269.375	−	79.9461i	0.442323	−	0.131274i
$610$	148.175	+	52.8088i	0.242911	+	0.0865718i
$611$	−26.2387	+	15.1489i	−0.0429439	+	0.0247937i
$612$	80.3422	+	396.722i	0.131278	+	0.648238i
$613$	−512.287	−	295.769i	−0.835705	−	0.482495i	0.0200968	−	0.999798i	$-0.493603\pi$
$613$	−512.287	−	295.769i	−0.835705	−	0.482495i	−0.855802	+	0.517303i	$0.826936\pi$
$614$	−32.6413	+	18.8455i	−0.0531618	+	0.0306930i
$615$	809.788	−	15.6682i	1.31673	−	0.0254768i
$616$	−43.0948	+	587.658i	−0.0699590	+	0.953990i
$617$	−426.832			−0.691785			−0.345893	−	0.938274i	$-0.612424\pi$
$617$	−426.832			−0.691785			−0.345893	+	0.938274i	$0.612424\pi$
$618$	−422.743	−	345.713i	−0.684050	−	0.559406i
$619$	93.5484	−	162.031i	0.151128	−	0.261762i	−0.780514	−	0.625138i	$-0.785043\pi$
$619$	93.5484	−	162.031i	0.151128	−	0.261762i	0.931643	+	0.363376i	$0.118376\pi$
$620$	555.262	−	472.302i	0.895584	−	0.761777i
$621$	26.6142	+	701.519i	0.0428570	+	1.12966i
$622$			47.7403i			0.0767528i
$623$	713.973	+	485.109i	1.14602	+	0.778666i
$624$	58.5081	−	22.1366i	0.0937629	−	0.0354753i
$625$	467.830	−	414.439i	0.748528	−	0.663103i
$626$	−12.3521	−	7.13147i	−0.0197317	−	0.0113921i
$627$	11.8659	−	72.6535i	0.0189249	−	0.115875i
$628$	−660.235	+	381.187i	−1.05133	+	0.606986i
$629$			358.393i			0.569783i
$630$	−247.096	−	225.326i	−0.392216	−	0.357660i
$631$	−1073.17			−1.70075			−0.850375	−	0.526177i	$-0.823625\pi$
$631$	−1073.17			−1.70075			−0.850375	+	0.526177i	$0.823625\pi$
$632$	319.653	+	553.655i	0.505780	+	0.876036i
$633$	610.713	+	99.7431i	0.964791	+	0.157572i
$634$	−76.6280	+	132.724i	−0.120864	+	0.209343i
$635$	−1201.01	+	220.086i	−1.89136	+	0.346592i
$636$	−94.6694	−	250.215i	−0.148851	−	0.393421i
$637$	213.794	+	169.380i	0.335626	+	0.265902i
$638$	−163.875			−0.256858
$639$	228.128	−	679.769i	0.357008	−	1.06380i
$640$	423.447	−	360.181i	0.661636	−	0.562782i
$641$	−806.425	−	465.590i	−1.25807	−	0.726349i	−0.285374	−	0.958416i	$-0.592118\pi$
$641$	−806.425	−	465.590i	−1.25807	−	0.726349i	−0.972700	+	0.232067i	$0.925451\pi$
$642$	−336.753	+	411.786i	−0.524537	+	0.641412i
$643$		−	400.552i		−	0.622942i	−0.950256	−	0.311471i	$-0.899178\pi$
$643$		−	400.552i		−	0.622942i	0.950256	−	0.311471i	$-0.100822\pi$
$644$	−227.631	−	470.754i	−0.353464	−	0.730985i
$645$	−582.423	+	11.2690i	−0.902981	+	0.0174714i
$646$	−17.6744	−	30.6129i	−0.0273597	−	0.0473885i
$647$	−335.990	+	581.952i	−0.519305	+	0.899462i	0.480444	+	0.877026i	$0.340476\pi$
$647$	−335.990	+	581.952i	−0.519305	+	0.899462i	−0.999748	+	0.0224363i	$0.992858\pi$
$648$	471.361	+	356.528i	0.727409	+	0.550198i
$649$	−652.656	−	1130.43i	−1.00563	−	1.74181i
$650$	−93.4367	+	114.436i	−0.143749	+	0.176056i
$651$	−1036.35	−	248.231i	−1.59194	−	0.381308i
$652$		−	440.931i		−	0.676275i
$653$	145.162	+	251.429i	0.222301	+	0.385036i	0.955506	−	0.294971i	$-0.0953100\pi$
$653$	145.162	+	251.429i	0.222301	+	0.385036i	−0.733205	+	0.680007i	$0.761977\pi$
$654$	−239.978	−	39.1938i	−0.366940	−	0.0599294i
$655$	−167.101	−	196.453i	−0.255117	−	0.299928i
$656$	175.168	−	101.134i	0.267025	−	0.154167i
$657$	−11.6948	−	13.2426i	−0.0178004	−	0.0201562i
$658$	40.3393	+	2.95821i	0.0613059	+	0.00449575i
$659$		−	293.143i		−	0.444830i	−0.974952	−	0.222415i	$-0.928606\pi$
$659$		−	293.143i		−	0.444830i	0.974952	−	0.222415i	$-0.0713940\pi$
$660$	−256.868	−	425.672i	−0.389193	−	0.644958i
$661$	−391.459	+	678.026i	−0.592222	+	1.02576i	0.401711	+	0.915767i	$0.368416\pi$
$661$	−391.459	+	678.026i	−0.592222	+	1.02576i	−0.993933	+	0.109992i	$0.964918\pi$
$662$	271.899	−	470.942i	0.410723	−	0.711393i
$663$	−202.369	−	165.494i	−0.305232	−	0.249614i
$664$	520.698			0.784183
$665$	−68.1095	−	30.0540i	−0.102420	−	0.0451939i
$666$	144.794	+	163.957i	0.217409	+	0.246182i
$667$	301.292	−	173.951i	0.451712	−	0.260796i
$668$	257.457	−	445.928i	0.385414	−	0.667557i
$669$	36.5683	−	223.903i	0.0546611	−	0.334683i
$670$	142.068	−	26.0339i	0.212041	−	0.0388566i
$671$		−	341.890i		−	0.509523i
$672$	−677.255	−	162.219i	−1.00782	−	0.241397i
$673$			287.467i			0.427143i	0.976927	+	0.213571i	$0.0685096\pi$
$673$			287.467i			0.427143i	−0.976927	+	0.213571i	$0.931490\pi$
$674$	−472.154	+	272.598i	−0.700525	+	0.404448i
$675$	669.884	+	82.9503i	0.992420	+	0.122889i
$676$	198.256	−	343.390i	0.293278	−	0.507973i
$677$	−522.319	−	904.683i	−0.771520	−	1.33631i	−0.936730	−	0.350053i	$-0.886164\pi$
$677$	−522.319	−	904.683i	−0.771520	−	1.33631i	0.165211	−	0.986258i	$-0.447170\pi$
$678$	7.17872	+	18.9737i	0.0105881	+	0.0279848i
$679$	6.45262	−	3.12013i	0.00950313	−	0.00459519i
$680$	−537.965	−	191.727i	−0.791124	−	0.281952i
$681$	−289.495	+	353.999i	−0.425103	+	0.519822i
$682$	538.242	+	310.754i	0.789212	+	0.455651i
$683$	−198.216	+	343.320i	−0.290214	+	0.502665i	−0.973860	−	0.227148i	$-0.927060\pi$
$683$	−198.216	+	343.320i	−0.290214	+	0.502665i	0.683646	+	0.729814i	$0.260393\pi$
$684$	52.1401	+	17.4980i	0.0762283	+	0.0255819i
$685$	−676.663	−	241.159i	−0.987830	−	0.352056i
$686$	−108.997	−	347.437i	−0.158887	−	0.506467i
$687$	−322.070	−	851.246i	−0.468807	−	1.23908i
$688$	−125.986	+	72.7381i	−0.183119	+	0.105724i
$689$	149.632	+	86.3900i	0.217173	+	0.125385i
$690$	−362.509	−	200.046i	−0.525375	−	0.289922i
$691$	296.958	+	514.346i	0.429751	+	0.744350i	0.996851	−	0.0792990i	$-0.0252682\pi$
$691$	296.958	+	514.346i	0.429751	+	0.744350i	−0.567100	+	0.823649i	$0.691935\pi$
$692$	300.787			0.434663
$693$	−281.016	+	670.286i	−0.405506	+	0.967224i
$694$	156.028			0.224824
$695$	−1.65893	−	9.05284i	−0.00238695	−	0.0130257i
$696$	47.2095	−	289.057i	0.0678297	−	0.415312i
$697$	−732.032	−	422.639i	−1.05026	−	0.606369i
$698$	−269.193	−	466.256i	−0.385664	−	0.667989i
$699$	146.351	+	386.812i	0.209372	+	0.553379i
$700$	−481.882	+	143.420i	−0.688403	+	0.204886i
$701$		−	152.343i		−	0.217322i	−0.994079	−	0.108661i	$-0.965344\pi$
$701$		−	152.343i		−	0.217322i	0.994079	−	0.108661i	$-0.0346563\pi$
$702$	−159.441	+	6.04884i	−0.227123	+	0.00861658i
$703$	42.1719	+	24.3480i	0.0599885	+	0.0346344i
$704$	202.037	+	116.646i	0.286984	+	0.165690i
$705$	−69.9023	+	42.1819i	−0.0991523	+	0.0598324i
$706$	−384.865			−0.545134
$707$	60.6370	−	826.871i	0.0857666	−	1.16955i
$708$	912.088	−	345.090i	1.28826	−	0.487415i
$709$	31.1663	+	53.9817i	0.0439581	+	0.0761377i	0.887167	−	0.461448i	$-0.152670\pi$
$709$	31.1663	+	53.9817i	0.0439581	+	0.0761377i	−0.843209	+	0.537586i	$0.819337\pi$
$710$	273.995	+	322.123i	0.385909	+	0.453694i
$711$	156.520	+	772.881i	0.220141	+	1.08703i
$712$	779.196	−	449.869i	1.09438	−	0.631839i
$713$	−1319.44			−1.85055
$714$	99.2962	+	334.574i	0.139070	+	0.468591i
$715$	302.460	+	107.795i	0.423021	+	0.150762i
$716$	203.275	−	117.361i	0.283903	−	0.163912i
$717$	171.771	−	1051.73i	0.239570	−	1.46685i
$718$	345.717	+	199.600i	0.481500	+	0.277994i
$719$	−699.337	+	403.762i	−0.972652	+	0.561561i	−0.900044	−	0.435799i	$-0.856466\pi$
$719$	−699.337	+	403.762i	−0.972652	+	0.561561i	−0.0726086	+	0.997361i	$0.523132\pi$
$720$	156.478	−	62.6901i	0.217330	−	0.0870696i
$721$	992.805	+	674.562i	1.37698	+	0.935592i
$722$	378.438			0.524153
$723$	234.680	−	286.971i	0.324593	−	0.396917i
$724$	116.057	−	201.017i	0.160300	−	0.277648i
$725$	−118.615	−	312.773i	−0.163606	−	0.431411i
$726$	24.3851	−	29.8184i	0.0335882	−	0.0410722i
$727$			437.949i			0.602406i	0.953560	+	0.301203i	$0.0973882\pi$
$727$			437.949i			0.602406i	−0.953560	+	0.301203i	$0.902612\pi$
$728$	255.956	−	123.766i	0.351588	−	0.170008i
$729$	411.286	+	601.901i	0.564179	+	0.825653i
$730$	10.2493	−	1.87818i	0.0140401	−	0.00257285i
$731$	526.499	+	303.974i	0.720244	+	0.415833i
$732$	252.083	+	41.1709i	0.344376	+	0.0562443i
$733$	419.443	−	242.166i	0.572228	−	0.330376i	−0.185811	−	0.982586i	$-0.559491\pi$
$733$	419.443	−	242.166i	0.572228	−	0.330376i	0.758039	+	0.652209i	$0.226158\pi$
$734$		−	316.277i		−	0.430895i
$735$	584.829	+	445.196i	0.795686	+	0.605709i
$736$	−862.254			−1.17154
$737$	−156.958	−	271.859i	−0.212969	−	0.368872i
$738$	−505.639	+	102.400i	−0.685148	+	0.138753i
$739$	283.380	−	490.829i	0.383464	−	0.664179i	−0.608091	−	0.793868i	$-0.708064\pi$
$739$	283.380	−	490.829i	0.383464	−	0.664179i	0.991555	+	0.129688i	$0.0413976\pi$
$740$	323.484	−	59.2784i	0.437140	−	0.0801060i
$741$	−33.2218	+	12.5695i	−0.0448337	+	0.0169629i
$742$	−100.412	−	207.658i	−0.135326	−	0.279863i
$743$	−277.502			−0.373489			−0.186744	−	0.982409i	$-0.559794\pi$
$743$	−277.502			−0.373489			−0.186744	+	0.982409i	$0.559794\pi$
$744$	−703.192	+	859.874i	−0.945150	+	1.15574i
$745$	−380.332	−	447.138i	−0.510513	−	0.600185i
$746$	−218.461	−	126.129i	−0.292844	−	0.169073i
$747$	608.896	+	204.343i	0.815122	+	0.273552i
$748$			518.862i			0.693666i
$749$	657.079	−	967.074i	0.877275	−	1.29115i
$750$	−245.770	+	313.183i	−0.327694	+	0.417577i
$751$	−426.468	−	738.664i	−0.567866	−	0.983574i	−0.996777	−	0.0802265i	$-0.974436\pi$
$751$	−426.468	−	738.664i	−0.567866	−	0.983574i	0.428910	−	0.903347i	$-0.358898\pi$
$752$	−10.1945	+	17.6573i	−0.0135564	+	0.0234805i
$753$	−92.3226	+	565.278i	−0.122606	+	0.750701i
$754$	39.5353	+	68.4772i	0.0524341	+	0.0908186i
$755$	−1185.01	−	422.329i	−1.56954	−	0.559376i
$756$	−460.377	−	287.916i	−0.608964	−	0.380841i
$757$		−	162.899i		−	0.215191i	−0.994195	−	0.107595i	$-0.965685\pi$
$757$		−	162.899i		−	0.215191i	0.994195	−	0.107595i	$-0.0343151\pi$
$758$	19.8089	+	34.3100i	0.0261331	+	0.0452639i
$759$	−145.051	+	888.124i	−0.191107	+	1.17012i
$760$	−59.1078	+	50.2766i	−0.0777734	+	0.0661535i
$761$	405.009	−	233.832i	0.532207	−	0.307270i	−0.209708	−	0.977764i	$-0.567251\pi$
$761$	405.009	−	233.832i	0.532207	−	0.307270i	0.741915	+	0.670494i	$0.233918\pi$
$762$	727.419	−	275.220i	0.954618	−	0.361181i
$763$	533.010	+	39.0873i	0.698572	+	0.0512284i
$764$			964.456i			1.26238i
$765$	−553.846	−	435.323i	−0.723982	−	0.569049i
$766$	−279.321	+	483.797i	−0.364648	+	0.631589i
$767$	−314.910	+	545.440i	−0.410573	+	0.711134i
$768$	−377.780	+	461.955i	−0.491901	+	0.601504i
$769$	−221.050			−0.287452			−0.143726	−	0.989618i	$-0.545908\pi$
$769$	−221.050			−0.287452			−0.143726	+	0.989618i	$0.545908\pi$
$770$	−253.109	−	345.956i	−0.328714	−	0.449294i
$771$	191.700	+	506.671i	0.248638	+	0.657160i
$772$	31.9368	−	18.4387i	0.0413689	−	0.0238843i
$773$	42.3039	−	73.2725i	0.0547269	−	0.0947897i	−0.837364	−	0.546646i	$-0.815905\pi$
$773$	42.3039	−	73.2725i	0.0547269	−	0.0947897i	0.892091	+	0.451856i	$0.149238\pi$
$774$	363.670	−	73.6487i	0.469858	−	0.0951534i
$775$	−203.522	+	1252.22i	−0.262609	+	1.61576i
$776$		−	7.47092i		−	0.00962747i
$777$	−348.915	−	330.760i	−0.449054	−	0.425689i
$778$		−	95.9138i		−	0.123282i
$779$	−99.4633	+	57.4251i	−0.127681	+	0.0737165i
$780$	−115.902	+	210.030i	−0.148592	+	0.269269i
$781$	459.561	−	795.984i	0.588427	−	1.01919i
$782$	216.054	+	374.216i	0.276284	+	0.478537i
$783$	168.644	−	319.492i	0.215382	−	0.408036i
$784$	181.589	+	26.7769i	0.231618	+	0.0341542i
$785$	445.420	−	1249.80i	0.567415	−	1.59210i
$786$	127.170	+	103.997i	0.161793	+	0.132312i
$787$	−484.582	−	279.774i	−0.615733	−	0.355494i	0.159473	−	0.987202i	$-0.449021\pi$
$787$	−484.582	−	279.774i	−0.615733	−	0.355494i	−0.775206	+	0.631709i	$0.782354\pi$
$788$	113.769	−	197.053i	0.144377	−	0.250068i
$789$	330.363	−	403.973i	0.418711	−	0.512006i
$790$	−438.095	−	156.134i	−0.554550	−	0.197638i
$791$	−19.4100	−	40.1411i	−0.0245386	−	0.0507473i
$792$	501.482	+	567.852i	0.633185	+	0.716985i
$793$	−142.863	+	82.4818i	−0.180155	+	0.104012i
$794$	−234.558	−	135.422i	−0.295414	−	0.170557i
$795$	407.640	+	224.951i	0.512754	+	0.282957i
$796$	7.77618	+	13.4687i	0.00976908	+	0.0169205i
$797$	209.388			0.262720			0.131360	−	0.991335i	$-0.458066\pi$
$797$	209.388			0.262720			0.131360	+	0.991335i	$0.458066\pi$
$798$	46.1149	+	11.0456i	0.0577881	+	0.0138417i
$799$	85.2056			0.106640
$800$	−133.002	+	818.324i	−0.166252	+	1.02291i
$801$	1087.73	−	220.281i	1.35796	−	0.275008i
$802$	108.495	+	62.6398i	0.135281	+	0.0781045i
$803$	−11.3235	−	19.6128i	−0.0141015	−	0.0244245i
$804$	219.349	−	82.9909i	0.272822	−	0.103223i
$805$	832.578	+	367.383i	1.03426	+	0.456377i
$806$		−	299.881i		−	0.372061i
$807$	−401.767	−	328.559i	−0.497852	−	0.407136i
$808$	−748.420	−	432.100i	−0.926262	−	0.534778i
$809$	−1146.24	−	661.779i	−1.41685	−	0.818021i	−0.420833	−	0.907138i	$-0.638262\pi$
$809$	−1146.24	−	661.779i	−1.41685	−	0.818021i	−0.996021	+	0.0891169i	$0.971596\pi$
$810$	−429.247	+	24.6081i	−0.529935	+	0.0303804i
$811$	242.337			0.298812			0.149406	−	0.988776i	$-0.452264\pi$
$811$	242.337			0.298812			0.149406	+	0.988776i	$0.452264\pi$
$812$	−19.6804	+	268.370i	−0.0242370	+	0.330505i
$813$	264.373	+	698.750i	0.325182	+	0.859471i
$814$	140.197	+	242.828i	0.172232	+	0.298314i
$815$	497.190	+	584.522i	0.610049	+	0.717205i
$816$	−173.623	−	28.3565i	−0.212773	−	0.0347506i
$817$	71.5368	−	41.3018i	0.0875604	−	0.0505530i
$818$	428.972			0.524416
$819$	347.882	−	44.2825i	0.424765	−	0.0540690i
$820$	−260.393	+	730.633i	−0.317553	+	0.891016i
$821$	−676.286	+	390.454i	−0.823735	+	0.475584i	−0.851703	−	0.524025i	$-0.824430\pi$
$821$	−676.286	+	390.454i	−0.823735	+	0.475584i	0.0279677	+	0.999609i	$0.491096\pi$
$822$	451.583	+	73.7537i	0.549371	+	0.0897246i
$823$	−17.6320	−	10.1799i	−0.0214241	−	0.0123692i	0.489250	−	0.872144i	$-0.337271\pi$
$823$	−17.6320	−	10.1799i	−0.0214241	−	0.0123692i	−0.510674	+	0.859775i	$0.670604\pi$
$824$	1083.50	−	625.560i	1.31493	−	0.759174i
$825$	820.502	+	274.653i	0.994548	+	0.332912i
$826$	756.959	−	366.023i	0.916415	−	0.443127i
$827$	783.381			0.947256			0.473628	−	0.880725i	$-0.342944\pi$
$827$	783.381			0.947256			0.473628	+	0.880725i	$0.342944\pi$
$828$	−637.367	−	213.898i	−0.769767	−	0.258331i
$829$	−187.112	+	324.087i	−0.225708	+	0.390938i	−0.956532	−	0.291629i	$-0.905803\pi$
$829$	−187.112	+	324.087i	−0.225708	+	0.390938i	0.730824	+	0.682566i	$0.239136\pi$
$830$	−288.538	+	245.429i	−0.347637	+	0.295697i
$831$	−389.091	−	318.193i	−0.468221	−	0.382904i
$832$		−	112.564i		−	0.135294i
$833$	−282.522	−	713.145i	−0.339162	−	0.856117i
$834$	2.07452	+	5.48305i	0.00248743	+	0.00657439i
$835$	161.526	+	881.452i	0.193444	+	1.05563i
$836$	61.0541	+	35.2496i	0.0730313	+	0.0421646i
$837$	−1159.75	+	729.562i	−1.38561	+	0.871639i
$838$	−284.120	+	164.037i	−0.339045	+	0.195748i
$839$		−	823.397i		−	0.981403i	−0.871328	−	0.490702i	$-0.836740\pi$
$839$		−	823.397i		−	0.981403i	0.871328	−	0.490702i	$-0.163260\pi$
$840$	683.142	−	346.792i	0.813264	−	0.412848i
$841$	661.966			0.787117
$842$	91.8710	+	159.125i	0.109110	+	0.188985i
$843$	56.9512	−	348.705i	0.0675578	−	0.413647i
$844$	−296.302	+	513.211i	−0.351069	+	0.608070i
$845$	124.384	+	678.768i	0.147200	+	0.803276i
$846$	38.9798	−	34.4239i	0.0460754	−	0.0406902i
$847$	−47.5807	+	70.0282i	−0.0561755	+	0.0826779i
$848$	116.272			0.137113
$849$	−617.683	−	505.132i	−0.727542	−	0.594973i
$850$	388.477	−	147.324i	0.457031	−	0.173322i
$851$	−515.514	−	297.632i	−0.605774	−	0.349744i
$852$	531.556	+	434.698i	0.623892	+	0.510209i
$853$		−	960.760i		−	1.12633i	−0.826344	−	0.563166i	$-0.809583\pi$
$853$		−	960.760i		−	1.12633i	0.826344	−	0.563166i	$-0.190417\pi$
$854$	219.637	+	16.1066i	0.257186	+	0.0188602i
$855$	−88.8504	+	35.5964i	−0.103919	+	0.0416332i
$856$	−609.347	−	1055.42i	−0.711854	−	1.23297i
$857$	−616.927	+	1068.55i	−0.719868	+	1.24685i	0.241183	+	0.970480i	$0.422465\pi$
$857$	−616.927	+	1068.55i	−0.719868	+	1.24685i	−0.961052	+	0.276369i	$0.910869\pi$
$858$	−201.852	−	32.9669i	−0.235259	−	0.0384230i
$859$	−603.799	−	1045.81i	−0.702910	−	1.21748i	−0.967441	−	0.253098i	$-0.918550\pi$
$859$	−603.799	−	1045.81i	−0.702910	−	1.21748i	0.264531	−	0.964377i	$-0.414783\pi$
$860$	187.282	−	525.492i	0.217770	−	0.611037i
$861$	1087.05	−	322.619i	1.26254	−	0.374703i
$862$			12.6046i			0.0146225i
$863$	581.346	+	1006.92i	0.673634	+	1.16677i	0.976866	+	0.213852i	$0.0686009\pi$
$863$	581.346	+	1006.92i	0.673634	+	1.16677i	−0.303232	+	0.952917i	$0.598066\pi$
$864$	−757.898	+	476.769i	−0.877197	+	0.551816i
$865$	−398.739	+	339.165i	−0.460970	+	0.392098i
$866$	42.5333	−	24.5566i	0.0491147	−	0.0283564i
$867$	−46.6445	−	123.284i	−0.0537999	−	0.142196i
$868$	573.546	−	844.132i	0.660767	−	0.972503i
$869$			1010.83i			1.16321i
$870$	110.085	+	182.430i	0.126535	+	0.209689i
$871$	−75.7329	+	131.173i	−0.0869494	+	0.150601i
$872$	278.537	−	482.440i	0.319423	−	0.553257i
$873$	2.93190	−	8.73638i	0.00335842	−	0.0100073i
$874$	58.7117			0.0671758
$875$	477.090	−	733.492i	0.545246	−	0.838276i
$876$	15.8246	−	5.98726i	0.0180646	−	0.00683477i
$877$	−1167.92	+	674.300i	−1.33172	+	0.768871i	−0.985564	−	0.169304i	$-0.945848\pi$
$877$	−1167.92	+	674.300i	−1.33172	+	0.768871i	−0.346160	+	0.938175i	$0.612515\pi$
$878$	−87.8001	+	152.074i	−0.100000	+	0.173205i
$879$	0.348527	+	0.0569223i	0.000396504	+	6.47580e-5i
$880$	212.541	−	38.9481i	0.241524	−	0.0442592i
$881$			48.4832i			0.0550320i	0.999621	+	0.0275160i	$0.00875971\pi$
$881$			48.4832i			0.0550320i	−0.999621	+	0.0275160i	$0.991240\pi$
$882$	−417.365	−	212.107i	−0.473203	−	0.240484i
$883$			922.339i			1.04455i	0.852777	+	0.522276i	$0.174917\pi$
$883$			922.339i			1.04455i	−0.852777	+	0.522276i	$0.825083\pi$
$884$	216.813	−	125.177i	0.245263	−	0.141603i
$885$	−819.993	+	1485.93i	−0.926546	+	1.67902i
$886$	361.887	−	626.807i	0.408450	−	0.707457i
$887$	527.551	+	913.745i	0.594758	+	1.03015i	0.993581	+	0.113124i	$0.0360856\pi$
$887$	527.551	+	913.745i	0.594758	+	1.03015i	−0.398822	+	0.917028i	$0.630581\pi$
$888$	−468.707	+	177.336i	−0.527824	+	0.199703i
$889$	−1538.94	+	744.148i	−1.73110	+	0.837062i
$890$	−219.738	+	616.560i	−0.246897	+	0.692764i
$891$	363.577	+	860.840i	0.408056	+	0.966151i
$892$	188.156	+	108.632i	0.210937	+	0.121785i
$893$	5.78856	−	10.0261i	0.00648215	−	0.0112274i
$894$	289.445	+	236.704i	0.323764	+	0.264769i
$895$	−137.137	+	384.790i	−0.153226	+	0.429933i
$896$	437.390	−	643.741i	0.488159	−	0.718461i
$897$	406.107	−	153.651i	0.452739	−	0.171294i
$898$	658.040	−	379.920i	0.732784	−	0.423073i
$899$	588.031	+	339.500i	0.654095	+	0.377642i
$900$	−301.313	+	571.901i	−0.334793	+	0.635445i
$901$	−242.952	−	420.805i	−0.269647	−	0.467042i
$902$	−661.313			−0.733163
$903$	−781.838	+	232.037i	−0.865823	+	0.256962i
$904$	−46.4758			−0.0514113
$905$	72.8135	+	397.345i	0.0804569	+	0.439055i
$906$	790.834	+	129.161i	0.872886	+	0.142562i
$907$	1051.66	+	607.177i	1.15949	+	0.669434i	0.951183	−	0.308629i	$-0.0998700\pi$
$907$	1051.66	+	607.177i	1.15949	+	0.669434i	0.208311	+	0.978063i	$0.433203\pi$
$908$	−218.969	−	379.265i	−0.241155	−	0.417693i
$909$	−705.617	−	799.003i	−0.776256	−	0.878991i
$910$	−83.4984	+	189.227i	−0.0917565	+	0.207942i
$911$		−	759.541i		−	0.833744i	−0.908965	−	0.416872i	$-0.863126\pi$
$911$		−	759.541i		−	0.833744i	0.908965	−	0.416872i	$-0.136874\pi$
$912$	−15.1320	+	18.5037i	−0.0165921	+	0.0202891i
$913$	712.995	+	411.648i	0.780936	+	0.450874i
$914$	424.565	+	245.123i	0.464513	+	0.268187i
$915$	−380.599	+	229.669i	−0.415956	+	0.251004i
$916$	871.603			0.951531
$917$	−298.656	−	202.922i	−0.325688	−	0.221289i
$918$	396.822	+	209.463i	0.432268	+	0.228173i
$919$	607.913	+	1052.94i	0.661494	+	1.14574i	0.980223	+	0.197896i	$0.0634108\pi$
$919$	607.913	+	1052.94i	0.661494	+	1.14574i	−0.318729	+	0.947846i	$0.603256\pi$
$920$	722.540	−	614.587i	0.785370	−	0.668030i
$921$	17.1681	−	105.118i	0.0186407	−	0.114135i
$922$	−606.398	+	350.104i	−0.657699	+	0.379723i
$923$	−443.481			−0.480478
$924$	−505.139	−	478.856i	−0.546687	−	0.518242i
$925$	−361.986	+	443.340i	−0.391336	+	0.479287i
$926$	−340.393	+	196.526i	−0.367595	+	0.212231i
$927$	1512.53	−	306.309i	1.63164	−	0.330431i
$928$	384.278	+	221.863i	0.414093	+	0.239077i
$929$	−277.778	+	160.375i	−0.299008	+	0.172632i	−0.641997	−	0.766707i	$-0.721894\pi$
$929$	−277.778	+	160.375i	−0.299008	+	0.172632i	0.342989	+	0.939339i	$0.388561\pi$
$930$	−15.6324	−	807.935i	−0.0168090	−	0.868748i
$931$	−103.109	−	15.2043i	−0.110751	−	0.0163312i
$932$	−396.062			−0.424959
$933$	−104.434	−	85.4047i	−0.111934	−	0.0915377i
$934$	−7.44148	+	12.8890i	−0.00796733	+	0.0137998i
$935$	−585.065	−	687.832i	−0.625738	−	0.735649i
$936$	116.300	−	346.546i	0.124252	−	0.370241i
$937$			1263.22i			1.34815i	0.738661	+	0.674077i	$0.235458\pi$
$937$			1263.22i			1.34815i	−0.738661	+	0.674077i	$0.764542\pi$
$938$	182.042	−	88.0252i	0.194074	−	0.0938435i
$939$	37.6976	−	14.2629i	0.0401465	−	0.0151895i
$940$	−14.0930	−	76.9061i	−0.0149926	−	0.0818150i
$941$	1258.18	+	726.408i	1.33706	+	0.771953i	0.986371	−	0.164538i	$-0.0526134\pi$
$941$	1258.18	+	726.408i	1.33706	+	0.771953i	0.350691	+	0.936491i	$0.385947\pi$
$942$	−136.223	+	834.075i	−0.144611	+	0.885430i
$943$	1215.85	−	701.971i	1.28934	−	0.744402i
$944$			423.836i			0.448979i
$945$	934.952	−	137.440i	0.989367	−	0.145439i
$946$	475.635			0.502786
$947$	−452.463	−	783.689i	−0.477786	−	0.827549i	0.521890	−	0.853013i	$-0.325227\pi$
$947$	−452.463	−	783.689i	−0.477786	−	0.827549i	−0.999676	+	0.0254634i	$0.991894\pi$
$948$	−745.309	−	121.726i	−0.786190	−	0.128402i
$949$	−5.46364	+	9.46329i	−0.00575726	+	0.00997186i
$950$	9.05620	−	55.7204i	0.00953284	−	0.0586531i
$951$	−153.256	−	405.063i	−0.161153	−	0.425933i
$952$	−797.411	−	58.4766i	−0.837617	−	0.0614250i
$953$	−1057.16			−1.10930			−0.554648	−	0.832085i	$-0.687147\pi$
$953$	−1057.16			−1.10930			−0.554648	+	0.832085i	$0.687147\pi$
$954$	−281.154	−	94.3544i	−0.294711	−	0.0989040i
$955$	−1087.51	−	1278.54i	−1.13876	−	1.33878i
$956$	883.821	+	510.274i	0.924499	+	0.533760i
$957$	293.164	−	358.485i	0.306336	−	0.374593i
$958$		−	178.739i		−	0.186575i
$959$	−1003.00	−	73.5531i	−1.04588	−	0.0766977i
$960$	−5.86784	−	303.270i	−0.00611233	−	0.315906i
$961$	−807.077	−	1397.90i	−0.839830	−	1.45463i
$962$	67.6455	−	117.165i	0.0703176	−	0.121794i
$963$	−298.371	−	1473.33i	−0.309834	−	1.52993i
$964$	177.508	+	307.453i	0.184137	+	0.318935i
$965$	−21.5458	+	60.4550i	−0.0223273	+	0.0626477i
$966$	−563.714	−	135.023i	−0.583555	−	0.139776i
$967$		−	1580.68i		−	1.63462i	−0.576196	−	0.817311i	$-0.695464\pi$
$967$		−	1580.68i		−	1.63462i	0.576196	−	0.817311i	$-0.304536\pi$
$968$	44.1243	+	76.4254i	0.0455829	+	0.0789519i
$969$	98.5858	+	16.1013i	0.101740	+	0.0166164i
$970$	3.52139	+	4.13992i	0.00363029	+	0.00426796i
$971$	−1527.53	+	881.919i	−1.57315	+	0.908258i	−0.577370	+	0.816483i	$0.695921\pi$
$971$	−1527.53	+	881.919i	−1.57315	+	0.908258i	−0.995780	+	0.0917752i	$0.970746\pi$
$972$	−678.500	+	164.410i	−0.698045	+	0.169147i
$973$	−5.60914	−	11.6001i	−0.00576479	−	0.0119219i
$974$			463.797i			0.476178i
$975$	−83.1814	−	409.117i	−0.0853143	−	0.419607i
$976$	−55.5060	+	96.1392i	−0.0568709	+	0.0985033i
$977$	299.246	−	518.309i	0.306290	−	0.530510i	−0.671257	−	0.741224i	$-0.734245\pi$
$977$	299.246	−	518.309i	0.306290	−	0.530510i	0.977548	+	0.210714i	$0.0675788\pi$
$978$	−378.378	−	309.432i	−0.386889	−	0.316392i
$979$	1422.61			1.45313
$980$	−596.952	+	372.957i	−0.609134	+	0.380569i
$981$	515.046	−	454.849i	0.525022	−	0.463658i
$982$	−95.4152	+	55.0880i	−0.0971642	+	0.0560978i
$983$	463.467	−	802.748i	0.471482	−	0.816631i	−0.527986	−	0.849253i	$-0.677053\pi$
$983$	463.467	−	802.748i	0.471482	−	0.816631i	0.999468	+	0.0326225i	$0.0103859\pi$
$984$	190.512	−	1166.48i	0.193610	−	1.18545i
$985$	71.3777	+	389.510i	0.0724646	+	0.395441i
$986$		−	222.368i		−	0.225525i
$987$	−78.6360	+	82.9521i	−0.0796717	+	0.0840447i
$988$		−	34.0162i		−	0.0344294i
$989$	−874.474	+	504.878i	−0.884201	+	0.510493i
$990$	−545.545	−	78.2968i	−0.551056	−	0.0790877i
$991$	203.029	−	351.657i	0.204873	−	0.354851i	−0.745219	−	0.666820i	$-0.767655\pi$
$991$	203.029	−	351.657i	0.204873	−	0.354851i	0.950092	+	0.311969i	$0.100989\pi$
$992$	−841.431	−	1457.40i	−0.848217	−	1.46915i
$993$	543.797	+	1437.28i	0.547630	+	1.44741i
$994$	489.705	+	332.730i	0.492661	+	0.334738i
$995$	−25.4958	−	9.08654i	−0.0256239	−	0.00913220i
$996$	−389.377	+	476.136i	−0.390941	+	0.478048i
$997$	888.128	+	512.761i	0.890801	+	0.514304i	0.874204	−	0.485558i	$-0.161384\pi$
$997$	888.128	+	512.761i	0.890801	+	0.514304i	0.0165963	+	0.999862i	$0.494717\pi$
$998$	140.897	−	244.040i	0.141179	−	0.244529i
$999$	−617.694	+	23.4340i	−0.618312	+	0.0234575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.o.a.74.5	yes	16
3.2	odd	2	inner	105.3.o.a.74.3	yes	16
5.4	even	2	inner	105.3.o.a.74.4	yes	16
7.2	even	3	inner	105.3.o.a.44.6	yes	16
15.14	odd	2	inner	105.3.o.a.74.6	yes	16
21.2	odd	6	inner	105.3.o.a.44.4	yes	16
35.9	even	6	inner	105.3.o.a.44.3	✓	16
105.44	odd	6	inner	105.3.o.a.44.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.o.a.44.3	✓	16	35.9	even	6	inner
105.3.o.a.44.4	yes	16	21.2	odd	6	inner
105.3.o.a.44.5	yes	16	105.44	odd	6	inner
105.3.o.a.44.6	yes	16	7.2	even	3	inner
105.3.o.a.74.3	yes	16	3.2	odd	2	inner
105.3.o.a.74.4	yes	16	5.4	even	2	inner
105.3.o.a.74.5	yes	16	1.1	even	1	trivial
105.3.o.a.74.6	yes	16	15.14	odd	2	inner

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.530805 + 0.919382i) q^{2} +(-2.96077 - 0.483560i) q^{3} +(1.43649 - 2.48808i) q^{4} +(0.901243 + 4.91811i) q^{5} +(-1.12702 - 2.97876i) q^{6} +(3.04726 + 6.30192i) q^{7} +7.29643 q^{8} +(8.53234 + 2.86342i) q^{9} +O(q^{10})\)	\(q+(0.530805 + 0.919382i) q^{2} +(-2.96077 - 0.483560i) q^{3} +(1.43649 - 2.48808i) q^{4} +(0.901243 + 4.91811i) q^{5} +(-1.12702 - 2.97876i) q^{6} +(3.04726 + 6.30192i) q^{7} +7.29643 q^{8} +(8.53234 + 2.86342i) q^{9} +(-4.04323 + 3.43914i) q^{10} +(9.99105 + 5.76833i) q^{11} +(-5.45626 + 6.67200i) q^{12} -5.56650i q^{13} +(-4.17637 + 6.14669i) q^{14} +(-0.290174 - 14.9972i) q^{15} +(-1.87298 - 3.24410i) q^{16} +(-7.82724 + 13.5572i) q^{17} +(1.89643 + 9.36440i) q^{18} +(1.06351 + 1.84205i) q^{19} +(13.5313 + 4.82246i) q^{20} +(-5.97488 - 20.1321i) q^{21} +12.2474i q^{22} +(-13.0004 - 22.5174i) q^{23} +(-21.6031 - 3.52826i) q^{24} +(-23.3755 + 8.86482i) q^{25} +(5.11774 - 2.95473i) q^{26} +(-23.8777 - 12.6038i) q^{27} +(20.0570 + 1.47084i) q^{28} +13.3804i q^{29} +(13.6341 - 8.22737i) q^{30} +(25.3730 - 43.9473i) q^{31} +(16.5812 - 28.7195i) q^{32} +(-26.7919 - 21.9100i) q^{33} -16.6190 q^{34} +(-28.2472 + 20.6663i) q^{35} +(19.3810 - 17.1158i) q^{36} +(19.8268 - 11.4470i) q^{37} +(-1.12903 + 1.95554i) q^{38} +(-2.69174 + 16.4811i) q^{39} +(6.57586 + 35.8846i) q^{40} +53.9959i q^{41} +(15.3376 - 16.1794i) q^{42} -38.8354i q^{43} +(28.7041 - 16.5723i) q^{44} +(-6.39291 + 44.5436i) q^{45} +(13.8014 - 23.9047i) q^{46} +(-2.72145 - 4.71368i) q^{47} +(3.97676 + 10.5107i) q^{48} +(-30.4284 + 38.4072i) q^{49} +(-20.5580 - 16.7855i) q^{50} +(29.7304 - 36.3547i) q^{51} +(-13.8499 - 7.99623i) q^{52} +(-15.5196 + 26.8808i) q^{53} +(-1.08665 - 28.6429i) q^{54} +(-19.3649 + 54.3357i) q^{55} +(22.2341 + 45.9815i) q^{56} +(-2.25806 - 5.96816i) q^{57} +(-12.3017 + 7.10237i) q^{58} +(-97.9861 - 56.5723i) q^{59} +(-37.7310 - 20.8214i) q^{60} +(-14.8175 - 25.6647i) q^{61} +53.8724 q^{62} +(7.95518 + 62.4957i) q^{63} +20.2218 q^{64} +(27.3766 - 5.01677i) q^{65} +(5.92238 - 36.2619i) q^{66} +(-23.5648 - 13.6051i) q^{67} +(22.4875 + 38.9495i) q^{68} +(27.6028 + 72.9555i) q^{69} +(-33.9940 - 15.0002i) q^{70} -79.6697i q^{71} +(62.2556 + 20.8928i) q^{72} +(-1.70004 - 0.981521i) q^{73} +(21.0483 + 12.1523i) q^{74} +(73.4963 - 14.9432i) q^{75} +6.11088 q^{76} +(-5.90628 + 80.5404i) q^{77} +(-16.5812 + 6.27354i) q^{78} +(43.8095 + 75.8802i) q^{79} +(14.2668 - 12.1353i) q^{80} +(64.6016 + 48.8634i) q^{81} +(-49.6429 + 28.6613i) q^{82} +71.3633 q^{83} +(-58.6730 - 14.0536i) q^{84} +(-73.7298 - 26.2769i) q^{85} +(35.7046 - 20.6141i) q^{86} +(6.47022 - 39.6162i) q^{87} +(72.8990 + 42.0883i) q^{88} +(106.791 - 61.6560i) q^{89} +(-44.3459 + 17.7664i) q^{90} +(35.0796 - 16.9626i) q^{91} -74.7001 q^{92} +(-96.3748 + 117.849i) q^{93} +(2.88912 - 5.00410i) q^{94} +(-8.10092 + 6.89058i) q^{95} +(-62.9809 + 77.0140i) q^{96} -1.02391i q^{97} +(-51.4624 - 7.58861i) q^{98} +(68.7298 + 77.8260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} - 80 q^{6} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^4 - 80 * q^6 - 8 * q^9	\( 16 q - 8 q^{4} - 80 q^{6} - 8 q^{9} - 40 q^{10} - 80 q^{15} + 32 q^{16} + 48 q^{19} - 8 q^{21} + 40 q^{30} + 344 q^{31} - 80 q^{34} + 496 q^{36} - 32 q^{39} + 120 q^{40} - 80 q^{45} - 120 q^{46} - 208 q^{49} - 40 q^{51} + 200 q^{54} + 40 q^{60} - 392 q^{61} - 544 q^{64} + 120 q^{66} - 240 q^{69} - 760 q^{70} + 200 q^{75} - 336 q^{76} + 608 q^{79} - 328 q^{81} - 344 q^{84} - 560 q^{85} + 80 q^{90} + 1088 q^{91} + 480 q^{94} - 400 q^{96} + 480 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 - 80 * q^6 - 8 * q^9 - 40 * q^10 - 80 * q^15 + 32 * q^16 + 48 * q^19 - 8 * q^21 + 40 * q^30 + 344 * q^31 - 80 * q^34 + 496 * q^36 - 32 * q^39 + 120 * q^40 - 80 * q^45 - 120 * q^46 - 208 * q^49 - 40 * q^51 + 200 * q^54 + 40 * q^60 - 392 * q^61 - 544 * q^64 + 120 * q^66 - 240 * q^69 - 760 * q^70 + 200 * q^75 - 336 * q^76 + 608 * q^79 - 328 * q^81 - 344 * q^84 - 560 * q^85 + 80 * q^90 + 1088 * q^91 + 480 * q^94 - 400 * q^96 + 480 * q^99

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