LMFDB - Embedded newform 105.3.o.a.74.4

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			74.4
Root			$-2.18880 - 2.65755i$ of defining polynomial
Character	$\chi$	$=$	105.74
Dual form			105.3.o.a.44.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.530805 - 0.919382i) q^{2} +(2.96077 + 0.483560i) q^{3} +(1.43649 - 2.48808i) q^{4} +(-3.80858 - 3.23955i) q^{5} +(-1.12702 - 2.97876i) q^{6} +(-3.04726 - 6.30192i) q^{7} -7.29643 q^{8} +(8.53234 + 2.86342i) q^{9} +O(q^{10})$	\(q+(-0.530805 - 0.919382i) q^{2} +(2.96077 + 0.483560i) q^{3} +(1.43649 - 2.48808i) q^{4} +(-3.80858 - 3.23955i) q^{5} +(-1.12702 - 2.97876i) q^{6} +(-3.04726 - 6.30192i) q^{7} -7.29643 q^{8} +(8.53234 + 2.86342i) q^{9} +(-0.956769 + 5.22111i) q^{10} +(9.99105 + 5.76833i) q^{11} +(5.45626 - 6.67200i) q^{12} +5.56650i q^{13} +(-4.17637 + 6.14669i) q^{14} +(-9.70983 - 11.4333i) 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} +(4.01061 + 24.6762i) q^{25} +(5.11774 - 2.95473i) q^{26} +(23.8777 + 12.6038i) q^{27} +(-20.0570 - 1.47084i) q^{28} +13.3804i q^{29} +(-5.35750 + 14.9959i) q^{30} +(25.3730 - 43.9473i) q^{31} +(-16.5812 + 28.7195i) q^{32} +(26.7919 + 21.9100i) q^{33} -16.6190 q^{34} +(-8.80966 + 33.8731i) 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} +(27.7891 + 23.6372i) q^{40} +53.9959i q^{41} +(-15.3376 + 16.1794i) q^{42} +38.8354i q^{43} +(28.7041 - 16.5723i) q^{44} +(-23.2199 - 38.5465i) 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} +(-42.3949 + 7.73502i) q^{60} +(-14.8175 - 25.6647i) q^{61} -53.8724 q^{62} +(-7.95518 - 62.4957i) q^{63} +20.2218 q^{64} +(18.0330 - 21.2005i) 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} +(35.8186 - 9.88060i) q^{70} -79.6697i q^{71} +(-62.2556 - 20.8928i) q^{72} +(1.70004 + 0.981521i) q^{73} +(21.0483 + 12.1523i) q^{74} +(-0.0579441 + 75.0000i) q^{75} +6.11088 q^{76} +(5.90628 - 80.5404i) q^{77} +(16.5812 - 6.27354i) q^{78} +(43.8095 + 75.8802i) q^{79} +(-3.37603 + 18.4231i) 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} +(-23.1137 + 41.8087i) q^{90} +(35.0796 - 16.9626i) q^{91} +74.7001 q^{92} +(96.3748 - 117.849i) q^{93} +(2.88912 - 5.00410i) q^{94} +(1.91696 - 10.4609i) 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	0.702266	−	0.711914i	$-0.252172\pi$
$2$	−0.530805	−	0.919382i	−0.265403	−	0.459691i	−0.967669	+	0.252223i	$0.918838\pi$
$3$	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
$5$	−3.80858	−	3.23955i	−0.761717	−	0.647910i
$5$	−3.80858	−	3.23955i	−0.761717	−	0.647910i
$6$	−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
$10$	−0.956769	+	5.22111i	−0.0956769	+	0.522111i
$11$	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	$0.0686806\pi$
$13$			5.56650i			0.428192i	−0.976813	+	0.214096i	$0.931319\pi$
$14$	−4.17637	+	6.14669i	−0.298312	+	0.439049i
$15$	−9.70983	−	11.4333i	−0.647322	−	0.762217i
$16$	−1.87298	−	3.24410i	−0.117061	−	0.202756i
$17$	7.82724	−	13.5572i	0.460426	−	0.797481i	−0.538556	−	0.842589i	$-0.681030\pi$
$17$	7.82724	−	13.5572i	0.460426	−	0.797481i	0.998982	+	0.0451088i	$0.0143635\pi$
$18$	−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	$0.0245485\pi$
$23$	13.0004	+	22.5174i	0.565237	+	0.979019i	−0.431791	+	0.901974i	$0.642118\pi$
$24$	−21.6031	−	3.52826i	−0.900128	−	0.147011i
$25$	4.01061	+	24.6762i	0.160424	+	0.987048i
$26$	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	$0.925900\pi$
$30$	−5.35750	+	14.9959i	−0.178583	+	0.499862i
$31$	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
$35$	−8.80966	+	33.8731i	−0.251705	+	0.967804i
$36$	19.3810	−	17.1158i	0.538362	−	0.475440i
$37$	−19.8268	+	11.4470i	−0.535859	+	0.309378i	−0.743399	−	0.668848i	$-0.766788\pi$
$37$	−19.8268	+	11.4470i	−0.535859	+	0.309378i	0.207540	+	0.978227i	$0.433454\pi$
$38$	1.12903	−	1.95554i	0.0297114	−	0.0514616i
$39$	−2.69174	+	16.4811i	−0.0690189	+	0.422593i
$40$	27.7891	+	23.6372i	0.694727	+	0.590929i
$41$			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	$0.149138\pi$
$43$			38.8354i			0.903150i	−0.892233	+	0.451575i	$0.850862\pi$
$44$	28.7041	−	16.5723i	0.652366	−	0.376644i
$45$	−23.2199	−	38.5465i	−0.515998	−	0.856590i
$46$	13.8014	−	23.9047i	0.300031	−	0.519668i
$47$	2.72145	+	4.71368i	0.0579031	+	0.100291i	0.893524	−	0.449016i	$-0.148225\pi$
$47$	2.72145	+	4.71368i	0.0579031	+	0.100291i	−0.835621	+	0.549307i	$0.814892\pi$
$48$	−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	−0.681653	−	0.731676i	$-0.738739\pi$
$53$	15.5196	−	26.8808i	0.292823	−	0.507185i	0.974476	+	0.224491i	$0.0720719\pi$
$54$	−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	$-0.741704\pi$
$60$	−42.3949	+	7.73502i	−0.706582	+	0.128917i
$61$	−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
$65$	18.0330	−	21.2005i	0.277430	−	0.326161i
$66$	5.92238	−	36.2619i	0.0897330	−	0.549423i
$67$	23.5648	+	13.6051i	0.351713	+	0.203062i	0.665439	−	0.746452i	$-0.268244\pi$
$67$	23.5648	+	13.6051i	0.351713	+	0.203062i	−0.313727	+	0.949513i	$0.601578\pi$
$68$	−22.4875	−	38.9495i	−0.330699	−	0.572787i
$69$	27.6028	+	72.9555i	0.400041	+	1.05733i
$70$	35.8186	−	9.88060i	0.511694	−	0.141151i
$71$		−	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	0.511599	−	0.859224i	$-0.329053\pi$
$73$	1.70004	+	0.981521i	0.0232883	+	0.0134455i	−0.488311	+	0.872670i	$0.662387\pi$
$74$	21.0483	+	12.1523i	0.284437	+	0.164220i
$75$	−0.0579441	+	75.0000i	−0.000772588	+	1.00000i
$76$	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	$0.646224\pi$
$80$	−3.37603	+	18.4231i	−0.0422003	+	0.230288i
$81$	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	$-0.641451\pi$
$83$	−71.3633			−0.859799			−0.429900	+	0.902877i	$0.641451\pi$
$84$	−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	$0.0897259\pi$
$90$	−23.1137	+	41.8087i	−0.256819	+	0.464541i
$91$	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
$95$	1.91696	−	10.4609i	0.0201785	−	0.110115i
$96$	−62.9809	+	77.0140i	−0.656051	+	0.802229i
$97$			1.02391i			0.0105558i	0.999986	+	0.00527791i	$0.00168002\pi$
$97$			1.02391i			0.0105558i	−0.999986	+	0.00527791i	$0.998320\pi$
$98$	51.4624	+	7.58861i	0.525127	+	0.0774348i
$99$	68.7298	+	77.8260i	0.694241	+	0.786121i
$100$	67.1575	+	25.4685i	0.671575	+	0.254685i
$101$	−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	−0.997965	−	0.0637681i	$-0.979688\pi$
$103$	−148.497	+	85.7350i	−1.44172	+	0.832379i	−0.443758	+	0.896147i	$0.646355\pi$
$104$		−	40.6156i		−	0.390534i
$105$	−42.4631	+	96.0306i	−0.404411	+	0.914578i
$106$	−32.9516			−0.310864
$107$	83.5130	+	144.649i	0.780495	+	1.35186i	0.931654	+	0.363348i	$0.118366\pi$
$107$	83.5130	+	144.649i	0.780495	+	1.35186i	−0.151158	+	0.988510i	$0.548300\pi$
$108$	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	$0.0527722\pi$
$110$	−39.6762	+	46.6454i	−0.360693	+	0.424049i
$111$	−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	$-0.491027\pi$
$113$	6.36966			0.0563687			0.0281843	+	0.999603i	$0.491027\pi$
$114$	4.28843	−	5.24395i	0.0376178	−	0.0459996i
$115$	23.4331	−	127.875i	0.203766	−	1.11196i
$116$	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
$120$	70.8471	+	83.4219i	0.590392	+	0.695183i
$121$	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	$-0.588698\pi$
$127$		−	244.202i		−	1.92285i	0.275061	−	0.961427i	$-0.411302\pi$
$128$	55.5911	+	96.2867i	0.434306	+	0.752240i
$129$	−18.7793	+	114.983i	−0.145576	+	0.891340i
$130$	−29.0633	−	5.32585i	−0.223564	−	0.0409681i
$131$	−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
$135$	−50.1093	−	125.356i	−0.371180	−	0.928561i
$136$	−57.1109	+	98.9190i	−0.419933	+	0.727345i
$137$	71.8353	−	124.422i	0.524345	−	0.908192i	−0.475253	−	0.879849i	$-0.657644\pi$
$137$	71.8353	−	124.422i	0.524345	−	0.908192i	0.999598	−	0.0283432i	$-0.00902313\pi$
$138$	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	$0.502108\pi$
$140$	71.6240	+	70.5776i	0.511600	+	0.504126i
$141$	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
$145$	43.3464	−	50.9602i	0.298941	−	0.351450i
$146$		−	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	$0.462231\pi$
$150$	68.9844	−	39.7571i	0.459896	−	0.265047i
$151$	−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	0.999182	−	0.0404444i	$-0.0128774\pi$
$157$	229.808	+	132.680i	1.46375	+	0.845095i	0.464565	+	0.885539i	$0.346211\pi$
$158$	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	−0.848834	−	0.528659i	$-0.822695\pi$
$163$	−132.913	+	76.7375i	−0.815419	+	0.470782i	0.0334153	+	0.999442i	$0.489362\pi$
$164$	134.346	+	77.5647i	0.819183	+	0.472956i
$165$	−31.0605	−	170.240i	−0.188246	−	1.03176i
$166$	37.8800	+	65.6101i	0.228193	+	0.395242i
$167$	−179.226			−1.07321			−0.536605	−	0.843834i	$-0.680293\pi$
$167$	−179.226			−1.07321			−0.536605	+	0.843834i	$0.680293\pi$
$168$	43.5953	+	146.892i	0.259496	+	0.874359i
$169$	138.014			0.816651
$170$	63.2946	+	53.8380i	0.372321	+	0.316694i
$171$	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	0.674135	−	0.738609i	$-0.264517\pi$
$173$	−52.3475	−	90.6684i	−0.302586	−	0.524095i	−0.976721	+	0.214513i	$0.931183\pi$
$174$	39.8569	−	15.0799i	0.229062	−	0.0866661i
$175$	143.286	−	100.469i	0.818778	−	0.574110i
$176$		−	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	$0.593379\pi$
$180$	−129.262	+	2.40113i	−0.718122	+	0.0133396i
$181$	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
$185$	112.595	+	20.6331i	0.608622	+	0.111530i
$186$	−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	0.470925	−	0.882173i	$-0.343920\pi$
$193$	−11.1162	−	6.41797i	−0.0575971	−	0.0332537i	−0.528522	+	0.848920i	$0.677254\pi$
$194$	0.941368	−	0.543499i	0.00485241	−	0.00280154i
$195$	63.6432	−	54.0497i	0.326375	−	0.277178i
$196$	51.8498	+	130.880i	0.264540	+	0.667754i
$197$	−79.1991			−0.402026			−0.201013	−	0.979589i	$-0.564423\pi$
$197$	−79.1991			−0.402026			−0.201013	+	0.979589i	$0.564423\pi$
$198$	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	$0.170996\pi$
$200$	−29.2631	−	180.048i	−0.146316	−	0.900241i
$201$	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
$205$	174.923	−	205.648i	0.853281	−	1.00316i
$206$	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
$210$	110.828	−	11.9338i	0.527754	−	0.0568274i
$211$	−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
$215$	125.809	−	147.908i	0.585160	−	0.687944i
$216$	−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
$220$	−163.009	−	29.8714i	−0.740950	−	0.135779i
$221$	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	$-0.945766\pi$
$223$		−	75.6231i		−	0.339117i	0.985520	−	0.169558i	$-0.0542341\pi$
$224$	231.516	+	16.9778i	1.03355	+	0.0757936i
$225$	−36.4386	+	222.030i	−0.161949	+	0.986799i
$226$	−3.38105	−	5.85615i	−0.0149604	−	0.0259122i
$227$	−76.2166	+	132.011i	−0.335756	+	0.581546i	−0.983630	−	0.180202i	$-0.942325\pi$
$227$	−76.2166	+	132.011i	−0.335756	+	0.581546i	0.647874	+	0.761748i	$0.275658\pi$
$228$	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	0.975178	−	0.221423i	$-0.0710700\pi$
$233$	68.9287	+	119.388i	0.295831	+	0.512395i	−0.679347	+	0.733818i	$0.737737\pi$
$234$	52.1269	−	10.5565i	0.222765	−	0.0451132i
$235$	4.90537	−	26.7687i	0.0208739	−	0.113909i
$236$	−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	$0.733334\pi$
$240$	−18.9043	+	52.9140i	−0.0787679	+	0.220475i
$241$	−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
$245$	240.311	−	47.7024i	0.980862	−	0.194704i
$246$	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
$250$	−132.674	−	2.66960i	−0.530698	−	0.0106784i
$251$		−	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
$255$	−231.004	+	42.1470i	−0.905897	+	0.165282i
$256$	99.4597	−	172.269i	0.388514	−	0.672927i
$257$	90.2872	+	156.382i	0.351312	+	0.608490i	0.986480	−	0.163884i	$-0.0524023\pi$
$257$	90.2872	+	156.382i	0.351312	+	0.608490i	−0.635168	+	0.772374i	$0.719069\pi$
$258$	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	−0.651943	−	0.758268i	$-0.726046\pi$
$263$	86.9761	−	150.647i	0.330707	−	0.572802i	0.982651	+	0.185466i	$0.0593793\pi$
$264$	−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	$0.562458\pi$
$270$	−88.6515	+	112.609i	−0.328339	+	0.417070i
$271$	−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
$275$	−102.270	+	269.676i	−0.371893	+	0.980639i
$276$	221.170	+	36.1220i	0.801341	+	0.130877i
$277$	−145.097	−	83.7720i	−0.523817	−	0.302426i	0.214678	−	0.976685i	$-0.431130\pi$
$277$	−145.097	−	83.7720i	−0.523817	−	0.302426i	−0.738495	+	0.674259i	$0.764463\pi$
$278$	0.977062	+	1.69232i	0.00351461	+	0.00608749i
$279$	342.331	−	302.320i	1.22699	−	1.08358i
$280$	64.2791	−	247.153i	0.229568	−	0.882689i
$281$			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	0.0343889	−	0.999409i	$-0.489052\pi$
$283$	−230.342	−	132.988i	−0.813930	−	0.469923i	−0.848319	+	0.529486i	$0.822385\pi$
$284$	−198.224	−	114.445i	−0.697973	−	0.402975i
$285$	10.7341	−	30.0453i	0.0376637	−	0.105422i
$286$	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
$290$	−69.8604	−	12.8019i	−0.240898	−	0.0441446i
$291$	−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	$-0.499936\pi$
$293$	0.117715			0.000401758			0.000200879		1.00000i	$0.499936\pi$
$294$	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
$300$	186.522	+	107.881i	0.621742	+	0.359603i
$301$	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
$305$	−26.7084	+	145.748i	−0.0875686	+	0.477864i
$306$	−141.799	−	47.5871i	−0.463394	−	0.155513i
$307$		−	35.5036i		−	0.115647i	−0.998327	−	0.0578234i	$-0.981584\pi$
$307$		−	35.5036i		−	0.115647i	0.998327	−	0.0578234i	$-0.0184160\pi$
$308$	−191.906	−	130.391i	−0.623073	−	0.423347i
$309$	−481.125	+	182.034i	−1.55704	+	0.589108i
$310$	205.178	+	174.523i	0.661863	+	0.562976i
$311$	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	−0.481298	−	0.876557i	$-0.659835\pi$
$313$	11.6352	−	6.71759i	0.0371732	−	0.0214620i	0.518471	+	0.855095i	$0.326501\pi$
$314$		−	281.709i		−	0.897161i
$315$	−172.160	+	263.791i	−0.546540	+	0.837433i
$316$	251.728			0.796607
$317$	−72.1809	−	125.021i	−0.227700	−	0.394388i	0.729426	−	0.684060i	$-0.239787\pi$
$317$	−72.1809	−	125.021i	−0.227700	−	0.394388i	−0.957126	+	0.289672i	$0.906454\pi$
$318$	−97.5622	−	15.9341i	−0.306799	−	0.0501072i
$319$	−77.1825	+	133.684i	−0.241951	+	0.419072i
$320$	−77.0163	−	65.5095i	−0.240676	−	0.204717i
$321$	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
$325$	−137.360	+	22.3250i	−0.422646	+	0.0686924i
$326$	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
$330$	−140.028	+	118.921i	−0.424328	+	0.360365i
$331$	−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	$-0.724241\pi$
$337$		−	513.556i		−	1.52390i	0.647633	−	0.761952i	$-0.275759\pi$
$338$	−73.2586	−	126.888i	−0.216741	−	0.375407i
$339$	18.8591	+	3.08012i	0.0556316	+	0.00908589i
$340$	−40.5334	+	221.192i	−0.119216	+	0.650565i
$341$	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
$345$	131.215	−	367.278i	0.380335	−	1.06457i
$346$	−55.5726	+	96.2546i	−0.160614	+	0.278192i
$347$	−73.4865	+	127.282i	−0.211777	+	0.366808i	−0.952271	−	0.305255i	$-0.901258\pi$
$347$	−73.4865	+	127.282i	−0.211777	+	0.366808i	0.740494	+	0.672063i	$0.234592\pi$
$348$	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	$0.758884\pi$
$350$	−168.427	−	78.4050i	−0.481219	−	0.224014i
$351$	−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	$-0.661683\pi$
$353$	181.265	−	313.960i	0.513497	−	0.889404i	0.999877	−	0.0156563i	$-0.00498376\pi$
$354$	−58.0831	+	355.635i	−0.164077	+	1.00462i
$355$	−258.094	+	303.429i	−0.727026	+	0.854728i
$356$		−	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	$0.157877\pi$
$360$	169.422	+	281.252i	0.470618	+	0.781256i
$361$	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	0.808471	−	0.588537i	$-0.200296\pi$
$367$	258.008	+	148.961i	0.703018	+	0.405888i	−0.105452	+	0.994424i	$0.533629\pi$
$368$	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	−0.198109	−	0.980180i	$-0.563480\pi$
$373$	205.783	−	118.809i	0.551697	−	0.318522i	0.749806	+	0.661658i	$0.230147\pi$
$374$	−166.041	−	95.8637i	−0.443959	−	0.256320i
$375$	243.187	−	285.456i	0.648499	−	0.761216i
$376$	−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	$0.484322\pi$
$380$	−23.2738	−	19.7965i	−0.0612469	−	0.0520961i
$381$	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	$-0.925606\pi$
$383$	−263.110	−	455.720i	−0.686972	−	1.18987i	0.285841	−	0.958277i	$-0.407727\pi$
$384$	118.032	+	311.965i	0.307376	+	0.812408i
$385$	−283.409	+	287.611i	−0.736128	+	0.747042i
$386$			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	$0.703715\pi$
$390$	−83.4745	−	29.8225i	−0.214037	−	0.0764680i
$391$	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
$395$	78.9660	−	430.919i	0.199914	−	1.09093i
$396$	292.367	−	59.2087i	0.738300	−	0.149517i
$397$	220.946	−	127.563i	0.556539	−	0.321318i	−0.195216	−	0.980760i	$-0.562541\pi$
$397$	220.946	−	127.563i	0.556539	−	0.321318i	0.751755	+	0.659442i	$0.229208\pi$
$398$	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
$405$	−87.7451	−	395.381i	−0.216655	−	0.976248i
$406$	−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	$0.00220785\pi$
$410$	−281.919	−	51.6616i	−0.687607	−	0.126004i
$411$	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
$415$	271.793	+	231.185i	0.654923	+	0.557073i
$416$	−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	$0.879777\pi$
$420$	177.934	+	243.599i	0.423652	+	0.579997i
$421$	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
$425$	365.931	+	138.774i	0.861015	+	0.326527i
$426$	−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
$430$	−202.764	−	37.1565i	−0.471545	−	0.0864106i
$431$	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	$0.0170127\pi$
$433$			46.2629i			0.106843i	−0.998572	+	0.0534214i	$0.982987\pi$
$434$	164.163	+	339.500i	0.378256	+	0.782258i
$435$	152.981	−	129.921i	0.351681	−	0.298669i
$436$	−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	$0.112824\pi$
$443$	340.885	+	590.430i	0.769492	+	1.33280i	−0.168347	+	0.985728i	$0.553843\pi$
$444$	−31.8057	+	194.742i	−0.0716345	+	0.438608i
$445$	−606.462	−	111.134i	−1.36284	−	0.249740i
$446$	−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	$-0.293602\pi$
$450$	223.472	−	84.3536i	0.496604	−	0.187452i
$451$	−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
$455$	−188.555	−	49.0390i	−0.414406	−	0.107778i
$456$	−16.4758	−	43.5463i	−0.0361311	−	0.0954962i
$457$	−399.925	+	230.897i	−0.875110	+	0.505245i	−0.869043	−	0.494737i	$-0.835265\pi$
$457$	−399.925	+	230.897i	−0.875110	+	0.505245i	−0.00606692	+	0.999982i	$0.501931\pi$
$458$	161.035	−	278.921i	0.351605	−	0.608998i
$459$	357.769	−	225.060i	0.779452	−	0.490328i
$460$	−284.502	−	241.995i	−0.618482	−	0.526076i
$461$			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	$-0.869070\pi$
$463$		−	370.241i		−	0.799656i	0.916590	−	0.399828i	$-0.130930\pi$
$464$	43.4073	−	25.0612i	0.0935502	−	0.0540112i
$465$	−748.828	+	136.625i	−1.61038	+	0.293817i
$466$	73.1754	−	126.744i	0.157029	−	0.271982i
$467$	−7.00962	−	12.1410i	−0.0150099	−	0.0259979i	0.858423	−	0.512943i	$-0.171445\pi$
$467$	−7.00962	−	12.1410i	−0.0150099	−	0.0259979i	−0.873433	+	0.486945i	$0.838111\pi$
$468$	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	$0.722901\pi$
$480$	489.359	−	89.2843i	1.01950	−	0.186009i
$481$	−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
$485$	3.31702	−	3.89966i	0.00683922	−	0.00804054i
$486$	72.7450	−	247.502i	0.149681	−	0.509264i
$487$	−378.350	−	218.440i	−0.776899	−	0.448543i	0.0584311	−	0.998291i	$-0.481390\pi$
$487$	−378.350	−	218.440i	−0.776899	−	0.448543i	−0.835330	+	0.549749i	$0.814724\pi$
$488$	108.115	+	187.261i	0.221547	+	0.383731i
$489$	−430.633	+	162.931i	−0.880640	+	0.333192i
$490$	−171.415	−	195.617i	−0.349827	−	0.399218i
$491$			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
$495$	−9.64192	−	519.061i	−0.0194786	−	1.04861i
$496$	−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	$0.919026\pi$
$500$	−173.268	−	314.559i	−0.346537	−	0.629118i
$501$	−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	$-0.511071\pi$
$503$	−34.9818			−0.0695462			−0.0347731	+	0.999395i	$0.511071\pi$
$504$	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	$0.218593\pi$
$510$	161.367	+	190.009i	0.316406	+	0.372566i
$511$	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
$515$	843.308	+	154.536i	1.63749	+	0.300070i
$516$	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
$520$	−131.576	+	154.688i	−0.253031	+	0.297477i
$521$	−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	−0.439404	−	0.898289i	$-0.644811\pi$
$523$	62.1505	−	35.8826i	0.118835	−	0.0686092i	0.558239	+	0.829680i	$0.311477\pi$
$524$			148.193i			0.282812i
$525$	472.821	−	228.179i	0.900611	−	0.434627i
$526$	−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
$530$	125.499	+	106.748i	0.236790	+	0.201412i
$531$	−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
$535$	150.531	−	821.451i	0.281366	−	1.53542i
$536$	−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
$540$	−383.876	−	55.3967i	−0.710882	−	0.102587i
$541$	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	$-0.887747\pi$
$547$		−	377.855i		−	0.690777i	0.938460	−	0.345389i	$-0.112253\pi$
$548$	−206.382	−	357.463i	−0.376609	−	0.652305i
$549$	−52.9393	−	261.409i	−0.0964286	−	0.476155i
$550$	302.221	−	49.1197i	0.549492	−	0.0893085i
$551$	−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
$555$	323.391	+	115.536i	0.582687	+	0.208173i
$556$	−2.64417	+	4.57984i	−0.00475571	+	0.00823713i
$557$	−73.2928	+	126.947i	−0.131585	+	0.227912i	−0.924288	−	0.381696i	$-0.875340\pi$
$557$	−73.2928	+	126.947i	−0.131585	+	0.227912i	0.792703	+	0.609608i	$0.208673\pi$
$558$	−459.658	−	154.260i	−0.823760	−	0.276451i
$559$	−216.177			−0.386722
$560$	126.388	−	34.8644i	0.225693	−	0.0622578i
$561$	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	−0.886964	−	0.461839i	$-0.847190\pi$
$563$	−24.5005	+	42.4361i	−0.0435178	+	0.0753750i	0.843446	+	0.537214i	$0.180523\pi$
$564$	46.2986	+	7.56160i	0.0820897	+	0.0134071i
$565$	−24.2594	−	20.6349i	−0.0429370	−	0.0365219i
$566$			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	$0.152149\pi$
$570$	−33.3209	+	6.07945i	−0.0584577	+	0.0106657i
$571$	−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	−0.172735	−	0.984968i	$-0.555260\pi$
$577$	−641.687	−	370.478i	−1.11211	−	0.642077i	−0.939375	+	0.342892i	$0.888594\pi$
$578$	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
$585$	214.569	−	129.254i	0.366785	−	0.220946i
$586$	−0.0624837	−	0.108225i	−0.000106628	−	0.000184684i
$587$	779.387			1.32775			0.663873	−	0.747845i	$-0.268912\pi$
$587$	779.387			1.32775			0.663873	+	0.747845i	$0.268912\pi$
$588$	90.2272	+	412.578i	0.153448	+	0.701663i
$589$	107.938			0.183256
$590$	389.121	−	457.470i	0.659526	−	0.775373i
$591$	−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	0.652945	−	0.757405i	$-0.273533\pi$
$593$	−195.369	−	338.390i	−0.329459	−	0.570641i	−0.982405	+	0.186765i	$0.940200\pi$
$594$	154.365	−	292.441i	0.259874	−	0.492324i
$595$	390.269	+	384.567i	0.655914	+	0.646331i
$596$			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	$0.483586\pi$
$600$	0.422785	−	547.232i	0.000704642	−	0.912054i
$601$	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
$605$	10.9003	−	59.4833i	0.0180170	−	0.0983194i
$606$	−60.8023	+	372.284i	−0.100334	+	0.614330i
$607$	359.361	−	207.477i	0.592027	−	0.341807i	−0.173871	−	0.984768i	$-0.555628\pi$
$607$	359.361	−	207.477i	0.592027	−	0.341807i	0.765899	+	0.642961i	$0.222294\pi$
$608$	−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	0.855802	−	0.517303i	$-0.173064\pi$
$613$	512.287	+	295.769i	0.835705	+	0.482495i	−0.0200968	+	0.999798i	$0.506397\pi$
$614$	−32.6413	+	18.8455i	−0.0531618	+	0.0306930i
$615$	617.349	−	524.291i	1.00382	−	0.852506i
$616$	−43.0948	+	587.658i	−0.0699590	+	0.953990i
$617$	426.832			0.691785			0.345893	−	0.938274i	$-0.387576\pi$
$617$	426.832			0.691785			0.345893	+	0.938274i	$0.387576\pi$
$618$	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	$0.118376\pi$
$620$	−131.394	+	717.022i	−0.211926	+	1.15649i
$621$	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
$625$	−592.830	+	197.933i	−0.948528	+	0.316693i
$626$	−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
$630$	333.908	+	18.2591i	0.530013	+	0.0289827i
$631$	−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
$635$	−791.106	+	930.065i	−1.24584	+	1.46467i
$636$	−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
$640$	100.202	−	546.806i	0.156566	−	0.854385i
$641$	−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	$0.100822\pi$
$643$			400.552i			0.622942i	−0.950256	+	0.311471i	$0.899178\pi$
$644$	−227.631	−	470.754i	−0.353464	−	0.730985i
$645$	444.015	−	377.085i	0.688396	−	0.584628i
$646$	−17.6744	−	30.6129i	−0.0273597	−	0.0473885i
$647$	335.990	−	581.952i	0.519305	−	0.899462i	−0.480444	−	0.877026i	$-0.659524\pi$
$647$	335.990	−	581.952i	0.519305	−	0.899462i	0.999748	−	0.0224363i	$-0.00714230\pi$
$648$	−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	0.733205	−	0.680007i	$-0.238023\pi$
$653$	−145.162	−	251.429i	−0.222301	−	0.385036i	−0.955506	+	0.294971i	$0.904690\pi$
$654$	−239.978	−	39.1938i	−0.366940	−	0.0599294i
$655$	253.684	+	46.4876i	0.387304	+	0.0709735i
$656$	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	$-0.0713940\pi$
$660$	−468.188	−	167.267i	−0.709375	−	0.253435i
$661$	−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
$665$	−71.7652	+	19.7965i	−0.107918	+	0.0297692i
$666$	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
$670$	−93.5799	+	110.017i	−0.139671	+	0.164205i
$671$		−	341.890i		−	0.509523i
$672$	677.255	+	162.219i	1.00782	+	0.241397i
$673$		−	287.467i		−	0.427143i	−0.976927	−	0.213571i	$-0.931490\pi$
$673$		−	287.467i		−	0.427143i	0.976927	−	0.213571i	$-0.0685096\pi$
$674$	−472.154	+	272.598i	−0.700525	+	0.404448i
$675$	−215.251	+	639.759i	−0.318890	+	0.947792i
$676$	198.256	−	343.390i	0.293278	−	0.507973i
$677$	522.319	+	904.683i	0.771520	+	1.33631i	0.936730	+	0.350053i	$0.113836\pi$
$677$	522.319	+	904.683i	0.771520	+	1.33631i	−0.165211	+	0.986258i	$0.552830\pi$
$678$	−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	−0.683646	−	0.729814i	$-0.739607\pi$
$683$	198.216	−	343.320i	0.290214	−	0.502665i	0.973860	+	0.227148i	$0.0729402\pi$
$684$	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
$690$	−407.318	+	74.3159i	−0.590316	+	0.107704i
$691$	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
$695$	7.01052	+	5.96310i	0.0100871	+	0.00858000i
$696$	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
$700$	−44.1460	−	500.830i	−0.0630657	−	0.715472i
$701$		−	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
$705$	27.4680	−	76.8841i	0.0389617	−	0.109055i
$706$	−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	$0.819337\pi$
$710$	415.964	+	76.2255i	0.585865	+	0.107360i
$711$	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	$0.523132\pi$
$720$	−81.5584	+	147.525i	−0.113276	+	0.204896i
$721$	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
$725$	−330.177	+	53.6634i	−0.455416	+	0.0740185i
$726$	24.3851	−	29.8184i	0.0335882	−	0.0410722i
$727$		−	437.949i		−	0.602406i	−0.953560	−	0.301203i	$-0.902612\pi$
$727$		−	437.949i		−	0.602406i	0.953560	−	0.301203i	$-0.0973882\pi$
$728$	−255.956	+	123.766i	−0.351588	+	0.170008i
$729$	411.286	+	601.901i	0.564179	+	0.825653i
$730$	−6.75118	+	7.93703i	−0.00924819	+	0.0108726i
$731$	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	−0.758039	−	0.652209i	$-0.773842\pi$
$733$	−419.443	+	242.166i	−0.572228	+	0.330376i	0.185811	+	0.982586i	$0.440509\pi$
$734$		−	316.277i		−	0.430895i
$735$	734.574	−	25.0311i	0.999420	−	0.0340559i
$736$	−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	$0.0413976\pi$
$740$	213.079	−	250.506i	0.287944	−	0.338522i
$741$	−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	$-0.440206\pi$
$743$	277.502			0.373489			0.186744	+	0.982409i	$0.440206\pi$
$744$	−703.192	+	859.874i	−0.945150	+	1.15574i
$745$	577.398	+	105.808i	0.775032	+	0.142025i
$746$	−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
$750$	−391.528	−	72.0602i	−0.522037	−	0.0960802i
$751$	−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	$0.0343151\pi$
$757$			162.899i			0.215191i	−0.994195	+	0.107595i	$0.965685\pi$
$758$	−19.8089	−	34.3100i	−0.0261331	−	0.0452639i
$759$	−145.051	+	888.124i	−0.191107	+	1.17012i
$760$	−13.9870	+	76.3272i	−0.0184039	+	0.100430i
$761$	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
$765$	−704.330	+	13.0834i	−0.920692	+	0.0171025i
$766$	−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	$0.545908\pi$
$770$	414.860	+	107.896i	0.538779	+	0.140125i
$771$	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	−0.892091	−	0.451856i	$-0.850762\pi$
$773$	−42.3039	+	73.2725i	−0.0547269	+	0.0947897i	0.837364	+	0.546646i	$0.184095\pi$
$774$	363.670	−	73.6487i	0.469858	−	0.0951534i
$775$	1186.21	+	449.854i	1.53060	+	0.580456i
$776$		−	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
$780$	−43.0570	−	235.991i	−0.0552012	−	0.302553i
$781$	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	0.775206	−	0.631709i	$-0.217646\pi$
$787$	484.582	+	279.774i	0.615733	+	0.355494i	−0.159473	+	0.987202i	$0.550979\pi$
$788$	−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
$795$	−458.028	+	83.5679i	−0.576136	+	0.105117i
$796$	7.77618	+	13.4687i	0.00976908	+	0.0169205i
$797$	−209.388			−0.262720			−0.131360	−	0.991335i	$-0.541934\pi$
$797$	−209.388			−0.262720			−0.131360	+	0.991335i	$0.541934\pi$
$798$	−46.1149	−	11.0456i	−0.0577881	−	0.0138417i
$799$	85.2056			0.106640
$800$	−775.190	−	293.979i	−0.968988	−	0.367474i
$801$	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
$805$	−877.266	+	241.995i	−1.08977	+	0.300615i
$806$		−	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	$0.971596\pi$
$810$	−316.930	+	290.541i	−0.391272	+	0.358693i
$811$	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
$815$	754.806	+	138.318i	0.926143	+	0.169716i
$816$	−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	0.510674	−	0.859775i	$-0.329396\pi$
$823$	17.6320	+	10.1799i	0.0214241	+	0.0123692i	−0.489250	+	0.872144i	$0.662729\pi$
$824$	1083.50	−	625.560i	1.31493	−	0.759174i
$825$	−433.204	+	748.994i	−0.525096	+	0.907872i
$826$	756.959	−	366.023i	0.916415	−	0.443127i
$827$	−783.381			−0.947256			−0.473628	−	0.880725i	$-0.657056\pi$
$827$	−783.381			−0.947256			−0.473628	+	0.880725i	$0.657056\pi$
$828$	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	$0.239136\pi$
$830$	68.2782	−	372.596i	0.0822629	−	0.448911i
$831$	−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
$835$	682.597	+	580.612i	0.817481	+	0.695343i
$836$	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	$-0.163260\pi$
$840$	309.829	−	700.681i	0.368844	−	0.834144i
$841$	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
$845$	−525.638	−	447.104i	−0.622057	−	0.529117i
$846$	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
$850$	−66.6521	−	410.093i	−0.0784142	−	0.482462i
$851$	−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	$0.190417\pi$
$853$			960.760i			1.12633i	−0.826344	+	0.563166i	$0.809583\pi$
$854$	219.637	+	16.1066i	0.257186	+	0.0188602i
$855$	46.3101	−	83.7668i	0.0541639	−	0.0979729i
$856$	−609.347	−	1055.42i	−0.711854	−	1.23297i
$857$	616.927	−	1068.55i	0.719868	−	1.24685i	−0.241183	−	0.970480i	$-0.577535\pi$
$857$	616.927	−	1068.55i	0.719868	−	1.24685i	0.961052	−	0.276369i	$-0.0891312\pi$
$858$	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	$-0.931399\pi$
$863$	−581.346	−	1006.92i	−0.673634	−	1.16677i	0.303232	−	0.952917i	$-0.401934\pi$
$864$	−757.898	+	476.769i	−0.877197	+	0.551816i
$865$	−94.3555	+	514.901i	−0.109082	+	0.595261i
$866$	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
$870$	−200.650	−	71.6853i	−0.230632	−	0.0823969i
$871$	−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
$875$	−871.193	−	81.5372i	−0.995649	−	0.0931854i
$876$	15.8246	−	5.98726i	0.0180646	−	0.00683477i
$877$	1167.92	−	674.300i	1.33172	−	0.768871i	0.346160	−	0.938175i	$-0.387485\pi$
$877$	1167.92	−	674.300i	1.33172	−	0.768871i	0.985564	+	0.169304i	$0.0541520\pi$
$878$	87.8001	−	152.074i	0.100000	−	0.173205i
$879$	0.348527	+	0.0569223i	0.000396504	+	6.47580e-5i
$880$	−140.000	+	164.592i	−0.159091	+	0.187036i
$881$			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	$-0.825083\pi$
$883$		−	922.339i		−	1.04455i	0.852777	−	0.522276i	$-0.174917\pi$
$884$	216.813	−	125.177i	0.245263	−	0.141603i
$885$	304.623	+	1669.61i	0.344206	+	1.88656i
$886$	361.887	−	626.807i	0.408450	−	0.707457i
$887$	−527.551	−	913.745i	−0.594758	−	1.03015i	−0.993581	−	0.113124i	$-0.963914\pi$
$887$	−527.551	−	913.745i	−0.594758	−	1.03015i	0.398822	−	0.917028i	$-0.369419\pi$
$888$	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
$900$	500.083	+	409.606i	0.555648	+	0.455118i
$901$	−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
$905$	−307.704	−	261.731i	−0.340005	−	0.289205i
$906$	790.834	+	129.161i	0.872886	+	0.142562i
$907$	−1051.66	−	607.177i	−1.15949	−	0.669434i	−0.208311	−	0.978063i	$-0.566797\pi$
$907$	−1051.66	−	607.177i	−1.15949	−	0.669434i	−0.951183	+	0.308629i	$0.900130\pi$
$908$	218.969	+	379.265i	0.241155	+	0.417693i
$909$	−705.617	−	799.003i	−0.776256	−	0.878991i
$910$	55.0003	+	199.384i	0.0604399	+	0.219103i
$911$		−	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
$915$	−149.556	+	418.613i	−0.163449	+	0.457500i
$916$	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	$0.603256\pi$
$920$	−170.978	+	933.032i	−0.185846	+	1.01417i
$921$	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	$0.388561\pi$
$930$	523.092	+	615.937i	0.562465	+	0.662298i
$931$	−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
$935$	−888.212	−	162.765i	−0.949960	−	0.174080i
$936$	116.300	−	346.546i	0.124252	−	0.370241i
$937$		−	1263.22i		−	1.34815i	−0.738661	−	0.674077i	$-0.764542\pi$
$937$		−	1263.22i		−	1.34815i	0.738661	−	0.674077i	$-0.235458\pi$
$938$	−182.042	+	88.0252i	−0.194074	+	0.0938435i
$939$	37.6976	−	14.2629i	0.0401465	−	0.0151895i
$940$	−59.5561	−	50.6580i	−0.0633576	−	0.0538915i
$941$	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
$945$	−637.286	+	697.776i	−0.674377	+	0.738387i
$946$	475.635			0.502786
$947$	452.463	+	783.689i	0.477786	+	0.827549i	0.999676	−	0.0254634i	$-0.00810614\pi$
$947$	452.463	+	783.689i	0.477786	+	0.827549i	−0.521890	+	0.853013i	$0.674773\pi$
$948$	745.309	+	121.726i	0.786190	+	0.128402i
$949$	−5.46364	+	9.46329i	−0.00575726	+	0.00997186i
$950$	52.7834	+	20.0173i	0.0555615	+	0.0210709i
$951$	−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	$-0.312853\pi$
$953$	1057.16			1.10930			0.554648	+	0.832085i	$0.312853\pi$
$954$	−281.154	−	94.3544i	−0.294711	−	0.0989040i
$955$	1651.00	+	302.546i	1.72880	+	0.316802i
$956$	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
$960$	−196.350	−	231.201i	−0.204531	−	0.240834i
$961$	−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	$0.304536\pi$
$967$			1580.68i			1.63462i	−0.576196	+	0.817311i	$0.695464\pi$
$968$	−44.1243	−	76.4254i	−0.0455829	−	0.0789519i
$969$	98.5858	+	16.1013i	0.101740	+	0.0166164i
$970$	−5.34597	−	0.979649i	−0.00551131	−	0.00100995i
$971$	−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
$975$	−417.487	−	0.322546i	−0.428192	−	0.000330816i
$976$	−55.5060	+	96.1392i	−0.0568709	+	0.0985033i
$977$	−299.246	+	518.309i	−0.306290	+	0.530510i	−0.977548	−	0.210714i	$-0.932421\pi$
$977$	−299.246	+	518.309i	−0.306290	+	0.530510i	0.671257	+	0.741224i	$0.265755\pi$
$978$	378.378	+	309.432i	0.386889	+	0.316392i
$979$	1422.61			1.45313
$980$	226.518	−	666.437i	0.231141	−	0.680038i
$981$	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	−0.999468	−	0.0326225i	$-0.989614\pi$
$983$	−463.467	+	802.748i	−0.471482	+	0.816631i	0.527986	+	0.849253i	$0.322947\pi$
$984$	190.512	−	1166.48i	0.193610	−	1.18545i
$985$	301.636	+	256.570i	0.306230	+	0.260477i
$986$		−	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
$990$	−472.097	+	284.385i	−0.476865	+	0.287257i
$991$	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	−0.0165963	−	0.999862i	$-0.505283\pi$
$997$	−888.128	−	512.761i	−0.890801	−	0.514304i	−0.874204	+	0.485558i	$0.838616\pi$
$998$	−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.74.4	yes	16
3.2	odd	2	inner	105.3.o.a.74.6	yes	16
5.4	even	2	inner	105.3.o.a.74.5	yes	16
7.2	even	3	inner	105.3.o.a.44.3	✓	16
15.14	odd	2	inner	105.3.o.a.74.3	yes	16
21.2	odd	6	inner	105.3.o.a.44.5	yes	16
35.9	even	6	inner	105.3.o.a.44.6	yes	16
105.44	odd	6	inner	105.3.o.a.44.4	yes	16

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

\(f(q)\)	\(=\)	\(q+(-0.530805 - 0.919382i) q^{2} +(2.96077 + 0.483560i) q^{3} +(1.43649 - 2.48808i) q^{4} +(-3.80858 - 3.23955i) q^{5} +(-1.12702 - 2.97876i) q^{6} +(-3.04726 - 6.30192i) q^{7} -7.29643 q^{8} +(8.53234 + 2.86342i) q^{9} +O(q^{10})\)	\(q+(-0.530805 - 0.919382i) q^{2} +(2.96077 + 0.483560i) q^{3} +(1.43649 - 2.48808i) q^{4} +(-3.80858 - 3.23955i) q^{5} +(-1.12702 - 2.97876i) q^{6} +(-3.04726 - 6.30192i) q^{7} -7.29643 q^{8} +(8.53234 + 2.86342i) q^{9} +(-0.956769 + 5.22111i) q^{10} +(9.99105 + 5.76833i) q^{11} +(5.45626 - 6.67200i) q^{12} +5.56650i q^{13} +(-4.17637 + 6.14669i) q^{14} +(-9.70983 - 11.4333i) 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} +(4.01061 + 24.6762i) q^{25} +(5.11774 - 2.95473i) q^{26} +(23.8777 + 12.6038i) q^{27} +(-20.0570 - 1.47084i) q^{28} +13.3804i q^{29} +(-5.35750 + 14.9959i) q^{30} +(25.3730 - 43.9473i) q^{31} +(-16.5812 + 28.7195i) q^{32} +(26.7919 + 21.9100i) q^{33} -16.6190 q^{34} +(-8.80966 + 33.8731i) 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} +(27.7891 + 23.6372i) q^{40} +53.9959i q^{41} +(-15.3376 + 16.1794i) q^{42} +38.8354i q^{43} +(28.7041 - 16.5723i) q^{44} +(-23.2199 - 38.5465i) 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} +(-42.3949 + 7.73502i) q^{60} +(-14.8175 - 25.6647i) q^{61} -53.8724 q^{62} +(-7.95518 - 62.4957i) q^{63} +20.2218 q^{64} +(18.0330 - 21.2005i) 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} +(35.8186 - 9.88060i) q^{70} -79.6697i q^{71} +(-62.2556 - 20.8928i) q^{72} +(1.70004 + 0.981521i) q^{73} +(21.0483 + 12.1523i) q^{74} +(-0.0579441 + 75.0000i) q^{75} +6.11088 q^{76} +(5.90628 - 80.5404i) q^{77} +(16.5812 - 6.27354i) q^{78} +(43.8095 + 75.8802i) q^{79} +(-3.37603 + 18.4231i) 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} +(-23.1137 + 41.8087i) q^{90} +(35.0796 - 16.9626i) q^{91} +74.7001 q^{92} +(96.3748 - 117.849i) q^{93} +(2.88912 - 5.00410i) q^{94} +(1.91696 - 10.4609i) 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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