LMFDB - Embedded newform 207.4.o.a.11.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(5,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$207 = 3^{2} \cdot 23$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	207.o (of order $66$ , degree $20$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.24
Character	$\chi$	$=$	207.11
Dual form			207.4.o.a.113.24

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28970 + 0.109072i) q^{2} +(-4.03437 + 3.27473i) q^{3} +(-2.73296 + 0.260966i) q^{4} +(9.32648 + 8.89278i) q^{5} +(8.88031 - 7.93816i) q^{6} +(2.38597 + 12.3796i) q^{7} +(24.3809 - 3.50544i) q^{8} +(5.55235 - 26.4229i) q^{9} +(-22.3248 - 19.3445i) q^{10} +(23.3283 - 12.0266i) q^{11} +(10.1712 - 10.0025i) q^{12} +(54.3018 + 10.4658i) q^{13} +(-6.81342 - 28.0853i) q^{14} +(-66.7479 - 5.33514i) q^{15} +(-33.8762 + 6.52911i) q^{16} +(-14.8472 - 32.5108i) q^{17} +(-9.83120 + 61.1061i) q^{18} +(56.3288 + 25.7245i) q^{19} +(-27.8096 - 21.8697i) q^{20} +(-50.1657 - 42.1305i) q^{21} +(-52.1030 + 30.0817i) q^{22} +(110.039 + 7.64275i) q^{23} +(-86.8822 + 93.9829i) q^{24} +(1.95394 + 41.0183i) q^{25} +(-125.476 - 18.0408i) q^{26} +(64.1276 + 124.782i) q^{27} +(-9.75142 - 33.2103i) q^{28} +(-29.4662 + 308.583i) q^{29} +(153.414 + 4.93555i) q^{30} +(121.450 - 95.5096i) q^{31} +(-114.644 + 27.8123i) q^{32} +(-54.7314 + 124.914i) q^{33} +(37.5416 + 72.8205i) q^{34} +(-87.8364 + 136.676i) q^{35} +(-8.27886 + 73.6618i) q^{36} +(-11.8987 + 40.5234i) q^{37} +(-131.782 - 52.7574i) q^{38} +(-253.347 + 135.601i) q^{39} +(258.561 + 184.120i) q^{40} +(-263.418 + 276.265i) q^{41} +(119.459 + 90.9945i) q^{42} +(134.484 - 171.010i) q^{43} +(-60.6168 + 38.9561i) q^{44} +(286.757 - 197.057i) q^{45} +(-252.790 - 5.49743i) q^{46} +(-210.513 - 121.540i) q^{47} +(115.288 - 137.276i) q^{48} +(170.869 - 68.4055i) q^{49} +(-8.94788 - 93.7065i) q^{50} +(166.363 + 82.5403i) q^{51} +(-151.136 - 14.4317i) q^{52} +(-52.5883 - 60.6901i) q^{53} +(-160.443 - 278.719i) q^{54} +(324.521 + 95.2879i) q^{55} +(101.568 + 293.462i) q^{56} +(-311.492 + 80.6791i) q^{57} +(33.8108 - 709.777i) q^{58} +(-3.98824 + 20.6930i) q^{59} +(183.812 - 2.83821i) q^{60} +(-336.254 + 839.923i) q^{61} +(-267.667 + 231.935i) q^{62} +(340.353 + 5.69146i) q^{63} +(524.284 - 153.944i) q^{64} +(413.375 + 580.504i) q^{65} +(111.694 - 291.984i) q^{66} +(279.430 - 542.019i) q^{67} +(49.0610 + 84.9761i) q^{68} +(-468.967 + 329.514i) q^{69} +(186.211 - 322.527i) q^{70} +(-384.634 - 598.503i) q^{71} +(42.7471 - 663.678i) q^{72} +(-94.0395 + 205.918i) q^{73} +(22.8245 - 94.0840i) q^{74} +(-142.207 - 159.085i) q^{75} +(-160.658 - 55.6041i) q^{76} +(204.545 + 260.100i) q^{77} +(565.297 - 338.117i) q^{78} +(304.244 - 105.300i) q^{79} +(-374.008 - 240.360i) q^{80} +(-667.343 - 293.419i) q^{81} +(573.015 - 661.295i) q^{82} +(-449.780 + 428.864i) q^{83} +(148.095 + 102.050i) q^{84} +(150.639 - 435.244i) q^{85} +(-289.275 + 406.231i) q^{86} +(-891.649 - 1341.43i) q^{87} +(526.606 - 374.994i) q^{88} +(180.318 - 1254.14i) q^{89} +(-635.094 + 482.478i) q^{90} +697.206i q^{91} +(-302.727 + 7.82912i) q^{92} +(-177.208 + 783.038i) q^{93} +(495.267 + 255.328i) q^{94} +(296.587 + 740.839i) q^{95} +(371.439 - 487.633i) q^{96} +(663.581 + 160.983i) q^{97} +(-383.776 + 175.265i) q^{98} +(-188.251 - 683.178i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$1400 q - 27 q^{2} - 22 q^{3} - 281 q^{4} - 33 q^{5} + 29 q^{6} - 11 q^{7} - 22 q^{9} - 44 q^{10} - 33 q^{11} + 86 q^{12} - 9 q^{13} - 33 q^{14} + 726 q^{15} + 999 q^{16} + 51 q^{18} - 44 q^{19} - 33 q^{20}+ \cdots - 9262 q^{99}+O(q^{100})$ 1400 * q - 27 * q^2 - 22 * q^3 - 281 * q^4 - 33 * q^5 + 29 * q^6 - 11 * q^7 - 22 * q^9 - 44 * q^10 - 33 * q^11 + 86 * q^12 - 9 * q^13 - 33 * q^14 + 726 * q^15 + 999 * q^16 + 51 * q^18 - 44 * q^19 - 33 * q^20 + 638 * q^21 + 252 * q^23 - 2564 * q^24 + 1397 * q^25 - 178 * q^27 - 44 * q^28 - 135 * q^29 - 1518 * q^30 - 45 * q^31 - 339 * q^32 + 1914 * q^33 - 11 * q^34 - 2137 * q^36 - 44 * q^37 - 33 * q^38 + 374 * q^39 + 979 * q^40 + 441 * q^41 - 22 * q^42 - 11 * q^43 + 516 * q^46 - 1992 * q^47 - 20 * q^48 - 4633 * q^49 - 6231 * q^50 - 22 * q^51 + 178 * q^52 + 2640 * q^54 + 256 * q^55 + 17391 * q^56 + 2090 * q^57 + 320 * q^58 - 2061 * q^59 + 418 * q^60 - 11 * q^61 - 2112 * q^63 + 8546 * q^64 - 12969 * q^65 - 5775 * q^66 - 11 * q^67 - 519 * q^69 - 1582 * q^70 - 4156 * q^72 - 36 * q^73 - 10065 * q^74 - 7876 * q^75 - 11 * q^76 + 1317 * q^77 - 10053 * q^78 - 11 * q^79 + 12442 * q^81 + 698 * q^82 + 14025 * q^83 + 16720 * q^84 + 241 * q^85 - 33 * q^86 + 11672 * q^87 - 1419 * q^88 - 37136 * q^90 + 3141 * q^92 + 1138 * q^93 + 396 * q^94 + 5883 * q^95 + 9218 * q^96 + 6325 * q^97 - 9262 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$ .

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−2.28970	+	0.109072i	−0.809530	+	0.0385627i	−0.448265	−	0.893901i	$-0.647958\pi$
$2$	−2.28970	+	0.109072i	−0.809530	+	0.0385627i	−0.361265	+	0.932463i	$0.617655\pi$
$3$	−4.03437	+	3.27473i	−0.776416	+	0.630221i
$3$	−4.03437	+	3.27473i	−0.776416	+	0.630221i
$4$	−2.73296	+	0.260966i	−0.341620	+	0.0326208i
$5$	9.32648	+	8.89278i	0.834186	+	0.795395i	0.981049	−	0.193762i	$-0.0620690\pi$
$5$	9.32648	+	8.89278i	0.834186	+	0.795395i	−0.146863	+	0.989157i	$0.546918\pi$
$6$	8.88031	−	7.93816i	0.604229	−	0.540124i
$7$	2.38597	+	12.3796i	0.128830	+	0.668436i	0.987715	+	0.156266i	$0.0499458\pi$
$7$	2.38597	+	12.3796i	0.128830	+	0.668436i	−0.858885	+	0.512169i	$0.828842\pi$
$8$	24.3809	−	3.50544i	1.07749	−	0.154920i
$9$	5.55235	−	26.4229i	0.205643	−	0.978627i
$10$	−22.3248	−	19.3445i	−0.705971	−	0.611727i
$11$	23.3283	−	12.0266i	0.639432	−	0.329650i	−0.107840	−	0.994168i	$-0.534394\pi$
$11$	23.3283	−	12.0266i	0.639432	−	0.329650i	0.747272	+	0.664518i	$0.231363\pi$
$12$	10.1712	−	10.0025i	0.244681	−	0.240623i
$13$	54.3018	+	10.4658i	1.15851	+	0.223284i	0.732068	−	0.681231i	$-0.238555\pi$
$13$	54.3018	+	10.4658i	1.15851	+	0.223284i	0.426441	+	0.904516i	$0.359767\pi$
$14$	−6.81342	−	28.0853i	−0.130069	−	0.536151i
$15$	−66.7479	−	5.33514i	−1.14895	−	0.0918352i
$16$	−33.8762	+	6.52911i	−0.529316	+	0.102017i
$17$	−14.8472	−	32.5108i	−0.211822	−	0.463825i	0.773661	−	0.633600i	$-0.218423\pi$
$17$	−14.8472	−	32.5108i	−0.211822	−	0.463825i	−0.985483	+	0.169775i	$0.945696\pi$
$18$	−9.83120	+	61.1061i	−0.128735	+	0.800158i
$19$	56.3288	+	25.7245i	0.680143	+	0.310611i	0.725363	−	0.688366i	$-0.241672\pi$
$19$	56.3288	+	25.7245i	0.680143	+	0.310611i	−0.0452207	+	0.998977i	$0.514399\pi$
$20$	−27.8096	−	21.8697i	−0.310921	−	0.244511i
$21$	−50.1657	−	42.1305i	−0.521288	−	0.437792i
$22$	−52.1030	+	30.0817i	−0.504927	+	0.291520i
$23$	110.039	+	7.64275i	0.997597	+	0.0692880i
$23$	110.039	+	7.64275i	0.997597	+	0.0692880i
$24$	−86.8822	+	93.9829i	−0.738948	+	0.799341i
$25$	1.95394	+	41.0183i	0.0156316	+	0.328147i
$26$	−125.476	−	18.0408i	−0.946458	−	0.136080i
$27$	64.1276	+	124.782i	0.457088	+	0.889422i
$28$	−9.75142	−	33.2103i	−0.0658159	−	0.224148i
$29$	−29.4662	+	308.583i	−0.188680	+	1.97595i	0.0276064	+	0.999619i	$0.491211\pi$
$29$	−29.4662	+	308.583i	−0.188680	+	1.97595i	−0.216287	+	0.976330i	$0.569395\pi$
$30$	153.414	+	4.93555i	0.933651	+	0.0300368i
$31$	121.450	−	95.5096i	0.703649	−	0.553356i	−0.200959	−	0.979600i	$-0.564406\pi$
$31$	121.450	−	95.5096i	0.703649	−	0.553356i	0.904608	+	0.426244i	$0.140163\pi$
$32$	−114.644	+	27.8123i	−0.633324	+	0.153643i
$33$	−54.7314	+	124.914i	−0.288712	+	0.658929i
$34$	37.5416	+	72.8205i	0.189362	+	0.367312i
$35$	−87.8364	+	136.676i	−0.424202	+	0.660071i
$36$	−8.27886	+	73.6618i	−0.0383280	+	0.341027i
$37$	−11.8987	+	40.5234i	−0.0528686	+	0.180054i	−0.981694	−	0.190463i	$-0.939001\pi$
$37$	−11.8987	+	40.5234i	−0.0528686	+	0.180054i	0.928826	+	0.370517i	$0.120819\pi$
$38$	−131.782	−	52.7574i	−0.562574	−	0.225221i
$39$	−253.347	+	135.601i	−1.04020	+	0.556755i
$40$	258.561	+	184.120i	1.02205	+	0.727800i
$41$	−263.418	+	276.265i	−1.00339	+	1.05233i	−0.00476140	+	0.999989i	$0.501516\pi$
$41$	−263.418	+	276.265i	−1.00339	+	1.05233i	−0.998629	+	0.0523374i	$0.983333\pi$
$42$	119.459	+	90.9945i	0.438881	+	0.334304i
$43$	134.484	−	171.010i	0.476945	−	0.606485i	−0.486733	−	0.873551i	$-0.661812\pi$
$43$	134.484	−	171.010i	0.476945	−	0.606485i	0.963678	+	0.267066i	$0.0860541\pi$
$44$	−60.6168	+	38.9561i	−0.207689	+	0.133474i
$45$	286.757	−	197.057i	0.949939	−	0.652790i
$46$	−252.790	−	5.49743i	−0.810256	−	0.0176207i
$47$	−210.513	−	121.540i	−0.653328	−	0.377199i	0.136402	−	0.990654i	$-0.456446\pi$
$47$	−210.513	−	121.540i	−0.653328	−	0.377199i	−0.789730	+	0.613454i	$0.789779\pi$
$48$	115.288	−	137.276i	0.346676	−	0.412794i
$49$	170.869	−	68.4055i	0.498159	−	0.199433i
$50$	−8.94788	−	93.7065i	−0.0253084	−	0.265042i
$51$	166.363	+	82.5403i	0.456774	+	0.226626i
$52$	−151.136	−	14.4317i	−0.403054	−	0.0384869i
$53$	−52.5883	−	60.6901i	−0.136294	−	0.157291i	0.683500	−	0.729951i	$-0.260457\pi$
$53$	−52.5883	−	60.6901i	−0.136294	−	0.157291i	−0.819793	+	0.572660i	$0.805912\pi$
$54$	−160.443	−	278.719i	−0.404325	−	0.702387i
$55$	324.521	+	95.2879i	0.795607	+	0.233611i
$56$	101.568	+	293.462i	0.242368	+	0.700276i
$57$	−311.492	+	80.6791i	−0.723827	+	0.187477i
$58$	33.8108	−	709.777i	0.0765445	−	1.60687i
$59$	−3.98824	+	20.6930i	−0.00880042	+	0.0456609i	−0.986063	−	0.166370i	$-0.946796\pi$
$59$	−3.98824	+	20.6930i	−0.00880042	+	0.0456609i	0.977263	+	0.212031i	$0.0680076\pi$
$60$	183.812	−	2.83821i	0.395500	−	0.00610685i
$61$	−336.254	+	839.923i	−0.705786	+	1.76297i	−0.0615982	+	0.998101i	$0.519620\pi$
$61$	−336.254	+	839.923i	−0.705786	+	1.76297i	−0.644188	+	0.764867i	$0.722805\pi$
$62$	−267.667	+	231.935i	−0.548286	+	0.475093i
$63$	340.353	+	5.69146i	0.680642	+	0.0113818i
$64$	524.284	−	153.944i	1.02399	−	0.300671i
$65$	413.375	+	580.504i	0.788813	+	1.10773i
$66$	111.694	−	291.984i	0.208311	−	0.544556i
$67$	279.430	−	542.019i	0.509520	−	0.988332i	−0.484042	−	0.875045i	$-0.660832\pi$
$67$	279.430	−	542.019i	0.509520	−	0.988332i	0.993562	−	0.113287i	$-0.0361379\pi$
$68$	49.0610	+	84.9761i	0.0874929	+	0.151542i
$69$	−468.967	+	329.514i	−0.818216	+	0.574910i
$70$	186.211	−	322.527i	0.317950	−	0.550705i
$71$	−384.634	−	598.503i	−0.642925	−	1.00041i	−0.997851	−	0.0655169i	$-0.979130\pi$
$71$	−384.634	−	598.503i	−0.642925	−	1.00041i	0.354926	−	0.934894i	$-0.384506\pi$
$72$	42.7471	−	663.678i	0.0699693	−	1.08632i
$73$	−94.0395	+	205.918i	−0.150774	+	0.330149i	−0.969915	−	0.243443i	$-0.921723\pi$
$73$	−94.0395	+	205.918i	−0.150774	+	0.330149i	0.819141	+	0.573592i	$0.194450\pi$
$74$	22.8245	−	94.0840i	0.0358554	−	0.147798i
$75$	−142.207	−	159.085i	−0.218942	−	0.244927i
$76$	−160.658	−	55.6041i	−0.242483	−	0.0839241i
$77$	204.545	+	260.100i	0.302728	+	0.384950i
$78$	565.297	−	338.117i	0.820606	−	0.490823i
$79$	304.244	−	105.300i	0.433293	−	0.149964i	−0.101711	−	0.994814i	$-0.532432\pi$
$79$	304.244	−	105.300i	0.433293	−	0.149964i	0.535003	+	0.844850i	$0.320310\pi$
$80$	−374.008	−	240.360i	−0.522692	−	0.335914i
$81$	−667.343	−	293.419i	−0.915422	−	0.402495i
$82$	573.015	−	661.295i	0.771695	−	0.890583i
$83$	−449.780	+	428.864i	−0.594816	+	0.567156i	−0.926529	−	0.376224i	$-0.877222\pi$
$83$	−449.780	+	428.864i	−0.594816	+	0.567156i	0.331712	+	0.943381i	$0.392374\pi$
$84$	148.095	+	102.050i	0.192364	+	0.132554i
$85$	150.639	−	435.244i	0.192225	−	0.555398i
$86$	−289.275	+	406.231i	−0.362714	+	0.509360i
$87$	−891.649	−	1341.43i	−1.09879	−	1.65307i
$88$	526.606	−	374.994i	0.637914	−	0.454256i
$89$	180.318	−	1254.14i	0.214760	−	1.49369i	−0.542210	−	0.840243i	$-0.682412\pi$
$89$	180.318	−	1254.14i	0.214760	−	1.49369i	0.756971	−	0.653449i	$-0.226679\pi$
$90$	−635.094	+	482.478i	−0.743831	+	0.565085i
$91$			697.206i			0.803154i
$92$	−302.727	+	7.82912i	−0.343059	+	0.00887220i
$93$	−177.208	+	783.038i	−0.197588	+	0.873089i
$94$	495.267	+	255.328i	0.543435	+	0.280160i
$95$	296.587	+	740.839i	0.320307	+	0.800089i
$96$	371.439	−	487.633i	0.394894	−	0.518425i
$97$	663.581	+	160.983i	0.694603	+	0.168509i	0.567491	−	0.823380i	$-0.307914\pi$
$97$	663.581	+	160.983i	0.694603	+	0.168509i	0.127112	+	0.991888i	$0.459429\pi$
$98$	−383.776	+	175.265i	−0.395584	+	0.180657i
$99$	−188.251	−	683.178i	−0.191110	−	0.693555i
$100$	−16.0445	−	111.592i	−0.0160445	−	0.111592i
$101$	1037.00	+	1087.58i	1.02164	+	1.07146i	0.997422	+	0.0717574i	$0.0228607\pi$
$101$	1037.00	+	1087.58i	1.02164	+	1.07146i	0.0242169	+	0.999707i	$0.492291\pi$
$102$	−389.924	−	170.847i	−0.378512	−	0.165847i
$103$	−830.081	−	39.5416i	−0.794081	−	0.0378267i	−0.353379	−	0.935480i	$-0.614967\pi$
$103$	−830.081	−	39.5416i	−0.794081	−	0.0378267i	−0.440702	+	0.897654i	$0.645270\pi$
$104$	1360.61	+	64.8140i	1.28288	+	0.0611109i
$105$	−93.2118	−	839.042i	−0.0866337	−	0.779830i
$106$	127.031	+	133.226i	0.116399	+	0.122076i
$107$	83.6643	+	581.898i	0.0755900	+	0.525740i	0.992073	+	0.125666i	$0.0401066\pi$
$107$	83.6643	+	581.898i	0.0755900	+	0.525740i	−0.916483	+	0.400074i	$0.868984\pi$
$108$	−207.822	−	324.290i	−0.185164	−	0.288934i
$109$	492.595	−	224.960i	0.432862	−	0.197682i	−0.187054	−	0.982350i	$-0.559894\pi$
$109$	492.595	−	224.960i	0.432862	−	0.197682i	0.619916	+	0.784668i	$0.287167\pi$
$110$	−753.447	−	182.784i	−0.653076	−	0.158435i
$111$	−84.6989	−	202.451i	−0.0724258	−	0.173116i
$112$	−161.656	−	403.796i	−0.136384	−	0.340671i
$113$	−1288.54	−	664.291i	−1.07271	−	0.553020i	−0.170959	−	0.985278i	$-0.554687\pi$
$113$	−1288.54	−	664.291i	−1.07271	−	0.553020i	−0.901750	+	0.432258i	$0.857717\pi$
$114$	704.422	−	218.706i	0.578730	−	0.179681i
$115$	958.312	+	1049.83i	0.777070	+	0.851282i
$116$		−	851.036i		−	0.681179i
$117$	578.040	−	1376.70i	0.456751	−	1.08783i
$118$	6.87485	−	47.8156i	0.00536340	−	0.0373032i
$119$	367.046	−	261.372i	0.282748	−	0.201344i
$120$	−1646.08	+	103.905i	−1.25221	+	0.0790435i
$121$	−372.484	+	523.081i	−0.279853	+	0.392999i
$122$	678.309	−	1959.84i	0.503370	−	1.45439i
$123$	158.035	−	1977.18i	0.115850	−	1.44940i
$124$	−306.994	+	292.718i	−0.222330	+	0.211991i
$125$	708.323	−	817.449i	0.506835	−	0.584919i
$126$	−779.926	+	24.0912i	−0.551439	+	0.0170334i
$127$	1021.24	+	656.311i	0.713547	+	0.458569i	0.846387	−	0.532569i	$-0.178773\pi$
$127$	1021.24	+	656.311i	0.713547	+	0.458569i	−0.132840	+	0.991137i	$0.542410\pi$
$128$	−291.812	+	100.997i	−0.201506	+	0.0697419i
$129$	17.4531	+	1130.32i	0.0119121	+	0.771465i
$130$	−1009.82	−	1284.09i	−0.681285	−	0.866324i
$131$	−957.372	−	331.350i	−0.638519	−	0.220994i	−0.0114220	−	0.999935i	$-0.503636\pi$
$131$	−957.372	−	331.350i	−0.638519	−	0.220994i	−0.627097	+	0.778941i	$0.715757\pi$
$132$	116.980	−	355.667i	0.0771352	−	0.234521i
$133$	−184.060	+	758.706i	−0.120000	+	0.494648i
$134$	−580.692	+	1271.54i	−0.374359	+	0.819733i
$135$	−511.578	+	1734.05i	−0.326145	+	1.10551i
$136$	−475.952	−	740.596i	−0.300092	−	0.466953i
$137$	−1024.53	+	1774.53i	−0.638913	+	1.10663i	0.346758	+	0.937955i	$0.387282\pi$
$137$	−1024.53	+	1774.53i	−0.638913	+	1.10663i	−0.985672	+	0.168676i	$0.946051\pi$
$138$	1037.85	−	805.638i	0.640201	−	0.496960i
$139$	826.219	+	1431.05i	0.504165	+	0.873240i	0.999988	+	0.00481630i	$0.00153308\pi$
$139$	826.219	+	1431.05i	0.504165	+	0.873240i	−0.495823	+	0.868424i	$0.665134\pi$
$140$	204.385	−	396.453i	0.123384	−	0.239331i
$141$	1247.30	−	199.035i	0.744973	−	0.118878i
$142$	945.976	+	1328.44i	0.559046	+	0.785070i
$143$	1392.64	−	408.915i	0.814393	−	0.239127i
$144$	−15.5744	+	931.361i	−0.00901298	+	0.538982i
$145$	−3018.98	+	2615.96i	−1.72905	+	1.49823i
$146$	192.862	−	481.746i	0.109325	−	0.273079i
$147$	−465.339	+	835.521i	−0.261092	+	0.468793i
$148$	21.9435	−	113.854i	0.0121875	−	0.0632347i
$149$	−106.557	+	2236.91i	−0.0585873	+	1.22990i	0.757836	+	0.652445i	$0.226256\pi$
$149$	−106.557	+	2236.91i	−0.0585873	+	1.22990i	−0.816424	+	0.577453i	$0.804047\pi$
$150$	342.962	+	348.745i	0.186685	+	0.189833i
$151$	−317.549	−	917.498i	−0.171138	−	0.494470i	0.826518	−	0.562911i	$-0.190319\pi$
$151$	−317.549	−	917.498i	−0.171138	−	0.494470i	−0.997655	+	0.0684414i	$0.978197\pi$
$152$	1463.52	+	429.728i	0.780968	+	0.229313i
$153$	−941.467	+	211.795i	−0.497471	+	0.111912i
$154$	−496.715	−	573.240i	−0.259912	−	0.299955i
$155$	1982.05	+	189.263i	1.02711	+	0.0980772i
$156$	656.999	−	436.706i	0.337192	−	0.224131i
$157$	58.0696	+	608.132i	0.0295188	+	0.309135i	0.998158	+	0.0606644i	$0.0193219\pi$
$157$	58.0696	+	608.132i	0.0295188	+	0.309135i	−0.968639	+	0.248471i	$0.920072\pi$
$158$	−685.141	+	274.289i	−0.344980	+	0.138109i
$159$	410.904	+	72.6345i	0.204949	+	0.0362282i
$160$	−1316.55	−	760.113i	−0.650517	−	0.375576i
$161$	167.936	+	1380.47i	0.0822062	+	0.675755i
$162$	1560.02	+	599.052i	0.756583	+	0.290530i
$163$	−711.460	+	457.228i	−0.341877	+	0.219711i	−0.700300	−	0.713848i	$-0.746951\pi$
$163$	−711.460	+	457.228i	−0.341877	+	0.219711i	0.358424	+	0.933559i	$0.383314\pi$
$164$	647.816	−	823.765i	0.308451	−	0.392227i
$165$	−1621.28	+	678.289i	−0.764948	+	0.320029i
$166$	983.082	−	1031.03i	0.459651	−	0.482068i
$167$	−488.822	−	348.089i	−0.226504	−	0.161293i	0.461171	−	0.887311i	$-0.347429\pi$
$167$	−488.822	−	348.089i	−0.226504	−	0.161293i	−0.687675	+	0.726018i	$0.741369\pi$
$168$	−1370.77	−	851.326i	−0.629507	−	0.390960i
$169$	799.530	+	320.083i	0.363919	+	0.145691i
$170$	−297.446	+	1013.01i	−0.134194	+	0.457024i
$171$	992.473	−	1345.54i	0.443838	−	0.601731i
$172$	−322.912	+	502.461i	−0.143150	+	0.222746i
$173$	1635.19	+	3171.83i	0.718621	+	1.39393i	0.910915	+	0.412593i	$0.135377\pi$
$173$	1635.19	+	3171.83i	0.718621	+	1.39393i	−0.192294	+	0.981337i	$0.561593\pi$
$174$	2187.92	+	2974.23i	0.953251	+	1.29584i
$175$	−503.129	+	122.058i	−0.217331	+	0.0527240i
$176$	−711.752	+	559.728i	−0.304832	+	0.239722i
$177$	−51.6737	−	96.5435i	−0.0219437	−	0.0409981i
$178$	−276.083	+	2891.27i	−0.116254	+	1.21747i
$179$	456.672	+	1555.28i	0.190689	+	0.649426i	0.998222	+	0.0596039i	$0.0189838\pi$
$179$	456.672	+	1555.28i	0.190689	+	0.649426i	−0.807534	+	0.589822i	$0.799198\pi$
$180$	−732.271	+	613.383i	−0.303224	+	0.253994i
$181$	4057.89	+	583.436i	1.66641	+	0.239594i	0.910031	−	0.414539i	$-0.136057\pi$
$181$	4057.89	+	583.436i	1.66641	+	0.239594i	0.756379	+	0.654133i	$0.226966\pi$
$182$	−76.0454	−	1596.39i	−0.0309718	−	0.650178i
$183$	−1393.94	−	4489.70i	−0.563077	−	1.81360i
$184$	2709.64	−	199.398i	1.08564	−	0.0798905i
$185$	−471.339	+	272.128i	−0.187316	+	0.108147i
$186$	320.346	−	1812.25i	0.126285	−	0.714411i
$187$	−737.353	−	579.861i	−0.288346	−	0.226757i
$188$	607.040	+	277.226i	0.235495	+	0.107547i
$189$	−1391.75	+	1091.60i	−0.535634	+	0.420118i
$190$	−759.899	−	1663.95i	−0.290152	−	0.635344i
$191$	−3066.94	+	591.104i	−1.16186	+	0.223931i	−0.733509	−	0.679680i	$-0.762119\pi$
$191$	−3066.94	+	591.104i	−1.16186	+	0.223931i	−0.428354	+	0.903611i	$0.640907\pi$
$192$	−1611.03	+	2337.95i	−0.605554	+	0.878787i
$193$	−870.278	−	3587.33i	−0.324580	−	1.33794i	−0.867200	−	0.497960i	$-0.834083\pi$
$193$	−870.278	−	3587.33i	−0.324580	−	1.33794i	0.542620	−	0.839978i	$-0.317432\pi$
$194$	−1536.96	−	296.224i	−0.568800	−	0.109627i
$195$	−3568.70	−	988.280i	−1.31056	−	0.362934i
$196$	−449.126	+	231.540i	−0.163675	+	0.0843806i
$197$	−630.695	−	546.500i	−0.228097	−	0.197647i	0.533312	−	0.845918i	$-0.320947\pi$
$197$	−630.695	−	546.500i	−0.228097	−	0.197647i	−0.761410	+	0.648271i	$0.775492\pi$
$198$	505.552	+	1543.74i	0.181455	+	0.554084i
$199$	3921.02	−	563.758i	1.39675	−	0.200823i	0.597525	−	0.801850i	$-0.296151\pi$
$199$	3921.02	−	563.758i	1.39675	−	0.200823i	0.799228	+	0.601027i	$0.205242\pi$
$200$	191.426	+	993.214i	0.0676794	+	0.351154i
$201$	647.638	+	3101.77i	0.227268	+	1.08847i
$202$	−2493.04	−	2377.11i	−0.868366	−	0.827985i
$203$	−3890.45	+	371.492i	−1.34510	+	0.128442i
$204$	−476.204	−	182.164i	−0.163436	−	0.0625198i
$205$	−4913.53	+	234.060i	−1.67403	+	0.0797438i
$206$	1904.95			0.644291
$207$	812.919	−	2865.12i	0.272955	−	0.962027i
$208$	−1907.87			−0.635996
$209$	1623.43	−	77.3336i	0.537298	−	0.0255946i
$210$	304.942	+	1910.99i	0.100205	+	0.627955i
$211$	−2535.74	+	242.134i	−0.827333	+	0.0790008i	−0.500127	−	0.865952i	$-0.666713\pi$
$211$	−2535.74	+	242.134i	−0.827333	+	0.0790008i	−0.327207	+	0.944953i	$0.606107\pi$
$212$	159.560	+	152.140i	0.0516916	+	0.0492878i
$213$	3511.69	+	1155.01i	1.12966	+	0.371550i
$214$	−255.034	−	1323.24i	−0.0814663	−	0.422687i
$215$	2775.02	−	398.988i	0.880256	−	0.126562i
$216$	2000.90	+	2817.51i	0.630298	+	0.887533i
$217$	1472.15	+	1275.62i	0.460534	+	0.399055i
$218$	−1103.36	+	568.819i	−0.342792	+	0.176722i
$219$	−294.934	−	1138.70i	−0.0910035	−	0.351353i
$220$	−911.769	−	175.729i	−0.279416	−	0.0538530i
$221$	−465.977	−	1920.78i	−0.141833	−	0.584642i
$222$	216.017	+	454.314i	0.0653067	+	0.137349i
$223$	548.885	−	105.789i	0.164825	−	0.0317675i	−0.106171	−	0.994348i	$-0.533859\pi$
$223$	548.885	−	105.789i	0.164825	−	0.0317675i	0.270996	+	0.962580i	$0.412647\pi$
$224$	−617.843	−	1352.89i	−0.184292	−	0.403543i
$225$	1094.67	+	176.119i	0.324348	+	0.0521835i
$226$	3022.83	+	1380.48i	0.889716	+	0.406320i
$227$	−4057.53	−	3190.88i	−1.18638	−	0.932977i	−0.187591	−	0.982247i	$-0.560068\pi$
$227$	−4057.53	−	3190.88i	−1.18638	−	0.932977i	−0.998785	+	0.0492700i	$0.984311\pi$
$228$	830.241	−	301.782i	0.241158	−	0.0876578i
$229$	−2147.94	+	1240.11i	−0.619825	+	0.357856i	−0.776801	−	0.629746i	$-0.783159\pi$
$229$	−2147.94	+	1240.11i	−0.619825	+	0.357856i	0.156976	+	0.987602i	$0.449826\pi$
$230$	−2308.75	−	2299.28i	−0.661889	−	0.659173i
$231$	−1676.97	−	379.512i	−0.477646	−	0.108096i
$232$	363.311	+	7626.83i	0.102813	+	2.15830i
$233$	464.831	+	66.8327i	0.130696	+	0.0187912i	0.207352	−	0.978266i	$-0.433515\pi$
$233$	464.831	+	66.8327i	0.130696	+	0.0187912i	−0.0766565	+	0.997058i	$0.524424\pi$
$234$	−1173.38	+	3215.28i	−0.327804	+	0.898246i
$235$	−882.518	−	3005.58i	−0.244975	−	0.834308i
$236$	5.49954	−	57.5938i	0.00151691	−	0.0158858i
$237$	−882.606	+	1421.13i	−0.241905	+	0.389505i
$238$	−811.915	+	638.497i	−0.221129	+	0.173898i
$239$	5309.07	−	1287.97i	1.43688	−	0.348584i	0.559683	−	0.828707i	$-0.310923\pi$
$239$	5309.07	−	1287.97i	1.43688	−	0.348584i	0.877201	+	0.480123i	$0.159408\pi$
$240$	2296.00	−	255.070i	0.617526	−	0.0686029i
$241$	−2807.33	−	5445.46i	−0.750357	−	1.45549i	−0.885488	−	0.464662i	$-0.846176\pi$
$241$	−2807.33	−	5445.46i	−0.750357	−	1.45549i	0.135131	−	0.990828i	$-0.456855\pi$
$242$	795.823	−	1238.32i	0.211394	−	0.328936i
$243$	3653.18	−	1001.60i	0.964409	−	0.264415i
$244$	699.778	−	2383.23i	0.183601	−	0.625289i
$245$	2201.92	+	881.515i	0.574185	+	0.229869i
$246$	−146.199	+	4544.38i	−0.0378915	+	1.17780i
$247$	2789.53	+	1986.41i	0.718597	+	0.511710i
$248$	2626.26	−	2754.34i	0.672451	−	0.705246i
$249$	410.168	−	3203.10i	0.104391	−	0.815215i
$250$	−1532.69	+	1948.97i	−0.387742	+	0.493054i
$251$	5289.44	−	3399.31i	1.33014	−	0.854832i	0.334001	−	0.942573i	$-0.391601\pi$
$251$	5289.44	−	3399.31i	1.33014	−	0.854832i	0.996143	+	0.0877409i	$0.0279647\pi$
$252$	−931.657	+	73.2661i	−0.232892	+	0.0183148i
$253$	2658.94	−	1145.10i	0.660736	−	0.284553i
$254$	−2409.92	−	1391.37i	−0.595321	−	0.343709i
$255$	817.569	+	2249.24i	0.200777	+	0.552364i
$256$	−3401.07	+	1361.58i	−0.830339	+	0.332418i
$257$	−102.223	−	1070.52i	−0.0248112	−	0.259835i	−0.999363	−	0.0356743i	$-0.988642\pi$
$257$	−102.223	−	1070.52i	−0.0248112	−	0.259835i	0.974552	−	0.224160i	$-0.0719639\pi$
$258$	−163.248	−	2586.18i	−0.0393929	−	0.624065i
$259$	−530.053	−	50.6139i	−0.127166	−	0.0121428i
$260$	−1281.23	−	1478.62i	−0.305609	−	0.352692i
$261$	7990.07	+	2491.94i	1.89492	+	0.590987i
$262$	2228.23	+	654.268i	0.525422	+	0.154278i
$263$	−1949.96	−	5634.04i	−0.457185	−	1.32095i	−0.904462	−	0.426555i	$-0.859727\pi$
$263$	−1949.96	−	5634.04i	−0.457185	−	1.32095i	0.447276	−	0.894396i	$-0.352394\pi$
$264$	−896.522	+	3237.36i	−0.209004	+	0.754718i
$265$	49.2403	−	1033.68i	0.0114144	−	0.239617i
$266$	338.688	−	1757.28i	0.0780688	−	0.405060i
$267$	3379.49	+	5650.16i	0.774613	+	1.29507i
$268$	−622.224	+	1554.24i	−0.141822	+	0.354255i
$269$	−1297.08	+	1123.92i	−0.293993	+	0.254746i	−0.789351	−	0.613943i	$-0.789583\pi$
$269$	−1297.08	+	1123.92i	−0.293993	+	0.254746i	0.495357	+	0.868689i	$0.335037\pi$
$270$	982.222	−	4026.26i	0.221393	−	0.907519i
$271$	4764.59	−	1399.01i	1.06800	−	0.313594i	0.299933	−	0.953960i	$-0.403036\pi$
$271$	4764.59	−	1399.01i	1.06800	−	0.313594i	0.768069	+	0.640367i	$0.221218\pi$
$272$	715.233	+	1004.40i	0.159439	+	0.223901i
$273$	−2283.16	−	2812.79i	−0.506165	−	0.623582i
$274$	2152.30	−	4174.88i	0.474545	−	0.920489i
$275$	538.893	+	933.389i	0.118169	+	0.204675i
$276$	1195.67	−	1022.93i	0.260765	−	0.223092i
$277$	924.983	−	1602.12i	0.200638	−	0.347516i	−0.748096	−	0.663591i	$-0.769032\pi$
$277$	924.983	−	1602.12i	0.200638	−	0.347516i	0.948734	+	0.316075i	$0.102365\pi$
$278$	−2047.88	−	3186.56i	−0.441811	−	0.687472i
$279$	−1849.31	−	3739.38i	−0.396829	−	0.802404i
$280$	−1662.42	+	3640.19i	−0.354816	+	0.776938i
$281$	−1088.54	+	4487.04i	−0.231093	+	0.952579i	0.731546	+	0.681792i	$0.238799\pi$
$281$	−1088.54	+	4487.04i	−0.231093	+	0.952579i	−0.962639	+	0.270787i	$0.912716\pi$
$282$	−2834.22	+	591.775i	−0.598494	+	0.124963i
$283$	−3276.97	−	1134.17i	−0.688324	−	0.238231i	−0.0395560	−	0.999217i	$-0.512594\pi$
$283$	−3276.97	−	1134.17i	−0.688324	−	0.238231i	−0.648768	+	0.760986i	$0.724716\pi$
$284$	1207.38	+	1535.31i	0.252270	+	0.320788i
$285$	−3622.59	−	2017.58i	−0.752924	−	0.419337i
$286$	−3144.12	+	1088.19i	−0.650054	+	0.224986i
$287$	−4048.56	−	2601.85i	−0.832679	−	0.535131i
$288$	98.3400	+	3183.65i	0.0201206	+	0.651384i
$289$	2380.82	−	2747.61i	0.484595	−	0.559253i
$290$	6627.22	−	6319.05i	1.34194	−	1.27954i
$291$	−3204.31	+	1523.58i	−0.645498	+	0.306920i
$292$	203.269	−	587.306i	0.0407377	−	0.117704i
$293$	−1769.56	+	2485.00i	−0.352829	+	0.495479i	−0.952404	−	0.304840i	$-0.901397\pi$
$293$	−1769.56	+	2485.00i	−0.352829	+	0.495479i	0.599575	+	0.800319i	$0.295336\pi$
$294$	974.353	−	1963.84i	0.193284	−	0.389571i
$295$	−221.214	+	157.526i	−0.0436596	+	0.0310899i
$296$	−148.049	+	1029.71i	−0.0290716	+	0.202197i
$297$	2996.69	+	2139.73i	0.585474	+	0.418046i
$298$		−	5133.47i		−	0.997899i
$299$	5895.33	+	1566.66i	1.14025	+	0.303018i
$300$	430.161	+	397.661i	0.0827846	+	0.0765299i
$301$	2437.92	+	1256.83i	0.466841	+	0.240673i
$302$	827.164	+	2066.16i	0.157609	+	0.393688i
$303$	−7745.17	−	991.793i	−1.46848	−	0.188043i
$304$	−2076.17	−	503.672i	−0.391698	−	0.0950249i
$305$	−10605.3	+	4843.29i	−1.99101	+	0.909265i
$306$	2132.57	−	587.634i	0.398402	−	0.109780i
$307$	−657.169	−	4570.71i	−0.122171	−	0.849721i	−0.955088	−	0.296322i	$-0.904240\pi$
$307$	−657.169	−	4570.71i	−0.122171	−	0.849721i	0.832917	−	0.553399i	$-0.186669\pi$
$308$	−626.890	−	657.464i	−0.115975	−	0.121631i
$309$	3478.35	−	2558.76i	0.640376	−	0.471077i
$310$	−4558.94	−	217.169i	−0.835259	−	0.0397883i
$311$	−1490.74	−	71.0128i	−0.271808	−	0.0129478i	−0.0887644	−	0.996053i	$-0.528292\pi$
$311$	−1490.74	−	71.0128i	−0.271808	−	0.0129478i	−0.183043	+	0.983105i	$0.558595\pi$
$312$	−5701.47	+	4194.15i	−1.03456	+	0.761048i
$313$	−3709.75	−	3890.68i	−0.669929	−	0.702601i	0.297791	−	0.954631i	$-0.403750\pi$
$313$	−3709.75	−	3890.68i	−0.669929	−	0.702601i	−0.967719	+	0.252030i	$0.918902\pi$
$314$	−199.292	−	1386.10i	−0.0358175	−	0.249116i
$315$	3123.68	+	3079.77i	0.558729	+	0.550874i
$316$	−804.007	+	367.178i	−0.143130	+	0.0653651i
$317$	−1084.21	−	263.026i	−0.192099	−	0.0466026i	0.138555	−	0.990355i	$-0.455754\pi$
$317$	−1084.21	−	263.026i	−0.192099	−	0.0466026i	−0.330654	+	0.943752i	$0.607269\pi$
$318$	−948.769	−	121.493i	−0.167309	−	0.0214245i
$319$	3023.81	+	7553.11i	0.530723	+	1.32568i
$320$	6258.71	+	3226.59i	1.09335	+	0.563662i
$321$	−2243.09	−	2073.62i	−0.390022	−	0.360554i
$322$	−535.093	−	3142.55i	−0.0926074	−	0.543874i
$323$		−	2213.23i		−	0.381261i
$324$	1900.39	+	627.748i	0.325856	+	0.107638i
$325$	−323.188	+	2247.82i	−0.0551607	+	0.383651i
$326$	1579.16	−	1124.51i	0.268287	−	0.191046i
$327$	−1250.63	+	2520.69i	−0.211498	+	0.426282i
$328$	−5453.94	+	7658.98i	−0.918120	+	1.28932i
$329$	1002.33	−	2896.05i	0.167965	−	0.485303i
$330$	3638.26	−	1729.91i	0.606908	−	0.288571i
$331$	−2178.86	+	2077.54i	−0.361815	+	0.344990i	−0.849080	−	0.528264i	$-0.822843\pi$
$331$	−2178.86	+	2077.54i	−0.361815	+	0.344990i	0.487265	+	0.873254i	$0.337995\pi$
$332$	1117.31	−	1289.45i	0.184700	−	0.213155i
$333$	1004.68	+	539.399i	0.165334	+	0.0887655i
$334$	1157.22	+	743.701i	0.189582	+	0.121837i
$335$	7426.17	−	2570.22i	1.21115	−	0.419183i
$336$	1974.50	+	1099.69i	0.320589	+	0.178550i
$337$	−5789.26	−	7361.64i	−0.935789	−	1.18995i	−0.981590	−	0.191002i	$-0.938826\pi$
$337$	−5789.26	−	7361.64i	−0.935789	−	1.18995i	0.0458005	−	0.998951i	$-0.485416\pi$
$338$	−1865.59	−	645.688i	−0.300222	−	0.103908i
$339$	7373.84	−	1539.63i	1.18139	−	0.246671i
$340$	−298.108	+	1228.82i	−0.0475505	+	0.196006i
$341$	1684.58	−	3688.71i	0.267522	−	0.585791i
$342$	−2125.70	+	3189.13i	−0.336096	+	0.504235i
$343$	3592.44	+	5589.95i	0.565520	+	0.879967i
$344$	2679.37	−	4640.81i	0.419948	−	0.727371i
$345$	−7304.10	−	1097.21i	−1.13983	−	0.171223i
$346$	−4090.06	−	7084.18i	−0.635499	−	1.10072i
$347$	167.212	−	324.347i	0.0258687	−	0.0501782i	−0.875547	−	0.483133i	$-0.839499\pi$
$347$	167.212	−	324.347i	0.0258687	−	0.0501782i	0.901416	+	0.432955i	$0.142529\pi$
$348$	2786.91	+	3433.40i	0.429293	+	0.528878i
$349$	−1891.38	−	2656.08i	−0.290096	−	0.407382i	0.643650	−	0.765320i	$-0.277419\pi$
$349$	−1891.38	−	2656.08i	−0.290096	−	0.407382i	−0.933745	+	0.357938i	$0.883480\pi$
$350$	1138.70	−	334.352i	0.173903	−	0.0510625i
$351$	2176.30	+	7447.06i	0.330946	+	1.13246i
$352$	−2339.96	+	2027.59i	−0.354319	+	0.307019i
$353$	2795.03	−	6981.66i	0.421430	−	1.05268i	−0.554029	−	0.832497i	$-0.686910\pi$
$353$	2795.03	−	6981.66i	0.421430	−	1.05268i	0.975459	−	0.220183i	$-0.0706655\pi$
$354$	128.847	+	215.419i	0.0193451	+	0.0323430i
$355$	1735.07	−	9002.39i	0.259403	−	1.34591i
$356$	−165.514	+	3474.57i	−0.0246411	+	0.517281i
$357$	−624.878	+	2256.45i	−0.0926388	+	0.334520i
$358$	−1215.28	−	3511.31i	−0.179412	−	0.518376i
$359$	2449.44	+	719.221i	0.360102	+	0.105735i	0.456779	−	0.889580i	$-0.349003\pi$
$359$	2449.44	+	719.221i	0.360102	+	0.105735i	−0.0966769	+	0.995316i	$0.530821\pi$
$360$	6300.62	−	5809.64i	0.922422	−	0.850541i
$361$	−1980.51	−	2285.63i	−0.288746	−	0.333231i
$362$	−9354.97	−	893.291i	−1.35825	−	0.129697i
$363$	−210.206	−	3330.09i	−0.0303938	−	0.481500i
$364$	−181.947	−	1905.44i	−0.0261995	−	0.274374i
$365$	−2708.24	+	1084.22i	−0.388372	+	0.155481i
$366$	3681.40	+	10128.0i	0.525765	+	1.44645i
$367$	8107.73	+	4681.00i	1.15319	+	0.665793i	0.949662	−	0.313276i	$-0.101427\pi$
$367$	8107.73	+	4681.00i	1.15319	+	0.665793i	0.203526	+	0.979070i	$0.434760\pi$
$368$	−3777.61	+	459.549i	−0.535113	+	0.0650969i
$369$	5837.15	+	8494.20i	0.823495	+	1.19835i
$370$	1049.54	−	674.499i	0.147468	−	0.0947718i
$371$	625.845	−	795.827i	0.0875802	−	0.111367i
$372$	279.957	−	2186.26i	0.0390191	−	0.304710i
$373$	−3283.74	+	3443.89i	−0.455833	+	0.478064i	−0.911038	−	0.412323i	$-0.864718\pi$
$373$	−3283.74	+	3443.89i	−0.455833	+	0.478064i	0.455205	+	0.890387i	$0.349566\pi$
$374$	1751.56	+	1247.28i	0.242169	+	0.172448i
$375$	−180.721	+	5617.46i	−0.0248864	+	0.773558i
$376$	−5558.53	−	2225.30i	−0.762392	−	0.305216i
$377$	−4829.64	+	16448.3i	−0.659786	+	2.24702i
$378$	3067.62	−	2651.24i	0.417411	−	0.360754i
$379$	−1553.25	+	2416.91i	−0.210515	+	0.327568i	−0.930414	−	0.366511i	$-0.880552\pi$
$379$	−1553.25	+	2416.91i	−0.210515	+	0.327568i	0.719898	+	0.694080i	$0.244188\pi$
$380$	−1003.89	−	1947.28i	−0.135523	−	0.262878i
$381$	−6269.30	+	696.476i	−0.843008	+	0.0936524i
$382$	6957.89	−	1687.97i	0.931928	−	0.226083i
$383$	−9154.01	+	7198.80i	−1.22127	+	0.960421i	−0.999891	−	0.0147657i	$-0.995300\pi$
$383$	−9154.01	+	7198.80i	−1.22127	+	0.960421i	−0.221384	+	0.975187i	$0.571057\pi$
$384$	846.540	−	1363.06i	0.112500	−	0.181142i
$385$	−405.328	+	4244.79i	−0.0536557	+	0.561908i
$386$	2383.95	+	8118.99i	0.314352	+	1.07058i
$387$	−3771.90	−	4502.97i	−0.495442	−	0.591470i
$388$	−1855.55	−	266.788i	−0.242787	−	0.0349075i
$389$	−372.343	−	7816.44i	−0.0485309	−	1.01879i	−0.883482	−	0.468465i	$-0.844807\pi$
$389$	−372.343	−	7816.44i	−0.0485309	−	1.01879i	0.834951	−	0.550324i	$-0.185496\pi$
$390$	8279.03	+	1873.62i	1.07494	+	0.243267i
$391$	−1385.30	−	3690.93i	−0.179175	−	0.477387i
$392$	3926.13	−	2266.75i	0.505867	−	0.292062i
$393$	4947.48	−	1798.34i	0.635031	−	0.230825i
$394$	1503.71	+	1182.53i	0.192273	+	0.151206i
$395$	3773.93	+	1723.50i	0.480727	+	0.219541i
$396$	692.768	+	1817.97i	0.0879113	+	0.230698i
$397$	1790.53	+	3920.71i	0.226358	+	0.495655i	0.988400	−	0.151873i	$-0.0485303\pi$
$397$	1790.53	+	3920.71i	0.226358	+	0.495655i	−0.762042	+	0.647528i	$0.775803\pi$
$398$	−8916.46	+	1718.51i	−1.12297	+	0.216435i
$399$	−1741.99	−	3663.65i	−0.218567	−	0.459679i
$400$	−334.006	−	1376.79i	−0.0417507	−	0.172099i
$401$	2360.91	+	455.028i	0.294010	+	0.0566658i	0.334123	−	0.942529i	$-0.391560\pi$
$401$	2360.91	+	455.028i	0.294010	+	0.0566658i	−0.0401133	+	0.999195i	$0.512772\pi$
$402$	−1821.21	−	7031.47i	−0.225954	−	0.872382i
$403$	7594.56	−	3915.27i	0.938740	−	0.483954i
$404$	−3117.91	−	2701.68i	−0.383964	−	0.332707i
$405$	−3614.65	−	8671.10i	−0.443490	−	1.06388i
$406$	8867.42	−	1274.94i	1.08395	−	0.155848i
$407$	209.780	+	1088.44i	0.0255489	+	0.132560i
$408$	4345.42	+	1429.23i	0.527280	+	0.173425i
$409$	9579.54	+	9134.07i	1.15814	+	1.10428i	0.993013	+	0.118007i	$0.0376507\pi$
$409$	9579.54	+	9134.07i	1.15814	+	1.10428i	0.165123	+	0.986273i	$0.447198\pi$
$410$	11225.0	−	1071.85i	1.35210	−	0.129110i
$411$	−1677.78	−	10514.2i	−0.201360	−	1.26186i
$412$	2278.90	−	108.557i	0.272508	−	0.0129812i
$413$	−265.686			−0.0316551
$414$	−1548.83	+	6648.92i	−0.183867	+	0.789315i
$415$	−8008.66			−0.947300
$416$	−6516.45	+	310.417i	−0.768018	+	0.0365852i
$417$	−8019.58	−	3067.76i	−0.941776	−	0.360261i
$418$	−3708.73	+	354.141i	−0.433972	+	0.0414393i
$419$	−1064.27	−	1014.78i	−0.124088	−	0.118318i	0.625495	−	0.780228i	$-0.284897\pi$
$419$	−1064.27	−	1014.78i	−0.124088	−	0.118318i	−0.749583	+	0.661911i	$0.769746\pi$
$420$	473.706	+	2268.74i	0.0550345	+	0.263579i
$421$	−113.600	−	589.412i	−0.0131509	−	0.0682333i	0.974760	−	0.223254i	$-0.0716678\pi$
$421$	−113.600	−	589.412i	−0.0131509	−	0.0682333i	−0.987911	+	0.155020i	$0.950456\pi$
$422$	5779.66	−	830.990i	0.666705	−	0.0958577i
$423$	−4380.27	+	4887.53i	−0.503490	+	0.561797i
$424$	−1494.89	−	1295.33i	−0.171223	−	0.148365i
$425$	1304.53	−	672.531i	0.148892	−	0.0767590i
$426$	−8166.69	−	2261.60i	−0.928820	−	0.257218i
$427$	−11200.2	−	2158.66i	−1.26936	−	0.244649i
$428$	−380.507	−	1568.47i	−0.0429731	−	0.177138i
$429$	−4279.34	+	6210.22i	−0.481604	+	0.698910i
$430$	−6310.44	+	1216.24i	−0.707713	+	0.136400i
$431$	−2516.91	−	5511.26i	−0.281288	−	0.615936i	0.715268	−	0.698850i	$-0.246304\pi$
$431$	−2516.91	−	5511.26i	−0.281288	−	0.615936i	−0.996557	+	0.0829144i	$0.973577\pi$
$432$	−2987.12	−	3808.46i	−0.332680	−	0.424154i
$433$	3714.06	+	1696.16i	0.412209	+	0.188249i	0.610716	−	0.791850i	$-0.290882\pi$
$433$	3714.06	+	1696.16i	0.412209	+	0.188249i	−0.198507	+	0.980100i	$0.563609\pi$
$434$	−3509.91	−	2760.22i	−0.388205	−	0.305288i
$435$	3613.14	−	20440.1i	0.398246	−	2.25294i
$436$	−1287.53	+	743.358i	−0.141426	+	0.0816523i
$437$	6001.76	+	3261.20i	0.656986	+	0.356990i
$438$	799.509	+	2575.11i	0.0872192	+	0.280922i
$439$	770.245	+	16169.4i	0.0837398	+	1.75791i	0.516390	+	0.856353i	$0.327275\pi$
$439$	770.245	+	16169.4i	0.0837398	+	1.75791i	−0.432651	+	0.901562i	$0.642422\pi$
$440$	8246.13	+	1185.61i	0.893452	+	0.128459i
$441$	−858.751	−	4894.66i	−0.0927277	−	0.528524i
$442$	1276.45	+	4347.19i	0.137363	+	0.467816i
$443$	342.231	−	3584.00i	0.0367040	−	0.384382i	−0.958391	−	0.285458i	$-0.907854\pi$
$443$	342.231	−	3584.00i	0.0367040	−	0.384382i	0.995095	−	0.0989231i	$-0.0315398\pi$
$444$	284.312	+	531.188i	0.0303893	+	0.0567772i
$445$	12834.5	−	10093.2i	1.36722	−	1.07520i
$446$	−1245.24	+	302.092i	−0.132206	+	0.0320728i
$447$	−6895.37	−	9373.48i	−0.729620	−	0.991835i
$448$	3156.69	+	6123.12i	0.332901	+	0.645737i
$449$	−6175.65	+	9609.50i	−0.649102	+	1.01002i	0.348257	+	0.937399i	$0.386774\pi$
$449$	−6175.65	+	9609.50i	−0.649102	+	1.01002i	−0.997359	+	0.0726241i	$0.976863\pi$
$450$	−2525.68	−	283.862i	−0.264582	−	0.0297364i
$451$	−2822.58	+	9612.82i	−0.294701	+	1.00366i
$452$	3694.90	+	1479.21i	0.384499	+	0.153930i
$453$	4285.66	+	2661.64i	0.444499	+	0.276059i
$454$	9638.54	+	6863.58i	0.996386	+	0.709523i
$455$	−6200.10	+	6502.48i	−0.638825	+	0.669980i
$456$	−7311.63	+	3058.94i	−0.750874	+	0.314141i
$457$	−7953.81	+	10114.1i	−0.814144	+	1.03527i	0.184481	+	0.982836i	$0.440940\pi$
$457$	−7953.81	+	10114.1i	−0.814144	+	1.03527i	−0.998625	+	0.0524318i	$0.983303\pi$
$458$	4782.87	−	3073.77i	0.487967	−	0.313597i
$459$	3104.66	−	3937.51i	0.315715	−	0.400408i
$460$	−2893.00	−	2619.07i	−0.293232	−	0.265466i
$461$	11368.1	+	6563.37i	1.14851	+	0.663095i	0.948525	−	0.316704i	$-0.102576\pi$
$461$	11368.1	+	6563.37i	1.14851	+	0.663095i	0.199989	+	0.979798i	$0.435909\pi$
$462$	3881.14	+	686.059i	0.390838	+	0.0690873i
$463$	9341.77	−	3739.88i	0.937686	−	0.375393i	0.148058	−	0.988979i	$-0.452698\pi$
$463$	9341.77	−	3739.88i	0.937686	−	0.375393i	0.789628	+	0.613586i	$0.210274\pi$
$464$	−1016.57	−	10646.0i	−0.101710	−	1.06515i
$465$	−8616.12	+	5727.11i	−0.859275	+	0.571158i
$466$	−1071.61	−	102.327i	−0.106527	−	0.0101721i
$467$	−3194.53	−	3686.69i	−0.316542	−	0.365309i	0.575074	−	0.818102i	$-0.304973\pi$
$467$	−3194.53	−	3686.69i	−0.316542	−	0.365309i	−0.891616	+	0.452792i	$0.850428\pi$
$468$	−1220.49	+	3913.33i	−0.120549	+	0.386525i
$469$	7376.70	+	2165.99i	0.726278	+	0.213254i
$470$	2348.52	+	6785.61i	0.230488	+	0.665951i
$471$	−2225.74	−	2263.27i	−0.217742	−	0.221414i
$472$	−24.6989	+	518.493i	−0.00240860	+	0.0505627i
$473$	1080.62	−	5606.77i	0.105046	−	0.545031i
$474$	1865.89	−	3350.23i	0.180809	−	0.324644i
$475$	−945.113	+	2360.78i	−0.0912942	+	0.228042i
$476$	−934.912	+	810.106i	−0.0900244	+	0.0780066i
$477$	−1895.60	+	1052.56i	−0.181957	+	0.101035i
$478$	−12015.7	+	3528.12i	−1.14976	+	0.337600i
$479$	6832.15	+	9594.42i	0.651710	+	0.915199i	0.999752	−	0.0222805i	$-0.00709268\pi$
$479$	6832.15	+	9594.42i	0.651710	+	0.915199i	−0.348042	+	0.937479i	$0.613153\pi$
$480$	7800.63	−	1244.77i	0.741767	−	0.118366i
$481$	−1070.23	+	2075.96i	−0.101452	+	0.196789i
$482$	7021.88	+	12162.3i	0.663564	+	1.14933i
$483$	−5198.19	−	5019.41i	−0.489702	−	0.472859i
$484$	881.479	−	1526.77i	0.0827835	−	0.143385i
$485$	4757.29	+	7402.49i	0.445397	+	0.693051i
$486$	−8255.42	+	2691.83i	−0.770521	+	0.251242i
$487$	5440.49	−	11913.0i	0.506226	−	1.10848i	−0.468169	−	0.883639i	$-0.655086\pi$
$487$	5440.49	−	11913.0i	0.506226	−	1.10848i	0.974395	−	0.224842i	$-0.0721867\pi$
$488$	−5253.87	+	21656.8i	−0.487360	+	2.00893i
$489$	1373.00	−	4174.47i	0.126972	−	0.386045i
$490$	−5137.87	−	1778.23i	−0.473685	−	0.163944i
$491$	2676.91	+	3403.97i	0.246043	+	0.312869i	0.893351	−	0.449359i	$-0.148348\pi$
$491$	2676.91	+	3403.97i	0.246043	+	0.312869i	−0.647308	+	0.762229i	$0.724105\pi$
$492$	84.0722	+	5444.80i	0.00770380	+	0.498923i
$493$	10469.8	−	3623.63i	0.956461	−	0.331034i
$494$	−6603.83	−	4244.03i	−0.601459	−	0.386534i
$495$	4319.64	−	8045.72i	0.392229	−	0.730562i
$496$	−3490.69	+	4028.47i	−0.316001	+	0.364685i
$497$	6491.50	−	6189.63i	0.585882	−	0.558637i
$498$	−589.791	+	7378.87i	−0.0530707	+	0.663966i
$499$	−1044.94	+	3019.16i	−0.0937436	+	0.270854i	−0.982118	−	0.188265i	$-0.939714\pi$
$499$	−1044.94	+	3019.16i	−0.0937436	+	0.270854i	0.888375	+	0.459119i	$0.151835\pi$
$500$	−1722.49	+	2418.90i	−0.154065	+	0.216353i
$501$	3111.99	−	196.438i	0.277512	−	0.0175174i
$502$	−11740.4	+	8360.33i	−1.04383	+	0.743306i
$503$	−1063.92	+	7399.70i	−0.0943095	+	0.655937i	0.886753	+	0.462244i	$0.152956\pi$
$503$	−1063.92	+	7399.70i	−0.0943095	+	0.655937i	−0.981062	+	0.193693i	$0.937953\pi$
$504$	8318.06	−	1054.32i	0.735150	−	0.0931813i
$505$			19365.1i			1.70641i
$506$	−5963.27	+	2911.95i	−0.523912	+	0.255834i
$507$	−4273.79	+	1326.90i	−0.374370	+	0.116233i
$508$	−2962.28	−	1527.16i	−0.258721	−	0.133380i
$509$	−6357.56	−	15880.4i	−0.553622	−	1.38288i	−0.896308	−	0.443432i	$-0.853761\pi$
$509$	−6357.56	−	15880.4i	−0.553622	−	1.38288i	0.342686	−	0.939450i	$-0.388663\pi$
$510$	−2117.31	−	5060.91i	−0.183836	−	0.439413i
$511$	−2773.55	−	672.857i	−0.240107	−	0.0582494i
$512$	9886.03	−	4514.80i	0.853330	−	0.389703i
$513$	402.265	+	8678.49i	0.0346208	+	0.746910i
$514$	350.823	+	2440.03i	0.0301053	+	0.209387i
$515$	−7390.10	−	7750.52i	−0.632324	−	0.663162i
$516$	−342.673	−	3084.56i	−0.0292352	−	0.263159i
$517$	−6372.61	−	303.565i	−0.542103	−	0.0258235i
$518$	1219.18	+	58.0768i	0.103413	+	0.00492615i
$519$	−16983.9	−	7441.55i	−1.43643	−	0.629379i
$520$	12113.4	+	12704.1i	1.02155	+	1.07137i
$521$	2087.92	+	14521.8i	0.175573	+	1.22114i	0.866858	+	0.498555i	$0.166136\pi$
$521$	2087.92	+	14521.8i	0.175573	+	1.22114i	−0.691285	+	0.722582i	$0.742955\pi$
$522$	−18566.6	−	4834.31i	−1.55678	−	0.405348i
$523$	11662.9	−	5326.29i	0.975115	−	0.445320i	0.136855	−	0.990591i	$-0.456301\pi$
$523$	11662.9	−	5326.29i	0.975115	−	0.445320i	0.838260	+	0.545271i	$0.183573\pi$
$524$	2702.93	+	655.724i	0.225340	+	0.0546669i
$525$	1630.10	−	2140.03i	0.135512	−	0.177902i
$526$	5079.33	+	12687.6i	0.421045	+	1.05172i
$527$	−4908.29	−	2530.40i	−0.405709	−	0.209157i
$528$	1038.52	−	4588.95i	0.0855980	−	0.378235i
$529$	12050.2	+	1682.00i	0.990398	+	0.138243i
$530$			2372.19i			0.194418i
$531$	524.625	+	220.276i	0.0428753	+	0.0180022i
$532$	305.032	−	2121.55i	0.0248587	−	0.172896i
$533$	−17195.4	+	12244.8i	−1.39741	+	0.995088i
$534$	−8354.29	−	12568.6i	−0.677014	−	1.01853i
$535$	−4394.40	+	6171.07i	−0.355115	+	0.498689i
$536$	4912.74	−	14194.4i	0.395892	−	1.14385i
$537$	−6935.50	−	4779.11i	−0.557335	−	0.384048i
$538$	2847.32	−	2714.92i	0.228173	−	0.217562i
$539$	3163.39	−	3650.75i	0.252796	−	0.291742i
$540$	945.593	−	4872.60i	0.0753553	−	0.388303i
$541$	−6098.51	−	3919.27i	−0.484649	−	0.311465i	0.275401	−	0.961329i	$-0.411189\pi$
$541$	−6098.51	−	3919.27i	−0.484649	−	0.311465i	−0.760050	+	0.649864i	$0.774826\pi$
$542$	−10756.9	+	3722.99i	−0.852487	+	0.295048i
$543$	−18281.6	+	10934.7i	−1.44482	+	0.864183i
$544$	2606.34	+	3314.23i	0.205415	+	0.261207i
$545$	6594.70	+	2282.45i	0.518323	+	0.179393i
$546$	5534.54	+	6191.41i	0.433803	+	0.485289i
$547$	4522.63	−	18642.6i	0.353517	−	1.45722i	−0.466318	−	0.884617i	$-0.654420\pi$
$547$	4522.63	−	18642.6i	0.353517	−	1.45722i	0.819835	−	0.572600i	$-0.194065\pi$
$548$	2336.90	−	5117.09i	0.182167	−	0.398889i
$549$	20326.2	+	13548.4i	1.58015	+	1.05324i
$550$	−1335.71	−	2078.40i	−0.103554	−	0.161133i
$551$	−9597.95	+	16624.1i	−0.742080	+	1.28532i
$552$	−10278.7	+	9677.77i	−0.792557	+	0.746220i
$553$	2029.49	+	3515.18i	0.156063	+	0.270308i
$554$	−1943.19	+	3769.25i	−0.149022	+	0.289062i
$555$	1010.41	−	2641.37i	0.0772787	−	0.202018i
$556$	−2631.48	−	3695.40i	−0.200719	−	0.281870i
$557$	−7340.39	+	2155.33i	−0.558388	+	0.163958i	−0.548736	−	0.835996i	$-0.684891\pi$
$557$	−7340.39	+	2155.33i	−0.558388	+	0.163958i	−0.00965255	+	0.999953i	$0.503073\pi$
$558$	4642.22	+	8360.33i	0.352188	+	0.634267i
$559$	9092.50	−	7878.69i	0.687964	−	0.596124i
$560$	2083.19	−	5203.56i	0.157198	−	0.392662i
$561$	4873.64	−	75.2532i	0.366783	−	0.00566344i
$562$	2003.03	−	10392.7i	0.150343	−	0.780053i
$563$	52.3275	−	1098.49i	0.00391712	−	0.0822305i	−0.996062	−	0.0886569i	$-0.971743\pi$
$563$	52.3275	−	1098.49i	0.00391712	−	0.0822305i	0.999979	+	0.00642632i	$0.00204557\pi$
$564$	−3356.87	+	869.457i	−0.250620	+	0.0649127i
$565$	−6110.19	−	17654.2i	−0.454970	−	1.31455i
$566$	7626.98	+	2239.48i	0.566406	+	0.166312i
$567$	2040.14	−	8961.53i	0.151108	−	0.663754i
$568$	−11475.7	−	13243.7i	−0.847731	−	0.978334i
$569$	−3639.44	−	347.525i	−0.268143	−	0.0256046i	−0.0398815	−	0.999204i	$-0.512698\pi$
$569$	−3639.44	−	347.525i	−0.268143	−	0.0256046i	−0.228261	+	0.973600i	$0.573304\pi$
$570$	8514.68	+	4224.52i	0.625686	+	0.310431i
$571$	−1782.21	−	18664.1i	−0.130618	−	1.36790i	−0.788620	−	0.614881i	$-0.789204\pi$
$571$	−1782.21	−	18664.1i	−0.130618	−	1.36790i	0.658001	−	0.753017i	$-0.271402\pi$
$572$	−3699.31	+	1480.98i	−0.270412	+	0.108257i
$573$	10437.5	−	12428.1i	0.760963	−	0.906094i
$574$	9553.77	+	5515.87i	0.694715	+	0.401094i
$575$	−98.4827	+	4528.55i	−0.00714263	+	0.328441i
$576$	−1156.64	−	14707.9i	−0.0836687	−	1.06394i
$577$	4024.07	−	2586.11i	0.290337	−	0.186588i	−0.387362	−	0.921928i	$-0.626614\pi$
$577$	4024.07	−	2586.11i	0.290337	−	0.186588i	0.677699	+	0.735340i	$0.262977\pi$
$578$	−5151.66	+	6550.87i	−0.370728	+	0.471419i
$579$	15258.6	+	11622.7i	1.09521	+	0.834239i
$580$	7568.08	−	7937.17i	0.541806	−	0.568230i
$581$	−6382.33	−	4544.84i	−0.455738	−	0.324529i
$582$	7170.72	−	3838.04i	0.510715	−	0.273353i
$583$	−1956.69	−	783.341i	−0.139001	−	0.0556478i
$584$	−1570.93	+	5350.10i	−0.111311	+	0.379091i
$585$	17633.8	−	7699.41i	1.24627	−	0.544157i
$586$	3780.72	−	5882.91i	0.266519	−	0.414711i
$587$	−7578.81	−	14700.8i	−0.532897	−	1.03368i	−0.989571	−	0.144043i	$-0.953990\pi$
$587$	−7578.81	−	14700.8i	−0.532897	−	1.03368i	0.456674	−	0.889634i	$-0.349041\pi$
$588$	1053.71	−	2404.88i	0.0739018	−	0.168666i
$589$	9298.09	−	2255.69i	0.650460	−	0.157800i
$590$	489.332	−	384.815i	0.0341449	−	0.0268518i
$591$	4334.10	+	139.434i	0.301660	+	0.00970481i
$592$	138.503	−	1450.47i	0.00961559	−	0.100699i
$593$	−7781.71	−	26502.1i	−0.538881	−	1.83526i	−0.549764	−	0.835320i	$-0.685282\pi$
$593$	−7781.71	−	26502.1i	−0.538881	−	1.83526i	0.0108824	−	0.999941i	$-0.496536\pi$
$594$	−7094.90	−	4572.47i	−0.490080	−	0.315843i
$595$	5747.57	+	826.376i	0.396012	+	0.0569380i
$596$	−292.541	−	6141.19i	−0.0201056	−	0.422069i
$597$	−13972.7	+	15114.7i	−0.957898	+	1.03619i
$598$	−13669.4	−	2944.17i	−0.934755	−	0.201331i
$599$	100.098	−	57.7914i	0.00682785	−	0.00394206i	−0.496582	−	0.867990i	$-0.665412\pi$
$599$	100.098	−	57.7914i	0.00682785	−	0.00394206i	0.503410	+	0.864048i	$0.332079\pi$
$600$	−4024.79	−	3380.13i	−0.273852	−	0.229989i
$601$	−765.386	−	601.906i	−0.0519480	−	0.0408524i	0.591847	−	0.806050i	$-0.298399\pi$
$601$	−765.386	−	601.906i	−0.0519480	−	0.0408524i	−0.643795	+	0.765198i	$0.722641\pi$
$602$	−5719.17	−	2611.86i	−0.387203	−	0.176830i
$603$	−12770.3	−	10392.9i	−0.862429	−	0.701874i
$604$	1107.28	+	2424.62i	0.0745940	+	0.163338i
$605$	−8125.62	+	1566.08i	−0.546039	+	0.105240i
$606$	17842.3	+	1426.13i	1.19603	+	0.0955981i
$607$	−5987.39	−	24680.4i	−0.400364	−	1.65032i	−0.713531	−	0.700624i	$-0.752905\pi$
$607$	−5987.39	−	24680.4i	−0.400364	−	1.65032i	0.313167	−	0.949698i	$-0.398610\pi$
$608$	−7173.21	−	1382.52i	−0.478474	−	0.0922183i
$609$	14479.0	−	14238.9i	0.963412	−	0.947436i
$610$	23754.7	−	12246.4i	1.57672	−	0.812856i
$611$	−10159.2	−	8803.01i	−0.672664	−	0.582867i
$612$	2517.72	−	824.518i	0.166296	−	0.0544594i
$613$	4471.81	−	642.949i	0.294641	−	0.0423629i	0.00659061	−	0.999978i	$-0.497902\pi$
$613$	4471.81	−	642.949i	0.294641	−	0.0423629i	0.288050	+	0.957615i	$0.406993\pi$
$614$	2003.25	+	10393.9i	0.131669	+	0.683163i
$615$	19056.5	−	17034.8i	1.24949	−	1.11692i
$616$	5898.75	+	5624.45i	0.385824	+	0.367882i
$617$	951.446	−	90.8521i	0.0620807	−	0.00592798i	−0.0639695	−	0.997952i	$-0.520376\pi$
$617$	951.446	−	90.8521i	0.0620807	−	0.00592798i	0.126050	+	0.992024i	$0.459770\pi$
$618$	−7685.27	+	6238.18i	−0.500238	+	0.406046i
$619$	22140.8	−	1054.70i	1.43766	−	0.0684843i	0.685793	−	0.727796i	$-0.259455\pi$
$619$	22140.8	−	1054.70i	1.43766	−	0.0684843i	0.751869	+	0.659312i	$0.229152\pi$
$620$	−5466.26			−0.354081
$621$	6102.86	+	14221.0i	0.394363	+	0.918955i
$622$	3421.09			0.220536
$623$	15956.0	−	760.077i	1.02610	−	0.0488794i
$624$	7697.08	−	6247.76i	0.493798	−	0.400818i
$625$	18985.4	−	1812.89i	1.21507	−	0.116025i
$626$	8918.58	+	8503.84i	0.569422	+	0.542942i
$627$	−6296.29	+	5628.29i	−0.401036	+	0.358488i
$628$	−317.404	−	1646.85i	−0.0201684	−	0.104644i
$629$	1494.11	−	214.821i	0.0947123	−	0.0136176i
$630$	−7488.21	−	6711.03i	−0.473551	−	0.424403i
$631$	−14365.3	−	12447.6i	−0.906297	−	0.785311i	0.0709357	−	0.997481i	$-0.477401\pi$
$631$	−14365.3	−	12447.6i	−0.906297	−	0.785311i	−0.977233	+	0.212170i	$0.931947\pi$
$632$	7048.61	−	3633.81i	0.443637	−	0.228711i
$633$	9437.19	−	9280.70i	0.592567	−	0.582741i
$634$	2511.20	+	483.994i	0.157307	+	0.0303184i
$635$	3688.15	+	15202.7i	0.230488	+	0.950083i
$636$	−1141.94	−	91.2750i	−0.0711964	−	0.00569071i
$637$	9994.39	−	1926.26i	0.621652	−	0.119814i
$638$	−7747.43	−	16964.5i	−0.480758	−	1.05271i
$639$	−17949.8	+	6840.07i	−1.11124	+	0.423457i
$640$	−3619.72	−	1653.07i	−0.223566	−	0.102099i
$641$	3944.17	+	3101.73i	0.243035	+	0.191125i	0.732245	−	0.681041i	$-0.238473\pi$
$641$	3944.17	+	3101.73i	0.243035	+	0.191125i	−0.489210	+	0.872166i	$0.662715\pi$
$642$	5362.17	+	4503.29i	0.329638	+	0.276839i
$643$	9177.01	−	5298.35i	0.562840	−	0.324956i	−0.191445	−	0.981503i	$-0.561317\pi$
$643$	9177.01	−	5298.35i	0.562840	−	0.324956i	0.754284	+	0.656548i	$0.227984\pi$
$644$	−819.219	−	3728.96i	−0.0501270	−	0.228170i
$645$	−9888.90	+	10697.1i	−0.603682	+	0.653020i
$646$	241.401	+	5067.63i	0.0147025	+	0.308642i
$647$	−23639.0	−	3398.78i	−1.43639	−	0.206522i	−0.620265	−	0.784393i	$-0.712975\pi$
$647$	−23639.0	−	3398.78i	−1.43639	−	0.206522i	−0.816128	+	0.577871i	$0.803884\pi$
$648$	−17299.0	−	4814.47i	−1.04872	−	0.291868i
$649$	155.827	+	530.697i	0.00942485	+	0.0320981i
$650$	494.828	−	5182.08i	0.0298596	−	0.312704i
$651$	−10116.5	−	325.462i	−0.609059	−	0.0195943i
$652$	1825.07	−	1435.25i	0.109625	−	0.0862099i
$653$	30008.9	−	7280.07i	1.79837	−	0.436281i	0.809760	−	0.586761i	$-0.199597\pi$
$653$	30008.9	−	7280.07i	1.79837	−	0.436281i	0.988613	+	0.150480i	$0.0480820\pi$
$654$	2588.62	−	5908.02i	0.154775	−	0.353244i
$655$	−5982.29	−	11604.0i	−0.356866	−	0.692224i
$656$	7119.85	−	11078.7i	0.423756	−	0.659376i
$657$	4918.81	+	3628.13i	0.292087	+	0.215444i
$658$	−1979.16	+	6740.41i	−0.117258	+	0.399344i
$659$	983.553	+	393.755i	0.0581393	+	0.0232754i	0.400550	−	0.916275i	$-0.368819\pi$
$659$	983.553	+	393.755i	0.0581393	+	0.0232754i	−0.342411	+	0.939550i	$0.611243\pi$
$660$	4253.88	−	2276.84i	0.250882	−	0.134281i
$661$	−5826.46	−	4149.01i	−0.342849	−	0.244142i	0.395642	−	0.918405i	$-0.370522\pi$
$661$	−5826.46	−	4149.01i	−0.342849	−	0.244142i	−0.738491	+	0.674263i	$0.764461\pi$
$662$	4762.32	−	4994.58i	0.279597	−	0.293232i
$663$	8169.96	+	6223.21i	0.478575	+	0.364539i
$664$	−9462.67	+	12032.8i	−0.553046	+	0.703256i
$665$	−8463.64	+	5439.25i	−0.493542	+	0.317181i
$666$	−2359.25	−	1125.48i	−0.137266	−	0.0654826i
$667$	−5600.85	+	33731.0i	−0.325136	+	1.95813i
$668$	1426.77	+	823.747i	0.0826399	+	0.0477121i
$669$	−1867.98	+	2224.24i	−0.107952	+	0.128541i
$670$	−16723.3	+	6695.01i	−0.964296	+	0.386046i
$671$	2257.15	+	23638.0i	0.129860	+	1.35996i
$672$	6922.94	+	3434.79i	0.397408	+	0.197172i
$673$	−9851.24	−	940.679i	−0.564246	−	0.0538789i	−0.190964	−	0.981597i	$-0.561161\pi$
$673$	−9851.24	−	940.679i	−0.564246	−	0.0538789i	−0.373282	+	0.927718i	$0.621767\pi$
$674$	14058.6	+	16224.5i	0.803437	+	0.927216i
$675$	−4993.07	+	2874.23i	−0.284716	+	0.163895i
$676$	−2268.61	−	666.125i	−0.129075	−	0.0378997i
$677$	2376.74	+	6867.15i	0.134927	+	0.389846i	0.992143	−	0.125111i	$-0.0399288\pi$
$677$	2376.74	+	6867.15i	0.134927	+	0.389846i	−0.857216	+	0.514958i	$0.827808\pi$
$678$	−16715.9	+	4329.57i	−0.946861	+	0.245245i
$679$	−409.619	+	8598.97i	−0.0231513	+	0.486006i
$680$	2147.00	−	11139.7i	0.121079	−	0.628217i
$681$	26818.8	−	414.105i	1.50910	−	0.0233018i
$682$	−3454.84	+	8629.77i	−0.193977	+	0.484532i
$683$	−25584.4	+	22169.0i	−1.43332	+	1.24198i	−0.508783	+	0.860895i	$0.669905\pi$
$683$	−25584.4	+	22169.0i	−1.43332	+	1.24198i	−0.924539	+	0.381087i	$0.875550\pi$
$684$	−2361.25	+	3936.31i	−0.131995	+	0.220042i
$685$	−25335.7	+	7439.24i	−1.41318	+	0.414947i
$686$	−8835.30	−	12407.4i	−0.491740	−	0.690552i
$687$	4604.56	−	12037.0i	0.255713	−	0.668472i
$688$	−3439.27	+	6671.25i	−0.190583	+	0.369679i
$689$	−2220.47	−	3845.96i	−0.122777	−	0.212655i
$690$	16843.9	+	1715.61i	0.929326	+	0.0946554i
$691$	7777.45	−	13470.9i	0.428174	−	0.741619i	−0.568537	−	0.822658i	$-0.692490\pi$
$691$	7777.45	−	13470.9i	0.428174	−	0.741619i	0.996711	+	0.0810388i	$0.0258238\pi$
$692$	−5296.66	−	8241.76i	−0.290967	−	0.452753i
$693$	8008.31	−	3960.51i	0.438976	−	0.217096i
$694$	−347.489	+	760.894i	−0.0190065	+	0.0416183i
$695$	−5020.33	+	20694.1i	−0.274003	+	1.12945i
$696$	−26441.5	−	29579.7i	−1.44003	−	1.61094i
$697$	12892.6	+	4462.18i	0.700635	+	0.242492i
$698$	4620.40	+	5875.31i	0.250551	+	0.318601i
$699$	−2094.16	+	1252.57i	−0.113317	+	0.0677775i
$700$	1343.18	−	464.878i	0.0725248	−	0.0251011i
$701$	−25741.9	−	16543.3i	−1.38696	−	0.891344i	−0.387426	−	0.921901i	$-0.626636\pi$
$701$	−25741.9	−	16543.3i	−1.38696	−	0.891344i	−0.999533	+	0.0305566i	$0.990272\pi$
$702$	−5795.32	−	16814.1i	−0.311582	−	0.904001i
$703$	−1712.68	+	1976.54i	−0.0918849	+	0.106041i
$704$	10379.2	−	9896.59i	0.555657	−	0.529818i
$705$	13402.9	+	9235.63i	0.716001	+	0.493381i
$706$	−5638.28	+	16290.7i	−0.300566	+	0.868428i
$707$	−10989.5	+	15432.6i	−0.584587	+	0.820937i
$708$	166.417	+	250.365i	0.00883379	+	0.0132899i
$709$	2313.60	−	1647.51i	0.122552	−	0.0872686i	−0.517138	−	0.855902i	$-0.673002\pi$
$709$	2313.60	−	1647.51i	0.122552	−	0.0872686i	0.639689	+	0.768634i	$0.279063\pi$
$710$	−2990.88	+	20802.0i	−0.158092	+	1.09956i
$711$	−1093.06	−	8623.68i	−0.0576555	−	0.454871i
$712$		−	31209.1i		−	1.64271i
$713$	14094.2	−	9581.57i	0.740299	−	0.503272i
$714$	1184.67	−	5234.73i	0.0620939	−	0.274377i
$715$	16624.8	+	8570.68i	0.869556	+	0.448287i
$716$	−1653.94	−	4131.35i	−0.0863278	−	0.215636i
$717$	−17201.0	+	22581.9i	−0.895934	+	1.17620i
$718$	−5686.92	−	1379.63i	−0.295591	−	0.0717095i
$719$	24025.8	−	10972.2i	1.24619	−	0.569116i	0.320446	−	0.947267i	$-0.396167\pi$
$719$	24025.8	−	10972.2i	1.24619	−	0.569116i	0.925744	+	0.378151i	$0.123440\pi$
$720$	−8427.65	+	8547.83i	−0.436222	+	0.442443i
$721$	−1491.04	−	10370.4i	−0.0770170	−	0.535665i
$722$	4784.06	+	5017.38i	0.246599	+	0.258625i
$723$	29158.2	+	12775.8i	1.49987	+	0.657174i
$724$	−11242.3	−	535.537i	−0.577095	−	0.0274904i
$725$	−12715.2	−	605.698i	−0.651351	−	0.0310277i
$726$	844.526	+	7601.97i	0.0431726	+	0.388616i
$727$	−12201.5	−	12796.5i	−0.622459	−	0.652816i	0.334718	−	0.942318i	$-0.391359\pi$
$727$	−12201.5	−	12796.5i	−0.622459	−	0.652816i	−0.957177	+	0.289502i	$0.906510\pi$
$728$	2444.01	+	16998.5i	0.124425	+	0.865393i
$729$	−11458.3	+	16004.0i	−0.582142	+	0.813087i
$730$	6082.79	−	2777.92i	0.308403	−	0.140843i
$731$	−7556.40	−	1833.16i	−0.382330	−	0.0927523i
$732$	4981.24	+	11906.4i	0.251519	+	0.601193i
$733$	10279.5	+	25676.8i	0.517982	+	1.29386i	0.924837	+	0.380363i	$0.124201\pi$
$733$	10279.5	+	25676.8i	0.517982	+	1.29386i	−0.406856	+	0.913492i	$0.633375\pi$
$734$	−19074.8	−	9833.74i	−0.959215	−	0.494510i
$735$	−11770.1	+	3654.31i	−0.590675	+	0.183390i
$736$	−12827.9	+	2184.25i	−0.642448	+	0.109392i
$737$		−	16005.0i		−	0.799934i
$738$	−14291.8	−	18812.5i	−0.712856	−	0.938343i
$739$	1286.64	−	8948.76i	0.0640456	−	0.445447i	−0.932415	−	0.361389i	$-0.882303\pi$
$739$	1286.64	−	8948.76i	0.0640456	−	0.445447i	0.996461	−	0.0840584i	$-0.0267882\pi$
$740$	1217.13	−	866.717i	0.0604632	−	0.0430556i
$741$	−17759.0	+	1121.00i	−0.880420	+	0.0555749i
$742$	−1346.19	+	1890.46i	−0.0666042	+	0.0935325i
$743$	1110.71	−	3209.19i	0.0548425	−	0.158457i	−0.914252	−	0.405145i	$-0.867221\pi$
$743$	1110.71	−	3209.19i	0.0548425	−	0.158457i	0.969095	+	0.246688i	$0.0793422\pi$
$744$	−1575.60	+	19712.3i	−0.0776403	+	0.971357i
$745$	−20886.2	+	19914.9i	−1.02713	+	0.979364i
$746$	7143.15	−	8243.63i	0.350575	−	0.404586i
$747$	8834.52	+	14265.7i	0.432715	+	0.698735i
$748$	2166.48	+	1392.31i	0.105902	+	0.0680588i
$749$	−7004.04	+	2424.12i	−0.341685	+	0.118258i
$750$	−198.909	−	12882.0i	−0.00968416	−	0.627178i
$751$	24220.9	+	30799.4i	1.17688	+	1.49652i	0.829242	+	0.558890i	$0.188773\pi$
$751$	24220.9	+	30799.4i	1.17688	+	1.49652i	0.347635	+	0.937630i	$0.386985\pi$
$752$	7924.92	+	2742.84i	0.384298	+	0.133007i
$753$	−10207.7	+	31035.6i	−0.494012	+	1.50199i
$754$	9264.38	−	38188.3i	0.447465	−	1.84448i
$755$	5197.49	−	11380.9i	0.250538	−	0.548601i
$756$	3518.73	−	3346.50i	0.169279	−	0.160994i
$757$	−4122.35	−	6414.51i	−0.197925	−	0.307978i	0.728077	−	0.685495i	$-0.240414\pi$
$757$	−4122.35	−	6414.51i	−0.197925	−	0.307978i	−0.926003	+	0.377517i	$0.876778\pi$
$758$	3292.86	−	5703.41i	0.157787	−	0.273294i
$759$	−6977.27	+	13327.1i	−0.333674	+	0.637341i
$760$	9828.02	+	17022.6i	0.469078	+	0.812468i
$761$	−10639.8	+	20638.4i	−0.506825	+	0.983103i	0.487132	+	0.873328i	$0.338043\pi$
$761$	−10639.8	+	20638.4i	−0.506825	+	0.983103i	−0.993957	+	0.109774i	$0.964987\pi$
$762$	14278.8	−	2278.52i	0.678829	−	0.108323i
$763$	3960.24	+	5561.37i	0.187903	+	0.263873i
$764$	8227.56	−	2415.83i	0.389611	−	0.114400i
$765$	−10664.0	−	6396.96i	−0.503998	−	0.302330i
$766$	20174.7	−	17481.5i	0.951622	−	0.824585i
$767$	−433.137	+	1081.93i	−0.0203907	+	0.0509336i
$768$	9262.38	−	16630.7i	0.435192	−	0.781392i
$769$	−4387.80	+	22766.1i	−0.205758	+	1.06757i	0.721290	+	0.692633i	$0.243549\pi$
$769$	−4387.80	+	22766.1i	−0.205758	+	1.06757i	−0.927048	+	0.374942i	$0.877663\pi$
$770$	465.093	−	9763.50i	0.0217672	−	0.456951i
$771$	3918.08	+	3984.15i	0.183017	+	0.186103i
$772$	3314.61	+	9576.93i	0.154528	+	0.446478i
$773$	30438.8	+	8937.63i	1.41631	+	0.415865i	0.898252	−	0.439481i	$-0.144838\pi$
$773$	30438.8	+	8937.63i	1.41631	+	0.415865i	0.518056	+	0.855347i	$0.326656\pi$
$774$	9127.64	+	9899.04i	0.423884	+	0.459708i
$775$	4154.95	+	4795.07i	0.192581	+	0.222250i
$776$	16743.0	+	1598.76i	0.774535	+	0.0739591i
$777$	2304.18	−	1531.58i	0.106386	−	0.0707146i
$778$	1705.10	+	17856.7i	0.0785745	+	0.822869i
$779$	−21944.8	+	8785.38i	−1.00931	+	0.404068i
$780$	10011.0	+	1769.62i	0.459554	+	0.0812341i
$781$	−16170.8	−	9336.22i	−0.740892	−	0.427754i
$782$	3574.49	+	8300.01i	0.163457	+	0.379550i
$783$	−40395.4	+	16111.9i	−1.84370	+	0.735365i
$784$	−5341.76	+	3432.94i	−0.243338	+	0.156384i
$785$	−4866.40	+	6188.13i	−0.221260	+	0.281355i
$786$	−11132.1	+	4657.29i	−0.505175	+	0.211349i
$787$	20341.0	−	21333.0i	0.921318	−	0.966251i	−0.0782107	−	0.996937i	$-0.524921\pi$
$787$	20341.0	−	21333.0i	0.921318	−	0.966251i	0.999529	+	0.0306860i	$0.00976918\pi$
$788$	1866.28	+	1328.97i	0.0843700	+	0.0600796i
$789$	26316.8	+	16344.2i	1.18746	+	0.737479i
$790$	−8829.15	−	3534.66i	−0.397629	−	0.159187i
$791$	5149.22	−	17536.6i	0.231461	−	0.788283i
$792$	−6984.55	−	15996.6i	−0.313365	−	0.717694i
$793$	−27049.7	+	42090.1i	−1.21130	+	1.88482i
$794$	−4527.41	−	8781.95i	−0.202357	−	0.392519i
$795$	3186.37	+	4331.51i	0.142150	+	0.193236i
$796$	−10568.9	+	2563.98i	−0.470608	+	0.114168i
$797$	3537.49	−	2781.91i	0.157220	−	0.123639i	−0.536450	−	0.843932i	$-0.680235\pi$
$797$	3537.49	−	2781.91i	0.157220	−	0.123639i	0.693670	+	0.720293i	$0.255993\pi$
$798$	4388.22	+	8198.64i	0.194663	+	0.363695i
$799$	−825.827	+	8648.46i	−0.0365653	+	0.382929i
$800$	−1364.82	−	4648.16i	−0.0603172	−	0.205422i
$801$	−32136.9	−	11728.0i	−1.41760	−	0.517337i
$802$	−5455.39	−	784.367i	−0.240195	−	0.0345349i
$803$	282.704	+	5934.69i	0.0124239	+	0.260810i
$804$	−2579.42	−	8308.00i	−0.113146	−	0.364428i
$805$	−10710.0	+	14368.4i	−0.468917	+	0.629092i
$806$	−16962.2	+	9793.13i	−0.741275	+	0.427976i
$807$	1552.35	−	8781.90i	0.0677142	−	0.383070i
$808$	29095.4	+	22880.9i	1.26680	+	0.996222i
$809$	34649.6	+	15823.9i	1.50583	+	0.687688i	0.986025	−	0.166598i	$-0.0532782\pi$
$809$	34649.6	+	15823.9i	1.50583	+	0.687688i	0.519803	+	0.854286i	$0.326005\pi$
$810$	9222.23	+	19459.9i	0.400045	+	0.844139i
$811$	−14748.4	−	32294.4i	−0.638576	−	1.39829i	−0.901206	−	0.433390i	$-0.857317\pi$
$811$	−14748.4	−	32294.4i	−0.638576	−	1.39829i	0.262630	−	0.964897i	$-0.415410\pi$
$812$	10535.5	−	2030.55i	0.455324	−	0.0877565i
$813$	−14640.8	+	21246.9i	−0.631580	+	0.916556i
$814$	−599.051	−	2469.32i	−0.0257945	−	0.106326i
$815$	−10701.5	−	2062.54i	−0.459945	−	0.0886472i
$816$	−6174.67	−	1709.95i	−0.264898	−	0.0733582i
$817$	11974.5	−	6173.27i	0.512771	−	0.264352i
$818$	−22930.5	−	19869.4i	−0.980130	−	0.849287i
$819$	18422.2	+	3871.13i	0.785989	+	0.165163i
$820$	13367.4	−	1921.94i	0.569281	−	0.0818502i
$821$	2321.97	+	12047.5i	0.0987057	+	0.512134i	0.997305	+	0.0733640i	$0.0233735\pi$
$821$	2321.97	+	12047.5i	0.0987057	+	0.512134i	−0.898600	+	0.438770i	$0.855414\pi$
$822$	4988.41	+	23891.2i	0.211667	+	1.01375i
$823$	−3145.23	−	2998.97i	−0.133215	−	0.127020i	0.620543	−	0.784173i	$-0.286912\pi$
$823$	−3145.23	−	2998.97i	−0.133215	−	0.127020i	−0.753758	+	0.657152i	$0.771761\pi$
$824$	−20376.7	+	1945.74i	−0.861476	+	0.0822610i
$825$	−5230.69	−	2000.92i	−0.220738	−	0.0844400i
$826$	608.341	−	28.9789i	0.0256258	−	0.00122071i
$827$	24863.0			1.04543			0.522716	−	0.852507i	$-0.324919\pi$
$827$	24863.0			1.04543			0.522716	+	0.852507i	$0.324919\pi$
$828$	−1473.98	+	8042.40i	−0.0618650	+	0.337552i
$829$	−33477.3			−1.40255			−0.701275	−	0.712891i	$-0.747385\pi$
$829$	−33477.3			−1.40255			−0.701275	+	0.712891i	$0.747385\pi$
$830$	18337.4	−	873.518i	0.766868	−	0.0365304i
$831$	1514.77	+	9492.61i	0.0632331	+	0.396263i
$832$	30080.7	−	2872.36i	1.25344	−	0.119689i
$833$	−4760.83	−	4539.45i	−0.198023	−	0.188814i
$834$	18697.0	+	6149.54i	0.776289	+	0.255325i
$835$	−1463.51	−	7593.43i	−0.0606551	−	0.314708i
$836$	−4416.60	+	635.011i	−0.182717	+	0.0262707i
$837$	19706.2	+	9030.07i	0.813796	+	0.372909i
$838$	2547.53	+	2207.45i	0.105016	+	0.0909965i
$839$	21069.7	−	10862.2i	0.866994	−	0.446966i	0.0334634	−	0.999440i	$-0.489346\pi$
$839$	21069.7	−	10862.2i	0.866994	−	0.446966i	0.833530	+	0.552474i	$0.186316\pi$
$840$	−5213.80	−	20129.8i	−0.214158	−	0.826840i
$841$	−70407.3	−	13569.9i	−2.88684	−	0.556394i
$842$	324.398	+	1337.19i	0.0132773	+	0.0547297i
$843$	−10302.2	−	21667.1i	−0.420911	−	0.885237i
$844$	6866.88	−	1323.48i	0.280057	−	0.0539765i
$845$	4610.37	+	10095.3i	0.187694	+	0.410993i
$846$	9496.40	−	11668.7i	0.385926	−	0.474207i
$847$	−7364.27	−	3363.15i	−0.298748	−	0.136434i
$848$	2177.75	+	1712.60i	0.0881888	+	0.0693524i
$849$	16934.6	−	6155.51i	0.684564	−	0.248830i
$850$	−2913.62	+	1682.18i	−0.117572	+	0.0678803i
$851$	−1619.03	+	4368.21i	−0.0652172	+	0.175958i
$852$	−9898.73	−	2240.17i	−0.398034	−	0.0900786i
$853$	−1815.34	−	38108.6i	−0.0728674	−	1.52967i	−0.678897	−	0.734233i	$-0.737542\pi$
$853$	−1815.34	−	38108.6i	−0.0728674	−	1.52967i	0.606030	−	0.795442i	$-0.292761\pi$
$854$	25880.5	+	3721.06i	1.03702	+	0.149101i
$855$	21221.9	−	3723.31i	0.848857	−	0.148929i
$856$	4079.62	+	13893.9i	0.162895	+	0.554771i
$857$	3910.88	−	40956.5i	0.155884	−	1.63250i	−0.491886	−	0.870660i	$-0.663692\pi$
$857$	3910.88	−	40956.5i	0.155884	−	1.63250i	0.647770	−	0.761836i	$-0.275702\pi$
$858$	9121.02	−	14686.3i	0.362921	−	0.584361i
$859$	24129.5	−	18975.7i	0.958427	−	0.753715i	−0.0107857	−	0.999942i	$-0.503433\pi$
$859$	24129.5	−	18975.7i	0.958427	−	0.753715i	0.969212	+	0.246227i	$0.0791908\pi$
$860$	−7479.90	+	1814.61i	−0.296584	+	0.0719506i
$861$	24853.8	−	2761.08i	0.983756	−	0.109288i
$862$	6364.08	+	12344.6i	0.251463	+	0.487771i
$863$	5482.86	−	8531.50i	0.216267	−	0.336519i	−0.716121	−	0.697976i	$-0.754084\pi$
$863$	5482.86	−	8531.50i	0.216267	−	0.336519i	0.932389	+	0.361457i	$0.117721\pi$
$864$	−10822.3	−	12522.0i	−0.426138	−	0.493064i
$865$	−12955.8	+	44123.5i	−0.509261	+	1.73438i
$866$	−8689.08	−	3478.58i	−0.340955	−	0.136498i
$867$	−607.441	+	18881.4i	−0.0237944	+	0.739615i
$868$	−4356.22	−	3102.05i	−0.170345	−	0.121302i
$869$	5831.10	−	6115.48i	0.227625	−	0.238727i
$870$	−6043.56	+	47195.7i	−0.235513	+	1.83918i
$871$	20846.3	−	26508.2i	0.810963	−	1.03122i
$872$	11221.3	−	7211.49i	0.435781	−	0.280060i
$873$	7938.08	−	16639.9i	0.307747	−	0.645104i
$874$	−14097.9	−	6812.55i	−0.545617	−	0.263659i
$875$	11809.7	+	6818.35i	0.456276	+	0.263431i
$876$	1103.20	+	3035.06i	0.0425500	+	0.117061i
$877$	−22868.9	+	9155.31i	−0.880532	+	0.352512i	−0.767477	−	0.641077i	$-0.778488\pi$
$877$	−22868.9	+	9155.31i	−0.880532	+	0.352512i	−0.113055	+	0.993589i	$0.536064\pi$
$878$	−3527.25	−	36939.1i	−0.135580	−	1.41986i
$879$	−998.624	−	15820.3i	−0.0383194	−	0.607058i
$880$	−11615.7	−	1109.16i	−0.444960	−	0.0424885i
$881$	−12621.3	−	14565.8i	−0.482659	−	0.557019i	0.461230	−	0.887281i	$-0.347408\pi$
$881$	−12621.3	−	14565.8i	−0.482659	−	0.557019i	−0.943889	+	0.330262i	$0.892863\pi$
$882$	2500.15	+	11113.6i	0.0954472	+	0.424280i
$883$	−3269.68	−	960.066i	−0.124613	−	0.0365898i	0.218831	−	0.975763i	$-0.429776\pi$
$883$	−3269.68	−	960.066i	−0.124613	−	0.0365898i	−0.343445	+	0.939173i	$0.611594\pi$
$884$	1774.76	+	5127.82i	0.0675243	+	0.195099i
$885$	376.607	−	1359.93i	0.0143045	−	0.0516539i
$886$	−392.691	+	8243.60i	−0.0148902	+	0.312584i
$887$	−2904.72	+	15071.1i	−0.109956	+	0.570505i	0.884604	+	0.466342i	$0.154429\pi$
$887$	−2904.72	+	15071.1i	−0.109956	+	0.570505i	−0.994560	+	0.104163i	$0.966784\pi$
$888$	−2774.72	−	4639.04i	−0.104857	−	0.175311i
$889$	−5688.22	+	14208.5i	−0.214597	+	0.536037i
$890$	−28286.3	+	24510.2i	−1.06535	+	0.923129i
$891$	−19096.8	+	1180.89i	−0.718032	+	0.0444010i
$892$	−1472.47	+	432.357i	−0.0552714	+	0.0162291i
$893$	−8731.38	−	12261.5i	−0.327194	−	0.459480i
$894$	16810.7	+	20710.3i	0.628897	+	0.774784i
$895$	−9571.64	+	18566.4i	−0.357480	+	0.693414i
$896$	−1946.56	−	3371.54i	−0.0725781	−	0.125709i
$897$	−28914.4	+	12985.1i	−1.07628	+	0.483344i
$898$	13092.2	−	22676.4i	0.486519	−	0.842675i
$899$	25894.0	+	40291.9i	0.960638	+	1.49478i
$900$	−3037.66	−	195.654i	−0.112506	−	0.00724644i
$901$	−1192.30	+	2610.77i	−0.0440856	+	0.0965341i
$902$	5414.36	−	22318.3i	0.199865	−	0.823856i
$903$	−13951.3	+	2912.97i	−0.514140	+	0.107351i
$904$	−33744.5	−	11679.1i	−1.24151	−	0.429691i
$905$	32657.4	+	41527.3i	1.19952	+	1.52532i
$906$	−10103.2	−	5626.91i	−0.370481	−	0.206337i
$907$	−34571.2	+	11965.2i	−1.26562	+	0.438036i	−0.875719	−	0.482820i	$-0.839612\pi$
$907$	−34571.2	+	11965.2i	−1.26562	+	0.438036i	−0.389902	+	0.920856i	$0.627491\pi$
$908$	11921.8	+	7661.66i	0.435725	+	0.280023i
$909$	34494.7	−	21362.0i	1.25866	−	0.779465i
$910$	13487.1	−	15565.0i	0.491312	−	0.567004i
$911$	6433.86	−	6134.68i	0.233988	−	0.223107i	−0.564009	−	0.825769i	$-0.690742\pi$
$911$	6433.86	−	6134.68i	0.233988	−	0.223107i	0.797997	+	0.602661i	$0.205893\pi$
$912$	10025.4	−	4766.87i	0.364007	−	0.173078i
$913$	−5334.83	+	15414.0i	−0.193381	+	0.558739i
$914$	17108.7	−	24025.7i	0.619151	−	0.869476i
$915$	26925.4	−	54269.1i	0.972815	−	1.96075i
$916$	5546.61	−	3949.72i	0.200071	−	0.142470i
$917$	1817.71	−	12642.5i	0.0654593	−	0.455279i
$918$	−6679.26	+	9354.33i	−0.240140	+	0.336317i
$919$			12246.7i			0.439586i	0.975546	+	0.219793i	$0.0705383\pi$
$919$			12246.7i			0.439586i	−0.975546	+	0.219793i	$0.929462\pi$
$920$	27044.6	+	22236.5i	0.969168	+	0.796867i
$921$	17619.1	+	16287.9i	0.630368	+	0.582742i
$922$	−26745.4	−	13788.2i	−0.955327	−	0.492505i
$923$	−14622.5	−	36525.3i	−0.521459	−	1.30254i
$924$	4682.12	+	599.561i	0.166700	+	0.0213464i
$925$	−1685.45	−	408.886i	−0.0599106	−	0.0145341i
$926$	−20981.9	+	9582.11i	−0.744609	+	0.340052i
$927$	−5653.71	+	21713.6i	−0.200315	+	0.769330i
$928$	−5204.31	−	36196.7i	−0.184095	−	1.28041i
$929$	5303.78	+	5562.45i	0.187311	+	0.196446i	0.810693	−	0.585471i	$-0.199091\pi$
$929$	5303.78	+	5562.45i	0.187311	+	0.196446i	−0.623383	+	0.781917i	$0.714242\pi$
$930$	19103.6	−	14053.1i	0.673584	−	0.495506i
$931$	11384.5	+	542.311i	0.400765	+	0.0190908i
$932$	−1287.81	−	61.3458i	−0.0452613	−	0.00215606i
$933$	6246.76	−	4595.28i	0.219196	−	0.161246i
$934$	7716.62	+	8092.96i	0.270338	+	0.283522i
$935$	−1720.33	−	11965.2i	−0.0601721	−	0.418506i
$936$	9267.17	−	35591.5i	0.323619	−	1.24289i
$937$	−15755.6	+	7195.35i	−0.549321	+	0.250866i	−0.670686	−	0.741742i	$-0.734000\pi$
$937$	−15755.6	+	7195.35i	−0.549321	+	0.250866i	0.121365	+	0.992608i	$0.461273\pi$
$938$	−17126.7	−	4154.88i	−0.596167	−	0.144629i
$939$	27707.4	+	3548.03i	0.962937	+	0.123307i
$940$	3196.24	+	7983.82i	0.110904	+	0.277025i
$941$	−11955.8	−	6163.62i	−0.414183	−	0.213526i	0.238524	−	0.971137i	$-0.423336\pi$
$941$	−11955.8	−	6163.62i	−0.414183	−	0.213526i	−0.652707	+	0.757610i	$0.726367\pi$
$942$	5343.13	+	4939.44i	0.184807	+	0.170845i
$943$	−31097.7	+	28386.7i	−1.07389	+	0.980274i
$944$		−	727.039i		−	0.0250669i
$945$	−22687.5	−	2195.73i	−0.780978	−	0.0755841i
$946$	−1862.74	+	12955.7i	−0.0640201	+	0.445270i
$947$	1350.15	−	961.439i	0.0463295	−	0.0329911i	−0.556658	−	0.830742i	$-0.687916\pi$
$947$	1350.15	−	961.439i	0.0463295	−	0.0329911i	0.602987	+	0.797751i	$0.293977\pi$
$948$	2041.26	−	4114.23i	0.0699335	−	0.140954i
$949$	−7261.61	+	10197.5i	−0.248390	+	0.348815i
$950$	1906.53	−	5508.55i	0.0651115	−	0.188127i
$951$	5235.44	−	2489.34i	0.178518	−	0.0848816i
$952$	8032.67	−	7659.14i	0.273467	−	0.260750i
$953$	18987.2	−	21912.4i	0.645390	−	0.744820i	−0.334928	−	0.942244i	$-0.608712\pi$
$953$	18987.2	−	21912.4i	0.645390	−	0.744820i	0.980318	+	0.197424i	$0.0632575\pi$
$954$	4225.54	−	2616.81i	0.143404	−	0.0888075i
$955$	−33860.3	−	21760.7i	−1.14732	−	0.737340i
$956$	−14173.4	+	4905.45i	−0.479497	+	0.165956i
$957$	−36933.5	−	20569.9i	−1.24754	−	0.694808i
$958$	−16690.0	−	21223.1i	−0.562871	−	0.715749i
$959$	−24412.5	−	8449.24i	−0.822023	−	0.284505i
$960$	−35816.2	+	7478.29i	−1.20413	+	0.251418i
$961$	−1395.39	+	5751.89i	−0.0468394	+	0.193075i
$962$	2224.08	−	4870.06i	0.0745397	−	0.163219i
$963$	15840.0	+	1020.24i	0.530048	+	0.0341401i
$964$	9093.40	+	14149.6i	0.303816	+	0.472747i
$965$	23784.8	−	41196.4i	0.793428	−	1.37426i
$966$	12449.8	+	10925.9i	0.414663	+	0.363909i
$967$	25722.6	+	44552.9i	0.855413	+	1.48162i	0.876262	+	0.481836i	$0.160030\pi$
$967$	25722.6	+	44552.9i	0.855413	+	1.48162i	−0.0208491	+	0.999783i	$0.506637\pi$
$968$	−7247.87	+	14058.9i	−0.240656	+	0.466808i
$969$	7247.72	+	8929.00i	0.240279	+	0.296017i
$970$	−11700.2	−	16430.6i	−0.387288	−	0.543870i
$971$	18911.4	−	5552.90i	0.625023	−	0.183523i	0.0461412	−	0.998935i	$-0.485308\pi$
$971$	18911.4	−	5552.90i	0.625023	−	0.183523i	0.578881	+	0.815412i	$0.303489\pi$
$972$	−9722.60	+	3690.70i	−0.320836	+	0.121789i
$973$	−15744.5	+	13642.7i	−0.518753	+	0.449502i
$974$	−11157.7	+	27870.6i	−0.367060	+	0.916870i
$975$	−6057.13	−	10126.9i	−0.198957	−	0.332636i
$976$	5907.08	−	30648.9i	0.193731	−	1.00517i
$977$	2830.05	−	59410.1i	0.0926728	−	1.94544i	−0.180711	−	0.983536i	$-0.557840\pi$
$977$	2830.05	−	59410.1i	0.0926728	−	1.94544i	0.273384	−	0.961905i	$-0.411857\pi$
$978$	−2688.44	+	9708.02i	−0.0879007	+	0.317411i
$979$	−10876.5	−	31425.6i	−0.355071	−	1.02591i
$980$	−6247.80	−	1834.52i	−0.203652	−	0.0597975i
$981$	−3209.06	−	14264.9i	−0.104442	−	0.464263i
$982$	−6500.59	−	7502.08i	−0.211244	−	0.243789i
$983$	−25208.1	−	2407.08i	−0.817918	−	0.0781017i	−0.322295	−	0.946639i	$-0.604454\pi$
$983$	−25208.1	−	2407.08i	−0.817918	−	0.0781017i	−0.495623	+	0.868538i	$0.665060\pi$
$984$	−3077.84	−	48759.3i	−0.0997135	−	1.57967i
$985$	−1022.26	−	10705.6i	−0.0330678	−	0.346302i
$986$	−23577.4	+	9438.97i	−0.761519	+	0.304866i
$987$	5439.99	+	14966.1i	0.175437	+	0.482652i
$988$	−8142.05	−	4700.82i	−0.262179	−	0.151369i
$989$	16105.5	−	17790.0i	0.517821	−	0.571981i
$990$	−9013.10	+	18893.4i	−0.289349	+	0.606537i
$991$	−10312.0	+	6627.10i	−0.330545	+	0.212429i	−0.695377	−	0.718645i	$-0.744763\pi$
$991$	−10312.0	+	6627.10i	−0.330545	+	0.212429i	0.364832	+	0.931073i	$0.381126\pi$
$992$	−11267.2	+	14327.4i	−0.360619	+	0.458564i
$993$	1986.97	−	15516.7i	0.0634989	−	0.495879i
$994$	−14188.4	+	14880.4i	−0.452747	+	0.474827i
$995$	41582.7	+	29610.9i	1.32489	+	0.943447i
$996$	−285.070	+	8861.00i	−0.00906907	+	0.281899i
$997$	50937.8	+	20392.4i	1.61807	+	0.647778i	0.991324	−	0.131444i	$-0.0419615\pi$
$997$	50937.8	+	20392.4i	1.61807	+	0.647778i	0.626748	+	0.779222i	$0.284386\pi$
$998$	2063.30	−	7026.94i	0.0654434	−	0.222880i
$999$	−5819.64	+	1113.91i	−0.184310	+	0.0352779i

Display

a_p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.o.a.11.24	✓	1400
9.5	odd	6	inner	207.4.o.a.149.24	yes	1400
23.21	odd	22	inner	207.4.o.a.182.24	yes	1400
207.113	even	66	inner	207.4.o.a.113.24	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.o.a.11.24	✓	1400	1.1	even	1	trivial
207.4.o.a.113.24	yes	1400	207.113	even	66	inner
207.4.o.a.149.24	yes	1400	9.5	odd	6	inner
207.4.o.a.182.24	yes	1400	23.21	odd	22	inner

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	207.4.o.a.11.24

Level	$207$
Weight	$4$
Character	207.11
Analytic conductor	$12.213$
Analytic rank	$0$
Dimension	$1400$
Inner twists	$4$