LMFDB - Embedded newform 570.4.i.i.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,4,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("570.121");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	570.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$33.6310887033$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{481})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 121x^{2} + 120x + 14400 $ x^4 - x^3 + 121x^2 + 120x + 14400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-5.23293 - 9.06370i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.4.i.i.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} -9.46586 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} -9.46586 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} -31.3976 q^{11} -12.0000 q^{12} +(32.7329 - 56.6951i) q^{13} +(-9.46586 - 16.3953i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-56.3293 - 97.5652i) q^{17} -18.0000 q^{18} +(-82.4939 + 7.33165i) q^{19} -20.0000 q^{20} +(-14.1988 - 24.5930i) q^{21} +(-31.3976 - 54.3822i) q^{22} +(25.4659 - 44.1082i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +130.932 q^{26} -27.0000 q^{27} +(18.9317 - 32.7907i) q^{28} +(-60.3012 + 104.445i) q^{29} -30.0000 q^{30} +209.932 q^{31} +(16.0000 - 27.7128i) q^{32} +(-47.0964 - 81.5733i) q^{33} +(112.659 - 195.130i) q^{34} +(-23.6646 - 40.9884i) q^{35} +(-18.0000 - 31.1769i) q^{36} -164.398 q^{37} +(-95.1927 - 135.552i) q^{38} +196.398 q^{39} +(-20.0000 - 34.6410i) q^{40} +(-72.6024 - 125.751i) q^{41} +(28.3976 - 49.1860i) q^{42} +(-7.66464 - 13.2755i) q^{43} +(62.7951 - 108.764i) q^{44} -45.0000 q^{45} +101.863 q^{46} +(261.988 - 453.776i) q^{47} +(24.0000 - 41.5692i) q^{48} -253.398 q^{49} -50.0000 q^{50} +(168.988 - 292.696i) q^{51} +(130.932 + 226.780i) q^{52} +(-146.590 + 253.902i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(-78.4939 - 135.955i) q^{55} +75.7268 q^{56} +(-142.789 - 203.328i) q^{57} -241.205 q^{58} +(-2.90365 - 5.02927i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(-356.624 + 617.692i) q^{61} +(209.932 + 363.612i) q^{62} +(42.5964 - 73.7790i) q^{63} +64.0000 q^{64} +327.329 q^{65} +(94.1927 - 163.147i) q^{66} +(27.7329 - 48.0348i) q^{67} +450.634 q^{68} +152.795 q^{69} +(47.3293 - 81.9767i) q^{70} +(-112.482 - 194.824i) q^{71} +(36.0000 - 62.3538i) q^{72} +(-177.516 - 307.467i) q^{73} +(-164.398 - 284.745i) q^{74} -75.0000 q^{75} +(139.590 - 300.431i) q^{76} +297.205 q^{77} +(196.398 + 340.171i) q^{78} +(-261.649 - 453.189i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(145.205 - 251.502i) q^{82} +499.020 q^{83} +113.590 q^{84} +(281.646 - 487.826i) q^{85} +(15.3293 - 26.5511i) q^{86} -361.807 q^{87} +251.181 q^{88} +(148.743 - 257.630i) q^{89} +(-45.0000 - 77.9423i) q^{90} +(-309.845 + 536.668i) q^{91} +(101.863 + 176.433i) q^{92} +(314.898 + 545.419i) q^{93} +1047.95 q^{94} +(-237.982 - 338.880i) q^{95} +96.0000 q^{96} +(-182.261 - 315.685i) q^{97} +(-253.398 - 438.897i) q^{98} +(141.289 - 244.720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 12 q^{6} + 6 q^{7} - 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 12 * q^6 + 6 * q^7 - 32 * q^8 - 18 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 12 q^{6} + 6 q^{7} - 32 q^{8} - 18 q^{9} - 20 q^{10} + 6 q^{11} - 48 q^{12} + 109 q^{13} + 6 q^{14} - 30 q^{15} - 32 q^{16} - 6 q^{17} - 72 q^{18} - q^{19} - 80 q^{20} + 9 q^{21} + 6 q^{22} + 58 q^{23} - 48 q^{24} - 50 q^{25} + 436 q^{26} - 108 q^{27} - 12 q^{28} - 307 q^{29} - 120 q^{30} + 752 q^{31} + 64 q^{32} + 9 q^{33} + 12 q^{34} + 15 q^{35} - 72 q^{36} - 526 q^{37} + 14 q^{38} + 654 q^{39} - 80 q^{40} - 422 q^{41} - 18 q^{42} + 79 q^{43} - 12 q^{44} - 180 q^{45} + 232 q^{46} + 390 q^{47} + 96 q^{48} - 882 q^{49} - 200 q^{50} + 18 q^{51} + 436 q^{52} - 60 q^{53} - 108 q^{54} + 15 q^{55} - 48 q^{56} + 21 q^{57} - 1228 q^{58} - 209 q^{59} - 120 q^{60} - 944 q^{61} + 752 q^{62} - 27 q^{63} + 256 q^{64} + 1090 q^{65} - 18 q^{66} + 89 q^{67} + 48 q^{68} + 348 q^{69} - 30 q^{70} + 537 q^{71} + 144 q^{72} + 233 q^{73} - 526 q^{74} - 300 q^{75} + 32 q^{76} + 1452 q^{77} + 654 q^{78} - 1880 q^{79} + 160 q^{80} - 162 q^{81} + 844 q^{82} - 548 q^{83} - 72 q^{84} + 30 q^{85} - 158 q^{86} - 1842 q^{87} - 48 q^{88} - 699 q^{89} - 180 q^{90} - 77 q^{91} + 232 q^{92} + 1128 q^{93} + 1560 q^{94} + 35 q^{95} + 384 q^{96} - 422 q^{97} - 882 q^{98} - 27 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 12 * q^6 + 6 * q^7 - 32 * q^8 - 18 * q^9 - 20 * q^10 + 6 * q^11 - 48 * q^12 + 109 * q^13 + 6 * q^14 - 30 * q^15 - 32 * q^16 - 6 * q^17 - 72 * q^18 - q^19 - 80 * q^20 + 9 * q^21 + 6 * q^22 + 58 * q^23 - 48 * q^24 - 50 * q^25 + 436 * q^26 - 108 * q^27 - 12 * q^28 - 307 * q^29 - 120 * q^30 + 752 * q^31 + 64 * q^32 + 9 * q^33 + 12 * q^34 + 15 * q^35 - 72 * q^36 - 526 * q^37 + 14 * q^38 + 654 * q^39 - 80 * q^40 - 422 * q^41 - 18 * q^42 + 79 * q^43 - 12 * q^44 - 180 * q^45 + 232 * q^46 + 390 * q^47 + 96 * q^48 - 882 * q^49 - 200 * q^50 + 18 * q^51 + 436 * q^52 - 60 * q^53 - 108 * q^54 + 15 * q^55 - 48 * q^56 + 21 * q^57 - 1228 * q^58 - 209 * q^59 - 120 * q^60 - 944 * q^61 + 752 * q^62 - 27 * q^63 + 256 * q^64 + 1090 * q^65 - 18 * q^66 + 89 * q^67 + 48 * q^68 + 348 * q^69 - 30 * q^70 + 537 * q^71 + 144 * q^72 + 233 * q^73 - 526 * q^74 - 300 * q^75 + 32 * q^76 + 1452 * q^77 + 654 * q^78 - 1880 * q^79 + 160 * q^80 - 162 * q^81 + 844 * q^82 - 548 * q^83 - 72 * q^84 + 30 * q^85 - 158 * q^86 - 1842 * q^87 - 48 * q^88 - 699 * q^89 - 180 * q^90 - 77 * q^91 + 232 * q^92 + 1128 * q^93 + 1560 * q^94 + 35 * q^95 + 384 * q^96 - 422 * q^97 - 882 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−3.00000	+	5.19615i	−0.204124	+	0.353553i
$7$	−9.46586			−0.511108			−0.255554	−	0.966795i	$-0.582258\pi$
$7$	−9.46586			−0.511108			−0.255554	+	0.966795i	$0.582258\pi$
$8$	−8.00000			−0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−5.00000	+	8.66025i	−0.158114	+	0.273861i
$11$	−31.3976			−0.860611			−0.430306	−	0.902683i	$-0.641594\pi$
$11$	−31.3976			−0.860611			−0.430306	+	0.902683i	$0.641594\pi$
$12$	−12.0000			−0.288675
$13$	32.7329	−	56.6951i	0.698345	−	1.20957i	−0.270695	−	0.962665i	$-0.587254\pi$
$13$	32.7329	−	56.6951i	0.698345	−	1.20957i	0.969040	−	0.246903i	$-0.0794130\pi$
$14$	−9.46586	−	16.3953i	−0.180704	−	0.312989i
$15$	−7.50000	+	12.9904i	−0.129099	+	0.223607i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−56.3293	−	97.5652i	−0.803639	−	1.39194i	−0.917206	−	0.398413i	$-0.869561\pi$
$17$	−56.3293	−	97.5652i	−0.803639	−	1.39194i	0.113568	−	0.993530i	$-0.463772\pi$
$18$	−18.0000			−0.235702
$19$	−82.4939	+	7.33165i	−0.996074	+	0.0885261i
$19$	−82.4939	+	7.33165i	−0.996074	+	0.0885261i
$20$	−20.0000			−0.223607
$21$	−14.1988	−	24.5930i	−0.147544	−	0.255554i
$22$	−31.3976	−	54.3822i	−0.304272	−	0.527015i
$23$	25.4659	−	44.1082i	0.230869	−	0.399878i	−0.727195	−	0.686431i	$-0.759176\pi$
$23$	25.4659	−	44.1082i	0.230869	−	0.399878i	0.958064	+	0.286554i	$0.0925096\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	130.932			0.987609
$27$	−27.0000			−0.192450
$28$	18.9317	−	32.7907i	0.127777	−	0.221316i
$29$	−60.3012	+	104.445i	−0.386126	+	0.668790i	−0.991925	−	0.126828i	$-0.959520\pi$
$29$	−60.3012	+	104.445i	−0.386126	+	0.668790i	0.605799	+	0.795618i	$0.292854\pi$
$30$	−30.0000			−0.182574
$31$	209.932			1.21629			0.608143	−	0.793828i	$-0.291915\pi$
$31$	209.932			1.21629			0.608143	+	0.793828i	$0.291915\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−47.0964	−	81.5733i	−0.248437	−	0.430306i
$34$	112.659	−	195.130i	0.568258	−	0.984252i
$35$	−23.6646	−	40.9884i	−0.114287	−	0.197951i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	−164.398			−0.730454			−0.365227	−	0.930919i	$-0.619009\pi$
$37$	−164.398			−0.730454			−0.365227	+	0.930919i	$0.619009\pi$
$38$	−95.1927	−	135.552i	−0.406376	−	0.578669i
$39$	196.398			0.806379
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	−72.6024	−	125.751i	−0.276551	−	0.479001i	0.693974	−	0.720000i	$-0.255858\pi$
$41$	−72.6024	−	125.751i	−0.276551	−	0.479001i	−0.970525	+	0.240999i	$0.922525\pi$
$42$	28.3976	−	49.1860i	0.104330	−	0.180704i
$43$	−7.66464	−	13.2755i	−0.0271825	−	0.0470814i	0.852114	−	0.523356i	$-0.175320\pi$
$43$	−7.66464	−	13.2755i	−0.0271825	−	0.0470814i	−0.879297	+	0.476275i	$0.841987\pi$
$44$	62.7951	−	108.764i	0.215153	−	0.372656i
$45$	−45.0000			−0.149071
$46$	101.863			0.326499
$47$	261.988	−	453.776i	0.813082	−	1.40830i	−0.0976150	−	0.995224i	$-0.531121\pi$
$47$	261.988	−	453.776i	0.813082	−	1.40830i	0.910697	−	0.413075i	$-0.135545\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	−253.398			−0.738768
$50$	−50.0000			−0.141421
$51$	168.988	−	292.696i	0.463981	−	0.803639i
$52$	130.932	+	226.780i	0.349172	+	0.604784i
$53$	−146.590	+	253.902i	−0.379919	+	0.658040i	−0.991050	−	0.133490i	$-0.957382\pi$
$53$	−146.590	+	253.902i	−0.379919	+	0.658040i	0.611131	+	0.791530i	$0.290715\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	−78.4939	−	135.955i	−0.192439	−	0.333313i
$56$	75.7268			0.180704
$57$	−142.789	−	203.328i	−0.331805	−	0.472482i
$58$	−241.205			−0.546065
$59$	−2.90365	−	5.02927i	−0.00640716	−	0.0110975i	0.862804	−	0.505539i	$-0.168706\pi$
$59$	−2.90365	−	5.02927i	−0.00640716	−	0.0110975i	−0.869211	+	0.494441i	$0.835373\pi$
$60$	−30.0000	−	51.9615i	−0.0645497	−	0.111803i
$61$	−356.624	+	617.692i	−0.748542	+	1.29651i	0.199979	+	0.979800i	$0.435913\pi$
$61$	−356.624	+	617.692i	−0.748542	+	1.29651i	−0.948521	+	0.316713i	$0.897421\pi$
$62$	209.932	+	363.612i	0.430022	+	0.744820i
$63$	42.5964	−	73.7790i	0.0851847	−	0.147544i
$64$	64.0000			0.125000
$65$	327.329			0.624618
$66$	94.1927	−	163.147i	0.175672	−	0.304272i
$67$	27.7329	−	48.0348i	0.0505689	−	0.0875879i	−0.839633	−	0.543154i	$-0.817230\pi$
$67$	27.7329	−	48.0348i	0.0505689	−	0.0875879i	0.890202	+	0.455566i	$0.150563\pi$
$68$	450.634			0.803639
$69$	152.795			0.266585
$70$	47.3293	−	81.9767i	0.0808133	−	0.139973i
$71$	−112.482	−	194.824i	−0.188016	−	0.325653i	0.756573	−	0.653910i	$-0.226872\pi$
$71$	−112.482	−	194.824i	−0.188016	−	0.325653i	−0.944589	+	0.328256i	$0.893539\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	−177.516	−	307.467i	−0.284612	−	0.492962i	0.687903	−	0.725803i	$-0.258531\pi$
$73$	−177.516	−	307.467i	−0.284612	−	0.492962i	−0.972515	+	0.232840i	$0.925198\pi$
$74$	−164.398	−	284.745i	−0.258254	−	0.447310i
$75$	−75.0000			−0.115470
$76$	139.590	−	300.431i	0.210686	−	0.453444i
$77$	297.205			0.439865
$78$	196.398	+	340.171i	0.285098	+	0.493804i
$79$	−261.649	−	453.189i	−0.372630	−	0.645414i	0.617339	−	0.786697i	$-0.288211\pi$
$79$	−261.649	−	453.189i	−0.372630	−	0.645414i	−0.989969	+	0.141283i	$0.954877\pi$
$80$	40.0000	−	69.2820i	0.0559017	−	0.0968246i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	145.205	−	251.502i	0.195551	−	0.338705i
$83$	499.020			0.659934			0.329967	−	0.943992i	$-0.392962\pi$
$83$	499.020			0.659934			0.329967	+	0.943992i	$0.392962\pi$
$84$	113.590			0.147544
$85$	281.646	−	487.826i	0.359398	−	0.622496i
$86$	15.3293	−	26.5511i	0.0192209	−	0.0332916i
$87$	−361.807			−0.445860
$88$	251.181			0.304272
$89$	148.743	−	257.630i	0.177154	−	0.306840i	−0.763751	−	0.645511i	$-0.776644\pi$
$89$	148.743	−	257.630i	0.177154	−	0.306840i	0.940905	+	0.338672i	$0.109978\pi$
$90$	−45.0000	−	77.9423i	−0.0527046	−	0.0912871i
$91$	−309.845	+	536.668i	−0.356930	+	0.618220i
$92$	101.863	+	176.433i	0.115435	+	0.199939i
$93$	314.898	+	545.419i	0.351111	+	0.608143i
$94$	1047.95			1.14987
$95$	−237.982	−	338.880i	−0.257015	−	0.365983i
$96$	96.0000			0.102062
$97$	−182.261	−	315.685i	−0.190781	−	0.330443i	0.754728	−	0.656038i	$-0.227769\pi$
$97$	−182.261	−	315.685i	−0.190781	−	0.330443i	−0.945509	+	0.325595i	$0.894436\pi$
$98$	−253.398	−	438.897i	−0.261194	−	0.452401i
$99$	141.289	−	244.720i	0.143435	−	0.248437i
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	316.948	−	548.969i	0.312252	−	0.540837i	−0.666597	−	0.745418i	$-0.732250\pi$
$101$	316.948	−	548.969i	0.312252	−	0.540837i	0.978850	+	0.204581i	$0.0655833\pi$
$102$	675.951			0.656168
$103$	1815.42			1.73668			0.868342	−	0.495967i	$-0.165186\pi$
$103$	1815.42			1.73668			0.868342	+	0.495967i	$0.165186\pi$
$104$	−261.863	+	453.561i	−0.246902	+	0.427647i
$105$	70.9939	−	122.965i	0.0659838	−	0.114287i
$106$	−586.361			−0.537287
$107$	−1540.20			−1.39156			−0.695779	−	0.718256i	$-0.744941\pi$
$107$	−1540.20			−1.39156			−0.695779	+	0.718256i	$0.744941\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	362.482	+	627.837i	0.318527	+	0.551705i	0.980181	−	0.198104i	$-0.0634785\pi$
$109$	362.482	+	627.837i	0.318527	+	0.551705i	−0.661654	+	0.749809i	$0.730145\pi$
$110$	156.988	−	271.911i	0.136075	−	0.235688i
$111$	−246.596	−	427.117i	−0.210864	−	0.365227i
$112$	75.7268	+	131.163i	0.0638885	+	0.110658i
$113$	−1283.29			−1.06834			−0.534168	−	0.845378i	$-0.679375\pi$
$113$	−1283.29			−1.06834			−0.534168	+	0.845378i	$0.679375\pi$
$114$	209.385	−	450.646i	0.172024	−	0.370236i
$115$	254.659			0.206496
$116$	−241.205	−	417.779i	−0.193063	−	0.334395i
$117$	294.596	+	510.256i	0.232782	+	0.403189i
$118$	5.80730	−	10.0585i	0.00453055	−	0.00784714i
$119$	533.205	+	923.538i	0.410746	+	0.711433i
$120$	60.0000	−	103.923i	0.0456435	−	0.0790569i
$121$	−345.193			−0.259348
$122$	−1426.50			−1.05860
$123$	217.807	−	377.253i	0.159667	−	0.276551i
$124$	−419.863	+	727.225i	−0.304071	+	0.526667i
$125$	−125.000			−0.0894427
$126$	170.385			0.120469
$127$	−804.088	+	1392.72i	−0.561821	+	0.973103i	0.435517	+	0.900181i	$0.356566\pi$
$127$	−804.088	+	1392.72i	−0.561821	+	0.973103i	−0.997338	+	0.0729218i	$0.976768\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	22.9939	−	39.8266i	0.0156938	−	0.0271825i
$130$	327.329	+	566.951i	0.220836	+	0.382499i
$131$	−1441.26	−	2496.33i	−0.961245	−	1.66493i	−0.719381	−	0.694616i	$-0.755574\pi$
$131$	−1441.26	−	2496.33i	−0.961245	−	1.66493i	−0.241865	−	0.970310i	$-0.577759\pi$
$132$	376.771			0.248437
$133$	780.876	−	69.4003i	0.509102	−	0.0452464i
$134$	110.932			0.0715152
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	450.634	+	780.521i	0.284129	+	0.492126i
$137$	143.049	−	247.768i	0.0892078	−	0.154512i	−0.817969	−	0.575263i	$-0.804900\pi$
$137$	143.049	−	247.768i	0.0892078	−	0.154512i	0.907176	+	0.420750i	$0.138233\pi$
$138$	152.795	+	264.649i	0.0942521	+	0.163249i
$139$	919.174	−	1592.06i	0.560887	−	0.971486i	−0.436532	−	0.899689i	$-0.643793\pi$
$139$	919.174	−	1592.06i	0.560887	−	0.971486i	0.997419	−	0.0717968i	$-0.0228733\pi$
$140$	189.317			0.114287
$141$	1571.93			0.938866
$142$	224.964	−	389.648i	0.132947	−	0.230272i
$143$	−1027.73	+	1780.09i	−0.601003	+	1.04097i
$144$	144.000			0.0833333
$145$	−603.012			−0.345362
$146$	355.032	−	614.933i	0.201251	−	0.348577i
$147$	−380.096	−	658.346i	−0.213264	−	0.369384i
$148$	328.795	−	569.490i	0.182613	−	0.316296i
$149$	200.165	+	346.695i	0.110055	+	0.190620i	0.915792	−	0.401653i	$-0.131564\pi$
$149$	200.165	+	346.695i	0.110055	+	0.190620i	−0.805738	+	0.592273i	$0.798231\pi$
$150$	−75.0000	−	129.904i	−0.0408248	−	0.0707107i
$151$	534.739			0.288188			0.144094	−	0.989564i	$-0.453973\pi$
$151$	534.739			0.288188			0.144094	+	0.989564i	$0.453973\pi$
$152$	659.951	−	58.6532i	0.352165	−	0.0312987i
$153$	1013.93			0.535759
$154$	297.205	+	514.774i	0.155516	+	0.269361i
$155$	524.829	+	909.031i	0.271970	+	0.471065i
$156$	−392.795	+	680.341i	−0.201595	+	0.349172i
$157$	161.733	+	280.130i	0.0822146	+	0.142400i	0.904201	−	0.427107i	$-0.140467\pi$
$157$	161.733	+	280.130i	0.0822146	+	0.142400i	−0.821986	+	0.569507i	$0.807134\pi$
$158$	523.297	−	906.378i	0.263489	−	0.456377i
$159$	−879.542			−0.438693
$160$	160.000			0.0790569
$161$	−241.056	+	417.521i	−0.117999	+	0.204381i
$162$	81.0000	−	140.296i	0.0392837	−	0.0680414i
$163$	−1548.45			−0.744072			−0.372036	−	0.928218i	$-0.621340\pi$
$163$	−1548.45			−0.744072			−0.372036	+	0.928218i	$0.621340\pi$
$164$	580.819			0.276551
$165$	235.482	−	407.866i	0.111104	−	0.192439i
$166$	499.020	+	864.327i	0.233322	+	0.404125i
$167$	−87.8073	+	152.087i	−0.0406870	+	0.0704720i	−0.885652	−	0.464350i	$-0.846288\pi$
$167$	−87.8073	+	152.087i	−0.0406870	+	0.0704720i	0.844965	+	0.534822i	$0.179621\pi$
$168$	113.590	+	196.744i	0.0521648	+	0.0903520i
$169$	−1044.39	−	1808.94i	−0.475371	−	0.823366i
$170$	1126.59			0.508266
$171$	314.078	−	675.969i	0.140457	−	0.302296i
$172$	61.3171			0.0271825
$173$	408.329	+	707.247i	0.179449	+	0.310815i	0.941692	−	0.336476i	$-0.109235\pi$
$173$	408.329	+	707.247i	0.179449	+	0.310815i	−0.762243	+	0.647291i	$0.775902\pi$
$174$	−361.807	−	626.669i	−0.157635	−	0.273032i
$175$	118.323	−	204.942i	0.0511108	−	0.0885265i
$176$	251.181	+	435.057i	0.107576	+	0.186328i
$177$	8.71094	−	15.0878i	0.00369918	−	0.00640716i
$178$	594.971			0.250534
$179$	−2331.87			−0.973700			−0.486850	−	0.873486i	$-0.661854\pi$
$179$	−2331.87			−0.973700			−0.486850	+	0.873486i	$0.661854\pi$
$180$	90.0000	−	155.885i	0.0372678	−	0.0645497i
$181$	−1142.57	+	1978.98i	−0.469206	+	0.812688i	−0.999380	−	0.0352002i	$-0.988793\pi$
$181$	−1142.57	+	1978.98i	−0.469206	+	0.812688i	0.530174	+	0.847889i	$0.322126\pi$
$182$	−1239.38			−0.504775
$183$	−2139.75			−0.864342
$184$	−203.727	+	352.865i	−0.0816247	+	0.141378i
$185$	−410.994	−	711.862i	−0.163334	−	0.282904i
$186$	−629.795	+	1090.84i	−0.248273	+	0.430022i
$187$	1768.60	+	3063.31i	0.691620	+	1.19792i
$188$	1047.95	+	1815.11i	0.406541	+	0.704150i
$189$	255.578			0.0983628
$190$	348.976	−	751.077i	0.133249	−	0.286783i
$191$	−2159.56			−0.818118			−0.409059	−	0.912508i	$-0.634143\pi$
$191$	−2159.56			−0.818118			−0.409059	+	0.912508i	$0.634143\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	1257.17	+	2177.48i	0.468876	+	0.812117i	0.999367	−	0.0355735i	$-0.0113258\pi$
$193$	1257.17	+	2177.48i	0.468876	+	0.812117i	−0.530491	+	0.847691i	$0.677992\pi$
$194$	364.522	−	631.371i	0.134903	−	0.233659i
$195$	490.994	+	850.426i	0.180312	+	0.312309i
$196$	506.795	−	877.795i	0.184692	−	0.319896i
$197$	−5315.00			−1.92222			−0.961112	−	0.276159i	$-0.910938\pi$
$197$	−5315.00			−1.92222			−0.961112	+	0.276159i	$0.910938\pi$
$198$	565.156			0.202848
$199$	791.395	−	1370.74i	0.281912	−	0.488286i	−0.689944	−	0.723863i	$-0.742365\pi$
$199$	791.395	−	1370.74i	0.281912	−	0.488286i	0.971856	+	0.235577i	$0.0756980\pi$
$200$	100.000	−	173.205i	0.0353553	−	0.0612372i
$201$	166.398			0.0583919
$202$	1267.79			0.441591
$203$	570.803	−	988.659i	0.197352	−	0.341824i
$204$	675.951	+	1170.78i	0.231990	+	0.401819i
$205$	363.012	−	628.756i	0.123677	−	0.214216i
$206$	1815.42	+	3144.39i	0.614010	+	1.06350i
$207$	229.193	+	396.973i	0.0769565	+	0.133293i
$208$	−1047.45			−0.349172
$209$	2590.11	−	230.196i	0.857232	−	0.0761865i
$210$	283.976			0.0933152
$211$	−590.332	−	1022.48i	−0.192607	−	0.333605i	0.753506	−	0.657441i	$-0.228361\pi$
$211$	−590.332	−	1022.48i	−0.192607	−	0.333605i	−0.946113	+	0.323835i	$0.895028\pi$
$212$	−586.361	−	1015.61i	−0.189960	−	0.329020i
$213$	337.445	−	584.472i	0.108551	−	0.188016i
$214$	−1540.20	−	2667.71i	−0.491990	−	0.852152i
$215$	38.3232	−	66.3777i	0.0121564	−	0.0210555i
$216$	216.000			0.0680414
$217$	−1987.18			−0.621653
$218$	−724.964	+	1255.67i	−0.225233	+	0.390114i
$219$	532.548	−	922.400i	0.164321	−	0.284612i
$220$	627.951			0.192439
$221$	−7375.29			−2.24487
$222$	493.193	−	854.235i	0.149103	−	0.258254i
$223$	1930.92	+	3344.45i	0.579837	+	1.00431i	0.995498	+	0.0947877i	$0.0302172\pi$
$223$	1930.92	+	3344.45i	0.579837	+	1.00431i	−0.415660	+	0.909520i	$0.636449\pi$
$224$	−151.454	+	262.325i	−0.0451760	+	0.0782471i
$225$	−112.500	−	194.856i	−0.0333333	−	0.0577350i
$226$	−1283.29	−	2222.73i	−0.377714	−	0.654220i
$227$	−5807.25			−1.69798			−0.848988	−	0.528412i	$-0.822788\pi$
$227$	−5807.25			−1.69798			−0.848988	+	0.528412i	$0.822788\pi$
$228$	989.927	−	87.9798i	0.287542	−	0.0255553i
$229$	−2586.63			−0.746416			−0.373208	−	0.927748i	$-0.621742\pi$
$229$	−2586.63			−0.746416			−0.373208	+	0.927748i	$0.621742\pi$
$230$	254.659	+	441.082i	0.0730073	+	0.126452i
$231$	445.807	+	772.161i	0.126978	+	0.219933i
$232$	482.410	−	835.558i	0.136516	−	0.236453i
$233$	−207.442	−	359.299i	−0.0583260	−	0.101024i	0.835388	−	0.549661i	$-0.185243\pi$
$233$	−207.442	−	359.299i	−0.0583260	−	0.101024i	−0.893714	+	0.448637i	$0.851910\pi$
$234$	−589.193	+	1020.51i	−0.164601	+	0.285098i
$235$	2619.88			0.727243
$236$	23.2292			0.00640716
$237$	784.946	−	1359.57i	0.215138	−	0.372630i
$238$	−1066.41	+	1847.08i	−0.290441	+	0.503059i
$239$	5546.06			1.50102			0.750512	−	0.660857i	$-0.229807\pi$
$239$	5546.06			1.50102			0.750512	+	0.660857i	$0.229807\pi$
$240$	240.000			0.0645497
$241$	−393.583	+	681.706i	−0.105199	+	0.182210i	−0.913819	−	0.406121i	$-0.866881\pi$
$241$	−393.583	+	681.706i	−0.105199	+	0.182210i	0.808621	+	0.588330i	$0.200215\pi$
$242$	−345.193	−	597.891i	−0.0916935	−	0.158818i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−1426.50	−	2470.77i	−0.374271	−	0.648257i
$245$	−633.494	−	1097.24i	−0.165194	−	0.286124i
$246$	871.229			0.225803
$247$	−2284.60	+	4916.99i	−0.588525	+	1.26664i
$248$	−1679.45			−0.430022
$249$	748.529	+	1296.49i	0.190507	+	0.329967i
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	626.128	−	1084.49i	0.157454	−	0.272718i	−0.776496	−	0.630122i	$-0.783005\pi$
$251$	626.128	−	1084.49i	0.157454	−	0.272718i	0.933950	+	0.357404i	$0.116338\pi$
$252$	170.385	+	295.116i	0.0425923	+	0.0737721i
$253$	−799.566	+	1384.89i	−0.198689	+	0.344139i
$254$	−3216.35			−0.794535
$255$	1689.88			0.414997
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−966.293	+	1673.67i	−0.234536	+	0.406228i	−0.959138	−	0.282940i	$-0.908690\pi$
$257$	−966.293	+	1673.67i	−0.234536	+	0.406228i	0.724602	+	0.689168i	$0.242024\pi$
$258$	91.9757			0.0221944
$259$	1556.16			0.373341
$260$	−654.659	+	1133.90i	−0.156155	+	0.270468i
$261$	−542.711	−	940.003i	−0.128709	−	0.222930i
$262$	2882.51	−	4992.66i	0.679703	−	1.17728i
$263$	−535.153	−	926.913i	−0.125471	−	0.217323i	0.796446	−	0.604710i	$-0.206711\pi$
$263$	−535.153	−	926.913i	−0.125471	−	0.217323i	−0.921917	+	0.387387i	$0.873378\pi$
$264$	376.771	+	652.586i	0.0878358	+	0.152136i
$265$	−1465.90			−0.339810
$266$	901.080	+	1283.12i	0.207702	+	0.295763i
$267$	892.457			0.204560
$268$	110.932	+	192.139i	0.0252845	+	0.0437940i
$269$	−3700.48	−	6409.43i	−0.838745	−	1.45275i	−0.890944	−	0.454113i	$-0.849956\pi$
$269$	−3700.48	−	6409.43i	−0.838745	−	1.45275i	0.0521986	−	0.998637i	$-0.483377\pi$
$270$	135.000	−	233.827i	0.0304290	−	0.0527046i
$271$	1182.60	+	2048.32i	0.265084	+	0.459139i	0.967586	−	0.252543i	$-0.0812670\pi$
$271$	1182.60	+	2048.32i	0.265084	+	0.459139i	−0.702502	+	0.711682i	$0.747934\pi$
$272$	−901.268	+	1561.04i	−0.200910	+	0.347986i
$273$	−1859.07			−0.412147
$274$	572.195			0.126159
$275$	392.470	−	679.777i	0.0860611	−	0.149062i
$276$	−305.590	+	529.298i	−0.0666463	+	0.115435i
$277$	5235.96			1.13573			0.567867	−	0.823121i	$-0.307769\pi$
$277$	5235.96			1.13573			0.567867	+	0.823121i	$0.307769\pi$
$278$	3676.70			0.793215
$279$	−944.693	+	1636.26i	−0.202714	+	0.351111i
$280$	189.317	+	327.907i	0.0404067	+	0.0699864i
$281$	−3956.10	+	6852.16i	−0.839861	+	1.45468i	0.0501488	+	0.998742i	$0.484030\pi$
$281$	−3956.10	+	6852.16i	−0.839861	+	1.45468i	−0.890010	+	0.455941i	$0.849303\pi$
$282$	1571.93	+	2722.66i	0.331939	+	0.574936i
$283$	2520.00	+	4364.76i	0.529323	+	0.916814i	0.999415	+	0.0341967i	$0.0108873\pi$
$283$	2520.00	+	4364.76i	0.529323	+	0.916814i	−0.470092	+	0.882617i	$0.655779\pi$
$284$	899.854			0.188016
$285$	523.464	−	1126.61i	0.108798	−	0.234158i
$286$	−4110.94			−0.849947
$287$	687.244	+	1190.34i	0.141348	+	0.244821i
$288$	144.000	+	249.415i	0.0294628	+	0.0510310i
$289$	−3889.48	+	6736.77i	−0.791670	+	1.37121i
$290$	−603.012	−	1044.45i	−0.122104	−	0.211490i
$291$	546.783	−	947.056i	0.110148	−	0.190781i
$292$	1420.13			0.284612
$293$	−336.152			−0.0670245			−0.0335123	−	0.999438i	$-0.510669\pi$
$293$	−336.152			−0.0670245			−0.0335123	+	0.999438i	$0.510669\pi$
$294$	760.193	−	1316.69i	0.150800	−	0.261194i
$295$	14.5182	−	25.1463i	0.00286537	−	0.00496297i
$296$	1315.18			0.258254
$297$	847.734			0.165625
$298$	−400.329	+	693.391i	−0.0778203	+	0.134789i
$299$	−1667.14	−	2887.58i	−0.322453	−	0.558505i
$300$	150.000	−	259.808i	0.0288675	−	0.0500000i
$301$	72.5524	+	125.664i	0.0138932	+	0.0240637i
$302$	534.739	+	926.195i	0.101890	+	0.176479i
$303$	1901.69			0.360558
$304$	761.542	+	1084.42i	0.143676	+	0.204591i
$305$	−3566.24			−0.669517
$306$	1013.93	+	1756.17i	0.189419	+	0.328084i
$307$	2153.57	+	3730.09i	0.400360	+	0.693444i	0.993769	−	0.111457i	$-0.0355518\pi$
$307$	2153.57	+	3730.09i	0.400360	+	0.693444i	−0.593409	+	0.804901i	$0.702218\pi$
$308$	−594.410	+	1029.55i	−0.109966	+	0.190467i
$309$	2723.13	+	4716.59i	0.501337	+	0.868342i
$310$	−1049.66	+	1818.06i	−0.192312	+	0.333093i
$311$	−9483.69			−1.72917			−0.864583	−	0.502490i	$-0.832417\pi$
$311$	−9483.69			−1.72917			−0.864583	+	0.502490i	$0.832417\pi$
$312$	−1571.18			−0.285098
$313$	2104.86	−	3645.72i	0.380107	−	0.658365i	−0.610970	−	0.791654i	$-0.709220\pi$
$313$	2104.86	−	3645.72i	0.380107	−	0.658365i	0.991077	+	0.133289i	$0.0425538\pi$
$314$	−323.466	+	560.259i	−0.0581345	+	0.100692i
$315$	425.964			0.0761915
$316$	2093.19			0.372630
$317$	−4429.65	+	7672.37i	−0.784838	+	1.35938i	0.144257	+	0.989540i	$0.453921\pi$
$317$	−4429.65	+	7672.37i	−0.784838	+	1.35938i	−0.929096	+	0.369840i	$0.879413\pi$
$318$	−879.542	−	1523.41i	−0.155101	−	0.268644i
$319$	1893.31	−	3279.31i	0.332304	−	0.575568i
$320$	160.000	+	277.128i	0.0279508	+	0.0484123i
$321$	−2310.30	−	4001.56i	−0.401708	−	0.695779i
$322$	−964.225			−0.166876
$323$	5362.14	+	7635.55i	0.923707	+	1.31534i
$324$	324.000			0.0555556
$325$	818.323	+	1417.38i	0.139669	+	0.241914i
$326$	−1548.45	−	2681.99i	−0.263069	−	0.455649i
$327$	−1087.45	+	1883.51i	−0.183902	+	0.318527i
$328$	580.819	+	1006.01i	0.0977756	+	0.169352i
$329$	−2479.94	+	4295.38i	−0.415573	+	0.719793i
$330$	941.927			0.157125
$331$	−11577.5			−1.92253			−0.961263	−	0.275632i	$-0.911113\pi$
$331$	−11577.5			−1.92253			−0.961263	+	0.275632i	$0.911113\pi$
$332$	−998.039	+	1728.65i	−0.164984	+	0.285760i
$333$	739.789	−	1281.35i	0.121742	−	0.210864i
$334$	−351.229			−0.0575401
$335$	277.329			0.0452302
$336$	−227.181	+	393.488i	−0.0368861	+	0.0638885i
$337$	−3149.68	−	5455.41i	−0.509122	−	0.881826i	−0.999944	−	0.0105658i	$-0.996637\pi$
$337$	−3149.68	−	5455.41i	−0.509122	−	0.881826i	0.490822	−	0.871260i	$-0.336697\pi$
$338$	2088.78	−	3617.87i	0.336138	−	0.582208i
$339$	−1924.94	−	3334.09i	−0.308402	−	0.534168i
$340$	1126.59	+	1951.30i	0.179699	+	0.311248i
$341$	−6591.35			−1.04675
$342$	1484.89	−	131.970i	0.234777	−	0.0208658i
$343$	5645.41			0.888699
$344$	61.3171	+	106.204i	0.00961046	+	0.0166458i
$345$	381.988	+	661.622i	0.0596102	+	0.103248i
$346$	−816.659	+	1414.49i	−0.126890	+	0.219779i
$347$	−2098.99	−	3635.56i	−0.324725	−	0.562441i	0.656731	−	0.754125i	$-0.271939\pi$
$347$	−2098.99	−	3635.56i	−0.324725	−	0.562441i	−0.981457	+	0.191684i	$0.938605\pi$
$348$	723.615	−	1253.34i	0.111465	−	0.193063i
$349$	3662.09			0.561683			0.280841	−	0.959754i	$-0.409387\pi$
$349$	3662.09			0.561683			0.280841	+	0.959754i	$0.409387\pi$
$350$	473.293			0.0722816
$351$	−883.789	+	1530.77i	−0.134396	+	0.232782i
$352$	−502.361	+	870.115i	−0.0760680	+	0.131754i
$353$	6923.15			1.04386			0.521930	−	0.852989i	$-0.325212\pi$
$353$	6923.15			1.04386			0.521930	+	0.852989i	$0.325212\pi$
$354$	34.8438			0.00523143
$355$	562.409	−	974.121i	0.0840833	−	0.145636i
$356$	594.971	+	1030.52i	0.0885770	+	0.153420i
$357$	−1599.61	+	2770.61i	−0.237144	+	0.410746i
$358$	−2331.87	−	4038.92i	−0.344255	−	0.596267i
$359$	534.689	+	926.108i	0.0786066	+	0.136151i	0.902649	−	0.430378i	$-0.141620\pi$
$359$	534.689	+	926.108i	0.0786066	+	0.136151i	−0.824042	+	0.566528i	$0.808286\pi$
$360$	360.000			0.0527046
$361$	6751.49	−	1209.63i	0.984326	−	0.176357i
$362$	−4570.26			−0.663557
$363$	−517.789	−	896.837i	−0.0748674	−	0.129674i
$364$	−1239.38	−	2146.67i	−0.178465	−	0.309110i
$365$	887.580	−	1537.33i	0.127282	−	0.220459i
$366$	−2139.75	−	3706.15i	−0.305591	−	0.529299i
$367$	5737.85	−	9938.25i	0.816113	−	1.41355i	−0.0924134	−	0.995721i	$-0.529458\pi$
$367$	5737.85	−	9938.25i	0.816113	−	1.41355i	0.908526	−	0.417828i	$-0.137209\pi$
$368$	−814.907			−0.115435
$369$	1306.84			0.184367
$370$	821.988	−	1423.72i	0.115495	−	0.200043i
$371$	1387.60	−	2403.40i	0.194180	−	0.336329i
$372$	−2519.18			−0.351111
$373$	7551.41			1.04825			0.524125	−	0.851641i	$-0.324392\pi$
$373$	7551.41			1.04825			0.524125	+	0.851641i	$0.324392\pi$
$374$	−3537.20	+	6126.62i	−0.489049	+	0.847059i
$375$	−187.500	−	324.760i	−0.0258199	−	0.0447214i
$376$	−2095.90	+	3630.21i	−0.287468	+	0.497909i
$377$	3947.67	+	6837.57i	0.539298	+	0.934092i
$378$	255.578	+	442.674i	0.0347765	+	0.0602347i
$379$	5449.18			0.738537			0.369269	−	0.929323i	$-0.379608\pi$
$379$	5449.18			0.738537			0.369269	+	0.929323i	$0.379608\pi$
$380$	1649.88	−	146.633i	0.222729	−	0.0197950i
$381$	−4824.53			−0.648735
$382$	−2159.56	−	3740.47i	−0.289248	−	0.500993i
$383$	−1407.45	−	2437.77i	−0.187773	−	0.325233i	0.756734	−	0.653723i	$-0.226794\pi$
$383$	−1407.45	−	2437.77i	−0.187773	−	0.325233i	−0.944508	+	0.328490i	$0.893460\pi$
$384$	−192.000	+	332.554i	−0.0255155	+	0.0441942i
$385$	743.012	+	1286.93i	0.0983569	+	0.170359i
$386$	−2514.34	+	4354.96i	−0.331545	+	0.574253i
$387$	137.964			0.0181217
$388$	1458.09			0.190781
$389$	−1434.38	+	2484.43i	−0.186957	+	0.323819i	−0.944234	−	0.329275i	$-0.893196\pi$
$389$	−1434.38	+	2484.43i	−0.186957	+	0.323819i	0.757277	+	0.653093i	$0.226529\pi$
$390$	−981.988	+	1700.85i	−0.127500	+	0.220836i
$391$	−5737.89			−0.742143
$392$	2027.18			0.261194
$393$	4323.77	−	7488.99i	0.554975	−	0.961245i
$394$	−5315.00	−	9205.85i	−0.679609	−	1.17712i
$395$	1308.24	−	2265.94i	0.166645	−	0.288638i
$396$	565.156	+	978.879i	0.0717176	+	0.124219i
$397$	−1404.03	−	2431.85i	−0.177497	−	0.307433i	0.763526	−	0.645777i	$-0.223467\pi$
$397$	−1404.03	−	2431.85i	−0.177497	−	0.307433i	−0.941022	+	0.338344i	$0.890133\pi$
$398$	3165.58			0.398684
$399$	1351.62	+	1924.67i	0.169588	+	0.241489i
$400$	400.000			0.0500000
$401$	4243.89	+	7350.64i	0.528503	+	0.915395i	0.999448	+	0.0332317i	$0.0105799\pi$
$401$	4243.89	+	7350.64i	0.528503	+	0.915395i	−0.470944	+	0.882163i	$0.656087\pi$
$402$	166.398	+	288.209i	0.0206447	+	0.0357576i
$403$	6871.68	−	11902.1i	0.849386	−	1.47118i
$404$	1267.79	+	2195.88i	0.156126	+	0.270418i
$405$	202.500	−	350.740i	0.0248452	−	0.0430331i
$406$	2283.21			0.279098
$407$	5161.68			0.628637
$408$	−1351.90	+	2341.56i	−0.164042	+	0.284129i
$409$	979.037	−	1695.74i	0.118363	−	0.205010i	−0.800756	−	0.598990i	$-0.795569\pi$
$409$	979.037	−	1695.74i	0.118363	−	0.205010i	0.919119	+	0.393980i	$0.128902\pi$
$410$	1452.05			0.174906
$411$	858.292			0.103008
$412$	−3630.83	+	6288.79i	−0.434171	+	0.752006i
$413$	27.4855	+	47.6063i	0.00327475	+	0.00567204i
$414$	−458.385	+	793.947i	−0.0544165	+	0.0942521i
$415$	1247.55	+	2160.82i	0.147566	+	0.255591i
$416$	−1047.45	−	1814.24i	−0.123451	−	0.213824i
$417$	5515.05			0.647657
$418$	2988.82	+	4256.00i	0.349732	+	0.498009i
$419$	6227.21			0.726060			0.363030	−	0.931777i	$-0.381742\pi$
$419$	6227.21			0.726060			0.363030	+	0.931777i	$0.381742\pi$
$420$	283.976	+	491.860i	0.0329919	+	0.0571436i
$421$	4638.03	+	8033.31i	0.536921	+	0.929975i	0.999068	+	0.0431711i	$0.0137461\pi$
$421$	4638.03	+	8033.31i	0.536921	+	0.929975i	−0.462147	+	0.886804i	$0.652921\pi$
$422$	1180.66	−	2044.97i	0.136194	−	0.235895i
$423$	2357.89	+	4083.99i	0.271027	+	0.469433i
$424$	1172.72	−	2031.21i	0.134322	−	0.232652i
$425$	2816.46			0.321455
$426$	1349.78			0.153514
$427$	3375.76	−	5846.98i	0.382586	−	0.662659i
$428$	3080.40	−	5335.41i	0.347890	−	0.602563i
$429$	−6166.41			−0.693979
$430$	153.293			0.0171917
$431$	3955.74	−	6851.54i	0.442091	−	0.765724i	−0.555753	−	0.831347i	$-0.687570\pi$
$431$	3955.74	−	6851.54i	0.442091	−	0.765724i	0.997844	+	0.0656230i	$0.0209035\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	1239.72	−	2147.26i	0.137592	−	0.238316i	−0.788993	−	0.614402i	$-0.789397\pi$
$433$	1239.72	−	2147.26i	0.137592	−	0.238316i	0.926585	+	0.376087i	$0.122730\pi$
$434$	−1987.18	−	3441.90i	−0.219788	−	0.380683i
$435$	−904.518	−	1566.67i	−0.0996973	−	0.172681i
$436$	−2899.85			−0.318527
$437$	−1777.39	+	3825.36i	−0.194563	+	0.418746i
$438$	2130.19			0.232385
$439$	−6448.71	−	11169.5i	−0.701094	−	1.21433i	−0.968083	−	0.250630i	$-0.919362\pi$
$439$	−6448.71	−	11169.5i	−0.701094	−	1.21433i	0.266989	−	0.963699i	$-0.413971\pi$
$440$	627.951	+	1087.64i	0.0680373	+	0.117844i
$441$	1140.29	−	1975.04i	0.123128	−	0.213264i
$442$	−7375.29	−	12774.4i	−0.793680	−	1.37469i
$443$	301.508	−	522.227i	0.0323365	−	0.0560085i	−0.849404	−	0.527743i	$-0.823039\pi$
$443$	301.508	−	522.227i	0.0323365	−	0.0560085i	0.881741	+	0.471734i	$0.156372\pi$
$444$	1972.77			0.210864
$445$	1487.43			0.158451
$446$	−3861.83	+	6688.89i	−0.410007	+	0.710153i
$447$	−600.494	+	1040.09i	−0.0635400	+	0.110055i
$448$	−605.815			−0.0638885
$449$	−11358.0			−1.19380			−0.596902	−	0.802314i	$-0.703602\pi$
$449$	−11358.0			−1.19380			−0.596902	+	0.802314i	$0.703602\pi$
$450$	225.000	−	389.711i	0.0235702	−	0.0408248i
$451$	2279.54	+	3948.28i	0.238003	+	0.412233i
$452$	2566.59	−	4445.46i	0.267084	−	0.462603i
$453$	802.109	+	1389.29i	0.0831928	+	0.144094i
$454$	−5807.25	−	10058.5i	−0.600325	−	1.03979i
$455$	−3098.45			−0.319248
$456$	1142.31	+	1626.62i	0.117311	+	0.167047i
$457$	−164.122			−0.0167994			−0.00839970	−	0.999965i	$-0.502674\pi$
$457$	−164.122			−0.0167994			−0.00839970	+	0.999965i	$0.502674\pi$
$458$	−2586.63	−	4480.17i	−0.263898	−	0.457085i
$459$	1520.89	+	2634.26i	0.154660	+	0.267880i
$460$	−509.317	+	882.163i	−0.0516240	+	0.0894154i
$461$	−2552.00	−	4420.19i	−0.257827	−	0.446570i	0.707832	−	0.706380i	$-0.249673\pi$
$461$	−2552.00	−	4420.19i	−0.257827	−	0.446570i	−0.965660	+	0.259811i	$0.916340\pi$
$462$	−891.615	+	1544.32i	−0.0897872	+	0.155516i
$463$	−6575.52			−0.660022			−0.330011	−	0.943977i	$-0.607052\pi$
$463$	−6575.52			−0.660022			−0.330011	+	0.943977i	$0.607052\pi$
$464$	1929.64			0.193063
$465$	−1574.49	+	2727.09i	−0.157022	+	0.271970i
$466$	414.883	−	718.599i	0.0412427	−	0.0714344i
$467$	−8860.46			−0.877972			−0.438986	−	0.898494i	$-0.644662\pi$
$467$	−8860.46			−0.877972			−0.438986	+	0.898494i	$0.644662\pi$
$468$	−2356.77			−0.232782
$469$	−262.516	+	454.691i	−0.0258462	+	0.0447669i
$470$	2619.88	+	4537.76i	0.257119	+	0.445343i
$471$	−485.199	+	840.389i	−0.0474666	+	0.0822146i
$472$	23.2292	+	40.2341i	0.00226527	+	0.00392357i
$473$	240.651	+	416.820i	0.0233935	+	0.0405188i
$474$	3139.78			0.304251
$475$	872.439	−	1877.69i	0.0842742	−	0.181378i
$476$	−4265.64			−0.410746
$477$	−1319.31	−	2285.12i	−0.126640	−	0.219347i
$478$	5546.06	+	9606.05i	0.530692	+	0.919185i
$479$	1343.78	−	2327.50i	0.128182	−	0.222017i	−0.794790	−	0.606884i	$-0.792419\pi$
$479$	1343.78	−	2327.50i	0.128182	−	0.222017i	0.922972	+	0.384867i	$0.125753\pi$
$480$	240.000	+	415.692i	0.0228218	+	0.0395285i
$481$	−5381.21	+	9320.54i	−0.510109	+	0.883534i
$482$	−1574.33			−0.148774
$483$	−1446.34			−0.136254
$484$	690.385	−	1195.78i	0.0648371	−	0.112301i
$485$	911.305	−	1578.43i	0.0853201	−	0.147779i
$486$	486.000			0.0453609
$487$	18255.0			1.69859			0.849294	−	0.527920i	$-0.177028\pi$
$487$	18255.0			1.69859			0.849294	+	0.527920i	$0.177028\pi$
$488$	2853.00	−	4941.53i	0.264650	−	0.458387i
$489$	−2322.67	−	4022.98i	−0.214795	−	0.372036i
$490$	1266.99	−	2194.49i	0.116810	−	0.202320i
$491$	−490.199	−	849.050i	−0.0450558	−	0.0780389i	0.842618	−	0.538512i	$-0.181013\pi$
$491$	−490.199	−	849.050i	−0.0450558	−	0.0780389i	−0.887674	+	0.460473i	$0.847680\pi$
$492$	871.229	+	1509.01i	0.0798334	+	0.138276i
$493$	13586.9			1.24122
$494$	−10801.1	+	959.945i	−0.983731	+	0.0874291i
$495$	1412.89			0.128292
$496$	−1679.45	−	2908.90i	−0.152036	−	0.263334i
$497$	1064.74	+	1844.18i	0.0960965	+	0.166444i
$498$	−1497.06	+	2592.98i	−0.134708	+	0.233322i
$499$	5501.54	+	9528.94i	0.493552	+	0.854858i	0.999972	−	0.00742933i	$-0.00236485\pi$
$499$	5501.54	+	9528.94i	0.493552	+	0.854858i	−0.506420	+	0.862287i	$0.669032\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$	−526.844			−0.0469813
$502$	2504.51			0.222673
$503$	6754.71	−	11699.5i	0.598763	−	1.03709i	−0.394241	−	0.919007i	$-0.628993\pi$
$503$	6754.71	−	11699.5i	0.598763	−	1.03709i	0.993004	−	0.118080i	$-0.0376740\pi$
$504$	−340.771	+	590.232i	−0.0301173	+	0.0521648i
$505$	3169.48			0.279287
$506$	−3198.26			−0.280988
$507$	3133.17	−	5426.81i	0.274455	−	0.475371i
$508$	−3216.35	−	5570.88i	−0.280910	−	0.486551i
$509$	10523.1	−	18226.5i	0.916360	−	1.58718i	0.111462	−	0.993769i	$-0.464447\pi$
$509$	10523.1	−	18226.5i	0.916360	−	1.58718i	0.804898	−	0.593413i	$-0.202220\pi$
$510$	1689.88	+	2926.96i	0.146724	+	0.254133i
$511$	1680.34	+	2910.43i	0.145467	+	0.251957i
$512$	−512.000			−0.0441942
$513$	2227.34	−	197.954i	0.191695	−	0.0170368i
$514$	−3865.17			−0.331684
$515$	4538.54	+	7860.99i	0.388334	+	0.672615i
$516$	91.9757	+	159.307i	0.00784691	+	0.0135912i
$517$	−8225.78	+	14247.5i	−0.699747	+	1.21200i
$518$	1556.16	+	2695.35i	0.131996	+	0.228624i
$519$	−1224.99	+	2121.74i	−0.103605	+	0.179449i
$520$	−2618.63			−0.220836
$521$	20773.2			1.74681			0.873407	−	0.486991i	$-0.161906\pi$
$521$	20773.2			1.74681			0.873407	+	0.486991i	$0.161906\pi$
$522$	1085.42	−	1880.01i	0.0910108	−	0.157635i
$523$	1998.43	−	3461.39i	0.167085	−	0.289399i	−0.770309	−	0.637671i	$-0.779898\pi$
$523$	1998.43	−	3461.39i	0.167085	−	0.289399i	0.937394	+	0.348272i	$0.113231\pi$
$524$	11530.1			0.961245
$525$	709.939			0.0590177
$526$	1070.31	−	1853.83i	0.0887217	−	0.153670i
$527$	−11825.3	−	20482.0i	−0.977454	−	1.69300i
$528$	−753.542	+	1305.17i	−0.0621093	+	0.107576i
$529$	4786.48	+	8290.43i	0.393399	+	0.681386i
$530$	−1465.90	−	2539.02i	−0.120141	−	0.208090i
$531$	52.2657			0.00427144
$532$	−1321.34	+	2843.83i	−0.107683	+	0.231759i
$533$	−9505.96			−0.772512
$534$	892.457	+	1545.78i	0.0723228	+	0.125267i
$535$	−3850.50	−	6669.26i	−0.311162	−	0.538948i
$536$	−221.863	+	384.279i	−0.0178788	+	0.0309670i
$537$	−3497.81	−	6058.38i	−0.281083	−	0.486850i
$538$	7400.97	−	12818.9i	0.593083	−	1.02725i
$539$	7956.07			0.635792
$540$	540.000			0.0430331
$541$	9474.21	−	16409.8i	0.752917	−	1.30409i	−0.193486	−	0.981103i	$-0.561979\pi$
$541$	9474.21	−	16409.8i	0.752917	−	1.30409i	0.946403	−	0.322988i	$-0.104687\pi$
$542$	−2365.20	+	4096.64i	−0.187443	+	0.324660i
$543$	−6855.40			−0.541792
$544$	−3605.07			−0.284129
$545$	−1812.41	+	3139.18i	−0.142450	+	0.246730i
$546$	−1859.07	−	3220.01i	−0.145716	−	0.252387i
$547$	5452.79	−	9444.50i	0.426224	−	0.738241i	−0.570310	−	0.821429i	$-0.693177\pi$
$547$	5452.79	−	9444.50i	0.426224	−	0.738241i	0.996534	+	0.0831885i	$0.0265103\pi$
$548$	572.195	+	991.070i	0.0446039	+	0.0772562i
$549$	−3209.62	−	5559.22i	−0.249514	−	0.432171i
$550$	1569.88			0.121709
$551$	4208.73	−	9058.17i	0.325405	−	0.700346i
$552$	−1222.36			−0.0942521
$553$	2476.73	+	4289.82i	0.190454	+	0.329877i
$554$	5235.96	+	9068.94i	0.401542	+	0.695492i
$555$	1232.98	−	2135.59i	0.0943012	−	0.163334i
$556$	3676.70	+	6368.23i	0.280444	+	0.485743i
$557$	315.378	−	546.251i	0.0239910	−	0.0415536i	−0.853781	−	0.520633i	$-0.825696\pi$
$557$	315.378	−	546.251i	0.0239910	−	0.0415536i	0.877772	+	0.479079i	$0.159029\pi$
$558$	−3778.77			−0.286681
$559$	−1003.54			−0.0759310
$560$	−378.634	+	655.814i	−0.0285718	+	0.0494878i
$561$	−5305.81	+	9189.93i	−0.399307	+	0.691620i
$562$	−15824.4			−1.18774
$563$	14014.8			1.04912			0.524561	−	0.851373i	$-0.324230\pi$
$563$	14014.8			1.04912			0.524561	+	0.851373i	$0.324230\pi$
$564$	−3143.85	+	5445.32i	−0.234717	+	0.406541i
$565$	−3208.23	−	5556.82i	−0.238887	−	0.413765i
$566$	−5040.00	+	8729.53i	−0.374288	+	0.648285i
$567$	383.367	+	664.011i	0.0283949	+	0.0491814i
$568$	899.854	+	1558.59i	0.0664737	+	0.115136i
$569$	23499.5			1.73137			0.865685	−	0.500589i	$-0.166883\pi$
$569$	23499.5			1.73137			0.865685	+	0.500589i	$0.166883\pi$
$570$	2474.82	−	219.949i	0.181857	−	0.0161626i
$571$	−19021.1			−1.39406			−0.697031	−	0.717041i	$-0.745496\pi$
$571$	−19021.1			−1.39406			−0.697031	+	0.717041i	$0.745496\pi$
$572$	−4110.94	−	7120.35i	−0.300502	−	0.520484i
$573$	−3239.35	−	5610.71i	−0.236170	−	0.409059i
$574$	−1374.49	+	2380.68i	−0.0999478	+	0.173115i
$575$	636.646	+	1102.70i	0.0461739	+	0.0799755i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−15685.2			−1.13169			−0.565844	−	0.824512i	$-0.691450\pi$
$577$	−15685.2			−1.13169			−0.565844	+	0.824512i	$0.691450\pi$
$578$	−15557.9			−1.11959
$579$	−3771.51	+	6532.45i	−0.270706	+	0.468876i
$580$	1206.02	−	2088.90i	0.0863404	−	0.149546i
$581$	−4723.65			−0.337298
$582$	2187.13			0.155772
$583$	4602.58	−	7971.90i	0.326963	−	0.566316i
$584$	1420.13	+	2459.73i	0.100625	+	0.174288i
$585$	−1472.98	+	2551.28i	−0.104103	+	0.180312i
$586$	−336.152	−	582.232i	−0.0236967	−	0.0410440i
$587$	−221.699	−	383.993i	−0.0155886	−	0.0270002i	0.858126	−	0.513439i	$-0.171629\pi$
$587$	−221.699	−	383.993i	−0.0155886	−	0.0270002i	−0.873714	+	0.486439i	$0.838296\pi$
$588$	3040.77			0.213264
$589$	−17318.1	+	1539.15i	−1.21151	+	0.107673i
$590$	58.0730			0.00405225
$591$	−7972.50	−	13808.8i	−0.554898	−	0.961112i
$592$	1315.18	+	2277.96i	0.0913067	+	0.158148i
$593$	10926.6	−	18925.4i	0.756662	−	1.31058i	−0.187882	−	0.982192i	$-0.560162\pi$
$593$	10926.6	−	18925.4i	0.756662	−	1.31058i	0.944544	−	0.328385i	$-0.106504\pi$
$594$	847.734	+	1468.32i	0.0585572	+	0.101424i
$595$	−2666.02	+	4617.69i	−0.183691	+	0.318163i
$596$	−1601.32			−0.110055
$597$	4748.37			0.325524
$598$	3334.29	−	5775.16i	0.228009	−	0.394923i
$599$	−7466.47	+	12932.3i	−0.509302	+	0.882137i	0.490640	+	0.871362i	$0.336763\pi$
$599$	−7466.47	+	12932.3i	−0.509302	+	0.882137i	−0.999942	+	0.0107744i	$0.996570\pi$
$600$	600.000			0.0408248
$601$	−22409.9			−1.52100			−0.760499	−	0.649339i	$-0.775046\pi$
$601$	−22409.9			−1.52100			−0.760499	+	0.649339i	$0.775046\pi$
$602$	−145.105	+	251.329i	−0.00982397	+	0.0170156i
$603$	249.596	+	432.314i	0.0168563	+	0.0291960i
$604$	−1069.48	+	1852.39i	−0.0720471	+	0.124789i
$605$	−862.982	−	1494.73i	−0.0579921	−	0.100445i
$606$	1901.69	+	3293.82i	0.127476	+	0.220796i
$607$	18731.1			1.25250			0.626252	−	0.779620i	$-0.284588\pi$
$607$	18731.1			1.25250			0.626252	+	0.779620i	$0.284588\pi$
$608$	−1116.72	+	2403.44i	−0.0744886	+	0.160317i
$609$	3424.82			0.227883
$610$	−3566.24	−	6176.92i	−0.236710	−	0.409993i
$611$	−17151.3	−	29706.9i	−1.13562	−	1.96696i
$612$	−2027.85	+	3512.35i	−0.133940	+	0.231990i
$613$	6866.35	+	11892.9i	0.452413	+	0.783603i	0.998535	−	0.0541027i	$-0.0172299\pi$
$613$	6866.35	+	11892.9i	0.452413	+	0.783603i	−0.546122	+	0.837706i	$0.683897\pi$
$614$	−4307.13	+	7460.17i	−0.283097	+	0.490339i
$615$	2178.07			0.142810
$616$	−2377.64			−0.155516
$617$	1906.74	−	3302.57i	0.124412	−	0.215488i	−0.797091	−	0.603859i	$-0.793629\pi$
$617$	1906.74	−	3302.57i	0.124412	−	0.215488i	0.921503	+	0.388371i	$0.126962\pi$
$618$	−5446.25	+	9433.18i	−0.354499	+	0.614010i
$619$	15487.6			1.00565			0.502826	−	0.864387i	$-0.332294\pi$
$619$	15487.6			1.00565			0.502826	+	0.864387i	$0.332294\pi$
$620$	−4198.63			−0.271970
$621$	−687.578	+	1190.92i	−0.0444309	+	0.0769565i
$622$	−9483.69	−	16426.2i	−0.611353	−	1.05889i
$623$	−1407.98	+	2438.69i	−0.0905448	+	0.156828i
$624$	−1571.18	−	2721.36i	−0.100797	−	0.174586i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	8419.42			0.537552
$627$	4483.23	+	6384.01i	0.285555	+	0.406623i
$628$	−1293.86			−0.0822146
$629$	9260.40	+	16039.5i	0.587021	+	1.01675i
$630$	425.964	+	737.790i	0.0269378	+	0.0466576i
$631$	10776.7	−	18665.7i	0.679893	−	1.17761i	−0.295119	−	0.955460i	$-0.595359\pi$
$631$	10776.7	−	18665.7i	0.679893	−	1.17761i	0.975013	−	0.222149i	$-0.0713072\pi$
$632$	2093.19	+	3625.51i	0.131745	+	0.228188i
$633$	1770.99	−	3067.45i	0.111202	−	0.192607i
$634$	−17718.6			−1.10993
$635$	−8040.88			−0.502508
$636$	1759.08	−	3046.82i	0.109673	−	0.189960i
$637$	−8294.44	+	14366.4i	−0.515915	+	0.893591i
$638$	7573.25			0.469949
$639$	2024.67			0.125344
$640$	−320.000	+	554.256i	−0.0197642	+	0.0342327i
$641$	3324.85	+	5758.81i	0.204873	+	0.354851i	0.950092	−	0.311969i	$-0.100988\pi$
$641$	3324.85	+	5758.81i	0.204873	+	0.354851i	−0.745219	+	0.666820i	$0.767655\pi$
$642$	4620.60	−	8003.12i	0.284051	−	0.491990i
$643$	14372.1	+	24893.2i	0.881462	+	1.52674i	0.849716	+	0.527240i	$0.176773\pi$
$643$	14372.1	+	24893.2i	0.881462	+	1.52674i	0.0317454	+	0.999496i	$0.489893\pi$
$644$	−964.225	−	1670.09i	−0.0589996	−	0.102190i
$645$	229.939			0.0140370
$646$	−7863.02	+	16923.0i	−0.478895	+	1.03069i
$647$	5967.56			0.362610			0.181305	−	0.983427i	$-0.441968\pi$
$647$	5967.56			0.362610			0.181305	+	0.983427i	$0.441968\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	91.1675	+	157.907i	0.00551408	+	0.00955066i
$650$	−1636.65	+	2834.75i	−0.0987609	+	0.171059i
$651$	−2980.78	−	5162.85i	−0.179456	−	0.310827i
$652$	3096.89	−	5363.97i	0.186018	−	0.322192i
$653$	12877.8			0.771744			0.385872	−	0.922552i	$-0.373901\pi$
$653$	12877.8			0.771744			0.385872	+	0.922552i	$0.373901\pi$
$654$	−4349.78			−0.260076
$655$	7206.28	−	12481.6i	0.429882	−	0.744578i
$656$	−1161.64	+	2012.02i	−0.0691378	+	0.119750i
$657$	3195.29			0.189741
$658$	−9919.76			−0.587709
$659$	−4061.24	+	7034.27i	−0.240066	+	0.415806i	−0.960733	−	0.277475i	$-0.910502\pi$
$659$	−4061.24	+	7034.27i	−0.240066	+	0.415806i	0.720667	+	0.693281i	$0.243836\pi$
$660$	941.927	+	1631.47i	0.0555522	+	0.0962193i
$661$	−208.269	+	360.732i	−0.0122552	+	0.0212267i	−0.872088	−	0.489349i	$-0.837234\pi$
$661$	−208.269	+	360.732i	−0.0122552	+	0.0212267i	0.859833	+	0.510576i	$0.170568\pi$
$662$	−11577.5	−	20052.8i	−0.679716	−	1.17730i
$663$	−11062.9	−	19161.6i	−0.648037	−	1.12243i
$664$	−3992.16			−0.233322
$665$	2252.70	+	3207.79i	0.131362	+	0.187057i
$666$	2959.16			0.172170
$667$	3071.24	+	5319.55i	0.178289	+	0.308806i
$668$	−351.229	−	608.347i	−0.0203435	−	0.0352360i
$669$	−5792.75	+	10033.3i	−0.334769	+	0.579837i
$670$	277.329	+	480.348i	0.0159913	+	0.0276977i
$671$	11197.1	−	19394.0i	0.644204	−	1.11579i
$672$	−908.722			−0.0521648
$673$	22256.9			1.27480			0.637400	−	0.770533i	$-0.280010\pi$
$673$	22256.9			1.27480			0.637400	+	0.770533i	$0.280010\pi$
$674$	6299.37	−	10910.8i	0.360004	−	0.623545i
$675$	337.500	−	584.567i	0.0192450	−	0.0333333i
$676$	8355.11			0.475371
$677$	−3857.05			−0.218964			−0.109482	−	0.993989i	$-0.534919\pi$
$677$	−3857.05			−0.218964			−0.109482	+	0.993989i	$0.534919\pi$
$678$	3849.88	−	6668.19i	0.218073	−	0.377714i
$679$	1725.26	+	2988.23i	0.0975100	+	0.168892i
$680$	−2253.17	+	3902.61i	−0.127066	+	0.220086i
$681$	−8710.87	−	15087.7i	−0.490164	−	0.848988i
$682$	−6591.35	−	11416.5i	−0.370082	−	0.641000i
$683$	13692.5			0.767100			0.383550	−	0.923520i	$-0.374701\pi$
$683$	13692.5			0.767100			0.383550	+	0.923520i	$0.374701\pi$
$684$	1713.47	+	2439.94i	0.0957838	+	0.136394i
$685$	1430.49			0.0797899
$686$	5645.41	+	9778.14i	0.314202	+	0.544215i
$687$	−3879.94	−	6720.26i	−0.215472	−	0.373208i
$688$	−122.634	+	212.409i	−0.00679562	+	0.0117704i
$689$	9596.66	+	16621.9i	0.530629	+	0.919077i
$690$	−763.976	+	1323.24i	−0.0421508	+	0.0730073i
$691$	−13079.0			−0.720042			−0.360021	−	0.932944i	$-0.617231\pi$
$691$	−13079.0			−0.720042			−0.360021	+	0.932944i	$0.617231\pi$
$692$	−3266.63			−0.179449
$693$	−1337.42	+	2316.48i	−0.0733109	+	0.126978i
$694$	4197.98	−	7271.12i	0.229616	−	0.397706i
$695$	9191.74			0.501673
$696$	2894.46			0.157635
$697$	−8179.29	+	14166.9i	−0.444494	+	0.769887i
$698$	3662.09	+	6342.93i	0.198585	+	0.343959i
$699$	622.325	−	1077.90i	0.0336745	−	0.0583260i
$700$	473.293	+	819.767i	0.0255554	+	0.0442633i
$701$	−11458.1	−	19845.9i	−0.617353	−	1.06929i	−0.989967	−	0.141301i	$-0.954872\pi$
$701$	−11458.1	−	19845.9i	−0.617353	−	1.06929i	0.372613	−	0.927987i	$-0.378462\pi$
$702$	−3535.16			−0.190065
$703$	13561.8	−	1205.30i	0.727586	−	0.0646642i
$704$	−2009.44			−0.107576
$705$	3929.82	+	6806.64i	0.209937	+	0.363621i
$706$	6923.15	+	11991.3i	0.369060	+	0.639230i
$707$	−3000.18	+	5196.47i	−0.159595	+	0.276426i
$708$	34.8438	+	60.3512i	0.00184959	+	0.00320358i
$709$	−13994.2	+	24238.6i	−0.741271	+	1.28392i	0.210645	+	0.977563i	$0.432443\pi$
$709$	−13994.2	+	24238.6i	−0.741271	+	1.28392i	−0.951917	+	0.306357i	$0.900890\pi$
$710$	2249.64			0.118912
$711$	4709.68			0.248420
$712$	−1189.94	+	2061.04i	−0.0626334	+	0.108484i
$713$	5346.09	−	9259.70i	0.280803	−	0.486365i
$714$	−6398.46			−0.335373
$715$	−10277.3			−0.537554
$716$	4663.74	−	8077.84i	0.243425	−	0.421624i
$717$	8319.08	+	14409.1i	0.433308	+	0.750512i
$718$	−1069.38	+	1852.22i	−0.0555833	+	0.0962731i
$719$	−1680.24	−	2910.26i	−0.0871521	−	0.150952i	0.819154	−	0.573573i	$-0.194443\pi$
$719$	−1680.24	−	2910.26i	−0.0871521	−	0.150952i	−0.906306	+	0.422622i	$0.861110\pi$
$720$	360.000	+	623.538i	0.0186339	+	0.0322749i
$721$	−17184.5			−0.887633
$722$	8846.64	+	10484.3i	0.456008	+	0.540423i
$723$	−2361.50			−0.121473
$724$	−4570.26	−	7915.93i	−0.234603	−	0.406344i
$725$	−1507.53	−	2611.12i	−0.0772252	−	0.133758i
$726$	1035.58	−	1793.67i	0.0529393	−	0.0916935i
$727$	9213.39	+	15958.1i	0.470022	+	0.814101i	0.999412	−	0.0342769i	$-0.0109128\pi$
$727$	9213.39	+	15958.1i	0.470022	+	0.814101i	−0.529391	+	0.848378i	$0.677579\pi$
$728$	2478.76	−	4293.34i	0.126194	−	0.218574i
$729$	729.000			0.0370370
$730$	3550.32			0.180004
$731$	−863.487	+	1495.60i	−0.0436898	+	0.0756729i
$732$	4279.49	−	7412.30i	0.216086	−	0.374271i
$733$	−32470.5			−1.63619			−0.818093	−	0.575086i	$-0.804969\pi$
$733$	−32470.5			−1.63619			−0.818093	+	0.575086i	$0.804969\pi$
$734$	22951.4			1.15416
$735$	1900.48	−	3291.73i	0.0953746	−	0.165194i
$736$	−814.907	−	1411.46i	−0.0408123	−	0.0706891i
$737$	−870.747	+	1508.18i	−0.0435202	+	0.0753791i
$738$	1306.84	+	2263.52i	0.0651837	+	0.112902i
$739$	−13815.5	−	23929.2i	−0.687703	−	1.19114i	−0.972579	−	0.232572i	$-0.925286\pi$
$739$	−13815.5	−	23929.2i	−0.687703	−	1.19114i	0.284876	−	0.958564i	$-0.408048\pi$
$740$	3287.95			0.163334
$741$	−16201.6	+	1439.92i	−0.803213	+	0.0713855i
$742$	5550.41			0.274612
$743$	−17707.4	−	30670.2i	−0.874324	−	1.51437i	−0.857481	−	0.514515i	$-0.827972\pi$
$743$	−17707.4	−	30670.2i	−0.874324	−	1.51437i	−0.0168429	−	0.999858i	$-0.505362\pi$
$744$	−2519.18	−	4363.35i	−0.124137	−	0.215011i
$745$	−1000.82	+	1733.48i	−0.0492179	+	0.0852479i
$746$	7551.41	+	13079.4i	0.370612	+	0.641919i
$747$	−2245.59	+	3889.47i	−0.109989	+	0.190507i
$748$	−14148.8			−0.691620
$749$	14579.3			0.711237
$750$	375.000	−	649.519i	0.0182574	−	0.0316228i
$751$	−15992.8	+	27700.3i	−0.777076	+	1.34594i	0.156544	+	0.987671i	$0.449965\pi$
$751$	−15992.8	+	27700.3i	−0.777076	+	1.34594i	−0.933620	+	0.358264i	$0.883369\pi$
$752$	−8383.61			−0.406541
$753$	3756.77			0.181812
$754$	−7895.34	+	13675.1i	−0.381341	+	0.660503i
$755$	1336.85	+	2315.49i	0.0644409	+	0.111615i
$756$	−511.156	+	885.349i	−0.0245907	+	0.0425923i
$757$	10980.0	+	19017.8i	0.527178	+	0.913098i	0.999498	+	0.0316716i	$0.0100831\pi$
$757$	10980.0	+	19017.8i	0.527178	+	0.913098i	−0.472321	+	0.881427i	$0.656584\pi$
$758$	5449.18	+	9438.26i	0.261112	+	0.452260i
$759$	−4797.40			−0.229426
$760$	1903.85	+	2711.04i	0.0908685	+	0.129394i
$761$	−24827.1			−1.18263			−0.591316	−	0.806440i	$-0.701391\pi$
$761$	−24827.1			−1.18263			−0.591316	+	0.806440i	$0.701391\pi$
$762$	−4824.53	−	8356.33i	−0.229362	−	0.397267i
$763$	−3431.20	−	5943.01i	−0.162802	−	0.281981i
$764$	4319.13	−	7480.95i	0.204530	−	0.354256i
$765$	2534.82	+	4390.43i	0.119799	+	0.207499i
$766$	2814.89	−	4875.54i	0.132776	−	0.229974i
$767$	−380.180			−0.0178976
$768$	−768.000			−0.0360844
$769$	−14112.5	+	24443.5i	−0.661779	+	1.14623i	0.318369	+	0.947967i	$0.396865\pi$
$769$	−14112.5	+	24443.5i	−0.661779	+	1.14623i	−0.980148	+	0.198268i	$0.936468\pi$
$770$	−1486.02	+	2573.87i	−0.0695488	+	0.120462i
$771$	−5797.76			−0.270819
$772$	−10057.4			−0.468876
$773$	66.0794	−	114.453i	0.00307466	−	0.00532547i	−0.864484	−	0.502660i	$-0.832355\pi$
$773$	66.0794	−	114.453i	0.00307466	−	0.00532547i	0.867559	+	0.497335i	$0.165688\pi$
$774$	137.964	+	238.960i	0.00640697	+	0.0110972i
$775$	−2624.15	+	4545.15i	−0.121629	+	0.210667i
$776$	1458.09	+	2525.48i	0.0674514	+	0.116829i
$777$	2334.25	+	4043.03i	0.107774	+	0.186670i
$778$	−5737.54			−0.264397
$779$	6911.22	+	9841.41i	0.317869	+	0.452638i
$780$	−3927.95			−0.180312
$781$	3531.65	+	6117.00i	0.161809	+	0.280261i
$782$	−5737.89	−	9938.32i	−0.262387	−	0.454468i
$783$	1628.13	−	2820.01i	0.0743100	−	0.128709i
$784$	2027.18	+	3511.18i	0.0923461	+	0.159948i
$785$	−808.665	+	1400.65i	−0.0367675	+	0.0636832i
$786$	17295.1			0.784854
$787$	20434.1			0.925538			0.462769	−	0.886479i	$-0.346856\pi$
$787$	20434.1			0.925538			0.462769	+	0.886479i	$0.346856\pi$
$788$	10630.0	−	18411.7i	0.480556	−	0.832347i
$789$	1605.46	−	2780.74i	0.0724409	−	0.125471i
$790$	5232.97			0.235672
$791$	12147.5			0.546036
$792$	−1130.31	+	1957.76i	−0.0507120	+	0.0878358i
$793$	23346.7	+	40437.7i	1.04548	+	1.81083i
$794$	2808.06	−	4863.69i	0.125509	−	0.217388i
$795$	−2198.85	−	3808.53i	−0.0980947	−	0.169905i
$796$	3165.58	+	5482.95i	0.140956	+	0.244143i
$797$	−41468.4			−1.84302			−0.921510	−	0.388355i	$-0.873043\pi$
$797$	−41468.4			−1.84302			−0.921510	+	0.388355i	$0.873043\pi$
$798$	−1982.01	+	4265.75i	−0.0879229	+	0.189230i
$799$	−59030.3			−2.61370
$800$	400.000	+	692.820i	0.0176777	+	0.0306186i
$801$	1338.68	+	2318.67i	0.0590513	+	0.102280i
$802$	−8487.78	+	14701.3i	−0.373708	+	0.647282i
$803$	5573.57	+	9653.70i	0.244940	+	0.424249i
$804$	−332.795	+	576.418i	−0.0145980	+	0.0252845i
$805$	−2410.56			−0.105542
$806$	27486.7			1.20121
$807$	11101.5	−	19228.3i	0.484250	−	0.838745i
$808$	−2535.58	+	4391.76i	−0.110398	+	0.191215i
$809$	19100.8			0.830097			0.415048	−	0.909799i	$-0.363765\pi$
$809$	19100.8			0.830097			0.415048	+	0.909799i	$0.363765\pi$
$810$	810.000			0.0351364
$811$	17238.3	−	29857.6i	0.746385	−	1.29278i	−0.203159	−	0.979146i	$-0.565121\pi$
$811$	17238.3	−	29857.6i	0.746385	−	1.29278i	0.949545	−	0.313632i	$-0.101546\pi$
$812$	2283.21	+	3954.64i	0.0986761	+	0.170912i
$813$	−3547.80	+	6144.96i	−0.153046	+	0.265084i
$814$	5161.68	+	8940.30i	0.222257	+	0.384960i
$815$	−3871.12	−	6704.97i	−0.166379	−	0.288178i
$816$	−5407.61			−0.231990
$817$	729.618	+	1038.96i	0.0312437	+	0.0444902i
$818$	3916.15			0.167390
$819$	−2788.61	−	4830.01i	−0.118977	−	0.206073i
$820$	1452.05	+	2515.02i	0.0618387	+	0.107108i
$821$	−7308.71	+	12659.1i	−0.310689	+	0.538129i	−0.978512	−	0.206191i	$-0.933893\pi$
$821$	−7308.71	+	12659.1i	−0.310689	+	0.538129i	0.667823	+	0.744321i	$0.267227\pi$
$822$	858.292	+	1486.61i	0.0364189	+	0.0630794i
$823$	−11259.3	+	19501.7i	−0.476882	+	0.825984i	−0.999649	−	0.0264916i	$-0.991566\pi$
$823$	−11259.3	+	19501.7i	−0.476882	+	0.825984i	0.522767	+	0.852476i	$0.324900\pi$
$824$	−14523.3			−0.614010
$825$	2354.82			0.0993748
$826$	−54.9710	+	95.2126i	−0.00231560	+	0.00401074i
$827$	−12420.1	+	21512.3i	−0.522237	+	0.904542i	0.477428	+	0.878671i	$0.341569\pi$
$827$	−12420.1	+	21512.3i	−0.522237	+	0.904542i	−0.999665	+	0.0258708i	$0.991764\pi$
$828$	−1833.54			−0.0769565
$829$	−24002.3			−1.00559			−0.502795	−	0.864405i	$-0.667695\pi$
$829$	−24002.3			−1.00559			−0.502795	+	0.864405i	$0.667695\pi$
$830$	−2495.10	+	4321.64i	−0.104345	+	0.180730i
$831$	7853.94	+	13603.4i	0.327858	+	0.567867i
$832$	2094.91	−	3628.49i	0.0872931	−	0.151196i
$833$	14273.7	+	24722.8i	0.593703	+	1.02832i
$834$	5515.05	+	9552.34i	0.228981	+	0.396607i
$835$	−878.073			−0.0363916
$836$	−4382.80	+	9432.79i	−0.181318	+	0.390239i
$837$	−5668.16			−0.234074
$838$	6227.21	+	10785.9i	0.256701	+	0.444619i
$839$	12877.6	+	22304.6i	0.529897	+	0.917809i	0.999392	+	0.0348735i	$0.0111028\pi$
$839$	12877.6	+	22304.6i	0.529897	+	0.917809i	−0.469495	+	0.882935i	$0.655564\pi$
$840$	−567.951	+	983.721i	−0.0233288	+	0.0404067i
$841$	4922.03	+	8525.20i	0.201813	+	0.349551i
$842$	−9276.06	+	16066.6i	−0.379661	+	0.657591i
$843$	−23736.6			−0.969788
$844$	4722.65			0.192607
$845$	5221.95	−	9044.68i	0.212592	−	0.368220i
$846$	−4715.78	+	8167.97i	−0.191645	+	0.331939i
$847$	3267.54			0.132555
$848$	4690.89			0.189960
$849$	−7559.99	+	13094.3i	−0.305605	+	0.529323i
$850$	2816.46	+	4878.26i	0.113652	+	0.196850i
$851$	−4186.52	+	7251.27i	−0.168640	+	0.292092i
$852$	1349.78	+	2337.89i	0.0542755	+	0.0940080i
$853$	10403.0	+	18018.6i	0.417577	+	0.723265i	0.995695	−	0.0926880i	$-0.0295459\pi$
$853$	10403.0	+	18018.6i	0.417577	+	0.723265i	−0.578118	+	0.815953i	$0.696213\pi$
$854$	13503.0			0.541058
$855$	3712.23	−	329.924i	0.148486	−	0.0131967i
$856$	12321.6			0.491990
$857$	19663.3	+	34057.8i	0.783764	+	1.35752i	0.929735	+	0.368230i	$0.120036\pi$
$857$	19663.3	+	34057.8i	0.783764	+	1.35752i	−0.145971	+	0.989289i	$0.546630\pi$
$858$	−6166.41	−	10680.5i	−0.245359	−	0.424973i
$859$	14633.3	−	25345.6i	0.581237	−	1.00673i	−0.414096	−	0.910233i	$-0.635902\pi$
$859$	14633.3	−	25345.6i	0.581237	−	1.00673i	0.995333	−	0.0964984i	$-0.0307643\pi$
$860$	153.293	+	265.511i	0.00607819	+	0.0105277i
$861$	−2061.73	+	3571.03i	−0.0816070	+	0.141348i
$862$	15823.0			0.625211
$863$	8053.05			0.317647			0.158823	−	0.987307i	$-0.449230\pi$
$863$	8053.05			0.317647			0.158823	+	0.987307i	$0.449230\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	−2041.65	+	3536.24i	−0.0802521	+	0.139001i
$866$	4958.89			0.194584
$867$	−23336.9			−0.914142
$868$	3974.37	−	6883.81i	0.155413	−	0.269184i
$869$	8215.13	+	14229.0i	0.320690	+	0.555451i
$870$	1809.04	−	3133.34i	0.0704966	−	0.122104i
$871$	−1815.56	−	3144.64i	−0.0706290	−	0.122333i
$872$	−2899.85	−	5022.69i	−0.112616	−	0.195057i
$873$	3280.70			0.127188
$874$	−8403.11	+	746.827i	−0.325217	+	0.0289036i
$875$	1183.23			0.0457149
$876$	2130.19	+	3689.60i	0.0821604	+	0.142306i
$877$	−11930.3	−	20663.8i	−0.459357	−	0.795629i	0.539570	−	0.841941i	$-0.318587\pi$
$877$	−11930.3	−	20663.8i	−0.459357	−	0.795629i	−0.998927	+	0.0463112i	$0.985253\pi$
$878$	12897.4	−	22339.0i	0.495748	−	0.858661i
$879$	−504.227	−	873.347i	−0.0193483	−	0.0335123i
$880$	−1255.90	+	2175.29i	−0.0481096	+	0.0833283i
$881$	−17274.7			−0.660612			−0.330306	−	0.943874i	$-0.607152\pi$
$881$	−17274.7			−0.660612			−0.330306	+	0.943874i	$0.607152\pi$
$882$	4561.16			0.174129
$883$	−19530.1	+	33827.1i	−0.744326	+	1.28921i	0.206182	+	0.978514i	$0.433896\pi$
$883$	−19530.1	+	33827.1i	−0.744326	+	1.28921i	−0.950509	+	0.310698i	$0.899437\pi$
$884$	14750.6	−	25548.8i	0.561217	−	0.972056i
$885$	87.1094			0.00330865
$886$	1206.03			0.0457307
$887$	18713.8	−	32413.2i	0.708395	−	1.22698i	−0.257057	−	0.966396i	$-0.582753\pi$
$887$	18713.8	−	32413.2i	0.708395	−	1.22698i	0.965452	−	0.260580i	$-0.0839139\pi$
$888$	1972.77	+	3416.94i	0.0745516	+	0.129127i
$889$	7611.38	−	13183.3i	0.287151	−	0.497361i
$890$	1487.43	+	2576.30i	0.0560210	+	0.0970312i
$891$	1271.60	+	2202.48i	0.0478117	+	0.0828123i
$892$	−15447.3			−0.579837
$893$	−18285.5	+	39354.6i	−0.685219	+	1.47475i
$894$	−2401.98			−0.0898592
$895$	−5829.68	−	10097.3i	−0.217726	−	0.377112i
$896$	−605.815	−	1049.30i	−0.0225880	−	0.0391236i
$897$	5001.43	−	8662.73i	0.186168	−	0.322453i
$898$	−11358.0	−	19672.7i	−0.422073	−	0.731053i
$899$	−12659.1	+	21926.3i	−0.469639	+	0.813439i
$900$	900.000			0.0333333
$901$	33029.3			1.22127
$902$	−4559.08	+	7896.56i	−0.168294	+	0.291493i
$903$	−217.657	+	376.993i	−0.00802124	+	0.0138932i
$904$	10266.3			0.377714
$905$	−11425.7			−0.419670
$906$	−1604.22	+	2778.59i	−0.0588262	+	0.101890i
$907$	7325.87	+	12688.8i	0.268193	+	0.464525i	0.968395	−	0.249420i	$-0.0802401\pi$
$907$	7325.87	+	12688.8i	0.268193	+	0.464525i	−0.700202	+	0.713945i	$0.746907\pi$
$908$	11614.5	−	20116.9i	0.424494	−	0.735245i
$909$	2852.53	+	4940.72i	0.104084	+	0.180279i
$910$	−3098.45	−	5366.68i	−0.112871	−	0.195498i
$911$	47811.0			1.73880			0.869401	−	0.494108i	$-0.164505\pi$
$911$	47811.0			1.73880			0.869401	+	0.494108i	$0.164505\pi$
$912$	−1675.08	+	3605.17i	−0.0608197	+	0.130898i
$913$	−15668.0			−0.567947
$914$	−164.122	−	284.268i	−0.00593948	−	0.0102875i
$915$	−5349.37	−	9265.37i	−0.193273	−	0.334758i
$916$	5173.26	−	8960.35i	0.186604	−	0.323208i
$917$	13642.7	+	23629.9i	0.491300	+	0.850957i
$918$	−3041.78	+	5268.52i	−0.109361	+	0.189419i
$919$	−17167.4			−0.616212			−0.308106	−	0.951352i	$-0.599695\pi$
$919$	−17167.4			−0.616212			−0.308106	+	0.951352i	$0.599695\pi$
$920$	−2037.27			−0.0730073
$921$	−6460.70	+	11190.3i	−0.231148	+	0.400360i
$922$	5103.99	−	8840.37i	0.182311	−	0.315772i
$923$	−14727.4			−0.525200
$924$	−3566.46			−0.126978
$925$	2054.97	−	3559.31i	0.0730454	−	0.126518i
$926$	−6575.52	−	11389.1i	−0.233353	−	0.404179i
$927$	−8169.38	+	14149.8i	−0.289447	+	0.501337i
$928$	1929.64	+	3342.23i	0.0682581	+	0.118226i
$929$	−7579.34	−	13127.8i	−0.267675	−	0.463627i	0.700586	−	0.713568i	$-0.252922\pi$
$929$	−7579.34	−	13127.8i	−0.267675	−	0.463627i	−0.968261	+	0.249941i	$0.919589\pi$
$930$	−6297.95			−0.222062
$931$	20903.8	−	1857.82i	0.735868	−	0.0654003i
$932$	1659.53			0.0583260
$933$	−14225.5	−	24639.3i	−0.499167	−	0.864583i
$934$	−8860.46	−	15346.8i	−0.310410	−	0.537646i
$935$	−8843.01	+	15316.5i	−0.309302	+	0.535727i
$936$	−2356.77	−	4082.05i	−0.0823007	−	0.142549i
$937$	−6382.57	+	11054.9i	−0.222529	+	0.385431i	−0.955575	−	0.294747i	$-0.904764\pi$
$937$	−6382.57	+	11054.9i	−0.222529	+	0.385431i	0.733046	+	0.680179i	$0.238098\pi$
$938$	−1050.06			−0.0365520
$939$	12629.1			0.438910
$940$	−5239.76	+	9075.53i	−0.181811	+	0.314905i
$941$	4798.87	−	8311.88i	0.166247	−	0.287949i	−0.770850	−	0.637016i	$-0.780168\pi$
$941$	4798.87	−	8311.88i	0.166247	−	0.287949i	0.937097	+	0.349068i	$0.113502\pi$
$942$	−1940.80			−0.0671279
$943$	−7395.53			−0.255389
$944$	−46.4584	+	80.4682i	−0.00160179	+	0.00277438i
$945$	638.945	+	1106.69i	0.0219946	+	0.0380958i
$946$	−481.302	+	833.640i	−0.0165417	+	0.0286511i
$947$	−1199.30	−	2077.25i	−0.0411531	−	0.0712793i	0.844715	−	0.535216i	$-0.179770\pi$
$947$	−1199.30	−	2077.25i	−0.0411531	−	0.0712793i	−0.885868	+	0.463937i	$0.846436\pi$
$948$	3139.78	+	5438.27i	0.107569	+	0.186315i
$949$	−23242.5			−0.795029
$950$	4124.70	−	366.582i	0.140866	−	0.0125195i
$951$	−26577.9			−0.906253
$952$	−4265.64	−	7388.30i	−0.145221	−	0.251530i
$953$	−2719.93	−	4711.05i	−0.0924523	−	0.160132i	0.816090	−	0.577925i	$-0.196137\pi$
$953$	−2719.93	−	4711.05i	−0.0924523	−	0.160132i	−0.908542	+	0.417793i	$0.862804\pi$
$954$	2638.62	−	4570.23i	0.0895478	−	0.155101i
$955$	−5398.91	−	9351.19i	−0.182937	−	0.316856i
$956$	−11092.1	+	19212.1i	−0.375256	+	0.649962i
$957$	11359.9			0.383712
$958$	5375.14			0.181276
$959$	−1354.08	+	2345.33i	−0.0455948	+	0.0789726i
$960$	−480.000	+	831.384i	−0.0161374	+	0.0279508i
$961$	14280.3			0.479350
$962$	−21524.9			−0.721402
$963$	6930.90	−	12004.7i	0.231926	−	0.401708i
$964$	−1574.33	−	2726.82i	−0.0525994	−	0.0911049i
$965$	−6285.85	+	10887.4i	−0.209688	+	0.363190i
$966$	−1446.34	−	2505.13i	−0.0481730	−	0.0834381i
$967$	28267.7	+	48961.1i	0.940049	+	1.62821i	0.765373	+	0.643586i	$0.222554\pi$
$967$	28267.7	+	48961.1i	0.940049	+	1.62821i	0.174676	+	0.984626i	$0.444112\pi$
$968$	2761.54			0.0916935
$969$	−11794.5	+	25384.6i	−0.391016	+	0.841558i
$970$	3645.22			0.120661
$971$	−963.799	−	1669.35i	−0.0318535	−	0.0551719i	0.849659	−	0.527332i	$-0.176808\pi$
$971$	−963.799	−	1669.35i	−0.0318535	−	0.0551719i	−0.881513	+	0.472160i	$0.843474\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	−8700.77	+	15070.2i	−0.286674	+	0.496534i
$974$	18255.0	+	31618.6i	0.600542	+	1.04017i
$975$	−2454.97	+	4252.13i	−0.0806379	+	0.139669i
$976$	11412.0			0.374271
$977$	53049.3			1.73715			0.868576	−	0.495557i	$-0.165036\pi$
$977$	53049.3			1.73715			0.868576	+	0.495557i	$0.165036\pi$
$978$	4645.34	−	8045.96i	0.151883	−	0.263069i
$979$	−4670.16	+	8088.96i	−0.152461	+	0.264070i
$980$	5067.95			0.165194
$981$	−6524.67			−0.212351
$982$	980.399	−	1698.10i	0.0318592	−	0.0551818i
$983$	−25590.8	−	44324.5i	−0.830335	−	1.43818i	−0.897773	−	0.440458i	$-0.854816\pi$
$983$	−25590.8	−	44324.5i	−0.830335	−	1.43818i	0.0674386	−	0.997723i	$-0.478517\pi$
$984$	−1742.46	+	3018.03i	−0.0564508	+	0.0977756i
$985$	−13287.5	−	23014.6i	−0.429822	−	0.744474i
$986$	13586.9	+	23533.2i	0.438839	+	0.760091i
$987$	−14879.6			−0.479862
$988$	−12463.7	−	17748.1i	−0.401341	−	0.571499i
$989$	−780.747			−0.0251024
$990$	1412.89	+	2447.20i	0.0453582	+	0.0785627i
$991$	9939.12	+	17215.1i	0.318594	+	0.551821i	0.980195	−	0.198035i	$-0.0634560\pi$
$991$	9939.12	+	17215.1i	0.318594	+	0.551821i	−0.661601	+	0.749856i	$0.730123\pi$
$992$	3358.91	−	5817.80i	0.107505	−	0.186205i
$993$	−17366.2	−	30079.2i	−0.554986	−	0.961263i
$994$	−2129.47	+	3688.35i	−0.0679505	+	0.117694i
$995$	7913.95			0.252150
$996$	−5988.24			−0.190507
$997$	−13568.2	+	23500.8i	−0.431003	+	0.746519i	−0.996960	−	0.0779159i	$-0.975173\pi$
$997$	−13568.2	+	23500.8i	−0.431003	+	0.746519i	0.565957	+	0.824435i	$0.308507\pi$
$998$	−11003.1	+	19057.9i	−0.348994	+	0.604476i
$999$	4438.73			0.140576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.4.i.i.121.1	✓	4
19.11	even	3	inner	570.4.i.i.391.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.i.i.121.1	✓	4	1.1	even	1	trivial
570.4.i.i.391.1	yes	4	19.11	even	3	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} -9.46586 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-3.00000 + 5.19615i) q^{6} -9.46586 q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-5.00000 + 8.66025i) q^{10} -31.3976 q^{11} -12.0000 q^{12} +(32.7329 - 56.6951i) q^{13} +(-9.46586 - 16.3953i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-56.3293 - 97.5652i) q^{17} -18.0000 q^{18} +(-82.4939 + 7.33165i) q^{19} -20.0000 q^{20} +(-14.1988 - 24.5930i) q^{21} +(-31.3976 - 54.3822i) q^{22} +(25.4659 - 44.1082i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} +130.932 q^{26} -27.0000 q^{27} +(18.9317 - 32.7907i) q^{28} +(-60.3012 + 104.445i) q^{29} -30.0000 q^{30} +209.932 q^{31} +(16.0000 - 27.7128i) q^{32} +(-47.0964 - 81.5733i) q^{33} +(112.659 - 195.130i) q^{34} +(-23.6646 - 40.9884i) q^{35} +(-18.0000 - 31.1769i) q^{36} -164.398 q^{37} +(-95.1927 - 135.552i) q^{38} +196.398 q^{39} +(-20.0000 - 34.6410i) q^{40} +(-72.6024 - 125.751i) q^{41} +(28.3976 - 49.1860i) q^{42} +(-7.66464 - 13.2755i) q^{43} +(62.7951 - 108.764i) q^{44} -45.0000 q^{45} +101.863 q^{46} +(261.988 - 453.776i) q^{47} +(24.0000 - 41.5692i) q^{48} -253.398 q^{49} -50.0000 q^{50} +(168.988 - 292.696i) q^{51} +(130.932 + 226.780i) q^{52} +(-146.590 + 253.902i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(-78.4939 - 135.955i) q^{55} +75.7268 q^{56} +(-142.789 - 203.328i) q^{57} -241.205 q^{58} +(-2.90365 - 5.02927i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(-356.624 + 617.692i) q^{61} +(209.932 + 363.612i) q^{62} +(42.5964 - 73.7790i) q^{63} +64.0000 q^{64} +327.329 q^{65} +(94.1927 - 163.147i) q^{66} +(27.7329 - 48.0348i) q^{67} +450.634 q^{68} +152.795 q^{69} +(47.3293 - 81.9767i) q^{70} +(-112.482 - 194.824i) q^{71} +(36.0000 - 62.3538i) q^{72} +(-177.516 - 307.467i) q^{73} +(-164.398 - 284.745i) q^{74} -75.0000 q^{75} +(139.590 - 300.431i) q^{76} +297.205 q^{77} +(196.398 + 340.171i) q^{78} +(-261.649 - 453.189i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(145.205 - 251.502i) q^{82} +499.020 q^{83} +113.590 q^{84} +(281.646 - 487.826i) q^{85} +(15.3293 - 26.5511i) q^{86} -361.807 q^{87} +251.181 q^{88} +(148.743 - 257.630i) q^{89} +(-45.0000 - 77.9423i) q^{90} +(-309.845 + 536.668i) q^{91} +(101.863 + 176.433i) q^{92} +(314.898 + 545.419i) q^{93} +1047.95 q^{94} +(-237.982 - 338.880i) q^{95} +96.0000 q^{96} +(-182.261 - 315.685i) q^{97} +(-253.398 - 438.897i) q^{98} +(141.289 - 244.720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 12 q^{6} + 6 q^{7} - 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 12 * q^6 + 6 * q^7 - 32 * q^8 - 18 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 12 q^{6} + 6 q^{7} - 32 q^{8} - 18 q^{9} - 20 q^{10} + 6 q^{11} - 48 q^{12} + 109 q^{13} + 6 q^{14} - 30 q^{15} - 32 q^{16} - 6 q^{17} - 72 q^{18} - q^{19} - 80 q^{20} + 9 q^{21} + 6 q^{22} + 58 q^{23} - 48 q^{24} - 50 q^{25} + 436 q^{26} - 108 q^{27} - 12 q^{28} - 307 q^{29} - 120 q^{30} + 752 q^{31} + 64 q^{32} + 9 q^{33} + 12 q^{34} + 15 q^{35} - 72 q^{36} - 526 q^{37} + 14 q^{38} + 654 q^{39} - 80 q^{40} - 422 q^{41} - 18 q^{42} + 79 q^{43} - 12 q^{44} - 180 q^{45} + 232 q^{46} + 390 q^{47} + 96 q^{48} - 882 q^{49} - 200 q^{50} + 18 q^{51} + 436 q^{52} - 60 q^{53} - 108 q^{54} + 15 q^{55} - 48 q^{56} + 21 q^{57} - 1228 q^{58} - 209 q^{59} - 120 q^{60} - 944 q^{61} + 752 q^{62} - 27 q^{63} + 256 q^{64} + 1090 q^{65} - 18 q^{66} + 89 q^{67} + 48 q^{68} + 348 q^{69} - 30 q^{70} + 537 q^{71} + 144 q^{72} + 233 q^{73} - 526 q^{74} - 300 q^{75} + 32 q^{76} + 1452 q^{77} + 654 q^{78} - 1880 q^{79} + 160 q^{80} - 162 q^{81} + 844 q^{82} - 548 q^{83} - 72 q^{84} + 30 q^{85} - 158 q^{86} - 1842 q^{87} - 48 q^{88} - 699 q^{89} - 180 q^{90} - 77 q^{91} + 232 q^{92} + 1128 q^{93} + 1560 q^{94} + 35 q^{95} + 384 q^{96} - 422 q^{97} - 882 q^{98} - 27 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 12 * q^6 + 6 * q^7 - 32 * q^8 - 18 * q^9 - 20 * q^10 + 6 * q^11 - 48 * q^12 + 109 * q^13 + 6 * q^14 - 30 * q^15 - 32 * q^16 - 6 * q^17 - 72 * q^18 - q^19 - 80 * q^20 + 9 * q^21 + 6 * q^22 + 58 * q^23 - 48 * q^24 - 50 * q^25 + 436 * q^26 - 108 * q^27 - 12 * q^28 - 307 * q^29 - 120 * q^30 + 752 * q^31 + 64 * q^32 + 9 * q^33 + 12 * q^34 + 15 * q^35 - 72 * q^36 - 526 * q^37 + 14 * q^38 + 654 * q^39 - 80 * q^40 - 422 * q^41 - 18 * q^42 + 79 * q^43 - 12 * q^44 - 180 * q^45 + 232 * q^46 + 390 * q^47 + 96 * q^48 - 882 * q^49 - 200 * q^50 + 18 * q^51 + 436 * q^52 - 60 * q^53 - 108 * q^54 + 15 * q^55 - 48 * q^56 + 21 * q^57 - 1228 * q^58 - 209 * q^59 - 120 * q^60 - 944 * q^61 + 752 * q^62 - 27 * q^63 + 256 * q^64 + 1090 * q^65 - 18 * q^66 + 89 * q^67 + 48 * q^68 + 348 * q^69 - 30 * q^70 + 537 * q^71 + 144 * q^72 + 233 * q^73 - 526 * q^74 - 300 * q^75 + 32 * q^76 + 1452 * q^77 + 654 * q^78 - 1880 * q^79 + 160 * q^80 - 162 * q^81 + 844 * q^82 - 548 * q^83 - 72 * q^84 + 30 * q^85 - 158 * q^86 - 1842 * q^87 - 48 * q^88 - 699 * q^89 - 180 * q^90 - 77 * q^91 + 232 * q^92 + 1128 * q^93 + 1560 * q^94 + 35 * q^95 + 384 * q^96 - 422 * q^97 - 882 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

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