LMFDB - Embedded newform 207.4.o.a.11.51

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			11.51
Character	$\chi$	$=$	207.11
Dual form			207.4.o.a.113.51

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.85982 - 0.136230i) q^{2} +(-2.90453 - 4.30856i) q^{3} +(0.196263 - 0.0187409i) q^{4} +(-0.0350831 - 0.0334517i) q^{5} +(-8.89340 - 11.9260i) q^{6} +(4.71344 + 24.4557i) q^{7} +(-22.1127 + 3.17932i) q^{8} +(-10.1274 + 25.0287i) q^{9} +(-0.104889 - 0.0908867i) q^{10} +(-14.4660 + 7.45776i) q^{11} +(-0.650798 - 0.791178i) q^{12} +(87.7165 + 16.9060i) q^{13} +(16.8112 + 69.2968i) q^{14} +(-0.0422287 + 0.248319i) q^{15} +(-64.3540 + 12.4032i) q^{16} +(24.8521 + 54.4184i) q^{17} +(-25.5530 + 72.9573i) q^{18} +(34.6094 + 15.8056i) q^{19} +(-0.00751244 - 0.00590785i) q^{20} +(91.6784 - 91.3404i) q^{21} +(-40.3544 + 23.2986i) q^{22} +(-97.4342 - 51.7066i) q^{23} +(77.9253 + 86.0394i) q^{24} +(-5.94763 - 124.856i) q^{25} +(253.157 + 36.3985i) q^{26} +(137.253 - 29.0620i) q^{27} +(1.38340 + 4.71141i) q^{28} +(-22.8664 + 239.467i) q^{29} +(-0.0869382 + 0.715903i) q^{30} +(-149.614 + 117.658i) q^{31} +(-8.66879 + 2.10303i) q^{32} +(74.1493 + 40.6665i) q^{33} +(78.4860 + 152.242i) q^{34} +(0.652722 - 1.01565i) q^{35} +(-1.51858 + 5.10201i) q^{36} +(-105.841 + 360.462i) q^{37} +(101.130 + 40.4863i) q^{38} +(-181.935 - 427.036i) q^{39} +(0.882136 + 0.628166i) q^{40} +(-171.214 + 179.564i) q^{41} +(249.741 - 273.707i) q^{42} +(61.3107 - 77.9629i) q^{43} +(-2.69938 + 1.73479i) q^{44} +(1.19255 - 0.539306i) q^{45} +(-285.689 - 134.598i) q^{46} +(58.1359 + 33.5648i) q^{47} +(240.358 + 241.248i) q^{48} +(-257.433 + 103.061i) q^{49} +(-34.0183 - 356.256i) q^{50} +(162.282 - 265.137i) q^{51} +(17.5323 + 1.67414i) q^{52} +(-202.494 - 233.690i) q^{53} +(388.561 - 101.810i) q^{54} +(0.756989 + 0.222272i) q^{55} +(-181.979 - 525.795i) q^{56} +(-32.4247 - 195.024i) q^{57} +(-32.7711 + 687.950i) q^{58} +(-135.929 + 705.265i) q^{59} +(-0.00363423 + 0.0495273i) q^{60} +(300.776 - 751.302i) q^{61} +(-411.841 + 356.862i) q^{62} +(-659.829 - 129.701i) q^{63} +(478.564 - 140.519i) q^{64} +(-2.51184 - 3.52738i) q^{65} +(217.594 + 106.198i) q^{66} +(-105.702 + 205.033i) q^{67} +(5.89739 + 10.2146i) q^{68} +(60.2196 + 569.985i) q^{69} +(1.72831 - 2.99352i) q^{70} +(-262.688 - 408.751i) q^{71} +(144.370 - 585.650i) q^{72} +(269.534 - 590.196i) q^{73} +(-253.582 + 1045.28i) q^{74} +(-520.675 + 388.274i) q^{75} +(7.08875 + 2.45344i) q^{76} +(-250.569 - 318.625i) q^{77} +(-578.477 - 1196.46i) q^{78} +(-415.964 + 143.966i) q^{79} +(2.67265 + 1.71761i) q^{80} +(-523.871 - 506.952i) q^{81} +(-465.180 + 536.847i) q^{82} +(565.683 - 539.378i) q^{83} +(16.2813 - 19.6449i) q^{84} +(0.948501 - 2.74051i) q^{85} +(164.717 - 231.313i) q^{86} +(1098.18 - 597.019i) q^{87} +(296.172 - 210.903i) q^{88} +(-53.3400 + 370.988i) q^{89} +(3.33703 - 1.70478i) q^{90} +2224.85i q^{91} +(-20.0918 - 8.32210i) q^{92} +(941.493 + 302.880i) q^{93} +(170.831 + 88.0695i) q^{94} +(-0.685482 - 1.71225i) q^{95} +(34.2398 + 31.2417i) q^{96} +(1102.10 + 267.367i) q^{97} +(-722.174 + 329.806i) q^{98} +(-40.1545 - 437.594i) 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

)

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

$2$	2.85982	−	0.136230i	1.01110	−	0.0481647i	0.464513	−	0.885566i	$-0.346229\pi$
$2$	2.85982	−	0.136230i	1.01110	−	0.0481647i	0.546588	+	0.837402i	$0.315926\pi$
$3$	−2.90453	−	4.30856i	−0.558977	−	0.829183i
$3$	−2.90453	−	4.30856i	−0.558977	−	0.829183i
$4$	0.196263	−	0.0187409i	0.0245329	−	0.00234261i
$5$	−0.0350831	−	0.0334517i	−0.00313793	−	0.00299201i	0.688508	−	0.725228i	$-0.258266\pi$
$5$	−0.0350831	−	0.0334517i	−0.00313793	−	0.00299201i	−0.691646	+	0.722236i	$0.743114\pi$
$6$	−8.89340	−	11.9260i	−0.605119	−	0.811465i
$7$	4.71344	+	24.4557i	0.254502	+	1.32048i	0.854070	+	0.520158i	$0.174127\pi$
$7$	4.71344	+	24.4557i	0.254502	+	1.32048i	−0.599568	+	0.800324i	$0.704661\pi$
$8$	−22.1127	+	3.17932i	−0.977252	+	0.140508i
$9$	−10.1274	+	25.0287i	−0.375089	+	0.926989i
$10$	−0.104889	−	0.0908867i	−0.00331687	−	0.00287409i
$11$	−14.4660	+	7.45776i	−0.396516	+	0.204418i	−0.644940	−	0.764233i	$-0.723118\pi$
$11$	−14.4660	+	7.45776i	−0.396516	+	0.204418i	0.248424	+	0.968651i	$0.420087\pi$
$12$	−0.650798	−	0.791178i	−0.0156558	−	0.0190328i
$13$	87.7165	+	16.9060i	1.87140	+	0.360682i	0.993085	−	0.117402i	$-0.0374565\pi$
$13$	87.7165	+	16.9060i	1.87140	+	0.360682i	0.878314	+	0.478084i	$0.158669\pi$
$14$	16.8112	+	69.2968i	0.320928	+	1.32288i
$15$	−0.0422287	+	0.248319i	−0.000726894	+	0.00427439i
$16$	−64.3540	+	12.4032i	−1.00553	+	0.193800i
$17$	24.8521	+	54.4184i	0.354559	+	0.776377i	0.999922	+	0.0125004i	$0.00397910\pi$
$17$	24.8521	+	54.4184i	0.354559	+	0.776377i	−0.645362	+	0.763877i	$0.723294\pi$
$18$	−25.5530	+	72.9573i	−0.334605	+	0.955345i
$19$	34.6094	+	15.8056i	0.417891	+	0.190844i	0.613253	−	0.789887i	$-0.289861\pi$
$19$	34.6094	+	15.8056i	0.417891	+	0.190844i	−0.195362	+	0.980731i	$0.562588\pi$
$20$	−0.00751244	−	0.00590785i	−8.39917e−5	−	6.60518e-5i
$21$	91.6784	−	91.3404i	0.952661	−	0.949148i
$22$	−40.3544	+	23.2986i	−0.391072	+	0.225785i
$23$	−97.4342	−	51.7066i	−0.883324	−	0.468764i
$23$	−97.4342	−	51.7066i	−0.883324	−	0.468764i
$24$	77.9253	+	86.0394i	0.662768	+	0.731780i
$25$	−5.94763	−	124.856i	−0.0475810	−	0.998849i
$26$	253.157	+	36.3985i	1.90954	+	0.274551i
$27$	137.253	−	29.0620i	0.978310	−	0.207148i
$28$	1.38340	+	4.71141i	0.00933704	+	0.0317990i
$29$	−22.8664	+	239.467i	−0.146420	+	1.53338i	0.561732	+	0.827319i	$0.310135\pi$
$29$	−22.8664	+	239.467i	−0.146420	+	1.53338i	−0.708152	+	0.706060i	$0.750471\pi$
$30$	−0.0869382	+	0.715903i	−0.000529089	+	0.00435685i
$31$	−149.614	+	117.658i	−0.866821	+	0.681675i	−0.949114	−	0.314933i	$-0.898018\pi$
$31$	−149.614	+	117.658i	−0.866821	+	0.681675i	0.0822933	+	0.996608i	$0.473776\pi$
$32$	−8.66879	+	2.10303i	−0.0478888	+	0.0116177i
$33$	74.1493	+	40.6665i	0.391143	+	0.214519i
$34$	78.4860	+	152.242i	0.395889	+	0.767918i
$35$	0.652722	−	1.01565i	0.00315229	−	0.00490506i
$36$	−1.51858	+	5.10201i	−0.00703046	+	0.0236204i
$37$	−105.841	+	360.462i	−0.470276	+	1.60161i	0.293385	+	0.955994i	$0.405218\pi$
$37$	−105.841	+	360.462i	−0.470276	+	1.60161i	−0.763661	+	0.645618i	$0.776600\pi$
$38$	101.130	+	40.4863i	0.431722	+	0.172835i
$39$	−181.935	−	427.036i	−0.746997	−	1.75335i
$40$	0.882136	+	0.628166i	0.00348695	+	0.00248305i
$41$	−171.214	+	179.564i	−0.652174	+	0.683981i	−0.963922	−	0.266184i	$-0.914237\pi$
$41$	−171.214	+	179.564i	−0.652174	+	0.683981i	0.311748	+	0.950165i	$0.399086\pi$
$42$	249.741	−	273.707i	0.917521	−	1.00557i
$43$	61.3107	−	77.9629i	0.217437	−	0.276494i	−0.665082	−	0.746770i	$-0.731603\pi$
$43$	61.3107	−	77.9629i	0.217437	−	0.276494i	0.882519	+	0.470277i	$0.155846\pi$
$44$	−2.69938	+	1.73479i	−0.00924881	+	0.00594385i
$45$	1.19255	−	0.539306i	0.00395057	−	0.00178656i
$46$	−285.689	−	134.598i	−0.915707	−	0.431423i
$47$	58.1359	+	33.5648i	0.180425	+	0.104169i	0.587493	−	0.809230i	$-0.300115\pi$
$47$	58.1359	+	33.5648i	0.180425	+	0.104169i	−0.407067	+	0.913398i	$0.633448\pi$
$48$	240.358	+	241.248i	0.722765	+	0.725440i
$49$	−257.433	+	103.061i	−0.750534	+	0.300469i
$50$	−34.0183	−	356.256i	−0.0962184	−	1.00764i
$51$	162.282	−	265.137i	0.445568	−	0.727972i
$52$	17.5323	+	1.67414i	0.0467558	+	0.00446463i
$53$	−202.494	−	233.690i	−0.524804	−	0.605656i	0.430023	−	0.902818i	$-0.358505\pi$
$53$	−202.494	−	233.690i	−0.524804	−	0.605656i	−0.954827	+	0.297162i	$0.903960\pi$
$54$	388.561	−	101.810i	0.979192	−	0.256567i
$55$	0.756989	+	0.222272i	0.00185586	+	0.000544930i
$56$	−181.979	−	525.795i	−0.434250	−	1.25468i
$57$	−32.4247	−	195.024i	−0.0753465	−	0.453186i
$58$	−32.7711	+	687.950i	−0.0741906	+	1.55745i
$59$	−135.929	+	705.265i	−0.299939	+	1.55623i	0.448963	+	0.893550i	$0.351793\pi$
$59$	−135.929	+	705.265i	−0.299939	+	1.55623i	−0.748902	+	0.662681i	$0.769419\pi$
$60$	−0.00363423	+	0.0495273i	−7.81961e−6	+	0.000106566i
$61$	300.776	−	751.302i	0.631318	−	1.57696i	−0.174411	−	0.984673i	$-0.555802\pi$
$61$	300.776	−	751.302i	0.631318	−	1.57696i	0.805729	−	0.592284i	$-0.201774\pi$
$62$	−411.841	+	356.862i	−0.843610	+	0.730993i
$63$	−659.829	−	129.701i	−1.31953	−	0.259378i
$64$	478.564	−	140.519i	0.934696	−	0.274451i
$65$	−2.51184	−	3.52738i	−0.00479316	−	0.00673104i
$66$	217.594	+	106.198i	0.405817	+	0.198061i
$67$	−105.702	+	205.033i	−0.192740	+	0.373863i	−0.965326	−	0.261047i	$-0.915932\pi$
$67$	−105.702	+	205.033i	−0.192740	+	0.373863i	0.772586	+	0.634910i	$0.218963\pi$
$68$	5.89739	+	10.2146i	0.0105171	+	0.0182162i
$69$	60.2196	+	569.985i	0.105066	+	0.994465i
$70$	1.72831	−	2.99352i	0.00295103	−	0.00511134i
$71$	−262.688	−	408.751i	−0.439090	−	0.683237i	0.549223	−	0.835676i	$-0.314924\pi$
$71$	−262.688	−	408.751i	−0.439090	−	0.683237i	−0.988313	+	0.152439i	$0.951287\pi$
$72$	144.370	−	585.650i	0.236308	−	0.958604i
$73$	269.534	−	590.196i	0.432144	−	0.946263i	−0.560830	−	0.827931i	$-0.689518\pi$
$73$	269.534	−	590.196i	0.432144	−	0.946263i	0.992974	−	0.118332i	$-0.0377549\pi$
$74$	−253.582	+	1045.28i	−0.398355	+	1.64204i
$75$	−520.675	+	388.274i	−0.801632	+	0.597787i
$76$	7.08875	+	2.45344i	0.0106992	+	0.00370301i
$77$	−250.569	−	318.625i	−0.370845	−	0.471567i
$78$	−578.477	−	1196.46i	−0.839738	−	1.73683i
$79$	−415.964	+	143.966i	−0.592400	+	0.205032i	−0.606786	−	0.794865i	$-0.707542\pi$
$79$	−415.964	+	143.966i	−0.592400	+	0.205032i	0.0143865	+	0.999897i	$0.495420\pi$
$80$	2.67265	+	1.71761i	0.00373514	+	0.00240043i
$81$	−523.871	−	506.952i	−0.718616	−	0.695407i
$82$	−465.180	+	536.847i	−0.626470	+	0.722985i
$83$	565.683	−	539.378i	0.748094	−	0.713306i	−0.216722	−	0.976233i	$-0.569536\pi$
$83$	565.683	−	539.378i	0.748094	−	0.713306i	0.964816	+	0.262927i	$0.0846879\pi$
$84$	16.2813	−	19.6449i	0.0211480	−	0.0255171i
$85$	0.948501	−	2.74051i	0.00121035	−	0.00349706i
$86$	164.717	−	231.313i	0.206534	−	0.290036i
$87$	1098.18	−	597.019i	1.35330	−	0.735715i
$88$	296.172	−	210.903i	0.358773	−	0.255481i
$89$	−53.3400	+	370.988i	−0.0635284	+	0.441850i	0.933087	+	0.359649i	$0.117104\pi$
$89$	−53.3400	+	370.988i	−0.0635284	+	0.441850i	−0.996616	+	0.0822000i	$0.973805\pi$
$90$	3.33703	−	1.70478i	0.00390837	−	0.00199667i
$91$			2224.85i			2.56294i
$92$	−20.0918	−	8.32210i	−0.0227686	−	0.00943085i
$93$	941.493	+	302.880i	1.04977	+	0.337712i
$94$	170.831	+	88.0695i	0.187446	+	0.0966349i
$95$	−0.685482	−	1.71225i	−0.000740305	−	0.00184919i
$96$	34.2398	+	31.2417i	0.0364019	+	0.0332145i
$97$	1102.10	+	267.367i	1.15363	+	0.279866i	0.766552	−	0.642182i	$-0.221971\pi$
$97$	1102.10	+	267.367i	1.15363	+	0.279866i	0.387073	+	0.922049i	$0.373486\pi$
$98$	−722.174	+	329.806i	−0.744394	+	0.339953i
$99$	−40.1545	−	437.594i	−0.0407644	−	0.444241i
$100$	−3.50721	−	24.3932i	−0.00350721	−	0.0243932i
$101$	844.845	+	886.048i	0.832329	+	0.872921i	0.993480	−	0.114008i	$-0.0363691\pi$
$101$	844.845	+	886.048i	0.832329	+	0.872921i	−0.161151	+	0.986930i	$0.551521\pi$
$102$	427.977	−	780.352i	0.415452	−	0.757513i
$103$	1314.49	+	62.6170i	1.25748	+	0.0599013i	0.665715	−	0.746206i	$-0.268127\pi$
$103$	1314.49	+	62.6170i	1.25748	+	0.0599013i	0.591769	+	0.806108i	$0.298430\pi$
$104$	−1993.40	−	94.9572i	−1.87951	−	0.0895319i
$105$	−6.27186	+	0.137708i	−0.00582925	+	0.000127989i
$106$	−610.932	−	640.727i	−0.559801	−	0.587103i
$107$	−246.000	−	1710.97i	−0.222259	−	1.54584i	−0.729465	−	0.684019i	$-0.760231\pi$
$107$	−246.000	−	1710.97i	−0.222259	−	1.54584i	0.507206	−	0.861825i	$-0.330678\pi$
$108$	26.3931	−	8.27604i	0.0235155	−	0.00737372i
$109$	1397.79	−	638.348i	1.22829	−	0.560941i	0.307704	−	0.951482i	$-0.400439\pi$
$109$	1397.79	−	638.348i	1.22829	−	0.560941i	0.920586	+	0.390541i	$0.127712\pi$
$110$	2.19514	+	0.532534i	0.00190271	+	0.000461592i
$111$	1860.49	−	590.950i	1.59090	−	0.505320i
$112$	−606.658	−	1515.36i	−0.511820	−	1.27846i
$113$	−1183.59	−	610.184i	−0.985335	−	0.507976i	−0.111273	−	0.993790i	$-0.535493\pi$
$113$	−1183.59	−	610.184i	−0.985335	−	0.507976i	−0.874062	+	0.485814i	$0.838523\pi$
$114$	−119.297	−	553.318i	−0.0980105	−	0.454588i
$115$	1.68863	+	5.07337i	0.00136926	+	0.00411386i
$116$			47.4272i			0.0379612i
$117$	−1311.48	+	2024.22i	−1.03629	+	1.59948i
$118$	−292.654	+	2035.45i	−0.228313	+	1.58795i
$119$	−1213.70	+	864.272i	−0.934956	+	0.665779i
$120$	0.144303	−	5.62527i	0.000109775	−	0.00427929i
$121$	−618.408	+	868.432i	−0.464619	+	0.652466i
$122$	757.816	−	2189.57i	0.562373	−	1.62487i
$123$	1270.96	+	216.137i	0.931696	+	0.158442i
$124$	−27.1587	+	25.8957i	−0.0196687	+	0.0187541i
$125$	−7.93605	+	9.15869i	−0.00567858	+	0.00655343i
$126$	−1904.66	−	281.035i	−1.34667	−	0.198703i
$127$	1145.53	+	736.188i	0.800389	+	0.514379i	0.875743	−	0.482778i	$-0.160372\pi$
$127$	1145.53	+	736.188i	0.800389	+	0.514379i	−0.0753537	+	0.997157i	$0.524009\pi$
$128$	1416.90	−	490.395i	0.978420	−	0.338635i
$129$	−513.987	−	37.7154i	−0.350806	−	0.0257415i
$130$	−7.66395	−	9.74551i	−0.00517056	−	0.00657490i
$131$	−1459.08	−	504.994i	−0.973135	−	0.336805i	−0.206186	−	0.978513i	$-0.566105\pi$
$131$	−1459.08	−	504.994i	−0.973135	−	0.336805i	−0.766950	+	0.641707i	$0.778226\pi$
$132$	15.3149	+	6.59172i	0.0100984	+	0.00434648i
$133$	−223.406	+	920.894i	−0.145653	+	0.600388i
$134$	−274.358	+	600.759i	−0.176872	+	0.387296i
$135$	−5.78744	−	3.57176i	−0.00368966	−	0.00227710i
$136$	−722.560	−	1124.32i	−0.455581	−	0.708897i
$137$	1099.64	−	1904.63i	0.685755	−	1.18776i	−0.287444	−	0.957798i	$-0.592805\pi$
$137$	1099.64	−	1904.63i	0.685755	−	1.18776i	0.973199	−	0.229965i	$-0.0738612\pi$
$138$	249.867	+	1621.85i	0.154131	+	1.00044i
$139$	−506.582	−	877.426i	−0.309121	−	0.535412i	0.669050	−	0.743218i	$-0.266701\pi$
$139$	−506.582	−	877.426i	−0.309121	−	0.535412i	−0.978170	+	0.207805i	$0.933368\pi$
$140$	0.109071	−	0.211568i	6.58441e−5	−	0.000127720i
$141$	−24.2415	−	347.972i	−0.0144788	−	0.207834i
$142$	−806.927	−	1133.17i	−0.476872	−	0.669673i
$143$	−1394.99	+	409.606i	−0.815769	+	0.239531i
$144$	341.303	−	1736.31i	0.197513	−	1.00481i
$145$	8.81282	−	7.63635i	0.00504734	−	0.00437355i
$146$	690.416	−	1724.58i	0.391365	−	0.977582i
$147$	1191.77	+	809.824i	0.668675	+	0.454375i
$148$	−14.0174	+	72.7290i	−0.00778528	+	0.0403939i
$149$	−112.501	+	2361.69i	−0.0618554	+	1.29850i	0.728156	+	0.685412i	$0.240378\pi$
$149$	−112.501	+	2361.69i	−0.0618554	+	1.29850i	−0.790011	+	0.613093i	$0.789925\pi$
$150$	−1436.14	+	1181.33i	−0.781738	+	0.643033i
$151$	−8.75309	−	25.2904i	−0.00471733	−	0.0136298i	0.942618	−	0.333874i	$-0.108356\pi$
$151$	−8.75309	−	25.2904i	−0.00471733	−	0.0136298i	−0.947335	+	0.320245i	$0.896235\pi$
$152$	−815.557	−	239.469i	−0.435200	−	0.127786i
$153$	−1613.71	+	70.8968i	−0.852684	+	0.0374619i
$154$	−759.991	−	877.076i	−0.397674	−	0.458940i
$155$	9.18477	+	0.877040i	0.00475961	+	0.000454487i
$156$	−43.7101	−	80.4018i	−0.0224334	−	0.0412647i
$157$	95.9162	+	1004.48i	0.0487576	+	0.510613i	0.986555	+	0.163430i	$0.0522557\pi$
$157$	95.9162	+	1004.48i	0.0487576	+	0.510613i	−0.937797	+	0.347183i	$0.887138\pi$
$158$	−1169.97	+	468.386i	−0.589101	+	0.235840i
$159$	−418.719	+	1551.22i	−0.208847	+	0.773707i
$160$	0.374478	+	0.216205i	0.000185032	+	0.000106828i
$161$	805.269	−	2626.54i	0.394187	−	1.28571i
$162$	−1567.24	−	1378.43i	−0.760087	−	0.668515i
$163$	−1569.56	+	1008.69i	−0.754216	+	0.484705i	−0.860386	−	0.509643i	$-0.829777\pi$
$163$	−1569.56	+	1008.69i	−0.754216	+	0.484705i	0.106170	+	0.994348i	$0.466141\pi$
$164$	−30.2378	+	38.4505i	−0.0143974	+	0.0183078i
$165$	−1.24102	−	3.90713i	−0.000585537	−	0.00184345i
$166$	1544.28	−	1619.59i	0.722042	−	0.757256i
$167$	−264.318	−	188.220i	−0.122476	−	0.0872149i	0.517177	−	0.855878i	$-0.326983\pi$
$167$	−264.318	−	188.220i	−0.122476	−	0.0872149i	−0.639654	+	0.768663i	$0.720922\pi$
$168$	−1736.86	+	2311.26i	−0.797627	+	1.06141i
$169$	5368.75	+	2149.32i	2.44367	+	0.978299i
$170$	2.33921	−	7.96660i	0.00105535	−	0.00359418i
$171$	−746.096	+	706.158i	−0.333657	+	0.315797i
$172$	10.5719	−	16.4503i	0.00468665	−	0.00729256i
$173$	−629.398	−	1220.86i	−0.276602	−	0.536534i	0.709084	−	0.705124i	$-0.249109\pi$
$173$	−629.398	−	1220.86i	−0.276602	−	0.536534i	−0.985686	+	0.168590i	$0.946078\pi$
$174$	3059.26	−	1856.97i	1.33288	−	0.809063i
$175$	3025.41	−	733.955i	1.30685	−	0.317039i
$176$	838.447	−	659.362i	0.359093	−	0.282394i
$177$	3433.48	−	1462.81i	1.45806	−	0.621193i
$178$	−102.003	+	1068.23i	−0.0429520	+	0.449814i
$179$	−46.3805	−	157.958i	−0.0193667	−	0.0659570i	0.949243	−	0.314545i	$-0.101852\pi$
$179$	−46.3805	−	157.958i	−0.0193667	−	0.0659570i	−0.968609	+	0.248588i	$0.920034\pi$
$180$	0.223947	−	0.128195i	9.27336e−5	−	5.30840e-5i
$181$	2341.23	+	336.617i	0.961447	+	0.138235i	0.605127	−	0.796129i	$-0.293122\pi$
$181$	2341.23	+	336.617i	0.961447	+	0.138235i	0.356320	+	0.934364i	$0.384031\pi$
$182$	303.092	+	6362.68i	0.123443	+	2.59139i
$183$	−4110.64	+	886.267i	−1.66048	+	0.358004i
$184$	2318.92	+	833.596i	0.929094	+	0.333987i
$185$	15.7713	−	9.10558i	0.00626774	−	0.00361868i
$186$	2733.77	+	737.925i	1.07769	+	0.290899i
$187$	−765.350	−	601.878i	−0.299294	−	0.235367i
$188$	12.0390	+	5.49801i	0.00467038	+	0.00213289i
$189$	1357.67	+	3219.63i	0.522517	+	1.23912i
$190$	−2.19362	−	4.80336i	−0.000837589	−	0.00183406i
$191$	−1027.67	+	198.068i	−0.389319	+	0.0750350i	−0.380154	−	0.924923i	$-0.624129\pi$
$191$	−1027.67	+	198.068i	−0.389319	+	0.0750350i	−0.00916409	+	0.999958i	$0.502917\pi$
$192$	−1995.44	−	1653.78i	−0.750044	−	0.621622i
$193$	1074.09	+	4427.45i	0.400594	+	1.65127i	0.712883	+	0.701283i	$0.247389\pi$
$193$	1074.09	+	4427.45i	0.400594	+	1.65127i	−0.312290	+	0.949987i	$0.601096\pi$
$194$	3188.25	+	614.484i	1.17991	+	0.227409i
$195$	−7.90224	+	21.0678i	−0.00290201	+	0.00773690i
$196$	−48.5932	+	25.0515i	−0.0177089	+	0.00912957i
$197$	2270.78	+	1967.64i	0.821249	+	0.711617i	0.960391	−	0.278656i	$-0.0898889\pi$
$197$	2270.78	+	1967.64i	0.821249	+	0.711617i	−0.139142	+	0.990272i	$0.544434\pi$
$198$	−174.448	−	1245.97i	−0.0626136	−	0.447209i
$199$	−1633.79	+	234.903i	−0.581991	+	0.0836777i	−0.427021	−	0.904242i	$-0.640437\pi$
$199$	−1633.79	+	234.903i	−0.581991	+	0.0836777i	−0.154970	+	0.987919i	$0.549528\pi$
$200$	528.476	+	2741.99i	0.186844	+	0.969441i
$201$	1190.41	−	140.102i	0.417738	−	0.0491642i
$202$	2536.82	+	2418.85i	0.883612	+	0.842523i
$203$	−5964.12	+	569.504i	−2.06206	+	0.196903i
$204$	26.8810	−	55.0778i	0.00922572	−	0.0189030i
$205$	12.0135	−	0.572272i	0.00409296	−	0.000194972i
$206$	3767.75			1.27433
$207$	2280.91	−	1915.00i	0.765864	−	0.643002i
$208$	−5854.60			−1.95165
$209$	−618.534	+	29.4644i	−0.204712	+	0.00975166i
$210$	−17.9177	+	1.24824i	−0.00588779	+	0.000410174i
$211$	−1036.76	+	98.9983i	−0.338262	+	0.0323001i	−0.262805	−	0.964849i	$-0.584648\pi$
$211$	−1036.76	+	98.9983i	−0.338262	+	0.0323001i	−0.0754571	+	0.997149i	$0.524042\pi$
$212$	−44.1216	−	42.0698i	−0.0142938	−	0.0136291i
$213$	−998.143	+	2319.04i	−0.321087	+	0.746000i
$214$	−936.601	−	4859.55i	−0.299181	−	1.55230i
$215$	−4.75897	+	0.684236i	−0.00150958	+	0.000217044i
$216$	−2942.64	+	1079.01i	−0.926949	+	0.339895i
$217$	−3582.59	−	3104.33i	−1.12075	−	0.971134i
$218$	3910.46	−	2015.98i	1.21491	−	0.626328i
$219$	−3325.76	+	552.940i	−1.02618	+	0.170613i
$220$	0.152735	+	0.0294372i	4.68062e−5	+	9.02116e-6i
$221$	1259.94	+	5193.54i	0.383496	+	1.58079i
$222$	5240.18	−	1943.47i	1.58423	−	0.587555i
$223$	3071.56	−	591.994i	0.922362	−	0.177771i	0.294102	−	0.955774i	$-0.404980\pi$
$223$	3071.56	−	591.994i	0.922362	−	0.177771i	0.628260	+	0.778003i	$0.283767\pi$
$224$	−92.2908	−	202.089i	−0.0275287	−	0.0602795i
$225$	3185.22	+	1115.61i	0.943768	+	0.330550i
$226$	−3467.99	−	1583.78i	−1.02074	−	0.466156i
$227$	−2824.21	−	2220.98i	−0.825767	−	0.649391i	0.113133	−	0.993580i	$-0.463911\pi$
$227$	−2824.21	−	2220.98i	−0.825767	−	0.649391i	−0.938900	+	0.344189i	$0.888154\pi$
$228$	−10.0187	−	37.6684i	−0.00291010	−	0.0109415i
$229$	−1446.58	+	835.183i	−0.417435	+	0.241006i	−0.693979	−	0.719995i	$-0.744144\pi$
$229$	−1446.58	+	835.183i	−0.417435	+	0.241006i	0.276544	+	0.961001i	$0.410811\pi$
$230$	5.52032	+	14.2789i	0.00158260	+	0.00409358i
$231$	−645.029	+	2005.05i	−0.183722	+	0.571093i
$232$	−255.708	−	5367.97i	−0.0723622	−	1.51907i
$233$	3528.57	+	507.331i	0.992121	+	0.142645i	0.619213	−	0.785223i	$-0.287452\pi$
$233$	3528.57	+	507.331i	0.992121	+	0.142645i	0.372908	+	0.927868i	$0.378361\pi$
$234$	−3474.83	+	5967.56i	−0.970756	+	1.66714i
$235$	−0.916791	−	3.12230i	−0.000254489	−	0.000866709i
$236$	−13.4605	+	140.965i	−0.00371273	+	0.0388815i
$237$	1828.47	+	1374.05i	0.501147	+	0.376600i
$238$	−3353.23	+	2637.01i	−0.913267	+	0.718201i
$239$	4504.81	−	1092.86i	1.21921	−	0.295778i	0.426001	−	0.904723i	$-0.359922\pi$
$239$	4504.81	−	1092.86i	1.21921	−	0.295778i	0.793213	+	0.608945i	$0.208407\pi$
$240$	−0.362372	−	16.5041i	−9.74624e−5	−	0.00443890i
$241$	−1304.87	−	2531.09i	−0.348771	−	0.676522i	0.647568	−	0.762007i	$-0.275786\pi$
$241$	−1304.87	−	2531.09i	−0.348771	−	0.676522i	−0.996339	+	0.0854858i	$0.972756\pi$
$242$	−1650.23	+	2567.81i	−0.438351	+	0.682087i
$243$	−662.635	+	3729.59i	−0.174930	+	0.984581i
$244$	44.9512	−	153.090i	0.0117939	−	0.0401662i
$245$	12.4791	+	4.99589i	0.00325413	+	0.00130276i
$246$	3664.17	+	444.971i	0.949670	+	0.115326i
$247$	2768.60	+	1971.51i	0.713207	+	0.507872i
$248$	2934.29	−	3077.40i	0.751321	−	0.787963i
$249$	−3966.99	−	870.642i	−1.00963	−	0.221585i
$250$	−21.4480	+	27.2734i	−0.00542597	+	0.00689968i
$251$	4756.71	−	3056.95i	1.19618	−	0.768738i	0.217888	−	0.975974i	$-0.430083\pi$
$251$	4756.71	−	3056.95i	1.19618	−	0.768738i	0.978291	+	0.207236i	$0.0664468\pi$
$252$	−131.931	−	13.0898i	−0.0329796	−	0.00327215i
$253$	1795.10	+	21.3483i	0.446076	+	0.00530498i
$254$	3376.31	+	1949.31i	0.834049	+	0.481538i
$255$	−14.5626	+	3.87323i	−0.00357626	+	0.000951180i
$256$	280.970	−	112.483i	0.0685961	−	0.0274617i
$257$	−85.0797	−	890.995i	−0.0206503	−	0.216260i	−0.999907	−	0.0136362i	$-0.995659\pi$
$257$	−85.0797	−	890.995i	−0.0206503	−	0.216260i	0.979257	−	0.202623i	$-0.0649467\pi$
$258$	−1475.05	−	37.8389i	−0.355940	−	0.00913080i
$259$	−9314.23	−	889.401i	−2.23459	−	0.213377i
$260$	−0.559087	−	0.645221i	−0.000133358	−	0.000153904i
$261$	−5761.98	−	2997.50i	−1.36650	−	0.710884i
$262$	−4241.52	−	1245.42i	−1.00016	−	0.293673i
$263$	762.015	+	2201.70i	0.178661	+	0.516207i	0.998401	−	0.0565288i	$-0.0180033\pi$
$263$	762.015	+	2201.70i	0.178661	+	0.516207i	−0.819740	+	0.572736i	$0.805882\pi$
$264$	−1768.93	−	663.501i	−0.412387	−	0.154681i
$265$	−0.713220	+	14.9723i	−0.000165331	+	0.00347073i
$266$	−513.450	+	2664.03i	−0.118352	+	0.614068i
$267$	1753.35	−	847.726i	0.401885	−	0.194307i
$268$	−16.9029	+	42.2214i	−0.00385265	+	0.00962345i
$269$	1343.05	−	1163.76i	0.304413	−	0.263775i	−0.489236	−	0.872151i	$-0.662724\pi$
$269$	1343.05	−	1163.76i	0.304413	−	0.263775i	0.793649	+	0.608376i	$0.208179\pi$
$270$	−17.0377	−	9.42619i	−0.00384029	−	0.00212467i
$271$	−661.062	+	194.105i	−0.148180	+	0.0435094i	−0.354981	−	0.934873i	$-0.615513\pi$
$271$	−661.062	+	194.105i	−0.148180	+	0.0435094i	0.206802	+	0.978383i	$0.433695\pi$
$272$	−2274.29	−	3193.80i	−0.506983	−	0.711958i
$273$	9585.91	−	6462.15i	2.12515	−	1.43263i
$274$	2885.30	−	5596.71i	0.636159	−	1.23398i
$275$	1017.19	+	1761.82i	0.223049	+	0.386333i
$276$	22.5009	+	110.738i	0.00490722	+	0.0241510i
$277$	1122.09	−	1943.52i	0.243393	−	0.421569i	−0.718286	−	0.695748i	$-0.755073\pi$
$277$	1122.09	−	1943.52i	0.243393	−	0.421569i	0.961679	+	0.274179i	$0.0884062\pi$
$278$	−1568.27	−	2440.27i	−0.338340	−	0.526467i
$279$	−1429.62	−	4936.21i	−0.306770	−	1.05922i
$280$	−11.2043	+	24.5341i	−0.00239138	+	0.00523640i
$281$	−1109.79	+	4574.61i	−0.235603	+	0.971169i	0.723997	+	0.689803i	$0.242303\pi$
$281$	−1109.79	+	4574.61i	−0.235603	+	0.971169i	−0.959600	+	0.281367i	$0.909212\pi$
$282$	−116.731	−	991.837i	−0.0246497	−	0.209443i
$283$	−7409.38	−	2564.41i	−1.55633	−	0.538652i	−0.592594	−	0.805502i	$-0.701896\pi$
$283$	−7409.38	−	2564.41i	−1.55633	−	0.538652i	−0.963738	+	0.266850i	$0.914017\pi$
$284$	−59.2164	−	75.2997i	−0.0123727	−	0.0157332i
$285$	−5.38634	+	7.92673i	−0.00111951	+	0.00164750i
$286$	−3933.63	+	1361.44i	−0.813288	+	0.281482i
$287$	−5198.37	−	3340.79i	−1.06916	−	0.687110i
$288$	35.1564	−	238.267i	0.00719310	−	0.0487500i
$289$	873.591	−	1008.18i	0.177812	−	0.205206i
$290$	24.1628	−	23.0392i	0.00489272	−	0.00466520i
$291$	−2049.12	−	5525.06i	−0.412789	−	1.11301i
$292$	41.8387	−	120.885i	0.00838502	−	0.0242269i
$293$	−1407.95	+	1977.19i	−0.280728	+	0.394227i	−0.930731	−	0.365704i	$-0.880828\pi$
$293$	−1407.95	+	1977.19i	−0.280728	+	0.394227i	0.650003	+	0.759932i	$0.274768\pi$
$294$	3518.56	+	2153.60i	0.697982	+	0.427213i
$295$	28.3611	−	20.1959i	0.00559745	−	0.00398593i
$296$	1194.41	−	8307.29i	0.234539	−	1.63126i
$297$	−1768.77	+	1444.01i	−0.345571	+	0.282121i
$298$			6769.34i			1.31590i
$299$	−7672.44	−	6182.74i	−1.48398	−	1.19584i
$300$	−94.9127	+	85.9617i	−0.0182660	+	0.0165433i
$301$	2195.62	+	1131.92i	0.420443	+	0.216754i
$302$	−28.4776	−	71.1336i	−0.00542617	−	0.0135539i
$303$	1363.72	−	6213.62i	0.258559	−	1.17810i
$304$	−2423.29	−	587.884i	−0.457188	−	0.110913i
$305$	−35.6845	+	16.2966i	−0.00669931	+	0.00305947i
$306$	−4605.27	+	422.588i	−0.860345	+	0.0789469i
$307$	−273.138	−	1899.72i	−0.0507780	−	0.353169i	−0.999332	−	0.0365524i	$-0.988362\pi$
$307$	−273.138	−	1899.72i	−0.0507780	−	0.353169i	0.948554	−	0.316616i	$-0.102547\pi$
$308$	−55.1488	−	57.8384i	−0.0102026	−	0.0107002i
$309$	−3548.19	−	5845.45i	−0.653235	−	1.07617i
$310$	26.3863	+	1.25694i	0.00483433	+	0.000230288i
$311$	8552.16	+	407.390i	1.55932	+	0.0742796i	0.809404	−	0.587252i	$-0.199790\pi$
$311$	8552.16	+	407.390i	1.55932	+	0.0742796i	0.749917	+	0.661532i	$0.230093\pi$
$312$	5380.75	+	8864.48i	0.976362	+	1.60850i
$313$	−3819.41	−	4005.68i	−0.689730	−	0.723368i	0.282012	−	0.959411i	$-0.408998\pi$
$313$	−3819.41	−	4005.68i	−0.689730	−	0.723368i	−0.971743	+	0.236042i	$0.924150\pi$
$314$	411.144	+	2859.57i	0.0738924	+	0.513933i
$315$	18.8101	+	26.6227i	0.00336454	+	0.00476197i
$316$	−78.9403	+	36.0508i	−0.0140530	+	0.00641778i
$317$	529.456	+	128.445i	0.0938083	+	0.0227576i	0.282388	−	0.959300i	$-0.408873\pi$
$317$	529.456	+	128.445i	0.0938083	+	0.0227576i	−0.188580	+	0.982058i	$0.560388\pi$
$318$	−986.141	+	4493.25i	−0.173900	+	0.792355i
$319$	−1455.10	−	3634.68i	−0.255393	−	0.637940i
$320$	−21.4901	−	11.0789i	−0.00375417	−	0.00193541i
$321$	−6657.29	+	6029.45i	−1.15755	+	1.04838i
$322$	1945.11	−	7621.13i	0.336636	−	1.31897i
$323$			2276.19i			0.392107i
$324$	−112.317	−	89.6782i	−0.0192588	−	0.0153769i
$325$	1589.11	−	11052.5i	0.271224	−	1.88641i
$326$	−4351.24	+	3098.51i	−0.739242	+	0.526412i
$327$	−6810.27	−	4168.35i	−1.15171	−	0.704924i
$328$	3215.11	−	4514.99i	0.541234	−	0.760057i
$329$	−546.829	+	1579.96i	−0.0916342	+	0.264760i
$330$	−4.08138	−	11.0046i	−0.000680826	−	0.00183571i
$331$	2372.21	−	2261.90i	0.393924	−	0.375605i	−0.467071	−	0.884220i	$-0.654691\pi$
$331$	2372.21	−	2261.90i	0.393924	−	0.375605i	0.860994	+	0.508615i	$0.169842\pi$
$332$	100.914	−	116.461i	0.0166819	−	0.0192520i
$333$	−7950.01	−	6299.62i	−1.30828	−	1.03669i
$334$	−781.544	−	502.268i	−0.128036	−	0.0822840i
$335$	10.5671	−	3.65730i	0.00172341	−	0.000596477i
$336$	−4766.96	+	7015.23i	−0.773985	+	1.13902i
$337$	6739.37	+	8569.80i	1.08937	+	1.38524i	0.916376	+	0.400320i	$0.131101\pi$
$337$	6739.37	+	8569.80i	1.08937	+	1.38524i	0.172992	+	0.984923i	$0.444657\pi$
$338$	15646.5	+	5415.30i	2.51792	+	0.871460i
$339$	808.762	+	6871.87i	0.129575	+	1.10097i
$340$	0.134796	−	0.555638i	2.15010e−5	−	8.86285e-5i
$341$	1286.86	−	2817.82i	0.204361	−	0.447489i
$342$	−2037.50	+	2121.13i	−0.322151	+	0.335373i
$343$	884.702	+	1376.62i	0.139269	+	0.216707i
$344$	−1107.87	+	1918.90i	−0.173641	+	0.300756i
$345$	16.9543	−	22.0113i	0.00264576	−	0.00343492i
$346$	−1966.28	−	3405.71i	−0.305515	−	0.529167i
$347$	670.178	−	1299.96i	0.103680	−	0.201111i	−0.831289	−	0.555840i	$-0.812397\pi$
$347$	670.178	−	1299.96i	0.103680	−	0.201111i	0.934969	+	0.354729i	$0.115427\pi$
$348$	204.343	−	137.754i	0.0314768	−	0.0212194i
$349$	3297.66	+	4630.91i	0.505786	+	0.710278i	0.985976	−	0.166887i	$-0.0533715\pi$
$349$	3297.66	+	4630.91i	0.505786	+	0.710278i	−0.480190	+	0.877165i	$0.659432\pi$
$350$	8552.14	−	2511.14i	1.30609	−	0.383502i
$351$	12530.7	−	228.821i	1.90552	−	0.0347964i
$352$	109.719	−	95.0722i	0.0166138	−	0.0143959i
$353$	168.569	−	421.065i	0.0254165	−	0.0634873i	−0.915117	−	0.403189i	$-0.867902\pi$
$353$	168.569	−	421.065i	0.0254165	−	0.0634873i	0.940533	+	0.339701i	$0.110326\pi$
$354$	9619.89	−	4651.11i	1.44433	−	0.698316i
$355$	−4.45749	+	23.1276i	−0.000666420	+	0.00345771i
$356$	−3.51604	+	73.8108i	−0.000523455	+	0.0109887i
$357$	7249.00	+	2719.00i	1.07467	+	0.403094i
$358$	−154.159	−	445.413i	−0.0227585	−	0.0657564i
$359$	−8999.13	−	2642.38i	−1.32300	−	0.388467i	−0.457424	−	0.889249i	$-0.651228\pi$
$359$	−8999.13	−	2642.38i	−1.32300	−	0.388467i	−0.865574	+	0.500782i	$0.833046\pi$
$360$	−24.6559	+	15.7170i	−0.00360967	+	0.00230100i
$361$	−3543.70	−	4089.65i	−0.516649	−	0.596245i
$362$	6741.35	+	643.721i	0.978778	+	0.0934620i
$363$	5537.88	+	142.061i	0.800725	+	0.0205407i
$364$	41.6956	+	436.656i	0.00600397	+	0.0628764i
$365$	−29.1992	+	11.6896i	−0.00418727	+	0.00167633i
$366$	−11635.0	+	3094.56i	−1.66167	+	0.441955i
$367$	7032.82	+	4060.40i	1.00030	+	0.577524i	0.908337	−	0.418239i	$-0.137352\pi$
$367$	7032.82	+	4060.40i	1.00030	+	0.577524i	0.0919634	+	0.995762i	$0.470686\pi$
$368$	6911.61	+	2119.03i	0.979056	+	0.300168i
$369$	−2760.30	−	6103.79i	−0.389419	−	0.861112i
$370$	43.8628	−	28.1889i	0.00616302	−	0.00396073i
$371$	4760.60	−	6053.60i	0.666195	−	0.847135i
$372$	190.457	+	41.7999i	0.0265449	+	0.00582587i
$373$	352.386	−	369.572i	0.0489166	−	0.0513022i	−0.698821	−	0.715297i	$-0.746292\pi$
$373$	352.386	−	369.572i	0.0489166	−	0.0513022i	0.747738	+	0.663994i	$0.231140\pi$
$374$	−2270.76	−	1617.00i	−0.313953	−	0.223565i
$375$	62.5113	+	7.59128i	0.00860818	+	0.00104536i
$376$	−1392.25	−	557.375i	−0.190958	−	0.0764479i
$377$	−6054.19	+	20618.7i	−0.827073	+	2.81675i
$378$	4321.30	+	9022.63i	0.587999	+	1.22771i
$379$	−3081.92	+	4795.56i	−0.417698	+	0.649952i	−0.984799	−	0.173697i	$-0.944429\pi$
$379$	−3081.92	+	4795.56i	−0.417698	+	0.649952i	0.567101	+	0.823648i	$0.308065\pi$
$380$	−0.166624	−	0.323205i	−2.24938e−5	−	4.36318e-5i
$381$	−155.317	−	7073.87i	−0.0208848	−	0.951195i
$382$	−2911.98	+	706.440i	−0.390026	+	0.0946193i
$383$	−1370.75	+	1077.97i	−0.182877	+	0.143816i	−0.705401	−	0.708809i	$-0.749233\pi$
$383$	−1370.75	+	1077.97i	−0.182877	+	0.143816i	0.522524	+	0.852625i	$0.324991\pi$
$384$	−6228.34	−	4680.45i	−0.827704	−	0.622001i
$385$	−1.86779	+	19.5603i	−0.000247250	+	0.00258932i
$386$	3674.86	+	12515.4i	0.484573	+	1.65031i
$387$	1330.39	+	2324.09i	0.174748	+	0.305272i
$388$	221.313	+	31.8200i	0.0289574	+	0.00416344i
$389$	−402.343	−	8446.22i	−0.0524411	−	1.10088i	−0.859740	−	0.510732i	$-0.829374\pi$
$389$	−402.343	−	8446.22i	−0.0524411	−	1.10088i	0.807299	−	0.590143i	$-0.200929\pi$
$390$	−19.7289	+	61.3267i	−0.00256157	+	0.00796256i
$391$	392.350	−	6587.23i	0.0507468	−	0.851997i
$392$	5364.87	−	3097.41i	0.691243	−	0.399089i
$393$	2062.16	+	7753.32i	0.264687	+	0.995174i
$394$	6762.08	+	5317.75i	0.864641	+	0.679961i
$395$	19.4092	+	8.86391i	0.00247237	+	0.00112909i
$396$	−16.0817	−	85.1310i	−0.00204075	−	0.0108030i
$397$	1642.83	+	3597.29i	0.207685	+	0.454768i	0.984596	−	0.174843i	$-0.0559417\pi$
$397$	1642.83	+	3597.29i	0.207685	+	0.454768i	−0.776911	+	0.629611i	$0.783214\pi$
$398$	−4640.35	+	894.354i	−0.584421	+	0.112638i
$399$	4616.62	−	1712.20i	0.579248	−	0.214830i
$400$	1931.37	+	7961.22i	0.241421	+	0.995152i
$401$	−13325.6	−	2568.30i	−1.65948	−	0.319838i	−0.728535	−	0.685009i	$-0.759798\pi$
$401$	−13325.6	−	2568.30i	−1.65948	−	0.319838i	−0.930940	+	0.365171i	$0.881010\pi$
$402$	3385.29	−	562.837i	0.420007	−	0.0698302i
$403$	−15112.7	+	7791.15i	−1.86804	+	0.963039i
$404$	182.417	+	158.065i	0.0224643	+	0.0194655i
$405$	1.42064	+	35.3099i	0.000174301	+	0.00433225i
$406$	−16978.7	+	2441.17i	−2.07547	+	0.298408i
$407$	−1157.14	−	6003.80i	−0.140927	−	0.731198i
$408$	−2745.53	+	6378.83i	−0.333147	+	0.774017i
$409$	8128.62	+	7750.63i	0.982725	+	0.937027i	0.998023	−	0.0628565i	$-0.0200210\pi$
$409$	8128.62	+	7750.63i	0.982725	+	0.937027i	−0.0152974	+	0.999883i	$0.504870\pi$
$410$	34.2784	−	3.27319i	0.00412900	−	0.000394272i
$411$	−11400.1	+	794.193i	−1.36819	+	0.0953155i
$412$	259.160	−	12.3453i	0.0309900	−	0.00147624i
$413$	−17888.4			−2.13131
$414$	6262.11	−	5787.28i	0.743396	−	0.687028i
$415$	−37.8891			−0.00448169
$416$	−795.950	+	37.9158i	−0.0938093	+	0.00446869i
$417$	−2309.06	+	4731.15i	−0.271164	+	0.555601i
$418$	−1764.89	+	168.526i	−0.206515	+	0.0197198i
$419$	−2090.66	−	1993.44i	−0.243760	−	0.232425i	0.558343	−	0.829610i	$-0.311437\pi$
$419$	−2090.66	−	1993.44i	−0.243760	−	0.232425i	−0.802103	+	0.597185i	$0.796286\pi$
$420$	−1.22835	+	0.144567i	−0.000142708	+	1.67956e-5i
$421$	−510.598	−	2649.23i	−0.0591093	−	0.306688i	0.940327	−	0.340273i	$-0.110520\pi$
$421$	−510.598	−	2649.23i	−0.0591093	−	0.306688i	−0.999436	+	0.0335851i	$0.989308\pi$
$422$	−2951.46	+	424.356i	−0.340461	+	0.0489510i
$423$	−1428.85	+	1115.14i	−0.164239	+	0.128180i
$424$	5220.65	+	4523.72i	0.597965	+	0.518140i
$425$	6646.66	−	3426.59i	0.758613	−	0.391092i
$426$	−2538.59	+	6768.02i	−0.288721	+	0.769746i
$427$	19791.3	+	3814.46i	2.24302	+	0.432306i
$428$	−80.3456	−	331.189i	−0.00907395	−	0.0374033i
$429$	5816.61	+	4820.69i	0.654612	+	0.542529i
$430$	−13.5166	+	2.60511i	−0.00151588	+	0.000292162i
$431$	1546.47	+	3386.30i	0.172833	+	0.378451i	0.976149	−	0.217102i	$-0.0696604\pi$
$431$	1546.47	+	3386.30i	0.172833	+	0.378451i	−0.803316	+	0.595553i	$0.796933\pi$
$432$	−8472.32	+	3572.64i	−0.943576	+	0.397890i
$433$	4387.56	+	2003.73i	0.486958	+	0.222386i	0.643736	−	0.765248i	$-0.277383\pi$
$433$	4387.56	+	2003.73i	0.486958	+	0.222386i	−0.156778	+	0.987634i	$0.550111\pi$
$434$	−10668.5	−	8389.80i	−1.17996	−	0.927933i
$435$	−58.4988	−	15.7906i	−0.00644782	−	0.00174046i
$436$	262.371	−	151.480i	0.0288194	−	0.0166389i
$437$	−2554.88	−	3329.53i	−0.279672	−	0.364470i
$438$	−9435.78	+	2034.38i	−1.02936	+	0.221933i
$439$	−379.527	−	7967.26i	−0.0412616	−	0.866188i	−0.920723	−	0.390217i	$-0.872400\pi$
$439$	−379.527	−	7967.26i	−0.0412616	−	0.866188i	0.879461	−	0.475971i	$-0.157903\pi$
$440$	−17.4457	−	2.50832i	−0.00189021	−	0.000271771i
$441$	27.6576	−	7486.95i	0.00298646	−	0.808439i
$442$	4310.72	+	14681.0i	0.463892	+	1.57987i
$443$	−340.030	+	3560.96i	−0.0364680	+	0.381910i	0.958751	+	0.284246i	$0.0917432\pi$
$443$	−340.030	+	3560.96i	−0.0364680	+	0.381910i	−0.995219	+	0.0976641i	$0.968863\pi$
$444$	354.071	−	150.849i	0.0378457	−	0.0161238i
$445$	14.2815	−	11.2311i	0.00152137	−	0.00119642i
$446$	8703.47	−	2111.44i	0.924038	−	0.224169i
$447$	10502.2	−	6374.88i	1.11127	−	0.674545i
$448$	5692.18	+	11041.3i	0.600290	+	1.16440i
$449$	2857.14	−	4445.80i	0.300305	−	0.467284i	−0.658005	−	0.753013i	$-0.728600\pi$
$449$	2857.14	−	4445.80i	0.300305	−	0.467284i	0.958310	+	0.285730i	$0.0922359\pi$
$450$	9261.15	+	2756.52i	0.970166	+	0.288763i
$451$	1137.64	−	3874.46i	0.118779	−	0.404526i
$452$	−243.731	−	97.5751i	−0.0253631	−	0.0101539i
$453$	−83.5416	+	111.170i	−0.00866474	+	0.0115303i
$454$	−8379.30	−	5966.87i	−0.866212	−	0.616827i
$455$	74.4251	−	78.0548i	0.00766836	−	0.00804234i
$456$	1337.04	+	4209.42i	0.137309	+	0.432290i
$457$	3865.07	−	4914.84i	0.395625	−	0.503078i	−0.546908	−	0.837193i	$-0.684195\pi$
$457$	3865.07	−	4914.84i	0.395625	−	0.503078i	0.942532	+	0.334115i	$0.108438\pi$
$458$	−4023.19	+	2585.55i	−0.410461	+	0.263787i
$459$	4992.53	+	6746.84i	0.507694	+	0.686091i
$460$	0.426494	+	0.964070i	4.32291e−5	+	9.77173e-5i
$461$	4184.51	+	2415.93i	0.422759	+	0.244080i	0.696257	−	0.717792i	$-0.254847\pi$
$461$	4184.51	+	2415.93i	0.422759	+	0.244080i	−0.273498	+	0.961873i	$0.588181\pi$
$462$	−1571.52	+	5821.96i	−0.158255	+	0.586282i
$463$	8726.04	−	3493.38i	0.875883	−	0.350650i	0.110231	−	0.993906i	$-0.464841\pi$
$463$	8726.04	−	3493.38i	0.875883	−	0.350650i	0.765652	+	0.643256i	$0.222417\pi$
$464$	−1498.62	−	15694.3i	−0.149939	−	1.57024i
$465$	−22.8987	−	42.1206i	−0.00228366	−	0.00420063i
$466$	10160.2	+	970.181i	1.01000	+	0.0964437i
$467$	7217.71	+	8329.68i	0.715194	+	0.825378i	0.990720	−	0.135915i	$-0.0433975\pi$
$467$	7217.71	+	8329.68i	0.715194	+	0.825378i	−0.275526	+	0.961294i	$0.588852\pi$
$468$	−219.459	+	421.857i	−0.0216763	+	0.0416674i
$469$	−5512.45	−	1618.60i	−0.542732	−	0.159360i
$470$	−3.04721	−	8.80435i	−0.000299059	−	0.000864073i
$471$	4049.27	−	3330.80i	0.396137	−	0.325850i
$472$	763.482	−	16027.4i	0.0744536	−	1.56297i
$473$	−305.494	+	1585.05i	−0.0296969	+	0.154082i
$474$	5416.29	+	3680.45i	0.524849	+	0.356643i
$475$	1767.58	−	4415.19i	0.170741	−	0.426491i
$476$	−222.007	+	192.371i	−0.0213775	+	0.0185237i
$477$	7899.69	−	2701.47i	0.758285	−	0.259312i
$478$	12734.1	−	3739.07i	1.21850	−	0.357784i
$479$	−3419.30	−	4801.74i	−0.326162	−	0.458031i	0.618639	−	0.785676i	$-0.287685\pi$
$479$	−3419.30	−	4801.74i	−0.326162	−	0.458031i	−0.944801	+	0.327645i	$0.893745\pi$
$480$	−0.156150	−	2.24144i	−1.48484e−5	−	0.000213140i
$481$	−15378.0	+	29829.2i	−1.45775	+	2.82763i
$482$	−4076.50	−	7060.71i	−0.385227	−	0.667233i
$483$	−13655.5	+	4159.30i	−1.28643	+	0.391832i
$484$	−105.095	+	182.031i	−0.00986997	+	0.0170953i
$485$	−29.7214	−	46.2473i	−0.00278263	−	0.00432986i
$486$	−1386.94	+	10756.2i	−0.129450	+	1.00394i
$487$	−4875.30	+	10675.4i	−0.453637	+	0.993326i	0.535255	+	0.844690i	$0.320215\pi$
$487$	−4875.30	+	10675.4i	−0.453637	+	0.993326i	−0.988892	+	0.148636i	$0.952512\pi$
$488$	−4262.33	+	17569.6i	−0.395382	+	1.62979i
$489$	8904.84	+	3832.75i	0.823498	+	0.354444i
$490$	36.3687	+	12.5873i	0.00335300	+	0.00116048i
$491$	−735.054	−	934.697i	−0.0675611	−	0.0859110i	0.751098	−	0.660191i	$-0.229525\pi$
$491$	−735.054	−	934.697i	−0.0675611	−	0.0859110i	−0.818659	+	0.574280i	$0.805282\pi$
$492$	253.493	+	18.6009i	0.0232284	+	0.00170445i
$493$	−13599.7	+	4706.91i	−1.24239	+	0.429997i
$494$	8186.30	+	5261.02i	0.745585	+	0.479158i
$495$	−13.2295	+	16.6954i	−0.00120126	+	0.00151596i
$496$	8168.92	−	9427.43i	0.739507	−	0.853436i
$497$	8758.11	−	8350.85i	0.790453	−	0.753695i
$498$	−11463.5	−	1949.46i	−1.03151	−	0.175417i
$499$	3077.90	−	8893.01i	0.276124	−	0.797807i	−0.718619	−	0.695404i	$-0.755225\pi$
$499$	3077.90	−	8893.01i	0.276124	−	0.797807i	0.994743	−	0.102404i	$-0.0326533\pi$
$500$	−1.38591	+	1.94624i	−0.000123960	+	0.000174077i
$501$	−43.2380	+	1685.52i	−0.00385575	+	0.150306i
$502$	13186.9	−	9390.36i	1.17243	−	0.834885i
$503$	2339.70	−	16273.0i	0.207400	−	1.44250i	−0.574200	−	0.818715i	$-0.694687\pi$
$503$	2339.70	−	16273.0i	0.207400	−	1.44250i	0.781599	−	0.623781i	$-0.214404\pi$
$504$	15002.9	+	770.236i	1.32596	+	0.0680735i
$505$		−	59.3469i		−	0.00522951i
$506$	5136.59	−	183.495i	0.451283	−	0.0161212i
$507$	−6333.20	−	29374.4i	−0.554768	−	2.57310i
$508$	238.622	+	123.018i	0.0208408	+	0.0107442i
$509$	1717.13	+	4289.17i	0.149529	+	0.373505i	0.984155	−	0.177312i	$-0.0567403\pi$
$509$	1717.13	+	4289.17i	0.149529	+	0.373505i	−0.834626	+	0.550818i	$0.814316\pi$
$510$	−41.1189	+	13.0606i	−0.00357015	+	0.00113399i
$511$	15704.1	+	3809.77i	1.35951	+	0.329813i
$512$	−10122.8	+	4622.92i	−0.873766	+	0.399035i
$513$	5209.58	+	1163.54i	0.448360	+	0.100140i
$514$	−364.693	−	2536.50i	−0.0312956	−	0.217666i
$515$	−44.0219	−	46.1688i	−0.00376667	−	0.00395037i
$516$	−101.583	+	2.23041i	−0.00866660	+	0.000190287i
$517$	−1091.31	−	51.9857i	−0.0928355	−	0.00442230i
$518$	−26758.2	−	1274.65i	−2.26967	−	0.108118i
$519$	−3432.05	+	6257.83i	−0.290270	+	0.529264i
$520$	66.7581	+	70.0139i	0.00562988	+	0.00590445i
$521$	−1878.32	−	13064.0i	−0.157948	−	1.09855i	−0.902408	−	0.430883i	$-0.858202\pi$
$521$	−1878.32	−	13064.0i	−0.157948	−	1.09855i	0.744460	−	0.667667i	$-0.232707\pi$
$522$	−16886.6	−	7787.37i	−1.41591	−	0.652958i
$523$	−8524.58	+	3893.05i	−0.712723	+	0.325490i	−0.738570	−	0.674176i	$-0.764499\pi$
$523$	−8524.58	+	3893.05i	−0.712723	+	0.325490i	0.0258478	+	0.999666i	$0.491771\pi$
$524$	−295.828	−	71.7672i	−0.0246628	−	0.00598314i
$525$	−11949.7	−	10903.4i	−0.993384	−	0.906402i
$526$	2479.17	+	6192.66i	0.205507	+	0.513332i
$527$	−10121.0	−	5217.72i	−0.836576	−	0.431285i
$528$	−5276.20	−	1697.36i	−0.434881	−	0.139902i
$529$	6819.86	+	10076.0i	0.560521	+	0.828140i
$530$			42.9154i			0.00351722i
$531$	−16275.2	−	10544.6i	−1.33010	−	0.861766i
$532$	−26.5881	+	184.924i	−0.00216681	+	0.0150705i
$533$	−18054.0	+	12856.2i	−1.46718	+	1.04477i
$534$	4898.79	−	2663.21i	0.396988	−	0.215821i
$535$	−48.6043	+	68.2552i	−0.00392775	+	0.00551575i
$536$	1685.49	−	4869.90i	0.135825	−	0.392439i
$537$	−545.857	+	658.626i	−0.0438649	+	0.0529270i
$538$	3682.34	−	3511.10i	0.295087	−	0.281365i
$539$	2955.44	−	3410.75i	0.236177	−	0.272563i
$540$	−1.20280	−	0.592544i	−9.58523e−5	−	4.72204e-5i
$541$	3804.21	+	2444.82i	0.302321	+	0.194290i	0.683002	−	0.730416i	$-0.260674\pi$
$541$	3804.21	+	2444.82i	0.302321	+	0.194290i	−0.380681	+	0.924707i	$0.624310\pi$
$542$	−1864.08	+	645.164i	−0.147729	+	0.0511294i
$543$	−5349.82	−	11065.0i	−0.422805	−	0.874486i
$544$	−329.881	−	419.478i	−0.0259991	−	0.0330606i
$545$	−70.3926	−	24.3631i	−0.00553263	−	0.00191486i
$546$	26533.7	−	19786.5i	2.07974	−	1.55089i
$547$	−1940.29	+	7997.99i	−0.151665	+	0.625172i	0.844335	+	0.535816i	$0.179996\pi$
$547$	−1940.29	+	7997.99i	−0.151665	+	0.625172i	−0.996000	+	0.0893560i	$0.971519\pi$
$548$	180.124	−	394.417i	0.0140411	−	0.0307457i
$549$	15758.0	+	15136.8i	1.22502	+	1.17672i
$550$	3148.98	+	4899.91i	0.244133	+	0.379878i
$551$	−4576.31	+	7926.40i	−0.353824	+	0.612842i
$552$	−3143.78	−	12412.4i	−0.242406	−	0.957080i
$553$	−5481.42	−	9494.10i	−0.421508	−	0.730073i
$554$	2944.21	−	5710.98i	0.225790	−	0.437972i
$555$	−85.0403	−	41.5043i	−0.00650407	−	0.00317434i
$556$	−115.867	−	162.713i	−0.00883788	−	0.0124111i
$557$	1534.94	−	450.699i	0.116764	−	0.0342850i	−0.222829	−	0.974858i	$-0.571529\pi$
$557$	1534.94	−	450.699i	0.116764	−	0.0342850i	0.339592	+	0.940573i	$0.389711\pi$
$558$	−4760.91	−	13921.9i	−0.361193	−	1.05620i
$559$	6696.00	−	5802.12i	0.506638	−	0.439004i
$560$	−29.4079	+	73.4573i	−0.00221912	+	0.00554310i
$561$	−370.247	+	5045.73i	−0.0278642	+	0.379734i
$562$	−2550.60	+	13233.8i	−0.191442	+	0.993298i
$563$	−440.228	+	9241.52i	−0.0329545	+	0.691800i	0.920587	+	0.390538i	$0.127711\pi$
$563$	−440.228	+	9241.52i	−0.0329545	+	0.691800i	−0.953541	+	0.301262i	$0.902592\pi$
$564$	−11.2790	−	67.8398i	−0.000842078	−	0.00506484i
$565$	21.1124	+	61.0003i	0.00157205	+	0.00454213i
$566$	−21538.9	−	6324.38i	−1.59955	−	0.469671i
$567$	9928.61	−	15201.1i	0.735384	−	1.12590i
$568$	7108.29	+	8203.41i	0.525101	+	0.605999i
$569$	10015.4	+	956.358i	0.737907	+	0.0704615i	0.457239	−	0.889344i	$-0.348838\pi$
$569$	10015.4	+	956.358i	0.737907	+	0.0704615i	0.280667	+	0.959805i	$0.409444\pi$
$570$	−14.3241	+	23.4028i	−0.00105258	+	0.00171971i
$571$	456.359	+	4779.21i	0.0334466	+	0.350269i	0.996668	+	0.0815611i	$0.0259906\pi$
$571$	456.359	+	4779.21i	0.0334466	+	0.350269i	−0.963222	+	0.268708i	$0.913403\pi$
$572$	−266.109	+	106.534i	−0.0194520	+	0.00778742i
$573$	3838.30	+	3852.50i	0.279838	+	0.280874i
$574$	−15321.5	−	8845.90i	−1.11413	−	0.643242i
$575$	−5876.38	+	12472.8i	−0.426195	+	0.904611i
$576$	−1329.61	+	13400.9i	−0.0961811	+	0.969396i
$577$	−12919.4	+	8302.82i	−0.932137	+	0.599048i	−0.916155	−	0.400824i	$-0.868724\pi$
$577$	−12919.4	+	8302.82i	−0.932137	+	0.599048i	−0.0159821	+	0.999872i	$0.505087\pi$
$578$	2360.97	−	3002.22i	0.169902	−	0.216048i
$579$	15956.2	−	17487.4i	1.14528	−	1.25519i
$580$	1.58652	−	1.66389i	0.000113580	−	0.000119120i
$581$	15857.2	+	11291.8i	1.13230	+	0.806307i
$582$	−6612.81	−	15521.5i	−0.470979	−	1.10548i
$583$	4672.08	+	1870.42i	0.331900	+	0.132873i
$584$	−4083.68	+	13907.8i	−0.289356	+	0.985457i
$585$	113.724	−	27.1448i	0.00803746	−	0.00191846i
$586$	−3757.14	+	5846.22i	−0.264856	+	0.412125i
$587$	261.308	+	506.867i	0.0183737	+	0.0356399i	0.897844	−	0.440314i	$-0.145133\pi$
$587$	261.308	+	506.867i	0.0183737	+	0.0356399i	−0.879470	+	0.475954i	$0.842103\pi$
$588$	249.076	+	136.604i	0.0174689	+	0.00958069i
$589$	−7037.68	+	1707.32i	−0.492331	+	0.119438i
$590$	78.3565	−	61.6202i	0.00546760	−	0.00429977i
$591$	1882.16	−	15498.8i	0.131001	−	1.07874i
$592$	2340.42	−	24510.0i	0.162484	−	1.70161i
$593$	2489.72	+	8479.20i	0.172412	+	0.587182i	0.999678	+	0.0253715i	$0.00807686\pi$
$593$	2489.72	+	8479.20i	0.172412	+	0.587182i	−0.827266	+	0.561811i	$0.810105\pi$
$594$	−4861.65	+	4370.58i	−0.335818	+	0.301898i
$595$	71.4918	+	10.2790i	0.00492585	+	0.000708230i
$596$	22.1803	+	465.621i	0.00152439	+	0.0320010i
$597$	5757.49	+	6357.00i	0.394704	+	0.435803i
$598$	−22784.1	−	16636.3i	−1.55805	−	1.13764i
$599$	−15218.2	+	8786.21i	−1.03806	+	0.599324i	−0.919283	−	0.393598i	$-0.871230\pi$
$599$	−15218.2	+	8786.21i	−1.03806	+	0.599324i	−0.118776	+	0.992921i	$0.537897\pi$
$600$	10279.1	−	10241.2i	0.699402	−	0.696823i
$601$	−769.758	−	605.344i	−0.0522447	−	0.0410857i	0.591695	−	0.806162i	$-0.298459\pi$
$601$	−769.758	−	605.344i	−0.0522447	−	0.0410857i	−0.643940	+	0.765076i	$0.722701\pi$
$602$	6433.29	+	2937.99i	0.435550	+	0.198909i
$603$	−4061.23	−	4722.04i	−0.274272	−	0.318899i
$604$	−2.19187	−	4.79953i	−0.000147659	−	0.000323328i
$605$	50.7462	−	9.78054i	0.00341013	−	0.000657248i
$606$	3053.50	−	17955.6i	0.204687	−	1.20363i
$607$	−329.053	−	1356.38i	−0.0220031	−	0.0906978i	0.959751	−	0.280851i	$-0.0906167\pi$
$607$	−329.053	−	1356.38i	−0.0220031	−	0.0906978i	−0.981754	+	0.190153i	$0.939102\pi$
$608$	−333.261	−	64.2308i	−0.0222295	−	0.00428438i
$609$	19776.7	+	24042.6i	1.31591	+	1.59976i
$610$	−99.8313	+	51.4666i	−0.00662632	+	0.00341610i
$611$	4532.03	+	3927.03i	0.300076	+	0.260017i
$612$	−315.383	+	44.1567i	−0.0208310	+	0.00291655i
$613$	3222.28	−	463.293i	0.212311	−	0.0305257i	−0.0353386	−	0.999375i	$-0.511251\pi$
$613$	3222.28	−	463.293i	0.212311	−	0.0305257i	0.247649	+	0.968850i	$0.420342\pi$
$614$	−1039.93	−	5395.66i	−0.0683519	−	0.354643i
$615$	−37.3591	−	50.0986i	−0.00244954	−	0.00328483i
$616$	6553.77	+	6249.01i	0.428667	+	0.408733i
$617$	27759.6	−	2650.72i	1.81128	−	0.172956i	0.866178	−	0.499735i	$-0.166569\pi$
$617$	27759.6	−	2650.72i	1.81128	−	0.172956i	0.945101	+	0.326779i	$0.105963\pi$
$618$	−10943.5	−	16233.6i	−0.712320	−	1.05665i
$619$	−12029.9	+	573.053i	−0.781132	+	0.0372099i	−0.434360	−	0.900739i	$-0.643025\pi$
$619$	−12029.9	+	573.053i	−0.781132	+	0.0372099i	−0.346772	+	0.937949i	$0.612722\pi$
$620$	1.81907			0.000117832
$621$	−14875.8	−	4265.25i	−0.961267	−	0.275618i
$622$	24513.2			1.58021
$623$	−9324.17	+	444.165i	−0.599623	+	0.0285635i
$624$	17004.9	+	25224.9i	1.09093	+	1.61828i
$625$	−15553.4	+	1485.17i	−0.995416	+	0.0950507i
$626$	−11468.5	−	10935.2i	−0.732228	−	0.698178i
$627$	1923.50	+	2579.41i	0.122515	+	0.164293i
$628$	37.6496	+	195.345i	0.00239233	+	0.0124126i
$629$	−22246.2	+	3198.52i	−1.41020	+	0.202756i
$630$	57.4205	+	73.5738i	0.00363125	+	0.00465278i
$631$	971.905	+	842.160i	0.0613168	+	0.0531313i	0.684980	−	0.728562i	$-0.259811\pi$
$631$	971.905	+	842.160i	0.0613168	+	0.0531313i	−0.623663	+	0.781693i	$0.714356\pi$
$632$	8740.36	−	4505.97i	0.550115	−	0.283604i
$633$	3437.83	+	4179.39i	0.215864	+	0.262426i
$634$	1531.65	+	295.201i	0.0959458	+	0.0184920i
$635$	−15.5621	−	64.1478i	−0.000972539	−	0.00400886i
$636$	−53.1081	+	312.294i	−0.00331112	+	0.0194705i
$637$	−24323.5	+	4687.97i	−1.51292	+	0.291592i
$638$	−4656.50	−	10196.3i	−0.288954	−	0.632720i
$639$	12890.9	−	2435.16i	0.798051	−	0.150756i
$640$	−66.1140	−	30.1933i	−0.00408341	−	0.00186483i
$641$	−5563.52	−	4375.20i	−0.342817	−	0.269594i	0.431874	−	0.901934i	$-0.357852\pi$
$641$	−5563.52	−	4375.20i	−0.342817	−	0.269594i	−0.774691	+	0.632339i	$0.782095\pi$
$642$	−18217.3	+	18150.1i	−1.11990	+	1.11578i
$643$	−11994.7	+	6925.16i	−0.735655	+	0.424730i	−0.820487	−	0.571665i	$-0.806298\pi$
$643$	−11994.7	+	6925.16i	−0.735655	+	0.424730i	0.0848326	+	0.996395i	$0.472964\pi$
$644$	108.821	−	530.584i	0.00665862	−	0.0324657i
$645$	16.7706	+	18.5169i	0.00102379	+	0.00113039i
$646$	310.086	+	6509.50i	0.0188857	+	0.396459i
$647$	−21196.8	−	3047.64i	−1.28799	−	0.185186i	−0.535922	−	0.844267i	$-0.680036\pi$
$647$	−21196.8	−	3047.64i	−1.28799	−	0.185186i	−0.752071	+	0.659082i	$0.770945\pi$
$648$	13196.0	+	9544.51i	0.799979	+	0.578617i
$649$	−3293.35	−	11216.1i	−0.199191	−	0.678383i
$650$	3038.89	−	31824.7i	0.183377	−	1.92041i
$651$	−2969.47	+	24452.5i	−0.178775	+	1.47215i
$652$	−289.142	+	227.384i	−0.0173676	+	0.0136580i
$653$	3863.31	−	937.229i	0.231521	−	0.0561663i	−0.118320	−	0.992976i	$-0.537751\pi$
$653$	3863.31	−	937.229i	0.231521	−	0.0561663i	0.349841	+	0.936809i	$0.386236\pi$
$654$	−20044.0	−	10993.0i	−1.19845	−	0.657278i
$655$	34.2963	+	66.5256i	0.00204591	+	0.00396851i
$656$	8791.14	−	13679.3i	0.523226	−	0.814156i
$657$	12042.2	+	12723.2i	0.715083	+	0.755526i
$658$	−1348.60	+	4592.90i	−0.0798994	+	0.272112i
$659$	−6776.11	−	2712.75i	−0.400546	−	0.160355i	0.162638	−	0.986686i	$-0.448000\pi$
$659$	−6776.11	−	2712.75i	−0.400546	−	0.160355i	−0.563184	+	0.826331i	$0.690424\pi$
$660$	−0.316790	−	0.743568i	−1.86834e−5	−	4.38535e-5i
$661$	2336.00	+	1663.46i	0.137458	+	0.0978836i	0.646718	−	0.762729i	$-0.276141\pi$
$661$	2336.00	+	1663.46i	0.137458	+	0.0978836i	−0.509259	+	0.860613i	$0.670081\pi$
$662$	6475.98	−	6791.81i	0.380206	−	0.398748i
$663$	18717.2	−	20513.3i	1.09640	−	1.20162i
$664$	−10793.9	+	13725.6i	−0.630851	+	0.802193i
$665$	38.6433	−	24.8345i	0.00225342	−	0.00144818i
$666$	−23593.8	−	16932.8i	−1.37274	−	0.985183i
$667$	14610.0	−	22150.0i	0.848129	−	1.28583i
$668$	−55.4032	−	31.9871i	−0.00320900	−	0.00185272i
$669$	−11472.1	−	11514.5i	−0.662983	−	0.665437i
$670$	29.7218	−	11.8988i	0.00171381	−	0.000686105i
$671$	1251.99	+	13111.5i	0.0720308	+	0.754341i
$672$	−602.650	+	984.613i	−0.0345948	+	0.0565212i
$673$	7490.17	+	715.224i	0.429011	+	0.0409656i	0.307329	−	0.951603i	$-0.400565\pi$
$673$	7490.17	+	715.224i	0.429011	+	0.0409656i	0.121683	+	0.992569i	$0.461171\pi$
$674$	20440.9	+	23590.0i	1.16818	+	1.34815i
$675$	−4444.90	−	16964.0i	−0.253458	−	0.967327i
$676$	1093.97	+	321.218i	0.0622421	+	0.0182759i
$677$	8971.33	+	25921.0i	0.509300	+	1.47153i	0.847675	+	0.530516i	$0.178002\pi$
$677$	8971.33	+	25921.0i	0.509300	+	1.47153i	−0.338375	+	0.941011i	$0.609877\pi$
$678$	3249.07	+	19542.2i	0.184041	+	1.10695i
$679$	−1343.95	+	28212.9i	−0.0759587	+	1.59457i
$680$	−12.2609	+	63.6157i	−0.000691448	+	0.00358757i
$681$	−1366.24	+	18619.2i	−0.0768788	+	1.04771i
$682$	3296.31	−	8233.79i	0.185077	−	0.462299i
$683$	2374.60	−	2057.60i	0.133033	−	0.115274i	−0.585803	−	0.810454i	$-0.699221\pi$
$683$	2374.60	−	2057.60i	0.133033	−	0.115274i	0.718836	+	0.695180i	$0.244675\pi$
$684$	−133.197	+	152.575i	−0.00744579	+	0.00852903i
$685$	−102.292	+	30.0356i	−0.00570565	+	0.00167533i
$686$	2717.63	+	3816.38i	0.151253	+	0.212405i
$687$	7800.07	+	3806.86i	0.433175	+	0.211413i
$688$	−2978.60	+	5777.68i	−0.165055	+	0.320163i
$689$	−13811.3	−	23921.8i	−0.763668	−	1.32271i
$690$	45.4876	−	65.2582i	0.00250969	−	0.00360049i
$691$	7983.08	−	13827.1i	0.439494	−	0.761226i	−0.558156	−	0.829736i	$-0.688491\pi$
$691$	7983.08	−	13827.1i	0.439494	−	0.761226i	0.997650	+	0.0685095i	$0.0218243\pi$
$692$	−146.408	−	227.815i	−0.00804274	−	0.0125148i
$693$	10512.4	−	3044.58i	0.576237	−	0.166889i
$694$	1739.50	−	3808.96i	0.0951446	−	0.208338i
$695$	−11.5789	+	47.7289i	−0.000631961	+	0.00260498i
$696$	−22385.5	+	16693.1i	−1.21914	+	0.909127i
$697$	−14026.6	−	4854.66i	−0.762262	−	0.263821i
$698$	10061.6	+	12794.3i	0.545611	+	0.693801i
$699$	−8062.96	−	16676.6i	−0.436293	−	0.902385i
$700$	580.021	−	200.747i	0.0313182	−	0.0108393i
$701$	15457.5	+	9933.91i	0.832839	+	0.535233i	0.886179	−	0.463343i	$-0.153350\pi$
$701$	15457.5	+	9933.91i	0.832839	+	0.535233i	−0.0533398	+	0.998576i	$0.516987\pi$
$702$	35804.4	−	2361.44i	1.92500	−	0.126962i
$703$	−9360.41	+	10802.5i	−0.502183	+	0.579550i
$704$	−5874.97	+	5601.77i	−0.314519	+	0.299893i
$705$	−10.7898	+	13.0189i	−0.000576407	+	0.000695488i
$706$	424.716	−	1227.14i	0.0226408	−	0.0654162i
$707$	−17686.8	+	24837.6i	−0.940848	+	1.32124i
$708$	646.452	−	351.441i	0.0343152	−	0.0186553i
$709$	21597.1	−	15379.2i	1.14400	−	0.814640i	0.159016	−	0.987276i	$-0.449168\pi$
$709$	21597.1	−	15379.2i	1.14400	−	0.814640i	0.984986	+	0.172636i	$0.0552284\pi$
$710$	−9.59695	+	66.7483i	−0.000507278	+	0.00352819i
$711$	609.345	−	11869.0i	0.0321409	−	0.626053i
$712$		−	8373.12i		−	0.440724i
$713$	20661.2	−	3727.86i	1.08523	−	0.195806i
$714$	21101.3	+	6788.33i	1.10602	+	0.355808i
$715$	62.6427	+	32.2946i	0.00327651	+	0.00168916i
$716$	−12.0631	−	30.1320i	−0.000629633	−	0.00157275i
$717$	−17793.0	−	16235.0i	−0.926767	−	0.845618i
$718$	−26095.9	−	6330.80i	−1.35639	−	0.329058i
$719$	1561.38	−	713.056i	0.0809868	−	0.0369854i	−0.374510	−	0.927223i	$-0.622189\pi$
$719$	1561.38	−	713.056i	0.0809868	−	0.0369854i	0.455497	+	0.890238i	$0.349462\pi$
$720$	−70.0565	+	49.4980i	−0.00362618	+	0.00256206i
$721$	4664.45	+	32442.0i	0.240934	+	1.67573i
$722$	−10691.5	−	11212.9i	−0.551102	−	0.577980i
$723$	−7115.33	+	12973.7i	−0.366005	+	0.667355i
$724$	465.805	+	22.1890i	0.0239109	+	0.00113902i
$725$	30035.0	+	1430.74i	1.53858	+	0.0732916i
$726$	15856.7	−	348.157i	0.810603	−	0.0177979i
$727$	10101.0	+	10593.6i	0.515303	+	0.540434i	0.929048	−	0.369958i	$-0.120628\pi$
$727$	10101.0	+	10593.6i	0.515303	+	0.540434i	−0.413745	+	0.910393i	$0.635780\pi$
$728$	−7073.52	−	49197.4i	−0.360113	−	2.50464i
$729$	17993.8	−	7977.70i	0.914180	−	0.405309i
$730$	−81.9120	+	37.4080i	−0.00415301	+	0.00189662i
$731$	5766.32	+	1398.89i	0.291758	+	0.0707797i
$732$	−790.158	+	250.979i	−0.0398977	+	0.0126727i
$733$	−8291.35	−	20710.8i	−0.417801	−	1.04362i	−0.976744	−	0.214410i	$-0.931217\pi$
$733$	−8291.35	−	20710.8i	−0.417801	−	1.04362i	0.558943	−	0.829206i	$-0.311207\pi$
$734$	20665.8	+	10654.0i	1.03922	+	0.535756i
$735$	−14.7209	−	68.2778i	−0.000738760	−	0.00342648i
$736$	953.377	+	243.327i	0.0477472	+	0.0121863i
$737$		−	3754.32i		−	0.187642i
$738$	−8725.50	−	17079.7i	−0.435217	−	0.851915i
$739$	260.701	−	1813.22i	0.0129771	−	0.0902574i	−0.982304	−	0.187296i	$-0.940028\pi$
$739$	260.701	−	1813.22i	0.0129771	−	0.0902574i	0.995281	+	0.0970382i	$0.0309369\pi$
$740$	2.92468	−	2.08266i	0.000145289	−	0.000103460i
$741$	452.897	−	17655.0i	0.0224529	−	0.875268i
$742$	12789.8	−	17960.8i	0.632788	−	0.888626i
$743$	−7862.79	+	22718.1i	−0.388234	+	1.12173i	0.566447	+	0.824098i	$0.308318\pi$
$743$	−7862.79	+	22718.1i	−0.388234	+	1.12173i	−0.954681	+	0.297631i	$0.903804\pi$
$744$	−21781.9	−	3704.19i	−1.07334	−	0.182530i
$745$	82.9495	−	79.0921i	0.00407924	−	0.00388955i
$746$	957.416	−	1104.92i	0.0469886	−	0.0542277i
$747$	7771.02	+	19620.8i	0.380625	+	0.961028i
$748$	−161.490	−	103.783i	−0.00789392	−	0.00507311i
$749$	40683.3	−	14080.6i	1.98469	−	0.686909i
$750$	179.805	+	13.1938i	0.00875409	+	0.000642359i
$751$	3356.81	+	4268.53i	0.163105	+	0.207405i	0.860735	−	0.509054i	$-0.170005\pi$
$751$	3356.81	+	4268.53i	0.163105	+	0.207405i	−0.697630	+	0.716458i	$0.745762\pi$
$752$	−4157.59	−	1438.96i	−0.201611	−	0.0697784i
$753$	−26987.1	−	11615.6i	−1.30606	−	0.562145i
$754$	−14505.0	+	59790.5i	−0.700586	+	2.88786i
$755$	−0.538921	+	1.18007i	−2.59779e−5	+	5.68837e-5i
$756$	326.798	+	606.452i	0.0157216	+	0.0291752i
$757$	−17815.7	−	27721.7i	−0.855378	−	1.33099i	−0.942297	−	0.334779i	$-0.891338\pi$
$757$	−17815.7	−	27721.7i	−0.855378	−	1.33099i	0.0869188	−	0.996215i	$-0.472298\pi$
$758$	−8160.46	+	14134.3i	−0.391031	+	0.677285i
$759$	−5121.95	−	7796.32i	−0.244947	−	0.372844i
$760$	20.6016	+	35.6831i	0.000983290	+	0.00170311i
$761$	−3025.36	+	5868.38i	−0.144112	+	0.279538i	−0.949833	−	0.312757i	$-0.898748\pi$
$761$	−3025.36	+	5868.38i	−0.144112	+	0.279538i	0.805721	+	0.592295i	$0.201778\pi$
$762$	−1407.85	−	20208.9i	−0.0669307	−	0.960748i
$763$	22199.6	+	31175.0i	1.05332	+	1.47917i
$764$	−197.982	+	58.1329i	−0.00937533	+	0.00275285i
$765$	58.9856	+	51.4941i	0.00278775	+	0.00243369i
$766$	−3773.24	+	3269.53i	−0.177980	+	0.154221i
$767$	−23846.4	+	59565.3i	−1.12261	+	2.80415i
$768$	−1300.73	−	883.864i	−0.0611145	−	0.0415283i
$769$	1971.20	−	10227.5i	0.0924358	−	0.479602i	−0.905979	−	0.423322i	$-0.860864\pi$
$769$	1971.20	−	10227.5i	0.0924358	−	0.479602i	0.998415	−	0.0562803i	$-0.0179240\pi$
$770$	−2.67683	+	56.1936i	−0.000125281	+	0.00262997i
$771$	−3591.79	+	2954.49i	−0.167776	+	0.138007i
$772$	293.778	+	848.816i	0.0136960	+	0.0395720i
$773$	6973.08	+	2047.48i	0.324456	+	0.0952687i	0.439904	−	0.898045i	$-0.355012\pi$
$773$	6973.08	+	2047.48i	0.324456	+	0.0952687i	−0.115449	+	0.993313i	$0.536831\pi$
$774$	4121.30	+	6465.25i	0.191391	+	0.300244i
$775$	15580.1	+	17980.4i	0.722135	+	0.833388i
$776$	−25220.5	−	2408.27i	−1.16671	−	0.111407i
$777$	23221.4	+	42714.2i	1.07215	+	1.97215i
$778$	−2301.26	−	24099.9i	−0.106047	−	1.11057i
$779$	−8763.72	+	3508.47i	−0.403072	+	0.161366i
$780$	−1.15609	+	4.28293i	−5.30701e−5	+	0.000196607i
$781$	6848.43	+	3953.94i	0.313772	+	0.181156i
$782$	224.672	−	18891.8i	0.0102740	−	0.863899i
$783$	3820.92	+	33532.2i	0.174392	+	1.53045i
$784$	15288.6	−	9825.37i	0.696455	−	0.447584i
$785$	30.2365	−	38.4489i	0.00137476	−	0.00174815i
$786$	6953.64	+	21892.2i	0.315557	+	0.993473i
$787$	15728.1	−	16495.1i	0.712383	−	0.747126i	−0.263681	−	0.964610i	$-0.584937\pi$
$787$	15728.1	−	16495.1i	0.712383	−	0.747126i	0.976064	+	0.217484i	$0.0697851\pi$
$788$	482.545	+	343.619i	0.0218147	+	0.0155341i
$789$	7272.86	−	9678.08i	0.328163	−	0.436691i
$790$	56.7146	+	22.7051i	0.00255420	+	0.00102255i
$791$	9343.66	−	31821.6i	0.420003	−	1.43040i
$792$	2279.17	+	9548.71i	0.102256	+	0.428407i
$793$	39084.5	−	60816.7i	1.75023	−	2.72341i
$794$	5188.26	+	10063.8i	0.231895	+	0.449813i
$795$	66.5808	−	40.4146i	0.00297029	−	0.00180297i
$796$	−316.250	+	76.7215i	−0.0140819	+	0.00341623i
$797$	−9355.31	+	7357.10i	−0.415787	+	0.326978i	−0.804041	−	0.594574i	$-0.797321\pi$
$797$	−9355.31	+	7357.10i	−0.415787	+	0.326978i	0.388254	+	0.921552i	$0.373078\pi$
$798$	12969.5	−	5525.52i	0.575331	−	0.245115i
$799$	−381.745	+	3997.82i	−0.0169026	+	0.177012i
$800$	314.134	+	1069.84i	0.0138829	+	0.0472808i
$801$	−8745.14	−	5092.17i	−0.385761	−	0.224623i
$802$	−38458.8	−	5529.54i	−1.69330	−	0.243460i
$803$	502.459	+	10547.9i	0.0220814	+	0.463546i
$804$	231.009	−	49.8062i	0.0101331	−	0.00218474i
$805$	−116.113	+	65.2095i	−0.00508380	+	0.00285507i
$806$	−42158.3	+	24340.1i	−1.84239	+	1.06370i
$807$	−8915.04	−	2406.43i	−0.388878	−	0.104970i
$808$	−21498.8	−	16906.9i	−0.936047	−	0.736115i
$809$	19052.4	+	8700.93i	0.827993	+	0.378132i	0.783893	−	0.620896i	$-0.213231\pi$
$809$	19052.4	+	8700.93i	0.827993	+	0.378132i	0.0440994	+	0.999027i	$0.485958\pi$
$810$	8.87304	+	100.786i	0.000384897	+	0.00437194i
$811$	2550.30	+	5584.37i	0.110423	+	0.241793i	0.956774	−	0.290833i	$-0.0939325\pi$
$811$	2550.30	+	5584.37i	0.110423	+	0.241793i	−0.846351	+	0.532626i	$0.821205\pi$
$812$	−1159.86	+	223.545i	−0.0501271	+	0.00966121i
$813$	2756.39	+	2284.44i	0.118906	+	0.0985472i
$814$	−4127.11	−	17012.2i	−0.177709	−	0.732527i
$815$	88.8075	+	17.1162i	0.00381692	+	0.000735651i
$816$	−7154.93	+	19075.4i	−0.306952	+	0.818350i
$817$	3354.17	−	1729.20i	0.143632	−	0.0740476i
$818$	24302.3	+	21058.1i	1.03877	+	0.900096i
$819$	−55685.1	−	22532.0i	−2.37582	−	0.961333i
$820$	2.34707	−	0.337458i	9.99554e−5	−	1.43714e-5i
$821$	−2894.52	−	15018.2i	−0.123044	−	0.638414i	−0.990118	−	0.140235i	$-0.955214\pi$
$821$	−2894.52	−	15018.2i	−0.123044	−	0.638414i	0.867074	−	0.498179i	$-0.165998\pi$
$822$	−32494.2	+	3824.30i	−1.37879	+	0.162272i
$823$	−23187.8	−	22109.5i	−0.982109	−	0.936439i	0.0158769	−	0.999874i	$-0.494946\pi$
$823$	−23187.8	−	22109.5i	−0.982109	−	0.936439i	−0.997986	+	0.0634348i	$0.979795\pi$
$824$	−29266.0	+	2794.57i	−1.23729	+	0.118147i
$825$	4636.45	−	9499.85i	0.195661	−	0.400900i
$826$	−51157.7	+	2436.94i	−2.15497	+	0.102654i
$827$	166.795			0.00701334			0.00350667	−	0.999994i	$-0.498884\pi$
$827$	166.795			0.00701334			0.00350667	+	0.999994i	$0.498884\pi$
$828$	411.769	−	418.589i	0.0172826	−	0.0175688i
$829$	29237.9			1.22494			0.612469	−	0.790495i	$-0.290176\pi$
$829$	29237.9			1.22494			0.612469	+	0.790495i	$0.290176\pi$
$830$	−108.356	+	5.16164i	−0.00453144	+	0.000215859i
$831$	−11632.9	+	810.408i	−0.485609	+	0.0338300i
$832$	44353.6	−	4235.25i	1.84818	−	0.176480i
$833$	−12006.1	−	11447.8i	−0.499386	−	0.476163i
$834$	−5958.99	+	13844.8i	−0.247414	+	0.574829i
$835$	2.97682	+	15.4452i	0.000123374	+	0.000640125i
$836$	−120.843	+	17.3746i	−0.00499934	+	0.000718797i
$837$	−17115.6	+	20496.9i	−0.706812	+	0.846449i
$838$	−6250.49	−	5416.08i	−0.257661	−	0.223264i
$839$	40030.0	−	20636.9i	1.64719	−	0.849183i	0.651274	−	0.758843i	$-0.274235\pi$
$839$	40030.0	−	20636.9i	1.64719	−	0.849183i	0.995911	−	0.0903403i	$-0.0287955\pi$
$840$	138.250	−	22.9854i	0.00567866	−	0.000944131i
$841$	−32873.5	−	6335.85i	−1.34788	−	0.259783i
$842$	−1821.13	−	7506.79i	−0.0745370	−	0.307246i
$843$	22933.4	−	8505.51i	0.936974	−	0.347503i
$844$	−201.622	+	38.8595i	−0.00822288	+	0.00158483i
$845$	−116.454	−	254.999i	−0.00474100	−	0.0103813i
$846$	−3934.34	+	3383.76i	−0.159888	+	0.137513i
$847$	−24152.9	−	11030.3i	−0.979816	−	0.447467i
$848$	15929.8	+	12527.3i	0.645084	+	0.507299i
$849$	10471.8	+	39372.2i	0.423313	+	1.59158i
$850$	18541.5	−	10704.9i	0.748197	−	0.431972i
$851$	28950.9	−	29648.7i	1.16618	−	1.19429i
$852$	−152.438	+	473.848i	−0.00612962	+	0.0190537i
$853$	1658.15	+	34808.9i	0.0665581	+	1.39723i	0.747194	+	0.664606i	$0.231400\pi$
$853$	1658.15	+	34808.9i	0.0665581	+	1.39723i	−0.680636	+	0.732621i	$0.738297\pi$
$854$	57119.3	+	8212.51i	2.28874	+	0.329071i
$855$	49.7976	+	0.183957i	0.00199186	+	7.35814e-6i
$856$	10879.4	+	37051.9i	0.434405	+	1.47945i
$857$	49.2734	−	516.015i	0.00196400	−	0.0205679i	−0.994437	−	0.105335i	$-0.966409\pi$
$857$	49.2734	−	516.015i	0.00196400	−	0.0205679i	0.996401	+	0.0847670i	$0.0270146\pi$
$858$	17291.2	+	12993.9i	0.688009	+	0.517023i
$859$	17674.3	−	13899.2i	0.702023	−	0.552077i	−0.202092	−	0.979367i	$-0.564774\pi$
$859$	17674.3	−	13899.2i	0.702023	−	0.552077i	0.904115	+	0.427290i	$0.140532\pi$
$860$	−0.921186	+	0.223477i	−3.65258e−5	+	8.86107e-6i
$861$	704.822	+	32100.9i	0.0278981	+	1.27061i
$862$	4883.95	+	9473.55i	0.192979	+	0.374328i
$863$	−809.127	+	1259.03i	−0.0319154	+	0.0496614i	−0.856845	−	0.515575i	$-0.827579\pi$
$863$	−809.127	+	1259.03i	−0.0319154	+	0.0496614i	0.824929	+	0.565236i	$0.191215\pi$
$864$	−1128.70	+	540.579i	−0.0444435	+	0.0212857i
$865$	−18.7586	+	63.8861i	−0.000737356	+	0.00251120i
$866$	12820.6	+	5132.61i	0.503075	+	0.201401i
$867$	−6881.16	−	835.638i	−0.269546	−	0.0327333i
$868$	−761.309	−	542.126i	−0.0297702	−	0.0211992i
$869$	4943.68	−	5184.78i	0.192984	−	0.202396i
$870$	−169.447	−	37.1890i	−0.00660323	−	0.00144922i
$871$	−12738.1	+	16197.8i	−0.495539	+	0.630128i
$872$	−28879.3	+	18559.6i	−1.12153	+	0.720765i
$873$	−17853.3	+	24876.5i	−0.692146	+	0.964423i
$874$	−7760.10	−	9173.83i	−0.300331	−	0.355045i
$875$	−261.388	−	150.912i	−0.0100989	−	0.00583060i
$876$	−642.362	+	170.849i	−0.0247756	+	0.00658958i
$877$	−40822.5	+	16342.9i	−1.57181	+	0.629258i	−0.983747	−	0.179558i	$-0.942533\pi$
$877$	−40822.5	+	16342.9i	−1.57181	+	0.629258i	−0.588062	+	0.808816i	$0.700109\pi$
$878$	−2170.76	−	22733.3i	−0.0834393	−	0.873816i
$879$	12608.3	+	323.435i	0.483807	+	0.0124109i
$880$	−51.4722	−	4.91500i	−0.00197173	−	0.000188278i
$881$	7991.77	+	9223.00i	0.305618	+	0.352702i	0.887695	−	0.460431i	$-0.152305\pi$
$881$	7991.77	+	9223.00i	0.305618	+	0.352702i	−0.582077	+	0.813134i	$0.697760\pi$
$882$	−940.854	−	21415.1i	−0.0359186	−	0.817557i
$883$	23007.4	+	6755.59i	0.876854	+	0.257468i	0.689028	−	0.724735i	$-0.258038\pi$
$883$	23007.4	+	6755.59i	0.876854	+	0.257468i	0.187826	+	0.982202i	$0.439856\pi$
$884$	344.611	+	995.689i	0.0131115	+	0.0378831i
$885$	−169.391	−	63.5361i	−0.00643391	−	0.00241327i
$886$	−487.316	+	10230.0i	−0.0184782	+	0.387906i
$887$	381.232	−	1978.02i	0.0144312	−	0.0748764i	−0.973999	−	0.226552i	$-0.927255\pi$
$887$	381.232	−	1978.02i	0.0144312	−	0.0748764i	0.988430	+	0.151675i	$0.0484669\pi$
$888$	−39261.7	+	18982.6i	−1.48371	+	0.717359i
$889$	−12604.6	+	31484.7i	−0.475527	+	1.18781i
$890$	39.3126	−	34.0646i	0.00148063	−	0.00128297i
$891$	11359.1	+	3426.68i	0.427096	+	0.128842i
$892$	591.739	−	173.750i	0.0222118	−	0.00652196i
$893$	1481.54	+	2080.53i	0.0555182	+	0.0779644i
$894$	29166.1	−	19661.8i	1.09112	−	0.735557i
$895$	−3.65678	+	7.09316i	−0.000136573	+	0.000264914i
$896$	18671.4	+	32339.9i	0.696171	+	1.20580i
$897$	−4353.90	+	51015.1i	−0.162065	+	1.89894i
$898$	7565.28	−	13103.4i	0.281132	−	0.486935i
$899$	−24754.0	−	38518.0i	−0.918347	−	1.42898i
$900$	646.048	+	159.259i	0.0239277	+	0.00589848i
$901$	7684.66	−	16827.1i	0.284143	−	0.622187i
$902$	2725.64	−	11235.2i	0.100614	−	0.414737i
$903$	−1500.29	−	12747.7i	−0.0552897	−	0.469785i
$904$	28112.3	+	9729.78i	1.03430	+	0.357973i
$905$	−70.8771	−	90.1276i	−0.00260335	−	0.00331043i
$906$	−223.770	+	329.307i	−0.00820557	+	0.0120756i
$907$	−36900.7	+	12771.5i	−1.35090	+	0.467552i	−0.904192	−	0.427126i	$-0.859526\pi$
$907$	−36900.7	+	12771.5i	−1.35090	+	0.467552i	−0.446711	+	0.894678i	$0.647405\pi$
$908$	−595.911	−	382.969i	−0.0217797	−	0.0139970i
$909$	−30732.7	+	12172.0i	−1.12139	+	0.444136i
$910$	202.209	−	233.362i	0.00736612	−	0.00850096i
$911$	25474.2	−	24289.6i	0.926452	−	0.883370i	−0.0669847	−	0.997754i	$-0.521338\pi$
$911$	25474.2	−	24289.6i	0.926452	−	0.883370i	0.993437	+	0.114384i	$0.0364894\pi$
$912$	4505.59	+	12148.4i	0.163591	+	0.441091i
$913$	−4160.64	+	12021.4i	−0.150818	+	0.435761i
$914$	10383.9	−	14582.1i	0.375786	−	0.527717i
$915$	173.861	+	106.415i	0.00628162	+	0.00384478i
$916$	−268.258	+	191.026i	−0.00967631	+	0.00689047i
$917$	5472.65	−	38063.1i	0.197081	−	1.37073i
$918$	15196.9	+	18614.7i	0.546375	+	0.669254i
$919$		−	36108.2i		−	1.29608i	−0.761606	−	0.648041i	$-0.775589\pi$
$919$		−	36108.2i		−	1.29608i	0.761606	−	0.648041i	$-0.224411\pi$
$920$	−53.4699	−	106.817i	−0.00191614	−	0.00382789i
$921$	−7391.72	+	6694.63i	−0.264458	+	0.239517i
$922$	12296.1	+	6339.07i	0.439208	+	0.226428i
$923$	−16131.8	−	40295.2i	−0.575280	−	1.43698i
$924$	−89.0190	+	405.606i	−0.00316938	+	0.0144410i
$925$	45635.4	+	11071.0i	1.62214	+	0.393528i
$926$	24479.1	−	11179.2i	0.868717	−	0.396730i
$927$	−14879.6	+	32265.9i	−0.527197	+	1.14321i
$928$	−305.382	−	2123.98i	−0.0108024	−	0.0751327i
$929$	11378.3	+	11933.2i	0.401841	+	0.421439i	0.893299	−	0.449462i	$-0.148384\pi$
$929$	11378.3	+	11933.2i	0.401841	+	0.421439i	−0.491458	+	0.870901i	$0.663536\pi$
$930$	−71.2243	−	117.338i	−0.00251133	−	0.00413727i
$931$	−10538.5	−	502.012i	−0.370984	−	0.0176722i
$932$	702.035	+	33.4421i	0.0246737	+	0.00117536i
$933$	−23084.8	−	38030.8i	−0.810033	−	1.33448i
$934$	21776.1	+	22838.2i	0.762888	+	0.800094i
$935$	6.71704	+	46.7181i	0.000234942	+	0.00163406i
$936$	22564.6	−	48930.4i	0.787978	−	1.70870i
$937$	2938.55	−	1341.99i	0.102453	−	0.0467886i	−0.363529	−	0.931583i	$-0.618428\pi$
$937$	2938.55	−	1341.99i	0.102453	−	0.0467886i	0.465982	+	0.884794i	$0.345701\pi$
$938$	−15985.1	−	3877.95i	−0.556432	−	0.134989i
$939$	−6165.13	+	28090.8i	−0.214261	+	0.976259i
$940$	−0.238447	−	0.595612i	−8.27371e−6	−	2.06667e-5i
$941$	−16084.3	−	8292.03i	−0.557208	−	0.287261i	0.156530	−	0.987673i	$-0.449969\pi$
$941$	−16084.3	−	8292.03i	−0.557208	−	0.287261i	−0.713738	+	0.700412i	$0.752999\pi$
$942$	11126.5	−	10077.1i	0.384840	−	0.348547i
$943$	25966.8	−	8642.80i	0.896707	−	0.298461i
$944$		−	47072.6i		−	1.62297i
$945$	60.0711	−	158.371i	0.00206784	−	0.00545165i
$946$	−657.728	+	4574.60i	−0.0226053	+	0.157223i
$947$	−18589.0	+	13237.2i	−0.637868	+	0.454224i	−0.852681	−	0.522431i	$-0.825025\pi$
$947$	−18589.0	+	13237.2i	−0.637868	+	0.454224i	0.214813	+	0.976655i	$0.431086\pi$
$948$	384.612	+	235.409i	0.0131768	+	0.00806510i
$949$	33620.4	−	47213.2i	1.15001	−	1.61497i
$950$	4453.48	−	12867.5i	0.152095	−	0.439449i
$951$	−984.410	−	2654.27i	−0.0335664	−	0.0905053i
$952$	24090.4	−	22970.1i	0.820140	−	0.782002i
$953$	35479.9	−	40946.0i	1.20599	−	1.39179i	0.308222	−	0.951314i	$-0.400266\pi$
$953$	35479.9	−	40946.0i	1.20599	−	1.39179i	0.897767	−	0.440471i	$-0.145189\pi$
$954$	22223.7	−	8801.92i	0.754213	−	0.298713i
$955$	42.6797	+	27.4286i	0.00144616	+	0.000929391i
$956$	863.647	−	298.911i	0.0292179	−	0.0101124i
$957$	−11433.8	+	16826.4i	−0.386210	+	0.568361i
$958$	−10432.7	−	13266.3i	−0.351844	−	0.447406i
$959$	51762.1	+	17915.0i	1.74295	+	0.603239i
$960$	14.6845	+	124.771i	0.000493687	+	0.00419475i
$961$	1517.49	−	6255.19i	0.0509379	−	0.209969i
$962$	−39914.7	+	87401.1i	−1.33774	+	2.92924i
$963$	45314.6	+	11170.6i	1.51635	+	0.373798i
$964$	−303.532	−	472.305i	−0.0101412	−	0.0157800i
$965$	110.423	−	191.259i	0.00368358	−	0.00638015i
$966$	−38485.8	+	13755.2i	−1.28184	+	0.458142i
$967$	−26070.5	−	45155.4i	−0.866980	−	1.50165i	−0.865067	−	0.501656i	$-0.832724\pi$
$967$	−26070.5	−	45155.4i	−0.866980	−	1.50165i	−0.00191331	−	0.999998i	$-0.500609\pi$
$968$	10913.6	−	21169.5i	0.362373	−	0.702906i
$969$	9807.10	−	6611.25i	0.325128	−	0.219179i
$970$	−91.2982	−	128.210i	−0.00302207	−	0.00424390i
$971$	−39958.1	+	11732.8i	−1.32062	+	0.387768i	−0.864715	−	0.502263i	$-0.832501\pi$
$971$	−39958.1	+	11732.8i	−1.32062	+	0.387768i	−0.455900	+	0.890031i	$0.650683\pi$
$972$	−60.1551	+	744.399i	−0.00198506	+	0.0245644i
$973$	19070.3	−	16524.5i	0.628331	−	0.544452i
$974$	−12488.2	+	31194.0i	−0.410829	+	1.02620i
$975$	−52235.9	+	25255.5i	−1.71578	+	0.829563i
$976$	−10037.6	+	52079.9i	−0.329196	+	1.70803i
$977$	−2037.12	+	42764.5i	−0.0667077	+	1.40037i	0.679022	+	0.734118i	$0.262404\pi$
$977$	−2037.12	+	42764.5i	−0.0667077	+	1.40037i	−0.745730	+	0.666249i	$0.767899\pi$
$978$	25988.4	+	9747.89i	0.849711	+	0.318715i
$979$	−1995.12	−	5764.52i	−0.0651320	−	0.188187i
$980$	2.54282	+	0.746639i	8.28851e−5	+	2.43373e-5i
$981$	1821.05	+	41449.6i	0.0592676	+	1.34901i
$982$	−2229.46	−	2572.93i	−0.0724490	−	0.0836106i
$983$	−29734.8	−	2839.32i	−0.964793	−	0.0921265i	−0.399247	−	0.916843i	$-0.630728\pi$
$983$	−29734.8	−	2839.32i	−0.964793	−	0.0921265i	−0.565546	+	0.824717i	$0.691334\pi$
$984$	−28791.5	−	738.577i	−0.932764	−	0.0239278i
$985$	−13.8451	−	144.992i	−0.000447859	−	0.00469019i
$986$	−38251.6	+	15313.6i	−1.23548	+	0.494610i
$987$	8395.63	−	2232.99i	0.270756	−	0.0720130i
$988$	580.323	+	335.049i	0.0186868	+	0.0107888i
$989$	−10005.0	+	4426.09i	−0.321678	+	0.142307i
$990$	−35.5597	+	49.5482i	−0.00114158	+	0.00159065i
$991$	7414.82	−	4765.22i	0.237679	−	0.152747i	−0.416380	−	0.909191i	$-0.636701\pi$
$991$	7414.82	−	4765.22i	0.237679	−	0.152747i	0.654059	+	0.756444i	$0.273065\pi$
$992$	1049.53	−	1334.59i	0.0335915	−	0.0427150i
$993$	−16635.7	−	3651.07i	−0.531640	−	0.116680i
$994$	23909.0	−	25075.1i	0.762926	−	0.800134i
$995$	65.1764	+	46.4119i	0.00207661	+	0.00147875i
$996$	−794.890	−	96.5302i	−0.0252882	−	0.00307096i
$997$	−31208.4	−	12494.0i	−0.991355	−	0.396879i	−0.181425	−	0.983405i	$-0.558071\pi$
$997$	−31208.4	−	12494.0i	−0.991355	−	0.396879i	−0.809930	+	0.586526i	$0.800495\pi$
$998$	7590.76	−	25851.8i	0.240763	−	0.819963i
$999$	−4051.29	+	52550.5i	−0.128305	+	1.66429i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.o.a.11.51	✓	1400
9.5	odd	6	inner	207.4.o.a.149.51	yes	1400
23.21	odd	22	inner	207.4.o.a.182.51	yes	1400
207.113	even	66	inner	207.4.o.a.113.51	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.o.a.11.51	✓	1400	1.1	even	1	trivial
207.4.o.a.113.51	yes	1400	207.113	even	66	inner
207.4.o.a.149.51	yes	1400	9.5	odd	6	inner
207.4.o.a.182.51	yes	1400	23.21	odd	22	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

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.11.51

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