LMFDB - Embedded newform 153.3.t.a.7.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(7,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([32, 33])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.t (of order $48$, degree $16$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			7.19
Character	$\chi$	$=$	153.7
Dual form			153.3.t.a.22.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.286178 + 0.372954i) q^{2} +(-1.53721 - 2.57624i) q^{3} +(0.978079 - 3.65024i) q^{4} +(-1.59407 + 1.39796i) q^{5} +(0.520903 - 1.31057i) q^{6} +(-2.48802 - 2.18193i) q^{7} +(3.37853 - 1.39943i) q^{8} +(-4.27399 + 7.92042i) q^{9} +(-0.977562 - 0.194449i) q^{10} +(-0.351962 - 5.36990i) q^{11} +(-10.9074 + 3.09141i) q^{12} +(-20.2258 - 5.41948i) q^{13} +(0.101746 - 1.55234i) q^{14} +(6.05190 + 1.95774i) q^{15} +(-11.6021 - 6.69847i) q^{16} +(-5.36360 + 16.1317i) q^{17} +(-4.17707 + 0.672646i) q^{18} +(10.2395 - 24.7203i) q^{19} +(3.54377 + 7.18606i) q^{20} +(-1.79658 + 9.76381i) q^{21} +(1.90200 - 1.66801i) q^{22} +(9.44455 - 19.1517i) q^{23} +(-8.79877 - 6.55268i) q^{24} +(-2.67639 + 20.3292i) q^{25} +(-3.76694 - 9.09421i) q^{26} +(26.9749 - 1.16452i) q^{27} +(-10.3981 + 6.94776i) q^{28} +(9.14303 - 26.9345i) q^{29} +(1.00177 + 2.81734i) q^{30} +(-1.07994 + 16.4768i) q^{31} +(-2.73132 - 20.7464i) q^{32} +(-13.2931 + 9.16138i) q^{33} +(-7.55132 + 2.61616i) q^{34} +7.01634 q^{35} +(24.7311 + 23.3479i) q^{36} +(30.4130 - 45.5163i) q^{37} +(12.1498 - 3.25554i) q^{38} +(17.1293 + 60.4372i) q^{39} +(-3.42926 + 6.95385i) q^{40} +(68.3251 - 23.1932i) q^{41} +(-4.15559 + 2.12414i) q^{42} +(-36.5791 - 4.81573i) q^{43} +(-19.9457 - 3.96744i) q^{44} +(-4.25941 - 18.6006i) q^{45} +(9.84550 - 1.95839i) q^{46} +(22.2515 + 83.0436i) q^{47} +(0.577975 + 40.1866i) q^{48} +(-4.96638 - 37.7234i) q^{49} +(-8.34779 + 4.81960i) q^{50} +(49.8040 - 10.9799i) q^{51} +(-39.5648 + 68.5282i) q^{52} +(-4.56444 + 11.0195i) q^{53} +(8.15392 + 9.72712i) q^{54} +(8.06796 + 8.06796i) q^{55} +(-11.4593 - 3.88992i) q^{56} +(-79.4255 + 11.6209i) q^{57} +(12.6618 - 4.29812i) q^{58} +(-16.4582 - 12.6288i) q^{59} +(13.0655 - 20.1761i) q^{60} +(-21.9331 + 25.0099i) q^{61} +(-6.45413 + 4.31251i) q^{62} +(27.9156 - 10.3806i) q^{63} +(-30.9364 + 30.9364i) q^{64} +(39.8175 - 19.6358i) q^{65} +(-7.22096 - 2.33593i) q^{66} +(71.7411 - 41.4198i) q^{67} +(53.6386 + 35.3565i) q^{68} +(-63.8574 + 5.10867i) q^{69} +(2.00792 + 2.61677i) q^{70} +(30.5912 - 45.7830i) q^{71} +(-3.35570 + 32.7405i) q^{72} +(-4.26575 - 21.4454i) q^{73} +(25.6790 - 1.68309i) q^{74} +(56.4871 - 24.3552i) q^{75} +(-80.2200 - 61.5549i) q^{76} +(-10.8411 + 14.1284i) q^{77} +(-17.6383 + 23.6842i) q^{78} +(-4.20332 - 64.1302i) q^{79} +(27.8587 - 5.54145i) q^{80} +(-44.4661 - 67.7035i) q^{81} +(28.2031 + 18.8447i) q^{82} +(3.20366 - 2.45825i) q^{83} +(33.8831 + 16.1077i) q^{84} +(-14.0016 - 33.2132i) q^{85} +(-8.67207 - 15.0205i) q^{86} +(-83.4443 + 17.8493i) q^{87} +(-8.70393 - 17.6498i) q^{88} +(32.5868 + 32.5868i) q^{89} +(5.71821 - 6.91163i) q^{90} +(38.4971 + 57.6150i) q^{91} +(-60.6706 - 53.2067i) q^{92} +(44.1082 - 22.5460i) q^{93} +(-24.6036 + 32.0640i) q^{94} +(18.2356 + 53.7202i) q^{95} +(-49.2491 + 38.9281i) q^{96} +(6.33637 - 18.6663i) q^{97} +(12.6478 - 12.6478i) q^{98} +(44.0361 + 20.1632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) $ 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.286178	+	0.372954i	0.143089	+	0.186477i	0.859400	−	0.511304i	$-0.170837\pi$
$2$	0.286178	+	0.372954i	0.143089	+	0.186477i	−0.716311	+	0.697781i	$0.754171\pi$
$3$	−1.53721	−	2.57624i	−0.512402	−	0.858745i
$3$	−1.53721	−	2.57624i	−0.512402	−	0.858745i
$4$	0.978079	−	3.65024i	0.244520	−	0.912560i
$5$	−1.59407	+	1.39796i	−0.318814	+	0.279592i	−0.803762	−	0.594950i	$-0.797172\pi$
$5$	−1.59407	+	1.39796i	−0.318814	+	0.279592i	0.484948	+	0.874543i	$0.338838\pi$
$6$	0.520903	−	1.31057i	0.0868172	−	0.218428i
$7$	−2.48802	−	2.18193i	−0.355431	−	0.311705i	0.462946	−	0.886387i	$-0.346792\pi$
$7$	−2.48802	−	2.18193i	−0.355431	−	0.311705i	−0.818377	+	0.574682i	$0.805126\pi$
$8$	3.37853	−	1.39943i	0.422316	−	0.174929i
$9$	−4.27399	+	7.92042i	−0.474888	+	0.880046i
$10$	−0.977562	−	0.194449i	−0.0977562	−	0.0194449i
$11$	−0.351962	−	5.36990i	−0.0319965	−	0.488173i	−0.983544	−	0.180670i	$-0.942173\pi$
$11$	−0.351962	−	5.36990i	−0.0319965	−	0.488173i	0.951547	−	0.307503i	$-0.0994933\pi$
$12$	−10.9074	+	3.09141i	−0.908950	+	0.257618i
$13$	−20.2258	−	5.41948i	−1.55583	−	0.416883i	−0.624488	−	0.781034i	$-0.714692\pi$
$13$	−20.2258	−	5.41948i	−1.55583	−	0.416883i	−0.931340	+	0.364151i	$0.881359\pi$
$14$	0.101746	−	1.55234i	0.00726754	−	0.110881i
$15$	6.05190	+	1.95774i	0.403460	+	0.130516i
$16$	−11.6021	−	6.69847i	−0.725130	−	0.418654i
$17$	−5.36360	+	16.1317i	−0.315506	+	0.948924i
$17$	−5.36360	+	16.1317i	−0.315506	+	0.948924i
$18$	−4.17707	+	0.672646i	−0.232059	+	0.0373692i
$19$	10.2395	−	24.7203i	0.538920	−	1.30107i	−0.386558	−	0.922265i	$-0.626336\pi$
$19$	10.2395	−	24.7203i	0.538920	−	1.30107i	0.925478	−	0.378802i	$-0.123664\pi$
$20$	3.54377	+	7.18606i	0.177189	+	0.359303i
$21$	−1.79658	+	9.76381i	−0.0855513	+	0.464943i
$22$	1.90200	−	1.66801i	0.0864546	−	0.0758186i
$23$	9.44455	−	19.1517i	0.410633	−	0.832681i	−0.589065	−	0.808086i	$-0.700504\pi$
$23$	9.44455	−	19.1517i	0.410633	−	0.832681i	0.999697	−	0.0245949i	$-0.00782960\pi$
$24$	−8.79877	−	6.55268i	−0.366616	−	0.273028i
$25$	−2.67639	+	20.3292i	−0.107056	+	0.813169i
$26$	−3.76694	−	9.09421i	−0.144882	−	0.349777i
$27$	26.9749	−	1.16452i	0.999069	−	0.0431305i
$28$	−10.3981	+	6.94776i	−0.371359	+	0.248134i
$29$	9.14303	−	26.9345i	0.315277	−	0.928775i	−0.667601	−	0.744519i	$-0.732679\pi$
$29$	9.14303	−	26.9345i	0.315277	−	0.928775i	0.982878	−	0.184256i	$-0.0589877\pi$
$30$	1.00177	+	2.81734i	0.0333923	+	0.0939113i
$31$	−1.07994	+	16.4768i	−0.0348369	+	0.531509i	0.944401	+	0.328795i	$0.106643\pi$
$31$	−1.07994	+	16.4768i	−0.0348369	+	0.531509i	−0.979238	+	0.202713i	$0.935024\pi$
$32$	−2.73132	−	20.7464i	−0.0853538	−	0.648326i
$33$	−13.2931	+	9.16138i	−0.402821	+	0.277618i
$34$	−7.55132	+	2.61616i	−0.222098	+	0.0769458i
$35$	7.01634			0.200467
$36$	24.7311	+	23.3479i	0.686976	+	0.648552i
$37$	30.4130	−	45.5163i	0.821974	−	1.23017i	−0.148487	−	0.988914i	$-0.547440\pi$
$37$	30.4130	−	45.5163i	0.821974	−	1.23017i	0.970461	−	0.241257i	$-0.0775597\pi$
$38$	12.1498	−	3.25554i	0.319732	−	0.0856720i
$39$	17.1293	+	60.4372i	0.439214	+	1.54967i
$40$	−3.42926	+	6.95385i	−0.0857315	+	0.173846i
$41$	68.3251	−	23.1932i	1.66646	−	0.565689i	0.680515	−	0.732734i	$-0.261756\pi$
$41$	68.3251	−	23.1932i	1.66646	−	0.565689i	0.985949	+	0.167045i	$0.0534226\pi$
$42$	−4.15559	+	2.12414i	−0.0989426	+	0.0505748i
$43$	−36.5791	−	4.81573i	−0.850677	−	0.111994i	−0.307434	−	0.951569i	$-0.599470\pi$
$43$	−36.5791	−	4.81573i	−0.850677	−	0.111994i	−0.543243	+	0.839576i	$0.682804\pi$
$44$	−19.9457	−	3.96744i	−0.453311	−	0.0901691i
$45$	−4.25941	−	18.6006i	−0.0946535	−	0.413346i
$46$	9.84550	−	1.95839i	0.214033	−	0.0425737i
$47$	22.2515	+	83.0436i	0.473436	+	1.76689i	0.627283	+	0.778791i	$0.284167\pi$
$47$	22.2515	+	83.0436i	0.473436	+	1.76689i	−0.153847	+	0.988095i	$0.549166\pi$
$48$	0.577975	+	40.1866i	0.0120411	+	0.837222i
$49$	−4.96638	−	37.7234i	−0.101355	−	0.769866i
$50$	−8.34779	+	4.81960i	−0.166956	+	0.0963919i
$51$	49.8040	−	10.9799i	0.976550	−	0.215292i
$52$	−39.5648	+	68.5282i	−0.760862	+	1.31785i
$53$	−4.56444	+	11.0195i	−0.0861216	+	0.207916i	−0.961073	−	0.276295i	$-0.910893\pi$
$53$	−4.56444	+	11.0195i	−0.0861216	+	0.207916i	0.874951	+	0.484211i	$0.160893\pi$
$54$	8.15392	+	9.72712i	0.150998	+	0.180132i
$55$	8.06796	+	8.06796i	0.146690	+	0.146690i
$56$	−11.4593	−	3.88992i	−0.204631	−	0.0694628i
$57$	−79.4255	+	11.6209i	−1.39343	+	0.203875i
$58$	12.6618	−	4.29812i	0.218308	−	0.0741055i
$59$	−16.4582	−	12.6288i	−0.278953	−	0.214048i	0.459804	−	0.888021i	$-0.347920\pi$
$59$	−16.4582	−	12.6288i	−0.278953	−	0.214048i	−0.738756	+	0.673973i	$0.764586\pi$
$60$	13.0655	−	20.1761i	0.217758	−	0.336268i
$61$	−21.9331	+	25.0099i	−0.359558	+	0.409998i	−0.903131	−	0.429364i	$-0.858738\pi$
$61$	−21.9331	+	25.0099i	−0.359558	+	0.409998i	0.543573	+	0.839362i	$0.317071\pi$
$62$	−6.45413	+	4.31251i	−0.104099	+	0.0695567i
$63$	27.9156	−	10.3806i	0.443105	−	0.164771i
$64$	−30.9364	+	30.9364i	−0.483382	+	0.483382i
$65$	39.8175	−	19.6358i	0.612577	−	0.302090i
$66$	−7.22096	−	2.33593i	−0.109408	−	0.0353928i
$67$	71.7411	−	41.4198i	1.07076	−	0.618205i	0.142373	−	0.989813i	$-0.454527\pi$
$67$	71.7411	−	41.4198i	1.07076	−	0.618205i	0.928390	+	0.371608i	$0.121193\pi$
$68$	53.6386	+	35.3565i	0.788803	+	0.519949i
$69$	−63.8574	+	5.10867i	−0.925470	+	0.0740387i
$70$	2.00792	+	2.61677i	0.0286845	+	0.0373824i
$71$	30.5912	−	45.7830i	0.430862	−	0.644831i	−0.550982	−	0.834517i	$-0.685747\pi$
$71$	30.5912	−	45.7830i	0.430862	−	0.644831i	0.981845	+	0.189686i	$0.0607469\pi$
$72$	−3.35570	+	32.7405i	−0.0466070	+	0.454730i
$73$	−4.26575	−	21.4454i	−0.0584350	−	0.293772i	0.940506	−	0.339776i	$-0.110351\pi$
$73$	−4.26575	−	21.4454i	−0.0584350	−	0.293772i	−0.998941	+	0.0460038i	$0.985351\pi$
$74$	25.6790	−	1.68309i	0.347014	−	0.0227445i
$75$	56.4871	−	24.3552i	0.753161	−	0.324736i
$76$	−80.2200	−	61.5549i	−1.05553	−	0.809933i
$77$	−10.8411	+	14.1284i	−0.140793	+	0.183485i
$78$	−17.6383	+	23.6842i	−0.226132	+	0.303644i
$79$	−4.20332	−	64.1302i	−0.0532065	−	0.811775i	−0.938183	−	0.346139i	$-0.887492\pi$
$79$	−4.20332	−	64.1302i	−0.0532065	−	0.811775i	0.884977	−	0.465636i	$-0.154174\pi$
$80$	27.8587	−	5.54145i	0.348234	−	0.0692681i
$81$	−44.4661	−	67.7035i	−0.548964	−	0.835846i
$82$	28.2031	+	18.8447i	0.343940	+	0.229814i
$83$	3.20366	−	2.45825i	0.0385983	−	0.0296175i	−0.589282	−	0.807927i	$-0.700589\pi$
$83$	3.20366	−	2.45825i	0.0385983	−	0.0296175i	0.627880	+	0.778310i	$0.283923\pi$
$84$	33.8831	+	16.1077i	0.403370	+	0.191759i
$85$	−14.0016	−	33.2132i	−0.164724	−	0.390743i
$86$	−8.67207	−	15.0205i	−0.100838	−	0.174657i
$87$	−83.4443	+	17.8493i	−0.959130	+	0.205164i
$88$	−8.70393	−	17.6498i	−0.0989083	−	0.200566i
$89$	32.5868	+	32.5868i	0.366144	+	0.366144i	0.866069	−	0.499925i	$-0.166639\pi$
$89$	32.5868	+	32.5868i	0.366144	+	0.366144i	−0.499925	+	0.866069i	$0.666639\pi$
$90$	5.71821	−	6.91163i	0.0635356	−	0.0767959i
$91$	38.4971	+	57.6150i	0.423045	+	0.633132i
$92$	−60.6706	−	53.2067i	−0.659464	−	0.578334i
$93$	44.1082	−	22.5460i	0.474281	−	0.242430i
$94$	−24.6036	+	32.0640i	−0.261740	+	0.341106i
$95$	18.2356	+	53.7202i	0.191953	+	0.565476i
$96$	−49.2491	+	38.9281i	−0.513012	+	0.405501i
$97$	6.33637	−	18.6663i	0.0653234	−	0.192436i	−0.909367	−	0.415994i	$-0.863434\pi$
$97$	6.33637	−	18.6663i	0.0653234	−	0.192436i	0.974691	+	0.223558i	$0.0717671\pi$
$98$	12.6478	−	12.6478i	0.129059	−	0.129059i
$99$	44.0361	+	20.1632i	0.444809	+	0.203669i
$100$	71.5888	+	29.6531i	0.715888	+	0.296531i
$101$	−73.1428	−	42.2290i	−0.724186	−	0.418109i	0.0921051	−	0.995749i	$-0.470640\pi$
$101$	−73.1428	−	42.2290i	−0.724186	−	0.418109i	−0.816292	+	0.577640i	$0.803974\pi$
$102$	18.3478	+	15.4324i	0.179880	+	0.151298i
$103$	−16.6233	−	28.7924i	−0.161391	−	0.279538i	0.773977	−	0.633214i	$-0.218265\pi$
$103$	−16.6233	−	28.7924i	−0.161391	−	0.279538i	−0.935368	+	0.353676i	$0.884931\pi$
$104$	−75.9176	+	9.99474i	−0.729977	+	0.0961033i
$105$	−10.7856	−	18.0757i	−0.102720	−	0.172150i
$106$	−5.41602	+	1.45122i	−0.0510945	+	0.0136907i
$107$	20.9618	+	105.382i	0.195904	+	0.984878i	0.946152	+	0.323721i	$0.104934\pi$
$107$	20.9618	+	105.382i	0.195904	+	0.984878i	−0.750248	+	0.661156i	$0.770066\pi$
$108$	22.1328	−	99.6038i	0.204933	−	0.922257i
$109$	−3.82359	+	19.2225i	−0.0350788	+	0.176353i	−0.994353	−	0.106124i	$-0.966156\pi$
$109$	−3.82359	+	19.2225i	−0.0350788	+	0.176353i	0.959274	+	0.282477i	$0.0911561\pi$
$110$	−0.700108	+	5.31785i	−0.00636462	+	0.0483441i
$111$	−164.012	−	8.38315i	−1.47759	−	0.0755239i
$112$	14.2506	+	41.9809i	0.127237	+	0.374829i
$113$	−175.048	−	86.3239i	−1.54909	−	0.763929i	−0.551561	−	0.834134i	$-0.685968\pi$
$113$	−175.048	−	86.3239i	−1.54909	−	0.763929i	−0.997533	+	0.0702058i	$0.977634\pi$
$114$	−27.0638	−	26.2964i	−0.237402	−	0.230670i
$115$	11.7180	+	43.7322i	0.101896	+	0.380280i
$116$	−89.3748	−	59.7183i	−0.770472	−	0.514813i
$117$	129.369	−	137.034i	1.10572	−	1.17123i
$118$		−	9.75224i		−	0.0826461i
$119$	48.5430	−	28.4330i	0.407925	−	0.238932i
$120$	23.1863	−	1.85493i	0.193219	−	0.0154577i
$121$	91.2529	−	12.0137i	0.754156	−	0.0992865i
$122$	−15.6043	−	1.02276i	−0.127904	−	0.00838326i
$123$	−164.781	−	140.369i	−1.33968	−	1.14121i
$124$	59.0879	+	20.0577i	0.476516	+	0.161755i
$125$	−53.6015	−	80.2203i	−0.428812	−	0.641762i
$126$	11.8603	+	7.44053i	0.0941293	+	0.0590519i
$127$	5.64008	−	2.33620i	0.0444101	−	0.0183953i	−0.360368	−	0.932810i	$-0.617349\pi$
$127$	5.64008	−	2.33620i	0.0444101	−	0.0183953i	0.404778	+	0.914415i	$0.367349\pi$
$128$	−103.377	−	13.6098i	−0.807632	−	0.106327i
$129$	43.8232	+	101.639i	0.339715	+	0.787900i
$130$	18.7181	+	9.23076i	0.143986	+	0.0710058i
$131$	55.5209	+	63.3095i	0.423824	+	0.483279i	0.923862	−	0.382725i	$-0.125014\pi$
$131$	55.5209	+	63.3095i	0.423824	+	0.483279i	−0.500039	+	0.866003i	$0.666681\pi$
$132$	20.4396	+	57.4835i	0.154845	+	0.435481i
$133$	−79.4140	+	39.1627i	−0.597098	+	0.294456i
$134$	35.9784	+	14.9027i	0.268495	+	0.111214i
$135$	−41.3719	+	39.5662i	−0.306458	+	0.293083i
$136$	4.45416	+	62.0075i	0.0327512	+	0.455937i
$137$	−122.515	+	212.202i	−0.894271	+	1.54892i	−0.0595658	+	0.998224i	$0.518972\pi$
$137$	−122.515	+	212.202i	−0.894271	+	1.54892i	−0.834705	+	0.550698i	$0.814362\pi$
$138$	−20.1799	−	22.3539i	−0.146231	−	0.161985i
$139$	−22.3167	−	1.46271i	−0.160551	−	0.0105231i	−0.0150846	−	0.999886i	$-0.504802\pi$
$139$	−22.3167	−	1.46271i	−0.160551	−	0.0105231i	−0.145467	+	0.989363i	$0.546468\pi$
$140$	6.86253	−	25.6113i	0.0490181	−	0.182938i
$141$	179.735	−	184.980i	1.27472	−	1.31192i
$142$	25.8295	−	1.69295i	0.181898	−	0.0119222i
$143$	−21.9833	+	110.518i	−0.153730	+	0.772851i
$144$	102.642	−	63.2642i	0.712790	−	0.439335i
$145$	23.0788	+	55.7170i	0.159164	+	0.384255i
$146$	6.77738	−	7.72812i	0.0464204	−	0.0529323i
$147$	−89.5501	+	70.7833i	−0.609184	+	0.481519i
$148$	−136.399	−	155.534i	−0.921617	−	1.05090i
$149$	−0.602534	−	0.161448i	−0.00404385	−	0.00108355i	0.256797	−	0.966465i	$-0.417333\pi$
$149$	−0.602534	−	0.161448i	−0.00404385	−	0.00108355i	−0.260840	+	0.965382i	$0.584000\pi$
$150$	25.2487	+	14.0972i	0.168325	+	0.0939810i
$151$	−25.7587	+	19.7653i	−0.170587	+	0.130896i	−0.690527	−	0.723307i	$-0.742621\pi$
$151$	−25.7587	+	19.7653i	−0.170587	+	0.130896i	0.519939	+	0.854203i	$0.325955\pi$
$152$		−	97.8477i		−	0.643735i
$153$	−104.846	−	111.429i	−0.685267	−	0.728292i
$154$	−8.37170			−0.0543617
$155$	−21.3124	−	27.7749i	−0.137499	−	0.179193i
$156$	237.364	−	3.41384i	1.52157	−	0.0218836i
$157$	−45.7356	+	170.688i	−0.291310	+	1.08718i	0.652795	+	0.757535i	$0.273596\pi$
$157$	−45.7356	+	170.688i	−0.291310	+	1.08718i	−0.944104	+	0.329647i	$0.893070\pi$
$158$	22.7147	−	19.9203i	0.143764	−	0.126078i
$159$	35.4054	−	5.18023i	0.222676	−	0.0325801i
$160$	33.3566	+	29.2530i	0.208479	+	0.182831i
$161$	−65.2859	+	27.0423i	−0.405502	+	0.167965i
$162$	12.5251	−	35.9590i	0.0773155	−	0.221969i
$163$	172.050	+	34.2228i	1.05552	+	0.209956i	0.692198	−	0.721708i	$-0.256643\pi$
$163$	172.050	+	34.2228i	1.05552	+	0.209956i	0.363322	+	0.931664i	$0.381643\pi$
$164$	−17.8336	−	272.088i	−0.108741	−	1.65907i
$165$	8.38285	−	33.1871i	0.0508051	−	0.201134i
$166$	1.83363	+	0.491319i	0.0110460	+	0.00295975i
$167$	−12.6531	+	193.049i	−0.0757670	+	1.15598i	0.775535	+	0.631305i	$0.217480\pi$
$167$	−12.6531	+	193.049i	−0.0757670	+	1.15598i	−0.851302	+	0.524676i	$0.824186\pi$
$168$	7.59401	+	35.5015i	0.0452024	+	0.211319i
$169$	233.353	+	134.726i	1.38078	+	0.797196i
$170$	8.38005	−	14.7268i	0.0492944	−	0.0866282i
$171$	152.032	+	186.755i	0.889073	+	1.09214i
$172$	−53.3558	+	128.812i	−0.310208	+	0.748909i
$173$	82.9973	+	168.302i	0.479753	+	0.972844i	0.993385	+	0.114833i	$0.0366332\pi$
$173$	82.9973	+	168.302i	0.479753	+	0.972844i	−0.513631	+	0.858011i	$0.671700\pi$
$174$	−30.5369	−	26.0128i	−0.175499	−	0.149499i
$175$	51.0159	−	44.7398i	0.291520	−	0.255656i
$176$	−31.8866	+	64.6596i	−0.181174	+	0.367384i
$177$	−7.23517	+	61.8133i	−0.0408766	+	0.349228i
$178$	−2.82776	+	21.4790i	−0.0158863	+	0.120668i
$179$	55.1724	+	133.198i	0.308226	+	0.744123i	0.999763	+	0.0217818i	$0.00693390\pi$
$179$	55.1724	+	133.198i	0.308226	+	0.744123i	−0.691537	+	0.722341i	$0.743066\pi$
$180$	−72.0626	−	2.64497i	−0.400348	−	0.0146943i
$181$	203.964	−	136.284i	1.12687	−	0.752953i	0.154873	−	0.987934i	$-0.450503\pi$
$181$	203.964	−	136.284i	1.12687	−	0.752953i	0.972000	+	0.234982i	$0.0755030\pi$
$182$	−10.4707	+	30.8458i	−0.0575315	+	0.169482i
$183$	98.1469	+	18.0594i	0.536322	+	0.0986852i
$184$	5.10725	−	77.9215i	0.0277568	−	0.423486i
$185$	15.1496	+	115.073i	0.0818896	+	0.622014i
$186$	21.0314	+	9.99814i	0.113072	+	0.0537535i
$187$	88.5134	+	23.1242i	0.473334	+	0.123659i
$188$	324.893			1.72815
$189$	−69.6549	−	55.9600i	−0.368544	−	0.296085i
$190$	−14.8166	+	22.1746i	−0.0779819	+	0.116708i
$191$	47.3735	−	12.6937i	0.248029	−	0.0664591i	−0.132663	−	0.991161i	$-0.542353\pi$
$191$	47.3735	−	12.6937i	0.248029	−	0.0664591i	0.380691	+	0.924702i	$0.375686\pi$
$192$	127.255	+	32.1438i	0.662788	+	0.167416i
$193$	154.255	−	312.797i	0.799247	−	1.62071i	0.0153002	−	0.999883i	$-0.495130\pi$
$193$	154.255	−	312.797i	0.799247	−	1.62071i	0.783946	−	0.620829i	$-0.213204\pi$
$194$	8.77501	−	2.97871i	0.0452320	−	0.0153542i
$195$	−111.794	−	72.3950i	−0.573304	−	0.371256i
$196$	−142.557	−	18.7680i	−0.727332	−	0.0957551i
$197$	−332.670	−	66.1722i	−1.68868	−	0.335900i	−0.745078	−	0.666977i	$-0.767588\pi$
$197$	−332.670	−	66.1722i	−1.68868	−	0.335900i	−0.943604	+	0.331078i	$0.892588\pi$
$198$	5.08221	+	22.1937i	0.0256677	+	0.112089i
$199$	−74.0170	+	14.7229i	−0.371945	+	0.0739844i	−0.377523	−	0.926000i	$-0.623224\pi$
$199$	−74.0170	+	14.7229i	−0.371945	+	0.0739844i	0.00557872	+	0.999984i	$0.498224\pi$
$200$	19.4071	+	72.4284i	0.0970356	+	0.362142i
$201$	−216.988	−	121.151i	−1.07954	−	0.602743i
$202$	−5.18236	−	39.3639i	−0.0256552	−	0.194871i
$203$	−81.5173	+	47.0640i	−0.401563	+	0.231842i
$204$	8.63310	−	192.536i	0.0423191	−	0.943804i
$205$	−76.4917	+	132.487i	−0.373130	+	0.646280i
$206$	5.98102	−	14.4395i	0.0290341	−	0.0700945i
$207$	111.323	+	156.659i	0.537793	+	0.756806i
$208$	198.359	+	198.359i	0.953648	+	0.953648i
$209$	−136.349	−	46.2843i	−0.652389	−	0.221456i
$210$	3.65483	−	9.19539i	0.0174040	−	0.0437876i
$211$	112.365	−	38.1427i	0.532535	−	0.180771i	−0.0422027	−	0.999109i	$-0.513438\pi$
$211$	112.365	−	38.1427i	0.532535	−	0.180771i	0.574737	+	0.818338i	$0.305104\pi$
$212$	35.7596	+	27.4393i	0.168677	+	0.129431i
$213$	−164.973	−	8.43226i	−0.774521	−	0.0395881i
$214$	−33.3038	+	37.9757i	−0.155625	+	0.177457i
$215$	65.0418	−	43.4596i	0.302520	−	0.202137i
$216$	89.5058	−	41.6839i	0.414379	−	0.192981i
$217$	38.6382	−	38.6382i	0.178056	−	0.178056i
$218$	−8.26333	+	4.07503i	−0.0379052	+	0.0186928i
$219$	−48.6911	+	43.9556i	−0.222334	+	0.200711i
$220$	37.3411	−	21.5589i	0.169732	−	0.0979950i
$221$	195.908	−	297.208i	0.886463	−	1.34483i
$222$	−43.8100	−	63.5680i	−0.197342	−	0.286342i
$223$	−75.3462	−	98.1930i	−0.337875	−	0.440328i	0.593255	−	0.805015i	$-0.297843\pi$
$223$	−75.3462	−	98.1930i	−0.337875	−	0.440328i	−0.931130	+	0.364687i	$0.881176\pi$
$224$	−38.4718	+	57.5771i	−0.171749	+	0.257041i
$225$	−149.577	−	108.085i	−0.664787	−	0.480378i
$226$	−17.8999	−	89.9886i	−0.0792029	−	0.398180i
$227$	119.762	−	7.84965i	0.527588	−	0.0345800i	0.200718	−	0.979649i	$-0.435673\pi$
$227$	119.762	−	7.84965i	0.527588	−	0.0345800i	0.326870	+	0.945069i	$0.394006\pi$
$228$	−35.2654	+	301.288i	−0.154673	+	1.32144i
$229$	−163.803	−	125.691i	−0.715298	−	0.548868i	0.185744	−	0.982598i	$-0.440530\pi$
$229$	−163.803	−	125.691i	−0.715298	−	0.548868i	−0.901043	+	0.433730i	$0.857197\pi$
$230$	−12.9567	+	16.8854i	−0.0563333	+	0.0734150i
$231$	53.0630	+	6.21095i	0.229710	+	0.0268872i
$232$	−6.80302	−	103.794i	−0.0293234	−	0.447388i
$233$	−38.4078	+	7.63979i	−0.164840	+	0.0327888i	−0.276820	−	0.960922i	$-0.589281\pi$
$233$	−38.4078	+	7.63979i	−0.164840	+	0.0327888i	0.111980	+	0.993710i	$0.464281\pi$
$234$	88.1298	+	9.03276i	0.376623	+	0.0386015i
$235$	−151.562	−	101.271i	−0.644946	−	0.430939i
$236$	−62.1957	+	47.7244i	−0.263541	+	0.202222i
$237$	−158.753	+	109.410i	−0.669845	+	0.461646i
$238$	24.4961	+	9.96744i	0.102925	+	0.0418800i
$239$	29.6562	+	51.3660i	0.124085	+	0.214921i	0.921375	−	0.388675i	$-0.127067\pi$
$239$	29.6562	+	51.3660i	0.124085	+	0.214921i	−0.797290	+	0.603596i	$0.793734\pi$
$240$	−57.1007	−	63.2523i	−0.237920	−	0.263551i
$241$	72.2906	+	146.591i	0.299961	+	0.608261i	0.993714	−	0.111953i	$-0.0357105\pi$
$241$	72.2906	+	146.591i	0.299961	+	0.608261i	−0.693753	+	0.720213i	$0.744044\pi$
$242$	30.5951	+	30.5951i	0.126426	+	0.126426i
$243$	−106.067	+	218.629i	−0.436489	+	0.899710i
$244$	69.8397	+	104.523i	0.286228	+	0.428371i
$245$	60.6526	+	53.1909i	0.247562	+	0.217106i
$246$	5.19441	−	101.626i	0.0211155	−	0.413114i
$247$	−341.072	+	444.494i	−1.38086	+	1.79957i
$248$	19.4095	+	57.1786i	0.0782642	+	0.230559i
$249$	−11.2577	−	4.47453i	−0.0452117	−	0.0179700i
$250$	14.5789	−	42.9481i	0.0583157	−	0.171792i
$251$	20.5006	−	20.5006i	0.0816757	−	0.0816757i	−0.665089	−	0.746764i	$-0.731606\pi$
$251$	20.5006	−	20.5006i	0.0816757	−	0.0816757i	0.746764	+	0.665089i	$0.231606\pi$
$252$	−10.5880	−	112.052i	−0.0420159	−	0.444650i
$253$	−106.167	−	43.9756i	−0.419631	−	0.173817i
$254$	2.48536	+	1.43492i	0.00978488	+	0.00564930i
$255$	−64.0417	+	87.1268i	−0.251144	+	0.341674i
$256$	62.9931	+	109.107i	0.246067	+	0.426200i
$257$	−279.568	+	36.8058i	−1.08781	+	0.143213i	−0.653037	−	0.757326i	$-0.726506\pi$
$257$	−279.568	+	36.8058i	−1.08781	+	0.143213i	−0.434775	+	0.900539i	$0.643172\pi$
$258$	−25.3655	+	45.4309i	−0.0983159	+	0.176089i
$259$	−174.982	+	46.8863i	−0.675606	+	0.181028i
$260$	−32.7308	−	164.549i	−0.125888	−	0.632880i
$261$	174.255	+	187.534i	0.667644	+	0.718522i
$262$	−7.72267	+	38.8245i	−0.0294759	+	0.148185i
$263$	41.8171	−	317.632i	0.159000	−	1.20773i	−0.706827	−	0.707386i	$-0.749874\pi$
$263$	41.8171	−	317.632i	0.159000	−	1.20773i	0.865828	−	0.500342i	$-0.166792\pi$
$264$	−32.0904	+	49.5548i	−0.121554	+	0.187708i
$265$	−8.12886	−	23.9468i	−0.0306749	−	0.0903654i
$266$	−37.3324	−	18.4103i	−0.140347	−	0.0692116i
$267$	33.8586	−	134.044i	0.126811	−	0.502037i
$268$	−81.0236	−	302.384i	−0.302327	−	1.12830i
$269$	60.3485	+	40.3235i	0.224344	+	0.149902i	0.662663	−	0.748918i	$-0.269426\pi$
$269$	60.3485	+	40.3235i	0.224344	+	0.149902i	−0.438319	+	0.898819i	$0.644426\pi$
$270$	−26.5961	−	4.10685i	−0.0985039	−	0.0152106i
$271$		−	369.308i		−	1.36276i	−0.731930	−	0.681380i	$-0.761380\pi$
$271$		−	369.308i		−	1.36276i	0.731930	−	0.681380i	$-0.238620\pi$
$272$	170.287	−	151.233i	0.626054	−	0.556005i
$273$	89.2519	−	187.744i	0.326930	−	0.687707i
$274$	−114.203	+	15.0351i	−0.416798	+	0.0548725i
$275$	110.108	+	7.21685i	0.400392	+	0.0262431i
$276$	−43.8098	+	238.092i	−0.158731	+	0.862651i
$277$	−5.21989	−	1.77192i	−0.0188444	−	0.00639681i	0.312001	−	0.950082i	$-0.399001\pi$
$277$	−5.21989	−	1.77192i	−0.0188444	−	0.00639681i	−0.330846	+	0.943685i	$0.607334\pi$
$278$	−5.84100	−	8.74168i	−0.0210108	−	0.0314449i
$279$	−125.887	−	78.9752i	−0.451209	−	0.283065i
$280$	23.7049	−	9.81890i	0.0846604	−	0.0350675i
$281$	411.125	+	54.1256i	1.46308	+	0.192618i	0.819639	−	0.572881i	$-0.194174\pi$
$281$	411.125	+	54.1256i	1.46308	+	0.192618i	0.643438	+	0.765498i	$0.277507\pi$
$282$	120.425	+	14.0956i	0.427040	+	0.0499844i
$283$	−61.9998	−	30.5749i	−0.219081	−	0.108039i	0.329437	−	0.944178i	$-0.393141\pi$
$283$	−61.9998	−	30.5749i	−0.219081	−	0.108039i	−0.548518	+	0.836139i	$0.684808\pi$
$284$	−137.198	−	156.445i	−0.483093	−	0.550862i
$285$	110.364	−	129.558i	0.387243	−	0.454590i
$286$	−47.5092	+	23.4289i	−0.166116	+	0.0819193i
$287$	−220.600	−	91.3756i	−0.768641	−	0.318382i
$288$	175.994	+	67.0368i	0.611091	+	0.232767i
$289$	−231.464	−	173.048i	−0.800912	−	0.598782i
$290$	−14.1753	+	24.5523i	−0.0488802	+	0.0846630i
$291$	−57.8292	+	12.3700i	−0.198726	+	0.0425088i
$292$	−82.4531	−	5.40426i	−0.282374	−	0.0185077i
$293$	74.1715	−	276.812i	0.253145	−	0.944750i	−0.715968	−	0.698133i	$-0.754014\pi$
$293$	74.1715	−	276.812i	0.253145	−	0.944750i	0.969113	−	0.246617i	$-0.0793189\pi$
$294$	−52.0261	−	13.1415i	−0.176960	−	0.0446988i
$295$	43.8901	−	2.87671i	0.148780	−	0.00975156i
$296$	39.0543	−	196.339i	0.131940	−	0.663309i
$297$	−15.7475	−	144.442i	−0.0530219	−	0.486338i
$298$	−0.112219	−	0.270920i	−0.000376573	−	0.000909128i
$299$	−294.815	+	336.172i	−0.986004	+	1.12432i
$300$	−33.6536	−	230.013i	−0.112179	−	0.766709i
$301$	80.5019	+	91.7948i	0.267448	+	0.304966i
$302$	−14.7431	−	3.95040i	−0.0488182	−	0.0130808i
$303$	3.64372	+	253.348i	0.0120255	+	0.836132i
$304$	−284.387	+	218.218i	−0.935484	+	0.717822i
$305$		−	70.5290i		−	0.231243i
$306$	11.5532	−	70.9910i	0.0377555	−	0.231997i
$307$	33.8423			0.110236			0.0551178	−	0.998480i	$-0.482447\pi$
$307$	33.8423			0.110236			0.0551178	+	0.998480i	$0.482447\pi$
$308$	40.9685	+	53.3912i	0.133015	+	0.173348i
$309$	−48.6226	+	87.0854i	−0.157355	+	0.281830i
$310$	4.25961	−	15.8971i	0.0137407	−	0.0512809i
$311$	150.307	−	131.815i	0.483301	−	0.423844i	−0.382710	−	0.923869i	$-0.625009\pi$
$311$	150.307	−	131.815i	0.483301	−	0.423844i	0.866011	+	0.500025i	$0.166676\pi$
$312$	142.450	+	180.218i	0.456570	+	0.577621i
$313$	186.865	+	163.876i	0.597013	+	0.523567i	0.903657	−	0.428258i	$-0.140873\pi$
$313$	186.865	+	163.876i	0.597013	+	0.523567i	−0.306643	+	0.951825i	$0.599206\pi$
$314$	−76.7471	+	31.7897i	−0.244418	+	0.101241i
$315$	−29.9877	+	55.5723i	−0.0951991	+	0.176420i
$316$	−238.202	−	47.3813i	−0.753804	−	0.149941i
$317$	−21.1251	−	322.307i	−0.0666407	−	1.01674i	−0.891972	−	0.452091i	$-0.850678\pi$
$317$	−21.1251	−	322.307i	−0.0666407	−	1.01674i	0.825331	−	0.564649i	$-0.190988\pi$
$318$	12.0642	+	11.7221i	0.0379378	+	0.0368620i
$319$	−147.853	−	39.6172i	−0.463490	−	0.124192i
$320$	6.06688	−	92.5628i	0.0189590	−	0.289259i
$321$	239.266	−	215.996i	0.745377	−	0.672886i
$322$	−28.7689	−	16.6097i	−0.0893443	−	0.0515830i
$323$	343.860	+	297.770i	1.06458	+	0.921888i
$324$	−290.626	+	96.0924i	−0.896993	+	0.296582i
$325$	164.306	−	396.669i	0.505557	−	1.22052i
$326$	36.4732	+	73.9604i	0.111881	+	0.226872i
$327$	55.3994	−	19.6985i	0.169417	−	0.0602400i
$328$	198.381	−	173.975i	0.604820	−	0.530413i
$329$	125.834	−	255.165i	0.382473	−	0.775579i
$330$	14.7762	−	6.37099i	0.0447765	−	0.0193060i
$331$	53.8815	−	409.271i	0.162784	−	1.23647i	−0.693689	−	0.720275i	$-0.744016\pi$
$331$	53.8815	−	409.271i	0.162784	−	1.23647i	0.856473	−	0.516192i	$-0.172651\pi$
$332$	−5.83978	−	14.0985i	−0.0175897	−	0.0424653i
$333$	230.523	+	435.420i	0.692263	+	1.30757i
$334$	−75.6193	+	50.5272i	−0.226405	+	0.151279i
$335$	−56.4571	+	166.317i	−0.168529	+	0.496470i
$336$	86.2466	−	101.246i	0.256686	−	0.301328i
$337$	−33.4410	+	510.211i	−0.0992314	+	1.51398i	0.600530	+	0.799602i	$0.294956\pi$
$337$	−33.4410	+	510.211i	−0.0992314	+	1.51398i	−0.699761	+	0.714377i	$0.746710\pi$
$338$	16.5336	+	125.585i	0.0489160	+	0.371554i
$339$	46.6936	+	583.662i	0.137739	+	1.72172i
$340$	−134.931	+	18.6239i	−0.396855	+	0.0547763i
$341$	88.8587			0.260583
$342$	−26.1430	+	110.146i	−0.0764415	+	0.322064i
$343$	−160.041	+	239.518i	−0.466591	+	0.698303i
$344$	−130.323	+	34.9199i	−0.378846	+	0.101511i
$345$	94.6515	−	97.4138i	0.274352	−	0.282359i
$346$	−39.0169	+	79.1184i	−0.112766	+	0.228666i
$347$	286.438	−	97.2326i	0.825470	−	0.280209i	0.123436	−	0.992353i	$-0.460609\pi$
$347$	286.438	−	97.2326i	0.825470	−	0.280209i	0.702034	+	0.712143i	$0.252275\pi$
$348$	−16.4609	+	322.050i	−0.0473016	+	0.925431i
$349$	−345.073	−	45.4297i	−0.988748	−	0.130171i	−0.381233	−	0.924479i	$-0.624500\pi$
$349$	−345.073	−	45.4297i	−0.988748	−	0.130171i	−0.607515	+	0.794308i	$0.707834\pi$
$350$	31.2855	+	6.22307i	0.0893871	+	0.0177802i
$351$	−551.899	−	122.636i	−1.57236	−	0.349391i
$352$	−110.445	+	21.9689i	−0.313764	+	0.0624115i
$353$	144.015	+	537.472i	0.407975	+	1.52258i	0.798502	+	0.601992i	$0.205626\pi$
$353$	144.015	+	537.472i	0.407975	+	1.52258i	−0.390528	+	0.920591i	$0.627707\pi$
$354$	−25.1241	+	14.9912i	−0.0709719	+	0.0423480i
$355$	15.2383	+	115.747i	0.0429249	+	0.326047i
$356$	150.822	−	87.0772i	0.423658	−	0.244599i
$357$	−147.871	−	81.3510i	−0.414204	−	0.227874i
$358$	−33.8876	+	58.6950i	−0.0946581	+	0.163953i
$359$	222.053	−	536.084i	0.618533	−	1.49327i	−0.234874	−	0.972026i	$-0.575468\pi$
$359$	222.053	−	536.084i	0.618533	−	1.49327i	0.853407	−	0.521245i	$-0.174532\pi$
$360$	−40.4208	−	56.8819i	−0.112280	−	0.158005i
$361$	−250.980	−	250.980i	−0.695235	−	0.695235i
$362$	109.198	+	37.0676i	0.301651	+	0.102397i
$363$	−171.225	−	216.622i	−0.471693	−	0.596754i
$364$	247.962	−	84.1718i	0.681214	−	0.231241i
$365$	36.7797	+	28.2221i	0.100766	+	0.0773208i
$366$	21.3521	+	41.7725i	0.0583391	+	0.114132i
$367$	448.219	−	511.096i	1.22130	−	1.39263i	0.327089	−	0.944993i	$-0.393932\pi$
$367$	448.219	−	511.096i	1.22130	−	1.39263i	0.894215	−	0.447638i	$-0.147734\pi$
$368$	−237.863	+	158.935i	−0.646367	+	0.431889i
$369$	−108.320	+	640.291i	−0.293551	+	1.73520i
$370$	−38.5813	+	38.5813i	−0.104274	+	0.104274i
$371$	35.4003	−	17.4575i	0.0954187	−	0.0470553i
$372$	−39.1572	−	183.057i	−0.105261	−	0.492089i
$373$	322.414	−	186.146i	0.864381	−	0.499051i	−0.00109585	−	0.999999i	$-0.500349\pi$
$373$	322.414	−	186.146i	0.864381	−	0.499051i	0.865477	+	0.500949i	$0.167015\pi$
$374$	16.7063	+	39.6290i	0.0446692	+	0.105960i
$375$	−124.270	+	261.405i	−0.331386	+	0.697081i
$376$	191.391	+	249.426i	0.509020	+	0.663367i
$377$	−330.896	+	495.220i	−0.877707	+	1.31358i
$378$	0.936842	−	41.9926i	0.00247842	−	0.111091i
$379$	38.1116	+	191.600i	0.100558	+	0.505541i	0.997932	+	0.0642707i	$0.0204721\pi$
$379$	38.1116	+	191.600i	0.100558	+	0.505541i	−0.897374	+	0.441271i	$0.854528\pi$
$380$	213.928	−	14.0216i	0.562968	−	0.0368988i
$381$	−14.6886	−	10.9390i	−0.0385527	−	0.0287112i
$382$	18.2914	+	14.0355i	0.0478832	+	0.0367421i
$383$	−387.894	+	505.514i	−1.01278	+	1.31988i	−0.0660609	+	0.997816i	$0.521043\pi$
$383$	−387.894	+	505.514i	−1.01278	+	1.31988i	−0.946718	+	0.322064i	$0.895623\pi$
$384$	123.850	+	287.244i	0.322525	+	0.748033i
$385$	−2.46948	−	37.6770i	−0.00641424	−	0.0978624i
$386$	160.803	−	31.9857i	0.416589	−	0.0828646i
$387$	194.481	−	269.139i	0.502535	−	0.695451i
$388$	−61.9392	−	41.3864i	−0.159637	−	0.106666i
$389$	599.184	−	459.770i	1.54032	−	1.18193i	0.624035	−	0.781396i	$-0.285492\pi$
$389$	599.184	−	459.770i	1.54032	−	1.18193i	0.916283	−	0.400531i	$-0.131174\pi$
$390$	−4.99303	−	62.4119i	−0.0128026	−	0.160031i
$391$	258.292	+	255.078i	0.660594	+	0.652375i
$392$	−69.5705	−	120.500i	−0.177476	−	0.307397i
$393$	77.7530	−	240.355i	0.197845	−	0.611590i
$394$	−70.5236	−	143.008i	−0.178994	−	0.362964i
$395$	96.3520	+	96.3520i	0.243929	+	0.243929i
$396$	116.671	−	141.021i	0.294625	−	0.356114i
$397$	35.9176	+	53.7545i	0.0904725	+	0.135402i	0.873945	−	0.486025i	$-0.161553\pi$
$397$	35.9176	+	53.7545i	0.0904725	+	0.135402i	−0.783473	+	0.621426i	$0.786553\pi$
$398$	−26.6730	−	23.3916i	−0.0670175	−	0.0587728i
$399$	222.968	+	144.388i	0.558817	+	0.361875i
$400$	167.226	−	217.934i	0.418066	−	0.544834i
$401$	21.3956	+	63.0295i	0.0533557	+	0.157181i	0.970341	−	0.241740i	$-0.0777181\pi$
$401$	21.3956	+	63.0295i	0.0533557	+	0.157181i	−0.916985	+	0.398921i	$0.869385\pi$
$402$	−16.9133	−	115.597i	−0.0420728	−	0.287556i
$403$	111.138	−	327.403i	0.275777	−	0.812414i
$404$	−225.686	+	225.686i	−0.558628	+	0.558628i
$405$	165.529	+	45.7623i	0.408713	+	0.112993i
$406$	−40.8811	−	16.9335i	−0.100692	−	0.0417082i
$407$	−255.122	−	147.295i	−0.626836	−	0.361904i
$408$	152.899	−	106.793i	0.374752	−	0.261748i
$409$	187.943	+	325.526i	0.459517	+	0.795907i	0.998935	−	0.0461307i	$-0.0146891\pi$
$409$	187.943	+	325.526i	0.459517	+	0.795907i	−0.539418	+	0.842038i	$0.681356\pi$
$410$	−71.3019	+	9.38707i	−0.173907	+	0.0228953i
$411$	735.014	−	10.5712i	1.78836	−	0.0257206i
$412$	−121.358	+	32.5178i	−0.294558	+	0.0789267i
$413$	13.3931	+	67.3315i	0.0324287	+	0.163030i
$414$	−26.5683	+	86.3506i	−0.0641746	+	0.208576i
$415$	−1.67031	+	8.39721i	−0.00402484	+	0.0202342i
$416$	−57.1918	+	434.415i	−0.137480	+	1.04427i
$417$	30.5370	+	59.7415i	0.0732303	+	0.143265i
$418$	−21.7582	−	64.0975i	−0.0520531	−	0.153343i
$419$	549.914	+	271.188i	1.31244	+	0.647226i	0.957708	−	0.287741i	$-0.0929041\pi$
$419$	549.914	+	271.188i	1.31244	+	0.647226i	0.354736	+	0.934967i	$0.384571\pi$
$420$	−76.5299	+	21.6904i	−0.182214	+	0.0516438i
$421$	−38.6113	−	144.099i	−0.0917133	−	0.342279i	0.904787	−	0.425864i	$-0.140030\pi$
$421$	−38.6113	−	144.099i	−0.0917133	−	0.342279i	−0.996501	+	0.0835849i	$0.973363\pi$
$422$	46.3818	+	30.9913i	0.109909	+	0.0734391i
$423$	−752.843	−	178.686i	−1.77977	−	0.422427i
$424$			43.6175i			0.102871i
$425$	−313.590	−	152.213i	−0.737859	−	0.358147i
$426$	−44.0667	−	63.9404i	−0.103443	−	0.150095i
$427$	109.140	−	14.3685i	0.255596	−	0.0336499i
$428$	405.172	+	26.5564i	0.946663	+	0.0620476i
$429$	318.513	−	113.254i	0.742454	−	0.263996i
$430$	34.8219	+	11.8204i	0.0809812	+	0.0274894i
$431$	−61.5090	−	92.0547i	−0.142712	−	0.213584i	0.753227	−	0.657761i	$-0.228496\pi$
$431$	−61.5090	−	92.0547i	−0.142712	−	0.213584i	−0.895939	+	0.444177i	$0.853496\pi$
$432$	−320.765	−	167.179i	−0.742512	−	0.386989i
$433$	−457.317	+	189.427i	−1.05616	+	0.437475i	−0.842086	−	0.539343i	$-0.818673\pi$
$433$	−457.317	+	189.427i	−1.05616	+	0.437475i	−0.214072	+	0.976818i	$0.568673\pi$
$434$	25.4676	+	3.35288i	0.0586812	+	0.00772552i
$435$	108.063	−	145.105i	0.248422	−	0.333575i
$436$	66.4270	+	32.7582i	0.152356	+	0.0751334i
$437$	−376.727	−	429.575i	−0.862076	−	0.983009i
$438$	−30.3277	−	5.58041i	−0.0692413	−	0.0127407i
$439$	453.995	−	223.886i	1.03416	−	0.509990i	0.155697	−	0.987805i	$-0.450238\pi$
$439$	453.995	−	223.886i	1.03416	−	0.509990i	0.878461	+	0.477815i	$0.158571\pi$
$440$	38.5485	+	15.9673i	0.0876101	+	0.0362893i
$441$	320.011	+	121.894i	0.725650	+	0.276403i
$442$	166.909	−	11.9896i	0.377623	−	0.0271257i
$443$	326.907	−	566.219i	0.737939	−	1.27815i	−0.215483	−	0.976508i	$-0.569133\pi$
$443$	326.907	−	566.219i	0.737939	−	1.27815i	0.953422	−	0.301640i	$-0.0975341\pi$
$444$	−191.017	+	590.484i	−0.430219	+	1.32992i
$445$	−97.5007	−	6.39053i	−0.219103	−	0.0143608i
$446$	15.0591	−	56.2013i	0.0337648	−	0.126012i
$447$	0.510290	+	1.80045i	0.00114159	+	0.00402785i
$448$	144.472	−	9.46917i	0.322481	−	0.0211365i
$449$	90.6297	−	455.627i	0.201848	−	1.01476i	−0.738425	−	0.674336i	$-0.764430\pi$
$449$	90.6297	−	455.627i	0.201848	−	1.01476i	0.940273	−	0.340422i	$-0.110570\pi$
$450$	−2.49489	−	86.7169i	−0.00554419	−	0.192704i
$451$	−148.593	−	358.735i	−0.329475	−	0.795422i
$452$	−486.314	+	554.534i	−1.07591	+	1.22685i
$453$	90.5166	+	35.9770i	0.199816	+	0.0794195i
$454$	37.2009	+	42.4195i	0.0819403	+	0.0934350i
$455$	−141.911	−	38.0249i	−0.311892	−	0.0835711i
$456$	−252.079	+	150.412i	−0.552804	+	0.329851i
$457$	67.4054	−	51.7220i	0.147495	−	0.113177i	−0.532378	−	0.846507i	$-0.678701\pi$
$457$	67.4054	−	51.7220i	0.147495	−	0.113177i	0.679873	+	0.733330i	$0.262035\pi$
$458$		−	97.0609i		−	0.211923i
$459$	−125.897	+	441.397i	−0.274285	+	0.961649i
$460$	171.094			0.371944
$461$	−269.903	−	351.745i	−0.585474	−	0.763004i	0.402868	−	0.915258i	$-0.368014\pi$
$461$	−269.903	−	351.745i	−0.585474	−	0.763004i	−0.988341	+	0.152254i	$0.951347\pi$
$462$	12.8690	+	21.5675i	0.0278551	+	0.0466829i
$463$	−129.561	+	483.529i	−0.279830	+	1.04434i	0.672706	+	0.739910i	$0.265132\pi$
$463$	−129.561	+	483.529i	−0.279830	+	1.04434i	−0.952535	+	0.304428i	$0.901535\pi$
$464$	−286.498	+	251.252i	−0.617452	+	0.541491i
$465$	−38.7930	+	97.6015i	−0.0834258	+	0.209896i
$466$	−13.8407	−	12.1380i	−0.0297012	−	0.0260472i
$467$	109.122	−	45.2000i	0.233667	−	0.0967880i	−0.262778	−	0.964856i	$-0.584639\pi$
$467$	109.122	−	45.2000i	0.233667	−	0.0967880i	0.496445	+	0.868068i	$0.334639\pi$
$468$	−373.673	−	606.259i	−0.798446	−	1.29542i
$469$	−268.868	−	53.4813i	−0.573280	−	0.114033i
$470$	−5.60443	−	85.5071i	−0.0119243	−	0.181930i
$471$	510.037	−	144.557i	1.08288	−	0.306914i
$472$	−73.2778	−	19.6347i	−0.155249	−	0.0415990i
$473$	−12.9855	+	198.121i	−0.0274536	+	0.418860i
$474$	−86.2365	−	27.8969i	−0.181934	−	0.0588542i
$475$	475.139	+	274.322i	1.00029	+	0.577519i
$476$	−56.3082	−	205.003i	−0.118295	−	0.430680i
$477$	−67.7710	−	83.2497i	−0.142078	−	0.174528i
$478$	−10.6702	+	25.7602i	−0.0223226	+	0.0538916i
$479$	38.6409	+	78.3560i	0.0806700	+	0.163583i	0.933470	−	0.358654i	$-0.116764\pi$
$479$	38.6409	+	78.3560i	0.0806700	+	0.163583i	−0.852800	+	0.522237i	$0.825098\pi$
$480$	24.0865	−	130.902i	0.0501803	−	0.272714i
$481$	−861.802	+	755.780i	−1.79169	+	1.57127i
$482$	−33.9837	+	68.9120i	−0.0705055	+	0.142971i
$483$	170.025	+	126.622i	0.352019	+	0.262158i
$484$	45.3998	−	344.845i	0.0938012	−	0.712491i
$485$	15.9942	+	38.6134i	0.0329778	+	0.0796154i
$486$	−111.893	+	23.0088i	−0.230232	+	0.0473433i
$487$	−704.507	+	470.736i	−1.44663	+	0.966604i	−0.449310	+	0.893376i	$0.648330\pi$
$487$	−704.507	+	470.736i	−1.44663	+	0.966604i	−0.997315	+	0.0732286i	$0.976670\pi$
$488$	−39.1019	+	115.190i	−0.0801268	+	0.236046i
$489$	−176.310	−	495.848i	−0.360552	−	1.01400i
$490$	−2.48034	+	37.8427i	−0.00506192	+	0.0772300i
$491$	−14.2165	−	107.985i	−0.0289542	−	0.219929i	0.970851	−	0.239685i	$-0.0770443\pi$
$491$	−14.2165	−	107.985i	−0.0289542	−	0.219929i	−0.999805	+	0.0197562i	$0.993711\pi$
$492$	−673.548	+	464.199i	−1.36900	+	0.943493i
$493$	385.460	+	291.958i	0.781865	+	0.592207i
$494$	−263.383			−0.533164
$495$	−98.3840	+	29.4193i	−0.198756	+	0.0594329i
$496$	122.899	−	183.931i	0.247780	−	0.370829i
$497$	−176.007	+	47.1609i	−0.354139	+	0.0948912i
$498$	−1.55291	−	5.47912i	−0.00311830	−	0.0110022i
$499$	−36.9305	+	74.8877i	−0.0740090	+	0.150075i	−0.930733	−	0.365700i	$-0.880830\pi$
$499$	−36.9305	+	74.8877i	−0.0740090	+	0.150075i	0.856724	+	0.515776i	$0.172496\pi$
$500$	−345.250	+	117.197i	−0.690500	+	0.234393i
$501$	516.790	−	264.159i	1.03152	−	0.527263i
$502$	13.5126	+	1.77897i	0.0269175	+	0.00354376i
$503$	−22.5176	−	4.47903i	−0.0447666	−	0.00890463i	0.172656	−	0.984982i	$-0.444765\pi$
$503$	−22.5176	−	4.47903i	−0.0447666	−	0.00890463i	−0.217423	+	0.976078i	$0.569765\pi$
$504$	79.7868	−	74.1372i	0.158307	−	0.147098i
$505$	175.629	−	34.9349i	0.347781	−	0.0691779i
$506$	−13.9816	−	52.1801i	−0.0276316	−	0.103123i
$507$	−11.6248	−	808.273i	−0.0229286	−	1.59423i
$508$	−3.01124	−	22.8726i	−0.00592764	−	0.0450249i
$509$	−552.317	+	318.880i	−1.08510	+	0.626484i	−0.932268	−	0.361768i	$-0.882173\pi$
$509$	−552.317	+	318.880i	−1.08510	+	0.626484i	−0.152834	+	0.988252i	$0.548840\pi$
$510$	−50.8216	+	1.04916i	−0.0996501	+	0.00205717i
$511$	−36.1791	+	62.6641i	−0.0708007	+	0.122630i
$512$	−182.273	+	440.045i	−0.356001	+	0.859464i
$513$	247.421	−	678.751i	0.482303	−	1.32310i
$514$	−93.7329	−	93.7329i	−0.182360	−	0.182360i
$515$	66.7494	+	22.6584i	0.129610	+	0.0439968i
$516$	413.870	−	60.5541i	0.802074	−	0.117353i
$517$	438.104	−	148.716i	0.847397	−	0.287653i
$518$	−67.5623	−	51.8424i	−0.130429	−	0.100082i
$519$	306.001	−	472.536i	0.589598	−	0.910473i
$520$	107.046	−	122.062i	0.205857	−	0.234735i
$521$	−387.058	+	258.624i	−0.742914	+	0.496399i	−0.868503	−	0.495683i	$-0.834918\pi$
$521$	−387.058	+	258.624i	−0.742914	+	0.496399i	0.125590	+	0.992082i	$0.459918\pi$
$522$	−20.0737	+	118.657i	−0.0384553	+	0.227313i
$523$	−220.583	+	220.583i	−0.421764	+	0.421764i	−0.885811	−	0.464046i	$-0.846397\pi$
$523$	−220.583	+	220.583i	−0.421764	+	0.421764i	0.464046	+	0.885811i	$0.346397\pi$
$524$	285.399	−	140.743i	0.544654	−	0.268594i
$525$	−193.682	−	62.6548i	−0.368919	−	0.119342i
$526$	130.429	−	75.3034i	0.247965	−	0.143162i
$527$	−260.006	−	105.796i	−0.493370	−	0.200752i
$528$	215.595	−	17.2478i	0.408323	−	0.0326663i
$529$	44.4484	+	57.9263i	0.0840234	+	0.109501i
$530$	6.60477	−	9.88473i	0.0124618	−	0.0186504i
$531$	170.368	−	76.3804i	0.320843	−	0.143843i
$532$	65.2800	+	328.184i	0.122707	+	0.616888i
$533$	−1507.62	+	98.8147i	−2.82856	+	0.185394i
$534$	59.6818	−	25.7327i	0.111764	−	0.0481885i
$535$	−180.734	−	138.682i	−0.337821	−	0.259219i
$536$	184.415	−	240.335i	0.344059	−	0.448386i
$537$	258.338	−	346.890i	0.481076	−	0.645978i
$538$	2.23155	+	34.0469i	0.00414786	+	0.0632842i
$539$	−200.823	+	39.9462i	−0.372584	+	0.0741116i
$540$	103.961	+	189.716i	0.192521	+	0.351326i
$541$	292.981	+	195.764i	0.541555	+	0.361856i	0.796062	−	0.605215i	$-0.206913\pi$
$541$	292.981	+	195.764i	0.541555	+	0.361856i	−0.254507	+	0.967071i	$0.581913\pi$
$542$	137.735	−	105.688i	0.254123	−	0.194996i
$543$	−664.636	−	315.962i	−1.22401	−	0.581883i
$544$	349.325	+	67.2147i	0.642142	+	0.123556i
$545$	−20.7773	−	35.9873i	−0.0381234	−	0.0660317i
$546$	95.5617	−	20.4413i	0.175021	−	0.0374382i
$547$	−328.800	−	666.740i	−0.601097	−	1.21890i	−0.958537	−	0.284968i	$-0.908017\pi$
$547$	−328.800	−	666.740i	−0.601097	−	1.21890i	0.357440	−	0.933936i	$-0.383650\pi$
$548$	654.760	+	654.760i	1.19482	+	1.19482i
$549$	−104.347	−	280.611i	−0.190067	−	0.511131i
$550$	28.8188	+	43.1304i	0.0523979	+	0.0784190i
$551$	−572.208	−	501.813i	−1.03849	−	0.910732i
$552$	−208.595	+	106.624i	−0.377890	+	0.193159i
$553$	−129.470	+	168.729i	−0.234123	+	0.305115i
$554$	−0.832974	−	2.45386i	−0.00150356	−	0.00442935i
$555$	273.166	−	215.919i	0.492191	−	0.389044i
$556$	−27.1667	+	80.0305i	−0.0488610	+	0.143940i
$557$	86.4064	−	86.4064i	0.155128	−	0.155128i	−0.625276	−	0.780404i	$-0.715013\pi$
$557$	86.4064	−	86.4064i	0.155128	−	0.155128i	0.780404	+	0.625276i	$0.215013\pi$
$558$	−6.57203	−	69.5511i	−0.0117778	−	0.124643i
$559$	713.741	+	295.641i	1.27682	+	0.528875i
$560$	−81.4041	−	46.9987i	−0.145364	−	0.0839262i
$561$	−76.4899	−	263.578i	−0.136346	−	0.469836i
$562$	97.4683	+	168.820i	0.173431	+	0.300391i
$563$	783.670	−	103.172i	1.39195	−	0.183254i	0.603017	−	0.797728i	$-0.293965\pi$
$563$	783.670	−	103.172i	1.39195	−	0.183254i	0.788937	+	0.614474i	$0.210632\pi$
$564$	−499.428	−	837.001i	−0.885511	−	1.48404i
$565$	399.716	−	107.103i	0.707461	−	0.189564i
$566$	−6.33992	−	31.8729i	−0.0112013	−	0.0563126i
$567$	−37.0923	+	265.470i	−0.0654185	+	0.468200i
$568$	39.2832	−	197.490i	0.0691605	−	0.347693i
$569$	18.2195	−	138.391i	0.0320203	−	0.243218i	−0.967948	−	0.251150i	$-0.919191\pi$
$569$	18.2195	−	138.391i	0.0320203	−	0.243218i	0.999969	+	0.00793143i	$0.00252468\pi$
$570$	79.9030	+	4.08408i	0.140181	+	0.00716506i
$571$	−257.862	−	759.638i	−0.451598	−	1.33036i	−0.899749	−	0.436407i	$-0.856251\pi$
$571$	−257.862	−	759.638i	−0.451598	−	1.33036i	0.448151	−	0.893958i	$-0.352083\pi$
$572$	381.915	+	188.340i	0.667684	+	0.329265i
$573$	−105.525	−	102.532i	−0.184162	−	0.178940i
$574$	−29.0519	−	108.423i	−0.0506131	−	0.188891i
$575$	364.061	+	243.258i	0.633150	+	0.423057i
$576$	−112.808	−	377.251i	−0.195846	−	0.654950i
$577$			272.110i			0.471594i	0.971802	+	0.235797i	$0.0757700\pi$
$577$			272.110i			0.471594i	−0.971802	+	0.235797i	$0.924230\pi$
$578$	−1.70082	−	135.848i	−0.00294259	−	0.235031i
$579$	−1042.96	+	83.4381i	−1.80131	+	0.144107i
$580$	225.954	−	29.7473i	0.389575	−	0.0512885i
$581$	−13.3345	−	0.873989i	−0.0229509	−	0.00150428i
$582$	−21.1629	−	18.0276i	−0.0363623	−	0.0309753i
$583$	60.7803	+	20.6321i	0.104254	+	0.0353896i
$584$	−44.4234	−	66.4843i	−0.0760674	−	0.113843i
$585$	−14.6556	+	399.295i	−0.0250523	+	0.682555i
$586$	124.464	−	51.5548i	0.212396	−	0.0879774i
$587$	493.985	+	65.0344i	0.841542	+	0.110791i	0.538959	−	0.842332i	$-0.318818\pi$
$587$	493.985	+	65.0344i	0.841542	+	0.110791i	0.302583	+	0.953123i	$0.402151\pi$
$588$	170.789	+	396.111i	0.290457	+	0.673658i
$589$	396.252	+	195.410i	0.672755	+	0.331766i
$590$	13.6333	+	15.5457i	0.0231072	+	0.0263487i
$591$	340.908	+	958.758i	0.576832	+	1.62226i
$592$	−657.744	+	324.364i	−1.11105	+	0.547912i
$593$	377.599	+	156.407i	0.636760	+	0.263755i	0.677622	−	0.735410i	$-0.263010\pi$
$593$	377.599	+	156.407i	0.636760	+	0.263755i	−0.0408622	+	0.999165i	$0.513010\pi$
$594$	49.3638	−	47.2093i	0.0831040	−	0.0794769i
$595$	−37.6328	+	113.185i	−0.0632484	+	0.190228i
$596$	−1.17865	+	2.04148i	−0.00197760	+	0.00342531i
$597$	151.709	+	168.053i	0.254119	+	0.281496i
$598$	−209.746	−	13.7475i	−0.350746	−	0.0229891i
$599$	−168.132	+	627.479i	−0.280689	+	1.04754i	0.671244	+	0.741236i	$0.265760\pi$
$599$	−168.132	+	627.479i	−0.280689	+	1.04754i	−0.951933	+	0.306308i	$0.900906\pi$
$600$	156.760	−	161.335i	0.261266	−	0.268891i
$601$	248.980	−	16.3190i	0.414277	−	0.0271531i	0.143160	−	0.989700i	$-0.454274\pi$
$601$	248.980	−	16.3190i	0.414277	−	0.0271531i	0.271117	+	0.962546i	$0.412607\pi$
$602$	−11.1974	+	56.2931i	−0.0186003	+	0.0935101i
$603$	21.4411	+	745.247i	0.0355574	+	1.23590i
$604$	46.9542	+	113.357i	0.0777387	+	0.187678i
$605$	−128.669	+	146.719i	−0.212676	+	0.242510i
$606$	−93.4444	+	73.8615i	−0.154199	+	0.121884i
$607$	−484.228	−	552.156i	−0.797740	−	0.909648i	0.199794	−	0.979838i	$-0.435973\pi$
$607$	−484.228	−	552.156i	−0.797740	−	0.909648i	−0.997534	+	0.0701901i	$0.977639\pi$
$608$	−540.825	−	144.914i	−0.889515	−	0.238345i
$609$	246.557	+	137.661i	0.404855	+	0.226044i
$610$	26.3041	−	20.1838i	0.0431214	−	0.0330882i
$611$		−	1800.21i		−	2.94634i
$612$	−509.289	+	273.727i	−0.832172	+	0.447266i
$613$	−184.332			−0.300705			−0.150352	−	0.988632i	$-0.548041\pi$
$613$	−184.332			−0.300705			−0.150352	+	0.988632i	$0.548041\pi$
$614$	9.68492	+	12.6216i	0.0157735	+	0.0205564i
$615$	458.902	−	6.60006i	0.746183	−	0.0107318i
$616$	−16.8552	+	62.9045i	−0.0273624	+	0.102118i
$617$	120.994	−	106.109i	0.196101	−	0.171976i	−0.555664	−	0.831407i	$-0.687536\pi$
$617$	120.994	−	106.109i	0.196101	−	0.171976i	0.751765	+	0.659431i	$0.229203\pi$
$618$	−46.3935	+	6.78792i	−0.0750704	+	0.0109837i
$619$	449.831	+	394.491i	0.726706	+	0.637304i	0.940586	−	0.339556i	$-0.110277\pi$
$619$	449.831	+	394.491i	0.726706	+	0.637304i	−0.213880	+	0.976860i	$0.568610\pi$
$620$	−122.230	+	50.6294i	−0.197145	+	0.0816603i
$621$	232.463	−	527.612i	0.374337	−	0.849617i
$622$	92.1755	+	18.3348i	0.148192	+	0.0294772i
$623$	−9.97432	−	152.179i	−0.0160101	−	0.244268i
$624$	206.101	−	815.938i	0.330289	−	1.30759i
$625$	−297.560	−	79.7309i	−0.476096	−	0.127569i
$626$	−7.64170	+	116.590i	−0.0122072	+	0.186246i
$627$	90.3577	+	422.417i	0.144111	+	0.673711i
$628$	578.318	+	333.892i	0.920888	+	0.531675i
$629$	571.133	+	734.746i	0.908001	+	1.16812i
$630$	−29.3077	+	4.71951i	−0.0465202	+	0.00749128i
$631$	−242.675	+	585.868i	−0.384587	+	0.928476i	0.606478	+	0.795100i	$0.292582\pi$
$631$	−242.675	+	585.868i	−0.384587	+	0.928476i	−0.991066	+	0.133376i	$0.957418\pi$
$632$	−103.947	−	210.784i	−0.164473	−	0.333518i
$633$	−270.993	−	230.845i	−0.428108	−	0.364684i
$634$	114.160	−	100.116i	0.180063	−	0.157911i
$635$	−5.72477	+	11.6087i	−0.00901538	+	0.0182814i
$636$	15.7202	−	134.305i	0.0247173	−	0.211171i
$637$	−103.992	+	789.900i	−0.163253	+	1.24003i
$638$	−27.5369	−	66.4801i	−0.0431614	−	0.104201i
$639$	231.874	+	437.971i	0.362870	+	0.685401i
$640$	183.816	−	122.822i	0.287213	−	0.191909i
$641$	−188.066	+	554.023i	−0.293394	+	0.864311i	0.695869	+	0.718168i	$0.255019\pi$
$641$	−188.066	+	554.023i	−0.293394	+	0.864311i	−0.989264	+	0.146143i	$0.953314\pi$
$642$	149.029	+	27.4219i	0.232133	+	0.0427133i
$643$	50.3853	−	768.731i	0.0783597	−	1.19554i	−0.759816	−	0.650138i	$-0.774711\pi$
$643$	50.3853	−	768.731i	0.0783597	−	1.19554i	0.838176	−	0.545400i	$-0.183622\pi$
$644$	34.8561	+	264.759i	0.0541244	+	0.411116i
$645$	−211.945	−	100.757i	−0.328597	−	0.156212i
$646$	−12.6494	+	213.459i	−0.0195812	+	0.330432i
$647$	422.729			0.653367			0.326684	−	0.945134i	$-0.394069\pi$
$647$	422.729			0.653367			0.326684	+	0.945134i	$0.394069\pi$
$648$	−244.977	−	166.511i	−0.378050	−	0.256962i
$649$	−62.0228	+	92.8237i	−0.0955668	+	0.143026i
$650$	194.960	−	52.2394i	0.299939	−	0.0803683i
$651$	−158.936	−	40.1462i	−0.244141	−	0.0616685i
$652$	293.200	−	594.550i	0.449693	−	0.911887i
$653$	−877.451	+	297.854i	−1.34372	+	0.456132i	−0.898377	−	0.439226i	$-0.855253\pi$
$653$	−877.451	+	297.854i	−1.34372	+	0.456132i	−0.445346	+	0.895358i	$0.646919\pi$
$654$	23.2007	+	15.0241i	0.0354751	+	0.0229727i
$655$	−177.008	−	23.3036i	−0.270242	−	0.0355780i
$656$	−948.072	−	188.583i	−1.44523	−	0.287474i
$657$	188.088	+	57.8708i	0.286283	+	0.0880834i
$658$	131.176	−	26.0925i	0.199355	−	0.0396542i
$659$	286.081	+	1067.67i	0.434114	+	1.62013i	0.743178	+	0.669093i	$0.233317\pi$
$659$	286.081	+	1067.67i	0.434114	+	1.62013i	−0.309065	+	0.951041i	$0.600016\pi$
$660$	−112.942	−	63.0591i	−0.171124	−	0.0955440i
$661$	144.162	+	1095.02i	0.218097	+	1.65661i	0.653907	+	0.756575i	$0.273129\pi$
$661$	144.162	+	1095.02i	0.218097	+	1.65661i	−0.435810	+	0.900039i	$0.643538\pi$
$662$	168.059	−	97.0288i	0.253865	−	0.146569i
$663$	−1066.83	−	47.8355i	−1.60910	−	0.0721500i
$664$	7.38349	−	12.7886i	0.0111197	−	0.0192599i
$665$	71.8436	−	173.446i	0.108035	−	0.260821i
$666$	−96.4210	+	210.582i	−0.144776	+	0.316189i
$667$	−429.488	−	429.488i	−0.643910	−	0.643910i
$668$	692.299	+	235.004i	1.03638	+	0.351802i
$669$	−137.146	+	345.053i	−0.205001	+	0.515774i
$670$	−78.1855	+	26.5404i	−0.116695	+	0.0396125i
$671$	142.020	+	108.976i	0.211654	+	0.162408i
$672$	207.471	+	10.6045i	0.308737	+	0.0157805i
$673$	795.071	−	906.605i	1.18138	−	1.34711i	0.256646	−	0.966506i	$-0.417383\pi$
$673$	795.071	−	906.605i	1.18138	−	1.34711i	0.924738	−	0.380604i	$-0.124284\pi$
$674$	−199.855	+	133.539i	−0.296521	+	0.198129i
$675$	−48.5215	+	551.495i	−0.0718838	+	0.817030i
$676$	720.020	−	720.020i	1.06512	−	1.06512i
$677$	18.7279	−	9.23557i	0.0276630	−	0.0136419i	−0.428405	−	0.903587i	$-0.640924\pi$
$677$	18.7279	−	9.23557i	0.0276630	−	0.0136419i	0.456068	+	0.889945i	$0.349258\pi$
$678$	−204.316	+	184.445i	−0.301351	+	0.272043i
$679$	−56.4937	+	32.6167i	−0.0832014	+	0.0480363i
$680$	−93.7843	−	92.6175i	−0.137918	−	0.136202i
$681$	−204.322	−	296.470i	−0.300033	−	0.435345i
$682$	25.4294	+	33.1402i	0.0372865	+	0.0485927i
$683$	−506.112	+	757.450i	−0.741013	+	1.10900i	0.249066	+	0.968487i	$0.419876\pi$
$683$	−506.112	+	757.450i	−0.741013	+	1.10900i	−0.990078	+	0.140517i	$0.955124\pi$
$684$	830.400	−	372.291i	1.21404	−	0.544285i
$685$	−101.353	−	509.537i	−0.147961	−	0.743849i
$686$	−135.129	+	8.85684i	−0.196981	+	0.0129108i
$687$	−72.0093	+	615.209i	−0.104817	+	0.895500i
$688$	392.136	+	300.896i	0.569965	+	0.437349i
$689$	152.040	−	198.142i	0.220667	−	0.287579i
$690$	63.4180	+	7.42299i	0.0919101	+	0.0107580i
$691$	71.4473	+	1090.07i	0.103397	+	1.57753i	0.662902	+	0.748706i	$0.269324\pi$
$691$	71.4473	+	1090.07i	0.103397	+	1.57753i	−0.559505	+	0.828827i	$0.689009\pi$
$692$	695.521	−	138.348i	1.00509	−	0.199924i
$693$	−65.5679	−	146.250i	−0.0946146	−	0.211039i
$694$	118.235	+	79.0024i	0.170368	+	0.113836i
$695$	37.6191	−	28.8662i	0.0541282	−	0.0415340i
$696$	−256.940	+	177.079i	−0.369167	+	0.254424i
$697$	7.67824	+	1226.60i	0.0110161	+	1.75983i
$698$	−81.8089	−	141.697i	−0.117205	−	0.203005i
$699$	78.7227	+	87.2037i	0.112622	+	0.124755i
$700$	−113.413	−	229.980i	−0.162019	−	0.328542i
$701$	−235.366	−	235.366i	−0.335758	−	0.335758i	0.519010	−	0.854768i	$-0.326301\pi$
$701$	−235.366	−	235.366i	−0.335758	−	0.335758i	−0.854768	+	0.519010i	$0.826301\pi$
$702$	−112.203	−	240.928i	−0.159834	−	0.343203i
$703$	−813.763	−	1217.88i	−1.15756	−	1.73241i
$704$	177.014	+	155.237i	0.251440	+	0.220507i
$705$	−27.9146	+	546.134i	−0.0395951	+	0.774658i
$706$	−159.238	+	207.523i	−0.225550	+	0.293942i
$707$	89.8398	+	264.659i	0.127072	+	0.374342i
$708$	218.557	+	86.8684i	0.308696	+	0.122696i
$709$	−267.749	+	788.764i	−0.377643	+	1.11250i	0.577508	+	0.816385i	$0.304025\pi$
$709$	−267.749	+	788.764i	−0.377643	+	1.11250i	−0.955152	+	0.296117i	$0.904308\pi$
$710$	−38.8073	+	38.8073i	−0.0546582	+	0.0546582i
$711$	525.903	+	240.800i	0.739667	+	0.338678i
$712$	155.699	+	64.4925i	0.218678	+	0.0905793i
$713$	305.358	+	176.299i	0.428272	+	0.247263i
$714$	−11.9771	−	78.4298i	−0.0167747	−	0.109846i
$715$	−119.457	−	206.905i	−0.167072	−	0.289377i
$716$	540.168	−	71.1144i	0.754424	−	0.0993218i
$717$	86.7433	−	155.362i	0.120981	−	0.216683i
$718$	263.481	−	70.5996i	0.366966	−	0.0983282i
$719$	−177.980	−	894.766i	−0.247538	−	1.24446i	−0.881905	−	0.471427i	$-0.843739\pi$
$719$	−177.980	−	894.766i	−0.247538	−	1.24446i	0.634367	−	0.773032i	$-0.281261\pi$
$720$	−75.1773	+	244.337i	−0.104413	+	0.339357i
$721$	−21.4640	+	107.907i	−0.0297698	+	0.149663i
$722$	21.7791	−	165.429i	0.0301650	−	0.229126i
$723$	266.527	−	411.578i	0.368640	−	0.569264i
$724$	−297.978	−	877.815i	−0.411572	−	1.21245i
$725$	523.087	+	257.958i	0.721499	+	0.355804i
$726$	31.7892	−	125.851i	0.0437867	−	0.173349i
$727$	−143.641	−	536.076i	−0.197580	−	0.737380i	−0.991584	−	0.129467i	$-0.958673\pi$
$727$	−143.641	−	536.076i	−0.197580	−	0.737380i	0.794003	−	0.607914i	$-0.207993\pi$
$728$	210.692	+	140.780i	0.289412	+	0.193379i
$729$	726.288	−	62.8257i	0.996280	−	0.0861806i
$730$			21.7937i			0.0298544i
$731$	273.881	−	564.253i	0.374667	−	0.771892i
$732$	161.917	−	340.596i	0.221198	−	0.465296i
$733$	−171.790	+	22.6166i	−0.234366	+	0.0308549i	−0.246794	−	0.969068i	$-0.579377\pi$
$733$	−171.790	+	22.6166i	−0.234366	+	0.0308549i	0.0124282	+	0.999923i	$0.496044\pi$
$734$	318.885	+	20.9008i	0.434448	+	0.0284753i
$735$	43.7968	−	238.021i	0.0595874	−	0.323838i
$736$	−423.125	−	143.631i	−0.574898	−	0.195151i
$737$	−247.670	−	370.664i	−0.336052	−	0.502937i
$738$	−269.798	+	142.838i	−0.365580	+	0.193548i
$739$	571.846	−	236.866i	0.773811	−	0.320523i	0.0393958	−	0.999224i	$-0.487457\pi$
$739$	571.846	−	236.866i	0.773811	−	0.320523i	0.734415	+	0.678701i	$0.237457\pi$
$740$	434.860	+	57.2504i	0.587649	+	0.0773654i
$741$	1669.42	+	195.403i	2.25293	+	0.263702i
$742$	16.6416	+	8.20674i	0.0224281	+	0.0110603i
$743$	396.241	+	451.826i	0.533299	+	0.608110i	0.954264	−	0.298966i	$-0.0966419\pi$
$743$	396.241	+	451.826i	0.533299	+	0.608110i	−0.420965	+	0.907077i	$0.638309\pi$
$744$	117.469	−	137.899i	0.157889	−	0.185348i
$745$	1.18618	−	0.584959i	0.00159219	−	0.000785180i
$746$	161.692	+	66.9748i	0.216745	+	0.0897786i
$747$	5.77800	+	35.8808i	0.00773493	+	0.0480332i
$748$	170.982	−	300.478i	0.228586	−	0.401708i
$749$	177.783	−	307.929i	0.237361	−	0.411121i
$750$	−133.055	+	28.4614i	−0.177407	+	0.0379485i
$751$	−1239.72	−	81.2554i	−1.65076	−	0.108196i	−0.788622	−	0.614878i	$-0.789205\pi$
$751$	−1239.72	−	81.2554i	−1.65076	−	0.108196i	−0.862133	+	0.506681i	$0.830872\pi$
$752$	298.102	−	1112.53i	0.396412	−	1.47943i
$753$	−84.3281	−	21.3007i	−0.111989	−	0.0282878i
$754$	−279.389	+	18.3121i	−0.370543	+	0.0242866i
$755$	13.4300	−	67.5170i	0.0177880	−	0.0894264i
$756$	−272.396	+	199.524i	−0.360312	+	0.263920i
$757$	219.920	+	530.935i	0.290516	+	0.701367i	0.999994	−	0.00335986i	$-0.00106948\pi$
$757$	219.920	+	530.935i	0.290516	+	0.701367i	−0.709479	+	0.704727i	$0.751069\pi$
$758$	−60.5513	+	69.0456i	−0.0798830	+	0.0910891i
$759$	49.9084	+	341.110i	0.0657555	+	0.449420i
$760$	136.787	+	155.976i	0.179983	+	0.205232i
$761$	−837.354	−	224.368i	−1.10033	−	0.294833i	−0.337433	−	0.941349i	$-0.609559\pi$
$761$	−837.354	−	224.368i	−1.10033	−	0.294833i	−0.762900	+	0.646516i	$0.776225\pi$
$762$	−0.123812	−	8.60864i	−0.000162483	−	0.0112974i
$763$	51.4554	−	39.4831i	0.0674383	−	0.0517472i
$764$		−	185.340i		−	0.242592i
$765$	322.905	+	31.0545i	0.422098	+	0.0405941i
$766$	−299.540			−0.391044
$767$	264.438	+	344.622i	0.344769	+	0.449312i
$768$	184.253	−	330.006i	0.239912	−	0.429695i
$769$	19.1815	−	71.5863i	0.0249434	−	0.0930902i	−0.952332	−	0.305063i	$-0.901322\pi$
$769$	19.1815	−	71.5863i	0.0249434	−	0.0930902i	0.977275	+	0.211973i	$0.0679890\pi$
$770$	13.3451	−	11.7033i	0.0173313	−	0.0151991i
$771$	524.574	+	663.655i	0.680382	+	0.860771i
$772$	−990.913	−	869.007i	−1.28357	−	1.12566i
$773$	−791.934	+	328.030i	−1.02449	+	0.424360i	−0.830722	−	0.556687i	$-0.812072\pi$
$773$	−791.934	+	328.030i	−1.02449	+	0.424360i	−0.193772	+	0.981047i	$0.562072\pi$
$774$	156.033	−	4.48914i	0.201593	−	0.00579992i
$775$	−332.070	−	66.0528i	−0.428477	−	0.0852294i
$776$	−4.71468	−	71.9321i	−0.00607562	−	0.0926961i
$777$	389.773	+	378.721i	0.501639	+	0.487414i
$778$	342.946	+	91.8921i	0.440804	+	0.118113i
$779$	126.270	−	1926.50i	0.162092	−	2.47304i
$780$	−373.603	+	337.268i	−0.478978	+	0.432395i
$781$	−256.617	−	148.158i	−0.328575	−	0.189703i
$782$	−21.2151	+	169.329i	−0.0271293	+	0.216533i
$783$	215.266	−	737.202i	0.274925	−	0.941509i
$784$	−195.069	+	470.937i	−0.248812	+	0.600685i
$785$	−165.709	−	336.025i	−0.211094	−	0.428057i
$786$	111.892	−	39.7859i	0.142357	−	0.0506182i
$787$	115.743	−	101.504i	0.147069	−	0.128976i	−0.582650	−	0.812723i	$-0.697984\pi$
$787$	115.743	−	101.504i	0.147069	−	0.128976i	0.729719	+	0.683747i	$0.239651\pi$
$788$	−566.923	+	1149.61i	−0.719445	+	1.45889i
$789$	−882.578	+	380.536i	−1.11860	+	0.482302i
$790$	−8.36107	+	63.5086i	−0.0105836	+	0.0803906i
$791$	247.169	+	596.718i	0.312476	+	0.754384i
$792$	176.994	+	6.49636i	0.223478	+	0.00820248i
$793$	579.153	−	386.978i	0.730332	−	0.487992i
$794$	−9.76913	+	28.7789i	−0.0123037	+	0.0362455i
$795$	−49.1970	+	57.7531i	−0.0618830	+	0.0726454i
$796$	−18.6524	+	284.580i	−0.0234326	+	0.357513i
$797$	−60.3918	−	458.722i	−0.0757739	−	0.575560i	−0.986647	−	0.162874i	$-0.947924\pi$
$797$	−60.3918	−	458.722i	−0.0757739	−	0.575560i	0.910873	−	0.412687i	$-0.135410\pi$
$798$	9.95834	+	124.477i	0.0124791	+	0.155987i
$799$	−1458.98	−	86.4584i	−1.82601	−	0.108208i
$800$	429.069			0.536336
$801$	−397.377	+	118.825i	−0.496101	+	0.148346i
$802$	−17.3841	+	26.0172i	−0.0216760	+	0.0324404i
$803$	−113.658	+	30.4546i	−0.141542	+	0.0379261i
$804$	−654.463	+	673.563i	−0.814009	+	0.837765i
$805$	66.2661	−	134.374i	0.0823182	−	0.166925i
$806$	153.911	−	52.2459i	0.190957	−	0.0648212i
$807$	11.1149	−	217.458i	0.0137731	−	0.269464i
$808$	−306.212	−	40.3136i	−0.378975	−	0.0498931i
$809$	−766.807	−	152.527i	−0.947846	−	0.188538i	−0.303120	−	0.952952i	$-0.598028\pi$
$809$	−766.807	−	152.527i	−0.947846	−	0.188538i	−0.644726	+	0.764414i	$0.723028\pi$
$810$	30.3034	+	74.8308i	0.0374116	+	0.0923837i
$811$	254.137	−	50.5509i	0.313362	−	0.0623316i	−0.0359038	−	0.999355i	$-0.511431\pi$
$811$	254.137	−	50.5509i	0.313362	−	0.0623316i	0.349266	+	0.937024i	$0.386431\pi$
$812$	92.0647	+	343.590i	0.113380	+	0.423140i
$813$	−951.424	+	567.703i	−1.17026	+	0.698281i
$814$	−18.0761	−	137.301i	−0.0222065	−	0.168675i
$815$	−322.101	+	185.965i	−0.395217	+	0.228178i
$816$	−651.379	−	206.221i	−0.798258	−	0.252722i
$817$	−493.597	+	854.935i	−0.604158	+	1.04643i
$818$	−67.6213	+	163.252i	−0.0826666	+	0.199575i
$819$	−620.872	+	58.6675i	−0.758085	+	0.0716331i
$820$	408.796	+	408.796i	0.498532	+	0.498532i
$821$	507.393	+	172.237i	0.618018	+	0.209789i	0.612852	−	0.790198i	$-0.290022\pi$
$821$	507.393	+	172.237i	0.618018	+	0.209789i	0.00516608	+	0.999987i	$0.498356\pi$
$822$	214.287	+	271.101i	0.260690	+	0.329807i
$823$	478.758	−	162.517i	0.581724	−	0.197469i	−0.0150383	−	0.999887i	$-0.504787\pi$
$823$	478.758	−	162.517i	0.581724	−	0.197469i	0.596762	+	0.802418i	$0.296454\pi$
$824$	−96.4554	−	74.0128i	−0.117058	−	0.0898214i
$825$	−150.666	−	294.758i	−0.182626	−	0.357282i
$826$	−21.2787	+	24.2637i	−0.0257612	+	0.0293750i
$827$	717.870	−	479.665i	0.868041	−	0.580006i	−0.0398535	−	0.999206i	$-0.512689\pi$
$827$	717.870	−	479.665i	0.868041	−	0.580006i	0.907894	+	0.419199i	$0.137689\pi$
$828$	680.725	−	253.132i	0.822132	−	0.305715i
$829$	−446.964	+	446.964i	−0.539161	+	0.539161i	−0.923282	−	0.384122i	$-0.874504\pi$
$829$	−446.964	+	446.964i	−0.539161	+	0.539161i	0.384122	+	0.923282i	$0.374504\pi$
$830$	−3.60978	+	1.78015i	−0.00434913	+	0.00214475i
$831$	3.45919	+	16.1715i	0.00416268	+	0.0194603i
$832$	793.372	−	458.054i	0.953572	−	0.550545i
$833$	635.181	+	122.217i	0.762522	+	0.146719i
$834$	−13.5418	+	28.4856i	−0.0162372	+	0.0341554i
$835$	−249.705	−	325.422i	−0.299048	−	0.389727i
$836$	−302.309	+	452.438i	−0.361614	+	0.541194i
$837$	−9.94381	+	445.717i	−0.0118803	+	0.532517i
$838$	56.2326	+	282.700i	0.0671033	+	0.337351i
$839$	−301.834	+	19.7832i	−0.359754	+	0.0235795i	−0.244209	−	0.969723i	$-0.578528\pi$
$839$	−301.834	+	19.7832i	−0.359754	+	0.0235795i	−0.115545	+	0.993302i	$0.536862\pi$
$840$	−61.7352	−	45.9758i	−0.0734942	−	0.0547331i
$841$	25.3387	+	19.4430i	0.0301292	+	0.0231189i
$842$	42.6927	−	55.6382i	0.0507040	−	0.0660787i
$843$	−492.543	−	1142.36i	−0.584275	−	1.35511i
$844$	−29.3284	−	447.465i	−0.0347493	−	0.530172i
$845$	−560.322	+	111.455i	−0.663103	+	0.131899i
$846$	−148.805	−	331.912i	−0.175892	−	0.392331i
$847$	−253.252	−	169.218i	−0.298999	−	0.199785i
$848$	126.771	−	97.2749i	0.149494	−	0.114711i
$849$	16.5383	+	206.726i	0.0194798	+	0.243494i
$850$	−32.9741	−	160.514i	−0.0387931	−	0.188840i
$851$	−584.476	−	1012.34i	−0.686811	−	1.18959i
$852$	−192.136	+	593.944i	−0.225512	+	0.697117i
$853$	−414.010	−	839.529i	−0.485357	−	0.984207i	−0.992488	−	0.122338i	$-0.960961\pi$
$853$	−414.010	−	839.529i	−0.485357	−	0.984207i	0.507131	−	0.861869i	$-0.330706\pi$
$854$	36.5921	+	36.5921i	0.0428479	+	0.0428479i
$855$	−503.425	−	85.1663i	−0.588802	−	0.0996098i
$856$	218.295	+	326.702i	0.255018	+	0.381661i
$857$	−744.232	−	652.674i	−0.868415	−	0.761579i	0.104064	−	0.994571i	$-0.466815\pi$
$857$	−744.232	−	652.674i	−0.868415	−	0.761579i	−0.972479	+	0.232991i	$0.925149\pi$
$858$	133.390	+	86.3797i	0.155466	+	0.100676i
$859$	525.895	−	685.360i	0.612218	−	0.797858i	−0.379650	−	0.925130i	$-0.623956\pi$
$859$	525.895	−	685.360i	0.612218	−	0.797858i	0.991868	+	0.127272i	$0.0406222\pi$
$860$	−95.0218	−	279.925i	−0.110490	−	0.325494i
$861$	103.703	+	708.781i	0.120445	+	0.823207i
$862$	16.7297	−	49.2840i	0.0194080	−	0.0571740i
$863$	617.835	−	617.835i	0.715915	−	0.715915i	−0.251851	−	0.967766i	$-0.581039\pi$
$863$	617.835	−	617.835i	0.715915	−	0.715915i	0.967766	+	0.251851i	$0.0810392\pi$
$864$	−97.8367	−	556.452i	−0.113237	−	0.644041i
$865$	−367.583	−	152.258i	−0.424952	−	0.176021i
$866$	−201.521	−	116.348i	−0.232703	−	0.134351i
$867$	−90.0047	+	862.316i	−0.103812	+	0.994597i
$868$	−103.247	−	178.830i	−0.118949	−	0.206025i
$869$	−342.893	+	45.1428i	−0.394584	+	0.0519479i
$870$	85.0428	−	1.22311i	0.0977503	−	0.00140587i
$871$	−1675.49	+	448.947i	−1.92364	+	0.515439i
$872$	13.9825	+	70.2947i	0.0160350	+	0.0806132i
$873$	120.764	+	129.966i	0.138332	+	0.148873i
$874$	52.4008	−	263.436i	0.0599551	−	0.301415i
$875$	−41.6739	+	316.544i	−0.0476273	+	0.361765i
$876$	112.825	+	220.726i	0.128795	+	0.251970i
$877$	−264.644	−	779.616i	−0.301760	−	0.888958i	−0.987011	−	0.160650i	$-0.948641\pi$
$877$	−264.644	−	779.616i	−0.301760	−	0.888958i	0.685251	−	0.728307i	$-0.259693\pi$
$878$	213.422	+	105.248i	0.243078	+	0.119873i
$879$	−827.149	+	234.434i	−0.941012	+	0.266705i
$880$	−39.5622	−	147.648i	−0.0449571	−	0.167782i
$881$	−289.890	−	193.698i	−0.329047	−	0.219862i	0.380062	−	0.924961i	$-0.375903\pi$
$881$	−289.890	−	193.698i	−0.329047	−	0.219862i	−0.709109	+	0.705099i	$0.750903\pi$
$882$	46.1194	+	154.233i	0.0522896	+	0.174867i
$883$			524.201i			0.593659i	0.954930	+	0.296830i	$0.0959294\pi$
$883$			524.201i			0.593659i	−0.954930	+	0.296830i	$0.904071\pi$
$884$	−893.268	−	1005.81i	−1.01048	−	1.13779i
$885$	−74.8793	−	108.649i	−0.0846094	−	0.122768i
$886$	304.727	−	40.1181i	0.343936	−	0.0452800i
$887$	437.190	+	28.6549i	0.492886	+	0.0323055i	0.309820	−	0.950795i	$-0.399731\pi$
$887$	437.190	+	28.6549i	0.492886	+	0.0323055i	0.183066	+	0.983101i	$0.441398\pi$
$888$	−565.851	+	201.201i	−0.637220	+	0.226578i
$889$	−19.1301	−	6.49378i	−0.0215186	−	0.00730459i
$890$	−25.5191	−	38.1921i	−0.0286732	−	0.0429125i
$891$	−347.911	+	262.607i	−0.390472	+	0.294733i
$892$	−432.123	+	178.991i	−0.484443	+	0.200663i
$893$	2280.71	+	300.261i	2.55398	+	0.336238i
$894$	−0.525451	+	0.705563i	−0.000587753	+	0.000789220i
$895$	−274.154	−	135.198i	−0.306318	−	0.151059i
$896$	227.508	+	259.423i	0.253915	+	0.289535i
$897$	1319.25	+	242.747i	1.47074	+	0.270621i
$898$	195.864	−	96.5894i	0.218111	−	0.107561i
$899$	433.919	+	179.735i	0.482669	+	0.199928i
$900$	−540.835	+	440.277i	−0.600927	+	0.489196i
$901$	−153.282	−	132.737i	−0.170124	−	0.147321i
$902$	91.2678	−	158.080i	0.101184	−	0.175255i
$903$	112.737	−	348.499i	0.124847	−	0.385935i
$904$	−712.208	−	46.6806i	−0.787841	−	0.0516378i
$905$	−134.613	+	502.381i	−0.148743	+	0.555117i
$906$	12.4860	+	44.0543i	0.0137815	+	0.0486251i
$907$	186.499	−	12.2238i	0.205622	−	0.0134772i	0.0377558	−	0.999287i	$-0.487979\pi$
$907$	186.499	−	12.2238i	0.205622	−	0.0134772i	0.167866	+	0.985810i	$0.446312\pi$
$908$	88.4841	−	444.840i	0.0974494	−	0.489911i
$909$	647.083	−	398.835i	0.711863	−	0.438763i
$910$	−26.4301	−	63.8080i	−0.0290441	−	0.0701187i
$911$	487.096	−	555.426i	0.534683	−	0.609689i	−0.419924	−	0.907559i	$-0.637943\pi$
$911$	487.096	−	555.426i	0.534683	−	0.609689i	0.954606	+	0.297871i	$0.0962764\pi$
$912$	999.343	+	397.202i	1.09577	+	0.435529i
$913$	−14.3281	−	16.3381i	−0.0156935	−	0.0178950i
$914$	38.5798	+	10.3374i	0.0422099	+	0.0113101i
$915$	−181.699	+	108.418i	−0.198579	+	0.118489i
$916$	−619.014	+	474.986i	−0.675780	+	0.518544i
$917$		−	278.658i		−	0.303880i
$918$	−200.649	+	79.3642i	−0.218572	+	0.0864534i
$919$	1553.83			1.69078			0.845390	−	0.534149i	$-0.179368\pi$
$919$	1553.83			1.69078			0.845390	+	0.534149i	$0.179368\pi$
$920$	100.790	+	131.352i	0.109554	+	0.142774i
$921$	−52.0227	−	87.1858i	−0.0564850	−	0.0946643i
$922$	53.9443	−	201.323i	0.0585080	−	0.218355i
$923$	−866.851	+	760.208i	−0.939167	+	0.823627i
$924$	74.5713	−	187.618i	0.0807048	−	0.203050i
$925$	843.915	+	740.093i	0.912340	+	0.800101i
$926$	−217.411	+	90.0548i	−0.234786	+	0.0972514i
$927$	299.096	−	8.60513i	0.322649	−	0.00928277i
$928$	−583.767	−	116.118i	−0.629059	−	0.125128i
$929$	70.8126	+	1080.39i	0.0762245	+	1.16296i	0.849039	+	0.528330i	$0.177182\pi$
$929$	70.8126	+	1080.39i	0.0762245	+	1.16296i	−0.772815	+	0.634632i	$0.781152\pi$
$930$	−47.5025	+	13.4633i	−0.0510780	+	0.0144767i
$931$	−983.386	−	263.498i	−1.05627	−	0.283026i
$932$	−9.67881	+	147.670i	−0.0103850	+	0.158444i
$933$	−570.640	−	184.598i	−0.611619	−	0.197854i
$934$	48.0859	+	27.7624i	0.0514839	+	0.0297242i
$935$	−173.423	+	86.8767i	−0.185479	+	0.0929162i
$936$	245.308	−	644.016i	0.262082	−	0.688052i
$937$	700.014	−	1689.98i	0.747080	−	1.80361i	0.172791	−	0.984959i	$-0.444722\pi$
$937$	700.014	−	1689.98i	0.747080	−	1.80361i	0.574289	−	0.818652i	$-0.305278\pi$
$938$	−56.9981	−	115.581i	−0.0607655	−	0.123220i
$939$	134.934	−	733.321i	0.143699	−	0.780959i
$940$	−517.902	+	454.188i	−0.550960	+	0.483179i
$941$	461.382	−	935.591i	0.490311	−	0.994252i	−0.501334	−	0.865254i	$-0.667157\pi$
$941$	461.382	−	935.591i	0.490311	−	0.994252i	0.991645	−	0.128998i	$-0.0411761\pi$
$942$	199.874	+	148.851i	0.212180	+	0.158016i
$943$	201.111	−	1527.59i	0.213267	−	1.61992i
$944$	106.356	+	256.765i	0.112665	+	0.271997i
$945$	189.265	−	8.17068i	0.200280	−	0.00864622i
$946$	−77.6061	+	51.8548i	−0.0820361	+	0.0548148i
$947$	−65.9469	+	194.273i	−0.0696377	+	0.205146i	−0.976177	−	0.216975i	$-0.930381\pi$
$947$	−65.9469	+	194.273i	−0.0696377	+	0.205146i	0.906539	+	0.422121i	$0.138714\pi$
$948$	244.100	+	686.499i	0.257490	+	0.724155i
$949$	−29.9447	+	456.868i	−0.0315539	+	0.481420i
$950$	33.6648	+	255.710i	0.0354367	+	0.269168i
$951$	−797.864	+	549.875i	−0.838974	+	0.578207i
$952$	124.214	−	163.994i	0.130477	−	0.172263i
$953$	1697.31			1.78102			0.890510	−	0.454963i	$-0.150347\pi$
$953$	1697.31			1.78102			0.890510	+	0.454963i	$0.150347\pi$
$954$	11.6538	−	49.0996i	0.0122157	−	0.0514671i
$955$	−57.7713	+	86.4609i	−0.0604935	+	0.0905350i
$956$	216.505	−	58.0122i	0.226469	−	0.0606822i
$957$	125.218	+	441.805i	0.130844	+	0.461656i
$958$	−18.1650	+	36.8350i	−0.0189614	+	0.0384499i
$959$	767.831	−	260.644i	0.800658	−	0.271787i
$960$	−247.790	+	126.658i	−0.258114	+	0.131936i
$961$	682.461	+	89.8476i	0.710157	+	0.0934939i
$962$	−528.499	−	105.125i	−0.549376	−	0.109278i
$963$	−924.259	−	284.375i	−0.959771	−	0.295301i
$964$	605.798	−	120.501i	0.628421	−	0.125001i
$965$	191.386	+	714.263i	0.198328	+	0.740169i
$966$	1.43316	+	99.6480i	0.00148361	+	0.103155i
$967$	42.5980	+	323.564i	0.0440517	+	0.334606i	0.999253	+	0.0386485i	$0.0123053\pi$
$967$	42.5980	+	323.564i	0.0440517	+	0.334606i	−0.955201	+	0.295957i	$0.904361\pi$
$968$	291.488	−	168.291i	0.301124	−	0.173854i
$969$	238.542	−	1343.60i	0.246173	−	1.38658i
$970$	−9.82385	+	17.0154i	−0.0101277	+	0.0175417i
$971$	−70.5216	+	170.254i	−0.0726278	+	0.175339i	−0.956024	−	0.293287i	$-0.905251\pi$
$971$	−70.5216	+	170.254i	−0.0726278	+	0.175339i	0.883397	+	0.468626i	$0.155251\pi$
$972$	694.309	+	601.006i	0.714309	+	0.618319i
$973$	52.3327	+	52.3327i	0.0537849	+	0.0537849i
$974$	−377.177	−	128.034i	−0.387245	−	0.131452i
$975$	−1274.49	+	186.472i	−1.30717	+	0.191254i
$976$	421.997	−	143.249i	0.432374	−	0.146771i
$977$	784.829	+	602.220i	0.803305	+	0.616397i	0.926632	−	0.375969i	$-0.122690\pi$
$977$	784.829	+	602.220i	0.803305	+	0.616397i	−0.123328	+	0.992366i	$0.539357\pi$
$978$	134.473	−	207.656i	0.137498	−	0.212327i
$979$	163.518	−	186.457i	0.167026	−	0.190457i
$980$	253.483	−	169.372i	0.258656	−	0.172828i
$981$	−135.908	−	112.441i	−0.138541	−	0.114619i
$982$	36.2051	−	36.2051i	0.0368687	−	0.0368687i
$983$	−534.135	+	263.406i	−0.543373	+	0.267962i	−0.693194	−	0.720751i	$-0.743797\pi$
$983$	−534.135	+	263.406i	−0.543373	+	0.267962i	0.149821	+	0.988713i	$0.452130\pi$
$984$	−753.155	−	243.640i	−0.765401	−	0.247602i
$985$	622.806	−	359.577i	0.632290	−	0.365053i
$986$	1.42291	+	227.311i	0.00144312	+	0.230538i
$987$	−850.799	+	68.0649i	−0.862005	+	0.0689614i
$988$	1288.91	+	1679.75i	1.30457	+	1.70015i
$989$	−437.702	+	655.068i	−0.442571	+	0.662354i
$990$	−39.1273	−	28.2736i	−0.0395226	−	0.0285592i
$991$	−70.7396	−	355.632i	−0.0713821	−	0.358862i	0.928541	−	0.371229i	$-0.121063\pi$
$991$	−70.7396	−	355.632i	−0.0713821	−	0.358862i	−0.999924	+	0.0123668i	$0.996063\pi$
$992$	344.784	−	22.5983i	0.347565	−	0.0227806i
$993$	−1137.21	+	490.322i	−1.14522	+	0.493779i
$994$	−67.9581	−	52.1461i	−0.0683683	−	0.0524609i
$995$	97.4062	−	126.942i	0.0978957	−	0.127580i
$996$	−27.3441	+	36.7169i	−0.0274539	+	0.0368644i
$997$	120.529	+	1838.92i	0.120892	+	1.84445i	0.441528	+	0.897247i	$0.354436\pi$
$997$	120.529	+	1838.92i	0.120892	+	1.84445i	−0.320637	+	0.947202i	$0.603897\pi$
$998$	−38.4983	+	7.65779i	−0.0385755	+	0.00767314i
$999$	767.383	−	1263.21i	0.768152	−	1.26448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.7.19	✓	544
9.4	even	3	inner	153.3.t.a.58.16	yes	544
17.5	odd	16	inner	153.3.t.a.124.16	yes	544
153.22	odd	48	inner	153.3.t.a.22.19	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.19	✓	544	1.1	even	1	trivial
153.3.t.a.22.19	yes	544	153.22	odd	48	inner
153.3.t.a.58.16	yes	544	9.4	even	3	inner
153.3.t.a.124.16	yes	544	17.5	odd	16	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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.t (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.286178 + 0.372954i) q^{2} +(-1.53721 - 2.57624i) q^{3} +(0.978079 - 3.65024i) q^{4} +(-1.59407 + 1.39796i) q^{5} +(0.520903 - 1.31057i) q^{6} +(-2.48802 - 2.18193i) q^{7} +(3.37853 - 1.39943i) q^{8} +(-4.27399 + 7.92042i) q^{9} +(-0.977562 - 0.194449i) q^{10} +(-0.351962 - 5.36990i) q^{11} +(-10.9074 + 3.09141i) q^{12} +(-20.2258 - 5.41948i) q^{13} +(0.101746 - 1.55234i) q^{14} +(6.05190 + 1.95774i) q^{15} +(-11.6021 - 6.69847i) q^{16} +(-5.36360 + 16.1317i) q^{17} +(-4.17707 + 0.672646i) q^{18} +(10.2395 - 24.7203i) q^{19} +(3.54377 + 7.18606i) q^{20} +(-1.79658 + 9.76381i) q^{21} +(1.90200 - 1.66801i) q^{22} +(9.44455 - 19.1517i) q^{23} +(-8.79877 - 6.55268i) q^{24} +(-2.67639 + 20.3292i) q^{25} +(-3.76694 - 9.09421i) q^{26} +(26.9749 - 1.16452i) q^{27} +(-10.3981 + 6.94776i) q^{28} +(9.14303 - 26.9345i) q^{29} +(1.00177 + 2.81734i) q^{30} +(-1.07994 + 16.4768i) q^{31} +(-2.73132 - 20.7464i) q^{32} +(-13.2931 + 9.16138i) q^{33} +(-7.55132 + 2.61616i) q^{34} +7.01634 q^{35} +(24.7311 + 23.3479i) q^{36} +(30.4130 - 45.5163i) q^{37} +(12.1498 - 3.25554i) q^{38} +(17.1293 + 60.4372i) q^{39} +(-3.42926 + 6.95385i) q^{40} +(68.3251 - 23.1932i) q^{41} +(-4.15559 + 2.12414i) q^{42} +(-36.5791 - 4.81573i) q^{43} +(-19.9457 - 3.96744i) q^{44} +(-4.25941 - 18.6006i) q^{45} +(9.84550 - 1.95839i) q^{46} +(22.2515 + 83.0436i) q^{47} +(0.577975 + 40.1866i) q^{48} +(-4.96638 - 37.7234i) q^{49} +(-8.34779 + 4.81960i) q^{50} +(49.8040 - 10.9799i) q^{51} +(-39.5648 + 68.5282i) q^{52} +(-4.56444 + 11.0195i) q^{53} +(8.15392 + 9.72712i) q^{54} +(8.06796 + 8.06796i) q^{55} +(-11.4593 - 3.88992i) q^{56} +(-79.4255 + 11.6209i) q^{57} +(12.6618 - 4.29812i) q^{58} +(-16.4582 - 12.6288i) q^{59} +(13.0655 - 20.1761i) q^{60} +(-21.9331 + 25.0099i) q^{61} +(-6.45413 + 4.31251i) q^{62} +(27.9156 - 10.3806i) q^{63} +(-30.9364 + 30.9364i) q^{64} +(39.8175 - 19.6358i) q^{65} +(-7.22096 - 2.33593i) q^{66} +(71.7411 - 41.4198i) q^{67} +(53.6386 + 35.3565i) q^{68} +(-63.8574 + 5.10867i) q^{69} +(2.00792 + 2.61677i) q^{70} +(30.5912 - 45.7830i) q^{71} +(-3.35570 + 32.7405i) q^{72} +(-4.26575 - 21.4454i) q^{73} +(25.6790 - 1.68309i) q^{74} +(56.4871 - 24.3552i) q^{75} +(-80.2200 - 61.5549i) q^{76} +(-10.8411 + 14.1284i) q^{77} +(-17.6383 + 23.6842i) q^{78} +(-4.20332 - 64.1302i) q^{79} +(27.8587 - 5.54145i) q^{80} +(-44.4661 - 67.7035i) q^{81} +(28.2031 + 18.8447i) q^{82} +(3.20366 - 2.45825i) q^{83} +(33.8831 + 16.1077i) q^{84} +(-14.0016 - 33.2132i) q^{85} +(-8.67207 - 15.0205i) q^{86} +(-83.4443 + 17.8493i) q^{87} +(-8.70393 - 17.6498i) q^{88} +(32.5868 + 32.5868i) q^{89} +(5.71821 - 6.91163i) q^{90} +(38.4971 + 57.6150i) q^{91} +(-60.6706 - 53.2067i) q^{92} +(44.1082 - 22.5460i) q^{93} +(-24.6036 + 32.0640i) q^{94} +(18.2356 + 53.7202i) q^{95} +(-49.2491 + 38.9281i) q^{96} +(6.33637 - 18.6663i) q^{97} +(12.6478 - 12.6478i) q^{98} +(44.0361 + 20.1632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) \) 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Introduction

L-functions

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