LMFDB - Embedded newform 75.3.h.a.14.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(14,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.h (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.13
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.27392 - 0.925557i) q^{2} +(-1.60087 + 2.53717i) q^{3} +(-0.469852 + 1.44606i) q^{4} +(2.47338 + 4.34538i) q^{5} +(0.308913 + 4.71384i) q^{6} -3.45468i q^{7} +(2.68623 + 8.26736i) q^{8} +(-3.87443 - 8.12335i) q^{9} +(7.17279 + 3.24641i) q^{10} +(4.67438 + 6.43373i) q^{11} +(-2.91672 - 3.50704i) q^{12} +(9.39120 - 12.9259i) q^{13} +(-3.19750 - 4.40098i) q^{14} +(-14.9845 - 0.681003i) q^{15} +(6.15359 + 4.47085i) q^{16} +(-5.07678 - 15.6247i) q^{17} +(-12.4543 - 6.76248i) q^{18} +(-0.909136 - 2.79803i) q^{19} +(-7.44580 + 1.53497i) q^{20} +(8.76509 + 5.53049i) q^{21} +(11.9096 + 3.86965i) q^{22} +(3.91892 - 2.84726i) q^{23} +(-25.2760 - 6.41956i) q^{24} +(-12.7647 + 21.4956i) q^{25} -25.1586i q^{26} +(26.8128 + 3.17434i) q^{27} +(4.99566 + 1.62319i) q^{28} +(-2.93429 - 0.953408i) q^{29} +(-19.7194 + 13.0015i) q^{30} +(9.46440 + 29.1284i) q^{31} -22.7941 q^{32} +(-23.8065 + 1.56012i) q^{33} +(-20.9290 - 15.2058i) q^{34} +(15.0119 - 8.54475i) q^{35} +(13.5672 - 1.78588i) q^{36} +(36.9883 - 50.9101i) q^{37} +(-3.74791 - 2.72301i) q^{38} +(17.7610 + 44.5197i) q^{39} +(-29.2808 + 32.1211i) q^{40} +(5.01027 - 6.89605i) q^{41} +(16.2848 - 1.06719i) q^{42} -76.9353i q^{43} +(-11.4998 + 3.73651i) q^{44} +(25.7161 - 36.9281i) q^{45} +(2.35708 - 7.25436i) q^{46} +(-21.0904 + 64.9097i) q^{47} +(-21.1944 + 8.45545i) q^{48} +37.0652 q^{49} +(3.63417 + 39.1982i) q^{50} +(47.7698 + 12.1325i) q^{51} +(14.2791 + 19.6535i) q^{52} +(19.3602 - 59.5846i) q^{53} +(37.0953 - 20.7729i) q^{54} +(-16.3955 + 36.2250i) q^{55} +(28.5611 - 9.28005i) q^{56} +(8.55449 + 2.17266i) q^{57} +(-4.62048 + 1.50128i) q^{58} +(-63.2466 + 87.0514i) q^{59} +(8.02529 - 21.3485i) q^{60} +(-60.5497 + 43.9919i) q^{61} +(39.0169 + 28.3474i) q^{62} +(-28.0635 + 13.3849i) q^{63} +(-53.6522 + 38.9806i) q^{64} +(79.3960 + 8.83771i) q^{65} +(-28.8836 + 24.0217i) q^{66} +(-74.5516 + 24.2233i) q^{67} +24.9796 q^{68} +(0.950298 + 14.5010i) q^{69} +(11.2153 - 24.7797i) q^{70} +(-35.3941 - 11.5002i) q^{71} +(56.7510 - 53.8525i) q^{72} +(8.18118 + 11.2604i) q^{73} -99.0901i q^{74} +(-34.1033 - 66.7979i) q^{75} +4.47328 q^{76} +(22.2264 - 16.1485i) q^{77} +(63.8316 + 40.2757i) q^{78} +(23.1785 - 71.3362i) q^{79} +(-4.20735 + 37.7979i) q^{80} +(-50.9775 + 62.9467i) q^{81} -13.4223i q^{82} +(15.7098 + 48.3497i) q^{83} +(-12.1157 + 10.0763i) q^{84} +(55.3386 - 60.7065i) q^{85} +(-71.2080 - 98.0094i) q^{86} +(7.11637 - 5.91850i) q^{87} +(-40.6335 + 55.9272i) q^{88} +(-80.9329 - 111.395i) q^{89} +(-1.41877 - 70.8451i) q^{90} +(-44.6548 - 32.4436i) q^{91} +(2.27599 + 7.00477i) q^{92} +(-89.0550 - 22.6181i) q^{93} +(33.2101 + 102.210i) q^{94} +(9.90989 - 10.8712i) q^{95} +(36.4903 - 57.8324i) q^{96} +(-151.453 - 49.2101i) q^{97} +(47.2181 - 34.3059i) q^{98} +(34.1528 - 62.8986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) $ 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.27392	−	0.925557i	0.636960	−	0.462778i	−0.221845	−	0.975082i	$-0.571208\pi$
$2$	1.27392	−	0.925557i	0.636960	−	0.462778i	0.858804	+	0.512304i	$0.171208\pi$
$3$	−1.60087	+	2.53717i	−0.533623	+	0.845722i
$3$	−1.60087	+	2.53717i	−0.533623	+	0.845722i
$4$	−0.469852	+	1.44606i	−0.117463	+	0.361514i
$5$	2.47338	+	4.34538i	0.494677	+	0.869077i
$5$	2.47338	+	4.34538i	0.494677	+	0.869077i
$6$	0.308913	+	4.71384i	0.0514855	+	0.785640i
$7$		−	3.45468i		−	0.493525i	−0.969076	−	0.246763i	$-0.920633\pi$
$7$		−	3.45468i		−	0.493525i	0.969076	−	0.246763i	$-0.0793668\pi$
$8$	2.68623	+	8.26736i	0.335779	+	1.03342i
$9$	−3.87443	−	8.12335i	−0.430493	−	0.902594i
$10$	7.17279	+	3.24641i	0.717279	+	0.324641i
$11$	4.67438	+	6.43373i	0.424943	+	0.584884i	0.966783	−	0.255597i	$-0.0822722\pi$
$11$	4.67438	+	6.43373i	0.424943	+	0.584884i	−0.541840	+	0.840482i	$0.682272\pi$
$12$	−2.91672	−	3.50704i	−0.243060	−	0.292254i
$13$	9.39120	−	12.9259i	0.722400	−	0.994299i	−0.277040	−	0.960858i	$-0.589354\pi$
$13$	9.39120	−	12.9259i	0.722400	−	0.994299i	0.999441	−	0.0334405i	$-0.0106464\pi$
$14$	−3.19750	−	4.40098i	−0.228393	−	0.314356i
$15$	−14.9845	−	0.681003i	−0.998969	−	0.0454002i
$16$	6.15359	+	4.47085i	0.384600	+	0.279428i
$17$	−5.07678	−	15.6247i	−0.298634	−	0.919101i	−0.981976	−	0.189003i	$-0.939474\pi$
$17$	−5.07678	−	15.6247i	−0.298634	−	0.919101i	0.683342	−	0.730098i	$-0.260526\pi$
$18$	−12.4543	−	6.76248i	−0.691907	−	0.375693i
$19$	−0.909136	−	2.79803i	−0.0478493	−	0.147265i	0.924277	−	0.381722i	$-0.124669\pi$
$19$	−0.909136	−	2.79803i	−0.0478493	−	0.147265i	−0.972126	+	0.234457i	$0.924669\pi$
$20$	−7.44580	+	1.53497i	−0.372290	+	0.0767483i
$21$	8.76509	+	5.53049i	0.417385	+	0.263357i
$22$	11.9096	+	3.86965i	0.541343	+	0.175893i
$23$	3.91892	−	2.84726i	0.170388	−	0.123794i	−0.499323	−	0.866416i	$-0.666418\pi$
$23$	3.91892	−	2.84726i	0.170388	−	0.123794i	0.669711	+	0.742622i	$0.266418\pi$
$24$	−25.2760	−	6.41956i	−1.05317	−	0.267482i
$25$	−12.7647	+	21.4956i	−0.510589	+	0.859825i
$26$		−	25.1586i		−	0.967639i
$27$	26.8128	+	3.17434i	0.993065	+	0.117568i
$28$	4.99566	+	1.62319i	0.178416	+	0.0579710i
$29$	−2.93429	−	0.953408i	−0.101182	−	0.0328761i	0.257988	−	0.966148i	$-0.416940\pi$
$29$	−2.93429	−	0.953408i	−0.101182	−	0.0328761i	−0.359171	+	0.933272i	$0.616940\pi$
$30$	−19.7194	+	13.0015i	−0.657313	+	0.433383i
$31$	9.46440	+	29.1284i	0.305303	+	0.939627i	0.979564	+	0.201133i	$0.0644625\pi$
$31$	9.46440	+	29.1284i	0.305303	+	0.939627i	−0.674261	+	0.738494i	$0.735538\pi$
$32$	−22.7941			−0.712315
$33$	−23.8065	+	1.56012i	−0.721409	+	0.0472762i
$34$	−20.9290	−	15.2058i	−0.615558	−	0.447229i
$35$	15.0119	−	8.54475i	0.428911	−	0.244136i
$36$	13.5672	−	1.78588i	0.376868	−	0.0496077i
$37$	36.9883	−	50.9101i	0.999684	−	1.37595i	0.0741655	−	0.997246i	$-0.476371\pi$
$37$	36.9883	−	50.9101i	0.999684	−	1.37595i	0.925519	−	0.378701i	$-0.123629\pi$
$38$	−3.74791	−	2.72301i	−0.0986291	−	0.0716582i
$39$	17.7610	+	44.5197i	0.455411	+	1.14153i
$40$	−29.2808	+	32.1211i	−0.732020	+	0.803027i
$41$	5.01027	−	6.89605i	0.122202	−	0.168196i	−0.743533	−	0.668699i	$-0.766851\pi$
$41$	5.01027	−	6.89605i	0.122202	−	0.168196i	0.865735	+	0.500503i	$0.166851\pi$
$42$	16.2848	−	1.06719i	0.387733	−	0.0254094i
$43$		−	76.9353i		−	1.78919i	−0.446875	−	0.894597i	$-0.647463\pi$
$43$		−	76.9353i		−	1.78919i	0.446875	−	0.894597i	$-0.352537\pi$
$44$	−11.4998	+	3.73651i	−0.261359	+	0.0849207i
$45$	25.7161	−	36.9281i	0.571469	−	0.820624i
$46$	2.35708	−	7.25436i	0.0512409	−	0.157703i
$47$	−21.0904	+	64.9097i	−0.448733	+	1.38106i	0.429605	+	0.903017i	$0.358653\pi$
$47$	−21.0904	+	64.9097i	−0.448733	+	1.38106i	−0.878338	+	0.478040i	$0.841347\pi$
$48$	−21.1944	+	8.45545i	−0.441550	+	0.176155i
$49$	37.0652			0.756433
$50$	3.63417	+	39.1982i	0.0726834	+	0.783963i
$51$	47.7698	+	12.1325i	0.936663	+	0.237892i
$52$	14.2791	+	19.6535i	0.274598	+	0.377951i
$53$	19.3602	−	59.5846i	0.365287	−	1.12424i	−0.584514	−	0.811384i	$-0.698715\pi$
$53$	19.3602	−	59.5846i	0.365287	−	1.12424i	0.949801	−	0.312855i	$-0.101285\pi$
$54$	37.0953	−	20.7729i	0.686950	−	0.384683i
$55$	−16.3955	+	36.2250i	−0.298100	+	0.658637i
$56$	28.5611	−	9.28005i	0.510019	−	0.165715i
$57$	8.55449	+	2.17266i	0.150079	+	0.0381168i
$58$	−4.62048	+	1.50128i	−0.0796634	+	0.0258842i
$59$	−63.2466	+	87.0514i	−1.07198	+	1.47545i	−0.203915	+	0.978989i	$0.565367\pi$
$59$	−63.2466	+	87.0514i	−1.07198	+	1.47545i	−0.868060	+	0.496459i	$0.834633\pi$
$60$	8.02529	−	21.3485i	0.133755	−	0.355809i
$61$	−60.5497	+	43.9919i	−0.992617	+	0.721179i	−0.960493	−	0.278305i	$-0.910227\pi$
$61$	−60.5497	+	43.9919i	−0.992617	+	0.721179i	−0.0321247	+	0.999484i	$0.510227\pi$
$62$	39.0169	+	28.3474i	0.629305	+	0.457217i
$63$	−28.0635	+	13.3849i	−0.445453	+	0.212459i
$64$	−53.6522	+	38.9806i	−0.838316	+	0.609072i
$65$	79.3960	+	8.83771i	1.22148	+	0.135965i
$66$	−28.8836	+	24.0217i	−0.437630	+	0.363966i
$67$	−74.5516	+	24.2233i	−1.11271	+	0.361541i	−0.806981	−	0.590577i	$-0.798900\pi$
$67$	−74.5516	+	24.2233i	−1.11271	+	0.361541i	−0.305729	+	0.952119i	$0.598900\pi$
$68$	24.9796			0.367347
$69$	0.950298	+	14.5010i	0.0137724	+	0.210160i
$70$	11.2153	−	24.7797i	0.160219	−	0.353995i
$71$	−35.3941	−	11.5002i	−0.498508	−	0.161975i	0.0489616	−	0.998801i	$-0.484409\pi$
$71$	−35.3941	−	11.5002i	−0.498508	−	0.161975i	−0.547470	+	0.836826i	$0.684409\pi$
$72$	56.7510	−	53.8525i	0.788209	−	0.747952i
$73$	8.18118	+	11.2604i	0.112071	+	0.154252i	0.861368	−	0.507982i	$-0.169608\pi$
$73$	8.18118	+	11.2604i	0.112071	+	0.154252i	−0.749297	+	0.662234i	$0.769608\pi$
$74$		−	99.0901i		−	1.33906i
$75$	−34.1033	−	66.7979i	−0.454711	−	0.890639i
$76$	4.47328			0.0588589
$77$	22.2264	−	16.1485i	0.288655	−	0.209720i
$78$	63.8316	+	40.2757i	0.818354	+	0.516355i
$79$	23.1785	−	71.3362i	0.293399	−	0.902990i	−0.690355	−	0.723471i	$-0.742546\pi$
$79$	23.1785	−	71.3362i	0.293399	−	0.902990i	0.983754	−	0.179519i	$-0.0574543\pi$
$80$	−4.20735	+	37.7979i	−0.0525918	+	0.472473i
$81$	−50.9775	+	62.9467i	−0.629352	+	0.777120i
$82$		−	13.4223i		−	0.163687i
$83$	15.7098	+	48.3497i	0.189274	+	0.582526i	0.999996	−	0.00290563i	$-0.000924893\pi$
$83$	15.7098	+	48.3497i	0.189274	+	0.582526i	−0.810721	+	0.585432i	$0.800925\pi$
$84$	−12.1157	+	10.0763i	−0.144235	+	0.119956i
$85$	55.3386	−	60.7065i	0.651042	−	0.714194i
$86$	−71.2080	−	98.0094i	−0.828000	−	1.13964i
$87$	7.11637	−	5.91850i	0.0817973	−	0.0680287i
$88$	−40.6335	+	55.9272i	−0.461744	+	0.635537i
$89$	−80.9329	−	111.395i	−0.909359	−	1.25163i	−0.967385	−	0.253310i	$-0.918481\pi$
$89$	−80.9329	−	111.395i	−0.909359	−	1.25163i	0.0580262	−	0.998315i	$-0.481519\pi$
$90$	−1.41877	−	70.8451i	−0.0157641	−	0.787168i
$91$	−44.6548	−	32.4436i	−0.490712	−	0.356523i
$92$	2.27599	+	7.00477i	0.0247390	+	0.0761388i
$93$	−89.0550	−	22.6181i	−0.957581	−	0.243205i
$94$	33.2101	+	102.210i	0.353299	+	1.08734i
$95$	9.90989	−	10.8712i	0.104315	−	0.114433i
$96$	36.4903	−	57.8324i	0.380108	−	0.602421i
$97$	−151.453	−	49.2101i	−1.56137	−	0.507320i	−0.604198	−	0.796834i	$-0.706506\pi$
$97$	−151.453	−	49.2101i	−1.56137	−	0.507320i	−0.957174	+	0.289514i	$0.906506\pi$
$98$	47.2181	−	34.3059i	0.481817	−	0.350061i
$99$	34.1528	−	62.8986i	0.344978	−	0.635340i
$100$	−25.0863	−	28.5583i	−0.250863	−	0.285583i
$101$			0.307054i			0.00304014i	0.999999	+	0.00152007i	$0.000483853\pi$
$101$			0.307054i			0.00304014i	−0.999999	+	0.00152007i	$0.999516\pi$
$102$	72.0842	−	28.7578i	0.706708	−	0.281939i
$103$	21.0182	+	6.82924i	0.204060	+	0.0663033i	0.409264	−	0.912416i	$-0.365786\pi$
$103$	21.0182	+	6.82924i	0.204060	+	0.0663033i	−0.205203	+	0.978719i	$0.565786\pi$
$104$	132.090	+	42.9186i	1.27010	+	0.412679i
$105$	−2.35265	+	51.7667i	−0.0224062	+	0.493016i
$106$	−30.4856	−	93.8250i	−0.287600	−	0.885142i
$107$	−139.254			−1.30144			−0.650721	−	0.759317i	$-0.725533\pi$
$107$	−139.254			−1.30144			−0.650721	+	0.759317i	$0.725533\pi$
$108$	−17.1883	+	37.2813i	−0.159151	+	0.345197i
$109$	81.6553	+	59.3261i	0.749131	+	0.544276i	0.895558	−	0.444946i	$-0.146777\pi$
$109$	81.6553	+	59.3261i	0.749131	+	0.544276i	−0.146426	+	0.989222i	$0.546777\pi$
$110$	12.6418	+	61.3227i	0.114925	+	0.557479i
$111$	69.9538	+	175.346i	0.630215	+	1.57969i
$112$	15.4453	−	21.2587i	0.137905	−	0.189810i
$113$	57.8390	+	42.0225i	0.511849	+	0.371880i	0.813525	−	0.581530i	$-0.197546\pi$
$113$	57.8390	+	42.0225i	0.511849	+	0.371880i	−0.301675	+	0.953411i	$0.597546\pi$
$114$	12.9086	−	5.14987i	0.113234	−	0.0451743i
$115$	22.0654	+	9.98683i	0.191873	+	0.0868420i
$116$	2.75736	−	3.79519i	0.0237704	−	0.0327171i
$117$	−141.387	−	26.2075i	−1.20844	−	0.223996i
$118$			169.435i			1.43589i
$119$	−53.9784	+	17.5386i	−0.453600	+	0.147383i
$120$	−34.6218	−	125.712i	−0.288515	−	1.04760i
$121$	17.8480	−	54.9305i	0.147504	−	0.453971i
$122$	−36.4184	+	112.084i	−0.298511	+	0.918724i
$123$	9.47563	+	23.7516i	0.0770377	+	0.193102i
$124$	−46.5683			−0.375550
$125$	−124.979	−	2.30075i	−0.999831	−	0.0184060i
$126$	−23.3622	+	43.0257i	−0.185414	+	0.341474i
$127$	79.5270	+	109.460i	0.626197	+	0.861886i	0.997786	−	0.0665113i	$-0.0211868\pi$
$127$	79.5270	+	109.460i	0.626197	+	0.861886i	−0.371589	+	0.928397i	$0.621187\pi$
$128$	−4.09479	+	12.6025i	−0.0319906	+	0.0984568i
$129$	195.198	+	123.163i	1.51316	+	0.954755i
$130$	109.324	−	62.2270i	0.840953	−	0.478669i
$131$	123.408	−	40.0976i	0.942044	−	0.306089i	0.202565	−	0.979269i	$-0.435072\pi$
$131$	123.408	−	40.0976i	0.942044	−	0.306089i	0.739478	+	0.673180i	$0.235072\pi$
$132$	8.92953	−	35.1586i	0.0676479	−	0.266353i
$133$	−9.66630	+	3.14077i	−0.0726790	+	0.0236148i
$134$	−72.5527	+	99.8602i	−0.541438	+	0.745225i
$135$	52.5245	+	124.363i	0.389071	+	0.921208i
$136$	115.538	−	83.9432i	0.849543	−	0.617229i
$137$	34.2523	+	24.8857i	0.250017	+	0.181648i	0.705734	−	0.708477i	$-0.250617\pi$
$137$	34.2523	+	24.8857i	0.250017	+	0.181648i	−0.455718	+	0.890124i	$0.650617\pi$
$138$	14.6321	+	17.5936i	0.106030	+	0.127490i
$139$	137.253	−	99.7198i	0.987428	−	0.717409i	0.0280720	−	0.999606i	$-0.491063\pi$
$139$	137.253	−	99.7198i	0.987428	−	0.717409i	0.959356	+	0.282197i	$0.0910632\pi$
$140$	5.30281	+	25.7228i	0.0378772	+	0.183735i
$141$	−130.924	−	157.422i	−0.928537	−	1.11647i
$142$	−55.7333	+	18.1088i	−0.392488	+	0.127527i
$143$	127.060			0.888529
$144$	12.4766	−	67.3098i	0.0866428	−	0.467429i
$145$	−3.11470	−	15.1088i	−0.0214807	−	0.104198i
$146$	20.8443	+	6.77273i	0.142769	+	0.0463886i
$147$	−59.3366	+	94.0406i	−0.403650	+	0.639732i
$148$	56.2398	+	77.4074i	0.379999	+	0.523023i
$149$		−	227.208i		−	1.52489i	−0.647054	−	0.762444i	$-0.723999\pi$
$149$		−	227.208i		−	1.52489i	0.647054	−	0.762444i	$-0.276001\pi$
$150$	−105.270	−	53.5307i	−0.701801	−	0.356871i
$151$	−68.4391			−0.453239			−0.226620	−	0.973983i	$-0.572767\pi$
$151$	−68.4391			−0.453239			−0.226620	+	0.973983i	$0.572767\pi$
$152$	20.6902	−	15.0323i	0.136120	−	0.0988969i
$153$	−107.255	+	101.777i	−0.701016	+	0.665212i
$154$	13.3684	−	41.1437i	0.0868077	−	0.267167i
$155$	−103.165	+	113.172i	−0.665582	+	0.730144i
$156$	−72.7231	+	4.76577i	−0.466174	+	0.0305498i
$157$			148.456i			0.945582i	0.881175	+	0.472791i	$0.156753\pi$
$157$			148.456i			0.945582i	−0.881175	+	0.472791i	$0.843247\pi$
$158$	−36.4981	−	112.330i	−0.231001	−	0.710947i
$159$	120.183	+	144.507i	0.755868	+	0.908851i
$160$	−56.3785	−	99.0490i	−0.352366	−	0.619056i
$161$	−9.83636	−	13.5386i	−0.0610954	−	0.0840906i
$162$	−6.68051	+	127.372i	−0.0412377	+	0.786245i
$163$	91.0894	−	125.374i	0.558830	−	0.769164i	−0.432347	−	0.901707i	$-0.642314\pi$
$163$	91.0894	−	125.374i	0.558830	−	0.769164i	0.991177	+	0.132543i	$0.0423144\pi$
$164$	7.61799	+	10.4853i	0.0464512	+	0.0639345i
$165$	−65.6619	−	99.5897i	−0.397951	−	0.603574i
$166$	64.7634	+	47.0533i	0.390141	+	0.283454i
$167$	−16.3877	−	50.4362i	−0.0981300	−	0.302013i	0.889927	−	0.456103i	$-0.150755\pi$
$167$	−16.3877	−	50.4362i	−0.0981300	−	0.302013i	−0.988057	+	0.154090i	$0.950755\pi$
$168$	−22.1775	+	87.3204i	−0.132009	+	0.519764i
$169$	−26.6599	−	82.0507i	−0.157751	−	0.485507i
$170$	14.3096	−	128.554i	0.0841741	−	0.756201i
$171$	−19.2070	+	18.2260i	−0.112322	+	0.106585i
$172$	111.253	+	36.1482i	0.646819	+	0.210164i
$173$	−25.5804	+	18.5852i	−0.147863	+	0.107429i	−0.659257	−	0.751917i	$-0.729129\pi$
$173$	−25.5804	+	18.5852i	−0.147863	+	0.107429i	0.511394	+	0.859346i	$0.329129\pi$
$174$	3.58778	−	14.1263i	0.0206194	−	0.0811856i
$175$	74.2604	+	44.0980i	0.424345	+	0.251989i
$176$			60.4890i			0.343687i
$177$	−119.614	−	299.825i	−0.675788	−	1.69393i
$178$	−206.204	−	66.9998i	−1.15845	−	0.376403i
$179$	77.9997	+	25.3436i	0.435753	+	0.141585i	0.518675	−	0.854971i	$-0.326425\pi$
$179$	77.9997	+	25.3436i	0.435753	+	0.141585i	−0.0829226	+	0.996556i	$0.526425\pi$
$180$	41.3173	+	54.5377i	0.229541	+	0.302987i
$181$	27.7033	+	85.2621i	0.153057	+	0.471061i	0.997959	−	0.0638602i	$-0.0203412\pi$
$181$	27.7033	+	85.2621i	0.153057	+	0.471061i	−0.844902	+	0.534922i	$0.820341\pi$
$182$	−86.9149			−0.477555
$183$	−14.6827	−	224.050i	−0.0802333	−	1.22432i
$184$	34.0664	+	24.7507i	0.185144	+	0.134515i
$185$	312.710	+	34.8083i	1.69032	+	0.188153i
$186$	−134.383	+	53.6118i	−0.722490	+	0.288236i
$187$	76.7944	−	105.698i	0.410665	−	0.565232i
$188$	−83.9537	−	60.9959i	−0.446562	−	0.324446i
$189$	10.9663	−	92.6294i	0.0580228	−	0.490103i
$190$	2.56252	−	23.0211i	0.0134870	−	0.121164i
$191$	−0.866643	+	1.19283i	−0.00453740	+	0.00624519i	−0.811280	−	0.584658i	$-0.801229\pi$
$191$	−0.866643	+	1.19283i	−0.00453740	+	0.00624519i	0.806742	+	0.590903i	$0.201229\pi$
$192$	−13.0101	−	198.527i	−0.0677611	−	1.03400i
$193$			141.376i			0.732518i	0.930513	+	0.366259i	$0.119362\pi$
$193$			141.376i			0.732518i	−0.930513	+	0.366259i	$0.880638\pi$
$194$	−238.486	+	77.4887i	−1.22931	+	0.399426i
$195$	−149.525	+	187.293i	−0.766797	+	0.960476i
$196$	−17.4152	+	53.5984i	−0.0888529	+	0.273461i
$197$	−30.8463	+	94.9352i	−0.156580	+	0.481905i	−0.998318	−	0.0579827i	$-0.981533\pi$
$197$	−30.8463	+	94.9352i	−0.156580	+	0.481905i	0.841737	+	0.539887i	$0.181533\pi$
$198$	−14.7083	−	111.738i	−0.0742842	−	0.564334i
$199$	−250.393			−1.25826			−0.629128	−	0.777301i	$-0.716588\pi$
$199$	−250.393			−1.25826			−0.629128	+	0.777301i	$0.716588\pi$
$200$	−212.001	−	47.7885i	−1.06001	−	0.238943i
$201$	57.8889	−	227.928i	0.288004	−	1.13397i
$202$	0.284196	+	0.391162i	0.00140691	+	0.00193645i
$203$	−3.29372	+	10.1370i	−0.0162252	+	0.0499361i
$204$	−39.9890	+	63.3773i	−0.196025	+	0.310673i
$205$	42.3583	+	4.71498i	0.206626	+	0.0229999i
$206$	33.0964	−	10.7537i	0.160662	−	0.0522022i
$207$	−38.3128	−	20.8032i	−0.185086	−	0.100499i
$208$	115.579	−	37.5540i	0.555670	−	0.180548i
$209$	13.7521	−	18.9282i	0.0657997	−	0.0905655i
$210$	44.9160	+	68.1241i	0.213885	+	0.324401i
$211$	38.3969	−	27.8970i	0.181976	−	0.132213i	−0.493068	−	0.869991i	$-0.664125\pi$
$211$	38.3969	−	27.8970i	0.181976	−	0.132213i	0.675044	+	0.737778i	$0.264125\pi$
$212$	77.0663	+	55.9920i	0.363520	+	0.264113i
$213$	85.8393	−	71.3903i	0.403001	−	0.335166i
$214$	−177.399	+	128.888i	−0.828966	+	0.602279i
$215$	334.313	−	190.291i	1.55495	−	0.885073i
$216$	45.7818	+	230.198i	0.211953	+	1.06573i
$217$	100.629	−	32.6965i	0.463730	−	0.150675i
$218$	158.932			0.729046
$219$	−41.6666	+	2.73054i	−0.190258	+	0.0124682i
$220$	−44.6800	−	40.7292i	−0.203091	−	0.185133i
$221$	−249.640	−	81.1131i	−1.12959	−	0.367028i
$222$	251.408	+	158.630i	1.13247	+	0.714551i
$223$	−108.162	−	148.872i	−0.485029	−	0.667586i	0.494432	−	0.869216i	$-0.335376\pi$
$223$	−108.162	−	148.872i	−0.485029	−	0.667586i	−0.979462	+	0.201630i	$0.935376\pi$
$224$			78.7462i			0.351545i
$225$	224.072	+	20.4090i	0.995878	+	0.0907068i
$226$	112.576			0.498126
$227$	174.859	−	127.043i	0.770305	−	0.559659i	−0.131749	−	0.991283i	$-0.542059\pi$
$227$	174.859	−	127.043i	0.770305	−	0.559659i	0.902054	+	0.431624i	$0.142059\pi$
$228$	−7.16113	+	11.3494i	−0.0314085	+	0.0497783i
$229$	−32.4904	+	99.9953i	−0.141880	+	0.436661i	−0.996597	−	0.0824337i	$-0.973731\pi$
$229$	−32.4904	+	99.9953i	−0.141880	+	0.436661i	0.854717	+	0.519094i	$0.173731\pi$
$230$	37.3529	−	7.70038i	0.162404	−	0.0334799i
$231$	5.38969	+	82.2438i	0.0233320	+	0.356034i
$232$		−	26.8199i		−	0.115603i
$233$	62.4520	+	192.208i	0.268034	+	0.824925i	0.990979	+	0.134019i	$0.0427883\pi$
$233$	62.4520	+	192.208i	0.268034	+	0.824925i	−0.722944	+	0.690906i	$0.757212\pi$
$234$	−204.372	+	97.4754i	−0.873386	+	0.416562i
$235$	−334.222	+	68.9006i	−1.42222	+	0.293194i
$236$	−96.1648	−	132.359i	−0.407478	−	0.560845i
$237$	143.886	+	173.008i	0.607114	+	0.729991i
$238$	−52.5311	+	72.3028i	−0.220719	+	0.303793i
$239$	44.7563	+	61.6017i	0.187265	+	0.257748i	0.892319	−	0.451406i	$-0.149077\pi$
$239$	44.7563	+	61.6017i	0.187265	+	0.257748i	−0.705054	+	0.709154i	$0.749077\pi$
$240$	−89.1641	−	71.1842i	−0.371517	−	0.296601i
$241$	191.906	+	139.428i	0.796290	+	0.578538i	0.909823	−	0.414996i	$-0.136217\pi$
$241$	191.906	+	139.428i	0.796290	+	0.578538i	−0.113534	+	0.993534i	$0.536217\pi$
$242$	−28.1044	−	86.4964i	−0.116134	−	0.357423i
$243$	−78.0980	−	230.108i	−0.321391	−	0.946947i
$244$	−35.1654	−	108.228i	−0.144120	−	0.443557i
$245$	91.6765	+	161.063i	0.374190	+	0.657398i
$246$	34.0546	+	21.4874i	0.138433	+	0.0873470i
$247$	−44.7049	−	14.5255i	−0.180992	−	0.0588078i
$248$	−215.392	+	156.491i	−0.868515	+	0.631013i
$249$	−147.821	−	37.5432i	−0.593657	−	0.150776i
$250$	−161.342	+	112.744i	−0.645370	+	0.450976i
$251$			329.960i			1.31458i	0.753637	+	0.657291i	$0.228298\pi$
$251$			329.960i			1.31458i	−0.753637	+	0.657291i	$0.771702\pi$
$252$	−6.16963	−	46.8704i	−0.0244826	−	0.185994i
$253$	36.6370	+	11.9041i	0.144810	+	0.0470517i
$254$	202.622	+	65.8359i	0.797724	+	0.259196i
$255$	65.4327	+	237.586i	0.256599	+	0.931712i
$256$	−75.5254	−	232.443i	−0.295021	−	0.907981i
$257$	113.930			0.443306			0.221653	−	0.975126i	$-0.428855\pi$
$257$	113.930			0.443306			0.221653	+	0.975126i	$0.428855\pi$
$258$	362.661	−	23.7663i	1.40566	−	0.0921175i
$259$	−175.878	−	127.783i	−0.679065	−	0.493370i
$260$	−50.0842	+	110.659i	−0.192632	+	0.425610i
$261$	3.62384	+	27.5302i	0.0138844	+	0.105480i
$262$	120.099	−	165.302i	0.458393	−	0.630923i
$263$	−190.229	−	138.210i	−0.723304	−	0.525511i	0.164134	−	0.986438i	$-0.447517\pi$
$263$	−190.229	−	138.210i	−0.723304	−	0.525511i	−0.887438	+	0.460927i	$0.847517\pi$
$264$	−76.8478	−	192.626i	−0.291090	−	0.729645i
$265$	306.803	−	63.2481i	1.15775	−	0.238672i
$266$	−9.40713	+	12.9478i	−0.0353651	+	0.0486760i
$267$	412.190	−	27.0121i	1.54378	−	0.101169i
$268$		−	119.187i		−	0.444728i
$269$	−158.804	+	51.5986i	−0.590350	+	0.191816i	−0.588932	−	0.808183i	$-0.700451\pi$
$269$	−158.804	+	51.5986i	−0.590350	+	0.191816i	−0.00141812	+	0.999999i	$0.500451\pi$
$270$	182.017	+	109.814i	0.674137	+	0.406719i
$271$	−164.547	+	506.424i	−0.607185	+	1.86872i	−0.126174	+	0.992008i	$0.540270\pi$
$271$	−164.547	+	506.424i	−0.607185	+	1.86872i	−0.481011	+	0.876715i	$0.659730\pi$
$272$	38.6153	−	118.846i	0.141968	−	0.436933i
$273$	153.801	−	61.3586i	0.563374	−	0.224757i
$274$	66.6678			0.243313
$275$	−197.964	+	18.3538i	−0.719869	+	0.0667410i
$276$	−21.4158	−	5.43916i	−0.0775935	−	0.0197071i
$277$	−11.6322	−	16.0104i	−0.0419935	−	0.0577991i	0.787504	−	0.616310i	$-0.211373\pi$
$277$	−11.6322	−	16.0104i	−0.0419935	−	0.0577991i	−0.829497	+	0.558511i	$0.811373\pi$
$278$	82.5524	−	254.070i	0.296951	−	0.913921i
$279$	199.951	−	189.739i	0.716671	−	0.680067i
$280$	110.968	+	101.156i	0.396314	+	0.361270i
$281$	25.0374	−	8.13516i	0.0891012	−	0.0289507i	−0.264127	−	0.964488i	$-0.585084\pi$
$281$	25.0374	−	8.13516i	0.0891012	−	0.0289507i	0.353228	+	0.935537i	$0.385084\pi$
$282$	−312.489	−	79.3655i	−1.10812	−	0.281438i
$283$	−46.4423	+	15.0900i	−0.164107	+	0.0533216i	−0.389918	−	0.920849i	$-0.627497\pi$
$283$	−46.4423	+	15.0900i	−0.164107	+	0.0533216i	0.225811	+	0.974171i	$0.427497\pi$
$284$	33.2600	−	45.7784i	0.117113	−	0.161192i
$285$	11.7175	+	42.5464i	0.0411141	+	0.149285i
$286$	161.864	−	117.601i	0.565957	−	0.411192i
$287$	−23.8236	−	17.3089i	−0.0830091	−	0.0603097i
$288$	88.3141	+	185.164i	0.306646	+	0.642931i
$289$	15.4477	−	11.2234i	0.0534523	−	0.0388354i
$290$	−17.9519	−	16.3645i	−0.0619031	−	0.0564293i
$291$	367.311	−	305.483i	1.26224	−	1.04977i
$292$	−20.1272	+	6.53971i	−0.0689286	+	0.0223963i
$293$	−290.824			−0.992572			−0.496286	−	0.868159i	$-0.665303\pi$
$293$	−290.824			−0.992572			−0.496286	+	0.868159i	$0.665303\pi$
$294$	11.4499	+	174.720i	0.0389453	+	0.594284i
$295$	−534.705	−	59.5189i	−1.81256	−	0.201759i
$296$	520.251	+	169.040i	1.75760	+	0.571080i
$297$	104.910	+	187.344i	0.353233	+	0.630788i
$298$	−210.294	−	289.445i	−0.705685	−	0.971293i
$299$		−	77.3946i		−	0.258845i
$300$	112.617	−	17.9301i	0.375390	−	0.0597671i
$301$	−265.787			−0.883012
$302$	−87.1860	+	63.3443i	−0.288695	+	0.209749i
$303$	−0.779047	−	0.491554i	−0.00257111	−	0.00162229i
$304$	6.91513	−	21.2826i	0.0227471	−	0.0700085i
$305$	−340.924	−	154.303i	−1.11778	−	0.505910i
$306$	−42.4340	+	228.927i	−0.138673	+	0.748128i
$307$			273.816i			0.891909i	0.895056	+	0.445954i	$0.147136\pi$
$307$			273.816i			0.891909i	−0.895056	+	0.445954i	$0.852864\pi$
$308$	12.9084	+	39.7281i	0.0419105	+	0.128987i
$309$	−50.9744	+	42.3940i	−0.164966	+	0.137198i
$310$	−26.6767	+	239.658i	−0.0860539	+	0.773089i
$311$	18.4022	+	25.3284i	0.0591710	+	0.0814418i	0.837577	−	0.546319i	$-0.183971\pi$
$311$	18.4022	+	25.3284i	0.0591710	+	0.0814418i	−0.778406	+	0.627761i	$0.783971\pi$
$312$	−320.350	+	266.427i	−1.02676	+	0.853933i
$313$	11.2273	−	15.4531i	0.0358700	−	0.0493709i	−0.790705	−	0.612197i	$-0.790286\pi$
$313$	11.2273	−	15.4531i	0.0358700	−	0.0493709i	0.826575	+	0.562826i	$0.190286\pi$
$314$	137.405	+	189.121i	0.437595	+	0.602297i
$315$	−127.575	−	88.8408i	−0.404999	−	0.282034i
$316$	92.2657	+	67.0350i	0.291980	+	0.212136i
$317$	−103.121	−	317.375i	−0.325304	−	1.00118i	−0.971303	−	0.237845i	$-0.923559\pi$
$317$	−103.121	−	317.375i	−0.325304	−	1.00118i	0.645999	−	0.763338i	$-0.276441\pi$
$318$	286.853	+	72.8546i	0.902054	+	0.229102i
$319$	−7.58200	−	23.3350i	−0.0237680	−	0.0731505i
$320$	−302.088	−	136.725i	−0.944026	−	0.427267i
$321$	222.928	−	353.312i	0.694480	−	1.10066i
$322$	−25.0615	−	8.14296i	−0.0778306	−	0.0252887i
$323$	−39.1030	+	28.4100i	−0.121062	+	0.0879567i
$324$	−67.0726	−	103.292i	−0.207014	−	0.318803i
$325$	157.974	+	366.865i	0.486073	+	1.12882i
$326$		−	244.024i		−	0.748541i
$327$	−281.240	+	112.200i	−0.860060	+	0.343119i
$328$	70.4709	+	22.8974i	0.214850	+	0.0698091i
$329$	224.242	+	72.8606i	0.681587	+	0.221461i
$330$	−175.824	−	66.0953i	−0.532800	−	0.200289i
$331$	−29.9792	−	92.2664i	−0.0905715	−	0.278750i	0.895503	−	0.445056i	$-0.146816\pi$
$331$	−29.9792	−	92.2664i	−0.0905715	−	0.278750i	−0.986074	+	0.166306i	$0.946816\pi$
$332$	−77.2977			−0.232824
$333$	−556.869	−	103.221i	−1.67228	−	0.309974i
$334$	−67.5581	−	49.0839i	−0.202270	−	0.146958i
$335$	−289.654	−	264.042i	−0.864639	−	0.788185i
$336$	29.2109	+	73.2198i	0.0869371	+	0.217916i
$337$	35.9558	−	49.4890i	0.106694	−	0.146852i	−0.752331	−	0.658785i	$-0.771071\pi$
$337$	35.9558	−	49.4890i	0.106694	−	0.146852i	0.859025	+	0.511934i	$0.171071\pi$
$338$	−109.905	−	79.8507i	−0.325163	−	0.236245i
$339$	−199.211	+	79.4746i	−0.587642	+	0.234438i
$340$	61.7841	+	108.546i	0.181718	+	0.319252i
$341$	−143.164	+	197.049i	−0.419836	+	0.577855i
$342$	−7.59897	+	40.9957i	−0.0222192	+	0.119870i
$343$		−	297.327i		−	0.866844i
$344$	636.052	−	206.666i	1.84899	−	0.600773i
$345$	−60.6621	+	39.9960i	−0.175832	+	0.115931i
$346$	−15.3856	+	47.3522i	−0.0444672	+	0.136856i
$347$	110.008	−	338.571i	0.317027	−	0.975709i	−0.657885	−	0.753119i	$-0.728549\pi$
$347$	110.008	−	338.571i	0.317027	−	0.975709i	0.974912	−	0.222591i	$-0.0714513\pi$
$348$	5.21484	+	13.0715i	0.0149852	+	0.0375618i
$349$	120.930			0.346506			0.173253	−	0.984877i	$-0.444572\pi$
$349$	120.930			0.346506			0.173253	+	0.984877i	$0.444572\pi$
$350$	135.417	−	12.5549i	0.386906	−	0.0358711i
$351$	292.835	−	316.768i	0.834288	−	0.902472i
$352$	−106.548	−	146.651i	−0.302693	−	0.416622i
$353$	−131.712	+	405.367i	−0.373121	+	1.14835i	0.571617	+	0.820520i	$0.306316\pi$
$353$	−131.712	+	405.367i	−0.373121	+	1.14835i	−0.944738	+	0.327827i	$0.893684\pi$
$354$	−429.884	−	271.243i	−1.21436	−	0.766223i
$355$	−37.5702	−	182.245i	−0.105832	−	0.513367i
$356$	199.110	−	64.6946i	0.559296	−	0.181726i
$357$	41.9139	−	165.029i	0.117406	−	0.462267i
$358$	122.822	−	39.9074i	0.343079	−	0.111473i
$359$	−103.927	+	143.043i	−0.289491	+	0.398450i	−0.928849	−	0.370460i	$-0.879200\pi$
$359$	−103.927	+	143.043i	−0.289491	+	0.398450i	0.639358	+	0.768909i	$0.279200\pi$
$360$	374.377	+	113.407i	1.03994	+	0.315020i
$361$	285.053	−	207.103i	0.789620	−	0.573692i
$362$	114.207	+	82.9761i	0.315488	+	0.229216i
$363$	110.796	+	133.220i	0.305222	+	0.366997i
$364$	67.8964	−	49.3296i	0.186529	−	0.135521i
$365$	−28.6957	+	63.4017i	−0.0786183	+	0.173703i
$366$	−226.075	−	271.832i	−0.617693	−	0.742710i
$367$	257.659	−	83.7185i	0.702068	−	0.228116i	0.0638366	−	0.997960i	$-0.479666\pi$
$367$	257.659	−	83.7185i	0.702068	−	0.228116i	0.638231	+	0.769845i	$0.279666\pi$
$368$	36.8451			0.100122
$369$	−75.4310	−	13.9819i	−0.204420	−	0.0378913i
$370$	430.585	−	245.088i	1.16374	−	0.662400i
$371$	−205.846	−	66.8833i	−0.554840	−	0.180278i
$372$	74.5497	−	118.151i	0.200402	−	0.317611i
$373$	371.550	+	511.394i	0.996111	+	1.37103i	0.927681	+	0.373374i	$0.121799\pi$
$373$	371.550	+	511.394i	0.996111	+	1.37103i	0.0684302	+	0.997656i	$0.478201\pi$
$374$		−	205.729i		−	0.550077i
$375$	205.912	−	313.409i	0.549099	−	0.835757i
$376$	−593.286			−1.57789
$377$	−39.8801	+	28.9746i	−0.105783	+	0.0768558i
$378$	−71.7636	−	128.152i	−0.189851	−	0.339027i
$379$	−8.13290	+	25.0305i	−0.0214588	+	0.0660435i	−0.961212	−	0.275809i	$-0.911054\pi$
$379$	−8.13290	+	25.0305i	−0.0214588	+	0.0660435i	0.939754	+	0.341852i	$0.111054\pi$
$380$	11.0641	+	19.4381i	0.0291161	+	0.0511529i
$381$	−405.030	+	26.5429i	−1.06307	+	0.0696663i
$382$			2.32170i			0.00607775i
$383$	8.00232	+	24.6286i	0.0208938	+	0.0643045i	0.960960	−	0.276688i	$-0.0892369\pi$
$383$	8.00232	+	24.6286i	0.0208938	+	0.0643045i	−0.940066	+	0.340993i	$0.889237\pi$
$384$	−25.4194	−	30.5641i	−0.0661962	−	0.0795940i
$385$	125.146	+	56.6411i	0.325054	+	0.147120i
$386$	130.851	+	180.102i	0.338993	+	0.466584i
$387$	−624.972	+	298.081i	−1.61492	+	0.770234i
$388$	142.321	−	195.888i	0.366807	−	0.504867i
$389$	−92.7133	−	127.609i	−0.238338	−	0.328044i	0.673047	−	0.739600i	$-0.264985\pi$
$389$	−92.7133	−	127.609i	−0.238338	−	0.328044i	−0.911384	+	0.411556i	$0.864985\pi$
$390$	−17.1331	+	376.990i	−0.0439311	+	0.966642i
$391$	−64.3831	−	46.7770i	−0.164663	−	0.119634i
$392$	99.5656	+	306.432i	0.253994	+	0.781713i
$393$	−95.8254	+	377.297i	−0.243830	+	0.960043i
$394$	48.5722	+	149.490i	0.123280	+	0.379416i
$395$	367.313	−	75.7222i	0.929906	−	0.191702i
$396$	74.9082	+	78.9400i	0.189162	+	0.199343i
$397$	−468.010	−	152.066i	−1.17887	−	0.383037i	−0.346921	−	0.937894i	$-0.612773\pi$
$397$	−468.010	−	152.066i	−1.17887	−	0.383037i	−0.831945	+	0.554858i	$0.812773\pi$
$398$	−318.981	+	231.753i	−0.801459	+	0.582294i
$399$	7.50583	−	29.5530i	0.0188116	−	0.0740677i
$400$	−174.653	+	75.2061i	−0.436632	+	0.188015i
$401$			590.500i			1.47257i	0.676672	+	0.736285i	$0.263421\pi$
$401$			590.500i			1.47257i	−0.676672	+	0.736285i	$0.736579\pi$
$402$	−137.215	−	343.941i	−0.341330	−	0.855576i
$403$	465.393	+	151.215i	1.15482	+	0.375224i
$404$	−0.444018	−	0.144270i	−0.00109905	−	0.000357104i
$405$	−399.615	−	65.8255i	−0.986703	−	0.162532i
$406$	5.18645	+	15.9623i	0.0127745	+	0.0393159i
$407$	500.439			1.22958
$408$	28.0168	+	427.521i	0.0686686	+	1.04785i
$409$	602.755	+	437.927i	1.47373	+	1.07073i	0.979511	+	0.201390i	$0.0645457\pi$
$409$	602.755	+	437.927i	1.47373	+	1.07073i	0.494218	+	0.869338i	$0.335454\pi$
$410$	58.3251	−	33.1985i	0.142256	−	0.0809720i
$411$	−117.973	+	47.0649i	−0.287038	+	0.114513i
$412$	−19.7509	+	27.1848i	−0.0479391	+	0.0659826i
$413$	300.735	+	218.496i	0.728171	+	0.529047i
$414$	−68.0620	+	8.95911i	−0.164401	+	0.0216404i
$415$	−171.242	+	187.852i	−0.412631	+	0.452656i
$416$	−214.064	+	294.634i	−0.514576	+	0.708254i
$417$	33.2824	+	507.871i	0.0798139	+	1.21792i
$418$		−	36.8414i		−	0.0881373i
$419$	187.721	−	60.9941i	0.448020	−	0.145571i	−0.0763126	−	0.997084i	$-0.524315\pi$
$419$	187.721	−	60.9941i	0.448020	−	0.145571i	0.524333	+	0.851513i	$0.324315\pi$
$420$	−73.7522	−	27.7248i	−0.175601	−	0.0660114i
$421$	47.9058	−	147.439i	0.113791	−	0.350211i	−0.877902	−	0.478840i	$-0.841058\pi$
$421$	47.9058	−	147.439i	0.113791	−	0.350211i	0.991693	+	0.128629i	$0.0410575\pi$
$422$	23.0943	−	71.0770i	0.0547259	−	0.168429i
$423$	608.997	−	80.1633i	1.43971	−	0.189511i
$424$	544.614			1.28447
$425$	400.667	+	90.3169i	0.942745	+	0.212510i
$426$	43.2766	−	170.395i	0.101588	−	0.399987i
$427$	151.978	+	209.180i	0.355920	+	0.489882i
$428$	65.4290	−	201.370i	0.152871	−	0.470490i
$429$	−203.406	+	322.371i	−0.474140	+	0.751449i
$430$	249.764	−	551.841i	0.580846	−	1.28335i
$431$	−218.609	+	71.0303i	−0.507213	+	0.164804i	−0.551434	−	0.834218i	$-0.685919\pi$
$431$	−218.609	+	71.0303i	−0.507213	+	0.164804i	0.0442213	+	0.999022i	$0.485919\pi$
$432$	150.803	+	139.409i	0.349081	+	0.322707i
$433$	−526.213	+	170.977i	−1.21527	+	0.394866i	−0.845358	−	0.534200i	$-0.820613\pi$
$433$	−526.213	+	170.977i	−1.21527	+	0.394866i	−0.369915	+	0.929066i	$0.620613\pi$
$434$	97.9313	−	134.791i	0.225648	−	0.310578i
$435$	43.3197	+	16.2846i	0.0995854	+	0.0374359i
$436$	−124.155	+	90.2038i	−0.284759	+	0.206889i
$437$	−11.5296	−	8.37671i	−0.0263834	−	0.0191687i
$438$	−50.5526	+	42.0433i	−0.115417	+	0.0959892i
$439$	42.8442	−	31.1281i	0.0975950	−	0.0709069i	−0.537918	−	0.842997i	$-0.680789\pi$
$439$	42.8442	−	31.1281i	0.0975950	−	0.0709069i	0.635513	+	0.772091i	$0.280789\pi$
$440$	−343.528	−	38.2387i	−0.780745	−	0.0869061i
$441$	−143.607	−	301.094i	−0.325639	−	0.682752i
$442$	−393.096	+	127.725i	−0.889359	+	0.288970i
$443$	−260.488			−0.588009			−0.294004	−	0.955804i	$-0.594988\pi$
$443$	−260.488			−0.588009			−0.294004	+	0.955804i	$0.594988\pi$
$444$	−286.428	+	18.7705i	−0.645108	+	0.0422760i
$445$	283.874	−	627.207i	0.637920	−	1.40945i
$446$	−275.578	−	89.5408i	−0.617888	−	0.200764i
$447$	576.466	+	363.731i	1.28963	+	0.813716i
$448$	134.665	+	185.351i	0.300592	+	0.413730i
$449$			757.399i			1.68686i	0.537241	+	0.843429i	$0.319467\pi$
$449$			757.399i			1.68686i	−0.537241	+	0.843429i	$0.680533\pi$
$450$	304.340	−	181.392i	0.676311	−	0.403094i
$451$	67.7872			0.150304
$452$	−87.9427	+	63.8941i	−0.194563	+	0.141359i
$453$	109.562	−	173.642i	0.241859	−	0.383315i
$454$	105.171	−	323.684i	0.231655	−	0.712961i
$455$	30.5314	−	274.288i	0.0671020	−	0.602830i
$456$	5.01717	+	76.5593i	0.0110026	+	0.167893i
$457$		−	28.8112i		−	0.0630442i	−0.999503	−	0.0315221i	$-0.989965\pi$
$457$		−	28.8112i		−	0.0630442i	0.999503	−	0.0315221i	$-0.0100355\pi$
$458$	51.1611	+	157.458i	0.111705	+	0.343794i
$459$	−86.5243	−	435.057i	−0.188506	−	0.947837i
$460$	−24.8090	+	27.2155i	−0.0539326	+	0.0591642i
$461$	7.46952	+	10.2809i	0.0162029	+	0.0223013i	0.817042	−	0.576579i	$-0.195613\pi$
$461$	7.46952	+	10.2809i	0.0162029	+	0.0223013i	−0.800839	+	0.598880i	$0.795613\pi$
$462$	82.9873	+	99.7835i	0.179626	+	0.215982i
$463$	−275.156	+	378.719i	−0.594289	+	0.817969i	−0.995171	−	0.0981613i	$-0.968704\pi$
$463$	−275.156	+	378.719i	−0.594289	+	0.817969i	0.400882	+	0.916130i	$0.368704\pi$
$464$	−13.7939	−	18.9856i	−0.0297282	−	0.0409173i
$465$	−121.983	−	442.921i	−0.262329	−	0.952519i
$466$	257.458	+	187.054i	0.552485	+	0.401404i
$467$	−109.488	−	336.968i	−0.234449	−	0.721559i	−0.997194	−	0.0748600i	$-0.976149\pi$
$467$	−109.488	−	336.968i	−0.234449	−	0.721559i	0.762745	−	0.646699i	$-0.223851\pi$
$468$	104.329	−	192.140i	0.222924	−	0.410556i
$469$	83.6836	+	257.552i	0.178430	+	0.549151i
$470$	−362.001	+	397.115i	−0.770215	+	0.844926i
$471$	−376.658	−	237.659i	−0.799699	−	0.504584i
$472$	−889.580	−	289.042i	−1.88470	−	0.612378i
$473$	494.981	−	359.624i	1.04647	−	0.760305i
$474$	343.428	+	87.2233i	0.724531	+	0.184015i
$475$	71.7504	+	16.1737i	0.151053	+	0.0340499i
$476$		−	86.2964i		−	0.181295i
$477$	−559.037	+	73.5869i	−1.17198	+	0.154270i
$478$	114.032	+	37.0512i	0.238560	+	0.0775129i
$479$	−845.986	−	274.877i	−1.76615	−	0.573857i	−0.768342	−	0.640039i	$-0.778918\pi$
$479$	−845.986	−	274.877i	−1.76615	−	0.573857i	−0.997808	+	0.0661825i	$0.978918\pi$
$480$	341.559	+	15.5228i	0.711580	+	0.0323393i
$481$	−310.693	−	956.213i	−0.645931	−	1.98797i
$482$	373.521			0.774940
$483$	50.0964	−	3.28297i	0.103719	−	0.00679705i
$484$	71.0467	+	51.6185i	0.146791	+	0.106650i
$485$	−160.765	−	779.837i	−0.331474	−	1.60791i
$486$	−312.469	−	220.855i	−0.642939	−	0.454434i
$487$	367.869	−	506.328i	0.755377	−	1.03969i	−0.242207	−	0.970225i	$-0.577871\pi$
$487$	367.869	−	506.328i	0.755377	−	1.03969i	0.997585	−	0.0694630i	$-0.0221286\pi$
$488$	−526.347	−	382.414i	−1.07858	−	0.783635i
$489$	172.272	+	431.816i	0.352294	+	0.883059i
$490$	265.861	+	120.329i	0.542574	+	0.245569i
$491$	87.2230	−	120.052i	0.177644	−	0.244505i	−0.710905	−	0.703288i	$-0.751714\pi$
$491$	87.2230	−	120.052i	0.177644	−	0.244505i	0.888548	+	0.458783i	$0.151714\pi$
$492$	−38.7983	+	2.54257i	−0.0788583	+	0.00516783i
$493$			50.6877i			0.102815i
$494$	−70.3947	+	22.8726i	−0.142499	+	0.0463009i
$495$	357.792	−	7.16529i	0.722812	−	0.0144753i
$496$	−71.9887	+	221.559i	−0.145139	+	0.446691i
$497$	−39.7296	+	122.275i	−0.0799388	+	0.246026i
$498$	−223.060	+	88.9892i	−0.447911	+	0.178693i
$499$	−162.393			−0.325437			−0.162719	−	0.986673i	$-0.552026\pi$
$499$	−162.393			−0.325437			−0.162719	+	0.986673i	$0.552026\pi$
$500$	62.0486	−	179.645i	0.124097	−	0.359291i
$501$	154.200	+	39.1634i	0.307784	+	0.0781704i
$502$	305.397	+	420.342i	0.608360	+	0.837335i
$503$	89.5586	−	275.633i	0.178049	−	0.547978i	−0.821711	−	0.569905i	$-0.806980\pi$
$503$	89.5586	−	275.633i	0.178049	−	0.547978i	0.999760	+	0.0219268i	$0.00698008\pi$
$504$	−186.043	−	196.057i	−0.369133	−	0.389001i
$505$	−1.33427	+	0.759463i	−0.00264211	+	0.00150389i
$506$	57.6904	−	18.7448i	0.114013	−	0.0370450i
$507$	250.855	+	63.7119i	0.494784	+	0.125664i
$508$	−195.651	+	63.5708i	−0.385139	+	0.125139i
$509$	229.058	−	315.271i	0.450016	−	0.619394i	−0.522385	−	0.852710i	$-0.674958\pi$
$509$	229.058	−	315.271i	0.450016	−	0.619394i	0.972401	+	0.233316i	$0.0749577\pi$
$510$	303.256	+	242.104i	0.594619	+	0.474714i
$511$	38.9011	−	28.2633i	0.0761275	−	0.0553098i
$512$	−354.234	−	257.366i	−0.691863	−	0.502668i
$513$	−15.4945	−	77.9089i	−0.0302038	−	0.151869i
$514$	145.137	−	105.448i	0.282368	−	0.205152i
$515$	22.3105	+	108.224i	0.0433214	+	0.210143i
$516$	−269.815	+	224.398i	−0.522898	+	0.434881i
$517$	−516.196	+	167.722i	−0.998444	+	0.324414i
$518$	−342.324			−0.660858
$519$	−6.20299	−	94.6542i	−0.0119518	−	0.182378i
$520$	140.211	+	680.136i	0.269637	+	1.30795i
$521$	62.7140	+	20.3770i	0.120372	+	0.0391113i	0.368584	−	0.929595i	$-0.379843\pi$
$521$	62.7140	+	20.3770i	0.120372	+	0.0391113i	−0.248211	+	0.968706i	$0.579843\pi$
$522$	30.0972	+	31.7171i	0.0576575	+	0.0607608i
$523$	−195.827	−	269.533i	−0.374430	−	0.515359i	0.579668	−	0.814853i	$-0.303182\pi$
$523$	−195.827	−	269.533i	−0.374430	−	0.515359i	−0.954098	+	0.299494i	$0.903182\pi$
$524$			197.295i			0.376516i
$525$	−230.765	+	117.816i	−0.439553	+	0.224411i
$526$	−370.257			−0.703911
$527$	407.075	−	295.757i	0.772438	−	0.561209i
$528$	−153.471	−	96.8349i	−0.290664	−	0.183400i
$529$	−156.219	+	480.793i	−0.295310	+	0.908871i
$530$	332.303	−	364.537i	0.626987	−	0.687806i
$531$	952.193	+	176.499i	1.79321	+	0.332390i
$532$		−	15.4537i		−	0.0290484i
$533$	−42.0850	−	129.524i	−0.0789588	−	0.243010i
$534$	500.095	−	415.916i	0.936508	−	0.778870i
$535$	−344.430	−	605.114i	−0.643794	−	1.13105i
$536$	−400.525	−	551.276i	−0.747249	−	1.02850i
$537$	−189.168	+	157.326i	−0.352269	+	0.292973i
$538$	−154.546	+	212.715i	−0.287261	+	0.395381i
$539$	173.257	+	238.467i	0.321441	+	0.442426i
$540$	−204.515	+	17.5212i	−0.378731	+	0.0324467i
$541$	−127.353	−	92.5277i	−0.235404	−	0.171031i	0.463829	−	0.885925i	$-0.346475\pi$
$541$	−127.353	−	92.5277i	−0.235404	−	0.171031i	−0.699233	+	0.714894i	$0.746475\pi$
$542$	259.104	+	797.441i	0.478052	+	1.47129i
$543$	−260.674	−	66.2055i	−0.480062	−	0.121925i
$544$	115.720	+	356.151i	0.212721	+	0.654689i
$545$	−55.8295	+	501.560i	−0.102439	+	0.920294i
$546$	139.139	−	220.518i	0.254834	−	0.403879i
$547$	60.8679	+	19.7772i	0.111276	+	0.0361557i	0.364126	−	0.931350i	$-0.381368\pi$
$547$	60.8679	+	19.7772i	0.111276	+	0.0361557i	−0.252850	+	0.967506i	$0.581368\pi$
$548$	−52.0797	+	37.8381i	−0.0950359	+	0.0690477i
$549$	591.957	+	321.422i	1.07825	+	0.585469i
$550$	−235.203	+	206.608i	−0.427641	+	0.375651i
$551$			9.07702i			0.0164737i
$552$	−117.333	+	46.8096i	−0.212559	+	0.0847999i
$553$	−246.444	−	80.0744i	−0.445648	−	0.144800i
$554$	−29.6370	−	9.62964i	−0.0534964	−	0.0173820i
$555$	−588.923	+	737.674i	−1.06112	+	1.32914i
$556$	79.7121	+	245.329i	0.143367	+	0.441239i
$557$	−934.176			−1.67716			−0.838578	−	0.544781i	$-0.816613\pi$
$557$	−934.176			−1.67716			−0.838578	+	0.544781i	$0.816613\pi$
$558$	79.1077	−	426.778i	0.141770	−	0.764835i
$559$	−994.457	−	722.515i	−1.77899	−	1.29251i
$560$	130.579	+	14.5350i	0.233178	+	0.0259554i
$561$	145.237	+	364.050i	0.258889	+	0.648930i
$562$	24.3661	−	33.5371i	0.0433561	−	0.0596746i
$563$	583.167	+	423.696i	1.03582	+	0.752568i	0.969465	−	0.245228i	$-0.0788627\pi$
$563$	583.167	+	423.696i	1.03582	+	0.752568i	0.0663559	+	0.997796i	$0.478863\pi$
$564$	289.156	−	115.358i	0.512688	−	0.204535i
$565$	−39.5458	+	355.270i	−0.0699925	+	0.628797i
$566$	−45.1971	+	62.2084i	−0.0798535	+	0.109909i
$567$	217.461	+	176.111i	0.383528	+	0.310601i
$568$		−	323.508i		−	0.569556i
$569$	560.605	−	182.152i	0.985246	−	0.320126i	0.228291	−	0.973593i	$-0.426686\pi$
$569$	560.605	−	182.152i	0.985246	−	0.320126i	0.756955	+	0.653467i	$0.226686\pi$
$570$	54.3062	+	43.3554i	0.0952741	+	0.0760621i
$571$	23.9750	−	73.7873i	0.0419877	−	0.129225i	−0.927865	−	0.372915i	$-0.878358\pi$
$571$	23.9750	−	73.7873i	0.0419877	−	0.129225i	0.969853	+	0.243691i	$0.0783582\pi$
$572$	−59.6993	+	183.735i	−0.104369	+	0.321216i
$573$	−1.63903	−	4.10839i	−0.00286044	−	0.00716996i
$574$	−46.3697			−0.0807835
$575$	11.1797	+	120.584i	0.0194429	+	0.209711i
$576$	524.525	+	284.808i	0.910633	+	0.494458i
$577$	618.037	+	850.656i	1.07112	+	1.47427i	0.868935	+	0.494926i	$0.164805\pi$
$577$	618.037	+	850.656i	1.07112	+	1.47427i	0.202187	+	0.979347i	$0.435195\pi$
$578$	9.29123	−	28.5955i	0.0160748	−	0.0494731i
$579$	−358.694	−	226.324i	−0.619507	−	0.390888i
$580$	23.3116	+	2.59485i	0.0401924	+	0.00447388i
$581$	167.033	−	54.2722i	0.287492	−	0.0934117i
$582$	185.183	−	729.127i	0.318183	−	1.25280i
$583$	473.848	−	153.963i	0.812776	−	0.264087i
$584$	−71.1175	+	97.8849i	−0.121777	+	0.167611i
$585$	−235.823	−	679.202i	−0.403116	−	1.16103i
$586$	−370.486	+	269.174i	−0.632228	+	0.459341i
$587$	−229.514	−	166.752i	−0.390994	−	0.284074i	0.374868	−	0.927078i	$-0.377688\pi$
$587$	−229.514	−	166.752i	−0.390994	−	0.284074i	−0.765863	+	0.643004i	$0.777688\pi$
$588$	−108.109	−	129.989i	−0.183858	−	0.221070i
$589$	72.8979	−	52.9634i	0.123766	−	0.0899210i
$590$	−736.259	+	419.077i	−1.24790	+	0.710301i
$591$	−191.486	−	230.241i	−0.324003	−	0.389579i
$592$	455.222	−	147.911i	0.768957	−	0.249849i
$593$	924.858			1.55962			0.779812	−	0.626013i	$-0.215314\pi$
$593$	924.858			1.55962			0.779812	+	0.626013i	$0.215314\pi$
$594$	307.044	+	141.561i	0.516910	+	0.238318i
$595$	−209.721	−	191.177i	−0.352473	−	0.321306i
$596$	328.556	+	106.754i	0.551269	+	0.179118i
$597$	400.847	−	635.289i	0.671435	−	1.06414i
$598$	−71.6331	−	98.5945i	−0.119788	−	0.164874i
$599$			620.049i			1.03514i	0.855641	+	0.517570i	$0.173163\pi$
$599$			620.049i			1.03514i	−0.855641	+	0.517570i	$0.826837\pi$
$600$	460.634	−	461.379i	0.767723	−	0.768965i
$601$	738.329			1.22850			0.614251	−	0.789111i	$-0.289458\pi$
$601$	738.329			1.22850			0.614251	+	0.789111i	$0.289458\pi$
$602$	−338.591	+	246.001i	−0.562443	+	0.408639i
$603$	485.619	+	511.757i	0.805339	+	0.848685i
$604$	32.1563	−	98.9669i	0.0532389	−	0.163852i
$605$	282.839	−	58.3079i	0.467503	−	0.0963766i
$606$	−1.44740	+	0.0948530i	−0.00238846	+	0.000156523i
$607$		−	43.7863i		−	0.0721355i	−0.999349	−	0.0360678i	$-0.988517\pi$
$607$		−	43.7863i		−	0.0721355i	0.999349	−	0.0360678i	$-0.0114832\pi$
$608$	20.7229	+	63.7786i	0.0340838	+	0.104899i
$609$	−20.4465	−	24.5848i	−0.0335739	−	0.0403691i
$610$	−577.126	+	118.976i	−0.946108	+	0.195042i
$611$	640.950	+	882.192i	1.04902	+	1.44385i
$612$	−96.7817	−	202.918i	−0.158140	−	0.331565i
$613$	−99.1056	+	136.407i	−0.161673	+	0.222524i	−0.882166	−	0.470938i	$-0.843916\pi$
$613$	−99.1056	+	136.407i	−0.161673	+	0.222524i	0.720493	+	0.693462i	$0.243916\pi$
$614$	253.432	+	348.820i	0.412756	+	0.568110i
$615$	−79.7728	+	99.9220i	−0.129712	+	0.162475i
$616$	193.211	+	140.376i	0.313653	+	0.227883i
$617$	29.9101	+	92.0539i	0.0484767	+	0.149196i	0.972365	−	0.233467i	$-0.0750071\pi$
$617$	29.9101	+	92.0539i	0.0484767	+	0.149196i	−0.923888	+	0.382663i	$0.875007\pi$
$618$	−25.6991	+	101.186i	−0.0415844	+	0.163732i
$619$	−268.240	−	825.556i	−0.433343	−	1.33369i	−0.894775	−	0.446518i	$-0.852664\pi$
$619$	−268.240	−	825.556i	−0.433343	−	1.33369i	0.461431	−	0.887176i	$-0.347336\pi$
$620$	−115.181	−	202.357i	−0.185776	−	0.326382i
$621$	114.115	−	63.9029i	0.183760	−	0.102903i
$622$	46.8858	+	15.2341i	0.0753790	+	0.0244921i
$623$	−384.833	+	279.597i	−0.617709	+	0.448792i
$624$	−89.7467	+	353.363i	−0.143825	+	0.566287i
$625$	−299.123	−	548.772i	−0.478597	−	0.878035i
$626$		−	30.0775i		−	0.0480471i
$627$	26.0086	+	65.1931i	0.0414810	+	0.103976i
$628$	−214.676	−	69.7525i	−0.341841	−	0.111071i
$629$	−983.237	−	319.473i	−1.56317	−	0.507906i
$630$	−244.747	+	4.90140i	−0.388487	+	0.00778000i
$631$	177.485	+	546.241i	0.281275	+	0.865676i	0.987490	+	0.157679i	$0.0504010\pi$
$631$	177.485	+	546.241i	0.281275	+	0.865676i	−0.706215	+	0.707997i	$0.749599\pi$
$632$	652.025			1.03169
$633$	9.31087	+	142.079i	0.0147091	+	0.224453i
$634$	−425.117	−	308.866i	−0.670532	−	0.487170i
$635$	−278.943	+	616.311i	−0.439280	+	0.970569i
$636$	−265.434	+	105.894i	−0.417349	+	0.166500i
$637$	348.087	−	479.101i	0.546447	−	0.752120i
$638$	−31.2567	−	22.7093i	−0.0489917	−	0.0355946i
$639$	43.7116	+	332.075i	0.0684062	+	0.519679i
$640$	−64.8906	+	13.3773i	−0.101392	+	0.0209021i
$641$	666.711	−	917.650i	1.04011	−	1.43159i	0.143034	−	0.989718i	$-0.454314\pi$
$641$	666.711	−	917.650i	1.04011	−	1.43159i	0.897078	−	0.441873i	$-0.145686\pi$
$642$	−43.0175	−	656.423i	−0.0670054	−	1.02247i
$643$		−	21.4999i		−	0.0334368i	−0.999860	−	0.0167184i	$-0.994678\pi$
$643$		−	21.4999i		−	0.0334368i	0.999860	−	0.0167184i	$-0.00532189\pi$
$644$	24.1992	−	7.86280i	0.0375764	−	0.0122093i
$645$	−52.3932	+	1152.84i	−0.0812298	+	1.78735i
$646$	−23.5190	+	72.3841i	−0.0364072	+	0.112050i
$647$	230.085	−	708.129i	0.355619	−	1.09448i	−0.600031	−	0.799976i	$-0.704845\pi$
$647$	230.085	−	708.129i	0.355619	−	1.09448i	0.955650	−	0.294505i	$-0.0951547\pi$
$648$	−657.341	−	252.360i	−1.01441	−	0.389445i
$649$	−855.703			−1.31849
$650$	540.800	+	321.143i	0.832000	+	0.494066i
$651$	−78.1381	+	307.656i	−0.120028	+	0.472590i
$652$	138.499	+	190.628i	0.212422	+	0.292374i
$653$	−290.386	+	893.717i	−0.444696	+	1.36863i	0.438121	+	0.898916i	$0.355644\pi$
$653$	−290.386	+	893.717i	−0.444696	+	1.36863i	−0.882817	+	0.469717i	$0.844356\pi$
$654$	−254.429	+	403.237i	−0.389036	+	0.616570i
$655$	479.474	+	437.077i	0.732022	+	0.667293i
$656$	61.6624	−	20.0353i	0.0939975	−	0.0305416i
$657$	59.7749	−	110.086i	0.0909816	−	0.167559i
$658$	353.103	−	114.730i	0.536630	−	0.174362i
$659$	695.825	−	957.721i	1.05588	−	1.45329i	0.172283	−	0.985047i	$-0.444886\pi$
$659$	695.825	−	957.721i	1.05588	−	1.45329i	0.883597	−	0.468247i	$-0.155114\pi$
$660$	174.864	−	48.1585i	0.264945	−	0.0729674i
$661$	676.253	−	491.327i	1.02308	−	0.743308i	0.0561650	−	0.998422i	$-0.482113\pi$
$661$	676.253	−	491.327i	1.02308	−	0.743308i	0.966911	+	0.255113i	$0.0821127\pi$
$662$	−123.589	−	89.7925i	−0.186690	−	0.135638i
$663$	605.439	−	503.528i	0.913181	−	0.759469i
$664$	−357.524	+	259.757i	−0.538440	+	0.391200i
$665$	−37.5564	−	34.2355i	−0.0564757	−	0.0514819i
$666$	−804.943	+	383.918i	−1.20862	+	0.576453i
$667$	−14.2138	+	4.61835i	−0.0213101	+	0.00692407i
$668$	80.6334			0.120709
$669$	550.865	−	36.0999i	0.823415	−	0.0539610i
$670$	−613.382	−	68.2766i	−0.915495	−	0.101905i
$671$	−566.064	−	183.925i	−0.843612	−	0.274106i
$672$	−199.792	−	126.062i	−0.297310	−	0.187593i
$673$	−188.307	−	259.183i	−0.279803	−	0.385116i	0.645866	−	0.763451i	$-0.276497\pi$
$673$	−188.307	−	259.183i	−0.279803	−	0.385116i	−0.925669	+	0.378335i	$0.876497\pi$
$674$		−	96.3241i		−	0.142914i
$675$	−410.492	+	535.837i	−0.608136	+	0.793833i
$676$	131.176			0.194048
$677$	−418.668	+	304.180i	−0.618416	+	0.449306i	−0.852368	−	0.522943i	$-0.824834\pi$
$677$	−418.668	+	304.180i	−0.618416	+	0.449306i	0.233952	+	0.972248i	$0.424834\pi$
$678$	−180.220	+	285.625i	−0.265811	+	0.421276i
$679$	−170.005	+	523.221i	−0.250375	+	0.770576i
$680$	650.535	+	294.433i	0.956669	+	0.432989i
$681$	42.4016	+	647.026i	0.0622638	+	0.950111i
$682$			383.531i			0.562362i
$683$	−170.064	−	523.402i	−0.248995	−	0.766328i	−0.994954	−	0.100336i	$-0.968008\pi$
$683$	−170.064	−	523.402i	−0.248995	−	0.766328i	0.745958	−	0.665993i	$-0.231992\pi$
$684$	−17.3314	−	36.3380i	−0.0253383	−	0.0531257i
$685$	−23.4190	+	210.391i	−0.0341884	+	0.307141i
$686$	−275.193	−	378.771i	−0.401157	−	0.552145i
$687$	−201.692	−	242.513i	−0.293583	−	0.353003i
$688$	343.966	−	473.429i	0.499951	−	0.688123i
$689$	−588.368	−	809.819i	−0.853945	−	1.17535i
$690$	−40.2600	+	107.098i	−0.0583479	+	0.155214i
$691$	600.331	+	436.166i	0.868786	+	0.631210i	0.930261	−	0.366899i	$-0.119581\pi$
$691$	600.331	+	436.166i	0.868786	+	0.631210i	−0.0614752	+	0.998109i	$0.519581\pi$
$692$	−14.8563	−	45.7230i	−0.0214686	−	0.0660737i
$693$	−217.294	−	117.987i	−0.313556	−	0.170255i
$694$	−173.225	−	533.131i	−0.249604	−	0.768201i
$695$	772.799	+	349.770i	1.11194	+	0.503266i
$696$	68.0466	+	42.9352i	0.0977681	+	0.0616885i
$697$	−133.185	−	43.2744i	−0.191083	−	0.0620866i
$698$	154.056	−	111.928i	0.220710	−	0.160355i
$699$	−587.640	−	149.248i	−0.840687	−	0.213517i
$700$	−98.6597	+	86.6652i	−0.140942	+	0.123807i
$701$		−	684.914i		−	0.977053i	−0.872549	−	0.488527i	$-0.837535\pi$
$701$		−	684.914i		−	0.977053i	0.872549	−	0.488527i	$-0.162465\pi$
$702$	79.8619	−	674.572i	0.113763	−	0.960929i
$703$	−176.075	−	57.2104i	−0.250463	−	0.0813804i
$704$	−501.581	−	162.974i	−0.712473	−	0.231497i
$705$	360.234	−	958.279i	0.510970	−	1.35926i
$706$	207.400	+	638.311i	0.293767	+	0.904123i
$707$	1.06077			0.00150039
$708$	489.765	−	32.0959i	0.691759	−	0.0453331i
$709$	648.335	+	471.043i	0.914435	+	0.664376i	0.942133	−	0.335240i	$-0.108817\pi$
$709$	648.335	+	471.043i	0.914435	+	0.664376i	−0.0276973	+	0.999616i	$0.508817\pi$
$710$	−216.540	−	197.392i	−0.304986	−	0.278018i
$711$	−669.293	+	88.1000i	−0.941340	+	0.123910i
$712$	703.536	−	968.334i	0.988112	−	1.36002i
$713$	120.026	+	87.2043i	0.168340	+	0.122306i
$714$	−99.3490	−	249.028i	−0.139144	−	0.348778i
$715$	314.267	+	552.123i	0.439535	+	0.772200i
$716$	−73.2967	+	100.884i	−0.102370	+	0.140900i
$717$	−227.943	+	14.9378i	−0.317912	+	0.0208338i
$718$			278.416i			0.387766i
$719$	−803.024	+	260.918i	−1.11686	+	0.362890i	−0.808569	−	0.588401i	$-0.799758\pi$
$719$	−803.024	+	260.918i	−1.11686	+	0.362890i	−0.308293	+	0.951292i	$0.599758\pi$
$720$	323.346	−	112.268i	0.449092	−	0.155927i
$721$	23.5928	−	72.6112i	0.0327223	−	0.100709i
$722$	171.449	−	527.665i	0.237464	−	0.730838i
$723$	−660.968	+	263.692i	−0.914202	+	0.364719i
$724$	−136.310			−0.188274
$725$	57.9495	−	50.9043i	0.0799303	−	0.0702129i
$726$	264.447	+	67.1640i	0.364253	+	0.0925123i
$727$	389.355	+	535.901i	0.535563	+	0.737140i	0.987966	−	0.154674i	$-0.0494328\pi$
$727$	389.355	+	535.901i	0.535563	+	0.737140i	−0.452402	+	0.891814i	$0.649433\pi$
$728$	148.270	−	456.328i	0.203668	−	0.626824i
$729$	708.847	+	170.225i	0.972356	+	0.233505i
$730$	22.1259	+	107.328i	0.0303095	+	0.147025i
$731$	−1202.09	+	390.584i	−1.64445	+	0.534314i
$732$	330.888	+	84.0384i	0.452032	+	0.114807i
$733$	−84.9829	+	27.6126i	−0.115938	+	0.0376707i	−0.366412	−	0.930453i	$-0.619414\pi$
$733$	−84.9829	+	27.6126i	−0.115938	+	0.0376707i	0.250473	+	0.968124i	$0.419414\pi$
$734$	250.751	−	345.128i	0.341622	−	0.470202i
$735$	−555.405	−	25.2415i	−0.755653	−	0.0343422i
$736$	−89.3280	+	64.9006i	−0.121370	+	0.0881802i
$737$	−504.328	−	366.416i	−0.684299	−	0.497172i
$738$	−109.034	+	52.0038i	−0.147743	+	0.0704659i
$739$	−295.965	+	215.031i	−0.400494	+	0.290976i	−0.769742	−	0.638355i	$-0.779615\pi$
$739$	−295.965	+	215.031i	−0.400494	+	0.290976i	0.369248	+	0.929331i	$0.379615\pi$
$740$	−197.262	+	435.842i	−0.266571	+	0.588975i
$741$	108.420	−	90.1705i	0.146316	−	0.121688i
$742$	−324.135	+	105.318i	−0.436840	+	0.141938i
$743$	−1066.14			−1.43491			−0.717454	−	0.696606i	$-0.754692\pi$
$743$	−1066.14			−1.43491			−0.717454	+	0.696606i	$0.754692\pi$
$744$	−52.2304	−	797.007i	−0.0702021	−	1.07125i
$745$	987.308	−	561.974i	1.32525	−	0.754327i
$746$	946.648	+	307.585i	1.26897	+	0.412312i
$747$	331.895	−	314.944i	0.444304	−	0.421611i
$748$	116.764	+	160.712i	0.156101	+	0.214855i
$749$			481.079i			0.642295i
$750$	−27.7622	−	589.841i	−0.0370163	−	0.786455i
$751$	−312.398			−0.415976			−0.207988	−	0.978131i	$-0.566691\pi$
$751$	−312.398			−0.415976			−0.207988	+	0.978131i	$0.566691\pi$
$752$	−419.983	+	305.136i	−0.558488	+	0.405766i
$753$	−837.164	−	528.223i	−1.11177	−	0.701491i
$754$	−23.9864	+	73.8227i	−0.0318122	+	0.0979080i
$755$	−169.276	−	297.394i	−0.224207	−	0.393900i
$756$	128.795	+	59.3800i	0.170364	+	0.0785450i
$757$		−	657.769i		−	0.868915i	−0.900692	−	0.434458i	$-0.856940\pi$
$757$		−	657.769i		−	0.868915i	0.900692	−	0.434458i	$-0.143060\pi$
$758$	12.8065	+	39.4143i	0.0168951	+	0.0519978i
$759$	−88.8536	+	73.8972i	−0.117067	+	0.0973613i
$760$	116.496	+	52.7262i	0.153284	+	0.0693766i
$761$	55.8262	+	76.8382i	0.0733590	+	0.100970i	0.844120	−	0.536155i	$-0.180124\pi$
$761$	55.8262	+	76.8382i	0.0733590	+	0.100970i	−0.770761	+	0.637125i	$0.780124\pi$
$762$	−491.408	+	408.691i	−0.644892	+	0.536340i
$763$	204.952	−	282.093i	0.268614	−	0.369715i
$764$	−1.31771	−	1.81367i	−0.00172475	−	0.00237391i
$765$	−707.546	−	214.331i	−0.924896	−	0.280172i
$766$	32.9895	+	23.9683i	0.0430672	+	0.0312902i
$767$	531.255	+	1635.04i	0.692640	+	2.13173i
$768$	710.654	+	180.491i	0.925330	+	0.235014i
$769$	−174.903	−	538.297i	−0.227443	−	0.699997i	−0.998034	−	0.0626676i	$-0.980039\pi$
$769$	−174.903	−	538.297i	−0.227443	−	0.699997i	0.770592	−	0.637329i	$-0.219961\pi$
$770$	211.850	−	43.6733i	0.275130	−	0.0567186i
$771$	−182.386	+	289.058i	−0.236558	+	0.374914i
$772$	−204.438	−	66.4258i	−0.264816	−	0.0860438i
$773$	1165.39	−	846.708i	1.50762	−	1.09535i	0.540406	−	0.841404i	$-0.318271\pi$
$773$	1165.39	−	846.708i	1.50762	−	1.09535i	0.967218	−	0.253949i	$-0.0817294\pi$
$774$	−520.274	+	958.178i	−0.672188	+	1.23796i
$775$	−746.944	−	168.374i	−0.963799	−	0.217256i
$776$		−	1384.31i		−	1.78390i
$777$	605.763	−	241.668i	0.779618	−	0.311027i
$778$	−236.219	−	76.7521i	−0.303623	−	0.0986531i
$779$	−23.8504	−	7.74946i	−0.0306167	−	0.00994796i
$780$	−200.581	−	304.222i	−0.257156	−	0.390028i
$781$	−91.4558	−	281.472i	−0.117101	−	0.360400i
$782$	−125.314			−0.160248
$783$	−75.6499	−	34.8779i	−0.0966155	−	0.0445439i
$784$	228.084	+	165.713i	0.290924	+	0.211369i
$785$	−645.100	+	367.190i	−0.821783	+	0.467757i
$786$	227.136	+	569.338i	0.288977	+	0.724348i
$787$	197.252	−	271.494i	0.250638	−	0.344973i	−0.665097	−	0.746757i	$-0.731610\pi$
$787$	197.252	−	271.494i	0.250638	−	0.344973i	0.915735	+	0.401784i	$0.131610\pi$
$788$	−122.789	−	89.2111i	−0.155823	−	0.113212i
$789$	655.193	−	261.388i	0.830409	−	0.331290i
$790$	397.842	−	436.433i	0.503597	−	0.552447i
$791$	145.174	−	199.815i	0.183532	−	0.252611i
$792$	611.748	+	113.394i	0.772409	+	0.143174i
$793$			1195.79i			1.50794i
$794$	−736.952	+	239.450i	−0.928151	+	0.301575i
$795$	−330.681	+	879.664i	−0.415951	+	1.10650i
$796$	117.648	−	362.083i	0.147799	−	0.454878i
$797$	−209.068	+	643.446i	−0.262319	+	0.807335i	0.729980	+	0.683469i	$0.239529\pi$
$797$	−209.068	+	643.446i	−0.262319	+	0.807335i	−0.992299	+	0.123866i	$0.960471\pi$
$798$	−17.7912	−	44.5952i	−0.0222947	−	0.0558837i
$799$	1121.27			1.40334
$800$	290.960	−	489.973i	0.363700	−	0.612466i
$801$	−591.328	+	1089.04i	−0.738237	+	1.35960i
$802$	546.541	+	752.250i	0.681473	+	0.937967i
$803$	−34.2046	+	105.271i	−0.0425960	+	0.131097i
$804$	302.398	+	190.803i	0.376117	+	0.237317i
$805$	34.5013	−	76.2289i	0.0428587	−	0.0946943i
$806$	732.831	−	238.111i	0.909220	−	0.295424i
$807$	123.310	−	485.515i	0.152801	−	0.601630i
$808$	−2.53853	+	0.824818i	−0.00314174	+	0.00102081i
$809$	−519.696	+	715.300i	−0.642393	+	0.884178i	−0.998740	−	0.0501756i	$-0.984022\pi$
$809$	−519.696	+	715.300i	−0.642393	+	0.884178i	0.356348	+	0.934353i	$0.384022\pi$
$810$	−570.002	+	286.010i	−0.703707	+	0.353098i
$811$	319.492	−	232.125i	0.393949	−	0.286220i	−0.373123	−	0.927782i	$-0.621713\pi$
$811$	319.492	−	232.125i	0.393949	−	0.286220i	0.767072	+	0.641561i	$0.221713\pi$
$812$	−13.1111	−	9.52580i	−0.0161467	−	0.0117313i
$813$	−1021.46	−	1228.20i	−1.25641	−	1.51070i
$814$	637.519	−	463.184i	0.783192	−	0.569023i
$815$	770.096	+	85.7208i	0.944903	+	0.105179i
$816$	239.713	+	288.230i	0.293766	+	0.353223i
$817$	−215.268	+	69.9447i	−0.263485	+	0.0856116i
$818$	1173.19			1.43422
$819$	−90.5386	+	488.447i	−0.110548	+	0.596394i
$820$	−26.7203	+	59.0372i	−0.0325857	+	0.0719966i
$821$	−942.860	−	306.354i	−1.14843	−	0.373147i	−0.327878	−	0.944720i	$-0.606333\pi$
$821$	−942.860	−	306.354i	−1.14843	−	0.373147i	−0.820551	+	0.571573i	$0.806333\pi$
$822$	−106.726	+	169.147i	−0.129838	+	0.205775i
$823$	−303.986	−	418.401i	−0.369364	−	0.508385i	0.583364	−	0.812211i	$-0.301736\pi$
$823$	−303.986	−	418.401i	−0.369364	−	0.508385i	−0.952728	+	0.303825i	$0.901736\pi$
$824$			192.110i			0.233143i
$825$	270.348	−	531.650i	0.327695	−	0.644424i
$826$	585.342			0.708647
$827$	−866.409	+	629.483i	−1.04765	+	0.761164i	−0.971765	−	0.235952i	$-0.924179\pi$
$827$	−866.409	+	629.483i	−1.04765	+	0.761164i	−0.0758880	+	0.997116i	$0.524179\pi$
$828$	48.0840	−	45.6281i	0.0580724	−	0.0551064i
$829$	−35.7199	+	109.935i	−0.0430880	+	0.132611i	−0.970286	−	0.241960i	$-0.922210\pi$
$829$	−35.7199	+	109.935i	−0.0430880	+	0.132611i	0.927198	+	0.374571i	$0.122210\pi$
$830$	−44.2801	+	397.803i	−0.0533495	+	0.479280i
$831$	59.2426	−	3.88236i	0.0712908	−	0.00467191i
$832$			1059.58i			1.27353i
$833$	−188.172	−	579.133i	−0.225897	−	0.695238i
$834$	512.463	+	616.182i	0.614463	+	0.738827i
$835$	178.631	−	195.959i	0.213930	−	0.234681i
$836$	20.9098	+	28.7798i	0.0250117	+	0.0344256i
$837$	161.303	+	811.057i	0.192716	+	0.969004i
$838$	182.687	−	251.448i	0.218004	−	0.300057i
$839$	304.872	+	419.620i	0.363375	+	0.500143i	0.951085	−	0.308929i	$-0.0999705\pi$
$839$	304.872	+	419.620i	0.363375	+	0.500143i	−0.587710	+	0.809072i	$0.699970\pi$
$840$	−434.294	+	119.607i	−0.517017	+	0.142389i
$841$	−672.682	−	488.732i	−0.799860	−	0.581132i
$842$	−75.4349	−	232.165i	−0.0895902	−	0.275730i
$843$	−19.4414	+	76.5475i	−0.0230622	+	0.0908037i
$844$	22.2997	+	68.6316i	0.0264215	+	0.0813170i
$845$	290.602	−	318.790i	0.343907	−	0.377267i
$846$	701.618	−	665.783i	0.829335	−	0.786978i
$847$	−189.767	−	61.6591i	−0.224046	−	0.0727971i
$848$	385.529	−	280.103i	0.454633	−	0.330310i
$849$	36.0621	−	141.989i	0.0424760	−	0.167243i
$850$	594.011	−	255.783i	0.698836	−	0.300922i
$851$		−	304.827i		−	0.358199i
$852$	62.9026	+	157.671i	0.0738294	+	0.185060i
$853$	−748.148	−	243.088i	−0.877079	−	0.284980i	−0.164335	−	0.986405i	$-0.552548\pi$
$853$	−748.148	−	243.088i	−0.877079	−	0.284980i	−0.712744	+	0.701424i	$0.752548\pi$
$854$	387.215	+	125.814i	0.453413	+	0.147323i
$855$	−126.705	−	38.3819i	−0.148193	−	0.0448911i
$856$	−374.069	−	1151.27i	−0.436997	−	1.34494i
$857$	977.865			1.14103			0.570517	−	0.821286i	$-0.306743\pi$
$857$	977.865			1.14103			0.570517	+	0.821286i	$0.306743\pi$
$858$	39.2504	+	598.939i	0.0457463	+	0.698064i
$859$	268.364	+	194.978i	0.312414	+	0.226982i	0.732932	−	0.680302i	$-0.238151\pi$
$859$	268.364	+	194.978i	0.312414	+	0.226982i	−0.420518	+	0.907284i	$0.638151\pi$
$860$	118.093	+	572.845i	0.137318	+	0.666099i
$861$	82.0540	−	32.7353i	0.0953008	−	0.0380200i
$862$	−212.747	+	292.822i	−0.246807	+	0.339700i
$863$	353.404	+	256.763i	0.409507	+	0.297524i	0.773402	−	0.633916i	$-0.218553\pi$
$863$	353.404	+	256.763i	0.409507	+	0.297524i	−0.363895	+	0.931440i	$0.618553\pi$
$864$	−611.172	−	72.3560i	−0.707375	−	0.0837454i
$865$	−144.030	−	65.1881i	−0.166509	−	0.0753620i
$866$	−512.104	+	704.851i	−0.591344	+	0.813916i
$867$	3.74592	+	57.1607i	0.00432055	+	0.0659292i
$868$			160.878i			0.185344i
$869$	567.303	−	184.328i	0.652823	−	0.212115i
$870$	70.2581	−	19.3495i	0.0807565	−	0.0222408i
$871$	−387.022	+	1191.13i	−0.444342	+	1.36754i
$872$	−271.125	+	834.438i	−0.310923	+	0.956924i
$873$	187.044	+	1420.97i	0.214254	+	1.62768i
$874$	−22.4408			−0.0256760
$875$	−7.94833	+	431.761i	−0.00908381	+	0.493442i
$876$	15.6286	−	61.5352i	0.0178409	−	0.0702457i
$877$	−909.561	−	1251.90i	−1.03713	−	1.42748i	−0.899459	−	0.437005i	$-0.856039\pi$
$877$	−909.561	−	1251.90i	−1.03713	−	1.42748i	−0.137668	−	0.990478i	$-0.543961\pi$
$878$	25.7692	−	79.3094i	0.0293499	−	0.0903297i
$879$	465.571	−	737.868i	0.529659	−	0.839440i
$880$	−262.848	+	149.612i	−0.298691	+	0.170014i
$881$	−265.263	+	86.1891i	−0.301093	+	0.0978310i	−0.455667	−	0.890150i	$-0.650599\pi$
$881$	−265.263	+	86.1891i	−0.301093	+	0.0978310i	0.154574	+	0.987981i	$0.450599\pi$
$882$	−461.622	−	250.653i	−0.523381	−	0.284187i
$883$	866.868	−	281.662i	0.981730	−	0.318983i	0.226188	−	0.974084i	$-0.427374\pi$
$883$	866.868	−	281.662i	0.981730	−	0.318983i	0.755542	+	0.655100i	$0.227374\pi$
$884$	234.588	−	322.883i	0.265371	−	0.365252i
$885$	1007.00	−	1261.35i	1.13786	−	1.42526i
$886$	−331.841	+	241.096i	−0.374538	+	0.272118i
$887$	725.289	+	526.953i	0.817687	+	0.594085i	0.916049	−	0.401066i	$-0.131360\pi$
$887$	725.289	+	526.953i	0.817687	+	0.594085i	−0.0983617	+	0.995151i	$0.531360\pi$
$888$	−1261.74	+	1049.35i	−1.42087	+	1.18170i
$889$	378.147	−	274.740i	0.425363	−	0.309044i
$890$	−218.882	−	1061.75i	−0.245935	−	1.19298i
$891$	−643.270	−	33.7389i	−0.721964	−	0.0378663i
$892$	266.097	−	86.4601i	0.298315	−	0.0969283i
$893$	200.794			0.224853
$894$	1071.02	−	70.1876i	1.19801	−	0.0785096i
$895$	82.7954	+	401.623i	0.0925089	+	0.448741i
$896$	43.5375	+	14.1462i	0.0485909	+	0.0157882i
$897$	196.363	+	123.899i	0.218911	+	0.138126i
$898$	701.016	+	964.865i	0.780641	+	1.07446i
$899$		−	94.4947i		−	0.105111i
$900$	−134.794	+	314.432i	−0.149771	+	0.349369i
$901$	−1029.28			−1.14238
$902$	86.3554	−	62.7409i	0.0957377	−	0.0695575i
$903$	425.490	−	674.345i	0.471196	−	0.746783i
$904$	−192.046	+	591.058i	−0.212441	+	0.653825i
$905$	−301.976	+	331.268i	−0.333675	+	0.366042i
$906$	−21.1417	−	322.611i	−0.0233353	−	0.356083i
$907$		−	324.877i		−	0.358189i	−0.983832	−	0.179094i	$-0.942683\pi$
$907$		−	324.877i		−	0.358189i	0.983832	−	0.179094i	$-0.0573168\pi$
$908$	101.553	+	312.548i	0.111842	+	0.344215i
$909$	2.49431	−	1.18966i	0.00274401	−	0.00130876i
$910$	−214.974	−	377.679i	−0.236235	−	0.415032i
$911$	−140.444	−	193.304i	−0.154164	−	0.212189i	0.724948	−	0.688804i	$-0.241864\pi$
$911$	−140.444	−	193.304i	−0.154164	−	0.212189i	−0.879112	+	0.476615i	$0.841864\pi$
$912$	42.9272	+	51.6155i	0.0470693	+	0.0565959i
$913$	−237.635	+	327.077i	−0.260280	+	0.358244i
$914$	−26.6664	−	36.7031i	−0.0291755	−	0.0401566i
$915$	937.267	−	617.964i	1.02434	−	0.675370i
$916$	−129.333	−	93.9661i	−0.141193	−	0.102583i
$917$	−138.524	−	426.334i	−0.151062	−	0.464922i
$918$	−512.895	−	474.145i	−0.558709	−	0.516497i
$919$	414.828	+	1276.71i	0.451391	+	1.38924i	0.875320	+	0.483544i	$0.160651\pi$
$919$	414.828	+	1276.71i	0.451391	+	1.38924i	−0.423929	+	0.905695i	$0.639349\pi$
$920$	−23.2920	+	209.250i	−0.0253173	+	0.227445i
$921$	−694.717	−	438.344i	−0.754307	−	0.475943i
$922$	19.0311	+	6.18359i	0.0206411	+	0.00670671i
$923$	−481.044	+	349.499i	−0.521174	+	0.378655i
$924$	−121.462	−	30.8486i	−0.131452	−	0.0333860i
$925$	622.197	+	1444.94i	0.672645	+	1.56210i
$926$			737.130i			0.796037i
$927$	−25.9575	−	197.198i	−0.0280016	−	0.212727i
$928$	66.8844	+	21.7321i	0.0720737	+	0.0234182i
$929$	−498.160	−	161.862i	−0.536232	−	0.174232i	0.0283670	−	0.999598i	$-0.490969\pi$
$929$	−498.160	−	161.862i	−0.536232	−	0.174232i	−0.564599	+	0.825365i	$0.690969\pi$
$930$	−565.345	−	451.344i	−0.607898	−	0.485316i
$931$	−33.6973	−	103.710i	−0.0361948	−	0.111396i
$932$	−307.286			−0.329706
$933$	−93.7219	+	6.14189i	−0.100452	+	0.00658295i
$934$	−451.361	−	327.933i	−0.483256	−	0.351106i
$935$	649.242	+	72.2683i	0.694377	+	0.0772923i
$936$	−163.131	−	1239.30i	−0.174285	−	1.32404i
$937$	−845.258	+	1163.40i	−0.902089	+	1.24162i	0.0677073	+	0.997705i	$0.478432\pi$
$937$	−845.258	+	1163.40i	−0.902089	+	1.24162i	−0.969797	+	0.243914i	$0.921568\pi$
$938$	344.985	+	250.646i	0.367788	+	0.267213i
$939$	21.2336	+	53.2240i	0.0226130	+	0.0566815i
$940$	57.4010	−	515.678i	0.0610649	−	0.548593i
$941$	660.110	−	908.564i	0.701498	−	0.965530i	−0.298440	−	0.954428i	$-0.596466\pi$
$941$	660.110	−	908.564i	0.701498	−	0.965530i	0.999938	−	0.0111014i	$-0.00353375\pi$
$942$	−699.800	+	45.8601i	−0.742887	+	0.0486837i
$943$		−	41.2906i		−	0.0437864i
$944$	−778.387	+	252.913i	−0.824563	+	0.267917i
$945$	429.634	−	181.455i	0.454639	−	0.192016i
$946$	297.713	−	916.265i	0.314707	−	0.968568i
$947$	134.922	−	415.247i	0.142473	−	0.438487i	−0.854204	−	0.519938i	$-0.825955\pi$
$947$	134.922	−	415.247i	0.142473	−	0.438487i	0.996677	+	0.0814503i	$0.0259552\pi$
$948$	−317.784	+	126.779i	−0.335216	+	0.133733i
$949$	222.382			0.234333
$950$	106.374	−	45.8050i	0.111972	−	0.0482158i
$951$	970.318	+	246.440i	1.02031	+	0.259138i
$952$	−289.997	−	399.146i	−0.304618	−	0.419271i
$953$	48.3303	−	148.745i	0.0507138	−	0.156081i	−0.922492	−	0.386015i	$-0.873851\pi$
$953$	48.3303	−	148.745i	0.0507138	−	0.156081i	0.973206	+	0.229934i	$0.0738511\pi$
$954$	−644.059	+	611.164i	−0.675114	+	0.640633i
$955$	−7.32686	−	0.815565i	−0.00767210	−	0.000853995i
$956$	−110.108	+	35.7764i	−0.115176	+	0.0374230i
$957$	71.3426	+	18.1195i	0.0745481	+	0.0189336i
$958$	−1332.13	+	432.836i	−1.39053	+	0.451812i
$959$	85.9722	−	118.331i	0.0896477	−	0.123390i
$960$	830.499	−	547.569i	0.865103	−	0.570384i
$961$	18.5744	−	13.4951i	0.0193282	−	0.0140427i
$962$	−1280.83	−	930.575i	−1.33142	−	0.967334i
$963$	539.532	+	1131.21i	0.560261	+	1.17467i
$964$	−291.788	+	211.996i	−0.302685	+	0.219913i
$965$	−614.333	+	349.677i	−0.636614	+	0.362360i
$966$	60.7802	−	50.5493i	0.0629194	−	0.0523284i
$967$	−405.235	+	131.669i	−0.419064	+	0.136162i	−0.510956	−	0.859607i	$-0.670709\pi$
$967$	−405.235	+	131.669i	−0.419064	+	0.136162i	0.0918918	+	0.995769i	$0.470709\pi$
$968$	502.075			0.518672
$969$	−9.48210	−	144.692i	−0.00978544	−	0.149321i
$970$	−926.585	−	844.653i	−0.955242	−	0.870776i
$971$	871.013	+	283.009i	0.897026	+	0.291462i	0.721009	−	0.692926i	$-0.243679\pi$
$971$	871.013	+	283.009i	0.897026	+	0.291462i	0.176017	+	0.984387i	$0.443679\pi$
$972$	369.444	−	4.81732i	0.380086	−	0.00495609i
$973$	−344.500	−	474.163i	−0.354059	−	0.487321i
$974$		−	985.504i		−	1.01181i
$975$	−1183.69	−	186.498i	−1.21404	−	0.191280i
$976$	−569.279			−0.583278
$977$	565.618	−	410.945i	0.578933	−	0.420620i	−0.259406	−	0.965768i	$-0.583527\pi$
$977$	565.618	−	410.945i	0.578933	−	0.420620i	0.838339	+	0.545149i	$0.183527\pi$
$978$	619.131	+	390.651i	0.633058	+	0.399439i
$979$	338.372	−	1041.40i	0.345630	−	1.06374i
$980$	−275.980	+	56.8938i	−0.281612	+	0.0580549i
$981$	165.558	−	893.169i	0.168765	−	0.910468i
$982$		−	233.667i		−	0.237950i
$983$	−106.423	−	327.536i	−0.108263	−	0.333201i	0.882219	−	0.470839i	$-0.156049\pi$
$983$	−106.423	−	327.536i	−0.108263	−	0.333201i	−0.990483	+	0.137639i	$0.956049\pi$
$984$	−170.909	+	142.141i	−0.173688	+	0.144452i
$985$	−488.825	+	100.772i	−0.496269	+	0.102307i
$986$	46.9143	+	64.5720i	0.0475804	+	0.0654889i
$987$	−543.842	+	452.299i	−0.551005	+	0.458256i
$988$	42.0095	−	57.8211i	0.0425197	−	0.0585233i
$989$	−219.055	−	301.503i	−0.221491	−	0.304856i
$990$	449.166	−	340.285i	0.453703	−	0.343722i
$991$	187.691	+	136.365i	0.189395	+	0.137604i	0.678442	−	0.734654i	$-0.262655\pi$
$991$	187.691	+	136.365i	0.189395	+	0.137604i	−0.489047	+	0.872257i	$0.662655\pi$
$992$	−215.732	−	663.956i	−0.217472	−	0.669310i
$993$	282.088	+	71.6443i	0.284076	+	0.0721493i
$994$	62.5602	+	192.541i	0.0629378	+	0.193703i
$995$	−619.318	−	1088.05i	−0.622431	−	1.09352i
$996$	123.744	−	196.117i	0.124240	−	0.196905i
$997$	−903.277	−	293.493i	−0.905995	−	0.294376i	−0.181286	−	0.983430i	$-0.558026\pi$
$997$	−903.277	−	293.493i	−0.905995	−	0.294376i	−0.724709	+	0.689055i	$0.758026\pi$
$998$	−206.876	+	150.304i	−0.207290	+	0.150605i
$999$	1153.36	−	1247.63i	1.15452	−	1.24887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.14.13	yes	72
3.2	odd	2	inner	75.3.h.a.14.6	✓	72
5.2	odd	4		375.3.j.b.176.25		144
5.3	odd	4		375.3.j.b.176.12		144
5.4	even	2		375.3.h.a.74.6		72
15.2	even	4		375.3.j.b.176.11		144
15.8	even	4		375.3.j.b.176.26		144
15.14	odd	2		375.3.h.a.74.13		72
25.9	even	10	inner	75.3.h.a.59.6	yes	72
25.12	odd	20		375.3.j.b.326.11		144
25.13	odd	20		375.3.j.b.326.26		144
25.16	even	5		375.3.h.a.299.13		72
75.38	even	20		375.3.j.b.326.12		144
75.41	odd	10		375.3.h.a.299.6		72
75.59	odd	10	inner	75.3.h.a.59.13	yes	72
75.62	even	20		375.3.j.b.326.25		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.6	✓	72	3.2	odd	2	inner
75.3.h.a.14.13	yes	72	1.1	even	1	trivial
75.3.h.a.59.6	yes	72	25.9	even	10	inner
75.3.h.a.59.13	yes	72	75.59	odd	10	inner
375.3.h.a.74.6		72	5.4	even	2
375.3.h.a.74.13		72	15.14	odd	2
375.3.h.a.299.6		72	75.41	odd	10
375.3.h.a.299.13		72	25.16	even	5
375.3.j.b.176.11		144	15.2	even	4
375.3.j.b.176.12		144	5.3	odd	4
375.3.j.b.176.25		144	5.2	odd	4
375.3.j.b.176.26		144	15.8	even	4
375.3.j.b.326.11		144	25.12	odd	20
375.3.j.b.326.12		144	75.38	even	20
375.3.j.b.326.25		144	75.62	even	20
375.3.j.b.326.26		144	25.13	odd	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27392 - 0.925557i) q^{2} +(-1.60087 + 2.53717i) q^{3} +(-0.469852 + 1.44606i) q^{4} +(2.47338 + 4.34538i) q^{5} +(0.308913 + 4.71384i) q^{6} -3.45468i q^{7} +(2.68623 + 8.26736i) q^{8} +(-3.87443 - 8.12335i) q^{9} +(7.17279 + 3.24641i) q^{10} +(4.67438 + 6.43373i) q^{11} +(-2.91672 - 3.50704i) q^{12} +(9.39120 - 12.9259i) q^{13} +(-3.19750 - 4.40098i) q^{14} +(-14.9845 - 0.681003i) q^{15} +(6.15359 + 4.47085i) q^{16} +(-5.07678 - 15.6247i) q^{17} +(-12.4543 - 6.76248i) q^{18} +(-0.909136 - 2.79803i) q^{19} +(-7.44580 + 1.53497i) q^{20} +(8.76509 + 5.53049i) q^{21} +(11.9096 + 3.86965i) q^{22} +(3.91892 - 2.84726i) q^{23} +(-25.2760 - 6.41956i) q^{24} +(-12.7647 + 21.4956i) q^{25} -25.1586i q^{26} +(26.8128 + 3.17434i) q^{27} +(4.99566 + 1.62319i) q^{28} +(-2.93429 - 0.953408i) q^{29} +(-19.7194 + 13.0015i) q^{30} +(9.46440 + 29.1284i) q^{31} -22.7941 q^{32} +(-23.8065 + 1.56012i) q^{33} +(-20.9290 - 15.2058i) q^{34} +(15.0119 - 8.54475i) q^{35} +(13.5672 - 1.78588i) q^{36} +(36.9883 - 50.9101i) q^{37} +(-3.74791 - 2.72301i) q^{38} +(17.7610 + 44.5197i) q^{39} +(-29.2808 + 32.1211i) q^{40} +(5.01027 - 6.89605i) q^{41} +(16.2848 - 1.06719i) q^{42} -76.9353i q^{43} +(-11.4998 + 3.73651i) q^{44} +(25.7161 - 36.9281i) q^{45} +(2.35708 - 7.25436i) q^{46} +(-21.0904 + 64.9097i) q^{47} +(-21.1944 + 8.45545i) q^{48} +37.0652 q^{49} +(3.63417 + 39.1982i) q^{50} +(47.7698 + 12.1325i) q^{51} +(14.2791 + 19.6535i) q^{52} +(19.3602 - 59.5846i) q^{53} +(37.0953 - 20.7729i) q^{54} +(-16.3955 + 36.2250i) q^{55} +(28.5611 - 9.28005i) q^{56} +(8.55449 + 2.17266i) q^{57} +(-4.62048 + 1.50128i) q^{58} +(-63.2466 + 87.0514i) q^{59} +(8.02529 - 21.3485i) q^{60} +(-60.5497 + 43.9919i) q^{61} +(39.0169 + 28.3474i) q^{62} +(-28.0635 + 13.3849i) q^{63} +(-53.6522 + 38.9806i) q^{64} +(79.3960 + 8.83771i) q^{65} +(-28.8836 + 24.0217i) q^{66} +(-74.5516 + 24.2233i) q^{67} +24.9796 q^{68} +(0.950298 + 14.5010i) q^{69} +(11.2153 - 24.7797i) q^{70} +(-35.3941 - 11.5002i) q^{71} +(56.7510 - 53.8525i) q^{72} +(8.18118 + 11.2604i) q^{73} -99.0901i q^{74} +(-34.1033 - 66.7979i) q^{75} +4.47328 q^{76} +(22.2264 - 16.1485i) q^{77} +(63.8316 + 40.2757i) q^{78} +(23.1785 - 71.3362i) q^{79} +(-4.20735 + 37.7979i) q^{80} +(-50.9775 + 62.9467i) q^{81} -13.4223i q^{82} +(15.7098 + 48.3497i) q^{83} +(-12.1157 + 10.0763i) q^{84} +(55.3386 - 60.7065i) q^{85} +(-71.2080 - 98.0094i) q^{86} +(7.11637 - 5.91850i) q^{87} +(-40.6335 + 55.9272i) q^{88} +(-80.9329 - 111.395i) q^{89} +(-1.41877 - 70.8451i) q^{90} +(-44.6548 - 32.4436i) q^{91} +(2.27599 + 7.00477i) q^{92} +(-89.0550 - 22.6181i) q^{93} +(33.2101 + 102.210i) q^{94} +(9.90989 - 10.8712i) q^{95} +(36.4903 - 57.8324i) q^{96} +(-151.453 - 49.2101i) q^{97} +(47.2181 - 34.3059i) q^{98} +(34.1528 - 62.8986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) \) 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

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