LMFDB - Embedded newform 75.3.h.a.14.6

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			14.6
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.6

$q$-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} +(0.196179 - 2.99358i) q^{3} +(-0.469852 + 1.44606i) q^{4} +(-2.47338 - 4.34538i) q^{5} +(2.52081 + 3.99515i) q^{6} -3.45468i q^{7} +(-2.68623 - 8.26736i) q^{8} +(-8.92303 - 1.17455i) q^{9} +(7.17279 + 3.24641i) q^{10} +(-4.67438 - 6.43373i) q^{11} +(4.23671 + 1.69023i) q^{12} +(9.39120 - 12.9259i) q^{13} +(3.19750 + 4.40098i) q^{14} +(-13.4935 + 6.55180i) 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} +(-10.3418 - 0.677734i) 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} +(-5.26662 + 26.4814i) q^{27} +(4.99566 + 1.62319i) q^{28} +(2.93429 + 0.953408i) q^{29} +(11.1255 - 20.8354i) q^{30} +(9.46440 + 29.1284i) q^{31} +22.7941 q^{32} +(-20.1769 + 12.7310i) q^{33} +(-20.9290 - 15.2058i) q^{34} +(-15.0119 + 8.54475i) q^{35} +(5.89098 - 12.3513i) q^{36} +(36.9883 - 50.9101i) q^{37} +(3.74791 + 2.72301i) q^{38} +(-36.8523 - 30.6491i) q^{39} +(-29.2808 + 32.1211i) q^{40} +(-5.01027 + 6.89605i) q^{41} +(13.8020 - 8.70859i) q^{42} -76.9353i q^{43} +(11.4998 - 3.73651i) q^{44} +(16.9662 + 41.6791i) q^{45} +(2.35708 - 7.25436i) q^{46} +(21.0904 - 64.9097i) q^{47} +(14.5910 - 17.5442i) 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} +(-17.8007 - 38.6097i) 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} +(-3.13433 - 22.5907i) q^{60} +(-60.5497 + 43.9919i) q^{61} +(-39.0169 - 28.3474i) q^{62} +(-4.05770 + 30.8262i) q^{63} +(-53.6522 + 38.9806i) q^{64} +(-79.3960 - 8.83771i) q^{65} +(13.9205 - 34.8931i) q^{66} +(-74.5516 + 24.2233i) q^{67} -24.9796 q^{68} +(7.75469 + 12.2902i) q^{69} +(11.2153 - 24.7797i) q^{70} +(35.3941 + 11.5002i) q^{71} +(14.2588 + 76.9250i) q^{72} +(8.18118 + 11.2604i) q^{73} +99.0901i q^{74} +(61.8447 + 42.4292i) q^{75} +4.47328 q^{76} +(-22.2264 + 16.1485i) q^{77} +(75.3143 + 4.93559i) q^{78} +(23.1785 - 71.3362i) q^{79} +(4.20735 - 37.7979i) q^{80} +(78.2409 + 20.9611i) q^{81} -13.4223i q^{82} +(-15.7098 - 48.3497i) q^{83} +(5.83918 - 14.6365i) q^{84} +(55.3386 - 60.7065i) q^{85} +(71.2080 + 98.0094i) q^{86} +(3.42975 - 8.59698i) q^{87} +(-40.6335 + 55.9272i) q^{88} +(80.9329 + 111.395i) q^{89} +(-60.1899 - 37.3926i) 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} +(4.47171 - 68.2359i) 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	−0.858804	−	0.512304i	$-0.828792\pi$
$2$	−1.27392	+	0.925557i	−0.636960	+	0.462778i	0.221845	+	0.975082i	$0.428792\pi$
$3$	0.196179	−	2.99358i	0.0653929	−	0.997860i
$3$	0.196179	−	2.99358i	0.0653929	−	0.997860i
$4$	−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
$6$	2.52081	+	3.99515i	0.420135	+	0.665859i
$7$		−	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
$9$	−8.92303	−	1.17455i	−0.991448	−	0.130506i
$10$	7.17279	+	3.24641i	0.717279	+	0.324641i
$11$	−4.67438	−	6.43373i	−0.424943	−	0.584884i	0.541840	−	0.840482i	$-0.317728\pi$
$11$	−4.67438	−	6.43373i	−0.424943	−	0.584884i	−0.966783	+	0.255597i	$0.917728\pi$
$12$	4.23671	+	1.69023i	0.353059	+	0.140852i
$13$	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
$15$	−13.4935	+	6.55180i	−0.899565	+	0.436787i
$16$	6.15359	+	4.47085i	0.384600	+	0.279428i
$17$	5.07678	+	15.6247i	0.298634	+	0.919101i	0.981976	+	0.189003i	$0.0605256\pi$
$17$	5.07678	+	15.6247i	0.298634	+	0.919101i	−0.683342	+	0.730098i	$0.739474\pi$
$18$	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
$21$	−10.3418	−	0.677734i	−0.492469	−	0.0322730i
$22$	11.9096	+	3.86965i	0.541343	+	0.175893i
$23$	−3.91892	+	2.84726i	−0.170388	+	0.123794i	−0.669711	−	0.742622i	$-0.733582\pi$
$23$	−3.91892	+	2.84726i	−0.170388	+	0.123794i	0.499323	+	0.866416i	$0.333582\pi$
$24$	−25.2760	+	6.41956i	−1.05317	+	0.267482i
$25$	−12.7647	+	21.4956i	−0.510589	+	0.859825i
$26$			25.1586i			0.967639i
$27$	−5.26662	+	26.4814i	−0.195060	+	0.980791i
$28$	4.99566	+	1.62319i	0.178416	+	0.0579710i
$29$	2.93429	+	0.953408i	0.101182	+	0.0328761i	0.359171	−	0.933272i	$-0.383060\pi$
$29$	2.93429	+	0.953408i	0.101182	+	0.0328761i	−0.257988	+	0.966148i	$0.583060\pi$
$30$	11.1255	−	20.8354i	0.370851	−	0.694515i
$31$	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
$33$	−20.1769	+	12.7310i	−0.611421	+	0.385786i
$34$	−20.9290	−	15.2058i	−0.615558	−	0.447229i
$35$	−15.0119	+	8.54475i	−0.428911	+	0.244136i
$36$	5.89098	−	12.3513i	0.163638	−	0.343093i
$37$	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
$39$	−36.8523	−	30.6491i	−0.944931	−	0.785874i
$40$	−29.2808	+	32.1211i	−0.732020	+	0.803027i
$41$	−5.01027	+	6.89605i	−0.122202	+	0.168196i	−0.865735	−	0.500503i	$-0.833149\pi$
$41$	−5.01027	+	6.89605i	−0.122202	+	0.168196i	0.743533	+	0.668699i	$0.233149\pi$
$42$	13.8020	−	8.70859i	0.328618	−	0.207347i
$43$		−	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
$45$	16.9662	+	41.6791i	0.377027	+	0.926202i
$46$	2.35708	−	7.25436i	0.0512409	−	0.157703i
$47$	21.0904	−	64.9097i	0.448733	−	1.38106i	−0.429605	−	0.903017i	$-0.641347\pi$
$47$	21.0904	−	64.9097i	0.448733	−	1.38106i	0.878338	−	0.478040i	$-0.158653\pi$
$48$	14.5910	−	17.5442i	0.303980	−	0.365504i
$49$	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	$0.301285\pi$
$53$	−19.3602	+	59.5846i	−0.365287	+	1.12424i	−0.949801	+	0.312855i	$0.898715\pi$
$54$	−17.8007	−	38.6097i	−0.329644	−	0.714994i
$55$	−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	$-0.434633\pi$
$59$	63.2466	−	87.0514i	1.07198	−	1.47545i	0.868060	−	0.496459i	$-0.165367\pi$
$60$	−3.13433	−	22.5907i	−0.0522389	−	0.376512i
$61$	−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
$63$	−4.05770	+	30.8262i	−0.0644079	+	0.489304i
$64$	−53.6522	+	38.9806i	−0.838316	+	0.609072i
$65$	−79.3960	−	8.83771i	−1.22148	−	0.135965i
$66$	13.9205	−	34.8931i	0.210917	−	0.528683i
$67$	−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
$69$	7.75469	+	12.2902i	0.112387	+	0.178118i
$70$	11.2153	−	24.7797i	0.160219	−	0.353995i
$71$	35.3941	+	11.5002i	0.498508	+	0.161975i	0.547470	−	0.836826i	$-0.315591\pi$
$71$	35.3941	+	11.5002i	0.498508	+	0.161975i	−0.0489616	+	0.998801i	$0.515591\pi$
$72$	14.2588	+	76.9250i	0.198040	+	1.06840i
$73$	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
$75$	61.8447	+	42.4292i	0.824595	+	0.565723i
$76$	4.47328			0.0588589
$77$	−22.2264	+	16.1485i	−0.288655	+	0.209720i
$78$	75.3143	+	4.93559i	0.965568	+	0.0632767i
$79$	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
$81$	78.2409	+	20.9611i	0.965936	+	0.258779i
$82$		−	13.4223i		−	0.163687i
$83$	−15.7098	−	48.3497i	−0.189274	−	0.582526i	0.810721	−	0.585432i	$-0.199075\pi$
$83$	−15.7098	−	48.3497i	−0.189274	−	0.582526i	−0.999996	+	0.00290563i	$0.999075\pi$
$84$	5.83918	−	14.6365i	0.0695141	−	0.174244i
$85$	55.3386	−	60.7065i	0.651042	−	0.714194i
$86$	71.2080	+	98.0094i	0.828000	+	1.13964i
$87$	3.42975	−	8.59698i	0.0394224	−	0.0988159i
$88$	−40.6335	+	55.9272i	−0.461744	+	0.635537i
$89$	80.9329	+	111.395i	0.909359	+	1.25163i	0.967385	+	0.253310i	$0.0815193\pi$
$89$	80.9329	+	111.395i	0.909359	+	1.25163i	−0.0580262	+	0.998315i	$0.518481\pi$
$90$	−60.1899	−	37.3926i	−0.668777	−	0.415474i
$91$	−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
$96$	4.47171	−	68.2359i	0.0465803	−	0.710790i
$97$	−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	$-0.999516\pi$
$101$		−	0.307054i		−	0.00304014i	0.999999	−	0.00152007i	$-0.000483853\pi$
$102$	−49.6255	+	59.6695i	−0.486525	+	0.584995i
$103$	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
$105$	22.6344	+	46.6156i	0.215565	+	0.443958i
$106$	−30.4856	−	93.8250i	−0.287600	−	0.885142i
$107$	139.254			1.30144			0.650721	−	0.759317i	$-0.274467\pi$
$107$	139.254			1.30144			0.650721	+	0.759317i	$0.274467\pi$
$108$	−35.8190	−	20.0582i	−0.331658	−	0.185724i
$109$	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
$111$	−145.147	−	120.715i	−1.30763	−	1.08752i
$112$	15.4453	−	21.2587i	0.137905	−	0.189810i
$113$	−57.8390	−	42.0225i	−0.511849	−	0.371880i	0.301675	−	0.953411i	$-0.402454\pi$
$113$	−57.8390	−	42.0225i	−0.511849	−	0.371880i	−0.813525	+	0.581530i	$0.802454\pi$
$114$	8.88681	−	10.6855i	0.0779545	−	0.0937320i
$115$	22.0654	+	9.98683i	0.191873	+	0.0868420i
$116$	−2.75736	+	3.79519i	−0.0237704	+	0.0327171i
$117$	−98.9801	+	104.308i	−0.845984	+	0.891518i
$118$			169.435i			1.43589i
$119$	53.9784	−	17.5386i	0.453600	−	0.147383i
$120$	90.4127	+	93.9558i	0.753439	+	0.782965i
$121$	17.8480	−	54.9305i	0.147504	−	0.453971i
$122$	36.4184	−	112.084i	0.298511	−	0.918724i
$123$	19.6610	+	16.3515i	0.159845	+	0.132939i
$124$	−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
$129$	−230.312	−	15.0931i	−1.78536	−	0.117000i
$130$	109.324	−	62.2270i	0.840953	−	0.478669i
$131$	−123.408	+	40.0976i	−0.942044	+	0.306089i	−0.739478	−	0.673180i	$-0.764928\pi$
$131$	−123.408	+	40.0976i	−0.942044	+	0.306089i	−0.202565	+	0.979269i	$0.564928\pi$
$132$	−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
$135$	128.098	−	42.6131i	0.948875	−	0.315653i
$136$	115.538	−	83.9432i	0.849543	−	0.617229i
$137$	−34.2523	−	24.8857i	−0.250017	−	0.181648i	0.455718	−	0.890124i	$-0.349383\pi$
$137$	−34.2523	−	24.8857i	−0.250017	−	0.181648i	−0.705734	+	0.708477i	$0.749383\pi$
$138$	−21.2541	−	8.47926i	−0.154015	−	0.0614439i
$139$	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
$141$	−190.175	−	75.8698i	−1.34876	−	0.538083i
$142$	−55.7333	+	18.1088i	−0.392488	+	0.127527i
$143$	−127.060			−0.888529
$144$	−49.6575	−	47.1212i	−0.344843	−	0.327231i
$145$	−3.11470	−	15.1088i	−0.0214807	−	0.104198i
$146$	−20.8443	−	6.77273i	−0.142769	−	0.0463886i
$147$	7.27140	−	110.958i	0.0494653	−	0.754814i
$148$	56.2398	+	77.4074i	0.379999	+	0.523023i
$149$			227.208i			1.52489i	0.647054	+	0.762444i	$0.276001\pi$
$149$			227.208i			1.52489i	−0.647054	+	0.762444i	$0.723999\pi$
$150$	−118.056	+	3.18932i	−0.787038	+	0.0212622i
$151$	−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
$153$	−26.9482	−	145.383i	−0.176132	−	0.950214i
$154$	13.3684	−	41.1437i	0.0868077	−	0.267167i
$155$	103.165	−	113.172i	0.665582	−	0.730144i
$156$	61.6355	−	38.8900i	0.395099	−	0.249295i
$157$			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
$159$	174.573	+	69.6456i	1.09794	+	0.438023i
$160$	−56.3785	−	99.0490i	−0.352366	−	0.619056i
$161$	9.83636	+	13.5386i	0.0610954	+	0.0840906i
$162$	−119.073	+	45.7136i	−0.735020	+	0.282182i
$163$	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
$165$	105.226	+	56.1878i	0.637734	+	0.340532i
$166$	64.7634	+	47.0533i	0.390141	+	0.283454i
$167$	16.3877	+	50.4362i	0.0981300	+	0.302013i	0.988057	−	0.154090i	$-0.0492447\pi$
$167$	16.3877	+	50.4362i	0.0981300	+	0.302013i	−0.889927	+	0.456103i	$0.849245\pi$
$168$	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
$171$	4.82581	+	26.0348i	0.0282211	+	0.152250i
$172$	111.253	+	36.1482i	0.646819	+	0.210164i
$173$	25.5804	−	18.5852i	0.147863	−	0.107429i	−0.511394	−	0.859346i	$-0.670871\pi$
$173$	25.5804	−	18.5852i	0.147863	−	0.107429i	0.659257	+	0.751917i	$0.270871\pi$
$174$	3.58778	+	14.1263i	0.0206194	+	0.0811856i
$175$	74.2604	+	44.0980i	0.424345	+	0.251989i
$176$		−	60.4890i		−	0.343687i
$177$	−248.188	−	206.411i	−1.40219	−	1.16616i
$178$	−206.204	−	66.9998i	−1.15845	−	0.376403i
$179$	−77.9997	−	25.3436i	−0.435753	−	0.141585i	0.0829226	−	0.996556i	$-0.473575\pi$
$179$	−77.9997	−	25.3436i	−0.435753	−	0.141585i	−0.518675	+	0.854971i	$0.673575\pi$
$180$	−68.2420	+	4.95106i	−0.379122	+	0.0275059i
$181$	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
$183$	119.815	+	189.890i	0.654725	+	1.03765i
$184$	34.0664	+	24.7507i	0.185144	+	0.134515i
$185$	−312.710	−	34.8083i	−1.69032	−	0.188153i
$186$	−92.5146	+	111.239i	−0.497390	+	0.598059i
$187$	76.7944	−	105.698i	0.410665	−	0.565232i
$188$	83.9537	+	60.9959i	0.446562	+	0.324446i
$189$	91.4846	+	18.1945i	0.484045	+	0.0962671i
$190$	2.56252	−	23.0211i	0.0134870	−	0.121164i
$191$	0.866643	−	1.19283i	0.00453740	−	0.00624519i	−0.806742	−	0.590903i	$-0.798771\pi$
$191$	0.866643	−	1.19283i	0.00453740	−	0.00624519i	0.811280	+	0.584658i	$0.198771\pi$
$192$	106.166	+	168.259i	0.552948	+	0.876350i
$193$			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
$195$	−42.0322	+	235.944i	−0.215550	+	1.20997i
$196$	−17.4152	+	53.5984i	−0.0888529	+	0.273461i
$197$	30.8463	−	94.9352i	0.156580	−	0.481905i	−0.841737	−	0.539887i	$-0.818467\pi$
$197$	30.8463	−	94.9352i	0.156580	−	0.481905i	0.998318	+	0.0579827i	$0.0184668\pi$
$198$	−101.724	−	48.5174i	−0.513759	−	0.245037i
$199$	−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
$204$	−4.90046	+	74.7783i	−0.0240219	+	0.366560i
$205$	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
$210$	−71.9797	−	38.4351i	−0.342761	−	0.183024i
$211$	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
$213$	41.3704	−	103.699i	0.194227	−	0.486849i
$214$	−177.399	+	128.888i	−0.828966	+	0.602279i
$215$	−334.313	+	190.291i	−1.55495	+	0.885073i
$216$	233.078	−	27.5939i	1.07907	−	0.127750i
$217$	100.629	−	32.6965i	0.463730	−	0.150675i
$218$	−158.932			−0.729046
$219$	35.3139	−	22.2819i	0.161251	−	0.101744i
$220$	−44.6800	−	40.7292i	−0.203091	−	0.185133i
$221$	249.640	+	81.1131i	1.12959	+	0.367028i
$222$	296.634	+	19.4394i	1.33619	+	0.0875647i
$223$	−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
$225$	139.148	−	176.813i	0.618435	−	0.785836i
$226$	112.576			0.498126
$227$	−174.859	+	127.043i	−0.770305	+	0.559659i	−0.902054	−	0.431624i	$-0.857941\pi$
$227$	−174.859	+	127.043i	−0.770305	+	0.559659i	0.131749	+	0.991283i	$0.457941\pi$
$228$	0.877561	−	13.3911i	0.00384895	−	0.0587329i
$229$	−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
$231$	43.9813	+	69.7046i	0.190395	+	0.301752i
$232$		−	26.8199i		−	0.115603i
$233$	−62.4520	−	192.208i	−0.268034	−	0.824925i	−0.990979	−	0.134019i	$-0.957212\pi$
$233$	−62.4520	−	192.208i	−0.268034	−	0.824925i	0.722944	−	0.690906i	$-0.242788\pi$
$234$	29.5501	−	224.491i	0.126283	−	0.959364i
$235$	−334.222	+	68.9006i	−1.42222	+	0.293194i
$236$	96.1648	+	132.359i	0.407478	+	0.560845i
$237$	−209.003	−	83.3814i	−0.881871	−	0.351820i
$238$	−52.5311	+	72.3028i	−0.220719	+	0.303793i
$239$	−44.7563	−	61.6017i	−0.187265	−	0.257748i	0.705054	−	0.709154i	$-0.250923\pi$
$239$	−44.7563	−	61.6017i	−0.187265	−	0.257748i	−0.892319	+	0.451406i	$0.850923\pi$
$240$	−112.325	−	20.0102i	−0.468023	−	0.0833757i
$241$	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
$246$	−40.1807	−	2.63317i	−0.163336	−	0.0107039i
$247$	−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	$-0.771702\pi$
$251$		−	329.960i		−	1.31458i	0.753637	−	0.657291i	$-0.228298\pi$
$252$	−42.6699	−	20.3514i	−0.169325	−	0.0807596i
$253$	36.6370	+	11.9041i	0.144810	+	0.0470517i
$254$	−202.622	−	65.8359i	−0.797724	−	0.259196i
$255$	−170.873	−	177.570i	−0.670092	−	0.696352i
$256$	−75.5254	−	232.443i	−0.295021	−	0.907981i
$257$	−113.930			−0.443306			−0.221653	−	0.975126i	$-0.571145\pi$
$257$	−113.930			−0.443306			−0.221653	+	0.975126i	$0.571145\pi$
$258$	307.368	−	193.939i	1.19135	−	0.751703i
$259$	−175.878	−	127.783i	−0.679065	−	0.493370i
$260$	50.0842	−	110.659i	0.192632	−	0.425610i
$261$	−25.0629	−	11.9538i	−0.0960265	−	0.0457999i
$262$	120.099	−	165.302i	0.458393	−	0.630923i
$263$	190.229	+	138.210i	0.723304	+	0.525511i	0.887438	−	0.460927i	$-0.152483\pi$
$263$	190.229	+	138.210i	0.723304	+	0.525511i	−0.164134	+	0.986438i	$0.552483\pi$
$264$	159.451	+	132.611i	0.603982	+	0.502316i
$265$	306.803	−	63.2481i	1.15775	−	0.238672i
$266$	9.40713	−	12.9478i	0.0353651	−	0.0486760i
$267$	349.346	−	220.426i	1.30841	−	0.825565i
$268$		−	119.187i		−	0.444728i
$269$	158.804	−	51.5986i	0.590350	−	0.191816i	0.00141812	−	0.999999i	$-0.499549\pi$
$269$	158.804	−	51.5986i	0.590350	−	0.191816i	0.588932	+	0.808183i	$0.299549\pi$
$270$	−123.746	+	172.848i	−0.458318	+	0.640177i
$271$	−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
$273$	−105.883	+	127.313i	−0.387849	+	0.466347i
$274$	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
$279$	−50.2383	−	271.030i	−0.180065	−	0.971435i
$280$	110.968	+	101.156i	0.396314	+	0.361270i
$281$	−25.0374	+	8.13516i	−0.0891012	+	0.0289507i	−0.353228	−	0.935537i	$-0.614916\pi$
$281$	−25.0374	+	8.13516i	−0.0891012	+	0.0289507i	0.264127	+	0.964488i	$0.414916\pi$
$282$	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
$285$	30.5996	+	31.7987i	0.107367	+	0.111574i
$286$	161.864	−	117.601i	0.565957	−	0.411192i
$287$	23.8236	+	17.3089i	0.0830091	+	0.0603097i
$288$	−203.392	−	26.7728i	−0.706223	−	0.0929612i
$289$	15.4477	−	11.2234i	0.0534523	−	0.0388354i
$290$	17.9519	+	16.3645i	0.0619031	+	0.0564293i
$291$	−177.026	+	443.733i	−0.608337	+	1.52485i
$292$	−20.1272	+	6.53971i	−0.0689286	+	0.0223963i
$293$	290.824			0.992572			0.496286	−	0.868159i	$-0.334697\pi$
$293$	290.824			0.992572			0.496286	+	0.868159i	$0.334697\pi$
$294$	93.4344	+	148.081i	0.317804	+	0.503677i
$295$	−534.705	−	59.5189i	−1.81256	−	0.201759i
$296$	−520.251	−	169.040i	−1.75760	−	0.571080i
$297$	194.992	−	89.8998i	0.656539	−	0.302693i
$298$	−210.294	−	289.445i	−0.705685	−	0.971293i
$299$			77.3946i			0.258845i
$300$	−90.4129	+	69.4954i	−0.301376	+	0.231651i
$301$	−265.787			−0.883012
$302$	87.1860	−	63.3443i	0.288695	−	0.209749i
$303$	−0.919191	−	0.0602375i	−0.00303363	−	0.000198803i
$304$	6.91513	−	21.2826i	0.0227471	−	0.0700085i
$305$	340.924	+	154.303i	1.11778	+	0.505910i
$306$	168.890	+	160.264i	0.551927	+	0.523738i
$307$			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
$309$	24.5672	−	61.5800i	0.0795054	−	0.199288i
$310$	−26.6767	+	239.658i	−0.0860539	+	0.773089i
$311$	−18.4022	−	25.3284i	−0.0591710	−	0.0814418i	0.778406	−	0.627761i	$-0.216029\pi$
$311$	−18.4022	−	25.3284i	−0.0591710	−	0.0814418i	−0.837577	+	0.546319i	$0.816029\pi$
$312$	−154.393	+	387.002i	−0.494851	+	1.24039i
$313$	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
$315$	143.988	−	58.6127i	0.457104	−	0.186072i
$316$	92.2657	+	67.0350i	0.291980	+	0.212136i
$317$	103.121	+	317.375i	0.325304	+	1.00118i	0.971303	+	0.237845i	$0.0764410\pi$
$317$	103.121	+	317.375i	0.325304	+	1.00118i	−0.645999	+	0.763338i	$0.723559\pi$
$318$	−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
$321$	27.3187	−	416.869i	0.0851051	−	1.29866i
$322$	−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
$327$	193.616	−	232.803i	0.592099	−	0.711936i
$328$	70.4709	+	22.8974i	0.214850	+	0.0698091i
$329$	−224.242	−	72.8606i	−0.681587	−	0.221461i
$330$	−186.054	+	25.8140i	−0.563801	+	0.0782243i
$331$	−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
$333$	−389.844	+	410.827i	−1.17070	+	1.23372i
$334$	−67.5581	−	49.0839i	−0.202270	−	0.146958i
$335$	289.654	+	264.042i	0.864639	+	0.788185i
$336$	−60.6095	−	50.4073i	−0.180385	−	0.150022i
$337$	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
$339$	−137.144	+	164.902i	−0.404556	+	0.486436i
$340$	61.7841	+	108.546i	0.181718	+	0.319252i
$341$	143.164	−	197.049i	0.419836	−	0.577855i
$342$	−30.2443	−	28.6996i	−0.0884338	−	0.0839170i
$343$		−	297.327i		−	0.866844i
$344$	−636.052	+	206.666i	−1.84899	+	0.600773i
$345$	34.2251	−	64.0954i	0.0992032	−	0.185784i
$346$	−15.3856	+	47.3522i	−0.0444672	+	0.136856i
$347$	−110.008	+	338.571i	−0.317027	+	0.975709i	0.657885	+	0.753119i	$0.271451\pi$
$347$	−110.008	+	338.571i	−0.317027	+	0.975709i	−0.974912	+	0.222591i	$0.928549\pi$
$348$	10.8203	+	8.99892i	0.0310927	+	0.0258590i
$349$	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	$-0.693684\pi$
$353$	131.712	−	405.367i	0.373121	−	1.14835i	0.944738	−	0.327827i	$-0.106316\pi$
$354$	507.216	+	33.2395i	1.43281	+	0.0938968i
$355$	−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	−0.639358	−	0.768909i	$-0.720800\pi$
$359$	103.927	−	143.043i	0.289491	−	0.398450i	0.928849	+	0.370460i	$0.120800\pi$
$360$	299.001	−	252.225i	0.830559	−	0.700626i
$361$	285.053	−	207.103i	0.789620	−	0.573692i
$362$	−114.207	−	82.9761i	−0.315488	−	0.229216i
$363$	−160.937	−	64.2056i	−0.443354	−	0.176875i
$364$	67.8964	−	49.3296i	0.186529	−	0.135521i
$365$	28.6957	−	63.4017i	0.0786183	−	0.173703i
$366$	−328.389	−	131.010i	−0.897237	−	0.357950i
$367$	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
$369$	52.8066	−	55.6488i	0.143107	−	0.150810i
$370$	430.585	−	245.088i	1.16374	−	0.662400i
$371$	205.846	+	66.8833i	0.554840	+	0.180278i
$372$	−9.13570	+	139.406i	−0.0245583	+	0.374747i
$373$	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
$375$	31.4056	−	373.683i	0.0837484	−	0.996487i
$376$	−593.286			−1.57789
$377$	39.8801	−	28.9746i	0.105783	−	0.0768558i
$378$	−133.384	+	61.4958i	−0.352868	+	0.162687i
$379$	−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
$381$	343.277	−	216.597i	0.900990	−	0.568495i
$382$			2.32170i			0.00607775i
$383$	−8.00232	−	24.6286i	−0.0208938	−	0.0643045i	0.940066	−	0.340993i	$-0.110763\pi$
$383$	−8.00232	−	24.6286i	−0.0208938	−	0.0643045i	−0.960960	+	0.276688i	$0.910763\pi$
$384$	−36.9232	−	14.7304i	−0.0961541	−	0.0383605i
$385$	125.146	+	56.6411i	0.325054	+	0.147120i
$386$	−130.851	−	180.102i	−0.338993	−	0.466584i
$387$	−90.3645	+	686.496i	−0.233500	+	1.77389i
$388$	142.321	−	195.888i	0.366807	−	0.504867i
$389$	92.7133	+	127.609i	0.238338	+	0.328044i	0.911384	−	0.411556i	$-0.135015\pi$
$389$	92.7133	+	127.609i	0.238338	+	0.328044i	−0.673047	+	0.739600i	$0.735015\pi$
$390$	−164.834	−	339.477i	−0.422652	−	0.870455i
$391$	−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
$396$	−107.002	+	19.8339i	−0.270206	+	0.0500856i
$397$	−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	$-0.736579\pi$
$401$		−	590.500i		−	1.47257i	0.676672	−	0.736285i	$-0.263421\pi$
$402$	−284.706	−	236.783i	−0.708224	−	0.589012i
$403$	465.393	+	151.215i	1.15482	+	0.375224i
$404$	0.444018	+	0.144270i	0.00109905	+	0.000357104i
$405$	−102.436	−	391.832i	−0.252927	−	0.967485i
$406$	5.18645	+	15.9623i	0.0127745	+	0.0393159i
$407$	−500.439			−1.22958
$408$	−228.624	−	362.340i	−0.560354	−	0.888087i
$409$	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
$411$	−81.2170	+	97.6548i	−0.197608	+	0.237603i
$412$	−19.7509	+	27.1848i	−0.0479391	+	0.0659826i
$413$	−300.735	−	218.496i	−0.728171	−	0.529047i
$414$	−29.5529	+	61.9623i	−0.0713839	+	0.149667i
$415$	−171.242	+	187.852i	−0.412631	+	0.452656i
$416$	214.064	−	294.634i	0.514576	−	0.708254i
$417$	−271.593	−	430.439i	−0.651302	−	1.03223i
$418$		−	36.8414i		−	0.0881373i
$419$	−187.721	+	60.9941i	−0.448020	+	0.145571i	−0.524333	−	0.851513i	$-0.675685\pi$
$419$	−187.721	+	60.9941i	−0.448020	+	0.145571i	0.0763126	+	0.997084i	$0.475685\pi$
$420$	−78.0436	+	10.8281i	−0.185818	+	0.0257812i
$421$	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
$423$	−264.430	+	554.419i	−0.625131	+	1.31068i
$424$	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
$429$	−24.9264	+	380.363i	−0.0581035	+	0.886627i
$430$	249.764	−	551.841i	0.580846	−	1.28335i
$431$	218.609	−	71.0303i	0.507213	−	0.164804i	−0.0442213	−	0.999022i	$-0.514081\pi$
$431$	218.609	−	71.0303i	0.507213	−	0.164804i	0.551434	+	0.834218i	$0.314081\pi$
$432$	−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
$435$	−45.8403	+	6.36008i	−0.105380	+	0.0146209i
$436$	−124.155	+	90.2038i	−0.284759	+	0.206889i
$437$	11.5296	+	8.37671i	0.0263834	+	0.0191687i
$438$	−24.3639	+	61.0705i	−0.0556254	+	0.139430i
$439$	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
$441$	−330.734	−	43.5350i	−0.749963	−	0.0987189i
$442$	−393.096	+	127.725i	−0.889359	+	0.288970i
$443$	260.488			0.588009			0.294004	−	0.955804i	$-0.405012\pi$
$443$	260.488			0.588009			0.294004	+	0.955804i	$0.405012\pi$
$444$	242.758	−	153.173i	0.546753	−	0.344983i
$445$	283.874	−	627.207i	0.637920	−	1.40945i
$446$	275.578	+	89.5408i	0.617888	+	0.200764i
$447$	680.166	+	44.5734i	1.52162	+	0.0997169i
$448$	134.665	+	185.351i	0.300592	+	0.413730i
$449$		−	757.399i		−	1.68686i	−0.537241	−	0.843429i	$-0.680533\pi$
$449$		−	757.399i		−	1.68686i	0.537241	−	0.843429i	$-0.319467\pi$
$450$	−13.6125	+	354.035i	−0.0302501	+	0.786744i
$451$	67.7872			0.150304
$452$	87.9427	−	63.8941i	0.194563	−	0.141359i
$453$	−13.4263	+	204.878i	−0.0296386	+	0.452269i
$454$	105.171	−	323.684i	0.231655	−	0.712961i
$455$	−30.5314	+	274.288i	−0.0671020	+	0.602830i
$456$	40.9415	+	64.8868i	0.0897839	+	0.142296i
$457$		−	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
$459$	−440.501	+	52.1505i	−0.959698	+	0.113618i
$460$	−24.8090	+	27.2155i	−0.0539326	+	0.0591642i
$461$	−7.46952	−	10.2809i	−0.0162029	−	0.0223013i	0.800839	−	0.598880i	$-0.204387\pi$
$461$	−7.46952	−	10.2809i	−0.0162029	−	0.0223013i	−0.817042	+	0.576579i	$0.804387\pi$
$462$	−120.544	−	48.0908i	−0.260918	−	0.104093i
$463$	−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
$465$	−318.551	−	331.035i	−0.685057	−	0.711903i
$466$	257.458	+	187.054i	0.552485	+	0.401404i
$467$	109.488	+	336.968i	0.234449	+	0.721559i	0.997194	+	0.0748600i	$0.0238510\pi$
$467$	109.488	+	336.968i	0.234449	+	0.721559i	−0.762745	+	0.646699i	$0.776149\pi$
$468$	−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
$471$	444.416	+	29.1240i	0.943558	+	0.0618343i
$472$	−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
$477$	242.737	−	508.936i	0.508883	−	1.06695i
$478$	114.032	+	37.0512i	0.238560	+	0.0775129i
$479$	845.986	+	274.877i	1.76615	+	0.573857i	0.997808	−	0.0661825i	$-0.0210820\pi$
$479$	845.986	+	274.877i	1.76615	+	0.573857i	0.768342	+	0.640039i	$0.221082\pi$
$480$	−307.571	+	149.342i	−0.640774	+	0.311130i
$481$	−310.693	−	956.213i	−0.645931	−	1.98797i
$482$	−373.521			−0.774940
$483$	42.4585	−	26.7899i	0.0879058	−	0.0554657i
$484$	71.0467	+	51.6185i	0.146791	+	0.106650i
$485$	160.765	+	779.837i	0.331474	+	1.60791i
$486$	113.487	+	365.423i	0.233513	+	0.751900i
$487$	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
$489$	−357.446	−	297.279i	−0.730974	−	0.607932i
$490$	265.861	+	120.329i	0.542574	+	0.245569i
$491$	−87.2230	+	120.052i	−0.177644	+	0.244505i	−0.888548	−	0.458783i	$-0.848286\pi$
$491$	−87.2230	+	120.052i	−0.177644	+	0.244505i	0.710905	+	0.703288i	$0.248286\pi$
$492$	−32.8829	+	20.7481i	−0.0668353	+	0.0421709i
$493$			50.6877i			0.102815i
$494$	70.3947	−	22.8726i	0.142499	−	0.0463009i
$495$	188.846	−	303.980i	0.381506	−	0.614100i
$496$	−71.9887	+	221.559i	−0.145139	+	0.446691i
$497$	39.7296	−	122.275i	0.0799388	−	0.246026i
$498$	153.563	−	184.643i	0.308360	−	0.370770i
$499$	−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	−0.999760	−	0.0219268i	$-0.993020\pi$
$503$	−89.5586	+	275.633i	−0.178049	+	0.547978i	0.821711	+	0.569905i	$0.193020\pi$
$504$	265.751	−	49.2597i	0.527284	−	0.0977375i
$505$	−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	−0.972401	−	0.233316i	$-0.925042\pi$
$509$	−229.058	+	315.271i	−0.450016	+	0.619394i	0.522385	+	0.852710i	$0.325042\pi$
$510$	382.030	+	68.0565i	0.749078	+	0.133444i
$511$	38.9011	−	28.2633i	0.0761275	−	0.0553098i
$512$	354.234	+	257.366i	0.691863	+	0.502668i
$513$	78.8838	−	9.33898i	0.153770	−	0.0182046i
$514$	145.137	−	105.448i	0.282368	−	0.205152i
$515$	−22.3105	−	108.224i	−0.0433214	−	0.210143i
$516$	130.038	−	325.953i	0.252012	−	0.631691i
$517$	−516.196	+	167.722i	−0.998444	+	0.324414i
$518$	342.324			0.660858
$519$	−50.6180	−	80.2229i	−0.0975299	−	0.154572i
$520$	140.211	+	680.136i	0.269637	+	1.30795i
$521$	−62.7140	−	20.3770i	−0.120372	−	0.0391113i	0.248211	−	0.968706i	$-0.420157\pi$
$521$	−62.7140	−	20.3770i	−0.120372	−	0.0391113i	−0.368584	+	0.929595i	$0.620157\pi$
$522$	42.9920	−	7.96901i	0.0823602	−	0.0152663i
$523$	−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
$525$	146.579	−	213.653i	0.279199	−	0.406959i
$526$	−370.257			−0.703911
$527$	−407.075	+	295.757i	−0.772438	+	0.561209i
$528$	−181.078	−	11.8666i	−0.342952	−	0.0224747i
$529$	−156.219	+	480.793i	−0.295310	+	0.908871i
$530$	−332.303	+	364.537i	−0.626987	+	0.687806i
$531$	−666.597	+	702.476i	−1.25536	+	1.32293i
$532$		−	15.4537i		−	0.0290484i
$533$	42.0850	+	129.524i	0.0789588	+	0.243010i
$534$	−241.022	+	604.144i	−0.451352	+	1.13136i
$535$	−344.430	−	605.114i	−0.643794	−	1.13105i
$536$	400.525	+	551.276i	0.747249	+	1.02850i
$537$	−91.1701	+	228.526i	−0.169777	+	0.425561i
$538$	−154.546	+	212.715i	−0.287261	+	0.395381i
$539$	−173.257	−	238.467i	−0.321441	−	0.442426i
$540$	1.43378	+	205.259i	0.00265515	+	0.380109i
$541$	−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
$546$	17.0509	−	260.187i	0.0312287	−	0.476532i
$547$	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
$552$	80.7763	−	97.1250i	0.146334	−	0.175951i
$553$	−246.444	−	80.0744i	−0.445648	−	0.144800i
$554$	29.6370	+	9.62964i	0.0534964	+	0.0173820i
$555$	−165.548	+	929.294i	−0.298286	+	1.67440i
$556$	79.7121	+	245.329i	0.143367	+	0.441239i
$557$	934.176			1.67716			0.838578	−	0.544781i	$-0.183387\pi$
$557$	934.176			1.67716			0.838578	+	0.544781i	$0.183387\pi$
$558$	314.853	+	298.772i	0.564253	+	0.535434i
$559$	−994.457	−	722.515i	−1.77899	−	1.29251i
$560$	−130.579	−	14.5350i	−0.233178	−	0.0259554i
$561$	−301.351	−	250.626i	−0.537168	−	0.446748i
$562$	24.3661	−	33.5371i	0.0433561	−	0.0596746i
$563$	−583.167	−	423.696i	−1.03582	−	0.752568i	−0.0663559	−	0.997796i	$-0.521137\pi$
$563$	−583.167	−	423.696i	−1.03582	−	0.752568i	−0.969465	+	0.245228i	$0.921137\pi$
$564$	199.066	−	239.356i	0.352954	−	0.424390i
$565$	−39.5458	+	355.270i	−0.0699925	+	0.628797i
$566$	45.1971	−	62.2084i	0.0798535	−	0.109909i
$567$	72.4139	−	270.297i	0.127714	−	0.476714i
$568$		−	323.508i		−	0.569556i
$569$	−560.605	+	182.152i	−0.985246	+	0.320126i	−0.756955	−	0.653467i	$-0.773314\pi$
$569$	−560.605	+	182.152i	−0.985246	+	0.320126i	−0.228291	+	0.973593i	$0.573314\pi$
$570$	−68.4129	−	12.1874i	−0.120023	−	0.0213814i
$571$	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
$573$	−3.40082	−	2.82837i	−0.00593511	−	0.00493608i
$574$	−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
$579$	423.220	+	27.7349i	0.730950	+	0.0479014i
$580$	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
$585$	698.072	+	172.114i	1.19329	+	0.294212i
$586$	−370.486	+	269.174i	−0.632228	+	0.459341i
$587$	229.514	+	166.752i	0.390994	+	0.284074i	0.765863	−	0.643004i	$-0.222312\pi$
$587$	229.514	+	166.752i	0.390994	+	0.284074i	−0.374868	+	0.927078i	$0.622312\pi$
$588$	157.035	+	62.6486i	0.267066	+	0.106545i
$589$	72.8979	−	52.9634i	0.123766	−	0.0899210i
$590$	736.259	−	419.077i	1.24790	−	0.710301i
$591$	−278.145	−	110.965i	−0.470634	−	0.187758i
$592$	455.222	−	147.911i	0.768957	−	0.249849i
$593$	−924.858			−1.55962			−0.779812	−	0.626013i	$-0.784686\pi$
$593$	−924.858			−1.55962			−0.779812	+	0.626013i	$0.784686\pi$
$594$	−165.197	+	295.001i	−0.278109	+	0.496635i
$595$	−209.721	−	191.177i	−0.352473	−	0.321306i
$596$	−328.556	−	106.754i	−0.551269	−	0.179118i
$597$	−49.1218	+	749.571i	−0.0822810	+	1.25556i
$598$	−71.6331	−	98.5945i	−0.119788	−	0.164874i
$599$		−	620.049i		−	1.03514i	−0.855641	−	0.517570i	$-0.826837\pi$
$599$		−	620.049i		−	1.03514i	0.855641	−	0.517570i	$-0.173163\pi$
$600$	184.649	−	625.267i	0.307748	−	1.04211i
$601$	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
$603$	693.677	−	128.580i	1.15038	−	0.213234i
$604$	32.1563	−	98.9669i	0.0532389	−	0.163852i
$605$	−282.839	+	58.3079i	−0.467503	+	0.0963766i
$606$	1.22673	−	0.774025i	0.00202430	−	0.00127727i
$607$		−	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
$609$	−29.6998	−	11.8487i	−0.0487682	−	0.0194559i
$610$	−577.126	+	118.976i	−0.946108	+	0.195042i
$611$	−640.950	−	882.192i	−1.04902	−	1.44385i
$612$	222.893	+	29.3398i	0.364205	+	0.0479409i
$613$	−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
$615$	22.4245	−	125.878i	0.0364625	−	0.204680i
$616$	193.211	+	140.376i	0.313653	+	0.227883i
$617$	−29.9101	−	92.0539i	−0.0484767	−	0.149196i	0.923888	−	0.382663i	$-0.124993\pi$
$617$	−29.9101	−	92.0539i	−0.0484767	−	0.149196i	−0.972365	+	0.233467i	$0.924993\pi$
$618$	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
$621$	−54.7598	−	118.774i	−0.0881801	−	0.191262i
$622$	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
$627$	53.9652	+	44.8814i	0.0860689	+	0.0715812i
$628$	−214.676	−	69.7525i	−0.341841	−	0.111071i
$629$	983.237	+	319.473i	1.56317	+	0.507906i
$630$	−129.180	+	207.937i	−0.205047	+	0.330058i
$631$	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
$633$	−75.9792	−	120.417i	−0.120030	−	0.190232i
$634$	−425.117	−	308.866i	−0.670532	−	0.487170i
$635$	278.943	−	616.311i	0.439280	−	0.970569i
$636$	−182.735	+	219.720i	−0.287319	+	0.345471i
$637$	348.087	−	479.101i	0.546447	−	0.752120i
$638$	31.2567	+	22.7093i	0.0489917	+	0.0355946i
$639$	−302.315	−	144.189i	−0.473106	−	0.225648i
$640$	−64.8906	+	13.3773i	−0.101392	+	0.0209021i
$641$	−666.711	+	917.650i	−1.04011	+	1.43159i	−0.143034	+	0.989718i	$0.545686\pi$
$641$	−666.711	+	917.650i	−1.04011	+	1.43159i	−0.897078	+	0.441873i	$0.854314\pi$
$642$	351.034	+	556.342i	0.546782	+	0.866577i
$643$		−	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
$645$	504.065	+	1038.12i	0.781496	+	1.60950i
$646$	−23.5190	+	72.3841i	−0.0364072	+	0.112050i
$647$	−230.085	+	708.129i	−0.355619	+	1.09448i	0.600031	+	0.799976i	$0.295155\pi$
$647$	−230.085	+	708.129i	−0.355619	+	1.09448i	−0.955650	+	0.294505i	$0.904845\pi$
$648$	−36.8796	−	703.152i	−0.0569129	−	1.08511i
$649$	−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	$-0.644356\pi$
$653$	290.386	−	893.717i	0.444696	−	1.36863i	0.882817	−	0.469717i	$-0.155644\pi$
$654$	−31.1791	+	475.775i	−0.0476744	+	0.727485i
$655$	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	$0.555114\pi$
$659$	−695.825	+	957.721i	−1.05588	+	1.45329i	−0.883597	+	0.468247i	$0.844886\pi$
$660$	−130.691	+	125.763i	−0.198017	+	0.190550i
$661$	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
$663$	291.793	−	731.406i	0.440109	−	1.10318i
$664$	−357.524	+	259.757i	−0.538440	+	0.391200i
$665$	37.5564	+	34.2355i	0.0564757	+	0.0514819i
$666$	116.387	−	884.184i	0.174755	−	1.32760i
$667$	−14.2138	+	4.61835i	−0.0213101	+	0.00692407i
$668$	−80.6334			−0.120709
$669$	−466.878	+	294.585i	−0.697874	+	0.440336i
$670$	−613.382	−	68.2766i	−0.915495	−	0.101905i
$671$	566.064	+	183.925i	0.843612	+	0.274106i
$672$	−235.733	−	15.4483i	−0.350793	−	0.0229886i
$673$	−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
$675$	−502.006	−	451.237i	−0.743713	−	0.668499i
$676$	131.176			0.194048
$677$	418.668	−	304.180i	0.618416	−	0.449306i	−0.233952	−	0.972248i	$-0.575166\pi$
$677$	418.668	−	304.180i	0.618416	−	0.449306i	0.852368	+	0.522943i	$0.175166\pi$
$678$	22.0851	−	337.006i	0.0325739	−	0.497059i
$679$	−170.005	+	523.221i	−0.250375	+	0.770576i
$680$	−650.535	−	294.433i	−0.956669	−	0.432989i
$681$	346.008	+	548.378i	0.508089	+	0.805254i
$682$			383.531i			0.562362i
$683$	170.064	+	523.402i	0.248995	+	0.766328i	0.994954	+	0.100336i	$0.0319917\pi$
$683$	170.064	+	523.402i	0.248995	+	0.766328i	−0.745958	+	0.665993i	$0.768008\pi$
$684$	−39.9152	−	5.25410i	−0.0583555	−	0.00768143i
$685$	−23.4190	+	210.391i	−0.0341884	+	0.307141i
$686$	275.193	+	378.771i	0.401157	+	0.552145i
$687$	292.970	+	116.880i	0.426448	+	0.170130i
$688$	343.966	−	473.429i	0.499951	−	0.688123i
$689$	588.368	+	809.819i	0.853945	+	1.17535i
$690$	15.7238	+	113.330i	0.0227882	+	0.164246i
$691$	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
$696$	−80.2875	−	5.26149i	−0.115356	−	0.00755961i
$697$	−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	$0.162465\pi$
$701$			684.914i			0.977053i	−0.872549	+	0.488527i	$0.837535\pi$
$702$	−666.235	−	132.501i	−0.949052	−	0.188748i
$703$	−176.075	−	57.2104i	−0.250463	−	0.0813804i
$704$	501.581	+	162.974i	0.712473	+	0.231497i
$705$	140.692	+	1014.04i	0.199563	+	1.43835i
$706$	207.400	+	638.311i	0.293767	+	0.904123i
$707$	−1.06077			−0.00150039
$708$	415.094	−	261.911i	0.586291	−	0.369930i
$709$	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
$711$	−290.611	+	609.311i	−0.408735	+	0.856977i
$712$	703.536	−	968.334i	0.988112	−	1.36002i
$713$	−120.026	−	87.2043i	−0.168340	−	0.122306i
$714$	206.139	+	171.440i	0.288710	+	0.240112i
$715$	314.267	+	552.123i	0.439535	+	0.772200i
$716$	73.2967	−	100.884i	0.102370	−	0.140900i
$717$	−193.190	+	121.896i	−0.269442	+	0.170009i
$718$			278.416i			0.387766i
$719$	803.024	−	260.918i	1.11686	−	0.362890i	0.308293	−	0.951292i	$-0.400242\pi$
$719$	803.024	−	260.918i	1.11686	−	0.362890i	0.808569	+	0.588401i	$0.200242\pi$
$720$	−81.9378	+	332.330i	−0.113803	+	0.461569i
$721$	23.5928	−	72.6112i	0.0327223	−	0.100709i
$722$	−171.449	+	527.665i	−0.237464	+	0.730838i
$723$	455.036	−	547.132i	0.629372	−	0.756753i
$724$	−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
$729$	−673.525	−	278.935i	−0.923903	−	0.382627i
$730$	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
$735$	−500.138	+	242.844i	−0.680461	+	0.330400i
$736$	−89.3280	+	64.9006i	−0.121370	+	0.0881802i
$737$	504.328	+	366.416i	0.684299	+	0.497172i
$738$	−15.7652	+	119.768i	−0.0213621	+	0.162287i
$739$	−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
$741$	−52.2534	+	130.978i	−0.0705175	+	0.176759i
$742$	−324.135	+	105.318i	−0.436840	+	0.141938i
$743$	1066.14			1.43491			0.717454	−	0.696606i	$-0.245308\pi$
$743$	1066.14			1.43491			0.717454	+	0.696606i	$0.245308\pi$
$744$	−426.214	−	675.493i	−0.572868	−	0.907920i
$745$	987.308	−	561.974i	1.32525	−	0.754327i
$746$	−946.648	−	307.585i	−1.26897	−	0.412312i
$747$	83.3894	+	449.878i	0.111632	+	0.602246i
$748$	116.764	+	160.712i	0.156101	+	0.214855i
$749$		−	481.079i		−	0.642295i
$750$	305.856	+	505.109i	0.407808	+	0.673479i
$751$	−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
$753$	−987.761	−	64.7311i	−1.31177	−	0.0859643i
$754$	−23.9864	+	73.8227i	−0.0318122	+	0.0979080i
$755$	169.276	+	297.394i	0.224207	+	0.393900i
$756$	−69.2945	+	123.743i	−0.0916594	+	0.163681i
$757$		−	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
$759$	42.8232	−	107.340i	0.0564205	−	0.141423i
$760$	116.496	+	52.7262i	0.153284	+	0.0693766i
$761$	−55.8262	−	76.8382i	−0.0733590	−	0.100970i	0.770761	−	0.637125i	$-0.219876\pi$
$761$	−55.8262	−	76.8382i	−0.0733590	−	0.100970i	−0.844120	+	0.536155i	$0.819876\pi$
$762$	−236.835	+	593.649i	−0.310807	+	0.779067i
$763$	204.952	−	282.093i	0.268614	−	0.369715i
$764$	1.31771	+	1.81367i	0.00172475	+	0.00237391i
$765$	−565.091	+	476.688i	−0.738681	+	0.623121i
$766$	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
$771$	−22.3506	+	341.057i	−0.0289890	+	0.442357i
$772$	−204.438	−	66.4258i	−0.264816	−	0.0860438i
$773$	−1165.39	+	846.708i	−1.50762	+	1.09535i	−0.540406	+	0.841404i	$0.681729\pi$
$773$	−1165.39	+	846.708i	−1.50762	+	1.09535i	−0.967218	+	0.253949i	$0.918271\pi$
$774$	−520.274	−	958.178i	−0.672188	−	1.23796i
$775$	−746.944	−	168.374i	−0.963799	−	0.217256i
$776$			1384.31i			1.78390i
$777$	−417.031	+	501.436i	−0.536720	+	0.645349i
$778$	−236.219	−	76.7521i	−0.303623	−	0.0986531i
$779$	23.8504	+	7.74946i	0.0306167	+	0.00994796i
$780$	−321.440	−	171.640i	−0.412103	−	0.220051i
$781$	−91.4558	−	281.472i	−0.117101	−	0.360400i
$782$	125.314			0.160248
$783$	−40.7013	+	72.6827i	−0.0519813	+	0.0928259i
$784$	228.084	+	165.713i	0.290924	+	0.211369i
$785$	645.100	−	367.190i	0.821783	−	0.467757i
$786$	−471.284	−	391.954i	−0.599597	−	0.498669i
$787$	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
$789$	451.060	−	542.352i	0.571686	−	0.687392i
$790$	397.842	−	436.433i	0.503597	−	0.552447i
$791$	−145.174	+	199.815i	−0.183532	+	0.252611i
$792$	428.263	−	451.314i	0.540737	−	0.569841i
$793$			1195.79i			1.50794i
$794$	736.952	−	239.450i	0.928151	−	0.301575i
$795$	−129.150	−	930.848i	−0.162453	−	1.17088i
$796$	117.648	−	362.083i	0.147799	−	0.454878i
$797$	209.068	−	643.446i	0.262319	−	0.807335i	−0.729980	−	0.683469i	$-0.760471\pi$
$797$	209.068	−	643.446i	0.262319	−	0.807335i	0.992299	−	0.123866i	$-0.0395294\pi$
$798$	−36.9148	−	30.7011i	−0.0462591	−	0.0384725i
$799$	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
$804$	−356.796	−	23.3820i	−0.443776	−	0.0290821i
$805$	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	−0.356348	−	0.934353i	$-0.615978\pi$
$809$	519.696	−	715.300i	0.642393	−	0.884178i	0.998740	+	0.0501756i	$0.0159781\pi$
$810$	493.157	+	404.352i	0.608836	+	0.499200i
$811$	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
$813$	1483.74	+	591.934i	1.82502	+	0.728086i
$814$	637.519	−	463.184i	0.783192	−	0.569023i
$815$	−770.096	−	85.7208i	−0.944903	−	0.105179i
$816$	348.198	+	138.913i	0.426714	+	0.170236i
$817$	−215.268	+	69.9447i	−0.263485	+	0.0856116i
$818$	−1173.19			−1.43422
$819$	360.349	+	341.944i	0.439986	+	0.417514i
$820$	−26.7203	+	59.0372i	−0.0325857	+	0.0719966i
$821$	942.860	+	306.354i	1.14843	+	0.373147i	0.820551	−	0.571573i	$-0.193667\pi$
$821$	942.860	+	306.354i	1.14843	+	0.373147i	0.327878	+	0.944720i	$0.393667\pi$
$822$	13.0788	−	199.575i	0.0159109	−	0.242792i
$823$	−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
$825$	−16.1072	−	596.222i	−0.0195238	−	0.722693i
$826$	585.342			0.708647
$827$	866.409	−	629.483i	1.04765	−	0.761164i	0.0758880	−	0.997116i	$-0.475821\pi$
$827$	866.409	−	629.483i	1.04765	−	0.761164i	0.971765	+	0.235952i	$0.0758209\pi$
$828$	12.0812	+	65.1770i	0.0145909	+	0.0787162i
$829$	−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
$831$	−50.2103	+	31.6810i	−0.0604215	+	0.0381240i
$832$			1059.58i			1.27353i
$833$	188.172	+	579.133i	0.225897	+	0.695238i
$834$	744.384	+	296.970i	0.892546	+	0.356079i
$835$	178.631	−	195.959i	0.213930	−	0.234681i
$836$	−20.9098	−	28.7798i	−0.0250117	−	0.0344256i
$837$	−821.206	+	97.2218i	−0.981131	+	0.116155i
$838$	182.687	−	251.448i	0.218004	−	0.300057i
$839$	−304.872	−	419.620i	−0.363375	−	0.500143i	0.587710	−	0.809072i	$-0.300030\pi$
$839$	−304.872	−	419.620i	−0.363375	−	0.500143i	−0.951085	+	0.308929i	$0.900030\pi$
$840$	324.587	−	312.347i	0.386413	−	0.371841i
$841$	−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
$846$	−176.283	−	951.030i	−0.208373	−	1.12415i
$847$	−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
$852$	130.516	+	108.547i	0.153188	+	0.127403i
$853$	−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
$855$	101.195	−	85.3640i	0.118357	−	0.0998409i
$856$	−374.069	−	1151.27i	−0.436997	−	1.34494i
$857$	−977.865			−1.14103			−0.570517	−	0.821286i	$-0.693257\pi$
$857$	−977.865			−1.14103			−0.570517	+	0.821286i	$0.693257\pi$
$858$	−320.293	−	507.623i	−0.373302	−	0.591635i
$859$	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
$861$	56.4892	−	67.9222i	0.0656088	−	0.0788876i
$862$	−212.747	+	292.822i	−0.246807	+	0.339700i
$863$	−353.404	−	256.763i	−0.409507	−	0.297524i	0.363895	−	0.931440i	$-0.381447\pi$
$863$	−353.404	−	256.763i	−0.409507	−	0.297524i	−0.773402	+	0.633916i	$0.781447\pi$
$864$	−120.048	+	603.618i	−0.138944	+	0.698632i
$865$	−144.030	−	65.1881i	−0.166509	−	0.0753620i
$866$	512.104	−	704.851i	0.591344	−	0.813916i
$867$	−30.5677	−	48.4457i	−0.0352568	−	0.0558774i
$868$			160.878i			0.185344i
$869$	−567.303	+	184.328i	−0.652823	+	0.212115i
$870$	52.5102	−	50.5300i	0.0603566	−	0.0580805i
$871$	−387.022	+	1191.13i	−0.444342	+	1.36754i
$872$	271.125	−	834.438i	0.310923	−	0.956924i
$873$	1293.62	+	616.993i	1.48181	+	0.706750i
$874$	−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
$879$	57.0534	−	870.603i	0.0649071	−	0.990447i
$880$	−262.848	+	149.612i	−0.298691	+	0.170014i
$881$	265.263	−	86.1891i	0.301093	−	0.0978310i	−0.154574	−	0.987981i	$-0.549401\pi$
$881$	265.263	−	86.1891i	0.301093	−	0.0978310i	0.455667	+	0.890150i	$0.349401\pi$
$882$	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
$885$	−283.072	+	1589.01i	−0.319856	+	1.79549i
$886$	−331.841	+	241.096i	−0.374538	+	0.272118i
$887$	−725.289	−	526.953i	−0.817687	−	0.594085i	0.0983617	−	0.995151i	$-0.468640\pi$
$887$	−725.289	−	526.953i	−0.817687	−	0.594085i	−0.916049	+	0.401066i	$0.868640\pi$
$888$	−608.096	+	1524.25i	−0.684793	+	1.71650i
$889$	378.147	−	274.740i	0.425363	−	0.309044i
$890$	218.882	+	1061.75i	0.245935	+	1.19298i
$891$	−230.869	−	601.360i	−0.259112	−	0.674928i
$892$	266.097	−	86.4601i	0.298315	−	0.0969283i
$893$	−200.794			−0.224853
$894$	−907.732	+	572.749i	−1.01536	+	0.640659i
$895$	82.7954	+	401.623i	0.0925089	+	0.448741i
$896$	−43.5375	−	14.1462i	−0.0485909	−	0.0157882i
$897$	231.687	+	15.1832i	0.258291	+	0.0169266i
$898$	701.016	+	964.865i	0.780641	+	1.07446i
$899$			94.4947i			0.105111i
$900$	190.303	+	284.292i	0.211448	+	0.315880i
$901$	−1029.28			−1.14238
$902$	−86.3554	+	62.7409i	−0.0957377	+	0.0695575i
$903$	−52.1417	+	795.653i	−0.0577427	+	0.881122i
$904$	−192.046	+	591.058i	−0.212441	+	0.653825i
$905$	301.976	−	331.268i	0.333675	−	0.366042i
$906$	−172.522	−	273.425i	−0.190422	−	0.301793i
$907$		−	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
$909$	−0.360651	+	2.73985i	−0.000396756	+	0.00301414i
$910$	−214.974	−	377.679i	−0.236235	−	0.415032i
$911$	140.444	+	193.304i	0.154164	+	0.212189i	0.879112	−	0.476615i	$-0.158136\pi$
$911$	140.444	+	193.304i	0.154164	+	0.212189i	−0.724948	+	0.688804i	$0.758136\pi$
$912$	−62.3545	−	24.8762i	−0.0683711	−	0.0272765i
$913$	−237.635	+	327.077i	−0.260280	+	0.358244i
$914$	26.6664	+	36.7031i	0.0291755	+	0.0401566i
$915$	528.799	−	990.313i	0.577923	−	1.08231i
$916$	−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
$921$	819.690	+	53.7169i	0.890000	+	0.0583245i
$922$	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
$927$	−179.525	−	85.6245i	−0.193662	−	0.0923673i
$928$	66.8844	+	21.7321i	0.0720737	+	0.0234182i
$929$	498.160	+	161.862i	0.536232	+	0.174232i	0.564599	−	0.825365i	$-0.309031\pi$
$929$	498.160	+	161.862i	0.536232	+	0.174232i	−0.0283670	+	0.999598i	$0.509031\pi$
$930$	712.200	+	126.875i	0.765807	+	0.136424i
$931$	−33.6973	−	103.710i	−0.0361948	−	0.111396i
$932$	307.286			0.329706
$933$	−79.4327	+	50.1194i	−0.0851369	+	0.0537186i
$934$	−451.361	−	327.933i	−0.483256	−	0.351106i
$935$	−649.242	−	72.2683i	−0.694377	−	0.0772923i
$936$	1128.23	+	538.110i	1.20538	+	0.574904i
$937$	−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
$939$	−44.0575	−	36.6414i	−0.0469196	−	0.0390218i
$940$	57.4010	−	515.678i	0.0610649	−	0.548593i
$941$	−660.110	+	908.564i	−0.701498	+	0.965530i	0.298440	+	0.954428i	$0.403534\pi$
$941$	−660.110	+	908.564i	−0.701498	+	0.965530i	−0.999938	+	0.0111014i	$0.996466\pi$
$942$	−593.106	+	374.230i	−0.629624	+	0.397272i
$943$		−	41.2906i		−	0.0437864i
$944$	778.387	−	252.913i	0.824563	−	0.267917i
$945$	−147.215	−	442.538i	−0.155783	−	0.468294i
$946$	297.713	−	916.265i	0.314707	−	0.968568i
$947$	−134.922	+	415.247i	−0.142473	+	0.438487i	−0.996677	−	0.0814503i	$-0.974045\pi$
$947$	−134.922	+	415.247i	−0.142473	+	0.438487i	0.854204	+	0.519938i	$0.174045\pi$
$948$	218.775	−	263.054i	0.230775	−	0.277483i
$949$	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	−0.973206	−	0.229934i	$-0.926149\pi$
$953$	−48.3303	+	148.745i	−0.0507138	+	0.156081i	0.922492	+	0.386015i	$0.126149\pi$
$954$	161.821	+	873.010i	0.169624	+	0.915105i
$955$	−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
$960$	468.561	−	877.502i	0.488085	−	0.914065i
$961$	18.5744	−	13.4951i	0.0193282	−	0.0140427i
$962$	1280.83	+	930.575i	1.33142	+	0.967334i
$963$	−1242.57	−	163.562i	−1.29031	−	0.169846i
$964$	−291.788	+	211.996i	−0.302685	+	0.219913i
$965$	614.333	−	349.677i	0.636614	−	0.362360i
$966$	−29.2931	+	73.4260i	−0.0303241	+	0.0760103i
$967$	−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
$969$	−77.3764	−	122.631i	−0.0798518	−	0.126555i
$970$	−926.585	−	844.653i	−0.955242	−	0.870776i
$971$	−871.013	−	283.009i	−0.897026	−	0.291462i	−0.176017	−	0.984387i	$-0.556321\pi$
$971$	−871.013	−	283.009i	−0.897026	−	0.291462i	−0.721009	+	0.692926i	$0.756321\pi$
$972$	296.055	+	221.051i	0.304583	+	0.227419i
$973$	−344.500	−	474.163i	−0.354059	−	0.487321i
$974$			985.504i			1.01181i
$975$	1129.23	−	400.935i	1.15819	−	0.411216i
$976$	−569.279			−0.583278
$977$	−565.618	+	410.945i	−0.578933	+	0.420620i	−0.838339	−	0.545149i	$-0.816473\pi$
$977$	−565.618	+	410.945i	−0.578933	+	0.420620i	0.259406	+	0.965768i	$0.416473\pi$
$978$	730.506	+	47.8724i	0.746939	+	0.0489493i
$979$	338.372	−	1041.40i	0.345630	−	1.06374i
$980$	275.980	−	56.8938i	0.281612	−	0.0580549i
$981$	−658.931	−	625.277i	−0.671693	−	0.637387i
$982$		−	233.667i		−	0.237950i
$983$	106.423	+	327.536i	0.108263	+	0.333201i	0.990483	−	0.137639i	$-0.0439512\pi$
$983$	106.423	+	327.536i	0.108263	+	0.333201i	−0.882219	+	0.470839i	$0.843951\pi$
$984$	82.3700	−	206.468i	0.0837093	−	0.209825i
$985$	−488.825	+	100.772i	−0.496269	+	0.102307i
$986$	−46.9143	−	64.5720i	−0.0475804	−	0.0654889i
$987$	−262.106	+	656.992i	−0.265558	+	0.665646i
$988$	42.0095	−	57.8211i	0.0425197	−	0.0585233i
$989$	219.055	+	301.503i	0.221491	+	0.304856i
$990$	40.7764	+	562.033i	0.0411883	+	0.567710i
$991$	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
$996$	15.1642	−	231.397i	0.0152251	−	0.232326i
$997$	−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.14.6	✓	72
3.2	odd	2	inner	75.3.h.a.14.13	yes	72
5.2	odd	4		375.3.j.b.176.11		144
5.3	odd	4		375.3.j.b.176.26		144
5.4	even	2		375.3.h.a.74.13		72
15.2	even	4		375.3.j.b.176.25		144
15.8	even	4		375.3.j.b.176.12		144
15.14	odd	2		375.3.h.a.74.6		72
25.9	even	10	inner	75.3.h.a.59.13	yes	72
25.12	odd	20		375.3.j.b.326.25		144
25.13	odd	20		375.3.j.b.326.12		144
25.16	even	5		375.3.h.a.299.6		72
75.38	even	20		375.3.j.b.326.26		144
75.41	odd	10		375.3.h.a.299.13		72
75.59	odd	10	inner	75.3.h.a.59.6	yes	72
75.62	even	20		375.3.j.b.326.11		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.6	✓	72	1.1	even	1	trivial
75.3.h.a.14.13	yes	72	3.2	odd	2	inner
75.3.h.a.59.6	yes	72	75.59	odd	10	inner
75.3.h.a.59.13	yes	72	25.9	even	10	inner
375.3.h.a.74.6		72	15.14	odd	2
375.3.h.a.74.13		72	5.4	even	2
375.3.h.a.299.6		72	25.16	even	5
375.3.h.a.299.13		72	75.41	odd	10
375.3.j.b.176.11		144	5.2	odd	4
375.3.j.b.176.12		144	15.8	even	4
375.3.j.b.176.25		144	15.2	even	4
375.3.j.b.176.26		144	5.3	odd	4
375.3.j.b.326.11		144	75.62	even	20
375.3.j.b.326.12		144	25.13	odd	20
375.3.j.b.326.25		144	25.12	odd	20
375.3.j.b.326.26		144	75.38	even	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} +(0.196179 - 2.99358i) q^{3} +(-0.469852 + 1.44606i) q^{4} +(-2.47338 - 4.34538i) q^{5} +(2.52081 + 3.99515i) q^{6} -3.45468i q^{7} +(-2.68623 - 8.26736i) q^{8} +(-8.92303 - 1.17455i) q^{9} +(7.17279 + 3.24641i) q^{10} +(-4.67438 - 6.43373i) q^{11} +(4.23671 + 1.69023i) q^{12} +(9.39120 - 12.9259i) q^{13} +(3.19750 + 4.40098i) q^{14} +(-13.4935 + 6.55180i) 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} +(-10.3418 - 0.677734i) 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} +(-5.26662 + 26.4814i) q^{27} +(4.99566 + 1.62319i) q^{28} +(2.93429 + 0.953408i) q^{29} +(11.1255 - 20.8354i) q^{30} +(9.46440 + 29.1284i) q^{31} +22.7941 q^{32} +(-20.1769 + 12.7310i) q^{33} +(-20.9290 - 15.2058i) q^{34} +(-15.0119 + 8.54475i) q^{35} +(5.89098 - 12.3513i) q^{36} +(36.9883 - 50.9101i) q^{37} +(3.74791 + 2.72301i) q^{38} +(-36.8523 - 30.6491i) q^{39} +(-29.2808 + 32.1211i) q^{40} +(-5.01027 + 6.89605i) q^{41} +(13.8020 - 8.70859i) q^{42} -76.9353i q^{43} +(11.4998 - 3.73651i) q^{44} +(16.9662 + 41.6791i) q^{45} +(2.35708 - 7.25436i) q^{46} +(21.0904 - 64.9097i) q^{47} +(14.5910 - 17.5442i) 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} +(-17.8007 - 38.6097i) 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} +(-3.13433 - 22.5907i) q^{60} +(-60.5497 + 43.9919i) q^{61} +(-39.0169 - 28.3474i) q^{62} +(-4.05770 + 30.8262i) q^{63} +(-53.6522 + 38.9806i) q^{64} +(-79.3960 - 8.83771i) q^{65} +(13.9205 - 34.8931i) q^{66} +(-74.5516 + 24.2233i) q^{67} -24.9796 q^{68} +(7.75469 + 12.2902i) q^{69} +(11.2153 - 24.7797i) q^{70} +(35.3941 + 11.5002i) q^{71} +(14.2588 + 76.9250i) q^{72} +(8.18118 + 11.2604i) q^{73} +99.0901i q^{74} +(61.8447 + 42.4292i) q^{75} +4.47328 q^{76} +(-22.2264 + 16.1485i) q^{77} +(75.3143 + 4.93559i) q^{78} +(23.1785 - 71.3362i) q^{79} +(4.20735 - 37.7979i) q^{80} +(78.2409 + 20.9611i) q^{81} -13.4223i q^{82} +(-15.7098 - 48.3497i) q^{83} +(5.83918 - 14.6365i) q^{84} +(55.3386 - 60.7065i) q^{85} +(71.2080 + 98.0094i) q^{86} +(3.42975 - 8.59698i) q^{87} +(-40.6335 + 55.9272i) q^{88} +(80.9329 + 111.395i) q^{89} +(-60.1899 - 37.3926i) 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} +(4.47171 - 68.2359i) 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

Introduction

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