LMFDB - Embedded newform 75.3.h.a.14.17

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			14.17
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.79240 - 2.02880i) q^{2} +(-1.49624 - 2.60025i) q^{3} +(2.44541 - 7.52621i) q^{4} +(1.27184 + 4.83554i) q^{5} +(-9.45346 - 4.22537i) q^{6} +4.79411i q^{7} +(-4.17417 - 12.8468i) q^{8} +(-4.52255 + 7.78116i) q^{9} +(13.3618 + 10.9224i) q^{10} +(-3.78331 - 5.20729i) q^{11} +(-23.2289 + 4.90231i) q^{12} +(10.0282 - 13.8026i) q^{13} +(9.72627 + 13.3871i) q^{14} +(10.6706 - 10.5422i) q^{15} +(-12.1108 - 8.79899i) q^{16} +(7.53221 + 23.1818i) q^{17} +(3.15763 + 30.9035i) q^{18} +(-2.98003 - 9.17158i) q^{19} +(39.5034 + 2.25272i) q^{20} +(12.4659 - 7.17312i) q^{21} +(-21.1291 - 6.86525i) q^{22} +(-28.8553 + 20.9646i) q^{23} +(-27.1592 + 30.0757i) q^{24} +(-21.7648 + 12.3001i) q^{25} -58.8876i q^{26} +(26.9997 + 0.117285i) q^{27} +(36.0814 + 11.7236i) q^{28} +(-11.9737 - 3.89048i) q^{29} +(8.40858 - 51.0866i) q^{30} +(-16.0217 - 49.3096i) q^{31} +2.36210 q^{32} +(-7.87949 + 17.6289i) q^{33} +(68.0641 + 49.4514i) q^{34} +(-23.1821 + 6.09735i) q^{35} +(47.5031 + 53.0658i) q^{36} +(-16.7155 + 23.0069i) q^{37} +(-26.9287 - 19.5649i) q^{38} +(-50.8947 - 5.42377i) q^{39} +(56.8122 - 36.5234i) q^{40} +(-9.29508 + 12.7936i) q^{41} +(20.2568 - 45.3209i) q^{42} -8.20810i q^{43} +(-48.4429 + 15.7400i) q^{44} +(-43.3781 - 11.9725i) q^{45} +(-38.0427 + 117.083i) q^{46} +(-1.74488 + 5.37018i) q^{47} +(-4.75896 + 44.6564i) q^{48} +26.0166 q^{49} +(-35.8217 + 78.5032i) q^{50} +(49.0083 - 54.2710i) q^{51} +(-79.3583 - 109.227i) q^{52} +(-0.677064 + 2.08379i) q^{53} +(75.6321 - 54.4495i) q^{54} +(20.3682 - 24.9172i) q^{55} +(61.5888 - 20.0114i) q^{56} +(-19.3895 + 21.4717i) q^{57} +(-41.3282 + 13.4284i) q^{58} +(46.4201 - 63.8918i) q^{59} +(-53.2488 - 106.089i) q^{60} +(-13.8436 + 10.0580i) q^{61} +(-144.778 - 105.187i) q^{62} +(-37.3037 - 21.6816i) q^{63} +(55.0390 - 39.9882i) q^{64} +(79.4974 + 30.9369i) q^{65} +(13.7627 + 65.2128i) q^{66} +(13.6362 - 4.43067i) q^{67} +192.890 q^{68} +(97.6876 + 43.6629i) q^{69} +(-52.3633 + 64.0580i) q^{70} +(-18.4263 - 5.98707i) q^{71} +(118.841 + 25.6203i) q^{72} +(-76.5887 - 105.415i) q^{73} +98.1567i q^{74} +(64.5486 + 38.1900i) q^{75} -76.3146 q^{76} +(24.9643 - 18.1376i) q^{77} +(-153.122 + 88.1098i) q^{78} +(-5.48956 + 16.8951i) q^{79} +(27.1448 - 69.7530i) q^{80} +(-40.0930 - 70.3815i) q^{81} +54.5826i q^{82} +(10.3048 + 31.7148i) q^{83} +(-23.5022 - 111.362i) q^{84} +(-102.516 + 65.9059i) q^{85} +(-16.6526 - 22.9203i) q^{86} +(7.79923 + 36.9555i) q^{87} +(-51.1046 + 70.3395i) q^{88} +(-32.2511 - 44.3899i) q^{89} +(-145.419 + 54.5732i) q^{90} +(66.1712 + 48.0762i) q^{91} +(87.2210 + 268.439i) q^{92} +(-104.245 + 115.439i) q^{93} +(6.02261 + 18.5357i) q^{94} +(40.5594 - 26.0748i) q^{95} +(-3.53425 - 6.14203i) q^{96} +(149.045 + 48.4277i) q^{97} +(72.6486 - 52.7823i) q^{98} +(57.6290 - 5.88837i) 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 $

$2$	2.79240	−	2.02880i	1.39620	−	1.01440i	0.401048	−	0.916057i	$-0.368646\pi$
$2$	2.79240	−	2.02880i	1.39620	−	1.01440i	0.995153	−	0.0983417i	$-0.0313538\pi$
$3$	−1.49624	−	2.60025i	−0.498745	−	0.866748i
$3$	−1.49624	−	2.60025i	−0.498745	−	0.866748i
$4$	2.44541	−	7.52621i	0.611353	−	1.88155i
$5$	1.27184	+	4.83554i	0.254369	+	0.967107i
$5$	1.27184	+	4.83554i	0.254369	+	0.967107i
$6$	−9.45346	−	4.22537i	−1.57558	−	0.704228i
$7$			4.79411i			0.684872i	0.939541	+	0.342436i	$0.111252\pi$
$7$			4.79411i			0.684872i	−0.939541	+	0.342436i	$0.888748\pi$
$8$	−4.17417	−	12.8468i	−0.521771	−	1.60585i
$9$	−4.52255	+	7.78116i	−0.502506	+	0.864574i
$10$	13.3618	+	10.9224i	1.33618	+	1.09224i
$11$	−3.78331	−	5.20729i	−0.343938	−	0.473390i	0.601649	−	0.798761i	$-0.294511\pi$
$11$	−3.78331	−	5.20729i	−0.343938	−	0.473390i	−0.945586	+	0.325371i	$0.894511\pi$
$12$	−23.2289	+	4.90231i	−1.93574	+	0.408526i
$13$	10.0282	−	13.8026i	0.771399	−	1.06174i	−0.224780	−	0.974409i	$-0.572166\pi$
$13$	10.0282	−	13.8026i	0.771399	−	1.06174i	0.996179	−	0.0873303i	$-0.0278336\pi$
$14$	9.72627	+	13.3871i	0.694734	+	0.956219i
$15$	10.6706	−	10.5422i	0.711374	−	0.702814i
$16$	−12.1108	−	8.79899i	−0.756923	−	0.549937i
$17$	7.53221	+	23.1818i	0.443071	+	1.36363i	0.884585	+	0.466379i	$0.154442\pi$
$17$	7.53221	+	23.1818i	0.443071	+	1.36363i	−0.441514	+	0.897254i	$0.645558\pi$
$18$	3.15763	+	30.9035i	0.175424	+	1.71686i
$19$	−2.98003	−	9.17158i	−0.156844	−	0.482715i	0.841500	−	0.540258i	$-0.181673\pi$
$19$	−2.98003	−	9.17158i	−0.156844	−	0.482715i	−0.998343	+	0.0575432i	$0.981673\pi$
$20$	39.5034	+	2.25272i	1.97517	+	0.112636i
$21$	12.4659	−	7.17312i	0.593612	−	0.341577i
$22$	−21.1291	−	6.86525i	−0.960412	−	0.312057i
$23$	−28.8553	+	20.9646i	−1.25458	+	0.911506i	−0.998478	−	0.0551437i	$-0.982438\pi$
$23$	−28.8553	+	20.9646i	−1.25458	+	0.911506i	−0.256102	+	0.966650i	$0.582438\pi$
$24$	−27.1592	+	30.0757i	−1.13163	+	1.25315i
$25$	−21.7648	+	12.3001i	−0.870593	+	0.492004i
$26$		−	58.8876i		−	2.26491i
$27$	26.9997	+	0.117285i	0.999991	+	0.00434390i
$28$	36.0814	+	11.7236i	1.28862	+	0.418699i
$29$	−11.9737	−	3.89048i	−0.412885	−	0.134154i	0.0952067	−	0.995458i	$-0.469649\pi$
$29$	−11.9737	−	3.89048i	−0.412885	−	0.134154i	−0.508091	+	0.861303i	$0.669649\pi$
$30$	8.40858	−	51.0866i	0.280286	−	1.70289i
$31$	−16.0217	−	49.3096i	−0.516828	−	1.59063i	−0.779932	−	0.625865i	$-0.784746\pi$
$31$	−16.0217	−	49.3096i	−0.516828	−	1.59063i	0.263104	−	0.964768i	$-0.415254\pi$
$32$	2.36210			0.0738155
$33$	−7.87949	+	17.6289i	−0.238772	+	0.534208i
$34$	68.0641	+	49.4514i	2.00188	+	1.45445i
$35$	−23.1821	+	6.09735i	−0.662345	+	0.174210i
$36$	47.5031	+	53.0658i	1.31953	+	1.47405i
$37$	−16.7155	+	23.0069i	−0.451769	+	0.621807i	−0.972777	−	0.231745i	$-0.925556\pi$
$37$	−16.7155	+	23.0069i	−0.451769	+	0.621807i	0.521007	+	0.853552i	$0.325556\pi$
$38$	−26.9287	−	19.5649i	−0.708650	−	0.514865i
$39$	−50.8947	−	5.42377i	−1.30499	−	0.139071i
$40$	56.8122	−	36.5234i	1.42030	−	0.913086i
$41$	−9.29508	+	12.7936i	−0.226709	+	0.312039i	−0.907185	−	0.420732i	$-0.861773\pi$
$41$	−9.29508	+	12.7936i	−0.226709	+	0.312039i	0.680476	+	0.732771i	$0.261773\pi$
$42$	20.2568	−	45.3209i	0.482306	−	1.07907i
$43$		−	8.20810i		−	0.190886i	−0.995435	−	0.0954430i	$-0.969573\pi$
$43$		−	8.20810i		−	0.190886i	0.995435	−	0.0954430i	$-0.0304268\pi$
$44$	−48.4429	+	15.7400i	−1.10097	+	0.357728i
$45$	−43.3781	−	11.9725i	−0.963957	−	0.266057i
$46$	−38.0427	+	117.083i	−0.827015	+	2.54529i
$47$	−1.74488	+	5.37018i	−0.0371250	+	0.114259i	−0.967902	−	0.251329i	$-0.919132\pi$
$47$	−1.74488	+	5.37018i	−0.0371250	+	0.114259i	0.930777	+	0.365589i	$0.119132\pi$
$48$	−4.75896	+	44.6564i	−0.0991449	+	0.930341i
$49$	26.0166			0.530950
$50$	−35.8217	+	78.5032i	−0.716434	+	1.57006i
$51$	49.0083	−	54.2710i	0.960947	−	1.06414i
$52$	−79.3583	−	109.227i	−1.52612	−	2.10053i
$53$	−0.677064	+	2.08379i	−0.0127748	+	0.0393167i	−0.957241	−	0.289293i	$-0.906580\pi$
$53$	−0.677064	+	2.08379i	−0.0127748	+	0.0393167i	0.944466	+	0.328609i	$0.106580\pi$
$54$	75.6321	−	54.4495i	1.40059	−	1.00832i
$55$	20.3682	−	24.9172i	0.370332	−	0.453040i
$56$	61.5888	−	20.0114i	1.09980	−	0.357347i
$57$	−19.3895	+	21.4717i	−0.340167	+	0.376696i
$58$	−41.3282	+	13.4284i	−0.712556	+	0.231523i
$59$	46.4201	−	63.8918i	0.786782	−	1.08291i	−0.207720	−	0.978188i	$-0.566604\pi$
$59$	46.4201	−	63.8918i	0.786782	−	1.08291i	0.994501	−	0.104724i	$-0.0333958\pi$
$60$	−53.2488	−	106.089i	−0.887481	−	1.76815i
$61$	−13.8436	+	10.0580i	−0.226945	+	0.164885i	−0.695447	−	0.718577i	$-0.744794\pi$
$61$	−13.8436	+	10.0580i	−0.226945	+	0.164885i	0.468502	+	0.883462i	$0.344794\pi$
$62$	−144.778	−	105.187i	−2.33513	−	1.69657i
$63$	−37.3037	−	21.6816i	−0.592123	−	0.344152i
$64$	55.0390	−	39.9882i	0.859984	−	0.624815i
$65$	79.4974	+	30.9369i	1.22304	+	0.475952i
$66$	13.7627	+	65.2128i	0.208526	+	0.988072i
$67$	13.6362	−	4.43067i	0.203525	−	0.0661294i	−0.205480	−	0.978661i	$-0.565876\pi$
$67$	13.6362	−	4.43067i	0.203525	−	0.0661294i	0.409006	+	0.912532i	$0.365876\pi$
$68$	192.890			2.83662
$69$	97.6876	+	43.6629i	1.41576	+	0.632796i
$70$	−52.3633	+	64.0580i	−0.748048	+	0.915114i
$71$	−18.4263	−	5.98707i	−0.259526	−	0.0843250i	0.176364	−	0.984325i	$-0.443566\pi$
$71$	−18.4263	−	5.98707i	−0.259526	−	0.0843250i	−0.435890	+	0.900000i	$0.643566\pi$
$72$	118.841	+	25.6203i	1.65057	+	0.355838i
$73$	−76.5887	−	105.415i	−1.04916	−	1.44405i	−0.889534	−	0.456868i	$-0.848971\pi$
$73$	−76.5887	−	105.415i	−1.04916	−	1.44405i	−0.159626	−	0.987177i	$-0.551029\pi$
$74$			98.1567i			1.32644i
$75$	64.5486	+	38.1900i	0.860648	+	0.509201i
$76$	−76.3146			−1.00414
$77$	24.9643	−	18.1376i	0.324211	−	0.235553i
$78$	−153.122	+	88.1098i	−1.96311	+	1.12961i
$79$	−5.48956	+	16.8951i	−0.0694881	+	0.213862i	−0.979770	−	0.200126i	$-0.935865\pi$
$79$	−5.48956	+	16.8951i	−0.0694881	+	0.213862i	0.910282	+	0.413989i	$0.135865\pi$
$80$	27.1448	−	69.7530i	0.339310	−	0.871913i
$81$	−40.0930	−	70.3815i	−0.494976	−	0.868907i
$82$			54.5826i			0.665642i
$83$	10.3048	+	31.7148i	0.124154	+	0.382106i	0.993746	−	0.111664i	$-0.0356182\pi$
$83$	10.3048	+	31.7148i	0.124154	+	0.382106i	−0.869592	+	0.493771i	$0.835618\pi$
$84$	−23.5022	−	111.362i	−0.279788	−	1.32574i
$85$	−102.516	+	65.9059i	−1.20608	+	0.775363i
$86$	−16.6526	−	22.9203i	−0.193635	−	0.266515i
$87$	7.79923	+	36.9555i	0.0896463	+	0.424776i
$88$	−51.1046	+	70.3395i	−0.580734	+	0.799312i
$89$	−32.2511	−	44.3899i	−0.362372	−	0.498763i	0.588436	−	0.808544i	$-0.299744\pi$
$89$	−32.2511	−	44.3899i	−0.362372	−	0.498763i	−0.950808	+	0.309782i	$0.899744\pi$
$90$	−145.419	+	54.5732i	−1.61577	+	0.606369i
$91$	66.1712	+	48.0762i	0.727156	+	0.528310i
$92$	87.2210	+	268.439i	0.948054	+	2.91781i
$93$	−104.245	+	115.439i	−1.12091	+	1.24128i
$94$	6.02261	+	18.5357i	0.0640703	+	0.197188i
$95$	40.5594	−	26.0748i	0.426941	−	0.274472i
$96$	−3.53425	−	6.14203i	−0.0368151	−	0.0639795i
$97$	149.045	+	48.4277i	1.53655	+	0.499255i	0.950421	−	0.310965i	$-0.100652\pi$
$97$	149.045	+	48.4277i	1.53655	+	0.499255i	0.586126	+	0.810220i	$0.300652\pi$
$98$	72.6486	−	52.7823i	0.741313	−	0.538595i
$99$	57.6290	−	5.88837i	0.582111	−	0.0594785i
$100$	39.3491	+	193.885i	0.393491	+	1.93885i
$101$			92.0605i			0.911490i	0.890110	+	0.455745i	$0.150627\pi$
$101$			92.0605i			0.911490i	−0.890110	+	0.455745i	$0.849373\pi$
$102$	26.7459	−	250.974i	0.262215	−	2.46053i
$103$	174.917	+	56.8339i	1.69822	+	0.551786i	0.988304	−	0.152499i	$-0.0487320\pi$
$103$	174.917	+	56.8339i	1.69822	+	0.551786i	0.709918	+	0.704284i	$0.248732\pi$
$104$	−219.178	−	71.2154i	−2.10749	−	0.684764i
$105$	50.5405	+	51.1560i	0.481338	+	0.487200i
$106$	2.33695	+	7.19239i	0.0220467	+	0.0678528i
$107$	−32.7249			−0.305840			−0.152920	−	0.988239i	$-0.548868\pi$
$107$	−32.7249			−0.305840			−0.152920	+	0.988239i	$0.548868\pi$
$108$	66.9082	−	202.919i	0.619521	−	1.87888i
$109$	−42.7420	−	31.0538i	−0.392128	−	0.284898i	0.374199	−	0.927348i	$-0.377918\pi$
$109$	−42.7420	−	31.0538i	−0.392128	−	0.284898i	−0.766327	+	0.642451i	$0.777918\pi$
$110$	6.32429	−	110.902i	0.0574935	−	1.00820i
$111$	84.8338	+	9.04060i	0.764268	+	0.0814469i
$112$	42.1833	−	58.0603i	0.376637	−	0.518396i
$113$	4.49772	+	3.26779i	0.0398028	+	0.0289185i	0.607509	−	0.794313i	$-0.292169\pi$
$113$	4.49772	+	3.26779i	0.0398028	+	0.0289185i	−0.567706	+	0.823231i	$0.692169\pi$
$114$	−10.5817	+	99.2949i	−0.0928219	+	0.871008i
$115$	−138.075	−	112.867i	−1.20065	−	0.981455i
$116$	−58.5611	+	80.6024i	−0.504837	+	0.694848i
$117$	62.0474	+	140.454i	0.530320	+	1.20046i
$118$		−	272.589i		−	2.31007i
$119$	−111.136	+	36.1102i	−0.933915	+	0.303447i
$120$	−179.974	−	93.0778i	−1.49979	−	0.775649i
$121$	24.5887	−	75.6762i	0.203212	−	0.625423i
$122$	−18.2514	+	56.1719i	−0.149601	+	0.460425i
$123$	47.1741	+	5.02727i	0.383529	+	0.0408721i
$124$	−410.294			−3.30882
$125$	−87.1590	−	89.6008i	−0.697272	−	0.716806i
$126$	−148.155	+	15.1380i	−1.17583	+	0.120143i
$127$	−9.97381	−	13.7278i	−0.0785339	−	0.108093i	0.767943	−	0.640519i	$-0.221281\pi$
$127$	−9.97381	−	13.7278i	−0.0785339	−	0.108093i	−0.846477	+	0.532426i	$0.821281\pi$
$128$	69.6433	−	214.340i	0.544088	−	1.67453i
$129$	−21.3431	+	12.2813i	−0.165450	+	0.0952035i
$130$	284.753	−	74.8958i	2.19041	−	0.576122i
$131$	141.214	−	45.8832i	1.07797	−	0.350254i	0.284383	−	0.958711i	$-0.408211\pi$
$131$	141.214	−	45.8832i	1.07797	−	0.350254i	0.793587	+	0.608457i	$0.208211\pi$
$132$	113.410	+	102.413i	0.859166	+	0.775852i
$133$	43.9695	−	14.2866i	0.330598	−	0.107418i
$134$	29.0888	−	40.0373i	0.217080	−	0.298786i
$135$	33.7723	+	130.707i	0.250165	+	0.968203i
$136$	266.370	−	193.529i	1.95860	−	1.42301i
$137$	90.4373	+	65.7066i	0.660127	+	0.479610i	0.866706	−	0.498820i	$-0.166233\pi$
$137$	90.4373	+	65.7066i	0.660127	+	0.479610i	−0.206579	+	0.978430i	$0.566233\pi$
$138$	361.366	−	76.2641i	2.61860	−	0.552638i
$139$	−9.29046	+	6.74992i	−0.0668379	+	0.0485605i	−0.620702	−	0.784046i	$-0.713153\pi$
$139$	−9.29046	+	6.74992i	−0.0668379	+	0.0485605i	0.553865	+	0.832607i	$0.313153\pi$
$140$	−10.7998	+	189.384i	−0.0771414	+	1.35274i
$141$	16.5745	−	3.49795i	0.117550	−	0.0248082i
$142$	−63.6002	+	20.6650i	−0.447889	+	0.145528i
$143$	−109.814			−0.767930
$144$	123.238	−	54.4420i	0.855819	−	0.378069i
$145$	3.58392	−	62.8471i	0.0247167	−	0.433428i
$146$	−427.733	−	138.979i	−2.92968	−	0.951910i
$147$	−38.9269	−	67.6494i	−0.264809	−	0.460200i
$148$	132.278	+	182.065i	0.893771	+	1.23017i
$149$		−	24.7843i		−	0.166337i	−0.996535	−	0.0831687i	$-0.973496\pi$
$149$		−	24.7843i		−	0.166337i	0.996535	−	0.0831687i	$-0.0265040\pi$
$150$	257.725	−	24.3142i	1.71817	−	0.162094i
$151$	−50.5081			−0.334491			−0.167245	−	0.985915i	$-0.553487\pi$
$151$	−50.5081			−0.334491			−0.167245	+	0.985915i	$0.553487\pi$
$152$	−105.386	+	76.5675i	−0.693329	+	0.503733i
$153$	−214.446	−	46.2314i	−1.40161	−	0.302166i
$154$	32.9127	−	101.295i	0.213719	−	0.657759i
$155$	218.061	−	140.187i	1.40685	−	0.904435i
$156$	−165.279	+	369.781i	−1.05948	+	2.37039i
$157$			124.494i			0.792952i	0.918045	+	0.396476i	$0.129767\pi$
$157$			124.494i			0.792952i	−0.918045	+	0.396476i	$0.870233\pi$
$158$	18.9477	+	58.3151i	0.119922	+	0.369083i
$159$	6.43141	−	1.35731i	0.0404491	−	0.00853652i
$160$	3.00422	+	11.4220i	0.0187764	+	0.0713875i
$161$	−100.507	−	138.336i	−0.624265	−	0.859227i
$162$	−254.746	−	115.193i	−1.57250	−	0.711065i
$163$	−85.4298	+	117.584i	−0.524109	+	0.721374i	−0.986218	−	0.165449i	$-0.947093\pi$
$163$	−85.4298	+	117.584i	−0.524109	+	0.721374i	0.462109	+	0.886823i	$0.347093\pi$
$164$	73.5568	+	101.242i	0.448517	+	0.617331i
$165$	−95.2666	−	15.6804i	−0.577373	−	0.0950325i
$166$	93.1180	+	67.6542i	0.560952	+	0.407556i
$167$	−36.0606	−	110.983i	−0.215932	−	0.664569i	−0.999086	−	0.0427419i	$-0.986391\pi$
$167$	−36.0606	−	110.983i	−0.215932	−	0.664569i	0.783155	−	0.621827i	$-0.213609\pi$
$168$	−144.186	−	130.204i	−0.858250	−	0.775025i
$169$	−37.7238	−	116.102i	−0.223218	−	0.686994i
$170$	−152.557	+	392.021i	−0.897396	+	2.30600i
$171$	84.8429	+	18.2909i	0.496157	+	0.106964i
$172$	−61.7758	−	20.0722i	−0.359162	−	0.116699i
$173$	61.6697	−	44.8057i	0.356472	−	0.258992i	−0.395107	−	0.918635i	$-0.629292\pi$
$173$	61.6697	−	44.8057i	0.356472	−	0.258992i	0.751579	+	0.659643i	$0.229292\pi$
$174$	96.7538	+	87.3716i	0.556057	+	0.502135i
$175$	−58.9680	−	104.343i	−0.336960	−	0.596245i
$176$			96.3536i			0.547464i
$177$	−235.590	−	25.1064i	−1.33102	−	0.141844i
$178$	−180.116	−	58.5233i	−1.01189	−	0.328782i
$179$	−24.5279	−	7.96958i	−0.137027	−	0.0445228i	0.239701	−	0.970847i	$-0.422951\pi$
$179$	−24.5279	−	7.96958i	−0.137027	−	0.0445228i	−0.376728	+	0.926324i	$0.622951\pi$
$180$	−196.185	+	297.195i	−1.08992	+	1.65108i
$181$	45.9748	+	141.496i	0.254004	+	0.781745i	0.994024	+	0.109160i	$0.0348160\pi$
$181$	45.9748	+	141.496i	0.254004	+	0.781745i	−0.740020	+	0.672585i	$0.765184\pi$
$182$	282.313			1.55117
$183$	46.8666	+	20.9477i	0.256102	+	0.114468i
$184$	389.775	+	283.188i	2.11834	+	1.53907i
$185$	−132.510	−	51.5671i	−0.716270	−	0.278741i
$186$	−56.8909	+	533.844i	−0.305865	+	2.87013i
$187$	92.2174	−	126.926i	0.493141	−	0.678750i
$188$	36.1501	+	26.2646i	0.192288	+	0.139705i
$189$	−0.562279	+	129.440i	−0.00297502	+	0.684866i
$190$	60.3574	−	155.098i	0.317671	−	0.816306i
$191$	−9.46693	+	13.0301i	−0.0495651	+	0.0682205i	−0.833080	−	0.553152i	$-0.813425\pi$
$191$	−9.46693	+	13.0301i	−0.0495651	+	0.0682205i	0.783515	+	0.621373i	$0.213425\pi$
$192$	−186.330	−	83.2832i	−0.970471	−	0.433766i
$193$			199.019i			1.03119i	0.856834	+	0.515593i	$0.172428\pi$
$193$			199.019i			1.03119i	−0.856834	+	0.515593i	$0.827572\pi$
$194$	514.444	−	167.153i	2.65177	−	0.861613i
$195$	−38.5033	−	253.002i	−0.197453	−	1.29744i
$196$	63.6212	−	195.806i	0.324598	−	0.999010i
$197$	−10.3055	+	31.7172i	−0.0523123	+	0.161001i	−0.973800	−	0.227408i	$-0.926975\pi$
$197$	−10.3055	+	31.7172i	−0.0523123	+	0.161001i	0.921487	+	0.388408i	$0.126975\pi$
$198$	148.977	−	133.360i	0.752409	−	0.673537i
$199$	−210.659			−1.05859			−0.529293	−	0.848439i	$-0.677543\pi$
$199$	−210.659			−1.05859			−0.529293	+	0.848439i	$0.677543\pi$
$200$	248.867	+	228.265i	1.24433	+	1.14133i
$201$	−31.9238	−	28.8281i	−0.158825	−	0.143423i
$202$	186.772	+	257.070i	0.924615	+	1.27262i
$203$	18.6514	−	57.4030i	0.0918786	−	0.282773i
$204$	−288.609	−	501.562i	−1.41475	−	2.45864i
$205$	−73.6857	−	28.6753i	−0.359443	−	0.139879i
$206$	603.742	−	196.168i	2.93079	−	0.952271i
$207$	−32.6295	−	319.342i	−0.157630	−	1.54271i
$208$	−242.898	+	78.9224i	−1.16778	+	0.379435i
$209$	−36.4847	+	50.2168i	−0.174568	+	0.240272i
$210$	244.914	+	40.3116i	1.16626	+	0.191960i
$211$	−98.7969	+	71.7801i	−0.468232	+	0.340190i	−0.796752	−	0.604307i	$-0.793450\pi$
$211$	−98.7969	+	71.7801i	−0.468232	+	0.340190i	0.328520	+	0.944497i	$0.393450\pi$
$212$	14.0273	+	10.1914i	0.0661666	+	0.0480728i
$213$	12.0023	+	56.8710i	0.0563487	+	0.267000i
$214$	−91.3810	+	66.3922i	−0.427014	+	0.310244i
$215$	39.6906	−	10.4394i	0.184607	−	0.0485554i
$216$	−111.195	−	347.349i	−0.514791	−	1.60810i
$217$	236.395	−	76.8095i	1.08938	−	0.353961i
$218$	−182.355			−0.836489
$219$	−159.511	+	356.876i	−0.728360	+	1.62957i
$220$	−137.723	−	214.228i	−0.626015	−	0.973765i
$221$	395.504	+	128.507i	1.78961	+	0.581479i
$222$	255.231	−	146.866i	1.14969	−	0.661557i
$223$	−13.5458	−	18.6442i	−0.0607437	−	0.0836065i	0.777564	−	0.628803i	$-0.216455\pi$
$223$	−13.5458	−	18.6442i	−0.0607437	−	0.0836065i	−0.838308	+	0.545197i	$0.816455\pi$
$224$			11.3241i			0.0505542i
$225$	2.72352	−	224.984i	0.0121045	−	0.999927i
$226$	19.1891			0.0849076
$227$	−43.3598	+	31.5027i	−0.191012	+	0.138779i	−0.679181	−	0.733971i	$-0.737665\pi$
$227$	−43.3598	+	31.5027i	−0.191012	+	0.138779i	0.488169	+	0.872749i	$0.337665\pi$
$228$	114.185	+	198.437i	0.500810	+	0.870336i
$229$	88.7679	−	273.199i	0.387633	−	1.19301i	−0.546920	−	0.837185i	$-0.684200\pi$
$229$	88.7679	−	273.199i	0.387633	−	1.19301i	0.934552	−	0.355826i	$-0.115800\pi$
$230$	−614.545	−	35.0451i	−2.67194	−	0.152370i
$231$	−84.5147	−	37.7751i	−0.365864	−	0.163529i
$232$			170.062i			0.733027i
$233$	124.366	+	382.758i	0.533758	+	1.64274i	0.746318	+	0.665589i	$0.231820\pi$
$233$	124.366	+	382.758i	0.533758	+	1.64274i	−0.212561	+	0.977148i	$0.568180\pi$
$234$	458.214	+	266.322i	1.95818	+	1.13813i
$235$	−28.1869	−	1.60739i	−0.119944	−	0.00683994i
$236$	−367.347	−	505.609i	−1.55655	−	2.14241i
$237$	52.1451	−	11.0049i	0.220022	−	0.0464342i
$238$	−237.075	+	326.306i	−0.996115	+	1.37104i
$239$	−148.380	−	204.228i	−0.620838	−	0.854510i	0.376575	−	0.926386i	$-0.377102\pi$
$239$	−148.380	−	204.228i	−0.620838	−	0.854510i	−0.997414	+	0.0718756i	$0.977102\pi$
$240$	−221.990	+	33.7838i	−0.924959	+	0.140766i
$241$	−26.1809	−	19.0215i	−0.108634	−	0.0789275i	0.532142	−	0.846655i	$-0.321387\pi$
$241$	−26.1809	−	19.0215i	−0.108634	−	0.0789275i	−0.640776	+	0.767728i	$0.721387\pi$
$242$	−84.8703	−	261.204i	−0.350704	−	1.07935i
$243$	−123.020	+	209.559i	−0.506257	+	0.862383i
$244$	41.8451	+	128.786i	0.171496	+	0.527812i
$245$	33.0890	+	125.804i	0.135057	+	0.513486i
$246$	141.928	−	81.6685i	0.576944	−	0.331986i
$247$	−156.476	−	50.8422i	−0.633506	−	0.205839i
$248$	−566.592	+	411.653i	−2.28465	+	1.65989i
$249$	67.0480	−	74.2478i	0.269269	−	0.298184i
$250$	−425.165	−	73.3733i	−1.70066	−	0.293493i
$251$			405.814i			1.61679i	0.588641	+	0.808394i	$0.299663\pi$
$251$			405.814i			1.61679i	−0.588641	+	0.808394i	$0.700337\pi$
$252$	−254.403	+	227.735i	−1.00954	+	0.903711i
$253$	218.338	+	70.9422i	0.862995	+	0.280404i
$254$	−55.7017	−	18.0986i	−0.219298	−	0.0712543i
$255$	324.760	+	167.957i	1.27357	+	0.658656i
$256$	−156.289	−	481.007i	−0.610502	−	1.87893i
$257$	−332.036			−1.29197			−0.645984	−	0.763351i	$-0.723553\pi$
$257$	−332.036			−1.29197			−0.645984	+	0.763351i	$0.723553\pi$
$258$	−34.6822	+	77.5950i	−0.134427	+	0.300756i
$259$	−110.297	−	80.1357i	−0.425858	−	0.309404i
$260$	427.241	−	522.660i	1.64324	−	2.01023i
$261$	84.4239	−	75.5741i	0.323463	−	0.289556i
$262$	301.238	−	414.619i	1.14976	−	1.58252i
$263$	−338.632	−	246.031i	−1.28757	−	0.935477i	−0.287821	−	0.957684i	$-0.592931\pi$
$263$	−338.632	−	246.031i	−1.28757	−	0.935477i	−0.999753	+	0.0222068i	$0.992931\pi$
$264$	259.365	+	27.6401i	0.982441	+	0.104697i
$265$	−10.9373	−	0.623713i	−0.0412730	−	0.00235364i
$266$	93.7960	−	129.099i	0.352616	−	0.485335i
$267$	−67.1692	+	150.279i	−0.251570	+	0.562841i
$268$		−	113.464i		−	0.423372i
$269$	−43.7184	+	14.2050i	−0.162522	+	0.0528066i	−0.389148	−	0.921175i	$-0.627231\pi$
$269$	−43.7184	+	14.2050i	−0.162522	+	0.0528066i	0.226626	+	0.973982i	$0.427231\pi$
$270$	359.485	+	296.470i	1.33143	+	1.09804i
$271$	−120.577	+	371.096i	−0.444932	+	1.36936i	0.437626	+	0.899157i	$0.355819\pi$
$271$	−120.577	+	371.096i	−0.444932	+	1.36936i	−0.882558	+	0.470203i	$0.844181\pi$
$272$	112.755	−	347.025i	0.414541	−	1.27583i
$273$	26.0021	−	243.995i	0.0952459	−	0.893754i
$274$	385.843			1.40818
$275$	146.393	+	66.8005i	0.532339	+	0.242911i
$276$	567.503	−	628.443i	2.05617	−	2.27697i
$277$	204.852	+	281.954i	0.739536	+	1.01788i	0.998645	+	0.0520364i	$0.0165712\pi$
$277$	204.852	+	281.954i	0.739536	+	1.01788i	−0.259109	+	0.965848i	$0.583429\pi$
$278$	−12.2485	+	37.6969i	−0.0440593	+	0.135601i
$279$	456.145	+	98.3381i	1.63493	+	0.352466i
$280$	175.097	+	272.363i	0.625347	+	0.972727i
$281$	−382.974	+	124.436i	−1.36290	+	0.442832i	−0.897009	−	0.442012i	$-0.854265\pi$
$281$	−382.974	+	124.436i	−1.36290	+	0.442832i	−0.465888	+	0.884844i	$0.654265\pi$
$282$	39.1861	−	43.3941i	0.138958	−	0.153880i
$283$	224.653	−	72.9942i	0.793827	−	0.257930i	0.116094	−	0.993238i	$-0.462963\pi$
$283$	224.653	−	72.9942i	0.793827	−	0.257930i	0.677733	+	0.735308i	$0.262963\pi$
$284$	−90.1199	+	124.039i	−0.317324	+	0.436758i
$285$	−128.487	−	66.4502i	−0.450833	−	0.233159i
$286$	−306.645	+	222.790i	−1.07218	+	0.778987i
$287$	−61.3338	−	44.5616i	−0.213707	−	0.155267i
$288$	−10.6827	+	18.3799i	−0.0370927	+	0.0638189i
$289$	−246.854	+	179.350i	−0.854167	+	0.620588i
$290$	−117.496	−	182.765i	−0.405160	−	0.630226i
$291$	−97.0828	−	460.013i	−0.333618	−	1.58080i
$292$	−980.669	+	318.639i	−3.35845	+	1.09123i
$293$	392.633			1.34005			0.670023	−	0.742341i	$-0.266284\pi$
$293$	392.633			1.34005			0.670023	+	0.742341i	$0.266284\pi$
$294$	−245.947	−	109.929i	−0.836553	−	0.373910i
$295$	367.990	+	143.206i	1.24742	+	0.485443i
$296$	365.337	+	118.705i	1.23425	+	0.401031i
$297$	−101.538	−	141.039i	−0.341878	−	0.474879i
$298$	−50.2823	−	69.2076i	−0.168732	−	0.232240i
$299$			608.517i			2.03517i
$300$	445.274	−	392.416i	1.48425	−	1.30805i
$301$	39.3505			0.130733
$302$	−141.039	+	102.471i	−0.467016	+	0.339307i
$303$	239.380	−	137.744i	0.790033	−	0.454602i
$304$	−44.6102	+	137.296i	−0.146744	+	0.451632i
$305$	−66.2427	−	54.1492i	−0.217189	−	0.177538i
$306$	−692.613	+	305.971i	−2.26344	+	0.999905i
$307$		−	21.4763i		−	0.0699554i	−0.999388	−	0.0349777i	$-0.988864\pi$
$307$		−	21.4763i		−	0.0699554i	0.999388	−	0.0349777i	$-0.0111360\pi$
$308$	−75.4594	−	232.240i	−0.244998	−	0.754027i
$309$	−113.935	−	539.864i	−0.368721	−	1.74713i
$310$	324.503	−	833.862i	1.04678	−	2.68988i
$311$	11.2806	+	15.5264i	0.0362720	+	0.0499241i	0.826768	−	0.562543i	$-0.190177\pi$
$311$	11.2806	+	15.5264i	0.0362720	+	0.0499241i	−0.790496	+	0.612467i	$0.790177\pi$
$312$	142.765	+	676.473i	0.457581	+	2.16818i
$313$	288.515	−	397.107i	0.921774	−	1.26871i	−0.0412095	−	0.999151i	$-0.513121\pi$
$313$	288.515	−	397.107i	0.921774	−	1.26871i	0.962983	−	0.269562i	$-0.0868789\pi$
$314$	252.572	+	347.636i	0.804370	+	1.10712i
$315$	57.3976	−	207.959i	0.182215	−	0.660188i
$316$	113.732	+	82.6311i	0.359911	+	0.261491i
$317$	−60.0015	−	184.666i	−0.189279	−	0.582541i	0.810717	−	0.585439i	$-0.199078\pi$
$317$	−60.0015	−	184.666i	−0.189279	−	0.582541i	−0.999996	+	0.00289745i	$0.999078\pi$
$318$	15.2054	−	16.8382i	0.0478156	−	0.0529502i
$319$	25.0413	+	77.0691i	0.0784993	+	0.241596i
$320$	263.365	+	215.284i	0.823017	+	0.672764i
$321$	48.9642	+	85.0928i	0.152536	+	0.265087i
$322$	−561.310	−	182.381i	−1.74320	−	0.566399i
$323$	190.167	−	138.165i	0.588753	−	0.427754i
$324$	−627.749	+	129.637i	−1.93750	+	0.400113i
$325$	−48.4883	+	423.759i	−0.149195	+	1.30387i
$326$			501.661i			1.53884i
$327$	−16.7956	+	157.603i	−0.0513625	+	0.481968i
$328$	203.156	+	66.0092i	0.619377	+	0.201248i
$329$	−25.7452	−	8.36513i	−0.0782529	−	0.0254259i
$330$	−297.835	+	149.491i	−0.902529	+	0.453002i
$331$	46.5225	+	143.182i	0.140551	+	0.432573i	0.996412	−	0.0846337i	$-0.0269720\pi$
$331$	46.5225	+	143.182i	0.140551	+	0.432573i	−0.855861	+	0.517206i	$0.826972\pi$
$332$	263.892			0.794855
$333$	−103.424	−	234.115i	−0.310581	−	0.703050i
$334$	−325.858	−	236.749i	−0.975622	−	0.708831i
$335$	38.7678	+	60.3032i	0.115725	+	0.180010i
$336$	−214.087	−	22.8149i	−0.637164	−	0.0679016i
$337$	20.2430	−	27.8621i	0.0600683	−	0.0826769i	−0.777926	−	0.628356i	$-0.783728\pi$
$337$	20.2430	−	27.8621i	0.0600683	−	0.0826769i	0.837994	+	0.545679i	$0.183728\pi$
$338$	−340.887	−	247.669i	−1.00854	−	0.732749i
$339$	1.76739	−	16.5846i	0.00521354	−	0.0489220i
$340$	245.326	+	932.727i	0.721547	+	2.74332i
$341$	−196.154	+	269.983i	−0.575232	+	0.791739i
$342$	274.024	−	121.054i	0.801239	−	0.353958i
$343$			359.637i			1.04851i
$344$	−105.448	+	34.2620i	−0.306534	+	0.0995988i
$345$	−86.8903	+	527.905i	−0.251856	+	1.53016i
$346$	81.3049	−	250.231i	0.234985	−	0.723210i
$347$	155.034	−	477.144i	0.446783	−	1.37506i	−0.433734	−	0.901041i	$-0.642804\pi$
$347$	155.034	−	477.144i	0.446783	−	1.37506i	0.880517	−	0.474015i	$-0.157196\pi$
$348$	297.207	+	31.6729i	0.854044	+	0.0910141i
$349$	295.702			0.847282			0.423641	−	0.905830i	$-0.360752\pi$
$349$	295.702			0.847282			0.423641	+	0.905830i	$0.360752\pi$
$350$	−376.353	−	171.733i	−1.07529	−	0.490666i
$351$	272.377	−	371.491i	0.776004	−	1.05838i
$352$	−8.93655	−	12.3001i	−0.0253879	−	0.0349435i
$353$	105.425	−	324.465i	0.298655	−	0.919165i	−0.683315	−	0.730124i	$-0.739462\pi$
$353$	105.425	−	324.465i	0.298655	−	0.919165i	0.981969	−	0.189041i	$-0.0605378\pi$
$354$	−708.797	+	407.857i	−2.00225	+	1.15214i
$355$	5.51531	−	96.7157i	0.0155361	−	0.272439i
$356$	−412.955	+	134.177i	−1.15998	+	0.376902i
$357$	260.181	+	234.951i	0.728798	+	0.658126i
$358$	−84.6603	+	27.5078i	−0.236481	+	0.0768374i
$359$	−33.1665	+	45.6498i	−0.0923858	+	0.127158i	−0.852708	−	0.522388i	$-0.825041\pi$
$359$	−33.1665	+	45.6498i	−0.0923858	+	0.127158i	0.760322	+	0.649546i	$0.225041\pi$
$360$	27.2589	+	607.244i	0.0757193	+	1.68679i
$361$	216.818	−	157.527i	0.600603	−	0.436364i
$362$	415.446	+	301.839i	1.14764	+	0.833810i
$363$	−233.567	+	49.2929i	−0.643436	+	0.135793i
$364$	523.647	−	380.452i	1.43859	−	1.04520i
$365$	412.331	−	504.419i	1.12967	−	1.38197i
$366$	173.369	−	36.5884i	0.473686	−	0.0999684i
$367$	−607.364	+	197.344i	−1.65494	+	0.537723i	−0.979803	−	0.199967i	$-0.935917\pi$
$367$	−607.364	+	197.344i	−1.65494	+	0.537723i	−0.675139	+	0.737690i	$0.735917\pi$
$368$	533.928			1.45089
$369$	−57.5115	−	130.186i	−0.155858	−	0.352808i
$370$	−474.640	+	124.840i	−1.28281	+	0.337405i
$371$	−9.98990	−	3.24591i	−0.0269269	−	0.00874909i
$372$	613.897	+	1066.86i	1.65026	+	2.86792i
$373$	−139.077	−	191.423i	−0.372859	−	0.513197i	0.580816	−	0.814035i	$-0.302734\pi$
$373$	−139.077	−	191.423i	−0.372859	−	0.513197i	−0.953675	+	0.300838i	$0.902734\pi$
$374$		−	541.519i		−	1.44791i
$375$	−102.574	+	360.699i	−0.273530	+	0.961864i
$376$	76.2729			0.202853
$377$	−173.773	+	126.253i	−0.460936	+	0.334890i
$378$	261.037	+	362.588i	0.690573	+	0.959228i
$379$	−36.7734	+	113.177i	−0.0970276	+	0.298620i	−0.987777	−	0.155875i	$-0.950180\pi$
$379$	−36.7734	+	113.177i	−0.0970276	+	0.298620i	0.890749	+	0.454495i	$0.150180\pi$
$380$	−97.0602	−	369.022i	−0.255422	−	0.971111i
$381$	−20.7724	+	46.4743i	−0.0545207	+	0.121980i
$382$			55.5918i			0.145528i
$383$	232.170	+	714.546i	0.606188	+	1.86565i	0.488410	+	0.872614i	$0.337577\pi$
$383$	232.170	+	714.546i	0.606188	+	1.86565i	0.117778	+	0.993040i	$0.462423\pi$
$384$	−661.540	+	139.614i	−1.72276	+	0.363577i
$385$	119.456	+	97.6475i	0.310275	+	0.253630i
$386$	403.769	+	555.740i	1.04603	+	1.43974i
$387$	63.8686	+	37.1216i	0.165035	+	0.0959213i
$388$	728.954	−	1003.32i	1.87875	−	2.58587i
$389$	−122.928	−	169.196i	−0.316010	−	0.434951i	0.621233	−	0.783626i	$-0.286632\pi$
$389$	−122.928	−	169.196i	−0.316010	−	0.434951i	−0.937244	+	0.348674i	$0.886632\pi$
$390$	−620.806	−	628.366i	−1.59181	−	1.61120i
$391$	−703.342	−	511.008i	−1.79883	−	1.30693i
$392$	−108.598	−	334.229i	−0.277034	−	0.852625i
$393$	−330.597	−	298.539i	−0.841214	−	0.759641i
$394$	35.5705	+	109.475i	0.0902806	+	0.277855i
$395$	−88.6788	−	5.05700i	−0.224503	−	0.0128025i
$396$	96.6096	−	448.127i	0.243964	−	1.13163i
$397$	372.824	+	121.138i	0.939104	+	0.305133i	0.738280	−	0.674494i	$-0.235638\pi$
$397$	372.824	+	121.138i	0.939104	+	0.305133i	0.200824	+	0.979627i	$0.435638\pi$
$398$	−588.243	+	427.384i	−1.47800	+	1.07383i
$399$	−102.937	−	92.9555i	−0.257988	−	0.232971i
$400$	371.817	+	42.5449i	0.929543	+	0.106362i
$401$		−	453.902i		−	1.13193i	−0.824431	−	0.565963i	$-0.808504\pi$
$401$		−	453.902i		−	1.13193i	0.824431	−	0.565963i	$-0.191496\pi$
$402$	−147.630	−	15.7327i	−0.367240	−	0.0391362i
$403$	−841.270	−	273.345i	−2.08752	−	0.678276i
$404$	692.866	+	225.126i	1.71502	+	0.557242i
$405$	289.340	−	283.386i	0.714420	−	0.699717i
$406$	−64.3770	−	198.132i	−0.158564	−	0.488010i
$407$	183.043			0.449737
$408$	−901.777	−	403.062i	−2.21024	−	0.987898i
$409$	181.431	+	131.817i	0.443597	+	0.322292i	0.787063	−	0.616873i	$-0.211601\pi$
$409$	181.431	+	131.817i	0.443597	+	0.322292i	−0.343466	+	0.939165i	$0.611601\pi$
$410$	−263.936	+	69.4206i	−0.643747	+	0.169319i
$411$	35.5376	−	333.472i	0.0864661	−	0.811367i
$412$	855.488	−	1177.48i	2.07643	−	2.85796i
$413$	306.304	+	222.543i	0.741656	+	0.538845i
$414$	−738.995	−	825.532i	−1.78501	−	1.99404i
$415$	−140.252	+	90.1654i	−0.337957	+	0.217266i
$416$	23.6875	−	32.6031i	0.0569412	−	0.0783728i
$417$	31.4522	+	14.0580i	0.0754249	+	0.0337123i
$418$			214.245i			0.512549i
$419$	−41.6295	+	13.5262i	−0.0993543	+	0.0322822i	−0.358272	−	0.933617i	$-0.616634\pi$
$419$	−41.6295	+	13.5262i	−0.0993543	+	0.0322822i	0.258918	+	0.965899i	$0.416634\pi$
$420$	508.603	−	255.281i	1.21096	−	0.607811i
$421$	−164.969	+	507.723i	−0.391851	+	1.20599i	0.539536	+	0.841963i	$0.318600\pi$
$421$	−164.969	+	507.723i	−0.391851	+	1.20599i	−0.931387	+	0.364031i	$0.881400\pi$
$422$	−130.253	+	400.878i	−0.308657	+	0.949947i
$423$	−33.8950	−	37.8641i	−0.0801299	−	0.0895132i
$424$	29.5961			0.0698022
$425$	−449.075	−	411.900i	−1.05665	−	0.969177i
$426$	148.895	+	134.456i	0.349519	+	0.315626i
$427$	−48.2191	−	66.3679i	−0.112925	−	0.155428i
$428$	−80.0259	+	246.294i	−0.186976	+	0.575454i
$429$	164.308	+	285.543i	0.383002	+	0.665602i
$430$	89.6525	−	109.675i	0.208494	−	0.255059i
$431$	397.203	−	129.059i	0.921584	−	0.299441i	0.190468	−	0.981693i	$-0.439000\pi$
$431$	397.203	−	129.059i	0.921584	−	0.299441i	0.731116	+	0.682253i	$0.239000\pi$
$432$	−325.956	−	238.991i	−0.754527	−	0.553220i
$433$	647.730	−	210.460i	1.49591	−	0.486052i	0.557090	−	0.830452i	$-0.311918\pi$
$433$	647.730	−	210.460i	1.49591	−	0.486052i	0.938823	+	0.344400i	$0.111918\pi$
$434$	504.280	−	694.082i	1.16193	−	1.59927i
$435$	−168.780	+	84.7151i	−0.388001	+	0.194747i
$436$	−338.239	+	245.745i	−0.775778	+	0.563636i
$437$	278.269	+	202.174i	0.636770	+	0.462641i
$438$	278.610	+	1320.16i	0.636097	+	3.01405i
$439$	188.505	−	136.957i	0.429396	−	0.311975i	−0.352011	−	0.935996i	$-0.614502\pi$
$439$	188.505	−	136.957i	0.429396	−	0.311975i	0.781407	+	0.624021i	$0.214502\pi$
$440$	−405.126	−	157.657i	−0.920742	−	0.358312i
$441$	−117.661	+	202.439i	−0.266806	+	0.459045i
$442$	1365.12	−	443.554i	3.08850	−	1.00352i
$443$	−171.589			−0.387334			−0.193667	−	0.981067i	$-0.562038\pi$
$443$	−171.589			−0.387334			−0.193667	+	0.981067i	$0.562038\pi$
$444$	275.495	−	616.368i	0.620484	−	1.38822i
$445$	173.630	−	212.408i	0.390181	−	0.477322i
$446$	−75.6508	−	24.5804i	−0.169621	−	0.0551131i
$447$	−64.4452	+	37.0831i	−0.144173	+	0.0829600i
$448$	191.708	+	263.863i	0.427919	+	0.588979i
$449$		−	55.7697i		−	0.124209i	−0.998070	−	0.0621044i	$-0.980219\pi$
$449$		−	55.7697i		−	0.124209i	0.998070	−	0.0621044i	$-0.0197812\pi$
$450$	−448.841	−	633.770i	−0.997424	−	1.40838i
$451$	101.786			0.225690
$452$	35.5928	−	25.8597i	0.0787452	−	0.0572117i
$453$	75.5721	+	131.333i	0.166826	+	0.289919i
$454$	−57.1652	+	175.936i	−0.125915	+	0.387525i
$455$	−148.315	+	381.119i	−0.325966	+	0.837623i
$456$	356.777	+	159.467i	0.782405	+	0.349708i
$457$		−	450.546i		−	0.985878i	−0.870064	−	0.492939i	$-0.835923\pi$
$457$		−	450.546i		−	0.985878i	0.870064	−	0.492939i	$-0.164077\pi$
$458$	−306.391	−	942.974i	−0.668976	−	2.05890i
$459$	200.649	+	626.785i	0.437144	+	1.36555i
$460$	−1187.11	+	763.172i	−2.58068	+	1.65907i
$461$	−354.983	−	488.592i	−0.770028	−	1.05985i	−0.996313	−	0.0857918i	$-0.972658\pi$
$461$	−354.983	−	488.592i	−0.770028	−	1.05985i	0.226285	−	0.974061i	$-0.427342\pi$
$462$	−312.637	+	65.9800i	−0.676703	+	0.142814i
$463$	−175.681	+	241.804i	−0.379440	+	0.522254i	−0.955436	−	0.295198i	$-0.904614\pi$
$463$	−175.681	+	241.804i	−0.379440	+	0.522254i	0.575996	+	0.817452i	$0.304614\pi$
$464$	110.778	+	152.473i	0.238746	+	0.328605i
$465$	−690.793	−	357.259i	−1.48558	−	0.768300i
$466$	1123.82	+	816.500i	2.41162	+	1.75215i
$467$	−5.00217	−	15.3951i	−0.0107113	−	0.0329660i	0.945558	−	0.325454i	$-0.105517\pi$
$467$	−5.00217	−	15.3951i	−0.0107113	−	0.0329660i	−0.956269	+	0.292488i	$0.905517\pi$
$468$	1208.82	−	123.514i	2.58294	−	0.263918i
$469$	21.2411	+	65.3733i	0.0452902	+	0.139389i
$470$	−81.9702	+	52.6971i	−0.174405	+	0.112121i
$471$	323.714	−	186.272i	0.687290	−	0.395481i
$472$	−1014.57	−	329.654i	−2.14951	−	0.698418i
$473$	−42.7419	+	31.0538i	−0.0903634	+	0.0656529i
$474$	123.283	−	136.522i	0.260092	−	0.288021i
$475$	177.671	+	162.963i	0.374044	+	0.343080i
$476$			924.736i			1.94272i
$477$	−13.1522	−	14.6924i	−0.0275728	−	0.0308016i
$478$	−828.675	−	269.253i	−1.73363	−	0.563290i
$479$	−163.124	−	53.0022i	−0.340551	−	0.110652i	0.133748	−	0.991015i	$-0.457299\pi$
$479$	−163.124	−	53.0022i	−0.340551	−	0.110652i	−0.474299	+	0.880364i	$0.657299\pi$
$480$	25.2050	−	24.9017i	0.0525104	−	0.0518786i
$481$	149.929	+	461.434i	0.311703	+	0.959323i
$482$	−111.698			−0.231739
$483$	−209.325	+	468.325i	−0.433385	+	0.969617i
$484$	−509.425	−	370.119i	−1.05253	−	0.764709i
$485$	−44.6118	+	782.306i	−0.0919830	+	1.61300i
$486$	81.6307	+	834.756i	0.167964	+	1.71761i
$487$	−402.271	+	553.679i	−0.826019	+	1.13692i	0.162632	+	0.986687i	$0.448002\pi$
$487$	−402.271	+	553.679i	−0.826019	+	1.13692i	−0.988651	+	0.150231i	$0.951998\pi$
$488$	186.999	+	135.862i	0.383194	+	0.278407i
$489$	433.570	+	46.2049i	0.886647	+	0.0944886i
$490$	347.629	+	284.164i	0.709446	+	0.579927i
$491$	−288.681	+	397.336i	−0.587946	+	0.809238i	−0.994538	−	0.104372i	$-0.966717\pi$
$491$	−288.681	+	397.336i	−0.587946	+	0.809238i	0.406593	+	0.913610i	$0.366717\pi$
$492$	153.196	−	342.748i	0.311375	−	0.696643i
$493$		−	306.874i		−	0.622463i
$494$	−540.092	+	175.487i	−1.09330	+	0.355236i
$495$	101.768	+	271.178i	0.205593	+	0.547834i
$496$	−239.840	+	738.152i	−0.483549	+	1.48821i
$497$	28.7027	−	88.3377i	0.0577518	−	0.177742i
$498$	36.5910	−	343.356i	0.0734758	−	0.689471i
$499$	830.622			1.66457			0.832286	−	0.554346i	$-0.187031\pi$
$499$	830.622			1.66457			0.832286	+	0.554346i	$0.187031\pi$
$500$	−887.494	+	436.866i	−1.77499	+	0.873732i
$501$	−234.628	+	259.823i	−0.468319	+	0.518609i
$502$	823.314	+	1133.20i	1.64007	+	2.25736i
$503$	−68.0929	+	209.569i	−0.135374	+	0.416637i	−0.995648	−	0.0931942i	$-0.970292\pi$
$503$	−68.0929	+	209.569i	−0.135374	+	0.416637i	0.860274	+	0.509831i	$0.170292\pi$
$504$	−122.826	+	569.735i	−0.243703	+	1.13043i
$505$	−445.162	+	117.087i	−0.881509	+	0.231855i
$506$	753.614	−	244.864i	1.48936	−	0.483921i
$507$	−245.450	+	271.807i	−0.484122	+	0.536109i
$508$	−127.708	+	41.4949i	−0.251394	+	0.0816828i
$509$	477.759	−	657.579i	0.938623	−	1.29190i	−0.0177765	−	0.999842i	$-0.505659\pi$
$509$	477.759	−	657.579i	0.938623	−	1.29190i	0.956399	−	0.292062i	$-0.0943413\pi$
$510$	1247.61	−	189.869i	2.44630	−	0.372293i
$511$	505.372	−	367.174i	0.988987	−	0.718541i
$512$	−682.971	−	496.208i	−1.33393	−	0.969155i
$513$	−79.3843	−	247.980i	−0.154745	−	0.483391i
$514$	−927.178	+	673.634i	−1.80385	+	1.31057i
$515$	−52.3556	+	918.101i	−0.101661	+	1.78272i
$516$	40.2387	+	190.665i	0.0779819	+	0.369506i
$517$	34.5655	−	11.2310i	0.0668578	−	0.0217234i
$518$	−470.573			−0.908443
$519$	−208.778	−	93.3165i	−0.402270	−	0.179801i
$520$	65.6039	−	1150.42i	0.126161	−	2.21235i
$521$	−695.445	−	225.964i	−1.33483	−	0.433712i	−0.447266	−	0.894401i	$-0.647602\pi$
$521$	−695.445	−	225.964i	−1.33483	−	0.433712i	−0.887561	+	0.460689i	$0.847602\pi$
$522$	82.4209	−	382.312i	0.157894	−	0.732399i
$523$	−411.764	−	566.744i	−0.787311	−	1.08364i	−0.994438	−	0.105326i	$-0.966411\pi$
$523$	−411.764	−	566.744i	−0.787311	−	1.08364i	0.207127	−	0.978314i	$-0.433589\pi$
$524$		−	1175.01i		−	2.24238i
$525$	−183.087	+	309.453i	−0.348737	+	0.589434i
$526$	−1444.74			−2.74666
$527$	1022.41	−	742.821i	1.94005	−	1.40953i
$528$	250.543	−	144.168i	0.474513	−	0.273045i
$529$	229.645	−	706.775i	0.434112	−	1.33606i
$530$	−31.8068	+	20.4480i	−0.0600129	+	0.0385812i
$531$	287.215	+	650.157i	0.540895	+	1.22440i
$532$		−	365.860i		−	0.687707i
$533$	83.3721	+	256.593i	0.156420	+	0.481413i
$534$	117.321	+	555.911i	0.219703	+	1.04103i
$535$	−41.6210	−	158.242i	−0.0777962	−	0.295780i
$536$	−113.840	−	156.687i	−0.212387	−	0.292326i
$537$	15.9766	+	75.7028i	0.0297516	+	0.140974i
$538$	−93.2604	+	128.362i	−0.173346	+	0.238591i
$539$	−98.4288	−	135.476i	−0.182614	−	0.251346i
$540$	1066.32	+	65.4561i	1.97466	+	0.121215i
$541$	225.950	+	164.163i	0.417653	+	0.303443i	0.776693	−	0.629879i	$-0.216896\pi$
$541$	225.950	+	164.163i	0.417653	+	0.303443i	−0.359040	+	0.933322i	$0.616896\pi$
$542$	416.182	+	1280.88i	0.767863	+	2.36324i
$543$	299.135	−	331.257i	0.550892	−	0.610049i
$544$	17.7918	+	54.7575i	0.0327055	+	0.100657i
$545$	95.8009	−	246.176i	0.175782	−	0.451699i
$546$	−422.408	−	734.084i	−0.773640	−	1.34448i
$547$	−509.525	−	165.555i	−0.931491	−	0.302660i	−0.196319	−	0.980540i	$-0.562899\pi$
$547$	−509.525	−	165.555i	−0.931491	−	0.302660i	−0.735172	+	0.677881i	$0.762899\pi$
$548$	715.678	−	519.970i	1.30598	−	0.948851i
$549$	−15.6543	−	153.207i	−0.0285142	−	0.279066i
$550$	544.313	−	110.469i	0.989661	−	0.200852i
$551$			121.411i			0.220347i
$552$	153.163	−	1437.23i	0.277469	−	2.60367i
$553$	−80.9970	−	26.3175i	−0.146468	−	0.0475904i
$554$	1144.06	+	371.726i	2.06508	+	0.670986i
$555$	64.1792	+	421.715i	0.115638	+	0.759847i
$556$	28.0822	+	86.4283i	0.0505076	+	0.155447i
$557$	−215.531			−0.386950			−0.193475	−	0.981105i	$-0.561976\pi$
$557$	−215.531			−0.386950			−0.193475	+	0.981105i	$0.561976\pi$
$558$	1473.25	−	650.826i	2.64023	−	1.16636i
$559$	−113.293	−	82.3124i	−0.202671	−	0.147249i
$560$	334.403	+	130.135i	0.597149	+	0.232384i
$561$	−468.018	−	49.8760i	−0.834258	−	0.0889055i
$562$	−816.962	+	1124.45i	−1.45367	+	2.00080i
$563$	−604.915	−	439.496i	−1.07445	−	0.780633i	−0.0977424	−	0.995212i	$-0.531162\pi$
$563$	−604.915	−	439.496i	−1.07445	−	0.780633i	−0.976707	+	0.214579i	$0.931162\pi$
$564$	14.2053	−	133.297i	0.0251867	−	0.236343i
$565$	−10.0811	+	25.9050i	−0.0178427	+	0.0458496i
$566$	479.231	−	659.605i	0.846698	−	1.16538i
$567$	337.416	−	192.210i	0.595090	−	0.338995i
$568$			261.710i			0.460757i
$569$	557.452	−	181.127i	0.979705	−	0.318325i	0.224978	−	0.974364i	$-0.427769\pi$
$569$	557.452	−	181.127i	0.979705	−	0.318325i	0.754727	+	0.656039i	$0.227769\pi$
$570$	−493.602	+	75.1194i	−0.865969	+	0.131788i
$571$	171.096	−	526.579i	0.299643	−	0.922206i	−0.681979	−	0.731371i	$-0.738881\pi$
$571$	171.096	−	526.579i	0.299643	−	0.922206i	0.981622	−	0.190834i	$-0.0611193\pi$
$572$	−268.540	+	826.483i	−0.469476	+	1.44490i
$573$	48.0462	+	5.12021i	0.0838503	+	0.00893580i
$574$	−261.675			−0.455880
$575$	370.165	−	811.215i	0.643765	−	1.41081i
$576$	62.2378	+	609.116i	0.108052	+	1.05749i
$577$	−538.708	−	741.467i	−0.933635	−	1.28504i	−0.958425	−	0.285346i	$-0.907891\pi$
$577$	−538.708	−	741.467i	−0.933635	−	1.28504i	0.0247892	−	0.999693i	$-0.492109\pi$
$578$	−325.451	+	1001.63i	−0.563064	+	1.73293i
$579$	517.498	−	297.779i	0.893778	−	0.514299i
$580$	−464.236	−	180.660i	−0.800407	−	0.311484i
$581$	−152.044	+	49.4022i	−0.261694	+	0.0850296i
$582$	−1204.37	−	1087.58i	−2.06936	−	1.86869i
$583$	13.4124	−	4.35796i	0.0230059	−	0.00747506i
$584$	−1034.55	+	1423.94i	−1.77149	+	2.43825i
$585$	−600.256	+	478.668i	−1.02608	+	0.818236i
$586$	1096.39	−	796.574i	1.87097	−	1.35934i
$587$	−488.615	−	355.000i	−0.832394	−	0.604770i	0.0878416	−	0.996134i	$-0.472003\pi$
$587$	−488.615	−	355.000i	−0.832394	−	0.604770i	−0.920236	+	0.391365i	$0.872003\pi$
$588$	−604.336	+	127.541i	−1.02778	+	0.216907i
$589$	−404.502	+	293.888i	−0.686760	+	0.498961i
$590$	1318.11	−	346.690i	2.23409	−	0.587610i
$591$	97.8919	−	20.6595i	0.165638	−	0.0349568i
$592$	404.874	−	131.552i	0.683909	−	0.222216i
$593$	14.7174			0.0248185			0.0124093	−	0.999923i	$-0.496050\pi$
$593$	14.7174			0.0248185			0.0124093	+	0.999923i	$0.496050\pi$
$594$	−569.674	−	187.838i	−0.959047	−	0.316226i
$595$	−315.960	−	491.475i	−0.531025	−	0.826008i
$596$	−186.532	−	60.6078i	−0.312972	−	0.101691i
$597$	315.195	+	547.764i	0.527965	+	0.917528i
$598$	1234.56	+	1699.22i	2.06448	+	2.84151i
$599$			1048.47i			1.75037i	0.483786	+	0.875186i	$0.339261\pi$
$599$			1048.47i			1.75037i	−0.483786	+	0.875186i	$0.660739\pi$
$600$	221.182	−	988.653i	0.368637	−	1.64776i
$601$	128.346			0.213555			0.106777	−	0.994283i	$-0.465947\pi$
$601$	128.346			0.213555			0.106777	+	0.994283i	$0.465947\pi$
$602$	109.882	−	79.8342i	0.182529	−	0.132615i
$603$	−27.1946	+	126.143i	−0.0450989	+	0.209193i
$604$	−123.513	+	380.134i	−0.204492	+	0.629362i
$605$	397.208	+	22.6512i	0.656543	+	0.0374400i
$606$	388.989	−	870.291i	0.641897	−	1.43612i
$607$			603.019i			0.993442i	0.867910	+	0.496721i	$0.165463\pi$
$607$			603.019i			0.993442i	−0.867910	+	0.496721i	$0.834537\pi$
$608$	−7.03911	−	21.6641i	−0.0115775	−	0.0356318i
$609$	−177.169	+	37.3903i	−0.290917	+	0.0613962i
$610$	−294.834	−	16.8132i	−0.483335	−	0.0275626i
$611$	56.6246	+	77.9370i	0.0926752	+	0.127557i
$612$	−872.356	+	1500.91i	−1.42542	+	2.45247i
$613$	−380.744	+	524.050i	−0.621116	+	0.854893i	−0.997434	−	0.0715974i	$-0.977190\pi$
$613$	−380.744	+	524.050i	−0.621116	+	0.854893i	0.376317	+	0.926491i	$0.377190\pi$
$614$	−43.5711	−	59.9704i	−0.0709627	−	0.0976717i
$615$	35.6885	+	234.506i	0.0580301	+	0.381310i
$616$	−337.215	−	245.001i	−0.547427	−	0.397729i
$617$	−32.4788	−	99.9594i	−0.0526398	−	0.162009i	0.921281	−	0.388898i	$-0.127144\pi$
$617$	−32.4788	−	99.9594i	−0.0526398	−	0.162009i	−0.973920	+	0.226890i	$0.927144\pi$
$618$	−1413.43	−	1276.36i	−2.28710	−	2.06532i
$619$	227.844	+	701.232i	0.368084	+	1.13285i	0.948027	+	0.318190i	$0.103075\pi$
$619$	227.844	+	701.232i	0.368084	+	1.13285i	−0.579943	+	0.814657i	$0.696925\pi$
$620$	−521.830	−	1983.99i	−0.841661	−	3.19998i
$621$	−781.546	+	562.656i	−1.25853	+	0.906048i
$622$	62.9998	+	20.4699i	0.101286	+	0.0329098i
$623$	212.810	−	154.615i	0.341589	−	0.248179i
$624$	568.651	+	513.508i	0.911299	+	0.822930i
$625$	322.415	−	535.419i	0.515865	−	0.856670i
$626$		−	1694.22i		−	2.70642i
$627$	185.166	+	19.7328i	0.295320	+	0.0314718i
$628$	936.964	+	304.438i	1.49198	+	0.484774i
$629$	−659.244	−	214.201i	−1.04808	−	0.340543i
$630$	−261.630	−	697.153i	−0.415285	−	1.10659i
$631$	−356.940	−	1098.55i	−0.565674	−	1.74096i	−0.665942	−	0.746004i	$-0.731970\pi$
$631$	−356.940	−	1098.55i	−0.565674	−	1.74096i	0.100268	−	0.994960i	$-0.468030\pi$
$632$	239.962			0.379687
$633$	334.469	+	149.496i	0.528388	+	0.236171i
$634$	−542.197	−	393.929i	−0.855201	−	0.621340i
$635$	53.6960	−	65.6883i	0.0845607	−	0.103446i
$636$	5.51207	−	51.7233i	0.00866677	−	0.0813259i
$637$	260.899	−	359.097i	0.409574	−	0.563731i
$638$	226.283	+	164.404i	0.354676	+	0.257687i
$639$	129.920	−	116.301i	0.203318	−	0.182005i
$640$	1125.02	+	64.1557i	1.75785	+	0.100243i
$641$	−322.461	+	443.829i	−0.503059	+	0.692402i	−0.982730	−	0.185047i	$-0.940756\pi$
$641$	−322.461	+	443.829i	−0.503059	+	0.692402i	0.479670	+	0.877449i	$0.340756\pi$
$642$	309.364	+	138.275i	0.481875	+	0.215381i
$643$			823.590i			1.28086i	0.768018	+	0.640428i	$0.221243\pi$
$643$			823.590i			1.28086i	−0.768018	+	0.640428i	$0.778757\pi$
$644$	−1286.92	+	418.146i	−1.99833	+	0.649296i
$645$	−86.5315	−	87.5854i	−0.134157	−	0.135791i
$646$	250.715	−	771.622i	0.388104	−	1.19446i
$647$	−120.454	+	370.718i	−0.186172	+	0.572980i	−0.999967	−	0.00817339i	$-0.997398\pi$
$647$	−120.454	+	370.718i	−0.186172	+	0.572980i	0.813794	+	0.581153i	$0.197398\pi$
$648$	−736.820	+	808.850i	−1.13707	+	1.24823i
$649$	−508.325			−0.783243
$650$	724.323	+	1281.68i	1.11434	+	1.97181i
$651$	−553.427	−	499.761i	−0.850118	−	0.767682i
$652$	676.050	+	930.504i	1.03689	+	1.42715i
$653$	221.753	−	682.485i	0.339591	−	1.04515i	−0.624826	−	0.780764i	$-0.714830\pi$
$653$	221.753	−	682.485i	0.339591	−	1.04515i	0.964416	−	0.264388i	$-0.0851701\pi$
$654$	272.846	+	474.167i	0.417195	+	0.725026i
$655$	401.472	+	624.489i	0.612935	+	0.953419i
$656$	225.141	−	73.1528i	0.343203	−	0.111513i
$657$	1166.63	−	119.203i	1.77569	−	0.181435i
$658$	−88.8621	+	28.8730i	−0.135049	+	0.0438800i
$659$	−60.3180	+	83.0206i	−0.0915296	+	0.125980i	−0.852326	−	0.523011i	$-0.824809\pi$
$659$	−60.3180	+	83.0206i	−0.0915296	+	0.125980i	0.760796	+	0.648991i	$0.224809\pi$
$660$	−350.980	+	678.651i	−0.531787	+	1.02826i
$661$	565.922	−	411.166i	0.856161	−	0.622037i	−0.0706772	−	0.997499i	$-0.522516\pi$
$661$	565.922	−	411.166i	0.856161	−	0.622037i	0.926838	+	0.375462i	$0.122516\pi$
$662$	420.396	+	305.435i	0.635039	+	0.461383i
$663$	−257.617	−	1220.68i	−0.388563	−	1.84115i
$664$	364.419	−	264.766i	0.548824	−	0.398744i
$665$	125.006	+	194.446i	0.187978	+	0.292400i
$666$	−763.773	−	443.919i	−1.14681	−	0.666545i
$667$	427.066	−	138.762i	0.640280	−	0.208039i
$668$	−923.464			−1.38243
$669$	−28.2118	+	63.1187i	−0.0421702	+	0.0943478i
$670$	230.598	+	89.7387i	0.344176	+	0.133938i
$671$	104.750	+	34.0352i	0.156110	+	0.0507232i
$672$	29.4455	−	16.9436i	0.0438178	−	0.0252137i
$673$	−420.099	−	578.216i	−0.624218	−	0.859163i	0.373433	−	0.927657i	$-0.378180\pi$
$673$	−420.099	−	578.216i	−0.624218	−	0.859163i	−0.997652	+	0.0684944i	$0.978180\pi$
$674$		−	118.871i		−	0.176367i
$675$	−589.087	+	329.547i	−0.872722	+	0.488217i
$676$	−966.058			−1.42908
$677$	−201.589	+	146.463i	−0.297769	+	0.216342i	−0.726630	−	0.687029i	$-0.758915\pi$
$677$	−201.589	+	146.463i	−0.297769	+	0.216342i	0.428862	+	0.903370i	$0.358915\pi$
$678$	−28.7115	−	49.8964i	−0.0423473	−	0.0735935i
$679$	−232.167	+	714.538i	−0.341926	+	1.05234i
$680$	1274.60	+	1041.90i	1.87441	+	1.53221i
$681$	146.791	+	65.6105i	0.215553	+	0.0963444i
$682$			1151.86i			1.68894i
$683$	−305.750	−	941.001i	−0.447657	−	1.37775i	−0.879543	−	0.475819i	$-0.842152\pi$
$683$	−305.750	−	941.001i	−0.447657	−	1.37775i	0.431886	−	0.901928i	$-0.357848\pi$
$684$	345.137	−	593.816i	0.504586	−	0.868153i
$685$	−202.704	+	520.882i	−0.295919	+	0.760411i
$686$	729.631	+	1004.25i	1.06360	+	1.46392i
$687$	−843.203	+	177.953i	−1.22737	+	0.259029i
$688$	−72.2230	+	99.4064i	−0.104975	+	0.144486i
$689$	21.9720	+	30.2419i	0.0318897	+	0.0438924i
$690$	828.379	+	1650.40i	1.20055	+	2.39189i
$691$	−263.711	−	191.598i	−0.381637	−	0.277276i	0.380383	−	0.924829i	$-0.375792\pi$
$691$	−263.711	−	191.598i	−0.381637	−	0.277276i	−0.762020	+	0.647553i	$0.775792\pi$
$692$	−186.409	−	573.707i	−0.269377	−	0.829057i
$693$	28.2295	+	276.279i	0.0407351	+	0.398672i
$694$	−535.113	−	1646.91i	−0.771057	−	2.37307i
$695$	−44.4555	−	36.3395i	−0.0639647	−	0.0522871i
$696$	442.204	−	254.454i	0.635350	−	0.365594i
$697$	−366.590	−	119.112i	−0.525955	−	0.170893i
$698$	825.717	−	599.919i	1.18298	−	0.859482i
$699$	809.184	−	896.077i	1.15763	−	1.28194i
$700$	−929.507	+	188.644i	−1.32787	+	0.269491i
$701$		−	165.328i		−	0.235846i	−0.993023	−	0.117923i	$-0.962376\pi$
$701$		−	165.328i		−	0.235846i	0.993023	−	0.117923i	$-0.0376236\pi$
$702$	6.90666	−	1589.95i	0.00983854	−	2.26489i
$703$	260.822	+	84.7461i	0.371012	+	0.120549i
$704$	−416.460	−	135.316i	−0.591562	−	0.192210i
$705$	37.9947	+	75.6979i	0.0538932	+	0.107373i
$706$	−363.885	−	1119.92i	−0.515418	−	1.58629i
$707$	−441.348			−0.624254
$708$	−765.071	+	1711.70i	−1.08061	+	2.41766i
$709$	−22.5573	−	16.3888i	−0.0318156	−	0.0231154i	0.571764	−	0.820418i	$-0.306259\pi$
$709$	−22.5573	−	16.3888i	−0.0318156	−	0.0231154i	−0.603579	+	0.797303i	$0.706259\pi$
$710$	−180.816	−	281.259i	−0.254670	−	0.396139i
$711$	−106.637	−	119.124i	−0.149982	−	0.167545i
$712$	−435.645	+	599.614i	−0.611861	+	0.842154i
$713$	1496.07	+	1086.96i	2.09827	+	1.52448i
$714$	1203.20	+	128.223i	1.68515	+	0.179584i
$715$	−139.666	−	531.009i	−0.195337	−	0.742671i
$716$	−119.961	+	165.113i	−0.167544	+	0.230604i
$717$	−309.031	+	691.399i	−0.431005	+	0.964294i
$718$			194.761i			0.271254i
$719$	114.908	−	37.3358i	0.159816	−	0.0519274i	−0.228016	−	0.973657i	$-0.573224\pi$
$719$	114.908	−	37.3358i	0.159816	−	0.0519274i	0.387832	+	0.921730i	$0.373224\pi$
$720$	419.996	+	526.680i	0.583328	+	0.731500i
$721$	−272.468	+	838.570i	−0.377903	+	1.16306i
$722$	285.851	−	879.759i	0.395916	−	1.21850i
$723$	−10.2878	+	96.5375i	−0.0142294	+	0.133523i
$724$	1177.35			1.62618
$725$	308.458	−	62.6016i	0.425459	−	0.0863470i
$726$	−552.208	+	611.506i	−0.760617	+	0.842295i
$727$	−125.521	−	172.765i	−0.172657	−	0.237641i	0.713916	−	0.700232i	$-0.246920\pi$
$727$	−125.521	−	172.765i	−0.172657	−	0.237641i	−0.886572	+	0.462591i	$0.846920\pi$
$728$	341.414	−	1050.76i	0.468976	−	1.44336i
$729$	728.972	+	6.33335i	0.999962	+	0.00868773i
$730$	128.028	−	2245.08i	0.175381	−	3.07545i
$731$	190.278	−	61.8251i	0.260299	−	0.0845761i
$732$	272.265	−	301.502i	0.371947	−	0.411888i
$733$	−1126.46	+	366.010i	−1.53678	+	0.499331i	−0.950487	−	0.310765i	$-0.899415\pi$
$733$	−1126.46	+	366.010i	−1.53678	+	0.499331i	−0.586297	+	0.810096i	$0.699415\pi$
$734$	−1295.63	+	1783.28i	−1.76516	+	2.42954i
$735$	277.612	−	274.272i	0.377704	−	0.373159i
$736$	−68.1591	+	49.5205i	−0.0926075	+	0.0672833i
$737$	−74.6618	−	54.2449i	−0.101305	−	0.0736024i
$738$	−424.717	−	246.853i	−0.575497	−	0.334489i
$739$	755.924	−	549.211i	1.02290	−	0.743181i	0.0560255	−	0.998429i	$-0.482157\pi$
$739$	755.924	−	549.211i	1.02290	−	0.743181i	0.966876	+	0.255248i	$0.0821572\pi$
$740$	−712.146	+	871.195i	−0.962360	+	1.17729i
$741$	101.923	+	482.948i	0.137548	+	0.651752i
$742$	−34.4811	+	11.2036i	−0.0464705	+	0.0150992i
$743$	79.6348			0.107180			0.0535900	−	0.998563i	$-0.482934\pi$
$743$	79.6348			0.107180			0.0535900	+	0.998563i	$0.482934\pi$
$744$	1918.16	+	857.348i	2.57817	+	1.15235i
$745$	119.845	−	31.5217i	0.160866	−	0.0423110i
$746$	−776.715	−	252.370i	−1.04117	−	0.338298i
$747$	−293.382	−	63.2489i	−0.392747	−	0.0846705i
$748$	−729.764	−	1004.43i	−0.975620	−	1.34283i
$749$		−	156.887i		−	0.209461i
$750$	445.358	+	1215.32i	0.593811	+	1.62042i
$751$	627.018			0.834911			0.417455	−	0.908697i	$-0.362922\pi$
$751$	627.018			0.834911			0.417455	+	0.908697i	$0.362922\pi$
$752$	68.3840	−	49.6839i	0.0909361	−	0.0660690i
$753$	1055.22	−	607.194i	1.40135	−	0.806366i
$754$	−229.101	+	705.100i	−0.303847	+	0.935146i
$755$	−64.2384	−	244.234i	−0.0850840	−	0.323488i
$756$	972.814	+	320.765i	1.28679	+	0.424293i
$757$			438.031i			0.578641i	0.957232	+	0.289320i	$0.0934293\pi$
$757$			438.031i			0.578641i	−0.957232	+	0.289320i	$0.906571\pi$
$758$	126.927	+	390.642i	0.167450	+	0.515358i
$759$	−142.218	−	673.878i	−0.187375	−	0.887850i
$760$	−504.279	−	412.216i	−0.663526	−	0.542390i
$761$	555.927	+	765.168i	0.730521	+	1.00548i	0.999108	+	0.0422209i	$0.0134433\pi$
$761$	555.927	+	765.168i	0.730521	+	1.00548i	−0.268587	+	0.963255i	$0.586557\pi$
$762$	36.2822	+	171.918i	0.0476144	+	0.225614i
$763$	148.875	−	204.909i	0.195119	−	0.268558i
$764$	74.9167	+	103.114i	0.0980586	+	0.134966i
$765$	−49.1883	−	1095.76i	−0.0642984	−	1.43237i
$766$	2097.98	+	1524.27i	2.73888	+	1.98991i
$767$	−416.365	−	1281.44i	−0.542848	−	1.67071i
$768$	−1016.89	+	1126.09i	−1.32408	+	1.46626i
$769$	−243.815	−	750.386i	−0.317055	−	0.975794i	−0.974900	−	0.222641i	$-0.928532\pi$
$769$	−243.815	−	750.386i	−0.317055	−	0.975794i	0.657846	−	0.753153i	$-0.271468\pi$
$770$	531.675	+	30.3193i	0.690487	+	0.0393757i
$771$	496.804	+	863.375i	0.644364	+	1.11981i
$772$	1497.86	+	486.683i	1.94023	+	0.630418i
$773$	−554.735	+	403.039i	−0.717640	+	0.521396i	−0.885629	−	0.464393i	$-0.846272\pi$
$773$	−554.735	+	403.039i	−0.717640	+	0.521396i	0.167990	+	0.985789i	$0.446272\pi$
$774$	253.659	−	25.9181i	0.327724	−	0.0334860i
$775$	955.221	+	876.147i	1.23254	+	1.13051i
$776$		−	2116.89i		−	2.72796i
$777$	−43.3416	+	406.702i	−0.0557807	+	0.523426i
$778$	−686.529	−	223.067i	−0.882428	−	0.286718i
$779$	145.037	+	47.1254i	0.186183	+	0.0604947i
$780$	−1998.30	−	328.909i	−2.56192	−	0.421679i
$781$	38.5361	+	118.602i	0.0493421	+	0.151859i
$782$	−3000.74			−3.83727
$783$	−322.829	−	106.446i	−0.412298	−	0.135947i
$784$	−315.081	−	228.919i	−0.401888	−	0.291989i
$785$	−601.993	+	158.336i	−0.766870	+	0.201702i
$786$	−1528.84	−	162.926i	−1.94508	−	0.207284i
$787$	617.749	−	850.258i	0.784941	−	1.08038i	−0.209779	−	0.977749i	$-0.567274\pi$
$787$	617.749	−	850.258i	0.784941	−	1.08038i	0.994720	−	0.102630i	$-0.0327257\pi$
$788$	213.509	+	155.123i	0.270950	+	0.196857i
$789$	−133.066	+	1248.65i	−0.168652	+	1.58257i
$790$	−257.886	+	165.790i	−0.326439	+	0.209861i
$791$	−15.6661	+	21.5626i	−0.0198054	+	0.0272599i
$792$	−316.200	−	715.768i	−0.399242	−	0.903747i
$793$			291.942i			0.368149i
$794$	1286.84	−	418.119i	1.62070	−	0.526599i
$795$	14.7431	+	29.3730i	0.0185447	+	0.0369472i
$796$	−515.147	+	1585.46i	−0.647170	+	1.99178i
$797$	−484.162	+	1490.10i	−0.607481	+	1.86963i	−0.128737	+	0.991679i	$0.541092\pi$
$797$	−484.162	+	1490.10i	−0.607481	+	1.86963i	−0.478743	+	0.877955i	$0.658908\pi$
$798$	−476.030	−	50.7298i	−0.596529	−	0.0635712i
$799$	−137.633			−0.172257
$800$	−51.4106	+	29.0540i	−0.0642632	+	0.0363175i
$801$	491.262	−	50.1958i	0.613311	−	0.0626664i
$802$	−920.876	−	1267.48i	−1.14822	−	1.58040i
$803$	−259.169	+	797.639i	−0.322750	+	0.993324i
$804$	−295.033	+	169.768i	−0.366957	+	0.211155i
$805$	541.098	−	661.945i	0.672171	−	0.822292i
$806$	−2903.72	+	943.477i	−3.60264	+	1.17057i
$807$	102.350	+	92.4247i	0.126827	+	0.114529i
$808$	1182.68	−	384.276i	1.46371	−	0.475589i
$809$	−678.239	+	933.516i	−0.838367	+	1.15391i	0.147940	+	0.988996i	$0.452736\pi$
$809$	−678.239	+	933.516i	−0.838367	+	1.15391i	−0.986307	+	0.164917i	$0.947264\pi$
$810$	233.021	−	1378.34i	0.287681	−	1.70165i
$811$	−207.383	+	150.673i	−0.255713	+	0.185786i	−0.708255	−	0.705957i	$-0.750517\pi$
$811$	−207.383	+	150.673i	−0.255713	+	0.185786i	0.452542	+	0.891743i	$0.350517\pi$
$812$	−386.416	−	280.748i	−0.475882	−	0.345749i
$813$	1145.35	−	241.719i	1.40880	−	0.297318i
$814$	511.130	−	371.358i	0.627924	−	0.456213i
$815$	−677.235	−	263.550i	−0.830963	−	0.323375i
$816$	−1071.06	+	226.040i	−1.31257	+	0.277010i
$817$	−75.2812	+	24.4604i	−0.0921435	+	0.0299392i
$818$	774.060			0.946283
$819$	−673.352	+	297.462i	−0.822163	+	0.363201i
$820$	−396.008	+	484.451i	−0.482937	+	0.590794i
$821$	1412.69	+	459.010i	1.72069	+	0.559086i	0.992054	−	0.125815i	$-0.0401547\pi$
$821$	1412.69	+	459.010i	1.72069	+	0.559086i	0.728636	+	0.684901i	$0.240155\pi$
$822$	−577.312	−	1003.29i	−0.702326	−	1.22054i
$823$	379.623	+	522.507i	0.461268	+	0.634880i	0.974771	−	0.223207i	$-0.0716526\pi$
$823$	379.623	+	522.507i	0.461268	+	0.634880i	−0.513503	+	0.858088i	$0.671653\pi$
$824$		−	2484.35i		−	3.01499i
$825$	−45.3412	−	480.608i	−0.0549590	−	0.582555i
$826$	1306.82			1.58210
$827$	852.084	−	619.076i	1.03033	−	0.748580i	0.0619568	−	0.998079i	$-0.480266\pi$
$827$	852.084	−	619.076i	1.03033	−	0.748580i	0.968375	+	0.249499i	$0.0802659\pi$
$828$	−2483.23	−	535.347i	−2.99906	−	0.646554i
$829$	−440.918	+	1357.00i	−0.531867	+	1.63692i	0.218457	+	0.975847i	$0.429898\pi$
$829$	−440.918	+	1357.00i	−0.531867	+	1.63692i	−0.750323	+	0.661071i	$0.770102\pi$
$830$	−208.713	+	536.321i	−0.251461	+	0.646170i
$831$	426.643	−	954.534i	0.513409	−	1.14866i
$832$		−	1160.69i		−	1.39506i
$833$	195.962	+	603.110i	0.235249	+	0.724021i
$834$	116.348	−	24.5545i	0.139506	−	0.0294418i
$835$	490.799	−	315.525i	0.587783	−	0.377875i
$836$	288.722	+	397.392i	0.345361	+	0.475349i
$837$	−426.797	−	1333.23i	−0.509913	−	1.59286i
$838$	−88.8042	+	122.228i	−0.105972	+	0.145857i
$839$	−199.569	−	274.683i	−0.237865	−	0.327393i	0.673350	−	0.739324i	$-0.264855\pi$
$839$	−199.569	−	274.683i	−0.237865	−	0.327393i	−0.911215	+	0.411931i	$0.864855\pi$
$840$	446.225	−	862.816i	0.531220	−	1.02716i
$841$	−552.151	−	401.161i	−0.656541	−	0.477005i
$842$	569.407	+	1752.46i	0.676256	+	2.08130i
$843$	896.583	+	809.641i	1.06356	+	0.960428i
$844$	298.633	+	919.098i	0.353830	+	1.08898i
$845$	513.436	−	330.078i	0.607617	−	0.390625i
$846$	−171.467	−	36.9657i	−0.202680	−	0.0436947i
$847$	362.800	+	117.881i	0.428335	+	0.139175i
$848$	26.5350	−	19.2788i	0.0312913	−	0.0227344i
$849$	−525.937	−	474.937i	−0.619478	−	0.559407i
$850$	−2089.66	−	239.108i	−2.45842	−	0.281303i
$851$		−	1014.30i		−	1.19190i
$852$	457.373	+	48.7416i	0.536823	+	0.0572084i
$853$	1425.16	+	463.062i	1.67076	+	0.542863i	0.983084	−	0.183153i	$-0.0586305\pi$
$853$	1425.16	+	463.062i	1.67076	+	0.542863i	0.687677	+	0.726017i	$0.258630\pi$
$854$	−269.294	−	87.4989i	−0.315333	−	0.102458i
$855$	19.4607	+	433.524i	0.0227611	+	0.507046i
$856$	136.599	+	420.410i	0.159579	+	0.491133i
$857$	280.524			0.327333			0.163666	−	0.986516i	$-0.447668\pi$
$857$	280.524			0.327333			0.163666	+	0.986516i	$0.447668\pi$
$858$	1038.12	+	464.004i	1.20993	+	0.540797i
$859$	253.517	+	184.191i	0.295130	+	0.214425i	0.725490	−	0.688233i	$-0.241613\pi$
$859$	253.517	+	184.191i	0.295130	+	0.214425i	−0.430360	+	0.902658i	$0.641613\pi$
$860$	18.4906	−	324.248i	0.0215007	−	0.377033i
$861$	−24.1013	+	226.158i	−0.0279922	+	0.262668i
$862$	847.315	−	1166.23i	0.982963	−	1.35293i
$863$	−474.919	−	345.049i	−0.550311	−	0.399825i	0.277589	−	0.960700i	$-0.410465\pi$
$863$	−474.919	−	345.049i	−0.550311	−	0.399825i	−0.827900	+	0.560875i	$0.810465\pi$
$864$	63.7760	+	0.277039i	0.0738148	+	0.000320647i
$865$	295.094	+	241.220i	0.341149	+	0.278867i
$866$	1381.74	−	1901.80i	1.59554	−	2.19608i
$867$	835.706	+	373.531i	0.963906	+	0.430832i
$868$		−	1966.99i		−	2.26612i
$869$	108.746	−	35.3339i	0.125140	−	0.0406604i
$870$	−299.433	+	578.980i	−0.344175	+	0.665494i
$871$	75.5915	−	232.647i	0.0867870	−	0.267103i
$872$	−220.530	+	678.720i	−0.252901	+	0.778349i
$873$	−1050.89	+	940.728i	−1.20377	+	1.07758i
$874$	1187.21			1.35836
$875$	429.556	−	417.850i	0.490921	−	0.477542i
$876$	2295.85	+	2073.22i	2.62083	+	2.36669i
$877$	286.619	+	394.497i	0.326817	+	0.449825i	0.940533	−	0.339701i	$-0.110326\pi$
$877$	286.619	+	394.497i	0.326817	+	0.449825i	−0.613716	+	0.789527i	$0.710326\pi$
$878$	248.524	−	764.877i	0.283057	−	0.871158i
$879$	−587.472	−	1020.94i	−0.668342	−	1.16148i
$880$	−465.921	+	122.547i	−0.529456	+	0.139258i
$881$	18.7206	−	6.08269i	0.0212492	−	0.00690430i	−0.298373	−	0.954449i	$-0.596444\pi$
$881$	18.7206	−	6.08269i	0.0212492	−	0.00690430i	0.319622	+	0.947545i	$0.396444\pi$
$882$	82.1506	+	804.002i	0.0931413	+	0.911567i
$883$	−1177.85	+	382.707i	−1.33392	+	0.433416i	−0.887252	−	0.461285i	$-0.847389\pi$
$883$	−1177.85	+	382.707i	−1.33392	+	0.433416i	−0.446666	+	0.894701i	$0.647389\pi$
$884$	1934.34	−	2662.39i	2.18817	−	3.01175i
$885$	−178.230	−	1171.13i	−0.201390	−	1.32332i
$886$	−479.145	+	348.119i	−0.540795	+	0.392911i
$887$	756.749	+	549.811i	0.853156	+	0.619854i	0.926014	−	0.377488i	$-0.123212\pi$
$887$	756.749	+	549.811i	0.853156	+	0.619854i	−0.0728585	+	0.997342i	$0.523212\pi$
$888$	−237.968	−	1127.58i	−0.267982	−	1.26979i
$889$	65.8124	−	47.8155i	0.0740297	−	0.0537857i
$890$	53.9118	−	945.391i	0.0605751	−	1.06224i
$891$	−214.812	+	475.051i	−0.241091	+	0.533166i
$892$	−173.446	+	56.3559i	−0.194446	+	0.0631792i
$893$	54.4528			0.0609774
$894$	−104.723	+	234.297i	−0.117139	+	0.262077i
$895$	7.34161	−	128.741i	0.00820291	−	0.143845i
$896$	1027.57	+	333.877i	1.14684	+	0.372631i
$897$	1582.29	−	910.485i	1.76398	−	1.01503i
$898$	−113.146	−	155.731i	−0.125997	−	0.173420i
$899$			652.748i			0.726082i
$900$	−1686.61	−	570.675i	−1.87401	−	0.634084i
$901$	−53.4057			−0.0592738
$902$	284.227	−	206.503i	0.315108	−	0.228939i
$903$	−58.8776	−	102.321i	−0.0652023	−	0.113312i
$904$	23.2063	−	71.4215i	0.0256706	−	0.0790061i
$905$	−625.735	+	402.273i	−0.691420	+	0.444501i
$906$	477.476	+	213.415i	0.527016	+	0.235558i
$907$		−	1496.48i		−	1.64992i	−0.565192	−	0.824959i	$-0.691198\pi$
$907$		−	1496.48i		−	1.64992i	0.565192	−	0.824959i	$-0.308802\pi$
$908$	131.063	+	403.372i	0.144343	+	0.444242i
$909$	−716.338	−	416.349i	−0.788051	−	0.458029i
$910$	359.059	+	1365.14i	0.394570	+	1.50015i
$911$	25.1739	+	34.6490i	0.0276333	+	0.0380340i	0.822610	−	0.568606i	$-0.192517\pi$
$911$	25.1739	+	34.6490i	0.0276333	+	0.0380340i	−0.794977	+	0.606640i	$0.792517\pi$
$912$	423.751	−	89.4300i	0.464639	−	0.0980592i
$913$	126.162	−	173.647i	0.138184	−	0.190194i
$914$	−914.067	−	1258.11i	−1.00007	−	1.37648i
$915$	−41.6865	+	253.267i	−0.0455590	+	0.276795i
$916$	−1839.08	−	1336.17i	−2.00773	−	1.45870i
$917$	219.969	+	676.995i	0.239879	+	0.738271i
$918$	1831.91	+	1343.16i	1.99555	+	1.46314i
$919$	33.9736	+	104.560i	0.0369680	+	0.113776i	0.967838	−	0.251576i	$-0.0809488\pi$
$919$	33.9736	+	104.560i	0.0369680	+	0.113776i	−0.930870	+	0.365352i	$0.880949\pi$
$920$	−873.634	+	2244.94i	−0.949602	+	2.44016i
$921$	−55.8437	+	32.1336i	−0.0606337	+	0.0348899i
$922$	−1982.51	−	644.156i	−2.15023	−	0.698651i
$923$	−267.420	+	194.292i	−0.289729	+	0.210500i
$924$	−490.976	+	543.699i	−0.531360	+	0.588419i
$925$	80.8226	−	706.342i	0.0873757	−	0.763613i
$926$			1031.63i			1.11408i
$927$	−1233.30	+	1104.02i	−1.33043	+	1.19096i
$928$	−28.2829	−	9.18968i	−0.0304773	−	0.00990267i
$929$	−1367.63	−	444.370i	−1.47215	−	0.478332i	−0.540395	−	0.841411i	$-0.681725\pi$
$929$	−1367.63	−	444.370i	−1.47215	−	0.478332i	−0.931758	+	0.363080i	$0.881725\pi$
$930$	−2653.78	+	403.868i	−2.85352	+	0.434267i
$931$	−77.5300	−	238.613i	−0.0832761	−	0.256297i
$932$	3184.84			3.41721
$933$	23.4940	−	52.5634i	0.0251811	−	0.0563381i
$934$	−45.2016	−	32.8409i	−0.0483957	−	0.0351616i
$935$	731.043	+	284.490i	0.781864	+	0.304267i
$936$	1545.39	−	1383.39i	1.65105	−	1.47798i
$937$	−689.179	+	948.573i	−0.735516	+	1.01235i	0.263348	+	0.964701i	$0.415173\pi$
$937$	−689.179	+	948.573i	−0.735516	+	1.01235i	−0.998864	+	0.0476503i	$0.984827\pi$
$938$	191.943	+	139.455i	0.204630	+	0.148672i
$939$	−1464.26	−	156.044i	−1.55939	−	0.166181i
$940$	−81.0262	+	208.210i	−0.0861980	+	0.221500i
$941$	30.1867	−	41.5484i	0.0320794	−	0.0441535i	−0.792676	−	0.609643i	$-0.791313\pi$
$941$	30.1867	−	41.5484i	0.0320794	−	0.0441535i	0.824755	+	0.565490i	$0.191313\pi$
$942$	526.031	−	1176.89i	0.558419	−	1.24936i
$943$		−	564.031i		−	0.598124i
$944$	−1124.37	+	365.329i	−1.19107	+	0.387001i
$945$	−626.625	+	161.908i	−0.663095	+	0.171331i
$946$	−56.3506	+	173.429i	−0.0595673	+	0.183329i
$947$	−339.478	+	1044.81i	−0.358477	+	1.10328i	0.595489	+	0.803364i	$0.296958\pi$
$947$	−339.478	+	1044.81i	−0.358477	+	1.10328i	−0.953966	+	0.299915i	$0.903042\pi$
$948$	44.6912	−	419.367i	0.0471427	−	0.442370i
$949$	−2223.05			−2.34252
$950$	826.748	+	94.5999i	0.870261	+	0.0995789i
$951$	−390.399	+	432.322i	−0.410515	+	0.454597i
$952$	927.800	+	1277.01i	0.974580	+	1.34139i
$953$	282.837	−	870.484i	0.296786	−	0.913415i	−0.685829	−	0.727763i	$-0.740560\pi$
$953$	282.837	−	870.484i	0.296786	−	0.913415i	0.982616	−	0.185652i	$-0.0594397\pi$
$954$	−66.5342	−	14.3438i	−0.0697423	−	0.0150354i
$955$	−75.0480	−	29.2054i	−0.0785843	−	0.0305816i
$956$	−1899.91	+	617.319i	−1.98736	+	0.645731i
$957$	162.931	−	180.427i	0.170252	−	0.188534i
$958$	−563.038	+	182.942i	−0.587722	+	0.190963i
$959$	−315.004	+	433.566i	−0.328472	+	0.452102i
$960$	165.735	−	1006.93i	0.172641	−	1.04889i
$961$	−1397.28	+	1015.18i	−1.45398	+	1.05638i
$962$	1354.82	+	984.334i	1.40834	+	1.02322i
$963$	148.000	−	254.638i	0.153687	−	0.264421i
$964$	−207.183	+	150.527i	−0.214920	+	0.156149i
$965$	−962.363	+	253.121i	−0.997267	+	0.262301i
$966$	365.618	+	1732.43i	0.378486	+	1.79340i
$967$	−384.880	+	125.055i	−0.398015	+	0.129323i	−0.501183	−	0.865341i	$-0.667102\pi$
$967$	−384.880	+	125.055i	−0.398015	+	0.129323i	0.103169	+	0.994664i	$0.467102\pi$
$968$	−1074.83			−1.11036
$969$	−643.797	−	287.755i	−0.664393	−	0.296960i
$970$	1462.57	+	2275.02i	1.50780	+	2.34538i
$971$	497.083	+	161.512i	0.511929	+	0.166336i	0.553580	−	0.832796i	$-0.313261\pi$
$971$	497.083	+	161.512i	0.511929	+	0.166336i	−0.0416501	+	0.999132i	$0.513261\pi$
$972$	1276.35	+	1438.34i	1.31312	+	1.47977i
$973$	−32.3598	−	44.5395i	−0.0332578	−	0.0457754i
$974$			2362.22i			2.42528i
$975$	1174.43	−	507.963i	1.20454	−	0.520987i
$976$	256.157			0.262456
$977$	−669.765	+	486.613i	−0.685533	+	0.498069i	−0.875189	−	0.483782i	$-0.839263\pi$
$977$	−669.765	+	486.613i	−0.685533	+	0.498069i	0.189656	+	0.981851i	$0.439263\pi$
$978$	1304.44	−	750.604i	1.33379	−	0.767489i
$979$	−109.135	+	335.882i	−0.111476	+	0.343086i
$980$	1027.74	+	58.6081i	1.04872	+	0.0598042i
$981$	434.938	−	192.139i	0.443362	−	0.195861i
$982$			1695.20i			1.72627i
$983$	−199.079	−	612.701i	−0.202521	−	0.623297i	−0.999806	−	0.0196933i	$-0.993731\pi$
$983$	−199.079	−	612.701i	−0.202521	−	0.623297i	0.797285	−	0.603603i	$-0.206269\pi$
$984$	−132.328	−	627.020i	−0.134480	−	0.637215i
$985$	−166.477	−	9.49349i	−0.169012	−	0.00963806i
$986$	−622.586	−	856.916i	−0.631426	−	0.869083i
$987$	16.7695	+	79.4601i	0.0169904	+	0.0805067i
$988$	−765.297	+	1053.34i	−0.774592	+	1.06613i
$989$	172.080	+	236.848i	0.173994	+	0.239482i
$990$	834.344	+	550.770i	0.842771	+	0.556333i
$991$	400.041	+	290.647i	0.403674	+	0.293286i	0.771036	−	0.636792i	$-0.219739\pi$
$991$	400.041	+	290.647i	0.403674	+	0.293286i	−0.367362	+	0.930078i	$0.619739\pi$
$992$	−37.8447	−	116.474i	−0.0381499	−	0.117413i
$993$	302.698	−	335.203i	0.304832	−	0.337566i
$994$	−99.0700	−	304.906i	−0.0996680	−	0.306747i
$995$	−267.925	−	1018.65i	−0.269271	−	1.02377i
$996$	−394.845	−	686.183i	−0.396430	−	0.688939i
$997$	−1302.86	−	423.324i	−1.30678	−	0.424598i	−0.428844	−	0.903379i	$-0.641079\pi$
$997$	−1302.86	−	423.324i	−1.30678	−	0.424598i	−0.877934	+	0.478781i	$0.841079\pi$
$998$	2319.43	−	1685.16i	2.32408	−	1.68854i
$999$	−454.012	+	619.219i	−0.454466	+	0.619839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.14.17	yes	72
3.2	odd	2	inner	75.3.h.a.14.2	✓	72
5.2	odd	4		375.3.j.b.176.33		144
5.3	odd	4		375.3.j.b.176.4		144
5.4	even	2		375.3.h.a.74.2		72
15.2	even	4		375.3.j.b.176.3		144
15.8	even	4		375.3.j.b.176.34		144
15.14	odd	2		375.3.h.a.74.17		72
25.9	even	10	inner	75.3.h.a.59.2	yes	72
25.12	odd	20		375.3.j.b.326.3		144
25.13	odd	20		375.3.j.b.326.34		144
25.16	even	5		375.3.h.a.299.17		72
75.38	even	20		375.3.j.b.326.4		144
75.41	odd	10		375.3.h.a.299.2		72
75.59	odd	10	inner	75.3.h.a.59.17	yes	72
75.62	even	20		375.3.j.b.326.33		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.2	✓	72	3.2	odd	2	inner
75.3.h.a.14.17	yes	72	1.1	even	1	trivial
75.3.h.a.59.2	yes	72	25.9	even	10	inner
75.3.h.a.59.17	yes	72	75.59	odd	10	inner
375.3.h.a.74.2		72	5.4	even	2
375.3.h.a.74.17		72	15.14	odd	2
375.3.h.a.299.2		72	75.41	odd	10
375.3.h.a.299.17		72	25.16	even	5
375.3.j.b.176.3		144	15.2	even	4
375.3.j.b.176.4		144	5.3	odd	4
375.3.j.b.176.33		144	5.2	odd	4
375.3.j.b.176.34		144	15.8	even	4
375.3.j.b.326.3		144	25.12	odd	20
375.3.j.b.326.4		144	75.38	even	20
375.3.j.b.326.33		144	75.62	even	20
375.3.j.b.326.34		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+(2.79240 - 2.02880i) q^{2} +(-1.49624 - 2.60025i) q^{3} +(2.44541 - 7.52621i) q^{4} +(1.27184 + 4.83554i) q^{5} +(-9.45346 - 4.22537i) q^{6} +4.79411i q^{7} +(-4.17417 - 12.8468i) q^{8} +(-4.52255 + 7.78116i) q^{9} +(13.3618 + 10.9224i) q^{10} +(-3.78331 - 5.20729i) q^{11} +(-23.2289 + 4.90231i) q^{12} +(10.0282 - 13.8026i) q^{13} +(9.72627 + 13.3871i) q^{14} +(10.6706 - 10.5422i) q^{15} +(-12.1108 - 8.79899i) q^{16} +(7.53221 + 23.1818i) q^{17} +(3.15763 + 30.9035i) q^{18} +(-2.98003 - 9.17158i) q^{19} +(39.5034 + 2.25272i) q^{20} +(12.4659 - 7.17312i) q^{21} +(-21.1291 - 6.86525i) q^{22} +(-28.8553 + 20.9646i) q^{23} +(-27.1592 + 30.0757i) q^{24} +(-21.7648 + 12.3001i) q^{25} -58.8876i q^{26} +(26.9997 + 0.117285i) q^{27} +(36.0814 + 11.7236i) q^{28} +(-11.9737 - 3.89048i) q^{29} +(8.40858 - 51.0866i) q^{30} +(-16.0217 - 49.3096i) q^{31} +2.36210 q^{32} +(-7.87949 + 17.6289i) q^{33} +(68.0641 + 49.4514i) q^{34} +(-23.1821 + 6.09735i) q^{35} +(47.5031 + 53.0658i) q^{36} +(-16.7155 + 23.0069i) q^{37} +(-26.9287 - 19.5649i) q^{38} +(-50.8947 - 5.42377i) q^{39} +(56.8122 - 36.5234i) q^{40} +(-9.29508 + 12.7936i) q^{41} +(20.2568 - 45.3209i) q^{42} -8.20810i q^{43} +(-48.4429 + 15.7400i) q^{44} +(-43.3781 - 11.9725i) q^{45} +(-38.0427 + 117.083i) q^{46} +(-1.74488 + 5.37018i) q^{47} +(-4.75896 + 44.6564i) q^{48} +26.0166 q^{49} +(-35.8217 + 78.5032i) q^{50} +(49.0083 - 54.2710i) q^{51} +(-79.3583 - 109.227i) q^{52} +(-0.677064 + 2.08379i) q^{53} +(75.6321 - 54.4495i) q^{54} +(20.3682 - 24.9172i) q^{55} +(61.5888 - 20.0114i) q^{56} +(-19.3895 + 21.4717i) q^{57} +(-41.3282 + 13.4284i) q^{58} +(46.4201 - 63.8918i) q^{59} +(-53.2488 - 106.089i) q^{60} +(-13.8436 + 10.0580i) q^{61} +(-144.778 - 105.187i) q^{62} +(-37.3037 - 21.6816i) q^{63} +(55.0390 - 39.9882i) q^{64} +(79.4974 + 30.9369i) q^{65} +(13.7627 + 65.2128i) q^{66} +(13.6362 - 4.43067i) q^{67} +192.890 q^{68} +(97.6876 + 43.6629i) q^{69} +(-52.3633 + 64.0580i) q^{70} +(-18.4263 - 5.98707i) q^{71} +(118.841 + 25.6203i) q^{72} +(-76.5887 - 105.415i) q^{73} +98.1567i q^{74} +(64.5486 + 38.1900i) q^{75} -76.3146 q^{76} +(24.9643 - 18.1376i) q^{77} +(-153.122 + 88.1098i) q^{78} +(-5.48956 + 16.8951i) q^{79} +(27.1448 - 69.7530i) q^{80} +(-40.0930 - 70.3815i) q^{81} +54.5826i q^{82} +(10.3048 + 31.7148i) q^{83} +(-23.5022 - 111.362i) q^{84} +(-102.516 + 65.9059i) q^{85} +(-16.6526 - 22.9203i) q^{86} +(7.79923 + 36.9555i) q^{87} +(-51.1046 + 70.3395i) q^{88} +(-32.2511 - 44.3899i) q^{89} +(-145.419 + 54.5732i) q^{90} +(66.1712 + 48.0762i) q^{91} +(87.2210 + 268.439i) q^{92} +(-104.245 + 115.439i) q^{93} +(6.02261 + 18.5357i) q^{94} +(40.5594 - 26.0748i) q^{95} +(-3.53425 - 6.14203i) q^{96} +(149.045 + 48.4277i) q^{97} +(72.6486 - 52.7823i) q^{98} +(57.6290 - 5.88837i) 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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