LMFDB - Embedded newform 75.3.h.a.29.2

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			29.2
Character	$\chi$	$=$	75.29
Dual form			75.3.h.a.44.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10327 + 3.39551i) q^{2} +(-0.907156 + 2.85956i) q^{3} +(-7.07623 - 5.14118i) q^{4} +(2.46900 + 4.34788i) q^{5} +(-8.70882 - 6.23512i) q^{6} +0.132726i q^{7} +(13.7104 - 9.96116i) q^{8} +(-7.35413 - 5.18813i) q^{9} +(-17.4872 + 3.58664i) q^{10} +(4.25956 + 1.38402i) q^{11} +(21.1208 - 15.5710i) q^{12} +(18.9526 - 6.15806i) q^{13} +(-0.450674 - 0.146433i) q^{14} +(-14.6728 + 3.11604i) q^{15} +(7.88551 + 24.2691i) q^{16} +(-18.9405 + 13.7611i) q^{17} +(25.7300 - 19.2472i) q^{18} +(-18.1615 + 13.1951i) q^{19} +(4.88202 - 43.4602i) q^{20} +(-0.379539 - 0.120404i) q^{21} +(-9.39889 + 12.9365i) q^{22} +(-8.14650 + 25.0723i) q^{23} +(16.0471 + 48.2419i) q^{24} +(-12.8081 + 21.4698i) q^{25} +71.1477i q^{26} +(21.5071 - 16.3231i) q^{27} +(0.682371 - 0.939203i) q^{28} +(13.8383 - 19.0467i) q^{29} +(5.60745 - 53.2594i) q^{30} +(19.3057 - 14.0264i) q^{31} -23.3181 q^{32} +(-7.82176 + 10.9249i) q^{33} +(-25.8295 - 79.4951i) q^{34} +(-0.577078 + 0.327701i) q^{35} +(25.3664 + 74.5214i) q^{36} +(29.3131 - 9.52439i) q^{37} +(-24.7671 - 76.2254i) q^{38} +(0.416390 + 59.7823i) q^{39} +(77.1608 + 35.0169i) q^{40} +(31.0138 - 10.0770i) q^{41} +(0.827565 - 1.15589i) q^{42} +52.1832i q^{43} +(-23.0262 - 31.6928i) q^{44} +(4.40000 - 44.7844i) q^{45} +(-76.1457 - 55.3231i) q^{46} +(-8.72933 - 6.34223i) q^{47} +(-76.5523 + 0.533195i) q^{48} +48.9824 q^{49} +(-58.7703 - 67.1770i) q^{50} +(-22.1687 - 66.6451i) q^{51} +(-165.773 - 53.8628i) q^{52} +(16.7363 + 12.1596i) q^{53} +(31.6972 + 91.0364i) q^{54} +(4.49933 + 21.9372i) q^{55} +(1.32211 + 1.81973i) q^{56} +(-21.2569 - 63.9039i) q^{57} +(49.4061 + 68.0017i) q^{58} +(-56.7282 + 18.4321i) q^{59} +(119.848 + 53.3856i) q^{60} +(26.7105 - 82.2063i) q^{61} +(26.3274 + 81.0275i) q^{62} +(0.688602 - 0.976087i) q^{63} +(-5.81589 + 17.8995i) q^{64} +(73.5684 + 67.1992i) q^{65} +(-28.4663 - 38.6120i) q^{66} +(14.7506 + 20.3024i) q^{67} +204.776 q^{68} +(-64.3056 - 46.0399i) q^{69} +(-0.476042 - 2.32102i) q^{70} +(14.2320 - 19.5886i) q^{71} +(-152.508 + 2.12457i) q^{72} +(-23.3069 - 7.57287i) q^{73} +110.041i q^{74} +(-49.7753 - 56.1019i) q^{75} +196.354 q^{76} +(-0.183695 + 0.565356i) q^{77} +(-203.451 - 64.5421i) q^{78} +(5.10413 + 3.70837i) q^{79} +(-86.0498 + 94.2057i) q^{80} +(27.1666 + 76.3084i) q^{81} +116.425i q^{82} +(0.0376952 - 0.0273872i) q^{83} +(2.06669 + 2.80328i) q^{84} +(-106.596 - 48.3750i) q^{85} +(-177.189 - 57.5721i) q^{86} +(41.9118 + 56.8497i) q^{87} +(72.1866 - 23.4548i) q^{88} +(42.9445 + 13.9535i) q^{89} +(147.212 + 64.3494i) q^{90} +(0.817337 + 2.51550i) q^{91} +(186.548 - 135.535i) q^{92} +(22.5960 + 67.9298i) q^{93} +(31.1659 - 22.6434i) q^{94} +(-102.212 - 46.3853i) q^{95} +(21.1532 - 66.6795i) q^{96} +(75.4840 - 103.895i) q^{97} +(-54.0407 + 166.320i) q^{98} +(-24.1449 - 32.2774i) 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.10327	+	3.39551i	−0.551634	+	1.69776i	0.153035	+	0.988221i	$0.451095\pi$
$2$	−1.10327	+	3.39551i	−0.551634	+	1.69776i	−0.704670	+	0.709535i	$0.748905\pi$
$3$	−0.907156	+	2.85956i	−0.302385	+	0.953186i
$3$	−0.907156	+	2.85956i	−0.302385	+	0.953186i
$4$	−7.07623	−	5.14118i	−1.76906	−	1.28530i
$5$	2.46900	+	4.34788i	0.493800	+	0.869575i
$5$	2.46900	+	4.34788i	0.493800	+	0.869575i
$6$	−8.70882	−	6.23512i	−1.45147	−	1.03919i
$7$			0.132726i			0.0189609i	0.999955	+	0.00948045i	$0.00301777\pi$
$7$			0.132726i			0.0189609i	−0.999955	+	0.00948045i	$0.996982\pi$
$8$	13.7104	−	9.96116i	1.71380	−	1.24515i
$9$	−7.35413	−	5.18813i	−0.817126	−	0.576459i
$10$	−17.4872	+	3.58664i	−1.74872	+	0.358664i
$11$	4.25956	+	1.38402i	0.387233	+	0.125820i	0.496162	−	0.868230i	$-0.334742\pi$
$11$	4.25956	+	1.38402i	0.387233	+	0.125820i	−0.108929	+	0.994050i	$0.534742\pi$
$12$	21.1208	−	15.5710i	1.76006	−	1.29759i
$13$	18.9526	−	6.15806i	1.45789	−	0.473697i	0.530465	−	0.847707i	$-0.322017\pi$
$13$	18.9526	−	6.15806i	1.45789	−	0.473697i	0.927425	+	0.374010i	$0.122017\pi$
$14$	−0.450674	−	0.146433i	−0.0321910	−	0.0104595i
$15$	−14.6728	+	3.11604i	−0.978185	+	0.207736i
$16$	7.88551	+	24.2691i	0.492844	+	1.51682i
$17$	−18.9405	+	13.7611i	−1.11415	+	0.809477i	−0.983312	−	0.181926i	$-0.941767\pi$
$17$	−18.9405	+	13.7611i	−1.11415	+	0.809477i	−0.130838	+	0.991404i	$0.541767\pi$
$18$	25.7300	−	19.2472i	1.42944	−	1.06929i
$19$	−18.1615	+	13.1951i	−0.955870	+	0.694480i	−0.952188	−	0.305513i	$-0.901172\pi$
$19$	−18.1615	+	13.1951i	−0.955870	+	0.694480i	−0.00368181	+	0.999993i	$0.501172\pi$
$20$	4.88202	−	43.4602i	0.244101	−	2.17301i
$21$	−0.379539	−	0.120404i	−0.0180733	−	0.00573350i
$22$	−9.39889	+	12.9365i	−0.427222	+	0.588021i
$23$	−8.14650	+	25.0723i	−0.354196	+	1.09010i	0.602279	+	0.798286i	$0.294259\pi$
$23$	−8.14650	+	25.0723i	−0.354196	+	1.09010i	−0.956474	+	0.291816i	$0.905741\pi$
$24$	16.0471	+	48.2419i	0.668628	+	2.01008i
$25$	−12.8081	+	21.4698i	−0.512323	+	0.858793i
$26$			71.1477i			2.73645i
$27$	21.5071	−	16.3231i	0.796560	−	0.604560i
$28$	0.682371	−	0.939203i	0.0243704	−	0.0335429i
$29$	13.8383	−	19.0467i	0.477182	−	0.656784i	−0.500779	−	0.865575i	$-0.666953\pi$
$29$	13.8383	−	19.0467i	0.477182	−	0.656784i	0.977960	+	0.208791i	$0.0669529\pi$
$30$	5.60745	−	53.2594i	0.186915	−	1.77531i
$31$	19.3057	−	14.0264i	0.622764	−	0.452464i	−0.231122	−	0.972925i	$-0.574240\pi$
$31$	19.3057	−	14.0264i	0.622764	−	0.452464i	0.853886	+	0.520460i	$0.174240\pi$
$32$	−23.3181			−0.728691
$33$	−7.82176	+	10.9249i	−0.237023	+	0.331059i
$34$	−25.8295	−	79.4951i	−0.759692	−	2.33809i
$35$	−0.577078	+	0.327701i	−0.0164879	+	0.00936290i
$36$	25.3664	+	74.5214i	0.704623	+	2.07004i
$37$	29.3131	−	9.52439i	0.792245	−	0.257416i	0.115185	−	0.993344i	$-0.463254\pi$
$37$	29.3131	−	9.52439i	0.792245	−	0.257416i	0.677060	+	0.735928i	$0.263254\pi$
$38$	−24.7671	−	76.2254i	−0.651767	−	2.00593i
$39$	0.416390	+	59.7823i	0.0106767	+	1.53288i
$40$	77.1608	+	35.0169i	1.92902	+	0.875422i
$41$	31.0138	−	10.0770i	0.756433	−	0.245780i	0.0946862	−	0.995507i	$-0.469815\pi$
$41$	31.0138	−	10.0770i	0.756433	−	0.245780i	0.661747	+	0.749727i	$0.269815\pi$
$42$	0.827565	−	1.15589i	0.0197039	−	0.0275212i
$43$			52.1832i			1.21356i	0.794869	+	0.606781i	$0.207540\pi$
$43$			52.1832i			1.21356i	−0.794869	+	0.606781i	$0.792460\pi$
$44$	−23.0262	−	31.6928i	−0.523322	−	0.720292i
$45$	4.40000	−	44.7844i	0.0977777	−	0.995208i
$46$	−76.1457	−	55.3231i	−1.65534	−	1.20268i
$47$	−8.72933	−	6.34223i	−0.185731	−	0.134941i	0.491035	−	0.871140i	$-0.336619\pi$
$47$	−8.72933	−	6.34223i	−0.185731	−	0.134941i	−0.676765	+	0.736199i	$0.736619\pi$
$48$	−76.5523	+	0.533195i	−1.59484	+	0.0111082i
$49$	48.9824			0.999640
$50$	−58.7703	−	67.1770i	−1.17541	−	1.34354i
$51$	−22.1687	−	66.6451i	−0.434679	−	1.30677i
$52$	−165.773	−	53.8628i	−3.18793	−	1.03582i
$53$	16.7363	+	12.1596i	0.315779	+	0.229427i	0.734372	−	0.678747i	$-0.237477\pi$
$53$	16.7363	+	12.1596i	0.315779	+	0.229427i	−0.418593	+	0.908174i	$0.637477\pi$
$54$	31.6972	+	91.0364i	0.586986	+	1.68586i
$55$	4.49933	+	21.9372i	0.0818060	+	0.398858i
$56$	1.32211	+	1.81973i	0.0236091	+	0.0324951i
$57$	−21.2569	−	63.9039i	−0.372927	−	1.12112i
$58$	49.4061	+	68.0017i	0.851830	+	1.17244i
$59$	−56.7282	+	18.4321i	−0.961496	+	0.312409i	−0.747378	−	0.664399i	$-0.768688\pi$
$59$	−56.7282	+	18.4321i	−0.961496	+	0.312409i	−0.214118	+	0.976808i	$0.568688\pi$
$60$	119.848	+	53.3856i	1.99747	+	0.889760i
$61$	26.7105	−	82.2063i	0.437876	−	1.34764i	−0.452234	−	0.891899i	$-0.649373\pi$
$61$	26.7105	−	82.2063i	0.437876	−	1.34764i	0.890110	−	0.455745i	$-0.150627\pi$
$62$	26.3274	+	81.0275i	0.424636	+	1.30690i
$63$	0.688602	−	0.976087i	0.0109302	−	0.0154934i
$64$	−5.81589	+	17.8995i	−0.0908733	+	0.279679i
$65$	73.5684	+	67.1992i	1.13182	+	1.03383i
$66$	−28.4663	−	38.6120i	−0.431307	−	0.585031i
$67$	14.7506	+	20.3024i	0.220158	+	0.303021i	0.904782	−	0.425875i	$-0.140034\pi$
$67$	14.7506	+	20.3024i	0.220158	+	0.303021i	−0.684624	+	0.728896i	$0.740034\pi$
$68$	204.776			3.01141
$69$	−64.3056	−	46.0399i	−0.931966	−	0.667245i
$70$	−0.476042	−	2.32102i	−0.00680060	−	0.0331574i
$71$	14.2320	−	19.5886i	0.200450	−	0.275896i	−0.696944	−	0.717126i	$-0.745457\pi$
$71$	14.2320	−	19.5886i	0.200450	−	0.275896i	0.897394	+	0.441229i	$0.145457\pi$
$72$	−152.508	+	2.12457i	−2.11816	+	0.0295079i
$73$	−23.3069	−	7.57287i	−0.319273	−	0.103738i	0.144996	−	0.989432i	$-0.453683\pi$
$73$	−23.3069	−	7.57287i	−0.319273	−	0.103738i	−0.464269	+	0.885694i	$0.653683\pi$
$74$			110.041i			1.48704i
$75$	−49.7753	−	56.1019i	−0.663670	−	0.748025i
$76$	196.354			2.58360
$77$	−0.183695	+	0.565356i	−0.00238565	+	0.00734229i
$78$	−203.451	−	64.5421i	−2.60834	−	0.827462i
$79$	5.10413	+	3.70837i	0.0646093	+	0.0469414i	0.619621	−	0.784901i	$-0.287286\pi$
$79$	5.10413	+	3.70837i	0.0646093	+	0.0469414i	−0.555012	+	0.831842i	$0.687286\pi$
$80$	−86.0498	+	94.2057i	−1.07562	+	1.17757i
$81$	27.1666	+	76.3084i	0.335390	+	0.942079i
$82$			116.425i			1.41982i
$83$	0.0376952	−	0.0273872i	0.000454159	−	0.000329966i	−0.587558	−	0.809182i	$-0.699911\pi$
$83$	0.0376952	−	0.0273872i	0.000454159	−	0.000329966i	0.588012	+	0.808852i	$0.299911\pi$
$84$	2.06669	+	2.80328i	0.0246034	+	0.0333724i
$85$	−106.596	−	48.3750i	−1.25407	−	0.569118i
$86$	−177.189	−	57.5721i	−2.06033	−	0.669443i
$87$	41.9118	+	56.8497i	0.481745	+	0.653445i
$88$	72.1866	−	23.4548i	0.820302	−	0.266532i
$89$	42.9445	+	13.9535i	0.482522	+	0.156781i	0.540170	−	0.841556i	$-0.318360\pi$
$89$	42.9445	+	13.9535i	0.482522	+	0.156781i	−0.0576478	+	0.998337i	$0.518360\pi$
$90$	147.212	+	64.3494i	1.63568	+	0.714994i
$91$	0.817337	+	2.51550i	0.00898173	+	0.0276429i
$92$	186.548	−	135.535i	2.02770	−	1.47321i
$93$	22.5960	+	67.9298i	0.242968	+	0.730428i
$94$	31.1659	−	22.6434i	0.331552	−	0.240887i
$95$	−102.212	−	46.3853i	−1.07591	−	0.488267i
$96$	21.1532	−	66.6795i	0.220346	−	0.694578i
$97$	75.4840	−	103.895i	0.778186	−	1.07108i	−0.217294	−	0.976106i	$-0.569723\pi$
$97$	75.4840	−	103.895i	0.778186	−	1.07108i	0.995480	−	0.0949744i	$-0.0302769\pi$
$98$	−54.0407	+	166.320i	−0.551436	+	1.69715i
$99$	−24.1449	−	32.2774i	−0.243888	−	0.326035i
$100$	201.013	−	86.0768i	2.01013	−	0.860768i
$101$		−	8.59255i		−	0.0850747i	−0.999095	−	0.0425374i	$-0.986456\pi$
$101$		−	8.59255i		−	0.0850747i	0.999095	−	0.0425374i	$-0.0135441\pi$
$102$	250.752	−	1.74652i	2.45835	−	0.0171227i
$103$	18.2784	−	25.1580i	0.177460	−	0.244252i	−0.711016	−	0.703176i	$-0.751765\pi$
$103$	18.2784	−	25.1580i	0.177460	−	0.244252i	0.888476	+	0.458923i	$0.151765\pi$
$104$	198.505	−	273.219i	1.90870	−	2.62710i
$105$	−0.413581	−	1.94746i	−0.00393887	−	0.0185473i
$106$	−59.7527	+	43.4129i	−0.563705	+	0.409555i
$107$	−2.91437			−0.0272371			−0.0136185	−	0.999907i	$-0.504335\pi$
$107$	−2.91437			−0.0272371			−0.0136185	+	0.999907i	$0.504335\pi$
$108$	−236.110	+	4.93422i	−2.18620	+	0.0456872i
$109$	28.0957	+	86.4698i	0.257759	+	0.793301i	0.993274	+	0.115792i	$0.0369405\pi$
$109$	28.0957	+	86.4698i	0.257759	+	0.793301i	−0.735514	+	0.677509i	$0.763059\pi$
$110$	−79.4520	−	8.92509i	−0.722291	−	0.0811372i
$111$	0.644011	+	92.4625i	0.00580190	+	0.832995i
$112$	−3.22115	+	1.04661i	−0.0287603	+	0.00934478i
$113$	5.22653	+	16.0856i	0.0462525	+	0.142350i	0.971516	−	0.236975i	$-0.0761560\pi$
$113$	5.22653	+	16.0856i	0.0462525	+	0.142350i	−0.925263	+	0.379326i	$0.876156\pi$
$114$	240.439	−	1.67468i	2.10911	−	0.0146902i
$115$	−129.125	+	26.4836i	−1.12283	+	0.230293i
$116$	−195.846	+	63.6341i	−1.68832	+	0.548570i
$117$	−171.329	−	53.0412i	−1.46435	−	0.453343i
$118$		−	212.957i		−	1.80472i
$119$	−1.82646	−	2.51391i	−0.0153484	−	0.0211253i
$120$	−170.130	+	188.880i	−1.41775	+	1.57400i
$121$	−81.6627	−	59.3314i	−0.674898	−	0.490342i
$122$	249.664	+	181.391i	2.04642	+	1.48681i
$123$	0.681376	+	97.8270i	0.00553964	+	0.795342i
$124$	−208.724			−1.68326
$125$	−124.971	−	2.67896i	−0.999770	−	0.0214316i
$126$	2.55460	+	3.41504i	0.0202746	+	0.0271035i
$127$	78.8693	+	25.6262i	0.621018	+	0.201781i	0.602592	−	0.798049i	$-0.294135\pi$
$127$	78.8693	+	25.6262i	0.621018	+	0.201781i	0.0184259	+	0.999830i	$0.494135\pi$
$128$	−129.820	−	94.3200i	−1.01422	−	0.736875i
$129$	−149.221	−	47.3383i	−1.15675	−	0.366964i
$130$	−309.341	+	175.664i	−2.37955	+	1.35126i
$131$	3.29343	+	4.53302i	0.0251407	+	0.0346032i	0.821402	−	0.570349i	$-0.193192\pi$
$131$	3.29343	+	4.53302i	0.0251407	+	0.0346032i	−0.796262	+	0.604952i	$0.793192\pi$
$132$	111.516	−	37.0943i	0.844817	−	0.281018i
$133$	−1.75134	−	2.41051i	−0.0131680	−	0.0181242i
$134$	−85.2110	+	27.6867i	−0.635903	+	0.206618i
$135$	124.072	+	53.2085i	0.919052	+	0.394137i
$136$	−122.605	+	377.340i	−0.901508	+	2.77456i
$137$	−63.1504	−	194.357i	−0.460952	−	1.41866i	−0.864003	−	0.503487i	$-0.832050\pi$
$137$	−63.1504	−	194.357i	−0.460952	−	1.41866i	0.403051	−	0.915177i	$-0.367950\pi$
$138$	227.275	−	167.556i	1.64692	−	1.21418i
$139$	22.1430	−	68.1492i	0.159302	−	0.490282i	−0.839269	−	0.543716i	$-0.817017\pi$
$139$	22.1430	−	68.1492i	0.159302	−	0.490282i	0.998571	+	0.0534344i	$0.0170168\pi$
$140$	5.76831	+	0.647972i	0.0412022	+	0.00462837i
$141$	26.0548	−	19.2086i	0.184786	−	0.136231i
$142$	50.8118	+	69.9364i	0.357829	+	0.492510i
$143$	89.2525			0.624144
$144$	67.9202	−	219.389i	0.471668	−	1.52354i
$145$	116.980	+	13.1407i	0.806756	+	0.0906254i
$146$	51.4276	−	70.7840i	0.352244	−	0.484822i
$147$	−44.4347	+	140.068i	−0.302277	+	0.952843i
$148$	−256.393	−	83.3070i	−1.73238	−	0.562885i
$149$		−	244.350i		−	1.63993i	−0.572412	−	0.819966i	$-0.693992\pi$
$149$		−	244.350i		−	1.63993i	0.572412	−	0.819966i	$-0.306008\pi$
$150$	245.410	−	107.117i	1.63607	−	0.714113i
$151$	111.778			0.740250			0.370125	−	0.928982i	$-0.379315\pi$
$151$	111.778			0.740250			0.370125	+	0.928982i	$0.379315\pi$
$152$	−117.562	+	361.820i	−0.773437	+	2.38039i
$153$	210.686	−	2.93504i	1.37703	−	0.0191833i
$154$	−1.71701	−	1.24748i	−0.0111494	−	0.00810052i
$155$	108.651	+	49.3075i	0.700973	+	0.318113i
$156$	304.405	−	425.174i	1.95132	−	2.72548i
$157$			237.336i			1.51169i	0.654750	+	0.755846i	$0.272774\pi$
$157$			237.336i			1.51169i	−0.654750	+	0.755846i	$0.727226\pi$
$158$	−18.2231	+	13.2398i	−0.115336	+	0.0837963i
$159$	−49.9535	+	36.8276i	−0.314173	+	0.231620i
$160$	−57.5724	−	101.384i	−0.359828	−	0.633652i
$161$	−3.32776	−	1.08125i	−0.0206693	−	0.00671587i
$162$	−289.078	+	8.05580i	−1.78443	+	0.0497271i
$163$	−131.840	+	42.8374i	−0.808835	+	0.262806i	−0.684104	−	0.729384i	$-0.739807\pi$
$163$	−131.840	+	42.8374i	−0.808835	+	0.262806i	−0.124730	+	0.992191i	$0.539807\pi$
$164$	−271.268	−	88.1404i	−1.65408	−	0.537442i
$165$	−66.8123	−	7.03437i	−0.404923	−	0.0426326i
$166$	0.0514056	+	0.158210i	0.000309672	+	0.000953073i
$167$	−228.108	+	165.730i	−1.36592	+	0.992398i	−0.367875	+	0.929875i	$0.619915\pi$
$167$	−228.108	+	165.730i	−1.36592	+	0.992398i	−0.998044	+	0.0625226i	$0.980085\pi$
$168$	−6.40297	+	2.12987i	−0.0381129	+	0.0126778i
$169$	184.554	−	134.086i	1.09204	−	0.793411i
$170$	281.862	−	308.577i	1.65801	−	1.81516i
$171$	202.020	−	2.81432i	1.18141	−	0.0164580i
$172$	268.283	−	369.260i	1.55979	−	2.14686i
$173$	56.1084	−	172.684i	0.324326	−	0.998174i	−0.647418	−	0.762136i	$-0.724151\pi$
$173$	56.1084	−	172.684i	0.324326	−	0.998174i	0.971744	−	0.236038i	$-0.0758490\pi$
$174$	−239.274	+	79.5915i	−1.37514	+	0.457422i
$175$	−2.84961	−	1.69997i	−0.0162835	−	0.00971411i
$176$			114.289i			0.649372i
$177$	−1.24633	−	178.938i	−0.00704139	−	1.01095i
$178$	−94.7586	+	130.424i	−0.532351	+	0.732719i
$179$	131.220	−	180.609i	0.733073	−	1.00899i	−0.265914	−	0.963997i	$-0.585674\pi$
$179$	131.220	−	180.609i	0.733073	−	1.00899i	0.998987	−	0.0449920i	$-0.0143262\pi$
$180$	−261.380	+	294.284i	−1.45211	+	1.63491i
$181$	−76.5018	+	55.5818i	−0.422662	+	0.307082i	−0.778708	−	0.627387i	$-0.784125\pi$
$181$	−76.5018	+	55.5818i	−0.422662	+	0.307082i	0.356046	+	0.934468i	$0.384125\pi$
$182$	−9.44317			−0.0518855
$183$	210.843	+	150.954i	1.15215	+	0.824886i
$184$	138.058	+	424.899i	0.750316	+	2.30924i
$185$	113.785	+	103.934i	0.615053	+	0.561805i
$186$	−255.586	+	1.78018i	−1.37412	+	0.00957088i
$187$	−99.7241	+	32.4023i	−0.533284	+	0.173274i
$188$	29.1642	+	89.7582i	0.155129	+	0.477437i
$189$	2.16651	+	2.85456i	0.0114630	+	0.0151035i
$190$	270.269	−	295.885i	1.42247	−	1.55729i
$191$	202.401	−	65.7641i	1.05969	−	0.344315i	0.273227	−	0.961950i	$-0.411909\pi$
$191$	202.401	−	65.7641i	1.05969	−	0.344315i	0.786465	+	0.617635i	$0.211909\pi$
$192$	−45.9087	−	32.8685i	−0.239108	−	0.171190i
$193$		−	117.770i		−	0.610205i	−0.952319	−	0.305103i	$-0.901309\pi$
$193$		−	117.770i		−	0.610205i	0.952319	−	0.305103i	$-0.0986908\pi$
$194$	269.497	+	370.931i	1.38916	+	1.91201i
$195$	−258.898	+	149.413i	−1.32768	+	0.766220i
$196$	−346.611	−	251.827i	−1.76842	−	1.28483i
$197$	77.3876	+	56.2254i	0.392830	+	0.285408i	0.766614	−	0.642108i	$-0.221940\pi$
$197$	77.3876	+	56.2254i	0.392830	+	0.285408i	−0.373784	+	0.927516i	$0.621940\pi$
$198$	136.237	−	46.3738i	0.688064	−	0.234211i
$199$	109.035			0.547916			0.273958	−	0.961742i	$-0.411667\pi$
$199$	109.035			0.547916			0.273958	+	0.961742i	$0.411667\pi$
$200$	38.2610	+	421.942i	0.191305	+	2.10971i
$201$	−71.4371	+	23.7627i	−0.355408	+	0.118222i
$202$	29.1761	+	9.47989i	0.144436	+	0.0469301i
$203$	2.52800	+	1.83670i	0.0124532	+	0.00904780i
$204$	−185.764	+	585.569i	−0.910608	+	2.87044i
$205$	120.386	+	109.964i	0.587251	+	0.536410i
$206$	65.2583	+	89.8204i	0.316788	+	0.436021i
$207$	189.989	−	142.120i	0.917821	−	0.686571i
$208$	298.901	+	411.402i	1.43703	+	1.97790i
$209$	−95.6224	+	31.0696i	−0.457524	+	0.148658i
$210$	7.06893	+	0.744257i	0.0336616	+	0.00354408i
$211$	16.4332	−	50.5763i	0.0778826	−	0.239698i	−0.904534	−	0.426403i	$-0.859781\pi$
$211$	16.4332	−	50.5763i	0.0778826	−	0.239698i	0.982416	+	0.186705i	$0.0597807\pi$
$212$	−55.9149	−	172.088i	−0.263750	−	0.811738i
$213$	43.1042	+	58.4671i	0.202367	+	0.274494i
$214$	3.21533	−	9.89578i	0.0150249	−	0.0462420i
$215$	−226.886	+	128.840i	−1.05528	+	0.599257i
$216$	132.273	−	438.032i	0.612375	−	2.02792i
$217$	1.86167	+	2.56237i	0.00857913	+	0.0118082i
$218$	−324.606			−1.48902
$219$	42.7981	−	59.7776i	0.195425	−	0.272957i
$220$	80.9449	−	178.365i	0.367931	−	0.810748i
$221$	−274.230	+	377.446i	−1.24086	+	1.70790i
$222$	−314.668	−	99.8242i	−1.41742	−	0.449659i
$223$	−291.289	−	94.6454i	−1.30623	−	0.424419i	−0.428483	−	0.903550i	$-0.640952\pi$
$223$	−291.289	−	94.6454i	−1.30623	−	0.424419i	−0.877743	+	0.479131i	$0.840952\pi$
$224$		−	3.09493i		−	0.0138166i
$225$	205.581	−	91.4420i	0.913691	−	0.406409i
$226$	−60.3851			−0.267191
$227$	72.1388	−	222.021i	0.317792	−	0.978064i	−0.656798	−	0.754067i	$-0.728089\pi$
$227$	72.1388	−	222.021i	0.317792	−	0.978064i	0.974590	−	0.223997i	$-0.0719106\pi$
$228$	−178.124	+	561.485i	−0.781244	+	2.46265i
$229$	85.0610	+	61.8004i	0.371445	+	0.269871i	0.757810	−	0.652475i	$-0.226269\pi$
$229$	85.0610	+	61.8004i	0.371445	+	0.269871i	−0.386365	+	0.922346i	$0.626269\pi$
$230$	52.5342	−	467.665i	0.228410	−	2.03332i
$231$	−1.45003	−	1.03815i	−0.00627718	−	0.00449417i
$232$		−	398.983i		−	1.71975i
$233$	−59.6300	+	43.3237i	−0.255923	+	0.185939i	−0.708348	−	0.705864i	$-0.750559\pi$
$233$	−59.6300	+	43.3237i	−0.255923	+	0.185939i	0.452425	+	0.891803i	$0.350559\pi$
$234$	369.123	−	523.230i	1.57745	−	2.23602i
$235$	6.02252	−	53.6130i	0.0256278	−	0.228141i
$236$	496.185	+	161.220i	2.10248	+	0.683137i
$237$	−15.2345	+	11.2315i	−0.0642808	+	0.0473903i
$238$	10.5511	−	3.42826i	0.0443323	−	0.0144044i
$239$	68.5286	+	22.2663i	0.286730	+	0.0931644i	0.448851	−	0.893607i	$-0.351833\pi$
$239$	68.5286	+	22.2663i	0.286730	+	0.0931644i	−0.162121	+	0.986771i	$0.551833\pi$
$240$	−191.326	−	331.523i	−0.797191	−	1.38135i
$241$	58.2895	+	179.396i	0.241865	+	0.744384i	0.996136	+	0.0878209i	$0.0279903\pi$
$241$	58.2895	+	179.396i	0.241865	+	0.744384i	−0.754271	+	0.656563i	$0.772010\pi$
$242$	291.556	−	211.828i	1.20478	−	0.875323i
$243$	−242.853	+	8.46076i	−0.999394	+	0.0348179i
$244$	−611.647	+	444.388i	−2.50675	+	1.82126i
$245$	120.938	+	212.969i	0.493623	+	0.869263i
$246$	−332.925	−	105.616i	−1.35335	−	0.429333i
$247$	−262.951	+	361.921i	−1.06458	+	1.46527i
$248$	124.969	−	384.614i	0.503906	−	1.55086i
$249$	0.0441198	+	0.132636i	0.000177188	+	0.000532675i
$250$	146.973	−	421.386i	0.587893	−	1.68554i
$251$		−	230.944i		−	0.920095i	−0.887894	−	0.460048i	$-0.847832\pi$
$251$		−	230.944i		−	0.920095i	0.887894	−	0.460048i	$-0.152168\pi$
$252$	−9.89095	+	3.36679i	−0.0392498	+	0.0133603i
$253$	−69.4010	+	95.5223i	−0.274312	+	0.377559i
$254$	−174.028	+	239.529i	−0.685150	+	0.943028i
$255$	235.030	−	260.933i	0.921687	−	1.02327i
$256$	402.587	−	292.496i	1.57260	−	1.14256i
$257$	−420.523			−1.63628			−0.818138	−	0.575022i	$-0.804994\pi$
$257$	−420.523			−1.63628			−0.818138	+	0.575022i	$0.804994\pi$
$258$	325.368	−	454.454i	1.26112	−	1.76145i
$259$	1.26414	+	3.89061i	0.00488084	+	0.0150217i
$260$	−175.104	−	853.746i	−0.673476	−	3.28364i
$261$	−200.585	+	68.2776i	−0.768527	+	0.261600i
$262$	−19.0255	+	6.18175i	−0.0726163	+	0.0235945i
$263$	28.6326	+	88.1221i	0.108869	+	0.335065i	0.990619	−	0.136652i	$-0.0436343\pi$
$263$	28.6326	+	88.1221i	0.108869	+	0.335065i	−0.881750	+	0.471717i	$0.843634\pi$
$264$	1.58595	+	227.699i	0.00600737	+	0.862496i
$265$	−11.5466	+	102.789i	−0.0435723	+	0.387884i
$266$	10.1171	−	3.28725i	0.0380343	−	0.0123581i
$267$	−78.8582	+	110.144i	−0.295349	+	0.412525i
$268$		−	219.500i		−	0.819031i
$269$	76.2251	+	104.915i	0.283365	+	0.390018i	0.926845	−	0.375445i	$-0.122510\pi$
$269$	76.2251	+	104.915i	0.283365	+	0.390018i	−0.643480	+	0.765463i	$0.722510\pi$
$270$	−317.555	+	362.585i	−1.17613	+	1.34291i
$271$	17.3266	+	12.5885i	0.0639357	+	0.0464520i	0.619294	−	0.785159i	$-0.287419\pi$
$271$	17.3266	+	12.5885i	0.0639357	+	0.0464520i	−0.555358	+	0.831611i	$0.687419\pi$
$272$	−483.326	−	351.157i	−1.77693	−	1.29102i
$273$	−7.93468	+	0.0552659i	−0.0290648	+	0.000202439i
$274$	729.613			2.66282
$275$	−84.2714	+	73.7255i	−0.306441	+	0.268093i
$276$	218.342	+	656.396i	0.791095	+	2.37825i
$277$	−56.8011	−	18.4558i	−0.205058	−	0.0666275i	0.204687	−	0.978827i	$-0.434382\pi$
$277$	−56.8011	−	18.4558i	−0.205058	−	0.0666275i	−0.409745	+	0.912200i	$0.634382\pi$
$278$	206.972	+	150.374i	0.744502	+	0.540913i
$279$	−214.747	+	2.99162i	−0.769704	+	0.0107227i
$280$	−4.64766	+	10.2413i	−0.0165988	+	0.0365760i
$281$	125.832	+	173.192i	0.447799	+	0.616343i	0.971923	−	0.235299i	$-0.0756071\pi$
$281$	125.832	+	173.192i	0.447799	+	0.616343i	−0.524124	+	0.851642i	$0.675607\pi$
$282$	36.4777	+	109.662i	0.129353	+	0.388872i
$283$	−238.025	−	327.613i	−0.841076	−	1.15764i	−0.985759	−	0.168164i	$-0.946216\pi$
$283$	−238.025	−	327.613i	−0.841076	−	1.15764i	0.144683	−	0.989478i	$-0.453784\pi$
$284$	−201.418	+	65.4446i	−0.709217	+	0.230439i
$285$	225.363	−	250.201i	0.790749	−	0.877898i
$286$	−98.4695	+	303.058i	−0.344299	+	1.05964i
$287$	1.33748	+	4.11634i	0.00466021	+	0.0143427i
$288$	171.485	+	120.977i	0.595432	+	0.420060i
$289$	80.0702	−	246.431i	0.277060	−	0.852702i
$290$	−173.679	+	382.708i	−0.598894	+	1.31968i
$291$	228.617	+	310.100i	0.785627	+	1.06563i
$292$	125.992	+	173.413i	0.431478	+	0.593879i
$293$	50.9833			0.174004			0.0870021	−	0.996208i	$-0.472271\pi$
$293$	50.9833			0.174004			0.0870021	+	0.996208i	$0.472271\pi$
$294$	−426.579	−	305.411i	−1.45095	−	1.03881i
$295$	−220.203	−	201.139i	−0.746450	−	0.681826i
$296$	307.019	−	422.575i	1.03723	−	1.42762i
$297$	114.202	−	39.7632i	0.384520	−	0.133883i
$298$	829.693	+	269.584i	2.78420	+	0.904643i
$299$			525.352i			1.75703i
$300$	63.7910	+	652.894i	0.212637	+	2.17631i
$301$	−6.92608			−0.0230102
$302$	−123.321	+	379.543i	−0.408348	+	1.25676i
$303$	24.5709	+	7.79478i	0.0810920	+	0.0257254i
$304$	−463.447	−	336.714i	−1.52450	−	1.10761i
$305$	423.371	−	86.8337i	1.38810	−	0.284701i
$306$	−222.477	+	718.624i	−0.727049	+	2.34845i
$307$		−	452.266i		−	1.47318i	−0.676339	−	0.736590i	$-0.736435\pi$
$307$		−	452.266i		−	1.47318i	0.676339	−	0.736590i	$-0.263565\pi$
$308$	4.20647	−	3.05618i	0.0136574	−	0.00992267i
$309$	55.3594	+	75.0902i	0.179157	+	0.243010i
$310$	−287.295	+	314.525i	−0.926759	+	1.01460i
$311$	−552.577	−	179.543i	−1.77678	−	0.577309i	−0.778070	−	0.628177i	$-0.783801\pi$
$311$	−552.577	−	179.543i	−1.77678	−	0.577309i	−0.998705	+	0.0508679i	$0.983801\pi$
$312$	601.210	+	815.489i	1.92695	+	2.61375i
$313$	−47.2081	+	15.3388i	−0.150825	+	0.0490059i	−0.383456	−	0.923559i	$-0.625266\pi$
$313$	−47.2081	+	15.3388i	−0.150825	+	0.0490059i	0.232632	+	0.972565i	$0.425266\pi$
$314$	−805.876	−	261.845i	−2.56648	−	0.833901i
$315$	5.94407	+	0.583996i	0.0188700	+	0.00185395i
$316$	−17.0526	−	52.4826i	−0.0539640	−	0.166084i
$317$	−43.3818	+	31.5187i	−0.136851	+	0.0994282i	−0.654105	−	0.756404i	$-0.726954\pi$
$317$	−43.3818	+	31.5187i	−0.136851	+	0.0994282i	0.517254	+	0.855832i	$0.326954\pi$
$318$	−69.9366	−	210.249i	−0.219926	−	0.661159i
$319$	85.3060	−	61.9784i	0.267417	−	0.194290i
$320$	−92.1842	+	18.9070i	−0.288076	+	0.0590845i
$321$	2.64379	−	8.33381i	0.00823610	−	0.0259620i
$322$	7.34283	−	10.1065i	0.0228038	−	0.0313868i
$323$	162.410	−	499.846i	0.502816	−	1.54751i
$324$	200.079	−	679.645i	0.617526	−	2.09767i
$325$	−110.533	+	485.781i	−0.340103	+	1.49471i
$326$		−	494.926i		−	1.51818i
$327$	−272.753	+	1.89975i	−0.834106	+	0.00580963i
$328$	324.832	−	447.092i	0.990340	−	1.36309i
$329$	0.841781	−	1.15861i	0.00255861	−	0.00352162i
$330$	97.5972	−	219.101i	0.295749	−	0.663943i
$331$	−125.098	+	90.8888i	−0.377939	+	0.274588i	−0.760495	−	0.649344i	$-0.775044\pi$
$331$	−125.098	+	90.8888i	−0.377939	+	0.274588i	0.382557	+	0.923932i	$0.375044\pi$
$332$	−0.407543			−0.00122754
$333$	−264.986	−	82.0363i	−0.795753	−	0.246355i
$334$	−311.075	−	957.390i	−0.931362	−	2.86644i
$335$	−51.8533	+	114.260i	−0.154786	+	0.341076i
$336$	−0.0707690	−	10.1605i	−0.000210622	−	0.0302396i
$337$	440.561	−	143.147i	1.30730	−	0.424769i	0.429187	−	0.903216i	$-0.358800\pi$
$337$	440.561	−	143.147i	1.30730	−	0.424769i	0.878117	+	0.478447i	$0.158800\pi$
$338$	251.679	+	774.590i	0.744614	+	2.29168i
$339$	−50.7390	+	0.353402i	−0.149673	+	0.00104248i
$340$	505.592	+	890.342i	1.48704	+	2.61865i
$341$	101.646	−	33.0269i	0.298084	−	0.0968532i
$342$	−213.327	+	689.067i	−0.623762	+	2.01482i
$343$			13.0048i			0.0379150i
$344$	519.805	+	715.450i	1.51106	+	2.07980i
$345$	41.4052	−	393.266i	0.120015	−	1.13990i
$346$	524.448	+	381.034i	1.51575	+	1.10125i
$347$	478.959	+	347.984i	1.38029	+	1.00284i	0.996853	+	0.0792673i	$0.0252581\pi$
$347$	478.959	+	347.984i	1.38029	+	1.00284i	0.383432	+	0.923569i	$0.374742\pi$
$348$	−4.30275	−	617.758i	−0.0123642	−	1.77517i
$349$	−191.403			−0.548432			−0.274216	−	0.961668i	$-0.588418\pi$
$349$	−191.403			−0.548432			−0.274216	+	0.961668i	$0.588418\pi$
$350$	8.91615	−	7.80036i	0.0254747	−	0.0222868i
$351$	307.096	−	441.807i	0.874918	−	1.25871i
$352$	−99.3250	−	32.2726i	−0.282173	−	0.0916836i
$353$	33.5112	+	24.3473i	0.0949326	+	0.0689725i	0.634239	−	0.773137i	$-0.281314\pi$
$353$	33.5112	+	24.3473i	0.0949326	+	0.0689725i	−0.539306	+	0.842110i	$0.681314\pi$
$354$	608.963	+	193.185i	1.72023	+	0.545721i
$355$	120.308	+	13.5145i	0.338895	+	0.0380692i
$356$	−232.148	−	319.524i	−0.652100	−	0.897538i
$357$	8.84556	−	2.94236i	0.0247775	−	0.00824192i
$358$	468.489	+	644.820i	1.30863	+	1.80117i
$359$	671.276	−	218.111i	1.86985	−	0.607551i	0.878252	−	0.478198i	$-0.158710\pi$
$359$	671.276	−	218.111i	1.86985	−	0.607551i	0.991599	−	0.129353i	$-0.0412900\pi$
$360$	−385.779	−	657.839i	−1.07161	−	1.82733i
$361$	44.1746	−	135.955i	0.122367	−	0.376608i
$362$	−104.327	−	321.085i	−0.288195	−	0.886974i
$363$	243.742	−	179.696i	0.671467	−	0.495031i
$364$	7.14901	−	22.0024i	0.0196401	−	0.0604461i
$365$	−24.6188	−	120.033i	−0.0674489	−	0.328858i
$366$	−745.183	+	549.378i	−2.03602	+	1.50103i
$367$	85.0328	+	117.038i	0.231697	+	0.318903i	0.908996	−	0.416804i	$-0.136850\pi$
$367$	85.0328	+	117.038i	0.231697	+	0.318903i	−0.677299	+	0.735707i	$0.736850\pi$
$368$	−672.722			−1.82805
$369$	−280.360	−	86.7960i	−0.759784	−	0.235219i
$370$	−478.444	+	271.691i	−1.29309	+	0.734299i
$371$	−1.61390	+	2.22134i	−0.00435014	+	0.00598745i
$372$	189.345	−	596.857i	0.508992	−	1.60446i
$373$	−172.799	−	56.1458i	−0.463268	−	0.150525i	0.0680776	−	0.997680i	$-0.478313\pi$
$373$	−172.799	−	56.1458i	−0.463268	−	0.150525i	−0.531346	+	0.847155i	$0.678313\pi$
$374$		−	374.363i		−	1.00097i
$375$	121.029	−	354.932i	0.322744	−	0.946486i
$376$	−182.858			−0.486325
$377$	144.980	−	446.202i	0.384561	−	1.18356i
$378$	−12.0829	+	4.20706i	−0.0319654	+	0.0111298i
$379$	−443.326	−	322.095i	−1.16972	−	0.849854i	−0.178748	−	0.983895i	$-0.557205\pi$
$379$	−443.326	−	322.095i	−1.16972	−	0.849854i	−0.990976	+	0.134040i	$0.957205\pi$
$380$	484.797	+	853.722i	1.27578	+	2.24664i
$381$	−144.826	+	202.284i	−0.380122	+	0.530930i
$382$			759.811i			1.98904i
$383$	−108.840	+	79.0765i	−0.284176	+	0.206466i	−0.720737	−	0.693209i	$-0.756196\pi$
$383$	−108.840	+	79.0765i	−0.284176	+	0.206466i	0.436561	+	0.899675i	$0.356196\pi$
$384$	387.481	−	285.666i	1.00907	−	0.743921i
$385$	−2.91164	+	0.597180i	−0.00756271	+	0.00155112i
$386$	399.888	+	129.932i	1.03598	+	0.336610i
$387$	270.733	−	383.762i	0.699569	−	0.991633i
$388$	−1068.28	+	347.107i	−2.75331	+	0.894605i
$389$	−368.230	−	119.645i	−0.946606	−	0.307571i	−0.205270	−	0.978705i	$-0.565807\pi$
$389$	−368.230	−	119.645i	−0.946606	−	0.307571i	−0.741336	+	0.671134i	$0.765807\pi$
$390$	−221.699	−	1043.93i	−0.568459	−	2.67675i
$391$	−190.724	−	586.989i	−0.487786	−	1.50125i
$392$	671.566	−	487.922i	1.71318	−	1.24470i
$393$	−15.9501	+	5.30560i	−0.0405855	+	0.0135003i
$394$	−276.293	+	200.739i	−0.701252	+	0.509489i
$395$	−3.52143	+	31.3481i	−0.00891502	+	0.0793623i
$396$	4.91114	+	352.536i	0.0124019	+	0.890243i
$397$	−454.944	+	626.177i	−1.14595	+	1.57727i	−0.392528	+	0.919740i	$0.628399\pi$
$397$	−454.944	+	626.177i	−1.14595	+	1.57727i	−0.753427	+	0.657531i	$0.771601\pi$
$398$	−120.295	+	370.231i	−0.302250	+	0.930229i
$399$	8.48174	−	2.82134i	0.0212575	−	0.00707104i
$400$	−622.052	−	141.540i	−1.55513	−	0.353850i
$401$			597.305i			1.48954i	0.667322	+	0.744769i	$0.267441\pi$
$401$			597.305i			1.48954i	−0.667322	+	0.744769i	$0.732559\pi$
$402$	−1.87210	−	268.782i	−0.00465695	−	0.668612i
$403$	279.517	−	384.722i	0.693590	−	0.954644i
$404$	−44.1759	+	60.8029i	−0.109346	+	0.150502i
$405$	−264.705	+	306.523i	−0.653593	+	0.756846i
$406$	−9.02561	+	6.55749i	−0.0222306	+	0.0161515i
$407$	138.043			0.339171
$408$	−967.803	−	692.903i	−2.37207	−	1.69829i
$409$	125.658	+	386.736i	0.307232	+	0.945564i	0.978835	+	0.204652i	$0.0656064\pi$
$409$	125.658	+	386.736i	0.307232	+	0.945564i	−0.671602	+	0.740912i	$0.734394\pi$
$410$	−506.203	+	287.454i	−1.23464	+	0.701107i
$411$	613.062	−	4.27004i	1.49164	−	0.0103894i
$412$	−258.684	+	84.0515i	−0.627873	+	0.204008i
$413$	−2.44643	−	7.52933i	−0.00592356	−	0.0182308i
$414$	272.962	+	801.907i	0.659329	+	1.93697i
$415$	0.212146	+	0.0962753i	0.000511194	+	0.000231989i
$416$	−441.938	+	143.594i	−1.06235	+	0.345179i
$417$	174.789	+	125.141i	0.419159	+	0.300099i
$418$		−	358.965i		−	0.858769i
$419$	345.036	+	474.902i	0.823475	+	1.13342i	0.989103	+	0.147228i	$0.0470351\pi$
$419$	345.036	+	474.902i	0.823475	+	1.13342i	−0.165627	+	0.986188i	$0.552965\pi$
$420$	−7.08567	+	15.9070i	−0.0168707	+	0.0378738i
$421$	−8.87461	−	6.44778i	−0.0210798	−	0.0153154i	0.577195	−	0.816606i	$-0.304147\pi$
$421$	−8.87461	−	6.44778i	−0.0210798	−	0.0153154i	−0.598275	+	0.801291i	$0.704147\pi$
$422$	153.602	+	111.598i	0.363986	+	0.264451i
$423$	31.2924	+	91.9306i	0.0739772	+	0.217330i
$424$	350.584			0.826849
$425$	−52.8567	−	582.904i	−0.124369	−	1.37154i
$426$	−246.081	+	81.8559i	−0.577656	+	0.192150i
$427$	10.9109	+	3.54518i	0.0255526	+	0.00830253i
$428$	20.6228	+	14.9833i	0.0481840	+	0.0350077i
$429$	−80.9660	+	255.223i	−0.188732	+	0.594925i
$430$	−187.162	−	912.540i	−0.435261	−	2.12219i
$431$	−20.5759	−	28.3202i	−0.0477398	−	0.0657082i	0.784480	−	0.620154i	$-0.212930\pi$
$431$	−20.5759	−	28.3202i	−0.0477398	−	0.0657082i	−0.832220	+	0.554446i	$0.812930\pi$
$432$	565.742	+	393.242i	1.30959	+	0.910283i
$433$	427.498	+	588.400i	0.987293	+	1.35889i	0.932807	+	0.360377i	$0.117352\pi$
$433$	427.498	+	588.400i	0.987293	+	1.35889i	0.0544860	+	0.998515i	$0.482648\pi$
$434$	−10.7545	+	3.49434i	−0.0247799	+	0.00805149i
$435$	−143.695	+	322.589i	−0.330334	+	0.741584i
$436$	245.745	−	756.326i	0.563636	−	1.73469i
$437$	−182.880	−	562.846i	−0.418489	−	1.28798i
$438$	155.758	+	211.272i	0.355612	+	0.482357i
$439$	−82.2579	+	253.164i	−0.187376	+	0.576683i	−0.999981	−	0.00613099i	$-0.998048\pi$
$439$	−82.2579	+	253.164i	−0.187376	+	0.576683i	0.812605	+	0.582814i	$0.198048\pi$
$440$	280.207	+	255.948i	0.636835	+	0.581701i
$441$	−360.223	−	254.127i	−0.816832	−	0.576252i
$442$	−979.071	−	1347.58i	−2.21509	−	3.04881i
$443$	−651.199			−1.46998			−0.734988	−	0.678080i	$-0.762812\pi$
$443$	−651.199			−1.46998			−0.734988	+	0.678080i	$0.762812\pi$
$444$	470.809	−	657.597i	1.06038	−	1.48107i
$445$	45.3618	+	221.168i	0.101937	+	0.497008i
$446$	642.739	−	884.655i	1.44112	−	1.98353i
$447$	698.732	+	221.664i	1.56316	+	0.495892i
$448$	−2.37573	−	0.771922i	−0.00530297	−	0.00172304i
$449$			99.9364i			0.222576i	0.993788	+	0.111288i	$0.0354975\pi$
$449$			99.9364i			0.222576i	−0.993788	+	0.111288i	$0.964502\pi$
$450$	83.6817	+	798.936i	0.185959	+	1.77541i
$451$	146.052			0.323840
$452$	45.7149	−	140.696i	0.101139	−	0.311274i
$453$	−101.400	+	319.635i	−0.223841	+	0.705596i
$454$	674.285	+	489.897i	1.48521	+	1.07907i
$455$	−8.91910	+	9.76446i	−0.0196024	+	0.0214604i
$456$	−927.997	−	664.403i	−2.03508	−	1.45703i
$457$		−	416.103i		−	0.910510i	−0.890361	−	0.455255i	$-0.849548\pi$
$457$		−	416.103i		−	0.910510i	0.890361	−	0.455255i	$-0.150452\pi$
$458$	−303.689	+	220.643i	−0.663077	+	0.481754i
$459$	−182.732	+	605.131i	−0.398109	+	1.31837i
$460$	1049.88	+	476.452i	2.28234	+	1.03576i
$461$	−419.749	−	136.385i	−0.910518	−	0.295845i	−0.183947	−	0.982936i	$-0.558887\pi$
$461$	−419.749	−	136.385i	−0.910518	−	0.295845i	−0.726571	+	0.687091i	$0.758887\pi$
$462$	5.12484	−	3.77823i	0.0110927	−	0.00817798i
$463$	222.796	−	72.3907i	0.481200	−	0.156351i	−0.0583649	−	0.998295i	$-0.518589\pi$
$463$	222.796	−	72.3907i	0.481200	−	0.156351i	0.539565	+	0.841944i	$0.318589\pi$
$464$	571.369	+	185.649i	1.23140	+	0.400106i
$465$	−239.561	+	265.963i	−0.515185	+	0.571964i
$466$	−81.3183	−	250.272i	−0.174503	−	0.537065i
$467$	−614.767	+	446.654i	−1.31642	+	0.956433i	−0.316448	+	0.948610i	$0.602490\pi$
$467$	−614.767	+	446.654i	−1.31642	+	0.956433i	−0.999969	+	0.00782298i	$0.997510\pi$
$468$	939.667	+	1256.16i	2.00783	+	2.68411i
$469$	−2.69467	+	1.95779i	−0.00574556	+	0.00417439i
$470$	175.399	+	79.5992i	0.373190	+	0.169360i
$471$	−678.675	−	215.300i	−1.44092	−	0.457114i
$472$	−594.160	+	817.790i	−1.25881	+	1.73261i
$473$	−72.2224	+	222.278i	−0.152690	+	0.469931i
$474$	−21.3289	−	64.1204i	−0.0449976	−	0.135275i
$475$	−50.6827	−	558.929i	−0.106700	−	1.17669i
$476$			27.1792i			0.0570991i
$477$	−59.9951	−	176.253i	−0.125776	−	0.369504i
$478$	−151.211	+	208.124i	−0.316341	+	0.435406i
$479$	454.682	−	625.816i	0.949232	−	1.30651i	−0.00263575	−	0.999997i	$-0.500839\pi$
$479$	454.682	−	625.816i	0.949232	−	1.30651i	0.951868	−	0.306509i	$-0.0991610\pi$
$480$	342.141	−	72.6602i	0.712795	−	0.151375i
$481$	496.906	−	361.023i	1.03307	−	0.750568i
$482$	−673.452			−1.39720
$483$	6.11071	−	8.53505i	0.0126516	−	0.0176709i
$484$	272.830	+	839.686i	0.563699	+	1.73489i
$485$	638.092	+	71.6789i	1.31565	+	0.147791i
$486$	239.203	−	833.944i	0.492188	−	1.71593i
$487$	−267.330	+	86.8608i	−0.548933	+	0.178359i	−0.570335	−	0.821412i	$-0.693187\pi$
$487$	−267.330	+	86.8608i	−0.548933	+	0.178359i	0.0214028	+	0.999771i	$0.493187\pi$
$488$	−452.661	−	1393.15i	−0.927583	−	2.85481i
$489$	−2.89654	−	415.864i	−0.00592339	−	0.850438i
$490$	−856.567	+	175.682i	−1.74810	+	0.358535i
$491$	209.331	−	68.0156i	0.426335	−	0.138525i	−0.0879873	−	0.996122i	$-0.528043\pi$
$491$	209.331	−	68.0156i	0.426335	−	0.138525i	0.514322	+	0.857597i	$0.328043\pi$
$492$	498.125	−	695.750i	1.01245	−	1.41413i
$493$			551.186i			1.11802i
$494$	−938.802	−	1292.15i	−1.90041	−	2.61569i
$495$	80.7244	−	184.672i	0.163080	−	0.373075i
$496$	492.643	+	357.926i	0.993232	+	0.721625i
$497$	2.59993	+	1.88896i	0.00523124	+	0.00380072i
$498$	−0.499044	+	0.00347589i	−0.00100210	+	6.97970e-6i
$499$	−614.075			−1.23061			−0.615306	−	0.788289i	$-0.710967\pi$
$499$	−614.075			−1.23061			−0.615306	+	0.788289i	$0.710967\pi$
$500$	870.553	+	661.457i	1.74111	+	1.32291i
$501$	−266.986	−	802.632i	−0.532906	−	1.60206i
$502$	784.173	+	254.793i	1.56210	+	0.507556i
$503$	−524.185	−	380.843i	−1.04212	−	0.757143i	−0.0714197	−	0.997446i	$-0.522753\pi$
$503$	−524.185	−	380.843i	−1.04212	−	0.757143i	−0.970698	+	0.240304i	$0.922753\pi$
$504$	−0.281986	−	20.2418i	−0.000559496	−	0.0401623i
$505$	37.3593	−	21.2150i	0.0739789	−	0.0420099i
$506$	−247.779	−	341.039i	−0.489682	−	0.673990i
$507$	216.008	+	649.381i	0.426052	+	1.28083i
$508$	−426.349	−	586.819i	−0.839269	−	1.15515i
$509$	−946.342	+	307.485i	−1.85922	+	0.604097i	−0.864354	+	0.502883i	$0.832273\pi$
$509$	−946.342	+	307.485i	−1.85922	+	0.604097i	−0.994865	+	0.101214i	$0.967727\pi$
$510$	626.701	+	1085.93i	1.22882	+	2.12927i
$511$	1.00512	−	3.09344i	0.00196697	−	0.00605370i
$512$	350.666	+	1079.24i	0.684894	+	2.10789i
$513$	−175.216	+	580.242i	−0.341552	+	1.13108i
$514$	463.950	−	1427.89i	0.902626	−	2.77800i
$515$	154.513	+	17.3569i	0.300026	+	0.0337028i
$516$	812.546	+	1102.15i	1.57470	+	2.13595i
$517$	−28.4054	−	39.0967i	−0.0549428	−	0.0756222i
$518$	−14.6053			−0.0281956
$519$	442.901	+	317.097i	0.853373	+	0.610976i
$520$	1678.03	+	188.499i	3.22698	+	0.362497i
$521$	−243.112	+	334.615i	−0.466626	+	0.642255i	−0.975866	−	0.218369i	$-0.929926\pi$
$521$	−243.112	+	334.615i	−0.466626	+	0.642255i	0.509241	+	0.860624i	$0.329926\pi$
$522$	−10.5376	−	756.419i	−0.0201869	−	1.44908i
$523$	885.885	+	287.841i	1.69385	+	0.550366i	0.987517	−	0.157512i	$-0.0503473\pi$
$523$	885.885	+	287.841i	1.69385	+	0.550366i	0.706335	+	0.707878i	$0.250347\pi$
$524$		−	49.0089i		−	0.0935284i
$525$	7.44620	−	6.60649i	0.0141832	−	0.0125838i
$526$	−330.809			−0.628915
$527$	−172.641	+	531.335i	−0.327593	+	1.00823i
$528$	−326.817	−	103.678i	−0.618972	−	0.196361i
$529$	−134.287	−	97.5650i	−0.253850	−	0.184433i
$530$	−336.283	−	152.611i	−0.634497	−	0.287945i
$531$	512.815	+	158.761i	0.965754	+	0.298985i
$532$			26.0613i			0.0489874i
$533$	525.736	−	381.969i	0.986371	−	0.716641i
$534$	−286.994	−	389.282i	−0.537442	−	0.728993i
$535$	−7.19558	−	12.6713i	−0.0134497	−	0.0236847i
$536$	404.472	+	131.421i	0.754612	+	0.245188i
$537$	397.425	+	539.072i	0.740083	+	1.00386i
$538$	−440.336	+	143.074i	−0.818469	+	0.265937i
$539$	208.644	+	67.7924i	0.387094	+	0.125774i
$540$	−604.408	−	1014.39i	−1.11927	−	1.87850i
$541$	134.787	+	414.830i	0.249143	+	0.766784i	0.994927	+	0.100596i	$0.0320751\pi$
$541$	134.787	+	414.830i	0.249143	+	0.766784i	−0.745784	+	0.666188i	$0.767925\pi$
$542$	−61.8602	+	44.9441i	−0.114133	+	0.0829227i
$543$	−89.5403	−	269.183i	−0.164899	−	0.495732i
$544$	441.658	−	320.883i	0.811871	−	0.589859i
$545$	−306.592	+	335.651i	−0.562554	+	0.615873i
$546$	8.56643	−	27.0033i	0.0156894	−	0.0494566i
$547$	324.413	−	446.516i	0.593077	−	0.816300i	−0.401976	−	0.915650i	$-0.631676\pi$
$547$	324.413	−	446.516i	0.593077	−	0.816300i	0.995053	+	0.0993502i	$0.0316764\pi$
$548$	−552.358	+	1699.98i	−1.00795	+	3.10216i
$549$	−622.930	+	465.979i	−1.13466	+	0.848778i
$550$	−157.362	−	367.484i	−0.286112	−	0.668152i
$551$			528.515i			0.959193i
$552$	−1340.26	+	9.33509i	−2.42802	+	0.0169114i
$553$	−0.492198	+	0.677453i	−0.000890051	+	0.00122505i
$554$	125.334	−	172.507i	0.226234	−	0.311385i
$555$	−400.425	+	231.090i	−0.721487	+	0.416378i
$556$	−507.057	+	368.398i	−0.911972	+	0.662587i
$557$	361.786			0.649526			0.324763	−	0.945795i	$-0.394715\pi$
$557$	361.786			0.649526			0.324763	+	0.945795i	$0.394715\pi$
$558$	226.766	−	732.478i	0.406391	−	1.31268i
$559$	321.347	+	989.005i	0.574861	+	1.76924i
$560$	−12.5036	−	11.4211i	−0.0223278	−	0.0203948i
$561$	−2.19095	−	314.561i	−0.00390543	−	0.560714i
$562$	−726.903	+	236.185i	−1.29342	+	0.420258i
$563$	−273.396	−	841.426i	−0.485606	−	1.49454i	−0.831102	−	0.556121i	$-0.812289\pi$
$563$	−273.396	−	841.426i	−0.485606	−	1.49454i	0.345496	−	0.938420i	$-0.387711\pi$
$564$	−283.125	+	1.97200i	−0.501995	+	0.00349645i
$565$	−57.0339	+	62.4397i	−0.100945	+	0.110513i
$566$	1375.02	−	446.770i	2.42936	−	0.789347i
$567$	−10.1281	+	3.60572i	−0.0178627	+	0.00635930i
$568$		−	410.334i		−	0.722420i
$569$	−151.672	−	208.758i	−0.266558	−	0.366886i	0.654666	−	0.755919i	$-0.272809\pi$
$569$	−151.672	−	208.758i	−0.266558	−	0.366886i	−0.921224	+	0.389032i	$0.872809\pi$
$570$	600.924	+	1041.26i	1.05425	+	1.82678i
$571$	−281.646	−	204.628i	−0.493250	−	0.358367i	0.313183	−	0.949693i	$-0.398605\pi$
$571$	−281.646	−	204.628i	−0.493250	−	0.358367i	−0.806433	+	0.591326i	$0.798605\pi$
$572$	−631.572	−	458.864i	−1.10415	−	0.802209i
$573$	4.44678	+	638.436i	0.00776052	+	1.11420i
$574$	−15.4527			−0.0269211
$575$	−433.958	−	496.032i	−0.754709	−	0.862665i
$576$	135.636	−	101.462i	0.235479	−	0.176149i
$577$	780.937	+	253.742i	1.35344	+	0.439761i	0.893849	−	0.448368i	$-0.147995\pi$
$577$	780.937	+	253.742i	1.35344	+	0.439761i	0.459595	+	0.888129i	$0.347995\pi$
$578$	748.420	+	543.759i	1.29484	+	0.940759i
$579$	336.769	+	106.835i	0.581639	+	0.184517i
$580$	−760.216	−	694.400i	−1.31072	−	1.19724i
$581$	0.00363500	+	0.00500315i	6.25646e−6	+	8.61127e-6i
$582$	−1305.17	+	434.150i	−2.24257	+	0.745962i
$583$	54.4601	+	74.9579i	0.0934136	+	0.128573i
$584$	−394.981	+	128.337i	−0.676337	+	0.219755i
$585$	−192.394	−	875.874i	−0.328878	−	1.49722i
$586$	−56.2482	+	173.114i	−0.0959867	+	0.295417i
$587$	110.506	+	340.103i	0.188256	+	0.579391i	0.999989	−	0.00463659i	$-0.00147588\pi$
$587$	110.506	+	340.103i	0.188256	+	0.579391i	−0.811734	+	0.584028i	$0.801476\pi$
$588$	1034.55	−	762.707i	1.75943	−	1.29712i
$589$	−165.541	+	509.481i	−0.281053	+	0.864994i
$590$	925.911	−	525.791i	1.56934	−	0.891171i
$591$	−230.982	+	170.289i	−0.390833	+	0.288137i
$592$	462.297	+	636.297i	0.780907	+	1.07483i
$593$	814.522			1.37356			0.686781	−	0.726865i	$-0.259023\pi$
$593$	814.522			1.37356			0.686781	+	0.726865i	$0.259023\pi$
$594$	9.02053	+	431.645i	0.0151861	+	0.726675i
$595$	6.42064	−	14.1481i	0.0107910	−	0.0237783i
$596$	−1256.25	+	1729.08i	−2.10780	+	2.90114i
$597$	−98.9121	+	311.793i	−0.165682	+	0.522266i
$598$	−1783.84	−	579.604i	−2.98301	−	0.969238i
$599$		−	590.758i		−	0.986241i	−0.869961	−	0.493120i	$-0.835856\pi$
$599$		−	590.758i		−	0.986241i	0.869961	−	0.493120i	$-0.164144\pi$
$600$	−1241.28	−	273.358i	−2.06880	−	0.455597i
$601$	−694.182			−1.15505			−0.577523	−	0.816375i	$-0.695980\pi$
$601$	−694.182			−1.15505			−0.577523	+	0.816375i	$0.695980\pi$
$602$	7.64133	−	23.5176i	0.0126932	−	0.0390658i
$603$	−3.14608	−	225.835i	−0.00521738	−	0.374519i
$604$	−790.966	−	574.670i	−1.30955	−	0.951441i
$605$	56.3405	−	501.549i	0.0931248	−	0.829006i
$606$	−53.5756	+	74.8310i	−0.0884085	+	0.123483i
$607$		−	716.601i		−	1.18056i	−0.807198	−	0.590281i	$-0.799017\pi$
$607$		−	716.601i		−	1.18056i	0.807198	−	0.590281i	$-0.200983\pi$
$608$	423.492	−	307.685i	0.696534	−	0.506061i
$609$	−7.54545	+	5.56280i	−0.0123899	+	0.00913431i
$610$	−172.247	+	1533.36i	−0.282373	+	2.51371i
$611$	−204.499	−	66.4458i	−0.334696	−	0.108749i
$612$	−1505.95	−	1062.41i	−2.46071	−	1.73596i
$613$	436.901	−	141.958i	0.712726	−	0.231579i	0.0698593	−	0.997557i	$-0.477745\pi$
$613$	436.901	−	141.958i	0.712726	−	0.231579i	0.642867	+	0.765978i	$0.277745\pi$
$614$	1535.68	+	498.972i	2.50110	+	0.812657i
$615$	−423.658	+	244.498i	−0.688874	+	0.397557i
$616$	3.11308	+	9.58106i	0.00505369	+	0.0155537i
$617$	950.755	−	690.764i	1.54093	−	1.11955i	0.591183	−	0.806537i	$-0.298661\pi$
$617$	950.755	−	690.764i	1.54093	−	1.11955i	0.949748	−	0.313015i	$-0.101339\pi$
$618$	−316.046	+	105.129i	−0.511401	+	0.170111i
$619$	694.219	−	504.380i	1.12152	−	0.814830i	0.137079	−	0.990560i	$-0.456229\pi$
$619$	694.219	−	504.380i	1.12152	−	0.814830i	0.984438	+	0.175730i	$0.0562286\pi$
$620$	−515.339	−	907.505i	−0.831192	−	1.46372i
$621$	234.051	+	672.210i	0.376894	+	1.08246i
$622$	1219.28	−	1678.20i	1.96026	−	2.69807i
$623$	−1.85200	+	5.69986i	−0.00297271	+	0.00914905i
$624$	−1447.58	+	481.519i	−2.31984	+	0.771665i
$625$	−296.906	−	549.974i	−0.475050	−	0.879959i
$626$		−	177.219i		−	0.283097i
$627$	−2.10083	−	301.623i	−0.00335061	−	0.481057i
$628$	1220.19	−	1679.44i	1.94297	−	2.67427i
$629$	−424.139	+	583.777i	−0.674307	+	0.928104i
$630$	−8.54087	+	19.5388i	−0.0135569	+	0.0310140i
$631$	−664.762	+	482.978i	−1.05351	+	0.765417i	−0.972876	−	0.231328i	$-0.925693\pi$
$631$	−664.762	+	482.978i	−1.05351	+	0.765417i	−0.0806296	+	0.996744i	$0.525693\pi$
$632$	106.919			0.169176
$633$	129.718	+	92.8723i	0.204926	+	0.146718i
$634$	−59.1604	−	182.077i	−0.0933130	−	0.287188i
$635$	83.3088	+	406.185i	0.131195	+	0.639662i
$636$	542.820	−	3.78080i	0.853491	−	0.00594466i
$637$	928.342	−	301.637i	1.45737	−	0.473527i
$638$	116.333	+	358.036i	0.182340	+	0.561186i
$639$	−206.292	+	70.2201i	−0.322836	+	0.109891i
$640$	89.5654	−	797.319i	0.139946	−	1.24581i
$641$	−28.4173	+	9.23334i	−0.0443328	+	0.0144046i	−0.331099	−	0.943596i	$-0.607420\pi$
$641$	−28.4173	+	9.23334i	−0.0443328	+	0.0144046i	0.286767	+	0.958000i	$0.407420\pi$
$642$	25.3807	+	18.1714i	0.0395339	+	0.0283044i
$643$		−	49.5295i		−	0.0770287i	−0.999258	−	0.0385144i	$-0.987737\pi$
$643$		−	49.5295i		−	0.0770287i	0.999258	−	0.0385144i	$-0.0122625\pi$
$644$	17.9891	+	24.7598i	0.0279333	+	0.0384470i
$645$	−162.605	−	765.672i	−0.252101	−	1.18709i
$646$	1518.05	+	1102.93i	2.34992	+	1.70732i
$647$	−45.1044	−	32.7702i	−0.0697131	−	0.0506495i	0.552383	−	0.833591i	$-0.313719\pi$
$647$	−45.1044	−	32.7702i	−0.0697131	−	0.0506495i	−0.622096	+	0.782941i	$0.713719\pi$
$648$	1132.58	+	775.605i	1.74782	+	1.19692i
$649$	−267.148			−0.411630
$650$	−1527.53	−	911.265i	−2.35004	−	1.40195i
$651$	−9.01607	+	2.99909i	−0.0138496	+	0.00460689i
$652$	1153.17	+	374.686i	1.76866	+	0.574672i
$653$	−394.531	−	286.643i	−0.604182	−	0.438964i	0.243179	−	0.969981i	$-0.421810\pi$
$653$	−394.531	−	286.643i	−0.604182	−	0.438964i	−0.847361	+	0.531018i	$0.821810\pi$
$654$	294.469	−	928.231i	0.450258	−	1.41931i
$655$	−11.5775	+	25.5115i	−0.0176756	+	0.0389488i
$656$	489.119	+	673.214i	0.745608	+	1.02624i
$657$	132.113	+	176.611i	0.201085	+	0.268815i
$658$	3.00537	+	4.13654i	0.00456743	+	0.00628653i
$659$	517.104	−	168.017i	0.784681	−	0.254958i	0.110843	−	0.993838i	$-0.464645\pi$
$659$	517.104	−	168.017i	0.784681	−	0.254958i	0.673837	+	0.738880i	$0.264645\pi$
$660$	436.614	+	393.271i	0.661537	+	0.595865i
$661$	−59.9549	+	184.522i	−0.0907033	+	0.279156i	−0.986110	−	0.166093i	$-0.946885\pi$
$661$	−59.9549	+	184.522i	−0.0907033	+	0.279156i	0.895407	+	0.445249i	$0.146885\pi$
$662$	−170.598	−	525.045i	−0.257700	−	0.793120i
$663$	−830.557	−	1126.58i	−1.25273	−	1.69921i
$664$	0.244007	−	0.750977i	0.000367481	−	0.00113099i
$665$	6.15655	−	13.5662i	0.00925798	−	0.0204002i
$666$	570.906	−	809.255i	0.857216	−	1.21510i
$667$	364.813	+	502.122i	0.546946	+	0.752806i
$668$	2466.20			3.69192
$669$	534.888	−	747.098i	0.799534	−	1.11674i
$670$	−330.765	−	302.129i	−0.493679	−	0.450938i
$671$	227.550	−	313.195i	0.339120	−	0.466759i
$672$	8.85012	+	2.80758i	0.0131698	+	0.00417795i
$673$	−313.307	−	101.800i	−0.465538	−	0.151262i	0.0668500	−	0.997763i	$-0.478705\pi$
$673$	−313.307	−	101.800i	−0.465538	−	0.151262i	−0.532388	+	0.846501i	$0.678705\pi$
$674$			1653.86i			2.45380i
$675$	74.9898	+	670.822i	0.111096	+	0.993810i
$676$	−1995.31			−2.95165
$677$	83.9234	−	258.290i	0.123964	−	0.381521i	−0.869747	−	0.493497i	$-0.835718\pi$
$677$	83.9234	−	258.290i	0.123964	−	0.381521i	0.993711	+	0.111977i	$0.0357182\pi$
$678$	54.7788	−	172.675i	0.0807946	−	0.254682i
$679$	13.7896	+	10.0187i	0.0203087	+	0.0147551i
$680$	−1943.34	+	398.580i	−2.85785	+	0.586147i
$681$	569.439	+	407.693i	0.836181	+	0.598667i
$682$			381.580i			0.559501i
$683$	−498.066	+	361.866i	−0.729233	+	0.529819i	−0.889321	−	0.457284i	$-0.848822\pi$
$683$	−498.066	+	361.866i	−0.729233	+	0.529819i	0.160087	+	0.987103i	$0.448822\pi$
$684$	−1444.01	−	1018.71i	−2.11113	−	1.48934i
$685$	689.122	−	754.438i	1.00602	−	1.10137i
$686$	−44.1581	−	14.3478i	−0.0643704	−	0.0209152i
$687$	−253.885	+	187.174i	−0.369557	+	0.272451i
$688$	−1266.44	+	411.491i	−1.84075	+	0.598097i
$689$	392.075	+	127.393i	0.569049	+	0.184895i
$690$	1289.66	+	574.470i	1.86907	+	0.832565i
$691$	230.907	+	710.658i	0.334163	+	1.02845i	0.967133	+	0.254272i	$0.0818359\pi$
$691$	230.907	+	710.658i	0.334163	+	1.02845i	−0.632969	+	0.774177i	$0.718164\pi$
$692$	−1284.84	+	933.489i	−1.85670	+	1.34897i
$693$	4.28406	−	3.20467i	0.00618191	−	0.00462434i
$694$	−1710.01	+	1242.39i	−2.46398	+	1.79019i
$695$	350.975	−	71.9852i	0.505001	−	0.103576i
$696$	1140.91	+	361.940i	1.63925	+	0.520029i
$697$	−448.747	+	617.648i	−0.643827	+	0.886152i
$698$	211.169	−	649.910i	0.302534	−	0.931103i
$699$	−69.7930	−	209.817i	−0.0998469	−	0.300167i
$700$	11.4247	+	26.6798i	0.0163209	+	0.0381139i
$701$		−	113.358i		−	0.161710i	−0.996726	−	0.0808548i	$-0.974235\pi$
$701$		−	113.358i		−	0.161710i	0.996726	−	0.0808548i	$-0.0257650\pi$
$702$	1161.35	+	1530.18i	1.65435	+	2.17974i
$703$	−406.694	+	559.767i	−0.578512	+	0.796254i
$704$	−49.5463	+	68.1947i	−0.0703783	+	0.0968675i
$705$	147.846	+	65.8572i	0.209711	+	0.0934144i
$706$	−119.643	+	86.9260i	−0.169467	+	0.123125i
$707$	1.14046			0.00161309
$708$	−911.137	+	1272.62i	−1.28692	+	1.79748i
$709$	−292.719	−	900.895i	−0.412861	−	1.27066i	−0.914150	−	0.405376i	$-0.867141\pi$
$709$	−292.719	−	900.895i	−0.412861	−	1.27066i	0.501289	−	0.865280i	$-0.332859\pi$
$710$	−178.621	+	393.596i	−0.251578	+	0.554361i
$711$	−18.2970	−	53.7528i	−0.0257341	−	0.0756016i
$712$	727.777	−	236.469i	1.02216	−	0.332120i
$713$	194.401	+	598.304i	0.272652	+	0.839137i
$714$	0.231809	+	33.2814i	0.000324662	+	0.0466126i
$715$	220.365	+	388.059i	0.308202	+	0.542740i
$716$	−1857.09	+	603.405i	−2.59370	+	0.842744i
$717$	−125.838	+	175.762i	−0.175506	+	0.245136i
$718$			2519.96i			3.50970i
$719$	65.2834	+	89.8548i	0.0907974	+	0.124972i	0.851999	−	0.523543i	$-0.175390\pi$
$719$	65.2834	+	89.8548i	0.0907974	+	0.124972i	−0.761202	+	0.648515i	$0.775390\pi$
$720$	1121.57	−	246.364i	1.55774	−	0.342172i
$721$	3.33913	+	2.42602i	0.00463125	+	0.00336480i
$722$	412.902	+	299.991i	0.571887	+	0.415500i
$723$	−565.872	+	3.94136i	−0.782672	+	0.00545140i
$724$	827.101			1.14241
$725$	231.689	+	541.057i	0.319570	+	0.746286i
$726$	341.247	+	1025.88i	0.470038	+	1.41306i
$727$	−1176.94	−	382.410i	−1.61889	−	0.526011i	−0.647214	−	0.762309i	$-0.724066\pi$
$727$	−1176.94	−	382.410i	−1.61889	−	0.526011i	−0.971681	+	0.236298i	$0.924066\pi$
$728$	36.2633	+	26.3469i	0.0498123	+	0.0361907i
$729$	196.111	−	702.126i	0.269014	−	0.963136i
$730$	434.735	+	48.8351i	0.595527	+	0.0668974i
$731$	−718.099	−	988.378i	−0.982351	−	1.35209i
$732$	−715.893	−	2152.17i	−0.977995	−	2.94012i
$733$	−257.518	−	354.444i	−0.351321	−	0.483552i	0.596384	−	0.802699i	$-0.296604\pi$
$733$	−257.518	−	354.444i	−0.351321	−	0.483552i	−0.947705	+	0.319147i	$0.896604\pi$
$734$	−491.217	+	159.606i	−0.669232	+	0.217447i
$735$	−718.707	+	152.631i	−0.977833	+	0.207661i
$736$	189.961	−	584.640i	0.258099	−	0.794347i
$737$	34.7322	+	106.895i	0.0471264	+	0.145040i
$738$	604.029	−	856.207i	0.818468	−	1.16017i
$739$	−251.331	+	773.516i	−0.340096	+	1.04671i	0.624061	+	0.781375i	$0.285481\pi$
$739$	−251.331	+	773.516i	−0.340096	+	1.04671i	−0.964157	+	0.265332i	$0.914519\pi$
$740$	−270.825	−	1320.45i	−0.365979	−	1.78439i
$741$	−796.396	−	1080.24i	−1.07476	−	1.45782i
$742$	−5.76203	−	7.93076i	−0.00776554	−	0.0106884i
$743$	1125.92			1.51536			0.757682	−	0.652623i	$-0.226332\pi$
$743$	1125.92			1.51536			0.757682	+	0.652623i	$0.226332\pi$
$744$	986.459	+	706.260i	1.32589	+	0.949274i
$745$	1062.40	−	603.300i	1.42604	−	0.809798i
$746$	381.287	−	524.797i	0.511109	−	0.703481i
$747$	−0.419304	+	0.00584128i	−0.000561318	+	7.81965e-6i
$748$	872.257	+	283.414i	1.16612	+	0.378895i
$749$		−	0.386814i		−	0.000516440i
$750$	1071.65	+	802.542i	1.42887	+	1.07006i
$751$	1171.01			1.55927			0.779636	−	0.626233i	$-0.215404\pi$
$751$	1171.01			1.55927			0.779636	+	0.626233i	$0.215404\pi$
$752$	85.0851	−	261.865i	0.113145	−	0.348225i
$753$	660.397	+	209.502i	0.877022	+	0.278223i
$754$	1355.13	+	984.561i	1.79726	+	1.30578i
$755$	275.979	+	485.996i	0.365536	+	0.643703i
$756$	−0.654901	−	31.3380i	−0.000866271	−	0.0414523i
$757$		−	310.927i		−	0.410736i	−0.978685	−	0.205368i	$-0.934161\pi$
$757$		−	310.927i		−	0.410736i	0.978685	−	0.205368i	$-0.0658392\pi$
$758$	1582.78	−	1149.96i	2.08811	−	1.51710i
$759$	−210.194	−	285.110i	−0.276935	−	0.375639i
$760$	−1863.41	+	382.186i	−2.45185	+	0.502877i
$761$	508.366	+	165.178i	0.668023	+	0.217054i	0.623344	−	0.781948i	$-0.285774\pi$
$761$	508.366	+	165.178i	0.668023	+	0.217054i	0.0446788	+	0.999001i	$0.485774\pi$
$762$	−527.077	−	714.934i	−0.691702	−	0.938233i
$763$	−11.4768	+	3.72904i	−0.0150417	+	0.00488734i
$764$	−1770.34	−	575.220i	−2.31720	−	0.752905i
$765$	532.945	+	908.789i	0.696659	+	1.18796i
$766$	−148.426	−	456.809i	−0.193768	−	0.596356i
$767$	−961.640	+	698.672i	−1.25377	+	0.910915i
$768$	471.201	+	1416.56i	0.613543	+	1.84448i
$769$	398.449	−	289.490i	0.518140	−	0.376450i	−0.297763	−	0.954640i	$-0.596241\pi$
$769$	398.449	−	289.490i	0.518140	−	0.376450i	0.815903	+	0.578189i	$0.196241\pi$
$770$	1.18459	−	10.5454i	0.00153843	−	0.0136953i
$771$	381.480	−	1202.51i	0.494786	−	1.55968i
$772$	−605.475	+	833.365i	−0.784295	+	1.07949i
$773$	45.1535	−	138.968i	0.0584133	−	0.179778i	−0.917592	−	0.397522i	$-0.869870\pi$
$773$	45.1535	−	138.968i	0.0584133	−	0.179778i	0.976006	+	0.217745i	$0.0698701\pi$
$774$	1004.38	+	1342.67i	1.29765	+	1.73472i
$775$	53.8756	+	594.140i	0.0695169	+	0.766633i
$776$		−	2176.34i		−	2.80457i
$777$	−12.2722	+	0.0854772i	−0.0157943	+	0.000110009i
$778$	812.513	−	1118.33i	1.04436	−	1.43744i
$779$	−430.290	+	592.244i	−0.552362	+	0.760262i
$780$	2600.18	+	273.762i	3.33357	+	0.350977i
$781$	87.7330	−	63.7418i	0.112334	−	0.0816156i
$782$	2203.55			2.81784
$783$	−13.2812	−	635.524i	−0.0169619	−	0.811653i
$784$	386.251	+	1188.76i	0.492667	+	1.51627i
$785$	−1031.91	+	585.982i	−1.31453	+	0.746473i
$786$	−0.417992	−	60.0123i	−0.000531796	−	0.0763515i
$787$	−777.307	+	252.563i	−0.987684	+	0.320918i	−0.757934	−	0.652332i	$-0.773791\pi$
$787$	−777.307	+	252.563i	−0.987684	+	0.320918i	−0.229750	+	0.973250i	$0.573791\pi$
$788$	−258.548	−	795.728i	−0.328106	−	1.00981i
$789$	−277.964	+	1.93605i	−0.352300	+	0.00245380i
$790$	−102.558	−	46.5425i	−0.129820	−	0.0589145i
$791$	−2.13498	+	0.693698i	−0.00269909	+	0.000876989i
$792$	−652.557	−	202.023i	−0.823935	−	0.255080i
$793$		−	1722.51i		−	2.17214i
$794$	−1624.27	−	2235.61i	−2.04567	−	2.81563i
$795$	−283.457	−	126.264i	−0.356550	−	0.158823i
$796$	−771.560	−	560.571i	−0.969296	−	0.704235i
$797$	−692.495	−	503.127i	−0.868877	−	0.631276i	0.0614085	−	0.998113i	$-0.480441\pi$
$797$	−692.495	−	503.127i	−0.868877	−	0.631276i	−0.930285	+	0.366837i	$0.880441\pi$
$798$	0.222274	+	31.9125i	0.000278539	+	0.0399907i
$799$	252.615			0.316163
$800$	298.660	−	500.636i	0.373325	−	0.625795i
$801$	−243.427	−	325.417i	−0.303904	−	0.406264i
$802$	−2028.16	−	658.988i	−2.52887	−	0.821681i
$803$	−88.7963	−	64.5143i	−0.110581	−	0.0803416i
$804$	627.674	+	199.121i	0.780689	+	0.247663i
$805$	−3.51508	−	17.1383i	−0.00436655	−	0.0212898i
$806$	997.945	+	1373.55i	1.23815	+	1.70416i
$807$	−369.158	+	122.796i	−0.457445	+	0.152163i
$808$	−85.5917	−	117.807i	−0.105930	−	0.145801i
$809$	−222.792	+	72.3895i	−0.275392	+	0.0894802i	−0.443457	−	0.896296i	$-0.646248\pi$
$809$	−222.792	+	72.3895i	−0.275392	+	0.0894802i	0.168065	+	0.985776i	$0.446248\pi$
$810$	−748.760	−	1236.99i	−0.924395	−	1.52714i
$811$	−80.7742	+	248.597i	−0.0995983	+	0.306532i	−0.988425	−	0.151712i	$-0.951521\pi$
$811$	−80.7742	+	248.597i	−0.0995983	+	0.306532i	0.888826	+	0.458244i	$0.151521\pi$
$812$	−8.44592	−	25.9939i	−0.0104014	−	0.0320122i
$813$	−51.7154	+	38.1266i	−0.0636106	+	0.0468962i
$814$	−152.298	+	468.726i	−0.187099	+	0.575830i
$815$	−511.765	−	467.459i	−0.627932	−	0.573569i
$816$	1442.60	−	1063.54i	1.76790	−	1.30336i
$817$	−688.563	−	947.726i	−0.842795	−	1.16001i
$818$	−1451.80			−1.77482
$819$	7.03996	−	22.7398i	0.00859580	−	0.0277653i
$820$	−286.538	−	1397.06i	−0.349436	−	1.70373i
$821$	−423.908	+	583.459i	−0.516331	+	0.710669i	−0.984971	−	0.172720i	$-0.944744\pi$
$821$	−423.908	+	583.459i	−0.516331	+	0.710669i	0.468639	+	0.883390i	$0.344744\pi$
$822$	−661.873	+	2086.37i	−0.805199	+	2.53816i
$823$	1196.12	+	388.643i	1.45337	+	0.472227i	0.926036	−	0.377434i	$-0.123194\pi$
$823$	1196.12	+	388.643i	1.45337	+	0.472227i	0.527329	+	0.849661i	$0.323194\pi$
$824$		−	526.999i		−	0.639562i
$825$	−134.375	−	307.859i	−0.162879	−	0.373163i
$826$	28.2650			0.0342191
$827$	128.762	−	396.289i	0.155698	−	0.479188i	−0.842533	−	0.538644i	$-0.818937\pi$
$827$	128.762	−	396.289i	0.155698	−	0.479188i	0.998231	+	0.0594560i	$0.0189366\pi$
$828$	−2075.07	+	28.9076i	−2.50613	+	0.0349126i
$829$	−815.878	−	592.770i	−0.984171	−	0.715042i	−0.0255344	−	0.999674i	$-0.508129\pi$
$829$	−815.878	−	592.770i	−0.984171	−	0.715042i	−0.958637	+	0.284632i	$0.908129\pi$
$830$	−0.560958	+	0.614126i	−0.000675853	+	0.000739911i
$831$	104.303	−	145.684i	0.125515	−	0.175311i
$832$			375.056i			0.450788i
$833$	−927.753	+	674.052i	−1.11375	+	0.809186i
$834$	−617.758	+	455.435i	−0.740717	+	0.546085i
$835$	−1283.78	−	582.599i	−1.53746	−	0.697723i
$836$	836.381	+	271.757i	1.00046	+	0.325068i
$837$	186.255	−	616.796i	0.222526	−	0.736913i
$838$	−1993.20	+	647.630i	−2.37852	+	0.772829i
$839$	1341.31	+	435.818i	1.59870	+	0.519449i	0.966786	−	0.255588i	$-0.0822692\pi$
$839$	1341.31	+	435.818i	1.59870	+	0.519449i	0.631915	+	0.775038i	$0.282269\pi$
$840$	−25.0693	−	22.5807i	−0.0298445	−	0.0268818i
$841$	88.6026	+	272.691i	0.105354	+	0.324246i
$842$	31.6846	−	23.0202i	0.0376302	−	0.0273399i
$843$	−609.402	+	202.710i	−0.722897	+	0.240463i
$844$	−376.307	+	273.403i	−0.445862	+	0.323938i
$845$	1038.66	+	471.360i	1.22918	+	0.557822i
$846$	−346.675	+	4.82949i	−0.409782	+	0.00570862i
$847$	7.87484	−	10.8388i	0.00929733	−	0.0127967i
$848$	−163.129	+	502.059i	−0.192369	+	0.592051i
$849$	1152.75	−	383.449i	1.35778	−	0.451648i
$850$	2037.57	+	463.624i	2.39714	+	0.545440i
$851$			812.537i			0.954803i
$852$	−4.42517	−	635.334i	−0.00519386	−	0.745697i
$853$	−714.220	+	983.040i	−0.837304	+	1.15245i	0.149215	+	0.988805i	$0.452325\pi$
$853$	−714.220	+	983.040i	−0.837304	+	1.15245i	−0.986519	+	0.163645i	$0.947675\pi$
$854$	−24.0754	+	33.1370i	−0.0281913	+	0.0388021i
$855$	511.024	+	871.411i	0.597689	+	1.01919i
$856$	−39.9571	+	29.0305i	−0.0466788	+	0.0339141i
$857$	58.4151			0.0681623			0.0340811	−	0.999419i	$-0.489150\pi$
$857$	58.4151			0.0681623			0.0340811	+	0.999419i	$0.489150\pi$
$858$	−777.285	−	556.500i	−0.905926	−	0.648602i
$859$	−271.371	−	835.193i	−0.315915	−	0.972285i	−0.975376	−	0.220547i	$-0.929216\pi$
$859$	−271.371	−	835.193i	−0.315915	−	0.972285i	0.659462	−	0.751738i	$-0.270784\pi$
$860$	2267.89	+	254.759i	2.63708	+	0.296232i
$861$	−12.9842	+	0.0904365i	−0.0150804	+	0.000105037i
$862$	118.862	−	38.6207i	0.137891	−	0.0448036i
$863$	399.565	+	1229.73i	0.462995	+	1.42495i	0.861487	+	0.507780i	$0.169534\pi$
$863$	399.565	+	1229.73i	0.462995	+	1.42495i	−0.398492	+	0.917172i	$0.630466\pi$
$864$	−501.505	+	380.624i	−0.580446	+	0.440538i
$865$	889.341	−	182.404i	1.02814	−	0.210872i
$866$	−2469.56	+	802.410i	−2.85169	+	0.926571i
$867$	632.047	+	452.517i	0.729004	+	0.521934i
$868$		−	27.7031i		−	0.0319161i
$869$	16.6089	+	22.8602i	0.0191127	+	0.0263064i
$870$	−936.821	−	843.822i	−1.07681	−	0.969910i
$871$	404.585	+	293.948i	0.464506	+	0.337484i
$872$	1246.54	+	905.666i	1.42952	+	1.03861i
$873$	−1094.14	+	372.436i	−1.25331	+	0.426616i
$874$	2112.92			2.41752
$875$	0.355568	−	16.5870i	0.000406363	−	0.0189565i
$876$	−610.177	+	202.968i	−0.696549	+	0.231698i
$877$	−731.731	−	237.754i	−0.834357	−	0.271099i	−0.139478	−	0.990225i	$-0.544542\pi$
$877$	−731.731	−	237.754i	−0.834357	−	0.271099i	−0.694880	+	0.719126i	$0.744542\pi$
$878$	−768.869	−	558.616i	−0.875704	−	0.636237i
$879$	−46.2498	+	145.790i	−0.0526164	+	0.165858i
$880$	−496.917	+	282.181i	−0.564678	+	0.320660i
$881$	289.701	+	398.739i	0.328832	+	0.452598i	0.941138	−	0.338023i	$-0.109758\pi$
$881$	289.701	+	398.739i	0.328832	+	0.452598i	−0.612306	+	0.790621i	$0.709758\pi$
$882$	1260.31	−	942.771i	1.42893	−	1.06890i
$883$	−297.460	−	409.419i	−0.336874	−	0.463668i	0.606651	−	0.794968i	$-0.292513\pi$
$883$	−297.460	−	409.419i	−0.336874	−	0.463668i	−0.943525	+	0.331301i	$0.892513\pi$
$884$	3881.03	−	1261.02i	4.39031	−	1.42650i
$885$	774.925	−	447.218i	0.875622	−	0.505331i
$886$	718.448	−	2211.15i	0.810889	−	2.49566i
$887$	156.799	+	482.578i	0.176775	+	0.544056i	0.999710	−	0.0240787i	$-0.00766524\pi$
$887$	156.799	+	482.578i	0.176775	+	0.544056i	−0.822936	+	0.568135i	$0.807665\pi$
$888$	929.863	+	1261.28i	1.04714	+	1.42036i
$889$	−3.40127	+	10.4680i	−0.00382595	+	0.0117751i
$890$	−801.026	−	89.9818i	−0.900030	−	0.101103i
$891$	10.1057	+	362.640i	0.0113420	+	0.407003i
$892$	1574.64	+	2167.30i	1.76529	+	2.42971i
$893$	242.225			0.271248
$894$	−1523.55	+	2128.00i	−1.70420	+	2.38031i
$895$	1109.25	+	124.605i	1.23938	+	0.139224i
$896$	12.5188	−	17.2306i	0.0139718	−	0.0192306i
$897$	−1502.27	−	476.576i	−1.67478	−	0.531300i
$898$	−339.335	−	110.257i	−0.377879	−	0.122780i
$899$		−	561.811i		−	0.624929i
$900$	−1924.86	−	409.863i	−2.13873	−	0.455403i
$901$	−484.324			−0.537540
$902$	−161.134	+	495.921i	−0.178641	+	0.549801i
$903$	6.28304	−	19.8055i	0.00695796	−	0.0219330i
$904$	231.889	+	168.477i	0.256514	+	0.186369i
$905$	−430.546	−	195.389i	−0.475741	−	0.215899i
$906$	−973.453	−	696.948i	−1.07445	−	0.769258i
$907$		−	197.513i		−	0.217765i	−0.994055	−	0.108883i	$-0.965273\pi$
$907$		−	197.513i		−	0.217765i	0.994055	−	0.108883i	$-0.0347273\pi$
$908$	−1651.92	+	1200.19i	−1.81930	+	1.32180i
$909$	−44.5792	+	63.1907i	−0.0490421	+	0.0695168i
$910$	−23.3152	−	41.0577i	−0.0256211	−	0.0451184i
$911$	453.991	+	147.511i	0.498344	+	0.161922i	0.547395	−	0.836875i	$-0.315620\pi$
$911$	453.991	+	147.511i	0.498344	+	0.161922i	−0.0490509	+	0.998796i	$0.515620\pi$
$912$	1383.27	−	1019.80i	1.51674	−	1.11820i
$913$	0.198470	−	0.0644867i	0.000217382	−	7.06316e-5i
$914$	1412.88	+	459.074i	1.54582	+	0.502269i
$915$	−135.758	+	1289.43i	−0.148369	+	1.40921i
$916$	−284.184	−	874.629i	−0.310245	−	0.954835i
$917$	−0.601652	+	0.437125i	−0.000656109	+	0.000476691i
$918$	−1853.13	−	1288.09i	−2.01866	−	1.40315i
$919$	−483.268	+	351.115i	−0.525863	+	0.382062i	−0.818808	−	0.574067i	$-0.805365\pi$
$919$	−483.268	+	351.115i	−0.525863	+	0.382062i	0.292945	+	0.956129i	$0.405365\pi$
$920$	−1506.55	+	1649.34i	−1.63755	+	1.79276i
$921$	1293.28	+	410.276i	1.40421	+	0.445468i
$922$	926.192	−	1274.79i	1.00455	−	1.38264i
$923$	149.104	−	458.896i	0.161543	−	0.497179i
$924$	4.92340	+	14.8011i	0.00532835	+	0.0160185i
$925$	−170.957	+	751.335i	−0.184818	+	0.812254i
$926$			836.372i			0.903209i
$927$	−264.944	+	90.1848i	−0.285808	+	0.0972867i
$928$	−322.682	+	444.134i	−0.347718	+	0.478593i
$929$	228.336	−	314.278i	0.245787	−	0.338297i	−0.668243	−	0.743943i	$-0.732953\pi$
$929$	228.336	−	314.278i	0.245787	−	0.338297i	0.914030	+	0.405646i	$0.132953\pi$
$930$	−638.782	−	1106.86i	−0.686862	−	1.19017i
$931$	−889.595	+	646.328i	−0.955526	+	0.694230i
$932$	644.691			0.691729
$933$	1014.69	−	1417.25i	1.08755	−	1.51903i
$934$	−838.367	−	2580.23i	−0.897609	−	2.76256i
$935$	−387.100	−	353.587i	−0.414011	−	0.378168i
$936$	−2877.33	+	979.418i	−3.07407	+	1.04639i
$937$	−639.798	+	207.883i	−0.682816	+	0.221860i	−0.629828	−	0.776735i	$-0.716874\pi$
$937$	−639.798	+	207.883i	−0.682816	+	0.221860i	−0.0529879	+	0.998595i	$0.516874\pi$
$938$	−3.67476	−	11.3097i	−0.00391765	−	0.0120573i
$939$	−1.03717	−	148.909i	−0.00110454	−	0.158583i
$940$	−318.251	+	348.416i	−0.338565	+	0.370655i
$941$	1700.87	−	552.645i	1.80751	−	0.587295i	0.807512	−	0.589851i	$-0.200813\pi$
$941$	1700.87	−	552.645i	1.80751	−	0.587295i	0.999997	+	0.00255532i	$0.000813386\pi$
$942$	1479.82	−	2066.91i	1.57093	−	2.19418i
$943$			859.680i			0.911643i
$944$	−894.662	−	1231.40i	−0.947736	−	1.30445i
$945$	−7.06217	+	16.4676i	−0.00747319	+	0.0174261i
$946$	−675.066	−	490.464i	−0.713600	−	0.518461i
$947$	−1120.42	−	814.034i	−1.18313	−	0.859593i	−0.190607	−	0.981666i	$-0.561046\pi$
$947$	−1120.42	−	814.034i	−1.18313	−	0.859593i	−0.992521	+	0.122074i	$0.961046\pi$
$948$	165.546	−	1.15305i	0.174627	−	0.00121630i
$949$	−488.360			−0.514605
$950$	1953.77	+	444.555i	2.05660	+	0.467953i
$951$	−50.7755	−	152.645i	−0.0533917	−	0.160510i
$952$	−50.0829	−	16.2729i	−0.0526081	−	0.0170934i
$953$	−530.363	−	385.331i	−0.556519	−	0.404335i	0.273664	−	0.961825i	$-0.411764\pi$
$953$	−530.363	−	385.331i	−0.556519	−	0.404335i	−0.830183	+	0.557490i	$0.811764\pi$
$954$	664.661	−	9.25932i	0.696710	−	0.00970579i
$955$	785.663	+	717.644i	0.822684	+	0.751460i
$956$	−370.449	−	509.880i	−0.387499	−	0.533347i
$957$	99.8450	+	300.161i	0.104331	+	0.313648i
$958$	1623.33	+	2234.32i	1.69450	+	2.33228i
$959$	25.7963	−	8.38172i	0.0268992	−	0.00874007i
$960$	29.5597	−	280.758i	0.0307914	−	0.292456i
$961$	−120.996	+	372.387i	−0.125906	+	0.387500i
$962$	677.638	+	2085.56i	0.704405	+	2.16794i
$963$	21.4327	+	15.1201i	0.0222561	+	0.0157011i
$964$	509.841	−	1569.13i	0.528880	−	1.62773i
$965$	512.048	−	290.773i	0.530620	−	0.301319i
$966$	22.2391	+	30.1654i	0.0230219	+	0.0312272i
$967$	691.985	+	952.435i	0.715599	+	0.984938i	0.999659	+	0.0261313i	$0.00831881\pi$
$967$	691.985	+	952.435i	0.715599	+	0.984938i	−0.284059	+	0.958807i	$0.591681\pi$
$968$	−1710.63			−1.76718
$969$	1282.01	+	917.858i	1.32302	+	0.947222i
$970$	−947.373	+	2087.57i	−0.976674	+	2.15213i
$971$	297.531	−	409.516i	0.306417	−	0.421746i	−0.627843	−	0.778340i	$-0.716062\pi$
$971$	297.531	−	409.516i	0.306417	−	0.421746i	0.934260	+	0.356594i	$0.116062\pi$
$972$	1761.98	+	1188.68i	1.81274	+	1.22292i
$973$	9.04519	+	2.93896i	0.00929619	+	0.00302051i
$974$		−	1003.55i		−	1.03034i
$975$	−1288.85	−	756.756i	−1.32190	−	0.776160i
$976$	2205.70			2.25994
$977$	247.962	−	763.149i	0.253799	−	0.781114i	−0.740264	−	0.672316i	$-0.765300\pi$
$977$	247.962	−	763.149i	0.253799	−	0.781114i	0.994064	−	0.108799i	$-0.0347003\pi$
$978$	1415.27	+	448.975i	1.44710	+	0.459075i
$979$	163.613	+	118.872i	0.167122	+	0.121421i
$980$	239.133	−	2128.78i	0.244013	−	2.17223i
$981$	241.997	−	781.675i	0.246684	−	0.796814i
$982$			785.824i			0.800228i
$983$	178.360	−	129.586i	0.181444	−	0.131827i	−0.493356	−	0.869828i	$-0.664230\pi$
$983$	178.360	−	129.586i	0.181444	−	0.131827i	0.674800	+	0.738001i	$0.264230\pi$
$984$	983.813	+	1334.46i	0.999810	+	1.35616i
$985$	−53.3911	+	475.292i	−0.0542041	+	0.482530i
$986$	−1871.56	−	608.106i	−1.89813	−	0.616740i
$987$	2.54949	+	3.45816i	0.00258307	+	0.00350371i
$988$	3721.41	−	1209.16i	3.76661	−	1.22384i
$989$	−1308.35	−	425.110i	−1.32291	−	0.429838i
$990$	537.996	+	477.844i	0.543430	+	0.482670i
$991$	215.220	+	662.380i	0.217175	+	0.668396i	0.998992	+	0.0448878i	$0.0142930\pi$
$991$	215.220	+	662.380i	0.217175	+	0.668396i	−0.781817	+	0.623508i	$0.785707\pi$
$992$	−450.172	+	327.069i	−0.453802	+	0.329707i
$993$	−146.419	−	440.174i	−0.147451	−	0.443277i
$994$	−9.28240	+	6.74406i	−0.00933843	+	0.00678477i
$995$	269.208	+	474.072i	0.270561	+	0.476455i
$996$	0.369705	−	1.16539i	0.000371190	−	0.00117007i
$997$	402.160	−	553.526i	0.403370	−	0.555191i	−0.558216	−	0.829696i	$-0.688514\pi$
$997$	402.160	−	553.526i	0.403370	−	0.555191i	0.961586	+	0.274505i	$0.0885139\pi$
$998$	677.490	−	2085.10i	0.678848	−	2.08928i
$999$	474.971	−	683.323i	0.475447	−	0.684007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.29.2	✓	72
3.2	odd	2	inner	75.3.h.a.29.17	yes	72
5.2	odd	4		375.3.j.b.101.4		144
5.3	odd	4		375.3.j.b.101.33		144
5.4	even	2		375.3.h.a.149.17		72
15.2	even	4		375.3.j.b.101.34		144
15.8	even	4		375.3.j.b.101.3		144
15.14	odd	2		375.3.h.a.149.2		72
25.6	even	5		375.3.h.a.224.2		72
25.8	odd	20		375.3.j.b.26.3		144
25.17	odd	20		375.3.j.b.26.34		144
25.19	even	10	inner	75.3.h.a.44.17	yes	72
75.8	even	20		375.3.j.b.26.33		144
75.17	even	20		375.3.j.b.26.4		144
75.44	odd	10	inner	75.3.h.a.44.2	yes	72
75.56	odd	10		375.3.h.a.224.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.29.2	✓	72	1.1	even	1	trivial
75.3.h.a.29.17	yes	72	3.2	odd	2	inner
75.3.h.a.44.2	yes	72	75.44	odd	10	inner
75.3.h.a.44.17	yes	72	25.19	even	10	inner
375.3.h.a.149.2		72	15.14	odd	2
375.3.h.a.149.17		72	5.4	even	2
375.3.h.a.224.2		72	25.6	even	5
375.3.h.a.224.17		72	75.56	odd	10
375.3.j.b.26.3		144	25.8	odd	20
375.3.j.b.26.4		144	75.17	even	20
375.3.j.b.26.33		144	75.8	even	20
375.3.j.b.26.34		144	25.17	odd	20
375.3.j.b.101.3		144	15.8	even	4
375.3.j.b.101.4		144	5.2	odd	4
375.3.j.b.101.33		144	5.3	odd	4
375.3.j.b.101.34		144	15.2	even	4

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+(-1.10327 + 3.39551i) q^{2} +(-0.907156 + 2.85956i) q^{3} +(-7.07623 - 5.14118i) q^{4} +(2.46900 + 4.34788i) q^{5} +(-8.70882 - 6.23512i) q^{6} +0.132726i q^{7} +(13.7104 - 9.96116i) q^{8} +(-7.35413 - 5.18813i) q^{9} +(-17.4872 + 3.58664i) q^{10} +(4.25956 + 1.38402i) q^{11} +(21.1208 - 15.5710i) q^{12} +(18.9526 - 6.15806i) q^{13} +(-0.450674 - 0.146433i) q^{14} +(-14.6728 + 3.11604i) q^{15} +(7.88551 + 24.2691i) q^{16} +(-18.9405 + 13.7611i) q^{17} +(25.7300 - 19.2472i) q^{18} +(-18.1615 + 13.1951i) q^{19} +(4.88202 - 43.4602i) q^{20} +(-0.379539 - 0.120404i) q^{21} +(-9.39889 + 12.9365i) q^{22} +(-8.14650 + 25.0723i) q^{23} +(16.0471 + 48.2419i) q^{24} +(-12.8081 + 21.4698i) q^{25} +71.1477i q^{26} +(21.5071 - 16.3231i) q^{27} +(0.682371 - 0.939203i) q^{28} +(13.8383 - 19.0467i) q^{29} +(5.60745 - 53.2594i) q^{30} +(19.3057 - 14.0264i) q^{31} -23.3181 q^{32} +(-7.82176 + 10.9249i) q^{33} +(-25.8295 - 79.4951i) q^{34} +(-0.577078 + 0.327701i) q^{35} +(25.3664 + 74.5214i) q^{36} +(29.3131 - 9.52439i) q^{37} +(-24.7671 - 76.2254i) q^{38} +(0.416390 + 59.7823i) q^{39} +(77.1608 + 35.0169i) q^{40} +(31.0138 - 10.0770i) q^{41} +(0.827565 - 1.15589i) q^{42} +52.1832i q^{43} +(-23.0262 - 31.6928i) q^{44} +(4.40000 - 44.7844i) q^{45} +(-76.1457 - 55.3231i) q^{46} +(-8.72933 - 6.34223i) q^{47} +(-76.5523 + 0.533195i) q^{48} +48.9824 q^{49} +(-58.7703 - 67.1770i) q^{50} +(-22.1687 - 66.6451i) q^{51} +(-165.773 - 53.8628i) q^{52} +(16.7363 + 12.1596i) q^{53} +(31.6972 + 91.0364i) q^{54} +(4.49933 + 21.9372i) q^{55} +(1.32211 + 1.81973i) q^{56} +(-21.2569 - 63.9039i) q^{57} +(49.4061 + 68.0017i) q^{58} +(-56.7282 + 18.4321i) q^{59} +(119.848 + 53.3856i) q^{60} +(26.7105 - 82.2063i) q^{61} +(26.3274 + 81.0275i) q^{62} +(0.688602 - 0.976087i) q^{63} +(-5.81589 + 17.8995i) q^{64} +(73.5684 + 67.1992i) q^{65} +(-28.4663 - 38.6120i) q^{66} +(14.7506 + 20.3024i) q^{67} +204.776 q^{68} +(-64.3056 - 46.0399i) q^{69} +(-0.476042 - 2.32102i) q^{70} +(14.2320 - 19.5886i) q^{71} +(-152.508 + 2.12457i) q^{72} +(-23.3069 - 7.57287i) q^{73} +110.041i q^{74} +(-49.7753 - 56.1019i) q^{75} +196.354 q^{76} +(-0.183695 + 0.565356i) q^{77} +(-203.451 - 64.5421i) q^{78} +(5.10413 + 3.70837i) q^{79} +(-86.0498 + 94.2057i) q^{80} +(27.1666 + 76.3084i) q^{81} +116.425i q^{82} +(0.0376952 - 0.0273872i) q^{83} +(2.06669 + 2.80328i) q^{84} +(-106.596 - 48.3750i) q^{85} +(-177.189 - 57.5721i) q^{86} +(41.9118 + 56.8497i) q^{87} +(72.1866 - 23.4548i) q^{88} +(42.9445 + 13.9535i) q^{89} +(147.212 + 64.3494i) q^{90} +(0.817337 + 2.51550i) q^{91} +(186.548 - 135.535i) q^{92} +(22.5960 + 67.9298i) q^{93} +(31.1659 - 22.6434i) q^{94} +(-102.212 - 46.3853i) q^{95} +(21.1532 - 66.6795i) q^{96} +(75.4840 - 103.895i) q^{97} +(-54.0407 + 166.320i) q^{98} +(-24.1449 - 32.2774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) \) 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

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