LMFDB - Embedded newform 48.4.k.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, degree $2$, 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:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.775594 - 2.72001i) q^{2} +(-2.65327 - 4.46768i) q^{3} +(-6.79691 + 4.21925i) q^{4} +(5.27809 - 5.27809i) q^{5} +(-10.0943 + 10.6820i) q^{6} -22.9284 q^{7} +(16.7480 + 15.2152i) q^{8} +(-12.9203 + 23.7079i) q^{9} +O(q^{10})$	\(q+(-0.775594 - 2.72001i) q^{2} +(-2.65327 - 4.46768i) q^{3} +(-6.79691 + 4.21925i) q^{4} +(5.27809 - 5.27809i) q^{5} +(-10.0943 + 10.6820i) q^{6} -22.9284 q^{7} +(16.7480 + 15.2152i) q^{8} +(-12.9203 + 23.7079i) q^{9} +(-18.4501 - 10.2628i) q^{10} +(-10.6369 - 10.6369i) q^{11} +(36.8843 + 19.1716i) q^{12} +(12.7359 - 12.7359i) q^{13} +(17.7831 + 62.3654i) q^{14} +(-37.5850 - 9.57663i) q^{15} +(28.3959 - 57.3557i) q^{16} -134.550i q^{17} +(74.5067 + 16.7557i) q^{18} +(-46.9113 - 46.9113i) q^{19} +(-13.6051 + 58.1443i) q^{20} +(60.8352 + 102.437i) q^{21} +(-20.6826 + 37.1824i) q^{22} -93.7270i q^{23} +(23.5398 - 115.195i) q^{24} +69.2835i q^{25} +(-44.5198 - 24.7640i) q^{26} +(140.200 - 5.17956i) q^{27} +(155.842 - 96.7405i) q^{28} +(161.072 + 161.072i) q^{29} +(3.10219 + 109.659i) q^{30} -120.518i q^{31} +(-178.032 - 32.7525i) q^{32} +(-19.2997 + 75.7449i) q^{33} +(-365.978 + 104.356i) q^{34} +(-121.018 + 121.018i) q^{35} +(-12.2112 - 215.655i) q^{36} +(2.42940 + 2.42940i) q^{37} +(-91.2151 + 163.983i) q^{38} +(-90.6920 - 23.1082i) q^{39} +(168.705 - 8.09026i) q^{40} -253.093 q^{41} +(231.445 - 244.922i) q^{42} +(-135.701 + 135.701i) q^{43} +(117.178 + 27.4184i) q^{44} +(56.9379 + 193.327i) q^{45} +(-254.938 + 72.6941i) q^{46} +468.668 q^{47} +(-331.589 + 25.3161i) q^{48} +182.711 q^{49} +(188.452 - 53.7358i) q^{50} +(-601.128 + 356.998i) q^{51} +(-32.8289 + 140.301i) q^{52} +(321.633 - 321.633i) q^{53} +(-122.827 - 377.329i) q^{54} -112.285 q^{55} +(-384.005 - 348.861i) q^{56} +(-85.1164 + 334.053i) q^{57} +(313.191 - 563.045i) q^{58} +(-119.500 - 119.500i) q^{59} +(295.868 - 93.4890i) q^{60} +(310.130 - 310.130i) q^{61} +(-327.811 + 93.4734i) q^{62} +(296.242 - 543.584i) q^{63} +(48.9933 + 509.651i) q^{64} -134.443i q^{65} +(220.996 - 6.25183i) q^{66} +(705.631 + 705.631i) q^{67} +(567.701 + 914.526i) q^{68} +(-418.742 + 248.683i) q^{69} +(423.031 + 235.310i) q^{70} -501.730i q^{71} +(-577.112 + 200.475i) q^{72} -641.954i q^{73} +(4.72376 - 8.49222i) q^{74} +(309.536 - 183.828i) q^{75} +(516.782 + 120.921i) q^{76} +(243.887 + 243.887i) q^{77} +(7.48553 + 264.606i) q^{78} +1232.86i q^{79} +(-152.852 - 452.605i) q^{80} +(-395.130 - 612.628i) q^{81} +(196.297 + 688.414i) q^{82} +(87.3585 - 87.3585i) q^{83} +(-845.697 - 439.574i) q^{84} +(-710.169 - 710.169i) q^{85} +(474.356 + 263.859i) q^{86} +(292.251 - 1146.99i) q^{87} +(-16.3042 - 339.990i) q^{88} -1196.04 q^{89} +(481.691 - 304.815i) q^{90} +(-292.014 + 292.014i) q^{91} +(395.457 + 637.054i) q^{92} +(-538.438 + 319.768i) q^{93} +(-363.496 - 1274.78i) q^{94} -495.204 q^{95} +(326.038 + 882.290i) q^{96} -1058.49 q^{97} +(-141.709 - 496.975i) q^{98} +(389.611 - 114.747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.775594	−	2.72001i	−0.274214	−	0.961669i
$2$	−0.775594	−	2.72001i	−0.274214	−	0.961669i
$3$	−2.65327	−	4.46768i	−0.510622	−	0.859805i
$3$	−2.65327	−	4.46768i	−0.510622	−	0.859805i
$4$	−6.79691	+	4.21925i	−0.849613	+	0.527406i
$5$	5.27809	−	5.27809i	0.472087	−	0.472087i	−0.430502	−	0.902589i	$-0.641664\pi$
$5$	5.27809	−	5.27809i	0.472087	−	0.472087i	0.902589	+	0.430502i	$0.141664\pi$
$6$	−10.0943	+	10.6820i	−0.686828	+	0.726820i
$7$	−22.9284			−1.23802			−0.619008	−	0.785385i	$-0.712465\pi$
$7$	−22.9284			−1.23802			−0.619008	+	0.785385i	$0.712465\pi$
$8$	16.7480	+	15.2152i	0.740166	+	0.672425i
$9$	−12.9203	+	23.7079i	−0.478531	+	0.878071i
$10$	−18.4501	−	10.2628i	−0.583444	−	0.324538i
$11$	−10.6369	−	10.6369i	−0.291559	−	0.291559i	0.546137	−	0.837696i	$-0.316098\pi$
$11$	−10.6369	−	10.6369i	−0.291559	−	0.291559i	−0.837696	+	0.546137i	$0.816098\pi$
$12$	36.8843	+	19.1716i	0.887298	+	0.461197i
$13$	12.7359	−	12.7359i	0.271716	−	0.271716i	−0.558074	−	0.829791i	$-0.688460\pi$
$13$	12.7359	−	12.7359i	0.271716	−	0.271716i	0.829791	+	0.558074i	$0.188460\pi$
$14$	17.7831	+	62.3654i	0.339481	+	1.19056i
$15$	−37.5850	−	9.57663i	−0.646961	−	0.164845i
$16$	28.3959	−	57.3557i	0.443686	−	0.896182i
$17$		−	134.550i		−	1.91960i	−0.280679	−	0.959802i	$-0.590560\pi$
$17$		−	134.550i		−	1.91960i	0.280679	−	0.959802i	$-0.409440\pi$
$18$	74.5067	+	16.7557i	0.975633	+	0.219409i
$19$	−46.9113	−	46.9113i	−0.566431	−	0.566431i	0.364696	−	0.931127i	$-0.381173\pi$
$19$	−46.9113	−	46.9113i	−0.566431	−	0.566431i	−0.931127	+	0.364696i	$0.881173\pi$
$20$	−13.6051	+	58.1443i	−0.152110	+	0.650073i
$21$	60.8352	+	102.437i	0.632158	+	1.06445i
$22$	−20.6826	+	37.1824i	−0.200434	+	0.360333i
$23$		−	93.7270i		−	0.849715i	−0.905260	−	0.424857i	$-0.860324\pi$
$23$		−	93.7270i		−	0.849715i	0.905260	−	0.424857i	$-0.139676\pi$
$24$	23.5398	−	115.195i	0.200210	−	0.979753i
$25$			69.2835i			0.554268i
$26$	−44.5198	−	24.7640i	−0.335810	−	0.186793i
$27$	140.200	−	5.17956i	0.999318	−	0.0369188i
$28$	155.842	−	96.7405i	1.05184	−	0.652937i
$29$	161.072	+	161.072i	1.03139	+	1.03139i	0.999491	+	0.0319009i	$0.0101561\pi$
$29$	161.072	+	161.072i	1.03139	+	1.03139i	0.0319009	+	0.999491i	$0.489844\pi$
$30$	3.10219	+	109.659i	0.0188793	+	0.667365i
$31$		−	120.518i		−	0.698250i	−0.937076	−	0.349125i	$-0.886479\pi$
$31$		−	120.518i		−	0.698250i	0.937076	−	0.349125i	$-0.113521\pi$
$32$	−178.032	−	32.7525i	−0.983495	−	0.180934i
$33$	−19.2997	+	75.7449i	−0.101808	+	0.399560i
$34$	−365.978	+	104.356i	−1.84602	+	0.526382i
$35$	−121.018	+	121.018i	−0.584451	+	0.584451i
$36$	−12.2112	−	215.655i	−0.0565335	−	0.998401i
$37$	2.42940	+	2.42940i	0.0107943	+	0.0107943i	0.712483	−	0.701689i	$-0.247570\pi$
$37$	2.42940	+	2.42940i	0.0107943	+	0.0107943i	−0.701689	+	0.712483i	$0.747570\pi$
$38$	−91.2151	+	163.983i	−0.389396	+	0.700042i
$39$	−90.6920	−	23.1082i	−0.372368	−	0.0948789i
$40$	168.705	−	8.09026i	0.666865	−	0.0319795i
$41$	−253.093			−0.964059			−0.482029	−	0.876155i	$-0.660100\pi$
$41$	−253.093			−0.964059			−0.482029	+	0.876155i	$0.660100\pi$
$42$	231.445	−	244.922i	0.850305	−	0.899815i
$43$	−135.701	+	135.701i	−0.481260	+	0.481260i	−0.905534	−	0.424274i	$-0.860529\pi$
$43$	−135.701	+	135.701i	−0.481260	+	0.481260i	0.424274	+	0.905534i	$0.360529\pi$
$44$	117.178	+	27.4184i	0.401482	+	0.0939426i
$45$	56.9379	+	193.327i	0.188618	+	0.640434i
$46$	−254.938	+	72.6941i	−0.817144	+	0.233004i
$47$	468.668			1.45452			0.727258	−	0.686364i	$-0.240794\pi$
$47$	468.668			1.45452			0.727258	+	0.686364i	$0.240794\pi$
$48$	−331.589	+	25.3161i	−0.997098	+	0.0761264i
$49$	182.711			0.532684
$50$	188.452	−	53.7358i	0.533022	−	0.151988i
$51$	−601.128	+	356.998i	−1.65049	+	0.980191i
$52$	−32.8289	+	140.301i	−0.0875491	+	0.374159i
$53$	321.633	−	321.633i	0.833580	−	0.833580i	−0.154425	−	0.988005i	$-0.549352\pi$
$53$	321.633	−	321.633i	0.833580	−	0.833580i	0.988005	+	0.154425i	$0.0493524\pi$
$54$	−122.827	−	377.329i	−0.309531	−	0.950889i
$55$	−112.285			−0.275282
$56$	−384.005	−	348.861i	−0.916337	−	0.832473i
$57$	−85.1164	+	334.053i	−0.197788	+	0.776252i
$58$	313.191	−	563.045i	0.709035	−	1.27468i
$59$	−119.500	−	119.500i	−0.263688	−	0.263688i	0.562863	−	0.826550i	$-0.309700\pi$
$59$	−119.500	−	119.500i	−0.263688	−	0.263688i	−0.826550	+	0.562863i	$0.809700\pi$
$60$	295.868	−	93.4890i	0.636607	−	0.201156i
$61$	310.130	−	310.130i	0.650953	−	0.650953i	−0.302270	−	0.953222i	$-0.597744\pi$
$61$	310.130	−	310.130i	0.650953	−	0.650953i	0.953222	+	0.302270i	$0.0977443\pi$
$62$	−327.811	+	93.4734i	−0.671485	+	0.191470i
$63$	296.242	−	543.584i	0.592429	−	1.08707i
$64$	48.9933	+	509.651i	0.0956900	+	0.995411i
$65$		−	134.443i		−	0.256548i
$66$	220.996	−	6.25183i	0.412162	−	0.0116598i
$67$	705.631	+	705.631i	1.28666	+	1.28666i	0.936800	+	0.349865i	$0.113772\pi$
$67$	705.631	+	705.631i	1.28666	+	1.28666i	0.349865	+	0.936800i	$0.386228\pi$
$68$	567.701	+	914.526i	1.01241	+	1.63092i
$69$	−418.742	+	248.683i	−0.730589	+	0.433883i
$70$	423.031	+	235.310i	0.722313	+	0.401784i
$71$		−	501.730i		−	0.838654i	−0.907835	−	0.419327i	$-0.862266\pi$
$71$		−	501.730i		−	0.838654i	0.907835	−	0.419327i	$-0.137734\pi$
$72$	−577.112	+	200.475i	−0.944628	+	0.328142i
$73$		−	641.954i		−	1.02925i	−0.857416	−	0.514624i	$-0.827932\pi$
$73$		−	641.954i		−	1.02925i	0.857416	−	0.514624i	$-0.172068\pi$
$74$	4.72376	−	8.49222i	0.00742062	−	0.0133405i
$75$	309.536	−	183.828i	0.476562	−	0.283021i
$76$	516.782	+	120.921i	0.779986	+	0.182508i
$77$	243.887	+	243.887i	0.360955	+	0.360955i
$78$	7.48553	+	264.606i	0.0108663	+	0.384111i
$79$			1232.86i			1.75580i	0.478847	+	0.877899i	$0.341055\pi$
$79$			1232.86i			1.75580i	−0.478847	+	0.877899i	$0.658945\pi$
$80$	−152.852	−	452.605i	−0.213617	−	0.632534i
$81$	−395.130	−	612.628i	−0.542017	−	0.840368i
$82$	196.297	+	688.414i	0.264358	+	0.927105i
$83$	87.3585	−	87.3585i	0.115528	−	0.115528i	−0.646979	−	0.762508i	$-0.723968\pi$
$83$	87.3585	−	87.3585i	0.115528	−	0.115528i	0.762508	+	0.646979i	$0.223968\pi$
$84$	−845.697	−	439.574i	−1.09849	−	0.570970i
$85$	−710.169	−	710.169i	−0.906220	−	0.906220i
$86$	474.356	+	263.859i	0.594781	+	0.330844i
$87$	292.251	−	1146.99i	0.360145	−	1.41345i
$88$	−16.3042	−	339.990i	−0.0197504	−	0.411854i
$89$	−1196.04			−1.42450			−0.712250	−	0.701926i	$-0.752324\pi$
$89$	−1196.04			−1.42450			−0.712250	+	0.701926i	$0.752324\pi$
$90$	481.691	−	304.815i	0.564164	−	0.357004i
$91$	−292.014	+	292.014i	−0.336389	+	0.336389i
$92$	395.457	+	637.054i	0.448144	+	0.721929i
$93$	−538.438	+	319.768i	−0.600359	+	0.356542i
$94$	−363.496	−	1274.78i	−0.398849	−	1.39876i
$95$	−495.204			−0.534809
$96$	326.038	+	882.290i	0.346627	+	0.938003i
$97$	−1058.49			−1.10798			−0.553989	−	0.832524i	$-0.686895\pi$
$97$	−1058.49			−1.10798			−0.553989	+	0.832524i	$0.686895\pi$
$98$	−141.709	−	496.975i	−0.146069	−	0.512266i
$99$	389.611	−	114.747i	0.395529	−	0.116490i
$100$	−292.324	−	470.913i	−0.292324	−	0.470913i
$101$	40.2249	−	40.2249i	0.0396290	−	0.0396290i	−0.687015	−	0.726644i	$-0.741079\pi$
$101$	40.2249	−	40.2249i	0.0396290	−	0.0396290i	0.726644	+	0.687015i	$0.241079\pi$
$102$	1437.27	+	1358.19i	1.39521	+	1.31844i
$103$	355.450			0.340034			0.170017	−	0.985441i	$-0.445618\pi$
$103$	355.450			0.340034			0.170017	+	0.985441i	$0.445618\pi$
$104$	407.082	−	19.5216i	0.383824	−	0.0184063i
$105$	861.764	+	219.577i	0.800948	+	0.204081i
$106$	−1124.30	−	625.389i	−1.03021	−	0.573048i
$107$	−272.818	−	272.818i	−0.246489	−	0.246489i	0.573039	−	0.819528i	$-0.305764\pi$
$107$	−272.818	−	272.818i	−0.246489	−	0.246489i	−0.819528	+	0.573039i	$0.805764\pi$
$108$	−931.076	+	626.745i	−0.829563	+	0.558413i
$109$	422.130	−	422.130i	0.370942	−	0.370942i	−0.496878	−	0.867820i	$-0.665520\pi$
$109$	422.130	−	422.130i	0.370942	−	0.370942i	0.867820	+	0.496878i	$0.165520\pi$
$110$	87.0877	+	305.417i	0.0754863	+	0.264731i
$111$	4.40793	−	17.2996i	0.00376921	−	0.0147929i
$112$	−651.072	+	1315.07i	−0.549291	+	1.10949i
$113$			209.116i			0.174089i	0.996204	+	0.0870443i	$0.0277422\pi$
$113$			209.116i			0.174089i	−0.996204	+	0.0870443i	$0.972258\pi$
$114$	974.643	−	27.5720i	0.800734	−	0.0226523i
$115$	−494.700	−	494.700i	−0.401139	−	0.401139i
$116$	−1774.40	−	415.190i	−1.42025	−	0.332322i
$117$	137.390	+	466.495i	0.108562	+	0.368611i
$118$	−232.358	+	417.725i	−0.181273	+	0.325887i
$119$			3085.02i			2.37650i
$120$	−483.765	−	732.255i	−0.368012	−	0.557045i
$121$		−	1104.71i		−	0.829987i
$122$	−1084.09	−	603.022i	−0.804501	−	0.447501i
$123$	671.523	+	1130.74i	0.492270	+	0.828903i
$124$	508.497	+	819.153i	0.368261	+	0.593243i
$125$	1025.45	+	1025.45i	0.733750	+	0.733750i
$126$	−1708.32	−	384.181i	−1.20785	−	0.271632i
$127$		−	95.6660i		−	0.0668424i	−0.999441	−	0.0334212i	$-0.989360\pi$
$127$		−	95.6660i		−	0.0668424i	0.999441	−	0.0334212i	$-0.0106403\pi$
$128$	1348.26	−	528.544i	0.931016	−	0.364978i
$129$	966.318	+	246.217i	0.659532	+	0.168048i
$130$	−365.686	+	104.273i	−0.246714	+	0.0703489i
$131$	634.537	−	634.537i	0.423204	−	0.423204i	−0.463101	−	0.886305i	$-0.653263\pi$
$131$	634.537	−	634.537i	0.423204	−	0.423204i	0.886305	+	0.463101i	$0.153263\pi$
$132$	−188.408	−	596.262i	−0.124233	−	0.393166i
$133$	1075.60	+	1075.60i	0.701251	+	0.701251i
$134$	1372.04	−	2466.61i	0.884524	−	1.59017i
$135$	712.653	−	767.329i	0.454336	−	0.489194i
$136$	2047.22	−	2253.45i	1.29079	−	1.42082i
$137$	59.7796			0.0372797			0.0186398	−	0.999826i	$-0.494066\pi$
$137$	59.7796			0.0372797			0.0186398	+	0.999826i	$0.494066\pi$
$138$	1001.19	+	946.106i	0.617589	+	0.583608i
$139$	527.801	−	527.801i	0.322068	−	0.322068i	−0.527492	−	0.849560i	$-0.676867\pi$
$139$	527.801	−	527.801i	0.322068	−	0.322068i	0.849560	+	0.527492i	$0.176867\pi$
$140$	311.944	−	1333.15i	0.188315	−	0.804801i
$141$	−1243.50	−	2093.86i	−0.742708	−	1.25060i
$142$	−1364.71	+	389.139i	−0.806507	+	0.229970i
$143$	−270.942			−0.158443
$144$	992.898	+	1414.26i	0.574594	+	0.818439i
$145$	1700.31			0.973813
$146$	−1746.12	+	497.896i	−0.989795	+	0.282234i
$147$	−484.781	−	816.293i	−0.272000	−	0.458005i
$148$	−26.7626	−	6.26217i	−0.0148640	−	0.00347802i
$149$	−334.922	+	334.922i	−0.184147	+	0.184147i	−0.793160	−	0.609013i	$-0.791566\pi$
$149$	−334.922	+	334.922i	−0.184147	+	0.184147i	0.609013	+	0.793160i	$0.291566\pi$
$150$	−740.088	−	699.366i	−0.402853	−	0.380687i
$151$	−1791.49			−0.965495			−0.482747	−	0.875760i	$-0.660361\pi$
$151$	−1791.49			−0.965495			−0.482747	+	0.875760i	$0.660361\pi$
$152$	−71.9056	−	1499.44i	−0.0383705	−	0.800135i
$153$	3189.91	+	1738.43i	1.68555	+	0.918589i
$154$	474.218	−	852.533i	0.248140	−	0.446098i
$155$	−636.108	−	636.108i	−0.329635	−	0.329635i
$156$	713.924	−	225.587i	0.366408	−	0.115778i
$157$	−730.387	+	730.387i	−0.371281	+	0.371281i	−0.867944	−	0.496662i	$-0.834559\pi$
$157$	−730.387	+	730.387i	−0.371281	+	0.371281i	0.496662	+	0.867944i	$0.334559\pi$
$158$	3353.40	−	956.201i	1.68850	−	0.481464i
$159$	−2290.33	−	583.575i	−1.14236	−	0.291072i
$160$	−1112.54	+	766.797i	−0.549712	+	0.378879i
$161$			2149.01i			1.05196i
$162$	−1359.89	+	1549.91i	−0.659527	+	0.751681i
$163$	−741.068	−	741.068i	−0.356104	−	0.356104i	0.506271	−	0.862375i	$-0.331024\pi$
$163$	−741.068	−	741.068i	−0.356104	−	0.356104i	−0.862375	+	0.506271i	$0.831024\pi$
$164$	1720.25	−	1067.86i	0.819077	−	0.508450i
$165$	297.923	+	501.654i	0.140565	+	0.236689i
$166$	−305.371	−	169.861i	−0.142779	−	0.0794205i
$167$			2270.55i			1.05210i	0.850454	+	0.526049i	$0.176327\pi$
$167$			2270.55i			1.05210i	−0.850454	+	0.526049i	$0.823673\pi$
$168$	−539.729	+	2641.23i	−0.247863	+	1.21295i
$169$			1872.59i			0.852340i
$170$	−1380.86	+	2482.47i	−0.622985	+	1.11998i
$171$	1718.28	−	506.059i	0.768421	−	0.226312i
$172$	349.791	−	1494.90i	0.155066	−	0.662704i
$173$	−1798.49	−	1798.49i	−0.790385	−	0.790385i	0.191172	−	0.981557i	$-0.438771\pi$
$173$	−1798.49	−	1798.49i	−0.790385	−	0.790385i	−0.981557	+	0.191172i	$0.938771\pi$
$174$	−3346.49	+	94.6700i	−1.45803	+	0.0412466i
$175$		−	1588.56i		−	0.686193i
$176$	−912.132	+	308.042i	−0.390651	+	0.131929i
$177$	−216.822	+	850.953i	−0.0920754	+	0.361365i
$178$	927.645	+	3253.25i	0.390618	+	1.36990i
$179$	1440.56	−	1440.56i	0.601523	−	0.601523i	−0.339194	−	0.940716i	$-0.610154\pi$
$179$	1440.56	−	1440.56i	0.601523	−	0.601523i	0.940716	+	0.339194i	$0.110154\pi$
$180$	−1202.70	−	1073.79i	−0.498021	−	0.444643i
$181$	−876.030	−	876.030i	−0.359750	−	0.359750i	0.503971	−	0.863721i	$-0.331872\pi$
$181$	−876.030	−	876.030i	−0.359750	−	0.359750i	−0.863721	+	0.503971i	$0.831872\pi$
$182$	1020.77	+	567.798i	0.415738	+	0.231252i
$183$	−2208.42	−	562.704i	−0.892083	−	0.227302i
$184$	1426.08	−	1569.74i	0.571369	−	0.628929i
$185$	25.6452			0.0101917
$186$	1287.38	+	1216.55i	0.507502	+	0.479578i
$187$	−1431.20	+	1431.20i	−0.559678	+	0.559678i
$188$	−3185.50	+	1977.43i	−1.23578	+	0.767121i
$189$	−3214.57	+	118.759i	−1.23717	+	0.0457061i
$190$	384.077	+	1346.96i	0.146652	+	0.514309i
$191$	364.086			0.137928			0.0689642	−	0.997619i	$-0.478031\pi$
$191$	364.086			0.137928			0.0689642	+	0.997619i	$0.478031\pi$
$192$	2146.96	−	1571.13i	0.806999	−	0.590553i
$193$	524.279			0.195536			0.0977680	−	0.995209i	$-0.468830\pi$
$193$	524.279			0.195536			0.0977680	+	0.995209i	$0.468830\pi$
$194$	820.962	+	2879.11i	0.303823	+	1.06551i
$195$	−600.648	+	356.713i	−0.220581	+	0.130999i
$196$	−1241.87	+	770.902i	−0.452576	+	0.280941i
$197$	3063.36	−	3063.36i	1.10790	−	1.10790i	0.114469	−	0.993427i	$-0.463483\pi$
$197$	3063.36	−	3063.36i	1.10790	−	1.10790i	0.993427	−	0.114469i	$-0.0365167\pi$
$198$	−614.292	−	970.750i	−0.220484	−	0.348425i
$199$	3850.52			1.37164			0.685819	−	0.727772i	$-0.259444\pi$
$199$	3850.52			1.37164			0.685819	+	0.727772i	$0.259444\pi$
$200$	−1054.16	+	1160.36i	−0.372703	+	0.410250i
$201$	1280.30	−	5024.76i	0.449282	−	1.76328i
$202$	−140.610	−	78.2140i	−0.0489768	−	0.0272432i
$203$	−3693.13	−	3693.13i	−1.27688	−	1.27688i
$204$	2579.55	−	4962.79i	0.885316	−	1.70326i
$205$	−1335.85	+	1335.85i	−0.455120	+	0.455120i
$206$	−275.685	−	966.827i	−0.0932421	−	0.327000i
$207$	2222.07	+	1210.98i	0.746110	+	0.406615i
$208$	−368.830	−	1092.13i	−0.122951	−	0.364064i
$209$			997.983i			0.330296i
$210$	−71.1282	−	2514.31i	−0.0233729	−	0.826209i
$211$	−387.294	−	387.294i	−0.126362	−	0.126362i	0.641097	−	0.767460i	$-0.278479\pi$
$211$	−387.294	−	387.294i	−0.126362	−	0.126362i	−0.767460	+	0.641097i	$0.778479\pi$
$212$	−829.062	+	3543.16i	−0.268586	+	1.14786i
$213$	−2241.57	+	1331.22i	−0.721079	+	0.428235i
$214$	−530.472	+	953.663i	−0.169450	+	0.304631i
$215$			1432.48i			0.454393i
$216$	2426.89	+	2046.44i	0.764486	+	0.644640i
$217$			2763.29i			0.864445i
$218$	−1475.60	−	820.796i	−0.458441	−	0.255006i
$219$	−2868.05	+	1703.28i	−0.884952	+	0.525556i
$220$	763.192	−	473.759i	0.233884	−	0.145186i
$221$	−1713.62	−	1713.62i	−0.521588	−	0.521588i
$222$	−50.4739	+	1.42788i	−0.0152594	+	0.000431679i
$223$		−	1726.98i		−	0.518597i	−0.965797	−	0.259298i	$-0.916509\pi$
$223$		−	1726.98i		−	0.518597i	0.965797	−	0.259298i	$-0.0834913\pi$
$224$	4081.98	+	750.961i	1.21758	+	0.223999i
$225$	−1642.57	−	895.165i	−0.486686	−	0.265234i
$226$	568.798	−	162.189i	0.167416	−	0.0477375i
$227$	3123.12	−	3123.12i	0.913165	−	0.913165i	−0.0833548	−	0.996520i	$-0.526563\pi$
$227$	3123.12	−	3123.12i	0.913165	−	0.913165i	0.996520	+	0.0833548i	$0.0265635\pi$
$228$	−830.923	−	2629.65i	−0.241356	−	0.763829i
$229$	2822.16	+	2822.16i	0.814383	+	0.814383i	0.985288	−	0.170905i	$-0.0546691\pi$
$229$	2822.16	+	2822.16i	0.814383	+	0.814383i	−0.170905	+	0.985288i	$0.554669\pi$
$230$	−961.902	+	1729.28i	−0.275765	+	0.495761i
$231$	442.512	−	1736.71i	0.126040	−	0.494662i
$232$	246.891	+	5148.40i	0.0698673	+	1.45693i
$233$	−1826.16			−0.513459			−0.256729	−	0.966483i	$-0.582645\pi$
$233$	−1826.16			−0.513459			−0.256729	+	0.966483i	$0.582645\pi$
$234$	1162.31	−	735.513i	0.324712	−	0.205479i
$235$	2473.67	−	2473.67i	0.686658	−	0.686658i
$236$	1316.43	+	308.031i	0.363103	+	0.0849622i
$237$	5508.04	−	3271.12i	1.50964	−	0.896548i
$238$	8391.29	−	2392.72i	2.28541	−	0.651669i
$239$	−4210.91			−1.13967			−0.569835	−	0.821759i	$-0.692993\pi$
$239$	−4210.91			−1.13967			−0.569835	+	0.821759i	$0.692993\pi$
$240$	−1616.54	+	1883.78i	−0.434779	+	0.506655i
$241$	2256.00			0.602994			0.301497	−	0.953467i	$-0.402514\pi$
$241$	2256.00			0.602994			0.301497	+	0.953467i	$0.402514\pi$
$242$	−3004.83	+	856.808i	−0.798172	+	0.227594i
$243$	−1688.64	+	3390.78i	−0.445787	+	0.895139i
$244$	−799.411	+	3416.44i	−0.209742	+	0.896374i
$245$	964.364	−	964.364i	0.251473	−	0.251473i
$246$	2554.79	−	2703.54i	0.662143	−	0.700697i
$247$	−1194.92			−0.307817
$248$	1833.72	−	2018.45i	0.469521	−	0.516821i
$249$	−622.076	−	158.504i	−0.158323	−	0.0403406i
$250$	1993.89	−	3584.55i	0.504420	−	0.906828i
$251$	4234.49	+	4234.49i	1.06486	+	1.06486i	0.997746	+	0.0671099i	$0.0213778\pi$
$251$	4234.49	+	4234.49i	1.06486	+	1.06486i	0.0671099	+	0.997746i	$0.478622\pi$
$252$	279.984	+	4944.61i	0.0699894	+	1.23604i
$253$	−996.966	+	996.966i	−0.247742	+	0.247742i
$254$	−260.212	+	74.1979i	−0.0642802	+	0.0183291i
$255$	−1288.54	+	5057.08i	−0.316437	+	1.24191i
$256$	−2483.34	−	3257.33i	−0.606285	−	0.795247i
$257$		−	3349.78i		−	0.813050i	−0.913640	−	0.406525i	$-0.866740\pi$
$257$		−	3349.78i		−	0.813050i	0.913640	−	0.406525i	$-0.133260\pi$
$258$	−79.7579	−	2819.36i	−0.0192462	−	0.680332i
$259$	−55.7022	−	55.7022i	−0.0133636	−	0.0133636i
$260$	567.248	+	913.796i	0.135305	+	0.217966i
$261$	−5899.79	+	1737.58i	−1.39919	+	0.412082i
$262$	−2218.09	−	1233.80i	−0.523031	−	0.290934i
$263$		−	426.421i		−	0.0999780i	−0.998750	−	0.0499890i	$-0.984081\pi$
$263$		−	426.421i		−	0.0999780i	0.998750	−	0.0499890i	$-0.0159186\pi$
$264$	−1475.71	+	974.928i	−0.344029	+	0.227283i
$265$		−	3395.22i		−	0.787044i
$266$	2091.41	−	3759.87i	0.482078	−	0.866664i
$267$	3173.43	+	5343.55i	0.727381	+	1.22479i
$268$	−7773.34	−	1818.88i	−1.77176	−	0.414573i
$269$	5493.24	+	5493.24i	1.24509	+	1.24509i	0.957863	+	0.287224i	$0.0927324\pi$
$269$	5493.24	+	5493.24i	1.24509	+	1.24509i	0.287224	+	0.957863i	$0.407268\pi$
$270$	−2639.87	−	1343.29i	−0.595028	−	0.302777i
$271$			2721.90i			0.610124i	0.952332	+	0.305062i	$0.0986772\pi$
$271$			2721.90i			0.610124i	−0.952332	+	0.305062i	$0.901323\pi$
$272$	−7717.22	−	3820.68i	−1.72031	−	0.851701i
$273$	2079.42	+	529.834i	0.460997	+	0.117462i
$274$	−46.3647	−	162.601i	−0.0102226	−	0.0358507i
$275$	736.962	−	736.962i	0.161602	−	0.161602i
$276$	1796.90	−	3457.05i	0.391886	−	0.753950i
$277$	−3710.99	−	3710.99i	−0.804951	−	0.804951i	0.178913	−	0.983865i	$-0.442742\pi$
$277$	−3710.99	−	3710.99i	−0.804951	−	0.804951i	−0.983865	+	0.178913i	$0.942742\pi$
$278$	−1844.98	−	1026.26i	−0.398038	−	0.221407i
$279$	2857.24	+	1557.14i	0.613113	+	0.334134i
$280$	−3868.14	+	185.496i	−0.825590	+	0.0395912i
$281$	1134.95			0.240944			0.120472	−	0.992717i	$-0.461559\pi$
$281$	1134.95			0.240944			0.120472	+	0.992717i	$0.461559\pi$
$282$	−4730.87	+	5006.33i	−0.999003	+	1.05717i
$283$	2248.53	−	2248.53i	0.472302	−	0.472302i	−0.430357	−	0.902659i	$-0.641612\pi$
$283$	2248.53	−	2248.53i	0.472302	−	0.472302i	0.902659	+	0.430357i	$0.141612\pi$
$284$	2116.92	+	3410.21i	0.442311	+	0.712532i
$285$	1313.91	+	2212.41i	0.273085	+	0.459832i
$286$	210.141	+	736.965i	0.0434472	+	0.152369i
$287$	5803.00			1.19352
$288$	3076.72	−	3797.59i	0.629505	−	0.776996i
$289$	−13190.8			−2.68488
$290$	−1318.75	−	4624.86i	−0.267033	−	0.936486i
$291$	2808.47	+	4729.01i	0.565757	+	0.952645i
$292$	2708.56	+	4363.30i	0.542831	+	0.874462i
$293$	−1246.92	+	1246.92i	−0.248621	+	0.248621i	−0.820405	−	0.571784i	$-0.806252\pi$
$293$	−1246.92	+	1246.92i	−0.248621	+	0.248621i	0.571784	+	0.820405i	$0.306252\pi$
$294$	−1844.33	+	1951.72i	−0.365863	+	0.387165i
$295$	−1261.46			−0.248967
$296$	3.72378	+	77.6515i	0.000731217	+	0.0152480i
$297$	−1546.39	−	1436.21i	−0.302124	−	0.280596i
$298$	1170.75	+	651.227i	0.227584	+	0.126593i
$299$	−1193.70	−	1193.70i	−0.230881	−	0.230881i
$300$	−1328.28	+	2555.47i	−0.255627	+	0.491800i
$301$	3111.40	−	3111.40i	0.595808	−	0.595808i
$302$	1389.47	+	4872.88i	0.264752	+	0.928486i
$303$	−286.440	−	72.9846i	−0.0543087	−	0.0138378i
$304$	−4022.72	+	1358.54i	−0.758943	+	0.256308i
$305$		−	3273.79i		−	0.614613i
$306$	2254.49	−	10024.9i	0.421178	−	1.87283i
$307$	2404.62	+	2404.62i	0.447032	+	0.447032i	0.894367	−	0.447335i	$-0.147627\pi$
$307$	2404.62	+	2404.62i	0.447032	+	0.447032i	−0.447335	+	0.894367i	$0.647627\pi$
$308$	−2686.70	−	628.659i	−0.497042	−	0.116302i
$309$	−943.104	−	1588.04i	−0.173629	−	0.292363i
$310$	−1236.86	+	2223.58i	−0.226609	+	0.407390i
$311$		−	5394.10i		−	0.983509i	−0.870734	−	0.491754i	$-0.836356\pi$
$311$		−	5394.10i		−	0.983509i	0.870734	−	0.491754i	$-0.163644\pi$
$312$	−1167.31	−	1766.92i	−0.211815	−	0.320615i
$313$			3696.52i			0.667538i	0.942655	+	0.333769i	$0.108321\pi$
$313$			3696.52i			0.667538i	−0.942655	+	0.333769i	$0.891679\pi$
$314$	2553.14	+	1420.18i	0.458860	+	0.255239i
$315$	−1305.49	−	4432.68i	−0.233512	−	0.792868i
$316$	−5201.75	−	8379.66i	−0.926018	−	1.49175i
$317$	3129.07	+	3129.07i	0.554405	+	0.554405i	0.927709	−	0.373304i	$-0.121775\pi$
$317$	3129.07	+	3129.07i	0.554405	+	0.554405i	−0.373304	+	0.927709i	$0.621775\pi$
$318$	189.039	+	6682.35i	0.0333359	+	1.17839i
$319$		−	3426.62i		−	0.601423i
$320$	2948.57	+	2431.39i	0.515095	+	0.424747i
$321$	−495.004	+	1942.72i	−0.0860699	+	0.337795i
$322$	5845.33	−	1666.76i	1.01164	−	0.288462i
$323$	−6311.93	+	6311.93i	−1.08732	+	1.08732i
$324$	5270.49	+	2496.82i	0.903720	+	0.428125i
$325$	882.390	+	882.390i	0.150604	+	0.150604i
$326$	−1440.94	+	2590.48i	−0.244805	+	0.440103i
$327$	−3005.97	−	765.917i	−0.508349	−	0.129527i
$328$	−4238.80	−	3850.86i	−0.713563	−	0.648257i
$329$	−10745.8			−1.80072
$330$	1133.44	−	1199.43i	0.189072	−	0.200081i
$331$	−2951.06	+	2951.06i	−0.490045	+	0.490045i	−0.908320	−	0.418275i	$-0.862635\pi$
$331$	−2951.06	+	2951.06i	−0.490045	+	0.490045i	0.418275	+	0.908320i	$0.362635\pi$
$332$	−225.181	+	962.355i	−0.0372241	+	0.159085i
$333$	−88.9846	+	26.2073i	−0.0146436	+	0.00431277i
$334$	6175.92	−	1761.03i	1.01177	−	0.288500i
$335$	7448.77			1.21484
$336$	7602.79	−	580.458i	1.23442	−	0.0942457i
$337$	8323.57			1.34544			0.672720	−	0.739897i	$-0.265126\pi$
$337$	8323.57			1.34544			0.672720	+	0.739897i	$0.265126\pi$
$338$	5093.47	−	1452.37i	0.819669	−	0.233724i
$339$	934.265	−	554.842i	0.149682	−	0.0888934i
$340$	7823.33	+	1830.58i	1.24788	+	0.291991i
$341$	−1281.94	+	1281.94i	−0.203581	+	0.203581i
$342$	−2709.17	−	4281.24i	−0.428349	−	0.676909i
$343$	3675.17			0.578544
$344$	−4337.44	+	208.002i	−0.679823	+	0.0326009i
$345$	−897.589	+	3522.73i	−0.140071	+	0.549732i
$346$	−3497.01	+	6286.81i	−0.543354	+	0.976823i
$347$	−4148.13	−	4148.13i	−0.641739	−	0.641739i	0.309244	−	0.950983i	$-0.399924\pi$
$347$	−4148.13	−	4148.13i	−0.641739	−	0.641739i	−0.950983	+	0.309244i	$0.899924\pi$
$348$	2853.02	+	9029.05i	0.439476	+	1.39083i
$349$	−3221.89	+	3221.89i	−0.494165	+	0.494165i	−0.909616	−	0.415451i	$-0.863624\pi$
$349$	−3221.89	+	3221.89i	−0.494165	+	0.494165i	0.415451	+	0.909616i	$0.363624\pi$
$350$	−4320.89	+	1232.08i	−0.659890	+	0.188164i
$351$	1719.62	−	1851.55i	0.261500	−	0.281563i
$352$	1545.32	+	2242.09i	0.233994	+	0.339500i
$353$			1084.64i			0.163540i	0.996651	+	0.0817701i	$0.0260573\pi$
$353$			1084.64i			0.163540i	−0.996651	+	0.0817701i	$0.973943\pi$
$354$	2482.77	−	70.2359i	0.372762	−	0.0105452i
$355$	−2648.18	−	2648.18i	−0.395918	−	0.395918i
$356$	8129.41	−	5046.41i	1.21027	−	0.751290i
$357$	13782.9	−	8185.39i	2.04333	−	1.21349i
$358$	−5035.63	−	2801.05i	−0.743411	−	0.413520i
$359$		−	5935.87i		−	0.872655i	−0.899788	−	0.436328i	$-0.856279\pi$
$359$		−	5935.87i		−	0.872655i	0.899788	−	0.436328i	$-0.143721\pi$
$360$	−1987.92	+	4104.17i	−0.291035	+	0.600858i
$361$		−	2457.66i		−	0.358312i
$362$	−1703.37	+	3062.25i	−0.247312	+	0.444609i
$363$	−4935.50	+	2931.10i	−0.713627	+	0.423809i
$364$	752.714	−	3216.88i	0.108387	−	0.463215i
$365$	−3388.29	−	3388.29i	−0.485894	−	0.485894i
$366$	182.279	+	6443.36i	0.0260324	+	0.920218i
$367$		−	2623.54i		−	0.373154i	−0.982440	−	0.186577i	$-0.940261\pi$
$367$		−	2623.54i		−	0.373154i	0.982440	−	0.186577i	$-0.0597394\pi$
$368$	−5375.78	−	2661.46i	−0.761499	−	0.377007i
$369$	3270.04	−	6000.30i	0.461332	−	0.846512i
$370$	−19.8903	−	69.7552i	−0.00279472	−	0.00980108i
$371$	−7374.53	+	7374.53i	−1.03199	+	1.03199i
$372$	2310.53	−	4445.24i	0.322031	−	0.619556i
$373$	2239.51	+	2239.51i	0.310878	+	0.310878i	0.845250	−	0.534372i	$-0.179452\pi$
$373$	2239.51	+	2239.51i	0.310878	+	0.310878i	−0.534372	+	0.845250i	$0.679452\pi$
$374$	5002.91	+	2782.85i	0.691696	+	0.384753i
$375$	1860.58	−	7302.15i	0.256213	−	1.00555i
$376$	7849.27	+	7130.90i	1.07658	+	0.978053i
$377$	4102.81			0.560492
$378$	2816.23	+	8651.55i	0.383204	+	1.17722i
$379$	4858.63	−	4858.63i	0.658499	−	0.658499i	−0.296526	−	0.955025i	$-0.595828\pi$
$379$	4858.63	−	4858.63i	0.658499	−	0.658499i	0.955025	+	0.296526i	$0.0958282\pi$
$380$	3365.86	−	2089.39i	0.454381	−	0.282062i
$381$	−427.405	+	253.827i	−0.0574714	+	0.0341312i
$382$	−282.383	−	990.318i	−0.0378219	−	0.132642i
$383$	−2179.82			−0.290819			−0.145410	−	0.989372i	$-0.546450\pi$
$383$	−2179.82			−0.290819			−0.145410	+	0.989372i	$0.546450\pi$
$384$	−5938.65	−	4621.21i	−0.789207	−	0.614127i
$385$	2574.52			0.340804
$386$	−406.628	−	1426.04i	−0.0536187	−	0.188041i
$387$	−1463.88	−	4970.48i	−0.192283	−	0.652878i
$388$	7194.49	−	4466.05i	0.941352	−	0.584354i
$389$	357.917	−	357.917i	0.0466506	−	0.0466506i	−0.683397	−	0.730047i	$-0.739498\pi$
$389$	357.917	−	357.917i	0.0466506	−	0.0466506i	0.730047	+	0.683397i	$0.239498\pi$
$390$	1436.12	+	1357.10i	0.186464	+	0.176204i
$391$	−12611.0			−1.63111
$392$	3060.05	+	2779.99i	0.394275	+	0.358190i
$393$	−4518.51	−	1151.31i	−0.579971	−	0.147776i
$394$	−10708.3	−	5956.45i	−1.36923	−	0.761628i
$395$	6507.17	+	6507.17i	0.828889	+	0.828889i
$396$	−2164.01	+	2423.79i	−0.274610	+	0.307576i
$397$	2747.60	−	2747.60i	0.347350	−	0.347350i	−0.511771	−	0.859122i	$-0.671011\pi$
$397$	2747.60	−	2747.60i	0.347350	−	0.347350i	0.859122	+	0.511771i	$0.171011\pi$
$398$	−2986.44	−	10473.4i	−0.376122	−	1.31906i
$399$	1951.58	−	7659.29i	0.244865	−	0.961013i
$400$	3973.80	+	1967.37i	0.496725	+	0.245921i
$401$		−	5326.53i		−	0.663328i	−0.943398	−	0.331664i	$-0.892390\pi$
$401$		−	5326.53i		−	0.663328i	0.943398	−	0.331664i	$-0.107610\pi$
$402$	−14660.4	+	414.734i	−1.81889	+	0.0514553i
$403$	−1534.92	−	1534.92i	−0.189726	−	0.189726i
$404$	−103.686	+	443.124i	−0.0127688	+	0.0545699i
$405$	−5319.04	−	1147.97i	−0.652606	−	0.140848i
$406$	−7180.97	+	12909.7i	−0.877797	+	1.57807i
$407$		−	51.6826i		−	0.00629438i
$408$	−15499.5	−	3167.28i	−1.88074	−	0.384323i
$409$			10928.8i			1.32126i	0.750713	+	0.660629i	$0.229710\pi$
$409$			10928.8i			1.32126i	−0.750713	+	0.660629i	$0.770290\pi$
$410$	4669.59	+	2597.44i	0.562474	+	0.312874i
$411$	−158.611	−	267.076i	−0.0190358	−	0.0320532i
$412$	−2415.96	+	1499.73i	−0.288898	+	0.179336i
$413$	2739.94	+	2739.94i	0.326450	+	0.326450i
$414$	1570.46	−	6983.29i	0.186435	−	0.829010i
$415$		−	922.173i		−	0.109079i
$416$	−2684.53	+	1850.27i	−0.316394	+	0.218069i
$417$	−3758.44	−	957.648i	−0.441371	−	0.112461i
$418$	2714.52	−	774.029i	0.317635	−	0.0905718i
$419$	−6156.01	+	6156.01i	−0.717758	+	0.717758i	−0.968146	−	0.250387i	$-0.919442\pi$
$419$	−6156.01	+	6156.01i	−0.717758	+	0.717758i	0.250387	+	0.968146i	$0.419442\pi$
$420$	−6783.78	+	2143.55i	−0.788130	+	0.249035i
$421$	10186.5	+	10186.5i	1.17924	+	1.17924i	0.979939	+	0.199298i	$0.0638662\pi$
$421$	10186.5	+	10186.5i	1.17924	+	1.17924i	0.199298	+	0.979939i	$0.436134\pi$
$422$	−753.061	+	1353.83i	−0.0868683	+	0.156169i
$423$	−6055.35	+	11111.1i	−0.696031	+	1.27717i
$424$	10280.4	−	492.999i	1.17751	−	0.0564673i
$425$	9322.12			1.06397
$426$	5359.49	+	5064.60i	0.609550	+	0.576011i
$427$	−7110.79	+	7110.79i	−0.805890	+	0.805890i
$428$	3005.40	+	703.232i	0.339420	+	0.0794206i
$429$	718.882	+	1210.48i	0.0809043	+	0.136230i
$430$	3896.37	−	1111.03i	0.436976	−	0.124601i
$431$	−6076.07			−0.679058			−0.339529	−	0.940596i	$-0.610268\pi$
$431$	−6076.07			−0.679058			−0.339529	+	0.940596i	$0.610268\pi$
$432$	3684.04	−	8188.37i	0.410298	−	0.911952i
$433$	1951.79			0.216621			0.108311	−	0.994117i	$-0.465456\pi$
$433$	1951.79			0.216621			0.108311	+	0.994117i	$0.465456\pi$
$434$	7516.19	−	2143.19i	0.831310	−	0.237043i
$435$	−4511.38	−	7596.43i	−0.497250	−	0.837290i
$436$	−1088.11	+	4650.25i	−0.119520	+	0.510795i
$437$	−4396.86	+	4396.86i	−0.481305	+	0.481305i
$438$	6857.37	+	6480.06i	0.748077	+	0.706916i
$439$	2714.36			0.295101			0.147551	−	0.989055i	$-0.452861\pi$
$439$	2714.36			0.295101			0.147551	+	0.989055i	$0.452861\pi$
$440$	−1880.56	−	1708.45i	−0.203755	−	0.185107i
$441$	−2360.68	+	4331.69i	−0.254906	+	0.467735i
$442$	−3332.00	+	5990.15i	−0.358568	+	0.644621i
$443$	1752.77	+	1752.77i	0.187984	+	0.187984i	0.794824	−	0.606840i	$-0.207563\pi$
$443$	1752.77	+	1752.77i	0.187984	+	0.187984i	−0.606840	+	0.794824i	$0.707563\pi$
$444$	43.0311	+	136.182i	0.00459947	+	0.0145561i
$445$	−6312.84	+	6312.84i	−0.672488	+	0.672488i
$446$	−4697.40	+	1339.43i	−0.498718	+	0.142206i
$447$	2384.96	+	607.686i	0.252360	+	0.0643010i
$448$	−1123.34	−	11685.5i	−0.118466	−	1.23234i
$449$			8284.17i			0.870722i	0.900256	+	0.435361i	$0.143379\pi$
$449$			8284.17i			0.870722i	−0.900256	+	0.435361i	$0.856621\pi$
$450$	−1160.89	+	5162.08i	−0.121611	+	0.540762i
$451$	2692.12	+	2692.12i	0.281080	+	0.281080i
$452$	−882.313	−	1421.34i	−0.0918153	−	0.147908i
$453$	4753.31	+	8003.82i	0.493003	+	0.830138i
$454$	−10917.2	−	6072.64i	−1.12856	−	0.627760i
$455$			3082.56i			0.317610i
$456$	−6508.22	+	4299.66i	−0.668367	+	0.441557i
$457$		−	10981.7i		−	1.12407i	−0.827113	−	0.562036i	$-0.810018\pi$
$457$		−	10981.7i		−	1.12407i	0.827113	−	0.562036i	$-0.189982\pi$
$458$	5487.45	−	9865.16i	0.559851	−	1.00648i
$459$	−696.912	−	18864.0i	−0.0708694	−	1.91829i
$460$	5449.69	+	1275.17i	0.552376	+	0.129250i
$461$	−3446.67	−	3446.67i	−0.348216	−	0.348216i	0.511229	−	0.859445i	$-0.329190\pi$
$461$	−3446.67	−	3446.67i	−0.348216	−	0.348216i	−0.859445	+	0.511229i	$0.829190\pi$
$462$	−5067.07	+	143.344i	−0.510263	+	0.0144350i
$463$			5145.65i			0.516498i	0.966078	+	0.258249i	$0.0831455\pi$
$463$			5145.65i			0.516498i	−0.966078	+	0.258249i	$0.916855\pi$
$464$	13812.2	−	4664.61i	1.38193	−	0.466701i
$465$	−1154.16	+	4529.69i	−0.115103	+	0.451741i
$466$	1416.36	+	4967.18i	0.140797	+	0.493777i
$467$	11172.9	−	11172.9i	1.10711	−	1.10711i	0.113583	−	0.993529i	$-0.463767\pi$
$467$	11172.9	−	11172.9i	1.10711	−	1.10711i	0.993529	−	0.113583i	$-0.0362328\pi$
$468$	−2902.08	−	2591.04i	−0.286643	−	0.255921i
$469$	−16179.0	−	16179.0i	−1.59291	−	1.59291i
$470$	−8646.99	−	4809.85i	−0.848629	−	0.472047i
$471$	5201.05	+	1325.22i	0.508814	+	0.129645i
$472$	−183.169	−	3819.61i	−0.0178624	−	0.372483i
$473$	2886.87			0.280631
$474$	−13169.5	−	12444.9i	−1.27615	−	1.20593i
$475$	3250.18	−	3250.18i	0.313954	−	0.313954i
$476$	−13016.5	−	20968.6i	−1.25338	−	2.01911i
$477$	3469.65	+	11780.9i	0.333049	+	1.13084i
$478$	3265.96	+	11453.7i	0.312513	+	1.09598i
$479$	−5754.44			−0.548908			−0.274454	−	0.961600i	$-0.588497\pi$
$479$	−5754.44			−0.548908			−0.274454	+	0.961600i	$0.588497\pi$
$480$	6377.67	+	2935.95i	0.606457	+	0.279181i
$481$	61.8813			0.00586600
$482$	−1749.74	−	6136.34i	−0.165349	−	0.579881i
$483$	9601.09	−	5701.90i	0.904481	−	0.537154i
$484$	4661.05	+	7508.63i	0.437740	+	0.705168i
$485$	−5586.83	+	5586.83i	−0.523062	+	0.523062i
$486$	10532.7	+	1963.25i	0.983068	+	0.183240i
$487$	15071.9			1.40240			0.701202	−	0.712963i	$-0.252647\pi$
$487$	15071.9			1.40240			0.701202	+	0.712963i	$0.252647\pi$
$488$	9912.78	−	475.367i	0.919529	−	0.0440960i
$489$	−1344.60	+	5277.11i	−0.124346	+	0.488015i
$490$	−3371.04	−	1875.13i	−0.310792	−	0.172877i
$491$	11081.7	+	11081.7i	1.01855	+	1.01855i	0.999825	+	0.0187273i	$0.00596145\pi$
$491$	11081.7	+	11081.7i	1.01855	+	1.01855i	0.0187273	+	0.999825i	$0.494039\pi$
$492$	−9335.13	−	4852.19i	−0.855407	−	0.444621i
$493$	21672.3	−	21672.3i	1.97986	−	1.97986i
$494$	926.772	+	3250.19i	0.0844077	+	0.296018i
$495$	1450.76	−	2662.05i	0.131731	−	0.241718i
$496$	−6912.42	−	3422.23i	−0.625759	−	0.309804i
$497$			11503.9i			1.03827i
$498$	51.3448	+	1814.99i	0.00462012	+	0.163316i
$499$	8365.34	+	8365.34i	0.750469	+	0.750469i	0.974567	−	0.224098i	$-0.0719435\pi$
$499$	8365.34	+	8365.34i	0.750469	+	0.750469i	−0.224098	+	0.974567i	$0.571944\pi$
$500$	−11296.5	−	2643.25i	−1.01039	−	0.236420i
$501$	10144.1	−	6024.38i	0.904600	−	0.537225i
$502$	8233.61	−	14802.1i	0.732040	−	1.31604i
$503$			6889.74i			0.610732i	0.952235	+	0.305366i	$0.0987788\pi$
$503$			6889.74i			0.610732i	−0.952235	+	0.305366i	$0.901221\pi$
$504$	13232.2	−	4596.57i	1.16947	−	0.406245i
$505$		−	424.622i		−	0.0374167i
$506$	3485.00	+	1938.52i	0.306180	+	0.170311i
$507$	8366.14	−	4968.49i	0.732847	−	0.435224i
$508$	403.638	+	650.233i	0.0352531	+	0.0567902i
$509$	−7441.04	−	7441.04i	−0.647973	−	0.647973i	0.304529	−	0.952503i	$-0.401501\pi$
$509$	−7441.04	−	7441.04i	−0.647973	−	0.647973i	−0.952503	+	0.304529i	$0.901501\pi$
$510$	14754.7	−	417.401i	1.28108	−	0.0362408i
$511$			14719.0i			1.27422i
$512$	−6933.91	+	9281.09i	−0.598513	+	0.801113i
$513$	−6819.96	−	6334.00i	−0.586957	−	0.545133i
$514$	−9111.45	+	2598.07i	−0.781885	+	0.222950i
$515$	1876.10	−	1876.10i	0.160526	−	0.160526i
$516$	−7606.83	+	2403.62i	−0.648977	+	0.205065i
$517$	−4985.18	−	4985.18i	−0.424078	−	0.424078i
$518$	−108.308	+	194.713i	−0.00918685	+	0.0165158i
$519$	−3263.20	+	12807.0i	−0.275990	+	1.08317i
$520$	2045.58	−	2251.65i	0.172509	−	0.189888i
$521$	18192.4			1.52980			0.764900	−	0.644149i	$-0.222788\pi$
$521$	18192.4			1.52980			0.764900	+	0.644149i	$0.222788\pi$
$522$	9302.08	+	14699.8i	0.779964	+	1.23256i
$523$	−10642.0	+	10642.0i	−0.889756	+	0.889756i	−0.994499	−	0.104743i	$-0.966598\pi$
$523$	−10642.0	+	10642.0i	−0.889756	+	0.889756i	0.104743	+	0.994499i	$0.466598\pi$
$524$	−1635.62	+	6990.16i	−0.136360	+	0.582760i
$525$	−7097.17	+	4214.87i	−0.589992	+	0.350385i
$526$	−1159.87	+	330.729i	−0.0961457	+	0.0274154i
$527$	−16215.8			−1.34036
$528$	3796.37	+	3257.80i	0.312908	+	0.268518i
$529$	3382.24			0.277985
$530$	−9235.03	+	2633.31i	−0.756876	+	0.215818i
$531$	4377.07	−	1289.12i	0.357719	−	0.105354i
$532$	−11849.0	−	2772.53i	−0.965636	−	0.225948i
$533$	−3223.37	+	3223.37i	−0.261951	+	0.261951i
$534$	12073.2	−	12776.2i	0.978387	−	1.03535i
$535$	−2879.92			−0.232728
$536$	1081.59	+	22554.3i	0.0871597	+	1.81753i
$537$	−10258.2	−	2613.77i	−0.824343	−	0.210042i
$538$	10681.1	−	19202.2i	0.855941	−	1.53878i
$539$	−1943.48	−	1943.48i	−0.155309	−	0.155309i
$540$	−1606.28	+	8222.33i	−0.128006	+	0.655245i
$541$	−12016.8	+	12016.8i	−0.954974	+	0.954974i	−0.999029	−	0.0440548i	$-0.985972\pi$
$541$	−12016.8	+	12016.8i	−0.954974	+	0.954974i	0.0440548	+	0.999029i	$0.485972\pi$
$542$	7403.59	−	2111.09i	0.586737	−	0.167304i
$543$	−1589.48	+	6238.16i	−0.125619	+	0.493011i
$544$	−4406.86	+	23954.2i	−0.347321	+	1.88792i
$545$		−	4456.08i		−	0.350234i
$546$	−171.631	−	6066.98i	−0.0134526	−	0.475536i
$547$	−14646.2	−	14646.2i	−1.14484	−	1.14484i	−0.987554	−	0.157283i	$-0.949726\pi$
$547$	−14646.2	−	14646.2i	−1.14484	−	1.14484i	−0.157283	−	0.987554i	$-0.550274\pi$
$548$	−406.316	+	252.225i	−0.0316733	+	0.0196615i
$549$	3345.56	+	11359.5i	0.260082	+	0.883083i
$550$	−2576.13	−	1432.96i	−0.199721	−	0.111094i
$551$		−	15112.2i		−	1.16842i
$552$	−10796.9	−	2206.31i	−0.832511	−	0.170121i
$553$		−	28267.6i		−	2.17371i
$554$	−7215.70	+	12972.1i	−0.553368	+	0.994826i
$555$	−68.0436	−	114.574i	−0.00520412	−	0.00876291i
$556$	−1360.49	+	5814.34i	−0.103773	+	0.443494i
$557$	−18470.0	−	18470.0i	−1.40503	−	1.40503i	−0.782985	−	0.622041i	$-0.786304\pi$
$557$	−18470.0	−	18470.0i	−1.40503	−	1.40503i	−0.622041	−	0.782985i	$-0.713696\pi$
$558$	2019.37	−	8979.43i	0.153202	−	0.681236i
$559$			3456.55i			0.261532i
$560$	3504.65	+	10377.5i	0.264462	+	0.783088i
$561$	10191.5	+	2596.79i	0.766998	+	0.195430i
$562$	−880.257	−	3087.06i	−0.0660701	−	0.231708i
$563$	7487.33	−	7487.33i	0.560486	−	0.560486i	−0.368960	−	0.929445i	$-0.620286\pi$
$563$	7487.33	−	7487.33i	0.560486	−	0.560486i	0.929445	+	0.368960i	$0.120286\pi$
$564$	17286.5	+	8985.13i	1.29059	+	0.670819i
$565$	1103.74	+	1103.74i	0.0821849	+	0.0821849i
$566$	−7859.98	−	4372.08i	−0.583709	−	0.324686i
$567$	9059.70	+	14046.6i	0.671026	+	1.04039i
$568$	7633.94	−	8402.99i	0.563932	−	0.620743i
$569$	7740.75			0.570315			0.285157	−	0.958481i	$-0.407954\pi$
$569$	7740.75			0.570315			0.285157	+	0.958481i	$0.407954\pi$
$570$	4998.73	−	5289.78i	0.367322	−	0.388710i
$571$	−5808.73	+	5808.73i	−0.425723	+	0.425723i	−0.887169	−	0.461445i	$-0.847331\pi$
$571$	−5808.73	+	5808.73i	−0.425723	+	0.425723i	0.461445	+	0.887169i	$0.347331\pi$
$572$	1841.57	−	1143.17i	0.134615	−	0.0835636i
$573$	−966.018	−	1626.62i	−0.0704293	−	0.118592i
$574$	−4500.77	−	15784.2i	−0.327280	−	1.14777i
$575$	6493.73			0.470969
$576$	−12715.8	−	5423.32i	−0.919832	−	0.392312i
$577$	−16485.8			−1.18945			−0.594726	−	0.803928i	$-0.702740\pi$
$577$	−16485.8			−1.18945			−0.594726	+	0.803928i	$0.702740\pi$
$578$	10230.7	+	35879.1i	0.736230	+	2.58196i
$579$	−1391.05	−	2342.31i	−0.0998449	−	0.168123i
$580$	−11556.8	+	7174.02i	−0.827365	+	0.513595i
$581$	−2002.99	+	2002.99i	−0.143026	+	0.143026i
$582$	10684.7	−	11306.9i	0.760990	−	0.805300i
$583$	−6842.37			−0.486075
$584$	9767.48	−	10751.5i	0.692091	−	0.761813i
$585$	3187.36	+	1737.05i	0.225267	+	0.122766i
$586$	4358.75	+	2424.54i	0.307266	+	0.170916i
$587$	−5625.07	−	5625.07i	−0.395522	−	0.395522i	0.481128	−	0.876650i	$-0.340227\pi$
$587$	−5625.07	−	5625.07i	−0.395522	−	0.395522i	−0.876650	+	0.481128i	$0.840227\pi$
$588$	6739.15	+	3502.86i	0.472650	+	0.245673i
$589$	−5653.68	+	5653.68i	−0.395511	+	0.395511i
$590$	978.384	+	3431.20i	0.0682702	+	0.239424i
$591$	−21814.0	−	5558.20i	−1.51829	−	0.386859i
$592$	208.325	−	70.3548i	0.0144630	−	0.00488440i
$593$		−	17499.9i		−	1.21186i	−0.795516	−	0.605932i	$-0.792800\pi$
$593$		−	17499.9i		−	1.21186i	0.795516	−	0.605932i	$-0.207200\pi$
$594$	−2707.12	+	5320.12i	−0.186994	+	0.367487i
$595$	16283.0	+	16283.0i	1.12191	+	1.12191i
$596$	863.315	−	3689.55i	0.0593335	−	0.253574i
$597$	−10216.5	−	17202.9i	−0.700388	−	1.17934i
$598$	−2321.05	+	4172.71i	−0.158721	+	0.285342i
$599$		−	19054.7i		−	1.29976i	−0.760038	−	0.649878i	$-0.774820\pi$
$599$		−	19054.7i		−	1.29976i	0.760038	−	0.649878i	$-0.225180\pi$
$600$	7981.11	+	1630.92i	0.543046	+	0.110970i
$601$			2428.46i			0.164823i	0.996598	+	0.0824117i	$0.0262622\pi$
$601$			2428.46i			0.164823i	−0.996598	+	0.0824117i	$0.973738\pi$
$602$	−10876.2	−	6049.86i	−0.736348	−	0.409591i
$603$	−25846.0	+	7612.05i	−1.74549	+	0.514074i
$604$	12176.6	−	7558.75i	0.820297	−	0.509208i
$605$	−5830.77	−	5830.77i	−0.391826	−	0.391826i
$606$	23.6421	+	835.725i	0.00158481	+	0.0560215i
$607$		−	510.635i		−	0.0341450i	−0.999854	−	0.0170725i	$-0.994565\pi$
$607$		−	510.635i		−	0.0341450i	0.999854	−	0.0170725i	$-0.00543461\pi$
$608$	6815.23	+	9888.15i	0.454596	+	0.659568i
$609$	−6700.85	+	26298.6i	−0.445866	+	1.74987i
$610$	−8904.75	+	2539.13i	−0.591054	+	0.168535i
$611$	5968.93	−	5968.93i	0.395216	−	0.395216i
$612$	−29016.4	+	1643.03i	−1.91653	+	0.108522i
$613$	−3775.57	−	3775.57i	−0.248767	−	0.248767i	0.571698	−	0.820464i	$-0.306285\pi$
$613$	−3775.57	−	3775.57i	−0.248767	−	0.248767i	−0.820464	+	0.571698i	$0.806285\pi$
$614$	4675.58	−	8405.59i	0.307314	−	0.552479i
$615$	9512.49	+	2423.77i	0.623708	+	0.158920i
$616$	373.830	+	7795.43i	0.0244514	+	0.509881i
$617$	2253.48			0.147037			0.0735185	−	0.997294i	$-0.476577\pi$
$617$	2253.48			0.147037			0.0735185	+	0.997294i	$0.476577\pi$
$618$	−3588.01	+	3796.92i	−0.233545	+	0.247143i
$619$	6167.00	−	6167.00i	0.400440	−	0.400440i	−0.477948	−	0.878388i	$-0.658619\pi$
$619$	6167.00	−	6167.00i	0.400440	−	0.400440i	0.878388	+	0.477948i	$0.158619\pi$
$620$	7007.46	+	1639.67i	0.453914	+	0.106211i
$621$	−485.465	−	13140.6i	−0.0313704	−	0.849135i
$622$	−14672.0	+	4183.63i	−0.945810	+	0.269692i
$623$	27423.4			1.76355
$624$	−3900.67	+	4545.52i	−0.250243	+	0.291613i
$625$	2164.37			0.138519
$626$	10054.6	−	2867.00i	0.641951	−	0.183048i
$627$	4458.67	−	2647.92i	0.283990	−	0.168656i
$628$	1882.69	−	8046.05i	0.119630	−	0.511262i
$629$	326.877	−	326.877i	0.0207209	−	0.0207209i
$630$	−11044.4	+	6988.92i	−0.698444	+	0.441976i
$631$	−4568.99			−0.288255			−0.144127	−	0.989559i	$-0.546037\pi$
$631$	−4568.99			−0.288255			−0.144127	+	0.989559i	$0.546037\pi$
$632$	−18758.3	+	20648.0i	−1.18064	+	1.29958i
$633$	−702.711	+	2757.90i	−0.0441236	+	0.173170i
$634$	6084.22	−	10938.0i	0.381128	−	0.685179i
$635$	−504.934	−	504.934i	−0.0315554	−	0.0315554i
$636$	18029.4	−	5696.98i	1.12408	−	0.355188i
$637$	2326.99	−	2326.99i	0.144739	−	0.144739i
$638$	−9320.45	+	2657.67i	−0.578370	+	0.164919i
$639$	11895.0	+	6482.52i	0.736397	+	0.401322i
$640$	4326.51	−	9905.92i	0.267219	−	0.611822i
$641$			19078.5i			1.17560i	0.809008	+	0.587798i	$0.200005\pi$
$641$			19078.5i			1.17560i	−0.809008	+	0.587798i	$0.799995\pi$
$642$	5668.15	−	160.348i	0.348448	−	0.00985739i
$643$	−1491.99	−	1491.99i	−0.0915059	−	0.0915059i	0.659872	−	0.751378i	$-0.270610\pi$
$643$	−1491.99	−	1491.99i	−0.0915059	−	0.0915059i	−0.751378	+	0.659872i	$0.770610\pi$
$644$	−9067.20	−	14606.6i	−0.554810	−	0.893760i
$645$	6399.87	−	3800.76i	0.390690	−	0.232023i
$646$	22064.0	+	12273.0i	1.34380	+	0.747485i
$647$			14416.3i			0.875985i	0.898979	+	0.437992i	$0.144310\pi$
$647$			14416.3i			0.875985i	−0.898979	+	0.437992i	$0.855690\pi$
$648$	2703.63	−	16272.3i	0.163902	−	0.986477i
$649$			2542.22i			0.153761i
$650$	1715.73	−	3084.49i	0.103533	−	0.186128i
$651$	12345.5	−	7331.76i	0.743255	−	0.441405i
$652$	8163.72	+	1910.22i	0.490362	+	0.114739i
$653$	7610.82	+	7610.82i	0.456102	+	0.456102i	0.897373	−	0.441272i	$-0.145473\pi$
$653$	7610.82	+	7610.82i	0.456102	+	0.456102i	−0.441272	+	0.897373i	$0.645473\pi$
$654$	248.106	+	8770.30i	0.0148344	+	0.524382i
$655$		−	6698.29i		−	0.399578i
$656$	−7186.79	+	14516.3i	−0.427740	+	0.863972i
$657$	15219.4	+	8294.26i	0.903752	+	0.492526i
$658$	8334.38	+	29228.7i	0.493781	+	1.73169i
$659$	−18086.0	+	18086.0i	−1.06909	+	1.06909i	−0.0716615	+	0.997429i	$0.522830\pi$
$659$	−18086.0	+	18086.0i	−1.06909	+	1.06909i	−0.997429	+	0.0716615i	$0.977170\pi$
$660$	−4141.56	−	2152.69i	−0.244257	−	0.126960i
$661$	2628.00	+	2628.00i	0.154641	+	0.154641i	0.780187	−	0.625546i	$-0.215124\pi$
$661$	2628.00	+	2628.00i	0.154641	+	0.154641i	−0.625546	+	0.780187i	$0.715124\pi$
$662$	10315.7	+	5738.09i	0.605638	+	0.336884i
$663$	−3109.22	+	12202.6i	−0.182130	+	0.714798i
$664$	2792.26	−	133.903i	0.163194	−	0.00782597i
$665$	11354.2			0.662103
$666$	140.300	+	221.713i	0.00816294	+	0.0128997i
$667$	15096.8	−	15096.8i	0.876389	−	0.876389i
$668$	−9580.01	−	15432.7i	−0.554883	−	0.893877i
$669$	−7715.59	+	4582.14i	−0.445892	+	0.264807i
$670$	−5777.22	−	20260.7i	−0.333125	−	1.16827i
$671$	−6597.66			−0.379582
$672$	−7475.53	−	20229.5i	−0.429129	−	1.16126i
$673$	25842.2			1.48015			0.740076	−	0.672523i	$-0.234789\pi$
$673$	25842.2			1.48015			0.740076	+	0.672523i	$0.234789\pi$
$674$	−6455.71	−	22640.2i	−0.368939	−	1.29387i
$675$	358.858	+	9713.58i	0.0204629	+	0.553890i
$676$	−7900.93	−	12727.8i	−0.449529	−	0.724160i
$677$	14698.6	−	14698.6i	0.834437	−	0.834437i	−0.153683	−	0.988120i	$-0.549114\pi$
$677$	14698.6	−	14698.6i	0.834437	−	0.834437i	0.988120	+	0.153683i	$0.0491136\pi$
$678$	−2233.79	−	2110.88i	−0.126531	−	0.119569i
$679$	24269.6			1.37169
$680$	−1088.55	−	22699.3i	−0.0613880	−	1.28012i
$681$	−22239.5	−	5666.62i	−1.25143	−	0.318862i
$682$	4481.17	+	2492.63i	0.251602	+	0.139953i
$683$	−7696.74	−	7696.74i	−0.431197	−	0.431197i	0.457838	−	0.889035i	$-0.348624\pi$
$683$	−7696.74	−	7696.74i	−0.431197	−	0.431197i	−0.889035	+	0.457838i	$0.848624\pi$
$684$	−9543.79	+	10689.5i	−0.533503	+	0.597547i
$685$	315.522	−	315.522i	0.0175992	−	0.0175992i
$686$	−2850.44	−	9996.51i	−0.158645	−	0.556368i
$687$	5120.56	−	20096.5i	0.284369	−	1.11605i
$688$	3929.86	+	11636.6i	0.217768	+	0.644825i
$689$		−	8192.60i		−	0.452995i
$690$	10278.0	−	290.759i	0.567070	−	0.0160420i
$691$	−4345.29	−	4345.29i	−0.239222	−	0.239222i	0.577306	−	0.816528i	$-0.304104\pi$
$691$	−4345.29	−	4345.29i	−0.239222	−	0.239222i	−0.816528	+	0.577306i	$0.804104\pi$
$692$	19812.4	+	4635.90i	1.08838	+	0.254668i
$693$	−8933.16	+	2630.95i	−0.489672	+	0.144216i
$694$	−8065.69	+	14500.2i	−0.441167	+	0.793114i
$695$		−	5571.56i		−	0.304088i
$696$	22346.3	−	14763.1i	1.21700	−	0.804015i
$697$			34053.7i			1.85061i
$698$	11262.4	+	6264.69i	0.610730	+	0.339716i
$699$	4845.30	+	8158.71i	0.262183	+	0.441474i
$700$	6702.52	+	10797.3i	0.361902	+	0.582998i
$701$	9985.70	+	9985.70i	0.538024	+	0.538024i	0.922948	−	0.384924i	$-0.125773\pi$
$701$	9985.70	+	9985.70i	0.538024	+	0.538024i	−0.384924	+	0.922948i	$0.625773\pi$
$702$	−6369.96	−	3241.33i	−0.342477	−	0.174268i
$703$		−	227.932i		−	0.0122285i
$704$	4899.97	−	5942.25i	0.262322	−	0.318120i
$705$	−17614.9	−	4488.26i	−0.941015	−	0.239770i
$706$	2950.24	−	841.242i	0.157271	−	0.0448450i
$707$	−922.293	+	922.293i	−0.0490614	+	0.0490614i
$708$	−2116.66	−	6698.68i	−0.112357	−	0.355582i
$709$	11552.4	+	11552.4i	0.611932	+	0.611932i	0.943449	−	0.331517i	$-0.107560\pi$
$709$	11552.4	+	11552.4i	0.611932	+	0.611932i	−0.331517	+	0.943449i	$0.607560\pi$
$710$	−5149.16	+	9256.98i	−0.272175	+	0.489308i
$711$	−29228.6	−	15929.0i	−1.54171	−	0.840203i
$712$	−20031.4	−	18198.1i	−1.05437	−	0.957869i
$713$	−11295.8			−0.593313
$714$	−32954.3	−	31141.1i	−1.72729	−	1.63225i
$715$	−1430.06	+	1430.06i	−0.0747988	+	0.0747988i
$716$	−3713.28	+	15869.4i	−0.193815	+	0.828308i
$717$	11172.7	+	18813.0i	0.581940	+	0.979894i
$718$	−16145.6	+	4603.82i	−0.839205	+	0.239294i
$719$	−11158.4			−0.578772			−0.289386	−	0.957212i	$-0.593451\pi$
$719$	−11158.4			−0.578772			−0.289386	+	0.957212i	$0.593451\pi$
$720$	12705.2	+	2224.00i	0.657633	+	0.115116i
$721$	−8149.89			−0.420968
$722$	−6684.87	+	1906.15i	−0.344578	+	0.0982541i
$723$	−5985.77	−	10079.1i	−0.307902	−	0.518458i
$724$	9650.48	+	2258.11i	0.495383	+	0.115914i
$725$	−11159.6	+	11159.6i	−0.571667	+	0.571667i
$726$	11800.6	+	11151.3i	0.603251	+	0.570058i
$727$	−30801.0			−1.57132			−0.785658	−	0.618661i	$-0.787675\pi$
$727$	−30801.0			−1.57132			−0.785658	+	0.618661i	$0.787675\pi$
$728$	−9333.74	+	447.599i	−0.475180	+	0.0227873i
$729$	19629.3	−	1452.35i	0.997274	−	0.0737873i
$730$	−6588.25	+	11844.1i	−0.334030	+	0.600508i
$731$	18258.6	+	18258.6i	0.923828	+	0.923828i
$732$	17384.6	−	5493.23i	0.877806	−	0.277371i
$733$	8931.06	−	8931.06i	0.450036	−	0.450036i	−0.445331	−	0.895366i	$-0.646914\pi$
$733$	8931.06	−	8931.06i	0.450036	−	0.450036i	0.895366	+	0.445331i	$0.146914\pi$
$734$	−7136.05	+	2034.80i	−0.358850	+	0.102324i
$735$	−6867.19	−	1749.75i	−0.344626	−	0.0878104i
$736$	−3069.79	+	16686.4i	−0.153742	+	0.835690i
$737$		−	15011.5i		−	0.750278i
$738$	−18857.1	−	4240.75i	−0.940568	−	0.211523i
$739$	−4939.23	−	4939.23i	−0.245863	−	0.245863i	0.573408	−	0.819270i	$-0.305621\pi$
$739$	−4939.23	−	4939.23i	−0.245863	−	0.245863i	−0.819270	+	0.573408i	$0.805621\pi$
$740$	−174.308	+	108.203i	−0.00865904	+	0.00537518i
$741$	3170.44	+	5338.51i	0.157178	+	0.264663i
$742$	25778.4	+	14339.2i	1.27541	+	0.709443i
$743$			7164.72i			0.353766i	0.984232	+	0.176883i	$0.0566014\pi$
$743$			7164.72i			0.353766i	−0.984232	+	0.176883i	$0.943399\pi$
$744$	−13883.1	−	2836.98i	−0.684113	−	0.139797i
$745$			3535.50i			0.173867i
$746$	4354.54	−	7828.44i	0.213715	−	0.384209i
$747$	942.387	+	3199.79i	0.0461582	+	0.156726i
$748$	3689.15	−	15766.3i	0.180332	−	0.770687i
$749$	6255.27	+	6255.27i	0.305157	+	0.305157i
$750$	−21305.0	+	602.704i	−1.03726	+	0.0293435i
$751$			5225.64i			0.253910i	0.991908	+	0.126955i	$0.0405203\pi$
$751$			5225.64i			0.253910i	−0.991908	+	0.126955i	$0.959480\pi$
$752$	13308.3	−	26880.8i	0.645349	−	1.30351i
$753$	7683.11	−	30153.6i	0.371830	−	1.45931i
$754$	−3182.12	−	11159.7i	−0.153695	−	0.539008i
$755$	−9455.67	+	9455.67i	−0.455798	+	0.455798i
$756$	21348.1	−	14370.3i	1.02701	−	0.691324i
$757$	20074.4	+	20074.4i	0.963828	+	0.963828i	0.999368	−	0.0355400i	$-0.0113151\pi$
$757$	20074.4	+	20074.4i	0.963828	+	0.963828i	−0.0355400	+	0.999368i	$0.511315\pi$
$758$	−16983.8	−	9447.20i	−0.813827	−	0.452688i
$759$	7099.35	+	1808.91i	0.339512	+	0.0865074i
$760$	−8293.70	−	7534.65i	−0.395847	−	0.359619i
$761$	−6376.16			−0.303726			−0.151863	−	0.988402i	$-0.548527\pi$
$761$	−6376.16			−0.303726			−0.151863	+	0.988402i	$0.548527\pi$
$762$	1021.91	+	965.678i	0.0485823	+	0.0459092i
$763$	−9678.76	+	9678.76i	−0.459233	+	0.459233i
$764$	−2474.66	+	1536.17i	−0.117186	+	0.0727443i
$765$	26012.3	−	7661.01i	1.22938	−	0.362071i
$766$	1690.66	+	5929.15i	0.0797467	+	0.279672i
$767$	−3043.89			−0.143297
$768$	−7963.74	+	19737.4i	−0.374176	+	0.927358i
$769$	−19537.7			−0.916185			−0.458092	−	0.888905i	$-0.651467\pi$
$769$	−19537.7			−0.916185			−0.458092	+	0.888905i	$0.651467\pi$
$770$	−1996.78	−	7002.72i	−0.0934532	−	0.327741i
$771$	−14965.8	+	8887.88i	−0.699065	+	0.415161i
$772$	−3563.48	+	2212.06i	−0.166130	+	0.103127i
$773$	−16886.8	+	16886.8i	−0.785740	+	0.785740i	−0.980793	−	0.195053i	$-0.937512\pi$
$773$	−16886.8	+	16886.8i	−0.785740	+	0.785740i	0.195053	+	0.980793i	$0.437512\pi$
$774$	−12384.4	+	7836.85i	−0.575126	+	0.363940i
$775$	8349.94			0.387018
$776$	−17727.7	−	16105.2i	−0.820087	−	0.745031i
$777$	−101.067	+	396.652i	−0.00466634	+	0.0183138i
$778$	−1251.13	−	695.939i	−0.0576547	−	0.0320702i
$779$	11872.9	+	11872.9i	0.546073	+	0.546073i
$780$	2577.49	−	4958.83i	0.118319	−	0.227634i
$781$	−5336.86	+	5336.86i	−0.244517	+	0.244517i
$782$	9781.02	+	34302.1i	0.447274	+	1.56859i
$783$	23416.7	+	21748.1i	1.06877	+	0.992611i
$784$	5188.24	−	10479.5i	0.236345	−	0.477382i
$785$			7710.10i			0.350554i
$786$	372.948	+	13183.3i	0.0169245	+	0.598262i
$787$	−24395.2	−	24395.2i	−1.10495	−	1.10495i	−0.993804	−	0.111145i	$-0.964548\pi$
$787$	−24395.2	−	24395.2i	−1.10495	−	1.10495i	−0.111145	−	0.993804i	$-0.535452\pi$
$788$	−7896.31	+	33746.5i	−0.356973	+	1.52559i
$789$	−1905.11	+	1131.41i	−0.0859616	+	0.0510510i
$790$	12652.6	−	22746.5i	0.569824	−	1.02441i
$791$		−	4794.70i		−	0.215524i
$792$	8271.12	+	4006.25i	0.371088	+	0.179742i
$793$		−	7899.60i		−	0.353749i
$794$	−9604.52	−	5342.48i	−0.429284	−	0.238788i
$795$	−15168.8	+	9008.43i	−0.676705	+	0.401882i
$796$	−26171.6	+	16246.3i	−1.16536	+	0.723410i
$797$	19285.8	+	19285.8i	0.857139	+	0.857139i	0.991000	−	0.133861i	$-0.0427376\pi$
$797$	19285.8	+	19285.8i	0.857139	+	0.857139i	−0.133861	+	0.991000i	$0.542738\pi$
$798$	−22347.0	+	632.182i	−0.991322	+	0.0280439i
$799$		−	63059.5i		−	2.79210i
$800$	2269.20	−	12334.7i	0.100286	−	0.545120i
$801$	15453.3	−	28355.7i	0.681667	−	1.25081i
$802$	−14488.2	+	4131.23i	−0.637901	+	0.181894i
$803$	−6828.41	+	6828.41i	−0.300086	+	0.300086i
$804$	12498.6	+	39554.8i	0.548248	+	1.73506i
$805$	11342.7	+	11342.7i	0.496617	+	0.496617i
$806$	−2984.51	+	5365.46i	−0.130428	+	0.234479i
$807$	9966.99	−	39117.1i	0.434764	−	1.70630i
$808$	1285.72	−	61.6567i	0.0559796	−	0.00268450i
$809$	−26695.5			−1.16015			−0.580077	−	0.814561i	$-0.696978\pi$
$809$	−26695.5			−1.16015			−0.580077	+	0.814561i	$0.696978\pi$
$810$	1002.92	+	15358.2i	0.0435048	+	0.666213i
$811$	14691.0	−	14691.0i	0.636094	−	0.636094i	−0.313496	−	0.949590i	$-0.601500\pi$
$811$	14691.0	−	14691.0i	0.636094	−	0.636094i	0.949590	+	0.313496i	$0.101500\pi$
$812$	40684.1	+	9519.63i	1.75829	+	0.411421i
$813$	12160.6	−	7221.93i	0.524588	−	0.311543i
$814$	−140.577	+	40.0847i	−0.00605311	+	0.00172601i
$815$	−7822.85			−0.336224
$816$	3406.29	+	44615.4i	0.146133	+	1.91403i
$817$	12731.8			0.545201
$818$	29726.4	−	8476.31i	1.27061	−	0.362307i
$819$	−3150.13	−	10696.0i	−0.134401	−	0.456346i
$820$	3443.36	−	14715.9i	0.146643	−	0.626709i
$821$	25860.0	−	25860.0i	1.09930	−	1.09930i	0.104802	−	0.994493i	$-0.466579\pi$
$821$	25860.0	−	25860.0i	1.09930	−	1.09930i	0.994493	−	0.104802i	$-0.0334209\pi$
$822$	−603.431	+	638.567i	−0.0256047	+	0.0270956i
$823$	−21062.2			−0.892081			−0.446041	−	0.895013i	$-0.647166\pi$
$823$	−21062.2			−0.892081			−0.446041	+	0.895013i	$0.647166\pi$
$824$	5953.09	+	5408.25i	0.251682	+	0.228647i
$825$	−5247.87	−	1337.15i	−0.221464	−	0.0564287i
$826$	5327.59	−	9577.75i	0.224419	−	0.403453i
$827$	−10436.6	−	10436.6i	−0.438836	−	0.438836i	0.452784	−	0.891620i	$-0.350431\pi$
$827$	−10436.6	−	10436.6i	−0.438836	−	0.438836i	−0.891620	+	0.452784i	$0.850431\pi$
$828$	−20212.7	+	1144.52i	−0.848356	+	0.0480373i
$829$	−26644.7	+	26644.7i	−1.11629	+	1.11629i	−0.124014	+	0.992280i	$0.539577\pi$
$829$	−26644.7	+	26644.7i	−1.11629	+	1.11629i	−0.992280	+	0.124014i	$0.960423\pi$
$830$	−2508.32	+	715.232i	−0.104898	+	0.0299109i
$831$	−6733.26	+	26425.7i	−0.281076	+	1.10313i
$832$	7114.85	+	5866.90i	0.296470	+	0.244469i
$833$		−	24583.8i		−	1.02254i
$834$	310.214	+	10965.7i	0.0128799	+	0.455291i
$835$	11984.2	+	11984.2i	0.496682	+	0.496682i
$836$	−4210.73	−	6783.20i	−0.174200	−	0.280624i
$837$	−624.233	−	16896.7i	−0.0257786	−	0.697774i
$838$	21519.0	+	11969.8i	0.887065	+	0.493426i
$839$		−	9701.30i		−	0.399197i	−0.979878	−	0.199598i	$-0.936036\pi$
$839$		−	9701.30i		−	0.399197i	0.979878	−	0.199598i	$-0.0639638\pi$
$840$	11091.9	+	16789.4i	0.455605	+	0.689631i
$841$			27499.5i			1.12754i
$842$	19806.8	−	35607.9i	0.810672	−	1.45740i
$843$	−3011.32	−	5070.57i	−0.123031	−	0.207165i
$844$	4266.49	+	998.313i	0.174003	+	0.0407149i
$845$	9883.71	+	9883.71i	0.402379	+	0.402379i
$846$	34918.9	+	7852.87i	1.41907	+	0.319134i
$847$			25329.3i			1.02754i
$848$	−9314.42	−	27580.6i	−0.377192	−	1.11689i
$849$	−16011.7	−	4079.76i	−0.647255	−	0.164920i
$850$	−7230.18	−	25356.2i	−0.291756	−	1.02319i
$851$	227.700	−	227.700i	0.00917211	−	0.00917211i
$852$	9618.98	−	18505.9i	0.386785	−	0.744135i
$853$	−14896.8	−	14896.8i	−0.597958	−	0.597958i	0.341811	−	0.939769i	$-0.388960\pi$
$853$	−14896.8	−	14896.8i	−0.597958	−	0.597958i	−0.939769	+	0.341811i	$0.888960\pi$
$854$	24856.5	+	13826.3i	0.995986	+	0.554013i
$855$	6398.20	−	11740.3i	0.255923	−	0.469600i
$856$	−418.175	−	8720.15i	−0.0166973	−	0.348188i
$857$	−43753.5			−1.74398			−0.871989	−	0.489525i	$-0.837170\pi$
$857$	−43753.5			−1.74398			−0.871989	+	0.489525i	$0.837170\pi$
$858$	2734.96	−	2894.21i	0.108823	−	0.115159i
$859$	18526.6	−	18526.6i	0.735880	−	0.735880i	−0.235898	−	0.971778i	$-0.575803\pi$
$859$	18526.6	−	18526.6i	0.735880	−	0.735880i	0.971778	+	0.235898i	$0.0758030\pi$
$860$	−6044.00	−	9736.45i	−0.239650	−	0.386059i
$861$	−15396.9	−	25926.0i	−0.609438	−	1.02620i
$862$	4712.56	+	16527.0i	0.186207	+	0.653028i
$863$	6795.73			0.268052			0.134026	−	0.990978i	$-0.457209\pi$
$863$	6795.73			0.268052			0.134026	+	0.990978i	$0.457209\pi$
$864$	−25129.8	−	3669.78i	−0.989505	−	0.144501i
$865$	−18985.2			−0.746261
$866$	−1513.80	−	5308.89i	−0.0594006	−	0.208318i
$867$	34998.7	+	58932.3i	1.37096	+	2.30847i
$868$	−11659.0	−	18781.9i	−0.455913	−	0.734444i
$869$	13113.9	−	13113.9i	0.511919	−	0.511919i
$870$	−17163.4	+	18162.7i	−0.668843	+	0.707787i
$871$	17973.7			0.699216
$872$	13492.7	−	647.040i	0.523989	−	0.0251279i
$873$	13676.1	−	25094.7i	0.530201	−	0.972883i
$874$	15369.7	+	8549.32i	0.594836	+	0.330875i
$875$	−23511.8	−	23511.8i	−0.908394	−	0.908394i
$876$	12307.3	−	23678.0i	0.474686	−	0.913249i
$877$	16260.9	−	16260.9i	0.626103	−	0.626103i	−0.320982	−	0.947085i	$-0.604013\pi$
$877$	16260.9	−	16260.9i	0.626103	−	0.626103i	0.947085	+	0.320982i	$0.104013\pi$
$878$	−2105.24	−	7383.09i	−0.0809208	−	0.283789i
$879$	8879.27	+	2262.43i	0.340717	+	0.0868144i
$880$	−3188.44	+	6440.19i	−0.122139	+	0.246703i
$881$			30505.1i			1.16656i	0.812269	+	0.583282i	$0.198232\pi$
$881$			30505.1i			1.16656i	−0.812269	+	0.583282i	$0.801768\pi$
$882$	13613.2	+	3061.45i	0.519705	+	0.116876i
$883$	17328.5	+	17328.5i	0.660419	+	0.660419i	0.955479	−	0.295059i	$-0.0953394\pi$
$883$	17328.5	+	17328.5i	0.660419	+	0.660419i	−0.295059	+	0.955479i	$0.595339\pi$
$884$	18877.6	+	4417.14i	0.718236	+	0.168060i
$885$	3347.00	+	5635.82i	0.127128	+	0.214063i
$886$	3408.12	−	6127.00i	0.129230	−	0.232326i
$887$			3034.76i			0.114878i	0.998349	+	0.0574392i	$0.0182935\pi$
$887$			3034.76i			0.114878i	−0.998349	+	0.0574392i	$0.981706\pi$
$888$	337.042	−	222.667i	0.0127369	−	0.00841466i
$889$			2193.47i			0.0827519i
$890$	22067.2	+	12274.8i	0.831116	+	0.462305i
$891$	−2313.51	+	10719.4i	−0.0869869	+	0.403047i
$892$	7286.55	+	11738.1i	0.273511	+	0.440607i
$893$	−21985.8	−	21985.8i	−0.823883	−	0.823883i
$894$	−196.850	−	6958.44i	−0.00736425	−	0.260319i
$895$		−	15206.8i		−	0.567942i
$896$	−30913.3	+	12118.7i	−1.15261	+	0.451848i
$897$	−2165.87	+	8500.29i	−0.0806200	+	0.316406i
$898$	22533.0	−	6425.15i	0.837346	−	0.238764i
$899$	19412.2	−	19412.2i	0.720170	−	0.720170i
$900$	14941.3	−	846.037i	0.553381	−	0.0313347i
$901$	−43275.9	−	43275.9i	−1.60014	−	1.60014i
$902$	5234.61	−	9410.60i	0.193230	−	0.347382i
$903$	−22156.1	−	5645.36i	−0.816511	−	0.208046i
$904$	−3181.75	+	3502.29i	−0.117061	+	0.128854i
$905$	−9247.53			−0.339667
$906$	18083.8	−	19136.8i	0.663129	−	0.701741i
$907$	−23264.5	+	23264.5i	−0.851692	+	0.851692i	−0.990342	−	0.138649i	$-0.955724\pi$
$907$	−23264.5	+	23264.5i	−0.851692	+	0.851692i	0.138649	+	0.990342i	$0.455724\pi$
$908$	−8050.34	+	34404.7i	−0.294229	+	1.25745i
$909$	433.930	+	1473.37i	0.0158334	+	0.0537608i
$910$	8384.59	−	2390.81i	0.305436	−	0.0870931i
$911$	52041.6			1.89266			0.946331	−	0.323199i	$-0.104758\pi$
$911$	52041.6			1.89266			0.946331	+	0.323199i	$0.104758\pi$
$912$	16742.9	+	14367.6i	0.607908	+	0.521667i
$913$	−1858.45			−0.0673666
$914$	−29870.2	+	8517.32i	−1.08098	+	0.308236i
$915$	−14626.3	+	8686.25i	−0.528447	+	0.313835i
$916$	−31089.4	−	7274.58i	−1.12142	−	0.262400i
$917$	−14548.9	+	14548.9i	−0.523934	+	0.523934i
$918$	−50769.8	+	16526.4i	−1.82533	+	0.594176i
$919$	37426.1			1.34339			0.671694	−	0.740829i	$-0.265567\pi$
$919$	37426.1			1.34339			0.671694	+	0.740829i	$0.265567\pi$
$920$	−758.276	−	15812.2i	−0.0271735	−	0.566645i
$921$	4362.97	−	17123.2i	0.156096	−	0.612625i
$922$	−6701.76	+	12048.2i	−0.239383	+	0.430354i
$923$	−6390.00	−	6390.00i	−0.227876	−	0.227876i
$924$	4319.89	+	13671.3i	0.153803	+	0.486746i
$925$	−168.317	+	168.317i	−0.00598296	+	0.00598296i
$926$	13996.2	−	3990.93i	0.496700	−	0.141631i
$927$	−4592.53	+	8426.97i	−0.162717	+	0.298574i
$928$	−23400.4	−	33951.5i	−0.827756	−	1.20098i
$929$			13155.3i			0.464597i	0.972644	+	0.232299i	$0.0746247\pi$
$929$			13155.3i			0.464597i	−0.972644	+	0.232299i	$0.925375\pi$
$930$	13216.0	−	373.871i	0.465988	−	0.0131825i
$931$	−8571.20	−	8571.20i	−0.301729	−	0.301729i
$932$	12412.3	−	7705.03i	0.436241	−	0.270801i
$933$	−24099.1	+	14312.0i	−0.845626	+	0.502201i
$934$	−39056.1	−	21724.8i	−1.36826	−	0.761089i
$935$			15108.0i			0.528433i
$936$	−4796.82	+	9903.29i	−0.167510	+	0.345833i
$937$		−	2012.42i		−	0.0701630i	−0.999384	−	0.0350815i	$-0.988831\pi$
$937$		−	2012.42i		−	0.0701630i	0.999384	−	0.0350815i	$-0.0111691\pi$
$938$	−31458.7	+	56555.3i	−1.09506	+	1.96865i
$939$	16514.9	−	9807.85i	0.573953	−	0.340860i
$940$	−6376.30	+	27250.4i	−0.221247	+	0.945542i
$941$	32019.9	+	32019.9i	1.10927	+	1.10927i	0.993247	+	0.116018i	$0.0370130\pi$
$941$	32019.9	+	32019.9i	1.10927	+	1.10927i	0.116018	+	0.993247i	$0.462987\pi$
$942$	−429.284	−	15174.7i	−0.0148480	−	0.524861i
$943$			23721.6i			0.819175i
$944$	−10247.3	+	3460.69i	−0.353307	+	0.119318i
$945$	−16340.0	+	17593.6i	−0.562476	+	0.605630i
$946$	−2239.04	−	7852.33i	−0.0769530	−	0.269874i
$947$	−27561.7	+	27561.7i	−0.945761	+	0.945761i	−0.998603	−	0.0528415i	$-0.983172\pi$
$947$	−27561.7	+	27561.7i	−0.945761	+	0.945761i	0.0528415	+	0.998603i	$0.483172\pi$
$948$	−23636.0	+	45473.3i	−0.809769	+	1.55791i
$949$	−8175.89	−	8175.89i	−0.279663	−	0.279663i
$950$	−11361.3	−	6319.70i	−0.388011	−	0.215829i
$951$	5677.43	−	22282.0i	0.193589	−	0.759771i
$952$	−46939.3	+	51668.1i	−1.59802	+	1.75900i
$953$	13766.6			0.467937			0.233969	−	0.972244i	$-0.424829\pi$
$953$	13766.6			0.467937			0.233969	+	0.972244i	$0.424829\pi$
$954$	29353.0	−	18574.6i	0.996163	−	0.630373i
$955$	1921.68	−	1921.68i	0.0651142	−	0.0651142i
$956$	28621.2	−	17766.9i	0.968279	−	0.601069i
$957$	−15309.1	+	9091.75i	−0.517107	+	0.307100i
$958$	4463.11	+	15652.1i	0.150518	+	0.527868i
$959$	−1370.65			−0.0461528
$960$	3039.32	−	19624.4i	0.102181	−	0.659766i
$961$	15266.3			0.512447
$962$	−47.9948	−	168.318i	−0.00160854	−	0.00564115i
$963$	9992.84	−	2943.05i	0.334387	−	0.0984822i
$964$	−15333.8	+	9518.61i	−0.512312	+	0.318023i
$965$	2767.19	−	2767.19i	0.0923100	−	0.0923100i
$966$	−22955.8	−	21692.7i	−0.764586	−	0.722516i
$967$	−18327.2			−0.609475			−0.304737	−	0.952436i	$-0.598569\pi$
$967$	−18327.2			−0.609475			−0.304737	+	0.952436i	$0.598569\pi$
$968$	16808.5	−	18501.8i	0.558104	−	0.614327i
$969$	44946.9	+	11452.4i	1.49010	+	0.379675i
$970$	19529.3	+	10863.1i	0.646443	+	0.359581i
$971$	12094.8	+	12094.8i	0.399734	+	0.399734i	0.878139	−	0.478405i	$-0.158785\pi$
$971$	12094.8	+	12094.8i	0.399734	+	0.399734i	−0.478405	+	0.878139i	$0.658785\pi$
$972$	−2829.02	−	30171.6i	−0.0933547	−	0.995633i
$973$	−12101.6	+	12101.6i	−0.398726	+	0.398726i
$974$	−11689.6	−	40995.6i	−0.384559	−	1.34865i
$975$	1601.02	−	6283.45i	0.0525883	−	0.206391i
$976$	−8981.29	−	26594.2i	−0.294554	−	0.872191i
$977$			4537.40i			0.148582i	0.997237	+	0.0742908i	$0.0236693\pi$
$977$			4537.40i			0.148582i	−0.997237	+	0.0742908i	$0.976331\pi$
$978$	15396.7	−	435.562i	0.503406	−	0.0142410i
$979$	12722.2	+	12722.2i	0.415326	+	0.415326i
$980$	−2485.80	+	10623.6i	−0.0810267	+	0.346284i
$981$	4553.76	+	15461.9i	0.148206	+	0.503221i
$982$	21547.4	−	38737.1i	0.700208	−	1.25881i
$983$			46650.8i			1.51366i	0.653611	+	0.756831i	$0.273253\pi$
$983$			46650.8i			1.51366i	−0.653611	+	0.756831i	$0.726747\pi$
$984$	−5957.74	+	29155.0i	−0.193014	+	0.944540i
$985$		−	32337.4i		−	1.04605i
$986$	−75757.9	−	42140.0i	−2.44688	−	1.36107i
$987$	28511.5	+	48008.8i	0.919485	+	1.54827i
$988$	8121.75	−	5041.66i	0.261526	−	0.162345i
$989$	12718.8	+	12718.8i	0.408934	+	0.408934i
$990$	−8366.00	−	1881.42i	−0.268575	−	0.0603994i
$991$		−	35234.9i		−	1.12944i	−0.825283	−	0.564719i	$-0.808985\pi$
$991$		−	35234.9i		−	1.12944i	0.825283	−	0.564719i	$-0.191015\pi$
$992$	−3947.28	+	21456.1i	−0.126337	+	0.686726i
$993$	21014.4	+	5354.44i	0.671571	+	0.171116i
$994$	31290.6	−	8922.33i	0.998469	−	0.284707i
$995$	20323.4	−	20323.4i	0.647533	−	0.647533i
$996$	4896.96	−	1547.35i	0.155789	−	0.0492266i
$997$	22326.4	+	22326.4i	0.709212	+	0.709212i	0.966369	−	0.257158i	$-0.0827860\pi$
$997$	22326.4	+	22326.4i	0.709212	+	0.709212i	−0.257158	+	0.966369i	$0.582786\pi$
$998$	16265.7	−	29241.9i	0.515913	−	0.927491i
$999$	353.186	+	328.020i	0.0111855	+	0.0103885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.k.a.11.9	✓	44
3.2	odd	2	inner	48.4.k.a.11.14	yes	44
4.3	odd	2		192.4.k.a.143.15		44
8.3	odd	2		384.4.k.a.287.8		44
8.5	even	2		384.4.k.b.287.15		44
12.11	even	2		192.4.k.a.143.18		44
16.3	odd	4	inner	48.4.k.a.35.14	yes	44
16.5	even	4		384.4.k.a.95.5		44
16.11	odd	4		384.4.k.b.95.18		44
16.13	even	4		192.4.k.a.47.18		44
24.5	odd	2		384.4.k.b.287.18		44
24.11	even	2		384.4.k.a.287.5		44
48.5	odd	4		384.4.k.a.95.8		44
48.11	even	4		384.4.k.b.95.15		44
48.29	odd	4		192.4.k.a.47.15		44
48.35	even	4	inner	48.4.k.a.35.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.9	✓	44	1.1	even	1	trivial
48.4.k.a.11.14	yes	44	3.2	odd	2	inner
48.4.k.a.35.9	yes	44	48.35	even	4	inner
48.4.k.a.35.14	yes	44	16.3	odd	4	inner
192.4.k.a.47.15		44	48.29	odd	4
192.4.k.a.47.18		44	16.13	even	4
192.4.k.a.143.15		44	4.3	odd	2
192.4.k.a.143.18		44	12.11	even	2
384.4.k.a.95.5		44	16.5	even	4
384.4.k.a.95.8		44	48.5	odd	4
384.4.k.a.287.5		44	24.11	even	2
384.4.k.a.287.8		44	8.3	odd	2
384.4.k.b.95.15		44	48.11	even	4
384.4.k.b.95.18		44	16.11	odd	4
384.4.k.b.287.15		44	8.5	even	2
384.4.k.b.287.18		44	24.5	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.775594 - 2.72001i) q^{2} +(-2.65327 - 4.46768i) q^{3} +(-6.79691 + 4.21925i) q^{4} +(5.27809 - 5.27809i) q^{5} +(-10.0943 + 10.6820i) q^{6} -22.9284 q^{7} +(16.7480 + 15.2152i) q^{8} +(-12.9203 + 23.7079i) q^{9} +O(q^{10})\)	\(q+(-0.775594 - 2.72001i) q^{2} +(-2.65327 - 4.46768i) q^{3} +(-6.79691 + 4.21925i) q^{4} +(5.27809 - 5.27809i) q^{5} +(-10.0943 + 10.6820i) q^{6} -22.9284 q^{7} +(16.7480 + 15.2152i) q^{8} +(-12.9203 + 23.7079i) q^{9} +(-18.4501 - 10.2628i) q^{10} +(-10.6369 - 10.6369i) q^{11} +(36.8843 + 19.1716i) q^{12} +(12.7359 - 12.7359i) q^{13} +(17.7831 + 62.3654i) q^{14} +(-37.5850 - 9.57663i) q^{15} +(28.3959 - 57.3557i) q^{16} -134.550i q^{17} +(74.5067 + 16.7557i) q^{18} +(-46.9113 - 46.9113i) q^{19} +(-13.6051 + 58.1443i) q^{20} +(60.8352 + 102.437i) q^{21} +(-20.6826 + 37.1824i) q^{22} -93.7270i q^{23} +(23.5398 - 115.195i) q^{24} +69.2835i q^{25} +(-44.5198 - 24.7640i) q^{26} +(140.200 - 5.17956i) q^{27} +(155.842 - 96.7405i) q^{28} +(161.072 + 161.072i) q^{29} +(3.10219 + 109.659i) q^{30} -120.518i q^{31} +(-178.032 - 32.7525i) q^{32} +(-19.2997 + 75.7449i) q^{33} +(-365.978 + 104.356i) q^{34} +(-121.018 + 121.018i) q^{35} +(-12.2112 - 215.655i) q^{36} +(2.42940 + 2.42940i) q^{37} +(-91.2151 + 163.983i) q^{38} +(-90.6920 - 23.1082i) q^{39} +(168.705 - 8.09026i) q^{40} -253.093 q^{41} +(231.445 - 244.922i) q^{42} +(-135.701 + 135.701i) q^{43} +(117.178 + 27.4184i) q^{44} +(56.9379 + 193.327i) q^{45} +(-254.938 + 72.6941i) q^{46} +468.668 q^{47} +(-331.589 + 25.3161i) q^{48} +182.711 q^{49} +(188.452 - 53.7358i) q^{50} +(-601.128 + 356.998i) q^{51} +(-32.8289 + 140.301i) q^{52} +(321.633 - 321.633i) q^{53} +(-122.827 - 377.329i) q^{54} -112.285 q^{55} +(-384.005 - 348.861i) q^{56} +(-85.1164 + 334.053i) q^{57} +(313.191 - 563.045i) q^{58} +(-119.500 - 119.500i) q^{59} +(295.868 - 93.4890i) q^{60} +(310.130 - 310.130i) q^{61} +(-327.811 + 93.4734i) q^{62} +(296.242 - 543.584i) q^{63} +(48.9933 + 509.651i) q^{64} -134.443i q^{65} +(220.996 - 6.25183i) q^{66} +(705.631 + 705.631i) q^{67} +(567.701 + 914.526i) q^{68} +(-418.742 + 248.683i) q^{69} +(423.031 + 235.310i) q^{70} -501.730i q^{71} +(-577.112 + 200.475i) q^{72} -641.954i q^{73} +(4.72376 - 8.49222i) q^{74} +(309.536 - 183.828i) q^{75} +(516.782 + 120.921i) q^{76} +(243.887 + 243.887i) q^{77} +(7.48553 + 264.606i) q^{78} +1232.86i q^{79} +(-152.852 - 452.605i) q^{80} +(-395.130 - 612.628i) q^{81} +(196.297 + 688.414i) q^{82} +(87.3585 - 87.3585i) q^{83} +(-845.697 - 439.574i) q^{84} +(-710.169 - 710.169i) q^{85} +(474.356 + 263.859i) q^{86} +(292.251 - 1146.99i) q^{87} +(-16.3042 - 339.990i) q^{88} -1196.04 q^{89} +(481.691 - 304.815i) q^{90} +(-292.014 + 292.014i) q^{91} +(395.457 + 637.054i) q^{92} +(-538.438 + 319.768i) q^{93} +(-363.496 - 1274.78i) q^{94} -495.204 q^{95} +(326.038 + 882.290i) q^{96} -1058.49 q^{97} +(-141.709 - 496.975i) q^{98} +(389.611 - 114.747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

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