LMFDB - Embedded newform 48.4.k.a.11.14

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			11.14
Character	$\chi$	$=$	48.11
Dual form			48.4.k.a.35.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.775594 + 2.72001i) q^{2} +(-4.46768 - 2.65327i) q^{3} +(-6.79691 + 4.21925i) q^{4} +(-5.27809 + 5.27809i) q^{5} +(3.75181 - 14.2100i) q^{6} -22.9284 q^{7} +(-16.7480 - 15.2152i) q^{8} +(12.9203 + 23.7079i) q^{9} +O(q^{10})$	\(q+(0.775594 + 2.72001i) q^{2} +(-4.46768 - 2.65327i) q^{3} +(-6.79691 + 4.21925i) q^{4} +(-5.27809 + 5.27809i) q^{5} +(3.75181 - 14.2100i) 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} +(41.5612 - 0.816220i) 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} +(-54.4648 + 53.5311i) q^{18} +(-46.9113 - 46.9113i) q^{19} +(13.6051 - 58.1443i) q^{20} +(102.437 + 60.8352i) q^{21} +(-20.6826 + 37.1824i) q^{22} +93.7270i q^{23} +(34.4547 + 112.414i) q^{24} +69.2835i q^{25} +(44.5198 + 24.7640i) q^{26} +(5.17956 - 140.200i) q^{27} +(155.842 - 96.7405i) q^{28} +(-161.072 - 161.072i) q^{29} +(55.1993 + 94.8041i) 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} +(-187.848 - 106.626i) 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} +(-86.0230 + 325.812i) q^{42} +(-135.701 + 135.701i) q^{43} +(-117.178 - 27.4184i) q^{44} +(-193.327 - 56.9379i) q^{45} +(-254.938 + 72.6941i) q^{46} -468.668 q^{47} +(-279.044 + 180.905i) q^{48} +182.711 q^{49} +(-188.452 + 53.7358i) q^{50} +(356.998 - 601.128i) q^{51} +(-32.8289 + 140.301i) q^{52} +(-321.633 + 321.633i) q^{53} +(385.364 - 94.6502i) 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} +(-215.056 + 223.672i) 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} +(191.058 - 111.243i) q^{66} +(705.631 + 705.631i) q^{67} +(-567.701 - 914.526i) q^{68} +(248.683 - 418.742i) q^{69} +(423.031 + 235.310i) q^{70} +501.730i q^{71} +(144.331 - 593.647i) q^{72} -641.954i q^{73} +(-4.72376 + 8.49222i) q^{74} +(183.828 - 309.536i) q^{75} +(516.782 + 120.921i) q^{76} +(-243.887 - 243.887i) q^{77} +(-133.195 - 228.760i) 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} +(-952.931 + 18.7146i) 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} +(4.92809 - 570.013i) q^{90} +(-292.014 + 292.014i) q^{91} +(-395.457 - 637.054i) q^{92} +(-319.768 + 538.438i) q^{93} +(-363.496 - 1274.78i) q^{94} +495.204 q^{95} +(-708.487 - 618.693i) q^{96} -1058.49 q^{97} +(141.709 + 496.975i) q^{98} +(-114.747 + 389.611i) 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
$3$	−4.46768	−	2.65327i	−0.859805	−	0.510622i
$3$	−4.46768	−	2.65327i	−0.859805	−	0.510622i
$4$	−6.79691	+	4.21925i	−0.849613	+	0.527406i
$5$	−5.27809	+	5.27809i	−0.472087	+	0.472087i	−0.902589	−	0.430502i	$-0.858336\pi$
$5$	−5.27809	+	5.27809i	−0.472087	+	0.472087i	0.430502	+	0.902589i	$0.358336\pi$
$6$	3.75181	−	14.2100i	0.255278	−	0.966868i
$7$	−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	0.837696	−	0.546137i	$-0.183902\pi$
$11$	10.6369	+	10.6369i	0.291559	+	0.291559i	−0.546137	+	0.837696i	$0.683902\pi$
$12$	41.5612	−	0.816220i	0.999807	−	0.0196352i
$13$	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	$0.409440\pi$
$17$			134.550i			1.91960i	−0.280679	+	0.959802i	$0.590560\pi$
$18$	−54.4648	+	53.5311i	−0.713193	+	0.700967i
$19$	−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
$21$	102.437	+	60.8352i	1.06445	+	0.632158i
$22$	−20.6826	+	37.1824i	−0.200434	+	0.360333i
$23$			93.7270i			0.849715i	0.905260	+	0.424857i	$0.139676\pi$
$23$			93.7270i			0.849715i	−0.905260	+	0.424857i	$0.860324\pi$
$24$	34.4547	+	112.414i	0.293044	+	0.956099i
$25$			69.2835i			0.554268i
$26$	44.5198	+	24.7640i	0.335810	+	0.186793i
$27$	5.17956	−	140.200i	0.0369188	−	0.999318i
$28$	155.842	−	96.7405i	1.05184	−	0.652937i
$29$	−161.072	−	161.072i	−1.03139	−	1.03139i	−0.999491	−	0.0319009i	$-0.989844\pi$
$29$	−161.072	−	161.072i	−1.03139	−	1.03139i	−0.0319009	−	0.999491i	$-0.510156\pi$
$30$	55.1993	+	94.8041i	0.335932	+	0.576959i
$31$		−	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
$36$	−187.848	−	106.626i	−0.869666	−	0.493641i
$37$	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	$-0.339900\pi$
$41$	253.093			0.964059			0.482029	+	0.876155i	$0.339900\pi$
$42$	−86.0230	+	325.812i	−0.316039	+	1.19700i
$43$	−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
$45$	−193.327	−	56.9379i	−0.640434	−	0.188618i
$46$	−254.938	+	72.6941i	−0.817144	+	0.233004i
$47$	−468.668			−1.45452			−0.727258	−	0.686364i	$-0.759206\pi$
$47$	−468.668			−1.45452			−0.727258	+	0.686364i	$0.759206\pi$
$48$	−279.044	+	180.905i	−0.839094	+	0.543986i
$49$	182.711			0.532684
$50$	−188.452	+	53.7358i	−0.533022	+	0.151988i
$51$	356.998	−	601.128i	0.980191	−	1.65049i
$52$	−32.8289	+	140.301i	−0.0875491	+	0.374159i
$53$	−321.633	+	321.633i	−0.833580	+	0.833580i	−0.988005	−	0.154425i	$-0.950648\pi$
$53$	−321.633	+	321.633i	−0.833580	+	0.833580i	0.154425	+	0.988005i	$0.450648\pi$
$54$	385.364	−	94.6502i	0.971137	−	0.238523i
$55$	−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	0.826550	−	0.562863i	$-0.190300\pi$
$59$	119.500	+	119.500i	0.263688	+	0.263688i	−0.562863	+	0.826550i	$0.690300\pi$
$60$	−215.056	+	223.672i	−0.462726	+	0.481265i
$61$	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
$66$	191.058	−	111.243i	0.356328	−	0.207470i
$67$	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
$69$	248.683	−	418.742i	0.433883	−	0.730589i
$70$	423.031	+	235.310i	0.722313	+	0.401784i
$71$			501.730i			0.838654i	0.907835	+	0.419327i	$0.137734\pi$
$71$			501.730i			0.838654i	−0.907835	+	0.419327i	$0.862266\pi$
$72$	144.331	−	593.647i	0.236245	−	0.971694i
$73$		−	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
$75$	183.828	−	309.536i	0.283021	−	0.476562i
$76$	516.782	+	120.921i	0.779986	+	0.182508i
$77$	−243.887	−	243.887i	−0.360955	−	0.360955i
$78$	−133.195	−	228.760i	−0.193350	−	0.332077i
$79$			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	−0.762508	−	0.646979i	$-0.776032\pi$
$83$	−87.3585	+	87.3585i	−0.115528	+	0.115528i	0.646979	+	0.762508i	$0.276032\pi$
$84$	−952.931	+	18.7146i	−1.23778	+	0.0243087i
$85$	−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	$-0.247676\pi$
$89$	1196.04			1.42450			0.712250	+	0.701926i	$0.247676\pi$
$90$	4.92809	−	570.013i	0.00577185	−	0.667607i
$91$	−292.014	+	292.014i	−0.336389	+	0.336389i
$92$	−395.457	−	637.054i	−0.448144	−	0.721929i
$93$	−319.768	+	538.438i	−0.356542	+	0.600359i
$94$	−363.496	−	1274.78i	−0.398849	−	1.39876i
$95$	495.204			0.534809
$96$	−708.487	−	618.693i	−0.753226	−	0.657762i
$97$	−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
$99$	−114.747	+	389.611i	−0.116490	+	0.395529i
$100$	−292.324	−	470.913i	−0.292324	−	0.470913i
$101$	−40.2249	+	40.2249i	−0.0396290	+	0.0396290i	−0.726644	−	0.687015i	$-0.758921\pi$
$101$	−40.2249	+	40.2249i	−0.0396290	+	0.0396290i	0.687015	+	0.726644i	$0.258921\pi$
$102$	1911.96	+	504.808i	1.85600	+	0.490033i
$103$	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	0.819528	−	0.573039i	$-0.194236\pi$
$107$	272.818	+	272.818i	0.246489	+	0.246489i	−0.573039	+	0.819528i	$0.694236\pi$
$108$	556.335	+	974.784i	0.495680	+	0.868505i
$109$	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	$-0.972258\pi$
$113$		−	209.116i		−	0.174089i	0.996204	−	0.0870443i	$-0.0277422\pi$
$114$	−842.611	+	490.607i	−0.692261	+	0.403066i
$115$	−494.700	−	494.700i	−0.401139	−	0.401139i
$116$	1774.40	+	415.190i	1.42025	+	0.332322i
$117$	466.495	+	137.390i	0.368611	+	0.108562i
$118$	−232.358	+	417.725i	−0.181273	+	0.325887i
$119$		−	3085.02i		−	2.37650i
$120$	−775.186	−	411.475i	−0.589704	−	0.313020i
$121$		−	1104.71i		−	0.829987i
$122$	1084.09	+	603.022i	0.804501	+	0.447501i
$123$	−1130.74	−	671.523i	−0.828903	−	0.492270i
$124$	508.497	+	819.153i	0.368261	+	0.593243i
$125$	−1025.45	−	1025.45i	−0.733750	−	0.733750i
$126$	1248.79	−	1227.38i	0.882945	−	0.867809i
$127$		−	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	−0.886305	−	0.463101i	$-0.846737\pi$
$131$	−634.537	+	634.537i	−0.423204	+	0.423204i	0.463101	+	0.886305i	$0.346737\pi$
$132$	450.765	+	433.401i	0.297228	+	0.285778i
$133$	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	$-0.505934\pi$
$137$	−59.7796			−0.0372797			−0.0186398	+	0.999826i	$0.505934\pi$
$138$	1331.86	+	351.646i	0.821562	+	0.216914i
$139$	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
$141$	2093.86	+	1243.50i	1.25060	+	0.742708i
$142$	−1364.71	+	389.139i	−0.806507	+	0.229970i
$143$	270.942			0.158443
$144$	1726.67	−	67.8462i	0.999229	−	0.0392629i
$145$	1700.31			0.973813
$146$	1746.12	−	497.896i	0.989795	−	0.282234i
$147$	−816.293	−	484.781i	−0.458005	−	0.272000i
$148$	−26.7626	−	6.26217i	−0.0148640	−	0.00347802i
$149$	334.922	−	334.922i	0.184147	−	0.184147i	−0.609013	−	0.793160i	$-0.708434\pi$
$149$	334.922	−	334.922i	0.184147	−	0.184147i	0.793160	+	0.609013i	$0.208434\pi$
$150$	984.518	+	259.939i	0.535904	+	0.141493i
$151$	−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
$156$	518.926	−	539.716i	0.266329	−	0.276999i
$157$	−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
$162$	−1972.82	−	599.607i	−0.956784	−	0.290800i
$163$	−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
$165$	501.654	+	297.923i	0.236689	+	0.140565i
$166$	−305.371	−	169.861i	−0.142779	−	0.0794205i
$167$		−	2270.55i		−	1.05210i	−0.850454	−	0.526049i	$-0.823673\pi$
$167$		−	2270.55i		−	1.05210i	0.850454	−	0.526049i	$-0.176327\pi$
$168$	−789.992	−	2577.47i	−0.362793	−	1.18367i
$169$			1872.59i			0.852340i
$170$	1380.86	−	2482.47i	0.622985	−	1.11998i
$171$	506.059	−	1718.28i	0.226312	−	0.768421i
$172$	349.791	−	1494.90i	0.155066	−	0.662704i
$173$	1798.49	+	1798.49i	0.790385	+	0.790385i	0.981557	−	0.191172i	$-0.0612287\pi$
$173$	1798.49	+	1798.49i	0.790385	+	0.790385i	−0.191172	+	0.981557i	$0.561229\pi$
$174$	−2893.15	+	1684.52i	−1.26051	+	0.733927i
$175$		−	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	−0.940716	−	0.339194i	$-0.889846\pi$
$179$	−1440.56	+	1440.56i	−0.601523	+	0.601523i	0.339194	+	0.940716i	$0.389846\pi$
$180$	1554.26	−	428.694i	0.643599	−	0.177516i
$181$	−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
$186$	−1712.57	−	452.163i	−0.675116	−	0.178248i
$187$	−1431.20	+	1431.20i	−0.559678	+	0.559678i
$188$	3185.50	−	1977.43i	1.23578	−	0.767121i
$189$	−118.759	+	3214.57i	−0.0457061	+	1.23717i
$190$	384.077	+	1346.96i	0.146652	+	0.514309i
$191$	−364.086			−0.137928			−0.0689642	−	0.997619i	$-0.521969\pi$
$191$	−364.086			−0.137928			−0.0689642	+	0.997619i	$0.521969\pi$
$192$	1133.35	−	2406.95i	0.426004	−	0.904721i
$193$	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
$195$	356.713	−	600.648i	0.130999	−	0.220581i
$196$	−1241.87	+	770.902i	−0.452576	+	0.280941i
$197$	−3063.36	+	3063.36i	−1.10790	+	1.10790i	−0.114469	+	0.993427i	$0.536517\pi$
$197$	−3063.36	+	3063.36i	−1.10790	+	1.10790i	−0.993427	+	0.114469i	$0.963483\pi$
$198$	−1148.74	−	9.93155i	−0.412311	−	0.00356467i
$199$	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
$204$	109.823	+	5592.07i	0.0376918	+	1.91923i
$205$	−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
$210$	−1265.63	−	2173.70i	−0.415889	−	0.714285i
$211$	−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
$213$	1331.22	−	2241.57i	0.428235	−	0.721079i
$214$	−530.472	+	953.663i	−0.169450	+	0.304631i
$215$		−	1432.48i		−	0.454393i
$216$	−2219.93	+	2269.27i	−0.699292	+	0.714836i
$217$			2763.29i			0.864445i
$218$	1475.60	+	820.796i	0.458441	+	0.255006i
$219$	−1703.28	+	2868.05i	−0.525556	+	0.884952i
$220$	763.192	−	473.759i	0.233884	−	0.145186i
$221$	1713.62	+	1713.62i	0.521588	+	0.521588i
$222$	43.6364	−	25.4071i	0.0131923	−	0.00768114i
$223$		−	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	−0.996520	−	0.0833548i	$-0.973437\pi$
$227$	−3123.12	+	3123.12i	−0.913165	+	0.913165i	0.0833548	+	0.996520i	$0.473437\pi$
$228$	−1987.98	−	1911.40i	−0.577444	−	0.555200i
$229$	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	$-0.417355\pi$
$233$	1826.16			0.513459			0.256729	+	0.966483i	$0.417355\pi$
$234$	−11.8914	+	1375.43i	−0.00332207	+	0.384251i
$235$	2473.67	−	2473.67i	0.686658	−	0.686658i
$236$	−1316.43	−	308.031i	−0.363103	−	0.0849622i
$237$	3271.12	−	5508.04i	0.896548	−	1.50964i
$238$	8391.29	−	2392.72i	2.28541	−	0.651669i
$239$	4210.91			1.13967			0.569835	−	0.821759i	$-0.307007\pi$
$239$	4210.91			1.13967			0.569835	+	0.821759i	$0.307007\pi$
$240$	517.987	−	2427.65i	0.139316	−	0.652934i
$241$	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
$243$	3390.78	−	1688.64i	0.895139	−	0.445787i
$244$	−799.411	+	3416.44i	−0.209742	+	0.896374i
$245$	−964.364	+	964.364i	−0.251473	+	0.251473i
$246$	949.556	−	3596.44i	0.246103	−	0.932117i
$247$	−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	$-0.978622\pi$
$251$	−4234.49	−	4234.49i	−1.06486	−	1.06486i	−0.0671099	−	0.997746i	$-0.521378\pi$
$252$	4307.05	+	2444.77i	1.07666	+	0.611136i
$253$	−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	$0.133260\pi$
$257$			3349.78i			0.813050i	−0.913640	+	0.406525i	$0.866740\pi$
$258$	1419.18	+	2437.43i	0.342459	+	0.588170i
$259$	−55.7022	−	55.7022i	−0.0133636	−	0.0133636i
$260$	−567.248	−	913.796i	−0.135305	−	0.217966i
$261$	1737.58	−	5899.79i	0.412082	−	1.39919i
$262$	−2218.09	−	1233.80i	−0.523031	−	0.290934i
$263$			426.421i			0.0999780i	0.998750	+	0.0499890i	$0.0159186\pi$
$263$			426.421i			0.0999780i	−0.998750	+	0.0499890i	$0.984081\pi$
$264$	−829.244	+	1562.23i	−0.193320	+	0.364199i
$265$		−	3395.22i		−	0.787044i
$266$	−2091.41	+	3759.87i	−0.482078	+	0.866664i
$267$	−5343.55	−	3173.43i	−1.22479	−	0.727381i
$268$	−7773.34	−	1818.88i	−1.77176	−	0.414573i
$269$	−5493.24	−	5493.24i	−1.24509	−	1.24509i	−0.957863	−	0.287224i	$-0.907268\pi$
$269$	−5493.24	−	5493.24i	−1.24509	−	1.24509i	−0.287224	−	0.957863i	$-0.592732\pi$
$270$	−1534.41	+	2533.56i	−0.345857	+	0.571065i
$271$			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
$276$	76.5019	+	3895.41i	0.0166843	+	0.849551i
$277$	−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	$-0.538441\pi$
$281$	−1134.95			−0.240944			−0.120472	+	0.992717i	$0.538441\pi$
$282$	−1758.36	+	6659.77i	−0.371307	+	1.40633i
$283$	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
$285$	−2212.41	−	1313.91i	−0.459832	−	0.273085i
$286$	210.141	+	736.965i	0.0434472	+	0.152369i
$287$	−5803.00			−1.19352
$288$	1523.74	+	4643.93i	0.311760	+	0.950161i
$289$	−13190.8			−2.68488
$290$	1318.75	+	4624.86i	0.267033	+	0.936486i
$291$	4729.01	+	2808.47i	0.952645	+	0.565757i
$292$	2708.56	+	4363.30i	0.542831	+	0.874462i
$293$	1246.92	−	1246.92i	0.248621	−	0.248621i	−0.571784	−	0.820405i	$-0.693748\pi$
$293$	1246.92	−	1246.92i	0.248621	−	0.248621i	0.820405	+	0.571784i	$0.193748\pi$
$294$	685.496	−	2596.32i	0.135983	−	0.515035i
$295$	−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
$300$	56.5506	+	2879.50i	0.0108832	+	0.554161i
$301$	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
$306$	−7202.63	−	7328.26i	−1.34558	−	1.36905i
$307$	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
$309$	−1588.04	−	943.104i	−0.292363	−	0.173629i
$310$	−1236.86	+	2223.58i	−0.226609	+	0.407390i
$311$			5394.10i			0.983509i	0.870734	+	0.491754i	$0.163644\pi$
$311$			5394.10i			0.983509i	−0.870734	+	0.491754i	$0.836356\pi$
$312$	1870.51	+	992.882i	0.339413	+	0.180163i
$313$			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
$315$	4432.68	+	1305.49i	0.792868	+	0.233512i
$316$	−5201.75	−	8379.66i	−0.926018	−	1.49175i
$317$	−3129.07	−	3129.07i	−0.554405	−	0.554405i	0.373304	−	0.927709i	$-0.378225\pi$
$317$	−3129.07	−	3129.07i	−0.554405	−	0.554405i	−0.927709	+	0.373304i	$0.878225\pi$
$318$	3363.70	+	5777.11i	0.593166	+	1.01876i
$319$		−	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
$324$	100.834	−	5831.13i	0.0172899	−	0.999851i
$325$	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
$330$	−421.273	+	1595.57i	−0.0702737	+	0.266162i
$331$	−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
$333$	−26.2073	+	88.9846i	−0.00431277	+	0.0146436i
$334$	6175.92	−	1761.03i	1.01177	−	0.288500i
$335$	−7448.77			−1.21484
$336$	6398.02	−	4147.85i	1.03881	−	0.673464i
$337$	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
$339$	−554.842	+	934.265i	−0.0888934	+	0.149682i
$340$	7823.33	+	1830.58i	1.24788	+	0.291991i
$341$	1281.94	−	1281.94i	0.203581	−	0.203581i
$342$	5066.23	+	43.8005i	0.801024	+	0.00692532i
$343$	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	0.950983	−	0.309244i	$-0.100076\pi$
$347$	4148.13	+	4148.13i	0.641739	+	0.641739i	−0.309244	+	0.950983i	$0.600076\pi$
$348$	−6825.83	−	6562.89i	−1.05144	−	1.01094i
$349$	−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	$-0.973943\pi$
$353$		−	1084.64i		−	0.163540i	0.996651	−	0.0817701i	$-0.0260573\pi$
$354$	2146.44	−	1249.75i	0.322265	−	0.187637i
$355$	−2648.18	−	2648.18i	−0.395918	−	0.395918i
$356$	−8129.41	+	5046.41i	−1.21027	+	0.751290i
$357$	−8185.39	+	13782.9i	−1.21349	+	2.04333i
$358$	−5035.63	−	2801.05i	−0.743411	−	0.413520i
$359$			5935.87i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$359$			5935.87i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$360$	2371.53	+	3895.12i	0.347196	+	0.570252i
$361$		−	2457.66i		−	0.358312i
$362$	1703.37	−	3062.25i	0.247312	−	0.444609i
$363$	−2931.10	+	4935.50i	−0.423809	+	0.713627i
$364$	752.714	−	3216.88i	0.108387	−	0.463215i
$365$	3388.29	+	3388.29i	0.485894	+	0.485894i
$366$	−3243.40	−	5570.50i	−0.463211	−	0.795559i
$367$		−	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
$372$	−98.3696	−	5008.89i	−0.0137103	−	0.698116i
$373$	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
$378$	−8835.77	+	2170.18i	−1.20228	+	0.295296i
$379$	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
$381$	−253.827	+	427.405i	−0.0341312	+	0.0574714i
$382$	−282.383	−	990.318i	−0.0378219	−	0.132642i
$383$	2179.82			0.290819			0.145410	−	0.989372i	$-0.453550\pi$
$383$	2179.82			0.290819			0.145410	+	0.989372i	$0.453550\pi$
$384$	7425.94	+	1215.92i	0.986858	+	0.161587i
$385$	2574.52			0.340804
$386$	406.628	+	1426.04i	0.0536187	+	0.188041i
$387$	−4970.48	−	1463.88i	−0.652878	−	0.192283i
$388$	7194.49	−	4466.05i	0.941352	−	0.584354i
$389$	−357.917	+	357.917i	−0.0466506	+	0.0466506i	−0.730047	−	0.683397i	$-0.760502\pi$
$389$	−357.917	+	357.917i	−0.0466506	+	0.0466506i	0.683397	+	0.730047i	$0.260502\pi$
$390$	1910.43	+	504.405i	0.248048	+	0.0654911i
$391$	−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
$396$	−863.945	−	3132.30i	−0.109633	−	0.397484i
$397$	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	$0.107610\pi$
$401$			5326.53i			0.663328i	−0.943398	+	0.331664i	$0.892390\pi$
$402$	12674.4	−	7379.62i	1.57249	−	0.915577i
$403$	−1534.92	−	1534.92i	−0.189726	−	0.189726i
$404$	103.686	−	443.124i	0.0127688	−	0.0545699i
$405$	−1147.97	−	5319.04i	−0.140848	−	0.652606i
$406$	−7180.97	+	12909.7i	−0.877797	+	1.57807i
$407$			51.6826i			0.00629438i
$408$	−15125.3	+	4635.90i	−1.83533	+	0.562527i
$409$			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
$411$	267.076	+	158.611i	0.0320532	+	0.0190358i
$412$	−2415.96	+	1499.73i	−0.288898	+	0.179336i
$413$	−2739.94	−	2739.94i	−0.326450	−	0.326450i
$414$	−5017.31	−	5104.83i	−0.595622	−	0.606011i
$415$		−	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	−0.250387	−	0.968146i	$-0.580558\pi$
$419$	6156.01	−	6156.01i	0.717758	−	0.717758i	0.968146	+	0.250387i	$0.0805580\pi$
$420$	4930.88	−	5128.44i	0.572863	−	0.595815i
$421$	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
$426$	7129.58	+	1882.40i	0.810867	+	0.214090i
$427$	−7110.79	+	7110.79i	−0.805890	+	0.805890i
$428$	−3005.40	−	703.232i	−0.339420	−	0.0794206i
$429$	−1210.48	−	718.882i	−0.136230	−	0.0809043i
$430$	3896.37	−	1111.03i	0.436976	−	0.124601i
$431$	6076.07			0.679058			0.339529	−	0.940596i	$-0.389732\pi$
$431$	6076.07			0.679058			0.339529	+	0.940596i	$0.389732\pi$
$432$	−7894.21	−	4278.20i	−0.879191	−	0.476470i
$433$	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
$435$	−7596.43	−	4511.38i	−0.837290	−	0.497250i
$436$	−1088.11	+	4650.25i	−0.119520	+	0.510795i
$437$	4396.86	−	4396.86i	0.481305	−	0.481305i
$438$	−9122.16	−	2408.49i	−0.995146	−	0.262745i
$439$	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	0.606840	−	0.794824i	$-0.292437\pi$
$443$	−1752.77	−	1752.77i	−0.187984	−	0.187984i	−0.794824	+	0.606840i	$0.792437\pi$
$444$	102.952	+	98.9858i	0.0110042	+	0.0105803i
$445$	−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	$-0.856621\pi$
$449$		−	8284.17i		−	0.870722i	0.900256	−	0.435361i	$-0.143379\pi$
$450$	−3708.82	−	3773.51i	−0.388524	−	0.395300i
$451$	2692.12	+	2692.12i	0.281080	+	0.281080i
$452$	882.313	+	1421.34i	0.0918153	+	0.147908i
$453$	8003.82	+	4753.31i	0.830138	+	0.493003i
$454$	−10917.2	−	6072.64i	−1.12856	−	0.627760i
$455$		−	3082.56i		−	0.317610i
$456$	3657.16	−	6889.79i	0.375575	−	0.707553i
$457$		−	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
$459$	18864.0	+	696.912i	1.91829	+	0.0708694i
$460$	5449.69	+	1275.17i	0.552376	+	0.129250i
$461$	3446.67	+	3446.67i	0.348216	+	0.348216i	0.859445	−	0.511229i	$-0.170810\pi$
$461$	3446.67	+	3446.67i	0.348216	+	0.348216i	−0.511229	+	0.859445i	$0.670810\pi$
$462$	−4380.65	+	2550.62i	−0.441140	+	0.256852i
$463$			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	$0.536233\pi$
$467$	−11172.9	+	11172.9i	−1.10711	+	1.10711i	−0.993529	+	0.113583i	$0.963767\pi$
$468$	−3750.41	+	1034.43i	−0.370433	+	0.102172i
$469$	−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
$474$	17519.0	+	4625.47i	1.69762	+	0.448217i
$475$	3250.18	−	3250.18i	0.313954	−	0.313954i
$476$	13016.5	+	20968.6i	1.25338	+	2.01911i
$477$	−11780.9	−	3469.65i	−1.13084	−	0.333049i
$478$	3265.96	+	11453.7i	0.312513	+	1.09598i
$479$	5754.44			0.548908			0.274454	−	0.961600i	$-0.411503\pi$
$479$	5754.44			0.548908			0.274454	+	0.961600i	$0.411503\pi$
$480$	7004.98	−	473.941i	0.666109	−	0.0450674i
$481$	61.8813			0.00586600
$482$	1749.74	+	6136.34i	0.165349	+	0.579881i
$483$	−5701.90	+	9601.09i	−0.537154	+	0.904481i
$484$	4661.05	+	7508.63i	0.437740	+	0.705168i
$485$	5586.83	−	5586.83i	0.523062	−	0.523062i
$486$	7222.99	+	7913.26i	0.674159	+	0.738586i
$487$	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	$-0.994039\pi$
$491$	−11081.7	−	11081.7i	−1.01855	−	1.01855i	−0.0187273	−	0.999825i	$-0.505961\pi$
$492$	10518.8	−	206.579i	0.963873	−	0.0189295i
$493$	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
$498$	913.611	+	1569.12i	0.0822086	+	0.141192i
$499$	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
$501$	−6024.38	+	10144.1i	−0.537225	+	0.904600i
$502$	8233.61	−	14802.1i	0.732040	−	1.31604i
$503$		−	6889.74i		−	0.610732i	−0.952235	−	0.305366i	$-0.901221\pi$
$503$		−	6889.74i		−	0.610732i	0.952235	−	0.305366i	$-0.0987788\pi$
$504$	−3309.28	+	13611.4i	−0.292475	+	1.20297i
$505$		−	424.622i		−	0.0374167i
$506$	−3485.00	−	1938.52i	−0.306180	−	0.170311i
$507$	4968.49	−	8366.14i	0.435224	−	0.732847i
$508$	403.638	+	650.233i	0.0352531	+	0.0567902i
$509$	7441.04	+	7441.04i	0.647973	+	0.647973i	0.952503	−	0.304529i	$-0.0984992\pi$
$509$	7441.04	+	7441.04i	0.647973	+	0.647973i	−0.304529	+	0.952503i	$0.598499\pi$
$510$	−12755.9	+	7427.08i	−1.10753	+	0.644856i
$511$			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
$516$	−5529.13	+	5750.65i	−0.471718	+	0.490617i
$517$	−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	$-0.777212\pi$
$521$	−18192.4			−1.52980			−0.764900	+	0.644149i	$0.777212\pi$
$522$	17395.2	+	150.391i	1.45855	+	0.0126100i
$523$	−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
$525$	−4214.87	+	7097.17i	−0.350385	+	0.589992i
$526$	−1159.87	+	330.729i	−0.0961457	+	0.0274154i
$527$	16215.8			1.34036
$528$	−4892.43	−	1043.90i	−0.403250	−	0.0860413i
$529$	3382.24			0.277985
$530$	9235.03	−	2633.31i	0.756876	−	0.215818i
$531$	−1289.12	+	4377.07i	−0.105354	+	0.357719i
$532$	−11849.0	−	2772.53i	−0.965636	−	0.225948i
$533$	3223.37	−	3223.37i	0.261951	−	0.261951i
$534$	4487.34	−	16995.8i	0.363644	−	1.37730i
$535$	−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
$540$	−8081.39	−	2208.61i	−0.644014	−	0.176006i
$541$	−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
$546$	3053.94	+	5245.11i	0.239371	+	0.411117i
$547$	−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
$549$	11359.5	+	3345.56i	0.883083	+	0.260082i
$550$	−2576.13	−	1432.96i	−0.199721	−	0.111094i
$551$			15112.2i			1.16842i
$552$	−10536.2	+	3229.34i	−0.812411	+	0.249003i
$553$		−	28267.6i		−	2.17371i
$554$	7215.70	−	12972.1i	0.553368	−	0.994826i
$555$	114.574	+	68.0436i	0.00876291	+	0.00520412i
$556$	−1360.49	+	5814.34i	−0.103773	+	0.443494i
$557$	18470.0	+	18470.0i	1.40503	+	1.40503i	0.782985	+	0.622041i	$0.213696\pi$
$557$	18470.0	+	18470.0i	1.40503	+	1.40503i	0.622041	+	0.782985i	$0.286304\pi$
$558$	6451.49	+	6564.02i	0.489451	+	0.497988i
$559$			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	−0.929445	−	0.368960i	$-0.879714\pi$
$563$	−7487.33	+	7487.33i	−0.560486	+	0.560486i	0.368960	+	0.929445i	$0.379714\pi$
$564$	−19478.4	+	382.537i	−1.45424	+	0.0285597i
$565$	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	$-0.592046\pi$
$569$	−7740.75			−0.570315			−0.285157	+	0.958481i	$0.592046\pi$
$570$	1857.91	−	7036.85i	0.136525	−	0.517090i
$571$	−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
$573$	1626.62	+	966.018i	0.118592	+	0.0704293i
$574$	−4500.77	−	15784.2i	−0.327280	−	1.14777i
$575$	−6493.73			−0.470969
$576$	−11449.7	+	7746.38i	−0.828251	+	0.560357i
$577$	−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
$579$	−2342.31	−	1391.05i	−0.168123	−	0.0998449i
$580$	−11556.8	+	7174.02i	−0.827365	+	0.513595i
$581$	2002.99	−	2002.99i	0.143026	−	0.143026i
$582$	−3971.27	+	15041.2i	−0.282843	+	1.07127i
$583$	−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	0.876650	−	0.481128i	$-0.159773\pi$
$587$	5625.07	+	5625.07i	0.395522	+	0.395522i	−0.481128	+	0.876650i	$0.659773\pi$
$588$	7593.68	−	149.132i	0.532582	−	0.0104594i
$589$	−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	$0.207200\pi$
$593$			17499.9i			1.21186i	−0.795516	+	0.605932i	$0.792800\pi$
$594$	5105.87	+	3092.30i	0.352687	+	0.213600i
$595$	16283.0	+	16283.0i	1.12191	+	1.12191i
$596$	−863.315	+	3689.55i	−0.0593335	+	0.253574i
$597$	−17202.9	−	10216.5i	−1.17934	−	0.700388i
$598$	−2321.05	+	4172.71i	−0.158721	+	0.285342i
$599$			19054.7i			1.29976i	0.760038	+	0.649878i	$0.225180\pi$
$599$			19054.7i			1.29976i	−0.760038	+	0.649878i	$0.774820\pi$
$600$	−7788.42	+	2387.14i	−0.529935	+	0.162425i
$601$			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
$603$	−7612.05	+	25846.0i	−0.514074	+	1.74549i
$604$	12176.6	−	7558.75i	0.820297	−	0.509208i
$605$	5830.77	+	5830.77i	0.391826	+	0.391826i
$606$	420.680	+	722.512i	0.0281996	+	0.0484324i
$607$		−	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
$612$	14346.6	−	25275.0i	0.947595	−	1.66941i
$613$	−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	$-0.523423\pi$
$617$	−2253.48			−0.147037			−0.0735185	+	0.997294i	$0.523423\pi$
$618$	1333.58	−	5050.94i	0.0868034	−	0.328768i
$619$	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
$621$	13140.6	+	485.465i	0.849135	+	0.0313704i
$622$	−14672.0	+	4183.63i	−0.945810	+	0.269692i
$623$	−27423.4			−1.76355
$624$	−1249.89	+	5857.88i	−0.0801855	+	0.375806i
$625$	2164.37			0.138519
$626$	−10054.6	+	2867.00i	−0.641951	+	0.183048i
$627$	−2647.92	+	4458.67i	−0.168656	+	0.283990i
$628$	1882.69	−	8046.05i	0.119630	−	0.511262i
$629$	−326.877	+	326.877i	−0.0207209	+	0.0207209i
$630$	−112.993	+	13069.5i	−0.00714564	+	0.826508i
$631$	−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
$636$	−13104.9	+	13630.0i	−0.817051	+	0.849787i
$637$	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	$-0.799995\pi$
$641$		−	19078.5i		−	1.17560i	0.809008	−	0.587798i	$-0.200005\pi$
$642$	4900.30	−	2853.18i	0.301245	−	0.175399i
$643$	−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
$645$	−3800.76	+	6399.87i	−0.232023	+	0.390690i
$646$	22064.0	+	12273.0i	1.34380	+	0.747485i
$647$		−	14416.3i		−	0.875985i	−0.898979	−	0.437992i	$-0.855690\pi$
$647$		−	14416.3i		−	0.875985i	0.898979	−	0.437992i	$-0.144310\pi$
$648$	15938.9	−	4248.32i	0.966266	−	0.257546i
$649$			2542.22i			0.153761i
$650$	−1715.73	+	3084.49i	−0.103533	+	0.186128i
$651$	7331.76	−	12345.5i	0.441405	−	0.743255i
$652$	8163.72	+	1910.22i	0.490362	+	0.114739i
$653$	−7610.82	−	7610.82i	−0.456102	−	0.456102i	0.441272	−	0.897373i	$-0.354527\pi$
$653$	−7610.82	−	7610.82i	−0.456102	−	0.456102i	−0.897373	+	0.441272i	$0.854527\pi$
$654$	−4414.71	−	7582.21i	−0.263959	−	0.453346i
$655$		−	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	$-0.477170\pi$
$659$	18086.0	−	18086.0i	1.06909	−	1.06909i	0.997429	−	0.0716615i	$-0.0228301\pi$
$660$	−4666.71	+	91.6495i	−0.275229	+	0.00540523i
$661$	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
$666$	−262.365	−	2.26830i	−0.0152649	−	0.000131974i
$667$	15096.8	−	15096.8i	0.876389	−	0.876389i
$668$	9580.01	+	15432.7i	0.554883	+	0.893877i
$669$	−4582.14	+	7715.59i	−0.264807	+	0.445892i
$670$	−5777.22	−	20260.7i	−0.333125	−	1.16827i
$671$	6597.66			0.379582
$672$	16244.5	+	14185.6i	0.932506	+	0.814320i
$673$	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
$675$	9713.58	+	358.858i	0.553890	+	0.0204629i
$676$	−7900.93	−	12727.8i	−0.449529	−	0.724160i
$677$	−14698.6	+	14698.6i	−0.834437	+	0.834437i	−0.988120	−	0.153683i	$-0.950886\pi$
$677$	−14698.6	+	14698.6i	−0.834437	+	0.834437i	0.153683	+	0.988120i	$0.450886\pi$
$678$	−2971.54	−	784.565i	−0.168321	−	0.0444411i
$679$	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	0.889035	−	0.457838i	$-0.151376\pi$
$683$	7696.74	+	7696.74i	0.431197	+	0.431197i	−0.457838	+	0.889035i	$0.651376\pi$
$684$	3810.20	+	13814.2i	0.212992	+	0.772219i
$685$	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
$690$	−8885.70	+	5173.66i	−0.490251	+	0.285446i
$691$	−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
$693$	2630.95	−	8933.16i	0.144216	−	0.489672i
$694$	−8065.69	+	14500.2i	−0.441167	+	0.793114i
$695$			5571.56i			0.304088i
$696$	12557.0	−	23656.5i	0.683870	−	1.28836i
$697$			34053.7i			1.85061i
$698$	−11262.4	−	6264.69i	−0.610730	−	0.339716i
$699$	−8158.71	−	4845.30i	−0.441474	−	0.262183i
$700$	6702.52	+	10797.3i	0.361902	+	0.582998i
$701$	−9985.70	−	9985.70i	−0.538024	−	0.538024i	0.384924	−	0.922948i	$-0.374227\pi$
$701$	−9985.70	−	9985.70i	−0.538024	−	0.538024i	−0.922948	+	0.384924i	$0.874227\pi$
$702$	3702.51	−	6113.43i	0.199063	−	0.328684i
$703$		−	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
$708$	5064.10	+	4869.03i	0.268814	+	0.258459i
$709$	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
$714$	−43838.1	−	11574.4i	−2.29776	−	0.606669i
$715$	−1430.06	+	1430.06i	−0.0747988	+	0.0747988i
$716$	3713.28	−	15869.4i	0.193815	−	0.828308i
$717$	−18813.0	−	11172.7i	−0.979894	−	0.581940i
$718$	−16145.6	+	4603.82i	−0.839205	+	0.239294i
$719$	11158.4			0.578772			0.289386	−	0.957212i	$-0.406549\pi$
$719$	11158.4			0.578772			0.289386	+	0.957212i	$0.406549\pi$
$720$	−8755.41	+	9471.61i	−0.453187	+	0.490258i
$721$	−8149.89			−0.420968
$722$	6684.87	−	1906.15i	0.344578	−	0.0982541i
$723$	−10079.1	−	5985.77i	−0.518458	−	0.307902i
$724$	9650.48	+	2258.11i	0.495383	+	0.115914i
$725$	11159.6	−	11159.6i	0.571667	−	0.571667i
$726$	−15698.0	−	4144.67i	−0.802487	−	0.211878i
$727$	−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
$732$	12636.3	−	13142.5i	0.638046	−	0.663609i
$733$	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
$738$	−13784.6	+	13548.3i	−0.687561	+	0.675774i
$739$	−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
$741$	5338.51	+	3170.44i	0.264663	+	0.157178i
$742$	25778.4	+	14339.2i	1.27541	+	0.709443i
$743$		−	7164.72i		−	0.353766i	−0.984232	−	0.176883i	$-0.943399\pi$
$743$		−	7164.72i		−	0.353766i	0.984232	−	0.176883i	$-0.0566014\pi$
$744$	13547.9	−	4152.43i	0.667596	−	0.204618i
$745$			3535.50i			0.173867i
$746$	−4354.54	+	7828.44i	−0.213715	+	0.384209i
$747$	−3199.79	−	942.387i	−0.156726	−	0.0461582i
$748$	3689.15	−	15766.3i	0.180332	−	0.770687i
$749$	−6255.27	−	6255.27i	−0.305157	−	0.305157i
$750$	−18418.9	+	10724.3i	−0.896749	+	0.522128i
$751$			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
$756$	−12755.9	−	22350.2i	−0.613659	−	1.07522i
$757$	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	$-0.451473\pi$
$761$	6376.16			0.303726			0.151863	+	0.988402i	$0.451473\pi$
$762$	−1359.41	−	358.921i	−0.0646277	−	0.0170634i
$763$	−9678.76	+	9678.76i	−0.459233	+	0.459233i
$764$	2474.66	−	1536.17i	0.117186	−	0.0727443i
$765$	7661.01	−	26012.3i	0.362071	−	1.22938i
$766$	1690.66	+	5929.15i	0.0797467	+	0.279672i
$767$	3043.89			0.143297
$768$	2452.21	+	21141.7i	0.115217	+	0.993340i
$769$	−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
$771$	8887.88	−	14965.8i	0.415161	−	0.699065i
$772$	−3563.48	+	2212.06i	−0.166130	+	0.103127i
$773$	16886.8	−	16886.8i	0.785740	−	0.785740i	−0.195053	−	0.980793i	$-0.562488\pi$
$773$	16886.8	−	16886.8i	0.785740	−	0.785740i	0.980793	+	0.195053i	$0.0624878\pi$
$774$	126.702	−	14655.1i	0.00588400	−	0.680579i
$775$	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
$780$	109.735	+	5587.61i	0.00503737	+	0.256498i
$781$	−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
$786$	6636.10	+	11397.4i	0.301148	+	0.517217i
$787$	−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
$789$	1131.41	−	1905.11i	0.0510510	−	0.0859616i
$790$	12652.6	−	22746.5i	0.569824	−	1.02441i
$791$			4794.70i			0.215524i
$792$	7849.81	−	4779.33i	0.352185	−	0.214427i
$793$		−	7899.60i		−	0.353749i
$794$	9604.52	+	5342.48i	0.429284	+	0.238788i
$795$	−9008.43	+	15168.8i	−0.401882	+	0.676705i
$796$	−26171.6	+	16246.3i	−1.16536	+	0.723410i
$797$	−19285.8	−	19285.8i	−0.857139	−	0.857139i	0.133861	−	0.991000i	$-0.457262\pi$
$797$	−19285.8	−	19285.8i	−0.857139	−	0.857139i	−0.991000	+	0.133861i	$0.957262\pi$
$798$	19319.7	−	11248.8i	0.857031	−	0.499002i
$799$		−	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
$804$	29902.8	+	28750.9i	1.31168	+	1.26115i
$805$	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	$-0.303022\pi$
$809$	26695.5			1.16015			0.580077	+	0.814561i	$0.303022\pi$
$810$	13577.5	−	7247.92i	0.588968	−	0.314402i
$811$	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
$813$	7221.93	−	12160.6i	0.311543	−	0.524588i
$814$	−140.577	+	40.0847i	−0.00605311	+	0.00172601i
$815$	7822.85			0.336224
$816$	−24340.8	−	37545.4i	−1.04424	−	1.61073i
$817$	12731.8			0.545201
$818$	−29726.4	+	8476.31i	−1.27061	+	0.362307i
$819$	−10696.0	−	3150.13i	−0.456346	−	0.134401i
$820$	3443.36	−	14715.9i	0.146643	−	0.626709i
$821$	−25860.0	+	25860.0i	−1.09930	+	1.09930i	−0.104802	+	0.994493i	$0.533421\pi$
$821$	−25860.0	+	25860.0i	−1.09930	+	1.09930i	−0.994493	+	0.104802i	$0.966579\pi$
$822$	−224.282	+	849.467i	−0.00951669	+	0.0360445i
$823$	−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	0.891620	−	0.452784i	$-0.149569\pi$
$827$	10436.6	+	10436.6i	0.438836	+	0.438836i	−0.452784	+	0.891620i	$0.649569\pi$
$828$	9993.78	−	17606.4i	0.419454	−	0.738968i
$829$	−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
$834$	−5519.84	−	9480.25i	−0.229180	−	0.393614i
$835$	11984.2	+	11984.2i	0.496682	+	0.496682i
$836$	4210.73	+	6783.20i	0.174200	+	0.280624i
$837$	−16896.7	−	624.233i	−0.697774	−	0.0257786i
$838$	21519.0	+	11969.8i	0.887065	+	0.493426i
$839$			9701.30i			0.399197i	0.979878	+	0.199598i	$0.0639638\pi$
$839$			9701.30i			0.399197i	−0.979878	+	0.199598i	$0.936036\pi$
$840$	17773.8	+	9434.46i	0.730063	+	0.387524i
$841$			27499.5i			1.12754i
$842$	−19806.8	+	35607.9i	−0.810672	+	1.45740i
$843$	5070.57	+	3011.32i	0.207165	+	0.123031i
$844$	4266.49	+	998.313i	0.174003	+	0.0407149i
$845$	−9883.71	−	9883.71i	−0.402379	−	0.402379i
$846$	25525.9	−	25088.3i	1.03735	−	1.01957i
$847$			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
$852$	409.522	+	20852.5i	0.0164671	+	0.838492i
$853$	−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	$-0.162830\pi$
$857$	43753.5			1.74398			0.871989	+	0.489525i	$0.162830\pi$
$858$	1016.52	−	3850.09i	0.0404470	−	0.153193i
$859$	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
$861$	25926.0	+	15396.9i	1.02620	+	0.609438i
$862$	4712.56	+	16527.0i	0.186207	+	0.653028i
$863$	−6795.73			−0.268052			−0.134026	−	0.990978i	$-0.542791\pi$
$863$	−6795.73			−0.268052			−0.134026	+	0.990978i	$0.542791\pi$
$864$	5514.04	−	24790.5i	0.217120	−	0.976145i
$865$	−18985.2			−0.746261
$866$	1513.80	+	5308.89i	0.0594006	+	0.208318i
$867$	58932.3	+	34998.7i	2.30847	+	1.37096i
$868$	−11659.0	−	18781.9i	−0.455913	−	0.734444i
$869$	−13113.9	+	13113.9i	−0.511919	+	0.511919i
$870$	6379.24	−	24161.4i	0.248594	−	0.941549i
$871$	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
$876$	−523.976	−	26680.4i	−0.0202095	−	1.02905i
$877$	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	$-0.801768\pi$
$881$		−	30505.1i		−	1.16656i	0.812269	−	0.583282i	$-0.198232\pi$
$882$	−9951.31	+	9780.71i	−0.379907	+	0.373394i
$883$	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
$885$	5635.82	+	3347.00i	0.214063	+	0.127128i
$886$	3408.12	−	6127.00i	0.129230	−	0.232326i
$887$		−	3034.76i		−	0.114878i	−0.998349	−	0.0574392i	$-0.981706\pi$
$887$		−	3034.76i		−	0.114878i	0.998349	−	0.0574392i	$-0.0182935\pi$
$888$	−189.394	+	356.802i	−0.00715725	+	0.0134837i
$889$			2193.47i			0.0827519i
$890$	−22067.2	−	12274.8i	−0.831116	−	0.462305i
$891$	−10719.4	+	2313.51i	−0.403047	+	0.0869869i
$892$	7286.55	+	11738.1i	0.273511	+	0.440607i
$893$	21985.8	+	21985.8i	0.823883	+	0.823883i
$894$	−3502.67	−	6015.80i	−0.131037	−	0.225054i
$895$		−	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
$900$	7387.45	−	13014.7i	0.273609	−	0.482028i
$901$	−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
$906$	−6721.35	+	25457.1i	−0.246470	+	0.933506i
$907$	−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
$909$	−1473.37	−	433.930i	−0.0537608	−	0.0158334i
$910$	8384.59	−	2390.81i	0.305436	−	0.0870931i
$911$	−52041.6			−1.89266			−0.946331	−	0.323199i	$-0.895242\pi$
$911$	−52041.6			−1.89266			−0.946331	+	0.323199i	$0.895242\pi$
$912$	21576.8	+	4603.83i	0.783420	+	0.167158i
$913$	−1858.45			−0.0673666
$914$	29870.2	−	8517.32i	1.08098	−	0.308236i
$915$	8686.25	−	14626.3i	0.313835	−	0.528447i
$916$	−31089.4	−	7274.58i	−1.12142	−	0.262400i
$917$	14548.9	−	14548.9i	0.523934	−	0.523934i
$918$	12735.2	+	51850.9i	0.457870	+	1.86420i
$919$	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
$924$	−10335.3	−	9937.18i	−0.367973	−	0.353798i
$925$	−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	$-0.925375\pi$
$929$		−	13155.3i		−	0.464597i	0.972644	−	0.232299i	$-0.0746247\pi$
$930$	11425.6	−	6652.53i	0.402862	−	0.234565i
$931$	−8571.20	−	8571.20i	−0.301729	−	0.301729i
$932$	−12412.3	+	7705.03i	−0.436241	+	0.270801i
$933$	14312.0	−	24099.1i	0.502201	−	0.845626i
$934$	−39056.1	−	21724.8i	−1.36826	−	0.761089i
$935$		−	15108.0i		−	0.528433i
$936$	−5722.45	−	9398.84i	−0.199834	−	0.328217i
$937$		−	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
$939$	9807.85	−	16514.9i	0.340860	−	0.573953i
$940$	−6376.30	+	27250.4i	−0.221247	+	0.945542i
$941$	−32019.9	−	32019.9i	−1.10927	−	1.10927i	−0.993247	−	0.116018i	$-0.962987\pi$
$941$	−32019.9	−	32019.9i	−1.10927	−	1.10927i	−0.116018	−	0.993247i	$-0.537013\pi$
$942$	7638.52	+	13119.1i	0.264200	+	0.453760i
$943$			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	−0.0528415	−	0.998603i	$-0.516828\pi$
$947$	27561.7	−	27561.7i	0.945761	−	0.945761i	0.998603	+	0.0528415i	$0.0168278\pi$
$948$	1006.29	+	51239.3i	0.0344754	+	1.75546i
$949$	−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	$-0.575171\pi$
$953$	−13766.6			−0.467937			−0.233969	+	0.972244i	$0.575171\pi$
$954$	300.305	−	34735.1i	0.0101915	−	1.17882i
$955$	1921.68	−	1921.68i	0.0651142	−	0.0651142i
$956$	−28621.2	+	17766.9i	−0.968279	+	0.601069i
$957$	−9091.75	+	15309.1i	−0.307100	+	0.517107i
$958$	4463.11	+	15652.1i	0.150518	+	0.527868i
$959$	1370.65			0.0461528
$960$	6722.15	+	18686.0i	0.225996	+	0.628218i
$961$	15266.3			0.512447
$962$	47.9948	+	168.318i	0.00160854	+	0.00564115i
$963$	−2943.05	+	9992.84i	−0.0984822	+	0.334387i
$964$	−15333.8	+	9518.61i	−0.512312	+	0.318023i
$965$	−2767.19	+	2767.19i	−0.0923100	+	0.0923100i
$966$	−30537.4	−	8062.68i	−1.01711	−	0.268543i
$967$	−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	0.478405	−	0.878139i	$-0.341215\pi$
$971$	−12094.8	−	12094.8i	−0.399734	−	0.399734i	−0.878139	+	0.478405i	$0.841215\pi$
$972$	−15922.0	+	25784.1i	−0.525411	+	0.850848i
$973$	−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	$-0.976331\pi$
$977$		−	4537.40i		−	0.148582i	0.997237	−	0.0742908i	$-0.0236693\pi$
$978$	−13310.9	+	7750.23i	−0.435211	+	0.253400i
$979$	12722.2	+	12722.2i	0.415326	+	0.415326i
$980$	2485.80	−	10623.6i	0.0810267	−	0.346284i
$981$	15461.9	+	4553.76i	0.503221	+	0.148206i
$982$	21547.4	−	38737.1i	0.700208	−	1.25881i
$983$		−	46650.8i		−	1.51366i	−0.653611	−	0.756831i	$-0.726747\pi$
$983$		−	46650.8i		−	1.51366i	0.653611	−	0.756831i	$-0.273253\pi$
$984$	8720.24	+	28451.1i	0.282511	+	0.921736i
$985$		−	32337.4i		−	1.04605i
$986$	75757.9	+	42140.0i	2.44688	+	1.36107i
$987$	−48008.8	−	28511.5i	−1.54827	−	0.919485i
$988$	8121.75	−	5041.66i	0.261526	−	0.162345i
$989$	−12718.8	−	12718.8i	−0.408934	−	0.408934i
$990$	6115.60	−	6010.76i	0.196330	−	0.192964i
$991$		−	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
$996$	−3559.42	+	3702.03i	−0.113238	+	0.117774i
$997$	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.11.14	yes	44
3.2	odd	2	inner	48.4.k.a.11.9	✓	44
4.3	odd	2		192.4.k.a.143.18		44
8.3	odd	2		384.4.k.a.287.5		44
8.5	even	2		384.4.k.b.287.18		44
12.11	even	2		192.4.k.a.143.15		44
16.3	odd	4	inner	48.4.k.a.35.9	yes	44
16.5	even	4		384.4.k.a.95.8		44
16.11	odd	4		384.4.k.b.95.15		44
16.13	even	4		192.4.k.a.47.15		44
24.5	odd	2		384.4.k.b.287.15		44
24.11	even	2		384.4.k.a.287.8		44
48.5	odd	4		384.4.k.a.95.5		44
48.11	even	4		384.4.k.b.95.18		44
48.29	odd	4		192.4.k.a.47.18		44
48.35	even	4	inner	48.4.k.a.35.14	yes	44

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

\(f(q)\)	\(=\)	\(q+(0.775594 + 2.72001i) q^{2} +(-4.46768 - 2.65327i) q^{3} +(-6.79691 + 4.21925i) q^{4} +(-5.27809 + 5.27809i) q^{5} +(3.75181 - 14.2100i) q^{6} -22.9284 q^{7} +(-16.7480 - 15.2152i) q^{8} +(12.9203 + 23.7079i) q^{9} +O(q^{10})\)	\(q+(0.775594 + 2.72001i) q^{2} +(-4.46768 - 2.65327i) q^{3} +(-6.79691 + 4.21925i) q^{4} +(-5.27809 + 5.27809i) q^{5} +(3.75181 - 14.2100i) 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} +(41.5612 - 0.816220i) 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} +(-54.4648 + 53.5311i) q^{18} +(-46.9113 - 46.9113i) q^{19} +(13.6051 - 58.1443i) q^{20} +(102.437 + 60.8352i) q^{21} +(-20.6826 + 37.1824i) q^{22} +93.7270i q^{23} +(34.4547 + 112.414i) q^{24} +69.2835i q^{25} +(44.5198 + 24.7640i) q^{26} +(5.17956 - 140.200i) q^{27} +(155.842 - 96.7405i) q^{28} +(-161.072 - 161.072i) q^{29} +(55.1993 + 94.8041i) 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} +(-187.848 - 106.626i) 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} +(-86.0230 + 325.812i) q^{42} +(-135.701 + 135.701i) q^{43} +(-117.178 - 27.4184i) q^{44} +(-193.327 - 56.9379i) q^{45} +(-254.938 + 72.6941i) q^{46} -468.668 q^{47} +(-279.044 + 180.905i) q^{48} +182.711 q^{49} +(-188.452 + 53.7358i) q^{50} +(356.998 - 601.128i) q^{51} +(-32.8289 + 140.301i) q^{52} +(-321.633 + 321.633i) q^{53} +(385.364 - 94.6502i) 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} +(-215.056 + 223.672i) 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} +(191.058 - 111.243i) q^{66} +(705.631 + 705.631i) q^{67} +(-567.701 - 914.526i) q^{68} +(248.683 - 418.742i) q^{69} +(423.031 + 235.310i) q^{70} +501.730i q^{71} +(144.331 - 593.647i) q^{72} -641.954i q^{73} +(-4.72376 + 8.49222i) q^{74} +(183.828 - 309.536i) q^{75} +(516.782 + 120.921i) q^{76} +(-243.887 - 243.887i) q^{77} +(-133.195 - 228.760i) 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} +(-952.931 + 18.7146i) 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} +(4.92809 - 570.013i) q^{90} +(-292.014 + 292.014i) q^{91} +(-395.457 - 637.054i) q^{92} +(-319.768 + 538.438i) q^{93} +(-363.496 - 1274.78i) q^{94} +495.204 q^{95} +(-708.487 - 618.693i) q^{96} -1058.49 q^{97} +(141.709 + 496.975i) q^{98} +(-114.747 + 389.611i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more