LMFDB - Embedded newform 42.4.d.a.41.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,4,Mod(41,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.41"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	42.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.47808022024$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.116876510171136.13
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 15x^{6} + 455x^{4} + 5097x^{2} + 21904 $ x^8 + 15x^6 + 455x^4 + 5097*x^2 + 21904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.4
Root			$0.696949 + 2.67617i$ of defining polynomial
Character	$\chi$	$=$	42.41
Dual form			42.4.d.a.41.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000i q^{2} +(4.30448 - 2.91058i) q^{3} -4.00000 q^{4} +11.3967 q^{5} +(-5.82116 - 8.60895i) q^{6} +(-17.0570 - 7.21506i) q^{7} +8.00000i q^{8} +(10.0570 - 25.0570i) q^{9} -22.7935i q^{10} +20.1141i q^{11} +(-17.2179 + 11.6423i) q^{12} +19.7601i q^{13} +(-14.4301 + 34.1141i) q^{14} +(49.0570 - 33.1711i) q^{15} +16.0000 q^{16} +55.4238 q^{17} +(-50.1141 - 20.1141i) q^{18} +126.838i q^{19} -45.5870 q^{20} +(-94.4217 + 18.5889i) q^{21} +40.2282 q^{22} +154.228i q^{23} +(23.2846 + 34.4358i) q^{24} +4.88590 q^{25} +39.5203 q^{26} +(-29.6402 - 137.129i) q^{27} +(68.2282 + 28.8602i) q^{28} -57.8859i q^{29} +(-66.3423 - 98.1141i) q^{30} -318.286i q^{31} -32.0000i q^{32} +(58.5437 + 86.5807i) q^{33} -110.848i q^{34} +(-194.395 - 82.2282i) q^{35} +(-40.2282 + 100.228i) q^{36} -74.0000 q^{37} +253.675 q^{38} +(57.5134 + 85.0570i) q^{39} +91.1740i q^{40} +307.626 q^{41} +(37.1777 + 188.843i) q^{42} -492.913 q^{43} -80.4564i q^{44} +(114.618 - 285.569i) q^{45} +308.456 q^{46} -455.697 q^{47} +(68.8716 - 46.5693i) q^{48} +(238.886 + 246.135i) q^{49} -9.77180i q^{50} +(238.570 - 161.315i) q^{51} -79.0405i q^{52} -247.027i q^{53} +(-274.259 + 59.2804i) q^{54} +229.235i q^{55} +(57.7205 - 136.456i) q^{56} +(369.171 + 545.970i) q^{57} -115.772 q^{58} -83.7204 q^{59} +(-196.228 + 132.685i) q^{60} +305.416i q^{61} -636.572 q^{62} +(-352.332 + 354.837i) q^{63} -64.0000 q^{64} +225.201i q^{65} +(173.161 - 117.087i) q^{66} -8.22820 q^{67} -221.695 q^{68} +(448.893 + 663.872i) q^{69} +(-164.456 + 388.790i) q^{70} -765.483i q^{71} +(200.456 + 80.4564i) q^{72} -397.803i q^{73} +148.000i q^{74} +(21.0312 - 14.2208i) q^{75} -507.351i q^{76} +(145.124 - 343.087i) q^{77} +(170.114 - 115.027i) q^{78} +36.9731 q^{79} +182.348 q^{80} +(-526.711 - 504.000i) q^{81} -615.251i q^{82} +1062.02 q^{83} +(377.687 - 74.3554i) q^{84} +631.651 q^{85} +985.826i q^{86} +(-168.482 - 249.169i) q^{87} -160.913 q^{88} +374.360 q^{89} +(-571.138 - 229.235i) q^{90} +(142.570 - 337.050i) q^{91} -616.913i q^{92} +(-926.396 - 1370.05i) q^{93} +911.394i q^{94} +1445.54i q^{95} +(-93.1386 - 137.743i) q^{96} -273.695i q^{97} +(492.270 - 477.772i) q^{98} +(504.000 + 202.289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 4 q^{7} - 60 q^{9} + 252 q^{15} + 128 q^{16} - 120 q^{18} - 168 q^{21} - 240 q^{22} + 320 q^{25} - 16 q^{28} + 312 q^{30} + 240 q^{36} - 592 q^{37} - 804 q^{39} - 216 q^{42} - 1696 q^{43}+ \cdots + 4032 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 4 * q^7 - 60 * q^9 + 252 * q^15 + 128 * q^16 - 120 * q^18 - 168 * q^21 - 240 * q^22 + 320 * q^25 - 16 * q^28 + 312 * q^30 + 240 * q^36 - 592 * q^37 - 804 * q^39 - 216 * q^42 - 1696 * q^43 + 1344 * q^46 + 2192 * q^49 + 504 * q^51 + 2532 * q^57 - 1488 * q^58 - 1008 * q^60 - 2496 * q^63 - 512 * q^64 + 496 * q^67 - 192 * q^70 + 480 * q^72 + 1080 * q^78 + 2824 * q^79 + 672 * q^84 - 3936 * q^85 + 960 * q^88 - 264 * q^91 - 1512 * q^93 + 4032 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	4.30448	−	2.91058i	0.828397	−	0.560141i
$3$	4.30448	−	2.91058i	0.828397	−	0.560141i
$4$	−4.00000			−0.500000
$5$	11.3967			1.01936			0.509678	−	0.860365i	$-0.329764\pi$
$5$	11.3967			1.01936			0.509678	+	0.860365i	$0.329764\pi$
$6$	−5.82116	−	8.60895i	−0.396080	−	0.585765i
$7$	−17.0570	−	7.21506i	−0.920994	−	0.389576i
$7$	−17.0570	−	7.21506i	−0.920994	−	0.389576i
$8$			8.00000i			0.353553i
$9$	10.0570	−	25.0570i	0.372483	−	0.928039i
$10$		−	22.7935i		−	0.720794i
$11$			20.1141i			0.551330i	0.961254	+	0.275665i	$0.0888980\pi$
$11$			20.1141i			0.551330i	−0.961254	+	0.275665i	$0.911102\pi$
$12$	−17.2179	+	11.6423i	−0.414199	+	0.280071i
$13$			19.7601i			0.421575i	0.977532	+	0.210788i	$0.0676028\pi$
$13$			19.7601i			0.421575i	−0.977532	+	0.210788i	$0.932397\pi$
$14$	−14.4301	+	34.1141i	−0.275472	+	0.651241i
$15$	49.0570	−	33.1711i	0.844432	−	0.570984i
$16$	16.0000			0.250000
$17$	55.4238			0.790720			0.395360	−	0.918526i	$-0.370620\pi$
$17$	55.4238			0.790720			0.395360	+	0.918526i	$0.370620\pi$
$18$	−50.1141	−	20.1141i	−0.656223	−	0.263385i
$19$			126.838i			1.53150i	0.643137	+	0.765751i	$0.277633\pi$
$19$			126.838i			1.53150i	−0.643137	+	0.765751i	$0.722367\pi$
$20$	−45.5870			−0.509678
$21$	−94.4217	+	18.5889i	−0.981167	+	0.193163i
$22$	40.2282			0.389849
$23$			154.228i			1.39821i	0.715020	+	0.699104i	$0.246418\pi$
$23$			154.228i			1.39821i	−0.715020	+	0.699104i	$0.753582\pi$
$24$	23.2846	+	34.4358i	0.198040	+	0.292883i
$25$	4.88590			0.0390872
$26$	39.5203			0.298099
$27$	−29.6402	−	137.129i	−0.211269	−	0.977428i
$28$	68.2282	+	28.8602i	0.460497	+	0.194788i
$29$		−	57.8859i		−	0.370660i	−0.982676	−	0.185330i	$-0.940665\pi$
$29$		−	57.8859i		−	0.370660i	0.982676	−	0.185330i	$-0.0593354\pi$
$30$	−66.3423	−	98.1141i	−0.403746	−	0.597103i
$31$		−	318.286i		−	1.84406i	−0.387120	−	0.922029i	$-0.626530\pi$
$31$		−	318.286i		−	1.84406i	0.387120	−	0.922029i	$-0.373470\pi$
$32$		−	32.0000i		−	0.176777i
$33$	58.5437	+	86.5807i	0.308823	+	0.456720i
$34$		−	110.848i		−	0.559124i
$35$	−194.395	−	82.2282i	−0.938821	−	0.397117i
$36$	−40.2282	+	100.228i	−0.186242	+	0.464019i
$37$	−74.0000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−74.0000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	253.675			1.08294
$39$	57.5134	+	85.0570i	0.236142	+	0.349231i
$40$			91.1740i			0.360397i
$41$	307.626			1.17178			0.585891	−	0.810390i	$-0.300745\pi$
$41$	307.626			1.17178			0.585891	+	0.810390i	$0.300745\pi$
$42$	37.1777	+	188.843i	0.136587	+	0.693790i
$43$	−492.913			−1.74810			−0.874052	−	0.485832i	$-0.838517\pi$
$43$	−492.913			−1.74810			−0.874052	+	0.485832i	$0.838517\pi$
$44$		−	80.4564i		−	0.275665i
$45$	114.618	−	285.569i	0.379693	−	0.946002i
$46$	308.456			0.988683
$47$	−455.697			−1.41426			−0.707130	−	0.707083i	$-0.750010\pi$
$47$	−455.697			−1.41426			−0.707130	+	0.707083i	$0.750010\pi$
$48$	68.8716	−	46.5693i	0.207099	−	0.140035i
$49$	238.886	+	246.135i	0.696460	+	0.717595i
$50$		−	9.77180i		−	0.0276388i
$51$	238.570	−	161.315i	0.655030	−	0.442915i
$52$		−	79.0405i		−	0.210788i
$53$		−	247.027i		−	0.640222i	−0.947380	−	0.320111i	$-0.896280\pi$
$53$		−	247.027i		−	0.640222i	0.947380	−	0.320111i	$-0.103720\pi$
$54$	−274.259	+	59.2804i	−0.691146	+	0.149390i
$55$			229.235i			0.562002i
$56$	57.7205	−	136.456i	0.137736	−	0.325621i
$57$	369.171	+	545.970i	0.857858	+	1.26869i
$58$	−115.772			−0.262096
$59$	−83.7204			−0.184737			−0.0923683	−	0.995725i	$-0.529444\pi$
$59$	−83.7204			−0.184737			−0.0923683	+	0.995725i	$0.529444\pi$
$60$	−196.228	+	132.685i	−0.422216	+	0.285492i
$61$			305.416i			0.641057i	0.947239	+	0.320528i	$0.103860\pi$
$61$			305.416i			0.641057i	−0.947239	+	0.320528i	$0.896140\pi$
$62$	−636.572			−1.30395
$63$	−352.332	+	354.837i	−0.704597	+	0.709608i
$64$	−64.0000			−0.125000
$65$			225.201i			0.429735i
$66$	173.161	−	117.087i	0.322950	−	0.218371i
$67$	−8.22820			−0.0150035			−0.00750175	−	0.999972i	$-0.502388\pi$
$67$	−8.22820			−0.0150035			−0.00750175	+	0.999972i	$0.502388\pi$
$68$	−221.695			−0.395360
$69$	448.893	+	663.872i	0.783195	+	1.15827i
$70$	−164.456	+	388.790i	−0.280804	+	0.663847i
$71$		−	765.483i		−	1.27952i	−0.768573	−	0.639762i	$-0.779033\pi$
$71$		−	765.483i		−	1.27952i	0.768573	−	0.639762i	$-0.220967\pi$
$72$	200.456	+	80.4564i	0.328111	+	0.131693i
$73$		−	397.803i		−	0.637800i	−0.947788	−	0.318900i	$-0.896687\pi$
$73$		−	397.803i		−	0.637800i	0.947788	−	0.318900i	$-0.103313\pi$
$74$			148.000i			0.232495i
$75$	21.0312	−	14.2208i	0.0323797	−	0.0218944i
$76$		−	507.351i		−	0.765751i
$77$	145.124	−	343.087i	0.214785	−	0.507772i
$78$	170.114	−	115.027i	0.246944	−	0.166977i
$79$	36.9731			0.0526557			0.0263278	−	0.999653i	$-0.491619\pi$
$79$	36.9731			0.0526557			0.0263278	+	0.999653i	$0.491619\pi$
$80$	182.348			0.254839
$81$	−526.711	−	504.000i	−0.722512	−	0.691358i
$82$		−	615.251i		−	0.828575i
$83$	1062.02			1.40448			0.702241	−	0.711939i	$-0.252183\pi$
$83$	1062.02			1.40448			0.702241	+	0.711939i	$0.252183\pi$
$84$	377.687	−	74.3554i	0.490583	−	0.0965814i
$85$	631.651			0.806026
$86$			985.826i			1.23610i
$87$	−168.482	−	249.169i	−0.207622	−	0.307054i
$88$	−160.913			−0.194925
$89$	374.360			0.445866			0.222933	−	0.974834i	$-0.428437\pi$
$89$	374.360			0.445866			0.222933	+	0.974834i	$0.428437\pi$
$90$	−571.138	−	229.235i	−0.668925	−	0.268484i
$91$	142.570	−	337.050i	0.164236	−	0.388268i
$92$		−	616.913i		−	0.699104i
$93$	−926.396	−	1370.05i	−1.03293	−	1.52761i
$94$			911.394i			1.00003i
$95$			1445.54i			1.56115i
$96$	−93.1386	−	137.743i	−0.0990199	−	0.146441i
$97$		−	273.695i		−	0.286490i	−0.989687	−	0.143245i	$-0.954246\pi$
$97$		−	273.695i		−	0.286490i	0.989687	−	0.143245i	$-0.0457537\pi$
$98$	492.270	−	477.772i	0.507416	−	0.492472i
$99$	504.000	+	202.289i	0.511656	+	0.205361i
$100$	−19.5436			−0.0195436
$101$	−1112.51			−1.09602			−0.548012	−	0.836470i	$-0.684615\pi$
$101$	−1112.51			−1.09602			−0.548012	+	0.836470i	$0.684615\pi$
$102$	−322.631	−	477.141i	−0.313188	−	0.463176i
$103$		−	910.917i		−	0.871411i	−0.900089	−	0.435705i	$-0.856499\pi$
$103$		−	910.917i		−	0.871411i	0.900089	−	0.435705i	$-0.143501\pi$
$104$	−158.081			−0.149049
$105$	−1076.10	+	211.853i	−1.00016	+	0.196902i
$106$	−494.054			−0.452705
$107$			679.430i			0.613859i	0.951732	+	0.306930i	$0.0993016\pi$
$107$			679.430i			0.613859i	−0.951732	+	0.306930i	$0.900698\pi$
$108$	118.561	+	548.517i	0.105634	+	0.488714i
$109$	283.141			0.248807			0.124404	−	0.992232i	$-0.460298\pi$
$109$	283.141			0.248807			0.124404	+	0.992232i	$0.460298\pi$
$110$	458.471			0.397395
$111$	−318.531	+	215.383i	−0.272375	+	0.184173i
$112$	−272.913	−	115.441i	−0.230249	−	0.0973941i
$113$			983.134i			0.818456i	0.912432	+	0.409228i	$0.134202\pi$
$113$			983.134i			0.818456i	−0.912432	+	0.409228i	$0.865798\pi$
$114$	1091.94	−	738.342i	0.897101	−	0.606597i
$115$			1757.70i			1.42527i
$116$			231.544i			0.185330i
$117$	495.131	+	198.729i	0.391238	+	0.157030i
$118$			167.441i			0.130629i
$119$	−945.367	−	399.886i	−0.728249	−	0.308046i
$120$	265.369	+	392.456i	0.201873	+	0.298552i
$121$	926.423			0.696035
$122$	610.831			0.453296
$123$	1324.17	−	895.369i	0.970701	−	0.656364i
$124$			1273.14i			0.922029i
$125$	−1368.91			−0.979512
$126$	709.674	+	704.663i	0.501768	+	0.498225i
$127$	−1300.56			−0.908712			−0.454356	−	0.890820i	$-0.650131\pi$
$127$	−1300.56			−0.908712			−0.454356	+	0.890820i	$0.650131\pi$
$128$			128.000i			0.0883883i
$129$	−2121.73	+	1434.66i	−1.44812	+	0.979186i
$130$	450.403			0.303869
$131$	2204.12			1.47004			0.735020	−	0.678046i	$-0.237173\pi$
$131$	2204.12			1.47004			0.735020	+	0.678046i	$0.237173\pi$
$132$	−234.175	−	346.323i	−0.154411	−	0.228360i
$133$	915.141	−	2163.48i	0.596638	−	1.41051i
$134$			16.4564i			0.0106091i
$135$	−337.802	−	1562.83i	−0.215358	−	0.996347i
$136$			443.390i			0.279562i
$137$		−	632.336i		−	0.394336i	−0.980370	−	0.197168i	$-0.936825\pi$
$137$		−	632.336i		−	0.394336i	0.980370	−	0.197168i	$-0.0631745\pi$
$138$	1327.74	−	897.787i	0.819022	−	0.553802i
$139$			1907.68i			1.16408i	0.813160	+	0.582040i	$0.197745\pi$
$139$			1907.68i			1.16408i	−0.813160	+	0.582040i	$0.802255\pi$
$140$	777.580	+	328.913i	0.469411	+	0.198559i
$141$	−1961.54	+	1326.34i	−1.17157	+	0.792186i
$142$	−1530.97			−0.904760
$143$	−397.457			−0.232427
$144$	160.913	−	400.913i	0.0931208	−	0.232010i
$145$		−	659.711i		−	0.377835i
$146$	−795.607			−0.450992
$147$	1744.68	+	364.187i	0.978900	+	0.204338i
$148$	296.000			0.164399
$149$			3563.13i			1.95908i	0.201243	+	0.979541i	$0.435502\pi$
$149$			3563.13i			1.95908i	−0.201243	+	0.979541i	$0.564498\pi$
$150$	−28.4416	−	42.0625i	−0.0154816	−	0.0228959i
$151$	−1470.63			−0.792571			−0.396286	−	0.918127i	$-0.629701\pi$
$151$	−1470.63			−0.792571			−0.396286	+	0.918127i	$0.629701\pi$
$152$	−1014.70			−0.541468
$153$	557.400	−	1388.76i	0.294530	−	0.733819i
$154$	−686.174	−	290.249i	−0.359049	−	0.151876i
$155$		−	3627.42i		−	1.87975i
$156$	−230.054	−	340.228i	−0.118071	−	0.174616i
$157$		−	1013.14i		−	0.515016i	−0.966276	−	0.257508i	$-0.917099\pi$
$157$		−	1013.14i		−	0.515016i	0.966276	−	0.257508i	$-0.0829013\pi$
$158$		−	73.9462i		−	0.0372332i
$159$	−718.992	−	1063.32i	−0.358615	−	0.530358i
$160$		−	364.696i		−	0.180198i
$161$	1112.77	−	2630.68i	0.544709	−	1.28774i
$162$	−1008.00	+	1053.42i	−0.488864	+	0.510893i
$163$	316.577			0.152124			0.0760620	−	0.997103i	$-0.475765\pi$
$163$	316.577			0.152124			0.0760620	+	0.997103i	$0.475765\pi$
$164$	−1230.50			−0.585891
$165$	667.208	+	986.738i	0.314800	+	0.465560i
$166$		−	2124.04i		−	0.993119i
$167$	677.738			0.314042			0.157021	−	0.987595i	$-0.449811\pi$
$167$	677.738			0.314042			0.157021	+	0.987595i	$0.449811\pi$
$168$	−148.711	−	755.373i	−0.0682934	−	0.346895i
$169$	1806.54			0.822275
$170$		−	1263.30i		−	0.569946i
$171$	3178.18	+	1275.61i	1.42129	+	0.570459i
$172$	1971.65			0.874052
$173$	683.068			0.300189			0.150095	−	0.988672i	$-0.452042\pi$
$173$	683.068			0.300189			0.150095	+	0.988672i	$0.452042\pi$
$174$	−498.337	+	336.963i	−0.217120	+	0.146811i
$175$	−83.3390	−	35.2520i	−0.0359991	−	0.0152275i
$176$			321.826i			0.137832i
$177$	−360.372	+	243.675i	−0.153035	+	0.103479i
$178$		−	748.719i		−	0.315275i
$179$		−	887.537i		−	0.370601i	−0.982682	−	0.185301i	$-0.940674\pi$
$179$		−	887.537i		−	0.370601i	0.982682	−	0.185301i	$-0.0593259\pi$
$180$	−458.471	+	1142.28i	−0.189847	+	0.473001i
$181$			369.549i			0.151759i	0.997117	+	0.0758794i	$0.0241764\pi$
$181$			369.549i			0.151759i	−0.997117	+	0.0758794i	$0.975824\pi$
$182$	−674.099	−	285.141i	−0.274547	−	0.116132i
$183$	888.936	+	1314.65i	0.359082	+	0.531049i
$184$	−1233.83			−0.494341
$185$	−843.359			−0.335162
$186$	−2740.11	+	1852.79i	−1.08019	+	0.730394i
$187$			1114.80i			0.435948i
$188$	1822.79			0.707130
$189$	−483.822	+	2552.88i	−0.186206	+	0.982511i
$190$	2891.07			1.10390
$191$			526.409i			0.199422i	0.995016	+	0.0997111i	$0.0317918\pi$
$191$			526.409i			0.199422i	−0.995016	+	0.0997111i	$0.968208\pi$
$192$	−275.487	+	186.277i	−0.103550	+	0.0700177i
$193$	−3441.03			−1.28337			−0.641685	−	0.766968i	$-0.721764\pi$
$193$	−3441.03			−1.28337			−0.641685	+	0.766968i	$0.721764\pi$
$194$	−547.390			−0.202579
$195$	655.466	+	969.374i	0.240712	+	0.355991i
$196$	−955.544	−	984.541i	−0.348230	−	0.358798i
$197$		−	2684.84i		−	0.970999i	−0.874237	−	0.485500i	$-0.838638\pi$
$197$		−	2684.84i		−	0.970999i	0.874237	−	0.485500i	$-0.161362\pi$
$198$	404.577	−	1008.00i	0.145212	−	0.361795i
$199$			1862.27i			0.663380i	0.943389	+	0.331690i	$0.107619\pi$
$199$			1862.27i			0.663380i	−0.943389	+	0.331690i	$0.892381\pi$
$200$			39.0872i			0.0138194i
$201$	−35.4181	+	23.9488i	−0.0124289	+	0.00840408i
$202$			2225.01i			0.775006i
$203$	−417.650	+	987.363i	−0.144400	+	0.341376i
$204$	−954.282	+	645.262i	−0.327515	+	0.221458i
$205$	3505.93			1.19446
$206$	−1821.83			−0.616180
$207$	3864.50	+	1551.08i	1.29759	+	0.520809i
$208$			316.162i			0.105394i
$209$	−2551.23			−0.844363
$210$	423.705	+	2152.20i	0.139231	+	0.707219i
$211$	1156.12			0.377207			0.188603	−	0.982053i	$-0.439604\pi$
$211$	1156.12			0.377207			0.188603	+	0.982053i	$0.439604\pi$
$212$			988.108i			0.320111i
$213$	−2228.00	−	3295.01i	−0.716714	−	1.05995i
$214$	1358.86			0.434064
$215$	−5617.60			−1.78194
$216$	1097.03	−	237.122i	0.345573	−	0.0746948i
$217$	−2296.45	+	5429.02i	−0.718402	+	1.69837i
$218$		−	566.282i		−	0.175933i
$219$	−1157.84	−	1712.34i	−0.357258	−	0.528351i
$220$		−	916.941i		−	0.281001i
$221$			1095.18i			0.333348i
$222$	430.766	+	637.063i	0.130230	+	0.192598i
$223$		−	4405.86i		−	1.32304i	−0.749927	−	0.661521i	$-0.769911\pi$
$223$		−	4405.86i		−	1.32304i	0.749927	−	0.661521i	$-0.230089\pi$
$224$	−230.882	+	545.826i	−0.0688680	+	0.162810i
$225$	49.1377	−	122.426i	0.0145593	−	0.0362744i
$226$	1966.27			0.578736
$227$	5108.00			1.49352			0.746762	−	0.665091i	$-0.231607\pi$
$227$	5108.00			1.49352			0.746762	+	0.665091i	$0.231607\pi$
$228$	−1476.68	−	2183.88i	−0.428929	−	0.634346i
$229$			307.670i			0.0887835i	0.999014	+	0.0443917i	$0.0141350\pi$
$229$			307.670i			0.0887835i	−0.999014	+	0.0443917i	$0.985865\pi$
$230$	3515.40			1.00782
$231$	−373.898	−	1899.21i	−0.106496	−	0.540947i
$232$	463.087			0.131048
$233$		−	1624.91i		−	0.456874i	−0.973559	−	0.228437i	$-0.926639\pi$
$233$		−	1624.91i		−	0.456874i	0.973559	−	0.228437i	$-0.0733614\pi$
$234$	397.457	−	990.261i	0.111037	−	0.276647i
$235$	−5193.46			−1.44163
$236$	334.881			0.0923683
$237$	159.150	−	107.613i	0.0436198	−	0.0294946i
$238$	−799.772	+	1890.73i	−0.217821	+	0.514950i
$239$			5289.87i			1.43169i	0.698261	+	0.715843i	$0.253957\pi$
$239$			5289.87i			1.43169i	−0.698261	+	0.715843i	$0.746043\pi$
$240$	784.913	−	530.738i	0.211108	−	0.142746i
$241$		−	3851.67i		−	1.02949i	−0.857342	−	0.514747i	$-0.827886\pi$
$241$		−	3851.67i		−	1.02949i	0.857342	−	0.514747i	$-0.172114\pi$
$242$		−	1852.85i		−	0.492171i
$243$	−3734.15	−	636.421i	−0.985785	−	0.168010i
$244$		−	1221.66i		−	0.320528i
$245$	2722.52	+	2805.14i	0.709941	+	0.731485i
$246$	−1790.74	−	2648.34i	−0.464119	−	0.686389i
$247$	−2506.33			−0.645643
$248$	2546.29			0.651973
$249$	4571.45	−	3091.10i	1.16347	−	0.786708i
$250$			2737.82i			0.692620i
$251$	1314.57			0.330577			0.165289	−	0.986245i	$-0.447144\pi$
$251$	1314.57			0.330577			0.165289	+	0.986245i	$0.447144\pi$
$252$	1409.33	−	1419.35i	0.352299	−	0.354804i
$253$	−3102.16			−0.770874
$254$			2601.13i			0.642556i
$255$	2718.93	−	1838.47i	0.667709	−	0.451488i
$256$	256.000			0.0625000
$257$	420.639			0.102096			0.0510481	−	0.998696i	$-0.483744\pi$
$257$	420.639			0.102096			0.0510481	+	0.998696i	$0.483744\pi$
$258$	2869.32	+	4243.46i	0.692389	+	1.02398i
$259$	1262.22	+	533.914i	0.302821	+	0.128092i
$260$		−	900.805i		−	0.214868i
$261$	−1450.45	−	582.161i	−0.343987	−	0.138065i
$262$		−	4408.25i		−	1.03948i
$263$			747.886i			0.175348i	0.996149	+	0.0876742i	$0.0279434\pi$
$263$			747.886i			0.175348i	−0.996149	+	0.0876742i	$0.972057\pi$
$264$	−692.645	+	468.350i	−0.161475	+	0.109185i
$265$		−	2815.30i		−	0.652614i
$266$	−4326.95	−	1830.28i	−0.997378	−	0.421886i
$267$	1611.42	−	1089.60i	0.369354	−	0.249748i
$268$	32.9128			0.00750175
$269$	3799.63			0.861217			0.430608	−	0.902539i	$-0.358299\pi$
$269$	3799.63			0.861217			0.430608	+	0.902539i	$0.358299\pi$
$270$	−3125.66	+	675.604i	−0.704524	+	0.152281i
$271$		−	257.445i		−	0.0577074i	−0.999584	−	0.0288537i	$-0.990814\pi$
$271$		−	257.445i		−	0.0577074i	0.999584	−	0.0288537i	$-0.00918569\pi$
$272$	886.781			0.197680
$273$	−367.318	−	1865.79i	−0.0814327	−	0.413635i
$274$	−1264.67			−0.278838
$275$			98.2755i			0.0215499i
$276$	−1795.57	−	2655.49i	−0.391597	−	0.579136i
$277$	3415.92			0.740949			0.370474	−	0.928843i	$-0.379195\pi$
$277$	3415.92			0.740949			0.370474	+	0.928843i	$0.379195\pi$
$278$	3815.35			0.823129
$279$	−7975.30	−	3201.02i	−1.71136	−	0.686881i
$280$	657.826	−	1555.16i	0.140402	−	0.331923i
$281$			842.497i			0.178858i	0.995993	+	0.0894291i	$0.0285043\pi$
$281$			842.497i			0.178858i	−0.995993	+	0.0894291i	$0.971496\pi$
$282$	2652.68	+	3923.07i	0.560160	+	0.828424i
$283$			261.868i			0.0550051i	0.999622	+	0.0275026i	$0.00875544\pi$
$283$			261.868i			0.0550051i	−0.999622	+	0.0275026i	$0.991245\pi$
$284$			3061.93i			0.639762i
$285$	4207.35	+	6222.28i	0.874463	+	1.29325i
$286$			794.915i			0.164351i
$287$	−5247.19	−	2219.54i	−1.07920	−	0.456499i
$288$	−801.826	−	321.826i	−0.164056	−	0.0658464i
$289$	−1841.20			−0.374761
$290$	−1319.42			−0.267169
$291$	−796.611	−	1178.11i	−0.160475	−	0.237327i
$292$			1591.21i			0.318900i
$293$	−3823.98			−0.762455			−0.381227	−	0.924481i	$-0.624498\pi$
$293$	−3823.98			−0.762455			−0.381227	+	0.924481i	$0.624498\pi$
$294$	728.374	−	3489.35i	0.144488	−	0.692187i
$295$	−954.140			−0.188312
$296$		−	592.000i		−	0.116248i
$297$	2758.23	−	596.186i	0.538885	−	0.116479i
$298$	7126.27			1.38528
$299$	−3047.57			−0.589450
$300$	−84.1250	+	56.8832i	−0.0161899	+	0.0109472i
$301$	8407.64	+	3556.39i	1.60999	+	0.681020i
$302$			2941.26i			0.560432i
$303$	−4788.76	+	3238.04i	−0.907943	+	0.613929i
$304$			2029.40i			0.382876i
$305$			3480.74i			0.653465i
$306$	−2777.51	−	1114.80i	−0.518889	−	0.208264i
$307$			662.440i			0.123151i	0.998102	+	0.0615757i	$0.0196126\pi$
$307$			662.440i			0.123151i	−0.998102	+	0.0615757i	$0.980387\pi$
$308$	−580.498	+	1372.35i	−0.107393	+	0.253886i
$309$	−2651.30	−	3921.02i	−0.488113	−	0.721874i
$310$	−7254.85			−1.32919
$311$	3623.91			0.660749			0.330375	−	0.943850i	$-0.392825\pi$
$311$	3623.91			0.660749			0.330375	+	0.943850i	$0.392825\pi$
$312$	−680.456	+	460.108i	−0.123472	+	0.0834887i
$313$			8340.17i			1.50612i	0.657954	+	0.753058i	$0.271422\pi$
$313$			8340.17i			1.50612i	−0.657954	+	0.753058i	$0.728578\pi$
$314$	−2026.28			−0.364171
$315$	−4015.44	+	4043.99i	−0.718235	+	0.723343i
$316$	−147.892			−0.0263278
$317$		−	7466.56i		−	1.32291i	−0.749983	−	0.661457i	$-0.769938\pi$
$317$		−	7466.56i		−	1.32291i	0.749983	−	0.661457i	$-0.230062\pi$
$318$	−2126.64	+	1437.98i	−0.375020	+	0.253579i
$319$	1164.32			0.204356
$320$	−729.392			−0.127420
$321$	1977.53	+	2924.59i	0.343848	+	0.508519i
$322$	−5261.36	−	2225.53i	−0.910571	−	0.385168i
$323$			7029.83i			1.21099i
$324$	2106.85	+	2016.00i	0.361256	+	0.345679i
$325$			96.5460i			0.0164782i
$326$		−	633.154i		−	0.107568i
$327$	1218.77	−	824.104i	0.206111	−	0.139367i
$328$			2461.01i			0.414288i
$329$	7772.85	+	3287.88i	1.30253	+	0.550962i
$330$	1973.48	−	1334.42i	0.329201	−	0.222597i
$331$	11152.0			1.85186			0.925932	−	0.377689i	$-0.123281\pi$
$331$	11152.0			1.85186			0.925932	+	0.377689i	$0.123281\pi$
$332$	−4248.09			−0.702241
$333$	−744.222	+	1854.22i	−0.122472	+	0.305137i
$334$		−	1355.48i		−	0.222061i
$335$	−93.7747			−0.0152939
$336$	−1510.75	+	297.422i	−0.245292	+	0.0482907i
$337$	2827.44			0.457034			0.228517	−	0.973540i	$-0.426612\pi$
$337$	2827.44			0.457034			0.228517	+	0.973540i	$0.426612\pi$
$338$		−	3613.07i		−	0.581436i
$339$	2861.49	+	4231.88i	0.458451	+	0.678006i
$340$	−2526.60			−0.403013
$341$	6402.03			1.01668
$342$	2551.23	−	6356.36i	0.403376	−	1.00501i
$343$	−2298.81	−	5921.92i	−0.361878	−	0.932226i
$344$		−	3943.30i		−	0.618048i
$345$	5115.93	+	7565.98i	0.798354	+	1.18069i
$346$		−	1366.14i		−	0.212266i
$347$		−	12356.0i		−	1.91153i	−0.294124	−	0.955767i	$-0.595028\pi$
$347$		−	12356.0i		−	1.91153i	0.294124	−	0.955767i	$-0.404972\pi$
$348$	673.926	+	996.674i	0.103811	+	0.153527i
$349$		−	4451.06i		−	0.682693i	−0.939937	−	0.341347i	$-0.889117\pi$
$349$		−	4451.06i		−	0.682693i	0.939937	−	0.341347i	$-0.110883\pi$
$350$	−70.5041	+	166.678i	−0.0107674	+	0.0254552i
$351$	2709.69	−	585.694i	0.412059	−	0.0890657i
$352$	643.651			0.0974623
$353$	−9082.26			−1.36941			−0.684703	−	0.728823i	$-0.740068\pi$
$353$	−9082.26			−1.36941			−0.684703	+	0.728823i	$0.740068\pi$
$354$	487.350	+	720.745i	0.0731705	+	0.108212i
$355$		−	8724.02i		−	1.30429i
$356$	−1497.44			−0.222933
$357$	−5233.21	+	1030.27i	−0.775829	+	0.152738i
$358$	−1775.07			−0.262055
$359$		−	7818.24i		−	1.14939i	−0.818368	−	0.574695i	$-0.805121\pi$
$359$		−	7818.24i		−	1.14939i	0.818368	−	0.574695i	$-0.194879\pi$
$360$	2284.55	+	916.941i	0.334462	+	0.134242i
$361$	−9228.79			−1.34550
$362$	739.098			0.107310
$363$	3987.77	−	2696.43i	0.576594	−	0.389878i
$364$	−570.282	+	1348.20i	−0.0821179	+	0.194134i
$365$		−	4533.67i		−	0.650145i
$366$	2629.31	−	1777.87i	0.375509	−	0.253910i
$367$			3511.72i			0.499483i	0.968313	+	0.249741i	$0.0803456\pi$
$367$			3511.72i			0.499483i	−0.968313	+	0.249741i	$0.919654\pi$
$368$			2467.65i			0.349552i
$369$	3093.81	−	7708.19i	0.436469	−	1.08746i
$370$			1686.72i			0.236996i
$371$	−1782.31	+	4213.55i	−0.249415	+	0.589640i
$372$	3705.58	+	5480.22i	0.516467	+	0.763806i
$373$	−5709.68			−0.792589			−0.396295	−	0.918123i	$-0.629704\pi$
$373$	−5709.68			−0.792589			−0.396295	+	0.918123i	$0.629704\pi$
$374$	2229.60			0.308262
$375$	−5892.44	+	3984.32i	−0.811425	+	0.548665i
$376$		−	3645.58i		−	0.500016i
$377$	1143.83			0.156261
$378$	5105.76	+	967.643i	0.694740	+	0.131667i
$379$	−4903.68			−0.664604			−0.332302	−	0.943173i	$-0.607825\pi$
$379$	−4903.68			−0.664604			−0.332302	+	0.943173i	$0.607825\pi$
$380$		−	5782.15i		−	0.780574i
$381$	−5598.25	+	3785.40i	−0.752774	+	0.509007i
$382$	1052.82			0.141013
$383$	−4897.57			−0.653405			−0.326703	−	0.945127i	$-0.605938\pi$
$383$	−4897.57			−0.653405			−0.326703	+	0.945127i	$0.605938\pi$
$384$	372.554	+	550.973i	0.0495100	+	0.0732206i
$385$	1653.95	−	3910.08i	0.218943	−	0.517600i
$386$			6882.05i			0.907480i
$387$	−4957.25	+	12350.9i	−0.651140	+	1.62231i
$388$			1094.78i			0.143245i
$389$			242.437i			0.0315991i	0.999875	+	0.0157995i	$0.00502936\pi$
$389$			242.437i			0.0315991i	−0.999875	+	0.0157995i	$0.994971\pi$
$390$	1938.75	−	1310.93i	0.251724	−	0.170209i
$391$			8547.91i			1.10559i
$392$	−1969.08	+	1911.09i	−0.253708	+	0.246236i
$393$	9487.60	−	6415.28i	1.21778	−	0.823430i
$394$	−5369.68			−0.686600
$395$	421.373			0.0536749
$396$	−2016.00	−	809.154i	−0.255828	−	0.102681i
$397$		−	2490.99i		−	0.314910i	−0.987526	−	0.157455i	$-0.949671\pi$
$397$		−	2490.99i		−	0.314910i	0.987526	−	0.157455i	$-0.0503289\pi$
$398$	3724.53			0.469080
$399$	−2357.77	−	11976.2i	−0.295830	−	1.50266i
$400$	78.1744			0.00977180
$401$		−	4713.97i		−	0.587043i	−0.955952	−	0.293522i	$-0.905173\pi$
$401$		−	4713.97i		−	0.587043i	0.955952	−	0.293522i	$-0.0948273\pi$
$402$	47.8977	+	70.8362i	0.00594258	+	0.00878853i
$403$	6289.37			0.777409
$404$	4450.02			0.548012
$405$	−6002.80	−	5743.96i	−0.736497	−	0.704740i
$406$	1974.73	+	835.300i	0.241389	+	0.102107i
$407$		−	1488.44i		−	0.181276i
$408$	1290.52	+	1908.56i	0.156594	+	0.231588i
$409$			928.032i			0.112196i	0.998425	+	0.0560981i	$0.0178659\pi$
$409$			928.032i			0.112196i	−0.998425	+	0.0560981i	$0.982134\pi$
$410$		−	7011.87i		−	0.844613i
$411$	−1840.46	−	2721.88i	−0.220884	−	0.326667i
$412$			3643.67i			0.435705i
$413$	1428.02	+	604.047i	0.170141	+	0.0719691i
$414$	3102.16	−	7729.01i	0.368268	−	0.917536i
$415$	12103.6			1.43167
$416$	632.324			0.0745246
$417$	5552.45	+	8211.55i	0.652049	+	0.964320i
$418$			5102.45i			0.597055i
$419$	−597.138			−0.0696231			−0.0348116	−	0.999394i	$-0.511083\pi$
$419$	−597.138			−0.0696231			−0.0348116	+	0.999394i	$0.511083\pi$
$420$	4304.40	−	847.410i	0.500079	−	0.0984509i
$421$	−4195.70			−0.485715			−0.242858	−	0.970062i	$-0.578085\pi$
$421$	−4195.70			−0.485715			−0.242858	+	0.970062i	$0.578085\pi$
$422$		−	2312.24i		−	0.266725i
$423$	−4582.97	+	11418.4i	−0.526788	+	1.31249i
$424$	1976.22			0.226353
$425$	270.795			0.0309070
$426$	−6590.01	+	4456.00i	−0.749500	+	0.506793i
$427$	2203.59	−	5209.49i	0.249741	−	0.590409i
$428$		−	2717.72i		−	0.306930i
$429$	−1710.85	+	1156.83i	−0.192542	+	0.130192i
$430$			11235.2i			1.26002i
$431$			13476.0i			1.50607i	0.657980	+	0.753035i	$0.271411\pi$
$431$			13476.0i			1.50607i	−0.657980	+	0.753035i	$0.728589\pi$
$432$	−474.243	−	2194.07i	−0.0528172	−	0.244357i
$433$			10824.9i			1.20142i	0.799469	+	0.600708i	$0.205114\pi$
$433$			10824.9i			1.20142i	−0.799469	+	0.600708i	$0.794886\pi$
$434$	10858.0	+	4592.90i	1.20093	+	0.507987i
$435$	−1920.14	−	2839.71i	−0.211641	−	0.312997i
$436$	−1132.56			−0.124404
$437$	−19561.9			−2.14136
$438$	−3424.67	+	2315.68i	−0.373601	+	0.252619i
$439$		−	10858.9i		−	1.18057i	−0.807196	−	0.590284i	$-0.799016\pi$
$439$		−	10858.9i		−	1.18057i	0.807196	−	0.590284i	$-0.200984\pi$
$440$	−1833.88			−0.198698
$441$	8569.91	−	3510.38i	0.925376	−	0.379050i
$442$	2190.36			0.235713
$443$			11094.5i			1.18987i	0.803773	+	0.594937i	$0.202823\pi$
$443$			11094.5i			1.18987i	−0.803773	+	0.594937i	$0.797177\pi$
$444$	1274.13	−	861.532i	0.136188	−	0.0920867i
$445$	4266.48			0.454496
$446$	−8811.72			−0.935532
$447$	10370.8	+	15337.4i	1.09736	+	1.62290i
$448$	1091.65	+	461.764i	0.115124	+	0.0486971i
$449$			12421.1i			1.30554i	0.757556	+	0.652770i	$0.226393\pi$
$449$			12421.1i			1.30554i	−0.757556	+	0.652770i	$0.773607\pi$
$450$	−244.852	−	98.2755i	−0.0256499	−	0.0102950i
$451$			6187.61i			0.646039i
$452$		−	3932.54i		−	0.409228i
$453$	−6330.30	+	4280.39i	−0.656564	+	0.443952i
$454$		−	10216.0i		−	1.05608i
$455$	1624.84	−	3841.27i	0.167415	−	0.395784i
$456$	−4367.76	+	2953.37i	−0.448551	+	0.303299i
$457$	−14629.8			−1.49749			−0.748744	−	0.662859i	$-0.769343\pi$
$457$	−14629.8			−1.49749			−0.748744	+	0.662859i	$0.769343\pi$
$458$	615.340			0.0627794
$459$	−1642.77	−	7600.23i	−0.167055	−	0.772872i
$460$		−	7030.80i		−	0.712636i
$461$	2859.63			0.288907			0.144454	−	0.989512i	$-0.453858\pi$
$461$	2859.63			0.288907			0.144454	+	0.989512i	$0.453858\pi$
$462$	−3798.41	+	747.796i	−0.382507	+	0.0753044i
$463$	2467.82			0.247709			0.123855	−	0.992300i	$-0.460474\pi$
$463$	2467.82			0.247709			0.123855	+	0.992300i	$0.460474\pi$
$464$		−	926.174i		−	0.0926650i
$465$	−10557.9	−	15614.2i	−1.05293	−	1.55718i
$466$	−3249.83			−0.323059
$467$	3388.17			0.335730			0.167865	−	0.985810i	$-0.446313\pi$
$467$	3388.17			0.335730			0.167865	+	0.985810i	$0.446313\pi$
$468$	−1980.52	−	794.915i	−0.195619	−	0.0785148i
$469$	140.349	+	59.3669i	0.0138181	+	0.00584501i
$470$			10386.9i			1.01939i
$471$	−2948.83	−	4361.04i	−0.288482	−	0.426638i
$472$		−	669.763i		−	0.0653143i
$473$		−	9914.50i		−	0.963782i
$474$	−215.226	−	318.300i	−0.0208559	−	0.0308439i
$475$			619.716i			0.0598622i
$476$	3781.47	+	1599.54i	0.364124	+	0.154023i
$477$	−6189.77	−	2484.36i	−0.594151	−	0.238472i
$478$	10579.7			1.01236
$479$	15923.4			1.51891			0.759455	−	0.650560i	$-0.225466\pi$
$479$	15923.4			1.51891			0.759455	+	0.650560i	$0.225466\pi$
$480$	−1061.48	−	1569.83i	−0.100937	−	0.149276i
$481$		−	1462.25i		−	0.138613i
$482$	−7703.34			−0.727962
$483$	−2866.93	−	14562.5i	−0.270082	−	1.37188i
$484$	−3705.69			−0.348018
$485$		−	3119.23i		−	0.292035i
$486$	−1272.84	+	7468.30i	−0.118801	+	0.697055i
$487$	10110.8			0.940791			0.470395	−	0.882456i	$-0.344111\pi$
$487$	10110.8			0.940791			0.470395	+	0.882456i	$0.344111\pi$
$488$	−2443.32			−0.226648
$489$	1362.70	−	921.423i	0.126019	−	0.0852110i
$490$	5610.28	−	5445.05i	0.517238	−	0.502004i
$491$		−	301.711i		−	0.0277313i	−0.999904	−	0.0138656i	$-0.995586\pi$
$491$		−	301.711i		−	0.0277313i	0.999904	−	0.0138656i	$-0.00441371\pi$
$492$	−5296.67	+	3581.48i	−0.485350	+	0.328182i
$493$		−	3208.26i		−	0.293088i
$494$			5012.66i			0.456539i
$495$	5743.96	+	2305.43i	0.521559	+	0.209336i
$496$		−	5092.57i		−	0.461015i
$497$	−5523.01	+	13056.9i	−0.498472	+	1.17843i
$498$	−6182.20	−	9142.89i	−0.556287	−	0.822696i
$499$	−1175.22			−0.105431			−0.0527155	−	0.998610i	$-0.516788\pi$
$499$	−1175.22			−0.105431			−0.0527155	+	0.998610i	$0.516788\pi$
$500$	5475.64			0.489756
$501$	2917.31	−	1972.61i	0.260151	−	0.175908i
$502$		−	2629.14i		−	0.233753i
$503$	13867.3			1.22925			0.614625	−	0.788820i	$-0.289308\pi$
$503$	13867.3			1.22925			0.614625	+	0.788820i	$0.289308\pi$
$504$	−2838.70	−	2818.65i	−0.250884	−	0.249113i
$505$	−12678.9			−1.11724
$506$			6204.32i			0.545090i
$507$	7776.20	−	5258.07i	0.681170	−	0.460590i
$508$	5202.26			0.454356
$509$	18205.8			1.58538			0.792690	−	0.609625i	$-0.208680\pi$
$509$	18205.8			1.58538			0.792690	+	0.609625i	$0.208680\pi$
$510$	−3676.94	−	5437.86i	−0.319250	−	0.472142i
$511$	−2870.17	+	6785.35i	−0.248472	+	0.587410i
$512$		−	512.000i		−	0.0441942i
$513$	17393.2	−	3759.49i	1.49693	−	0.323559i
$514$		−	841.278i		−	0.0721930i
$515$		−	10381.5i		−	0.888278i
$516$	8486.93	−	5738.65i	0.724062	−	0.489593i
$517$		−	9165.93i		−	0.779724i
$518$	1067.83	−	2524.44i	0.0905747	−	0.214127i
$519$	2940.25	−	1988.12i	0.248676	−	0.168148i
$520$	−1801.61			−0.151934
$521$	−3553.23			−0.298790			−0.149395	−	0.988778i	$-0.547733\pi$
$521$	−3553.23			−0.298790			−0.149395	+	0.988778i	$0.547733\pi$
$522$	−1164.32	+	2900.90i	−0.0976265	+	0.243236i
$523$			14199.4i			1.18718i	0.804768	+	0.593590i	$0.202290\pi$
$523$			14199.4i			1.18718i	−0.804768	+	0.593590i	$0.797710\pi$
$524$	−8816.50			−0.735020
$525$	−461.335	+	90.8233i	−0.0383511	+	0.00755020i
$526$	1495.77			0.123990
$527$		−	17640.6i		−	1.45813i
$528$	936.699	+	1385.29i	0.0772057	+	0.114180i
$529$	−11619.3			−0.954988
$530$	−5630.61			−0.461468
$531$	−841.980	+	2097.79i	−0.0688113	+	0.171443i
$532$	−3660.56	+	8653.91i	−0.298319	+	0.705253i
$533$			6078.73i			0.493994i
$534$	−2179.21	−	3222.85i	−0.176598	−	0.261173i
$535$			7743.29i			0.625741i
$536$		−	65.8256i		−	0.00530454i
$537$	−2583.25	−	3820.38i	−0.207589	−	0.307005i
$538$		−	7599.25i		−	0.608972i
$539$	−4950.79	+	4804.97i	−0.395632	+	0.383979i
$540$	1351.21	+	6251.32i	0.107679	+	0.498174i
$541$	−1935.11			−0.153784			−0.0768920	−	0.997039i	$-0.524500\pi$
$541$	−1935.11			−0.153784			−0.0768920	+	0.997039i	$0.524500\pi$
$542$	−514.891			−0.0408053
$543$	1075.60	+	1590.71i	0.0850064	+	0.125717i
$544$		−	1773.56i		−	0.139781i
$545$	3226.89			0.253623
$546$	−3731.57	+	734.637i	−0.292484	+	0.0575816i
$547$	−522.054			−0.0408070			−0.0204035	−	0.999792i	$-0.506495\pi$
$547$	−522.054			−0.0408070			−0.0204035	+	0.999792i	$0.506495\pi$
$548$			2529.34i			0.197168i
$549$	7652.81	+	3071.58i	0.594926	+	0.238783i
$550$	196.551			0.0152381
$551$	7342.11			0.567667
$552$	−5310.97	+	3591.15i	−0.409511	+	0.276901i
$553$	−630.652	−	266.763i	−0.0484956	−	0.0205134i
$554$		−	6831.84i		−	0.523930i
$555$	−3630.22	+	2454.67i	−0.277647	+	0.187738i
$556$		−	7630.71i		−	0.582040i
$557$			10838.8i			0.824518i	0.911067	+	0.412259i	$0.135260\pi$
$557$			10838.8i			0.824518i	−0.911067	+	0.412259i	$0.864740\pi$
$558$	−6402.03	+	15950.6i	−0.485698	+	1.21011i
$559$		−	9740.02i		−	0.736957i
$560$	−3110.32	−	1315.65i	−0.234705	−	0.0992793i
$561$	3244.71	+	4798.63i	0.244192	+	0.361138i
$562$	1684.99			0.126472
$563$	−12328.9			−0.922918			−0.461459	−	0.887161i	$-0.652674\pi$
$563$	−12328.9			−0.922918			−0.461459	+	0.887161i	$0.652674\pi$
$564$	7846.15	−	5305.37i	0.585784	−	0.396093i
$565$			11204.5i			0.834298i
$566$	523.736			0.0388945
$567$	5347.76	+	12397.0i	0.396093	+	0.918210i
$568$	6123.87			0.452380
$569$			8075.58i			0.594984i	0.954724	+	0.297492i	$0.0961501\pi$
$569$			8075.58i			0.594984i	−0.954724	+	0.297492i	$0.903850\pi$
$570$	12444.6	−	8414.70i	0.914466	−	0.618339i
$571$	−19067.1			−1.39743			−0.698717	−	0.715398i	$-0.746245\pi$
$571$	−19067.1			−1.39743			−0.698717	+	0.715398i	$0.746245\pi$
$572$	1589.83			0.116213
$573$	1532.16	+	2265.92i	0.111705	+	0.165201i
$574$	−4439.07	+	10494.4i	−0.322793	+	0.763113i
$575$			753.544i			0.0546521i
$576$	−643.651	+	1603.65i	−0.0465604	+	0.116005i
$577$		−	11243.2i		−	0.811195i	−0.914052	−	0.405598i	$-0.867063\pi$
$577$		−	11243.2i		−	0.811195i	0.914052	−	0.405598i	$-0.132937\pi$
$578$			3682.40i			0.264996i
$579$	−14811.8	+	10015.4i	−1.06314	+	0.718869i
$580$			2638.84i			0.188917i
$581$	−18115.0	−	7662.54i	−1.29352	−	0.547153i
$582$	−2356.23	+	1593.22i	−0.167816	+	0.113473i
$583$	4968.72			0.352973
$584$	3182.43			0.225496
$585$	5642.88	+	2264.86i	0.398811	+	0.160069i
$586$			7647.96i			0.539137i
$587$	−11283.4			−0.793382			−0.396691	−	0.917952i	$-0.629842\pi$
$587$	−11283.4			−0.793382			−0.396691	+	0.917952i	$0.629842\pi$
$588$	−6978.70	−	1456.75i	−0.489450	−	0.102169i
$589$	40370.6			2.82418
$590$			1908.28i			0.133157i
$591$	−7814.44	−	11556.8i	−0.543897	−	0.804373i
$592$	−1184.00			−0.0821995
$593$	−18072.4			−1.25151			−0.625756	−	0.780019i	$-0.715209\pi$
$593$	−18072.4			−1.25151			−0.625756	+	0.780019i	$0.715209\pi$
$594$	−1192.37	−	5516.47i	−0.0823630	−	0.381049i
$595$	−10774.1	−	4557.40i	−0.742345	−	0.314009i
$596$		−	14252.5i		−	0.979541i
$597$	5420.27	+	8016.08i	0.371586	+	0.549542i
$598$			6095.14i			0.416804i
$599$			1956.58i			0.133462i	0.997771	+	0.0667311i	$0.0212570\pi$
$599$			1956.58i			0.133462i	−0.997771	+	0.0667311i	$0.978743\pi$
$600$	113.766	+	168.250i	0.00774082	+	0.0114480i
$601$			21338.4i			1.44827i	0.689658	+	0.724135i	$0.257761\pi$
$601$			21338.4i			1.44827i	−0.689658	+	0.724135i	$0.742239\pi$
$602$	7112.79	−	16815.3i	0.481554	−	1.13844i
$603$	−82.7514	+	206.174i	−0.00558855	+	0.0139238i
$604$	5882.52			0.396286
$605$	10558.2			0.709508
$606$	6476.07	+	9577.51i	0.434113	+	0.642013i
$607$			14240.1i			0.952203i	0.879390	+	0.476102i	$0.157951\pi$
$607$			14240.1i			0.952203i	−0.879390	+	0.476102i	$0.842049\pi$
$608$	4058.81			0.270734
$609$	1076.03	+	5465.68i	0.0715978	+	0.363679i
$610$	6961.49			0.462070
$611$		−	9004.63i		−	0.596217i
$612$	−2229.60	+	5555.03i	−0.147265	+	0.366910i
$613$	−5847.24			−0.385265			−0.192633	−	0.981271i	$-0.561703\pi$
$613$	−5847.24			−0.385265			−0.192633	+	0.981271i	$0.561703\pi$
$614$	1324.88			0.0870812
$615$	15091.2	−	10204.3i	0.989490	−	0.669068i
$616$	2744.70	+	1161.00i	0.179524	+	0.0759380i
$617$		−	18432.4i		−	1.20269i	−0.798988	−	0.601346i	$-0.794631\pi$
$617$		−	18432.4i		−	1.20269i	0.798988	−	0.601346i	$-0.205369\pi$
$618$	−7842.04	+	5302.59i	−0.510442	+	0.345148i
$619$		−	23346.7i		−	1.51596i	−0.652276	−	0.757982i	$-0.726186\pi$
$619$		−	23346.7i		−	1.51596i	0.652276	−	0.757982i	$-0.273814\pi$
$620$			14509.7i			0.939876i
$621$	21149.2	−	4571.35i	1.36665	−	0.295398i
$622$		−	7247.82i		−	0.467220i
$623$	−6385.47	−	2701.03i	−0.410640	−	0.173699i
$624$	920.215	+	1360.91i	0.0590354	+	0.0873079i
$625$	−16211.9			−1.03756
$626$	16680.3			1.06498
$627$	−10981.7	+	7425.55i	−0.699468	+	0.472963i
$628$			4052.57i			0.257508i
$629$	−4101.36			−0.259987
$630$	8087.98	+	8030.87i	0.511481	+	0.507869i
$631$	−1055.71			−0.0666041			−0.0333021	−	0.999445i	$-0.510602\pi$
$631$	−1055.71			−0.0666041			−0.0333021	+	0.999445i	$0.510602\pi$
$632$			295.785i			0.0186166i
$633$	4976.49	−	3364.98i	0.312477	−	0.211289i
$634$	−14933.1			−0.935441
$635$	−14822.2			−0.926301
$636$	2875.97	+	4253.29i	0.179307	+	0.265179i
$637$	−4863.66	+	4720.42i	−0.302520	+	0.293610i
$638$		−	2328.65i		−	0.144502i
$639$	−19180.8	−	7698.50i	−1.18745	−	0.476601i
$640$			1458.78i			0.0900992i
$641$		−	16537.6i		−	1.01903i	−0.860462	−	0.509514i	$-0.829825\pi$
$641$		−	16537.6i		−	1.01903i	0.860462	−	0.509514i	$-0.170175\pi$
$642$	5849.18	−	3955.07i	0.359577	−	0.243137i
$643$		−	7150.79i		−	0.438568i	−0.975661	−	0.219284i	$-0.929628\pi$
$643$		−	7150.79i		−	0.438568i	0.975661	−	0.219284i	$-0.0703722\pi$
$644$	−4451.06	+	10522.7i	−0.272355	+	0.643871i
$645$	−24180.8	+	16350.5i	−1.47615	+	0.998139i
$646$	14059.7			0.856300
$647$	23066.7			1.40161			0.700807	−	0.713351i	$-0.252823\pi$
$647$	23066.7			1.40161			0.700807	+	0.713351i	$0.252823\pi$
$648$	4032.00	−	4213.69i	0.244432	−	0.255447i
$649$		−	1683.96i		−	0.101851i
$650$	193.092			0.0116518
$651$	5916.57	+	30053.1i	0.356204	+	1.80933i
$652$	−1266.31			−0.0760620
$653$			14207.3i			0.851418i	0.904860	+	0.425709i	$0.139975\pi$
$653$			14207.3i			0.851418i	−0.904860	+	0.425709i	$0.860025\pi$
$654$	−1648.21	−	2437.55i	−0.0985475	−	0.145743i
$655$	25119.8			1.49849
$656$	4922.01			0.292946
$657$	−9967.78	−	4000.73i	−0.591903	−	0.237570i
$658$	6575.76	−	15545.7i	0.389589	−	0.921024i
$659$		−	8857.27i		−	0.523566i	−0.965127	−	0.261783i	$-0.915689\pi$
$659$		−	8857.27i		−	0.523566i	0.965127	−	0.261783i	$-0.0843105\pi$
$660$	−2668.83	−	3946.95i	−0.157400	−	0.232780i
$661$		−	24205.8i		−	1.42435i	−0.702000	−	0.712177i	$-0.747709\pi$
$661$		−	24205.8i		−	1.42435i	0.702000	−	0.712177i	$-0.252291\pi$
$662$		−	22303.9i		−	1.30947i
$663$	3187.61	+	4714.19i	0.186722	+	0.276144i
$664$			8496.17i			0.496559i
$665$	10429.6	−	24656.6i	0.608186	−	1.43781i
$666$	3708.44	+	1488.44i	0.215765	+	0.0866006i
$667$	8927.64			0.518260
$668$	−2710.95			−0.157021
$669$	−12823.6	−	18964.9i	−0.741091	−	1.09600i
$670$			187.549i			0.0108144i
$671$	−6143.16			−0.353434
$672$	594.843	+	3021.49i	0.0341467	+	0.173447i
$673$	−10334.9			−0.591947			−0.295974	−	0.955196i	$-0.595644\pi$
$673$	−10334.9			−0.591947			−0.295974	+	0.955196i	$0.595644\pi$
$674$		−	5654.89i		−	0.323172i
$675$	−144.819	−	670.000i	−0.00825791	−	0.0382049i
$676$	−7226.15			−0.411137
$677$	−5022.07			−0.285101			−0.142551	−	0.989788i	$-0.545530\pi$
$677$	−5022.07			−0.285101			−0.142551	+	0.989788i	$0.545530\pi$
$678$	8463.76	−	5722.98i	0.479423	−	0.324174i
$679$	−1974.73	+	4668.43i	−0.111610	+	0.263856i
$680$			5053.21i			0.284973i
$681$	21987.3	−	14867.2i	1.23723	−	0.836585i
$682$		−	12804.1i		−	0.718905i
$683$			27859.9i			1.56080i	0.625279	+	0.780401i	$0.284985\pi$
$683$			27859.9i			1.56080i	−0.625279	+	0.780401i	$0.715015\pi$
$684$	−12712.7	−	5102.45i	−0.710647	−	0.285230i
$685$		−	7206.57i		−	0.401969i
$686$	−11843.8	+	4597.62i	−0.659183	+	0.255886i
$687$	895.499	+	1324.36i	0.0497313	+	0.0735480i
$688$	−7886.60			−0.437026
$689$	4881.28			0.269902
$690$	15132.0	−	10231.9i	0.834875	−	0.564522i
$691$		−	28475.3i		−	1.56766i	−0.620977	−	0.783828i	$-0.713264\pi$
$691$		−	28475.3i		−	1.56766i	0.620977	−	0.783828i	$-0.286736\pi$
$692$	−2732.27			−0.150095
$693$	−7137.23	−	7086.83i	−0.391228	−	0.388465i
$694$	−24711.9			−1.35166
$695$			21741.3i			1.18661i
$696$	1993.35	−	1347.85i	0.108560	−	0.0734055i
$697$	17049.8			0.926552
$698$	−8902.13			−0.482737
$699$	−4729.44	−	6994.40i	−0.255914	−	0.378473i
$700$	333.356	+	141.008i	0.0179995	+	0.00761373i
$701$			8813.22i			0.474851i	0.971406	+	0.237426i	$0.0763036\pi$
$701$			8813.22i			0.474851i	−0.971406	+	0.237426i	$0.923696\pi$
$702$	−1171.39	−	5419.39i	−0.0629789	−	0.291370i
$703$		−	9385.99i		−	0.503555i
$704$		−	1287.30i		−	0.0689162i
$705$	−22355.1	+	15116.0i	−1.19425	+	0.807519i
$706$			18164.5i			0.968316i
$707$	18976.1	+	8026.79i	1.00943	+	0.426985i
$708$	1441.49	−	974.699i	0.0765177	−	0.0517393i
$709$	15687.4			0.830961			0.415480	−	0.909602i	$-0.363613\pi$
$709$	15687.4			0.830961			0.415480	+	0.909602i	$0.363613\pi$
$710$	−17448.0			−0.922272
$711$	371.840	−	926.437i	0.0196134	−	0.0488665i
$712$			2994.88i			0.157637i
$713$	49088.6			2.57838
$714$	2060.53	+	10466.4i	0.108002	+	0.548594i
$715$	−4529.72			−0.236926
$716$			3550.15i			0.185301i
$717$	15396.6	+	22770.1i	0.801947	+	1.18600i
$718$	−15636.5			−0.812741
$719$	−12216.1			−0.633635			−0.316817	−	0.948487i	$-0.602614\pi$
$719$	−12216.1			−0.633635			−0.316817	+	0.948487i	$0.602614\pi$
$720$	1833.88	−	4569.10i	0.0949233	−	0.236501i
$721$	−6572.32	+	15537.6i	−0.339481	+	0.802564i
$722$			18457.6i			0.951413i
$723$	−11210.6	−	16579.4i	−0.576662	−	0.852829i
$724$		−	1478.20i		−	0.0758794i
$725$		−	282.825i		−	0.0144881i
$726$	−5392.86	−	7975.53i	−0.275685	−	0.407713i
$727$			24122.4i			1.23061i	0.788291	+	0.615303i	$0.210966\pi$
$727$			24122.4i			1.23061i	−0.788291	+	0.615303i	$0.789034\pi$
$728$	2696.40	+	1140.56i	0.137274	+	0.0580661i
$729$	−17925.9	+	8129.08i	−0.910731	+	0.413000i
$730$	−9067.33			−0.459722
$731$	−27319.1			−1.38226
$732$	−3555.75	−	5258.62i	−0.179541	−	0.265525i
$733$			25765.3i			1.29831i	0.760655	+	0.649157i	$0.224878\pi$
$733$			25765.3i			1.29831i	−0.760655	+	0.649157i	$0.775122\pi$
$734$	7023.44			0.353188
$735$	19883.6	+	4150.55i	0.997848	+	0.208293i
$736$	4935.30			0.247171
$737$		−	165.503i		−	0.00827188i
$738$	−15416.4	−	6187.61i	−0.768950	−	0.308630i
$739$	21233.2			1.05694			0.528468	−	0.848953i	$-0.322767\pi$
$739$	21233.2			1.05694			0.528468	+	0.848953i	$0.322767\pi$
$740$	3373.44			0.167581
$741$	−10788.4	+	7294.87i	−0.534849	+	0.361652i
$742$	8427.10	+	3564.63i	0.416939	+	0.176363i
$743$		−	9740.21i		−	0.480934i	−0.970657	−	0.240467i	$-0.922699\pi$
$743$		−	9740.21i		−	0.480934i	0.970657	−	0.240467i	$-0.0773005\pi$
$744$	10960.4	−	7411.17i	0.540093	−	0.365197i
$745$			40608.2i			1.99700i
$746$			11419.4i			0.560445i
$747$	10680.8	−	26611.1i	0.523146	−	1.30341i
$748$		−	4459.20i		−	0.217974i
$749$	4902.12	−	11589.1i	0.239145	−	0.565361i
$750$	7968.65	+	11784.9i	0.387965	+	0.573764i
$751$	−26128.4			−1.26956			−0.634779	−	0.772694i	$-0.718909\pi$
$751$	−26128.4			−1.26956			−0.634779	+	0.772694i	$0.718909\pi$
$752$	−7291.15			−0.353565
$753$	5658.53	−	3826.16i	0.273849	−	0.185170i
$754$		−	2287.67i		−	0.110493i
$755$	−16760.4			−0.807912
$756$	1935.29	−	10211.5i	0.0931028	−	0.491255i
$757$	24595.2			1.18088			0.590441	−	0.807081i	$-0.298954\pi$
$757$	24595.2			1.18088			0.590441	+	0.807081i	$0.298954\pi$
$758$			9807.35i			0.469946i
$759$	−13353.2	+	9029.09i	−0.638590	+	0.431799i
$760$	−11564.3			−0.551949
$761$	5671.31			0.270151			0.135075	−	0.990835i	$-0.456872\pi$
$761$	5671.31			0.270151			0.135075	+	0.990835i	$0.456872\pi$
$762$	7570.79	+	11196.5i	0.359922	+	0.532292i
$763$	−4829.55	−	2042.88i	−0.229150	−	0.0969294i
$764$		−	2105.64i		−	0.0997111i
$765$	6352.55	−	15827.3i	0.300231	−	0.748023i
$766$			9795.14i			0.462027i
$767$		−	1654.33i		−	0.0778804i
$768$	1101.95	−	745.108i	0.0517748	−	0.0350088i
$769$		−	14542.6i		−	0.681950i	−0.940072	−	0.340975i	$-0.889243\pi$
$769$		−	14542.6i		−	0.681950i	0.940072	−	0.340975i	$-0.110757\pi$
$770$	−7820.16	−	3307.89i	−0.365999	−	0.154816i
$771$	1810.63	−	1224.30i	0.0845762	−	0.0571883i
$772$	13764.1			0.641685
$773$	7326.80			0.340914			0.170457	−	0.985365i	$-0.445476\pi$
$773$	7326.80			0.340914			0.170457	+	0.985365i	$0.445476\pi$
$774$	24701.9	+	9914.50i	1.14715	+	0.460425i
$775$		−	1555.11i		−	0.0720791i
$776$	2189.56			0.101289
$777$	6987.20	−	1375.58i	0.322606	−	0.0635116i
$778$	484.874			0.0223439
$779$			39018.5i			1.79459i
$780$	−2621.87	−	3877.50i	−0.120356	−	0.177996i
$781$	15397.0			0.705439
$782$	17095.8			0.781772
$783$	−7937.86	+	1715.75i	−0.362294	+	0.0783089i
$784$	3822.17	+	3938.16i	0.174115	+	0.179399i
$785$		−	11546.5i		−	0.524985i
$786$	−12830.6	−	18975.2i	−0.582253	−	0.861098i
$787$			21254.9i			0.962715i	0.876524	+	0.481358i	$0.159856\pi$
$787$			21254.9i			0.962715i	−0.876524	+	0.481358i	$0.840144\pi$
$788$			10739.4i			0.485500i
$789$	2176.78	+	3219.26i	0.0982199	+	0.145258i
$790$		−	842.746i		−	0.0379539i
$791$	7093.37	−	16769.4i	0.318851	−	0.753793i
$792$	−1618.31	+	4032.00i	−0.0726062	+	0.180898i
$793$	−6035.05			−0.270253
$794$	−4981.98			−0.222675
$795$	−8194.17	−	12118.4i	−0.365556	−	0.540624i
$796$		−	7449.06i		−	0.331690i
$797$	−17739.5			−0.788412			−0.394206	−	0.919022i	$-0.628980\pi$
$797$	−17739.5			−0.788412			−0.394206	+	0.919022i	$0.628980\pi$
$798$	−23952.5	+	4715.53i	−1.06254	+	0.209183i
$799$	−25256.5			−1.11828
$800$		−	156.349i		−	0.00690971i
$801$	3764.95	−	9380.35i	0.166078	−	0.413781i
$802$	−9427.93			−0.415102
$803$	8001.46			0.351638
$804$	141.672	−	95.7953i	0.00621443	−	0.00420204i
$805$	12681.9	−	29981.2i	0.555253	−	1.31267i
$806$		−	12578.7i		−	0.549711i
$807$	16355.4	−	11059.1i	0.713430	−	0.482403i
$808$		−	8900.05i		−	0.387503i
$809$			32496.1i			1.41224i	0.708091	+	0.706121i	$0.249556\pi$
$809$			32496.1i			1.41224i	−0.708091	+	0.706121i	$0.750444\pi$
$810$	−11487.9	+	12005.6i	−0.498327	+	0.520782i
$811$		−	11851.6i		−	0.513153i	−0.966524	−	0.256576i	$-0.917405\pi$
$811$		−	11851.6i		−	0.513153i	0.966524	−	0.256576i	$-0.0825945\pi$
$812$	1670.60	−	3949.45i	0.0722002	−	0.170688i
$813$	−749.315	−	1108.17i	−0.0323243	−	0.0478046i
$814$	−2976.89			−0.128182
$815$	3607.95			0.155069
$816$	3817.13	−	2581.05i	0.163758	−	0.110729i
$817$		−	62519.9i		−	2.67723i
$818$	1856.06			0.0793346
$819$	−7011.63	−	6962.12i	−0.299153	−	0.297041i
$820$	−14023.7			−0.597232
$821$			39153.8i			1.66440i	0.554472	+	0.832202i	$0.312920\pi$
$821$			39153.8i			1.66440i	−0.554472	+	0.832202i	$0.687080\pi$
$822$	−5443.75	+	3680.93i	−0.230989	+	0.156189i
$823$	−27730.9			−1.17453			−0.587265	−	0.809395i	$-0.699795\pi$
$823$	−27730.9			−1.17453			−0.587265	+	0.809395i	$0.699795\pi$
$824$	7287.33			0.308090
$825$	286.039	+	423.025i	0.0120710	+	0.0178519i
$826$	1208.09	−	2856.05i	0.0508898	−	0.120308i
$827$		−	27135.3i		−	1.14098i	−0.821306	−	0.570488i	$-0.806754\pi$
$827$		−	27135.3i		−	1.14098i	0.821306	−	0.570488i	$-0.193246\pi$
$828$	−15458.0	−	6204.32i	−0.648796	−	0.260405i
$829$			32701.0i			1.37003i	0.728531	+	0.685013i	$0.240204\pi$
$829$			32701.0i			1.37003i	−0.728531	+	0.685013i	$0.759796\pi$
$830$		−	24207.2i		−	1.01234i
$831$	14703.8	−	9942.31i	0.613800	−	0.415036i
$832$		−	1264.65i		−	0.0526969i
$833$	13240.0	+	13641.7i	0.550705	+	0.567417i
$834$	16423.1	−	11104.9i	0.681877	−	0.461068i
$835$	7724.01			0.320120
$836$	10204.9			0.422182
$837$	−43646.3	+	9434.05i	−1.80243	+	0.389592i
$838$			1194.28i			0.0492310i
$839$	−30299.6			−1.24679			−0.623396	−	0.781906i	$-0.714247\pi$
$839$	−30299.6			−1.24679			−0.623396	+	0.781906i	$0.714247\pi$
$840$	−1694.82	−	8608.80i	−0.0696153	−	0.353609i
$841$	21038.2			0.862611
$842$			8391.41i			0.343453i
$843$	2452.16	+	3626.51i	0.100186	+	0.148166i
$844$	−4624.48			−0.188603
$845$	20588.7			0.838191
$846$	22836.8	+	9165.93i	0.928069	+	0.372496i
$847$	−15802.0	−	6684.19i	−0.641044	−	0.271159i
$848$		−	3952.43i		−	0.160055i
$849$	762.188	+	1127.21i	0.0308106	+	0.0455661i
$850$		−	541.590i		−	0.0218546i
$851$		−	11412.9i		−	0.459728i
$852$	8912.00	+	13180.0i	0.358357	+	0.529977i
$853$		−	34643.9i		−	1.39060i	−0.718718	−	0.695301i	$-0.755271\pi$
$853$		−	34643.9i		−	1.39060i	0.718718	−	0.695301i	$-0.244729\pi$
$854$	−10419.0	−	4407.18i	−0.417483	−	0.176593i
$855$	36220.9	+	14537.8i	1.44881	+	0.581501i
$856$	−5435.44			−0.217032
$857$	−3623.96			−0.144448			−0.0722241	−	0.997388i	$-0.523010\pi$
$857$	−3623.96			−0.144448			−0.0722241	+	0.997388i	$0.523010\pi$
$858$	2313.66	+	3421.69i	0.0920596	+	0.136148i
$859$			16781.9i			0.666578i	0.942825	+	0.333289i	$0.108158\pi$
$859$			16781.9i			0.666578i	−0.942825	+	0.333289i	$0.891842\pi$
$860$	22470.4			0.890971
$861$	−29046.5	+	5718.41i	−1.14971	+	0.226345i
$862$	26952.0			1.06495
$863$		−	25243.4i		−	0.995707i	−0.867261	−	0.497853i	$-0.834122\pi$
$863$		−	25243.4i		−	0.995707i	0.867261	−	0.497853i	$-0.165878\pi$
$864$	−4388.14	+	948.486i	−0.172786	+	0.0373474i
$865$	7784.76			0.306000
$866$	21649.9			0.849529
$867$	−7925.41	+	5358.97i	−0.310451	+	0.209919i
$868$	9185.80	−	21716.1i	0.359201	−	0.849183i
$869$			743.681i			0.0290307i
$870$	−5679.42	+	3840.28i	−0.221322	+	0.149653i
$871$		−	162.590i		−	0.00632510i
$872$			2265.13i			0.0879666i
$873$	−6857.99	−	2752.56i	−0.265874	−	0.106713i
$874$			39123.9i			1.51417i
$875$	23349.6	+	9876.77i	0.902125	+	0.381595i
$876$	4631.35	+	6849.34i	0.178629	+	0.264176i
$877$	−20237.6			−0.779219			−0.389610	−	0.920980i	$-0.627390\pi$
$877$	−20237.6			−0.779219			−0.389610	+	0.920980i	$0.627390\pi$
$878$	−21717.9			−0.834787
$879$	−16460.2	+	11130.0i	−0.631615	+	0.427082i
$880$			3667.77i			0.140500i
$881$	−33855.3			−1.29468			−0.647340	−	0.762201i	$-0.724119\pi$
$881$	−33855.3			−1.29468			−0.647340	+	0.762201i	$0.724119\pi$
$882$	−7020.76	−	17139.8i	−0.268029	−	0.654340i
$883$	−5294.24			−0.201773			−0.100886	−	0.994898i	$-0.532168\pi$
$883$	−5294.24			−0.201773			−0.100886	+	0.994898i	$0.532168\pi$
$884$		−	4380.73i		−	0.166674i
$885$	−4107.07	+	2777.10i	−0.155998	+	0.105482i
$886$	22188.9			0.841368
$887$	15305.5			0.579377			0.289688	−	0.957121i	$-0.406448\pi$
$887$	15305.5			0.579377			0.289688	+	0.957121i	$0.406448\pi$
$888$	−1723.06	−	2548.25i	−0.0651151	−	0.0962992i
$889$	22183.8	+	9383.64i	0.836918	+	0.354013i
$890$		−	8532.97i		−	0.321377i
$891$	10137.5	−	10594.3i	0.381166	−	0.398343i
$892$			17623.4i			0.661521i
$893$		−	57799.5i		−	2.16594i
$894$	30674.9	−	20741.6i	1.14756	−	0.775953i
$895$		−	10115.0i		−	0.377775i
$896$	923.527	−	2183.30i	0.0344340	−	0.0814051i
$897$	−13118.2	+	8870.20i	−0.488299	+	0.330175i
$898$	24842.2			0.923156
$899$	−18424.3			−0.683519
$900$	−196.551	+	489.705i	−0.00727967	+	0.0181372i
$901$		−	13691.2i		−	0.506236i
$902$	12375.2			0.456818
$903$	46541.7	−	9162.68i	1.71518	−	0.337669i
$904$	−7865.08			−0.289368
$905$			4211.66i			0.154696i
$906$	8560.78	+	12660.6i	0.313921	+	0.464261i
$907$	4475.65			0.163849			0.0819247	−	0.996639i	$-0.473893\pi$
$907$	4475.65			0.163849			0.0819247	+	0.996639i	$0.473893\pi$
$908$	−20432.0			−0.746762
$909$	−11188.5	+	27876.1i	−0.408251	+	1.01715i
$910$	−7682.54	−	3249.68i	−0.279861	−	0.118380i
$911$		−	8307.63i		−	0.302134i	−0.988524	−	0.151067i	$-0.951729\pi$
$911$		−	8307.63i		−	0.302134i	0.988524	−	0.151067i	$-0.0482709\pi$
$912$	5906.74	+	8735.52i	0.214465	+	0.317173i
$913$			21361.6i			0.774333i
$914$			29259.6i			1.05888i
$915$	10131.0	+	14982.8i	0.366033	+	0.541329i
$916$		−	1230.68i		−	0.0443917i
$917$	−37595.9	−	15902.9i	−1.35390	−	0.572693i
$918$	−15200.5	+	3285.55i	−0.546503	+	0.118125i
$919$	38868.6			1.39516			0.697582	−	0.716505i	$-0.254259\pi$
$919$	38868.6			1.39516			0.697582	+	0.716505i	$0.254259\pi$
$920$	−14061.6			−0.503910
$921$	1928.09	+	2851.46i	0.0689822	+	0.102018i
$922$		−	5719.26i		−	0.204288i
$923$	15126.1			0.539415
$924$	1495.59	+	7596.83i	0.0532482	+	0.270473i
$925$	−361.557			−0.0128518
$926$		−	4935.64i		−	0.175157i
$927$	−22824.9	−	9161.13i	−0.808703	−	0.324586i
$928$	−1852.35			−0.0655241
$929$	−52959.0			−1.87032			−0.935160	−	0.354225i	$-0.884745\pi$
$929$	−52959.0			−1.87032			−0.935160	+	0.354225i	$0.884745\pi$
$930$	−31228.3	+	21115.8i	−1.10109	+	0.744532i
$931$	−31219.2	+	30299.7i	−1.09900	+	1.06663i
$932$			6499.65i			0.228437i
$933$	15599.0	−	10547.7i	0.547363	−	0.370113i
$934$		−	6776.35i		−	0.237397i
$935$			12705.1i			0.444386i
$936$	−1589.83	+	3961.05i	−0.0555184	+	0.138324i
$937$			19402.2i			0.676460i	0.941063	+	0.338230i	$0.109828\pi$
$937$			19402.2i			0.676460i	−0.941063	+	0.338230i	$0.890172\pi$
$938$	118.734	−	280.698i	0.00413305	−	0.00977090i
$939$	24274.7	+	35900.1i	0.843638	+	1.24766i
$940$	20773.9			0.720817
$941$	28112.1			0.973886			0.486943	−	0.873434i	$-0.338112\pi$
$941$	28112.1			0.973886			0.486943	+	0.873434i	$0.338112\pi$
$942$	−8722.09	+	5897.66i	−0.301678	+	0.203987i
$943$			47444.6i			1.63840i
$944$	−1339.53			−0.0461842
$945$	−5513.99	+	29094.5i	−0.189810	+	1.00153i
$946$	−19829.0			−0.681497
$947$		−	10995.9i		−	0.377317i	−0.982043	−	0.188659i	$-0.939586\pi$
$947$		−	10995.9i		−	0.377317i	0.982043	−	0.188659i	$-0.0604140\pi$
$948$	−636.600	+	430.453i	−0.0218099	+	0.0147473i
$949$	7860.65			0.268880
$950$	1239.43			0.0423289
$951$	−21732.0	−	32139.6i	−0.741019	−	1.09590i
$952$	3199.09	−	7562.93i	0.108911	−	0.257475i
$953$			8056.15i			0.273834i	0.990582	+	0.136917i	$0.0437194\pi$
$953$			8056.15i			0.273834i	−0.990582	+	0.136917i	$0.956281\pi$
$954$	−4968.72	+	12379.5i	−0.168625	+	0.420128i
$955$			5999.35i			0.203282i
$956$		−	21159.5i		−	0.715843i
$957$	5011.80	−	3388.85i	0.169288	−	0.114468i
$958$		−	31846.8i		−	1.07403i
$959$	−4562.34	+	10785.8i	−0.153624	+	0.363182i
$960$	−3139.65	+	2122.95i	−0.105554	+	0.0713729i
$961$	−71514.8			−2.40055
$962$	−2924.50			−0.0980142
$963$	17024.5	+	6833.06i	0.569685	+	0.228652i
$964$			15406.7i			0.514747i
$965$	−39216.5			−1.30821
$966$	−29125.0	+	5733.85i	−0.970063	+	0.190977i
$967$	−56661.7			−1.88430			−0.942150	−	0.335191i	$-0.891199\pi$
$967$	−56661.7			−1.88430			−0.942150	+	0.335191i	$0.891199\pi$
$968$			7411.38i			0.246086i
$969$	20460.9	+	30259.7i	0.678326	+	1.00318i
$970$	−6238.47			−0.206500
$971$	51301.3			1.69551			0.847754	−	0.530390i	$-0.177954\pi$
$971$	51301.3			1.69551			0.847754	+	0.530390i	$0.177954\pi$
$972$	14936.6	+	2545.68i	0.492893	+	0.0840050i
$973$	13764.0	−	32539.3i	0.453498	−	1.07211i
$974$		−	20221.6i		−	0.665239i
$975$	281.005	+	415.580i	0.00923011	+	0.0136505i
$976$			4886.65i			0.160264i
$977$			30641.0i			1.00337i	0.865050	+	0.501686i	$0.167287\pi$
$977$			30641.0i			1.00337i	−0.865050	+	0.501686i	$0.832713\pi$
$978$	−1842.85	−	2725.40i	−0.0602533	−	0.0891090i
$979$			7529.91i			0.245819i
$980$	−10890.1	−	11220.6i	−0.354971	−	0.365743i
$981$	2847.56	−	7094.68i	0.0926765	−	0.230903i
$982$	−603.423			−0.0196090
$983$	−3134.58			−0.101707			−0.0508533	−	0.998706i	$-0.516194\pi$
$983$	−3134.58			−0.101707			−0.0508533	+	0.998706i	$0.516194\pi$
$984$	7162.95	+	10593.3i	0.232060	+	0.343195i
$985$		−	30598.4i		−	0.989794i
$986$	−6416.51			−0.207245
$987$	43027.7	−	8470.88i	1.38762	−	0.273183i
$988$	10025.3			0.322822
$989$		−	76021.1i		−	2.44422i
$990$	4610.86	−	11487.9i	0.148023	−	0.368798i
$991$	46982.4			1.50600			0.753000	−	0.658021i	$-0.228606\pi$
$991$	46982.4			1.50600			0.753000	+	0.658021i	$0.228606\pi$
$992$	−10185.1			−0.325987
$993$	48003.4	−	32458.7i	1.53408	−	1.03731i
$994$	26113.8	+	11046.0i	0.833278	+	0.352473i
$995$			21223.8i			0.676220i
$996$	−18285.8	+	12364.4i	−0.581734	+	0.393354i
$997$		−	6029.60i		−	0.191534i	−0.995404	−	0.0957670i	$-0.969470\pi$
$997$		−	6029.60i		−	0.191534i	0.995404	−	0.0957670i	$-0.0305304\pi$
$998$			2350.44i			0.0745510i
$999$	2193.37	+	10147.6i	0.0694648	+	0.321376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.4.d.a.41.4	yes	8
3.2	odd	2	inner	42.4.d.a.41.5	yes	8
4.3	odd	2		336.4.k.c.209.2		8
7.2	even	3		294.4.f.b.227.3		16
7.3	odd	6		294.4.f.b.215.8		16
7.4	even	3		294.4.f.b.215.5		16
7.5	odd	6		294.4.f.b.227.2		16
7.6	odd	2	inner	42.4.d.a.41.1	✓	8
12.11	even	2		336.4.k.c.209.8		8
21.2	odd	6		294.4.f.b.227.8		16
21.5	even	6		294.4.f.b.227.5		16
21.11	odd	6		294.4.f.b.215.2		16
21.17	even	6		294.4.f.b.215.3		16
21.20	even	2	inner	42.4.d.a.41.8	yes	8
28.27	even	2		336.4.k.c.209.7		8
84.83	odd	2		336.4.k.c.209.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.d.a.41.1	✓	8	7.6	odd	2	inner
42.4.d.a.41.4	yes	8	1.1	even	1	trivial
42.4.d.a.41.5	yes	8	3.2	odd	2	inner
42.4.d.a.41.8	yes	8	21.20	even	2	inner
294.4.f.b.215.2		16	21.11	odd	6
294.4.f.b.215.3		16	21.17	even	6
294.4.f.b.215.5		16	7.4	even	3
294.4.f.b.215.8		16	7.3	odd	6
294.4.f.b.227.2		16	7.5	odd	6
294.4.f.b.227.3		16	7.2	even	3
294.4.f.b.227.5		16	21.5	even	6
294.4.f.b.227.8		16	21.2	odd	6
336.4.k.c.209.1		8	84.83	odd	2
336.4.k.c.209.2		8	4.3	odd	2
336.4.k.c.209.7		8	28.27	even	2
336.4.k.c.209.8		8	12.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	42.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +(4.30448 - 2.91058i) q^{3} -4.00000 q^{4} +11.3967 q^{5} +(-5.82116 - 8.60895i) q^{6} +(-17.0570 - 7.21506i) q^{7} +8.00000i q^{8} +(10.0570 - 25.0570i) q^{9} -22.7935i q^{10} +20.1141i q^{11} +(-17.2179 + 11.6423i) q^{12} +19.7601i q^{13} +(-14.4301 + 34.1141i) q^{14} +(49.0570 - 33.1711i) q^{15} +16.0000 q^{16} +55.4238 q^{17} +(-50.1141 - 20.1141i) q^{18} +126.838i q^{19} -45.5870 q^{20} +(-94.4217 + 18.5889i) q^{21} +40.2282 q^{22} +154.228i q^{23} +(23.2846 + 34.4358i) q^{24} +4.88590 q^{25} +39.5203 q^{26} +(-29.6402 - 137.129i) q^{27} +(68.2282 + 28.8602i) q^{28} -57.8859i q^{29} +(-66.3423 - 98.1141i) q^{30} -318.286i q^{31} -32.0000i q^{32} +(58.5437 + 86.5807i) q^{33} -110.848i q^{34} +(-194.395 - 82.2282i) q^{35} +(-40.2282 + 100.228i) q^{36} -74.0000 q^{37} +253.675 q^{38} +(57.5134 + 85.0570i) q^{39} +91.1740i q^{40} +307.626 q^{41} +(37.1777 + 188.843i) q^{42} -492.913 q^{43} -80.4564i q^{44} +(114.618 - 285.569i) q^{45} +308.456 q^{46} -455.697 q^{47} +(68.8716 - 46.5693i) q^{48} +(238.886 + 246.135i) q^{49} -9.77180i q^{50} +(238.570 - 161.315i) q^{51} -79.0405i q^{52} -247.027i q^{53} +(-274.259 + 59.2804i) q^{54} +229.235i q^{55} +(57.7205 - 136.456i) q^{56} +(369.171 + 545.970i) q^{57} -115.772 q^{58} -83.7204 q^{59} +(-196.228 + 132.685i) q^{60} +305.416i q^{61} -636.572 q^{62} +(-352.332 + 354.837i) q^{63} -64.0000 q^{64} +225.201i q^{65} +(173.161 - 117.087i) q^{66} -8.22820 q^{67} -221.695 q^{68} +(448.893 + 663.872i) q^{69} +(-164.456 + 388.790i) q^{70} -765.483i q^{71} +(200.456 + 80.4564i) q^{72} -397.803i q^{73} +148.000i q^{74} +(21.0312 - 14.2208i) q^{75} -507.351i q^{76} +(145.124 - 343.087i) q^{77} +(170.114 - 115.027i) q^{78} +36.9731 q^{79} +182.348 q^{80} +(-526.711 - 504.000i) q^{81} -615.251i q^{82} +1062.02 q^{83} +(377.687 - 74.3554i) q^{84} +631.651 q^{85} +985.826i q^{86} +(-168.482 - 249.169i) q^{87} -160.913 q^{88} +374.360 q^{89} +(-571.138 - 229.235i) q^{90} +(142.570 - 337.050i) q^{91} -616.913i q^{92} +(-926.396 - 1370.05i) q^{93} +911.394i q^{94} +1445.54i q^{95} +(-93.1386 - 137.743i) q^{96} -273.695i q^{97} +(492.270 - 477.772i) q^{98} +(504.000 + 202.289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 4 q^{7} - 60 q^{9} + 252 q^{15} + 128 q^{16} - 120 q^{18} - 168 q^{21} - 240 q^{22} + 320 q^{25} - 16 q^{28} + 312 q^{30} + 240 q^{36} - 592 q^{37} - 804 q^{39} - 216 q^{42} - 1696 q^{43}+ \cdots + 4032 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 4 * q^7 - 60 * q^9 + 252 * q^15 + 128 * q^16 - 120 * q^18 - 168 * q^21 - 240 * q^22 + 320 * q^25 - 16 * q^28 + 312 * q^30 + 240 * q^36 - 592 * q^37 - 804 * q^39 - 216 * q^42 - 1696 * q^43 + 1344 * q^46 + 2192 * q^49 + 504 * q^51 + 2532 * q^57 - 1488 * q^58 - 1008 * q^60 - 2496 * q^63 - 512 * q^64 + 496 * q^67 - 192 * q^70 + 480 * q^72 + 1080 * q^78 + 2824 * q^79 + 672 * q^84 - 3936 * q^85 + 960 * q^88 - 264 * q^91 - 1512 * q^93 + 4032 * q^99

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