LMFDB - Embedded newform 42.4.f.a.17.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,4,Mod(5,42)] 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("42.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.8
Root			$2.99617 - 0.151487i$ of defining polynomial
Character	$\chi$	$=$	42.17
Dual form			42.4.f.a.5.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(5.18952 + 0.262384i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-2.24534 - 3.88904i) q^{5} +(9.25090 - 4.73506i) q^{6} +(-9.71288 + 15.7690i) q^{7} -8.00000i q^{8} +(26.8623 + 2.72329i) q^{9} +(-7.77808 - 4.49068i) q^{10} +(-20.2835 - 11.7107i) q^{11} +(11.2880 - 17.4523i) q^{12} -5.91384i q^{13} +(-1.05425 + 37.0255i) q^{14} +(-10.6318 - 20.7714i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-58.0418 + 100.531i) q^{17} +(49.2502 - 22.1454i) q^{18} +(8.02533 - 4.63343i) q^{19} -17.9627 q^{20} +(-54.5428 + 79.2849i) q^{21} -46.8428 q^{22} +(-107.721 + 62.1928i) q^{23} +(2.09907 - 41.5162i) q^{24} +(52.4169 - 90.7888i) q^{25} +(-5.91384 - 10.2431i) q^{26} +(138.688 + 21.1808i) q^{27} +(35.1995 + 65.1843i) q^{28} -207.807i q^{29} +(-39.1862 - 25.3453i) q^{30} +(122.764 + 70.8780i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-102.189 - 66.0951i) q^{33} +232.167i q^{34} +(83.1348 + 2.36716i) q^{35} +(63.1584 - 87.6072i) q^{36} +(-149.838 - 259.526i) q^{37} +(9.26685 - 16.0507i) q^{38} +(1.55170 - 30.6900i) q^{39} +(-31.1123 + 17.9627i) q^{40} +508.379 q^{41} +(-15.1860 + 191.868i) q^{42} +391.127 q^{43} +(-81.1341 + 46.8428i) q^{44} +(-49.7240 - 110.583i) q^{45} +(-124.386 + 215.442i) q^{46} +(40.2575 + 69.7281i) q^{47} +(-37.8805 - 74.0072i) q^{48} +(-154.320 - 306.324i) q^{49} -209.668i q^{50} +(-327.587 + 506.481i) q^{51} +(-20.4862 - 11.8277i) q^{52} +(-258.697 - 149.359i) q^{53} +(261.396 - 102.002i) q^{54} +105.178i q^{55} +(126.152 + 77.7031i) q^{56} +(42.8634 - 21.9396i) q^{57} +(-207.807 - 359.932i) q^{58} +(-102.276 + 177.147i) q^{59} +(-93.2179 - 4.71312i) q^{60} +(-543.757 + 313.939i) q^{61} +283.512 q^{62} +(-303.854 + 397.139i) q^{63} -64.0000 q^{64} +(-22.9992 + 13.2786i) q^{65} +(-243.092 - 12.2908i) q^{66} +(51.3894 - 89.0091i) q^{67} +(232.167 + 402.126i) q^{68} +(-575.340 + 294.487i) q^{69} +(146.361 - 79.0348i) q^{70} -46.9785i q^{71} +(21.7863 - 214.898i) q^{72} +(-228.182 - 131.741i) q^{73} +(-519.053 - 299.675i) q^{74} +(295.840 - 457.397i) q^{75} -37.0674i q^{76} +(381.677 - 206.105i) q^{77} +(-28.0024 - 54.7084i) q^{78} +(533.634 + 924.281i) q^{79} +(-35.9254 + 62.2246i) q^{80} +(714.167 + 146.308i) q^{81} +(880.538 - 508.379i) q^{82} +270.436 q^{83} +(165.565 + 347.511i) q^{84} +521.294 q^{85} +(677.452 - 391.127i) q^{86} +(54.5252 - 1078.42i) q^{87} +(-93.6856 + 162.268i) q^{88} +(-443.765 - 768.624i) q^{89} +(-196.708 - 141.812i) q^{90} +(93.2551 + 57.4405i) q^{91} +497.543i q^{92} +(618.491 + 400.034i) q^{93} +(139.456 + 80.5151i) q^{94} +(-36.0392 - 20.8072i) q^{95} +(-139.618 - 90.3038i) q^{96} -219.564i q^{97} +(-573.614 - 376.249i) q^{98} +(-512.971 - 369.815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36}+ \cdots - 4284 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

Character values

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

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	5.18952	+	0.262384i	0.998724	+	0.0504958i
$3$	5.18952	+	0.262384i	0.998724	+	0.0504958i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	−2.24534	−	3.88904i	−0.200829	−	0.347846i	0.747967	−	0.663736i	$-0.231030\pi$
$5$	−2.24534	−	3.88904i	−0.200829	−	0.347846i	−0.948796	+	0.315890i	$0.897697\pi$
$6$	9.25090	−	4.73506i	0.629444	−	0.322180i
$7$	−9.71288	+	15.7690i	−0.524446	+	0.851443i
$7$	−9.71288	+	15.7690i	−0.524446	+	0.851443i
$8$		−	8.00000i		−	0.353553i
$9$	26.8623	+	2.72329i	0.994900	+	0.100863i
$10$	−7.77808	−	4.49068i	−0.245964	−	0.142008i
$11$	−20.2835	−	11.7107i	−0.555974	−	0.320992i	0.195554	−	0.980693i	$-0.437350\pi$
$11$	−20.2835	−	11.7107i	−0.555974	−	0.320992i	−0.751528	+	0.659701i	$0.770683\pi$
$12$	11.2880	−	17.4523i	0.271546	−	0.419836i
$13$		−	5.91384i		−	0.126170i	−0.998008	−	0.0630848i	$-0.979906\pi$
$13$		−	5.91384i		−	0.126170i	0.998008	−	0.0630848i	$-0.0200939\pi$
$14$	−1.05425	+	37.0255i	−0.0201258	+	0.706820i
$15$	−10.6318	−	20.7714i	−0.183008	−	0.357544i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−58.0418	+	100.531i	−0.828071	+	1.43426i	0.0714778	+	0.997442i	$0.477228\pi$
$17$	−58.0418	+	100.531i	−0.828071	+	1.43426i	−0.899549	+	0.436819i	$0.856105\pi$
$18$	49.2502	−	22.1454i	0.644910	−	0.289985i
$19$	8.02533	−	4.63343i	0.0969019	−	0.0559464i	−0.450766	−	0.892642i	$-0.648849\pi$
$19$	8.02533	−	4.63343i	0.0969019	−	0.0559464i	0.547668	+	0.836696i	$0.315516\pi$
$20$	−17.9627			−0.200829
$21$	−54.5428	+	79.2849i	−0.566772	+	0.823875i
$22$	−46.8428			−0.453951
$23$	−107.721	+	62.1928i	−0.976583	+	0.563830i	−0.901237	−	0.433327i	$-0.857339\pi$
$23$	−107.721	+	62.1928i	−0.976583	+	0.563830i	−0.0753461	+	0.997157i	$0.524006\pi$
$24$	2.09907	−	41.5162i	0.0178530	−	0.353102i
$25$	52.4169	−	90.7888i	0.419335	−	0.726310i
$26$	−5.91384	−	10.2431i	−0.0446077	−	0.0772628i
$27$	138.688	+	21.1808i	0.988538	+	0.150972i
$28$	35.1995	+	65.1843i	0.237574	+	0.439953i
$29$		−	207.807i		−	1.33065i	−0.746555	−	0.665324i	$-0.768293\pi$
$29$		−	207.807i		−	1.33065i	0.746555	−	0.665324i	$-0.231707\pi$
$30$	−39.1862	−	25.3453i	−0.238480	−	0.154247i
$31$	122.764	+	70.8780i	0.711262	+	0.410647i	0.811528	−	0.584314i	$-0.198636\pi$
$31$	122.764	+	70.8780i	0.711262	+	0.410647i	−0.100266	+	0.994961i	$0.531970\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−102.189	−	66.0951i	−0.539056	−	0.348657i
$34$			232.167i			1.17107i
$35$	83.1348	+	2.36716i	0.401496	+	0.0114321i
$36$	63.1584	−	87.6072i	0.292400	−	0.405589i
$37$	−149.838	−	259.526i	−0.665761	−	1.15313i	−0.979078	−	0.203483i	$-0.934774\pi$
$37$	−149.838	−	259.526i	−0.665761	−	1.15313i	0.313317	−	0.949648i	$-0.398560\pi$
$38$	9.26685	−	16.0507i	0.0395601	−	0.0685200i
$39$	1.55170	−	30.6900i	0.00637103	−	0.126009i
$40$	−31.1123	+	17.9627i	−0.122982	+	0.0710038i
$41$	508.379			1.93647			0.968237	−	0.250032i	$-0.0804412\pi$
$41$	508.379			1.93647			0.968237	+	0.250032i	$0.0804412\pi$
$42$	−15.1860	+	191.868i	−0.0557916	+	0.704902i
$43$	391.127			1.38712			0.693562	−	0.720397i	$-0.256041\pi$
$43$	391.127			1.38712			0.693562	+	0.720397i	$0.256041\pi$
$44$	−81.1341	+	46.8428i	−0.277987	+	0.160496i
$45$	−49.7240	−	110.583i	−0.164720	−	0.366329i
$46$	−124.386	+	215.442i	−0.398688	+	0.690548i
$47$	40.2575	+	69.7281i	0.124940	+	0.216402i	0.921709	−	0.387881i	$-0.126793\pi$
$47$	40.2575	+	69.7281i	0.124940	+	0.216402i	−0.796770	+	0.604283i	$0.793460\pi$
$48$	−37.8805	−	74.0072i	−0.113908	−	0.222542i
$49$	−154.320	−	306.324i	−0.449912	−	0.893073i
$50$		−	209.668i		−	0.593030i
$51$	−327.587	+	506.481i	−0.899439	+	1.39062i
$52$	−20.4862	−	11.8277i	−0.0546330	−	0.0315424i
$53$	−258.697	−	149.359i	−0.670467	−	0.387094i	0.125786	−	0.992057i	$-0.459855\pi$
$53$	−258.697	−	149.359i	−0.670467	−	0.387094i	−0.796254	+	0.604963i	$0.793188\pi$
$54$	261.396	−	102.002i	0.658730	−	0.257050i
$55$			105.178i			0.257858i
$56$	126.152	+	77.7031i	0.301031	+	0.185420i
$57$	42.8634	−	21.9396i	0.0996034	−	0.0509818i
$58$	−207.807	−	359.932i	−0.470455	−	0.814852i
$59$	−102.276	+	177.147i	−0.225682	+	0.390892i	−0.956524	−	0.291655i	$-0.905794\pi$
$59$	−102.276	+	177.147i	−0.225682	+	0.390892i	0.730842	+	0.682547i	$0.239128\pi$
$60$	−93.2179	−	4.71312i	−0.200573	−	0.0101410i
$61$	−543.757	+	313.939i	−1.14133	+	0.658946i	−0.946759	−	0.321943i	$-0.895664\pi$
$61$	−543.757	+	313.939i	−1.14133	+	0.658946i	−0.194569	+	0.980889i	$0.562331\pi$
$62$	283.512			0.580743
$63$	−303.854	+	397.139i	−0.607651	+	0.794204i
$64$	−64.0000			−0.125000
$65$	−22.9992	+	13.2786i	−0.0438876	+	0.0253385i
$66$	−243.092	−	12.2908i	−0.453372	−	0.0229226i
$67$	51.3894	−	89.0091i	0.0937048	−	0.162301i	−0.815363	−	0.578951i	$-0.803462\pi$
$67$	51.3894	−	89.0091i	0.0937048	−	0.162301i	0.909067	+	0.416649i	$0.136796\pi$
$68$	232.167	+	402.126i	0.414036	+	0.717131i
$69$	−575.340	+	294.487i	−1.00381	+	0.513798i
$70$	146.361	−	79.0348i	0.249907	−	0.134949i
$71$		−	46.9785i		−	0.0785256i	−0.999229	−	0.0392628i	$-0.987499\pi$
$71$		−	46.9785i		−	0.0785256i	0.999229	−	0.0392628i	$-0.0125010\pi$
$72$	21.7863	−	214.898i	0.0356604	−	0.351750i
$73$	−228.182	−	131.741i	−0.365845	−	0.211221i	0.305797	−	0.952097i	$-0.401077\pi$
$73$	−228.182	−	131.741i	−0.365845	−	0.211221i	−0.671642	+	0.740876i	$0.734411\pi$
$74$	−519.053	−	299.675i	−0.815387	−	0.470764i
$75$	295.840	−	457.397i	0.455476	−	0.704209i
$76$		−	37.0674i		−	0.0559464i
$77$	381.677	−	206.105i	0.564885	−	0.305038i
$78$	−28.0024	−	54.7084i	−0.0406493	−	0.0794167i
$79$	533.634	+	924.281i	0.759981	+	1.31633i	0.942860	+	0.333190i	$0.108125\pi$
$79$	533.634	+	924.281i	0.759981	+	1.31633i	−0.182878	+	0.983136i	$0.558541\pi$
$80$	−35.9254	+	62.2246i	−0.0502073	+	0.0869616i
$81$	714.167	+	146.308i	0.979653	+	0.200697i
$82$	880.538	−	508.379i	1.18584	−	0.684647i
$83$	270.436			0.357642			0.178821	−	0.983882i	$-0.442772\pi$
$83$	270.436			0.357642			0.178821	+	0.983882i	$0.442772\pi$
$84$	165.565	+	347.511i	0.215055	+	0.451388i
$85$	521.294			0.665203
$86$	677.452	−	391.127i	0.849436	−	0.490422i
$87$	54.5252	−	1078.42i	0.0671921	−	1.32895i
$88$	−93.6856	+	162.268i	−0.113488	+	0.196567i
$89$	−443.765	−	768.624i	−0.528528	−	0.915438i	−0.999447	−	0.0332610i	$-0.989411\pi$
$89$	−443.765	−	768.624i	−0.528528	−	0.915438i	0.470918	−	0.882177i	$-0.343923\pi$
$90$	−196.708	−	141.812i	−0.230387	−	0.166092i
$91$	93.2551	+	57.4405i	0.107426	+	0.0661692i
$92$			497.543i			0.563830i
$93$	618.491	+	400.034i	0.689618	+	0.446039i
$94$	139.456	+	80.5151i	0.153019	+	0.0883457i
$95$	−36.0392	−	20.8072i	−0.0389215	−	0.0224713i
$96$	−139.618	−	90.3038i	−0.148435	−	0.0960061i
$97$		−	219.564i		−	0.229828i	−0.993375	−	0.114914i	$-0.963341\pi$
$97$		−	219.564i		−	0.229828i	0.993375	−	0.114914i	$-0.0366593\pi$
$98$	−573.614	−	376.249i	−0.591263	−	0.387825i
$99$	−512.971	−	369.815i	−0.520763	−	0.375432i
$100$	−209.668	−	363.155i	−0.209668	−	0.363155i
$101$	−492.533	+	853.093i	−0.485237	+	0.840455i	−0.999856	−	0.0169642i	$-0.994600\pi$
$101$	−492.533	+	853.093i	−0.485237	+	0.840455i	0.514619	+	0.857419i	$0.327933\pi$
$102$	−60.9169	+	1204.84i	−0.0591341	+	1.16958i
$103$	−1112.87	+	642.516i	−1.06461	+	0.614650i	−0.926703	−	0.375796i	$-0.877369\pi$
$103$	−1112.87	+	642.516i	−1.06461	+	0.614650i	−0.137903	+	0.990446i	$0.544036\pi$
$104$	−47.3107			−0.0446077
$105$	430.809	+	34.0976i	0.400406	+	0.0316913i
$106$	−597.435			−0.547434
$107$	−158.409	+	91.4575i	−0.143121	+	0.0826311i	−0.569851	−	0.821748i	$-0.692999\pi$
$107$	−158.409	+	91.4575i	−0.143121	+	0.0826311i	0.426729	+	0.904379i	$0.359666\pi$
$108$	350.749	−	438.068i	0.312507	−	0.390306i
$109$	291.471	−	504.843i	0.256127	−	0.443625i	−0.709074	−	0.705134i	$-0.750887\pi$
$109$	291.471	−	504.843i	0.256127	−	0.443625i	0.965201	+	0.261509i	$0.0842201\pi$
$110$	105.178	+	182.174i	0.0911666	+	0.157905i
$111$	−709.490	−	1386.13i	−0.606683	−	1.18528i
$112$	296.204	+	8.43404i	0.249899	+	0.00711555i
$113$			2283.94i			1.90137i	0.310152	+	0.950687i	$0.399620\pi$
$113$			2283.94i			1.90137i	−0.310152	+	0.950687i	$0.600380\pi$
$114$	52.3020	−	80.8638i	0.0429696	−	0.0664350i
$115$	483.741	+	279.288i	0.392253	+	0.226467i
$116$	−719.865	−	415.614i	−0.576188	−	0.332662i
$117$	16.1051	−	158.859i	0.0127258	−	0.125526i
$118$			409.104i			0.319162i
$119$	−1021.52	−	1891.71i	−0.786914	−	1.45725i
$120$	−166.171	+	85.0545i	−0.126411	+	0.0647032i
$121$	−391.219	−	677.611i	−0.293928	−	0.509099i
$122$	−627.877	+	1087.51i	−0.465945	+	0.807041i
$123$	2638.25	+	133.390i	1.93400	+	0.0977838i
$124$	491.057	−	283.512i	0.355631	−	0.205324i
$125$	−1032.11			−0.738517
$126$	−129.151	+	991.720i	−0.0913150	+	0.701186i
$127$	−1554.48			−1.08613			−0.543064	−	0.839692i	$-0.682736\pi$
$127$	−1554.48			−1.08613			−0.543064	+	0.839692i	$0.682736\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	2029.76	+	102.625i	1.38535	+	0.0700439i
$130$	−26.5572	+	45.9983i	−0.0179170	+	0.0310332i
$131$	1047.46	+	1814.26i	0.698605	+	1.21002i	0.968950	+	0.247256i	$0.0795288\pi$
$131$	1047.46	+	1814.26i	0.698605	+	1.21002i	−0.270345	+	0.962763i	$0.587138\pi$
$132$	−433.338	+	221.804i	−0.285737	+	0.146254i
$133$	−4.88481	+	171.555i	−0.00318471	+	0.111847i
$134$		−	205.558i		−	0.132519i
$135$	−229.028	−	586.921i	−0.146012	−	0.374179i
$136$	804.251	+	464.335i	0.507088	+	0.292767i
$137$	−529.002	−	305.420i	−0.329896	−	0.190465i	0.325899	−	0.945405i	$-0.394333\pi$
$137$	−529.002	−	305.420i	−0.329896	−	0.190465i	−0.655795	+	0.754939i	$0.727666\pi$
$138$	−702.031	+	1085.41i	−0.433049	+	0.669535i
$139$		−	1806.61i		−	1.10241i	−0.834370	−	0.551204i	$-0.814169\pi$
$139$		−	1806.61i		−	1.10241i	0.834370	−	0.551204i	$-0.185831\pi$
$140$	174.470	−	283.253i	0.105324	−	0.170995i
$141$	190.622	+	372.419i	0.113853	+	0.222435i
$142$	−46.9785	−	81.3691i	−0.0277630	−	0.0480869i
$143$	−69.2553	+	119.954i	−0.0404994	+	0.0701470i
$144$	−177.163	−	394.001i	−0.102525	−	0.228010i
$145$	−808.170	+	466.597i	−0.462861	+	0.267233i
$146$	−526.964			−0.298711
$147$	−720.472	−	1630.17i	−0.404242	−	0.914652i
$148$	−1198.70			−0.665761
$149$	2341.75	−	1352.01i	1.28754	−	0.743363i	0.309328	−	0.950956i	$-0.399896\pi$
$149$	2341.75	−	1352.01i	1.28754	−	0.743363i	0.978215	+	0.207592i	$0.0665627\pi$
$150$	55.0134	−	1088.08i	0.0299455	−	0.592273i
$151$	−770.352	+	1334.29i	−0.415168	+	0.719092i	−0.995446	−	0.0953266i	$-0.969610\pi$
$151$	−770.352	+	1334.29i	−0.415168	+	0.719092i	0.580278	+	0.814418i	$0.302944\pi$
$152$	−37.0674	−	64.2026i	−0.0197800	−	0.0342600i
$153$	−1832.91	+	2542.44i	−0.968512	+	1.34343i
$154$	454.979	−	738.662i	0.238073	−	0.386514i
$155$		−	636.580i		−	0.329880i
$156$	−103.210	−	66.7553i	−0.0529706	−	0.0342609i
$157$	477.498	+	275.684i	0.242729	+	0.140140i	0.616430	−	0.787409i	$-0.288578\pi$
$157$	477.498	+	275.684i	0.242729	+	0.140140i	−0.373701	+	0.927549i	$0.621911\pi$
$158$	1848.56	+	1067.27i	0.930783	+	0.537388i
$159$	−1303.32	−	842.979i	−0.650065	−	0.420456i
$160$			143.702i			0.0710038i
$161$	65.5670	−	2302.72i	0.0320957	−	1.12720i
$162$	1383.28	−	460.755i	0.670870	−	0.223459i
$163$	1155.82	+	2001.94i	0.555403	+	0.961986i	0.997872	+	0.0652023i	$0.0207693\pi$
$163$	1155.82	+	2001.94i	0.555403	+	0.961986i	−0.442469	+	0.896784i	$0.645897\pi$
$164$	1016.76	−	1761.08i	0.484119	−	0.838518i
$165$	−27.5970	+	545.824i	−0.0130207	+	0.257529i
$166$	468.410	−	270.436i	0.219010	−	0.126445i
$167$	2580.87			1.19589			0.597944	−	0.801538i	$-0.295984\pi$
$167$	2580.87			1.19589			0.597944	+	0.801538i	$0.295984\pi$
$168$	634.279	+	436.342i	0.291284	+	0.200384i
$169$	2162.03			0.984081
$170$	902.908	−	521.294i	0.407352	−	0.235185i
$171$	228.197	−	102.609i	0.102051	−	0.0458873i
$172$	782.254	−	1354.90i	0.346781	−	0.600642i
$173$	501.050	+	867.845i	0.220197	+	0.381393i	0.954868	−	0.297031i	$-0.0959965\pi$
$173$	501.050	+	867.845i	0.220197	+	0.381393i	−0.734670	+	0.678424i	$0.762663\pi$
$174$	−983.979	−	1922.40i	−0.428708	−	0.837569i
$175$	922.524	+	1708.38i	0.398493	+	0.737951i
$176$			374.743i			0.160496i
$177$	−577.245	+	892.475i	−0.245132	+	0.378997i
$178$	−1537.25	−	887.530i	−0.647312	−	0.373726i
$179$	−2598.36	−	1500.17i	−1.08498	−	0.626411i	−0.152742	−	0.988266i	$-0.548810\pi$
$179$	−2598.36	−	1500.17i	−1.08498	−	0.626411i	−0.932234	+	0.361855i	$0.882144\pi$
$180$	−482.520	−	48.9177i	−0.199805	−	0.0202562i
$181$		−	967.850i		−	0.397457i	−0.980055	−	0.198729i	$-0.936319\pi$
$181$		−	967.850i		−	0.397457i	0.980055	−	0.198729i	$-0.0636812\pi$
$182$	218.963	+	6.23469i	0.0891792	+	0.00253927i
$183$	−2904.21	+	1486.52i	−1.17315	+	0.600473i
$184$	497.543	+	861.769i	0.199344	+	0.345274i
$185$	−672.872	+	1165.45i	−0.267408	+	0.463165i
$186$	1471.29	+	74.3889i	0.580002	+	0.0293250i
$187$	2354.59	−	1359.42i	0.920773	−	0.531608i
$188$	322.060			0.124940
$189$	−1681.06	+	1981.24i	−0.646980	+	0.762507i
$190$	−83.2289			−0.0317792
$191$	−356.214	+	205.660i	−0.134946	+	0.0779113i	−0.565953	−	0.824437i	$-0.691492\pi$
$191$	−356.214	+	205.660i	−0.134946	+	0.0779113i	0.431007	+	0.902349i	$0.358158\pi$
$192$	−332.130	−	16.7926i	−0.124841	−	0.00631197i
$193$	−408.212	+	707.043i	−0.152247	+	0.263700i	−0.932053	−	0.362321i	$-0.881984\pi$
$193$	−408.212	+	707.043i	−0.152247	+	0.263700i	0.779806	+	0.626021i	$0.215318\pi$
$194$	−219.564	−	380.296i	−0.0812566	−	0.140741i
$195$	−122.839	+	62.8749i	−0.0451111	+	0.0230901i
$196$	−1369.78	−	78.0686i	−0.499190	−	0.0284507i
$197$			633.331i			0.229051i	0.993420	+	0.114525i	$0.0365347\pi$
$197$			633.331i			0.229051i	−0.993420	+	0.114525i	$0.963465\pi$
$198$	−1258.31	−	127.567i	−0.451636	−	0.0457867i
$199$	−2964.48	−	1711.54i	−1.05601	−	0.609688i	−0.131685	−	0.991292i	$-0.542039\pi$
$199$	−2964.48	−	1711.54i	−1.05601	−	0.609688i	−0.924326	+	0.381603i	$0.875372\pi$
$200$	−726.310	−	419.335i	−0.256789	−	0.148257i
$201$	290.041	−	448.431i	0.101781	−	0.157363i
$202$			1970.13i			0.686228i
$203$	3276.90	+	2018.41i	1.13297	+	0.697854i
$204$	1099.33	+	2147.76i	0.377295	+	0.737123i
$205$	−1141.48	−	1977.11i	−0.388901	−	0.673596i
$206$	−1285.03	+	2225.74i	−0.434623	+	0.752790i
$207$	−3063.01	+	1377.29i	−1.02847	+	0.462454i
$208$	−81.9446	+	47.3107i	−0.0273165	+	0.0157712i
$209$	−217.043			−0.0718333
$210$	780.281	−	371.750i	0.256402	−	0.122158i
$211$	1023.65			0.333986			0.166993	−	0.985958i	$-0.446594\pi$
$211$	1023.65			0.333986			0.166993	+	0.985958i	$0.446594\pi$
$212$	−1034.79	+	597.435i	−0.335234	+	0.193547i
$213$	12.3264	−	243.796i	0.00396521	−	0.0784254i
$214$	−182.915	+	316.818i	−0.0584290	+	0.101202i
$215$	−878.212	−	1521.11i	−0.278575	−	0.482506i
$216$	169.447	−	1109.50i	0.0533768	−	0.349501i
$217$	−2310.07	+	1247.43i	−0.722661	+	0.390237i
$218$		−	1165.88i		−	0.362219i
$219$	−1149.59	−	743.545i	−0.354713	−	0.229425i
$220$	364.347	+	210.356i	0.111656	+	0.0644645i
$221$	594.527	+	343.250i	0.180960	+	0.104477i
$222$	−2615.01	−	1691.36i	−0.790576	−	0.511337i
$223$		−	1521.32i		−	0.456840i	−0.973563	−	0.228420i	$-0.926644\pi$
$223$		−	1521.32i		−	0.456840i	0.973563	−	0.228420i	$-0.0733559\pi$
$224$	521.475	−	281.596i	0.155547	−	0.0839952i
$225$	1655.28	−	2296.05i	0.490454	−	0.680311i
$226$	2283.94	+	3955.90i	0.672237	+	1.16435i
$227$	−729.575	+	1263.66i	−0.213320	+	0.369481i	−0.952752	−	0.303751i	$-0.901761\pi$
$227$	−729.575	+	1263.66i	−0.213320	+	0.369481i	0.739432	+	0.673232i	$0.235094\pi$
$228$	9.72589	−	192.362i	0.00282505	−	0.0558750i
$229$	4152.17	−	2397.26i	1.19818	−	0.691770i	0.238031	−	0.971257i	$-0.423498\pi$
$229$	4152.17	−	2397.26i	1.19818	−	0.691770i	0.960149	+	0.279488i	$0.0901646\pi$
$230$	1117.15			0.320273
$231$	2034.80	−	969.443i	0.579568	−	0.276124i
$232$	−1662.46			−0.470455
$233$	−1445.76	+	834.708i	−0.406501	+	0.234693i	−0.689285	−	0.724490i	$-0.742075\pi$
$233$	−1445.76	+	834.708i	−0.406501	+	0.234693i	0.282784	+	0.959183i	$0.408742\pi$
$234$	−130.965	−	291.258i	−0.0365873	−	0.0813680i
$235$	180.784	−	313.126i	0.0501831	−	0.0869196i
$236$	409.104	+	708.590i	0.112841	+	0.195446i
$237$	2526.79	+	4936.60i	0.692543	+	1.35302i
$238$	−3661.04	−	2255.01i	−0.997100	−	0.614163i
$239$		−	3529.25i		−	0.955181i	−0.878583	−	0.477590i	$-0.841510\pi$
$239$		−	3529.25i		−	0.955181i	0.878583	−	0.477590i	$-0.158490\pi$
$240$	−202.762	+	313.490i	−0.0545344	+	0.0843154i
$241$	−4269.15	−	2464.80i	−1.14108	−	0.658803i	−0.194382	−	0.980926i	$-0.562270\pi$
$241$	−4269.15	−	2464.80i	−1.14108	−	0.658803i	−0.946698	+	0.322123i	$0.895603\pi$
$242$	−1355.22	−	782.438i	−0.359987	−	0.207839i
$243$	3667.80	+	946.654i	0.968269	+	0.249909i
$244$			2511.51i			0.658946i
$245$	−844.806	+	1287.96i	−0.220297	+	0.335855i
$246$	4702.97	−	2407.21i	1.21890	−	0.623894i
$247$	−27.4014	−	47.4605i	−0.00705873	−	0.0122261i
$248$	567.024	−	982.114i	0.145186	−	0.251469i
$249$	1403.44	+	70.9581i	0.357185	+	0.0180594i
$250$	−1787.67	+	1032.11i	−0.452248	+	0.261105i
$251$	1294.99			0.325652			0.162826	−	0.986655i	$-0.447939\pi$
$251$	1294.99			0.325652			0.162826	+	0.986655i	$0.447939\pi$
$252$	768.024	+	1846.86i	0.191988	+	0.461672i
$253$	2913.29			0.723940
$254$	−2692.45	+	1554.48i	−0.665114	+	0.384004i
$255$	2705.27	+	136.779i	0.664355	+	0.0335900i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	728.040	+	1261.00i	0.176708	+	0.306067i	0.940751	−	0.339098i	$-0.110122\pi$
$257$	728.040	+	1261.00i	0.176708	+	0.306067i	−0.764043	+	0.645165i	$0.776789\pi$
$258$	3618.28	−	1852.01i	0.873117	−	0.446904i
$259$	5547.82	+	157.967i	1.33098	+	0.0378980i
$260$			106.229i			0.0253385i
$261$	565.920	−	5582.18i	0.134213	−	1.32386i
$262$	3628.52	+	2094.93i	0.855613	+	0.493988i
$263$	−1850.30	−	1068.27i	−0.433820	−	0.250466i	0.267153	−	0.963654i	$-0.413917\pi$
$263$	−1850.30	−	1068.27i	−0.433820	−	0.250466i	−0.700973	+	0.713188i	$0.747251\pi$
$264$	−528.760	+	817.514i	−0.123269	+	0.190585i
$265$			1341.44i			0.310959i
$266$	163.094	+	302.027i	0.0375938	+	0.0696182i
$267$	−2101.26	−	4105.23i	−0.481628	−	0.940958i
$268$	−205.558	−	356.036i	−0.0468524	−	0.0811507i
$269$	1443.73	−	2500.61i	0.327233	−	0.566784i	−0.654729	−	0.755864i	$-0.727217\pi$
$269$	1443.73	−	2500.61i	0.327233	−	0.566784i	0.981962	+	0.189080i	$0.0605506\pi$
$270$	−983.610	−	787.549i	−0.221706	−	0.177514i
$271$	−5072.92	+	2928.85i	−1.13711	+	0.656513i	−0.945714	−	0.324999i	$-0.894636\pi$
$271$	−5072.92	+	2928.85i	−1.13711	+	0.656513i	−0.191400	+	0.981512i	$0.561303\pi$
$272$	1857.34			0.414036
$273$	468.878	+	322.557i	0.103948	+	0.0715094i
$274$	−1221.68			−0.269359
$275$	−2126.40	+	1227.68i	−0.466279	+	0.269206i
$276$	−130.547	+	2582.01i	−0.0284711	+	0.563111i
$277$	1401.52	−	2427.50i	0.304003	−	0.526549i	−0.673036	−	0.739610i	$-0.735010\pi$
$277$	1401.52	−	2427.50i	0.304003	−	0.526549i	0.977039	+	0.213061i	$0.0683433\pi$
$278$	−1806.61	−	3129.14i	−0.389760	−	0.675085i
$279$	3104.71	+	2238.27i	0.666215	+	0.480293i
$280$	18.9373	−	665.078i	0.00404185	−	0.141950i
$281$		−	4665.53i		−	0.990469i	−0.868759	−	0.495235i	$-0.835082\pi$
$281$		−	4665.53i		−	0.990469i	0.868759	−	0.495235i	$-0.164918\pi$
$282$	702.585	+	454.426i	0.148363	+	0.0959598i
$283$	4654.53	+	2687.29i	0.977679	+	0.564463i	0.901569	−	0.432636i	$-0.142417\pi$
$283$	4654.53	+	2687.29i	0.977679	+	0.564463i	0.0761103	+	0.997099i	$0.475750\pi$
$284$	−162.738	−	93.9569i	−0.0340026	−	0.0196314i
$285$	−181.567	−	117.436i	−0.0377371	−	0.0244080i
$286$			277.021i			0.0572748i
$287$	−4937.83	+	8016.61i	−1.01558	+	1.64880i
$288$	−700.857	−	505.267i	−0.143397	−	0.103379i
$289$	−4281.21	−	7415.27i	−0.871404	−	1.50932i
$290$	−933.194	+	1616.34i	−0.188962	+	0.327292i
$291$	57.6101	−	1139.43i	0.0116054	−	0.229535i
$292$	−912.729	+	526.964i	−0.182923	+	0.105610i
$293$	−1302.13			−0.259630			−0.129815	−	0.991538i	$-0.541438\pi$
$293$	−1302.13			−0.259630			−0.129815	+	0.991538i	$0.541438\pi$
$294$	−2878.06	−	2103.06i	−0.570925	−	0.417187i
$295$	918.578			0.181294
$296$	−2076.21	+	1198.70i	−0.407694	+	0.235382i
$297$	−2565.04	−	2053.76i	−0.501141	−	0.401249i
$298$	2704.02	−	4683.51i	0.525637	−	0.910430i
$299$	367.799	+	637.046i	0.0711383	+	0.123215i
$300$	−992.789	−	1939.61i	−0.191062	−	0.373279i
$301$	−3798.97	+	6167.66i	−0.727472	+	1.18106i
$302$			3081.41i			0.587136i
$303$	−2779.85	+	4297.91i	−0.527057	+	0.814880i
$304$	−128.405	−	74.1348i	−0.0242255	−	0.0139866i
$305$	2441.84	+	1409.80i	0.458424	+	0.264671i
$306$	−632.260	+	6236.55i	−0.118117	+	1.16510i
$307$			644.894i			0.119889i	0.998202	+	0.0599447i	$0.0190924\pi$
$307$			644.894i			0.119889i	−0.998202	+	0.0599447i	$0.980908\pi$
$308$	49.3842	−	1734.38i	0.00913613	−	0.320862i
$309$	−5943.85	+	3042.35i	−1.09428	+	0.560108i
$310$	−636.580	−	1102.59i	−0.116630	−	0.202009i
$311$	−668.420	+	1157.74i	−0.121873	+	0.211091i	−0.920506	−	0.390727i	$-0.872224\pi$
$311$	−668.420	+	1157.74i	−0.121873	+	0.211091i	0.798633	+	0.601818i	$0.205557\pi$
$312$	−245.520	−	12.4136i	−0.0445508	−	0.00225250i
$313$	−1459.67	+	842.739i	−0.263595	+	0.152187i	−0.625973	−	0.779844i	$-0.715298\pi$
$313$	−1459.67	+	842.739i	−0.263595	+	0.152187i	0.362378	+	0.932031i	$0.381965\pi$
$314$	1102.73			0.198188
$315$	2226.75	+	289.988i	0.398295	+	0.0518697i
$316$	4269.07			0.759981
$317$	−2609.95	+	1506.85i	−0.462427	+	0.266982i	−0.713064	−	0.701099i	$-0.752693\pi$
$317$	−2609.95	+	1506.85i	−0.462427	+	0.266982i	0.250637	+	0.968081i	$0.419360\pi$
$318$	−3100.40	−	156.757i	−0.546736	−	0.0276431i
$319$	−2433.57	+	4215.06i	−0.427127	+	0.739806i
$320$	143.702	+	248.899i	0.0251036	+	0.0434808i
$321$	−846.064	+	433.057i	−0.147111	+	0.0752987i
$322$	−2189.16	−	4054.00i	−0.378872	−	0.701616i
$323$			1075.73i			0.185310i
$324$	1935.16	−	2181.33i	0.331818	−	0.374028i
$325$	−536.910	−	309.985i	−0.0916382	−	0.0529074i
$326$	4003.87	+	2311.64i	0.680227	+	0.392729i
$327$	1645.06	−	2543.42i	0.278202	−	0.430126i
$328$		−	4067.03i		−	0.684647i
$329$	−1490.56	−	42.4417i	−0.249778	−	0.00711211i
$330$	498.024	+	972.991i	0.0830768	+	0.162307i
$331$	394.460	+	683.225i	0.0655030	+	0.113454i	0.896917	−	0.442199i	$-0.145801\pi$
$331$	394.460	+	683.225i	0.0655030	+	0.113454i	−0.831414	+	0.555653i	$0.812468\pi$
$332$	540.873	−	936.819i	0.0894104	−	0.154863i
$333$	−3318.22	−	7379.53i	−0.546058	−	1.21440i
$334$	4470.19	−	2580.87i	0.732329	−	0.422811i
$335$	−461.547			−0.0752746
$336$	1534.95	+	121.488i	0.249221	+	0.0197253i
$337$	1906.16			0.308116			0.154058	−	0.988062i	$-0.450766\pi$
$337$	1906.16			0.308116			0.154058	+	0.988062i	$0.450766\pi$
$338$	3744.74	−	2162.03i	0.602624	−	0.347925i
$339$	−599.269	+	11852.6i	−0.0960113	+	1.89895i
$340$	1042.59	−	1805.82i	0.166301	−	0.288042i
$341$	−1660.06	−	2875.31i	−0.263629	−	0.456618i
$342$	292.640	−	405.921i	0.0462694	−	0.0641805i
$343$	6329.30	+	541.828i	0.996356	+	0.0852944i
$344$		−	3129.02i		−	0.490422i
$345$	2437.10	+	1576.30i	0.380317	+	0.245985i
$346$	1735.69	+	1002.10i	0.269686	+	0.155703i
$347$	4538.98	+	2620.58i	0.702205	+	0.405418i	0.808168	−	0.588952i	$-0.200459\pi$
$347$	4538.98	+	2620.58i	0.702205	+	0.405418i	−0.105963	+	0.994370i	$0.533793\pi$
$348$	−3626.70	−	2345.72i	−0.558654	−	0.361333i
$349$			4502.54i			0.690588i	0.938495	+	0.345294i	$0.112221\pi$
$349$			4502.54i			0.690588i	−0.938495	+	0.345294i	$0.887779\pi$
$350$	3306.24	+	2036.48i	0.504931	+	0.311012i
$351$	125.260	−	820.179i	0.0190481	−	0.124723i
$352$	374.743	+	649.073i	0.0567439	+	0.0982833i
$353$	4799.70	−	8313.33i	0.723689	−	1.25347i	−0.235822	−	0.971796i	$-0.575778\pi$
$353$	4799.70	−	8313.33i	0.723689	−	1.25347i	0.959511	−	0.281671i	$-0.0908885\pi$
$354$	−107.342	+	2123.06i	−0.0161163	+	0.318755i
$355$	−182.701	+	105.483i	−0.0273148	+	0.0157702i
$356$	−3550.12			−0.528528
$357$	−4804.86	−	10085.1i	−0.712325	−	1.49513i
$358$	−6000.66			−0.885879
$359$	8803.94	−	5082.96i	1.29430	−	0.747265i	0.314888	−	0.949129i	$-0.398033\pi$
$359$	8803.94	−	5082.96i	1.29430	−	0.747265i	0.979414	+	0.201863i	$0.0646997\pi$
$360$	−884.666	+	397.792i	−0.129517	+	0.0582374i
$361$	−3386.56	+	5865.70i	−0.493740	+	0.855183i
$362$	−967.850	−	1676.37i	−0.140522	−	0.243392i
$363$	−1852.44	−	3619.13i	−0.267846	−	0.523292i
$364$	385.490	−	208.164i	0.0555087	−	0.0299746i
$365$			1183.21i			0.169677i
$366$	−3543.73	+	5478.94i	−0.506103	+	0.782483i
$367$	332.544	+	191.995i	0.0472988	+	0.0273080i	0.523463	−	0.852048i	$-0.324640\pi$
$367$	332.544	+	191.995i	0.0472988	+	0.0273080i	−0.476164	+	0.879356i	$0.657973\pi$
$368$	1723.54	+	995.085i	0.244146	+	0.140958i
$369$	13656.2	+	1384.47i	1.92660	+	0.195318i
$370$			2691.49i			0.378173i
$371$	4867.92	−	2628.68i	0.681213	−	0.367855i
$372$	2622.74	−	1342.45i	0.365545	−	0.187104i
$373$	1481.79	+	2566.54i	0.205695	+	0.356275i	0.950354	−	0.311171i	$-0.100721\pi$
$373$	1481.79	+	2566.54i	0.205695	+	0.356275i	−0.744659	+	0.667445i	$0.767388\pi$
$374$	2718.84	−	4709.17i	0.375904	−	0.651085i
$375$	−5356.16	−	270.809i	−0.737575	−	0.0372920i
$376$	557.825	−	322.060i	0.0765096	−	0.0441728i
$377$	−1228.94			−0.167887
$378$	−930.443	+	5112.67i	−0.126605	+	0.695680i
$379$	−13195.4			−1.78839			−0.894195	−	0.447677i	$-0.852251\pi$
$379$	−13195.4			−1.78839			−0.894195	+	0.447677i	$0.852251\pi$
$380$	−144.157	+	83.2289i	−0.0194607	+	0.0112357i
$381$	−8067.03	−	407.871i	−1.08474	−	0.0548448i
$382$	−411.321	+	712.428i	−0.0550916	+	0.0954214i
$383$	−4475.95	−	7752.57i	−0.597155	−	1.03430i	−0.993239	−	0.116088i	$-0.962964\pi$
$383$	−4475.95	−	7752.57i	−0.597155	−	1.03430i	0.396084	−	0.918214i	$-0.370369\pi$
$384$	−592.058	+	303.044i	−0.0786805	+	0.0402725i
$385$	−1658.55	−	1021.58i	−0.219552	−	0.135233i
$386$			1632.85i			0.215310i
$387$	10506.6	+	1065.15i	1.38005	+	0.139909i
$388$	−760.593	−	439.128i	−0.0995186	−	0.0574571i
$389$	7594.74	+	4384.82i	0.989893	+	0.571515i	0.905242	−	0.424896i	$-0.139689\pi$
$389$	7594.74	+	4384.82i	0.989893	+	0.571515i	0.0846507	+	0.996411i	$0.473023\pi$
$390$	−149.888	+	231.741i	−0.0194612	+	0.0300889i
$391$		−	14439.1i		−	1.86757i
$392$	−2450.59	+	1234.56i	−0.315749	+	0.159068i
$393$	4959.80	+	9689.97i	0.636613	+	1.24375i
$394$	633.331	+	1096.96i	0.0809816	+	0.140264i
$395$	2396.38	−	4150.65i	0.305253	−	0.528713i
$396$	−2307.02	+	1037.35i	−0.292758	+	0.131639i
$397$	−1187.30	+	685.490i	−0.150098	+	0.0866594i	−0.573168	−	0.819438i	$-0.694286\pi$
$397$	−1187.30	+	685.490i	−0.150098	+	0.0866594i	0.423070	+	0.906097i	$0.360953\pi$
$398$	−6846.17			−0.862229
$399$	−70.3631	+	889.007i	−0.00882847	+	0.111544i
$400$	−1677.34			−0.209668
$401$	2392.14	−	1381.10i	0.297899	−	0.171992i	−0.343599	−	0.939116i	$-0.611646\pi$
$401$	2392.14	−	1381.10i	0.297899	−	0.171992i	0.641499	+	0.767124i	$0.278313\pi$
$402$	53.9350	−	1066.75i	0.00669163	−	0.132349i
$403$	419.161	−	726.008i	0.0518112	−	0.0897396i
$404$	1970.13	+	3412.37i	0.242618	+	0.420227i
$405$	−1034.55	−	3105.94i	−0.126931	−	0.381075i
$406$	7694.16	+	219.081i	0.940529	+	0.0267804i
$407$			7018.82i			0.854815i
$408$	4051.85	+	2620.70i	0.491658	+	0.318000i
$409$	2310.01	+	1333.69i	0.279273	+	0.161239i	0.633094	−	0.774075i	$-0.281784\pi$
$409$	2310.01	+	1333.69i	0.279273	+	0.161239i	−0.353821	+	0.935313i	$0.615118\pi$
$410$	−3954.21	−	2282.97i	−0.476304	−	0.274994i
$411$	−2665.13	−	1723.78i	−0.319857	−	0.206881i
$412$			5140.13i			0.614650i
$413$	−1800.03	−	3333.40i	−0.214465	−	0.397157i
$414$	−3928.00	+	5448.54i	−0.466306	+	0.646814i
$415$	−607.221	−	1051.74i	−0.0718249	−	0.124404i
$416$	−94.6215	+	163.889i	−0.0111519	+	0.0193157i
$417$	474.025	−	9375.45i	0.0556670	−	1.10100i
$418$	−375.929	+	217.043i	−0.0439887	+	0.0253969i
$419$	−14480.6			−1.68836			−0.844179	−	0.536061i	$-0.819912\pi$
$419$	−14480.6			−1.68836			−0.844179	+	0.536061i	$0.819912\pi$
$420$	979.735	−	1424.17i	0.113824	−	0.165458i
$421$	14248.8			1.64951			0.824753	−	0.565494i	$-0.191314\pi$
$421$	14248.8			1.64951			0.824753	+	0.565494i	$0.191314\pi$
$422$	1773.02	−	1023.65i	0.204524	−	0.118082i
$423$	891.520	+	1982.69i	0.102476	+	0.227900i
$424$	−1194.87	+	2069.58i	−0.136859	+	0.237046i
$425$	6084.75	+	10539.1i	0.694479	+	1.20287i
$426$	−222.446	−	434.593i	−0.0252994	−	0.0494275i
$427$	330.971	−	11623.7i	0.0375101	−	1.31736i
$428$			731.660i			0.0826311i
$429$	−390.876	+	604.331i	−0.0439899	+	0.0680125i
$430$	−3042.22	−	1756.42i	−0.341183	−	0.196982i
$431$	4826.49	+	2786.57i	0.539405	+	0.311426i	0.744838	−	0.667246i	$-0.232527\pi$
$431$	4826.49	+	2786.57i	0.539405	+	0.311426i	−0.205433	+	0.978671i	$0.565860\pi$
$432$	−816.014	−	2091.16i	−0.0908808	−	0.232896i
$433$			2939.93i			0.326291i	0.986602	+	0.163146i	$0.0521640\pi$
$433$			2939.93i			0.326291i	−0.986602	+	0.163146i	$0.947836\pi$
$434$	−2753.72	+	4470.69i	−0.304568	+	0.494469i
$435$	−4316.44	+	2209.37i	−0.475765	+	0.243520i
$436$	−1165.88	−	2019.37i	−0.128064	−	0.221813i
$437$	−576.332	+	998.236i	−0.0630885	+	0.109273i
$438$	−2734.69	−	138.267i	−0.298330	−	0.0150837i
$439$	−8290.73	+	4786.66i	−0.901355	+	0.520398i	−0.877640	−	0.479321i	$-0.840883\pi$
$439$	−8290.73	+	4786.66i	−0.901355	+	0.520398i	−0.0237157	+	0.999719i	$0.507550\pi$
$440$	841.424			0.0911666
$441$	−3311.18	−	8648.83i	−0.357540	−	0.933898i
$442$	1373.00			0.147753
$443$	−6197.42	+	3578.08i	−0.664669	+	0.383747i	−0.794054	−	0.607848i	$-0.792033\pi$
$443$	−6197.42	+	3578.08i	−0.664669	+	0.383747i	0.129385	+	0.991594i	$0.458700\pi$
$444$	−6220.69	−	314.520i	−0.664912	−	0.0336181i
$445$	−1992.81	+	3451.64i	−0.212288	+	0.367693i
$446$	−1521.32	−	2635.01i	−0.161517	−	0.279756i
$447$	12507.3	−	6401.86i	1.32344	−	0.677400i
$448$	621.625	−	1009.21i	0.0655558	−	0.106430i
$449$			14839.2i			1.55970i	0.625964	+	0.779852i	$0.284706\pi$
$449$			14839.2i			1.55970i	−0.625964	+	0.779852i	$0.715294\pi$
$450$	570.986	−	5632.16i	0.0598146	−	0.590005i
$451$	−10311.7	−	5953.48i	−1.07663	−	0.621593i
$452$	7911.81	+	4567.88i	0.823319	+	0.475343i
$453$	−4347.85	+	6722.19i	−0.450949	+	0.697210i
$454$			2918.30i			0.301680i
$455$	13.9990	−	491.646i	0.00144238	−	0.0506565i
$456$	−175.516	−	342.907i	−0.0180248	−	0.0352151i
$457$	3787.42	+	6560.00i	0.387676	+	0.671474i	0.992136	−	0.125161i	$-0.0399447\pi$
$457$	3787.42	+	6560.00i	0.387676	+	0.671474i	−0.604461	+	0.796635i	$0.706611\pi$
$458$	4794.52	−	8304.35i	0.489155	−	0.847242i
$459$	−10179.0	+	12713.1i	−1.03511	+	1.29281i
$460$	1934.96	−	1117.15i	0.196126	−	0.113234i
$461$	−14850.5			−1.50034			−0.750170	−	0.661245i	$-0.770029\pi$
$461$	−14850.5			−1.50034			−0.750170	+	0.661245i	$0.770029\pi$
$462$	2554.94	−	3713.93i	0.257287	−	0.373999i
$463$	3361.43			0.337406			0.168703	−	0.985667i	$-0.446042\pi$
$463$	3361.43			0.337406			0.168703	+	0.985667i	$0.446042\pi$
$464$	−2879.46	+	1662.46i	−0.288094	+	0.166331i
$465$	167.028	−	3303.55i	0.0166575	−	0.329459i
$466$	−1669.42	+	2891.51i	−0.165953	+	0.287439i
$467$	115.422	+	199.917i	0.0114371	+	0.0198096i	0.871687	−	0.490063i	$-0.163026\pi$
$467$	115.422	+	199.917i	0.0114371	+	0.0198096i	−0.860250	+	0.509872i	$0.829693\pi$
$468$	−518.095	−	373.509i	−0.0511730	−	0.0368920i
$469$	904.441	+	1674.89i	0.0890473	+	0.164903i
$470$		−	723.134i		−	0.0709696i
$471$	2405.65	+	1555.95i	0.235343	+	0.152218i
$472$	1417.18	+	818.209i	0.138201	+	0.0797905i
$473$	−7933.44	−	4580.37i	−0.771205	−	0.445255i
$474$	9313.12	+	6023.64i	0.902460	+	0.583703i
$475$		−	971.480i		−	0.0938411i
$476$	−8596.11	−	244.763i	−0.827736	−	0.0235687i
$477$	−6542.45	−	4716.63i	−0.628005	−	0.452745i
$478$	−3529.25	−	6112.84i	−0.337707	−	0.584926i
$479$	2200.43	−	3811.26i	0.209896	−	0.363551i	−0.741786	−	0.670637i	$-0.766021\pi$
$479$	2200.43	−	3811.26i	0.209896	−	0.363551i	0.951682	+	0.307087i	$0.0993541\pi$
$480$	−37.7050	+	745.743i	−0.00358539	+	0.0709132i
$481$	−1534.80	+	886.116i	−0.145490	+	0.0839988i
$482$	−9859.18			−0.931688
$483$	944.458	−	11932.8i	0.0889738	−	1.12415i
$484$	−3129.75			−0.293928
$485$	−853.894	+	492.996i	−0.0799450	+	0.0461563i
$486$	7299.47	−	2028.15i	0.681298	−	0.189298i
$487$	5972.31	−	10344.3i	0.555711	−	0.962520i	−0.442137	−	0.896948i	$-0.645779\pi$
$487$	5972.31	−	10344.3i	0.555711	−	0.962520i	0.997848	−	0.0655721i	$-0.0208872\pi$
$488$	2511.51	+	4350.06i	0.232973	+	0.403520i
$489$	5472.87	+	10692.4i	0.506118	+	0.988804i
$490$	−175.290	+	3075.61i	−0.0161608	+	0.283555i
$491$		−	19916.7i		−	1.83060i	−0.402768	−	0.915302i	$-0.631952\pi$
$491$		−	19916.7i		−	1.83060i	0.402768	−	0.915302i	$-0.368048\pi$
$492$	5738.57	−	8872.37i	0.525843	−	0.813003i
$493$	20891.1	+	12061.5i	1.90850	+	1.10187i
$494$	−94.9211	−	54.8027i	−0.00864514	−	0.00499128i
$495$	−286.430	+	2825.32i	−0.0260083	+	0.256543i
$496$		−	2268.09i		−	0.205324i
$497$	740.801	+	456.296i	0.0668601	+	0.0411825i
$498$	2501.78	−	1280.53i	0.225115	−	0.115225i
$499$	−665.569	−	1152.80i	−0.0597093	−	0.103420i	0.834626	−	0.550818i	$-0.185684\pi$
$499$	−665.569	−	1152.80i	−0.0597093	−	0.103420i	−0.894335	+	0.447398i	$0.852351\pi$
$500$	−2064.22	+	3575.33i	−0.184629	+	0.319787i
$501$	13393.5	+	677.177i	1.19436	+	0.0603873i
$502$	2242.98	−	1294.99i	0.199421	−	0.115136i
$503$	10393.2			0.921288			0.460644	−	0.887585i	$-0.347618\pi$
$503$	10393.2			0.921288			0.460644	+	0.887585i	$0.347618\pi$
$504$	3177.12	+	2430.83i	0.280794	+	0.214837i
$505$	4423.62			0.389799
$506$	5045.96	−	2913.29i	0.443321	−	0.255951i
$507$	11219.9	+	567.281i	0.982826	+	0.0496919i
$508$	−3108.97	+	5384.89i	−0.271532	+	0.470307i
$509$	−5132.02	−	8888.91i	−0.446901	−	0.774055i	0.551281	−	0.834319i	$-0.314139\pi$
$509$	−5132.02	−	8888.91i	−0.446901	−	0.774055i	−0.998182	+	0.0602640i	$0.980806\pi$
$510$	4822.44	−	2468.36i	0.418708	−	0.214315i
$511$	4293.73	−	2318.61i	0.371709	−	0.200723i
$512$			512.000i			0.0441942i
$513$	1211.16	−	472.618i	0.104238	−	0.0406756i
$514$	2522.00	+	1456.08i	0.216422	+	0.124951i
$515$	4997.54	+	2885.33i	0.427608	+	0.246879i
$516$	4415.03	−	6826.05i	0.376668	−	0.582365i
$517$		−	1885.78i		−	0.160418i
$518$	9767.06	−	5274.21i	0.828456	−	0.447366i
$519$	2372.50	+	4635.17i	0.200658	+	0.392026i
$520$	106.229	+	183.993i	0.00895852	+	0.0155166i
$521$	−1549.97	+	2684.63i	−0.130337	+	0.225750i	−0.923806	−	0.382860i	$-0.874939\pi$
$521$	−1549.97	+	2684.63i	−0.130337	+	0.225750i	0.793470	+	0.608610i	$0.208273\pi$
$522$	−4601.98	−	10234.5i	−0.385868	−	0.858148i
$523$	−8265.94	+	4772.34i	−0.691098	+	0.399005i	−0.804023	−	0.594598i	$-0.797311\pi$
$523$	−8265.94	+	4772.34i	−0.691098	+	0.399005i	0.112925	+	0.993603i	$0.463978\pi$
$524$	8379.70			0.698605
$525$	4339.21	+	9107.74i	0.360721	+	0.757132i
$526$	−4273.10			−0.354213
$527$	−14250.9	+	8227.77i	−1.17795	+	0.680090i
$528$	−98.3264	+	1944.74i	−0.00810437	+	0.160291i
$529$	1652.39	−	2862.03i	0.135809	−	0.235229i
$530$	1341.44	+	2323.45i	0.109941	+	0.190423i
$531$	−3229.80	+	4480.06i	−0.263957	+	0.366136i
$532$	584.514	+	360.031i	0.0476352	+	0.0293409i
$533$		−	3006.47i		−	0.244324i
$534$	−7744.71	−	5009.21i	−0.627615	−	0.405936i
$535$	711.364	+	410.706i	0.0574859	+	0.0331895i
$536$	−712.073	−	411.115i	−0.0573822	−	0.0331296i
$537$	−13090.6	−	8466.91i	−1.05196	−	0.680399i
$538$		−	5774.91i		−	0.462777i
$539$	−457.119	+	8020.53i	−0.0365297	+	0.640944i
$540$	−2491.21	−	380.465i	−0.198527	−	0.0303196i
$541$	3403.83	+	5895.60i	0.270503	+	0.468524i	0.968991	−	0.247098i	$-0.0794768\pi$
$541$	3403.83	+	5895.60i	0.270503	+	0.468524i	−0.698488	+	0.715622i	$0.746143\pi$
$542$	−5857.70	+	10145.8i	−0.464225	+	0.804061i
$543$	253.948	−	5022.68i	0.0200699	−	0.396950i
$544$	3217.01	−	1857.34i	0.253544	−	0.146384i
$545$	−2617.80			−0.205751
$546$	1134.68	+	89.8074i	0.0889372	+	0.00703920i
$547$	−14906.9			−1.16521			−0.582606	−	0.812754i	$-0.697967\pi$
$547$	−14906.9			−1.16521			−0.582606	+	0.812754i	$0.697967\pi$
$548$	−2116.01	+	1221.68i	−0.164948	+	0.0952327i
$549$	−15461.5	+	6952.30i	−1.20197	+	0.540468i
$550$	−2455.36	+	4252.80i	−0.190358	+	0.329709i
$551$	−962.859	−	1667.72i	−0.0744449	−	0.128942i
$552$	2355.89	+	4602.72i	0.181655	+	0.354900i
$553$	−19758.1	−	562.586i	−1.51935	−	0.0432615i
$554$		−	5606.06i		−	0.429925i
$555$	−3797.68	+	5871.57i	−0.290455	+	0.449071i
$556$	−6258.29	−	3613.22i	−0.477357	−	0.275602i
$557$	10661.9	+	6155.67i	0.811061	+	0.468266i	0.847324	−	0.531076i	$-0.178212\pi$
$557$	10661.9	+	6155.67i	0.811061	+	0.468266i	−0.0362634	+	0.999342i	$0.511546\pi$
$558$	7615.78	+	772.086i	0.577781	+	0.0585753i
$559$		−	2313.06i		−	0.175013i
$560$	−632.278	−	1170.89i	−0.0477118	−	0.0883554i
$561$	12575.9	−	6436.95i	0.946442	−	0.484435i
$562$	−4665.53	−	8080.93i	−0.350184	−	0.606536i
$563$	417.925	−	723.867i	0.0312850	−	0.0541872i	−0.849959	−	0.526849i	$-0.823373\pi$
$563$	417.925	−	723.867i	0.0312850	−	0.0541872i	0.881244	+	0.472662i	$0.156707\pi$
$564$	1671.34	+	84.5034i	0.124780	+	0.00630893i
$565$	8882.34	−	5128.22i	0.661386	−	0.381851i
$566$	10749.2			0.798271
$567$	−9243.75	+	9840.60i	−0.684658	+	0.728865i
$568$	−375.828			−0.0277630
$569$	5291.04	−	3054.78i	0.389828	−	0.225067i	−0.292258	−	0.956340i	$-0.594407\pi$
$569$	5291.04	−	3054.78i	0.389828	−	0.225067i	0.682086	+	0.731272i	$0.261073\pi$
$570$	−431.918	−	21.8379i	−0.0317387	−	0.00160472i
$571$	6319.69	−	10946.0i	0.463171	−	0.802236i	−0.535946	−	0.844252i	$-0.680045\pi$
$571$	6319.69	−	10946.0i	0.463171	−	0.802236i	0.999117	+	0.0420166i	$0.0133782\pi$
$572$	277.021	+	479.815i	0.0202497	+	0.0350735i
$573$	−1902.54	+	973.814i	−0.138708	+	0.0709977i
$574$	−535.961	+	18823.0i	−0.0389731	+	1.36874i
$575$			13039.8i			0.945736i
$576$	−1719.19	−	174.291i	−0.124363	−	0.0126078i
$577$	−15334.7	−	8853.51i	−1.10640	−	0.638781i	−0.168506	−	0.985701i	$-0.553894\pi$
$577$	−15334.7	−	8853.51i	−1.10640	−	0.638781i	−0.937895	+	0.346920i	$0.887228\pi$
$578$	−14830.5	−	8562.42i	−1.06725	−	0.616176i
$579$	−2303.94	+	3562.11i	−0.165369	+	0.255676i
$580$			3732.78i			0.267233i
$581$	−2626.72	+	4264.50i	−0.187564	+	0.304512i
$582$	−1039.65	−	2031.17i	−0.0740462	−	0.144664i
$583$	3498.19	+	6059.05i	0.248508	+	0.430429i
$584$	−1053.93	+	1825.46i	−0.0746779	+	0.129346i
$585$	−653.972	+	294.060i	−0.0462195	+	0.0207827i
$586$	−2255.36	+	1302.13i	−0.158990	+	0.0917929i
$587$	11725.2			0.824446			0.412223	−	0.911083i	$-0.364752\pi$
$587$	11725.2			0.824446			0.412223	+	0.911083i	$0.364752\pi$
$588$	−7088.01	−	764.546i	−0.497116	−	0.0536213i
$589$	1313.63			0.0918968
$590$	1591.02	−	918.578i	0.111019	−	0.0640970i
$591$	−166.176	+	3286.69i	−0.0115661	+	0.228758i
$592$	−2397.40	+	4152.42i	−0.166440	+	0.288283i
$593$	−7523.76	−	13031.5i	−0.521018	−	0.902430i	−0.999701	−	0.0244425i	$-0.992219\pi$
$593$	−7523.76	−	13031.5i	−0.521018	−	0.902430i	0.478683	−	0.877988i	$-0.341114\pi$
$594$	−6496.54	−	992.170i	−0.448748	−	0.0685340i
$595$	−5063.27	+	8220.26i	−0.348864	+	0.566383i
$596$		−	10816.1i		−	0.743363i
$597$	−14935.1	−	9659.91i	−1.02388	−	0.662234i
$598$	1274.09	+	735.597i	0.0871262	+	0.0503023i
$599$	−5292.70	−	3055.74i	−0.361025	−	0.208438i	0.308505	−	0.951223i	$-0.400171\pi$
$599$	−5292.70	−	3055.74i	−0.361025	−	0.208438i	−0.669530	+	0.742785i	$0.733505\pi$
$600$	−3659.18	−	2366.72i	−0.248975	−	0.161035i
$601$			7494.08i			0.508636i	0.967121	+	0.254318i	$0.0818509\pi$
$601$			7494.08i			0.508636i	−0.967121	+	0.254318i	$0.918149\pi$
$602$	−412.347	+	14481.7i	−0.0279170	+	0.980447i
$603$	1622.84	−	2251.04i	0.109597	−	0.152022i
$604$	3081.41	+	5337.15i	0.207584	+	0.359546i
$605$	−1756.84	+	3042.93i	−0.118059	+	0.204484i
$606$	−516.931	+	10224.1i	−0.0346516	+	0.685353i
$607$	17917.1	−	10344.5i	1.19808	−	0.691711i	0.237953	−	0.971277i	$-0.423524\pi$
$607$	17917.1	−	10344.5i	1.19808	−	0.691711i	0.960127	+	0.279565i	$0.0901904\pi$
$608$	−296.539			−0.0197800
$609$	16476.0	+	11334.4i	1.09629	+	0.754174i
$610$	5639.19			0.374302
$611$	412.361	−	238.077i	0.0273033	−	0.0157636i
$612$	5141.45	+	11434.3i	0.339592	+	0.755234i
$613$	11645.5	−	20170.6i	0.767305	−	1.32901i	−0.171714	−	0.985147i	$-0.554931\pi$
$613$	11645.5	−	20170.6i	0.767305	−	1.32901i	0.939019	−	0.343865i	$-0.111736\pi$
$614$	644.894	+	1116.99i	0.0423873	+	0.0734169i
$615$	−5404.99	−	10559.7i	−0.354391	−	0.692374i
$616$	−1648.84	−	3053.42i	−0.107847	−	0.199717i
$617$		−	11640.9i		−	0.759554i	−0.925078	−	0.379777i	$-0.876001\pi$
$617$		−	11640.9i		−	0.759554i	0.925078	−	0.379777i	$-0.123999\pi$
$618$	−7252.70	+	11213.4i	−0.472082	+	0.729883i
$619$	−13978.4	−	8070.44i	−0.907657	−	0.524036i	−0.0279803	−	0.999608i	$-0.508908\pi$
$619$	−13978.4	−	8070.44i	−0.907657	−	0.524036i	−0.879676	+	0.475573i	$0.842241\pi$
$620$	−2205.18	−	1273.16i	−0.142842	−	0.0824699i
$621$	−16256.9	+	6343.78i	−1.05051	+	0.409931i
$622$			2673.68i			0.172355i
$623$	16430.6	+	467.841i	1.05663	+	0.0300861i
$624$	−437.667	+	224.019i	−0.0280781	+	0.0143717i
$625$	−4234.68	−	7334.68i	−0.271019	−	0.469420i
$626$	−1685.48	+	2919.33i	−0.107612	+	0.186390i
$627$	−1126.35	−	56.9485i	−0.0717417	−	0.00362728i
$628$	1909.99	−	1102.73i	0.121365	−	0.0700699i
$629$	34787.4			2.20519
$630$	4146.83	−	1724.47i	0.262244	−	0.109055i
$631$	9424.67			0.594596			0.297298	−	0.954785i	$-0.403914\pi$
$631$	9424.67			0.594596			0.297298	+	0.954785i	$0.403914\pi$
$632$	7394.25	−	4269.07i	0.465392	−	0.268694i
$633$	5312.26	+	268.589i	0.333560	+	0.0168649i
$634$	−3013.71	+	5219.90i	−0.188785	+	0.326985i
$635$	3490.34	+	6045.45i	0.218126	+	0.377805i
$636$	−5526.81	+	2828.89i	−0.344579	+	0.176372i
$637$	−1811.55	+	912.623i	−0.112679	+	0.0567652i
$638$			9734.27i			0.604049i
$639$	127.936	−	1261.95i	0.00792031	−	0.0781252i
$640$	497.797	+	287.403i	0.0307456	+	0.0177510i
$641$	−1459.54	−	842.666i	−0.0899351	−	0.0519241i	0.454358	−	0.890819i	$-0.349869\pi$
$641$	−1459.54	−	842.666i	−0.0899351	−	0.0519241i	−0.544293	+	0.838895i	$0.683202\pi$
$642$	−1032.37	+	1596.14i	−0.0634648	+	0.0981225i
$643$			10186.5i			0.624752i	0.949958	+	0.312376i	$0.101125\pi$
$643$			10186.5i			0.624752i	−0.949958	+	0.312376i	$0.898875\pi$
$644$	−7845.72	−	4832.57i	−0.480070	−	0.295699i
$645$	−4158.39	−	8124.26i	−0.253855	−	0.495957i
$646$	1075.73	+	1863.22i	0.0655171	+	0.113479i
$647$	163.793	−	283.698i	0.00995266	−	0.0172385i	−0.861006	−	0.508594i	$-0.830165\pi$
$647$	163.793	−	283.698i	0.00995266	−	0.0172385i	0.870959	+	0.491356i	$0.163499\pi$
$648$	1170.46	−	5713.34i	0.0709570	−	0.346360i
$649$	4149.04	−	2395.45i	0.250946	−	0.144884i
$650$	−1239.94			−0.0748223
$651$	−12315.4	+	5867.46i	−0.741445	+	0.353247i
$652$	9246.55			0.555403
$653$	1769.92	−	1021.87i	0.106068	−	0.0612384i	−0.446028	−	0.895019i	$-0.647162\pi$
$653$	1769.92	−	1021.87i	0.106068	−	0.0612384i	0.552096	+	0.833781i	$0.313828\pi$
$654$	305.909	−	6050.38i	0.0182905	−	0.361756i
$655$	4703.82	−	8147.25i	0.280600	−	0.486014i
$656$	−4067.03	−	7044.31i	−0.242059	−	0.419259i
$657$	−5770.73	−	4160.28i	−0.342675	−	0.247044i
$658$	−2624.16	+	1417.04i	−0.155472	+	0.0839546i
$659$		−	27567.4i		−	1.62955i	−0.579778	−	0.814774i	$-0.696861\pi$
$659$		−	27567.4i		−	1.62955i	0.579778	−	0.814774i	$-0.303139\pi$
$660$	1835.59	+	1187.25i	0.108258	+	0.0700204i
$661$	18417.0	+	10633.0i	1.08372	+	0.625684i	0.931897	−	0.362724i	$-0.118153\pi$
$661$	18417.0	+	10633.0i	1.08372	+	0.625684i	0.151820	+	0.988408i	$0.451487\pi$
$662$	1366.45	+	788.920i	0.0802244	+	0.0463176i
$663$	2995.25	+	1937.30i	0.175454	+	0.113482i
$664$		−	2163.49i		−	0.126445i
$665$	678.152	−	366.202i	0.0395453	−	0.0213544i
$666$	−13126.9	−	9463.50i	−0.763747	−	0.550606i
$667$	12924.1	+	22385.2i	0.750260	+	1.29949i
$668$	5161.73	−	8940.38i	0.298972	−	0.517835i
$669$	399.170	−	7894.94i	0.0230685	−	0.456257i
$670$	−799.422	+	461.547i	−0.0460961	+	0.0266136i
$671$	14705.8			0.846065
$672$	2780.09	−	1324.52i	0.159590	−	0.0760336i
$673$	−9377.40			−0.537106			−0.268553	−	0.963265i	$-0.586545\pi$
$673$	−9377.40			−0.537106			−0.268553	+	0.963265i	$0.586545\pi$
$674$	3301.56	−	1906.16i	0.188682	−	0.108935i
$675$	9192.58	−	11481.1i	0.524182	−	0.654677i
$676$	4324.05	−	7489.48i	0.246020	−	0.426120i
$677$	5342.31	+	9253.15i	0.303282	+	0.525299i	0.976877	−	0.213801i	$-0.0685844\pi$
$677$	5342.31	+	9253.15i	0.303282	+	0.525299i	−0.673596	+	0.739100i	$0.735251\pi$
$678$	10814.6	+	21128.5i	0.612585	+	1.19681i
$679$	3462.30	+	2132.60i	0.195686	+	0.120533i
$680$		−	4170.35i		−	0.235185i
$681$	−4117.71	+	6366.37i	−0.231705	+	0.358238i
$682$	−5750.62	−	3320.12i	−0.322878	−	0.186414i
$683$	−24985.9	−	14425.6i	−1.39979	−	0.808172i	−0.405424	−	0.914129i	$-0.632876\pi$
$683$	−24985.9	−	14425.6i	−1.39979	−	0.808172i	−0.994371	+	0.105957i	$0.966209\pi$
$684$	100.945	−	995.716i	0.00564290	−	0.0556611i
$685$			2743.08i			0.153004i
$686$	11504.5	−	5390.83i	0.640297	−	0.300033i
$687$	22176.8	−	11351.2i	1.23158	−	0.630384i
$688$	−3129.02	−	5419.61i	−0.173390	−	0.300321i
$689$	−883.284	+	1529.89i	−0.0488395	+	0.0845926i
$690$	5797.48	+	293.122i	0.319864	+	0.0161724i
$691$	−1139.99	+	658.171i	−0.0627599	+	0.0362344i	−0.531052	−	0.847339i	$-0.678203\pi$
$691$	−1139.99	+	658.171i	−0.0627599	+	0.0362344i	0.468292	+	0.883574i	$0.344870\pi$
$692$	4008.40			0.220197
$693$	10814.0	−	4497.05i	0.592771	−	0.246506i
$694$	10482.3			0.573348
$695$	−7025.98	+	4056.45i	−0.383469	+	0.221396i
$696$	−8627.36	−	436.202i	−0.469855	−	0.0237560i
$697$	−29507.3	+	51108.1i	−1.60354	+	2.77741i
$698$	4502.54	+	7798.62i	0.244160	+	0.422897i
$699$	−7721.80	+	3952.39i	−0.417833	+	0.213867i
$700$	7763.05	+	221.043i	0.419165	+	0.0119352i
$701$			12811.2i			0.690259i	0.938555	+	0.345129i	$0.112165\pi$
$701$			12811.2i			0.690259i	−0.938555	+	0.345129i	$0.887835\pi$
$702$	−603.222	−	1545.85i	−0.0324319	−	0.0831117i
$703$	−2404.99	−	1388.52i	−0.129027	−	0.0744938i
$704$	1298.15	+	749.485i	0.0694968	+	0.0401240i
$705$	1020.34	−	1577.54i	0.0545081	−	0.0842747i
$706$		−	19198.8i		−	1.02345i
$707$	−8668.46	−	16052.7i	−0.461119	−	0.853925i
$708$	1937.13	+	3784.58i	0.102828	+	0.200895i
$709$	−16482.9	−	28549.2i	−0.873101	−	1.51226i	−0.858772	−	0.512358i	$-0.828772\pi$
$709$	−16482.9	−	28549.2i	−0.873101	−	1.51226i	−0.0143290	−	0.999897i	$-0.504561\pi$
$710$	−210.965	+	365.402i	−0.0111512	+	0.0193145i
$711$	11817.6	+	26281.6i	0.623337	+	1.38627i
$712$	−6148.99	+	3550.12i	−0.323656	+	0.186863i
$713$	−17632.4			−0.926141
$714$	−18407.4	−	12663.0i	−0.964815	−	0.663729i
$715$	622.006			0.0325339
$716$	−10393.4	+	6000.66i	−0.542488	+	0.313206i
$717$	926.018	−	18315.1i	0.0482326	−	0.953962i
$718$	10165.9	−	17607.9i	0.528396	−	0.915210i
$719$	4307.48	+	7460.77i	0.223424	+	0.386982i	0.955845	−	0.293870i	$-0.0949432\pi$
$719$	4307.48	+	7460.77i	0.223424	+	0.386982i	−0.732421	+	0.680851i	$0.761610\pi$
$720$	−1134.50	+	1573.66i	−0.0587224	+	0.0814541i
$721$	677.375	−	23789.5i	0.0349886	−	1.22880i
$722$			13546.3i			0.698254i
$723$	−21508.1	−	13911.3i	−1.10636	−	0.715582i
$724$	−3352.73	−	1935.70i	−0.172104	−	0.0993643i
$725$	−18866.5	−	10892.6i	−0.966463	−	0.557988i
$726$	−6827.66	−	4416.07i	−0.349033	−	0.225751i
$727$			26635.3i			1.35880i	0.733768	+	0.679400i	$0.237760\pi$
$727$			26635.3i			1.35880i	−0.733768	+	0.679400i	$0.762240\pi$
$728$	459.524	−	746.041i	0.0233943	−	0.0379809i
$729$	18785.7	+	5875.05i	0.954415	+	0.298484i
$730$	1183.21	+	2049.38i	0.0599900	+	0.103906i
$731$	−22701.7	+	39320.5i	−1.14864	+	1.98950i
$732$	−658.979	+	13033.5i	−0.0332740	+	0.658105i
$733$	−5328.35	+	3076.33i	−0.268496	+	0.155016i	−0.628204	−	0.778049i	$-0.716210\pi$
$733$	−5328.35	+	3076.33i	−0.268496	+	0.155016i	0.359708	+	0.933065i	$0.382876\pi$
$734$	767.978			0.0386193
$735$	−4722.08	+	6462.22i	−0.236975	+	0.324303i
$736$	3980.34			0.199344
$737$	−2084.72	+	1203.61i	−0.104195	+	0.0601569i
$738$	25037.8	−	11258.3i	1.24885	−	0.561548i
$739$	−7364.30	+	12755.3i	−0.366577	+	0.634929i	−0.989028	−	0.147729i	$-0.952804\pi$
$739$	−7364.30	+	12755.3i	−0.366577	+	0.634929i	0.622451	+	0.782659i	$0.286137\pi$
$740$	2691.49	+	4661.80i	0.133704	+	0.231582i
$741$	−129.747	−	253.487i	−0.00643236	−	0.0125669i
$742$	5802.82	−	9420.93i	0.287100	−	0.466109i
$743$			27255.1i			1.34575i	0.739755	+	0.672876i	$0.234941\pi$
$743$			27255.1i			1.34575i	−0.739755	+	0.672876i	$0.765059\pi$
$744$	3200.27	−	4947.93i	0.157699	−	0.243817i
$745$	−10516.1	−	6071.45i	−0.517152	−	0.298578i
$746$	5133.08	+	2963.59i	0.251924	+	0.145449i
$747$	7264.55	+	736.478i	0.355818	+	0.0360727i
$748$		−	10875.4i		−	0.531608i
$749$	96.4195	−	3386.26i	0.00470373	−	0.165195i
$750$	−9547.94	+	4887.10i	−0.464855	+	0.237936i
$751$	3075.69	+	5327.25i	0.149445	+	0.258847i	0.931023	−	0.364961i	$-0.118918\pi$
$751$	3075.69	+	5327.25i	0.149445	+	0.258847i	−0.781577	+	0.623809i	$0.785585\pi$
$752$	644.121	−	1115.65i	0.0312349	−	0.0541005i
$753$	6720.36	+	339.783i	0.325237	+	0.0164441i
$754$	−2128.58	+	1228.94i	−0.102810	+	0.0593571i
$755$	6918.80			0.333511
$756$	3501.09	+	9785.84i	0.168430	+	0.470777i
$757$	−21107.3			−1.01342			−0.506710	−	0.862117i	$-0.669139\pi$
$757$	−21107.3			−1.01342			−0.506710	+	0.862117i	$0.669139\pi$
$758$	−22855.0	+	13195.4i	−1.09516	+	0.632292i
$759$	15118.6	+	764.399i	0.723016	+	0.0365559i
$760$	−166.458	+	288.313i	−0.00794481	+	0.0137608i
$761$	7530.97	+	13044.0i	0.358735	+	0.621348i	0.987750	−	0.156046i	$-0.0498748\pi$
$761$	7530.97	+	13044.0i	0.358735	+	0.621348i	−0.629015	+	0.777393i	$0.716541\pi$
$762$	−14380.4	+	7360.58i	−0.683657	+	0.349929i
$763$	5129.82	+	9499.67i	0.243397	+	0.450736i
$764$			1645.28i			0.0779113i
$765$	14003.2	+	1419.64i	0.661811	+	0.0670942i
$766$	−15505.1	−	8951.90i	−0.731362	−	0.422252i
$767$	1047.62	+	604.845i	0.0493187	+	0.0284742i
$768$	−722.430	+	1116.95i	−0.0339433	+	0.0524795i
$769$		−	26099.2i		−	1.22387i	−0.790906	−	0.611937i	$-0.790390\pi$
$769$		−	26099.2i		−	1.22387i	0.790906	−	0.611937i	$-0.209610\pi$
$770$	−3894.27	−	110.884i	−0.182259	−	0.00518960i
$771$	3447.31	+	6735.03i	0.161027	+	0.314599i
$772$	1632.85	+	2828.17i	0.0761236	+	0.131850i
$773$	−8.84542	+	15.3207i	−0.000411575	+	0.000712869i	−0.866231	−	0.499644i	$-0.833464\pi$
$773$	−8.84542	+	15.3207i	−0.000411575	+	0.000712869i	0.865820	+	0.500356i	$0.166798\pi$
$774$	19263.1	−	8661.67i	0.894569	−	0.402245i
$775$	12869.8	−	7430.41i	0.596514	−	0.344398i
$776$	−1756.51			−0.0812566
$777$	28749.1	+	2275.43i	1.32737	+	0.105059i
$778$	17539.3			0.808244
$779$	4079.91	−	2355.54i	0.187648	−	0.108339i
$780$	−27.8727	+	551.276i	−0.00127949	+	0.0253062i
$781$	−550.151	+	952.889i	−0.0252061	+	0.0436582i
$782$	−14439.1	−	25009.3i	−0.660285	−	1.14365i
$783$	4401.53	−	28820.4i	0.200891	−	1.31540i
$784$	−3009.99	+	4588.91i	−0.137117	+	0.209043i
$785$		−	2476.01i		−	0.112577i
$786$	18280.6	+	11823.7i	0.829577	+	0.536563i
$787$	2066.21	+	1192.93i	0.0935865	+	0.0540322i	0.546063	−	0.837744i	$-0.316126\pi$
$787$	2066.21	+	1192.93i	0.0935865	+	0.0540322i	−0.452476	+	0.891776i	$0.649459\pi$
$788$	2193.92	+	1266.66i	0.0991819	+	0.0572627i
$789$	−9321.90	−	6029.32i	−0.420619	−	0.272053i
$790$		−	9585.51i		−	0.431693i
$791$	−36015.4	−	22183.7i	−1.61891	−	0.997169i
$792$	−2958.52	+	4103.77i	−0.132735	+	0.184117i
$793$	1856.58	+	3215.70i	0.0831390	+	0.144001i
$794$	−1370.98	+	2374.61i	−0.0612774	+	0.106136i
$795$	−351.973	+	6961.45i	−0.0157021	+	0.310563i
$796$	−11857.9	+	6846.17i	−0.528005	+	0.304844i
$797$	−13183.5			−0.585927			−0.292964	−	0.956124i	$-0.594641\pi$
$797$	−13183.5			−0.585927			−0.292964	+	0.956124i	$0.594641\pi$
$798$	767.134	+	1610.17i	0.0340304	+	0.0714277i
$799$	−9346.49			−0.413836
$800$	−2905.24	+	1677.34i	−0.128395	+	0.0741287i
$801$	−9827.37	−	21855.5i	−0.433499	−	0.964078i
$802$	2762.20	−	4784.28i	0.121617	−	0.210647i
$803$	3085.56	+	5344.35i	0.135600	+	0.234867i
$804$	−973.329	−	1901.59i	−0.0426948	−	0.0834130i
$805$	−9102.59	+	4915.39i	−0.398539	+	0.215211i
$806$		−	1676.64i		−	0.0732721i
$807$	8148.37	−	12598.2i	0.355435	−	0.549537i
$808$	6824.74	+	3940.27i	0.297146	+	0.171557i
$809$	−26645.9	−	15384.0i	−1.15800	−	0.668570i	−0.207174	−	0.978304i	$-0.566426\pi$
$809$	−26645.9	−	15384.0i	−1.15800	−	0.668570i	−0.950823	+	0.309734i	$0.899760\pi$
$810$	−4897.83	−	4345.09i	−0.212459	−	0.188483i
$811$			42776.4i			1.85214i	0.377357	+	0.926068i	$0.376833\pi$
$811$			42776.4i			1.85214i	−0.377357	+	0.926068i	$0.623167\pi$
$812$	13545.8	−	7314.70i	0.585422	−	0.316128i
$813$	−27094.5	+	13868.3i	−1.16881	+	0.598256i
$814$	7018.82	+	12156.9i	0.302223	+	0.523465i
$815$	5190.41	−	8990.05i	0.223082	−	0.386390i
$816$	9638.70	+	487.335i	0.413507	+	0.0209071i
$817$	3138.92	−	1812.26i	0.134415	−	0.0776045i
$818$	5334.75			0.228026
$819$	2348.62	+	1796.94i	0.100204	+	0.0766671i
$820$	−9131.86			−0.388901
$821$	36141.5	−	20866.3i	1.53635	−	0.887014i	0.537305	−	0.843388i	$-0.319442\pi$
$821$	36141.5	−	20866.3i	1.53635	−	0.887014i	0.999048	−	0.0436263i	$-0.0138911\pi$
$822$	−6339.93	−	320.549i	−0.269015	−	0.0136015i
$823$	7822.35	−	13548.7i	0.331312	−	0.573850i	−0.651457	−	0.758685i	$-0.725842\pi$
$823$	7822.35	−	13548.7i	0.331312	−	0.573850i	0.982769	+	0.184836i	$0.0591753\pi$
$824$	5140.13	+	8902.96i	0.217312	+	0.376395i
$825$	−11357.1	+	5813.13i	−0.479278	+	0.245318i
$826$	−6451.15	−	3973.58i	−0.271748	−	0.167383i
$827$			24395.1i			1.02576i	0.858461	+	0.512879i	$0.171421\pi$
$827$			24395.1i			1.02576i	−0.858461	+	0.512879i	$0.828579\pi$
$828$	−1354.95	+	13365.1i	−0.0568695	+	0.560955i
$829$	32786.9	+	18929.5i	1.37362	+	0.793062i	0.991382	−	0.131000i	$-0.0418188\pi$
$829$	32786.9	+	18929.5i	1.37362	+	0.793062i	0.382242	+	0.924062i	$0.375152\pi$
$830$	−2103.48	−	1214.44i	−0.0879671	−	0.0507878i
$831$	7910.13	−	12229.8i	0.330204	−	0.510526i
$832$			378.486i			0.0157712i
$833$	39752.2	+	2265.62i	1.65346	+	0.0942367i
$834$	−8554.42	−	16712.8i	−0.355174	−	0.693905i
$835$	−5794.92	−	10037.1i	−0.240169	−	0.415986i
$836$	−434.085	+	751.858i	−0.0179583	+	0.0311047i
$837$	15524.7	+	12430.2i	0.641113	+	0.513321i
$838$	−25081.1	+	14480.6i	−1.03390	+	0.596925i
$839$	−40533.9			−1.66792			−0.833960	−	0.551826i	$-0.813931\pi$
$839$	−40533.9			−1.66792			−0.833960	+	0.551826i	$0.813931\pi$
$840$	272.781	−	3446.47i	0.0112046	−	0.141565i
$841$	−18794.8			−0.770625
$842$	24679.6	−	14248.8i	1.01011	−	0.583188i
$843$	1224.16	−	24211.9i	0.0500145	−	0.989206i
$844$	2047.30	−	3546.03i	0.0834965	−	0.144620i
$845$	−4854.48	−	8408.21i	−0.197632	−	0.342309i
$846$	3526.85	+	2542.60i	0.143328	+	0.103329i
$847$	14485.1	+	412.444i	0.587619	+	0.0167317i
$848$			4779.48i			0.193547i
$849$	23449.7	+	15167.1i	0.947929	+	0.613112i
$850$	21078.2	+	12169.5i	0.850560	+	0.491071i
$851$	32281.4	+	18637.6i	1.30034	+	0.750752i
$852$	−819.881	−	530.292i	−0.0329679	−	0.0213233i
$853$		−	38466.5i		−	1.54404i	−0.635598	−	0.772021i	$-0.719246\pi$
$853$		−	38466.5i		−	1.54404i	0.635598	−	0.772021i	$-0.280754\pi$
$854$	−11050.5	−	20463.9i	−0.442786	−	0.819976i
$855$	−911.431	−	657.075i	−0.0364565	−	0.0262824i
$856$	731.660	+	1267.27i	0.0292145	+	0.0506010i
$857$	−13054.1	+	22610.3i	−0.520326	+	0.901230i	0.479395	+	0.877599i	$0.340856\pi$
$857$	−13054.1	+	22610.3i	−0.520326	+	0.901230i	−0.999721	+	0.0236312i	$0.992477\pi$
$858$	−72.6858	+	1437.61i	−0.00289214	+	0.0572018i
$859$	21033.3	−	12143.6i	0.835445	−	0.482345i	−0.0202681	−	0.999795i	$-0.506452\pi$
$859$	21033.3	−	12143.6i	0.835445	−	0.482345i	0.855713	+	0.517450i	$0.173119\pi$
$860$	−7025.70			−0.278575
$861$	−27728.4	+	40306.8i	−1.09754	+	1.59541i
$862$	11146.3			0.440423
$863$	32475.9	−	18750.0i	1.28099	−	0.739579i	0.303960	−	0.952685i	$-0.401691\pi$
$863$	32475.9	−	18750.0i	1.28099	−	0.739579i	0.977029	+	0.213106i	$0.0683579\pi$
$864$	−3504.54	−	2805.99i	−0.137994	−	0.110488i
$865$	2250.06	−	3897.21i	0.0884441	−	0.153190i
$866$	2939.93	+	5092.11i	0.115361	+	0.199812i
$867$	−20271.8	−	39605.1i	−0.794079	−	1.55139i
$868$	−298.894	+	10497.2i	−0.0116879	+	0.410481i
$869$		−	24996.9i		−	0.975791i
$870$	−5266.93	+	8143.18i	−0.205248	+	0.317333i
$871$	−526.386	−	303.909i	−0.0204775	−	0.0118227i
$872$	−4038.74	−	2331.77i	−0.156845	−	0.0905546i
$873$	597.938	−	5898.00i	0.0231811	−	0.228656i
$874$			2305.33i			0.0892206i
$875$	10024.8	−	16275.3i	0.387313	−	0.628806i
$876$	−4874.89	+	2495.21i	−0.188022	+	0.0962389i
$877$	7420.70	+	12853.0i	0.285723	+	0.494887i	0.972784	−	0.231713i	$-0.0744329\pi$
$877$	7420.70	+	12853.0i	0.285723	+	0.494887i	−0.687061	+	0.726600i	$0.741100\pi$
$878$	−9573.31	+	16581.5i	−0.367977	+	0.637355i
$879$	−6757.45	−	341.659i	−0.259298	−	0.0131102i
$880$	1457.39	−	841.424i	0.0558279	−	0.0322323i
$881$	30469.3			1.16520			0.582598	−	0.812760i	$-0.302036\pi$
$881$	30469.3			1.16520			0.582598	+	0.812760i	$0.302036\pi$
$882$	−14384.0	−	11669.0i	−0.549130	−	0.445484i
$883$	−6758.53			−0.257580			−0.128790	−	0.991672i	$-0.541109\pi$
$883$	−6758.53			−0.257580			−0.128790	+	0.991672i	$0.541109\pi$
$884$	2378.11	−	1373.00i	0.0904801	−	0.0522387i
$885$	4766.98	+	241.020i	0.181062	+	0.00915457i
$886$	−7156.17	+	12394.8i	−0.271350	+	0.469992i
$887$	17666.5	+	30599.4i	0.668754	+	1.15832i	0.978253	+	0.207416i	$0.0665053\pi$
$887$	17666.5	+	30599.4i	0.668754	+	1.15832i	−0.309499	+	0.950900i	$0.600161\pi$
$888$	−11089.1	+	5675.92i	−0.419059	+	0.214495i
$889$	15098.5	−	24512.6i	0.569616	−	0.924776i
$890$			7971.22i			0.300220i
$891$	−12772.5	−	11331.0i	−0.480240	−	0.426043i
$892$	−5270.02	−	3042.65i	−0.197818	−	0.114210i
$893$	646.160	+	373.061i	0.0242138	+	0.0139798i
$894$	15261.5	−	23595.7i	0.570940	−	0.882727i
$895$			13473.5i			0.503207i
$896$	67.4723	−	2369.63i	0.00251573	−	0.0883525i
$897$	1741.55	+	3402.47i	0.0648257	+	0.126650i
$898$	14839.2	+	25702.3i	0.551439	+	0.955120i
$899$	14728.9	−	25511.3i	0.546427	−	0.946439i
$900$	−4643.18	−	10326.2i	−0.171970	−	0.382451i
$901$	30030.5	−	17338.1i	1.11039	−	0.641084i
$902$	−23813.9			−0.879065
$903$	−21333.1	+	31010.4i	−0.786182	+	1.14282i
$904$	18271.5			0.672237
$905$	−3764.01	+	2173.15i	−0.138254	+	0.0798210i
$906$	−808.511	+	15991.0i	−0.0296479	+	0.586387i
$907$	10481.2	−	18153.9i	0.383706	−	0.664598i	−0.607883	−	0.794027i	$-0.707981\pi$
$907$	10481.2	−	18153.9i	0.383706	−	0.664598i	0.991589	+	0.129429i	$0.0413144\pi$
$908$	2918.30	+	5054.65i	0.106660	+	0.184740i
$909$	−15553.8	+	21574.7i	−0.567533	+	0.787226i
$910$	−467.399	−	865.555i	−0.0170265	−	0.0315306i
$911$		−	5419.65i		−	0.197103i	−0.995132	−	0.0985516i	$-0.968579\pi$
$911$		−	5419.65i		−	0.197103i	0.995132	−	0.0985516i	$-0.0314209\pi$
$912$	−646.910	−	418.416i	−0.0234883	−	0.0151920i
$913$	−5485.41	−	3167.00i	−0.198840	−	0.114800i
$914$	13120.0	+	7574.83i	0.474804	+	0.274128i
$915$	12302.1	+	7956.87i	0.444474	+	0.287482i
$916$		−	19178.1i		−	0.691770i
$917$	−38782.8	−	1104.29i	−1.39664	−	0.0397677i
$918$	−4917.50	+	32198.8i	−0.176799	+	1.15765i
$919$	−12706.3	−	22007.9i	−0.456084	−	0.789961i	0.542666	−	0.839949i	$-0.317415\pi$
$919$	−12706.3	−	22007.9i	−0.456084	−	0.789961i	−0.998750	+	0.0499878i	$0.984082\pi$
$920$	2234.30	−	3869.93i	0.0800682	−	0.138682i
$921$	−169.210	+	3346.69i	−0.00605390	+	0.119736i
$922$	−25721.8	+	14850.5i	−0.918767	+	0.530450i
$923$	−277.823			−0.00990754
$924$	711.354	−	8987.65i	0.0253266	−	0.319991i
$925$	−31416.1			−1.11671
$926$	5822.17	−	3361.43i	0.206618	−	0.119291i
$927$	−31644.0	+	14228.8i	−1.12117	+	0.504137i
$928$	−3324.91	+	5758.92i	−0.117614	+	0.203713i
$929$	−276.744	−	479.335i	−0.00977360	−	0.0169284i	0.861097	−	0.508440i	$-0.169778\pi$
$929$	−276.744	−	479.335i	−0.00977360	−	0.0169284i	−0.870871	+	0.491512i	$0.836444\pi$
$930$	−3014.25	−	5888.94i	−0.106281	−	0.207641i
$931$	−2657.80	−	1743.32i	−0.0935615	−	0.0613696i
$932$			6677.66i			0.234693i
$933$	−3772.55	+	5832.73i	−0.132377	+	0.204668i
$934$	399.835	+	230.845i	0.0140075	+	0.00808723i
$935$	−10573.7	−	6104.72i	−0.369836	−	0.213525i
$936$	−1270.88	−	128.841i	−0.0443802	−	0.00449925i
$937$		−	18956.6i		−	0.660923i	−0.943819	−	0.330462i	$-0.892796\pi$
$937$		−	18956.6i		−	0.660923i	0.943819	−	0.330462i	$-0.107204\pi$
$938$	3241.43	+	1996.56i	0.112832	+	0.0694989i
$939$	−7796.09	+	3990.42i	−0.270943	+	0.138682i
$940$	−723.134	−	1252.51i	−0.0250915	−	0.0434598i
$941$	−16542.7	+	28652.8i	−0.573089	+	0.992619i	0.423157	+	0.906056i	$0.360922\pi$
$941$	−16542.7	+	28652.8i	−0.573089	+	0.992619i	−0.996246	+	0.0865632i	$0.972412\pi$
$942$	5722.67	+	289.340i	0.197935	+	0.0100076i
$943$	−54763.2	+	31617.5i	−1.89113	+	1.09184i
$944$	3272.83			0.112841
$945$	11479.7	+	2089.16i	0.395168	+	0.0719158i
$946$	−18321.5			−0.629686
$947$	11619.3	−	6708.40i	0.398708	−	0.230194i	−0.287219	−	0.957865i	$-0.592731\pi$
$947$	11619.3	−	6708.40i	0.398708	−	0.230194i	0.685926	+	0.727671i	$0.259397\pi$
$948$	22154.4	+	1120.14i	0.759012	+	0.0383758i
$949$	−779.096	+	1349.43i	−0.0266497	+	0.0461586i
$950$	−971.480	−	1682.65i	−0.0331779	−	0.0574657i
$951$	−13939.8	+	7135.05i	−0.475319	+	0.243291i
$952$	−15133.7	+	8172.17i	−0.515215	+	0.278216i
$953$			36353.5i			1.23568i	0.786303	+	0.617841i	$0.211993\pi$
$953$			36353.5i			1.23568i	−0.786303	+	0.617841i	$0.788007\pi$
$954$	−16048.5	−	1626.99i	−0.544642	−	0.0552157i
$955$	1599.64	+	923.554i	0.0542023	+	0.0312937i
$956$	−12225.7	−	7058.50i	−0.413605	−	0.238795i
$957$	−13735.0	+	21235.6i	−0.463939	+	0.717294i
$958$		−	8801.72i		−	0.296838i
$959$	9954.29	−	5375.31i	0.335183	−	0.180999i
$960$	680.436	+	1329.37i	0.0228760	+	0.0446929i
$961$	−4848.13	−	8397.21i	−0.162738	−	0.281871i
$962$	−1772.23	+	3069.60i	−0.0593961	+	0.102877i
$963$	−4504.30	+	2025.37i	−0.150726	+	0.0677741i
$964$	−17076.6	+	9859.18i	−0.570540	+	0.329401i
$965$	3666.29			0.122303
$966$	−10297.0	−	21612.7i	−0.342960	−	0.719852i
$967$	3453.28			0.114840			0.0574198	−	0.998350i	$-0.481713\pi$
$967$	3453.28			0.114840			0.0574198	+	0.998350i	$0.481713\pi$
$968$	−5420.89	+	3129.75i	−0.179994	+	0.103919i
$969$	−282.254	+	5582.53i	−0.00935739	+	0.185074i
$970$	−985.992	+	1707.79i	−0.0326374	+	0.0565296i
$971$	−25320.0	−	43855.6i	−0.836826	−	1.44943i	−0.892535	−	0.450978i	$-0.851075\pi$
$971$	−25320.0	−	43855.6i	−0.836826	−	1.44943i	0.0557091	−	0.998447i	$-0.482258\pi$
$972$	10614.9	−	10812.3i	0.350281	−	0.356796i
$973$	28488.4	+	17547.4i	0.938638	+	0.578154i
$974$		−	23889.2i		−	0.785894i
$975$	−2704.97	−	1749.55i	−0.0888497	−	0.0574672i
$976$	8700.12	+	5023.02i	0.285332	+	0.164737i
$977$	26914.6	+	15539.1i	0.881344	+	0.508844i	0.871101	−	0.491103i	$-0.163406\pi$
$977$	26914.6	+	15539.1i	0.881344	+	0.508844i	0.0102426	+	0.999948i	$0.496740\pi$
$978$	20171.7	+	13046.8i	0.659528	+	0.426577i
$979$			20787.2i			0.678613i
$980$	2772.00	+	5502.41i	0.0903554	+	0.179355i
$981$	9204.42	−	12767.5i	0.299566	−	0.415529i
$982$	−19916.7	−	34496.7i	−0.647216	−	1.12101i
$983$	20154.8	−	34909.1i	0.653956	−	1.13268i	−0.328199	−	0.944609i	$-0.606442\pi$
$983$	20154.8	−	34909.1i	0.653956	−	1.13268i	0.982155	−	0.188076i	$-0.0602251\pi$
$984$	1067.12	−	21106.0i	0.0345718	−	0.683774i
$985$	2463.05	−	1422.04i	0.0796744	−	0.0460001i
$986$	48246.0			1.55828
$987$	−7724.14	−	611.350i	−0.249100	−	0.0197158i
$988$	−219.211			−0.00705873
$989$	−42132.6	+	24325.3i	−1.35464	+	0.782102i
$990$	2329.21	+	5180.03i	0.0747749	+	0.166295i
$991$	−2007.28	+	3476.71i	−0.0643425	+	0.111444i	−0.896402	−	0.443242i	$-0.853828\pi$
$991$	−2007.28	+	3476.71i	−0.0643425	+	0.111444i	0.832060	+	0.554686i	$0.187162\pi$
$992$	−2268.09	−	3928.46i	−0.0725928	−	0.125734i
$993$	1867.79	+	3649.11i	0.0596904	+	0.116617i
$994$	1739.40	+	49.5273i	0.0555035	+	0.00158039i
$995$			15372.0i			0.489773i
$996$	3052.68	−	4719.73i	0.0971163	−	0.150151i
$997$	36113.8	+	20850.3i	1.14718	+	0.662323i	0.948198	−	0.317680i	$-0.102904\pi$
$997$	36113.8	+	20850.3i	1.14718	+	0.662323i	0.198980	+	0.980004i	$0.436237\pi$
$998$	−2305.60	−	1331.14i	−0.0731287	−	0.0422209i
$999$	−15283.7	−	39166.9i	−0.484039	−	1.24043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.4.f.a.17.8	yes	16
3.2	odd	2	inner	42.4.f.a.17.3	yes	16
4.3	odd	2		336.4.bc.e.17.1		16
7.2	even	3		294.4.f.a.215.2		16
7.3	odd	6		294.4.d.a.293.14		16
7.4	even	3		294.4.d.a.293.11		16
7.5	odd	6	inner	42.4.f.a.5.3	✓	16
7.6	odd	2		294.4.f.a.227.5		16
12.11	even	2		336.4.bc.e.17.3		16
21.2	odd	6		294.4.f.a.215.5		16
21.5	even	6	inner	42.4.f.a.5.8	yes	16
21.11	odd	6		294.4.d.a.293.6		16
21.17	even	6		294.4.d.a.293.3		16
21.20	even	2		294.4.f.a.227.2		16
28.19	even	6		336.4.bc.e.257.3		16
84.47	odd	6		336.4.bc.e.257.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.3	✓	16	7.5	odd	6	inner
42.4.f.a.5.8	yes	16	21.5	even	6	inner
42.4.f.a.17.3	yes	16	3.2	odd	2	inner
42.4.f.a.17.8	yes	16	1.1	even	1	trivial
294.4.d.a.293.3		16	21.17	even	6
294.4.d.a.293.6		16	21.11	odd	6
294.4.d.a.293.11		16	7.4	even	3
294.4.d.a.293.14		16	7.3	odd	6
294.4.f.a.215.2		16	7.2	even	3
294.4.f.a.215.5		16	21.2	odd	6
294.4.f.a.227.2		16	21.20	even	2
294.4.f.a.227.5		16	7.6	odd	2
336.4.bc.e.17.1		16	4.3	odd	2
336.4.bc.e.17.3		16	12.11	even	2
336.4.bc.e.257.1		16	84.47	odd	6
336.4.bc.e.257.3		16	28.19	even	6

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.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(5.18952 + 0.262384i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-2.24534 - 3.88904i) q^{5} +(9.25090 - 4.73506i) q^{6} +(-9.71288 + 15.7690i) q^{7} -8.00000i q^{8} +(26.8623 + 2.72329i) q^{9} +(-7.77808 - 4.49068i) q^{10} +(-20.2835 - 11.7107i) q^{11} +(11.2880 - 17.4523i) q^{12} -5.91384i q^{13} +(-1.05425 + 37.0255i) q^{14} +(-10.6318 - 20.7714i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-58.0418 + 100.531i) q^{17} +(49.2502 - 22.1454i) q^{18} +(8.02533 - 4.63343i) q^{19} -17.9627 q^{20} +(-54.5428 + 79.2849i) q^{21} -46.8428 q^{22} +(-107.721 + 62.1928i) q^{23} +(2.09907 - 41.5162i) q^{24} +(52.4169 - 90.7888i) q^{25} +(-5.91384 - 10.2431i) q^{26} +(138.688 + 21.1808i) q^{27} +(35.1995 + 65.1843i) q^{28} -207.807i q^{29} +(-39.1862 - 25.3453i) q^{30} +(122.764 + 70.8780i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-102.189 - 66.0951i) q^{33} +232.167i q^{34} +(83.1348 + 2.36716i) q^{35} +(63.1584 - 87.6072i) q^{36} +(-149.838 - 259.526i) q^{37} +(9.26685 - 16.0507i) q^{38} +(1.55170 - 30.6900i) q^{39} +(-31.1123 + 17.9627i) q^{40} +508.379 q^{41} +(-15.1860 + 191.868i) q^{42} +391.127 q^{43} +(-81.1341 + 46.8428i) q^{44} +(-49.7240 - 110.583i) q^{45} +(-124.386 + 215.442i) q^{46} +(40.2575 + 69.7281i) q^{47} +(-37.8805 - 74.0072i) q^{48} +(-154.320 - 306.324i) q^{49} -209.668i q^{50} +(-327.587 + 506.481i) q^{51} +(-20.4862 - 11.8277i) q^{52} +(-258.697 - 149.359i) q^{53} +(261.396 - 102.002i) q^{54} +105.178i q^{55} +(126.152 + 77.7031i) q^{56} +(42.8634 - 21.9396i) q^{57} +(-207.807 - 359.932i) q^{58} +(-102.276 + 177.147i) q^{59} +(-93.2179 - 4.71312i) q^{60} +(-543.757 + 313.939i) q^{61} +283.512 q^{62} +(-303.854 + 397.139i) q^{63} -64.0000 q^{64} +(-22.9992 + 13.2786i) q^{65} +(-243.092 - 12.2908i) q^{66} +(51.3894 - 89.0091i) q^{67} +(232.167 + 402.126i) q^{68} +(-575.340 + 294.487i) q^{69} +(146.361 - 79.0348i) q^{70} -46.9785i q^{71} +(21.7863 - 214.898i) q^{72} +(-228.182 - 131.741i) q^{73} +(-519.053 - 299.675i) q^{74} +(295.840 - 457.397i) q^{75} -37.0674i q^{76} +(381.677 - 206.105i) q^{77} +(-28.0024 - 54.7084i) q^{78} +(533.634 + 924.281i) q^{79} +(-35.9254 + 62.2246i) q^{80} +(714.167 + 146.308i) q^{81} +(880.538 - 508.379i) q^{82} +270.436 q^{83} +(165.565 + 347.511i) q^{84} +521.294 q^{85} +(677.452 - 391.127i) q^{86} +(54.5252 - 1078.42i) q^{87} +(-93.6856 + 162.268i) q^{88} +(-443.765 - 768.624i) q^{89} +(-196.708 - 141.812i) q^{90} +(93.2551 + 57.4405i) q^{91} +497.543i q^{92} +(618.491 + 400.034i) q^{93} +(139.456 + 80.5151i) q^{94} +(-36.0392 - 20.8072i) q^{95} +(-139.618 - 90.3038i) q^{96} -219.564i q^{97} +(-573.614 - 376.249i) q^{98} +(-512.971 - 369.815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36}+ \cdots - 4284 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more