LMFDB - Embedded newform 490.4.c.c.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(99,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.43197465600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 16x^{3} + 1521x^{2} - 624x + 128 $ x^6 - 16x^3 + 1521x^2 - 624*x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-4.51508 + 4.51508i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.c.99.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -10.2673i q^{3} -4.00000 q^{4} +(8.27790 + 7.51508i) q^{5} -20.5347 q^{6} +8.00000i q^{8} -78.4181 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -10.2673i q^{3} -4.00000 q^{4} +(8.27790 + 7.51508i) q^{5} -20.5347 q^{6} +8.00000i q^{8} -78.4181 q^{9} +(15.0302 - 16.5558i) q^{10} -30.8834 q^{11} +41.0693i q^{12} -53.3367i q^{13} +(77.1598 - 84.9919i) q^{15} +16.0000 q^{16} -1.41810i q^{17} +156.836i q^{18} -88.3588 q^{19} +(-33.1116 - 30.0603i) q^{20} +61.7669i q^{22} +85.0451i q^{23} +82.1387 q^{24} +(12.0472 + 124.418i) q^{25} -106.673 q^{26} +527.927i q^{27} +49.5810 q^{29} +(-169.984 - 154.320i) q^{30} -62.7218 q^{31} -32.0000i q^{32} +317.091i q^{33} -2.83620 q^{34} +313.672 q^{36} +251.672i q^{37} +176.718i q^{38} -547.625 q^{39} +(-60.1206 + 66.2232i) q^{40} +197.322 q^{41} +93.8838i q^{43} +123.534 q^{44} +(-649.137 - 589.318i) q^{45} +170.090 q^{46} -211.112i q^{47} -164.277i q^{48} +(248.836 - 24.0945i) q^{50} -14.5601 q^{51} +213.347i q^{52} -388.997i q^{53} +1055.85 q^{54} +(-255.650 - 232.091i) q^{55} +907.209i q^{57} -99.1620i q^{58} -384.238 q^{59} +(-308.639 + 339.968i) q^{60} +114.476 q^{61} +125.444i q^{62} -64.0000 q^{64} +(400.829 - 441.515i) q^{65} +634.181 q^{66} +313.164i q^{67} +5.67241i q^{68} +873.186 q^{69} -345.783 q^{71} -627.345i q^{72} +381.137i q^{73} +503.345 q^{74} +(1277.44 - 123.693i) q^{75} +353.435 q^{76} +1095.25i q^{78} -957.577 q^{79} +(132.446 + 120.241i) q^{80} +3303.11 q^{81} -394.645i q^{82} +135.761i q^{83} +(10.6571 - 11.7389i) q^{85} +187.768 q^{86} -509.064i q^{87} -247.068i q^{88} -184.287 q^{89} +(-1178.64 + 1298.27i) q^{90} -340.180i q^{92} +643.985i q^{93} -422.225 q^{94} +(-731.425 - 664.023i) q^{95} -328.555 q^{96} -1259.42i q^{97} +2421.82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{4} + 16 q^{5} - 28 q^{6} - 152 q^{9}+O(q^{10}) $ 6 * q - 24 * q^4 + 16 * q^5 - 28 * q^6 - 152 * q^9	$ 6 q - 24 q^{4} + 16 q^{5} - 28 q^{6} - 152 q^{9} + 36 q^{10} + 38 q^{11} + 110 q^{15} + 96 q^{16} + 312 q^{19} - 64 q^{20} + 112 q^{24} + 486 q^{25} - 164 q^{26} - 182 q^{29} + 80 q^{30} - 340 q^{31} + 620 q^{34} + 608 q^{36} - 1598 q^{39} - 144 q^{40} + 12 q^{41} - 152 q^{44} - 1988 q^{45} + 200 q^{46} + 856 q^{50} - 238 q^{51} + 1876 q^{54} - 1636 q^{55} + 1180 q^{59} - 440 q^{60} - 704 q^{61} - 384 q^{64} + 586 q^{65} + 620 q^{66} + 4500 q^{69} + 1448 q^{71} + 472 q^{74} + 1960 q^{75} - 1248 q^{76} - 2074 q^{79} + 256 q^{80} + 4814 q^{81} - 82 q^{85} - 864 q^{86} - 2096 q^{89} - 2608 q^{90} + 316 q^{94} + 100 q^{95} - 448 q^{96} + 6556 q^{99}+O(q^{100}) $ 6 * q - 24 * q^4 + 16 * q^5 - 28 * q^6 - 152 * q^9 + 36 * q^10 + 38 * q^11 + 110 * q^15 + 96 * q^16 + 312 * q^19 - 64 * q^20 + 112 * q^24 + 486 * q^25 - 164 * q^26 - 182 * q^29 + 80 * q^30 - 340 * q^31 + 620 * q^34 + 608 * q^36 - 1598 * q^39 - 144 * q^40 + 12 * q^41 - 152 * q^44 - 1988 * q^45 + 200 * q^46 + 856 * q^50 - 238 * q^51 + 1876 * q^54 - 1636 * q^55 + 1180 * q^59 - 440 * q^60 - 704 * q^61 - 384 * q^64 + 586 * q^65 + 620 * q^66 + 4500 * q^69 + 1448 * q^71 + 472 * q^74 + 1960 * q^75 - 1248 * q^76 - 2074 * q^79 + 256 * q^80 + 4814 * q^81 - 82 * q^85 - 864 * q^86 - 2096 * q^89 - 2608 * q^90 + 316 * q^94 + 100 * q^95 - 448 * q^96 + 6556 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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
$3$		−	10.2673i		−	1.97595i	−0.154617	−	0.987974i	$-0.549414\pi$
$3$		−	10.2673i		−	1.97595i	0.154617	−	0.987974i	$-0.450586\pi$
$4$	−4.00000			−0.500000
$5$	8.27790	+	7.51508i	0.740398	+	0.672169i
$5$	8.27790	+	7.51508i	0.740398	+	0.672169i
$6$	−20.5347			−1.39721
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	−78.4181			−2.90437
$10$	15.0302	−	16.5558i	0.475295	−	0.523540i
$11$	−30.8834			−0.846519			−0.423259	−	0.906009i	$-0.639114\pi$
$11$	−30.8834			−0.846519			−0.423259	+	0.906009i	$0.639114\pi$
$12$			41.0693i			0.987974i
$13$		−	53.3367i		−	1.13792i	−0.822366	−	0.568959i	$-0.807346\pi$
$13$		−	53.3367i		−	1.13792i	0.822366	−	0.568959i	$-0.192654\pi$
$14$		0			0
$15$	77.1598	−	84.9919i	1.32817	−	1.46299i
$16$	16.0000			0.250000
$17$		−	1.41810i		−	0.0202318i	−0.999949	−	0.0101159i	$-0.996780\pi$
$17$		−	1.41810i		−	0.0202318i	0.999949	−	0.0101159i	$-0.00322004\pi$
$18$			156.836i			2.05370i
$19$	−88.3588			−1.06689			−0.533444	−	0.845835i	$-0.679103\pi$
$19$	−88.3588			−1.06689			−0.533444	+	0.845835i	$0.679103\pi$
$20$	−33.1116	−	30.0603i	−0.370199	−	0.336084i
$21$		0			0
$22$			61.7669i			0.598579i
$23$			85.0451i			0.771006i	0.922707	+	0.385503i	$0.125972\pi$
$23$			85.0451i			0.771006i	−0.922707	+	0.385503i	$0.874028\pi$
$24$	82.1387			0.698603
$25$	12.0472	+	124.418i	0.0963779	+	0.995345i
$26$	−106.673			−0.804629
$27$			527.927i			3.76295i
$28$		0			0
$29$	49.5810			0.317481			0.158741	−	0.987320i	$-0.449257\pi$
$29$	49.5810			0.317481			0.158741	+	0.987320i	$0.449257\pi$
$30$	−169.984	−	154.320i	−1.03449	−	0.939159i
$31$	−62.7218			−0.363392			−0.181696	−	0.983355i	$-0.558159\pi$
$31$	−62.7218			−0.363392			−0.181696	+	0.983355i	$0.558159\pi$
$32$		−	32.0000i		−	0.176777i
$33$			317.091i			1.67268i
$34$	−2.83620			−0.0143060
$35$		0			0
$36$	313.672			1.45219
$37$			251.672i			1.11823i	0.829088	+	0.559117i	$0.188860\pi$
$37$			251.672i			1.11823i	−0.829088	+	0.559117i	$0.811140\pi$
$38$			176.718i			0.754404i
$39$	−547.625			−2.24847
$40$	−60.1206	+	66.2232i	−0.237648	+	0.261770i
$41$	197.322			0.751624			0.375812	−	0.926696i	$-0.377364\pi$
$41$	197.322			0.751624			0.375812	+	0.926696i	$0.377364\pi$
$42$		0			0
$43$			93.8838i			0.332957i	0.986045	+	0.166478i	$0.0532396\pi$
$43$			93.8838i			0.332957i	−0.986045	+	0.166478i	$0.946760\pi$
$44$	123.534			0.423259
$45$	−649.137	−	589.318i	−2.15039	−	1.95223i
$46$	170.090			0.545183
$47$		−	211.112i		−	0.655189i	−0.944818	−	0.327595i	$-0.893762\pi$
$47$		−	211.112i		−	0.655189i	0.944818	−	0.327595i	$-0.106238\pi$
$48$		−	164.277i		−	0.493987i
$49$		0			0
$50$	248.836	−	24.0945i	0.703815	−	0.0681494i
$51$	−14.5601			−0.0399770
$52$			213.347i			0.568959i
$53$		−	388.997i		−	1.00817i	−0.863655	−	0.504083i	$-0.831831\pi$
$53$		−	388.997i		−	1.00817i	0.863655	−	0.504083i	$-0.168169\pi$
$54$	1055.85			2.66080
$55$	−255.650	−	232.091i	−0.626761	−	0.569004i
$56$		0			0
$57$			907.209i			2.10812i
$58$		−	99.1620i		−	0.224493i
$59$	−384.238			−0.847857			−0.423928	−	0.905696i	$-0.639349\pi$
$59$	−384.238			−0.847857			−0.423928	+	0.905696i	$0.639349\pi$
$60$	−308.639	+	339.968i	−0.664086	+	0.731494i
$61$	114.476			0.240280			0.120140	−	0.992757i	$-0.461666\pi$
$61$	114.476			0.240280			0.120140	+	0.992757i	$0.461666\pi$
$62$			125.444i			0.256957i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	400.829	−	441.515i	0.764873	−	0.842512i
$66$	634.181			1.18276
$67$			313.164i			0.571031i	0.958374	+	0.285515i	$0.0921647\pi$
$67$			313.164i			0.571031i	−0.958374	+	0.285515i	$0.907835\pi$
$68$			5.67241i			0.0101159i
$69$	873.186			1.52347
$70$		0			0
$71$	−345.783			−0.577984			−0.288992	−	0.957332i	$-0.593320\pi$
$71$	−345.783			−0.577984			−0.288992	+	0.957332i	$0.593320\pi$
$72$		−	627.345i		−	1.02685i
$73$			381.137i			0.611078i	0.952179	+	0.305539i	$0.0988367\pi$
$73$			381.137i			0.611078i	−0.952179	+	0.305539i	$0.901163\pi$
$74$	503.345			0.790711
$75$	1277.44	−	123.693i	1.96675	−	0.190438i
$76$	353.435			0.533444
$77$		0			0
$78$			1095.25i			1.58991i
$79$	−957.577			−1.36375			−0.681873	−	0.731471i	$-0.738834\pi$
$79$	−957.577			−1.36375			−0.681873	+	0.731471i	$0.738834\pi$
$80$	132.446	+	120.241i	0.185099	+	0.168042i
$81$	3303.11			4.53102
$82$		−	394.645i		−	0.531478i
$83$			135.761i			0.179538i	0.995963	+	0.0897690i	$0.0286129\pi$
$83$			135.761i			0.179538i	−0.995963	+	0.0897690i	$0.971387\pi$
$84$		0			0
$85$	10.6571	−	11.7389i	0.0135992	−	0.0149796i
$86$	187.768			0.235436
$87$		−	509.064i		−	0.627327i
$88$		−	247.068i		−	0.299290i
$89$	−184.287			−0.219487			−0.109743	−	0.993960i	$-0.535003\pi$
$89$	−184.287			−0.219487			−0.109743	+	0.993960i	$0.535003\pi$
$90$	−1178.64	+	1298.27i	−1.38044	+	1.52056i
$91$		0			0
$92$		−	340.180i		−	0.385503i
$93$			643.985i			0.718045i
$94$	−422.225			−0.463289
$95$	−731.425	−	664.023i	−0.789922	−	0.717130i
$96$	−328.555			−0.349302
$97$		−	1259.42i		−	1.31829i	−0.752015	−	0.659146i	$-0.770918\pi$
$97$		−	1259.42i		−	1.31829i	0.752015	−	0.659146i	$-0.229082\pi$
$98$		0			0
$99$	2421.82			2.45861
$100$	−48.1889	−	497.672i	−0.0481889	−	0.497672i
$101$	−86.7354			−0.0854505			−0.0427252	−	0.999087i	$-0.513604\pi$
$101$	−86.7354			−0.0854505			−0.0427252	+	0.999087i	$0.513604\pi$
$102$			29.1203i			0.0282680i
$103$		−	540.782i		−	0.517329i	−0.965967	−	0.258664i	$-0.916718\pi$
$103$		−	540.782i		−	0.517329i	0.965967	−	0.258664i	$-0.0832824\pi$
$104$	426.693			0.402315
$105$		0			0
$106$	−777.993			−0.712881
$107$		−	1997.38i		−	1.80462i	−0.431092	−	0.902308i	$-0.641871\pi$
$107$		−	1997.38i		−	1.80462i	0.431092	−	0.902308i	$-0.358129\pi$
$108$		−	2111.71i		−	1.88147i
$109$	−1537.05			−1.35067			−0.675335	−	0.737511i	$-0.736001\pi$
$109$	−1537.05			−1.35067			−0.675335	+	0.737511i	$0.736001\pi$
$110$	−464.183	+	511.300i	−0.402346	+	0.443187i
$111$	2584.00			2.20957
$112$		0			0
$113$			470.700i			0.391856i	0.980618	+	0.195928i	$0.0627719\pi$
$113$			470.700i			0.391856i	−0.980618	+	0.195928i	$0.937228\pi$
$114$	1814.42			1.49066
$115$	−639.120	+	703.995i	−0.518246	+	0.570851i
$116$	−198.324			−0.158741
$117$			4182.56i			3.30494i
$118$			768.476i			0.599525i
$119$		0			0
$120$	679.936	+	617.278i	0.517244	+	0.469580i
$121$	−377.213			−0.283406
$122$		−	228.951i		−	0.169904i
$123$		−	2025.97i		−	1.48517i
$124$	250.887			0.181696
$125$	−835.286	+	1120.46i	−0.597682	+	0.801733i
$126$		0			0
$127$			1132.37i			0.791196i	0.918424	+	0.395598i	$0.129463\pi$
$127$			1132.37i			0.791196i	−0.918424	+	0.395598i	$0.870537\pi$
$128$			128.000i			0.0883883i
$129$	963.936			0.657905
$130$	−883.031	−	801.658i	−0.595746	−	0.540847i
$131$	−2766.44			−1.84508			−0.922538	−	0.385905i	$-0.873889\pi$
$131$	−2766.44			−1.84508			−0.922538	+	0.385905i	$0.873889\pi$
$132$		−	1268.36i		−	0.836339i
$133$		0			0
$134$	626.328			0.403780
$135$	−3967.41	+	4370.12i	−2.52934	+	2.78608i
$136$	11.3448			0.00715302
$137$			3054.72i			1.90498i	0.304572	+	0.952489i	$0.401487\pi$
$137$			3054.72i			1.90498i	−0.304572	+	0.952489i	$0.598513\pi$
$138$		−	1746.37i		−	1.07725i
$139$	−1057.41			−0.645239			−0.322619	−	0.946529i	$-0.604563\pi$
$139$	−1057.41			−0.645239			−0.322619	+	0.946529i	$0.604563\pi$
$140$		0			0
$141$	−2167.56			−1.29462
$142$			691.565i			0.408696i
$143$			1647.22i			0.963269i
$144$	−1254.69			−0.726094
$145$	410.426	+	372.605i	0.235062	+	0.213401i
$146$	762.274			0.432098
$147$		0			0
$148$		−	1006.69i		−	0.559117i
$149$	510.799			0.280848			0.140424	−	0.990091i	$-0.455153\pi$
$149$	510.799			0.280848			0.140424	+	0.990091i	$0.455153\pi$
$150$	−247.386	−	2554.88i	−0.134660	−	1.39070i
$151$	2393.68			1.29003			0.645017	−	0.764168i	$-0.276850\pi$
$151$	2393.68			1.29003			0.645017	+	0.764168i	$0.276850\pi$
$152$		−	706.870i		−	0.377202i
$153$			111.205i			0.0587607i
$154$		0			0
$155$	−519.205	−	471.359i	−0.269055	−	0.244261i
$156$	2190.50			1.12423
$157$			395.381i			0.200986i	0.994938	+	0.100493i	$0.0320420\pi$
$157$			395.381i			0.200986i	−0.994938	+	0.100493i	$0.967958\pi$
$158$			1915.15i			0.964313i
$159$	−3993.96			−1.99208
$160$	240.482	−	264.893i	0.118824	−	0.130885i
$161$		0			0
$162$		−	6606.22i		−	3.20391i
$163$		−	3027.47i		−	1.45479i	−0.686221	−	0.727393i	$-0.740732\pi$
$163$		−	3027.47i		−	1.45479i	0.686221	−	0.727393i	$-0.259268\pi$
$164$	−789.290			−0.375812
$165$	−2382.96	+	2624.84i	−1.12432	+	1.23845i
$166$	271.521			0.126953
$167$		−	714.032i		−	0.330859i	−0.986222	−	0.165430i	$-0.947099\pi$
$167$		−	714.032i		−	0.330859i	0.986222	−	0.165430i	$-0.0529010\pi$
$168$		0			0
$169$	−647.799			−0.294856
$170$	−23.4778	−	21.3143i	−0.0105922	−	0.00961607i
$171$	6928.93			3.09864
$172$		−	375.535i		−	0.166478i
$173$		−	1137.15i		−	0.499745i	−0.968279	−	0.249872i	$-0.919611\pi$
$173$		−	1137.15i		−	0.499745i	0.968279	−	0.249872i	$-0.0803886\pi$
$174$	−1018.13			−0.443587
$175$		0			0
$176$	−494.135			−0.211630
$177$			3945.10i			1.67532i
$178$			368.573i			0.155201i
$179$	407.397			0.170113			0.0850566	−	0.996376i	$-0.472893\pi$
$179$	407.397			0.170113			0.0850566	+	0.996376i	$0.472893\pi$
$180$	2596.55	+	2357.27i	1.07520	+	0.976115i
$181$	−2517.81			−1.03396			−0.516981	−	0.855997i	$-0.672944\pi$
$181$	−2517.81			−1.03396			−0.516981	+	0.855997i	$0.672944\pi$
$182$		0			0
$183$		−	1175.36i		−	0.474782i
$184$	−680.361			−0.272592
$185$	−1891.34	+	2083.32i	−0.751643	+	0.827939i
$186$	1287.97			0.507734
$187$			43.7959i			0.0171266i
$188$			844.449i			0.327595i
$189$		0			0
$190$	−1328.05	+	1462.85i	−0.507087	+	0.558559i
$191$	−1165.88			−0.441674			−0.220837	−	0.975311i	$-0.570879\pi$
$191$	−1165.88			−0.441674			−0.220837	+	0.975311i	$0.570879\pi$
$192$			657.109i			0.246994i
$193$		−	168.672i		−	0.0629080i	−0.999505	−	0.0314540i	$-0.989986\pi$
$193$		−	168.672i		−	0.0629080i	0.999505	−	0.0314540i	$-0.0100138\pi$
$194$	−2518.83			−0.932173
$195$	−4533.19	−	4115.45i	−1.66476	−	1.51135i
$196$		0			0
$197$			2929.19i			1.05937i	0.848194	+	0.529686i	$0.177690\pi$
$197$			2929.19i			1.05937i	−0.848194	+	0.529686i	$0.822310\pi$
$198$		−	4843.64i		−	1.73850i
$199$	−4731.19			−1.68535			−0.842677	−	0.538419i	$-0.819022\pi$
$199$	−4731.19			−1.68535			−0.842677	+	0.538419i	$0.819022\pi$
$200$	−995.345	+	96.3779i	−0.351908	+	0.0340747i
$201$	3215.36			1.12833
$202$			173.471i			0.0604226i
$203$		0			0
$204$	58.2405			0.0199885
$205$	1633.41	+	1482.89i	0.556501	+	0.505218i
$206$	−1081.56			−0.365807
$207$		−	6669.07i		−	2.23929i
$208$		−	853.387i		−	0.284479i
$209$	2728.82			0.903141
$210$		0			0
$211$	2372.31			0.774013			0.387006	−	0.922077i	$-0.373509\pi$
$211$	2372.31			0.774013			0.387006	+	0.922077i	$0.373509\pi$
$212$			1555.99i			0.504083i
$213$			3550.26i			1.14207i
$214$	−3994.76			−1.27606
$215$	−705.544	+	777.160i	−0.223803	+	0.246520i
$216$	−4223.41			−1.33040
$217$		0			0
$218$			3074.11i			0.955067i
$219$	3913.26			1.20746
$220$	1022.60	+	928.366i	0.313380	+	0.284502i
$221$	−75.6368			−0.0230221
$222$		−	5168.01i		−	1.56241i
$223$		−	5490.39i		−	1.64872i	−0.566069	−	0.824358i	$-0.691537\pi$
$223$		−	5490.39i		−	1.64872i	0.566069	−	0.824358i	$-0.308463\pi$
$224$		0			0
$225$	−944.721	−	9756.63i	−0.279917	−	2.89085i
$226$	941.400			0.277084
$227$			1178.68i			0.344634i	0.985042	+	0.172317i	$0.0551253\pi$
$227$			1178.68i			0.344634i	−0.985042	+	0.172317i	$0.944875\pi$
$228$		−	3628.83i		−	1.05406i
$229$	6353.35			1.83337			0.916684	−	0.399613i	$-0.130855\pi$
$229$	6353.35			1.83337			0.916684	+	0.399613i	$0.130855\pi$
$230$	1407.99	+	1278.24i	0.403653	+	0.366455i
$231$		0			0
$232$			396.648i			0.112247i
$233$		−	1458.02i		−	0.409947i	−0.978767	−	0.204974i	$-0.934289\pi$
$233$		−	1458.02i		−	0.409947i	0.978767	−	0.204974i	$-0.0657109\pi$
$234$	8365.12			2.33694
$235$	1586.53	−	1747.57i	0.440398	−	0.485101i
$236$	1536.95			0.423928
$237$			9831.76i			2.69469i
$238$		0			0
$239$	−4642.36			−1.25644			−0.628220	−	0.778036i	$-0.716216\pi$
$239$	−4642.36			−1.25644			−0.628220	+	0.778036i	$0.716216\pi$
$240$	1234.56	−	1359.87i	0.332043	−	0.365747i
$241$	−5389.12			−1.44043			−0.720216	−	0.693750i	$-0.755957\pi$
$241$	−5389.12			−1.44043			−0.720216	+	0.693750i	$0.755957\pi$
$242$			754.426i			0.200398i
$243$		−	19660.1i		−	5.19011i
$244$	−457.903			−0.120140
$245$		0			0
$246$	−4051.95			−1.05017
$247$			4712.76i			1.21403i
$248$		−	501.774i		−	0.128479i
$249$	1393.90			0.354758
$250$	2240.91	+	1670.57i	0.566911	+	0.422625i
$251$	3350.16			0.842470			0.421235	−	0.906952i	$-0.361597\pi$
$251$	3350.16			0.842470			0.421235	+	0.906952i	$0.361597\pi$
$252$		0			0
$253$		−	2626.48i		−	0.652671i
$254$	2264.75			0.559460
$255$	−120.527	−	109.420i	−0.0295989	−	0.0268713i
$256$	256.000			0.0625000
$257$		−	1165.91i		−	0.282985i	−0.989939	−	0.141493i	$-0.954810\pi$
$257$		−	1165.91i		−	0.282985i	0.989939	−	0.141493i	$-0.0451901\pi$
$258$		−	1927.87i		−	0.465209i
$259$		0			0
$260$	−1603.32	+	1766.06i	−0.382436	+	0.421256i
$261$	−3888.05			−0.922085
$262$			5532.88i			1.30467i
$263$			1241.81i			0.291152i	0.989347	+	0.145576i	$0.0465036\pi$
$263$			1241.81i			0.291152i	−0.989347	+	0.145576i	$0.953496\pi$
$264$	−2536.72			−0.591381
$265$	2923.34	−	3220.07i	0.677658	−	0.746444i
$266$		0			0
$267$			1892.13i			0.433695i
$268$		−	1252.66i		−	0.285515i
$269$	1513.58			0.343066			0.171533	−	0.985178i	$-0.445128\pi$
$269$	1513.58			0.343066			0.171533	+	0.985178i	$0.445128\pi$
$270$	8740.25	+	7934.82i	1.97005	+	1.78851i
$271$	−7113.17			−1.59444			−0.797222	−	0.603687i	$-0.793698\pi$
$271$	−7113.17			−1.59444			−0.797222	+	0.603687i	$0.793698\pi$
$272$		−	22.6896i		−	0.00505795i
$273$		0			0
$274$	6109.43			1.34702
$275$	−372.060	−	3842.46i	−0.0815857	−	0.842578i
$276$	−3492.74			−0.761734
$277$			4851.92i			1.05243i	0.850351	+	0.526216i	$0.176390\pi$
$277$			4851.92i			1.05243i	−0.850351	+	0.526216i	$0.823610\pi$
$278$			2114.82i			0.456253i
$279$	4918.52			1.05543
$280$		0			0
$281$	−8726.67			−1.85263			−0.926315	−	0.376749i	$-0.877042\pi$
$281$	−8726.67			−1.85263			−0.926315	+	0.376749i	$0.877042\pi$
$282$			4335.12i			0.915435i
$283$			1671.69i			0.351136i	0.984467	+	0.175568i	$0.0561762\pi$
$283$			1671.69i			0.351136i	−0.984467	+	0.175568i	$0.943824\pi$
$284$	1383.13			0.288992
$285$	−6817.74	+	7509.78i	−1.41701	+	1.56085i
$286$	3294.44			0.681134
$287$		0			0
$288$			2509.38i			0.513426i
$289$	4910.99			0.999591
$290$	745.210	−	820.853i	0.150897	−	0.166214i
$291$	−12930.8			−2.60488
$292$		−	1524.55i		−	0.305539i
$293$		−	5658.60i		−	1.12825i	−0.825688	−	0.564127i	$-0.809213\pi$
$293$		−	5658.60i		−	1.12825i	0.825688	−	0.564127i	$-0.190787\pi$
$294$		0			0
$295$	−3180.69	−	2887.58i	−0.627751	−	0.569903i
$296$	−2013.38			−0.395356
$297$		−	16304.2i		−	3.18540i
$298$		−	1021.60i		−	0.198589i
$299$	4536.02			0.877341
$300$	−5109.77	+	494.772i	−0.983375	+	0.0952189i
$301$		0			0
$302$		−	4787.37i		−	0.912192i
$303$			890.542i			0.168846i
$304$	−1413.74			−0.266722
$305$	947.618	+	860.293i	0.177903	+	0.161509i
$306$	222.410			0.0415501
$307$			3231.56i			0.600764i	0.953819	+	0.300382i	$0.0971142\pi$
$307$			3231.56i			0.600764i	−0.953819	+	0.300382i	$0.902886\pi$
$308$		0			0
$309$	−5552.39			−1.02222
$310$	−942.718	+	1038.41i	−0.172719	+	0.190251i
$311$	−5952.20			−1.08527			−0.542634	−	0.839970i	$-0.682573\pi$
$311$	−5952.20			−1.08527			−0.542634	+	0.839970i	$0.682573\pi$
$312$		−	4381.00i		−	0.794953i
$313$			8920.21i			1.61086i	0.592689	+	0.805431i	$0.298066\pi$
$313$			8920.21i			1.61086i	−0.592689	+	0.805431i	$0.701934\pi$
$314$	790.762			0.142119
$315$		0			0
$316$	3830.31			0.681873
$317$		−	8045.97i		−	1.42557i	−0.701381	−	0.712787i	$-0.747433\pi$
$317$		−	8045.97i		−	1.42557i	0.701381	−	0.712787i	$-0.252567\pi$
$318$			7987.91i			1.40862i
$319$	−1531.23			−0.268754
$320$	−529.786	−	480.965i	−0.0925497	−	0.0840211i
$321$	−20507.8			−3.56583
$322$		0			0
$323$			125.302i			0.0215851i
$324$	−13212.4			−2.26551
$325$	6636.05	−	642.559i	1.13262	−	0.109670i
$326$	−6054.95			−1.02869
$327$			15781.4i			2.66885i
$328$			1578.58i			0.265739i
$329$		0			0
$330$	5249.69	+	4765.92i	0.875714	+	0.795016i
$331$	5583.61			0.927200			0.463600	−	0.886045i	$-0.346557\pi$
$331$	5583.61			0.927200			0.463600	+	0.886045i	$0.346557\pi$
$332$		−	543.042i		−	0.0897690i
$333$		−	19735.7i		−	3.24777i
$334$	−1428.06			−0.233953
$335$	−2353.45	+	2592.34i	−0.383829	+	0.422790i
$336$		0			0
$337$		−	4267.42i		−	0.689796i	−0.938640	−	0.344898i	$-0.887913\pi$
$337$		−	4267.42i		−	0.689796i	0.938640	−	0.344898i	$-0.112087\pi$
$338$			1295.60i			0.208495i
$339$	4832.83			0.774288
$340$	−42.6286	+	46.9556i	−0.00679959	+	0.00748978i
$341$	1937.06			0.307619
$342$		−	13857.9i		−	2.19107i
$343$		0			0
$344$	−751.070			−0.117718
$345$	7228.15	+	6562.06i	1.12797	+	1.02403i
$346$	−2274.30			−0.353373
$347$			8052.36i			1.24574i	0.782323	+	0.622872i	$0.214034\pi$
$347$			8052.36i			1.24574i	−0.782323	+	0.622872i	$0.785966\pi$
$348$			2036.26i			0.313663i
$349$	8817.10			1.35235			0.676173	−	0.736743i	$-0.263637\pi$
$349$	8817.10			1.35235			0.676173	+	0.736743i	$0.263637\pi$
$350$		0			0
$351$	28157.8			4.28192
$352$			988.270i			0.149645i
$353$		−	7561.81i		−	1.14016i	−0.821591	−	0.570078i	$-0.806913\pi$
$353$		−	7561.81i		−	1.14016i	0.821591	−	0.570078i	$-0.193087\pi$
$354$	7890.20			1.18463
$355$	−2862.35	−	2598.58i	−0.427938	−	0.388503i
$356$	737.146			0.109743
$357$		0			0
$358$		−	814.794i		−	0.120288i
$359$	−9873.62			−1.45156			−0.725779	−	0.687928i	$-0.758521\pi$
$359$	−9873.62			−1.45156			−0.725779	+	0.687928i	$0.758521\pi$
$360$	4714.54	−	5193.10i	0.690218	−	0.760278i
$361$	948.269			0.138252
$362$			5035.62i			0.731122i
$363$			3872.97i			0.559996i
$364$		0			0
$365$	−2864.27	+	3155.01i	−0.410748	+	0.452441i
$366$	−2350.72			−0.335721
$367$			4845.75i			0.689226i	0.938745	+	0.344613i	$0.111990\pi$
$367$			4845.75i			0.689226i	−0.938745	+	0.344613i	$0.888010\pi$
$368$			1360.72i			0.192751i
$369$	−15473.6			−2.18300
$370$	4166.64	+	3782.68i	0.585441	+	0.531492i
$371$		0			0
$372$		−	2575.94i		−	0.359022i
$373$			4775.10i			0.662856i	0.943480	+	0.331428i	$0.107530\pi$
$373$			4775.10i			0.662856i	−0.943480	+	0.331428i	$0.892470\pi$
$374$	87.5917			0.0121103
$375$	11504.1	+	8576.16i	1.58418	+	1.18099i
$376$	1688.90			0.231644
$377$		−	2644.48i		−	0.361268i
$378$		0			0
$379$	5614.29			0.760914			0.380457	−	0.924799i	$-0.375767\pi$
$379$	5614.29			0.760914			0.380457	+	0.924799i	$0.375767\pi$
$380$	2925.70	+	2656.09i	0.394961	+	0.358565i
$381$	11626.4			1.56336
$382$			2331.75i			0.312311i
$383$		−	8369.30i		−	1.11658i	−0.829645	−	0.558291i	$-0.811457\pi$
$383$		−	8369.30i		−	1.11658i	0.829645	−	0.558291i	$-0.188543\pi$
$384$	1314.22			0.174651
$385$		0			0
$386$	−337.343			−0.0444827
$387$		−	7362.19i		−	0.967031i
$388$			5037.67i			0.659146i
$389$	4412.56			0.575130			0.287565	−	0.957761i	$-0.407154\pi$
$389$	4412.56			0.575130			0.287565	+	0.957761i	$0.407154\pi$
$390$	−8230.89	+	9066.37i	−1.06869	+	1.17716i
$391$	120.603			0.0155988
$392$		0			0
$393$			28404.0i			3.64578i
$394$	5858.39			0.749090
$395$	−7926.73	−	7196.27i	−1.00971	−	0.916667i
$396$	−9687.28			−1.22930
$397$			1865.36i			0.235819i	0.993024	+	0.117909i	$0.0376192\pi$
$397$			1865.36i			0.235819i	−0.993024	+	0.117909i	$0.962381\pi$
$398$			9462.39i			1.19173i
$399$		0			0
$400$	192.756	+	1990.69i	0.0240945	+	0.248836i
$401$	−12981.9			−1.61667			−0.808335	−	0.588722i	$-0.799631\pi$
$401$	−12981.9			−1.61667			−0.808335	+	0.588722i	$0.799631\pi$
$402$		−	6430.71i		−	0.797848i
$403$			3345.37i			0.413511i
$404$	346.942			0.0427252
$405$	27342.8	+	24823.1i	3.35475	+	3.04561i
$406$		0			0
$407$		−	7772.51i		−	0.946607i
$408$		−	116.481i		−	0.0141340i
$409$	6240.07			0.754405			0.377203	−	0.926131i	$-0.376886\pi$
$409$	6240.07			0.754405			0.377203	+	0.926131i	$0.376886\pi$
$410$	2965.79	−	3266.83i	0.357243	−	0.393505i
$411$	31363.8			3.76414
$412$			2163.13i			0.258664i
$413$		0			0
$414$	−13338.1			−1.58342
$415$	−1020.25	+	1123.81i	−0.120680	+	0.132930i
$416$	−1706.77			−0.201157
$417$			10856.8i			1.27496i
$418$		−	5457.64i		−	0.638617i
$419$	−6690.95			−0.780130			−0.390065	−	0.920787i	$-0.627547\pi$
$419$	−6690.95			−0.780130			−0.390065	+	0.920787i	$0.627547\pi$
$420$		0			0
$421$	1955.47			0.226375			0.113187	−	0.993574i	$-0.463894\pi$
$421$	1955.47			0.226375			0.113187	+	0.993574i	$0.463894\pi$
$422$		−	4744.62i		−	0.547310i
$423$			16555.0i			1.90291i
$424$	3111.97			0.356440
$425$	176.438	−	17.0842i	0.0201376	−	0.00194990i
$426$	7100.53			0.807563
$427$		0			0
$428$			7989.52i			0.902308i
$429$	16912.5			1.90337
$430$	1554.32	+	1411.09i	0.174316	+	0.158253i
$431$	−1069.96			−0.119578			−0.0597890	−	0.998211i	$-0.519043\pi$
$431$	−1069.96			−0.119578			−0.0597890	+	0.998211i	$0.519043\pi$
$432$			8446.83i			0.940737i
$433$		−	8915.27i		−	0.989470i	−0.869044	−	0.494735i	$-0.835265\pi$
$433$		−	8915.27i		−	0.989470i	0.869044	−	0.494735i	$-0.164735\pi$
$434$		0			0
$435$	3825.66	−	4213.98i	0.421670	−	0.464471i
$436$	6148.21			0.675335
$437$		−	7514.48i		−	0.822577i
$438$		−	7826.52i		−	0.853803i
$439$	10152.4			1.10375			0.551874	−	0.833927i	$-0.313913\pi$
$439$	10152.4			1.10375			0.551874	+	0.833927i	$0.313913\pi$
$440$	1856.73	−	2045.20i	0.201173	−	0.221593i
$441$		0			0
$442$			151.274i			0.0162791i
$443$		−	7518.21i		−	0.806323i	−0.915129	−	0.403161i	$-0.867911\pi$
$443$		−	7518.21i		−	0.806323i	0.915129	−	0.403161i	$-0.132089\pi$
$444$	−10336.0			−1.10479
$445$	−1525.51	−	1384.93i	−0.162508	−	0.147532i
$446$	−10980.8			−1.16582
$447$		−	5244.55i		−	0.554941i
$448$		0			0
$449$	13126.5			1.37968			0.689841	−	0.723961i	$-0.257680\pi$
$449$	13126.5			1.37968			0.689841	+	0.723961i	$0.257680\pi$
$450$	−19513.3	+	1889.44i	−2.04414	+	0.197931i
$451$	−6093.99			−0.636264
$452$		−	1882.80i		−	0.195928i
$453$		−	24576.7i		−	2.54904i
$454$	2357.37			0.243693
$455$		0			0
$456$	−7257.67			−0.745332
$457$		−	8051.71i		−	0.824164i	−0.911147	−	0.412082i	$-0.864802\pi$
$457$		−	8051.71i		−	0.824164i	0.911147	−	0.412082i	$-0.135198\pi$
$458$		−	12706.7i		−	1.29639i
$459$	748.654			0.0761311
$460$	2556.48	−	2815.98i	0.259123	−	0.285425i
$461$	−7347.87			−0.742352			−0.371176	−	0.928563i	$-0.621045\pi$
$461$	−7347.87			−0.742352			−0.371176	+	0.928563i	$0.621045\pi$
$462$		0			0
$463$			2631.71i			0.264160i	0.991239	+	0.132080i	$0.0421656\pi$
$463$			2631.71i			0.264160i	−0.991239	+	0.132080i	$0.957834\pi$
$464$	793.296			0.0793703
$465$	−4839.60	+	5330.85i	−0.482647	+	0.531639i
$466$	−2916.03			−0.289877
$467$		−	1125.26i		−	0.111500i	−0.998445	−	0.0557502i	$-0.982245\pi$
$467$		−	1125.26i		−	0.111500i	0.998445	−	0.0557502i	$-0.0177550\pi$
$468$		−	16730.2i		−	1.65247i
$469$		0			0
$470$	−3495.13	−	3173.05i	−0.343018	−	0.311408i
$471$	4059.51			0.397138
$472$		−	3073.91i		−	0.299763i
$473$		−	2899.45i		−	0.281854i
$474$	19663.5			1.90543
$475$	−1064.48	−	10993.4i	−0.102824	−	1.06192i
$476$		0			0
$477$			30504.4i			2.92809i
$478$			9284.72i			0.888438i
$479$	−10870.4			−1.03691			−0.518456	−	0.855104i	$-0.673493\pi$
$479$	−10870.4			−1.03691			−0.518456	+	0.855104i	$0.673493\pi$
$480$	−2719.74	−	2469.11i	−0.258622	−	0.234790i
$481$	13423.4			1.27246
$482$			10778.2i			1.01854i
$483$		0			0
$484$	1508.85			0.141703
$485$	9464.61	−	10425.3i	0.886115	−	0.976061i
$486$	−39320.2			−3.66996
$487$		−	8442.38i		−	0.785546i	−0.919636	−	0.392773i	$-0.871516\pi$
$487$		−	8442.38i		−	0.785546i	0.919636	−	0.392773i	$-0.128484\pi$
$488$			915.805i			0.0849519i
$489$	−31084.1			−2.87458
$490$		0			0
$491$	−501.323			−0.0460782			−0.0230391	−	0.999735i	$-0.507334\pi$
$491$	−501.323			−0.0460782			−0.0230391	+	0.999735i	$0.507334\pi$
$492$			8103.90i			0.742585i
$493$		−	70.3109i		−	0.00642321i
$494$	9425.52			0.858450
$495$	20047.6	+	18200.2i	1.82035	+	1.65260i
$496$	−1003.55			−0.0908481
$497$		0			0
$498$		−	2787.80i		−	0.250852i
$499$	−13927.4			−1.24945			−0.624723	−	0.780846i	$-0.714788\pi$
$499$	−13927.4			−1.24945			−0.624723	+	0.780846i	$0.714788\pi$
$500$	3341.14	−	4481.83i	0.298841	−	0.400867i
$501$	−7331.20			−0.653761
$502$		−	6700.31i		−	0.595716i
$503$			15884.2i			1.40803i	0.710184	+	0.704016i	$0.248612\pi$
$503$			15884.2i			1.40803i	−0.710184	+	0.704016i	$0.751388\pi$
$504$		0			0
$505$	−717.987	−	651.824i	−0.0632674	−	0.0574372i
$506$	−5252.97			−0.461508
$507$			6651.17i			0.582621i
$508$		−	4529.49i		−	0.395598i
$509$	−13411.1			−1.16785			−0.583926	−	0.811807i	$-0.698484\pi$
$509$	−13411.1			−1.16785			−0.583926	+	0.811807i	$0.698484\pi$
$510$	−218.841	+	241.055i	−0.0190009	+	0.0209296i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$		−	46646.9i		−	4.01465i
$514$	−2331.81			−0.200101
$515$	4064.02	−	4476.54i	0.347732	−	0.383029i
$516$	−3855.74			−0.328953
$517$			6519.87i			0.554630i
$518$		0			0
$519$	−11675.5			−0.987470
$520$	3532.12	+	3206.63i	0.297873	+	0.270423i
$521$	10095.8			0.848954			0.424477	−	0.905439i	$-0.360458\pi$
$521$	10095.8			0.848954			0.424477	+	0.905439i	$0.360458\pi$
$522$			7776.09i			0.652012i
$523$			2577.01i			0.215458i	0.994180	+	0.107729i	$0.0343580\pi$
$523$			2577.01i			0.215458i	−0.994180	+	0.107729i	$0.965642\pi$
$524$	11065.8			0.922538
$525$		0			0
$526$	2483.61			0.205876
$527$			88.9459i			0.00735208i
$528$			5073.45i			0.418169i
$529$	4934.33			0.405550
$530$	−6440.15	−	5846.68i	−0.527816	−	0.479176i
$531$	30131.2			2.46249
$532$		0			0
$533$		−	10524.5i		−	0.855286i
$534$	3784.26			0.306669
$535$	15010.5	−	16534.1i	1.21301	−	1.33613i
$536$	−2505.31			−0.201890
$537$		−	4182.88i		−	0.336135i
$538$		−	3027.16i		−	0.242584i
$539$		0			0
$540$	15869.6	−	17480.5i	1.26467	−	1.39304i
$541$	6017.19			0.478187			0.239094	−	0.970996i	$-0.423150\pi$
$541$	6017.19			0.478187			0.239094	+	0.970996i	$0.423150\pi$
$542$			14226.3i			1.12744i
$543$			25851.2i			2.04306i
$544$	−45.3793			−0.00357651
$545$	−12723.6	−	11551.1i	−1.00003	−	0.907878i
$546$		0			0
$547$		−	9577.80i		−	0.748660i	−0.927296	−	0.374330i	$-0.877873\pi$
$547$		−	9577.80i		−	0.748660i	0.927296	−	0.374330i	$-0.122127\pi$
$548$		−	12218.9i		−	0.952489i
$549$	−8976.96			−0.697864
$550$	−7684.92	+	744.120i	−0.595793	+	0.0576898i
$551$	−4380.91			−0.338717
$552$			6985.49i			0.538627i
$553$		0			0
$554$	9703.84			0.744182
$555$	21390.1	+	19419.0i	1.63596	+	1.48521i
$556$	4229.63			0.322619
$557$			7960.95i			0.605595i	0.953055	+	0.302797i	$0.0979205\pi$
$557$			7960.95i			0.605595i	−0.953055	+	0.302797i	$0.902079\pi$
$558$		−	9837.05i		−	0.746300i
$559$	5007.45			0.378877
$560$		0			0
$561$	449.667			0.0338413
$562$			17453.3i			1.31001i
$563$			3005.30i			0.224970i	0.993653	+	0.112485i	$0.0358810\pi$
$563$			3005.30i			0.224970i	−0.993653	+	0.112485i	$0.964119\pi$
$564$	8670.24			0.647310
$565$	−3537.35	+	3896.41i	−0.263393	+	0.290129i
$566$	3343.37			0.248291
$567$		0			0
$568$		−	2766.26i		−	0.204348i
$569$	−22062.8			−1.62552			−0.812760	−	0.582599i	$-0.802036\pi$
$569$	−22062.8			−1.62552			−0.812760	+	0.582599i	$0.802036\pi$
$570$	15019.6	+	13635.5i	1.10368	+	1.00198i
$571$	14840.8			1.08768			0.543841	−	0.839188i	$-0.316969\pi$
$571$	14840.8			1.08768			0.543841	+	0.839188i	$0.316969\pi$
$572$		−	6588.88i		−	0.481634i
$573$			11970.4i			0.872726i
$574$		0			0
$575$	−10581.1	+	1024.56i	−0.767416	+	0.0743079i
$576$	5018.76			0.363047
$577$			24793.9i			1.78888i	0.447191	+	0.894438i	$0.352424\pi$
$577$			24793.9i			1.78888i	−0.447191	+	0.894438i	$0.647576\pi$
$578$		−	9821.98i		−	0.706817i
$579$	−1731.81			−0.124303
$580$	−1641.71	−	1490.42i	−0.117531	−	0.106701i
$581$		0			0
$582$			25861.7i			1.84193i
$583$			12013.6i			0.853431i
$584$	−3049.10			−0.216049
$585$	−31432.3	+	34622.8i	−2.22148	+	2.44697i
$586$	−11317.2			−0.797797
$587$			16347.8i			1.14948i	0.818336	+	0.574740i	$0.194897\pi$
$587$			16347.8i			1.14948i	−0.818336	+	0.574740i	$0.805103\pi$
$588$		0			0
$589$	5542.02			0.387699
$590$	−5775.16	+	6361.37i	−0.402982	+	0.443887i
$591$	30075.0			2.09327
$592$			4026.76i			0.279559i
$593$			5639.89i			0.390561i	0.980747	+	0.195280i	$0.0625617\pi$
$593$			5639.89i			0.390561i	−0.980747	+	0.195280i	$0.937438\pi$
$594$	−32608.4			−2.25242
$595$		0			0
$596$	−2043.20			−0.140424
$597$			48576.7i			3.33017i
$598$		−	9072.04i		−	0.620374i
$599$	−2109.20			−0.143872			−0.0719362	−	0.997409i	$-0.522918\pi$
$599$	−2109.20			−0.143872			−0.0719362	+	0.997409i	$0.522918\pi$
$600$	989.544	+	10219.5i	0.0673299	+	0.695351i
$601$	−17482.0			−1.18653			−0.593265	−	0.805007i	$-0.702161\pi$
$601$	−17482.0			−1.18653			−0.593265	+	0.805007i	$0.702161\pi$
$602$		0			0
$603$		−	24557.7i		−	1.65849i
$604$	−9574.73			−0.645017
$605$	−3122.53	−	2834.79i	−0.209833	−	0.190497i
$606$	1781.08			0.119392
$607$			161.215i			0.0107801i	0.999985	+	0.00539005i	$0.00171571\pi$
$607$			161.215i			0.0107801i	−0.999985	+	0.00539005i	$0.998284\pi$
$608$			2827.48i			0.188601i
$609$		0			0
$610$	1720.59	−	1895.24i	0.114204	−	0.125796i
$611$	−11260.0			−0.745551
$612$		−	444.820i		−	0.0293803i
$613$		−	24640.1i		−	1.62350i	−0.584005	−	0.811750i	$-0.698515\pi$
$613$		−	24640.1i		−	1.62350i	0.584005	−	0.811750i	$-0.301485\pi$
$614$	6463.11			0.424805
$615$	15225.4	−	16770.8i	0.998285	−	1.09962i
$616$		0			0
$617$		−	11946.3i		−	0.779483i	−0.920924	−	0.389742i	$-0.872564\pi$
$617$		−	11946.3i		−	0.779483i	0.920924	−	0.389742i	$-0.127436\pi$
$618$			11104.8i			0.722815i
$619$	5280.50			0.342877			0.171439	−	0.985195i	$-0.445158\pi$
$619$	5280.50			0.342877			0.171439	+	0.985195i	$0.445158\pi$
$620$	2076.82	+	1885.44i	0.134527	+	0.122131i
$621$	−44897.6			−2.90125
$622$			11904.4i			0.767400i
$623$		0			0
$624$	−8762.00			−0.562117
$625$	−15334.7	+	2997.79i	−0.981423	+	0.191858i
$626$	17840.4			1.13905
$627$		−	28017.7i		−	1.78456i
$628$		−	1581.52i		−	0.100493i
$629$	356.897			0.0226239
$630$		0			0
$631$	4395.90			0.277334			0.138667	−	0.990339i	$-0.455718\pi$
$631$	4395.90			0.277334			0.138667	+	0.990339i	$0.455718\pi$
$632$		−	7660.62i		−	0.482157i
$633$		−	24357.3i		−	1.52941i
$634$	−16091.9			−1.00803
$635$	−8509.87	+	9373.67i	−0.531817	+	0.585799i
$636$	15975.8			0.996042
$637$		0			0
$638$			3062.46i			0.190038i
$639$	27115.6			1.67868
$640$	−961.930	+	1059.57i	−0.0594119	+	0.0654425i
$641$	7642.31			0.470910			0.235455	−	0.971885i	$-0.424342\pi$
$641$	7642.31			0.470910			0.235455	+	0.971885i	$0.424342\pi$
$642$			41015.5i			2.52142i
$643$		−	17425.2i		−	1.06871i	−0.845259	−	0.534357i	$-0.820554\pi$
$643$		−	17425.2i		−	1.06871i	0.845259	−	0.534357i	$-0.179446\pi$
$644$		0			0
$645$	7979.36	+	7244.05i	0.487112	+	0.442224i
$646$	250.603			0.0152629
$647$		−	25912.2i		−	1.57452i	−0.616623	−	0.787258i	$-0.711500\pi$
$647$		−	25912.2i		−	1.57452i	0.616623	−	0.787258i	$-0.288500\pi$
$648$			26424.9i			1.60196i
$649$	11866.6			0.717727
$650$	−1285.12	−	13272.1i	−0.0775485	−	0.800883i
$651$		0			0
$652$			12109.9i			0.727393i
$653$		−	17119.2i		−	1.02592i	−0.858412	−	0.512960i	$-0.828549\pi$
$653$		−	17119.2i		−	1.02592i	0.858412	−	0.512960i	$-0.171451\pi$
$654$	31562.9			1.88716
$655$	−22900.3	−	20790.0i	−1.36609	−	1.24020i
$656$	3157.16			0.187906
$657$		−	29888.0i		−	1.77480i
$658$		0			0
$659$	15073.4			0.891011			0.445506	−	0.895279i	$-0.353024\pi$
$659$	15073.4			0.891011			0.445506	+	0.895279i	$0.353024\pi$
$660$	9531.84	−	10499.4i	0.562161	−	0.619224i
$661$	30781.4			1.81128			0.905641	−	0.424045i	$-0.139390\pi$
$661$	30781.4			1.81128			0.905641	+	0.424045i	$0.139390\pi$
$662$		−	11167.2i		−	0.655629i
$663$			776.588i			0.0454905i
$664$	−1086.08			−0.0634763
$665$		0			0
$666$	−39471.3			−2.29652
$667$			4216.62i			0.244780i
$668$			2856.13i			0.165430i
$669$	−56371.6			−3.25778
$670$	5184.68	+	4706.90i	0.298958	+	0.271408i
$671$	−3535.40			−0.203402
$672$		0			0
$673$			7432.97i			0.425735i	0.977081	+	0.212868i	$0.0682803\pi$
$673$			7432.97i			0.425735i	−0.977081	+	0.212868i	$0.931720\pi$
$674$	−8534.84			−0.487760
$675$	−65683.6	+	6360.06i	−3.74543	+	0.362665i
$676$	2591.20			0.147428
$677$		−	23124.5i		−	1.31277i	−0.754426	−	0.656386i	$-0.772084\pi$
$677$		−	23124.5i		−	1.31277i	0.754426	−	0.656386i	$-0.227916\pi$
$678$		−	9665.67i		−	0.547504i
$679$		0			0
$680$	93.9113	+	85.2572i	0.00529608	+	0.00480803i
$681$	12101.9			0.680979
$682$		−	3874.13i		−	0.217519i
$683$		−	3852.56i		−	0.215833i	−0.994160	−	0.107917i	$-0.965582\pi$
$683$		−	3852.56i		−	0.215833i	0.994160	−	0.107917i	$-0.0344180\pi$
$684$	−27715.7			−1.54932
$685$	−22956.4	+	25286.6i	−1.28047	+	1.41044i
$686$		0			0
$687$		−	65232.0i		−	3.62264i
$688$			1502.14i			0.0832392i
$689$	−20747.8			−1.14721
$690$	13124.1	−	14456.3i	0.724097	−	0.797597i
$691$	−16586.9			−0.913162			−0.456581	−	0.889682i	$-0.650926\pi$
$691$	−16586.9			−0.913162			−0.456581	+	0.889682i	$0.650926\pi$
$692$			4548.59i			0.249872i
$693$		0			0
$694$	16104.7			0.880875
$695$	−8753.12	−	7946.51i	−0.477734	−	0.433710i
$696$	4072.52			0.221794
$697$		−	279.823i		−	0.0152067i
$698$		−	17634.2i		−	0.956252i
$699$	−14969.9			−0.810035
$700$		0			0
$701$	1063.40			0.0572953			0.0286477	−	0.999590i	$-0.490880\pi$
$701$	1063.40			0.0572953			0.0286477	+	0.999590i	$0.490880\pi$
$702$		−	56315.7i		−	3.02778i
$703$		−	22237.5i		−	1.19303i
$704$	1976.54			0.105815
$705$	−17942.8	−	16289.4i	−0.958534	−	0.870204i
$706$	−15123.6			−0.806211
$707$		0			0
$708$		−	15780.4i		−	0.837661i
$709$	−1693.47			−0.0897032			−0.0448516	−	0.998994i	$-0.514282\pi$
$709$	−1693.47			−0.0897032			−0.0448516	+	0.998994i	$0.514282\pi$
$710$	−5197.17	+	5724.71i	−0.274713	+	0.302598i
$711$	75091.4			3.96083
$712$		−	1474.29i		−	0.0776003i
$713$		−	5334.18i		−	0.280178i
$714$		0			0
$715$	−12379.0	+	13635.5i	−0.647479	+	0.713202i
$716$	−1629.59			−0.0850566
$717$			47664.6i			2.48266i
$718$			19747.2i			1.02641i
$719$	21006.9			1.08960			0.544801	−	0.838566i	$-0.316605\pi$
$719$	21006.9			1.08960			0.544801	+	0.838566i	$0.316605\pi$
$720$	−10386.2	−	9429.09i	−0.537598	−	0.488058i
$721$		0			0
$722$		−	1896.54i		−	0.0977588i
$723$			55331.9i			2.84622i
$724$	10071.2			0.516981
$725$	597.314	+	6168.77i	0.0305982	+	0.316003i
$726$	7745.95			0.395977
$727$		−	32859.1i		−	1.67631i	−0.545434	−	0.838154i	$-0.683635\pi$
$727$		−	32859.1i		−	1.67631i	0.545434	−	0.838154i	$-0.316365\pi$
$728$		0			0
$729$	−112673.			−5.72437
$730$	6310.03	+	5728.55i	0.319924	+	0.290443i
$731$	133.137			0.00673631
$732$			4701.44i			0.237391i
$733$			5065.14i			0.255232i	0.991824	+	0.127616i	$0.0407326\pi$
$733$			5065.14i			0.255232i	−0.991824	+	0.127616i	$0.959267\pi$
$734$	9691.49			0.487356
$735$		0			0
$736$	2721.44			0.136296
$737$		−	9671.57i		−	0.483388i
$738$			30947.3i			1.54361i
$739$	38168.0			1.89991			0.949955	−	0.312386i	$-0.101128\pi$
$739$	38168.0			1.89991			0.949955	+	0.312386i	$0.101128\pi$
$740$	7565.35	−	8333.28i	0.375821	−	0.413969i
$741$	48387.5			2.39886
$742$		0			0
$743$		−	16378.0i		−	0.808682i	−0.914608	−	0.404341i	$-0.867501\pi$
$743$		−	16378.0i		−	0.808682i	0.914608	−	0.404341i	$-0.132499\pi$
$744$	−5151.88			−0.253867
$745$	4228.35	+	3838.70i	0.207939	+	0.188777i
$746$	9550.20			0.468710
$747$		−	10646.1i		−	0.521446i
$748$		−	175.183i		−	0.00856329i
$749$		0			0
$750$	17152.3	−	23008.2i	0.835085	−	1.12019i
$751$	27993.2			1.36017			0.680085	−	0.733133i	$-0.261943\pi$
$751$	27993.2			1.36017			0.680085	+	0.733133i	$0.261943\pi$
$752$		−	3377.80i		−	0.163797i
$753$		−	34397.2i		−	1.66468i
$754$	−5288.97			−0.255455
$755$	19814.7	+	17988.7i	0.955138	+	0.867121i
$756$		0			0
$757$		−	5832.05i		−	0.280013i	−0.990151	−	0.140006i	$-0.955288\pi$
$757$		−	5832.05i		−	0.280013i	0.990151	−	0.140006i	$-0.0447123\pi$
$758$		−	11228.6i		−	0.538048i
$759$	−26967.0			−1.28964
$760$	5312.18	−	5851.40i	0.253544	−	0.279280i
$761$	−37005.8			−1.76276			−0.881380	−	0.472409i	$-0.843385\pi$
$761$	−37005.8			−1.76276			−0.881380	+	0.472409i	$0.843385\pi$
$762$		−	23252.9i		−	1.10546i
$763$		0			0
$764$	4663.50			0.220837
$765$	−835.713	+	920.543i	−0.0394971	+	0.0435063i
$766$	−16738.6			−0.789543
$767$			20494.0i			0.964791i
$768$		−	2628.44i		−	0.123497i
$769$	9854.24			0.462098			0.231049	−	0.972942i	$-0.425784\pi$
$769$	9854.24			0.462098			0.231049	+	0.972942i	$0.425784\pi$
$770$		0			0
$771$	−11970.7			−0.559164
$772$			674.687i			0.0314540i
$773$			4627.79i			0.215330i	0.994187	+	0.107665i	$0.0343374\pi$
$773$			4627.79i			0.215330i	−0.994187	+	0.107665i	$0.965663\pi$
$774$	−14724.4			−0.683794
$775$	−755.624	−	7803.73i	−0.0350230	−	0.361701i
$776$	10075.3			0.466087
$777$		0			0
$778$		−	8825.11i		−	0.406678i
$779$	−17435.2			−0.801899
$780$	18132.7	+	16461.8i	0.832380	+	0.755675i
$781$	10679.0			0.489274
$782$		−	241.205i		−	0.0110300i
$783$			26175.1i			1.19467i
$784$		0			0
$785$	−2971.32	+	3272.92i	−0.135097	+	0.148810i
$786$	56807.9			2.57795
$787$		−	14843.9i		−	0.672335i	−0.941802	−	0.336167i	$-0.890869\pi$
$787$		−	14843.9i		−	0.672335i	0.941802	−	0.336167i	$-0.109131\pi$
$788$		−	11716.8i		−	0.529686i
$789$	12750.0			0.575302
$790$	−14392.5	+	15853.5i	−0.648182	+	0.713976i
$791$		0			0
$792$			19374.6i			0.869249i
$793$		−	6105.75i		−	0.273419i
$794$	3730.73			0.166749
$795$	−33061.6	−	30014.9i	−1.47494	−	1.33902i
$796$	18924.8			0.842677
$797$		−	1004.72i		−	0.0446536i	−0.999751	−	0.0223268i	$-0.992893\pi$
$797$		−	1004.72i		−	0.0446536i	0.999751	−	0.0223268i	$-0.00710743\pi$
$798$		0			0
$799$	−299.379			−0.0132556
$800$	3981.38	−	385.511i	0.175954	−	0.0170374i
$801$	14451.4			0.637472
$802$			25963.8i			1.14316i
$803$		−	11770.8i		−	0.517289i
$804$	−12861.4			−0.564164
$805$		0			0
$806$	6690.74			0.292396
$807$		−	15540.4i		−	0.677880i
$808$		−	693.884i		−	0.0302113i
$809$	28142.0			1.22301			0.611507	−	0.791239i	$-0.290564\pi$
$809$	28142.0			1.22301			0.611507	+	0.791239i	$0.290564\pi$
$810$	49646.3	−	54685.6i	2.15357	−	2.37217i
$811$	−20279.7			−0.878073			−0.439036	−	0.898469i	$-0.644680\pi$
$811$	−20279.7			−0.878073			−0.439036	+	0.898469i	$0.644680\pi$
$812$		0			0
$813$			73033.3i			3.15054i
$814$	−15545.0			−0.669352
$815$	22751.7	−	25061.1i	0.977862	−	1.07712i
$816$	−232.962			−0.00999424
$817$		−	8295.45i		−	0.355228i
$818$		−	12480.1i		−	0.533445i
$819$		0			0
$820$	−6533.66	−	5931.57i	−0.278250	−	0.252609i
$821$	−1362.32			−0.0579113			−0.0289556	−	0.999581i	$-0.509218\pi$
$821$	−1362.32			−0.0579113			−0.0289556	+	0.999581i	$0.509218\pi$
$822$		−	62727.6i		−	2.66165i
$823$			10733.0i			0.454593i	0.973826	+	0.227296i	$0.0729886\pi$
$823$			10733.0i			0.454593i	−0.973826	+	0.227296i	$0.927011\pi$
$824$	4326.26			0.182903
$825$	−39451.8	+	3820.06i	−1.66489	+	0.161209i
$826$		0			0
$827$			5942.61i			0.249873i	0.992165	+	0.124936i	$0.0398727\pi$
$827$			5942.61i			0.249873i	−0.992165	+	0.124936i	$0.960127\pi$
$828$			26676.3i			1.11964i
$829$	15157.6			0.635038			0.317519	−	0.948252i	$-0.397150\pi$
$829$	15157.6			0.635038			0.317519	+	0.948252i	$0.397150\pi$
$830$	2247.62	+	2040.50i	0.0939954	+	0.0853336i
$831$	49816.3			2.07955
$832$			3413.55i			0.142240i
$833$		0			0
$834$	21713.5			0.901532
$835$	5366.01	−	5910.69i	0.222393	−	0.244967i
$836$	−10915.3			−0.451571
$837$		−	33112.5i		−	1.36743i
$838$			13381.9i			0.551635i
$839$	25178.7			1.03607			0.518036	−	0.855359i	$-0.326663\pi$
$839$	25178.7			1.03607			0.518036	+	0.855359i	$0.326663\pi$
$840$		0			0
$841$	−21930.7			−0.899206
$842$		−	3910.94i		−	0.160071i
$843$			89599.6i			3.66070i
$844$	−9489.25			−0.387006
$845$	−5362.42	−	4868.26i	−0.218311	−	0.198193i
$846$	33110.0			1.34556
$847$		0			0
$848$		−	6223.95i		−	0.252041i
$849$	17163.8			0.693827
$850$	−34.1684	−	352.875i	−0.00137878	−	0.0142394i
$851$	−21403.5			−0.862165
$852$		−	14201.1i		−	0.571033i
$853$		−	9293.60i		−	0.373044i	−0.982451	−	0.186522i	$-0.940278\pi$
$853$		−	9293.60i		−	0.373044i	0.982451	−	0.186522i	$-0.0597216\pi$
$854$		0			0
$855$	57356.9	+	52071.4i	2.29423	+	2.08281i
$856$	15979.0			0.638028
$857$		−	33470.9i		−	1.33412i	−0.745003	−	0.667061i	$-0.767552\pi$
$857$		−	33470.9i		−	1.33412i	0.745003	−	0.667061i	$-0.232448\pi$
$858$		−	33825.1i		−	1.34589i
$859$	5396.02			0.214330			0.107165	−	0.994241i	$-0.465823\pi$
$859$	5396.02			0.214330			0.107165	+	0.994241i	$0.465823\pi$
$860$	2822.17	−	3108.64i	0.111902	−	0.123260i
$861$		0			0
$862$			2139.92i			0.0845544i
$863$			18020.0i			0.710786i	0.934717	+	0.355393i	$0.115653\pi$
$863$			18020.0i			0.710786i	−0.934717	+	0.355393i	$0.884347\pi$
$864$	16893.7			0.665201
$865$	8545.76	−	9413.20i	0.335913	−	0.370010i
$866$	−17830.5			−0.699661
$867$		−	50422.8i		−	1.97514i
$868$		0			0
$869$	29573.3			1.15444
$870$	−8427.97	−	7651.32i	−0.328431	−	0.298165i
$871$	16703.1			0.649786
$872$		−	12296.4i		−	0.477534i
$873$			98761.0i			3.82881i
$874$	−15029.0			−0.581650
$875$		0			0
$876$	−15653.0			−0.603730
$877$		−	10837.0i		−	0.417263i	−0.977994	−	0.208631i	$-0.933099\pi$
$877$		−	10837.0i		−	0.417263i	0.977994	−	0.208631i	$-0.0669009\pi$
$878$		−	20304.7i		−	0.780468i
$879$	−58098.7			−2.22937
$880$	−4090.40	−	3713.46i	−0.156690	−	0.142251i
$881$	28672.0			1.09646			0.548232	−	0.836327i	$-0.315301\pi$
$881$	28672.0			1.09646			0.548232	+	0.836327i	$0.315301\pi$
$882$		0			0
$883$		−	22769.4i		−	0.867783i	−0.900965	−	0.433891i	$-0.857140\pi$
$883$		−	22769.4i		−	0.867783i	0.900965	−	0.433891i	$-0.142860\pi$
$884$	302.547			0.0115110
$885$	−29647.7	+	32657.2i	−1.12610	+	1.24040i
$886$	−15036.4			−0.570156
$887$		−	46488.4i		−	1.75978i	−0.475176	−	0.879891i	$-0.657616\pi$
$887$		−	46488.4i		−	1.75978i	0.475176	−	0.879891i	$-0.342384\pi$
$888$			20672.0i			0.781203i
$889$		0			0
$890$	−2769.85	+	3051.01i	−0.104321	+	0.114910i
$891$	−102011.			−3.83559
$892$			21961.6i			0.824358i
$893$			18653.6i			0.699014i
$894$	−10489.1			−0.392402
$895$	3372.39	+	3061.62i	0.125951	+	0.114345i
$896$		0			0
$897$		−	46572.8i		−	1.73358i
$898$		−	26253.0i		−	0.975583i
$899$	−3109.81			−0.115370
$900$	3778.88	+	39026.5i	0.139959	+	1.44543i
$901$	−551.637			−0.0203970
$902$			12188.0i			0.449906i
$903$		0			0
$904$	−3765.60			−0.138542
$905$	−20842.2	−	18921.5i	−0.765544	−	0.694998i
$906$	−49153.5			−1.80244
$907$		−	3677.74i		−	0.134639i	−0.997731	−	0.0673193i	$-0.978555\pi$
$907$		−	3677.74i		−	0.134639i	0.997731	−	0.0673193i	$-0.0214446\pi$
$908$		−	4714.73i		−	0.172317i
$909$	6801.63			0.248180
$910$		0			0
$911$	−11721.1			−0.426277			−0.213138	−	0.977022i	$-0.568369\pi$
$911$	−11721.1			−0.426277			−0.213138	+	0.977022i	$0.568369\pi$
$912$			14515.3i			0.527029i
$913$		−	4192.75i		−	0.151982i
$914$	−16103.4			−0.582772
$915$	8832.92	−	9729.51i	0.319134	−	0.351527i
$916$	−25413.4			−0.916684
$917$		0			0
$918$		−	1497.31i		−	0.0538328i
$919$	30983.7			1.11214			0.556070	−	0.831136i	$-0.312309\pi$
$919$	30983.7			1.11214			0.556070	+	0.831136i	$0.312309\pi$
$920$	−5631.96	−	5112.96i	−0.201826	−	0.183228i
$921$	33179.5			1.18708
$922$			14695.7i			0.524922i
$923$			18442.9i			0.657698i
$924$		0			0
$925$	−31312.6	+	3031.96i	−1.11303	+	0.107773i
$926$	5263.43			0.186789
$927$			42407.1i			1.50252i
$928$		−	1586.59i		−	0.0561233i
$929$	35616.6			1.25785			0.628925	−	0.777466i	$-0.283495\pi$
$929$	35616.6			1.25785			0.628925	+	0.777466i	$0.283495\pi$
$930$	10661.7	+	9679.20i	0.375925	+	0.341283i
$931$		0			0
$932$			5832.06i			0.204974i
$933$			61113.2i			2.14443i
$934$	−2250.51			−0.0788426
$935$	−329.129	+	362.538i	−0.0115120	+	0.0126805i
$936$	−33460.5			−1.16847
$937$			30571.1i			1.06586i	0.846159	+	0.532931i	$0.178910\pi$
$937$			30571.1i			1.06586i	−0.846159	+	0.532931i	$0.821090\pi$
$938$		0			0
$939$	91586.7			3.18298
$940$	−6346.10	+	6990.26i	−0.220199	+	0.242550i
$941$	21649.7			0.750011			0.375006	−	0.927023i	$-0.377641\pi$
$941$	21649.7			0.750011			0.375006	+	0.927023i	$0.377641\pi$
$942$		−	8119.01i		−	0.280819i
$943$			16781.3i			0.579506i
$944$	−6147.81			−0.211964
$945$		0			0
$946$	−5798.91			−0.199301
$947$			45534.0i			1.56247i	0.624239	+	0.781234i	$0.285409\pi$
$947$			45534.0i			1.56247i	−0.624239	+	0.781234i	$0.714591\pi$
$948$		−	39327.1i		−	1.34735i
$949$	20328.6			0.695357
$950$	−21986.9	+	2128.96i	−0.750892	+	0.0727079i
$951$	−82610.6			−2.81686
$952$		0			0
$953$		−	17096.3i		−	0.581114i	−0.956858	−	0.290557i	$-0.906159\pi$
$953$		−	17096.3i		−	0.581114i	0.956858	−	0.290557i	$-0.0938406\pi$
$954$	61008.8			2.07047
$955$	−9651.00	−	8761.64i	−0.327015	−	0.296880i
$956$	18569.4			0.628220
$957$			15721.7i			0.531044i
$958$			21740.8i			0.733208i
$959$		0			0
$960$	−4938.23	+	5439.48i	−0.166021	+	0.182874i
$961$	−25857.0			−0.867946
$962$		−	26846.7i		−	0.899764i
$963$			156631.i			5.24128i
$964$	21556.5			0.720216
$965$	1267.58	−	1396.25i	0.0422848	−	0.0465770i
$966$		0			0
$967$			54908.9i			1.82601i	0.407950	+	0.913004i	$0.366244\pi$
$967$			54908.9i			1.82601i	−0.407950	+	0.913004i	$0.633756\pi$
$968$		−	3017.71i		−	0.100199i
$969$	1286.51			0.0426510
$970$	−20850.6	−	18929.2i	−0.690179	−	0.626578i
$971$	−2599.26			−0.0859053			−0.0429527	−	0.999077i	$-0.513676\pi$
$971$	−2599.26			−0.0859053			−0.0429527	+	0.999077i	$0.513676\pi$
$972$			78640.4i			2.59505i
$973$		0			0
$974$	−16884.8			−0.555465
$975$	−6597.37	−	68134.5i	−0.216702	−	2.23800i
$976$	1831.61			0.0600701
$977$			51337.7i			1.68110i	0.541732	+	0.840551i	$0.317769\pi$
$977$			51337.7i			1.68110i	−0.541732	+	0.840551i	$0.682231\pi$
$978$			62168.2i			2.03264i
$979$	5691.40			0.185800
$980$		0			0
$981$	120533.			3.92285
$982$			1002.65i			0.0325822i
$983$		−	1330.13i		−	0.0431583i	−0.999767	−	0.0215791i	$-0.993131\pi$
$983$		−	1330.13i		−	0.0431583i	0.999767	−	0.0215791i	$-0.00686938\pi$
$984$	16207.8			0.525087
$985$	−22013.1	+	24247.6i	−0.712077	+	0.784357i
$986$	−140.622			−0.00454190
$987$		0			0
$988$		−	18851.0i		−	0.607016i
$989$	−7984.35			−0.256711
$990$	36400.3	−	40095.2i	1.16856	−	1.28718i
$991$	−2630.07			−0.0843057			−0.0421529	−	0.999111i	$-0.513422\pi$
$991$	−2630.07			−0.0843057			−0.0421529	+	0.999111i	$0.513422\pi$
$992$			2007.10i			0.0642393i
$993$		−	57328.8i		−	1.83210i
$994$		0			0
$995$	−39164.3	−	35555.3i	−1.24783	−	1.13284i
$996$	−5575.60			−0.177379
$997$			15573.6i			0.494706i	0.968925	+	0.247353i	$0.0795607\pi$
$997$			15573.6i			0.494706i	−0.968925	+	0.247353i	$0.920439\pi$
$998$			27854.7i			0.883492i
$999$	−132865.			−4.20786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.c.99.1		6
5.2	odd	4		2450.4.a.cg.1.1		3
5.3	odd	4		2450.4.a.cf.1.3		3
5.4	even	2	inner	490.4.c.c.99.6		6
7.6	odd	2		70.4.c.b.29.3	✓	6
21.20	even	2		630.4.g.j.379.5		6
28.27	even	2		560.4.g.e.449.1		6
35.13	even	4		350.4.a.w.1.1		3
35.27	even	4		350.4.a.x.1.3		3
35.34	odd	2		70.4.c.b.29.4	yes	6
105.104	even	2		630.4.g.j.379.2		6
140.139	even	2		560.4.g.e.449.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.c.b.29.3	✓	6	7.6	odd	2
70.4.c.b.29.4	yes	6	35.34	odd	2
350.4.a.w.1.1		3	35.13	even	4
350.4.a.x.1.3		3	35.27	even	4
490.4.c.c.99.1		6	1.1	even	1	trivial
490.4.c.c.99.6		6	5.4	even	2	inner
560.4.g.e.449.1		6	28.27	even	2
560.4.g.e.449.6		6	140.139	even	2
630.4.g.j.379.2		6	105.104	even	2
630.4.g.j.379.5		6	21.20	even	2
2450.4.a.cf.1.3		3	5.3	odd	4
2450.4.a.cg.1.1		3	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -10.2673i q^{3} -4.00000 q^{4} +(8.27790 + 7.51508i) q^{5} -20.5347 q^{6} +8.00000i q^{8} -78.4181 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -10.2673i q^{3} -4.00000 q^{4} +(8.27790 + 7.51508i) q^{5} -20.5347 q^{6} +8.00000i q^{8} -78.4181 q^{9} +(15.0302 - 16.5558i) q^{10} -30.8834 q^{11} +41.0693i q^{12} -53.3367i q^{13} +(77.1598 - 84.9919i) q^{15} +16.0000 q^{16} -1.41810i q^{17} +156.836i q^{18} -88.3588 q^{19} +(-33.1116 - 30.0603i) q^{20} +61.7669i q^{22} +85.0451i q^{23} +82.1387 q^{24} +(12.0472 + 124.418i) q^{25} -106.673 q^{26} +527.927i q^{27} +49.5810 q^{29} +(-169.984 - 154.320i) q^{30} -62.7218 q^{31} -32.0000i q^{32} +317.091i q^{33} -2.83620 q^{34} +313.672 q^{36} +251.672i q^{37} +176.718i q^{38} -547.625 q^{39} +(-60.1206 + 66.2232i) q^{40} +197.322 q^{41} +93.8838i q^{43} +123.534 q^{44} +(-649.137 - 589.318i) q^{45} +170.090 q^{46} -211.112i q^{47} -164.277i q^{48} +(248.836 - 24.0945i) q^{50} -14.5601 q^{51} +213.347i q^{52} -388.997i q^{53} +1055.85 q^{54} +(-255.650 - 232.091i) q^{55} +907.209i q^{57} -99.1620i q^{58} -384.238 q^{59} +(-308.639 + 339.968i) q^{60} +114.476 q^{61} +125.444i q^{62} -64.0000 q^{64} +(400.829 - 441.515i) q^{65} +634.181 q^{66} +313.164i q^{67} +5.67241i q^{68} +873.186 q^{69} -345.783 q^{71} -627.345i q^{72} +381.137i q^{73} +503.345 q^{74} +(1277.44 - 123.693i) q^{75} +353.435 q^{76} +1095.25i q^{78} -957.577 q^{79} +(132.446 + 120.241i) q^{80} +3303.11 q^{81} -394.645i q^{82} +135.761i q^{83} +(10.6571 - 11.7389i) q^{85} +187.768 q^{86} -509.064i q^{87} -247.068i q^{88} -184.287 q^{89} +(-1178.64 + 1298.27i) q^{90} -340.180i q^{92} +643.985i q^{93} -422.225 q^{94} +(-731.425 - 664.023i) q^{95} -328.555 q^{96} -1259.42i q^{97} +2421.82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{4} + 16 q^{5} - 28 q^{6} - 152 q^{9}+O(q^{10}) \) 6 * q - 24 * q^4 + 16 * q^5 - 28 * q^6 - 152 * q^9	\( 6 q - 24 q^{4} + 16 q^{5} - 28 q^{6} - 152 q^{9} + 36 q^{10} + 38 q^{11} + 110 q^{15} + 96 q^{16} + 312 q^{19} - 64 q^{20} + 112 q^{24} + 486 q^{25} - 164 q^{26} - 182 q^{29} + 80 q^{30} - 340 q^{31} + 620 q^{34} + 608 q^{36} - 1598 q^{39} - 144 q^{40} + 12 q^{41} - 152 q^{44} - 1988 q^{45} + 200 q^{46} + 856 q^{50} - 238 q^{51} + 1876 q^{54} - 1636 q^{55} + 1180 q^{59} - 440 q^{60} - 704 q^{61} - 384 q^{64} + 586 q^{65} + 620 q^{66} + 4500 q^{69} + 1448 q^{71} + 472 q^{74} + 1960 q^{75} - 1248 q^{76} - 2074 q^{79} + 256 q^{80} + 4814 q^{81} - 82 q^{85} - 864 q^{86} - 2096 q^{89} - 2608 q^{90} + 316 q^{94} + 100 q^{95} - 448 q^{96} + 6556 q^{99}+O(q^{100}) \) 6 * q - 24 * q^4 + 16 * q^5 - 28 * q^6 - 152 * q^9 + 36 * q^10 + 38 * q^11 + 110 * q^15 + 96 * q^16 + 312 * q^19 - 64 * q^20 + 112 * q^24 + 486 * q^25 - 164 * q^26 - 182 * q^29 + 80 * q^30 - 340 * q^31 + 620 * q^34 + 608 * q^36 - 1598 * q^39 - 144 * q^40 + 12 * q^41 - 152 * q^44 - 1988 * q^45 + 200 * q^46 + 856 * q^50 - 238 * q^51 + 1876 * q^54 - 1636 * q^55 + 1180 * q^59 - 440 * q^60 - 704 * q^61 - 384 * q^64 + 586 * q^65 + 620 * q^66 + 4500 * q^69 + 1448 * q^71 + 472 * q^74 + 1960 * q^75 - 1248 * q^76 - 2074 * q^79 + 256 * q^80 + 4814 * q^81 - 82 * q^85 - 864 * q^86 - 2096 * q^89 - 2608 * q^90 + 316 * q^94 + 100 * q^95 - 448 * q^96 + 6556 * q^99

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