LMFDB - Embedded newform 490.4.c.c.99.5

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			99.5
Root			$4.30950 + 4.30950i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.c.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +3.17488i q^{3} -4.00000 q^{4} +(-11.1034 + 1.30950i) q^{5} -6.34975 q^{6} -8.00000i q^{8} +16.9202 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +3.17488i q^{3} -4.00000 q^{4} +(-11.1034 + 1.30950i) q^{5} -6.34975 q^{6} -8.00000i q^{8} +16.9202 q^{9} +(-2.61901 - 22.2068i) q^{10} +50.2699 q^{11} -12.6995i q^{12} +17.8744i q^{13} +(-4.15751 - 35.2519i) q^{15} +16.0000 q^{16} -93.9202i q^{17} +33.8403i q^{18} +84.9965 q^{19} +(44.4135 - 5.23801i) q^{20} +100.540i q^{22} -119.688i q^{23} +25.3990 q^{24} +(121.570 - 29.0798i) q^{25} -35.7488 q^{26} +139.441i q^{27} -165.509 q^{29} +(70.5038 - 8.31502i) q^{30} +134.227 q^{31} +32.0000i q^{32} +159.601i q^{33} +187.840 q^{34} -67.6806 q^{36} +129.681i q^{37} +169.993i q^{38} -56.7490 q^{39} +(10.4760 + 88.8271i) q^{40} +118.486 q^{41} +533.246i q^{43} -201.080 q^{44} +(-187.871 + 22.1570i) q^{45} +239.375 q^{46} +142.504i q^{47} +50.7980i q^{48} +(58.1597 + 243.141i) q^{50} +298.185 q^{51} -71.4975i q^{52} +549.664i q^{53} -278.882 q^{54} +(-558.166 + 65.8286i) q^{55} +269.853i q^{57} -331.018i q^{58} +566.008 q^{59} +(16.6300 + 141.008i) q^{60} -523.703 q^{61} +268.455i q^{62} -64.0000 q^{64} +(-23.4066 - 198.466i) q^{65} -319.202 q^{66} -503.840i q^{67} +375.681i q^{68} +379.993 q^{69} +179.059 q^{71} -135.361i q^{72} -1105.92i q^{73} -259.361 q^{74} +(92.3249 + 385.971i) q^{75} -339.986 q^{76} -113.498i q^{78} +499.227 q^{79} +(-177.654 + 20.9521i) q^{80} +14.1359 q^{81} +236.971i q^{82} +626.803i q^{83} +(122.989 + 1042.83i) q^{85} -1066.49 q^{86} -525.471i q^{87} -402.159i q^{88} +721.623 q^{89} +(-44.3140 - 375.742i) q^{90} +478.750i q^{92} +426.156i q^{93} -285.009 q^{94} +(-943.749 + 111.303i) q^{95} -101.596 q^{96} +543.221i q^{97} +850.575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			3.17488i			0.611005i	0.952191	+	0.305503i	$0.0988245\pi$
$3$			3.17488i			0.611005i	−0.952191	+	0.305503i	$0.901176\pi$
$4$	−4.00000			−0.500000
$5$	−11.1034	+	1.30950i	−0.993117	+	0.117126i
$5$	−11.1034	+	1.30950i	−0.993117	+	0.117126i
$6$	−6.34975			−0.432046
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	16.9202			0.626672
$10$	−2.61901	−	22.2068i	−0.0828203	−	0.702240i
$11$	50.2699			1.37790			0.688952	−	0.724807i	$-0.258071\pi$
$11$	50.2699			1.37790			0.688952	+	0.724807i	$0.258071\pi$
$12$		−	12.6995i		−	0.305503i
$13$			17.8744i			0.381343i	0.981654	+	0.190672i	$0.0610666\pi$
$13$			17.8744i			0.381343i	−0.981654	+	0.190672i	$0.938933\pi$
$14$		0			0
$15$	−4.15751	−	35.2519i	−0.0715643	−	0.606800i
$16$	16.0000			0.250000
$17$		−	93.9202i		−	1.33994i	−0.742388	−	0.669970i	$-0.766307\pi$
$17$		−	93.9202i		−	1.33994i	0.742388	−	0.669970i	$-0.233693\pi$
$18$			33.8403i			0.443124i
$19$	84.9965			1.02629			0.513146	−	0.858302i	$-0.328480\pi$
$19$	84.9965			1.02629			0.513146	+	0.858302i	$0.328480\pi$
$20$	44.4135	−	5.23801i	0.496559	−	0.0585628i
$21$		0			0
$22$			100.540i			0.974326i
$23$		−	119.688i		−	1.08507i	−0.840033	−	0.542535i	$-0.817465\pi$
$23$		−	119.688i		−	1.08507i	0.840033	−	0.542535i	$-0.182535\pi$
$24$	25.3990			0.216023
$25$	121.570	−	29.0798i	0.972563	−	0.232639i
$26$	−35.7488			−0.269650
$27$			139.441i			0.993906i
$28$		0			0
$29$	−165.509			−1.05980			−0.529902	−	0.848059i	$-0.677771\pi$
$29$	−165.509			−1.05980			−0.529902	+	0.848059i	$0.677771\pi$
$30$	70.5038	−	8.31502i	0.429072	−	0.0506036i
$31$	134.227			0.777676			0.388838	−	0.921306i	$-0.372877\pi$
$31$	134.227			0.777676			0.388838	+	0.921306i	$0.372877\pi$
$32$			32.0000i			0.176777i
$33$			159.601i			0.841907i
$34$	187.840			0.947481
$35$		0			0
$36$	−67.6806			−0.313336
$37$			129.681i			0.576199i	0.957600	+	0.288100i	$0.0930234\pi$
$37$			129.681i			0.576199i	−0.957600	+	0.288100i	$0.906977\pi$
$38$			169.993i			0.725698i
$39$	−56.7490			−0.233003
$40$	10.4760	+	88.8271i	0.0414101	+	0.351120i
$41$	118.486			0.451326			0.225663	−	0.974205i	$-0.427545\pi$
$41$	118.486			0.451326			0.225663	+	0.974205i	$0.427545\pi$
$42$		0			0
$43$			533.246i			1.89115i	0.325411	+	0.945573i	$0.394497\pi$
$43$			533.246i			1.89115i	−0.325411	+	0.945573i	$0.605503\pi$
$44$	−201.080			−0.688952
$45$	−187.871	+	22.1570i	−0.622359	+	0.0733993i
$46$	239.375			0.767260
$47$			142.504i			0.442264i	0.975244	+	0.221132i	$0.0709751\pi$
$47$			142.504i			0.442264i	−0.975244	+	0.221132i	$0.929025\pi$
$48$			50.7980i			0.152751i
$49$		0			0
$50$	58.1597	+	243.141i	0.164500	+	0.687706i
$51$	298.185			0.818711
$52$		−	71.4975i		−	0.190672i
$53$			549.664i			1.42457i	0.701891	+	0.712284i	$0.252339\pi$
$53$			549.664i			1.42457i	−0.701891	+	0.712284i	$0.747661\pi$
$54$	−278.882			−0.702797
$55$	−558.166	+	65.8286i	−1.36842	+	0.161388i
$56$		0			0
$57$			269.853i			0.627070i
$58$		−	331.018i		−	0.749394i
$59$	566.008			1.24895			0.624474	−	0.781045i	$-0.285313\pi$
$59$	566.008			1.24895			0.624474	+	0.781045i	$0.285313\pi$
$60$	16.6300	+	141.008i	0.0357822	+	0.303400i
$61$	−523.703			−1.09923			−0.549617	−	0.835417i	$-0.685226\pi$
$61$	−523.703			−1.09923			−0.549617	+	0.835417i	$0.685226\pi$
$62$			268.455i			0.549900i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−23.4066	−	198.466i	−0.0446650	−	0.378719i
$66$	−319.202			−0.595318
$67$		−	503.840i		−	0.918715i	−0.888252	−	0.459357i	$-0.848080\pi$
$67$		−	503.840i		−	0.918715i	0.888252	−	0.459357i	$-0.151920\pi$
$68$			375.681i			0.669970i
$69$	379.993			0.662983
$70$		0			0
$71$	179.059			0.299301			0.149651	−	0.988739i	$-0.452185\pi$
$71$	179.059			0.299301			0.149651	+	0.988739i	$0.452185\pi$
$72$		−	135.361i		−	0.221562i
$73$		−	1105.92i		−	1.77313i	−0.462606	−	0.886564i	$-0.653086\pi$
$73$		−	1105.92i		−	1.77313i	0.462606	−	0.886564i	$-0.346914\pi$
$74$	−259.361			−0.407434
$75$	92.3249	+	385.971i	0.142144	+	0.594241i
$76$	−339.986			−0.513146
$77$		0			0
$78$		−	113.498i		−	0.164758i
$79$	499.227			0.710980			0.355490	−	0.934680i	$-0.384314\pi$
$79$	499.227			0.710980			0.355490	+	0.934680i	$0.384314\pi$
$80$	−177.654	+	20.9521i	−0.248279	+	0.0292814i
$81$	14.1359			0.0193908
$82$			236.971i			0.319135i
$83$			626.803i			0.828922i	0.910067	+	0.414461i	$0.136030\pi$
$83$			626.803i			0.828922i	−0.910067	+	0.414461i	$0.863970\pi$
$84$		0			0
$85$	122.989	+	1042.83i	0.156941	+	1.33072i
$86$	−1066.49			−1.33724
$87$		−	525.471i		−	0.647545i
$88$		−	402.159i		−	0.487163i
$89$	721.623			0.859459			0.429730	−	0.902958i	$-0.358609\pi$
$89$	721.623			0.859459			0.429730	+	0.902958i	$0.358609\pi$
$90$	−44.3140	−	375.742i	−0.0519012	−	0.440074i
$91$		0			0
$92$			478.750i			0.542535i
$93$			426.156i			0.475164i
$94$	−285.009			−0.312728
$95$	−943.749	+	111.303i	−1.01923	+	0.120205i
$96$	−101.596			−0.108012
$97$			543.221i			0.568616i	0.958733	+	0.284308i	$0.0917638\pi$
$97$			543.221i			0.568616i	−0.958733	+	0.284308i	$0.908236\pi$
$98$		0			0
$99$	850.575			0.863495
$100$	−486.282	+	116.319i	−0.486282	+	0.116319i
$101$	923.244			0.909567			0.454783	−	0.890602i	$-0.349717\pi$
$101$	923.244			0.909567			0.454783	+	0.890602i	$0.349717\pi$
$102$			596.370i			0.578916i
$103$			561.917i			0.537547i	0.963203	+	0.268773i	$0.0866183\pi$
$103$			561.917i			0.537547i	−0.963203	+	0.268773i	$0.913382\pi$
$104$	142.995			0.134825
$105$		0			0
$106$	−1099.33			−1.00732
$107$		−	1053.44i		−	0.951779i	−0.879505	−	0.475890i	$-0.842126\pi$
$107$		−	1053.44i		−	0.951779i	0.879505	−	0.475890i	$-0.157874\pi$
$108$		−	557.764i		−	0.496953i
$109$	−1766.04			−1.55189			−0.775946	−	0.630800i	$-0.782727\pi$
$109$	−1766.04			−1.55189			−0.775946	+	0.630800i	$0.782727\pi$
$110$	−131.657	−	1116.33i	−0.114118	−	0.967619i
$111$	−411.720			−0.352061
$112$		0			0
$113$			134.333i			0.111831i	0.998435	+	0.0559157i	$0.0178078\pi$
$113$			134.333i			0.111831i	−0.998435	+	0.0559157i	$0.982192\pi$
$114$	−539.707			−0.443405
$115$	156.731	+	1328.94i	0.127089	+	1.07760i
$116$	662.037			0.529902
$117$			302.437i			0.238977i
$118$			1132.02i			0.883140i
$119$		0			0
$120$	−282.015	+	33.2601i	−0.214536	+	0.0253018i
$121$	1196.06			0.898620
$122$		−	1047.41i		−	0.777275i
$123$			376.177i			0.275762i
$124$	−536.910			−0.388838
$125$	−1311.76	+	482.082i	−0.938621	+	0.344950i
$126$		0			0
$127$			194.736i			0.136063i	0.997683	+	0.0680316i	$0.0216719\pi$
$127$			194.736i			0.136063i	−0.997683	+	0.0680316i	$0.978328\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−1692.99			−1.15550
$130$	396.932	−	46.8131i	0.267794	−	0.0315829i
$131$	1874.59			1.25026			0.625129	−	0.780522i	$-0.285047\pi$
$131$	1874.59			1.25026			0.625129	+	0.780522i	$0.285047\pi$
$132$		−	638.403i		−	0.420953i
$133$		0			0
$134$	1007.68			0.649629
$135$	−182.599	−	1548.27i	−0.116412	−	0.987065i
$136$	−751.361			−0.473740
$137$			437.479i			0.272820i	0.990652	+	0.136410i	$0.0435564\pi$
$137$			437.479i			0.272820i	−0.990652	+	0.136410i	$0.956444\pi$
$138$			759.987i			0.468800i
$139$	−727.734			−0.444069			−0.222034	−	0.975039i	$-0.571270\pi$
$139$	−727.734			−0.444069			−0.222034	+	0.975039i	$0.571270\pi$
$140$		0			0
$141$	−452.434			−0.270225
$142$			358.118i			0.211638i
$143$			898.544i			0.525455i
$144$	270.722			0.156668
$145$	1837.71	−	216.735i	1.05251	−	0.124130i
$146$	2211.84			1.25379
$147$		0			0
$148$		−	518.722i		−	0.288100i
$149$	3079.34			1.69308			0.846541	−	0.532324i	$-0.178681\pi$
$149$	3079.34			1.69308			0.846541	+	0.532324i	$0.178681\pi$
$150$	−771.942	+	184.650i	−0.420192	+	0.100511i
$151$	1735.58			0.935362			0.467681	−	0.883897i	$-0.345090\pi$
$151$	1735.58			0.935362			0.467681	+	0.883897i	$0.345090\pi$
$152$		−	679.972i		−	0.362849i
$153$		−	1589.14i		−	0.839704i
$154$		0			0
$155$	−1490.38	+	175.771i	−0.772323	+	0.0910857i
$156$	226.996			0.116501
$157$			1864.22i			0.947652i	0.880619	+	0.473826i	$0.157127\pi$
$157$			1864.22i			0.947652i	−0.880619	+	0.473826i	$0.842873\pi$
$158$			998.454i			0.502739i
$159$	−1745.11			−0.870419
$160$	−41.9041	−	355.308i	−0.0207051	−	0.175560i
$161$		0			0
$162$			28.2718i			0.0137114i
$163$			2659.74i			1.27808i	0.769175	+	0.639039i	$0.220668\pi$
$163$			2659.74i			1.27808i	−0.769175	+	0.639039i	$0.779332\pi$
$164$	−473.943			−0.225663
$165$	−208.998	−	1772.11i	−0.0986088	−	0.836112i
$166$	−1253.61			−0.586137
$167$		−	3051.35i		−	1.41389i	−0.707266	−	0.706947i	$-0.750072\pi$
$167$		−	3051.35i		−	1.41389i	0.707266	−	0.706947i	$-0.249928\pi$
$168$		0			0
$169$	1877.51			0.854577
$170$	−2085.66	+	245.978i	−0.940959	+	0.110974i
$171$	1438.15			0.643149
$172$		−	2132.98i		−	0.945573i
$173$			2717.13i			1.19410i	0.802204	+	0.597050i	$0.203661\pi$
$173$			2717.13i			1.19410i	−0.802204	+	0.597050i	$0.796339\pi$
$174$	1050.94			0.457884
$175$		0			0
$176$	804.319			0.344476
$177$			1797.01i			0.763114i
$178$			1443.25i			0.607729i
$179$	760.380			0.317505			0.158753	−	0.987318i	$-0.449253\pi$
$179$	760.380			0.317505			0.158753	+	0.987318i	$0.449253\pi$
$180$	751.484	−	88.6280i	0.311180	−	0.0366997i
$181$	−1629.22			−0.669056			−0.334528	−	0.942386i	$-0.608577\pi$
$181$	−1629.22			−0.669056			−0.334528	+	0.942386i	$0.608577\pi$
$182$		0			0
$183$		−	1662.69i		−	0.671638i
$184$	−957.501			−0.383630
$185$	−169.817	−	1439.89i	−0.0674876	−	0.572233i
$186$	−852.311			−0.335992
$187$		−	4721.36i		−	1.84631i
$188$		−	570.017i		−	0.221132i
$189$		0			0
$190$	−222.606	−	1887.50i	−0.0849977	−	0.720703i
$191$	−1436.35			−0.544140			−0.272070	−	0.962277i	$-0.587708\pi$
$191$	−1436.35			−0.544140			−0.272070	+	0.962277i	$0.587708\pi$
$192$		−	203.192i		−	0.0763757i
$193$			2622.38i			0.978045i	0.872271	+	0.489023i	$0.162646\pi$
$193$			2622.38i			0.978045i	−0.872271	+	0.489023i	$0.837354\pi$
$194$	−1086.44			−0.402072
$195$	630.106	−	74.3130i	0.231399	−	0.0272906i
$196$		0			0
$197$		−	5329.93i		−	1.92763i	−0.266581	−	0.963813i	$-0.585894\pi$
$197$		−	5329.93i		−	1.92763i	0.266581	−	0.963813i	$-0.414106\pi$
$198$			1701.15i			0.610583i
$199$	4558.21			1.62373			0.811867	−	0.583843i	$-0.198452\pi$
$199$	4558.21			1.62373			0.811867	+	0.583843i	$0.198452\pi$
$200$	−232.639	−	972.563i	−0.0822502	−	0.343853i
$201$	1599.63			0.561340
$202$			1846.49i			0.643161i
$203$		0			0
$204$	−1192.74			−0.409355
$205$	−1315.59	+	155.157i	−0.448219	+	0.0528617i
$206$	−1123.83			−0.380103
$207$		−	2025.13i		−	0.679983i
$208$			285.990i			0.0953358i
$209$	4272.77			1.41413
$210$		0			0
$211$	−2728.87			−0.890347			−0.445174	−	0.895444i	$-0.646858\pi$
$211$	−2728.87			−0.890347			−0.445174	+	0.895444i	$0.646858\pi$
$212$		−	2198.66i		−	0.712284i
$213$			568.491i			0.182875i
$214$	2106.89			0.673010
$215$	−698.287	−	5920.84i	−0.221501	−	1.87813i
$216$	1115.53			0.351399
$217$		0			0
$218$		−	3532.09i		−	1.09735i
$219$	3511.17			1.08339
$220$	2232.67	−	263.314i	0.684210	−	0.0806939i
$221$	1678.77			0.510977
$222$		−	823.440i		−	0.248944i
$223$		−	611.653i		−	0.183674i	−0.995774	−	0.0918370i	$-0.970726\pi$
$223$		−	611.653i		−	0.183674i	0.995774	−	0.0918370i	$-0.0292739\pi$
$224$		0			0
$225$	2056.99	−	492.035i	0.609479	−	0.145788i
$226$	−268.665			−0.0790767
$227$			1803.39i			0.527292i	0.964620	+	0.263646i	$0.0849251\pi$
$227$			1803.39i			0.527292i	−0.964620	+	0.263646i	$0.915075\pi$
$228$		−	1079.41i		−	0.313535i
$229$	−1192.02			−0.343978			−0.171989	−	0.985099i	$-0.555019\pi$
$229$	−1192.02			−0.343978			−0.171989	+	0.985099i	$0.555019\pi$
$230$	−2657.88	+	313.463i	−0.761979	+	0.0898657i
$231$		0			0
$232$			1324.07i			0.374697i
$233$			1436.20i			0.403815i	0.979405	+	0.201907i	$0.0647140\pi$
$233$			1436.20i			0.403815i	−0.979405	+	0.201907i	$0.935286\pi$
$234$	−604.875			−0.168982
$235$	−186.610	−	1582.28i	−0.0518004	−	0.439220i
$236$	−2264.03			−0.624474
$237$			1584.98i			0.434412i
$238$		0			0
$239$	1887.15			0.510752			0.255376	−	0.966842i	$-0.417801\pi$
$239$	1887.15			0.510752			0.255376	+	0.966842i	$0.417801\pi$
$240$	−66.5202	−	564.030i	−0.0178911	−	0.151700i
$241$	1718.30			0.459275			0.229638	−	0.973276i	$-0.426246\pi$
$241$	1718.30			0.459275			0.229638	+	0.973276i	$0.426246\pi$
$242$			2392.13i			0.635421i
$243$			3809.79i			1.00575i
$244$	2094.81			0.549617
$245$		0			0
$246$	−752.355			−0.194993
$247$			1519.26i			0.391369i
$248$		−	1073.82i		−	0.274950i
$249$	−1990.02			−0.506476
$250$	−964.163	−	2623.53i	−0.243916	−	0.663705i
$251$	−3320.10			−0.834912			−0.417456	−	0.908697i	$-0.637078\pi$
$251$	−3320.10			−0.834912			−0.417456	+	0.908697i	$0.637078\pi$
$252$		0			0
$253$		−	6016.69i		−	1.49512i
$254$	−389.472			−0.0962112
$255$	−3310.86	+	390.474i	−0.813076	+	0.0958919i
$256$	256.000			0.0625000
$257$		−	2609.13i		−	0.633281i	−0.948546	−	0.316641i	$-0.897445\pi$
$257$		−	2609.13i		−	0.633281i	0.948546	−	0.316641i	$-0.102555\pi$
$258$		−	3385.98i		−	0.817062i
$259$		0			0
$260$	93.6263	+	793.865i	0.0223325	+	0.189359i
$261$	−2800.44			−0.664149
$262$			3749.18i			0.884065i
$263$			1058.86i			0.248258i	0.992266	+	0.124129i	$0.0396137\pi$
$263$			1058.86i			0.248258i	−0.992266	+	0.124129i	$0.960386\pi$
$264$	1276.81			0.297659
$265$	−719.787	−	6103.13i	−0.166853	−	1.41476i
$266$		0			0
$267$			2291.06i			0.525134i
$268$			2015.36i			0.459357i
$269$	−1571.46			−0.356184			−0.178092	−	0.984014i	$-0.556992\pi$
$269$	−1571.46			−0.356184			−0.178092	+	0.984014i	$0.556992\pi$
$270$	3096.54	−	365.197i	0.697960	−	0.0823155i
$271$	−3967.40			−0.889307			−0.444654	−	0.895703i	$-0.646673\pi$
$271$	−3967.40			−0.889307			−0.444654	+	0.895703i	$0.646673\pi$
$272$		−	1502.72i		−	0.334985i
$273$		0			0
$274$	−874.957			−0.192913
$275$	6111.33	−	1461.84i	1.34010	−	0.320554i
$276$	−1519.97			−0.331492
$277$		−	4059.99i		−	0.880653i	−0.897838	−	0.440327i	$-0.854863\pi$
$277$		−	4059.99i		−	0.880653i	0.897838	−	0.440327i	$-0.145137\pi$
$278$		−	1455.47i		−	0.314004i
$279$	2271.15			0.487348
$280$		0			0
$281$	8768.49			1.86151			0.930755	−	0.365643i	$-0.119151\pi$
$281$	8768.49			1.86151			0.930755	+	0.365643i	$0.119151\pi$
$282$		−	904.867i		−	0.191078i
$283$		−	4138.47i		−	0.869281i	−0.900604	−	0.434641i	$-0.856875\pi$
$283$		−	4138.47i		−	0.869281i	0.900604	−	0.434641i	$-0.143125\pi$
$284$	−716.236			−0.149651
$285$	−353.374	−	2996.29i	−0.0734459	−	0.622753i
$286$	−1797.09			−0.371552
$287$		0			0
$288$			541.445i			0.110781i
$289$	−3908.00			−0.795440
$290$	433.470	+	3675.43i	0.0877732	+	0.744236i
$291$	−1724.66			−0.347427
$292$			4423.69i			0.886564i
$293$			9248.12i			1.84396i	0.387234	+	0.921982i	$0.373431\pi$
$293$			9248.12i			1.84396i	−0.387234	+	0.921982i	$0.626569\pi$
$294$		0			0
$295$	−6284.61	+	741.189i	−1.24035	+	0.146284i
$296$	1037.44			0.203717
$297$			7009.69i			1.36951i
$298$			6158.67i			1.19719i
$299$	2139.34			0.413784
$300$	−369.300	−	1543.88i	−0.0710718	−	0.297121i
$301$		0			0
$302$			3471.16i			0.661400i
$303$			2931.19i			0.555750i
$304$	1359.94			0.256573
$305$	5814.87	−	685.790i	1.09167	−	0.128748i
$306$	3178.29			0.593760
$307$		−	6805.83i		−	1.26524i	−0.774461	−	0.632621i	$-0.781979\pi$
$307$		−	6805.83i		−	1.26524i	0.774461	−	0.632621i	$-0.218021\pi$
$308$		0			0
$309$	−1784.02			−0.328444
$310$	−351.543	−	2980.76i	−0.0644073	−	0.546115i
$311$	−1901.30			−0.346665			−0.173333	−	0.984863i	$-0.555454\pi$
$311$	−1901.30			−0.346665			−0.173333	+	0.984863i	$0.555454\pi$
$312$			453.992i			0.0823789i
$313$			8870.98i			1.60197i	0.598683	+	0.800986i	$0.295691\pi$
$313$			8870.98i			1.60197i	−0.598683	+	0.800986i	$0.704309\pi$
$314$	−3728.45			−0.670091
$315$		0			0
$316$	−1996.91			−0.355490
$317$		−	9550.80i		−	1.69220i	−0.533027	−	0.846098i	$-0.678946\pi$
$317$		−	9550.80i		−	1.69220i	0.533027	−	0.846098i	$-0.321054\pi$
$318$		−	3490.23i		−	0.615479i
$319$	−8320.13			−1.46031
$320$	710.617	−	83.8082i	0.124140	−	0.0146407i
$321$	3344.56			0.581542
$322$		0			0
$323$		−	7982.89i		−	1.37517i
$324$	−56.5436			−0.00969540
$325$	519.784	+	2173.00i	0.0887152	+	0.370880i
$326$	−5319.47			−0.903737
$327$		−	5606.97i		−	0.948214i
$328$		−	947.885i		−	0.159568i
$329$		0			0
$330$	3544.22	−	417.996i	0.591221	−	0.0697270i
$331$	2564.72			0.425891			0.212946	−	0.977064i	$-0.431694\pi$
$331$	2564.72			0.425891			0.212946	+	0.977064i	$0.431694\pi$
$332$		−	2507.21i		−	0.414461i
$333$			2194.22i			0.361088i
$334$	6102.70			0.999774
$335$	659.781	+	5594.33i	0.107605	+	0.912391i
$336$		0			0
$337$			3535.22i			0.571442i	0.958313	+	0.285721i	$0.0922330\pi$
$337$			3535.22i			0.571442i	−0.958313	+	0.285721i	$0.907767\pi$
$338$			3755.01i			0.604277i
$339$	−426.489			−0.0683295
$340$	−491.955	−	4171.33i	−0.0784706	−	0.665359i
$341$	6747.60			1.07156
$342$			2876.31i			0.454775i
$343$		0			0
$344$	4265.97			0.668621
$345$	−4219.21	+	497.603i	−0.658420	+	0.0776522i
$346$	−5434.25			−0.844356
$347$			4382.81i			0.678045i	0.940778	+	0.339023i	$0.110096\pi$
$347$			4382.81i			0.678045i	−0.940778	+	0.339023i	$0.889904\pi$
$348$			2101.89i			0.323773i
$349$	2414.14			0.370276			0.185138	−	0.982713i	$-0.440727\pi$
$349$	2414.14			0.370276			0.185138	+	0.982713i	$0.440727\pi$
$350$		0			0
$351$	−2492.42			−0.379019
$352$			1608.64i			0.243581i
$353$		−	11564.0i		−	1.74360i	−0.489860	−	0.871801i	$-0.662952\pi$
$353$		−	11564.0i		−	1.74360i	0.489860	−	0.871801i	$-0.337048\pi$
$354$	−3594.01			−0.539603
$355$	−1988.16	+	234.478i	−0.297241	+	0.0350558i
$356$	−2886.49			−0.429730
$357$		0			0
$358$			1520.76i			0.224510i
$359$	−6453.41			−0.948742			−0.474371	−	0.880325i	$-0.657324\pi$
$359$	−6453.41			−0.948742			−0.474371	+	0.880325i	$0.657324\pi$
$360$	177.256	+	1502.97i	0.0259506	+	0.220037i
$361$	365.407			0.0532740
$362$		−	3258.44i		−	0.473094i
$363$			3797.36i			0.549062i
$364$		0			0
$365$	1448.21	+	12279.5i	0.207679	+	1.76092i
$366$	3325.38			0.474919
$367$		−	5131.76i		−	0.729907i	−0.931026	−	0.364953i	$-0.881085\pi$
$367$		−	5131.76i		−	0.729907i	0.931026	−	0.364953i	$-0.118915\pi$
$368$		−	1915.00i		−	0.271267i
$369$	2004.80			0.282833
$370$	2879.79	−	339.634i	0.404630	−	0.0477210i
$371$		0			0
$372$		−	1704.62i		−	0.237582i
$373$			6506.75i			0.903235i	0.892212	+	0.451617i	$0.149153\pi$
$373$			6506.75i			0.903235i	−0.892212	+	0.451617i	$0.850847\pi$
$374$	9442.72			1.30554
$375$	−1530.55	−	4164.69i	−0.210766	−	0.573503i
$376$	1140.03			0.156364
$377$		−	2958.38i		−	0.404149i
$378$		0			0
$379$	−12932.0			−1.75270			−0.876350	−	0.481676i	$-0.840028\pi$
$379$	−12932.0			−1.75270			−0.876350	+	0.481676i	$0.840028\pi$
$380$	3775.00	−	445.213i	0.509614	−	0.0601025i
$381$	−618.263			−0.0831353
$382$		−	2872.70i		−	0.384765i
$383$			13062.0i			1.74266i	0.490701	+	0.871328i	$0.336741\pi$
$383$			13062.0i			1.74266i	−0.490701	+	0.871328i	$0.663259\pi$
$384$	406.384			0.0540058
$385$		0			0
$386$	−5244.75			−0.691582
$387$			9022.60i			1.18513i
$388$		−	2172.88i		−	0.284308i
$389$	12364.3			1.61156			0.805780	−	0.592215i	$-0.201746\pi$
$389$	12364.3			1.61156			0.805780	+	0.592215i	$0.201746\pi$
$390$	148.626	+	1260.21i	0.0192974	+	0.163624i
$391$	−11241.1			−1.45393
$392$		0			0
$393$			5951.59i			0.763914i
$394$	10659.9			1.36304
$395$	−5543.11	+	653.739i	−0.706086	+	0.0832739i
$396$	−3402.30			−0.431747
$397$			5195.33i			0.656792i	0.944540	+	0.328396i	$0.106508\pi$
$397$			5195.33i			0.656792i	−0.944540	+	0.328396i	$0.893492\pi$
$398$			9116.42i			1.14815i
$399$		0			0
$400$	1945.13	−	465.278i	0.243141	−	0.0581597i
$401$	−9343.04			−1.16351			−0.581757	−	0.813363i	$-0.697634\pi$
$401$	−9343.04			−1.16351			−0.581757	+	0.813363i	$0.697634\pi$
$402$			3199.26i			0.396927i
$403$			2399.23i			0.296562i
$404$	−3692.98			−0.454783
$405$	−156.956	+	18.5110i	−0.0192573	+	0.00227116i
$406$		0			0
$407$			6519.03i			0.793947i
$408$		−	2385.48i		−	0.289458i
$409$	−11930.1			−1.44231			−0.721155	−	0.692774i	$-0.756388\pi$
$409$	−11930.1			−1.44231			−0.721155	+	0.692774i	$0.756388\pi$
$410$	−310.315	−	2631.18i	−0.0373789	−	0.316939i
$411$	−1388.94			−0.166694
$412$		−	2247.67i		−	0.268773i
$413$		0			0
$414$	4050.27			0.480821
$415$	−820.800	−	6959.63i	−0.0970880	−	0.823217i
$416$	−571.980			−0.0674126
$417$		−	2310.47i		−	0.271328i
$418$			8545.53i			0.999942i
$419$	−5113.86			−0.596250			−0.298125	−	0.954527i	$-0.596361\pi$
$419$	−5113.86			−0.596250			−0.298125	+	0.954527i	$0.596361\pi$
$420$		0			0
$421$	14255.5			1.65028			0.825141	−	0.564927i	$-0.191096\pi$
$421$	14255.5			1.65028			0.825141	+	0.564927i	$0.191096\pi$
$422$		−	5457.74i		−	0.629571i
$423$			2411.20i			0.277154i
$424$	4397.31			0.503661
$425$	−2731.18	−	11417.9i	−0.311722	−	1.30318i
$426$	−1136.98			−0.129312
$427$		0			0
$428$			4213.78i			0.475890i
$429$	−2852.77			−0.321056
$430$	11841.7	−	1396.57i	1.32804	−	0.156625i
$431$	−8773.25			−0.980494			−0.490247	−	0.871584i	$-0.663093\pi$
$431$	−8773.25			−0.980494			−0.490247	+	0.871584i	$0.663093\pi$
$432$			2231.06i			0.248476i
$433$			2530.92i			0.280897i	0.990088	+	0.140448i	$0.0448544\pi$
$433$			2530.92i			0.280897i	−0.990088	+	0.140448i	$0.955146\pi$
$434$		0			0
$435$	688.107	+	5834.51i	0.0758441	+	0.643088i
$436$	7064.17			0.775946
$437$		−	10173.0i		−	1.11360i
$438$			7022.33i			0.766073i
$439$	−13842.6			−1.50494			−0.752472	−	0.658624i	$-0.771139\pi$
$439$	−13842.6			−1.50494			−0.752472	+	0.658624i	$0.771139\pi$
$440$	526.629	+	4465.33i	0.0570592	+	0.483810i
$441$		0			0
$442$			3357.53i			0.361315i
$443$		−	16388.0i		−	1.75760i	−0.477190	−	0.878800i	$-0.658345\pi$
$443$		−	16388.0i		−	1.75760i	0.477190	−	0.878800i	$-0.341655\pi$
$444$	1646.88			0.176030
$445$	−8012.46	+	944.967i	−0.853544	+	0.100665i
$446$	1223.31			0.129877
$447$			9776.52i			1.03448i
$448$		0			0
$449$	3165.01			0.332664			0.166332	−	0.986070i	$-0.446808\pi$
$449$	3165.01			0.332664			0.166332	+	0.986070i	$0.446808\pi$
$450$	984.071	+	4113.98i	0.103088	+	0.430966i
$451$	5956.26			0.621883
$452$		−	537.330i		−	0.0559157i
$453$			5510.26i			0.571511i
$454$	−3606.78			−0.372852
$455$		0			0
$456$	2158.83			0.221703
$457$		−	10685.9i		−	1.09380i	−0.837198	−	0.546899i	$-0.815808\pi$
$457$		−	10685.9i		−	1.09380i	0.837198	−	0.546899i	$-0.184192\pi$
$458$		−	2384.04i		−	0.243229i
$459$	13096.3			1.33177
$460$	−626.925	−	5315.75i	−0.0635447	−	0.538800i
$461$	14153.1			1.42988			0.714941	−	0.699185i	$-0.246453\pi$
$461$	14153.1			1.42988			0.714941	+	0.699185i	$0.246453\pi$
$462$		0			0
$463$			5347.76i			0.536785i	0.963310	+	0.268392i	$0.0864924\pi$
$463$			5347.76i			0.536785i	−0.963310	+	0.268392i	$0.913508\pi$
$464$	−2648.15			−0.264951
$465$	−558.052	−	4731.77i	−0.0556539	−	0.471894i
$466$	−2872.41			−0.285540
$467$		−	863.874i		−	0.0856002i	−0.999084	−	0.0428001i	$-0.986372\pi$
$467$		−	863.874i		−	0.0856002i	0.999084	−	0.0428001i	$-0.0136279\pi$
$468$		−	1209.75i		−	0.119489i
$469$		0			0
$470$	3164.56	−	373.220i	0.310575	−	0.0366284i
$471$	−5918.68			−0.579020
$472$		−	4528.06i		−	0.441570i
$473$			26806.2i			2.60582i
$474$	−3169.97			−0.307176
$475$	10333.1	−	2471.69i	0.998133	−	0.238755i
$476$		0			0
$477$			9300.40i			0.892738i
$478$			3774.31i			0.361156i
$479$	−935.617			−0.0892473			−0.0446236	−	0.999004i	$-0.514209\pi$
$479$	−935.617			−0.0892473			−0.0446236	+	0.999004i	$0.514209\pi$
$480$	1128.06	−	133.040i	0.107268	−	0.0126509i
$481$	−2317.96			−0.219730
$482$			3436.60i			0.324757i
$483$		0			0
$484$	−4784.26			−0.449310
$485$	−711.350	−	6031.59i	−0.0665994	−	0.564702i
$486$	−7619.58			−0.711175
$487$			4610.03i			0.428954i	0.976729	+	0.214477i	$0.0688047\pi$
$487$			4610.03i			0.428954i	−0.976729	+	0.214477i	$0.931195\pi$
$488$			4189.62i			0.388638i
$489$	−8444.33			−0.780912
$490$		0			0
$491$	−16184.3			−1.48755			−0.743775	−	0.668430i	$-0.766967\pi$
$491$	−16184.3			−1.48755			−0.743775	+	0.668430i	$0.766967\pi$
$492$		−	1504.71i		−	0.137881i
$493$			15544.7i			1.42007i
$494$	−3038.52			−0.276740
$495$	−9444.26	+	1113.83i	−0.857551	+	0.101137i
$496$	2147.64			0.194419
$497$		0			0
$498$		−	3980.04i		−	0.358133i
$499$	−777.051			−0.0697106			−0.0348553	−	0.999392i	$-0.511097\pi$
$499$	−777.051			−0.0697106			−0.0348553	+	0.999392i	$0.511097\pi$
$500$	5247.05	−	1928.33i	0.469311	−	0.172475i
$501$	9687.65			0.863897
$502$		−	6640.20i		−	0.590372i
$503$		−	2775.36i		−	0.246018i	−0.992406	−	0.123009i	$-0.960746\pi$
$503$		−	2775.36i		−	0.246018i	0.992406	−	0.123009i	$-0.0392544\pi$
$504$		0			0
$505$	−10251.1	+	1208.99i	−0.903306	+	0.106533i
$506$	12033.4			1.05721
$507$			5960.85i			0.522151i
$508$		−	778.944i		−	0.0680316i
$509$	6544.58			0.569908			0.284954	−	0.958541i	$-0.408022\pi$
$509$	6544.58			0.569908			0.284954	+	0.958541i	$0.408022\pi$
$510$	−780.948	−	6621.73i	−0.0678058	−	0.574931i
$511$		0			0
$512$			512.000i			0.0441942i
$513$			11852.0i			1.02004i
$514$	5218.27			0.447797
$515$	−735.832	−	6239.18i	−0.0629605	−	0.533847i
$516$	6771.96			0.577750
$517$			7163.68i			0.609397i
$518$		0			0
$519$	−8626.54			−0.729601
$520$	−1587.73	+	187.253i	−0.133897	+	0.0157915i
$521$	14477.2			1.21739			0.608694	−	0.793405i	$-0.291694\pi$
$521$	14477.2			1.21739			0.608694	+	0.793405i	$0.291694\pi$
$522$		−	5600.88i		−	0.469625i
$523$			18110.0i			1.51414i	0.653334	+	0.757070i	$0.273370\pi$
$523$			18110.0i			1.51414i	−0.653334	+	0.757070i	$0.726630\pi$
$524$	−7498.36			−0.625129
$525$		0			0
$526$	−2117.72			−0.175545
$527$		−	12606.7i		−	1.04204i
$528$			2553.61i			0.210477i
$529$	−2158.12			−0.177375
$530$	12206.3	−	1439.57i	1.00039	−	0.117983i
$531$	9576.94			0.782682
$532$		0			0
$533$			2117.86i			0.172110i
$534$	−4582.13			−0.371326
$535$	1379.49	+	11696.8i	0.111478	+	0.945228i
$536$	−4030.72			−0.324815
$537$			2414.11i			0.193998i
$538$		−	3142.91i		−	0.251860i
$539$		0			0
$540$	730.394	+	6193.07i	0.0582059	+	0.493532i
$541$	−6723.03			−0.534280			−0.267140	−	0.963658i	$-0.586079\pi$
$541$	−6723.03			−0.534280			−0.267140	+	0.963658i	$0.586079\pi$
$542$		−	7934.79i		−	0.628835i
$543$		−	5172.58i		−	0.408796i
$544$	3005.44			0.236870
$545$	19609.1	−	2312.64i	1.54121	−	0.181766i
$546$		0			0
$547$		−	8128.96i		−	0.635410i	−0.948190	−	0.317705i	$-0.897088\pi$
$547$		−	8128.96i		−	0.635410i	0.948190	−	0.317705i	$-0.102912\pi$
$548$		−	1749.91i		−	0.136410i
$549$	−8861.13			−0.688859
$550$	2923.68	+	12222.7i	0.226666	+	0.947593i
$551$	−14067.7			−1.08767
$552$		−	3039.95i		−	0.234400i
$553$		0			0
$554$	8119.97			0.622716
$555$	4571.49	−	539.149i	0.349637	−	0.0412353i
$556$	2910.94			0.222034
$557$		−	22542.4i		−	1.71481i	−0.514638	−	0.857407i	$-0.672074\pi$
$557$		−	22542.4i		−	1.71481i	0.514638	−	0.857407i	$-0.327926\pi$
$558$			4542.30i			0.344607i
$559$	−9531.44			−0.721175
$560$		0			0
$561$	14989.7			1.12811
$562$			17537.0i			1.31629i
$563$		−	22232.9i		−	1.66431i	−0.554545	−	0.832154i	$-0.687108\pi$
$563$		−	22232.9i		−	1.66431i	0.554545	−	0.832154i	$-0.312892\pi$
$564$	1809.73			0.135113
$565$	−175.909	−	1491.55i	−0.0130983	−	0.111062i
$566$	8276.94			0.614675
$567$		0			0
$568$		−	1432.47i		−	0.105819i
$569$	6113.48			0.450423			0.225211	−	0.974310i	$-0.427693\pi$
$569$	6113.48			0.450423			0.225211	+	0.974310i	$0.427693\pi$
$570$	5992.57	−	706.748i	0.440353	−	0.0519341i
$571$	22721.7			1.66528			0.832640	−	0.553815i	$-0.186828\pi$
$571$	22721.7			1.66528			0.832640	+	0.553815i	$0.186828\pi$
$572$		−	3594.17i		−	0.262727i
$573$		−	4560.24i		−	0.332472i
$574$		0			0
$575$	−3480.50	−	14550.5i	−0.252429	−	1.05530i
$576$	−1082.89			−0.0783341
$577$			1519.61i			0.109640i	0.998496	+	0.0548199i	$0.0174585\pi$
$577$			1519.61i			0.109640i	−0.998496	+	0.0548199i	$0.982542\pi$
$578$		−	7815.99i		−	0.562461i
$579$	−8325.72			−0.597591
$580$	−7350.85	+	866.940i	−0.526254	+	0.0620650i
$581$		0			0
$582$		−	3449.32i		−	0.245668i
$583$			27631.5i			1.96292i
$584$	−8847.37			−0.626895
$585$	−396.043	−	3358.08i	−0.0279903	−	0.237332i
$586$	−18496.2			−1.30388
$587$			10440.9i			0.734143i	0.930193	+	0.367071i	$0.119640\pi$
$587$			10440.9i			0.734143i	−0.930193	+	0.367071i	$0.880360\pi$
$588$		0			0
$589$	11408.9			0.798122
$590$	−1482.38	−	12569.2i	−0.103438	−	0.877061i
$591$	16921.9			1.17779
$592$			2074.89i			0.144050i
$593$		−	19081.2i		−	1.32136i	−0.750666	−	0.660682i	$-0.770267\pi$
$593$		−	19081.2i		−	1.32136i	0.750666	−	0.660682i	$-0.229733\pi$
$594$	−14019.4			−0.968388
$595$		0			0
$596$	−12317.3			−0.846541
$597$			14471.8i			0.992110i
$598$			4278.68i			0.292589i
$599$	−5175.38			−0.353022			−0.176511	−	0.984299i	$-0.556481\pi$
$599$	−5175.38			−0.353022			−0.176511	+	0.984299i	$0.556481\pi$
$600$	3087.77	−	738.599i	0.210096	−	0.0502553i
$601$	−4472.56			−0.303560			−0.151780	−	0.988414i	$-0.548500\pi$
$601$	−4472.56			−0.303560			−0.151780	+	0.988414i	$0.548500\pi$
$602$		0			0
$603$		−	8525.06i		−	0.575733i
$604$	−6942.32			−0.467681
$605$	−13280.4	+	1566.25i	−0.892435	+	0.105251i
$606$	−5862.37			−0.392975
$607$		−	15446.8i		−	1.03289i	−0.856319	−	0.516447i	$-0.827254\pi$
$607$		−	15446.8i		−	1.03289i	0.856319	−	0.516447i	$-0.172746\pi$
$608$			2719.89i			0.181424i
$609$		0			0
$610$	1371.58	+	11629.7i	0.0910388	+	0.771926i
$611$	−2547.18			−0.168654
$612$			6356.57i			0.419852i
$613$		−	8024.00i		−	0.528689i	−0.964428	−	0.264344i	$-0.914844\pi$
$613$		−	8024.00i		−	0.528689i	0.964428	−	0.264344i	$-0.0851555\pi$
$614$	13611.7			0.894661
$615$	−492.605	−	4176.84i	−0.0322988	−	0.273864i
$616$		0			0
$617$		−	10712.9i		−	0.699003i	−0.936936	−	0.349501i	$-0.886351\pi$
$617$		−	10712.9i		−	0.699003i	0.936936	−	0.349501i	$-0.113649\pi$
$618$		−	3568.03i		−	0.232245i
$619$	−7260.60			−0.471451			−0.235726	−	0.971820i	$-0.575747\pi$
$619$	−7260.60			−0.471451			−0.235726	+	0.971820i	$0.575747\pi$
$620$	5961.52	−	703.085i	0.386162	−	0.0455429i
$621$	16689.4			1.07846
$622$		−	3802.60i		−	0.245129i
$623$		0			0
$624$	−907.984			−0.0582507
$625$	13933.7	−	7070.50i	0.891758	−	0.452512i
$626$	−17742.0			−1.13277
$627$			13565.5i			0.864042i
$628$		−	7456.90i		−	0.473826i
$629$	12179.6			0.772072
$630$		0			0
$631$	5154.44			0.325190			0.162595	−	0.986693i	$-0.448014\pi$
$631$	5154.44			0.325190			0.162595	+	0.986693i	$0.448014\pi$
$632$		−	3993.81i		−	0.251369i
$633$		−	8663.83i		−	0.544007i
$634$	19101.6			1.19656
$635$	−255.007	−	2162.23i	−0.0159365	−	0.135127i
$636$	6980.46			0.435209
$637$		0			0
$638$		−	16640.3i		−	1.03259i
$639$	3029.71			0.187564
$640$	167.616	+	1421.23i	0.0103525	+	0.0877800i
$641$	−2623.50			−0.161657			−0.0808284	−	0.996728i	$-0.525757\pi$
$641$	−2623.50			−0.161657			−0.0808284	+	0.996728i	$0.525757\pi$
$642$			6689.12i			0.411212i
$643$			1598.88i			0.0980614i	0.998797	+	0.0490307i	$0.0156132\pi$
$643$			1598.88i			0.0980614i	−0.998797	+	0.0490307i	$0.984387\pi$
$644$		0			0
$645$	18797.9	−	2216.98i	1.14755	−	0.135339i
$646$	15965.8			0.972391
$647$		−	873.932i		−	0.0531033i	−0.999647	−	0.0265516i	$-0.991547\pi$
$647$		−	873.932i		−	0.0531033i	0.999647	−	0.0265516i	$-0.00845264\pi$
$648$		−	113.087i		−	0.00685569i
$649$	28453.2			1.72093
$650$	−4345.99	+	1039.57i	−0.262252	+	0.0627311i
$651$		0			0
$652$		−	10638.9i		−	0.639039i
$653$		−	5974.47i		−	0.358039i	−0.983846	−	0.179019i	$-0.942708\pi$
$653$		−	5974.47i		−	0.358039i	0.983846	−	0.179019i	$-0.0572925\pi$
$654$	11213.9			0.670489
$655$	−20814.3	+	2454.78i	−1.24165	+	0.146437i
$656$	1895.77			0.112831
$657$		−	18712.4i		−	1.11117i
$658$		0			0
$659$	−20011.0			−1.18288			−0.591439	−	0.806350i	$-0.701440\pi$
$659$	−20011.0			−1.18288			−0.591439	+	0.806350i	$0.701440\pi$
$660$	835.991	+	7088.44i	0.0493044	+	0.418056i
$661$	−22177.7			−1.30501			−0.652506	−	0.757784i	$-0.726282\pi$
$661$	−22177.7			−1.30501			−0.652506	+	0.757784i	$0.726282\pi$
$662$			5129.45i			0.301151i
$663$			5329.87i			0.312210i
$664$	5014.42			0.293068
$665$		0			0
$666$	−4388.43			−0.255328
$667$			19809.4i			1.14996i
$668$			12205.4i			0.706947i
$669$	1941.92			0.112226
$670$	−11188.7	+	1319.56i	−0.645158	+	0.0760882i
$671$	−26326.5			−1.51464
$672$		0			0
$673$		−	13666.5i		−	0.782770i	−0.920227	−	0.391385i	$-0.871996\pi$
$673$		−	13666.5i		−	0.782770i	0.920227	−	0.391385i	$-0.128004\pi$
$674$	−7070.45			−0.404070
$675$	4054.93	+	16951.9i	0.231221	+	0.966636i
$676$	−7510.03			−0.427289
$677$		−	14583.9i		−	0.827923i	−0.910294	−	0.413962i	$-0.864145\pi$
$677$		−	14583.9i		−	0.827923i	0.910294	−	0.413962i	$-0.135855\pi$
$678$		−	852.978i		−	0.0483163i
$679$		0			0
$680$	8342.65	−	983.910i	0.470480	−	0.0554871i
$681$	−5725.54			−0.322178
$682$			13495.2i			0.757710i
$683$			920.211i			0.0515533i	0.999668	+	0.0257766i	$0.00820587\pi$
$683$			920.211i			0.0515533i	−0.999668	+	0.0257766i	$0.991794\pi$
$684$	−5752.62			−0.321574
$685$	−572.880	−	4857.49i	−0.0319542	−	0.270942i
$686$		0			0
$687$		−	3784.52i		−	0.210173i
$688$			8531.93i			0.472786i
$689$	−9824.90			−0.543250
$690$	−995.205	−	8438.43i	−0.0549084	−	0.465573i
$691$	16707.7			0.919815			0.459907	−	0.887967i	$-0.347883\pi$
$691$	16707.7			0.919815			0.459907	+	0.887967i	$0.347883\pi$
$692$		−	10868.5i		−	0.597050i
$693$		0			0
$694$	−8765.62			−0.479450
$695$	8080.31	−	952.970i	0.441012	−	0.0520118i
$696$	−4203.77			−0.228942
$697$		−	11128.2i		−	0.604749i
$698$			4828.29i			0.261824i
$699$	−4559.77			−0.246733
$700$		0			0
$701$	11097.6			0.597931			0.298966	−	0.954264i	$-0.403358\pi$
$701$	11097.6			0.597931			0.298966	+	0.954264i	$0.403358\pi$
$702$		−	4984.85i		−	0.268007i
$703$			11022.4i			0.591348i
$704$	−3217.27			−0.172238
$705$	5023.55	−	592.463i	0.268366	−	0.0316503i
$706$	23128.1			1.23291
$707$		0			0
$708$		−	7188.02i		−	0.381557i
$709$	−29650.1			−1.57057			−0.785284	−	0.619136i	$-0.787483\pi$
$709$	−29650.1			−1.57057			−0.785284	+	0.619136i	$0.787483\pi$
$710$	−468.957	−	3976.33i	−0.0247882	−	0.210181i
$711$	8447.00			0.445551
$712$		−	5772.98i		−	0.303865i
$713$		−	16065.4i		−	0.843832i
$714$		0			0
$715$	−1176.65	−	9976.88i	−0.0615441	−	0.521838i
$716$	−3041.52			−0.158753
$717$			5991.48i			0.312072i
$718$		−	12906.8i		−	0.670862i
$719$	2341.15			0.121433			0.0607164	−	0.998155i	$-0.480661\pi$
$719$	2341.15			0.121433			0.0607164	+	0.998155i	$0.480661\pi$
$720$	−3005.94	+	354.512i	−0.155590	+	0.0183498i
$721$		0			0
$722$			730.813i			0.0376704i
$723$			5455.39i			0.280620i
$724$	6516.88			0.334528
$725$	−20121.0	+	4812.98i	−1.03073	+	0.246551i
$726$	−7594.71			−0.388245
$727$		−	24729.2i		−	1.26156i	−0.775961	−	0.630781i	$-0.782734\pi$
$727$		−	24729.2i		−	1.26156i	0.775961	−	0.630781i	$-0.217266\pi$
$728$		0			0
$729$	−11713.9			−0.595130
$730$	−24559.0	+	2896.42i	−1.24516	+	0.146851i
$731$	50082.5			2.53402
$732$			6650.77i			0.335819i
$733$		−	18246.1i		−	0.919420i	−0.888069	−	0.459710i	$-0.847953\pi$
$733$		−	18246.1i		−	0.919420i	0.888069	−	0.459710i	$-0.152047\pi$
$734$	10263.5			0.516122
$735$		0			0
$736$	3830.00			0.191815
$737$		−	25328.0i		−	1.26590i
$738$			4009.59i			0.199993i
$739$	−34838.2			−1.73416			−0.867080	−	0.498168i	$-0.834006\pi$
$739$	−34838.2			−1.73416			−0.867080	+	0.498168i	$0.834006\pi$
$740$	679.269	+	5759.58i	0.0337438	+	0.286117i
$741$	−4823.46			−0.239129
$742$		0			0
$743$		−	12774.2i		−	0.630739i	−0.948969	−	0.315370i	$-0.897872\pi$
$743$		−	12774.2i		−	0.630739i	0.948969	−	0.315370i	$-0.102128\pi$
$744$	3409.24			0.167996
$745$	−34191.1	+	4032.40i	−1.68143	+	0.198303i
$746$	−13013.5			−0.638684
$747$			10605.6i			0.519463i
$748$			18885.4i			0.923155i
$749$		0			0
$750$	8329.37	−	3061.10i	0.405528	−	0.149034i
$751$	17229.9			0.837189			0.418594	−	0.908173i	$-0.362523\pi$
$751$	17229.9			0.837189			0.418594	+	0.908173i	$0.362523\pi$
$752$			2280.07i			0.110566i
$753$		−	10540.9i		−	0.510136i
$754$	5916.75			0.285776
$755$	−19270.8	+	2272.75i	−0.928924	+	0.109555i
$756$		0			0
$757$			3671.89i			0.176297i	0.996107	+	0.0881486i	$0.0280950\pi$
$757$			3671.89i			0.176297i	−0.996107	+	0.0881486i	$0.971905\pi$
$758$		−	25864.0i		−	1.23935i
$759$	19102.2			0.913527
$760$	890.426	+	7549.99i	0.0424989	+	0.360351i
$761$	−29675.3			−1.41357			−0.706786	−	0.707427i	$-0.749856\pi$
$761$	−29675.3			−1.41357			−0.706786	+	0.707427i	$0.749856\pi$
$762$		−	1236.53i		−	0.0587856i
$763$		0			0
$764$	5745.40			0.272070
$765$	2080.99	+	17644.9i	0.0983507	+	0.833924i
$766$	−26124.0			−1.23224
$767$			10117.0i			0.476278i
$768$			812.769i			0.0381878i
$769$	1561.06			0.0732032			0.0366016	−	0.999330i	$-0.488347\pi$
$769$	1561.06			0.0732032			0.0366016	+	0.999330i	$0.488347\pi$
$770$		0			0
$771$	8283.68			0.386938
$772$		−	10489.5i		−	0.489023i
$773$			5248.94i			0.244232i	0.992516	+	0.122116i	$0.0389679\pi$
$773$			5248.94i			0.244232i	−0.992516	+	0.122116i	$0.961032\pi$
$774$	−18045.2			−0.838012
$775$	16318.1	−	3903.31i	0.756339	−	0.180918i
$776$	4345.77			0.201036
$777$		0			0
$778$			24728.7i			1.13954i
$779$	10070.9			0.463192
$780$	−2520.42	+	297.252i	−0.115700	+	0.0136453i
$781$	9001.29			0.412409
$782$		−	22482.2i		−	1.02808i
$783$		−	23078.8i		−	1.05334i
$784$		0			0
$785$	−2441.21	−	20699.2i	−0.110994	−	0.941129i
$786$	−11903.2			−0.540169
$787$		−	14479.1i		−	0.655813i	−0.944710	−	0.327907i	$-0.893657\pi$
$787$		−	14479.1i		−	0.655813i	0.944710	−	0.327907i	$-0.106343\pi$
$788$			21319.7i			0.963813i
$789$	−3361.74			−0.151687
$790$	−1307.48	−	11086.2i	−0.0588835	−	0.499278i
$791$		0			0
$792$		−	6804.60i		−	0.305291i
$793$		−	9360.86i		−	0.419185i
$794$	−10390.7			−0.464422
$795$	19376.7	−	2285.23i	0.864428	−	0.101948i
$796$	−18232.8			−0.811867
$797$			34842.2i			1.54853i	0.632864	+	0.774263i	$0.281879\pi$
$797$			34842.2i			1.54853i	−0.632864	+	0.774263i	$0.718121\pi$
$798$		0			0
$799$	13384.0			0.592607
$800$	930.555	+	3890.25i	0.0411251	+	0.171927i
$801$	12210.0			0.538599
$802$		−	18686.1i		−	0.822728i
$803$		−	55594.6i		−	2.44320i
$804$	−6398.52			−0.280670
$805$		0			0
$806$	−4798.47			−0.209701
$807$		−	4989.18i		−	0.217630i
$808$		−	7385.95i		−	0.321580i
$809$	−608.467			−0.0264432			−0.0132216	−	0.999913i	$-0.504209\pi$
$809$	−608.467			−0.0264432			−0.0132216	+	0.999913i	$0.504209\pi$
$810$	−37.0220	−	313.913i	−0.00160595	−	0.0136170i
$811$	−1060.59			−0.0459217			−0.0229609	−	0.999736i	$-0.507309\pi$
$811$	−1060.59			−0.0459217			−0.0229609	+	0.999736i	$0.507309\pi$
$812$		0			0
$813$		−	12596.0i		−	0.543371i
$814$	−13038.1			−0.561405
$815$	−3482.93	−	29532.1i	−0.149695	−	1.26928i
$816$	4770.96			0.204678
$817$			45324.0i			1.94087i
$818$		−	23860.2i		−	1.01987i
$819$		0			0
$820$	5262.37	−	620.629i	0.224110	−	0.0264309i
$821$	12614.1			0.536216			0.268108	−	0.963389i	$-0.413602\pi$
$821$	12614.1			0.536216			0.268108	+	0.963389i	$0.413602\pi$
$822$		−	2777.88i		−	0.117871i
$823$		−	24322.8i		−	1.03018i	−0.857135	−	0.515091i	$-0.827758\pi$
$823$		−	24322.8i		−	1.03018i	0.857135	−	0.515091i	$-0.172242\pi$
$824$	4495.34			0.190051
$825$	4641.17	+	19402.7i	0.195860	+	0.818808i
$826$		0			0
$827$		−	5878.95i		−	0.247196i	−0.992332	−	0.123598i	$-0.960557\pi$
$827$		−	5878.95i		−	0.247196i	0.992332	−	0.123598i	$-0.0394434\pi$
$828$			8100.53i			0.339991i
$829$	13627.4			0.570927			0.285464	−	0.958390i	$-0.407852\pi$
$829$	13627.4			0.570927			0.285464	+	0.958390i	$0.407852\pi$
$830$	13919.3	−	1641.60i	0.582102	−	0.0686516i
$831$	12890.0			0.538084
$832$		−	1143.96i		−	0.0476679i
$833$		0			0
$834$	4620.93			0.191858
$835$	3995.75	+	33880.3i	0.165603	+	1.40416i
$836$	−17091.1			−0.707066
$837$			18716.8i			0.772937i
$838$		−	10227.7i		−	0.421612i
$839$	−26823.3			−1.10374			−0.551872	−	0.833929i	$-0.686086\pi$
$839$	−26823.3			−1.10374			−0.551872	+	0.833929i	$0.686086\pi$
$840$		0			0
$841$	3004.31			0.123183
$842$			28510.9i			1.16693i
$843$			27838.9i			1.13739i
$844$	10915.5			0.445174
$845$	−20846.7	+	2458.60i	−0.848695	+	0.100093i
$846$	−4822.39			−0.195978
$847$		0			0
$848$			8794.62i			0.356142i
$849$	13139.1			0.531135
$850$	22835.8	−	5462.37i	0.921485	−	0.220421i
$851$	15521.2			0.625216
$852$		−	2273.96i		−	0.0914374i
$853$			22815.2i			0.915799i	0.889004	+	0.457899i	$0.151398\pi$
$853$			22815.2i			0.915799i	−0.889004	+	0.457899i	$0.848602\pi$
$854$		0			0
$855$	−15968.4	+	1883.27i	−0.638722	+	0.0753291i
$856$	−8427.56			−0.336505
$857$			16137.1i			0.643210i	0.946874	+	0.321605i	$0.104222\pi$
$857$			16137.1i			0.643210i	−0.946874	+	0.321605i	$0.895778\pi$
$858$		−	5705.53i		−	0.227021i
$859$	−30538.8			−1.21301			−0.606503	−	0.795081i	$-0.707428\pi$
$859$	−30538.8			−1.21301			−0.606503	+	0.795081i	$0.707428\pi$
$860$	2793.15	+	23683.3i	0.110751	+	0.939064i
$861$		0			0
$862$		−	17546.5i		−	0.693314i
$863$		−	25921.0i		−	1.02243i	−0.859451	−	0.511217i	$-0.829195\pi$
$863$		−	25921.0i		−	1.02243i	0.859451	−	0.511217i	$-0.170805\pi$
$864$	−4462.11			−0.175699
$865$	−3558.09	−	30169.3i	−0.139860	−	1.18588i
$866$	−5061.84			−0.198624
$867$		−	12407.4i		−	0.486018i
$868$		0			0
$869$	25096.1			0.979662
$870$	−11669.0	+	1376.21i	−0.454732	+	0.0536299i
$871$	9005.84			0.350346
$872$			14128.3i			0.548677i
$873$			9191.39i			0.356336i
$874$	20346.1			0.787432
$875$		0			0
$876$	−14044.7			−0.541695
$877$			24691.0i			0.950689i	0.879800	+	0.475345i	$0.157677\pi$
$877$			24691.0i			0.950689i	−0.879800	+	0.475345i	$0.842323\pi$
$878$		−	27685.2i		−	1.06416i
$879$	−29361.7			−1.12667
$880$	−8930.66	+	1053.26i	−0.342105	+	0.0403469i
$881$	5281.51			0.201974			0.100987	−	0.994888i	$-0.467800\pi$
$881$	5281.51			0.201974			0.100987	+	0.994888i	$0.467800\pi$
$882$		0			0
$883$			41189.3i			1.56980i	0.619625	+	0.784898i	$0.287285\pi$
$883$			41189.3i			1.56980i	−0.619625	+	0.784898i	$0.712715\pi$
$884$	−6715.06			−0.255489
$885$	−2353.19	−	19952.9i	−0.0893802	−	0.757862i
$886$	32776.0			1.24281
$887$			29315.1i			1.10970i	0.831951	+	0.554850i	$0.187224\pi$
$887$			29315.1i			1.10970i	−0.831951	+	0.554850i	$0.812776\pi$
$888$			3293.76i			0.124472i
$889$		0			0
$890$	−1889.93	−	16024.9i	−0.0711806	−	0.603546i
$891$	710.610			0.0267187
$892$			2446.61i			0.0918370i
$893$			12112.4i			0.453891i
$894$	−19553.0			−0.731489
$895$	−8442.79	+	995.720i	−0.315320	+	0.0371880i
$896$		0			0
$897$			6792.15i			0.252824i
$898$			6330.03i			0.235229i
$899$	−22215.9			−0.824184
$900$	−8227.96	+	1968.14i	−0.304739	+	0.0728941i
$901$	51624.5			1.90884
$902$			11912.5i			0.439738i
$903$		0			0
$904$	1074.66			0.0395383
$905$	18089.9	−	2133.47i	0.664450	−	0.0783635i
$906$	−11020.5			−0.404119
$907$		−	19000.2i		−	0.695581i	−0.937572	−	0.347791i	$-0.886932\pi$
$907$		−	19000.2i		−	0.695581i	0.937572	−	0.347791i	$-0.113068\pi$
$908$		−	7213.56i		−	0.263646i
$909$	15621.4			0.570000
$910$		0			0
$911$	19449.0			0.707327			0.353664	−	0.935373i	$-0.384936\pi$
$911$	19449.0			0.707327			0.353664	+	0.935373i	$0.384936\pi$
$912$			4317.66i			0.156767i
$913$			31509.3i			1.14218i
$914$	21371.8			0.773433
$915$	2177.30	+	18461.5i	0.0786659	+	0.667015i
$916$	4768.09			0.171989
$917$		0			0
$918$			26192.7i			0.941706i
$919$	25521.1			0.916064			0.458032	−	0.888936i	$-0.348555\pi$
$919$	25521.1			0.916064			0.458032	+	0.888936i	$0.348555\pi$
$920$	10631.5	−	1253.85i	0.380989	−	0.0449329i
$921$	21607.7			0.773070
$922$			28306.2i			1.01108i
$923$			3200.57i			0.114137i
$924$		0			0
$925$	3771.09	+	15765.3i	0.134046	+	0.560390i
$926$	−10695.5			−0.379564
$927$			9507.72i			0.336866i
$928$		−	5296.30i		−	0.187349i
$929$	30156.2			1.06501			0.532504	−	0.846428i	$-0.321251\pi$
$929$	30156.2			1.06501			0.532504	+	0.846428i	$0.321251\pi$
$930$	9463.54	−	1116.10i	0.333679	−	0.0393532i
$931$		0			0
$932$		−	5744.81i		−	0.201907i
$933$		−	6036.39i		−	0.211814i
$934$	1727.75			0.0605285
$935$	6182.63	+	52423.1i	0.216250	+	1.83360i
$936$	2419.50			0.0844912
$937$		−	7569.52i		−	0.263912i	−0.991256	−	0.131956i	$-0.957874\pi$
$937$		−	7569.52i		−	0.263912i	0.991256	−	0.131956i	$-0.0421257\pi$
$938$		0			0
$939$	−28164.3			−0.978814
$940$	746.440	+	6329.12i	0.0259002	+	0.219610i
$941$	38612.4			1.33765			0.668824	−	0.743420i	$-0.266798\pi$
$941$	38612.4			1.33765			0.668824	+	0.743420i	$0.266798\pi$
$942$		−	11837.4i		−	0.409429i
$943$		−	14181.3i		−	0.489719i
$944$	9056.13			0.312237
$945$		0			0
$946$	−53612.4			−1.84259
$947$		−	15811.3i		−	0.542555i	−0.962501	−	0.271278i	$-0.912554\pi$
$947$		−	15811.3i		−	0.542555i	0.962501	−	0.271278i	$-0.0874462\pi$
$948$		−	6339.93i		−	0.217206i
$949$	19767.7			0.676170
$950$	4943.37	+	20666.1i	0.168825	+	0.705787i
$951$	30322.6			1.03394
$952$		0			0
$953$			19159.9i			0.651259i	0.945497	+	0.325630i	$0.105576\pi$
$953$			19159.9i			0.651259i	−0.945497	+	0.325630i	$0.894424\pi$
$954$	−18600.8			−0.631261
$955$	15948.4	−	1880.91i	0.540395	−	0.0637327i
$956$	−7548.61			−0.255376
$957$		−	26415.4i		−	0.892256i
$958$		−	1871.23i		−	0.0631074i
$959$		0			0
$960$	266.081	+	2256.12i	0.00894554	+	0.0758500i
$961$	−11774.0			−0.395220
$962$		−	4635.92i		−	0.155372i
$963$		−	17824.5i		−	0.596454i
$964$	−6873.19			−0.229638
$965$	−3434.01	−	29117.3i	−0.114554	−	0.971313i
$966$		0			0
$967$			32756.8i			1.08933i	0.838652	+	0.544667i	$0.183344\pi$
$967$			32756.8i			1.08933i	−0.838652	+	0.544667i	$0.816656\pi$
$968$		−	9568.51i		−	0.317710i
$969$	25344.7			0.840236
$970$	12063.2	−	1422.70i	0.399305	−	0.0470929i
$971$	−27170.3			−0.897977			−0.448989	−	0.893537i	$-0.648216\pi$
$971$	−27170.3			−0.897977			−0.448989	+	0.893537i	$0.648216\pi$
$972$		−	15239.2i		−	0.502877i
$973$		0			0
$974$	−9220.06			−0.303316
$975$	−6899.00	+	1650.25i	−0.226610	+	0.0542055i
$976$	−8379.24			−0.274808
$977$			39982.6i			1.30927i	0.755945	+	0.654635i	$0.227178\pi$
$977$			39982.6i			1.30927i	−0.755945	+	0.654635i	$0.772822\pi$
$978$		−	16888.7i		−	0.552188i
$979$	36275.9			1.18425
$980$		0			0
$981$	−29881.7			−0.972528
$982$		−	32368.6i		−	1.05186i
$983$		−	24423.6i		−	0.792462i	−0.918151	−	0.396231i	$-0.870318\pi$
$983$		−	24423.6i		−	0.792462i	0.918151	−	0.396231i	$-0.129682\pi$
$984$	3009.42			0.0974967
$985$	6979.57	+	59180.3i	0.225774	+	1.91436i
$986$	−31089.3			−1.00414
$987$		0			0
$988$		−	6077.04i		−	0.195685i
$989$	63822.9			2.05202
$990$	−2227.66	−	18888.5i	−0.0715149	−	0.606380i
$991$	−44963.2			−1.44127			−0.720637	−	0.693313i	$-0.756150\pi$
$991$	−44963.2			−1.44127			−0.720637	+	0.693313i	$0.756150\pi$
$992$			4295.28i			0.137475i
$993$			8142.68i			0.260222i
$994$		0			0
$995$	−50611.6	+	5968.99i	−1.61256	+	0.190181i
$996$	7960.09			0.253238
$997$		−	39374.4i		−	1.25075i	−0.780323	−	0.625376i	$-0.784945\pi$
$997$		−	39374.4i		−	1.25075i	0.780323	−	0.625376i	$-0.215055\pi$
$998$		−	1554.10i		−	0.0492928i
$999$	−18082.8			−0.572687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.c.99.5		6
5.2	odd	4		2450.4.a.cf.1.2		3
5.3	odd	4		2450.4.a.cg.1.2		3
5.4	even	2	inner	490.4.c.c.99.2		6
7.6	odd	2		70.4.c.b.29.5	yes	6
21.20	even	2		630.4.g.j.379.1		6
28.27	even	2		560.4.g.e.449.4		6
35.13	even	4		350.4.a.x.1.2		3
35.27	even	4		350.4.a.w.1.2		3
35.34	odd	2		70.4.c.b.29.2	✓	6
105.104	even	2		630.4.g.j.379.4		6
140.139	even	2		560.4.g.e.449.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.c.b.29.2	✓	6	35.34	odd	2
70.4.c.b.29.5	yes	6	7.6	odd	2
350.4.a.w.1.2		3	35.27	even	4
350.4.a.x.1.2		3	35.13	even	4
490.4.c.c.99.2		6	5.4	even	2	inner
490.4.c.c.99.5		6	1.1	even	1	trivial
560.4.g.e.449.3		6	140.139	even	2
560.4.g.e.449.4		6	28.27	even	2
630.4.g.j.379.1		6	21.20	even	2
630.4.g.j.379.4		6	105.104	even	2
2450.4.a.cf.1.2		3	5.2	odd	4
2450.4.a.cg.1.2		3	5.3	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)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +3.17488i q^{3} -4.00000 q^{4} +(-11.1034 + 1.30950i) q^{5} -6.34975 q^{6} -8.00000i q^{8} +16.9202 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +3.17488i q^{3} -4.00000 q^{4} +(-11.1034 + 1.30950i) q^{5} -6.34975 q^{6} -8.00000i q^{8} +16.9202 q^{9} +(-2.61901 - 22.2068i) q^{10} +50.2699 q^{11} -12.6995i q^{12} +17.8744i q^{13} +(-4.15751 - 35.2519i) q^{15} +16.0000 q^{16} -93.9202i q^{17} +33.8403i q^{18} +84.9965 q^{19} +(44.4135 - 5.23801i) q^{20} +100.540i q^{22} -119.688i q^{23} +25.3990 q^{24} +(121.570 - 29.0798i) q^{25} -35.7488 q^{26} +139.441i q^{27} -165.509 q^{29} +(70.5038 - 8.31502i) q^{30} +134.227 q^{31} +32.0000i q^{32} +159.601i q^{33} +187.840 q^{34} -67.6806 q^{36} +129.681i q^{37} +169.993i q^{38} -56.7490 q^{39} +(10.4760 + 88.8271i) q^{40} +118.486 q^{41} +533.246i q^{43} -201.080 q^{44} +(-187.871 + 22.1570i) q^{45} +239.375 q^{46} +142.504i q^{47} +50.7980i q^{48} +(58.1597 + 243.141i) q^{50} +298.185 q^{51} -71.4975i q^{52} +549.664i q^{53} -278.882 q^{54} +(-558.166 + 65.8286i) q^{55} +269.853i q^{57} -331.018i q^{58} +566.008 q^{59} +(16.6300 + 141.008i) q^{60} -523.703 q^{61} +268.455i q^{62} -64.0000 q^{64} +(-23.4066 - 198.466i) q^{65} -319.202 q^{66} -503.840i q^{67} +375.681i q^{68} +379.993 q^{69} +179.059 q^{71} -135.361i q^{72} -1105.92i q^{73} -259.361 q^{74} +(92.3249 + 385.971i) q^{75} -339.986 q^{76} -113.498i q^{78} +499.227 q^{79} +(-177.654 + 20.9521i) q^{80} +14.1359 q^{81} +236.971i q^{82} +626.803i q^{83} +(122.989 + 1042.83i) q^{85} -1066.49 q^{86} -525.471i q^{87} -402.159i q^{88} +721.623 q^{89} +(-44.3140 - 375.742i) q^{90} +478.750i q^{92} +426.156i q^{93} -285.009 q^{94} +(-943.749 + 111.303i) q^{95} -101.596 q^{96} +543.221i q^{97} +850.575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{4} + 16 q^{5} - 28 q^{6} - 152 q^{9}+O(q^{10}) \) 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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