LMFDB - Embedded newform 490.4.c.d.99.4

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:	$8$
Coefficient field:	8.0.6654810844696576.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1325x^{4} + 9604 $ x^8 + 1325*x^4 + 9604
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$-1.16183 + 1.16183i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.d.99.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +6.02497i q^{3} -4.00000 q^{4} +(7.18680 - 8.56445i) q^{5} +12.0499 q^{6} +8.00000i q^{8} -9.30030 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +6.02497i q^{3} -4.00000 q^{4} +(7.18680 - 8.56445i) q^{5} +12.0499 q^{6} +8.00000i q^{8} -9.30030 q^{9} +(-17.1289 - 14.3736i) q^{10} -54.9009 q^{11} -24.0999i q^{12} -10.6723i q^{13} +(51.6006 + 43.3003i) q^{15} +16.0000 q^{16} +12.1327i q^{17} +18.6006i q^{18} -27.4523 q^{19} +(-28.7472 + 34.2578i) q^{20} +109.802i q^{22} +181.003i q^{23} -48.1998 q^{24} +(-21.6997 - 123.102i) q^{25} -21.3446 q^{26} +106.640i q^{27} +124.300 q^{29} +(86.6006 - 103.201i) q^{30} -334.478 q^{31} -32.0000i q^{32} -330.776i q^{33} +24.2654 q^{34} +37.2012 q^{36} +88.1982i q^{37} +54.9046i q^{38} +64.3003 q^{39} +(68.5156 + 57.4944i) q^{40} -134.110 q^{41} -190.402i q^{43} +219.604 q^{44} +(-66.8394 + 79.6520i) q^{45} +362.006 q^{46} -177.746i q^{47} +96.3996i q^{48} +(-246.204 + 43.3994i) q^{50} -73.0991 q^{51} +42.6892i q^{52} +211.802i q^{53} +213.280 q^{54} +(-394.562 + 470.196i) q^{55} -165.399i q^{57} -248.601i q^{58} -342.679 q^{59} +(-206.402 - 173.201i) q^{60} -659.891 q^{61} +668.955i q^{62} -64.0000 q^{64} +(-91.4024 - 76.6997i) q^{65} -661.553 q^{66} +572.805i q^{67} -48.5307i q^{68} -1090.54 q^{69} -743.405 q^{71} -74.4024i q^{72} +1163.33i q^{73} +176.396 q^{74} +(741.687 - 130.740i) q^{75} +109.809 q^{76} -128.601i q^{78} -1007.11 q^{79} +(114.989 - 137.031i) q^{80} -893.612 q^{81} +268.221i q^{82} -348.189i q^{83} +(103.910 + 87.1952i) q^{85} -380.805 q^{86} +748.906i q^{87} -439.207i q^{88} +1060.06 q^{89} +(159.304 + 133.679i) q^{90} -724.012i q^{92} -2015.22i q^{93} -355.491 q^{94} +(-197.294 + 235.114i) q^{95} +192.799 q^{96} -578.020i q^{97} +510.595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 60 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 + 60 * q^9	$ 8 q - 32 q^{4} + 60 q^{9} - 36 q^{11} + 144 q^{15} + 128 q^{16} - 308 q^{25} + 860 q^{29} + 424 q^{30} - 240 q^{36} + 380 q^{39} + 144 q^{44} + 208 q^{46} - 88 q^{50} - 988 q^{51} - 576 q^{60} - 512 q^{64} + 344 q^{65} - 3528 q^{71} + 3024 q^{74} - 3084 q^{79} - 1504 q^{81} - 3604 q^{85} - 896 q^{86} - 4132 q^{95} + 6504 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 60 * q^9 - 36 * q^11 + 144 * q^15 + 128 * q^16 - 308 * q^25 + 860 * q^29 + 424 * q^30 - 240 * q^36 + 380 * q^39 + 144 * q^44 + 208 * q^46 - 88 * q^50 - 988 * q^51 - 576 * q^60 - 512 * q^64 + 344 * q^65 - 3528 * q^71 + 3024 * q^74 - 3084 * q^79 - 1504 * q^81 - 3604 * q^85 - 896 * q^86 - 4132 * q^95 + 6504 * 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
$3$			6.02497i			1.15951i	0.814792	+	0.579753i	$0.196851\pi$
$3$			6.02497i			1.15951i	−0.814792	+	0.579753i	$0.803149\pi$
$4$	−4.00000			−0.500000
$5$	7.18680	−	8.56445i	0.642807	−	0.766028i
$5$	7.18680	−	8.56445i	0.642807	−	0.766028i
$6$	12.0499			0.819895
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	−9.30030			−0.344455
$10$	−17.1289	−	14.3736i	−0.541664	−	0.454533i
$11$	−54.9009			−1.50484			−0.752420	−	0.658684i	$-0.771114\pi$
$11$	−54.9009			−1.50484			−0.752420	+	0.658684i	$0.771114\pi$
$12$		−	24.0999i		−	0.579753i
$13$		−	10.6723i		−	0.227689i	−0.993499	−	0.113845i	$-0.963683\pi$
$13$		−	10.6723i		−	0.227689i	0.993499	−	0.113845i	$-0.0363166\pi$
$14$		0			0
$15$	51.6006	+	43.3003i	0.888214	+	0.745339i
$16$	16.0000			0.250000
$17$			12.1327i			0.173095i	0.996248	+	0.0865473i	$0.0275834\pi$
$17$			12.1327i			0.173095i	−0.996248	+	0.0865473i	$0.972417\pi$
$18$			18.6006i			0.243567i
$19$	−27.4523			−0.331473			−0.165737	−	0.986170i	$-0.553000\pi$
$19$	−27.4523			−0.331473			−0.165737	+	0.986170i	$0.553000\pi$
$20$	−28.7472	+	34.2578i	−0.321404	+	0.383014i
$21$		0			0
$22$			109.802i			1.06408i
$23$			181.003i			1.64094i	0.571686	+	0.820472i	$0.306289\pi$
$23$			181.003i			1.64094i	−0.571686	+	0.820472i	$0.693711\pi$
$24$	−48.1998			−0.409947
$25$	−21.6997	−	123.102i	−0.173598	−	0.984817i
$26$	−21.3446			−0.161001
$27$			106.640i			0.760108i
$28$		0			0
$29$	124.300			0.795931			0.397965	−	0.917400i	$-0.369716\pi$
$29$	124.300			0.795931			0.397965	+	0.917400i	$0.369716\pi$
$30$	86.6006	−	103.201i	0.527034	−	0.628062i
$31$	−334.478			−1.93787			−0.968935	−	0.247316i	$-0.920452\pi$
$31$	−334.478			−1.93787			−0.968935	+	0.247316i	$0.920452\pi$
$32$		−	32.0000i		−	0.176777i
$33$		−	330.776i		−	1.74487i
$34$	24.2654			0.122396
$35$		0			0
$36$	37.2012			0.172228
$37$			88.1982i			0.391884i	0.980616	+	0.195942i	$0.0627764\pi$
$37$			88.1982i			0.391884i	−0.980616	+	0.195942i	$0.937224\pi$
$38$			54.9046i			0.234387i
$39$	64.3003			0.264007
$40$	68.5156	+	57.4944i	0.270832	+	0.227267i
$41$	−134.110			−0.510842			−0.255421	−	0.966830i	$-0.582214\pi$
$41$	−134.110			−0.510842			−0.255421	+	0.966830i	$0.582214\pi$
$42$		0			0
$43$		−	190.402i		−	0.675258i	−0.941279	−	0.337629i	$-0.890375\pi$
$43$		−	190.402i		−	0.675258i	0.941279	−	0.337629i	$-0.109625\pi$
$44$	219.604			0.752420
$45$	−66.8394	+	79.6520i	−0.221418	+	0.263863i
$46$	362.006			1.16032
$47$		−	177.746i		−	0.551636i	−0.961210	−	0.275818i	$-0.911051\pi$
$47$		−	177.746i		−	0.551636i	0.961210	−	0.275818i	$-0.0889486\pi$
$48$			96.3996i			0.289877i
$49$		0			0
$50$	−246.204	+	43.3994i	−0.696371	+	0.122752i
$51$	−73.0991			−0.200704
$52$			42.6892i			0.113845i
$53$			211.802i			0.548929i	0.961597	+	0.274464i	$0.0885005\pi$
$53$			211.802i			0.548929i	−0.961597	+	0.274464i	$0.911499\pi$
$54$	213.280			0.537478
$55$	−394.562	+	470.196i	−0.967322	+	1.15275i
$56$		0			0
$57$		−	165.399i		−	0.384345i
$58$		−	248.601i		−	0.562808i
$59$	−342.679			−0.756152			−0.378076	−	0.925775i	$-0.623414\pi$
$59$	−342.679			−0.756152			−0.378076	+	0.925775i	$0.623414\pi$
$60$	−206.402	−	173.201i	−0.444107	−	0.372670i
$61$	−659.891			−1.38509			−0.692544	−	0.721375i	$-0.743510\pi$
$61$	−659.891			−1.38509			−0.692544	+	0.721375i	$0.743510\pi$
$62$			668.955i			1.37028i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−91.4024	−	76.6997i	−0.174416	−	0.146360i
$66$	−661.553			−1.23381
$67$			572.805i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$67$			572.805i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$68$		−	48.5307i		−	0.0865473i
$69$	−1090.54			−1.90269
$70$		0			0
$71$	−743.405			−1.24262			−0.621310	−	0.783565i	$-0.713399\pi$
$71$	−743.405			−1.24262			−0.621310	+	0.783565i	$0.713399\pi$
$72$		−	74.4024i		−	0.121783i
$73$			1163.33i			1.86518i	0.360941	+	0.932589i	$0.382456\pi$
$73$			1163.33i			1.86518i	−0.360941	+	0.932589i	$0.617544\pi$
$74$	176.396			0.277104
$75$	741.687	−	130.740i	1.14190	−	0.201288i
$76$	109.809			0.165737
$77$		0			0
$78$		−	128.601i		−	0.186681i
$79$	−1007.11			−1.43429			−0.717145	−	0.696924i	$-0.754551\pi$
$79$	−1007.11			−1.43429			−0.717145	+	0.696924i	$0.754551\pi$
$80$	114.989	−	137.031i	0.160702	−	0.191507i
$81$	−893.612			−1.22581
$82$			268.221i			0.361220i
$83$		−	348.189i		−	0.460467i	−0.973135	−	0.230233i	$-0.926051\pi$
$83$		−	348.189i		−	0.460467i	0.973135	−	0.230233i	$-0.0739490\pi$
$84$		0			0
$85$	103.910	+	87.1952i	0.132595	+	0.111266i
$86$	−380.805			−0.477479
$87$			748.906i			0.922887i
$88$		−	439.207i		−	0.532041i
$89$	1060.06			1.26255			0.631273	−	0.775561i	$-0.282533\pi$
$89$	1060.06			1.26255			0.631273	+	0.775561i	$0.282533\pi$
$90$	159.304	+	133.679i	0.186579	+	0.156567i
$91$		0			0
$92$		−	724.012i		−	0.820472i
$93$		−	2015.22i		−	2.24697i
$94$	−355.491			−0.390065
$95$	−197.294	+	235.114i	−0.213073	+	0.253918i
$96$	192.799			0.204974
$97$		−	578.020i		−	0.605041i	−0.953143	−	0.302521i	$-0.902172\pi$
$97$		−	578.020i		−	0.605041i	0.953143	−	0.302521i	$-0.0978281\pi$
$98$		0			0
$99$	510.595			0.518350
$100$	86.7988	+	492.408i	0.0867988	+	0.492408i
$101$	−1668.37			−1.64366			−0.821829	−	0.569734i	$-0.807046\pi$
$101$	−1668.37			−1.64366			−0.821829	+	0.569734i	$0.807046\pi$
$102$			146.198i			0.141919i
$103$		−	869.571i		−	0.831858i	−0.909397	−	0.415929i	$-0.863456\pi$
$103$		−	869.571i		−	0.831858i	0.909397	−	0.415929i	$-0.136544\pi$
$104$	85.3784			0.0805004
$105$		0			0
$106$	423.604			0.388151
$107$			1718.41i			1.55257i	0.630380	+	0.776287i	$0.282899\pi$
$107$			1718.41i			1.55257i	−0.630380	+	0.776287i	$0.717101\pi$
$108$		−	426.561i		−	0.380054i
$109$	1771.71			1.55687			0.778437	−	0.627723i	$-0.216013\pi$
$109$	1771.71			1.55687			0.778437	+	0.627723i	$0.216013\pi$
$110$	940.392	+	789.124i	0.815117	+	0.684000i
$111$	−531.392			−0.454392
$112$		0			0
$113$		−	270.985i		−	0.225594i	−0.993618	−	0.112797i	$-0.964019\pi$
$113$		−	270.985i		−	0.225594i	0.993618	−	0.112797i	$-0.0359810\pi$
$114$	−330.799			−0.271773
$115$	1550.19	+	1300.83i	1.25701	+	1.05481i
$116$	−497.201			−0.397965
$117$			99.2555i			0.0784289i
$118$			685.358i			0.534680i
$119$		0			0
$120$	−346.402	+	412.805i	−0.263517	+	0.314031i
$121$	1683.11			1.26454
$122$			1319.78i			0.979405i
$123$		−	808.012i		−	0.592325i
$124$	1337.91			0.968935
$125$	−1210.25	−	698.864i	−0.865987	−	0.500067i
$126$		0			0
$127$			1094.60i			0.764804i	0.923996	+	0.382402i	$0.124903\pi$
$127$			1094.60i			0.764804i	−0.923996	+	0.382402i	$0.875097\pi$
$128$			128.000i			0.0883883i
$129$	1147.17			0.782966
$130$	−153.399	+	182.805i	−0.103492	+	0.123331i
$131$	−2369.79			−1.58053			−0.790265	−	0.612765i	$-0.790057\pi$
$131$	−2369.79			−1.58053			−0.790265	+	0.612765i	$0.790057\pi$
$132$			1323.11i			0.872436i
$133$		0			0
$134$	1145.61			0.738549
$135$	913.315	+	766.402i	0.582264	+	0.488603i
$136$	−97.0615			−0.0611982
$137$		−	1220.02i		−	0.760830i	−0.924816	−	0.380415i	$-0.875781\pi$
$137$		−	1220.02i		−	0.760830i	0.924816	−	0.380415i	$-0.124219\pi$
$138$			2181.08i			1.34540i
$139$	−681.602			−0.415919			−0.207960	−	0.978137i	$-0.566682\pi$
$139$	−681.602			−0.415919			−0.207960	+	0.978137i	$0.566682\pi$
$140$		0			0
$141$	1070.91			0.639625
$142$			1486.81i			0.878665i
$143$			585.919i			0.342636i
$144$	−148.805			−0.0861139
$145$	893.322	−	1064.56i	0.511630	−	0.609705i
$146$	2326.67			1.31888
$147$		0			0
$148$		−	352.793i		−	0.195942i
$149$	2008.44			1.10428			0.552140	−	0.833752i	$-0.313811\pi$
$149$	2008.44			1.10428			0.552140	+	0.833752i	$0.313811\pi$
$150$	−261.480	−	1483.37i	−0.142332	−	0.807446i
$151$	1749.34			0.942776			0.471388	−	0.881926i	$-0.343753\pi$
$151$	1749.34			0.942776			0.471388	+	0.881926i	$0.343753\pi$
$152$		−	219.618i		−	0.117193i
$153$		−	112.838i		−	0.0596234i
$154$		0			0
$155$	−2403.83	+	2864.62i	−1.24568	+	1.48446i
$156$	−257.201			−0.132004
$157$		−	2701.44i		−	1.37324i	−0.727017	−	0.686619i	$-0.759094\pi$
$157$		−	2701.44i		−	1.37324i	0.727017	−	0.686619i	$-0.240906\pi$
$158$			2014.22i			1.01420i
$159$	−1276.10			−0.636486
$160$	−274.062	−	229.978i	−0.135416	−	0.113633i
$161$		0			0
$162$			1787.22i			0.866776i
$163$			305.237i			0.146675i	0.997307	+	0.0733374i	$0.0233650\pi$
$163$			305.237i			0.146675i	−0.997307	+	0.0733374i	$0.976635\pi$
$164$	536.442			0.255421
$165$	−2832.92	−	2377.22i	−1.33662	−	1.12162i
$166$	−696.379			−0.325599
$167$		−	4034.39i		−	1.86940i	−0.355432	−	0.934702i	$-0.615666\pi$
$167$		−	4034.39i		−	1.86940i	0.355432	−	0.934702i	$-0.384334\pi$
$168$		0			0
$169$	2083.10			0.948158
$170$	174.390	−	207.820i	0.0786773	−	0.0937591i
$171$	255.315			0.114178
$172$			761.610i			0.337629i
$173$			1210.08i			0.531798i	0.964001	+	0.265899i	$0.0856687\pi$
$173$			1210.08i			0.531798i	−0.964001	+	0.265899i	$0.914331\pi$
$174$	1497.81			0.652579
$175$		0			0
$176$	−878.414			−0.376210
$177$		−	2064.63i		−	0.876763i
$178$		−	2120.13i		−	0.892755i
$179$	1011.57			0.422392			0.211196	−	0.977444i	$-0.432264\pi$
$179$	1011.57			0.422392			0.211196	+	0.977444i	$0.432264\pi$
$180$	267.358	−	318.608i	0.110709	−	0.131931i
$181$	1386.21			0.569261			0.284631	−	0.958637i	$-0.408129\pi$
$181$	1386.21			0.569261			0.284631	+	0.958637i	$0.408129\pi$
$182$		0			0
$183$		−	3975.83i		−	1.60602i
$184$	−1448.02			−0.580162
$185$	755.369	+	633.863i	0.300194	+	0.251906i
$186$	−4030.44			−1.58885
$187$		−	666.095i		−	0.260480i
$188$			710.983i			0.275818i
$189$		0			0
$190$	470.228	+	394.589i	0.179547	+	0.150666i
$191$	197.285			0.0747386			0.0373693	−	0.999302i	$-0.488102\pi$
$191$	197.285			0.0747386			0.0373693	+	0.999302i	$0.488102\pi$
$192$		−	385.598i		−	0.144938i
$193$			3711.83i			1.38437i	0.721721	+	0.692184i	$0.243351\pi$
$193$			3711.83i			1.38437i	−0.721721	+	0.692184i	$0.756649\pi$
$194$	−1156.04			−0.427829
$195$	462.114	−	550.697i	0.169706	−	0.202237i
$196$		0			0
$197$		−	509.423i		−	0.184238i	−0.995748	−	0.0921190i	$-0.970636\pi$
$197$		−	509.423i		−	0.184238i	0.995748	−	0.0921190i	$-0.0293640\pi$
$198$		−	1021.19i		−	0.366529i
$199$	4504.16			1.60448			0.802240	−	0.597002i	$-0.203641\pi$
$199$	4504.16			1.60448			0.802240	+	0.597002i	$0.203641\pi$
$200$	984.817	−	173.598i	0.348185	−	0.0613760i
$201$	−3451.13			−1.21107
$202$			3336.75i			1.16224i
$203$		0			0
$204$	292.396			0.100352
$205$	−963.826	+	1148.58i	−0.328373	+	0.391320i
$206$	−1739.14			−0.588212
$207$		−	1683.38i		−	0.565232i
$208$		−	170.757i		−	0.0569224i
$209$	1507.16			0.498814
$210$		0			0
$211$	−2469.10			−0.805591			−0.402796	−	0.915290i	$-0.631961\pi$
$211$	−2469.10			−0.805591			−0.402796	+	0.915290i	$0.631961\pi$
$212$		−	847.207i		−	0.274464i
$213$		−	4479.00i		−	1.44083i
$214$	3436.83			1.09784
$215$	−1630.69	−	1368.38i	−0.517266	−	0.434061i
$216$	−853.122			−0.268739
$217$		0			0
$218$		−	3543.42i		−	1.10088i
$219$	−7009.06			−2.16269
$220$	1578.25	−	1880.78i	0.483661	−	0.576375i
$221$	129.484			0.0394118
$222$			1062.78i			0.321303i
$223$			1826.84i			0.548584i	0.961646	+	0.274292i	$0.0884435\pi$
$223$			1826.84i			0.548584i	−0.961646	+	0.274292i	$0.911557\pi$
$224$		0			0
$225$	201.814	+	1144.89i	0.0597966	+	0.339225i
$226$	−541.970			−0.159519
$227$		−	4245.55i		−	1.24135i	−0.784067	−	0.620676i	$-0.786858\pi$
$227$		−	4245.55i		−	1.24135i	0.784067	−	0.620676i	$-0.213142\pi$
$228$			661.598i			0.192173i
$229$	−3252.06			−0.938438			−0.469219	−	0.883082i	$-0.655464\pi$
$229$	−3252.06			−0.938438			−0.469219	+	0.883082i	$0.655464\pi$
$230$	2601.67	−	3100.38i	0.745864	−	0.888840i
$231$		0			0
$232$			994.402i			0.281404i
$233$		−	3894.39i		−	1.09498i	−0.836813	−	0.547489i	$-0.815584\pi$
$233$		−	3894.39i		−	1.09498i	0.836813	−	0.547489i	$-0.184416\pi$
$234$	198.511			0.0554576
$235$	−1522.29	−	1277.42i	−0.422568	−	0.354595i
$236$	1370.72			0.378076
$237$		−	6067.82i		−	1.66307i
$238$		0			0
$239$	641.099			0.173512			0.0867558	−	0.996230i	$-0.472350\pi$
$239$	641.099			0.173512			0.0867558	+	0.996230i	$0.472350\pi$
$240$	825.610	+	692.805i	0.222054	+	0.186335i
$241$	4403.72			1.17705			0.588524	−	0.808480i	$-0.299709\pi$
$241$	4403.72			1.17705			0.588524	+	0.808480i	$0.299709\pi$
$242$		−	3366.22i		−	0.894168i
$243$		−	2504.70i		−	0.661222i
$244$	2639.56			0.692544
$245$		0			0
$246$	−1616.02			−0.418837
$247$			292.979i			0.0754729i
$248$		−	2675.82i		−	0.685140i
$249$	2097.83			0.533914
$250$	−1397.73	+	2420.51i	−0.353601	+	0.612345i
$251$	4207.24			1.05800			0.529001	−	0.848621i	$-0.322567\pi$
$251$	4207.24			1.05800			0.529001	+	0.848621i	$0.322567\pi$
$252$		0			0
$253$		−	9937.22i		−	2.46936i
$254$	2189.20			0.540798
$255$	−525.349	+	626.054i	−0.129014	+	0.153745i
$256$	256.000			0.0625000
$257$		−	83.2133i		−	0.0201973i	−0.999949	−	0.0100986i	$-0.996785\pi$
$257$		−	83.2133i		−	0.0201973i	0.999949	−	0.0100986i	$-0.00321455\pi$
$258$		−	2294.34i		−	0.553641i
$259$		0			0
$260$	365.610	+	306.799i	0.0872082	+	0.0731802i
$261$	−1156.03			−0.274163
$262$			4739.58i			1.11760i
$263$			5040.00i			1.18167i	0.806792	+	0.590836i	$0.201202\pi$
$263$			5040.00i			1.18167i	−0.806792	+	0.590836i	$0.798798\pi$
$264$	2646.21			0.616905
$265$	1813.97	+	1522.18i	0.420495	+	0.352855i
$266$		0			0
$267$			6386.86i			1.46393i
$268$		−	2291.22i		−	0.522233i
$269$	−5090.54			−1.15381			−0.576907	−	0.816810i	$-0.695741\pi$
$269$	−5090.54			−1.15381			−0.576907	+	0.816810i	$0.695741\pi$
$270$	1532.80	−	1826.63i	0.345495	−	0.411723i
$271$	1671.78			0.374737			0.187368	−	0.982290i	$-0.440004\pi$
$271$	1671.78			0.374737			0.187368	+	0.982290i	$0.440004\pi$
$272$			194.123i			0.0432737i
$273$		0			0
$274$	−2440.05			−0.537988
$275$	1191.33	+	6758.41i	0.261237	+	1.48199i
$276$	4362.15			0.951343
$277$			3064.68i			0.664760i	0.943145	+	0.332380i	$0.107852\pi$
$277$			3064.68i			0.664760i	−0.943145	+	0.332380i	$0.892148\pi$
$278$			1363.20i			0.294099i
$279$	3110.74			0.667510
$280$		0			0
$281$	−1788.29			−0.379645			−0.189823	−	0.981818i	$-0.560791\pi$
$281$	−1788.29			−0.379645			−0.189823	+	0.981818i	$0.560791\pi$
$282$		−	2141.83i		−	0.452283i
$283$			4343.06i			0.912255i	0.889914	+	0.456128i	$0.150764\pi$
$283$			4343.06i			0.912255i	−0.889914	+	0.456128i	$0.849236\pi$
$284$	2973.62			0.621310
$285$	−1416.56	−	1188.69i	−0.294419	−	0.247060i
$286$	1171.84			0.242280
$287$		0			0
$288$			297.610i			0.0608917i
$289$	4765.80			0.970038
$290$	−2129.13	−	1786.64i	−0.431127	−	0.361777i
$291$	3482.55			0.701549
$292$		−	4653.34i		−	0.932589i
$293$		−	7302.49i		−	1.45603i	−0.685563	−	0.728013i	$-0.740444\pi$
$293$		−	7302.49i		−	1.45603i	0.685563	−	0.728013i	$-0.259556\pi$
$294$		0			0
$295$	−2462.77	+	2934.86i	−0.486060	+	0.579234i
$296$	−705.586			−0.138552
$297$		−	5854.64i		−	1.14384i
$298$		−	4016.88i		−	0.780844i
$299$	1931.72			0.373626
$300$	−2966.75	+	522.960i	−0.570951	+	0.100644i
$301$		0			0
$302$		−	3498.68i		−	0.666643i
$303$		−	10051.9i		−	1.90583i
$304$	−439.237			−0.0828683
$305$	−4742.51	+	5651.61i	−0.890345	+	1.06102i
$306$	−225.675			−0.0421601
$307$			5837.81i			1.08528i	0.839965	+	0.542641i	$0.182575\pi$
$307$			5837.81i			1.08528i	−0.839965	+	0.542641i	$0.817425\pi$
$308$		0			0
$309$	5239.14			0.964545
$310$	5729.24	+	4807.65i	1.04967	+	0.880827i
$311$	5809.92			1.05933			0.529663	−	0.848208i	$-0.322319\pi$
$311$	5809.92			1.05933			0.529663	+	0.848208i	$0.322319\pi$
$312$			514.402i			0.0933407i
$313$			5186.92i			0.936684i	0.883547	+	0.468342i	$0.155148\pi$
$313$			5186.92i			0.936684i	−0.883547	+	0.468342i	$0.844852\pi$
$314$	−5402.88			−0.971026
$315$		0			0
$316$	4028.44			0.717145
$317$			8132.32i			1.44087i	0.693521	+	0.720436i	$0.256058\pi$
$317$			8132.32i			1.44087i	−0.693521	+	0.720436i	$0.743942\pi$
$318$			2552.20i			0.450064i
$319$	−6824.20			−1.19775
$320$	−459.955	+	548.125i	−0.0803509	+	0.0957535i
$321$	−10353.4			−1.80022
$322$		0			0
$323$		−	333.070i		−	0.0573762i
$324$	3574.45			0.612903
$325$	−1313.78	+	231.586i	−0.224232	+	0.0395263i
$326$	610.474			0.103715
$327$			10674.5i			1.80520i
$328$		−	1072.88i		−	0.180610i
$329$		0			0
$330$	−4754.45	+	5665.84i	−0.793103	+	0.945134i
$331$	5765.99			0.957485			0.478743	−	0.877955i	$-0.341093\pi$
$331$	5765.99			0.957485			0.478743	+	0.877955i	$0.341093\pi$
$332$			1392.76i			0.230233i
$333$		−	820.270i		−	0.134986i
$334$	−8068.78			−1.32187
$335$	4905.76	+	4116.64i	0.800090	+	0.671391i
$336$		0			0
$337$			6697.82i			1.08265i	0.840813	+	0.541326i	$0.182077\pi$
$337$			6697.82i			1.08265i	−0.840813	+	0.541326i	$0.817923\pi$
$338$		−	4166.20i		−	0.670449i
$339$	1632.68			0.261578
$340$	−415.639	−	348.781i	−0.0662977	−	0.0556332i
$341$	18363.1			2.91618
$342$		−	510.629i		−	0.0807359i
$343$		0			0
$344$	1523.22			0.238740
$345$	−7837.48	+	9339.86i	−1.22306	+	1.45751i
$346$	2420.17			0.376038
$347$		−	8793.32i		−	1.36038i	−0.733038	−	0.680188i	$-0.761898\pi$
$347$		−	8793.32i		−	1.36038i	0.733038	−	0.680188i	$-0.238102\pi$
$348$		−	2995.62i		−	0.461443i
$349$	−4678.89			−0.717637			−0.358818	−	0.933407i	$-0.616820\pi$
$349$	−4678.89			−0.717637			−0.358818	+	0.933407i	$0.616820\pi$
$350$		0			0
$351$	1138.10			0.173069
$352$			1756.83i			0.266021i
$353$			5008.06i			0.755105i	0.925988	+	0.377552i	$0.123234\pi$
$353$			5008.06i			0.755105i	−0.925988	+	0.377552i	$0.876766\pi$
$354$	−4129.26			−0.619965
$355$	−5342.71	+	6366.86i	−0.798765	+	0.951881i
$356$	−4240.26			−0.631273
$357$		0			0
$358$		−	2023.14i		−	0.298676i
$359$	−4554.91			−0.669634			−0.334817	−	0.942283i	$-0.608675\pi$
$359$	−4554.91			−0.669634			−0.334817	+	0.942283i	$0.608675\pi$
$360$	−637.216	−	534.715i	−0.0932895	−	0.0782833i
$361$	−6105.37			−0.890126
$362$		−	2772.42i		−	0.402528i
$363$			10140.7i			1.46625i
$364$		0			0
$365$	9963.32	+	8360.65i	1.42878	+	1.19895i
$366$	−7951.65			−1.13563
$367$			8341.17i			1.18639i	0.805058	+	0.593195i	$0.202134\pi$
$367$			8341.17i			1.18639i	−0.805058	+	0.593195i	$0.797866\pi$
$368$			2896.05i			0.410236i
$369$	1247.27			0.175962
$370$	1267.73	−	1510.74i	0.178124	−	0.212269i
$371$		0			0
$372$			8060.88i			1.12349i
$373$		−	2842.93i		−	0.394641i	−0.980339	−	0.197321i	$-0.936776\pi$
$373$		−	2842.93i		−	0.394641i	0.980339	−	0.197321i	$-0.0632240\pi$
$374$	−1332.19			−0.184187
$375$	4210.64	−	7291.74i	0.579831	−	1.00412i
$376$	1421.97			0.195033
$377$		−	1326.57i		−	0.181225i
$378$		0			0
$379$	1311.25			0.177717			0.0888584	−	0.996044i	$-0.471678\pi$
$379$	1311.25			0.177717			0.0888584	+	0.996044i	$0.471678\pi$
$380$	789.177	−	940.456i	0.106537	−	0.126959i
$381$	−6594.94			−0.886795
$382$		−	394.571i		−	0.0528482i
$383$		−	11802.6i		−	1.57464i	−0.616547	−	0.787318i	$-0.711469\pi$
$383$		−	11802.6i		−	1.57464i	0.616547	−	0.787318i	$-0.288531\pi$
$384$	−771.197			−0.102487
$385$		0			0
$386$	7423.65			0.978896
$387$			1770.80i			0.232596i
$388$			2312.08i			0.302521i
$389$	3508.24			0.457262			0.228631	−	0.973513i	$-0.426575\pi$
$389$	3508.24			0.457262			0.228631	+	0.973513i	$0.426575\pi$
$390$	−1101.39	−	924.227i	−0.143003	−	0.120000i
$391$	−2196.05			−0.284039
$392$		0			0
$393$		−	14277.9i		−	1.83263i
$394$	−1018.85			−0.130276
$395$	−7237.91	+	8625.35i	−0.921971	+	1.09871i
$396$	−2042.38			−0.259175
$397$			3728.41i			0.471344i	0.971833	+	0.235672i	$0.0757290\pi$
$397$			3728.41i			0.471344i	−0.971833	+	0.235672i	$0.924271\pi$
$398$		−	9008.32i		−	1.13454i
$399$		0			0
$400$	−347.195	−	1969.63i	−0.0433994	−	0.246204i
$401$	8353.81			1.04032			0.520161	−	0.854068i	$-0.325872\pi$
$401$	8353.81			1.04032			0.520161	+	0.854068i	$0.325872\pi$
$402$			6902.27i			0.856353i
$403$			3569.65i			0.441232i
$404$	6673.50			0.821829
$405$	−6422.22	+	7653.30i	−0.787957	+	0.939002i
$406$		0			0
$407$		−	4842.16i		−	0.589722i
$408$		−	584.793i		−	0.0709597i
$409$	−11362.2			−1.37366			−0.686829	−	0.726819i	$-0.740998\pi$
$409$	−11362.2			−1.37366			−0.686829	+	0.726819i	$0.740998\pi$
$410$	2297.17	+	1927.65i	0.276705	+	0.232195i
$411$	7350.61			0.882187
$412$			3478.28i			0.415929i
$413$		0			0
$414$	−3366.76			−0.399680
$415$	−2982.05	−	2502.37i	−0.352730	−	0.295991i
$416$	−341.513			−0.0402502
$417$		−	4106.64i		−	0.482261i
$418$		−	3014.31i		−	0.352715i
$419$	7444.97			0.868044			0.434022	−	0.900902i	$-0.357094\pi$
$419$	7444.97			0.868044			0.434022	+	0.900902i	$0.357094\pi$
$420$		0			0
$421$	−9173.07			−1.06192			−0.530960	−	0.847397i	$-0.678168\pi$
$421$	−9173.07			−1.06192			−0.530960	+	0.847397i	$0.678168\pi$
$422$			4938.20i			0.569639i
$423$			1653.09i			0.190014i
$424$	−1694.41			−0.194076
$425$	1493.56	−	263.276i	0.170466	−	0.0300488i
$426$	−8957.99			−1.01882
$427$		0			0
$428$		−	6873.66i		−	0.776287i
$429$	−3530.14			−0.397289
$430$	−2736.77	+	3261.38i	−0.306927	+	0.365763i
$431$	6715.89			0.750563			0.375282	−	0.926911i	$-0.377546\pi$
$431$	6715.89			0.750563			0.375282	+	0.926911i	$0.377546\pi$
$432$			1706.24i			0.190027i
$433$			4741.46i			0.526235i	0.964764	+	0.263118i	$0.0847507\pi$
$433$			4741.46i			0.526235i	−0.964764	+	0.263118i	$0.915249\pi$
$434$		0			0
$435$	6413.97	+	5382.24i	0.706957	+	0.593238i
$436$	−7086.85			−0.778437
$437$		−	4968.95i		−	0.543929i
$438$			14018.1i			1.52925i
$439$	−137.434			−0.0149416			−0.00747080	−	0.999972i	$-0.502378\pi$
$439$	−137.434			−0.0149416			−0.00747080	+	0.999972i	$0.502378\pi$
$440$	−3761.57	−	3156.50i	−0.407559	−	0.342000i
$441$		0			0
$442$		−	258.967i		−	0.0278684i
$443$		−	11003.6i		−	1.18012i	−0.807358	−	0.590062i	$-0.799103\pi$
$443$		−	11003.6i		−	1.18012i	0.807358	−	0.590062i	$-0.200897\pi$
$444$	2125.57			0.227196
$445$	7618.47	−	9078.87i	0.811574	−	0.967145i
$446$	3653.68			0.387907
$447$			12100.8i			1.28042i
$448$		0			0
$449$	−16849.9			−1.77104			−0.885519	−	0.464604i	$-0.846197\pi$
$449$	−16849.9			−1.77104			−0.885519	+	0.464604i	$0.846197\pi$
$450$	2289.77	−	403.627i	0.239869	−	0.0422826i
$451$	7362.78			0.768736
$452$			1083.94i			0.112797i
$453$			10539.7i			1.09316i
$454$	−8491.10			−0.877769
$455$		0			0
$456$	1323.20			0.135887
$457$		−	4262.78i		−	0.436333i	−0.975912	−	0.218167i	$-0.929992\pi$
$457$		−	4262.78i		−	0.436333i	0.975912	−	0.218167i	$-0.0700077\pi$
$458$			6504.12i			0.663576i
$459$	−1293.83			−0.131571
$460$	−6200.77	−	5203.33i	−0.628505	−	0.527406i
$461$	3616.84			0.365408			0.182704	−	0.983168i	$-0.441515\pi$
$461$	3616.84			0.365408			0.182704	+	0.983168i	$0.441515\pi$
$462$		0			0
$463$		−	15914.0i		−	1.59738i	−0.601741	−	0.798691i	$-0.705526\pi$
$463$		−	15914.0i		−	1.59738i	0.601741	−	0.798691i	$-0.294474\pi$
$464$	1988.80			0.198983
$465$	−17259.2	−	14483.0i	−1.72124	−	1.44437i
$466$	−7788.78			−0.774267
$467$		−	17975.7i		−	1.78119i	−0.454793	−	0.890597i	$-0.650287\pi$
$467$		−	17975.7i		−	1.78119i	0.454793	−	0.890597i	$-0.349713\pi$
$468$		−	397.022i		−	0.0392144i
$469$		0			0
$470$	−2554.85	+	3044.59i	−0.250737	+	0.298801i
$471$	16276.1			1.59228
$472$		−	2741.43i		−	0.267340i
$473$			10453.3i			1.01616i
$474$	−12135.6			−1.17597
$475$	595.707	+	3379.44i	0.0575430	+	0.326440i
$476$		0			0
$477$		−	1969.82i		−	0.189081i
$478$		−	1282.20i		−	0.122691i
$479$	−12545.9			−1.19674			−0.598369	−	0.801221i	$-0.704184\pi$
$479$	−12545.9			−1.19674			−0.598369	+	0.801221i	$0.704184\pi$
$480$	1385.61	−	1651.22i	0.131759	−	0.157016i
$481$	941.278			0.0892278
$482$		−	8807.44i		−	0.832298i
$483$		0			0
$484$	−6732.43			−0.632272
$485$	−4950.42	−	4154.11i	−0.463478	−	0.388925i
$486$	−5009.41			−0.467554
$487$			8373.44i			0.779131i	0.920999	+	0.389565i	$0.127375\pi$
$487$			8373.44i			0.779131i	−0.920999	+	0.389565i	$0.872625\pi$
$488$		−	5279.13i		−	0.489703i
$489$	−1839.04			−0.170070
$490$		0			0
$491$	−978.998			−0.0899828			−0.0449914	−	0.998987i	$-0.514326\pi$
$491$	−978.998			−0.0899828			−0.0449914	+	0.998987i	$0.514326\pi$
$492$			3232.05i			0.296163i
$493$			1508.10i			0.137771i
$494$	585.958			0.0533674
$495$	3669.54	−	4372.96i	0.333199	−	0.397071i
$496$	−5351.64			−0.484467
$497$		0			0
$498$		−	4195.66i		−	0.377534i
$499$	7427.49			0.666333			0.333166	−	0.942868i	$-0.391883\pi$
$499$	7427.49			0.666333			0.333166	+	0.942868i	$0.391883\pi$
$500$	4841.01	+	2795.46i	0.432993	+	0.250033i
$501$	24307.1			2.16759
$502$		−	8414.47i		−	0.748120i
$503$			7872.21i			0.697822i	0.937156	+	0.348911i	$0.113448\pi$
$503$			7872.21i			0.697822i	−0.937156	+	0.348911i	$0.886552\pi$
$504$		0			0
$505$	−11990.3	+	14288.7i	−1.05656	+	1.25909i
$506$	−19874.4			−1.74610
$507$			12550.6i			1.09939i
$508$		−	4378.40i		−	0.382402i
$509$	12082.5			1.05216			0.526078	−	0.850436i	$-0.323662\pi$
$509$	12082.5			1.05216			0.526078	+	0.850436i	$0.323662\pi$
$510$	1252.11	+	1050.70i	0.108714	+	0.0912268i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$		−	2927.52i		−	0.251956i
$514$	−166.427			−0.0142816
$515$	−7447.40	−	6249.44i	−0.637226	−	0.534724i
$516$	−4588.68			−0.391483
$517$			9758.40i			0.830123i
$518$		0			0
$519$	−7290.73			−0.616623
$520$	613.598	−	731.219i	0.0517462	−	0.0616655i
$521$	−19728.8			−1.65899			−0.829497	−	0.558511i	$-0.811373\pi$
$521$	−19728.8			−1.65899			−0.829497	+	0.558511i	$0.811373\pi$
$522$			2312.06i			0.193862i
$523$		−	90.0382i		−	0.00752791i	−0.999993	−	0.00376396i	$-0.998802\pi$
$523$		−	90.0382i		−	0.00752791i	0.999993	−	0.00376396i	$-0.00119811\pi$
$524$	9479.16			0.790265
$525$		0			0
$526$	10080.0			0.835568
$527$		−	4058.11i		−	0.335435i
$528$		−	5292.42i		−	0.436218i
$529$	−20595.1			−1.69270
$530$	3044.36	−	3627.93i	0.249506	−	0.297335i
$531$	3187.01			0.260461
$532$		0			0
$533$			1431.27i			0.116313i
$534$	12773.7			1.03516
$535$	14717.3	+	12349.9i	1.18931	+	0.998006i
$536$	−4582.44			−0.369275
$537$			6094.67i			0.489766i
$538$			10181.1i			0.815870i
$539$		0			0
$540$	−3653.26	−	3065.61i	−0.291132	−	0.244302i
$541$	−4428.92			−0.351967			−0.175984	−	0.984393i	$-0.556311\pi$
$541$	−4428.92			−0.351967			−0.175984	+	0.984393i	$0.556311\pi$
$542$		−	3343.57i		−	0.264979i
$543$			8351.89i			0.660062i
$544$	388.246			0.0305991
$545$	12732.9	−	15173.7i	1.00077	−	1.19261i
$546$		0			0
$547$			7292.17i			0.570001i	0.958527	+	0.285000i	$0.0919938\pi$
$547$			7292.17i			0.570001i	−0.958527	+	0.285000i	$0.908006\pi$
$548$			4880.10i			0.380415i
$549$	6137.18			0.477101
$550$	13516.8	−	2382.67i	1.04793	−	0.184722i
$551$	−3412.33			−0.263830
$552$		−	8724.30i		−	0.672701i
$553$		0			0
$554$	6129.36			0.470057
$555$	−3819.01	+	4551.08i	−0.292086	+	0.348077i
$556$	2726.41			0.207960
$557$		−	95.2982i		−	0.00724940i	−0.999993	−	0.00362470i	$-0.998846\pi$
$557$		−	95.2982i		−	0.00724940i	0.999993	−	0.00362470i	$-0.00115378\pi$
$558$		−	6221.48i		−	0.472001i
$559$	−2032.03			−0.153749
$560$		0			0
$561$	4013.21			0.302028
$562$			3576.58i			0.268450i
$563$		−	15610.4i		−	1.16856i	−0.811553	−	0.584279i	$-0.801377\pi$
$563$		−	15610.4i		−	1.16856i	0.811553	−	0.584279i	$-0.198623\pi$
$564$	−4283.65			−0.319813
$565$	−2320.84	−	1947.52i	−0.172811	−	0.145014i
$566$	8686.12			0.645062
$567$		0			0
$568$		−	5947.24i		−	0.439332i
$569$	−3870.40			−0.285159			−0.142580	−	0.989783i	$-0.545540\pi$
$569$	−3870.40			−0.285159			−0.142580	+	0.989783i	$0.545540\pi$
$570$	−2377.39	+	2833.11i	−0.174698	+	0.208186i
$571$	7447.18			0.545805			0.272903	−	0.962042i	$-0.412016\pi$
$571$	7447.18			0.545805			0.272903	+	0.962042i	$0.412016\pi$
$572$		−	2343.67i		−	0.171318i
$573$			1188.64i			0.0866599i
$574$		0			0
$575$	22281.8	−	3927.71i	1.61603	−	0.284864i
$576$	595.219			0.0430569
$577$		−	16956.1i		−	1.22338i	−0.791097	−	0.611691i	$-0.790490\pi$
$577$		−	16956.1i		−	1.22338i	0.791097	−	0.611691i	$-0.209510\pi$
$578$		−	9531.60i		−	0.685921i
$579$	−22363.6			−1.60518
$580$	−3573.29	+	4258.26i	−0.255815	+	0.304853i
$581$		0			0
$582$		−	6965.10i		−	0.496070i
$583$		−	11628.1i		−	0.826050i
$584$	−9306.67			−0.659440
$585$	850.069	+	713.330i	0.0600787	+	0.0504146i
$586$	−14605.0			−1.02957
$587$			1037.11i			0.0729238i	0.999335	+	0.0364619i	$0.0116087\pi$
$587$			1037.11i			0.0729238i	−0.999335	+	0.0364619i	$0.988391\pi$
$588$		0			0
$589$	9182.18			0.642352
$590$	5869.71	+	4925.53i	0.409580	+	0.343696i
$591$	3069.26			0.213625
$592$			1411.17i			0.0979709i
$593$			11649.7i			0.806737i	0.915038	+	0.403368i	$0.132161\pi$
$593$			11649.7i			0.806737i	−0.915038	+	0.403368i	$0.867839\pi$
$594$	−11709.3			−0.808818
$595$		0			0
$596$	−8033.75			−0.552140
$597$			27137.5i			1.86041i
$598$		−	3863.43i		−	0.264193i
$599$	−18549.7			−1.26531			−0.632656	−	0.774433i	$-0.718035\pi$
$599$	−18549.7			−1.26531			−0.632656	+	0.774433i	$0.718035\pi$
$600$	1045.92	+	5933.49i	0.0711659	+	0.403723i
$601$	−4808.55			−0.326364			−0.163182	−	0.986596i	$-0.552176\pi$
$601$	−4808.55			−0.326364			−0.163182	+	0.986596i	$0.552176\pi$
$602$		0			0
$603$		−	5327.25i		−	0.359772i
$604$	−6997.36			−0.471388
$605$	12096.2	−	14414.9i	0.812858	−	0.968676i
$606$	−20103.8			−1.34763
$607$			7157.03i			0.478575i	0.970949	+	0.239287i	$0.0769138\pi$
$607$			7157.03i			0.478575i	−0.970949	+	0.239287i	$0.923086\pi$
$608$			878.474i			0.0585967i
$609$		0			0
$610$	11303.2	+	9485.01i	0.750252	+	0.629569i
$611$	−1896.95			−0.125602
$612$			451.350i			0.0298117i
$613$		−	24865.2i		−	1.63833i	−0.573557	−	0.819165i	$-0.694437\pi$
$613$		−	24865.2i		−	1.63833i	0.573557	−	0.819165i	$-0.305563\pi$
$614$	11675.6			0.767410
$615$	−6920.18	−	5807.02i	−0.453738	−	0.380751i
$616$		0			0
$617$			24953.7i			1.62820i	0.580726	+	0.814099i	$0.302769\pi$
$617$			24953.7i			1.62820i	−0.580726	+	0.814099i	$0.697231\pi$
$618$		−	10478.3i		−	0.682036i
$619$	17423.5			1.13136			0.565678	−	0.824626i	$-0.308615\pi$
$619$	17423.5			1.13136			0.565678	+	0.824626i	$0.308615\pi$
$620$	9615.30	−	11458.5i	0.622838	−	0.742231i
$621$	−19302.2			−1.24730
$622$		−	11619.8i		−	0.749056i
$623$		0			0
$624$	1028.80			0.0660018
$625$	−14683.2	+	5342.56i	−0.939728	+	0.341924i
$626$	10373.8			0.662335
$627$			9080.57i			0.578378i
$628$			10805.8i			0.686619i
$629$	−1070.08			−0.0678330
$630$		0			0
$631$	14833.8			0.935858			0.467929	−	0.883766i	$-0.345000\pi$
$631$	14833.8			0.935858			0.467929	+	0.883766i	$0.345000\pi$
$632$		−	8056.89i		−	0.507098i
$633$		−	14876.3i		−	0.934089i
$634$	16264.6			1.01885
$635$	9374.66	+	7866.68i	0.585861	+	0.491622i
$636$	5104.40			0.318243
$637$		0			0
$638$			13648.4i			0.846936i
$639$	6913.89			0.428027
$640$	1096.25	+	919.911i	0.0677079	+	0.0568167i
$641$	8833.77			0.544326			0.272163	−	0.962251i	$-0.412261\pi$
$641$	8833.77			0.544326			0.272163	+	0.962251i	$0.412261\pi$
$642$			20706.8i			1.27295i
$643$			10067.6i			0.617462i	0.951149	+	0.308731i	$0.0999043\pi$
$643$			10067.6i			0.617462i	−0.951149	+	0.308731i	$0.900096\pi$
$644$		0			0
$645$	8244.48	−	9824.88i	0.503296	−	0.599774i
$646$	−666.140			−0.0405711
$647$			21455.5i			1.30372i	0.758341	+	0.651858i	$0.226010\pi$
$647$			21455.5i			1.30372i	−0.758341	+	0.651858i	$0.773990\pi$
$648$		−	7148.90i		−	0.433388i
$649$	18813.4			1.13789
$650$	463.171	+	2627.56i	0.0279493	+	0.158556i
$651$		0			0
$652$		−	1220.95i		−	0.0733374i
$653$		−	8688.51i		−	0.520685i	−0.965516	−	0.260343i	$-0.916164\pi$
$653$		−	8688.51i		−	0.520685i	0.965516	−	0.260343i	$-0.0838355\pi$
$654$	21349.0			1.27647
$655$	−17031.2	+	20295.9i	−1.01598	+	1.21073i
$656$	−2145.77			−0.127711
$657$		−	10819.4i		−	0.642471i
$658$		0			0
$659$	−3196.76			−0.188965			−0.0944827	−	0.995527i	$-0.530120\pi$
$659$	−3196.76			−0.188965			−0.0944827	+	0.995527i	$0.530120\pi$
$660$	11331.7	+	9508.90i	0.668310	+	0.560808i
$661$	4906.23			0.288699			0.144350	−	0.989527i	$-0.453891\pi$
$661$	4906.23			0.288699			0.144350	+	0.989527i	$0.453891\pi$
$662$		−	11532.0i		−	0.677044i
$663$			780.135i			0.0456983i
$664$	2785.52			0.162800
$665$		0			0
$666$	−1640.54			−0.0954499
$667$			22498.7i			1.30608i
$668$			16137.6i			0.934702i
$669$	−11006.7			−0.636087
$670$	8233.27	−	9811.52i	0.474745	−	0.565749i
$671$	36228.6			2.08434
$672$		0			0
$673$			27838.8i			1.59451i	0.603643	+	0.797255i	$0.293715\pi$
$673$			27838.8i			1.59451i	−0.603643	+	0.797255i	$0.706285\pi$
$674$	13395.6			0.765550
$675$	13127.6	−	2314.06i	0.748567	−	0.131953i
$676$	−8332.41			−0.474079
$677$		−	17110.3i		−	0.971350i	−0.874140	−	0.485675i	$-0.838574\pi$
$677$		−	17110.3i		−	0.971350i	0.874140	−	0.485675i	$-0.161426\pi$
$678$		−	3265.36i		−	0.184963i
$679$		0			0
$680$	−697.562	+	831.279i	−0.0393386	+	0.0468795i
$681$	25579.3			1.43936
$682$		−	36726.2i		−	2.06205i
$683$		−	3308.61i		−	0.185359i	−0.995696	−	0.0926797i	$-0.970457\pi$
$683$		−	3308.61i		−	0.185359i	0.995696	−	0.0926797i	$-0.0295433\pi$
$684$	−1021.26			−0.0570889
$685$	−10448.8	−	8768.07i	−0.582817	−	0.489067i
$686$		0			0
$687$		−	19593.6i		−	1.08812i
$688$		−	3046.44i		−	0.168814i
$689$	2260.41			0.124985
$690$	18679.7	+	15675.0i	1.03062	+	0.864834i
$691$	−28127.2			−1.54849			−0.774246	−	0.632885i	$-0.781871\pi$
$691$	−28127.2			−1.54849			−0.774246	+	0.632885i	$0.781871\pi$
$692$		−	4840.34i		−	0.265899i
$693$		0			0
$694$	−17586.6			−0.961930
$695$	−4898.54	+	5837.55i	−0.267356	+	0.318606i
$696$	−5991.25			−0.326290
$697$		−	1627.12i		−	0.0884241i
$698$			9357.78i			0.507446i
$699$	23463.6			1.26963
$700$		0			0
$701$	−21962.0			−1.18330			−0.591650	−	0.806195i	$-0.701523\pi$
$701$	−21962.0			−1.18330			−0.591650	+	0.806195i	$0.701523\pi$
$702$		−	2276.19i		−	0.122378i
$703$		−	2421.24i		−	0.129899i
$704$	3513.66			0.188105
$705$	7696.44	−	9171.78i	0.411156	−	0.489971i
$706$	10016.1			0.533940
$707$		0			0
$708$			8258.52i			0.438382i
$709$	−16353.0			−0.866222			−0.433111	−	0.901341i	$-0.642584\pi$
$709$	−16353.0			−0.866222			−0.433111	+	0.901341i	$0.642584\pi$
$710$	12733.7	+	10685.4i	0.673082	+	0.564812i
$711$	9366.43			0.494049
$712$			8480.51i			0.446377i
$713$		−	60541.5i		−	3.17994i
$714$		0			0
$715$	5018.07	+	4210.88i	0.262469	+	0.220249i
$716$	−4046.27			−0.211196
$717$			3862.60i			0.201188i
$718$			9109.81i			0.473503i
$719$	18095.8			0.938607			0.469303	−	0.883037i	$-0.344505\pi$
$719$	18095.8			0.938607			0.469303	+	0.883037i	$0.344505\pi$
$720$	−1069.43	+	1274.43i	−0.0553546	+	0.0659656i
$721$		0			0
$722$			12210.7i			0.629414i
$723$			26532.3i			1.36479i
$724$	−5544.84			−0.284631
$725$	−2697.28	−	15301.6i	−0.138172	−	0.783846i
$726$	20281.4			1.03679
$727$		−	9732.61i		−	0.496510i	−0.968695	−	0.248255i	$-0.920143\pi$
$727$		−	9732.61i		−	0.496510i	0.968695	−	0.248255i	$-0.0798571\pi$
$728$		0			0
$729$	−9036.76			−0.459115
$730$	16721.3	−	19926.6i	0.847785	−	1.01030i
$731$	2310.09			0.116884
$732$			15903.3i			0.803010i
$733$			31738.9i			1.59932i	0.600452	+	0.799661i	$0.294987\pi$
$733$			31738.9i			1.59932i	−0.600452	+	0.799661i	$0.705013\pi$
$734$	16682.3			0.838905
$735$		0			0
$736$	5792.10			0.290081
$737$		−	31447.5i		−	1.57175i
$738$		−	2494.53i		−	0.124424i
$739$	6082.66			0.302780			0.151390	−	0.988474i	$-0.451625\pi$
$739$	6082.66			0.302780			0.151390	+	0.988474i	$0.451625\pi$
$740$	−3021.48	−	2535.45i	−0.150097	−	0.125953i
$741$	−1765.19			−0.0875114
$742$		0			0
$743$		−	21355.5i		−	1.05445i	−0.849726	−	0.527225i	$-0.823232\pi$
$743$		−	21355.5i		−	1.05445i	0.849726	−	0.527225i	$-0.176768\pi$
$744$	16121.8			0.794425
$745$	14434.3	−	17201.2i	0.709839	−	0.845909i
$746$	−5685.85			−0.279053
$747$			3238.26i			0.158610i
$748$			2664.38i			0.130240i
$749$		0			0
$750$	−14583.5	−	8421.28i	−0.710018	−	0.410002i
$751$	955.107			0.0464079			0.0232040	−	0.999731i	$-0.492613\pi$
$751$	955.107			0.0464079			0.0232040	+	0.999731i	$0.492613\pi$
$752$		−	2843.93i		−	0.137909i
$753$			25348.5i			1.22676i
$754$	−2653.14			−0.128145
$755$	12572.2	−	14982.1i	0.606023	−	0.722193i
$756$		0			0
$757$		−	32116.3i		−	1.54199i	−0.636840	−	0.770996i	$-0.719759\pi$
$757$		−	32116.3i		−	1.54199i	0.636840	−	0.770996i	$-0.280241\pi$
$758$		−	2622.51i		−	0.125665i
$759$	59871.5			2.86324
$760$	−1880.91	−	1578.35i	−0.0897735	−	0.0753328i
$761$	−9234.12			−0.439864			−0.219932	−	0.975515i	$-0.570584\pi$
$761$	−9234.12			−0.439864			−0.219932	+	0.975515i	$0.570584\pi$
$762$			13189.9i			0.627059i
$763$		0			0
$764$	−789.142			−0.0373693
$765$	−966.392	−	810.942i	−0.0456732	−	0.0383264i
$766$	−23605.2			−1.11344
$767$			3657.17i			0.172168i
$768$			1542.39i			0.0724692i
$769$	−29271.9			−1.37266			−0.686328	−	0.727292i	$-0.740778\pi$
$769$	−29271.9			−1.37266			−0.686328	+	0.727292i	$0.740778\pi$
$770$		0			0
$771$	501.358			0.0234189
$772$		−	14847.3i		−	0.692184i
$773$			9256.13i			0.430686i	0.976539	+	0.215343i	$0.0690869\pi$
$773$			9256.13i			0.430686i	−0.976539	+	0.215343i	$0.930913\pi$
$774$	3541.60			0.164470
$775$	7258.07	+	41174.9i	0.336410	+	1.90845i
$776$	4624.16			0.213914
$777$		0			0
$778$		−	7016.48i		−	0.323333i
$779$	3681.64			0.169331
$780$	−1848.45	+	2202.79i	−0.0848529	+	0.101119i
$781$	40813.6			1.86994
$782$			4392.10i			0.200846i
$783$			13255.4i			0.604993i
$784$		0			0
$785$	−23136.4	−	19414.7i	−1.05194	−	0.882727i
$786$	−28555.8			−1.29587
$787$			21454.9i			0.971772i	0.874022	+	0.485886i	$0.161503\pi$
$787$			21454.9i			0.971772i	−0.874022	+	0.485886i	$0.838497\pi$
$788$			2037.69i			0.0921190i
$789$	−30365.9			−1.37016
$790$	17250.7	+	14475.8i	0.776902	+	0.651932i
$791$		0			0
$792$			4084.76i			0.183265i
$793$			7042.55i			0.315370i
$794$	7456.81			0.333290
$795$	−9171.08	+	10929.1i	−0.409138	+	0.487566i
$796$	−18016.6			−0.802240
$797$		−	9524.52i		−	0.423307i	−0.977345	−	0.211654i	$-0.932115\pi$
$797$		−	9524.52i		−	0.423307i	0.977345	−	0.211654i	$-0.0678848\pi$
$798$		0			0
$799$	2156.53			0.0954851
$800$	−3939.27	+	694.390i	−0.174093	+	0.0306880i
$801$	−9858.91			−0.434891
$802$		−	16707.6i		−	0.735619i
$803$		−	63868.1i		−	2.80679i
$804$	13804.5			0.605533
$805$		0			0
$806$	7139.29			0.311998
$807$		−	30670.4i		−	1.33786i
$808$		−	13347.0i		−	0.581121i
$809$	−26558.5			−1.15420			−0.577099	−	0.816674i	$-0.695815\pi$
$809$	−26558.5			−1.15420			−0.577099	+	0.816674i	$0.695815\pi$
$810$	15306.6	+	12844.4i	0.663974	+	0.557170i
$811$	−5940.88			−0.257229			−0.128614	−	0.991695i	$-0.541053\pi$
$811$	−5940.88			−0.257229			−0.128614	+	0.991695i	$0.541053\pi$
$812$		0			0
$813$			10072.5i			0.434510i
$814$	−9684.32			−0.416997
$815$	2614.19	+	2193.68i	0.112357	+	0.0942837i
$816$	−1169.59			−0.0501761
$817$			5226.98i			0.223830i
$818$			22724.5i			0.971323i
$819$		0			0
$820$	3855.30	−	4594.33i	0.164187	−	0.195660i
$821$	−15988.9			−0.679679			−0.339839	−	0.940483i	$-0.610373\pi$
$821$	−15988.9			−0.679679			−0.339839	+	0.940483i	$0.610373\pi$
$822$		−	14701.2i		−	0.623800i
$823$		−	15330.7i		−	0.649325i	−0.945830	−	0.324662i	$-0.894749\pi$
$823$		−	15330.7i		−	0.649325i	0.945830	−	0.324662i	$-0.105251\pi$
$824$	6956.57			0.294106
$825$	−40719.3	+	7177.75i	−1.71838	+	0.302906i
$826$		0			0
$827$		−	7892.50i		−	0.331861i	−0.986137	−	0.165931i	$-0.946937\pi$
$827$		−	7892.50i		−	0.331861i	0.986137	−	0.165931i	$-0.0530628\pi$
$828$			6733.53i			0.282616i
$829$	−17664.6			−0.740069			−0.370034	−	0.929018i	$-0.620654\pi$
$829$	−17664.6			−0.740069			−0.370034	+	0.929018i	$0.620654\pi$
$830$	−5004.74	+	5964.10i	−0.209298	+	0.249418i
$831$	−18464.6			−0.770794
$832$			683.027i			0.0284612i
$833$		0			0
$834$	−8213.27			−0.341010
$835$	−34552.3	−	28994.4i	−1.43202	−	1.20167i
$836$	−6028.62			−0.249407
$837$		−	35668.8i		−	1.47299i
$838$		−	14889.9i		−	0.613800i
$839$	−2826.25			−0.116297			−0.0581484	−	0.998308i	$-0.518520\pi$
$839$	−2826.25			−0.116297			−0.0581484	+	0.998308i	$0.518520\pi$
$840$		0			0
$841$	−8938.44			−0.366495
$842$			18346.1i			0.750890i
$843$		−	10774.4i		−	0.440201i
$844$	9876.40			0.402796
$845$	14970.8	−	17840.6i	0.609483	−	0.726315i
$846$	3306.18			0.134360
$847$		0			0
$848$			3388.83i			0.137232i
$849$	−26166.8			−1.05777
$850$	−526.551	−	2987.12i	−0.0212477	−	0.120538i
$851$	−15964.1			−0.643060
$852$			17916.0i			0.720413i
$853$		−	46441.9i		−	1.86417i	−0.362234	−	0.932087i	$-0.617986\pi$
$853$		−	46441.9i		−	1.86417i	0.362234	−	0.932087i	$-0.382014\pi$
$854$		0			0
$855$	1834.90	−	2186.63i	0.0733943	−	0.0874634i
$856$	−13747.3			−0.548918
$857$		−	5995.48i		−	0.238975i	−0.992836	−	0.119488i	$-0.961875\pi$
$857$		−	5995.48i		−	0.238975i	0.992836	−	0.119488i	$-0.0381252\pi$
$858$			7060.29i			0.280926i
$859$	4671.33			0.185546			0.0927729	−	0.995687i	$-0.470427\pi$
$859$	4671.33			0.185546			0.0927729	+	0.995687i	$0.470427\pi$
$860$	6522.77	+	5473.54i	0.258633	+	0.217030i
$861$		0			0
$862$		−	13431.8i		−	0.530729i
$863$			40220.0i			1.58645i	0.608930	+	0.793224i	$0.291599\pi$
$863$			40220.0i			1.58645i	−0.608930	+	0.793224i	$0.708401\pi$
$864$	3412.49			0.134369
$865$	10363.7	+	8696.64i	0.407372	+	0.341844i
$866$	9482.91			0.372104
$867$			28713.8i			1.12477i
$868$		0			0
$869$	55291.3			2.15838
$870$	10764.5	−	12827.9i	0.419483	−	0.499894i
$871$	6113.14			0.237814
$872$			14173.7i			0.550438i
$873$			5375.75i			0.208410i
$874$	−9937.90			−0.384616
$875$		0			0
$876$	28036.2			1.08134
$877$		−	15820.2i		−	0.609135i	−0.952491	−	0.304567i	$-0.901488\pi$
$877$		−	15820.2i		−	0.609135i	0.952491	−	0.304567i	$-0.0985119\pi$
$878$			274.868i			0.0105653i
$879$	43997.3			1.68827
$880$	−6312.99	+	7523.14i	−0.241831	+	0.288187i
$881$	4103.34			0.156918			0.0784592	−	0.996917i	$-0.475000\pi$
$881$	4103.34			0.156918			0.0784592	+	0.996917i	$0.475000\pi$
$882$		0			0
$883$			25725.3i			0.980436i	0.871600	+	0.490218i	$0.163083\pi$
$883$			25725.3i			0.980436i	−0.871600	+	0.490218i	$0.836917\pi$
$884$	−517.935			−0.0197059
$885$	−17682.4	−	14838.1i	−0.671625	−	0.563590i
$886$	−22007.1			−0.834473
$887$		−	16215.9i		−	0.613840i	−0.951735	−	0.306920i	$-0.900702\pi$
$887$		−	16215.9i		−	0.613840i	0.951735	−	0.306920i	$-0.0992983\pi$
$888$		−	4251.13i		−	0.160652i
$889$		0			0
$890$	−18157.7	−	15236.9i	−0.683875	−	0.573869i
$891$	49060.1			1.84464
$892$		−	7307.36i		−	0.274292i
$893$			4879.53i			0.182852i
$894$	24201.6			0.905393
$895$	7269.94	−	8663.53i	0.271517	−	0.323564i
$896$		0			0
$897$			11638.5i			0.433222i
$898$			33699.8i			1.25231i
$899$	−41575.7			−1.54241
$900$	−807.255	−	4579.54i	−0.0298983	−	0.169613i
$901$	−2569.72			−0.0950166
$902$		−	14725.6i		−	0.543578i
$903$		0			0
$904$	2167.88			0.0797596
$905$	9962.43	−	11872.1i	0.365925	−	0.436070i
$906$	21079.4			0.772977
$907$			633.923i			0.0232073i	0.999933	+	0.0116037i	$0.00369365\pi$
$907$			633.923i			0.0232073i	−0.999933	+	0.0116037i	$0.996306\pi$
$908$			16982.2i			0.620676i
$909$	15516.4			0.566167
$910$		0			0
$911$	−35153.6			−1.27848			−0.639238	−	0.769009i	$-0.720750\pi$
$911$	−35153.6			−1.27848			−0.639238	+	0.769009i	$0.720750\pi$
$912$		−	2646.39i		−	0.0960863i
$913$			19115.9i			0.692929i
$914$	−8525.56			−0.308534
$915$	−34050.8	−	28573.5i	−1.23026	−	1.03236i
$916$	13008.2			0.469219
$917$		0			0
$918$			2587.66i			0.0930345i
$919$	−12758.7			−0.457964			−0.228982	−	0.973431i	$-0.573540\pi$
$919$	−12758.7			−0.457964			−0.228982	+	0.973431i	$0.573540\pi$
$920$	−10406.7	+	12401.5i	−0.372932	+	0.444420i
$921$	−35172.6			−1.25839
$922$		−	7233.68i		−	0.258382i
$923$			7933.84i			0.282931i
$924$		0			0
$925$	10857.4	−	1913.88i	0.385934	−	0.0680301i
$926$	−31828.1			−1.12952
$927$			8087.27i			0.286538i
$928$		−	3977.61i		−	0.140702i
$929$	−14821.9			−0.523457			−0.261728	−	0.965142i	$-0.584292\pi$
$929$	−14821.9			−0.523457			−0.261728	+	0.965142i	$0.584292\pi$
$930$	−28966.0	+	34518.5i	−1.02132	+	1.21710i
$931$		0			0
$932$			15577.6i			0.547489i
$933$			35004.6i			1.22829i
$934$	−35951.5			−1.25949
$935$	−5704.74	−	4787.10i	−0.199535	−	0.167438i
$936$	−794.044			−0.0277288
$937$			30747.5i			1.07201i	0.844214	+	0.536006i	$0.180068\pi$
$937$			30747.5i			1.07201i	−0.844214	+	0.536006i	$0.819932\pi$
$938$		0			0
$939$	−31251.0			−1.08609
$940$	6089.18	+	5109.69i	0.211284	+	0.177298i
$941$	−14309.1			−0.495711			−0.247855	−	0.968797i	$-0.579726\pi$
$941$	−14309.1			−0.495711			−0.247855	+	0.968797i	$0.579726\pi$
$942$		−	32552.2i		−	1.12591i
$943$		−	24274.4i		−	0.838264i
$944$	−5482.86			−0.189038
$945$		0			0
$946$	20906.5			0.718530
$947$		−	29708.6i		−	1.01943i	−0.860343	−	0.509715i	$-0.829751\pi$
$947$		−	29708.6i		−	1.01943i	0.860343	−	0.509715i	$-0.170249\pi$
$948$			24271.3i			0.831534i
$949$	12415.4			0.424681
$950$	6758.87	−	1191.41i	0.230828	−	0.0406890i
$951$	−48997.0			−1.67070
$952$		0			0
$953$			31956.6i			1.08623i	0.839659	+	0.543114i	$0.182755\pi$
$953$			31956.6i			1.08623i	−0.839659	+	0.543114i	$0.817245\pi$
$954$	−3939.64			−0.133701
$955$	1417.85	−	1689.64i	0.0480425	−	0.0572519i
$956$	−2564.40			−0.0867558
$957$		−	41115.6i		−	1.38880i
$958$			25091.8i			0.846221i
$959$		0			0
$960$	−3302.44	−	2771.22i	−0.111027	−	0.0931674i
$961$	82084.3			2.75534
$962$		−	1882.56i		−	0.0630936i
$963$		−	15981.8i		−	0.534792i
$964$	−17614.9			−0.588524
$965$	31789.8	+	26676.2i	1.06046	+	0.889882i
$966$		0			0
$967$			32350.5i			1.07582i	0.843001	+	0.537911i	$0.180786\pi$
$967$			32350.5i			1.07582i	−0.843001	+	0.537911i	$0.819214\pi$
$968$			13464.9i			0.447084i
$969$	2006.74			0.0665281
$970$	−8308.23	+	9900.84i	−0.275011	+	0.327729i
$971$	−7988.02			−0.264004			−0.132002	−	0.991249i	$-0.542140\pi$
$971$	−7988.02			−0.264004			−0.132002	+	0.991249i	$0.542140\pi$
$972$			10018.8i			0.330611i
$973$		0			0
$974$	16746.9			0.550928
$975$	−1395.30	−	7915.50i	−0.0458311	−	0.259999i
$976$	−10558.3			−0.346272
$977$			43075.2i			1.41054i	0.708939	+	0.705270i	$0.249174\pi$
$977$			43075.2i			1.41054i	−0.708939	+	0.705270i	$0.750826\pi$
$978$			3678.09i			0.120258i
$979$	−58198.5			−1.89993
$980$		0			0
$981$	−16477.4			−0.536274
$982$			1958.00i			0.0636275i
$983$			28618.9i			0.928587i	0.885681	+	0.464294i	$0.153692\pi$
$983$			28618.9i			0.928587i	−0.885681	+	0.464294i	$0.846308\pi$
$984$	6464.10			0.209419
$985$	−4362.93	−	3661.12i	−0.141132	−	0.118430i
$986$	3016.19			0.0974190
$987$		0			0
$988$		−	1171.92i		−	0.0377365i
$989$	34463.4			1.10806
$990$	−8745.93	−	7339.09i	−0.280772	−	0.235608i
$991$	−13783.9			−0.441836			−0.220918	−	0.975292i	$-0.570905\pi$
$991$	−13783.9			−0.441836			−0.220918	+	0.975292i	$0.570905\pi$
$992$			10703.3i			0.342570i
$993$			34740.0i			1.11021i
$994$		0			0
$995$	32370.5	−	38575.7i	1.03137	−	1.22908i
$996$	−8391.33			−0.266957
$997$			8857.97i			0.281379i	0.990054	+	0.140689i	$0.0449319\pi$
$997$			8857.97i			0.281379i	−0.990054	+	0.140689i	$0.955068\pi$
$998$		−	14855.0i		−	0.471168i
$999$	−9405.48			−0.297874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.d.99.4	yes	8
5.2	odd	4		2450.4.a.cs.1.4		4
5.3	odd	4		2450.4.a.cm.1.1		4
5.4	even	2	inner	490.4.c.d.99.5	yes	8
7.6	odd	2	inner	490.4.c.d.99.1	✓	8
35.13	even	4		2450.4.a.cm.1.4		4
35.27	even	4		2450.4.a.cs.1.1		4
35.34	odd	2	inner	490.4.c.d.99.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.c.d.99.1	✓	8	7.6	odd	2	inner
490.4.c.d.99.4	yes	8	1.1	even	1	trivial
490.4.c.d.99.5	yes	8	5.4	even	2	inner
490.4.c.d.99.8	yes	8	35.34	odd	2	inner
2450.4.a.cm.1.1		4	5.3	odd	4
2450.4.a.cm.1.4		4	35.13	even	4
2450.4.a.cs.1.1		4	35.27	even	4
2450.4.a.cs.1.4		4	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)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +6.02497i q^{3} -4.00000 q^{4} +(7.18680 - 8.56445i) q^{5} +12.0499 q^{6} +8.00000i q^{8} -9.30030 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +6.02497i q^{3} -4.00000 q^{4} +(7.18680 - 8.56445i) q^{5} +12.0499 q^{6} +8.00000i q^{8} -9.30030 q^{9} +(-17.1289 - 14.3736i) q^{10} -54.9009 q^{11} -24.0999i q^{12} -10.6723i q^{13} +(51.6006 + 43.3003i) q^{15} +16.0000 q^{16} +12.1327i q^{17} +18.6006i q^{18} -27.4523 q^{19} +(-28.7472 + 34.2578i) q^{20} +109.802i q^{22} +181.003i q^{23} -48.1998 q^{24} +(-21.6997 - 123.102i) q^{25} -21.3446 q^{26} +106.640i q^{27} +124.300 q^{29} +(86.6006 - 103.201i) q^{30} -334.478 q^{31} -32.0000i q^{32} -330.776i q^{33} +24.2654 q^{34} +37.2012 q^{36} +88.1982i q^{37} +54.9046i q^{38} +64.3003 q^{39} +(68.5156 + 57.4944i) q^{40} -134.110 q^{41} -190.402i q^{43} +219.604 q^{44} +(-66.8394 + 79.6520i) q^{45} +362.006 q^{46} -177.746i q^{47} +96.3996i q^{48} +(-246.204 + 43.3994i) q^{50} -73.0991 q^{51} +42.6892i q^{52} +211.802i q^{53} +213.280 q^{54} +(-394.562 + 470.196i) q^{55} -165.399i q^{57} -248.601i q^{58} -342.679 q^{59} +(-206.402 - 173.201i) q^{60} -659.891 q^{61} +668.955i q^{62} -64.0000 q^{64} +(-91.4024 - 76.6997i) q^{65} -661.553 q^{66} +572.805i q^{67} -48.5307i q^{68} -1090.54 q^{69} -743.405 q^{71} -74.4024i q^{72} +1163.33i q^{73} +176.396 q^{74} +(741.687 - 130.740i) q^{75} +109.809 q^{76} -128.601i q^{78} -1007.11 q^{79} +(114.989 - 137.031i) q^{80} -893.612 q^{81} +268.221i q^{82} -348.189i q^{83} +(103.910 + 87.1952i) q^{85} -380.805 q^{86} +748.906i q^{87} -439.207i q^{88} +1060.06 q^{89} +(159.304 + 133.679i) q^{90} -724.012i q^{92} -2015.22i q^{93} -355.491 q^{94} +(-197.294 + 235.114i) q^{95} +192.799 q^{96} -578.020i q^{97} +510.595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 60 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 + 60 * q^9	\( 8 q - 32 q^{4} + 60 q^{9} - 36 q^{11} + 144 q^{15} + 128 q^{16} - 308 q^{25} + 860 q^{29} + 424 q^{30} - 240 q^{36} + 380 q^{39} + 144 q^{44} + 208 q^{46} - 88 q^{50} - 988 q^{51} - 576 q^{60} - 512 q^{64} + 344 q^{65} - 3528 q^{71} + 3024 q^{74} - 3084 q^{79} - 1504 q^{81} - 3604 q^{85} - 896 q^{86} - 4132 q^{95} + 6504 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 60 * q^9 - 36 * q^11 + 144 * q^15 + 128 * q^16 - 308 * q^25 + 860 * q^29 + 424 * q^30 - 240 * q^36 + 380 * q^39 + 144 * q^44 + 208 * q^46 - 88 * q^50 - 988 * q^51 - 576 * q^60 - 512 * q^64 + 344 * q^65 - 3528 * q^71 + 3024 * q^74 - 3084 * q^79 - 1504 * q^81 - 3604 * q^85 - 896 * q^86 - 4132 * q^95 + 6504 * q^99

Introduction

L-functions

Modular forms

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