LMFDB - Embedded newform 490.4.c.g.99.3

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 438 x^{18} + 80439 x^{16} + 8097428 x^{14} + 488971671 x^{12} + 18162509334 x^{10} + \cdots + 9871083181584 $ x^20 + 438x^18 + 80439x^16 + 8097428x^14 + 488971671x^12 + 18162509334x^10 + 407198911753x^8 + 5129420990112x^6 + 30509282328120x^4 + 52488428698656*x^2 + 9871083181584
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{23}\cdot 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.3
Root			$5.79189i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.g.99.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -6.79189i q^{3} -4.00000 q^{4} +(10.7861 + 2.94297i) q^{5} -13.5838 q^{6} +8.00000i q^{8} -19.1298 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -6.79189i q^{3} -4.00000 q^{4} +(10.7861 + 2.94297i) q^{5} -13.5838 q^{6} +8.00000i q^{8} -19.1298 q^{9} +(5.88595 - 21.5721i) q^{10} +69.2093 q^{11} +27.1676i q^{12} +28.3716i q^{13} +(19.9884 - 73.2577i) q^{15} +16.0000 q^{16} +11.3106i q^{17} +38.2596i q^{18} +74.2184 q^{19} +(-43.1442 - 11.7719i) q^{20} -138.419i q^{22} +66.6640i q^{23} +54.3351 q^{24} +(107.678 + 63.4861i) q^{25} +56.7433 q^{26} -53.4536i q^{27} +134.560 q^{29} +(-146.515 - 39.9767i) q^{30} +160.637 q^{31} -32.0000i q^{32} -470.062i q^{33} +22.6212 q^{34} +76.5192 q^{36} -284.750i q^{37} -148.437i q^{38} +192.697 q^{39} +(-23.5438 + 86.2884i) q^{40} -149.376 q^{41} +513.925i q^{43} -276.837 q^{44} +(-206.335 - 56.2985i) q^{45} +133.328 q^{46} -411.615i q^{47} -108.670i q^{48} +(126.972 - 215.356i) q^{50} +76.8204 q^{51} -113.487i q^{52} +354.813i q^{53} -106.907 q^{54} +(746.495 + 203.681i) q^{55} -504.083i q^{57} -269.119i q^{58} +210.828 q^{59} +(-79.9534 + 293.031i) q^{60} -587.114 q^{61} -321.273i q^{62} -64.0000 q^{64} +(-83.4970 + 306.018i) q^{65} -940.124 q^{66} +1034.20i q^{67} -45.2424i q^{68} +452.774 q^{69} -1033.04 q^{71} -153.038i q^{72} -743.489i q^{73} -569.500 q^{74} +(431.191 - 731.336i) q^{75} -296.874 q^{76} -385.394i q^{78} -609.837 q^{79} +(172.577 + 47.0876i) q^{80} -879.555 q^{81} +298.752i q^{82} -1149.96i q^{83} +(-33.2868 + 121.997i) q^{85} +1027.85 q^{86} -913.914i q^{87} +553.675i q^{88} -735.658 q^{89} +(-112.597 + 412.670i) q^{90} -266.656i q^{92} -1091.03i q^{93} -823.230 q^{94} +(800.523 + 218.423i) q^{95} -217.341 q^{96} +333.373i q^{97} -1323.96 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) $ 20 * q - 80 * q^4 - 316 * q^9	$ 20 q - 80 q^{4} - 316 q^{9} + 104 q^{11} - 360 q^{15} + 320 q^{16} - 440 q^{25} - 216 q^{29} + 224 q^{30} + 1264 q^{36} - 504 q^{39} - 416 q^{44} + 1600 q^{46} + 952 q^{50} - 296 q^{51} + 1440 q^{60} - 1280 q^{64} + 2732 q^{65} - 1872 q^{71} - 5968 q^{74} - 6424 q^{79} + 2020 q^{81} + 428 q^{85} + 3616 q^{86} + 3568 q^{95} + 624 q^{99}+O(q^{100}) $ 20 * q - 80 * q^4 - 316 * q^9 + 104 * q^11 - 360 * q^15 + 320 * q^16 - 440 * q^25 - 216 * q^29 + 224 * q^30 + 1264 * q^36 - 504 * q^39 - 416 * q^44 + 1600 * q^46 + 952 * q^50 - 296 * q^51 + 1440 * q^60 - 1280 * q^64 + 2732 * q^65 - 1872 * q^71 - 5968 * q^74 - 6424 * q^79 + 2020 * q^81 + 428 * q^85 + 3616 * q^86 + 3568 * q^95 + 624 * 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
$3$		−	6.79189i		−	1.30710i	−0.756883	−	0.653550i	$-0.773279\pi$
$3$		−	6.79189i		−	1.30710i	0.756883	−	0.653550i	$-0.226721\pi$
$4$	−4.00000			−0.500000
$5$	10.7861	+	2.94297i	0.964734	+	0.263228i
$5$	10.7861	+	2.94297i	0.964734	+	0.263228i
$6$	−13.5838			−0.924259
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	−19.1298			−0.708511
$10$	5.88595	−	21.5721i	0.186130	−	0.682170i
$11$	69.2093			1.89704			0.948518	−	0.316724i	$-0.102583\pi$
$11$	69.2093			1.89704			0.948518	+	0.316724i	$0.102583\pi$
$12$			27.1676i			0.653550i
$13$			28.3716i			0.605298i	0.953102	+	0.302649i	$0.0978710\pi$
$13$			28.3716i			0.605298i	−0.953102	+	0.302649i	$0.902129\pi$
$14$		0			0
$15$	19.9884	−	73.2577i	0.344065	−	1.26100i
$16$	16.0000			0.250000
$17$			11.3106i			0.161366i	0.996740	+	0.0806831i	$0.0257102\pi$
$17$			11.3106i			0.161366i	−0.996740	+	0.0806831i	$0.974290\pi$
$18$			38.2596i			0.500993i
$19$	74.2184			0.896151			0.448075	−	0.893996i	$-0.352110\pi$
$19$	74.2184			0.896151			0.448075	+	0.893996i	$0.352110\pi$
$20$	−43.1442	−	11.7719i	−0.482367	−	0.131614i
$21$		0			0
$22$		−	138.419i		−	1.34141i
$23$			66.6640i			0.604365i	0.953250	+	0.302183i	$0.0977152\pi$
$23$			66.6640i			0.604365i	−0.953250	+	0.302183i	$0.902285\pi$
$24$	54.3351			0.462130
$25$	107.678	+	63.4861i	0.861422	+	0.507889i
$26$	56.7433			0.428010
$27$		−	53.4536i		−	0.381006i
$28$		0			0
$29$	134.560			0.861624			0.430812	−	0.902442i	$-0.358227\pi$
$29$	134.560			0.861624			0.430812	+	0.902442i	$0.358227\pi$
$30$	−146.515	−	39.9767i	−0.891664	−	0.243291i
$31$	160.637			0.930684			0.465342	−	0.885131i	$-0.345931\pi$
$31$	160.637			0.930684			0.465342	+	0.885131i	$0.345931\pi$
$32$		−	32.0000i		−	0.176777i
$33$		−	470.062i		−	2.47962i
$34$	22.6212			0.114103
$35$		0			0
$36$	76.5192			0.354255
$37$		−	284.750i		−	1.26521i	−0.774476	−	0.632603i	$-0.781986\pi$
$37$		−	284.750i		−	1.26521i	0.774476	−	0.632603i	$-0.218014\pi$
$38$		−	148.437i		−	0.633674i
$39$	192.697			0.791185
$40$	−23.5438	+	86.2884i	−0.0930650	+	0.341085i
$41$	−149.376			−0.568990			−0.284495	−	0.958678i	$-0.591826\pi$
$41$	−149.376			−0.568990			−0.284495	+	0.958678i	$0.591826\pi$
$42$		0			0
$43$			513.925i			1.82262i	0.411717	+	0.911312i	$0.364929\pi$
$43$			513.925i			1.82262i	−0.411717	+	0.911312i	$0.635071\pi$
$44$	−276.837			−0.948518
$45$	−206.335	−	56.2985i	−0.683524	−	0.186500i
$46$	133.328			0.427351
$47$		−	411.615i		−	1.27745i	−0.769435	−	0.638726i	$-0.779462\pi$
$47$		−	411.615i		−	1.27745i	0.769435	−	0.638726i	$-0.220538\pi$
$48$		−	108.670i		−	0.326775i
$49$		0			0
$50$	126.972	−	215.356i	0.359132	−	0.609118i
$51$	76.8204			0.210922
$52$		−	113.487i		−	0.302649i
$53$			354.813i			0.919571i	0.888030	+	0.459785i	$0.152074\pi$
$53$			354.813i			0.919571i	−0.888030	+	0.459785i	$0.847926\pi$
$54$	−106.907			−0.269412
$55$	746.495	+	203.681i	1.83013	+	0.499352i
$56$		0			0
$57$		−	504.083i		−	1.17136i
$58$		−	269.119i		−	0.609260i
$59$	210.828			0.465212			0.232606	−	0.972571i	$-0.425275\pi$
$59$	210.828			0.465212			0.232606	+	0.972571i	$0.425275\pi$
$60$	−79.9534	+	293.031i	−0.172032	+	0.630502i
$61$	−587.114			−1.23233			−0.616166	−	0.787616i	$-0.711315\pi$
$61$	−587.114			−1.23233			−0.616166	+	0.787616i	$0.711315\pi$
$62$		−	321.273i		−	0.658093i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−83.4970	+	306.018i	−0.159331	+	0.583952i
$66$	−940.124			−1.75335
$67$			1034.20i			1.88578i	0.333102	+	0.942891i	$0.391905\pi$
$67$			1034.20i			1.88578i	−0.333102	+	0.942891i	$0.608095\pi$
$68$		−	45.2424i		−	0.0806831i
$69$	452.774			0.789966
$70$		0			0
$71$	−1033.04			−1.72675			−0.863373	−	0.504566i	$-0.831653\pi$
$71$	−1033.04			−1.72675			−0.863373	+	0.504566i	$0.831653\pi$
$72$		−	153.038i		−	0.250496i
$73$		−	743.489i		−	1.19204i	−0.802970	−	0.596019i	$-0.796748\pi$
$73$		−	743.489i		−	1.19204i	0.802970	−	0.596019i	$-0.203252\pi$
$74$	−569.500			−0.894636
$75$	431.191	−	731.336i	0.663862	−	1.12597i
$76$	−296.874			−0.448075
$77$		0			0
$78$		−	385.394i		−	0.559453i
$79$	−609.837			−0.868507			−0.434254	−	0.900791i	$-0.642988\pi$
$79$	−609.837			−0.868507			−0.434254	+	0.900791i	$0.642988\pi$
$80$	172.577	+	47.0876i	0.241183	+	0.0658069i
$81$	−879.555			−1.20652
$82$			298.752i			0.402337i
$83$		−	1149.96i		−	1.52078i	−0.649466	−	0.760391i	$-0.725007\pi$
$83$		−	1149.96i		−	1.52078i	0.649466	−	0.760391i	$-0.274993\pi$
$84$		0			0
$85$	−33.2868	+	121.997i	−0.0424760	+	0.155675i
$86$	1027.85			1.28879
$87$		−	913.914i		−	1.12623i
$88$			553.675i			0.670703i
$89$	−735.658			−0.876175			−0.438087	−	0.898932i	$-0.644344\pi$
$89$	−735.658			−0.876175			−0.438087	+	0.898932i	$0.644344\pi$
$90$	−112.597	+	412.670i	−0.131875	+	0.483325i
$91$		0			0
$92$		−	266.656i		−	0.302183i
$93$		−	1091.03i		−	1.21650i
$94$	−823.230			−0.903294
$95$	800.523	+	218.423i	0.864547	+	0.235892i
$96$	−217.341			−0.231065
$97$			333.373i			0.348958i	0.984661	+	0.174479i	$0.0558241\pi$
$97$			333.373i			0.348958i	−0.984661	+	0.174479i	$0.944176\pi$
$98$		0			0
$99$	−1323.96			−1.34407
$100$	−430.711	−	253.945i	−0.430711	−	0.253945i
$101$	−3.00584			−0.00296131			−0.00148065	−	0.999999i	$-0.500471\pi$
$101$	−3.00584			−0.00296131			−0.00148065	+	0.999999i	$0.500471\pi$
$102$		−	153.641i		−	0.149144i
$103$			746.724i			0.714339i	0.934040	+	0.357170i	$0.116258\pi$
$103$			746.724i			0.714339i	−0.934040	+	0.357170i	$0.883742\pi$
$104$	−226.973			−0.214005
$105$		0			0
$106$	709.625			0.650235
$107$		−	771.055i		−	0.696642i	−0.937375	−	0.348321i	$-0.886752\pi$
$107$		−	771.055i		−	0.696642i	0.937375	−	0.348321i	$-0.113248\pi$
$108$			213.814i			0.190503i
$109$	845.588			0.743052			0.371526	−	0.928423i	$-0.378835\pi$
$109$	845.588			0.743052			0.371526	+	0.928423i	$0.378835\pi$
$110$	407.362	−	1492.99i	0.353095	−	1.29410i
$111$	−1933.99			−1.65375
$112$		0			0
$113$		−	881.711i		−	0.734021i	−0.930217	−	0.367011i	$-0.880381\pi$
$113$		−	881.711i		−	0.734021i	0.930217	−	0.367011i	$-0.119619\pi$
$114$	−1008.17			−0.828276
$115$	−196.190	+	719.041i	−0.159086	+	0.583051i
$116$	−538.238			−0.430812
$117$		−	542.744i		−	0.428860i
$118$		−	421.657i		−	0.328955i
$119$		0			0
$120$	586.062	+	159.907i	0.445832	+	0.121645i
$121$	3458.93			2.59874
$122$			1174.23i			0.871391i
$123$			1014.54i			0.743727i
$124$	−642.547			−0.465342
$125$	974.580	+	1001.66i	0.697353	+	0.716728i
$126$		0			0
$127$		−	486.055i		−	0.339610i	−0.985478	−	0.169805i	$-0.945686\pi$
$127$		−	486.055i		−	0.339610i	0.985478	−	0.169805i	$-0.0543137\pi$
$128$			128.000i			0.0883883i
$129$	3490.52			2.38235
$130$	612.036	+	166.994i	0.412916	+	0.112664i
$131$	−1171.60			−0.781398			−0.390699	−	0.920518i	$-0.627767\pi$
$131$	−1171.60			−0.781398			−0.390699	+	0.920518i	$0.627767\pi$
$132$			1880.25i			1.23981i
$133$		0			0
$134$	2068.40			1.33345
$135$	157.313	−	576.553i	0.100291	−	0.367569i
$136$	−90.4849			−0.0570516
$137$		−	663.078i		−	0.413508i	−0.978393	−	0.206754i	$-0.933710\pi$
$137$		−	663.078i		−	0.413508i	0.978393	−	0.206754i	$-0.0662899\pi$
$138$		−	905.549i		−	0.558590i
$139$	−1395.82			−0.851741			−0.425870	−	0.904784i	$-0.640032\pi$
$139$	−1395.82			−0.851741			−0.425870	+	0.904784i	$0.640032\pi$
$140$		0			0
$141$	−2795.64			−1.66976
$142$			2066.08i			1.22099i
$143$			1963.58i			1.14827i
$144$	−306.077			−0.177128
$145$	1451.37	+	396.005i	0.831238	+	0.226803i
$146$	−1486.98			−0.842898
$147$		0			0
$148$			1139.00i			0.632603i
$149$	−710.861			−0.390845			−0.195423	−	0.980719i	$-0.562608\pi$
$149$	−710.861			−0.390845			−0.195423	+	0.980719i	$0.562608\pi$
$150$	−1462.67	−	862.382i	−0.796178	−	0.469421i
$151$	1739.00			0.937204			0.468602	−	0.883409i	$-0.344758\pi$
$151$	1739.00			0.937204			0.468602	+	0.883409i	$0.344758\pi$
$152$			593.747i			0.316837i
$153$		−	216.370i		−	0.114330i
$154$		0			0
$155$	1732.64	+	472.749i	0.897862	+	0.244982i
$156$	−770.788			−0.395593
$157$		−	3551.13i		−	1.80517i	−0.430517	−	0.902583i	$-0.641669\pi$
$157$		−	3551.13i		−	1.80517i	0.430517	−	0.902583i	$-0.358331\pi$
$158$			1219.67i			0.614127i
$159$	2409.85			1.20197
$160$	94.1752	−	345.154i	0.0465325	−	0.170542i
$161$		0			0
$162$			1759.11i			0.853141i
$163$			2446.20i			1.17547i	0.809055	+	0.587733i	$0.199979\pi$
$163$			2446.20i			1.17547i	−0.809055	+	0.587733i	$0.800021\pi$
$164$	597.503			0.284495
$165$	1383.38	−	5070.11i	0.652703	−	2.39217i
$166$	−2299.93			−1.07536
$167$		−	2080.53i		−	0.964049i	−0.876158	−	0.482025i	$-0.839902\pi$
$167$		−	2080.53i		−	0.964049i	0.876158	−	0.482025i	$-0.160098\pi$
$168$		0			0
$169$	1392.05			0.633614
$170$	243.994	+	66.5736i	0.110079	+	0.0300351i
$171$	−1419.78			−0.634933
$172$		−	2055.70i		−	0.911312i
$173$			2513.87i			1.10477i	0.833588	+	0.552387i	$0.186283\pi$
$173$			2513.87i			1.10477i	−0.833588	+	0.552387i	$0.813717\pi$
$174$	−1827.83			−0.796364
$175$		0			0
$176$	1107.35			0.474259
$177$		−	1431.92i		−	0.608079i
$178$			1471.32i			0.619549i
$179$	−990.726			−0.413689			−0.206844	−	0.978374i	$-0.566319\pi$
$179$	−990.726			−0.413689			−0.206844	+	0.978374i	$0.566319\pi$
$180$	825.340	+	225.194i	0.341762	+	0.0932498i
$181$	1777.12			0.729792			0.364896	−	0.931048i	$-0.381105\pi$
$181$	1777.12			0.729792			0.364896	+	0.931048i	$0.381105\pi$
$182$		0			0
$183$			3987.62i			1.61078i
$184$	−533.312			−0.213675
$185$	838.012	−	3071.33i	0.333037	−	1.22059i
$186$	−2182.05			−0.860193
$187$			782.800i			0.306117i
$188$			1646.46i			0.638726i
$189$		0			0
$190$	436.846	−	1601.05i	0.166801	−	0.611327i
$191$	2336.71			0.885226			0.442613	−	0.896713i	$-0.354051\pi$
$191$	2336.71			0.885226			0.442613	+	0.896713i	$0.354051\pi$
$192$			434.681i			0.163388i
$193$		−	800.791i		−	0.298664i	−0.988787	−	0.149332i	$-0.952288\pi$
$193$		−	800.791i		−	0.298664i	0.988787	−	0.149332i	$-0.0477124\pi$
$194$	666.746			0.246750
$195$	2078.44	+	567.102i	0.763283	+	0.208262i
$196$		0			0
$197$		−	2168.24i		−	0.784167i	−0.919930	−	0.392083i	$-0.871754\pi$
$197$		−	2168.24i		−	0.784167i	0.919930	−	0.392083i	$-0.128246\pi$
$198$			2647.92i			0.950401i
$199$	1625.98			0.579210			0.289605	−	0.957146i	$-0.406476\pi$
$199$	1625.98			0.579210			0.289605	+	0.957146i	$0.406476\pi$
$200$	−507.889	+	861.422i	−0.179566	+	0.304559i
$201$	7024.16			2.46491
$202$			6.01168i			0.00209396i
$203$		0			0
$204$	−307.282			−0.105461
$205$	−1611.18	−	439.609i	−0.548924	−	0.149774i
$206$	1493.45			0.505114
$207$		−	1275.27i		−	0.428199i
$208$			453.946i			0.151325i
$209$	5136.60			1.70003
$210$		0			0
$211$	−818.927			−0.267191			−0.133595	−	0.991036i	$-0.542652\pi$
$211$	−818.927			−0.267191			−0.133595	+	0.991036i	$0.542652\pi$
$212$		−	1419.25i		−	0.459785i
$213$			7016.28i			2.25703i
$214$	−1542.11			−0.492600
$215$	−1512.47	+	5543.22i	−0.479765	+	1.75835i
$216$	427.629			0.134706
$217$		0			0
$218$		−	1691.18i		−	0.525417i
$219$	−5049.69			−1.55811
$220$	−2985.98	−	814.725i	−0.915067	−	0.249676i
$221$	−320.901			−0.0976747
$222$			3867.99i			1.16938i
$223$		−	4820.46i		−	1.44754i	−0.690040	−	0.723771i	$-0.742407\pi$
$223$		−	4820.46i		−	1.44754i	0.690040	−	0.723771i	$-0.257593\pi$
$224$		0			0
$225$	−2059.85	−	1214.48i	−0.610327	−	0.359845i
$226$	−1763.42			−0.519031
$227$			5000.05i			1.46196i	0.682399	+	0.730980i	$0.260937\pi$
$227$			5000.05i			1.46196i	−0.682399	+	0.730980i	$0.739063\pi$
$228$			2016.33i			0.585679i
$229$	−6313.04			−1.82173			−0.910867	−	0.412700i	$-0.864586\pi$
$229$	−6313.04			−1.82173			−0.910867	+	0.412700i	$0.864586\pi$
$230$	1438.08	+	392.381i	0.412280	+	0.112490i
$231$		0			0
$232$			1076.48i			0.304630i
$233$			4697.78i			1.32087i	0.750885	+	0.660433i	$0.229627\pi$
$233$			4697.78i			1.32087i	−0.750885	+	0.660433i	$0.770373\pi$
$234$	−1085.49			−0.303250
$235$	1211.37	−	4439.70i	0.336260	−	1.23240i
$236$	−843.314			−0.232606
$237$			4141.95i			1.13523i
$238$		0			0
$239$	−4151.19			−1.12351			−0.561753	−	0.827305i	$-0.689873\pi$
$239$	−4151.19			−1.12351			−0.561753	+	0.827305i	$0.689873\pi$
$240$	319.814	−	1172.12i	0.0860162	−	0.315251i
$241$	−2451.44			−0.655232			−0.327616	−	0.944811i	$-0.606245\pi$
$241$	−2451.44			−0.655232			−0.327616	+	0.944811i	$0.606245\pi$
$242$		−	6917.86i		−	1.83759i
$243$			4530.60i			1.19604i
$244$	2348.46			0.616166
$245$		0			0
$246$	2029.09			0.525894
$247$			2105.70i			0.542438i
$248$			1285.09i			0.329046i
$249$	−7810.43			−1.98781
$250$	2003.32	−	1949.16i	0.506803	−	0.493103i
$251$	3104.12			0.780598			0.390299	−	0.920688i	$-0.372372\pi$
$251$	3104.12			0.780598			0.390299	+	0.920688i	$0.372372\pi$
$252$		0			0
$253$			4613.77i			1.14650i
$254$	−972.111			−0.240140
$255$	828.589	+	226.081i	0.203483	+	0.0555204i
$256$	256.000			0.0625000
$257$		−	7683.54i		−	1.86493i	−0.361265	−	0.932463i	$-0.617655\pi$
$257$		−	7683.54i		−	1.86493i	0.361265	−	0.932463i	$-0.382345\pi$
$258$		−	6981.05i		−	1.68458i
$259$		0			0
$260$	333.988	−	1224.07i	0.0796656	−	0.291976i
$261$	−2574.10			−0.610470
$262$			2343.20i			0.552532i
$263$			3678.45i			0.862445i	0.902246	+	0.431222i	$0.141918\pi$
$263$			3678.45i			0.862445i	−0.902246	+	0.431222i	$0.858082\pi$
$264$	3760.50			0.876677
$265$	−1044.20	+	3827.03i	−0.242056	+	0.887141i
$266$		0			0
$267$			4996.51i			1.14525i
$268$		−	4136.79i		−	0.942891i
$269$	3612.17			0.818729			0.409364	−	0.912371i	$-0.365751\pi$
$269$	3612.17			0.818729			0.409364	+	0.912371i	$0.365751\pi$
$270$	−1153.11	−	314.625i	−0.259910	−	0.0709166i
$271$	−2374.98			−0.532360			−0.266180	−	0.963923i	$-0.585762\pi$
$271$	−2374.98			−0.532360			−0.266180	+	0.963923i	$0.585762\pi$
$272$			180.970i			0.0403416i
$273$		0			0
$274$	−1326.16			−0.292394
$275$	7452.31	+	4393.83i	1.63415	+	0.963484i
$276$	−1811.10			−0.394983
$277$		−	1964.57i		−	0.426136i	−0.977037	−	0.213068i	$-0.931654\pi$
$277$		−	1964.57i		−	0.426136i	0.977037	−	0.213068i	$-0.0683455\pi$
$278$			2791.64i			0.602272i
$279$	−3072.95			−0.659400
$280$		0			0
$281$	4525.40			0.960721			0.480360	−	0.877071i	$-0.340506\pi$
$281$	4525.40			0.960721			0.480360	+	0.877071i	$0.340506\pi$
$282$			5591.29i			1.18070i
$283$			167.067i			0.0350922i	0.999846	+	0.0175461i	$0.00558538\pi$
$283$			167.067i			0.0350922i	−0.999846	+	0.0175461i	$0.994415\pi$
$284$	4132.15			0.863373
$285$	1483.50	−	5437.07i	0.308334	−	1.13005i
$286$	3927.16			0.811951
$287$		0			0
$288$			612.153i			0.125248i
$289$	4785.07			0.973961
$290$	792.011	−	2902.73i	0.160374	−	0.587774i
$291$	2264.23			0.456123
$292$			2973.95i			0.596019i
$293$		−	1220.67i		−	0.243388i	−0.992568	−	0.121694i	$-0.961167\pi$
$293$		−	1220.67i		−	0.243388i	0.992568	−	0.121694i	$-0.0388326\pi$
$294$		0			0
$295$	2274.01	+	620.463i	0.448806	+	0.122457i
$296$	2278.00			0.447318
$297$		−	3699.49i		−	0.722781i
$298$			1421.72i			0.276369i
$299$	−1891.37			−0.365821
$300$	−1724.76	+	2925.34i	−0.331931	+	0.562983i
$301$		0			0
$302$		−	3478.00i		−	0.662704i
$303$			20.4153i			0.00387073i
$304$	1187.49			0.224038
$305$	−6332.65	−	1727.86i	−1.18887	−	0.324384i
$306$	−432.739			−0.0808433
$307$			6193.89i			1.15148i	0.817633	+	0.575739i	$0.195286\pi$
$307$			6193.89i			1.15148i	−0.817633	+	0.575739i	$0.804714\pi$
$308$		0			0
$309$	5071.67			0.933713
$310$	945.499	−	3465.27i	0.173228	−	0.634884i
$311$	5280.54			0.962803			0.481402	−	0.876500i	$-0.340128\pi$
$311$	5280.54			0.962803			0.481402	+	0.876500i	$0.340128\pi$
$312$			1541.58i			0.279726i
$313$			7753.59i			1.40019i	0.714051	+	0.700094i	$0.246858\pi$
$313$			7753.59i			1.40019i	−0.714051	+	0.700094i	$0.753142\pi$
$314$	−7102.26			−1.27644
$315$		0			0
$316$	2439.35			0.434254
$317$		−	212.730i		−	0.0376912i	−0.999822	−	0.0188456i	$-0.994001\pi$
$317$		−	212.730i		−	0.0376912i	0.999822	−	0.0188456i	$-0.00599909\pi$
$318$		−	4819.70i		−	0.849922i
$319$	9312.78			1.63453
$320$	−690.307	−	188.350i	−0.120592	−	0.0329034i
$321$	−5236.92			−0.910581
$322$		0			0
$323$			839.455i			0.144608i
$324$	3518.22			0.603262
$325$	−1801.21	+	3055.00i	−0.307424	+	0.521417i
$326$	4892.39			0.831180
$327$		−	5743.14i		−	0.971243i
$328$		−	1195.01i		−	0.201168i
$329$		0			0
$330$	−10140.2	−	2766.76i	−1.69152	−	0.461531i
$331$	−12028.8			−1.99747			−0.998736	−	0.0502714i	$-0.983991\pi$
$331$	−12028.8			−1.99747			−0.998736	+	0.0502714i	$0.983991\pi$
$332$			4599.85i			0.760391i
$333$			5447.21i			0.896413i
$334$	−4161.06			−0.681686
$335$	−3043.62	+	11154.9i	−0.496390	+	1.81928i
$336$		0			0
$337$		−	1044.91i		−	0.168901i	−0.996428	−	0.0844507i	$-0.973086\pi$
$337$		−	1044.91i		−	0.168901i	0.996428	−	0.0844507i	$-0.0269135\pi$
$338$		−	2784.10i		−	0.448033i
$339$	−5988.49			−0.959439
$340$	133.147	−	487.987i	0.0212380	−	0.0778377i
$341$	11117.6			1.76554
$342$			2839.56i			0.448965i
$343$		0			0
$344$	−4111.40			−0.644395
$345$	4883.65	+	1332.50i	0.762107	+	0.207941i
$346$	5027.74			0.781193
$347$			7390.86i			1.14341i	0.820460	+	0.571703i	$0.193717\pi$
$347$			7390.86i			1.14341i	−0.820460	+	0.571703i	$0.806283\pi$
$348$			3655.66i			0.563114i
$349$	−9299.14			−1.42628			−0.713140	−	0.701022i	$-0.752728\pi$
$349$	−9299.14			−1.42628			−0.713140	+	0.701022i	$0.752728\pi$
$350$		0			0
$351$	1516.57			0.230622
$352$		−	2214.70i		−	0.335352i
$353$		−	1872.73i		−	0.282367i	−0.989983	−	0.141183i	$-0.954909\pi$
$353$		−	1872.73i		−	0.282367i	0.989983	−	0.141183i	$-0.0450907\pi$
$354$	−2863.85			−0.429977
$355$	−11142.4	−	3040.20i	−1.66585	−	0.454527i
$356$	2942.63			0.438087
$357$		0			0
$358$			1981.45i			0.292522i
$359$	4300.48			0.632230			0.316115	−	0.948721i	$-0.397621\pi$
$359$	4300.48			0.632230			0.316115	+	0.948721i	$0.397621\pi$
$360$	450.388	−	1650.68i	0.0659376	−	0.241662i
$361$	−1350.63			−0.196914
$362$		−	3554.24i		−	0.516041i
$363$		−	23492.7i		−	3.39682i
$364$		0			0
$365$	2188.07	−	8019.31i	0.313777	−	1.15000i
$366$	7975.24			1.13900
$367$		−	9618.48i		−	1.36807i	−0.729451	−	0.684033i	$-0.760224\pi$
$367$		−	9618.48i		−	1.36807i	0.729451	−	0.684033i	$-0.239776\pi$
$368$			1066.62i			0.151091i
$369$	2857.53			0.403136
$370$	−6142.66	−	1676.02i	−0.863086	−	0.235493i
$371$		0			0
$372$			4364.11i			0.608248i
$373$		−	9483.14i		−	1.31640i	−0.752842	−	0.658202i	$-0.771317\pi$
$373$		−	9483.14i		−	1.31640i	0.752842	−	0.658202i	$-0.228683\pi$
$374$	1565.60			0.216458
$375$	6803.15	−	6619.24i	0.936835	−	0.911510i
$376$	3292.92			0.451647
$377$			3817.68i			0.521539i
$378$		0			0
$379$	−558.846			−0.0757414			−0.0378707	−	0.999283i	$-0.512057\pi$
$379$	−558.846			−0.0757414			−0.0378707	+	0.999283i	$0.512057\pi$
$380$	−3202.09	−	873.691i	−0.432274	−	0.117946i
$381$	−3301.24			−0.443904
$382$		−	4673.42i		−	0.625950i
$383$		−	2251.51i		−	0.300383i	−0.988657	−	0.150191i	$-0.952011\pi$
$383$		−	2251.51i		−	0.300383i	0.988657	−	0.150191i	$-0.0479890\pi$
$384$	869.362			0.115532
$385$		0			0
$386$	−1601.58			−0.211188
$387$		−	9831.28i		−	1.29135i
$388$		−	1333.49i		−	0.174479i
$389$	−5246.70			−0.683851			−0.341926	−	0.939727i	$-0.611079\pi$
$389$	−5246.70			−0.683851			−0.341926	+	0.939727i	$0.611079\pi$
$390$	1134.20	−	4156.88i	0.147263	−	0.539723i
$391$	−754.010			−0.0975241
$392$		0			0
$393$			7957.38i			1.02137i
$394$	−4336.48			−0.554490
$395$	−6577.74	−	1794.74i	−0.837878	−	0.228615i
$396$	5295.84			0.672035
$397$		−	4750.94i		−	0.600612i	−0.953843	−	0.300306i	$-0.902911\pi$
$397$		−	4750.94i		−	0.600612i	0.953843	−	0.300306i	$-0.0970888\pi$
$398$		−	3251.96i		−	0.409563i
$399$		0			0
$400$	1722.84	+	1015.78i	0.215356	+	0.126972i
$401$	−10598.9			−1.31991			−0.659956	−	0.751305i	$-0.729425\pi$
$401$	−10598.9			−1.31991			−0.659956	+	0.751305i	$0.729425\pi$
$402$		−	14048.3i		−	1.74295i
$403$			4557.53i			0.563341i
$404$	12.0234			0.00148065
$405$	−9486.93	−	2588.51i	−1.16397	−	0.317590i
$406$		0			0
$407$		−	19707.4i		−	2.40014i
$408$			614.563i			0.0745721i
$409$	−5914.26			−0.715016			−0.357508	−	0.933910i	$-0.616373\pi$
$409$	−5914.26			−0.715016			−0.357508	+	0.933910i	$0.616373\pi$
$410$	−879.218	+	3222.35i	−0.105906	+	0.388148i
$411$	−4503.55			−0.540496
$412$		−	2986.90i		−	0.357170i
$413$		0			0
$414$	−2550.54			−0.302783
$415$	3384.31	−	12403.6i	0.400312	−	1.46715i
$416$	907.892			0.107003
$417$			9480.26i			1.11331i
$418$		−	10273.2i		−	1.20210i
$419$	483.168			0.0563349			0.0281674	−	0.999603i	$-0.491033\pi$
$419$	483.168			0.0563349			0.0281674	+	0.999603i	$0.491033\pi$
$420$		0			0
$421$	−5789.84			−0.670260			−0.335130	−	0.942172i	$-0.608780\pi$
$421$	−5789.84			−0.670260			−0.335130	+	0.942172i	$0.608780\pi$
$422$			1637.85i			0.188932i
$423$			7874.11i			0.905088i
$424$	−2838.50			−0.325117
$425$	−718.067	+	1217.90i	−0.0819561	+	0.139004i
$426$	14032.6			1.59596
$427$		0			0
$428$			3084.22i			0.348321i
$429$	13336.4			1.50091
$430$	11086.4	+	3024.94i	1.24334	+	0.339245i
$431$	642.154			0.0717668			0.0358834	−	0.999356i	$-0.488576\pi$
$431$	642.154			0.0717668			0.0358834	+	0.999356i	$0.488576\pi$
$432$		−	855.258i		−	0.0952514i
$433$		−	2336.33i		−	0.259300i	−0.991560	−	0.129650i	$-0.958615\pi$
$433$		−	2336.33i		−	0.259300i	0.991560	−	0.129650i	$-0.0413853\pi$
$434$		0			0
$435$	2689.63	−	9857.53i	0.296454	−	1.08651i
$436$	−3382.35			−0.371526
$437$			4947.69i			0.541602i
$438$			10099.4i			1.10175i
$439$	−8930.85			−0.970948			−0.485474	−	0.874251i	$-0.661353\pi$
$439$	−8930.85			−0.970948			−0.485474	+	0.874251i	$0.661353\pi$
$440$	−1629.45	+	5971.96i	−0.176548	+	0.647050i
$441$		0			0
$442$			641.801i			0.0690664i
$443$			7112.29i			0.762788i	0.924413	+	0.381394i	$0.124556\pi$
$443$			7112.29i			0.762788i	−0.924413	+	0.381394i	$0.875444\pi$
$444$	7735.97			0.826876
$445$	−7934.84	−	2165.02i	−0.845275	−	0.230633i
$446$	−9640.92			−1.02357
$447$			4828.09i			0.510874i
$448$		0			0
$449$	4508.90			0.473916			0.236958	−	0.971520i	$-0.423850\pi$
$449$	4508.90			0.473916			0.236958	+	0.971520i	$0.423850\pi$
$450$	−2428.95	+	4119.71i	−0.254449	+	0.431566i
$451$	−10338.2			−1.07939
$452$			3526.84i			0.367011i
$453$		−	11811.1i		−	1.22502i
$454$	10000.1			1.03376
$455$		0			0
$456$	4032.67			0.414138
$457$			2048.24i			0.209656i	0.994490	+	0.104828i	$0.0334292\pi$
$457$			2048.24i			0.209656i	−0.994490	+	0.104828i	$0.966571\pi$
$458$			12626.1i			1.28816i
$459$	604.593			0.0614814
$460$	784.761	−	2876.16i	0.0795428	−	0.291526i
$461$	9007.55			0.910030			0.455015	−	0.890484i	$-0.349634\pi$
$461$	9007.55			0.910030			0.455015	+	0.890484i	$0.349634\pi$
$462$		0			0
$463$			3016.17i			0.302750i	0.988476	+	0.151375i	$0.0483702\pi$
$463$			3016.17i			0.302750i	−0.988476	+	0.151375i	$0.951630\pi$
$464$	2152.95			0.215406
$465$	3210.86	−	11767.9i	0.320216	−	1.17360i
$466$	9395.56			0.933993
$467$			9182.69i			0.909902i	0.890516	+	0.454951i	$0.150343\pi$
$467$			9182.69i			0.909902i	−0.890516	+	0.454951i	$0.849657\pi$
$468$			2170.97i			0.214430i
$469$		0			0
$470$	−8879.40	−	2422.74i	−0.871439	−	0.237772i
$471$	−24118.9			−2.35953
$472$			1686.63i			0.164477i
$473$			35568.4i			3.45758i
$474$	8283.90			0.802726
$475$	7991.67	+	4711.84i	0.771965	+	0.455145i
$476$		0			0
$477$		−	6787.49i		−	0.651526i
$478$			8302.38i			0.794439i
$479$	−19335.2			−1.84436			−0.922181	−	0.386760i	$-0.873594\pi$
$479$	−19335.2			−1.84436			−0.922181	+	0.386760i	$0.873594\pi$
$480$	−2344.25	−	639.627i	−0.222916	−	0.0608226i
$481$	8078.83			0.765827
$482$			4902.87i			0.463319i
$483$		0			0
$484$	−13835.7			−1.29937
$485$	−981.108	+	3595.78i	−0.0918553	+	0.336651i
$486$	9061.20			0.845729
$487$		−	9704.88i		−	0.903019i	−0.892266	−	0.451509i	$-0.850886\pi$
$487$		−	9704.88i		−	0.903019i	0.892266	−	0.451509i	$-0.149114\pi$
$488$		−	4696.92i		−	0.435695i
$489$	16614.3			1.53645
$490$		0			0
$491$	−2284.05			−0.209934			−0.104967	−	0.994476i	$-0.533474\pi$
$491$	−2284.05			−0.209934			−0.104967	+	0.994476i	$0.533474\pi$
$492$		−	4058.18i		−	0.371863i
$493$			1521.95i			0.139037i
$494$	4211.39			0.383562
$495$	−14280.3	−	3896.38i	−1.29667	−	0.353796i
$496$	2570.19			0.232671
$497$		0			0
$498$			15620.9i			1.40560i
$499$	−6801.94			−0.610214			−0.305107	−	0.952318i	$-0.598692\pi$
$499$	−6801.94			−0.610214			−0.305107	+	0.952318i	$0.598692\pi$
$500$	−3898.32	−	4006.63i	−0.348676	−	0.358364i
$501$	−14130.7			−1.26011
$502$		−	6208.23i		−	0.551966i
$503$			8820.72i			0.781902i	0.920412	+	0.390951i	$0.127854\pi$
$503$			8820.72i			0.781902i	−0.920412	+	0.390951i	$0.872146\pi$
$504$		0			0
$505$	−32.4211	−	8.84610i	−0.00285687	−	0.000779498i
$506$	9227.53			0.810700
$507$		−	9454.65i		−	0.828197i
$508$			1944.22i			0.169805i
$509$	11132.7			0.969449			0.484724	−	0.874667i	$-0.338920\pi$
$509$	11132.7			0.969449			0.484724	+	0.874667i	$0.338920\pi$
$510$	452.161	−	1657.18i	0.0392589	−	0.143884i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$		−	3967.24i		−	0.341438i
$514$	−15367.1			−1.31870
$515$	−2197.59	+	8054.21i	−0.188034	+	0.689147i
$516$	−13962.1			−1.19118
$517$		−	28487.6i		−	2.42337i
$518$		0			0
$519$	17073.9			1.44405
$520$	−2448.14	−	667.976i	−0.206458	−	0.0563321i
$521$	4640.75			0.390240			0.195120	−	0.980779i	$-0.437490\pi$
$521$	4640.75			0.390240			0.195120	+	0.980779i	$0.437490\pi$
$522$			5148.19i			0.431667i
$523$			201.305i			0.0168307i	0.999965	+	0.00841534i	$0.00267872\pi$
$523$			201.305i			0.0168307i	−0.999965	+	0.00841534i	$0.997321\pi$
$524$	4686.40			0.390699
$525$		0			0
$526$	7356.90			0.609840
$527$			1816.90i			0.150181i
$528$		−	7520.99i		−	0.619904i
$529$	7722.92			0.634743
$530$	7654.05	+	2088.41i	0.627303	+	0.171160i
$531$	−4033.11			−0.329608
$532$		0			0
$533$		−	4238.04i		−	0.344409i
$534$	9993.01			0.809813
$535$	2269.19	−	8316.64i	0.183375	−	0.672074i
$536$	−8273.58			−0.666725
$537$			6728.90i			0.540733i
$538$		−	7224.34i		−	0.578929i
$539$		0			0
$540$	−629.250	+	2306.21i	−0.0501456	+	0.183784i
$541$	3721.35			0.295736			0.147868	−	0.989007i	$-0.452759\pi$
$541$	3721.35			0.295736			0.147868	+	0.989007i	$0.452759\pi$
$542$			4749.96i			0.376436i
$543$		−	12070.0i		−	0.953912i
$544$	361.939			0.0285258
$545$	9120.55	+	2488.54i	0.716847	+	0.195592i
$546$		0			0
$547$			5900.64i			0.461231i	0.973045	+	0.230615i	$0.0740739\pi$
$547$			5900.64i			0.461231i	−0.973045	+	0.230615i	$0.925926\pi$
$548$			2652.31i			0.206754i
$549$	11231.4			0.873121
$550$	8787.66	−	14904.6i	0.681286	−	1.15552i
$551$	9986.80			0.772145
$552$			3622.20i			0.279295i
$553$		0			0
$554$	−3929.14			−0.301323
$555$	−20860.1	−	5691.69i	−1.59543	−	0.435313i
$556$	5583.28			0.425870
$557$		−	11769.4i		−	0.895309i	−0.894206	−	0.447655i	$-0.852259\pi$
$557$		−	11769.4i		−	0.895309i	0.894206	−	0.447655i	$-0.147741\pi$
$558$			6145.89i			0.466266i
$559$	−14580.9			−1.10323
$560$		0			0
$561$	5316.69			0.400126
$562$		−	9050.79i		−	0.679332i
$563$			11661.6i			0.872965i	0.899713	+	0.436482i	$0.143776\pi$
$563$			11661.6i			0.872965i	−0.899713	+	0.436482i	$0.856224\pi$
$564$	11182.6			0.834878
$565$	2594.85	−	9510.18i	0.193215	−	0.708135i
$566$	334.133			0.0248139
$567$		0			0
$568$		−	8264.30i		−	0.610497i
$569$	−10613.7			−0.781986			−0.390993	−	0.920394i	$-0.627868\pi$
$569$	−10613.7			−0.781986			−0.390993	+	0.920394i	$0.627868\pi$
$570$	−10874.1	−	2967.01i	−0.799066	−	0.218025i
$571$	−5276.34			−0.386704			−0.193352	−	0.981129i	$-0.561936\pi$
$571$	−5276.34			−0.386704			−0.193352	+	0.981129i	$0.561936\pi$
$572$		−	7854.33i		−	0.574136i
$573$		−	15870.7i		−	1.15708i
$574$		0			0
$575$	−4232.24	+	7178.23i	−0.306950	+	0.520614i
$576$	1224.31			0.0885639
$577$		−	5712.12i		−	0.412129i	−0.978538	−	0.206065i	$-0.933934\pi$
$577$		−	5712.12i		−	0.412129i	0.978538	−	0.206065i	$-0.0660657\pi$
$578$		−	9570.14i		−	0.688694i
$579$	−5438.89			−0.390384
$580$	−5805.47	−	1584.02i	−0.415619	−	0.113402i
$581$		0			0
$582$		−	4528.47i		−	0.322528i
$583$			24556.3i			1.74446i
$584$	5947.91			0.421449
$585$	1597.28	−	5854.06i	0.112888	−	0.413736i
$586$	−2441.35			−0.172101
$587$			18045.4i			1.26885i	0.772985	+	0.634424i	$0.218763\pi$
$587$			18045.4i			1.26885i	−0.772985	+	0.634424i	$0.781237\pi$
$588$		0			0
$589$	11922.2			0.834033
$590$	1240.93	−	4548.01i	0.0865900	−	0.317354i
$591$	−14726.5			−1.02498
$592$		−	4556.00i		−	0.316302i
$593$			26700.2i			1.84898i	0.381204	+	0.924491i	$0.375510\pi$
$593$			26700.2i			1.84898i	−0.381204	+	0.924491i	$0.624490\pi$
$594$	−7398.97			−0.511083
$595$		0			0
$596$	2843.44			0.195423
$597$		−	11043.5i		−	0.757086i
$598$			3782.73i			0.258675i
$599$	23229.1			1.58450			0.792249	−	0.610197i	$-0.208910\pi$
$599$	23229.1			1.58450			0.792249	+	0.610197i	$0.208910\pi$
$600$	5850.69	+	3449.53i	0.398089	+	0.234711i
$601$	−28766.2			−1.95241			−0.976205	−	0.216850i	$-0.930422\pi$
$601$	−28766.2			−1.95241			−0.976205	+	0.216850i	$0.930422\pi$
$602$		0			0
$603$		−	19784.0i		−	1.33610i
$604$	−6956.00			−0.468602
$605$	37308.2	+	10179.5i	2.50710	+	0.684061i
$606$	40.8307			0.00273702
$607$		−	1266.07i		−	0.0846592i	−0.999104	−	0.0423296i	$-0.986522\pi$
$607$		−	1266.07i		−	0.0846592i	0.999104	−	0.0423296i	$-0.0134780\pi$
$608$		−	2374.99i		−	0.158419i
$609$		0			0
$610$	−3455.72	+	12665.3i	−0.229374	+	0.840660i
$611$	11678.2			0.773239
$612$			865.478i			0.0571649i
$613$			11761.1i			0.774920i	0.921887	+	0.387460i	$0.126647\pi$
$613$			11761.1i			0.774920i	−0.921887	+	0.387460i	$0.873353\pi$
$614$	12387.8			0.814218
$615$	−2985.78	+	10942.9i	−0.195769	+	0.717498i
$616$		0			0
$617$		−	1282.04i		−	0.0836518i	−0.999125	−	0.0418259i	$-0.986683\pi$
$617$		−	1282.04i		−	0.0836518i	0.999125	−	0.0418259i	$-0.0133175\pi$
$618$		−	10143.3i		−	0.660235i
$619$	−2004.70			−0.130171			−0.0650854	−	0.997880i	$-0.520732\pi$
$619$	−2004.70			−0.130171			−0.0650854	+	0.997880i	$0.520732\pi$
$620$	−6930.54	−	1891.00i	−0.448931	−	0.122491i
$621$	3563.43			0.230266
$622$		−	10561.1i		−	0.680805i
$623$		0			0
$624$	3083.15			0.197796
$625$	7564.02	+	13672.1i	0.484097	+	0.875014i
$626$	15507.2			0.990082
$627$		−	34887.3i		−	2.22211i
$628$			14204.5i			0.902583i
$629$	3220.70			0.204162
$630$		0			0
$631$	−28022.2			−1.76790			−0.883949	−	0.467582i	$-0.845125\pi$
$631$	−28022.2			−1.76790			−0.883949	+	0.467582i	$0.845125\pi$
$632$		−	4878.70i		−	0.307064i
$633$			5562.06i			0.349245i
$634$	−425.460			−0.0266517
$635$	1430.45	−	5242.62i	0.0893946	−	0.327633i
$636$	−9639.39			−0.600986
$637$		0			0
$638$		−	18625.6i		−	1.15579i
$639$	19761.8			1.22342
$640$	−376.701	+	1380.61i	−0.0232662	+	0.0852712i
$641$	13405.5			0.826030			0.413015	−	0.910724i	$-0.364476\pi$
$641$	13405.5			0.826030			0.413015	+	0.910724i	$0.364476\pi$
$642$			10473.8i			0.643878i
$643$			8670.90i			0.531799i	0.964001	+	0.265899i	$0.0856689\pi$
$643$			8670.90i			0.531799i	−0.964001	+	0.265899i	$0.914331\pi$
$644$		0			0
$645$	37649.0	+	10272.5i	2.29834	+	0.627101i
$646$	1678.91			0.102254
$647$			21187.8i			1.28745i	0.765259	+	0.643723i	$0.222611\pi$
$647$			21187.8i			1.28745i	−0.765259	+	0.643723i	$0.777389\pi$
$648$		−	7036.44i		−	0.426570i
$649$	14591.3			0.882525
$650$	6109.99	+	3602.41i	0.368698	+	0.217382i
$651$		0			0
$652$		−	9784.79i		−	0.587733i
$653$		−	22491.4i		−	1.34787i	−0.738793	−	0.673933i	$-0.764604\pi$
$653$		−	22491.4i		−	1.34787i	0.738793	−	0.673933i	$-0.235396\pi$
$654$	−11486.3			−0.686772
$655$	−12636.9	−	3447.99i	−0.753841	−	0.205686i
$656$	−2390.01			−0.142247
$657$			14222.8i			0.844572i
$658$		0			0
$659$	−16930.9			−1.00081			−0.500406	−	0.865791i	$-0.666816\pi$
$659$	−16930.9			−1.00081			−0.500406	+	0.865791i	$0.666816\pi$
$660$	−5533.52	+	20280.5i	−0.326352	+	1.19608i
$661$	510.961			0.0300667			0.0150333	−	0.999887i	$-0.495215\pi$
$661$	510.961			0.0300667			0.0150333	+	0.999887i	$0.495215\pi$
$662$			24057.6i			1.41243i
$663$			2179.52i			0.127671i
$664$	9199.71			0.537678
$665$		0			0
$666$	10894.4			0.633859
$667$			8970.28i			0.520735i
$668$			8322.12i			0.482025i
$669$	−32740.0			−1.89208
$670$	22309.8	+	6087.23i	1.28642	+	0.351001i
$671$	−40633.8			−2.33778
$672$		0			0
$673$			33178.8i			1.90037i	0.311683	+	0.950186i	$0.399107\pi$
$673$			33178.8i			1.90037i	−0.311683	+	0.950186i	$0.600893\pi$
$674$	−2089.82			−0.119431
$675$	3393.56	−	5755.77i	0.193509	−	0.328207i
$676$	−5568.20			−0.316807
$677$			5258.20i			0.298507i	0.988799	+	0.149253i	$0.0476870\pi$
$677$			5258.20i			0.298507i	−0.988799	+	0.149253i	$0.952313\pi$
$678$			11977.0i			0.678426i
$679$		0			0
$680$	−975.974	−	266.295i	−0.0550396	−	0.0150175i
$681$	33959.8			1.91093
$682$		−	22235.1i		−	1.24843i
$683$		−	20819.9i		−	1.16640i	−0.812328	−	0.583201i	$-0.801800\pi$
$683$		−	20819.9i		−	1.16640i	0.812328	−	0.583201i	$-0.198200\pi$
$684$	5679.13			0.317466
$685$	1951.42	−	7151.99i	0.108847	−	0.398925i
$686$		0			0
$687$			42877.5i			2.38119i
$688$			8222.80i			0.455656i
$689$	−10066.6			−0.556614
$690$	2665.01	−	9767.30i	0.147036	−	0.538891i
$691$	2113.50			0.116355			0.0581775	−	0.998306i	$-0.481471\pi$
$691$	2113.50			0.116355			0.0581775	+	0.998306i	$0.481471\pi$
$692$		−	10055.5i		−	0.552387i
$693$		0			0
$694$	14781.7			0.808511
$695$	−15055.4	−	4107.86i	−0.821703	−	0.224202i
$696$	7311.31			0.398182
$697$		−	1689.53i		−	0.0918158i
$698$			18598.3i			1.00853i
$699$	31906.8			1.72650
$700$		0			0
$701$	−7392.50			−0.398304			−0.199152	−	0.979969i	$-0.563819\pi$
$701$	−7392.50			−0.398304			−0.199152	+	0.979969i	$0.563819\pi$
$702$		−	3033.13i		−	0.163074i
$703$		−	21133.7i		−	1.13382i
$704$	−4429.40			−0.237129
$705$	−30154.0	−	8227.51i	−1.61087	−	0.439526i
$706$	−3745.46			−0.199663
$707$		0			0
$708$			5727.70i			0.304040i
$709$	16827.4			0.891351			0.445675	−	0.895195i	$-0.352964\pi$
$709$	16827.4			0.891351			0.445675	+	0.895195i	$0.352964\pi$
$710$	−6080.41	+	22284.8i	−0.321399	+	1.17793i
$711$	11666.1			0.615347
$712$		−	5885.26i		−	0.309775i
$713$			10708.7i			0.562473i
$714$		0			0
$715$	−5778.77	+	21179.3i	−0.302257	+	1.10778i
$716$	3962.90			0.206844
$717$			28194.4i			1.46854i
$718$		−	8600.96i		−	0.447054i
$719$	−31417.3			−1.62958			−0.814790	−	0.579757i	$-0.803148\pi$
$719$	−31417.3			−1.62958			−0.814790	+	0.579757i	$0.803148\pi$
$720$	−3301.36	−	900.776i	−0.170881	−	0.0466249i
$721$		0			0
$722$			2701.26i			0.139239i
$723$			16649.9i			0.856454i
$724$	−7108.49			−0.364896
$725$	14489.1	+	8542.67i	0.742222	+	0.437609i
$726$	−46985.3			−2.40191
$727$			12784.5i			0.652201i	0.945335	+	0.326101i	$0.105735\pi$
$727$			12784.5i			0.652201i	−0.945335	+	0.326101i	$0.894265\pi$
$728$		0			0
$729$	7023.33			0.356822
$730$	−16038.6	−	4376.13i	−0.813172	−	0.221874i
$731$	−5812.80			−0.294110
$732$		−	15950.5i		−	0.805391i
$733$			3569.49i			0.179867i	0.995948	+	0.0899333i	$0.0286654\pi$
$733$			3569.49i			0.179867i	−0.995948	+	0.0899333i	$0.971335\pi$
$734$	−19237.0			−0.967369
$735$		0			0
$736$	2133.25			0.106838
$737$			71576.1i			3.57740i
$738$		−	5715.06i		−	0.285060i
$739$	20274.7			1.00922			0.504612	−	0.863346i	$-0.331636\pi$
$739$	20274.7			1.00922			0.504612	+	0.863346i	$0.331636\pi$
$740$	−3352.05	+	12285.3i	−0.166519	+	0.610294i
$741$	14301.7			0.709021
$742$		0			0
$743$		−	23416.6i		−	1.15622i	−0.815959	−	0.578109i	$-0.803791\pi$
$743$		−	23416.6i		−	1.15622i	0.815959	−	0.578109i	$-0.196209\pi$
$744$	8728.21			0.430097
$745$	−7667.38	−	2092.04i	−0.377062	−	0.102881i
$746$	−18966.3			−0.930838
$747$			21998.6i			1.07749i
$748$		−	3131.20i		−	0.153059i
$749$		0			0
$750$	−13238.5	−	13606.3i	−0.644535	−	0.662442i
$751$	27051.6			1.31442			0.657209	−	0.753708i	$-0.271737\pi$
$751$	27051.6			1.31442			0.657209	+	0.753708i	$0.271737\pi$
$752$		−	6585.84i		−	0.319363i
$753$		−	21082.8i		−	1.02032i
$754$	7635.35			0.368784
$755$	18756.9	+	5117.83i	0.904153	+	0.246698i
$756$		0			0
$757$			7695.13i			0.369464i	0.982789	+	0.184732i	$0.0591417\pi$
$757$			7695.13i			0.369464i	−0.982789	+	0.184732i	$0.940858\pi$
$758$			1117.69i			0.0535572i
$759$	31336.2			1.49859
$760$	−1747.38	+	6404.19i	−0.0834003	+	0.305664i
$761$	19601.5			0.933709			0.466854	−	0.884334i	$-0.345387\pi$
$761$	19601.5			0.933709			0.466854	+	0.884334i	$0.345387\pi$
$762$			6602.47i			0.313887i
$763$		0			0
$764$	−9346.83			−0.442613
$765$	636.770	−	2333.77i	0.0300947	−	0.110298i
$766$	−4503.01			−0.212403
$767$			5981.55i			0.281592i
$768$		−	1738.72i		−	0.0816938i
$769$	9832.15			0.461062			0.230531	−	0.973065i	$-0.425954\pi$
$769$	9832.15			0.461062			0.230531	+	0.973065i	$0.425954\pi$
$770$		0			0
$771$	−52185.8			−2.43765
$772$			3203.16i			0.149332i
$773$			33561.5i			1.56161i	0.624776	+	0.780804i	$0.285190\pi$
$773$			33561.5i			1.56161i	−0.624776	+	0.780804i	$0.714810\pi$
$774$	−19662.6			−0.913121
$775$	17297.0	+	10198.2i	0.801712	+	0.472684i
$776$	−2666.99			−0.123375
$777$		0			0
$778$			10493.4i			0.483556i
$779$	−11086.4			−0.509901
$780$	−8313.76	−	2268.41i	−0.381642	−	0.104131i
$781$	−71495.8			−3.27570
$782$			1508.02i			0.0689600i
$783$		−	7192.70i		−	0.328283i
$784$		0			0
$785$	10450.9	−	38302.7i	0.475169	−	1.74150i
$786$	15914.8			0.722215
$787$			19916.4i			0.902087i	0.892502	+	0.451044i	$0.148948\pi$
$787$			19916.4i			0.902087i	−0.892502	+	0.451044i	$0.851052\pi$
$788$			8672.97i			0.392083i
$789$	24983.6			1.12730
$790$	−3589.47	+	13155.5i	−0.161655	+	0.592469i
$791$		0			0
$792$		−	10591.7i		−	0.475201i
$793$		−	16657.4i		−	0.745929i
$794$	−9501.88			−0.424697
$795$	25992.7	+	7092.12i	1.15958	+	0.316392i
$796$	−6503.93			−0.289605
$797$		−	2485.71i		−	0.110475i	−0.998473	−	0.0552373i	$-0.982408\pi$
$797$		−	2485.71i		−	0.110475i	0.998473	−	0.0552373i	$-0.0175915\pi$
$798$		0			0
$799$	4655.62			0.206137
$800$	2031.56	−	3445.69i	0.0897829	−	0.152279i
$801$	14073.0			0.620779
$802$			21197.8i			0.933318i
$803$		−	51456.3i		−	2.26134i
$804$	−28096.6			−1.23245
$805$		0			0
$806$	9115.05			0.398342
$807$		−	24533.5i		−	1.07016i
$808$		−	24.0467i		−	0.00104698i
$809$	−7580.66			−0.329446			−0.164723	−	0.986340i	$-0.552673\pi$
$809$	−7580.66			−0.329446			−0.164723	+	0.986340i	$0.552673\pi$
$810$	−5177.02	+	18973.9i	−0.224570	+	0.823054i
$811$	18439.3			0.798387			0.399193	−	0.916867i	$-0.369290\pi$
$811$	18439.3			0.798387			0.399193	+	0.916867i	$0.369290\pi$
$812$		0			0
$813$			16130.6i			0.695848i
$814$	−39414.7			−1.69716
$815$	−7199.09	+	26384.8i	−0.309415	+	1.13401i
$816$	1229.13			0.0527305
$817$			38142.7i			1.63335i
$818$			11828.5i			0.505592i
$819$		0			0
$820$	6444.70	+	1758.44i	0.274462	+	0.0748869i
$821$	−6651.55			−0.282754			−0.141377	−	0.989956i	$-0.545153\pi$
$821$	−6651.55			−0.282754			−0.141377	+	0.989956i	$0.545153\pi$
$822$			9007.11i			0.382188i
$823$		−	7392.45i		−	0.313104i	−0.987670	−	0.156552i	$-0.949962\pi$
$823$		−	7392.45i		−	0.313104i	0.987670	−	0.156552i	$-0.0500379\pi$
$824$	−5973.80			−0.252557
$825$	29842.4	−	50615.3i	1.25937	−	2.13600i
$826$		0			0
$827$		−	6122.78i		−	0.257449i	−0.991680	−	0.128724i	$-0.958912\pi$
$827$		−	6122.78i		−	0.257449i	0.991680	−	0.128724i	$-0.0410882\pi$
$828$			5101.07i			0.214100i
$829$	383.866			0.0160823			0.00804115	−	0.999968i	$-0.497440\pi$
$829$	383.866			0.0160823			0.00804115	+	0.999968i	$0.497440\pi$
$830$	−24807.1	−	6768.63i	−1.03743	−	0.283063i
$831$	−13343.1			−0.557002
$832$		−	1815.78i		−	0.0756623i
$833$		0			0
$834$	18960.5			0.787229
$835$	6122.95	−	22440.7i	0.253764	−	0.930051i
$836$	−20546.4			−0.850015
$837$		−	8586.61i		−	0.354596i
$838$		−	966.336i		−	0.0398348i
$839$	27506.6			1.13186			0.565932	−	0.824452i	$-0.308516\pi$
$839$	27506.6			1.13186			0.565932	+	0.824452i	$0.308516\pi$
$840$		0			0
$841$	−6282.71			−0.257604
$842$			11579.7i			0.473946i
$843$		−	30736.0i		−	1.25576i
$844$	3275.71			0.133595
$845$	15014.7	+	4096.77i	0.611269	+	0.166785i
$846$	15748.2			0.639994
$847$		0			0
$848$			5677.00i			0.229893i
$849$	1134.70			0.0458690
$850$	2435.80	+	1436.13i	0.0982910	+	0.0579517i
$851$	18982.6			0.764647
$852$		−	28065.1i		−	1.12852i
$853$			36571.5i			1.46798i	0.679162	+	0.733988i	$0.262343\pi$
$853$			36571.5i			1.46798i	−0.679162	+	0.733988i	$0.737657\pi$
$854$		0			0
$855$	−15313.8	−	4178.38i	−0.612541	−	0.167132i
$856$	6168.44			0.246300
$857$		−	29925.1i		−	1.19279i	−0.802690	−	0.596396i	$-0.796599\pi$
$857$		−	29925.1i		−	1.19279i	0.802690	−	0.596396i	$-0.203401\pi$
$858$		−	26672.9i		−	1.06130i
$859$	1497.15			0.0594668			0.0297334	−	0.999558i	$-0.490534\pi$
$859$	1497.15			0.0594668			0.0297334	+	0.999558i	$0.490534\pi$
$860$	6049.87	−	22172.9i	0.239882	−	0.879173i
$861$		0			0
$862$		−	1284.31i		−	0.0507468i
$863$			2753.12i			0.108595i	0.998525	+	0.0542975i	$0.0172919\pi$
$863$			2753.12i			0.108595i	−0.998525	+	0.0542975i	$0.982708\pi$
$864$	−1710.52			−0.0673529
$865$	−7398.25	+	27114.7i	−0.290807	+	1.06581i
$866$	−4672.65			−0.183352
$867$		−	32499.7i		−	1.27306i
$868$		0			0
$869$	−42206.4			−1.64759
$870$	−19715.1	−	5379.25i	−0.768279	−	0.209625i
$871$	−29341.9			−1.14146
$872$			6764.70i			0.262708i
$873$		−	6377.36i		−	0.247240i
$874$	9895.38			0.382971
$875$		0			0
$876$	20198.8			0.779056
$877$		−	45447.4i		−	1.74989i	−0.484226	−	0.874943i	$-0.660899\pi$
$877$		−	45447.4i		−	1.74989i	0.484226	−	0.874943i	$-0.339101\pi$
$878$			17861.7i			0.686564i
$879$	−8290.69			−0.318132
$880$	11943.9	+	3258.90i	0.457534	+	0.124838i
$881$	−41341.0			−1.58095			−0.790473	−	0.612497i	$-0.790165\pi$
$881$	−41341.0			−1.58095			−0.790473	+	0.612497i	$0.790165\pi$
$882$		0			0
$883$			24941.7i			0.950572i	0.879831	+	0.475286i	$0.157655\pi$
$883$			24941.7i			0.950572i	−0.879831	+	0.475286i	$0.842345\pi$
$884$	1283.60			0.0488373
$885$	4214.12	−	15444.8i	0.160063	−	0.586635i
$886$	14224.6			0.539373
$887$			14450.7i			0.547022i	0.961869	+	0.273511i	$0.0881850\pi$
$887$			14450.7i			0.547022i	−0.961869	+	0.273511i	$0.911815\pi$
$888$		−	15471.9i		−	0.584690i
$889$		0			0
$890$	−4330.04	+	15869.7i	−0.163082	+	0.597700i
$891$	−60873.4			−2.28882
$892$			19281.8i			0.723771i
$893$		−	30549.4i		−	1.14479i
$894$	9656.18			0.361243
$895$	−10686.0	−	2915.68i	−0.399100	−	0.108894i
$896$		0			0
$897$			12846.0i			0.478165i
$898$		−	9017.81i		−	0.335109i
$899$	21615.2			0.801899
$900$	8239.42	+	4857.91i	0.305164	+	0.179922i
$901$	−4013.15			−0.148388
$902$			20676.4i			0.763247i
$903$		0			0
$904$	7053.69			0.259516
$905$	19168.1	+	5230.02i	0.704055	+	0.192101i
$906$	−23622.2			−0.866220
$907$		−	7808.12i		−	0.285848i	−0.989734	−	0.142924i	$-0.954350\pi$
$907$		−	7808.12i		−	0.285848i	0.989734	−	0.142924i	$-0.0456505\pi$
$908$		−	20000.2i		−	0.730980i
$909$	57.5011			0.00209812
$910$		0			0
$911$	−17340.9			−0.630659			−0.315330	−	0.948982i	$-0.602115\pi$
$911$	−17340.9			−0.630659			−0.315330	+	0.948982i	$0.602115\pi$
$912$		−	8065.33i		−	0.292840i
$913$		−	79588.2i		−	2.88498i
$914$	4096.49			0.148249
$915$	−11735.5	+	43010.7i	−0.424002	+	1.55398i
$916$	25252.1			0.910867
$917$		0			0
$918$		−	1209.19i		−	0.0434739i
$919$	−3716.76			−0.133411			−0.0667055	−	0.997773i	$-0.521249\pi$
$919$	−3716.76			−0.133411			−0.0667055	+	0.997773i	$0.521249\pi$
$920$	−5752.33	−	1569.52i	−0.206140	−	0.0562452i
$921$	42068.2			1.50510
$922$		−	18015.1i		−	0.643488i
$923$		−	29309.0i		−	1.04520i
$924$		0			0
$925$	18077.7	−	30661.3i	0.642585	−	1.08988i
$926$	6032.34			0.214077
$927$		−	14284.7i		−	0.506117i
$928$		−	4305.91i		−	0.152315i
$929$	−19318.5			−0.682261			−0.341131	−	0.940016i	$-0.610810\pi$
$929$	−19318.5			−0.682261			−0.341131	+	0.940016i	$0.610810\pi$
$930$	−23535.7	−	6421.73i	−0.829857	−	0.226427i
$931$		0			0
$932$		−	18791.1i		−	0.660433i
$933$		−	35864.8i		−	1.25848i
$934$	18365.4			0.643398
$935$	−2303.76	+	8443.32i	−0.0805786	+	0.295322i
$936$	4341.95			0.151625
$937$		−	19563.7i		−	0.682090i	−0.940047	−	0.341045i	$-0.889219\pi$
$937$		−	19563.7i		−	0.682090i	0.940047	−	0.341045i	$-0.110781\pi$
$938$		0			0
$939$	52661.5			1.83019
$940$	−4845.49	+	17758.8i	−0.168130	+	0.616200i
$941$	44457.2			1.54013			0.770065	−	0.637966i	$-0.220224\pi$
$941$	44457.2			1.54013			0.770065	+	0.637966i	$0.220224\pi$
$942$			48237.8i			1.66844i
$943$		−	9957.99i		−	0.343878i
$944$	3373.26			0.116303
$945$		0			0
$946$	71136.8			2.44488
$947$			32366.4i			1.11063i	0.831640	+	0.555316i	$0.187403\pi$
$947$			32366.4i			1.11063i	−0.831640	+	0.555316i	$0.812597\pi$
$948$		−	16567.8i		−	0.567613i
$949$	21094.0			0.721538
$950$	9423.68	−	15983.3i	0.321836	−	0.545861i
$951$	−1444.84			−0.0492661
$952$		0			0
$953$		−	38984.4i		−	1.32511i	−0.749013	−	0.662555i	$-0.769472\pi$
$953$		−	38984.4i		−	1.32511i	0.749013	−	0.662555i	$-0.230528\pi$
$954$	−13575.0			−0.460698
$955$	25203.9	+	6876.87i	0.854008	+	0.233016i
$956$	16604.8			0.561753
$957$		−	63251.4i		−	2.13650i
$958$			38670.5i			1.30416i
$959$		0			0
$960$	−1279.25	+	4688.49i	−0.0430081	+	0.157625i
$961$	−3986.86			−0.133828
$962$		−	16157.7i		−	0.541522i
$963$			14750.1i			0.493578i
$964$	9805.74			0.327616
$965$	2356.71	−	8637.37i	0.0786167	−	0.288132i
$966$		0			0
$967$		−	9949.53i		−	0.330874i	−0.986220	−	0.165437i	$-0.947097\pi$
$967$		−	9949.53i		−	0.330874i	0.986220	−	0.165437i	$-0.0529035\pi$
$968$			27671.4i			0.918795i
$969$	5701.49			0.189018
$970$	7191.56	+	1962.22i	0.238049	+	0.0649515i
$971$	40427.1			1.33612			0.668058	−	0.744110i	$-0.267126\pi$
$971$	40427.1			1.33612			0.668058	+	0.744110i	$0.267126\pi$
$972$		−	18122.4i		−	0.598021i
$973$		0			0
$974$	−19409.8			−0.638531
$975$	20749.2	+	12233.6i	0.681545	+	0.401834i
$976$	−9393.83			−0.308083
$977$			37619.1i			1.23187i	0.787796	+	0.615937i	$0.211222\pi$
$977$			37619.1i			1.23187i	−0.787796	+	0.615937i	$0.788778\pi$
$978$		−	33228.6i		−	1.08644i
$979$	−50914.4			−1.66213
$980$		0			0
$981$	−16175.9			−0.526460
$982$			4568.10i			0.148446i
$983$		−	8270.45i		−	0.268348i	−0.990958	−	0.134174i	$-0.957162\pi$
$983$		−	8270.45i		−	0.268348i	0.990958	−	0.134174i	$-0.0428381\pi$
$984$	−8116.36			−0.262947
$985$	6381.08	−	23386.8i	0.206414	−	0.756512i
$986$	3043.90			0.0983140
$987$		0			0
$988$		−	8422.79i		−	0.271219i
$989$	−34260.3			−1.10153
$990$	−7792.76	+	28560.6i	−0.250172	+	0.916884i
$991$	−7181.21			−0.230190			−0.115095	−	0.993354i	$-0.536717\pi$
$991$	−7181.21			−0.230190			−0.115095	+	0.993354i	$0.536717\pi$
$992$		−	5140.37i		−	0.164523i
$993$			81698.3i			2.61089i
$994$		0			0
$995$	17537.9	+	4785.22i	0.558784	+	0.152464i
$996$	31241.7			0.993907
$997$			11574.8i			0.367680i	0.982956	+	0.183840i	$0.0588528\pi$
$997$			11574.8i			0.367680i	−0.982956	+	0.183840i	$0.941147\pi$
$998$			13603.9i			0.431486i
$999$	−15220.9			−0.482051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.g.99.3	✓	20
5.2	odd	4		2450.4.a.dc.1.3		10
5.3	odd	4		2450.4.a.db.1.8		10
5.4	even	2	inner	490.4.c.g.99.18	yes	20
7.6	odd	2	inner	490.4.c.g.99.8	yes	20
35.13	even	4		2450.4.a.db.1.3		10
35.27	even	4		2450.4.a.dc.1.8		10
35.34	odd	2	inner	490.4.c.g.99.13	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.c.g.99.3	✓	20	1.1	even	1	trivial
490.4.c.g.99.8	yes	20	7.6	odd	2	inner
490.4.c.g.99.13	yes	20	35.34	odd	2	inner
490.4.c.g.99.18	yes	20	5.4	even	2	inner
2450.4.a.db.1.3		10	35.13	even	4
2450.4.a.db.1.8		10	5.3	odd	4
2450.4.a.dc.1.3		10	5.2	odd	4
2450.4.a.dc.1.8		10	35.27	even	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)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -6.79189i q^{3} -4.00000 q^{4} +(10.7861 + 2.94297i) q^{5} -13.5838 q^{6} +8.00000i q^{8} -19.1298 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -6.79189i q^{3} -4.00000 q^{4} +(10.7861 + 2.94297i) q^{5} -13.5838 q^{6} +8.00000i q^{8} -19.1298 q^{9} +(5.88595 - 21.5721i) q^{10} +69.2093 q^{11} +27.1676i q^{12} +28.3716i q^{13} +(19.9884 - 73.2577i) q^{15} +16.0000 q^{16} +11.3106i q^{17} +38.2596i q^{18} +74.2184 q^{19} +(-43.1442 - 11.7719i) q^{20} -138.419i q^{22} +66.6640i q^{23} +54.3351 q^{24} +(107.678 + 63.4861i) q^{25} +56.7433 q^{26} -53.4536i q^{27} +134.560 q^{29} +(-146.515 - 39.9767i) q^{30} +160.637 q^{31} -32.0000i q^{32} -470.062i q^{33} +22.6212 q^{34} +76.5192 q^{36} -284.750i q^{37} -148.437i q^{38} +192.697 q^{39} +(-23.5438 + 86.2884i) q^{40} -149.376 q^{41} +513.925i q^{43} -276.837 q^{44} +(-206.335 - 56.2985i) q^{45} +133.328 q^{46} -411.615i q^{47} -108.670i q^{48} +(126.972 - 215.356i) q^{50} +76.8204 q^{51} -113.487i q^{52} +354.813i q^{53} -106.907 q^{54} +(746.495 + 203.681i) q^{55} -504.083i q^{57} -269.119i q^{58} +210.828 q^{59} +(-79.9534 + 293.031i) q^{60} -587.114 q^{61} -321.273i q^{62} -64.0000 q^{64} +(-83.4970 + 306.018i) q^{65} -940.124 q^{66} +1034.20i q^{67} -45.2424i q^{68} +452.774 q^{69} -1033.04 q^{71} -153.038i q^{72} -743.489i q^{73} -569.500 q^{74} +(431.191 - 731.336i) q^{75} -296.874 q^{76} -385.394i q^{78} -609.837 q^{79} +(172.577 + 47.0876i) q^{80} -879.555 q^{81} +298.752i q^{82} -1149.96i q^{83} +(-33.2868 + 121.997i) q^{85} +1027.85 q^{86} -913.914i q^{87} +553.675i q^{88} -735.658 q^{89} +(-112.597 + 412.670i) q^{90} -266.656i q^{92} -1091.03i q^{93} -823.230 q^{94} +(800.523 + 218.423i) q^{95} -217.341 q^{96} +333.373i q^{97} -1323.96 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) \) 20 * q - 80 * q^4 - 316 * q^9	\( 20 q - 80 q^{4} - 316 q^{9} + 104 q^{11} - 360 q^{15} + 320 q^{16} - 440 q^{25} - 216 q^{29} + 224 q^{30} + 1264 q^{36} - 504 q^{39} - 416 q^{44} + 1600 q^{46} + 952 q^{50} - 296 q^{51} + 1440 q^{60} - 1280 q^{64} + 2732 q^{65} - 1872 q^{71} - 5968 q^{74} - 6424 q^{79} + 2020 q^{81} + 428 q^{85} + 3616 q^{86} + 3568 q^{95} + 624 q^{99}+O(q^{100}) \) 20 * q - 80 * q^4 - 316 * q^9 + 104 * q^11 - 360 * q^15 + 320 * q^16 - 440 * q^25 - 216 * q^29 + 224 * q^30 + 1264 * q^36 - 504 * q^39 - 416 * q^44 + 1600 * q^46 + 952 * q^50 - 296 * q^51 + 1440 * q^60 - 1280 * q^64 + 2732 * q^65 - 1872 * q^71 - 5968 * q^74 - 6424 * q^79 + 2020 * q^81 + 428 * q^85 + 3616 * q^86 + 3568 * q^95 + 624 * q^99

Introduction

L-functions

Modular forms

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