LMFDB - Embedded newform 490.4.c.f.99.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 185x^{10} + 12748x^{8} + 405460x^{6} + 5908496x^{4} + 33016000x^{2} + 60840000 $ x^12 + 185x^10 + 12748x^8 + 405460x^6 + 5908496x^4 + 33016000*x^2 + 60840000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.5
Root			$5.44232i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.f.99.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +6.44232i q^{3} -4.00000 q^{4} +(-6.24768 + 9.27181i) q^{5} +12.8846 q^{6} +8.00000i q^{8} -14.5035 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +6.44232i q^{3} -4.00000 q^{4} +(-6.24768 + 9.27181i) q^{5} +12.8846 q^{6} +8.00000i q^{8} -14.5035 q^{9} +(18.5436 + 12.4954i) q^{10} +48.3846 q^{11} -25.7693i q^{12} +93.4871i q^{13} +(-59.7320 - 40.2496i) q^{15} +16.0000 q^{16} +20.2793i q^{17} +29.0071i q^{18} +31.0581 q^{19} +(24.9907 - 37.0872i) q^{20} -96.7692i q^{22} +21.0487i q^{23} -51.5386 q^{24} +(-46.9329 - 115.855i) q^{25} +186.974 q^{26} +80.5063i q^{27} -69.5116 q^{29} +(-80.4992 + 119.464i) q^{30} +161.116 q^{31} -32.0000i q^{32} +311.709i q^{33} +40.5585 q^{34} +58.0141 q^{36} +162.582i q^{37} -62.1162i q^{38} -602.274 q^{39} +(-74.1745 - 49.9815i) q^{40} -365.073 q^{41} -254.518i q^{43} -193.538 q^{44} +(90.6134 - 134.474i) q^{45} +42.0975 q^{46} -468.802i q^{47} +103.077i q^{48} +(-231.709 + 93.8658i) q^{50} -130.646 q^{51} -373.949i q^{52} +587.150i q^{53} +161.013 q^{54} +(-302.292 + 448.613i) q^{55} +200.086i q^{57} +139.023i q^{58} -536.945 q^{59} +(238.928 + 160.998i) q^{60} -625.824 q^{61} -322.232i q^{62} -64.0000 q^{64} +(-866.795 - 584.078i) q^{65} +623.419 q^{66} -123.074i q^{67} -81.1171i q^{68} -135.603 q^{69} +210.060 q^{71} -116.028i q^{72} -141.783i q^{73} +325.164 q^{74} +(746.373 - 302.357i) q^{75} -124.232 q^{76} +1204.55i q^{78} -513.424 q^{79} +(-99.9629 + 148.349i) q^{80} -910.243 q^{81} +730.146i q^{82} -117.376i q^{83} +(-188.025 - 126.698i) q^{85} -509.037 q^{86} -447.816i q^{87} +387.077i q^{88} +61.2589 q^{89} +(-268.948 - 181.227i) q^{90} -84.1950i q^{92} +1037.96i q^{93} -937.604 q^{94} +(-194.041 + 287.965i) q^{95} +206.154 q^{96} +436.654i q^{97} -701.748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9}+O(q^{10}) $ 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9	$ 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9} - 12 q^{10} + 62 q^{11} + 86 q^{15} + 192 q^{16} - 186 q^{19} - 32 q^{20} - 112 q^{24} - 126 q^{25} + 236 q^{26} - 338 q^{29} - 28 q^{30} + 652 q^{31} - 272 q^{34} + 248 q^{36} + 868 q^{39} + 48 q^{40} + 396 q^{41} - 248 q^{44} - 664 q^{45} - 376 q^{46} + 160 q^{50} + 1448 q^{51} - 1540 q^{54} + 298 q^{55} - 1336 q^{59} - 344 q^{60} + 314 q^{61} - 768 q^{64} - 1862 q^{65} + 1600 q^{66} + 90 q^{69} + 2216 q^{71} + 1012 q^{74} + 4550 q^{75} + 744 q^{76} + 1772 q^{79} + 128 q^{80} - 1228 q^{81} + 2282 q^{85} - 396 q^{86} - 6094 q^{89} + 100 q^{90} - 3604 q^{94} - 1166 q^{95} + 448 q^{96} - 8546 q^{99}+O(q^{100}) $ 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9 - 12 * q^10 + 62 * q^11 + 86 * q^15 + 192 * q^16 - 186 * q^19 - 32 * q^20 - 112 * q^24 - 126 * q^25 + 236 * q^26 - 338 * q^29 - 28 * q^30 + 652 * q^31 - 272 * q^34 + 248 * q^36 + 868 * q^39 + 48 * q^40 + 396 * q^41 - 248 * q^44 - 664 * q^45 - 376 * q^46 + 160 * q^50 + 1448 * q^51 - 1540 * q^54 + 298 * q^55 - 1336 * q^59 - 344 * q^60 + 314 * q^61 - 768 * q^64 - 1862 * q^65 + 1600 * q^66 + 90 * q^69 + 2216 * q^71 + 1012 * q^74 + 4550 * q^75 + 744 * q^76 + 1772 * q^79 + 128 * q^80 - 1228 * q^81 + 2282 * q^85 - 396 * q^86 - 6094 * q^89 + 100 * q^90 - 3604 * q^94 - 1166 * q^95 + 448 * q^96 - 8546 * 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
$3$			6.44232i			1.23983i	0.784671	+	0.619913i	$0.212832\pi$
$3$			6.44232i			1.23983i	−0.784671	+	0.619913i	$0.787168\pi$
$4$	−4.00000			−0.500000
$5$	−6.24768	+	9.27181i	−0.558810	+	0.829296i
$5$	−6.24768	+	9.27181i	−0.558810	+	0.829296i
$6$	12.8846			0.876689
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	−14.5035			−0.537168
$10$	18.5436	+	12.4954i	0.586401	+	0.395138i
$11$	48.3846			1.32623			0.663114	−	0.748518i	$-0.269234\pi$
$11$	48.3846			1.32623			0.663114	+	0.748518i	$0.269234\pi$
$12$		−	25.7693i		−	0.619913i
$13$			93.4871i			1.99451i	0.0740250	+	0.997256i	$0.476416\pi$
$13$			93.4871i			1.99451i	−0.0740250	+	0.997256i	$0.523584\pi$
$14$		0			0
$15$	−59.7320	−	40.2496i	−1.02818	−	0.692827i
$16$	16.0000			0.250000
$17$			20.2793i			0.289320i	0.989481	+	0.144660i	$0.0462089\pi$
$17$			20.2793i			0.289320i	−0.989481	+	0.144660i	$0.953791\pi$
$18$			29.0071i			0.379835i
$19$	31.0581			0.375011			0.187506	−	0.982264i	$-0.439960\pi$
$19$	31.0581			0.375011			0.187506	+	0.982264i	$0.439960\pi$
$20$	24.9907	−	37.0872i	0.279405	−	0.414648i
$21$		0			0
$22$		−	96.7692i		−	0.937785i
$23$			21.0487i			0.190825i	0.995438	+	0.0954123i	$0.0304170\pi$
$23$			21.0487i			0.190825i	−0.995438	+	0.0954123i	$0.969583\pi$
$24$	−51.5386			−0.438345
$25$	−46.9329	−	115.855i	−0.375463	−	0.926837i
$26$	186.974			1.41033
$27$			80.5063i			0.573831i
$28$		0			0
$29$	−69.5116			−0.445103			−0.222551	−	0.974921i	$-0.571438\pi$
$29$	−69.5116			−0.445103			−0.222551	+	0.974921i	$0.571438\pi$
$30$	−80.4992	+	119.464i	−0.489902	+	0.727035i
$31$	161.116			0.933462			0.466731	−	0.884399i	$-0.345432\pi$
$31$	161.116			0.933462			0.466731	+	0.884399i	$0.345432\pi$
$32$		−	32.0000i		−	0.176777i
$33$			311.709i			1.64429i
$34$	40.5585			0.204580
$35$		0			0
$36$	58.0141			0.268584
$37$			162.582i			0.722386i	0.932491	+	0.361193i	$0.117630\pi$
$37$			162.582i			0.722386i	−0.932491	+	0.361193i	$0.882370\pi$
$38$		−	62.1162i		−	0.265173i
$39$	−602.274			−2.47285
$40$	−74.1745	−	49.9815i	−0.293200	−	0.197569i
$41$	−365.073			−1.39060			−0.695302	−	0.718717i	$-0.744730\pi$
$41$	−365.073			−1.39060			−0.695302	+	0.718717i	$0.744730\pi$
$42$		0			0
$43$		−	254.518i		−	0.902644i	−0.892361	−	0.451322i	$-0.850953\pi$
$43$		−	254.518i		−	0.902644i	0.892361	−	0.451322i	$-0.149047\pi$
$44$	−193.538			−0.663114
$45$	90.6134	−	134.474i	0.300175	−	0.445471i
$46$	42.0975			0.134933
$47$		−	468.802i		−	1.45493i	−0.686144	−	0.727466i	$-0.740698\pi$
$47$		−	468.802i		−	1.45493i	0.686144	−	0.727466i	$-0.259302\pi$
$48$			103.077i			0.309956i
$49$		0			0
$50$	−231.709	+	93.8658i	−0.655373	+	0.265493i
$51$	−130.646			−0.358707
$52$		−	373.949i		−	0.997256i
$53$			587.150i			1.52172i	0.648915	+	0.760861i	$0.275223\pi$
$53$			587.150i			1.52172i	−0.648915	+	0.760861i	$0.724777\pi$
$54$	161.013			0.405760
$55$	−302.292	+	448.613i	−0.741109	+	1.09984i
$56$		0			0
$57$			200.086i			0.464949i
$58$			139.023i			0.314735i
$59$	−536.945			−1.18482			−0.592409	−	0.805637i	$-0.701823\pi$
$59$	−536.945			−1.18482			−0.592409	+	0.805637i	$0.701823\pi$
$60$	238.928	+	160.998i	0.514091	+	0.346413i
$61$	−625.824			−1.31358			−0.656791	−	0.754072i	$-0.728087\pi$
$61$	−625.824			−1.31358			−0.656791	+	0.754072i	$0.728087\pi$
$62$		−	322.232i		−	0.660057i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−866.795	−	584.078i	−1.65404	−	1.11455i
$66$	623.419			1.16269
$67$		−	123.074i		−	0.224416i	−0.993685	−	0.112208i	$-0.964208\pi$
$67$		−	123.074i		−	0.224416i	0.993685	−	0.112208i	$-0.0357922\pi$
$68$		−	81.1171i		−	0.144660i
$69$	−135.603			−0.236589
$70$		0			0
$71$	210.060			0.351121			0.175560	−	0.984469i	$-0.443826\pi$
$71$	210.060			0.351121			0.175560	+	0.984469i	$0.443826\pi$
$72$		−	116.028i		−	0.189917i
$73$		−	141.783i		−	0.227322i	−0.993520	−	0.113661i	$-0.963742\pi$
$73$		−	141.783i		−	0.227322i	0.993520	−	0.113661i	$-0.0362578\pi$
$74$	325.164			0.510804
$75$	746.373	−	302.357i	1.14912	−	0.465509i
$76$	−124.232			−0.187506
$77$		0			0
$78$			1204.55i			1.74857i
$79$	−513.424			−0.731198			−0.365599	−	0.930772i	$-0.619136\pi$
$79$	−513.424			−0.731198			−0.365599	+	0.930772i	$0.619136\pi$
$80$	−99.9629	+	148.349i	−0.139702	+	0.207324i
$81$	−910.243			−1.24862
$82$			730.146i			0.983306i
$83$		−	117.376i		−	0.155225i	−0.996984	−	0.0776125i	$-0.975270\pi$
$83$		−	117.376i		−	0.155225i	0.996984	−	0.0776125i	$-0.0247297\pi$
$84$		0			0
$85$	−188.025	−	126.698i	−0.239932	−	0.161675i
$86$	−509.037			−0.638266
$87$		−	447.816i		−	0.551850i
$88$			387.077i			0.468892i
$89$	61.2589			0.0729598			0.0364799	−	0.999334i	$-0.488386\pi$
$89$	61.2589			0.0729598			0.0364799	+	0.999334i	$0.488386\pi$
$90$	−268.948	−	181.227i	−0.314996	−	0.212255i
$91$		0			0
$92$		−	84.1950i		−	0.0954123i
$93$			1037.96i			1.15733i
$94$	−937.604			−1.02879
$95$	−194.041	+	287.965i	−0.209560	+	0.310995i
$96$	206.154			0.219172
$97$			436.654i			0.457067i	0.973536	+	0.228533i	$0.0733930\pi$
$97$			436.654i			0.457067i	−0.973536	+	0.228533i	$0.926607\pi$
$98$		0			0
$99$	−701.748			−0.712407
$100$	187.732	+	463.419i	0.187732	+	0.463419i
$101$	1768.21			1.74201			0.871007	−	0.491271i	$-0.163468\pi$
$101$	1768.21			1.74201			0.871007	+	0.491271i	$0.163468\pi$
$102$			261.291i			0.253644i
$103$		−	849.407i		−	0.812568i	−0.913747	−	0.406284i	$-0.866824\pi$
$103$		−	849.407i		−	0.812568i	0.913747	−	0.406284i	$-0.133176\pi$
$104$	−747.897			−0.705167
$105$		0			0
$106$	1174.30			1.07602
$107$			1282.58i			1.15880i	0.815044	+	0.579399i	$0.196713\pi$
$107$			1282.58i			1.15880i	−0.815044	+	0.579399i	$0.803287\pi$
$108$		−	322.025i		−	0.286916i
$109$	598.398			0.525836			0.262918	−	0.964818i	$-0.415315\pi$
$109$	598.398			0.525836			0.262918	+	0.964818i	$0.415315\pi$
$110$	897.226	+	604.583i	0.777701	+	0.524043i
$111$	−1047.40			−0.895633
$112$		0			0
$113$		−	860.218i		−	0.716128i	−0.933697	−	0.358064i	$-0.883437\pi$
$113$		−	860.218i		−	0.716128i	0.933697	−	0.358064i	$-0.116563\pi$
$114$	400.172			0.328768
$115$	−195.160	−	131.506i	−0.158250	−	0.106635i
$116$	278.046			0.222551
$117$		−	1355.89i		−	1.07139i
$118$			1073.89i			0.837793i
$119$		0			0
$120$	321.997	−	477.856i	0.244951	−	0.363517i
$121$	1010.07			0.758881
$122$			1251.65i			0.928843i
$123$		−	2351.92i		−	1.72411i
$124$	−644.465			−0.466731
$125$	1367.40	+	288.670i	0.978435	+	0.206555i
$126$		0			0
$127$			971.435i			0.678748i	0.940652	+	0.339374i	$0.110215\pi$
$127$			971.435i			0.678748i	−0.940652	+	0.339374i	$0.889785\pi$
$128$			128.000i			0.0883883i
$129$	1639.69			1.11912
$130$	−1168.16	+	1733.59i	−0.788108	+	1.16958i
$131$	149.593			0.0997713			0.0498856	−	0.998755i	$-0.484114\pi$
$131$	149.593			0.0997713			0.0498856	+	0.998755i	$0.484114\pi$
$132$		−	1246.84i		−	0.822146i
$133$		0			0
$134$	−246.147			−0.158686
$135$	−746.439	−	502.978i	−0.475876	−	0.320663i
$136$	−162.234			−0.102290
$137$		−	495.245i		−	0.308844i	−0.988005	−	0.154422i	$-0.950648\pi$
$137$		−	495.245i		−	0.308844i	0.988005	−	0.154422i	$-0.0493516\pi$
$138$			271.206i			0.167294i
$139$	466.520			0.284674			0.142337	−	0.989818i	$-0.454538\pi$
$139$	466.520			0.284674			0.142337	+	0.989818i	$0.454538\pi$
$140$		0			0
$141$	3020.17			1.80386
$142$		−	420.121i		−	0.248280i
$143$			4523.34i			2.64518i
$144$	−232.056			−0.134292
$145$	434.286	−	644.498i	0.248728	−	0.369122i
$146$	−283.567			−0.160741
$147$		0			0
$148$		−	650.327i		−	0.361193i
$149$	178.554			0.0981723			0.0490862	−	0.998795i	$-0.484369\pi$
$149$	178.554			0.0981723			0.0490862	+	0.998795i	$0.484369\pi$
$150$	−604.714	−	1492.75i	−0.329165	−	0.812548i
$151$	831.668			0.448213			0.224107	−	0.974565i	$-0.428054\pi$
$151$	831.668			0.448213			0.224107	+	0.974565i	$0.428054\pi$
$152$			248.465i			0.132587i
$153$		−	294.121i		−	0.155413i
$154$		0			0
$155$	−1006.60	+	1493.84i	−0.521628	+	0.774116i
$156$	2409.10			1.23642
$157$		−	167.697i		−	0.0852462i	−0.999091	−	0.0426231i	$-0.986429\pi$
$157$		−	167.697i		−	0.0852462i	0.999091	−	0.0426231i	$-0.0135715\pi$
$158$			1026.85i			0.517035i
$159$	−3782.61			−1.88667
$160$	296.698	+	199.926i	0.146600	+	0.0987845i
$161$		0			0
$162$			1820.49i			0.882907i
$163$			1612.09i			0.774655i	0.921942	+	0.387327i	$0.126602\pi$
$163$			1612.09i			0.774655i	−0.921942	+	0.387327i	$0.873398\pi$
$164$	1460.29			0.695302
$165$	−2890.11	−	1947.46i	−1.36360	−	0.918846i
$166$	−234.752			−0.109761
$167$			1590.69i			0.737073i	0.929613	+	0.368536i	$0.120141\pi$
$167$			1590.69i			0.737073i	−0.929613	+	0.368536i	$0.879859\pi$
$168$		0			0
$169$	−6542.84			−2.97808
$170$	−253.397	+	376.051i	−0.114321	+	0.169658i
$171$	−450.452			−0.201444
$172$			1018.07i			0.451322i
$173$			1742.41i			0.765739i	0.923802	+	0.382870i	$0.125064\pi$
$173$			1742.41i			0.765739i	−0.923802	+	0.382870i	$0.874936\pi$
$174$	−895.632			−0.390217
$175$		0			0
$176$	774.154			0.331557
$177$		−	3459.17i		−	1.46897i
$178$		−	122.518i		−	0.0515904i
$179$	2429.37			1.01441			0.507205	−	0.861825i	$-0.330679\pi$
$179$	2429.37			1.01441			0.507205	+	0.861825i	$0.330679\pi$
$180$	−362.454	+	537.896i	−0.150087	+	0.222735i
$181$	2628.61			1.07946			0.539732	−	0.841837i	$-0.318526\pi$
$181$	2628.61			1.07946			0.539732	+	0.841837i	$0.318526\pi$
$182$		0			0
$183$		−	4031.76i		−	1.62861i
$184$	−168.390			−0.0674667
$185$	−1507.43	−	1015.76i	−0.599072	−	0.403676i
$186$	2075.92			0.818356
$187$			981.204i			0.383705i
$188$			1875.21i			0.727466i
$189$		0			0
$190$	575.929	+	388.082i	0.219907	+	0.148181i
$191$	1124.82			0.426122			0.213061	−	0.977039i	$-0.431657\pi$
$191$	1124.82			0.426122			0.213061	+	0.977039i	$0.431657\pi$
$192$		−	412.309i		−	0.154978i
$193$		−	2216.08i		−	0.826514i	−0.910615	−	0.413257i	$-0.864391\pi$
$193$		−	2216.08i		−	0.826514i	0.910615	−	0.413257i	$-0.135609\pi$
$194$	873.308			0.323195
$195$	3762.82	−	5584.17i	1.38185	−	2.05072i
$196$		0			0
$197$		−	3125.56i		−	1.13039i	−0.824958	−	0.565194i	$-0.808801\pi$
$197$		−	3125.56i		−	1.13039i	0.824958	−	0.565194i	$-0.191199\pi$
$198$			1403.50i			0.503748i
$199$	−4539.34			−1.61701			−0.808506	−	0.588488i	$-0.799724\pi$
$199$	−4539.34			−1.61701			−0.808506	+	0.588488i	$0.799724\pi$
$200$	926.837	−	375.463i	0.327686	−	0.132746i
$201$	792.881			0.278236
$202$		−	3536.42i		−	1.23179i
$203$		0			0
$204$	522.582			0.179353
$205$	2280.86	−	3384.89i	0.777084	−	1.15322i
$206$	−1698.81			−0.574573
$207$		−	305.281i		−	0.102505i
$208$			1495.79i			0.498628i
$209$	1502.73			0.497350
$210$		0			0
$211$	2520.40			0.822331			0.411165	−	0.911561i	$-0.365122\pi$
$211$	2520.40			0.822331			0.411165	+	0.911561i	$0.365122\pi$
$212$		−	2348.60i		−	0.760861i
$213$			1353.28i			0.435329i
$214$	2565.15			0.819394
$215$	2359.85	+	1590.15i	0.748559	+	0.504406i
$216$	−644.051			−0.202880
$217$		0			0
$218$		−	1196.80i		−	0.371822i
$219$	913.415			0.281839
$220$	1209.17	−	1794.45i	0.370555	−	0.549918i
$221$	−1895.85			−0.577053
$222$			2094.81i			0.633308i
$223$			5800.58i			1.74186i	0.491405	+	0.870931i	$0.336484\pi$
$223$			5800.58i			1.74186i	−0.491405	+	0.870931i	$0.663516\pi$
$224$		0			0
$225$	680.693	+	1680.30i	0.201687	+	0.497867i
$226$	−1720.44			−0.506379
$227$		−	6626.47i		−	1.93751i	−0.248026	−	0.968753i	$-0.579782\pi$
$227$		−	6626.47i		−	1.93751i	0.248026	−	0.968753i	$-0.420218\pi$
$228$		−	800.345i		−	0.232474i
$229$	−507.845			−0.146547			−0.0732736	−	0.997312i	$-0.523345\pi$
$229$	−507.845			−0.146547			−0.0732736	+	0.997312i	$0.523345\pi$
$230$	−263.012	+	390.320i	−0.0754021	+	0.111900i
$231$		0			0
$232$		−	556.093i		−	0.157368i
$233$		−	6307.82i		−	1.77356i	−0.462193	−	0.886779i	$-0.652937\pi$
$233$		−	6307.82i		−	1.77356i	0.462193	−	0.886779i	$-0.347063\pi$
$234$	−2711.79			−0.757586
$235$	4346.64	+	2928.92i	1.20657	+	0.813030i
$236$	2147.78			0.592409
$237$		−	3307.64i		−	0.906559i
$238$		0			0
$239$	4615.12			1.24907			0.624535	−	0.780997i	$-0.285289\pi$
$239$	4615.12			1.24907			0.624535	+	0.780997i	$0.285289\pi$
$240$	−955.712	−	643.993i	−0.257046	−	0.173207i
$241$	1550.70			0.414480			0.207240	−	0.978290i	$-0.433552\pi$
$241$	1550.70			0.414480			0.207240	+	0.978290i	$0.433552\pi$
$242$		−	2020.14i		−	0.536610i
$243$		−	3690.41i		−	0.974238i
$244$	2503.30			0.656791
$245$		0			0
$246$	−4703.83			−1.21913
$247$			2903.53i			0.747965i
$248$			1288.93i			0.330029i
$249$	756.173			0.192452
$250$	577.340	−	2734.81i	0.146057	−	0.691858i
$251$	762.543			0.191758			0.0958790	−	0.995393i	$-0.469434\pi$
$251$	762.543			0.191758			0.0958790	+	0.995393i	$0.469434\pi$
$252$		0			0
$253$			1018.44i			0.253077i
$254$	1942.87			0.479947
$255$	816.232	−	1211.32i	0.200449	−	0.297474i
$256$	256.000			0.0625000
$257$		−	2302.36i		−	0.558822i	−0.960172	−	0.279411i	$-0.909861\pi$
$257$		−	2302.36i		−	0.558822i	0.960172	−	0.279411i	$-0.0901392\pi$
$258$		−	3279.38i		−	0.791338i
$259$		0			0
$260$	3467.18	+	2336.31i	0.827021	+	0.557277i
$261$	1008.16			0.239095
$262$		−	299.187i		−	0.0705490i
$263$		−	4833.50i		−	1.13326i	−0.823974	−	0.566628i	$-0.808248\pi$
$263$		−	4833.50i		−	1.13326i	0.823974	−	0.566628i	$-0.191752\pi$
$264$	−2493.67			−0.581345
$265$	−5443.94	−	3668.33i	−1.26196	−	0.850353i
$266$		0			0
$267$			394.649i			0.0904575i
$268$			492.295i			0.112208i
$269$	−4830.35			−1.09484			−0.547420	−	0.836858i	$-0.684390\pi$
$269$	−4830.35			−1.09484			−0.547420	+	0.836858i	$0.684390\pi$
$270$	−1005.96	+	1492.88i	−0.226743	+	0.336495i
$271$	−5950.37			−1.33380			−0.666899	−	0.745149i	$-0.732379\pi$
$271$	−5950.37			−1.33380			−0.666899	+	0.745149i	$0.732379\pi$
$272$			324.468i			0.0723301i
$273$		0			0
$274$	−990.491			−0.218386
$275$	−2270.83	−	5605.58i	−0.497950	−	1.22920i
$276$	542.411			0.118295
$277$			7668.90i			1.66346i	0.555177	+	0.831732i	$0.312651\pi$
$277$			7668.90i			1.66346i	−0.555177	+	0.831732i	$0.687349\pi$
$278$		−	933.040i		−	0.201295i
$279$	−2336.75			−0.501426
$280$		0			0
$281$	−6314.18			−1.34047			−0.670235	−	0.742149i	$-0.733807\pi$
$281$	−6314.18			−1.34047			−0.670235	+	0.742149i	$0.733807\pi$
$282$		−	6040.35i		−	1.27552i
$283$			6122.72i			1.28607i	0.765836	+	0.643035i	$0.222325\pi$
$283$			6122.72i			1.28607i	−0.765836	+	0.643035i	$0.777675\pi$
$284$	−840.242			−0.175560
$285$	−1855.16	−	1250.08i	−0.385580	−	0.259818i
$286$	9046.68			1.87042
$287$		0			0
$288$			464.113i			0.0949587i
$289$	4501.75			0.916294
$290$	−1289.00	−	868.573i	−0.261009	−	0.175877i
$291$	−2813.07			−0.566683
$292$			567.134i			0.113661i
$293$		−	1646.67i		−	0.328326i	−0.986433	−	0.164163i	$-0.947508\pi$
$293$		−	1646.67i		−	0.328326i	0.986433	−	0.164163i	$-0.0524923\pi$
$294$		0			0
$295$	3354.66	−	4978.45i	0.662088	−	0.982564i
$296$	−1300.65			−0.255402
$297$			3895.27i			0.761031i
$298$		−	357.107i		−	0.0694183i
$299$	−1967.79			−0.380602
$300$	−2985.49	+	1209.43i	−0.574558	+	0.232755i
$301$		0			0
$302$		−	1663.34i		−	0.316934i
$303$			11391.4i			2.15979i
$304$	496.929			0.0937528
$305$	3909.95	−	5802.52i	0.734043	−	1.08935i
$306$	−588.242			−0.109894
$307$			7890.42i			1.46687i	0.679758	+	0.733436i	$0.262085\pi$
$307$			7890.42i			1.46687i	−0.679758	+	0.733436i	$0.737915\pi$
$308$		0			0
$309$	5472.15			1.00744
$310$	2987.68	+	2013.21i	0.547383	+	0.368846i
$311$	−3436.98			−0.626667			−0.313333	−	0.949643i	$-0.601446\pi$
$311$	−3436.98			−0.626667			−0.313333	+	0.949643i	$0.601446\pi$
$312$		−	4818.19i		−	0.874284i
$313$			7209.81i			1.30199i	0.759082	+	0.650995i	$0.225648\pi$
$313$			7209.81i			1.30199i	−0.759082	+	0.650995i	$0.774352\pi$
$314$	−335.393			−0.0602782
$315$		0			0
$316$	2053.69			0.365599
$317$			885.804i			0.156945i	0.996916	+	0.0784727i	$0.0250043\pi$
$317$			885.804i			0.156945i	−0.996916	+	0.0784727i	$0.974996\pi$
$318$			7565.22i			1.33408i
$319$	−3363.29			−0.590308
$320$	399.852	−	593.396i	0.0698512	−	0.103662i
$321$	−8262.77			−1.43671
$322$		0			0
$323$			629.835i			0.108498i
$324$	3640.97			0.624309
$325$	10830.9	−	4387.62i	1.84859	−	0.748866i
$326$	3224.18			0.547764
$327$			3855.08i			0.651945i
$328$		−	2920.58i		−	0.491653i
$329$		0			0
$330$	−3894.92	+	5780.22i	−0.649722	+	0.964214i
$331$	−1766.18			−0.293288			−0.146644	−	0.989189i	$-0.546847\pi$
$331$	−1766.18			−0.293288			−0.146644	+	0.989189i	$0.546847\pi$
$332$			469.504i			0.0776125i
$333$		−	2358.01i		−	0.388042i
$334$	3181.38			0.521189
$335$	1141.12	+	768.925i	0.186107	+	0.125406i
$336$		0			0
$337$			7521.34i			1.21577i	0.794026	+	0.607883i	$0.207981\pi$
$337$			7521.34i			1.21577i	−0.794026	+	0.607883i	$0.792019\pi$
$338$			13085.7i			2.10582i
$339$	5541.80			0.887874
$340$	752.102	+	506.794i	0.119966	+	0.0808375i
$341$	7795.54			1.23798
$342$			900.904i			0.142442i
$343$		0			0
$344$	2036.15			0.319133
$345$	847.203	−	1257.28i	0.132208	−	0.196203i
$346$	3484.82			0.541459
$347$			4658.53i			0.720700i	0.932817	+	0.360350i	$0.117343\pi$
$347$			4658.53i			0.720700i	−0.932817	+	0.360350i	$0.882657\pi$
$348$			1791.26i			0.275925i
$349$	7198.15			1.10403			0.552017	−	0.833833i	$-0.313858\pi$
$349$	7198.15			1.10403			0.552017	+	0.833833i	$0.313858\pi$
$350$		0			0
$351$	−7526.30			−1.14451
$352$		−	1548.31i		−	0.234446i
$353$			3640.08i			0.548844i	0.961609	+	0.274422i	$0.0884865\pi$
$353$			3640.08i			0.548844i	−0.961609	+	0.274422i	$0.911514\pi$
$354$	−6918.34			−1.03872
$355$	−1312.39	+	1947.64i	−0.196210	+	0.291183i
$356$	−245.035			−0.0364799
$357$		0			0
$358$		−	4858.73i		−	0.717296i
$359$	5469.89			0.804150			0.402075	−	0.915607i	$-0.368289\pi$
$359$	5469.89			0.804150			0.402075	+	0.915607i	$0.368289\pi$
$360$	1075.79	+	724.908i	0.157498	+	0.106128i
$361$	−5894.40			−0.859367
$362$		−	5257.22i		−	0.763296i
$363$			6507.20i			0.940880i
$364$		0			0
$365$	1314.59	+	885.818i	0.188517	+	0.127030i
$366$	−8063.52			−1.15160
$367$		−	65.0871i		−	0.00925754i	−0.999989	−	0.00462877i	$-0.998527\pi$
$367$		−	65.0871i		−	0.00925754i	0.999989	−	0.00462877i	$-0.00147339\pi$
$368$			336.780i			0.0477062i
$369$	5294.84			0.746988
$370$	−2031.52	+	3014.85i	−0.285442	+	0.423608i
$371$		0			0
$372$		−	4151.85i		−	0.578665i
$373$			10153.4i			1.40944i	0.709484	+	0.704721i	$0.248928\pi$
$373$			10153.4i			1.40944i	−0.709484	+	0.704721i	$0.751072\pi$
$374$	1962.41			0.271320
$375$	−1859.71	+	8809.26i	−0.256093	+	1.21309i
$376$	3750.41			0.514396
$377$		−	6498.44i		−	0.887763i
$378$		0			0
$379$	−1453.96			−0.197057			−0.0985287	−	0.995134i	$-0.531414\pi$
$379$	−1453.96			−0.197057			−0.0985287	+	0.995134i	$0.531414\pi$
$380$	776.164	−	1151.86i	0.104780	−	0.155498i
$381$	−6258.30			−0.841529
$382$		−	2249.65i		−	0.301314i
$383$		−	577.301i		−	0.0770201i	−0.999258	−	0.0385101i	$-0.987739\pi$
$383$		−	577.301i		−	0.0770201i	0.999258	−	0.0385101i	$-0.0122612\pi$
$384$	−824.617			−0.109586
$385$		0			0
$386$	−4432.16			−0.584433
$387$			3691.41i			0.484871i
$388$		−	1746.62i		−	0.228533i
$389$	2071.00			0.269933			0.134966	−	0.990850i	$-0.456907\pi$
$389$	2071.00			0.269933			0.134966	+	0.990850i	$0.456907\pi$
$390$	−11168.3	−	7525.64i	−1.45008	−	0.977117i
$391$	−426.853			−0.0552094
$392$		0			0
$393$			963.729i			0.123699i
$394$	−6251.11			−0.799306
$395$	3207.71	−	4760.37i	0.408601	−	0.606380i
$396$	2806.99			0.356203
$397$		−	5033.42i		−	0.636322i	−0.948037	−	0.318161i	$-0.896935\pi$
$397$		−	5033.42i		−	0.636322i	0.948037	−	0.318161i	$-0.103065\pi$
$398$			9078.68i			1.14340i
$399$		0			0
$400$	−750.927	−	1853.67i	−0.0938658	−	0.231709i
$401$	−4946.88			−0.616048			−0.308024	−	0.951379i	$-0.599668\pi$
$401$	−4946.88			−0.616048			−0.308024	+	0.951379i	$0.599668\pi$
$402$		−	1585.76i		−	0.196743i
$403$			15062.3i			1.86180i
$404$	−7072.83			−0.871007
$405$	5686.91	−	8439.60i	0.697740	−	1.03547i
$406$		0			0
$407$			7866.46i			0.958049i
$408$		−	1045.16i		−	0.126822i
$409$	9389.84			1.13520			0.567601	−	0.823304i	$-0.307872\pi$
$409$	9389.84			1.13520			0.567601	+	0.823304i	$0.307872\pi$
$410$	−6769.77	−	4561.72i	−0.815452	−	0.549481i
$411$	3190.53			0.382913
$412$			3397.63i			0.406284i
$413$		0			0
$414$	−610.562			−0.0724819
$415$	1088.29	+	733.327i	0.128727	+	0.0867413i
$416$	2991.59			0.352583
$417$			3005.47i			0.352946i
$418$		−	3005.47i		−	0.351680i
$419$	−8423.77			−0.982167			−0.491084	−	0.871112i	$-0.663399\pi$
$419$	−8423.77			−0.982167			−0.491084	+	0.871112i	$0.663399\pi$
$420$		0			0
$421$	5680.15			0.657562			0.328781	−	0.944406i	$-0.393362\pi$
$421$	5680.15			0.657562			0.328781	+	0.944406i	$0.393362\pi$
$422$		−	5040.81i		−	0.581476i
$423$			6799.28i			0.781542i
$424$	−4697.20			−0.538010
$425$	2349.45	−	951.765i	0.268153	−	0.108629i
$426$	2706.55			0.307824
$427$		0			0
$428$		−	5130.31i		−	0.579399i
$429$	−29140.8			−3.27956
$430$	3180.30	−	4719.69i	0.356669	−	0.529311i
$431$	12348.4			1.38005			0.690023	−	0.723787i	$-0.257600\pi$
$431$	12348.4			1.38005			0.690023	+	0.723787i	$0.257600\pi$
$432$			1288.10i			0.143458i
$433$			9031.93i			1.00242i	0.865326	+	0.501209i	$0.167111\pi$
$433$			9031.93i			1.00242i	−0.865326	+	0.501209i	$0.832889\pi$
$434$		0			0
$435$	4152.07	+	2797.81i	0.457647	+	0.308379i
$436$	−2393.59			−0.262918
$437$			653.734i			0.0715614i
$438$		−	1826.83i		−	0.199291i
$439$	10657.4			1.15866			0.579329	−	0.815094i	$-0.303315\pi$
$439$	10657.4			1.15866			0.579329	+	0.815094i	$0.303315\pi$
$440$	−3588.90	−	2418.33i	−0.388851	−	0.262022i
$441$		0			0
$442$			3791.70i			0.408038i
$443$		−	901.320i		−	0.0966660i	−0.998831	−	0.0483330i	$-0.984609\pi$
$443$		−	901.320i		−	0.0966660i	0.998831	−	0.0483330i	$-0.0153909\pi$
$444$	4189.62			0.447816
$445$	−382.726	+	567.980i	−0.0407707	+	0.0605053i
$446$	11601.2			1.23168
$447$			1150.30i			0.121717i
$448$		0			0
$449$	7771.88			0.816877			0.408438	−	0.912786i	$-0.366074\pi$
$449$	7771.88			0.816877			0.408438	+	0.912786i	$0.366074\pi$
$450$	3360.60	−	1361.39i	0.352045	−	0.142614i
$451$	−17663.9			−1.84426
$452$			3440.87i			0.358064i
$453$			5357.87i			0.555706i
$454$	−13252.9			−1.37002
$455$		0			0
$456$	−1600.69			−0.164384
$457$		−	2760.35i		−	0.282547i	−0.989971	−	0.141273i	$-0.954880\pi$
$457$		−	2760.35i		−	0.282547i	0.989971	−	0.141273i	$-0.0451196\pi$
$458$			1015.69i			0.103625i
$459$	−1632.61			−0.166021
$460$	780.640	+	526.024i	0.0791250	+	0.0533173i
$461$	−16482.3			−1.66520			−0.832602	−	0.553872i	$-0.813150\pi$
$461$	−16482.3			−1.66520			−0.832602	+	0.553872i	$0.813150\pi$
$462$		0			0
$463$			9949.16i			0.998653i	0.866414	+	0.499327i	$0.166419\pi$
$463$			9949.16i			0.998653i	−0.866414	+	0.499327i	$0.833581\pi$
$464$	−1112.19			−0.111276
$465$	−9623.79	−	6484.86i	−0.959769	−	0.646727i
$466$	−12615.6			−1.25410
$467$		−	2101.55i		−	0.208240i	−0.994565	−	0.104120i	$-0.966797\pi$
$467$		−	2101.55i		−	0.208240i	0.994565	−	0.104120i	$-0.0332027\pi$
$468$			5423.57i			0.535694i
$469$		0			0
$470$	5857.85	−	8693.28i	0.574899	−	0.853173i
$471$	1080.36			0.105690
$472$		−	4295.56i		−	0.418896i
$473$		−	12314.8i		−	1.19711i
$474$	−6615.28			−0.641034
$475$	−1457.65	−	3598.22i	−0.140803	−	0.347574i
$476$		0			0
$477$		−	8515.74i		−	0.817420i
$478$		−	9230.25i		−	0.883225i
$479$	8009.97			0.764060			0.382030	−	0.924150i	$-0.375225\pi$
$479$	8009.97			0.764060			0.382030	+	0.924150i	$0.375225\pi$
$480$	−1287.99	+	1911.42i	−0.122476	+	0.181759i
$481$	−15199.3			−1.44081
$482$		−	3101.41i		−	0.293082i
$483$		0			0
$484$	−4040.28			−0.379441
$485$	−4048.57	−	2728.08i	−0.379044	−	0.255413i
$486$	−7380.82			−0.688890
$487$		−	5382.59i		−	0.500839i	−0.968137	−	0.250420i	$-0.919431\pi$
$487$		−	5382.59i		−	0.500839i	0.968137	−	0.250420i	$-0.0805685\pi$
$488$		−	5006.59i		−	0.464422i
$489$	−10385.6			−0.960437
$490$		0			0
$491$	−3456.93			−0.317737			−0.158869	−	0.987300i	$-0.550785\pi$
$491$	−3456.93			−0.317737			−0.158869	+	0.987300i	$0.550785\pi$
$492$			9407.67i			0.862054i
$493$		−	1409.64i		−	0.128777i
$494$	5807.06			0.528891
$495$	4384.30	−	6506.47i	0.398100	−	0.590796i
$496$	2577.86			0.233365
$497$		0			0
$498$		−	1512.35i		−	0.136084i
$499$	12098.2			1.08535			0.542674	−	0.839943i	$-0.317412\pi$
$499$	12098.2			1.08535			0.542674	+	0.839943i	$0.317412\pi$
$500$	−5469.62	−	1154.68i	−0.489217	−	0.103278i
$501$	−10247.7			−0.913842
$502$		−	1525.09i		−	0.135593i
$503$			1508.10i			0.133684i	0.997764	+	0.0668418i	$0.0212923\pi$
$503$			1508.10i			0.133684i	−0.997764	+	0.0668418i	$0.978708\pi$
$504$		0			0
$505$	−11047.2	+	16394.5i	−0.973454	+	1.44464i
$506$	2036.87			0.178952
$507$		−	42151.1i		−	3.69230i
$508$		−	3885.74i		−	0.339374i
$509$	10363.5			0.902460			0.451230	−	0.892408i	$-0.350985\pi$
$509$	10363.5			0.902460			0.451230	+	0.892408i	$0.350985\pi$
$510$	−2422.64	−	1632.46i	−0.210346	−	0.141739i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$			2500.37i			0.215193i
$514$	−4604.72			−0.395147
$515$	7875.54	+	5306.82i	0.673860	+	0.454071i
$516$	−6558.76			−0.559561
$517$		−	22682.8i		−	1.92957i
$518$		0			0
$519$	−11225.2			−0.949383
$520$	4672.62	−	6934.36i	0.394054	−	0.584792i
$521$	4650.70			0.391077			0.195538	−	0.980696i	$-0.437355\pi$
$521$	4650.70			0.391077			0.195538	+	0.980696i	$0.437355\pi$
$522$		−	2016.33i		−	0.169066i
$523$			6457.71i			0.539916i	0.962872	+	0.269958i	$0.0870098\pi$
$523$			6457.71i			0.539916i	−0.962872	+	0.269958i	$0.912990\pi$
$524$	−598.374			−0.0498856
$525$		0			0
$526$	−9667.00			−0.801333
$527$			3267.32i			0.270069i
$528$			4987.35i			0.411073i
$529$	11724.0			0.963586
$530$	−7336.65	+	10887.9i	−0.601290	+	0.892339i
$531$	7787.59			0.636446
$532$		0			0
$533$		−	34129.6i		−	2.77358i
$534$	789.299			0.0639631
$535$	−11891.8	−	8013.13i	−0.960986	−	0.647548i
$536$	984.590			0.0793429
$537$			15650.8i			1.25769i
$538$			9660.70i			0.774168i
$539$		0			0
$540$	2985.76	+	2011.91i	0.237938	+	0.160331i
$541$	−23030.2			−1.83021			−0.915106	−	0.403214i	$-0.867893\pi$
$541$	−23030.2			−1.83021			−0.915106	+	0.403214i	$0.867893\pi$
$542$			11900.7i			0.943137i
$543$			16934.4i			1.33835i
$544$	648.936			0.0511451
$545$	−3738.60	+	5548.24i	−0.293842	+	0.436074i
$546$		0			0
$547$			6553.72i			0.512280i	0.966640	+	0.256140i	$0.0824508\pi$
$547$			6553.72i			0.512280i	−0.966640	+	0.256140i	$0.917549\pi$
$548$			1980.98i			0.154422i
$549$	9076.66			0.705614
$550$	−11211.2	+	4541.66i	−0.869174	+	0.352104i
$551$	−2158.90			−0.166919
$552$		−	1084.82i		−	0.0836469i
$553$		0			0
$554$	15337.8			1.17625
$555$	6543.85	−	9711.33i	0.500488	−	0.742745i
$556$	−1866.08			−0.142337
$557$		−	5254.73i		−	0.399731i	−0.979823	−	0.199865i	$-0.935949\pi$
$557$		−	5254.73i		−	0.399731i	0.979823	−	0.199865i	$-0.0640505\pi$
$558$			4673.51i			0.354561i
$559$	23794.2			1.80034
$560$		0			0
$561$	−6321.24			−0.475727
$562$			12628.4i			0.947856i
$563$			9759.11i			0.730546i	0.930900	+	0.365273i	$0.119024\pi$
$563$			9759.11i			0.730546i	−0.930900	+	0.365273i	$0.880976\pi$
$564$	−12080.7			−0.901931
$565$	7975.78	+	5374.37i	0.593882	+	0.400179i
$566$	12245.4			0.909389
$567$		0			0
$568$			1680.48i			0.124140i
$569$	−4063.44			−0.299382			−0.149691	−	0.988733i	$-0.547828\pi$
$569$	−4063.44			−0.299382			−0.149691	+	0.988733i	$0.547828\pi$
$570$	−2500.15	+	3710.32i	−0.183719	+	0.272646i
$571$	−23907.0			−1.75215			−0.876075	−	0.482175i	$-0.839847\pi$
$571$	−23907.0			−1.75215			−0.876075	+	0.482175i	$0.839847\pi$
$572$		−	18093.4i		−	1.32259i
$573$			7246.48i			0.528317i
$574$		0			0
$575$	2438.60	−	987.879i	0.176863	−	0.0716477i
$576$	928.226			0.0671460
$577$			15145.4i			1.09274i	0.837545	+	0.546369i	$0.183990\pi$
$577$			15145.4i			1.09274i	−0.837545	+	0.546369i	$0.816010\pi$
$578$		−	9003.50i		−	0.647918i
$579$	14276.7			1.02473
$580$	−1737.15	+	2577.99i	−0.124364	+	0.184561i
$581$		0			0
$582$			5626.13i			0.400706i
$583$			28409.0i			2.01815i
$584$	1134.27			0.0803704
$585$	12571.6	+	8471.19i	0.888498	+	0.598702i
$586$	−3293.34			−0.232162
$587$			10865.9i			0.764025i	0.924157	+	0.382013i	$0.124769\pi$
$587$			10865.9i			0.764025i	−0.924157	+	0.382013i	$0.875231\pi$
$588$		0			0
$589$	5003.96			0.350059
$590$	−9956.90	−	6709.32i	−0.694778	−	0.468167i
$591$	20135.8			1.40149
$592$			2601.31i			0.180596i
$593$		−	4578.29i		−	0.317045i	−0.987355	−	0.158523i	$-0.949327\pi$
$593$		−	4578.29i		−	0.317045i	0.987355	−	0.158523i	$-0.0506731\pi$
$594$	7790.53			0.538130
$595$		0			0
$596$	−714.214			−0.0490862
$597$		−	29243.9i		−	2.00481i
$598$			3935.57i			0.269126i
$599$	20561.5			1.40254			0.701270	−	0.712896i	$-0.252617\pi$
$599$	20561.5			1.40254			0.701270	+	0.712896i	$0.252617\pi$
$600$	2418.86	+	5970.98i	0.164582	+	0.406274i
$601$	−1254.44			−0.0851406			−0.0425703	−	0.999093i	$-0.513555\pi$
$601$	−1254.44			−0.0851406			−0.0425703	+	0.999093i	$0.513555\pi$
$602$		0			0
$603$			1785.00i			0.120549i
$604$	−3326.67			−0.224107
$605$	−6310.60	+	9365.18i	−0.424070	+	0.629337i
$606$	22782.7			1.52720
$607$		−	10861.4i		−	0.726277i	−0.931735	−	0.363139i	$-0.881705\pi$
$607$		−	10861.4i		−	0.726277i	0.931735	−	0.363139i	$-0.118295\pi$
$608$		−	993.859i		−	0.0662933i
$609$		0			0
$610$	−11605.0	−	7819.90i	−0.770286	−	0.519047i
$611$	43826.9			2.90188
$612$			1176.48i			0.0777067i
$613$		−	21385.7i		−	1.40907i	−0.709668	−	0.704536i	$-0.751155\pi$
$613$		−	21385.7i		−	1.40907i	0.709668	−	0.704536i	$-0.248845\pi$
$614$	15780.8			1.03724
$615$	21806.5	+	14694.0i	1.42980	+	0.963448i
$616$		0			0
$617$		−	11863.3i		−	0.774066i	−0.922066	−	0.387033i	$-0.873500\pi$
$617$		−	11863.3i		−	0.774066i	0.922066	−	0.387033i	$-0.126500\pi$
$618$		−	10944.3i		−	0.712370i
$619$	8098.60			0.525864			0.262932	−	0.964814i	$-0.415310\pi$
$619$	8098.60			0.525864			0.262932	+	0.964814i	$0.415310\pi$
$620$	4026.41	−	5975.35i	0.260814	−	0.387058i
$621$	−1694.56			−0.109501
$622$			6873.96i			0.443120i
$623$		0			0
$624$	−9636.39			−0.618212
$625$	−11219.6	+	10874.8i	−0.718055	+	0.695987i
$626$	14419.6			0.920645
$627$			9681.10i			0.616628i
$628$			670.787i			0.0426231i
$629$	−3297.04			−0.209001
$630$		0			0
$631$	28405.4			1.79208			0.896038	−	0.443977i	$-0.146433\pi$
$631$	28405.4			1.79208			0.896038	+	0.443977i	$0.146433\pi$
$632$		−	4107.39i		−	0.258518i
$633$			16237.3i			1.01955i
$634$	1771.61			0.110977
$635$	−9006.96	−	6069.22i	−0.562883	−	0.379291i
$636$	15130.4			0.943335
$637$		0			0
$638$			6726.58i			0.417411i
$639$	−3046.62			−0.188611
$640$	−1186.79	−	799.703i	−0.0733001	−	0.0493923i
$641$	4854.85			0.299150			0.149575	−	0.988750i	$-0.452209\pi$
$641$	4854.85			0.299150			0.149575	+	0.988750i	$0.452209\pi$
$642$			16525.5i			1.01591i
$643$		−	23838.8i		−	1.46207i	−0.682342	−	0.731033i	$-0.739038\pi$
$643$		−	23838.8i		−	1.46207i	0.682342	−	0.731033i	$-0.260962\pi$
$644$		0			0
$645$	−10244.3	+	15202.9i	−0.625376	+	0.928083i
$646$	1259.67			0.0767199
$647$			16912.8i			1.02768i	0.857886	+	0.513841i	$0.171778\pi$
$647$			16912.8i			1.02768i	−0.857886	+	0.513841i	$0.828222\pi$
$648$		−	7281.94i		−	0.441453i
$649$	−25979.9			−1.57134
$650$	−8775.25	−	21661.8i	−0.529529	−	1.30715i
$651$		0			0
$652$		−	6448.37i		−	0.387327i
$653$		−	14301.5i		−	0.857059i	−0.903528	−	0.428530i	$-0.859032\pi$
$653$		−	14301.5i		−	0.857059i	0.903528	−	0.428530i	$-0.140968\pi$
$654$	7710.15			0.460995
$655$	−934.612	+	1387.00i	−0.0557532	+	0.0827399i
$656$	−5841.17			−0.347651
$657$			2056.36i			0.122110i
$658$		0			0
$659$	8601.03			0.508420			0.254210	−	0.967149i	$-0.418185\pi$
$659$	8601.03			0.508420			0.254210	+	0.967149i	$0.418185\pi$
$660$	11560.4	+	7789.84i	0.681802	+	0.459423i
$661$	−794.288			−0.0467386			−0.0233693	−	0.999727i	$-0.507439\pi$
$661$	−794.288			−0.0467386			−0.0233693	+	0.999727i	$0.507439\pi$
$662$			3532.37i			0.207386i
$663$		−	12213.7i		−	0.715445i
$664$	939.007			0.0548803
$665$		0			0
$666$	−4716.02			−0.274387
$667$		−	1463.13i		−	0.0849366i
$668$		−	6362.75i		−	0.368536i
$669$	−37369.2			−2.15961
$670$	1537.85	−	2282.23i	0.0886752	−	0.131597i
$671$	−30280.3			−1.74211
$672$		0			0
$673$		−	3100.85i		−	0.177606i	−0.996049	−	0.0888031i	$-0.971696\pi$
$673$		−	3100.85i		−	0.177606i	0.996049	−	0.0888031i	$-0.0283042\pi$
$674$	15042.7			0.859677
$675$	9327.03	−	3778.40i	0.531848	−	0.215453i
$676$	26171.4			1.48904
$677$			3236.73i			0.183748i	0.995771	+	0.0918742i	$0.0292858\pi$
$677$			3236.73i			0.183748i	−0.995771	+	0.0918742i	$0.970714\pi$
$678$		−	11083.6i		−	0.627822i
$679$		0			0
$680$	1013.59	−	1504.20i	0.0571607	−	0.0848288i
$681$	42689.8			2.40217
$682$		−	15591.1i		−	0.875386i
$683$		−	9415.00i		−	0.527460i	−0.964597	−	0.263730i	$-0.915047\pi$
$683$		−	9415.00i		−	0.527460i	0.964597	−	0.263730i	$-0.0849527\pi$
$684$	1801.81			0.100722
$685$	4591.82	+	3094.14i	0.256123	+	0.172585i
$686$		0			0
$687$		−	3271.70i		−	0.181693i
$688$		−	4072.29i		−	0.225661i
$689$	−54891.0			−3.03509
$690$	−2514.57	−	1694.41i	−0.138736	−	0.0934855i
$691$	−22798.5			−1.25513			−0.627565	−	0.778564i	$-0.715948\pi$
$691$	−22798.5			−1.25513			−0.627565	+	0.778564i	$0.715948\pi$
$692$		−	6969.63i		−	0.382870i
$693$		0			0
$694$	9317.06			0.509612
$695$	−2914.67	+	4325.49i	−0.159079	+	0.236079i
$696$	3582.53			0.195108
$697$		−	7403.41i		−	0.402330i
$698$		−	14396.3i		−	0.780670i
$699$	40637.0			2.19890
$700$		0			0
$701$	33797.9			1.82101			0.910506	−	0.413496i	$-0.135692\pi$
$701$	33797.9			1.82101			0.910506	+	0.413496i	$0.135692\pi$
$702$			15052.6i			0.809294i
$703$			5049.48i			0.270903i
$704$	−3096.62			−0.165779
$705$	−18869.1	+	28002.5i	−1.00802	+	1.49593i
$706$	7280.16			0.388091
$707$		0			0
$708$			13836.7i			0.734484i
$709$	26226.1			1.38920			0.694599	−	0.719397i	$-0.255582\pi$
$709$	26226.1			1.38920			0.694599	+	0.719397i	$0.255582\pi$
$710$	3895.28	+	2624.78i	0.205898	+	0.138741i
$711$	7446.45			0.392776
$712$			490.071i			0.0257952i
$713$			3391.29i			0.178128i
$714$		0			0
$715$	−41939.5	−	28260.4i	−2.19364	−	1.47815i
$716$	−9717.47			−0.507205
$717$			29732.1i			1.54863i
$718$		−	10939.8i		−	0.568620i
$719$	8593.89			0.445755			0.222878	−	0.974846i	$-0.428455\pi$
$719$	8593.89			0.445755			0.222878	+	0.974846i	$0.428455\pi$
$720$	1449.82	−	2151.58i	0.0750436	−	0.111368i
$721$		0			0
$722$			11788.8i			0.607664i
$723$			9990.14i			0.513883i
$724$	−10514.4			−0.539732
$725$	3262.38	+	8053.24i	0.167120	+	0.412538i
$726$	13014.4			0.665303
$727$		−	26368.9i		−	1.34521i	−0.740001	−	0.672606i	$-0.765175\pi$
$727$		−	26368.9i		−	1.34521i	0.740001	−	0.672606i	$-0.234825\pi$
$728$		0			0
$729$	−801.754			−0.0407333
$730$	1771.64	−	2629.18i	0.0898235	−	0.133302i
$731$	5161.45			0.261153
$732$			16127.0i			0.814307i
$733$			16495.5i			0.831207i	0.909546	+	0.415604i	$0.136430\pi$
$733$			16495.5i			0.831207i	−0.909546	+	0.415604i	$0.863570\pi$
$734$	−130.174			−0.00654607
$735$		0			0
$736$	673.560			0.0337333
$737$		−	5954.87i		−	0.297626i
$738$		−	10589.7i		−	0.528200i
$739$	−8670.04			−0.431573			−0.215786	−	0.976441i	$-0.569232\pi$
$739$	−8670.04			−0.431573			−0.215786	+	0.976441i	$0.569232\pi$
$740$	6029.71	+	4063.04i	0.299536	+	0.201838i
$741$	−18705.5			−0.927346
$742$		0			0
$743$			30923.0i			1.52686i	0.645891	+	0.763430i	$0.276486\pi$
$743$			30923.0i			1.52686i	−0.645891	+	0.763430i	$0.723514\pi$
$744$	−8303.70			−0.409178
$745$	−1115.55	+	1655.51i	−0.0548596	+	0.0814139i
$746$	20306.8			0.996627
$747$			1702.36i			0.0833819i
$748$		−	3924.82i		−	0.191852i
$749$		0			0
$750$	17618.5	+	3719.41i	0.857783	+	0.181085i
$751$	13168.0			0.639822			0.319911	−	0.947448i	$-0.396347\pi$
$751$	13168.0			0.639822			0.319911	+	0.947448i	$0.396347\pi$
$752$		−	7500.83i		−	0.363733i
$753$			4912.55i			0.237747i
$754$	−12996.9			−0.627743
$755$	−5196.00	+	7711.07i	−0.250466	+	0.371701i
$756$		0			0
$757$			31713.3i			1.52264i	0.648375	+	0.761321i	$0.275449\pi$
$757$			31713.3i			1.52264i	−0.648375	+	0.761321i	$0.724551\pi$
$758$			2907.91i			0.139341i
$759$	−6561.09			−0.313771
$760$	−2303.72	−	1552.33i	−0.109953	−	0.0740906i
$761$	−818.651			−0.0389962			−0.0194981	−	0.999810i	$-0.506207\pi$
$761$	−818.651			−0.0389962			−0.0194981	+	0.999810i	$0.506207\pi$
$762$			12516.6i			0.595051i
$763$		0			0
$764$	−4499.29			−0.213061
$765$	2727.03	+	1837.57i	0.128884	+	0.0868466i
$766$	−1154.60			−0.0544615
$767$		−	50197.4i		−	2.36313i
$768$			1649.23i			0.0774891i
$769$	−28514.9			−1.33716			−0.668578	−	0.743642i	$-0.733097\pi$
$769$	−28514.9			−1.33716			−0.668578	+	0.743642i	$0.733097\pi$
$770$		0			0
$771$	14832.6			0.692842
$772$			8864.33i			0.413257i
$773$		−	28791.0i		−	1.33964i	−0.742525	−	0.669819i	$-0.766372\pi$
$773$		−	28791.0i		−	1.33964i	0.742525	−	0.669819i	$-0.233628\pi$
$774$	7382.83			0.342856
$775$	−7561.65	−	18666.1i	−0.350481	−	0.865167i
$776$	−3493.23			−0.161598
$777$		0			0
$778$		−	4142.00i		−	0.190871i
$779$	−11338.5			−0.521493
$780$	−15051.3	+	22336.7i	−0.690926	+	1.02536i
$781$	10163.7			0.465666
$782$			853.706i			0.0390390i
$783$		−	5596.12i		−	0.255414i
$784$		0			0
$785$	1554.85	+	1047.72i	0.0706943	+	0.0476364i
$786$	1927.46			0.0874684
$787$			7485.80i			0.339059i	0.985525	+	0.169530i	$0.0542249\pi$
$787$			7485.80i			0.339059i	−0.985525	+	0.169530i	$0.945775\pi$
$788$			12502.2i			0.565194i
$789$	31139.0			1.40504
$790$	−9520.73	−	6415.42i	−0.428775	−	0.288924i
$791$		0			0
$792$		−	5613.98i		−	0.251874i
$793$		−	58506.5i		−	2.61996i
$794$	−10066.8			−0.449948
$795$	23632.5	−	35071.6i	1.05429	−	1.56461i
$796$	18157.4			0.808506
$797$			2323.41i			0.103261i	0.998666	+	0.0516307i	$0.0164419\pi$
$797$			2323.41i			0.103261i	−0.998666	+	0.0516307i	$0.983558\pi$
$798$		0			0
$799$	9506.96			0.420941
$800$	−3707.35	+	1501.85i	−0.163843	+	0.0663732i
$801$	−888.469			−0.0391917
$802$			9893.76i			0.435612i
$803$		−	6860.14i		−	0.301481i
$804$	−3171.52			−0.139118
$805$		0			0
$806$	30124.6			1.31649
$807$		−	31118.7i		−	1.35741i
$808$			14145.7i			0.615895i
$809$	9103.69			0.395635			0.197818	−	0.980239i	$-0.436615\pi$
$809$	9103.69			0.395635			0.197818	+	0.980239i	$0.436615\pi$
$810$	−16879.2	−	11373.8i	−0.732191	−	0.493377i
$811$	−4516.19			−0.195542			−0.0977711	−	0.995209i	$-0.531171\pi$
$811$	−4516.19			−0.195542			−0.0977711	+	0.995209i	$0.531171\pi$
$812$		0			0
$813$		−	38334.2i		−	1.65368i
$814$	15732.9			0.677443
$815$	−14947.0	−	10071.8i	−0.642418	−	0.432885i
$816$	−2090.33			−0.0896767
$817$		−	7904.86i		−	0.338502i
$818$		−	18779.7i		−	0.802709i
$819$		0			0
$820$	−9123.44	+	13539.5i	−0.388542	+	0.576612i
$821$	−6046.44			−0.257031			−0.128515	−	0.991708i	$-0.541021\pi$
$821$	−6046.44			−0.257031			−0.128515	+	0.991708i	$0.541021\pi$
$822$		−	6381.06i		−	0.270760i
$823$			44591.3i			1.88864i	0.329022	+	0.944322i	$0.393281\pi$
$823$			44591.3i			1.88864i	−0.329022	+	0.944322i	$0.606719\pi$
$824$	6795.25			0.287286
$825$	36113.0	−	14629.4i	1.52399	−	0.617371i
$826$		0			0
$827$		−	17170.6i		−	0.721982i	−0.932569	−	0.360991i	$-0.882439\pi$
$827$		−	17170.6i		−	0.721982i	0.932569	−	0.360991i	$-0.117561\pi$
$828$			1221.12i			0.0512524i
$829$	30509.9			1.27823			0.639115	−	0.769111i	$-0.279301\pi$
$829$	30509.9			1.27823			0.639115	+	0.769111i	$0.279301\pi$
$830$	1466.65	−	2176.57i	0.0613353	−	0.0910241i
$831$	−49405.5			−2.06241
$832$		−	5983.18i		−	0.249314i
$833$		0			0
$834$	6010.95			0.249571
$835$	−14748.6	−	9938.12i	−0.611251	−	0.411883i
$836$	−6010.93			−0.248675
$837$			12970.9i			0.535650i
$838$			16847.5i			0.694497i
$839$	34089.6			1.40275			0.701373	−	0.712794i	$-0.252571\pi$
$839$	34089.6			1.40275			0.701373	+	0.712794i	$0.252571\pi$
$840$		0			0
$841$	−19557.1			−0.801884
$842$		−	11360.3i		−	0.464966i
$843$		−	40678.0i		−	1.66195i
$844$	−10081.6			−0.411165
$845$	40877.6	−	60664.0i	1.66418	−	2.46971i
$846$	13598.6			0.552634
$847$		0			0
$848$			9394.40i			0.380430i
$849$	−39444.6			−1.59450
$850$	−1903.53	−	4698.89i	−0.0768124	−	0.189613i
$851$	−3422.14			−0.137849
$852$		−	5413.11i		−	0.217664i
$853$		−	5078.39i		−	0.203846i	−0.994792	−	0.101923i	$-0.967500\pi$
$853$		−	5078.39i		−	0.203846i	0.994792	−	0.101923i	$-0.0324995\pi$
$854$		0			0
$855$	2814.28	−	4176.50i	0.112569	−	0.167057i
$856$	−10260.6			−0.409697
$857$			85.5262i			0.00340901i	0.999999	+	0.00170450i	$0.000542561\pi$
$857$			85.5262i			0.00340901i	−0.999999	+	0.00170450i	$0.999457\pi$
$858$			58281.6i			2.31900i
$859$	−32320.1			−1.28376			−0.641878	−	0.766807i	$-0.721844\pi$
$859$	−32320.1			−1.28376			−0.641878	+	0.766807i	$0.721844\pi$
$860$	−9439.39	−	6360.60i	−0.374279	−	0.252203i
$861$		0			0
$862$		−	24696.7i		−	0.975840i
$863$			20936.2i			0.825813i	0.910773	+	0.412907i	$0.135486\pi$
$863$			20936.2i			0.825813i	−0.910773	+	0.412907i	$0.864514\pi$
$864$	2576.20			0.101440
$865$	−16155.3	−	10886.0i	−0.635024	−	0.427902i
$866$	18063.9			0.708816
$867$			29001.7i			1.13604i
$868$		0			0
$869$	−24841.8			−0.969736
$870$	5595.63	−	8304.13i	0.218057	−	0.323605i
$871$	11505.8			0.447600
$872$			4787.19i			0.185911i
$873$		−	6333.02i		−	0.245522i
$874$	1307.47			0.0506015
$875$		0			0
$876$	−3653.66			−0.140920
$877$			24078.1i			0.927093i	0.886073	+	0.463546i	$0.153423\pi$
$877$			24078.1i			0.927093i	−0.886073	+	0.463546i	$0.846577\pi$
$878$		−	21314.8i		−	0.819295i
$879$	10608.4			0.407067
$880$	−4836.67	+	7177.81i	−0.185277	+	0.274959i
$881$	23196.8			0.887081			0.443541	−	0.896254i	$-0.353722\pi$
$881$	23196.8			0.887081			0.443541	+	0.896254i	$0.353722\pi$
$882$		0			0
$883$			31800.2i			1.21196i	0.795479	+	0.605981i	$0.207219\pi$
$883$			31800.2i			1.21196i	−0.795479	+	0.605981i	$0.792781\pi$
$884$	7583.40			0.288526
$885$	32072.8	+	21611.8i	1.21821	+	0.820873i
$886$	−1802.64			−0.0683532
$887$			34200.2i			1.29462i	0.762226	+	0.647311i	$0.224107\pi$
$887$			34200.2i			1.29462i	−0.762226	+	0.647311i	$0.775893\pi$
$888$		−	8379.24i		−	0.316654i
$889$		0			0
$890$	1135.96	+	765.452i	0.0427837	+	0.0288292i
$891$	−44041.8			−1.65595
$892$		−	23202.3i		−	0.870931i
$893$		−	14560.1i		−	0.545616i
$894$	2300.60			0.0860666
$895$	−15177.9	+	22524.6i	−0.566862	+	0.841246i
$896$		0			0
$897$		−	12677.1i		−	0.471880i
$898$		−	15543.8i		−	0.577619i
$899$	−11199.4			−0.415486
$900$	−2722.77	−	6721.20i	−0.100843	−	0.248934i
$901$	−11907.0			−0.440265
$902$			35327.8i			1.30409i
$903$		0			0
$904$	6881.74			0.253190
$905$	−16422.7	+	24372.0i	−0.603215	+	0.895195i
$906$	10715.7			0.392944
$907$			4793.39i			0.175482i	0.996143	+	0.0877409i	$0.0279648\pi$
$907$			4793.39i			0.175482i	−0.996143	+	0.0877409i	$0.972035\pi$
$908$			26505.9i			0.968753i
$909$	−25645.3			−0.935753
$910$		0			0
$911$	−25153.4			−0.914787			−0.457393	−	0.889264i	$-0.651217\pi$
$911$	−25153.4			−0.914787			−0.457393	+	0.889264i	$0.651217\pi$
$912$			3201.38i			0.116237i
$913$		−	5679.19i		−	0.205864i
$914$	−5520.70			−0.199791
$915$	37381.7	+	25189.2i	1.35060	+	0.910085i
$916$	2031.38			0.0732736
$917$		0			0
$918$			3265.22i			0.117395i
$919$	20437.0			0.733573			0.366786	−	0.930305i	$-0.380458\pi$
$919$	20437.0			0.733573			0.366786	+	0.930305i	$0.380458\pi$
$920$	1052.05	−	1561.28i	0.0377010	−	0.0559499i
$921$	−50832.6			−1.81867
$922$			32964.7i			1.17748i
$923$			19637.9i			0.700315i
$924$		0			0
$925$	18835.9	−	7630.44i	0.669534	−	0.271229i
$926$	19898.3			0.706155
$927$			12319.4i			0.436485i
$928$			2224.37i			0.0786838i
$929$	−1282.13			−0.0452802			−0.0226401	−	0.999744i	$-0.507207\pi$
$929$	−1282.13			−0.0452802			−0.0226401	+	0.999744i	$0.507207\pi$
$930$	−12969.7	+	19247.6i	−0.457305	+	0.678659i
$931$		0			0
$932$			25231.3i			0.886779i
$933$		−	22142.1i		−	0.776957i
$934$	−4203.11			−0.147248
$935$	−9097.54	−	6130.25i	−0.318205	−	0.214418i
$936$	10847.1			0.378793
$937$		−	16878.5i		−	0.588472i	−0.955733	−	0.294236i	$-0.904935\pi$
$937$		−	16878.5i		−	0.588472i	0.955733	−	0.294236i	$-0.0950651\pi$
$938$		0			0
$939$	−46447.9			−1.61424
$940$	−17386.6	−	11715.7i	−0.603284	−	0.406515i
$941$	14931.6			0.517275			0.258637	−	0.965974i	$-0.416726\pi$
$941$	14931.6			0.517275			0.258637	+	0.965974i	$0.416726\pi$
$942$		−	2160.71i		−	0.0747344i
$943$		−	7684.33i		−	0.265362i
$944$	−8591.11			−0.296204
$945$		0			0
$946$	−24629.5			−0.846486
$947$			37545.7i			1.28835i	0.764877	+	0.644177i	$0.222800\pi$
$947$			37545.7i			1.28835i	−0.764877	+	0.644177i	$0.777200\pi$
$948$			13230.6i			0.453279i
$949$	13254.9			0.453396
$950$	−7196.45	+	2915.29i	−0.245772	+	0.0995628i
$951$	−5706.63			−0.194585
$952$		0			0
$953$		−	437.260i		−	0.0148628i	−0.999972	−	0.00743140i	$-0.997634\pi$
$953$		−	437.260i		−	0.0148628i	0.999972	−	0.00743140i	$-0.00236551\pi$
$954$	−17031.5			−0.578003
$955$	−7027.54	+	10429.1i	−0.238121	+	0.353381i
$956$	−18460.5			−0.624535
$957$		−	21667.4i		−	0.731879i
$958$		−	16019.9i		−	0.540272i
$959$		0			0
$960$	3822.85	+	2575.97i	0.128523	+	0.0866033i
$961$	−3832.58			−0.128649
$962$			30398.6i			1.01881i
$963$		−	18601.9i		−	0.622469i
$964$	−6202.82			−0.207240
$965$	20547.1	+	13845.4i	0.685424	+	0.461864i
$966$		0			0
$967$		−	52372.7i		−	1.74167i	−0.491577	−	0.870834i	$-0.663579\pi$
$967$		−	52372.7i		−	1.74167i	0.491577	−	0.870834i	$-0.336421\pi$
$968$			8080.57i			0.268305i
$969$	−4057.60			−0.134519
$970$	−5456.15	+	8097.14i	−0.180605	+	0.268024i
$971$	40759.4			1.34710			0.673548	−	0.739144i	$-0.264769\pi$
$971$	40759.4			1.34710			0.673548	+	0.739144i	$0.264769\pi$
$972$			14761.6i			0.487119i
$973$		0			0
$974$	−10765.2			−0.354147
$975$	28266.5	+	69776.3i	0.928464	+	2.29193i
$976$	−10013.2			−0.328396
$977$		−	37637.9i		−	1.23249i	−0.787554	−	0.616246i	$-0.788653\pi$
$977$		−	37637.9i		−	1.23249i	0.787554	−	0.616246i	$-0.211347\pi$
$978$			20771.2i			0.679132i
$979$	2963.99			0.0967614
$980$		0			0
$981$	−8678.89			−0.282462
$982$			6913.86i			0.224674i
$983$		−	8799.74i		−	0.285522i	−0.989757	−	0.142761i	$-0.954402\pi$
$983$		−	8799.74i		−	0.285522i	0.989757	−	0.142761i	$-0.0455980\pi$
$984$	18815.3			0.609564
$985$	28979.6	+	19527.5i	0.937427	+	0.631672i
$986$	−2819.29			−0.0910592
$987$		0			0
$988$		−	11614.1i		−	0.373982i
$989$	5357.29			0.172247
$990$	−13012.9	−	8768.59i	−0.417756	−	0.281499i
$991$	−43972.1			−1.40950			−0.704752	−	0.709454i	$-0.748942\pi$
$991$	−43972.1			−1.40950			−0.704752	+	0.709454i	$0.748942\pi$
$992$		−	5155.72i		−	0.165014i
$993$		−	11378.3i		−	0.363626i
$994$		0			0
$995$	28360.4	−	42087.9i	0.903602	−	1.34098i
$996$	−3024.69			−0.0962260
$997$		−	10052.7i		−	0.319329i	−0.987171	−	0.159664i	$-0.948959\pi$
$997$		−	10052.7i		−	0.319329i	0.987171	−	0.159664i	$-0.0510412\pi$
$998$		−	24196.3i		−	0.767457i
$999$	−13088.9			−0.414528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.f.99.5		12
5.2	odd	4		2450.4.a.cy.1.5		6
5.3	odd	4		2450.4.a.cv.1.2		6
5.4	even	2	inner	490.4.c.f.99.8		12
7.2	even	3		70.4.i.a.39.2	yes	24
7.4	even	3		70.4.i.a.9.11	yes	24
7.6	odd	2		490.4.c.e.99.2		12
35.2	odd	12		350.4.e.n.151.2		12
35.4	even	6		70.4.i.a.9.2	✓	24
35.9	even	6		70.4.i.a.39.11	yes	24
35.13	even	4		2450.4.a.cw.1.5		6
35.18	odd	12		350.4.e.o.51.5		12
35.23	odd	12		350.4.e.o.151.5		12
35.27	even	4		2450.4.a.cx.1.2		6
35.32	odd	12		350.4.e.n.51.2		12
35.34	odd	2		490.4.c.e.99.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.i.a.9.2	✓	24	35.4	even	6
70.4.i.a.9.11	yes	24	7.4	even	3
70.4.i.a.39.2	yes	24	7.2	even	3
70.4.i.a.39.11	yes	24	35.9	even	6
350.4.e.n.51.2		12	35.32	odd	12
350.4.e.n.151.2		12	35.2	odd	12
350.4.e.o.51.5		12	35.18	odd	12
350.4.e.o.151.5		12	35.23	odd	12
490.4.c.e.99.2		12	7.6	odd	2
490.4.c.e.99.11		12	35.34	odd	2
490.4.c.f.99.5		12	1.1	even	1	trivial
490.4.c.f.99.8		12	5.4	even	2	inner
2450.4.a.cv.1.2		6	5.3	odd	4
2450.4.a.cw.1.5		6	35.13	even	4
2450.4.a.cx.1.2		6	35.27	even	4
2450.4.a.cy.1.5		6	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)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +6.44232i q^{3} -4.00000 q^{4} +(-6.24768 + 9.27181i) q^{5} +12.8846 q^{6} +8.00000i q^{8} -14.5035 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +6.44232i q^{3} -4.00000 q^{4} +(-6.24768 + 9.27181i) q^{5} +12.8846 q^{6} +8.00000i q^{8} -14.5035 q^{9} +(18.5436 + 12.4954i) q^{10} +48.3846 q^{11} -25.7693i q^{12} +93.4871i q^{13} +(-59.7320 - 40.2496i) q^{15} +16.0000 q^{16} +20.2793i q^{17} +29.0071i q^{18} +31.0581 q^{19} +(24.9907 - 37.0872i) q^{20} -96.7692i q^{22} +21.0487i q^{23} -51.5386 q^{24} +(-46.9329 - 115.855i) q^{25} +186.974 q^{26} +80.5063i q^{27} -69.5116 q^{29} +(-80.4992 + 119.464i) q^{30} +161.116 q^{31} -32.0000i q^{32} +311.709i q^{33} +40.5585 q^{34} +58.0141 q^{36} +162.582i q^{37} -62.1162i q^{38} -602.274 q^{39} +(-74.1745 - 49.9815i) q^{40} -365.073 q^{41} -254.518i q^{43} -193.538 q^{44} +(90.6134 - 134.474i) q^{45} +42.0975 q^{46} -468.802i q^{47} +103.077i q^{48} +(-231.709 + 93.8658i) q^{50} -130.646 q^{51} -373.949i q^{52} +587.150i q^{53} +161.013 q^{54} +(-302.292 + 448.613i) q^{55} +200.086i q^{57} +139.023i q^{58} -536.945 q^{59} +(238.928 + 160.998i) q^{60} -625.824 q^{61} -322.232i q^{62} -64.0000 q^{64} +(-866.795 - 584.078i) q^{65} +623.419 q^{66} -123.074i q^{67} -81.1171i q^{68} -135.603 q^{69} +210.060 q^{71} -116.028i q^{72} -141.783i q^{73} +325.164 q^{74} +(746.373 - 302.357i) q^{75} -124.232 q^{76} +1204.55i q^{78} -513.424 q^{79} +(-99.9629 + 148.349i) q^{80} -910.243 q^{81} +730.146i q^{82} -117.376i q^{83} +(-188.025 - 126.698i) q^{85} -509.037 q^{86} -447.816i q^{87} +387.077i q^{88} +61.2589 q^{89} +(-268.948 - 181.227i) q^{90} -84.1950i q^{92} +1037.96i q^{93} -937.604 q^{94} +(-194.041 + 287.965i) q^{95} +206.154 q^{96} +436.654i q^{97} -701.748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9}+O(q^{10}) \) 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9	\( 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9} - 12 q^{10} + 62 q^{11} + 86 q^{15} + 192 q^{16} - 186 q^{19} - 32 q^{20} - 112 q^{24} - 126 q^{25} + 236 q^{26} - 338 q^{29} - 28 q^{30} + 652 q^{31} - 272 q^{34} + 248 q^{36} + 868 q^{39} + 48 q^{40} + 396 q^{41} - 248 q^{44} - 664 q^{45} - 376 q^{46} + 160 q^{50} + 1448 q^{51} - 1540 q^{54} + 298 q^{55} - 1336 q^{59} - 344 q^{60} + 314 q^{61} - 768 q^{64} - 1862 q^{65} + 1600 q^{66} + 90 q^{69} + 2216 q^{71} + 1012 q^{74} + 4550 q^{75} + 744 q^{76} + 1772 q^{79} + 128 q^{80} - 1228 q^{81} + 2282 q^{85} - 396 q^{86} - 6094 q^{89} + 100 q^{90} - 3604 q^{94} - 1166 q^{95} + 448 q^{96} - 8546 q^{99}+O(q^{100}) \) 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9 - 12 * q^10 + 62 * q^11 + 86 * q^15 + 192 * q^16 - 186 * q^19 - 32 * q^20 - 112 * q^24 - 126 * q^25 + 236 * q^26 - 338 * q^29 - 28 * q^30 + 652 * q^31 - 272 * q^34 + 248 * q^36 + 868 * q^39 + 48 * q^40 + 396 * q^41 - 248 * q^44 - 664 * q^45 - 376 * q^46 + 160 * q^50 + 1448 * q^51 - 1540 * q^54 + 298 * q^55 - 1336 * q^59 - 344 * q^60 + 314 * q^61 - 768 * q^64 - 1862 * q^65 + 1600 * q^66 + 90 * q^69 + 2216 * q^71 + 1012 * q^74 + 4550 * q^75 + 744 * q^76 + 1772 * q^79 + 128 * q^80 - 1228 * q^81 + 2282 * q^85 - 396 * q^86 - 6094 * q^89 + 100 * q^90 - 3604 * q^94 - 1166 * q^95 + 448 * q^96 - 8546 * q^99

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