Properties

 Label 560.4.q.b.81.1 Level $560$ Weight $4$ Character 560.81 Analytic conductor $33.041$ Analytic rank $0$ Dimension $2$ Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,4,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 560.q (of order $$3$$, degree $$2$$, not 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: $$33.0410696032$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 35) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 81.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 560.81 Dual form 560.4.q.b.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{5} +(14.0000 + 12.1244i) q^{7} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$$ $$q+(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{5} +(14.0000 + 12.1244i) q^{7} +(11.5000 + 19.9186i) q^{9} +(-22.5000 + 38.9711i) q^{11} +59.0000 q^{13} +10.0000 q^{15} +(27.0000 - 46.7654i) q^{17} +(-60.5000 - 104.789i) q^{19} +(-35.0000 + 12.1244i) q^{21} +(34.5000 + 59.7558i) q^{23} +(-12.5000 + 21.6506i) q^{25} -100.000 q^{27} -162.000 q^{29} +(-44.0000 + 76.2102i) q^{31} +(-45.0000 - 77.9423i) q^{33} +(17.5000 - 90.9327i) q^{35} +(129.500 + 224.301i) q^{37} +(-59.0000 + 102.191i) q^{39} +195.000 q^{41} +286.000 q^{43} +(57.5000 - 99.5929i) q^{45} +(22.5000 + 38.9711i) q^{47} +(49.0000 + 339.482i) q^{49} +(54.0000 + 93.5307i) q^{51} +(-298.500 + 517.017i) q^{53} +225.000 q^{55} +242.000 q^{57} +(-180.000 + 311.769i) q^{59} +(-196.000 - 339.482i) q^{61} +(-80.5000 + 418.290i) q^{63} +(-147.500 - 255.477i) q^{65} +(-140.000 + 242.487i) q^{67} -138.000 q^{69} -48.0000 q^{71} +(-334.000 + 578.505i) q^{73} +(-25.0000 - 43.3013i) q^{75} +(-787.500 + 272.798i) q^{77} +(391.000 + 677.232i) q^{79} +(-210.500 + 364.597i) q^{81} -768.000 q^{83} -270.000 q^{85} +(162.000 - 280.592i) q^{87} +(597.000 + 1034.03i) q^{89} +(826.000 + 715.337i) q^{91} +(-88.0000 - 152.420i) q^{93} +(-302.500 + 523.945i) q^{95} +902.000 q^{97} -1035.00 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{3} - 5 q^{5} + 28 q^{7} + 23 q^{9}+O(q^{10})$$ 2 * q - 2 * q^3 - 5 * q^5 + 28 * q^7 + 23 * q^9 $$2 q - 2 q^{3} - 5 q^{5} + 28 q^{7} + 23 q^{9} - 45 q^{11} + 118 q^{13} + 20 q^{15} + 54 q^{17} - 121 q^{19} - 70 q^{21} + 69 q^{23} - 25 q^{25} - 200 q^{27} - 324 q^{29} - 88 q^{31} - 90 q^{33} + 35 q^{35} + 259 q^{37} - 118 q^{39} + 390 q^{41} + 572 q^{43} + 115 q^{45} + 45 q^{47} + 98 q^{49} + 108 q^{51} - 597 q^{53} + 450 q^{55} + 484 q^{57} - 360 q^{59} - 392 q^{61} - 161 q^{63} - 295 q^{65} - 280 q^{67} - 276 q^{69} - 96 q^{71} - 668 q^{73} - 50 q^{75} - 1575 q^{77} + 782 q^{79} - 421 q^{81} - 1536 q^{83} - 540 q^{85} + 324 q^{87} + 1194 q^{89} + 1652 q^{91} - 176 q^{93} - 605 q^{95} + 1804 q^{97} - 2070 q^{99}+O(q^{100})$$ 2 * q - 2 * q^3 - 5 * q^5 + 28 * q^7 + 23 * q^9 - 45 * q^11 + 118 * q^13 + 20 * q^15 + 54 * q^17 - 121 * q^19 - 70 * q^21 + 69 * q^23 - 25 * q^25 - 200 * q^27 - 324 * q^29 - 88 * q^31 - 90 * q^33 + 35 * q^35 + 259 * q^37 - 118 * q^39 + 390 * q^41 + 572 * q^43 + 115 * q^45 + 45 * q^47 + 98 * q^49 + 108 * q^51 - 597 * q^53 + 450 * q^55 + 484 * q^57 - 360 * q^59 - 392 * q^61 - 161 * q^63 - 295 * q^65 - 280 * q^67 - 276 * q^69 - 96 * q^71 - 668 * q^73 - 50 * q^75 - 1575 * q^77 + 782 * q^79 - 421 * q^81 - 1536 * q^83 - 540 * q^85 + 324 * q^87 + 1194 * q^89 + 1652 * q^91 - 176 * q^93 - 605 * q^95 + 1804 * q^97 - 2070 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$351$$ $$421$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$1$$

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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.00000 + 1.73205i −0.192450 + 0.333333i −0.946062 0.323987i $$-0.894977\pi$$
0.753612 + 0.657320i $$0.228310\pi$$
$$4$$ 0 0
$$5$$ −2.50000 4.33013i −0.223607 0.387298i
$$6$$ 0 0
$$7$$ 14.0000 + 12.1244i 0.755929 + 0.654654i
$$8$$ 0 0
$$9$$ 11.5000 + 19.9186i 0.425926 + 0.737725i
$$10$$ 0 0
$$11$$ −22.5000 + 38.9711i −0.616728 + 1.06820i 0.373351 + 0.927690i $$0.378209\pi$$
−0.990079 + 0.140514i $$0.955125\pi$$
$$12$$ 0 0
$$13$$ 59.0000 1.25874 0.629371 0.777105i $$-0.283312\pi$$
0.629371 + 0.777105i $$0.283312\pi$$
$$14$$ 0 0
$$15$$ 10.0000 0.172133
$$16$$ 0 0
$$17$$ 27.0000 46.7654i 0.385204 0.667192i −0.606594 0.795012i $$-0.707465\pi$$
0.991797 + 0.127820i $$0.0407979\pi$$
$$18$$ 0 0
$$19$$ −60.5000 104.789i −0.730508 1.26528i −0.956666 0.291186i $$-0.905950\pi$$
0.226158 0.974091i $$-0.427383\pi$$
$$20$$ 0 0
$$21$$ −35.0000 + 12.1244i −0.363696 + 0.125988i
$$22$$ 0 0
$$23$$ 34.5000 + 59.7558i 0.312772 + 0.541736i 0.978961 0.204046i $$-0.0654092\pi$$
−0.666190 + 0.745782i $$0.732076\pi$$
$$24$$ 0 0
$$25$$ −12.5000 + 21.6506i −0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ −100.000 −0.712778
$$28$$ 0 0
$$29$$ −162.000 −1.03733 −0.518666 0.854977i $$-0.673571\pi$$
−0.518666 + 0.854977i $$0.673571\pi$$
$$30$$ 0 0
$$31$$ −44.0000 + 76.2102i −0.254924 + 0.441541i −0.964875 0.262710i $$-0.915384\pi$$
0.709951 + 0.704251i $$0.248717\pi$$
$$32$$ 0 0
$$33$$ −45.0000 77.9423i −0.237379 0.411152i
$$34$$ 0 0
$$35$$ 17.5000 90.9327i 0.0845154 0.439155i
$$36$$ 0 0
$$37$$ 129.500 + 224.301i 0.575396 + 0.996616i 0.995998 + 0.0893706i $$0.0284856\pi$$
−0.420602 + 0.907245i $$0.638181\pi$$
$$38$$ 0 0
$$39$$ −59.0000 + 102.191i −0.242245 + 0.419581i
$$40$$ 0 0
$$41$$ 195.000 0.742778 0.371389 0.928477i $$-0.378882\pi$$
0.371389 + 0.928477i $$0.378882\pi$$
$$42$$ 0 0
$$43$$ 286.000 1.01429 0.507146 0.861860i $$-0.330700\pi$$
0.507146 + 0.861860i $$0.330700\pi$$
$$44$$ 0 0
$$45$$ 57.5000 99.5929i 0.190480 0.329921i
$$46$$ 0 0
$$47$$ 22.5000 + 38.9711i 0.0698290 + 0.120947i 0.898826 0.438306i $$-0.144421\pi$$
−0.828997 + 0.559253i $$0.811088\pi$$
$$48$$ 0 0
$$49$$ 49.0000 + 339.482i 0.142857 + 0.989743i
$$50$$ 0 0
$$51$$ 54.0000 + 93.5307i 0.148265 + 0.256802i
$$52$$ 0 0
$$53$$ −298.500 + 517.017i −0.773625 + 1.33996i 0.161939 + 0.986801i $$0.448225\pi$$
−0.935564 + 0.353157i $$0.885108\pi$$
$$54$$ 0 0
$$55$$ 225.000 0.551618
$$56$$ 0 0
$$57$$ 242.000 0.562345
$$58$$ 0 0
$$59$$ −180.000 + 311.769i −0.397187 + 0.687947i −0.993378 0.114895i $$-0.963347\pi$$
0.596191 + 0.802843i $$0.296680\pi$$
$$60$$ 0 0
$$61$$ −196.000 339.482i −0.411397 0.712561i 0.583646 0.812009i $$-0.301626\pi$$
−0.995043 + 0.0994477i $$0.968292\pi$$
$$62$$ 0 0
$$63$$ −80.5000 + 418.290i −0.160985 + 0.836502i
$$64$$ 0 0
$$65$$ −147.500 255.477i −0.281463 0.487509i
$$66$$ 0 0
$$67$$ −140.000 + 242.487i −0.255279 + 0.442157i −0.964971 0.262355i $$-0.915501\pi$$
0.709692 + 0.704512i $$0.248834\pi$$
$$68$$ 0 0
$$69$$ −138.000 −0.240772
$$70$$ 0 0
$$71$$ −48.0000 −0.0802331 −0.0401166 0.999195i $$-0.512773\pi$$
−0.0401166 + 0.999195i $$0.512773\pi$$
$$72$$ 0 0
$$73$$ −334.000 + 578.505i −0.535503 + 0.927519i 0.463635 + 0.886026i $$0.346545\pi$$
−0.999139 + 0.0414929i $$0.986789\pi$$
$$74$$ 0 0
$$75$$ −25.0000 43.3013i −0.0384900 0.0666667i
$$76$$ 0 0
$$77$$ −787.500 + 272.798i −1.16551 + 0.403743i
$$78$$ 0 0
$$79$$ 391.000 + 677.232i 0.556847 + 0.964488i 0.997757 + 0.0669365i $$0.0213225\pi$$
−0.440910 + 0.897551i $$0.645344\pi$$
$$80$$ 0 0
$$81$$ −210.500 + 364.597i −0.288752 + 0.500133i
$$82$$ 0 0
$$83$$ −768.000 −1.01565 −0.507825 0.861460i $$-0.669550\pi$$
−0.507825 + 0.861460i $$0.669550\pi$$
$$84$$ 0 0
$$85$$ −270.000 −0.344537
$$86$$ 0 0
$$87$$ 162.000 280.592i 0.199635 0.345778i
$$88$$ 0 0
$$89$$ 597.000 + 1034.03i 0.711032 + 1.23154i 0.964470 + 0.264192i $$0.0851054\pi$$
−0.253438 + 0.967352i $$0.581561\pi$$
$$90$$ 0 0
$$91$$ 826.000 + 715.337i 0.951520 + 0.824041i
$$92$$ 0 0
$$93$$ −88.0000 152.420i −0.0981202 0.169949i
$$94$$ 0 0
$$95$$ −302.500 + 523.945i −0.326693 + 0.565849i
$$96$$ 0 0
$$97$$ 902.000 0.944167 0.472084 0.881554i $$-0.343502\pi$$
0.472084 + 0.881554i $$0.343502\pi$$
$$98$$ 0 0
$$99$$ −1035.00 −1.05072
$$100$$ 0 0
$$101$$ −342.000 + 592.361i −0.336933 + 0.583586i −0.983854 0.178971i $$-0.942723\pi$$
0.646921 + 0.762557i $$0.276056\pi$$
$$102$$ 0 0
$$103$$ −758.000 1312.89i −0.725126 1.25595i −0.958922 0.283669i $$-0.908448\pi$$
0.233796 0.972286i $$-0.424885\pi$$
$$104$$ 0 0
$$105$$ 140.000 + 121.244i 0.130120 + 0.112687i
$$106$$ 0 0
$$107$$ −366.000 633.931i −0.330678 0.572751i 0.651967 0.758247i $$-0.273944\pi$$
−0.982645 + 0.185496i $$0.940611\pi$$
$$108$$ 0 0
$$109$$ 800.000 1385.64i 0.702992 1.21762i −0.264420 0.964408i $$-0.585180\pi$$
0.967411 0.253210i $$-0.0814863\pi$$
$$110$$ 0 0
$$111$$ −518.000 −0.442940
$$112$$ 0 0
$$113$$ −1392.00 −1.15883 −0.579417 0.815031i $$-0.696720\pi$$
−0.579417 + 0.815031i $$0.696720\pi$$
$$114$$ 0 0
$$115$$ 172.500 298.779i 0.139876 0.242272i
$$116$$ 0 0
$$117$$ 678.500 + 1175.20i 0.536131 + 0.928606i
$$118$$ 0 0
$$119$$ 945.000 327.358i 0.727966 0.252175i
$$120$$ 0 0
$$121$$ −347.000 601.022i −0.260706 0.451556i
$$122$$ 0 0
$$123$$ −195.000 + 337.750i −0.142948 + 0.247593i
$$124$$ 0 0
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ −803.000 −0.561061 −0.280530 0.959845i $$-0.590510\pi$$
−0.280530 + 0.959845i $$0.590510\pi$$
$$128$$ 0 0
$$129$$ −286.000 + 495.367i −0.195201 + 0.338098i
$$130$$ 0 0
$$131$$ 1009.50 + 1748.51i 0.673286 + 1.16617i 0.976967 + 0.213391i $$0.0684509\pi$$
−0.303681 + 0.952774i $$0.598216\pi$$
$$132$$ 0 0
$$133$$ 423.500 2200.57i 0.276106 1.43469i
$$134$$ 0 0
$$135$$ 250.000 + 433.013i 0.159382 + 0.276058i
$$136$$ 0 0
$$137$$ −30.0000 + 51.9615i −0.0187086 + 0.0324042i −0.875228 0.483710i $$-0.839289\pi$$
0.856520 + 0.516115i $$0.172622\pi$$
$$138$$ 0 0
$$139$$ 1708.00 1.04224 0.521118 0.853485i $$-0.325515\pi$$
0.521118 + 0.853485i $$0.325515\pi$$
$$140$$ 0 0
$$141$$ −90.0000 −0.0537544
$$142$$ 0 0
$$143$$ −1327.50 + 2299.30i −0.776302 + 1.34459i
$$144$$ 0 0
$$145$$ 405.000 + 701.481i 0.231955 + 0.401757i
$$146$$ 0 0
$$147$$ −637.000 254.611i −0.357407 0.142857i
$$148$$ 0 0
$$149$$ 543.000 + 940.504i 0.298552 + 0.517108i 0.975805 0.218643i $$-0.0701629\pi$$
−0.677253 + 0.735751i $$0.736830\pi$$
$$150$$ 0 0
$$151$$ −1433.00 + 2482.03i −0.772291 + 1.33765i 0.164014 + 0.986458i $$0.447556\pi$$
−0.936305 + 0.351189i $$0.885778\pi$$
$$152$$ 0 0
$$153$$ 1242.00 0.656273
$$154$$ 0 0
$$155$$ 440.000 0.228011
$$156$$ 0 0
$$157$$ 114.500 198.320i 0.0582044 0.100813i −0.835455 0.549559i $$-0.814796\pi$$
0.893659 + 0.448746i $$0.148129\pi$$
$$158$$ 0 0
$$159$$ −597.000 1034.03i −0.297768 0.515750i
$$160$$ 0 0
$$161$$ −241.500 + 1254.87i −0.118217 + 0.614271i
$$162$$ 0 0
$$163$$ −614.000 1063.48i −0.295044 0.511031i 0.679951 0.733258i $$-0.262001\pi$$
−0.974995 + 0.222226i $$0.928668\pi$$
$$164$$ 0 0
$$165$$ −225.000 + 389.711i −0.106159 + 0.183873i
$$166$$ 0 0
$$167$$ 1929.00 0.893835 0.446918 0.894575i $$-0.352522\pi$$
0.446918 + 0.894575i $$0.352522\pi$$
$$168$$ 0 0
$$169$$ 1284.00 0.584433
$$170$$ 0 0
$$171$$ 1391.50 2410.15i 0.622285 1.07783i
$$172$$ 0 0
$$173$$ 349.500 + 605.352i 0.153595 + 0.266035i 0.932547 0.361049i $$-0.117581\pi$$
−0.778951 + 0.627084i $$0.784248\pi$$
$$174$$ 0 0
$$175$$ −437.500 + 151.554i −0.188982 + 0.0654654i
$$176$$ 0 0
$$177$$ −360.000 623.538i −0.152877 0.264791i
$$178$$ 0 0
$$179$$ 1558.50 2699.40i 0.650770 1.12717i −0.332167 0.943221i $$-0.607780\pi$$
0.982936 0.183945i $$-0.0588870\pi$$
$$180$$ 0 0
$$181$$ −1798.00 −0.738366 −0.369183 0.929357i $$-0.620362\pi$$
−0.369183 + 0.929357i $$0.620362\pi$$
$$182$$ 0 0
$$183$$ 784.000 0.316694
$$184$$ 0 0
$$185$$ 647.500 1121.50i 0.257325 0.445700i
$$186$$ 0 0
$$187$$ 1215.00 + 2104.44i 0.475132 + 0.822952i
$$188$$ 0 0
$$189$$ −1400.00 1212.44i −0.538810 0.466623i
$$190$$ 0 0
$$191$$ −1194.00 2068.07i −0.452329 0.783457i 0.546201 0.837654i $$-0.316073\pi$$
−0.998530 + 0.0541974i $$0.982740\pi$$
$$192$$ 0 0
$$193$$ −136.000 + 235.559i −0.0507228 + 0.0878544i −0.890272 0.455429i $$-0.849486\pi$$
0.839549 + 0.543284i $$0.182819\pi$$
$$194$$ 0 0
$$195$$ 590.000 0.216671
$$196$$ 0 0
$$197$$ −2109.00 −0.762741 −0.381371 0.924422i $$-0.624548\pi$$
−0.381371 + 0.924422i $$0.624548\pi$$
$$198$$ 0 0
$$199$$ 712.000 1233.22i 0.253630 0.439300i −0.710893 0.703301i $$-0.751709\pi$$
0.964522 + 0.264001i $$0.0850422\pi$$
$$200$$ 0 0
$$201$$ −280.000 484.974i −0.0982571 0.170186i
$$202$$ 0 0
$$203$$ −2268.00 1964.15i −0.784150 0.679094i
$$204$$ 0 0
$$205$$ −487.500 844.375i −0.166090 0.287677i
$$206$$ 0 0
$$207$$ −793.500 + 1374.38i −0.266435 + 0.461479i
$$208$$ 0 0
$$209$$ 5445.00 1.80210
$$210$$ 0 0
$$211$$ 3625.00 1.18273 0.591363 0.806405i $$-0.298590\pi$$
0.591363 + 0.806405i $$0.298590\pi$$
$$212$$ 0 0
$$213$$ 48.0000 83.1384i 0.0154409 0.0267444i
$$214$$ 0 0
$$215$$ −715.000 1238.42i −0.226803 0.392834i
$$216$$ 0 0
$$217$$ −1540.00 + 533.472i −0.481760 + 0.166887i
$$218$$ 0 0
$$219$$ −668.000 1157.01i −0.206115 0.357002i
$$220$$ 0 0
$$221$$ 1593.00 2759.16i 0.484872 0.839823i
$$222$$ 0 0
$$223$$ 4960.00 1.48944 0.744722 0.667374i $$-0.232582\pi$$
0.744722 + 0.667374i $$0.232582\pi$$
$$224$$ 0 0
$$225$$ −575.000 −0.170370
$$226$$ 0 0
$$227$$ −750.000 + 1299.04i −0.219292 + 0.379825i −0.954592 0.297917i $$-0.903708\pi$$
0.735300 + 0.677742i $$0.237041\pi$$
$$228$$ 0 0
$$229$$ −3046.00 5275.83i −0.878975 1.52243i −0.852467 0.522781i $$-0.824894\pi$$
−0.0265085 0.999649i $$-0.508439\pi$$
$$230$$ 0 0
$$231$$ 315.000 1636.79i 0.0897207 0.466202i
$$232$$ 0 0
$$233$$ −69.0000 119.512i −0.0194006 0.0336028i 0.856162 0.516707i $$-0.172842\pi$$
−0.875563 + 0.483104i $$0.839509\pi$$
$$234$$ 0 0
$$235$$ 112.500 194.856i 0.0312285 0.0540893i
$$236$$ 0 0
$$237$$ −1564.00 −0.428661
$$238$$ 0 0
$$239$$ 5502.00 1.48910 0.744550 0.667567i $$-0.232664\pi$$
0.744550 + 0.667567i $$0.232664\pi$$
$$240$$ 0 0
$$241$$ −1775.50 + 3075.26i −0.474564 + 0.821970i −0.999576 0.0291256i $$-0.990728\pi$$
0.525011 + 0.851095i $$0.324061\pi$$
$$242$$ 0 0
$$243$$ −1771.00 3067.46i −0.467530 0.809785i
$$244$$ 0 0
$$245$$ 1347.50 1060.88i 0.351382 0.276642i
$$246$$ 0 0
$$247$$ −3569.50 6182.56i −0.919522 1.59266i
$$248$$ 0 0
$$249$$ 768.000 1330.22i 0.195462 0.338550i
$$250$$ 0 0
$$251$$ −7065.00 −1.77665 −0.888324 0.459216i $$-0.848130\pi$$
−0.888324 + 0.459216i $$0.848130\pi$$
$$252$$ 0 0
$$253$$ −3105.00 −0.771580
$$254$$ 0 0
$$255$$ 270.000 467.654i 0.0663061 0.114846i
$$256$$ 0 0
$$257$$ 2040.00 + 3533.38i 0.495143 + 0.857613i 0.999984 0.00559954i $$-0.00178240\pi$$
−0.504842 + 0.863212i $$0.668449\pi$$
$$258$$ 0 0
$$259$$ −906.500 + 4710.31i −0.217479 + 1.13006i
$$260$$ 0 0
$$261$$ −1863.00 3226.81i −0.441827 0.765267i
$$262$$ 0 0
$$263$$ −1644.00 + 2847.49i −0.385450 + 0.667619i −0.991832 0.127555i $$-0.959287\pi$$
0.606381 + 0.795174i $$0.292620\pi$$
$$264$$ 0 0
$$265$$ 2985.00 0.691951
$$266$$ 0 0
$$267$$ −2388.00 −0.547353
$$268$$ 0 0
$$269$$ 1632.00 2826.71i 0.369906 0.640697i −0.619644 0.784883i $$-0.712723\pi$$
0.989551 + 0.144186i $$0.0460564\pi$$
$$270$$ 0 0
$$271$$ −1376.00 2383.30i −0.308436 0.534226i 0.669585 0.742736i $$-0.266472\pi$$
−0.978020 + 0.208510i $$0.933139\pi$$
$$272$$ 0 0
$$273$$ −2065.00 + 715.337i −0.457800 + 0.158587i
$$274$$ 0 0
$$275$$ −562.500 974.279i −0.123346 0.213641i
$$276$$ 0 0
$$277$$ 2345.00 4061.66i 0.508655 0.881016i −0.491295 0.870993i $$-0.663476\pi$$
0.999950 0.0100228i $$-0.00319040\pi$$
$$278$$ 0 0
$$279$$ −2024.00 −0.434314
$$280$$ 0 0
$$281$$ 7821.00 1.66036 0.830181 0.557494i $$-0.188237\pi$$
0.830181 + 0.557494i $$0.188237\pi$$
$$282$$ 0 0
$$283$$ −329.000 + 569.845i −0.0691061 + 0.119695i −0.898508 0.438957i $$-0.855348\pi$$
0.829402 + 0.558652i $$0.188681\pi$$
$$284$$ 0 0
$$285$$ −605.000 1047.89i −0.125744 0.217795i
$$286$$ 0 0
$$287$$ 2730.00 + 2364.25i 0.561487 + 0.486262i
$$288$$ 0 0
$$289$$ 998.500 + 1729.45i 0.203236 + 0.352016i
$$290$$ 0 0
$$291$$ −902.000 + 1562.31i −0.181705 + 0.314722i
$$292$$ 0 0
$$293$$ −5997.00 −1.19573 −0.597864 0.801597i $$-0.703984\pi$$
−0.597864 + 0.801597i $$0.703984\pi$$
$$294$$ 0 0
$$295$$ 1800.00 0.355254
$$296$$ 0 0
$$297$$ 2250.00 3897.11i 0.439590 0.761392i
$$298$$ 0 0
$$299$$ 2035.50 + 3525.59i 0.393699 + 0.681907i
$$300$$ 0 0
$$301$$ 4004.00 + 3467.57i 0.766733 + 0.664011i
$$302$$ 0 0
$$303$$ −684.000 1184.72i −0.129686 0.224622i
$$304$$ 0 0
$$305$$ −980.000 + 1697.41i −0.183982 + 0.318667i
$$306$$ 0 0
$$307$$ 6226.00 1.15745 0.578724 0.815523i $$-0.303551\pi$$
0.578724 + 0.815523i $$0.303551\pi$$
$$308$$ 0 0
$$309$$ 3032.00 0.558202
$$310$$ 0 0
$$311$$ 2340.00 4053.00i 0.426653 0.738985i −0.569920 0.821700i $$-0.693026\pi$$
0.996573 + 0.0827149i $$0.0263591\pi$$
$$312$$ 0 0
$$313$$ −514.000 890.274i −0.0928211 0.160771i 0.815876 0.578227i $$-0.196255\pi$$
−0.908697 + 0.417456i $$0.862922\pi$$
$$314$$ 0 0
$$315$$ 2012.50 697.150i 0.359973 0.124698i
$$316$$ 0 0
$$317$$ −4311.00 7466.87i −0.763817 1.32297i −0.940870 0.338768i $$-0.889990\pi$$
0.177053 0.984201i $$-0.443344\pi$$
$$318$$ 0 0
$$319$$ 3645.00 6313.33i 0.639752 1.10808i
$$320$$ 0 0
$$321$$ 1464.00 0.254556
$$322$$ 0 0
$$323$$ −6534.00 −1.12558
$$324$$ 0 0
$$325$$ −737.500 + 1277.39i −0.125874 + 0.218021i
$$326$$ 0 0
$$327$$ 1600.00 + 2771.28i 0.270582 + 0.468661i
$$328$$ 0 0
$$329$$ −157.500 + 818.394i −0.0263929 + 0.137141i
$$330$$ 0 0
$$331$$ −999.500 1731.18i −0.165974 0.287476i 0.771027 0.636803i $$-0.219744\pi$$
−0.937001 + 0.349327i $$0.886410\pi$$
$$332$$ 0 0
$$333$$ −2978.50 + 5158.91i −0.490153 + 0.848969i
$$334$$ 0 0
$$335$$ 1400.00 0.228329
$$336$$ 0 0
$$337$$ 5114.00 0.826639 0.413319 0.910586i $$-0.364369\pi$$
0.413319 + 0.910586i $$0.364369\pi$$
$$338$$ 0 0
$$339$$ 1392.00 2411.01i 0.223018 0.386278i
$$340$$ 0 0
$$341$$ −1980.00 3429.46i −0.314437 0.544621i
$$342$$ 0 0
$$343$$ −3430.00 + 5346.84i −0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 345.000 + 597.558i 0.0538382 + 0.0932505i
$$346$$ 0 0
$$347$$ 2160.00 3741.23i 0.334164 0.578789i −0.649160 0.760652i $$-0.724879\pi$$
0.983324 + 0.181863i $$0.0582128\pi$$
$$348$$ 0 0
$$349$$ 7922.00 1.21506 0.607529 0.794298i $$-0.292161\pi$$
0.607529 + 0.794298i $$0.292161\pi$$
$$350$$ 0 0
$$351$$ −5900.00 −0.897204
$$352$$ 0 0
$$353$$ −414.000 + 717.069i −0.0624221 + 0.108118i −0.895548 0.444966i $$-0.853216\pi$$
0.833125 + 0.553084i $$0.186549\pi$$
$$354$$ 0 0
$$355$$ 120.000 + 207.846i 0.0179407 + 0.0310742i
$$356$$ 0 0
$$357$$ −378.000 + 1964.15i −0.0560389 + 0.291187i
$$358$$ 0 0
$$359$$ −675.000 1169.13i −0.0992344 0.171879i 0.812134 0.583472i $$-0.198306\pi$$
−0.911368 + 0.411593i $$0.864973\pi$$
$$360$$ 0 0
$$361$$ −3891.00 + 6739.41i −0.567284 + 0.982564i
$$362$$ 0 0
$$363$$ 1388.00 0.200692
$$364$$ 0 0
$$365$$ 3340.00 0.478969
$$366$$ 0 0
$$367$$ 1400.50 2425.74i 0.199198 0.345020i −0.749071 0.662490i $$-0.769500\pi$$
0.948268 + 0.317470i $$0.102833\pi$$
$$368$$ 0 0
$$369$$ 2242.50 + 3884.12i 0.316368 + 0.547966i
$$370$$ 0 0
$$371$$ −10447.5 + 3619.12i −1.46201 + 0.506456i
$$372$$ 0 0
$$373$$ −3301.00 5717.50i −0.458229 0.793675i 0.540639 0.841255i $$-0.318183\pi$$
−0.998867 + 0.0475795i $$0.984849\pi$$
$$374$$ 0 0
$$375$$ −125.000 + 216.506i −0.0172133 + 0.0298142i
$$376$$ 0 0
$$377$$ −9558.00 −1.30573
$$378$$ 0 0
$$379$$ 8305.00 1.12559 0.562796 0.826596i $$-0.309726\pi$$
0.562796 + 0.826596i $$0.309726\pi$$
$$380$$ 0 0
$$381$$ 803.000 1390.84i 0.107976 0.187020i
$$382$$ 0 0
$$383$$ 472.500 + 818.394i 0.0630382 + 0.109185i 0.895822 0.444413i $$-0.146588\pi$$
−0.832784 + 0.553598i $$0.813254\pi$$
$$384$$ 0 0
$$385$$ 3150.00 + 2727.98i 0.416984 + 0.361119i
$$386$$ 0 0
$$387$$ 3289.00 + 5696.72i 0.432014 + 0.748270i
$$388$$ 0 0
$$389$$ −6018.00 + 10423.5i −0.784382 + 1.35859i 0.144985 + 0.989434i $$0.453687\pi$$
−0.929367 + 0.369156i $$0.879647\pi$$
$$390$$ 0 0
$$391$$ 3726.00 0.481923
$$392$$ 0 0
$$393$$ −4038.00 −0.518296
$$394$$ 0 0
$$395$$ 1955.00 3386.16i 0.249030 0.431332i
$$396$$ 0 0
$$397$$ 1349.00 + 2336.54i 0.170540 + 0.295384i 0.938609 0.344983i $$-0.112115\pi$$
−0.768069 + 0.640367i $$0.778782\pi$$
$$398$$ 0 0
$$399$$ 3388.00 + 2934.09i 0.425093 + 0.368141i
$$400$$ 0 0
$$401$$ −3526.50 6108.08i −0.439165 0.760655i 0.558461 0.829531i $$-0.311392\pi$$
−0.997625 + 0.0688756i $$0.978059\pi$$
$$402$$ 0 0
$$403$$ −2596.00 + 4496.40i −0.320883 + 0.555786i
$$404$$ 0 0
$$405$$ 2105.00 0.258267
$$406$$ 0 0
$$407$$ −11655.0 −1.41945
$$408$$ 0 0
$$409$$ 5435.00 9413.70i 0.657074 1.13809i −0.324295 0.945956i $$-0.605127\pi$$
0.981369 0.192130i $$-0.0615396\pi$$
$$410$$ 0 0
$$411$$ −60.0000 103.923i −0.00720093 0.0124724i
$$412$$ 0 0
$$413$$ −6300.00 + 2182.38i −0.750612 + 0.260020i
$$414$$ 0 0
$$415$$ 1920.00 + 3325.54i 0.227106 + 0.393360i
$$416$$ 0 0
$$417$$ −1708.00 + 2958.34i −0.200578 + 0.347412i
$$418$$ 0 0
$$419$$ 9729.00 1.13435 0.567175 0.823597i $$-0.308036\pi$$
0.567175 + 0.823597i $$0.308036\pi$$
$$420$$ 0 0
$$421$$ −12550.0 −1.45285 −0.726425 0.687246i $$-0.758819\pi$$
−0.726425 + 0.687246i $$0.758819\pi$$
$$422$$ 0 0
$$423$$ −517.500 + 896.336i −0.0594840 + 0.103029i
$$424$$ 0 0
$$425$$ 675.000 + 1169.13i 0.0770407 + 0.133438i
$$426$$ 0 0
$$427$$ 1372.00 7129.12i 0.155494 0.807968i
$$428$$ 0 0
$$429$$ −2655.00 4598.59i −0.298799 0.517534i
$$430$$ 0 0
$$431$$ 1494.00 2587.68i 0.166969 0.289198i −0.770384 0.637580i $$-0.779935\pi$$
0.937353 + 0.348382i $$0.113269\pi$$
$$432$$ 0 0
$$433$$ 16616.0 1.84414 0.922072 0.387019i $$-0.126495\pi$$
0.922072 + 0.387019i $$0.126495\pi$$
$$434$$ 0 0
$$435$$ −1620.00 −0.178559
$$436$$ 0 0
$$437$$ 4174.50 7230.45i 0.456964 0.791485i
$$438$$ 0 0
$$439$$ 3673.00 + 6361.82i 0.399323 + 0.691647i 0.993642 0.112581i $$-0.0359119\pi$$
−0.594320 + 0.804229i $$0.702579\pi$$
$$440$$ 0 0
$$441$$ −6198.50 + 4880.05i −0.669312 + 0.526947i
$$442$$ 0 0
$$443$$ 6.00000 + 10.3923i 0.000643496 + 0.00111457i 0.866347 0.499443i $$-0.166462\pi$$
−0.865703 + 0.500557i $$0.833129\pi$$
$$444$$ 0 0
$$445$$ 2985.00 5170.17i 0.317983 0.550763i
$$446$$ 0 0
$$447$$ −2172.00 −0.229826
$$448$$ 0 0
$$449$$ 9669.00 1.01628 0.508138 0.861275i $$-0.330334\pi$$
0.508138 + 0.861275i $$0.330334\pi$$
$$450$$ 0 0
$$451$$ −4387.50 + 7599.37i −0.458092 + 0.793438i
$$452$$ 0 0
$$453$$ −2866.00 4964.06i −0.297255 0.514860i
$$454$$ 0 0
$$455$$ 1032.50 5365.03i 0.106383 0.552783i
$$456$$ 0 0
$$457$$ 4817.00 + 8343.29i 0.493063 + 0.854010i 0.999968 0.00799181i $$-0.00254390\pi$$
−0.506905 + 0.862002i $$0.669211\pi$$
$$458$$ 0 0
$$459$$ −2700.00 + 4676.54i −0.274565 + 0.475560i
$$460$$ 0 0
$$461$$ −342.000 −0.0345521 −0.0172761 0.999851i $$-0.505499\pi$$
−0.0172761 + 0.999851i $$0.505499\pi$$
$$462$$ 0 0
$$463$$ −2411.00 −0.242006 −0.121003 0.992652i $$-0.538611\pi$$
−0.121003 + 0.992652i $$0.538611\pi$$
$$464$$ 0 0
$$465$$ −440.000 + 762.102i −0.0438807 + 0.0760035i
$$466$$ 0 0
$$467$$ −603.000 1044.43i −0.0597506 0.103491i 0.834603 0.550852i $$-0.185697\pi$$
−0.894353 + 0.447361i $$0.852364\pi$$
$$468$$ 0 0
$$469$$ −4900.00 + 1697.41i −0.482433 + 0.167120i
$$470$$ 0 0
$$471$$ 229.000 + 396.640i 0.0224029 + 0.0388030i
$$472$$ 0 0
$$473$$ −6435.00 + 11145.7i −0.625543 + 1.08347i
$$474$$ 0 0
$$475$$ 3025.00 0.292203
$$476$$ 0 0
$$477$$ −13731.0 −1.31803
$$478$$ 0 0
$$479$$ −216.000 + 374.123i −0.0206039 + 0.0356871i −0.876144 0.482050i $$-0.839892\pi$$
0.855540 + 0.517737i $$0.173226\pi$$
$$480$$ 0 0
$$481$$ 7640.50 + 13233.7i 0.724276 + 1.25448i
$$482$$ 0 0
$$483$$ −1932.00 1673.16i −0.182006 0.157622i
$$484$$ 0 0
$$485$$ −2255.00 3905.77i −0.211122 0.365674i
$$486$$ 0 0
$$487$$ −5948.00 + 10302.2i −0.553449 + 0.958602i 0.444574 + 0.895742i $$0.353355\pi$$
−0.998022 + 0.0628592i $$0.979978\pi$$
$$488$$ 0 0
$$489$$ 2456.00 0.227125
$$490$$ 0 0
$$491$$ 12276.0 1.12833 0.564163 0.825663i $$-0.309199\pi$$
0.564163 + 0.825663i $$0.309199\pi$$
$$492$$ 0 0
$$493$$ −4374.00 + 7575.99i −0.399584 + 0.692100i
$$494$$ 0 0
$$495$$ 2587.50 + 4481.68i 0.234948 + 0.406943i
$$496$$ 0 0
$$497$$ −672.000 581.969i −0.0606505 0.0525249i
$$498$$ 0 0
$$499$$ −5438.00 9418.89i −0.487852 0.844985i 0.512050 0.858956i $$-0.328886\pi$$
−0.999902 + 0.0139706i $$0.995553\pi$$
$$500$$ 0 0
$$501$$ −1929.00 + 3341.13i −0.172019 + 0.297945i
$$502$$ 0 0
$$503$$ −12000.0 −1.06372 −0.531862 0.846831i $$-0.678508\pi$$
−0.531862 + 0.846831i $$0.678508\pi$$
$$504$$ 0 0
$$505$$ 3420.00 0.301362
$$506$$ 0 0
$$507$$ −1284.00 + 2223.95i −0.112474 + 0.194811i
$$508$$ 0 0
$$509$$ 5841.00 + 10116.9i 0.508640 + 0.880990i 0.999950 + 0.0100055i $$0.00318492\pi$$
−0.491310 + 0.870985i $$0.663482\pi$$
$$510$$ 0 0
$$511$$ −11690.0 + 4049.53i −1.01201 + 0.350569i
$$512$$ 0 0
$$513$$ 6050.00 + 10478.9i 0.520690 + 0.901862i
$$514$$ 0 0
$$515$$ −3790.00 + 6564.47i −0.324286 + 0.561680i
$$516$$ 0 0
$$517$$ −2025.00 −0.172262
$$518$$ 0 0
$$519$$ −1398.00 −0.118238
$$520$$ 0 0
$$521$$ −4804.50 + 8321.64i −0.404010 + 0.699765i −0.994206 0.107495i $$-0.965717\pi$$
0.590196 + 0.807260i $$0.299050\pi$$
$$522$$ 0 0
$$523$$ 10594.0 + 18349.3i 0.885742 + 1.53415i 0.844860 + 0.534987i $$0.179683\pi$$
0.0408820 + 0.999164i $$0.486983\pi$$
$$524$$ 0 0
$$525$$ 175.000 909.327i 0.0145479 0.0755929i
$$526$$ 0 0
$$527$$ 2376.00 + 4115.35i 0.196395 + 0.340166i
$$528$$ 0 0
$$529$$ 3703.00 6413.78i 0.304348 0.527146i
$$530$$ 0 0
$$531$$ −8280.00 −0.676688
$$532$$ 0 0
$$533$$ 11505.0 0.934966
$$534$$ 0 0
$$535$$ −1830.00 + 3169.65i −0.147884 + 0.256142i
$$536$$ 0 0
$$537$$ 3117.00 + 5398.80i 0.250481 + 0.433846i
$$538$$ 0 0
$$539$$ −14332.5 5728.76i −1.14535 0.457802i
$$540$$ 0 0
$$541$$ −4036.00 6990.56i −0.320742 0.555541i 0.659900 0.751354i $$-0.270599\pi$$
−0.980641 + 0.195813i $$0.937265\pi$$
$$542$$ 0 0
$$543$$ 1798.00 3114.23i 0.142099 0.246122i
$$544$$ 0 0
$$545$$ −8000.00 −0.628775
$$546$$ 0 0
$$547$$ −344.000 −0.0268892 −0.0134446 0.999910i $$-0.504280\pi$$
−0.0134446 + 0.999910i $$0.504280\pi$$
$$548$$ 0 0
$$549$$ 4508.00 7808.09i 0.350449 0.606996i
$$550$$ 0 0
$$551$$ 9801.00 + 16975.8i 0.757780 + 1.31251i
$$552$$ 0 0
$$553$$ −2737.00 + 14221.9i −0.210468 + 1.09363i
$$554$$ 0 0
$$555$$ 1295.00 + 2243.01i 0.0990445 + 0.171550i
$$556$$ 0 0
$$557$$ −9181.50 + 15902.8i −0.698443 + 1.20974i 0.270563 + 0.962702i $$0.412790\pi$$
−0.969006 + 0.247036i $$0.920543\pi$$
$$558$$ 0 0
$$559$$ 16874.0 1.27673
$$560$$ 0 0
$$561$$ −4860.00 −0.365756
$$562$$ 0 0
$$563$$ −3147.00 + 5450.76i −0.235578 + 0.408033i −0.959440 0.281912i $$-0.909032\pi$$
0.723863 + 0.689944i $$0.242365\pi$$
$$564$$ 0 0
$$565$$ 3480.00 + 6027.54i 0.259123 + 0.448815i
$$566$$ 0 0
$$567$$ −7367.50 + 2552.18i −0.545689 + 0.189032i
$$568$$ 0 0
$$569$$ −5866.50 10161.1i −0.432226 0.748637i 0.564839 0.825201i $$-0.308938\pi$$
−0.997065 + 0.0765642i $$0.975605\pi$$
$$570$$ 0 0
$$571$$ 526.000 911.059i 0.0385506 0.0667717i −0.846106 0.533014i $$-0.821059\pi$$
0.884657 + 0.466242i $$0.154393\pi$$
$$572$$ 0 0
$$573$$ 4776.00 0.348203
$$574$$ 0 0
$$575$$ −1725.00 −0.125109
$$576$$ 0 0
$$577$$ 6578.00 11393.4i 0.474603 0.822036i −0.524974 0.851118i $$-0.675925\pi$$
0.999577 + 0.0290821i $$0.00925844\pi$$
$$578$$ 0 0
$$579$$ −272.000 471.118i −0.0195232 0.0338152i
$$580$$ 0 0
$$581$$ −10752.0 9311.51i −0.767759 0.664899i
$$582$$ 0 0
$$583$$ −13432.5 23265.8i −0.954232 1.65278i
$$584$$ 0 0
$$585$$ 3392.50 5875.98i 0.239765 0.415285i
$$586$$ 0 0
$$587$$ 13368.0 0.939960 0.469980 0.882677i $$-0.344261\pi$$
0.469980 + 0.882677i $$0.344261\pi$$
$$588$$ 0 0
$$589$$ 10648.0 0.744895
$$590$$ 0 0
$$591$$ 2109.00 3652.90i 0.146790 0.254247i
$$592$$ 0 0
$$593$$ −13332.0 23091.7i −0.923237 1.59909i −0.794372 0.607431i $$-0.792200\pi$$
−0.128865 0.991662i $$-0.541133\pi$$
$$594$$ 0 0
$$595$$ −3780.00 3273.58i −0.260445 0.225552i
$$596$$ 0 0
$$597$$ 1424.00 + 2466.44i 0.0976222 + 0.169087i
$$598$$ 0 0
$$599$$ 3807.00 6593.92i 0.259682 0.449783i −0.706474 0.707739i $$-0.749715\pi$$
0.966157 + 0.257955i $$0.0830488\pi$$
$$600$$ 0 0
$$601$$ 6410.00 0.435057 0.217529 0.976054i $$-0.430200\pi$$
0.217529 + 0.976054i $$0.430200\pi$$
$$602$$ 0 0
$$603$$ −6440.00 −0.434921
$$604$$ 0 0
$$605$$ −1735.00 + 3005.11i −0.116591 + 0.201942i
$$606$$ 0 0
$$607$$ −10734.5 18592.7i −0.717792 1.24325i −0.961873 0.273498i $$-0.911819\pi$$
0.244080 0.969755i $$-0.421514\pi$$
$$608$$ 0 0
$$609$$ 5670.00 1964.15i 0.377274 0.130692i
$$610$$ 0 0
$$611$$ 1327.50 + 2299.30i 0.0878967 + 0.152242i
$$612$$ 0 0
$$613$$ −1868.50 + 3236.34i −0.123113 + 0.213237i −0.920994 0.389578i $$-0.872621\pi$$
0.797881 + 0.602815i $$0.205954\pi$$
$$614$$ 0 0
$$615$$ 1950.00 0.127856
$$616$$ 0 0
$$617$$ 18078.0 1.17957 0.589784 0.807561i $$-0.299213\pi$$
0.589784 + 0.807561i $$0.299213\pi$$
$$618$$ 0 0
$$619$$ 6143.50 10640.9i 0.398915 0.690940i −0.594678 0.803964i $$-0.702720\pi$$
0.993592 + 0.113024i $$0.0360537\pi$$
$$620$$ 0 0
$$621$$ −3450.00 5975.58i −0.222937 0.386138i
$$622$$ 0 0
$$623$$ −4179.00 + 21714.7i −0.268745 + 1.39644i
$$624$$ 0 0
$$625$$ −312.500 541.266i −0.0200000 0.0346410i
$$626$$ 0 0
$$627$$ −5445.00 + 9431.02i −0.346814 + 0.600699i
$$628$$ 0 0
$$629$$ 13986.0 0.886579
$$630$$ 0 0
$$631$$ 9580.00 0.604396 0.302198 0.953245i $$-0.402280\pi$$
0.302198 + 0.953245i $$0.402280\pi$$
$$632$$ 0 0
$$633$$ −3625.00 + 6278.68i −0.227616 + 0.394242i
$$634$$ 0 0
$$635$$ 2007.50 + 3477.09i 0.125457 + 0.217298i
$$636$$ 0 0
$$637$$ 2891.00 + 20029.4i 0.179820 + 1.24583i
$$638$$ 0 0
$$639$$ −552.000 956.092i −0.0341734 0.0591900i
$$640$$ 0 0
$$641$$ −5389.50 + 9334.89i −0.332094 + 0.575204i −0.982922 0.184021i $$-0.941089\pi$$
0.650828 + 0.759225i $$0.274422\pi$$
$$642$$ 0 0
$$643$$ −8882.00 −0.544746 −0.272373 0.962192i $$-0.587809\pi$$
−0.272373 + 0.962192i $$0.587809\pi$$
$$644$$ 0 0
$$645$$ 2860.00 0.174593
$$646$$ 0 0
$$647$$ −5509.50 + 9542.73i −0.334777 + 0.579851i −0.983442 0.181223i $$-0.941994\pi$$
0.648665 + 0.761074i $$0.275328\pi$$
$$648$$ 0 0
$$649$$ −8100.00 14029.6i −0.489912 0.848552i
$$650$$ 0 0
$$651$$ 616.000 3200.83i 0.0370859 0.192704i
$$652$$ 0 0
$$653$$ −11161.5 19332.3i −0.668887 1.15855i −0.978216 0.207591i $$-0.933438\pi$$
0.309329 0.950955i $$-0.399896\pi$$
$$654$$ 0 0
$$655$$ 5047.50 8742.53i 0.301103 0.521525i
$$656$$ 0 0
$$657$$ −15364.0 −0.912339
$$658$$ 0 0
$$659$$ 11856.0 0.700826 0.350413 0.936595i $$-0.386041\pi$$
0.350413 + 0.936595i $$0.386041\pi$$
$$660$$ 0 0
$$661$$ 16622.0 28790.1i 0.978095 1.69411i 0.308777 0.951134i $$-0.400080\pi$$
0.669318 0.742976i $$-0.266586\pi$$
$$662$$ 0 0
$$663$$ 3186.00 + 5518.31i 0.186627 + 0.323248i
$$664$$ 0 0
$$665$$ −10587.5 + 3667.62i −0.617392 + 0.213871i
$$666$$ 0 0
$$667$$ −5589.00 9680.43i −0.324448 0.561961i
$$668$$ 0 0
$$669$$ −4960.00 + 8590.97i −0.286644 + 0.496482i
$$670$$ 0 0
$$671$$ 17640.0 1.01488
$$672$$ 0 0
$$673$$ −12322.0 −0.705763 −0.352881 0.935668i $$-0.614798\pi$$
−0.352881 + 0.935668i $$0.614798\pi$$
$$674$$ 0 0
$$675$$ 1250.00 2165.06i 0.0712778 0.123457i
$$676$$ 0 0
$$677$$ 6298.50 + 10909.3i 0.357564 + 0.619320i 0.987553 0.157285i $$-0.0502740\pi$$
−0.629989 + 0.776604i $$0.716941\pi$$
$$678$$ 0 0
$$679$$ 12628.0 + 10936.2i 0.713723 + 0.618103i
$$680$$ 0 0
$$681$$ −1500.00 2598.08i −0.0844055 0.146195i
$$682$$ 0 0
$$683$$ −4170.00 + 7222.65i −0.233617 + 0.404637i −0.958870 0.283846i $$-0.908390\pi$$
0.725253 + 0.688483i $$0.241723\pi$$
$$684$$ 0 0
$$685$$ 300.000 0.0167334
$$686$$ 0 0
$$687$$ 12184.0 0.676636
$$688$$ 0 0
$$689$$ −17611.5 + 30504.0i −0.973795 + 1.68666i
$$690$$ 0 0
$$691$$ −10100.0 17493.7i −0.556038 0.963086i −0.997822 0.0659643i $$-0.978988\pi$$
0.441784 0.897121i $$-0.354346\pi$$
$$692$$ 0 0
$$693$$ −14490.0 12548.7i −0.794271 0.687859i
$$694$$ 0 0
$$695$$ −4270.00 7395.86i −0.233051 0.403656i
$$696$$ 0 0
$$697$$ 5265.00 9119.25i 0.286121 0.495576i
$$698$$ 0 0
$$699$$ 276.000 0.0149346
$$700$$ 0 0
$$701$$ 474.000 0.0255388 0.0127694 0.999918i $$-0.495935\pi$$
0.0127694 + 0.999918i $$0.495935\pi$$
$$702$$ 0 0
$$703$$ 15669.5 27140.4i 0.840663 1.45607i
$$704$$ 0 0
$$705$$ 225.000 + 389.711i 0.0120198 + 0.0208190i
$$706$$ 0 0
$$707$$ −11970.0 + 4146.53i −0.636744 + 0.220575i
$$708$$ 0 0
$$709$$ 12563.0 + 21759.8i 0.665463 + 1.15262i 0.979160 + 0.203093i $$0.0650993\pi$$
−0.313696 + 0.949523i $$0.601567\pi$$
$$710$$ 0 0
$$711$$ −8993.00 + 15576.3i −0.474351 + 0.821601i
$$712$$ 0 0
$$713$$ −6072.00 −0.318932
$$714$$ 0 0
$$715$$ 13275.0 0.694345
$$716$$ 0 0
$$717$$ −5502.00 + 9529.74i −0.286577 + 0.496367i
$$718$$ 0 0
$$719$$ −3648.00 6318.52i −0.189218 0.327734i 0.755772 0.654835i $$-0.227262\pi$$
−0.944990 + 0.327100i $$0.893928\pi$$
$$720$$ 0 0
$$721$$ 5306.00 27570.8i 0.274072 1.42412i
$$722$$ 0 0
$$723$$ −3551.00 6150.51i −0.182660 0.316376i
$$724$$ 0 0
$$725$$ 2025.00 3507.40i 0.103733 0.179671i
$$726$$ 0 0
$$727$$ 15421.0 0.786703 0.393352 0.919388i $$-0.371316\pi$$
0.393352 + 0.919388i $$0.371316\pi$$
$$728$$ 0 0
$$729$$ −4283.00 −0.217599
$$730$$ 0 0
$$731$$ 7722.00 13374.9i 0.390709 0.676728i
$$732$$ 0 0
$$733$$ 14583.5 + 25259.4i 0.734862 + 1.27282i 0.954784 + 0.297301i $$0.0960864\pi$$
−0.219922 + 0.975517i $$0.570580\pi$$
$$734$$ 0 0
$$735$$ 490.000 + 3394.82i 0.0245904 + 0.170367i
$$736$$ 0 0
$$737$$ −6300.00 10911.9i −0.314876 0.545381i
$$738$$ 0 0
$$739$$ −6690.50 + 11588.3i −0.333037 + 0.576836i −0.983106 0.183039i $$-0.941407\pi$$
0.650069 + 0.759875i $$0.274740\pi$$
$$740$$ 0 0
$$741$$ 14278.0 0.707848
$$742$$ 0 0
$$743$$ −5487.00 −0.270927 −0.135463 0.990782i $$-0.543252\pi$$
−0.135463 + 0.990782i $$0.543252\pi$$
$$744$$ 0 0
$$745$$ 2715.00 4702.52i 0.133517 0.231258i
$$746$$ 0 0
$$747$$ −8832.00 15297.5i −0.432592 0.749271i
$$748$$ 0 0
$$749$$ 2562.00 13312.5i 0.124985 0.649439i
$$750$$ 0 0
$$751$$ 3319.00 + 5748.68i 0.161268 + 0.279324i 0.935324 0.353793i $$-0.115108\pi$$
−0.774056 + 0.633117i $$0.781775\pi$$
$$752$$ 0 0
$$753$$ 7065.00 12236.9i 0.341916 0.592216i
$$754$$ 0 0
$$755$$ 14330.0 0.690758
$$756$$ 0 0
$$757$$ 14846.0 0.712797 0.356398 0.934334i $$-0.384005\pi$$
0.356398 + 0.934334i $$0.384005\pi$$
$$758$$ 0 0
$$759$$ 3105.00 5378.02i 0.148491 0.257193i
$$760$$ 0 0
$$761$$ 1825.50 + 3161.86i 0.0869571 + 0.150614i 0.906223 0.422799i $$-0.138952\pi$$
−0.819266 + 0.573413i $$0.805619\pi$$
$$762$$ 0 0
$$763$$ 28000.0 9699.48i 1.32853 0.460216i
$$764$$ 0 0
$$765$$ −3105.00 5378.02i −0.146747 0.254173i
$$766$$ 0 0
$$767$$ −10620.0 + 18394.4i −0.499956 + 0.865949i
$$768$$ 0 0
$$769$$ 29855.0 1.40000 0.699999 0.714144i $$-0.253184\pi$$
0.699999 + 0.714144i $$0.253184\pi$$
$$770$$ 0 0
$$771$$ −8160.00 −0.381161
$$772$$ 0 0
$$773$$ 3259.50 5645.62i 0.151664 0.262689i −0.780175 0.625561i $$-0.784870\pi$$
0.931839 + 0.362871i $$0.118204\pi$$
$$774$$ 0 0
$$775$$ −1100.00 1905.26i −0.0509847 0.0883081i
$$776$$ 0 0
$$777$$ −7252.00 6280.42i −0.334831 0.289973i
$$778$$ 0 0
$$779$$ −11797.5 20433.9i −0.542605 0.939819i
$$780$$ 0 0
$$781$$ 1080.00 1870.61i 0.0494820 0.0857053i
$$782$$ 0 0
$$783$$ 16200.0 0.739388
$$784$$ 0 0
$$785$$ −1145.00 −0.0520596