# Properties

 Label 147.4.e.j.67.2 Level $147$ Weight $4$ Character 147.67 Analytic conductor $8.673$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 147.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.67328077084$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.2 Root $$0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 147.67 Dual form 147.4.e.j.79.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.207107 + 0.358719i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(3.91421 - 6.77962i) q^{4} +(0.0502525 + 0.0870399i) q^{5} -1.24264 q^{6} +6.55635 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$$ $$q+(0.207107 + 0.358719i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(3.91421 - 6.77962i) q^{4} +(0.0502525 + 0.0870399i) q^{5} -1.24264 q^{6} +6.55635 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-0.0208153 + 0.0360531i) q^{10} +(21.9706 - 38.0541i) q^{11} +(11.7426 + 20.3389i) q^{12} -16.6447 q^{13} -0.301515 q^{15} +(-29.9558 - 51.8850i) q^{16} +(60.8198 - 105.343i) q^{17} +(1.86396 - 3.22848i) q^{18} +(63.5563 + 110.083i) q^{19} +0.786797 q^{20} +18.2010 q^{22} +(-26.7990 - 46.4172i) q^{23} +(-9.83452 + 17.0339i) q^{24} +(62.4949 - 108.244i) q^{25} +(-3.44722 - 5.97076i) q^{26} +27.0000 q^{27} +235.681 q^{29} +(-0.0624458 - 0.108159i) q^{30} +(9.35534 - 16.2039i) q^{31} +(38.6335 - 66.9152i) q^{32} +(65.9117 + 114.162i) q^{33} +50.3848 q^{34} -70.4558 q^{36} +(95.9411 + 166.175i) q^{37} +(-26.3259 + 45.5978i) q^{38} +(24.9670 - 43.2441i) q^{39} +(0.329473 + 0.570664i) q^{40} -319.713 q^{41} -218.579 q^{43} +(-171.995 - 297.904i) q^{44} +(0.452273 - 0.783359i) q^{45} +(11.1005 - 19.2266i) q^{46} +(-200.777 - 347.755i) q^{47} +179.735 q^{48} +51.7725 q^{50} +(182.459 + 316.029i) q^{51} +(-65.1508 + 112.844i) q^{52} +(-321.558 + 556.956i) q^{53} +(5.59188 + 9.68543i) q^{54} +4.41631 q^{55} -381.338 q^{57} +(48.8112 + 84.5434i) q^{58} +(5.80613 - 10.0565i) q^{59} +(-1.18019 + 2.04416i) q^{60} +(6.12132 + 10.6024i) q^{61} +7.75022 q^{62} -447.288 q^{64} +(-0.836436 - 1.44875i) q^{65} +(-27.3015 + 47.2876i) q^{66} +(-334.524 + 579.412i) q^{67} +(-476.123 - 824.670i) q^{68} +160.794 q^{69} +822.098 q^{71} +(-29.5036 - 51.1017i) q^{72} +(-257.550 + 446.089i) q^{73} +(-39.7401 + 68.8319i) q^{74} +(187.485 + 324.733i) q^{75} +995.092 q^{76} +20.6833 q^{78} +(402.877 + 697.804i) q^{79} +(3.01071 - 5.21471i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-66.2147 - 114.687i) q^{82} -394.863 q^{83} +12.2254 q^{85} +(-45.2691 - 78.4084i) q^{86} +(-353.522 + 612.318i) q^{87} +(144.047 - 249.496i) q^{88} +(-336.709 - 583.197i) q^{89} +0.374675 q^{90} -419.588 q^{92} +(28.0660 + 48.6118i) q^{93} +(83.1644 - 144.045i) q^{94} +(-6.38773 + 11.0639i) q^{95} +(115.901 + 200.746i) q^{96} -1091.11 q^{97} -395.470 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{2} - 6q^{3} + 10q^{4} + 20q^{5} + 12q^{6} - 36q^{8} - 18q^{9} + O(q^{10})$$ $$4q - 2q^{2} - 6q^{3} + 10q^{4} + 20q^{5} + 12q^{6} - 36q^{8} - 18q^{9} + 48q^{10} + 20q^{11} + 30q^{12} - 208q^{13} - 120q^{15} - 18q^{16} + 116q^{17} - 18q^{18} + 192q^{19} + 88q^{20} + 152q^{22} - 28q^{23} + 54q^{24} - 146q^{25} + 204q^{26} + 108q^{27} + 592q^{29} + 144q^{30} - 104q^{31} - 18q^{32} + 60q^{33} + 128q^{34} - 180q^{36} + 248q^{37} + 104q^{38} + 312q^{39} - 488q^{40} - 40q^{41} - 1440q^{43} - 292q^{44} + 180q^{45} + 84q^{46} - 96q^{47} + 108q^{48} + 1412q^{50} + 348q^{51} - 320q^{52} - 268q^{53} - 54q^{54} - 944q^{55} - 1152q^{57} - 48q^{58} - 616q^{59} - 132q^{60} + 16q^{61} + 608q^{62} + 236q^{64} - 1740q^{65} - 228q^{66} + 144q^{67} - 940q^{68} + 168q^{69} + 1976q^{71} + 162q^{72} + 104q^{73} + 56q^{74} - 438q^{75} + 2272q^{76} - 1224q^{78} + 944q^{79} - 828q^{80} - 162q^{81} - 856q^{82} - 2032q^{83} - 200q^{85} + 1120q^{86} - 888q^{87} + 876q^{88} - 388q^{89} - 864q^{90} - 728q^{92} - 312q^{93} + 904q^{94} - 1304q^{95} - 54q^{96} - 976q^{97} - 360q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$$.

 $$n$$ $$50$$ $$52$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.207107 + 0.358719i 0.0732233 + 0.126826i 0.900312 0.435245i $$-0.143338\pi$$
−0.827089 + 0.562071i $$0.810005\pi$$
$$3$$ −1.50000 + 2.59808i −0.288675 + 0.500000i
$$4$$ 3.91421 6.77962i 0.489277 0.847452i
$$5$$ 0.0502525 + 0.0870399i 0.00449472 + 0.00778509i 0.868264 0.496102i $$-0.165236\pi$$
−0.863769 + 0.503887i $$0.831903\pi$$
$$6$$ −1.24264 −0.0845510
$$7$$ 0 0
$$8$$ 6.55635 0.289752
$$9$$ −4.50000 7.79423i −0.166667 0.288675i
$$10$$ −0.0208153 + 0.0360531i −0.000658237 + 0.00114010i
$$11$$ 21.9706 38.0541i 0.602216 1.04307i −0.390269 0.920701i $$-0.627618\pi$$
0.992485 0.122368i $$-0.0390487\pi$$
$$12$$ 11.7426 + 20.3389i 0.282484 + 0.489277i
$$13$$ −16.6447 −0.355108 −0.177554 0.984111i $$-0.556818\pi$$
−0.177554 + 0.984111i $$0.556818\pi$$
$$14$$ 0 0
$$15$$ −0.301515 −0.00519006
$$16$$ −29.9558 51.8850i −0.468060 0.810704i
$$17$$ 60.8198 105.343i 0.867704 1.50291i 0.00336718 0.999994i $$-0.498928\pi$$
0.864337 0.502913i $$-0.167738\pi$$
$$18$$ 1.86396 3.22848i 0.0244078 0.0422755i
$$19$$ 63.5563 + 110.083i 0.767412 + 1.32920i 0.938962 + 0.344021i $$0.111789\pi$$
−0.171550 + 0.985175i $$0.554878\pi$$
$$20$$ 0.786797 0.00879665
$$21$$ 0 0
$$22$$ 18.2010 0.176385
$$23$$ −26.7990 46.4172i −0.242955 0.420811i 0.718599 0.695424i $$-0.244784\pi$$
−0.961555 + 0.274613i $$0.911450\pi$$
$$24$$ −9.83452 + 17.0339i −0.0836443 + 0.144876i
$$25$$ 62.4949 108.244i 0.499960 0.865955i
$$26$$ −3.44722 5.97076i −0.0260021 0.0450370i
$$27$$ 27.0000 0.192450
$$28$$ 0 0
$$29$$ 235.681 1.50913 0.754567 0.656223i $$-0.227847\pi$$
0.754567 + 0.656223i $$0.227847\pi$$
$$30$$ −0.0624458 0.108159i −0.000380033 0.000658237i
$$31$$ 9.35534 16.2039i 0.0542022 0.0938810i −0.837651 0.546205i $$-0.816072\pi$$
0.891853 + 0.452324i $$0.149405\pi$$
$$32$$ 38.6335 66.9152i 0.213422 0.369658i
$$33$$ 65.9117 + 114.162i 0.347689 + 0.602216i
$$34$$ 50.3848 0.254145
$$35$$ 0 0
$$36$$ −70.4558 −0.326184
$$37$$ 95.9411 + 166.175i 0.426287 + 0.738351i 0.996540 0.0831185i $$-0.0264880\pi$$
−0.570253 + 0.821469i $$0.693155\pi$$
$$38$$ −26.3259 + 45.5978i −0.112385 + 0.194656i
$$39$$ 24.9670 43.2441i 0.102511 0.177554i
$$40$$ 0.329473 + 0.570664i 0.00130236 + 0.00225575i
$$41$$ −319.713 −1.21782 −0.608912 0.793238i $$-0.708394\pi$$
−0.608912 + 0.793238i $$0.708394\pi$$
$$42$$ 0 0
$$43$$ −218.579 −0.775184 −0.387592 0.921831i $$-0.626693\pi$$
−0.387592 + 0.921831i $$0.626693\pi$$
$$44$$ −171.995 297.904i −0.589300 1.02070i
$$45$$ 0.452273 0.783359i 0.00149824 0.00259503i
$$46$$ 11.1005 19.2266i 0.0355800 0.0616264i
$$47$$ −200.777 347.755i −0.623113 1.07926i −0.988903 0.148565i $$-0.952535\pi$$
0.365790 0.930697i $$-0.380799\pi$$
$$48$$ 179.735 0.540469
$$49$$ 0 0
$$50$$ 51.7725 0.146435
$$51$$ 182.459 + 316.029i 0.500969 + 0.867704i
$$52$$ −65.1508 + 112.844i −0.173746 + 0.300937i
$$53$$ −321.558 + 556.956i −0.833386 + 1.44347i 0.0619521 + 0.998079i $$0.480267\pi$$
−0.895338 + 0.445387i $$0.853066\pi$$
$$54$$ 5.59188 + 9.68543i 0.0140918 + 0.0244078i
$$55$$ 4.41631 0.0108272
$$56$$ 0 0
$$57$$ −381.338 −0.886131
$$58$$ 48.8112 + 84.5434i 0.110504 + 0.191398i
$$59$$ 5.80613 10.0565i 0.0128118 0.0221906i −0.859548 0.511054i $$-0.829255\pi$$
0.872360 + 0.488864i $$0.162588\pi$$
$$60$$ −1.18019 + 2.04416i −0.00253937 + 0.00439833i
$$61$$ 6.12132 + 10.6024i 0.0128484 + 0.0222541i 0.872378 0.488832i $$-0.162577\pi$$
−0.859530 + 0.511086i $$0.829243\pi$$
$$62$$ 7.75022 0.0158755
$$63$$ 0 0
$$64$$ −447.288 −0.873610
$$65$$ −0.836436 1.44875i −0.00159611 0.00276454i
$$66$$ −27.3015 + 47.2876i −0.0509179 + 0.0881925i
$$67$$ −334.524 + 579.412i −0.609979 + 1.05651i 0.381264 + 0.924466i $$0.375489\pi$$
−0.991243 + 0.132049i $$0.957844\pi$$
$$68$$ −476.123 824.670i −0.849095 1.47068i
$$69$$ 160.794 0.280541
$$70$$ 0 0
$$71$$ 822.098 1.37416 0.687078 0.726584i $$-0.258893\pi$$
0.687078 + 0.726584i $$0.258893\pi$$
$$72$$ −29.5036 51.1017i −0.0482921 0.0836443i
$$73$$ −257.550 + 446.089i −0.412930 + 0.715217i −0.995209 0.0977730i $$-0.968828\pi$$
0.582278 + 0.812990i $$0.302161\pi$$
$$74$$ −39.7401 + 68.8319i −0.0624283 + 0.108129i
$$75$$ 187.485 + 324.733i 0.288652 + 0.499960i
$$76$$ 995.092 1.50191
$$77$$ 0 0
$$78$$ 20.6833 0.0300247
$$79$$ 402.877 + 697.804i 0.573762 + 0.993786i 0.996175 + 0.0873819i $$0.0278500\pi$$
−0.422413 + 0.906404i $$0.638817\pi$$
$$80$$ 3.01071 5.21471i 0.00420760 0.00728778i
$$81$$ −40.5000 + 70.1481i −0.0555556 + 0.0962250i
$$82$$ −66.2147 114.687i −0.0891730 0.154452i
$$83$$ −394.863 −0.522191 −0.261095 0.965313i $$-0.584084\pi$$
−0.261095 + 0.965313i $$0.584084\pi$$
$$84$$ 0 0
$$85$$ 12.2254 0.0156004
$$86$$ −45.2691 78.4084i −0.0567616 0.0983139i
$$87$$ −353.522 + 612.318i −0.435650 + 0.754567i
$$88$$ 144.047 249.496i 0.174493 0.302232i
$$89$$ −336.709 583.197i −0.401024 0.694593i 0.592826 0.805331i $$-0.298012\pi$$
−0.993850 + 0.110737i $$0.964679\pi$$
$$90$$ 0.374675 0.000438825
$$91$$ 0 0
$$92$$ −419.588 −0.475490
$$93$$ 28.0660 + 48.6118i 0.0312937 + 0.0542022i
$$94$$ 83.1644 144.045i 0.0912527 0.158054i
$$95$$ −6.38773 + 11.0639i −0.00689861 + 0.0119487i
$$96$$ 115.901 + 200.746i 0.123219 + 0.213422i
$$97$$ −1091.11 −1.14212 −0.571061 0.820908i $$-0.693468\pi$$
−0.571061 + 0.820908i $$0.693468\pi$$
$$98$$ 0 0
$$99$$ −395.470 −0.401477
$$100$$ −489.237 847.384i −0.489237 0.847384i
$$101$$ 685.395 1187.14i 0.675242 1.16955i −0.301157 0.953575i $$-0.597373\pi$$
0.976398 0.215978i $$-0.0692940\pi$$
$$102$$ −75.5772 + 130.903i −0.0733652 + 0.127072i
$$103$$ 706.978 + 1224.52i 0.676316 + 1.17141i 0.976082 + 0.217401i $$0.0697581\pi$$
−0.299766 + 0.954013i $$0.596909\pi$$
$$104$$ −109.128 −0.102893
$$105$$ 0 0
$$106$$ −266.388 −0.244093
$$107$$ 171.770 + 297.514i 0.155192 + 0.268801i 0.933129 0.359542i $$-0.117067\pi$$
−0.777937 + 0.628343i $$0.783734\pi$$
$$108$$ 105.684 183.050i 0.0941613 0.163092i
$$109$$ 158.828 275.099i 0.139569 0.241740i −0.787765 0.615976i $$-0.788762\pi$$
0.927333 + 0.374236i $$0.122095\pi$$
$$110$$ 0.914647 + 1.58421i 0.000792801 + 0.00137317i
$$111$$ −575.647 −0.492234
$$112$$ 0 0
$$113$$ 798.373 0.664643 0.332321 0.943166i $$-0.392168\pi$$
0.332321 + 0.943166i $$0.392168\pi$$
$$114$$ −78.9777 136.793i −0.0648854 0.112385i
$$115$$ 2.69343 4.66516i 0.00218404 0.00378286i
$$116$$ 922.507 1597.83i 0.738384 1.27892i
$$117$$ 74.9010 + 129.732i 0.0591846 + 0.102511i
$$118$$ 4.80996 0.00375248
$$119$$ 0 0
$$120$$ −1.97684 −0.00150383
$$121$$ −299.911 519.462i −0.225328 0.390279i
$$122$$ −2.53553 + 4.39167i −0.00188161 + 0.00325904i
$$123$$ 479.569 830.638i 0.351555 0.608912i
$$124$$ −73.2376 126.851i −0.0530398 0.0918676i
$$125$$ 25.1253 0.0179782
$$126$$ 0 0
$$127$$ 1071.40 0.748593 0.374297 0.927309i $$-0.377884\pi$$
0.374297 + 0.927309i $$0.377884\pi$$
$$128$$ −401.705 695.773i −0.277391 0.480455i
$$129$$ 327.868 567.884i 0.223776 0.387592i
$$130$$ 0.346463 0.600092i 0.000233745 0.000404858i
$$131$$ 1257.51 + 2178.07i 0.838695 + 1.45266i 0.890986 + 0.454031i $$0.150014\pi$$
−0.0522910 + 0.998632i $$0.516652\pi$$
$$132$$ 1031.97 0.680465
$$133$$ 0 0
$$134$$ −277.129 −0.178659
$$135$$ 1.35682 + 2.35008i 0.000865010 + 0.00149824i
$$136$$ 398.756 690.665i 0.251419 0.435471i
$$137$$ −125.532 + 217.428i −0.0782841 + 0.135592i −0.902510 0.430670i $$-0.858277\pi$$
0.824226 + 0.566262i $$0.191611\pi$$
$$138$$ 33.3015 + 57.6799i 0.0205421 + 0.0355800i
$$139$$ 886.067 0.540685 0.270343 0.962764i $$-0.412863\pi$$
0.270343 + 0.962764i $$0.412863\pi$$
$$140$$ 0 0
$$141$$ 1204.66 0.719508
$$142$$ 170.262 + 294.902i 0.100620 + 0.174279i
$$143$$ −365.693 + 633.398i −0.213851 + 0.370401i
$$144$$ −269.603 + 466.965i −0.156020 + 0.270235i
$$145$$ 11.8436 + 20.5137i 0.00678314 + 0.0117487i
$$146$$ −213.361 −0.120945
$$147$$ 0 0
$$148$$ 1502.14 0.834289
$$149$$ −291.313 504.569i −0.160170 0.277422i 0.774760 0.632256i $$-0.217871\pi$$
−0.934929 + 0.354834i $$0.884537\pi$$
$$150$$ −77.6588 + 134.509i −0.0422721 + 0.0732174i
$$151$$ 1405.88 2435.06i 0.757676 1.31233i −0.186357 0.982482i $$-0.559668\pi$$
0.944033 0.329851i $$-0.106999\pi$$
$$152$$ 416.698 + 721.741i 0.222359 + 0.385138i
$$153$$ −1094.76 −0.578469
$$154$$ 0 0
$$155$$ 1.88052 0.000974496
$$156$$ −195.452 338.533i −0.100312 0.173746i
$$157$$ 845.672 1464.75i 0.429885 0.744583i −0.566978 0.823733i $$-0.691887\pi$$
0.996863 + 0.0791504i $$0.0252207\pi$$
$$158$$ −166.877 + 289.040i −0.0840256 + 0.145537i
$$159$$ −964.675 1670.87i −0.481156 0.833386i
$$160$$ 7.76573 0.00383709
$$161$$ 0 0
$$162$$ −33.5513 −0.0162718
$$163$$ 20.3616 + 35.2674i 0.00978432 + 0.0169469i 0.870876 0.491503i $$-0.163552\pi$$
−0.861092 + 0.508450i $$0.830219\pi$$
$$164$$ −1251.42 + 2167.53i −0.595852 + 1.03205i
$$165$$ −6.62446 + 11.4739i −0.00312554 + 0.00541359i
$$166$$ −81.7788 141.645i −0.0382365 0.0662276i
$$167$$ 2900.47 1.34398 0.671990 0.740560i $$-0.265440\pi$$
0.671990 + 0.740560i $$0.265440\pi$$
$$168$$ 0 0
$$169$$ −1919.96 −0.873899
$$170$$ 2.53196 + 4.38549i 0.00114231 + 0.00197854i
$$171$$ 572.007 990.745i 0.255804 0.443065i
$$172$$ −855.563 + 1481.88i −0.379280 + 0.656932i
$$173$$ 1073.07 + 1858.62i 0.471585 + 0.816810i 0.999472 0.0325052i $$-0.0103485\pi$$
−0.527886 + 0.849315i $$0.677015\pi$$
$$174$$ −292.867 −0.127599
$$175$$ 0 0
$$176$$ −2632.59 −1.12749
$$177$$ 17.4184 + 30.1695i 0.00739688 + 0.0128118i
$$178$$ 139.470 241.568i 0.0587286 0.101721i
$$179$$ −601.770 + 1042.30i −0.251276 + 0.435222i −0.963877 0.266347i $$-0.914183\pi$$
0.712602 + 0.701569i $$0.247517\pi$$
$$180$$ −3.54058 6.13247i −0.00146611 0.00253937i
$$181$$ −2990.47 −1.22807 −0.614033 0.789280i $$-0.710454\pi$$
−0.614033 + 0.789280i $$0.710454\pi$$
$$182$$ 0 0
$$183$$ −36.7279 −0.0148361
$$184$$ −175.704 304.327i −0.0703969 0.121931i
$$185$$ −9.64257 + 16.7014i −0.00383209 + 0.00663737i
$$186$$ −11.6253 + 20.1357i −0.00458285 + 0.00793773i
$$187$$ −2672.49 4628.89i −1.04509 1.81015i
$$188$$ −3143.53 −1.21950
$$189$$ 0 0
$$190$$ −5.29177 −0.00202056
$$191$$ 1403.70 + 2431.29i 0.531772 + 0.921057i 0.999312 + 0.0370847i $$0.0118071\pi$$
−0.467540 + 0.883972i $$0.654860\pi$$
$$192$$ 670.933 1162.09i 0.252190 0.436805i
$$193$$ −1668.18 + 2889.38i −0.622169 + 1.07763i 0.366913 + 0.930255i $$0.380415\pi$$
−0.989081 + 0.147372i $$0.952919\pi$$
$$194$$ −225.977 391.404i −0.0836299 0.144851i
$$195$$ 5.01862 0.00184303
$$196$$ 0 0
$$197$$ −4226.65 −1.52861 −0.764305 0.644855i $$-0.776918\pi$$
−0.764305 + 0.644855i $$0.776918\pi$$
$$198$$ −81.9045 141.863i −0.0293975 0.0509179i
$$199$$ −2192.85 + 3798.12i −0.781140 + 1.35297i 0.150139 + 0.988665i $$0.452028\pi$$
−0.931278 + 0.364309i $$0.881305\pi$$
$$200$$ 409.739 709.688i 0.144865 0.250913i
$$201$$ −1003.57 1738.24i −0.352172 0.609979i
$$202$$ 567.800 0.197774
$$203$$ 0 0
$$204$$ 2856.74 0.980450
$$205$$ −16.0664 27.8278i −0.00547378 0.00948086i
$$206$$ −292.840 + 507.213i −0.0990442 + 0.171550i
$$207$$ −241.191 + 417.755i −0.0809852 + 0.140270i
$$208$$ 498.605 + 863.609i 0.166212 + 0.287887i
$$209$$ 5585.48 1.84859
$$210$$ 0 0
$$211$$ 2291.56 0.747665 0.373833 0.927496i $$-0.378043\pi$$
0.373833 + 0.927496i $$0.378043\pi$$
$$212$$ 2517.30 + 4360.09i 0.815513 + 1.41251i
$$213$$ −1233.15 + 2135.87i −0.396684 + 0.687078i
$$214$$ −71.1493 + 123.234i −0.0227274 + 0.0393650i
$$215$$ −10.9841 19.0251i −0.00348424 0.00603488i
$$216$$ 177.021 0.0557629
$$217$$ 0 0
$$218$$ 131.578 0.0408788
$$219$$ −772.649 1338.27i −0.238406 0.412930i
$$220$$ 17.2864 29.9409i 0.00529748 0.00917551i
$$221$$ −1012.33 + 1753.40i −0.308128 + 0.533694i
$$222$$ −119.220 206.496i −0.0360430 0.0624283i
$$223$$ −217.970 −0.0654544 −0.0327272 0.999464i $$-0.510419\pi$$
−0.0327272 + 0.999464i $$0.510419\pi$$
$$224$$ 0 0
$$225$$ −1124.91 −0.333306
$$226$$ 165.349 + 286.392i 0.0486674 + 0.0842943i
$$227$$ −917.680 + 1589.47i −0.268320 + 0.464743i −0.968428 0.249293i $$-0.919802\pi$$
0.700108 + 0.714037i $$0.253135\pi$$
$$228$$ −1492.64 + 2585.33i −0.433563 + 0.750954i
$$229$$ −1387.00 2402.36i −0.400244 0.693243i 0.593511 0.804826i $$-0.297741\pi$$
−0.993755 + 0.111583i $$0.964408\pi$$
$$230$$ 2.23131 0.000639689
$$231$$ 0 0
$$232$$ 1545.21 0.437275
$$233$$ 494.356 + 856.250i 0.138997 + 0.240750i 0.927117 0.374771i $$-0.122279\pi$$
−0.788120 + 0.615522i $$0.788945\pi$$
$$234$$ −31.0250 + 53.7369i −0.00866738 + 0.0150123i
$$235$$ 20.1791 34.9512i 0.00560144 0.00970197i
$$236$$ −45.4529 78.7267i −0.0125370 0.0217147i
$$237$$ −2417.26 −0.662524
$$238$$ 0 0
$$239$$ −837.928 −0.226783 −0.113391 0.993550i $$-0.536171\pi$$
−0.113391 + 0.993550i $$0.536171\pi$$
$$240$$ 9.03214 + 15.6441i 0.00242926 + 0.00420760i
$$241$$ 1727.49 2992.11i 0.461733 0.799745i −0.537315 0.843382i $$-0.680561\pi$$
0.999047 + 0.0436371i $$0.0138945\pi$$
$$242$$ 124.227 215.168i 0.0329985 0.0571551i
$$243$$ −121.500 210.444i −0.0320750 0.0555556i
$$244$$ 95.8406 0.0251458
$$245$$ 0 0
$$246$$ 397.288 0.102968
$$247$$ −1057.87 1832.29i −0.272514 0.472008i
$$248$$ 61.3369 106.239i 0.0157052 0.0272022i
$$249$$ 592.294 1025.88i 0.150743 0.261095i
$$250$$ 5.20361 + 9.01292i 0.00131642 + 0.00228011i
$$251$$ 5635.01 1.41705 0.708523 0.705688i $$-0.249362\pi$$
0.708523 + 0.705688i $$0.249362\pi$$
$$252$$ 0 0
$$253$$ −2355.16 −0.585246
$$254$$ 221.894 + 384.332i 0.0548145 + 0.0949414i
$$255$$ −18.3381 + 31.7625i −0.00450344 + 0.00780018i
$$256$$ −1622.76 + 2810.71i −0.396182 + 0.686208i
$$257$$ 1135.58 + 1966.88i 0.275624 + 0.477395i 0.970292 0.241935i $$-0.0777821\pi$$
−0.694668 + 0.719330i $$0.744449\pi$$
$$258$$ 271.615 0.0655426
$$259$$ 0 0
$$260$$ −13.0960 −0.00312376
$$261$$ −1060.57 1836.95i −0.251522 0.435650i
$$262$$ −520.877 + 902.186i −0.122824 + 0.212737i
$$263$$ −81.9336 + 141.913i −0.0192101 + 0.0332728i −0.875471 0.483271i $$-0.839448\pi$$
0.856261 + 0.516544i $$0.172782\pi$$
$$264$$ 432.140 + 748.489i 0.100744 + 0.174493i
$$265$$ −64.6365 −0.0149834
$$266$$ 0 0
$$267$$ 2020.26 0.463062
$$268$$ 2618.80 + 4535.89i 0.596897 + 1.03386i
$$269$$ 2583.55 4474.84i 0.585582 1.01426i −0.409220 0.912436i $$-0.634199\pi$$
0.994803 0.101823i $$-0.0324675\pi$$
$$270$$ −0.562013 + 0.973434i −0.000126678 + 0.000219412i
$$271$$ 811.136 + 1404.93i 0.181819 + 0.314920i 0.942500 0.334206i $$-0.108468\pi$$
−0.760681 + 0.649126i $$0.775135\pi$$
$$272$$ −7287.63 −1.62455
$$273$$ 0 0
$$274$$ −103.994 −0.0229289
$$275$$ −2746.10 4756.38i −0.602167 1.04298i
$$276$$ 629.382 1090.12i 0.137262 0.237745i
$$277$$ 2306.18 3994.43i 0.500235 0.866433i −0.499765 0.866161i $$-0.666580\pi$$
1.00000 0.000271708i $$-8.64874e-5\pi$$
$$278$$ 183.511 + 317.850i 0.0395908 + 0.0685732i
$$279$$ −168.396 −0.0361348
$$280$$ 0 0
$$281$$ −2125.22 −0.451174 −0.225587 0.974223i $$-0.572430\pi$$
−0.225587 + 0.974223i $$0.572430\pi$$
$$282$$ 249.493 + 432.135i 0.0526848 + 0.0912527i
$$283$$ −1285.77 + 2227.02i −0.270075 + 0.467783i −0.968881 0.247528i $$-0.920382\pi$$
0.698806 + 0.715311i $$0.253715\pi$$
$$284$$ 3217.87 5573.51i 0.672342 1.16453i
$$285$$ −19.1632 33.1916i −0.00398291 0.00689861i
$$286$$ −302.950 −0.0626356
$$287$$ 0 0
$$288$$ −695.403 −0.142281
$$289$$ −4941.60 8559.10i −1.00582 1.74213i
$$290$$ −4.90577 + 8.49704i −0.000993368 + 0.00172056i
$$291$$ 1636.67 2834.80i 0.329702 0.571061i
$$292$$ 2016.21 + 3492.18i 0.404075 + 0.699878i
$$293$$ −3324.96 −0.662957 −0.331478 0.943463i $$-0.607547\pi$$
−0.331478 + 0.943463i $$0.607547\pi$$
$$294$$ 0 0
$$295$$ 1.16709 0.000230341
$$296$$ 629.024 + 1089.50i 0.123518 + 0.213939i
$$297$$ 593.205 1027.46i 0.115896 0.200739i
$$298$$ 120.666 208.999i 0.0234563 0.0406275i
$$299$$ 446.060 + 772.599i 0.0862753 + 0.149433i
$$300$$ 2935.42 0.564922
$$301$$ 0 0
$$302$$ 1164.67 0.221918
$$303$$ 2056.19 + 3561.42i 0.389851 + 0.675242i
$$304$$ 3807.77 6595.25i 0.718390 1.24429i
$$305$$ −0.615224 + 1.06560i −0.000115500 + 0.000200052i
$$306$$ −226.731 392.710i −0.0423574 0.0733652i
$$307$$ 887.096 0.164916 0.0824580 0.996595i $$-0.473723\pi$$
0.0824580 + 0.996595i $$0.473723\pi$$
$$308$$ 0 0
$$309$$ −4241.87 −0.780943
$$310$$ 0.389468 + 0.674578i 7.13558e−5 + 0.000123592i
$$311$$ −2255.41 + 3906.48i −0.411230 + 0.712271i −0.995025 0.0996300i $$-0.968234\pi$$
0.583794 + 0.811902i $$0.301567\pi$$
$$312$$ 163.692 283.523i 0.0297027 0.0514466i
$$313$$ 1857.89 + 3217.96i 0.335509 + 0.581118i 0.983582 0.180459i $$-0.0577584\pi$$
−0.648074 + 0.761578i $$0.724425\pi$$
$$314$$ 700.577 0.125910
$$315$$ 0 0
$$316$$ 6307.79 1.12291
$$317$$ −3477.26 6022.79i −0.616096 1.06711i −0.990191 0.139719i $$-0.955380\pi$$
0.374095 0.927390i $$-0.377953\pi$$
$$318$$ 399.582 692.096i 0.0704636 0.122047i
$$319$$ 5178.05 8968.64i 0.908825 1.57413i
$$320$$ −22.4774 38.9320i −0.00392664 0.00680113i
$$321$$ −1030.62 −0.179201
$$322$$ 0 0
$$323$$ 15461.9 2.66355
$$324$$ 317.051 + 549.149i 0.0543641 + 0.0941613i
$$325$$ −1040.21 + 1801.69i −0.177539 + 0.307507i
$$326$$ −8.43406 + 14.6082i −0.00143288 + 0.00248182i
$$327$$ 476.485 + 825.297i 0.0805801 + 0.139569i
$$328$$ −2096.15 −0.352867
$$329$$ 0 0
$$330$$ −5.48788 −0.000915448
$$331$$ 4931.59 + 8541.76i 0.818926 + 1.41842i 0.906474 + 0.422262i $$0.138764\pi$$
−0.0875478 + 0.996160i $$0.527903\pi$$
$$332$$ −1545.58 + 2677.02i −0.255496 + 0.442532i
$$333$$ 863.470 1495.57i 0.142096 0.246117i
$$334$$ 600.706 + 1040.45i 0.0984107 + 0.170452i
$$335$$ −67.2427 −0.0109668
$$336$$ 0 0
$$337$$ −5945.06 −0.960974 −0.480487 0.877002i $$-0.659540\pi$$
−0.480487 + 0.877002i $$0.659540\pi$$
$$338$$ −397.636 688.725i −0.0639897 0.110833i
$$339$$ −1197.56 + 2074.24i −0.191866 + 0.332321i
$$340$$ 47.8528 82.8835i 0.00763289 0.0132206i
$$341$$ −411.084 712.019i −0.0652829 0.113073i
$$342$$ 473.866 0.0749232
$$343$$ 0 0
$$344$$ −1433.08 −0.224612
$$345$$ 8.08030 + 13.9955i 0.00126095 + 0.00218404i
$$346$$ −444.482 + 769.865i −0.0690621 + 0.119619i
$$347$$ −584.786 + 1012.88i −0.0904697 + 0.156698i −0.907709 0.419601i $$-0.862170\pi$$
0.817239 + 0.576299i $$0.195503\pi$$
$$348$$ 2767.52 + 4793.49i 0.426306 + 0.738384i
$$349$$ 9176.66 1.40749 0.703747 0.710451i $$-0.251509\pi$$
0.703747 + 0.710451i $$0.251509\pi$$
$$350$$ 0 0
$$351$$ −449.406 −0.0683405
$$352$$ −1697.60 2940.33i −0.257052 0.445228i
$$353$$ 5293.60 9168.78i 0.798158 1.38245i −0.122656 0.992449i $$-0.539141\pi$$
0.920814 0.390001i $$-0.127526\pi$$
$$354$$ −7.21494 + 12.4966i −0.00108325 + 0.00187624i
$$355$$ 41.3125 + 71.5553i 0.00617645 + 0.0106979i
$$356$$ −5271.81 −0.784846
$$357$$ 0 0
$$358$$ −498.522 −0.0735970
$$359$$ −4307.61 7460.99i −0.633278 1.09687i −0.986877 0.161472i $$-0.948376\pi$$
0.353599 0.935397i $$-0.384958\pi$$
$$360$$ 2.96526 5.13598i 0.000434119 0.000751916i
$$361$$ −4649.32 + 8052.86i −0.677842 + 1.17406i
$$362$$ −619.347 1072.74i −0.0899230 0.155751i
$$363$$ 1799.47 0.260186
$$364$$ 0 0
$$365$$ −51.7701 −0.00742403
$$366$$ −7.60660 13.1750i −0.00108635 0.00188161i
$$367$$ 4148.89 7186.10i 0.590110 1.02210i −0.404107 0.914712i $$-0.632418\pi$$
0.994217 0.107389i $$-0.0342492\pi$$
$$368$$ −1605.57 + 2780.93i −0.227436 + 0.393930i
$$369$$ 1438.71 + 2491.91i 0.202971 + 0.351555i
$$370$$ −7.98817 −0.00112239
$$371$$ 0 0
$$372$$ 439.426 0.0612450
$$373$$ 2561.93 + 4437.39i 0.355634 + 0.615977i 0.987226 0.159324i $$-0.0509315\pi$$
−0.631592 + 0.775301i $$0.717598\pi$$
$$374$$ 1106.98 1917.35i 0.153050 0.265090i
$$375$$ −37.6879 + 65.2773i −0.00518985 + 0.00898908i
$$376$$ −1316.36 2280.01i −0.180548 0.312719i
$$377$$ −3922.83 −0.535905
$$378$$ 0 0
$$379$$ −1502.49 −0.203635 −0.101817 0.994803i $$-0.532466\pi$$
−0.101817 + 0.994803i $$0.532466\pi$$
$$380$$ 50.0059 + 86.6128i 0.00675066 + 0.0116925i
$$381$$ −1607.10 + 2783.58i −0.216100 + 0.374297i
$$382$$ −581.434 + 1007.07i −0.0778763 + 0.134886i
$$383$$ −5436.47 9416.24i −0.725301 1.25626i −0.958850 0.283914i $$-0.908367\pi$$
0.233548 0.972345i $$-0.424966\pi$$
$$384$$ 2410.23 0.320303
$$385$$ 0 0
$$386$$ −1381.97 −0.182229
$$387$$ 983.604 + 1703.65i 0.129197 + 0.223776i
$$388$$ −4270.85 + 7397.33i −0.558814 + 0.967894i
$$389$$ −2309.50 + 4000.16i −0.301018 + 0.521379i −0.976367 0.216120i $$-0.930660\pi$$
0.675349 + 0.737499i $$0.263993\pi$$
$$390$$ 1.03939 + 1.80028i 0.000134953 + 0.000233745i
$$391$$ −6519.64 −0.843254
$$392$$ 0 0
$$393$$ −7545.05 −0.968442
$$394$$ −875.367 1516.18i −0.111930 0.193868i
$$395$$ −40.4912 + 70.1328i −0.00515781 + 0.00893358i
$$396$$ −1547.95 + 2681.14i −0.196433 + 0.340233i
$$397$$ 4803.48 + 8319.86i 0.607253 + 1.05179i 0.991691 + 0.128642i $$0.0410620\pi$$
−0.384438 + 0.923151i $$0.625605\pi$$
$$398$$ −1816.61 −0.228791
$$399$$ 0 0
$$400$$ −7488.36 −0.936044
$$401$$ 5250.52 + 9094.17i 0.653862 + 1.13252i 0.982178 + 0.187954i $$0.0601857\pi$$
−0.328316 + 0.944568i $$0.606481\pi$$
$$402$$ 415.693 720.002i 0.0515743 0.0893294i
$$403$$ −155.716 + 269.709i −0.0192476 + 0.0333378i
$$404$$ −5365.57 9293.44i −0.660760 1.14447i
$$405$$ −8.14091 −0.000998827
$$406$$ 0 0
$$407$$ 8431.52 1.02687
$$408$$ 1196.27 + 2072.00i 0.145157 + 0.251419i
$$409$$ −6033.47 + 10450.3i −0.729427 + 1.26340i 0.227699 + 0.973732i $$0.426880\pi$$
−0.957126 + 0.289673i $$0.906453\pi$$
$$410$$ 6.65491 11.5266i 0.000801616 0.00138844i
$$411$$ −376.596 652.283i −0.0451973 0.0782841i
$$412$$ 11069.0 1.32362
$$413$$ 0 0
$$414$$ −199.809 −0.0237200
$$415$$ −19.8429 34.3688i −0.00234710 0.00406530i
$$416$$ −643.042 + 1113.78i −0.0757878 + 0.131268i
$$417$$ −1329.10 + 2302.07i −0.156082 + 0.270343i
$$418$$ 1156.79 + 2003.62i 0.135360 + 0.234450i
$$419$$ 6366.31 0.742278 0.371139 0.928577i $$-0.378967\pi$$
0.371139 + 0.928577i $$0.378967\pi$$
$$420$$ 0 0
$$421$$ −4731.84 −0.547781 −0.273890 0.961761i $$-0.588311\pi$$
−0.273890 + 0.961761i $$0.588311\pi$$
$$422$$ 474.597 + 822.026i 0.0547465 + 0.0948237i
$$423$$ −1806.99 + 3129.80i −0.207704 + 0.359754i
$$424$$ −2108.25 + 3651.60i −0.241476 + 0.418248i
$$425$$ −7601.86 13166.8i −0.867634 1.50279i
$$426$$ −1021.57 −0.116186
$$427$$ 0 0
$$428$$ 2689.37 0.303728
$$429$$ −1097.08 1900.19i −0.123467 0.213851i
$$430$$ 4.54978 7.88044i 0.000510255 0.000883788i
$$431$$ −1876.39 + 3250.01i −0.209704 + 0.363219i −0.951621 0.307273i $$-0.900584\pi$$
0.741917 + 0.670492i $$0.233917\pi$$
$$432$$ −808.808 1400.90i −0.0900782 0.156020i
$$433$$ −11709.2 −1.29956 −0.649780 0.760122i $$-0.725139\pi$$
−0.649780 + 0.760122i $$0.725139\pi$$
$$434$$ 0 0
$$435$$ −71.0615 −0.00783250
$$436$$ −1243.38 2153.59i −0.136576 0.236556i
$$437$$ 3406.49 5900.22i 0.372894 0.645871i
$$438$$ 320.042 554.329i 0.0349137 0.0604723i
$$439$$ −7462.36 12925.2i −0.811296 1.40521i −0.911957 0.410285i $$-0.865429\pi$$
0.100661 0.994921i $$-0.467904\pi$$
$$440$$ 28.9548 0.00313720
$$441$$ 0 0
$$442$$ −838.638 −0.0902487
$$443$$ 4258.83 + 7376.51i 0.456756 + 0.791125i 0.998787 0.0492333i $$-0.0156778\pi$$
−0.542031 + 0.840359i $$0.682344\pi$$
$$444$$ −2253.20 + 3902.66i −0.240839 + 0.417145i
$$445$$ 33.8410 58.6143i 0.00360498 0.00624401i
$$446$$ −45.1430 78.1900i −0.00479279 0.00830135i
$$447$$ 1747.88 0.184948
$$448$$ 0 0
$$449$$ −5965.73 −0.627038 −0.313519 0.949582i $$-0.601508\pi$$
−0.313519 + 0.949582i $$0.601508\pi$$
$$450$$ −232.976 403.527i −0.0244058 0.0422721i
$$451$$ −7024.27 + 12166.4i −0.733392 + 1.27027i
$$452$$ 3125.00 5412.67i 0.325194 0.563253i
$$453$$ 4217.65 + 7305.18i 0.437444 + 0.757676i
$$454$$ −760.231 −0.0785890
$$455$$ 0 0
$$456$$ −2500.19 −0.256759
$$457$$ 6930.28 + 12003.6i 0.709376 + 1.22868i 0.965089 + 0.261923i $$0.0843567\pi$$
−0.255712 + 0.966753i $$0.582310\pi$$
$$458$$ 574.516 995.091i 0.0586143 0.101523i
$$459$$ 1642.13 2844.26i 0.166990 0.289235i
$$460$$ −21.0854 36.5209i −0.00213719 0.00370173i
$$461$$ 149.312 0.0150850 0.00754249 0.999972i $$-0.497599\pi$$
0.00754249 + 0.999972i $$0.497599\pi$$
$$462$$ 0 0
$$463$$ 5403.95 0.542425 0.271213 0.962519i $$-0.412575\pi$$
0.271213 + 0.962519i $$0.412575\pi$$
$$464$$ −7060.03 12228.3i −0.706366 1.22346i
$$465$$ −2.82078 + 4.88573i −0.000281313 + 0.000487248i
$$466$$ −204.769 + 354.670i −0.0203557 + 0.0352571i
$$467$$ 1852.33 + 3208.33i 0.183545 + 0.317909i 0.943085 0.332551i $$-0.107909\pi$$
−0.759540 + 0.650460i $$0.774576\pi$$
$$468$$ 1172.71 0.115831
$$469$$ 0 0
$$470$$ 16.7169 0.00164062
$$471$$ 2537.02 + 4394.24i 0.248194 + 0.429885i
$$472$$ 38.0670 65.9340i 0.00371224 0.00642979i
$$473$$ −4802.30 + 8317.82i −0.466828 + 0.808570i
$$474$$ −500.632 867.119i −0.0485122 0.0840256i
$$475$$ 15887.8 1.53470
$$476$$ 0 0
$$477$$ 5788.05 0.555591
$$478$$ −173.540 300.581i −0.0166058 0.0287620i
$$479$$ −5335.88 + 9242.02i −0.508982 + 0.881583i 0.490963 + 0.871180i $$0.336645\pi$$
−0.999946 + 0.0104033i $$0.996688\pi$$
$$480$$ −11.6486 + 20.1760i −0.00110767 + 0.00191855i
$$481$$ −1596.91 2765.92i −0.151378 0.262194i
$$482$$ 1431.10 0.135238
$$483$$ 0 0
$$484$$ −4695.67 −0.440990
$$485$$ −54.8312 94.9705i −0.00513352 0.00889152i
$$486$$ 50.3269 87.1688i 0.00469728 0.00813592i
$$487$$ −2926.96 + 5069.65i −0.272348 + 0.471720i −0.969463 0.245239i $$-0.921133\pi$$
0.697115 + 0.716959i $$0.254467\pi$$
$$488$$ 40.1335 + 69.5133i 0.00372287 + 0.00644819i
$$489$$ −122.170 −0.0112980
$$490$$ 0 0
$$491$$ 4065.31 0.373656 0.186828 0.982393i $$-0.440179\pi$$
0.186828 + 0.982393i $$0.440179\pi$$
$$492$$ −3754.27 6502.59i −0.344016 0.595852i
$$493$$ 14334.1 24827.4i 1.30948 2.26809i
$$494$$ 438.186 758.960i 0.0399087 0.0691239i
$$495$$ −19.8734 34.4217i −0.00180453 0.00312554i
$$496$$ −1120.99 −0.101480
$$497$$ 0 0
$$498$$ 490.673 0.0441517
$$499$$ −2405.59 4166.61i −0.215810 0.373794i 0.737713 0.675115i $$-0.235906\pi$$
−0.953523 + 0.301321i $$0.902572\pi$$
$$500$$ 98.3456 170.340i 0.00879630 0.0152356i
$$501$$ −4350.70 + 7535.63i −0.387974 + 0.671990i
$$502$$ 1167.05 + 2021.39i 0.103761 + 0.179719i
$$503$$ −17001.2 −1.50705 −0.753526 0.657418i $$-0.771649\pi$$
−0.753526 + 0.657418i $$0.771649\pi$$
$$504$$ 0 0
$$505$$ 137.771 0.0121401
$$506$$ −487.769 844.840i −0.0428537 0.0742248i
$$507$$ 2879.93 4988.19i 0.252273 0.436949i
$$508$$ 4193.69 7263.68i 0.366269 0.634397i
$$509$$ 6898.61 + 11948.7i 0.600738 + 1.04051i 0.992710 + 0.120531i $$0.0384597\pi$$
−0.391972 + 0.919977i $$0.628207\pi$$
$$510$$ −15.1918 −0.00131903
$$511$$ 0 0
$$512$$ −7771.61 −0.670820
$$513$$ 1716.02 + 2972.24i 0.147688 + 0.255804i
$$514$$ −470.372 + 814.708i −0.0403642 + 0.0699129i
$$515$$ −71.0548 + 123.071i −0.00607971 + 0.0105304i
$$516$$ −2566.69 4445.64i −0.218977 0.379280i
$$517$$ −17644.7 −1.50099
$$518$$ 0 0
$$519$$ −6438.44 −0.544540
$$520$$ −5.48397 9.49851i −0.000462477 0.000801033i
$$521$$ 1968.31 3409.21i 0.165515 0.286680i −0.771323 0.636443i $$-0.780405\pi$$
0.936838 + 0.349764i $$0.113738\pi$$
$$522$$ 439.301 760.891i 0.0368346 0.0637994i
$$523$$ 8729.63 + 15120.2i 0.729866 + 1.26417i 0.956939 + 0.290288i $$0.0937510\pi$$
−0.227073 + 0.973878i $$0.572916\pi$$
$$524$$ 19688.6 1.64142
$$525$$ 0 0
$$526$$ −67.8760 −0.00562649
$$527$$ −1137.98 1971.04i −0.0940630 0.162922i
$$528$$ 3948.88 6839.66i 0.325479 0.563746i
$$529$$ 4647.13 8049.06i 0.381945 0.661549i
$$530$$ −13.3867 23.1864i −0.00109713 0.00190029i
$$531$$ −104.510 −0.00854118
$$532$$ 0 0
$$533$$ 5321.51 0.432458
$$534$$ 418.409 + 724.705i 0.0339069 + 0.0587286i
$$535$$ −17.2637 + 29.9016i −0.00139509 + 0.00241637i
$$536$$ −2193.26 + 3798.83i −0.176743 + 0.306128i
$$537$$ −1805.31 3126.89i −0.145074 0.251276i
$$538$$ 2140.28 0.171513
$$539$$ 0 0
$$540$$ 21.2435 0.00169292
$$541$$ −9550.66 16542.2i −0.758992 1.31461i −0.943365 0.331757i $$-0.892359\pi$$
0.184373 0.982856i $$-0.440975\pi$$
$$542$$ −335.983 + 581.940i −0.0266268 + 0.0461190i
$$543$$ 4485.71 7769.47i 0.354512 0.614033i
$$544$$ −4699.37 8139.54i −0.370374 0.641507i
$$545$$ 31.9261 0.00250929
$$546$$ 0 0
$$547$$ 15413.5 1.20481 0.602407 0.798189i $$-0.294208\pi$$
0.602407 + 0.798189i $$0.294208\pi$$
$$548$$ 982.718 + 1702.12i 0.0766052 + 0.132684i
$$549$$ 55.0919 95.4219i 0.00428281 0.00741805i
$$550$$ 1137.47 1970.16i 0.0881853 0.152741i
$$551$$ 14979.0 + 25944.5i 1.15813 + 2.00594i
$$552$$ 1054.22 0.0812874
$$553$$ 0 0
$$554$$ 1910.51 0.146516
$$555$$ −28.9277 50.1043i −0.00221246 0.00383209i
$$556$$ 3468.26 6007.20i 0.264545 0.458205i
$$557$$ 10246.4 17747.3i 0.779453 1.35005i −0.152804 0.988257i $$-0.548830\pi$$
0.932257 0.361796i $$-0.117836\pi$$
$$558$$ −34.8760 60.4070i −0.00264591 0.00458285i
$$559$$ 3638.17 0.275274
$$560$$ 0 0
$$561$$ 16034.9 1.20677
$$562$$ −440.147 762.357i −0.0330364 0.0572208i
$$563$$ −3571.24 + 6185.57i −0.267336 + 0.463039i −0.968173 0.250282i $$-0.919477\pi$$
0.700837 + 0.713321i $$0.252810\pi$$
$$564$$ 4715.30 8167.13i 0.352039 0.609749i
$$565$$ 40.1203 + 69.4904i 0.00298739 + 0.00517430i
$$566$$ −1065.17 −0.0791030
$$567$$ 0 0
$$568$$ 5389.96 0.398165
$$569$$ −2048.96 3548.90i −0.150961 0.261472i 0.780620 0.625006i $$-0.214903\pi$$
−0.931581 + 0.363534i $$0.881570\pi$$
$$570$$ 7.93766 13.7484i 0.000583284 0.00101028i
$$571$$ 1419.24 2458.20i 0.104016 0.180162i −0.809320 0.587369i $$-0.800164\pi$$
0.913336 + 0.407207i $$0.133497\pi$$
$$572$$ 2862.80 + 4958.51i 0.209265 + 0.362458i
$$573$$ −8422.23 −0.614038
$$574$$ 0 0
$$575$$ −6699.21 −0.485872
$$576$$ 2012.80 + 3486.27i 0.145602 + 0.252190i
$$577$$ −7732.23 + 13392.6i −0.557881 + 0.966277i 0.439793 + 0.898099i $$0.355052\pi$$
−0.997673 + 0.0681781i $$0.978281\pi$$
$$578$$ 2046.88 3545.29i 0.147299 0.255129i
$$579$$ −5004.55 8668.14i −0.359209 0.622169i
$$580$$ 185.433 0.0132753
$$581$$ 0 0
$$582$$ 1355.86 0.0965675
$$583$$ 14129.6 + 24473.3i 1.00376 + 1.73856i
$$584$$ −1688.59 + 2924.72i −0.119648 + 0.207236i
$$585$$ −7.52793 + 13.0388i −0.000532037 + 0.000921515i
$$586$$ −688.622 1192.73i −0.0485439 0.0840805i
$$587$$ −14003.6 −0.984652 −0.492326 0.870411i $$-0.663853\pi$$
−0.492326 + 0.870411i $$0.663853\pi$$
$$588$$ 0 0
$$589$$ 2378.36 0.166382
$$590$$ 0.241713 + 0.418658i 1.68664e−5 + 2.92134e-5i
$$591$$ 6339.97 10981.1i 0.441272 0.764305i
$$592$$ 5747.99 9955.82i 0.399056 0.691185i
$$593$$ 3252.25 + 5633.06i 0.225217 + 0.390088i 0.956385 0.292110i $$-0.0943574\pi$$
−0.731167 + 0.682198i $$0.761024\pi$$
$$594$$ 491.427 0.0339453
$$595$$ 0 0
$$596$$ −4561.04 −0.313469
$$597$$ −6578.54 11394.4i −0.450991 0.781140i
$$598$$ −184.764 + 320.021i −0.0126347 + 0.0218840i
$$599$$ 6308.05 10925.9i 0.430284 0.745273i −0.566614 0.823983i $$-0.691747\pi$$
0.996898 + 0.0787104i $$0.0250802\pi$$
$$600$$ 1229.22 + 2129.06i 0.0836376 + 0.144865i
$$601$$ −8270.87 −0.561358 −0.280679 0.959802i $$-0.590560\pi$$
−0.280679 + 0.959802i $$0.590560\pi$$
$$602$$ 0 0
$$603$$ 6021.43 0.406653
$$604$$ −11005.8 19062.7i −0.741426 1.28419i
$$605$$ 30.1426 52.2085i 0.00202557 0.00350839i
$$606$$ −851.700 + 1475.19i −0.0570923 + 0.0988868i
$$607$$ 1905.92 + 3301.15i 0.127445 + 0.220740i 0.922686 0.385553i $$-0.125989\pi$$
−0.795241 + 0.606293i $$0.792656\pi$$
$$608$$ 9821.62 0.655130
$$609$$ 0 0
$$610$$ −0.509668 −3.38293e−5
$$611$$ 3341.86 + 5788.27i 0.221272 + 0.383254i
$$612$$ −4285.11 + 7422.03i −0.283032 + 0.490225i
$$613$$ −5679.63 + 9837.42i −0.374222 + 0.648172i −0.990210 0.139583i $$-0.955424\pi$$
0.615988 + 0.787756i $$0.288757\pi$$
$$614$$ 183.724 + 318.219i 0.0120757 + 0.0209157i
$$615$$ 96.3983 0.00632057
$$616$$ 0 0
$$617$$ −18272.2 −1.19224 −0.596118 0.802896i $$-0.703291\pi$$
−0.596118 + 0.802896i $$0.703291\pi$$
$$618$$ −878.519 1521.64i −0.0571832 0.0990442i
$$619$$ 14800.1 25634.6i 0.961013 1.66452i 0.241048 0.970513i $$-0.422509\pi$$
0.719965 0.694010i $$-0.244158\pi$$
$$620$$ 7.36075 12.7492i 0.000476798 0.000825838i
$$621$$ −723.573 1253.26i −0.0467568 0.0809852i
$$622$$ −1868.44 −0.120447
$$623$$ 0 0
$$624$$ −2991.63 −0.191925
$$625$$ −7810.61 13528.4i −0.499879 0.865815i
$$626$$ −769.564 + 1332.92i −0.0491341 + 0.0851028i
$$627$$ −8378.21 + 14511.5i −0.533642 + 0.924295i
$$628$$ −6620.28 11466.7i −0.420665 0.728614i
$$629$$ 23340.5 1.47956
$$630$$ 0 0
$$631$$ 7185.41 0.453322 0.226661 0.973974i $$-0.427219\pi$$
0.226661 + 0.973974i $$0.427219\pi$$
$$632$$ 2641.40 + 4575.05i 0.166249 + 0.287952i
$$633$$ −3437.34 + 5953.64i −0.215832 + 0.373833i
$$634$$ 1440.33 2494.72i 0.0902252 0.156275i
$$635$$ 53.8405 + 93.2545i 0.00336472 + 0.00582786i
$$636$$ −15103.8 −0.941673
$$637$$ 0 0
$$638$$ 4289.64 0.266189
$$639$$ −3699.44 6407.62i −0.229026 0.396684i
$$640$$ 40.3733 69.9287i 0.00249359 0.00431902i
$$641$$ 116.491 201.768i 0.00717803 0.0124327i −0.862414 0.506203i $$-0.831048\pi$$
0.869592 + 0.493771i $$0.164382\pi$$
$$642$$ −213.448 369.702i −0.0131217 0.0227274i
$$643$$ 1837.96 0.112725 0.0563624 0.998410i $$-0.482050\pi$$
0.0563624 + 0.998410i $$0.482050\pi$$
$$644$$ 0 0
$$645$$ 65.9048 0.00402325
$$646$$ 3202.27 + 5546.50i 0.195034 + 0.337808i
$$647$$ −9297.35 + 16103.5i −0.564941 + 0.978506i 0.432114 + 0.901819i $$0.357768\pi$$
−0.997055 + 0.0766874i $$0.975566\pi$$
$$648$$ −265.532 + 459.915i −0.0160974 + 0.0278814i
$$649$$ −255.128 441.895i −0.0154309 0.0267271i
$$650$$ −861.736 −0.0520001
$$651$$ 0 0
$$652$$ 318.799 0.0191490
$$653$$ 14432.3 + 24997.6i 0.864902 + 1.49805i 0.867144 + 0.498057i $$0.165953\pi$$
−0.00224162 + 0.999997i $$0.500714\pi$$
$$654$$ −197.367 + 341.849i −0.0118007 + 0.0204394i
$$655$$ −126.386 + 218.907i −0.00753940 + 0.0130586i
$$656$$ 9577.27 + 16588.3i 0.570014 + 0.987294i
$$657$$ 4635.90 0.275287
$$658$$ 0 0
$$659$$ −29066.3 −1.71815 −0.859076 0.511847i $$-0.828961\pi$$
−0.859076 + 0.511847i $$0.828961\pi$$
$$660$$ 51.8591 + 89.8226i 0.00305850 + 0.00529748i
$$661$$ −1989.75 + 3446.36i −0.117084 + 0.202795i −0.918611 0.395163i $$-0.870688\pi$$
0.801527 + 0.597959i $$0.204021\pi$$
$$662$$ −2042.73 + 3538.11i −0.119929 + 0.207723i
$$663$$ −3036.98 5260.20i −0.177898 0.308128i
$$664$$ −2588.86 −0.151306
$$665$$ 0 0
$$666$$ 715.322 0.0416189
$$667$$ −6316.02 10939.7i −0.366653 0.635061i
$$668$$ 11353.0 19664.0i 0.657578 1.13896i
$$669$$ 326.955 566.302i 0.0188951 0.0327272i
$$670$$ −13.9264 24.1213i −0.000803022 0.00139087i
$$671$$ 537.955 0.0309501
$$672$$ 0 0
$$673$$ −184.229 −0.0105520 −0.00527601 0.999986i $$-0.501679\pi$$
−0.00527601 + 0.999986i $$0.501679\pi$$
$$674$$ −1231.26 2132.61i −0.0703657 0.121877i
$$675$$ 1687.36 2922.60i 0.0962173 0.166653i
$$676$$ −7515.11 + 13016.6i −0.427578 + 0.740587i
$$677$$ −8341.73 14448.3i −0.473558 0.820227i 0.525984 0.850495i $$-0.323697\pi$$
−0.999542 + 0.0302680i $$0.990364\pi$$
$$678$$ −992.091 −0.0561962
$$679$$ 0 0
$$680$$ 80.1540 0.00452024
$$681$$ −2753.04 4768.41i −0.154914 0.268320i
$$682$$ 170.277 294.928i 0.00956045 0.0165592i
$$683$$ −8904.11 + 15422.4i −0.498838 + 0.864013i −0.999999 0.00134107i $$-0.999573\pi$$
0.501161 + 0.865354i $$0.332906\pi$$
$$684$$ −4477.92 7755.98i −0.250318 0.433563i
$$685$$ −25.2332 −0.00140746
$$686$$ 0 0
$$687$$ 8322.03 0.462162
$$688$$ 6547.71 + 11341.0i 0.362833 + 0.628445i
$$689$$ 5352.23 9270.34i 0.295942 0.512586i
$$690$$ −3.34697 + 5.79712i −0.000184662 + 0.000319845i
$$691$$ −10072.8 17446.7i −0.554542 0.960495i −0.997939 0.0641695i $$-0.979560\pi$$
0.443397 0.896325i $$-0.353773\pi$$
$$692$$ 16801.0 0.922943
$$693$$ 0 0
$$694$$ −484.453 −0.0264980
$$695$$ 44.5271 + 77.1232i 0.00243023 + 0.00420928i
$$696$$ −2317.81 + 4014.57i −0.126231 + 0.218638i
$$697$$ −19444.9 + 33679.5i −1.05671 + 1.83028i
$$698$$ 1900.55 + 3291.85i 0.103061 + 0.178507i
$$699$$ −2966.14 −0.160500
$$700$$ 0 0
$$701$$ −2719.67 −0.146534 −0.0732672 0.997312i $$-0.523343\pi$$
−0.0732672 + 0.997312i $$0.523343\pi$$
$$702$$ −93.0750 161.211i −0.00500412 0.00866738i
$$703$$ −12195.3 + 21122.9i −0.654276 + 1.13324i
$$704$$ −9827.18 + 17021.2i −0.526102 + 0.911235i
$$705$$ 60.5372 + 104.854i 0.00323399 + 0.00560144i
$$706$$ 4385.36 0.233775
$$707$$ 0 0
$$708$$ 272.717 0.0144765
$$709$$ 312.854 + 541.879i 0.0165719 + 0.0287034i 0.874192 0.485580i $$-0.161391\pi$$
−0.857621 + 0.514283i $$0.828058\pi$$
$$710$$ −17.1122 + 29.6392i −0.000904520 + 0.00156667i
$$711$$ 3625.89 6280.23i 0.191254 0.331262i
$$712$$ −2207.58 3823.65i −0.116198 0.201260i
$$713$$ −1002.85 −0.0526749
$$714$$ 0 0
$$715$$ −73.5079 −0.00384481
$$716$$ 4710.91 + 8159.53i 0.245887 + 0.425888i
$$717$$ 1256.89 2177.00i 0.0654665 0.113391i
$$718$$ 1784.27 3090.44i 0.0927414 0.160633i
$$719$$ −4788.77 8294.39i −0.248388 0.430221i 0.714691 0.699441i $$-0.246567\pi$$
−0.963079 + 0.269220i $$0.913234\pi$$
$$720$$ −54.1929 −0.00280507
$$721$$ 0 0
$$722$$ −3851.62 −0.198535
$$723$$ 5182.48 + 8976.32i 0.266582 + 0.461733i
$$724$$ −11705.3 + 20274.2i −0.600864 + 1.04073i
$$725$$ 14728.9 25511.2i 0.754506 1.30684i
$$726$$ 372.682 + 645.504i 0.0190517 + 0.0329985i
$$727$$ 16741.2 0.854053 0.427027 0.904239i $$-0.359561\pi$$
0.427027 + 0.904239i $$0.359561\pi$$
$$728$$ 0 0
$$729$$ 729.000 0.0370370
$$730$$ −10.7219 18.5710i −0.000543612 0.000941564i
$$731$$ −13293.9 + 23025.7i −0.672631 + 1.16503i
$$732$$ −143.761 + 249.001i −0.00725896 + 0.0125729i
$$733$$ −3248.02 5625.74i −0.163668 0.283481i 0.772514 0.634998i $$-0.218999\pi$$
−0.936181 + 0.351517i $$0.885666\pi$$
$$734$$ 3437.06 0.172839
$$735$$ 0 0
$$736$$ −4141.36 −0.207408
$$737$$ 14699.4 + 25460.0i 0.734678 + 1.27250i
$$738$$ −595.932 + 1032.18i −0.0297243 + 0.0514841i
$$739$$ −249.640 + 432.389i −0.0124265 + 0.0215233i −0.872172 0.489200i $$-0.837289\pi$$
0.859745 + 0.510723i $$0.170622\pi$$
$$740$$ 75.4861 + 130.746i 0.00374990 + 0.00649502i
$$741$$ 6347.24 0.314672
$$742$$ 0 0
$$743$$ −6367.30 −0.314393 −0.157196 0.987567i $$-0.550246\pi$$
−0.157196 + 0.987567i $$0.550246\pi$$
$$744$$ 184.011 + 318.716i 0.00906741 + 0.0157052i
$$745$$ 29.2784 50.7117i 0.00143984 0.00249387i
$$746$$ −1061.19 + 1838.03i −0.0520814 + 0.0902077i
$$747$$ 1776.88 + 3077.65i 0.0870318 + 0.150743i
$$748$$ −41842.8 −2.04535
$$749$$ 0 0
$$750$$ −31.2217 −0.00152007
$$751$$ −248.049 429.634i −0.0120525 0.0208756i 0.859936 0.510401i $$-0.170503\pi$$
−0.871989 + 0.489526i $$0.837170\pi$$
$$752$$ −12028.9 + 20834.6i −0.583308 + 1.01032i
$$753$$ −8452.51 + 14640.2i −0.409066 + 0.708523i
$$754$$ −812.446 1407.20i −0.0392407 0.0679670i
$$755$$ 282.597 0.0136222
$$756$$ 0 0
$$757$$ 13025.9 0.625408 0.312704 0.949851i $$-0.398765\pi$$
0.312704 + 0.949851i $$0.398765\pi$$
$$758$$ −311.175 538.971i −0.0149108 0.0258263i
$$759$$ 3532.73 6118.87i 0.168946 0.292623i
$$760$$ −41.8802 + 72.5387i −0.00199889 + 0.00346218i
$$761$$ −12737.3 22061.6i −0.606736 1.05090i −0.991775 0.127997i $$-0.959145\pi$$
0.385039 0.922900i $$-0.374188\pi$$
$$762$$ −1331.36 −0.0632943
$$763$$ 0 0
$$764$$ 21977.6 1.04074
$$765$$ −55.0143 95.2875i −0.00260006 0.00450344i
$$766$$ 2251.86 3900.33i 0.106218 0.183975i
$$767$$ −96.6411 + 167.387i −0.00454955 + 0.00788006i
$$768$$ −4868.29 8432.12i −0.228736 0.396182i
$$769$$ 29054.0 1.36244 0.681218 0.732080i $$-0.261450\pi$$
0.681218 + 0.732080i $$0.261450\pi$$
$$770$$ 0 0
$$771$$ −6813.47 −0.318263
$$772$$ 13059.3 + 22619.3i 0.608825 + 1.05452i
$$773$$ 948.677 1643.16i 0.0441417 0.0764557i −0.843110 0.537740i $$-0.819278\pi$$
0.887252 + 0.461285i $$0.152611\pi$$
$$774$$ −407.422 + 705.676i −0.0189205 + 0.0327713i
$$775$$ −1169.32 2025.33i −0.0541978 0.0938734i
$$776$$ −7153.72 −0.330933
$$777$$ 0 0
$$778$$ −1913.25 −0.0881662