# Properties

 Label 16.4.e.a.5.1 Level 16 Weight 4 Character 16.5 Analytic conductor 0.944 Analytic rank 0 Dimension 10 CM no Inner twists 2

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$16 = 2^{4}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 16.e (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.944030560092$$ Analytic rank: $$0$$ Dimension: $$10$$ Relative dimension: $$5$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ Defining polynomial: $$x^{10} - 2 x^{9} - x^{8} + 6 x^{7} + 14 x^{6} - 80 x^{5} + 56 x^{4} + 96 x^{3} - 64 x^{2} - 512 x + 1024$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{10}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 5.1 Root $$1.28199 - 1.53509i$$ of defining polynomial Character $$\chi$$ $$=$$ 16.5 Dual form 16.4.e.a.13.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.81708 - 0.253099i) q^{2} +(5.49618 - 5.49618i) q^{3} +(7.87188 + 1.42600i) q^{4} +(-4.66372 - 4.66372i) q^{5} +(-16.8743 + 14.0921i) q^{6} +24.8965i q^{7} +(-21.8148 - 6.00953i) q^{8} -33.4160i q^{9} +O(q^{10})$$ $$q+(-2.81708 - 0.253099i) q^{2} +(5.49618 - 5.49618i) q^{3} +(7.87188 + 1.42600i) q^{4} +(-4.66372 - 4.66372i) q^{5} +(-16.8743 + 14.0921i) q^{6} +24.8965i q^{7} +(-21.8148 - 6.00953i) q^{8} -33.4160i q^{9} +(11.9577 + 14.3185i) q^{10} +(22.3431 + 22.3431i) q^{11} +(51.1028 - 35.4277i) q^{12} +(-11.2714 + 11.2714i) q^{13} +(6.30129 - 70.1355i) q^{14} -51.2653 q^{15} +(59.9330 + 22.4506i) q^{16} -88.4846 q^{17} +(-8.45756 + 94.1356i) q^{18} +(37.8187 - 37.8187i) q^{19} +(-30.0618 - 43.3627i) q^{20} +(136.836 + 136.836i) q^{21} +(-57.2873 - 68.5974i) q^{22} -48.1224i q^{23} +(-152.928 + 86.8686i) q^{24} -81.4994i q^{25} +(34.6053 - 28.8997i) q^{26} +(-35.2635 - 35.2635i) q^{27} +(-35.5025 + 195.982i) q^{28} +(10.4432 - 10.4432i) q^{29} +(144.419 + 12.9752i) q^{30} -96.9578 q^{31} +(-163.154 - 78.4142i) q^{32} +245.604 q^{33} +(249.268 + 22.3954i) q^{34} +(116.110 - 116.110i) q^{35} +(47.6513 - 263.047i) q^{36} +(-163.279 - 163.279i) q^{37} +(-116.110 + 96.9665i) q^{38} +123.899i q^{39} +(73.7114 + 129.765i) q^{40} +360.519i q^{41} +(-350.844 - 420.110i) q^{42} +(-100.249 - 100.249i) q^{43} +(144.021 + 207.744i) q^{44} +(-155.843 + 155.843i) q^{45} +(-12.1797 + 135.565i) q^{46} +220.669 q^{47} +(452.796 - 206.010i) q^{48} -276.837 q^{49} +(-20.6274 + 229.590i) q^{50} +(-486.327 + 486.327i) q^{51} +(-104.800 + 72.6542i) q^{52} +(-175.752 - 175.752i) q^{53} +(90.4150 + 108.265i) q^{54} -208.404i q^{55} +(149.616 - 543.113i) q^{56} -415.717i q^{57} +(-32.0624 + 26.7761i) q^{58} +(405.008 + 405.008i) q^{59} +(-403.555 - 73.1044i) q^{60} +(664.576 - 664.576i) q^{61} +(273.138 + 24.5399i) q^{62} +831.942 q^{63} +(439.771 + 262.193i) q^{64} +105.133 q^{65} +(-691.885 - 62.1621i) q^{66} +(-107.377 + 107.377i) q^{67} +(-696.540 - 126.179i) q^{68} +(-264.489 - 264.489i) q^{69} +(-356.480 + 297.705i) q^{70} -215.050i q^{71} +(-200.814 + 728.964i) q^{72} +668.587i q^{73} +(418.644 + 501.296i) q^{74} +(-447.935 - 447.935i) q^{75} +(351.634 - 243.775i) q^{76} +(-556.266 + 556.266i) q^{77} +(31.3588 - 349.035i) q^{78} -822.956 q^{79} +(-174.808 - 384.215i) q^{80} +514.603 q^{81} +(91.2471 - 1015.61i) q^{82} +(326.873 - 326.873i) q^{83} +(882.027 + 1272.28i) q^{84} +(412.668 + 412.668i) q^{85} +(257.037 + 307.783i) q^{86} -114.795i q^{87} +(-353.139 - 621.682i) q^{88} +262.733i q^{89} +(478.466 - 399.578i) q^{90} +(-280.619 - 280.619i) q^{91} +(68.6226 - 378.814i) q^{92} +(-532.898 + 532.898i) q^{93} +(-621.643 - 55.8512i) q^{94} -352.752 q^{95} +(-1327.70 + 465.745i) q^{96} -150.801 q^{97} +(779.871 + 70.0671i) q^{98} +(746.618 - 746.618i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} + O(q^{10})$$ $$10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} - 68q^{10} + 18q^{11} + 100q^{12} - 2q^{13} + 188q^{14} - 124q^{15} + 280q^{16} - 4q^{17} + 174q^{18} - 26q^{19} - 196q^{20} + 52q^{21} - 588q^{22} - 848q^{24} - 264q^{26} + 184q^{27} + 280q^{28} - 202q^{29} + 1236q^{30} + 368q^{31} + 968q^{32} - 4q^{33} + 436q^{34} + 476q^{35} - 596q^{36} - 10q^{37} - 1232q^{38} - 1336q^{40} - 680q^{42} - 838q^{43} + 868q^{44} + 194q^{45} + 1132q^{46} - 944q^{47} + 1768q^{48} + 94q^{49} + 726q^{50} - 1500q^{51} - 236q^{52} - 378q^{53} - 1376q^{54} - 488q^{56} + 8q^{58} + 1706q^{59} - 192q^{60} + 910q^{61} - 80q^{62} + 2628q^{63} + 512q^{64} - 492q^{65} - 428q^{66} + 1942q^{67} - 880q^{68} + 580q^{69} + 160q^{70} + 1092q^{72} - 452q^{74} - 2954q^{75} - 1228q^{76} - 268q^{77} - 772q^{78} - 4416q^{79} - 2648q^{80} + 482q^{81} - 704q^{82} - 2562q^{83} + 1960q^{84} - 12q^{85} + 3764q^{86} + 1528q^{88} + 1896q^{90} + 3332q^{91} + 632q^{92} - 2192q^{93} - 3248q^{94} + 6900q^{95} - 4432q^{96} - 4q^{97} + 314q^{98} + 4958q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$15$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.81708 0.253099i −0.995988 0.0894841i
$$3$$ 5.49618 5.49618i 1.05774 1.05774i 0.0595129 0.998228i $$-0.481045\pi$$
0.998228 0.0595129i $$-0.0189548\pi$$
$$4$$ 7.87188 + 1.42600i 0.983985 + 0.178250i
$$5$$ −4.66372 4.66372i −0.417136 0.417136i 0.467079 0.884215i $$-0.345306\pi$$
−0.884215 + 0.467079i $$0.845306\pi$$
$$6$$ −16.8743 + 14.0921i −1.14815 + 0.958846i
$$7$$ 24.8965i 1.34429i 0.740422 + 0.672143i $$0.234626\pi$$
−0.740422 + 0.672143i $$0.765374\pi$$
$$8$$ −21.8148 6.00953i −0.964087 0.265586i
$$9$$ 33.4160i 1.23763i
$$10$$ 11.9577 + 14.3185i 0.378136 + 0.452790i
$$11$$ 22.3431 + 22.3431i 0.612427 + 0.612427i 0.943578 0.331151i $$-0.107437\pi$$
−0.331151 + 0.943578i $$0.607437\pi$$
$$12$$ 51.1028 35.4277i 1.22934 0.852259i
$$13$$ −11.2714 + 11.2714i −0.240471 + 0.240471i −0.817045 0.576574i $$-0.804389\pi$$
0.576574 + 0.817045i $$0.304389\pi$$
$$14$$ 6.30129 70.1355i 0.120292 1.33889i
$$15$$ −51.2653 −0.882443
$$16$$ 59.9330 + 22.4506i 0.936454 + 0.350791i
$$17$$ −88.4846 −1.26239 −0.631196 0.775623i $$-0.717436\pi$$
−0.631196 + 0.775623i $$0.717436\pi$$
$$18$$ −8.45756 + 94.1356i −0.110748 + 1.23266i
$$19$$ 37.8187 37.8187i 0.456643 0.456643i −0.440909 0.897552i $$-0.645344\pi$$
0.897552 + 0.440909i $$0.145344\pi$$
$$20$$ −30.0618 43.3627i −0.336101 0.484810i
$$21$$ 136.836 + 136.836i 1.42191 + 1.42191i
$$22$$ −57.2873 68.5974i −0.555168 0.664773i
$$23$$ 48.1224i 0.436270i −0.975919 0.218135i $$-0.930003\pi$$
0.975919 0.218135i $$-0.0699973\pi$$
$$24$$ −152.928 + 86.8686i −1.30068 + 0.738833i
$$25$$ 81.4994i 0.651995i
$$26$$ 34.6053 28.8997i 0.261025 0.217988i
$$27$$ −35.2635 35.2635i −0.251351 0.251351i
$$28$$ −35.5025 + 195.982i −0.239619 + 1.32276i
$$29$$ 10.4432 10.4432i 0.0668705 0.0668705i −0.672881 0.739751i $$-0.734943\pi$$
0.739751 + 0.672881i $$0.234943\pi$$
$$30$$ 144.419 + 12.9752i 0.878903 + 0.0789646i
$$31$$ −96.9578 −0.561746 −0.280873 0.959745i $$-0.590624\pi$$
−0.280873 + 0.959745i $$0.590624\pi$$
$$32$$ −163.154 78.4142i −0.901307 0.433181i
$$33$$ 245.604 1.29558
$$34$$ 249.268 + 22.3954i 1.25733 + 0.112964i
$$35$$ 116.110 116.110i 0.560750 0.560750i
$$36$$ 47.6513 263.047i 0.220608 1.21781i
$$37$$ −163.279 163.279i −0.725484 0.725484i 0.244233 0.969717i $$-0.421464\pi$$
−0.969717 + 0.244233i $$0.921464\pi$$
$$38$$ −116.110 + 96.9665i −0.495673 + 0.413949i
$$39$$ 123.899i 0.508713i
$$40$$ 73.7114 + 129.765i 0.291370 + 0.512941i
$$41$$ 360.519i 1.37326i 0.727008 + 0.686629i $$0.240910\pi$$
−0.727008 + 0.686629i $$0.759090\pi$$
$$42$$ −350.844 420.110i −1.28896 1.54344i
$$43$$ −100.249 100.249i −0.355531 0.355531i 0.506632 0.862163i $$-0.330890\pi$$
−0.862163 + 0.506632i $$0.830890\pi$$
$$44$$ 144.021 + 207.744i 0.493454 + 0.711785i
$$45$$ −155.843 + 155.843i −0.516260 + 0.516260i
$$46$$ −12.1797 + 135.565i −0.0390392 + 0.434520i
$$47$$ 220.669 0.684849 0.342425 0.939545i $$-0.388752\pi$$
0.342425 + 0.939545i $$0.388752\pi$$
$$48$$ 452.796 206.010i 1.36157 0.619479i
$$49$$ −276.837 −0.807104
$$50$$ −20.6274 + 229.590i −0.0583432 + 0.649379i
$$51$$ −486.327 + 486.327i −1.33528 + 1.33528i
$$52$$ −104.800 + 72.6542i −0.279484 + 0.193756i
$$53$$ −175.752 175.752i −0.455498 0.455498i 0.441676 0.897174i $$-0.354384\pi$$
−0.897174 + 0.441676i $$0.854384\pi$$
$$54$$ 90.4150 + 108.265i 0.227850 + 0.272834i
$$55$$ 208.404i 0.510931i
$$56$$ 149.616 543.113i 0.357024 1.29601i
$$57$$ 415.717i 0.966019i
$$58$$ −32.0624 + 26.7761i −0.0725861 + 0.0606184i
$$59$$ 405.008 + 405.008i 0.893687 + 0.893687i 0.994868 0.101181i $$-0.0322622\pi$$
−0.101181 + 0.994868i $$0.532262\pi$$
$$60$$ −403.555 73.1044i −0.868311 0.157296i
$$61$$ 664.576 664.576i 1.39492 1.39492i 0.581061 0.813860i $$-0.302638\pi$$
0.813860 0.581061i $$-0.197362\pi$$
$$62$$ 273.138 + 24.5399i 0.559493 + 0.0502674i
$$63$$ 831.942 1.66373
$$64$$ 439.771 + 262.193i 0.858928 + 0.512096i
$$65$$ 105.133 0.200619
$$66$$ −691.885 62.1621i −1.29038 0.115934i
$$67$$ −107.377 + 107.377i −0.195794 + 0.195794i −0.798194 0.602400i $$-0.794211\pi$$
0.602400 + 0.798194i $$0.294211\pi$$
$$68$$ −696.540 126.179i −1.24218 0.225022i
$$69$$ −264.489 264.489i −0.461461 0.461461i
$$70$$ −356.480 + 297.705i −0.608679 + 0.508322i
$$71$$ 215.050i 0.359461i −0.983716 0.179731i $$-0.942477\pi$$
0.983716 0.179731i $$-0.0575226\pi$$
$$72$$ −200.814 + 728.964i −0.328697 + 1.19318i
$$73$$ 668.587i 1.07195i 0.844235 + 0.535974i $$0.180055\pi$$
−0.844235 + 0.535974i $$0.819945\pi$$
$$74$$ 418.644 + 501.296i 0.657654 + 0.787492i
$$75$$ −447.935 447.935i −0.689642 0.689642i
$$76$$ 351.634 243.775i 0.530726 0.367933i
$$77$$ −556.266 + 556.266i −0.823277 + 0.823277i
$$78$$ 31.3588 349.035i 0.0455217 0.506672i
$$79$$ −822.956 −1.17202 −0.586012 0.810303i $$-0.699303\pi$$
−0.586012 + 0.810303i $$0.699303\pi$$
$$80$$ −174.808 384.215i −0.244301 0.536956i
$$81$$ 514.603 0.705902
$$82$$ 91.2471 1015.61i 0.122885 1.36775i
$$83$$ 326.873 326.873i 0.432277 0.432277i −0.457125 0.889402i $$-0.651121\pi$$
0.889402 + 0.457125i $$0.151121\pi$$
$$84$$ 882.027 + 1272.28i 1.14568 + 1.65259i
$$85$$ 412.668 + 412.668i 0.526589 + 0.526589i
$$86$$ 257.037 + 307.783i 0.322290 + 0.385919i
$$87$$ 114.795i 0.141463i
$$88$$ −353.139 621.682i −0.427781 0.753086i
$$89$$ 262.733i 0.312918i 0.987684 + 0.156459i $$0.0500079\pi$$
−0.987684 + 0.156459i $$0.949992\pi$$
$$90$$ 478.466 399.578i 0.560386 0.467992i
$$91$$ −280.619 280.619i −0.323262 0.323262i
$$92$$ 68.6226 378.814i 0.0777652 0.429283i
$$93$$ −532.898 + 532.898i −0.594182 + 0.594182i
$$94$$ −621.643 55.8512i −0.682102 0.0612831i
$$95$$ −352.752 −0.380964
$$96$$ −1327.70 + 465.745i −1.41154 + 0.495155i
$$97$$ −150.801 −0.157850 −0.0789251 0.996881i $$-0.525149\pi$$
−0.0789251 + 0.996881i $$0.525149\pi$$
$$98$$ 779.871 + 70.0671i 0.803866 + 0.0722229i
$$99$$ 746.618 746.618i 0.757958 0.757958i
$$100$$ 116.218 641.553i 0.116218 0.641553i
$$101$$ 487.985 + 487.985i 0.480755 + 0.480755i 0.905373 0.424617i $$-0.139591\pi$$
−0.424617 + 0.905373i $$0.639591\pi$$
$$102$$ 1493.11 1246.93i 1.44941 1.21044i
$$103$$ 1840.58i 1.76075i 0.474275 + 0.880377i $$0.342710\pi$$
−0.474275 + 0.880377i $$0.657290\pi$$
$$104$$ 313.620 178.148i 0.295701 0.167970i
$$105$$ 1276.33i 1.18626i
$$106$$ 450.625 + 539.590i 0.412911 + 0.494431i
$$107$$ −79.4098 79.4098i −0.0717461 0.0717461i 0.670323 0.742069i $$-0.266155\pi$$
−0.742069 + 0.670323i $$0.766155\pi$$
$$108$$ −227.304 327.876i −0.202522 0.292129i
$$109$$ 952.979 952.979i 0.837421 0.837421i −0.151098 0.988519i $$-0.548281\pi$$
0.988519 + 0.151098i $$0.0482809\pi$$
$$110$$ −52.7469 + 587.091i −0.0457202 + 0.508881i
$$111$$ −1794.82 −1.53475
$$112$$ −558.942 + 1492.12i −0.471563 + 1.25886i
$$113$$ −720.469 −0.599788 −0.299894 0.953973i $$-0.596951\pi$$
−0.299894 + 0.953973i $$0.596951\pi$$
$$114$$ −105.218 + 1171.11i −0.0864433 + 0.962144i
$$115$$ −224.430 + 224.430i −0.181984 + 0.181984i
$$116$$ 97.0993 67.3153i 0.0777193 0.0538799i
$$117$$ 376.646 + 376.646i 0.297615 + 0.297615i
$$118$$ −1038.43 1243.45i −0.810131 0.970072i
$$119$$ 2202.96i 1.69702i
$$120$$ 1118.34 + 308.080i 0.850752 + 0.234365i
$$121$$ 332.571i 0.249865i
$$122$$ −2040.37 + 1703.96i −1.51415 + 1.26450i
$$123$$ 1981.48 + 1981.48i 1.45255 + 1.45255i
$$124$$ −763.240 138.262i −0.552750 0.100131i
$$125$$ −963.056 + 963.056i −0.689107 + 0.689107i
$$126$$ −2343.65 210.564i −1.65705 0.148877i
$$127$$ 2622.35 1.83225 0.916124 0.400895i $$-0.131301\pi$$
0.916124 + 0.400895i $$0.131301\pi$$
$$128$$ −1172.51 849.925i −0.809658 0.586902i
$$129$$ −1101.97 −0.752119
$$130$$ −296.169 26.6092i −0.199814 0.0179522i
$$131$$ 657.574 657.574i 0.438569 0.438569i −0.452961 0.891530i $$-0.649632\pi$$
0.891530 + 0.452961i $$0.149632\pi$$
$$132$$ 1933.36 + 350.231i 1.27483 + 0.230937i
$$133$$ 941.555 + 941.555i 0.613858 + 0.613858i
$$134$$ 329.666 275.312i 0.212529 0.177488i
$$135$$ 328.919i 0.209695i
$$136$$ 1930.27 + 531.751i 1.21706 + 0.335274i
$$137$$ 2511.52i 1.56623i −0.621874 0.783117i $$-0.713629\pi$$
0.621874 0.783117i $$-0.286371\pi$$
$$138$$ 678.146 + 812.030i 0.418316 + 0.500903i
$$139$$ −1086.02 1086.02i −0.662697 0.662697i 0.293318 0.956015i $$-0.405241\pi$$
−0.956015 + 0.293318i $$0.905241\pi$$
$$140$$ 1079.58 748.434i 0.651723 0.451816i
$$141$$ 1212.84 1212.84i 0.724393 0.724393i
$$142$$ −54.4290 + 605.813i −0.0321661 + 0.358019i
$$143$$ −503.677 −0.294543
$$144$$ 750.210 2002.72i 0.434149 1.15898i
$$145$$ −97.4080 −0.0557882
$$146$$ 169.219 1883.46i 0.0959222 1.06765i
$$147$$ −1521.54 + 1521.54i −0.853706 + 0.853706i
$$148$$ −1052.48 1518.15i −0.584547 0.843183i
$$149$$ −2284.63 2284.63i −1.25614 1.25614i −0.952922 0.303214i $$-0.901940\pi$$
−0.303214 0.952922i $$-0.598060\pi$$
$$150$$ 1148.50 + 1375.24i 0.625163 + 0.748587i
$$151$$ 2814.39i 1.51677i 0.651809 + 0.758383i $$0.274010\pi$$
−0.651809 + 0.758383i $$0.725990\pi$$
$$152$$ −1052.28 + 597.735i −0.561521 + 0.318965i
$$153$$ 2956.80i 1.56237i
$$154$$ 1707.84 1426.25i 0.893645 0.746304i
$$155$$ 452.184 + 452.184i 0.234325 + 0.234325i
$$156$$ −176.681 + 975.322i −0.0906781 + 0.500566i
$$157$$ −906.308 + 906.308i −0.460709 + 0.460709i −0.898888 0.438179i $$-0.855624\pi$$
0.438179 + 0.898888i $$0.355624\pi$$
$$158$$ 2318.33 + 208.290i 1.16732 + 0.104877i
$$159$$ −1931.93 −0.963598
$$160$$ 395.203 + 1126.61i 0.195272 + 0.556663i
$$161$$ 1198.08 0.586472
$$162$$ −1449.68 130.246i −0.703070 0.0631670i
$$163$$ 1392.36 1392.36i 0.669067 0.669067i −0.288433 0.957500i $$-0.593134\pi$$
0.957500 + 0.288433i $$0.0931342\pi$$
$$164$$ −514.101 + 2837.96i −0.244784 + 1.35127i
$$165$$ −1145.43 1145.43i −0.540433 0.540433i
$$166$$ −1003.56 + 838.097i −0.469225 + 0.391861i
$$167$$ 1221.66i 0.566075i 0.959109 + 0.283038i $$0.0913421\pi$$
−0.959109 + 0.283038i $$0.908658\pi$$
$$168$$ −2162.73 3807.36i −0.993202 1.74848i
$$169$$ 1942.91i 0.884347i
$$170$$ −1058.07 1266.96i −0.477356 0.571598i
$$171$$ −1263.75 1263.75i −0.565155 0.565155i
$$172$$ −646.193 932.104i −0.286464 0.413211i
$$173$$ −563.418 + 563.418i −0.247606 + 0.247606i −0.819988 0.572381i $$-0.806020\pi$$
0.572381 + 0.819988i $$0.306020\pi$$
$$174$$ −29.0545 + 323.387i −0.0126587 + 0.140896i
$$175$$ 2029.05 0.876468
$$176$$ 837.474 + 1840.71i 0.358676 + 0.788344i
$$177$$ 4451.99 1.89058
$$178$$ 66.4976 740.141i 0.0280012 0.311662i
$$179$$ −2202.23 + 2202.23i −0.919565 + 0.919565i −0.996998 0.0774329i $$-0.975328\pi$$
0.0774329 + 0.996998i $$0.475328\pi$$
$$180$$ −1449.01 + 1004.55i −0.600016 + 0.415969i
$$181$$ 121.294 + 121.294i 0.0498104 + 0.0498104i 0.731573 0.681763i $$-0.238786\pi$$
−0.681763 + 0.731573i $$0.738786\pi$$
$$182$$ 719.502 + 861.551i 0.293039 + 0.350892i
$$183$$ 7305.26i 2.95093i
$$184$$ −289.193 + 1049.78i −0.115867 + 0.420602i
$$185$$ 1522.98i 0.605251i
$$186$$ 1636.09 1366.34i 0.644968 0.538628i
$$187$$ −1977.02 1977.02i −0.773124 0.773124i
$$188$$ 1737.08 + 314.675i 0.673882 + 0.122074i
$$189$$ 877.939 877.939i 0.337887 0.337887i
$$190$$ 993.731 + 89.2813i 0.379436 + 0.0340902i
$$191$$ 3927.65 1.48793 0.743966 0.668218i $$-0.232942\pi$$
0.743966 + 0.668218i $$0.232942\pi$$
$$192$$ 3858.12 976.000i 1.45019 0.366858i
$$193$$ −3249.02 −1.21176 −0.605880 0.795556i $$-0.707179\pi$$
−0.605880 + 0.795556i $$0.707179\pi$$
$$194$$ 424.817 + 38.1675i 0.157217 + 0.0141251i
$$195$$ 577.833 577.833i 0.212202 0.212202i
$$196$$ −2179.23 394.769i −0.794178 0.143866i
$$197$$ 2420.90 + 2420.90i 0.875545 + 0.875545i 0.993070 0.117525i $$-0.0374961\pi$$
−0.117525 + 0.993070i $$0.537496\pi$$
$$198$$ −2292.25 + 1914.31i −0.822743 + 0.687093i
$$199$$ 1371.30i 0.488488i −0.969714 0.244244i $$-0.921460\pi$$
0.969714 0.244244i $$-0.0785397\pi$$
$$200$$ −489.773 + 1777.89i −0.173161 + 0.628580i
$$201$$ 1180.33i 0.414198i
$$202$$ −1251.18 1498.20i −0.435807 0.521847i
$$203$$ 259.998 + 259.998i 0.0898931 + 0.0898931i
$$204$$ −4521.82 + 3134.81i −1.55191 + 1.07588i
$$205$$ 1681.36 1681.36i 0.572836 0.572836i
$$206$$ 465.849 5185.06i 0.157559 1.75369i
$$207$$ −1608.06 −0.539941
$$208$$ −928.580 + 422.480i −0.309546 + 0.140835i
$$209$$ 1689.98 0.559321
$$210$$ −323.038 + 3595.52i −0.106151 + 1.18150i
$$211$$ −1620.50 + 1620.50i −0.528719 + 0.528719i −0.920190 0.391471i $$-0.871966\pi$$
0.391471 + 0.920190i $$0.371966\pi$$
$$212$$ −1132.88 1634.12i −0.367011 0.529396i
$$213$$ −1181.95 1181.95i −0.380217 0.380217i
$$214$$ 203.605 + 243.802i 0.0650382 + 0.0778784i
$$215$$ 935.068i 0.296610i
$$216$$ 557.350 + 981.184i 0.175569 + 0.309079i
$$217$$ 2413.91i 0.755148i
$$218$$ −2925.82 + 2443.42i −0.908997 + 0.759125i
$$219$$ 3674.67 + 3674.67i 1.13384 + 1.13384i
$$220$$ 297.185 1640.53i 0.0910736 0.502749i
$$221$$ 997.347 997.347i 0.303569 0.303569i
$$222$$ 5056.15 + 454.268i 1.52859 + 0.137335i
$$223$$ −419.617 −0.126007 −0.0630036 0.998013i $$-0.520068\pi$$
−0.0630036 + 0.998013i $$0.520068\pi$$
$$224$$ 1952.24 4061.97i 0.582320 1.21161i
$$225$$ −2723.38 −0.806929
$$226$$ 2029.62 + 182.350i 0.597381 + 0.0536714i
$$227$$ −2133.64 + 2133.64i −0.623853 + 0.623853i −0.946515 0.322661i $$-0.895423\pi$$
0.322661 + 0.946515i $$0.395423\pi$$
$$228$$ 592.813 3272.48i 0.172193 0.950548i
$$229$$ −1574.42 1574.42i −0.454325 0.454325i 0.442462 0.896787i $$-0.354105\pi$$
−0.896787 + 0.442462i $$0.854105\pi$$
$$230$$ 689.039 575.433i 0.197539 0.164969i
$$231$$ 6114.67i 1.74163i
$$232$$ −290.574 + 165.057i −0.0822289 + 0.0467091i
$$233$$ 1194.86i 0.335957i −0.985791 0.167978i $$-0.946276\pi$$
0.985791 0.167978i $$-0.0537239\pi$$
$$234$$ −965.712 1156.37i −0.269789 0.323052i
$$235$$ −1029.14 1029.14i −0.285675 0.285675i
$$236$$ 2610.63 + 3765.71i 0.720075 + 1.03867i
$$237$$ −4523.12 + 4523.12i −1.23970 + 1.23970i
$$238$$ −557.567 + 6205.91i −0.151856 + 1.69021i
$$239$$ −4241.03 −1.14782 −0.573911 0.818917i $$-0.694575\pi$$
−0.573911 + 0.818917i $$0.694575\pi$$
$$240$$ −3072.49 1150.94i −0.826367 0.309553i
$$241$$ −5571.19 −1.48910 −0.744548 0.667569i $$-0.767335\pi$$
−0.744548 + 0.667569i $$0.767335\pi$$
$$242$$ −84.1734 + 936.878i −0.0223590 + 0.248863i
$$243$$ 3780.46 3780.46i 0.998012 0.998012i
$$244$$ 6179.15 4283.77i 1.62123 1.12394i
$$245$$ 1291.09 + 1291.09i 0.336672 + 0.336672i
$$246$$ −5080.47 6083.49i −1.31674 1.57670i
$$247$$ 852.541i 0.219619i
$$248$$ 2115.12 + 582.671i 0.541572 + 0.149192i
$$249$$ 3593.11i 0.914474i
$$250$$ 2956.75 2469.26i 0.748006 0.624678i
$$251$$ −482.728 482.728i −0.121393 0.121393i 0.643801 0.765193i $$-0.277357\pi$$
−0.765193 + 0.643801i $$0.777357\pi$$
$$252$$ 6548.95 + 1186.35i 1.63708 + 0.296560i
$$253$$ 1075.20 1075.20i 0.267184 0.267184i
$$254$$ −7387.36 663.713i −1.82490 0.163957i
$$255$$ 4536.19 1.11399
$$256$$ 3087.94 + 2691.07i 0.753891 + 0.656999i
$$257$$ 8093.12 1.96434 0.982169 0.188002i $$-0.0602013\pi$$
0.982169 + 0.188002i $$0.0602013\pi$$
$$258$$ 3104.35 + 278.909i 0.749102 + 0.0673027i
$$259$$ 4065.08 4065.08i 0.975257 0.975257i
$$260$$ 827.598 + 149.921i 0.197406 + 0.0357603i
$$261$$ −348.969 348.969i −0.0827610 0.0827610i
$$262$$ −2018.87 + 1686.01i −0.476054 + 0.397564i
$$263$$ 410.300i 0.0961984i 0.998843 + 0.0480992i $$0.0153164\pi$$
−0.998843 + 0.0480992i $$0.984684\pi$$
$$264$$ −5357.79 1475.96i −1.24905 0.344088i
$$265$$ 1639.32i 0.380009i
$$266$$ −2414.13 2890.74i −0.556465 0.666326i
$$267$$ 1444.03 + 1444.03i 0.330986 + 0.330986i
$$268$$ −998.378 + 692.139i −0.227558 + 0.157758i
$$269$$ −4.77962 + 4.77962i −0.00108334 + 0.00108334i −0.707648 0.706565i $$-0.750244\pi$$
0.706565 + 0.707648i $$0.250244\pi$$
$$270$$ 83.2490 926.590i 0.0187643 0.208854i
$$271$$ −2833.98 −0.635247 −0.317623 0.948217i $$-0.602885\pi$$
−0.317623 + 0.948217i $$0.602885\pi$$
$$272$$ −5303.15 1986.54i −1.18217 0.442836i
$$273$$ −3084.67 −0.683855
$$274$$ −635.665 + 7075.17i −0.140153 + 1.55995i
$$275$$ 1820.95 1820.95i 0.399300 0.399300i
$$276$$ −1704.87 2459.19i −0.371815 0.536326i
$$277$$ 1525.80 + 1525.80i 0.330962 + 0.330962i 0.852952 0.521989i $$-0.174810\pi$$
−0.521989 + 0.852952i $$0.674810\pi$$
$$278$$ 2784.53 + 3334.27i 0.600738 + 0.719339i
$$279$$ 3239.94i 0.695234i
$$280$$ −3230.70 + 1835.16i −0.689539 + 0.391684i
$$281$$ 4750.23i 1.00845i −0.863572 0.504226i $$-0.831778\pi$$
0.863572 0.504226i $$-0.168222\pi$$
$$282$$ −3723.63 + 3109.69i −0.786308 + 0.656665i
$$283$$ 644.104 + 644.104i 0.135293 + 0.135293i 0.771510 0.636217i $$-0.219502\pi$$
−0.636217 + 0.771510i $$0.719502\pi$$
$$284$$ 306.662 1692.85i 0.0640740 0.353705i
$$285$$ −1938.79 + 1938.79i −0.402961 + 0.402961i
$$286$$ 1418.90 + 127.480i 0.293361 + 0.0263569i
$$287$$ −8975.67 −1.84605
$$288$$ −2620.29 + 5451.95i −0.536118 + 1.11548i
$$289$$ 2916.53 0.593635
$$290$$ 274.406 + 24.6539i 0.0555644 + 0.00499216i
$$291$$ −828.827 + 828.827i −0.166965 + 0.166965i
$$292$$ −953.405 + 5263.03i −0.191075 + 1.05478i
$$293$$ −1433.16 1433.16i −0.285755 0.285755i 0.549644 0.835399i $$-0.314763\pi$$
−0.835399 + 0.549644i $$0.814763\pi$$
$$294$$ 4671.41 3901.21i 0.926675 0.773888i
$$295$$ 3777.69i 0.745578i
$$296$$ 2580.67 + 4543.13i 0.506751 + 0.892108i
$$297$$ 1575.79i 0.307868i
$$298$$ 5857.75 + 7014.23i 1.13869 + 1.36350i
$$299$$ 542.407 + 542.407i 0.104910 + 0.104910i
$$300$$ −2887.34 4164.85i −0.555668 0.801526i
$$301$$ 2495.85 2495.85i 0.477935 0.477935i
$$302$$ 712.319 7928.36i 0.135726 1.51068i
$$303$$ 5364.10 1.01703
$$304$$ 3115.65 1417.54i 0.587811 0.267439i
$$305$$ −6198.79 −1.16374
$$306$$ 748.364 8329.55i 0.139808 1.55611i
$$307$$ −231.211 + 231.211i −0.0429834 + 0.0429834i −0.728272 0.685288i $$-0.759676\pi$$
0.685288 + 0.728272i $$0.259676\pi$$
$$308$$ −5172.09 + 3585.62i −0.956842 + 0.663343i
$$309$$ 10116.2 + 10116.2i 1.86242 + 1.86242i
$$310$$ −1159.39 1388.29i −0.212416 0.254353i
$$311$$ 871.410i 0.158885i −0.996839 0.0794423i $$-0.974686\pi$$
0.996839 0.0794423i $$-0.0253140\pi$$
$$312$$ 744.577 2702.84i 0.135107 0.490443i
$$313$$ 3515.02i 0.634762i 0.948298 + 0.317381i $$0.102803\pi$$
−0.948298 + 0.317381i $$0.897197\pi$$
$$314$$ 2782.53 2323.76i 0.500087 0.417634i
$$315$$ −3879.95 3879.95i −0.694001 0.694001i
$$316$$ −6478.22 1173.54i −1.15325 0.208913i
$$317$$ 4723.77 4723.77i 0.836951 0.836951i −0.151506 0.988456i $$-0.548412\pi$$
0.988456 + 0.151506i $$0.0484121\pi$$
$$318$$ 5442.40 + 488.970i 0.959732 + 0.0862266i
$$319$$ 466.665 0.0819067
$$320$$ −828.174 3273.77i −0.144676 0.571904i
$$321$$ −872.901 −0.151778
$$322$$ −3375.09 303.233i −0.584119 0.0524799i
$$323$$ −3346.38 + 3346.38i −0.576462 + 0.576462i
$$324$$ 4050.89 + 733.824i 0.694597 + 0.125827i
$$325$$ 918.613 + 918.613i 0.156786 + 0.156786i
$$326$$ −4274.79 + 3569.98i −0.726254 + 0.606512i
$$327$$ 10475.5i 1.77155i
$$328$$ 2166.55 7864.65i 0.364718 1.32394i
$$329$$ 5493.90i 0.920633i
$$330$$ 2936.85 + 3516.67i 0.489904 + 0.586625i
$$331$$ −1820.26 1820.26i −0.302268 0.302268i 0.539633 0.841901i $$-0.318563\pi$$
−0.841901 + 0.539633i $$0.818563\pi$$
$$332$$ 3039.23 2106.99i 0.502408 0.348301i
$$333$$ −5456.13 + 5456.13i −0.897880 + 0.897880i
$$334$$ 309.200 3441.50i 0.0506547 0.563804i
$$335$$ 1001.55 0.163345
$$336$$ 5128.93 + 11273.0i 0.832757 + 1.83034i
$$337$$ 74.0970 0.0119772 0.00598861 0.999982i $$-0.498094\pi$$
0.00598861 + 0.999982i $$0.498094\pi$$
$$338$$ 491.749 5473.33i 0.0791350 0.880799i
$$339$$ −3959.83 + 3959.83i −0.634420 + 0.634420i
$$340$$ 2660.01 + 3836.94i 0.424292 + 0.612021i
$$341$$ −2166.34 2166.34i −0.344029 0.344029i
$$342$$ 3240.23 + 3879.94i 0.512315 + 0.613460i
$$343$$ 1647.24i 0.259307i
$$344$$ 1584.46 + 2789.36i 0.248339 + 0.437187i
$$345$$ 2467.01i 0.384984i
$$346$$ 1729.80 1444.59i 0.268770 0.224456i
$$347$$ 2102.73 + 2102.73i 0.325305 + 0.325305i 0.850798 0.525493i $$-0.176119\pi$$
−0.525493 + 0.850798i $$0.676119\pi$$
$$348$$ 163.698 903.652i 0.0252159 0.139198i
$$349$$ −6612.85 + 6612.85i −1.01426 + 1.01426i −0.0143661 + 0.999897i $$0.504573\pi$$
−0.999897 + 0.0143661i $$0.995427\pi$$
$$350$$ −5716.00 513.551i −0.872951 0.0784299i
$$351$$ 794.940 0.120885
$$352$$ −1893.35 5397.38i −0.286693 0.817277i
$$353$$ 2216.90 0.334259 0.167130 0.985935i $$-0.446550\pi$$
0.167130 + 0.985935i $$0.446550\pi$$
$$354$$ −12541.6 1126.80i −1.88299 0.169177i
$$355$$ −1002.93 + 1002.93i −0.149944 + 0.149944i
$$356$$ −374.658 + 2068.21i −0.0557776 + 0.307906i
$$357$$ −12107.9 12107.9i −1.79500 1.79500i
$$358$$ 6761.23 5646.46i 0.998162 0.833589i
$$359$$ 2082.23i 0.306117i 0.988217 + 0.153059i $$0.0489123\pi$$
−0.988217 + 0.153059i $$0.951088\pi$$
$$360$$ 4336.23 2463.14i 0.634831 0.360608i
$$361$$ 3998.49i 0.582955i
$$362$$ −310.995 372.393i −0.0451533 0.0540678i
$$363$$ −1827.87 1827.87i −0.264293 0.264293i
$$364$$ −1808.84 2609.16i −0.260464 0.375707i
$$365$$ 3118.10 3118.10i 0.447148 0.447148i
$$366$$ −1848.95 + 20579.5i −0.264061 + 2.93909i
$$367$$ 4509.22 0.641360 0.320680 0.947188i $$-0.396089\pi$$
0.320680 + 0.947188i $$0.396089\pi$$
$$368$$ 1080.38 2884.12i 0.153040 0.408547i
$$369$$ 12047.1 1.69959
$$370$$ 385.464 4290.34i 0.0541603 0.602823i
$$371$$ 4375.61 4375.61i 0.612320 0.612320i
$$372$$ −4954.82 + 3434.99i −0.690579 + 0.478753i
$$373$$ −8661.56 8661.56i −1.20236 1.20236i −0.973448 0.228908i $$-0.926485\pi$$
−0.228908 0.973448i $$-0.573515\pi$$
$$374$$ 5069.05 + 6069.81i 0.700840 + 0.839205i
$$375$$ 10586.3i 1.45779i
$$376$$ −4813.86 1326.12i −0.660254 0.181886i
$$377$$ 235.418i 0.0321609i
$$378$$ −2695.43 + 2251.02i −0.366767 + 0.306296i
$$379$$ 3522.46 + 3522.46i 0.477405 + 0.477405i 0.904301 0.426896i $$-0.140393\pi$$
−0.426896 + 0.904301i $$0.640393\pi$$
$$380$$ −2776.82 503.025i −0.374863 0.0679069i
$$381$$ 14412.9 14412.9i 1.93804 1.93804i
$$382$$ −11064.5 994.086i −1.48196 0.133146i
$$383$$ 3044.88 0.406229 0.203115 0.979155i $$-0.434894\pi$$
0.203115 + 0.979155i $$0.434894\pi$$
$$384$$ −11115.7 + 1772.98i −1.47720 + 0.235618i
$$385$$ 5188.54 0.686837
$$386$$ 9152.75 + 822.325i 1.20690 + 0.108433i
$$387$$ −3349.92 + 3349.92i −0.440016 + 0.440016i
$$388$$ −1187.08 215.042i −0.155322 0.0281368i
$$389$$ 1932.73 + 1932.73i 0.251911 + 0.251911i 0.821754 0.569843i $$-0.192996\pi$$
−0.569843 + 0.821754i $$0.692996\pi$$
$$390$$ −1774.05 + 1481.55i −0.230340 + 0.192362i
$$391$$ 4258.09i 0.550744i
$$392$$ 6039.14 + 1663.66i 0.778119 + 0.214356i
$$393$$ 7228.29i 0.927784i
$$394$$ −6207.15 7432.61i −0.793685 0.950379i
$$395$$ 3838.04 + 3838.04i 0.488893 + 0.488893i
$$396$$ 6941.96 4812.61i 0.880926 0.610714i
$$397$$ −672.457 + 672.457i −0.0850117 + 0.0850117i −0.748334 0.663322i $$-0.769146\pi$$
0.663322 + 0.748334i $$0.269146\pi$$
$$398$$ −347.075 + 3863.07i −0.0437119 + 0.486528i
$$399$$ 10349.9 1.29861
$$400$$ 1829.71 4884.51i 0.228714 0.610563i
$$401$$ −7606.74 −0.947288 −0.473644 0.880716i $$-0.657062\pi$$
−0.473644 + 0.880716i $$0.657062\pi$$
$$402$$ 298.740 3325.07i 0.0370641 0.412536i
$$403$$ 1092.85 1092.85i 0.135084 0.135084i
$$404$$ 3145.49 + 4537.23i 0.387361 + 0.558751i
$$405$$ −2399.96 2399.96i −0.294457 0.294457i
$$406$$ −666.631 798.241i −0.0814885 0.0975765i
$$407$$ 7296.32i 0.888612i
$$408$$ 13531.7 7686.54i 1.64196 0.932697i
$$409$$ 4981.58i 0.602257i −0.953584 0.301129i $$-0.902637\pi$$
0.953584 0.301129i $$-0.0973634\pi$$
$$410$$ −5162.08 + 4310.98i −0.621797 + 0.519278i
$$411$$ −13803.8 13803.8i −1.65667 1.65667i
$$412$$ −2624.67 + 14488.8i −0.313855 + 1.73256i
$$413$$ −10083.3 + 10083.3i −1.20137 + 1.20137i
$$414$$ 4530.03 + 406.998i 0.537775 + 0.0483161i
$$415$$ −3048.89 −0.360637
$$416$$ 2722.81 955.136i 0.320906 0.112571i
$$417$$ −11937.9 −1.40192
$$418$$ −4760.80 427.732i −0.557077 0.0500503i
$$419$$ −3433.38 + 3433.38i −0.400314 + 0.400314i −0.878344 0.478030i $$-0.841351\pi$$
0.478030 + 0.878344i $$0.341351\pi$$
$$420$$ 1820.05 10047.1i 0.211450 1.16726i
$$421$$ 7973.72 + 7973.72i 0.923077 + 0.923077i 0.997246 0.0741686i $$-0.0236303\pi$$
−0.0741686 + 0.997246i $$0.523630\pi$$
$$422$$ 4975.22 4154.93i 0.573910 0.479286i
$$423$$ 7373.88i 0.847590i
$$424$$ 2777.81 + 4890.18i 0.318166 + 0.560114i
$$425$$ 7211.44i 0.823074i
$$426$$ 3030.51 + 3628.81i 0.344668 + 0.412715i
$$427$$ 16545.6 + 16545.6i 1.87517 + 1.87517i
$$428$$ −511.866 738.343i −0.0578084 0.0833859i
$$429$$ −2768.30 + 2768.30i −0.311550 + 0.311550i
$$430$$ 236.665 2634.16i 0.0265418 0.295420i
$$431$$ 4800.16 0.536463 0.268232 0.963354i $$-0.413561\pi$$
0.268232 + 0.963354i $$0.413561\pi$$
$$432$$ −1321.76 2905.14i −0.147207 0.323550i
$$433$$ 6242.32 0.692810 0.346405 0.938085i $$-0.387402\pi$$
0.346405 + 0.938085i $$0.387402\pi$$
$$434$$ −610.959 + 6800.18i −0.0675737 + 0.752118i
$$435$$ −535.372 + 535.372i −0.0590095 + 0.0590095i
$$436$$ 8860.69 6142.79i 0.973280 0.674739i
$$437$$ −1819.93 1819.93i −0.199220 0.199220i
$$438$$ −9421.79 11281.9i −1.02783 1.23075i
$$439$$ 4929.27i 0.535903i −0.963432 0.267951i $$-0.913653\pi$$
0.963432 0.267951i $$-0.0863466\pi$$
$$440$$ −1252.41 + 4546.30i −0.135696 + 0.492582i
$$441$$ 9250.77i 0.998896i
$$442$$ −3062.03 + 2557.18i −0.329516 + 0.275187i
$$443$$ −7670.67 7670.67i −0.822674 0.822674i 0.163817 0.986491i $$-0.447619\pi$$
−0.986491 + 0.163817i $$0.947619\pi$$
$$444$$ −14128.6 2559.42i −1.51017 0.273569i
$$445$$ 1225.32 1225.32i 0.130529 0.130529i
$$446$$ 1182.09 + 106.205i 0.125502 + 0.0112756i
$$447$$ −25113.5 −2.65733
$$448$$ −6527.70 + 10948.8i −0.688404 + 1.15464i
$$449$$ −11515.2 −1.21032 −0.605162 0.796102i $$-0.706892\pi$$
−0.605162 + 0.796102i $$0.706892\pi$$
$$450$$ 7671.99 + 689.286i 0.803691 + 0.0722073i
$$451$$ −8055.12 + 8055.12i −0.841021 + 0.841021i
$$452$$ −5671.44 1027.39i −0.590182 0.106912i
$$453$$ 15468.4 + 15468.4i 1.60434 + 1.60434i
$$454$$ 6550.66 5470.61i 0.677176 0.565526i
$$455$$ 2617.46i 0.269689i
$$456$$ −2498.26 + 9068.79i −0.256561 + 0.931326i
$$457$$ 4829.89i 0.494383i −0.968967 0.247191i $$-0.920492\pi$$
0.968967 0.247191i $$-0.0795076\pi$$
$$458$$ 4036.78 + 4833.74i 0.411848 + 0.493157i
$$459$$ 3120.28 + 3120.28i 0.317303 + 0.317303i
$$460$$ −2086.72 + 1446.65i −0.211508 + 0.146631i
$$461$$ 8265.79 8265.79i 0.835090 0.835090i −0.153118 0.988208i $$-0.548931\pi$$
0.988208 + 0.153118i $$0.0489315\pi$$
$$462$$ 1547.62 17225.5i 0.155848 1.73464i
$$463$$ −5043.86 −0.506281 −0.253141 0.967430i $$-0.581464\pi$$
−0.253141 + 0.967430i $$0.581464\pi$$
$$464$$ 860.346 391.435i 0.0860788 0.0391636i
$$465$$ 4970.57 0.495709
$$466$$ −302.418 + 3366.02i −0.0300628 + 0.334609i
$$467$$ 12438.8 12438.8i 1.23255 1.23255i 0.269564 0.962982i $$-0.413120\pi$$
0.962982 0.269564i $$-0.0868796\pi$$
$$468$$ 2427.81 + 3502.01i 0.239798 + 0.345898i
$$469$$ −2673.31 2673.31i −0.263203 0.263203i
$$470$$ 2638.70 + 3159.64i 0.258966 + 0.310093i
$$471$$ 9962.47i 0.974621i
$$472$$ −6401.26 11269.1i −0.624241 1.09894i
$$473$$ 4479.75i 0.435474i
$$474$$ 13886.8 11597.2i 1.34566 1.12379i
$$475$$ −3082.20 3082.20i −0.297729 0.297729i
$$476$$ 3141.42 17341.4i 0.302493 1.66984i
$$477$$ −5872.93 + 5872.93i −0.563738 + 0.563738i
$$478$$ 11947.3 + 1073.40i 1.14322 + 0.102712i
$$479$$ 13059.7 1.24575 0.622875 0.782321i $$-0.285964\pi$$
0.622875 + 0.782321i $$0.285964\pi$$
$$480$$ 8364.14 + 4019.93i 0.795352 + 0.382258i
$$481$$ 3680.77 0.348916
$$482$$ 15694.5 + 1410.06i 1.48312 + 0.133250i
$$483$$ 6584.87 6584.87i 0.620335 0.620335i
$$484$$ 474.246 2617.96i 0.0445385 0.245864i
$$485$$ 703.292 + 703.292i 0.0658450 + 0.0658450i
$$486$$ −11606.7 + 9693.04i −1.08331 + 0.904702i
$$487$$ 15549.3i 1.44683i −0.690414 0.723414i $$-0.742572\pi$$
0.690414 0.723414i $$-0.257428\pi$$
$$488$$ −18491.4 + 10503.8i −1.71530 + 0.974354i
$$489$$ 15305.3i 1.41540i
$$490$$ −3310.33 3963.88i −0.305195 0.365448i
$$491$$ −8628.34 8628.34i −0.793058 0.793058i 0.188932 0.981990i $$-0.439497\pi$$
−0.981990 + 0.188932i $$0.939497\pi$$
$$492$$ 12772.4 + 18423.5i 1.17037 + 1.68821i
$$493$$ −924.059 + 924.059i −0.0844169 + 0.0844169i
$$494$$ 215.777 2401.68i 0.0196524 0.218738i
$$495$$ −6964.03 −0.632344
$$496$$ −5810.98 2176.76i −0.526049 0.197056i
$$497$$ 5354.00 0.483219
$$498$$ −909.413 + 10122.1i −0.0818309 + 0.910806i
$$499$$ 1732.42 1732.42i 0.155418 0.155418i −0.625115 0.780533i $$-0.714948\pi$$
0.780533 + 0.625115i $$0.214948\pi$$
$$500$$ −8954.38 + 6207.74i −0.800904 + 0.555237i
$$501$$ 6714.44 + 6714.44i 0.598761 + 0.598761i
$$502$$ 1237.71 + 1482.06i 0.110043 + 0.131768i
$$503$$ 16579.6i 1.46968i 0.678241 + 0.734839i $$0.262742\pi$$
−0.678241 + 0.734839i $$0.737258\pi$$
$$504$$ −18148.7 4999.58i −1.60398 0.441863i
$$505$$ 4551.65i 0.401081i
$$506$$ −3301.07 + 2756.80i −0.290021 + 0.242203i
$$507$$ 10678.6 + 10678.6i 0.935410 + 0.935410i
$$508$$ 20642.8 + 3739.47i 1.80291 + 0.326599i
$$509$$ −7830.92 + 7830.92i −0.681924 + 0.681924i −0.960434 0.278509i $$-0.910160\pi$$
0.278509 + 0.960434i $$0.410160\pi$$
$$510$$ −12778.8 1148.11i −1.10952 0.0996844i
$$511$$ −16645.5 −1.44100
$$512$$ −8017.86 8362.51i −0.692076 0.721825i
$$513$$ −2667.24 −0.229555
$$514$$ −22799.0 2048.36i −1.95646 0.175777i
$$515$$ 8583.95 8583.95i 0.734474 0.734474i
$$516$$ −8674.61 1571.42i −0.740074 0.134065i
$$517$$ 4930.44 + 4930.44i 0.419420 + 0.419420i
$$518$$ −12480.5 + 10422.8i −1.05861 + 0.884075i
$$519$$ 6193.30i 0.523807i
$$520$$ −2293.47 631.803i −0.193414 0.0532815i
$$521$$ 3400.02i 0.285907i 0.989729 + 0.142953i $$0.0456599\pi$$
−0.989729 + 0.142953i $$0.954340\pi$$
$$522$$ 894.749 + 1071.40i 0.0750232 + 0.0898348i
$$523$$ −2019.50 2019.50i −0.168847 0.168847i 0.617626 0.786472i $$-0.288095\pi$$
−0.786472 + 0.617626i $$0.788095\pi$$
$$524$$ 6114.05 4238.64i 0.509720 0.353370i
$$525$$ 11152.0 11152.0i 0.927075 0.927075i
$$526$$ 103.847 1155.85i 0.00860822 0.0958124i
$$527$$ 8579.28 0.709144
$$528$$ 14719.8 + 5513.95i 1.21325 + 0.454477i
$$529$$ 9851.23 0.809668
$$530$$ 414.910 4618.09i 0.0340048 0.378485i
$$531$$ 13533.7 13533.7i 1.10605 1.10605i
$$532$$ 6069.15 + 8754.47i 0.494607 + 0.713448i
$$533$$ −4063.56 4063.56i −0.330229 0.330229i
$$534$$ −3702.47 4433.43i −0.300040 0.359276i
$$535$$ 740.691i 0.0598558i
$$536$$ 2987.69 1697.12i 0.240762 0.136762i
$$537$$ 24207.7i 1.94532i
$$538$$ 14.6743 12.2548i 0.00117594 0.000982052i
$$539$$ −6185.39 6185.39i −0.494293 0.494293i
$$540$$ −469.038 + 2589.21i −0.0373781 + 0.206337i
$$541$$ −13432.6 + 13432.6i −1.06749 + 1.06749i −0.0699388 + 0.997551i $$0.522280\pi$$
−0.997551 + 0.0699388i $$0.977720\pi$$
$$542$$ 7983.54 + 717.278i 0.632699 + 0.0568445i
$$543$$ 1333.30 0.105373
$$544$$ 14436.6 + 6938.45i 1.13780 + 0.546845i
$$545$$ −8888.86 −0.698637
$$546$$ 8689.75 + 780.726i 0.681112 + 0.0611941i
$$547$$ −5376.46 + 5376.46i −0.420257 + 0.420257i −0.885292 0.465035i $$-0.846042\pi$$
0.465035 + 0.885292i $$0.346042\pi$$
$$548$$ 3581.44 19770.4i 0.279181 1.54115i
$$549$$ −22207.5 22207.5i −1.72640 1.72640i
$$550$$ −5590.64 + 4668.88i −0.433429 + 0.361967i
$$551$$ 789.894i 0.0610719i
$$552$$ 4180.33 + 7359.24i 0.322331 + 0.567446i
$$553$$ 20488.7i 1.57553i
$$554$$ −3912.13 4684.49i −0.300019 0.359251i
$$555$$ 8370.55 + 8370.55i 0.640198 + 0.640198i
$$556$$ −7000.34 10097.7i −0.533958 0.770210i
$$557$$ −2076.28 + 2076.28i −0.157944 + 0.157944i −0.781655 0.623711i $$-0.785624\pi$$
0.623711 + 0.781655i $$0.285624\pi$$
$$558$$ 820.027 9127.18i 0.0622124 0.692445i
$$559$$ 2259.90 0.170990
$$560$$ 9565.61 4352.10i 0.721823 0.328410i
$$561$$ −21732.1 −1.63553
$$562$$ −1202.28 + 13381.8i −0.0902405 + 1.00441i
$$563$$ −16643.1 + 16643.1i −1.24587 + 1.24587i −0.288339 + 0.957528i $$0.593103\pi$$
−0.957528 + 0.288339i $$0.906897\pi$$
$$564$$ 11276.8 7817.81i 0.841915 0.583669i
$$565$$ 3360.07 + 3360.07i 0.250193 + 0.250193i
$$566$$ −1651.47 1977.51i −0.122644 0.146857i
$$567$$ 12811.8i 0.948934i
$$568$$ −1292.35 + 4691.28i −0.0954679 + 0.346552i
$$569$$ 5659.60i 0.416982i −0.978024 0.208491i $$-0.933145\pi$$
0.978024 0.208491i $$-0.0668551\pi$$
$$570$$ 5952.43 4971.02i 0.437403 0.365286i
$$571$$ 4872.67 + 4872.67i 0.357119 + 0.357119i 0.862750 0.505631i $$-0.168740\pi$$
−0.505631 + 0.862750i $$0.668740\pi$$
$$572$$ −3964.89 718.244i −0.289825 0.0525023i
$$573$$ 21587.1 21587.1i 1.57385 1.57385i
$$574$$ 25285.2 + 2271.73i 1.83865 + 0.165192i
$$575$$ −3921.95 −0.284446
$$576$$ 8761.45 14695.4i 0.633786 1.06303i
$$577$$ 10652.2 0.768556 0.384278 0.923217i $$-0.374450\pi$$
0.384278 + 0.923217i $$0.374450\pi$$
$$578$$ −8216.10 738.171i −0.591254 0.0531209i
$$579$$ −17857.2 + 17857.2i −1.28173 + 1.28173i
$$580$$ −766.784 138.904i −0.0548948 0.00994426i
$$581$$ 8138.01 + 8138.01i 0.581104 + 0.581104i
$$582$$ 2544.65 2125.10i 0.181235 0.151354i
$$583$$ 7853.69i 0.557919i
$$584$$ 4017.89 14585.1i 0.284694 1.03345i
$$585$$ 3513.14i 0.248291i
$$586$$ 3674.61 + 4400.07i 0.259039 + 0.310180i
$$587$$ 9903.95 + 9903.95i 0.696388 + 0.696388i 0.963630 0.267242i $$-0.0861122\pi$$
−0.267242 + 0.963630i $$0.586112\pi$$
$$588$$ −14147.1 + 9807.69i −0.992208 + 0.687861i
$$589$$ −3666.82 + 3666.82i −0.256517 + 0.256517i
$$590$$ −956.129 + 10642.0i −0.0667173 + 0.742587i
$$591$$ 26611.5 1.85220
$$592$$ −6120.09 13451.5i −0.424889 0.933875i
$$593$$ −3528.04 −0.244316 −0.122158 0.992511i $$-0.538981\pi$$
−0.122158 + 0.992511i $$0.538981\pi$$
$$594$$ −398.832 + 4439.14i −0.0275493 + 0.306633i
$$595$$ −10274.0 + 10274.0i −0.707887 + 0.707887i
$$596$$ −14726.5 21242.2i −1.01211 1.45993i
$$597$$ −7536.93 7536.93i −0.516693 0.516693i
$$598$$ −1390.72 1665.29i −0.0951018 0.113877i
$$599$$ 19024.9i 1.29772i −0.760907 0.648861i $$-0.775246\pi$$
0.760907 0.648861i $$-0.224754\pi$$
$$600$$ 7079.74 + 12463.5i 0.481715 + 0.848034i
$$601$$ 1065.92i 0.0723460i −0.999346 0.0361730i $$-0.988483\pi$$
0.999346 0.0361730i $$-0.0115167\pi$$
$$602$$ −7662.72 + 6399.32i −0.518786 + 0.433250i
$$603$$ 3588.11 + 3588.11i 0.242320 + 0.242320i
$$604$$ −4013.32 + 22154.5i −0.270364 + 1.49248i
$$605$$ −1551.02 + 1551.02i −0.104228 + 0.104228i
$$606$$ −15111.1 1357.65i −1.01295 0.0910079i
$$607$$ 12909.7 0.863242 0.431621 0.902055i $$-0.357942\pi$$
0.431621 + 0.902055i $$0.357942\pi$$
$$608$$ −9135.80 + 3204.75i −0.609384 + 0.213766i
$$609$$ 2858.00 0.190167
$$610$$ 17462.5 + 1568.91i 1.15908 + 0.104137i
$$611$$ −2487.25 + 2487.25i −0.164687 + 0.164687i
$$612$$ −4216.40 + 23275.6i −0.278494 + 1.53735i
$$613$$ −8763.41 8763.41i −0.577408 0.577408i 0.356781 0.934188i $$-0.383874\pi$$
−0.934188 + 0.356781i $$0.883874\pi$$
$$614$$ 709.859 592.820i 0.0466573 0.0389646i
$$615$$ 18482.1i 1.21182i
$$616$$ 15477.7 8791.93i 1.01236 0.575060i
$$617$$ 18921.2i 1.23459i 0.786733 + 0.617293i $$0.211771\pi$$
−0.786733 + 0.617293i $$0.788229\pi$$
$$618$$ −25937.6 31058.4i −1.68829 2.02161i
$$619$$ −15116.6 15116.6i −0.981565 0.981565i 0.0182677 0.999833i $$-0.494185\pi$$
−0.999833 + 0.0182677i $$0.994185\pi$$
$$620$$ 2914.73 + 4204.36i 0.188804 + 0.272340i
$$621$$ −1696.97 + 1696.97i −0.109657 + 0.109657i
$$622$$ −220.553 + 2454.83i −0.0142176 + 0.158247i
$$623$$ −6541.15 −0.420651
$$624$$ −2781.62 + 7425.67i −0.178452 + 0.476386i
$$625$$ −1204.57 −0.0770926
$$626$$ 889.648 9902.09i 0.0568011 0.632216i
$$627$$ 9288.42 9288.42i 0.591617 0.591617i
$$628$$ −8426.75 + 5841.95i −0.535452 + 0.371209i
$$629$$ 14447.7 + 14447.7i 0.915845 + 0.915845i
$$630$$ 9948.11 + 11912.1i 0.629115 + 0.753319i
$$631$$ 9602.80i 0.605834i 0.953017 + 0.302917i $$0.0979605\pi$$
−0.953017 + 0.302917i $$0.902039\pi$$
$$632$$ 17952.6 + 4945.58i 1.12993 + 0.311273i
$$633$$ 17813.1i 1.11849i
$$634$$ −14502.8 + 12111.7i −0.908487 + 0.758699i
$$635$$ −12229.9 12229.9i −0.764297 0.764297i
$$636$$ −15207.9 2754.93i −0.948166 0.171761i
$$637$$ 3120.34 3120.34i 0.194085 0.194085i
$$638$$ −1314.63 118.113i −0.0815781 0.00732935i
$$639$$ −7186.12 −0.444880
$$640$$ 1504.44 + 9432.08i 0.0929194 + 0.582556i
$$641$$ 4450.84 0.274256 0.137128 0.990553i $$-0.456213\pi$$
0.137128 + 0.990553i $$0.456213\pi$$
$$642$$ 2459.03 + 220.931i 0.151169 + 0.0135817i
$$643$$ 6491.27 6491.27i 0.398119 0.398119i −0.479450 0.877569i $$-0.659164\pi$$
0.877569 + 0.479450i $$0.159164\pi$$
$$644$$ 9431.15 + 1708.46i 0.577080 + 0.104539i
$$645$$ 5139.30 + 5139.30i 0.313736 + 0.313736i
$$646$$ 10274.0 8580.05i 0.625734 0.522566i
$$647$$ 5546.17i 0.337005i 0.985701 + 0.168503i $$0.0538932\pi$$
−0.985701 + 0.168503i $$0.946107\pi$$
$$648$$ −11226.0 3092.52i −0.680551 0.187478i
$$649$$ 18098.3i 1.09464i
$$650$$ −2355.31 2820.31i −0.142127 0.170187i
$$651$$ −13267.3 13267.3i −0.798750 0.798750i
$$652$$ 12946.0 8974.98i 0.777613 0.539091i
$$653$$ 6327.58 6327.58i 0.379200 0.379200i −0.491614 0.870813i $$-0.663593\pi$$
0.870813 + 0.491614i $$0.163593\pi$$
$$654$$ −2651.34 + 29510.3i −0.158525 + 1.76444i
$$655$$ −6133.49 −0.365886
$$656$$ −8093.88 + 21607.0i −0.481727 + 1.28599i
$$657$$ 22341.5 1.32667
$$658$$ 1390.50 15476.7i 0.0823820 0.916940i
$$659$$ 15135.2 15135.2i 0.894663 0.894663i −0.100294 0.994958i $$-0.531978\pi$$
0.994958 + 0.100294i $$0.0319785\pi$$
$$660$$ −7383.28 10650.0i −0.435445 0.628110i
$$661$$ −23460.1 23460.1i −1.38047 1.38047i −0.843777 0.536694i $$-0.819673\pi$$
−0.536694 0.843777i $$-0.680327\pi$$
$$662$$ 4667.12 + 5588.53i 0.274007 + 0.328103i
$$663$$ 10963.2i 0.642195i
$$664$$ −9095.03 + 5166.32i −0.531560 + 0.301946i
$$665$$ 8782.30i 0.512125i
$$666$$ 16751.3 13989.4i 0.974624 0.813932i
$$667$$ −502.550 502.550i −0.0291736 0.0291736i
$$668$$ −1742.08 + 9616.73i −0.100903 + 0.557009i
$$669$$ −2306.29 + 2306.29i −0.133283 + 0.133283i
$$670$$ −2821.45 253.492i −0.162690 0.0146168i
$$671$$ 29697.4 1.70858
$$672$$ −11595.4 33055.2i −0.665630 1.89752i
$$673$$ 30638.5 1.75487 0.877436 0.479694i $$-0.159252\pi$$
0.877436 + 0.479694i $$0.159252\pi$$
$$674$$ −208.737 18.7539i −0.0119292 0.00107177i
$$675$$ −2873.96 + 2873.96i −0.163879 + 0.163879i
$$676$$ −2770.59 + 15294.4i −0.157635 + 0.870184i
$$677$$ −12468.9 12468.9i −0.707855 0.707855i 0.258229 0.966084i $$-0.416861\pi$$
−0.966084 + 0.258229i $$0.916861\pi$$
$$678$$ 12157.4 10152.9i 0.688645 0.575104i
$$679$$ 3754.41i 0.212196i
$$680$$ −6522.33 11482.2i −0.367823 0.647533i
$$681$$ 23453.8i 1.31975i
$$682$$ 5554.45 + 6651.05i 0.311864 + 0.373434i
$$683$$ 13838.5 + 13838.5i 0.775280 + 0.775280i 0.979024 0.203744i $$-0.0653111\pi$$
−0.203744 + 0.979024i $$0.565311\pi$$
$$684$$ −8145.99 11750.2i −0.455365 0.656843i
$$685$$ −11713.1 + 11713.1i −0.653333 + 0.653333i
$$686$$ 416.914 4640.40i 0.0232039 0.258267i
$$687$$ −17306.6 −0.961116
$$688$$ −3757.58 8258.89i −0.208221 0.457656i
$$689$$ 3961.95 0.219068
$$690$$ 624.398 6949.77i 0.0344499 0.383439i
$$691$$ −106.012 + 106.012i −0.00583628 + 0.00583628i −0.710019 0.704183i $$-0.751314\pi$$
0.704183 + 0.710019i $$0.251314\pi$$
$$692$$ −5238.60 + 3631.73i −0.287777 + 0.199505i
$$693$$ 18588.2 + 18588.2i 1.01891 + 1.01891i
$$694$$ −5391.37 6455.77i −0.294890 0.353109i
$$695$$ 10129.8i 0.552870i
$$696$$ −689.863 + 2504.23i −0.0375707 + 0.136383i
$$697$$ 31900.4i 1.73359i
$$698$$ 20302.6 16955.2i 1.10095 0.919434i
$$699$$ −6567.17 6567.17i −0.355355 0.355355i
$$700$$ 15972.4 + 2893.43i 0.862431 + 0.156231i
$$701$$ 7839.35 7839.35i 0.422380 0.422380i −0.463643 0.886022i $$-0.653458\pi$$
0.886022 + 0.463643i $$0.153458\pi$$
$$702$$ −2239.41 201.199i −0.120400 0.0108173i
$$703$$ −12350.0 −0.662574
$$704$$ 3967.64 + 15684.1i 0.212409 + 0.839653i
$$705$$ −11312.7 −0.604341
$$706$$ −6245.17 561.095i −0.332918 0.0299109i
$$707$$ −12149.1 + 12149.1i −0.646273 + 0.646273i
$$708$$ 35045.5 + 6348.55i 1.86030 + 0.336996i
$$709$$ 2728.30 + 2728.30i 0.144518 + 0.144518i 0.775664 0.631146i $$-0.217415\pi$$
−0.631146 + 0.775664i $$0.717415\pi$$
$$710$$ 3079.19 2571.50i 0.162760 0.135925i
$$711$$ 27499.9i 1.45053i
$$712$$ 1578.90 5731.48i 0.0831066 0.301680i
$$713$$ 4665.84i 0.245073i
$$714$$ 31044.3 + 37173.3i 1.62718 + 1.94843i
$$715$$ 2349.01 + 2349.01i 0.122864 + 0.122864i
$$716$$ −20476.0 + 14195.3i −1.06875 + 0.740925i
$$717$$ −23309.5 + 23309.5i −1.21410 + 1.21410i
$$718$$ 527.011 5865.82i 0.0273926 0.304889i
$$719$$ −32717.8 −1.69704 −0.848519 0.529166i $$-0.822505\pi$$
−0.848519 + 0.529166i $$0.822505\pi$$
$$720$$ −12838.9 + 5841.37i −0.664553 + 0.302354i
$$721$$ −45824.0 −2.36696
$$722$$ 1012.01 11264.1i 0.0521652 0.580616i
$$723$$ −30620.3 + 30620.3i −1.57508 + 1.57508i
$$724$$ 781.844 + 1127.77i 0.0401340 + 0.0578914i
$$725$$ −851.111 851.111i −0.0435993 0.0435993i
$$726$$ 4686.62 + 5611.88i 0.239582 + 0.286882i
$$727$$ 25847.2i 1.31859i −0.751883 0.659297i $$-0.770854\pi$$
0.751883 0.659297i $$-0.229146\pi$$
$$728$$ 4435.26 + 7808.03i 0.225799 + 0.397507i
$$729$$ 27662.0i 1.40537i
$$730$$ −9573.13 + 7994.75i −0.485366 + 0.405341i
$$731$$ 8870.50 + 8870.50i 0.448820 + 0.448820i
$$732$$ 10417.3 57506.1i 0.526004 2.90367i
$$733$$ 10131.9 10131.9i 0.510547 0.510547i −0.404147 0.914694i $$-0.632432\pi$$
0.914694 + 0.404147i $$0.132432\pi$$
$$734$$ −12702.8 1141.28i −0.638787 0.0573915i
$$735$$ 14192.1 0.712223
$$736$$ −3773.48 + 7851.36i −0.188984 + 0.393213i
$$737$$ −4798.27 −0.239819
$$738$$ −33937.7 3049.11i −1.69277 0.152086i
$$739$$ 19163.7 19163.7i 0.953921 0.953921i −0.0450633 0.998984i $$-0.514349\pi$$
0.998984 + 0.0450633i $$0.0143490\pi$$
$$740$$ −2171.76 + 11988.7i −0.107886 + 0.595558i
$$741$$ 4685.72 + 4685.72i 0.232300 + 0.232300i
$$742$$ −13433.9 + 11219.0i −0.664656 + 0.555070i
$$743$$ 23322.1i 1.15155i 0.817607 + 0.575777i $$0.195301\pi$$
−0.817607 + 0.575777i $$0.804699\pi$$
$$744$$ 14827.5 8422.59i 0.730650 0.415037i
$$745$$ 21309.8i 1.04796i
$$746$$ 22208.1 + 26592.5i 1.08994 + 1.30512i
$$747$$ −10922.8 10922.8i −0.534999 0.534999i
$$748$$ −12743.6 18382.1i −0.622933 0.898552i
$$749$$ 1977.03 1977.03i 0.0964473 0.0964473i
$$750$$ 2679.37 29822.3i 0.130449 1.45194i
$$751$$ 25994.0 1.26303 0.631515 0.775364i $$-0.282434\pi$$
0.631515 + 0.775364i $$0.282434\pi$$
$$752$$ 13225.4 + 4954.16i 0.641330 + 0.240239i
$$753$$ −5306.32 −0.256804
$$754$$ 59.5842 663.192i 0.00287789 0.0320319i
$$755$$ 13125.5 13125.5i 0.632698 0.632698i
$$756$$ 8162.97 5659.09i 0.392704 0.272247i
$$757$$ 22145.0 + 22145.0i 1.06324 + 1.06324i 0.997860 + 0.0653808i $$0.0208262\pi$$
0.0653808 + 0.997860i $$0.479174\pi$$
$$758$$ −9031.52 10814.6i −0.432770 0.518210i
$$759$$ 11819.0i 0.565222i
$$760$$ 7695.22 + 2119.87i 0.367283 + 0.101179i
$$761$$ 16497.5i 0.785853i −0.919570 0.392926i $$-0.871463\pi$$
0.919570 0.392926i $$-0.128537\pi$$
$$762$$ −44250.1 + 36954.4i −2.10369 + 1.75684i
$$763$$ 23725.9 + 23725.9i 1.12573 + 1.12573i
$$764$$ 30918.0 + 5600.84i 1.46410 + 0.265224i
$$765$$ 13789.7 13789.7i 0.651723 0.651723i
$$766$$ −8577.66 770.656i −0.404600 0.0363511i
$$767$$ −9130.02 −0.429812
$$768$$ 31762.5 2181.27i 1.49236 0.102487i
$$769$$ −24867.3 −1.16611 −0.583055 0.812433i $$-0.698143\pi$$
−0.583055 + 0.812433i $$0.698143\pi$$
$$770$$ −14616.5 1313.21i −0.684082 0.0614610i
$$771$$ 44481.2 44481.2i 2.07776 2.07776i
$$772$$ −25575.9 4633.11i −1.19235 0.215996i
$$773$$ 1881.72 + 1881.72i 0.0875559 + 0.0875559i 0.749528 0.661972i $$-0.230280\pi$$
−0.661972 + 0.749528i $$0.730280\pi$$
$$774$$ 10284.9