# Properties

 Label 177.3.c.a.58.18 Level $177$ Weight $3$ Character 177.58 Analytic conductor $4.823$ Analytic rank $0$ Dimension $20$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$177 = 3 \cdot 59$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 177.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.82290067918$$ Analytic rank: $$0$$ Dimension: $$20$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ Defining polynomial: $$x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{7}\cdot 3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 58.18 Root $$3.07256i$$ of defining polynomial Character $$\chi$$ $$=$$ 177.58 Dual form 177.3.c.a.58.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.07256i q^{2} +1.73205 q^{3} -5.44061 q^{4} -6.03179 q^{5} +5.32183i q^{6} -9.30133 q^{7} -4.42637i q^{8} +3.00000 q^{9} +O(q^{10})$$ $$q+3.07256i q^{2} +1.73205 q^{3} -5.44061 q^{4} -6.03179 q^{5} +5.32183i q^{6} -9.30133 q^{7} -4.42637i q^{8} +3.00000 q^{9} -18.5330i q^{10} -12.6629i q^{11} -9.42342 q^{12} +16.7819i q^{13} -28.5789i q^{14} -10.4474 q^{15} -8.16217 q^{16} +14.0828 q^{17} +9.21767i q^{18} -37.4075 q^{19} +32.8166 q^{20} -16.1104 q^{21} +38.9074 q^{22} +27.8025i q^{23} -7.66670i q^{24} +11.3824 q^{25} -51.5635 q^{26} +5.19615 q^{27} +50.6050 q^{28} +39.1159 q^{29} -32.1001i q^{30} +0.257147i q^{31} -42.7842i q^{32} -21.9327i q^{33} +43.2703i q^{34} +56.1036 q^{35} -16.3218 q^{36} +54.7014i q^{37} -114.937i q^{38} +29.0672i q^{39} +26.6989i q^{40} -11.3202 q^{41} -49.5001i q^{42} +7.36421i q^{43} +68.8937i q^{44} -18.0954 q^{45} -85.4249 q^{46} +28.7287i q^{47} -14.1373 q^{48} +37.5148 q^{49} +34.9732i q^{50} +24.3922 q^{51} -91.3041i q^{52} -47.3053 q^{53} +15.9655i q^{54} +76.3796i q^{55} +41.1711i q^{56} -64.7917 q^{57} +120.186i q^{58} +(-28.6844 + 51.5578i) q^{59} +56.8401 q^{60} -84.0505i q^{61} -0.790099 q^{62} -27.9040 q^{63} +98.8084 q^{64} -101.225i q^{65} +67.3895 q^{66} -81.5123i q^{67} -76.6193 q^{68} +48.1554i q^{69} +172.382i q^{70} -6.96917 q^{71} -13.2791i q^{72} +131.681i q^{73} -168.073 q^{74} +19.7150 q^{75} +203.520 q^{76} +117.781i q^{77} -89.3106 q^{78} +51.9880 q^{79} +49.2325 q^{80} +9.00000 q^{81} -34.7820i q^{82} +16.5553i q^{83} +87.6504 q^{84} -84.9447 q^{85} -22.6270 q^{86} +67.7508 q^{87} -56.0505 q^{88} +69.2544i q^{89} -55.5990i q^{90} -156.094i q^{91} -151.263i q^{92} +0.445392i q^{93} -88.2705 q^{94} +225.634 q^{95} -74.1045i q^{96} -110.495i q^{97} +115.266i q^{98} -37.9886i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10})$$ $$20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$$.

 $$n$$ $$61$$ $$119$$ $$\chi(n)$$ $$-1$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 3.07256i 1.53628i 0.640282 + 0.768140i $$0.278817\pi$$
−0.640282 + 0.768140i $$0.721183\pi$$
$$3$$ 1.73205 0.577350
$$4$$ −5.44061 −1.36015
$$5$$ −6.03179 −1.20636 −0.603179 0.797606i $$-0.706099\pi$$
−0.603179 + 0.797606i $$0.706099\pi$$
$$6$$ 5.32183i 0.886971i
$$7$$ −9.30133 −1.32876 −0.664381 0.747394i $$-0.731305\pi$$
−0.664381 + 0.747394i $$0.731305\pi$$
$$8$$ 4.42637i 0.553296i
$$9$$ 3.00000 0.333333
$$10$$ 18.5330i 1.85330i
$$11$$ 12.6629i 1.15117i −0.817742 0.575584i $$-0.804775\pi$$
0.817742 0.575584i $$-0.195225\pi$$
$$12$$ −9.42342 −0.785285
$$13$$ 16.7819i 1.29092i 0.763795 + 0.645459i $$0.223334\pi$$
−0.763795 + 0.645459i $$0.776666\pi$$
$$14$$ 28.5789i 2.04135i
$$15$$ −10.4474 −0.696491
$$16$$ −8.16217 −0.510136
$$17$$ 14.0828 0.828402 0.414201 0.910185i $$-0.364061\pi$$
0.414201 + 0.910185i $$0.364061\pi$$
$$18$$ 9.21767i 0.512093i
$$19$$ −37.4075 −1.96882 −0.984408 0.175902i $$-0.943716\pi$$
−0.984408 + 0.175902i $$0.943716\pi$$
$$20$$ 32.8166 1.64083
$$21$$ −16.1104 −0.767161
$$22$$ 38.9074 1.76852
$$23$$ 27.8025i 1.20881i 0.796679 + 0.604403i $$0.206588\pi$$
−0.796679 + 0.604403i $$0.793412\pi$$
$$24$$ 7.66670i 0.319446i
$$25$$ 11.3824 0.455298
$$26$$ −51.5635 −1.98321
$$27$$ 5.19615 0.192450
$$28$$ 50.6050 1.80732
$$29$$ 39.1159 1.34882 0.674412 0.738355i $$-0.264397\pi$$
0.674412 + 0.738355i $$0.264397\pi$$
$$30$$ 32.1001i 1.07000i
$$31$$ 0.257147i 0.00829506i 0.999991 + 0.00414753i $$0.00132020\pi$$
−0.999991 + 0.00414753i $$0.998680\pi$$
$$32$$ 42.7842i 1.33701i
$$33$$ 21.9327i 0.664627i
$$34$$ 43.2703i 1.27266i
$$35$$ 56.1036 1.60296
$$36$$ −16.3218 −0.453385
$$37$$ 54.7014i 1.47842i 0.673477 + 0.739208i $$0.264800\pi$$
−0.673477 + 0.739208i $$0.735200\pi$$
$$38$$ 114.937i 3.02465i
$$39$$ 29.0672i 0.745312i
$$40$$ 26.6989i 0.667473i
$$41$$ −11.3202 −0.276102 −0.138051 0.990425i $$-0.544084\pi$$
−0.138051 + 0.990425i $$0.544084\pi$$
$$42$$ 49.5001i 1.17857i
$$43$$ 7.36421i 0.171261i 0.996327 + 0.0856303i $$0.0272904\pi$$
−0.996327 + 0.0856303i $$0.972710\pi$$
$$44$$ 68.8937i 1.56577i
$$45$$ −18.0954 −0.402119
$$46$$ −85.4249 −1.85706
$$47$$ 28.7287i 0.611248i 0.952152 + 0.305624i $$0.0988651\pi$$
−0.952152 + 0.305624i $$0.901135\pi$$
$$48$$ −14.1373 −0.294527
$$49$$ 37.5148 0.765608
$$50$$ 34.9732i 0.699464i
$$51$$ 24.3922 0.478278
$$52$$ 91.3041i 1.75585i
$$53$$ −47.3053 −0.892552 −0.446276 0.894895i $$-0.647250\pi$$
−0.446276 + 0.894895i $$0.647250\pi$$
$$54$$ 15.9655i 0.295657i
$$55$$ 76.3796i 1.38872i
$$56$$ 41.1711i 0.735199i
$$57$$ −64.7917 −1.13670
$$58$$ 120.186i 2.07217i
$$59$$ −28.6844 + 51.5578i −0.486176 + 0.873861i
$$60$$ 56.8401 0.947334
$$61$$ 84.0505i 1.37788i −0.724820 0.688938i $$-0.758077\pi$$
0.724820 0.688938i $$-0.241923\pi$$
$$62$$ −0.790099 −0.0127435
$$63$$ −27.9040 −0.442921
$$64$$ 98.8084 1.54388
$$65$$ 101.225i 1.55731i
$$66$$ 67.3895 1.02105
$$67$$ 81.5123i 1.21660i −0.793707 0.608300i $$-0.791852\pi$$
0.793707 0.608300i $$-0.208148\pi$$
$$68$$ −76.6193 −1.12675
$$69$$ 48.1554i 0.697905i
$$70$$ 172.382i 2.46260i
$$71$$ −6.96917 −0.0981573 −0.0490787 0.998795i $$-0.515628\pi$$
−0.0490787 + 0.998795i $$0.515628\pi$$
$$72$$ 13.2791i 0.184432i
$$73$$ 131.681i 1.80385i 0.431896 + 0.901923i $$0.357845\pi$$
−0.431896 + 0.901923i $$0.642155\pi$$
$$74$$ −168.073 −2.27126
$$75$$ 19.7150 0.262866
$$76$$ 203.520 2.67789
$$77$$ 117.781i 1.52963i
$$78$$ −89.3106 −1.14501
$$79$$ 51.9880 0.658076 0.329038 0.944317i $$-0.393276\pi$$
0.329038 + 0.944317i $$0.393276\pi$$
$$80$$ 49.2325 0.615406
$$81$$ 9.00000 0.111111
$$82$$ 34.7820i 0.424170i
$$83$$ 16.5553i 0.199461i 0.995014 + 0.0997305i $$0.0317981\pi$$
−0.995014 + 0.0997305i $$0.968202\pi$$
$$84$$ 87.6504 1.04346
$$85$$ −84.9447 −0.999349
$$86$$ −22.6270 −0.263104
$$87$$ 67.7508 0.778744
$$88$$ −56.0505 −0.636937
$$89$$ 69.2544i 0.778139i 0.921208 + 0.389070i $$0.127203\pi$$
−0.921208 + 0.389070i $$0.872797\pi$$
$$90$$ 55.5990i 0.617767i
$$91$$ 156.094i 1.71532i
$$92$$ 151.263i 1.64416i
$$93$$ 0.445392i 0.00478916i
$$94$$ −88.2705 −0.939048
$$95$$ 225.634 2.37509
$$96$$ 74.1045i 0.771922i
$$97$$ 110.495i 1.13912i −0.821949 0.569560i $$-0.807113\pi$$
0.821949 0.569560i $$-0.192887\pi$$
$$98$$ 115.266i 1.17619i
$$99$$ 37.9886i 0.383723i
$$100$$ −61.9275 −0.619275
$$101$$ 159.617i 1.58037i −0.612868 0.790186i $$-0.709984\pi$$
0.612868 0.790186i $$-0.290016\pi$$
$$102$$ 74.9464i 0.734769i
$$103$$ 26.7475i 0.259684i −0.991535 0.129842i $$-0.958553\pi$$
0.991535 0.129842i $$-0.0414470\pi$$
$$104$$ 74.2831 0.714260
$$105$$ 97.1744 0.925470
$$106$$ 145.348i 1.37121i
$$107$$ −35.3863 −0.330713 −0.165356 0.986234i $$-0.552877\pi$$
−0.165356 + 0.986234i $$0.552877\pi$$
$$108$$ −28.2703 −0.261762
$$109$$ 68.2150i 0.625826i 0.949782 + 0.312913i $$0.101305\pi$$
−0.949782 + 0.312913i $$0.898695\pi$$
$$110$$ −234.681 −2.13346
$$111$$ 94.7456i 0.853564i
$$112$$ 75.9191 0.677849
$$113$$ 120.908i 1.06998i −0.844858 0.534990i $$-0.820315\pi$$
0.844858 0.534990i $$-0.179685\pi$$
$$114$$ 199.076i 1.74628i
$$115$$ 167.699i 1.45825i
$$116$$ −212.815 −1.83461
$$117$$ 50.3458i 0.430306i
$$118$$ −158.414 88.1345i −1.34249 0.746902i
$$119$$ −130.989 −1.10075
$$120$$ 46.2439i 0.385366i
$$121$$ −39.3479 −0.325189
$$122$$ 258.250 2.11680
$$123$$ −19.6072 −0.159408
$$124$$ 1.39904i 0.0112826i
$$125$$ 82.1382 0.657105
$$126$$ 85.7367i 0.680450i
$$127$$ −158.088 −1.24479 −0.622393 0.782705i $$-0.713839\pi$$
−0.622393 + 0.782705i $$0.713839\pi$$
$$128$$ 132.458i 1.03482i
$$129$$ 12.7552i 0.0988774i
$$130$$ 311.020 2.39246
$$131$$ 130.513i 0.996282i 0.867096 + 0.498141i $$0.165984\pi$$
−0.867096 + 0.498141i $$0.834016\pi$$
$$132$$ 119.327i 0.903995i
$$133$$ 347.939 2.61609
$$134$$ 250.451 1.86904
$$135$$ −31.3421 −0.232164
$$136$$ 62.3359i 0.458352i
$$137$$ 208.921 1.52497 0.762487 0.647004i $$-0.223978\pi$$
0.762487 + 0.647004i $$0.223978\pi$$
$$138$$ −147.960 −1.07218
$$139$$ −73.8315 −0.531162 −0.265581 0.964089i $$-0.585564\pi$$
−0.265581 + 0.964089i $$0.585564\pi$$
$$140$$ −305.238 −2.18027
$$141$$ 49.7595i 0.352904i
$$142$$ 21.4132i 0.150797i
$$143$$ 212.507 1.48606
$$144$$ −24.4865 −0.170045
$$145$$ −235.939 −1.62716
$$146$$ −404.597 −2.77121
$$147$$ 64.9775 0.442024
$$148$$ 297.609i 2.01087i
$$149$$ 66.3172i 0.445082i 0.974923 + 0.222541i $$0.0714351\pi$$
−0.974923 + 0.222541i $$0.928565\pi$$
$$150$$ 60.5754i 0.403836i
$$151$$ 103.185i 0.683347i 0.939819 + 0.341673i $$0.110994\pi$$
−0.939819 + 0.341673i $$0.889006\pi$$
$$152$$ 165.579i 1.08934i
$$153$$ 42.2485 0.276134
$$154$$ −361.890 −2.34994
$$155$$ 1.55106i 0.0100068i
$$156$$ 158.143i 1.01374i
$$157$$ 251.051i 1.59905i 0.600630 + 0.799527i $$0.294916\pi$$
−0.600630 + 0.799527i $$0.705084\pi$$
$$158$$ 159.736i 1.01099i
$$159$$ −81.9351 −0.515315
$$160$$ 258.065i 1.61291i
$$161$$ 258.601i 1.60622i
$$162$$ 27.6530i 0.170698i
$$163$$ −96.4209 −0.591539 −0.295770 0.955259i $$-0.595576\pi$$
−0.295770 + 0.955259i $$0.595576\pi$$
$$164$$ 61.5888 0.375542
$$165$$ 132.293i 0.801778i
$$166$$ −50.8670 −0.306428
$$167$$ 78.3907 0.469405 0.234703 0.972067i $$-0.424588\pi$$
0.234703 + 0.972067i $$0.424588\pi$$
$$168$$ 71.3105i 0.424467i
$$169$$ −112.633 −0.666470
$$170$$ 260.997i 1.53528i
$$171$$ −112.222 −0.656272
$$172$$ 40.0658i 0.232941i
$$173$$ 52.2561i 0.302058i 0.988529 + 0.151029i $$0.0482587\pi$$
−0.988529 + 0.151029i $$0.951741\pi$$
$$174$$ 208.168i 1.19637i
$$175$$ −105.872 −0.604982
$$176$$ 103.356i 0.587252i
$$177$$ −49.6828 + 89.3007i −0.280694 + 0.504524i
$$178$$ −212.788 −1.19544
$$179$$ 117.505i 0.656453i −0.944599 0.328226i $$-0.893549\pi$$
0.944599 0.328226i $$-0.106451\pi$$
$$180$$ 98.4499 0.546944
$$181$$ 160.180 0.884972 0.442486 0.896776i $$-0.354097\pi$$
0.442486 + 0.896776i $$0.354097\pi$$
$$182$$ 479.609 2.63521
$$183$$ 145.580i 0.795517i
$$184$$ 123.064 0.668828
$$185$$ 329.947i 1.78350i
$$186$$ −1.36849 −0.00735748
$$187$$ 178.329i 0.953630i
$$188$$ 156.302i 0.831391i
$$189$$ −48.3311 −0.255720
$$190$$ 693.274i 3.64881i
$$191$$ 14.2938i 0.0748369i −0.999300 0.0374184i $$-0.988087\pi$$
0.999300 0.0374184i $$-0.0119134\pi$$
$$192$$ 171.141 0.891360
$$193$$ 71.9463 0.372779 0.186389 0.982476i $$-0.440321\pi$$
0.186389 + 0.982476i $$0.440321\pi$$
$$194$$ 339.501 1.75001
$$195$$ 175.327i 0.899113i
$$196$$ −204.103 −1.04134
$$197$$ −44.5489 −0.226137 −0.113068 0.993587i $$-0.536068\pi$$
−0.113068 + 0.993587i $$0.536068\pi$$
$$198$$ 116.722 0.589505
$$199$$ −125.217 −0.629233 −0.314617 0.949219i $$-0.601876\pi$$
−0.314617 + 0.949219i $$0.601876\pi$$
$$200$$ 50.3829i 0.251915i
$$201$$ 141.183i 0.702405i
$$202$$ 490.434 2.42789
$$203$$ −363.830 −1.79227
$$204$$ −132.708 −0.650532
$$205$$ 68.2810 0.333078
$$206$$ 82.1831 0.398947
$$207$$ 83.4076i 0.402935i
$$208$$ 136.977i 0.658544i
$$209$$ 473.686i 2.26644i
$$210$$ 298.574i 1.42178i
$$211$$ 106.781i 0.506071i −0.967457 0.253035i $$-0.918571\pi$$
0.967457 0.253035i $$-0.0814289\pi$$
$$212$$ 257.370 1.21401
$$213$$ −12.0710 −0.0566711
$$214$$ 108.726i 0.508067i
$$215$$ 44.4193i 0.206602i
$$216$$ 23.0001i 0.106482i
$$217$$ 2.39181i 0.0110222i
$$218$$ −209.595 −0.961443
$$219$$ 228.078i 1.04145i
$$220$$ 415.552i 1.88887i
$$221$$ 236.337i 1.06940i
$$222$$ −291.111 −1.31131
$$223$$ −37.6647 −0.168900 −0.0844501 0.996428i $$-0.526913\pi$$
−0.0844501 + 0.996428i $$0.526913\pi$$
$$224$$ 397.950i 1.77656i
$$225$$ 34.1473 0.151766
$$226$$ 371.496 1.64379
$$227$$ 189.636i 0.835399i −0.908585 0.417699i $$-0.862837\pi$$
0.908585 0.417699i $$-0.137163\pi$$
$$228$$ 352.507 1.54608
$$229$$ 206.938i 0.903658i 0.892104 + 0.451829i $$0.149228\pi$$
−0.892104 + 0.451829i $$0.850772\pi$$
$$230$$ 515.265 2.24028
$$231$$ 204.003i 0.883131i
$$232$$ 173.142i 0.746300i
$$233$$ 213.272i 0.915330i 0.889125 + 0.457665i $$0.151314\pi$$
−0.889125 + 0.457665i $$0.848686\pi$$
$$234$$ −154.690 −0.661070
$$235$$ 173.285i 0.737384i
$$236$$ 156.061 280.506i 0.661274 1.18858i
$$237$$ 90.0458 0.379940
$$238$$ 402.472i 1.69106i
$$239$$ −142.148 −0.594760 −0.297380 0.954759i $$-0.596113\pi$$
−0.297380 + 0.954759i $$0.596113\pi$$
$$240$$ 85.2732 0.355305
$$241$$ −391.267 −1.62351 −0.811756 0.583996i $$-0.801488\pi$$
−0.811756 + 0.583996i $$0.801488\pi$$
$$242$$ 120.899i 0.499581i
$$243$$ 15.5885 0.0641500
$$244$$ 457.286i 1.87412i
$$245$$ −226.281 −0.923596
$$246$$ 60.2441i 0.244895i
$$247$$ 627.770i 2.54158i
$$248$$ 1.13823 0.00458963
$$249$$ 28.6745i 0.115159i
$$250$$ 252.374i 1.00950i
$$251$$ 135.007 0.537877 0.268938 0.963157i $$-0.413327\pi$$
0.268938 + 0.963157i $$0.413327\pi$$
$$252$$ 151.815 0.602440
$$253$$ 352.060 1.39154
$$254$$ 485.734i 1.91234i
$$255$$ −147.128 −0.576974
$$256$$ −11.7500 −0.0458983
$$257$$ −133.333 −0.518807 −0.259403 0.965769i $$-0.583526\pi$$
−0.259403 + 0.965769i $$0.583526\pi$$
$$258$$ −39.1910 −0.151903
$$259$$ 508.796i 1.96446i
$$260$$ 550.727i 2.11818i
$$261$$ 117.348 0.449608
$$262$$ −401.009 −1.53057
$$263$$ 272.345 1.03553 0.517765 0.855523i $$-0.326764\pi$$
0.517765 + 0.855523i $$0.326764\pi$$
$$264$$ −97.0823 −0.367736
$$265$$ 285.335 1.07674
$$266$$ 1069.06i 4.01904i
$$267$$ 119.952i 0.449259i
$$268$$ 443.477i 1.65476i
$$269$$ 275.151i 1.02287i 0.859323 + 0.511434i $$0.170886\pi$$
−0.859323 + 0.511434i $$0.829114\pi$$
$$270$$ 96.3004i 0.356668i
$$271$$ −142.359 −0.525308 −0.262654 0.964890i $$-0.584598\pi$$
−0.262654 + 0.964890i $$0.584598\pi$$
$$272$$ −114.947 −0.422598
$$273$$ 270.363i 0.990342i
$$274$$ 641.923i 2.34278i
$$275$$ 144.134i 0.524124i
$$276$$ 261.995i 0.949257i
$$277$$ −282.049 −1.01823 −0.509114 0.860699i $$-0.670027\pi$$
−0.509114 + 0.860699i $$0.670027\pi$$
$$278$$ 226.852i 0.816013i
$$279$$ 0.771441i 0.00276502i
$$280$$ 248.336i 0.886913i
$$281$$ −273.179 −0.972168 −0.486084 0.873912i $$-0.661575\pi$$
−0.486084 + 0.873912i $$0.661575\pi$$
$$282$$ −152.889 −0.542159
$$283$$ 240.930i 0.851343i 0.904878 + 0.425671i $$0.139962\pi$$
−0.904878 + 0.425671i $$0.860038\pi$$
$$284$$ 37.9166 0.133509
$$285$$ 390.810 1.37126
$$286$$ 652.941i 2.28301i
$$287$$ 105.293 0.366874
$$288$$ 128.353i 0.445669i
$$289$$ −90.6737 −0.313750
$$290$$ 724.936i 2.49978i
$$291$$ 191.382i 0.657672i
$$292$$ 716.424i 2.45351i
$$293$$ −321.271 −1.09649 −0.548245 0.836318i $$-0.684704\pi$$
−0.548245 + 0.836318i $$0.684704\pi$$
$$294$$ 199.647i 0.679072i
$$295$$ 173.018 310.986i 0.586502 1.05419i
$$296$$ 242.129 0.818002
$$297$$ 65.7981i 0.221542i
$$298$$ −203.763 −0.683770
$$299$$ −466.581 −1.56047
$$300$$ −107.262 −0.357539
$$301$$ 68.4969i 0.227565i
$$302$$ −317.043 −1.04981
$$303$$ 276.466i 0.912428i
$$304$$ 305.326 1.00436
$$305$$ 506.974i 1.66221i
$$306$$ 129.811i 0.424219i
$$307$$ −569.638 −1.85550 −0.927750 0.373203i $$-0.878259\pi$$
−0.927750 + 0.373203i $$0.878259\pi$$
$$308$$ 640.803i 2.08053i
$$309$$ 46.3280i 0.149929i
$$310$$ 4.76571 0.0153733
$$311$$ −357.447 −1.14935 −0.574673 0.818383i $$-0.694871\pi$$
−0.574673 + 0.818383i $$0.694871\pi$$
$$312$$ 128.662 0.412378
$$313$$ 540.979i 1.72837i 0.503176 + 0.864184i $$0.332165\pi$$
−0.503176 + 0.864184i $$0.667835\pi$$
$$314$$ −771.370 −2.45659
$$315$$ 168.311 0.534320
$$316$$ −282.847 −0.895084
$$317$$ 431.328 1.36066 0.680328 0.732908i $$-0.261837\pi$$
0.680328 + 0.732908i $$0.261837\pi$$
$$318$$ 251.750i 0.791668i
$$319$$ 495.319i 1.55272i
$$320$$ −595.991 −1.86247
$$321$$ −61.2908 −0.190937
$$322$$ 794.566 2.46760
$$323$$ −526.804 −1.63097
$$324$$ −48.9655 −0.151128
$$325$$ 191.019i 0.587752i
$$326$$ 296.259i 0.908770i
$$327$$ 118.152i 0.361321i
$$328$$ 50.1074i 0.152766i
$$329$$ 267.215i 0.812203i
$$330$$ −406.479 −1.23176
$$331$$ 241.399 0.729301 0.364650 0.931145i $$-0.381189\pi$$
0.364650 + 0.931145i $$0.381189\pi$$
$$332$$ 90.0708i 0.271297i
$$333$$ 164.104i 0.492805i
$$334$$ 240.860i 0.721138i
$$335$$ 491.664i 1.46766i
$$336$$ 131.496 0.391356
$$337$$ 122.088i 0.362278i −0.983457 0.181139i $$-0.942022\pi$$
0.983457 0.181139i $$-0.0579784\pi$$
$$338$$ 346.073i 1.02388i
$$339$$ 209.419i 0.617754i
$$340$$ 462.151 1.35927
$$341$$ 3.25621 0.00954901
$$342$$ 344.810i 1.00822i
$$343$$ 106.828 0.311452
$$344$$ 32.5967 0.0947579
$$345$$ 290.463i 0.841922i
$$346$$ −160.560 −0.464046
$$347$$ 403.930i 1.16406i −0.813166 0.582032i $$-0.802258\pi$$
0.813166 0.582032i $$-0.197742\pi$$
$$348$$ −368.606 −1.05921
$$349$$ 449.445i 1.28781i 0.765106 + 0.643904i $$0.222686\pi$$
−0.765106 + 0.643904i $$0.777314\pi$$
$$350$$ 325.298i 0.929422i
$$351$$ 87.2015i 0.248437i
$$352$$ −541.771 −1.53912
$$353$$ 213.176i 0.603899i 0.953324 + 0.301950i $$0.0976374\pi$$
−0.953324 + 0.301950i $$0.902363\pi$$
$$354$$ −274.382 152.653i −0.775089 0.431224i
$$355$$ 42.0365 0.118413
$$356$$ 376.786i 1.05839i
$$357$$ −226.880 −0.635518
$$358$$ 361.041 1.00849
$$359$$ 405.372 1.12917 0.564585 0.825375i $$-0.309036\pi$$
0.564585 + 0.825375i $$0.309036\pi$$
$$360$$ 80.0968i 0.222491i
$$361$$ 1038.32 2.87623
$$362$$ 492.162i 1.35956i
$$363$$ −68.1525 −0.187748
$$364$$ 849.249i 2.33310i
$$365$$ 794.270i 2.17608i
$$366$$ 447.302 1.22214
$$367$$ 541.192i 1.47464i 0.675546 + 0.737318i $$0.263908\pi$$
−0.675546 + 0.737318i $$0.736092\pi$$
$$368$$ 226.929i 0.616655i
$$369$$ −33.9606 −0.0920341
$$370$$ 1013.78 2.73995
$$371$$ 440.002 1.18599
$$372$$ 2.42320i 0.00651399i
$$373$$ −107.068 −0.287046 −0.143523 0.989647i $$-0.545843\pi$$
−0.143523 + 0.989647i $$0.545843\pi$$
$$374$$ 547.926 1.46504
$$375$$ 142.268 0.379380
$$376$$ 127.164 0.338201
$$377$$ 656.441i 1.74122i
$$378$$ 148.500i 0.392858i
$$379$$ −204.702 −0.540112 −0.270056 0.962845i $$-0.587042\pi$$
−0.270056 + 0.962845i $$0.587042\pi$$
$$380$$ −1227.59 −3.23049
$$381$$ −273.816 −0.718678
$$382$$ 43.9187 0.114970
$$383$$ −4.98048 −0.0130039 −0.00650193 0.999979i $$-0.502070\pi$$
−0.00650193 + 0.999979i $$0.502070\pi$$
$$384$$ 229.423i 0.597456i
$$385$$ 710.432i 1.84528i
$$386$$ 221.059i 0.572692i
$$387$$ 22.0926i 0.0570869i
$$388$$ 601.159i 1.54938i
$$389$$ 138.904 0.357079 0.178539 0.983933i $$-0.442863\pi$$
0.178539 + 0.983933i $$0.442863\pi$$
$$390$$ 538.702 1.38129
$$391$$ 391.539i 1.00138i
$$392$$ 166.054i 0.423608i
$$393$$ 226.055i 0.575204i
$$394$$ 136.879i 0.347409i
$$395$$ −313.580 −0.793874
$$396$$ 206.681i 0.521922i
$$397$$ 266.530i 0.671359i −0.941976 0.335679i $$-0.891034\pi$$
0.941976 0.335679i $$-0.108966\pi$$
$$398$$ 384.738i 0.966678i
$$399$$ 602.649 1.51040
$$400$$ −92.9055 −0.232264
$$401$$ 515.725i 1.28610i 0.765825 + 0.643049i $$0.222331\pi$$
−0.765825 + 0.643049i $$0.777669\pi$$
$$402$$ 433.794 1.07909
$$403$$ −4.31542 −0.0107082
$$404$$ 868.417i 2.14955i
$$405$$ −54.2861 −0.134040
$$406$$ 1117.89i 2.75342i
$$407$$ 692.676 1.70191
$$408$$ 107.969i 0.264630i
$$409$$ 53.2453i 0.130184i 0.997879 + 0.0650920i $$0.0207341\pi$$
−0.997879 + 0.0650920i $$0.979266\pi$$
$$410$$ 209.797i 0.511701i
$$411$$ 361.862 0.880444
$$412$$ 145.523i 0.353210i
$$413$$ 266.803 479.556i 0.646012 1.16115i
$$414$$ −256.275 −0.619021
$$415$$ 99.8578i 0.240621i
$$416$$ 718.002 1.72597
$$417$$ −127.880 −0.306667
$$418$$ −1455.43 −3.48188
$$419$$ 275.166i 0.656721i −0.944553 0.328360i $$-0.893504\pi$$
0.944553 0.328360i $$-0.106496\pi$$
$$420$$ −528.688 −1.25878
$$421$$ 508.314i 1.20740i −0.797213 0.603699i $$-0.793693\pi$$
0.797213 0.603699i $$-0.206307\pi$$
$$422$$ 328.091 0.777466
$$423$$ 86.1860i 0.203749i
$$424$$ 209.391i 0.493846i
$$425$$ 160.297 0.377170
$$426$$ 37.0887i 0.0870627i
$$427$$ 781.781i 1.83087i
$$428$$ 192.523 0.449820
$$429$$ 368.073 0.857980
$$430$$ 136.481 0.317398
$$431$$ 331.069i 0.768141i 0.923304 + 0.384070i $$0.125478\pi$$
−0.923304 + 0.384070i $$0.874522\pi$$
$$432$$ −42.4119 −0.0981757
$$433$$ 216.406 0.499783 0.249891 0.968274i $$-0.419605\pi$$
0.249891 + 0.968274i $$0.419605\pi$$
$$434$$ 7.34897 0.0169331
$$435$$ −408.658 −0.939444
$$436$$ 371.132i 0.851219i
$$437$$ 1040.02i 2.37992i
$$438$$ −700.782 −1.59996
$$439$$ 594.843 1.35500 0.677498 0.735525i $$-0.263064\pi$$
0.677498 + 0.735525i $$0.263064\pi$$
$$440$$ 338.085 0.768374
$$441$$ 112.544 0.255203
$$442$$ −726.160 −1.64290
$$443$$ 101.223i 0.228495i −0.993452 0.114247i $$-0.963554\pi$$
0.993452 0.114247i $$-0.0364456\pi$$
$$444$$ 515.474i 1.16098i
$$445$$ 417.728i 0.938714i
$$446$$ 115.727i 0.259478i
$$447$$ 114.865i 0.256968i
$$448$$ −919.049 −2.05145
$$449$$ 612.041 1.36312 0.681561 0.731762i $$-0.261302\pi$$
0.681561 + 0.731762i $$0.261302\pi$$
$$450$$ 104.920i 0.233155i
$$451$$ 143.346i 0.317840i
$$452$$ 657.813i 1.45534i
$$453$$ 178.722i 0.394530i
$$454$$ 582.666 1.28341
$$455$$ 941.528i 2.06929i
$$456$$ 286.792i 0.628930i
$$457$$ 406.851i 0.890264i −0.895465 0.445132i $$-0.853157\pi$$
0.895465 0.445132i $$-0.146843\pi$$
$$458$$ −635.828 −1.38827
$$459$$ 73.1766 0.159426
$$460$$ 912.385i 1.98345i
$$461$$ −852.748 −1.84978 −0.924889 0.380236i $$-0.875843\pi$$
−0.924889 + 0.380236i $$0.875843\pi$$
$$462$$ −626.812 −1.35674
$$463$$ 727.640i 1.57158i 0.618495 + 0.785788i $$0.287743\pi$$
−0.618495 + 0.785788i $$0.712257\pi$$
$$464$$ −319.271 −0.688084
$$465$$ 2.68651i 0.00577743i
$$466$$ −655.290 −1.40620
$$467$$ 24.1720i 0.0517602i −0.999665 0.0258801i $$-0.991761\pi$$
0.999665 0.0258801i $$-0.00823880\pi$$
$$468$$ 273.912i 0.585282i
$$469$$ 758.173i 1.61657i
$$470$$ 532.429 1.13283
$$471$$ 434.834i 0.923214i
$$472$$ 228.214 + 126.968i 0.483504 + 0.268999i
$$473$$ 93.2519 0.197150
$$474$$ 276.671i 0.583694i
$$475$$ −425.789 −0.896397
$$476$$ 712.661 1.49719
$$477$$ −141.916 −0.297517
$$478$$ 436.757i 0.913717i
$$479$$ −540.528 −1.12845 −0.564225 0.825621i $$-0.690825\pi$$
−0.564225 + 0.825621i $$0.690825\pi$$
$$480$$ 446.982i 0.931213i
$$481$$ −917.996 −1.90851
$$482$$ 1202.19i 2.49417i
$$483$$ 447.909i 0.927349i
$$484$$ 214.077 0.442307
$$485$$ 666.481i 1.37419i
$$486$$ 47.8964i 0.0985524i
$$487$$ −564.800 −1.15975 −0.579877 0.814704i $$-0.696899\pi$$
−0.579877 + 0.814704i $$0.696899\pi$$
$$488$$ −372.038 −0.762374
$$489$$ −167.006 −0.341525
$$490$$ 695.262i 1.41890i
$$491$$ 8.09712 0.0164911 0.00824554 0.999966i $$-0.497375\pi$$
0.00824554 + 0.999966i $$0.497375\pi$$
$$492$$ 106.675 0.216819
$$493$$ 550.863 1.11737
$$494$$ 1928.86 3.90458
$$495$$ 229.139i 0.462907i
$$496$$ 2.09888i 0.00423161i
$$497$$ 64.8226 0.130428
$$498$$ −88.1042 −0.176916
$$499$$ 719.073 1.44103 0.720514 0.693440i $$-0.243906\pi$$
0.720514 + 0.693440i $$0.243906\pi$$
$$500$$ −446.882 −0.893764
$$501$$ 135.777 0.271011
$$502$$ 414.817i 0.826329i
$$503$$ 524.427i 1.04260i −0.853374 0.521299i $$-0.825448\pi$$
0.853374 0.521299i $$-0.174552\pi$$
$$504$$ 123.513i 0.245066i
$$505$$ 962.778i 1.90649i
$$506$$ 1081.72i 2.13779i
$$507$$ −195.087 −0.384787
$$508$$ 860.095 1.69310
$$509$$ 749.520i 1.47253i 0.676691 + 0.736267i $$0.263413\pi$$
−0.676691 + 0.736267i $$0.736587\pi$$
$$510$$ 452.061i 0.886394i
$$511$$ 1224.81i 2.39688i
$$512$$ 493.728i 0.964312i
$$513$$ −194.375 −0.378899
$$514$$ 409.674i 0.797032i
$$515$$ 161.335i 0.313272i
$$516$$ 69.3960i 0.134488i
$$517$$ 363.787 0.703650
$$518$$ 1563.31 3.01796
$$519$$ 90.5102i 0.174393i
$$520$$ −448.060 −0.861653
$$521$$ −191.543 −0.367646 −0.183823 0.982959i $$-0.558847\pi$$
−0.183823 + 0.982959i $$0.558847\pi$$
$$522$$ 360.558i 0.690724i
$$523$$ 985.876 1.88504 0.942520 0.334149i $$-0.108449\pi$$
0.942520 + 0.334149i $$0.108449\pi$$
$$524$$ 710.071i 1.35510i
$$525$$ −183.375 −0.349287
$$526$$ 836.795i 1.59086i
$$527$$ 3.62136i 0.00687165i
$$528$$ 179.019i 0.339050i
$$529$$ −243.981 −0.461212
$$530$$ 876.709i 1.65417i
$$531$$ −86.0532 + 154.673i −0.162059 + 0.291287i
$$532$$ −1893.00 −3.55828
$$533$$ 189.975i 0.356426i
$$534$$ −368.560 −0.690187
$$535$$ 213.443 0.398958
$$536$$ −360.804 −0.673141
$$537$$ 203.525i 0.379003i
$$538$$ −845.419 −1.57141
$$539$$ 475.044i 0.881343i
$$540$$ 170.520 0.315778
$$541$$ 239.083i 0.441928i −0.975282 0.220964i $$-0.929080\pi$$
0.975282 0.220964i $$-0.0709204\pi$$
$$542$$ 437.405i 0.807020i
$$543$$ 277.440 0.510939
$$544$$ 602.523i 1.10758i
$$545$$ 411.458i 0.754969i
$$546$$ 830.707 1.52144
$$547$$ 106.125 0.194013 0.0970065 0.995284i $$-0.469073\pi$$
0.0970065 + 0.995284i $$0.469073\pi$$
$$548$$ −1136.66 −2.07420
$$549$$ 252.151i 0.459292i
$$550$$ 442.861 0.805201
$$551$$ −1463.23 −2.65559
$$552$$ 213.154 0.386148
$$553$$ −483.557 −0.874426
$$554$$ 866.613i 1.56428i
$$555$$ 571.485i 1.02970i
$$556$$ 401.689 0.722462
$$557$$ 8.64276 0.0155166 0.00775831 0.999970i $$-0.497530\pi$$
0.00775831 + 0.999970i $$0.497530\pi$$
$$558$$ −2.37030 −0.00424784
$$559$$ −123.586 −0.221084
$$560$$ −457.928 −0.817728
$$561$$ 308.875i 0.550579i
$$562$$ 839.359i 1.49352i
$$563$$ 327.402i 0.581530i −0.956794 0.290765i $$-0.906090\pi$$
0.956794 0.290765i $$-0.0939099\pi$$
$$564$$ 270.722i 0.480004i
$$565$$ 729.290i 1.29078i
$$566$$ −740.272 −1.30790
$$567$$ −83.7120 −0.147640
$$568$$ 30.8481i 0.0543101i
$$569$$ 616.454i 1.08340i −0.840572 0.541700i $$-0.817781\pi$$
0.840572 0.541700i $$-0.182219\pi$$
$$570$$ 1200.79i 2.10664i
$$571$$ 518.165i 0.907470i 0.891137 + 0.453735i $$0.149909\pi$$
−0.891137 + 0.453735i $$0.850091\pi$$
$$572$$ −1156.17 −2.02128
$$573$$ 24.7577i 0.0432071i
$$574$$ 323.519i 0.563621i
$$575$$ 316.461i 0.550367i
$$576$$ 296.425 0.514627
$$577$$ 787.940 1.36558 0.682790 0.730614i $$-0.260766\pi$$
0.682790 + 0.730614i $$0.260766\pi$$
$$578$$ 278.600i 0.482007i
$$579$$ 124.615 0.215224
$$580$$ 1283.65 2.21319
$$581$$ 153.986i 0.265036i
$$582$$ 588.034 1.01037
$$583$$ 599.020i 1.02748i
$$584$$ 582.868 0.998062
$$585$$ 303.675i 0.519103i
$$586$$ 987.125i 1.68451i
$$587$$ 782.879i 1.33370i −0.745194 0.666848i $$-0.767643\pi$$
0.745194 0.666848i $$-0.232357\pi$$
$$588$$ −353.517 −0.601220
$$589$$ 9.61922i 0.0163314i
$$590$$ 955.521 + 531.608i 1.61953 + 0.901031i
$$591$$ −77.1610 −0.130560
$$592$$ 446.482i 0.754193i
$$593$$ 1037.25 1.74916 0.874580 0.484881i $$-0.161137\pi$$
0.874580 + 0.484881i $$0.161137\pi$$
$$594$$ 202.169 0.340351
$$595$$ 790.098 1.32790
$$596$$ 360.806i 0.605380i
$$597$$ −216.883 −0.363288
$$598$$ 1433.60i 2.39732i
$$599$$ 673.671 1.12466 0.562330 0.826913i $$-0.309905\pi$$
0.562330 + 0.826913i $$0.309905\pi$$
$$600$$ 87.2658i 0.145443i
$$601$$ 962.944i 1.60224i 0.598506 + 0.801118i $$0.295761\pi$$
−0.598506 + 0.801118i $$0.704239\pi$$
$$602$$ 210.461 0.349603
$$603$$ 244.537i 0.405534i
$$604$$ 561.392i 0.929457i
$$605$$ 237.338 0.392294
$$606$$ 849.457 1.40174
$$607$$ −790.355 −1.30207 −0.651034 0.759049i $$-0.725664\pi$$
−0.651034 + 0.759049i $$0.725664\pi$$
$$608$$ 1600.45i 2.63232i
$$609$$ −630.172 −1.03477
$$610$$ −1557.71 −2.55362
$$611$$ −482.123 −0.789071
$$612$$ −229.858 −0.375585
$$613$$ 953.011i 1.55467i −0.629088 0.777334i $$-0.716572\pi$$
0.629088 0.777334i $$-0.283428\pi$$
$$614$$ 1750.25i 2.85056i
$$615$$ 118.266 0.192303
$$616$$ 521.344 0.846338
$$617$$ 419.167 0.679364 0.339682 0.940540i $$-0.389681\pi$$
0.339682 + 0.940540i $$0.389681\pi$$
$$618$$ 142.345 0.230332
$$619$$ −209.634 −0.338666 −0.169333 0.985559i $$-0.554161\pi$$
−0.169333 + 0.985559i $$0.554161\pi$$
$$620$$ 8.43869i 0.0136108i
$$621$$ 144.466i 0.232635i
$$622$$ 1098.28i 1.76572i
$$623$$ 644.158i 1.03396i
$$624$$ 237.251i 0.380210i
$$625$$ −780.001 −1.24800
$$626$$ −1662.19 −2.65526
$$627$$ 820.448i 1.30853i
$$628$$ 1365.87i 2.17496i
$$629$$ 770.351i 1.22472i
$$630$$ 517.145i 0.820865i
$$631$$ −612.575 −0.970800 −0.485400 0.874292i $$-0.661326\pi$$
−0.485400 + 0.874292i $$0.661326\pi$$
$$632$$ 230.118i 0.364111i
$$633$$ 184.950i 0.292180i
$$634$$ 1325.28i 2.09035i
$$635$$ 953.552 1.50166
$$636$$ 445.777 0.700908
$$637$$ 629.571i 0.988337i
$$638$$ 1521.90 2.38542
$$639$$ −20.9075 −0.0327191
$$640$$ 798.955i 1.24837i
$$641$$ 198.748 0.310060 0.155030 0.987910i $$-0.450453\pi$$
0.155030 + 0.987910i $$0.450453\pi$$
$$642$$ 188.320i 0.293333i
$$643$$ −157.384 −0.244766 −0.122383 0.992483i $$-0.539054\pi$$
−0.122383 + 0.992483i $$0.539054\pi$$
$$644$$ 1406.95i 2.18470i
$$645$$ 76.9365i 0.119281i
$$646$$ 1618.63i 2.50563i
$$647$$ 1214.33 1.87686 0.938430 0.345470i $$-0.112280\pi$$
0.938430 + 0.345470i $$0.112280\pi$$
$$648$$ 39.8373i 0.0614774i
$$649$$ 652.869 + 363.226i 1.00596 + 0.559671i
$$650$$ −586.918 −0.902951
$$651$$ 4.14273i 0.00636365i
$$652$$ 524.589 0.804584
$$653$$ −404.646 −0.619673 −0.309836 0.950790i $$-0.600274\pi$$
−0.309836 + 0.950790i $$0.600274\pi$$
$$654$$ −363.028 −0.555089
$$655$$ 787.226i 1.20187i
$$656$$ 92.3974 0.140850
$$657$$ 395.042i 0.601282i
$$658$$ 821.033 1.24777
$$659$$ 1245.68i 1.89025i 0.326703 + 0.945127i $$0.394062\pi$$
−0.326703 + 0.945127i $$0.605938\pi$$
$$660$$ 719.757i 1.09054i
$$661$$ 96.3638 0.145785 0.0728924 0.997340i $$-0.476777\pi$$
0.0728924 + 0.997340i $$0.476777\pi$$
$$662$$ 741.711i 1.12041i
$$663$$ 409.348i 0.617418i
$$664$$ 73.2797 0.110361
$$665$$ −2098.70 −3.15593
$$666$$ −504.220 −0.757087
$$667$$ 1087.52i 1.63047i
$$668$$ −426.493 −0.638463
$$669$$ −65.2372 −0.0975146
$$670$$ −1510.67 −2.25473
$$671$$ −1064.32 −1.58617
$$672$$ 689.270i 1.02570i
$$673$$ 786.566i 1.16875i 0.811485 + 0.584373i $$0.198660\pi$$
−0.811485 + 0.584373i $$0.801340\pi$$
$$674$$ 375.122 0.556561
$$675$$ 59.1449 0.0876221
$$676$$ 612.795 0.906502
$$677$$ −797.643 −1.17820 −0.589101 0.808059i $$-0.700518\pi$$
−0.589101 + 0.808059i $$0.700518\pi$$
$$678$$ 643.451 0.949042
$$679$$ 1027.75i 1.51362i
$$680$$ 375.997i 0.552936i
$$681$$ 328.458i 0.482318i
$$682$$ 10.0049i 0.0146700i
$$683$$ 743.492i 1.08857i −0.838901 0.544284i $$-0.816801\pi$$
0.838901 0.544284i $$-0.183199\pi$$
$$684$$ 610.559 0.892630
$$685$$ −1260.17 −1.83966
$$686$$ 328.235i 0.478477i
$$687$$ 358.427i 0.521727i
$$688$$ 60.1079i 0.0873662i
$$689$$ 793.874i 1.15221i
$$690$$ 892.465 1.29343
$$691$$ 652.050i 0.943632i −0.881697 0.471816i $$-0.843599\pi$$
0.881697 0.471816i $$-0.156401\pi$$
$$692$$ 284.305i 0.410845i
$$693$$ 353.344i 0.509876i
$$694$$ 1241.10 1.78833
$$695$$ 445.336 0.640771
$$696$$ 299.890i 0.430877i
$$697$$ −159.420 −0.228724
$$698$$ −1380.95 −1.97843
$$699$$ 369.398i 0.528466i
$$700$$ 576.008 0.822869
$$701$$ 24.8059i 0.0353864i 0.999843 + 0.0176932i $$0.00563221\pi$$
−0.999843 + 0.0176932i $$0.994368\pi$$
$$702$$ −267.932 −0.381669
$$703$$ 2046.24i 2.91073i
$$704$$ 1251.20i 1.77727i
$$705$$ 300.139i 0.425729i
$$706$$ −654.997 −0.927758
$$707$$ 1484.66i 2.09994i
$$708$$ 270.305 485.851i 0.381787 0.686230i
$$709$$ 521.844 0.736028 0.368014 0.929820i $$-0.380038\pi$$
0.368014 + 0.929820i $$0.380038\pi$$
$$710$$ 129.160i 0.181915i
$$711$$ 155.964 0.219359
$$712$$ 306.546 0.430542
$$713$$ −7.14934 −0.0100271
$$714$$ 697.102i 0.976333i
$$715$$ −1281.80 −1.79272
$$716$$ 639.299i 0.892876i
$$717$$ −246.207 −0.343385
$$718$$ 1245.53i 1.73472i
$$719$$ 997.450i 1.38727i 0.720325 + 0.693637i $$0.243993\pi$$
−0.720325 + 0.693637i $$0.756007\pi$$
$$720$$ 147.697 0.205135
$$721$$ 248.787i 0.345058i
$$722$$ 3190.30i 4.41870i
$$723$$ −677.693 −0.937335
$$724$$ −871.477 −1.20370
$$725$$ 445.235 0.614117
$$726$$ 209.403i 0.288433i
$$727$$ −570.949 −0.785349 −0.392675 0.919677i $$-0.628450\pi$$
−0.392675 + 0.919677i $$0.628450\pi$$
$$728$$ −690.932 −0.949082
$$729$$ 27.0000 0.0370370
$$730$$ 2440.44 3.34307
$$731$$ 103.709i 0.141873i
$$732$$ 792.043i 1.08203i
$$733$$ −337.572 −0.460535 −0.230268 0.973127i $$-0.573960\pi$$
−0.230268 + 0.973127i $$0.573960\pi$$
$$734$$ −1662.84 −2.26545
$$735$$ −391.930 −0.533239
$$736$$ 1189.51 1.61618
$$737$$ −1032.18 −1.40051
$$738$$ 104.346i 0.141390i
$$739$$ 1041.04i 1.40872i −0.709843 0.704360i $$-0.751234\pi$$
0.709843 0.704360i $$-0.248766\pi$$
$$740$$ 1795.12i 2.42583i
$$741$$ 1087.33i 1.46738i
$$742$$ 1351.93i 1.82201i
$$743$$ 955.497 1.28600 0.643000 0.765867i $$-0.277690\pi$$
0.643000 + 0.765867i $$0.277690\pi$$
$$744$$ 1.97147 0.00264982
$$745$$ 400.011i 0.536928i
$$746$$ 328.974i 0.440983i
$$747$$ 49.6658i 0.0664870i
$$748$$ 970.219i 1.29708i
$$749$$ 329.140 0.439439
$$750$$ 437.125i 0.582834i
$$751$$ 450.913i 0.600416i −0.953874 0.300208i $$-0.902944\pi$$
0.953874 0.300208i $$-0.0970561\pi$$
$$752$$ 234.488i 0.311820i
$$753$$ 233.839 0.310543
$$754$$ −2016.95 −2.67500
$$755$$ 622.392i 0.824360i
$$756$$ 262.951 0.347819
$$757$$ 410.015 0.541632 0.270816 0.962631i $$-0.412707\pi$$
0.270816 + 0.962631i $$0.412707\pi$$
$$758$$ 628.960i 0.829763i
$$759$$ 609.785 0.803406
$$760$$ 998.740i 1.31413i
$$761$$ 1469.25 1.93068 0.965339 0.260998i $$-0.0840517\pi$$
0.965339 + 0.260998i $$0.0840517\pi$$
$$762$$ 841.316i 1.10409i
$$763$$ 634.490i 0.831573i
$$764$$ 77.7673i 0.101790i
$$765$$ −254.834 −0.333116
$$766$$ 15.3028i 0.0199776i
$$767$$ −865.240 481.380i −1.12808 0.627614i
$$768$$ −20.3515 −0.0264994
$$769$$ 469.742i 0.610848i −0.952216 0.305424i $$-0.901202\pi$$
0.952216 0.305424i $$-0.0987982\pi$$
$$770$$ 2182.84 2.83486
$$771$$ −230.940 −0.299533
$$772$$ −391.432 −0.507037
$$773$$ 373.454i 0.483122i −0.970386 0.241561i $$-0.922341\pi$$
0.970386 0.241561i $$-0.0776595\pi$$
$$774$$ −67.8809 −0.0877014
$$775$$ 2.92696i 0.00377672i
$$776$$ −489.091 −0.630271
$$777$$ 881.260i 1.13418i
$$778$$ 426.789i 0.548572i
$$779$$ 423.460 0.543594
$$780$$ 953.886i 1.22293i
$$781$$ 88.2496i 0.112996i
$$782$$ −1203.03 −1.53840
$$783$$ 203.252 0.259581
$$784$$ −306.202 −0.390564
$$785$$ 1514.29i 1.92903i
$$786$$ −694.567 −0.883674
$$787$$ −97.7362 −0.124188 −0.0620942 0.998070i $$-0.519778\pi$$
−0.0620942 + 0.998070i $$0.519778\pi$$
$$788$$ 242.374 0.307581
$$789$$ 471.715 0.597864
$$790$$ 963.494i 1.21961i
$$791$$ 1124.60i 1.42175i