# Properties

 Label 240.3.c.e.209.3 Level $240$ Weight $3$ Character 240.209 Analytic conductor $6.540$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 240.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.53952634465$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ Defining polynomial: $$x^{12} + 34 x^{10} + 305 x^{8} + 616 x^{6} + 305 x^{4} + 34 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{15}\cdot 3^{2}$$ Twist minimal: no (minimal twist has level 120) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 209.3 Root $$-0.304307i$$ of defining polynomial Character $$\chi$$ $$=$$ 240.209 Dual form 240.3.c.e.209.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.49147 - 1.67109i) q^{3} +(4.19906 - 2.71439i) q^{5} +12.7692i q^{7} +(3.41489 + 8.32698i) q^{9} +O(q^{10})$$ $$q+(-2.49147 - 1.67109i) q^{3} +(4.19906 - 2.71439i) q^{5} +12.7692i q^{7} +(3.41489 + 8.32698i) q^{9} -12.6296i q^{11} +7.44085i q^{13} +(-14.9978 - 0.254179i) q^{15} +14.0550 q^{17} +31.0176 q^{19} +(21.3386 - 31.8142i) q^{21} +7.50423 q^{23} +(10.2641 - 22.7958i) q^{25} +(5.40707 - 26.4530i) q^{27} +15.7298i q^{29} +20.4893 q^{31} +(-21.1053 + 31.4663i) q^{33} +(34.6607 + 53.6186i) q^{35} +12.9261i q^{37} +(12.4344 - 18.5387i) q^{39} -13.8451i q^{41} +30.0797i q^{43} +(36.9420 + 25.6961i) q^{45} +20.2570 q^{47} -114.053 q^{49} +(-35.0176 - 23.4872i) q^{51} -29.1185 q^{53} +(-34.2817 - 53.0324i) q^{55} +(-77.2795 - 51.8333i) q^{57} -47.6333i q^{59} +43.0176 q^{61} +(-106.329 + 43.6054i) q^{63} +(20.1974 + 31.2445i) q^{65} +0.630153i q^{67} +(-18.6966 - 12.5403i) q^{69} +90.4047i q^{71} -46.2193i q^{73} +(-63.6667 + 39.6427i) q^{75} +161.270 q^{77} -37.9610 q^{79} +(-57.6771 + 56.8713i) q^{81} -80.2267 q^{83} +(59.0176 - 38.1507i) q^{85} +(26.2860 - 39.1904i) q^{87} +140.923i q^{89} -95.0138 q^{91} +(-51.0486 - 34.2396i) q^{93} +(130.245 - 84.1939i) q^{95} +10.3429i q^{97} +(105.166 - 43.1286i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 8 q^{9} + O(q^{10})$$ $$12 q + 8 q^{9} - 16 q^{15} + 4 q^{21} + 36 q^{25} + 48 q^{31} + 128 q^{39} - 68 q^{45} - 252 q^{49} - 48 q^{51} + 48 q^{55} + 144 q^{61} + 268 q^{69} - 304 q^{75} - 432 q^{79} - 188 q^{81} + 336 q^{85} + 560 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$97$$ $$161$$ $$181$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −2.49147 1.67109i −0.830491 0.557032i
$$4$$ 0 0
$$5$$ 4.19906 2.71439i 0.839811 0.542879i
$$6$$ 0 0
$$7$$ 12.7692i 1.82417i 0.409998 + 0.912086i $$0.365529\pi$$
−0.409998 + 0.912086i $$0.634471\pi$$
$$8$$ 0 0
$$9$$ 3.41489 + 8.32698i 0.379432 + 0.925220i
$$10$$ 0 0
$$11$$ 12.6296i 1.14815i −0.818804 0.574073i $$-0.805363\pi$$
0.818804 0.574073i $$-0.194637\pi$$
$$12$$ 0 0
$$13$$ 7.44085i 0.572373i 0.958174 + 0.286187i $$0.0923877\pi$$
−0.958174 + 0.286187i $$0.907612\pi$$
$$14$$ 0 0
$$15$$ −14.9978 0.254179i −0.999856 0.0169452i
$$16$$ 0 0
$$17$$ 14.0550 0.826763 0.413381 0.910558i $$-0.364348\pi$$
0.413381 + 0.910558i $$0.364348\pi$$
$$18$$ 0 0
$$19$$ 31.0176 1.63250 0.816252 0.577696i $$-0.196048\pi$$
0.816252 + 0.577696i $$0.196048\pi$$
$$20$$ 0 0
$$21$$ 21.3386 31.8142i 1.01612 1.51496i
$$22$$ 0 0
$$23$$ 7.50423 0.326271 0.163135 0.986604i $$-0.447839\pi$$
0.163135 + 0.986604i $$0.447839\pi$$
$$24$$ 0 0
$$25$$ 10.2641 22.7958i 0.410565 0.911831i
$$26$$ 0 0
$$27$$ 5.40707 26.4530i 0.200262 0.979742i
$$28$$ 0 0
$$29$$ 15.7298i 0.542407i 0.962522 + 0.271204i $$0.0874217\pi$$
−0.962522 + 0.271204i $$0.912578\pi$$
$$30$$ 0 0
$$31$$ 20.4893 0.660945 0.330473 0.943816i $$-0.392792\pi$$
0.330473 + 0.943816i $$0.392792\pi$$
$$32$$ 0 0
$$33$$ −21.1053 + 31.4663i −0.639553 + 0.953525i
$$34$$ 0 0
$$35$$ 34.6607 + 53.6186i 0.990305 + 1.53196i
$$36$$ 0 0
$$37$$ 12.9261i 0.349355i 0.984626 + 0.174677i $$0.0558883\pi$$
−0.984626 + 0.174677i $$0.944112\pi$$
$$38$$ 0 0
$$39$$ 12.4344 18.5387i 0.318830 0.475351i
$$40$$ 0 0
$$41$$ 13.8451i 0.337685i −0.985643 0.168843i $$-0.945997\pi$$
0.985643 0.168843i $$-0.0540029\pi$$
$$42$$ 0 0
$$43$$ 30.0797i 0.699528i 0.936838 + 0.349764i $$0.113738\pi$$
−0.936838 + 0.349764i $$0.886262\pi$$
$$44$$ 0 0
$$45$$ 36.9420 + 25.6961i 0.820933 + 0.571024i
$$46$$ 0 0
$$47$$ 20.2570 0.431000 0.215500 0.976504i $$-0.430862\pi$$
0.215500 + 0.976504i $$0.430862\pi$$
$$48$$ 0 0
$$49$$ −114.053 −2.32761
$$50$$ 0 0
$$51$$ −35.0176 23.4872i −0.686619 0.460533i
$$52$$ 0 0
$$53$$ −29.1185 −0.549406 −0.274703 0.961529i $$-0.588580\pi$$
−0.274703 + 0.961529i $$0.588580\pi$$
$$54$$ 0 0
$$55$$ −34.2817 53.0324i −0.623304 0.964226i
$$56$$ 0 0
$$57$$ −77.2795 51.8333i −1.35578 0.909356i
$$58$$ 0 0
$$59$$ 47.6333i 0.807344i −0.914904 0.403672i $$-0.867734\pi$$
0.914904 0.403672i $$-0.132266\pi$$
$$60$$ 0 0
$$61$$ 43.0176 0.705206 0.352603 0.935773i $$-0.385297\pi$$
0.352603 + 0.935773i $$0.385297\pi$$
$$62$$ 0 0
$$63$$ −106.329 + 43.6054i −1.68776 + 0.692149i
$$64$$ 0 0
$$65$$ 20.1974 + 31.2445i 0.310729 + 0.480685i
$$66$$ 0 0
$$67$$ 0.630153i 0.00940527i 0.999989 + 0.00470264i $$0.00149690\pi$$
−0.999989 + 0.00470264i $$0.998503\pi$$
$$68$$ 0 0
$$69$$ −18.6966 12.5403i −0.270965 0.181743i
$$70$$ 0 0
$$71$$ 90.4047i 1.27330i 0.771151 + 0.636652i $$0.219681\pi$$
−0.771151 + 0.636652i $$0.780319\pi$$
$$72$$ 0 0
$$73$$ 46.2193i 0.633140i −0.948569 0.316570i $$-0.897469\pi$$
0.948569 0.316570i $$-0.102531\pi$$
$$74$$ 0 0
$$75$$ −63.6667 + 39.6427i −0.848890 + 0.528570i
$$76$$ 0 0
$$77$$ 161.270 2.09442
$$78$$ 0 0
$$79$$ −37.9610 −0.480519 −0.240260 0.970709i $$-0.577233\pi$$
−0.240260 + 0.970709i $$0.577233\pi$$
$$80$$ 0 0
$$81$$ −57.6771 + 56.8713i −0.712063 + 0.702115i
$$82$$ 0 0
$$83$$ −80.2267 −0.966587 −0.483294 0.875458i $$-0.660560\pi$$
−0.483294 + 0.875458i $$0.660560\pi$$
$$84$$ 0 0
$$85$$ 59.0176 38.1507i 0.694324 0.448832i
$$86$$ 0 0
$$87$$ 26.2860 39.1904i 0.302138 0.450465i
$$88$$ 0 0
$$89$$ 140.923i 1.58341i 0.610907 + 0.791703i $$0.290805\pi$$
−0.610907 + 0.791703i $$0.709195\pi$$
$$90$$ 0 0
$$91$$ −95.0138 −1.04411
$$92$$ 0 0
$$93$$ −51.0486 34.2396i −0.548909 0.368168i
$$94$$ 0 0
$$95$$ 130.245 84.1939i 1.37100 0.886252i
$$96$$ 0 0
$$97$$ 10.3429i 0.106628i 0.998578 + 0.0533138i $$0.0169784\pi$$
−0.998578 + 0.0533138i $$0.983022\pi$$
$$98$$ 0 0
$$99$$ 105.166 43.1286i 1.06229 0.435643i
$$100$$ 0 0
$$101$$ 19.2739i 0.190830i 0.995438 + 0.0954152i $$0.0304179\pi$$
−0.995438 + 0.0954152i $$0.969582\pi$$
$$102$$ 0 0
$$103$$ 6.97008i 0.0676707i 0.999427 + 0.0338353i $$0.0107722\pi$$
−0.999427 + 0.0338353i $$0.989228\pi$$
$$104$$ 0 0
$$105$$ 3.24566 191.511i 0.0309110 1.82391i
$$106$$ 0 0
$$107$$ −73.7731 −0.689468 −0.344734 0.938700i $$-0.612031\pi$$
−0.344734 + 0.938700i $$0.612031\pi$$
$$108$$ 0 0
$$109$$ 74.0314 0.679187 0.339593 0.940572i $$-0.389711\pi$$
0.339593 + 0.940572i $$0.389711\pi$$
$$110$$ 0 0
$$111$$ 21.6008 32.2051i 0.194602 0.290136i
$$112$$ 0 0
$$113$$ −147.215 −1.30279 −0.651394 0.758739i $$-0.725816\pi$$
−0.651394 + 0.758739i $$0.725816\pi$$
$$114$$ 0 0
$$115$$ 31.5107 20.3694i 0.274006 0.177126i
$$116$$ 0 0
$$117$$ −61.9598 + 25.4096i −0.529571 + 0.217176i
$$118$$ 0 0
$$119$$ 179.471i 1.50816i
$$120$$ 0 0
$$121$$ −38.5069 −0.318239
$$122$$ 0 0
$$123$$ −23.1364 + 34.4947i −0.188101 + 0.280444i
$$124$$ 0 0
$$125$$ −18.7770 123.582i −0.150216 0.988653i
$$126$$ 0 0
$$127$$ 90.0171i 0.708796i −0.935095 0.354398i $$-0.884686\pi$$
0.935095 0.354398i $$-0.115314\pi$$
$$128$$ 0 0
$$129$$ 50.2660 74.9428i 0.389659 0.580952i
$$130$$ 0 0
$$131$$ 11.2911i 0.0861917i 0.999071 + 0.0430958i $$0.0137221\pi$$
−0.999071 + 0.0430958i $$0.986278\pi$$
$$132$$ 0 0
$$133$$ 396.070i 2.97797i
$$134$$ 0 0
$$135$$ −49.0994 125.755i −0.363699 0.931516i
$$136$$ 0 0
$$137$$ 22.4905 0.164164 0.0820822 0.996626i $$-0.473843\pi$$
0.0820822 + 0.996626i $$0.473843\pi$$
$$138$$ 0 0
$$139$$ −91.0955 −0.655363 −0.327682 0.944788i $$-0.606267\pi$$
−0.327682 + 0.944788i $$0.606267\pi$$
$$140$$ 0 0
$$141$$ −50.4698 33.8514i −0.357942 0.240081i
$$142$$ 0 0
$$143$$ 93.9750 0.657168
$$144$$ 0 0
$$145$$ 42.6969 + 66.0504i 0.294461 + 0.455520i
$$146$$ 0 0
$$147$$ 284.159 + 190.593i 1.93306 + 1.29655i
$$148$$ 0 0
$$149$$ 228.330i 1.53242i −0.642593 0.766208i $$-0.722141\pi$$
0.642593 0.766208i $$-0.277859\pi$$
$$150$$ 0 0
$$151$$ 74.0390 0.490324 0.245162 0.969482i $$-0.421159\pi$$
0.245162 + 0.969482i $$0.421159\pi$$
$$152$$ 0 0
$$153$$ 47.9961 + 117.035i 0.313700 + 0.764937i
$$154$$ 0 0
$$155$$ 86.0358 55.6161i 0.555069 0.358813i
$$156$$ 0 0
$$157$$ 245.742i 1.56523i −0.622504 0.782616i $$-0.713885\pi$$
0.622504 0.782616i $$-0.286115\pi$$
$$158$$ 0 0
$$159$$ 72.5481 + 48.6598i 0.456277 + 0.306037i
$$160$$ 0 0
$$161$$ 95.8231i 0.595175i
$$162$$ 0 0
$$163$$ 60.1570i 0.369061i 0.982827 + 0.184531i $$0.0590765\pi$$
−0.982827 + 0.184531i $$0.940924\pi$$
$$164$$ 0 0
$$165$$ −3.21017 + 189.417i −0.0194556 + 1.14798i
$$166$$ 0 0
$$167$$ −81.5664 −0.488421 −0.244211 0.969722i $$-0.578529\pi$$
−0.244211 + 0.969722i $$0.578529\pi$$
$$168$$ 0 0
$$169$$ 113.634 0.672389
$$170$$ 0 0
$$171$$ 105.921 + 258.283i 0.619424 + 1.51043i
$$172$$ 0 0
$$173$$ −167.064 −0.965687 −0.482843 0.875707i $$-0.660396\pi$$
−0.482843 + 0.875707i $$0.660396\pi$$
$$174$$ 0 0
$$175$$ 291.084 + 131.065i 1.66334 + 0.748942i
$$176$$ 0 0
$$177$$ −79.5997 + 118.677i −0.449716 + 0.670492i
$$178$$ 0 0
$$179$$ 270.104i 1.50896i −0.656322 0.754481i $$-0.727889\pi$$
0.656322 0.754481i $$-0.272111\pi$$
$$180$$ 0 0
$$181$$ 86.9786 0.480545 0.240272 0.970705i $$-0.422763\pi$$
0.240272 + 0.970705i $$0.422763\pi$$
$$182$$ 0 0
$$183$$ −107.177 71.8865i −0.585668 0.392822i
$$184$$ 0 0
$$185$$ 35.0866 + 54.2776i 0.189657 + 0.293392i
$$186$$ 0 0
$$187$$ 177.509i 0.949244i
$$188$$ 0 0
$$189$$ 337.785 + 69.0440i 1.78722 + 0.365312i
$$190$$ 0 0
$$191$$ 302.223i 1.58232i −0.611610 0.791159i $$-0.709478\pi$$
0.611610 0.791159i $$-0.290522\pi$$
$$192$$ 0 0
$$193$$ 306.780i 1.58953i −0.606916 0.794766i $$-0.707593\pi$$
0.606916 0.794766i $$-0.292407\pi$$
$$194$$ 0 0
$$195$$ 1.89130 111.597i 0.00969900 0.572291i
$$196$$ 0 0
$$197$$ 289.956 1.47186 0.735930 0.677058i $$-0.236745\pi$$
0.735930 + 0.677058i $$0.236745\pi$$
$$198$$ 0 0
$$199$$ −382.595 −1.92259 −0.961293 0.275527i $$-0.911148\pi$$
−0.961293 + 0.275527i $$0.911148\pi$$
$$200$$ 0 0
$$201$$ 1.05305 1.57001i 0.00523903 0.00781100i
$$202$$ 0 0
$$203$$ −200.857 −0.989445
$$204$$ 0 0
$$205$$ −37.5810 58.1363i −0.183322 0.283592i
$$206$$ 0 0
$$207$$ 25.6261 + 62.4876i 0.123798 + 0.301872i
$$208$$ 0 0
$$209$$ 391.740i 1.87435i
$$210$$ 0 0
$$211$$ 321.115 1.52187 0.760937 0.648826i $$-0.224740\pi$$
0.760937 + 0.648826i $$0.224740\pi$$
$$212$$ 0 0
$$213$$ 151.075 225.241i 0.709271 1.05747i
$$214$$ 0 0
$$215$$ 81.6482 + 126.306i 0.379759 + 0.587471i
$$216$$ 0 0
$$217$$ 261.632i 1.20568i
$$218$$ 0 0
$$219$$ −77.2368 + 115.154i −0.352679 + 0.525818i
$$220$$ 0 0
$$221$$ 104.581i 0.473217i
$$222$$ 0 0
$$223$$ 292.432i 1.31135i 0.755042 + 0.655676i $$0.227616\pi$$
−0.755042 + 0.655676i $$0.772384\pi$$
$$224$$ 0 0
$$225$$ 224.871 + 7.62426i 0.999426 + 0.0338856i
$$226$$ 0 0
$$227$$ −370.155 −1.63064 −0.815319 0.579013i $$-0.803438\pi$$
−0.815319 + 0.579013i $$0.803438\pi$$
$$228$$ 0 0
$$229$$ −381.985 −1.66806 −0.834028 0.551722i $$-0.813971\pi$$
−0.834028 + 0.551722i $$0.813971\pi$$
$$230$$ 0 0
$$231$$ −401.800 269.498i −1.73939 1.16666i
$$232$$ 0 0
$$233$$ 144.262 0.619150 0.309575 0.950875i $$-0.399813\pi$$
0.309575 + 0.950875i $$0.399813\pi$$
$$234$$ 0 0
$$235$$ 85.0603 54.9855i 0.361959 0.233981i
$$236$$ 0 0
$$237$$ 94.5789 + 63.4365i 0.399067 + 0.267665i
$$238$$ 0 0
$$239$$ 249.478i 1.04384i 0.852994 + 0.521921i $$0.174784\pi$$
−0.852994 + 0.521921i $$0.825216\pi$$
$$240$$ 0 0
$$241$$ 30.4541 0.126366 0.0631829 0.998002i $$-0.479875\pi$$
0.0631829 + 0.998002i $$0.479875\pi$$
$$242$$ 0 0
$$243$$ 238.738 45.3095i 0.982463 0.186459i
$$244$$ 0 0
$$245$$ −478.914 + 309.584i −1.95475 + 1.26361i
$$246$$ 0 0
$$247$$ 230.797i 0.934401i
$$248$$ 0 0
$$249$$ 199.883 + 134.066i 0.802742 + 0.538420i
$$250$$ 0 0
$$251$$ 68.9183i 0.274575i 0.990531 + 0.137287i $$0.0438384\pi$$
−0.990531 + 0.137287i $$0.956162\pi$$
$$252$$ 0 0
$$253$$ 94.7755i 0.374607i
$$254$$ 0 0
$$255$$ −210.794 3.57247i −0.826644 0.0140097i
$$256$$ 0 0
$$257$$ −362.374 −1.41002 −0.705009 0.709199i $$-0.749057\pi$$
−0.705009 + 0.709199i $$0.749057\pi$$
$$258$$ 0 0
$$259$$ −165.057 −0.637284
$$260$$ 0 0
$$261$$ −130.982 + 53.7155i −0.501846 + 0.205807i
$$262$$ 0 0
$$263$$ −23.4485 −0.0891580 −0.0445790 0.999006i $$-0.514195\pi$$
−0.0445790 + 0.999006i $$0.514195\pi$$
$$264$$ 0 0
$$265$$ −122.270 + 79.0391i −0.461397 + 0.298261i
$$266$$ 0 0
$$267$$ 235.496 351.106i 0.882007 1.31500i
$$268$$ 0 0
$$269$$ 396.738i 1.47486i 0.675421 + 0.737432i $$0.263962\pi$$
−0.675421 + 0.737432i $$0.736038\pi$$
$$270$$ 0 0
$$271$$ 143.926 0.531092 0.265546 0.964098i $$-0.414448\pi$$
0.265546 + 0.964098i $$0.414448\pi$$
$$272$$ 0 0
$$273$$ 236.724 + 158.777i 0.867122 + 0.581601i
$$274$$ 0 0
$$275$$ −287.902 129.632i −1.04692 0.471389i
$$276$$ 0 0
$$277$$ 360.884i 1.30283i −0.758722 0.651415i $$-0.774176\pi$$
0.758722 0.651415i $$-0.225824\pi$$
$$278$$ 0 0
$$279$$ 69.9686 + 170.614i 0.250784 + 0.611520i
$$280$$ 0 0
$$281$$ 531.655i 1.89201i −0.324149 0.946006i $$-0.605078\pi$$
0.324149 0.946006i $$-0.394922\pi$$
$$282$$ 0 0
$$283$$ 257.400i 0.909541i −0.890609 0.454770i $$-0.849721\pi$$
0.890609 0.454770i $$-0.150279\pi$$
$$284$$ 0 0
$$285$$ −465.197 7.88400i −1.63227 0.0276632i
$$286$$ 0 0
$$287$$ 176.791 0.615996
$$288$$ 0 0
$$289$$ −91.4579 −0.316463
$$290$$ 0 0
$$291$$ 17.2839 25.7690i 0.0593949 0.0885533i
$$292$$ 0 0
$$293$$ −310.456 −1.05958 −0.529789 0.848130i $$-0.677729\pi$$
−0.529789 + 0.848130i $$0.677729\pi$$
$$294$$ 0 0
$$295$$ −129.295 200.015i −0.438290 0.678016i
$$296$$ 0 0
$$297$$ −334.091 68.2892i −1.12489 0.229930i
$$298$$ 0 0
$$299$$ 55.8379i 0.186749i
$$300$$ 0 0
$$301$$ −384.094 −1.27606
$$302$$ 0 0
$$303$$ 32.2085 48.0204i 0.106299 0.158483i
$$304$$ 0 0
$$305$$ 180.633 116.767i 0.592240 0.382841i
$$306$$ 0 0
$$307$$ 266.169i 0.866999i 0.901154 + 0.433499i $$0.142721\pi$$
−0.901154 + 0.433499i $$0.857279\pi$$
$$308$$ 0 0
$$309$$ 11.6477 17.3658i 0.0376947 0.0561999i
$$310$$ 0 0
$$311$$ 186.580i 0.599934i 0.953950 + 0.299967i $$0.0969757\pi$$
−0.953950 + 0.299967i $$0.903024\pi$$
$$312$$ 0 0
$$313$$ 20.5021i 0.0655019i −0.999464 0.0327510i $$-0.989573\pi$$
0.999464 0.0327510i $$-0.0104268\pi$$
$$314$$ 0 0
$$315$$ −328.119 + 471.720i −1.04165 + 1.49752i
$$316$$ 0 0
$$317$$ −18.9792 −0.0598711 −0.0299356 0.999552i $$-0.509530\pi$$
−0.0299356 + 0.999552i $$0.509530\pi$$
$$318$$ 0 0
$$319$$ 198.661 0.622763
$$320$$ 0 0
$$321$$ 183.804 + 123.282i 0.572597 + 0.384055i
$$322$$ 0 0
$$323$$ 435.951 1.34969
$$324$$ 0 0
$$325$$ 169.620 + 76.3739i 0.521908 + 0.234997i
$$326$$ 0 0
$$327$$ −184.447 123.713i −0.564059 0.378328i
$$328$$ 0 0
$$329$$ 258.666i 0.786219i
$$330$$ 0 0
$$331$$ −413.193 −1.24832 −0.624159 0.781297i $$-0.714558\pi$$
−0.624159 + 0.781297i $$0.714558\pi$$
$$332$$ 0 0
$$333$$ −107.636 + 44.1413i −0.323230 + 0.132556i
$$334$$ 0 0
$$335$$ 1.71048 + 2.64605i 0.00510592 + 0.00789865i
$$336$$ 0 0
$$337$$ 484.733i 1.43838i 0.694816 + 0.719188i $$0.255486\pi$$
−0.694816 + 0.719188i $$0.744514\pi$$
$$338$$ 0 0
$$339$$ 366.783 + 246.010i 1.08195 + 0.725694i
$$340$$ 0 0
$$341$$ 258.772i 0.758862i
$$342$$ 0 0
$$343$$ 830.672i 2.42178i
$$344$$ 0 0
$$345$$ −112.547 1.90741i −0.326224 0.00552874i
$$346$$ 0 0
$$347$$ −336.214 −0.968915 −0.484457 0.874815i $$-0.660983\pi$$
−0.484457 + 0.874815i $$0.660983\pi$$
$$348$$ 0 0
$$349$$ −428.261 −1.22711 −0.613555 0.789652i $$-0.710261\pi$$
−0.613555 + 0.789652i $$0.710261\pi$$
$$350$$ 0 0
$$351$$ 196.833 + 40.2332i 0.560778 + 0.114625i
$$352$$ 0 0
$$353$$ 558.817 1.58305 0.791525 0.611137i $$-0.209287\pi$$
0.791525 + 0.611137i $$0.209287\pi$$
$$354$$ 0 0
$$355$$ 245.394 + 379.614i 0.691250 + 1.06934i
$$356$$ 0 0
$$357$$ 299.913 447.147i 0.840092 1.25251i
$$358$$ 0 0
$$359$$ 206.915i 0.576365i −0.957576 0.288182i $$-0.906949\pi$$
0.957576 0.288182i $$-0.0930509\pi$$
$$360$$ 0 0
$$361$$ 601.090 1.66507
$$362$$ 0 0
$$363$$ 95.9389 + 64.3487i 0.264295 + 0.177269i
$$364$$ 0 0
$$365$$ −125.457 194.077i −0.343718 0.531718i
$$366$$ 0 0
$$367$$ 185.425i 0.505246i −0.967565 0.252623i $$-0.918707\pi$$
0.967565 0.252623i $$-0.0812932\pi$$
$$368$$ 0 0
$$369$$ 115.288 47.2794i 0.312433 0.128128i
$$370$$ 0 0
$$371$$ 371.821i 1.00221i
$$372$$ 0 0
$$373$$ 427.345i 1.14570i −0.819661 0.572848i $$-0.805838\pi$$
0.819661 0.572848i $$-0.194162\pi$$
$$374$$ 0 0
$$375$$ −159.734 + 339.279i −0.425958 + 0.904743i
$$376$$ 0 0
$$377$$ −117.043 −0.310459
$$378$$ 0 0
$$379$$ −117.727 −0.310626 −0.155313 0.987865i $$-0.549639\pi$$
−0.155313 + 0.987865i $$0.549639\pi$$
$$380$$ 0 0
$$381$$ −150.427 + 224.275i −0.394822 + 0.588649i
$$382$$ 0 0
$$383$$ 470.016 1.22720 0.613598 0.789619i $$-0.289722\pi$$
0.613598 + 0.789619i $$0.289722\pi$$
$$384$$ 0 0
$$385$$ 677.182 437.750i 1.75891 1.13701i
$$386$$ 0 0
$$387$$ −250.473 + 102.719i −0.647217 + 0.265423i
$$388$$ 0 0
$$389$$ 128.160i 0.329461i 0.986339 + 0.164730i $$0.0526754\pi$$
−0.986339 + 0.164730i $$0.947325\pi$$
$$390$$ 0 0
$$391$$ 105.472 0.269749
$$392$$ 0 0
$$393$$ 18.8685 28.1315i 0.0480115 0.0715814i
$$394$$ 0 0
$$395$$ −159.401 + 103.041i −0.403546 + 0.260864i
$$396$$ 0 0
$$397$$ 276.316i 0.696011i 0.937493 + 0.348005i $$0.113141\pi$$
−0.937493 + 0.348005i $$0.886859\pi$$
$$398$$ 0 0
$$399$$ 661.871 986.798i 1.65882 2.47318i
$$400$$ 0 0
$$401$$ 549.912i 1.37135i 0.727907 + 0.685675i $$0.240493\pi$$
−0.727907 + 0.685675i $$0.759507\pi$$
$$402$$ 0 0
$$403$$ 152.458i 0.378307i
$$404$$ 0 0
$$405$$ −87.8182 + 395.364i −0.216835 + 0.976208i
$$406$$ 0 0
$$407$$ 163.252 0.401110
$$408$$ 0 0
$$409$$ −219.166 −0.535858 −0.267929 0.963439i $$-0.586339\pi$$
−0.267929 + 0.963439i $$0.586339\pi$$
$$410$$ 0 0
$$411$$ −56.0346 37.5838i −0.136337 0.0914448i
$$412$$ 0 0
$$413$$ 608.240 1.47273
$$414$$ 0 0
$$415$$ −336.877 + 217.767i −0.811751 + 0.524740i
$$416$$ 0 0
$$417$$ 226.962 + 152.229i 0.544274 + 0.365058i
$$418$$ 0 0
$$419$$ 204.522i 0.488119i −0.969760 0.244060i $$-0.921521\pi$$
0.969760 0.244060i $$-0.0784792\pi$$
$$420$$ 0 0
$$421$$ 577.186 1.37099 0.685494 0.728078i $$-0.259586\pi$$
0.685494 + 0.728078i $$0.259586\pi$$
$$422$$ 0 0
$$423$$ 69.1754 + 168.680i 0.163535 + 0.398770i
$$424$$ 0 0
$$425$$ 144.262 320.394i 0.339440 0.753868i
$$426$$ 0 0
$$427$$ 549.301i 1.28642i
$$428$$ 0 0
$$429$$ −234.136 157.041i −0.545772 0.366063i
$$430$$ 0 0
$$431$$ 663.363i 1.53913i 0.638571 + 0.769563i $$0.279526\pi$$
−0.638571 + 0.769563i $$0.720474\pi$$
$$432$$ 0 0
$$433$$ 226.876i 0.523964i 0.965073 + 0.261982i $$0.0843760\pi$$
−0.965073 + 0.261982i $$0.915624\pi$$
$$434$$ 0 0
$$435$$ 3.99818 235.913i 0.00919122 0.542329i
$$436$$ 0 0
$$437$$ 232.763 0.532639
$$438$$ 0 0
$$439$$ −282.524 −0.643564 −0.321782 0.946814i $$-0.604282\pi$$
−0.321782 + 0.946814i $$0.604282\pi$$
$$440$$ 0 0
$$441$$ −389.477 949.715i −0.883168 2.15355i
$$442$$ 0 0
$$443$$ −455.605 −1.02845 −0.514227 0.857654i $$-0.671921\pi$$
−0.514227 + 0.857654i $$0.671921\pi$$
$$444$$ 0 0
$$445$$ 382.521 + 591.744i 0.859597 + 1.32976i
$$446$$ 0 0
$$447$$ −381.561 + 568.878i −0.853604 + 1.27266i
$$448$$ 0 0
$$449$$ 157.206i 0.350124i −0.984557 0.175062i $$-0.943987\pi$$
0.984557 0.175062i $$-0.0560127\pi$$
$$450$$ 0 0
$$451$$ −174.858 −0.387712
$$452$$ 0 0
$$453$$ −184.466 123.726i −0.407210 0.273126i
$$454$$ 0 0
$$455$$ −398.968 + 257.905i −0.876853 + 0.566824i
$$456$$ 0 0
$$457$$ 397.152i 0.869041i 0.900662 + 0.434520i $$0.143082\pi$$
−0.900662 + 0.434520i $$0.856918\pi$$
$$458$$ 0 0
$$459$$ 75.9962 371.797i 0.165569 0.810014i
$$460$$ 0 0
$$461$$ 350.730i 0.760803i 0.924821 + 0.380401i $$0.124214\pi$$
−0.924821 + 0.380401i $$0.875786\pi$$
$$462$$ 0 0
$$463$$ 308.385i 0.666058i 0.942917 + 0.333029i $$0.108071\pi$$
−0.942917 + 0.333029i $$0.891929\pi$$
$$464$$ 0 0
$$465$$ −307.296 5.20794i −0.660851 0.0111999i
$$466$$ 0 0
$$467$$ 800.129 1.71334 0.856669 0.515866i $$-0.172530\pi$$
0.856669 + 0.515866i $$0.172530\pi$$
$$468$$ 0 0
$$469$$ −8.04656 −0.0171568
$$470$$ 0 0
$$471$$ −410.657 + 612.259i −0.871884 + 1.29991i
$$472$$ 0 0
$$473$$ 379.895 0.803160
$$474$$ 0 0
$$475$$ 318.369 707.070i 0.670250 1.48857i
$$476$$ 0 0
$$477$$ −99.4364 242.469i −0.208462 0.508321i
$$478$$ 0 0
$$479$$ 630.135i 1.31552i −0.753227 0.657761i $$-0.771504\pi$$
0.753227 0.657761i $$-0.228496\pi$$
$$480$$ 0 0
$$481$$ −96.1814 −0.199961
$$482$$ 0 0
$$483$$ 160.130 238.741i 0.331531 0.494287i
$$484$$ 0 0
$$485$$ 28.0746 + 43.4303i 0.0578858 + 0.0895470i
$$486$$ 0 0
$$487$$ 103.952i 0.213454i −0.994288 0.106727i $$-0.965963\pi$$
0.994288 0.106727i $$-0.0340372\pi$$
$$488$$ 0 0
$$489$$ 100.528 149.879i 0.205579 0.306502i
$$490$$ 0 0
$$491$$ 286.049i 0.582585i −0.956634 0.291292i $$-0.905915\pi$$
0.956634 0.291292i $$-0.0940853\pi$$
$$492$$ 0 0
$$493$$ 221.082i 0.448442i
$$494$$ 0 0
$$495$$ 324.532 466.563i 0.655619 0.942551i
$$496$$ 0 0
$$497$$ −1154.40 −2.32273
$$498$$ 0 0
$$499$$ 528.285 1.05869 0.529344 0.848407i $$-0.322438\pi$$
0.529344 + 0.848407i $$0.322438\pi$$
$$500$$ 0 0
$$501$$ 203.220 + 136.305i 0.405630 + 0.272066i
$$502$$ 0 0
$$503$$ 733.418 1.45809 0.729044 0.684467i $$-0.239965\pi$$
0.729044 + 0.684467i $$0.239965\pi$$
$$504$$ 0 0
$$505$$ 52.3169 + 80.9321i 0.103598 + 0.160262i
$$506$$ 0 0
$$507$$ −283.116 189.893i −0.558413 0.374542i
$$508$$ 0 0
$$509$$ 312.619i 0.614183i −0.951680 0.307092i $$-0.900644\pi$$
0.951680 0.307092i $$-0.0993558\pi$$
$$510$$ 0 0
$$511$$ 590.183 1.15496
$$512$$ 0 0
$$513$$ 167.714 820.509i 0.326928 1.59943i
$$514$$ 0 0
$$515$$ 18.9195 + 29.2677i 0.0367370 + 0.0568306i
$$516$$ 0 0
$$517$$ 255.838i 0.494851i
$$518$$ 0 0
$$519$$ 416.235 + 279.179i 0.801995 + 0.537918i
$$520$$ 0 0
$$521$$ 715.719i 1.37374i 0.726780 + 0.686870i $$0.241016\pi$$
−0.726780 + 0.686870i $$0.758984\pi$$
$$522$$ 0 0
$$523$$ 109.080i 0.208567i −0.994548 0.104283i $$-0.966745\pi$$
0.994548 0.104283i $$-0.0332549\pi$$
$$524$$ 0 0
$$525$$ −506.207 812.974i −0.964203 1.54852i
$$526$$ 0 0
$$527$$ 287.977 0.546445
$$528$$ 0 0
$$529$$ −472.686 −0.893547
$$530$$ 0 0
$$531$$ 396.641 162.662i 0.746971 0.306332i
$$532$$ 0 0
$$533$$ 103.019 0.193282
$$534$$ 0 0
$$535$$ −309.777 + 200.249i −0.579023 + 0.374297i
$$536$$ 0 0
$$537$$ −451.370 + 672.958i −0.840540 + 1.25318i
$$538$$ 0 0
$$539$$ 1440.44i 2.67243i
$$540$$ 0 0
$$541$$ −14.9710 −0.0276729 −0.0138364 0.999904i $$-0.504404\pi$$
−0.0138364 + 0.999904i $$0.504404\pi$$
$$542$$ 0 0
$$543$$ −216.705 145.350i −0.399088 0.267679i
$$544$$ 0 0
$$545$$ 310.862 200.950i 0.570389 0.368716i
$$546$$ 0 0
$$547$$ 842.765i 1.54070i −0.637618 0.770352i $$-0.720080\pi$$
0.637618 0.770352i $$-0.279920\pi$$
$$548$$ 0 0
$$549$$ 146.900 + 358.206i 0.267578 + 0.652471i
$$550$$ 0 0
$$551$$ 487.901i 0.885482i
$$552$$ 0 0
$$553$$ 484.733i 0.876551i
$$554$$ 0 0
$$555$$ 3.28555 193.864i 0.00591990 0.349305i
$$556$$ 0 0
$$557$$ 845.989 1.51883 0.759415 0.650606i $$-0.225485\pi$$
0.759415 + 0.650606i $$0.225485\pi$$
$$558$$ 0 0
$$559$$ −223.819 −0.400391
$$560$$ 0 0
$$561$$ −296.634 + 442.258i −0.528759 + 0.788339i
$$562$$ 0 0
$$563$$ 336.509 0.597707 0.298853 0.954299i $$-0.403396\pi$$
0.298853 + 0.954299i $$0.403396\pi$$
$$564$$ 0 0
$$565$$ −618.164 + 399.600i −1.09410 + 0.707256i
$$566$$ 0 0
$$567$$ −726.202 736.491i −1.28078 1.29893i
$$568$$ 0 0
$$569$$ 552.736i 0.971416i 0.874121 + 0.485708i $$0.161438\pi$$
−0.874121 + 0.485708i $$0.838562\pi$$
$$570$$ 0 0
$$571$$ −772.222 −1.35240 −0.676202 0.736717i $$-0.736375\pi$$
−0.676202 + 0.736717i $$0.736375\pi$$
$$572$$ 0 0
$$573$$ −505.043 + 752.980i −0.881401 + 1.31410i
$$574$$ 0 0
$$575$$ 77.0245 171.065i 0.133956 0.297504i
$$576$$ 0 0
$$577$$ 848.557i 1.47064i −0.677722 0.735318i $$-0.737033\pi$$
0.677722 0.735318i $$-0.262967\pi$$
$$578$$ 0 0
$$579$$ −512.658 + 764.334i −0.885420 + 1.32009i
$$580$$ 0 0
$$581$$ 1024.43i 1.76322i
$$582$$ 0 0
$$583$$ 367.755i 0.630798i
$$584$$ 0 0
$$585$$ −191.201 + 274.880i −0.326839 + 0.469880i
$$586$$ 0 0
$$587$$ 575.536 0.980470 0.490235 0.871590i $$-0.336911\pi$$
0.490235 + 0.871590i $$0.336911\pi$$
$$588$$ 0 0
$$589$$ 635.529 1.07900
$$590$$ 0 0
$$591$$ −722.419 484.544i −1.22237 0.819872i
$$592$$ 0 0
$$593$$ −156.935 −0.264646 −0.132323 0.991207i $$-0.542244\pi$$
−0.132323 + 0.991207i $$0.542244\pi$$
$$594$$ 0 0
$$595$$ 487.154 + 753.608i 0.818747 + 1.26657i
$$596$$ 0 0
$$597$$ 953.225 + 639.352i 1.59669 + 1.07094i
$$598$$ 0 0
$$599$$ 517.564i 0.864047i −0.901862 0.432024i $$-0.857800\pi$$
0.901862 0.432024i $$-0.142200\pi$$
$$600$$ 0 0
$$601$$ −883.588 −1.47020 −0.735098 0.677961i $$-0.762864\pi$$
−0.735098 + 0.677961i $$0.762864\pi$$
$$602$$ 0 0
$$603$$ −5.24727 + 2.15190i −0.00870194 + 0.00356866i
$$604$$ 0 0
$$605$$ −161.693 + 104.523i −0.267260 + 0.172765i
$$606$$ 0 0
$$607$$ 242.929i 0.400212i −0.979774 0.200106i $$-0.935871\pi$$
0.979774 0.200106i $$-0.0641287\pi$$
$$608$$ 0 0
$$609$$ 500.431 + 335.652i 0.821725 + 0.551152i
$$610$$ 0 0
$$611$$ 150.729i 0.246693i
$$612$$ 0 0
$$613$$ 157.263i 0.256546i −0.991739 0.128273i $$-0.959057\pi$$
0.991739 0.128273i $$-0.0409434\pi$$
$$614$$ 0 0
$$615$$ −3.51912 + 207.646i −0.00572215 + 0.337637i
$$616$$ 0 0
$$617$$ −471.040 −0.763436 −0.381718 0.924279i $$-0.624667\pi$$
−0.381718 + 0.924279i $$0.624667\pi$$
$$618$$ 0 0
$$619$$ −550.320 −0.889047 −0.444524 0.895767i $$-0.646627\pi$$
−0.444524 + 0.895767i $$0.646627\pi$$
$$620$$ 0 0
$$621$$ 40.5759 198.510i 0.0653396 0.319662i
$$622$$ 0 0
$$623$$ −1799.48 −2.88841
$$624$$ 0 0
$$625$$ −414.295 467.958i −0.662872 0.748733i
$$626$$ 0 0
$$627$$ −654.634 + 976.009i −1.04407 + 1.55663i
$$628$$ 0 0
$$629$$ 181.676i 0.288834i
$$630$$ 0 0
$$631$$ 347.362 0.550495 0.275248 0.961373i $$-0.411240\pi$$
0.275248 + 0.961373i $$0.411240\pi$$
$$632$$ 0 0
$$633$$ −800.051 536.614i −1.26390 0.847732i
$$634$$ 0 0
$$635$$ −244.342 377.987i −0.384790 0.595255i
$$636$$ 0 0
$$637$$ 848.649i 1.33226i
$$638$$ 0 0
$$639$$ −752.798 + 308.721i −1.17809 + 0.483132i
$$640$$ 0 0
$$641$$ 333.802i 0.520752i −0.965507 0.260376i $$-0.916153\pi$$
0.965507 0.260376i $$-0.0838465\pi$$
$$642$$ 0 0
$$643$$ 495.512i 0.770625i −0.922786 0.385313i $$-0.874094\pi$$
0.922786 0.385313i $$-0.125906\pi$$
$$644$$ 0 0
$$645$$ 7.64561 451.131i 0.0118537 0.699428i
$$646$$ 0 0
$$647$$ −149.493 −0.231056 −0.115528 0.993304i $$-0.536856\pi$$
−0.115528 + 0.993304i $$0.536856\pi$$
$$648$$ 0 0
$$649$$ −601.590 −0.926948
$$650$$ 0 0
$$651$$ 437.212 651.850i 0.671601 1.00131i
$$652$$ 0 0
$$653$$ −261.846 −0.400990 −0.200495 0.979695i $$-0.564255\pi$$
−0.200495 + 0.979695i $$0.564255\pi$$
$$654$$ 0 0
$$655$$ 30.6485 + 47.4120i 0.0467916 + 0.0723847i
$$656$$ 0 0
$$657$$ 384.867 157.833i 0.585794 0.240234i
$$658$$ 0 0
$$659$$ 148.718i 0.225672i −0.993614 0.112836i $$-0.964006\pi$$
0.993614 0.112836i $$-0.0359935\pi$$
$$660$$ 0 0
$$661$$ −535.548 −0.810209 −0.405104 0.914270i $$-0.632765\pi$$
−0.405104 + 0.914270i $$0.632765\pi$$
$$662$$ 0 0
$$663$$ 174.765 260.561i 0.263597 0.393002i
$$664$$ 0 0
$$665$$ 1075.09 + 1663.12i 1.61668 + 2.50093i
$$666$$ 0 0
$$667$$ 118.040i 0.176972i
$$668$$ 0 0
$$669$$ 488.681 728.586i 0.730465 1.08907i
$$670$$ 0 0
$$671$$ 543.295i 0.809680i
$$672$$ 0 0
$$673$$ 678.388i 1.00801i 0.863702 + 0.504003i $$0.168140\pi$$
−0.863702 + 0.504003i $$0.831860\pi$$
$$674$$ 0 0
$$675$$ −547.519 394.776i −0.811139 0.584853i
$$676$$ 0 0
$$677$$ −809.743 −1.19608 −0.598038 0.801468i $$-0.704053\pi$$
−0.598038 + 0.801468i $$0.704053\pi$$
$$678$$ 0 0
$$679$$ −132.070 −0.194507
$$680$$ 0 0
$$681$$ 922.231 + 618.563i 1.35423 + 0.908316i
$$682$$ 0 0
$$683$$ −150.099 −0.219764 −0.109882 0.993945i $$-0.535047\pi$$
−0.109882 + 0.993945i $$0.535047\pi$$
$$684$$ 0 0
$$685$$ 94.4390 61.0481i 0.137867 0.0891214i
$$686$$ 0 0
$$687$$ 951.705 + 638.333i 1.38531 + 0.929160i
$$688$$ 0 0
$$689$$ 216.667i 0.314465i
$$690$$ 0 0
$$691$$ 334.001 0.483359 0.241679 0.970356i $$-0.422302\pi$$
0.241679 + 0.970356i $$0.422302\pi$$
$$692$$ 0 0
$$693$$ 550.719 + 1342.89i 0.794688 + 1.93780i
$$694$$ 0 0
$$695$$ −382.515 + 247.269i −0.550381 + 0.355783i
$$696$$ 0 0
$$697$$ 194.592i 0.279185i
$$698$$ 0 0
$$699$$ −359.425 241.076i −0.514199 0.344886i
$$700$$ 0 0
$$701$$ 924.471i 1.31879i 0.751797 + 0.659394i $$0.229187\pi$$
−0.751797 + 0.659394i $$0.770813\pi$$
$$702$$ 0 0
$$703$$ 400.937i 0.570324i
$$704$$ 0 0
$$705$$ −303.812 5.14890i −0.430938 0.00730340i
$$706$$ 0 0
$$707$$ −246.112 −0.348108
$$708$$ 0 0
$$709$$ 797.459 1.12477 0.562383 0.826877i $$-0.309885\pi$$
0.562383 + 0.826877i $$0.309885\pi$$
$$710$$ 0 0
$$711$$ −129.633 316.101i −0.182324 0.444586i
$$712$$ 0 0
$$713$$ 153.757 0.215647
$$714$$ 0 0
$$715$$ 394.606 255.085i 0.551897 0.356762i
$$716$$ 0 0
$$717$$ 416.902 621.568i 0.581453 0.866902i
$$718$$ 0 0
$$719$$ 907.966i 1.26282i 0.775450 + 0.631409i $$0.217523\pi$$
−0.775450 + 0.631409i $$0.782477\pi$$
$$720$$ 0 0
$$721$$ −89.0024 −0.123443
$$722$$ 0 0
$$723$$ −75.8757 50.8918i −0.104946 0.0703897i
$$724$$ 0 0
$$725$$ 358.573 + 161.453i 0.494584 + 0.222694i
$$726$$ 0 0
$$727$$ 1038.16i 1.42801i 0.700140 + 0.714005i $$0.253121\pi$$
−0.700140 + 0.714005i $$0.746879\pi$$
$$728$$ 0 0
$$729$$ −670.527 286.067i −0.919790 0.392410i
$$730$$ 0 0
$$731$$ 422.769i 0.578344i
$$732$$ 0 0
$$733$$ 399.107i 0.544485i 0.962229 + 0.272242i $$0.0877652\pi$$
−0.962229 + 0.272242i $$0.912235\pi$$
$$734$$ 0 0
$$735$$ 1710.55 + 28.9898i 2.32727 + 0.0394418i
$$736$$ 0 0
$$737$$ 7.95858 0.0107986
$$738$$ 0 0
$$739$$ −452.504 −0.612319 −0.306159 0.951980i $$-0.599044\pi$$
−0.306159 + 0.951980i $$0.599044\pi$$
$$740$$ 0 0
$$741$$ 385.684 575.025i 0.520491 0.776012i
$$742$$ 0 0
$$743$$ 486.909 0.655328 0.327664 0.944794i $$-0.393739\pi$$
0.327664 + 0.944794i $$0.393739\pi$$
$$744$$ 0 0
$$745$$ −619.777 958.770i −0.831916 1.28694i
$$746$$ 0 0
$$747$$ −273.965 668.046i −0.366754 0.894306i
$$748$$ 0 0
$$749$$ 942.024i 1.25771i
$$750$$ 0 0
$$751$$ 470.899 0.627029 0.313515 0.949583i $$-0.398494\pi$$
0.313515 + 0.949583i $$0.398494\pi$$
$$752$$ 0 0
$$753$$ 115.169 171.708i 0.152947 0.228032i
$$754$$ 0 0
$$755$$ 310.894 200.971i 0.411780 0.266187i
$$756$$ 0 0
$$757$$ 886.264i 1.17076i 0.810760 + 0.585379i $$0.199054\pi$$
−0.810760 + 0.585379i $$0.800946\pi$$
$$758$$ 0 0
$$759$$ −158.379 + 236.131i −0.208668 + 0.311108i
$$760$$ 0 0
$$761$$ 1022.30i 1.34336i −0.740841 0.671680i $$-0.765573\pi$$
0.740841 0.671680i $$-0.234427\pi$$
$$762$$ 0 0
$$763$$ 945.322i 1.23895i
$$764$$ 0 0
$$765$$ 519.218 + 361.158i 0.678717 + 0.472102i
$$766$$ 0 0
$$767$$ 354.432 0.462102
$$768$$ 0 0
$$769$$ 1051.96 1.36796 0.683982 0.729499i $$-0.260247\pi$$
0.683982 + 0.729499i $$0.260247\pi$$
$$770$$ 0 0
$$771$$ 902.847 + 605.562i 1.17101 + 0.785424i
$$772$$ 0 0
$$773$$ −983.554 −1.27238 −0.636192 0.771530i $$-0.719492\pi$$
−0.636192 + 0.771530i $$0.719492\pi$$
$$774$$ 0 0
$$775$$ 210.305 467.070i 0.271361 0.602671i
$$776$$ 0 0
$$777$$ 411.234 + 275.825i 0.529259 + 0.354987i
$$778$$ 0 0
$$779$$ 429.441i 0.551272i
$$780$$ 0 0
$$781$$ 1141.77 1.46194
$$782$$ 0 0
$$783$$ 416.101 + 85.0522i 0.531419 + 0.108624i
$$784$$ 0 0
$$785$$ −667.039 1031.88i −0.849731 1.31450i
$$786$$ 0 0
$$787$$ 984.726i 1.25124i −0.780128 0.625620i $$-0.784846\pi$$
0.780128 0.625620i $$-0.215154\pi$$
$$788$$ 0 0
$$789$$ 58.4214 + 39.1847i 0.0740449 + 0.0496638i
$$790$$ 0 0
$$791$$ 1879.82i 2.37651i
$$792$$ 0 0
$$793$$ 320.087i 0.403641i
$$794$$ 0 0
$$795$$ 436.715 + 7.40130i 0.549327 + 0.00930982i
$$796$$ 0 0
$$797$$ 359.710 0.451330 0.225665 0.974205i $$-0.427544\pi$$
0.225665 + 0.974205i $$0.427544\pi$$
$$798$$ 0 0
$$799$$ 284.712 0.356335