# Properties

 Label 384.3.i.d.353.3 Level $384$ Weight $3$ Character 384.353 Analytic conductor $10.463$ Analytic rank $0$ Dimension $20$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 384.i (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.4632421514$$ Analytic rank: $$0$$ Dimension: $$20$$ Relative dimension: $$10$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ Defining polynomial: $$x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{23}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 353.3 Root $$-1.85381 - 0.750590i$$ of defining polynomial Character $$\chi$$ $$=$$ 384.353 Dual form 384.3.i.d.161.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50491 - 2.59524i) q^{3} +(2.59897 - 2.59897i) q^{5} +7.30027i q^{7} +(-4.47050 + 7.81118i) q^{9} +O(q^{10})$$ $$q+(-1.50491 - 2.59524i) q^{3} +(2.59897 - 2.59897i) q^{5} +7.30027i q^{7} +(-4.47050 + 7.81118i) q^{9} +(-11.3161 + 11.3161i) q^{11} +(0.746462 - 0.746462i) q^{13} +(-10.6561 - 2.83373i) q^{15} -6.67452i q^{17} +(-22.1936 + 22.1936i) q^{19} +(18.9459 - 10.9862i) q^{21} +21.4389 q^{23} +11.4908i q^{25} +(26.9996 - 0.153096i) q^{27} +(-1.54272 - 1.54272i) q^{29} -14.6082 q^{31} +(46.3976 + 12.3382i) q^{33} +(18.9732 + 18.9732i) q^{35} +(50.1010 + 50.1010i) q^{37} +(-3.06060 - 0.813888i) q^{39} -15.0731 q^{41} +(-26.3634 - 26.3634i) q^{43} +(8.68231 + 31.9197i) q^{45} +36.6067i q^{47} -4.29399 q^{49} +(-17.3220 + 10.0445i) q^{51} +(-50.9270 + 50.9270i) q^{53} +58.8202i q^{55} +(90.9971 + 24.1983i) q^{57} +(12.1683 - 12.1683i) q^{59} +(27.5789 - 27.5789i) q^{61} +(-57.0238 - 32.6359i) q^{63} -3.88006i q^{65} +(4.84214 - 4.84214i) q^{67} +(-32.2636 - 55.6391i) q^{69} -74.9072 q^{71} -3.47110i q^{73} +(29.8212 - 17.2925i) q^{75} +(-82.6105 - 82.6105i) q^{77} +103.463 q^{79} +(-41.0292 - 69.8399i) q^{81} +(31.7254 + 31.7254i) q^{83} +(-17.3469 - 17.3469i) q^{85} +(-1.68207 + 6.32538i) q^{87} -78.2605 q^{89} +(5.44937 + 5.44937i) q^{91} +(21.9840 + 37.9118i) q^{93} +115.361i q^{95} -61.5651 q^{97} +(-37.8034 - 138.981i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q + 6q^{3} + O(q^{10})$$ $$20q + 6q^{3} - 92q^{13} - 116q^{15} + 52q^{19} - 48q^{21} - 18q^{27} - 80q^{31} + 60q^{33} + 116q^{37} - 172q^{43} - 60q^{45} - 364q^{49} - 128q^{51} + 244q^{61} + 296q^{63} - 356q^{67} + 20q^{69} + 146q^{75} + 384q^{79} - 188q^{81} - 48q^{85} - 136q^{91} + 132q^{93} + 472q^{97} + 452q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$133$$ $$257$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.50491 2.59524i −0.501636 0.865079i
$$4$$ 0 0
$$5$$ 2.59897 2.59897i 0.519793 0.519793i −0.397716 0.917509i $$-0.630197\pi$$
0.917509 + 0.397716i $$0.130197\pi$$
$$6$$ 0 0
$$7$$ 7.30027i 1.04290i 0.853283 + 0.521448i $$0.174608\pi$$
−0.853283 + 0.521448i $$0.825392\pi$$
$$8$$ 0 0
$$9$$ −4.47050 + 7.81118i −0.496723 + 0.867909i
$$10$$ 0 0
$$11$$ −11.3161 + 11.3161i −1.02873 + 1.02873i −0.0291601 + 0.999575i $$0.509283\pi$$
−0.999575 + 0.0291601i $$0.990717\pi$$
$$12$$ 0 0
$$13$$ 0.746462 0.746462i 0.0574201 0.0574201i −0.677814 0.735234i $$-0.737072\pi$$
0.735234 + 0.677814i $$0.237072\pi$$
$$14$$ 0 0
$$15$$ −10.6561 2.83373i −0.710409 0.188915i
$$16$$ 0 0
$$17$$ 6.67452i 0.392619i −0.980542 0.196310i $$-0.937104\pi$$
0.980542 0.196310i $$-0.0628957\pi$$
$$18$$ 0 0
$$19$$ −22.1936 + 22.1936i −1.16809 + 1.16809i −0.185428 + 0.982658i $$0.559367\pi$$
−0.982658 + 0.185428i $$0.940633\pi$$
$$20$$ 0 0
$$21$$ 18.9459 10.9862i 0.902187 0.523154i
$$22$$ 0 0
$$23$$ 21.4389 0.932128 0.466064 0.884751i $$-0.345672\pi$$
0.466064 + 0.884751i $$0.345672\pi$$
$$24$$ 0 0
$$25$$ 11.4908i 0.459630i
$$26$$ 0 0
$$27$$ 26.9996 0.153096i 0.999984 0.00567024i
$$28$$ 0 0
$$29$$ −1.54272 1.54272i −0.0531973 0.0531973i 0.680008 0.733205i $$-0.261976\pi$$
−0.733205 + 0.680008i $$0.761976\pi$$
$$30$$ 0 0
$$31$$ −14.6082 −0.471233 −0.235616 0.971846i $$-0.575711\pi$$
−0.235616 + 0.971846i $$0.575711\pi$$
$$32$$ 0 0
$$33$$ 46.3976 + 12.3382i 1.40599 + 0.373886i
$$34$$ 0 0
$$35$$ 18.9732 + 18.9732i 0.542090 + 0.542090i
$$36$$ 0 0
$$37$$ 50.1010 + 50.1010i 1.35408 + 1.35408i 0.881041 + 0.473039i $$0.156843\pi$$
0.473039 + 0.881041i $$0.343157\pi$$
$$38$$ 0 0
$$39$$ −3.06060 0.813888i −0.0784769 0.0208689i
$$40$$ 0 0
$$41$$ −15.0731 −0.367637 −0.183819 0.982960i $$-0.558846\pi$$
−0.183819 + 0.982960i $$0.558846\pi$$
$$42$$ 0 0
$$43$$ −26.3634 26.3634i −0.613102 0.613102i 0.330651 0.943753i $$-0.392732\pi$$
−0.943753 + 0.330651i $$0.892732\pi$$
$$44$$ 0 0
$$45$$ 8.68231 + 31.9197i 0.192940 + 0.709326i
$$46$$ 0 0
$$47$$ 36.6067i 0.778866i 0.921055 + 0.389433i $$0.127329\pi$$
−0.921055 + 0.389433i $$0.872671\pi$$
$$48$$ 0 0
$$49$$ −4.29399 −0.0876325
$$50$$ 0 0
$$51$$ −17.3220 + 10.0445i −0.339646 + 0.196952i
$$52$$ 0 0
$$53$$ −50.9270 + 50.9270i −0.960887 + 0.960887i −0.999263 0.0383765i $$-0.987781\pi$$
0.0383765 + 0.999263i $$0.487781\pi$$
$$54$$ 0 0
$$55$$ 58.8202i 1.06946i
$$56$$ 0 0
$$57$$ 90.9971 + 24.1983i 1.59644 + 0.424532i
$$58$$ 0 0
$$59$$ 12.1683 12.1683i 0.206242 0.206242i −0.596426 0.802668i $$-0.703413\pi$$
0.802668 + 0.596426i $$0.203413\pi$$
$$60$$ 0 0
$$61$$ 27.5789 27.5789i 0.452113 0.452113i −0.443943 0.896055i $$-0.646421\pi$$
0.896055 + 0.443943i $$0.146421\pi$$
$$62$$ 0 0
$$63$$ −57.0238 32.6359i −0.905139 0.518030i
$$64$$ 0 0
$$65$$ 3.88006i 0.0596932i
$$66$$ 0 0
$$67$$ 4.84214 4.84214i 0.0722707 0.0722707i −0.670047 0.742318i $$-0.733726\pi$$
0.742318 + 0.670047i $$0.233726\pi$$
$$68$$ 0 0
$$69$$ −32.2636 55.6391i −0.467589 0.806364i
$$70$$ 0 0
$$71$$ −74.9072 −1.05503 −0.527515 0.849546i $$-0.676876\pi$$
−0.527515 + 0.849546i $$0.676876\pi$$
$$72$$ 0 0
$$73$$ 3.47110i 0.0475494i −0.999717 0.0237747i $$-0.992432\pi$$
0.999717 0.0237747i $$-0.00756843\pi$$
$$74$$ 0 0
$$75$$ 29.8212 17.2925i 0.397616 0.230567i
$$76$$ 0 0
$$77$$ −82.6105 82.6105i −1.07286 1.07286i
$$78$$ 0 0
$$79$$ 103.463 1.30966 0.654831 0.755775i $$-0.272740\pi$$
0.654831 + 0.755775i $$0.272740\pi$$
$$80$$ 0 0
$$81$$ −41.0292 69.8399i −0.506533 0.862221i
$$82$$ 0 0
$$83$$ 31.7254 + 31.7254i 0.382233 + 0.382233i 0.871906 0.489673i $$-0.162884\pi$$
−0.489673 + 0.871906i $$0.662884\pi$$
$$84$$ 0 0
$$85$$ −17.3469 17.3469i −0.204081 0.204081i
$$86$$ 0 0
$$87$$ −1.68207 + 6.32538i −0.0193342 + 0.0727056i
$$88$$ 0 0
$$89$$ −78.2605 −0.879331 −0.439666 0.898162i $$-0.644903\pi$$
−0.439666 + 0.898162i $$0.644903\pi$$
$$90$$ 0 0
$$91$$ 5.44937 + 5.44937i 0.0598832 + 0.0598832i
$$92$$ 0 0
$$93$$ 21.9840 + 37.9118i 0.236387 + 0.407653i
$$94$$ 0 0
$$95$$ 115.361i 1.21433i
$$96$$ 0 0
$$97$$ −61.5651 −0.634692 −0.317346 0.948310i $$-0.602792\pi$$
−0.317346 + 0.948310i $$0.602792\pi$$
$$98$$ 0 0
$$99$$ −37.8034 138.981i −0.381853 1.40384i
$$100$$ 0 0
$$101$$ 56.9675 56.9675i 0.564034 0.564034i −0.366417 0.930451i $$-0.619415\pi$$
0.930451 + 0.366417i $$0.119415\pi$$
$$102$$ 0 0
$$103$$ 153.944i 1.49460i −0.664485 0.747301i $$-0.731349\pi$$
0.664485 0.747301i $$-0.268651\pi$$
$$104$$ 0 0
$$105$$ 20.6870 77.7927i 0.197019 0.740883i
$$106$$ 0 0
$$107$$ −76.9344 + 76.9344i −0.719013 + 0.719013i −0.968403 0.249390i $$-0.919770\pi$$
0.249390 + 0.968403i $$0.419770\pi$$
$$108$$ 0 0
$$109$$ −74.1271 + 74.1271i −0.680065 + 0.680065i −0.960015 0.279949i $$-0.909682\pi$$
0.279949 + 0.960015i $$0.409682\pi$$
$$110$$ 0 0
$$111$$ 54.6265 205.421i 0.492131 1.85064i
$$112$$ 0 0
$$113$$ 38.3909i 0.339742i 0.985466 + 0.169871i $$0.0543352\pi$$
−0.985466 + 0.169871i $$0.945665\pi$$
$$114$$ 0 0
$$115$$ 55.7191 55.7191i 0.484514 0.484514i
$$116$$ 0 0
$$117$$ 2.49369 + 9.16781i 0.0213136 + 0.0783573i
$$118$$ 0 0
$$119$$ 48.7259 0.409461
$$120$$ 0 0
$$121$$ 135.108i 1.11659i
$$122$$ 0 0
$$123$$ 22.6837 + 39.1184i 0.184420 + 0.318035i
$$124$$ 0 0
$$125$$ 94.8382 + 94.8382i 0.758706 + 0.758706i
$$126$$ 0 0
$$127$$ −43.3417 −0.341273 −0.170636 0.985334i $$-0.554582\pi$$
−0.170636 + 0.985334i $$0.554582\pi$$
$$128$$ 0 0
$$129$$ −28.7447 + 108.094i −0.222827 + 0.837935i
$$130$$ 0 0
$$131$$ −1.21414 1.21414i −0.00926827 0.00926827i 0.702457 0.711726i $$-0.252086\pi$$
−0.711726 + 0.702457i $$0.752086\pi$$
$$132$$ 0 0
$$133$$ −162.020 162.020i −1.21819 1.21819i
$$134$$ 0 0
$$135$$ 69.7730 70.5688i 0.516837 0.522732i
$$136$$ 0 0
$$137$$ −238.227 −1.73889 −0.869443 0.494033i $$-0.835522\pi$$
−0.869443 + 0.494033i $$0.835522\pi$$
$$138$$ 0 0
$$139$$ 26.5704 + 26.5704i 0.191154 + 0.191154i 0.796195 0.605041i $$-0.206843\pi$$
−0.605041 + 0.796195i $$0.706843\pi$$
$$140$$ 0 0
$$141$$ 95.0030 55.0897i 0.673780 0.390707i
$$142$$ 0 0
$$143$$ 16.8940i 0.118140i
$$144$$ 0 0
$$145$$ −8.01896 −0.0553032
$$146$$ 0 0
$$147$$ 6.46207 + 11.1439i 0.0439596 + 0.0758090i
$$148$$ 0 0
$$149$$ −133.254 + 133.254i −0.894321 + 0.894321i −0.994926 0.100605i $$-0.967922\pi$$
0.100605 + 0.994926i $$0.467922\pi$$
$$150$$ 0 0
$$151$$ 23.3716i 0.154779i −0.997001 0.0773895i $$-0.975342\pi$$
0.997001 0.0773895i $$-0.0246585\pi$$
$$152$$ 0 0
$$153$$ 52.1359 + 29.8385i 0.340758 + 0.195023i
$$154$$ 0 0
$$155$$ −37.9662 + 37.9662i −0.244943 + 0.244943i
$$156$$ 0 0
$$157$$ 95.8780 95.8780i 0.610688 0.610688i −0.332438 0.943125i $$-0.607871\pi$$
0.943125 + 0.332438i $$0.107871\pi$$
$$158$$ 0 0
$$159$$ 208.808 + 55.5272i 1.31326 + 0.349227i
$$160$$ 0 0
$$161$$ 156.510i 0.972113i
$$162$$ 0 0
$$163$$ 103.379 103.379i 0.634230 0.634230i −0.314896 0.949126i $$-0.601970\pi$$
0.949126 + 0.314896i $$0.101970\pi$$
$$164$$ 0 0
$$165$$ 152.652 88.5190i 0.925166 0.536479i
$$166$$ 0 0
$$167$$ 113.980 0.682515 0.341258 0.939970i $$-0.389147\pi$$
0.341258 + 0.939970i $$0.389147\pi$$
$$168$$ 0 0
$$169$$ 167.886i 0.993406i
$$170$$ 0 0
$$171$$ −74.1418 272.575i −0.433578 1.59401i
$$172$$ 0 0
$$173$$ −144.265 144.265i −0.833901 0.833901i 0.154147 0.988048i $$-0.450737\pi$$
−0.988048 + 0.154147i $$0.950737\pi$$
$$174$$ 0 0
$$175$$ −83.8857 −0.479347
$$176$$ 0 0
$$177$$ −49.8918 13.2674i −0.281875 0.0749573i
$$178$$ 0 0
$$179$$ 16.8240 + 16.8240i 0.0939888 + 0.0939888i 0.752538 0.658549i $$-0.228829\pi$$
−0.658549 + 0.752538i $$0.728829\pi$$
$$180$$ 0 0
$$181$$ −34.2037 34.2037i −0.188971 0.188971i 0.606280 0.795251i $$-0.292661\pi$$
−0.795251 + 0.606280i $$0.792661\pi$$
$$182$$ 0 0
$$183$$ −113.077 30.0700i −0.617909 0.164317i
$$184$$ 0 0
$$185$$ 260.421 1.40768
$$186$$ 0 0
$$187$$ 75.5295 + 75.5295i 0.403901 + 0.403901i
$$188$$ 0 0
$$189$$ 1.11765 + 197.104i 0.00591347 + 1.04288i
$$190$$ 0 0
$$191$$ 150.160i 0.786177i −0.919501 0.393088i $$-0.871407\pi$$
0.919501 0.393088i $$-0.128593\pi$$
$$192$$ 0 0
$$193$$ 117.637 0.609518 0.304759 0.952429i $$-0.401424\pi$$
0.304759 + 0.952429i $$0.401424\pi$$
$$194$$ 0 0
$$195$$ −10.0697 + 5.83913i −0.0516393 + 0.0299442i
$$196$$ 0 0
$$197$$ −31.8524 + 31.8524i −0.161688 + 0.161688i −0.783314 0.621626i $$-0.786472\pi$$
0.621626 + 0.783314i $$0.286472\pi$$
$$198$$ 0 0
$$199$$ 128.347i 0.644959i 0.946576 + 0.322480i $$0.104516\pi$$
−0.946576 + 0.322480i $$0.895484\pi$$
$$200$$ 0 0
$$201$$ −19.8535 5.27952i −0.0987735 0.0262663i
$$202$$ 0 0
$$203$$ 11.2623 11.2623i 0.0554793 0.0554793i
$$204$$ 0 0
$$205$$ −39.1746 + 39.1746i −0.191095 + 0.191095i
$$206$$ 0 0
$$207$$ −95.8429 + 167.464i −0.463009 + 0.809003i
$$208$$ 0 0
$$209$$ 502.290i 2.40330i
$$210$$ 0 0
$$211$$ −78.8045 + 78.8045i −0.373481 + 0.373481i −0.868743 0.495262i $$-0.835072\pi$$
0.495262 + 0.868743i $$0.335072\pi$$
$$212$$ 0 0
$$213$$ 112.728 + 194.402i 0.529241 + 0.912685i
$$214$$ 0 0
$$215$$ −137.035 −0.637372
$$216$$ 0 0
$$217$$ 106.644i 0.491447i
$$218$$ 0 0
$$219$$ −9.00834 + 5.22369i −0.0411340 + 0.0238525i
$$220$$ 0 0
$$221$$ −4.98228 4.98228i −0.0225442 0.0225442i
$$222$$ 0 0
$$223$$ −153.748 −0.689455 −0.344727 0.938703i $$-0.612029\pi$$
−0.344727 + 0.938703i $$0.612029\pi$$
$$224$$ 0 0
$$225$$ −89.7564 51.3695i −0.398917 0.228309i
$$226$$ 0 0
$$227$$ 43.6518 + 43.6518i 0.192299 + 0.192299i 0.796689 0.604390i $$-0.206583\pi$$
−0.604390 + 0.796689i $$0.706583\pi$$
$$228$$ 0 0
$$229$$ 111.882 + 111.882i 0.488566 + 0.488566i 0.907853 0.419288i $$-0.137720\pi$$
−0.419288 + 0.907853i $$0.637720\pi$$
$$230$$ 0 0
$$231$$ −90.0726 + 338.715i −0.389925 + 1.46630i
$$232$$ 0 0
$$233$$ −32.4793 −0.139396 −0.0696980 0.997568i $$-0.522204\pi$$
−0.0696980 + 0.997568i $$0.522204\pi$$
$$234$$ 0 0
$$235$$ 95.1395 + 95.1395i 0.404849 + 0.404849i
$$236$$ 0 0
$$237$$ −155.703 268.512i −0.656974 1.13296i
$$238$$ 0 0
$$239$$ 133.305i 0.557762i 0.960326 + 0.278881i $$0.0899636\pi$$
−0.960326 + 0.278881i $$0.910036\pi$$
$$240$$ 0 0
$$241$$ 159.670 0.662532 0.331266 0.943537i $$-0.392524\pi$$
0.331266 + 0.943537i $$0.392524\pi$$
$$242$$ 0 0
$$243$$ −119.506 + 211.583i −0.491793 + 0.870712i
$$244$$ 0 0
$$245$$ −11.1599 + 11.1599i −0.0455508 + 0.0455508i
$$246$$ 0 0
$$247$$ 33.1334i 0.134143i
$$248$$ 0 0
$$249$$ 34.5911 130.079i 0.138920 0.522404i
$$250$$ 0 0
$$251$$ 106.711 106.711i 0.425141 0.425141i −0.461828 0.886969i $$-0.652806\pi$$
0.886969 + 0.461828i $$0.152806\pi$$
$$252$$ 0 0
$$253$$ −242.605 + 242.605i −0.958913 + 0.958913i
$$254$$ 0 0
$$255$$ −18.9138 + 71.1246i −0.0741717 + 0.278920i
$$256$$ 0 0
$$257$$ 343.816i 1.33781i 0.743350 + 0.668903i $$0.233236\pi$$
−0.743350 + 0.668903i $$0.766764\pi$$
$$258$$ 0 0
$$259$$ −365.751 + 365.751i −1.41217 + 1.41217i
$$260$$ 0 0
$$261$$ 18.9472 5.15374i 0.0725948 0.0197461i
$$262$$ 0 0
$$263$$ −266.255 −1.01238 −0.506188 0.862423i $$-0.668946\pi$$
−0.506188 + 0.862423i $$0.668946\pi$$
$$264$$ 0 0
$$265$$ 264.715i 0.998925i
$$266$$ 0 0
$$267$$ 117.775 + 203.104i 0.441104 + 0.760691i
$$268$$ 0 0
$$269$$ 102.194 + 102.194i 0.379904 + 0.379904i 0.871067 0.491164i $$-0.163428\pi$$
−0.491164 + 0.871067i $$0.663428\pi$$
$$270$$ 0 0
$$271$$ −38.5636 −0.142301 −0.0711505 0.997466i $$-0.522667\pi$$
−0.0711505 + 0.997466i $$0.522667\pi$$
$$272$$ 0 0
$$273$$ 5.94161 22.3432i 0.0217641 0.0818433i
$$274$$ 0 0
$$275$$ −130.030 130.030i −0.472838 0.472838i
$$276$$ 0 0
$$277$$ 277.306 + 277.306i 1.00111 + 1.00111i 0.999999 + 0.00110593i $$0.000352027\pi$$
0.00110593 + 0.999999i $$0.499648\pi$$
$$278$$ 0 0
$$279$$ 65.3061 114.107i 0.234072 0.408987i
$$280$$ 0 0
$$281$$ 458.765 1.63262 0.816308 0.577617i $$-0.196017\pi$$
0.816308 + 0.577617i $$0.196017\pi$$
$$282$$ 0 0
$$283$$ −276.746 276.746i −0.977900 0.977900i 0.0218614 0.999761i $$-0.493041\pi$$
−0.999761 + 0.0218614i $$0.993041\pi$$
$$284$$ 0 0
$$285$$ 299.389 173.608i 1.05049 0.609149i
$$286$$ 0 0
$$287$$ 110.038i 0.383408i
$$288$$ 0 0
$$289$$ 244.451 0.845850
$$290$$ 0 0
$$291$$ 92.6499 + 159.776i 0.318384 + 0.549059i
$$292$$ 0 0
$$293$$ 306.513 306.513i 1.04612 1.04612i 0.0472370 0.998884i $$-0.484958\pi$$
0.998884 0.0472370i $$-0.0150416\pi$$
$$294$$ 0 0
$$295$$ 63.2500i 0.214407i
$$296$$ 0 0
$$297$$ −303.797 + 307.262i −1.02289 + 1.03455i
$$298$$ 0 0
$$299$$ 16.0033 16.0033i 0.0535229 0.0535229i
$$300$$ 0 0
$$301$$ 192.460 192.460i 0.639401 0.639401i
$$302$$ 0 0
$$303$$ −233.575 62.1133i −0.770874 0.204994i
$$304$$ 0 0
$$305$$ 143.353i 0.470010i
$$306$$ 0 0
$$307$$ 359.692 359.692i 1.17163 1.17163i 0.189814 0.981820i $$-0.439211\pi$$
0.981820 0.189814i $$-0.0607886\pi$$
$$308$$ 0 0
$$309$$ −399.521 + 231.672i −1.29295 + 0.749746i
$$310$$ 0 0
$$311$$ 572.008 1.83925 0.919626 0.392794i $$-0.128492\pi$$
0.919626 + 0.392794i $$0.128492\pi$$
$$312$$ 0 0
$$313$$ 333.314i 1.06490i 0.846461 + 0.532450i $$0.178729\pi$$
−0.846461 + 0.532450i $$0.821271\pi$$
$$314$$ 0 0
$$315$$ −233.022 + 63.3832i −0.739754 + 0.201217i
$$316$$ 0 0
$$317$$ 266.382 + 266.382i 0.840322 + 0.840322i 0.988901 0.148578i $$-0.0474697\pi$$
−0.148578 + 0.988901i $$0.547470\pi$$
$$318$$ 0 0
$$319$$ 34.9151 0.109452
$$320$$ 0 0
$$321$$ 315.442 + 83.8838i 0.982686 + 0.261320i
$$322$$ 0 0
$$323$$ 148.132 + 148.132i 0.458613 + 0.458613i
$$324$$ 0 0
$$325$$ 8.57741 + 8.57741i 0.0263920 + 0.0263920i
$$326$$ 0 0
$$327$$ 303.932 + 80.8229i 0.929455 + 0.247165i
$$328$$ 0 0
$$329$$ −267.239 −0.812276
$$330$$ 0 0
$$331$$ 212.431 + 212.431i 0.641787 + 0.641787i 0.950995 0.309208i $$-0.100064\pi$$
−0.309208 + 0.950995i $$0.600064\pi$$
$$332$$ 0 0
$$333$$ −615.325 + 167.371i −1.84782 + 0.502617i
$$334$$ 0 0
$$335$$ 25.1691i 0.0751317i
$$336$$ 0 0
$$337$$ −207.477 −0.615658 −0.307829 0.951442i $$-0.599602\pi$$
−0.307829 + 0.951442i $$0.599602\pi$$
$$338$$ 0 0
$$339$$ 99.6335 57.7748i 0.293904 0.170427i
$$340$$ 0 0
$$341$$ 165.308 165.308i 0.484773 0.484773i
$$342$$ 0 0
$$343$$ 326.366i 0.951505i
$$344$$ 0 0
$$345$$ −228.456 60.7521i −0.662192 0.176093i
$$346$$ 0 0
$$347$$ 98.4692 98.4692i 0.283773 0.283773i −0.550839 0.834612i $$-0.685692\pi$$
0.834612 + 0.550839i $$0.185692\pi$$
$$348$$ 0 0
$$349$$ 337.382 337.382i 0.966711 0.966711i −0.0327527 0.999463i $$-0.510427\pi$$
0.999463 + 0.0327527i $$0.0104274\pi$$
$$350$$ 0 0
$$351$$ 20.0399 20.2684i 0.0570936 0.0577448i
$$352$$ 0 0
$$353$$ 293.330i 0.830964i 0.909601 + 0.415482i $$0.136387\pi$$
−0.909601 + 0.415482i $$0.863613\pi$$
$$354$$ 0 0
$$355$$ −194.681 + 194.681i −0.548398 + 0.548398i
$$356$$ 0 0
$$357$$ −73.3279 126.455i −0.205400 0.354216i
$$358$$ 0 0
$$359$$ 305.954 0.852239 0.426119 0.904667i $$-0.359880\pi$$
0.426119 + 0.904667i $$0.359880\pi$$
$$360$$ 0 0
$$361$$ 624.114i 1.72885i
$$362$$ 0 0
$$363$$ −350.636 + 203.324i −0.965939 + 0.560122i
$$364$$ 0 0
$$365$$ −9.02128 9.02128i −0.0247158 0.0247158i
$$366$$ 0 0
$$367$$ 221.149 0.602585 0.301292 0.953532i $$-0.402582\pi$$
0.301292 + 0.953532i $$0.402582\pi$$
$$368$$ 0 0
$$369$$ 67.3845 117.739i 0.182614 0.319076i
$$370$$ 0 0
$$371$$ −371.781 371.781i −1.00211 1.00211i
$$372$$ 0 0
$$373$$ −147.216 147.216i −0.394682 0.394682i 0.481671 0.876352i $$-0.340030\pi$$
−0.876352 + 0.481671i $$0.840030\pi$$
$$374$$ 0 0
$$375$$ 103.405 388.850i 0.275746 1.03693i
$$376$$ 0 0
$$377$$ −2.30317 −0.00610919
$$378$$ 0 0
$$379$$ −298.572 298.572i −0.787790 0.787790i 0.193342 0.981131i $$-0.438067\pi$$
−0.981131 + 0.193342i $$0.938067\pi$$
$$380$$ 0 0
$$381$$ 65.2252 + 112.482i 0.171195 + 0.295228i
$$382$$ 0 0
$$383$$ 427.326i 1.11573i −0.829931 0.557866i $$-0.811620\pi$$
0.829931 0.557866i $$-0.188380\pi$$
$$384$$ 0 0
$$385$$ −429.404 −1.11533
$$386$$ 0 0
$$387$$ 323.787 88.0716i 0.836658 0.227575i
$$388$$ 0 0
$$389$$ 314.075 314.075i 0.807391 0.807391i −0.176847 0.984238i $$-0.556590\pi$$
0.984238 + 0.176847i $$0.0565899\pi$$
$$390$$ 0 0
$$391$$ 143.095i 0.365971i
$$392$$ 0 0
$$393$$ −1.32382 + 4.97816i −0.00336849 + 0.0126671i
$$394$$ 0 0
$$395$$ 268.898 268.898i 0.680753 0.680753i
$$396$$ 0 0
$$397$$ −189.839 + 189.839i −0.478185 + 0.478185i −0.904551 0.426366i $$-0.859794\pi$$
0.426366 + 0.904551i $$0.359794\pi$$
$$398$$ 0 0
$$399$$ −176.655 + 664.304i −0.442743 + 1.66492i
$$400$$ 0 0
$$401$$ 268.223i 0.668886i 0.942416 + 0.334443i $$0.108548\pi$$
−0.942416 + 0.334443i $$0.891452\pi$$
$$402$$ 0 0
$$403$$ −10.9045 + 10.9045i −0.0270582 + 0.0270582i
$$404$$ 0 0
$$405$$ −288.145 74.8780i −0.711469 0.184884i
$$406$$ 0 0
$$407$$ −1133.89 −2.78598
$$408$$ 0 0
$$409$$ 25.8478i 0.0631976i −0.999501 0.0315988i $$-0.989940\pi$$
0.999501 0.0315988i $$-0.0100599\pi$$
$$410$$ 0 0
$$411$$ 358.510 + 618.257i 0.872288 + 1.50427i
$$412$$ 0 0
$$413$$ 88.8319 + 88.8319i 0.215089 + 0.215089i
$$414$$ 0 0
$$415$$ 164.906 0.397365
$$416$$ 0 0
$$417$$ 28.9705 108.942i 0.0694735 0.261253i
$$418$$ 0 0
$$419$$ −243.361 243.361i −0.580813 0.580813i 0.354313 0.935127i $$-0.384715\pi$$
−0.935127 + 0.354313i $$0.884715\pi$$
$$420$$ 0 0
$$421$$ −115.847 115.847i −0.275171 0.275171i 0.556007 0.831178i $$-0.312333\pi$$
−0.831178 + 0.556007i $$0.812333\pi$$
$$422$$ 0 0
$$423$$ −285.942 163.650i −0.675985 0.386880i
$$424$$ 0 0
$$425$$ 76.6953 0.180460
$$426$$ 0 0
$$427$$ 201.333 + 201.333i 0.471507 + 0.471507i
$$428$$ 0 0
$$429$$ 43.8440 25.4240i 0.102201 0.0592634i
$$430$$ 0 0
$$431$$ 568.037i 1.31795i −0.752165 0.658975i $$-0.770990\pi$$
0.752165 0.658975i $$-0.229010\pi$$
$$432$$ 0 0
$$433$$ −647.222 −1.49474 −0.747370 0.664408i $$-0.768684\pi$$
−0.747370 + 0.664408i $$0.768684\pi$$
$$434$$ 0 0
$$435$$ 12.0678 + 20.8111i 0.0277421 + 0.0478416i
$$436$$ 0 0
$$437$$ −475.808 + 475.808i −1.08881 + 1.08881i
$$438$$ 0 0
$$439$$ 486.389i 1.10795i −0.832534 0.553973i $$-0.813111\pi$$
0.832534 0.553973i $$-0.186889\pi$$
$$440$$ 0 0
$$441$$ 19.1963 33.5412i 0.0435291 0.0760571i
$$442$$ 0 0
$$443$$ −258.469 + 258.469i −0.583451 + 0.583451i −0.935850 0.352399i $$-0.885366\pi$$
0.352399 + 0.935850i $$0.385366\pi$$
$$444$$ 0 0
$$445$$ −203.396 + 203.396i −0.457070 + 0.457070i
$$446$$ 0 0
$$447$$ 546.360 + 145.290i 1.22228 + 0.325035i
$$448$$ 0 0
$$449$$ 498.015i 1.10916i −0.832129 0.554582i $$-0.812878\pi$$
0.832129 0.554582i $$-0.187122\pi$$
$$450$$ 0 0
$$451$$ 170.569 170.569i 0.378201 0.378201i
$$452$$ 0 0
$$453$$ −60.6549 + 35.1721i −0.133896 + 0.0776427i
$$454$$ 0 0
$$455$$ 28.3255 0.0622538
$$456$$ 0 0
$$457$$ 466.468i 1.02072i −0.859961 0.510359i $$-0.829513\pi$$
0.859961 0.510359i $$-0.170487\pi$$
$$458$$ 0 0
$$459$$ −1.02185 180.209i −0.00222624 0.392613i
$$460$$ 0 0
$$461$$ −389.251 389.251i −0.844362 0.844362i 0.145061 0.989423i $$-0.453662\pi$$
−0.989423 + 0.145061i $$0.953662\pi$$
$$462$$ 0 0
$$463$$ 500.857 1.08177 0.540883 0.841098i $$-0.318090\pi$$
0.540883 + 0.841098i $$0.318090\pi$$
$$464$$ 0 0
$$465$$ 155.667 + 41.3957i 0.334768 + 0.0890229i
$$466$$ 0 0
$$467$$ 188.836 + 188.836i 0.404359 + 0.404359i 0.879766 0.475407i $$-0.157699\pi$$
−0.475407 + 0.879766i $$0.657699\pi$$
$$468$$ 0 0
$$469$$ 35.3489 + 35.3489i 0.0753709 + 0.0753709i
$$470$$ 0 0
$$471$$ −393.113 104.538i −0.834636 0.221950i
$$472$$ 0 0
$$473$$ 596.660 1.26144
$$474$$ 0 0
$$475$$ −255.022 255.022i −0.536888 0.536888i
$$476$$ 0 0
$$477$$ −170.131 625.470i −0.356668 1.31126i
$$478$$ 0 0
$$479$$ 326.344i 0.681303i 0.940190 + 0.340652i $$0.110648\pi$$
−0.940190 + 0.340652i $$0.889352\pi$$
$$480$$ 0 0
$$481$$ 74.7969 0.155503
$$482$$ 0 0
$$483$$ 406.181 235.533i 0.840954 0.487647i
$$484$$ 0 0
$$485$$ −160.006 + 160.006i −0.329909 + 0.329909i
$$486$$ 0 0
$$487$$ 196.238i 0.402952i 0.979493 + 0.201476i $$0.0645739\pi$$
−0.979493 + 0.201476i $$0.935426\pi$$
$$488$$ 0 0
$$489$$ −423.871 112.718i −0.866812 0.230506i
$$490$$ 0 0
$$491$$ 349.172 349.172i 0.711144 0.711144i −0.255631 0.966774i $$-0.582283\pi$$
0.966774 + 0.255631i $$0.0822831\pi$$
$$492$$ 0 0
$$493$$ −10.2969 + 10.2969i −0.0208863 + 0.0208863i
$$494$$ 0 0
$$495$$ −459.456 262.956i −0.928193 0.531224i
$$496$$ 0 0
$$497$$ 546.843i 1.10029i
$$498$$ 0 0
$$499$$ 321.326 321.326i 0.643940 0.643940i −0.307582 0.951522i $$-0.599520\pi$$
0.951522 + 0.307582i $$0.0995198\pi$$
$$500$$ 0 0
$$501$$ −171.530 295.805i −0.342374 0.590430i
$$502$$ 0 0
$$503$$ 623.698 1.23996 0.619978 0.784619i $$-0.287142\pi$$
0.619978 + 0.784619i $$0.287142\pi$$
$$504$$ 0 0
$$505$$ 296.113i 0.586362i
$$506$$ 0 0
$$507$$ 435.703 252.652i 0.859374 0.498328i
$$508$$ 0 0
$$509$$ 452.448 + 452.448i 0.888897 + 0.888897i 0.994417 0.105520i $$-0.0336508\pi$$
−0.105520 + 0.994417i $$0.533651\pi$$
$$510$$ 0 0
$$511$$ 25.3400 0.0495891
$$512$$ 0 0
$$513$$ −595.821 + 602.616i −1.16144 + 1.17469i
$$514$$ 0 0
$$515$$ −400.095 400.095i −0.776884 0.776884i
$$516$$ 0 0
$$517$$ −414.244 414.244i −0.801247 0.801247i
$$518$$ 0 0
$$519$$ −157.296 + 591.506i −0.303075 + 1.13970i
$$520$$ 0 0
$$521$$ 444.986 0.854100 0.427050 0.904228i $$-0.359553\pi$$
0.427050 + 0.904228i $$0.359553\pi$$
$$522$$ 0 0
$$523$$ −399.942 399.942i −0.764707 0.764707i 0.212462 0.977169i $$-0.431852\pi$$
−0.977169 + 0.212462i $$0.931852\pi$$
$$524$$ 0 0
$$525$$ 126.240 + 217.703i 0.240458 + 0.414673i
$$526$$ 0 0
$$527$$ 97.5029i 0.185015i
$$528$$ 0 0
$$529$$ −69.3715 −0.131137
$$530$$ 0 0
$$531$$ 40.6504 + 149.447i 0.0765544 + 0.281445i
$$532$$ 0 0
$$533$$ −11.2515 + 11.2515i −0.0211098 + 0.0211098i
$$534$$ 0 0
$$535$$ 399.900i 0.747476i
$$536$$ 0 0
$$537$$ 18.3437 68.9808i 0.0341595 0.128456i
$$538$$ 0 0
$$539$$ 48.5912 48.5912i 0.0901506 0.0901506i
$$540$$ 0 0
$$541$$ 116.940 116.940i 0.216155 0.216155i −0.590721 0.806876i $$-0.701156\pi$$
0.806876 + 0.590721i $$0.201156\pi$$
$$542$$ 0 0
$$543$$ −37.2932 + 140.240i −0.0686800 + 0.258269i
$$544$$ 0 0
$$545$$ 385.308i 0.706987i
$$546$$ 0 0
$$547$$ −85.6914 + 85.6914i −0.156657 + 0.156657i −0.781084 0.624427i $$-0.785333\pi$$
0.624427 + 0.781084i $$0.285333\pi$$
$$548$$ 0 0
$$549$$ 92.1322 + 338.715i 0.167818 + 0.616968i
$$550$$ 0 0
$$551$$ 68.4772 0.124278
$$552$$ 0 0
$$553$$ 755.311i 1.36584i
$$554$$ 0 0
$$555$$ −391.910 675.855i −0.706145 1.21776i
$$556$$ 0 0
$$557$$ 104.194 + 104.194i 0.187062 + 0.187062i 0.794425 0.607363i $$-0.207772\pi$$
−0.607363 + 0.794425i $$0.707772\pi$$
$$558$$ 0 0
$$559$$ −39.3585 −0.0704087
$$560$$ 0 0
$$561$$ 82.3519 309.682i 0.146795 0.552017i
$$562$$ 0 0
$$563$$ 776.673 + 776.673i 1.37953 + 1.37953i 0.845414 + 0.534111i $$0.179354\pi$$
0.534111 + 0.845414i $$0.320646\pi$$
$$564$$ 0 0
$$565$$ 99.7766 + 99.7766i 0.176596 + 0.176596i
$$566$$ 0 0
$$567$$ 509.850 299.524i 0.899207 0.528261i
$$568$$ 0 0
$$569$$ −456.546 −0.802366 −0.401183 0.915998i $$-0.631401\pi$$
−0.401183 + 0.915998i $$0.631401\pi$$
$$570$$ 0 0
$$571$$ 475.108 + 475.108i 0.832062 + 0.832062i 0.987799 0.155736i $$-0.0497750\pi$$
−0.155736 + 0.987799i $$0.549775\pi$$
$$572$$ 0 0
$$573$$ −389.700 + 225.977i −0.680105 + 0.394375i
$$574$$ 0 0
$$575$$ 246.350i 0.428434i
$$576$$ 0 0
$$577$$ 1127.70 1.95443 0.977213 0.212262i $$-0.0680832\pi$$
0.977213 + 0.212262i $$0.0680832\pi$$
$$578$$ 0 0
$$579$$ −177.033 305.296i −0.305756 0.527281i
$$580$$ 0 0
$$581$$ −231.604 + 231.604i −0.398630 + 0.398630i
$$582$$ 0 0
$$583$$ 1152.59i 1.97700i
$$584$$ 0 0
$$585$$ 30.3078 + 17.3458i 0.0518082 + 0.0296509i
$$586$$ 0 0
$$587$$ −584.236 + 584.236i −0.995292 + 0.995292i −0.999989 0.00469688i $$-0.998505\pi$$
0.00469688 + 0.999989i $$0.498505\pi$$
$$588$$ 0 0
$$589$$ 324.209 324.209i 0.550440 0.550440i
$$590$$ 0 0
$$591$$ 130.600 + 34.7296i 0.220981 + 0.0587642i
$$592$$ 0 0
$$593$$ 870.906i 1.46864i 0.678801 + 0.734322i $$0.262500\pi$$
−0.678801 + 0.734322i $$0.737500\pi$$
$$594$$ 0 0
$$595$$ 126.637 126.637i 0.212835 0.212835i
$$596$$ 0 0
$$597$$ 333.090 193.150i 0.557940 0.323535i
$$598$$ 0 0
$$599$$ −224.305 −0.374466 −0.187233 0.982316i $$-0.559952\pi$$
−0.187233 + 0.982316i $$0.559952\pi$$
$$600$$ 0 0
$$601$$ 234.358i 0.389946i 0.980809 + 0.194973i $$0.0624620\pi$$
−0.980809 + 0.194973i $$0.937538\pi$$
$$602$$ 0 0
$$603$$ 16.1760 + 59.4697i 0.0268259 + 0.0986230i
$$604$$ 0 0
$$605$$ −351.140 351.140i −0.580396 0.580396i
$$606$$ 0 0
$$607$$ −620.755 −1.02266 −0.511330 0.859384i $$-0.670847\pi$$
−0.511330 + 0.859384i $$0.670847\pi$$
$$608$$ 0 0
$$609$$ −46.1770 12.2796i −0.0758244 0.0201635i
$$610$$ 0 0
$$611$$ 27.3255 + 27.3255i 0.0447226 + 0.0447226i
$$612$$ 0 0
$$613$$ 645.945 + 645.945i 1.05374 + 1.05374i 0.998471 + 0.0552724i $$0.0176027\pi$$
0.0552724 + 0.998471i $$0.482397\pi$$
$$614$$ 0 0
$$615$$ 160.621 + 42.7131i 0.261173 + 0.0694523i
$$616$$ 0 0
$$617$$ −169.883 −0.275337 −0.137669 0.990478i $$-0.543961\pi$$
−0.137669 + 0.990478i $$0.543961\pi$$
$$618$$ 0 0
$$619$$ 647.603 + 647.603i 1.04621 + 1.04621i 0.998879 + 0.0473286i $$0.0150708\pi$$
0.0473286 + 0.998879i $$0.484929\pi$$
$$620$$ 0 0
$$621$$ 578.842 3.28222i 0.932113 0.00528539i
$$622$$ 0 0
$$623$$ 571.323i 0.917051i
$$624$$ 0 0
$$625$$ 205.694 0.329110
$$626$$ 0 0
$$627$$ −1303.56 + 755.900i −2.07904 + 1.20558i
$$628$$ 0 0
$$629$$ 334.400 334.400i 0.531638 0.531638i
$$630$$ 0 0
$$631$$ 975.374i 1.54576i 0.634553 + 0.772880i $$0.281184\pi$$
−0.634553 + 0.772880i $$0.718816\pi$$
$$632$$ 0 0
$$633$$ 323.110 + 85.9228i 0.510442 + 0.135739i
$$634$$ 0 0
$$635$$ −112.643 + 112.643i −0.177391 + 0.177391i
$$636$$ 0 0
$$637$$ −3.20530 + 3.20530i −0.00503187 + 0.00503187i
$$638$$ 0 0
$$639$$ 334.873 585.114i 0.524058 0.915671i
$$640$$ 0 0
$$641$$ 771.555i 1.20367i −0.798619 0.601837i $$-0.794436\pi$$
0.798619 0.601837i $$-0.205564\pi$$
$$642$$ 0 0
$$643$$ −319.214 + 319.214i −0.496445 + 0.496445i −0.910330 0.413884i $$-0.864172\pi$$
0.413884 + 0.910330i $$0.364172\pi$$
$$644$$ 0 0
$$645$$ 206.225 + 355.638i 0.319729 + 0.551377i
$$646$$ 0 0
$$647$$ 360.720 0.557527 0.278764 0.960360i $$-0.410075\pi$$
0.278764 + 0.960360i $$0.410075\pi$$
$$648$$ 0 0
$$649$$ 275.395i 0.424338i
$$650$$ 0 0
$$651$$ −276.766 + 160.489i −0.425140 + 0.246527i
$$652$$ 0 0
$$653$$ 415.043 + 415.043i 0.635595 + 0.635595i 0.949466 0.313871i $$-0.101626\pi$$
−0.313871 + 0.949466i $$0.601626\pi$$
$$654$$ 0 0
$$655$$ −6.31104 −0.00963517
$$656$$ 0 0
$$657$$ 27.1134 + 15.5176i 0.0412685 + 0.0236189i
$$658$$ 0 0
$$659$$ −363.535 363.535i −0.551646 0.551646i 0.375269 0.926916i $$-0.377550\pi$$
−0.926916 + 0.375269i $$0.877550\pi$$
$$660$$ 0 0
$$661$$ 151.997 + 151.997i 0.229951 + 0.229951i 0.812672 0.582721i $$-0.198012\pi$$
−0.582721 + 0.812672i $$0.698012\pi$$
$$662$$ 0 0
$$663$$ −5.43232 + 20.4280i −0.00819354 + 0.0308115i
$$664$$ 0 0
$$665$$ −842.166 −1.26642
$$666$$ 0 0
$$667$$ −33.0743 33.0743i −0.0495867 0.0495867i
$$668$$ 0 0
$$669$$ 231.377 + 399.013i 0.345855 + 0.596433i
$$670$$ 0 0
$$671$$ 624.170i 0.930208i
$$672$$ 0 0
$$673$$ −271.149 −0.402896 −0.201448 0.979499i $$-0.564565\pi$$
−0.201448 + 0.979499i $$0.564565\pi$$
$$674$$ 0 0
$$675$$ 1.75919 + 310.245i 0.00260621 + 0.459623i
$$676$$ 0 0
$$677$$ 639.750 639.750i 0.944978 0.944978i −0.0535849 0.998563i $$-0.517065\pi$$
0.998563 + 0.0535849i $$0.0170648\pi$$
$$678$$ 0 0
$$679$$ 449.442i 0.661918i
$$680$$ 0 0
$$681$$ 47.5948 178.979i 0.0698895 0.262817i
$$682$$ 0 0
$$683$$ −93.1730 + 93.1730i −0.136417 + 0.136417i −0.772018 0.635601i $$-0.780752\pi$$
0.635601 + 0.772018i $$0.280752\pi$$
$$684$$ 0 0
$$685$$ −619.145 + 619.145i −0.903861 + 0.903861i
$$686$$ 0 0
$$687$$ 121.988 458.731i 0.177566 0.667730i
$$688$$ 0 0
$$689$$ 76.0301i 0.110348i
$$690$$ 0 0
$$691$$ −303.844 + 303.844i −0.439716 + 0.439716i −0.891916 0.452200i $$-0.850639\pi$$
0.452200 + 0.891916i $$0.350639\pi$$
$$692$$ 0 0
$$693$$ 1014.60 275.975i 1.46406 0.398233i
$$694$$ 0 0
$$695$$ 138.111 0.198721
$$696$$ 0 0
$$697$$ 100.606i 0.144341i
$$698$$ 0 0
$$699$$ 48.8783 + 84.2914i 0.0699261 + 0.120589i
$$700$$ 0 0
$$701$$ −797.170 797.170i −1.13719 1.13719i −0.988952 0.148238i $$-0.952640\pi$$
−0.148238 0.988952i $$-0.547360\pi$$
$$702$$ 0 0
$$703$$ −2223.85 −3.16336
$$704$$ 0 0
$$705$$ 103.733 390.086i 0.147140 0.553313i
$$706$$ 0 0
$$707$$ 415.878 + 415.878i 0.588229 + 0.588229i
$$708$$ 0 0
$$709$$ −592.848 592.848i −0.836176 0.836176i 0.152178 0.988353i $$-0.451371\pi$$
−0.988353 + 0.152178i $$0.951371\pi$$
$$710$$ 0 0
$$711$$ −462.533 + 808.171i −0.650539 + 1.13667i
$$712$$ 0 0
$$713$$ −313.185 −0.439249
$$714$$ 0 0
$$715$$ 43.9070 + 43.9070i 0.0614084 + 0.0614084i
$$716$$ 0 0
$$717$$ 345.959 200.612i 0.482508 0.279794i
$$718$$ 0 0
$$719$$ 1252.89i 1.74255i 0.490799 + 0.871273i $$0.336705\pi$$
−0.490799 + 0.871273i $$0.663295\pi$$
$$720$$ 0 0
$$721$$ 1123.83 1.55872
$$722$$ 0 0
$$723$$ −240.289 414.382i −0.332350 0.573142i
$$724$$ 0 0
$$725$$ 17.7270 17.7270i 0.0244511 0.0244511i
$$726$$ 0 0
$$727$$ 1182.91i 1.62711i 0.581490 + 0.813553i $$0.302470\pi$$
−0.581490 + 0.813553i $$0.697530\pi$$
$$728$$ 0 0
$$729$$ 728.953 8.26707i 0.999936 0.0113403i
$$730$$ 0 0
$$731$$ −175.963 + 175.963i −0.240715 + 0.240715i
$$732$$ 0 0
$$733$$ −679.023 + 679.023i −0.926361 + 0.926361i −0.997469 0.0711072i $$-0.977347\pi$$
0.0711072 + 0.997469i $$0.477347\pi$$
$$734$$ 0 0
$$735$$ 45.7574 + 12.1680i 0.0622549 + 0.0165551i
$$736$$ 0 0
$$737$$ 109.588i 0.148695i
$$738$$ 0 0
$$739$$ −408.587 + 408.587i −0.552892 + 0.552892i −0.927274 0.374383i $$-0.877855\pi$$
0.374383 + 0.927274i $$0.377855\pi$$
$$740$$ 0 0
$$741$$ 85.9889 49.8627i 0.116044 0.0672911i
$$742$$ 0 0
$$743$$ −228.202 −0.307137 −0.153568 0.988138i $$-0.549077\pi$$
−0.153568 + 0.988138i $$0.549077\pi$$
$$744$$ 0 0
$$745$$ 692.644i 0.929724i
$$746$$ 0 0
$$747$$ −389.641 + 105.984i −0.521608 + 0.141880i
$$748$$ 0 0
$$749$$ −561.642 561.642i −0.749856 0.749856i
$$750$$ 0 0
$$751$$ 835.943 1.11311 0.556553 0.830812i $$-0.312124\pi$$
0.556553 + 0.830812i $$0.312124\pi$$
$$752$$ 0 0
$$753$$ −437.528 116.350i −0.581047 0.154515i
$$754$$ 0 0
$$755$$ −60.7421 60.7421i −0.0804530 0.0804530i
$$756$$ 0 0
$$757$$ −144.017 144.017i −0.190247 0.190247i 0.605556 0.795803i $$-0.292951\pi$$
−0.795803 + 0.605556i $$0.792951\pi$$
$$758$$ 0 0
$$759$$ 994.715 + 264.519i 1.31056 + 0.348510i
$$760$$ 0 0
$$761$$ −1238.49 −1.62745 −0.813727 0.581247i $$-0.802565\pi$$
−0.813727 + 0.581247i $$0.802565\pi$$
$$762$$ 0 0
$$763$$ −541.148 541.148i −0.709238 0.709238i
$$764$$ 0 0
$$765$$ 213.049 57.9503i 0.278495 0.0757520i
$$766$$ 0 0
$$767$$ 18.1663i 0.0236849i
$$768$$ 0 0
$$769$$ −906.729 −1.17910 −0.589551 0.807732i $$-0.700695\pi$$
−0.589551 + 0.807732i $$0.700695\pi$$
$$770$$ 0 0
$$771$$ 892.284 517.411i 1.15731 0.671091i
$$772$$ 0 0
$$773$$ −989.152 + 989.152i −1.27963 + 1.27963i −0.338752 + 0.940876i $$0.610005\pi$$
−0.940876 + 0.338752i $$0.889995\pi$$
$$774$$ 0 0
$$775$$ 167.859i 0.216593i
$$776$$ 0 0
$$777$$ 1499.63 + 398.789i 1.93003 + 0.513241i
$$778$$ 0 0
$$779$$ 334.528 334.528i 0.429432 0.429432i
$$780$$ 0 0
$$781$$ 847.656 847.656i 1.08535 1.08535i
$$782$$ 0 0
$$783$$ −41.8890 41.4166i −0.0534981 0.0528948i
$$784$$ 0 0
$$785$$ 498.367i 0.634862i
$$786$$ 0 0
$$787$$ −100.012 + 100.012i −0.127080 + 0.127080i −0.767786 0.640706i $$-0.778642\pi$$
0.640706 + 0.767786i $$0.278642\pi$$
$$788$$ 0 0
$$789$$ 400.689 + 690.994i 0.507844 + 0.875785i
$$790$$ 0 0
$$791$$ −280.264 −0.354316
$$792$$ 0 0
$$793$$ 41.1731i 0.0519207i
$$794$$ 0 0
$$795$$ 686.998 398.372i 0.864149 0.501097i
$$796$$ 0