# Properties

 Label 252.4.k.f.109.2 Level $252$ Weight $4$ Character 252.109 Analytic conductor $14.868$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 252.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.8684813214$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{193})$$ Defining polynomial: $$x^{4} - x^{3} + 49 x^{2} + 48 x + 2304$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 84) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 109.2 Root $$-3.22311 - 5.58259i$$ of defining polynomial Character $$\chi$$ $$=$$ 252.109 Dual form 252.4.k.f.37.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(6.22311 + 10.7787i) q^{5} +(15.3924 - 10.2992i) q^{7} +O(q^{10})$$ $$q+(6.22311 + 10.7787i) q^{5} +(15.3924 - 10.2992i) q^{7} +(-25.5618 + 44.2743i) q^{11} +37.2311 q^{13} +(11.1076 - 19.2389i) q^{17} +(-27.1693 - 47.0587i) q^{19} +(88.4622 + 153.221i) q^{23} +(-14.9542 + 25.9015i) q^{25} -61.0916 q^{29} +(-159.962 + 277.063i) q^{31} +(206.801 + 101.818i) q^{35} +(157.540 + 272.867i) q^{37} +206.032 q^{41} +339.661 q^{43} +(71.0320 + 123.031i) q^{47} +(130.855 - 317.058i) q^{49} +(155.008 - 268.482i) q^{53} -636.295 q^{55} +(-140.825 + 243.916i) q^{59} +(271.924 + 470.987i) q^{61} +(231.693 + 401.305i) q^{65} +(239.680 - 415.137i) q^{67} -1105.63 q^{71} +(-119.675 + 207.283i) q^{73} +(62.5298 + 944.754i) q^{77} +(-580.333 - 1005.17i) q^{79} +2.93158 q^{83} +276.494 q^{85} +(-639.371 - 1107.42i) q^{89} +(573.078 - 383.449i) q^{91} +(338.156 - 585.703i) q^{95} +79.0596 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 11q^{5} + 6q^{7} + O(q^{10})$$ $$4q + 11q^{5} + 6q^{7} - 5q^{11} + 10q^{13} + 100q^{17} - 67q^{19} + 76q^{23} + 93q^{25} - 550q^{29} - 362q^{31} + 466q^{35} + 5q^{37} + 324q^{41} + 1442q^{43} - 216q^{47} + 190q^{49} + 495q^{53} - 1406q^{55} + 173q^{59} + 532q^{61} + 510q^{65} - 111q^{67} - 3200q^{71} - 1215q^{73} + 653q^{77} - 1460q^{79} + 2818q^{83} + 328q^{85} - 1974q^{89} + 1945q^{91} + 658q^{95} + 1122q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 6.22311 + 10.7787i 0.556612 + 0.964080i 0.997776 + 0.0666538i $$0.0212323\pi$$
−0.441164 + 0.897426i $$0.645434\pi$$
$$6$$ 0 0
$$7$$ 15.3924 10.2992i 0.831114 0.556102i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −25.5618 + 44.2743i −0.700651 + 1.21356i 0.267587 + 0.963534i $$0.413774\pi$$
−0.968238 + 0.250030i $$0.919559\pi$$
$$12$$ 0 0
$$13$$ 37.2311 0.794312 0.397156 0.917751i $$-0.369997\pi$$
0.397156 + 0.917751i $$0.369997\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 11.1076 19.2389i 0.158469 0.274477i −0.775848 0.630920i $$-0.782677\pi$$
0.934317 + 0.356444i $$0.116011\pi$$
$$18$$ 0 0
$$19$$ −27.1693 47.0587i −0.328056 0.568210i 0.654070 0.756434i $$-0.273060\pi$$
−0.982126 + 0.188224i $$0.939727\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 88.4622 + 153.221i 0.801985 + 1.38908i 0.918308 + 0.395867i $$0.129556\pi$$
−0.116323 + 0.993211i $$0.537111\pi$$
$$24$$ 0 0
$$25$$ −14.9542 + 25.9015i −0.119634 + 0.207212i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −61.0916 −0.391187 −0.195593 0.980685i $$-0.562663\pi$$
−0.195593 + 0.980685i $$0.562663\pi$$
$$30$$ 0 0
$$31$$ −159.962 + 277.063i −0.926776 + 1.60522i −0.138097 + 0.990419i $$0.544099\pi$$
−0.788679 + 0.614805i $$0.789235\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 206.801 + 101.818i 0.998735 + 0.491727i
$$36$$ 0 0
$$37$$ 157.540 + 272.867i 0.699984 + 1.21241i 0.968471 + 0.249125i $$0.0801430\pi$$
−0.268487 + 0.963283i $$0.586524\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 206.032 0.784800 0.392400 0.919795i $$-0.371645\pi$$
0.392400 + 0.919795i $$0.371645\pi$$
$$42$$ 0 0
$$43$$ 339.661 1.20460 0.602301 0.798269i $$-0.294251\pi$$
0.602301 + 0.798269i $$0.294251\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 71.0320 + 123.031i 0.220449 + 0.381828i 0.954944 0.296785i $$-0.0959146\pi$$
−0.734496 + 0.678613i $$0.762581\pi$$
$$48$$ 0 0
$$49$$ 130.855 317.058i 0.381500 0.924369i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 155.008 268.482i 0.401736 0.695826i −0.592200 0.805791i $$-0.701740\pi$$
0.993936 + 0.109965i $$0.0350738\pi$$
$$54$$ 0 0
$$55$$ −636.295 −1.55996
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −140.825 + 243.916i −0.310743 + 0.538223i −0.978523 0.206136i $$-0.933911\pi$$
0.667780 + 0.744358i $$0.267245\pi$$
$$60$$ 0 0
$$61$$ 271.924 + 470.987i 0.570760 + 0.988585i 0.996488 + 0.0837341i $$0.0266846\pi$$
−0.425728 + 0.904851i $$0.639982\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 231.693 + 401.305i 0.442123 + 0.765780i
$$66$$ 0 0
$$67$$ 239.680 415.137i 0.437038 0.756971i −0.560422 0.828207i $$-0.689361\pi$$
0.997459 + 0.0712360i $$0.0226943\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −1105.63 −1.84809 −0.924046 0.382280i $$-0.875139\pi$$
−0.924046 + 0.382280i $$0.875139\pi$$
$$72$$ 0 0
$$73$$ −119.675 + 207.283i −0.191876 + 0.332338i −0.945872 0.324541i $$-0.894790\pi$$
0.753996 + 0.656879i $$0.228124\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 62.5298 + 944.754i 0.0925445 + 1.39824i
$$78$$ 0 0
$$79$$ −580.333 1005.17i −0.826488 1.43152i −0.900777 0.434282i $$-0.857002\pi$$
0.0742888 0.997237i $$-0.476331\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 2.93158 0.00387690 0.00193845 0.999998i $$-0.499383\pi$$
0.00193845 + 0.999998i $$0.499383\pi$$
$$84$$ 0 0
$$85$$ 276.494 0.352824
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −639.371 1107.42i −0.761496 1.31895i −0.942079 0.335390i $$-0.891132\pi$$
0.180583 0.983560i $$-0.442202\pi$$
$$90$$ 0 0
$$91$$ 573.078 383.449i 0.660163 0.441719i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 338.156 585.703i 0.365200 0.632545i
$$96$$ 0 0
$$97$$ 79.0596 0.0827555 0.0413777 0.999144i $$-0.486825\pi$$
0.0413777 + 0.999144i $$0.486825\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 686.052 1188.28i 0.675889 1.17067i −0.300319 0.953839i $$-0.597093\pi$$
0.976208 0.216835i $$-0.0695734\pi$$
$$102$$ 0 0
$$103$$ −129.265 223.894i −0.123659 0.214184i 0.797549 0.603254i $$-0.206130\pi$$
−0.921208 + 0.389070i $$0.872796\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −631.184 1093.24i −0.570270 0.987736i −0.996538 0.0831393i $$-0.973505\pi$$
0.426268 0.904597i $$-0.359828\pi$$
$$108$$ 0 0
$$109$$ −138.416 + 239.744i −0.121632 + 0.210673i −0.920411 0.390951i $$-0.872146\pi$$
0.798779 + 0.601624i $$0.205479\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −52.9156 −0.0440520 −0.0220260 0.999757i $$-0.507012\pi$$
−0.0220260 + 0.999757i $$0.507012\pi$$
$$114$$ 0 0
$$115$$ −1101.02 + 1907.02i −0.892789 + 1.54636i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −27.1715 410.531i −0.0209312 0.316247i
$$120$$ 0 0
$$121$$ −641.309 1110.78i −0.481825 0.834545i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1183.53 0.846866
$$126$$ 0 0
$$127$$ 443.700 0.310016 0.155008 0.987913i $$-0.450460\pi$$
0.155008 + 0.987913i $$0.450460\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1076.74 1864.97i −0.718133 1.24384i −0.961739 0.273968i $$-0.911664\pi$$
0.243606 0.969874i $$-0.421670\pi$$
$$132$$ 0 0
$$133$$ −902.867 444.527i −0.588635 0.289815i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 131.554 227.858i 0.0820394 0.142096i −0.822086 0.569363i $$-0.807190\pi$$
0.904126 + 0.427266i $$0.140523\pi$$
$$138$$ 0 0
$$139$$ 1165.77 0.711360 0.355680 0.934608i $$-0.384249\pi$$
0.355680 + 0.934608i $$0.384249\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −951.693 + 1648.38i −0.556536 + 0.963948i
$$144$$ 0 0
$$145$$ −380.180 658.490i −0.217739 0.377135i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −882.597 1528.70i −0.485270 0.840512i 0.514587 0.857438i $$-0.327945\pi$$
−0.999857 + 0.0169263i $$0.994612\pi$$
$$150$$ 0 0
$$151$$ −1346.16 + 2331.61i −0.725488 + 1.25658i 0.233285 + 0.972408i $$0.425052\pi$$
−0.958773 + 0.284173i $$0.908281\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3981.85 −2.06342
$$156$$ 0 0
$$157$$ 970.691 1681.29i 0.493437 0.854657i −0.506535 0.862220i $$-0.669074\pi$$
0.999971 + 0.00756226i $$0.00240716\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 2939.70 + 1447.36i 1.43901 + 0.708497i
$$162$$ 0 0
$$163$$ −1051.42 1821.11i −0.505236 0.875094i −0.999982 0.00605658i $$-0.998072\pi$$
0.494746 0.869038i $$-0.335261\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2344.22 1.08623 0.543116 0.839658i $$-0.317244\pi$$
0.543116 + 0.839658i $$0.317244\pi$$
$$168$$ 0 0
$$169$$ −810.844 −0.369069
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1735.32 + 3005.67i 0.762626 + 1.32091i 0.941493 + 0.337033i $$0.109424\pi$$
−0.178867 + 0.983873i $$0.557243\pi$$
$$174$$ 0 0
$$175$$ 36.5813 + 552.703i 0.0158017 + 0.238745i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −477.885 + 827.722i −0.199547 + 0.345625i −0.948381 0.317132i $$-0.897280\pi$$
0.748835 + 0.662757i $$0.230614\pi$$
$$180$$ 0 0
$$181$$ 4220.26 1.73309 0.866546 0.499098i $$-0.166335\pi$$
0.866546 + 0.499098i $$0.166335\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1960.78 + 3396.17i −0.779239 + 1.34968i
$$186$$ 0 0
$$187$$ 567.858 + 983.558i 0.222063 + 0.384625i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1759.02 3046.71i −0.666377 1.15420i −0.978910 0.204291i $$-0.934511\pi$$
0.312534 0.949907i $$-0.398822\pi$$
$$192$$ 0 0
$$193$$ 2508.84 4345.43i 0.935699 1.62068i 0.162317 0.986739i $$-0.448103\pi$$
0.773382 0.633940i $$-0.218563\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2838.14 1.02644 0.513221 0.858257i $$-0.328452\pi$$
0.513221 + 0.858257i $$0.328452\pi$$
$$198$$ 0 0
$$199$$ −177.451 + 307.354i −0.0632118 + 0.109486i −0.895899 0.444257i $$-0.853468\pi$$
0.832688 + 0.553743i $$0.186801\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −940.348 + 629.192i −0.325121 + 0.217540i
$$204$$ 0 0
$$205$$ 1282.16 + 2220.77i 0.436829 + 0.756610i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 2777.99 0.919413
$$210$$ 0 0
$$211$$ 752.672 0.245574 0.122787 0.992433i $$-0.460817\pi$$
0.122787 + 0.992433i $$0.460817\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 2113.75 + 3661.12i 0.670496 + 1.16133i
$$216$$ 0 0
$$217$$ 391.303 + 5912.15i 0.122412 + 1.84951i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 413.547 716.284i 0.125874 0.218020i
$$222$$ 0 0
$$223$$ −3077.75 −0.924221 −0.462111 0.886822i $$-0.652908\pi$$
−0.462111 + 0.886822i $$0.652908\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −3108.72 + 5384.46i −0.908955 + 1.57436i −0.0934368 + 0.995625i $$0.529785\pi$$
−0.815518 + 0.578731i $$0.803548\pi$$
$$228$$ 0 0
$$229$$ −251.627 435.831i −0.0726113 0.125766i 0.827434 0.561563i $$-0.189800\pi$$
−0.900045 + 0.435797i $$0.856467\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −134.170 232.389i −0.0377243 0.0653404i 0.846547 0.532314i $$-0.178678\pi$$
−0.884271 + 0.466974i $$0.845344\pi$$
$$234$$ 0 0
$$235$$ −884.080 + 1531.27i −0.245409 + 0.425060i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 5189.77 1.40459 0.702297 0.711884i $$-0.252158\pi$$
0.702297 + 0.711884i $$0.252158\pi$$
$$240$$ 0 0
$$241$$ −3085.47 + 5344.19i −0.824699 + 1.42842i 0.0774495 + 0.996996i $$0.475322\pi$$
−0.902149 + 0.431425i $$0.858011\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 4231.82 562.641i 1.10351 0.146718i
$$246$$ 0 0
$$247$$ −1011.54 1752.05i −0.260579 0.451336i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1891.91 −0.475763 −0.237882 0.971294i $$-0.576453\pi$$
−0.237882 + 0.971294i $$0.576453\pi$$
$$252$$ 0 0
$$253$$ −9045.01 −2.24765
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −3269.97 5663.75i −0.793676 1.37469i −0.923676 0.383174i $$-0.874831\pi$$
0.130000 0.991514i $$-0.458502\pi$$
$$258$$ 0 0
$$259$$ 5235.23 + 2577.56i 1.25599 + 0.618386i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 2687.95 4655.67i 0.630214 1.09156i −0.357294 0.933992i $$-0.616301\pi$$
0.987508 0.157570i $$-0.0503661\pi$$
$$264$$ 0 0
$$265$$ 3858.53 0.894443
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1619.44 + 2804.95i −0.367060 + 0.635766i −0.989104 0.147216i $$-0.952969\pi$$
0.622045 + 0.782982i $$0.286302\pi$$
$$270$$ 0 0
$$271$$ −678.729 1175.59i −0.152140 0.263514i 0.779874 0.625936i $$-0.215283\pi$$
−0.932014 + 0.362423i $$0.881950\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −764.513 1324.18i −0.167643 0.290366i
$$276$$ 0 0
$$277$$ 1280.82 2218.44i 0.277823 0.481203i −0.693021 0.720918i $$-0.743721\pi$$
0.970843 + 0.239715i $$0.0770539\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1786.17 −0.379196 −0.189598 0.981862i $$-0.560718\pi$$
−0.189598 + 0.981862i $$0.560718\pi$$
$$282$$ 0 0
$$283$$ 3694.14 6398.44i 0.775950 1.34398i −0.158309 0.987390i $$-0.550604\pi$$
0.934259 0.356595i $$-0.116063\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 3171.34 2121.96i 0.652258 0.436429i
$$288$$ 0 0
$$289$$ 2209.74 + 3827.39i 0.449775 + 0.779033i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −492.981 −0.0982945 −0.0491472 0.998792i $$-0.515650\pi$$
−0.0491472 + 0.998792i $$0.515650\pi$$
$$294$$ 0 0
$$295$$ −3505.48 −0.691853
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 3293.55 + 5704.59i 0.637026 + 1.10336i
$$300$$ 0 0
$$301$$ 5228.22 3498.23i 1.00116 0.669882i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −3384.43 + 5862.01i −0.635384 + 1.10052i
$$306$$ 0 0
$$307$$ −988.810 −0.183825 −0.0919126 0.995767i $$-0.529298\pi$$
−0.0919126 + 0.995767i $$0.529298\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −4798.28 + 8310.87i −0.874874 + 1.51533i −0.0179763 + 0.999838i $$0.505722\pi$$
−0.856897 + 0.515487i $$0.827611\pi$$
$$312$$ 0 0
$$313$$ −482.856 836.332i −0.0871970 0.151030i 0.819128 0.573610i $$-0.194458\pi$$
−0.906325 + 0.422581i $$0.861124\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −4492.99 7782.08i −0.796061 1.37882i −0.922163 0.386801i $$-0.873580\pi$$
0.126103 0.992017i $$-0.459753\pi$$
$$318$$ 0 0
$$319$$ 1561.61 2704.79i 0.274086 0.474730i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1207.14 −0.207947
$$324$$ 0 0
$$325$$ −556.762 + 964.340i −0.0950265 + 0.164591i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 2360.47 + 1162.18i 0.395553 + 0.194751i
$$330$$ 0 0
$$331$$ 1903.65 + 3297.22i 0.316115 + 0.547527i 0.979674 0.200597i $$-0.0642882\pi$$
−0.663559 + 0.748124i $$0.730955\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 5966.21 0.973041
$$336$$ 0 0
$$337$$ −1649.82 −0.266681 −0.133340 0.991070i $$-0.542570\pi$$
−0.133340 + 0.991070i $$0.542570\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −8177.84 14164.4i −1.29869 2.24940i
$$342$$ 0 0
$$343$$ −1251.26 6228.00i −0.196973 0.980409i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 2855.00 4945.00i 0.441684 0.765019i −0.556131 0.831095i $$-0.687715\pi$$
0.997815 + 0.0660760i $$0.0210480\pi$$
$$348$$ 0 0
$$349$$ −447.244 −0.0685973 −0.0342986 0.999412i $$-0.510920\pi$$
−0.0342986 + 0.999412i $$0.510920\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −5322.85 + 9219.45i −0.802569 + 1.39009i 0.115352 + 0.993325i $$0.463201\pi$$
−0.917920 + 0.396765i $$0.870133\pi$$
$$354$$ 0 0
$$355$$ −6880.48 11917.3i −1.02867 1.78171i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −4548.73 7878.64i −0.668727 1.15827i −0.978260 0.207381i $$-0.933506\pi$$
0.309533 0.950889i $$-0.399827\pi$$
$$360$$ 0 0
$$361$$ 1953.15 3382.96i 0.284758 0.493215i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2979.01 −0.427201
$$366$$ 0 0
$$367$$ −2643.91 + 4579.39i −0.376052 + 0.651341i −0.990484 0.137629i $$-0.956052\pi$$
0.614432 + 0.788970i $$0.289385\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −379.184 5729.04i −0.0530627 0.801717i
$$372$$ 0 0
$$373$$ −2947.51 5105.23i −0.409159 0.708683i 0.585637 0.810573i $$-0.300844\pi$$
−0.994796 + 0.101890i $$0.967511\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −2274.51 −0.310724
$$378$$ 0 0
$$379$$ 3842.41 0.520769 0.260384 0.965505i $$-0.416151\pi$$
0.260384 + 0.965505i $$0.416151\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 2506.87 + 4342.02i 0.334452 + 0.579287i 0.983379 0.181563i $$-0.0581156\pi$$
−0.648928 + 0.760850i $$0.724782\pi$$
$$384$$ 0 0
$$385$$ −9794.14 + 6553.30i −1.29651 + 0.867499i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 5591.24 9684.31i 0.728758 1.26225i −0.228650 0.973509i $$-0.573431\pi$$
0.957408 0.288738i $$-0.0932355\pi$$
$$390$$ 0 0
$$391$$ 3930.40 0.508360
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 7222.95 12510.5i 0.920066 1.59360i
$$396$$ 0 0
$$397$$ 1703.40 + 2950.37i 0.215343 + 0.372985i 0.953379 0.301777i $$-0.0975798\pi$$
−0.738036 + 0.674762i $$0.764246\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 41.5201 + 71.9149i 0.00517061 + 0.00895575i 0.868599 0.495515i $$-0.165021\pi$$
−0.863429 + 0.504471i $$0.831687\pi$$
$$402$$ 0 0
$$403$$ −5955.57 + 10315.4i −0.736149 + 1.27505i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −16108.0 −1.96178
$$408$$ 0 0
$$409$$ −1228.10 + 2127.13i −0.148473 + 0.257164i −0.930663 0.365876i $$-0.880769\pi$$
0.782190 + 0.623040i $$0.214103\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 344.489 + 5204.84i 0.0410440 + 0.620129i
$$414$$ 0 0
$$415$$ 18.2435 + 31.5987i 0.00215793 + 0.00373764i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 3437.96 0.400848 0.200424 0.979709i $$-0.435768\pi$$
0.200424 + 0.979709i $$0.435768\pi$$
$$420$$ 0 0
$$421$$ −5347.62 −0.619067 −0.309533 0.950889i $$-0.600173\pi$$
−0.309533 + 0.950889i $$0.600173\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 332.210 + 575.404i 0.0379166 + 0.0656734i
$$426$$ 0 0
$$427$$ 9036.35 + 4449.05i 1.02412 + 0.504226i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 425.821 737.544i 0.0475895 0.0824275i −0.841249 0.540647i $$-0.818179\pi$$
0.888839 + 0.458220i $$0.151513\pi$$
$$432$$ 0 0
$$433$$ −3433.42 −0.381061 −0.190531 0.981681i $$-0.561021\pi$$
−0.190531 + 0.981681i $$0.561021\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 4806.92 8325.83i 0.526192 0.911392i
$$438$$ 0 0
$$439$$ 4869.20 + 8433.70i 0.529371 + 0.916898i 0.999413 + 0.0342540i $$0.0109055\pi$$
−0.470042 + 0.882644i $$0.655761\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 4967.48 + 8603.93i 0.532759 + 0.922765i 0.999268 + 0.0382491i $$0.0121780\pi$$
−0.466509 + 0.884516i $$0.654489\pi$$
$$444$$ 0 0
$$445$$ 7957.75 13783.2i 0.847716 1.46829i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 7557.33 0.794327 0.397163 0.917748i $$-0.369995\pi$$
0.397163 + 0.917748i $$0.369995\pi$$
$$450$$ 0 0
$$451$$ −5266.54 + 9121.92i −0.549871 + 0.952405i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 7699.43 + 3790.81i 0.793307 + 0.390585i
$$456$$ 0 0
$$457$$ −7005.92 12134.6i −0.717118 1.24209i −0.962137 0.272567i $$-0.912127\pi$$
0.245018 0.969518i $$-0.421206\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 1669.61 0.168680 0.0843399 0.996437i $$-0.473122\pi$$
0.0843399 + 0.996437i $$0.473122\pi$$
$$462$$ 0 0
$$463$$ 14785.4 1.48409 0.742046 0.670349i $$-0.233856\pi$$
0.742046 + 0.670349i $$0.233856\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2301.58 + 3986.46i 0.228061 + 0.395014i 0.957233 0.289317i $$-0.0934280\pi$$
−0.729172 + 0.684330i $$0.760095\pi$$
$$468$$ 0 0
$$469$$ −586.309 8858.47i −0.0577255 0.872167i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −8682.35 + 15038.3i −0.844006 + 1.46186i
$$474$$ 0 0
$$475$$ 1625.18 0.156987
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 1738.68 3011.47i 0.165850 0.287261i −0.771107 0.636706i $$-0.780297\pi$$
0.936957 + 0.349445i $$0.113630\pi$$
$$480$$ 0 0
$$481$$ 5865.39 + 10159.2i 0.556006 + 0.963030i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 491.996 + 852.163i 0.0460627 + 0.0797829i
$$486$$ 0 0
$$487$$ −2172.08 + 3762.16i −0.202108 + 0.350061i −0.949207 0.314651i $$-0.898112\pi$$
0.747100 + 0.664712i $$0.231446\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −4982.89 −0.457993 −0.228997 0.973427i $$-0.573544\pi$$
−0.228997 + 0.973427i $$0.573544\pi$$
$$492$$ 0 0
$$493$$ −678.578 + 1175.33i −0.0619911 + 0.107372i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −17018.4 + 11387.1i −1.53598 + 1.02773i
$$498$$ 0 0
$$499$$ −7663.08 13272.8i −0.687468 1.19073i −0.972654 0.232257i $$-0.925389\pi$$
0.285187 0.958472i $$-0.407944\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 1516.04 0.134387 0.0671936 0.997740i $$-0.478595\pi$$
0.0671936 + 0.997740i $$0.478595\pi$$
$$504$$ 0 0
$$505$$ 17077.5 1.50483
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 1326.82 + 2298.12i 0.115541 + 0.200122i 0.917996 0.396590i $$-0.129807\pi$$
−0.802455 + 0.596713i $$0.796473\pi$$
$$510$$ 0 0
$$511$$ 292.752 + 4423.15i 0.0253436 + 0.382913i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 1608.86 2786.64i 0.137660 0.238435i
$$516$$ 0 0
$$517$$ −7262.82 −0.617830
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −6566.06 + 11372.8i −0.552139 + 0.956333i 0.445981 + 0.895042i $$0.352855\pi$$
−0.998120 + 0.0612905i $$0.980478\pi$$
$$522$$ 0 0
$$523$$ 1543.17 + 2672.85i 0.129021 + 0.223471i 0.923298 0.384085i $$-0.125483\pi$$
−0.794276 + 0.607557i $$0.792150\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 3553.58 + 6154.98i 0.293731 + 0.508757i
$$528$$ 0 0
$$529$$ −9567.63 + 16571.6i −0.786359 + 1.36201i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 7670.80 0.623376
$$534$$ 0 0
$$535$$ 7855.86 13606.7i 0.634838 1.09957i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 10692.7 + 13898.1i 0.854482 + 1.11064i
$$540$$ 0 0
$$541$$ −463.047 802.022i −0.0367985 0.0637368i 0.847040 0.531530i $$-0.178383\pi$$
−0.883838 + 0.467793i $$0.845049\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −3445.52 −0.270807
$$546$$ 0 0
$$547$$ 592.871 0.0463425 0.0231712 0.999732i $$-0.492624\pi$$
0.0231712 + 0.999732i $$0.492624\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1659.82 + 2874.89i 0.128331 + 0.222276i
$$552$$ 0 0
$$553$$ −19285.1 9495.02i −1.48298 0.730144i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −6122.67 + 10604.8i −0.465756 + 0.806713i −0.999235 0.0391003i $$-0.987551\pi$$
0.533480 + 0.845813i $$0.320884\pi$$
$$558$$ 0 0
$$559$$ 12646.0 0.956829
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 7297.31 12639.3i 0.546261 0.946152i −0.452266 0.891883i $$-0.649384\pi$$
0.998526 0.0542682i $$-0.0172826\pi$$
$$564$$ 0 0
$$565$$ −329.300 570.364i −0.0245199 0.0424697i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 11455.6 + 19841.7i 0.844015 + 1.46188i 0.886474 + 0.462779i $$0.153147\pi$$
−0.0424590 + 0.999098i $$0.513519\pi$$
$$570$$ 0 0
$$571$$ −2952.32 + 5113.57i −0.216376 + 0.374774i −0.953697 0.300768i $$-0.902757\pi$$
0.737321 + 0.675542i $$0.236090\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −5291.53 −0.383778
$$576$$ 0 0
$$577$$ −4756.61 + 8238.68i −0.343189 + 0.594421i −0.985023 0.172423i $$-0.944840\pi$$
0.641834 + 0.766844i $$0.278174\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 45.1242 30.1928i 0.00322214 0.00215595i
$$582$$ 0 0
$$583$$ 7924.56 + 13725.7i 0.562953 + 0.975064i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 22790.6 1.60250 0.801252 0.598327i $$-0.204167\pi$$
0.801252 + 0.598327i $$0.204167\pi$$
$$588$$ 0 0
$$589$$ 17384.3 1.21614
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −9131.39 15816.0i −0.632346 1.09526i −0.987071 0.160285i $$-0.948759\pi$$
0.354724 0.934971i $$-0.384575\pi$$
$$594$$ 0 0
$$595$$ 4255.92 2847.66i 0.293237 0.196206i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 3479.05 6025.88i 0.237312 0.411037i −0.722630 0.691235i $$-0.757067\pi$$
0.959942 + 0.280198i $$0.0904003\pi$$
$$600$$ 0 0
$$601$$ 2305.39 0.156471 0.0782353 0.996935i $$-0.475071\pi$$
0.0782353 + 0.996935i $$0.475071\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 7981.87 13825.0i 0.536379 0.929036i
$$606$$ 0 0
$$607$$ 8089.62 + 14011.6i 0.540935 + 0.936927i 0.998851 + 0.0479312i $$0.0152628\pi$$
−0.457916 + 0.888996i $$0.651404\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 2644.60 + 4580.58i 0.175105 + 0.303291i
$$612$$ 0 0
$$613$$ −10270.4 + 17788.8i −0.676699 + 1.17208i 0.299271 + 0.954168i $$0.403257\pi$$
−0.975969 + 0.217908i $$0.930077\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −6918.19 −0.451403 −0.225702 0.974196i $$-0.572467\pi$$
−0.225702 + 0.974196i $$0.572467\pi$$
$$618$$ 0 0
$$619$$ 4040.81 6998.89i 0.262381 0.454457i −0.704493 0.709711i $$-0.748826\pi$$
0.966874 + 0.255254i $$0.0821589\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −21247.0 10461.0i −1.36636 0.672728i
$$624$$ 0 0
$$625$$ 9234.52 + 15994.7i 0.591009 + 1.02366i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 6999.54 0.443704
$$630$$ 0 0
$$631$$ −27293.3 −1.72191 −0.860957 0.508677i $$-0.830135\pi$$
−0.860957 + 0.508677i $$0.830135\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 2761.20 + 4782.53i 0.172559 + 0.298880i
$$636$$ 0 0
$$637$$ 4871.86 11804.4i 0.303030 0.734237i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 9627.82 16675.9i 0.593254 1.02755i −0.400536 0.916281i $$-0.631176\pi$$
0.993791 0.111266i $$-0.0354905\pi$$
$$642$$ 0 0
$$643$$ −19996.4 −1.22641 −0.613204 0.789925i $$-0.710120\pi$$
−0.613204 + 0.789925i $$0.710120\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 3532.10 6117.77i 0.214623 0.371738i −0.738533 0.674218i $$-0.764481\pi$$
0.953156 + 0.302479i $$0.0978144\pi$$
$$648$$ 0 0
$$649$$ −7199.47 12469.8i −0.435445 0.754213i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −6910.53 11969.4i −0.414134 0.717302i 0.581203 0.813759i $$-0.302582\pi$$
−0.995337 + 0.0964570i $$0.969249\pi$$
$$654$$ 0 0
$$655$$ 13401.4 23211.9i 0.799443 1.38468i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 7802.80 0.461235 0.230617 0.973044i $$-0.425925\pi$$
0.230617 + 0.973044i $$0.425925\pi$$
$$660$$ 0 0
$$661$$ −7908.65 + 13698.2i −0.465372 + 0.806048i −0.999218 0.0395338i $$-0.987413\pi$$
0.533846 + 0.845581i $$0.320746\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −827.204 12498.1i −0.0482370 0.728806i
$$666$$ 0 0
$$667$$ −5404.29 9360.51i −0.313726 0.543389i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −27803.5 −1.59962
$$672$$ 0 0
$$673$$ 2943.30 0.168582 0.0842911 0.996441i $$-0.473137\pi$$
0.0842911 + 0.996441i $$0.473137\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1585.74 2746.58i −0.0900220 0.155923i 0.817498 0.575931i $$-0.195360\pi$$
−0.907520 + 0.420009i $$0.862027\pi$$
$$678$$ 0 0
$$679$$ 1216.92 814.247i 0.0687792 0.0460205i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12226.6 + 21177.1i −0.684975 + 1.18641i 0.288470 + 0.957489i $$0.406854\pi$$
−0.973445 + 0.228923i $$0.926480\pi$$
$$684$$ 0 0
$$685$$ 3274.70 0.182656
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 5771.12 9995.87i 0.319103 0.552703i
$$690$$ 0 0
$$691$$ −4297.95 7444.26i −0.236616 0.409831i 0.723125 0.690717i $$-0.242705\pi$$
−0.959741 + 0.280886i $$0.909372\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 7254.69 + 12565.5i 0.395951 + 0.685808i
$$696$$ 0 0
$$697$$ 2288.51 3963.82i 0.124367 0.215409i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 21476.1 1.15712 0.578561 0.815639i $$-0.303615\pi$$
0.578561 + 0.815639i $$0.303615\pi$$
$$702$$ 0 0
$$703$$ 8560.51 14827.2i 0.459269 0.795477i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1678.24 25356.3i −0.0892738 1.34883i
$$708$$ 0 0
$$709$$ 6769.46 + 11725.0i 0.358579 + 0.621077i 0.987724 0.156211i $$-0.0499281\pi$$
−0.629145 + 0.777288i $$0.716595\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −56602.5 −2.97304
$$714$$ 0 0
$$715$$ −23690.0 −1.23910
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 6941.84 + 12023.6i 0.360065 + 0.623652i 0.987971 0.154638i $$-0.0494210\pi$$
−0.627906 + 0.778289i $$0.716088\pi$$
$$720$$ 0 0
$$721$$ −4295.63 2114.95i −0.221883 0.109244i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 913.577 1582.36i 0.0467992 0.0810585i
$$726$$ 0 0
$$727$$ −18292.9 −0.933215 −0.466607 0.884465i $$-0.654524\pi$$
−0.466607 + 0.884465i $$0.654524\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 3772.81 6534.69i 0.190892 0.330635i
$$732$$ 0 0
$$733$$ −7122.92 12337.3i −0.358924 0.621674i 0.628857 0.777521i $$-0.283523\pi$$
−0.987781 + 0.155846i $$0.950190\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 12253.3 + 21223.3i 0.612422 + 1.06075i
$$738$$ 0 0
$$739$$ 681.947 1181.17i 0.0339456 0.0587956i −0.848553 0.529110i $$-0.822526\pi$$
0.882499 + 0.470314i $$0.155859\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −21789.4 −1.07588 −0.537938 0.842984i $$-0.680797\pi$$
−0.537938 + 0.842984i $$0.680797\pi$$
$$744$$ 0 0
$$745$$ 10985.0 19026.6i 0.540214 0.935678i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −20974.9 10327.0i −1.02324 0.503793i
$$750$$ 0 0
$$751$$ 1059.78 + 1835.59i 0.0514937 + 0.0891898i 0.890623 0.454742i $$-0.150268\pi$$
−0.839130 + 0.543932i $$0.816935\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −33509.1 −1.61526
$$756$$ 0 0
$$757$$ 28202.4 1.35408 0.677038 0.735948i $$-0.263263\pi$$
0.677038 + 0.735948i $$0.263263\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 5573.52 + 9653.62i 0.265493 + 0.459847i 0.967693 0.252133i $$-0.0811321\pi$$
−0.702200 + 0.711980i $$0.747799\pi$$
$$762$$ 0 0
$$763$$ 338.597 + 5115.82i 0.0160656 + 0.242733i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −5243.07 + 9081.26i −0.246827 + 0.427517i
$$768$$ 0 0
$$769$$ −4109.29 −0.192698 −0.0963491 0.995348i $$-0.530717\pi$$
−0.0963491 + 0.995348i $$0.530717\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 6945.68 12030.3i 0.323181 0.559766i −0.657962 0.753052i $$-0.728581\pi$$
0.981143 + 0.193286i $$0.0619144\pi$$
$$774$$ 0 0
$$775$$ −4784.22 8286.51i −0.221747 0.384078i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −5597.75 9695.59i −0.257459 0.445931i
$$780$$ 0 0
$$781$$ 28262.0 48951.2i 1.29487 2.24278i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 24162.9 1.09861
$$786$$ 0 0
$$787$$ 4671.18 8090.71i 0.211575 0.366458i −0.740633 0.671910i $$-0.765474\pi$$
0.952208 + 0.305452i $$0.0988074\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −814.500 + 544.986i −0.0366123 + 0.0244974i
$$792$$ 0 0
$$793$$ 10124.0 + 17535.4i 0.453361 + 0.785245i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 24324.3 1.08107 0.540534 0.841322i $$-0.318222\pi$$
0.540534 + 0.841322i $$0.318222\pi$$
$$798$$ 0 0
$$799$$ 3155.97 0.139737
$$800$$ 0 0