# Properties

 Label 160.4.c.d.129.1 Level $160$ Weight $4$ Character 160.129 Analytic conductor $9.440$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 160.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.44030560092$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.359712057600.22 Defining polynomial: $$x^{8} + 17x^{6} + 82x^{4} + 96x^{2} + 9$$ x^8 + 17*x^6 + 82*x^4 + 96*x^2 + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{22}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 129.1 Root $$1.24759i$$ of defining polynomial Character $$\chi$$ $$=$$ 160.129 Dual form 160.4.c.d.129.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-8.57295i q^{3} +(-0.582576 - 11.1652i) q^{5} -22.1403i q^{7} -46.4955 q^{9} +O(q^{10})$$ $$q-8.57295i q^{3} +(-0.582576 - 11.1652i) q^{5} -22.1403i q^{7} -46.4955 q^{9} +27.1347 q^{11} +70.3303i q^{13} +(-95.7183 + 4.99439i) q^{15} -73.3212i q^{17} +110.033 q^{19} -189.808 q^{21} +107.870i q^{23} +(-124.321 + 13.0091i) q^{25} +167.134i q^{27} -68.6424 q^{29} -137.167 q^{31} -232.624i q^{33} +(-247.200 + 12.8984i) q^{35} +60.3121i q^{37} +602.938 q^{39} +95.1470 q^{41} -501.479i q^{43} +(27.0871 + 519.129i) q^{45} -439.305i q^{47} -147.192 q^{49} -628.579 q^{51} +286.955i q^{53} +(-15.8080 - 302.963i) q^{55} -943.303i q^{57} +547.175 q^{59} +511.459 q^{61} +1029.42i q^{63} +(785.248 - 40.9727i) q^{65} +301.547i q^{67} +924.762 q^{69} +82.8978 q^{71} +763.267i q^{73} +(111.526 + 1065.80i) q^{75} -600.770i q^{77} -1011.45 q^{79} +177.450 q^{81} -704.554i q^{83} +(-818.642 + 42.7152i) q^{85} +588.468i q^{87} +743.212 q^{89} +1557.13 q^{91} +1175.93i q^{93} +(-64.1023 - 1228.53i) q^{95} -1136.00i q^{97} -1261.64 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 32 q^{5} - 152 q^{9}+O(q^{10})$$ 8 * q + 32 * q^5 - 152 * q^9 $$8 q + 32 q^{5} - 152 q^{9} - 272 q^{21} - 408 q^{25} + 624 q^{29} - 192 q^{41} + 400 q^{45} - 2424 q^{49} + 2112 q^{61} + 2176 q^{65} + 3952 q^{69} - 1000 q^{81} - 5376 q^{85} + 80 q^{89}+O(q^{100})$$ 8 * q + 32 * q^5 - 152 * q^9 - 272 * q^21 - 408 * q^25 + 624 * q^29 - 192 * q^41 + 400 * q^45 - 2424 * q^49 + 2112 * q^61 + 2176 * q^65 + 3952 * q^69 - 1000 * q^81 - 5376 * q^85 + 80 * q^89

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$97$$ $$101$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 8.57295i 1.64986i −0.565231 0.824932i $$-0.691213\pi$$
0.565231 0.824932i $$-0.308787\pi$$
$$4$$ 0 0
$$5$$ −0.582576 11.1652i −0.0521072 0.998641i
$$6$$ 0 0
$$7$$ 22.1403i 1.19546i −0.801696 0.597732i $$-0.796069\pi$$
0.801696 0.597732i $$-0.203931\pi$$
$$8$$ 0 0
$$9$$ −46.4955 −1.72205
$$10$$ 0 0
$$11$$ 27.1347 0.743765 0.371882 0.928280i $$-0.378712\pi$$
0.371882 + 0.928280i $$0.378712\pi$$
$$12$$ 0 0
$$13$$ 70.3303i 1.50047i 0.661171 + 0.750235i $$0.270060\pi$$
−0.661171 + 0.750235i $$0.729940\pi$$
$$14$$ 0 0
$$15$$ −95.7183 + 4.99439i −1.64762 + 0.0859698i
$$16$$ 0 0
$$17$$ 73.3212i 1.04606i −0.852315 0.523030i $$-0.824802\pi$$
0.852315 0.523030i $$-0.175198\pi$$
$$18$$ 0 0
$$19$$ 110.033 1.32859 0.664294 0.747471i $$-0.268732\pi$$
0.664294 + 0.747471i $$0.268732\pi$$
$$20$$ 0 0
$$21$$ −189.808 −1.97235
$$22$$ 0 0
$$23$$ 107.870i 0.977931i 0.872303 + 0.488965i $$0.162626\pi$$
−0.872303 + 0.488965i $$0.837374\pi$$
$$24$$ 0 0
$$25$$ −124.321 + 13.0091i −0.994570 + 0.104073i
$$26$$ 0 0
$$27$$ 167.134i 1.19129i
$$28$$ 0 0
$$29$$ −68.6424 −0.439537 −0.219769 0.975552i $$-0.570530\pi$$
−0.219769 + 0.975552i $$0.570530\pi$$
$$30$$ 0 0
$$31$$ −137.167 −0.794708 −0.397354 0.917665i $$-0.630072\pi$$
−0.397354 + 0.917665i $$0.630072\pi$$
$$32$$ 0 0
$$33$$ 232.624i 1.22711i
$$34$$ 0 0
$$35$$ −247.200 + 12.8984i −1.19384 + 0.0622922i
$$36$$ 0 0
$$37$$ 60.3121i 0.267980i 0.990983 + 0.133990i $$0.0427790\pi$$
−0.990983 + 0.133990i $$0.957221\pi$$
$$38$$ 0 0
$$39$$ 602.938 2.47557
$$40$$ 0 0
$$41$$ 95.1470 0.362426 0.181213 0.983444i $$-0.441998\pi$$
0.181213 + 0.983444i $$0.441998\pi$$
$$42$$ 0 0
$$43$$ 501.479i 1.77848i −0.457438 0.889241i $$-0.651233\pi$$
0.457438 0.889241i $$-0.348767\pi$$
$$44$$ 0 0
$$45$$ 27.0871 + 519.129i 0.0897313 + 1.71971i
$$46$$ 0 0
$$47$$ 439.305i 1.36339i −0.731637 0.681694i $$-0.761244\pi$$
0.731637 0.681694i $$-0.238756\pi$$
$$48$$ 0 0
$$49$$ −147.192 −0.429132
$$50$$ 0 0
$$51$$ −628.579 −1.72586
$$52$$ 0 0
$$53$$ 286.955i 0.743703i 0.928292 + 0.371851i $$0.121277\pi$$
−0.928292 + 0.371851i $$0.878723\pi$$
$$54$$ 0 0
$$55$$ −15.8080 302.963i −0.0387555 0.742755i
$$56$$ 0 0
$$57$$ 943.303i 2.19199i
$$58$$ 0 0
$$59$$ 547.175 1.20739 0.603696 0.797215i $$-0.293694\pi$$
0.603696 + 0.797215i $$0.293694\pi$$
$$60$$ 0 0
$$61$$ 511.459 1.07353 0.536767 0.843730i $$-0.319645\pi$$
0.536767 + 0.843730i $$0.319645\pi$$
$$62$$ 0 0
$$63$$ 1029.42i 2.05865i
$$64$$ 0 0
$$65$$ 785.248 40.9727i 1.49843 0.0781852i
$$66$$ 0 0
$$67$$ 301.547i 0.549848i 0.961466 + 0.274924i $$0.0886527\pi$$
−0.961466 + 0.274924i $$0.911347\pi$$
$$68$$ 0 0
$$69$$ 924.762 1.61345
$$70$$ 0 0
$$71$$ 82.8978 0.138566 0.0692828 0.997597i $$-0.477929\pi$$
0.0692828 + 0.997597i $$0.477929\pi$$
$$72$$ 0 0
$$73$$ 763.267i 1.22375i 0.790955 + 0.611874i $$0.209584\pi$$
−0.790955 + 0.611874i $$0.790416\pi$$
$$74$$ 0 0
$$75$$ 111.526 + 1065.80i 0.171706 + 1.64091i
$$76$$ 0 0
$$77$$ 600.770i 0.889144i
$$78$$ 0 0
$$79$$ −1011.45 −1.44047 −0.720236 0.693729i $$-0.755966\pi$$
−0.720236 + 0.693729i $$0.755966\pi$$
$$80$$ 0 0
$$81$$ 177.450 0.243416
$$82$$ 0 0
$$83$$ 704.554i 0.931745i −0.884852 0.465872i $$-0.845741\pi$$
0.884852 0.465872i $$-0.154259\pi$$
$$84$$ 0 0
$$85$$ −818.642 + 42.7152i −1.04464 + 0.0545072i
$$86$$ 0 0
$$87$$ 588.468i 0.725177i
$$88$$ 0 0
$$89$$ 743.212 0.885172 0.442586 0.896726i $$-0.354061\pi$$
0.442586 + 0.896726i $$0.354061\pi$$
$$90$$ 0 0
$$91$$ 1557.13 1.79376
$$92$$ 0 0
$$93$$ 1175.93i 1.31116i
$$94$$ 0 0
$$95$$ −64.1023 1228.53i −0.0692290 1.32678i
$$96$$ 0 0
$$97$$ 1136.00i 1.18911i −0.804056 0.594553i $$-0.797329\pi$$
0.804056 0.594553i $$-0.202671\pi$$
$$98$$ 0 0
$$99$$ −1261.64 −1.28080
$$100$$ 0 0
$$101$$ 291.212 0.286898 0.143449 0.989658i $$-0.454181\pi$$
0.143449 + 0.989658i $$0.454181\pi$$
$$102$$ 0 0
$$103$$ 200.445i 0.191751i −0.995393 0.0958757i $$-0.969435\pi$$
0.995393 0.0958757i $$-0.0305651\pi$$
$$104$$ 0 0
$$105$$ 110.577 + 2119.23i 0.102774 + 1.96967i
$$106$$ 0 0
$$107$$ 754.342i 0.681542i −0.940146 0.340771i $$-0.889312\pi$$
0.940146 0.340771i $$-0.110688\pi$$
$$108$$ 0 0
$$109$$ −501.680 −0.440846 −0.220423 0.975404i $$-0.570744\pi$$
−0.220423 + 0.975404i $$0.570744\pi$$
$$110$$ 0 0
$$111$$ 517.053 0.442130
$$112$$ 0 0
$$113$$ 497.248i 0.413958i −0.978345 0.206979i $$-0.933637\pi$$
0.978345 0.206979i $$-0.0663631\pi$$
$$114$$ 0 0
$$115$$ 1204.38 62.8423i 0.976602 0.0509572i
$$116$$ 0 0
$$117$$ 3270.04i 2.58389i
$$118$$ 0 0
$$119$$ −1623.35 −1.25053
$$120$$ 0 0
$$121$$ −594.709 −0.446814
$$122$$ 0 0
$$123$$ 815.690i 0.597954i
$$124$$ 0 0
$$125$$ 217.675 + 1380.49i 0.155756 + 0.987796i
$$126$$ 0 0
$$127$$ 915.221i 0.639470i −0.947507 0.319735i $$-0.896406\pi$$
0.947507 0.319735i $$-0.103594\pi$$
$$128$$ 0 0
$$129$$ −4299.15 −2.93426
$$130$$ 0 0
$$131$$ 607.419 0.405118 0.202559 0.979270i $$-0.435074\pi$$
0.202559 + 0.979270i $$0.435074\pi$$
$$132$$ 0 0
$$133$$ 2436.15i 1.58828i
$$134$$ 0 0
$$135$$ 1866.07 97.3679i 1.18967 0.0620748i
$$136$$ 0 0
$$137$$ 1418.98i 0.884900i 0.896793 + 0.442450i $$0.145891\pi$$
−0.896793 + 0.442450i $$0.854109\pi$$
$$138$$ 0 0
$$139$$ −3035.85 −1.85250 −0.926250 0.376910i $$-0.876987\pi$$
−0.926250 + 0.376910i $$0.876987\pi$$
$$140$$ 0 0
$$141$$ −3766.14 −2.24941
$$142$$ 0 0
$$143$$ 1908.39i 1.11600i
$$144$$ 0 0
$$145$$ 39.9894 + 766.403i 0.0229030 + 0.438940i
$$146$$ 0 0
$$147$$ 1261.87i 0.708011i
$$148$$ 0 0
$$149$$ 2649.26 1.45662 0.728308 0.685250i $$-0.240307\pi$$
0.728308 + 0.685250i $$0.240307\pi$$
$$150$$ 0 0
$$151$$ 283.297 0.152678 0.0763390 0.997082i $$-0.475677\pi$$
0.0763390 + 0.997082i $$0.475677\pi$$
$$152$$ 0 0
$$153$$ 3409.10i 1.80137i
$$154$$ 0 0
$$155$$ 79.9103 + 1531.49i 0.0414100 + 0.793629i
$$156$$ 0 0
$$157$$ 1414.88i 0.719235i −0.933100 0.359617i $$-0.882907\pi$$
0.933100 0.359617i $$-0.117093\pi$$
$$158$$ 0 0
$$159$$ 2460.05 1.22701
$$160$$ 0 0
$$161$$ 2388.27 1.16908
$$162$$ 0 0
$$163$$ 1725.68i 0.829239i 0.909995 + 0.414619i $$0.136085\pi$$
−0.909995 + 0.414619i $$0.863915\pi$$
$$164$$ 0 0
$$165$$ −2597.28 + 135.521i −1.22544 + 0.0639413i
$$166$$ 0 0
$$167$$ 1979.92i 0.917428i 0.888584 + 0.458714i $$0.151690\pi$$
−0.888584 + 0.458714i $$0.848310\pi$$
$$168$$ 0 0
$$169$$ −2749.35 −1.25141
$$170$$ 0 0
$$171$$ −5116.01 −2.28790
$$172$$ 0 0
$$173$$ 1468.72i 0.645460i 0.946491 + 0.322730i $$0.104601\pi$$
−0.946491 + 0.322730i $$0.895399\pi$$
$$174$$ 0 0
$$175$$ 288.025 + 2752.51i 0.124415 + 1.18897i
$$176$$ 0 0
$$177$$ 4690.90i 1.99203i
$$178$$ 0 0
$$179$$ 2978.59 1.24375 0.621873 0.783118i $$-0.286372\pi$$
0.621873 + 0.783118i $$0.286372\pi$$
$$180$$ 0 0
$$181$$ −1682.07 −0.690760 −0.345380 0.938463i $$-0.612250\pi$$
−0.345380 + 0.938463i $$0.612250\pi$$
$$182$$ 0 0
$$183$$ 4384.71i 1.77119i
$$184$$ 0 0
$$185$$ 673.394 35.1364i 0.267616 0.0139637i
$$186$$ 0 0
$$187$$ 1989.55i 0.778022i
$$188$$ 0 0
$$189$$ 3700.38 1.42414
$$190$$ 0 0
$$191$$ 274.334 0.103927 0.0519637 0.998649i $$-0.483452\pi$$
0.0519637 + 0.998649i $$0.483452\pi$$
$$192$$ 0 0
$$193$$ 2898.50i 1.08103i 0.841335 + 0.540514i $$0.181770\pi$$
−0.841335 + 0.540514i $$0.818230\pi$$
$$194$$ 0 0
$$195$$ −351.257 6731.90i −0.128995 2.47221i
$$196$$ 0 0
$$197$$ 2330.37i 0.842801i −0.906875 0.421400i $$-0.861539\pi$$
0.906875 0.421400i $$-0.138461\pi$$
$$198$$ 0 0
$$199$$ −1105.05 −0.393644 −0.196822 0.980439i $$-0.563062\pi$$
−0.196822 + 0.980439i $$0.563062\pi$$
$$200$$ 0 0
$$201$$ 2585.15 0.907175
$$202$$ 0 0
$$203$$ 1519.76i 0.525451i
$$204$$ 0 0
$$205$$ −55.4303 1062.33i −0.0188850 0.361933i
$$206$$ 0 0
$$207$$ 5015.45i 1.68405i
$$208$$ 0 0
$$209$$ 2985.70 0.988158
$$210$$ 0 0
$$211$$ 4749.82 1.54972 0.774860 0.632133i $$-0.217820\pi$$
0.774860 + 0.632133i $$0.217820\pi$$
$$212$$ 0 0
$$213$$ 710.679i 0.228615i
$$214$$ 0 0
$$215$$ −5599.08 + 292.149i −1.77607 + 0.0926717i
$$216$$ 0 0
$$217$$ 3036.92i 0.950044i
$$218$$ 0 0
$$219$$ 6543.45 2.01902
$$220$$ 0 0
$$221$$ 5156.70 1.56958
$$222$$ 0 0
$$223$$ 1889.71i 0.567462i −0.958904 0.283731i $$-0.908428\pi$$
0.958904 0.283731i $$-0.0915723\pi$$
$$224$$ 0 0
$$225$$ 5780.37 604.864i 1.71270 0.179219i
$$226$$ 0 0
$$227$$ 4154.11i 1.21462i 0.794466 + 0.607309i $$0.207751\pi$$
−0.794466 + 0.607309i $$0.792249\pi$$
$$228$$ 0 0
$$229$$ 888.642 0.256433 0.128216 0.991746i $$-0.459075\pi$$
0.128216 + 0.991746i $$0.459075\pi$$
$$230$$ 0 0
$$231$$ −5150.37 −1.46697
$$232$$ 0 0
$$233$$ 4919.38i 1.38317i −0.722294 0.691586i $$-0.756912\pi$$
0.722294 0.691586i $$-0.243088\pi$$
$$234$$ 0 0
$$235$$ −4904.91 + 255.929i −1.36154 + 0.0710423i
$$236$$ 0 0
$$237$$ 8671.13i 2.37658i
$$238$$ 0 0
$$239$$ 2178.00 0.589468 0.294734 0.955579i $$-0.404769\pi$$
0.294734 + 0.955579i $$0.404769\pi$$
$$240$$ 0 0
$$241$$ −3156.12 −0.843583 −0.421792 0.906693i $$-0.638599\pi$$
−0.421792 + 0.906693i $$0.638599\pi$$
$$242$$ 0 0
$$243$$ 2991.34i 0.789688i
$$244$$ 0 0
$$245$$ 85.7507 + 1643.43i 0.0223609 + 0.428549i
$$246$$ 0 0
$$247$$ 7738.62i 1.99351i
$$248$$ 0 0
$$249$$ −6040.10 −1.53725
$$250$$ 0 0
$$251$$ 2719.20 0.683801 0.341901 0.939736i $$-0.388929\pi$$
0.341901 + 0.939736i $$0.388929\pi$$
$$252$$ 0 0
$$253$$ 2927.01i 0.727350i
$$254$$ 0 0
$$255$$ 366.195 + 7018.18i 0.0899295 + 1.72351i
$$256$$ 0 0
$$257$$ 749.067i 0.181811i −0.995860 0.0909056i $$-0.971024\pi$$
0.995860 0.0909056i $$-0.0289762\pi$$
$$258$$ 0 0
$$259$$ 1335.33 0.320360
$$260$$ 0 0
$$261$$ 3191.56 0.756907
$$262$$ 0 0
$$263$$ 2546.04i 0.596942i −0.954419 0.298471i $$-0.903523\pi$$
0.954419 0.298471i $$-0.0964766\pi$$
$$264$$ 0 0
$$265$$ 3203.89 167.173i 0.742692 0.0387522i
$$266$$ 0 0
$$267$$ 6371.52i 1.46041i
$$268$$ 0 0
$$269$$ 7982.07 1.80920 0.904601 0.426260i $$-0.140169\pi$$
0.904601 + 0.426260i $$0.140169\pi$$
$$270$$ 0 0
$$271$$ 1686.58 0.378054 0.189027 0.981972i $$-0.439467\pi$$
0.189027 + 0.981972i $$0.439467\pi$$
$$272$$ 0 0
$$273$$ 13349.2i 2.95946i
$$274$$ 0 0
$$275$$ −3373.42 + 352.998i −0.739726 + 0.0774056i
$$276$$ 0 0
$$277$$ 1423.07i 0.308679i −0.988018 0.154339i $$-0.950675\pi$$
0.988018 0.154339i $$-0.0493249\pi$$
$$278$$ 0 0
$$279$$ 6377.65 1.36853
$$280$$ 0 0
$$281$$ 5418.67 1.15036 0.575180 0.818027i $$-0.304932\pi$$
0.575180 + 0.818027i $$0.304932\pi$$
$$282$$ 0 0
$$283$$ 8343.38i 1.75252i 0.481842 + 0.876258i $$0.339968\pi$$
−0.481842 + 0.876258i $$0.660032\pi$$
$$284$$ 0 0
$$285$$ −10532.1 + 549.545i −2.18901 + 0.114218i
$$286$$ 0 0
$$287$$ 2106.58i 0.433267i
$$288$$ 0 0
$$289$$ −463.000 −0.0942398
$$290$$ 0 0
$$291$$ −9738.87 −1.96186
$$292$$ 0 0
$$293$$ 2331.73i 0.464919i 0.972606 + 0.232459i $$0.0746772\pi$$
−0.972606 + 0.232459i $$0.925323\pi$$
$$294$$ 0 0
$$295$$ −318.771 6109.29i −0.0629137 1.20575i
$$296$$ 0 0
$$297$$ 4535.12i 0.886041i
$$298$$ 0 0
$$299$$ −7586.51 −1.46736
$$300$$ 0 0
$$301$$ −11102.9 −2.12611
$$302$$ 0 0
$$303$$ 2496.55i 0.473343i
$$304$$ 0 0
$$305$$ −297.964 5710.52i −0.0559388 1.07208i
$$306$$ 0 0
$$307$$ 2100.00i 0.390401i −0.980763 0.195200i $$-0.937464\pi$$
0.980763 0.195200i $$-0.0625357\pi$$
$$308$$ 0 0
$$309$$ −1718.40 −0.316364
$$310$$ 0 0
$$311$$ 8501.38 1.55006 0.775030 0.631924i $$-0.217735\pi$$
0.775030 + 0.631924i $$0.217735\pi$$
$$312$$ 0 0
$$313$$ 7257.73i 1.31064i 0.755350 + 0.655321i $$0.227467\pi$$
−0.755350 + 0.655321i $$0.772533\pi$$
$$314$$ 0 0
$$315$$ 11493.7 599.717i 2.05586 0.107271i
$$316$$ 0 0
$$317$$ 9639.14i 1.70785i 0.520397 + 0.853925i $$0.325784\pi$$
−0.520397 + 0.853925i $$0.674216\pi$$
$$318$$ 0 0
$$319$$ −1862.59 −0.326912
$$320$$ 0 0
$$321$$ −6466.93 −1.12445
$$322$$ 0 0
$$323$$ 8067.72i 1.38978i
$$324$$ 0 0
$$325$$ −914.933 8743.55i −0.156158 1.49232i
$$326$$ 0 0
$$327$$ 4300.88i 0.727337i
$$328$$ 0 0
$$329$$ −9726.34 −1.62988
$$330$$ 0 0
$$331$$ −360.466 −0.0598581 −0.0299290 0.999552i $$-0.509528\pi$$
−0.0299290 + 0.999552i $$0.509528\pi$$
$$332$$ 0 0
$$333$$ 2804.24i 0.461476i
$$334$$ 0 0
$$335$$ 3366.82 175.674i 0.549101 0.0286510i
$$336$$ 0 0
$$337$$ 2820.47i 0.455908i 0.973672 + 0.227954i $$0.0732036\pi$$
−0.973672 + 0.227954i $$0.926796\pi$$
$$338$$ 0 0
$$339$$ −4262.89 −0.682974
$$340$$ 0 0
$$341$$ −3721.99 −0.591076
$$342$$ 0 0
$$343$$ 4335.24i 0.682451i
$$344$$ 0 0
$$345$$ −538.744 10325.1i −0.0840725 1.61126i
$$346$$ 0 0
$$347$$ 8617.62i 1.33319i −0.745419 0.666597i $$-0.767750\pi$$
0.745419 0.666597i $$-0.232250\pi$$
$$348$$ 0 0
$$349$$ −735.067 −0.112743 −0.0563714 0.998410i $$-0.517953\pi$$
−0.0563714 + 0.998410i $$0.517953\pi$$
$$350$$ 0 0
$$351$$ −11754.6 −1.78750
$$352$$ 0 0
$$353$$ 4535.35i 0.683830i 0.939731 + 0.341915i $$0.111076\pi$$
−0.939731 + 0.341915i $$0.888924\pi$$
$$354$$ 0 0
$$355$$ −48.2943 925.567i −0.00722026 0.138377i
$$356$$ 0 0
$$357$$ 13916.9i 2.06320i
$$358$$ 0 0
$$359$$ −5426.44 −0.797762 −0.398881 0.917003i $$-0.630601\pi$$
−0.398881 + 0.917003i $$0.630601\pi$$
$$360$$ 0 0
$$361$$ 5248.15 0.765148
$$362$$ 0 0
$$363$$ 5098.41i 0.737182i
$$364$$ 0 0
$$365$$ 8521.99 444.661i 1.22209 0.0637660i
$$366$$ 0 0
$$367$$ 609.673i 0.0867157i 0.999060 + 0.0433579i $$0.0138056\pi$$
−0.999060 + 0.0433579i $$0.986194\pi$$
$$368$$ 0 0
$$369$$ −4423.90 −0.624117
$$370$$ 0 0
$$371$$ 6353.26 0.889069
$$372$$ 0 0
$$373$$ 5089.42i 0.706489i −0.935531 0.353244i $$-0.885078\pi$$
0.935531 0.353244i $$-0.114922\pi$$
$$374$$ 0 0
$$375$$ 11834.8 1866.12i 1.62973 0.256976i
$$376$$ 0 0
$$377$$ 4827.64i 0.659513i
$$378$$ 0 0
$$379$$ 910.876 0.123453 0.0617263 0.998093i $$-0.480339\pi$$
0.0617263 + 0.998093i $$0.480339\pi$$
$$380$$ 0 0
$$381$$ −7846.14 −1.05504
$$382$$ 0 0
$$383$$ 7686.98i 1.02555i 0.858522 + 0.512776i $$0.171383\pi$$
−0.858522 + 0.512776i $$0.828617\pi$$
$$384$$ 0 0
$$385$$ −6707.68 + 349.994i −0.887936 + 0.0463307i
$$386$$ 0 0
$$387$$ 23316.5i 3.06264i
$$388$$ 0 0
$$389$$ −4372.77 −0.569943 −0.284972 0.958536i $$-0.591984\pi$$
−0.284972 + 0.958536i $$0.591984\pi$$
$$390$$ 0 0
$$391$$ 7909.14 1.02297
$$392$$ 0 0
$$393$$ 5207.38i 0.668390i
$$394$$ 0 0
$$395$$ 589.247 + 11293.0i 0.0750589 + 1.43851i
$$396$$ 0 0
$$397$$ 12591.9i 1.59186i −0.605391 0.795928i $$-0.706983\pi$$
0.605391 0.795928i $$-0.293017\pi$$
$$398$$ 0 0
$$399$$ −20885.0 −2.62045
$$400$$ 0 0
$$401$$ 3614.48 0.450122 0.225061 0.974345i $$-0.427742\pi$$
0.225061 + 0.974345i $$0.427742\pi$$
$$402$$ 0 0
$$403$$ 9647.01i 1.19244i
$$404$$ 0 0
$$405$$ −103.378 1981.26i −0.0126837 0.243085i
$$406$$ 0 0
$$407$$ 1636.55i 0.199314i
$$408$$ 0 0
$$409$$ −639.314 −0.0772910 −0.0386455 0.999253i $$-0.512304\pi$$
−0.0386455 + 0.999253i $$0.512304\pi$$
$$410$$ 0 0
$$411$$ 12164.8 1.45997
$$412$$ 0 0
$$413$$ 12114.6i 1.44339i
$$414$$ 0 0
$$415$$ −7866.45 + 410.456i −0.930479 + 0.0485506i
$$416$$ 0 0
$$417$$ 26026.2i 3.05637i
$$418$$ 0 0
$$419$$ −11018.4 −1.28469 −0.642346 0.766415i $$-0.722039\pi$$
−0.642346 + 0.766415i $$0.722039\pi$$
$$420$$ 0 0
$$421$$ 16513.1 1.91164 0.955820 0.293952i $$-0.0949707\pi$$
0.955820 + 0.293952i $$0.0949707\pi$$
$$422$$ 0 0
$$423$$ 20425.7i 2.34783i
$$424$$ 0 0
$$425$$ 953.842 + 9115.38i 0.108866 + 1.04038i
$$426$$ 0 0
$$427$$ 11323.9i 1.28337i
$$428$$ 0 0
$$429$$ 16360.5 1.84124
$$430$$ 0 0
$$431$$ 6106.80 0.682492 0.341246 0.939974i $$-0.389151\pi$$
0.341246 + 0.939974i $$0.389151\pi$$
$$432$$ 0 0
$$433$$ 1757.88i 0.195100i 0.995231 + 0.0975500i $$0.0311006\pi$$
−0.995231 + 0.0975500i $$0.968899\pi$$
$$434$$ 0 0
$$435$$ 6570.33 342.827i 0.724192 0.0377869i
$$436$$ 0 0
$$437$$ 11869.2i 1.29927i
$$438$$ 0 0
$$439$$ −1055.02 −0.114700 −0.0573500 0.998354i $$-0.518265\pi$$
−0.0573500 + 0.998354i $$0.518265\pi$$
$$440$$ 0 0
$$441$$ 6843.78 0.738989
$$442$$ 0 0
$$443$$ 7775.51i 0.833918i −0.908925 0.416959i $$-0.863096\pi$$
0.908925 0.416959i $$-0.136904\pi$$
$$444$$ 0 0
$$445$$ −432.977 8298.08i −0.0461238 0.883970i
$$446$$ 0 0
$$447$$ 22712.0i 2.40322i
$$448$$ 0 0
$$449$$ 11245.1 1.18194 0.590969 0.806694i $$-0.298745\pi$$
0.590969 + 0.806694i $$0.298745\pi$$
$$450$$ 0 0
$$451$$ 2581.78 0.269560
$$452$$ 0 0
$$453$$ 2428.69i 0.251898i
$$454$$ 0 0
$$455$$ −907.148 17385.6i −0.0934676 1.79132i
$$456$$ 0 0
$$457$$ 13576.9i 1.38972i 0.719145 + 0.694860i $$0.244534\pi$$
−0.719145 + 0.694860i $$0.755466\pi$$
$$458$$ 0 0
$$459$$ 12254.4 1.24616
$$460$$ 0 0
$$461$$ −9605.08 −0.970397 −0.485199 0.874404i $$-0.661253\pi$$
−0.485199 + 0.874404i $$0.661253\pi$$
$$462$$ 0 0
$$463$$ 3226.71i 0.323883i −0.986800 0.161942i $$-0.948224\pi$$
0.986800 0.161942i $$-0.0517756\pi$$
$$464$$ 0 0
$$465$$ 13129.4 685.067i 1.30938 0.0683209i
$$466$$ 0 0
$$467$$ 20.6790i 0.00204906i 0.999999 + 0.00102453i $$0.000326118\pi$$
−0.999999 + 0.00102453i $$0.999674\pi$$
$$468$$ 0 0
$$469$$ 6676.34 0.657323
$$470$$ 0 0
$$471$$ −12129.7 −1.18664
$$472$$ 0 0
$$473$$ 13607.5i 1.32277i
$$474$$ 0 0
$$475$$ −13679.4 + 1431.42i −1.32137 + 0.138270i
$$476$$ 0 0
$$477$$ 13342.1i 1.28070i
$$478$$ 0 0
$$479$$ 12492.9 1.19168 0.595841 0.803102i $$-0.296819\pi$$
0.595841 + 0.803102i $$0.296819\pi$$
$$480$$ 0 0
$$481$$ −4241.77 −0.402096
$$482$$ 0 0
$$483$$ 20474.5i 1.92882i
$$484$$ 0 0
$$485$$ −12683.6 + 661.806i −1.18749 + 0.0619610i
$$486$$ 0 0
$$487$$ 4944.60i 0.460084i −0.973181 0.230042i $$-0.926114\pi$$
0.973181 0.230042i $$-0.0738864\pi$$
$$488$$ 0 0
$$489$$ 14794.2 1.36813
$$490$$ 0 0
$$491$$ −7712.73 −0.708902 −0.354451 0.935075i $$-0.615332\pi$$
−0.354451 + 0.935075i $$0.615332\pi$$
$$492$$ 0 0
$$493$$ 5032.95i 0.459782i
$$494$$ 0 0
$$495$$ 735.000 + 14086.4i 0.0667390 + 1.27906i
$$496$$ 0 0
$$497$$ 1835.38i 0.165650i
$$498$$ 0 0
$$499$$ 1492.41 0.133886 0.0669432 0.997757i $$-0.478675\pi$$
0.0669432 + 0.997757i $$0.478675\pi$$
$$500$$ 0 0
$$501$$ 16973.7 1.51363
$$502$$ 0 0
$$503$$ 3105.13i 0.275250i 0.990484 + 0.137625i $$0.0439469\pi$$
−0.990484 + 0.137625i $$0.956053\pi$$
$$504$$ 0 0
$$505$$ −169.653 3251.43i −0.0149494 0.286508i
$$506$$ 0 0
$$507$$ 23570.1i 2.06466i
$$508$$ 0 0
$$509$$ −15363.5 −1.33787 −0.668933 0.743322i $$-0.733249\pi$$
−0.668933 + 0.743322i $$0.733249\pi$$
$$510$$ 0 0
$$511$$ 16898.9 1.46295
$$512$$ 0 0
$$513$$ 18390.1i 1.58274i
$$514$$ 0 0
$$515$$ −2237.99 + 116.774i −0.191491 + 0.00999162i
$$516$$ 0 0
$$517$$ 11920.4i 1.01404i
$$518$$ 0 0
$$519$$ 12591.2 1.06492
$$520$$ 0 0
$$521$$ −9924.25 −0.834529 −0.417264 0.908785i $$-0.637011\pi$$
−0.417264 + 0.908785i $$0.637011\pi$$
$$522$$ 0 0
$$523$$ 455.146i 0.0380538i 0.999819 + 0.0190269i $$0.00605681\pi$$
−0.999819 + 0.0190269i $$0.993943\pi$$
$$524$$ 0 0
$$525$$ 23597.1 2469.22i 1.96164 0.205268i
$$526$$ 0 0
$$527$$ 10057.3i 0.831312i
$$528$$ 0 0
$$529$$ 531.111 0.0436517
$$530$$ 0 0
$$531$$ −25441.1 −2.07919
$$532$$ 0 0
$$533$$ 6691.72i 0.543809i
$$534$$ 0 0
$$535$$ −8422.34 + 439.461i −0.680616 + 0.0355132i
$$536$$ 0 0
$$537$$ 25535.3i 2.05201i
$$538$$ 0 0
$$539$$ −3994.02 −0.319174
$$540$$ 0 0
$$541$$ 23383.9 1.85832 0.929160 0.369678i $$-0.120532\pi$$
0.929160 + 0.369678i $$0.120532\pi$$
$$542$$ 0 0
$$543$$ 14420.3i 1.13966i
$$544$$ 0 0
$$545$$ 292.267 + 5601.34i 0.0229713 + 0.440248i
$$546$$ 0 0
$$547$$ 6908.03i 0.539974i 0.962864 + 0.269987i $$0.0870195\pi$$
−0.962864 + 0.269987i $$0.912981\pi$$
$$548$$ 0 0
$$549$$ −23780.5 −1.84868
$$550$$ 0 0
$$551$$ −7552.90 −0.583964
$$552$$ 0 0
$$553$$ 22393.8i 1.72203i
$$554$$ 0 0
$$555$$ −301.222 5772.97i −0.0230382 0.441530i
$$556$$ 0 0
$$557$$ 3221.81i 0.245085i 0.992463 + 0.122543i $$0.0391048\pi$$
−0.992463 + 0.122543i $$0.960895\pi$$
$$558$$ 0 0
$$559$$ 35269.1 2.66856
$$560$$ 0 0
$$561$$ −17056.3 −1.28363
$$562$$ 0 0
$$563$$ 14822.7i 1.10959i 0.831986 + 0.554796i $$0.187204\pi$$
−0.831986 + 0.554796i $$0.812796\pi$$
$$564$$ 0 0
$$565$$ −5551.85 + 289.685i −0.413395 + 0.0215701i
$$566$$ 0 0
$$567$$ 3928.79i 0.290994i
$$568$$ 0 0
$$569$$ −6434.10 −0.474045 −0.237022 0.971504i $$-0.576172\pi$$
−0.237022 + 0.971504i $$0.576172\pi$$
$$570$$ 0 0
$$571$$ −17760.3 −1.30165 −0.650827 0.759226i $$-0.725578\pi$$
−0.650827 + 0.759226i $$0.725578\pi$$
$$572$$ 0 0
$$573$$ 2351.85i 0.171466i
$$574$$ 0 0
$$575$$ −1403.29 13410.5i −0.101776 0.972620i
$$576$$ 0 0
$$577$$ 1341.96i 0.0968227i 0.998827 + 0.0484113i $$0.0154158\pi$$
−0.998827 + 0.0484113i $$0.984584\pi$$
$$578$$ 0 0
$$579$$ 24848.7 1.78355
$$580$$ 0 0
$$581$$ −15599.0 −1.11387
$$582$$ 0 0
$$583$$ 7786.42i 0.553140i
$$584$$ 0 0
$$585$$ −36510.5 + 1905.05i −2.58038 + 0.134639i
$$586$$ 0 0
$$587$$ 12957.3i 0.911082i −0.890215 0.455541i $$-0.849446\pi$$
0.890215 0.455541i $$-0.150554\pi$$
$$588$$ 0 0
$$589$$ −15092.8 −1.05584
$$590$$ 0 0
$$591$$ −19978.1 −1.39051
$$592$$ 0 0
$$593$$ 5966.63i 0.413187i −0.978427 0.206594i $$-0.933762\pi$$
0.978427 0.206594i $$-0.0662378\pi$$
$$594$$ 0 0
$$595$$ 945.726 + 18125.0i 0.0651613 + 1.24883i
$$596$$ 0 0
$$597$$ 9473.56i 0.649459i
$$598$$ 0 0
$$599$$ −10311.9 −0.703396 −0.351698 0.936114i $$-0.614396\pi$$
−0.351698 + 0.936114i $$0.614396\pi$$
$$600$$ 0 0
$$601$$ 2594.60 0.176100 0.0880499 0.996116i $$-0.471936\pi$$
0.0880499 + 0.996116i $$0.471936\pi$$
$$602$$ 0 0
$$603$$ 14020.6i 0.946868i
$$604$$ 0 0
$$605$$ 346.463 + 6640.02i 0.0232822 + 0.446207i
$$606$$ 0 0
$$607$$ 7796.08i 0.521306i 0.965432 + 0.260653i $$0.0839379\pi$$
−0.965432 + 0.260653i $$0.916062\pi$$
$$608$$ 0 0
$$609$$ 13028.9 0.866922
$$610$$ 0 0
$$611$$ 30896.5 2.04572
$$612$$ 0 0
$$613$$ 10443.5i 0.688106i 0.938950 + 0.344053i $$0.111800\pi$$
−0.938950 + 0.344053i $$0.888200\pi$$
$$614$$ 0 0
$$615$$ −9107.30 + 475.201i −0.597141 + 0.0311577i
$$616$$ 0 0
$$617$$ 18306.1i 1.19445i −0.802073 0.597226i $$-0.796270\pi$$
0.802073 0.597226i $$-0.203730\pi$$
$$618$$ 0 0
$$619$$ 149.857 0.00973066 0.00486533 0.999988i $$-0.498451\pi$$
0.00486533 + 0.999988i $$0.498451\pi$$
$$620$$ 0 0
$$621$$ −18028.7 −1.16500
$$622$$ 0 0
$$623$$ 16454.9i 1.05819i
$$624$$ 0 0
$$625$$ 15286.5 3234.61i 0.978338 0.207015i
$$626$$ 0 0
$$627$$ 25596.2i 1.63033i
$$628$$ 0 0
$$629$$ 4422.16 0.280323
$$630$$ 0 0
$$631$$ −24466.5 −1.54358 −0.771789 0.635879i $$-0.780638\pi$$
−0.771789 + 0.635879i $$0.780638\pi$$
$$632$$ 0 0
$$633$$ 40719.9i 2.55683i
$$634$$ 0 0
$$635$$ −10218.6 + 533.185i −0.638601 + 0.0333210i
$$636$$ 0 0
$$637$$ 10352.1i 0.643901i
$$638$$ 0 0
$$639$$ −3854.37 −0.238618
$$640$$ 0 0
$$641$$ −20274.7 −1.24930 −0.624652 0.780903i $$-0.714759\pi$$
−0.624652 + 0.780903i $$0.714759\pi$$
$$642$$ 0 0
$$643$$ 9167.25i 0.562241i 0.959672 + 0.281121i $$0.0907061\pi$$
−0.959672 + 0.281121i $$0.909294\pi$$
$$644$$ 0 0
$$645$$ 2504.58 + 48000.7i 0.152896 + 2.93027i
$$646$$ 0 0
$$647$$ 5459.82i 0.331758i 0.986146 + 0.165879i $$0.0530462\pi$$
−0.986146 + 0.165879i $$0.946954\pi$$
$$648$$ 0 0
$$649$$ 14847.4 0.898016
$$650$$ 0 0
$$651$$ 26035.4 1.56744
$$652$$ 0 0
$$653$$ 16280.5i 0.975659i −0.872939 0.487830i $$-0.837789\pi$$
0.872939 0.487830i $$-0.162211\pi$$
$$654$$ 0 0
$$655$$ −353.868 6781.93i −0.0211096 0.404568i
$$656$$ 0 0
$$657$$ 35488.4i 2.10736i
$$658$$ 0 0
$$659$$ 23975.9 1.41725 0.708625 0.705585i $$-0.249316\pi$$
0.708625 + 0.705585i $$0.249316\pi$$
$$660$$ 0 0
$$661$$ −13876.4 −0.816532 −0.408266 0.912863i $$-0.633866\pi$$
−0.408266 + 0.912863i $$0.633866\pi$$
$$662$$ 0 0
$$663$$ 44208.2i 2.58960i
$$664$$ 0 0
$$665$$ −27200.0 + 1419.24i −1.58612 + 0.0827607i
$$666$$ 0 0
$$667$$ 7404.44i 0.429837i
$$668$$ 0 0
$$669$$ −16200.3 −0.936236
$$670$$ 0 0
$$671$$ 13878.3 0.798458
$$672$$ 0 0
$$673$$ 30526.1i 1.74843i 0.485537 + 0.874216i $$0.338624\pi$$
−0.485537 + 0.874216i $$0.661376\pi$$
$$674$$ 0 0
$$675$$ −2174.26 20778.2i −0.123981 1.18482i
$$676$$ 0 0
$$677$$ 6992.09i 0.396939i −0.980107 0.198470i $$-0.936403\pi$$
0.980107 0.198470i $$-0.0635971\pi$$
$$678$$ 0 0
$$679$$ −25151.4 −1.42153
$$680$$ 0 0
$$681$$ 35613.0 2.00395
$$682$$ 0 0
$$683$$ 22479.2i 1.25936i 0.776854 + 0.629681i $$0.216814\pi$$
−0.776854 + 0.629681i $$0.783186\pi$$
$$684$$ 0 0
$$685$$ 15843.1 826.661i 0.883698 0.0461096i
$$686$$ 0 0
$$687$$ 7618.29i 0.423080i
$$688$$ 0 0
$$689$$ −20181.6 −1.11590
$$690$$ 0 0
$$691$$ 5536.97 0.304828 0.152414 0.988317i $$-0.451295\pi$$
0.152414 + 0.988317i $$0.451295\pi$$
$$692$$ 0 0
$$693$$ 27933.1i 1.53115i
$$694$$ 0 0
$$695$$ 1768.61 + 33895.7i 0.0965285 + 1.84998i
$$696$$ 0 0
$$697$$ 6976.29i 0.379119i
$$698$$ 0 0
$$699$$ −42173.6 −2.28205
$$700$$ 0 0
$$701$$ −16934.8 −0.912436 −0.456218 0.889868i $$-0.650796\pi$$
−0.456218 + 0.889868i $$0.650796\pi$$
$$702$$ 0 0
$$703$$ 6636.29i 0.356035i
$$704$$ 0 0
$$705$$ 2194.06 + 42049.5i 0.117210 + 2.24635i
$$706$$ 0 0
$$707$$ 6447.52i 0.342976i
$$708$$ 0 0
$$709$$ 4112.16 0.217821 0.108911 0.994052i $$-0.465264\pi$$
0.108911 + 0.994052i $$0.465264\pi$$
$$710$$ 0 0
$$711$$ 47027.9 2.48057
$$712$$ 0 0
$$713$$ 14796.2i 0.777169i
$$714$$ 0 0
$$715$$ 21307.5 1111.78i 1.11448 0.0581514i
$$716$$ 0 0
$$717$$ 18671.9i 0.972543i
$$718$$ 0 0
$$719$$ −34938.3 −1.81221 −0.906105 0.423053i $$-0.860958\pi$$
−0.906105 + 0.423053i $$0.860958\pi$$
$$720$$ 0 0
$$721$$ −4437.90 −0.229232
$$722$$ 0 0
$$723$$ 27057.3i 1.39180i
$$724$$ 0 0
$$725$$ 8533.71 892.976i 0.437150 0.0457438i
$$726$$ 0 0
$$727$$ 34679.2i 1.76916i 0.466389 + 0.884580i $$0.345555\pi$$
−0.466389 + 0.884580i $$0.654445\pi$$
$$728$$ 0 0
$$729$$ 30435.7 1.54629
$$730$$ 0 0
$$731$$ −36769.0 −1.86040
$$732$$ 0 0
$$733$$ 30802.4i 1.55213i 0.630652 + 0.776065i $$0.282787\pi$$
−0.630652 + 0.776065i $$0.717213\pi$$
$$734$$ 0 0
$$735$$ 14089.0 735.137i 0.707049 0.0368924i
$$736$$ 0 0
$$737$$ 8182.38i 0.408958i
$$738$$ 0 0
$$739$$ −16364.2 −0.814570 −0.407285 0.913301i $$-0.633524\pi$$
−0.407285 + 0.913301i $$0.633524\pi$$
$$740$$ 0 0
$$741$$ 66342.8 3.28902
$$742$$ 0 0
$$743$$ 4464.06i 0.220418i 0.993908 + 0.110209i $$0.0351520\pi$$
−0.993908 + 0.110209i $$0.964848\pi$$
$$744$$ 0 0
$$745$$ −1543.39 29579.4i −0.0759001 1.45464i
$$746$$ 0 0
$$747$$ 32758.5i 1.60451i
$$748$$ 0 0
$$749$$ −16701.3 −0.814758
$$750$$ 0 0
$$751$$ 17873.6 0.868463 0.434231 0.900801i $$-0.357020\pi$$
0.434231 + 0.900801i $$0.357020\pi$$
$$752$$ 0 0
$$753$$ 23311.5i 1.12818i
$$754$$ 0 0
$$755$$ −165.042 3163.05i −0.00795562 0.152471i
$$756$$ 0 0
$$757$$ 14305.3i 0.686834i −0.939183 0.343417i $$-0.888416\pi$$
0.939183 0.343417i $$-0.111584\pi$$
$$758$$ 0 0
$$759$$ 25093.1 1.20003
$$760$$ 0 0
$$761$$ 21819.9 1.03938 0.519692 0.854354i $$-0.326047\pi$$
0.519692 + 0.854354i $$0.326047\pi$$
$$762$$ 0 0
$$763$$ 11107.3i 0.527016i
$$764$$ 0 0
$$765$$ 38063.2 1986.06i 1.79892 0.0938643i
$$766$$ 0 0
$$767$$ 38483.0i 1.81166i
$$768$$ 0 0
$$769$$ 29446.6 1.38085 0.690423 0.723406i $$-0.257425\pi$$
0.690423 + 0.723406i $$0.257425\pi$$
$$770$$ 0 0
$$771$$ −6421.71 −0.299964
$$772$$ 0 0
$$773$$ 30232.4i 1.40671i 0.710840 + 0.703354i $$0.248315\pi$$
−0.710840 + 0.703354i $$0.751685\pi$$
$$774$$ 0 0
$$775$$ 17052.8 1784.42i 0.790393 0.0827075i
$$776$$ 0 0
$$777$$ 11447.7i 0.528551i
$$778$$ 0 0
$$779$$ 10469.3 0.481515
$$780$$ 0 0
$$781$$ 2249.41 0.103060
$$782$$ 0 0
$$783$$ 11472.5i 0.523617i
$$784$$ 0 0
$$785$$ −15797.4 + 824.276i −0.718258 + 0.0374773i
$$786$$ 0 0
$$787$$ 30871.6i 1.39829i −0.714980 0.699145i $$-0.753564\pi$$
0.714980 0.699145i $$-0.246436\pi$$
$$788$$ 0 0
$$789$$ −21827.1 −0.984873
$$790$$ 0 0
$$791$$ −11009.2 −0.494871
$$792$$ 0 0
$$793$$ 35971.1i 1.61081i
$$794$$ 0 0
$$795$$ −1433.16 27466.8i −0.0639359 1.22534i
$$796$$ 0 0
$$797$$ 4612.35i 0.204991i 0.994733 + 0.102496i $$0.0326828\pi$$
−0.994733 +