# Properties

 Label 441.4.e.p.361.1 Level $441$ Weight $4$ Character 441.361 Analytic conductor $26.020$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 441.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$26.0198423125$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-19})$$ Defining polynomial: $$x^{4} - x^{3} - 4 x^{2} - 5 x + 25$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$2.13746 + 0.656712i$$ of defining polynomial Character $$\chi$$ $$=$$ 441.361 Dual form 441.4.e.p.226.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.63746 - 4.56821i) q^{2} +(-9.91238 + 17.1687i) q^{4} +(-5.27492 - 9.13642i) q^{5} +62.3746 q^{8} +O(q^{10})$$ $$q+(-2.63746 - 4.56821i) q^{2} +(-9.91238 + 17.1687i) q^{4} +(-5.27492 - 9.13642i) q^{5} +62.3746 q^{8} +(-27.8248 + 48.1939i) q^{10} +(17.3746 - 30.0937i) q^{11} +37.2990 q^{13} +(-85.2114 - 147.590i) q^{16} +(5.27492 - 9.13642i) q^{17} +(-29.2990 - 50.7474i) q^{19} +209.148 q^{20} -183.299 q^{22} +(-62.6736 - 108.554i) q^{23} +(6.85050 - 11.8654i) q^{25} +(-98.3746 - 170.390i) q^{26} +35.4020 q^{29} +(145.897 - 252.701i) q^{31} +(-199.985 + 346.384i) q^{32} -55.6495 q^{34} +(129.949 + 225.077i) q^{37} +(-154.550 + 267.688i) q^{38} +(-329.021 - 569.881i) q^{40} -338.248 q^{41} +6.80397 q^{43} +(344.447 + 596.599i) q^{44} +(-330.598 + 572.613i) q^{46} +(-125.347 - 217.108i) q^{47} -72.2716 q^{50} +(-369.722 + 640.377i) q^{52} +(-268.450 + 464.969i) q^{53} -366.598 q^{55} +(-93.3713 - 161.724i) q^{58} +(17.9452 - 31.0820i) q^{59} +(28.8970 + 50.0511i) q^{61} -1539.19 q^{62} +746.423 q^{64} +(-196.749 - 340.780i) q^{65} +(-240.846 + 417.157i) q^{67} +(104.574 + 181.127i) q^{68} -363.752 q^{71} +(290.650 - 503.420i) q^{73} +(685.468 - 1187.26i) q^{74} +1161.69 q^{76} +(346.846 + 600.754i) q^{79} +(-898.966 + 1557.05i) q^{80} +(892.114 + 1545.19i) q^{82} +1334.39 q^{83} -111.299 q^{85} +(-17.9452 - 31.0820i) q^{86} +(1083.73 - 1877.08i) q^{88} +(176.519 + 305.740i) q^{89} +2484.98 q^{92} +(-661.196 + 1145.23i) q^{94} +(-309.100 + 535.376i) q^{95} -1445.88 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 3q^{2} - 17q^{4} - 6q^{5} + 174q^{8} + O(q^{10})$$ $$4q - 3q^{2} - 17q^{4} - 6q^{5} + 174q^{8} - 66q^{10} - 6q^{11} - 32q^{13} - 137q^{16} + 6q^{17} + 64q^{19} + 444q^{20} - 552q^{22} + 6q^{23} + 118q^{25} - 318q^{26} + 504q^{29} + 40q^{31} - 279q^{32} - 132q^{34} + 248q^{37} - 588q^{38} - 546q^{40} - 900q^{41} + 752q^{43} + 804q^{44} - 960q^{46} + 12q^{47} + 330q^{50} - 890q^{52} - 1104q^{53} - 1104q^{55} + 306q^{58} - 804q^{59} - 428q^{61} - 4224q^{62} + 2578q^{64} - 636q^{65} - 148q^{67} + 222q^{68} - 1908q^{71} + 1072q^{73} + 1398q^{74} + 3016q^{76} + 572q^{79} - 1950q^{80} + 1530q^{82} + 3888q^{83} - 264q^{85} + 804q^{86} + 1164q^{88} - 366q^{89} + 5712q^{92} - 1920q^{94} - 1176q^{95} - 1616q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$344$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.63746 4.56821i −0.932482 1.61511i −0.779063 0.626946i $$-0.784305\pi$$
−0.153420 0.988161i $$-0.549029\pi$$
$$3$$ 0 0
$$4$$ −9.91238 + 17.1687i −1.23905 + 2.14609i
$$5$$ −5.27492 9.13642i −0.471803 0.817187i 0.527677 0.849445i $$-0.323063\pi$$
−0.999480 + 0.0322587i $$0.989730\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 62.3746 2.75659
$$9$$ 0 0
$$10$$ −27.8248 + 48.1939i −0.879896 + 1.52402i
$$11$$ 17.3746 30.0937i 0.476240 0.824871i −0.523390 0.852093i $$-0.675333\pi$$
0.999629 + 0.0272223i $$0.00866619\pi$$
$$12$$ 0 0
$$13$$ 37.2990 0.795760 0.397880 0.917437i $$-0.369746\pi$$
0.397880 + 0.917437i $$0.369746\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −85.2114 147.590i −1.33143 2.30610i
$$17$$ 5.27492 9.13642i 0.0752562 0.130348i −0.825941 0.563756i $$-0.809356\pi$$
0.901198 + 0.433408i $$0.142689\pi$$
$$18$$ 0 0
$$19$$ −29.2990 50.7474i −0.353771 0.612750i 0.633136 0.774041i $$-0.281768\pi$$
−0.986907 + 0.161291i $$0.948434\pi$$
$$20$$ 209.148 2.33834
$$21$$ 0 0
$$22$$ −183.299 −1.77634
$$23$$ −62.6736 108.554i −0.568189 0.984132i −0.996745 0.0806171i $$-0.974311\pi$$
0.428556 0.903515i $$-0.359022\pi$$
$$24$$ 0 0
$$25$$ 6.85050 11.8654i 0.0548040 0.0949233i
$$26$$ −98.3746 170.390i −0.742032 1.28524i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 35.4020 0.226689 0.113345 0.993556i $$-0.463844\pi$$
0.113345 + 0.993556i $$0.463844\pi$$
$$30$$ 0 0
$$31$$ 145.897 252.701i 0.845286 1.46408i −0.0400859 0.999196i $$-0.512763\pi$$
0.885372 0.464883i $$-0.153904\pi$$
$$32$$ −199.985 + 346.384i −1.10477 + 1.91352i
$$33$$ 0 0
$$34$$ −55.6495 −0.280700
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 129.949 + 225.077i 0.577389 + 1.00007i 0.995778 + 0.0917993i $$0.0292618\pi$$
−0.418388 + 0.908268i $$0.637405\pi$$
$$38$$ −154.550 + 267.688i −0.659771 + 1.14276i
$$39$$ 0 0
$$40$$ −329.021 569.881i −1.30057 2.25265i
$$41$$ −338.248 −1.28842 −0.644212 0.764847i $$-0.722815\pi$$
−0.644212 + 0.764847i $$0.722815\pi$$
$$42$$ 0 0
$$43$$ 6.80397 0.0241301 0.0120651 0.999927i $$-0.496159\pi$$
0.0120651 + 0.999927i $$0.496159\pi$$
$$44$$ 344.447 + 596.599i 1.18017 + 2.04411i
$$45$$ 0 0
$$46$$ −330.598 + 572.613i −1.05965 + 1.83537i
$$47$$ −125.347 217.108i −0.389016 0.673796i 0.603301 0.797513i $$-0.293852\pi$$
−0.992317 + 0.123717i $$0.960518\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −72.2716 −0.204415
$$51$$ 0 0
$$52$$ −369.722 + 640.377i −0.985984 + 1.70777i
$$53$$ −268.450 + 464.969i −0.695745 + 1.20507i 0.274184 + 0.961677i $$0.411592\pi$$
−0.969929 + 0.243388i $$0.921741\pi$$
$$54$$ 0 0
$$55$$ −366.598 −0.898765
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −93.3713 161.724i −0.211384 0.366127i
$$59$$ 17.9452 31.0820i 0.0395977 0.0685853i −0.845547 0.533900i $$-0.820726\pi$$
0.885145 + 0.465315i $$0.154059\pi$$
$$60$$ 0 0
$$61$$ 28.8970 + 50.0511i 0.0606538 + 0.105056i 0.894758 0.446552i $$-0.147348\pi$$
−0.834104 + 0.551607i $$0.814015\pi$$
$$62$$ −1539.19 −3.15286
$$63$$ 0 0
$$64$$ 746.423 1.45786
$$65$$ −196.749 340.780i −0.375442 0.650285i
$$66$$ 0 0
$$67$$ −240.846 + 417.157i −0.439164 + 0.760654i −0.997625 0.0688767i $$-0.978059\pi$$
0.558462 + 0.829530i $$0.311392\pi$$
$$68$$ 104.574 + 181.127i 0.186492 + 0.323013i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −363.752 −0.608021 −0.304010 0.952669i $$-0.598326\pi$$
−0.304010 + 0.952669i $$0.598326\pi$$
$$72$$ 0 0
$$73$$ 290.650 503.420i 0.465999 0.807135i −0.533247 0.845960i $$-0.679028\pi$$
0.999246 + 0.0388253i $$0.0123616\pi$$
$$74$$ 685.468 1187.26i 1.07681 1.86509i
$$75$$ 0 0
$$76$$ 1161.69 1.75336
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 346.846 + 600.754i 0.493964 + 0.855571i 0.999976 0.00695559i $$-0.00221405\pi$$
−0.506012 + 0.862527i $$0.668881\pi$$
$$80$$ −898.966 + 1557.05i −1.25634 + 2.17605i
$$81$$ 0 0
$$82$$ 892.114 + 1545.19i 1.20143 + 2.08094i
$$83$$ 1334.39 1.76468 0.882341 0.470611i $$-0.155967\pi$$
0.882341 + 0.470611i $$0.155967\pi$$
$$84$$ 0 0
$$85$$ −111.299 −0.142024
$$86$$ −17.9452 31.0820i −0.0225009 0.0389728i
$$87$$ 0 0
$$88$$ 1083.73 1877.08i 1.31280 2.27383i
$$89$$ 176.519 + 305.740i 0.210236 + 0.364139i 0.951788 0.306756i $$-0.0992435\pi$$
−0.741552 + 0.670895i $$0.765910\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 2484.98 2.81605
$$93$$ 0 0
$$94$$ −661.196 + 1145.23i −0.725502 + 1.25661i
$$95$$ −309.100 + 535.376i −0.333821 + 0.578194i
$$96$$ 0 0
$$97$$ −1445.88 −1.51347 −0.756735 0.653722i $$-0.773207\pi$$
−0.756735 + 0.653722i $$0.773207\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 135.809 + 235.229i 0.135809 + 0.235229i
$$101$$ −237.426 + 411.234i −0.233909 + 0.405142i −0.958955 0.283558i $$-0.908485\pi$$
0.725046 + 0.688700i $$0.241818\pi$$
$$102$$ 0 0
$$103$$ −999.794 1731.69i −0.956433 1.65659i −0.731053 0.682320i $$-0.760971\pi$$
−0.225380 0.974271i $$-0.572362\pi$$
$$104$$ 2326.51 2.19359
$$105$$ 0 0
$$106$$ 2832.10 2.59508
$$107$$ 583.368 + 1010.42i 0.527068 + 0.912909i 0.999502 + 0.0315431i $$0.0100421\pi$$
−0.472434 + 0.881366i $$0.656625\pi$$
$$108$$ 0 0
$$109$$ 668.588 1158.03i 0.587515 1.01761i −0.407042 0.913410i $$-0.633440\pi$$
0.994557 0.104196i $$-0.0332270\pi$$
$$110$$ 966.887 + 1674.70i 0.838082 + 1.45160i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −906.578 −0.754723 −0.377361 0.926066i $$-0.623169\pi$$
−0.377361 + 0.926066i $$0.623169\pi$$
$$114$$ 0 0
$$115$$ −661.196 + 1145.23i −0.536146 + 0.928633i
$$116$$ −350.918 + 607.807i −0.280878 + 0.486496i
$$117$$ 0 0
$$118$$ −189.319 −0.147697
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 61.7475 + 106.950i 0.0463918 + 0.0803530i
$$122$$ 152.429 264.015i 0.113117 0.195925i
$$123$$ 0 0
$$124$$ 2892.37 + 5009.74i 2.09470 + 3.62813i
$$125$$ −1463.27 −1.04703
$$126$$ 0 0
$$127$$ −1714.89 −1.19820 −0.599101 0.800674i $$-0.704475\pi$$
−0.599101 + 0.800674i $$0.704475\pi$$
$$128$$ −368.782 638.749i −0.254656 0.441078i
$$129$$ 0 0
$$130$$ −1037.84 + 1797.58i −0.700186 + 1.21276i
$$131$$ −235.306 407.561i −0.156937 0.271823i 0.776826 0.629716i $$-0.216829\pi$$
−0.933763 + 0.357893i $$0.883495\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2540.88 1.63805
$$135$$ 0 0
$$136$$ 329.021 569.881i 0.207451 0.359315i
$$137$$ −221.955 + 384.438i −0.138415 + 0.239742i −0.926897 0.375316i $$-0.877534\pi$$
0.788482 + 0.615058i $$0.210868\pi$$
$$138$$ 0 0
$$139$$ −1669.98 −1.01904 −0.509518 0.860460i $$-0.670176\pi$$
−0.509518 + 0.860460i $$0.670176\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 959.382 + 1661.70i 0.566969 + 0.982019i
$$143$$ 648.055 1122.46i 0.378972 0.656400i
$$144$$ 0 0
$$145$$ −186.743 323.448i −0.106953 0.185247i
$$146$$ −3066.30 −1.73814
$$147$$ 0 0
$$148$$ −5152.39 −2.86165
$$149$$ 371.935 + 644.211i 0.204497 + 0.354200i 0.949973 0.312334i $$-0.101111\pi$$
−0.745475 + 0.666534i $$0.767777\pi$$
$$150$$ 0 0
$$151$$ −303.382 + 525.473i −0.163503 + 0.283195i −0.936123 0.351674i $$-0.885613\pi$$
0.772620 + 0.634869i $$0.218946\pi$$
$$152$$ −1827.51 3165.35i −0.975203 1.68910i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3078.38 −1.59523
$$156$$ 0 0
$$157$$ 1557.39 2697.48i 0.791678 1.37123i −0.133250 0.991083i $$-0.542541\pi$$
0.924927 0.380144i $$-0.124125\pi$$
$$158$$ 1829.58 3168.93i 0.921226 1.59561i
$$159$$ 0 0
$$160$$ 4219.61 2.08493
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −1206.54 2089.78i −0.579774 1.00420i −0.995505 0.0947109i $$-0.969807\pi$$
0.415730 0.909488i $$-0.363526\pi$$
$$164$$ 3352.84 5807.28i 1.59642 2.76508i
$$165$$ 0 0
$$166$$ −3519.40 6095.79i −1.64553 2.85015i
$$167$$ −610.475 −0.282874 −0.141437 0.989947i $$-0.545172\pi$$
−0.141437 + 0.989947i $$0.545172\pi$$
$$168$$ 0 0
$$169$$ −805.784 −0.366766
$$170$$ 293.547 + 508.437i 0.132435 + 0.229385i
$$171$$ 0 0
$$172$$ −67.4435 + 116.816i −0.0298984 + 0.0517855i
$$173$$ −1896.90 3285.54i −0.833636 1.44390i −0.895136 0.445792i $$-0.852922\pi$$
0.0615006 0.998107i $$-0.480411\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −5922.05 −2.53631
$$177$$ 0 0
$$178$$ 931.124 1612.75i 0.392082 0.679107i
$$179$$ −1402.34 + 2428.92i −0.585562 + 1.01422i 0.409243 + 0.912426i $$0.365793\pi$$
−0.994805 + 0.101798i $$0.967540\pi$$
$$180$$ 0 0
$$181$$ −3106.04 −1.27553 −0.637763 0.770232i $$-0.720140\pi$$
−0.637763 + 0.770232i $$0.720140\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −3909.24 6771.00i −1.56627 2.71285i
$$185$$ 1370.94 2374.53i 0.544828 0.943670i
$$186$$ 0 0
$$187$$ −183.299 317.483i −0.0716800 0.124153i
$$188$$ 4969.95 1.92804
$$189$$ 0 0
$$190$$ 3260.95 1.24513
$$191$$ 130.976 + 226.857i 0.0496182 + 0.0859413i 0.889768 0.456413i $$-0.150866\pi$$
−0.840150 + 0.542355i $$0.817533\pi$$
$$192$$ 0 0
$$193$$ −2025.54 + 3508.33i −0.755447 + 1.30847i 0.189704 + 0.981841i $$0.439247\pi$$
−0.945152 + 0.326632i $$0.894086\pi$$
$$194$$ 3813.44 + 6605.07i 1.41128 + 2.44442i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2874.83 1.03971 0.519855 0.854254i $$-0.325986\pi$$
0.519855 + 0.854254i $$0.325986\pi$$
$$198$$ 0 0
$$199$$ −1533.49 + 2656.07i −0.546261 + 0.946151i 0.452266 + 0.891883i $$0.350616\pi$$
−0.998526 + 0.0542680i $$0.982717\pi$$
$$200$$ 427.297 740.100i 0.151072 0.261665i
$$201$$ 0 0
$$202$$ 2504.81 0.872463
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 1784.23 + 3090.37i 0.607882 + 1.05288i
$$206$$ −5273.83 + 9134.54i −1.78371 + 3.08948i
$$207$$ 0 0
$$208$$ −3178.30 5504.98i −1.05950 1.83510i
$$209$$ −2036.23 −0.673919
$$210$$ 0 0
$$211$$ 595.422 0.194268 0.0971340 0.995271i $$-0.469032\pi$$
0.0971340 + 0.995271i $$0.469032\pi$$
$$212$$ −5321.96 9217.90i −1.72412 2.98626i
$$213$$ 0 0
$$214$$ 3077.22 5329.90i 0.982964 1.70254i
$$215$$ −35.8904 62.1640i −0.0113847 0.0197188i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −7053.49 −2.19139
$$219$$ 0 0
$$220$$ 3633.86 6294.03i 1.11361 1.92883i
$$221$$ 196.749 340.780i 0.0598859 0.103725i
$$222$$ 0 0
$$223$$ 3779.79 1.13504 0.567520 0.823360i $$-0.307903\pi$$
0.567520 + 0.823360i $$0.307903\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 2391.06 + 4141.44i 0.703766 + 1.21896i
$$227$$ −913.809 + 1582.76i −0.267188 + 0.462783i −0.968135 0.250431i $$-0.919428\pi$$
0.700947 + 0.713214i $$0.252761\pi$$
$$228$$ 0 0
$$229$$ −425.125 736.338i −0.122677 0.212483i 0.798146 0.602465i $$-0.205815\pi$$
−0.920823 + 0.389982i $$0.872481\pi$$
$$230$$ 6975.51 1.99979
$$231$$ 0 0
$$232$$ 2208.18 0.624890
$$233$$ −3295.55 5708.06i −0.926604 1.60492i −0.788962 0.614443i $$-0.789381\pi$$
−0.137642 0.990482i $$-0.543952\pi$$
$$234$$ 0 0
$$235$$ −1322.39 + 2290.45i −0.367078 + 0.635798i
$$236$$ 355.759 + 616.193i 0.0981269 + 0.169961i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 182.556 0.0494083 0.0247042 0.999695i $$-0.492136\pi$$
0.0247042 + 0.999695i $$0.492136\pi$$
$$240$$ 0 0
$$241$$ 761.949 1319.73i 0.203657 0.352745i −0.746047 0.665894i $$-0.768050\pi$$
0.949704 + 0.313149i $$0.101384\pi$$
$$242$$ 325.713 564.152i 0.0865191 0.149856i
$$243$$ 0 0
$$244$$ −1145.75 −0.300612
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1092.82 1892.83i −0.281517 0.487602i
$$248$$ 9100.27 15762.1i 2.33011 4.03587i
$$249$$ 0 0
$$250$$ 3859.32 + 6684.54i 0.976339 + 1.69107i
$$251$$ 2357.73 0.592903 0.296451 0.955048i $$-0.404197\pi$$
0.296451 + 0.955048i $$0.404197\pi$$
$$252$$ 0 0
$$253$$ −4355.71 −1.08238
$$254$$ 4522.94 + 7833.97i 1.11730 + 1.93522i
$$255$$ 0 0
$$256$$ 1040.40 1802.02i 0.254003 0.439946i
$$257$$ −1391.27 2409.76i −0.337686 0.584890i 0.646311 0.763074i $$-0.276311\pi$$
−0.983997 + 0.178185i $$0.942978\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 7801.01 1.86076
$$261$$ 0 0
$$262$$ −1241.22 + 2149.85i −0.292682 + 0.506940i
$$263$$ 1021.89 1769.97i 0.239591 0.414984i −0.721006 0.692929i $$-0.756320\pi$$
0.960597 + 0.277945i $$0.0896532\pi$$
$$264$$ 0 0
$$265$$ 5664.21 1.31302
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −4774.70 8270.03i −1.08829 1.88497i
$$269$$ −1726.42 + 2990.24i −0.391307 + 0.677763i −0.992622 0.121248i $$-0.961310\pi$$
0.601315 + 0.799012i $$0.294644\pi$$
$$270$$ 0 0
$$271$$ 1322.15 + 2290.02i 0.296364 + 0.513318i 0.975301 0.220879i $$-0.0708925\pi$$
−0.678937 + 0.734196i $$0.737559\pi$$
$$272$$ −1797.93 −0.400793
$$273$$ 0 0
$$274$$ 2341.59 0.516280
$$275$$ −238.049 412.313i −0.0521996 0.0904124i
$$276$$ 0 0
$$277$$ −1339.74 + 2320.50i −0.290604 + 0.503341i −0.973953 0.226751i $$-0.927190\pi$$
0.683349 + 0.730092i $$0.260523\pi$$
$$278$$ 4404.50 + 7628.82i 0.950232 + 1.64585i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1019.69 0.216476 0.108238 0.994125i $$-0.465479\pi$$
0.108238 + 0.994125i $$0.465479\pi$$
$$282$$ 0 0
$$283$$ 216.103 374.301i 0.0453922 0.0786216i −0.842437 0.538795i $$-0.818880\pi$$
0.887829 + 0.460174i $$0.152213\pi$$
$$284$$ 3605.65 6245.17i 0.753366 1.30487i
$$285$$ 0 0
$$286$$ −6836.87 −1.41354
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 2400.85 + 4158.40i 0.488673 + 0.846406i
$$290$$ −985.051 + 1706.16i −0.199463 + 0.345480i
$$291$$ 0 0
$$292$$ 5762.05 + 9980.17i 1.15479 + 2.00016i
$$293$$ −2245.92 −0.447809 −0.223904 0.974611i $$-0.571880\pi$$
−0.223904 + 0.974611i $$0.571880\pi$$
$$294$$ 0 0
$$295$$ −378.638 −0.0747293
$$296$$ 8105.48 + 14039.1i 1.59163 + 2.75678i
$$297$$ 0 0
$$298$$ 1961.93 3398.16i 0.381381 0.660571i
$$299$$ −2337.66 4048.95i −0.452142 0.783133i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 3200.63 0.609853
$$303$$ 0 0
$$304$$ −4993.22 + 8648.51i −0.942042 + 1.63166i
$$305$$ 304.859 528.031i 0.0572333 0.0991310i
$$306$$ 0 0
$$307$$ 3197.08 0.594354 0.297177 0.954822i $$-0.403955\pi$$
0.297177 + 0.954822i $$0.403955\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 8119.10 + 14062.7i 1.48753 + 2.57647i
$$311$$ 1677.80 2906.04i 0.305915 0.529860i −0.671550 0.740959i $$-0.734371\pi$$
0.977465 + 0.211100i $$0.0677045\pi$$
$$312$$ 0 0
$$313$$ −1128.20 1954.09i −0.203736 0.352881i 0.745993 0.665954i $$-0.231975\pi$$
−0.949729 + 0.313072i $$0.898642\pi$$
$$314$$ −16430.2 −2.95290
$$315$$ 0 0
$$316$$ −13752.3 −2.44818
$$317$$ −3069.59 5316.69i −0.543866 0.942004i −0.998677 0.0514158i $$-0.983627\pi$$
0.454811 0.890588i $$-0.349707\pi$$
$$318$$ 0 0
$$319$$ 615.095 1065.38i 0.107958 0.186989i
$$320$$ −3937.32 6819.64i −0.687821 1.19134i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −618.199 −0.106494
$$324$$ 0 0
$$325$$ 255.517 442.568i 0.0436108 0.0755362i
$$326$$ −6364.38 + 11023.4i −1.08126 + 1.87280i
$$327$$ 0 0
$$328$$ −21098.0 −3.55166
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −3514.91 6088.00i −0.583676 1.01096i −0.995039 0.0994849i $$-0.968280\pi$$
0.411363 0.911472i $$-0.365053\pi$$
$$332$$ −13227.0 + 22909.8i −2.18652 + 3.78717i
$$333$$ 0 0
$$334$$ 1610.10 + 2788.78i 0.263775 + 0.456872i
$$335$$ 5081.76 0.828795
$$336$$ 0 0
$$337$$ 10328.4 1.66951 0.834757 0.550619i $$-0.185608\pi$$
0.834757 + 0.550619i $$0.185608\pi$$
$$338$$ 2125.22 + 3680.99i 0.342003 + 0.592366i
$$339$$ 0 0
$$340$$ 1103.24 1910.86i 0.175975 0.304797i
$$341$$ −5069.80 8781.15i −0.805118 1.39450i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 424.395 0.0665170
$$345$$ 0 0
$$346$$ −10006.0 + 17330.9i −1.55470 + 2.69282i
$$347$$ 983.768 1703.94i 0.152194 0.263608i −0.779840 0.625980i $$-0.784699\pi$$
0.932034 + 0.362371i $$0.118033\pi$$
$$348$$ 0 0
$$349$$ 4365.46 0.669564 0.334782 0.942296i $$-0.391337\pi$$
0.334782 + 0.942296i $$0.391337\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 6949.30 + 12036.5i 1.05227 + 1.82258i
$$353$$ 3035.79 5258.15i 0.457731 0.792813i −0.541110 0.840952i $$-0.681996\pi$$
0.998841 + 0.0481389i $$0.0153290\pi$$
$$354$$ 0 0
$$355$$ 1918.76 + 3323.40i 0.286866 + 0.496866i
$$356$$ −6998.90 −1.04197
$$357$$ 0 0
$$358$$ 14794.4 2.18411
$$359$$ 4819.02 + 8346.79i 0.708463 + 1.22709i 0.965427 + 0.260673i $$0.0839443\pi$$
−0.256965 + 0.966421i $$0.582722\pi$$
$$360$$ 0 0
$$361$$ 1712.64 2966.37i 0.249692 0.432479i
$$362$$ 8192.06 + 14189.1i 1.18941 + 2.06011i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −6132.61 −0.879439
$$366$$ 0 0
$$367$$ 261.362 452.693i 0.0371744 0.0643879i −0.846840 0.531848i $$-0.821498\pi$$
0.884014 + 0.467460i $$0.154831\pi$$
$$368$$ −10681.0 + 18500.0i −1.51301 + 2.62060i
$$369$$ 0 0
$$370$$ −14463.1 −2.03217
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −1614.92 2797.12i −0.224175 0.388283i 0.731896 0.681416i $$-0.238636\pi$$
−0.956072 + 0.293133i $$0.905302\pi$$
$$374$$ −966.887 + 1674.70i −0.133681 + 0.231542i
$$375$$ 0 0
$$376$$ −7818.48 13542.0i −1.07236 1.85738i
$$377$$ 1320.46 0.180390
$$378$$ 0 0
$$379$$ 6639.71 0.899892 0.449946 0.893056i $$-0.351443\pi$$
0.449946 + 0.893056i $$0.351443\pi$$
$$380$$ −6127.82 10613.7i −0.827239 1.43282i
$$381$$ 0 0
$$382$$ 690.887 1196.65i 0.0925363 0.160278i
$$383$$ 7112.22 + 12318.7i 0.948871 + 1.64349i 0.747809 + 0.663914i $$0.231106\pi$$
0.201063 + 0.979578i $$0.435561\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 21369.1 2.81777
$$387$$ 0 0
$$388$$ 14332.1 24823.9i 1.87526 3.24805i
$$389$$ 1460.91 2530.37i 0.190414 0.329807i −0.754973 0.655755i $$-0.772350\pi$$
0.945388 + 0.325948i $$0.105684\pi$$
$$390$$ 0 0
$$391$$ −1322.39 −0.171039
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −7582.24 13132.8i −0.969512 1.67924i
$$395$$ 3659.16 6337.86i 0.466108 0.807322i
$$396$$ 0 0
$$397$$ 405.970 + 703.161i 0.0513226 + 0.0888933i 0.890545 0.454894i $$-0.150323\pi$$
−0.839223 + 0.543788i $$0.816990\pi$$
$$398$$ 16178.0 2.03751
$$399$$ 0 0
$$400$$ −2334.96 −0.291870
$$401$$ 1169.32 + 2025.32i 0.145618 + 0.252218i 0.929603 0.368561i $$-0.120150\pi$$
−0.783985 + 0.620780i $$0.786816\pi$$
$$402$$ 0 0
$$403$$ 5441.81 9425.50i 0.672645 1.16506i
$$404$$ −4706.91 8152.61i −0.579648 1.00398i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 9031.21 1.09990
$$408$$ 0 0
$$409$$ −1363.79 + 2362.15i −0.164877 + 0.285576i −0.936612 0.350369i $$-0.886056\pi$$
0.771734 + 0.635945i $$0.219390\pi$$
$$410$$ 9411.65 16301.5i 1.13368 1.96359i
$$411$$ 0 0
$$412$$ 39641.3 4.74026
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −7038.81 12191.6i −0.832582 1.44207i
$$416$$ −7459.23 + 12919.8i −0.879132 + 1.52270i
$$417$$ 0 0
$$418$$ 5370.48 + 9301.94i 0.628418 + 1.08845i
$$419$$ 13306.3 1.55144 0.775721 0.631076i $$-0.217386\pi$$
0.775721 + 0.631076i $$0.217386\pi$$
$$420$$ 0 0
$$421$$ −11007.5 −1.27428 −0.637138 0.770750i $$-0.719882\pi$$
−0.637138 + 0.770750i $$0.719882\pi$$
$$422$$ −1570.40 2720.01i −0.181151 0.313763i
$$423$$ 0 0
$$424$$ −16744.5 + 29002.3i −1.91789 + 3.32187i
$$425$$ −72.2716 125.178i −0.00824868 0.0142871i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −23130.2 −2.61225
$$429$$ 0 0
$$430$$ −189.319 + 327.910i −0.0212320 + 0.0367749i
$$431$$ −3262.81 + 5651.36i −0.364650 + 0.631592i −0.988720 0.149776i $$-0.952145\pi$$
0.624070 + 0.781368i $$0.285478\pi$$
$$432$$ 0 0
$$433$$ 11716.3 1.30034 0.650171 0.759788i $$-0.274697\pi$$
0.650171 + 0.759788i $$0.274697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 13254.6 + 22957.6i 1.45592 + 2.52172i
$$437$$ −3672.55 + 6361.04i −0.402018 + 0.696315i
$$438$$ 0 0
$$439$$ −7305.69 12653.8i −0.794264 1.37571i −0.923306 0.384066i $$-0.874524\pi$$
0.129042 0.991639i $$-0.458810\pi$$
$$440$$ −22866.4 −2.47753
$$441$$ 0 0
$$442$$ −2075.67 −0.223370
$$443$$ −7619.89 13198.0i −0.817228 1.41548i −0.907717 0.419583i $$-0.862176\pi$$
0.0904888 0.995897i $$-0.471157\pi$$
$$444$$ 0 0
$$445$$ 1862.25 3225.51i 0.198380 0.343604i
$$446$$ −9969.05 17266.9i −1.05840 1.83321i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −10678.8 −1.12241 −0.561206 0.827676i $$-0.689662\pi$$
−0.561206 + 0.827676i $$0.689662\pi$$
$$450$$ 0 0
$$451$$ −5876.91 + 10179.1i −0.613598 + 1.06278i
$$452$$ 8986.34 15564.8i 0.935137 1.61971i
$$453$$ 0 0
$$454$$ 9640.53 0.996592
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −2114.12 3661.76i −0.216399 0.374814i 0.737306 0.675559i $$-0.236098\pi$$
−0.953704 + 0.300746i $$0.902764\pi$$
$$458$$ −2242.50 + 3884.12i −0.228788 + 0.396273i
$$459$$ 0 0
$$460$$ −13108.0 22703.8i −1.32862 2.30124i
$$461$$ 910.121 0.0919492 0.0459746 0.998943i $$-0.485361\pi$$
0.0459746 + 0.998943i $$0.485361\pi$$
$$462$$ 0 0
$$463$$ 4456.16 0.447290 0.223645 0.974671i $$-0.428204\pi$$
0.223645 + 0.974671i $$0.428204\pi$$
$$464$$ −3016.65 5224.99i −0.301820 0.522768i
$$465$$ 0 0
$$466$$ −17383.8 + 30109.5i −1.72808 + 2.99313i
$$467$$ 2214.71 + 3835.99i 0.219453 + 0.380104i 0.954641 0.297759i $$-0.0962393\pi$$
−0.735188 + 0.677864i $$0.762906\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 13951.0 1.36918
$$471$$ 0 0
$$472$$ 1119.32 1938.73i 0.109155 0.189062i
$$473$$ 118.216 204.757i 0.0114917 0.0199043i
$$474$$ 0 0
$$475$$ −802.851 −0.0775523
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −481.485 833.957i −0.0460724 0.0797998i
$$479$$ −1376.43 + 2384.04i −0.131296 + 0.227411i −0.924176 0.381966i $$-0.875247\pi$$
0.792881 + 0.609377i $$0.208580\pi$$
$$480$$ 0 0
$$481$$ 4846.95 + 8395.16i 0.459463 + 0.795814i
$$482$$ −8038.43 −0.759628
$$483$$ 0 0
$$484$$ −2448.26 −0.229927
$$485$$ 7626.88 + 13210.1i 0.714060 + 1.23679i
$$486$$ 0 0
$$487$$ 335.299 580.755i 0.0311989 0.0540380i −0.850004 0.526776i $$-0.823401\pi$$
0.881203 + 0.472738i $$0.156734\pi$$
$$488$$ 1802.44 + 3121.92i 0.167198 + 0.289595i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 8244.70 0.757797 0.378898 0.925438i $$-0.376303\pi$$
0.378898 + 0.925438i $$0.376303\pi$$
$$492$$ 0 0
$$493$$ 186.743 323.448i 0.0170598 0.0295484i
$$494$$ −5764.56 + 9984.50i −0.525019 + 0.909360i
$$495$$ 0 0
$$496$$ −49728.3 −4.50175
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −4082.46 7071.02i −0.366244 0.634353i 0.622731 0.782436i $$-0.286023\pi$$
−0.988975 + 0.148083i $$0.952690\pi$$
$$500$$ 14504.5 25122.5i 1.29732 2.24703i
$$501$$ 0 0
$$502$$ −6218.42 10770.6i −0.552872 0.957602i
$$503$$ 8175.59 0.724715 0.362357 0.932039i $$-0.381972\pi$$
0.362357 + 0.932039i $$0.381972\pi$$
$$504$$ 0 0
$$505$$ 5009.61 0.441435
$$506$$ 11488.0 + 19897.8i 1.00930 + 1.74815i
$$507$$ 0 0
$$508$$ 16998.6 29442.4i 1.48463 2.57145i
$$509$$ 439.224 + 760.758i 0.0382480 + 0.0662475i 0.884516 0.466510i $$-0.154489\pi$$
−0.846268 + 0.532758i $$0.821156\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −16876.5 −1.45673
$$513$$ 0 0
$$514$$ −7338.86 + 12711.3i −0.629773 + 1.09080i
$$515$$ −10547.7 + 18269.1i −0.902496 + 1.56317i
$$516$$ 0 0
$$517$$ −8711.42 −0.741060
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −12272.1 21256.0i −1.03494 1.79257i
$$521$$ −5856.30 + 10143.4i −0.492455 + 0.852957i −0.999962 0.00869048i $$-0.997234\pi$$
0.507507 + 0.861647i $$0.330567\pi$$
$$522$$ 0 0
$$523$$ −3670.91 6358.20i −0.306917 0.531596i 0.670769 0.741666i $$-0.265964\pi$$
−0.977686 + 0.210070i $$0.932631\pi$$
$$524$$ 9329.75 0.777809
$$525$$ 0 0
$$526$$ −10780.8 −0.893659
$$527$$ −1539.19 2665.95i −0.127226 0.220362i
$$528$$ 0 0
$$529$$ −1772.46 + 3069.99i −0.145678 + 0.252321i
$$530$$ −14939.1 25875.3i −1.22437 2.12066i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −12616.3 −1.02528
$$534$$ 0 0
$$535$$ 6154.44 10659.8i 0.497345 0.861426i
$$536$$ −15022.6 + 26020.0i −1.21060 + 2.09681i
$$537$$ 0 0
$$538$$ 18213.4 1.45955
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 7934.36 + 13742.7i 0.630545 + 1.09214i 0.987440 + 0.157992i $$0.0505020\pi$$
−0.356895 + 0.934144i $$0.616165\pi$$
$$542$$ 6974.21 12079.7i 0.552709 0.957319i
$$543$$ 0 0
$$544$$ 2109.80 + 3654.29i 0.166282 + 0.288008i
$$545$$ −14107.0 −1.10877
$$546$$ 0 0
$$547$$ 2315.26 0.180975 0.0904875 0.995898i $$-0.471157\pi$$
0.0904875 + 0.995898i $$0.471157\pi$$
$$548$$ −4400.21 7621.38i −0.343006 0.594104i
$$549$$ 0 0
$$550$$ −1255.69 + 2174.92i −0.0973505 + 0.168616i
$$551$$ −1037.24 1796.56i −0.0801961 0.138904i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 14134.1 1.08393
$$555$$ 0 0
$$556$$ 16553.5 28671.5i 1.26263 2.18694i
$$557$$ −2409.52 + 4173.42i −0.183294 + 0.317475i −0.943000 0.332792i $$-0.892009\pi$$
0.759706 + 0.650266i $$0.225343\pi$$
$$558$$ 0 0
$$559$$ 253.781 0.0192018
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −2689.39 4658.17i −0.201860 0.349631i
$$563$$ −1270.43 + 2200.45i −0.0951017 + 0.164721i −0.909651 0.415373i $$-0.863651\pi$$
0.814549 + 0.580094i $$0.196984\pi$$
$$564$$ 0 0
$$565$$ 4782.12 + 8282.88i 0.356081 + 0.616750i
$$566$$ −2279.85 −0.169310
$$567$$ 0 0
$$568$$ −22688.9 −1.67607
$$569$$ −12110.0 20975.1i −0.892227 1.54538i −0.837200 0.546898i $$-0.815809\pi$$
−0.0550275 0.998485i $$-0.517525\pi$$
$$570$$ 0 0
$$571$$ 5886.04 10194.9i 0.431389 0.747188i −0.565604 0.824677i $$-0.691357\pi$$
0.996993 + 0.0774891i $$0.0246903\pi$$
$$572$$ 12847.5 + 22252.6i 0.939129 + 1.62662i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1717.38 −0.124556
$$576$$ 0 0
$$577$$ 5292.13 9166.24i 0.381827 0.661344i −0.609496 0.792789i $$-0.708628\pi$$
0.991324 + 0.131445i $$0.0419616\pi$$
$$578$$ 12664.3 21935.2i 0.911358 1.57852i
$$579$$ 0 0
$$580$$ 7404.25 0.530077
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 9328.42 + 16157.3i 0.662682 + 1.14780i
$$584$$ 18129.1 31400.6i 1.28457 2.22494i
$$585$$ 0 0
$$586$$ 5923.52 + 10259.8i 0.417574 + 0.723259i
$$587$$ −8712.63 −0.612621 −0.306311 0.951932i $$-0.599095\pi$$
−0.306311 + 0.951932i $$0.599095\pi$$
$$588$$ 0 0
$$589$$ −17098.6 −1.19615
$$590$$ 998.641 + 1729.70i 0.0696838 + 0.120696i
$$591$$ 0 0
$$592$$ 22146.2 38358.3i 1.53750 2.66304i
$$593$$ 7681.43 + 13304.6i 0.531937 + 0.921341i 0.999305 + 0.0372786i $$0.0118689\pi$$
−0.467368 + 0.884063i $$0.654798\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −14747.0 −1.01353
$$597$$ 0 0
$$598$$ −12331.0 + 21357.9i −0.843229 + 1.46052i
$$599$$ 13001.9 22519.9i 0.886883 1.53613i 0.0433430 0.999060i $$-0.486199\pi$$
0.843540 0.537066i $$-0.180467\pi$$
$$600$$ 0 0
$$601$$ −20567.7 −1.39596 −0.697982 0.716115i $$-0.745918\pi$$
−0.697982 + 0.716115i $$0.745918\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −6014.48 10417.4i −0.405175 0.701783i
$$605$$ 651.426 1128.30i 0.0437756 0.0758216i
$$606$$ 0 0
$$607$$ 9821.04 + 17010.5i 0.656711 + 1.13746i 0.981462 + 0.191657i $$0.0613862\pi$$
−0.324751 + 0.945800i $$0.605280\pi$$
$$608$$ 23437.4 1.56334
$$609$$ 0 0
$$610$$ −3216.21 −0.213476
$$611$$ −4675.33 8097.90i −0.309564 0.536180i
$$612$$ 0 0
$$613$$ −4227.29 + 7321.89i −0.278530 + 0.482428i −0.971020 0.239000i $$-0.923180\pi$$
0.692490 + 0.721428i $$0.256514\pi$$
$$614$$ −8432.16 14604.9i −0.554225 0.959946i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 24168.4 1.57696 0.788479 0.615061i $$-0.210869\pi$$
0.788479 + 0.615061i $$0.210869\pi$$
$$618$$ 0 0
$$619$$ −1018.78 + 1764.58i −0.0661523 + 0.114579i −0.897205 0.441615i $$-0.854406\pi$$
0.831052 + 0.556194i $$0.187739\pi$$
$$620$$ 30514.0 52851.9i 1.97657 3.42352i
$$621$$ 0 0
$$622$$ −17700.5 −1.14104
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 6862.33 + 11885.9i 0.439189 + 0.760698i
$$626$$ −5951.14 + 10307.7i −0.379961 + 0.658111i
$$627$$ 0 0
$$628$$ 30874.9 + 53476.9i 1.96185 + 3.39803i
$$629$$ 2741.87 0.173808
$$630$$ 0 0
$$631$$ 12339.5 0.778489 0.389244 0.921135i $$-0.372736\pi$$
0.389244 + 0.921135i $$0.372736\pi$$
$$632$$ 21634.3 + 37471.8i 1.36166 + 2.35846i
$$633$$ 0 0
$$634$$ −16191.9 + 28045.1i −1.01429 + 1.75680i
$$635$$ 9045.89 + 15667.9i 0.565315 + 0.979154i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −6489.15 −0.402677
$$639$$ 0 0
$$640$$ −3890.59 + 6738.70i −0.240295 + 0.416204i
$$641$$ −5111.32 + 8853.06i −0.314953 + 0.545515i −0.979428 0.201796i $$-0.935322\pi$$
0.664474 + 0.747311i $$0.268655\pi$$
$$642$$ 0 0
$$643$$ 1211.75 0.0743187 0.0371594 0.999309i $$-0.488169\pi$$
0.0371594 + 0.999309i $$0.488169\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 1630.48 + 2824.07i 0.0993037 + 0.171999i
$$647$$ 1408.61 2439.78i 0.0855922 0.148250i −0.820051 0.572290i $$-0.806055\pi$$
0.905643 + 0.424040i $$0.139388\pi$$
$$648$$ 0 0
$$649$$ −623.581 1080.07i −0.0377160 0.0653260i
$$650$$ −2695.66 −0.162665
$$651$$ 0 0
$$652$$ 47838.6 2.87347
$$653$$ 10493.1 + 18174.6i 0.628831 + 1.08917i 0.987787 + 0.155812i $$0.0497995\pi$$
−0.358956 + 0.933355i $$0.616867\pi$$
$$654$$ 0 0
$$655$$ −2482.44 + 4299.70i −0.148087 + 0.256494i
$$656$$ 28822.5 + 49922.1i 1.71544 + 2.97124i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 2384.09 0.140927 0.0704635 0.997514i $$-0.477552\pi$$
0.0704635 + 0.997514i $$0.477552\pi$$
$$660$$ 0 0
$$661$$ −3788.55 + 6561.96i −0.222931 + 0.386128i −0.955697 0.294353i $$-0.904896\pi$$
0.732766 + 0.680481i $$0.238229\pi$$
$$662$$ −18540.8 + 32113.7i −1.08854 + 1.88540i
$$663$$ 0 0
$$664$$ 83232.2 4.86451
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −2218.77 3843.02i −0.128802 0.223092i
$$668$$ 6051.26 10481.1i 0.350494 0.607074i
$$669$$ 0 0
$$670$$ −13402.9 23214.6i −0.772837 1.33859i
$$671$$ 2008.30 0.115543
$$672$$ 0 0
$$673$$ 11724.6 0.671547 0.335774 0.941943i $$-0.391002\pi$$
0.335774 + 0.941943i $$0.391002\pi$$
$$674$$ −27240.8 47182.5i −1.55679 2.69644i
$$675$$ 0 0
$$676$$ 7987.23 13834.3i 0.454440 0.787113i
$$677$$ −16152.1 27976.3i −0.916952 1.58821i −0.804018 0.594606i $$-0.797308\pi$$
−0.112935 0.993602i $$-0.536025\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −6942.23 −0.391503
$$681$$ 0 0
$$682$$ −26742.8 + 46319.9i −1.50152 + 2.60070i
$$683$$ 16683.6 28896.8i 0.934669 1.61889i 0.159446 0.987207i $$-0.449029\pi$$
0.775223 0.631687i $$-0.217637\pi$$
$$684$$ 0 0
$$685$$ 4683.18 0.261219
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −579.776 1004.20i −0.0321275 0.0556465i
$$689$$ −10012.9 + 17342.9i −0.553646 + 0.958943i
$$690$$ 0 0
$$691$$ −521.837 903.849i −0.0287288 0.0497598i 0.851304 0.524674i $$-0.175813\pi$$
−0.880032 + 0.474914i $$0.842479\pi$$
$$692$$ 75211.3 4.13166
$$693$$ 0 0
$$694$$ −10378.6 −0.567674
$$695$$ 8809.01 + 15257.6i 0.480784 + 0.832742i
$$696$$ 0 0
$$697$$ −1784.23 + 3090.37i −0.0969619 + 0.167943i
$$698$$ −11513.7 19942.4i −0.624357 1.08142i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 11305.7 0.609143 0.304572 0.952489i $$-0.401487\pi$$
0.304572 + 0.952489i $$0.401487\pi$$
$$702$$ 0 0
$$703$$ 7614.72 13189.1i 0.408527 0.707590i
$$704$$ 12968.8 22462.6i 0.694289 1.20254i
$$705$$ 0 0
$$706$$ −32027.1 −1.70730
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 6653.38 + 11524.0i 0.352430 + 0.610427i 0.986675 0.162706i $$-0.0520221\pi$$
−0.634245 + 0.773132i $$0.718689\pi$$
$$710$$ 10121.3 17530.6i 0.534995 0.926639i
$$711$$ 0 0
$$712$$ 11010.3 + 19070.4i 0.579535 + 1.00378i
$$713$$ −36575.6 −1.92113
$$714$$ 0 0
$$715$$ −13673.7 −0.715201
$$716$$ −27801.0 48152.8i −1.45108 2.51334i
$$717$$ 0 0
$$718$$ 25419.9 44028.6i 1.32126 2.28849i
$$719$$ −5350.62 9267.55i −0.277531 0.480697i 0.693240 0.720707i $$-0.256183\pi$$
−0.970770 + 0.240010i $$0.922849\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −18068.0 −0.931333
$$723$$ 0 0
$$724$$ 30788.3 53326.8i 1.58044 2.73740i
$$725$$ 242.521 420.059i 0.0124235 0.0215181i
$$726$$ 0 0
$$727$$ 2121.14 0.108210 0.0541051 0.998535i $$-0.482769\pi$$
0.0541051 + 0.998535i $$0.482769\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 16174.5 + 28015.1i 0.820062 + 1.42039i
$$731$$ 35.8904 62.1640i 0.00181594 0.00314531i
$$732$$ 0 0
$$733$$ −10792.0 18692.3i −0.543809 0.941906i −0.998681 0.0513484i $$-0.983648\pi$$
0.454871 0.890557i $$-0.349685\pi$$
$$734$$ −2757.33 −0.138658
$$735$$ 0 0
$$736$$ 50135.0 2.51087
$$737$$ 8369.18 + 14495.8i 0.418294 + 0.724507i
$$738$$ 0 0
$$739$$ 4972.61 8612.81i 0.247524 0.428724i −0.715314 0.698803i $$-0.753716\pi$$
0.962838 + 0.270079i $$0.0870497\pi$$
$$740$$ 27178.5 + 47074.5i 1.35013 + 2.33850i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −2867.01 −0.141562 −0.0707808 0.997492i $$-0.522549\pi$$
−0.0707808 + 0.997492i $$0.522549\pi$$
$$744$$ 0 0
$$745$$ 3923.86 6796.32i 0.192965 0.334225i
$$746$$ −8518.57 + 14754.6i −0.418079 + 0.724134i
$$747$$ 0 0
$$748$$ 7267.71 0.355259
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 5412.05 + 9373.94i 0.262967 + 0.455473i 0.967029 0.254666i $$-0.0819655\pi$$
−0.704062 + 0.710139i $$0.748632\pi$$
$$752$$ −21362.0 + 37000.1i −1.03589 + 1.79422i
$$753$$ 0 0
$$754$$ −3482.66 6032.14i −0.168211 0.291349i
$$755$$ 6401.26 0.308564
$$756$$ 0 0
$$757$$ −14512.0 −0.696761 −0.348381 0.937353i $$-0.613268\pi$$
−0.348381 + 0.937353i $$0.613268\pi$$
$$758$$ −17512.0 30331.6i −0.839134 1.45342i
$$759$$ 0 0
$$760$$ −19280.0 + 33393.9i −0.920208 + 1.59385i
$$761$$ 16537.9 + 28644.5i 0.787778 + 1.36447i 0.927325 + 0.374256i $$0.122102\pi$$
−0.139547 + 0.990215i $$0.544565\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −5193.13 −0.245917
$$765$$ 0 0
$$766$$ 37516.4 64980.3i 1.76961 3.06506i
$$767$$ 669.338 1159.33i 0.0315103 0.0545774i
$$768$$ 0 0
$$769$$ −6728.44 −0.315518 −0.157759 0.987478i $$-0.550427\pi$$
−0.157759 + 0.987478i $$0.550427\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −40155.8 69551.8i −1.87207 3.24252i
$$773$$ 12116.6 20986.6i 0.563784 0.976503i −0.433377 0.901213i $$-0.642678\pi$$
0.997162 0.0752907i $$-0.0239885\pi$$
$$774$$ 0 0
$$775$$ −1998.93 3462.26i −0.0926501 0.160475i
$$776$$ −90186.0 −4.17202
$$777$$ 0 0
$$778$$ −15412.4 −0.710231
$$779$$ 9910.32 + 17165.2i 0.455807 + 0.789481i
$$780$$ 0 0
$$781$$ −6320.05 + 10946.6i −0.289564 + 0.501539i
$$782$$ 3487.75 + 6040.97i 0.159491 + 0.276246i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −32860.5 −1.49406
$$786$$ 0 0
$$787$$ −8600.19 + 14896.0i −0.389535 + 0.674694i −0.992387 0.123159i $$-0.960697\pi$$
0.602852 + 0.797853i $$0.294031\pi$$
$$788$$ −28496.4 + 49357.2i −1.28825 + 2.23131i
$$789$$ 0 0