# Properties

 Label 441.4.e.q.226.1 Level $441$ Weight $4$ Character 441.226 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 226.1 Root $$2.13746 - 0.656712i$$ of defining polynomial Character $$\chi$$ $$=$$ 441.226 Dual form 441.4.e.q.361.1

## $q$-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 $$\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$$.

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

## 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 −0.153420 + 0.988161i $$0.549029\pi$$
−0.779063 + 0.626946i $$0.784305\pi$$
$$3$$ 0 0
$$4$$ −9.91238 17.1687i −1.23905 2.14609i
$$5$$ 5.27492 9.13642i 0.471803 0.817187i −0.527677 0.849445i $$-0.676937\pi$$
0.999480 + 0.0322587i $$0.0102700\pi$$
$$6$$ 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 0.999629 0.0272223i $$-0.00866619\pi$$
−0.523390 + 0.852093i $$0.675333\pi$$
$$12$$ 0 0
$$13$$ −37.2990 −0.795760 −0.397880 0.917437i $$-0.630254\pi$$
−0.397880 + 0.917437i $$0.630254\pi$$
$$14$$ 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 $$-0.190644\pi$$
−0.901198 + 0.433408i $$0.857311\pi$$
$$18$$ 0 0
$$19$$ 29.2990 50.7474i 0.353771 0.612750i −0.633136 0.774041i $$-0.718232\pi$$
0.986907 + 0.161291i $$0.0515658\pi$$
$$20$$ −209.148 −2.33834
$$21$$ 0 0
$$22$$ −183.299 −1.77634
$$23$$ −62.6736 + 108.554i −0.568189 + 0.984132i 0.428556 + 0.903515i $$0.359022\pi$$
−0.996745 + 0.0806171i $$0.974311\pi$$
$$24$$ 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 −0.885372 0.464883i $$-0.846096\pi$$
0.0400859 0.999196i $$-0.487237\pi$$
$$32$$ −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 −0.418388 0.908268i $$-0.637405\pi$$
0.995778 0.0917993i $$-0.0292618\pi$$
$$38$$ 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 $$-0.277185\pi$$
0.644212 + 0.764847i $$0.277185\pi$$
$$42$$ 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 $$-0.706148\pi$$
0.992317 + 0.123717i $$0.0394816\pi$$
$$48$$ 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 −0.969929 0.243388i $$-0.921741\pi$$
0.274184 0.961677i $$-0.411592\pi$$
$$54$$ 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 $$-0.179274\pi$$
−0.885145 + 0.465315i $$0.845941\pi$$
$$60$$ 0 0
$$61$$ −28.8970 + 50.0511i −0.0606538 + 0.105056i −0.894758 0.446552i $$-0.852652\pi$$
0.834104 + 0.551607i $$0.185985\pi$$
$$62$$ 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 0.558462 0.829530i $$-0.311392\pi$$
−0.997625 + 0.0688767i $$0.978059\pi$$
$$68$$ −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 $$-0.320972\pi$$
−0.999246 + 0.0388253i $$0.987638\pi$$
$$74$$ 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 −0.506012 0.862527i $$-0.668881\pi$$
0.999976 + 0.00695559i $$0.00221405\pi$$
$$80$$ 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 $$-0.844033\pi$$
−0.882341 + 0.470611i $$0.844033\pi$$
$$84$$ 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 $$-0.900757\pi$$
0.741552 + 0.670895i $$0.234090\pi$$
$$90$$ 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 $$-0.226793\pi$$
0.756735 + 0.653722i $$0.226793\pi$$
$$98$$ 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 $$-0.0915150\pi$$
−0.725046 + 0.688700i $$0.758182\pi$$
$$102$$ 0 0
$$103$$ 999.794 1731.69i 0.956433 1.65659i 0.225380 0.974271i $$-0.427638\pi$$
0.731053 0.682320i $$-0.239029\pi$$
$$104$$ −2326.51 −2.19359
$$105$$ 0 0
$$106$$ 2832.10 2.59508
$$107$$ 583.368 1010.42i 0.527068 0.912909i −0.472434 0.881366i $$-0.656625\pi$$
0.999502 0.0315431i $$-0.0100421\pi$$
$$108$$ 0 0
$$109$$ 668.588 + 1158.03i 0.587515 + 1.01761i 0.994557 + 0.104196i $$0.0332270\pi$$
−0.407042 + 0.913410i $$0.633440\pi$$
$$110$$ −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 $$-0.783171\pi$$
0.933763 + 0.357893i $$0.116505\pi$$
$$132$$ 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 0.788482 0.615058i $$-0.210868\pi$$
−0.926897 + 0.375316i $$0.877534\pi$$
$$138$$ 0 0
$$139$$ 1669.98 1.01904 0.509518 0.860460i $$-0.329824\pi$$
0.509518 + 0.860460i $$0.329824\pi$$
$$140$$ 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 −0.745475 0.666534i $$-0.767777\pi$$
0.949973 + 0.312334i $$0.101111\pi$$
$$150$$ 0 0
$$151$$ −303.382 525.473i −0.163503 0.283195i 0.772620 0.634869i $$-0.218946\pi$$
−0.936123 + 0.351674i $$0.885613\pi$$
$$152$$ 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 −0.924927 0.380144i $$-0.875875\pi$$
0.133250 0.991083i $$-0.457459\pi$$
$$158$$ 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 0.415730 + 0.909488i $$0.363526\pi$$
−0.995505 + 0.0947109i $$0.969807\pi$$
$$164$$ −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 $$-0.454828\pi$$
0.141437 + 0.989947i $$0.454828\pi$$
$$168$$ 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 −0.0615006 0.998107i $$-0.519589\pi$$
0.895136 0.445792i $$-0.147078\pi$$
$$174$$ 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 −0.994805 0.101798i $$-0.967540\pi$$
0.409243 0.912426i $$-0.365793\pi$$
$$180$$ 0 0
$$181$$ 3106.04 1.27553 0.637763 0.770232i $$-0.279860\pi$$
0.637763 + 0.770232i $$0.279860\pi$$
$$182$$ 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 −0.840150 0.542355i $$-0.817533\pi$$
0.889768 + 0.456413i $$0.150866\pi$$
$$192$$ 0 0
$$193$$ −2025.54 3508.33i −0.755447 1.30847i −0.945152 0.326632i $$-0.894086\pi$$
0.189704 0.981841i $$-0.439247\pi$$
$$194$$ −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 0.998526 + 0.0542680i $$0.0172825\pi$$
−0.452266 + 0.891883i $$0.649384\pi$$
$$200$$ 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 $$-0.692097\pi$$
−0.567520 + 0.823360i $$0.692097\pi$$
$$224$$ 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 $$-0.0805722\pi$$
−0.700947 + 0.713214i $$0.747239\pi$$
$$228$$ 0 0
$$229$$ 425.125 736.338i 0.122677 0.212483i −0.798146 0.602465i $$-0.794185\pi$$
0.920823 + 0.389982i $$0.127519\pi$$
$$230$$ −6975.51 −1.99979
$$231$$ 0 0
$$232$$ 2208.18 0.624890
$$233$$ −3295.55 + 5708.06i −0.926604 + 1.60492i −0.137642 + 0.990482i $$0.543952\pi$$
−0.788962 + 0.614443i $$0.789381\pi$$
$$234$$ 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 $$-0.231950\pi$$
−0.949704 + 0.313149i $$0.898616\pi$$
$$242$$ 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 $$-0.595803\pi$$
−0.296451 + 0.955048i $$0.595803\pi$$
$$252$$ 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 $$-0.723689\pi$$
0.983997 + 0.178185i $$0.0570224\pi$$
$$258$$ 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 0.960597 0.277945i $$-0.0896532\pi$$
−0.721006 + 0.692929i $$0.756320\pi$$
$$264$$ 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 $$-0.0386898\pi$$
−0.601315 + 0.799012i $$0.705356\pi$$
$$270$$ 0 0
$$271$$ −1322.15 + 2290.02i −0.296364 + 0.513318i −0.975301 0.220879i $$-0.929108\pi$$
0.678937 + 0.734196i $$0.262441\pi$$
$$272$$ 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 0.683349 0.730092i $$-0.260523\pi$$
−0.973953 + 0.226751i $$0.927190\pi$$
$$278$$ −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 $$-0.181120\pi$$
−0.887829 + 0.460174i $$0.847787\pi$$
$$284$$ 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 $$-0.428120\pi$$
0.223904 + 0.974611i $$0.428120\pi$$
$$294$$ 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 $$-0.596045\pi$$
−0.297177 + 0.954822i $$0.596045\pi$$
$$308$$ 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 $$-0.265629\pi$$
−0.977465 + 0.211100i $$0.932296\pi$$
$$312$$ 0 0
$$313$$ 1128.20 1954.09i 0.203736 0.352881i −0.745993 0.665954i $$-0.768025\pi$$
0.949729 + 0.313072i $$0.101358\pi$$
$$314$$ 16430.2 2.95290
$$315$$ 0 0
$$316$$ −13752.3 −2.44818
$$317$$ −3069.59 + 5316.69i −0.543866 + 0.942004i 0.454811 + 0.890588i $$0.349707\pi$$
−0.998677 + 0.0514158i $$0.983627\pi$$
$$318$$ 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 0.411363 + 0.911472i $$0.365053\pi$$
−0.995039 + 0.0994849i $$0.968280\pi$$
$$332$$ 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 0.932034 0.362371i $$-0.118033\pi$$
−0.779840 + 0.625980i $$0.784699\pi$$
$$348$$ 0 0
$$349$$ −4365.46 −0.669564 −0.334782 0.942296i $$-0.608663\pi$$
−0.334782 + 0.942296i $$0.608663\pi$$
$$350$$ 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 $$-0.318004\pi$$
−0.998841 + 0.0481389i $$0.984671\pi$$
$$354$$ 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 −0.256965 0.966421i $$-0.582722\pi$$
0.965427 0.260673i $$-0.0839443\pi$$
$$360$$ 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 $$-0.178502\pi$$
−0.884014 + 0.467460i $$0.845169\pi$$
$$368$$ −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 −0.956072 0.293133i $$-0.905302\pi$$
0.731896 + 0.681416i $$0.238636\pi$$
$$374$$ 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 −0.201063 + 0.979578i $$0.564439\pi$$
−0.747809 + 0.663914i $$0.768894\pi$$
$$384$$ 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 0.945388 0.325948i $$-0.105684\pi$$
−0.754973 + 0.655755i $$0.772350\pi$$
$$390$$ 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 $$-0.849677\pi$$
0.839223 + 0.543788i $$0.183010\pi$$
$$398$$ −16178.0 −2.03751
$$399$$ 0 0
$$400$$ −2334.96 −0.291870
$$401$$ 1169.32 2025.32i 0.145618 0.252218i −0.783985 0.620780i $$-0.786816\pi$$
0.929603 + 0.368561i $$0.120150\pi$$
$$402$$ 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 $$-0.113944\pi$$
−0.771734 + 0.635945i $$0.780610\pi$$
$$410$$ 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 $$-0.782614\pi$$
−0.775721 + 0.631076i $$0.782614\pi$$
$$420$$ 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 0.624070 0.781368i $$-0.285478\pi$$
−0.988720 + 0.149776i $$0.952145\pi$$
$$432$$ 0 0
$$433$$ −11716.3 −1.30034 −0.650171 0.759788i $$-0.725303\pi$$
−0.650171 + 0.759788i $$0.725303\pi$$
$$434$$ 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 −0.129042 0.991639i $$-0.541190\pi$$
0.923306 0.384066i $$-0.125476\pi$$
$$440$$ 22866.4 2.47753
$$441$$ 0 0
$$442$$ −2075.67 −0.223370
$$443$$ −7619.89 + 13198.0i −0.817228 + 1.41548i 0.0904888 + 0.995897i $$0.471157\pi$$
−0.907717 + 0.419583i $$0.862176\pi$$
$$444$$ 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 −0.953704 0.300746i $$-0.902764\pi$$
0.737306 + 0.675559i $$0.236098\pi$$
$$458$$ 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 $$-0.514639\pi$$
−0.0459746 + 0.998943i $$0.514639\pi$$
$$462$$ 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 $$-0.903761\pi$$
0.735188 + 0.677864i $$0.237094\pi$$
$$468$$ 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 $$-0.124753\pi$$
−0.792881 + 0.609377i $$0.791420\pi$$
$$480$$ 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 0.881203 0.472738i $$-0.156734\pi$$
−0.850004 + 0.526776i $$0.823401\pi$$
$$488$$ −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 −0.988975 0.148083i $$-0.952690\pi$$
0.622731 + 0.782436i $$0.286023\pi$$
$$500$$ −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 $$-0.618028\pi$$
−0.362357 + 0.932039i $$0.618028\pi$$
$$504$$ 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 $$-0.845511\pi$$
0.846268 + 0.532758i $$0.178844\pi$$
$$510$$ 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 $$-0.00276630\pi$$
−0.507507 + 0.861647i $$0.669433\pi$$
$$522$$ 0 0
$$523$$ 3670.91 6358.20i 0.306917 0.531596i −0.670769 0.741666i $$-0.734036\pi$$
0.977686 + 0.210070i $$0.0673692\pi$$
$$524$$ −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 −0.356895 0.934144i $$-0.616165\pi$$
0.987440 0.157992i $$-0.0505020\pi$$
$$542$$ −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 0.759706 0.650266i $$-0.225343\pi$$
−0.943000 + 0.332792i $$0.892009\pi$$
$$558$$ 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 $$-0.136349\pi$$
−0.814549 + 0.580094i $$0.803016\pi$$
$$564$$ 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 −0.0550275 + 0.998485i $$0.517525\pi$$
−0.837200 + 0.546898i $$0.815809\pi$$
$$570$$ 0 0
$$571$$ 5886.04 + 10194.9i 0.431389 + 0.747188i 0.996993 0.0774891i $$-0.0246903\pi$$
−0.565604 + 0.824677i $$0.691357\pi$$
$$572$$ −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 $$-0.291372\pi$$
−0.991324 + 0.131445i $$0.958038\pi$$
$$578$$ 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 $$-0.400905\pi$$
0.306311 + 0.951932i $$0.400905\pi$$
$$588$$ 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 0.467368 + 0.884063i $$0.345202\pi$$
−0.999305 + 0.0372786i $$0.988131\pi$$
$$594$$ 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 0.843540 + 0.537066i $$0.180467\pi$$
0.0433430 + 0.999060i $$0.486199\pi$$
$$600$$ 0 0
$$601$$ 20567.7 1.39596 0.697982 0.716115i $$-0.254082\pi$$
0.697982 + 0.716115i $$0.254082\pi$$
$$602$$ 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 0.324751 + 0.945800i $$0.394720\pi$$
−0.981462 + 0.191657i $$0.938614\pi$$
$$608$$ −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 0.692490 0.721428i $$-0.256514\pi$$
−0.971020 + 0.239000i $$0.923180\pi$$
$$614$$ 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 $$-0.145594\pi$$
−0.831052 + 0.556194i $$0.812261\pi$$
$$620$$ 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 0.664474 0.747311i $$-0.268655\pi$$
−0.979428 + 0.201796i $$0.935322\pi$$
$$642$$ 0 0
$$643$$ −1211.75 −0.0743187 −0.0371594 0.999309i $$-0.511831\pi$$
−0.0371594 + 0.999309i $$0.511831\pi$$
$$644$$ 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 $$-0.193945\pi$$
−0.905643 + 0.424040i $$0.860612\pi$$
$$648$$ 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 −0.358956 0.933355i $$-0.616867\pi$$
0.987787 0.155812i $$-0.0497995\pi$$
$$654$$ 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 $$-0.0951042\pi$$
−0.732766 + 0.680481i $$0.761771\pi$$
$$662$$ −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 0.112935 0.993602i $$-0.463975\pi$$
0.804018 0.594606i $$-0.202692\pi$$
$$678$$ 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 0.775223 + 0.631687i $$0.217637\pi$$
0.159446 + 0.987207i $$0.449029\pi$$
$$684$$ 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 $$-0.824187\pi$$
0.880032 + 0.474914i $$0.157521\pi$$
$$692$$ −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 −0.634245 0.773132i $$-0.718689\pi$$
0.986675 + 0.162706i $$0.0520221\pi$$
$$710$$ −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 $$-0.743817\pi$$
0.970770 + 0.240010i $$0.0771506\pi$$
$$720$$ 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 $$-0.517231\pi$$
−0.0541051 + 0.998535i $$0.517231\pi$$
$$728$$ 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 −0.454871 0.890557i $$-0.650315\pi$$
0.998681 0.0513484i $$-0.0163519\pi$$
$$734$$ 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 0.962838 0.270079i $$-0.0870497\pi$$
−0.715314 + 0.698803i $$0.753716\pi$$
$$740$$ −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 −0.704062 0.710139i $$-0.748632\pi$$
0.967029 + 0.254666i $$0.0819655\pi$$
$$752$$ 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 0.139547 + 0.990215i $$0.455435\pi$$
−0.927325 + 0.374256i $$0.877898\pi$$
$$762$$ 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 $$-0.449573\pi$$
0.157759 + 0.987478i $$0.449573\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −40155.8 + 69551.8i −1.87207 + 3.24252i
$$773$$ −12116.6 20986.6i −0.563784 0.976503i −0.997162 0.0752907i $$-0.976012\pi$$
0.433377 0.901213i $$-0.357322\pi$$
$$774$$ 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 $$-0.0393026\pi$$
−0.602852 + 0.797853i $$0.705969\pi$$
$$788$$ −28496.4 49357.2i −1.28825 2.23131i
$$789$$ 0 0
$$790$$ 38603.6