# Properties

 Label 105.4.d.b.64.2 Level $105$ Weight $4$ Character 105.64 Analytic conductor $6.195$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 105.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.19520055060$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Defining polynomial: $$x^{10} + 37 x^{8} + 398 x^{6} + 1149 x^{4} + 1040 x^{2} + 100$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{9}\cdot 5$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 64.2 Root $$-1.37042i$$ of defining polynomial Character $$\chi$$ $$=$$ 105.64 Dual form 105.4.d.b.64.9

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-4.88936i q^{2} +3.00000i q^{3} -15.9059 q^{4} +(-9.63020 + 5.67972i) q^{5} +14.6681 q^{6} +7.00000i q^{7} +38.6546i q^{8} -9.00000 q^{9} +O(q^{10})$$ $$q-4.88936i q^{2} +3.00000i q^{3} -15.9059 q^{4} +(-9.63020 + 5.67972i) q^{5} +14.6681 q^{6} +7.00000i q^{7} +38.6546i q^{8} -9.00000 q^{9} +(27.7702 + 47.0855i) q^{10} +54.9009 q^{11} -47.7176i q^{12} +49.7580i q^{13} +34.2255 q^{14} +(-17.0392 - 28.8906i) q^{15} +61.7496 q^{16} +133.661i q^{17} +44.0043i q^{18} -138.986 q^{19} +(153.177 - 90.3409i) q^{20} -21.0000 q^{21} -268.430i q^{22} -7.32751i q^{23} -115.964 q^{24} +(60.4815 - 109.394i) q^{25} +243.285 q^{26} -27.0000i q^{27} -111.341i q^{28} -87.2408 q^{29} +(-141.257 + 83.3106i) q^{30} -209.479 q^{31} +7.32107i q^{32} +164.703i q^{33} +653.519 q^{34} +(-39.7580 - 67.4114i) q^{35} +143.153 q^{36} -67.9041i q^{37} +679.555i q^{38} -149.274 q^{39} +(-219.547 - 372.252i) q^{40} +77.6804 q^{41} +102.677i q^{42} +197.692i q^{43} -873.246 q^{44} +(86.6718 - 51.1175i) q^{45} -35.8269 q^{46} +4.97613i q^{47} +185.249i q^{48} -49.0000 q^{49} +(-534.865 - 295.716i) q^{50} -400.984 q^{51} -791.444i q^{52} +53.0843i q^{53} -132.013 q^{54} +(-528.706 + 311.822i) q^{55} -270.582 q^{56} -416.959i q^{57} +426.552i q^{58} +683.950 q^{59} +(271.023 + 459.530i) q^{60} -26.8658 q^{61} +1024.22i q^{62} -63.0000i q^{63} +529.792 q^{64} +(-282.612 - 479.180i) q^{65} +805.291 q^{66} +149.300i q^{67} -2126.00i q^{68} +21.9825 q^{69} +(-329.599 + 194.391i) q^{70} +6.15571 q^{71} -347.892i q^{72} -294.545i q^{73} -332.008 q^{74} +(328.181 + 181.445i) q^{75} +2210.70 q^{76} +384.306i q^{77} +729.855i q^{78} +938.669 q^{79} +(-594.661 + 350.720i) q^{80} +81.0000 q^{81} -379.807i q^{82} -784.907i q^{83} +334.023 q^{84} +(-759.160 - 1287.19i) q^{85} +966.590 q^{86} -261.722i q^{87} +2122.17i q^{88} -275.928 q^{89} +(-249.932 - 423.770i) q^{90} -348.306 q^{91} +116.550i q^{92} -628.437i q^{93} +24.3301 q^{94} +(1338.47 - 789.404i) q^{95} -21.9632 q^{96} +1165.27i q^{97} +239.579i q^{98} -494.108 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + O(q^{10})$$ $$10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + 92q^{10} + 132q^{11} - 14q^{14} + 310q^{16} - 348q^{19} + 366q^{20} - 210q^{21} + 198q^{24} - 374q^{25} + 892q^{26} - 740q^{29} - 378q^{30} + 684q^{31} - 224q^{34} + 486q^{36} - 12q^{39} - 2156q^{40} + 1604q^{41} - 580q^{44} + 126q^{45} + 1280q^{46} - 490q^{49} - 2504q^{50} - 648q^{51} + 54q^{54} - 452q^{55} + 462q^{56} - 1408q^{59} - 852q^{60} + 1300q^{61} - 150q^{64} - 3296q^{65} + 3036q^{66} - 696q^{69} - 882q^{70} + 2940q^{71} + 2624q^{74} - 408q^{75} + 8740q^{76} + 1640q^{79} - 4126q^{80} + 810q^{81} + 1134q^{84} - 1704q^{85} + 1664q^{86} - 572q^{89} - 828q^{90} - 28q^{91} - 5080q^{94} + 1268q^{95} + 330q^{96} - 1188q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$$.

 $$n$$ $$22$$ $$31$$ $$71$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.88936i 1.72865i −0.502933 0.864325i $$-0.667746\pi$$
0.502933 0.864325i $$-0.332254\pi$$
$$3$$ 3.00000i 0.577350i
$$4$$ −15.9059 −1.98823
$$5$$ −9.63020 + 5.67972i −0.861351 + 0.508010i
$$6$$ 14.6681 0.998037
$$7$$ 7.00000i 0.377964i
$$8$$ 38.6546i 1.70831i
$$9$$ −9.00000 −0.333333
$$10$$ 27.7702 + 47.0855i 0.878171 + 1.48898i
$$11$$ 54.9009 1.50484 0.752420 0.658684i $$-0.228887\pi$$
0.752420 + 0.658684i $$0.228887\pi$$
$$12$$ 47.7176i 1.14791i
$$13$$ 49.7580i 1.06157i 0.847507 + 0.530784i $$0.178103\pi$$
−0.847507 + 0.530784i $$0.821897\pi$$
$$14$$ 34.2255 0.653368
$$15$$ −17.0392 28.8906i −0.293300 0.497301i
$$16$$ 61.7496 0.964837
$$17$$ 133.661i 1.90692i 0.301517 + 0.953461i $$0.402507\pi$$
−0.301517 + 0.953461i $$0.597493\pi$$
$$18$$ 44.0043i 0.576217i
$$19$$ −138.986 −1.67819 −0.839097 0.543983i $$-0.816916\pi$$
−0.839097 + 0.543983i $$0.816916\pi$$
$$20$$ 153.177 90.3409i 1.71257 1.01004i
$$21$$ −21.0000 −0.218218
$$22$$ 268.430i 2.60134i
$$23$$ 7.32751i 0.0664301i −0.999448 0.0332150i $$-0.989425\pi$$
0.999448 0.0332150i $$-0.0105746\pi$$
$$24$$ −115.964 −0.986293
$$25$$ 60.4815 109.394i 0.483852 0.875150i
$$26$$ 243.285 1.83508
$$27$$ 27.0000i 0.192450i
$$28$$ 111.341i 0.751481i
$$29$$ −87.2408 −0.558628 −0.279314 0.960200i $$-0.590107\pi$$
−0.279314 + 0.960200i $$0.590107\pi$$
$$30$$ −141.257 + 83.3106i −0.859660 + 0.507012i
$$31$$ −209.479 −1.21366 −0.606831 0.794831i $$-0.707560\pi$$
−0.606831 + 0.794831i $$0.707560\pi$$
$$32$$ 7.32107i 0.0404436i
$$33$$ 164.703i 0.868820i
$$34$$ 653.519 3.29640
$$35$$ −39.7580 67.4114i −0.192010 0.325560i
$$36$$ 143.153 0.662744
$$37$$ 67.9041i 0.301713i −0.988556 0.150856i $$-0.951797\pi$$
0.988556 0.150856i $$-0.0482031\pi$$
$$38$$ 679.555i 2.90101i
$$39$$ −149.274 −0.612897
$$40$$ −219.547 372.252i −0.867838 1.47145i
$$41$$ 77.6804 0.295894 0.147947 0.988995i $$-0.452734\pi$$
0.147947 + 0.988995i $$0.452734\pi$$
$$42$$ 102.677i 0.377222i
$$43$$ 197.692i 0.701112i 0.936542 + 0.350556i $$0.114007\pi$$
−0.936542 + 0.350556i $$0.885993\pi$$
$$44$$ −873.246 −2.99197
$$45$$ 86.6718 51.1175i 0.287117 0.169337i
$$46$$ −35.8269 −0.114834
$$47$$ 4.97613i 0.0154435i 0.999970 + 0.00772173i $$0.00245793\pi$$
−0.999970 + 0.00772173i $$0.997542\pi$$
$$48$$ 185.249i 0.557049i
$$49$$ −49.0000 −0.142857
$$50$$ −534.865 295.716i −1.51283 0.836412i
$$51$$ −400.984 −1.10096
$$52$$ 791.444i 2.11065i
$$53$$ 53.0843i 0.137579i 0.997631 + 0.0687895i $$0.0219137\pi$$
−0.997631 + 0.0687895i $$0.978086\pi$$
$$54$$ −132.013 −0.332679
$$55$$ −528.706 + 311.822i −1.29620 + 0.764473i
$$56$$ −270.582 −0.645680
$$57$$ 416.959i 0.968905i
$$58$$ 426.552i 0.965673i
$$59$$ 683.950 1.50920 0.754599 0.656186i $$-0.227831\pi$$
0.754599 + 0.656186i $$0.227831\pi$$
$$60$$ 271.023 + 459.530i 0.583148 + 0.988751i
$$61$$ −26.8658 −0.0563904 −0.0281952 0.999602i $$-0.508976\pi$$
−0.0281952 + 0.999602i $$0.508976\pi$$
$$62$$ 1024.22i 2.09800i
$$63$$ 63.0000i 0.125988i
$$64$$ 529.792 1.03475
$$65$$ −282.612 479.180i −0.539287 0.914383i
$$66$$ 805.291 1.50189
$$67$$ 149.300i 0.272237i 0.990693 + 0.136119i $$0.0434628\pi$$
−0.990693 + 0.136119i $$0.956537\pi$$
$$68$$ 2126.00i 3.79140i
$$69$$ 21.9825 0.0383534
$$70$$ −329.599 + 194.391i −0.562780 + 0.331918i
$$71$$ 6.15571 0.0102894 0.00514470 0.999987i $$-0.498362\pi$$
0.00514470 + 0.999987i $$0.498362\pi$$
$$72$$ 347.892i 0.569436i
$$73$$ 294.545i 0.472245i −0.971723 0.236123i $$-0.924123\pi$$
0.971723 0.236123i $$-0.0758767\pi$$
$$74$$ −332.008 −0.521556
$$75$$ 328.181 + 181.445i 0.505268 + 0.279352i
$$76$$ 2210.70 3.33664
$$77$$ 384.306i 0.568776i
$$78$$ 729.855i 1.05948i
$$79$$ 938.669 1.33682 0.668409 0.743794i $$-0.266976\pi$$
0.668409 + 0.743794i $$0.266976\pi$$
$$80$$ −594.661 + 350.720i −0.831063 + 0.490146i
$$81$$ 81.0000 0.111111
$$82$$ 379.807i 0.511496i
$$83$$ 784.907i 1.03801i −0.854772 0.519004i $$-0.826303\pi$$
0.854772 0.519004i $$-0.173697\pi$$
$$84$$ 334.023 0.433868
$$85$$ −759.160 1287.19i −0.968735 1.64253i
$$86$$ 966.590 1.21198
$$87$$ 261.722i 0.322524i
$$88$$ 2122.17i 2.57073i
$$89$$ −275.928 −0.328633 −0.164316 0.986408i $$-0.552542\pi$$
−0.164316 + 0.986408i $$0.552542\pi$$
$$90$$ −249.932 423.770i −0.292724 0.496325i
$$91$$ −348.306 −0.401235
$$92$$ 116.550i 0.132078i
$$93$$ 628.437i 0.700708i
$$94$$ 24.3301 0.0266963
$$95$$ 1338.47 789.404i 1.44551 0.852538i
$$96$$ −21.9632 −0.0233501
$$97$$ 1165.27i 1.21975i 0.792499 + 0.609873i $$0.208780\pi$$
−0.792499 + 0.609873i $$0.791220\pi$$
$$98$$ 239.579i 0.246950i
$$99$$ −494.108 −0.501613
$$100$$ −962.011 + 1740.00i −0.962011 + 1.74000i
$$101$$ −0.162999 −0.000160584 −8.02919e−5 1.00000i $$-0.500026\pi$$
−8.02919e−5 1.00000i $$0.500026\pi$$
$$102$$ 1960.56i 1.90318i
$$103$$ 1300.78i 1.24437i −0.782871 0.622184i $$-0.786245\pi$$
0.782871 0.622184i $$-0.213755\pi$$
$$104$$ −1923.38 −1.81349
$$105$$ 202.234 119.274i 0.187962 0.110857i
$$106$$ 259.548 0.237826
$$107$$ 1531.63i 1.38382i 0.721985 + 0.691908i $$0.243230\pi$$
−0.721985 + 0.691908i $$0.756770\pi$$
$$108$$ 429.458i 0.382636i
$$109$$ −1971.39 −1.73234 −0.866171 0.499748i $$-0.833426\pi$$
−0.866171 + 0.499748i $$0.833426\pi$$
$$110$$ 1524.61 + 2585.04i 1.32151 + 2.24067i
$$111$$ 203.712 0.174194
$$112$$ 432.247i 0.364674i
$$113$$ 262.817i 0.218794i 0.993998 + 0.109397i $$0.0348920\pi$$
−0.993998 + 0.109397i $$0.965108\pi$$
$$114$$ −2038.66 −1.67490
$$115$$ 41.6182 + 70.5654i 0.0337471 + 0.0572196i
$$116$$ 1387.64 1.11068
$$117$$ 447.822i 0.353856i
$$118$$ 3344.08i 2.60888i
$$119$$ −935.630 −0.720749
$$120$$ 1116.76 658.642i 0.849545 0.501046i
$$121$$ 1683.11 1.26454
$$122$$ 131.357i 0.0974793i
$$123$$ 233.041i 0.170834i
$$124$$ 3331.94 2.41304
$$125$$ 38.8765 + 1397.00i 0.0278177 + 0.999613i
$$126$$ −308.030 −0.217789
$$127$$ 569.649i 0.398017i 0.979998 + 0.199009i $$0.0637722\pi$$
−0.979998 + 0.199009i $$0.936228\pi$$
$$128$$ 2531.78i 1.74828i
$$129$$ −593.077 −0.404787
$$130$$ −2342.88 + 1381.79i −1.58065 + 0.932239i
$$131$$ 984.808 0.656817 0.328409 0.944536i $$-0.393488\pi$$
0.328409 + 0.944536i $$0.393488\pi$$
$$132$$ 2619.74i 1.72742i
$$133$$ 972.905i 0.634297i
$$134$$ 729.982 0.470603
$$135$$ 153.352 + 260.015i 0.0977665 + 0.165767i
$$136$$ −5166.63 −3.25761
$$137$$ 1377.35i 0.858942i −0.903081 0.429471i $$-0.858700\pi$$
0.903081 0.429471i $$-0.141300\pi$$
$$138$$ 107.481i 0.0662997i
$$139$$ −839.673 −0.512375 −0.256188 0.966627i $$-0.582466\pi$$
−0.256188 + 0.966627i $$0.582466\pi$$
$$140$$ 632.386 + 1072.24i 0.381760 + 0.647289i
$$141$$ −14.9284 −0.00891629
$$142$$ 30.0975i 0.0177868i
$$143$$ 2731.76i 1.59749i
$$144$$ −555.746 −0.321612
$$145$$ 840.147 495.504i 0.481175 0.283788i
$$146$$ −1440.14 −0.816347
$$147$$ 147.000i 0.0824786i
$$148$$ 1080.07i 0.599875i
$$149$$ 1470.33 0.808416 0.404208 0.914667i $$-0.367547\pi$$
0.404208 + 0.914667i $$0.367547\pi$$
$$150$$ 887.148 1604.60i 0.482902 0.873432i
$$151$$ −1695.79 −0.913916 −0.456958 0.889488i $$-0.651061\pi$$
−0.456958 + 0.889488i $$0.651061\pi$$
$$152$$ 5372.47i 2.86687i
$$153$$ 1202.95i 0.635641i
$$154$$ 1879.01 0.983215
$$155$$ 2017.32 1189.78i 1.04539 0.616552i
$$156$$ 2374.33 1.21858
$$157$$ 959.433i 0.487714i 0.969811 + 0.243857i $$0.0784127\pi$$
−0.969811 + 0.243857i $$0.921587\pi$$
$$158$$ 4589.49i 2.31089i
$$159$$ −159.253 −0.0794312
$$160$$ −41.5816 70.5033i −0.0205457 0.0348361i
$$161$$ 51.2926 0.0251082
$$162$$ 396.038i 0.192072i
$$163$$ 3865.27i 1.85737i 0.370869 + 0.928685i $$0.379060\pi$$
−0.370869 + 0.928685i $$0.620940\pi$$
$$164$$ −1235.57 −0.588305
$$165$$ −935.465 1586.12i −0.441369 0.748359i
$$166$$ −3837.69 −1.79435
$$167$$ 465.084i 0.215505i −0.994178 0.107752i $$-0.965635\pi$$
0.994178 0.107752i $$-0.0343653\pi$$
$$168$$ 811.747i 0.372784i
$$169$$ −278.860 −0.126927
$$170$$ −6293.52 + 3711.81i −2.83936 + 1.67460i
$$171$$ 1250.88 0.559398
$$172$$ 3144.47i 1.39397i
$$173$$ 2048.04i 0.900057i −0.893014 0.450028i $$-0.851414\pi$$
0.893014 0.450028i $$-0.148586\pi$$
$$174$$ −1279.66 −0.557531
$$175$$ 765.756 + 423.371i 0.330775 + 0.182879i
$$176$$ 3390.10 1.45192
$$177$$ 2051.85i 0.871336i
$$178$$ 1349.11i 0.568091i
$$179$$ 911.856 0.380756 0.190378 0.981711i $$-0.439029\pi$$
0.190378 + 0.981711i $$0.439029\pi$$
$$180$$ −1378.59 + 813.068i −0.570856 + 0.336681i
$$181$$ −2029.81 −0.833562 −0.416781 0.909007i $$-0.636842\pi$$
−0.416781 + 0.909007i $$0.636842\pi$$
$$182$$ 1702.99i 0.693595i
$$183$$ 80.5975i 0.0325570i
$$184$$ 283.242 0.113483
$$185$$ 385.677 + 653.930i 0.153273 + 0.259881i
$$186$$ −3072.66 −1.21128
$$187$$ 7338.13i 2.86961i
$$188$$ 79.1496i 0.0307052i
$$189$$ 189.000 0.0727393
$$190$$ −3859.68 6544.25i −1.47374 2.49879i
$$191$$ 4984.11 1.88815 0.944077 0.329725i $$-0.106956\pi$$
0.944077 + 0.329725i $$0.106956\pi$$
$$192$$ 1589.38i 0.597413i
$$193$$ 3393.44i 1.26562i 0.774306 + 0.632811i $$0.218099\pi$$
−0.774306 + 0.632811i $$0.781901\pi$$
$$194$$ 5697.43 2.10852
$$195$$ 1437.54 847.835i 0.527919 0.311358i
$$196$$ 779.387 0.284033
$$197$$ 762.475i 0.275757i 0.990449 + 0.137878i $$0.0440283\pi$$
−0.990449 + 0.137878i $$0.955972\pi$$
$$198$$ 2415.87i 0.867114i
$$199$$ 1272.32 0.453227 0.226613 0.973985i $$-0.427235\pi$$
0.226613 + 0.973985i $$0.427235\pi$$
$$200$$ 4228.57 + 2337.89i 1.49503 + 0.826569i
$$201$$ −447.900 −0.157176
$$202$$ 0.796959i 0.000277593i
$$203$$ 610.686i 0.211142i
$$204$$ 6378.00 2.18897
$$205$$ −748.077 + 441.203i −0.254868 + 0.150317i
$$206$$ −6360.00 −2.15108
$$207$$ 65.9476i 0.0221434i
$$208$$ 3072.53i 1.02424i
$$209$$ −7630.47 −2.52541
$$210$$ −583.174 988.796i −0.191633 0.324921i
$$211$$ 2010.72 0.656035 0.328017 0.944672i $$-0.393620\pi$$
0.328017 + 0.944672i $$0.393620\pi$$
$$212$$ 844.351i 0.273539i
$$213$$ 18.4671i 0.00594059i
$$214$$ 7488.70 2.39214
$$215$$ −1122.84 1903.82i −0.356172 0.603904i
$$216$$ 1043.67 0.328764
$$217$$ 1466.35i 0.458721i
$$218$$ 9638.85i 2.99461i
$$219$$ 883.635 0.272651
$$220$$ 8409.53 4959.79i 2.57714 1.51995i
$$221$$ −6650.73 −2.02433
$$222$$ 996.024i 0.301120i
$$223$$ 1516.44i 0.455374i −0.973734 0.227687i $$-0.926884\pi$$
0.973734 0.227687i $$-0.0731163\pi$$
$$224$$ −51.2475 −0.0152862
$$225$$ −544.334 + 984.543i −0.161284 + 0.291717i
$$226$$ 1285.01 0.378219
$$227$$ 4101.17i 1.19914i 0.800323 + 0.599568i $$0.204661\pi$$
−0.800323 + 0.599568i $$0.795339\pi$$
$$228$$ 6632.10i 1.92641i
$$229$$ 1029.24 0.297004 0.148502 0.988912i $$-0.452555\pi$$
0.148502 + 0.988912i $$0.452555\pi$$
$$230$$ 345.020 203.487i 0.0989128 0.0583370i
$$231$$ −1152.92 −0.328383
$$232$$ 3372.26i 0.954309i
$$233$$ 5578.41i 1.56847i −0.620463 0.784236i $$-0.713055\pi$$
0.620463 0.784236i $$-0.286945\pi$$
$$234$$ −2189.56 −0.611694
$$235$$ −28.2630 47.9211i −0.00784543 0.0133022i
$$236$$ −10878.8 −3.00064
$$237$$ 2816.01i 0.771812i
$$238$$ 4574.64i 1.24592i
$$239$$ −5389.67 −1.45870 −0.729348 0.684142i $$-0.760177\pi$$
−0.729348 + 0.684142i $$0.760177\pi$$
$$240$$ −1052.16 1783.98i −0.282986 0.479815i
$$241$$ 3976.27 1.06280 0.531399 0.847122i $$-0.321667\pi$$
0.531399 + 0.847122i $$0.321667\pi$$
$$242$$ 8229.31i 2.18595i
$$243$$ 243.000i 0.0641500i
$$244$$ 427.324 0.112117
$$245$$ 471.880 278.306i 0.123050 0.0725728i
$$246$$ 1139.42 0.295313
$$247$$ 6915.69i 1.78152i
$$248$$ 8097.33i 2.07331i
$$249$$ 2354.72 0.599294
$$250$$ 6830.45 190.081i 1.72798 0.0480871i
$$251$$ 7095.76 1.78438 0.892192 0.451655i $$-0.149166\pi$$
0.892192 + 0.451655i $$0.149166\pi$$
$$252$$ 1002.07i 0.250494i
$$253$$ 402.287i 0.0999666i
$$254$$ 2785.22 0.688033
$$255$$ 3861.56 2277.48i 0.948315 0.559299i
$$256$$ −8140.43 −1.98741
$$257$$ 2526.56i 0.613239i −0.951832 0.306619i $$-0.900802\pi$$
0.951832 0.306619i $$-0.0991979\pi$$
$$258$$ 2899.77i 0.699735i
$$259$$ 475.329 0.114037
$$260$$ 4495.18 + 7621.77i 1.07223 + 1.81801i
$$261$$ 785.167 0.186209
$$262$$ 4815.08i 1.13541i
$$263$$ 3842.34i 0.900871i 0.892809 + 0.450435i $$0.148731\pi$$
−0.892809 + 0.450435i $$0.851269\pi$$
$$264$$ −6366.52 −1.48421
$$265$$ −301.504 511.212i −0.0698914 0.118504i
$$266$$ −4756.88 −1.09648
$$267$$ 827.784i 0.189736i
$$268$$ 2374.75i 0.541271i
$$269$$ 8411.04 1.90643 0.953216 0.302291i $$-0.0977514\pi$$
0.953216 + 0.302291i $$0.0977514\pi$$
$$270$$ 1271.31 749.796i 0.286553 0.169004i
$$271$$ 5659.73 1.26865 0.634325 0.773067i $$-0.281278\pi$$
0.634325 + 0.773067i $$0.281278\pi$$
$$272$$ 8253.54i 1.83987i
$$273$$ 1044.92i 0.231653i
$$274$$ −6734.37 −1.48481
$$275$$ 3320.49 6005.81i 0.728120 1.31696i
$$276$$ −349.651 −0.0762555
$$277$$ 881.409i 0.191187i −0.995420 0.0955934i $$-0.969525\pi$$
0.995420 0.0955934i $$-0.0304749\pi$$
$$278$$ 4105.47i 0.885718i
$$279$$ 1885.31 0.404554
$$280$$ 2605.76 1536.83i 0.556157 0.328012i
$$281$$ −3853.71 −0.818124 −0.409062 0.912506i $$-0.634144\pi$$
−0.409062 + 0.912506i $$0.634144\pi$$
$$282$$ 72.9902i 0.0154131i
$$283$$ 1891.60i 0.397328i 0.980068 + 0.198664i $$0.0636603\pi$$
−0.980068 + 0.198664i $$0.936340\pi$$
$$284$$ −97.9118 −0.0204577
$$285$$ 2368.21 + 4015.40i 0.492213 + 0.834568i
$$286$$ 13356.6 2.76150
$$287$$ 543.763i 0.111837i
$$288$$ 65.8896i 0.0134812i
$$289$$ −12952.4 −2.63635
$$290$$ −2422.70 4107.78i −0.490571 0.831784i
$$291$$ −3495.81 −0.704221
$$292$$ 4684.99i 0.938933i
$$293$$ 4076.18i 0.812742i 0.913708 + 0.406371i $$0.133206\pi$$
−0.913708 + 0.406371i $$0.866794\pi$$
$$294$$ −718.736 −0.142577
$$295$$ −6586.58 + 3884.65i −1.29995 + 0.766687i
$$296$$ 2624.81 0.515419
$$297$$ 1482.32i 0.289607i
$$298$$ 7188.97i 1.39747i
$$299$$ 364.602 0.0705201
$$300$$ −5220.00 2886.03i −1.00459 0.555417i
$$301$$ −1383.85 −0.264995
$$302$$ 8291.33i 1.57984i
$$303$$ 0.488996i 9.27131e-5i
$$304$$ −8582.35 −1.61918
$$305$$ 258.723 152.590i 0.0485720 0.0286469i
$$306$$ −5881.67 −1.09880
$$307$$ 6201.87i 1.15296i 0.817110 + 0.576481i $$0.195575\pi$$
−0.817110 + 0.576481i $$0.804425\pi$$
$$308$$ 6112.72i 1.13086i
$$309$$ 3902.35 0.718437
$$310$$ −5817.28 9863.43i −1.06580 1.80711i
$$311$$ −6601.95 −1.20374 −0.601868 0.798595i $$-0.705577\pi$$
−0.601868 + 0.798595i $$0.705577\pi$$
$$312$$ 5770.13i 1.04702i
$$313$$ 2291.01i 0.413724i −0.978370 0.206862i $$-0.933675\pi$$
0.978370 0.206862i $$-0.0663251\pi$$
$$314$$ 4691.02 0.843087
$$315$$ 357.822 + 606.703i 0.0640032 + 0.108520i
$$316$$ −14930.3 −2.65790
$$317$$ 3124.07i 0.553517i 0.960939 + 0.276759i $$0.0892603\pi$$
−0.960939 + 0.276759i $$0.910740\pi$$
$$318$$ 778.644i 0.137309i
$$319$$ −4789.60 −0.840646
$$320$$ −5102.00 + 3009.07i −0.891283 + 0.525663i
$$321$$ −4594.89 −0.798947
$$322$$ 250.788i 0.0434033i
$$323$$ 18577.1i 3.20018i
$$324$$ −1288.37 −0.220915
$$325$$ 5443.21 + 3009.44i 0.929031 + 0.513642i
$$326$$ 18898.7 3.21074
$$327$$ 5914.18i 1.00017i
$$328$$ 3002.70i 0.505478i
$$329$$ −34.8329 −0.00583708
$$330$$ −7755.11 + 4573.83i −1.29365 + 0.762972i
$$331$$ 9825.49 1.63159 0.815797 0.578338i $$-0.196298\pi$$
0.815797 + 0.578338i $$0.196298\pi$$
$$332$$ 12484.6i 2.06380i
$$333$$ 611.137i 0.100571i
$$334$$ −2273.96 −0.372532
$$335$$ −847.983 1437.79i −0.138299 0.234492i
$$336$$ −1296.74 −0.210545
$$337$$ 8526.35i 1.37822i −0.724657 0.689110i $$-0.758002\pi$$
0.724657 0.689110i $$-0.241998\pi$$
$$338$$ 1363.45i 0.219413i
$$339$$ −788.451 −0.126321
$$340$$ 12075.1 + 20473.8i 1.92607 + 3.26573i
$$341$$ −11500.6 −1.82637
$$342$$ 6115.99i 0.967003i
$$343$$ 343.000i 0.0539949i
$$344$$ −7641.73 −1.19772
$$345$$ −211.696 + 124.855i −0.0330358 + 0.0194839i
$$346$$ −10013.6 −1.55588
$$347$$ 4164.54i 0.644277i 0.946693 + 0.322138i $$0.104402\pi$$
−0.946693 + 0.322138i $$0.895598\pi$$
$$348$$ 4162.92i 0.641253i
$$349$$ −2584.60 −0.396420 −0.198210 0.980160i $$-0.563513\pi$$
−0.198210 + 0.980160i $$0.563513\pi$$
$$350$$ 2070.01 3744.06i 0.316134 0.571795i
$$351$$ 1343.47 0.204299
$$352$$ 401.933i 0.0608611i
$$353$$ 4199.25i 0.633154i −0.948567 0.316577i $$-0.897466\pi$$
0.948567 0.316577i $$-0.102534\pi$$
$$354$$ 10032.2 1.50624
$$355$$ −59.2807 + 34.9627i −0.00886280 + 0.00522712i
$$356$$ 4388.87 0.653398
$$357$$ 2806.89i 0.416124i
$$358$$ 4458.39i 0.658194i
$$359$$ 990.277 0.145584 0.0727922 0.997347i $$-0.476809\pi$$
0.0727922 + 0.997347i $$0.476809\pi$$
$$360$$ 1975.93 + 3350.27i 0.289279 + 0.490485i
$$361$$ 12458.2 1.81633
$$362$$ 9924.48i 1.44094i
$$363$$ 5049.32i 0.730084i
$$364$$ 5540.11 0.797749
$$365$$ 1672.93 + 2836.53i 0.239905 + 0.406769i
$$366$$ −394.070 −0.0562797
$$367$$ 4179.24i 0.594427i 0.954811 + 0.297213i $$0.0960573\pi$$
−0.954811 + 0.297213i $$0.903943\pi$$
$$368$$ 452.471i 0.0640942i
$$369$$ −699.123 −0.0986312
$$370$$ 3197.30 1885.71i 0.449243 0.264955i
$$371$$ −371.590 −0.0519999
$$372$$ 9995.83i 1.39317i
$$373$$ 7365.36i 1.02242i 0.859455 + 0.511212i $$0.170803\pi$$
−0.859455 + 0.511212i $$0.829197\pi$$
$$374$$ 35878.8 4.96056
$$375$$ −4191.00 + 116.629i −0.577127 + 0.0160606i
$$376$$ −192.350 −0.0263822
$$377$$ 4340.93i 0.593022i
$$378$$ 924.089i 0.125741i
$$379$$ 6214.13 0.842213 0.421106 0.907011i $$-0.361642\pi$$
0.421106 + 0.907011i $$0.361642\pi$$
$$380$$ −21289.5 + 12556.2i −2.87402 + 1.69504i
$$381$$ −1708.95 −0.229795
$$382$$ 24369.1i 3.26396i
$$383$$ 1755.04i 0.234148i 0.993123 + 0.117074i $$0.0373514\pi$$
−0.993123 + 0.117074i $$0.962649\pi$$
$$384$$ 7595.33 1.00937
$$385$$ −2182.75 3700.94i −0.288944 0.489916i
$$386$$ 16591.7 2.18782
$$387$$ 1779.23i 0.233704i
$$388$$ 18534.6i 2.42514i
$$389$$ −8805.69 −1.14773 −0.573864 0.818950i $$-0.694556\pi$$
−0.573864 + 0.818950i $$0.694556\pi$$
$$390$$ −4145.37 7028.65i −0.538228 0.912588i
$$391$$ 979.406 0.126677
$$392$$ 1894.08i 0.244044i
$$393$$ 2954.42i 0.379214i
$$394$$ 3728.01 0.476687
$$395$$ −9039.57 + 5331.38i −1.15147 + 0.679116i
$$396$$ 7859.21 0.997324
$$397$$ 13717.2i 1.73413i −0.498199 0.867063i $$-0.666005\pi$$
0.498199 0.867063i $$-0.333995\pi$$
$$398$$ 6220.82i 0.783471i
$$399$$ 2918.71 0.366212
$$400$$ 3734.71 6755.01i 0.466838 0.844377i
$$401$$ 307.220 0.0382590 0.0191295 0.999817i $$-0.493911\pi$$
0.0191295 + 0.999817i $$0.493911\pi$$
$$402$$ 2189.95i 0.271703i
$$403$$ 10423.3i 1.28839i
$$404$$ 2.59263 0.000319278
$$405$$ −780.046 + 460.057i −0.0957057 + 0.0564455i
$$406$$ −2985.86 −0.364990
$$407$$ 3728.00i 0.454029i
$$408$$ 15499.9i 1.88078i
$$409$$ −12390.7 −1.49799 −0.748997 0.662573i $$-0.769464\pi$$
−0.748997 + 0.662573i $$0.769464\pi$$
$$410$$ 2157.20 + 3657.62i 0.259845 + 0.440578i
$$411$$ 4132.05 0.495910
$$412$$ 20690.1i 2.47409i
$$413$$ 4787.65i 0.570423i
$$414$$ 322.442 0.0382781
$$415$$ 4458.05 + 7558.81i 0.527318 + 0.894090i
$$416$$ −364.282 −0.0429336
$$417$$ 2519.02i 0.295820i
$$418$$ 37308.2i 4.36555i
$$419$$ −2664.10 −0.310620 −0.155310 0.987866i $$-0.549638\pi$$
−0.155310 + 0.987866i $$0.549638\pi$$
$$420$$ −3216.71 + 1897.16i −0.373713 + 0.220409i
$$421$$ −6851.11 −0.793118 −0.396559 0.918009i $$-0.629796\pi$$
−0.396559 + 0.918009i $$0.629796\pi$$
$$422$$ 9831.12i 1.13406i
$$423$$ 44.7851i 0.00514782i
$$424$$ −2051.95 −0.235027
$$425$$ 14621.7 + 8084.05i 1.66884 + 0.922668i
$$426$$ 90.2924 0.0102692
$$427$$ 188.061i 0.0213136i
$$428$$ 24361.9i 2.75135i
$$429$$ −8195.27 −0.922311
$$430$$ −9308.45 + 5489.96i −1.04394 + 0.615696i
$$431$$ −7651.38 −0.855114 −0.427557 0.903988i $$-0.640626\pi$$
−0.427557 + 0.903988i $$0.640626\pi$$
$$432$$ 1667.24i 0.185683i
$$433$$ 691.572i 0.0767548i −0.999263 0.0383774i $$-0.987781\pi$$
0.999263 0.0383774i $$-0.0122189\pi$$
$$434$$ −7169.53 −0.792969
$$435$$ 1486.51 + 2520.44i 0.163845 + 0.277807i
$$436$$ 31356.7 3.44430
$$437$$ 1018.42i 0.111483i
$$438$$ 4320.41i 0.471318i
$$439$$ −10621.7 −1.15478 −0.577389 0.816469i $$-0.695928\pi$$
−0.577389 + 0.816469i $$0.695928\pi$$
$$440$$ −12053.3 20436.9i −1.30596 2.21430i
$$441$$ 441.000 0.0476190
$$442$$ 32517.8i 3.49936i
$$443$$ 3133.67i 0.336084i 0.985780 + 0.168042i $$0.0537444\pi$$
−0.985780 + 0.168042i $$0.946256\pi$$
$$444$$ −3240.22 −0.346338
$$445$$ 2657.24 1567.19i 0.283068 0.166949i
$$446$$ −7414.43 −0.787182
$$447$$ 4410.99i 0.466739i
$$448$$ 3708.54i 0.391099i
$$449$$ 9144.92 0.961192 0.480596 0.876942i $$-0.340420\pi$$
0.480596 + 0.876942i $$0.340420\pi$$
$$450$$ 4813.79 + 2661.45i 0.504276 + 0.278804i
$$451$$ 4264.72 0.445272
$$452$$ 4180.33i 0.435014i
$$453$$ 5087.37i 0.527650i
$$454$$ 20052.1 2.07289
$$455$$ 3354.26 1978.28i 0.345604 0.203831i
$$456$$ 16117.4 1.65519
$$457$$ 8142.60i 0.833468i −0.909029 0.416734i $$-0.863175\pi$$
0.909029 0.416734i $$-0.136825\pi$$
$$458$$ 5032.32i 0.513417i
$$459$$ 3608.86 0.366987
$$460$$ −661.974 1122.40i −0.0670971 0.113766i
$$461$$ −9287.29 −0.938291 −0.469145 0.883121i $$-0.655438\pi$$
−0.469145 + 0.883121i $$0.655438\pi$$
$$462$$ 5637.04i 0.567659i
$$463$$ 2440.53i 0.244970i 0.992470 + 0.122485i $$0.0390864\pi$$
−0.992470 + 0.122485i $$0.960914\pi$$
$$464$$ −5387.08 −0.538985
$$465$$ 3569.35 + 6051.97i 0.355967 + 0.603556i
$$466$$ −27274.9 −2.71134
$$467$$ 12066.3i 1.19564i 0.801632 + 0.597818i $$0.203966\pi$$
−0.801632 + 0.597818i $$0.796034\pi$$
$$468$$ 7123.00i 0.703548i
$$469$$ −1045.10 −0.102896
$$470$$ −234.304 + 138.188i −0.0229949 + 0.0135620i
$$471$$ −2878.30 −0.281582
$$472$$ 26437.8i 2.57818i
$$473$$ 10853.5i 1.05506i
$$474$$ 13768.5 1.33419
$$475$$ −8406.11 + 15204.2i −0.811998 + 1.46867i
$$476$$ 14882.0 1.43302
$$477$$ 477.758i 0.0458596i
$$478$$ 26352.0i 2.52158i
$$479$$ −395.211 −0.0376987 −0.0188493 0.999822i $$-0.506000\pi$$
−0.0188493 + 0.999822i $$0.506000\pi$$
$$480$$ 211.510 124.745i 0.0201126 0.0118621i
$$481$$ 3378.77 0.320289
$$482$$ 19441.4i 1.83721i
$$483$$ 153.878i 0.0144962i
$$484$$ −26771.2 −2.51420
$$485$$ −6618.42 11221.8i −0.619643 1.05063i
$$486$$ 1188.11 0.110893
$$487$$ 9609.06i 0.894102i 0.894508 + 0.447051i $$0.147526\pi$$
−0.894508 + 0.447051i $$0.852474\pi$$
$$488$$ 1038.49i 0.0963323i
$$489$$ −11595.8 −1.07235
$$490$$ −1360.74 2307.19i −0.125453 0.212711i
$$491$$ 10941.0 1.00562 0.502810 0.864397i $$-0.332299\pi$$
0.502810 + 0.864397i $$0.332299\pi$$
$$492$$ 3706.72i 0.339658i
$$493$$ 11660.7i 1.06526i
$$494$$ −33813.3 −3.07962
$$495$$ 4758.36 2806.39i 0.432065 0.254824i
$$496$$ −12935.2 −1.17099
$$497$$ 43.0899i 0.00388903i
$$498$$ 11513.1i 1.03597i
$$499$$ −9269.90 −0.831618 −0.415809 0.909452i $$-0.636502\pi$$
−0.415809 + 0.909452i $$0.636502\pi$$
$$500$$ −618.363 22220.5i −0.0553081 1.98746i
$$501$$ 1395.25 0.124422
$$502$$ 34693.8i 3.08458i
$$503$$ 15085.4i 1.33723i 0.743609 + 0.668615i $$0.233112\pi$$
−0.743609 + 0.668615i $$0.766888\pi$$
$$504$$ 2435.24 0.215227
$$505$$ 1.56971 0.925787i 0.000138319 8.15781e-5i
$$506$$ −1966.93 −0.172807
$$507$$ 836.579i 0.0732816i
$$508$$ 9060.76i 0.791351i
$$509$$ −8650.44 −0.753289 −0.376645 0.926358i $$-0.622922\pi$$
−0.376645 + 0.926358i $$0.622922\pi$$
$$510$$ −11135.4 18880.6i −0.966833 1.63931i
$$511$$ 2061.82 0.178492
$$512$$ 19547.3i 1.68726i
$$513$$ 3752.63i 0.322968i
$$514$$ −12353.3 −1.06008
$$515$$ 7388.09 + 12526.8i 0.632151 + 1.07184i
$$516$$ 9433.40 0.804811
$$517$$ 273.194i 0.0232399i
$$518$$ 2324.06i 0.197130i
$$519$$ 6144.13 0.519648
$$520$$ 18522.5 10924.2i 1.56205 0.921269i
$$521$$ 10661.6 0.896535 0.448268 0.893899i $$-0.352041\pi$$
0.448268 + 0.893899i $$0.352041\pi$$
$$522$$ 3838.97i 0.321891i
$$523$$ 3449.22i 0.288382i 0.989550 + 0.144191i $$0.0460580\pi$$
−0.989550 + 0.144191i $$0.953942\pi$$
$$524$$ −15664.2 −1.30591
$$525$$ −1270.11 + 2297.27i −0.105585 + 0.190973i
$$526$$ 18786.6 1.55729
$$527$$ 27999.3i 2.31436i
$$528$$ 10170.3i 0.838269i
$$529$$ 12113.3 0.995587
$$530$$ −2499.50 + 1474.16i −0.204852 + 0.120818i
$$531$$ −6155.55 −0.503066
$$532$$ 15474.9i 1.26113i
$$533$$ 3865.22i 0.314111i
$$534$$ −4047.34 −0.327988
$$535$$ −8699.24 14749.9i −0.702992 1.19195i
$$536$$ −5771.14 −0.465066
$$537$$ 2735.57i 0.219829i
$$538$$ 41124.6i 3.29555i
$$539$$ −2690.14 −0.214977
$$540$$ −2439.20 4135.77i −0.194383 0.329584i
$$541$$ 13403.2 1.06516 0.532578 0.846381i $$-0.321223\pi$$
0.532578 + 0.846381i $$0.321223\pi$$
$$542$$ 27672.5i 2.19305i
$$543$$ 6089.43i 0.481257i
$$544$$ −978.544 −0.0771227
$$545$$ 18984.9 11197.0i 1.49215 0.880046i
$$546$$ −5108.98 −0.400447
$$547$$ 3670.29i 0.286893i −0.989658 0.143446i $$-0.954182\pi$$
0.989658 0.143446i $$-0.0458184\pi$$
$$548$$ 21907.9i 1.70778i
$$549$$ 241.792 0.0187968
$$550$$ −29364.6 16235.1i −2.27656 1.25867i
$$551$$ 12125.3 0.937486
$$552$$ 849.727i 0.0655195i
$$553$$ 6570.69i 0.505269i
$$554$$ −4309.53 −0.330495
$$555$$ −1961.79 + 1157.03i −0.150042 + 0.0884922i
$$556$$ 13355.7 1.01872
$$557$$ 521.169i 0.0396456i 0.999804 + 0.0198228i $$0.00631021\pi$$
−0.999804 + 0.0198228i $$0.993690\pi$$
$$558$$ 9217.97i 0.699333i
$$559$$ −9836.78 −0.744278
$$560$$ −2455.04 4162.62i −0.185258 0.314112i
$$561$$ −22014.4 −1.65677
$$562$$ 18842.2i 1.41425i
$$563$$ 17970.2i 1.34521i 0.740000 + 0.672606i $$0.234825\pi$$
−0.740000 + 0.672606i $$0.765175\pi$$
$$564$$ 237.449 0.0177277
$$565$$ −1492.73 2530.98i −0.111150 0.188459i
$$566$$ 9248.71 0.686842
$$567$$ 567.000i 0.0419961i
$$568$$ 237.947i 0.0175775i
$$569$$ 21808.6 1.60679 0.803396 0.595445i $$-0.203024\pi$$
0.803396 + 0.595445i $$0.203024\pi$$
$$570$$ 19632.7 11579.0i 1.44268 0.850865i
$$571$$ 6604.75 0.484064 0.242032 0.970268i $$-0.422186\pi$$
0.242032 + 0.970268i $$0.422186\pi$$
$$572$$ 43451.0i 3.17618i
$$573$$ 14952.3i 1.09013i
$$574$$ 2658.65 0.193327
$$575$$ −801.584 443.179i −0.0581363 0.0321423i
$$576$$ −4768.13 −0.344916
$$577$$ 25886.9i 1.86774i −0.357618 0.933868i $$-0.616411\pi$$
0.357618 0.933868i $$-0.383589\pi$$
$$578$$ 63328.9i 4.55733i
$$579$$ −10180.3 −0.730707
$$580$$ −13363.3 + 7881.41i −0.956688 + 0.564238i
$$581$$ 5494.35 0.392330
$$582$$ 17092.3i 1.21735i
$$583$$ 2914.37i 0.207034i
$$584$$ 11385.5 0.806741
$$585$$ 2543.50 + 4312.62i 0.179762 + 0.304794i
$$586$$ 19929.9 1.40495
$$587$$ 4949.88i 0.348046i −0.984742 0.174023i $$-0.944323\pi$$
0.984742 0.174023i $$-0.0556768\pi$$
$$588$$ 2338.16i 0.163987i
$$589$$ 29114.7 2.03676
$$590$$ 18993.4 + 32204.2i 1.32533 + 2.24716i
$$591$$ −2287.42 −0.159208
$$592$$ 4193.05i 0.291104i
$$593$$ 31.3988i 0.00217436i −0.999999 0.00108718i $$-0.999654\pi$$
0.999999 0.00108718i $$-0.000346059\pi$$
$$594$$ −7247.62 −0.500628
$$595$$ 9010.31 5314.12i 0.620818 0.366147i
$$596$$ −23386.8 −1.60732
$$597$$ 3816.95i 0.261671i
$$598$$ 1782.67i 0.121905i
$$599$$ 11870.4 0.809704 0.404852 0.914382i $$-0.367323\pi$$
0.404852 + 0.914382i $$0.367323\pi$$
$$600$$ −7013.67 + 12685.7i −0.477220 + 0.863154i
$$601$$ −967.320 −0.0656536 −0.0328268 0.999461i $$-0.510451\pi$$
−0.0328268 + 0.999461i $$0.510451\pi$$
$$602$$ 6766.13i 0.458084i
$$603$$ 1343.70i 0.0907458i
$$604$$ 26973.0 1.81708
$$605$$ −16208.6 + 9559.57i −1.08922 + 0.642400i
$$606$$ −2.39088 −0.000160269
$$607$$ 9518.28i 0.636466i −0.948013 0.318233i $$-0.896911\pi$$
0.948013 0.318233i $$-0.103089\pi$$
$$608$$ 1017.53i 0.0678721i
$$609$$ 1832.06 0.121903
$$610$$ −746.070 1264.99i −0.0495205 0.0839640i
$$611$$ −247.602 −0.0163943
$$612$$ 19134.0i 1.26380i
$$613$$ 3607.19i 0.237672i 0.992914 + 0.118836i $$0.0379163\pi$$
−0.992914 + 0.118836i $$0.962084\pi$$
$$614$$ 30323.2 1.99307
$$615$$ −1323.61 2244.23i −0.0867854 0.147148i
$$616$$ −14855.2 −0.971645
$$617$$ 22473.2i 1.46635i 0.680042 + 0.733173i $$0.261962\pi$$
−0.680042 + 0.733173i $$0.738038\pi$$
$$618$$ 19080.0i 1.24193i
$$619$$ −19200.1 −1.24672 −0.623358 0.781936i $$-0.714232\pi$$
−0.623358 + 0.781936i $$0.714232\pi$$
$$620$$ −32087.3 + 18924.5i −2.07848 + 1.22585i
$$621$$ −197.843 −0.0127845
$$622$$ 32279.3i 2.08084i
$$623$$ 1931.50i 0.124211i
$$624$$ −9217.60 −0.591345
$$625$$ −8308.97 13232.6i −0.531774 0.846886i
$$626$$ −11201.6 −0.715184
$$627$$ 22891.4i 1.45805i
$$628$$ 15260.6i 0.969689i
$$629$$ 9076.17 0.575343
$$630$$ 2966.39 1749.52i 0.187593 0.110639i
$$631$$ −6980.64 −0.440404 −0.220202 0.975454i $$-0.570672\pi$$
−0.220202 + 0.975454i $$0.570672\pi$$
$$632$$ 36283.9i 2.28370i
$$633$$ 6032.15i 0.378762i
$$634$$ 15274.7 0.956838
$$635$$ −3235.45 5485.83i −0.202197 0.342833i
$$636$$ 2533.05 0.157928
$$637$$ 2438.14i 0.151653i
$$638$$ 23418.1i 1.45318i
$$639$$ −55.4014 −0.00342980
$$640$$ 14379.8 + 24381.5i 0.888142 + 1.50588i
$$641$$ −1083.82 −0.0667837 −0.0333919 0.999442i $$-0.510631\pi$$
−0.0333919 + 0.999442i $$0.510631\pi$$
$$642$$ 22466.1i 1.38110i
$$643$$ 4151.42i 0.254613i −0.991863 0.127307i $$-0.959367\pi$$
0.991863 0.127307i $$-0.0406332\pi$$
$$644$$ −815.853 −0.0499210
$$645$$ 5711.45 3368.51i 0.348664 0.205636i
$$646$$ −90830.3 −5.53200
$$647$$ 3014.99i 0.183202i 0.995796 + 0.0916008i $$0.0291984\pi$$
−0.995796 + 0.0916008i $$0.970802\pi$$
$$648$$ 3131.02i 0.189812i
$$649$$ 37549.4 2.27110
$$650$$ 14714.2 26613.8i 0.887908 1.60597i
$$651$$ 4399.06 0.264843
$$652$$ 61480.5i 3.69288i
$$653$$ 21130.7i 1.26632i −0.774019 0.633162i $$-0.781757\pi$$
0.774019 0.633162i $$-0.218243\pi$$
$$654$$ −28916.6 −1.72894
$$655$$ −9483.90 + 5593.44i −0.565751 + 0.333670i
$$656$$ 4796.73 0.285489
$$657$$ 2650.91i 0.157415i
$$658$$ 170.311i 0.0100903i
$$659$$ 9961.24 0.588824 0.294412 0.955679i $$-0.404876\pi$$
0.294412 + 0.955679i $$0.404876\pi$$
$$660$$ 14879.4 + 25228.6i 0.877544 + 1.48791i
$$661$$ 1581.43 0.0930569 0.0465285 0.998917i $$-0.485184\pi$$
0.0465285 + 0.998917i $$0.485184\pi$$
$$662$$ 48040.4i 2.82046i
$$663$$ 19952.2i 1.16875i
$$664$$ 30340.3 1.77324
$$665$$ 5525.83 + 9369.27i 0.322229 + 0.546353i
$$666$$ 2988.07 0.173852
$$667$$ 639.258i 0.0371097i
$$668$$ 7397.56i 0.428473i
$$669$$ 4549.32 0.262910
$$670$$ −7029.87 + 4146.09i −0.405355 + 0.239071i
$$671$$ −1474.96 −0.0848586
$$672$$ 153.742i 0.00882551i
$$673$$ 11101.6i 0.635865i 0.948113 + 0.317932i $$0.102988\pi$$
−0.948113 + 0.317932i $$0.897012\pi$$
$$674$$ −41688.4 −2.38246
$$675$$ −2953.63 1633.00i −0.168423 0.0931174i
$$676$$ 4435.50 0.252361
$$677$$ 18249.8i 1.03603i 0.855370 + 0.518017i $$0.173330\pi$$
−0.855370 + 0.518017i $$0.826670\pi$$
$$678$$ 3855.02i 0.218365i
$$679$$ −8156.90 −0.461021
$$680$$ 49755.7 29345.0i 2.80595 1.65490i
$$681$$ −12303.5 −0.692322
$$682$$ 56230.5i 3.15715i
$$683$$ 14144.2i 0.792403i −0.918164 0.396202i $$-0.870328\pi$$
0.918164 0.396202i $$-0.129672\pi$$
$$684$$ −19896.3 −1.11221
$$685$$ 7822.97 + 13264.2i 0.436351 + 0.739851i
$$686$$ −1677.05 −0.0933384
$$687$$ 3087.71i 0.171475i
$$688$$ 12207.4i 0.676458i
$$689$$ −2641.37 −0.146049
$$690$$ 610.460 + 1035.06i 0.0336809 + 0.0571073i
$$691$$ 19621.7 1.08024 0.540120 0.841588i $$-0.318379\pi$$
0.540120 + 0.841588i $$0.318379\pi$$
$$692$$ 32575.9i 1.78952i
$$693$$ 3458.75i 0.189592i
$$694$$ 20361.9 1.11373
$$695$$ 8086.22 4769.11i 0.441335 0.260292i
$$696$$ 10116.8 0.550971
$$697$$ 10382.9i 0.564246i
$$698$$ 12637.1i 0.685272i
$$699$$ 16735.2 0.905557
$$700$$ −12180.0 6734.08i −0.657659 0.363606i
$$701$$ 21609.1 1.16428 0.582142 0.813087i $$-0.302215\pi$$
0.582142 + 0.813087i $$0.302215\pi$$
$$702$$ 6568.69i 0.353161i
$$703$$ 9437.75i 0.506332i
$$704$$ 29086.0 1.55713
$$705$$ 143.763 84.7890i 0.00768005 0.00452956i
$$706$$ −20531.6 −1.09450
$$707$$ 1.14099i 6.06950e-5i
$$708$$ 32636.4i 1.73242i
$$709$$ 12557.2 0.665158 0.332579 0.943075i $$-0.392081\pi$$
0.332579 + 0.943075i $$0.392081\pi$$
$$710$$ 170.945 + 289.845i 0.00903586 + 0.0153207i
$$711$$ −8448.02 −0.445606
$$712$$ 10665.9i 0.561406i
$$713$$ 1534.96i 0.0806237i
$$714$$ −13723.9 −0.719334
$$715$$ −15515.6 26307.4i −0.811540 1.37600i
$$716$$ −14503.9 −0.757031
$$717$$ 16169.0i 0.842179i
$$718$$ 4841.82i 0.251665i
$$719$$ −36151.9 −1.87516 −0.937580 0.347771i $$-0.886939\pi$$
−0.937580 + 0.347771i $$0.886939\pi$$
$$720$$ 5351.95 3156.48i 0.277021 0.163382i
$$721$$ 9105.48 0.470327
$$722$$ 60912.8i 3.13980i
$$723$$ 11928.8i 0.613606i
$$724$$ 32285.9 1.65731
$$725$$ −5276.46 + 9543.60i −0.270293 + 0.488883i
$$726$$ 24687.9 1.26206
$$727$$ 12007.2i 0.612550i −0.951943 0.306275i $$-0.900917\pi$$
0.951943 0.306275i $$-0.0990828\pi$$
$$728$$ 13463.6i 0.685434i
$$729$$ −729.000 −0.0370370
$$730$$ 13868.8 8179.58i 0.703162 0.414712i
$$731$$ −26423.9 −1.33697
$$732$$ 1281.97i 0.0647310i
$$733$$ 15920.2i 0.802220i −0.916030 0.401110i $$-0.868625\pi$$
0.916030 0.401110i $$-0.131375\pi$$
$$734$$ 20433.8 1.02756
$$735$$ 834.919 + 1415.64i 0.0418999 + 0.0710431i
$$736$$ 53.6452 0.00268667
$$737$$ 8196.70i 0.409674i
$$738$$ 3418.27i 0.170499i
$$739$$ 26581.1 1.32314 0.661571 0.749882i $$-0.269890\pi$$
0.661571 + 0.749882i $$0.269890\pi$$
$$740$$ −6134.52 10401.3i −0.304742 0.516703i
$$741$$ 20747.1 1.02856
$$742$$ 1816.84i 0.0898897i
$$743$$ 6601.38i 0.325950i −0.986630 0.162975i $$-0.947891\pi$$
0.986630 0.162975i $$-0.0521090\pi$$
$$744$$ 24292.0 1.19703
$$745$$ −14159.6 + 8351.06i −0.696330 + 0.410683i
$$746$$ 36011.9 1.76741
$$747$$ 7064.16i 0.346003i
$$748$$ 116719.i 5.70546i
$$749$$ −10721.4 −0.523034
$$750$$ 570.243 + 20491.3i 0.0277631 + 0.997651i
$$751$$ −29809.6 −1.44842 −0.724212 0.689578i $$-0.757796\pi$$
−0.724212 + 0.689578i $$0.757796\pi$$
$$752$$ 307.274i 0.0149004i
$$753$$ 21287.3i 1.03022i
$$754$$ −21224.4 −1.02513
$$755$$ 16330.8 9631.61i 0.787203 0.464278i
$$756$$ −3006.21 −0.144623
$$757$$ 8179.09i 0.392700i 0.980534 + 0.196350i $$0.0629089\pi$$
−0.980534 + 0.196350i $$0.937091\pi$$
$$758$$ 30383.2i 1.45589i
$$759$$ 1206.86 0.0577158
$$760$$ 30514.1 + 51737.9i 1.45640 + 2.46938i
$$761$$ −31616.8 −1.50605 −0.753027 0.657990i $$-0.771407\pi$$
−0.753027 + 0.657990i $$0.771407\pi$$
$$762$$ 8355.66i 0.397236i
$$763$$ 13799.8i 0.654763i
$$764$$ −79276.5 −3.75409
$$765$$ 6832.44 + 11584.7i 0.322912 + 0.547510i
$$766$$ 8581.05 0.404760
$$767$$ 34032.0i 1.60212i
$$768$$ 24421.3i 1.14743i
$$769$$ −24651.3 −1.15598 −0.577991 0.816043i $$-0.696163\pi$$
−0.577991 + 0.816043i $$0.696163\pi$$
$$770$$ −18095.3 + 10672.3i −0.846893 + 0.499483i
$$771$$ 7579.67 0.354054
$$772$$ 53975.6i 2.51635i
$$773$$ 7888.63i 0.367056i −0.983015 0.183528i $$-0.941248\pi$$
0.983015 0.183528i $$-0.0587518\pi$$
$$774$$ −8699.31 −0.403992
$$775$$ −12669.6 + 22915.7i −0.587233 + 1.06214i
$$776$$ −45043.1 −2.08370
$$777$$ 1425.99i 0.0658391i
$$778$$ 43054.2i 1.98402i
$$779$$ −10796.5 −0.496566
$$780$$ −22865.3 + 13485.5i −1.04963 + 0.619051i
$$781$$ 337.954 0.0154839
$$782$$ 4788.67i 0.218980i
$$783$$ 2355.50i 0.107508i
$$784$$ −3025.73 −0.137834