# Properties

 Label 168.4.q.f.121.2 Level $168$ Weight $4$ Character 168.121 Analytic conductor $9.912$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$168 = 2^{3} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 168.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.91232088096$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ Defining polynomial: $$x^{8} + 173 x^{6} + 9457 x^{4} + 168048 x^{2} + 746496$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{6}\cdot 7$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 121.2 Root $$8.34231i$$ of defining polynomial Character $$\chi$$ $$=$$ 168.121 Dual form 168.4.q.f.25.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 - 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(-18.1420 + 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$$ $$q+(-1.50000 - 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(-18.1420 + 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(32.2447 + 55.8495i) q^{11} +71.8475 q^{13} +2.17903 q^{15} +(-24.4517 - 42.3515i) q^{17} +(-17.1984 + 29.7885i) q^{19} +(36.8878 + 41.5487i) q^{21} +(0.451675 - 0.782324i) q^{23} +(62.2362 + 107.796i) q^{25} +27.0000 q^{27} +226.686 q^{29} +(137.898 + 238.846i) q^{31} +(96.7342 - 167.549i) q^{33} +(4.24627 - 12.7643i) q^{35} +(-147.605 + 255.658i) q^{37} +(-107.771 - 186.665i) q^{39} +186.604 q^{41} -455.317 q^{43} +(-3.26854 - 5.66128i) q^{45} +(-141.167 + 244.509i) q^{47} +(315.267 - 135.115i) q^{49} +(-73.3550 + 127.055i) q^{51} +(-178.107 - 308.491i) q^{53} -46.8414 q^{55} +103.191 q^{57} +(-364.685 - 631.653i) q^{59} +(-137.176 + 237.596i) q^{61} +(52.6150 - 158.160i) q^{63} +(-26.0929 + 45.1943i) q^{65} +(-96.6361 - 167.379i) q^{67} -2.71005 q^{69} +40.5277 q^{71} +(103.236 + 178.810i) q^{73} +(186.709 - 323.389i) q^{75} +(-792.958 - 893.151i) q^{77} +(-468.870 + 812.107i) q^{79} +(-40.5000 - 70.1481i) q^{81} +911.607 q^{83} +35.5206 q^{85} +(-340.029 - 588.948i) q^{87} +(474.988 - 822.703i) q^{89} +(-1303.46 + 267.546i) q^{91} +(413.693 - 716.537i) q^{93} +(-12.4919 - 21.6367i) q^{95} +39.4687 q^{97} -580.405 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 12q^{3} - 4q^{5} + 18q^{7} - 36q^{9} + O(q^{10})$$ $$8q - 12q^{3} - 4q^{5} + 18q^{7} - 36q^{9} - 14q^{11} + 44q^{13} + 24q^{15} - 96q^{17} + 26q^{19} - 36q^{21} - 96q^{23} - 110q^{25} + 216q^{27} - 152q^{29} - 238q^{31} - 42q^{33} + 152q^{35} - 562q^{37} - 66q^{39} + 856q^{41} - 516q^{43} - 36q^{45} + 80q^{47} + 156q^{49} - 288q^{51} + 2952q^{55} - 156q^{57} - 262q^{59} + 276q^{61} - 54q^{63} - 2196q^{65} - 150q^{67} + 576q^{69} - 1696q^{71} + 218q^{73} - 330q^{75} - 764q^{77} - 1762q^{79} - 324q^{81} + 6900q^{83} + 2904q^{85} + 228q^{87} + 344q^{89} - 2806q^{91} - 714q^{93} - 2004q^{95} - 1244q^{97} + 252q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$$.

 $$n$$ $$73$$ $$85$$ $$113$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.50000 2.59808i −0.288675 0.500000i
$$4$$ 0 0
$$5$$ −0.363171 + 0.629031i −0.0324830 + 0.0562622i −0.881810 0.471605i $$-0.843675\pi$$
0.849327 + 0.527867i $$0.177008\pi$$
$$6$$ 0 0
$$7$$ −18.1420 + 3.72380i −0.979578 + 0.201066i
$$8$$ 0 0
$$9$$ −4.50000 + 7.79423i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 32.2447 + 55.8495i 0.883832 + 1.53084i 0.847046 + 0.531519i $$0.178379\pi$$
0.0367856 + 0.999323i $$0.488288\pi$$
$$12$$ 0 0
$$13$$ 71.8475 1.53284 0.766420 0.642340i $$-0.222036\pi$$
0.766420 + 0.642340i $$0.222036\pi$$
$$14$$ 0 0
$$15$$ 2.17903 0.0375081
$$16$$ 0 0
$$17$$ −24.4517 42.3515i −0.348847 0.604221i 0.637198 0.770700i $$-0.280093\pi$$
−0.986045 + 0.166479i $$0.946760\pi$$
$$18$$ 0 0
$$19$$ −17.1984 + 29.7885i −0.207663 + 0.359682i −0.950978 0.309259i $$-0.899919\pi$$
0.743315 + 0.668941i $$0.233252\pi$$
$$20$$ 0 0
$$21$$ 36.8878 + 41.5487i 0.383313 + 0.431746i
$$22$$ 0 0
$$23$$ 0.451675 0.782324i 0.00409482 0.00709243i −0.863971 0.503542i $$-0.832030\pi$$
0.868066 + 0.496450i $$0.165363\pi$$
$$24$$ 0 0
$$25$$ 62.2362 + 107.796i 0.497890 + 0.862370i
$$26$$ 0 0
$$27$$ 27.0000 0.192450
$$28$$ 0 0
$$29$$ 226.686 1.45154 0.725769 0.687939i $$-0.241484\pi$$
0.725769 + 0.687939i $$0.241484\pi$$
$$30$$ 0 0
$$31$$ 137.898 + 238.846i 0.798940 + 1.38380i 0.920307 + 0.391197i $$0.127939\pi$$
−0.121367 + 0.992608i $$0.538728\pi$$
$$32$$ 0 0
$$33$$ 96.7342 167.549i 0.510281 0.883832i
$$34$$ 0 0
$$35$$ 4.24627 12.7643i 0.0205072 0.0616444i
$$36$$ 0 0
$$37$$ −147.605 + 255.658i −0.655839 + 1.13595i 0.325844 + 0.945423i $$0.394352\pi$$
−0.981683 + 0.190522i $$0.938982\pi$$
$$38$$ 0 0
$$39$$ −107.771 186.665i −0.442493 0.766420i
$$40$$ 0 0
$$41$$ 186.604 0.710798 0.355399 0.934715i $$-0.384345\pi$$
0.355399 + 0.934715i $$0.384345\pi$$
$$42$$ 0 0
$$43$$ −455.317 −1.61477 −0.807386 0.590023i $$-0.799119\pi$$
−0.807386 + 0.590023i $$0.799119\pi$$
$$44$$ 0 0
$$45$$ −3.26854 5.66128i −0.0108277 0.0187541i
$$46$$ 0 0
$$47$$ −141.167 + 244.509i −0.438114 + 0.758835i −0.997544 0.0700420i $$-0.977687\pi$$
0.559430 + 0.828877i $$0.311020\pi$$
$$48$$ 0 0
$$49$$ 315.267 135.115i 0.919145 0.393920i
$$50$$ 0 0
$$51$$ −73.3550 + 127.055i −0.201407 + 0.348847i
$$52$$ 0 0
$$53$$ −178.107 308.491i −0.461602 0.799518i 0.537439 0.843303i $$-0.319392\pi$$
−0.999041 + 0.0437844i $$0.986059\pi$$
$$54$$ 0 0
$$55$$ −46.8414 −0.114838
$$56$$ 0 0
$$57$$ 103.191 0.239788
$$58$$ 0 0
$$59$$ −364.685 631.653i −0.804711 1.39380i −0.916486 0.400066i $$-0.868987\pi$$
0.111776 0.993733i $$-0.464346\pi$$
$$60$$ 0 0
$$61$$ −137.176 + 237.596i −0.287928 + 0.498706i −0.973315 0.229473i $$-0.926300\pi$$
0.685387 + 0.728179i $$0.259633\pi$$
$$62$$ 0 0
$$63$$ 52.6150 158.160i 0.105220 0.316291i
$$64$$ 0 0
$$65$$ −26.0929 + 45.1943i −0.0497912 + 0.0862409i
$$66$$ 0 0
$$67$$ −96.6361 167.379i −0.176209 0.305202i 0.764370 0.644778i $$-0.223050\pi$$
−0.940579 + 0.339575i $$0.889717\pi$$
$$68$$ 0 0
$$69$$ −2.71005 −0.00472829
$$70$$ 0 0
$$71$$ 40.5277 0.0677429 0.0338715 0.999426i $$-0.489216\pi$$
0.0338715 + 0.999426i $$0.489216\pi$$
$$72$$ 0 0
$$73$$ 103.236 + 178.810i 0.165519 + 0.286687i 0.936839 0.349760i $$-0.113737\pi$$
−0.771320 + 0.636447i $$0.780403\pi$$
$$74$$ 0 0
$$75$$ 186.709 323.389i 0.287457 0.497890i
$$76$$ 0 0
$$77$$ −792.958 893.151i −1.17358 1.32187i
$$78$$ 0 0
$$79$$ −468.870 + 812.107i −0.667747 + 1.15657i 0.310785 + 0.950480i $$0.399408\pi$$
−0.978533 + 0.206092i $$0.933925\pi$$
$$80$$ 0 0
$$81$$ −40.5000 70.1481i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 911.607 1.20556 0.602782 0.797906i $$-0.294059\pi$$
0.602782 + 0.797906i $$0.294059\pi$$
$$84$$ 0 0
$$85$$ 35.5206 0.0453264
$$86$$ 0 0
$$87$$ −340.029 588.948i −0.419023 0.725769i
$$88$$ 0 0
$$89$$ 474.988 822.703i 0.565715 0.979846i −0.431268 0.902224i $$-0.641934\pi$$
0.996983 0.0776226i $$-0.0247329\pi$$
$$90$$ 0 0
$$91$$ −1303.46 + 267.546i −1.50154 + 0.308203i
$$92$$ 0 0
$$93$$ 413.693 716.537i 0.461268 0.798940i
$$94$$ 0 0
$$95$$ −12.4919 21.6367i −0.0134910 0.0233671i
$$96$$ 0 0
$$97$$ 39.4687 0.0413138 0.0206569 0.999787i $$-0.493424\pi$$
0.0206569 + 0.999787i $$0.493424\pi$$
$$98$$ 0 0
$$99$$ −580.405 −0.589221
$$100$$ 0 0
$$101$$ 158.437 + 274.421i 0.156090 + 0.270356i 0.933455 0.358694i $$-0.116778\pi$$
−0.777365 + 0.629049i $$0.783444\pi$$
$$102$$ 0 0
$$103$$ 161.317 279.409i 0.154321 0.267291i −0.778491 0.627656i $$-0.784014\pi$$
0.932811 + 0.360365i $$0.117348\pi$$
$$104$$ 0 0
$$105$$ −39.5320 + 8.11426i −0.0367421 + 0.00754163i
$$106$$ 0 0
$$107$$ −340.726 + 590.154i −0.307843 + 0.533200i −0.977890 0.209119i $$-0.932940\pi$$
0.670047 + 0.742318i $$0.266274\pi$$
$$108$$ 0 0
$$109$$ 227.984 + 394.879i 0.200338 + 0.346996i 0.948637 0.316365i $$-0.102463\pi$$
−0.748299 + 0.663361i $$0.769129\pi$$
$$110$$ 0 0
$$111$$ 885.627 0.757297
$$112$$ 0 0
$$113$$ −796.025 −0.662688 −0.331344 0.943510i $$-0.607502\pi$$
−0.331344 + 0.943510i $$0.607502\pi$$
$$114$$ 0 0
$$115$$ 0.328071 + 0.568235i 0.000266024 + 0.000460767i
$$116$$ 0 0
$$117$$ −323.314 + 559.996i −0.255473 + 0.442493i
$$118$$ 0 0
$$119$$ 601.312 + 677.290i 0.463212 + 0.521740i
$$120$$ 0 0
$$121$$ −1413.95 + 2449.03i −1.06232 + 1.83999i
$$122$$ 0 0
$$123$$ −279.907 484.813i −0.205190 0.355399i
$$124$$ 0 0
$$125$$ −181.202 −0.129658
$$126$$ 0 0
$$127$$ 2333.92 1.63072 0.815362 0.578952i $$-0.196538\pi$$
0.815362 + 0.578952i $$0.196538\pi$$
$$128$$ 0 0
$$129$$ 682.976 + 1182.95i 0.466145 + 0.807386i
$$130$$ 0 0
$$131$$ 943.489 1634.17i 0.629259 1.08991i −0.358441 0.933552i $$-0.616692\pi$$
0.987701 0.156357i $$-0.0499750\pi$$
$$132$$ 0 0
$$133$$ 201.088 604.468i 0.131102 0.394091i
$$134$$ 0 0
$$135$$ −9.80562 + 16.9838i −0.00625136 + 0.0108277i
$$136$$ 0 0
$$137$$ −1473.63 2552.40i −0.918983 1.59173i −0.800963 0.598714i $$-0.795678\pi$$
−0.118021 0.993011i $$-0.537655\pi$$
$$138$$ 0 0
$$139$$ 955.433 0.583013 0.291506 0.956569i $$-0.405844\pi$$
0.291506 + 0.956569i $$0.405844\pi$$
$$140$$ 0 0
$$141$$ 847.003 0.505890
$$142$$ 0 0
$$143$$ 2316.70 + 4012.65i 1.35477 + 2.34654i
$$144$$ 0 0
$$145$$ −82.3259 + 142.593i −0.0471503 + 0.0816667i
$$146$$ 0 0
$$147$$ −823.938 616.415i −0.462294 0.345857i
$$148$$ 0 0
$$149$$ −1091.87 + 1891.17i −0.600332 + 1.03981i 0.392439 + 0.919778i $$0.371631\pi$$
−0.992771 + 0.120027i $$0.961702\pi$$
$$150$$ 0 0
$$151$$ −202.360 350.497i −0.109058 0.188894i 0.806331 0.591465i $$-0.201450\pi$$
−0.915389 + 0.402570i $$0.868117\pi$$
$$152$$ 0 0
$$153$$ 440.130 0.232565
$$154$$ 0 0
$$155$$ −200.322 −0.103808
$$156$$ 0 0
$$157$$ 464.791 + 805.042i 0.236270 + 0.409231i 0.959641 0.281228i $$-0.0907418\pi$$
−0.723371 + 0.690459i $$0.757408\pi$$
$$158$$ 0 0
$$159$$ −534.322 + 925.472i −0.266506 + 0.461602i
$$160$$ 0 0
$$161$$ −5.28108 + 15.8749i −0.00258514 + 0.00777092i
$$162$$ 0 0
$$163$$ 712.840 1234.68i 0.342540 0.593296i −0.642364 0.766400i $$-0.722046\pi$$
0.984904 + 0.173104i $$0.0553796\pi$$
$$164$$ 0 0
$$165$$ 70.2621 + 121.698i 0.0331509 + 0.0574190i
$$166$$ 0 0
$$167$$ 4185.15 1.93926 0.969631 0.244572i $$-0.0786474\pi$$
0.969631 + 0.244572i $$0.0786474\pi$$
$$168$$ 0 0
$$169$$ 2965.07 1.34960
$$170$$ 0 0
$$171$$ −154.786 268.097i −0.0692209 0.119894i
$$172$$ 0 0
$$173$$ −1117.78 + 1936.05i −0.491231 + 0.850837i −0.999949 0.0100961i $$-0.996786\pi$$
0.508718 + 0.860933i $$0.330120\pi$$
$$174$$ 0 0
$$175$$ −1530.50 1723.89i −0.661115 0.744650i
$$176$$ 0 0
$$177$$ −1094.05 + 1894.96i −0.464600 + 0.804711i
$$178$$ 0 0
$$179$$ 470.740 + 815.345i 0.196563 + 0.340457i 0.947412 0.320017i $$-0.103689\pi$$
−0.750849 + 0.660474i $$0.770355\pi$$
$$180$$ 0 0
$$181$$ −467.540 −0.192000 −0.0960000 0.995381i $$-0.530605\pi$$
−0.0960000 + 0.995381i $$0.530605\pi$$
$$182$$ 0 0
$$183$$ 823.058 0.332471
$$184$$ 0 0
$$185$$ −107.211 185.696i −0.0426072 0.0737979i
$$186$$ 0 0
$$187$$ 1576.88 2731.23i 0.616645 1.06806i
$$188$$ 0 0
$$189$$ −489.835 + 100.543i −0.188520 + 0.0386953i
$$190$$ 0 0
$$191$$ −137.701 + 238.506i −0.0521660 + 0.0903542i −0.890929 0.454142i $$-0.849946\pi$$
0.838763 + 0.544496i $$0.183279\pi$$
$$192$$ 0 0
$$193$$ −820.148 1420.54i −0.305884 0.529806i 0.671574 0.740937i $$-0.265619\pi$$
−0.977458 + 0.211131i $$0.932285\pi$$
$$194$$ 0 0
$$195$$ 156.558 0.0574940
$$196$$ 0 0
$$197$$ 1303.88 0.471560 0.235780 0.971806i $$-0.424236\pi$$
0.235780 + 0.971806i $$0.424236\pi$$
$$198$$ 0 0
$$199$$ 663.678 + 1149.52i 0.236417 + 0.409485i 0.959683 0.281083i $$-0.0906937\pi$$
−0.723267 + 0.690569i $$0.757360\pi$$
$$200$$ 0 0
$$201$$ −289.908 + 502.136i −0.101734 + 0.176209i
$$202$$ 0 0
$$203$$ −4112.55 + 844.135i −1.42189 + 0.291855i
$$204$$ 0 0
$$205$$ −67.7693 + 117.380i −0.0230889 + 0.0399911i
$$206$$ 0 0
$$207$$ 4.06508 + 7.04092i 0.00136494 + 0.00236414i
$$208$$ 0 0
$$209$$ −2218.23 −0.734155
$$210$$ 0 0
$$211$$ −4753.28 −1.55085 −0.775426 0.631439i $$-0.782465\pi$$
−0.775426 + 0.631439i $$0.782465\pi$$
$$212$$ 0 0
$$213$$ −60.7915 105.294i −0.0195557 0.0338715i
$$214$$ 0 0
$$215$$ 165.358 286.408i 0.0524527 0.0908507i
$$216$$ 0 0
$$217$$ −3391.16 3819.64i −1.06086 1.19490i
$$218$$ 0 0
$$219$$ 309.709 536.431i 0.0955624 0.165519i
$$220$$ 0 0
$$221$$ −1756.79 3042.85i −0.534727 0.926174i
$$222$$ 0 0
$$223$$ 513.149 0.154094 0.0770470 0.997027i $$-0.475451\pi$$
0.0770470 + 0.997027i $$0.475451\pi$$
$$224$$ 0 0
$$225$$ −1120.25 −0.331926
$$226$$ 0 0
$$227$$ −1654.67 2865.97i −0.483808 0.837980i 0.516019 0.856577i $$-0.327413\pi$$
−0.999827 + 0.0185972i $$0.994080\pi$$
$$228$$ 0 0
$$229$$ 2954.73 5117.75i 0.852639 1.47681i −0.0261800 0.999657i $$-0.508334\pi$$
0.878819 0.477156i $$-0.158332\pi$$
$$230$$ 0 0
$$231$$ −1131.04 + 3399.89i −0.322151 + 0.968382i
$$232$$ 0 0
$$233$$ 176.786 306.202i 0.0497065 0.0860943i −0.840102 0.542429i $$-0.817505\pi$$
0.889808 + 0.456335i $$0.150838\pi$$
$$234$$ 0 0
$$235$$ −102.536 177.597i −0.0284625 0.0492985i
$$236$$ 0 0
$$237$$ 2813.22 0.771048
$$238$$ 0 0
$$239$$ −1652.55 −0.447259 −0.223629 0.974674i $$-0.571791\pi$$
−0.223629 + 0.974674i $$0.571791\pi$$
$$240$$ 0 0
$$241$$ 1553.47 + 2690.69i 0.415220 + 0.719182i 0.995452 0.0952696i $$-0.0303713\pi$$
−0.580232 + 0.814451i $$0.697038\pi$$
$$242$$ 0 0
$$243$$ −121.500 + 210.444i −0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ −29.5044 + 247.382i −0.00769374 + 0.0645088i
$$246$$ 0 0
$$247$$ −1235.66 + 2140.23i −0.318313 + 0.551335i
$$248$$ 0 0
$$249$$ −1367.41 2368.42i −0.348016 0.602782i
$$250$$ 0 0
$$251$$ 1771.77 0.445551 0.222776 0.974870i $$-0.428488\pi$$
0.222776 + 0.974870i $$0.428488\pi$$
$$252$$ 0 0
$$253$$ 58.2566 0.0144765
$$254$$ 0 0
$$255$$ −53.2808 92.2851i −0.0130846 0.0226632i
$$256$$ 0 0
$$257$$ −739.063 + 1280.09i −0.179383 + 0.310701i −0.941669 0.336539i $$-0.890743\pi$$
0.762286 + 0.647240i $$0.224077\pi$$
$$258$$ 0 0
$$259$$ 1725.82 5187.81i 0.414044 1.24461i
$$260$$ 0 0
$$261$$ −1020.09 + 1766.84i −0.241923 + 0.419023i
$$262$$ 0 0
$$263$$ 715.987 + 1240.13i 0.167869 + 0.290758i 0.937671 0.347525i $$-0.112978\pi$$
−0.769801 + 0.638284i $$0.779645\pi$$
$$264$$ 0 0
$$265$$ 258.734 0.0599769
$$266$$ 0 0
$$267$$ −2849.93 −0.653231
$$268$$ 0 0
$$269$$ −142.699 247.162i −0.0323439 0.0560213i 0.849400 0.527749i $$-0.176964\pi$$
−0.881744 + 0.471728i $$0.843631\pi$$
$$270$$ 0 0
$$271$$ 2624.66 4546.05i 0.588328 1.01901i −0.406123 0.913818i $$-0.633120\pi$$
0.994452 0.105196i $$-0.0335470\pi$$
$$272$$ 0 0
$$273$$ 2650.29 + 2985.17i 0.587557 + 0.661797i
$$274$$ 0 0
$$275$$ −4013.58 + 6951.72i −0.880102 + 1.52438i
$$276$$ 0 0
$$277$$ −3573.93 6190.24i −0.775224 1.34273i −0.934669 0.355520i $$-0.884304\pi$$
0.159445 0.987207i $$-0.449029\pi$$
$$278$$ 0 0
$$279$$ −2482.16 −0.532627
$$280$$ 0 0
$$281$$ 4228.36 0.897661 0.448831 0.893617i $$-0.351841\pi$$
0.448831 + 0.893617i $$0.351841\pi$$
$$282$$ 0 0
$$283$$ −4171.19 7224.71i −0.876154 1.51754i −0.855528 0.517756i $$-0.826768\pi$$
−0.0206255 0.999787i $$-0.506566\pi$$
$$284$$ 0 0
$$285$$ −37.4758 + 64.9100i −0.00778904 + 0.0134910i
$$286$$ 0 0
$$287$$ −3385.38 + 694.878i −0.696282 + 0.142918i
$$288$$ 0 0
$$289$$ 1260.73 2183.65i 0.256611 0.444464i
$$290$$ 0 0
$$291$$ −59.2030 102.543i −0.0119263 0.0206569i
$$292$$ 0 0
$$293$$ 5038.84 1.00468 0.502342 0.864669i $$-0.332472\pi$$
0.502342 + 0.864669i $$0.332472\pi$$
$$294$$ 0 0
$$295$$ 529.772 0.104558
$$296$$ 0 0
$$297$$ 870.608 + 1507.94i 0.170094 + 0.294611i
$$298$$ 0 0
$$299$$ 32.4517 56.2081i 0.00627670 0.0108716i
$$300$$ 0 0
$$301$$ 8260.38 1695.51i 1.58180 0.324677i
$$302$$ 0 0
$$303$$ 475.311 823.263i 0.0901186 0.156090i
$$304$$ 0 0
$$305$$ −99.6369 172.576i −0.0187055 0.0323990i
$$306$$ 0 0
$$307$$ −4869.67 −0.905300 −0.452650 0.891688i $$-0.649521\pi$$
−0.452650 + 0.891688i $$0.649521\pi$$
$$308$$ 0 0
$$309$$ −967.901 −0.178194
$$310$$ 0 0
$$311$$ 726.421 + 1258.20i 0.132449 + 0.229408i 0.924620 0.380891i $$-0.124383\pi$$
−0.792171 + 0.610299i $$0.791049\pi$$
$$312$$ 0 0
$$313$$ −2848.14 + 4933.12i −0.514333 + 0.890850i 0.485529 + 0.874221i $$0.338627\pi$$
−0.999862 + 0.0166299i $$0.994706\pi$$
$$314$$ 0 0
$$315$$ 80.3794 + 90.5356i 0.0143774 + 0.0161940i
$$316$$ 0 0
$$317$$ 1735.73 3006.38i 0.307535 0.532666i −0.670288 0.742101i $$-0.733829\pi$$
0.977822 + 0.209435i $$0.0671626\pi$$
$$318$$ 0 0
$$319$$ 7309.44 + 12660.3i 1.28291 + 2.22207i
$$320$$ 0 0
$$321$$ 2044.35 0.355466
$$322$$ 0 0
$$323$$ 1682.12 0.289770
$$324$$ 0 0
$$325$$ 4471.52 + 7744.90i 0.763185 + 1.32188i
$$326$$ 0 0
$$327$$ 683.951 1184.64i 0.115665 0.200338i
$$328$$ 0 0
$$329$$ 1650.56 4961.56i 0.276590 0.831428i
$$330$$ 0 0
$$331$$ −3127.19 + 5416.45i −0.519293 + 0.899441i 0.480456 + 0.877019i $$0.340471\pi$$
−0.999749 + 0.0224223i $$0.992862\pi$$
$$332$$ 0 0
$$333$$ −1328.44 2300.93i −0.218613 0.378649i
$$334$$ 0 0
$$335$$ 140.382 0.0228951
$$336$$ 0 0
$$337$$ 8006.96 1.29426 0.647132 0.762378i $$-0.275968\pi$$
0.647132 + 0.762378i $$0.275968\pi$$
$$338$$ 0 0
$$339$$ 1194.04 + 2068.13i 0.191302 + 0.331344i
$$340$$ 0 0
$$341$$ −8892.94 + 15403.0i −1.41226 + 2.44610i
$$342$$ 0 0
$$343$$ −5216.44 + 3625.25i −0.821169 + 0.570685i
$$344$$ 0 0
$$345$$ 0.984212 1.70471i 0.000153589 0.000266024i
$$346$$ 0 0
$$347$$ −3817.80 6612.62i −0.590634 1.02301i −0.994147 0.108034i $$-0.965544\pi$$
0.403513 0.914974i $$-0.367789\pi$$
$$348$$ 0 0
$$349$$ −10358.0 −1.58869 −0.794345 0.607468i $$-0.792185\pi$$
−0.794345 + 0.607468i $$0.792185\pi$$
$$350$$ 0 0
$$351$$ 1939.88 0.294995
$$352$$ 0 0
$$353$$ −1692.12 2930.83i −0.255134 0.441905i 0.709798 0.704405i $$-0.248786\pi$$
−0.964932 + 0.262500i $$0.915453\pi$$
$$354$$ 0 0
$$355$$ −14.7185 + 25.4931i −0.00220049 + 0.00381137i
$$356$$ 0 0
$$357$$ 857.683 2578.19i 0.127152 0.382219i
$$358$$ 0 0
$$359$$ 4097.31 7096.74i 0.602361 1.04332i −0.390102 0.920772i $$-0.627560\pi$$
0.992463 0.122548i $$-0.0391065\pi$$
$$360$$ 0 0
$$361$$ 2837.93 + 4915.44i 0.413752 + 0.716640i
$$362$$ 0 0
$$363$$ 8483.67 1.22666
$$364$$ 0 0
$$365$$ −149.970 −0.0215062
$$366$$ 0 0
$$367$$ −402.755 697.592i −0.0572851 0.0992208i 0.835961 0.548789i $$-0.184911\pi$$
−0.893246 + 0.449569i $$0.851578\pi$$
$$368$$ 0 0
$$369$$ −839.720 + 1454.44i −0.118466 + 0.205190i
$$370$$ 0 0
$$371$$ 4379.99 + 4933.41i 0.612931 + 0.690377i
$$372$$ 0 0
$$373$$ −3952.86 + 6846.55i −0.548716 + 0.950404i 0.449647 + 0.893206i $$0.351550\pi$$
−0.998363 + 0.0571977i $$0.981783\pi$$
$$374$$ 0 0
$$375$$ 271.803 + 470.777i 0.0374290 + 0.0648289i
$$376$$ 0 0
$$377$$ 16286.8 2.22497
$$378$$ 0 0
$$379$$ 3324.24 0.450540 0.225270 0.974296i $$-0.427674\pi$$
0.225270 + 0.974296i $$0.427674\pi$$
$$380$$ 0 0
$$381$$ −3500.88 6063.70i −0.470749 0.815362i
$$382$$ 0 0
$$383$$ 4235.38 7335.90i 0.565060 0.978712i −0.431984 0.901881i $$-0.642186\pi$$
0.997044 0.0768310i $$-0.0244802\pi$$
$$384$$ 0 0
$$385$$ 849.798 174.428i 0.112493 0.0230901i
$$386$$ 0 0
$$387$$ 2048.93 3548.85i 0.269129 0.466145i
$$388$$ 0 0
$$389$$ 3954.20 + 6848.88i 0.515388 + 0.892678i 0.999840 + 0.0178606i $$0.00568551\pi$$
−0.484452 + 0.874818i $$0.660981\pi$$
$$390$$ 0 0
$$391$$ −44.1769 −0.00571386
$$392$$ 0 0
$$393$$ −5660.93 −0.726606
$$394$$ 0 0
$$395$$ −340.560 589.868i −0.0433809 0.0751379i
$$396$$ 0 0
$$397$$ 4890.79 8471.10i 0.618292 1.07091i −0.371506 0.928431i $$-0.621158\pi$$
0.989797 0.142482i $$-0.0455083\pi$$
$$398$$ 0 0
$$399$$ −1872.09 + 384.261i −0.234891 + 0.0482134i
$$400$$ 0 0
$$401$$ 397.827 689.056i 0.0495424 0.0858100i −0.840191 0.542291i $$-0.817557\pi$$
0.889733 + 0.456481i $$0.150890\pi$$
$$402$$ 0 0
$$403$$ 9907.60 + 17160.5i 1.22465 + 2.12115i
$$404$$ 0 0
$$405$$ 58.8337 0.00721844
$$406$$ 0 0
$$407$$ −19037.9 −2.31860
$$408$$ 0 0
$$409$$ −4292.36 7434.59i −0.518933 0.898818i −0.999758 0.0220017i $$-0.992996\pi$$
0.480825 0.876817i $$-0.340337\pi$$
$$410$$ 0 0
$$411$$ −4420.89 + 7657.21i −0.530575 + 0.918983i
$$412$$ 0 0
$$413$$ 8968.27 + 10101.4i 1.06852 + 1.20353i
$$414$$ 0 0
$$415$$ −331.069 + 573.428i −0.0391603 + 0.0678277i
$$416$$ 0 0
$$417$$ −1433.15 2482.29i −0.168301 0.291506i
$$418$$ 0 0
$$419$$ −7447.09 −0.868292 −0.434146 0.900843i $$-0.642950\pi$$
−0.434146 + 0.900843i $$0.642950\pi$$
$$420$$ 0 0
$$421$$ −4446.76 −0.514779 −0.257390 0.966308i $$-0.582862\pi$$
−0.257390 + 0.966308i $$0.582862\pi$$
$$422$$ 0 0
$$423$$ −1270.50 2200.58i −0.146038 0.252945i
$$424$$ 0 0
$$425$$ 3043.56 5271.60i 0.347375 0.601671i
$$426$$ 0 0
$$427$$ 1603.89 4821.30i 0.181775 0.546414i
$$428$$ 0 0
$$429$$ 6950.11 12037.9i 0.782178 1.35477i
$$430$$ 0 0
$$431$$ 4481.85 + 7762.79i 0.500889 + 0.867565i 0.999999 + 0.00102683i $$0.000326850\pi$$
−0.499110 + 0.866538i $$0.666340\pi$$
$$432$$ 0 0
$$433$$ −16173.6 −1.79504 −0.897520 0.440973i $$-0.854633\pi$$
−0.897520 + 0.440973i $$0.854633\pi$$
$$434$$ 0 0
$$435$$ 493.955 0.0544445
$$436$$ 0 0
$$437$$ 15.5362 + 26.9095i 0.00170068 + 0.00294567i
$$438$$ 0 0
$$439$$ 3149.21 5454.60i 0.342378 0.593015i −0.642496 0.766289i $$-0.722101\pi$$
0.984874 + 0.173274i $$0.0554345\pi$$
$$440$$ 0 0
$$441$$ −365.585 + 3065.28i −0.0394757 + 0.330988i
$$442$$ 0 0
$$443$$ 8392.35 14536.0i 0.900074 1.55897i 0.0726770 0.997356i $$-0.476846\pi$$
0.827397 0.561618i $$-0.189821\pi$$
$$444$$ 0 0
$$445$$ 345.004 + 597.564i 0.0367522 + 0.0636567i
$$446$$ 0 0
$$447$$ 6551.22 0.693203
$$448$$ 0 0
$$449$$ 2733.88 0.287349 0.143674 0.989625i $$-0.454108\pi$$
0.143674 + 0.989625i $$0.454108\pi$$
$$450$$ 0 0
$$451$$ 6017.01 + 10421.8i 0.628226 + 1.08812i
$$452$$ 0 0
$$453$$ −607.079 + 1051.49i −0.0629648 + 0.109058i
$$454$$ 0 0
$$455$$ 305.084 917.081i 0.0314342 0.0944910i
$$456$$ 0 0
$$457$$ −4614.60 + 7992.72i −0.472345 + 0.818126i −0.999499 0.0316437i $$-0.989926\pi$$
0.527154 + 0.849770i $$0.323259\pi$$
$$458$$ 0 0
$$459$$ −660.195 1143.49i −0.0671357 0.116282i
$$460$$ 0 0
$$461$$ −19726.7 −1.99298 −0.996491 0.0837048i $$-0.973325\pi$$
−0.996491 + 0.0837048i $$0.973325\pi$$
$$462$$ 0 0
$$463$$ 368.924 0.0370310 0.0185155 0.999829i $$-0.494106\pi$$
0.0185155 + 0.999829i $$0.494106\pi$$
$$464$$ 0 0
$$465$$ 300.482 + 520.451i 0.0299667 + 0.0519039i
$$466$$ 0 0
$$467$$ 6654.78 11526.4i 0.659414 1.14214i −0.321353 0.946959i $$-0.604138\pi$$
0.980768 0.195179i $$-0.0625289\pi$$
$$468$$ 0 0
$$469$$ 2376.46 + 2676.73i 0.233976 + 0.263540i
$$470$$ 0 0
$$471$$ 1394.37 2415.12i 0.136410 0.236270i
$$472$$ 0 0
$$473$$ −14681.6 25429.2i −1.42719 2.47196i
$$474$$ 0 0
$$475$$ −4281.46 −0.413572
$$476$$ 0 0
$$477$$ 3205.93 0.307735
$$478$$ 0 0
$$479$$ −5781.39 10013.7i −0.551479 0.955189i −0.998168 0.0605002i $$-0.980730\pi$$
0.446689 0.894689i $$-0.352603\pi$$
$$480$$ 0 0
$$481$$ −10605.0 + 18368.4i −1.00530 + 1.74122i
$$482$$ 0 0
$$483$$ 49.1658 10.0917i 0.00463172 0.000950700i
$$484$$ 0 0
$$485$$ −14.3339 + 24.8270i −0.00134200 + 0.00232440i
$$486$$ 0 0
$$487$$ −1314.06 2276.02i −0.122271 0.211779i 0.798392 0.602138i $$-0.205684\pi$$
−0.920663 + 0.390359i $$0.872351\pi$$
$$488$$ 0 0
$$489$$ −4277.04 −0.395531
$$490$$ 0 0
$$491$$ −12319.9 −1.13236 −0.566181 0.824281i $$-0.691580\pi$$
−0.566181 + 0.824281i $$0.691580\pi$$
$$492$$ 0 0
$$493$$ −5542.86 9600.51i −0.506365 0.877049i
$$494$$ 0 0
$$495$$ 210.786 365.093i 0.0191397 0.0331509i
$$496$$ 0 0
$$497$$ −735.254 + 150.917i −0.0663595 + 0.0136208i
$$498$$ 0 0
$$499$$ 1652.90 2862.91i 0.148285 0.256837i −0.782309 0.622891i $$-0.785958\pi$$
0.930594 + 0.366054i $$0.119291\pi$$
$$500$$ 0 0
$$501$$ −6277.73 10873.3i −0.559817 0.969631i
$$502$$ 0 0
$$503$$ −3072.72 −0.272377 −0.136189 0.990683i $$-0.543485\pi$$
−0.136189 + 0.990683i $$0.543485\pi$$
$$504$$ 0 0
$$505$$ −230.159 −0.0202811
$$506$$ 0 0
$$507$$ −4447.60 7703.47i −0.389595 0.674799i
$$508$$ 0 0
$$509$$ −6784.91 + 11751.8i −0.590836 + 1.02336i 0.403284 + 0.915075i $$0.367869\pi$$
−0.994120 + 0.108284i $$0.965465\pi$$
$$510$$ 0 0
$$511$$ −2538.77 2859.55i −0.219782 0.247552i
$$512$$ 0 0
$$513$$ −464.357 + 804.291i −0.0399647 + 0.0692209i
$$514$$ 0 0
$$515$$ 117.171 + 202.947i 0.0100256 + 0.0173648i
$$516$$ 0 0
$$517$$ −18207.6 −1.54888
$$518$$ 0 0
$$519$$ 6706.66 0.567225
$$520$$ 0 0
$$521$$ 5366.68 + 9295.36i 0.451283 + 0.781645i 0.998466 0.0553681i $$-0.0176332\pi$$
−0.547183 + 0.837013i $$0.684300\pi$$
$$522$$ 0 0
$$523$$ −4174.07 + 7229.71i −0.348986 + 0.604461i −0.986070 0.166334i $$-0.946807\pi$$
0.637084 + 0.770794i $$0.280140\pi$$
$$524$$ 0 0
$$525$$ −2183.04 + 6562.20i −0.181477 + 0.545520i
$$526$$ 0 0
$$527$$ 6743.65 11680.3i 0.557416 0.965473i
$$528$$ 0 0
$$529$$ 6083.09 + 10536.2i 0.499966 + 0.865967i
$$530$$ 0 0
$$531$$ 6564.33 0.536474
$$532$$ 0 0
$$533$$ 13407.1 1.08954
$$534$$ 0 0
$$535$$ −247.483 428.654i −0.0199993 0.0346399i
$$536$$ 0 0
$$537$$ 1412.22 2446.04i 0.113486 0.196563i
$$538$$ 0 0
$$539$$ 17711.8 + 13250.7i 1.41540 + 1.05891i
$$540$$ 0 0
$$541$$ 11553.6 20011.5i 0.918170 1.59032i 0.115978 0.993252i $$-0.463000\pi$$
0.802192 0.597066i $$-0.203667\pi$$
$$542$$ 0 0
$$543$$ 701.310 + 1214.71i 0.0554256 + 0.0960000i
$$544$$ 0 0
$$545$$ −331.188 −0.0260304
$$546$$ 0 0
$$547$$ 13935.2 1.08926 0.544630 0.838676i $$-0.316670\pi$$
0.544630 + 0.838676i $$0.316670\pi$$
$$548$$ 0 0
$$549$$ −1234.59 2138.37i −0.0959761 0.166235i
$$550$$ 0 0
$$551$$ −3898.65 + 6752.65i −0.301430 + 0.522092i
$$552$$ 0 0
$$553$$ 5482.13 16479.3i 0.421562 1.26721i
$$554$$ 0 0
$$555$$ −321.634 + 557.087i −0.0245993 + 0.0426072i
$$556$$ 0 0
$$557$$ 7523.76 + 13031.5i 0.572337 + 0.991317i 0.996325 + 0.0856492i $$0.0272964\pi$$
−0.423988 + 0.905668i $$0.639370\pi$$
$$558$$ 0 0
$$559$$ −32713.4 −2.47519
$$560$$ 0 0
$$561$$ −9461.25 −0.712040
$$562$$ 0 0
$$563$$ −7721.08 13373.3i −0.577983 1.00110i −0.995710 0.0925239i $$-0.970507\pi$$
0.417727 0.908572i $$-0.362827\pi$$
$$564$$ 0 0
$$565$$ 289.093 500.724i 0.0215261 0.0372843i
$$566$$ 0 0
$$567$$ 995.970 + 1121.81i 0.0737686 + 0.0830895i
$$568$$ 0 0
$$569$$ 6681.06 11571.9i 0.492240 0.852585i −0.507720 0.861522i $$-0.669511\pi$$
0.999960 + 0.00893696i $$0.00284476\pi$$
$$570$$ 0 0
$$571$$ 11092.6 + 19213.0i 0.812981 + 1.40812i 0.910769 + 0.412917i $$0.135490\pi$$
−0.0977876 + 0.995207i $$0.531177\pi$$
$$572$$ 0 0
$$573$$ 826.208 0.0602362
$$574$$ 0 0
$$575$$ 112.442 0.00815507
$$576$$ 0 0
$$577$$ 9475.68 + 16412.4i 0.683671 + 1.18415i 0.973853 + 0.227181i $$0.0729508\pi$$
−0.290182 + 0.956971i $$0.593716\pi$$
$$578$$ 0 0
$$579$$ −2460.44 + 4261.61i −0.176602 + 0.305884i
$$580$$ 0 0
$$581$$ −16538.4 + 3394.64i −1.18094 + 0.242399i
$$582$$ 0 0
$$583$$ 11486.0 19894.4i 0.815957 1.41328i
$$584$$ 0 0
$$585$$ −234.836 406.749i −0.0165971 0.0287470i
$$586$$ 0 0
$$587$$ 19579.5 1.37672 0.688359 0.725371i $$-0.258332\pi$$
0.688359 + 0.725371i $$0.258332\pi$$
$$588$$ 0 0
$$589$$ −9486.48 −0.663640
$$590$$ 0 0
$$591$$ −1955.81 3387.57i −0.136128 0.235780i
$$592$$ 0 0
$$593$$ −2806.51 + 4861.01i −0.194350 + 0.336624i −0.946687 0.322154i $$-0.895593\pi$$
0.752337 + 0.658778i $$0.228926\pi$$
$$594$$ 0 0
$$595$$ −644.415 + 132.272i −0.0444007 + 0.00911362i
$$596$$ 0 0
$$597$$ 1991.03 3448.57i 0.136495 0.236417i
$$598$$ 0 0
$$599$$ −10962.8 18988.0i −0.747790 1.29521i −0.948880 0.315637i $$-0.897782\pi$$
0.201090 0.979573i $$-0.435552\pi$$
$$600$$ 0 0
$$601$$ −2067.51 −0.140326 −0.0701628 0.997536i $$-0.522352\pi$$
−0.0701628 + 0.997536i $$0.522352\pi$$
$$602$$ 0 0
$$603$$ 1739.45 0.117472
$$604$$ 0 0
$$605$$ −1027.01 1778.83i −0.0690146 0.119537i
$$606$$ 0 0
$$607$$ 5083.61 8805.07i 0.339930 0.588775i −0.644490 0.764613i $$-0.722930\pi$$
0.984419 + 0.175838i $$0.0562634\pi$$
$$608$$ 0 0
$$609$$ 8361.95 + 9418.51i 0.556393 + 0.626695i
$$610$$ 0 0
$$611$$ −10142.5 + 17567.3i −0.671558 + 1.16317i
$$612$$ 0 0
$$613$$ 9093.05 + 15749.6i 0.599127 + 1.03772i 0.992950 + 0.118532i $$0.0378188\pi$$
−0.393824 + 0.919186i $$0.628848\pi$$
$$614$$ 0 0
$$615$$ 406.616 0.0266607
$$616$$ 0 0
$$617$$ 6584.41 0.429625 0.214812 0.976655i $$-0.431086\pi$$
0.214812 + 0.976655i $$0.431086\pi$$
$$618$$ 0 0
$$619$$ 3889.86 + 6737.43i 0.252579 + 0.437480i 0.964235 0.265048i $$-0.0853878\pi$$
−0.711656 + 0.702528i $$0.752054\pi$$
$$620$$ 0 0
$$621$$ 12.1952 21.1228i 0.000788048 0.00136494i
$$622$$ 0 0
$$623$$ −5553.66 + 16694.3i −0.357147 + 1.07358i
$$624$$ 0 0
$$625$$ −7713.72 + 13360.6i −0.493678 + 0.855075i
$$626$$ 0 0
$$627$$ 3327.35 + 5763.14i 0.211932 + 0.367078i
$$628$$ 0 0
$$629$$ 14436.7 0.915150
$$630$$ 0 0
$$631$$ 3787.78 0.238969 0.119484 0.992836i $$-0.461876\pi$$
0.119484 + 0.992836i $$0.461876\pi$$
$$632$$ 0 0
$$633$$ 7129.93 + 12349.4i 0.447692 + 0.775426i
$$634$$ 0 0
$$635$$ −847.612 + 1468.11i −0.0529708 + 0.0917481i
$$636$$ 0 0
$$637$$ 22651.1 9707.66i 1.40890 0.603817i
$$638$$ 0 0
$$639$$ −182.374 + 315.882i −0.0112905 + 0.0195557i
$$640$$ 0 0
$$641$$ 9965.44 + 17260.6i 0.614058 + 1.06358i 0.990549 + 0.137159i $$0.0437973\pi$$
−0.376491 + 0.926420i $$0.622869\pi$$
$$642$$ 0 0
$$643$$ 3185.18 0.195352 0.0976759 0.995218i $$-0.468859\pi$$
0.0976759 + 0.995218i $$0.468859\pi$$
$$644$$ 0 0
$$645$$ −992.148 −0.0605671
$$646$$ 0 0
$$647$$ 8471.50 + 14673.1i 0.514759 + 0.891589i 0.999853 + 0.0171270i $$0.00545198\pi$$
−0.485094 + 0.874462i $$0.661215\pi$$
$$648$$ 0 0
$$649$$ 23518.3 40734.9i 1.42246 2.46377i
$$650$$ 0 0
$$651$$ −4836.98 + 14539.9i −0.291208 + 0.875369i
$$652$$ 0 0
$$653$$ 10039.4 17388.7i 0.601640 1.04207i −0.390932 0.920419i $$-0.627847\pi$$
0.992573 0.121652i $$-0.0388193\pi$$
$$654$$ 0 0
$$655$$ 685.295 + 1186.97i 0.0408805 + 0.0708070i
$$656$$ 0 0
$$657$$ −1858.25 −0.110346
$$658$$ 0 0
$$659$$ −9442.46 −0.558158 −0.279079 0.960268i $$-0.590029\pi$$
−0.279079 + 0.960268i $$0.590029\pi$$
$$660$$ 0 0
$$661$$ −380.995 659.902i −0.0224190 0.0388309i 0.854598 0.519290i $$-0.173803\pi$$
−0.877017 + 0.480459i $$0.840470\pi$$
$$662$$ 0 0
$$663$$ −5270.38 + 9128.56i −0.308725 + 0.534727i
$$664$$ 0 0
$$665$$ 307.200 + 346.016i 0.0179138 + 0.0201773i
$$666$$ 0 0
$$667$$ 102.389 177.342i 0.00594378 0.0102949i
$$668$$ 0 0
$$669$$ −769.723 1333.20i −0.0444831 0.0770470i
$$670$$ 0 0
$$671$$ −17692.8 −1.01792
$$672$$ 0 0
$$673$$ −16111.6 −0.922818 −0.461409 0.887188i $$-0.652656\pi$$
−0.461409 + 0.887188i $$0.652656\pi$$
$$674$$ 0 0
$$675$$ 1680.38 + 2910.50i 0.0958189 + 0.165963i
$$676$$ 0 0
$$677$$ −15620.7 + 27055.9i −0.886786 + 1.53596i −0.0431329 + 0.999069i $$0.513734\pi$$
−0.843653 + 0.536889i $$0.819599\pi$$
$$678$$ 0 0
$$679$$ −716.042 + 146.974i −0.0404700 + 0.00830682i
$$680$$ 0 0
$$681$$ −4964.01 + 8597.92i −0.279327 + 0.483808i
$$682$$ 0 0
$$683$$ 15056.8 + 26079.1i 0.843530 + 1.46104i 0.886892 + 0.461978i $$0.152860\pi$$
−0.0433614 + 0.999059i $$0.513807\pi$$
$$684$$ 0 0
$$685$$ 2140.72 0.119405
$$686$$ 0 0
$$687$$ −17728.4 −0.984542
$$688$$ 0 0
$$689$$ −12796.6 22164.3i −0.707562 1.22553i
$$690$$ 0 0
$$691$$ 4875.43 8444.49i 0.268408 0.464896i −0.700043 0.714101i $$-0.746836\pi$$
0.968451 + 0.249204i $$0.0801691\pi$$
$$692$$ 0 0
$$693$$ 10529.7 2161.31i 0.577188 0.118473i
$$694$$ 0 0
$$695$$ −346.986 + 600.997i −0.0189380 + 0.0328016i
$$696$$ 0 0
$$697$$ −4562.79 7902.99i −0.247960 0.429479i
$$698$$ 0 0
$$699$$ −1060.71 −0.0573962
$$700$$ 0 0
$$701$$ 11851.6 0.638559 0.319280 0.947661i $$-0.396559\pi$$
0.319280 + 0.947661i $$0.396559\pi$$
$$702$$ 0 0
$$703$$ −5077.13 8793.85i −0.272386 0.471787i
$$704$$ 0 0
$$705$$ −307.607 + 532.791i −0.0164328 + 0.0284625i
$$706$$ 0 0
$$707$$ −3896.26 4388.57i −0.207262 0.233450i
$$708$$ 0 0
$$709$$ −661.196 + 1145.22i −0.0350236 + 0.0606627i −0.883006 0.469362i $$-0.844484\pi$$
0.847982 + 0.530025i $$0.177817\pi$$
$$710$$ 0 0
$$711$$ −4219.83 7308.96i −0.222582 0.385524i
$$712$$ 0 0
$$713$$ 249.140 0.0130861
$$714$$ 0 0
$$715$$ −3365.44 −0.176028
$$716$$ 0 0
$$717$$ 2478.83 + 4293.46i 0.129112 + 0.223629i
$$718$$ 0 0
$$719$$ −3650.78 + 6323.33i −0.189362 + 0.327984i −0.945038 0.326962i $$-0.893975\pi$$
0.755676 + 0.654946i $$0.227309\pi$$
$$720$$ 0 0
$$721$$ −1886.15 + 5669.76i −0.0974257 + 0.292861i
$$722$$ 0 0
$$723$$ 4660.42 8072.08i 0.239727 0.415220i
$$724$$ 0 0
$$725$$ 14108.1 + 24435.9i 0.722705 + 1.25176i
$$726$$ 0 0
$$727$$ −6088.72 −0.310616 −0.155308 0.987866i $$-0.549637\pi$$
−0.155308 + 0.987866i $$0.549637\pi$$
$$728$$ 0 0
$$729$$ 729.000 0.0370370
$$730$$ 0 0
$$731$$ 11133.3 + 19283.4i 0.563309 + 0.975680i
$$732$$ 0 0
$$733$$ 13289.2 23017.6i 0.669644 1.15986i −0.308360 0.951270i $$-0.599780\pi$$
0.978004 0.208587i $$-0.0668865\pi$$
$$734$$ 0 0
$$735$$ 686.974 294.418i 0.0344754 0.0147752i
$$736$$ 0 0
$$737$$ 6232.01 10794.2i 0.311478 0.539495i
$$738$$ 0 0
$$739$$ −12609.9 21841.0i −0.627689 1.08719i −0.988014 0.154363i $$-0.950668\pi$$
0.360325 0.932827i $$-0.382666\pi$$
$$740$$ 0 0
$$741$$ 7413.98 0.367557
$$742$$ 0 0
$$743$$ 2634.28 0.130071 0.0650353 0.997883i $$-0.479284\pi$$
0.0650353 + 0.997883i $$0.479284\pi$$
$$744$$ 0 0
$$745$$ −793.071 1373.64i −0.0390012 0.0675520i
$$746$$ 0 0
$$747$$ −4102.23 + 7105.27i −0.200927 + 0.348016i
$$748$$ 0 0
$$749$$ 3983.84 11975.4i 0.194347 0.584207i
$$750$$ 0 0
$$751$$ −2883.64 + 4994.62i −0.140114 + 0.242685i −0.927539 0.373725i $$-0.878080\pi$$
0.787425 + 0.616410i $$0.211414\pi$$
$$752$$ 0 0
$$753$$ −2657.66 4603.20i −0.128619 0.222776i
$$754$$ 0 0
$$755$$ 293.965 0.0141702
$$756$$ 0 0
$$757$$ 33378.7 1.60260 0.801302 0.598260i $$-0.204141\pi$$
0.801302 + 0.598260i $$0.204141\pi$$
$$758$$ 0 0
$$759$$ −87.3849 151.355i −0.00417901 0.00723826i
$$760$$ 0 0
$$761$$ −1813.04 + 3140.28i −0.0863637 + 0.149586i −0.905971 0.423339i $$-0.860858\pi$$
0.819608 + 0.572925i $$0.194191\pi$$
$$762$$ 0 0
$$763$$ −5606.54 6314.95i −0.266016 0.299628i
$$764$$ 0 0
$$765$$ −159.843 + 276.855i −0.00755440 + 0.0130846i
$$766$$ 0 0
$$767$$ −26201.7 45382.7i −1.23349 2.13647i
$$768$$ 0 0
$$769$$ 3426.15 0.160663 0.0803316 0.996768i $$-0.474402\pi$$
0.0803316 + 0.996768i $$0.474402\pi$$
$$770$$ 0 0
$$771$$ 4434.38 0.207134
$$772$$ 0 0
$$773$$ −6554.09 11352.0i −0.304960 0.528207i 0.672292 0.740286i $$-0.265310\pi$$
−0.977252 + 0.212079i $$0.931976\pi$$
$$774$$ 0 0
$$775$$ −17164.4 + 29729.7i −0.795568 + 1.37796i
$$776$$ 0 0
$$777$$ −16067.1 + 3297.90i −0.741831 + 0.152267i
$$778$$ 0 0
$$779$$ −3209.30 + 5558.67i −0.147606 + 0.255661i
$$780$$ 0 0
$$781$$ 1306.80 + 2263.45i 0.0598734 + 0.103704i
$$782$$ 0 0
$$783$$ 6120.53 0.279348
$$784$$ 0 0
$$785$$ −675.194 −0.0306990
$$786$$ 0 0
$$787$$ −19659.9 34051.9i −0.890468 1.54234i −0.839315 0.543646i $$-0.817043\pi$$
−0.0511538 0.998691i $$-0.516290\pi$$
$$788$$ 0 0
$$789$$ 2147.96 3720.38i 0.0969195 0.167869i
$$790$$ 0 0
$$791$$ 14441.5 2964.24i 0.649154 0.133244i
$$792$$ 0 0
$$793$$ −9855.77 + 17070.7i −0.441348 + 0.764437i