# Properties

 Label 169.4.c.j.146.2 Level $169$ Weight $4$ Character 169.146 Analytic conductor $9.971$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$169 = 13^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 169.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.97132279097$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{17})$$ Defining polynomial: $$x^{4} - x^{3} + 5x^{2} + 4x + 16$$ x^4 - x^3 + 5*x^2 + 4*x + 16 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 13) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 146.2 Root $$1.28078 + 2.21837i$$ of defining polynomial Character $$\chi$$ $$=$$ 169.146 Dual form 169.4.c.j.22.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.28078 + 2.21837i) q^{2} +(1.84233 + 3.19101i) q^{3} +(0.719224 - 1.24573i) q^{4} -0.561553 q^{5} +(-4.71922 + 8.17394i) q^{6} +(9.08854 - 15.7418i) q^{7} +24.1771 q^{8} +(6.71165 - 11.6249i) q^{9} +O(q^{10})$$ $$q+(1.28078 + 2.21837i) q^{2} +(1.84233 + 3.19101i) q^{3} +(0.719224 - 1.24573i) q^{4} -0.561553 q^{5} +(-4.71922 + 8.17394i) q^{6} +(9.08854 - 15.7418i) q^{7} +24.1771 q^{8} +(6.71165 - 11.6249i) q^{9} +(-0.719224 - 1.24573i) q^{10} +(32.3693 + 56.0653i) q^{11} +5.30019 q^{12} +46.5616 q^{14} +(-1.03457 - 1.79192i) q^{15} +(25.2116 + 43.6679i) q^{16} +(12.7732 - 22.1238i) q^{17} +34.3845 q^{18} +(-53.9848 + 93.5045i) q^{19} +(-0.403882 + 0.699544i) q^{20} +66.9763 q^{21} +(-82.9157 + 143.614i) q^{22} +(-36.6307 - 63.4462i) q^{23} +(44.5421 + 77.1493i) q^{24} -124.685 q^{25} +148.946 q^{27} +(-13.0734 - 22.6438i) q^{28} +(-87.9545 - 152.342i) q^{29} +(2.65009 - 4.59010i) q^{30} +113.093 q^{31} +(32.1274 - 55.6462i) q^{32} +(-119.270 + 206.581i) q^{33} +65.4384 q^{34} +(-5.10370 + 8.83986i) q^{35} +(-9.65435 - 16.7218i) q^{36} +(57.4039 + 99.4264i) q^{37} -276.570 q^{38} -13.5767 q^{40} +(-34.8229 - 60.3151i) q^{41} +(85.7817 + 148.578i) q^{42} +(-219.151 + 379.581i) q^{43} +93.1231 q^{44} +(-3.76894 + 6.52800i) q^{45} +(93.8314 - 162.521i) q^{46} +31.9479 q^{47} +(-92.8963 + 160.901i) q^{48} +(6.29686 + 10.9065i) q^{49} +(-159.693 - 276.597i) q^{50} +94.1298 q^{51} +2.84658 q^{53} +(190.767 + 330.417i) q^{54} +(-18.1771 - 31.4836i) q^{55} +(219.734 - 380.591i) q^{56} -397.831 q^{57} +(225.300 - 390.231i) q^{58} +(35.8163 - 62.0356i) q^{59} -2.97633 q^{60} +(460.348 - 797.345i) q^{61} +(144.847 + 250.882i) q^{62} +(-121.998 - 211.307i) q^{63} +567.978 q^{64} -611.032 q^{66} +(-222.140 - 384.758i) q^{67} +(-18.3736 - 31.8240i) q^{68} +(134.972 - 233.778i) q^{69} -26.1468 q^{70} +(-270.859 + 469.142i) q^{71} +(162.268 - 281.056i) q^{72} -764.004 q^{73} +(-147.043 + 254.686i) q^{74} +(-229.710 - 397.870i) q^{75} +(77.6543 + 134.501i) q^{76} +1176.76 q^{77} -421.538 q^{79} +(-14.1577 - 24.5218i) q^{80} +(93.1932 + 161.415i) q^{81} +(89.2007 - 154.500i) q^{82} -603.797 q^{83} +(48.1710 - 83.4346i) q^{84} +(-7.17283 + 12.4237i) q^{85} -1122.73 q^{86} +(324.082 - 561.327i) q^{87} +(782.596 + 1355.50i) q^{88} +(-579.941 - 1004.49i) q^{89} -19.3087 q^{90} -105.383 q^{92} +(208.354 + 360.880i) q^{93} +(40.9181 + 70.8722i) q^{94} +(30.3153 - 52.5077i) q^{95} +236.757 q^{96} +(291.634 - 505.126i) q^{97} +(-16.1298 + 27.9375i) q^{98} +869.006 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9}+O(q^{10})$$ 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9 $$4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9} - 7 q^{10} + 80 q^{11} - 86 q^{12} + 178 q^{14} - 33 q^{15} + 39 q^{16} - 19 q^{17} + 220 q^{18} - 84 q^{19} + 19 q^{20} + 606 q^{21} - 142 q^{22} - 196 q^{23} + 273 q^{24} - 474 q^{25} + 670 q^{27} + 125 q^{28} + 44 q^{29} - 43 q^{30} + 172 q^{31} - 123 q^{32} - 106 q^{33} + 270 q^{34} - 107 q^{35} + 250 q^{36} + 209 q^{37} - 628 q^{38} - 178 q^{40} - 230 q^{41} - 197 q^{42} - 287 q^{43} + 356 q^{44} - 180 q^{45} - 4 q^{46} - 870 q^{47} - 285 q^{48} - 383 q^{49} - 144 q^{50} + 962 q^{51} - 236 q^{53} + 91 q^{54} + 18 q^{55} + 1015 q^{56} - 1212 q^{57} + 794 q^{58} - 368 q^{59} - 350 q^{60} + 1058 q^{61} + 332 q^{62} - 1560 q^{63} + 1538 q^{64} - 1636 q^{66} + 68 q^{67} + 211 q^{68} - 796 q^{69} + 250 q^{70} - 131 q^{71} + 1350 q^{72} - 912 q^{73} - 147 q^{74} + 516 q^{75} + 22 q^{76} + 1524 q^{77} - 2016 q^{79} - 69 q^{80} - 122 q^{81} - 72 q^{82} - 3916 q^{83} + 1409 q^{84} - 173 q^{85} - 2718 q^{86} + 2558 q^{87} + 1242 q^{88} - 720 q^{89} + 500 q^{90} - 1576 q^{92} + 652 q^{93} + 811 q^{94} + 146 q^{95} + 3726 q^{96} - 928 q^{97} - 650 q^{98} + 260 q^{99}+O(q^{100})$$ 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9 - 7 * q^10 + 80 * q^11 - 86 * q^12 + 178 * q^14 - 33 * q^15 + 39 * q^16 - 19 * q^17 + 220 * q^18 - 84 * q^19 + 19 * q^20 + 606 * q^21 - 142 * q^22 - 196 * q^23 + 273 * q^24 - 474 * q^25 + 670 * q^27 + 125 * q^28 + 44 * q^29 - 43 * q^30 + 172 * q^31 - 123 * q^32 - 106 * q^33 + 270 * q^34 - 107 * q^35 + 250 * q^36 + 209 * q^37 - 628 * q^38 - 178 * q^40 - 230 * q^41 - 197 * q^42 - 287 * q^43 + 356 * q^44 - 180 * q^45 - 4 * q^46 - 870 * q^47 - 285 * q^48 - 383 * q^49 - 144 * q^50 + 962 * q^51 - 236 * q^53 + 91 * q^54 + 18 * q^55 + 1015 * q^56 - 1212 * q^57 + 794 * q^58 - 368 * q^59 - 350 * q^60 + 1058 * q^61 + 332 * q^62 - 1560 * q^63 + 1538 * q^64 - 1636 * q^66 + 68 * q^67 + 211 * q^68 - 796 * q^69 + 250 * q^70 - 131 * q^71 + 1350 * q^72 - 912 * q^73 - 147 * q^74 + 516 * q^75 + 22 * q^76 + 1524 * q^77 - 2016 * q^79 - 69 * q^80 - 122 * q^81 - 72 * q^82 - 3916 * q^83 + 1409 * q^84 - 173 * q^85 - 2718 * q^86 + 2558 * q^87 + 1242 * q^88 - 720 * q^89 + 500 * q^90 - 1576 * q^92 + 652 * q^93 + 811 * q^94 + 146 * q^95 + 3726 * q^96 - 928 * q^97 - 650 * q^98 + 260 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$$.

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.28078 + 2.21837i 0.452823 + 0.784312i 0.998560 0.0536442i $$-0.0170837\pi$$
−0.545737 + 0.837956i $$0.683750\pi$$
$$3$$ 1.84233 + 3.19101i 0.354556 + 0.614110i 0.987042 0.160462i $$-0.0512985\pi$$
−0.632486 + 0.774572i $$0.717965\pi$$
$$4$$ 0.719224 1.24573i 0.0899029 0.155716i
$$5$$ −0.561553 −0.0502268 −0.0251134 0.999685i $$-0.507995\pi$$
−0.0251134 + 0.999685i $$0.507995\pi$$
$$6$$ −4.71922 + 8.17394i −0.321102 + 0.556166i
$$7$$ 9.08854 15.7418i 0.490735 0.849978i −0.509208 0.860643i $$-0.670062\pi$$
0.999943 + 0.0106654i $$0.00339497\pi$$
$$8$$ 24.1771 1.06849
$$9$$ 6.71165 11.6249i 0.248579 0.430552i
$$10$$ −0.719224 1.24573i −0.0227438 0.0393935i
$$11$$ 32.3693 + 56.0653i 0.887247 + 1.53676i 0.843116 + 0.537731i $$0.180718\pi$$
0.0441305 + 0.999026i $$0.485948\pi$$
$$12$$ 5.30019 0.127503
$$13$$ 0 0
$$14$$ 46.5616 0.888864
$$15$$ −1.03457 1.79192i −0.0178082 0.0308448i
$$16$$ 25.2116 + 43.6679i 0.393932 + 0.682310i
$$17$$ 12.7732 22.1238i 0.182233 0.315636i −0.760408 0.649446i $$-0.775001\pi$$
0.942641 + 0.333810i $$0.108334\pi$$
$$18$$ 34.3845 0.450250
$$19$$ −53.9848 + 93.5045i −0.651841 + 1.12902i 0.330835 + 0.943689i $$0.392670\pi$$
−0.982676 + 0.185333i $$0.940664\pi$$
$$20$$ −0.403882 + 0.699544i −0.00451554 + 0.00782114i
$$21$$ 66.9763 0.695973
$$22$$ −82.9157 + 143.614i −0.803531 + 1.39176i
$$23$$ −36.6307 63.4462i −0.332088 0.575193i 0.650833 0.759221i $$-0.274420\pi$$
−0.982921 + 0.184027i $$0.941086\pi$$
$$24$$ 44.5421 + 77.1493i 0.378839 + 0.656168i
$$25$$ −124.685 −0.997477
$$26$$ 0 0
$$27$$ 148.946 1.06165
$$28$$ −13.0734 22.6438i −0.0882371 0.152831i
$$29$$ −87.9545 152.342i −0.563198 0.975488i −0.997215 0.0745830i $$-0.976237\pi$$
0.434017 0.900905i $$-0.357096\pi$$
$$30$$ 2.65009 4.59010i 0.0161280 0.0279344i
$$31$$ 113.093 0.655228 0.327614 0.944812i $$-0.393755\pi$$
0.327614 + 0.944812i $$0.393755\pi$$
$$32$$ 32.1274 55.6462i 0.177480 0.307405i
$$33$$ −119.270 + 206.581i −0.629158 + 1.08973i
$$34$$ 65.4384 0.330077
$$35$$ −5.10370 + 8.83986i −0.0246481 + 0.0426917i
$$36$$ −9.65435 16.7218i −0.0446961 0.0774158i
$$37$$ 57.4039 + 99.4264i 0.255058 + 0.441773i 0.964911 0.262576i $$-0.0845722\pi$$
−0.709853 + 0.704349i $$0.751239\pi$$
$$38$$ −276.570 −1.18067
$$39$$ 0 0
$$40$$ −13.5767 −0.0536666
$$41$$ −34.8229 60.3151i −0.132645 0.229747i 0.792051 0.610455i $$-0.209014\pi$$
−0.924695 + 0.380708i $$0.875680\pi$$
$$42$$ 85.7817 + 148.578i 0.315153 + 0.545860i
$$43$$ −219.151 + 379.581i −0.777214 + 1.34617i 0.156327 + 0.987705i $$0.450035\pi$$
−0.933541 + 0.358469i $$0.883299\pi$$
$$44$$ 93.1231 0.319064
$$45$$ −3.76894 + 6.52800i −0.0124854 + 0.0216253i
$$46$$ 93.8314 162.521i 0.300754 0.520921i
$$47$$ 31.9479 0.0991506 0.0495753 0.998770i $$-0.484213\pi$$
0.0495753 + 0.998770i $$0.484213\pi$$
$$48$$ −92.8963 + 160.901i −0.279342 + 0.483835i
$$49$$ 6.29686 + 10.9065i 0.0183582 + 0.0317973i
$$50$$ −159.693 276.597i −0.451680 0.782334i
$$51$$ 94.1298 0.258447
$$52$$ 0 0
$$53$$ 2.84658 0.00737752 0.00368876 0.999993i $$-0.498826\pi$$
0.00368876 + 0.999993i $$0.498826\pi$$
$$54$$ 190.767 + 330.417i 0.480741 + 0.832669i
$$55$$ −18.1771 31.4836i −0.0445636 0.0771864i
$$56$$ 219.734 380.591i 0.524344 0.908190i
$$57$$ −397.831 −0.924457
$$58$$ 225.300 390.231i 0.510058 0.883446i
$$59$$ 35.8163 62.0356i 0.0790319 0.136887i −0.823801 0.566880i $$-0.808150\pi$$
0.902832 + 0.429992i $$0.141484\pi$$
$$60$$ −2.97633 −0.00640405
$$61$$ 460.348 797.345i 0.966253 1.67360i 0.260044 0.965597i $$-0.416263\pi$$
0.706209 0.708003i $$-0.250404\pi$$
$$62$$ 144.847 + 250.882i 0.296702 + 0.513903i
$$63$$ −121.998 211.307i −0.243973 0.422574i
$$64$$ 567.978 1.10933
$$65$$ 0 0
$$66$$ −611.032 −1.13959
$$67$$ −222.140 384.758i −0.405056 0.701577i 0.589272 0.807935i $$-0.299415\pi$$
−0.994328 + 0.106357i $$0.966081\pi$$
$$68$$ −18.3736 31.8240i −0.0327665 0.0567533i
$$69$$ 134.972 233.778i 0.235488 0.407877i
$$70$$ −26.1468 −0.0446448
$$71$$ −270.859 + 469.142i −0.452748 + 0.784182i −0.998556 0.0537283i $$-0.982890\pi$$
0.545808 + 0.837910i $$0.316223\pi$$
$$72$$ 162.268 281.056i 0.265604 0.460039i
$$73$$ −764.004 −1.22493 −0.612465 0.790498i $$-0.709822\pi$$
−0.612465 + 0.790498i $$0.709822\pi$$
$$74$$ −147.043 + 254.686i −0.230992 + 0.400090i
$$75$$ −229.710 397.870i −0.353662 0.612561i
$$76$$ 77.6543 + 134.501i 0.117205 + 0.203005i
$$77$$ 1176.76 1.74161
$$78$$ 0 0
$$79$$ −421.538 −0.600338 −0.300169 0.953886i $$-0.597043\pi$$
−0.300169 + 0.953886i $$0.597043\pi$$
$$80$$ −14.1577 24.5218i −0.0197859 0.0342703i
$$81$$ 93.1932 + 161.415i 0.127837 + 0.221420i
$$82$$ 89.2007 154.500i 0.120129 0.208069i
$$83$$ −603.797 −0.798498 −0.399249 0.916842i $$-0.630729\pi$$
−0.399249 + 0.916842i $$0.630729\pi$$
$$84$$ 48.1710 83.4346i 0.0625700 0.108374i
$$85$$ −7.17283 + 12.4237i −0.00915297 + 0.0158534i
$$86$$ −1122.73 −1.40776
$$87$$ 324.082 561.327i 0.399371 0.691731i
$$88$$ 782.596 + 1355.50i 0.948011 + 1.64200i
$$89$$ −579.941 1004.49i −0.690715 1.19635i −0.971604 0.236613i $$-0.923963\pi$$
0.280889 0.959740i $$-0.409371\pi$$
$$90$$ −19.3087 −0.0226146
$$91$$ 0 0
$$92$$ −105.383 −0.119423
$$93$$ 208.354 + 360.880i 0.232315 + 0.402382i
$$94$$ 40.9181 + 70.8722i 0.0448977 + 0.0777650i
$$95$$ 30.3153 52.5077i 0.0327399 0.0567071i
$$96$$ 236.757 0.251707
$$97$$ 291.634 505.126i 0.305268 0.528740i −0.672053 0.740503i $$-0.734587\pi$$
0.977321 + 0.211763i $$0.0679206\pi$$
$$98$$ −16.1298 + 27.9375i −0.0166260 + 0.0287971i
$$99$$ 869.006 0.882206
$$100$$ −89.6761 + 155.324i −0.0896761 + 0.155324i
$$101$$ −460.870 798.251i −0.454043 0.786425i 0.544590 0.838702i $$-0.316685\pi$$
−0.998633 + 0.0522775i $$0.983352\pi$$
$$102$$ 120.559 + 208.815i 0.117031 + 0.202703i
$$103$$ −930.712 −0.890347 −0.445174 0.895444i $$-0.646858\pi$$
−0.445174 + 0.895444i $$0.646858\pi$$
$$104$$ 0 0
$$105$$ −37.6107 −0.0349565
$$106$$ 3.64584 + 6.31478i 0.00334071 + 0.00578628i
$$107$$ −428.691 742.515i −0.387319 0.670857i 0.604769 0.796401i $$-0.293266\pi$$
−0.992088 + 0.125545i $$0.959932\pi$$
$$108$$ 107.125 185.547i 0.0954459 0.165317i
$$109$$ −671.853 −0.590384 −0.295192 0.955438i $$-0.595384\pi$$
−0.295192 + 0.955438i $$0.595384\pi$$
$$110$$ 46.5616 80.6470i 0.0403588 0.0699035i
$$111$$ −211.514 + 366.352i −0.180865 + 0.313267i
$$112$$ 916.548 0.773265
$$113$$ −320.737 + 555.532i −0.267012 + 0.462479i −0.968089 0.250607i $$-0.919370\pi$$
0.701077 + 0.713086i $$0.252703\pi$$
$$114$$ −509.533 882.537i −0.418615 0.725063i
$$115$$ 20.5701 + 35.6284i 0.0166797 + 0.0288901i
$$116$$ −253.036 −0.202533
$$117$$ 0 0
$$118$$ 183.491 0.143150
$$119$$ −232.179 402.147i −0.178856 0.309788i
$$120$$ −25.0128 43.3234i −0.0190279 0.0329572i
$$121$$ −1430.05 + 2476.91i −1.07441 + 1.86094i
$$122$$ 2358.41 1.75017
$$123$$ 128.311 222.240i 0.0940599 0.162917i
$$124$$ 81.3390 140.883i 0.0589069 0.102030i
$$125$$ 140.211 0.100327
$$126$$ 312.505 541.274i 0.220953 0.382703i
$$127$$ 276.587 + 479.063i 0.193253 + 0.334724i 0.946326 0.323212i $$-0.104763\pi$$
−0.753073 + 0.657937i $$0.771430\pi$$
$$128$$ 470.434 + 814.816i 0.324851 + 0.562658i
$$129$$ −1614.99 −1.10227
$$130$$ 0 0
$$131$$ 2056.40 1.37152 0.685758 0.727830i $$-0.259471\pi$$
0.685758 + 0.727830i $$0.259471\pi$$
$$132$$ 171.563 + 297.157i 0.113126 + 0.195941i
$$133$$ 981.287 + 1699.64i 0.639762 + 1.10810i
$$134$$ 569.024 985.578i 0.366837 0.635380i
$$135$$ −83.6411 −0.0533235
$$136$$ 308.819 534.890i 0.194713 0.337253i
$$137$$ −904.283 + 1566.26i −0.563928 + 0.976752i 0.433221 + 0.901288i $$0.357377\pi$$
−0.997149 + 0.0754639i $$0.975956\pi$$
$$138$$ 691.474 0.426537
$$139$$ −746.818 + 1293.53i −0.455714 + 0.789320i −0.998729 0.0504032i $$-0.983949\pi$$
0.543015 + 0.839723i $$0.317283\pi$$
$$140$$ 7.34140 + 12.7157i 0.00443187 + 0.00767622i
$$141$$ 58.8585 + 101.946i 0.0351545 + 0.0608894i
$$142$$ −1387.64 −0.820058
$$143$$ 0 0
$$144$$ 676.847 0.391694
$$145$$ 49.3911 + 85.5479i 0.0282876 + 0.0489956i
$$146$$ −978.518 1694.84i −0.554676 0.960727i
$$147$$ −23.2018 + 40.1867i −0.0130180 + 0.0225479i
$$148$$ 165.145 0.0917218
$$149$$ −1379.51 + 2389.38i −0.758482 + 1.31373i 0.185143 + 0.982712i $$0.440725\pi$$
−0.943625 + 0.331018i $$0.892608\pi$$
$$150$$ 588.415 1019.16i 0.320292 0.554763i
$$151$$ 976.355 0.526190 0.263095 0.964770i $$-0.415257\pi$$
0.263095 + 0.964770i $$0.415257\pi$$
$$152$$ −1305.20 + 2260.67i −0.696483 + 1.20634i
$$153$$ −171.458 296.975i −0.0905986 0.156921i
$$154$$ 1507.17 + 2610.49i 0.788642 + 1.36597i
$$155$$ −63.5076 −0.0329100
$$156$$ 0 0
$$157$$ −564.875 −0.287146 −0.143573 0.989640i $$-0.545859\pi$$
−0.143573 + 0.989640i $$0.545859\pi$$
$$158$$ −539.896 935.127i −0.271847 0.470853i
$$159$$ 5.24435 + 9.08347i 0.00261575 + 0.00453061i
$$160$$ −18.0412 + 31.2483i −0.00891427 + 0.0154400i
$$161$$ −1331.68 −0.651869
$$162$$ −238.719 + 413.474i −0.115775 + 0.200528i
$$163$$ 754.266 1306.43i 0.362446 0.627775i −0.625917 0.779890i $$-0.715275\pi$$
0.988363 + 0.152115i $$0.0486084\pi$$
$$164$$ −100.182 −0.0477005
$$165$$ 66.9763 116.006i 0.0316006 0.0547339i
$$166$$ −773.329 1339.45i −0.361578 0.626272i
$$167$$ 296.260 + 513.138i 0.137277 + 0.237771i 0.926465 0.376381i $$-0.122832\pi$$
−0.789188 + 0.614152i $$0.789498\pi$$
$$168$$ 1619.29 0.743638
$$169$$ 0 0
$$170$$ −36.7471 −0.0165787
$$171$$ 724.654 + 1255.14i 0.324068 + 0.561303i
$$172$$ 315.237 + 546.007i 0.139748 + 0.242050i
$$173$$ 2247.78 3893.28i 0.987838 1.71099i 0.359262 0.933237i $$-0.383028\pi$$
0.628576 0.777748i $$-0.283638\pi$$
$$174$$ 1660.31 0.723377
$$175$$ −1133.20 + 1962.76i −0.489497 + 0.847834i
$$176$$ −1632.17 + 2827.00i −0.699030 + 1.21076i
$$177$$ 263.941 0.112085
$$178$$ 1485.55 2573.05i 0.625543 1.08347i
$$179$$ 77.1425 + 133.615i 0.0322117 + 0.0557924i 0.881682 0.471844i $$-0.156412\pi$$
−0.849470 + 0.527637i $$0.823078\pi$$
$$180$$ 5.42143 + 9.39019i 0.00224494 + 0.00388835i
$$181$$ 1071.35 0.439959 0.219979 0.975505i $$-0.429401\pi$$
0.219979 + 0.975505i $$0.429401\pi$$
$$182$$ 0 0
$$183$$ 3392.45 1.37037
$$184$$ −885.623 1533.94i −0.354831 0.614586i
$$185$$ −32.2353 55.8332i −0.0128107 0.0221889i
$$186$$ −533.710 + 924.413i −0.210395 + 0.364415i
$$187$$ 1653.84 0.646742
$$188$$ 22.9777 39.7985i 0.00891393 0.0154394i
$$189$$ 1353.70 2344.68i 0.520991 0.902383i
$$190$$ 155.309 0.0593015
$$191$$ −338.601 + 586.475i −0.128274 + 0.222177i −0.923008 0.384781i $$-0.874277\pi$$
0.794734 + 0.606958i $$0.207610\pi$$
$$192$$ 1046.40 + 1812.42i 0.393321 + 0.681252i
$$193$$ 660.840 + 1144.61i 0.246468 + 0.426895i 0.962543 0.271128i $$-0.0873967\pi$$
−0.716075 + 0.698023i $$0.754063\pi$$
$$194$$ 1494.07 0.552929
$$195$$ 0 0
$$196$$ 18.1154 0.00660183
$$197$$ 633.683 + 1097.57i 0.229178 + 0.396948i 0.957565 0.288218i $$-0.0930629\pi$$
−0.728387 + 0.685166i $$0.759730\pi$$
$$198$$ 1113.00 + 1927.78i 0.399483 + 0.691925i
$$199$$ −1198.12 + 2075.21i −0.426796 + 0.739233i −0.996586 0.0825573i $$-0.973691\pi$$
0.569790 + 0.821790i $$0.307025\pi$$
$$200$$ −3014.51 −1.06579
$$201$$ 818.510 1417.70i 0.287230 0.497497i
$$202$$ 1180.54 2044.76i 0.411202 0.712222i
$$203$$ −3197.51 −1.10552
$$204$$ 67.7003 117.260i 0.0232352 0.0402445i
$$205$$ 19.5549 + 33.8701i 0.00666231 + 0.0115395i
$$206$$ −1192.03 2064.66i −0.403170 0.698310i
$$207$$ −983.409 −0.330201
$$208$$ 0 0
$$209$$ −6989.81 −2.31337
$$210$$ −48.1710 83.4346i −0.0158291 0.0274168i
$$211$$ 45.7769 + 79.2880i 0.0149356 + 0.0258692i 0.873397 0.487010i $$-0.161912\pi$$
−0.858461 + 0.512879i $$0.828579\pi$$
$$212$$ 2.04733 3.54608i 0.000663261 0.00114880i
$$213$$ −1996.05 −0.642099
$$214$$ 1098.12 1901.99i 0.350774 0.607558i
$$215$$ 123.065 213.155i 0.0390370 0.0676141i
$$216$$ 3601.08 1.13436
$$217$$ 1027.85 1780.29i 0.321543 0.556929i
$$218$$ −860.494 1490.42i −0.267339 0.463045i
$$219$$ −1407.55 2437.94i −0.434307 0.752241i
$$220$$ −52.2935 −0.0160256
$$221$$ 0 0
$$222$$ −1083.61 −0.327599
$$223$$ 617.709 + 1069.90i 0.185493 + 0.321282i 0.943742 0.330682i $$-0.107279\pi$$
−0.758250 + 0.651964i $$0.773945\pi$$
$$224$$ −583.982 1011.49i −0.174192 0.301709i
$$225$$ −836.839 + 1449.45i −0.247952 + 0.429466i
$$226$$ −1643.17 −0.483637
$$227$$ 1650.83 2859.32i 0.482685 0.836035i −0.517118 0.855914i $$-0.672995\pi$$
0.999802 + 0.0198797i $$0.00632833\pi$$
$$228$$ −286.130 + 495.591i −0.0831114 + 0.143953i
$$229$$ −211.283 −0.0609694 −0.0304847 0.999535i $$-0.509705\pi$$
−0.0304847 + 0.999535i $$0.509705\pi$$
$$230$$ −52.6913 + 91.2640i −0.0151059 + 0.0261642i
$$231$$ 2167.98 + 3755.05i 0.617500 + 1.06954i
$$232$$ −2126.48 3683.18i −0.601769 1.04230i
$$233$$ −256.724 −0.0721827 −0.0360913 0.999348i $$-0.511491\pi$$
−0.0360913 + 0.999348i $$0.511491\pi$$
$$234$$ 0 0
$$235$$ −17.9404 −0.00498002
$$236$$ −51.5198 89.2349i −0.0142104 0.0246131i
$$237$$ −776.612 1345.13i −0.212854 0.368674i
$$238$$ 594.740 1030.12i 0.161980 0.280558i
$$239$$ 3549.62 0.960694 0.480347 0.877078i $$-0.340511\pi$$
0.480347 + 0.877078i $$0.340511\pi$$
$$240$$ 52.1662 90.3545i 0.0140305 0.0243015i
$$241$$ −2515.05 + 4356.19i −0.672235 + 1.16434i 0.305034 + 0.952341i $$0.401332\pi$$
−0.977269 + 0.212003i $$0.932001\pi$$
$$242$$ −7326.27 −1.94608
$$243$$ 1667.39 2888.00i 0.440176 0.762408i
$$244$$ −662.186 1146.94i −0.173738 0.300923i
$$245$$ −3.53602 6.12457i −0.000922074 0.00159708i
$$246$$ 657.349 0.170370
$$247$$ 0 0
$$248$$ 2734.25 0.700102
$$249$$ −1112.39 1926.72i −0.283113 0.490366i
$$250$$ 179.579 + 311.040i 0.0454303 + 0.0786876i
$$251$$ 359.392 622.485i 0.0903770 0.156538i −0.817293 0.576223i $$-0.804526\pi$$
0.907670 + 0.419685i $$0.137859\pi$$
$$252$$ −350.976 −0.0877357
$$253$$ 2371.42 4107.42i 0.589288 1.02068i
$$254$$ −708.492 + 1227.14i −0.175019 + 0.303141i
$$255$$ −52.8588 −0.0129810
$$256$$ 1066.87 1847.87i 0.260466 0.451141i
$$257$$ −640.397 1109.20i −0.155435 0.269222i 0.777782 0.628534i $$-0.216345\pi$$
−0.933217 + 0.359312i $$0.883011\pi$$
$$258$$ −2068.45 3582.65i −0.499131 0.864520i
$$259$$ 2086.87 0.500663
$$260$$ 0 0
$$261$$ −2361.28 −0.559998
$$262$$ 2633.79 + 4561.86i 0.621054 + 1.07570i
$$263$$ −2612.77 4525.46i −0.612587 1.06103i −0.990803 0.135315i $$-0.956795\pi$$
0.378215 0.925718i $$-0.376538\pi$$
$$264$$ −2883.60 + 4994.54i −0.672247 + 1.16437i
$$265$$ −1.59851 −0.000370549
$$266$$ −2513.62 + 4353.71i −0.579398 + 1.00355i
$$267$$ 2136.89 3701.19i 0.489795 0.848350i
$$268$$ −639.074 −0.145663
$$269$$ −3221.90 + 5580.50i −0.730270 + 1.26487i 0.226497 + 0.974012i $$0.427273\pi$$
−0.956768 + 0.290854i $$0.906061\pi$$
$$270$$ −107.125 185.547i −0.0241461 0.0418223i
$$271$$ −1964.97 3403.42i −0.440455 0.762890i 0.557269 0.830332i $$-0.311849\pi$$
−0.997723 + 0.0674426i $$0.978516\pi$$
$$272$$ 1288.13 0.287149
$$273$$ 0 0
$$274$$ −4632.74 −1.02144
$$275$$ −4035.96 6990.48i −0.885009 1.53288i
$$276$$ −194.149 336.277i −0.0423421 0.0733387i
$$277$$ 2942.20 5096.04i 0.638194 1.10538i −0.347635 0.937630i $$-0.613015\pi$$
0.985829 0.167754i $$-0.0536516\pi$$
$$278$$ −3826.03 −0.825431
$$279$$ 759.039 1314.69i 0.162876 0.282110i
$$280$$ −123.392 + 213.722i −0.0263361 + 0.0456155i
$$281$$ −3529.79 −0.749358 −0.374679 0.927155i $$-0.622247\pi$$
−0.374679 + 0.927155i $$0.622247\pi$$
$$282$$ −150.769 + 261.140i −0.0318375 + 0.0551442i
$$283$$ 1305.50 + 2261.19i 0.274219 + 0.474961i 0.969938 0.243353i $$-0.0782474\pi$$
−0.695719 + 0.718314i $$0.744914\pi$$
$$284$$ 389.617 + 674.836i 0.0814067 + 0.141001i
$$285$$ 223.403 0.0464325
$$286$$ 0 0
$$287$$ −1265.96 −0.260373
$$288$$ −431.255 746.955i −0.0882359 0.152829i
$$289$$ 2130.19 + 3689.60i 0.433582 + 0.750987i
$$290$$ −126.518 + 219.136i −0.0256186 + 0.0443727i
$$291$$ 2149.15 0.432939
$$292$$ −549.490 + 951.744i −0.110125 + 0.190742i
$$293$$ −2745.51 + 4755.37i −0.547422 + 0.948163i 0.451028 + 0.892510i $$0.351057\pi$$
−0.998450 + 0.0556531i $$0.982276\pi$$
$$294$$ −118.865 −0.0235795
$$295$$ −20.1127 + 34.8363i −0.00396952 + 0.00687541i
$$296$$ 1387.86 + 2403.84i 0.272526 + 0.472028i
$$297$$ 4821.28 + 8350.70i 0.941950 + 1.63150i
$$298$$ −7067.37 −1.37383
$$299$$ 0 0
$$300$$ −660.852 −0.127181
$$301$$ 3983.53 + 6899.67i 0.762813 + 1.32123i
$$302$$ 1250.49 + 2165.92i 0.238271 + 0.412697i
$$303$$ 1698.15 2941.28i 0.321967 0.557664i
$$304$$ −5444.19 −1.02712
$$305$$ −258.509 + 447.751i −0.0485318 + 0.0840596i
$$306$$ 439.200 760.716i 0.0820502 0.142115i
$$307$$ 7307.59 1.35852 0.679261 0.733897i $$-0.262300\pi$$
0.679261 + 0.733897i $$0.262300\pi$$
$$308$$ 846.353 1465.93i 0.156576 0.271198i
$$309$$ −1714.68 2969.91i −0.315678 0.546771i
$$310$$ −81.3390 140.883i −0.0149024 0.0258117i
$$311$$ 7904.92 1.44131 0.720654 0.693295i $$-0.243842\pi$$
0.720654 + 0.693295i $$0.243842\pi$$
$$312$$ 0 0
$$313$$ 10002.4 1.80629 0.903145 0.429336i $$-0.141252\pi$$
0.903145 + 0.429336i $$0.141252\pi$$
$$314$$ −723.478 1253.10i −0.130026 0.225212i
$$315$$ 68.5084 + 118.660i 0.0122540 + 0.0212246i
$$316$$ −303.180 + 525.123i −0.0539722 + 0.0934825i
$$317$$ 6230.81 1.10397 0.551983 0.833856i $$-0.313871\pi$$
0.551983 + 0.833856i $$0.313871\pi$$
$$318$$ −13.4337 + 23.2678i −0.00236894 + 0.00410312i
$$319$$ 5694.06 9862.40i 0.999392 1.73100i
$$320$$ −318.950 −0.0557182
$$321$$ 1579.58 2735.91i 0.274653 0.475713i
$$322$$ −1705.58 2954.15i −0.295181 0.511269i
$$323$$ 1379.12 + 2388.70i 0.237573 + 0.411489i
$$324$$ 268.107 0.0459717
$$325$$ 0 0
$$326$$ 3864.19 0.656495
$$327$$ −1237.77 2143.89i −0.209324 0.362561i
$$328$$ −841.917 1458.24i −0.141729 0.245482i
$$329$$ 290.360 502.918i 0.0486567 0.0842758i
$$330$$ 343.127 0.0572379
$$331$$ −2317.25 + 4013.60i −0.384797 + 0.666488i −0.991741 0.128257i $$-0.959062\pi$$
0.606944 + 0.794745i $$0.292395\pi$$
$$332$$ −434.265 + 752.170i −0.0717874 + 0.124339i
$$333$$ 1541.10 0.253609
$$334$$ −758.886 + 1314.43i −0.124325 + 0.215337i
$$335$$ 124.743 + 216.062i 0.0203447 + 0.0352380i
$$336$$ 1688.58 + 2924.71i 0.274166 + 0.474870i
$$337$$ 3029.82 0.489747 0.244874 0.969555i $$-0.421254\pi$$
0.244874 + 0.969555i $$0.421254\pi$$
$$338$$ 0 0
$$339$$ −2363.61 −0.378684
$$340$$ 10.3177 + 17.8708i 0.00164576 + 0.00285054i
$$341$$ 3660.74 + 6340.58i 0.581349 + 1.00693i
$$342$$ −1856.24 + 3215.10i −0.293491 + 0.508342i
$$343$$ 6463.66 1.01751
$$344$$ −5298.43 + 9177.15i −0.830443 + 1.43837i
$$345$$ −75.7937 + 131.278i −0.0118278 + 0.0204864i
$$346$$ 11515.6 1.78926
$$347$$ −1420.80 + 2460.90i −0.219805 + 0.380714i −0.954748 0.297415i $$-0.903876\pi$$
0.734943 + 0.678129i $$0.237209\pi$$
$$348$$ −466.175 807.440i −0.0718093 0.124377i
$$349$$ 3782.84 + 6552.07i 0.580202 + 1.00494i 0.995455 + 0.0952339i $$0.0303599\pi$$
−0.415252 + 0.909706i $$0.636307\pi$$
$$350$$ −5805.51 −0.886622
$$351$$ 0 0
$$352$$ 4159.76 0.629875
$$353$$ −1169.72 2026.01i −0.176368 0.305478i 0.764266 0.644901i $$-0.223101\pi$$
−0.940634 + 0.339423i $$0.889768\pi$$
$$354$$ 338.050 + 585.520i 0.0507547 + 0.0879097i
$$355$$ 152.102 263.448i 0.0227401 0.0393870i
$$356$$ −1668.43 −0.248389
$$357$$ 855.502 1481.77i 0.126829 0.219674i
$$358$$ −197.605 + 342.261i −0.0291724 + 0.0505281i
$$359$$ 2531.68 0.372192 0.186096 0.982532i $$-0.440417\pi$$
0.186096 + 0.982532i $$0.440417\pi$$
$$360$$ −91.1221 + 157.828i −0.0133404 + 0.0231063i
$$361$$ −2399.23 4155.58i −0.349793 0.605858i
$$362$$ 1372.16 + 2376.64i 0.199223 + 0.345065i
$$363$$ −10538.5 −1.52376
$$364$$ 0 0
$$365$$ 429.028 0.0615243
$$366$$ 4344.97 + 7525.70i 0.620533 + 1.07479i
$$367$$ −3288.91 5696.55i −0.467792 0.810239i 0.531531 0.847039i $$-0.321617\pi$$
−0.999323 + 0.0368000i $$0.988284\pi$$
$$368$$ 1847.04 3199.17i 0.261640 0.453174i
$$369$$ −934.876 −0.131891
$$370$$ 82.5725 143.020i 0.0116020 0.0200952i
$$371$$ 25.8713 44.8104i 0.00362041 0.00627073i
$$372$$ 599.413 0.0835433
$$373$$ −1451.36 + 2513.83i −0.201471 + 0.348958i −0.949003 0.315268i $$-0.897905\pi$$
0.747532 + 0.664226i $$0.231239\pi$$
$$374$$ 2118.20 + 3668.83i 0.292859 + 0.507247i
$$375$$ 258.315 + 447.415i 0.0355716 + 0.0616117i
$$376$$ 772.407 0.105941
$$377$$ 0 0
$$378$$ 6935.16 0.943667
$$379$$ −932.867 1615.77i −0.126433 0.218989i 0.795859 0.605482i $$-0.207020\pi$$
−0.922292 + 0.386493i $$0.873686\pi$$
$$380$$ −43.6070 75.5296i −0.00588682 0.0101963i
$$381$$ −1019.13 + 1765.18i −0.137038 + 0.237357i
$$382$$ −1734.69 −0.232342
$$383$$ 5417.99 9384.24i 0.722837 1.25199i −0.237021 0.971504i $$-0.576171\pi$$
0.959858 0.280486i $$-0.0904955\pi$$
$$384$$ −1733.39 + 3002.32i −0.230356 + 0.398988i
$$385$$ −660.813 −0.0874757
$$386$$ −1692.78 + 2931.97i −0.223213 + 0.386616i
$$387$$ 2941.73 + 5095.22i 0.386399 + 0.669263i
$$388$$ −419.501 726.597i −0.0548890 0.0950705i
$$389$$ −9520.34 −1.24088 −0.620438 0.784256i $$-0.713045\pi$$
−0.620438 + 0.784256i $$0.713045\pi$$
$$390$$ 0 0
$$391$$ −1871.56 −0.242069
$$392$$ 152.240 + 263.687i 0.0196155 + 0.0339750i
$$393$$ 3788.57 + 6561.99i 0.486280 + 0.842261i
$$394$$ −1623.21 + 2811.49i −0.207554 + 0.359494i
$$395$$ 236.716 0.0301531
$$396$$ 625.009 1082.55i 0.0793129 0.137374i
$$397$$ −5054.42 + 8754.51i −0.638978 + 1.10674i 0.346680 + 0.937983i $$0.387309\pi$$
−0.985657 + 0.168758i $$0.946024\pi$$
$$398$$ −6138.10 −0.773053
$$399$$ −3615.71 + 6262.59i −0.453664 + 0.785768i
$$400$$ −3143.51 5444.71i −0.392938 0.680589i
$$401$$ 1042.19 + 1805.12i 0.129787 + 0.224797i 0.923594 0.383373i $$-0.125237\pi$$
−0.793807 + 0.608169i $$0.791904\pi$$
$$402$$ 4193.32 0.520258
$$403$$ 0 0
$$404$$ −1325.88 −0.163279
$$405$$ −52.3329 90.6432i −0.00642084 0.0111212i
$$406$$ −4095.30 7093.27i −0.500607 0.867076i
$$407$$ −3716.25 + 6436.73i −0.452599 + 0.783924i
$$408$$ 2275.78 0.276147
$$409$$ −4858.26 + 8414.76i −0.587349 + 1.01732i 0.407229 + 0.913326i $$0.366495\pi$$
−0.994578 + 0.103992i $$0.966838\pi$$
$$410$$ −50.0909 + 86.7600i −0.00603369 + 0.0104507i
$$411$$ −6663.95 −0.799777
$$412$$ −669.390 + 1159.42i −0.0800449 + 0.138642i
$$413$$ −651.035 1127.63i −0.0775674 0.134351i
$$414$$ −1259.53 2181.56i −0.149523 0.258981i
$$415$$ 339.064 0.0401060
$$416$$ 0 0
$$417$$ −5503.54 −0.646305
$$418$$ −8952.38 15506.0i −1.04755 1.81441i
$$419$$ −6690.94 11589.1i −0.780129 1.35122i −0.931866 0.362802i $$-0.881820\pi$$
0.151737 0.988421i $$-0.451513\pi$$
$$420$$ −27.0505 + 46.8529i −0.00314269 + 0.00544330i
$$421$$ 9463.37 1.09553 0.547763 0.836633i $$-0.315479\pi$$
0.547763 + 0.836633i $$0.315479\pi$$
$$422$$ −117.260 + 203.100i −0.0135264 + 0.0234284i
$$423$$ 214.423 371.391i 0.0246468 0.0426895i
$$424$$ 68.8221 0.00788278
$$425$$ −1592.62 + 2758.50i −0.181773 + 0.314840i
$$426$$ −2556.49 4427.97i −0.290757 0.503606i
$$427$$ −8367.77 14493.4i −0.948349 1.64259i
$$428$$ −1233.30 −0.139285
$$429$$ 0 0
$$430$$ 630.474 0.0707074
$$431$$ 2426.14 + 4202.20i 0.271144 + 0.469635i 0.969155 0.246452i $$-0.0792647\pi$$
−0.698011 + 0.716087i $$0.745931\pi$$
$$432$$ 3755.17 + 6504.15i 0.418220 + 0.724378i
$$433$$ 4104.00 7108.33i 0.455486 0.788925i −0.543230 0.839584i $$-0.682799\pi$$
0.998716 + 0.0506587i $$0.0161321\pi$$
$$434$$ 5265.78 0.582409
$$435$$ −181.989 + 315.215i −0.0200591 + 0.0347434i
$$436$$ −483.213 + 836.949i −0.0530773 + 0.0919325i
$$437$$ 7910.01 0.865874
$$438$$ 3605.50 6244.92i 0.393328 0.681264i
$$439$$ 1496.90 + 2592.71i 0.162741 + 0.281875i 0.935851 0.352397i $$-0.114633\pi$$
−0.773110 + 0.634272i $$0.781300\pi$$
$$440$$ −439.469 761.182i −0.0476156 0.0824726i
$$441$$ 169.049 0.0182539
$$442$$ 0 0
$$443$$ 9743.67 1.04500 0.522501 0.852639i $$-0.324999\pi$$
0.522501 + 0.852639i $$0.324999\pi$$
$$444$$ 304.251 + 526.979i 0.0325206 + 0.0563273i
$$445$$ 325.668 + 564.073i 0.0346924 + 0.0600890i
$$446$$ −1582.29 + 2740.61i −0.167990 + 0.290968i
$$447$$ −10166.0 −1.07570
$$448$$ 5162.09 8941.01i 0.544388 0.942908i
$$449$$ −280.729 + 486.237i −0.0295065 + 0.0511068i −0.880402 0.474229i $$-0.842727\pi$$
0.850895 + 0.525336i $$0.176060\pi$$
$$450$$ −4287.22 −0.449114
$$451$$ 2254.39 3904.71i 0.235377 0.407685i
$$452$$ 461.363 + 799.104i 0.0480104 + 0.0831564i
$$453$$ 1798.77 + 3115.56i 0.186564 + 0.323138i
$$454$$ 8457.38 0.874283
$$455$$ 0 0
$$456$$ −9618.40 −0.987770
$$457$$ 6879.20 + 11915.1i 0.704148 + 1.21962i 0.966998 + 0.254783i $$0.0820040\pi$$
−0.262851 + 0.964837i $$0.584663\pi$$
$$458$$ −270.606 468.704i −0.0276083 0.0478190i
$$459$$ 1902.52 3295.26i 0.193468 0.335097i
$$460$$ 59.1779 0.00599823
$$461$$ 6004.62 10400.3i 0.606644 1.05074i −0.385145 0.922856i $$-0.625849\pi$$
0.991789 0.127882i $$-0.0408179\pi$$
$$462$$ −5553.39 + 9618.75i −0.559236 + 0.968625i
$$463$$ −13635.7 −1.36870 −0.684348 0.729156i $$-0.739913\pi$$
−0.684348 + 0.729156i $$0.739913\pi$$
$$464$$ 4434.96 7681.57i 0.443724 0.768552i
$$465$$ −117.002 202.653i −0.0116685 0.0202104i
$$466$$ −328.806 569.509i −0.0326860 0.0566138i
$$467$$ 8821.95 0.874157 0.437079 0.899423i $$-0.356013\pi$$
0.437079 + 0.899423i $$0.356013\pi$$
$$468$$ 0 0
$$469$$ −8075.72 −0.795100
$$470$$ −22.9777 39.7985i −0.00225507 0.00390589i
$$471$$ −1040.69 1802.52i −0.101809 0.176339i
$$472$$ 865.933 1499.84i 0.0844445 0.146262i
$$473$$ −28375.1 −2.75832
$$474$$ 1989.33 3445.62i 0.192770 0.333888i
$$475$$ 6731.08 11658.6i 0.650196 1.12617i
$$476$$ −667.956 −0.0643187
$$477$$ 19.1053 33.0913i 0.00183390 0.00317641i
$$478$$ 4546.27 + 7874.37i 0.435024 + 0.753484i
$$479$$ −7310.02 12661.3i −0.697293 1.20775i −0.969402 0.245480i $$-0.921054\pi$$
0.272109 0.962267i $$-0.412279\pi$$
$$480$$ −132.951 −0.0126424
$$481$$ 0 0
$$482$$ −12884.9 −1.21761
$$483$$ −2453.39 4249.39i −0.231124 0.400319i
$$484$$ 2057.04 + 3562.91i 0.193186 + 0.334608i
$$485$$ −163.768 + 283.655i −0.0153326 + 0.0265569i
$$486$$ 8542.20 0.797288
$$487$$ −4899.43 + 8486.06i −0.455882 + 0.789610i −0.998738 0.0502150i $$-0.984009\pi$$
0.542857 + 0.839825i $$0.317343\pi$$
$$488$$ 11129.9 19277.5i 1.03243 1.78822i
$$489$$ 5558.43 0.514030
$$490$$ 9.05771 15.6884i 0.000835072 0.00144639i
$$491$$ 5418.03 + 9384.31i 0.497989 + 0.862542i 0.999997 0.00232091i $$-0.000738769\pi$$
−0.502009 + 0.864863i $$0.667405\pi$$
$$492$$ −184.568 319.681i −0.0169125 0.0292934i
$$493$$ −4493.84 −0.410532
$$494$$ 0 0
$$495$$ −487.993 −0.0443104
$$496$$ 2851.26 + 4938.52i 0.258115 + 0.447069i
$$497$$ 4923.43 + 8527.63i 0.444358 + 0.769651i
$$498$$ 2849.45 4935.40i 0.256400 0.444098i
$$499$$ −2589.96 −0.232349 −0.116175 0.993229i $$-0.537063\pi$$
−0.116175 + 0.993229i $$0.537063\pi$$
$$500$$ 100.843 174.665i 0.00901969 0.0156226i
$$501$$ −1091.62 + 1890.74i −0.0973451 + 0.168607i
$$502$$ 1841.20 0.163699
$$503$$ 8533.73 14780.9i 0.756462 1.31023i −0.188183 0.982134i $$-0.560260\pi$$
0.944644 0.328096i $$-0.106407\pi$$
$$504$$ −2949.56 5108.79i −0.260682 0.451515i
$$505$$ 258.803 + 448.260i 0.0228051 + 0.0394996i
$$506$$ 12149.0 1.06737
$$507$$ 0 0
$$508$$ 795.712 0.0694961
$$509$$ −506.447 877.192i −0.0441019 0.0763867i 0.843132 0.537707i $$-0.180709\pi$$
−0.887234 + 0.461320i $$0.847376\pi$$
$$510$$ −67.7003 117.260i −0.00587808 0.0101811i
$$511$$ −6943.68 + 12026.8i −0.601116 + 1.04116i
$$512$$ 12992.6 1.12148
$$513$$ −8040.83 + 13927.1i −0.692030 + 1.19863i
$$514$$ 1640.41 2841.28i 0.140769 0.243820i
$$515$$ 522.644 0.0447193
$$516$$ −1161.54 + 2011.85i −0.0990969 + 0.171641i
$$517$$ 1034.13 + 1791.17i 0.0879711 + 0.152370i
$$518$$ 2672.81 + 4629.45i 0.226712 + 0.392676i
$$519$$ 16564.6 1.40098
$$520$$ 0 0
$$521$$ −14367.7 −1.20818 −0.604089 0.796917i $$-0.706463\pi$$
−0.604089 + 0.796917i $$0.706463\pi$$
$$522$$ −3024.27 5238.19i −0.253580 0.439213i
$$523$$ 8109.96 + 14046.9i 0.678057 + 1.17443i 0.975565 + 0.219709i $$0.0705109\pi$$
−0.297509 + 0.954719i $$0.596156\pi$$
$$524$$ 1479.01 2561.72i 0.123303 0.213568i
$$525$$ −8350.92 −0.694217
$$526$$ 6692.76 11592.2i 0.554787 0.960919i
$$527$$ 1444.56 2502.05i 0.119404 0.206814i
$$528$$ −12028.0 −0.991382
$$529$$ 3399.89 5888.78i 0.279435 0.483996i
$$530$$ −2.04733 3.54608i −0.000167793 0.000290626i
$$531$$ −480.772 832.722i −0.0392914 0.0680547i
$$532$$ 2823.06 0.230066
$$533$$ 0 0
$$534$$ 10947.5 0.887161
$$535$$ 240.733 + 416.961i 0.0194538 + 0.0336950i
$$536$$ −5370.70 9302.32i −0.432796 0.749625i
$$537$$ −284.244 + 492.325i −0.0228418 + 0.0395631i
$$538$$ −16506.1 −1.32273
$$539$$ −407.650 + 706.071i −0.0325765 + 0.0564242i
$$540$$ −60.1566 + 104.194i −0.00479394 + 0.00830335i
$$541$$ −17592.2 −1.39806 −0.699029 0.715094i $$-0.746384\pi$$
−0.699029 + 0.715094i $$0.746384\pi$$
$$542$$ 5033.36 8718.04i 0.398896 0.690908i
$$543$$ 1973.77 + 3418.67i 0.155990 + 0.270183i
$$544$$ −820.738 1421.56i −0.0646854 0.112038i
$$545$$ 377.281 0.0296531
$$546$$ 0 0
$$547$$ 10504.6 0.821103 0.410552 0.911837i $$-0.365336\pi$$
0.410552 + 0.911837i $$0.365336\pi$$
$$548$$ 1300.76 + 2252.99i 0.101398 + 0.175626i
$$549$$ −6179.38 10703.0i −0.480382 0.832045i
$$550$$ 10338.3 17906.5i 0.801504 1.38825i
$$551$$ 18992.8 1.46846
$$552$$ 3263.22 5652.06i 0.251616 0.435811i
$$553$$ −3831.16 + 6635.77i −0.294607 + 0.510274i
$$554$$ 15073.2 1.15596
$$555$$ 118.776 205.726i 0.00908426 0.0157344i
$$556$$ 1074.26 + 1860.67i 0.0819401 + 0.141924i
$$557$$ −253.779 439.558i −0.0193051 0.0334375i 0.856211 0.516626i $$-0.172812\pi$$
−0.875517 + 0.483188i $$0.839479\pi$$
$$558$$ 3888.64 0.295016
$$559$$ 0 0
$$560$$ −514.690 −0.0388386
$$561$$ 3046.92 + 5277.41i 0.229306 + 0.397170i
$$562$$ −4520.87 7830.38i −0.339327 0.587731i
$$563$$ 1721.57 2981.85i 0.128873 0.223215i −0.794367 0.607438i $$-0.792197\pi$$
0.923240 + 0.384223i $$0.125531\pi$$
$$564$$ 169.330 0.0126420
$$565$$ 180.111 311.961i 0.0134112 0.0232288i
$$566$$ −3344.11 + 5792.16i −0.248345 + 0.430146i
$$567$$ 3387.96 0.250936
$$568$$ −6548.59 + 11342.5i −0.483755 + 0.837888i
$$569$$ −11986.1 20760.5i −0.883098 1.52957i −0.847879 0.530190i $$-0.822121\pi$$
−0.0352188 0.999380i $$-0.511213\pi$$
$$570$$ 286.130 + 495.591i 0.0210257 + 0.0364176i
$$571$$ −7458.32 −0.546622 −0.273311 0.961926i $$-0.588119\pi$$
−0.273311 + 0.961926i $$0.588119\pi$$
$$572$$ 0 0
$$573$$ −2495.26 −0.181922
$$574$$ −1621.41 2808.36i −0.117903 0.204214i
$$575$$ 4567.28 + 7910.77i 0.331250 + 0.573742i
$$576$$ 3812.07 6602.70i 0.275757 0.477626i
$$577$$ −5669.57 −0.409059 −0.204530 0.978860i $$-0.565566\pi$$
−0.204530 + 0.978860i $$0.565566\pi$$
$$578$$ −5456.60 + 9451.10i −0.392672 + 0.680128i
$$579$$ −2434.97 + 4217.49i −0.174774 + 0.302717i
$$580$$ 142.093 0.0101726
$$581$$ −5487.64 + 9504.87i −0.391851 + 0.678706i
$$582$$ 2752.58 + 4767.60i 0.196045 + 0.339559i
$$583$$ 92.1420 + 159.595i 0.00654568 + 0.0113375i
$$584$$ −18471.4 −1.30882
$$585$$ 0 0
$$586$$ −14065.6 −0.991541
$$587$$ 508.696 + 881.087i 0.0357685 + 0.0619529i 0.883355 0.468704i $$-0.155279\pi$$
−0.847587 + 0.530657i $$0.821945\pi$$
$$588$$ 33.3746 + 57.8064i 0.00234072 + 0.00405425i
$$589$$ −6105.30 + 10574.7i −0.427104 + 0.739766i
$$590$$ −103.040 −0.00718996
$$591$$ −2334.91 + 4044.18i −0.162513 + 0.281481i
$$592$$ −2894.49 + 5013.41i −0.200951 + 0.348057i
$$593$$ 10198.2 0.706221 0.353111 0.935582i $$-0.385124\pi$$
0.353111 + 0.935582i $$0.385124\pi$$
$$594$$ −12350.0 + 21390.8i −0.853073 + 1.47757i
$$595$$ 130.381 + 225.827i 0.00898336 + 0.0155596i
$$596$$ 1984.35 + 3437.00i 0.136380 + 0.236216i
$$597$$ −8829.33 −0.605294
$$598$$ 0 0
$$599$$ 12516.3 0.853763 0.426881 0.904308i $$-0.359612\pi$$
0.426881 + 0.904308i $$0.359612\pi$$
$$600$$ −5553.72 9619.33i −0.377883 0.654512i
$$601$$ −4813.73 8337.63i −0.326716 0.565888i 0.655142 0.755505i $$-0.272609\pi$$
−0.981858 + 0.189617i $$0.939275\pi$$
$$602$$ −10204.0 + 17673.9i −0.690838 + 1.19657i
$$603$$ −5963.70 −0.402754
$$604$$ 702.218 1216.28i 0.0473060 0.0819364i
$$605$$ 803.046 1390.92i 0.0539644 0.0934691i
$$606$$ 8699.80 0.583177
$$607$$ −3333.60 + 5773.96i −0.222910 + 0.386092i −0.955690 0.294373i $$-0.904889\pi$$
0.732780 + 0.680466i $$0.238222\pi$$
$$608$$ 3468.78 + 6008.11i 0.231378 + 0.400758i
$$609$$ −5890.87 10203.3i −0.391971 0.678913i
$$610$$ −1324.37 −0.0879053
$$611$$ 0 0
$$612$$ −493.268 −0.0325803
$$613$$ −11542.7 19992.5i −0.760530 1.31728i −0.942578 0.333987i $$-0.891606\pi$$
0.182047 0.983290i $$-0.441728\pi$$
$$614$$ 9359.39 + 16210.9i 0.615170 + 1.06551i
$$615$$ −72.0532 + 124.800i −0.00472433 + 0.00818278i
$$616$$ 28450.6 1.86089
$$617$$ 1524.62 2640.72i 0.0994796 0.172304i −0.811990 0.583672i $$-0.801616\pi$$
0.911469 + 0.411368i $$0.134949\pi$$
$$618$$ 4392.24 7607.58i 0.285893 0.495181i
$$619$$ −7296.58 −0.473787 −0.236894 0.971536i $$-0.576129\pi$$
−0.236894 + 0.971536i $$0.576129\pi$$
$$620$$ −45.6761 + 79.1134i −0.00295871 + 0.00512463i
$$621$$ −5455.99 9450.06i −0.352563 0.610657i
$$622$$ 10124.4 + 17536.0i 0.652657 + 1.13044i
$$623$$ −21083.3 −1.35583
$$624$$ 0 0
$$625$$ 15506.8 0.992438
$$626$$ 12810.8 + 22189.0i 0.817929 + 1.41670i
$$627$$ −12877.5 22304.5i −0.820222 1.42067i
$$628$$ −406.271 + 703.683i −0.0258153 + 0.0447134i
$$629$$ 2932.92 0.185920
$$630$$ −175.488 + 303.954i −0.0110978 + 0.0192219i
$$631$$ −11914.8 + 20637.0i −0.751694 + 1.30197i 0.195307 + 0.980742i $$0.437430\pi$$
−0.947001 + 0.321230i $$0.895904\pi$$
$$632$$ −10191.6 −0.641453
$$633$$ −168.672 + 292.149i −0.0105910 + 0.0183442i
$$634$$ 7980.27 + 13822.2i 0.499901 + 0.865853i
$$635$$ −155.318 269.019i −0.00970648 0.0168121i
$$636$$ 15.0874 0.000940653
$$637$$ 0 0
$$638$$ 29171.3 1.81019
$$639$$ 3635.82 + 6297.43i 0.225088 + 0.389863i
$$640$$ −264.174 457.562i −0.0163162 0.0282605i
$$641$$ −6702.63 + 11609.3i −0.413008 + 0.715351i −0.995217 0.0976883i $$-0.968855\pi$$
0.582209 + 0.813039i $$0.302188\pi$$
$$642$$ 8092.36 0.497477
$$643$$ 2625.76 4547.94i 0.161042 0.278932i −0.774201 0.632940i $$-0.781848\pi$$
0.935243 + 0.354008i $$0.115181\pi$$
$$644$$ −957.774 + 1658.91i −0.0586049 + 0.101507i
$$645$$ 906.904 0.0553633
$$646$$ −3532.68 + 6118.79i −0.215157 + 0.372663i
$$647$$ −10805.7 18716.1i −0.656595 1.13726i −0.981492 0.191506i $$-0.938663\pi$$
0.324897 0.945749i $$-0.394670\pi$$
$$648$$ 2253.14 + 3902.55i 0.136592 + 0.236584i
$$649$$ 4637.39 0.280483
$$650$$ 0 0
$$651$$ 7574.54 0.456021
$$652$$ −1084.97 1879.23i −0.0651699 0.112878i
$$653$$ 10797.9 + 18702.6i 0.647099 + 1.12081i 0.983813 + 0.179201i $$0.0573512\pi$$
−0.336714 + 0.941607i $$0.609316\pi$$
$$654$$ 3170.63 5491.68i 0.189574 0.328351i
$$655$$ −1154.78 −0.0688869
$$656$$ 1755.89 3041.28i 0.104506 0.181009i
$$657$$ −5127.72 + 8881.48i −0.304492 + 0.527396i
$$658$$ 1487.54 0.0881314
$$659$$ 8321.30 14412.9i 0.491884 0.851968i −0.508072 0.861315i $$-0.669642\pi$$
0.999956 + 0.00934609i $$0.00297500\pi$$
$$660$$ −96.3419 166.869i −0.00568198 0.00984147i
$$661$$ 13490.6 + 23366.3i 0.793831 + 1.37495i 0.923579 + 0.383408i $$0.125250\pi$$
−0.129748 + 0.991547i $$0.541417\pi$$
$$662$$ −11871.5 −0.696980
$$663$$ 0 0
$$664$$ −14598.1 −0.853185
$$665$$ −551.044 954.437i −0.0321332 0.0556564i
$$666$$ 1973.80 + 3418.73i 0.114840 + 0.198908i
$$667$$ −6443.67 + 11160.8i −0.374063 + 0.647896i
$$668$$ 852.310 0.0493665
$$669$$ −2276.05 + 3942.23i −0.131535 + 0.227826i
$$670$$ −319.537 + 553.454i −0.0184251 + 0.0319131i
$$671$$ 59604.5 3.42922
$$672$$ 2151.77 3726.98i 0.123521 0.213945i
$$673$$ −5574.62 9655.53i −0.319296 0.553036i 0.661046 0.750346i $$-0.270113\pi$$
−0.980341 + 0.197309i $$0.936780\pi$$
$$674$$ 3880.52 + 6721.26i 0.221769 + 0.384115i
$$675$$ −18571.3 −1.05898
$$676$$ 0 0
$$677$$ 3314.33 0.188154 0.0940769 0.995565i $$-0.470010\pi$$
0.0940769 + 0.995565i $$0.470010\pi$$
$$678$$ −3027.26 5243.36i −0.171477 0.297006i
$$679$$ −5301.06 9181.71i −0.299611 0.518942i
$$680$$ −173.418 + 300.369i −0.00977982 + 0.0169391i
$$681$$ 12165.5 0.684556
$$682$$ −9377.17 + 16241.7i −0.526496 + 0.911918i
$$683$$ 12252.6 21222.2i 0.686433 1.18894i −0.286552 0.958065i $$-0.592509\pi$$
0.972984 0.230872i $$-0.0741577\pi$$
$$684$$ 2084.75 0.116539
$$685$$ 507.803 879.540i 0.0283243 0.0490591i
$$686$$ 8278.50 + 14338.8i 0.460750 + 0.798042i
$$687$$ −389.253 674.206i −0.0216171 0.0374419i
$$688$$ −22100.6 −1.22468
$$689$$ 0 0
$$690$$ −388.299 −0.0214236
$$691$$ −10876.4 18838.5i −0.598782 1.03712i −0.993001 0.118105i $$-0.962318\pi$$
0.394219 0.919017i $$-0.371015\pi$$
$$692$$ −3233.32 5600.27i −0.177619 0.307645i
$$693$$ 7897.99 13679.7i 0.432929 0.749855i
$$694$$ −7278.90 −0.398132
$$695$$ 419.378 726.383i 0.0228891 0.0396450i
$$696$$ 7835.37 13571.3i 0.426722 0.739105i
$$697$$ −1779.20 −0.0966887
$$698$$ −9689.94 + 16783.5i −0.525458 + 0.910120i
$$699$$ −472.971 819.209i −0.0255928 0.0443281i
$$700$$ 1630.05 + 2823.33i 0.0880145 + 0.152446i
$$701$$ 34250.9 1.84542 0.922709 0.385496i $$-0.125970\pi$$
0.922709 + 0.385496i $$0.125970\pi$$
$$702$$ 0 0
$$703$$ −12395.8 −0.665028
$$704$$ 18385.1 + 31843.9i 0.984252 + 1.70477i
$$705$$ −33.0522 57.2480i −0.00176570 0.00305828i
$$706$$ 2996.30 5189.74i 0.159727 0.276655i
$$707$$ −16754.6 −0.891259
$$708$$ 189.833 328.800i 0.0100768 0.0174535i
$$709$$ −2763.56 + 4786.62i −0.146386 + 0.253548i −0.929889 0.367840i $$-0.880097\pi$$
0.783503 + 0.621388i $$0.213431\pi$$
$$710$$ 779.234 0.0411889
$$711$$ −2829.21 + 4900.34i −0.149232 + 0.258477i
$$712$$ −14021.3 24285.6i −0.738020 1.27829i
$$713$$ −4142.67 7175.31i −0.217593 0.376883i
$$714$$ 4382.83 0.229724
$$715$$ 0 0
$$716$$ 221.931 0.0115837
$$717$$ 6539.57 + 11326.9i 0.340620 + 0.589972i
$$718$$ 3242.51 + 5616.19i 0.168537 + 0.291914i
$$719$$ 1888.89 3271.65i 0.0979745 0.169697i −0.812872 0.582443i $$-0.802097\pi$$
0.910846 + 0.412746i $$0.135430\pi$$
$$720$$ −380.085 −0.0196735
$$721$$ −8458.81 + 14651.1i −0.436925 + 0.756776i
$$722$$ 6145.75 10644.7i 0.316788 0.548693i
$$723$$ −18534.2 −0.953380
$$724$$ 770.538 1334.61i 0.0395536 0.0685088i
$$725$$ 10966.6 + 18994.7i 0.561777 + 0.973027i
$$726$$ −13497.4 23378.2i −0.689994 1.19510i
$$727$$ 19076.8 0.973204 0.486602 0.873624i $$-0.338236\pi$$
0.486602 + 0.873624i $$0.338236\pi$$
$$728$$ 0 0
$$729$$ 17319.9 0.879944
$$730$$ 549.490 + 951.744i 0.0278596 + 0.0482543i
$$731$$ 5598.52 + 9696.92i 0.283268 + 0.490634i
$$732$$ 2439.93 4226.08i 0.123200 0.213388i
$$733$$ −7997.30 −0.402984 −0.201492 0.979490i $$-0.564579\pi$$
−0.201492 + 0.979490i $$0.564579\pi$$
$$734$$ 8424.71 14592.0i 0.423653 0.733789i
$$735$$ 13.0290 22.5669i 0.000653855 0.00113251i
$$736$$ −4707.39 −0.235756
$$737$$ 14381.0 24908.7i 0.718769 1.24494i
$$738$$ −1197.37 2073.90i −0.0597232 0.103444i
$$739$$ 14491.8 + 25100.6i 0.721367 + 1.24944i 0.960452 + 0.278445i $$0.0898190\pi$$
−0.239086 + 0.970998i $$0.576848\pi$$
$$740$$ −92.7376 −0.00460689
$$741$$ 0 0
$$742$$ 132.541 0.00655761
$$743$$ −9572.69 16580.4i −0.472662 0.818674i 0.526849 0.849959i $$-0.323373\pi$$
−0.999511 + 0.0312847i $$0.990040\pi$$
$$744$$ 5037.40 + 8725.02i 0.248226 + 0.429939i
$$745$$ 774.667 1341.76i 0.0380961 0.0659844i
$$746$$ −7435.47 −0.364922
$$747$$ −4052.47 + 7019.09i −0.198490 + 0.343795i
$$748$$ 1189.48 2060.24i 0.0581440 0.100708i
$$749$$ −15584.7 −0.760284
$$750$$ −661.688 + 1146.08i −0.0322152 + 0.0557984i
$$751$$ 12758.4 + 22098.3i 0.619923 + 1.07374i 0.989499 + 0.144538i $$0.0461695\pi$$
−0.369576 + 0.929200i $$0.620497\pi$$
$$752$$ 805.459 + 1395.10i 0.0390586 + 0.0676515i
$$753$$ 2648.47 0.128175
$$754$$ 0 0
$$755$$ −548.275 −0.0264288
$$756$$ −1947.23 3372.70i −0.0936773 0.162254i
$$757$$ 8615.31 + 14922.2i 0.413645 + 0.716453i 0.995285 0.0969925i $$-0.0309223\pi$$
−0.581641 + 0.813446i $$0.697589\pi$$
$$758$$ 2389.59 4138.89i 0.114504 0.198326i
$$759$$ 17475.7 0.835744
$$760$$ 732.936 1269.48i 0.0349821 0.0605908i
$$761$$ −1171.53 + 2029.15i −0.0558053 + 0.0966576i −0.892579 0.450892i $$-0.851106\pi$$
0.836773 + 0.547550i $$0.184439\pi$$
$$762$$ −5221.11 −0.248216
$$763$$ −6106.17 + 10576.2i −0.289722 + 0.501814i
$$764$$ 487.060 + 843.613i 0.0230644 + 0.0399488i
$$765$$ 96.2829 + 166.767i 0.00455048 + 0.00788166i
$$766$$ 27756.9 1.30927
$$767$$ 0 0
$$768$$ 7862.11 0.369400
$$769$$ −3550.09 6148.93i −0.166475 0.288344i 0.770703 0.637195i $$-0.219905\pi$$
−0.937178 + 0.348851i $$0.886572\pi$$
$$770$$ −846.353 1465.93i −0.0396110 0.0686082i
$$771$$ 2359.65 4087.03i 0.110221 0.190909i
$$772$$ 1901.17 0.0886328
$$773$$ 6135.22 10626.5i 0.285470 0.494449i −0.687253 0.726418i $$-0.741184\pi$$
0.972723 + 0.231969i $$0.0745169\pi$$
$$774$$ −7535.39