# Properties

 Label 12.4.b.a.11.1 Level 12 Weight 4 Character 12.11 Analytic conductor 0.708 Analytic rank 0 Dimension 4 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 12.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.708022920069$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{3}, \sqrt{-5})$$ Defining polynomial: $$x^{4} + x^{2} + 4$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 11.1 Root $$-0.866025 - 1.11803i$$ of defining polynomial Character $$\chi$$ $$=$$ 12.11 Dual form 12.4.b.a.11.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.73205 - 2.23607i) q^{2} +(3.46410 - 3.87298i) q^{3} +(-2.00000 + 7.74597i) q^{4} +8.94427i q^{5} +(-14.6603 - 1.03776i) q^{6} +7.74597i q^{7} +(20.7846 - 8.94427i) q^{8} +(-3.00000 - 26.8328i) q^{9} +O(q^{10})$$ $$q+(-1.73205 - 2.23607i) q^{2} +(3.46410 - 3.87298i) q^{3} +(-2.00000 + 7.74597i) q^{4} +8.94427i q^{5} +(-14.6603 - 1.03776i) q^{6} +7.74597i q^{7} +(20.7846 - 8.94427i) q^{8} +(-3.00000 - 26.8328i) q^{9} +(20.0000 - 15.4919i) q^{10} -34.6410 q^{11} +(23.0718 + 34.5788i) q^{12} -10.0000 q^{13} +(17.3205 - 13.4164i) q^{14} +(34.6410 + 30.9839i) q^{15} +(-56.0000 - 30.9839i) q^{16} +35.7771i q^{17} +(-54.8038 + 53.1840i) q^{18} -69.7137i q^{19} +(-69.2820 - 17.8885i) q^{20} +(30.0000 + 26.8328i) q^{21} +(60.0000 + 77.4597i) q^{22} +96.9948 q^{23} +(37.3590 - 111.482i) q^{24} +45.0000 q^{25} +(17.3205 + 22.3607i) q^{26} +(-114.315 - 81.3327i) q^{27} +(-60.0000 - 15.4919i) q^{28} -152.053i q^{29} +(9.28203 - 131.125i) q^{30} +224.633i q^{31} +(27.7128 + 178.885i) q^{32} +(-120.000 + 134.164i) q^{33} +(80.0000 - 61.9677i) q^{34} -69.2820 q^{35} +(213.846 + 30.4277i) q^{36} -130.000 q^{37} +(-155.885 + 120.748i) q^{38} +(-34.6410 + 38.7298i) q^{39} +(80.0000 + 185.903i) q^{40} -125.220i q^{41} +(8.03848 - 113.558i) q^{42} -224.633i q^{43} +(69.2820 - 268.328i) q^{44} +(240.000 - 26.8328i) q^{45} +(-168.000 - 216.887i) q^{46} +193.990 q^{47} +(-313.990 + 109.556i) q^{48} +283.000 q^{49} +(-77.9423 - 100.623i) q^{50} +(138.564 + 123.935i) q^{51} +(20.0000 - 77.4597i) q^{52} +545.601i q^{53} +(16.1347 + 396.489i) q^{54} -309.839i q^{55} +(69.2820 + 160.997i) q^{56} +(-270.000 - 241.495i) q^{57} +(-340.000 + 263.363i) q^{58} -173.205 q^{59} +(-309.282 + 206.360i) q^{60} -442.000 q^{61} +(502.295 - 389.076i) q^{62} +(207.846 - 23.2379i) q^{63} +(352.000 - 371.806i) q^{64} -89.4427i q^{65} +(507.846 + 35.9492i) q^{66} +735.867i q^{67} +(-277.128 - 71.5542i) q^{68} +(336.000 - 375.659i) q^{69} +(120.000 + 154.919i) q^{70} -1039.23 q^{71} +(-302.354 - 530.877i) q^{72} +410.000 q^{73} +(225.167 + 290.689i) q^{74} +(155.885 - 174.284i) q^{75} +(540.000 + 139.427i) q^{76} -268.328i q^{77} +(146.603 + 10.3776i) q^{78} -85.2056i q^{79} +(277.128 - 500.879i) q^{80} +(-711.000 + 160.997i) q^{81} +(-280.000 + 216.887i) q^{82} +1254.00 q^{83} +(-267.846 + 178.713i) q^{84} -320.000 q^{85} +(-502.295 + 389.076i) q^{86} +(-588.897 - 526.726i) q^{87} +(-720.000 + 309.839i) q^{88} +840.762i q^{89} +(-475.692 - 490.181i) q^{90} -77.4597i q^{91} +(-193.990 + 751.319i) q^{92} +(870.000 + 778.152i) q^{93} +(-336.000 - 433.774i) q^{94} +623.538 q^{95} +(788.820 + 512.346i) q^{96} +770.000 q^{97} +(-490.170 - 632.807i) q^{98} +(103.923 + 929.516i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 8q^{4} - 24q^{6} - 12q^{9} + O(q^{10})$$ $$4q - 8q^{4} - 24q^{6} - 12q^{9} + 80q^{10} + 120q^{12} - 40q^{13} - 224q^{16} - 240q^{18} + 120q^{21} + 240q^{22} + 288q^{24} + 180q^{25} - 240q^{28} - 240q^{30} - 480q^{33} + 320q^{34} + 24q^{36} - 520q^{37} + 320q^{40} + 240q^{42} + 960q^{45} - 672q^{46} - 480q^{48} + 1132q^{49} + 80q^{52} + 792q^{54} - 1080q^{57} - 1360q^{58} - 960q^{60} - 1768q^{61} + 1408q^{64} + 1200q^{66} + 1344q^{69} + 480q^{70} - 960q^{72} + 1640q^{73} + 2160q^{76} + 240q^{78} - 2844q^{81} - 1120q^{82} - 240q^{84} - 1280q^{85} - 2880q^{88} - 240q^{90} + 3480q^{93} - 1344q^{94} + 384q^{96} + 3080q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$7$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.73205 2.23607i −0.612372 0.790569i
$$3$$ 3.46410 3.87298i 0.666667 0.745356i
$$4$$ −2.00000 + 7.74597i −0.250000 + 0.968246i
$$5$$ 8.94427i 0.800000i 0.916515 + 0.400000i $$0.130990\pi$$
−0.916515 + 0.400000i $$0.869010\pi$$
$$6$$ −14.6603 1.03776i −0.997504 0.0706108i
$$7$$ 7.74597i 0.418243i 0.977890 + 0.209121i $$0.0670604\pi$$
−0.977890 + 0.209121i $$0.932940\pi$$
$$8$$ 20.7846 8.94427i 0.918559 0.395285i
$$9$$ −3.00000 26.8328i −0.111111 0.993808i
$$10$$ 20.0000 15.4919i 0.632456 0.489898i
$$11$$ −34.6410 −0.949514 −0.474757 0.880117i $$-0.657464\pi$$
−0.474757 + 0.880117i $$0.657464\pi$$
$$12$$ 23.0718 + 34.5788i 0.555021 + 0.831836i
$$13$$ −10.0000 −0.213346 −0.106673 0.994294i $$-0.534020\pi$$
−0.106673 + 0.994294i $$0.534020\pi$$
$$14$$ 17.3205 13.4164i 0.330650 0.256120i
$$15$$ 34.6410 + 30.9839i 0.596285 + 0.533333i
$$16$$ −56.0000 30.9839i −0.875000 0.484123i
$$17$$ 35.7771i 0.510425i 0.966885 + 0.255212i $$0.0821454\pi$$
−0.966885 + 0.255212i $$0.917855\pi$$
$$18$$ −54.8038 + 53.1840i −0.717633 + 0.696422i
$$19$$ 69.7137i 0.841759i −0.907117 0.420879i $$-0.861722\pi$$
0.907117 0.420879i $$-0.138278\pi$$
$$20$$ −69.2820 17.8885i −0.774597 0.200000i
$$21$$ 30.0000 + 26.8328i 0.311740 + 0.278829i
$$22$$ 60.0000 + 77.4597i 0.581456 + 0.750657i
$$23$$ 96.9948 0.879340 0.439670 0.898159i $$-0.355095\pi$$
0.439670 + 0.898159i $$0.355095\pi$$
$$24$$ 37.3590 111.482i 0.317745 0.948176i
$$25$$ 45.0000 0.360000
$$26$$ 17.3205 + 22.3607i 0.130647 + 0.168665i
$$27$$ −114.315 81.3327i −0.814815 0.579721i
$$28$$ −60.0000 15.4919i −0.404962 0.104561i
$$29$$ 152.053i 0.973637i −0.873503 0.486818i $$-0.838157\pi$$
0.873503 0.486818i $$-0.161843\pi$$
$$30$$ 9.28203 131.125i 0.0564886 0.798003i
$$31$$ 224.633i 1.30146i 0.759309 + 0.650730i $$0.225537\pi$$
−0.759309 + 0.650730i $$0.774463\pi$$
$$32$$ 27.7128 + 178.885i 0.153093 + 0.988212i
$$33$$ −120.000 + 134.164i −0.633010 + 0.707726i
$$34$$ 80.0000 61.9677i 0.403526 0.312570i
$$35$$ −69.2820 −0.334594
$$36$$ 213.846 + 30.4277i 0.990028 + 0.140869i
$$37$$ −130.000 −0.577618 −0.288809 0.957387i $$-0.593259\pi$$
−0.288809 + 0.957387i $$0.593259\pi$$
$$38$$ −155.885 + 120.748i −0.665469 + 0.515470i
$$39$$ −34.6410 + 38.7298i −0.142231 + 0.159019i
$$40$$ 80.0000 + 185.903i 0.316228 + 0.734847i
$$41$$ 125.220i 0.476977i −0.971145 0.238488i $$-0.923348\pi$$
0.971145 0.238488i $$-0.0766519\pi$$
$$42$$ 8.03848 113.558i 0.0295325 0.417199i
$$43$$ 224.633i 0.796656i −0.917243 0.398328i $$-0.869591\pi$$
0.917243 0.398328i $$-0.130409\pi$$
$$44$$ 69.2820 268.328i 0.237379 0.919363i
$$45$$ 240.000 26.8328i 0.795046 0.0888889i
$$46$$ −168.000 216.887i −0.538484 0.695179i
$$47$$ 193.990 0.602049 0.301025 0.953616i $$-0.402671\pi$$
0.301025 + 0.953616i $$0.402671\pi$$
$$48$$ −313.990 + 109.556i −0.944177 + 0.329438i
$$49$$ 283.000 0.825073
$$50$$ −77.9423 100.623i −0.220454 0.284605i
$$51$$ 138.564 + 123.935i 0.380448 + 0.340283i
$$52$$ 20.0000 77.4597i 0.0533366 0.206572i
$$53$$ 545.601i 1.41404i 0.707195 + 0.707019i $$0.249960\pi$$
−0.707195 + 0.707019i $$0.750040\pi$$
$$54$$ 16.1347 + 396.489i 0.0406602 + 0.999173i
$$55$$ 309.839i 0.759612i
$$56$$ 69.2820 + 160.997i 0.165325 + 0.384181i
$$57$$ −270.000 241.495i −0.627410 0.561173i
$$58$$ −340.000 + 263.363i −0.769727 + 0.596228i
$$59$$ −173.205 −0.382193 −0.191096 0.981571i $$-0.561204\pi$$
−0.191096 + 0.981571i $$0.561204\pi$$
$$60$$ −309.282 + 206.360i −0.665469 + 0.444017i
$$61$$ −442.000 −0.927743 −0.463871 0.885903i $$-0.653540\pi$$
−0.463871 + 0.885903i $$0.653540\pi$$
$$62$$ 502.295 389.076i 1.02890 0.796979i
$$63$$ 207.846 23.2379i 0.415653 0.0464714i
$$64$$ 352.000 371.806i 0.687500 0.726184i
$$65$$ 89.4427i 0.170677i
$$66$$ 507.846 + 35.9492i 0.947144 + 0.0670460i
$$67$$ 735.867i 1.34180i 0.741549 + 0.670899i $$0.234092\pi$$
−0.741549 + 0.670899i $$0.765908\pi$$
$$68$$ −277.128 71.5542i −0.494217 0.127606i
$$69$$ 336.000 375.659i 0.586227 0.655421i
$$70$$ 120.000 + 154.919i 0.204896 + 0.264520i
$$71$$ −1039.23 −1.73710 −0.868549 0.495603i $$-0.834947\pi$$
−0.868549 + 0.495603i $$0.834947\pi$$
$$72$$ −302.354 530.877i −0.494899 0.868950i
$$73$$ 410.000 0.657354 0.328677 0.944442i $$-0.393397\pi$$
0.328677 + 0.944442i $$0.393397\pi$$
$$74$$ 225.167 + 290.689i 0.353717 + 0.456647i
$$75$$ 155.885 174.284i 0.240000 0.268328i
$$76$$ 540.000 + 139.427i 0.815030 + 0.210440i
$$77$$ 268.328i 0.397128i
$$78$$ 146.603 + 10.3776i 0.212814 + 0.0150646i
$$79$$ 85.2056i 0.121347i −0.998158 0.0606733i $$-0.980675\pi$$
0.998158 0.0606733i $$-0.0193248\pi$$
$$80$$ 277.128 500.879i 0.387298 0.700000i
$$81$$ −711.000 + 160.997i −0.975309 + 0.220846i
$$82$$ −280.000 + 216.887i −0.377083 + 0.292087i
$$83$$ 1254.00 1.65837 0.829186 0.558973i $$-0.188804\pi$$
0.829186 + 0.558973i $$0.188804\pi$$
$$84$$ −267.846 + 178.713i −0.347910 + 0.232134i
$$85$$ −320.000 −0.408340
$$86$$ −502.295 + 389.076i −0.629812 + 0.487850i
$$87$$ −588.897 526.726i −0.725706 0.649091i
$$88$$ −720.000 + 309.839i −0.872185 + 0.375329i
$$89$$ 840.762i 1.00135i 0.865634 + 0.500677i $$0.166916\pi$$
−0.865634 + 0.500677i $$0.833084\pi$$
$$90$$ −475.692 490.181i −0.557137 0.574106i
$$91$$ 77.4597i 0.0892305i
$$92$$ −193.990 + 751.319i −0.219835 + 0.851417i
$$93$$ 870.000 + 778.152i 0.970052 + 0.867641i
$$94$$ −336.000 433.774i −0.368678 0.475962i
$$95$$ 623.538 0.673407
$$96$$ 788.820 + 512.346i 0.838632 + 0.544699i
$$97$$ 770.000 0.805996 0.402998 0.915201i $$-0.367968\pi$$
0.402998 + 0.915201i $$0.367968\pi$$
$$98$$ −490.170 632.807i −0.505252 0.652277i
$$99$$ 103.923 + 929.516i 0.105502 + 0.943635i
$$100$$ −90.0000 + 348.569i −0.0900000 + 0.348569i
$$101$$ 1493.69i 1.47156i −0.677218 0.735782i $$-0.736815\pi$$
0.677218 0.735782i $$-0.263185\pi$$
$$102$$ 37.1281 524.501i 0.0360415 0.509151i
$$103$$ 1355.54i 1.29675i −0.761319 0.648377i $$-0.775448\pi$$
0.761319 0.648377i $$-0.224552\pi$$
$$104$$ −207.846 + 89.4427i −0.195971 + 0.0843325i
$$105$$ −240.000 + 268.328i −0.223063 + 0.249392i
$$106$$ 1220.00 945.008i 1.11790 0.865918i
$$107$$ −644.323 −0.582141 −0.291070 0.956702i $$-0.594011\pi$$
−0.291070 + 0.956702i $$0.594011\pi$$
$$108$$ 858.631 722.818i 0.765016 0.644011i
$$109$$ −1066.00 −0.936737 −0.468368 0.883533i $$-0.655158\pi$$
−0.468368 + 0.883533i $$0.655158\pi$$
$$110$$ −692.820 + 536.656i −0.600526 + 0.465165i
$$111$$ −450.333 + 503.488i −0.385079 + 0.430531i
$$112$$ 240.000 433.774i 0.202481 0.365963i
$$113$$ 1037.54i 0.863745i −0.901935 0.431872i $$-0.857853\pi$$
0.901935 0.431872i $$-0.142147\pi$$
$$114$$ −72.3463 + 1022.02i −0.0594373 + 0.839658i
$$115$$ 867.548i 0.703472i
$$116$$ 1177.79 + 304.105i 0.942720 + 0.243409i
$$117$$ 30.0000 + 268.328i 0.0237051 + 0.212025i
$$118$$ 300.000 + 387.298i 0.234044 + 0.302150i
$$119$$ −277.128 −0.213481
$$120$$ 997.128 + 334.149i 0.758541 + 0.254196i
$$121$$ −131.000 −0.0984222
$$122$$ 765.566 + 988.342i 0.568124 + 0.733445i
$$123$$ −484.974 433.774i −0.355518 0.317985i
$$124$$ −1740.00 449.266i −1.26013 0.325365i
$$125$$ 1520.53i 1.08800i
$$126$$ −411.962 424.509i −0.291273 0.300145i
$$127$$ 1835.79i 1.28268i 0.767257 + 0.641340i $$0.221621\pi$$
−0.767257 + 0.641340i $$0.778379\pi$$
$$128$$ −1441.07 143.108i −0.995105 0.0988212i
$$129$$ −870.000 778.152i −0.593792 0.531104i
$$130$$ −200.000 + 154.919i −0.134932 + 0.104518i
$$131$$ 450.333 0.300350 0.150175 0.988659i $$-0.452016\pi$$
0.150175 + 0.988659i $$0.452016\pi$$
$$132$$ −799.230 1197.84i −0.527001 0.789841i
$$133$$ 540.000 0.352060
$$134$$ 1645.45 1274.56i 1.06078 0.821680i
$$135$$ 727.461 1022.47i 0.463777 0.651852i
$$136$$ 320.000 + 743.613i 0.201763 + 0.468855i
$$137$$ 89.4427i 0.0557782i 0.999611 + 0.0278891i $$0.00887852\pi$$
−0.999611 + 0.0278891i $$0.991121\pi$$
$$138$$ −1421.97 100.658i −0.877145 0.0620909i
$$139$$ 1959.73i 1.19584i −0.801555 0.597921i $$-0.795994\pi$$
0.801555 0.597921i $$-0.204006\pi$$
$$140$$ 138.564 536.656i 0.0836486 0.323970i
$$141$$ 672.000 751.319i 0.401366 0.448741i
$$142$$ 1800.00 + 2323.79i 1.06375 + 1.37330i
$$143$$ 346.410 0.202575
$$144$$ −663.384 + 1595.59i −0.383903 + 0.923373i
$$145$$ 1360.00 0.778909
$$146$$ −710.141 916.788i −0.402546 0.519684i
$$147$$ 980.341 1096.05i 0.550049 0.614973i
$$148$$ 260.000 1006.98i 0.144405 0.559276i
$$149$$ 1618.91i 0.890111i 0.895503 + 0.445055i $$0.146816\pi$$
−0.895503 + 0.445055i $$0.853184\pi$$
$$150$$ −659.711 46.6993i −0.359101 0.0254199i
$$151$$ 565.456i 0.304743i 0.988323 + 0.152371i $$0.0486909\pi$$
−0.988323 + 0.152371i $$0.951309\pi$$
$$152$$ −623.538 1448.97i −0.332734 0.773205i
$$153$$ 960.000 107.331i 0.507264 0.0567138i
$$154$$ −600.000 + 464.758i −0.313957 + 0.243190i
$$155$$ −2009.18 −1.04117
$$156$$ −230.718 345.788i −0.118412 0.177469i
$$157$$ −730.000 −0.371085 −0.185542 0.982636i $$-0.559404\pi$$
−0.185542 + 0.982636i $$0.559404\pi$$
$$158$$ −190.526 + 147.580i −0.0959329 + 0.0743093i
$$159$$ 2113.10 + 1890.02i 1.05396 + 0.942692i
$$160$$ −1600.00 + 247.871i −0.790569 + 0.122474i
$$161$$ 751.319i 0.367778i
$$162$$ 1591.49 + 1310.99i 0.771846 + 0.635809i
$$163$$ 255.617i 0.122831i −0.998112 0.0614155i $$-0.980439\pi$$
0.998112 0.0614155i $$-0.0195615\pi$$
$$164$$ 969.948 + 250.440i 0.461831 + 0.119244i
$$165$$ −1200.00 1073.31i −0.566181 0.506408i
$$166$$ −2172.00 2804.04i −1.01554 1.31106i
$$167$$ 13.8564 0.00642060 0.00321030 0.999995i $$-0.498978\pi$$
0.00321030 + 0.999995i $$0.498978\pi$$
$$168$$ 863.538 + 289.381i 0.396568 + 0.132894i
$$169$$ −2097.00 −0.954483
$$170$$ 554.256 + 715.542i 0.250056 + 0.322821i
$$171$$ −1870.61 + 209.141i −0.836547 + 0.0935288i
$$172$$ 1740.00 + 449.266i 0.771359 + 0.199164i
$$173$$ 1118.03i 0.491344i −0.969353 0.245672i $$-0.920991\pi$$
0.969353 0.245672i $$-0.0790086\pi$$
$$174$$ −157.795 + 2229.13i −0.0687493 + 0.971206i
$$175$$ 348.569i 0.150567i
$$176$$ 1939.90 + 1073.31i 0.830825 + 0.459682i
$$177$$ −600.000 + 670.820i −0.254795 + 0.284870i
$$178$$ 1880.00 1456.24i 0.791640 0.613202i
$$179$$ −1351.00 −0.564125 −0.282063 0.959396i $$-0.591019\pi$$
−0.282063 + 0.959396i $$0.591019\pi$$
$$180$$ −272.154 + 1912.70i −0.112695 + 0.792023i
$$181$$ 1262.00 0.518253 0.259126 0.965843i $$-0.416565\pi$$
0.259126 + 0.965843i $$0.416565\pi$$
$$182$$ −173.205 + 134.164i −0.0705429 + 0.0546423i
$$183$$ −1531.13 + 1711.86i −0.618495 + 0.691499i
$$184$$ 2016.00 867.548i 0.807725 0.347590i
$$185$$ 1162.76i 0.462094i
$$186$$ 233.116 3293.18i 0.0918972 1.29821i
$$187$$ 1239.35i 0.484656i
$$188$$ −387.979 + 1502.64i −0.150512 + 0.582931i
$$189$$ 630.000 885.483i 0.242464 0.340791i
$$190$$ −1080.00 1394.27i −0.412376 0.532375i
$$191$$ 2771.28 1.04986 0.524929 0.851146i $$-0.324092\pi$$
0.524929 + 0.851146i $$0.324092\pi$$
$$192$$ −220.636 2651.27i −0.0829325 0.996555i
$$193$$ −190.000 −0.0708627 −0.0354313 0.999372i $$-0.511281\pi$$
−0.0354313 + 0.999372i $$0.511281\pi$$
$$194$$ −1333.68 1721.77i −0.493570 0.637196i
$$195$$ −346.410 309.839i −0.127215 0.113785i
$$196$$ −566.000 + 2192.11i −0.206268 + 0.798873i
$$197$$ 2137.68i 0.773114i −0.922266 0.386557i $$-0.873664\pi$$
0.922266 0.386557i $$-0.126336\pi$$
$$198$$ 1898.46 1842.35i 0.681403 0.661262i
$$199$$ 255.617i 0.0910563i 0.998963 + 0.0455281i $$0.0144971\pi$$
−0.998963 + 0.0455281i $$0.985503\pi$$
$$200$$ 935.307 402.492i 0.330681 0.142302i
$$201$$ 2850.00 + 2549.12i 1.00012 + 0.894532i
$$202$$ −3340.00 + 2587.15i −1.16337 + 0.901146i
$$203$$ 1177.79 0.407217
$$204$$ −1237.13 + 825.442i −0.424590 + 0.283296i
$$205$$ 1120.00 0.381581
$$206$$ −3031.09 + 2347.87i −1.02517 + 0.794097i
$$207$$ −290.985 2602.64i −0.0977045 0.873895i
$$208$$ 560.000 + 309.839i 0.186678 + 0.103286i
$$209$$ 2414.95i 0.799262i
$$210$$ 1015.69 + 71.8983i 0.333759 + 0.0236260i
$$211$$ 549.964i 0.179436i 0.995967 + 0.0897181i $$0.0285966\pi$$
−0.995967 + 0.0897181i $$0.971403\pi$$
$$212$$ −4226.20 1091.20i −1.36914 0.353509i
$$213$$ −3600.00 + 4024.92i −1.15807 + 1.29476i
$$214$$ 1116.00 + 1440.75i 0.356487 + 0.460223i
$$215$$ 2009.18 0.637325
$$216$$ −3103.46 668.000i −0.977610 0.210424i
$$217$$ −1740.00 −0.544327
$$218$$ 1846.37 + 2383.65i 0.573632 + 0.740555i
$$219$$ 1420.28 1587.92i 0.438236 0.489963i
$$220$$ 2400.00 + 619.677i 0.735491 + 0.189903i
$$221$$ 357.771i 0.108897i
$$222$$ 1905.83 + 134.909i 0.576176 + 0.0407861i
$$223$$ 472.504i 0.141889i 0.997480 + 0.0709444i $$0.0226013\pi$$
−0.997480 + 0.0709444i $$0.977399\pi$$
$$224$$ −1385.64 + 214.663i −0.413313 + 0.0640301i
$$225$$ −135.000 1207.48i −0.0400000 0.357771i
$$226$$ −2320.00 + 1797.06i −0.682850 + 0.528933i
$$227$$ 505.759 0.147878 0.0739392 0.997263i $$-0.476443\pi$$
0.0739392 + 0.997263i $$0.476443\pi$$
$$228$$ 2410.61 1608.42i 0.700206 0.467194i
$$229$$ 4094.00 1.18139 0.590697 0.806894i $$-0.298853\pi$$
0.590697 + 0.806894i $$0.298853\pi$$
$$230$$ 1939.90 1502.64i 0.556144 0.430787i
$$231$$ −1039.23 929.516i −0.296001 0.264752i
$$232$$ −1360.00 3160.35i −0.384864 0.894342i
$$233$$ 5277.12i 1.48376i −0.670534 0.741879i $$-0.733935\pi$$
0.670534 0.741879i $$-0.266065\pi$$
$$234$$ 548.038 531.840i 0.153104 0.148579i
$$235$$ 1735.10i 0.481639i
$$236$$ 346.410 1341.64i 0.0955482 0.370057i
$$237$$ −330.000 295.161i −0.0904464 0.0808977i
$$238$$ 480.000 + 619.677i 0.130730 + 0.168772i
$$239$$ −5681.13 −1.53758 −0.768790 0.639502i $$-0.779141\pi$$
−0.768790 + 0.639502i $$0.779141\pi$$
$$240$$ −979.897 2808.41i −0.263550 0.755342i
$$241$$ −1198.00 −0.320207 −0.160104 0.987100i $$-0.551183\pi$$
−0.160104 + 0.987100i $$0.551183\pi$$
$$242$$ 226.899 + 292.925i 0.0602711 + 0.0778096i
$$243$$ −1839.44 + 3311.40i −0.485597 + 0.874183i
$$244$$ 884.000 3423.72i 0.231936 0.898283i
$$245$$ 2531.23i 0.660058i
$$246$$ −129.948 + 1835.75i −0.0336797 + 0.475786i
$$247$$ 697.137i 0.179586i
$$248$$ 2009.18 + 4668.91i 0.514448 + 1.19547i
$$249$$ 4344.00 4856.74i 1.10558 1.23608i
$$250$$ 3400.00 2633.63i 0.860140 0.666261i
$$251$$ 4260.84 1.07148 0.535741 0.844382i $$-0.320032\pi$$
0.535741 + 0.844382i $$0.320032\pi$$
$$252$$ −235.692 + 1656.44i −0.0589175 + 0.414072i
$$253$$ −3360.00 −0.834946
$$254$$ 4104.96 3179.69i 1.01405 0.785478i
$$255$$ −1108.51 + 1239.35i −0.272226 + 0.304358i
$$256$$ 2176.00 + 3470.19i 0.531250 + 0.847215i
$$257$$ 3148.38i 0.764166i 0.924128 + 0.382083i $$0.124793\pi$$
−0.924128 + 0.382083i $$0.875207\pi$$
$$258$$ −233.116 + 3293.18i −0.0562525 + 0.794668i
$$259$$ 1006.98i 0.241585i
$$260$$ 692.820 + 178.885i 0.165257 + 0.0426692i
$$261$$ −4080.00 + 456.158i −0.967608 + 0.108182i
$$262$$ −780.000 1006.98i −0.183926 0.237447i
$$263$$ −4253.92 −0.997368 −0.498684 0.866784i $$-0.666183\pi$$
−0.498684 + 0.866784i $$0.666183\pi$$
$$264$$ −1294.15 + 3861.86i −0.301703 + 0.900307i
$$265$$ −4880.00 −1.13123
$$266$$ −935.307 1207.48i −0.215592 0.278328i
$$267$$ 3256.26 + 2912.48i 0.746366 + 0.667570i
$$268$$ −5700.00 1471.73i −1.29919 0.335449i
$$269$$ 44.7214i 0.0101365i −0.999987 0.00506823i $$-0.998387\pi$$
0.999987 0.00506823i $$-0.00161328\pi$$
$$270$$ −3546.31 + 144.313i −0.799338 + 0.0325281i
$$271$$ 8760.69i 1.96374i −0.189552 0.981871i $$-0.560704\pi$$
0.189552 0.981871i $$-0.439296\pi$$
$$272$$ 1108.51 2003.52i 0.247108 0.446622i
$$273$$ −300.000 268.328i −0.0665085 0.0594870i
$$274$$ 200.000 154.919i 0.0440965 0.0341570i
$$275$$ −1558.85 −0.341825
$$276$$ 2237.85 + 3353.96i 0.488052 + 0.731467i
$$277$$ 6350.00 1.37738 0.688690 0.725055i $$-0.258186\pi$$
0.688690 + 0.725055i $$0.258186\pi$$
$$278$$ −4382.09 + 3394.35i −0.945396 + 0.732301i
$$279$$ 6027.54 673.899i 1.29340 0.144607i
$$280$$ −1440.00 + 619.677i −0.307344 + 0.132260i
$$281$$ 5563.34i 1.18107i 0.807012 + 0.590535i $$0.201083\pi$$
−0.807012 + 0.590535i $$0.798917\pi$$
$$282$$ −2843.94 201.315i −0.600546 0.0425112i
$$283$$ 6777.72i 1.42365i 0.702356 + 0.711826i $$0.252132\pi$$
−0.702356 + 0.711826i $$0.747868\pi$$
$$284$$ 2078.46 8049.84i 0.434275 1.68194i
$$285$$ 2160.00 2414.95i 0.448938 0.501928i
$$286$$ −600.000 774.597i −0.124052 0.160150i
$$287$$ 969.948 0.199492
$$288$$ 4716.86 1280.27i 0.965082 0.261946i
$$289$$ 3633.00 0.739467
$$290$$ −2355.59 3041.05i −0.476983 0.615782i
$$291$$ 2667.36 2982.20i 0.537331 0.600754i
$$292$$ −820.000 + 3175.85i −0.164339 + 0.636481i
$$293$$ 652.932i 0.130187i 0.997879 + 0.0650933i $$0.0207345\pi$$
−0.997879 + 0.0650933i $$0.979265\pi$$
$$294$$ −4148.85 293.687i −0.823013 0.0582591i
$$295$$ 1549.19i 0.305754i
$$296$$ −2702.00 + 1162.76i −0.530576 + 0.228324i
$$297$$ 3960.00 + 2817.45i 0.773678 + 0.550454i
$$298$$ 3620.00 2804.04i 0.703695 0.545079i
$$299$$ −969.948 −0.187604
$$300$$ 1038.23 + 1556.05i 0.199808 + 0.299461i
$$301$$ 1740.00 0.333196
$$302$$ 1264.40 979.398i 0.240920 0.186616i
$$303$$ −5785.05 5174.31i −1.09684 0.981043i
$$304$$ −2160.00 + 3903.97i −0.407515 + 0.736539i
$$305$$ 3953.37i 0.742194i
$$306$$ −1902.77 1960.72i −0.355471 0.366297i
$$307$$ 1556.94i 0.289444i −0.989472 0.144722i $$-0.953771\pi$$
0.989472 0.144722i $$-0.0462287\pi$$
$$308$$ 2078.46 + 536.656i 0.384517 + 0.0992819i
$$309$$ −5250.00 4695.74i −0.966544 0.864503i
$$310$$ 3480.00 + 4492.66i 0.637583 + 0.823116i
$$311$$ 3256.26 0.593715 0.296857 0.954922i $$-0.404061\pi$$
0.296857 + 0.954922i $$0.404061\pi$$
$$312$$ −373.590 + 1114.82i −0.0677896 + 0.202290i
$$313$$ −7030.00 −1.26952 −0.634759 0.772710i $$-0.718901\pi$$
−0.634759 + 0.772710i $$0.718901\pi$$
$$314$$ 1264.40 + 1632.33i 0.227242 + 0.293368i
$$315$$ 207.846 + 1859.03i 0.0371771 + 0.332522i
$$316$$ 660.000 + 170.411i 0.117493 + 0.0303367i
$$317$$ 491.935i 0.0871603i 0.999050 + 0.0435802i $$0.0138764\pi$$
−0.999050 + 0.0435802i $$0.986124\pi$$
$$318$$ 566.204 7998.64i 0.0998464 1.41051i
$$319$$ 5267.26i 0.924482i
$$320$$ 3325.54 + 3148.38i 0.580948 + 0.550000i
$$321$$ −2232.00 + 2495.45i −0.388094 + 0.433902i
$$322$$ 1680.00 1301.32i 0.290754 0.225217i
$$323$$ 2494.15 0.429654
$$324$$ 174.923 5829.38i 0.0299937 0.999550i
$$325$$ −450.000 −0.0768046
$$326$$ −571.577 + 442.741i −0.0971065 + 0.0752183i
$$327$$ −3692.73 + 4128.60i −0.624491 + 0.698202i
$$328$$ −1120.00 2602.64i −0.188542 0.438131i
$$329$$ 1502.64i 0.251803i
$$330$$ −321.539 + 4542.31i −0.0536368 + 0.757716i
$$331$$ 4237.04i 0.703592i 0.936077 + 0.351796i $$0.114429\pi$$
−0.936077 + 0.351796i $$0.885571\pi$$
$$332$$ −2508.01 + 9713.48i −0.414593 + 1.60571i
$$333$$ 390.000 + 3488.27i 0.0641798 + 0.574041i
$$334$$ −24.0000 30.9839i −0.00393180 0.00507593i
$$335$$ −6581.79 −1.07344
$$336$$ −848.616 2432.15i −0.137785 0.394895i
$$337$$ 1490.00 0.240847 0.120424 0.992723i $$-0.461575\pi$$
0.120424 + 0.992723i $$0.461575\pi$$
$$338$$ 3632.11 + 4689.03i 0.584499 + 0.754585i
$$339$$ −4018.36 3594.13i −0.643797 0.575830i
$$340$$ 640.000 2478.71i 0.102085 0.395373i
$$341$$ 7781.52i 1.23576i
$$342$$ 3707.65 + 3820.58i 0.586219 + 0.604074i
$$343$$ 4848.98i 0.763324i
$$344$$ −2009.18 4668.91i −0.314906 0.731775i
$$345$$ 3360.00 + 3005.28i 0.524337 + 0.468981i
$$346$$ −2500.00 + 1936.49i −0.388442 + 0.300886i
$$347$$ 1988.39 0.307616 0.153808 0.988101i $$-0.450846\pi$$
0.153808 + 0.988101i $$0.450846\pi$$
$$348$$ 5257.79 3508.13i 0.809906 0.540389i
$$349$$ −2074.00 −0.318105 −0.159053 0.987270i $$-0.550844\pi$$
−0.159053 + 0.987270i $$0.550844\pi$$
$$350$$ 779.423 603.738i 0.119034 0.0922033i
$$351$$ 1143.15 + 813.327i 0.173838 + 0.123681i
$$352$$ −960.000 6196.77i −0.145364 0.938321i
$$353$$ 8658.06i 1.30544i −0.757597 0.652722i $$-0.773627\pi$$
0.757597 0.652722i $$-0.226373\pi$$
$$354$$ 2539.23 + 179.746i 0.381239 + 0.0269870i
$$355$$ 9295.16i 1.38968i
$$356$$ −6512.51 1681.52i −0.969557 0.250339i
$$357$$ −960.000 + 1073.31i −0.142321 + 0.159120i
$$358$$ 2340.00 + 3020.93i 0.345455 + 0.445980i
$$359$$ 8106.00 1.19169 0.595847 0.803098i $$-0.296816\pi$$
0.595847 + 0.803098i $$0.296816\pi$$
$$360$$ 4748.31 2704.33i 0.695160 0.395919i
$$361$$ 1999.00 0.291442
$$362$$ −2185.85 2821.92i −0.317364 0.409715i
$$363$$ −453.797 + 507.361i −0.0656148 + 0.0733596i
$$364$$ 600.000 + 154.919i 0.0863971 + 0.0223076i
$$365$$ 3667.15i 0.525884i
$$366$$ 6479.83 + 458.691i 0.925427 + 0.0655087i
$$367$$ 7893.14i 1.12267i −0.827590 0.561333i $$-0.810289\pi$$
0.827590 0.561333i $$-0.189711\pi$$
$$368$$ −5431.71 3005.28i −0.769423 0.425709i
$$369$$ −3360.00 + 375.659i −0.474023 + 0.0529974i
$$370$$ −2600.00 + 2013.95i −0.365318 + 0.282974i
$$371$$ −4226.20 −0.591411
$$372$$ −7767.54 + 5182.69i −1.08260 + 0.722338i
$$373$$ 4910.00 0.681582 0.340791 0.940139i $$-0.389305\pi$$
0.340791 + 0.940139i $$0.389305\pi$$
$$374$$ −2771.28 + 2146.63i −0.383154 + 0.296790i
$$375$$ 5888.97 + 5267.26i 0.810947 + 0.725333i
$$376$$ 4032.00 1735.10i 0.553017 0.237981i
$$377$$ 1520.53i 0.207722i
$$378$$ −3071.19 + 124.979i −0.417897 + 0.0170058i
$$379$$ 3137.12i 0.425179i −0.977142 0.212590i $$-0.931810\pi$$
0.977142 0.212590i $$-0.0681897\pi$$
$$380$$ −1247.08 + 4829.91i −0.168352 + 0.652024i
$$381$$ 7110.00 + 6359.38i 0.956053 + 0.855120i
$$382$$ −4800.00 6196.77i −0.642904 0.829986i
$$383$$ 6207.67 0.828191 0.414095 0.910233i $$-0.364098\pi$$
0.414095 + 0.910233i $$0.364098\pi$$
$$384$$ −5546.26 + 5085.48i −0.737060 + 0.675827i
$$385$$ 2400.00 0.317702
$$386$$ 329.090 + 424.853i 0.0433944 + 0.0560219i
$$387$$ −6027.54 + 673.899i −0.791723 + 0.0885174i
$$388$$ −1540.00 + 5964.39i −0.201499 + 0.780403i
$$389$$ 9454.10i 1.23224i 0.787652 + 0.616120i $$0.211297\pi$$
−0.787652 + 0.616120i $$0.788703\pi$$
$$390$$ −92.8203 + 1311.25i −0.0120516 + 0.170251i
$$391$$ 3470.19i 0.448837i
$$392$$ 5882.04 2531.23i 0.757878 0.326139i
$$393$$ 1560.00 1744.13i 0.200233 0.223867i
$$394$$ −4780.00 + 3702.57i −0.611200 + 0.473434i
$$395$$ 762.102 0.0970773
$$396$$ −7407.85 1054.05i −0.940046 0.133757i
$$397$$ −10570.0 −1.33625 −0.668127 0.744047i $$-0.732904\pi$$
−0.668127 + 0.744047i $$0.732904\pi$$
$$398$$ 571.577 442.741i 0.0719863 0.0557604i
$$399$$ 1870.61 2091.41i 0.234706 0.262410i
$$400$$ −2520.00 1394.27i −0.315000 0.174284i
$$401$$ 1681.52i 0.209405i −0.994504 0.104702i $$-0.966611\pi$$
0.994504 0.104702i $$-0.0333890\pi$$
$$402$$ 763.655 10788.0i 0.0947454 1.33845i
$$403$$ 2246.33i 0.277662i
$$404$$ 11570.1 + 2987.39i 1.42484 + 0.367891i
$$405$$ −1440.00 6359.38i −0.176677 0.780247i
$$406$$ −2040.00 2633.63i −0.249368 0.321933i
$$407$$ 4503.33 0.548457
$$408$$ 3988.51 + 1336.60i 0.483973 + 0.162185i
$$409$$ −3574.00 −0.432085 −0.216043 0.976384i $$-0.569315\pi$$
−0.216043 + 0.976384i $$0.569315\pi$$
$$410$$ −1939.90 2504.40i −0.233670 0.301667i
$$411$$ 346.410 + 309.839i 0.0415746 + 0.0371854i
$$412$$ 10500.0 + 2711.09i 1.25558 + 0.324189i
$$413$$ 1341.64i 0.159849i
$$414$$ −5315.69 + 5158.57i −0.631043 + 0.612392i
$$415$$ 11216.2i 1.32670i
$$416$$ −277.128 1788.85i −0.0326618 0.210831i
$$417$$ −7590.00 6788.70i −0.891328 0.797228i
$$418$$ 5400.00 4182.82i 0.631872 0.489446i
$$419$$ −15346.0 −1.78926 −0.894630 0.446808i $$-0.852561\pi$$
−0.894630 + 0.446808i $$0.852561\pi$$
$$420$$ −1598.46 2395.69i −0.185707 0.278328i
$$421$$ 3518.00 0.407261 0.203630 0.979048i $$-0.434726\pi$$
0.203630 + 0.979048i $$0.434726\pi$$
$$422$$ 1229.76 952.565i 0.141857 0.109882i
$$423$$ −581.969 5205.29i −0.0668943 0.598321i
$$424$$ 4880.00 + 11340.1i 0.558948 + 1.29888i
$$425$$ 1609.97i 0.183753i
$$426$$ 15235.4 + 1078.47i 1.73276 + 0.122658i
$$427$$ 3423.72i 0.388022i
$$428$$ 1288.65 4990.90i 0.145535 0.563655i
$$429$$ 1200.00 1341.64i 0.135050 0.150991i
$$430$$ −3480.00 4492.66i −0.390280 0.503850i
$$431$$ −12886.5 −1.44018 −0.720091 0.693879i $$-0.755900\pi$$
−0.720091 + 0.693879i $$0.755900\pi$$
$$432$$ 3881.66 + 8096.56i 0.432307 + 0.901727i
$$433$$ 14450.0 1.60375 0.801874 0.597493i $$-0.203837\pi$$
0.801874 + 0.597493i $$0.203837\pi$$
$$434$$ 3013.77 + 3890.76i 0.333331 + 0.430328i
$$435$$ 4711.18 5267.26i 0.519273 0.580565i
$$436$$ 2132.00 8257.20i 0.234184 0.906991i
$$437$$ 6761.87i 0.740192i
$$438$$ −6010.70 425.483i −0.655714 0.0464163i
$$439$$ 15065.9i 1.63794i 0.573835 + 0.818971i $$0.305455\pi$$
−0.573835 + 0.818971i $$0.694545\pi$$
$$440$$ −2771.28 6439.88i −0.300263 0.697748i
$$441$$ −849.000 7593.69i −0.0916748 0.819964i
$$442$$ −800.000 + 619.677i −0.0860908 + 0.0666856i
$$443$$ 3041.48 0.326197 0.163098 0.986610i $$-0.447851\pi$$
0.163098 + 0.986610i $$0.447851\pi$$
$$444$$ −2999.33 4495.24i −0.320590 0.480484i
$$445$$ −7520.00 −0.801084
$$446$$ 1056.55 818.401i 0.112173 0.0868888i
$$447$$ 6270.02 + 5608.08i 0.663450 + 0.593407i
$$448$$ 2880.00 + 2726.58i 0.303721 + 0.287542i
$$449$$ 14310.8i 1.50416i 0.659069 + 0.752082i $$0.270951\pi$$
−0.659069 + 0.752082i $$0.729049\pi$$
$$450$$ −2466.17 + 2393.28i −0.258348 + 0.250712i
$$451$$ 4337.74i 0.452896i
$$452$$ 8036.72 + 2075.07i 0.836317 + 0.215936i
$$453$$ 2190.00 + 1958.80i 0.227142 + 0.203162i
$$454$$ −876.000 1130.91i −0.0905566 0.116908i
$$455$$ 692.820 0.0713844
$$456$$ −7771.84 2604.43i −0.798136 0.267464i
$$457$$ −3430.00 −0.351091 −0.175546 0.984471i $$-0.556169\pi$$
−0.175546 + 0.984471i $$0.556169\pi$$
$$458$$ −7091.02 9154.46i −0.723453 0.933974i
$$459$$ 2909.85 4089.87i 0.295904 0.415902i
$$460$$ −6720.00 1735.10i −0.681134 0.175868i
$$461$$ 3908.65i 0.394889i −0.980314 0.197445i $$-0.936736\pi$$
0.980314 0.197445i $$-0.0632642\pi$$
$$462$$ −278.461 + 3933.76i −0.0280415 + 0.396136i
$$463$$ 18179.8i 1.82481i −0.409291 0.912404i $$-0.634224\pi$$
0.409291 0.912404i $$-0.365776\pi$$
$$464$$ −4711.18 + 8514.95i −0.471360 + 0.851932i
$$465$$ −6960.00 + 7781.52i −0.694112 + 0.776041i
$$466$$ −11800.0 + 9140.24i −1.17301 + 0.908613i
$$467$$ −1849.83 −0.183298 −0.0916488 0.995791i $$-0.529214\pi$$
−0.0916488 + 0.995791i $$0.529214\pi$$
$$468$$ −2138.46 304.277i −0.211219 0.0300539i
$$469$$ −5700.00 −0.561197
$$470$$ 3879.79 3005.28i 0.380769 0.294943i
$$471$$ −2528.79 + 2827.28i −0.247390 + 0.276590i
$$472$$ −3600.00 + 1549.19i −0.351067 + 0.151075i
$$473$$ 7781.52i 0.756437i
$$474$$ −88.4232 + 1249.14i −0.00856838 + 0.121044i
$$475$$ 3137.12i 0.303033i
$$476$$ 554.256 2146.63i 0.0533704 0.206703i
$$477$$ 14640.0 1636.80i 1.40528 0.157115i
$$478$$ 9840.00 + 12703.4i 0.941571 + 1.21556i
$$479$$ 15242.0 1.45392 0.726959 0.686681i $$-0.240933\pi$$
0.726959 + 0.686681i $$0.240933\pi$$
$$480$$ −4582.56 + 7055.42i −0.435759 + 0.670905i
$$481$$ 1300.00 0.123233
$$482$$ 2075.00 + 2678.81i 0.196086 + 0.253146i
$$483$$ 2909.85 + 2602.64i 0.274125 + 0.245185i
$$484$$ 262.000 1014.72i 0.0246056 0.0952969i
$$485$$ 6887.09i 0.644797i
$$486$$ 10590.5 1622.41i 0.988468 0.151428i
$$487$$ 9783.16i 0.910302i −0.890414 0.455151i $$-0.849585\pi$$
0.890414 0.455151i $$-0.150415\pi$$
$$488$$ −9186.80 + 3953.37i −0.852186 + 0.366722i
$$489$$ −990.000 885.483i −0.0915529 0.0818874i
$$490$$ 5660.00 4384.22i 0.521822 0.404202i
$$491$$ 6893.56 0.633609 0.316805 0.948491i $$-0.397390\pi$$
0.316805 + 0.948491i $$0.397390\pi$$
$$492$$ 4329.95 2889.05i 0.396767 0.264732i
$$493$$ 5440.00 0.496968
$$494$$ 1558.85 1207.48i 0.141975 0.109974i
$$495$$ −8313.84 + 929.516i −0.754908 + 0.0844013i
$$496$$ 6960.00 12579.4i 0.630067 1.13878i
$$497$$ 8049.84i 0.726529i
$$498$$ −18384.0 1301.36i −1.65423 0.117099i
$$499$$ 1309.07i 0.117439i −0.998275 0.0587194i $$-0.981298\pi$$
0.998275 0.0587194i $$-0.0187017\pi$$
$$500$$ −11777.9 3041.05i −1.05345 0.272000i
$$501$$ 48.0000 53.6656i 0.00428040 0.00478564i
$$502$$ −7380.00 9527.54i −0.656146 0.847081i
$$503$$ −7939.72 −0.703806 −0.351903 0.936036i $$-0.614465\pi$$
−0.351903 + 0.936036i $$0.614465\pi$$
$$504$$ 4112.15 2342.02i 0.363432 0.206988i
$$505$$ 13360.0 1.17725
$$506$$ 5819.69 + 7513.19i 0.511298 + 0.660083i
$$507$$ −7264.22 + 8121.65i −0.636322 + 0.711430i
$$508$$ −14220.0 3671.59i −1.24195 0.320670i
$$509$$ 14534.4i 1.26567i −0.774285 0.632837i $$-0.781890\pi$$
0.774285 0.632837i $$-0.218110\pi$$
$$510$$ 4691.28 + 332.084i 0.407320 + 0.0288332i
$$511$$ 3175.85i 0.274934i
$$512$$ 3990.65 10876.2i 0.344459 0.938801i
$$513$$ −5670.00 + 7969.35i −0.487986 + 0.685878i
$$514$$ 7040.00 5453.16i 0.604127 0.467954i
$$515$$ 12124.4 1.03740
$$516$$ 7767.54 5182.69i 0.662687 0.442161i
$$517$$ −6720.00 −0.571654
$$518$$ −2251.67 + 1744.13i −0.190989 + 0.147940i
$$519$$ −4330.13 3872.98i −0.366226 0.327563i
$$520$$ −800.000 1859.03i −0.0674660 0.156777i
$$521$$ 9355.71i 0.786720i −0.919385 0.393360i $$-0.871313\pi$$
0.919385 0.393360i $$-0.128687\pi$$
$$522$$ 8086.77 + 8333.07i 0.678062 + 0.698714i
$$523$$ 10062.0i 0.841264i 0.907231 + 0.420632i $$0.138192\pi$$
−0.907231 + 0.420632i $$0.861808\pi$$
$$524$$ −900.666 + 3488.27i −0.0750874 + 0.290812i
$$525$$ 1350.00 + 1207.48i 0.112226 + 0.100378i
$$526$$ 7368.00 + 9512.05i 0.610761 + 0.788489i
$$527$$ −8036.72 −0.664298
$$528$$ 10876.9 3795.12i 0.896510 0.312806i
$$529$$ −2759.00 −0.226761
$$530$$ 8452.41 + 10912.0i 0.692734 + 0.894316i
$$531$$ 519.615 + 4647.58i 0.0424659 + 0.379826i
$$532$$ −1080.00 + 4182.82i −0.0880149 + 0.340880i
$$533$$ 1252.20i 0.101761i
$$534$$ 872.511 12325.8i 0.0707065 0.998855i
$$535$$ 5763.00i 0.465712i
$$536$$ 6581.79 + 15294.7i 0.530392 + 1.23252i
$$537$$ −4680.00 + 5232.40i −0.376084 + 0.420474i
$$538$$ −100.000 + 77.4597i −0.00801358 + 0.00620729i
$$539$$ −9803.41 −0.783419
$$540$$ 6465.08 + 7679.83i 0.515209 + 0.612013i
$$541$$ −23962.0 −1.90426 −0.952132 0.305687i $$-0.901114\pi$$
−0.952132 + 0.305687i $$0.901114\pi$$
$$542$$ −19589.5 + 15174.0i −1.55247 + 1.20254i
$$543$$ 4371.70 4887.70i 0.345502 0.386283i
$$544$$ −6400.00 + 991.484i −0.504408 + 0.0781425i
$$545$$ 9534.59i 0.749389i
$$546$$ −80.3848 + 1135.58i −0.00630064 + 0.0890078i
$$547$$ 15112.4i 1.18128i 0.806936 + 0.590639i $$0.201124\pi$$
−0.806936 + 0.590639i $$0.798876\pi$$
$$548$$ −692.820 178.885i −0.0540070 0.0139445i
$$549$$ 1326.00 + 11860.1i 0.103083 + 0.921998i
$$550$$ 2700.00 + 3485.69i 0.209324 + 0.270237i
$$551$$ −10600.2 −0.819567
$$552$$ 3623.63 10813.2i 0.279406 0.833770i
$$553$$ 660.000 0.0507524
$$554$$ −10998.5 14199.0i −0.843470 1.08892i
$$555$$ −4503.33 4027.90i −0.344425 0.308063i
$$556$$ 15180.0 + 3919.46i 1.15787 + 0.298961i
$$557$$ 16055.0i 1.22131i 0.791896 + 0.610656i $$0.209094\pi$$
−0.791896 + 0.610656i $$0.790906\pi$$
$$558$$ −11946.9 12310.8i −0.906365 0.933971i
$$559$$ 2246.33i 0.169964i
$$560$$ 3879.79 + 2146.63i 0.292770 + 0.161985i
$$561$$ −4800.00 4293.25i −0.361241 0.323104i
$$562$$ 12440.0 9635.98i 0.933718 0.723255i
$$563$$ 25142.4 1.88211 0.941055 0.338254i $$-0.109836\pi$$
0.941055 + 0.338254i $$0.109836\pi$$
$$564$$ 4475.69 + 6707.93i 0.334150 + 0.500806i
$$565$$ 9280.00 0.690996
$$566$$ 15155.4 11739.4i 1.12550 0.871806i
$$567$$ −1247.08 5507.38i −0.0923674 0.407916i
$$568$$ −21600.0 + 9295.16i −1.59563 + 0.686648i
$$569$$ 23416.1i 1.72523i −0.505864 0.862613i $$-0.668826\pi$$
0.505864 0.862613i $$-0.331174\pi$$
$$570$$ −9141.23 647.085i −0.671726 0.0475498i
$$571$$ 4918.69i 0.360492i 0.983622 + 0.180246i $$0.0576893\pi$$
−0.983622 + 0.180246i $$0.942311\pi$$
$$572$$ −692.820 + 2683.28i −0.0506438 + 0.196143i
$$573$$ 9600.00 10733.1i 0.699905 0.782518i
$$574$$ −1680.00 2168.87i −0.122163 0.157712i
$$575$$ 4364.77 0.316562
$$576$$ −11032.6 8329.73i −0.798077 0.602556i
$$577$$ 19490.0 1.40620 0.703102 0.711089i $$-0.251798\pi$$
0.703102 + 0.711089i $$0.251798\pi$$
$$578$$ −6292.54 8123.63i −0.452829 0.584600i
$$579$$ −658.179 + 735.867i −0.0472418 + 0.0528179i
$$580$$ −2720.00 + 10534.5i −0.194727 + 0.754176i
$$581$$ 9713.48i 0.693602i
$$582$$ −11288.4 799.077i −0.803985 0.0569121i
$$583$$ 18900.2i 1.34265i
$$584$$ 8521.69 3667.15i 0.603819 0.259842i
$$585$$ −2400.00 + 268.328i −0.169620 + 0.0189641i
$$586$$ 1460.00 1130.91i 0.102922 0.0797227i
$$587$$ −1364.86 −0.0959687 −0.0479844 0.998848i $$-0.515280\pi$$
−0.0479844 + 0.998848i $$0.515280\pi$$
$$588$$ 6529.32 + 9785.80i 0.457933 + 0.686326i
$$589$$ 15660.0 1.09552
$$590$$ −3464.10 + 2683.28i −0.241720 + 0.187236i
$$591$$ −8279.20 7405.14i −0.576245 0.515409i
$$592$$ 7280.00 + 4027.90i 0.505416 + 0.279638i
$$593$$ 25795.3i 1.78632i 0.449743 + 0.893158i $$0.351515\pi$$
−0.449743 + 0.893158i $$0.648485\pi$$
$$594$$ −558.921 13734.8i −0.0386074 0.948729i
$$595$$ 2478.71i 0.170785i
$$596$$ −12540.0 3237.83i −0.861846 0.222528i
$$597$$ 990.000 + 885.483i 0.0678694 + 0.0607042i
$$598$$ 1680.00 + 2168.87i 0.114883 + 0.148314i
$$599$$ 2424.87 0.165405 0.0827025 0.996574i $$-0.473645\pi$$
0.0827025 + 0.996574i $$0.473645\pi$$
$$600$$ 1681.15 5016.70i 0.114388 0.341343i
$$601$$ −8758.00 −0.594420 −0.297210 0.954812i $$-0.596056\pi$$
−0.297210 + 0.954812i $$0.596056\pi$$
$$602$$ −3013.77 3890.76i −0.204040 0.263414i
$$603$$ 19745.4 2207.60i 1.33349 0.149089i
$$604$$ −4380.00 1130.91i −0.295066 0.0761856i
$$605$$ 1171.70i 0.0787378i
$$606$$ −1550.10 + 21897.9i −0.103908 + 1.46789i
$$607$$ 19558.6i 1.30784i 0.756565 + 0.653919i $$0.226876\pi$$
−0.756565 + 0.653919i $$0.773124\pi$$
$$608$$ 12470.8 1931.96i 0.831836 0.128867i
$$609$$ 4080.00 4561.58i 0.271478 0.303521i
$$610$$ −8840.00 + 6847.43i −0.586756 + 0.454499i
$$611$$ −1939.90 −0.128445
$$612$$ −1088.62 + 7650.79i −0.0719031 + 0.505335i
$$613$$ −16450.0 −1.08386 −0.541932 0.840422i $$-0.682307\pi$$
−0.541932 + 0.840422i $$0.682307\pi$$
$$614$$ −3481.42 + 2696.70i −0.228825 + 0.177247i
$$615$$ 3879.79 4337.74i 0.254388 0.284414i
$$616$$ −2400.00 5577.10i −0.156978 0.364785i
$$617$$ 8461.28i 0.552088i 0.961145 + 0.276044i $$0.0890236\pi$$
−0.961145 + 0.276044i $$0.910976\pi$$
$$618$$ −1406.73 + 19872.6i −0.0915649 + 1.29352i
$$619$$ 19930.4i 1.29413i −0.762433 0.647067i $$-0.775995\pi$$
0.762433 0.647067i $$-0.224005\pi$$
$$620$$ 4018.36 15563.0i 0.260292 1.00811i
$$621$$ −11088.0 7888.85i −0.716499 0.509772i
$$622$$ −5640.00 7281.21i −0.363575 0.469373i
$$623$$ −6512.51 −0.418809
$$624$$ 3139.90 1095.56i 0.201437 0.0702843i
$$625$$ −7975.00 −0.510400
$$626$$ 12176.3 + 15719.6i 0.777418 + 1.00364i
$$627$$ 9353.07 + 8365.64i 0.595735 + 0.532842i
$$628$$ 1460.00 5654.56i 0.0927712 0.359301i
$$629$$ 4651.02i 0.294830i
$$630$$ 3796.92 3684.70i 0.240116 0.233019i
$$631$$ 12199.9i 0.769683i −0.922983 0.384842i $$-0.874256\pi$$
0.922983 0.384842i $$-0.125744\pi$$
$$632$$ −762.102 1770.97i −0.0479665 0.111464i
$$633$$ 2130.00 + 1905.13i 0.133744 + 0.119624i
$$634$$ 1100.00 852.056i 0.0689063 0.0533746i
$$635$$ −16419.8 −1.02614
$$636$$ −18866.2 + 12588.0i −1.17625 + 0.784821i
$$637$$ −2830.00 −0.176026
$$638$$ 11777.9 9123.16i 0.730867 0.566127i
$$639$$ 3117.69 + 27885.5i 0.193011 + 1.72634i
$$640$$ 1280.00 12889.3i 0.0790569 0.796084i
$$641$$ 7012.31i 0.432090i 0.976383 + 0.216045i $$0.0693158\pi$$
−0.976383 + 0.216045i $$0.930684\pi$$
$$642$$ 9445.94 + 668.654i 0.580688 + 0.0411054i
$$643$$ 15979.9i 0.980073i 0.871702 + 0.490036i $$0.163017\pi$$
−0.871702 + 0.490036i $$0.836983\pi$$
$$644$$ −5819.69 1502.64i −0.356099 0.0919444i
$$645$$ 6960.00 7781.52i 0.424883 0.475034i
$$646$$ −4320.00 5577.10i −0.263109 0.339672i
$$647$$ −17999.5 −1.09371 −0.546856 0.837226i $$-0.684176\pi$$
−0.546856 + 0.837226i $$0.684176\pi$$
$$648$$ −13337.9 + 9705.63i −0.808581 + 0.588385i
$$649$$ 6000.00 0.362898
$$650$$ 779.423 + 1006.23i 0.0470330 + 0.0607194i
$$651$$ −6027.54 + 6738.99i −0.362884 + 0.405717i
$$652$$ 1980.00 + 511.234i 0.118931 + 0.0307078i
$$653$$ 5196.62i 0.311423i −0.987803 0.155712i $$-0.950233\pi$$
0.987803 0.155712i $$-0.0497671\pi$$
$$654$$ 15627.8 + 1106.26i 0.934398 + 0.0661437i
$$655$$ 4027.90i 0.240280i
$$656$$ −3879.79 + 7012.31i −0.230915 + 0.417355i
$$657$$ −1230.00 11001.5i −0.0730394 0.653284i
$$658$$ 3360.00 2602.64i 0.199068 0.154197i
$$659$$ −6062.18 −0.358344 −0.179172 0.983818i $$-0.557342\pi$$
−0.179172 + 0.983818i $$0.557342\pi$$
$$660$$ 10713.8 7148.53i 0.631872 0.421601i
$$661$$ 9422.00 0.554423 0.277211 0.960809i $$-0.410590\pi$$
0.277211 + 0.960809i $$0.410590\pi$$
$$662$$ 9474.32 7338.78i 0.556238 0.430860i
$$663$$ −1385.64 1239.35i −0.0811672 0.0725981i
$$664$$ 26064.0 11216.2i 1.52331 0.655529i
$$665$$ 4829.91i 0.281648i
$$666$$ 7124.50 6913.92i 0.414518 0.402266i
$$667$$ 14748.3i 0.856158i
$$668$$ −27.7128 + 107.331i −0.00160515 + 0.00621672i
$$669$$ 1830.00 + 1636.80i 0.105758 + 0.0945925i
$$670$$ 11400.0 + 14717.3i 0.657344 + 0.848627i
$$671$$ 15311.3 0.880905
$$672$$ −3968.62 + 6110.18i −0.227816 + 0.350752i
$$673$$ −17470.0 −1.00062 −0.500311 0.865846i $$-0.666781\pi$$
−0.500311 + 0.865846i $$0.666781\pi$$
$$674$$ −2580.76 3331.74i −0.147488 0.190406i
$$675$$ −5144.19 3659.97i −0.293333 0.208700i
$$676$$ 4194.00 16243.3i 0.238621 0.924175i
$$677$$ 20813.3i 1.18157i −0.806830 0.590784i $$-0.798819\pi$$
0.806830 0.590784i $$-0.201181\pi$$
$$678$$ −1076.72 + 15210.5i −0.0609897 + 0.861589i
$$679$$ 5964.39i 0.337102i
$$680$$ −6651.08 + 2862.17i −0.375084 + 0.161410i
$$681$$ 1752.00 1958.80i 0.0985856 0.110222i
$$682$$ −17400.0 + 13478.0i −0.976951 + 0.756743i
$$683$$ −12616.3 −0.706805 −0.353402 0.935471i $$-0.614975\pi$$
−0.353402 + 0.935471i $$0.614975\pi$$
$$684$$ 2121.23 14908.0i 0.118578 0.833365i
$$685$$ −800.000 −0.0446225
$$686$$ 10842.6 8398.67i 0.603460 0.467438i
$$687$$ 14182.0 15856.0i 0.787596 0.880559i
$$688$$ −6960.00 + 12579.4i −0.385680 + 0.697074i
$$689$$ 5456.01i 0.301680i
$$690$$ 900.309 12718.5i 0.0496727 0.701716i
$$691$$ 3028.67i 0.166738i 0.996519 + 0.0833691i $$0.0265681\pi$$
−0.996519 + 0.0833691i $$0.973432\pi$$
$$692$$ 8660.25 + 2236.07i 0.475742 + 0.122836i
$$693$$ −7200.00 + 804.984i −0.394669 + 0.0441253i
$$694$$ −3444.00 4446.18i −0.188375 0.243191i
$$695$$ 17528.4 0.956674
$$696$$ −16951.2 5680.53i −0.923179 0.309368i
$$697$$ 4480.00 0.243461
$$698$$ 3592.27 + 4637.60i 0.194799 + 0.251484i
$$699$$ −20438.2 18280.5i −1.10593 0.989172i
$$700$$ −2700.00 697.137i −0.145786 0.0376419i
$$701$$ 17664.9i 0.951777i 0.879506 + 0.475888i $$0.157873\pi$$
−0.879506 + 0.475888i $$0.842127\pi$$
$$702$$ −161.347 3964.89i −0.00867470 0.213170i
$$703$$ 9062.78i 0.486215i
$$704$$ −12193.6 + 12879.8i −0.652791 + 0.689523i
$$705$$ 6720.00 + 6010.55i 0.358993 + 0.321093i
$$706$$ −19360.0 + 14996.2i −1.03204 + 0.799418i
$$707$$ 11570.1 0.615472
$$708$$ −3996.15 5989.22i −0.212125 0.317922i
$$709$$ 14174.0 0.750798 0.375399 0.926863i $$-0.377506\pi$$
0.375399 + 0.926863i $$0.377506\pi$$
$$710$$ −20784.6 + 16099.7i −1.09864 + 0.851001i
$$711$$ −2286.31 + 255.617i −0.120595 + 0.0134830i
$$712$$ 7520.00 + 17474.9i 0.395820 + 0.919803i
$$713$$ 21788.2i 1.14443i
$$714$$ 4062.77 + 287.593i 0.212949 + 0.0150741i
$$715$$ 3098.39i 0.162060i
$$716$$ 2702.00 10464.8i 0.141031 0.546212i
$$717$$ −19680.0 + 22002.9i −1.02505 + 1.14604i
$$718$$ −14040.0 18125.6i −0.729761 0.942117i
$$719$$ 32839.7 1.70336 0.851678 0.524065i $$-0.175585\pi$$
0.851678 + 0.524065i $$0.175585\pi$$
$$720$$ −14271.4 5933.49i −0.738699 0.307122i
$$721$$ 10500.0 0.542358
$$722$$ −3462.37 4469.90i −0.178471 0.230405i
$$723$$ −4149.99 + 4639.83i −0.213472 + 0.238668i
$$724$$ −2524.00 + 9775.41i −0.129563 + 0.501796i
$$725$$ 6842.37i 0.350509i
$$726$$ 1920.49 + 135.947i 0.0981766 + 0.00694967i
$$727$$ 8001.58i 0.408201i 0.978950 + 0.204101i $$0.0654270\pi$$
−0.978950 + 0.204101i $$0.934573\pi$$
$$728$$ −692.820 1609.97i −0.0352715 0.0819635i
$$729$$ 6453.00 + 18595.1i 0.327846 + 0.944731i
$$730$$ 8200.00 6351.69i 0.415747 0.322037i
$$731$$ 8036.72 0.406633
$$732$$ −10197.7 15283.8i −0.514917 0.771730i
$$733$$ 11750.0 0.592082 0.296041 0.955175i $$-0.404333\pi$$
0.296041 + 0.955175i $$0.404333\pi$$
$$734$$ −17649.6 + 13671.3i −0.887546 + 0.687490i
$$735$$ 9803.41 + 8768.43i 0.491978 + 0.440039i
$$736$$ 2688.00 + 17351.0i 0.134621 + 0.868974i
$$737$$ 25491.2i 1.27406i
$$738$$ 6659.69 + 6862.53i 0.332177 + 0.342294i
$$739$$ 19961.4i 0.993627i −0.867857 0.496814i $$-0.834503\pi$$
0.867857 0.496814i $$-0.165497\pi$$
$$740$$ 9006.66 + 2325.51i 0.447421 + 0.115524i
$$741$$ 2700.00 + 2414.95i 0.133856 + 0.119724i
$$742$$ 7320.00 + 9450.08i 0.362164 + 0.467552i
$$743$$ −25592.8 −1.26367 −0.631836 0.775102i $$-0.717698\pi$$
−0.631836 + 0.775102i $$0.717698\pi$$
$$744$$ 25042.6 + 8392.06i 1.23401 + 0.413532i
$$745$$ −14480.0 −0.712089
$$746$$ −8504.37 10979.1i −0.417382 0.538838i
$$747$$ −3762.01 33648.5i −0.184264 1.64810i
$$748$$ 9600.00 + 2478.71i 0.469266 + 0.121164i
$$749$$ 4990.90i 0.243476i
$$750$$ 1577.95 22291.3i 0.0768246 1.08528i
$$751$$ 5244.02i 0.254803i 0.991851 + 0.127401i $$0.0406637\pi$$
−0.991851 + 0.127401i $$0.959336\pi$$
$$752$$ −10863.4 6010.55i −0.526793 0.291466i
$$753$$ 14760.0 16502.2i 0.714322 0.798636i
$$754$$ 3400.00 2633.63i 0.164218 0.127203i
$$755$$ −5057.59 −0.243794
$$756$$ 5598.92 + 6650.92i 0.269353 + 0.319963i
$$757$$ −14290.0 −0.686102 −0.343051 0.939317i $$-0.611460\pi$$
−0.343051 + 0.939317i $$0.611460\pi$$
$$758$$ −7014.81 + 5433.65i −0.336134 + 0.260368i
$$759$$ −11639.4 + 13013.2i −0.556631 + 0.622332i
$$760$$ 12960.0 5577.10i 0.618564 0.266188i
$$761$$ 16976.2i 0.808657i −0.914614 0.404328i $$-0.867505\pi$$
0.914614 0.404328i $$-0.132495\pi$$
$$762$$ 1905.12 26913.2i 0.0905711 1.27948i
$$763$$ 8257.20i 0.391783i
$$764$$ −5542.56 + 21466.3i −0.262464 + 1.01652i
$$765$$ 960.000 + 8586.50i 0.0453711 + 0.405811i
$$766$$ −10752.0 13880.8i −0.507161 0.654742i
$$767$$ 1732.05 0.0815394
$$768$$ 20977.9 + 3593.49i 0.985644 + 0.168840i
$$769$$ −29566.0 −1.38645 −0.693223 0.720723i $$-0.743810\pi$$
−0.693223 + 0.720723i $$0.743810\pi$$
$$770$$ −4156.92 5366.56i −0.194552 0.251166i
$$771$$ 12193.6 + 10906.3i 0.569576 + 0.509444i
$$772$$ 380.000 1471.73i 0.0177157 0.0686125i
$$773$$ 21457.3i 0.998403i −0.866486 0.499202i $$-0.833627\pi$$
0.866486 0.499202i $$-0.166373\pi$$
$$774$$ 11946.9 + 12310.8i 0.554809 + 0.571707i
$$775$$ 10108.5i 0.468526i
$$776$$ 16004.1 6887.09i 0.740355 0.318598i
$$777$$ −3900.00 3488.27i −0.180067 0.161056i
$$778$$ 21140.0 16375.0i 0.974172 0.754590i
$$779$$ −8729.54 −0.401499
$$780$$ 3092.82 2063.60i 0.141975 0.0947293i
$$781$$ 36000.0 1.64940
$$782$$ 7759.59 6010.55i 0.354837 0.274855i
$$783$$ −12366.8 + 17381.9i −0.564438 + 0.793334i
$$784$$ −15848.0 8768.43i −0.721939