# Properties

 Label 108.5.d.a.55.12 Level 108 Weight 5 Character 108.55 Analytic conductor 11.164 Analytic rank 0 Dimension 16 CM no Inner twists 4

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 108.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.1639560131$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{32}\cdot 3^{26}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 55.12 Root $$-1.98442 + 2.21794i$$ of $$x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} - 7353 x^{8} - 22934 x^{7} - 36353 x^{6} - 16248 x^{5} + 360646 x^{4} + 1077384 x^{3} + 2005641 x^{2} + 2990790 x + 2924100$$ Character $$\chi$$ $$=$$ 108.55 Dual form 108.5.d.a.55.11

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.59266 + 3.66925i) q^{2} +(-10.9268 + 11.6878i) q^{4} +29.4580 q^{5} +32.9098i q^{7} +(-60.2882 - 21.4787i) q^{8} +O(q^{10})$$ $$q+(1.59266 + 3.66925i) q^{2} +(-10.9268 + 11.6878i) q^{4} +29.4580 q^{5} +32.9098i q^{7} +(-60.2882 - 21.4787i) q^{8} +(46.9167 + 108.089i) q^{10} +136.639i q^{11} +164.522 q^{13} +(-120.754 + 52.4142i) q^{14} +(-17.2082 - 255.421i) q^{16} -380.756 q^{17} +439.574i q^{19} +(-321.883 + 344.298i) q^{20} +(-501.364 + 217.620i) q^{22} +171.733i q^{23} +242.773 q^{25} +(262.028 + 603.673i) q^{26} +(-384.642 - 359.600i) q^{28} -1041.21 q^{29} -1181.17i q^{31} +(909.798 - 469.941i) q^{32} +(-606.417 - 1397.09i) q^{34} +969.456i q^{35} +2700.79 q^{37} +(-1612.91 + 700.094i) q^{38} +(-1775.97 - 632.718i) q^{40} +1556.42 q^{41} +2218.02i q^{43} +(-1597.01 - 1493.04i) q^{44} +(-630.130 + 273.512i) q^{46} -1292.12i q^{47} +1317.95 q^{49} +(386.655 + 890.794i) q^{50} +(-1797.71 + 1922.90i) q^{52} +1015.00 q^{53} +4025.12i q^{55} +(706.858 - 1984.07i) q^{56} +(-1658.29 - 3820.45i) q^{58} -2434.15i q^{59} +3839.98 q^{61} +(4334.02 - 1881.21i) q^{62} +(3173.33 + 2589.82i) q^{64} +4846.48 q^{65} +2352.60i q^{67} +(4160.46 - 4450.19i) q^{68} +(-3557.18 + 1544.02i) q^{70} +884.064i q^{71} +6921.45 q^{73} +(4301.45 + 9909.89i) q^{74} +(-5137.65 - 4803.16i) q^{76} -4496.77 q^{77} -10308.0i q^{79} +(-506.918 - 7524.19i) q^{80} +(2478.85 + 5710.89i) q^{82} -12322.0i q^{83} -11216.3 q^{85} +(-8138.47 + 3532.56i) q^{86} +(2934.83 - 8237.73i) q^{88} -5751.10 q^{89} +5414.38i q^{91} +(-2007.17 - 1876.49i) q^{92} +(4741.11 - 2057.91i) q^{94} +12949.0i q^{95} -8159.93 q^{97} +(2099.04 + 4835.88i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q - 14q^{4} + O(q^{10})$$ $$16q - 14q^{4} - 202q^{10} - 352q^{13} - 206q^{16} + 738q^{22} + 1632q^{25} + 342q^{28} - 2536q^{34} + 3200q^{37} - 2854q^{40} + 36q^{46} - 896q^{49} + 2288q^{52} + 2492q^{58} - 2752q^{61} + 682q^{64} - 14166q^{70} + 8240q^{73} - 33084q^{76} + 68q^{82} + 8800q^{85} + 48294q^{88} + 52596q^{94} - 6928q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$55$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.59266 + 3.66925i 0.398166 + 0.917313i
$$3$$ 0 0
$$4$$ −10.9268 + 11.6878i −0.682928 + 0.730486i
$$5$$ 29.4580 1.17832 0.589160 0.808017i $$-0.299459\pi$$
0.589160 + 0.808017i $$0.299459\pi$$
$$6$$ 0 0
$$7$$ 32.9098i 0.671628i 0.941928 + 0.335814i $$0.109011\pi$$
−0.941928 + 0.335814i $$0.890989\pi$$
$$8$$ −60.2882 21.4787i −0.942003 0.335604i
$$9$$ 0 0
$$10$$ 46.9167 + 108.089i 0.469167 + 1.08089i
$$11$$ 136.639i 1.12925i 0.825348 + 0.564625i $$0.190979\pi$$
−0.825348 + 0.564625i $$0.809021\pi$$
$$12$$ 0 0
$$13$$ 164.522 0.973503 0.486751 0.873541i $$-0.338182\pi$$
0.486751 + 0.873541i $$0.338182\pi$$
$$14$$ −120.754 + 52.4142i −0.616094 + 0.267420i
$$15$$ 0 0
$$16$$ −17.2082 255.421i −0.0672195 0.997738i
$$17$$ −380.756 −1.31750 −0.658748 0.752364i $$-0.728914\pi$$
−0.658748 + 0.752364i $$0.728914\pi$$
$$18$$ 0 0
$$19$$ 439.574i 1.21766i 0.793302 + 0.608829i $$0.208360\pi$$
−0.793302 + 0.608829i $$0.791640\pi$$
$$20$$ −321.883 + 344.298i −0.804707 + 0.860746i
$$21$$ 0 0
$$22$$ −501.364 + 217.620i −1.03588 + 0.449629i
$$23$$ 171.733i 0.324636i 0.986738 + 0.162318i $$0.0518971\pi$$
−0.986738 + 0.162318i $$0.948103\pi$$
$$24$$ 0 0
$$25$$ 242.773 0.388436
$$26$$ 262.028 + 603.673i 0.387616 + 0.893007i
$$27$$ 0 0
$$28$$ −384.642 359.600i −0.490615 0.458674i
$$29$$ −1041.21 −1.23806 −0.619029 0.785368i $$-0.712474\pi$$
−0.619029 + 0.785368i $$0.712474\pi$$
$$30$$ 0 0
$$31$$ 1181.17i 1.22911i −0.788876 0.614553i $$-0.789336\pi$$
0.788876 0.614553i $$-0.210664\pi$$
$$32$$ 909.798 469.941i 0.888474 0.458927i
$$33$$ 0 0
$$34$$ −606.417 1397.09i −0.524582 1.20856i
$$35$$ 969.456i 0.791393i
$$36$$ 0 0
$$37$$ 2700.79 1.97282 0.986410 0.164301i $$-0.0525370\pi$$
0.986410 + 0.164301i $$0.0525370\pi$$
$$38$$ −1612.91 + 700.094i −1.11697 + 0.484830i
$$39$$ 0 0
$$40$$ −1775.97 632.718i −1.10998 0.395449i
$$41$$ 1556.42 0.925887 0.462944 0.886388i $$-0.346793\pi$$
0.462944 + 0.886388i $$0.346793\pi$$
$$42$$ 0 0
$$43$$ 2218.02i 1.19958i 0.800158 + 0.599789i $$0.204749\pi$$
−0.800158 + 0.599789i $$0.795251\pi$$
$$44$$ −1597.01 1493.04i −0.824901 0.771196i
$$45$$ 0 0
$$46$$ −630.130 + 273.512i −0.297793 + 0.129259i
$$47$$ 1292.12i 0.584934i −0.956276 0.292467i $$-0.905524\pi$$
0.956276 0.292467i $$-0.0944761\pi$$
$$48$$ 0 0
$$49$$ 1317.95 0.548915
$$50$$ 386.655 + 890.794i 0.154662 + 0.356318i
$$51$$ 0 0
$$52$$ −1797.71 + 1922.90i −0.664832 + 0.711130i
$$53$$ 1015.00 0.361337 0.180669 0.983544i $$-0.442174\pi$$
0.180669 + 0.983544i $$0.442174\pi$$
$$54$$ 0 0
$$55$$ 4025.12i 1.33062i
$$56$$ 706.858 1984.07i 0.225401 0.632676i
$$57$$ 0 0
$$58$$ −1658.29 3820.45i −0.492952 1.13569i
$$59$$ 2434.15i 0.699268i −0.936886 0.349634i $$-0.886306\pi$$
0.936886 0.349634i $$-0.113694\pi$$
$$60$$ 0 0
$$61$$ 3839.98 1.03198 0.515988 0.856596i $$-0.327425\pi$$
0.515988 + 0.856596i $$0.327425\pi$$
$$62$$ 4334.02 1881.21i 1.12748 0.489388i
$$63$$ 0 0
$$64$$ 3173.33 + 2589.82i 0.774740 + 0.632280i
$$65$$ 4846.48 1.14710
$$66$$ 0 0
$$67$$ 2352.60i 0.524081i 0.965057 + 0.262040i $$0.0843954\pi$$
−0.965057 + 0.262040i $$0.915605\pi$$
$$68$$ 4160.46 4450.19i 0.899754 0.962412i
$$69$$ 0 0
$$70$$ −3557.18 + 1544.02i −0.725955 + 0.315106i
$$71$$ 884.064i 0.175375i 0.996148 + 0.0876874i $$0.0279476\pi$$
−0.996148 + 0.0876874i $$0.972052\pi$$
$$72$$ 0 0
$$73$$ 6921.45 1.29883 0.649413 0.760436i $$-0.275014\pi$$
0.649413 + 0.760436i $$0.275014\pi$$
$$74$$ 4301.45 + 9909.89i 0.785510 + 1.80969i
$$75$$ 0 0
$$76$$ −5137.65 4803.16i −0.889482 0.831572i
$$77$$ −4496.77 −0.758436
$$78$$ 0 0
$$79$$ 10308.0i 1.65165i −0.563924 0.825826i $$-0.690709\pi$$
0.563924 0.825826i $$-0.309291\pi$$
$$80$$ −506.918 7524.19i −0.0792060 1.17565i
$$81$$ 0 0
$$82$$ 2478.85 + 5710.89i 0.368657 + 0.849329i
$$83$$ 12322.0i 1.78865i −0.447417 0.894326i $$-0.647656\pi$$
0.447417 0.894326i $$-0.352344\pi$$
$$84$$ 0 0
$$85$$ −11216.3 −1.55243
$$86$$ −8138.47 + 3532.56i −1.10039 + 0.477631i
$$87$$ 0 0
$$88$$ 2934.83 8237.73i 0.378981 1.06376i
$$89$$ −5751.10 −0.726057 −0.363028 0.931778i $$-0.618257\pi$$
−0.363028 + 0.931778i $$0.618257\pi$$
$$90$$ 0 0
$$91$$ 5414.38i 0.653832i
$$92$$ −2007.17 1876.49i −0.237142 0.221703i
$$93$$ 0 0
$$94$$ 4741.11 2057.91i 0.536568 0.232901i
$$95$$ 12949.0i 1.43479i
$$96$$ 0 0
$$97$$ −8159.93 −0.867247 −0.433624 0.901094i $$-0.642765\pi$$
−0.433624 + 0.901094i $$0.642765\pi$$
$$98$$ 2099.04 + 4835.88i 0.218559 + 0.503527i
$$99$$ 0 0
$$100$$ −2652.74 + 2837.47i −0.265274 + 0.283747i
$$101$$ 11440.4 1.12150 0.560749 0.827986i $$-0.310513\pi$$
0.560749 + 0.827986i $$0.310513\pi$$
$$102$$ 0 0
$$103$$ 11724.0i 1.10510i −0.833479 0.552552i $$-0.813654\pi$$
0.833479 0.552552i $$-0.186346\pi$$
$$104$$ −9918.73 3533.71i −0.917043 0.326711i
$$105$$ 0 0
$$106$$ 1616.55 + 3724.28i 0.143872 + 0.331460i
$$107$$ 21224.4i 1.85382i 0.375286 + 0.926909i $$0.377544\pi$$
−0.375286 + 0.926909i $$0.622456\pi$$
$$108$$ 0 0
$$109$$ −5752.64 −0.484188 −0.242094 0.970253i $$-0.577834\pi$$
−0.242094 + 0.970253i $$0.577834\pi$$
$$110$$ −14769.2 + 6410.66i −1.22059 + 0.529806i
$$111$$ 0 0
$$112$$ 8405.85 566.318i 0.670109 0.0451465i
$$113$$ −6018.68 −0.471351 −0.235675 0.971832i $$-0.575730\pi$$
−0.235675 + 0.971832i $$0.575730\pi$$
$$114$$ 0 0
$$115$$ 5058.90i 0.382525i
$$116$$ 11377.1 12169.4i 0.845504 0.904384i
$$117$$ 0 0
$$118$$ 8931.52 3876.79i 0.641448 0.278425i
$$119$$ 12530.6i 0.884868i
$$120$$ 0 0
$$121$$ −4029.28 −0.275205
$$122$$ 6115.80 + 14089.9i 0.410898 + 0.946646i
$$123$$ 0 0
$$124$$ 13805.3 + 12906.5i 0.897845 + 0.839391i
$$125$$ −11259.6 −0.720617
$$126$$ 0 0
$$127$$ 7591.93i 0.470700i −0.971911 0.235350i $$-0.924376\pi$$
0.971911 0.235350i $$-0.0756237\pi$$
$$128$$ −4448.65 + 15768.5i −0.271524 + 0.962432i
$$129$$ 0 0
$$130$$ 7718.82 + 17783.0i 0.456735 + 1.05225i
$$131$$ 3334.49i 0.194306i −0.995269 0.0971532i $$-0.969026\pi$$
0.995269 0.0971532i $$-0.0309737\pi$$
$$132$$ 0 0
$$133$$ −14466.3 −0.817813
$$134$$ −8632.28 + 3746.90i −0.480746 + 0.208671i
$$135$$ 0 0
$$136$$ 22955.1 + 8178.14i 1.24109 + 0.442157i
$$137$$ −11823.7 −0.629960 −0.314980 0.949098i $$-0.601998\pi$$
−0.314980 + 0.949098i $$0.601998\pi$$
$$138$$ 0 0
$$139$$ 5544.34i 0.286959i −0.989653 0.143480i $$-0.954171\pi$$
0.989653 0.143480i $$-0.0458292\pi$$
$$140$$ −11330.8 10593.1i −0.578101 0.540464i
$$141$$ 0 0
$$142$$ −3243.85 + 1408.02i −0.160874 + 0.0698282i
$$143$$ 22480.2i 1.09933i
$$144$$ 0 0
$$145$$ −30671.8 −1.45883
$$146$$ 11023.5 + 25396.5i 0.517149 + 1.19143i
$$147$$ 0 0
$$148$$ −29511.1 + 31566.2i −1.34729 + 1.44112i
$$149$$ −11073.6 −0.498790 −0.249395 0.968402i $$-0.580232\pi$$
−0.249395 + 0.968402i $$0.580232\pi$$
$$150$$ 0 0
$$151$$ 27450.4i 1.20391i 0.798529 + 0.601956i $$0.205612\pi$$
−0.798529 + 0.601956i $$0.794388\pi$$
$$152$$ 9441.47 26501.1i 0.408651 1.14704i
$$153$$ 0 0
$$154$$ −7161.84 16499.8i −0.301984 0.695724i
$$155$$ 34794.9i 1.44828i
$$156$$ 0 0
$$157$$ 14606.6 0.592583 0.296291 0.955098i $$-0.404250\pi$$
0.296291 + 0.955098i $$0.404250\pi$$
$$158$$ 37822.5 16417.1i 1.51508 0.657632i
$$159$$ 0 0
$$160$$ 26800.8 13843.5i 1.04691 0.540762i
$$161$$ −5651.68 −0.218035
$$162$$ 0 0
$$163$$ 39065.5i 1.47034i −0.677883 0.735170i $$-0.737102\pi$$
0.677883 0.735170i $$-0.262898\pi$$
$$164$$ −17006.7 + 18191.1i −0.632314 + 0.676348i
$$165$$ 0 0
$$166$$ 45212.6 19624.8i 1.64075 0.712180i
$$167$$ 3123.15i 0.111985i 0.998431 + 0.0559926i $$0.0178323\pi$$
−0.998431 + 0.0559926i $$0.982168\pi$$
$$168$$ 0 0
$$169$$ −1493.53 −0.0522925
$$170$$ −17863.8 41155.5i −0.618125 1.42407i
$$171$$ 0 0
$$172$$ −25923.7 24235.9i −0.876274 0.819225i
$$173$$ 50749.6 1.69567 0.847834 0.530262i $$-0.177907\pi$$
0.847834 + 0.530262i $$0.177907\pi$$
$$174$$ 0 0
$$175$$ 7989.60i 0.260885i
$$176$$ 34900.5 2351.31i 1.12670 0.0759076i
$$177$$ 0 0
$$178$$ −9159.56 21102.2i −0.289091 0.666022i
$$179$$ 4456.66i 0.139092i −0.997579 0.0695462i $$-0.977845\pi$$
0.997579 0.0695462i $$-0.0221551\pi$$
$$180$$ 0 0
$$181$$ −8462.68 −0.258316 −0.129158 0.991624i $$-0.541227\pi$$
−0.129158 + 0.991624i $$0.541227\pi$$
$$182$$ −19866.7 + 8623.29i −0.599769 + 0.260334i
$$183$$ 0 0
$$184$$ 3688.59 10353.4i 0.108949 0.305808i
$$185$$ 79559.9 2.32461
$$186$$ 0 0
$$187$$ 52026.2i 1.48778i
$$188$$ 15102.0 + 14118.8i 0.427286 + 0.399467i
$$189$$ 0 0
$$190$$ −47513.1 + 20623.4i −1.31615 + 0.571284i
$$191$$ 17699.2i 0.485163i −0.970131 0.242582i $$-0.922006\pi$$
0.970131 0.242582i $$-0.0779942\pi$$
$$192$$ 0 0
$$193$$ 10944.5 0.293820 0.146910 0.989150i $$-0.453067\pi$$
0.146910 + 0.989150i $$0.453067\pi$$
$$194$$ −12996.0 29940.9i −0.345308 0.795538i
$$195$$ 0 0
$$196$$ −14401.0 + 15403.9i −0.374869 + 0.400975i
$$197$$ 10101.3 0.260284 0.130142 0.991495i $$-0.458457\pi$$
0.130142 + 0.991495i $$0.458457\pi$$
$$198$$ 0 0
$$199$$ 31394.8i 0.792777i 0.918083 + 0.396388i $$0.129737\pi$$
−0.918083 + 0.396388i $$0.870263\pi$$
$$200$$ −14636.3 5214.43i −0.365908 0.130361i
$$201$$ 0 0
$$202$$ 18220.7 + 41977.8i 0.446543 + 1.02877i
$$203$$ 34265.9i 0.831515i
$$204$$ 0 0
$$205$$ 45848.9 1.09099
$$206$$ 43018.5 18672.5i 1.01373 0.440015i
$$207$$ 0 0
$$208$$ −2831.12 42022.4i −0.0654383 0.971301i
$$209$$ −60063.1 −1.37504
$$210$$ 0 0
$$211$$ 83361.8i 1.87241i 0.351448 + 0.936207i $$0.385689\pi$$
−0.351448 + 0.936207i $$0.614311\pi$$
$$212$$ −11090.7 + 11863.1i −0.246767 + 0.263952i
$$213$$ 0 0
$$214$$ −77877.6 + 33803.3i −1.70053 + 0.738127i
$$215$$ 65338.3i 1.41349i
$$216$$ 0 0
$$217$$ 38872.1 0.825503
$$218$$ −9162.02 21107.9i −0.192787 0.444152i
$$219$$ 0 0
$$220$$ −47044.7 43981.8i −0.971997 0.908715i
$$221$$ −62642.8 −1.28259
$$222$$ 0 0
$$223$$ 13301.4i 0.267478i 0.991017 + 0.133739i $$0.0426983\pi$$
−0.991017 + 0.133739i $$0.957302\pi$$
$$224$$ 15465.7 + 29941.2i 0.308228 + 0.596724i
$$225$$ 0 0
$$226$$ −9585.73 22084.1i −0.187676 0.432377i
$$227$$ 50075.5i 0.971792i −0.874017 0.485896i $$-0.838493\pi$$
0.874017 0.485896i $$-0.161507\pi$$
$$228$$ 0 0
$$229$$ 60039.8 1.14490 0.572451 0.819939i $$-0.305993\pi$$
0.572451 + 0.819939i $$0.305993\pi$$
$$230$$ −18562.4 + 8057.12i −0.350895 + 0.152308i
$$231$$ 0 0
$$232$$ 62772.5 + 22363.7i 1.16625 + 0.415497i
$$233$$ −31252.0 −0.575659 −0.287830 0.957682i $$-0.592934\pi$$
−0.287830 + 0.957682i $$0.592934\pi$$
$$234$$ 0 0
$$235$$ 38063.2i 0.689239i
$$236$$ 28449.8 + 26597.6i 0.510805 + 0.477549i
$$237$$ 0 0
$$238$$ 45978.0 19957.0i 0.811701 0.352324i
$$239$$ 62883.1i 1.10087i 0.834876 + 0.550437i $$0.185539\pi$$
−0.834876 + 0.550437i $$0.814461\pi$$
$$240$$ 0 0
$$241$$ 64613.0 1.11246 0.556232 0.831027i $$-0.312247\pi$$
0.556232 + 0.831027i $$0.312247\pi$$
$$242$$ −6417.29 14784.5i −0.109577 0.252450i
$$243$$ 0 0
$$244$$ −41958.9 + 44880.9i −0.704765 + 0.753844i
$$245$$ 38824.0 0.646797
$$246$$ 0 0
$$247$$ 72319.6i 1.18539i
$$248$$ −25370.0 + 71210.7i −0.412493 + 1.15782i
$$249$$ 0 0
$$250$$ −17932.8 41314.5i −0.286925 0.661032i
$$251$$ 78853.1i 1.25162i −0.779977 0.625808i $$-0.784769\pi$$
0.779977 0.625808i $$-0.215231\pi$$
$$252$$ 0 0
$$253$$ −23465.4 −0.366595
$$254$$ 27856.7 12091.4i 0.431780 0.187417i
$$255$$ 0 0
$$256$$ −64943.8 + 8790.66i −0.990963 + 0.134135i
$$257$$ −25571.1 −0.387153 −0.193576 0.981085i $$-0.562009\pi$$
−0.193576 + 0.981085i $$0.562009\pi$$
$$258$$ 0 0
$$259$$ 88882.5i 1.32500i
$$260$$ −52956.8 + 56644.6i −0.783384 + 0.837938i
$$261$$ 0 0
$$262$$ 12235.1 5310.73i 0.178240 0.0773662i
$$263$$ 110011.i 1.59046i 0.606305 + 0.795232i $$0.292651\pi$$
−0.606305 + 0.795232i $$0.707349\pi$$
$$264$$ 0 0
$$265$$ 29899.8 0.425771
$$266$$ −23040.0 53080.5i −0.325625 0.750191i
$$267$$ 0 0
$$268$$ −27496.6 25706.5i −0.382834 0.357909i
$$269$$ −39818.1 −0.550270 −0.275135 0.961406i $$-0.588723\pi$$
−0.275135 + 0.961406i $$0.588723\pi$$
$$270$$ 0 0
$$271$$ 14054.7i 0.191375i −0.995411 0.0956873i $$-0.969495\pi$$
0.995411 0.0956873i $$-0.0305049\pi$$
$$272$$ 6552.12 + 97253.1i 0.0885614 + 1.31452i
$$273$$ 0 0
$$274$$ −18831.2 43384.2i −0.250829 0.577871i
$$275$$ 33172.3i 0.438642i
$$276$$ 0 0
$$277$$ −31583.7 −0.411627 −0.205813 0.978591i $$-0.565984\pi$$
−0.205813 + 0.978591i $$0.565984\pi$$
$$278$$ 20343.6 8830.27i 0.263232 0.114257i
$$279$$ 0 0
$$280$$ 20822.6 58446.8i 0.265595 0.745494i
$$281$$ 66899.3 0.847244 0.423622 0.905839i $$-0.360758\pi$$
0.423622 + 0.905839i $$0.360758\pi$$
$$282$$ 0 0
$$283$$ 160099.i 1.99901i −0.0314612 0.999505i $$-0.510016\pi$$
0.0314612 0.999505i $$-0.489984\pi$$
$$284$$ −10332.7 9660.03i −0.128109 0.119768i
$$285$$ 0 0
$$286$$ −82485.4 + 35803.3i −1.00843 + 0.437715i
$$287$$ 51221.4i 0.621852i
$$288$$ 0 0
$$289$$ 61454.3 0.735795
$$290$$ −48849.9 112543.i −0.580855 1.33820i
$$291$$ 0 0
$$292$$ −75629.6 + 80896.3i −0.887005 + 0.948775i
$$293$$ −92671.2 −1.07947 −0.539734 0.841836i $$-0.681475\pi$$
−0.539734 + 0.841836i $$0.681475\pi$$
$$294$$ 0 0
$$295$$ 71705.2i 0.823961i
$$296$$ −162826. 58009.4i −1.85840 0.662087i
$$297$$ 0 0
$$298$$ −17636.6 40631.9i −0.198601 0.457546i
$$299$$ 28253.8i 0.316034i
$$300$$ 0 0
$$301$$ −72994.5 −0.805670
$$302$$ −100722. + 43719.3i −1.10436 + 0.479357i
$$303$$ 0 0
$$304$$ 112277. 7564.28i 1.21490 0.0818503i
$$305$$ 113118. 1.21600
$$306$$ 0 0
$$307$$ 86852.2i 0.921518i 0.887525 + 0.460759i $$0.152423\pi$$
−0.887525 + 0.460759i $$0.847577\pi$$
$$308$$ 49135.5 52557.2i 0.517957 0.554027i
$$309$$ 0 0
$$310$$ 127671. 55416.6i 1.32853 0.576656i
$$311$$ 43940.9i 0.454306i −0.973859 0.227153i $$-0.927058\pi$$
0.973859 0.227153i $$-0.0729417\pi$$
$$312$$ 0 0
$$313$$ −100801. −1.02890 −0.514452 0.857519i $$-0.672005\pi$$
−0.514452 + 0.857519i $$0.672005\pi$$
$$314$$ 23263.4 + 53595.2i 0.235946 + 0.543584i
$$315$$ 0 0
$$316$$ 120477. + 112634.i 1.20651 + 1.12796i
$$317$$ −101986. −1.01490 −0.507449 0.861682i $$-0.669411\pi$$
−0.507449 + 0.861682i $$0.669411\pi$$
$$318$$ 0 0
$$319$$ 142270.i 1.39808i
$$320$$ 93480.0 + 76290.9i 0.912891 + 0.745028i
$$321$$ 0 0
$$322$$ −9001.23 20737.5i −0.0868141 0.200006i
$$323$$ 167371.i 1.60426i
$$324$$ 0 0
$$325$$ 39941.4 0.378144
$$326$$ 143341. 62218.2i 1.34876 0.585439i
$$327$$ 0 0
$$328$$ −93833.6 33429.8i −0.872189 0.310732i
$$329$$ 42523.4 0.392858
$$330$$ 0 0
$$331$$ 39677.8i 0.362153i 0.983469 + 0.181076i $$0.0579581\pi$$
−0.983469 + 0.181076i $$0.942042\pi$$
$$332$$ 144017. + 134641.i 1.30658 + 1.22152i
$$333$$ 0 0
$$334$$ −11459.6 + 4974.13i −0.102725 + 0.0445887i
$$335$$ 69302.8i 0.617534i
$$336$$ 0 0
$$337$$ −129324. −1.13873 −0.569364 0.822086i $$-0.692810\pi$$
−0.569364 + 0.822086i $$0.692810\pi$$
$$338$$ −2378.68 5480.12i −0.0208211 0.0479686i
$$339$$ 0 0
$$340$$ 122559. 131094.i 1.06020 1.13403i
$$341$$ 161394. 1.38797
$$342$$ 0 0
$$343$$ 122390.i 1.04030i
$$344$$ 47640.1 133720.i 0.402583 1.13001i
$$345$$ 0 0
$$346$$ 80827.1 + 186213.i 0.675157 + 1.55546i
$$347$$ 174482.i 1.44908i −0.689233 0.724540i $$-0.742052\pi$$
0.689233 0.724540i $$-0.257948\pi$$
$$348$$ 0 0
$$349$$ −39421.3 −0.323654 −0.161827 0.986819i $$-0.551739\pi$$
−0.161827 + 0.986819i $$0.551739\pi$$
$$350$$ −29315.9 + 12724.7i −0.239313 + 0.103875i
$$351$$ 0 0
$$352$$ 64212.4 + 124314.i 0.518243 + 1.00331i
$$353$$ −123080. −0.987733 −0.493866 0.869538i $$-0.664417\pi$$
−0.493866 + 0.869538i $$0.664417\pi$$
$$354$$ 0 0
$$355$$ 26042.7i 0.206647i
$$356$$ 62841.3 67217.5i 0.495844 0.530374i
$$357$$ 0 0
$$358$$ 16352.6 7097.96i 0.127591 0.0553818i
$$359$$ 20967.0i 0.162685i −0.996686 0.0813424i $$-0.974079\pi$$
0.996686 0.0813424i $$-0.0259207\pi$$
$$360$$ 0 0
$$361$$ −62904.6 −0.482690
$$362$$ −13478.2 31051.7i −0.102852 0.236956i
$$363$$ 0 0
$$364$$ −63282.1 59162.1i −0.477615 0.446520i
$$365$$ 203892. 1.53043
$$366$$ 0 0
$$367$$ 58300.8i 0.432855i −0.976299 0.216427i $$-0.930560\pi$$
0.976299 0.216427i $$-0.0694405\pi$$
$$368$$ 43864.1 2955.21i 0.323902 0.0218219i
$$369$$ 0 0
$$370$$ 126712. + 291925.i 0.925581 + 2.13240i
$$371$$ 33403.3i 0.242684i
$$372$$ 0 0
$$373$$ −79775.3 −0.573391 −0.286695 0.958022i $$-0.592557\pi$$
−0.286695 + 0.958022i $$0.592557\pi$$
$$374$$ 190897. 82860.3i 1.36476 0.592384i
$$375$$ 0 0
$$376$$ −27753.0 + 77899.5i −0.196306 + 0.551009i
$$377$$ −171301. −1.20525
$$378$$ 0 0
$$379$$ 80878.2i 0.563058i 0.959553 + 0.281529i $$0.0908415\pi$$
−0.959553 + 0.281529i $$0.909159\pi$$
$$380$$ −151345. 141491.i −1.04809 0.979857i
$$381$$ 0 0
$$382$$ 64943.0 28188.9i 0.445047 0.193176i
$$383$$ 99819.8i 0.680486i 0.940338 + 0.340243i $$0.110509\pi$$
−0.940338 + 0.340243i $$0.889491\pi$$
$$384$$ 0 0
$$385$$ −132466. −0.893680
$$386$$ 17430.9 + 40158.1i 0.116989 + 0.269525i
$$387$$ 0 0
$$388$$ 89162.3 95371.4i 0.592267 0.633512i
$$389$$ 15583.1 0.102981 0.0514903 0.998673i $$-0.483603\pi$$
0.0514903 + 0.998673i $$0.483603\pi$$
$$390$$ 0 0
$$391$$ 65388.3i 0.427707i
$$392$$ −79456.6 28307.7i −0.517080 0.184218i
$$393$$ 0 0
$$394$$ 16088.0 + 37064.4i 0.103636 + 0.238762i
$$395$$ 303652.i 1.94617i
$$396$$ 0 0
$$397$$ −67256.6 −0.426730 −0.213365 0.976973i $$-0.568442\pi$$
−0.213365 + 0.976973i $$0.568442\pi$$
$$398$$ −115195. + 50001.3i −0.727225 + 0.315657i
$$399$$ 0 0
$$400$$ −4177.68 62009.2i −0.0261105 0.387558i
$$401$$ 151843. 0.944288 0.472144 0.881521i $$-0.343480\pi$$
0.472144 + 0.881521i $$0.343480\pi$$
$$402$$ 0 0
$$403$$ 194329.i 1.19654i
$$404$$ −125008. + 133713.i −0.765903 + 0.819239i
$$405$$ 0 0
$$406$$ 125730. 54574.0i 0.762760 0.331081i
$$407$$ 369034.i 2.22781i
$$408$$ 0 0
$$409$$ −64170.7 −0.383610 −0.191805 0.981433i $$-0.561434\pi$$
−0.191805 + 0.981433i $$0.561434\pi$$
$$410$$ 73021.9 + 168231.i 0.434396 + 1.00078i
$$411$$ 0 0
$$412$$ 137028. + 128107.i 0.807262 + 0.754706i
$$413$$ 80107.4 0.469648
$$414$$ 0 0
$$415$$ 362982.i 2.10760i
$$416$$ 149682. 77315.6i 0.864932 0.446766i
$$417$$ 0 0
$$418$$ −95660.3 220387.i −0.547494 1.26134i
$$419$$ 85171.9i 0.485142i −0.970134 0.242571i $$-0.922009\pi$$
0.970134 0.242571i $$-0.0779907\pi$$
$$420$$ 0 0
$$421$$ 214896. 1.21245 0.606224 0.795294i $$-0.292683\pi$$
0.606224 + 0.795294i $$0.292683\pi$$
$$422$$ −305875. + 132767.i −1.71759 + 0.745532i
$$423$$ 0 0
$$424$$ −61192.3 21800.8i −0.340381 0.121266i
$$425$$ −92437.2 −0.511763
$$426$$ 0 0
$$427$$ 126373.i 0.693105i
$$428$$ −248066. 231915.i −1.35419 1.26602i
$$429$$ 0 0
$$430$$ −239743. + 104062.i −1.29661 + 0.562802i
$$431$$ 19885.9i 0.107051i 0.998566 + 0.0535254i $$0.0170458\pi$$
−0.998566 + 0.0535254i $$0.982954\pi$$
$$432$$ 0 0
$$433$$ 103996. 0.554679 0.277339 0.960772i $$-0.410547\pi$$
0.277339 + 0.960772i $$0.410547\pi$$
$$434$$ 61910.2 + 142632.i 0.328687 + 0.757244i
$$435$$ 0 0
$$436$$ 62858.2 67235.6i 0.330666 0.353693i
$$437$$ −75489.2 −0.395296
$$438$$ 0 0
$$439$$ 55956.4i 0.290349i 0.989406 + 0.145175i $$0.0463744\pi$$
−0.989406 + 0.145175i $$0.953626\pi$$
$$440$$ 86454.1 242667.i 0.446561 1.25345i
$$441$$ 0 0
$$442$$ −99768.9 229852.i −0.510682 1.17653i
$$443$$ 22607.4i 0.115198i 0.998340 + 0.0575988i $$0.0183444\pi$$
−0.998340 + 0.0575988i $$0.981656\pi$$
$$444$$ 0 0
$$445$$ −169416. −0.855527
$$446$$ −48806.2 + 21184.7i −0.245361 + 0.106501i
$$447$$ 0 0
$$448$$ −85230.4 + 104434.i −0.424657 + 0.520337i
$$449$$ 77577.5 0.384807 0.192404 0.981316i $$-0.438372\pi$$
0.192404 + 0.981316i $$0.438372\pi$$
$$450$$ 0 0
$$451$$ 212668.i 1.04556i
$$452$$ 65765.2 70345.0i 0.321899 0.344315i
$$453$$ 0 0
$$454$$ 183740. 79753.4i 0.891438 0.386934i
$$455$$ 159497.i 0.770423i
$$456$$ 0 0
$$457$$ −242860. −1.16285 −0.581425 0.813600i $$-0.697505\pi$$
−0.581425 + 0.813600i $$0.697505\pi$$
$$458$$ 95623.2 + 220301.i 0.455861 + 1.05023i
$$459$$ 0 0
$$460$$ −59127.2 55277.8i −0.279429 0.261237i
$$461$$ −199640. −0.939391 −0.469696 0.882828i $$-0.655636\pi$$
−0.469696 + 0.882828i $$0.655636\pi$$
$$462$$ 0 0
$$463$$ 63490.8i 0.296175i 0.988974 + 0.148088i $$0.0473118\pi$$
−0.988974 + 0.148088i $$0.952688\pi$$
$$464$$ 17917.3 + 265946.i 0.0832216 + 1.23526i
$$465$$ 0 0
$$466$$ −49773.9 114671.i −0.229208 0.528060i
$$467$$ 112982.i 0.518053i 0.965870 + 0.259026i $$0.0834017\pi$$
−0.965870 + 0.259026i $$0.916598\pi$$
$$468$$ 0 0
$$469$$ −77423.5 −0.351987
$$470$$ 139664. 60621.9i 0.632248 0.274431i
$$471$$ 0 0
$$472$$ −52282.3 + 146751.i −0.234677 + 0.658713i
$$473$$ −303068. −1.35462
$$474$$ 0 0
$$475$$ 106717.i 0.472982i
$$476$$ 146455. + 136920.i 0.646383 + 0.604301i
$$477$$ 0 0
$$478$$ −230734. + 100152.i −1.00985 + 0.438331i
$$479$$ 313437.i 1.36609i 0.730376 + 0.683045i $$0.239345\pi$$
−0.730376 + 0.683045i $$0.760655\pi$$
$$480$$ 0 0
$$481$$ 444339. 1.92055
$$482$$ 102907. + 237081.i 0.442945 + 1.02048i
$$483$$ 0 0
$$484$$ 44027.3 47093.4i 0.187945 0.201034i
$$485$$ −240375. −1.02189
$$486$$ 0 0
$$487$$ 64950.6i 0.273858i −0.990581 0.136929i $$-0.956277\pi$$
0.990581 0.136929i $$-0.0437232\pi$$
$$488$$ −231506. 82477.7i −0.972125 0.346336i
$$489$$ 0 0
$$490$$ 61833.6 + 142455.i 0.257533 + 0.593316i
$$491$$ 358585.i 1.48741i −0.668510 0.743703i $$-0.733068\pi$$
0.668510 0.743703i $$-0.266932\pi$$
$$492$$ 0 0
$$493$$ 396446. 1.63114
$$494$$ −265359. + 115181.i −1.08738 + 0.471983i
$$495$$ 0 0
$$496$$ −301696. + 20325.8i −1.22633 + 0.0826198i
$$497$$ −29094.4 −0.117787
$$498$$ 0 0
$$499$$ 12696.3i 0.0509890i −0.999675 0.0254945i $$-0.991884\pi$$
0.999675 0.0254945i $$-0.00811603\pi$$
$$500$$ 123032. 131600.i 0.492130 0.526401i
$$501$$ 0 0
$$502$$ 289332. 125586.i 1.14812 0.498351i
$$503$$ 114739.i 0.453498i −0.973953 0.226749i $$-0.927190\pi$$
0.973953 0.226749i $$-0.0728097\pi$$
$$504$$ 0 0
$$505$$ 337011. 1.32148
$$506$$ −37372.5 86100.5i −0.145966 0.336283i
$$507$$ 0 0
$$508$$ 88732.8 + 82955.8i 0.343840 + 0.321454i
$$509$$ −44847.2 −0.173101 −0.0865505 0.996247i $$-0.527584\pi$$
−0.0865505 + 0.996247i $$0.527584\pi$$
$$510$$ 0 0
$$511$$ 227783.i 0.872329i
$$512$$ −135689. 224295.i −0.517611 0.855616i
$$513$$ 0 0
$$514$$ −40726.1 93826.7i −0.154151 0.355141i
$$515$$ 345367.i 1.30216i
$$516$$ 0 0
$$517$$ 176554. 0.660536
$$518$$ −326132. + 141560.i −1.21544 + 0.527571i
$$519$$ 0 0
$$520$$ −292186. 104096.i −1.08057 0.384970i
$$521$$ 285591. 1.05213 0.526065 0.850444i $$-0.323667\pi$$
0.526065 + 0.850444i $$0.323667\pi$$
$$522$$ 0 0
$$523$$ 164178.i 0.600220i −0.953905 0.300110i $$-0.902977\pi$$
0.953905 0.300110i $$-0.0970234\pi$$
$$524$$ 38972.8 + 36435.5i 0.141938 + 0.132697i
$$525$$ 0 0
$$526$$ −403658. + 175210.i −1.45895 + 0.633269i
$$527$$ 449738.i 1.61934i
$$528$$ 0 0
$$529$$ 250349. 0.894611
$$530$$ 47620.3 + 109710.i 0.169527 + 0.390565i
$$531$$ 0 0
$$532$$ 158071. 169079.i 0.558507 0.597401i
$$533$$ 256065. 0.901354
$$534$$ 0 0
$$535$$ 625227.i 2.18439i
$$536$$ 50530.7 141834.i 0.175884 0.493686i
$$537$$ 0 0
$$538$$ −63416.9 146103.i −0.219099 0.504770i
$$539$$ 180083.i 0.619863i
$$540$$ 0 0
$$541$$ −300448. −1.02654 −0.513269 0.858228i $$-0.671566\pi$$
−0.513269 + 0.858228i $$0.671566\pi$$
$$542$$ 51570.4 22384.5i 0.175551 0.0761989i
$$543$$ 0 0
$$544$$ −346411. + 178933.i −1.17056 + 0.604634i
$$545$$ −169461. −0.570528
$$546$$ 0 0
$$547$$ 74251.6i 0.248160i −0.992272 0.124080i $$-0.960402\pi$$
0.992272 0.124080i $$-0.0395979\pi$$
$$548$$ 129196. 138193.i 0.430217 0.460177i
$$549$$ 0 0
$$550$$ −121717. + 52832.3i −0.402372 + 0.174652i
$$551$$ 457688.i 1.50753i
$$552$$ 0 0
$$553$$ 339233. 1.10930
$$554$$ −50302.2 115889.i −0.163896 0.377591i
$$555$$ 0 0
$$556$$ 64801.0 + 60582.1i 0.209620 + 0.195972i
$$557$$ 193413. 0.623411 0.311705 0.950179i $$-0.399100\pi$$
0.311705 + 0.950179i $$0.399100\pi$$
$$558$$ 0 0
$$559$$ 364913.i 1.16779i
$$560$$ 247619. 16682.6i 0.789603 0.0531970i
$$561$$ 0 0
$$562$$ 106548. + 245470.i 0.337344 + 0.777188i
$$563$$ 177354.i 0.559530i 0.960068 + 0.279765i $$0.0902566\pi$$
−0.960068 + 0.279765i $$0.909743\pi$$
$$564$$ 0 0
$$565$$ −177298. −0.555402
$$566$$ 587443. 254983.i 1.83372 0.795938i
$$567$$ 0 0
$$568$$ 18988.5 53298.6i 0.0588565 0.165204i
$$569$$ 590091. 1.82261 0.911306 0.411730i $$-0.135075\pi$$
0.911306 + 0.411730i $$0.135075\pi$$
$$570$$ 0 0
$$571$$ 524012.i 1.60720i −0.595172 0.803598i $$-0.702916\pi$$
0.595172 0.803598i $$-0.297084\pi$$
$$572$$ −262743. 245637.i −0.803044 0.750761i
$$573$$ 0 0
$$574$$ −187944. + 81578.4i −0.570433 + 0.247600i
$$575$$ 41692.0i 0.126100i
$$576$$ 0 0
$$577$$ −337273. −1.01305 −0.506523 0.862226i $$-0.669070\pi$$
−0.506523 + 0.862226i $$0.669070\pi$$
$$578$$ 97876.1 + 225492.i 0.292969 + 0.674955i
$$579$$ 0 0
$$580$$ 335146. 358486.i 0.996273 1.06565i
$$581$$ 405515. 1.20131
$$582$$ 0 0
$$583$$ 138688.i 0.408040i
$$584$$ −417282. 148663.i −1.22350 0.435892i
$$585$$ 0 0
$$586$$ −147594. 340034.i −0.429807 0.990210i
$$587$$ 4289.71i 0.0124495i −0.999981 0.00622475i $$-0.998019\pi$$
0.999981 0.00622475i $$-0.00198141\pi$$
$$588$$ 0 0
$$589$$ 519212. 1.49663
$$590$$ 263105. 114202.i 0.755830 0.328073i
$$591$$ 0 0
$$592$$ −46475.7 689839.i −0.132612 1.96836i
$$593$$ 150227. 0.427207 0.213604 0.976920i $$-0.431480\pi$$
0.213604 + 0.976920i $$0.431480\pi$$
$$594$$ 0 0
$$595$$ 369126.i 1.04266i
$$596$$ 121000. 129426.i 0.340637 0.364359i
$$597$$ 0 0
$$598$$ −103670. + 44998.8i −0.289902 + 0.125834i
$$599$$ 473108.i 1.31858i −0.751888 0.659290i $$-0.770857\pi$$
0.751888 0.659290i $$-0.229143\pi$$
$$600$$ 0 0
$$601$$ −83320.1 −0.230675 −0.115338 0.993326i $$-0.536795\pi$$
−0.115338 + 0.993326i $$0.536795\pi$$
$$602$$ −116256. 267835.i −0.320790 0.739052i
$$603$$ 0 0
$$604$$ −320834. 299946.i −0.879441 0.822185i
$$605$$ −118695. −0.324280
$$606$$ 0 0
$$607$$ 143905.i 0.390570i −0.980747 0.195285i $$-0.937437\pi$$
0.980747 0.195285i $$-0.0625632\pi$$
$$608$$ 206574. + 399924.i 0.558816 + 1.08186i
$$609$$ 0 0
$$610$$ 180159. + 415059.i 0.484169 + 1.11545i
$$611$$ 212582.i 0.569435i
$$612$$ 0 0
$$613$$ −5563.04 −0.0148044 −0.00740221 0.999973i $$-0.502356\pi$$
−0.00740221 + 0.999973i $$0.502356\pi$$
$$614$$ −318683. + 138326.i −0.845321 + 0.366917i
$$615$$ 0 0
$$616$$ 271102. + 96584.6i 0.714449 + 0.254534i
$$617$$ −300749. −0.790012 −0.395006 0.918679i $$-0.629257\pi$$
−0.395006 + 0.918679i $$0.629257\pi$$
$$618$$ 0 0
$$619$$ 158539.i 0.413767i 0.978366 + 0.206883i $$0.0663321\pi$$
−0.978366 + 0.206883i $$0.933668\pi$$
$$620$$ 406675. + 380199.i 1.05795 + 0.989070i
$$621$$ 0 0
$$622$$ 161230. 69983.1i 0.416741 0.180889i
$$623$$ 189267.i 0.487640i
$$624$$ 0 0
$$625$$ −483419. −1.23755
$$626$$ −160542. 369863.i −0.409675 0.943828i
$$627$$ 0 0
$$628$$ −159604. + 170718.i −0.404691 + 0.432873i
$$629$$ −1.02834e6 −2.59918
$$630$$ 0 0
$$631$$ 557374.i 1.39987i −0.714206 0.699936i $$-0.753212\pi$$
0.714206 0.699936i $$-0.246788\pi$$
$$632$$ −221401. + 621449.i −0.554301 + 1.55586i
$$633$$ 0 0
$$634$$ −162429. 374213.i −0.404098 0.930979i
$$635$$ 223643.i 0.554635i
$$636$$ 0 0
$$637$$ 216831. 0.534370
$$638$$ 522023. 226588.i 1.28247 0.556667i
$$639$$ 0 0
$$640$$ −131048. + 464508.i −0.319942 + 1.13405i
$$641$$ 101106. 0.246071 0.123036 0.992402i $$-0.460737\pi$$
0.123036 + 0.992402i $$0.460737\pi$$
$$642$$ 0 0
$$643$$ 406950.i 0.984281i 0.870516 + 0.492141i $$0.163785\pi$$
−0.870516 + 0.492141i $$0.836215\pi$$
$$644$$ 61755.1 66055.6i 0.148902 0.159271i
$$645$$ 0 0
$$646$$ 614126. 266565.i 1.47161 0.638761i
$$647$$ 427706.i 1.02173i 0.859660 + 0.510866i $$0.170675\pi$$
−0.859660 + 0.510866i $$0.829325\pi$$
$$648$$ 0 0
$$649$$ 332601. 0.789648
$$650$$ 63613.3 + 146555.i 0.150564 + 0.346876i
$$651$$ 0 0
$$652$$ 456588. + 426862.i 1.07406 + 1.00414i
$$653$$ 430055. 1.00855 0.504275 0.863543i $$-0.331760\pi$$
0.504275 + 0.863543i $$0.331760\pi$$
$$654$$ 0 0
$$655$$ 98227.4i 0.228955i
$$656$$ −26783.1 397542.i −0.0622377 0.923793i
$$657$$ 0 0
$$658$$ 67725.4 + 156029.i 0.156423 + 0.360374i
$$659$$ 179686.i 0.413755i −0.978367 0.206878i $$-0.933670\pi$$
0.978367 0.206878i $$-0.0663302\pi$$
$$660$$ 0 0
$$661$$ −539348. −1.23443 −0.617214 0.786795i $$-0.711739\pi$$
−0.617214 + 0.786795i $$0.711739\pi$$
$$662$$ −145588. + 63193.4i −0.332208 + 0.144197i
$$663$$ 0 0
$$664$$ −264660. + 742872.i −0.600279 + 1.68492i
$$665$$ −426148. −0.963645
$$666$$ 0 0
$$667$$ 178809.i 0.401918i
$$668$$ −36502.7 34126.2i −0.0818036 0.0764777i
$$669$$ 0 0
$$670$$ −254290. + 110376.i −0.566473 + 0.245881i
$$671$$ 524693.i 1.16536i
$$672$$ 0 0
$$673$$ −758520. −1.67470 −0.837350 0.546667i $$-0.815896\pi$$
−0.837350 + 0.546667i $$0.815896\pi$$
$$674$$ −205970. 474523.i −0.453403 1.04457i
$$675$$ 0 0
$$676$$ 16319.5 17456.0i 0.0357120 0.0381989i
$$677$$ −394155. −0.859982 −0.429991 0.902833i $$-0.641483\pi$$
−0.429991 + 0.902833i $$0.641483\pi$$
$$678$$ 0 0
$$679$$ 268542.i 0.582468i
$$680$$ 676211. + 240911.i 1.46239 + 0.521002i
$$681$$ 0 0
$$682$$ 257047. + 592197.i 0.552642 + 1.27320i
$$683$$ 483705.i 1.03691i 0.855106 + 0.518453i $$0.173492\pi$$
−0.855106 + 0.518453i $$0.826508\pi$$
$$684$$ 0 0
$$685$$ −348303. −0.742294
$$686$$ −449079. + 194926.i −0.954277 + 0.414210i
$$687$$ 0 0
$$688$$ 566528. 38168.1i 1.19686 0.0806349i
$$689$$ 166989. 0.351763
$$690$$ 0 0
$$691$$ 136607.i 0.286098i −0.989716 0.143049i $$-0.954309\pi$$
0.989716 0.143049i $$-0.0456907\pi$$
$$692$$ −554533. + 593150.i −1.15802 + 1.23866i
$$693$$ 0 0
$$694$$ 640219. 277891.i 1.32926 0.576974i
$$695$$ 163325.i 0.338130i
$$696$$ 0 0
$$697$$ −592615. −1.21985
$$698$$ −62784.9 144647.i −0.128868 0.296892i
$$699$$ 0 0
$$700$$ −93380.6 87301.1i −0.190573 0.178165i
$$701$$ 878847. 1.78845 0.894226 0.447617i $$-0.147727\pi$$
0.894226 + 0.447617i $$0.147727\pi$$
$$702$$ 0 0
$$703$$ 1.18720e6i 2.40222i
$$704$$ −353871. + 433602.i −0.714002 + 0.874875i
$$705$$ 0 0
$$706$$ −196026. 451613.i −0.393282 0.906061i
$$707$$ 376502.i 0.753231i
$$708$$ 0 0
$$709$$ 445304. 0.885857 0.442929 0.896557i $$-0.353939\pi$$
0.442929 + 0.896557i $$0.353939\pi$$
$$710$$ −95557.4 + 41477.3i −0.189560 + 0.0822800i
$$711$$ 0 0
$$712$$ 346723. + 123526.i 0.683948 + 0.243668i
$$713$$ 202846. 0.399012
$$714$$ 0 0
$$715$$ 662220.i 1.29536i
$$716$$ 52088.4 + 48697.2i 0.101605 + 0.0949900i
$$717$$ 0 0
$$718$$ 76933.2 33393.4i 0.149233 0.0647756i
$$719$$ 731078.i 1.41418i 0.707121 + 0.707092i $$0.249993\pi$$
−0.707121 + 0.707092i $$0.750007\pi$$
$$720$$ 0 0
$$721$$ 385836. 0.742219
$$722$$ −100186. 230813.i −0.192191 0.442778i
$$723$$ 0 0
$$724$$ 92470.3 98909.8i 0.176411 0.188696i
$$725$$ −252776. −0.480906
$$726$$ 0 0
$$727$$ 992100.i 1.87710i −0.345147 0.938549i $$-0.612171\pi$$
0.345147 0.938549i $$-0.387829\pi$$
$$728$$ 116294. 326423.i 0.219429 0.615912i
$$729$$ 0 0
$$730$$ 324731. + 748131.i 0.609366 + 1.40389i
$$731$$ 844524.i 1.58044i
$$732$$ 0 0
$$733$$ −121286. −0.225737 −0.112868 0.993610i $$-0.536004\pi$$
−0.112868 + 0.993610i $$0.536004\pi$$
$$734$$ 213920. 92853.6i 0.397064 0.172348i
$$735$$ 0 0
$$736$$ 80704.2 + 156242.i 0.148984 + 0.288431i
$$737$$ −321457. −0.591818
$$738$$ 0 0
$$739$$ 273800.i 0.501355i −0.968071 0.250677i $$-0.919347\pi$$
0.968071 0.250677i $$-0.0806534\pi$$
$$740$$ −869338. + 929878.i −1.58754 + 1.69810i
$$741$$ 0 0
$$742$$ −122565. + 53200.3i −0.222618 + 0.0966287i
$$743$$ 389402.i 0.705376i −0.935741 0.352688i $$-0.885268\pi$$
0.935741 0.352688i $$-0.114732\pi$$
$$744$$ 0 0
$$745$$ −326207. −0.587733
$$746$$ −127055. 292716.i −0.228305 0.525979i
$$747$$ 0 0
$$748$$ 608071. + 568483.i 1.08680 + 1.01605i
$$749$$ −698489. −1.24508
$$750$$ 0 0
$$751$$ 430569.i 0.763419i −0.924282 0.381710i $$-0.875335\pi$$
0.924282 0.381710i $$-0.124665\pi$$
$$752$$ −330034. + 22235.0i −0.583611 + 0.0393189i
$$753$$ 0 0
$$754$$ −272825. 628548.i −0.479891 1.10559i
$$755$$ 808633.i 1.41859i
$$756$$ 0 0
$$757$$ −1.04226e6 −1.81880 −0.909401 0.415920i $$-0.863460\pi$$
−0.909401 + 0.415920i $$0.863460\pi$$
$$758$$ −296762. + 128812.i −0.516500 + 0.224190i
$$759$$ 0 0
$$760$$ 278127. 780670.i 0.481521 1.35158i
$$761$$ −117139. −0.202271 −0.101135 0.994873i $$-0.532248\pi$$
−0.101135 + 0.994873i $$0.532248\pi$$
$$762$$ 0 0
$$763$$ 189318.i 0.325195i
$$764$$ 206865. + 193397.i 0.354405 + 0.331331i
$$765$$ 0 0
$$766$$ −366264. + 158979.i −0.624219 + 0.270946i
$$767$$ 400471.i 0.680739i
$$768$$ 0 0
$$769$$ −104458. −0.176639 −0.0883197 0.996092i $$-0.528150\pi$$
−0.0883197 + 0.996092i $$0.528150\pi$$
$$770$$ −210973. 486050.i −0.355833 0.819785i
$$771$$ 0 0
$$772$$ −119589. + 127917.i −0.200658 + 0.214631i
$$773$$ 34677.2 0.0580343 0.0290172 0.999579i $$-0.490762\pi$$
0.0290172 + 0.999579i $$0.490762\pi$$
$$774$$ 0 0
$$775$$ 286756.i 0.477429i
$$776$$ 491948. + 175264.i 0.816950 + 0.291052i
$$777$$ 0 0
$$778$$ 24818.7 + 57178.4i 0.0410034 + 0.0944654i
$$779$$ 684161.i 1.12741i
$$780$$ 0 0
$$781$$ −120798. −0.198042
$$782$$ 239926. 104142.i 0.392341 0.170298i
$$783$$ 0 0
$$784$$ −22679.4 336631.i −0.0368978 0.547674i
$$785$$ 430280. 0.698252
$$786$$ 0 0
$$787$$ 1.08172e6i 1.74649i −0.487285 0.873243i $$-0.662013\pi$$
0.487285