Properties

 Label 441.2.g.b.67.3 Level $441$ Weight $2$ Character 441.67 Analytic conductor $3.521$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

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Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.g (of order $$3$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$3.52140272914$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\zeta_{18})$$ Defining polynomial: $$x^{6} - x^{3} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 67.3 Root $$0.939693 + 0.342020i$$ of defining polynomial Character $$\chi$$ $$=$$ 441.67 Dual form 441.2.g.b.79.3

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.439693 - 0.761570i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} -1.34730 q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$$ $$q+(0.439693 - 0.761570i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} -1.34730 q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +(-0.592396 + 1.02606i) q^{10} +1.65270 q^{11} +(-0.726682 + 1.99654i) q^{12} +(-1.68479 + 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +(0.233956 - 0.405223i) q^{17} +(2.02094 + 1.69577i) q^{18} +(-1.61334 - 2.79439i) q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +8.94356 q^{23} +(3.15910 + 3.76487i) q^{24} -3.18479 q^{25} +(1.48158 + 2.56617i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(-2.02094 + 0.356347i) q^{30} +(4.61721 + 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(1.84002 + 2.19285i) q^{33} +(-0.205737 - 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 - 7.99724i) q^{37} -2.83750 q^{38} +(-5.74763 + 1.01346i) q^{39} -3.82295 q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 + 1.75573i) q^{44} +(0.701867 - 3.98048i) q^{45} +(3.93242 - 6.81115i) q^{46} +(4.67752 - 8.10170i) q^{47} +(0.0714517 - 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(0.798133 - 0.140732i) q^{51} -4.13341 q^{52} +(0.286989 - 0.497079i) q^{53} +4.56942i q^{54} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} -5.51249 q^{58} +(-5.19846 - 9.00400i) q^{59} +(0.979055 - 2.68993i) q^{60} +(3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(2.47906 - 0.437124i) q^{66} +(-0.298133 - 0.516382i) q^{67} +0.573978 q^{68} +(9.95723 + 11.8666i) q^{69} -0.554378 q^{71} +(-1.47818 + 8.38316i) q^{72} +(1.02481 - 1.77503i) q^{73} -8.12061 q^{74} +(-3.54576 - 4.22567i) q^{75} +(1.97906 - 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} +(-0.0282185 + 0.0488759i) q^{80} +(-8.45723 - 3.07818i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +3.87939 q^{86} +(3.71348 - 10.2027i) q^{87} +4.68954 q^{88} +(4.54323 + 7.86911i) q^{89} +(-2.72281 - 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(-5.47044 + 15.0299i) q^{93} +(-4.11334 - 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(-3.34002 + 9.17664i) q^{96} +(-0.949493 - 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q - 3q^{2} - 3q^{4} - 6q^{5} + 9q^{6} + 12q^{8} + O(q^{10})$$ $$6q - 3q^{2} - 3q^{4} - 6q^{5} + 9q^{6} + 12q^{8} + 12q^{11} + 9q^{12} - 3q^{13} - 9q^{15} - 3q^{16} + 6q^{17} + 9q^{18} - 3q^{19} - 6q^{20} - 9q^{22} + 24q^{23} - 18q^{24} - 12q^{25} - 3q^{26} - 27q^{27} - 9q^{29} - 9q^{30} - 3q^{31} - 9q^{33} + 9q^{34} - 27q^{36} + 3q^{37} - 12q^{38} - 18q^{39} + 18q^{40} + 3q^{43} - 15q^{44} + 18q^{45} + 3q^{47} + 6q^{50} - 9q^{51} + 42q^{52} - 6q^{53} - 9q^{57} - 18q^{58} - 3q^{59} + 9q^{60} + 6q^{61} + 60q^{62} + 24q^{64} - 15q^{65} + 18q^{66} + 12q^{67} - 12q^{68} + 9q^{69} + 18q^{71} + 45q^{72} - 21q^{73} - 60q^{74} + 9q^{75} + 15q^{76} + 54q^{78} + 21q^{79} - 15q^{80} - 9q^{82} - 18q^{83} - 9q^{85} + 12q^{86} - 36q^{87} + 54q^{88} + 12q^{89} - 27q^{90} - 3q^{92} - 27q^{93} - 18q^{94} + 12q^{95} - 3q^{97} + 18q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$344$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.439693 0.761570i 0.310910 0.538511i −0.667650 0.744475i $$-0.732700\pi$$
0.978560 + 0.205964i $$0.0660330\pi$$
$$3$$ 1.11334 + 1.32683i 0.642788 + 0.766044i
$$4$$ 0.613341 + 1.06234i 0.306670 + 0.531169i
$$5$$ −1.34730 −0.602529 −0.301265 0.953541i $$-0.597409\pi$$
−0.301265 + 0.953541i $$0.597409\pi$$
$$6$$ 1.50000 0.264490i 0.612372 0.107978i
$$7$$ 0 0
$$8$$ 2.83750 1.00321
$$9$$ −0.520945 + 2.95442i −0.173648 + 0.984808i
$$10$$ −0.592396 + 1.02606i −0.187332 + 0.324469i
$$11$$ 1.65270 0.498309 0.249154 0.968464i $$-0.419847\pi$$
0.249154 + 0.968464i $$0.419847\pi$$
$$12$$ −0.726682 + 1.99654i −0.209775 + 0.576352i
$$13$$ −1.68479 + 2.91815i −0.467277 + 0.809348i −0.999301 0.0373813i $$-0.988098\pi$$
0.532024 + 0.846729i $$0.321432\pi$$
$$14$$ 0 0
$$15$$ −1.50000 1.78763i −0.387298 0.461564i
$$16$$ 0.0209445 0.0362770i 0.00523613 0.00906925i
$$17$$ 0.233956 0.405223i 0.0567426 0.0982810i −0.836259 0.548335i $$-0.815262\pi$$
0.893001 + 0.450054i $$0.148595\pi$$
$$18$$ 2.02094 + 1.69577i 0.476341 + 0.399698i
$$19$$ −1.61334 2.79439i −0.370126 0.641077i 0.619459 0.785029i $$-0.287352\pi$$
−0.989585 + 0.143953i $$0.954019\pi$$
$$20$$ −0.826352 1.43128i −0.184778 0.320045i
$$21$$ 0 0
$$22$$ 0.726682 1.25865i 0.154929 0.268345i
$$23$$ 8.94356 1.86486 0.932431 0.361348i $$-0.117683\pi$$
0.932431 + 0.361348i $$0.117683\pi$$
$$24$$ 3.15910 + 3.76487i 0.644849 + 0.768501i
$$25$$ −3.18479 −0.636959
$$26$$ 1.48158 + 2.56617i 0.290562 + 0.503268i
$$27$$ −4.50000 + 2.59808i −0.866025 + 0.500000i
$$28$$ 0 0
$$29$$ −3.13429 5.42874i −0.582022 1.00809i −0.995239 0.0974595i $$-0.968928\pi$$
0.413217 0.910632i $$-0.364405\pi$$
$$30$$ −2.02094 + 0.356347i −0.368972 + 0.0650598i
$$31$$ 4.61721 + 7.99724i 0.829276 + 1.43635i 0.898607 + 0.438754i $$0.144580\pi$$
−0.0693317 + 0.997594i $$0.522087\pi$$
$$32$$ 2.81908 + 4.88279i 0.498347 + 0.863163i
$$33$$ 1.84002 + 2.19285i 0.320307 + 0.381727i
$$34$$ −0.205737 0.356347i −0.0352836 0.0611130i
$$35$$ 0 0
$$36$$ −3.45811 + 1.25865i −0.576352 + 0.209775i
$$37$$ −4.61721 7.99724i −0.759065 1.31474i −0.943328 0.331862i $$-0.892323\pi$$
0.184263 0.982877i $$-0.441010\pi$$
$$38$$ −2.83750 −0.460303
$$39$$ −5.74763 + 1.01346i −0.920357 + 0.162284i
$$40$$ −3.82295 −0.604461
$$41$$ 1.70574 2.95442i 0.266391 0.461403i −0.701536 0.712634i $$-0.747502\pi$$
0.967927 + 0.251231i $$0.0808353\pi$$
$$42$$ 0 0
$$43$$ 2.20574 + 3.82045i 0.336372 + 0.582613i 0.983747 0.179558i $$-0.0574668\pi$$
−0.647376 + 0.762171i $$0.724133\pi$$
$$44$$ 1.01367 + 1.75573i 0.152817 + 0.264686i
$$45$$ 0.701867 3.98048i 0.104628 0.593375i
$$46$$ 3.93242 6.81115i 0.579803 1.00425i
$$47$$ 4.67752 8.10170i 0.682286 1.18175i −0.291995 0.956420i $$-0.594319\pi$$
0.974281 0.225335i $$-0.0723475\pi$$
$$48$$ 0.0714517 0.0125989i 0.0103132 0.00181849i
$$49$$ 0 0
$$50$$ −1.40033 + 2.42544i −0.198037 + 0.343009i
$$51$$ 0.798133 0.140732i 0.111761 0.0197065i
$$52$$ −4.13341 −0.573201
$$53$$ 0.286989 0.497079i 0.0394210 0.0682791i −0.845642 0.533751i $$-0.820782\pi$$
0.885063 + 0.465472i $$0.154115\pi$$
$$54$$ 4.56942i 0.621819i
$$55$$ −2.22668 −0.300246
$$56$$ 0 0
$$57$$ 1.91147 5.25173i 0.253181 0.695609i
$$58$$ −5.51249 −0.723825
$$59$$ −5.19846 9.00400i −0.676782 1.17222i −0.975945 0.218019i $$-0.930041\pi$$
0.299162 0.954202i $$-0.403293\pi$$
$$60$$ 0.979055 2.68993i 0.126396 0.347269i
$$61$$ 3.81908 6.61484i 0.488983 0.846943i −0.510937 0.859618i $$-0.670701\pi$$
0.999920 + 0.0126752i $$0.00403474\pi$$
$$62$$ 8.12061 1.03132
$$63$$ 0 0
$$64$$ 5.04189 0.630236
$$65$$ 2.26991 3.93161i 0.281548 0.487656i
$$66$$ 2.47906 0.437124i 0.305151 0.0538063i
$$67$$ −0.298133 0.516382i −0.0364228 0.0630861i 0.847239 0.531211i $$-0.178263\pi$$
−0.883662 + 0.468125i $$0.844930\pi$$
$$68$$ 0.573978 0.0696051
$$69$$ 9.95723 + 11.8666i 1.19871 + 1.42857i
$$70$$ 0 0
$$71$$ −0.554378 −0.0657925 −0.0328963 0.999459i $$-0.510473\pi$$
−0.0328963 + 0.999459i $$0.510473\pi$$
$$72$$ −1.47818 + 8.38316i −0.174205 + 0.987965i
$$73$$ 1.02481 1.77503i 0.119946 0.207752i −0.799800 0.600266i $$-0.795061\pi$$
0.919746 + 0.392514i $$0.128395\pi$$
$$74$$ −8.12061 −0.944002
$$75$$ −3.54576 4.22567i −0.409429 0.487939i
$$76$$ 1.97906 3.42782i 0.227013 0.393198i
$$77$$ 0 0
$$78$$ −1.75537 + 4.82283i −0.198756 + 0.546078i
$$79$$ 1.20187 2.08169i 0.135221 0.234209i −0.790461 0.612512i $$-0.790159\pi$$
0.925682 + 0.378303i $$0.123492\pi$$
$$80$$ −0.0282185 + 0.0488759i −0.00315492 + 0.00546449i
$$81$$ −8.45723 3.07818i −0.939693 0.342020i
$$82$$ −1.50000 2.59808i −0.165647 0.286910i
$$83$$ −7.52481 13.0334i −0.825956 1.43060i −0.901187 0.433431i $$-0.857303\pi$$
0.0752309 0.997166i $$-0.476031\pi$$
$$84$$ 0 0
$$85$$ −0.315207 + 0.545955i −0.0341891 + 0.0592172i
$$86$$ 3.87939 0.418325
$$87$$ 3.71348 10.2027i 0.398127 1.09384i
$$88$$ 4.68954 0.499907
$$89$$ 4.54323 + 7.86911i 0.481582 + 0.834124i 0.999777 0.0211385i $$-0.00672911\pi$$
−0.518195 + 0.855263i $$0.673396\pi$$
$$90$$ −2.72281 2.28471i −0.287010 0.240830i
$$91$$ 0 0
$$92$$ 5.48545 + 9.50108i 0.571898 + 0.990556i
$$93$$ −5.47044 + 15.0299i −0.567258 + 1.55853i
$$94$$ −4.11334 7.12452i −0.424259 0.734838i
$$95$$ 2.17365 + 3.76487i 0.223012 + 0.386267i
$$96$$ −3.34002 + 9.17664i −0.340890 + 0.936587i
$$97$$ −0.949493 1.64457i −0.0964064 0.166981i 0.813788 0.581161i $$-0.197402\pi$$
−0.910195 + 0.414181i $$0.864068\pi$$
$$98$$ 0 0
$$99$$ −0.860967 + 4.88279i −0.0865304 + 0.490738i
$$100$$ −1.95336 3.38332i −0.195336 0.338332i
$$101$$ 1.70914 0.170066 0.0850329 0.996378i $$-0.472900\pi$$
0.0850329 + 0.996378i $$0.472900\pi$$
$$102$$ 0.243756 0.669713i 0.0241354 0.0663115i
$$103$$ 3.63816 0.358478 0.179239 0.983806i $$-0.442636\pi$$
0.179239 + 0.983806i $$0.442636\pi$$
$$104$$ −4.78059 + 8.28023i −0.468776 + 0.811943i
$$105$$ 0 0
$$106$$ −0.252374 0.437124i −0.0245127 0.0424573i
$$107$$ −3.56418 6.17334i −0.344562 0.596799i 0.640712 0.767781i $$-0.278639\pi$$
−0.985274 + 0.170982i $$0.945306\pi$$
$$108$$ −5.52007 3.18701i −0.531169 0.306670i
$$109$$ −0.201867 + 0.349643i −0.0193353 + 0.0334898i −0.875531 0.483162i $$-0.839488\pi$$
0.856196 + 0.516651i $$0.172822\pi$$
$$110$$ −0.979055 + 1.69577i −0.0933493 + 0.161686i
$$111$$ 5.47044 15.0299i 0.519231 1.42658i
$$112$$ 0 0
$$113$$ −7.18479 + 12.4444i −0.675888 + 1.17067i 0.300320 + 0.953839i $$0.402907\pi$$
−0.976208 + 0.216835i $$0.930427\pi$$
$$114$$ −3.15910 3.76487i −0.295877 0.352612i
$$115$$ −12.0496 −1.12363
$$116$$ 3.84477 6.65934i 0.356978 0.618304i
$$117$$ −7.74376 6.49778i −0.715910 0.600720i
$$118$$ −9.14290 −0.841672
$$119$$ 0 0
$$120$$ −4.25624 5.07239i −0.388540 0.463044i
$$121$$ −8.26857 −0.751688
$$122$$ −3.35844 5.81699i −0.304059 0.526646i
$$123$$ 5.81908 1.02606i 0.524689 0.0925168i
$$124$$ −5.66385 + 9.81007i −0.508629 + 0.880971i
$$125$$ 11.0273 0.986315
$$126$$ 0 0
$$127$$ −20.7716 −1.84318 −0.921589 0.388167i $$-0.873108\pi$$
−0.921589 + 0.388167i $$0.873108\pi$$
$$128$$ −3.42127 + 5.92582i −0.302401 + 0.523774i
$$129$$ −2.61334 + 7.18009i −0.230092 + 0.632172i
$$130$$ −1.99613 3.45740i −0.175072 0.303234i
$$131$$ 7.16519 0.626026 0.313013 0.949749i $$-0.398662\pi$$
0.313013 + 0.949749i $$0.398662\pi$$
$$132$$ −1.20099 + 3.29969i −0.104533 + 0.287201i
$$133$$ 0 0
$$134$$ −0.524348 −0.0452968
$$135$$ 6.06283 3.50038i 0.521806 0.301265i
$$136$$ 0.663848 1.14982i 0.0569245 0.0985961i
$$137$$ 2.56893 0.219478 0.109739 0.993960i $$-0.464998\pi$$
0.109739 + 0.993960i $$0.464998\pi$$
$$138$$ 13.4153 2.36549i 1.14199 0.201364i
$$139$$ −3.06670 + 5.31169i −0.260114 + 0.450531i −0.966272 0.257523i $$-0.917094\pi$$
0.706158 + 0.708055i $$0.250427\pi$$
$$140$$ 0 0
$$141$$ 15.9572 2.81369i 1.34384 0.236956i
$$142$$ −0.243756 + 0.422197i −0.0204555 + 0.0354300i
$$143$$ −2.78446 + 4.82283i −0.232848 + 0.403305i
$$144$$ 0.0962667 + 0.0807773i 0.00802222 + 0.00673144i
$$145$$ 4.22281 + 7.31412i 0.350685 + 0.607405i
$$146$$ −0.901207 1.56094i −0.0745844 0.129184i
$$147$$ 0 0
$$148$$ 5.66385 9.81007i 0.465565 0.806383i
$$149$$ 0.431074 0.0353150 0.0176575 0.999844i $$-0.494379\pi$$
0.0176575 + 0.999844i $$0.494379\pi$$
$$150$$ −4.77719 + 0.842347i −0.390056 + 0.0687774i
$$151$$ −2.47060 −0.201055 −0.100527 0.994934i $$-0.532053\pi$$
−0.100527 + 0.994934i $$0.532053\pi$$
$$152$$ −4.57785 7.92907i −0.371313 0.643132i
$$153$$ 1.07532 + 0.902302i 0.0869346 + 0.0729468i
$$154$$ 0 0
$$155$$ −6.22075 10.7747i −0.499663 0.865441i
$$156$$ −4.60189 5.48432i −0.368446 0.439097i
$$157$$ 5.06670 + 8.77579i 0.404367 + 0.700384i 0.994248 0.107106i $$-0.0341585\pi$$
−0.589881 + 0.807491i $$0.700825\pi$$
$$158$$ −1.05690 1.83061i −0.0840828 0.145636i
$$159$$ 0.979055 0.172634i 0.0776441 0.0136908i
$$160$$ −3.79813 6.57856i −0.300269 0.520081i
$$161$$ 0 0
$$162$$ −6.06283 + 5.08732i −0.476341 + 0.399698i
$$163$$ 1.29813 + 2.24843i 0.101678 + 0.176111i 0.912376 0.409353i $$-0.134246\pi$$
−0.810698 + 0.585464i $$0.800912\pi$$
$$164$$ 4.18479 0.326777
$$165$$ −2.47906 2.95442i −0.192994 0.230002i
$$166$$ −13.2344 −1.02719
$$167$$ −11.5915 + 20.0771i −0.896979 + 1.55361i −0.0656422 + 0.997843i $$0.520910\pi$$
−0.831337 + 0.555769i $$0.812424\pi$$
$$168$$ 0 0
$$169$$ 0.822948 + 1.42539i 0.0633037 + 0.109645i
$$170$$ 0.277189 + 0.480105i 0.0212594 + 0.0368224i
$$171$$ 9.09627 3.31077i 0.695609 0.253181i
$$172$$ −2.70574 + 4.68647i −0.206311 + 0.357340i
$$173$$ −2.37598 + 4.11532i −0.180643 + 0.312882i −0.942100 0.335333i $$-0.891151\pi$$
0.761457 + 0.648215i $$0.224484\pi$$
$$174$$ −6.13728 7.31412i −0.465266 0.554482i
$$175$$ 0 0
$$176$$ 0.0346151 0.0599551i 0.00260921 0.00451929i
$$177$$ 6.15910 16.9220i 0.462946 1.27193i
$$178$$ 7.99050 0.598914
$$179$$ 4.26604 7.38901i 0.318859 0.552280i −0.661391 0.750041i $$-0.730034\pi$$
0.980250 + 0.197761i $$0.0633670\pi$$
$$180$$ 4.65910 1.69577i 0.347269 0.126396i
$$181$$ 17.2344 1.28102 0.640512 0.767948i $$-0.278722\pi$$
0.640512 + 0.767948i $$0.278722\pi$$
$$182$$ 0 0
$$183$$ 13.0287 2.29731i 0.963108 0.169822i
$$184$$ 25.3773 1.87084
$$185$$ 6.22075 + 10.7747i 0.457359 + 0.792169i
$$186$$ 9.04101 + 10.7747i 0.662919 + 0.790036i
$$187$$ 0.386659 0.669713i 0.0282753 0.0489743i
$$188$$ 11.4757 0.836948
$$189$$ 0 0
$$190$$ 3.82295 0.277346
$$191$$ −6.45471 + 11.1799i −0.467046 + 0.808948i −0.999291 0.0376425i $$-0.988015\pi$$
0.532245 + 0.846590i $$0.321349\pi$$
$$192$$ 5.61334 + 6.68972i 0.405108 + 0.482789i
$$193$$ 0.319078 + 0.552659i 0.0229677 + 0.0397813i 0.877281 0.479977i $$-0.159355\pi$$
−0.854313 + 0.519759i $$0.826022\pi$$
$$194$$ −1.66994 −0.119895
$$195$$ 7.74376 1.36543i 0.554542 0.0977807i
$$196$$ 0 0
$$197$$ 11.4456 0.815467 0.407733 0.913101i $$-0.366319\pi$$
0.407733 + 0.913101i $$0.366319\pi$$
$$198$$ 3.34002 + 2.80261i 0.237365 + 0.199173i
$$199$$ −1.81908 + 3.15074i −0.128951 + 0.223350i −0.923270 0.384151i $$-0.874494\pi$$
0.794319 + 0.607500i $$0.207828\pi$$
$$200$$ −9.03684 −0.639001
$$201$$ 0.353226 0.970481i 0.0249147 0.0684524i
$$202$$ 0.751497 1.30163i 0.0528751 0.0915824i
$$203$$ 0 0
$$204$$ 0.639033 + 0.761570i 0.0447413 + 0.0533206i
$$205$$ −2.29813 + 3.98048i −0.160509 + 0.278009i
$$206$$ 1.59967 2.77071i 0.111454 0.193045i
$$207$$ −4.65910 + 26.4231i −0.323830 + 1.83653i
$$208$$ 0.0705744 + 0.122238i 0.00489345 + 0.00847571i
$$209$$ −2.66637 4.61830i −0.184437 0.319454i
$$210$$ 0 0
$$211$$ −2.91147 + 5.04282i −0.200434 + 0.347162i −0.948668 0.316273i $$-0.897569\pi$$
0.748234 + 0.663435i $$0.230902\pi$$
$$212$$ 0.704088 0.0483570
$$213$$ −0.617211 0.735564i −0.0422906 0.0504000i
$$214$$ −6.26857 −0.428511
$$215$$ −2.97178 5.14728i −0.202674 0.351041i
$$216$$ −12.7687 + 7.37203i −0.868802 + 0.501603i
$$217$$ 0 0
$$218$$ 0.177519 + 0.307471i 0.0120231 + 0.0208246i
$$219$$ 3.49613 0.616462i 0.236247 0.0416566i
$$220$$ −1.36571 2.36549i −0.0920765 0.159481i
$$221$$ 0.788333 + 1.36543i 0.0530290 + 0.0918490i
$$222$$ −9.04101 10.7747i −0.606793 0.723148i
$$223$$ 3.54189 + 6.13473i 0.237182 + 0.410812i 0.959905 0.280327i $$-0.0904428\pi$$
−0.722722 + 0.691139i $$0.757109\pi$$
$$224$$ 0 0
$$225$$ 1.65910 9.40923i 0.110607 0.627282i
$$226$$ 6.31820 + 10.9434i 0.420280 + 0.727947i
$$227$$ 11.9436 0.792722 0.396361 0.918095i $$-0.370273\pi$$
0.396361 + 0.918095i $$0.370273\pi$$
$$228$$ 6.75150 1.19047i 0.447129 0.0788409i
$$229$$ 17.5526 1.15991 0.579955 0.814649i $$-0.303070\pi$$
0.579955 + 0.814649i $$0.303070\pi$$
$$230$$ −5.29813 + 9.17664i −0.349349 + 0.605089i
$$231$$ 0 0
$$232$$ −8.89352 15.4040i −0.583888 1.01132i
$$233$$ −8.12701 14.0764i −0.532418 0.922175i −0.999284 0.0378470i $$-0.987950\pi$$
0.466865 0.884328i $$-0.345383\pi$$
$$234$$ −8.35339 + 3.04038i −0.546078 + 0.198756i
$$235$$ −6.30200 + 10.9154i −0.411097 + 0.712042i
$$236$$ 6.37686 11.0450i 0.415098 0.718971i
$$237$$ 4.10014 0.722965i 0.266333 0.0469616i
$$238$$ 0 0
$$239$$ 7.54963 13.0763i 0.488345 0.845838i −0.511565 0.859244i $$-0.670934\pi$$
0.999910 + 0.0134062i $$0.00426745\pi$$
$$240$$ −0.0962667 + 0.0169744i −0.00621399 + 0.00109569i
$$241$$ 15.6382 1.00734 0.503671 0.863896i $$-0.331982\pi$$
0.503671 + 0.863896i $$0.331982\pi$$
$$242$$ −3.63563 + 6.29710i −0.233707 + 0.404793i
$$243$$ −5.33157 14.6484i −0.342020 0.939693i
$$244$$ 9.36959 0.599826
$$245$$ 0 0
$$246$$ 1.77719 4.88279i 0.113309 0.311315i
$$247$$ 10.8726 0.691806
$$248$$ 13.1013 + 22.6922i 0.831935 + 1.44095i
$$249$$ 8.91534 24.4947i 0.564987 1.55229i
$$250$$ 4.84864 8.39809i 0.306655 0.531142i
$$251$$ −19.0651 −1.20338 −0.601690 0.798730i $$-0.705506\pi$$
−0.601690 + 0.798730i $$0.705506\pi$$
$$252$$ 0 0
$$253$$ 14.7811 0.929277
$$254$$ −9.13310 + 15.8190i −0.573062 + 0.992572i
$$255$$ −1.07532 + 0.189608i −0.0673393 + 0.0118737i
$$256$$ 8.05051 + 13.9439i 0.503157 + 0.871493i
$$257$$ −26.5817 −1.65812 −0.829061 0.559158i $$-0.811124\pi$$
−0.829061 + 0.559158i $$0.811124\pi$$
$$258$$ 4.31908 + 5.14728i 0.268894 + 0.320455i
$$259$$ 0 0
$$260$$ 5.56893 0.345370
$$261$$ 17.6716 6.43193i 1.09384 0.398127i
$$262$$ 3.15048 5.45680i 0.194637 0.337122i
$$263$$ −0.734118 −0.0452676 −0.0226338 0.999744i $$-0.507205\pi$$
−0.0226338 + 0.999744i $$0.507205\pi$$
$$264$$ 5.22106 + 6.22221i 0.321334 + 0.382951i
$$265$$ −0.386659 + 0.669713i −0.0237523 + 0.0411402i
$$266$$ 0 0
$$267$$ −5.38279 + 14.7891i −0.329421 + 0.905078i
$$268$$ 0.365715 0.633436i 0.0223396 0.0386933i
$$269$$ −10.4251 + 18.0569i −0.635632 + 1.10095i 0.350749 + 0.936470i $$0.385927\pi$$
−0.986381 + 0.164478i $$0.947406\pi$$
$$270$$ 6.15636i 0.374664i
$$271$$ 3.47906 + 6.02590i 0.211338 + 0.366047i 0.952133 0.305683i $$-0.0988847\pi$$
−0.740796 + 0.671730i $$0.765551\pi$$
$$272$$ −0.00980018 0.0169744i −0.000594223 0.00102922i
$$273$$ 0 0
$$274$$ 1.12954 1.95642i 0.0682379 0.118191i
$$275$$ −5.26352 −0.317402
$$276$$ −6.49912 + 17.8562i −0.391201 + 1.07482i
$$277$$ 17.8726 1.07386 0.536930 0.843627i $$-0.319584\pi$$
0.536930 + 0.843627i $$0.319584\pi$$
$$278$$ 2.69681 + 4.67102i 0.161744 + 0.280149i
$$279$$ −26.0326 + 9.47508i −1.55853 + 0.567258i
$$280$$ 0 0
$$281$$ −11.1552 19.3214i −0.665465 1.15262i −0.979159 0.203095i $$-0.934900\pi$$
0.313694 0.949524i $$-0.398433\pi$$
$$282$$ 4.87346 13.3897i 0.290210 0.797346i
$$283$$ −9.29726 16.1033i −0.552665 0.957243i −0.998081 0.0619196i $$-0.980278\pi$$
0.445417 0.895323i $$-0.353056\pi$$
$$284$$ −0.340022 0.588936i −0.0201766 0.0349469i
$$285$$ −2.57532 + 7.07564i −0.152549 + 0.419125i
$$286$$ 2.44862 + 4.24113i 0.144790 + 0.250783i
$$287$$ 0 0
$$288$$ −15.8944 + 5.78509i −0.936587 + 0.340890i
$$289$$ 8.39053 + 14.5328i 0.493561 + 0.854872i
$$290$$ 7.42696 0.436126
$$291$$ 1.12495 3.09078i 0.0659459 0.181185i
$$292$$ 2.51424 0.147135
$$293$$ 6.54576 11.3376i 0.382407 0.662349i −0.608998 0.793171i $$-0.708428\pi$$
0.991406 + 0.130822i $$0.0417618\pi$$
$$294$$ 0 0
$$295$$ 7.00387 + 12.1311i 0.407781 + 0.706298i
$$296$$ −13.1013 22.6922i −0.761499 1.31895i
$$297$$ −7.43717 + 4.29385i −0.431548 + 0.249154i
$$298$$ 0.189540 0.328293i 0.0109798 0.0190175i
$$299$$ −15.0680 + 26.0986i −0.871408 + 1.50932i
$$300$$ 2.31433 6.35857i 0.133618 0.367112i
$$301$$ 0 0
$$302$$ −1.08630 + 1.88153i −0.0625098 + 0.108270i
$$303$$ 1.90286 + 2.26774i 0.109316 + 0.130278i
$$304$$ −0.135163 −0.00775211
$$305$$ −5.14543 + 8.91215i −0.294626 + 0.510308i
$$306$$ 1.15998 0.422197i 0.0663115 0.0241354i
$$307$$ −6.31046 −0.360157 −0.180078 0.983652i $$-0.557635\pi$$
−0.180078 + 0.983652i $$0.557635\pi$$
$$308$$ 0 0
$$309$$ 4.05051 + 4.82721i 0.230425 + 0.274610i
$$310$$ −10.9409 −0.621400
$$311$$ −4.76217 8.24833i −0.270038 0.467720i 0.698833 0.715285i $$-0.253703\pi$$
−0.968871 + 0.247565i $$0.920370\pi$$
$$312$$ −16.3089 + 2.87569i −0.923308 + 0.162804i
$$313$$ −8.81433 + 15.2669i −0.498215 + 0.862934i −0.999998 0.00205946i $$-0.999344\pi$$
0.501782 + 0.864994i $$0.332678\pi$$
$$314$$ 8.91117 0.502886
$$315$$ 0 0
$$316$$ 2.94862 0.165873
$$317$$ −4.03849 + 6.99486i −0.226824 + 0.392871i −0.956865 0.290533i $$-0.906168\pi$$
0.730041 + 0.683403i $$0.239501\pi$$
$$318$$ 0.299011 0.821525i 0.0167677 0.0460688i
$$319$$ −5.18004 8.97210i −0.290027 0.502341i
$$320$$ −6.79292 −0.379736
$$321$$ 4.22281 11.6021i 0.235694 0.647565i
$$322$$ 0 0
$$323$$ −1.50980 −0.0840075
$$324$$ −1.91710 10.8724i −0.106506 0.604023i
$$325$$ 5.36571 9.29369i 0.297636 0.515521i
$$326$$ 2.28312 0.126450
$$327$$ −0.688663 + 0.121430i −0.0380831 + 0.00671509i
$$328$$ 4.84002 8.38316i 0.267246 0.462883i
$$329$$ 0 0
$$330$$ −3.34002 + 0.588936i −0.183862 + 0.0324199i
$$331$$ −11.5248 + 19.9616i −0.633461 + 1.09719i 0.353378 + 0.935481i $$0.385033\pi$$
−0.986839 + 0.161706i $$0.948300\pi$$
$$332$$ 9.23055 15.9878i 0.506592 0.877444i
$$333$$ 26.0326 9.47508i 1.42658 0.519231i
$$334$$ 10.1934 + 17.6555i 0.557759 + 0.966066i
$$335$$ 0.401674 + 0.695720i 0.0219458 + 0.0380112i
$$336$$ 0 0
$$337$$ −14.5116 + 25.1348i −0.790498 + 1.36918i 0.135161 + 0.990824i $$0.456845\pi$$
−0.925659 + 0.378359i $$0.876489\pi$$
$$338$$ 1.44738 0.0787269
$$339$$ −24.5107 + 4.32190i −1.33124 + 0.234734i
$$340$$ −0.773318 −0.0419391
$$341$$ 7.63088 + 13.2171i 0.413235 + 0.715745i
$$342$$ 1.47818 8.38316i 0.0799307 0.453310i
$$343$$ 0 0
$$344$$ 6.25877 + 10.8405i 0.337450 + 0.584481i
$$345$$ −13.4153 15.9878i −0.722258 0.860753i
$$346$$ 2.08940 + 3.61895i 0.112327 + 0.194556i
$$347$$ −6.47313 11.2118i −0.347496 0.601880i 0.638308 0.769781i $$-0.279635\pi$$
−0.985804 + 0.167901i $$0.946301\pi$$
$$348$$ 13.1163 2.31276i 0.703109 0.123977i
$$349$$ 0.731429 + 1.26687i 0.0391525 + 0.0678141i 0.884938 0.465710i $$-0.154201\pi$$
−0.845785 + 0.533524i $$0.820868\pi$$
$$350$$ 0 0
$$351$$ 17.5089i 0.934555i
$$352$$ 4.65910 + 8.06980i 0.248331 + 0.430122i
$$353$$ −14.3327 −0.762855 −0.381428 0.924399i $$-0.624567\pi$$
−0.381428 + 0.924399i $$0.624567\pi$$
$$354$$ −10.1792 12.1311i −0.541017 0.644759i
$$355$$ 0.746911 0.0396419
$$356$$ −5.57310 + 9.65289i −0.295374 + 0.511602i
$$357$$ 0 0
$$358$$ −3.75150 6.49778i −0.198273 0.343418i
$$359$$ 10.4684 + 18.1318i 0.552500 + 0.956958i 0.998093 + 0.0617224i $$0.0196594\pi$$
−0.445593 + 0.895235i $$0.647007\pi$$
$$360$$ 1.99154 11.2946i 0.104964 0.595278i
$$361$$ 4.29426 7.43788i 0.226014 0.391467i
$$362$$ 7.57785 13.1252i 0.398283 0.689846i
$$363$$ −9.20574 10.9710i −0.483176 0.575827i
$$364$$ 0 0
$$365$$ −1.38073 + 2.39149i −0.0722707 + 0.125176i
$$366$$ 3.97906 10.9324i 0.207989 0.571444i
$$367$$ 12.0574 0.629390 0.314695 0.949193i $$-0.398098\pi$$
0.314695 + 0.949193i $$0.398098\pi$$
$$368$$ 0.187319 0.324446i 0.00976466 0.0169129i
$$369$$ 7.84002 + 6.57856i 0.408135 + 0.342466i
$$370$$ 10.9409 0.568789
$$371$$ 0 0
$$372$$ −19.3221 + 3.40700i −1.00180 + 0.176645i
$$373$$ −0.781059 −0.0404417 −0.0202209 0.999796i $$-0.506437\pi$$
−0.0202209 + 0.999796i $$0.506437\pi$$
$$374$$ −0.340022 0.588936i −0.0175821 0.0304532i
$$375$$ 12.2772 + 14.6314i 0.633991 + 0.755561i
$$376$$ 13.2724 22.9885i 0.684474 1.18554i
$$377$$ 21.1225 1.08786
$$378$$ 0 0
$$379$$ −6.92396 −0.355660 −0.177830 0.984061i $$-0.556908\pi$$
−0.177830 + 0.984061i $$0.556908\pi$$
$$380$$ −2.66637 + 4.61830i −0.136782 + 0.236914i
$$381$$ −23.1258 27.5603i −1.18477 1.41196i
$$382$$ 5.67617 + 9.83142i 0.290418 + 0.503019i
$$383$$ −7.73236 −0.395105 −0.197553 0.980292i $$-0.563299\pi$$
−0.197553 + 0.980292i $$0.563299\pi$$
$$384$$ −11.6716 + 2.05802i −0.595613 + 0.105023i
$$385$$ 0 0
$$386$$ 0.561185 0.0285636
$$387$$ −12.4363 + 4.52644i −0.632172 + 0.230092i
$$388$$ 1.16473 2.01736i 0.0591300 0.102416i
$$389$$ 5.39961 0.273771 0.136886 0.990587i $$-0.456291\pi$$
0.136886 + 0.990587i $$0.456291\pi$$
$$390$$ 2.36500 6.49778i 0.119756 0.329028i
$$391$$ 2.09240 3.62414i 0.105817 0.183280i
$$392$$ 0 0
$$393$$ 7.97730 + 9.50698i 0.402402 + 0.479564i
$$394$$ 5.03256 8.71664i 0.253536 0.439138i
$$395$$ −1.61927 + 2.80466i −0.0814743 + 0.141118i
$$396$$ −5.71523 + 2.08017i −0.287201 + 0.104533i
$$397$$ −14.6172 25.3178i −0.733617 1.27066i −0.955328 0.295549i $$-0.904497\pi$$
0.221711 0.975112i $$-0.428836\pi$$
$$398$$ 1.59967 + 2.77071i 0.0801842 + 0.138883i
$$399$$ 0 0
$$400$$ −0.0667040 + 0.115535i −0.00333520 + 0.00577674i
$$401$$ −27.3979 −1.36818 −0.684092 0.729396i $$-0.739801\pi$$
−0.684092 + 0.729396i $$0.739801\pi$$
$$402$$ −0.583778 0.695720i −0.0291162 0.0346993i
$$403$$ −31.1162 −1.55001
$$404$$ 1.04829 + 1.81568i 0.0521542 + 0.0903337i
$$405$$ 11.3944 + 4.14722i 0.566192 + 0.206077i
$$406$$ 0 0
$$407$$ −7.63088 13.2171i −0.378249 0.655146i
$$408$$ 2.26470 0.399328i 0.112119 0.0197697i
$$409$$ −4.51249 7.81586i −0.223128 0.386469i 0.732628 0.680629i $$-0.238294\pi$$
−0.955756 + 0.294160i $$0.904960\pi$$
$$410$$ 2.02094 + 3.50038i 0.0998073 + 0.172871i
$$411$$ 2.86009 + 3.40852i 0.141078 + 0.168130i
$$412$$ 2.23143 + 3.86495i 0.109935 + 0.190412i
$$413$$ 0 0
$$414$$ 18.0744 + 15.1663i 0.888310 + 0.745381i
$$415$$ 10.1382 + 17.5598i 0.497662 + 0.861977i
$$416$$ −18.9982 −0.931466
$$417$$ −10.4620 + 1.84473i −0.512325 + 0.0903368i
$$418$$ −4.68954 −0.229373
$$419$$ 0.0876485 0.151812i 0.00428191 0.00741649i −0.863877 0.503704i $$-0.831970\pi$$
0.868158 + 0.496287i $$0.165304\pi$$
$$420$$ 0 0
$$421$$ 12.3525 + 21.3952i 0.602025 + 1.04274i 0.992514 + 0.122130i $$0.0389724\pi$$
−0.390490 + 0.920607i $$0.627694\pi$$
$$422$$ 2.56031 + 4.43458i 0.124634 + 0.215872i
$$423$$ 21.4991 + 18.0399i 1.04532 + 0.877130i
$$424$$ 0.814330 1.41046i 0.0395474 0.0684980i
$$425$$ −0.745100 + 1.29055i −0.0361427 + 0.0626009i
$$426$$ −0.831566 + 0.146628i −0.0402895 + 0.00710413i
$$427$$ 0 0
$$428$$ 4.37211 7.57272i 0.211334 0.366041i
$$429$$ −9.49912 + 1.67495i −0.458622 + 0.0808674i
$$430$$ −5.22668 −0.252053
$$431$$ 14.6596 25.3911i 0.706126 1.22305i −0.260157 0.965566i $$-0.583774\pi$$
0.966283 0.257481i $$-0.0828924\pi$$
$$432$$ 0.217662i 0.0104723i
$$433$$ −19.6554 −0.944578 −0.472289 0.881444i $$-0.656572\pi$$
−0.472289 + 0.881444i $$0.656572\pi$$
$$434$$ 0 0
$$435$$ −5.00316 + 13.7461i −0.239883 + 0.659073i
$$436$$ −0.495252 −0.0237183
$$437$$ −14.4290 24.9918i −0.690233 1.19552i
$$438$$ 1.06774 2.93360i 0.0510188 0.140173i
$$439$$ −10.9650 + 18.9919i −0.523330 + 0.906434i 0.476302 + 0.879282i $$0.341977\pi$$
−0.999631 + 0.0271516i $$0.991356\pi$$
$$440$$ −6.31820 −0.301208
$$441$$ 0 0
$$442$$ 1.38650 0.0659489
$$443$$ 9.35504 16.2034i 0.444471 0.769847i −0.553544 0.832820i $$-0.686725\pi$$
0.998015 + 0.0629732i $$0.0200583\pi$$
$$444$$ 19.3221 3.40700i 0.916985 0.161689i
$$445$$ −6.12108 10.6020i −0.290167 0.502584i
$$446$$ 6.22937 0.294969
$$447$$ 0.479933 + 0.571962i 0.0227000 + 0.0270529i
$$448$$ 0 0
$$449$$ 6.68004 0.315251 0.157625 0.987499i $$-0.449616\pi$$
0.157625 + 0.987499i $$0.449616\pi$$
$$450$$ −6.43629 5.40069i −0.303410 0.254591i
$$451$$ 2.81908 4.88279i 0.132745 0.229921i
$$452$$ −17.6269 −0.829100
$$453$$ −2.75062 3.27806i −0.129235 0.154017i
$$454$$ 5.25150 9.09586i 0.246465 0.426890i
$$455$$ 0 0
$$456$$ 5.42380 14.9018i 0.253993 0.697839i
$$457$$ 9.71436 16.8258i 0.454418 0.787076i −0.544236 0.838932i $$-0.683180\pi$$
0.998655 + 0.0518563i $$0.0165138\pi$$
$$458$$ 7.71776 13.3676i 0.360627 0.624625i
$$459$$ 2.43134i 0.113485i
$$460$$ −7.39053 12.8008i −0.344585 0.596839i
$$461$$ −0.482926 0.836452i −0.0224921 0.0389575i 0.854560 0.519352i $$-0.173827\pi$$
−0.877052 + 0.480395i $$0.840493\pi$$
$$462$$ 0 0
$$463$$ 0.222811 0.385920i 0.0103549 0.0179352i −0.860802 0.508941i $$-0.830037\pi$$
0.871156 + 0.491006i $$0.163371\pi$$
$$464$$ −0.262585 −0.0121902
$$465$$ 7.37030 20.2497i 0.341789 0.939059i
$$466$$ −14.2935 −0.662136
$$467$$ −17.1074 29.6309i −0.791637 1.37115i −0.924953 0.380081i $$-0.875896\pi$$
0.133317 0.991074i $$-0.457437\pi$$
$$468$$ 2.15328 12.2118i 0.0995352 0.564492i
$$469$$ 0 0
$$470$$ 5.54189 + 9.59883i 0.255628 + 0.442761i
$$471$$ −6.00299 + 16.4931i −0.276603 + 0.759961i
$$472$$ −14.7506 25.5488i −0.678952 1.17598i
$$473$$ 3.64543 + 6.31407i 0.167617 + 0.290321i
$$474$$ 1.25221 3.44042i 0.0575160 0.158024i
$$475$$ 5.13816 + 8.89955i 0.235755 + 0.408339i
$$476$$ 0 0
$$477$$ 1.31908 + 1.10684i 0.0603964 + 0.0506786i
$$478$$ −6.63903 11.4991i −0.303662 0.525959i
$$479$$ 21.7929 0.995744 0.497872 0.867251i $$-0.334115\pi$$
0.497872 + 0.867251i $$0.334115\pi$$
$$480$$ 4.50000 12.3636i 0.205396 0.564321i
$$481$$ 31.1162 1.41878
$$482$$ 6.87598 11.9095i 0.313192 0.542465i
$$483$$ 0 0
$$484$$ −5.07145 8.78401i −0.230521 0.399273i
$$485$$ 1.27925 + 2.21572i 0.0580877 + 0.100611i
$$486$$ −13.5000 2.38041i −0.612372 0.107978i
$$487$$ −9.69640 + 16.7947i −0.439386 + 0.761039i −0.997642 0.0686297i $$-0.978137\pi$$
0.558256 + 0.829669i $$0.311471\pi$$
$$488$$ 10.8366 18.7696i 0.490551 0.849659i
$$489$$ −1.53802 + 4.22567i −0.0695516 + 0.191091i
$$490$$ 0 0
$$491$$ −13.0783 + 22.6523i −0.590216 + 1.02228i 0.403987 + 0.914765i $$0.367624\pi$$
−0.994203 + 0.107519i $$0.965709\pi$$
$$492$$ 4.65910 + 5.55250i 0.210048 + 0.250326i
$$493$$ −2.93313 −0.132102
$$494$$ 4.78059 8.28023i 0.215089 0.372545i
$$495$$ 1.15998 6.57856i 0.0521371 0.295684i
$$496$$ 0.386821 0.0173688
$$497$$ 0 0
$$498$$ −14.7344 17.5598i −0.660265 0.786873i
$$499$$ −14.3013 −0.640214 −0.320107 0.947381i $$-0.603719\pi$$
−0.320107 + 0.947381i $$0.603719\pi$$
$$500$$ 6.76352 + 11.7148i 0.302474 + 0.523900i
$$501$$ −39.5442 + 6.97270i −1.76670 + 0.311517i
$$502$$ −8.38279 + 14.5194i −0.374142 + 0.648033i
$$503$$ −18.7033 −0.833937 −0.416969 0.908921i $$-0.636908\pi$$
−0.416969 + 0.908921i $$0.636908\pi$$
$$504$$ 0 0
$$505$$ −2.30272 −0.102470
$$506$$ 6.49912 11.2568i 0.288921 0.500426i
$$507$$ −0.975023 + 2.67885i −0.0433023 + 0.118972i
$$508$$ −12.7400 22.0664i −0.565248 0.979039i
$$509$$ 25.6091 1.13510 0.567551 0.823338i $$-0.307891\pi$$
0.567551 + 0.823338i $$0.307891\pi$$
$$510$$ −0.328411 + 0.902302i −0.0145423 + 0.0399546i
$$511$$ 0 0
$$512$$ 0.473897 0.0209435
$$513$$ 14.5201 + 8.38316i 0.641077 + 0.370126i
$$514$$ −11.6878 + 20.2438i −0.515526 + 0.892917i
$$515$$ −4.90167 −0.215994
$$516$$ −9.23055 + 1.62760i −0.406352 + 0.0716509i
$$517$$ 7.73055 13.3897i 0.339989 0.588879i
$$518$$ 0 0
$$519$$ −8.10560 + 1.42924i −0.355796 + 0.0627365i
$$520$$ 6.44087 11.1559i 0.282451 0.489220i
$$521$$ −10.6061 + 18.3702i −0.464660 + 0.804815i −0.999186 0.0403370i $$-0.987157\pi$$
0.534526 + 0.845152i $$0.320490\pi$$
$$522$$ 2.87170 16.2862i 0.125691 0.712829i
$$523$$ 10.4029 + 18.0183i 0.454885 + 0.787884i 0.998682 0.0513330i $$-0.0163470\pi$$
−0.543796 + 0.839217i $$0.683014\pi$$
$$524$$ 4.39470 + 7.61185i 0.191984 + 0.332525i
$$525$$ 0 0
$$526$$ −0.322786 + 0.559082i −0.0140741 + 0.0243771i
$$527$$ 4.32089 0.188221
$$528$$ 0.118089 0.0208222i 0.00513914 0.000906170i
$$529$$ 56.9873 2.47771
$$530$$ 0.340022 + 0.588936i 0.0147696 + 0.0255817i
$$531$$ 29.3097 10.6679i 1.27193 0.462946i
$$532$$ 0 0
$$533$$ 5.74763 + 9.95518i 0.248957 + 0.431207i
$$534$$ 8.89615 + 10.6020i 0.384974 + 0.458794i
$$535$$ 4.80200 + 8.31731i 0.207609 + 0.359589i
$$536$$ −0.845952 1.46523i −0.0365396 0.0632884i
$$537$$ 14.5535 2.56617i 0.628030 0.110739i
$$538$$ 9.16772 + 15.8790i 0.395248 + 0.684590i
$$539$$ 0 0
$$540$$ 7.43717 + 4.29385i 0.320045 + 0.184778i
$$541$$ −13.3648 23.1486i −0.574599 0.995235i −0.996085 0.0884001i $$-0.971825\pi$$
0.421486 0.906835i $$-0.361509\pi$$
$$542$$ 6.11886 0.262828
$$543$$ 19.1878 + 22.8671i 0.823427 + 0.981322i
$$544$$ 2.63816 0.113110
$$545$$ 0.271974 0.471073i 0.0116501 0.0201786i
$$546$$ 0 0
$$547$$ −18.3812 31.8372i −0.785923 1.36126i −0.928446 0.371467i $$-0.878855\pi$$
0.142523 0.989792i $$-0.454479\pi$$
$$548$$ 1.57563 + 2.72907i 0.0673074 + 0.116580i
$$549$$ 17.5535 + 14.7291i 0.749165 + 0.628624i
$$550$$ −2.31433 + 4.00854i −0.0986834 + 0.170925i
$$551$$ −10.1133 + 17.5168i −0.430843 + 0.746242i
$$552$$ 28.2536 + 33.6713i 1.20255 + 1.43315i
$$553$$ 0 0
$$554$$ 7.85844 13.6112i 0.333873 0.578285i
$$555$$ −7.37030 + 20.2497i −0.312852 + 0.859553i
$$556$$ −7.52374 −0.319078
$$557$$ −16.1694 + 28.0062i −0.685118 + 1.18666i 0.288282 + 0.957546i $$0.406916\pi$$
−0.973400 + 0.229114i $$0.926417\pi$$
$$558$$ −4.23039 + 23.9917i −0.179087 + 1.01565i
$$559$$ −14.8648 −0.628716
$$560$$ 0 0
$$561$$ 1.31908 0.232589i 0.0556915 0.00981992i
$$562$$ −19.6195 −0.827598
$$563$$ −8.87093 15.3649i −0.373865 0.647553i 0.616291 0.787518i $$-0.288634\pi$$
−0.990156 + 0.139965i $$0.955301\pi$$
$$564$$ 12.7763 + 15.2262i 0.537980 + 0.641139i
$$565$$ 9.68004 16.7663i 0.407243 0.705365i
$$566$$ −16.3517 −0.687315
$$567$$ 0 0
$$568$$ −1.57304 −0.0660035
$$569$$ 13.3007 23.0374i 0.557593 0.965779i −0.440104 0.897947i $$-0.645058\pi$$
0.997697 0.0678320i $$-0.0216082\pi$$
$$570$$ 4.25624 + 5.07239i 0.178274 + 0.212459i
$$571$$ 5.00862 + 8.67518i 0.209604 + 0.363045i 0.951590 0.307371i $$-0.0994491\pi$$
−0.741986 + 0.670416i $$0.766116\pi$$
$$572$$ −6.83130 −0.285631
$$573$$ −22.0201 + 3.88273i −0.919902 + 0.162203i
$$574$$ 0 0
$$575$$ −28.4834 −1.18784
$$576$$ −2.62654 + 14.8959i −0.109439 + 0.620661i
$$577$$ −16.4572 + 28.5048i −0.685124 + 1.18667i 0.288274 + 0.957548i $$0.406918\pi$$
−0.973398 + 0.229121i $$0.926415\pi$$
$$578$$ 14.7570 0.613811
$$579$$ −0.378041 + 1.03866i −0.0157109 + 0.0431652i
$$580$$ −5.18004 + 8.97210i −0.215090 + 0.372546i
$$581$$ 0 0
$$582$$ −1.85921 2.21572i −0.0770668 0.0918447i
$$583$$ 0.474308 0.821525i 0.0196438 0.0340241i
$$584$$ 2.90791 5.03665i 0.120330 0.208418i
$$585$$ 10.4331 + 8.75444i 0.431357 + 0.361951i
$$586$$ −5.75624 9.97011i −0.237788 0.411861i
$$587$$ −7.53643 13.0535i −0.311062 0.538774i 0.667531 0.744582i $$-0.267351\pi$$
−0.978592 + 0.205808i $$0.934018\pi$$
$$588$$ 0 0
$$589$$ 14.8983 25.8046i 0.613873 1.06326i
$$590$$ 12.3182 0.507132
$$591$$ 12.7429 + 15.1864i 0.524172 + 0.624684i
$$592$$ −0.386821 −0.0158983
$$593$$ 20.5005 + 35.5079i 0.841853 + 1.45813i 0.888326 + 0.459213i $$0.151869\pi$$
−0.0464729 + 0.998920i $$0.514798\pi$$
$$594$$ 7.55190i 0.309858i
$$595$$ 0 0
$$596$$ 0.264396 + 0.457947i 0.0108301 + 0.0187582i
$$597$$ −6.20574 + 1.09424i −0.253984 + 0.0447842i
$$598$$ 13.2506 + 22.9507i 0.541858 + 0.938526i
$$599$$ −3.03684 5.25996i −0.124082 0.214916i 0.797292 0.603594i $$-0.206265\pi$$
−0.921374 + 0.388678i $$0.872932\pi$$
$$600$$ −10.0611 11.9903i −0.410742 0.489503i
$$601$$ −7.06758 12.2414i −0.288293 0.499338i 0.685110 0.728440i $$-0.259754\pi$$
−0.973402 + 0.229102i $$0.926421\pi$$
$$602$$ 0 0
$$603$$ 1.68092 0.611806i 0.0684524 0.0249147i
$$604$$ −1.51532 2.62461i −0.0616575 0.106794i
$$605$$ 11.1402 0.452914
$$606$$ 2.56371 0.452051i 0.104144 0.0183633i
$$607$$ −46.0898 −1.87073 −0.935363 0.353689i $$-0.884927\pi$$
−0.935363 + 0.353689i $$0.884927\pi$$
$$608$$ 9.09627 15.7552i 0.368902 0.638958i
$$609$$ 0 0
$$610$$ 4.52481 + 7.83721i 0.183204 + 0.317319i
$$611$$ 15.7613 + 27.2994i 0.637634 + 1.10441i
$$612$$ −0.299011 + 1.69577i −0.0120868 + 0.0685476i
$$613$$ 13.2469 22.9443i 0.535038 0.926712i −0.464124 0.885770i $$-0.653631\pi$$
0.999162 0.0409421i $$-0.0130359\pi$$
$$614$$ −2.77466 + 4.80586i −0.111976 + 0.193949i
$$615$$ −7.84002 + 1.38241i −0.316140 + 0.0557440i
$$616$$ 0 0
$$617$$ 1.12495 1.94847i 0.0452889 0.0784426i −0.842492 0.538708i $$-0.818913\pi$$
0.887781 + 0.460266i $$0.152246\pi$$
$$618$$ 5.45723 0.962258i 0.219522 0.0387077i
$$619$$ −6.19078 −0.248828 −0.124414 0.992230i $$-0.539705\pi$$
−0.124414 + 0.992230i $$0.539705\pi$$
$$620$$ 7.63088 13.2171i 0.306464 0.530811i
$$621$$ −40.2460 + 23.2361i −1.61502 + 0.932431i
$$622$$ −8.37557 −0.335830
$$623$$ 0 0
$$624$$ −0.0836160 + 0.229733i −0.00334732 + 0.00919668i
$$625$$ 1.06687 0.0426746
$$626$$ 7.75119 + 13.4255i 0.309800 + 0.536589i
$$627$$ 3.15910 8.67956i 0.126162 0.346628i
$$628$$ −6.21523 + 10.7651i −0.248015 + 0.429574i
$$629$$ −4.32089 −0.172285
$$630$$ 0 0
$$631$$ 26.1661 1.04166 0.520829 0.853661i $$-0.325623\pi$$
0.520829 + 0.853661i $$0.325623\pi$$
$$632$$ 3.41029 5.90680i 0.135654 0.234960i
$$633$$ −9.93242 + 1.75135i −0.394778 + 0.0696100i
$$634$$ 3.55138 + 6.15118i 0.141043 + 0.244295i
$$635$$ 27.9855 1.11057
$$636$$ 0.783890 + 0.934204i 0.0310833 + 0.0370436i
$$637$$ 0 0
$$638$$ −9.11051 −0.360689
$$639$$ 0.288800 1.63787i 0.0114248 0.0647930i
$$640$$ 4.60947 7.98384i 0.182205 0.315589i
$$641$$ 4.88888 0.193099 0.0965496 0.995328i $$-0.469219\pi$$
0.0965496 + 0.995328i $$0.469219\pi$$
$$642$$ −6.97906 8.31731i −0.275441 0.328258i
$$643$$ −20.1839 + 34.9596i −0.795976 + 1.37867i 0.126242 + 0.992000i $$0.459709\pi$$
−0.922218 + 0.386671i $$0.873625\pi$$
$$644$$ 0 0
$$645$$ 3.52094 9.67372i 0.138637 0.380902i
$$646$$ −0.663848 + 1.14982i −0.0261188 + 0.0452390i
$$647$$ −1.14038 + 1.97519i −0.0448329 + 0.0776528i −0.887571 0.460671i $$-0.847609\pi$$
0.842738 + 0.538324i $$0.180942\pi$$
$$648$$ −23.9974 8.73433i −0.942706 0.343117i
$$649$$ −8.59152 14.8809i −0.337247 0.584128i
$$650$$ −4.71853 8.17273i −0.185076 0.320561i
$$651$$ 0 0
$$652$$ −1.59240 + 2.75811i −0.0623631 + 0.108016i
$$653$$ 23.4793 0.918815 0.459407 0.888226i $$-0.348062\pi$$
0.459407 + 0.888226i $$0.348062\pi$$
$$654$$ −0.210323 + 0.577857i −0.00822427 + 0.0225960i
$$655$$ −9.65364 −0.377199
$$656$$ −0.0714517 0.123758i −0.00278972 0.00483194i
$$657$$ 4.71032 + 3.95243i 0.183767 + 0.154199i
$$658$$ 0 0
$$659$$ 23.9812 + 41.5366i 0.934174 + 1.61804i 0.776101 + 0.630609i $$0.217195\pi$$
0.158073 + 0.987427i $$0.449472\pi$$
$$660$$ 1.61809 4.44566i 0.0629840 0.173047i
$$661$$ 14.6545 + 25.3824i 0.569995 + 0.987260i 0.996566 + 0.0828055i $$0.0263880\pi$$
−0.426571 + 0.904454i $$0.640279\pi$$
$$662$$ 10.1348 + 17.5539i 0.393898 + 0.682252i
$$663$$ −0.934011 + 2.56617i −0.0362740 + 0.0996620i
$$664$$ −21.3516 36.9821i −0.828604 1.43518i
$$665$$ 0 0
$$666$$ 4.23039 23.9917i 0.163924 0.929661i
$$667$$ −28.0317 48.5523i −1.08539 1.87995i
$$668$$ −28.4382 −1.10031
$$669$$ −4.19640 + 11.5295i −0.162242 + 0.445757i
$$670$$ 0.706452 0.0272926
$$671$$ 6.31180 10.9324i 0.243664 0.422039i
$$672$$ 0 0
$$673$$ −13.1591 22.7922i −0.507246 0.878576i −0.999965 0.00838731i $$-0.997330\pi$$
0.492719 0.870189i $$-0.336003\pi$$
$$674$$ 12.7613 + 22.1032i 0.491547 + 0.851384i
$$675$$ 14.3316 8.27433i 0.551622 0.318479i
$$676$$ −1.00950 + 1.74850i −0.0388267 + 0.0672499i
$$677$$ 17.9454 31.0823i 0.689697 1.19459i −0.282239 0.959344i $$-0.591077\pi$$
0.971936 0.235246i $$-0.0755895\pi$$
$$678$$ −7.48576 + 20.5669i −0.287489 + 0.789869i
$$679$$ 0 0
$$680$$ −0.894400 + 1.54915i −0.0342987 + 0.0594070i
$$681$$ 13.2973 + 15.8471i 0.509552 + 0.607260i
$$682$$ 13.4210 0.513915
$$683$$ −17.5321 + 30.3665i −0.670847 + 1.16194i 0.306818 + 0.951768i $$0.400736\pi$$
−0.977664 + 0.210172i $$0.932597\pi$$
$$684$$ 9.09627 + 7.63267i 0.347804 + 0.291843i
$$685$$ −3.46110 −0.132242
$$686$$ 0 0
$$687$$ 19.5421 + 23.2893i 0.745576 + 0.888543i
$$688$$ 0.184793 0.00704515
$$689$$ 0.967034 + 1.67495i 0.0368411 + 0.0638106i
$$690$$ −18.0744 + 3.18701i −0.688082 + 0.121327i
$$691$$ 1.03343 1.78996i 0.0393136 0.0680932i −0.845699 0.533660i $$-0.820816\pi$$
0.885013 + 0.465567i $$0.154150\pi$$
$$692$$ −5.82915 −0.221591
$$693$$ 0 0
$$694$$ −11.3847 −0.432159
$$695$$ 4.13176 7.15642i 0.156727 0.271458i
$$696$$ 10.5370 28.9501i 0.399403 1.09735i
$$697$$ −0.798133 1.38241i −0.0302315 0.0523624i
$$698$$ 1.28642 0.0486916
$$699$$ 9.62882 26.4550i 0.364196 1.00062i
$$700$$ 0 0
$$701$$ −7.36009 −0.277987 −0.138993 0.990293i $$-0.544387\pi$$
−0.138993 + 0.990293i $$0.544387\pi$$
$$702$$ −13.3342 7.69852i −0.503268 0.290562i
$$703$$ −14.8983 + 25.8046i −0.561899 + 0.973237i
$$704$$ 8.33275 0.314052
$$705$$ −21.4991 + 3.79088i −0.809704 + 0.142773i
$$706$$ −6.30200 + 10.9154i −0.237179 + 0.410806i
$$707$$ 0 0
$$708$$ 21.7545 3.83590i 0.817584 0.144162i
$$709$$ −4.55438 + 7.88841i −0.171043 + 0.296256i −0.938785 0.344504i $$-0.888047\pi$$
0.767742 + 0.640760i $$0.221380\pi$$
$$710$$ 0.328411 0.568825i 0.0123251 0.0213476i
$$711$$ 5.52410 + 4.63527i 0.207170 + 0.173836i
$$712$$ 12.8914 + 22.3286i 0.483126 + 0.836799i
$$713$$ 41.2943 + 71.5239i 1.54648 + 2.67859i
$$714$$ 0 0
$$715$$ 3.75150 6.49778i 0.140298 0.243003i
$$716$$ 10.4662 0.391139
$$717$$ 25.7554 4.54137i 0.961852 0.169600i
$$718$$ 18.4115 0.687110
$$719$$ −12.9768 22.4765i −0.483954 0.838233i 0.515876 0.856663i $$-0.327467\pi$$
−0.999830 + 0.0184300i $$0.994133\pi$$
$$720$$ −0.129700 0.108831i −0.00483362 0.00405589i
$$721$$ 0 0
$$722$$ −3.77631 6.54076i −0.140540 0.243422i
$$723$$ 17.4106 + 20.7491i 0.647507 + 0.771669i
$$724$$ 10.5706 + 18.3088i 0.392852 + 0.680440i
$$725$$ 9.98205 + 17.2894i 0.370724 + 0.642113i
$$726$$ −12.4029 + 2.18696i −0.460313 + 0.0811656i
$$727$$ −5.08007 8.79894i −0.188409 0.326335i 0.756311 0.654213i $$-0.227000\pi$$
−0.944720 + 0.327878i $$0.893667\pi$$
$$728$$ 0 0
$$729$$ 13.5000 23.3827i 0.500000 0.866025i
$$730$$ 1.21419 + 2.10304i 0.0449393 + 0.0778372i
$$731$$ 2.06418 0.0763464
$$732$$ 10.4315 + 12.4318i 0.385561 + 0.459494i
$$733$$ −40.6614 −1.50186 −0.750931 0.660381i $$-0.770395\pi$$
−0.750931 + 0.660381i $$0.770395\pi$$
$$734$$ 5.30154 9.18253i 0.195683 0.338933i
$$735$$ 0 0
$$736$$ 25.2126 + 43.6695i 0.929349 + 1.60968i
$$737$$ −0.492726 0.853427i −0.0181498 0.0314364i
$$738$$ 8.45723 3.07818i 0.311315 0.113309i
$$739$$ 12.6809 21.9640i 0.466475 0.807959i −0.532791 0.846247i $$-0.678857\pi$$
0.999267 + 0.0382877i $$0.0121903\pi$$
$$740$$ −7.63088 + 13.2171i −0.280517 + 0.485869i
$$741$$ 12.1049 + 14.4260i 0.444684 + 0.529954i
$$742$$ 0 0
$$743$$ 11.2221 19.4372i 0.411699 0.713083i −0.583377 0.812202i $$-0.698269\pi$$
0.995076 + 0.0991184i $$0.0316023\pi$$
$$744$$ −15.5223 + 42.6473i −0.569077 + 1.56353i
$$745$$ −0.580785 −0.0212783
$$746$$ −0.343426 + 0.594831i −0.0125737 + 0.0217783i
$$747$$ 42.4261 15.4418i 1.55229 0.564987i
$$748$$ 0.948615 0.0346848
$$749$$ 0 0
$$750$$ 16.5410 2.91663i 0.603992 0.106500i
$$751$$ 24.2172 0.883698 0.441849 0.897090i $$-0.354323\pi$$
0.441849 + 0.897090i $$0.354323\pi$$
$$752$$ −0.195937 0.339373i −0.00714508 0.0123756i
$$753$$ −21.2260 25.2961i −0.773517 0.921842i
$$754$$ 9.28740 16.0862i 0.338227 0.585827i
$$755$$ 3.32863 0.121141
$$756$$ 0 0
$$757$$ 9.11793 0.331397 0.165698 0.986176i $$-0.447012\pi$$
0.165698 + 0.986176i $$0.447012\pi$$
$$758$$ −3.04442 + 5.27308i −0.110578 + 0.191527i
$$759$$ 16.4564 + 19.6119i 0.597328 + 0.711868i
$$760$$ 6.16772 + 10.6828i 0.223727 + 0.387506i
$$761$$ 18.2722 0.662366 0.331183 0.943566i $$-0.392552\pi$$
0.331183 + 0.943566i $$0.392552\pi$$
$$762$$ −31.1573 + 5.49388i −1.12871 + 0.199022i
$$763$$ 0 0
$$764$$ −15.8357 −0.572917
$$765$$ −1.44878 1.21567i −0.0523807 0.0439526i
$$766$$ −3.39986 + 5.88874i −0.122842 + 0.212769i
$$767$$ 35.0333 1.26498
$$768$$ −9.53818 + 26.2059i −0.344179 + 0.945625i
$$769$$ 9.26470 16.0469i 0.334094 0.578667i −0.649217 0.760604i $$-0.724903\pi$$
0.983310 + 0.181936i $$0.0582365\pi$$
$$770$$ 0 0
$$771$$ −29.5945 35.2694i −1.06582 1.27020i
$$772$$ −0.391407 + 0.677937i −0.0140870 + 0.0243995i
$$773$$ −1.48040 + 2.56413i −0.0532463 + 0.0922253i −0.891420 0.453178i $$-0.850290\pi$$
0.838174 + 0.545403i $$0.183624\pi$$
$$774$$ −2.02094 + 11.4613i −0.0726414 + 0.411970i
$$775$$ −14.7049 25.4696i −0.528214 0.914894i
$$776$$ −2.69418 4.66646i −0.0967155 0.167516i
$$777$$ 0 0
$$778$$ 2.37417 4.11218i 0.0851181 0.147429i
$$779$$ −11.0077 −0.394393
$$780$$ 6.20011 + 7.38901i 0.222000 + 0.264569i</