Properties

 Label 750.2.l.c.143.4 Level $750$ Weight $2$ Character 750.143 Analytic conductor $5.989$ Analytic rank $0$ Dimension $80$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$750 = 2 \cdot 3 \cdot 5^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 750.l (of order $$20$$, degree $$8$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$5.98878015160$$ Analytic rank: $$0$$ Dimension: $$80$$ Relative dimension: $$10$$ over $$\Q(\zeta_{20})$$ Twist minimal: no (minimal twist has level 150) Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

 Embedding label 143.4 Character $$\chi$$ $$=$$ 750.143 Dual form 750.2.l.c.257.4

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.453990 + 0.891007i) q^{2} +(0.530925 - 1.64867i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(-0.152718 + 0.152718i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.43624 - 1.75064i) q^{9} +O(q^{10})$$ $$q+(-0.453990 + 0.891007i) q^{2} +(0.530925 - 1.64867i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(-0.152718 + 0.152718i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.43624 - 1.75064i) q^{9} +(4.88609 - 1.58759i) q^{11} +(-1.64587 + 0.539538i) q^{12} +(-1.32436 + 0.674795i) q^{13} +(-0.0667401 - 0.205405i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.762690 - 4.81543i) q^{17} +(2.66586 - 1.37593i) q^{18} +(-0.283032 + 0.389560i) q^{19} +(0.170700 + 0.332863i) q^{21} +(-0.803689 + 5.07429i) q^{22} +(-2.38239 - 1.21389i) q^{23} +(0.266479 - 1.71143i) q^{24} -1.48636i q^{26} +(-4.17969 + 3.08710i) q^{27} +(0.213317 + 0.0337860i) q^{28} +(7.59423 - 5.51753i) q^{29} +(-1.84019 - 1.33698i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.0232622 - 8.89846i) q^{33} +(4.63684 + 1.50660i) q^{34} +(0.0156850 + 2.99996i) q^{36} +(-1.95441 - 3.83574i) q^{37} +(-0.218606 - 0.429039i) q^{38} +(0.409380 + 2.54170i) q^{39} +(5.95547 + 1.93505i) q^{41} +(-0.374079 + 0.000977913i) q^{42} +(-2.72225 - 2.72225i) q^{43} +(-4.15636 - 3.01977i) q^{44} +(2.16317 - 1.57163i) q^{46} +(-10.0271 - 1.58814i) q^{47} +(1.40392 + 1.01441i) q^{48} +6.95335i q^{49} +(-8.34400 - 1.29921i) q^{51} +(1.32436 + 0.674795i) q^{52} +(1.20325 - 7.59700i) q^{53} +(-0.853081 - 5.12565i) q^{54} +(-0.126947 + 0.174728i) q^{56} +(0.491987 + 0.673453i) q^{57} +(1.46845 + 9.27141i) q^{58} +(1.54130 - 4.74363i) q^{59} +(-4.21680 - 12.9780i) q^{61} +(2.02668 - 1.03265i) q^{62} +(0.639411 - 0.104703i) q^{63} +(0.951057 - 0.309017i) q^{64} +(7.93914 + 4.01909i) q^{66} +(14.8405 - 2.35050i) q^{67} +(-3.44747 + 3.44747i) q^{68} +(-3.26618 + 3.28330i) q^{69} +(-7.13100 - 9.81498i) q^{71} +(-2.68010 - 1.34798i) q^{72} +(-4.26070 + 8.36209i) q^{73} +4.30495 q^{74} +0.481522 q^{76} +(-0.503741 + 0.988647i) q^{77} +(-2.45053 - 0.789148i) q^{78} +(1.28502 + 1.76867i) q^{79} +(2.87050 + 8.52996i) q^{81} +(-4.42787 + 4.42787i) q^{82} +(4.93895 - 0.782253i) q^{83} +(0.168957 - 0.333751i) q^{84} +(3.66142 - 1.18967i) q^{86} +(-5.06463 - 15.4498i) q^{87} +(4.57759 - 2.33240i) q^{88} +(3.38311 + 10.4121i) q^{89} +(0.0992002 - 0.305307i) q^{91} +(0.418278 + 2.64090i) q^{92} +(-3.18124 + 2.32404i) q^{93} +(5.96725 - 8.21321i) q^{94} +(-1.54121 + 0.790366i) q^{96} +(-1.57877 + 9.96799i) q^{97} +(-6.19548 - 3.15676i) q^{98} +(-14.6830 - 4.68606i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$80q + 4q^{3} + 4q^{7} + O(q^{10})$$ $$80q + 4q^{3} + 4q^{7} + 16q^{12} + 20q^{16} - 8q^{18} + 40q^{19} + 4q^{22} - 56q^{27} + 4q^{28} - 96q^{33} + 40q^{34} - 64q^{37} + 40q^{39} - 4q^{42} - 24q^{43} + 16q^{48} - 64q^{57} + 20q^{58} + 4q^{63} - 104q^{67} - 140q^{69} + 8q^{72} - 60q^{73} - 60q^{78} - 80q^{79} - 40q^{81} + 96q^{82} - 60q^{84} + 80q^{87} + 24q^{88} + 12q^{93} - 12q^{97} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$251$$ $$\chi(n)$$ $$e\left(\frac{3}{20}\right)$$ $$-1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.453990 + 0.891007i −0.321020 + 0.630037i
$$3$$ 0.530925 1.64867i 0.306530 0.951861i
$$4$$ −0.587785 0.809017i −0.293893 0.404508i
$$5$$ 0 0
$$6$$ 1.22794 + 1.22154i 0.501305 + 0.498691i
$$7$$ −0.152718 + 0.152718i −0.0577219 + 0.0577219i −0.735379 0.677657i $$-0.762996\pi$$
0.677657 + 0.735379i $$0.262996\pi$$
$$8$$ 0.987688 0.156434i 0.349201 0.0553079i
$$9$$ −2.43624 1.75064i −0.812079 0.583547i
$$10$$ 0 0
$$11$$ 4.88609 1.58759i 1.47321 0.478676i 0.541136 0.840935i $$-0.317995\pi$$
0.932077 + 0.362259i $$0.117995\pi$$
$$12$$ −1.64587 + 0.539538i −0.475123 + 0.155751i
$$13$$ −1.32436 + 0.674795i −0.367312 + 0.187155i −0.627897 0.778296i $$-0.716084\pi$$
0.260586 + 0.965451i $$0.416084\pi$$
$$14$$ −0.0667401 0.205405i −0.0178371 0.0548968i
$$15$$ 0 0
$$16$$ −0.309017 + 0.951057i −0.0772542 + 0.237764i
$$17$$ −0.762690 4.81543i −0.184979 1.16791i −0.889059 0.457793i $$-0.848640\pi$$
0.704080 0.710121i $$-0.251360\pi$$
$$18$$ 2.66586 1.37593i 0.628350 0.324309i
$$19$$ −0.283032 + 0.389560i −0.0649319 + 0.0893711i −0.840248 0.542202i $$-0.817591\pi$$
0.775316 + 0.631574i $$0.217591\pi$$
$$20$$ 0 0
$$21$$ 0.170700 + 0.332863i 0.0372498 + 0.0726367i
$$22$$ −0.803689 + 5.07429i −0.171347 + 1.08184i
$$23$$ −2.38239 1.21389i −0.496763 0.253114i 0.187612 0.982243i $$-0.439925\pi$$
−0.684376 + 0.729130i $$0.739925\pi$$
$$24$$ 0.266479 1.71143i 0.0543949 0.349344i
$$25$$ 0 0
$$26$$ 1.48636i 0.291500i
$$27$$ −4.17969 + 3.08710i −0.804382 + 0.594112i
$$28$$ 0.213317 + 0.0337860i 0.0403130 + 0.00638496i
$$29$$ 7.59423 5.51753i 1.41021 1.02458i 0.416921 0.908943i $$-0.363109\pi$$
0.993292 0.115637i $$-0.0368909\pi$$
$$30$$ 0 0
$$31$$ −1.84019 1.33698i −0.330508 0.240128i 0.410138 0.912023i $$-0.365480\pi$$
−0.740646 + 0.671895i $$0.765480\pi$$
$$32$$ −0.707107 0.707107i −0.125000 0.125000i
$$33$$ −0.0232622 8.89846i −0.00404943 1.54902i
$$34$$ 4.63684 + 1.50660i 0.795211 + 0.258380i
$$35$$ 0 0
$$36$$ 0.0156850 + 2.99996i 0.00261417 + 0.499993i
$$37$$ −1.95441 3.83574i −0.321303 0.630592i 0.672704 0.739912i $$-0.265133\pi$$
−0.994007 + 0.109320i $$0.965133\pi$$
$$38$$ −0.218606 0.429039i −0.0354627 0.0695994i
$$39$$ 0.409380 + 2.54170i 0.0655533 + 0.406998i
$$40$$ 0 0
$$41$$ 5.95547 + 1.93505i 0.930087 + 0.302204i 0.734598 0.678502i $$-0.237371\pi$$
0.195489 + 0.980706i $$0.437371\pi$$
$$42$$ −0.374079 0.000977913i −0.0577217 0.000150895i
$$43$$ −2.72225 2.72225i −0.415139 0.415139i 0.468385 0.883524i $$-0.344836\pi$$
−0.883524 + 0.468385i $$0.844836\pi$$
$$44$$ −4.15636 3.01977i −0.626595 0.455248i
$$45$$ 0 0
$$46$$ 2.16317 1.57163i 0.318942 0.231725i
$$47$$ −10.0271 1.58814i −1.46260 0.231654i −0.626154 0.779699i $$-0.715372\pi$$
−0.836448 + 0.548046i $$0.815372\pi$$
$$48$$ 1.40392 + 1.01441i 0.202638 + 0.146417i
$$49$$ 6.95335i 0.993336i
$$50$$ 0 0
$$51$$ −8.34400 1.29921i −1.16839 0.181926i
$$52$$ 1.32436 + 0.674795i 0.183656 + 0.0935773i
$$53$$ 1.20325 7.59700i 0.165279 1.04353i −0.755985 0.654589i $$-0.772842\pi$$
0.921264 0.388939i $$-0.127158\pi$$
$$54$$ −0.853081 5.12565i −0.116090 0.697512i
$$55$$ 0 0
$$56$$ −0.126947 + 0.174728i −0.0169640 + 0.0233490i
$$57$$ 0.491987 + 0.673453i 0.0651653 + 0.0892011i
$$58$$ 1.46845 + 9.27141i 0.192817 + 1.21740i
$$59$$ 1.54130 4.74363i 0.200660 0.617569i −0.799204 0.601061i $$-0.794745\pi$$
0.999864 0.0165081i $$-0.00525494\pi$$
$$60$$ 0 0
$$61$$ −4.21680 12.9780i −0.539906 1.66166i −0.732803 0.680440i $$-0.761789\pi$$
0.192898 0.981219i $$-0.438211\pi$$
$$62$$ 2.02668 1.03265i 0.257389 0.131146i
$$63$$ 0.639411 0.104703i 0.0805582 0.0131913i
$$64$$ 0.951057 0.309017i 0.118882 0.0386271i
$$65$$ 0 0
$$66$$ 7.93914 + 4.01909i 0.977241 + 0.494716i
$$67$$ 14.8405 2.35050i 1.81305 0.287159i 0.844425 0.535673i $$-0.179942\pi$$
0.968628 + 0.248514i $$0.0799422\pi$$
$$68$$ −3.44747 + 3.44747i −0.418067 + 0.418067i
$$69$$ −3.26618 + 3.28330i −0.393202 + 0.395263i
$$70$$ 0 0
$$71$$ −7.13100 9.81498i −0.846294 1.16482i −0.984667 0.174444i $$-0.944187\pi$$
0.138373 0.990380i $$-0.455813\pi$$
$$72$$ −2.68010 1.34798i −0.315853 0.158861i
$$73$$ −4.26070 + 8.36209i −0.498677 + 0.978708i 0.495259 + 0.868745i $$0.335073\pi$$
−0.993936 + 0.109963i $$0.964927\pi$$
$$74$$ 4.30495 0.500441
$$75$$ 0 0
$$76$$ 0.481522 0.0552344
$$77$$ −0.503741 + 0.988647i −0.0574066 + 0.112667i
$$78$$ −2.45053 0.789148i −0.277468 0.0893534i
$$79$$ 1.28502 + 1.76867i 0.144576 + 0.198991i 0.875163 0.483828i $$-0.160754\pi$$
−0.730588 + 0.682819i $$0.760754\pi$$
$$80$$ 0 0
$$81$$ 2.87050 + 8.52996i 0.318945 + 0.947773i
$$82$$ −4.42787 + 4.42787i −0.488976 + 0.488976i
$$83$$ 4.93895 0.782253i 0.542120 0.0858634i 0.120632 0.992697i $$-0.461508\pi$$
0.421488 + 0.906834i $$0.361508\pi$$
$$84$$ 0.168957 0.333751i 0.0184347 0.0364152i
$$85$$ 0 0
$$86$$ 3.66142 1.18967i 0.394821 0.128285i
$$87$$ −5.06463 15.4498i −0.542985 1.65639i
$$88$$ 4.57759 2.33240i 0.487972 0.248634i
$$89$$ 3.38311 + 10.4121i 0.358609 + 1.10368i 0.953887 + 0.300165i $$0.0970417\pi$$
−0.595279 + 0.803519i $$0.702958\pi$$
$$90$$ 0 0
$$91$$ 0.0992002 0.305307i 0.0103990 0.0320048i
$$92$$ 0.418278 + 2.64090i 0.0436085 + 0.275333i
$$93$$ −3.18124 + 2.32404i −0.329879 + 0.240991i
$$94$$ 5.96725 8.21321i 0.615475 0.847128i
$$95$$ 0 0
$$96$$ −1.54121 + 0.790366i −0.157299 + 0.0806664i
$$97$$ −1.57877 + 9.96799i −0.160300 + 1.01210i 0.768050 + 0.640390i $$0.221227\pi$$
−0.928350 + 0.371706i $$0.878773\pi$$
$$98$$ −6.19548 3.15676i −0.625838 0.318881i
$$99$$ −14.6830 4.68606i −1.47570 0.470967i
$$100$$ 0 0
$$101$$ 9.53700i 0.948967i 0.880264 + 0.474483i $$0.157365\pi$$
−0.880264 + 0.474483i $$0.842635\pi$$
$$102$$ 4.94570 6.84473i 0.489697 0.677729i
$$103$$ 9.98929 + 1.58215i 0.984274 + 0.155894i 0.627769 0.778400i $$-0.283968\pi$$
0.356505 + 0.934293i $$0.383968\pi$$
$$104$$ −1.20249 + 0.873663i −0.117914 + 0.0856697i
$$105$$ 0 0
$$106$$ 6.22271 + 4.52106i 0.604403 + 0.439125i
$$107$$ 7.80873 + 7.80873i 0.754898 + 0.754898i 0.975389 0.220491i $$-0.0707659\pi$$
−0.220491 + 0.975389i $$0.570766\pi$$
$$108$$ 4.95428 + 1.56689i 0.476725 + 0.150774i
$$109$$ 5.83194 + 1.89491i 0.558598 + 0.181500i 0.574690 0.818371i $$-0.305123\pi$$
−0.0160921 + 0.999871i $$0.505123\pi$$
$$110$$ 0 0
$$111$$ −7.36152 + 1.18569i −0.698725 + 0.112540i
$$112$$ −0.0980509 0.192436i −0.00926494 0.0181835i
$$113$$ 4.98756 + 9.78864i 0.469190 + 0.920838i 0.997423 + 0.0717385i $$0.0228547\pi$$
−0.528233 + 0.849099i $$0.677145\pi$$
$$114$$ −0.823409 + 0.132623i −0.0771193 + 0.0124212i
$$115$$ 0 0
$$116$$ −8.92755 2.90074i −0.828902 0.269327i
$$117$$ 4.40778 + 0.674520i 0.407500 + 0.0623594i
$$118$$ 3.52687 + 3.52687i 0.324675 + 0.324675i
$$119$$ 0.851879 + 0.618926i 0.0780916 + 0.0567369i
$$120$$ 0 0
$$121$$ 12.4543 9.04858i 1.13221 0.822598i
$$122$$ 13.4778 + 2.13468i 1.22023 + 0.193265i
$$123$$ 6.35216 8.79124i 0.572755 0.792680i
$$124$$ 2.27460i 0.204265i
$$125$$ 0 0
$$126$$ −0.196996 + 0.617253i −0.0175498 + 0.0549893i
$$127$$ 13.3979 + 6.82658i 1.18887 + 0.605761i 0.932624 0.360850i $$-0.117513\pi$$
0.256249 + 0.966611i $$0.417513\pi$$
$$128$$ −0.156434 + 0.987688i −0.0138270 + 0.0873001i
$$129$$ −5.93341 + 3.04279i −0.522407 + 0.267902i
$$130$$ 0 0
$$131$$ −5.12870 + 7.05905i −0.448097 + 0.616752i −0.971987 0.235034i $$-0.924480\pi$$
0.523891 + 0.851785i $$0.324480\pi$$
$$132$$ −7.18533 + 5.24920i −0.625403 + 0.456884i
$$133$$ −0.0162687 0.102717i −0.00141068 0.00890667i
$$134$$ −4.64313 + 14.2901i −0.401105 + 1.23447i
$$135$$ 0 0
$$136$$ −1.50660 4.63684i −0.129190 0.397605i
$$137$$ 2.51567 1.28180i 0.214928 0.109511i −0.343212 0.939258i $$-0.611515\pi$$
0.558140 + 0.829747i $$0.311515\pi$$
$$138$$ −1.44263 4.40077i −0.122805 0.374619i
$$139$$ 6.62014 2.15102i 0.561513 0.182447i −0.0144887 0.999895i $$-0.504612\pi$$
0.576002 + 0.817448i $$0.304612\pi$$
$$140$$ 0 0
$$141$$ −7.94195 + 15.6882i −0.668833 + 1.32119i
$$142$$ 11.9826 1.89786i 1.00556 0.159265i
$$143$$ −5.39965 + 5.39965i −0.451542 + 0.451542i
$$144$$ 2.41780 1.77602i 0.201483 0.148002i
$$145$$ 0 0
$$146$$ −5.51636 7.59261i −0.456537 0.628369i
$$147$$ 11.4638 + 3.69171i 0.945518 + 0.304487i
$$148$$ −1.95441 + 3.83574i −0.160651 + 0.315296i
$$149$$ −7.72360 −0.632742 −0.316371 0.948635i $$-0.602465\pi$$
−0.316371 + 0.948635i $$0.602465\pi$$
$$150$$ 0 0
$$151$$ −14.7868 −1.20333 −0.601667 0.798747i $$-0.705497\pi$$
−0.601667 + 0.798747i $$0.705497\pi$$
$$152$$ −0.218606 + 0.429039i −0.0177313 + 0.0347997i
$$153$$ −6.57201 + 13.0667i −0.531315 + 1.05638i
$$154$$ −0.652197 0.897673i −0.0525556 0.0723365i
$$155$$ 0 0
$$156$$ 1.81565 1.82517i 0.145369 0.146131i
$$157$$ −11.5941 + 11.5941i −0.925312 + 0.925312i −0.997398 0.0720863i $$-0.977034\pi$$
0.0720863 + 0.997398i $$0.477034\pi$$
$$158$$ −2.15928 + 0.341997i −0.171783 + 0.0272078i
$$159$$ −11.8861 6.01719i −0.942630 0.477194i
$$160$$ 0 0
$$161$$ 0.549217 0.178451i 0.0432843 0.0140639i
$$162$$ −8.90343 1.31488i −0.699520 0.103307i
$$163$$ 3.61543 1.84215i 0.283182 0.144289i −0.306630 0.951829i $$-0.599202\pi$$
0.589813 + 0.807540i $$0.299202\pi$$
$$164$$ −1.93505 5.95547i −0.151102 0.465044i
$$165$$ 0 0
$$166$$ −1.54524 + 4.75577i −0.119934 + 0.369119i
$$167$$ −2.16520 13.6706i −0.167549 1.05786i −0.917897 0.396818i $$-0.870114\pi$$
0.750349 0.661042i $$-0.229886\pi$$
$$168$$ 0.220670 + 0.302062i 0.0170250 + 0.0233046i
$$169$$ −6.34263 + 8.72988i −0.487894 + 0.671529i
$$170$$ 0 0
$$171$$ 1.37151 0.453573i 0.104882 0.0346856i
$$172$$ −0.602248 + 3.80244i −0.0459210 + 0.289934i
$$173$$ −0.809140 0.412278i −0.0615178 0.0313449i 0.422961 0.906148i $$-0.360991\pi$$
−0.484479 + 0.874803i $$0.660991\pi$$
$$174$$ 16.0652 + 2.50144i 1.21790 + 0.189633i
$$175$$ 0 0
$$176$$ 5.13754i 0.387257i
$$177$$ −7.00238 5.05961i −0.526331 0.380304i
$$178$$ −10.8132 1.71264i −0.810482 0.128368i
$$179$$ −9.58645 + 6.96496i −0.716525 + 0.520586i −0.885272 0.465074i $$-0.846028\pi$$
0.168747 + 0.985659i $$0.446028\pi$$
$$180$$ 0 0
$$181$$ 13.9076 + 10.1044i 1.03374 + 0.751057i 0.969054 0.246848i $$-0.0793949\pi$$
0.0646876 + 0.997906i $$0.479395\pi$$
$$182$$ 0.226994 + 0.226994i 0.0168259 + 0.0168259i
$$183$$ −23.6352 + 0.0617869i −1.74717 + 0.00456742i
$$184$$ −2.54296 0.826257i −0.187469 0.0609125i
$$185$$ 0 0
$$186$$ −0.626479 3.88960i −0.0459357 0.285199i
$$187$$ −11.3715 22.3178i −0.831566 1.63204i
$$188$$ 4.60895 + 9.04558i 0.336142 + 0.659716i
$$189$$ 0.166859 1.10977i 0.0121372 0.0807238i
$$190$$ 0 0
$$191$$ −4.70151 1.52761i −0.340189 0.110534i 0.133940 0.990989i $$-0.457237\pi$$
−0.474129 + 0.880455i $$0.657237\pi$$
$$192$$ −0.00452789 1.73204i −0.000326772 0.125000i
$$193$$ 2.38356 + 2.38356i 0.171572 + 0.171572i 0.787670 0.616098i $$-0.211287\pi$$
−0.616098 + 0.787670i $$0.711287\pi$$
$$194$$ −8.16479 5.93207i −0.586198 0.425898i
$$195$$ 0 0
$$196$$ 5.62538 4.08708i 0.401813 0.291934i
$$197$$ 7.24145 + 1.14693i 0.515932 + 0.0817156i 0.408970 0.912548i $$-0.365888\pi$$
0.106961 + 0.994263i $$0.465888\pi$$
$$198$$ 10.8412 10.9552i 0.770454 0.778553i
$$199$$ 8.34182i 0.591336i −0.955291 0.295668i $$-0.904458\pi$$
0.955291 0.295668i $$-0.0955422\pi$$
$$200$$ 0 0
$$201$$ 4.00398 25.7150i 0.282419 1.81380i
$$202$$ −8.49753 4.32971i −0.597884 0.304637i
$$203$$ −0.317149 + 2.00240i −0.0222595 + 0.140541i
$$204$$ 3.85340 + 7.51409i 0.269792 + 0.526092i
$$205$$ 0 0
$$206$$ −5.94475 + 8.18224i −0.414190 + 0.570084i
$$207$$ 3.67899 + 7.12804i 0.255707 + 0.495433i
$$208$$ −0.232519 1.46807i −0.0161223 0.101792i
$$209$$ −0.764459 + 2.35276i −0.0528787 + 0.162744i
$$210$$ 0 0
$$211$$ 1.32487 + 4.07753i 0.0912078 + 0.280709i 0.986247 0.165279i $$-0.0528525\pi$$
−0.895039 + 0.445988i $$0.852852\pi$$
$$212$$ −6.85335 + 3.49196i −0.470690 + 0.239828i
$$213$$ −19.9677 + 6.54566i −1.36817 + 0.448501i
$$214$$ −10.5027 + 3.41254i −0.717951 + 0.233276i
$$215$$ 0 0
$$216$$ −3.64531 + 3.70294i −0.248032 + 0.251953i
$$217$$ 0.485210 0.0768498i 0.0329382 0.00521690i
$$218$$ −4.33602 + 4.33602i −0.293672 + 0.293672i
$$219$$ 11.5242 + 11.4641i 0.778735 + 0.774674i
$$220$$ 0 0
$$221$$ 4.25951 + 5.86271i 0.286525 + 0.394369i
$$222$$ 2.28561 7.09746i 0.153400 0.476350i
$$223$$ −0.331831 + 0.651256i −0.0222211 + 0.0436113i −0.901850 0.432049i $$-0.857791\pi$$
0.879629 + 0.475660i $$0.157791\pi$$
$$224$$ 0.215976 0.0144305
$$225$$ 0 0
$$226$$ −10.9860 −0.730781
$$227$$ −1.50300 + 2.94981i −0.0997579 + 0.195786i −0.935492 0.353349i $$-0.885043\pi$$
0.835734 + 0.549135i $$0.185043\pi$$
$$228$$ 0.255652 0.793872i 0.0169310 0.0525755i
$$229$$ 6.20224 + 8.53665i 0.409855 + 0.564117i 0.963183 0.268846i $$-0.0866423\pi$$
−0.553328 + 0.832964i $$0.686642\pi$$
$$230$$ 0 0
$$231$$ 1.36251 + 1.35540i 0.0896463 + 0.0891788i
$$232$$ 6.63760 6.63760i 0.435780 0.435780i
$$233$$ 12.4340 1.96935i 0.814577 0.129016i 0.264774 0.964311i $$-0.414703\pi$$
0.549803 + 0.835294i $$0.314703\pi$$
$$234$$ −2.60209 + 3.62114i −0.170104 + 0.236721i
$$235$$ 0 0
$$236$$ −4.74363 + 1.54130i −0.308784 + 0.100330i
$$237$$ 3.59821 1.17954i 0.233729 0.0766192i
$$238$$ −0.938212 + 0.478043i −0.0608152 + 0.0309869i
$$239$$ −3.62951 11.1705i −0.234773 0.722558i −0.997151 0.0754263i $$-0.975968\pi$$
0.762378 0.647132i $$-0.224032\pi$$
$$240$$ 0 0
$$241$$ 0.375849 1.15675i 0.0242106 0.0745125i −0.938221 0.346036i $$-0.887527\pi$$
0.962432 + 0.271524i $$0.0875275\pi$$
$$242$$ 2.40821 + 15.2048i 0.154805 + 0.977403i
$$243$$ 15.5871 0.203749i 0.999915 0.0130705i
$$244$$ −8.02083 + 11.0397i −0.513481 + 0.706746i
$$245$$ 0 0
$$246$$ 4.94923 + 9.65096i 0.315552 + 0.615323i
$$247$$ 0.111963 0.706906i 0.00712403 0.0449793i
$$248$$ −2.02668 1.03265i −0.128695 0.0655732i
$$249$$ 1.33253 8.55802i 0.0844459 0.542343i
$$250$$ 0 0
$$251$$ 22.6123i 1.42728i 0.700515 + 0.713638i $$0.252954\pi$$
−0.700515 + 0.713638i $$0.747046\pi$$
$$252$$ −0.460543 0.455752i −0.0290115 0.0287097i
$$253$$ −13.5678 2.14892i −0.852998 0.135102i
$$254$$ −12.1651 + 8.83843i −0.763304 + 0.554573i
$$255$$ 0 0
$$256$$ −0.809017 0.587785i −0.0505636 0.0367366i
$$257$$ −2.98436 2.98436i −0.186159 0.186159i 0.607874 0.794033i $$-0.292022\pi$$
−0.794033 + 0.607874i $$0.792022\pi$$
$$258$$ −0.0174316 6.66810i −0.00108525 0.415138i
$$259$$ 0.884259 + 0.287313i 0.0549452 + 0.0178528i
$$260$$ 0 0
$$261$$ −28.1606 + 0.147235i −1.74309 + 0.00911361i
$$262$$ −3.96128 7.77445i −0.244729 0.480307i
$$263$$ −1.16756 2.29146i −0.0719947 0.141298i 0.852204 0.523210i $$-0.175266\pi$$
−0.924199 + 0.381912i $$0.875266\pi$$
$$264$$ −1.41500 8.78526i −0.0870873 0.540696i
$$265$$ 0 0
$$266$$ 0.0989071 + 0.0321369i 0.00606438 + 0.00197044i
$$267$$ 18.9624 0.0495712i 1.16048 0.00303371i
$$268$$ −10.6246 10.6246i −0.649002 0.649002i
$$269$$ 19.5493 + 14.2034i 1.19194 + 0.865996i 0.993468 0.114110i $$-0.0364018\pi$$
0.198473 + 0.980106i $$0.436402\pi$$
$$270$$ 0 0
$$271$$ −9.36464 + 6.80381i −0.568861 + 0.413302i −0.834691 0.550718i $$-0.814354\pi$$
0.265830 + 0.964020i $$0.414354\pi$$
$$272$$ 4.81543 + 0.762690i 0.291978 + 0.0462448i
$$273$$ −0.450683 0.325644i −0.0272766 0.0197088i
$$274$$ 2.82340i 0.170568i
$$275$$ 0 0
$$276$$ 4.57606 + 0.712519i 0.275446 + 0.0428886i
$$277$$ −6.71461 3.42126i −0.403442 0.205564i 0.240482 0.970654i $$-0.422695\pi$$
−0.643924 + 0.765090i $$0.722695\pi$$
$$278$$ −1.08891 + 6.87513i −0.0653087 + 0.412343i
$$279$$ 2.14257 + 6.47871i 0.128273 + 0.387870i
$$280$$ 0 0
$$281$$ 13.8790 19.1028i 0.827952 1.13958i −0.160349 0.987060i $$-0.551262\pi$$
0.988301 0.152517i $$-0.0487380\pi$$
$$282$$ −10.3727 14.1986i −0.617687 0.845516i
$$283$$ 1.54005 + 9.72347i 0.0915463 + 0.578000i 0.990234 + 0.139412i $$0.0445213\pi$$
−0.898688 + 0.438588i $$0.855479\pi$$
$$284$$ −3.74899 + 11.5382i −0.222462 + 0.684667i
$$285$$ 0 0
$$286$$ −2.35974 7.26252i −0.139534 0.429442i
$$287$$ −1.20502 + 0.613989i −0.0711302 + 0.0362426i
$$288$$ 0.484789 + 2.96057i 0.0285665 + 0.174453i
$$289$$ −6.43873 + 2.09207i −0.378749 + 0.123063i
$$290$$ 0 0
$$291$$ 15.5957 + 7.89513i 0.914238 + 0.462821i
$$292$$ 9.26944 1.46814i 0.542453 0.0859161i
$$293$$ 3.33944 3.33944i 0.195092 0.195092i −0.602800 0.797892i $$-0.705948\pi$$
0.797892 + 0.602800i $$0.205948\pi$$
$$294$$ −8.49379 + 8.53832i −0.495368 + 0.497965i
$$295$$ 0 0
$$296$$ −2.53039 3.48278i −0.147076 0.202433i
$$297$$ −15.5213 + 21.7195i −0.900640 + 1.26029i
$$298$$ 3.50644 6.88178i 0.203123 0.398651i
$$299$$ 3.97428 0.229838
$$300$$ 0 0
$$301$$ 0.831472 0.0479252
$$302$$ 6.71307 13.1751i 0.386294 0.758145i
$$303$$ 15.7234 + 5.06343i 0.903285 + 0.290887i
$$304$$ −0.283032 0.389560i −0.0162330 0.0223428i
$$305$$ 0 0
$$306$$ −8.65891 11.7879i −0.494997 0.673868i
$$307$$ −11.8133 + 11.8133i −0.674221 + 0.674221i −0.958686 0.284465i $$-0.908184\pi$$
0.284465 + 0.958686i $$0.408184\pi$$
$$308$$ 1.09592 0.173577i 0.0624460 0.00989048i
$$309$$ 7.91201 15.6291i 0.450098 0.889106i
$$310$$ 0 0
$$311$$ 28.7239 9.33296i 1.62878 0.529224i 0.654791 0.755810i $$-0.272756\pi$$
0.973991 + 0.226586i $$0.0727564\pi$$
$$312$$ 0.801950 + 2.44637i 0.0454015 + 0.138498i
$$313$$ 14.8624 7.57278i 0.840073 0.428039i 0.0196580 0.999807i $$-0.493742\pi$$
0.820415 + 0.571768i $$0.193742\pi$$
$$314$$ −5.06682 15.5941i −0.285937 0.880024i
$$315$$ 0 0
$$316$$ 0.675573 2.07920i 0.0380040 0.116964i
$$317$$ 1.69675 + 10.7129i 0.0952991 + 0.601695i 0.988404 + 0.151847i $$0.0485219\pi$$
−0.893105 + 0.449848i $$0.851478\pi$$
$$318$$ 10.7575 7.85886i 0.603253 0.440703i
$$319$$ 28.3466 39.0157i 1.58710 2.18446i
$$320$$ 0 0
$$321$$ 17.0199 8.72818i 0.949957 0.487160i
$$322$$ −0.0903379 + 0.570371i −0.00503433 + 0.0317855i
$$323$$ 2.09176 + 1.06581i 0.116389 + 0.0593031i
$$324$$ 5.21364 7.33607i 0.289647 0.407559i
$$325$$ 0 0
$$326$$ 4.05769i 0.224735i
$$327$$ 6.22041 8.60889i 0.343989 0.476073i
$$328$$ 6.18485 + 0.979584i 0.341501 + 0.0540885i
$$329$$ 1.77385 1.28878i 0.0977957 0.0710527i
$$330$$ 0 0
$$331$$ −7.79472 5.66319i −0.428436 0.311277i 0.352587 0.935779i $$-0.385302\pi$$
−0.781023 + 0.624502i $$0.785302\pi$$
$$332$$ −3.53590 3.53590i −0.194058 0.194058i
$$333$$ −1.95361 + 12.7662i −0.107057 + 0.699586i
$$334$$ 13.1635 + 4.27710i 0.720277 + 0.234032i
$$335$$ 0 0
$$336$$ −0.369321 + 0.0594848i −0.0201481 + 0.00324516i
$$337$$ 12.7818 + 25.0858i 0.696272 + 1.36651i 0.920023 + 0.391864i $$0.128170\pi$$
−0.223752 + 0.974646i $$0.571830\pi$$
$$338$$ −4.89888 9.61460i −0.266464 0.522965i
$$339$$ 18.7863 3.02582i 1.02033 0.164340i
$$340$$ 0 0
$$341$$ −11.1139 3.61113i −0.601852 0.195554i
$$342$$ −0.218517 + 1.42794i −0.0118161 + 0.0772143i
$$343$$ −2.13093 2.13093i −0.115059 0.115059i
$$344$$ −3.11459 2.26288i −0.167927 0.122006i
$$345$$ 0 0
$$346$$ 0.734684 0.533779i 0.0394969 0.0286962i
$$347$$ −19.0736 3.02097i −1.02393 0.162174i −0.378185 0.925730i $$-0.623452\pi$$
−0.645742 + 0.763556i $$0.723452\pi$$
$$348$$ −9.52222 + 13.1785i −0.510445 + 0.706443i
$$349$$ 14.4119i 0.771451i 0.922614 + 0.385725i $$0.126049\pi$$
−0.922614 + 0.385725i $$0.873951\pi$$
$$350$$ 0 0
$$351$$ 3.45226 6.90887i 0.184268 0.368768i
$$352$$ −4.57759 2.33240i −0.243986 0.124317i
$$353$$ 5.47696 34.5802i 0.291509 1.84052i −0.212929 0.977068i $$-0.568300\pi$$
0.504438 0.863448i $$-0.331700\pi$$
$$354$$ 7.68716 3.94215i 0.408568 0.209523i
$$355$$ 0 0
$$356$$ 6.43505 8.85709i 0.341057 0.469425i
$$357$$ 1.47269 1.07586i 0.0779430 0.0569408i
$$358$$ −1.85367 11.7036i −0.0979695 0.618555i
$$359$$ 10.6846 32.8840i 0.563914 1.73555i −0.107242 0.994233i $$-0.534202\pi$$
0.671156 0.741316i $$-0.265798\pi$$
$$360$$ 0 0
$$361$$ 5.79967 + 17.8496i 0.305246 + 0.939450i
$$362$$ −15.3170 + 7.80442i −0.805045 + 0.410191i
$$363$$ −8.30583 25.3372i −0.435943 1.32986i
$$364$$ −0.305307 + 0.0992002i −0.0160024 + 0.00519950i
$$365$$ 0 0
$$366$$ 10.6751 21.0872i 0.557997 1.10224i
$$367$$ 3.18996 0.505240i 0.166514 0.0263733i −0.0726205 0.997360i $$-0.523136\pi$$
0.239135 + 0.970986i $$0.423136\pi$$
$$368$$ 1.89068 1.89068i 0.0985584 0.0985584i
$$369$$ −11.1214 15.1401i −0.578954 0.788163i
$$370$$ 0 0
$$371$$ 0.976440 + 1.34395i 0.0506942 + 0.0697746i
$$372$$ 3.75007 + 1.20764i 0.194432 + 0.0626134i
$$373$$ −4.91900 + 9.65408i −0.254696 + 0.499869i −0.982582 0.185829i $$-0.940503\pi$$
0.727886 + 0.685698i $$0.240503\pi$$
$$374$$ 25.0479 1.29519
$$375$$ 0 0
$$376$$ −10.1521 −0.523554
$$377$$ −6.33429 + 12.4317i −0.326233 + 0.640268i
$$378$$ 0.913058 + 0.652497i 0.0469627 + 0.0335608i
$$379$$ −19.6854 27.0946i −1.01117 1.39176i −0.918213 0.396087i $$-0.870368\pi$$
−0.0929573 0.995670i $$-0.529632\pi$$
$$380$$ 0 0
$$381$$ 18.3681 18.4644i 0.941025 0.945958i
$$382$$ 3.49555 3.49555i 0.178848 0.178848i
$$383$$ 16.0484 2.54182i 0.820034 0.129881i 0.267699 0.963503i $$-0.413737\pi$$
0.552335 + 0.833622i $$0.313737\pi$$
$$384$$ 1.54532 + 0.782298i 0.0788592 + 0.0399215i
$$385$$ 0 0
$$386$$ −3.20588 + 1.04165i −0.163175 + 0.0530187i
$$387$$ 1.86636 + 11.3977i 0.0948724 + 0.579379i
$$388$$ 8.99225 4.58178i 0.456512 0.232605i
$$389$$ 0.804900 + 2.47723i 0.0408101 + 0.125600i 0.969386 0.245542i $$-0.0789660\pi$$
−0.928576 + 0.371143i $$0.878966\pi$$
$$390$$ 0 0
$$391$$ −4.02838 + 12.3981i −0.203724 + 0.626998i
$$392$$ 1.08774 + 6.86775i 0.0549394 + 0.346874i
$$393$$ 8.91510 + 12.2034i 0.449707 + 0.615578i
$$394$$ −4.30947 + 5.93148i −0.217108 + 0.298824i
$$395$$ 0 0
$$396$$ 4.83934 + 14.6332i 0.243186 + 0.735345i
$$397$$ 0.295160 1.86357i 0.0148137 0.0935298i −0.979174 0.203024i $$-0.934923\pi$$
0.993987 + 0.109494i $$0.0349231\pi$$
$$398$$ 7.43262 + 3.78711i 0.372563 + 0.189831i
$$399$$ −0.177984 0.0277131i −0.00891032 0.00138739i
$$400$$ 0 0
$$401$$ 7.16880i 0.357993i 0.983850 + 0.178996i $$0.0572850\pi$$
−0.983850 + 0.178996i $$0.942715\pi$$
$$402$$ 21.0945 + 15.2419i 1.05210 + 0.760199i
$$403$$ 3.33926 + 0.528887i 0.166341 + 0.0263458i
$$404$$ 7.71559 5.60571i 0.383865 0.278894i
$$405$$ 0 0
$$406$$ −1.64017 1.19165i −0.0814002 0.0591407i
$$407$$ −15.6390 15.6390i −0.775197 0.775197i
$$408$$ −8.44451 + 0.0220755i −0.418066 + 0.00109290i
$$409$$ −15.2838 4.96600i −0.755734 0.245553i −0.0942874 0.995545i $$-0.530057\pi$$
−0.661447 + 0.749992i $$0.730057\pi$$
$$410$$ 0 0
$$411$$ −0.777631 4.82805i −0.0383577 0.238150i
$$412$$ −4.59157 9.01147i −0.226211 0.443963i
$$413$$ 0.489054 + 0.959822i 0.0240648 + 0.0472297i
$$414$$ −8.02136 + 0.0419389i −0.394228 + 0.00206119i
$$415$$ 0 0
$$416$$ 1.41362 + 0.459312i 0.0693083 + 0.0225196i
$$417$$ −0.0315179 12.0565i −0.00154344 0.590408i
$$418$$ −1.74927 1.74927i −0.0855596 0.0855596i
$$419$$ −1.81333 1.31746i −0.0885872 0.0643624i 0.542610 0.839985i $$-0.317436\pi$$
−0.631197 + 0.775622i $$0.717436\pi$$
$$420$$ 0 0
$$421$$ 2.09500 1.52210i 0.102104 0.0741828i −0.535562 0.844496i $$-0.679900\pi$$
0.637666 + 0.770313i $$0.279900\pi$$
$$422$$ −4.23458 0.670692i −0.206136 0.0326488i
$$423$$ 21.6481 + 21.4229i 1.05257 + 1.04162i
$$424$$ 7.69169i 0.373542i
$$425$$ 0 0
$$426$$ 3.23292 20.7630i 0.156636 1.00597i
$$427$$ 2.62595 + 1.33799i 0.127079 + 0.0647498i
$$428$$ 1.72754 10.9072i 0.0835037 0.527222i
$$429$$ 6.03545 + 11.7691i 0.291394 + 0.568216i
$$430$$ 0 0
$$431$$ −0.661426 + 0.910375i −0.0318598 + 0.0438512i −0.824650 0.565644i $$-0.808628\pi$$
0.792790 + 0.609495i $$0.208628\pi$$
$$432$$ −1.64441 4.92909i −0.0791165 0.237151i
$$433$$ 3.21125 + 20.2750i 0.154323 + 0.974355i 0.936339 + 0.351097i $$0.114191\pi$$
−0.782016 + 0.623258i $$0.785809\pi$$
$$434$$ −0.151807 + 0.467215i −0.00728698 + 0.0224270i
$$435$$ 0 0
$$436$$ −1.89491 5.83194i −0.0907498 0.279299i
$$437$$ 1.14718 0.584515i 0.0548768 0.0279611i
$$438$$ −15.4465 + 5.06355i −0.738062 + 0.241946i
$$439$$ −22.3736 + 7.26963i −1.06783 + 0.346960i −0.789644 0.613565i $$-0.789735\pi$$
−0.278191 + 0.960526i $$0.589735\pi$$
$$440$$ 0 0
$$441$$ 12.1728 16.9400i 0.579659 0.806668i
$$442$$ −7.15749 + 1.13363i −0.340447 + 0.0539215i
$$443$$ 13.6168 13.6168i 0.646952 0.646952i −0.305303 0.952255i $$-0.598758\pi$$
0.952255 + 0.305303i $$0.0987577\pi$$
$$444$$ 5.28624 + 5.25867i 0.250874 + 0.249565i
$$445$$ 0 0
$$446$$ −0.429625 0.591328i −0.0203433 0.0280002i
$$447$$ −4.10066 + 12.7337i −0.193954 + 0.602283i
$$448$$ −0.0980509 + 0.192436i −0.00463247 + 0.00909173i
$$449$$ −19.2184 −0.906973 −0.453487 0.891263i $$-0.649820\pi$$
−0.453487 + 0.891263i $$0.649820\pi$$
$$450$$ 0 0
$$451$$ 32.1710 1.51487
$$452$$ 4.98756 9.78864i 0.234595 0.460419i
$$453$$ −7.85069 + 24.3786i −0.368858 + 1.14541i
$$454$$ −1.94595 2.67837i −0.0913281 0.125702i
$$455$$ 0 0
$$456$$ 0.591281 + 0.588198i 0.0276893 + 0.0275449i
$$457$$ 15.9563 15.9563i 0.746405 0.746405i −0.227397 0.973802i $$-0.573021\pi$$
0.973802 + 0.227397i $$0.0730215\pi$$
$$458$$ −10.4220 + 1.65068i −0.486986 + 0.0771311i
$$459$$ 18.0535 + 17.7725i 0.842666 + 0.829551i
$$460$$ 0 0
$$461$$ 15.2184 4.94475i 0.708790 0.230300i 0.0676337 0.997710i $$-0.478455\pi$$
0.641156 + 0.767410i $$0.278455\pi$$
$$462$$ −1.82624 + 0.598662i −0.0849642 + 0.0278523i
$$463$$ 5.51675 2.81092i 0.256385 0.130635i −0.321075 0.947054i $$-0.604044\pi$$
0.577460 + 0.816419i $$0.304044\pi$$
$$464$$ 2.90074 + 8.92755i 0.134663 + 0.414451i
$$465$$ 0 0
$$466$$ −3.89021 + 11.9728i −0.180210 + 0.554630i
$$467$$ −3.63127 22.9270i −0.168035 1.06093i −0.917164 0.398509i $$-0.869528\pi$$
0.749129 0.662424i $$-0.230472\pi$$
$$468$$ −2.04513 3.96244i −0.0945362 0.183164i
$$469$$ −1.90744 + 2.62537i −0.0880775 + 0.121228i
$$470$$ 0 0
$$471$$ 12.9593 + 25.2705i 0.597133 + 1.16440i
$$472$$ 0.780256 4.92635i 0.0359142 0.226753i
$$473$$ −17.6230 8.97936i −0.810305 0.412871i
$$474$$ −0.582577 + 3.74153i −0.0267587 + 0.171854i
$$475$$ 0 0
$$476$$ 1.05298i 0.0482633i
$$477$$ −16.2310 + 16.4016i −0.743167 + 0.750979i
$$478$$ 11.6007 + 1.83738i 0.530605 + 0.0840396i
$$479$$ 18.1330 13.1744i 0.828519 0.601954i −0.0906212 0.995885i $$-0.528885\pi$$
0.919140 + 0.393931i $$0.128885\pi$$
$$480$$ 0 0
$$481$$ 5.17668 + 3.76108i 0.236036 + 0.171491i
$$482$$ 0.860035 + 0.860035i 0.0391735 + 0.0391735i
$$483$$ −0.00261477 1.00022i −0.000118976 0.0455117i
$$484$$ −14.6409 4.75712i −0.665496 0.216233i
$$485$$ 0 0
$$486$$ −6.89486 + 13.9807i −0.312757 + 0.634179i
$$487$$ −9.62881 18.8976i −0.436323 0.856332i −0.999549 0.0300294i $$-0.990440\pi$$
0.563226 0.826303i $$-0.309560\pi$$
$$488$$ −6.19509 12.1585i −0.280438 0.550391i
$$489$$ −1.11758 6.93870i −0.0505389 0.313779i
$$490$$ 0 0
$$491$$ −29.6177 9.62339i −1.33663 0.434297i −0.448456 0.893805i $$-0.648026\pi$$
−0.888174 + 0.459507i $$0.848026\pi$$
$$492$$ −10.8460 + 0.0283534i −0.488974 + 0.00127827i
$$493$$ −32.3613 32.3613i −1.45748 1.45748i
$$494$$ 0.579028 + 0.420688i 0.0260517 + 0.0189277i
$$495$$ 0 0
$$496$$ 1.84019 1.33698i 0.0826270 0.0600320i
$$497$$ 2.58795 + 0.409892i 0.116086 + 0.0183862i
$$498$$ 7.02030 + 5.07256i 0.314587 + 0.227307i
$$499$$ 1.25659i 0.0562528i 0.999604 + 0.0281264i $$0.00895410\pi$$
−0.999604 + 0.0281264i $$0.991046\pi$$
$$500$$ 0 0
$$501$$ −23.6878 3.68833i −1.05829 0.164783i
$$502$$ −20.1477 10.2658i −0.899236 0.458184i
$$503$$ −4.11407 + 25.9752i −0.183437 + 1.15818i 0.708397 + 0.705815i $$0.249419\pi$$
−0.891834 + 0.452363i $$0.850581\pi$$
$$504$$ 0.615160 0.203439i 0.0274014 0.00906191i
$$505$$ 0 0
$$506$$ 8.07434 11.1134i 0.358948 0.494050i
$$507$$ 11.0252 + 15.0918i 0.489648 + 0.670251i
$$508$$ −2.35228 14.8517i −0.104366 0.658938i
$$509$$ 5.31690 16.3637i 0.235668 0.725310i −0.761365 0.648324i $$-0.775470\pi$$
0.997032 0.0769863i $$-0.0245298\pi$$
$$510$$ 0 0
$$511$$ −0.626355 1.92772i −0.0277083 0.0852775i
$$512$$ 0.891007 0.453990i 0.0393773 0.0200637i
$$513$$ −0.0196223 2.50199i −0.000866347 0.110465i
$$514$$ 4.01395 1.30421i 0.177048 0.0575263i
$$515$$ 0 0
$$516$$ 5.94923 + 3.01172i 0.261900 + 0.132584i
$$517$$ −51.5147 + 8.15912i −2.26561 + 0.358838i
$$518$$ −0.657443 + 0.657443i −0.0288864 + 0.0288864i
$$519$$ −1.10930 + 1.11512i −0.0486930 + 0.0489483i
$$520$$ 0 0
$$521$$ 7.91212 + 10.8901i 0.346636 + 0.477104i 0.946365 0.323099i $$-0.104725\pi$$
−0.599729 + 0.800203i $$0.704725\pi$$
$$522$$ 12.6534 25.1581i 0.553826 1.10114i
$$523$$ 11.6979 22.9585i 0.511514 1.00390i −0.480407 0.877046i $$-0.659511\pi$$
0.991921 0.126858i $$-0.0404891\pi$$
$$524$$ 8.72546 0.381174
$$525$$ 0 0
$$526$$ 2.57177 0.112134
$$527$$ −5.03463 + 9.88101i −0.219312 + 0.430424i
$$528$$ 8.47012 + 2.72765i 0.368615 + 0.118706i
$$529$$ −9.31679 12.8235i −0.405078 0.557542i
$$530$$ 0 0
$$531$$ −12.0594 + 8.85835i −0.523333 + 0.384420i
$$532$$ −0.0735370 + 0.0735370i −0.00318823 + 0.00318823i
$$533$$ −9.19295 + 1.45602i −0.398191 + 0.0630672i
$$534$$ −8.56457 + 16.9181i −0.370625 + 0.732118i
$$535$$ 0 0
$$536$$ 14.2901 4.64313i 0.617237 0.200553i
$$537$$ 6.39325 + 19.5028i 0.275889 + 0.841607i
$$538$$ −21.5305 + 10.9703i −0.928246 + 0.472965i
$$539$$ 11.0391 + 33.9747i 0.475486 + 1.46340i
$$540$$ 0 0
$$541$$ −6.47364 + 19.9238i −0.278323 + 0.856591i 0.709998 + 0.704204i $$0.248696\pi$$
−0.988321 + 0.152387i $$0.951304\pi$$
$$542$$ −1.81078 11.4328i −0.0777797 0.491082i
$$543$$ 24.0428 17.5643i 1.03177 0.753757i
$$544$$ −2.86572 + 3.94433i −0.122867 + 0.169112i
$$545$$ 0 0
$$546$$ 0.494756 0.253722i 0.0211736 0.0108583i
$$547$$ 6.82585 43.0967i 0.291852 1.84268i −0.209965 0.977709i $$-0.567335\pi$$
0.501817 0.864974i $$-0.332665\pi$$
$$548$$ −2.51567 1.28180i −0.107464 0.0547557i
$$549$$ −12.4467 + 38.9995i −0.531211 + 1.66446i
$$550$$ 0 0
$$551$$ 4.52004i 0.192560i
$$552$$ −2.71235 + 3.75382i −0.115445 + 0.159773i
$$553$$ −0.466353 0.0738630i −0.0198313 0.00314098i
$$554$$ 6.09674 4.42954i 0.259025 0.188193i
$$555$$ 0 0
$$556$$ −5.63143 4.09147i −0.238826 0.173517i
$$557$$ 20.7979 + 20.7979i 0.881236 + 0.881236i 0.993660 0.112424i $$-0.0358615\pi$$
−0.112424 + 0.993660i $$0.535861\pi$$
$$558$$ −6.74528 1.03223i −0.285551 0.0436976i
$$559$$ 5.44220 + 1.76828i 0.230181 + 0.0747902i
$$560$$ 0 0
$$561$$ −42.8322 + 6.89878i −1.80838 + 0.291267i
$$562$$ 10.7198 + 21.0388i 0.452187 + 0.887467i
$$563$$ 7.14045 + 14.0139i 0.300934 + 0.590616i 0.991113 0.133022i $$-0.0424682\pi$$
−0.690179 + 0.723639i $$0.742468\pi$$
$$564$$ 17.3602 2.79613i 0.730996 0.117738i
$$565$$ 0 0
$$566$$ −9.36284 3.04217i −0.393550 0.127872i
$$567$$ −1.74105 0.864300i −0.0731174 0.0362972i
$$568$$ −8.57861 8.57861i −0.359950 0.359950i
$$569$$ 3.20445 + 2.32817i 0.134338 + 0.0976021i 0.652925 0.757423i $$-0.273542\pi$$
−0.518587 + 0.855025i $$0.673542\pi$$
$$570$$ 0 0
$$571$$ −31.7943 + 23.0999i −1.33055 + 0.966702i −0.330815 + 0.943696i $$0.607324\pi$$
−0.999735 + 0.0230060i $$0.992676\pi$$
$$572$$ 7.54225 + 1.19457i 0.315357 + 0.0499477i
$$573$$ −5.01468 + 6.94020i −0.209491 + 0.289931i
$$574$$ 1.35243i 0.0564492i
$$575$$ 0 0
$$576$$ −2.85798 0.912121i −0.119082 0.0380050i
$$577$$ 16.8154 + 8.56788i 0.700034 + 0.356685i 0.767511 0.641036i $$-0.221495\pi$$
−0.0674769 + 0.997721i $$0.521495\pi$$
$$578$$ 1.05907 6.68673i 0.0440517 0.278131i
$$579$$ 5.19519 2.66421i 0.215905 0.110721i
$$580$$ 0 0
$$581$$ −0.634802 + 0.873729i −0.0263360 + 0.0362484i
$$582$$ −14.1149 + 10.3116i −0.585083 + 0.427429i
$$583$$ −6.18173 39.0299i −0.256021 1.61645i
$$584$$ −2.90012 + 8.92565i −0.120008 + 0.369346i
$$585$$ 0 0
$$586$$ 1.45939 + 4.49153i 0.0602867 + 0.185543i
$$587$$ 4.14963 2.11434i 0.171274 0.0872683i −0.366252 0.930516i $$-0.619359\pi$$
0.537526 + 0.843247i $$0.319359\pi$$
$$588$$ −3.75160 11.4443i −0.154713 0.471957i
$$589$$ 1.04166 0.338457i 0.0429210 0.0139459i
$$590$$ 0 0
$$591$$ 5.73558 11.3298i 0.235930 0.466047i
$$592$$ 4.25195 0.673443i 0.174754 0.0276783i
$$593$$ −32.4687 + 32.4687i −1.33333 + 1.33333i −0.430960 + 0.902371i $$0.641825\pi$$
−0.902371 + 0.430960i $$0.858175\pi$$
$$594$$ −12.3057 23.6901i −0.504907 0.972015i
$$595$$ 0 0
$$596$$ 4.53982 + 6.24853i 0.185958 + 0.255950i
$$597$$ −13.7529 4.42888i −0.562870 0.181262i
$$598$$ −1.80428 + 3.54111i −0.0737826 + 0.144807i
$$599$$ −18.2921 −0.747393 −0.373697 0.927551i $$-0.621910\pi$$
−0.373697 + 0.927551i $$0.621910\pi$$
$$600$$ 0 0
$$601$$ −0.981781 −0.0400477 −0.0200238 0.999800i $$-0.506374\pi$$
−0.0200238 + 0.999800i $$0.506374\pi$$
$$602$$ −0.377480 + 0.740847i −0.0153850 + 0.0301947i
$$603$$ −40.2698 20.2540i −1.63991 0.824807i
$$604$$ 8.69147 + 11.9628i 0.353651 + 0.486759i
$$605$$ 0 0
$$606$$ −11.6498 + 11.7109i −0.473241 + 0.475722i
$$607$$ −2.39455 + 2.39455i −0.0971917 + 0.0971917i −0.754031 0.656839i $$-0.771893\pi$$
0.656839 + 0.754031i $$0.271893\pi$$
$$608$$ 0.475594 0.0753267i 0.0192879 0.00305490i
$$609$$ 3.13292 + 1.58600i 0.126952 + 0.0642679i
$$610$$ 0 0
$$611$$ 14.3512 4.66298i 0.580586 0.188644i
$$612$$ 14.4341 2.36357i 0.583465 0.0955415i
$$613$$ −12.2470 + 6.24017i −0.494653 + 0.252038i −0.683476 0.729973i $$-0.739533\pi$$
0.188823 + 0.982011i $$0.439533\pi$$
$$614$$ −5.16261 15.8889i −0.208346 0.641223i
$$615$$ 0 0
$$616$$ −0.342880 + 1.05528i −0.0138150 + 0.0425183i
$$617$$ 1.60431 + 10.1292i 0.0645872 + 0.407787i 0.998707 + 0.0508287i $$0.0161863\pi$$
−0.934120 + 0.356959i $$0.883814\pi$$
$$618$$ 10.3336 + 14.1451i 0.415679 + 0.568999i
$$619$$ −27.3325 + 37.6199i −1.09859 + 1.51207i −0.261338 + 0.965247i $$0.584164\pi$$
−0.837247 + 0.546825i $$0.815836\pi$$
$$620$$ 0 0
$$621$$ 13.7051 2.28099i 0.549966 0.0915329i
$$622$$ −4.72465 + 29.8303i −0.189441 + 1.19608i
$$623$$ −2.10678 1.07346i −0.0844063 0.0430072i
$$624$$ −2.54381 0.396086i −0.101834 0.0158561i
$$625$$ 0 0
$$626$$ 16.6805i 0.666686i
$$627$$ 3.47306 + 2.50948i 0.138701 + 0.100219i
$$628$$ 16.1947 + 2.56499i 0.646239 + 0.102354i
$$629$$ −16.9802 + 12.3368i −0.677043 + 0.491900i
$$630$$ 0 0
$$631$$ −20.6748 15.0211i −0.823051 0.597981i 0.0945340 0.995522i $$-0.469864\pi$$
−0.917585 + 0.397540i $$0.869864\pi$$
$$632$$ 1.54588 + 1.54588i 0.0614917 + 0.0614917i
$$633$$ 7.42591 0.0194127i 0.295153 0.000771586i
$$634$$ −10.3155 3.35172i −0.409683 0.133114i
$$635$$ 0 0
$$636$$ 2.11847 + 13.1529i 0.0840030 + 0.521546i
$$637$$ −4.69209 9.20875i −0.185907 0.364864i
$$638$$ 21.8942 + 42.9697i 0.866798 + 1.70119i
$$639$$ 0.190290 + 36.3955i 0.00752777 + 1.43978i
$$640$$ 0 0
$$641$$ 0.702023 + 0.228101i 0.0277282 + 0.00900945i 0.322848 0.946451i $$-0.395360\pi$$
−0.295120 + 0.955460i $$0.595360\pi$$
$$642$$ 0.0500024 + 19.1273i 0.00197344 + 0.754896i
$$643$$ 17.1573 + 17.1573i 0.676616 + 0.676616i 0.959233 0.282617i $$-0.0912025\pi$$
−0.282617 + 0.959233i $$0.591203\pi$$
$$644$$ −0.467192 0.339435i −0.0184099 0.0133756i
$$645$$ 0 0
$$646$$ −1.89928 + 1.37991i −0.0747262 + 0.0542918i
$$647$$ 5.95524 + 0.943217i 0.234125 + 0.0370817i 0.272394 0.962186i $$-0.412185\pi$$
−0.0382696 + 0.999267i $$0.512185\pi$$
$$648$$ 4.16954 + 7.97590i 0.163795 + 0.313323i
$$649$$ 25.6248i 1.00586i
$$650$$ 0 0
$$651$$ 0.130910 0.840754i 0.00513078 0.0329517i
$$652$$ −3.61543 1.84215i −0.141591 0.0721443i
$$653$$ 1.57981 9.97451i 0.0618226 0.390333i −0.937303 0.348516i $$-0.886686\pi$$
0.999125 0.0418163i $$-0.0133144\pi$$
$$654$$ 4.84657 + 9.45078i 0.189516 + 0.369555i
$$655$$ 0 0
$$656$$ −3.68068 + 5.06602i −0.143706 + 0.197795i
$$657$$ 25.0191 12.9131i 0.976087 0.503787i
$$658$$ 0.342999 + 2.16561i 0.0133715 + 0.0844242i
$$659$$ −3.59331 + 11.0591i −0.139975 + 0.430800i −0.996331 0.0855871i $$-0.972723\pi$$
0.856355 + 0.516387i $$0.172723\pi$$
$$660$$ 0 0
$$661$$ 12.8291 + 39.4838i 0.498993 + 1.53574i 0.810641 + 0.585544i $$0.199119\pi$$
−0.311648 + 0.950197i $$0.600881\pi$$
$$662$$ 8.58467 4.37411i 0.333653 0.170005i
$$663$$ 11.9272 3.90987i 0.463213 0.151847i
$$664$$ 4.75577 1.54524i 0.184560 0.0599671i
$$665$$ 0 0
$$666$$ −10.4879 7.53643i −0.406397 0.292031i
$$667$$ −24.7901 + 3.92637i −0.959877 + 0.152030i
$$668$$ −9.78704 + 9.78704i −0.378672 + 0.378672i
$$669$$ 0.897530 + 0.892849i 0.0347005 + 0.0345195i
$$670$$ 0 0
$$671$$ −41.2074 56.7171i −1.59079 2.18954i
$$672$$ 0.114667 0.356073i 0.00442337 0.0137358i
$$673$$ 12.1800 23.9046i 0.469504 0.921454i −0.527890 0.849313i $$-0.677017\pi$$
0.997394 0.0721411i $$-0.0229832\pi$$
$$674$$ −28.1544 −1.08447
$$675$$ 0 0
$$676$$ 10.7907 0.415028
$$677$$ 10.0184 19.6621i 0.385037 0.755677i −0.614408 0.788988i $$-0.710605\pi$$
0.999445 + 0.0333112i $$0.0106052\pi$$
$$678$$ −5.83277 + 18.1124i −0.224006 + 0.695602i
$$679$$ −1.28118 1.76340i −0.0491673 0.0676729i
$$680$$ 0 0
$$681$$ 4.06529 + 4.04409i 0.155782 + 0.154970i
$$682$$ 8.26315 8.26315i 0.316413 0.316413i
$$683$$ −19.3379 + 3.06282i −0.739944 + 0.117196i −0.515017 0.857180i $$-0.672214\pi$$
−0.224927 + 0.974376i $$0.572214\pi$$
$$684$$ −1.17310 0.842973i −0.0448547 0.0322319i
$$685$$ 0 0
$$686$$ 2.86609 0.931249i 0.109428 0.0355552i
$$687$$ 17.3670 5.69313i 0.662594 0.217207i
$$688$$ 3.43023 1.74779i 0.130776 0.0666339i
$$689$$ 3.53289 + 10.8731i 0.134592 + 0.414232i
$$690$$ 0 0
$$691$$ 12.6136 38.8206i 0.479843 1.47681i −0.359469 0.933157i $$-0.617042\pi$$
0.839313 0.543649i $$-0.182958\pi$$
$$692$$ 0.142061 + 0.896939i 0.00540036 + 0.0340965i
$$693$$ 2.95800 1.52671i 0.112365 0.0579949i
$$694$$ 11.3510 15.6232i 0.430876 0.593050i
$$695$$ 0 0
$$696$$ −7.41915 14.4673i −0.281222 0.548381i
$$697$$ 4.77592 30.1540i 0.180901 1.14216i
$$698$$ −12.8411 6.54286i −0.486042 0.247651i
$$699$$ 3.35470 21.5451i 0.126886 0.814912i
$$700$$ 0 0
$$701$$ 1.34594i 0.0508356i 0.999677 + 0.0254178i $$0.00809161\pi$$
−0.999677 + 0.0254178i $$0.991908\pi$$
$$702$$ 4.58855 + 6.21255i 0.173184 + 0.234478i
$$703$$ 2.04741 + 0.324278i 0.0772195 + 0.0122304i
$$704$$ 4.15636 3.01977i 0.156649 0.113812i
$$705$$ 0 0
$$706$$ 28.3247 + 20.5791i 1.06601 + 0.774503i
$$707$$ −1.45647 1.45647i −0.0547762 0.0547762i
$$708$$ 0.0225840 + 8.63901i 0.000848758 + 0.324674i
$$709$$ 5.99345 + 1.94739i 0.225089 + 0.0731358i 0.419390 0.907806i $$-0.362244\pi$$
−0.194301 + 0.980942i $$0.562244\pi$$
$$710$$ 0 0
$$711$$ −0.0342906 6.55851i −0.00128600 0.245963i
$$712$$ 4.97027 + 9.75471i 0.186269 + 0.365573i
$$713$$ 2.76112 + 5.41900i 0.103405 + 0.202943i
$$714$$ 0.290016 + 1.80061i 0.0108536 + 0.0673861i
$$715$$ 0 0
$$716$$ 11.2695 + 3.66170i 0.421163 + 0.136844i
$$717$$ −20.3435 + 0.0531816i −0.759740 + 0.00198610i
$$718$$ 24.4491 + 24.4491i 0.912432 + 0.912432i
$$719$$ −15.2779 11.1001i −0.569770 0.413962i 0.265251 0.964179i $$-0.414545\pi$$
−0.835022 + 0.550217i $$0.814545\pi$$
$$720$$ 0 0
$$721$$ −1.76717 + 1.28392i −0.0658127 + 0.0478157i
$$722$$ −18.5371 2.93598i −0.689878 0.109266i
$$723$$ −1.70755 1.23380i −0.0635043 0.0458854i
$$724$$ 17.1907i 0.638888i
$$725$$ 0 0
$$726$$ 26.3463 + 4.10228i 0.977805 + 0.152250i
$$727$$ 11.0417 + 5.62601i 0.409513 + 0.208657i 0.646597 0.762832i $$-0.276192\pi$$
−0.237084 + 0.971489i $$0.576192\pi$$
$$728$$ 0.0502184 0.317066i 0.00186122 0.0117513i
$$729$$ 7.93968 25.8062i 0.294062 0.955786i
$$730$$ 0 0
$$731$$ −11.0326 + 15.1850i −0.408055 + 0.561639i
$$732$$ 13.9424 + 19.0850i 0.515327 + 0.705401i
$$733$$ 1.46889 + 9.27418i 0.0542545 + 0.342550i 0.999852 + 0.0172103i $$0.00547849\pi$$
−0.945597 + 0.325339i $$0.894522\pi$$
$$734$$ −0.998039 + 3.07165i −0.0368383 + 0.113377i
$$735$$ 0 0
$$736$$ 0.826257 + 2.54296i 0.0304562 + 0.0937346i
$$737$$ 68.7804 35.0454i 2.53356 1.29091i
$$738$$ 18.5389 3.03572i 0.682428 0.111746i
$$739$$ 18.0916 5.87832i 0.665511 0.216238i 0.0432699 0.999063i $$-0.486222\pi$$
0.622241 + 0.782826i $$0.286222\pi$$
$$740$$ 0 0
$$741$$ −1.10601 0.559904i −0.0406304 0.0205686i
$$742$$ −1.64077 + 0.259872i −0.0602344 + 0.00954019i
$$743$$ −23.1938 + 23.1938i −0.850899 + 0.850899i −0.990244 0.139345i $$-0.955500\pi$$
0.139345 + 0.990244i $$0.455500\pi$$
$$744$$ −2.77851 + 2.79308i −0.101865 + 0.102399i
$$745$$ 0 0
$$746$$ −6.36867 8.76572i −0.233174 0.320936i
$$747$$ −13.4019 6.74058i −0.490350 0.246625i
$$748$$ −11.3715 + 22.3178i −0.415783 + 0.816020i
$$749$$ −2.38506 −0.0871483
$$750$$ 0 0
$$751$$ 35.1267 1.28179 0.640895 0.767628i $$-0.278563\pi$$
0.640895 + 0.767628i $$0.278563\pi$$
$$752$$ 4.60895 9.04558i 0.168071 0.329858i
$$753$$ 37.2803 + 12.0054i 1.35857 + 0.437502i
$$754$$ −8.20106 11.2878i −0.298665 0.411077i
$$755$$ 0 0
$$756$$ −0.995899 + 0.517314i −0.0362205 + 0.0188145i
$$757$$ 20.0652 20.0652i 0.729283 0.729283i −0.241194 0.970477i $$-0.577539\pi$$
0.970477 + 0.241194i $$0.0775389\pi$$
$$758$$ 33.0785 5.23911i 1.20146 0.190293i
$$759$$ −10.7463 + 21.2279i −0.390067 + 0.770523i
$$760$$ 0 0
$$761$$ −30.4666 + 9.89919i −1.10441 + 0.358845i −0.803799 0.594901i $$-0.797191\pi$$
−0.300613 + 0.953746i $$0.597191\pi$$
$$762$$ 8.11294 + 24.7487i 0.293901 + 0.896552i
$$763$$ −1.18003 + 0.601254i −0.0427199 + 0.0217669i
$$764$$ 1.52761 + 4.70151i 0.0552671 + 0.170095i
$$765$$ 0 0
$$766$$ −5.02104 + 15.4532i −0.181418 + 0.558346i
$$767$$ 1.15975 + 7.32235i 0.0418760 + 0.264395i
$$768$$ −1.39859 + 1.02173i −0.0504674 + 0.0368686i
$$769$$ 8.74366 12.0346i 0.315305 0.433980i −0.621722 0.783238i $$-0.713567\pi$$
0.937026 + 0.349259i $$0.113567\pi$$
$$770$$ 0 0
$$771$$ −6.50470 + 3.33576i −0.234261 + 0.120134i
$$772$$ 0.527318 3.32936i 0.0189786 0.119826i
$$773$$ −19.8204 10.0990i −0.712889 0.363235i 0.0596354 0.998220i $$-0.481006\pi$$
−0.772524 + 0.634985i $$0.781006\pi$$
$$774$$ −11.0028 3.51152i −0.395486 0.126219i
$$775$$ 0 0
$$776$$ 10.0922i 0.362290i
$$777$$ 0.943161 1.30531i 0.0338357 0.0468278i
$$778$$ −2.57264 0.407467i −0.0922337 0.0146084i
$$779$$ −2.43940 + 1.77233i −0.0874006 + 0.0635003i
$$780$$ 0 0
$$781$$ −50.4249 36.6358i −1.80435 1.31093i
$$782$$ −9.21792 9.21792i −0.329632