Properties

 Label 495.2.n.g.136.2 Level $495$ Weight $2$ Character 495.136 Analytic conductor $3.953$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$495 = 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 495.n (of order $$5$$, degree $$4$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$3.95259490005$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$4$$ over $$\Q(\zeta_{5})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} - 172 x^{7} + 471 x^{6} - 430 x^{5} + 383 x^{4} + 70 x^{3} + 17 x^{2} + 4 x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

 Embedding label 136.2 Root $$0.0698401 + 0.214946i$$ of defining polynomial Character $$\chi$$ $$=$$ 495.136 Dual form 495.2.n.g.91.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.991861 - 0.720629i) q^{2} +(-0.153553 - 0.472586i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.139581 - 0.429587i) q^{7} +(-0.945971 + 2.91140i) q^{8} +O(q^{10})$$ $$q+(-0.991861 - 0.720629i) q^{2} +(-0.153553 - 0.472586i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.139581 - 0.429587i) q^{7} +(-0.945971 + 2.91140i) q^{8} +1.22601 q^{10} +(1.55234 + 2.93091i) q^{11} +(3.91592 + 2.84508i) q^{13} +(-0.171128 + 0.526677i) q^{14} +(2.23230 - 1.62186i) q^{16} +(0.598736 - 0.435007i) q^{17} +(2.10247 - 6.47075i) q^{19} +(0.402006 + 0.292074i) q^{20} +(0.572395 - 4.02572i) q^{22} +0.00634166 q^{23} +(0.309017 - 0.951057i) q^{25} +(-1.83380 - 5.64385i) q^{26} +(-0.181584 + 0.131928i) q^{28} +(0.100091 + 0.308048i) q^{29} +(4.53521 + 3.29503i) q^{31} +2.73956 q^{32} -0.907341 q^{34} +(0.365429 + 0.265500i) q^{35} +(2.27713 + 7.00828i) q^{37} +(-6.74837 + 4.90298i) q^{38} +(-0.945971 - 2.91140i) q^{40} +(3.39006 - 10.4335i) q^{41} -1.80668 q^{43} +(1.14674 - 1.18366i) q^{44} +(-0.00629004 - 0.00456998i) q^{46} +(0.518988 - 1.59728i) q^{47} +(5.49806 - 3.99457i) q^{49} +(-0.991861 + 0.720629i) q^{50} +(0.743247 - 2.28748i) q^{52} +(6.98948 + 5.07816i) q^{53} +(-2.97862 - 1.45871i) q^{55} +1.38274 q^{56} +(0.122712 - 0.377669i) q^{58} +(0.463691 + 1.42709i) q^{59} +(-10.5540 + 7.66790i) q^{61} +(-2.12381 - 6.53641i) q^{62} +(-7.18186 - 5.21793i) q^{64} -4.84034 q^{65} +9.60773 q^{67} +(-0.297516 - 0.216158i) q^{68} +(-0.171128 - 0.526677i) q^{70} +(9.23296 - 6.70814i) q^{71} +(3.16430 + 9.73870i) q^{73} +(2.79178 - 8.59220i) q^{74} -3.38083 q^{76} +(1.04241 - 1.07597i) q^{77} +(1.69866 + 1.23415i) q^{79} +(-0.852662 + 2.62422i) q^{80} +(-10.8812 + 7.90563i) q^{82} +(-12.8589 + 9.34255i) q^{83} +(-0.228697 + 0.703856i) q^{85} +(1.79197 + 1.30194i) q^{86} +(-10.0015 + 1.74692i) q^{88} +9.36925 q^{89} +(0.675622 - 2.07935i) q^{91} +(-0.000973778 - 0.00299698i) q^{92} +(-1.66581 + 1.21028i) q^{94} +(2.10247 + 6.47075i) q^{95} +(-4.75689 - 3.45608i) q^{97} -8.33191 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + O(q^{10})$$ $$16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$56$$ $$397$$ $$\chi(n)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.991861 0.720629i −0.701351 0.509562i 0.179021 0.983845i $$-0.442707\pi$$
−0.880372 + 0.474284i $$0.842707\pi$$
$$3$$ 0 0
$$4$$ −0.153553 0.472586i −0.0767763 0.236293i
$$5$$ −0.809017 + 0.587785i −0.361803 + 0.262866i
$$6$$ 0 0
$$7$$ −0.139581 0.429587i −0.0527568 0.162369i 0.921207 0.389073i $$-0.127205\pi$$
−0.973964 + 0.226705i $$0.927205\pi$$
$$8$$ −0.945971 + 2.91140i −0.334451 + 1.02933i
$$9$$ 0 0
$$10$$ 1.22601 0.387698
$$11$$ 1.55234 + 2.93091i 0.468048 + 0.883703i
$$12$$ 0 0
$$13$$ 3.91592 + 2.84508i 1.08608 + 0.789084i 0.978733 0.205138i $$-0.0657643\pi$$
0.107348 + 0.994222i $$0.465764\pi$$
$$14$$ −0.171128 + 0.526677i −0.0457358 + 0.140760i
$$15$$ 0 0
$$16$$ 2.23230 1.62186i 0.558074 0.405465i
$$17$$ 0.598736 0.435007i 0.145215 0.105505i −0.512806 0.858505i $$-0.671394\pi$$
0.658021 + 0.753000i $$0.271394\pi$$
$$18$$ 0 0
$$19$$ 2.10247 6.47075i 0.482340 1.48449i −0.353456 0.935451i $$-0.614993\pi$$
0.835796 0.549040i $$-0.185007\pi$$
$$20$$ 0.402006 + 0.292074i 0.0898912 + 0.0653098i
$$21$$ 0 0
$$22$$ 0.572395 4.02572i 0.122035 0.858286i
$$23$$ 0.00634166 0.00132233 0.000661164 1.00000i $$-0.499790\pi$$
0.000661164 1.00000i $$0.499790\pi$$
$$24$$ 0 0
$$25$$ 0.309017 0.951057i 0.0618034 0.190211i
$$26$$ −1.83380 5.64385i −0.359637 1.10685i
$$27$$ 0 0
$$28$$ −0.181584 + 0.131928i −0.0343162 + 0.0249321i
$$29$$ 0.100091 + 0.308048i 0.0185864 + 0.0572030i 0.959920 0.280276i $$-0.0904259\pi$$
−0.941333 + 0.337479i $$0.890426\pi$$
$$30$$ 0 0
$$31$$ 4.53521 + 3.29503i 0.814548 + 0.591804i 0.915146 0.403123i $$-0.132075\pi$$
−0.100597 + 0.994927i $$0.532075\pi$$
$$32$$ 2.73956 0.484291
$$33$$ 0 0
$$34$$ −0.907341 −0.155608
$$35$$ 0.365429 + 0.265500i 0.0617688 + 0.0448776i
$$36$$ 0 0
$$37$$ 2.27713 + 7.00828i 0.374358 + 1.15215i 0.943911 + 0.330200i $$0.107116\pi$$
−0.569553 + 0.821954i $$0.692884\pi$$
$$38$$ −6.74837 + 4.90298i −1.09473 + 0.795368i
$$39$$ 0 0
$$40$$ −0.945971 2.91140i −0.149571 0.460332i
$$41$$ 3.39006 10.4335i 0.529438 1.62944i −0.225931 0.974143i $$-0.572543\pi$$
0.755369 0.655299i $$-0.227457\pi$$
$$42$$ 0 0
$$43$$ −1.80668 −0.275516 −0.137758 0.990466i $$-0.543990\pi$$
−0.137758 + 0.990466i $$0.543990\pi$$
$$44$$ 1.14674 1.18366i 0.172878 0.178444i
$$45$$ 0 0
$$46$$ −0.00629004 0.00456998i −0.000927416 0.000673807i
$$47$$ 0.518988 1.59728i 0.0757022 0.232987i −0.906044 0.423184i $$-0.860912\pi$$
0.981746 + 0.190196i $$0.0609125\pi$$
$$48$$ 0 0
$$49$$ 5.49806 3.99457i 0.785437 0.570653i
$$50$$ −0.991861 + 0.720629i −0.140270 + 0.101912i
$$51$$ 0 0
$$52$$ 0.743247 2.28748i 0.103070 0.317216i
$$53$$ 6.98948 + 5.07816i 0.960079 + 0.697539i 0.953169 0.302438i $$-0.0978004\pi$$
0.00691024 + 0.999976i $$0.497800\pi$$
$$54$$ 0 0
$$55$$ −2.97862 1.45871i −0.401636 0.196693i
$$56$$ 1.38274 0.184776
$$57$$ 0 0
$$58$$ 0.122712 0.377669i 0.0161129 0.0495903i
$$59$$ 0.463691 + 1.42709i 0.0603674 + 0.185792i 0.976692 0.214643i $$-0.0688589\pi$$
−0.916325 + 0.400435i $$0.868859\pi$$
$$60$$ 0 0
$$61$$ −10.5540 + 7.66790i −1.35130 + 0.981774i −0.352350 + 0.935868i $$0.614617\pi$$
−0.998946 + 0.0459057i $$0.985383\pi$$
$$62$$ −2.12381 6.53641i −0.269724 0.830125i
$$63$$ 0 0
$$64$$ −7.18186 5.21793i −0.897733 0.652241i
$$65$$ −4.84034 −0.600371
$$66$$ 0 0
$$67$$ 9.60773 1.17377 0.586885 0.809670i $$-0.300354\pi$$
0.586885 + 0.809670i $$0.300354\pi$$
$$68$$ −0.297516 0.216158i −0.0360791 0.0262130i
$$69$$ 0 0
$$70$$ −0.171128 0.526677i −0.0204537 0.0629500i
$$71$$ 9.23296 6.70814i 1.09575 0.796110i 0.115390 0.993320i $$-0.463188\pi$$
0.980361 + 0.197211i $$0.0631883\pi$$
$$72$$ 0 0
$$73$$ 3.16430 + 9.73870i 0.370353 + 1.13983i 0.946561 + 0.322526i $$0.104532\pi$$
−0.576208 + 0.817303i $$0.695468\pi$$
$$74$$ 2.79178 8.59220i 0.324537 0.998823i
$$75$$ 0 0
$$76$$ −3.38083 −0.387807
$$77$$ 1.04241 1.07597i 0.118793 0.122618i
$$78$$ 0 0
$$79$$ 1.69866 + 1.23415i 0.191114 + 0.138852i 0.679228 0.733928i $$-0.262315\pi$$
−0.488114 + 0.872780i $$0.662315\pi$$
$$80$$ −0.852662 + 2.62422i −0.0953305 + 0.293397i
$$81$$ 0 0
$$82$$ −10.8812 + 7.90563i −1.20162 + 0.873030i
$$83$$ −12.8589 + 9.34255i −1.41145 + 1.02548i −0.418339 + 0.908291i $$0.637388\pi$$
−0.993110 + 0.117187i $$0.962612\pi$$
$$84$$ 0 0
$$85$$ −0.228697 + 0.703856i −0.0248056 + 0.0763439i
$$86$$ 1.79197 + 1.30194i 0.193233 + 0.140392i
$$87$$ 0 0
$$88$$ −10.0015 + 1.74692i −1.06617 + 0.186223i
$$89$$ 9.36925 0.993138 0.496569 0.867997i $$-0.334593\pi$$
0.496569 + 0.867997i $$0.334593\pi$$
$$90$$ 0 0
$$91$$ 0.675622 2.07935i 0.0708244 0.217975i
$$92$$ −0.000973778 0.00299698i −0.000101523 0.000312457i
$$93$$ 0 0
$$94$$ −1.66581 + 1.21028i −0.171815 + 0.124831i
$$95$$ 2.10247 + 6.47075i 0.215709 + 0.663885i
$$96$$ 0 0
$$97$$ −4.75689 3.45608i −0.482989 0.350912i 0.319493 0.947589i $$-0.396487\pi$$
−0.802482 + 0.596677i $$0.796487\pi$$
$$98$$ −8.33191 −0.841650
$$99$$ 0 0
$$100$$ −0.496906 −0.0496906
$$101$$ −1.78628 1.29781i −0.177742 0.129137i 0.495357 0.868689i $$-0.335037\pi$$
−0.673099 + 0.739552i $$0.735037\pi$$
$$102$$ 0 0
$$103$$ 2.99111 + 9.20568i 0.294723 + 0.907063i 0.983314 + 0.181914i $$0.0582292\pi$$
−0.688592 + 0.725149i $$0.741771\pi$$
$$104$$ −11.9875 + 8.70944i −1.17547 + 0.854031i
$$105$$ 0 0
$$106$$ −3.27313 10.0736i −0.317914 0.978439i
$$107$$ 3.63294 11.1810i 0.351210 1.08091i −0.606965 0.794729i $$-0.707613\pi$$
0.958175 0.286184i $$-0.0923869\pi$$
$$108$$ 0 0
$$109$$ −12.5091 −1.19816 −0.599078 0.800691i $$-0.704466\pi$$
−0.599078 + 0.800691i $$0.704466\pi$$
$$110$$ 1.90318 + 3.59332i 0.181461 + 0.342609i
$$111$$ 0 0
$$112$$ −1.00832 0.732586i −0.0952771 0.0692228i
$$113$$ −3.06115 + 9.42124i −0.287968 + 0.886276i 0.697525 + 0.716561i $$0.254285\pi$$
−0.985493 + 0.169715i $$0.945715\pi$$
$$114$$ 0 0
$$115$$ −0.00513051 + 0.00372753i −0.000478422 + 0.000347594i
$$116$$ 0.130210 0.0946030i 0.0120897 0.00878367i
$$117$$ 0 0
$$118$$ 0.568489 1.74963i 0.0523336 0.161066i
$$119$$ −0.270446 0.196491i −0.0247917 0.0180123i
$$120$$ 0 0
$$121$$ −6.18048 + 9.09954i −0.561862 + 0.827231i
$$122$$ 15.9938 1.44801
$$123$$ 0 0
$$124$$ 0.860790 2.64924i 0.0773012 0.237909i
$$125$$ 0.309017 + 0.951057i 0.0276393 + 0.0850651i
$$126$$ 0 0
$$127$$ 0.454312 0.330077i 0.0403137 0.0292896i −0.567446 0.823411i $$-0.692068\pi$$
0.607760 + 0.794121i $$0.292068\pi$$
$$128$$ 1.67007 + 5.13995i 0.147615 + 0.454312i
$$129$$ 0 0
$$130$$ 4.80095 + 3.48809i 0.421071 + 0.305926i
$$131$$ −3.03500 −0.265170 −0.132585 0.991172i $$-0.542328\pi$$
−0.132585 + 0.991172i $$0.542328\pi$$
$$132$$ 0 0
$$133$$ −3.07322 −0.266482
$$134$$ −9.52953 6.92361i −0.823226 0.598108i
$$135$$ 0 0
$$136$$ 0.700092 + 2.15466i 0.0600324 + 0.184761i
$$137$$ −16.7469 + 12.1674i −1.43079 + 1.03953i −0.440918 + 0.897547i $$0.645347\pi$$
−0.989869 + 0.141981i $$0.954653\pi$$
$$138$$ 0 0
$$139$$ 1.09662 + 3.37504i 0.0930139 + 0.286267i 0.986731 0.162364i $$-0.0519117\pi$$
−0.893717 + 0.448631i $$0.851912\pi$$
$$140$$ 0.0693589 0.213465i 0.00586190 0.0180411i
$$141$$ 0 0
$$142$$ −13.9919 −1.17417
$$143$$ −2.25985 + 15.8937i −0.188978 + 1.32910i
$$144$$ 0 0
$$145$$ −0.262041 0.190384i −0.0217613 0.0158105i
$$146$$ 3.87945 11.9397i 0.321065 0.988138i
$$147$$ 0 0
$$148$$ 2.96236 2.15228i 0.243504 0.176916i
$$149$$ 5.10052 3.70575i 0.417851 0.303587i −0.358921 0.933368i $$-0.616855\pi$$
0.776773 + 0.629781i $$0.216855\pi$$
$$150$$ 0 0
$$151$$ −1.13852 + 3.50400i −0.0926512 + 0.285151i −0.986634 0.162949i $$-0.947899\pi$$
0.893983 + 0.448100i $$0.147899\pi$$
$$152$$ 16.8500 + 12.2423i 1.36672 + 0.992980i
$$153$$ 0 0
$$154$$ −1.80929 + 0.316022i −0.145797 + 0.0254657i
$$155$$ −5.60583 −0.450271
$$156$$ 0 0
$$157$$ 0.874113 2.69024i 0.0697618 0.214705i −0.910097 0.414394i $$-0.863993\pi$$
0.979859 + 0.199690i $$0.0639934\pi$$
$$158$$ −0.795469 2.44820i −0.0632841 0.194768i
$$159$$ 0 0
$$160$$ −2.21635 + 1.61028i −0.175218 + 0.127303i
$$161$$ −0.000885178 0.00272430i −6.97618e−5 0.000214705i
$$162$$ 0 0
$$163$$ −7.16094 5.20273i −0.560888 0.407509i 0.270896 0.962609i $$-0.412680\pi$$
−0.831784 + 0.555099i $$0.812680\pi$$
$$164$$ −5.45129 −0.425674
$$165$$ 0 0
$$166$$ 19.4868 1.51247
$$167$$ −15.9249 11.5701i −1.23230 0.895320i −0.235241 0.971937i $$-0.575588\pi$$
−0.997061 + 0.0766171i $$0.975588\pi$$
$$168$$ 0 0
$$169$$ 3.22271 + 9.91849i 0.247901 + 0.762961i
$$170$$ 0.734054 0.533322i 0.0562994 0.0409039i
$$171$$ 0 0
$$172$$ 0.277420 + 0.853811i 0.0211531 + 0.0651025i
$$173$$ 0.899661 2.76887i 0.0684000 0.210513i −0.911014 0.412375i $$-0.864699\pi$$
0.979414 + 0.201862i $$0.0646992\pi$$
$$174$$ 0 0
$$175$$ −0.451695 −0.0341449
$$176$$ 8.21881 + 4.02499i 0.619516 + 0.303395i
$$177$$ 0 0
$$178$$ −9.29299 6.75175i −0.696539 0.506065i
$$179$$ −1.94467 + 5.98508i −0.145352 + 0.447346i −0.997056 0.0766763i $$-0.975569\pi$$
0.851704 + 0.524022i $$0.175569\pi$$
$$180$$ 0 0
$$181$$ 9.03200 6.56213i 0.671343 0.487759i −0.199131 0.979973i $$-0.563812\pi$$
0.870475 + 0.492213i $$0.163812\pi$$
$$182$$ −2.16856 + 1.57555i −0.160745 + 0.116788i
$$183$$ 0 0
$$184$$ −0.00599902 + 0.0184631i −0.000442254 + 0.00136112i
$$185$$ −5.96160 4.33136i −0.438306 0.318448i
$$186$$ 0 0
$$187$$ 2.20441 + 1.07956i 0.161202 + 0.0789455i
$$188$$ −0.834545 −0.0608655
$$189$$ 0 0
$$190$$ 2.57765 7.93318i 0.187002 0.575534i
$$191$$ −6.30228 19.3964i −0.456017 1.40348i −0.869937 0.493163i $$-0.835841\pi$$
0.413920 0.910313i $$-0.364159\pi$$
$$192$$ 0 0
$$193$$ 2.40629 1.74827i 0.173208 0.125843i −0.497804 0.867290i $$-0.665860\pi$$
0.671012 + 0.741447i $$0.265860\pi$$
$$194$$ 2.22762 + 6.85590i 0.159934 + 0.492225i
$$195$$ 0 0
$$196$$ −2.73202 1.98493i −0.195144 0.141781i
$$197$$ 5.20127 0.370575 0.185288 0.982684i $$-0.440678\pi$$
0.185288 + 0.982684i $$0.440678\pi$$
$$198$$ 0 0
$$199$$ 8.10264 0.574381 0.287191 0.957873i $$-0.407279\pi$$
0.287191 + 0.957873i $$0.407279\pi$$
$$200$$ 2.47658 + 1.79934i 0.175121 + 0.127233i
$$201$$ 0 0
$$202$$ 0.836505 + 2.57450i 0.0588563 + 0.181141i
$$203$$ 0.118363 0.0859955i 0.00830743 0.00603570i
$$204$$ 0 0
$$205$$ 3.39006 + 10.4335i 0.236772 + 0.728709i
$$206$$ 3.66712 11.2862i 0.255500 0.786349i
$$207$$ 0 0
$$208$$ 13.3558 0.926059
$$209$$ 22.2289 3.88264i 1.53761 0.268568i
$$210$$ 0 0
$$211$$ 1.06252 + 0.771967i 0.0731470 + 0.0531444i 0.623758 0.781618i $$-0.285605\pi$$
−0.550611 + 0.834762i $$0.685605\pi$$
$$212$$ 1.32661 4.08290i 0.0911122 0.280415i
$$213$$ 0 0
$$214$$ −11.6608 + 8.47204i −0.797113 + 0.579137i
$$215$$ 1.46163 1.06194i 0.0996826 0.0724236i
$$216$$ 0 0
$$217$$ 0.782470 2.40820i 0.0531175 0.163479i
$$218$$ 12.4073 + 9.01443i 0.840328 + 0.610534i
$$219$$ 0 0
$$220$$ −0.231994 + 1.63164i −0.0156411 + 0.110005i
$$221$$ 3.58223 0.240967
$$222$$ 0 0
$$223$$ 8.84861 27.2332i 0.592547 1.82367i 0.0259701 0.999663i $$-0.491733\pi$$
0.566577 0.824009i $$-0.308267\pi$$
$$224$$ −0.382392 1.17688i −0.0255497 0.0786338i
$$225$$ 0 0
$$226$$ 9.82545 7.13861i 0.653579 0.474853i
$$227$$ −2.43074 7.48104i −0.161334 0.496534i 0.837414 0.546570i $$-0.184067\pi$$
−0.998747 + 0.0500354i $$0.984067\pi$$
$$228$$ 0 0
$$229$$ 13.0664 + 9.49331i 0.863453 + 0.627336i 0.928822 0.370526i $$-0.120822\pi$$
−0.0653689 + 0.997861i $$0.520822\pi$$
$$230$$ 0.00777492 0.000512663
$$231$$ 0 0
$$232$$ −0.991532 −0.0650973
$$233$$ −14.9138 10.8355i −0.977035 0.709858i −0.0199914 0.999800i $$-0.506364\pi$$
−0.957044 + 0.289942i $$0.906364\pi$$
$$234$$ 0 0
$$235$$ 0.518988 + 1.59728i 0.0338551 + 0.104195i
$$236$$ 0.603224 0.438268i 0.0392665 0.0285288i
$$237$$ 0 0
$$238$$ 0.126648 + 0.389782i 0.00820937 + 0.0252658i
$$239$$ 6.91081 21.2693i 0.447023 1.37579i −0.433227 0.901285i $$-0.642625\pi$$
0.880250 0.474510i $$-0.157375\pi$$
$$240$$ 0 0
$$241$$ −13.2213 −0.851662 −0.425831 0.904803i $$-0.640018\pi$$
−0.425831 + 0.904803i $$0.640018\pi$$
$$242$$ 12.6876 4.57164i 0.815588 0.293876i
$$243$$ 0 0
$$244$$ 5.24433 + 3.81023i 0.335734 + 0.243925i
$$245$$ −2.10007 + 6.46335i −0.134169 + 0.412928i
$$246$$ 0 0
$$247$$ 26.6429 19.3572i 1.69525 1.23167i
$$248$$ −13.8833 + 10.0868i −0.881591 + 0.640513i
$$249$$ 0 0
$$250$$ 0.378857 1.16600i 0.0239610 0.0737444i
$$251$$ 16.9919 + 12.3454i 1.07252 + 0.779232i 0.976364 0.216134i $$-0.0693450\pi$$
0.0961569 + 0.995366i $$0.469345\pi$$
$$252$$ 0 0
$$253$$ 0.00984441 + 0.0185868i 0.000618913 + 0.00116854i
$$254$$ −0.688477 −0.0431989
$$255$$ 0 0
$$256$$ −3.43893 + 10.5839i −0.214933 + 0.661497i
$$257$$ −1.04068 3.20289i −0.0649160 0.199791i 0.913338 0.407203i $$-0.133496\pi$$
−0.978254 + 0.207412i $$0.933496\pi$$
$$258$$ 0 0
$$259$$ 2.69283 1.95645i 0.167324 0.121568i
$$260$$ 0.743247 + 2.28748i 0.0460942 + 0.141863i
$$261$$ 0 0
$$262$$ 3.01030 + 2.18711i 0.185977 + 0.135120i
$$263$$ 21.0450 1.29769 0.648845 0.760920i $$-0.275252\pi$$
0.648845 + 0.760920i $$0.275252\pi$$
$$264$$ 0 0
$$265$$ −8.63948 −0.530719
$$266$$ 3.04820 + 2.21465i 0.186897 + 0.135789i
$$267$$ 0 0
$$268$$ −1.47529 4.54048i −0.0901177 0.277354i
$$269$$ −18.9161 + 13.7434i −1.15334 + 0.837947i −0.988921 0.148444i $$-0.952573\pi$$
−0.164415 + 0.986391i $$0.552573\pi$$
$$270$$ 0 0
$$271$$ −6.34951 19.5418i −0.385705 1.18708i −0.935967 0.352087i $$-0.885472\pi$$
0.550262 0.834992i $$-0.314528\pi$$
$$272$$ 0.631036 1.94213i 0.0382622 0.117759i
$$273$$ 0 0
$$274$$ 25.3788 1.53319
$$275$$ 3.26716 0.570661i 0.197017 0.0344122i
$$276$$ 0 0
$$277$$ 15.8420 + 11.5099i 0.951856 + 0.691564i 0.951245 0.308436i $$-0.0998055\pi$$
0.000611096 1.00000i $$0.499805\pi$$
$$278$$ 1.34446 4.13783i 0.0806354 0.248170i
$$279$$ 0 0
$$280$$ −1.11866 + 0.812754i −0.0668527 + 0.0485714i
$$281$$ −11.1585 + 8.10711i −0.665659 + 0.483630i −0.868569 0.495567i $$-0.834960\pi$$
0.202910 + 0.979197i $$0.434960\pi$$
$$282$$ 0 0
$$283$$ 9.73949 29.9751i 0.578953 1.78183i −0.0433533 0.999060i $$-0.513804\pi$$
0.622306 0.782774i $$-0.286196\pi$$
$$284$$ −4.58792 3.33332i −0.272243 0.197796i
$$285$$ 0 0
$$286$$ 13.6949 14.1359i 0.809799 0.835872i
$$287$$ −4.95530 −0.292502
$$288$$ 0 0
$$289$$ −5.08404 + 15.6471i −0.299061 + 0.920415i
$$290$$ 0.122712 + 0.377669i 0.00720589 + 0.0221775i
$$291$$ 0 0
$$292$$ 4.11649 2.99080i 0.240899 0.175024i
$$293$$ −7.20413 22.1720i −0.420870 1.29530i −0.906894 0.421359i $$-0.861553\pi$$
0.486024 0.873945i $$-0.338447\pi$$
$$294$$ 0 0
$$295$$ −1.21396 0.881993i −0.0706794 0.0513516i
$$296$$ −22.5580 −1.31116
$$297$$ 0 0
$$298$$ −7.72948 −0.447757
$$299$$ 0.0248334 + 0.0180425i 0.00143615 + 0.00104343i
$$300$$ 0 0
$$301$$ 0.252179 + 0.776126i 0.0145353 + 0.0447352i
$$302$$ 3.65433 2.65503i 0.210283 0.152780i
$$303$$ 0 0
$$304$$ −5.80129 17.8545i −0.332727 1.02403i
$$305$$ 4.03125 12.4069i 0.230829 0.710418i
$$306$$ 0 0
$$307$$ −10.0938 −0.576083 −0.288042 0.957618i $$-0.593004\pi$$
−0.288042 + 0.957618i $$0.593004\pi$$
$$308$$ −0.668551 0.327409i −0.0380942 0.0186558i
$$309$$ 0 0
$$310$$ 5.56020 + 4.03972i 0.315798 + 0.229441i
$$311$$ −4.11778 + 12.6732i −0.233498 + 0.718632i 0.763819 + 0.645430i $$0.223322\pi$$
−0.997317 + 0.0732020i $$0.976678\pi$$
$$312$$ 0 0
$$313$$ −18.7435 + 13.6180i −1.05945 + 0.769732i −0.973986 0.226609i $$-0.927236\pi$$
−0.0854599 + 0.996342i $$0.527236\pi$$
$$314$$ −2.80566 + 2.03843i −0.158333 + 0.115036i
$$315$$ 0 0
$$316$$ 0.322407 0.992267i 0.0181368 0.0558194i
$$317$$ −5.60802 4.07446i −0.314978 0.228845i 0.419052 0.907962i $$-0.362363\pi$$
−0.734029 + 0.679118i $$0.762363\pi$$
$$318$$ 0 0
$$319$$ −0.747485 + 0.771552i −0.0418512 + 0.0431986i
$$320$$ 8.87727 0.496254
$$321$$ 0 0
$$322$$ −0.00108523 + 0.00334001i −6.04777e−5 + 0.000186131i
$$323$$ −1.55599 4.78886i −0.0865779 0.266459i
$$324$$ 0 0
$$325$$ 3.91592 2.84508i 0.217216 0.157817i
$$326$$ 3.35342 + 10.3208i 0.185729 + 0.571614i
$$327$$ 0 0
$$328$$ 27.1692 + 19.7396i 1.50017 + 1.08994i
$$329$$ −0.758613 −0.0418237
$$330$$ 0 0
$$331$$ −10.5717 −0.581075 −0.290538 0.956864i $$-0.593834\pi$$
−0.290538 + 0.956864i $$0.593834\pi$$
$$332$$ 6.38968 + 4.64237i 0.350679 + 0.254783i
$$333$$ 0 0
$$334$$ 7.45750 + 22.9518i 0.408056 + 1.25587i
$$335$$ −7.77281 + 5.64728i −0.424674 + 0.308544i
$$336$$ 0 0
$$337$$ −1.96123 6.03605i −0.106835 0.328805i 0.883322 0.468767i $$-0.155302\pi$$
−0.990157 + 0.139963i $$0.955302\pi$$
$$338$$ 3.95107 12.1601i 0.214910 0.661424i
$$339$$ 0 0
$$340$$ 0.367750 0.0199440
$$341$$ −2.61724 + 18.4073i −0.141731 + 0.996811i
$$342$$ 0 0
$$343$$ −5.04145 3.66283i −0.272213 0.197774i
$$344$$ 1.70906 5.25996i 0.0921466 0.283598i
$$345$$ 0 0
$$346$$ −2.88767 + 2.09801i −0.155242 + 0.112790i
$$347$$ −20.4210 + 14.8367i −1.09626 + 0.796477i −0.980445 0.196794i $$-0.936947\pi$$
−0.115811 + 0.993271i $$0.536947\pi$$
$$348$$ 0 0
$$349$$ −3.43118 + 10.5601i −0.183667 + 0.565269i −0.999923 0.0124217i $$-0.996046\pi$$
0.816256 + 0.577691i $$0.196046\pi$$
$$350$$ 0.448019 + 0.325504i 0.0239476 + 0.0173989i
$$351$$ 0 0
$$352$$ 4.25273 + 8.02942i 0.226672 + 0.427970i
$$353$$ 18.8552 1.00356 0.501780 0.864996i $$-0.332679\pi$$
0.501780 + 0.864996i $$0.332679\pi$$
$$354$$ 0 0
$$355$$ −3.52668 + 10.8540i −0.187177 + 0.576070i
$$356$$ −1.43867 4.42778i −0.0762494 0.234672i
$$357$$ 0 0
$$358$$ 6.24187 4.53498i 0.329893 0.239681i
$$359$$ 6.57983 + 20.2506i 0.347270 + 1.06879i 0.960357 + 0.278773i $$0.0899276\pi$$
−0.613087 + 0.790016i $$0.710072\pi$$
$$360$$ 0 0
$$361$$ −22.0789 16.0412i −1.16205 0.844275i
$$362$$ −13.6873 −0.719391
$$363$$ 0 0
$$364$$ −1.08642 −0.0569437
$$365$$ −8.28423 6.01885i −0.433617 0.315041i
$$366$$ 0 0
$$367$$ −9.66781 29.7545i −0.504656 1.55317i −0.801349 0.598197i $$-0.795884\pi$$
0.296693 0.954973i $$-0.404116\pi$$
$$368$$ 0.0141565 0.0102853i 0.000737957 0.000536157i
$$369$$ 0 0
$$370$$ 2.79178 + 8.59220i 0.145138 + 0.446687i
$$371$$ 1.20591 3.71141i 0.0626078 0.192687i
$$372$$ 0 0
$$373$$ 9.39368 0.486386 0.243193 0.969978i $$-0.421805\pi$$
0.243193 + 0.969978i $$0.421805\pi$$
$$374$$ −1.40850 2.65934i −0.0728319 0.137511i
$$375$$ 0 0
$$376$$ 4.15938 + 3.02196i 0.214503 + 0.155846i
$$377$$ −0.484473 + 1.49106i −0.0249517 + 0.0767933i
$$378$$ 0 0
$$379$$ 6.63173 4.81823i 0.340649 0.247496i −0.404287 0.914632i $$-0.632480\pi$$
0.744936 + 0.667136i $$0.232480\pi$$
$$380$$ 2.73515 1.98720i 0.140310 0.101941i
$$381$$ 0 0
$$382$$ −7.72664 + 23.7802i −0.395329 + 1.21670i
$$383$$ 27.2501 + 19.7984i 1.39242 + 1.01165i 0.995596 + 0.0937524i $$0.0298862\pi$$
0.396820 + 0.917897i $$0.370114\pi$$
$$384$$ 0 0
$$385$$ −0.210886 + 1.48319i −0.0107478 + 0.0755901i
$$386$$ −3.64656 −0.185605
$$387$$ 0 0
$$388$$ −0.902863 + 2.77873i −0.0458359 + 0.141069i
$$389$$ 10.1771 + 31.3219i 0.515999 + 1.58808i 0.781456 + 0.623960i $$0.214477\pi$$
−0.265457 + 0.964123i $$0.585523\pi$$
$$390$$ 0 0
$$391$$ 0.00379698 0.00275867i 0.000192021 0.000139512i
$$392$$ 6.42879 + 19.7858i 0.324703 + 0.999333i
$$393$$ 0 0
$$394$$ −5.15894 3.74819i −0.259904 0.188831i
$$395$$ −2.09965 −0.105645
$$396$$ 0 0
$$397$$ −15.3865 −0.772228 −0.386114 0.922451i $$-0.626183\pi$$
−0.386114 + 0.922451i $$0.626183\pi$$
$$398$$ −8.03669 5.83900i −0.402843 0.292683i
$$399$$ 0 0
$$400$$ −0.852662 2.62422i −0.0426331 0.131211i
$$401$$ −5.37426 + 3.90463i −0.268378 + 0.194988i −0.713832 0.700317i $$-0.753042\pi$$
0.445455 + 0.895305i $$0.353042\pi$$
$$402$$ 0 0
$$403$$ 8.38491 + 25.8061i 0.417682 + 1.28549i
$$404$$ −0.339039 + 1.04346i −0.0168678 + 0.0519138i
$$405$$ 0 0
$$406$$ −0.179370 −0.00890198
$$407$$ −17.0058 + 17.5533i −0.842945 + 0.870085i
$$408$$ 0 0
$$409$$ −19.8088 14.3919i −0.979482 0.711636i −0.0218895 0.999760i $$-0.506968\pi$$
−0.957593 + 0.288125i $$0.906968\pi$$
$$410$$ 4.15623 12.7916i 0.205262 0.631731i
$$411$$ 0 0
$$412$$ 3.89119 2.82711i 0.191705 0.139282i
$$413$$ 0.548339 0.398392i 0.0269820 0.0196036i
$$414$$ 0 0
$$415$$ 4.91167 15.1166i 0.241104 0.742043i
$$416$$ 10.7279 + 7.79428i 0.525979 + 0.382146i
$$417$$ 0 0
$$418$$ −24.8459 12.1678i −1.21526 0.595146i
$$419$$ 20.8656 1.01935 0.509676 0.860367i $$-0.329765\pi$$
0.509676 + 0.860367i $$0.329765\pi$$
$$420$$ 0 0
$$421$$ −5.23200 + 16.1025i −0.254992 + 0.784785i 0.738839 + 0.673882i $$0.235374\pi$$
−0.993831 + 0.110903i $$0.964626\pi$$
$$422$$ −0.497571 1.53137i −0.0242214 0.0745458i
$$423$$ 0 0
$$424$$ −21.3964 + 15.5454i −1.03910 + 0.754951i
$$425$$ −0.228697 0.703856i −0.0110934 0.0341420i
$$426$$ 0 0
$$427$$ 4.76717 + 3.46355i 0.230700 + 0.167613i
$$428$$ −5.84186 −0.282377
$$429$$ 0 0
$$430$$ −2.21500 −0.106817
$$431$$ −21.1677 15.3792i −1.01961 0.740791i −0.0534080 0.998573i $$-0.517008\pi$$
−0.966203 + 0.257782i $$0.917008\pi$$
$$432$$ 0 0
$$433$$ −7.74375 23.8328i −0.372141 1.14533i −0.945387 0.325949i $$-0.894316\pi$$
0.573246 0.819383i $$-0.305684\pi$$
$$434$$ −2.51152 + 1.82472i −0.120557 + 0.0875895i
$$435$$ 0 0
$$436$$ 1.92081 + 5.91163i 0.0919899 + 0.283116i
$$437$$ 0.0133332 0.0410353i 0.000637812 0.00196298i
$$438$$ 0 0
$$439$$ 5.11234 0.243999 0.121999 0.992530i $$-0.461069\pi$$
0.121999 + 0.992530i $$0.461069\pi$$
$$440$$ 7.06458 7.29203i 0.336791 0.347634i
$$441$$ 0 0
$$442$$ −3.55307 2.58146i −0.169003 0.122788i
$$443$$ 8.67635 26.7031i 0.412226 1.26870i −0.502483 0.864587i $$-0.667580\pi$$
0.914709 0.404113i $$-0.132420\pi$$
$$444$$ 0 0
$$445$$ −7.57988 + 5.50711i −0.359321 + 0.261062i
$$446$$ −28.4016 + 20.6350i −1.34486 + 0.977096i
$$447$$ 0 0
$$448$$ −1.23910 + 3.81356i −0.0585421 + 0.180174i
$$449$$ −29.9297 21.7452i −1.41247 1.02622i −0.992958 0.118467i $$-0.962202\pi$$
−0.419510 0.907751i $$-0.637798\pi$$
$$450$$ 0 0
$$451$$ 35.8422 6.26041i 1.68775 0.294791i
$$452$$ 4.92239 0.231530
$$453$$ 0 0
$$454$$ −2.98010 + 9.17181i −0.139863 + 0.430454i
$$455$$ 0.675622 + 2.07935i 0.0316736 + 0.0974815i
$$456$$ 0 0
$$457$$ −29.8092 + 21.6576i −1.39441 + 1.01310i −0.399050 + 0.916929i $$0.630660\pi$$
−0.995365 + 0.0961719i $$0.969340\pi$$
$$458$$ −6.11891 18.8321i −0.285918 0.879965i
$$459$$ 0 0
$$460$$ 0.00254938 + 0.00185224i 0.000118866 + 8.63609e-5i
$$461$$ 23.0013 1.07128 0.535640 0.844447i $$-0.320071\pi$$
0.535640 + 0.844447i $$0.320071\pi$$
$$462$$ 0 0
$$463$$ −36.1571 −1.68036 −0.840181 0.542306i $$-0.817551\pi$$
−0.840181 + 0.542306i $$0.817551\pi$$
$$464$$ 0.723042 + 0.525321i 0.0335664 + 0.0243874i
$$465$$ 0 0
$$466$$ 6.98403 + 21.4946i 0.323529 + 0.995720i
$$467$$ 1.83240 1.33132i 0.0847935 0.0616061i −0.544581 0.838708i $$-0.683311\pi$$
0.629374 + 0.777102i $$0.283311\pi$$
$$468$$ 0 0
$$469$$ −1.34106 4.12736i −0.0619244 0.190584i
$$470$$ 0.636283 1.95828i 0.0293496 0.0903287i
$$471$$ 0 0
$$472$$ −4.59348 −0.211432
$$473$$ −2.80458 5.29521i −0.128955 0.243474i
$$474$$ 0 0
$$475$$ −5.50435 3.99914i −0.252557 0.183493i
$$476$$ −0.0513310 + 0.157981i −0.00235275 + 0.00724103i
$$477$$ 0 0
$$478$$ −22.1818 + 16.1160i −1.01457 + 0.737130i
$$479$$ 24.7000 17.9456i 1.12857 0.819954i 0.143084 0.989711i $$-0.454298\pi$$
0.985486 + 0.169756i $$0.0542981\pi$$
$$480$$ 0 0
$$481$$ −11.0221 + 33.9225i −0.502564 + 1.54673i
$$482$$ 13.1137 + 9.52768i 0.597314 + 0.433974i
$$483$$ 0 0
$$484$$ 5.24935 + 1.52355i 0.238607 + 0.0692524i
$$485$$ 5.87983 0.266989
$$486$$ 0 0
$$487$$ −4.99195 + 15.3636i −0.226207 + 0.696193i 0.771960 + 0.635671i $$0.219277\pi$$
−0.998167 + 0.0605221i $$0.980723\pi$$
$$488$$ −12.3406 37.9804i −0.558632 1.71929i
$$489$$ 0 0
$$490$$ 6.74066 4.89737i 0.304512 0.221241i
$$491$$ −3.60828 11.1051i −0.162839 0.501168i 0.836031 0.548682i $$-0.184870\pi$$
−0.998871 + 0.0475137i $$0.984870\pi$$
$$492$$ 0 0
$$493$$ 0.193931 + 0.140899i 0.00873420 + 0.00634577i
$$494$$ −40.3754 −1.81658
$$495$$ 0 0
$$496$$ 15.4680 0.694534
$$497$$ −4.17048 3.03003i −0.187072 0.135916i
$$498$$ 0 0
$$499$$ −12.6501 38.9330i −0.566296 1.74288i −0.664068 0.747672i $$-0.731171\pi$$
0.0977712 0.995209i $$-0.468829\pi$$
$$500$$ 0.402006 0.292074i 0.0179782 0.0130620i
$$501$$ 0 0
$$502$$ −7.95720 24.4897i −0.355147 1.09303i
$$503$$ −0.131171 + 0.403703i −0.00584863 + 0.0180002i −0.953938 0.300003i $$-0.903012\pi$$
0.948090 + 0.318003i $$0.103012\pi$$
$$504$$ 0 0
$$505$$ 2.20797 0.0982533
$$506$$ 0.00362993 0.0255297i 0.000161370 0.00113493i
$$507$$ 0 0
$$508$$ −0.225751 0.164017i −0.0100161 0.00727710i
$$509$$ −6.12017 + 18.8360i −0.271272 + 0.834889i 0.718910 + 0.695103i $$0.244641\pi$$
−0.990182 + 0.139786i $$0.955359\pi$$
$$510$$ 0 0
$$511$$ 3.74195 2.71868i 0.165534 0.120267i
$$512$$ 19.7827 14.3729i 0.874278 0.635200i
$$513$$ 0 0
$$514$$ −1.27588 + 3.92677i −0.0562769 + 0.173202i
$$515$$ −7.83082 5.68943i −0.345067 0.250706i
$$516$$ 0 0
$$517$$ 5.48714 0.958415i 0.241324 0.0421510i
$$518$$ −4.08078 −0.179299
$$519$$ 0 0
$$520$$ 4.57882 14.0922i 0.200795 0.617982i
$$521$$ 11.3748 + 35.0079i 0.498337 + 1.53372i 0.811690 + 0.584088i $$0.198548\pi$$
−0.313353 + 0.949637i $$0.601452\pi$$
$$522$$ 0 0
$$523$$ 8.49589 6.17262i 0.371499 0.269910i −0.386333 0.922359i $$-0.626258\pi$$
0.757832 + 0.652449i $$0.226258\pi$$
$$524$$ 0.466033 + 1.43430i 0.0203587 + 0.0626577i
$$525$$ 0 0
$$526$$ −20.8737 15.1656i −0.910137 0.661253i
$$527$$ 4.14875 0.180723
$$528$$ 0 0
$$529$$ −23.0000 −0.999998
$$530$$ 8.56916 + 6.22586i 0.372220 + 0.270434i
$$531$$ 0 0
$$532$$ 0.471900 + 1.45236i 0.0204595 + 0.0629678i
$$533$$ 42.9594 31.2118i 1.86078 1.35193i
$$534$$ 0 0
$$535$$ 3.63294 + 11.1810i 0.157066 + 0.483399i
$$536$$ −9.08863 + 27.9719i −0.392569 + 1.20820i
$$537$$ 0 0
$$538$$ 28.6660 1.23588
$$539$$ 20.2426 + 9.91338i 0.871910 + 0.427000i
$$540$$ 0 0
$$541$$ −0.529593 0.384772i −0.0227690 0.0165426i 0.576343 0.817208i $$-0.304479\pi$$
−0.599112 + 0.800666i $$0.704479\pi$$
$$542$$ −7.78454 + 23.9584i −0.334375 + 1.02910i
$$543$$ 0 0
$$544$$ 1.64028 1.19173i 0.0703262 0.0510950i
$$545$$ 10.1201 7.35267i 0.433497 0.314954i
$$546$$ 0 0
$$547$$ −4.14573 + 12.7592i −0.177259 + 0.545546i −0.999729 0.0232616i $$-0.992595\pi$$
0.822471 + 0.568807i $$0.192595\pi$$
$$548$$ 8.32166 + 6.04604i 0.355484 + 0.258274i
$$549$$ 0 0
$$550$$ −3.65180 1.78839i −0.155713 0.0762574i
$$551$$ 2.20374 0.0938823
$$552$$ 0 0
$$553$$ 0.293073 0.901985i 0.0124627 0.0383563i
$$554$$ −7.41872 22.8325i −0.315191 0.970059i
$$555$$ 0 0
$$556$$ 1.42661 1.03649i 0.0605017 0.0439571i
$$557$$ −4.09205 12.5940i −0.173386 0.533626i 0.826171 0.563420i $$-0.190515\pi$$
−0.999556 + 0.0297943i $$0.990515\pi$$
$$558$$ 0 0
$$559$$ −7.07481 5.14015i −0.299232 0.217405i
$$560$$ 1.24635 0.0526679
$$561$$ 0 0
$$562$$ 16.9099 0.713300
$$563$$ 17.2822 + 12.5562i 0.728356 + 0.529182i 0.889043 0.457824i $$-0.151371\pi$$
−0.160687 + 0.987005i $$0.551371\pi$$
$$564$$ 0 0
$$565$$ −3.06115 9.42124i −0.128783 0.396355i
$$566$$ −31.2611 + 22.7125i −1.31400 + 0.954679i
$$567$$ 0 0
$$568$$ 10.7960 + 33.2265i 0.452988 + 1.39415i
$$569$$ 14.0100 43.1185i 0.587332 1.80762i −0.00236662 0.999997i $$-0.500753\pi$$
0.589698 0.807624i $$-0.299247\pi$$
$$570$$ 0 0
$$571$$ −25.1544 −1.05268 −0.526339 0.850275i $$-0.676436\pi$$
−0.526339 + 0.850275i $$0.676436\pi$$
$$572$$ 7.85817 1.37255i 0.328567 0.0573893i
$$573$$ 0 0
$$574$$ 4.91497 + 3.57093i 0.205147 + 0.149048i
$$575$$ 0.00195968 0.00603127i 8.17243e−5 0.000251522i
$$576$$ 0 0
$$577$$ −6.16999 + 4.48276i −0.256860 + 0.186620i −0.708762 0.705448i $$-0.750746\pi$$
0.451902 + 0.892068i $$0.350746\pi$$
$$578$$ 16.3184 11.8560i 0.678755 0.493144i
$$579$$ 0 0
$$580$$ −0.0497357 + 0.153071i −0.00206516 + 0.00635592i
$$581$$ 5.80831 + 4.21998i 0.240969 + 0.175074i
$$582$$ 0 0
$$583$$ −4.03358 + 28.3686i −0.167054 + 1.17491i
$$584$$ −31.3466 −1.29713
$$585$$ 0 0
$$586$$ −8.83232 + 27.1831i −0.364860 + 1.12292i
$$587$$ −2.43760 7.50217i −0.100611 0.309648i 0.888065 0.459719i $$-0.152050\pi$$
−0.988675 + 0.150071i $$0.952050\pi$$
$$588$$ 0 0
$$589$$ 30.8564 22.4185i 1.27142 0.923739i
$$590$$ 0.568489 + 1.74963i 0.0234043 + 0.0720310i
$$591$$ 0 0
$$592$$ 16.4497 + 11.9514i 0.676077 + 0.491199i
$$593$$ 8.68507 0.356653 0.178327 0.983971i $$-0.442932\pi$$
0.178327 + 0.983971i $$0.442932\pi$$
$$594$$ 0 0
$$595$$ 0.334290 0.0137045
$$596$$ −2.53448 1.84141i −0.103816 0.0754271i
$$597$$ 0 0
$$598$$ −0.0116293 0.0357914i −0.000475558 0.00146362i
$$599$$ −11.3275 + 8.22991i −0.462829 + 0.336265i −0.794640 0.607081i $$-0.792340\pi$$
0.331811 + 0.943346i $$0.392340\pi$$
$$600$$ 0 0
$$601$$ −3.18091 9.78983i −0.129752 0.399335i 0.864985 0.501798i $$-0.167328\pi$$
−0.994737 + 0.102462i $$0.967328\pi$$
$$602$$ 0.309173 0.951537i 0.0126010 0.0387817i
$$603$$ 0 0
$$604$$ 1.83076 0.0744927
$$605$$ −0.348460 10.9945i −0.0141669 0.446989i
$$606$$ 0 0
$$607$$ −22.2282 16.1497i −0.902214 0.655497i 0.0368195 0.999322i $$-0.488277\pi$$
−0.939034 + 0.343825i $$0.888277\pi$$
$$608$$ 5.75986 17.7270i 0.233593 0.718926i
$$609$$ 0 0
$$610$$ −12.9392 + 9.40090i −0.523894 + 0.380631i
$$611$$ 6.57671 4.77826i 0.266065 0.193308i
$$612$$ 0 0
$$613$$ −3.35530 + 10.3266i −0.135519 + 0.417086i −0.995670 0.0929536i $$-0.970369\pi$$
0.860151 + 0.510039i $$0.170369\pi$$
$$614$$ 10.0116 + 7.27388i 0.404037 + 0.293550i
$$615$$ 0 0
$$616$$ 2.14648 + 4.05269i 0.0864842 + 0.163287i
$$617$$ −18.2404 −0.734330 −0.367165 0.930156i $$-0.619671\pi$$
−0.367165 + 0.930156i $$0.619671\pi$$
$$618$$ 0 0
$$619$$ 6.08144 18.7167i 0.244434 0.752289i −0.751295 0.659966i $$-0.770571\pi$$
0.995729 0.0923233i $$-0.0294293\pi$$
$$620$$ 0.860790 + 2.64924i 0.0345701 + 0.106396i
$$621$$ 0 0
$$622$$ 13.2169 9.60267i 0.529951 0.385032i
$$623$$ −1.30777 4.02491i −0.0523948 0.161255i
$$624$$ 0 0
$$625$$ −0.809017 0.587785i −0.0323607 0.0235114i
$$626$$ 28.4044 1.13527
$$627$$ 0 0
$$628$$ −1.40559 −0.0560893
$$629$$ 4.41205 + 3.20554i 0.175920 + 0.127813i
$$630$$ 0 0
$$631$$ −9.40181 28.9358i −0.374280 1.15192i −0.943963 0.330051i $$-0.892934\pi$$
0.569683 0.821865i $$-0.307066\pi$$
$$632$$ −5.19997 + 3.77800i −0.206844 + 0.150281i
$$633$$ 0 0
$$634$$ 2.62619 + 8.08260i 0.104300 + 0.321001i
$$635$$ −0.173532 + 0.534076i −0.00688640 + 0.0211942i
$$636$$ 0 0
$$637$$ 32.8948 1.30334
$$638$$ 1.29740 0.226612i 0.0513647 0.00897166i
$$639$$ 0 0
$$640$$ −4.37230 3.17666i −0.172830 0.125569i
$$641$$ −11.5427 + 35.5247i −0.455908 + 1.40314i 0.414159 + 0.910205i $$0.364076\pi$$
−0.870066 + 0.492935i $$0.835924\pi$$
$$642$$ 0 0
$$643$$ −0.861554 + 0.625956i −0.0339764 + 0.0246853i −0.604644 0.796496i $$-0.706685\pi$$
0.570667 + 0.821181i $$0.306685\pi$$
$$644$$ −0.00115154 0.000836645i −4.53772e−5 3.29684e-5i
$$645$$ 0 0
$$646$$ −1.90766 + 5.87118i −0.0750559 + 0.230998i
$$647$$ −12.7864 9.28987i −0.502686 0.365223i 0.307356 0.951595i $$-0.400556\pi$$
−0.810042 + 0.586372i $$0.800556\pi$$
$$648$$ 0 0
$$649$$ −3.46288 + 3.57437i −0.135930 + 0.140306i
$$650$$ −5.93429 −0.232762
$$651$$ 0 0
$$652$$ −1.35916 + 4.18305i −0.0532287 + 0.163821i
$$653$$ −10.9241 33.6210i −0.427495 1.31569i −0.900585 0.434679i $$-0.856862\pi$$
0.473091 0.881014i $$-0.343138\pi$$
$$654$$ 0 0
$$655$$ 2.45537 1.78393i 0.0959393 0.0697040i
$$656$$ −9.35409 28.7889i −0.365216 1.12402i
$$657$$ 0 0
$$658$$ 0.752439 + 0.546679i 0.0293331 + 0.0213118i
$$659$$ 28.4474 1.10815 0.554077 0.832465i $$-0.313071\pi$$
0.554077 + 0.832465i $$0.313071\pi$$
$$660$$ 0 0
$$661$$ 39.5989 1.54022 0.770110 0.637911i $$-0.220201\pi$$
0.770110 + 0.637911i $$0.220201\pi$$
$$662$$ 10.4857 + 7.61830i 0.407538 + 0.296094i
$$663$$ 0 0
$$664$$ −15.0357 46.2752i −0.583499 1.79583i
$$665$$ 2.48629 1.80639i 0.0964140 0.0700489i
$$666$$ 0 0
$$667$$ 0.000634741 0.00195353i 2.45773e−5 7.56411e-5i
$$668$$ −3.02256 + 9.30248i −0.116946 + 0.359924i
$$669$$ 0 0
$$670$$ 11.7791 0.455068
$$671$$ −38.8573 19.0295i −1.50007 0.734627i
$$672$$ 0 0
$$673$$ 14.2080 + 10.3227i 0.547679 + 0.397912i 0.826929 0.562306i $$-0.190086\pi$$
−0.279250 + 0.960218i $$0.590086\pi$$
$$674$$ −2.40448 + 7.40024i −0.0926173 + 0.285047i
$$675$$ 0 0
$$676$$ 4.19248 3.04602i 0.161249 0.117155i
$$677$$ −36.4616 + 26.4909i −1.40133 + 1.01813i −0.406819 + 0.913509i $$0.633362\pi$$
−0.994512 + 0.104619i $$0.966638\pi$$
$$678$$ 0 0
$$679$$ −0.820716 + 2.52590i −0.0314962 + 0.0969353i
$$680$$ −1.83287 1.33165i −0.0702872 0.0510666i
$$681$$ 0 0
$$682$$ 15.8608 16.3714i 0.607340 0.626894i
$$683$$ −15.7677 −0.603334 −0.301667 0.953413i $$-0.597543\pi$$
−0.301667 + 0.953413i $$0.597543\pi$$
$$684$$ 0 0
$$685$$ 6.39676 19.6872i 0.244408 0.752210i
$$686$$ 2.36087 + 7.26603i 0.0901386 + 0.277418i
$$687$$ 0 0
$$688$$ −4.03304 + 2.93018i −0.153758 + 0.111712i
$$689$$ 12.9225 + 39.7713i 0.492307 + 1.51517i
$$690$$ 0 0
$$691$$ −2.39970 1.74348i −0.0912889 0.0663253i 0.541205 0.840891i $$-0.317968\pi$$
−0.632493 + 0.774566i $$0.717968\pi$$
$$692$$ −1.44668 −0.0549944
$$693$$ 0 0
$$694$$ 30.9465 1.17471
$$695$$ −2.87098 2.08589i −0.108903 0.0791224i
$$696$$ 0 0
$$697$$ −2.50891 7.72162i −0.0950316 0.292477i
$$698$$ 11.0132 8.00153i 0.416854 0.302862i
$$699$$ 0 0
$$700$$ 0.0693589 + 0.213465i 0.00262152 + 0.00806821i
$$701$$ −11.4738 + 35.3128i −0.433360 + 1.33375i 0.461397 + 0.887194i $$0.347348\pi$$
−0.894757 + 0.446553i $$0.852652\pi$$
$$702$$ 0 0
$$703$$ 50.1364 1.89093
$$704$$ 4.14459 29.1494i 0.156205 1.09861i
$$705$$ 0 0
$$706$$ −18.7017 13.5876i −0.703848 0.511375i
$$707$$ −0.308191 + 0.948516i −0.0115907 + 0.0356726i
$$708$$ 0 0
$$709$$ 25.6867 18.6625i 0.964683 0.700883i 0.0104495 0.999945i $$-0.496674\pi$$
0.954234 + 0.299062i $$0.0966738\pi$$
$$710$$ 11.3197 8.22423i 0.424820 0.308650i
$$711$$ 0 0
$$712$$ −8.86303 + 27.2776i −0.332156 + 1.02227i
$$713$$ 0.0287608 + 0.0208959i 0.00107710 + 0.000782558i
$$714$$ 0 0
$$715$$ −7.51386 14.1866i −0.281002 0.530549i
$$716$$ 3.12708 0.116864
$$717$$ 0 0
$$718$$ 8.06692 24.8274i 0.301055 0.926552i
$$719$$ 9.85059 + 30.3170i 0.367365 + 1.13063i 0.948487 + 0.316816i $$0.102614\pi$$
−0.581122 + 0.813816i $$0.697386\pi$$
$$720$$ 0 0
$$721$$ 3.53714 2.56989i 0.131730 0.0957075i
$$722$$ 10.3394 + 31.8213i 0.384792 + 1.18427i
$$723$$ 0 0
$$724$$ −4.48806 3.26077i −0.166797 0.121185i
$$725$$ 0.323900 0.0120294
$$726$$ 0 0
$$727$$ 41.4129 1.53592 0.767959 0.640499i $$-0.221272\pi$$
0.767959 + 0.640499i $$0.221272\pi$$
$$728$$ 5.41470 + 3.93401i 0.200682 + 0.145804i
$$729$$ 0 0
$$730$$ 3.87945 + 11.9397i 0.143585 + 0.441909i
$$731$$ −1.08172 + 0.785918i −0.0400090 + 0.0290682i
$$732$$ 0 0
$$733$$ 14.7376 + 45.3578i 0.544347 + 1.67533i 0.722537 + 0.691333i $$0.242976\pi$$
−0.178189 + 0.983996i $$0.557024\pi$$
$$734$$ −11.8528 + 36.4792i −0.437495 + 1.34647i
$$735$$ 0 0
$$736$$ 0.0173734 0.000640391
$$737$$ 14.9145 + 28.1594i 0.549381 + 1.03726i
$$738$$ 0 0
$$739$$ 10.0777 + 7.32187i 0.370714 + 0.269339i 0.757507 0.652827i $$-0.226417\pi$$
−0.386793 + 0.922167i $$0.626417\pi$$
$$740$$ −1.13152 + 3.48246i −0.0415955 + 0.128018i
$$741$$ 0 0
$$742$$ −3.87065 + 2.81219i −0.142096 + 0.103239i
$$743$$ −22.1446 + 16.0890i −0.812407 + 0.590249i −0.914528 0.404524i $$-0.867437\pi$$
0.102120 + 0.994772i $$0.467437\pi$$
$$744$$ 0 0
$$745$$ −1.94823 + 5.99603i −0.0713775 + 0.219677i
$$746$$ −9.31722 6.76936i −0.341128 0.247844i
$$747$$ 0 0
$$748$$ 0.171694 1.20754i 0.00627775 0.0441521i
$$749$$ −5.31033 −0.194035
$$750$$ 0 0
$$751$$ −12.9393 + 39.8231i −0.472162 + 1.45317i 0.377585 + 0.925975i $$0.376755\pi$$
−0.849747 + 0.527191i $$0.823245\pi$$
$$752$$ −1.43203 4.40733i −0.0522207 0.160719i
$$753$$ 0 0
$$754$$ 1.55503 1.12979i 0.0566308 0.0411447i
$$755$$ −1.13852 3.50400i −0.0414349 0.127523i
$$756$$ 0 0
$$757$$ −13.0407 9.47464i −0.473973 0.344362i 0.325015 0.945709i $$-0.394631\pi$$
−0.798988 + 0.601347i $$0.794631\pi$$
$$758$$ −10.0499 −0.365029
$$759$$ 0 0
$$760$$ −20.8278 −0.755504
$$761$$ 8.83760 + 6.42090i 0.320363 + 0.232757i 0.736330 0.676622i $$-0.236557\pi$$
−0.415967 + 0.909380i $$0.636557\pi$$
$$762$$ 0 0
$$763$$ 1.74604 + 5.37376i 0.0632109 + 0.194543i
$$764$$ −8.19875 + 5.95674i −0.296620 + 0.215507i
$$765$$ 0 0
$$766$$ −12.7610 39.2744i −0.461075 1.41904i
$$767$$ −2.24442 + 6.90762i −0.0810414 + 0.249420i
$$768$$ 0 0
$$769$$ −34.2074 −1.23355 −0.616775 0.787139i $$-0.711561\pi$$
−0.616775 + 0.787139i $$0.711561\pi$$
$$770$$ 1.27800 1.31914i 0.0460558 0.0475386i
$$771$$ 0 0
$$772$$ −1.19570 0.868727i −0.0430342 0.0312662i
$$773$$ 2.66894 8.21416i 0.0959952 0.295443i −0.891517 0.452988i $$-0.850358\pi$$
0.987512 + 0.157545i $$0.0503580\pi$$
$$774$$ 0 0
$$775$$ 4.53521 3.29503i 0.162910 0.118361i
$$776$$ 14.5619 10.5798i 0.522742 0.379794i
$$777$$ 0 0
$$778$$ 12.4772 38.4009i 0.447329 1.37674i
$$779$$ −60.3852 43.8724i −2.16352 1.57189i
$$780$$ 0 0
$$781$$ 33.9937 + 16.6477i 1.21639 + 0.595701i
$$782$$ −0.00575405 −0.000205764
$$783$$ 0 0
$$784$$ 5.79466 17.8341i 0.206952 0.636934i
$$785$$ 0.874113 + 2.69024i 0.0311984 + 0.0960189i
$$786$$ 0 0
$$787$$ 18.6918 13.5804i 0.666291 0.484089i −0.202491 0.979284i $$-0.564904\pi$$
0.868781 + 0.495196