# Properties

 Label 950.2.e.m.201.1 Level $950$ Weight $2$ Character 950.201 Analytic conductor $7.586$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.39075800976.1 Defining polynomial: $$x^{8} - x^{7} + 12 x^{6} - 13 x^{5} + 125 x^{4} - 116 x^{3} + 232 x^{2} + 96 x + 64$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 201.1 Root $$1.51772 - 2.62877i$$ of defining polynomial Character $$\chi$$ $$=$$ 950.201 Dual form 950.2.e.m.501.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.51772 + 2.62877i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.51772 + 2.62877i) q^{6} -4.93155 q^{7} -1.00000 q^{8} +(-3.10694 - 5.38138i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.51772 + 2.62877i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.51772 + 2.62877i) q^{6} -4.93155 q^{7} -1.00000 q^{8} +(-3.10694 - 5.38138i) q^{9} +1.28233 q^{11} +3.03544 q^{12} +(1.98349 + 3.43551i) q^{13} +(-2.46578 + 4.27085i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.10694 - 1.91728i) q^{17} -6.21388 q^{18} +(3.12466 - 3.03916i) q^{19} +(7.48471 - 12.9639i) q^{21} +(0.641165 - 1.11053i) q^{22} +(-3.84233 - 6.65511i) q^{23} +(1.51772 - 2.62877i) q^{24} +3.96699 q^{26} +9.75553 q^{27} +(2.46578 + 4.27085i) q^{28} +(2.14116 + 3.70861i) q^{29} -4.14543 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.94622 + 3.37094i) q^{33} +(-1.10694 - 1.91728i) q^{34} +(-3.10694 + 5.38138i) q^{36} +9.38864 q^{37} +(-1.06966 - 4.22562i) q^{38} -12.0415 q^{39} +(2.30005 - 3.98380i) q^{41} +(-7.48471 - 12.9639i) q^{42} +(3.32461 - 5.75839i) q^{43} +(-0.641165 - 1.11053i) q^{44} -7.68466 q^{46} +(-3.46578 - 6.00290i) q^{47} +(-1.51772 - 2.62877i) q^{48} +17.3202 q^{49} +(3.36005 + 5.81977i) q^{51} +(1.98349 - 3.43551i) q^{52} +(3.46578 + 6.00290i) q^{53} +(4.87777 - 8.44854i) q^{54} +4.93155 q^{56} +(3.24689 + 12.8266i) q^{57} +4.28233 q^{58} +(3.15888 - 5.47135i) q^{59} +(-5.64238 - 9.77288i) q^{61} +(-2.07272 + 3.59005i) q^{62} +(15.3220 + 26.5385i) q^{63} +1.00000 q^{64} +(1.94622 + 3.37094i) q^{66} +(0.965775 + 1.67277i) q^{67} -2.21388 q^{68} +23.3263 q^{69} +(-4.16010 + 7.20550i) q^{71} +(3.10694 + 5.38138i) q^{72} +(3.41383 - 5.91293i) q^{73} +(4.69432 - 8.13080i) q^{74} +(-4.19432 - 1.18645i) q^{76} -6.32387 q^{77} +(-6.02077 + 10.4283i) q^{78} +(-1.76961 + 3.06506i) q^{79} +(-5.48533 + 9.50088i) q^{81} +(-2.30005 - 3.98380i) q^{82} -3.28476 q^{83} -14.9694 q^{84} +(-3.32461 - 5.75839i) q^{86} -12.9987 q^{87} -1.28233 q^{88} +(-4.46699 - 7.73705i) q^{89} +(-9.78170 - 16.9424i) q^{91} +(-3.84233 + 6.65511i) q^{92} +(6.29160 - 10.8974i) q^{93} -6.93155 q^{94} -3.03544 q^{96} +(1.07150 - 1.85590i) q^{97} +(8.66010 - 14.9997i) q^{98} +(-3.98412 - 6.90070i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + O(q^{10})$$ $$8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + 10q^{11} + 2q^{12} - 9q^{13} - 6q^{14} - 4q^{16} - 5q^{17} - 22q^{18} - q^{21} + 5q^{22} - 6q^{23} + q^{24} - 18q^{26} - 16q^{27} + 6q^{28} + 17q^{29} + 22q^{31} + 4q^{32} + 4q^{33} + 5q^{34} - 11q^{36} + 8q^{37} - 36q^{39} + 7q^{41} + q^{42} + 13q^{43} - 5q^{44} - 12q^{46} - 14q^{47} - q^{48} + 44q^{49} - 9q^{51} - 9q^{52} + 14q^{53} - 8q^{54} + 12q^{56} + 48q^{57} + 34q^{58} + 14q^{59} - 9q^{61} + 11q^{62} + 45q^{63} + 8q^{64} - 4q^{66} - 6q^{67} + 10q^{68} + 54q^{69} + 14q^{71} + 11q^{72} + 11q^{73} + 4q^{74} + 10q^{77} - 18q^{78} - 17q^{79} - 36q^{81} - 7q^{82} + 46q^{83} + 2q^{84} - 13q^{86} + 2q^{87} - 10q^{88} + 14q^{89} - 25q^{91} - 6q^{92} - 13q^{93} - 28q^{94} - 2q^{96} + 17q^{97} + 22q^{98} - 60q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ −1.51772 + 2.62877i −0.876255 + 1.51772i −0.0208358 + 0.999783i $$0.506633\pi$$
−0.855419 + 0.517936i $$0.826701\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0
$$6$$ 1.51772 + 2.62877i 0.619606 + 1.07319i
$$7$$ −4.93155 −1.86395 −0.931975 0.362521i $$-0.881916\pi$$
−0.931975 + 0.362521i $$0.881916\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −3.10694 5.38138i −1.03565 1.79379i
$$10$$ 0 0
$$11$$ 1.28233 0.386637 0.193318 0.981136i $$-0.438075\pi$$
0.193318 + 0.981136i $$0.438075\pi$$
$$12$$ 3.03544 0.876255
$$13$$ 1.98349 + 3.43551i 0.550122 + 0.952840i 0.998265 + 0.0588778i $$0.0187522\pi$$
−0.448143 + 0.893962i $$0.647914\pi$$
$$14$$ −2.46578 + 4.27085i −0.659006 + 1.14143i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 1.10694 1.91728i 0.268472 0.465008i −0.699995 0.714148i $$-0.746815\pi$$
0.968468 + 0.249140i $$0.0801478\pi$$
$$18$$ −6.21388 −1.46463
$$19$$ 3.12466 3.03916i 0.716846 0.697232i
$$20$$ 0 0
$$21$$ 7.48471 12.9639i 1.63330 2.82895i
$$22$$ 0.641165 1.11053i 0.136697 0.236766i
$$23$$ −3.84233 6.65511i −0.801181 1.38769i −0.918839 0.394632i $$-0.870872\pi$$
0.117658 0.993054i $$-0.462461\pi$$
$$24$$ 1.51772 2.62877i 0.309803 0.536595i
$$25$$ 0 0
$$26$$ 3.96699 0.777990
$$27$$ 9.75553 1.87745
$$28$$ 2.46578 + 4.27085i 0.465988 + 0.807114i
$$29$$ 2.14116 + 3.70861i 0.397604 + 0.688671i 0.993430 0.114443i $$-0.0365083\pi$$
−0.595825 + 0.803114i $$0.703175\pi$$
$$30$$ 0 0
$$31$$ −4.14543 −0.744541 −0.372271 0.928124i $$-0.621421\pi$$
−0.372271 + 0.928124i $$0.621421\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ −1.94622 + 3.37094i −0.338793 + 0.586806i
$$34$$ −1.10694 1.91728i −0.189839 0.328810i
$$35$$ 0 0
$$36$$ −3.10694 + 5.38138i −0.517823 + 0.896896i
$$37$$ 9.38864 1.54348 0.771742 0.635936i $$-0.219386\pi$$
0.771742 + 0.635936i $$0.219386\pi$$
$$38$$ −1.06966 4.22562i −0.173522 0.685485i
$$39$$ −12.0415 −1.92819
$$40$$ 0 0
$$41$$ 2.30005 3.98380i 0.359207 0.622165i −0.628621 0.777711i $$-0.716380\pi$$
0.987829 + 0.155546i $$0.0497138\pi$$
$$42$$ −7.48471 12.9639i −1.15492 2.00037i
$$43$$ 3.32461 5.75839i 0.506998 0.878147i −0.492969 0.870047i $$-0.664088\pi$$
0.999967 0.00809994i $$-0.00257832\pi$$
$$44$$ −0.641165 1.11053i −0.0966592 0.167419i
$$45$$ 0 0
$$46$$ −7.68466 −1.13304
$$47$$ −3.46578 6.00290i −0.505535 0.875613i −0.999979 0.00640345i $$-0.997962\pi$$
0.494444 0.869209i $$-0.335372\pi$$
$$48$$ −1.51772 2.62877i −0.219064 0.379430i
$$49$$ 17.3202 2.47431
$$50$$ 0 0
$$51$$ 3.36005 + 5.81977i 0.470501 + 0.814931i
$$52$$ 1.98349 3.43551i 0.275061 0.476420i
$$53$$ 3.46578 + 6.00290i 0.476061 + 0.824562i 0.999624 0.0274254i $$-0.00873086\pi$$
−0.523563 + 0.851987i $$0.675398\pi$$
$$54$$ 4.87777 8.44854i 0.663780 1.14970i
$$55$$ 0 0
$$56$$ 4.93155 0.659006
$$57$$ 3.24689 + 12.8266i 0.430061 + 1.69892i
$$58$$ 4.28233 0.562297
$$59$$ 3.15888 5.47135i 0.411252 0.712309i −0.583775 0.811915i $$-0.698425\pi$$
0.995027 + 0.0996066i $$0.0317584\pi$$
$$60$$ 0 0
$$61$$ −5.64238 9.77288i −0.722432 1.25129i −0.960022 0.279924i $$-0.909691\pi$$
0.237590 0.971366i $$-0.423643\pi$$
$$62$$ −2.07272 + 3.59005i −0.263235 + 0.455937i
$$63$$ 15.3220 + 26.5385i 1.93039 + 3.34354i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 1.94622 + 3.37094i 0.239563 + 0.414935i
$$67$$ 0.965775 + 1.67277i 0.117988 + 0.204362i 0.918970 0.394327i $$-0.129022\pi$$
−0.800982 + 0.598688i $$0.795689\pi$$
$$68$$ −2.21388 −0.268472
$$69$$ 23.3263 2.80816
$$70$$ 0 0
$$71$$ −4.16010 + 7.20550i −0.493713 + 0.855135i −0.999974 0.00724489i $$-0.997694\pi$$
0.506261 + 0.862380i $$0.331027\pi$$
$$72$$ 3.10694 + 5.38138i 0.366156 + 0.634202i
$$73$$ 3.41383 5.91293i 0.399559 0.692056i −0.594113 0.804382i $$-0.702497\pi$$
0.993671 + 0.112326i $$0.0358300\pi$$
$$74$$ 4.69432 8.13080i 0.545704 0.945187i
$$75$$ 0 0
$$76$$ −4.19432 1.18645i −0.481122 0.136095i
$$77$$ −6.32387 −0.720672
$$78$$ −6.02077 + 10.4283i −0.681718 + 1.18077i
$$79$$ −1.76961 + 3.06506i −0.199097 + 0.344846i −0.948236 0.317567i $$-0.897134\pi$$
0.749139 + 0.662413i $$0.230468\pi$$
$$80$$ 0 0
$$81$$ −5.48533 + 9.50088i −0.609482 + 1.05565i
$$82$$ −2.30005 3.98380i −0.253998 0.439937i
$$83$$ −3.28476 −0.360549 −0.180274 0.983616i $$-0.557699\pi$$
−0.180274 + 0.983616i $$0.557699\pi$$
$$84$$ −14.9694 −1.63330
$$85$$ 0 0
$$86$$ −3.32461 5.75839i −0.358502 0.620944i
$$87$$ −12.9987 −1.39361
$$88$$ −1.28233 −0.136697
$$89$$ −4.46699 7.73705i −0.473500 0.820126i 0.526040 0.850460i $$-0.323676\pi$$
−0.999540 + 0.0303341i $$0.990343\pi$$
$$90$$ 0 0
$$91$$ −9.78170 16.9424i −1.02540 1.77605i
$$92$$ −3.84233 + 6.65511i −0.400591 + 0.693843i
$$93$$ 6.29160 10.8974i 0.652408 1.13000i
$$94$$ −6.93155 −0.714935
$$95$$ 0 0
$$96$$ −3.03544 −0.309803
$$97$$ 1.07150 1.85590i 0.108795 0.188438i −0.806488 0.591251i $$-0.798634\pi$$
0.915282 + 0.402813i $$0.131968\pi$$
$$98$$ 8.66010 14.9997i 0.874802 1.51520i
$$99$$ −3.98412 6.90070i −0.400419 0.693547i
$$100$$ 0 0
$$101$$ −5.27267 9.13253i −0.524650 0.908720i −0.999588 0.0287012i $$-0.990863\pi$$
0.474938 0.880019i $$-0.342470\pi$$
$$102$$ 6.72010 0.665389
$$103$$ −3.64311 −0.358967 −0.179483 0.983761i $$-0.557443\pi$$
−0.179483 + 0.983761i $$0.557443\pi$$
$$104$$ −1.98349 3.43551i −0.194498 0.336880i
$$105$$ 0 0
$$106$$ 6.93155 0.673252
$$107$$ 5.07456 0.490576 0.245288 0.969450i $$-0.421117\pi$$
0.245288 + 0.969450i $$0.421117\pi$$
$$108$$ −4.87777 8.44854i −0.469363 0.812961i
$$109$$ −2.37155 + 4.10765i −0.227153 + 0.393441i −0.956963 0.290209i $$-0.906275\pi$$
0.729810 + 0.683650i $$0.239609\pi$$
$$110$$ 0 0
$$111$$ −14.2493 + 24.6805i −1.35249 + 2.34257i
$$112$$ 2.46578 4.27085i 0.232994 0.403557i
$$113$$ −12.4414 −1.17039 −0.585196 0.810892i $$-0.698983\pi$$
−0.585196 + 0.810892i $$0.698983\pi$$
$$114$$ 12.7316 + 3.60140i 1.19242 + 0.337302i
$$115$$ 0 0
$$116$$ 2.14116 3.70861i 0.198802 0.344335i
$$117$$ 12.3252 21.3479i 1.13946 1.97361i
$$118$$ −3.15888 5.47135i −0.290799 0.503678i
$$119$$ −5.45893 + 9.45515i −0.500419 + 0.866752i
$$120$$ 0 0
$$121$$ −9.35563 −0.850512
$$122$$ −11.2848 −1.02167
$$123$$ 6.98165 + 12.0926i 0.629514 + 1.09035i
$$124$$ 2.07272 + 3.59005i 0.186135 + 0.322396i
$$125$$ 0 0
$$126$$ 30.6441 2.72999
$$127$$ −1.94806 3.37413i −0.172862 0.299406i 0.766557 0.642176i $$-0.221968\pi$$
−0.939419 + 0.342770i $$0.888635\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 10.0916 + 17.4792i 0.888520 + 1.53896i
$$130$$ 0 0
$$131$$ 5.41504 9.37913i 0.473115 0.819459i −0.526412 0.850230i $$-0.676463\pi$$
0.999526 + 0.0307711i $$0.00979629\pi$$
$$132$$ 3.89243 0.338793
$$133$$ −15.4094 + 14.9878i −1.33617 + 1.29961i
$$134$$ 1.93155 0.166861
$$135$$ 0 0
$$136$$ −1.10694 + 1.91728i −0.0949193 + 0.164405i
$$137$$ −10.2994 17.8391i −0.879939 1.52410i −0.851407 0.524506i $$-0.824250\pi$$
−0.0285321 0.999593i $$-0.509083\pi$$
$$138$$ 11.6632 20.2012i 0.992833 1.71964i
$$139$$ 3.39427 + 5.87905i 0.287898 + 0.498655i 0.973308 0.229503i $$-0.0737101\pi$$
−0.685409 + 0.728158i $$0.740377\pi$$
$$140$$ 0 0
$$141$$ 21.0403 1.77191
$$142$$ 4.16010 + 7.20550i 0.349108 + 0.604672i
$$143$$ 2.54349 + 4.40546i 0.212698 + 0.368403i
$$144$$ 6.21388 0.517823
$$145$$ 0 0
$$146$$ −3.41383 5.91293i −0.282531 0.489358i
$$147$$ −26.2872 + 45.5307i −2.16813 + 3.75531i
$$148$$ −4.69432 8.13080i −0.385871 0.668348i
$$149$$ −11.3790 + 19.7090i −0.932202 + 1.61462i −0.152654 + 0.988280i $$0.548782\pi$$
−0.779548 + 0.626342i $$0.784551\pi$$
$$150$$ 0 0
$$151$$ 11.5478 0.939743 0.469872 0.882735i $$-0.344300\pi$$
0.469872 + 0.882735i $$0.344300\pi$$
$$152$$ −3.12466 + 3.03916i −0.253443 + 0.246509i
$$153$$ −13.7568 −1.11217
$$154$$ −3.16194 + 5.47664i −0.254796 + 0.441320i
$$155$$ 0 0
$$156$$ 6.02077 + 10.4283i 0.482048 + 0.834931i
$$157$$ 5.44927 9.43841i 0.434899 0.753267i −0.562388 0.826873i $$-0.690117\pi$$
0.997287 + 0.0736060i $$0.0234507\pi$$
$$158$$ 1.76961 + 3.06506i 0.140783 + 0.243843i
$$159$$ −21.0403 −1.66860
$$160$$ 0 0
$$161$$ 18.9486 + 32.8200i 1.49336 + 2.58658i
$$162$$ 5.48533 + 9.50088i 0.430969 + 0.746460i
$$163$$ −11.8240 −0.926126 −0.463063 0.886325i $$-0.653250\pi$$
−0.463063 + 0.886325i $$0.653250\pi$$
$$164$$ −4.60010 −0.359207
$$165$$ 0 0
$$166$$ −1.64238 + 2.84468i −0.127473 + 0.220790i
$$167$$ −8.83549 15.3035i −0.683710 1.18422i −0.973840 0.227234i $$-0.927032\pi$$
0.290130 0.956987i $$-0.406302\pi$$
$$168$$ −7.48471 + 12.9639i −0.577458 + 1.00019i
$$169$$ −1.36850 + 2.37031i −0.105269 + 0.182331i
$$170$$ 0 0
$$171$$ −26.0630 7.37248i −1.99309 0.563787i
$$172$$ −6.64922 −0.506998
$$173$$ 6.22855 10.7882i 0.473548 0.820208i −0.525994 0.850488i $$-0.676307\pi$$
0.999541 + 0.0302799i $$0.00963987\pi$$
$$174$$ −6.49937 + 11.2572i −0.492716 + 0.853409i
$$175$$ 0 0
$$176$$ −0.641165 + 1.11053i −0.0483296 + 0.0837094i
$$177$$ 9.58859 + 16.6079i 0.720723 + 1.24833i
$$178$$ −8.93398 −0.669630
$$179$$ 13.7971 1.03124 0.515621 0.856817i $$-0.327561\pi$$
0.515621 + 0.856817i $$0.327561\pi$$
$$180$$ 0 0
$$181$$ 6.96883 + 12.0704i 0.517989 + 0.897183i 0.999782 + 0.0208980i $$0.00665251\pi$$
−0.481793 + 0.876285i $$0.660014\pi$$
$$182$$ −19.5634 −1.45014
$$183$$ 34.2542 2.53214
$$184$$ 3.84233 + 6.65511i 0.283260 + 0.490621i
$$185$$ 0 0
$$186$$ −6.29160 10.8974i −0.461322 0.799034i
$$187$$ 1.41946 2.45858i 0.103801 0.179789i
$$188$$ −3.46578 + 6.00290i −0.252768 + 0.437806i
$$189$$ −48.1099 −3.49948
$$190$$ 0 0
$$191$$ 4.28233 0.309859 0.154929 0.987926i $$-0.450485\pi$$
0.154929 + 0.987926i $$0.450485\pi$$
$$192$$ −1.51772 + 2.62877i −0.109532 + 0.189715i
$$193$$ −4.80310 + 8.31922i −0.345735 + 0.598830i −0.985487 0.169751i $$-0.945704\pi$$
0.639752 + 0.768581i $$0.279037\pi$$
$$194$$ −1.07150 1.85590i −0.0769294 0.133246i
$$195$$ 0 0
$$196$$ −8.66010 14.9997i −0.618578 1.07141i
$$197$$ 23.7834 1.69450 0.847248 0.531197i $$-0.178258\pi$$
0.847248 + 0.531197i $$0.178258\pi$$
$$198$$ −7.96824 −0.566278
$$199$$ −7.51588 13.0179i −0.532786 0.922813i −0.999267 0.0382818i $$-0.987812\pi$$
0.466481 0.884531i $$-0.345522\pi$$
$$200$$ 0 0
$$201$$ −5.86310 −0.413551
$$202$$ −10.5453 −0.741967
$$203$$ −10.5593 18.2892i −0.741115 1.28365i
$$204$$ 3.36005 5.81977i 0.235250 0.407466i
$$205$$ 0 0
$$206$$ −1.82156 + 3.15503i −0.126914 + 0.219821i
$$207$$ −23.8758 + 41.3541i −1.65948 + 2.87431i
$$208$$ −3.96699 −0.275061
$$209$$ 4.00684 3.89721i 0.277159 0.269576i
$$210$$ 0 0
$$211$$ −9.73281 + 16.8577i −0.670034 + 1.16053i 0.307859 + 0.951432i $$0.400387\pi$$
−0.977894 + 0.209102i $$0.932946\pi$$
$$212$$ 3.46578 6.00290i 0.238030 0.412281i
$$213$$ −12.6277 21.8718i −0.865237 1.49863i
$$214$$ 2.53728 4.39469i 0.173445 0.300415i
$$215$$ 0 0
$$216$$ −9.75553 −0.663780
$$217$$ 20.4434 1.38779
$$218$$ 2.37155 + 4.10765i 0.160622 + 0.278205i
$$219$$ 10.3625 + 17.9483i 0.700231 + 1.21284i
$$220$$ 0 0
$$221$$ 8.78244 0.590771
$$222$$ 14.2493 + 24.6805i 0.956352 + 1.65645i
$$223$$ 2.82582 4.89447i 0.189231 0.327758i −0.755763 0.654845i $$-0.772734\pi$$
0.944994 + 0.327087i $$0.106067\pi$$
$$224$$ −2.46578 4.27085i −0.164752 0.285358i
$$225$$ 0 0
$$226$$ −6.22072 + 10.7746i −0.413796 + 0.716716i
$$227$$ 8.45952 0.561478 0.280739 0.959784i $$-0.409420\pi$$
0.280739 + 0.959784i $$0.409420\pi$$
$$228$$ 9.48471 9.22519i 0.628140 0.610953i
$$229$$ 1.54291 0.101958 0.0509791 0.998700i $$-0.483766\pi$$
0.0509791 + 0.998700i $$0.483766\pi$$
$$230$$ 0 0
$$231$$ 9.59786 16.6240i 0.631493 1.09378i
$$232$$ −2.14116 3.70861i −0.140574 0.243482i
$$233$$ 2.04631 3.54432i 0.134058 0.232196i −0.791179 0.611585i $$-0.790532\pi$$
0.925237 + 0.379389i $$0.123866\pi$$
$$234$$ −12.3252 21.3479i −0.805723 1.39555i
$$235$$ 0 0
$$236$$ −6.31777 −0.411252
$$237$$ −5.37155 9.30380i −0.348920 0.604347i
$$238$$ 5.45893 + 9.45515i 0.353850 + 0.612886i
$$239$$ 25.1442 1.62644 0.813221 0.581955i $$-0.197712\pi$$
0.813221 + 0.581955i $$0.197712\pi$$
$$240$$ 0 0
$$241$$ −13.7170 23.7586i −0.883592 1.53043i −0.847319 0.531085i $$-0.821784\pi$$
−0.0362738 0.999342i $$-0.511549\pi$$
$$242$$ −4.67782 + 8.10221i −0.300701 + 0.520830i
$$243$$ −2.01709 3.49370i −0.129396 0.224121i
$$244$$ −5.64238 + 9.77288i −0.361216 + 0.625645i
$$245$$ 0 0
$$246$$ 13.9633 0.890268
$$247$$ 16.6388 + 4.70665i 1.05870 + 0.299477i
$$248$$ 4.14543 0.263235
$$249$$ 4.98533 8.63485i 0.315933 0.547212i
$$250$$ 0 0
$$251$$ −2.30263 3.98826i −0.145340 0.251737i 0.784159 0.620559i $$-0.213094\pi$$
−0.929500 + 0.368822i $$0.879761\pi$$
$$252$$ 15.3220 26.5385i 0.965197 1.67177i
$$253$$ −4.92713 8.53404i −0.309766 0.536531i
$$254$$ −3.89611 −0.244464
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −9.86247 17.0823i −0.615204 1.06556i −0.990349 0.138599i $$-0.955740\pi$$
0.375144 0.926966i $$-0.377593\pi$$
$$258$$ 20.1833 1.25656
$$259$$ −46.3006 −2.87698
$$260$$ 0 0
$$261$$ 13.3049 23.0448i 0.823555 1.42644i
$$262$$ −5.41504 9.37913i −0.334543 0.579445i
$$263$$ 4.16010 7.20550i 0.256523 0.444310i −0.708785 0.705424i $$-0.750757\pi$$
0.965308 + 0.261114i $$0.0840899\pi$$
$$264$$ 1.94622 3.37094i 0.119781 0.207467i
$$265$$ 0 0
$$266$$ 5.27509 + 20.8388i 0.323437 + 1.27771i
$$267$$ 27.1185 1.65963
$$268$$ 0.965775 1.67277i 0.0589941 0.102181i
$$269$$ −7.67281 + 13.2897i −0.467820 + 0.810287i −0.999324 0.0367683i $$-0.988294\pi$$
0.531504 + 0.847056i $$0.321627\pi$$
$$270$$ 0 0
$$271$$ −1.68039 + 2.91052i −0.102077 + 0.176802i −0.912540 0.408987i $$-0.865882\pi$$
0.810463 + 0.585789i $$0.199215\pi$$
$$272$$ 1.10694 + 1.91728i 0.0671181 + 0.116252i
$$273$$ 59.3835 3.59405
$$274$$ −20.5988 −1.24442
$$275$$ 0 0
$$276$$ −11.6632 20.2012i −0.702039 1.21597i
$$277$$ −31.2517 −1.87774 −0.938868 0.344278i $$-0.888124\pi$$
−0.938868 + 0.344278i $$0.888124\pi$$
$$278$$ 6.78855 0.407150
$$279$$ 12.8796 + 22.3081i 0.771082 + 1.33555i
$$280$$ 0 0
$$281$$ −1.46699 2.54090i −0.0875132 0.151577i 0.818946 0.573870i $$-0.194559\pi$$
−0.906459 + 0.422293i $$0.861225\pi$$
$$282$$ 10.5201 18.2214i 0.626465 1.08507i
$$283$$ −7.34660 + 12.7247i −0.436710 + 0.756404i −0.997433 0.0715995i $$-0.977190\pi$$
0.560724 + 0.828003i $$0.310523\pi$$
$$284$$ 8.32019 0.493713
$$285$$ 0 0
$$286$$ 5.08699 0.300800
$$287$$ −11.3428 + 19.6463i −0.669545 + 1.15969i
$$288$$ 3.10694 5.38138i 0.183078 0.317101i
$$289$$ 6.04937 + 10.4778i 0.355845 + 0.616342i
$$290$$ 0 0
$$291$$ 3.25248 + 5.63346i 0.190664 + 0.330239i
$$292$$ −6.82766 −0.399559
$$293$$ 8.58320 0.501436 0.250718 0.968060i $$-0.419333\pi$$
0.250718 + 0.968060i $$0.419333\pi$$
$$294$$ 26.2872 + 45.5307i 1.53310 + 2.65541i
$$295$$ 0 0
$$296$$ −9.38864 −0.545704
$$297$$ 12.5098 0.725893
$$298$$ 11.3790 + 19.7090i 0.659167 + 1.14171i
$$299$$ 15.2425 26.4007i 0.881495 1.52679i
$$300$$ 0 0
$$301$$ −16.3955 + 28.3978i −0.945020 + 1.63682i
$$302$$ 5.77388 10.0007i 0.332249 0.575473i
$$303$$ 32.0097 1.83891
$$304$$ 1.06966 + 4.22562i 0.0613493 + 0.242356i
$$305$$ 0 0
$$306$$ −6.87839 + 11.9137i −0.393212 + 0.681063i
$$307$$ −2.66757 + 4.62036i −0.152246 + 0.263698i −0.932053 0.362322i $$-0.881984\pi$$
0.779807 + 0.626020i $$0.215317\pi$$
$$308$$ 3.16194 + 5.47664i 0.180168 + 0.312060i
$$309$$ 5.52922 9.57689i 0.314546 0.544810i
$$310$$ 0 0
$$311$$ 23.2933 1.32084 0.660421 0.750896i $$-0.270378\pi$$
0.660421 + 0.750896i $$0.270378\pi$$
$$312$$ 12.0415 0.681718
$$313$$ 5.35699 + 9.27859i 0.302795 + 0.524457i 0.976768 0.214299i $$-0.0687468\pi$$
−0.673973 + 0.738756i $$0.735414\pi$$
$$314$$ −5.44927 9.43841i −0.307520 0.532640i
$$315$$ 0 0
$$316$$ 3.53923 0.199097
$$317$$ 7.16267 + 12.4061i 0.402296 + 0.696797i 0.994003 0.109356i $$-0.0348790\pi$$
−0.591707 + 0.806153i $$0.701546\pi$$
$$318$$ −10.5201 + 18.2214i −0.589940 + 1.02181i
$$319$$ 2.74568 + 4.75566i 0.153729 + 0.266266i
$$320$$ 0 0
$$321$$ −7.70175 + 13.3398i −0.429870 + 0.744556i
$$322$$ 37.8973 2.11193
$$323$$ −2.36810 9.35501i −0.131765 0.520527i
$$324$$ 10.9707 0.609482
$$325$$ 0 0
$$326$$ −5.91199 + 10.2399i −0.327435 + 0.567134i
$$327$$ −7.19870 12.4685i −0.398089 0.689510i
$$328$$ −2.30005 + 3.98380i −0.126999 + 0.219969i
$$329$$ 17.0916 + 29.6036i 0.942293 + 1.63210i
$$330$$ 0 0
$$331$$ −10.5695 −0.580953 −0.290476 0.956882i $$-0.593814\pi$$
−0.290476 + 0.956882i $$0.593814\pi$$
$$332$$ 1.64238 + 2.84468i 0.0901372 + 0.156122i
$$333$$ −29.1700 50.5238i −1.59850 2.76869i
$$334$$ −17.6710 −0.966913
$$335$$ 0 0
$$336$$ 7.48471 + 12.9639i 0.408324 + 0.707238i
$$337$$ 5.85931 10.1486i 0.319177 0.552831i −0.661140 0.750263i $$-0.729927\pi$$
0.980317 + 0.197432i $$0.0632602\pi$$
$$338$$ 1.36850 + 2.37031i 0.0744365 + 0.128928i
$$339$$ 18.8826 32.7057i 1.02556 1.77633i
$$340$$ 0 0
$$341$$ −5.31581 −0.287867
$$342$$ −19.4163 + 18.8850i −1.04991 + 1.02118i
$$343$$ −50.8946 −2.74805
$$344$$ −3.32461 + 5.75839i −0.179251 + 0.310472i
$$345$$ 0 0
$$346$$ −6.22855 10.7882i −0.334849 0.579975i
$$347$$ 10.4505 18.1008i 0.561011 0.971700i −0.436397 0.899754i $$-0.643746\pi$$
0.997409 0.0719459i $$-0.0229209\pi$$
$$348$$ 6.49937 + 11.2572i 0.348403 + 0.603452i
$$349$$ 35.4817 1.89929 0.949647 0.313322i $$-0.101442\pi$$
0.949647 + 0.313322i $$0.101442\pi$$
$$350$$ 0 0
$$351$$ 19.3500 + 33.5153i 1.03283 + 1.78891i
$$352$$ 0.641165 + 1.11053i 0.0341742 + 0.0591915i
$$353$$ 14.2984 0.761029 0.380515 0.924775i $$-0.375747\pi$$
0.380515 + 0.924775i $$0.375747\pi$$
$$354$$ 19.1772 1.01926
$$355$$ 0 0
$$356$$ −4.46699 + 7.73705i −0.236750 + 0.410063i
$$357$$ −16.5702 28.7005i −0.876990 1.51899i
$$358$$ 6.89854 11.9486i 0.364599 0.631504i
$$359$$ −2.11073 + 3.65589i −0.111400 + 0.192951i −0.916335 0.400413i $$-0.868867\pi$$
0.804935 + 0.593363i $$0.202200\pi$$
$$360$$ 0 0
$$361$$ 0.526988 18.9927i 0.0277362 0.999615i
$$362$$ 13.9377 0.732547
$$363$$ 14.1992 24.5938i 0.745266 1.29084i
$$364$$ −9.78170 + 16.9424i −0.512700 + 0.888023i
$$365$$ 0 0
$$366$$ 17.1271 29.6650i 0.895247 1.55061i
$$367$$ 7.08238 + 12.2670i 0.369697 + 0.640334i 0.989518 0.144409i $$-0.0461281\pi$$
−0.619821 + 0.784743i $$0.712795\pi$$
$$368$$ 7.68466 0.400591
$$369$$ −28.5845 −1.48805
$$370$$ 0 0
$$371$$ −17.0916 29.6036i −0.887354 1.53694i
$$372$$ −12.5832 −0.652408
$$373$$ −16.6541 −0.862315 −0.431158 0.902277i $$-0.641895\pi$$
−0.431158 + 0.902277i $$0.641895\pi$$
$$374$$ −1.41946 2.45858i −0.0733987 0.127130i
$$375$$ 0 0
$$376$$ 3.46578 + 6.00290i 0.178734 + 0.309576i
$$377$$ −8.49398 + 14.7120i −0.437462 + 0.757706i
$$378$$ −24.0550 + 41.6644i −1.23725 + 2.14299i
$$379$$ 3.36689 0.172946 0.0864728 0.996254i $$-0.472440\pi$$
0.0864728 + 0.996254i $$0.472440\pi$$
$$380$$ 0 0
$$381$$ 11.8264 0.605885
$$382$$ 2.14116 3.70861i 0.109552 0.189749i
$$383$$ 4.16010 7.20550i 0.212571 0.368184i −0.739947 0.672665i $$-0.765150\pi$$
0.952518 + 0.304481i $$0.0984830\pi$$
$$384$$ 1.51772 + 2.62877i 0.0774508 + 0.134149i
$$385$$ 0 0
$$386$$ 4.80310 + 8.31922i 0.244471 + 0.423437i
$$387$$ −41.3175 −2.10028
$$388$$ −2.14301 −0.108795
$$389$$ −12.4076 21.4905i −0.629089 1.08961i −0.987735 0.156140i $$-0.950095\pi$$
0.358646 0.933474i $$-0.383239\pi$$
$$390$$ 0 0
$$391$$ −17.0129 −0.860380
$$392$$ −17.3202 −0.874802
$$393$$ 16.4370 + 28.4698i 0.829138 + 1.43611i
$$394$$ 11.8917 20.5970i 0.599095 1.03766i
$$395$$ 0 0
$$396$$ −3.98412 + 6.90070i −0.200210 + 0.346773i
$$397$$ −6.15043 + 10.6529i −0.308681 + 0.534652i −0.978074 0.208257i $$-0.933221\pi$$
0.669393 + 0.742909i $$0.266554\pi$$
$$398$$ −15.0318 −0.753474
$$399$$ −16.0122 63.2550i −0.801613 3.16671i
$$400$$ 0 0
$$401$$ 7.52320 13.0306i 0.375691 0.650715i −0.614740 0.788730i $$-0.710739\pi$$
0.990430 + 0.138015i $$0.0440722\pi$$
$$402$$ −2.93155 + 5.07759i −0.146212 + 0.253247i
$$403$$ −8.22244 14.2417i −0.409589 0.709429i
$$404$$ −5.27267 + 9.13253i −0.262325 + 0.454360i
$$405$$ 0 0
$$406$$ −21.1185 −1.04809
$$407$$ 12.0393 0.596768
$$408$$ −3.36005 5.81977i −0.166347 0.288122i
$$409$$ −13.0170 22.5461i −0.643648 1.11483i −0.984612 0.174755i $$-0.944087\pi$$
0.340964 0.940077i $$-0.389247\pi$$
$$410$$ 0 0
$$411$$ 62.5265 3.08420
$$412$$ 1.82156 + 3.15503i 0.0897417 + 0.155437i
$$413$$ −15.5782 + 26.9822i −0.766553 + 1.32771i
$$414$$ 23.8758 + 41.3541i 1.17343 + 2.03244i
$$415$$ 0 0
$$416$$ −1.98349 + 3.43551i −0.0972488 + 0.168440i
$$417$$ −20.6062 −1.00909
$$418$$ −1.37166 5.41863i −0.0670901 0.265034i
$$419$$ 9.69640 0.473700 0.236850 0.971546i $$-0.423885\pi$$
0.236850 + 0.971546i $$0.423885\pi$$
$$420$$ 0 0
$$421$$ −9.04154 + 15.6604i −0.440658 + 0.763242i −0.997738 0.0672166i $$-0.978588\pi$$
0.557080 + 0.830459i $$0.311921\pi$$
$$422$$ 9.73281 + 16.8577i 0.473786 + 0.820621i
$$423$$ −21.5359 + 37.3013i −1.04711 + 1.81365i
$$424$$ −3.46578 6.00290i −0.168313 0.291527i
$$425$$ 0 0
$$426$$ −25.2554 −1.22363
$$427$$ 27.8257 + 48.1955i 1.34658 + 2.33234i
$$428$$ −2.53728 4.39469i −0.122644 0.212426i
$$429$$ −15.4412 −0.745510
$$430$$ 0 0
$$431$$ 9.08981 + 15.7440i 0.437841 + 0.758362i 0.997523 0.0703453i $$-0.0224101\pi$$
−0.559682 + 0.828707i $$0.689077\pi$$
$$432$$ −4.87777 + 8.44854i −0.234682 + 0.406481i
$$433$$ 2.35699 + 4.08243i 0.113270 + 0.196189i 0.917087 0.398687i $$-0.130534\pi$$
−0.803817 + 0.594877i $$0.797201\pi$$
$$434$$ 10.2217 17.7045i 0.490657 0.849844i
$$435$$ 0 0
$$436$$ 4.74310 0.227153
$$437$$ −32.2319 9.11749i −1.54186 0.436149i
$$438$$ 20.7249 0.990276
$$439$$ 7.08554 12.2725i 0.338174 0.585735i −0.645915 0.763409i $$-0.723524\pi$$
0.984089 + 0.177674i $$0.0568573\pi$$
$$440$$ 0 0
$$441$$ −53.8128 93.2065i −2.56251 4.43841i
$$442$$ 4.39122 7.60581i 0.208869 0.361772i
$$443$$ −6.24811 10.8220i −0.296856 0.514170i 0.678559 0.734546i $$-0.262605\pi$$
−0.975415 + 0.220376i $$0.929272\pi$$
$$444$$ 28.4986 1.35249
$$445$$ 0 0
$$446$$ −2.82582 4.89447i −0.133807 0.231760i
$$447$$ −34.5402 59.8253i −1.63369 2.82964i
$$448$$ −4.93155 −0.232994
$$449$$ −29.3326 −1.38429 −0.692146 0.721757i $$-0.743335\pi$$
−0.692146 + 0.721757i $$0.743335\pi$$
$$450$$ 0 0
$$451$$ 2.94942 5.10855i 0.138883 0.240552i
$$452$$ 6.22072 + 10.7746i 0.292598 + 0.506795i
$$453$$ −17.5263 + 30.3564i −0.823455 + 1.42627i
$$454$$ 4.22976 7.32616i 0.198512 0.343834i
$$455$$ 0 0
$$456$$ −3.24689 12.8266i −0.152050 0.600660i
$$457$$ 26.2126 1.22617 0.613087 0.790015i $$-0.289927\pi$$
0.613087 + 0.790015i $$0.289927\pi$$
$$458$$ 0.771454 1.33620i 0.0360477 0.0624364i
$$459$$ 10.7988 18.7041i 0.504044 0.873031i
$$460$$ 0 0
$$461$$ −4.85641 + 8.41155i −0.226186 + 0.391765i −0.956674 0.291160i $$-0.905959\pi$$
0.730489 + 0.682925i $$0.239292\pi$$
$$462$$ −9.59786 16.6240i −0.446533 0.773418i
$$463$$ 5.34146 0.248239 0.124119 0.992267i $$-0.460389\pi$$
0.124119 + 0.992267i $$0.460389\pi$$
$$464$$ −4.28233 −0.198802
$$465$$ 0 0
$$466$$ −2.04631 3.54432i −0.0947936 0.164187i
$$467$$ 30.3642 1.40509 0.702543 0.711641i $$-0.252048\pi$$
0.702543 + 0.711641i $$0.252048\pi$$
$$468$$ −24.6504 −1.13946
$$469$$ −4.76277 8.24936i −0.219924 0.380920i
$$470$$ 0 0
$$471$$ 16.5409 + 28.6497i 0.762165 + 1.32011i
$$472$$ −3.15888 + 5.47135i −0.145399 + 0.251839i
$$473$$ 4.26325 7.38416i 0.196024 0.339524i
$$474$$ −10.7431 −0.493447
$$475$$ 0 0
$$476$$ 10.9179 0.500419
$$477$$ 21.5359 37.3013i 0.986062 1.70791i
$$478$$ 12.5721 21.7755i 0.575034 0.995988i
$$479$$ −0.994997 1.72339i −0.0454626 0.0787435i 0.842399 0.538855i $$-0.181143\pi$$
−0.887861 + 0.460111i $$0.847810\pi$$
$$480$$ 0 0
$$481$$ 18.6223 + 32.2548i 0.849105 + 1.47069i
$$482$$ −27.4341 −1.24959
$$483$$ −115.035 −5.23427
$$484$$ 4.67782 + 8.10221i 0.212628 + 0.368282i
$$485$$ 0 0
$$486$$ −4.03418 −0.182994
$$487$$ −29.2102 −1.32364 −0.661820 0.749663i $$-0.730216\pi$$
−0.661820 + 0.749663i $$0.730216\pi$$
$$488$$ 5.64238 + 9.77288i 0.255418 + 0.442398i
$$489$$ 17.9455 31.0825i 0.811523 1.40560i
$$490$$ 0 0
$$491$$ 8.44853 14.6333i 0.381277 0.660391i −0.609968 0.792426i $$-0.708818\pi$$
0.991245 + 0.132035i $$0.0421511\pi$$
$$492$$ 6.98165 12.0926i 0.314757 0.545176i
$$493$$ 9.48057 0.426983
$$494$$ 12.3955 12.0563i 0.557699 0.542439i
$$495$$ 0 0
$$496$$ 2.07272 3.59005i 0.0930677 0.161198i
$$497$$ 20.5157 35.5343i 0.920256 1.59393i
$$498$$ −4.98533 8.63485i −0.223398 0.386937i
$$499$$ −0.629662 + 1.09061i −0.0281875 + 0.0488222i −0.879775 0.475390i $$-0.842307\pi$$
0.851588 + 0.524212i $$0.175640\pi$$
$$500$$ 0 0
$$501$$ 53.6391 2.39642
$$502$$ −4.60525 −0.205542
$$503$$ 4.56966 + 7.91489i 0.203751 + 0.352907i 0.949734 0.313058i $$-0.101353\pi$$
−0.745983 + 0.665965i $$0.768020\pi$$
$$504$$ −15.3220 26.5385i −0.682498 1.18212i
$$505$$ 0 0
$$506$$ −9.85427 −0.438076
$$507$$ −4.15399 7.19492i −0.184485 0.319538i
$$508$$ −1.94806 + 3.37413i −0.0864310 + 0.149703i
$$509$$ −17.3005 29.9654i −0.766832 1.32819i −0.939272 0.343172i $$-0.888498\pi$$
0.172440 0.985020i $$-0.444835\pi$$
$$510$$ 0 0
$$511$$ −16.8355 + 29.1599i −0.744758 + 1.28996i
$$512$$ −1.00000 −0.0441942
$$513$$ 30.4827 29.6486i 1.34584 1.30902i
$$514$$ −19.7249 −0.870030
$$515$$ 0 0
$$516$$ 10.0916 17.4792i 0.444260 0.769481i
$$517$$ −4.44427 7.69770i −0.195459 0.338544i
$$518$$ −23.1503 + 40.0975i −1.01717 + 1.76178i
$$519$$ 18.9064 + 32.7468i 0.829897 + 1.43742i
$$520$$ 0 0
$$521$$ 23.2542 1.01878 0.509392 0.860535i $$-0.329870\pi$$
0.509392 + 0.860535i $$0.329870\pi$$
$$522$$ −13.3049 23.0448i −0.582342 1.00865i
$$523$$ 11.7066 + 20.2765i 0.511896 + 0.886630i 0.999905 + 0.0137910i $$0.00438994\pi$$
−0.488009 + 0.872839i $$0.662277\pi$$
$$524$$ −10.8301 −0.473115
$$525$$ 0 0
$$526$$ −4.16010 7.20550i −0.181389 0.314175i
$$527$$ −4.58874 + 7.94794i −0.199889 + 0.346218i
$$528$$ −1.94622 3.37094i −0.0846982 0.146702i
$$529$$ −18.0270 + 31.2237i −0.783782 + 1.35755i
$$530$$ 0 0
$$531$$ −39.2579 −1.70365
$$532$$ 20.6845 + 5.85105i 0.896787 + 0.253675i
$$533$$ 18.2485 0.790432
$$534$$ 13.5593 23.4853i 0.586767 1.01631i
$$535$$ 0 0
$$536$$ −0.965775 1.67277i −0.0417151 0.0722527i
$$537$$ −20.9401 + 36.2693i −0.903631 + 1.56514i
$$538$$ 7.67281 + 13.2897i 0.330798 + 0.572960i
$$539$$ 22.2102 0.956661
$$540$$ 0 0
$$541$$ −3.39291 5.87669i −0.145873 0.252659i 0.783826 0.620981i $$-0.213266\pi$$
−0.929698 + 0.368322i $$0.879932\pi$$
$$542$$ 1.68039 + 2.91052i 0.0721790 + 0.125018i
$$543$$ −42.3069 −1.81556
$$544$$ 2.21388 0.0949193
$$545$$ 0 0
$$546$$ 29.6917 51.4276i 1.27069 2.20090i
$$547$$ −14.3705 24.8905i −0.614439 1.06424i −0.990483 0.137638i $$-0.956049\pi$$
0.376043 0.926602i $$-0.377284\pi$$
$$548$$ −10.2994 + 17.8391i −0.439969 + 0.762049i
$$549$$ −35.0611 + 60.7275i −1.49637 + 2.59179i
$$550$$ 0 0
$$551$$ 17.9615 + 5.08078i 0.765184 + 0.216449i
$$552$$ −23.3263 −0.992833
$$553$$ 8.72694 15.1155i 0.371107 0.642777i
$$554$$ −15.6259 + 27.0648i −0.663880 + 1.14987i
$$555$$ 0 0
$$556$$ 3.39427 5.87905i 0.143949 0.249327i
$$557$$ 5.48471 + 9.49979i 0.232394 + 0.402519i 0.958512 0.285051i $$-0.0920106\pi$$
−0.726118 + 0.687570i $$0.758677\pi$$
$$558$$ 25.7592 1.09047
$$559$$ 26.3774 1.11564
$$560$$ 0 0
$$561$$ 4.30869 + 7.46287i 0.181913 + 0.315083i
$$562$$ −2.93398 −0.123762
$$563$$ 1.10389 0.0465233 0.0232616 0.999729i $$-0.492595\pi$$
0.0232616 + 0.999729i $$0.492595\pi$$
$$564$$ −10.5201 18.2214i −0.442978 0.767260i
$$565$$ 0 0
$$566$$ 7.34660 + 12.7247i 0.308800 + 0.534858i
$$567$$ 27.0512 46.8541i 1.13604 1.96769i
$$568$$ 4.16010 7.20550i 0.174554 0.302336i
$$569$$ −3.17844 −0.133247 −0.0666236 0.997778i $$-0.521223\pi$$
−0.0666236 + 0.997778i $$0.521223\pi$$
$$570$$ 0 0
$$571$$ −33.3717 −1.39656 −0.698282 0.715823i $$-0.746052\pi$$
−0.698282 + 0.715823i $$0.746052\pi$$
$$572$$ 2.54349 4.40546i 0.106349 0.184202i
$$573$$ −6.49937 + 11.2572i −0.271515 + 0.470278i
$$574$$ 11.3428 + 19.6463i 0.473440 + 0.820021i
$$575$$ 0 0
$$576$$ −3.10694 5.38138i −0.129456 0.224224i
$$577$$ 6.96331 0.289886 0.144943 0.989440i $$-0.453700\pi$$
0.144943 + 0.989440i $$0.453700\pi$$
$$578$$ 12.0987 0.503241
$$579$$ −14.5795 25.2525i −0.605904 1.04946i
$$580$$ 0 0
$$581$$ 16.1989 0.672045
$$582$$ 6.50496 0.269639
$$583$$ 4.44427 + 7.69770i 0.184063 + 0.318806i
$$584$$ −3.41383 + 5.91293i −0.141265 + 0.244679i
$$585$$ 0 0
$$586$$ 4.29160 7.43327i 0.177284 0.307065i
$$587$$ −5.49500 + 9.51761i −0.226803 + 0.392834i −0.956859 0.290553i $$-0.906161\pi$$
0.730056 + 0.683387i $$0.239494\pi$$
$$588$$ 52.5744 2.16813
$$589$$ −12.9531 + 12.5986i −0.533722 + 0.519118i
$$590$$ 0 0
$$591$$ −36.0965 + 62.5210i −1.48481 + 2.57177i
$$592$$ −4.69432 + 8.13080i −0.192935 + 0.334174i
$$593$$ −19.3949 33.5929i −0.796451 1.37949i −0.921914 0.387396i $$-0.873375\pi$$
0.125462 0.992098i $$-0.459959\pi$$
$$594$$ 6.25491 10.8338i 0.256642 0.444517i
$$595$$ 0 0
$$596$$ 22.7580 0.932202
$$597$$ 45.6280 1.86743
$$598$$ −15.2425 26.4007i −0.623311 1.07961i
$$599$$ −1.47262 2.55065i −0.0601696 0.104217i 0.834372 0.551202i $$-0.185831\pi$$
−0.894541 + 0.446986i $$0.852497\pi$$
$$600$$ 0 0
$$601$$ −9.62059 −0.392432 −0.196216 0.980561i $$-0.562865\pi$$
−0.196216 + 0.980561i $$0.562865\pi$$
$$602$$ 16.3955 + 28.3978i 0.668230 + 1.15741i
$$603$$ 6.00121 10.3944i 0.244388 0.423293i
$$604$$ −5.77388 10.0007i −0.234936 0.406921i
$$605$$ 0 0
$$606$$ 16.0049 27.7212i 0.650153 1.12610i
$$607$$ 32.8499 1.33334 0.666668 0.745355i $$-0.267720\pi$$
0.666668 + 0.745355i $$0.267720\pi$$
$$608$$ 4.19432 + 1.18645i 0.170102 + 0.0481170i
$$609$$ 64.1040 2.59762
$$610$$ 0 0
$$611$$ 13.7487 23.8134i 0.556212 0.963388i
$$612$$ 6.87839 + 11.9137i 0.278043 + 0.481584i
$$613$$ −5.29101 + 9.16430i −0.213702 + 0.370143i −0.952870 0.303378i $$-0.901885\pi$$
0.739168 + 0.673521i $$0.235219\pi$$
$$614$$ 2.66757 + 4.62036i 0.107654 + 0.186463i
$$615$$ 0 0
$$616$$ 6.32387 0.254796
$$617$$ −14.0478 24.3314i −0.565542 0.979547i −0.996999 0.0774134i $$-0.975334\pi$$
0.431458 0.902133i $$-0.357999\pi$$
$$618$$ −5.52922 9.57689i −0.222418 0.385239i
$$619$$ 2.32903 0.0936115 0.0468058 0.998904i $$-0.485096\pi$$
0.0468058 + 0.998904i $$0.485096\pi$$
$$620$$ 0 0
$$621$$ −37.4840 64.9241i −1.50418 2.60532i
$$622$$ 11.6466 20.1726i 0.466988 0.808847i
$$623$$ 22.0292 + 38.1557i 0.882580 + 1.52867i
$$624$$ 6.02077 10.4283i 0.241024 0.417465i
$$625$$ 0 0
$$626$$ 10.7140 0.428217
$$627$$ 4.16359 + 16.4479i 0.166278 + 0.656867i
$$628$$ −10.8985 −0.434899
$$629$$ 10.3927 18.0006i 0.414383 0.717732i
$$630$$ 0 0
$$631$$ 6.20704 + 10.7509i 0.247098 + 0.427987i 0.962719 0.270502i $$-0.0871896\pi$$
−0.715621 + 0.698489i $$0.753856\pi$$
$$632$$ 1.76961 3.06506i 0.0703914 0.121922i
$$633$$ −29.5433 51.1706i −1.17424 2.03385i
$$634$$ 14.3253 0.568932
$$635$$ 0 0
$$636$$ 10.5201 + 18.2214i 0.417151 + 0.722526i
$$637$$ 34.3545 + 59.5037i 1.36117 + 2.35762i
$$638$$ 5.49136 0.217405
$$639$$ 51.7007 2.04525
$$640$$ 0 0
$$641$$ 11.2279 19.4473i 0.443476 0.768123i −0.554469 0.832205i $$-0.687078\pi$$
0.997945 + 0.0640815i $$0.0204118\pi$$
$$642$$ 7.70175 + 13.3398i 0.303964 + 0.526481i
$$643$$ −15.5465 + 26.9274i −0.613096 + 1.06191i 0.377619 + 0.925961i $$0.376743\pi$$
−0.990715 + 0.135952i $$0.956591\pi$$
$$644$$ 18.9486 32.8200i 0.746681 1.29329i
$$645$$ 0 0
$$646$$ −9.28573 2.62667i −0.365342 0.103345i
$$647$$ 23.8320 0.936934 0.468467 0.883481i $$-0.344806\pi$$
0.468467 + 0.883481i $$0.344806\pi$$
$$648$$ 5.48533 9.50088i 0.215484 0.373230i
$$649$$ 4.05073 7.01607i 0.159005 0.275405i
$$650$$ 0 0
$$651$$ −31.0273 + 53.7409i −1.21606 + 2.10627i
$$652$$ 5.91199 + 10.2399i 0.231531 + 0.401024i
$$653$$ 25.2762 0.989135 0.494568 0.869139i $$-0.335326\pi$$
0.494568 + 0.869139i $$0.335326\pi$$
$$654$$ −14.3974 −0.562983
$$655$$ 0 0
$$656$$ 2.30005 + 3.98380i 0.0898018 + 0.155541i
$$657$$ −42.4263 −1.65521
$$658$$ 34.1833 1.33260
$$659$$ 0.0195595 + 0.0338780i 0.000761929 + 0.00131970i 0.866406 0.499340i $$-0.166424\pi$$
−0.865644 + 0.500660i $$0.833091\pi$$
$$660$$ 0 0
$$661$$ 12.9014 + 22.3458i 0.501805 + 0.869151i 0.999998 + 0.00208512i $$0.000663715\pi$$
−0.498193 + 0.867066i $$0.666003\pi$$
$$662$$ −5.28476 + 9.15346i −0.205398 + 0.355760i
$$663$$ −13.3293 + 23.0870i −0.517666 + 0.896624i
$$664$$ 3.28476 0.127473
$$665$$ 0 0
$$666$$ −58.3399 −2.26063
$$667$$ 16.4541 28.4994i 0.637106 1.10350i
$$668$$ −8.83549 + 15.3035i −0.341855 + 0.592111i
$$669$$ 8.57761 + 14.8569i 0.331630 + 0.574399i
$$670$$ 0 0
$$671$$ −7.23539 12.5321i −0.279319 0.483795i
$$672$$ 14.9694 0.577458
$$673$$ 24.6682 0.950891 0.475445 0.879745i $$-0.342287\pi$$
0.475445 + 0.879745i $$0.342287\pi$$
$$674$$ −5.85931 10.1486i −0.225692 0.390910i
$$675$$ 0 0
$$676$$ 2.73700 0.105269
$$677$$ −47.3964 −1.82159 −0.910796 0.412858i $$-0.864531\pi$$
−0.910796 + 0.412858i $$0.864531\pi$$
$$678$$ −18.8826 32.7057i −0.725183 1.25605i
$$679$$ −5.28417 + 9.15245i −0.202788 + 0.351239i
$$680$$ 0 0
$$681$$ −12.8392 + 22.2381i −0.491998 + 0.852165i
$$682$$ −2.65790 + 4.60363i −0.101776 + 0.176282i
$$683$$ −1.61136 −0.0616569 −0.0308284 0.999525i $$-0.509815\pi$$
−0.0308284 + 0.999525i $$0.509815\pi$$
$$684$$ 6.64675 + 26.2575i 0.254145 + 1.00398i
$$685$$ 0 0
$$686$$ −25.4473 + 44.0760i −0.971582 + 1.68283i
$$687$$ −2.34170 + 4.05595i −0.0893415 + 0.154744i
$$688$$ 3.32461 + 5.75839i 0.126750 + 0.219537i
$$689$$ −13.7487 + 23.8134i −0.523783 + 0.907219i
$$690$$ 0 0
$$691$$ −30.9474 −1.17729 −0.588647 0.808391i $$-0.700339\pi$$
−0.588647 + 0.808391i $$0.700339\pi$$
$$692$$ −12.4571 −0.473548
$$693$$ 19.6479 + 34.0312i 0.746362 + 1.29274i
$$694$$ −10.4505 18.1008i −0.396695 0.687096i
$$695$$ 0 0
$$696$$ 12.9987 0.492716
$$697$$ −5.09203 8.81966i −0.192874 0.334068i
$$698$$ 17.7409 30.7281i 0.671502 1.16308i
$$699$$ 6.21145 + 10.7586i 0.234939 + 0.406926i
$$700$$ 0 0
$$701$$ −1.39904 + 2.42321i −0.0528410 + 0.0915234i −0.891236 0.453540i $$-0.850161\pi$$
0.838395 + 0.545063i $$0.183494\pi$$
$$702$$ 38.7001 1.46064
$$703$$ 29.3363 28.5336i 1.10644 1.07617i
$$704$$ 1.28233 0.0483296
$$705$$ 0 0
$$706$$ 7.14922 12.3828i 0.269064 0.466033i
$$707$$ 26.0024 + 45.0375i 0.977922 + 1.69381i
$$708$$ 9.58859 16.6079i 0.360361 0.624164i
$$709$$ −20.7910 36.0110i −0.780821 1.35242i −0.931464 0.363834i $$-0.881468\pi$$
0.150643 0.988588i $$-0.451866\pi$$
$$710$$ 0 0
$$711$$ 21.9923 0.824777
$$712$$ 4.46699 + 7.73705i 0.167407 + 0.289958i
$$713$$ 15.9281 + 27.5883i 0.596512 + 1.03319i
$$714$$ −33.1405 −1.24025
$$715$$ 0 0
$$716$$ −6.89854 11.9486i −0.257811 0.446541i
$$717$$ −38.1618 + 66.0982i −1.42518 + 2.46848i
$$718$$ 2.11073 + 3.65589i 0.0787717 + 0.136437i
$$719$$ −9.88375 + 17.1192i −0.368602 + 0.638437i −0.989347 0.145575i $$-0.953497\pi$$
0.620746 + 0.784012i $$0.286830\pi$$
$$720$$ 0 0
$$721$$ 17.9662 0.669096
$$722$$ −16.1847 9.95273i −0.602331 0.370402i
$$723$$ 83.2744 3.09701
$$724$$ 6.96883 12.0704i 0.258994 0.448592i
$$725$$ 0 0
$$726$$ −14.1992 24.5938i −0.526982 0.912760i
$$727$$ −8.38398 + 14.5215i −0.310945 + 0.538572i −0.978567 0.205928i $$-0.933979\pi$$
0.667622 + 0.744500i $$0.267312\pi$$
$$728$$ 9.78170 + 16.9424i 0.362534 + 0.627927i
$$729$$ −20.6665 −0.765426
$$730$$ 0 0
$$731$$ −7.36029 12.7484i −0.272230 0.471516i
$$732$$ −17.1271 29.6650i −0.633035 1.09645i
$$733$$ −7.20019 −0.265945 −0.132973 0.991120i $$-0.542452\pi$$
−0.132973 + 0.991120i $$0.542452\pi$$
$$734$$ 14.1648 0.522831
$$735$$ 0 0
$$736$$ 3.84233 6.65511i 0.141630 0.245311i
$$737$$ 1.23844 + 2.14505i 0.0456186 + 0.0790138i
$$738$$ −14.2922 + 24.7549i −0.526104 + 0.911239i
$$739$$ 1.26645 2.19356i 0.0465872 0.0806914i −0.841792 0.539803i $$-0.818499\pi$$
0.888379 + 0.459111i $$0.151832\pi$$
$$740$$ 0 0
$$741$$ −37.6257 + 36.5962i −1.38222 + 1.34440i
$$742$$ −34.1833 −1.25491
$$743$$ −10.1601 + 17.5978i −0.372738 + 0.645601i −0.989986 0.141168i $$-0.954914\pi$$
0.617248 + 0.786769i $$0.288248\pi$$
$$744$$ −6.29160 + 10.8974i −0.230661 + 0.399517i
$$745$$ 0 0
$$746$$ −8.32704 + 14.4228i −0.304874 + 0.528058i
$$747$$ 10.2055 + 17.6765i 0.373401 + 0.646750i
$$748$$ −2.83892 −0.103801
$$749$$ −25.0254 −0.914409
$$750$$ 0 0
$$751$$ −8.67855 15.0317i −0.316685 0.548514i 0.663109 0.748523i $$-0.269236\pi$$
−0.979794 + 0.200008i $$0.935903\pi$$
$$752$$ 6.93155 0.252768
$$753$$ 13.9790 0.509421
$$754$$ 8.49398 + 14.7120i 0.309332 + 0.535779i
$$755$$ 0 0
$$756$$ 24.0550 + 41.6644i 0.874870 + 1.51532i
$$757$$ 21.5624 37.3472i 0.783700 1.35741i −0.146073 0.989274i $$-0.546663\pi$$
0.929773 0.368134i $$-0.120003\pi$$
$$758$$ 1.68345 2.91581i 0.0611455 0.105907i
$$759$$ 29.9120 1.08574
$$760$$ 0 0
$$761$$ 13.1711 0.477451 0.238726 0.971087i $$-0.423270\pi$$
0.238726 + 0.971087i $$0.423270\pi$$
$$762$$ 5.91320 10.2420i 0.214213 0.371027i
$$763$$ 11.6954 20.2571i 0.423403 0.733355i
$$764$$ −2.14116 3.70861i −0.0774646 0.134173i
$$765$$ 0 0
$$766$$ −4.16010 7.20550i −0.150310 0.260345i
$$767$$ 25.0625 0.904955
$$768$$ 3.03544 0.109532
$$769$$ −11.3839 19.7174i −0.410513 0.711029i 0.584433 0.811442i $$-0.301317\pi$$
−0.994946 + 0.100413i $$0.967984\pi$$
$$770$$ 0 0
$$771$$ 59.8738 2.15630
$$772$$ 9.60620 0.345735
$$773$$ −5.64054 9.76970i −0.202876 0.351392i 0.746578 0.665298i $$-0.231696\pi$$
−0.949454 + 0.313906i $$0.898362\pi$$
$$774$$ −20.6587 + 35.7820i −0.742563 + 1.28616i
$$775$$ 0 0
$$776$$ −1.07150 + 1.85590i −0.0384647 + 0.0666228i
$$777$$ 70.2712 121.713i 2.52097 4.36644i
$$778$$ −24.8151 −0.889666
$$779$$ −4.92055 19.4382i −0.176297 0.696447i
$$780$$ 0 0
$$781$$ −5.33462 + 9.23983i −0.190888 + 0.330627i
$$782$$ −8.50646 + 14.7336i −0.304190 + 0.526873i
$$783$$ 20.8882 + 36.1794i 0.746484 + 1.29295i
$$784$$ −8.66010 + 14.9997i −0.309289 + 0.535705i
$$785$$ 0 0