# Properties

 Label 950.2.e.j.201.1 Level $950$ Weight $2$ Character 950.201 Analytic conductor $7.586$ Analytic rank $0$ Dimension $4$ 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: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-7})$$ Defining polynomial: $$x^{4} - x^{3} - x^{2} - 2 x + 4$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 201.1 Root $$1.39564 - 0.228425i$$ of defining polynomial Character $$\chi$$ $$=$$ 950.201 Dual form 950.2.e.j.501.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.39564 + 2.41733i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.39564 + 2.41733i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-2.39564 - 4.14938i) q^{9} -3.79129 q^{11} +2.79129 q^{12} +(-0.104356 - 0.180750i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.395644 + 0.685275i) q^{17} -4.79129 q^{18} +(-3.50000 - 2.59808i) q^{19} +(-1.39564 + 2.41733i) q^{21} +(-1.89564 + 3.28335i) q^{22} +(2.29129 + 3.96863i) q^{23} +(1.39564 - 2.41733i) q^{24} -0.208712 q^{26} +5.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-3.39564 - 5.88143i) q^{29} -4.79129 q^{31} +(0.500000 + 0.866025i) q^{32} +(5.29129 - 9.16478i) q^{33} +(0.395644 + 0.685275i) q^{34} +(-2.39564 + 4.14938i) q^{36} -3.58258 q^{37} +(-4.00000 + 1.73205i) q^{38} +0.582576 q^{39} +(5.68693 - 9.85005i) q^{41} +(1.39564 + 2.41733i) q^{42} +(2.89564 - 5.01540i) q^{43} +(1.89564 + 3.28335i) q^{44} +4.58258 q^{46} +(-6.08258 - 10.5353i) q^{47} +(-1.39564 - 2.41733i) q^{48} -6.00000 q^{49} +(-1.10436 - 1.91280i) q^{51} +(-0.104356 + 0.180750i) q^{52} +(-2.29129 - 3.96863i) q^{53} +(2.50000 - 4.33013i) q^{54} -1.00000 q^{56} +(11.1652 - 4.83465i) q^{57} -6.79129 q^{58} +(-2.29129 + 3.96863i) q^{59} +(-0.686932 - 1.18980i) q^{61} +(-2.39564 + 4.14938i) q^{62} +(-2.39564 - 4.14938i) q^{63} +1.00000 q^{64} +(-5.29129 - 9.16478i) q^{66} +(7.79129 + 13.4949i) q^{67} +0.791288 q^{68} -12.7913 q^{69} +(2.29129 - 3.96863i) q^{71} +(2.39564 + 4.14938i) q^{72} +(1.39564 - 2.41733i) q^{73} +(-1.79129 + 3.10260i) q^{74} +(-0.500000 + 4.33013i) q^{76} -3.79129 q^{77} +(0.291288 - 0.504525i) q^{78} +(-7.47822 + 12.9527i) q^{79} +(0.208712 - 0.361500i) q^{81} +(-5.68693 - 9.85005i) q^{82} -3.79129 q^{83} +2.79129 q^{84} +(-2.89564 - 5.01540i) q^{86} +18.9564 q^{87} +3.79129 q^{88} +(-2.29129 - 3.96863i) q^{89} +(-0.104356 - 0.180750i) q^{91} +(2.29129 - 3.96863i) q^{92} +(6.68693 - 11.5821i) q^{93} -12.1652 q^{94} -2.79129 q^{96} +(-6.18693 + 10.7161i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(9.08258 + 15.7315i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} - q^{3} - 2q^{4} + q^{6} + 4q^{7} - 4q^{8} - 5q^{9} + O(q^{10})$$ $$4q + 2q^{2} - q^{3} - 2q^{4} + q^{6} + 4q^{7} - 4q^{8} - 5q^{9} - 6q^{11} + 2q^{12} - 5q^{13} + 2q^{14} - 2q^{16} + 3q^{17} - 10q^{18} - 14q^{19} - q^{21} - 3q^{22} + q^{24} - 10q^{26} + 20q^{27} - 2q^{28} - 9q^{29} - 10q^{31} + 2q^{32} + 12q^{33} - 3q^{34} - 5q^{36} + 4q^{37} - 16q^{38} - 16q^{39} + 9q^{41} + q^{42} + 7q^{43} + 3q^{44} - 6q^{47} - q^{48} - 24q^{49} - 9q^{51} - 5q^{52} + 10q^{54} - 4q^{56} + 8q^{57} - 18q^{58} + 11q^{61} - 5q^{62} - 5q^{63} + 4q^{64} - 12q^{66} + 22q^{67} - 6q^{68} - 42q^{69} + 5q^{72} + q^{73} + 2q^{74} - 2q^{76} - 6q^{77} - 8q^{78} - 7q^{79} + 10q^{81} - 9q^{82} - 6q^{83} + 2q^{84} - 7q^{86} + 30q^{87} + 6q^{88} - 5q^{91} + 13q^{93} - 12q^{94} - 2q^{96} - 11q^{97} - 12q^{98} + 18q^{99} + O(q^{100})$$

## 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
$$3$$ −1.39564 + 2.41733i −0.805775 + 1.39564i 0.109991 + 0.993933i $$0.464918\pi$$
−0.915766 + 0.401711i $$0.868416\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0
$$6$$ 1.39564 + 2.41733i 0.569769 + 0.986869i
$$7$$ 1.00000 0.377964 0.188982 0.981981i $$-0.439481\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −2.39564 4.14938i −0.798548 1.38313i
$$10$$ 0 0
$$11$$ −3.79129 −1.14312 −0.571558 0.820562i $$-0.693661\pi$$
−0.571558 + 0.820562i $$0.693661\pi$$
$$12$$ 2.79129 0.805775
$$13$$ −0.104356 0.180750i −0.0289432 0.0501310i 0.851191 0.524856i $$-0.175881\pi$$
−0.880134 + 0.474725i $$0.842548\pi$$
$$14$$ 0.500000 0.866025i 0.133631 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −0.395644 + 0.685275i −0.0959577 + 0.166204i −0.910008 0.414591i $$-0.863925\pi$$
0.814050 + 0.580795i $$0.197258\pi$$
$$18$$ −4.79129 −1.12932
$$19$$ −3.50000 2.59808i −0.802955 0.596040i
$$20$$ 0 0
$$21$$ −1.39564 + 2.41733i −0.304554 + 0.527504i
$$22$$ −1.89564 + 3.28335i −0.404153 + 0.700013i
$$23$$ 2.29129 + 3.96863i 0.477767 + 0.827516i 0.999675 0.0254855i $$-0.00811315\pi$$
−0.521909 + 0.853001i $$0.674780\pi$$
$$24$$ 1.39564 2.41733i 0.284885 0.493435i
$$25$$ 0 0
$$26$$ −0.208712 −0.0409318
$$27$$ 5.00000 0.962250
$$28$$ −0.500000 0.866025i −0.0944911 0.163663i
$$29$$ −3.39564 5.88143i −0.630555 1.09215i −0.987438 0.158005i $$-0.949494\pi$$
0.356883 0.934149i $$-0.383839\pi$$
$$30$$ 0 0
$$31$$ −4.79129 −0.860541 −0.430270 0.902700i $$-0.641582\pi$$
−0.430270 + 0.902700i $$0.641582\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 5.29129 9.16478i 0.921095 1.59538i
$$34$$ 0.395644 + 0.685275i 0.0678524 + 0.117524i
$$35$$ 0 0
$$36$$ −2.39564 + 4.14938i −0.399274 + 0.691563i
$$37$$ −3.58258 −0.588972 −0.294486 0.955656i $$-0.595148\pi$$
−0.294486 + 0.955656i $$0.595148\pi$$
$$38$$ −4.00000 + 1.73205i −0.648886 + 0.280976i
$$39$$ 0.582576 0.0932868
$$40$$ 0 0
$$41$$ 5.68693 9.85005i 0.888150 1.53832i 0.0460888 0.998937i $$-0.485324\pi$$
0.842061 0.539383i $$-0.181342\pi$$
$$42$$ 1.39564 + 2.41733i 0.215353 + 0.373002i
$$43$$ 2.89564 5.01540i 0.441582 0.764842i −0.556225 0.831031i $$-0.687751\pi$$
0.997807 + 0.0661897i $$0.0210843\pi$$
$$44$$ 1.89564 + 3.28335i 0.285779 + 0.494984i
$$45$$ 0 0
$$46$$ 4.58258 0.675664
$$47$$ −6.08258 10.5353i −0.887235 1.53674i −0.843131 0.537709i $$-0.819290\pi$$
−0.0441043 0.999027i $$-0.514043\pi$$
$$48$$ −1.39564 2.41733i −0.201444 0.348911i
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ −1.10436 1.91280i −0.154641 0.267846i
$$52$$ −0.104356 + 0.180750i −0.0144716 + 0.0250655i
$$53$$ −2.29129 3.96863i −0.314733 0.545133i 0.664648 0.747157i $$-0.268582\pi$$
−0.979381 + 0.202024i $$0.935248\pi$$
$$54$$ 2.50000 4.33013i 0.340207 0.589256i
$$55$$ 0 0
$$56$$ −1.00000 −0.133631
$$57$$ 11.1652 4.83465i 1.47886 0.640365i
$$58$$ −6.79129 −0.891740
$$59$$ −2.29129 + 3.96863i −0.298300 + 0.516671i −0.975747 0.218900i $$-0.929753\pi$$
0.677447 + 0.735572i $$0.263086\pi$$
$$60$$ 0 0
$$61$$ −0.686932 1.18980i −0.0879526 0.152338i 0.818693 0.574232i $$-0.194699\pi$$
−0.906646 + 0.421893i $$0.861366\pi$$
$$62$$ −2.39564 + 4.14938i −0.304247 + 0.526971i
$$63$$ −2.39564 4.14938i −0.301823 0.522772i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −5.29129 9.16478i −0.651313 1.12811i
$$67$$ 7.79129 + 13.4949i 0.951857 + 1.64867i 0.741401 + 0.671062i $$0.234162\pi$$
0.210456 + 0.977603i $$0.432505\pi$$
$$68$$ 0.791288 0.0959577
$$69$$ −12.7913 −1.53989
$$70$$ 0 0
$$71$$ 2.29129 3.96863i 0.271926 0.470989i −0.697429 0.716654i $$-0.745673\pi$$
0.969355 + 0.245664i $$0.0790061\pi$$
$$72$$ 2.39564 + 4.14938i 0.282329 + 0.489009i
$$73$$ 1.39564 2.41733i 0.163348 0.282927i −0.772720 0.634748i $$-0.781104\pi$$
0.936067 + 0.351821i $$0.114437\pi$$
$$74$$ −1.79129 + 3.10260i −0.208233 + 0.360670i
$$75$$ 0 0
$$76$$ −0.500000 + 4.33013i −0.0573539 + 0.496700i
$$77$$ −3.79129 −0.432057
$$78$$ 0.291288 0.504525i 0.0329819 0.0571262i
$$79$$ −7.47822 + 12.9527i −0.841365 + 1.45729i 0.0473751 + 0.998877i $$0.484914\pi$$
−0.888741 + 0.458411i $$0.848419\pi$$
$$80$$ 0 0
$$81$$ 0.208712 0.361500i 0.0231902 0.0401667i
$$82$$ −5.68693 9.85005i −0.628017 1.08776i
$$83$$ −3.79129 −0.416148 −0.208074 0.978113i $$-0.566719\pi$$
−0.208074 + 0.978113i $$0.566719\pi$$
$$84$$ 2.79129 0.304554
$$85$$ 0 0
$$86$$ −2.89564 5.01540i −0.312245 0.540825i
$$87$$ 18.9564 2.03234
$$88$$ 3.79129 0.404153
$$89$$ −2.29129 3.96863i −0.242876 0.420674i 0.718656 0.695365i $$-0.244757\pi$$
−0.961532 + 0.274692i $$0.911424\pi$$
$$90$$ 0 0
$$91$$ −0.104356 0.180750i −0.0109395 0.0189478i
$$92$$ 2.29129 3.96863i 0.238883 0.413758i
$$93$$ 6.68693 11.5821i 0.693403 1.20101i
$$94$$ −12.1652 −1.25474
$$95$$ 0 0
$$96$$ −2.79129 −0.284885
$$97$$ −6.18693 + 10.7161i −0.628188 + 1.08805i 0.359727 + 0.933057i $$0.382870\pi$$
−0.987915 + 0.154996i $$0.950464\pi$$
$$98$$ −3.00000 + 5.19615i −0.303046 + 0.524891i
$$99$$ 9.08258 + 15.7315i 0.912833 + 1.58107i
$$100$$ 0 0
$$101$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$102$$ −2.20871 −0.218695
$$103$$ −5.16515 −0.508937 −0.254469 0.967081i $$-0.581901\pi$$
−0.254469 + 0.967081i $$0.581901\pi$$
$$104$$ 0.104356 + 0.180750i 0.0102330 + 0.0177240i
$$105$$ 0 0
$$106$$ −4.58258 −0.445099
$$107$$ −18.9564 −1.83259 −0.916294 0.400506i $$-0.868834\pi$$
−0.916294 + 0.400506i $$0.868834\pi$$
$$108$$ −2.50000 4.33013i −0.240563 0.416667i
$$109$$ 5.87386 10.1738i 0.562614 0.974476i −0.434653 0.900598i $$-0.643129\pi$$
0.997267 0.0738783i $$-0.0235376\pi$$
$$110$$ 0 0
$$111$$ 5.00000 8.66025i 0.474579 0.821995i
$$112$$ −0.500000 + 0.866025i −0.0472456 + 0.0818317i
$$113$$ −5.37386 −0.505531 −0.252765 0.967528i $$-0.581340\pi$$
−0.252765 + 0.967528i $$0.581340\pi$$
$$114$$ 1.39564 12.0866i 0.130714 1.13202i
$$115$$ 0 0
$$116$$ −3.39564 + 5.88143i −0.315278 + 0.546077i
$$117$$ −0.500000 + 0.866025i −0.0462250 + 0.0800641i
$$118$$ 2.29129 + 3.96863i 0.210930 + 0.365342i
$$119$$ −0.395644 + 0.685275i −0.0362686 + 0.0628191i
$$120$$ 0 0
$$121$$ 3.37386 0.306715
$$122$$ −1.37386 −0.124384
$$123$$ 15.8739 + 27.4943i 1.43130 + 2.47908i
$$124$$ 2.39564 + 4.14938i 0.215135 + 0.372625i
$$125$$ 0 0
$$126$$ −4.79129 −0.426842
$$127$$ 1.31307 + 2.27430i 0.116516 + 0.201812i 0.918385 0.395689i $$-0.129494\pi$$
−0.801869 + 0.597500i $$0.796161\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 8.08258 + 13.9994i 0.711631 + 1.23258i
$$130$$ 0 0
$$131$$ −5.76951 + 9.99308i −0.504084 + 0.873099i 0.495905 + 0.868377i $$0.334837\pi$$
−0.999989 + 0.00472247i $$0.998497\pi$$
$$132$$ −10.5826 −0.921095
$$133$$ −3.50000 2.59808i −0.303488 0.225282i
$$134$$ 15.5826 1.34613
$$135$$ 0 0
$$136$$ 0.395644 0.685275i 0.0339262 0.0587619i
$$137$$ 7.66515 + 13.2764i 0.654878 + 1.13428i 0.981924 + 0.189274i $$0.0606134\pi$$
−0.327046 + 0.945008i $$0.606053\pi$$
$$138$$ −6.39564 + 11.0776i −0.544433 + 0.942986i
$$139$$ 6.10436 + 10.5731i 0.517765 + 0.896795i 0.999787 + 0.0206359i $$0.00656907\pi$$
−0.482022 + 0.876159i $$0.660098\pi$$
$$140$$ 0 0
$$141$$ 33.9564 2.85965
$$142$$ −2.29129 3.96863i −0.192281 0.333040i
$$143$$ 0.395644 + 0.685275i 0.0330854 + 0.0573056i
$$144$$ 4.79129 0.399274
$$145$$ 0 0
$$146$$ −1.39564 2.41733i −0.115504 0.200059i
$$147$$ 8.37386 14.5040i 0.690665 1.19627i
$$148$$ 1.79129 + 3.10260i 0.147243 + 0.255032i
$$149$$ 11.3739 19.7001i 0.931783 1.61390i 0.151511 0.988456i $$-0.451586\pi$$
0.780272 0.625440i $$-0.215081\pi$$
$$150$$ 0 0
$$151$$ 15.7477 1.28153 0.640766 0.767736i $$-0.278617\pi$$
0.640766 + 0.767736i $$0.278617\pi$$
$$152$$ 3.50000 + 2.59808i 0.283887 + 0.210732i
$$153$$ 3.79129 0.306507
$$154$$ −1.89564 + 3.28335i −0.152755 + 0.264580i
$$155$$ 0 0
$$156$$ −0.291288 0.504525i −0.0233217 0.0403944i
$$157$$ −3.97822 + 6.89048i −0.317496 + 0.549920i −0.979965 0.199170i $$-0.936176\pi$$
0.662469 + 0.749090i $$0.269509\pi$$
$$158$$ 7.47822 + 12.9527i 0.594935 + 1.03046i
$$159$$ 12.7913 1.01442
$$160$$ 0 0
$$161$$ 2.29129 + 3.96863i 0.180579 + 0.312772i
$$162$$ −0.208712 0.361500i −0.0163980 0.0284021i
$$163$$ 14.5826 1.14220 0.571098 0.820882i $$-0.306518\pi$$
0.571098 + 0.820882i $$0.306518\pi$$
$$164$$ −11.3739 −0.888150
$$165$$ 0 0
$$166$$ −1.89564 + 3.28335i −0.147131 + 0.254838i
$$167$$ 5.76951 + 9.99308i 0.446458 + 0.773288i 0.998152 0.0607584i $$-0.0193519\pi$$
−0.551695 + 0.834046i $$0.686019\pi$$
$$168$$ 1.39564 2.41733i 0.107676 0.186501i
$$169$$ 6.47822 11.2206i 0.498325 0.863124i
$$170$$ 0 0
$$171$$ −2.39564 + 20.7469i −0.183199 + 1.58655i
$$172$$ −5.79129 −0.441582
$$173$$ −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i $$0.460934\pi$$
−0.920722 + 0.390218i $$0.872399\pi$$
$$174$$ 9.47822 16.4168i 0.718542 1.24455i
$$175$$ 0 0
$$176$$ 1.89564 3.28335i 0.142890 0.247492i
$$177$$ −6.39564 11.0776i −0.480726 0.832642i
$$178$$ −4.58258 −0.343479
$$179$$ −16.7477 −1.25178 −0.625892 0.779910i $$-0.715265\pi$$
−0.625892 + 0.779910i $$0.715265\pi$$
$$180$$ 0 0
$$181$$ 3.81307 + 6.60443i 0.283423 + 0.490903i 0.972226 0.234046i $$-0.0751966\pi$$
−0.688802 + 0.724949i $$0.741863\pi$$
$$182$$ −0.208712 −0.0154708
$$183$$ 3.83485 0.283480
$$184$$ −2.29129 3.96863i −0.168916 0.292571i
$$185$$ 0 0
$$186$$ −6.68693 11.5821i −0.490310 0.849241i
$$187$$ 1.50000 2.59808i 0.109691 0.189990i
$$188$$ −6.08258 + 10.5353i −0.443617 + 0.768368i
$$189$$ 5.00000 0.363696
$$190$$ 0 0
$$191$$ 15.9564 1.15457 0.577284 0.816544i $$-0.304113\pi$$
0.577284 + 0.816544i $$0.304113\pi$$
$$192$$ −1.39564 + 2.41733i −0.100722 + 0.174455i
$$193$$ −1.37386 + 2.37960i −0.0988929 + 0.171287i −0.911227 0.411905i $$-0.864863\pi$$
0.812334 + 0.583193i $$0.198197\pi$$
$$194$$ 6.18693 + 10.7161i 0.444196 + 0.769370i
$$195$$ 0 0
$$196$$ 3.00000 + 5.19615i 0.214286 + 0.371154i
$$197$$ −20.2087 −1.43981 −0.719906 0.694072i $$-0.755815\pi$$
−0.719906 + 0.694072i $$0.755815\pi$$
$$198$$ 18.1652 1.29094
$$199$$ −1.79129 3.10260i −0.126981 0.219938i 0.795525 0.605921i $$-0.207195\pi$$
−0.922506 + 0.385984i $$0.873862\pi$$
$$200$$ 0 0
$$201$$ −43.4955 −3.06793
$$202$$ 0 0
$$203$$ −3.39564 5.88143i −0.238327 0.412795i
$$204$$ −1.10436 + 1.91280i −0.0773204 + 0.133923i
$$205$$ 0 0
$$206$$ −2.58258 + 4.47315i −0.179937 + 0.311659i
$$207$$ 10.9782 19.0148i 0.763039 1.32162i
$$208$$ 0.208712 0.0144716
$$209$$ 13.2695 + 9.85005i 0.917871 + 0.681343i
$$210$$ 0 0
$$211$$ −11.9782 + 20.7469i −0.824615 + 1.42827i 0.0775988 + 0.996985i $$0.475275\pi$$
−0.902213 + 0.431290i $$0.858059\pi$$
$$212$$ −2.29129 + 3.96863i −0.157366 + 0.272566i
$$213$$ 6.39564 + 11.0776i 0.438222 + 0.759023i
$$214$$ −9.47822 + 16.4168i −0.647918 + 1.12223i
$$215$$ 0 0
$$216$$ −5.00000 −0.340207
$$217$$ −4.79129 −0.325254
$$218$$ −5.87386 10.1738i −0.397828 0.689059i
$$219$$ 3.89564 + 6.74745i 0.263243 + 0.455951i
$$220$$ 0 0
$$221$$ 0.165151 0.0111093
$$222$$ −5.00000 8.66025i −0.335578 0.581238i
$$223$$ 9.60436 16.6352i 0.643155 1.11398i −0.341569 0.939857i $$-0.610958\pi$$
0.984724 0.174121i $$-0.0557084\pi$$
$$224$$ 0.500000 + 0.866025i 0.0334077 + 0.0578638i
$$225$$ 0 0
$$226$$ −2.68693 + 4.65390i −0.178732 + 0.309573i
$$227$$ −7.74773 −0.514235 −0.257117 0.966380i $$-0.582773\pi$$
−0.257117 + 0.966380i $$0.582773\pi$$
$$228$$ −9.76951 7.25198i −0.647001 0.480274i
$$229$$ −25.3303 −1.67387 −0.836937 0.547300i $$-0.815656\pi$$
−0.836937 + 0.547300i $$0.815656\pi$$
$$230$$ 0 0
$$231$$ 5.29129 9.16478i 0.348141 0.602998i
$$232$$ 3.39564 + 5.88143i 0.222935 + 0.386135i
$$233$$ 4.58258 7.93725i 0.300215 0.519987i −0.675970 0.736929i $$-0.736275\pi$$
0.976184 + 0.216942i $$0.0696084\pi$$
$$234$$ 0.500000 + 0.866025i 0.0326860 + 0.0566139i
$$235$$ 0 0
$$236$$ 4.58258 0.298300
$$237$$ −20.8739 36.1546i −1.35590 2.34849i
$$238$$ 0.395644 + 0.685275i 0.0256458 + 0.0444198i
$$239$$ 16.5826 1.07264 0.536319 0.844015i $$-0.319814\pi$$
0.536319 + 0.844015i $$0.319814\pi$$
$$240$$ 0 0
$$241$$ 8.39564 + 14.5417i 0.540811 + 0.936712i 0.998858 + 0.0477840i $$0.0152159\pi$$
−0.458047 + 0.888928i $$0.651451\pi$$
$$242$$ 1.68693 2.92185i 0.108440 0.187824i
$$243$$ 8.08258 + 13.9994i 0.518497 + 0.898064i
$$244$$ −0.686932 + 1.18980i −0.0439763 + 0.0761692i
$$245$$ 0 0
$$246$$ 31.7477 2.02416
$$247$$ −0.104356 + 0.903750i −0.00664002 + 0.0575042i
$$248$$ 4.79129 0.304247
$$249$$ 5.29129 9.16478i 0.335322 0.580794i
$$250$$ 0 0
$$251$$ −6.56080 11.3636i −0.414114 0.717266i 0.581221 0.813746i $$-0.302575\pi$$
−0.995335 + 0.0964796i $$0.969242\pi$$
$$252$$ −2.39564 + 4.14938i −0.150911 + 0.261386i
$$253$$ −8.68693 15.0462i −0.546143 0.945947i
$$254$$ 2.62614 0.164778
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −5.60436 9.70703i −0.349590 0.605508i 0.636587 0.771205i $$-0.280346\pi$$
−0.986177 + 0.165697i $$0.947012\pi$$
$$258$$ 16.1652 1.00640
$$259$$ −3.58258 −0.222610
$$260$$ 0 0
$$261$$ −16.2695 + 28.1796i −1.00706 + 1.74427i
$$262$$ 5.76951 + 9.99308i 0.356441 + 0.617375i
$$263$$ −9.70871 + 16.8160i −0.598665 + 1.03692i 0.394354 + 0.918959i $$0.370969\pi$$
−0.993018 + 0.117959i $$0.962365\pi$$
$$264$$ −5.29129 + 9.16478i −0.325656 + 0.564053i
$$265$$ 0 0
$$266$$ −4.00000 + 1.73205i −0.245256 + 0.106199i
$$267$$ 12.7913 0.782814
$$268$$ 7.79129 13.4949i 0.475929 0.824333i
$$269$$ −6.56080 + 11.3636i −0.400019 + 0.692853i −0.993728 0.111827i $$-0.964330\pi$$
0.593709 + 0.804680i $$0.297663\pi$$
$$270$$ 0 0
$$271$$ 8.56080 14.8277i 0.520031 0.900721i −0.479698 0.877434i $$-0.659254\pi$$
0.999729 0.0232867i $$-0.00741305\pi$$
$$272$$ −0.395644 0.685275i −0.0239894 0.0415509i
$$273$$ 0.582576 0.0352591
$$274$$ 15.3303 0.926137
$$275$$ 0 0
$$276$$ 6.39564 + 11.0776i 0.384973 + 0.666792i
$$277$$ 8.74773 0.525600 0.262800 0.964850i $$-0.415354\pi$$
0.262800 + 0.964850i $$0.415354\pi$$
$$278$$ 12.2087 0.732230
$$279$$ 11.4782 + 19.8809i 0.687183 + 1.19024i
$$280$$ 0 0
$$281$$ −5.29129 9.16478i −0.315652 0.546725i 0.663924 0.747800i $$-0.268890\pi$$
−0.979576 + 0.201075i $$0.935556\pi$$
$$282$$ 16.9782 29.4071i 1.01104 1.75117i
$$283$$ 10.5608 18.2918i 0.627774 1.08734i −0.360223 0.932866i $$-0.617299\pi$$
0.987997 0.154471i $$-0.0493672\pi$$
$$284$$ −4.58258 −0.271926
$$285$$ 0 0
$$286$$ 0.791288 0.0467898
$$287$$ 5.68693 9.85005i 0.335689 0.581430i
$$288$$ 2.39564 4.14938i 0.141165 0.244504i
$$289$$ 8.18693 + 14.1802i 0.481584 + 0.834128i
$$290$$ 0 0
$$291$$ −17.2695 29.9117i −1.01236 1.75345i
$$292$$ −2.79129 −0.163348
$$293$$ −24.9564 −1.45797 −0.728985 0.684529i $$-0.760008\pi$$
−0.728985 + 0.684529i $$0.760008\pi$$
$$294$$ −8.37386 14.5040i −0.488374 0.845888i
$$295$$ 0 0
$$296$$ 3.58258 0.208233
$$297$$ −18.9564 −1.09996
$$298$$ −11.3739 19.7001i −0.658870 1.14120i
$$299$$ 0.478220 0.828301i 0.0276562 0.0479019i
$$300$$ 0 0
$$301$$ 2.89564 5.01540i 0.166902 0.289083i
$$302$$ 7.87386 13.6379i 0.453090 0.784775i
$$303$$ 0 0
$$304$$ 4.00000 1.73205i 0.229416 0.0993399i
$$305$$ 0 0
$$306$$ 1.89564 3.28335i 0.108367 0.187697i
$$307$$ −17.2477 + 29.8739i −0.984380 + 1.70500i −0.339719 + 0.940527i $$0.610332\pi$$
−0.644661 + 0.764469i $$0.723001\pi$$
$$308$$ 1.89564 + 3.28335i 0.108014 + 0.187086i
$$309$$ 7.20871 12.4859i 0.410089 0.710296i
$$310$$ 0 0
$$311$$ −15.0000 −0.850572 −0.425286 0.905059i $$-0.639826\pi$$
−0.425286 + 0.905059i $$0.639826\pi$$
$$312$$ −0.582576 −0.0329819
$$313$$ −5.87386 10.1738i −0.332010 0.575059i 0.650896 0.759167i $$-0.274394\pi$$
−0.982906 + 0.184108i $$0.941060\pi$$
$$314$$ 3.97822 + 6.89048i 0.224504 + 0.388852i
$$315$$ 0 0
$$316$$ 14.9564 0.841365
$$317$$ −4.58258 7.93725i −0.257383 0.445801i 0.708157 0.706055i $$-0.249527\pi$$
−0.965540 + 0.260254i $$0.916194\pi$$
$$318$$ 6.39564 11.0776i 0.358650 0.621200i
$$319$$ 12.8739 + 22.2982i 0.720798 + 1.24846i
$$320$$ 0 0
$$321$$ 26.4564 45.8239i 1.47665 2.55764i
$$322$$ 4.58258 0.255377
$$323$$ 3.16515 1.37055i 0.176114 0.0762595i
$$324$$ −0.417424 −0.0231902
$$325$$ 0 0
$$326$$ 7.29129 12.6289i 0.403827 0.699449i
$$327$$ 16.3956 + 28.3981i 0.906681 + 1.57042i
$$328$$ −5.68693 + 9.85005i −0.314008 + 0.543878i
$$329$$ −6.08258 10.5353i −0.335343 0.580832i
$$330$$ 0 0
$$331$$ −17.9129 −0.984581 −0.492290 0.870431i $$-0.663840\pi$$
−0.492290 + 0.870431i $$0.663840\pi$$
$$332$$ 1.89564 + 3.28335i 0.104037 + 0.180197i
$$333$$ 8.58258 + 14.8655i 0.470322 + 0.814622i
$$334$$ 11.5390 0.631387
$$335$$ 0 0
$$336$$ −1.39564 2.41733i −0.0761386 0.131876i
$$337$$ 11.6652 20.2046i 0.635441 1.10062i −0.350980 0.936383i $$-0.614152\pi$$
0.986421 0.164234i $$-0.0525151\pi$$
$$338$$ −6.47822 11.2206i −0.352369 0.610320i
$$339$$ 7.50000 12.9904i 0.407344 0.705541i
$$340$$ 0 0
$$341$$ 18.1652 0.983698
$$342$$ 16.7695 + 12.4481i 0.906791 + 0.673118i
$$343$$ −13.0000 −0.701934
$$344$$ −2.89564 + 5.01540i −0.156123 + 0.270412i
$$345$$ 0 0
$$346$$ 10.5000 + 18.1865i 0.564483 + 0.977714i
$$347$$ 1.81307 3.14033i 0.0973306 0.168582i −0.813248 0.581917i $$-0.802303\pi$$
0.910579 + 0.413335i $$0.135636\pi$$
$$348$$ −9.47822 16.4168i −0.508086 0.880031i
$$349$$ −5.41742 −0.289988 −0.144994 0.989433i $$-0.546316\pi$$
−0.144994 + 0.989433i $$0.546316\pi$$
$$350$$ 0 0
$$351$$ −0.521780 0.903750i −0.0278506 0.0482386i
$$352$$ −1.89564 3.28335i −0.101038 0.175003i
$$353$$ 13.7477 0.731718 0.365859 0.930670i $$-0.380775\pi$$
0.365859 + 0.930670i $$0.380775\pi$$
$$354$$ −12.7913 −0.679849
$$355$$ 0 0
$$356$$ −2.29129 + 3.96863i −0.121438 + 0.210337i
$$357$$ −1.10436 1.91280i −0.0584487 0.101236i
$$358$$ −8.37386 + 14.5040i −0.442572 + 0.766558i
$$359$$ 17.8521 30.9207i 0.942197 1.63193i 0.180928 0.983496i $$-0.442090\pi$$
0.761269 0.648437i $$-0.224577\pi$$
$$360$$ 0 0
$$361$$ 5.50000 + 18.1865i 0.289474 + 0.957186i
$$362$$ 7.62614 0.400821
$$363$$ −4.70871 + 8.15573i −0.247143 + 0.428065i
$$364$$ −0.104356 + 0.180750i −0.00546974 + 0.00947388i
$$365$$ 0 0
$$366$$ 1.91742 3.32108i 0.100225 0.173595i
$$367$$ 4.39564 + 7.61348i 0.229451 + 0.397420i 0.957645 0.287950i $$-0.0929737\pi$$
−0.728195 + 0.685370i $$0.759640\pi$$
$$368$$ −4.58258 −0.238883
$$369$$ −54.4955 −2.83692
$$370$$ 0 0
$$371$$ −2.29129 3.96863i −0.118958 0.206041i
$$372$$ −13.3739 −0.693403
$$373$$ 21.3739 1.10670 0.553348 0.832950i $$-0.313350\pi$$
0.553348 + 0.832950i $$0.313350\pi$$
$$374$$ −1.50000 2.59808i −0.0775632 0.134343i
$$375$$ 0 0
$$376$$ 6.08258 + 10.5353i 0.313685 + 0.543318i
$$377$$ −0.708712 + 1.22753i −0.0365005 + 0.0632208i
$$378$$ 2.50000 4.33013i 0.128586 0.222718i
$$379$$ 4.83485 0.248349 0.124175 0.992260i $$-0.460372\pi$$
0.124175 + 0.992260i $$0.460372\pi$$
$$380$$ 0 0
$$381$$ −7.33030 −0.375543
$$382$$ 7.97822 13.8187i 0.408201 0.707025i
$$383$$ 2.29129 3.96863i 0.117079 0.202787i −0.801530 0.597955i $$-0.795980\pi$$
0.918609 + 0.395168i $$0.129313\pi$$
$$384$$ 1.39564 + 2.41733i 0.0712212 + 0.123359i
$$385$$ 0 0
$$386$$ 1.37386 + 2.37960i 0.0699278 + 0.121119i
$$387$$ −27.7477 −1.41050
$$388$$ 12.3739 0.628188
$$389$$ −9.31307 16.1307i −0.472191 0.817859i 0.527302 0.849678i $$-0.323204\pi$$
−0.999494 + 0.0318184i $$0.989870\pi$$
$$390$$ 0 0
$$391$$ −3.62614 −0.183382
$$392$$ 6.00000 0.303046
$$393$$ −16.1044 27.8936i −0.812357 1.40704i
$$394$$ −10.1044 + 17.5013i −0.509050 + 0.881701i
$$395$$ 0 0
$$396$$ 9.08258 15.7315i 0.456417 0.790537i
$$397$$ −5.70871 + 9.88778i −0.286512 + 0.496253i −0.972975 0.230912i $$-0.925829\pi$$
0.686463 + 0.727165i $$0.259163\pi$$
$$398$$ −3.58258 −0.179578
$$399$$ 11.1652 4.83465i 0.558957 0.242035i
$$400$$ 0 0
$$401$$ 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i $$-0.736472\pi$$
0.976050 + 0.217545i $$0.0698049\pi$$
$$402$$ −21.7477 + 37.6682i −1.08468 + 1.87872i
$$403$$ 0.500000 + 0.866025i 0.0249068 + 0.0431398i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ −6.79129 −0.337046
$$407$$ 13.5826 0.673263
$$408$$ 1.10436 + 1.91280i 0.0546738 + 0.0946978i
$$409$$ 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i $$-0.0871450\pi$$
−0.715523 + 0.698589i $$0.753812\pi$$
$$410$$ 0 0
$$411$$ −42.7913 −2.11074
$$412$$ 2.58258 + 4.47315i 0.127234 + 0.220376i
$$413$$ −2.29129 + 3.96863i −0.112747 + 0.195283i
$$414$$ −10.9782 19.0148i −0.539550 0.934528i
$$415$$ 0 0
$$416$$ 0.104356 0.180750i 0.00511648 0.00886200i
$$417$$ −34.0780 −1.66881
$$418$$ 15.1652 6.56670i 0.741752 0.321188i
$$419$$ −22.7477 −1.11130 −0.555650 0.831417i $$-0.687530\pi$$
−0.555650 + 0.831417i $$0.687530\pi$$
$$420$$ 0 0
$$421$$ −10.0000 + 17.3205i −0.487370 + 0.844150i −0.999895 0.0145228i $$-0.995377\pi$$
0.512524 + 0.858673i $$0.328710\pi$$
$$422$$ 11.9782 + 20.7469i 0.583091 + 1.00994i
$$423$$ −29.1434 + 50.4778i −1.41700 + 2.45431i
$$424$$ 2.29129 + 3.96863i 0.111275 + 0.192734i
$$425$$ 0 0
$$426$$ 12.7913 0.619740
$$427$$ −0.686932 1.18980i −0.0332430 0.0575785i
$$428$$ 9.47822 + 16.4168i 0.458147 + 0.793534i
$$429$$ −2.20871 −0.106638
$$430$$ 0 0
$$431$$ −4.10436 7.10895i −0.197700 0.342426i 0.750082 0.661344i $$-0.230014\pi$$
−0.947782 + 0.318918i $$0.896680\pi$$
$$432$$ −2.50000 + 4.33013i −0.120281 + 0.208333i
$$433$$ 3.45644 + 5.98673i 0.166106 + 0.287704i 0.937047 0.349202i $$-0.113547\pi$$
−0.770942 + 0.636906i $$0.780214\pi$$
$$434$$ −2.39564 + 4.14938i −0.114995 + 0.199176i
$$435$$ 0 0
$$436$$ −11.7477 −0.562614
$$437$$ 2.29129 19.8431i 0.109607 0.949226i
$$438$$ 7.79129 0.372282
$$439$$ 12.6652 21.9367i 0.604475 1.04698i −0.387660 0.921803i $$-0.626716\pi$$
0.992134 0.125178i $$-0.0399503\pi$$
$$440$$ 0 0
$$441$$ 14.3739 + 24.8963i 0.684470 + 1.18554i
$$442$$ 0.0825757 0.143025i 0.00392773 0.00680302i
$$443$$ −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i $$-0.973557\pi$$
0.426414 0.904528i $$-0.359777\pi$$
$$444$$ −10.0000 −0.474579
$$445$$ 0 0
$$446$$ −9.60436 16.6352i −0.454779 0.787701i
$$447$$ 31.7477 + 54.9887i 1.50162 + 2.60088i
$$448$$ 1.00000 0.0472456
$$449$$ 3.33030 0.157167 0.0785834 0.996908i $$-0.474960\pi$$
0.0785834 + 0.996908i $$0.474960\pi$$
$$450$$ 0 0
$$451$$ −21.5608 + 37.3444i −1.01526 + 1.75848i
$$452$$ 2.68693 + 4.65390i 0.126383 + 0.218901i
$$453$$ −21.9782 + 38.0674i −1.03263 + 1.78856i
$$454$$ −3.87386 + 6.70973i −0.181809 + 0.314903i
$$455$$ 0 0
$$456$$ −11.1652 + 4.83465i −0.522856 + 0.226403i
$$457$$ 20.7477 0.970538 0.485269 0.874365i $$-0.338722\pi$$
0.485269 + 0.874365i $$0.338722\pi$$
$$458$$ −12.6652 + 21.9367i −0.591804 + 1.02503i
$$459$$ −1.97822 + 3.42638i −0.0923354 + 0.159930i
$$460$$ 0 0
$$461$$ −6.39564 + 11.0776i −0.297875 + 0.515934i −0.975650 0.219335i $$-0.929611\pi$$
0.677775 + 0.735270i $$0.262944\pi$$
$$462$$ −5.29129 9.16478i −0.246173 0.426384i
$$463$$ −17.9564 −0.834507 −0.417253 0.908790i $$-0.637007\pi$$
−0.417253 + 0.908790i $$0.637007\pi$$
$$464$$ 6.79129 0.315278
$$465$$ 0 0
$$466$$ −4.58258 7.93725i −0.212284 0.367686i
$$467$$ 12.3303 0.570578 0.285289 0.958441i $$-0.407910\pi$$
0.285289 + 0.958441i $$0.407910\pi$$
$$468$$ 1.00000 0.0462250
$$469$$ 7.79129 + 13.4949i 0.359768 + 0.623137i
$$470$$ 0 0
$$471$$ −11.1044 19.2333i −0.511662 0.886224i
$$472$$ 2.29129 3.96863i 0.105465 0.182671i
$$473$$ −10.9782 + 19.0148i −0.504779 + 0.874303i
$$474$$ −41.7477 −1.91754
$$475$$ 0 0
$$476$$ 0.791288 0.0362686
$$477$$ −10.9782 + 19.0148i −0.502658 + 0.870629i
$$478$$ 8.29129 14.3609i 0.379235 0.656854i
$$479$$ −15.8739 27.4943i −0.725295 1.25625i −0.958852 0.283905i $$-0.908370\pi$$
0.233557 0.972343i $$-0.424963\pi$$
$$480$$ 0 0
$$481$$ 0.373864 + 0.647551i 0.0170467 + 0.0295258i
$$482$$ 16.7913 0.764822
$$483$$ −12.7913 −0.582024
$$484$$ −1.68693 2.92185i −0.0766787 0.132811i
$$485$$ 0 0
$$486$$ 16.1652 0.733266
$$487$$ −23.0000 −1.04223 −0.521115 0.853487i $$-0.674484\pi$$
−0.521115 + 0.853487i $$0.674484\pi$$
$$488$$ 0.686932 + 1.18980i 0.0310959 + 0.0538597i
$$489$$ −20.3521 + 35.2508i −0.920353 + 1.59410i
$$490$$ 0 0
$$491$$ 15.7087 27.2083i 0.708924 1.22789i −0.256332 0.966589i $$-0.582514\pi$$
0.965257 0.261304i $$-0.0841525\pi$$
$$492$$ 15.8739 27.4943i 0.715649 1.23954i
$$493$$ 5.37386 0.242027
$$494$$ 0.730493 + 0.542250i 0.0328664 + 0.0243970i
$$495$$ 0 0
$$496$$ 2.39564 4.14938i 0.107568 0.186313i
$$497$$ 2.29129 3.96863i 0.102778 0.178017i
$$498$$ −5.29129 9.16478i −0.237108 0.410684i
$$499$$ 9.66515 16.7405i 0.432672 0.749409i −0.564431 0.825480i $$-0.690904\pi$$
0.997102 + 0.0760712i $$0.0242376\pi$$
$$500$$ 0 0
$$501$$ −32.2087 −1.43898
$$502$$ −13.1216 −0.585645
$$503$$ −2.29129 3.96863i −0.102163 0.176952i 0.810412 0.585860i $$-0.199243\pi$$
−0.912576 + 0.408908i $$0.865910\pi$$
$$504$$ 2.39564 + 4.14938i 0.106710 + 0.184828i
$$505$$ 0 0
$$506$$ −17.3739 −0.772362
$$507$$ 18.0826 + 31.3199i 0.803075 + 1.39097i
$$508$$ 1.31307 2.27430i 0.0582580 0.100906i
$$509$$ −11.2087 19.4141i −0.496817 0.860513i 0.503176 0.864184i $$-0.332165\pi$$
−0.999993 + 0.00367102i $$0.998831\pi$$
$$510$$ 0 0
$$511$$ 1.39564 2.41733i 0.0617397 0.106936i
$$512$$ −1.00000 −0.0441942
$$513$$ −17.5000 12.9904i −0.772644 0.573539i
$$514$$ −11.2087 −0.494395
$$515$$ 0 0
$$516$$ 8.08258 13.9994i 0.355816 0.616291i
$$517$$ 23.0608 + 39.9425i 1.01421 + 1.75667i
$$518$$ −1.79129 + 3.10260i −0.0787047 + 0.136320i
$$519$$ −29.3085 50.7638i −1.28650 2.22829i
$$520$$ 0 0
$$521$$ 13.2523 0.580593 0.290296 0.956937i $$-0.406246\pi$$
0.290296 + 0.956937i $$0.406246\pi$$
$$522$$ 16.2695 + 28.1796i 0.712097 + 1.23339i
$$523$$ −8.87386 15.3700i −0.388027 0.672082i 0.604157 0.796865i $$-0.293510\pi$$
−0.992184 + 0.124783i $$0.960177\pi$$
$$524$$ 11.5390 0.504084
$$525$$ 0 0
$$526$$ 9.70871 + 16.8160i 0.423320 + 0.733212i
$$527$$ 1.89564 3.28335i 0.0825755 0.143025i
$$528$$ 5.29129 + 9.16478i 0.230274 + 0.398846i
$$529$$ 1.00000 1.73205i 0.0434783 0.0753066i
$$530$$ 0 0
$$531$$ 21.9564 0.952828
$$532$$ −0.500000 + 4.33013i −0.0216777 + 0.187735i
$$533$$ −2.37386 −0.102823
$$534$$ 6.39564 11.0776i 0.276767 0.479374i
$$535$$ 0 0
$$536$$ −7.79129 13.4949i −0.336532 0.582891i
$$537$$ 23.3739 40.4847i 1.00866 1.74704i
$$538$$ 6.56080 + 11.3636i 0.282856 + 0.489921i
$$539$$ 22.7477 0.979814
$$540$$ 0 0
$$541$$ 8.56080 + 14.8277i 0.368057 + 0.637494i 0.989262 0.146155i $$-0.0466897\pi$$
−0.621204 + 0.783649i $$0.713356\pi$$
$$542$$ −8.56080 14.8277i −0.367718 0.636906i
$$543$$ −21.2867 −0.913502
$$544$$ −0.791288 −0.0339262
$$545$$ 0 0
$$546$$ 0.291288 0.504525i 0.0124660 0.0215917i
$$547$$ 8.41742 + 14.5794i 0.359903 + 0.623370i 0.987944 0.154810i $$-0.0494764\pi$$
−0.628041 + 0.778180i $$0.716143\pi$$
$$548$$ 7.66515 13.2764i 0.327439 0.567141i
$$549$$ −3.29129 + 5.70068i −0.140469 + 0.243299i
$$550$$ 0 0
$$551$$ −3.39564 + 29.4071i −0.144659 + 1.25279i
$$552$$ 12.7913 0.544433
$$553$$ −7.47822 + 12.9527i −0.318006 + 0.550803i
$$554$$ 4.37386 7.57575i 0.185828 0.321863i
$$555$$ 0 0
$$556$$ 6.10436 10.5731i 0.258882 0.448397i
$$557$$ 4.97822 + 8.62253i 0.210934 + 0.365348i 0.952007 0.306076i $$-0.0990162\pi$$
−0.741073 + 0.671424i $$0.765683\pi$$
$$558$$ 22.9564 0.971824
$$559$$ −1.20871 −0.0511231
$$560$$ 0 0
$$561$$ 4.18693 + 7.25198i 0.176772 + 0.306179i
$$562$$ −10.5826 −0.446399
$$563$$ 14.3739 0.605786 0.302893 0.953025i $$-0.402047\pi$$
0.302893 + 0.953025i $$0.402047\pi$$
$$564$$ −16.9782 29.4071i −0.714912 1.23826i
$$565$$ 0 0
$$566$$ −10.5608 18.2918i −0.443903 0.768863i
$$567$$ 0.208712 0.361500i 0.00876509 0.0151816i
$$568$$ −2.29129 + 3.96863i −0.0961403 + 0.166520i
$$569$$ −8.83485 −0.370376 −0.185188 0.982703i $$-0.559289\pi$$
−0.185188 + 0.982703i $$0.559289\pi$$
$$570$$ 0 0
$$571$$ −22.0000 −0.920671 −0.460336 0.887745i $$-0.652271\pi$$
−0.460336 + 0.887745i $$0.652271\pi$$
$$572$$ 0.395644 0.685275i 0.0165427 0.0286528i
$$573$$ −22.2695 + 38.5719i −0.930322 + 1.61137i
$$574$$ −5.68693 9.85005i −0.237368 0.411133i
$$575$$ 0 0
$$576$$ −2.39564 4.14938i −0.0998185 0.172891i
$$577$$ −14.0000 −0.582828 −0.291414 0.956597i $$-0.594126\pi$$
−0.291414 + 0.956597i $$0.594126\pi$$
$$578$$ 16.3739 0.681063
$$579$$ −3.83485 6.64215i −0.159371 0.276038i
$$580$$ 0 0
$$581$$ −3.79129 −0.157289
$$582$$ −34.5390 −1.43169
$$583$$ 8.68693 + 15.0462i 0.359776 + 0.623150i
$$584$$ −1.39564 + 2.41733i −0.0577522 + 0.100030i
$$585$$ 0 0
$$586$$ −12.4782 + 21.6129i −0.515471 + 0.892821i
$$587$$ −4.74773 + 8.22330i −0.195960 + 0.339412i −0.947215 0.320600i $$-0.896116\pi$$
0.751255 + 0.660012i $$0.229449\pi$$
$$588$$ −16.7477 −0.690665
$$589$$ 16.7695 + 12.4481i 0.690976 + 0.512916i
$$590$$ 0 0
$$591$$ 28.2042 48.8510i 1.16016 2.00946i
$$592$$ 1.79129 3.10260i 0.0736215 0.127516i
$$593$$ −5.91742 10.2493i −0.242999 0.420887i 0.718568 0.695457i $$-0.244798\pi$$
−0.961567 + 0.274569i $$0.911465\pi$$
$$594$$ −9.47822 + 16.4168i −0.388896 + 0.673588i
$$595$$ 0 0
$$596$$ −22.7477 −0.931783
$$597$$ 10.0000 0.409273
$$598$$ −0.478220 0.828301i −0.0195559 0.0338717i
$$599$$ 18.5608 + 32.1482i 0.758374 + 1.31354i 0.943680 + 0.330861i $$0.107339\pi$$
−0.185306 + 0.982681i $$0.559328\pi$$
$$600$$ 0 0
$$601$$ 9.91288 0.404355 0.202177 0.979349i $$-0.435198\pi$$
0.202177 + 0.979349i $$0.435198\pi$$
$$602$$ −2.89564 5.01540i −0.118018 0.204413i
$$603$$ 37.3303 64.6580i 1.52021 2.63308i
$$604$$ −7.87386 13.6379i −0.320383 0.554920i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 18.2087 0.739069 0.369534 0.929217i $$-0.379517\pi$$
0.369534 + 0.929217i $$0.379517\pi$$
$$608$$ 0.500000 4.33013i 0.0202777 0.175610i
$$609$$ 18.9564 0.768154
$$610$$ 0 0
$$611$$ −1.26951 + 2.19885i −0.0513588 + 0.0889560i
$$612$$ −1.89564 3.28335i −0.0766269 0.132722i
$$613$$ 7.24773 12.5534i 0.292733 0.507028i −0.681722 0.731611i $$-0.738769\pi$$
0.974455 + 0.224583i $$0.0721020\pi$$
$$614$$ 17.2477 + 29.8739i 0.696062 + 1.20561i
$$615$$ 0 0
$$616$$ 3.79129 0.152755
$$617$$ −16.5000 28.5788i −0.664265 1.15054i −0.979484 0.201522i $$-0.935411\pi$$
0.315219 0.949019i $$-0.397922\pi$$
$$618$$ −7.20871 12.4859i −0.289977 0.502255i
$$619$$ −24.3739 −0.979668 −0.489834 0.871816i $$-0.662943\pi$$
−0.489834 + 0.871816i $$0.662943\pi$$
$$620$$ 0 0
$$621$$ 11.4564 + 19.8431i 0.459731 + 0.796278i
$$622$$ −7.50000 + 12.9904i −0.300723 + 0.520867i
$$623$$ −2.29129 3.96863i −0.0917985 0.159000i
$$624$$ −0.291288 + 0.504525i −0.0116608 + 0.0201972i
$$625$$ 0 0
$$626$$ −11.7477 −0.469534
$$627$$ −42.3303 + 18.3296i −1.69051 + 0.732012i
$$628$$ 7.95644 0.317496
$$629$$ 1.41742 2.45505i 0.0565164 0.0978893i
$$630$$ 0 0
$$631$$ 18.1044 + 31.3577i 0.720723 + 1.24833i 0.960710 + 0.277553i $$0.0895234\pi$$
−0.239987 + 0.970776i $$0.577143\pi$$
$$632$$ 7.47822 12.9527i 0.297468 0.515229i
$$633$$ −33.4347 57.9105i −1.32891 2.30174i
$$634$$ −9.16515 −0.363995
$$635$$ 0 0
$$636$$ −6.39564 11.0776i −0.253604 0.439255i
$$637$$ 0.626136 + 1.08450i 0.0248084 + 0.0429695i
$$638$$ 25.7477 1.01936
$$639$$ −21.9564 −0.868583
$$640$$ 0 0
$$641$$ −8.52178 + 14.7602i −0.336590 + 0.582991i −0.983789 0.179330i $$-0.942607\pi$$
0.647199 + 0.762321i $$0.275940\pi$$
$$642$$ −26.4564 45.8239i −1.04415 1.80852i
$$643$$ 14.7477 25.5438i 0.581594 1.00735i −0.413697 0.910415i $$-0.635763\pi$$
0.995291 0.0969351i $$-0.0309039\pi$$
$$644$$ 2.29129 3.96863i 0.0902894 0.156386i
$$645$$ 0 0
$$646$$ 0.395644 3.42638i 0.0155664 0.134809i
$$647$$ −18.7913 −0.738762 −0.369381 0.929278i $$-0.620430\pi$$
−0.369381 + 0.929278i $$0.620430\pi$$
$$648$$ −0.208712 + 0.361500i −0.00819899 + 0.0142011i
$$649$$ 8.68693 15.0462i 0.340992 0.590615i
$$650$$ 0 0
$$651$$ 6.68693 11.5821i 0.262082 0.453939i
$$652$$ −7.29129 12.6289i −0.285549 0.494585i
$$653$$ 27.3303 1.06952 0.534759 0.845005i $$-0.320403\pi$$
0.534759 + 0.845005i $$0.320403\pi$$
$$654$$ 32.7913 1.28224
$$655$$ 0 0
$$656$$ 5.68693 + 9.85005i 0.222037 + 0.384580i
$$657$$ −13.3739 −0.521764
$$658$$ −12.1652 −0.474247
$$659$$ −0.873864 1.51358i −0.0340409 0.0589606i 0.848503 0.529190i $$-0.177504\pi$$
−0.882544 + 0.470230i $$0.844171\pi$$
$$660$$ 0 0
$$661$$ −23.4347 40.5900i −0.911503 1.57877i −0.811943 0.583737i $$-0.801590\pi$$
−0.0995599 0.995032i $$-0.531744\pi$$
$$662$$ −8.95644 + 15.5130i −0.348102 + 0.602930i
$$663$$ −0.230493 + 0.399225i −0.00895159 + 0.0155046i
$$664$$ 3.79129 0.147131
$$665$$ 0 0
$$666$$ 17.1652 0.665136
$$667$$ 15.5608 26.9521i 0.602516 1.04359i
$$668$$ 5.76951 9.99308i 0.223229 0.386644i
$$669$$ 26.8085 + 46.4337i 1.03648 + 1.79523i
$$670$$ 0 0
$$671$$ 2.60436 + 4.51088i 0.100540 + 0.174140i
$$672$$ −2.79129 −0.107676
$$673$$ −2.79129 −0.107596 −0.0537981 0.998552i $$-0.517133\pi$$
−0.0537981 + 0.998552i $$0.517133\pi$$
$$674$$ −11.6652 20.2046i −0.449325 0.778253i
$$675$$ 0 0
$$676$$ −12.9564 −0.498325
$$677$$ 35.2432 1.35451 0.677253 0.735750i $$-0.263170\pi$$
0.677253 + 0.735750i $$0.263170\pi$$
$$678$$ −7.50000 12.9904i −0.288036 0.498893i
$$679$$ −6.18693 + 10.7161i −0.237433 + 0.411245i
$$680$$ 0 0
$$681$$ 10.8131 18.7288i 0.414358 0.717689i
$$682$$ 9.08258 15.7315i 0.347790 0.602390i
$$683$$ 36.1652 1.38382 0.691911 0.721983i $$-0.256769\pi$$
0.691911 + 0.721983i $$0.256769\pi$$
$$684$$ 19.1652 8.29875i 0.732798 0.317311i
$$685$$ 0 0
$$686$$ −6.50000 + 11.2583i −0.248171 + 0.429845i
$$687$$ 35.3521 61.2316i 1.34877 2.33613i
$$688$$ 2.89564 + 5.01540i 0.110395 + 0.191210i
$$689$$ −0.478220 + 0.828301i −0.0182187 + 0.0315557i
$$690$$ 0 0
$$691$$ −32.1216 −1.22196 −0.610981 0.791645i $$-0.709225\pi$$
−0.610981 + 0.791645i $$0.709225\pi$$
$$692$$ 21.0000 0.798300
$$693$$ 9.08258 + 15.7315i 0.345019 + 0.597590i
$$694$$ −1.81307 3.14033i −0.0688231 0.119205i
$$695$$ 0 0
$$696$$ −18.9564 −0.718542
$$697$$ 4.50000 + 7.79423i 0.170450 + 0.295227i
$$698$$ −2.70871 + 4.69163i −0.102526 + 0.177581i
$$699$$ 12.7913 + 22.1552i 0.483811 + 0.837985i
$$700$$ 0 0
$$701$$ 6.47822 11.2206i 0.244679 0.423796i −0.717362 0.696700i $$-0.754651\pi$$
0.962041 + 0.272904i $$0.0879841\pi$$
$$702$$ −1.04356 −0.0393867
$$703$$ 12.5390 + 9.30780i 0.472918 + 0.351051i
$$704$$ −3.79129 −0.142890
$$705$$ 0 0
$$706$$ 6.87386 11.9059i 0.258701 0.448084i
$$707$$ 0 0
$$708$$ −6.39564 + 11.0776i −0.240363 + 0.416321i
$$709$$ 13.3739 + 23.1642i 0.502266 + 0.869950i 0.999997 + 0.00261852i $$0.000833501\pi$$
−0.497731 + 0.867332i $$0.665833\pi$$
$$710$$ 0 0
$$711$$ 71.6606 2.68748
$$712$$ 2.29129 + 3.96863i 0.0858696 + 0.148731i
$$713$$ −10.9782 19.0148i −0.411138 0.712111i
$$714$$ −2.20871 −0.0826590
$$715$$ 0 0
$$716$$ 8.37386 + 14.5040i 0.312946 + 0.542038i
$$717$$ −23.1434 + 40.0855i −0.864305 + 1.49702i
$$718$$ −17.8521 30.9207i −0.666234 1.15395i
$$719$$ 6.08258 10.5353i 0.226842 0.392902i −0.730029 0.683417i $$-0.760493\pi$$
0.956870 + 0.290515i $$0.0938266\pi$$
$$720$$ 0 0
$$721$$ −5.16515 −0.192360
$$722$$ 18.5000 + 4.33013i 0.688499 + 0.161151i
$$723$$ −46.8693 −1.74309
$$724$$ 3.81307 6.60443i 0.141712 0.245452i
$$725$$ 0 0
$$726$$ 4.70871 + 8.15573i 0.174757 + 0.302687i
$$727$$ −2.08258 + 3.60713i −0.0772385 + 0.133781i −0.902058 0.431616i $$-0.857944\pi$$
0.824819 + 0.565397i $$0.191277\pi$$
$$728$$ 0.104356 + 0.180750i 0.00386769 + 0.00669904i
$$729$$ −43.8693 −1.62479
$$730$$ 0 0
$$731$$ 2.29129 + 3.96863i 0.0847463 + 0.146785i
$$732$$ −1.91742 3.32108i −0.0708700 0.122751i
$$733$$ −12.7477 −0.470848 −0.235424 0.971893i $$-0.575648\pi$$
−0.235424 + 0.971893i $$0.575648\pi$$
$$734$$ 8.79129 0.324492
$$735$$ 0 0
$$736$$ −2.29129 + 3.96863i −0.0844580 + 0.146286i
$$737$$ −29.5390 51.1631i −1.08808 1.88462i
$$738$$ −27.2477 + 47.1944i −1.00300 + 1.73725i
$$739$$ 17.8739 30.9584i 0.657501 1.13882i −0.323760 0.946139i $$-0.604947\pi$$
0.981261 0.192685i $$-0.0617197\pi$$
$$740$$ 0 0
$$741$$ −2.03901 1.51358i −0.0749051 0.0556026i
$$742$$ −4.58258 −0.168232
$$743$$ 9.70871 16.8160i 0.356178 0.616919i −0.631141 0.775668i $$-0.717413\pi$$
0.987319 + 0.158750i $$0.0507463\pi$$
$$744$$ −6.68693 + 11.5821i −0.245155 + 0.424621i
$$745$$ 0 0
$$746$$ 10.6869 18.5103i 0.391276 0.677711i
$$747$$ 9.08258 + 15.7315i 0.332314 + 0.575585i
$$748$$ −3.00000 −0.109691
$$749$$ −18.9564 −0.692653
$$750$$ 0 0
$$751$$ −10.7913 18.6911i −0.393780 0.682046i 0.599165 0.800626i $$-0.295499\pi$$
−0.992945 + 0.118579i $$0.962166\pi$$
$$752$$ 12.1652 0.443617
$$753$$ 36.6261 1.33473
$$754$$ 0.708712 + 1.22753i 0.0258098 + 0.0447038i
$$755$$ 0 0
$$756$$ −2.50000 4.33013i −0.0909241 0.157485i
$$757$$ 22.8739 39.6187i 0.831365 1.43997i −0.0655915 0.997847i $$-0.520893\pi$$
0.896956 0.442119i $$-0.145773\pi$$
$$758$$ 2.41742 4.18710i 0.0878048 0.152082i
$$759$$ 48.4955 1.76027
$$760$$ 0 0
$$761$$ 25.2523 0.915394 0.457697 0.889108i $$-0.348674\pi$$
0.457697 + 0.889108i $$0.348674\pi$$
$$762$$ −3.66515 + 6.34823i −0.132774 + 0.229972i
$$763$$ 5.87386 10.1738i 0.212648 0.368317i
$$764$$ −7.97822 13.8187i −0.288642 0.499942i
$$765$$ 0 0
$$766$$ −2.29129 3.96863i −0.0827876 0.143392i
$$767$$ 0.956439 0.0345350
$$768$$ 2.79129 0.100722
$$769$$ 11.1652 + 19.3386i 0.402626 + 0.697368i 0.994042 0.108998i $$-0.0347643\pi$$
−0.591416 + 0.806366i $$0.701431\pi$$
$$770$$ 0 0
$$771$$ 31.2867 1.12676
$$772$$ 2.74773 0.0988929
$$773$$ −10.6652 18.4726i −0.383599 0.664413i 0.607975 0.793956i $$-0.291982\pi$$
−0.991574 + 0.129544i $$0.958649\pi$$
$$774$$ −13.8739 + 24.0302i −0.498686 + 0.863749i
$$775$$ 0 0
$$776$$ 6.18693 10.7161i 0.222098 0.384685i
$$777$$ 5.00000 8.66025i 0.179374 0.310685i
$$778$$ −18.6261 −0.667779
$$779$$ −45.4955 + 19.7001i −1.63004 + 0.705830i
$$780$$ 0 0
$$781$$ −8.68693 + 15.0462i −0.310843 + 0.538396i
$$782$$ −1.81307 + 3.14033i −0.0648352 + 0.112298i
$$783$$ −16.9782 29.4071i −0.606752 1.05093i
$$784$$ 3.00000 5.19615i 0.107143 0.185577i
$$785$$ 0 0