# Properties

 Label 39.2.k.b.11.1 Level $39$ Weight $2$ Character 39.11 Analytic conductor $0.311$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$39 = 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 39.k (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.311416567883$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$2$$ over $$\Q(\zeta_{12})$$ Coefficient field: 8.0.56070144.2 Defining polynomial: $$x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 63 x^{4} - 74 x^{3} + 70 x^{2} - 38 x + 13$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 11.1 Root $$0.500000 - 1.56488i$$ of defining polynomial Character $$\chi$$ $$=$$ 39.11 Dual form 39.2.k.b.32.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.45466 - 0.389774i) q^{2} +(0.239203 - 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.01660 + 2.40216i) q^{6} +(0.366025 + 1.36603i) q^{7} +(1.84443 + 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})$$ $$q+(-1.45466 - 0.389774i) q^{2} +(0.239203 - 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.01660 + 2.40216i) q^{6} +(0.366025 + 1.36603i) q^{7} +(1.84443 + 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +(-1.96410 + 1.13397i) q^{10} +(-1.06488 + 3.97420i) q^{11} +(0.285334 - 0.366025i) q^{12} +(3.59808 + 0.232051i) q^{13} -2.12976i q^{14} +(-1.57203 - 2.08148i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(2.51954 - 4.36397i) q^{17} +(3.87762 + 2.31853i) q^{18} +(-3.73205 + 1.00000i) q^{19} +(0.389774 - 0.104440i) q^{20} +(2.43091 - 0.301143i) q^{21} +(3.09808 - 5.36603i) q^{22} +(3.60523 - 2.72284i) q^{24} +2.73205i q^{25} +(-5.14352 - 1.73999i) q^{26} +(-2.09808 + 4.75374i) q^{27} +(-0.0980762 + 0.366025i) q^{28} +(-6.20840 + 3.58442i) q^{29} +(1.47546 + 3.64058i) q^{30} +(-2.46410 - 2.46410i) q^{31} +(0.389774 + 1.45466i) q^{32} +(6.56283 + 2.77739i) q^{33} +(-5.36603 + 5.36603i) q^{34} +(1.84443 + 1.06488i) q^{35} +(-0.559647 - 0.577032i) q^{36} +(-5.23205 - 1.40192i) q^{37} +5.81863 q^{38} +(1.25874 - 6.11683i) q^{39} +3.92820 q^{40} +(5.42885 + 1.45466i) q^{41} +(-3.65351 - 0.509445i) q^{42} +(1.90192 + 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(-3.94672 + 2.19886i) q^{45} +(-4.25953 - 4.25953i) q^{47} +(-7.16590 + 2.90422i) q^{48} +(4.33013 - 2.50000i) q^{49} +(1.06488 - 3.97420i) q^{50} +(-6.88351 - 5.36603i) q^{51} +(0.803848 + 0.535898i) q^{52} -0.779548i q^{53} +(4.90487 - 6.09729i) q^{54} +(3.09808 + 5.36603i) q^{55} +(-1.84443 + 3.19465i) q^{56} +(0.822738 + 6.64136i) q^{57} +(10.4282 - 2.79423i) q^{58} +(-2.90931 + 0.779548i) q^{59} +(-0.0859264 - 0.693622i) q^{60} +(3.50000 - 6.06218i) q^{61} +(2.62398 + 4.54486i) q^{62} +(0.0648824 - 4.24214i) q^{63} +6.66025i q^{64} +(4.07863 - 3.58442i) q^{65} +(-8.46410 - 6.59817i) q^{66} +(-1.53590 + 5.73205i) q^{67} +(1.16932 - 0.675108i) q^{68} +(-2.26795 - 2.26795i) q^{70} +(-0.779548 - 2.90931i) q^{71} +(-3.80853 - 6.83591i) q^{72} +(-0.901924 + 0.901924i) q^{73} +(7.06440 + 4.07863i) q^{74} +(4.68671 + 0.653513i) q^{75} +(-1.00000 - 0.267949i) q^{76} -5.81863 q^{77} +(-4.21522 + 8.40726i) q^{78} +2.00000 q^{79} +(-6.49373 - 1.73999i) q^{80} +(7.65296 + 4.73626i) q^{81} +(-7.33013 - 4.23205i) q^{82} +(2.90931 - 2.90931i) q^{83} +(0.604440 + 0.255799i) q^{84} +(-1.96410 - 7.33013i) q^{85} +(-2.33864 - 2.33864i) q^{86} +(4.66384 + 11.5076i) q^{87} +(-9.29423 + 5.36603i) q^{88} +(-2.41510 + 9.01327i) q^{89} +(6.59817 - 1.66025i) q^{90} +(1.00000 + 5.00000i) q^{91} +(-4.81647 + 3.63763i) q^{93} +(4.53590 + 7.85641i) q^{94} +(-2.90931 + 5.03908i) q^{95} +(2.58863 - 0.320682i) q^{96} +(1.63397 - 0.437822i) q^{97} +(-7.27328 + 1.94887i) q^{98} +(6.33434 - 10.5939i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{3} - 12q^{4} - 2q^{6} - 4q^{7} + 4q^{9} + O(q^{10})$$ $$8q - 2q^{3} - 12q^{4} - 2q^{6} - 4q^{7} + 4q^{9} + 12q^{10} + 8q^{13} - 14q^{15} - 4q^{16} + 4q^{18} - 16q^{19} + 4q^{21} + 4q^{22} + 18q^{24} + 4q^{27} + 20q^{28} + 18q^{30} + 8q^{31} + 16q^{33} - 36q^{34} - 36q^{36} - 28q^{37} - 14q^{39} - 24q^{40} - 16q^{42} + 36q^{43} - 20q^{45} - 14q^{48} + 48q^{52} + 46q^{54} + 4q^{55} + 16q^{57} + 28q^{58} + 44q^{60} + 28q^{61} - 8q^{63} - 40q^{66} - 40q^{67} - 32q^{70} + 12q^{72} - 28q^{73} + 12q^{75} - 8q^{76} - 80q^{78} + 16q^{79} + 4q^{81} - 24q^{82} + 4q^{84} + 12q^{85} - 34q^{87} - 12q^{88} + 8q^{91} + 4q^{93} + 64q^{94} + 16q^{96} + 20q^{97} + 40q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$$.

 $$n$$ $$14$$ $$28$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.45466 0.389774i −1.02860 0.275612i −0.295217 0.955430i $$-0.595392\pi$$
−0.733380 + 0.679818i $$0.762059\pi$$
$$3$$ 0.239203 1.71545i 0.138104 0.990418i
$$4$$ 0.232051 + 0.133975i 0.116025 + 0.0669873i
$$5$$ 1.06488 1.06488i 0.476230 0.476230i −0.427694 0.903924i $$-0.640674\pi$$
0.903924 + 0.427694i $$0.140674\pi$$
$$6$$ −1.01660 + 2.40216i −0.415024 + 0.980678i
$$7$$ 0.366025 + 1.36603i 0.138345 + 0.516309i 0.999962 + 0.00875026i $$0.00278533\pi$$
−0.861617 + 0.507559i $$0.830548\pi$$
$$8$$ 1.84443 + 1.84443i 0.652105 + 0.652105i
$$9$$ −2.88556 0.820682i −0.961855 0.273561i
$$10$$ −1.96410 + 1.13397i −0.621103 + 0.358594i
$$11$$ −1.06488 + 3.97420i −0.321074 + 1.19826i 0.597126 + 0.802148i $$0.296309\pi$$
−0.918200 + 0.396117i $$0.870357\pi$$
$$12$$ 0.285334 0.366025i 0.0823689 0.105662i
$$13$$ 3.59808 + 0.232051i 0.997927 + 0.0643593i
$$14$$ 2.12976i 0.569204i
$$15$$ −1.57203 2.08148i −0.405897 0.537436i
$$16$$ −2.23205 3.86603i −0.558013 0.966506i
$$17$$ 2.51954 4.36397i 0.611078 1.05842i −0.379981 0.924994i $$-0.624070\pi$$
0.991059 0.133424i $$-0.0425971\pi$$
$$18$$ 3.87762 + 2.31853i 0.913965 + 0.546482i
$$19$$ −3.73205 + 1.00000i −0.856191 + 0.229416i −0.660107 0.751171i $$-0.729489\pi$$
−0.196084 + 0.980587i $$0.562823\pi$$
$$20$$ 0.389774 0.104440i 0.0871561 0.0233534i
$$21$$ 2.43091 0.301143i 0.530468 0.0657148i
$$22$$ 3.09808 5.36603i 0.660512 1.14404i
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 3.60523 2.72284i 0.735914 0.555798i
$$25$$ 2.73205i 0.546410i
$$26$$ −5.14352 1.73999i −1.00873 0.341240i
$$27$$ −2.09808 + 4.75374i −0.403775 + 0.914858i
$$28$$ −0.0980762 + 0.366025i −0.0185347 + 0.0691723i
$$29$$ −6.20840 + 3.58442i −1.15287 + 0.665610i −0.949585 0.313509i $$-0.898495\pi$$
−0.203286 + 0.979119i $$0.565162\pi$$
$$30$$ 1.47546 + 3.64058i 0.269381 + 0.664675i
$$31$$ −2.46410 2.46410i −0.442566 0.442566i 0.450308 0.892873i $$-0.351314\pi$$
−0.892873 + 0.450308i $$0.851314\pi$$
$$32$$ 0.389774 + 1.45466i 0.0689030 + 0.257149i
$$33$$ 6.56283 + 2.77739i 1.14244 + 0.483482i
$$34$$ −5.36603 + 5.36603i −0.920266 + 0.920266i
$$35$$ 1.84443 + 1.06488i 0.311766 + 0.179998i
$$36$$ −0.559647 0.577032i −0.0932745 0.0961720i
$$37$$ −5.23205 1.40192i −0.860144 0.230475i −0.198323 0.980137i $$-0.563549\pi$$
−0.661821 + 0.749662i $$0.730216\pi$$
$$38$$ 5.81863 0.943906
$$39$$ 1.25874 6.11683i 0.201560 0.979476i
$$40$$ 3.92820 0.621103
$$41$$ 5.42885 + 1.45466i 0.847844 + 0.227179i 0.656483 0.754341i $$-0.272043\pi$$
0.191361 + 0.981520i $$0.438710\pi$$
$$42$$ −3.65351 0.509445i −0.563749 0.0786091i
$$43$$ 1.90192 + 1.09808i 0.290041 + 0.167455i 0.637960 0.770069i $$-0.279778\pi$$
−0.347920 + 0.937524i $$0.613112\pi$$
$$44$$ −0.779548 + 0.779548i −0.117521 + 0.117521i
$$45$$ −3.94672 + 2.19886i −0.588342 + 0.327786i
$$46$$ 0 0
$$47$$ −4.25953 4.25953i −0.621316 0.621316i 0.324552 0.945868i $$-0.394787\pi$$
−0.945868 + 0.324552i $$0.894787\pi$$
$$48$$ −7.16590 + 2.90422i −1.03431 + 0.419188i
$$49$$ 4.33013 2.50000i 0.618590 0.357143i
$$50$$ 1.06488 3.97420i 0.150597 0.562036i
$$51$$ −6.88351 5.36603i −0.963884 0.751394i
$$52$$ 0.803848 + 0.535898i 0.111474 + 0.0743157i
$$53$$ 0.779548i 0.107079i −0.998566 0.0535396i $$-0.982950\pi$$
0.998566 0.0535396i $$-0.0170503\pi$$
$$54$$ 4.90487 6.09729i 0.667468 0.829736i
$$55$$ 3.09808 + 5.36603i 0.417745 + 0.723555i
$$56$$ −1.84443 + 3.19465i −0.246472 + 0.426903i
$$57$$ 0.822738 + 6.64136i 0.108974 + 0.879670i
$$58$$ 10.4282 2.79423i 1.36929 0.366900i
$$59$$ −2.90931 + 0.779548i −0.378760 + 0.101489i −0.443176 0.896435i $$-0.646148\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$60$$ −0.0859264 0.693622i −0.0110931 0.0895462i
$$61$$ 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i $$-0.685424\pi$$
0.998264 + 0.0588933i $$0.0187572\pi$$
$$62$$ 2.62398 + 4.54486i 0.333246 + 0.577198i
$$63$$ 0.0648824 4.24214i 0.00817442 0.534460i
$$64$$ 6.66025i 0.832532i
$$65$$ 4.07863 3.58442i 0.505892 0.444593i
$$66$$ −8.46410 6.59817i −1.04186 0.812179i
$$67$$ −1.53590 + 5.73205i −0.187640 + 0.700281i 0.806410 + 0.591357i $$0.201407\pi$$
−0.994050 + 0.108925i $$0.965259\pi$$
$$68$$ 1.16932 0.675108i 0.141801 0.0818689i
$$69$$ 0 0
$$70$$ −2.26795 2.26795i −0.271072 0.271072i
$$71$$ −0.779548 2.90931i −0.0925153 0.345272i 0.904116 0.427288i $$-0.140531\pi$$
−0.996631 + 0.0820158i $$0.973864\pi$$
$$72$$ −3.80853 6.83591i −0.448840 0.805620i
$$73$$ −0.901924 + 0.901924i −0.105562 + 0.105562i −0.757915 0.652353i $$-0.773782\pi$$
0.652353 + 0.757915i $$0.273782\pi$$
$$74$$ 7.06440 + 4.07863i 0.821220 + 0.474132i
$$75$$ 4.68671 + 0.653513i 0.541174 + 0.0754612i
$$76$$ −1.00000 0.267949i −0.114708 0.0307359i
$$77$$ −5.81863 −0.663094
$$78$$ −4.21522 + 8.40726i −0.477279 + 0.951934i
$$79$$ 2.00000 0.225018 0.112509 0.993651i $$-0.464111\pi$$
0.112509 + 0.993651i $$0.464111\pi$$
$$80$$ −6.49373 1.73999i −0.726022 0.194537i
$$81$$ 7.65296 + 4.73626i 0.850329 + 0.526251i
$$82$$ −7.33013 4.23205i −0.809477 0.467352i
$$83$$ 2.90931 2.90931i 0.319339 0.319339i −0.529174 0.848513i $$-0.677498\pi$$
0.848513 + 0.529174i $$0.177498\pi$$
$$84$$ 0.604440 + 0.255799i 0.0659498 + 0.0279100i
$$85$$ −1.96410 7.33013i −0.213037 0.795064i
$$86$$ −2.33864 2.33864i −0.252182 0.252182i
$$87$$ 4.66384 + 11.5076i 0.500017 + 1.23375i
$$88$$ −9.29423 + 5.36603i −0.990768 + 0.572020i
$$89$$ −2.41510 + 9.01327i −0.256000 + 0.955405i 0.711531 + 0.702654i $$0.248002\pi$$
−0.967531 + 0.252751i $$0.918665\pi$$
$$90$$ 6.59817 1.66025i 0.695509 0.175006i
$$91$$ 1.00000 + 5.00000i 0.104828 + 0.524142i
$$92$$ 0 0
$$93$$ −4.81647 + 3.63763i −0.499445 + 0.377205i
$$94$$ 4.53590 + 7.85641i 0.467842 + 0.810326i
$$95$$ −2.90931 + 5.03908i −0.298489 + 0.516998i
$$96$$ 2.58863 0.320682i 0.264201 0.0327295i
$$97$$ 1.63397 0.437822i 0.165905 0.0444541i −0.174910 0.984584i $$-0.555964\pi$$
0.340815 + 0.940130i $$0.389297\pi$$
$$98$$ −7.27328 + 1.94887i −0.734712 + 0.196866i
$$99$$ 6.33434 10.5939i 0.636625 1.06472i
$$100$$ −0.366025 + 0.633975i −0.0366025 + 0.0633975i
$$101$$ −3.01375 5.21997i −0.299880 0.519407i 0.676229 0.736692i $$-0.263613\pi$$
−0.976108 + 0.217285i $$0.930280\pi$$
$$102$$ 7.92160 + 10.4887i 0.784356 + 1.03854i
$$103$$ 6.92820i 0.682656i −0.939944 0.341328i $$-0.889123\pi$$
0.939944 0.341328i $$-0.110877\pi$$
$$104$$ 6.20840 + 7.06440i 0.608784 + 0.692722i
$$105$$ 2.26795 2.90931i 0.221329 0.283920i
$$106$$ −0.303848 + 1.13397i −0.0295123 + 0.110141i
$$107$$ 16.4675 9.50749i 1.59197 0.919123i 0.598999 0.800749i $$-0.295565\pi$$
0.992969 0.118374i $$-0.0377682\pi$$
$$108$$ −1.12374 + 0.822021i −0.108132 + 0.0790990i
$$109$$ −13.1962 13.1962i −1.26396 1.26396i −0.949156 0.314806i $$-0.898060\pi$$
−0.314806 0.949156i $$-0.601940\pi$$
$$110$$ −2.41510 9.01327i −0.230271 0.859382i
$$111$$ −3.65646 + 8.64000i −0.347055 + 0.820072i
$$112$$ 4.46410 4.46410i 0.421818 0.421818i
$$113$$ −8.90883 5.14352i −0.838073 0.483861i 0.0185360 0.999828i $$-0.494099\pi$$
−0.856609 + 0.515967i $$0.827433\pi$$
$$114$$ 1.39183 9.98158i 0.130357 0.934861i
$$115$$ 0 0
$$116$$ −1.92089 −0.178350
$$117$$ −10.1920 3.62247i −0.942254 0.334898i
$$118$$ 4.53590 0.417563
$$119$$ 6.88351 + 1.84443i 0.631010 + 0.169079i
$$120$$ 0.939636 6.73865i 0.0857767 0.615152i
$$121$$ −5.13397 2.96410i −0.466725 0.269464i
$$122$$ −7.45418 + 7.45418i −0.674869 + 0.674869i
$$123$$ 3.79399 8.96499i 0.342093 0.808346i
$$124$$ −0.241670 0.901924i −0.0217026 0.0809951i
$$125$$ 8.23373 + 8.23373i 0.736447 + 0.736447i
$$126$$ −1.74786 + 6.14557i −0.155712 + 0.547491i
$$127$$ 7.90192 4.56218i 0.701182 0.404828i −0.106605 0.994301i $$-0.533998\pi$$
0.807788 + 0.589474i $$0.200665\pi$$
$$128$$ 3.37554 12.5977i 0.298359 1.11349i
$$129$$ 2.33864 3.00000i 0.205906 0.264135i
$$130$$ −7.33013 + 3.62436i −0.642895 + 0.317877i
$$131$$ 7.94839i 0.694454i 0.937781 + 0.347227i $$0.112877\pi$$
−0.937781 + 0.347227i $$0.887123\pi$$
$$132$$ 1.15081 + 1.52375i 0.100165 + 0.132625i
$$133$$ −2.73205 4.73205i −0.236899 0.410321i
$$134$$ 4.46841 7.73951i 0.386012 0.668592i
$$135$$ 2.82797 + 7.29638i 0.243393 + 0.627973i
$$136$$ 12.6962 3.40192i 1.08869 0.291713i
$$137$$ 6.49373 1.73999i 0.554797 0.148657i 0.0294822 0.999565i $$-0.490614\pi$$
0.525315 + 0.850908i $$0.323948\pi$$
$$138$$ 0 0
$$139$$ −9.19615 + 15.9282i −0.780007 + 1.35101i 0.151929 + 0.988391i $$0.451451\pi$$
−0.931937 + 0.362621i $$0.881882\pi$$
$$140$$ 0.285334 + 0.494214i 0.0241152 + 0.0417687i
$$141$$ −8.32592 + 6.28814i −0.701169 + 0.529557i
$$142$$ 4.53590i 0.380644i
$$143$$ −4.75374 + 14.0524i −0.397528 + 1.17512i
$$144$$ 3.26795 + 12.9875i 0.272329 + 1.08229i
$$145$$ −2.79423 + 10.4282i −0.232048 + 0.866015i
$$146$$ 1.66354 0.960443i 0.137675 0.0794868i
$$147$$ −3.25286 8.02614i −0.268291 0.661985i
$$148$$ −1.02628 1.02628i −0.0843597 0.0843597i
$$149$$ 2.23420 + 8.33816i 0.183033 + 0.683089i 0.995043 + 0.0994454i $$0.0317068\pi$$
−0.812010 + 0.583644i $$0.801626\pi$$
$$150$$ −6.56283 2.77739i −0.535853 0.226773i
$$151$$ 0.535898 0.535898i 0.0436108 0.0436108i −0.684965 0.728576i $$-0.740183\pi$$
0.728576 + 0.684965i $$0.240183\pi$$
$$152$$ −8.72794 5.03908i −0.707929 0.408723i
$$153$$ −10.8517 + 10.5248i −0.877310 + 0.850878i
$$154$$ 8.46410 + 2.26795i 0.682057 + 0.182757i
$$155$$ −5.24796 −0.421526
$$156$$ 1.11159 1.25078i 0.0889985 0.100142i
$$157$$ −4.80385 −0.383389 −0.191694 0.981455i $$-0.561398\pi$$
−0.191694 + 0.981455i $$0.561398\pi$$
$$158$$ −2.90931 0.779548i −0.231453 0.0620175i
$$159$$ −1.33728 0.186470i −0.106053 0.0147880i
$$160$$ 1.96410 + 1.13397i 0.155276 + 0.0896486i
$$161$$ 0 0
$$162$$ −9.28636 9.87256i −0.729605 0.775661i
$$163$$ −1.07180 4.00000i −0.0839496 0.313304i 0.911164 0.412045i $$-0.135185\pi$$
−0.995113 + 0.0987406i $$0.968519\pi$$
$$164$$ 1.06488 + 1.06488i 0.0831533 + 0.0831533i
$$165$$ 9.94624 4.03104i 0.774313 0.313816i
$$166$$ −5.36603 + 3.09808i −0.416484 + 0.240457i
$$167$$ 3.47998 12.9875i 0.269289 1.00500i −0.690283 0.723539i $$-0.742514\pi$$
0.959573 0.281461i $$-0.0908192\pi$$
$$168$$ 5.03908 + 3.92820i 0.388773 + 0.303067i
$$169$$ 12.8923 + 1.66987i 0.991716 + 0.128452i
$$170$$ 11.4284i 0.876516i
$$171$$ 11.5898 + 0.177262i 0.886291 + 0.0135556i
$$172$$ 0.294229 + 0.509619i 0.0224347 + 0.0388581i
$$173$$ −8.72794 + 15.1172i −0.663573 + 1.14934i 0.316097 + 0.948727i $$0.397627\pi$$
−0.979670 + 0.200615i $$0.935706\pi$$
$$174$$ −2.29892 18.5575i −0.174281 1.40684i
$$175$$ −3.73205 + 1.00000i −0.282117 + 0.0755929i
$$176$$ 17.7412 4.75374i 1.33729 0.358327i
$$177$$ 0.641364 + 5.17726i 0.0482078 + 0.389147i
$$178$$ 7.02628 12.1699i 0.526642 0.912171i
$$179$$ −13.2728 22.9892i −0.992056 1.71829i −0.604972 0.796247i $$-0.706816\pi$$
−0.387084 0.922045i $$-0.626518\pi$$
$$180$$ −1.21043 0.0185132i −0.0902201 0.00137989i
$$181$$ 3.00000i 0.222988i −0.993765 0.111494i $$-0.964436\pi$$
0.993765 0.111494i $$-0.0355636\pi$$
$$182$$ 0.494214 7.66306i 0.0366336 0.568024i
$$183$$ −9.56218 7.45418i −0.706857 0.551029i
$$184$$ 0 0
$$185$$ −7.06440 + 4.07863i −0.519385 + 0.299867i
$$186$$ 8.42417 3.41417i 0.617690 0.250339i
$$187$$ 14.6603 + 14.6603i 1.07206 + 1.07206i
$$188$$ −0.417759 1.55910i −0.0304682 0.113709i
$$189$$ −7.26168 1.12603i −0.528210 0.0819070i
$$190$$ 6.19615 6.19615i 0.449516 0.449516i
$$191$$ 4.18307 + 2.41510i 0.302677 + 0.174750i 0.643645 0.765324i $$-0.277421\pi$$
−0.340968 + 0.940075i $$0.610755\pi$$
$$192$$ 11.4254 + 1.59315i 0.824554 + 0.114976i
$$193$$ 0.133975 + 0.0358984i 0.00964370 + 0.00258402i 0.263638 0.964622i $$-0.415078\pi$$
−0.253994 + 0.967206i $$0.581744\pi$$
$$194$$ −2.54752 −0.182902
$$195$$ −5.17329 7.85411i −0.370467 0.562445i
$$196$$ 1.33975 0.0956961
$$197$$ −3.97420 1.06488i −0.283150 0.0758697i 0.114449 0.993429i $$-0.463490\pi$$
−0.397599 + 0.917559i $$0.630156\pi$$
$$198$$ −13.3435 + 12.9415i −0.948281 + 0.919711i
$$199$$ 11.1962 + 6.46410i 0.793674 + 0.458228i 0.841254 0.540639i $$-0.181818\pi$$
−0.0475802 + 0.998867i $$0.515151\pi$$
$$200$$ −5.03908 + 5.03908i −0.356317 + 0.356317i
$$201$$ 9.46568 + 4.00588i 0.667657 + 0.282553i
$$202$$ 2.34936 + 8.76795i 0.165301 + 0.616911i
$$203$$ −7.16884 7.16884i −0.503154 0.503154i
$$204$$ −0.878413 2.16741i −0.0615012 0.151749i
$$205$$ 7.33013 4.23205i 0.511958 0.295579i
$$206$$ −2.70043 + 10.0782i −0.188148 + 0.702178i
$$207$$ 0 0
$$208$$ −7.13397 14.4282i −0.494652 1.00042i
$$209$$ 15.8968i 1.09960i
$$210$$ −4.43306 + 3.34806i −0.305910 + 0.231038i
$$211$$ 0.901924 + 1.56218i 0.0620910 + 0.107545i 0.895400 0.445263i $$-0.146890\pi$$
−0.833309 + 0.552808i $$0.813556\pi$$
$$212$$ 0.104440 0.180895i 0.00717294 0.0124239i
$$213$$ −5.17726 + 0.641364i −0.354740 + 0.0439455i
$$214$$ −27.6603 + 7.41154i −1.89082 + 0.506643i
$$215$$ 3.19465 0.856003i 0.217873 0.0583789i
$$216$$ −12.6377 + 4.89819i −0.859887 + 0.333280i
$$217$$ 2.46410 4.26795i 0.167274 0.289727i
$$218$$ 14.0524 + 24.3394i 0.951745 + 1.64847i
$$219$$ 1.33147 + 1.76295i 0.0899722 + 0.119129i
$$220$$ 1.66025i 0.111934i
$$221$$ 10.0782 15.1172i 0.677930 1.01690i
$$222$$ 8.68653 11.1430i 0.583002 0.747872i
$$223$$ 6.70577 25.0263i 0.449052 1.67588i −0.255960 0.966687i $$-0.582391\pi$$
0.705011 0.709196i $$-0.250942\pi$$
$$224$$ −1.84443 + 1.06488i −0.123236 + 0.0711505i
$$225$$ 2.24214 7.88351i 0.149476 0.525567i
$$226$$ 10.9545 + 10.9545i 0.728681 + 0.728681i
$$227$$ 5.24796 + 19.5856i 0.348319 + 1.29994i 0.888686 + 0.458515i $$0.151619\pi$$
−0.540367 + 0.841429i $$0.681715\pi$$
$$228$$ −0.698857 + 1.65136i −0.0462829 + 0.109364i
$$229$$ −14.1244 + 14.1244i −0.933364 + 0.933364i −0.997914 0.0645507i $$-0.979439\pi$$
0.0645507 + 0.997914i $$0.479439\pi$$
$$230$$ 0 0
$$231$$ −1.39183 + 9.98158i −0.0915757 + 0.656740i
$$232$$ −18.0622 4.83975i −1.18584 0.317745i
$$233$$ 17.4559 1.14357 0.571786 0.820403i $$-0.306251\pi$$
0.571786 + 0.820403i $$0.306251\pi$$
$$234$$ 13.4140 + 9.24205i 0.876899 + 0.604172i
$$235$$ −9.07180 −0.591779
$$236$$ −0.779548 0.208879i −0.0507443 0.0135969i
$$237$$ 0.478405 3.43091i 0.0310757 0.222861i
$$238$$ −9.29423 5.36603i −0.602455 0.347828i
$$239$$ 6.59817 6.59817i 0.426800 0.426800i −0.460737 0.887537i $$-0.652415\pi$$
0.887537 + 0.460737i $$0.152415\pi$$
$$240$$ −4.53819 + 10.7235i −0.292939 + 0.692198i
$$241$$ 3.76795 + 14.0622i 0.242715 + 0.905825i 0.974518 + 0.224309i $$0.0720123\pi$$
−0.731803 + 0.681516i $$0.761321\pi$$
$$242$$ 6.31284 + 6.31284i 0.405805 + 0.405805i
$$243$$ 9.95544 11.9954i 0.638642 0.769504i
$$244$$ 1.62436 0.937822i 0.103989 0.0600379i
$$245$$ 1.94887 7.27328i 0.124509 0.464673i
$$246$$ −9.01327 + 11.5622i −0.574665 + 0.737178i
$$247$$ −13.6603 + 2.73205i −0.869181 + 0.173836i
$$248$$ 9.08973i 0.577198i
$$249$$ −4.29488 5.68671i −0.272177 0.360380i
$$250$$ −8.76795 15.1865i −0.554534 0.960481i
$$251$$ 0.494214 0.856003i 0.0311945 0.0540304i −0.850007 0.526772i $$-0.823402\pi$$
0.881201 + 0.472741i $$0.156736\pi$$
$$252$$ 0.583396 0.975700i 0.0367505 0.0614634i
$$253$$ 0 0
$$254$$ −13.2728 + 3.55644i −0.832810 + 0.223151i
$$255$$ −13.0443 + 1.61594i −0.816867 + 0.101194i
$$256$$ −3.16025 + 5.47372i −0.197516 + 0.342108i
$$257$$ 10.7533 + 18.6252i 0.670770 + 1.16181i 0.977686 + 0.210071i $$0.0673696\pi$$
−0.306916 + 0.951737i $$0.599297\pi$$
$$258$$ −4.57125 + 3.45243i −0.284593 + 0.214939i
$$259$$ 7.66025i 0.475985i
$$260$$ 1.42667 0.285334i 0.0884784 0.0176957i
$$261$$ 20.8564 5.24796i 1.29098 0.324840i
$$262$$ 3.09808 11.5622i 0.191400 0.714314i
$$263$$ −19.3003 + 11.1430i −1.19011 + 0.687109i −0.958331 0.285660i $$-0.907787\pi$$
−0.231777 + 0.972769i $$0.574454\pi$$
$$264$$ 6.98197 + 17.2274i 0.429710 + 1.06027i
$$265$$ −0.830127 0.830127i −0.0509943 0.0509943i
$$266$$ 2.12976 + 7.94839i 0.130584 + 0.487347i
$$267$$ 14.8842 + 6.29899i 0.910896 + 0.385492i
$$268$$ −1.12436 + 1.12436i −0.0686810 + 0.0686810i
$$269$$ −12.4168 7.16884i −0.757066 0.437092i 0.0711756 0.997464i $$-0.477325\pi$$
−0.828241 + 0.560372i $$0.810658\pi$$
$$270$$ −1.26979 11.7160i −0.0772769 0.713013i
$$271$$ 7.46410 + 2.00000i 0.453412 + 0.121491i 0.478295 0.878199i $$-0.341255\pi$$
−0.0248835 + 0.999690i $$0.507921\pi$$
$$272$$ −22.4950 −1.36396
$$273$$ 8.81647 0.519441i 0.533597 0.0314380i
$$274$$ −10.1244 −0.611635
$$275$$ −10.8577 2.90931i −0.654744 0.175438i
$$276$$ 0 0
$$277$$ 23.8923 + 13.7942i 1.43555 + 0.828815i 0.997536 0.0701536i $$-0.0223490\pi$$
0.438013 + 0.898969i $$0.355682\pi$$
$$278$$ 19.5856 19.5856i 1.17467 1.17467i
$$279$$ 5.08808 + 9.13257i 0.304615 + 0.546752i
$$280$$ 1.43782 + 5.36603i 0.0859263 + 0.320681i
$$281$$ −12.1315 12.1315i −0.723703 0.723703i 0.245655 0.969357i $$-0.420997\pi$$
−0.969357 + 0.245655i $$0.920997\pi$$
$$282$$ 14.5623 5.90185i 0.867172 0.351450i
$$283$$ −5.70577 + 3.29423i −0.339173 + 0.195822i −0.659906 0.751348i $$-0.729404\pi$$
0.320733 + 0.947170i $$0.396071\pi$$
$$284$$ 0.208879 0.779548i 0.0123947 0.0462577i
$$285$$ 7.94839 + 6.19615i 0.470822 + 0.367028i
$$286$$ 12.3923 18.5885i 0.732772 1.09916i
$$287$$ 7.94839i 0.469179i
$$288$$ 0.0690922 4.51739i 0.00407129 0.266189i
$$289$$ −4.19615 7.26795i −0.246832 0.427526i
$$290$$ 8.12929 14.0803i 0.477368 0.826826i
$$291$$ −0.360213 2.90774i −0.0211161 0.170455i
$$292$$ −0.330127 + 0.0884573i −0.0193192 + 0.00517657i
$$293$$ −1.73999 + 0.466229i −0.101651 + 0.0272374i −0.309286 0.950969i $$-0.600090\pi$$
0.207635 + 0.978206i $$0.433423\pi$$
$$294$$ 1.60341 + 12.9432i 0.0935127 + 0.754860i
$$295$$ −2.26795 + 3.92820i −0.132045 + 0.228709i
$$296$$ −7.06440 12.2359i −0.410610 0.711198i
$$297$$ −16.6581 13.4003i −0.966601 0.777567i
$$298$$ 13.0000i 0.753070i
$$299$$ 0 0
$$300$$ 1.00000 + 0.779548i 0.0577350 + 0.0450072i
$$301$$ −0.803848 + 3.00000i −0.0463330 + 0.172917i
$$302$$ −0.988427 + 0.570669i −0.0568776 + 0.0328383i
$$303$$ −9.67552 + 3.92132i −0.555844 + 0.225274i
$$304$$ 12.1962 + 12.1962i 0.699497 + 0.699497i
$$305$$ −2.72842 10.1826i −0.156229 0.583054i
$$306$$ 19.8878 11.0802i 1.13691 0.633414i
$$307$$ 8.39230 8.39230i 0.478974 0.478974i −0.425829 0.904803i $$-0.640018\pi$$
0.904803 + 0.425829i $$0.140018\pi$$
$$308$$ −1.35022 0.779548i −0.0769357 0.0444189i
$$309$$ −11.8850 1.65724i −0.676115 0.0942773i
$$310$$ 7.63397 + 2.04552i 0.433581 + 0.116178i
$$311$$ 10.0782 0.571480 0.285740 0.958307i $$-0.407761\pi$$
0.285740 + 0.958307i $$0.407761\pi$$
$$312$$ 13.6037 8.96040i 0.770159 0.507283i
$$313$$ 2.00000 0.113047 0.0565233 0.998401i $$-0.481998\pi$$
0.0565233 + 0.998401i $$0.481998\pi$$
$$314$$ 6.98795 + 1.87241i 0.394353 + 0.105666i
$$315$$ −4.44829 4.58648i −0.250633 0.258419i
$$316$$ 0.464102 + 0.267949i 0.0261078 + 0.0150733i
$$317$$ −11.3519 + 11.3519i −0.637587 + 0.637587i −0.949960 0.312373i $$-0.898876\pi$$
0.312373 + 0.949960i $$0.398876\pi$$
$$318$$ 1.87260 + 0.792486i 0.105010 + 0.0444404i
$$319$$ −7.63397 28.4904i −0.427421 1.59516i
$$320$$ 7.09239 + 7.09239i 0.396477 + 0.396477i
$$321$$ −12.3706 30.5234i −0.690460 1.70365i
$$322$$ 0 0
$$323$$ −5.03908 + 18.8061i −0.280382 + 1.04640i
$$324$$ 1.14134 + 2.12436i 0.0634076 + 0.118020i
$$325$$ −0.633975 + 9.83013i −0.0351666 + 0.545277i
$$326$$ 6.23638i 0.345401i
$$327$$ −25.7939 + 19.4808i −1.42641 + 1.07729i
$$328$$ 7.33013 + 12.6962i 0.404739 + 0.701028i
$$329$$ 4.25953 7.37772i 0.234835 0.406747i
$$330$$ −16.0396 + 1.98699i −0.882948 + 0.109380i
$$331$$ −33.0526 + 8.85641i −1.81673 + 0.486792i −0.996376 0.0850595i $$-0.972892\pi$$
−0.820357 + 0.571852i $$0.806225\pi$$
$$332$$ 1.06488 0.285334i 0.0584430 0.0156598i
$$333$$ 13.9469 + 8.33919i 0.764285 + 0.456985i
$$334$$ −10.1244 + 17.5359i −0.553980 + 0.959522i
$$335$$ 4.46841 + 7.73951i 0.244135 + 0.422855i
$$336$$ −6.59014 8.72579i −0.359521 0.476031i
$$337$$ 18.4641i 1.00580i 0.864344 + 0.502902i $$0.167734\pi$$
−0.864344 + 0.502902i $$0.832266\pi$$
$$338$$ −18.1030 7.45418i −0.984673 0.405454i
$$339$$ −10.9545 + 14.0524i −0.594966 + 0.763219i
$$340$$ 0.526279 1.96410i 0.0285415 0.106518i
$$341$$ 12.4168 7.16884i 0.672407 0.388215i
$$342$$ −16.7900 4.77524i −0.907900 0.258215i
$$343$$ 12.0000 + 12.0000i 0.647939 + 0.647939i
$$344$$ 1.48264 + 5.53329i 0.0799386 + 0.298335i
$$345$$ 0 0
$$346$$ 18.5885 18.5885i 0.999322 0.999322i
$$347$$ 17.8177 + 10.2870i 0.956502 + 0.552237i 0.895095 0.445876i $$-0.147108\pi$$
0.0614076 + 0.998113i $$0.480441\pi$$
$$348$$ −0.459481 + 3.29519i −0.0246308 + 0.176641i
$$349$$ 27.4904 + 7.36603i 1.47153 + 0.394294i 0.903454 0.428684i $$-0.141023\pi$$
0.568072 + 0.822979i $$0.307689\pi$$
$$350$$ 5.81863 0.311019
$$351$$ −8.65215 + 16.6175i −0.461818 + 0.886975i
$$352$$ −6.19615 −0.330256
$$353$$ 13.6626 + 3.66088i 0.727186 + 0.194849i 0.603376 0.797457i $$-0.293822\pi$$
0.123810 + 0.992306i $$0.460489\pi$$
$$354$$ 1.08500 7.78112i 0.0576670 0.413562i
$$355$$ −3.92820 2.26795i −0.208487 0.120370i
$$356$$ −1.76798 + 1.76798i −0.0937025 + 0.0937025i
$$357$$ 4.81059 11.3671i 0.254603 0.601613i
$$358$$ 10.3468 + 38.6147i 0.546845 + 2.04085i
$$359$$ 18.2354 + 18.2354i 0.962429 + 0.962429i 0.999319 0.0368904i $$-0.0117452\pi$$
−0.0368904 + 0.999319i $$0.511745\pi$$
$$360$$ −11.3351 3.22381i −0.597411 0.169909i
$$361$$ −3.52628 + 2.03590i −0.185594 + 0.107153i
$$362$$ −1.16932 + 4.36397i −0.0614582 + 0.229365i
$$363$$ −6.31284 + 8.09808i −0.331338 + 0.425039i
$$364$$ −0.437822 + 1.29423i −0.0229481 + 0.0678360i
$$365$$ 1.92089i 0.100544i
$$366$$ 11.0042 + 14.5704i 0.575201 + 0.761605i
$$367$$ −15.1962 26.3205i −0.793233 1.37392i −0.923955 0.382500i $$-0.875063\pi$$
0.130723 0.991419i $$-0.458270\pi$$
$$368$$ 0 0
$$369$$ −14.4715 8.65286i −0.753356 0.450450i
$$370$$ 11.8660 3.17949i 0.616885 0.165294i
$$371$$ 1.06488 0.285334i 0.0552859 0.0148138i
$$372$$ −1.60502 + 0.198831i −0.0832162 + 0.0103089i
$$373$$ −5.79423 + 10.0359i −0.300014 + 0.519639i −0.976139 0.217148i $$-0.930325\pi$$
0.676125 + 0.736787i $$0.263658\pi$$
$$374$$ −15.6114 27.0398i −0.807249 1.39820i
$$375$$ 16.0941 12.1550i 0.831096 0.627684i
$$376$$ 15.7128i 0.810326i
$$377$$ −23.1701 + 11.4564i −1.19332 + 0.590032i
$$378$$ 10.1244 + 4.46841i 0.520741 + 0.229830i
$$379$$ 3.83013 14.2942i 0.196740 0.734245i −0.795069 0.606519i $$-0.792565\pi$$
0.991809 0.127726i $$-0.0407679\pi$$
$$380$$ −1.35022 + 0.779548i −0.0692647 + 0.0399900i
$$381$$ −5.93605 14.6467i −0.304113 0.750372i
$$382$$ −5.14359 5.14359i −0.263169 0.263169i
$$383$$ −8.51906 31.7936i −0.435304 1.62458i −0.740339 0.672234i $$-0.765335\pi$$
0.305035 0.952341i $$-0.401332\pi$$
$$384$$ −20.8033 8.80399i −1.06162 0.449277i
$$385$$ −6.19615 + 6.19615i −0.315785 + 0.315785i
$$386$$ −0.180895 0.104440i −0.00920730 0.00531584i
$$387$$ −4.58695 4.72944i −0.233168 0.240411i
$$388$$ 0.437822 + 0.117314i 0.0222271 + 0.00595572i
$$389$$ 22.4950 1.14054 0.570270 0.821457i $$-0.306839\pi$$
0.570270 + 0.821457i $$0.306839\pi$$
$$390$$ 4.46403 + 13.4415i 0.226045 + 0.680634i
$$391$$ 0 0
$$392$$ 12.5977 + 3.37554i 0.636280 + 0.170491i
$$393$$ 13.6351 + 1.90128i 0.687800 + 0.0959066i
$$394$$ 5.36603 + 3.09808i 0.270336 + 0.156079i
$$395$$ 2.12976 2.12976i 0.107160 0.107160i
$$396$$ 2.88920 1.60968i 0.145188 0.0808892i
$$397$$ −3.56218 13.2942i −0.178781 0.667218i −0.995877 0.0907168i $$-0.971084\pi$$
0.817096 0.576501i $$-0.195582\pi$$
$$398$$ −13.7670 13.7670i −0.690078 0.690078i
$$399$$ −8.77113 + 3.55479i −0.439106 + 0.177962i
$$400$$ 10.5622 6.09808i 0.528109 0.304904i
$$401$$ −3.22263 + 12.0270i −0.160931 + 0.600601i 0.837594 + 0.546294i $$0.183962\pi$$
−0.998524 + 0.0543073i $$0.982705\pi$$
$$402$$ −12.2079 9.51666i −0.608876 0.474648i
$$403$$ −8.29423 9.43782i −0.413165 0.470131i
$$404$$ 1.61507i 0.0803525i
$$405$$ 13.1931 3.10594i 0.655569 0.154336i
$$406$$ 7.63397 + 13.2224i 0.378868 + 0.656218i
$$407$$ 11.1430 19.3003i 0.552340 0.956681i
$$408$$ −2.79889 22.5934i −0.138566 1.11854i
$$409$$ 28.9904 7.76795i 1.43348 0.384100i 0.543236 0.839580i $$-0.317199\pi$$
0.890246 + 0.455480i $$0.150532\pi$$
$$410$$ −12.3124 + 3.29909i −0.608064 + 0.162930i
$$411$$ −1.43156 11.5559i −0.0706135 0.570011i
$$412$$ 0.928203 1.60770i 0.0457293 0.0792055i
$$413$$ −2.12976 3.68886i −0.104799 0.181517i
$$414$$ 0 0
$$415$$ 6.19615i 0.304157i
$$416$$ 1.06488 + 5.32441i 0.0522102 + 0.261051i
$$417$$ 25.1244 + 19.5856i 1.23034 + 0.959113i
$$418$$ −6.19615 + 23.1244i −0.303064 + 1.13105i
$$419$$ −8.23373 + 4.75374i −0.402244 + 0.232236i −0.687452 0.726230i $$-0.741271\pi$$
0.285208 + 0.958466i $$0.407937\pi$$
$$420$$ 0.916053 0.371261i 0.0446988 0.0181157i
$$421$$ −7.83013 7.83013i −0.381617 0.381617i 0.490067 0.871685i $$-0.336972\pi$$
−0.871685 + 0.490067i $$0.836972\pi$$
$$422$$ −0.703093 2.62398i −0.0342260 0.127733i
$$423$$ 8.79543 + 15.7869i 0.427648 + 0.767584i
$$424$$ 1.43782 1.43782i 0.0698268 0.0698268i
$$425$$ 11.9226 + 6.88351i 0.578330 + 0.333899i
$$426$$ 7.78112 + 1.08500i 0.376997 + 0.0525683i
$$427$$ 9.56218 + 2.56218i 0.462746 + 0.123992i
$$428$$ 5.09505 0.246278
$$429$$ 22.9691 + 11.5162i 1.10896 + 0.556007i
$$430$$ −4.98076 −0.240194
$$431$$ −36.5473 9.79282i −1.76042 0.471704i −0.773622 0.633648i $$-0.781557\pi$$
−0.986800 + 0.161944i $$0.948224\pi$$
$$432$$ 23.0611 2.49938i 1.10953 0.120252i
$$433$$ −26.8923 15.5263i −1.29236 0.746145i −0.313289 0.949658i $$-0.601431\pi$$
−0.979072 + 0.203512i $$0.934764\pi$$
$$434$$ −5.24796 + 5.24796i −0.251910 + 0.251910i
$$435$$ 17.2207 + 7.28782i 0.825670 + 0.349424i
$$436$$ −1.29423 4.83013i −0.0619823 0.231321i
$$437$$ 0 0
$$438$$ −1.24967 3.08346i −0.0597117 0.147333i
$$439$$ 1.09808 0.633975i 0.0524083 0.0302580i −0.473567 0.880758i $$-0.657034\pi$$
0.525975 + 0.850500i $$0.323700\pi$$
$$440$$ −4.18307 + 15.6114i −0.199420 + 0.744247i
$$441$$ −14.5466 + 3.66025i −0.692694 + 0.174298i
$$442$$ −20.5526 + 18.0622i −0.977586 + 0.859130i
$$443$$ 11.2195i 0.533054i −0.963827 0.266527i $$-0.914124\pi$$
0.963827 0.266527i $$-0.0858762\pi$$
$$444$$ −2.00602 + 1.51505i −0.0952017 + 0.0719009i
$$445$$ 7.02628 + 12.1699i 0.333078 + 0.576907i
$$446$$ −19.5092 + 33.7909i −0.923787 + 1.60005i
$$447$$ 14.8382 1.83816i 0.701821 0.0869422i
$$448$$ −9.09808 + 2.43782i −0.429844 + 0.115176i
$$449$$ −19.8710 + 5.32441i −0.937769 + 0.251275i −0.695165 0.718851i $$-0.744669\pi$$
−0.242605 + 0.970125i $$0.578002\pi$$
$$450$$ −6.33434 + 10.5939i −0.298603 + 0.499400i
$$451$$ −11.5622 + 20.0263i −0.544442 + 0.943001i
$$452$$ −1.37820 2.38711i −0.0648251 0.112280i
$$453$$ −0.791121 1.04750i −0.0371701 0.0492157i
$$454$$ 30.5359i 1.43312i
$$455$$ 6.38929 + 4.25953i 0.299535 + 0.199690i
$$456$$ −10.7321 + 13.7670i −0.502574 + 0.644700i
$$457$$ −1.00962 + 3.76795i −0.0472280 + 0.176257i −0.985511 0.169611i $$-0.945749\pi$$
0.938283 + 0.345868i $$0.112416\pi$$
$$458$$ 26.0514 15.0408i 1.21730 0.702809i
$$459$$ 15.4590 + 21.1332i 0.721565 + 0.986412i
$$460$$ 0 0
$$461$$ −5.50531 20.5461i −0.256408 0.956927i −0.967302 0.253628i $$-0.918376\pi$$
0.710894 0.703299i $$-0.248290\pi$$
$$462$$ 5.91520 13.9773i 0.275200 0.650282i
$$463$$ 23.0526 23.0526i 1.07134 1.07134i 0.0740918 0.997251i $$-0.476394\pi$$
0.997251 0.0740918i $$-0.0236058\pi$$
$$464$$ 27.7149 + 16.0012i 1.28663 + 0.742838i
$$465$$ −1.25532 + 9.00263i −0.0582143 + 0.417487i
$$466$$ −25.3923 6.80385i −1.17628 0.315182i
$$467$$ −19.1679 −0.886984 −0.443492 0.896278i $$-0.646261\pi$$
−0.443492 + 0.896278i $$0.646261\pi$$
$$468$$ −1.87975 2.20607i −0.0868916 0.101976i
$$469$$ −8.39230 −0.387521
$$470$$ 13.1963 + 3.53595i 0.608702 + 0.163101i
$$471$$ −1.14909 + 8.24078i −0.0529474 + 0.379715i
$$472$$ −6.80385 3.92820i −0.313172 0.180810i
$$473$$ −6.38929 + 6.38929i −0.293780 + 0.293780i
$$474$$ −2.03319 + 4.80432i −0.0933877 + 0.220670i
$$475$$ −2.73205 10.1962i −0.125355 0.467832i
$$476$$ 1.35022 + 1.35022i 0.0618871 + 0.0618871i
$$477$$ −0.639761 + 2.24944i −0.0292926 + 0.102995i
$$478$$ −12.1699 + 7.02628i −0.556637 + 0.321375i
$$479$$ 5.32441 19.8710i 0.243279 0.907928i −0.730962 0.682418i $$-0.760928\pi$$
0.974241 0.225510i $$-0.0724049\pi$$
$$480$$ 2.41510 3.09808i 0.110234 0.141407i
$$481$$ −18.5000 6.25833i −0.843527 0.285355i
$$482$$ 21.9243i 0.998624i
$$483$$ 0 0
$$484$$ −0.794229 1.37564i −0.0361013 0.0625293i
$$485$$ 1.27376 2.20622i 0.0578385 0.100179i
$$486$$ −19.1572 + 13.5688i −0.868990 + 0.615492i
$$487$$ 5.56218 1.49038i 0.252046 0.0675356i −0.130584 0.991437i $$-0.541685\pi$$
0.382630 + 0.923902i $$0.375018\pi$$
$$488$$ 17.6368 4.72576i 0.798379 0.213925i
$$489$$ −7.11819 + 0.881808i −0.321896 + 0.0398767i
$$490$$ −5.66987 + 9.82051i −0.256139 + 0.443645i
$$491$$ 14.2612 + 24.7012i 0.643600 + 1.11475i 0.984623 + 0.174693i $$0.0558934\pi$$
−0.341023 + 0.940055i $$0.610773\pi$$
$$492$$ 2.08148 1.57203i 0.0938403 0.0708728i
$$493$$ 36.1244i 1.62696i
$$494$$ 20.9359 + 1.35022i 0.941949 + 0.0607491i
$$495$$ −4.53590 18.0265i −0.203873 0.810233i
$$496$$ −4.02628 + 15.0263i −0.180785 + 0.674700i
$$497$$ 3.68886 2.12976i 0.165468 0.0955330i
$$498$$ 4.03104 + 9.94624i 0.180635 + 0.445702i
$$499$$ −2.46410 2.46410i −0.110308 0.110308i 0.649798 0.760107i $$-0.274853\pi$$
−0.760107 + 0.649798i $$0.774853\pi$$
$$500$$ 0.807533 + 3.01375i 0.0361140 + 0.134779i
$$501$$ −21.4470 9.07638i −0.958181 0.405503i
$$502$$ −1.05256 + 1.05256i −0.0469780 + 0.0469780i
$$503$$ −2.83286 1.63555i −0.126311 0.0729256i 0.435513 0.900182i $$-0.356567\pi$$
−0.561824 + 0.827257i $$0.689900\pi$$
$$504$$ 7.94401 7.70467i 0.353854 0.343193i
$$505$$ −8.76795 2.34936i −0.390169 0.104545i
$$506$$ 0 0
$$507$$ 5.94846 21.7167i 0.264180 0.964473i
$$508$$ 2.44486 0.108473
$$509$$ 14.1568 + 3.79330i 0.627489 + 0.168135i 0.558530 0.829484i $$-0.311366\pi$$
0.0689588 + 0.997620i $$0.478032\pi$$
$$510$$ 19.6048 + 2.73370i 0.868117 + 0.121050i
$$511$$ −1.56218 0.901924i −0.0691067 0.0398988i
$$512$$ −11.7137 + 11.7137i −0.517678 + 0.517678i
$$513$$ 3.07638 19.8393i 0.135826 0.875926i
$$514$$ −8.38269 31.2846i −0.369744 1.37990i
$$515$$ −7.37772 7.37772i −0.325101 0.325101i
$$516$$ 0.944608 0.382834i 0.0415841 0.0168533i
$$517$$ 21.4641 12.3923i 0.943990 0.545013i
$$518$$ −2.98577 + 11.1430i −0.131187 + 0.489597i
$$519$$ 23.8452 + 18.5885i 1.04669 + 0.815943i
$$520$$ 14.1340 + 0.911543i 0.619816 + 0.0399738i
$$521$$ 2.49155i 0.109157i −0.998509 0.0545785i $$-0.982618\pi$$
0.998509 0.0545785i $$-0.0173815\pi$$
$$522$$ −32.3844 0.495311i −1.41743 0.0216792i
$$523$$ 19.4904 + 33.7583i 0.852255 + 1.47615i 0.879169 + 0.476511i $$0.158099\pi$$
−0.0269137 + 0.999638i $$0.508568\pi$$
$$524$$ −1.06488 + 1.84443i −0.0465196 + 0.0805743i
$$525$$ 0.822738 + 6.64136i 0.0359072 + 0.289853i
$$526$$ 32.4186 8.68653i 1.41352 0.378751i
$$527$$ −16.9617 + 4.54486i −0.738862 + 0.197977i
$$528$$ −3.91108 31.5713i −0.170208 1.37397i
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ 0.883988 + 1.53111i 0.0383980 + 0.0665072i
$$531$$ 9.03477 + 0.138184i 0.392076 + 0.00599669i
$$532$$ 1.46410i 0.0634769i
$$533$$ 19.1959 + 6.49373i 0.831465 + 0.281275i
$$534$$ −19.1962 14.9643i −0.830699 0.647570i
$$535$$ 7.41154 27.6603i 0.320429 1.19586i
$$536$$ −13.4052 + 7.73951i −0.579018 + 0.334296i
$$537$$ −42.6117 + 17.2698i −1.83883 + 0.745247i
$$538$$ 15.2679 + 15.2679i 0.658248 + 0.658248i
$$539$$ 5.32441 + 19.8710i 0.229339 + 0.855904i
$$540$$ −0.321296 + 2.07201i −0.0138264 + 0.0891650i
$$541$$ −12.6865 + 12.6865i −0.545437 + 0.545437i −0.925118 0.379681i $$-0.876034\pi$$
0.379681 + 0.925118i $$0.376034\pi$$
$$542$$ −10.0782 5.81863i −0.432894 0.249931i
$$543$$ −5.14636 0.717608i −0.220852 0.0307955i
$$544$$ 7.33013 + 1.96410i 0.314277 + 0.0842102i
$$545$$ −28.1047 −1.20387
$$546$$ −13.0274 2.68082i −0.557521 0.114729i
$$547$$ 2.00000 0.0855138 0.0427569 0.999086i $$-0.486386\pi$$
0.0427569 + 0.999086i $$0.486386\pi$$
$$548$$ 1.73999 + 0.466229i 0.0743287 + 0.0199163i
$$549$$ −15.0746 + 14.6204i −0.643368 + 0.623984i
$$550$$ 14.6603 + 8.46410i 0.625115 + 0.360911i
$$551$$ 19.5856 19.5856i 0.834376 0.834376i
$$552$$ 0 0
$$553$$ 0.732051 + 2.73205i 0.0311300 + 0.116179i
$$554$$ −29.3785 29.3785i −1.24817 1.24817i
$$555$$ 5.30689 + 13.0943i 0.225265 + 0.555821i
$$556$$ −4.26795 + 2.46410i −0.181001 + 0.104501i
$$557$$ 6.62616 24.7292i 0.280759 1.04781i −0.671123 0.741346i $$-0.734188\pi$$
0.951883 0.306462i $$-0.0991454\pi$$
$$558$$ −3.84177 15.2679i −0.162635 0.646344i
$$559$$ 6.58846 + 4.39230i 0.278662 + 0.185775i
$$560$$ 9.50749i 0.401765i
$$561$$ 28.6558 21.6422i 1.20985 0.913735i
$$562$$ 12.9186 + 22.3756i 0.544938 + 0.943860i
$$563$$ 5.03908 8.72794i 0.212372 0.367839i −0.740085 0.672514i $$-0.765215\pi$$
0.952456 + 0.304675i $$0.0985479\pi$$
$$564$$ −2.77449 + 0.343706i −0.116827 + 0.0144726i
$$565$$ −14.9641 + 4.00962i −0.629544 + 0.168686i
$$566$$ 9.58394 2.56801i 0.402843 0.107941i
$$567$$ −3.66867 + 12.1877i −0.154070 + 0.511837i
$$568$$ 3.92820 6.80385i 0.164824 0.285483i
$$569$$ 1.35022 + 2.33864i 0.0566040 + 0.0980411i 0.892939 0.450178i $$-0.148639\pi$$
−0.836335 + 0.548219i $$0.815306\pi$$
$$570$$ −9.14708 12.1113i −0.383129 0.507289i
$$571$$ 1.94744i 0.0814979i −0.999169 0.0407489i $$-0.987026\pi$$
0.999169 0.0407489i $$-0.0129744\pi$$
$$572$$ −2.98577 + 2.62398i −0.124841 + 0.109714i
$$573$$ 5.14359 6.59817i 0.214877 0.275643i
$$574$$ 3.09808 11.5622i 0.129311 0.482596i
$$575$$ 0 0
$$576$$ 5.46595 19.2186i 0.227748 0.800775i
$$577$$ −22.4904 22.4904i −0.936287 0.936287i 0.0618016 0.998088i $$-0.480315\pi$$
−0.998088 + 0.0618016i $$0.980315\pi$$
$$578$$ 3.27110 + 12.2079i 0.136060 + 0.507783i
$$579$$ 0.0936291 0.221240i 0.00389109 0.00919443i
$$580$$ −2.04552 + 2.04552i −0.0849355 + 0.0849355i
$$581$$ 5.03908 + 2.90931i 0.209056 + 0.120699i
$$582$$ −0.609374 + 4.37016i −0.0252594 + 0.181149i
$$583$$ 3.09808 + 0.830127i 0.128309 + 0.0343803i
$$584$$ −3.32707 −0.137675
$$585$$ −14.7108 + 6.99582i −0.608218 + 0.289241i
$$586$$ 2.71281 0.112065
$$587$$ 18.0265 + 4.83020i 0.744035 + 0.199364i 0.610871 0.791730i $$-0.290819\pi$$
0.133164 + 0.991094i $$0.457486\pi$$
$$588$$ 0.320471 2.29827i 0.0132160 0.0947792i
$$589$$ 11.6603 + 6.73205i 0.480452 + 0.277389i
$$590$$ 4.83020 4.83020i 0.198856 0.198856i
$$591$$ −2.77739 + 6.56283i −0.114247 + 0.269959i
$$592$$ 6.25833 + 23.3564i 0.257216 + 0.959942i
$$593$$ 10.3635 + 10.3635i 0.425578 + 0.425578i 0.887119 0.461541i $$-0.152703\pi$$
−0.461541 + 0.887119i $$0.652703\pi$$
$$594$$ 19.0087 + 25.9858i 0.779937 + 1.06621i
$$595$$ 9.29423 5.36603i 0.381026 0.219986i
$$596$$ −0.598653 + 2.23420i −0.0245218 + 0.0915166i
$$597$$ 13.7670 17.6603i 0.563446 0.722786i
$$598$$ 0 0
$$599$$ 20.7270i 0.846881i 0.905924 + 0.423441i $$0.139178\pi$$
−0.905924 + 0.423441i $$0.860822\pi$$
$$600$$ 7.43895 + 9.84967i 0.303694 + 0.402111i
$$601$$ −11.7942 20.4282i −0.481097 0.833284i 0.518668 0.854976i $$-0.326428\pi$$
−0.999765 + 0.0216919i $$0.993095\pi$$
$$602$$ 2.33864 4.05065i 0.0953160 0.165092i
$$603$$ 9.13612 15.2797i 0.372052 0.622238i
$$604$$ 0.196152 0.0525589i 0.00798133 0.00213859i
$$605$$ −8.62350 + 2.31066i −0.350595 + 0.0939417i
$$606$$ 15.6030 1.93291i 0.633828 0.0785192i
$$607$$ 0.0980762 0.169873i 0.00398079 0.00689493i −0.864028 0.503444i $$-0.832066\pi$$
0.868009 + 0.496549i $$0.165400\pi$$
$$608$$ −2.90931 5.03908i −0.117988 0.204362i
$$609$$ −14.0126 + 10.5830i −0.567820 + 0.428845i
$$610$$ 15.8756i 0.642786i
$$611$$ −14.3377 16.3145i −0.580041 0.660016i
$$612$$ −3.92820 + 0.988427i −0.158788 + 0.0399548i
$$613$$ −11.3564 + 42.3827i −0.458681 + 1.71182i 0.218354 + 0.975870i $$0.429931\pi$$
−0.677035 + 0.735951i $$0.736735\pi$$
$$614$$ −15.4790 + 8.93682i −0.624683 + 0.360661i
$$615$$ −5.50650 13.5868i −0.222044 0.547873i
$$616$$ −10.7321 10.7321i −0.432407 0.432407i
$$617$$ −4.78173 17.8457i −0.192505 0.718439i −0.992899 0.118964i $$-0.962043\pi$$
0.800393 0.599475i $$-0.204624\pi$$
$$618$$ 16.6427 + 7.04319i 0.669466 + 0.283319i
$$619$$ −31.6603 + 31.6603i −1.27253 + 1.27253i −0.327778 + 0.944755i $$0.606300\pi$$
−0.944755 + 0.327778i $$0.893700\pi$$
$$620$$ −1.21779 0.703093i −0.0489077 0.0282369i
$$621$$ 0 0
$$622$$ −14.6603 3.92820i −0.587823 0.157507i
$$623$$ −13.1963 −0.528701
$$624$$ −26.4574 + 8.78674i −1.05914 + 0.351751i
$$625$$ 3.87564 0.155026
$$626$$ −2.90931 0.779548i −0.116280 0.0311570i
$$627$$ −27.2702 3.80255i −1.08907 0.151859i
$$628$$ −1.11474 0.643594i −0.0444828 0.0256822i
$$629$$ −19.3003 + 19.3003i −0.769554 + 0.769554i
$$630$$ 4.68305 + 8.40558i 0.186577 + 0.334886i
$$631$$ 5.73205 + 21.3923i 0.228189 + 0.851614i 0.981102 + 0.193493i $$0.0619818\pi$$
−0.752912 + 0.658121i $$0.771352\pi$$
$$632$$ 3.68886 + 3.68886i 0.146735 + 0.146735i
$$633$$ 2.89559 1.17353i 0.115089 0.0466437i
$$634$$ 20.9378 12.0885i 0.831547 0.480094i
$$635$$ 3.55644 13.2728i 0.141133 0.526715i
$$636$$ −0.285334 0.222432i −0.0113142 0.00882000i
$$637$$ 16.1603 7.99038i 0.640293 0.316590i
$$638$$ 44.4192i 1.75857i
$$639$$ −0.138184 + 9.03477i −0.00546649 + 0.357410i
$$640$$ −9.82051 17.0096i −0.388190 0.672364i
$$641$$ −22.6758 + 39.2757i −0.895642 + 1.55130i −0.0626345 + 0.998037i $$0.519950\pi$$
−0.833008 + 0.553261i $$0.813383\pi$$
$$642$$ 6.09776 + 49.2228i 0.240659 + 1.94267i
$$643$$ 7.00000 1.87564i 0.276053 0.0739682i −0.118136 0.992997i $$-0.537692\pi$$
0.394190 + 0.919029i $$0.371025\pi$$
$$644$$ 0 0
$$645$$ −0.704266 5.68503i −0.0277305 0.223848i
$$646$$ 14.6603 25.3923i 0.576800 0.999047i
$$647$$ 8.23373 + 14.2612i 0.323701 + 0.560667i 0.981249 0.192746i $$-0.0617394\pi$$
−0.657547 + 0.753413i $$0.728406\pi$$
$$648$$ 5.37965 + 22.8511i 0.211333 + 0.897674i
$$649$$ 12.3923i 0.486441i
$$650$$ 4.75374 14.0524i 0.186457 0.551179i
$$651$$ −6.73205 5.24796i −0.263850 0.205684i
$$652$$ 0.287187 1.07180i 0.0112471 0.0419748i
$$653$$ 8.36615 4.83020i 0.327393 0.189020i −0.327290 0.944924i $$-0.606135\pi$$
0.654683 + 0.755904i $$0.272802\pi$$
$$654$$ 45.1145 18.2841i 1.76411 0.714966i
$$655$$ 8.46410 + 8.46410i 0.330720 + 0.330720i
$$656$$ −6.49373 24.2349i −0.253538 0.946216i
$$657$$ 3.34275 1.86237i 0.130413 0.0726578i
$$658$$ −9.07180 + 9.07180i −0.353655 + 0.353655i
$$659$$ −23.4834 13.5581i −0.914783 0.528150i −0.0328158 0.999461i $$-0.510447\pi$$
−0.881967 + 0.471311i $$0.843781\pi$$
$$660$$ 2.84809 + 0.397137i 0.110862 + 0.0154585i
$$661$$ 9.42820 + 2.52628i 0.366715 + 0.0982609i 0.437470 0.899233i $$-0.355874\pi$$
−0.0707559 + 0.997494i $$0.522541\pi$$
$$662$$ 51.5321 2.00285
$$663$$ −23.5222 20.9047i −0.913526 0.811871i
$$664$$ 10.7321 0.416484
$$665$$ −7.94839 2.12976i −0.308225 0.0825887i
$$666$$ −17.0375 17.5668i −0.660191 0.680699i
$$667$$ 0 0
$$668$$ 2.54752 2.54752i 0.0985666 0.0985666i
$$669$$ −41.3274 17.4898i −1.59781 0.676194i
$$670$$ −3.48334 13.0000i −0.134573 0.502234i
$$671$$ 20.3652 + 20.3652i 0.786189 + 0.786189i
$$672$$ 1.38556 + 3.41876i 0.0534493 + 0.131881i
$$673$$ −36.9904 + 21.3564i −1.42587 + 0.823229i −0.996792 0.0800364i $$-0.974496\pi$$
−0.429082 + 0.903265i $$0.641163\pi$$
$$674$$ 7.19683 26.8589i 0.277211 1.03457i
$$675$$ −12.9875 5.73205i −0.499888 0.220627i
$$676$$ 2.76795 + 2.11474i 0.106460 + 0.0813360i
$$677$$ 9.66040i 0.371279i 0.982618 + 0.185640i $$0.0594357\pi$$
−0.982618 + 0.185640i $$0.940564\pi$$
$$678$$ 21.4123 16.1716i 0.822333 0.621065i
$$679$$ 1.19615 + 2.07180i 0.0459041 + 0.0795083i
$$680$$ 9.89726 17.1426i 0.379543 0.657387i
$$681$$ 34.8536 4.31769i 1.33559 0.165454i
$$682$$ −20.8564 + 5.58846i −0.798633 + 0.213993i
$$683$$ 45.2752 12.1315i 1.73241 0.464198i 0.751673 0.659536i $$-0.229247\pi$$
0.980736 + 0.195338i $$0.0625804\pi$$
$$684$$ 2.66566 + 1.59387i 0.101924 + 0.0609430i
$$685$$ 5.06218 8.76795i 0.193416 0.335006i
$$686$$ −12.7786 22.1332i −0.487889 0.845048i
$$687$$ 20.8511 + 27.6083i 0.795519 + 1.05332i
$$688$$ 9.80385i 0.373768i
$$689$$ 0.180895 2.80487i 0.00689154 0.106857i
$$690$$ 0 0
$$691$$ 4.88269 18.2224i 0.185746 0.693214i −0.808723 0.588189i $$-0.799841\pi$$
0.994470 0.105025i $$-0.0334922\pi$$
$$692$$ −4.05065 + 2.33864i −0.153983 + 0.0889019i
$$693$$ 16.7900 + 4.77524i 0.637800 + 0.181396i
$$694$$ −21.9090 21.9090i −0.831653 0.831653i
$$695$$ 7.16884 + 26.7545i 0.271930 + 1.01486i
$$696$$ −12.6229 + 29.8272i −0.478469 + 1.13060i
$$697$$ 20.0263 20.0263i 0.758549 0.758549i
$$698$$ −37.1180 21.4301i −1.40494 0.811140i
$$699$$ 4.17549 29.9448i 0.157932 1.13261i
$$700$$ −1.00000 0.267949i −0.0377964 0.0101275i
$$701$$ 12.7786 0.482641 0.241320 0.970446i $$-0.422420\pi$$
0.241320 + 0.970446i $$0.422420\pi$$
$$702$$ 19.0630 20.8003i 0.719485 0.785058i
$$703$$ 20.9282 0.789322
$$704$$ −26.4692 7.09239i −0.997594 0.267304i
$$705$$ −2.17000 + 15.5622i −0.0817268 + 0.586108i
$$706$$ −18.4474 10.6506i −0.694279 0.400842i
$$707$$ 6.02751 6.02751i 0.226688 0.226688i
$$708$$ −0.544793 + 1.28731i −0.0204746 + 0.0483802i
$$709$$ −3.03590 11.3301i −0.114016 0.425512i 0.885196 0.465219i $$-0.154024\pi$$
−0.999211 + 0.0397068i $$0.987358\pi$$
$$710$$ 4.83020 + 4.83020i 0.181274 + 0.181274i
$$711$$ −5.77113 1.64136i −0.216434 0.0615559i
$$712$$ −21.0788 + 12.1699i −0.789963 + 0.456085i
$$713$$ 0 0
$$714$$ −11.4284 + 14.6603i −0.427696 + 0.548646i
$$715$$ 9.90192 + 20.0263i 0.370311 + 0.748940i
$$716$$ 7.11287i 0.265821i
$$717$$ −9.74056 12.8972i −0.363768 0.481653i
$$718$$ −19.4186 33.6340i −0.724695 1.25521i
$$719$$ 3.68886 6.38929i 0.137571 0.238280i −0.789005 0.614386i $$-0.789404\pi$$
0.926577 + 0.376106i $$0.122737\pi$$
$$720$$ 17.3101 + 10.3501i 0.645110 + 0.385727i
$$721$$ 9.46410 2.53590i 0.352462 0.0944418i
$$722$$ 5.92307 1.58708i 0.220434 0.0590650i
$$723$$ 25.0243 3.10003i 0.930665 0.115292i
$$724$$ 0.401924 0.696152i 0.0149374 0.0258723i
$$725$$ −9.79282 16.9617i −0.363696 0.629940i
$$726$$ 12.3394 9.31934i 0.457959 0.345873i
$$727$$ 19.5167i 0.723833i 0.932211 + 0.361916i $$0.117877\pi$$
−0.932211 + 0.361916i $$0.882123\pi$$
$$728$$ −7.37772 + 11.0666i −0.273437 + 0.410155i
$$729$$ −18.1962 19.9474i −0.673932 0.738794i
$$730$$ 0.748711 2.79423i 0.0277110 0.103419i
$$731$$ 9.58394 5.53329i 0.354475 0.204656i
$$732$$ −1.22024 3.01084i −0.0451014 0.111284i
$$733$$ −6.77757 6.77757i −0.250335 0.250335i 0.570773 0.821108i $$-0.306644\pi$$
−0.821108 + 0.570773i $$0.806644\pi$$
$$734$$ 11.8461 + 44.2104i 0.437249 + 1.63183i
$$735$$ −12.0108 5.08298i −0.443025 0.187489i
$$736$$ 0 0
$$737$$ −21.1447 12.2079i −0.778876 0.449685i
$$738$$ 17.6784 + 18.2276i 0.650750 + 0.670966i
$$739$$ −11.1244 2.98076i −0.409216 0.109649i 0.0483378 0.998831i $$-0.484608\pi$$
−0.457554 + 0.889182i $$0.651274\pi$$
$$740$$ −2.18573 −0.0803492
$$741$$ 1.41914 + 24.0870i 0.0521334 + 0.884860i
$$742$$ −1.66025 −0.0609498
$$743$$ −8.51906 2.28268i −0.312534 0.0837432i 0.0991426 0.995073i $$-0.468390\pi$$
−0.411677 + 0.911330i $$0.635057\pi$$
$$744$$ −15.5930 2.17429i −0.571667 0.0797132i
$$745$$ 11.2583 + 6.50000i 0.412473 + 0.238142i
$$746$$ 12.3403 12.3403i 0.451812 0.451812i
$$747$$ −10.7826 + 6.00739i −0.394516 + 0.219799i
$$748$$ 1.43782 + 5.36603i 0.0525720 + 0.196201i
$$749$$ 19.0150 + 19.0150i 0.694792 + 0.694792i
$$750$$ −28.1491 + 11.4084i −1.02786 + 0.416574i
$$751$$ −29.2750 + 16.9019i −1.06826 + 0.616760i −0.927705 0.373313i $$-0.878222\pi$$
−0.140554 + 0.990073i $$0.544888\pi$$
$$752$$ −6.95996 + 25.9749i −0.253804 + 0.947208i
$$753$$ −1.35022 1.05256i −0.0492046 0.0383574i
$$754$$ 38.1699 7.63397i 1.39006 0.278013i
$$755$$ 1.14134i 0.0415375i
$$756$$ −1.53422 1.23418i −0.0557990 0.0448866i
$$757$$ −8.39230 14.5359i −0.305024 0.528316i 0.672243 0.740331i $$-0.265331\pi$$
−0.977267 + 0.212014i $$0.931998\pi$$
$$758$$ −11.1430 + 19.3003i −0.404733 + 0.701019i
$$759$$ 0 0
$$760$$ −14.6603 + 3.92820i −0.531783 + 0.142491i
$$761$$ 17.7412 4.75374i 0.643118 0.172323i 0.0775029 0.996992i $$-0.475305\pi$$
0.565616 + 0.824669i $$0.308639\pi$$
$$762$$ 2.92602 + 23.6196i 0.105998 + 0.855647i
$$763$$ 13.1962 22.8564i 0.477733 0.827457i
$$764$$ 0.647124 + 1.12085i 0.0234121 + 0.0405510i
$$765$$ −0.348161 + 22.7635i −0.0125878 + 0.823014i
$$766$$ 49.5692i 1.79101i
$$767$$ −10.6488 + 2.12976i −0.384507 + 0.0769014i
$$768$$ 8.63397 + 6.73060i 0.311552 + 0.242870i
$$769$$ −10.8301 + 40.4186i −0.390544 + 1.45753i 0.438694 + 0.898636i $$0.355441\pi$$
−0.829238 + 0.558895i $$0.811225\pi$$
$$770$$ 11.4284 6.59817i 0.411850 0.237782i
$$771$$ 34.5229 13.9915i 1.24331 0.503893i
$$772$$ 0.0262794 + 0.0262794i 0.000945818 + 0.000945818i
$$773$$ 11.1430 +