# Properties

 Label 370.2.c.a.369.4 Level $370$ Weight $2$ Character 370.369 Analytic conductor $2.954$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$370 = 2 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 370.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.95446487479$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Defining polynomial: $$x^{10} + 19 x^{8} + 103 x^{6} + 210 x^{4} + 140 x^{2} + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 369.4 Root $$-0.987983i$$ of defining polynomial Character $$\chi$$ $$=$$ 370.369 Dual form 370.2.c.a.369.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -0.987983i q^{3} +1.00000 q^{4} +(-1.85396 - 1.25013i) q^{5} +0.987983i q^{6} +4.78937i q^{7} -1.00000 q^{8} +2.02389 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -0.987983i q^{3} +1.00000 q^{4} +(-1.85396 - 1.25013i) q^{5} +0.987983i q^{6} +4.78937i q^{7} -1.00000 q^{8} +2.02389 q^{9} +(1.85396 + 1.25013i) q^{10} -5.98732 q^{11} -0.987983i q^{12} -3.49410 q^{13} -4.78937i q^{14} +(-1.23510 + 1.83168i) q^{15} +1.00000 q^{16} +4.96343 q^{17} -2.02389 q^{18} +7.33092i q^{19} +(-1.85396 - 1.25013i) q^{20} +4.73182 q^{21} +5.98732 q^{22} -1.74873 q^{23} +0.987983i q^{24} +(1.87436 + 4.63538i) q^{25} +3.49410 q^{26} -4.96352i q^{27} +4.78937i q^{28} +7.85004i q^{29} +(1.23510 - 1.83168i) q^{30} +3.24097i q^{31} -1.00000 q^{32} +5.91537i q^{33} -4.96343 q^{34} +(5.98732 - 8.87932i) q^{35} +2.02389 q^{36} +(-3.96343 - 4.61424i) q^{37} -7.33092i q^{38} +3.45211i q^{39} +(1.85396 + 1.25013i) q^{40} -0.530665 q^{41} -4.73182 q^{42} +1.76838 q^{43} -5.98732 q^{44} +(-3.75222 - 2.53012i) q^{45} +1.74873 q^{46} +4.30638i q^{47} -0.987983i q^{48} -15.9381 q^{49} +(-1.87436 - 4.63538i) q^{50} -4.90379i q^{51} -3.49410 q^{52} +3.66238i q^{53} +4.96352i q^{54} +(11.1003 + 7.48491i) q^{55} -4.78937i q^{56} +7.24283 q^{57} -7.85004i q^{58} -2.15110i q^{59} +(-1.23510 + 1.83168i) q^{60} -3.06584i q^{61} -3.24097i q^{62} +9.69316i q^{63} +1.00000 q^{64} +(6.47793 + 4.36807i) q^{65} -5.91537i q^{66} +3.79622i q^{67} +4.96343 q^{68} +1.72772i q^{69} +(-5.98732 + 8.87932i) q^{70} -8.47719 q^{71} -2.02389 q^{72} -9.05445i q^{73} +(3.96343 + 4.61424i) q^{74} +(4.57968 - 1.85184i) q^{75} +7.33092i q^{76} -28.6755i q^{77} -3.45211i q^{78} -5.56622i q^{79} +(-1.85396 - 1.25013i) q^{80} +1.16780 q^{81} +0.530665 q^{82} +3.77680i q^{83} +4.73182 q^{84} +(-9.20203 - 6.20492i) q^{85} -1.76838 q^{86} +7.75571 q^{87} +5.98732 q^{88} -8.45791i q^{89} +(3.75222 + 2.53012i) q^{90} -16.7345i q^{91} -1.74873 q^{92} +3.20203 q^{93} -4.30638i q^{94} +(9.16459 - 13.5913i) q^{95} +0.987983i q^{96} +3.64747 q^{97} +15.9381 q^{98} -12.1177 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + O(q^{10})$$ $$10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + 3q^{10} - 2q^{13} - 10q^{15} + 10q^{16} + 18q^{17} + 8q^{18} - 3q^{20} - 12q^{21} + 10q^{23} + 5q^{25} + 2q^{26} + 10q^{30} - 10q^{32} - 18q^{34} - 8q^{36} - 8q^{37} + 3q^{40} - 4q^{41} + 12q^{42} - 10q^{43} + 20q^{45} - 10q^{46} - 8q^{49} - 5q^{50} - 2q^{52} + 5q^{55} + 12q^{57} - 10q^{60} + 10q^{64} + 2q^{65} + 18q^{68} - 20q^{71} + 8q^{72} + 8q^{74} + 25q^{75} - 3q^{80} + 58q^{81} + 4q^{82} - 12q^{84} - 28q^{85} + 10q^{86} - 10q^{87} - 20q^{90} + 10q^{92} - 32q^{93} + 2q^{95} + 2q^{97} + 8q^{98} - 82q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$297$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 0.987983i 0.570412i −0.958466 0.285206i $$-0.907938\pi$$
0.958466 0.285206i $$-0.0920621\pi$$
$$4$$ 1.00000 0.500000
$$5$$ −1.85396 1.25013i −0.829118 0.559074i
$$6$$ 0.987983i 0.403342i
$$7$$ 4.78937i 1.81021i 0.425186 + 0.905106i $$0.360209\pi$$
−0.425186 + 0.905106i $$0.639791\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 2.02389 0.674630
$$10$$ 1.85396 + 1.25013i 0.586275 + 0.395325i
$$11$$ −5.98732 −1.80525 −0.902623 0.430432i $$-0.858361\pi$$
−0.902623 + 0.430432i $$0.858361\pi$$
$$12$$ 0.987983i 0.285206i
$$13$$ −3.49410 −0.969088 −0.484544 0.874767i $$-0.661015\pi$$
−0.484544 + 0.874767i $$0.661015\pi$$
$$14$$ 4.78937i 1.28001i
$$15$$ −1.23510 + 1.83168i −0.318903 + 0.472939i
$$16$$ 1.00000 0.250000
$$17$$ 4.96343 1.20381 0.601905 0.798568i $$-0.294409\pi$$
0.601905 + 0.798568i $$0.294409\pi$$
$$18$$ −2.02389 −0.477035
$$19$$ 7.33092i 1.68183i 0.541168 + 0.840915i $$0.317982\pi$$
−0.541168 + 0.840915i $$0.682018\pi$$
$$20$$ −1.85396 1.25013i −0.414559 0.279537i
$$21$$ 4.73182 1.03257
$$22$$ 5.98732 1.27650
$$23$$ −1.74873 −0.364635 −0.182318 0.983240i $$-0.558360\pi$$
−0.182318 + 0.983240i $$0.558360\pi$$
$$24$$ 0.987983i 0.201671i
$$25$$ 1.87436 + 4.63538i 0.374873 + 0.927076i
$$26$$ 3.49410 0.685249
$$27$$ 4.96352i 0.955229i
$$28$$ 4.78937i 0.905106i
$$29$$ 7.85004i 1.45772i 0.684665 + 0.728858i $$0.259949\pi$$
−0.684665 + 0.728858i $$0.740051\pi$$
$$30$$ 1.23510 1.83168i 0.225498 0.334418i
$$31$$ 3.24097i 0.582096i 0.956708 + 0.291048i $$0.0940039\pi$$
−0.956708 + 0.291048i $$0.905996\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 5.91537i 1.02973i
$$34$$ −4.96343 −0.851222
$$35$$ 5.98732 8.87932i 1.01204 1.50088i
$$36$$ 2.02389 0.337315
$$37$$ −3.96343 4.61424i −0.651584 0.758576i
$$38$$ 7.33092i 1.18923i
$$39$$ 3.45211i 0.552780i
$$40$$ 1.85396 + 1.25013i 0.293137 + 0.197662i
$$41$$ −0.530665 −0.0828760 −0.0414380 0.999141i $$-0.513194\pi$$
−0.0414380 + 0.999141i $$0.513194\pi$$
$$42$$ −4.73182 −0.730135
$$43$$ 1.76838 0.269676 0.134838 0.990868i $$-0.456949\pi$$
0.134838 + 0.990868i $$0.456949\pi$$
$$44$$ −5.98732 −0.902623
$$45$$ −3.75222 2.53012i −0.559348 0.377168i
$$46$$ 1.74873 0.257836
$$47$$ 4.30638i 0.628150i 0.949398 + 0.314075i $$0.101694\pi$$
−0.949398 + 0.314075i $$0.898306\pi$$
$$48$$ 0.987983i 0.142603i
$$49$$ −15.9381 −2.27687
$$50$$ −1.87436 4.63538i −0.265075 0.655542i
$$51$$ 4.90379i 0.686668i
$$52$$ −3.49410 −0.484544
$$53$$ 3.66238i 0.503067i 0.967849 + 0.251534i $$0.0809349\pi$$
−0.967849 + 0.251534i $$0.919065\pi$$
$$54$$ 4.96352i 0.675449i
$$55$$ 11.1003 + 7.48491i 1.49676 + 1.00927i
$$56$$ 4.78937i 0.640007i
$$57$$ 7.24283 0.959336
$$58$$ 7.85004i 1.03076i
$$59$$ 2.15110i 0.280049i −0.990148 0.140025i $$-0.955282\pi$$
0.990148 0.140025i $$-0.0447182\pi$$
$$60$$ −1.23510 + 1.83168i −0.159451 + 0.236470i
$$61$$ 3.06584i 0.392541i −0.980550 0.196270i $$-0.937117\pi$$
0.980550 0.196270i $$-0.0628830\pi$$
$$62$$ 3.24097i 0.411604i
$$63$$ 9.69316i 1.22122i
$$64$$ 1.00000 0.125000
$$65$$ 6.47793 + 4.36807i 0.803489 + 0.541792i
$$66$$ 5.91537i 0.728132i
$$67$$ 3.79622i 0.463782i 0.972742 + 0.231891i $$0.0744912\pi$$
−0.972742 + 0.231891i $$0.925509\pi$$
$$68$$ 4.96343 0.601905
$$69$$ 1.72772i 0.207992i
$$70$$ −5.98732 + 8.87932i −0.715622 + 1.06128i
$$71$$ −8.47719 −1.00606 −0.503028 0.864270i $$-0.667781\pi$$
−0.503028 + 0.864270i $$0.667781\pi$$
$$72$$ −2.02389 −0.238518
$$73$$ 9.05445i 1.05974i −0.848078 0.529872i $$-0.822240\pi$$
0.848078 0.529872i $$-0.177760\pi$$
$$74$$ 3.96343 + 4.61424i 0.460740 + 0.536394i
$$75$$ 4.57968 1.85184i 0.528816 0.213832i
$$76$$ 7.33092i 0.840915i
$$77$$ 28.6755i 3.26788i
$$78$$ 3.45211i 0.390874i
$$79$$ 5.56622i 0.626248i −0.949712 0.313124i $$-0.898624\pi$$
0.949712 0.313124i $$-0.101376\pi$$
$$80$$ −1.85396 1.25013i −0.207279 0.139768i
$$81$$ 1.16780 0.129755
$$82$$ 0.530665 0.0586022
$$83$$ 3.77680i 0.414558i 0.978282 + 0.207279i $$0.0664607\pi$$
−0.978282 + 0.207279i $$0.933539\pi$$
$$84$$ 4.73182 0.516284
$$85$$ −9.20203 6.20492i −0.998100 0.673018i
$$86$$ −1.76838 −0.190690
$$87$$ 7.75571 0.831499
$$88$$ 5.98732 0.638251
$$89$$ 8.45791i 0.896537i −0.893899 0.448268i $$-0.852041\pi$$
0.893899 0.448268i $$-0.147959\pi$$
$$90$$ 3.75222 + 2.53012i 0.395519 + 0.266698i
$$91$$ 16.7345i 1.75426i
$$92$$ −1.74873 −0.182318
$$93$$ 3.20203 0.332035
$$94$$ 4.30638i 0.444169i
$$95$$ 9.16459 13.5913i 0.940267 1.39443i
$$96$$ 0.987983i 0.100836i
$$97$$ 3.64747 0.370345 0.185172 0.982706i $$-0.440716\pi$$
0.185172 + 0.982706i $$0.440716\pi$$
$$98$$ 15.9381 1.60999
$$99$$ −12.1177 −1.21787
$$100$$ 1.87436 + 4.63538i 0.187436 + 0.463538i
$$101$$ 2.30416 0.229272 0.114636 0.993408i $$-0.463430\pi$$
0.114636 + 0.993408i $$0.463430\pi$$
$$102$$ 4.90379i 0.485547i
$$103$$ −11.1716 −1.10077 −0.550383 0.834912i $$-0.685518\pi$$
−0.550383 + 0.834912i $$0.685518\pi$$
$$104$$ 3.49410 0.342625
$$105$$ −8.77262 5.91537i −0.856120 0.577281i
$$106$$ 3.66238i 0.355722i
$$107$$ 6.51807i 0.630126i −0.949071 0.315063i $$-0.897974\pi$$
0.949071 0.315063i $$-0.102026\pi$$
$$108$$ 4.96352i 0.477615i
$$109$$ 1.33812i 0.128169i −0.997944 0.0640846i $$-0.979587\pi$$
0.997944 0.0640846i $$-0.0204127\pi$$
$$110$$ −11.1003 7.48491i −1.05837 0.713659i
$$111$$ −4.55879 + 3.91580i −0.432701 + 0.371672i
$$112$$ 4.78937i 0.452553i
$$113$$ −1.39109 −0.130863 −0.0654315 0.997857i $$-0.520842\pi$$
−0.0654315 + 0.997857i $$0.520842\pi$$
$$114$$ −7.24283 −0.678353
$$115$$ 3.24208 + 2.18613i 0.302326 + 0.203858i
$$116$$ 7.85004i 0.728858i
$$117$$ −7.07167 −0.653776
$$118$$ 2.15110i 0.198025i
$$119$$ 23.7717i 2.17915i
$$120$$ 1.23510 1.83168i 0.112749 0.167209i
$$121$$ 24.8480 2.25891
$$122$$ 3.06584i 0.277568i
$$123$$ 0.524288i 0.0472735i
$$124$$ 3.24097i 0.291048i
$$125$$ 2.31981 10.9370i 0.207490 0.978237i
$$126$$ 9.69316i 0.863535i
$$127$$ 7.51024i 0.666426i 0.942852 + 0.333213i $$0.108133\pi$$
−0.942852 + 0.333213i $$0.891867\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 1.74713i 0.153827i
$$130$$ −6.47793 4.36807i −0.568152 0.383105i
$$131$$ 6.19975i 0.541675i 0.962625 + 0.270837i $$0.0873006\pi$$
−0.962625 + 0.270837i $$0.912699\pi$$
$$132$$ 5.91537i 0.514867i
$$133$$ −35.1105 −3.04447
$$134$$ 3.79622i 0.327943i
$$135$$ −6.20503 + 9.20218i −0.534044 + 0.791998i
$$136$$ −4.96343 −0.425611
$$137$$ 8.97186i 0.766518i 0.923641 + 0.383259i $$0.125198\pi$$
−0.923641 + 0.383259i $$0.874802\pi$$
$$138$$ 1.72772i 0.147073i
$$139$$ 5.04168 0.427629 0.213815 0.976874i $$-0.431411\pi$$
0.213815 + 0.976874i $$0.431411\pi$$
$$140$$ 5.98732 8.87932i 0.506021 0.750440i
$$141$$ 4.25463 0.358305
$$142$$ 8.47719 0.711390
$$143$$ 20.9203 1.74944
$$144$$ 2.02389 0.168657
$$145$$ 9.81355 14.5537i 0.814971 1.20862i
$$146$$ 9.05445i 0.749352i
$$147$$ 15.7466i 1.29875i
$$148$$ −3.96343 4.61424i −0.325792 0.379288i
$$149$$ −21.6451 −1.77324 −0.886619 0.462500i $$-0.846952\pi$$
−0.886619 + 0.462500i $$0.846952\pi$$
$$150$$ −4.57968 + 1.85184i −0.373929 + 0.151202i
$$151$$ 6.47544 0.526964 0.263482 0.964664i $$-0.415129\pi$$
0.263482 + 0.964664i $$0.415129\pi$$
$$152$$ 7.33092i 0.594616i
$$153$$ 10.0454 0.812126
$$154$$ 28.6755i 2.31074i
$$155$$ 4.05163 6.00865i 0.325435 0.482626i
$$156$$ 3.45211i 0.276390i
$$157$$ 13.1689i 1.05099i 0.850797 + 0.525495i $$0.176120\pi$$
−0.850797 + 0.525495i $$0.823880\pi$$
$$158$$ 5.56622i 0.442825i
$$159$$ 3.61837 0.286956
$$160$$ 1.85396 + 1.25013i 0.146569 + 0.0988312i
$$161$$ 8.37532i 0.660067i
$$162$$ −1.16780 −0.0917509
$$163$$ 18.7651 1.46979 0.734896 0.678180i $$-0.237231\pi$$
0.734896 + 0.678180i $$0.237231\pi$$
$$164$$ −0.530665 −0.0414380
$$165$$ 7.39497 10.9669i 0.575697 0.853771i
$$166$$ 3.77680i 0.293136i
$$167$$ 7.19692 0.556914 0.278457 0.960449i $$-0.410177\pi$$
0.278457 + 0.960449i $$0.410177\pi$$
$$168$$ −4.73182 −0.365068
$$169$$ −0.791278 −0.0608676
$$170$$ 9.20203 + 6.20492i 0.705763 + 0.475896i
$$171$$ 14.8370i 1.13461i
$$172$$ 1.76838 0.134838
$$173$$ 9.79406i 0.744629i 0.928107 + 0.372314i $$0.121436\pi$$
−0.928107 + 0.372314i $$0.878564\pi$$
$$174$$ −7.75571 −0.587959
$$175$$ −22.2006 + 8.97703i −1.67820 + 0.678600i
$$176$$ −5.98732 −0.451311
$$177$$ −2.12525 −0.159743
$$178$$ 8.45791i 0.633947i
$$179$$ 11.2829i 0.843320i 0.906754 + 0.421660i $$0.138552\pi$$
−0.906754 + 0.421660i $$0.861448\pi$$
$$180$$ −3.75222 2.53012i −0.279674 0.188584i
$$181$$ 1.82697 0.135798 0.0678989 0.997692i $$-0.478370\pi$$
0.0678989 + 0.997692i $$0.478370\pi$$
$$182$$ 16.7345i 1.24045i
$$183$$ −3.02900 −0.223910
$$184$$ 1.74873 0.128918
$$185$$ 1.57968 + 13.5094i 0.116140 + 0.993233i
$$186$$ −3.20203 −0.234784
$$187$$ −29.7177 −2.17317
$$188$$ 4.30638i 0.314075i
$$189$$ 23.7721 1.72917
$$190$$ −9.16459 + 13.5913i −0.664869 + 0.986014i
$$191$$ 23.8204i 1.72358i −0.507264 0.861791i $$-0.669343\pi$$
0.507264 0.861791i $$-0.330657\pi$$
$$192$$ 0.987983i 0.0713015i
$$193$$ 8.40405 0.604937 0.302468 0.953159i $$-0.402189\pi$$
0.302468 + 0.953159i $$0.402189\pi$$
$$194$$ −3.64747 −0.261873
$$195$$ 4.31558 6.40009i 0.309045 0.458320i
$$196$$ −15.9381 −1.13843
$$197$$ 4.22797i 0.301230i −0.988592 0.150615i $$-0.951875\pi$$
0.988592 0.150615i $$-0.0481254\pi$$
$$198$$ 12.1177 0.861166
$$199$$ 17.7545i 1.25858i 0.777170 + 0.629290i $$0.216654\pi$$
−0.777170 + 0.629290i $$0.783346\pi$$
$$200$$ −1.87436 4.63538i −0.132538 0.327771i
$$201$$ 3.75060 0.264547
$$202$$ −2.30416 −0.162120
$$203$$ −37.5968 −2.63878
$$204$$ 4.90379i 0.343334i
$$205$$ 0.983834 + 0.663399i 0.0687139 + 0.0463338i
$$206$$ 11.1716 0.778360
$$207$$ −3.53924 −0.245994
$$208$$ −3.49410 −0.242272
$$209$$ 43.8926i 3.03611i
$$210$$ 8.77262 + 5.91537i 0.605368 + 0.408200i
$$211$$ 4.57321 0.314833 0.157417 0.987532i $$-0.449683\pi$$
0.157417 + 0.987532i $$0.449683\pi$$
$$212$$ 3.66238i 0.251534i
$$213$$ 8.37532i 0.573867i
$$214$$ 6.51807i 0.445566i
$$215$$ −3.27852 2.21071i −0.223593 0.150769i
$$216$$ 4.96352i 0.337725i
$$217$$ −15.5222 −1.05372
$$218$$ 1.33812i 0.0906293i
$$219$$ −8.94565 −0.604491
$$220$$ 11.1003 + 7.48491i 0.748381 + 0.504633i
$$221$$ −17.3427 −1.16660
$$222$$ 4.55879 3.91580i 0.305966 0.262812i
$$223$$ 20.3205i 1.36076i 0.732860 + 0.680380i $$0.238185\pi$$
−0.732860 + 0.680380i $$0.761815\pi$$
$$224$$ 4.78937i 0.320003i
$$225$$ 3.79351 + 9.38150i 0.252900 + 0.625433i
$$226$$ 1.39109 0.0925341
$$227$$ −5.74303 −0.381178 −0.190589 0.981670i $$-0.561040\pi$$
−0.190589 + 0.981670i $$0.561040\pi$$
$$228$$ 7.24283 0.479668
$$229$$ 23.4383 1.54885 0.774423 0.632669i $$-0.218040\pi$$
0.774423 + 0.632669i $$0.218040\pi$$
$$230$$ −3.24208 2.18613i −0.213777 0.144149i
$$231$$ −28.3309 −1.86404
$$232$$ 7.85004i 0.515380i
$$233$$ 17.2961i 1.13310i −0.824027 0.566551i $$-0.808277\pi$$
0.824027 0.566551i $$-0.191723\pi$$
$$234$$ 7.07167 0.462289
$$235$$ 5.38352 7.98388i 0.351182 0.520811i
$$236$$ 2.15110i 0.140025i
$$237$$ −5.49933 −0.357220
$$238$$ 23.7717i 1.54089i
$$239$$ 3.68796i 0.238554i 0.992861 + 0.119277i $$0.0380577\pi$$
−0.992861 + 0.119277i $$0.961942\pi$$
$$240$$ −1.23510 + 1.83168i −0.0797256 + 0.118235i
$$241$$ 11.3613i 0.731844i 0.930646 + 0.365922i $$0.119246\pi$$
−0.930646 + 0.365922i $$0.880754\pi$$
$$242$$ −24.8480 −1.59729
$$243$$ 16.0443i 1.02924i
$$244$$ 3.06584i 0.196270i
$$245$$ 29.5486 + 19.9246i 1.88779 + 1.27294i
$$246$$ 0.524288i 0.0334274i
$$247$$ 25.6150i 1.62984i
$$248$$ 3.24097i 0.205802i
$$249$$ 3.73141 0.236469
$$250$$ −2.31981 + 10.9370i −0.146718 + 0.691718i
$$251$$ 12.8260i 0.809567i 0.914412 + 0.404784i $$0.132653\pi$$
−0.914412 + 0.404784i $$0.867347\pi$$
$$252$$ 9.69316i 0.610612i
$$253$$ 10.4702 0.658256
$$254$$ 7.51024i 0.471234i
$$255$$ −6.13036 + 9.09145i −0.383898 + 0.569328i
$$256$$ 1.00000 0.0625000
$$257$$ 14.0268 0.874965 0.437483 0.899227i $$-0.355870\pi$$
0.437483 + 0.899227i $$0.355870\pi$$
$$258$$ 1.74713i 0.108772i
$$259$$ 22.0993 18.9824i 1.37318 1.17951i
$$260$$ 6.47793 + 4.36807i 0.401744 + 0.270896i
$$261$$ 15.8876i 0.983419i
$$262$$ 6.19975i 0.383022i
$$263$$ 3.57182i 0.220248i 0.993918 + 0.110124i $$0.0351248\pi$$
−0.993918 + 0.110124i $$0.964875\pi$$
$$264$$ 5.91537i 0.364066i
$$265$$ 4.57844 6.78993i 0.281252 0.417102i
$$266$$ 35.1105 2.15276
$$267$$ −8.35627 −0.511396
$$268$$ 3.79622i 0.231891i
$$269$$ −0.458895 −0.0279793 −0.0139897 0.999902i $$-0.504453\pi$$
−0.0139897 + 0.999902i $$0.504453\pi$$
$$270$$ 6.20503 9.20218i 0.377626 0.560027i
$$271$$ 28.8897 1.75492 0.877462 0.479645i $$-0.159235\pi$$
0.877462 + 0.479645i $$0.159235\pi$$
$$272$$ 4.96343 0.300952
$$273$$ −16.5334 −1.00065
$$274$$ 8.97186i 0.542010i
$$275$$ −11.2224 27.7535i −0.676738 1.67360i
$$276$$ 1.72772i 0.103996i
$$277$$ 22.4482 1.34878 0.674391 0.738374i $$-0.264406\pi$$
0.674391 + 0.738374i $$0.264406\pi$$
$$278$$ −5.04168 −0.302380
$$279$$ 6.55937i 0.392699i
$$280$$ −5.98732 + 8.87932i −0.357811 + 0.530641i
$$281$$ 6.04908i 0.360858i 0.983588 + 0.180429i $$0.0577486\pi$$
−0.983588 + 0.180429i $$0.942251\pi$$
$$282$$ −4.25463 −0.253360
$$283$$ 10.8317 0.643878 0.321939 0.946760i $$-0.395665\pi$$
0.321939 + 0.946760i $$0.395665\pi$$
$$284$$ −8.47719 −0.503028
$$285$$ −13.4279 9.05445i −0.795403 0.536340i
$$286$$ −20.9203 −1.23704
$$287$$ 2.54155i 0.150023i
$$288$$ −2.02389 −0.119259
$$289$$ 7.63567 0.449157
$$290$$ −9.81355 + 14.5537i −0.576271 + 0.854622i
$$291$$ 3.60364i 0.211249i
$$292$$ 9.05445i 0.529872i
$$293$$ 23.3144i 1.36204i 0.732264 + 0.681021i $$0.238464\pi$$
−0.732264 + 0.681021i $$0.761536\pi$$
$$294$$ 15.7466i 0.918357i
$$295$$ −2.68915 + 3.98806i −0.156568 + 0.232194i
$$296$$ 3.96343 + 4.61424i 0.230370 + 0.268197i
$$297$$ 29.7182i 1.72442i
$$298$$ 21.6451 1.25387
$$299$$ 6.11023 0.353364
$$300$$ 4.57968 1.85184i 0.264408 0.106916i
$$301$$ 8.46945i 0.488171i
$$302$$ −6.47544 −0.372620
$$303$$ 2.27647i 0.130780i
$$304$$ 7.33092i 0.420457i
$$305$$ −3.83269 + 5.68396i −0.219459 + 0.325462i
$$306$$ −10.0454 −0.574260
$$307$$ 14.2651i 0.814153i 0.913394 + 0.407077i $$0.133452\pi$$
−0.913394 + 0.407077i $$0.866548\pi$$
$$308$$ 28.6755i 1.63394i
$$309$$ 11.0373i 0.627891i
$$310$$ −4.05163 + 6.00865i −0.230117 + 0.341268i
$$311$$ 22.5322i 1.27768i 0.769339 + 0.638841i $$0.220586\pi$$
−0.769339 + 0.638841i $$0.779414\pi$$
$$312$$ 3.45211i 0.195437i
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 13.1689i 0.743162i
$$315$$ 12.1177 17.9708i 0.682754 1.01254i
$$316$$ 5.56622i 0.313124i
$$317$$ 12.3877i 0.695764i −0.937538 0.347882i $$-0.886901\pi$$
0.937538 0.347882i $$-0.113099\pi$$
$$318$$ −3.61837 −0.202908
$$319$$ 47.0007i 2.63154i
$$320$$ −1.85396 1.25013i −0.103640 0.0698842i
$$321$$ −6.43975 −0.359432
$$322$$ 8.37532i 0.466738i
$$323$$ 36.3865i 2.02460i
$$324$$ 1.16780 0.0648777
$$325$$ −6.54921 16.1965i −0.363285 0.898419i
$$326$$ −18.7651 −1.03930
$$327$$ −1.32204 −0.0731092
$$328$$ 0.530665 0.0293011
$$329$$ −20.6249 −1.13709
$$330$$ −7.39497 + 10.9669i −0.407080 + 0.603707i
$$331$$ 19.0068i 1.04471i −0.852728 0.522355i $$-0.825054\pi$$
0.852728 0.522355i $$-0.174946\pi$$
$$332$$ 3.77680i 0.207279i
$$333$$ −8.02155 9.33871i −0.439578 0.511758i
$$334$$ −7.19692 −0.393798
$$335$$ 4.74575 7.03805i 0.259288 0.384530i
$$336$$ 4.73182 0.258142
$$337$$ 25.1046i 1.36753i −0.729701 0.683766i $$-0.760341\pi$$
0.729701 0.683766i $$-0.239659\pi$$
$$338$$ 0.791278 0.0430399
$$339$$ 1.37438i 0.0746459i
$$340$$ −9.20203 6.20492i −0.499050 0.336509i
$$341$$ 19.4047i 1.05083i
$$342$$ 14.8370i 0.802292i
$$343$$ 42.8078i 2.31140i
$$344$$ −1.76838 −0.0953449
$$345$$ 2.15986 3.20312i 0.116283 0.172450i
$$346$$ 9.79406i 0.526532i
$$347$$ 30.4282 1.63347 0.816736 0.577011i $$-0.195781\pi$$
0.816736 + 0.577011i $$0.195781\pi$$
$$348$$ 7.75571 0.415750
$$349$$ 15.1341 0.810111 0.405056 0.914292i $$-0.367252\pi$$
0.405056 + 0.914292i $$0.367252\pi$$
$$350$$ 22.2006 8.97703i 1.18667 0.479842i
$$351$$ 17.3430i 0.925702i
$$352$$ 5.98732 0.319125
$$353$$ −10.1331 −0.539332 −0.269666 0.962954i $$-0.586913\pi$$
−0.269666 + 0.962954i $$0.586913\pi$$
$$354$$ 2.12525 0.112956
$$355$$ 15.7164 + 10.5976i 0.834140 + 0.562460i
$$356$$ 8.45791i 0.448268i
$$357$$ 23.4861 1.24301
$$358$$ 11.2829i 0.596317i
$$359$$ −26.3685 −1.39168 −0.695838 0.718199i $$-0.744967\pi$$
−0.695838 + 0.718199i $$0.744967\pi$$
$$360$$ 3.75222 + 2.53012i 0.197759 + 0.133349i
$$361$$ −34.7424 −1.82855
$$362$$ −1.82697 −0.0960235
$$363$$ 24.5494i 1.28851i
$$364$$ 16.7345i 0.877128i
$$365$$ −11.3192 + 16.7866i −0.592475 + 0.878653i
$$366$$ 3.02900 0.158328
$$367$$ 2.21157i 0.115443i 0.998333 + 0.0577215i $$0.0183835\pi$$
−0.998333 + 0.0577215i $$0.981616\pi$$
$$368$$ −1.74873 −0.0911588
$$369$$ −1.07401 −0.0559106
$$370$$ −1.57968 13.5094i −0.0821235 0.702322i
$$371$$ −17.5405 −0.910658
$$372$$ 3.20203 0.166017
$$373$$ 6.08275i 0.314953i 0.987523 + 0.157476i $$0.0503358\pi$$
−0.987523 + 0.157476i $$0.949664\pi$$
$$374$$ 29.7177 1.53666
$$375$$ −10.8056 2.29193i −0.557998 0.118355i
$$376$$ 4.30638i 0.222085i
$$377$$ 27.4288i 1.41266i
$$378$$ −23.7721 −1.22271
$$379$$ −20.0919 −1.03205 −0.516025 0.856574i $$-0.672589\pi$$
−0.516025 + 0.856574i $$0.672589\pi$$
$$380$$ 9.16459 13.5913i 0.470133 0.697217i
$$381$$ 7.41999 0.380138
$$382$$ 23.8204i 1.21876i
$$383$$ 11.5368 0.589501 0.294751 0.955574i $$-0.404763\pi$$
0.294751 + 0.955574i $$0.404763\pi$$
$$384$$ 0.987983i 0.0504178i
$$385$$ −35.8480 + 53.1634i −1.82698 + 2.70946i
$$386$$ −8.40405 −0.427755
$$387$$ 3.57901 0.181932
$$388$$ 3.64747 0.185172
$$389$$ 8.55057i 0.433531i 0.976224 + 0.216766i $$0.0695507\pi$$
−0.976224 + 0.216766i $$0.930449\pi$$
$$390$$ −4.31558 + 6.40009i −0.218528 + 0.324081i
$$391$$ −8.67970 −0.438951
$$392$$ 15.9381 0.804995
$$393$$ 6.12525 0.308978
$$394$$ 4.22797i 0.213002i
$$395$$ −6.95848 + 10.3196i −0.350119 + 0.519234i
$$396$$ −12.1177 −0.608936
$$397$$ 9.84444i 0.494078i 0.969006 + 0.247039i $$0.0794576\pi$$
−0.969006 + 0.247039i $$0.920542\pi$$
$$398$$ 17.7545i 0.889951i
$$399$$ 34.6886i 1.73660i
$$400$$ 1.87436 + 4.63538i 0.0937182 + 0.231769i
$$401$$ 31.0959i 1.55285i −0.630207 0.776427i $$-0.717030\pi$$
0.630207 0.776427i $$-0.282970\pi$$
$$402$$ −3.75060 −0.187063
$$403$$ 11.3243i 0.564102i
$$404$$ 2.30416 0.114636
$$405$$ −2.16506 1.45990i −0.107582 0.0725428i
$$406$$ 37.5968 1.86590
$$407$$ 23.7304 + 27.6269i 1.17627 + 1.36942i
$$408$$ 4.90379i 0.242774i
$$409$$ 38.3150i 1.89455i 0.320417 + 0.947277i $$0.396177\pi$$
−0.320417 + 0.947277i $$0.603823\pi$$
$$410$$ −0.983834 0.663399i −0.0485881 0.0327629i
$$411$$ 8.86404 0.437231
$$412$$ −11.1716 −0.550383
$$413$$ 10.3024 0.506948
$$414$$ 3.53924 0.173944
$$415$$ 4.72148 7.00205i 0.231768 0.343717i
$$416$$ 3.49410 0.171312
$$417$$ 4.98109i 0.243925i
$$418$$ 43.8926i 2.14686i
$$419$$ 29.0183 1.41764 0.708819 0.705391i $$-0.249228\pi$$
0.708819 + 0.705391i $$0.249228\pi$$
$$420$$ −8.77262 5.91537i −0.428060 0.288641i
$$421$$ 23.6443i 1.15235i −0.817326 0.576175i $$-0.804545\pi$$
0.817326 0.576175i $$-0.195455\pi$$
$$422$$ −4.57321 −0.222621
$$423$$ 8.71564i 0.423769i
$$424$$ 3.66238i 0.177861i
$$425$$ 9.30328 + 23.0074i 0.451276 + 1.11602i
$$426$$ 8.37532i 0.405785i
$$427$$ 14.6834 0.710582
$$428$$ 6.51807i 0.315063i
$$429$$ 20.6689i 0.997904i
$$430$$ 3.27852 + 2.21071i 0.158104 + 0.106610i
$$431$$ 32.1126i 1.54681i 0.633912 + 0.773406i $$0.281448\pi$$
−0.633912 + 0.773406i $$0.718552\pi$$
$$432$$ 4.96352i 0.238807i
$$433$$ 13.0575i 0.627504i 0.949505 + 0.313752i $$0.101586\pi$$
−0.949505 + 0.313752i $$0.898414\pi$$
$$434$$ 15.5222 0.745091
$$435$$ −14.3788 9.69562i −0.689411 0.464869i
$$436$$ 1.33812i 0.0640846i
$$437$$ 12.8198i 0.613254i
$$438$$ 8.94565 0.427440
$$439$$ 28.0499i 1.33875i −0.742924 0.669375i $$-0.766562\pi$$
0.742924 0.669375i $$-0.233438\pi$$
$$440$$ −11.1003 7.48491i −0.529185 0.356829i
$$441$$ −32.2569 −1.53604
$$442$$ 17.3427 0.824909
$$443$$ 6.79629i 0.322902i −0.986881 0.161451i $$-0.948383\pi$$
0.986881 0.161451i $$-0.0516173\pi$$
$$444$$ −4.55879 + 3.91580i −0.216351 + 0.185836i
$$445$$ −10.5735 + 15.6807i −0.501230 + 0.743335i
$$446$$ 20.3205i 0.962203i
$$447$$ 21.3850i 1.01148i
$$448$$ 4.78937i 0.226277i
$$449$$ 17.3278i 0.817747i −0.912591 0.408874i $$-0.865922\pi$$
0.912591 0.408874i $$-0.134078\pi$$
$$450$$ −3.79351 9.38150i −0.178828 0.442248i
$$451$$ 3.17726 0.149611
$$452$$ −1.39109 −0.0654315
$$453$$ 6.39762i 0.300587i
$$454$$ 5.74303 0.269534
$$455$$ −20.9203 + 31.0252i −0.980758 + 1.45448i
$$456$$ −7.24283 −0.339176
$$457$$ 3.20960 0.150139 0.0750693 0.997178i $$-0.476082\pi$$
0.0750693 + 0.997178i $$0.476082\pi$$
$$458$$ −23.4383 −1.09520
$$459$$ 24.6361i 1.14991i
$$460$$ 3.24208 + 2.18613i 0.151163 + 0.101929i
$$461$$ 34.0347i 1.58515i 0.609773 + 0.792576i $$0.291261\pi$$
−0.609773 + 0.792576i $$0.708739\pi$$
$$462$$ 28.3309 1.31807
$$463$$ 26.0543 1.21085 0.605423 0.795904i $$-0.293004\pi$$
0.605423 + 0.795904i $$0.293004\pi$$
$$464$$ 7.85004i 0.364429i
$$465$$ −5.93644 4.00294i −0.275296 0.185632i
$$466$$ 17.2961i 0.801224i
$$467$$ −20.3289 −0.940710 −0.470355 0.882477i $$-0.655874\pi$$
−0.470355 + 0.882477i $$0.655874\pi$$
$$468$$ −7.07167 −0.326888
$$469$$ −18.1815 −0.839544
$$470$$ −5.38352 + 7.98388i −0.248323 + 0.368269i
$$471$$ 13.0106 0.599498
$$472$$ 2.15110i 0.0990123i
$$473$$ −10.5879 −0.486832
$$474$$ 5.49933 0.252593
$$475$$ −33.9816 + 13.7408i −1.55918 + 0.630472i
$$476$$ 23.7717i 1.08958i
$$477$$ 7.41226i 0.339384i
$$478$$ 3.68796i 0.168683i
$$479$$ 6.22972i 0.284643i −0.989820 0.142322i $$-0.954543\pi$$
0.989820 0.142322i $$-0.0454567\pi$$
$$480$$ 1.23510 1.83168i 0.0563745 0.0836046i
$$481$$ 13.8486 + 16.1226i 0.631443 + 0.735127i
$$482$$ 11.3613i 0.517492i
$$483$$ −8.27467 −0.376511
$$484$$ 24.8480 1.12946
$$485$$ −6.76228 4.55980i −0.307059 0.207050i
$$486$$ 16.0443i 0.727785i
$$487$$ −30.5352 −1.38368 −0.691841 0.722050i $$-0.743200\pi$$
−0.691841 + 0.722050i $$0.743200\pi$$
$$488$$ 3.06584i 0.138784i
$$489$$ 18.5396i 0.838387i
$$490$$ −29.5486 19.9246i −1.33487 0.900103i
$$491$$ 24.5944 1.10993 0.554965 0.831874i $$-0.312732\pi$$
0.554965 + 0.831874i $$0.312732\pi$$
$$492$$ 0.524288i 0.0236367i
$$493$$ 38.9632i 1.75481i
$$494$$ 25.6150i 1.15247i
$$495$$ 22.4657 + 15.1486i 1.00976 + 0.680881i
$$496$$ 3.24097i 0.145524i
$$497$$ 40.6004i 1.82118i
$$498$$ −3.73141 −0.167209
$$499$$ 33.5739i 1.50297i −0.659747 0.751487i $$-0.729337\pi$$
0.659747 0.751487i $$-0.270663\pi$$
$$500$$ 2.31981 10.9370i 0.103745 0.489119i
$$501$$ 7.11043i 0.317671i
$$502$$ 12.8260i 0.572451i
$$503$$ −1.77931 −0.0793357 −0.0396679 0.999213i $$-0.512630\pi$$
−0.0396679 + 0.999213i $$0.512630\pi$$
$$504$$ 9.69316i 0.431768i
$$505$$ −4.27183 2.88049i −0.190094 0.128180i
$$506$$ −10.4702 −0.465458
$$507$$ 0.781770i 0.0347196i
$$508$$ 7.51024i 0.333213i
$$509$$ 29.5114 1.30807 0.654035 0.756464i $$-0.273075\pi$$
0.654035 + 0.756464i $$0.273075\pi$$
$$510$$ 6.13036 9.09145i 0.271457 0.402576i
$$511$$ 43.3651 1.91836
$$512$$ −1.00000 −0.0441942
$$513$$ 36.3872 1.60653
$$514$$ −14.0268 −0.618694
$$515$$ 20.7117 + 13.9659i 0.912665 + 0.615410i
$$516$$ 1.74713i 0.0769133i
$$517$$ 25.7837i 1.13397i
$$518$$ −22.0993 + 18.9824i −0.970988 + 0.834037i
$$519$$ 9.67637 0.424745
$$520$$ −6.47793 4.36807i −0.284076 0.191552i
$$521$$ 29.2841 1.28296 0.641481 0.767139i $$-0.278320\pi$$
0.641481 + 0.767139i $$0.278320\pi$$
$$522$$ 15.8876i 0.695382i
$$523$$ −29.9729 −1.31062 −0.655312 0.755359i $$-0.727463\pi$$
−0.655312 + 0.755359i $$0.727463\pi$$
$$524$$ 6.19975i 0.270837i
$$525$$ 8.86915 + 21.9338i 0.387082 + 0.957269i
$$526$$ 3.57182i 0.155739i
$$527$$ 16.0864i 0.700732i
$$528$$ 5.91537i 0.257434i
$$529$$ −19.9419 −0.867041
$$530$$ −4.57844 + 6.78993i −0.198875 + 0.294936i
$$531$$ 4.35359i 0.188930i
$$532$$ −35.1105 −1.52223
$$533$$ 1.85420 0.0803141
$$534$$ 8.35627 0.361611
$$535$$ −8.14842 + 12.0843i −0.352287 + 0.522449i
$$536$$ 3.79622i 0.163972i
$$537$$ 11.1473 0.481040
$$538$$ 0.458895 0.0197844
$$539$$ 95.4264 4.11031
$$540$$ −6.20503 + 9.20218i −0.267022 + 0.395999i
$$541$$ 18.7155i 0.804644i −0.915498 0.402322i $$-0.868203\pi$$
0.915498 0.402322i $$-0.131797\pi$$
$$542$$ −28.8897 −1.24092
$$543$$ 1.80502i 0.0774607i
$$544$$ −4.96343 −0.212805
$$545$$ −1.67283 + 2.48084i −0.0716560 + 0.106267i
$$546$$ 16.5334 0.707566
$$547$$ −32.4792 −1.38871 −0.694355 0.719633i $$-0.744310\pi$$
−0.694355 + 0.719633i $$0.744310\pi$$
$$548$$ 8.97186i 0.383259i
$$549$$ 6.20492i 0.264820i
$$550$$ 11.2224 + 27.7535i 0.478526 + 1.18341i
$$551$$ −57.5480 −2.45163
$$552$$ 1.72772i 0.0735364i
$$553$$ 26.6587 1.13364
$$554$$ −22.4482 −0.953733
$$555$$ 13.3471 1.56069i 0.566552 0.0662478i
$$556$$ 5.04168 0.213815
$$557$$ −16.0158 −0.678612 −0.339306 0.940676i $$-0.610192\pi$$
−0.339306 + 0.940676i $$0.610192\pi$$
$$558$$ 6.55937i 0.277680i
$$559$$ −6.17891 −0.261340
$$560$$ 5.98732 8.87932i 0.253011 0.375220i
$$561$$ 29.3606i 1.23960i
$$562$$ 6.04908i 0.255165i
$$563$$ −15.3069 −0.645109 −0.322554 0.946551i $$-0.604542\pi$$
−0.322554 + 0.946551i $$0.604542\pi$$
$$564$$ 4.25463 0.179152
$$565$$ 2.57904 + 1.73904i 0.108501 + 0.0731621i
$$566$$ −10.8317 −0.455291
$$567$$ 5.59302i 0.234885i
$$568$$ 8.47719 0.355695
$$569$$ 26.6494i 1.11720i 0.829437 + 0.558601i $$0.188662\pi$$
−0.829437 + 0.558601i $$0.811338\pi$$
$$570$$ 13.4279 + 9.05445i 0.562435 + 0.379249i
$$571$$ 23.1683 0.969564 0.484782 0.874635i $$-0.338899\pi$$
0.484782 + 0.874635i $$0.338899\pi$$
$$572$$ 20.9203 0.874721
$$573$$ −23.5341 −0.983152
$$574$$ 2.54155i 0.106082i
$$575$$ −3.27776 8.10603i −0.136692 0.338045i
$$576$$ 2.02389 0.0843287
$$577$$ −3.54110 −0.147418 −0.0737091 0.997280i $$-0.523484\pi$$
−0.0737091 + 0.997280i $$0.523484\pi$$
$$578$$ −7.63567 −0.317602
$$579$$ 8.30306i 0.345063i
$$580$$ 9.81355 14.5537i 0.407485 0.604309i
$$581$$ −18.0885 −0.750437
$$582$$ 3.60364i 0.149376i
$$583$$ 21.9279i 0.908160i
$$584$$ 9.05445i 0.374676i
$$585$$ 13.1106 + 8.84048i 0.542057 + 0.365509i
$$586$$ 23.3144i 0.963109i
$$587$$ 12.0976 0.499320 0.249660 0.968334i $$-0.419681\pi$$
0.249660 + 0.968334i $$0.419681\pi$$
$$588$$ 15.7466i 0.649377i
$$589$$ −23.7593 −0.978986
$$590$$ 2.68915 3.98806i 0.110710 0.164186i
$$591$$ −4.17716 −0.171825
$$592$$ −3.96343 4.61424i −0.162896 0.189644i
$$593$$ 17.2007i 0.706348i 0.935558 + 0.353174i $$0.114898\pi$$
−0.935558 + 0.353174i $$0.885102\pi$$
$$594$$ 29.7182i 1.21935i
$$595$$ 29.7177 44.0719i 1.21831 1.80677i
$$596$$ −21.6451 −0.886619
$$597$$ 17.5411 0.717910
$$598$$ −6.11023 −0.249866
$$599$$ 2.41919 0.0988454 0.0494227 0.998778i $$-0.484262\pi$$
0.0494227 + 0.998778i $$0.484262\pi$$
$$600$$ −4.57968 + 1.85184i −0.186965 + 0.0756011i
$$601$$ −39.0483 −1.59281 −0.796407 0.604761i $$-0.793269\pi$$
−0.796407 + 0.604761i $$0.793269\pi$$
$$602$$ 8.46945i 0.345189i
$$603$$ 7.68313i 0.312881i
$$604$$ 6.47544 0.263482
$$605$$ −46.0674 31.0632i −1.87290 1.26290i
$$606$$ 2.27647i 0.0924752i
$$607$$ −38.0508 −1.54443 −0.772217 0.635359i $$-0.780852\pi$$
−0.772217 + 0.635359i $$0.780852\pi$$
$$608$$ 7.33092i 0.297308i
$$609$$ 37.1450i 1.50519i
$$610$$ 3.83269 5.68396i 0.155181 0.230137i
$$611$$ 15.0469i 0.608733i
$$612$$ 10.0454 0.406063
$$613$$ 7.12176i 0.287645i 0.989603 + 0.143823i $$0.0459395\pi$$
−0.989603 + 0.143823i $$0.954061\pi$$
$$614$$ 14.2651i 0.575693i
$$615$$ 0.655427 0.972011i 0.0264294 0.0391953i
$$616$$ 28.6755i 1.15537i
$$617$$ 42.6678i 1.71774i 0.512192 + 0.858871i $$0.328834\pi$$
−0.512192 + 0.858871i $$0.671166\pi$$
$$618$$ 11.0373i 0.443986i
$$619$$ −6.30429 −0.253391 −0.126695 0.991942i $$-0.540437\pi$$
−0.126695 + 0.991942i $$0.540437\pi$$
$$620$$ 4.05163 6.00865i 0.162717 0.241313i
$$621$$ 8.67985i 0.348310i
$$622$$ 22.5322i 0.903458i
$$623$$ 40.5081 1.62292
$$624$$ 3.45211i 0.138195i
$$625$$ −17.9735 + 17.3768i −0.718941 + 0.695072i
$$626$$ 10.0000 0.399680
$$627$$ −43.3651 −1.73184
$$628$$ 13.1689i 0.525495i
$$629$$ −19.6722 22.9025i −0.784383 0.913181i
$$630$$ −12.1177 + 17.9708i −0.482780 + 0.715973i
$$631$$ 32.6385i 1.29932i −0.760225 0.649660i $$-0.774911\pi$$
0.760225 0.649660i $$-0.225089\pi$$
$$632$$ 5.56622i 0.221412i
$$633$$ 4.51826i 0.179585i
$$634$$ 12.3877i 0.491979i
$$635$$ 9.38875 13.9237i 0.372581 0.552546i
$$636$$ 3.61837 0.143478
$$637$$ 55.6892 2.20649
$$638$$ 47.0007i 1.86078i
$$639$$ −17.1569 −0.678716
$$640$$ 1.85396 + 1.25013i 0.0732844 + 0.0494156i
$$641$$ −12.1721 −0.480767 −0.240384 0.970678i $$-0.577273\pi$$
−0.240384 + 0.970678i $$0.577273\pi$$
$$642$$ 6.43975 0.254156
$$643$$ 10.0853 0.397727 0.198864 0.980027i $$-0.436275\pi$$
0.198864 + 0.980027i $$0.436275\pi$$
$$644$$ 8.37532i 0.330034i
$$645$$ −2.18414 + 3.23912i −0.0860004 + 0.127540i
$$646$$ 36.3865i 1.43161i
$$647$$ −38.5061 −1.51383 −0.756916 0.653512i $$-0.773295\pi$$
−0.756916 + 0.653512i $$0.773295\pi$$
$$648$$ −1.16780 −0.0458754
$$649$$ 12.8793i 0.505558i
$$650$$ 6.54921 + 16.1965i 0.256881 + 0.635278i
$$651$$ 15.3357i 0.601053i
$$652$$ 18.7651 0.734896
$$653$$ −2.20349 −0.0862293 −0.0431146 0.999070i $$-0.513728\pi$$
−0.0431146 + 0.999070i $$0.513728\pi$$
$$654$$ 1.32204 0.0516960
$$655$$ 7.75048 11.4941i 0.302836 0.449112i
$$656$$ −0.530665 −0.0207190
$$657$$ 18.3252i 0.714935i
$$658$$ 20.6249 0.804041
$$659$$ −20.4048 −0.794859 −0.397430 0.917633i $$-0.630098\pi$$
−0.397430 + 0.917633i $$0.630098\pi$$
$$660$$ 7.39497 10.9669i 0.287849 0.426886i
$$661$$ 27.0306i 1.05137i −0.850680 0.525684i $$-0.823809\pi$$
0.850680 0.525684i $$-0.176191\pi$$
$$662$$ 19.0068i 0.738721i
$$663$$ 17.1343i 0.665442i
$$664$$ 3.77680i 0.146568i
$$665$$ 65.0936 + 43.8926i 2.52422 + 1.70208i
$$666$$ 8.02155 + 9.33871i 0.310829 + 0.361868i
$$667$$ 13.7276i 0.531535i
$$668$$ 7.19692 0.278457
$$669$$ 20.0763 0.776194
$$670$$ −4.74575 + 7.03805i −0.183344 + 0.271904i
$$671$$ 18.3562i 0.708632i
$$672$$ −4.73182 −0.182534
$$673$$ 11.6776i 0.450139i 0.974343 + 0.225070i $$0.0722609\pi$$
−0.974343 + 0.225070i $$0.927739\pi$$
$$674$$ 25.1046i 0.966991i
$$675$$ 23.0078 9.30344i 0.885570 0.358090i
$$676$$ −0.791278 −0.0304338
$$677$$ 37.2578i 1.43193i 0.698135 + 0.715966i $$0.254014\pi$$
−0.698135 + 0.715966i $$0.745986\pi$$
$$678$$ 1.37438i 0.0527826i
$$679$$ 17.4691i 0.670402i
$$680$$ 9.20203 + 6.20492i 0.352882 + 0.237948i
$$681$$ 5.67402i 0.217429i
$$682$$ 19.4047i 0.743046i
$$683$$ −46.3018 −1.77169 −0.885845 0.463981i $$-0.846420\pi$$
−0.885845 + 0.463981i $$0.846420\pi$$
$$684$$ 14.8370i 0.567306i
$$685$$ 11.2160 16.6335i 0.428540 0.635533i
$$686$$ 42.8078i 1.63441i
$$687$$ 23.1566i 0.883480i
$$688$$ 1.76838 0.0674190
$$689$$ 12.7967i 0.487516i
$$690$$ −2.15986 + 3.20312i −0.0822246 + 0.121941i
$$691$$ 29.7037 1.12998 0.564991 0.825097i $$-0.308879\pi$$
0.564991 + 0.825097i $$0.308879\pi$$
$$692$$ 9.79406i 0.372314i
$$693$$ 58.0361i 2.20461i
$$694$$ −30.4282 −1.15504
$$695$$ −9.34708 6.30273i −0.354555 0.239076i
$$696$$ −7.75571 −0.293979
$$697$$ −2.63392 −0.0997669
$$698$$ −15.1341 −0.572835
$$699$$ −17.0882 −0.646336
$$700$$ −22.2006 + 8.97703i −0.839102 + 0.339300i
$$701$$ 45.9214i 1.73443i 0.497936 + 0.867214i $$0.334091\pi$$
−0.497936 + 0.867214i $$0.665909\pi$$
$$702$$ 17.3430i 0.654570i
$$703$$ 33.8266 29.0556i 1.27580 1.09585i
$$704$$ −5.98732 −0.225656
$$705$$ −7.88793 5.31883i −0.297077 0.200319i
$$706$$ 10.1331 0.381365
$$707$$ 11.0355i 0.415031i
$$708$$ −2.12525 −0.0798717
$$709$$ 52.6575i 1.97759i 0.149266 + 0.988797i $$0.452309\pi$$
−0.149266 + 0.988797i $$0.547691\pi$$
$$710$$ −15.7164 10.5976i −0.589826 0.397719i
$$711$$ 11.2654i 0.422486i
$$712$$ 8.45791i 0.316974i
$$713$$ 5.66759i 0.212253i
$$714$$ −23.4861 −0.878944
$$715$$ −38.7855 26.1530i −1.45049 0.978068i
$$716$$ 11.2829i 0.421660i
$$717$$ 3.64364 0.136074
$$718$$ 26.3685 0.984063
$$719$$ −13.3494 −0.497850 −0.248925 0.968523i $$-0.580077\pi$$
−0.248925 + 0.968523i $$0.580077\pi$$
$$720$$ −3.75222 2.53012i −0.139837 0.0942920i
$$721$$ 53.5048i 1.99262i
$$722$$ 34.7424 1.29298
$$723$$ 11.2247 0.417453
$$724$$ 1.82697 0.0678989
$$725$$ −36.3879 + 14.7138i −1.35141 + 0.546458i
$$726$$ 24.5494i 0.911115i
$$727$$ 13.1733 0.488571 0.244286 0.969703i $$-0.421447\pi$$
0.244286 + 0.969703i $$0.421447\pi$$
$$728$$ 16.7345i 0.620223i
$$729$$ −12.3481 −0.457338
$$730$$ 11.3192 16.7866i 0.418943 0.621301i
$$731$$ 8.77726 0.324639
$$732$$ −3.02900 −0.111955
$$733$$ 32.3264i 1.19400i −0.802241 0.597001i $$-0.796359\pi$$
0.802241 0.597001i $$-0.203641\pi$$
$$734$$ 2.21157i 0.0816305i
$$735$$ 19.6852 29.1935i 0.726099 1.07682i
$$736$$ 1.74873 0.0644590
$$737$$ 22.7292i 0.837240i
$$738$$ 1.07401 0.0395348
$$739$$ 6.94169 0.255354 0.127677 0.991816i $$-0.459248\pi$$
0.127677 + 0.991816i $$0.459248\pi$$
$$740$$ 1.57968 + 13.5094i 0.0580701 + 0.496616i
$$741$$ −25.3072 −0.929681
$$742$$ 17.5405 0.643933
$$743$$ 36.0784i 1.32359i −0.749685 0.661795i $$-0.769795\pi$$
0.749685 0.661795i $$-0.230205\pi$$
$$744$$ −3.20203 −0.117392
$$745$$ 40.1293 + 27.0592i 1.47022 + 0.991371i
$$746$$ 6.08275i 0.222705i
$$747$$ 7.64382i 0.279673i
$$748$$ −29.7177 −1.08659
$$749$$ 31.2175 1.14066
$$750$$ 10.8056 + 2.29193i 0.394564 + 0.0836896i
$$751$$ −29.9052 −1.09126 −0.545629 0.838027i $$-0.683709\pi$$
−0.545629 + 0.838027i $$0.683709\pi$$
$$752$$ 4.30638i 0.157038i
$$753$$ 12.6718 0.461787
$$754$$ 27.4288i 0.998898i
$$755$$ −12.0052 8.09512i −0.436915 0.294612i
$$756$$ 23.7721 0.864584
$$757$$ 24.9464 0.906693 0.453347 0.891334i $$-0.350230\pi$$
0.453347 + 0.891334i $$0.350230\pi$$
$$758$$ 20.0919 0.729769
$$759$$ 10.3444i 0.375477i
$$760$$ −9.16459 + 13.5913i −0.332434 + 0.493007i
$$761$$ 11.7647 0.426469 0.213235 0.977001i $$-0.431600\pi$$
0.213235 + 0.977001i $$0.431600\pi$$
$$762$$ −7.41999 −0.268798
$$763$$ 6.40878 0.232013
$$764$$ 23.8204i 0.861791i
$$765$$ −18.6239 12.5581i −0.673348 0.454038i
$$766$$ −11.5368 −0.416840
$$767$$ 7.51615i 0.271392i
$$768$$ 0.987983i 0.0356508i
$$769$$ 26.7939i 0.966214i −0.875561 0.483107i $$-0.839508\pi$$
0.875561 0.483107i $$-0.160492\pi$$
$$770$$ 35.8480 53.1634i 1.29187 1.91587i
$$771$$ 13.8582i 0.499091i
$$772$$ 8.40405 0.302468
$$773$$ 2.77358i 0.0997589i 0.998755 + 0.0498794i $$0.0158837\pi$$
−0.998755 + 0.0498794i $$0.984116\pi$$
$$774$$ −3.57901 −0.128645
$$775$$ −15.0231 + 6.07477i −0.539647 + 0.218212i
$$776$$ −3.64747 −0.130937
$$777$$ −18.7542 21.8337i −0.672805 0.783281i
$$778$$ 8.55057i 0.306553i
$$779$$ 3.89026i 0.139383i
$$780$$ 4.31558 6.40009i 0.154522 0.229160i
$$781$$ 50.7556 1.81618
$$782$$ 8.67970 0.310386
$$783$$ 38.9638 1.39245
$$784$$ −15.9381 −0.569217
$$785$$ 16.4628 24.4146i 0.587581 0.871395i
$$786$$ −6.12525 −0.218480
$$787$$ 28.0910i 1.00134i −0.865639 0.500669i $$-0.833088\pi$$
0.865639 0.500669i $$-0.166912\pi$$