Properties

 Label 1050.2.d.a.1049.3 Level $1050$ Weight $2$ Character 1050.1049 Analytic conductor $8.384$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1050.d (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$8.38429221223$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 210) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 1049.3 Root $$0.618034i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.1049 Dual form 1050.2.d.a.1049.4

$q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +(0.618034 - 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} -1.00000 q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +(0.618034 - 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} -1.00000 q^{8} +(-2.23607 - 2.00000i) q^{9} +4.47214i q^{11} +(0.618034 - 1.61803i) q^{12} +1.23607 q^{13} +(-0.381966 - 2.61803i) q^{14} +1.00000 q^{16} -5.23607i q^{17} +(2.23607 + 2.00000i) q^{18} +8.47214i q^{19} +(4.47214 + 1.00000i) q^{21} -4.47214i q^{22} -4.00000 q^{23} +(-0.618034 + 1.61803i) q^{24} -1.23607 q^{26} +(-4.61803 + 2.38197i) q^{27} +(0.381966 + 2.61803i) q^{28} +7.70820i q^{29} +2.76393i q^{31} -1.00000 q^{32} +(7.23607 + 2.76393i) q^{33} +5.23607i q^{34} +(-2.23607 - 2.00000i) q^{36} +0.763932i q^{37} -8.47214i q^{38} +(0.763932 - 2.00000i) q^{39} +2.47214 q^{41} +(-4.47214 - 1.00000i) q^{42} +4.94427i q^{43} +4.47214i q^{44} +4.00000 q^{46} +6.47214i q^{47} +(0.618034 - 1.61803i) q^{48} +(-6.70820 + 2.00000i) q^{49} +(-8.47214 - 3.23607i) q^{51} +1.23607 q^{52} +0.472136 q^{53} +(4.61803 - 2.38197i) q^{54} +(-0.381966 - 2.61803i) q^{56} +(13.7082 + 5.23607i) q^{57} -7.70820i q^{58} +4.47214 q^{59} -7.23607i q^{61} -2.76393i q^{62} +(4.38197 - 6.61803i) q^{63} +1.00000 q^{64} +(-7.23607 - 2.76393i) q^{66} -12.0000i q^{67} -5.23607i q^{68} +(-2.47214 + 6.47214i) q^{69} -7.23607i q^{71} +(2.23607 + 2.00000i) q^{72} +11.2361 q^{73} -0.763932i q^{74} +8.47214i q^{76} +(-11.7082 + 1.70820i) q^{77} +(-0.763932 + 2.00000i) q^{78} +8.94427 q^{79} +(1.00000 + 8.94427i) q^{81} -2.47214 q^{82} +14.6525i q^{83} +(4.47214 + 1.00000i) q^{84} -4.94427i q^{86} +(12.4721 + 4.76393i) q^{87} -4.47214i q^{88} -5.52786 q^{89} +(0.472136 + 3.23607i) q^{91} -4.00000 q^{92} +(4.47214 + 1.70820i) q^{93} -6.47214i q^{94} +(-0.618034 + 1.61803i) q^{96} +0.763932 q^{97} +(6.70820 - 2.00000i) q^{98} +(8.94427 - 10.0000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{2} - 2q^{3} + 4q^{4} + 2q^{6} + 6q^{7} - 4q^{8} + O(q^{10})$$ $$4q - 4q^{2} - 2q^{3} + 4q^{4} + 2q^{6} + 6q^{7} - 4q^{8} - 2q^{12} - 4q^{13} - 6q^{14} + 4q^{16} - 16q^{23} + 2q^{24} + 4q^{26} - 14q^{27} + 6q^{28} - 4q^{32} + 20q^{33} + 12q^{39} - 8q^{41} + 16q^{46} - 2q^{48} - 16q^{51} - 4q^{52} - 16q^{53} + 14q^{54} - 6q^{56} + 28q^{57} + 22q^{63} + 4q^{64} - 20q^{66} + 8q^{69} + 36q^{73} - 20q^{77} - 12q^{78} + 4q^{81} + 8q^{82} + 32q^{87} - 40q^{89} - 16q^{91} - 16q^{92} + 2q^{96} + 12q^{97} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

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
$$3$$ 0.618034 1.61803i 0.356822 0.934172i
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ −0.618034 + 1.61803i −0.252311 + 0.660560i
$$7$$ 0.381966 + 2.61803i 0.144370 + 0.989524i
$$8$$ −1.00000 −0.353553
$$9$$ −2.23607 2.00000i −0.745356 0.666667i
$$10$$ 0 0
$$11$$ 4.47214i 1.34840i 0.738549 + 0.674200i $$0.235511\pi$$
−0.738549 + 0.674200i $$0.764489\pi$$
$$12$$ 0.618034 1.61803i 0.178411 0.467086i
$$13$$ 1.23607 0.342824 0.171412 0.985199i $$-0.445167\pi$$
0.171412 + 0.985199i $$0.445167\pi$$
$$14$$ −0.381966 2.61803i −0.102085 0.699699i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 5.23607i 1.26993i −0.772540 0.634967i $$-0.781014\pi$$
0.772540 0.634967i $$-0.218986\pi$$
$$18$$ 2.23607 + 2.00000i 0.527046 + 0.471405i
$$19$$ 8.47214i 1.94364i 0.235722 + 0.971821i $$0.424255\pi$$
−0.235722 + 0.971821i $$0.575745\pi$$
$$20$$ 0 0
$$21$$ 4.47214 + 1.00000i 0.975900 + 0.218218i
$$22$$ 4.47214i 0.953463i
$$23$$ −4.00000 −0.834058 −0.417029 0.908893i $$-0.636929\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ −0.618034 + 1.61803i −0.126156 + 0.330280i
$$25$$ 0 0
$$26$$ −1.23607 −0.242413
$$27$$ −4.61803 + 2.38197i −0.888741 + 0.458410i
$$28$$ 0.381966 + 2.61803i 0.0721848 + 0.494762i
$$29$$ 7.70820i 1.43138i 0.698419 + 0.715689i $$0.253887\pi$$
−0.698419 + 0.715689i $$0.746113\pi$$
$$30$$ 0 0
$$31$$ 2.76393i 0.496417i 0.968707 + 0.248208i $$0.0798418\pi$$
−0.968707 + 0.248208i $$0.920158\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 7.23607 + 2.76393i 1.25964 + 0.481139i
$$34$$ 5.23607i 0.897978i
$$35$$ 0 0
$$36$$ −2.23607 2.00000i −0.372678 0.333333i
$$37$$ 0.763932i 0.125590i 0.998026 + 0.0627948i $$0.0200014\pi$$
−0.998026 + 0.0627948i $$0.979999\pi$$
$$38$$ 8.47214i 1.37436i
$$39$$ 0.763932 2.00000i 0.122327 0.320256i
$$40$$ 0 0
$$41$$ 2.47214 0.386083 0.193041 0.981191i $$-0.438165\pi$$
0.193041 + 0.981191i $$0.438165\pi$$
$$42$$ −4.47214 1.00000i −0.690066 0.154303i
$$43$$ 4.94427i 0.753994i 0.926214 + 0.376997i $$0.123043\pi$$
−0.926214 + 0.376997i $$0.876957\pi$$
$$44$$ 4.47214i 0.674200i
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ 6.47214i 0.944058i 0.881583 + 0.472029i $$0.156478\pi$$
−0.881583 + 0.472029i $$0.843522\pi$$
$$48$$ 0.618034 1.61803i 0.0892055 0.233543i
$$49$$ −6.70820 + 2.00000i −0.958315 + 0.285714i
$$50$$ 0 0
$$51$$ −8.47214 3.23607i −1.18634 0.453140i
$$52$$ 1.23607 0.171412
$$53$$ 0.472136 0.0648529 0.0324264 0.999474i $$-0.489677\pi$$
0.0324264 + 0.999474i $$0.489677\pi$$
$$54$$ 4.61803 2.38197i 0.628435 0.324145i
$$55$$ 0 0
$$56$$ −0.381966 2.61803i −0.0510424 0.349850i
$$57$$ 13.7082 + 5.23607i 1.81570 + 0.693534i
$$58$$ 7.70820i 1.01214i
$$59$$ 4.47214 0.582223 0.291111 0.956689i $$-0.405975\pi$$
0.291111 + 0.956689i $$0.405975\pi$$
$$60$$ 0 0
$$61$$ 7.23607i 0.926484i −0.886232 0.463242i $$-0.846686\pi$$
0.886232 0.463242i $$-0.153314\pi$$
$$62$$ 2.76393i 0.351020i
$$63$$ 4.38197 6.61803i 0.552076 0.833794i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −7.23607 2.76393i −0.890698 0.340217i
$$67$$ 12.0000i 1.46603i −0.680211 0.733017i $$-0.738112\pi$$
0.680211 0.733017i $$-0.261888\pi$$
$$68$$ 5.23607i 0.634967i
$$69$$ −2.47214 + 6.47214i −0.297610 + 0.779154i
$$70$$ 0 0
$$71$$ 7.23607i 0.858763i −0.903123 0.429382i $$-0.858732\pi$$
0.903123 0.429382i $$-0.141268\pi$$
$$72$$ 2.23607 + 2.00000i 0.263523 + 0.235702i
$$73$$ 11.2361 1.31508 0.657541 0.753419i $$-0.271597\pi$$
0.657541 + 0.753419i $$0.271597\pi$$
$$74$$ 0.763932i 0.0888053i
$$75$$ 0 0
$$76$$ 8.47214i 0.971821i
$$77$$ −11.7082 + 1.70820i −1.33427 + 0.194668i
$$78$$ −0.763932 + 2.00000i −0.0864983 + 0.226455i
$$79$$ 8.94427 1.00631 0.503155 0.864196i $$-0.332173\pi$$
0.503155 + 0.864196i $$0.332173\pi$$
$$80$$ 0 0
$$81$$ 1.00000 + 8.94427i 0.111111 + 0.993808i
$$82$$ −2.47214 −0.273002
$$83$$ 14.6525i 1.60832i 0.594414 + 0.804159i $$0.297384\pi$$
−0.594414 + 0.804159i $$0.702616\pi$$
$$84$$ 4.47214 + 1.00000i 0.487950 + 0.109109i
$$85$$ 0 0
$$86$$ 4.94427i 0.533155i
$$87$$ 12.4721 + 4.76393i 1.33715 + 0.510747i
$$88$$ 4.47214i 0.476731i
$$89$$ −5.52786 −0.585952 −0.292976 0.956120i $$-0.594646\pi$$
−0.292976 + 0.956120i $$0.594646\pi$$
$$90$$ 0 0
$$91$$ 0.472136 + 3.23607i 0.0494933 + 0.339232i
$$92$$ −4.00000 −0.417029
$$93$$ 4.47214 + 1.70820i 0.463739 + 0.177132i
$$94$$ 6.47214i 0.667550i
$$95$$ 0 0
$$96$$ −0.618034 + 1.61803i −0.0630778 + 0.165140i
$$97$$ 0.763932 0.0775655 0.0387828 0.999248i $$-0.487652\pi$$
0.0387828 + 0.999248i $$0.487652\pi$$
$$98$$ 6.70820 2.00000i 0.677631 0.202031i
$$99$$ 8.94427 10.0000i 0.898933 1.00504i
$$100$$ 0 0
$$101$$ 12.4721 1.24102 0.620512 0.784197i $$-0.286925\pi$$
0.620512 + 0.784197i $$0.286925\pi$$
$$102$$ 8.47214 + 3.23607i 0.838866 + 0.320418i
$$103$$ 14.6525 1.44375 0.721876 0.692023i $$-0.243280\pi$$
0.721876 + 0.692023i $$0.243280\pi$$
$$104$$ −1.23607 −0.121206
$$105$$ 0 0
$$106$$ −0.472136 −0.0458579
$$107$$ −11.4164 −1.10367 −0.551833 0.833955i $$-0.686071\pi$$
−0.551833 + 0.833955i $$0.686071\pi$$
$$108$$ −4.61803 + 2.38197i −0.444371 + 0.229205i
$$109$$ −4.47214 −0.428353 −0.214176 0.976795i $$-0.568707\pi$$
−0.214176 + 0.976795i $$0.568707\pi$$
$$110$$ 0 0
$$111$$ 1.23607 + 0.472136i 0.117322 + 0.0448132i
$$112$$ 0.381966 + 2.61803i 0.0360924 + 0.247381i
$$113$$ −2.94427 −0.276974 −0.138487 0.990364i $$-0.544224\pi$$
−0.138487 + 0.990364i $$0.544224\pi$$
$$114$$ −13.7082 5.23607i −1.28389 0.490403i
$$115$$ 0 0
$$116$$ 7.70820i 0.715689i
$$117$$ −2.76393 2.47214i −0.255526 0.228549i
$$118$$ −4.47214 −0.411693
$$119$$ 13.7082 2.00000i 1.25663 0.183340i
$$120$$ 0 0
$$121$$ −9.00000 −0.818182
$$122$$ 7.23607i 0.655123i
$$123$$ 1.52786 4.00000i 0.137763 0.360668i
$$124$$ 2.76393i 0.248208i
$$125$$ 0 0
$$126$$ −4.38197 + 6.61803i −0.390377 + 0.589581i
$$127$$ 0.291796i 0.0258927i −0.999916 0.0129464i $$-0.995879\pi$$
0.999916 0.0129464i $$-0.00412107\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 8.00000 + 3.05573i 0.704361 + 0.269042i
$$130$$ 0 0
$$131$$ −5.41641 −0.473234 −0.236617 0.971603i $$-0.576039\pi$$
−0.236617 + 0.971603i $$0.576039\pi$$
$$132$$ 7.23607 + 2.76393i 0.629819 + 0.240569i
$$133$$ −22.1803 + 3.23607i −1.92328 + 0.280603i
$$134$$ 12.0000i 1.03664i
$$135$$ 0 0
$$136$$ 5.23607i 0.448989i
$$137$$ −3.52786 −0.301406 −0.150703 0.988579i $$-0.548154\pi$$
−0.150703 + 0.988579i $$0.548154\pi$$
$$138$$ 2.47214 6.47214i 0.210442 0.550945i
$$139$$ 11.5279i 0.977781i −0.872345 0.488890i $$-0.837402\pi$$
0.872345 0.488890i $$-0.162598\pi$$
$$140$$ 0 0
$$141$$ 10.4721 + 4.00000i 0.881913 + 0.336861i
$$142$$ 7.23607i 0.607237i
$$143$$ 5.52786i 0.462263i
$$144$$ −2.23607 2.00000i −0.186339 0.166667i
$$145$$ 0 0
$$146$$ −11.2361 −0.929904
$$147$$ −0.909830 + 12.0902i −0.0750415 + 0.997180i
$$148$$ 0.763932i 0.0627948i
$$149$$ 4.29180i 0.351598i 0.984426 + 0.175799i $$0.0562508\pi$$
−0.984426 + 0.175799i $$0.943749\pi$$
$$150$$ 0 0
$$151$$ 20.9443 1.70442 0.852210 0.523199i $$-0.175262\pi$$
0.852210 + 0.523199i $$0.175262\pi$$
$$152$$ 8.47214i 0.687181i
$$153$$ −10.4721 + 11.7082i −0.846622 + 0.946552i
$$154$$ 11.7082 1.70820i 0.943474 0.137651i
$$155$$ 0 0
$$156$$ 0.763932 2.00000i 0.0611635 0.160128i
$$157$$ −9.23607 −0.737118 −0.368559 0.929604i $$-0.620149\pi$$
−0.368559 + 0.929604i $$0.620149\pi$$
$$158$$ −8.94427 −0.711568
$$159$$ 0.291796 0.763932i 0.0231409 0.0605838i
$$160$$ 0 0
$$161$$ −1.52786 10.4721i −0.120413 0.825320i
$$162$$ −1.00000 8.94427i −0.0785674 0.702728i
$$163$$ 10.4721i 0.820241i 0.912031 + 0.410120i $$0.134513\pi$$
−0.912031 + 0.410120i $$0.865487\pi$$
$$164$$ 2.47214 0.193041
$$165$$ 0 0
$$166$$ 14.6525i 1.13725i
$$167$$ 0.944272i 0.0730700i 0.999332 + 0.0365350i $$0.0116320\pi$$
−0.999332 + 0.0365350i $$0.988368\pi$$
$$168$$ −4.47214 1.00000i −0.345033 0.0771517i
$$169$$ −11.4721 −0.882472
$$170$$ 0 0
$$171$$ 16.9443 18.9443i 1.29576 1.44870i
$$172$$ 4.94427i 0.376997i
$$173$$ 9.41641i 0.715916i −0.933738 0.357958i $$-0.883473\pi$$
0.933738 0.357958i $$-0.116527\pi$$
$$174$$ −12.4721 4.76393i −0.945510 0.361153i
$$175$$ 0 0
$$176$$ 4.47214i 0.337100i
$$177$$ 2.76393 7.23607i 0.207750 0.543896i
$$178$$ 5.52786 0.414331
$$179$$ 14.9443i 1.11699i 0.829509 + 0.558494i $$0.188620\pi$$
−0.829509 + 0.558494i $$0.811380\pi$$
$$180$$ 0 0
$$181$$ 16.1803i 1.20268i 0.798995 + 0.601338i $$0.205365\pi$$
−0.798995 + 0.601338i $$0.794635\pi$$
$$182$$ −0.472136 3.23607i −0.0349970 0.239873i
$$183$$ −11.7082 4.47214i −0.865495 0.330590i
$$184$$ 4.00000 0.294884
$$185$$ 0 0
$$186$$ −4.47214 1.70820i −0.327913 0.125252i
$$187$$ 23.4164 1.71238
$$188$$ 6.47214i 0.472029i
$$189$$ −8.00000 11.1803i −0.581914 0.813250i
$$190$$ 0 0
$$191$$ 7.23607i 0.523584i 0.965124 + 0.261792i $$0.0843134\pi$$
−0.965124 + 0.261792i $$0.915687\pi$$
$$192$$ 0.618034 1.61803i 0.0446028 0.116772i
$$193$$ 6.00000i 0.431889i 0.976406 + 0.215945i $$0.0692831\pi$$
−0.976406 + 0.215945i $$0.930717\pi$$
$$194$$ −0.763932 −0.0548471
$$195$$ 0 0
$$196$$ −6.70820 + 2.00000i −0.479157 + 0.142857i
$$197$$ −3.52786 −0.251350 −0.125675 0.992071i $$-0.540110\pi$$
−0.125675 + 0.992071i $$0.540110\pi$$
$$198$$ −8.94427 + 10.0000i −0.635642 + 0.710669i
$$199$$ 22.1803i 1.57232i −0.618021 0.786161i $$-0.712065\pi$$
0.618021 0.786161i $$-0.287935\pi$$
$$200$$ 0 0
$$201$$ −19.4164 7.41641i −1.36953 0.523113i
$$202$$ −12.4721 −0.877536
$$203$$ −20.1803 + 2.94427i −1.41638 + 0.206647i
$$204$$ −8.47214 3.23607i −0.593168 0.226570i
$$205$$ 0 0
$$206$$ −14.6525 −1.02089
$$207$$ 8.94427 + 8.00000i 0.621670 + 0.556038i
$$208$$ 1.23607 0.0857059
$$209$$ −37.8885 −2.62081
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ 0.472136 0.0324264
$$213$$ −11.7082 4.47214i −0.802233 0.306426i
$$214$$ 11.4164 0.780410
$$215$$ 0 0
$$216$$ 4.61803 2.38197i 0.314217 0.162072i
$$217$$ −7.23607 + 1.05573i −0.491216 + 0.0716675i
$$218$$ 4.47214 0.302891
$$219$$ 6.94427 18.1803i 0.469250 1.22851i
$$220$$ 0 0
$$221$$ 6.47214i 0.435363i
$$222$$ −1.23607 0.472136i −0.0829595 0.0316877i
$$223$$ −17.7082 −1.18583 −0.592915 0.805265i $$-0.702023\pi$$
−0.592915 + 0.805265i $$0.702023\pi$$
$$224$$ −0.381966 2.61803i −0.0255212 0.174925i
$$225$$ 0 0
$$226$$ 2.94427 0.195850
$$227$$ 0.763932i 0.0507039i −0.999679 0.0253520i $$-0.991929\pi$$
0.999679 0.0253520i $$-0.00807065\pi$$
$$228$$ 13.7082 + 5.23607i 0.907848 + 0.346767i
$$229$$ 8.76393i 0.579137i −0.957157 0.289568i $$-0.906488\pi$$
0.957157 0.289568i $$-0.0935118\pi$$
$$230$$ 0 0
$$231$$ −4.47214 + 20.0000i −0.294245 + 1.31590i
$$232$$ 7.70820i 0.506068i
$$233$$ 11.5279 0.755215 0.377608 0.925966i $$-0.376747\pi$$
0.377608 + 0.925966i $$0.376747\pi$$
$$234$$ 2.76393 + 2.47214i 0.180684 + 0.161609i
$$235$$ 0 0
$$236$$ 4.47214 0.291111
$$237$$ 5.52786 14.4721i 0.359073 0.940066i
$$238$$ −13.7082 + 2.00000i −0.888571 + 0.129641i
$$239$$ 0.180340i 0.0116652i −0.999983 0.00583261i $$-0.998143\pi$$
0.999983 0.00583261i $$-0.00185659\pi$$
$$240$$ 0 0
$$241$$ 17.8885i 1.15230i −0.817343 0.576151i $$-0.804554\pi$$
0.817343 0.576151i $$-0.195446\pi$$
$$242$$ 9.00000 0.578542
$$243$$ 15.0902 + 3.90983i 0.968035 + 0.250816i
$$244$$ 7.23607i 0.463242i
$$245$$ 0 0
$$246$$ −1.52786 + 4.00000i −0.0974131 + 0.255031i
$$247$$ 10.4721i 0.666326i
$$248$$ 2.76393i 0.175510i
$$249$$ 23.7082 + 9.05573i 1.50245 + 0.573883i
$$250$$ 0 0
$$251$$ 12.4721 0.787234 0.393617 0.919274i $$-0.371224\pi$$
0.393617 + 0.919274i $$0.371224\pi$$
$$252$$ 4.38197 6.61803i 0.276038 0.416897i
$$253$$ 17.8885i 1.12464i
$$254$$ 0.291796i 0.0183089i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 14.1803i 0.884545i −0.896881 0.442273i $$-0.854172\pi$$
0.896881 0.442273i $$-0.145828\pi$$
$$258$$ −8.00000 3.05573i −0.498058 0.190241i
$$259$$ −2.00000 + 0.291796i −0.124274 + 0.0181313i
$$260$$ 0 0
$$261$$ 15.4164 17.2361i 0.954252 1.06689i
$$262$$ 5.41641 0.334627
$$263$$ −12.9443 −0.798178 −0.399089 0.916912i $$-0.630674\pi$$
−0.399089 + 0.916912i $$0.630674\pi$$
$$264$$ −7.23607 2.76393i −0.445349 0.170108i
$$265$$ 0 0
$$266$$ 22.1803 3.23607i 1.35996 0.198416i
$$267$$ −3.41641 + 8.94427i −0.209081 + 0.547381i
$$268$$ 12.0000i 0.733017i
$$269$$ 4.47214 0.272671 0.136335 0.990663i $$-0.456467\pi$$
0.136335 + 0.990663i $$0.456467\pi$$
$$270$$ 0 0
$$271$$ 31.7082i 1.92614i −0.269258 0.963068i $$-0.586778\pi$$
0.269258 0.963068i $$-0.413222\pi$$
$$272$$ 5.23607i 0.317483i
$$273$$ 5.52786 + 1.23607i 0.334562 + 0.0748102i
$$274$$ 3.52786 0.213126
$$275$$ 0 0
$$276$$ −2.47214 + 6.47214i −0.148805 + 0.389577i
$$277$$ 17.1246i 1.02892i −0.857515 0.514459i $$-0.827993\pi$$
0.857515 0.514459i $$-0.172007\pi$$
$$278$$ 11.5279i 0.691395i
$$279$$ 5.52786 6.18034i 0.330945 0.370007i
$$280$$ 0 0
$$281$$ 20.0000i 1.19310i 0.802576 + 0.596550i $$0.203462\pi$$
−0.802576 + 0.596550i $$0.796538\pi$$
$$282$$ −10.4721 4.00000i −0.623607 0.238197i
$$283$$ −13.2361 −0.786803 −0.393401 0.919367i $$-0.628702\pi$$
−0.393401 + 0.919367i $$0.628702\pi$$
$$284$$ 7.23607i 0.429382i
$$285$$ 0 0
$$286$$ 5.52786i 0.326869i
$$287$$ 0.944272 + 6.47214i 0.0557386 + 0.382038i
$$288$$ 2.23607 + 2.00000i 0.131762 + 0.117851i
$$289$$ −10.4164 −0.612730
$$290$$ 0 0
$$291$$ 0.472136 1.23607i 0.0276771 0.0724596i
$$292$$ 11.2361 0.657541
$$293$$ 2.58359i 0.150935i −0.997148 0.0754675i $$-0.975955\pi$$
0.997148 0.0754675i $$-0.0240449\pi$$
$$294$$ 0.909830 12.0902i 0.0530624 0.705113i
$$295$$ 0 0
$$296$$ 0.763932i 0.0444026i
$$297$$ −10.6525 20.6525i −0.618119 1.19838i
$$298$$ 4.29180i 0.248617i
$$299$$ −4.94427 −0.285935
$$300$$ 0 0
$$301$$ −12.9443 + 1.88854i −0.746095 + 0.108854i
$$302$$ −20.9443 −1.20521
$$303$$ 7.70820 20.1803i 0.442825 1.15933i
$$304$$ 8.47214i 0.485910i
$$305$$ 0 0
$$306$$ 10.4721 11.7082i 0.598652 0.669313i
$$307$$ −18.1803 −1.03761 −0.518803 0.854894i $$-0.673622\pi$$
−0.518803 + 0.854894i $$0.673622\pi$$
$$308$$ −11.7082 + 1.70820i −0.667137 + 0.0973340i
$$309$$ 9.05573 23.7082i 0.515162 1.34871i
$$310$$ 0 0
$$311$$ −17.5279 −0.993914 −0.496957 0.867775i $$-0.665549\pi$$
−0.496957 + 0.867775i $$0.665549\pi$$
$$312$$ −0.763932 + 2.00000i −0.0432491 + 0.113228i
$$313$$ 5.70820 0.322647 0.161323 0.986902i $$-0.448424\pi$$
0.161323 + 0.986902i $$0.448424\pi$$
$$314$$ 9.23607 0.521221
$$315$$ 0 0
$$316$$ 8.94427 0.503155
$$317$$ 10.9443 0.614692 0.307346 0.951598i $$-0.400559\pi$$
0.307346 + 0.951598i $$0.400559\pi$$
$$318$$ −0.291796 + 0.763932i −0.0163631 + 0.0428392i
$$319$$ −34.4721 −1.93007
$$320$$ 0 0
$$321$$ −7.05573 + 18.4721i −0.393812 + 1.03101i
$$322$$ 1.52786 + 10.4721i 0.0851445 + 0.583589i
$$323$$ 44.3607 2.46829
$$324$$ 1.00000 + 8.94427i 0.0555556 + 0.496904i
$$325$$ 0 0
$$326$$ 10.4721i 0.579998i
$$327$$ −2.76393 + 7.23607i −0.152846 + 0.400155i
$$328$$ −2.47214 −0.136501
$$329$$ −16.9443 + 2.47214i −0.934168 + 0.136293i
$$330$$ 0 0
$$331$$ 3.05573 0.167958 0.0839790 0.996468i $$-0.473237\pi$$
0.0839790 + 0.996468i $$0.473237\pi$$
$$332$$ 14.6525i 0.804159i
$$333$$ 1.52786 1.70820i 0.0837264 0.0936090i
$$334$$ 0.944272i 0.0516683i
$$335$$ 0 0
$$336$$ 4.47214 + 1.00000i 0.243975 + 0.0545545i
$$337$$ 21.4164i 1.16663i 0.812247 + 0.583313i $$0.198244\pi$$
−0.812247 + 0.583313i $$0.801756\pi$$
$$338$$ 11.4721 0.624002
$$339$$ −1.81966 + 4.76393i −0.0988304 + 0.258741i
$$340$$ 0 0
$$341$$ −12.3607 −0.669368
$$342$$ −16.9443 + 18.9443i −0.916241 + 1.02439i
$$343$$ −7.79837 16.7984i −0.421073 0.907027i
$$344$$ 4.94427i 0.266577i
$$345$$ 0 0
$$346$$ 9.41641i 0.506229i
$$347$$ −2.47214 −0.132711 −0.0663556 0.997796i $$-0.521137\pi$$
−0.0663556 + 0.997796i $$0.521137\pi$$
$$348$$ 12.4721 + 4.76393i 0.668577 + 0.255374i
$$349$$ 20.1803i 1.08023i 0.841592 + 0.540114i $$0.181619\pi$$
−0.841592 + 0.540114i $$0.818381\pi$$
$$350$$ 0 0
$$351$$ −5.70820 + 2.94427i −0.304681 + 0.157154i
$$352$$ 4.47214i 0.238366i
$$353$$ 27.7082i 1.47476i −0.675479 0.737379i $$-0.736063\pi$$
0.675479 0.737379i $$-0.263937\pi$$
$$354$$ −2.76393 + 7.23607i −0.146901 + 0.384593i
$$355$$ 0 0
$$356$$ −5.52786 −0.292976
$$357$$ 5.23607 23.4164i 0.277122 1.23933i
$$358$$ 14.9443i 0.789829i
$$359$$ 12.1803i 0.642854i 0.946934 + 0.321427i $$0.104162\pi$$
−0.946934 + 0.321427i $$0.895838\pi$$
$$360$$ 0 0
$$361$$ −52.7771 −2.77774
$$362$$ 16.1803i 0.850420i
$$363$$ −5.56231 + 14.5623i −0.291945 + 0.764323i
$$364$$ 0.472136 + 3.23607i 0.0247466 + 0.169616i
$$365$$ 0 0
$$366$$ 11.7082 + 4.47214i 0.611998 + 0.233762i
$$367$$ −8.18034 −0.427010 −0.213505 0.976942i $$-0.568488\pi$$
−0.213505 + 0.976942i $$0.568488\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ −5.52786 4.94427i −0.287769 0.257389i
$$370$$ 0 0
$$371$$ 0.180340 + 1.23607i 0.00936278 + 0.0641735i
$$372$$ 4.47214 + 1.70820i 0.231869 + 0.0885662i
$$373$$ 32.1803i 1.66623i 0.553096 + 0.833117i $$0.313446\pi$$
−0.553096 + 0.833117i $$0.686554\pi$$
$$374$$ −23.4164 −1.21083
$$375$$ 0 0
$$376$$ 6.47214i 0.333775i
$$377$$ 9.52786i 0.490710i
$$378$$ 8.00000 + 11.1803i 0.411476 + 0.575055i
$$379$$ 17.8885 0.918873 0.459436 0.888211i $$-0.348051\pi$$
0.459436 + 0.888211i $$0.348051\pi$$
$$380$$ 0 0
$$381$$ −0.472136 0.180340i −0.0241883 0.00923909i
$$382$$ 7.23607i 0.370229i
$$383$$ 13.8885i 0.709671i −0.934929 0.354836i $$-0.884537\pi$$
0.934929 0.354836i $$-0.115463\pi$$
$$384$$ −0.618034 + 1.61803i −0.0315389 + 0.0825700i
$$385$$ 0 0
$$386$$ 6.00000i 0.305392i
$$387$$ 9.88854 11.0557i 0.502663 0.561994i
$$388$$ 0.763932 0.0387828
$$389$$ 30.1803i 1.53020i −0.643909 0.765102i $$-0.722689\pi$$
0.643909 0.765102i $$-0.277311\pi$$
$$390$$ 0 0
$$391$$ 20.9443i 1.05920i
$$392$$ 6.70820 2.00000i 0.338815 0.101015i
$$393$$ −3.34752 + 8.76393i −0.168860 + 0.442082i
$$394$$ 3.52786 0.177731
$$395$$ 0 0
$$396$$ 8.94427 10.0000i 0.449467 0.502519i
$$397$$ 23.1246 1.16059 0.580295 0.814406i $$-0.302937\pi$$
0.580295 + 0.814406i $$0.302937\pi$$
$$398$$ 22.1803i 1.11180i
$$399$$ −8.47214 + 37.8885i −0.424137 + 1.89680i
$$400$$ 0 0
$$401$$ 14.4721i 0.722704i 0.932429 + 0.361352i $$0.117685\pi$$
−0.932429 + 0.361352i $$0.882315\pi$$
$$402$$ 19.4164 + 7.41641i 0.968402 + 0.369897i
$$403$$ 3.41641i 0.170183i
$$404$$ 12.4721 0.620512
$$405$$ 0 0
$$406$$ 20.1803 2.94427i 1.00153 0.146122i
$$407$$ −3.41641 −0.169345
$$408$$ 8.47214 + 3.23607i 0.419433 + 0.160209i
$$409$$ 7.41641i 0.366718i 0.983046 + 0.183359i $$0.0586970\pi$$
−0.983046 + 0.183359i $$0.941303\pi$$
$$410$$ 0 0
$$411$$ −2.18034 + 5.70820i −0.107548 + 0.281565i
$$412$$ 14.6525 0.721876
$$413$$ 1.70820 + 11.7082i 0.0840552 + 0.576123i
$$414$$ −8.94427 8.00000i −0.439587 0.393179i
$$415$$ 0 0
$$416$$ −1.23607 −0.0606032
$$417$$ −18.6525 7.12461i −0.913416 0.348894i
$$418$$ 37.8885 1.85319
$$419$$ 36.8328 1.79940 0.899700 0.436508i $$-0.143785\pi$$
0.899700 + 0.436508i $$0.143785\pi$$
$$420$$ 0 0
$$421$$ −3.52786 −0.171938 −0.0859688 0.996298i $$-0.527399\pi$$
−0.0859688 + 0.996298i $$0.527399\pi$$
$$422$$ 8.00000 0.389434
$$423$$ 12.9443 14.4721i 0.629372 0.703659i
$$424$$ −0.472136 −0.0229289
$$425$$ 0 0
$$426$$ 11.7082 + 4.47214i 0.567264 + 0.216676i
$$427$$ 18.9443 2.76393i 0.916778 0.133756i
$$428$$ −11.4164 −0.551833
$$429$$ 8.94427 + 3.41641i 0.431834 + 0.164946i
$$430$$ 0 0
$$431$$ 39.5967i 1.90731i −0.300905 0.953654i $$-0.597289\pi$$
0.300905 0.953654i $$-0.402711\pi$$
$$432$$ −4.61803 + 2.38197i −0.222185 + 0.114602i
$$433$$ −26.6525 −1.28084 −0.640418 0.768026i $$-0.721239\pi$$
−0.640418 + 0.768026i $$0.721239\pi$$
$$434$$ 7.23607 1.05573i 0.347342 0.0506766i
$$435$$ 0 0
$$436$$ −4.47214 −0.214176
$$437$$ 33.8885i 1.62111i
$$438$$ −6.94427 + 18.1803i −0.331810 + 0.868690i
$$439$$ 10.1803i 0.485881i 0.970041 + 0.242941i $$0.0781120\pi$$
−0.970041 + 0.242941i $$0.921888\pi$$
$$440$$ 0 0
$$441$$ 19.0000 + 8.94427i 0.904762 + 0.425918i
$$442$$ 6.47214i 0.307848i
$$443$$ −18.4721 −0.877638 −0.438819 0.898576i $$-0.644603\pi$$
−0.438819 + 0.898576i $$0.644603\pi$$
$$444$$ 1.23607 + 0.472136i 0.0586612 + 0.0224066i
$$445$$ 0 0
$$446$$ 17.7082 0.838508
$$447$$ 6.94427 + 2.65248i 0.328453 + 0.125458i
$$448$$ 0.381966 + 2.61803i 0.0180462 + 0.123690i
$$449$$ 10.4721i 0.494211i 0.968989 + 0.247105i $$0.0794794\pi$$
−0.968989 + 0.247105i $$0.920521\pi$$
$$450$$ 0 0
$$451$$ 11.0557i 0.520594i
$$452$$ −2.94427 −0.138487
$$453$$ 12.9443 33.8885i 0.608175 1.59222i
$$454$$ 0.763932i 0.0358531i
$$455$$ 0 0
$$456$$ −13.7082 5.23607i −0.641945 0.245201i
$$457$$ 26.9443i 1.26040i 0.776433 + 0.630200i $$0.217027\pi$$
−0.776433 + 0.630200i $$0.782973\pi$$
$$458$$ 8.76393i 0.409512i
$$459$$ 12.4721 + 24.1803i 0.582149 + 1.12864i
$$460$$ 0 0
$$461$$ 6.94427 0.323427 0.161713 0.986838i $$-0.448298\pi$$
0.161713 + 0.986838i $$0.448298\pi$$
$$462$$ 4.47214 20.0000i 0.208063 0.930484i
$$463$$ 22.1803i 1.03081i 0.856947 + 0.515404i $$0.172358\pi$$
−0.856947 + 0.515404i $$0.827642\pi$$
$$464$$ 7.70820i 0.357844i
$$465$$ 0 0
$$466$$ −11.5279 −0.534018
$$467$$ 33.7082i 1.55983i 0.625886 + 0.779915i $$0.284738\pi$$
−0.625886 + 0.779915i $$0.715262\pi$$
$$468$$ −2.76393 2.47214i −0.127763 0.114275i
$$469$$ 31.4164 4.58359i 1.45067 0.211651i
$$470$$ 0 0
$$471$$ −5.70820 + 14.9443i −0.263020 + 0.688596i
$$472$$ −4.47214 −0.205847
$$473$$ −22.1115 −1.01669
$$474$$ −5.52786 + 14.4721i −0.253903 + 0.664727i
$$475$$ 0 0
$$476$$ 13.7082 2.00000i 0.628314 0.0916698i
$$477$$ −1.05573 0.944272i −0.0483385 0.0432352i
$$478$$ 0.180340i 0.00824855i
$$479$$ 37.8885 1.73117 0.865586 0.500761i $$-0.166946\pi$$
0.865586 + 0.500761i $$0.166946\pi$$
$$480$$ 0 0
$$481$$ 0.944272i 0.0430551i
$$482$$ 17.8885i 0.814801i
$$483$$ −17.8885 4.00000i −0.813957 0.182006i
$$484$$ −9.00000 −0.409091
$$485$$ 0 0
$$486$$ −15.0902 3.90983i −0.684504 0.177353i
$$487$$ 17.5967i 0.797385i 0.917085 + 0.398692i $$0.130536\pi$$
−0.917085 + 0.398692i $$0.869464\pi$$
$$488$$ 7.23607i 0.327561i
$$489$$ 16.9443 + 6.47214i 0.766246 + 0.292680i
$$490$$ 0 0
$$491$$ 13.4164i 0.605474i 0.953074 + 0.302737i $$0.0979004\pi$$
−0.953074 + 0.302737i $$0.902100\pi$$
$$492$$ 1.52786 4.00000i 0.0688814 0.180334i
$$493$$ 40.3607 1.81775
$$494$$ 10.4721i 0.471164i
$$495$$ 0 0
$$496$$ 2.76393i 0.124104i
$$497$$ 18.9443 2.76393i 0.849767 0.123979i
$$498$$ −23.7082 9.05573i −1.06239 0.405797i
$$499$$ −17.8885 −0.800801 −0.400401 0.916340i $$-0.631129\pi$$
−0.400401 + 0.916340i $$0.631129\pi$$
$$500$$ 0 0
$$501$$ 1.52786 + 0.583592i 0.0682599 + 0.0260730i
$$502$$ −12.4721 −0.556659
$$503$$ 28.3607i 1.26454i −0.774748 0.632270i $$-0.782123\pi$$
0.774748 0.632270i $$-0.217877\pi$$
$$504$$ −4.38197 + 6.61803i −0.195188 + 0.294791i
$$505$$ 0 0
$$506$$ 17.8885i 0.795243i
$$507$$ −7.09017 + 18.5623i −0.314886 + 0.824381i
$$508$$ 0.291796i 0.0129464i
$$509$$ 15.5279 0.688260 0.344130 0.938922i $$-0.388174\pi$$
0.344130 + 0.938922i $$0.388174\pi$$
$$510$$ 0 0
$$511$$ 4.29180 + 29.4164i 0.189858 + 1.30131i
$$512$$ −1.00000 −0.0441942
$$513$$ −20.1803 39.1246i −0.890984 1.72739i
$$514$$ 14.1803i 0.625468i
$$515$$ 0 0
$$516$$ 8.00000 + 3.05573i 0.352180 + 0.134521i
$$517$$ −28.9443 −1.27297
$$518$$ 2.00000 0.291796i 0.0878750 0.0128208i
$$519$$ −15.2361 5.81966i −0.668789 0.255455i
$$520$$ 0 0
$$521$$ 36.9443 1.61856 0.809279 0.587425i $$-0.199858\pi$$
0.809279 + 0.587425i $$0.199858\pi$$
$$522$$ −15.4164 + 17.2361i −0.674758 + 0.754402i
$$523$$ 42.5410 1.86019 0.930094 0.367320i $$-0.119725\pi$$
0.930094 + 0.367320i $$0.119725\pi$$
$$524$$ −5.41641 −0.236617
$$525$$ 0 0
$$526$$ 12.9443 0.564397
$$527$$ 14.4721 0.630416
$$528$$ 7.23607 + 2.76393i 0.314909 + 0.120285i
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ −10.0000 8.94427i −0.433963 0.388148i
$$532$$ −22.1803 + 3.23607i −0.961640 + 0.140301i
$$533$$ 3.05573 0.132358
$$534$$ 3.41641 8.94427i 0.147842 0.387056i
$$535$$ 0 0
$$536$$ 12.0000i 0.518321i
$$537$$ 24.1803 + 9.23607i 1.04346 + 0.398566i
$$538$$ −4.47214 −0.192807
$$539$$ −8.94427 30.0000i −0.385257 1.29219i
$$540$$ 0 0
$$541$$ 30.9443 1.33040 0.665199 0.746666i $$-0.268347\pi$$
0.665199 + 0.746666i $$0.268347\pi$$
$$542$$ 31.7082i 1.36198i
$$543$$ 26.1803 + 10.0000i 1.12351 + 0.429141i
$$544$$ 5.23607i 0.224495i
$$545$$ 0 0
$$546$$ −5.52786 1.23607i −0.236571 0.0528988i
$$547$$ 35.4164i 1.51430i −0.653243 0.757148i $$-0.726592\pi$$
0.653243 0.757148i $$-0.273408\pi$$
$$548$$ −3.52786 −0.150703
$$549$$ −14.4721 + 16.1803i −0.617656 + 0.690560i
$$550$$ 0 0
$$551$$ −65.3050 −2.78208
$$552$$ 2.47214 6.47214i 0.105221 0.275472i
$$553$$ 3.41641 + 23.4164i 0.145280 + 0.995767i
$$554$$ 17.1246i 0.727555i
$$555$$ 0 0
$$556$$ 11.5279i 0.488890i
$$557$$ 7.52786 0.318966 0.159483 0.987201i $$-0.449017\pi$$
0.159483 + 0.987201i $$0.449017\pi$$
$$558$$ −5.52786 + 6.18034i −0.234013 + 0.261635i
$$559$$ 6.11146i 0.258487i
$$560$$ 0 0
$$561$$ 14.4721 37.8885i 0.611014 1.59966i
$$562$$ 20.0000i 0.843649i
$$563$$ 40.1803i 1.69340i 0.532071 + 0.846700i $$0.321414\pi$$
−0.532071 + 0.846700i $$0.678586\pi$$
$$564$$ 10.4721 + 4.00000i 0.440956 + 0.168430i
$$565$$ 0 0
$$566$$ 13.2361 0.556353
$$567$$ −23.0344 + 6.03444i −0.967356 + 0.253423i
$$568$$ 7.23607i 0.303619i
$$569$$ 9.52786i 0.399429i −0.979854 0.199714i $$-0.935999\pi$$
0.979854 0.199714i $$-0.0640014\pi$$
$$570$$ 0 0
$$571$$ 18.8328 0.788129 0.394064 0.919083i $$-0.371069\pi$$
0.394064 + 0.919083i $$0.371069\pi$$
$$572$$ 5.52786i 0.231132i
$$573$$ 11.7082 + 4.47214i 0.489117 + 0.186826i
$$574$$ −0.944272 6.47214i −0.0394131 0.270142i
$$575$$ 0 0
$$576$$ −2.23607 2.00000i −0.0931695 0.0833333i
$$577$$ −8.18034 −0.340552 −0.170276 0.985396i $$-0.554466\pi$$
−0.170276 + 0.985396i $$0.554466\pi$$
$$578$$ 10.4164 0.433265
$$579$$ 9.70820 + 3.70820i 0.403459 + 0.154108i
$$580$$ 0 0
$$581$$ −38.3607 + 5.59675i −1.59147 + 0.232192i
$$582$$ −0.472136 + 1.23607i −0.0195707 + 0.0512367i
$$583$$ 2.11146i 0.0874476i
$$584$$ −11.2361 −0.464952
$$585$$ 0 0
$$586$$ 2.58359i 0.106727i
$$587$$ 10.2918i 0.424788i 0.977184 + 0.212394i $$0.0681260\pi$$
−0.977184 + 0.212394i $$0.931874\pi$$
$$588$$ −0.909830 + 12.0902i −0.0375208 + 0.498590i
$$589$$ −23.4164 −0.964856
$$590$$ 0 0
$$591$$ −2.18034 + 5.70820i −0.0896872 + 0.234804i
$$592$$ 0.763932i 0.0313974i
$$593$$ 29.0132i 1.19143i −0.803197 0.595714i $$-0.796869\pi$$
0.803197 0.595714i $$-0.203131\pi$$
$$594$$ 10.6525 + 20.6525i 0.437076 + 0.847381i
$$595$$ 0 0
$$596$$ 4.29180i 0.175799i
$$597$$ −35.8885 13.7082i −1.46882 0.561039i
$$598$$ 4.94427 0.202186
$$599$$ 36.7639i 1.50213i −0.660226 0.751067i $$-0.729540\pi$$
0.660226 0.751067i $$-0.270460\pi$$
$$600$$ 0 0
$$601$$ 5.52786i 0.225486i −0.993624 0.112743i $$-0.964036\pi$$
0.993624 0.112743i $$-0.0359637\pi$$
$$602$$ 12.9443 1.88854i 0.527569 0.0769713i
$$603$$ −24.0000 + 26.8328i −0.977356 + 1.09272i
$$604$$ 20.9443 0.852210
$$605$$ 0 0
$$606$$ −7.70820 + 20.1803i −0.313124 + 0.819770i
$$607$$ −19.2361 −0.780768 −0.390384 0.920652i $$-0.627658\pi$$
−0.390384 + 0.920652i $$0.627658\pi$$
$$608$$ 8.47214i 0.343590i
$$609$$ −7.70820 + 34.4721i −0.312352 + 1.39688i
$$610$$ 0 0
$$611$$ 8.00000i 0.323645i
$$612$$ −10.4721 + 11.7082i −0.423311 + 0.473276i
$$613$$ 38.0689i 1.53759i −0.639497 0.768794i $$-0.720857\pi$$
0.639497 0.768794i $$-0.279143\pi$$
$$614$$ 18.1803 0.733699
$$615$$ 0 0
$$616$$ 11.7082 1.70820i 0.471737 0.0688255i
$$617$$ 2.00000 0.0805170 0.0402585 0.999189i $$-0.487182\pi$$
0.0402585 + 0.999189i $$0.487182\pi$$
$$618$$ −9.05573 + 23.7082i −0.364275 + 0.953684i
$$619$$ 14.0000i 0.562708i 0.959604 + 0.281354i $$0.0907834\pi$$
−0.959604 + 0.281354i $$0.909217\pi$$
$$620$$ 0 0
$$621$$ 18.4721 9.52786i 0.741261 0.382340i
$$622$$ 17.5279 0.702803
$$623$$ −2.11146 14.4721i −0.0845937 0.579814i
$$624$$ 0.763932 2.00000i 0.0305818 0.0800641i
$$625$$ 0 0
$$626$$ −5.70820 −0.228146
$$627$$ −23.4164 + 61.3050i −0.935161 + 2.44828i
$$628$$ −9.23607 −0.368559
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ −5.88854 −0.234419 −0.117210 0.993107i $$-0.537395\pi$$
−0.117210 + 0.993107i $$0.537395\pi$$
$$632$$ −8.94427 −0.355784
$$633$$ −4.94427 + 12.9443i −0.196517 + 0.514489i
$$634$$ −10.9443 −0.434653
$$635$$ 0 0
$$636$$ 0.291796 0.763932i 0.0115705 0.0302919i
$$637$$ −8.29180 + 2.47214i −0.328533 + 0.0979496i
$$638$$ 34.4721 1.36476
$$639$$ −14.4721 + 16.1803i −0.572509 + 0.640084i
$$640$$ 0 0
$$641$$ 23.4164i 0.924893i 0.886647 + 0.462446i $$0.153028\pi$$
−0.886647 + 0.462446i $$0.846972\pi$$
$$642$$ 7.05573 18.4721i 0.278467 0.729037i
$$643$$ 12.2918 0.484741 0.242371 0.970184i $$-0.422075\pi$$
0.242371 + 0.970184i $$0.422075\pi$$
$$644$$ −1.52786 10.4721i −0.0602063 0.412660i
$$645$$ 0 0
$$646$$ −44.3607 −1.74535
$$647$$ 34.8328i 1.36942i −0.728816 0.684710i $$-0.759929\pi$$
0.728816 0.684710i $$-0.240071\pi$$
$$648$$ −1.00000 8.94427i −0.0392837 0.351364i
$$649$$ 20.0000i 0.785069i
$$650$$ 0 0
$$651$$ −2.76393 + 12.3607i −0.108327 + 0.484453i
$$652$$ 10.4721i 0.410120i
$$653$$ 23.8885 0.934831 0.467415 0.884038i $$-0.345185\pi$$
0.467415 + 0.884038i $$0.345185\pi$$
$$654$$ 2.76393 7.23607i 0.108078 0.282953i
$$655$$ 0 0
$$656$$ 2.47214 0.0965207
$$657$$ −25.1246 22.4721i −0.980204 0.876722i
$$658$$ 16.9443 2.47214i 0.660556 0.0963739i
$$659$$ 31.5279i 1.22815i 0.789247 + 0.614076i $$0.210471\pi$$
−0.789247 + 0.614076i $$0.789529\pi$$
$$660$$ 0 0
$$661$$ 18.2918i 0.711468i −0.934587 0.355734i $$-0.884231\pi$$
0.934587 0.355734i $$-0.115769\pi$$
$$662$$ −3.05573 −0.118764
$$663$$ −10.4721 4.00000i −0.406704 0.155347i
$$664$$ 14.6525i 0.568626i
$$665$$ 0 0
$$666$$ −1.52786 + 1.70820i −0.0592035 + 0.0661916i
$$667$$ 30.8328i 1.19385i
$$668$$ 0.944272i 0.0365350i
$$669$$ −10.9443 + 28.6525i −0.423130 + 1.10777i
$$670$$ 0 0
$$671$$ 32.3607 1.24927
$$672$$ −4.47214 1.00000i −0.172516 0.0385758i
$$673$$ 19.5279i 0.752744i −0.926469 0.376372i $$-0.877171\pi$$
0.926469 0.376372i $$-0.122829\pi$$
$$674$$ 21.4164i 0.824929i
$$675$$ 0 0
$$676$$ −11.4721 −0.441236
$$677$$ 18.0000i 0.691796i −0.938272 0.345898i $$-0.887574\pi$$
0.938272 0.345898i $$-0.112426\pi$$
$$678$$ 1.81966 4.76393i 0.0698836 0.182958i
$$679$$ 0.291796 + 2.00000i 0.0111981 + 0.0767530i
$$680$$ 0 0
$$681$$ −1.23607 0.472136i −0.0473662 0.0180923i
$$682$$ 12.3607 0.473315
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 16.9443 18.9443i 0.647880 0.724352i
$$685$$ 0 0
$$686$$ 7.79837 + 16.7984i 0.297743 + 0.641365i
$$687$$ −14.1803 5.41641i −0.541014 0.206649i
$$688$$ 4.94427i 0.188499i
$$689$$ 0.583592 0.0222331
$$690$$ 0 0
$$691$$ 21.0557i 0.800998i 0.916297 + 0.400499i $$0.131163\pi$$
−0.916297 + 0.400499i $$0.868837\pi$$
$$692$$ 9.41641i 0.357958i
$$693$$ 29.5967 + 19.5967i 1.12429 + 0.744419i
$$694$$ 2.47214 0.0938410
$$695$$ 0 0
$$696$$ −12.4721 4.76393i −0.472755 0.180576i
$$697$$ 12.9443i 0.490299i
$$698$$ 20.1803i 0.763837i
$$699$$ 7.12461 18.6525i 0.269478 0.705501i
$$700$$ 0 0
$$701$$ 44.0689i 1.66446i −0.554431 0.832229i $$-0.687064\pi$$
0.554431 0.832229i $$-0.312936\pi$$
$$702$$ 5.70820 2.94427i 0.215442 0.111124i
$$703$$ −6.47214 −0.244101
$$704$$ 4.47214i 0.168550i
$$705$$ 0 0
$$706$$ 27.7082i 1.04281i
$$707$$ 4.76393 + 32.6525i 0.179166 + 1.22802i
$$708$$ 2.76393 7.23607i 0.103875 0.271948i
$$709$$ 15.5279 0.583161 0.291581 0.956546i $$-0.405819\pi$$
0.291581 + 0.956546i $$0.405819\pi$$
$$710$$ 0 0
$$711$$ −20.0000 17.8885i −0.750059 0.670873i
$$712$$ 5.52786 0.207165
$$713$$ 11.0557i 0.414040i
$$714$$ −5.23607 + 23.4164i −0.195955 + 0.876337i
$$715$$ 0 0
$$716$$ 14.9443i 0.558494i
$$717$$ −0.291796 0.111456i −0.0108973 0.00416241i
$$718$$ 12.1803i 0.454566i
$$719$$ −34.4721 −1.28559 −0.642797 0.766037i $$-0.722226\pi$$
−0.642797 + 0.766037i $$0.722226\pi$$
$$720$$ 0 0
$$721$$ 5.59675 + 38.3607i 0.208434 + 1.42863i
$$722$$ 52.7771 1.96416
$$723$$ −28.9443 11.0557i −1.07645 0.411167i
$$724$$ 16.1803i 0.601338i
$$725$$ 0 0
$$726$$ 5.56231 14.5623i 0.206437 0.540458i
$$727$$ 26.2918 0.975109 0.487554 0.873093i $$-0.337889\pi$$
0.487554 + 0.873093i $$0.337889\pi$$
$$728$$ −0.472136 3.23607i −0.0174985 0.119937i
$$729$$ 15.6525 22.0000i 0.579721 0.814815i
$$730$$ 0 0
$$731$$ 25.8885 0.957522
$$732$$ −11.7082 4.47214i −0.432748 0.165295i
$$733$$ −20.0689 −0.741261 −0.370631 0.928780i $$-0.620858\pi$$
−0.370631 + 0.928780i $$0.620858\pi$$
$$734$$ 8.18034 0.301942
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 53.6656 1.97680
$$738$$ 5.52786 + 4.94427i 0.203483 + 0.182001i
$$739$$ −8.94427 −0.329020 −0.164510 0.986375i $$-0.552604\pi$$
−0.164510 + 0.986375i $$0.552604\pi$$
$$740$$ 0 0
$$741$$ 16.9443 + 6.47214i 0.622463 + 0.237760i
$$742$$ −0.180340 1.23607i −0.00662049 0.0453775i
$$743$$ 10.4721 0.384185 0.192093 0.981377i $$-0.438473\pi$$
0.192093 + 0.981377i $$0.438473\pi$$
$$744$$ −4.47214 1.70820i −0.163956 0.0626258i
$$745$$ 0 0
$$746$$ 32.1803i 1.17821i
$$747$$ 29.3050 32.7639i 1.07221 1.19877i
$$748$$ 23.4164 0.856189
$$749$$ −4.36068 29.8885i −0.159336 1.09210i
$$750$$ 0 0
$$751$$ 8.58359 0.313220 0.156610 0.987661i $$-0.449943\pi$$
0.156610 + 0.987661i $$0.449943\pi$$
$$752$$ 6.47214i 0.236015i
$$753$$ 7.70820 20.1803i 0.280903 0.735412i
$$754$$ 9.52786i 0.346984i
$$755$$ 0 0
$$756$$ −8.00000 11.1803i −0.290957 0.406625i
$$757$$ 2.65248i 0.0964059i −0.998838 0.0482029i $$-0.984651\pi$$
0.998838 0.0482029i $$-0.0153494\pi$$
$$758$$ −17.8885 −0.649741
$$759$$ −28.9443 11.0557i −1.05061 0.401298i
$$760$$ 0 0
$$761$$ 5.88854 0.213460 0.106730 0.994288i $$-0.465962\pi$$
0.106730 + 0.994288i $$0.465962\pi$$
$$762$$ 0.472136 + 0.180340i 0.0171037 + 0.00653302i
$$763$$ −1.70820 11.7082i −0.0618411 0.423865i
$$764$$ 7.23607i 0.261792i
$$765$$ 0 0
$$766$$ 13.8885i 0.501813i
$$767$$ 5.52786 0.199600
$$768$$ 0.618034 1.61803i 0.0223014 0.0583858i
$$769$$ 36.0000i 1.29819i −0.760706 0.649097i $$-0.775147\pi$$
0.760706 0.649097i $$-0.224853\pi$$
$$770$$ 0 0
$$771$$ −22.9443 8.76393i −0.826318 0.315625i
$$772$$ 6.00000i 0.215945i
$$773$$ 10.5836i 0.380665i 0.981720 + 0.190333i $$0.0609567\pi$$
−0.981720 + 0.190333i $$0.939043\pi$$
$$774$$ −9.88854 + 11.0557i −0.355436 + 0.397390i
$$775$$ 0 0
$$776$$ −0.763932 −0.0274236
$$777$$ −0.763932 + 3.41641i −0.0274059 + 0.122563i
$$778$$ 30.1803i 1.08202i
$$779$$ 20.9443i 0.750406i
$$780$$ 0 0
$$781$$ 32.3607 1.15796
$$782$$ 20.9443i 0.748966i
$$783$$ −18.3607 35.5967i −0.656157 1.27212i
$$784$$ −6.70820 + 2.00000i −0.239579 + 0.0714286i
$$785$$ 0 0
$$786$$ 3.34752 8.76393i 0.119402 0.312599i
$$787$$ 36.2918 1.29366 0.646831 0.762633i $$-0.276094\pi$$
0.646831 + 0.762633i $$0.276094\pi$$
$$788$$ −3.52786 −0.125675