# Properties

 Label 950.2.e.n.501.3 Level $950$ Weight $2$ Character 950.501 Analytic conductor $7.586$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$10$$ Relative dimension: $$5$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Defining polynomial: $$x^{10} + 10 x^{8} - 12 x^{7} + 85 x^{6} - 70 x^{5} + 186 x^{4} - 110 x^{3} + 285 x^{2} - 150 x + 100$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 501.3 Root $$0.341187 + 0.590953i$$ of defining polynomial Character $$\chi$$ $$=$$ 950.501 Dual form 950.2.e.n.201.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.341187 + 0.590953i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.341187 - 0.590953i) q^{6} -0.317626 q^{7} +1.00000 q^{8} +(1.26718 - 2.19482i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.341187 + 0.590953i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.341187 - 0.590953i) q^{6} -0.317626 q^{7} +1.00000 q^{8} +(1.26718 - 2.19482i) q^{9} -4.31087 q^{11} -0.682374 q^{12} +(-3.14836 + 5.45312i) q^{13} +(0.158813 + 0.275072i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.0669268 + 0.115921i) q^{17} -2.53437 q^{18} +(-4.05310 + 1.60387i) q^{19} +(-0.108370 - 0.187702i) q^{21} +(2.15544 + 3.73333i) q^{22} +(-1.98955 + 3.44600i) q^{23} +(0.341187 + 0.590953i) q^{24} +6.29672 q^{26} +3.77651 q^{27} +(0.158813 - 0.275072i) q^{28} +(4.57435 - 7.92301i) q^{29} -2.98584 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.47081 - 2.54753i) q^{33} +(0.0669268 - 0.115921i) q^{34} +(1.26718 + 2.19482i) q^{36} -5.07323 q^{37} +(3.41554 + 2.70815i) q^{38} -4.29672 q^{39} +(0.433073 + 0.750105i) q^{41} +(-0.108370 + 0.187702i) q^{42} +(-2.85199 - 4.93979i) q^{43} +(2.15544 - 3.73333i) q^{44} +3.97909 q^{46} +(-6.48617 + 11.2344i) q^{47} +(0.341187 - 0.590953i) q^{48} -6.89911 q^{49} +(-0.0456691 + 0.0791012i) q^{51} +(-3.14836 - 5.45312i) q^{52} +(-3.96261 + 6.86344i) q^{53} +(-1.88825 - 3.27055i) q^{54} -0.317626 q^{56} +(-2.33068 - 1.84797i) q^{57} -9.14871 q^{58} +(4.80717 + 8.32627i) q^{59} +(-3.08711 + 5.34704i) q^{61} +(1.49292 + 2.58582i) q^{62} +(-0.402490 + 0.697133i) q^{63} +1.00000 q^{64} +(-1.47081 + 2.54753i) q^{66} +(0.295518 - 0.511852i) q^{67} -0.133854 q^{68} -2.71523 q^{69} +(-5.83073 - 10.0991i) q^{71} +(1.26718 - 2.19482i) q^{72} +(4.13048 + 7.15420i) q^{73} +(2.53661 + 4.39354i) q^{74} +(0.637555 - 4.31202i) q^{76} +1.36924 q^{77} +(2.14836 + 3.72107i) q^{78} +(1.66112 + 2.87714i) q^{79} +(-2.51305 - 4.35273i) q^{81} +(0.433073 - 0.750105i) q^{82} -4.20708 q^{83} +0.216740 q^{84} +(-2.85199 + 4.93979i) q^{86} +6.24284 q^{87} -4.31087 q^{88} +(1.85992 - 3.22147i) q^{89} +(1.00000 - 1.73205i) q^{91} +(-1.98955 - 3.44600i) q^{92} +(-1.01873 - 1.76450i) q^{93} +12.9723 q^{94} -0.682374 q^{96} +(-2.42830 - 4.20594i) q^{97} +(3.44956 + 5.97481i) q^{98} +(-5.46266 + 9.46161i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} + O(q^{10})$$ $$10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} - 6q^{11} - 2q^{13} + 5q^{14} - 5q^{16} + 4q^{17} + 10q^{18} + 11q^{19} + 20q^{21} + 3q^{22} + 13q^{23} + 4q^{26} + 36q^{27} + 5q^{28} + 2q^{29} - 8q^{31} - 5q^{32} + 2q^{33} + 4q^{34} - 5q^{36} + 10q^{37} - 13q^{38} + 16q^{39} + q^{41} + 20q^{42} + 3q^{44} - 26q^{46} - 10q^{47} - 20q^{49} + 4q^{51} - 2q^{52} + 5q^{53} - 18q^{54} - 10q^{56} - 10q^{57} - 4q^{58} + 22q^{59} - 2q^{61} + 4q^{62} + 23q^{63} + 10q^{64} + 2q^{66} + 4q^{67} - 8q^{68} - 24q^{69} - 22q^{71} - 5q^{72} + 26q^{73} - 5q^{74} + 2q^{76} + 10q^{77} - 8q^{78} + 2q^{79} - 5q^{81} + q^{82} + 12q^{83} - 40q^{84} - 20q^{87} - 6q^{88} - q^{89} + 10q^{91} + 13q^{92} + 6q^{93} + 20q^{94} + 8q^{97} + 10q^{98} + 13q^{99} + O(q^{100})$$

## Character values

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

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ 0.341187 + 0.590953i 0.196984 + 0.341187i 0.947549 0.319610i $$-0.103552\pi$$
−0.750565 + 0.660797i $$0.770218\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ 0.341187 0.590953i 0.139289 0.241256i
$$7$$ −0.317626 −0.120051 −0.0600256 0.998197i $$-0.519118\pi$$
−0.0600256 + 0.998197i $$0.519118\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.26718 2.19482i 0.422394 0.731608i
$$10$$ 0 0
$$11$$ −4.31087 −1.29978 −0.649889 0.760029i $$-0.725184\pi$$
−0.649889 + 0.760029i $$0.725184\pi$$
$$12$$ −0.682374 −0.196984
$$13$$ −3.14836 + 5.45312i −0.873198 + 1.51242i −0.0145275 + 0.999894i $$0.504624\pi$$
−0.858670 + 0.512528i $$0.828709\pi$$
$$14$$ 0.158813 + 0.275072i 0.0424445 + 0.0735161i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 0.0669268 + 0.115921i 0.0162321 + 0.0281149i 0.874027 0.485877i $$-0.161500\pi$$
−0.857795 + 0.513992i $$0.828166\pi$$
$$18$$ −2.53437 −0.597356
$$19$$ −4.05310 + 1.60387i −0.929844 + 0.367953i
$$20$$ 0 0
$$21$$ −0.108370 0.187702i −0.0236482 0.0409599i
$$22$$ 2.15544 + 3.73333i 0.459541 + 0.795948i
$$23$$ −1.98955 + 3.44600i −0.414849 + 0.718540i −0.995413 0.0956753i $$-0.969499\pi$$
0.580564 + 0.814215i $$0.302832\pi$$
$$24$$ 0.341187 + 0.590953i 0.0696445 + 0.120628i
$$25$$ 0 0
$$26$$ 6.29672 1.23489
$$27$$ 3.77651 0.726789
$$28$$ 0.158813 0.275072i 0.0300128 0.0519837i
$$29$$ 4.57435 7.92301i 0.849436 1.47127i −0.0322757 0.999479i $$-0.510275\pi$$
0.881712 0.471788i $$-0.156391\pi$$
$$30$$ 0 0
$$31$$ −2.98584 −0.536274 −0.268137 0.963381i $$-0.586408\pi$$
−0.268137 + 0.963381i $$0.586408\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −1.47081 2.54753i −0.256036 0.443467i
$$34$$ 0.0669268 0.115921i 0.0114778 0.0198802i
$$35$$ 0 0
$$36$$ 1.26718 + 2.19482i 0.211197 + 0.365804i
$$37$$ −5.07323 −0.834033 −0.417017 0.908899i $$-0.636924\pi$$
−0.417017 + 0.908899i $$0.636924\pi$$
$$38$$ 3.41554 + 2.70815i 0.554074 + 0.439320i
$$39$$ −4.29672 −0.688026
$$40$$ 0 0
$$41$$ 0.433073 + 0.750105i 0.0676347 + 0.117147i 0.897860 0.440282i $$-0.145121\pi$$
−0.830225 + 0.557428i $$0.811788\pi$$
$$42$$ −0.108370 + 0.187702i −0.0167218 + 0.0289631i
$$43$$ −2.85199 4.93979i −0.434925 0.753311i 0.562365 0.826889i $$-0.309892\pi$$
−0.997289 + 0.0735777i $$0.976558\pi$$
$$44$$ 2.15544 3.73333i 0.324944 0.562820i
$$45$$ 0 0
$$46$$ 3.97909 0.586685
$$47$$ −6.48617 + 11.2344i −0.946105 + 1.63870i −0.192582 + 0.981281i $$0.561686\pi$$
−0.753523 + 0.657421i $$0.771647\pi$$
$$48$$ 0.341187 0.590953i 0.0492461 0.0852968i
$$49$$ −6.89911 −0.985588
$$50$$ 0 0
$$51$$ −0.0456691 + 0.0791012i −0.00639495 + 0.0110764i
$$52$$ −3.14836 5.45312i −0.436599 0.756211i
$$53$$ −3.96261 + 6.86344i −0.544306 + 0.942766i 0.454344 + 0.890826i $$0.349874\pi$$
−0.998650 + 0.0519397i $$0.983460\pi$$
$$54$$ −1.88825 3.27055i −0.256959 0.445066i
$$55$$ 0 0
$$56$$ −0.317626 −0.0424445
$$57$$ −2.33068 1.84797i −0.308706 0.244770i
$$58$$ −9.14871 −1.20128
$$59$$ 4.80717 + 8.32627i 0.625841 + 1.08399i 0.988378 + 0.152018i $$0.0485772\pi$$
−0.362537 + 0.931969i $$0.618089\pi$$
$$60$$ 0 0
$$61$$ −3.08711 + 5.34704i −0.395264 + 0.684618i −0.993135 0.116975i $$-0.962680\pi$$
0.597871 + 0.801593i $$0.296014\pi$$
$$62$$ 1.49292 + 2.58582i 0.189601 + 0.328399i
$$63$$ −0.402490 + 0.697133i −0.0507090 + 0.0878305i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −1.47081 + 2.54753i −0.181045 + 0.313579i
$$67$$ 0.295518 0.511852i 0.0361033 0.0625327i −0.847409 0.530940i $$-0.821839\pi$$
0.883512 + 0.468408i $$0.155172\pi$$
$$68$$ −0.133854 −0.0162321
$$69$$ −2.71523 −0.326875
$$70$$ 0 0
$$71$$ −5.83073 10.0991i −0.691981 1.19855i −0.971188 0.238315i $$-0.923405\pi$$
0.279207 0.960231i $$-0.409928\pi$$
$$72$$ 1.26718 2.19482i 0.149339 0.258663i
$$73$$ 4.13048 + 7.15420i 0.483436 + 0.837335i 0.999819 0.0190222i $$-0.00605532\pi$$
−0.516383 + 0.856358i $$0.672722\pi$$
$$74$$ 2.53661 + 4.39354i 0.294875 + 0.510739i
$$75$$ 0 0
$$76$$ 0.637555 4.31202i 0.0731326 0.494623i
$$77$$ 1.36924 0.156040
$$78$$ 2.14836 + 3.72107i 0.243254 + 0.421328i
$$79$$ 1.66112 + 2.87714i 0.186890 + 0.323703i 0.944212 0.329339i $$-0.106826\pi$$
−0.757322 + 0.653042i $$0.773492\pi$$
$$80$$ 0 0
$$81$$ −2.51305 4.35273i −0.279228 0.483637i
$$82$$ 0.433073 0.750105i 0.0478249 0.0828352i
$$83$$ −4.20708 −0.461787 −0.230894 0.972979i $$-0.574165\pi$$
−0.230894 + 0.972979i $$0.574165\pi$$
$$84$$ 0.216740 0.0236482
$$85$$ 0 0
$$86$$ −2.85199 + 4.93979i −0.307538 + 0.532672i
$$87$$ 6.24284 0.669303
$$88$$ −4.31087 −0.459541
$$89$$ 1.85992 3.22147i 0.197151 0.341476i −0.750453 0.660924i $$-0.770164\pi$$
0.947604 + 0.319449i $$0.103498\pi$$
$$90$$ 0 0
$$91$$ 1.00000 1.73205i 0.104828 0.181568i
$$92$$ −1.98955 3.44600i −0.207425 0.359270i
$$93$$ −1.01873 1.76450i −0.105638 0.182970i
$$94$$ 12.9723 1.33799
$$95$$ 0 0
$$96$$ −0.682374 −0.0696445
$$97$$ −2.42830 4.20594i −0.246556 0.427048i 0.716012 0.698088i $$-0.245966\pi$$
−0.962568 + 0.271040i $$0.912632\pi$$
$$98$$ 3.44956 + 5.97481i 0.348458 + 0.603547i
$$99$$ −5.46266 + 9.46161i −0.549018 + 0.950928i
$$100$$ 0 0
$$101$$ 1.25638 2.17611i 0.125014 0.216531i −0.796724 0.604343i $$-0.793436\pi$$
0.921739 + 0.387812i $$0.126769\pi$$
$$102$$ 0.0913382 0.00904383
$$103$$ −4.03297 −0.397380 −0.198690 0.980062i $$-0.563669\pi$$
−0.198690 + 0.980062i $$0.563669\pi$$
$$104$$ −3.14836 + 5.45312i −0.308722 + 0.534722i
$$105$$ 0 0
$$106$$ 7.92522 0.769765
$$107$$ −10.0000 −0.966736 −0.483368 0.875417i $$-0.660587\pi$$
−0.483368 + 0.875417i $$0.660587\pi$$
$$108$$ −1.88825 + 3.27055i −0.181697 + 0.314709i
$$109$$ 2.93197 + 5.07832i 0.280832 + 0.486415i 0.971590 0.236671i $$-0.0760564\pi$$
−0.690758 + 0.723086i $$0.742723\pi$$
$$110$$ 0 0
$$111$$ −1.73092 2.99804i −0.164292 0.284561i
$$112$$ 0.158813 + 0.275072i 0.0150064 + 0.0259919i
$$113$$ 18.0853 1.70132 0.850660 0.525716i $$-0.176202\pi$$
0.850660 + 0.525716i $$0.176202\pi$$
$$114$$ −0.435051 + 2.94241i −0.0407463 + 0.275582i
$$115$$ 0 0
$$116$$ 4.57435 + 7.92301i 0.424718 + 0.735633i
$$117$$ 7.97909 + 13.8202i 0.737667 + 1.27768i
$$118$$ 4.80717 8.32627i 0.442536 0.766495i
$$119$$ −0.0212577 0.0368194i −0.00194869 0.00337523i
$$120$$ 0 0
$$121$$ 7.58363 0.689421
$$122$$ 6.17422 0.558988
$$123$$ −0.295518 + 0.511852i −0.0266460 + 0.0461522i
$$124$$ 1.49292 2.58582i 0.134068 0.232213i
$$125$$ 0 0
$$126$$ 0.804980 0.0717133
$$127$$ 8.94845 15.4992i 0.794047 1.37533i −0.129396 0.991593i $$-0.541304\pi$$
0.923443 0.383736i $$-0.125363\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 1.94613 3.37079i 0.171347 0.296781i
$$130$$ 0 0
$$131$$ 5.90509 + 10.2279i 0.515930 + 0.893617i 0.999829 + 0.0184931i $$0.00588686\pi$$
−0.483899 + 0.875124i $$0.660780\pi$$
$$132$$ 2.94163 0.256036
$$133$$ 1.28737 0.509431i 0.111629 0.0441733i
$$134$$ −0.591036 −0.0510577
$$135$$ 0 0
$$136$$ 0.0669268 + 0.115921i 0.00573892 + 0.00994011i
$$137$$ 7.91554 13.7101i 0.676270 1.17133i −0.299825 0.953994i $$-0.596928\pi$$
0.976096 0.217341i $$-0.0697382\pi$$
$$138$$ 1.35762 + 2.35146i 0.115568 + 0.200169i
$$139$$ −0.583681 + 1.01096i −0.0495071 + 0.0857489i −0.889717 0.456512i $$-0.849098\pi$$
0.840210 + 0.542261i $$0.182432\pi$$
$$140$$ 0 0
$$141$$ −8.85199 −0.745472
$$142$$ −5.83073 + 10.0991i −0.489304 + 0.847500i
$$143$$ 13.5722 23.5077i 1.13496 1.96581i
$$144$$ −2.53437 −0.211197
$$145$$ 0 0
$$146$$ 4.13048 7.15420i 0.341841 0.592086i
$$147$$ −2.35389 4.07705i −0.194145 0.336270i
$$148$$ 2.53661 4.39354i 0.208508 0.361147i
$$149$$ 6.07575 + 10.5235i 0.497745 + 0.862120i 0.999997 0.00260182i $$-0.000828187\pi$$
−0.502252 + 0.864722i $$0.667495\pi$$
$$150$$ 0 0
$$151$$ −20.3803 −1.65853 −0.829263 0.558859i $$-0.811239\pi$$
−0.829263 + 0.558859i $$0.811239\pi$$
$$152$$ −4.05310 + 1.60387i −0.328750 + 0.130091i
$$153$$ 0.339234 0.0274254
$$154$$ −0.684622 1.18580i −0.0551684 0.0955545i
$$155$$ 0 0
$$156$$ 2.14836 3.72107i 0.172006 0.297924i
$$157$$ −2.46121 4.26294i −0.196426 0.340220i 0.750941 0.660369i $$-0.229600\pi$$
−0.947367 + 0.320149i $$0.896267\pi$$
$$158$$ 1.66112 2.87714i 0.132151 0.228893i
$$159$$ −5.40796 −0.428879
$$160$$ 0 0
$$161$$ 0.631931 1.09454i 0.0498032 0.0862616i
$$162$$ −2.51305 + 4.35273i −0.197444 + 0.341983i
$$163$$ −1.43727 −0.112576 −0.0562880 0.998415i $$-0.517927\pi$$
−0.0562880 + 0.998415i $$0.517927\pi$$
$$164$$ −0.866146 −0.0676347
$$165$$ 0 0
$$166$$ 2.10354 + 3.64344i 0.163266 + 0.282786i
$$167$$ −4.68750 + 8.11899i −0.362730 + 0.628266i −0.988409 0.151814i $$-0.951488\pi$$
0.625680 + 0.780080i $$0.284822\pi$$
$$168$$ −0.108370 0.187702i −0.00836091 0.0144815i
$$169$$ −13.3243 23.0784i −1.02495 1.77526i
$$170$$ 0 0
$$171$$ −1.61580 + 10.9282i −0.123563 + 0.835703i
$$172$$ 5.70398 0.434925
$$173$$ −3.88263 6.72491i −0.295191 0.511286i 0.679838 0.733362i $$-0.262050\pi$$
−0.975029 + 0.222076i $$0.928717\pi$$
$$174$$ −3.12142 5.40646i −0.236634 0.409863i
$$175$$ 0 0
$$176$$ 2.15544 + 3.73333i 0.162472 + 0.281410i
$$177$$ −3.28029 + 5.68163i −0.246562 + 0.427057i
$$178$$ −3.71984 −0.278814
$$179$$ −1.12249 −0.0838992 −0.0419496 0.999120i $$-0.513357\pi$$
−0.0419496 + 0.999120i $$0.513357\pi$$
$$180$$ 0 0
$$181$$ −7.89198 + 13.6693i −0.586606 + 1.01603i 0.408067 + 0.912952i $$0.366203\pi$$
−0.994673 + 0.103080i $$0.967130\pi$$
$$182$$ −2.00000 −0.148250
$$183$$ −4.21313 −0.311444
$$184$$ −1.98955 + 3.44600i −0.146671 + 0.254042i
$$185$$ 0 0
$$186$$ −1.01873 + 1.76450i −0.0746970 + 0.129379i
$$187$$ −0.288513 0.499719i −0.0210982 0.0365431i
$$188$$ −6.48617 11.2344i −0.473053 0.819351i
$$189$$ −1.19952 −0.0872520
$$190$$ 0 0
$$191$$ 18.2974 1.32395 0.661977 0.749524i $$-0.269717\pi$$
0.661977 + 0.749524i $$0.269717\pi$$
$$192$$ 0.341187 + 0.590953i 0.0246231 + 0.0426484i
$$193$$ −0.558777 0.967830i −0.0402216 0.0696659i 0.845214 0.534428i $$-0.179473\pi$$
−0.885435 + 0.464762i $$0.846140\pi$$
$$194$$ −2.42830 + 4.20594i −0.174342 + 0.301969i
$$195$$ 0 0
$$196$$ 3.44956 5.97481i 0.246397 0.426772i
$$197$$ 16.2594 1.15843 0.579217 0.815173i $$-0.303358\pi$$
0.579217 + 0.815173i $$0.303358\pi$$
$$198$$ 10.9253 0.776429
$$199$$ 6.89911 11.9496i 0.489065 0.847086i −0.510856 0.859667i $$-0.670671\pi$$
0.999921 + 0.0125807i $$0.00400467\pi$$
$$200$$ 0 0
$$201$$ 0.403308 0.0284471
$$202$$ −2.51276 −0.176797
$$203$$ −1.45293 + 2.51655i −0.101976 + 0.176627i
$$204$$ −0.0456691 0.0791012i −0.00319748 0.00553819i
$$205$$ 0 0
$$206$$ 2.01648 + 3.49265i 0.140495 + 0.243345i
$$207$$ 5.04224 + 8.73341i 0.350460 + 0.607014i
$$208$$ 6.29672 0.436599
$$209$$ 17.4724 6.91409i 1.20859 0.478257i
$$210$$ 0 0
$$211$$ 0.584458 + 1.01231i 0.0402358 + 0.0696904i 0.885442 0.464750i $$-0.153856\pi$$
−0.845206 + 0.534440i $$0.820522\pi$$
$$212$$ −3.96261 6.86344i −0.272153 0.471383i
$$213$$ 3.97874 6.89138i 0.272619 0.472190i
$$214$$ 5.00000 + 8.66025i 0.341793 + 0.592003i
$$215$$ 0 0
$$216$$ 3.77651 0.256959
$$217$$ 0.948381 0.0643803
$$218$$ 2.93197 5.07832i 0.198578 0.343947i
$$219$$ −2.81853 + 4.88184i −0.190459 + 0.329884i
$$220$$ 0 0
$$221$$ −0.842838 −0.0566954
$$222$$ −1.73092 + 2.99804i −0.116172 + 0.201215i
$$223$$ −3.15881 5.47122i −0.211530 0.366380i 0.740664 0.671876i $$-0.234511\pi$$
−0.952193 + 0.305496i $$0.901178\pi$$
$$224$$ 0.158813 0.275072i 0.0106111 0.0183790i
$$225$$ 0 0
$$226$$ −9.04264 15.6623i −0.601508 1.04184i
$$227$$ 3.77942 0.250849 0.125424 0.992103i $$-0.459971\pi$$
0.125424 + 0.992103i $$0.459971\pi$$
$$228$$ 2.76573 1.09444i 0.183165 0.0724811i
$$229$$ 5.43628 0.359239 0.179620 0.983736i $$-0.442513\pi$$
0.179620 + 0.983736i $$0.442513\pi$$
$$230$$ 0 0
$$231$$ 0.467169 + 0.809160i 0.0307374 + 0.0532388i
$$232$$ 4.57435 7.92301i 0.300321 0.520171i
$$233$$ −1.22461 2.12109i −0.0802270 0.138957i 0.823120 0.567867i $$-0.192231\pi$$
−0.903347 + 0.428910i $$0.858898\pi$$
$$234$$ 7.97909 13.8202i 0.521610 0.903454i
$$235$$ 0 0
$$236$$ −9.61434 −0.625841
$$237$$ −1.13350 + 1.96329i −0.0736289 + 0.127529i
$$238$$ −0.0212577 + 0.0368194i −0.00137793 + 0.00238664i
$$239$$ −9.45899 −0.611851 −0.305926 0.952055i $$-0.598966\pi$$
−0.305926 + 0.952055i $$0.598966\pi$$
$$240$$ 0 0
$$241$$ 8.43540 14.6105i 0.543372 0.941148i −0.455335 0.890320i $$-0.650481\pi$$
0.998707 0.0508279i $$-0.0161860\pi$$
$$242$$ −3.79182 6.56762i −0.243747 0.422183i
$$243$$ 7.37960 12.7819i 0.473402 0.819956i
$$244$$ −3.08711 5.34704i −0.197632 0.342309i
$$245$$ 0 0
$$246$$ 0.591036 0.0376831
$$247$$ 4.01451 27.1516i 0.255437 1.72761i
$$248$$ −2.98584 −0.189601
$$249$$ −1.43540 2.48619i −0.0909649 0.157556i
$$250$$ 0 0
$$251$$ −1.32814 + 2.30040i −0.0838311 + 0.145200i −0.904893 0.425640i $$-0.860049\pi$$
0.821061 + 0.570840i $$0.193382\pi$$
$$252$$ −0.402490 0.697133i −0.0253545 0.0439152i
$$253$$ 8.57668 14.8553i 0.539211 0.933942i
$$254$$ −17.8969 −1.12295
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −1.12373 + 1.94635i −0.0700961 + 0.121410i −0.898943 0.438065i $$-0.855664\pi$$
0.828847 + 0.559475i $$0.188997\pi$$
$$258$$ −3.89225 −0.242321
$$259$$ 1.61139 0.100127
$$260$$ 0 0
$$261$$ −11.5931 20.0798i −0.717594 1.24291i
$$262$$ 5.90509 10.2279i 0.364818 0.631883i
$$263$$ 15.9289 + 27.5897i 0.982219 + 1.70125i 0.653695 + 0.756758i $$0.273218\pi$$
0.328524 + 0.944496i $$0.393449\pi$$
$$264$$ −1.47081 2.54753i −0.0905224 0.156789i
$$265$$ 0 0
$$266$$ −1.08486 0.860178i −0.0665173 0.0527409i
$$267$$ 2.53832 0.155343
$$268$$ 0.295518 + 0.511852i 0.0180516 + 0.0312663i
$$269$$ 5.44763 + 9.43558i 0.332148 + 0.575297i 0.982933 0.183965i $$-0.0588933\pi$$
−0.650785 + 0.759262i $$0.725560\pi$$
$$270$$ 0 0
$$271$$ 5.96631 + 10.3340i 0.362428 + 0.627743i 0.988360 0.152134i $$-0.0486147\pi$$
−0.625932 + 0.779877i $$0.715281\pi$$
$$272$$ 0.0669268 0.115921i 0.00405803 0.00702872i
$$273$$ 1.36475 0.0825983
$$274$$ −15.8311 −0.956391
$$275$$ 0 0
$$276$$ 1.35762 2.35146i 0.0817188 0.141541i
$$277$$ −15.9065 −0.955730 −0.477865 0.878433i $$-0.658589\pi$$
−0.477865 + 0.878433i $$0.658589\pi$$
$$278$$ 1.16736 0.0700137
$$279$$ −3.78361 + 6.55341i −0.226519 + 0.392342i
$$280$$ 0 0
$$281$$ 10.4921 18.1729i 0.625909 1.08411i −0.362455 0.932001i $$-0.618062\pi$$
0.988364 0.152105i $$-0.0486052\pi$$
$$282$$ 4.42600 + 7.66605i 0.263564 + 0.456507i
$$283$$ 6.43083 + 11.1385i 0.382273 + 0.662116i 0.991387 0.130967i $$-0.0418081\pi$$
−0.609114 + 0.793083i $$0.708475\pi$$
$$284$$ 11.6615 0.691981
$$285$$ 0 0
$$286$$ −27.1444 −1.60508
$$287$$ −0.137555 0.238253i −0.00811963 0.0140636i
$$288$$ 1.26718 + 2.19482i 0.0746695 + 0.129331i
$$289$$ 8.49104 14.7069i 0.499473 0.865113i
$$290$$ 0 0
$$291$$ 1.65701 2.87002i 0.0971356 0.168244i
$$292$$ −8.26096 −0.483436
$$293$$ −12.1278 −0.708511 −0.354255 0.935149i $$-0.615266\pi$$
−0.354255 + 0.935149i $$0.615266\pi$$
$$294$$ −2.35389 + 4.07705i −0.137282 + 0.237779i
$$295$$ 0 0
$$296$$ −5.07323 −0.294875
$$297$$ −16.2801 −0.944664
$$298$$ 6.07575 10.5235i 0.351959 0.609611i
$$299$$ −12.5276 21.6985i −0.724491 1.25485i
$$300$$ 0 0
$$301$$ 0.905866 + 1.56901i 0.0522132 + 0.0904360i
$$302$$ 10.1902 + 17.6499i 0.586377 + 1.01564i
$$303$$ 1.71464 0.0985035
$$304$$ 3.41554 + 2.70815i 0.195895 + 0.155323i
$$305$$ 0 0
$$306$$ −0.169617 0.293785i −0.00969635 0.0167946i
$$307$$ −9.08409 15.7341i −0.518456 0.897992i −0.999770 0.0214442i $$-0.993174\pi$$
0.481314 0.876548i $$-0.340160\pi$$
$$308$$ −0.684622 + 1.18580i −0.0390100 + 0.0675673i
$$309$$ −1.37600 2.38330i −0.0782777 0.135581i
$$310$$ 0 0
$$311$$ 19.4766 1.10442 0.552210 0.833705i $$-0.313785\pi$$
0.552210 + 0.833705i $$0.313785\pi$$
$$312$$ −4.29672 −0.243254
$$313$$ 5.98987 10.3748i 0.338568 0.586416i −0.645596 0.763679i $$-0.723391\pi$$
0.984164 + 0.177263i $$0.0567243\pi$$
$$314$$ −2.46121 + 4.26294i −0.138894 + 0.240572i
$$315$$ 0 0
$$316$$ −3.32223 −0.186890
$$317$$ 0.564654 0.978009i 0.0317141 0.0549305i −0.849733 0.527214i $$-0.823237\pi$$
0.881447 + 0.472283i $$0.156570\pi$$
$$318$$ 2.70398 + 4.68343i 0.151632 + 0.262634i
$$319$$ −19.7195 + 34.1551i −1.10408 + 1.91232i
$$320$$ 0 0
$$321$$ −3.41187 5.90953i −0.190432 0.329838i
$$322$$ −1.26386 −0.0704323
$$323$$ −0.457182 0.362495i −0.0254383 0.0201698i
$$324$$ 5.02610 0.279228
$$325$$ 0 0
$$326$$ 0.718637 + 1.24472i 0.0398016 + 0.0689385i
$$327$$ −2.00070 + 3.46532i −0.110639 + 0.191632i
$$328$$ 0.433073 + 0.750105i 0.0239125 + 0.0414176i
$$329$$ 2.06017 3.56833i 0.113581 0.196728i
$$330$$ 0 0
$$331$$ −14.3080 −0.786437 −0.393218 0.919445i $$-0.628638\pi$$
−0.393218 + 0.919445i $$0.628638\pi$$
$$332$$ 2.10354 3.64344i 0.115447 0.199960i
$$333$$ −6.42871 + 11.1348i −0.352291 + 0.610186i
$$334$$ 9.37500 0.512977
$$335$$ 0 0
$$336$$ −0.108370 + 0.187702i −0.00591206 + 0.0102400i
$$337$$ −13.8589 24.0043i −0.754941 1.30760i −0.945404 0.325901i $$-0.894332\pi$$
0.190463 0.981694i $$-0.439001\pi$$
$$338$$ −13.3243 + 23.0784i −0.724748 + 1.25530i
$$339$$ 6.17047 + 10.6876i 0.335134 + 0.580469i
$$340$$ 0 0
$$341$$ 12.8716 0.697036
$$342$$ 10.2720 4.06480i 0.555448 0.219799i
$$343$$ 4.41472 0.238372
$$344$$ −2.85199 4.93979i −0.153769 0.266336i
$$345$$ 0 0
$$346$$ −3.88263 + 6.72491i −0.208731 + 0.361534i
$$347$$ 15.7098 + 27.2102i 0.843346 + 1.46072i 0.887050 + 0.461673i $$0.152751\pi$$
−0.0437044 + 0.999045i $$0.513916\pi$$
$$348$$ −3.12142 + 5.40646i −0.167326 + 0.289817i
$$349$$ 23.4539 1.25546 0.627729 0.778432i $$-0.283985\pi$$
0.627729 + 0.778432i $$0.283985\pi$$
$$350$$ 0 0
$$351$$ −11.8898 + 20.5937i −0.634631 + 1.09921i
$$352$$ 2.15544 3.73333i 0.114885 0.198987i
$$353$$ −17.3468 −0.923277 −0.461638 0.887068i $$-0.652738\pi$$
−0.461638 + 0.887068i $$0.652738\pi$$
$$354$$ 6.56058 0.348691
$$355$$ 0 0
$$356$$ 1.85992 + 3.22147i 0.0985755 + 0.170738i
$$357$$ 0.0145057 0.0251246i 0.000767722 0.00132973i
$$358$$ 0.561247 + 0.972108i 0.0296628 + 0.0513775i
$$359$$ −0.402934 0.697902i −0.0212660 0.0368339i 0.855197 0.518304i $$-0.173436\pi$$
−0.876463 + 0.481470i $$0.840103\pi$$
$$360$$ 0 0
$$361$$ 13.8552 13.0013i 0.729221 0.684279i
$$362$$ 15.7840 0.829587
$$363$$ 2.58744 + 4.48157i 0.135805 + 0.235222i
$$364$$ 1.00000 + 1.73205i 0.0524142 + 0.0907841i
$$365$$ 0 0
$$366$$ 2.10657 + 3.64868i 0.110112 + 0.190720i
$$367$$ −1.26908 + 2.19811i −0.0662455 + 0.114740i −0.897246 0.441531i $$-0.854435\pi$$
0.831000 + 0.556272i $$0.187769\pi$$
$$368$$ 3.97909 0.207425
$$369$$ 2.19513 0.114274
$$370$$ 0 0
$$371$$ 1.25863 2.18001i 0.0653446 0.113180i
$$372$$ 2.03746 0.105638
$$373$$ −12.4012 −0.642110 −0.321055 0.947060i $$-0.604038\pi$$
−0.321055 + 0.947060i $$0.604038\pi$$
$$374$$ −0.288513 + 0.499719i −0.0149186 + 0.0258399i
$$375$$ 0 0
$$376$$ −6.48617 + 11.2344i −0.334499 + 0.579369i
$$377$$ 28.8034 + 49.8890i 1.48345 + 2.56941i
$$378$$ 0.599758 + 1.03881i 0.0308482 + 0.0534307i
$$379$$ −12.6756 −0.651100 −0.325550 0.945525i $$-0.605549\pi$$
−0.325550 + 0.945525i $$0.605549\pi$$
$$380$$ 0 0
$$381$$ 12.2124 0.625660
$$382$$ −9.14871 15.8460i −0.468089 0.810753i
$$383$$ −7.97632 13.8154i −0.407571 0.705934i 0.587046 0.809554i $$-0.300291\pi$$
−0.994617 + 0.103620i $$0.966957\pi$$
$$384$$ 0.341187 0.590953i 0.0174111 0.0301570i
$$385$$ 0 0
$$386$$ −0.558777 + 0.967830i −0.0284410 + 0.0492612i
$$387$$ −14.4560 −0.734839
$$388$$ 4.85660 0.246556
$$389$$ 13.0991 22.6883i 0.664150 1.15034i −0.315365 0.948971i $$-0.602127\pi$$
0.979515 0.201372i $$-0.0645399\pi$$
$$390$$ 0 0
$$391$$ −0.532616 −0.0269355
$$392$$ −6.89911 −0.348458
$$393$$ −4.02948 + 6.97926i −0.203260 + 0.352057i
$$394$$ −8.12970 14.0811i −0.409568 0.709393i
$$395$$ 0 0
$$396$$ −5.46266 9.46161i −0.274509 0.475464i
$$397$$ 15.0639 + 26.0914i 0.756034 + 1.30949i 0.944858 + 0.327479i $$0.106199\pi$$
−0.188824 + 0.982011i $$0.560468\pi$$
$$398$$ −13.7982 −0.691643
$$399$$ 0.740283 + 0.586963i 0.0370605 + 0.0293849i
$$400$$ 0 0
$$401$$ 1.08591 + 1.88085i 0.0542278 + 0.0939254i 0.891865 0.452302i $$-0.149397\pi$$
−0.837637 + 0.546227i $$0.816064\pi$$
$$402$$ −0.201654 0.349275i −0.0100576 0.0174202i
$$403$$ 9.40051 16.2822i 0.468273 0.811072i
$$404$$ 1.25638 + 2.17611i 0.0625072 + 0.108266i
$$405$$ 0 0
$$406$$ 2.90587 0.144216
$$407$$ 21.8700 1.08406
$$408$$ −0.0456691 + 0.0791012i −0.00226096 + 0.00391609i
$$409$$ −16.0832 + 27.8569i −0.795262 + 1.37743i 0.127410 + 0.991850i $$0.459333\pi$$
−0.922673 + 0.385584i $$0.874000\pi$$
$$410$$ 0 0
$$411$$ 10.8027 0.532859
$$412$$ 2.01648 3.49265i 0.0993450 0.172071i
$$413$$ −1.52688 2.64464i −0.0751329 0.130134i
$$414$$ 5.04224 8.73341i 0.247812 0.429224i
$$415$$ 0 0
$$416$$ −3.14836 5.45312i −0.154361 0.267361i
$$417$$ −0.796577 −0.0390085
$$418$$ −14.7240 11.6745i −0.720173 0.571018i
$$419$$ −9.99674 −0.488373 −0.244186 0.969728i $$-0.578521\pi$$
−0.244186 + 0.969728i $$0.578521\pi$$
$$420$$ 0 0
$$421$$ 19.0856 + 33.0572i 0.930173 + 1.61111i 0.783023 + 0.621993i $$0.213677\pi$$
0.147150 + 0.989114i $$0.452990\pi$$
$$422$$ 0.584458 1.01231i 0.0284510 0.0492785i
$$423$$ 16.4383 + 28.4720i 0.799259 + 1.38436i
$$424$$ −3.96261 + 6.86344i −0.192441 + 0.333318i
$$425$$ 0 0
$$426$$ −7.95748 −0.385541
$$427$$ 0.980546 1.69836i 0.0474520 0.0821892i
$$428$$ 5.00000 8.66025i 0.241684 0.418609i
$$429$$ 18.5226 0.894280
$$430$$ 0 0
$$431$$ −1.73649 + 3.00769i −0.0836437 + 0.144875i −0.904812 0.425810i $$-0.859989\pi$$
0.821169 + 0.570685i $$0.193322\pi$$
$$432$$ −1.88825 3.27055i −0.0908487 0.157355i
$$433$$ 5.54742 9.60841i 0.266592 0.461751i −0.701388 0.712780i $$-0.747436\pi$$
0.967979 + 0.251029i $$0.0807691\pi$$
$$434$$ −0.474191 0.821322i −0.0227619 0.0394247i
$$435$$ 0 0
$$436$$ −5.86394 −0.280832
$$437$$ 2.53689 17.1579i 0.121356 0.820775i
$$438$$ 5.63706 0.269349
$$439$$ 6.51914 + 11.2915i 0.311141 + 0.538913i 0.978610 0.205725i $$-0.0659554\pi$$
−0.667468 + 0.744638i $$0.732622\pi$$
$$440$$ 0 0
$$441$$ −8.74244 + 15.1423i −0.416307 + 0.721064i
$$442$$ 0.421419 + 0.729919i 0.0200449 + 0.0347187i
$$443$$ −7.51250 + 13.0120i −0.356930 + 0.618221i −0.987446 0.157955i $$-0.949510\pi$$
0.630516 + 0.776176i $$0.282843\pi$$
$$444$$ 3.46184 0.164292
$$445$$ 0 0
$$446$$ −3.15881 + 5.47122i −0.149574 + 0.259070i
$$447$$ −4.14594 + 7.18097i −0.196096 + 0.339648i
$$448$$ −0.317626 −0.0150064
$$449$$ 14.4251 0.680761 0.340381 0.940288i $$-0.389444\pi$$
0.340381 + 0.940288i $$0.389444\pi$$
$$450$$ 0 0
$$451$$ −1.86692 3.23361i −0.0879100 0.152265i
$$452$$ −9.04264 + 15.6623i −0.425330 + 0.736693i
$$453$$ −6.95350 12.0438i −0.326704 0.565868i
$$454$$ −1.88971 3.27307i −0.0886884 0.153613i
$$455$$ 0 0
$$456$$ −2.33068 1.84797i −0.109144 0.0865392i
$$457$$ −32.1773 −1.50519 −0.752596 0.658483i $$-0.771199\pi$$
−0.752596 + 0.658483i $$0.771199\pi$$
$$458$$ −2.71814 4.70795i −0.127010 0.219988i
$$459$$ 0.252750 + 0.437775i 0.0117973 + 0.0204336i
$$460$$ 0 0
$$461$$ 7.75530 + 13.4326i 0.361200 + 0.625617i 0.988159 0.153435i $$-0.0490337\pi$$
−0.626958 + 0.779053i $$0.715700\pi$$
$$462$$ 0.467169 0.809160i 0.0217347 0.0376455i
$$463$$ −30.1477 −1.40108 −0.700541 0.713612i $$-0.747058\pi$$
−0.700541 + 0.713612i $$0.747058\pi$$
$$464$$ −9.14871 −0.424718
$$465$$ 0 0
$$466$$ −1.22461 + 2.12109i −0.0567290 + 0.0982576i
$$467$$ −34.5731 −1.59985 −0.799927 0.600098i $$-0.795128\pi$$
−0.799927 + 0.600098i $$0.795128\pi$$
$$468$$ −15.9582 −0.737667
$$469$$ −0.0938641 + 0.162577i −0.00433424 + 0.00750713i
$$470$$ 0 0
$$471$$ 1.67947 2.90892i 0.0773858 0.134036i
$$472$$ 4.80717 + 8.32627i 0.221268 + 0.383247i
$$473$$ 12.2946 + 21.2948i 0.565305 + 0.979137i
$$474$$ 2.26701 0.104127
$$475$$ 0 0
$$476$$ 0.0425153 0.00194869
$$477$$ 10.0427 + 17.3945i 0.459824 + 0.796438i
$$478$$ 4.72950 + 8.19173i 0.216322 + 0.374681i
$$479$$ −15.4238 + 26.7148i −0.704732 + 1.22063i 0.262056 + 0.965053i $$0.415600\pi$$
−0.966788 + 0.255579i $$0.917734\pi$$
$$480$$ 0 0
$$481$$ 15.9723 27.6649i 0.728276 1.26141i
$$482$$ −16.8708 −0.768444
$$483$$ 0.862427 0.0392418
$$484$$ −3.79182 + 6.56762i −0.172355 + 0.298528i
$$485$$ 0 0
$$486$$ −14.7592 −0.669491
$$487$$ −30.7745 −1.39453 −0.697263 0.716815i $$-0.745599\pi$$
−0.697263 + 0.716815i $$0.745599\pi$$
$$488$$ −3.08711 + 5.34704i −0.139747 + 0.242049i
$$489$$ −0.490380 0.849362i −0.0221757 0.0384095i
$$490$$ 0 0
$$491$$ 12.8571 + 22.2692i 0.580234 + 1.00499i 0.995451 + 0.0952719i $$0.0303720\pi$$
−0.415218 + 0.909722i $$0.636295\pi$$
$$492$$ −0.295518 0.511852i −0.0133230 0.0230761i
$$493$$ 1.22459 0.0551526
$$494$$ −25.5212 + 10.0991i −1.14825 + 0.454381i
$$495$$ 0 0
$$496$$ 1.49292 + 2.58582i 0.0670342 + 0.116107i
$$497$$ 1.85199 + 3.20774i 0.0830732 + 0.143887i
$$498$$ −1.43540 + 2.48619i −0.0643219 + 0.111409i
$$499$$ 0.201106 + 0.348326i 0.00900274 + 0.0155932i 0.870492 0.492183i $$-0.163801\pi$$
−0.861489 + 0.507776i $$0.830468\pi$$
$$500$$ 0 0
$$501$$ −6.39726 −0.285808
$$502$$ 2.65627 0.118555
$$503$$ −20.2327 + 35.0441i −0.902133 + 1.56254i −0.0774136 + 0.996999i $$0.524666\pi$$
−0.824720 + 0.565542i $$0.808667\pi$$
$$504$$ −0.402490 + 0.697133i −0.0179283 + 0.0310528i
$$505$$ 0 0
$$506$$ −17.1534 −0.762560
$$507$$ 9.09218 15.7481i 0.403798 0.699399i
$$508$$ 8.94845 + 15.4992i 0.397023 + 0.687665i
$$509$$ 5.72694 9.91935i 0.253842 0.439668i −0.710738 0.703457i $$-0.751639\pi$$
0.964580 + 0.263789i $$0.0849723\pi$$
$$510$$ 0 0
$$511$$ −1.31195 2.27236i −0.0580371 0.100523i
$$512$$ 1.00000 0.0441942
$$513$$ −15.3066 + 6.05703i −0.675801 + 0.267425i
$$514$$ 2.24745 0.0991308
$$515$$ 0 0
$$516$$ 1.94613 + 3.37079i 0.0856734 + 0.148391i
$$517$$ 27.9611 48.4300i 1.22973 2.12995i
$$518$$ −0.805694 1.39550i −0.0354002 0.0613149i
$$519$$ 2.64941 4.58891i 0.116296 0.201431i
$$520$$ 0 0
$$521$$ 1.66822 0.0730860 0.0365430 0.999332i $$-0.488365\pi$$
0.0365430 + 0.999332i $$0.488365\pi$$
$$522$$ −11.5931 + 20.0798i −0.507416 + 0.878870i
$$523$$ −21.9775 + 38.0662i −0.961011 + 1.66452i −0.241039 + 0.970515i $$0.577488\pi$$
−0.719971 + 0.694004i $$0.755845\pi$$
$$524$$ −11.8102 −0.515930
$$525$$ 0 0
$$526$$ 15.9289 27.5897i 0.694534 1.20297i
$$527$$ −0.199833 0.346121i −0.00870486 0.0150773i
$$528$$ −1.47081 + 2.54753i −0.0640090 + 0.110867i
$$529$$ 3.58341 + 6.20665i 0.155800 + 0.269854i
$$530$$ 0 0
$$531$$ 24.3663 1.05741
$$532$$ −0.202504 + 1.36961i −0.00877966 + 0.0593801i
$$533$$ −5.45388 −0.236234
$$534$$ −1.26916 2.19825i −0.0549220 0.0951276i
$$535$$ 0 0
$$536$$ 0.295518 0.511852i 0.0127644 0.0221086i
$$537$$ −0.382981 0.663342i −0.0165268 0.0286253i
$$538$$ 5.44763 9.43558i 0.234864 0.406797i
$$539$$ 29.7412 1.28104
$$540$$ 0 0
$$541$$ 14.7202 25.4961i 0.632870 1.09616i −0.354092 0.935211i $$-0.615210\pi$$
0.986962 0.160953i $$-0.0514567\pi$$
$$542$$ 5.96631 10.3340i 0.256275 0.443881i
$$543$$ −10.7706 −0.462209
$$544$$ −0.133854 −0.00573892
$$545$$ 0 0
$$546$$ −0.682374 1.18191i −0.0292029 0.0505809i
$$547$$ −10.2026 + 17.6714i −0.436231 + 0.755574i −0.997395 0.0721302i $$-0.977020\pi$$
0.561164 + 0.827704i $$0.310354\pi$$
$$548$$ 7.91554 + 13.7101i 0.338135 + 0.585667i
$$549$$ 7.82387 + 13.5513i 0.333915 + 0.578357i
$$550$$ 0 0
$$551$$ −5.83281 + 39.4494i −0.248486 + 1.68060i
$$552$$ −2.71523 −0.115568
$$553$$ −0.527613 0.913853i −0.0224364 0.0388610i
$$554$$ 7.95326 + 13.7754i 0.337902 + 0.585263i
$$555$$ 0 0
$$556$$ −0.583681 1.01096i −0.0247536 0.0428744i
$$557$$ 2.30575 3.99368i 0.0976977 0.169217i −0.813034 0.582217i $$-0.802185\pi$$
0.910731 + 0.412999i $$0.135519\pi$$
$$558$$ 7.56722 0.320346
$$559$$ 35.9164 1.51910
$$560$$ 0 0
$$561$$ 0.196874 0.340995i 0.00831202 0.0143968i
$$562$$ −20.9843 −0.885169
$$563$$ −5.13495 −0.216412 −0.108206 0.994128i $$-0.534511\pi$$
−0.108206 + 0.994128i $$0.534511\pi$$
$$564$$ 4.42600 7.66605i 0.186368 0.322799i
$$565$$ 0 0
$$566$$ 6.43083 11.1385i 0.270308 0.468187i
$$567$$ 0.798210 + 1.38254i 0.0335217 + 0.0580612i
$$568$$ −5.83073 10.0991i −0.244652 0.423750i
$$569$$ −23.0698 −0.967135 −0.483568 0.875307i $$-0.660659\pi$$
−0.483568 + 0.875307i $$0.660659\pi$$
$$570$$ 0 0
$$571$$ −24.7009 −1.03370 −0.516850 0.856076i $$-0.672896\pi$$
−0.516850 + 0.856076i $$0.672896\pi$$
$$572$$ 13.5722 + 23.5077i 0.567481 + 0.982906i
$$573$$ 6.24284 + 10.8129i 0.260799 + 0.451716i
$$574$$ −0.137555 + 0.238253i −0.00574144 + 0.00994447i
$$575$$ 0 0
$$576$$ 1.26718 2.19482i 0.0527993 0.0914510i
$$577$$ −34.0569 −1.41781 −0.708903 0.705306i $$-0.750810\pi$$
−0.708903 + 0.705306i $$0.750810\pi$$
$$578$$ −16.9821 −0.706362
$$579$$ 0.381295 0.660422i 0.0158461 0.0274462i
$$580$$ 0 0
$$581$$ 1.33628 0.0554381
$$582$$ −3.31402 −0.137370
$$583$$ 17.0823 29.5874i 0.707477 1.22539i
$$584$$ 4.13048 + 7.15420i 0.170920 + 0.296043i
$$585$$ 0 0
$$586$$ 6.06388 + 10.5029i 0.250496 + 0.433873i
$$587$$ −18.9701 32.8572i −0.782981 1.35616i −0.930198 0.367059i $$-0.880365\pi$$
0.147216 0.989104i $$-0.452969\pi$$
$$588$$ 4.70778 0.194145
$$589$$ 12.1019 4.78891i 0.498651 0.197324i
$$590$$ 0 0
$$591$$ 5.54750 + 9.60855i 0.228194 + 0.395243i
$$592$$ 2.53661 + 4.39354i 0.104254 + 0.180574i
$$593$$ −4.85602 + 8.41087i −0.199413 + 0.345393i −0.948338 0.317261i $$-0.897237\pi$$
0.748925 + 0.662654i $$0.230570\pi$$
$$594$$ 8.14003 + 14.0989i 0.333989 + 0.578486i
$$595$$ 0 0
$$596$$ −12.1515 −0.497745
$$597$$ 9.41556 0.385353
$$598$$ −12.5276 + 21.6985i −0.512292 + 0.887316i
$$599$$ 7.71001 13.3541i 0.315023 0.545635i −0.664420 0.747360i $$-0.731321\pi$$
0.979442 + 0.201725i $$0.0646546\pi$$
$$600$$ 0 0
$$601$$ −21.9383 −0.894881 −0.447441 0.894314i $$-0.647664\pi$$
−0.447441 + 0.894314i $$0.647664\pi$$
$$602$$ 0.905866 1.56901i 0.0369203 0.0639479i
$$603$$ −0.748951 1.29722i −0.0304996 0.0528269i
$$604$$ 10.1902 17.6499i 0.414631 0.718163i
$$605$$ 0 0
$$606$$ −0.857320 1.48492i −0.0348263 0.0603209i
$$607$$ 22.2900 0.904724 0.452362 0.891834i $$-0.350582\pi$$
0.452362 + 0.891834i $$0.350582\pi$$
$$608$$ 0.637555 4.31202i 0.0258563 0.174876i
$$609$$ −1.98289 −0.0803507
$$610$$ 0 0
$$611$$ −40.8416 70.7397i −1.65227 2.86182i
$$612$$ −0.169617 + 0.293785i −0.00685636 + 0.0118756i
$$613$$ 12.6028 + 21.8287i 0.509023 + 0.881654i 0.999945 + 0.0104504i $$0.00332654\pi$$
−0.490922 + 0.871203i $$0.663340\pi$$
$$614$$ −9.08409 + 15.7341i −0.366604 + 0.634977i
$$615$$ 0 0
$$616$$ 1.36924 0.0551684
$$617$$ −9.51333 + 16.4776i −0.382992 + 0.663362i −0.991488 0.130195i $$-0.958440\pi$$
0.608496 + 0.793557i $$0.291773\pi$$
$$618$$ −1.37600 + 2.38330i −0.0553507 + 0.0958702i
$$619$$ −33.9075 −1.36286 −0.681429 0.731884i $$-0.738641\pi$$
−0.681429 + 0.731884i $$0.738641\pi$$
$$620$$ 0 0
$$621$$ −7.51354 + 13.0138i −0.301508 + 0.522227i
$$622$$ −9.73832 16.8673i −0.390471 0.676316i
$$623$$ −0.590758 + 1.02322i −0.0236682 + 0.0409946i
$$624$$ 2.14836 + 3.72107i 0.0860032 + 0.148962i
$$625$$ 0 0
$$626$$ −11.9797 −0.478807
$$627$$ 10.0473 + 7.96637i 0.401249 + 0.318146i
$$628$$ 4.92242 0.196426
$$629$$ −0.339535 0.588091i −0.0135381 0.0234487i
$$630$$ 0 0
$$631$$ −4.27169 + 7.39878i −0.170053 + 0.294541i −0.938438 0.345447i $$-0.887727\pi$$
0.768385 + 0.639988i $$0.221061\pi$$
$$632$$ 1.66112 + 2.87714i 0.0660757 + 0.114446i
$$633$$ −0.398819 + 0.690775i −0.0158516 + 0.0274558i
$$634$$ −1.12931 −0.0448505
$$635$$ 0 0
$$636$$ 2.70398 4.68343i 0.107220 0.185710i
$$637$$ 21.7209 37.6217i 0.860613 1.49063i
$$638$$ 39.4389 1.56140
$$639$$ −29.5544 −1.16915
$$640$$ 0 0
$$641$$ −1.86302 3.22684i −0.0735847 0.127453i 0.826885 0.562371i $$-0.190111\pi$$
−0.900470 + 0.434918i $$0.856777\pi$$
$$642$$ −3.41187 + 5.90953i −0.134656 + 0.233231i
$$643$$ −16.1350 27.9466i −0.636300 1.10210i −0.986238 0.165332i $$-0.947131\pi$$
0.349938 0.936773i $$-0.386203\pi$$
$$644$$ 0.631931 + 1.09454i 0.0249016 + 0.0431308i
$$645$$ 0 0
$$646$$ −0.0853390 + 0.577179i −0.00335762 + 0.0227088i
$$647$$ 48.1241 1.89195 0.945977 0.324234i $$-0.105107\pi$$
0.945977 + 0.324234i $$0.105107\pi$$
$$648$$ −2.51305 4.35273i −0.0987220 0.170992i
$$649$$ −20.7231 35.8935i −0.813453 1.40894i
$$650$$ 0 0
$$651$$ 0.323575 + 0.560449i 0.0126819 + 0.0219657i
$$652$$ 0.718637 1.24472i 0.0281440 0.0487469i
$$653$$ 13.9774 0.546979 0.273489 0.961875i $$-0.411822\pi$$
0.273489 + 0.961875i $$0.411822\pi$$
$$654$$ 4.00140 0.156467
$$655$$ 0 0
$$656$$ 0.433073 0.750105i 0.0169087 0.0292867i
$$657$$ 20.9363 0.816802
$$658$$ −4.12035 −0.160628
$$659$$ 6.24517 10.8170i 0.243277 0.421369i −0.718369 0.695663i $$-0.755111\pi$$
0.961646 + 0.274294i $$0.0884441\pi$$
$$660$$ 0 0
$$661$$ −14.2429 + 24.6695i −0.553986 + 0.959531i 0.443996 + 0.896029i $$0.353560\pi$$
−0.997982 + 0.0635024i $$0.979773\pi$$
$$662$$ 7.15398 + 12.3911i 0.278047 + 0.481592i
$$663$$ −0.287566 0.498078i −0.0111681 0.0193438i
$$664$$ −4.20708 −0.163266
$$665$$ 0 0
$$666$$ 12.8574 0.498215
$$667$$ 18.2018 + 31.5264i 0.704776 + 1.22071i
$$668$$ −4.68750 8.11899i −0.181365 0.314133i
$$669$$ 2.15549 3.73342i 0.0833362 0.144342i
$$670$$ 0 0
$$671$$ 13.3082 23.0504i 0.513755 0.889851i
$$672$$ 0.216740 0.00836091
$$673$$ 31.6748 1.22097 0.610486 0.792027i $$-0.290974\pi$$
0.610486 + 0.792027i $$0.290974\pi$$
$$674$$ −13.8589 + 24.0043i −0.533824 + 0.924610i
$$675$$ 0 0
$$676$$ 26.6487 1.02495
$$677$$ −49.3049 −1.89494 −0.947470 0.319844i $$-0.896369\pi$$
−0.947470 + 0.319844i $$0.896369\pi$$
$$678$$ 6.17047 10.6876i 0.236975 0.410453i
$$679$$ 0.771290 + 1.33591i 0.0295994 + 0.0512677i
$$680$$ 0 0
$$681$$ 1.28949 + 2.23346i 0.0494133 + 0.0855863i
$$682$$ −6.43580 11.1471i −0.246440 0.426846i
$$683$$ −4.26771 −0.163299 −0.0816496 0.996661i $$-0.526019\pi$$
−0.0816496 + 0.996661i $$0.526019\pi$$
$$684$$ −8.65623 6.86344i −0.330979 0.262430i
$$685$$ 0 0
$$686$$ −2.20736 3.82326i −0.0842773 0.145973i
$$687$$ 1.85479 + 3.21259i 0.0707645 + 0.122568i
$$688$$ −2.85199 + 4.93979i −0.108731 + 0.188328i
$$689$$ −24.9514 43.2172i −0.950574 1.64644i
$$690$$ 0 0
$$691$$ 0.249546 0.00949319 0.00474659 0.999989i $$-0.498489\pi$$
0.00474659 + 0.999989i $$0.498489\pi$$
$$692$$ 7.76526 0.295191
$$693$$ 1.73508 3.00525i 0.0659104 0.114160i
$$694$$ 15.7098 27.2102i 0.596335 1.03288i
$$695$$ 0 0
$$696$$ 6.24284 0.236634
$$697$$ −0.0579684 + 0.100404i −0.00219571 + 0.00380308i
$$698$$ −11.7269 20.3117i −0.443871 0.768808i
$$699$$ 0.835643 1.44738i 0.0316069 0.0547448i
$$700$$ 0 0
$$701$$ −4.08961 7.08341i −0.154462 0.267537i 0.778401 0.627768i $$-0.216031\pi$$
−0.932863 + 0.360231i $$0.882698\pi$$
$$702$$ 23.7796 0.897504
$$703$$ 20.5623 8.13680i 0.775521 0.306885i
$$704$$ −4.31087 −0.162472
$$705$$ 0 0
$$706$$ 8.67340 + 15.0228i 0.326428 + 0.565389i
$$707$$ −0.399058 + 0.691189i −0.0150081 + 0.0259948i
$$708$$ −3.28029 5.68163i −0.123281 0.213529i
$$709$$ 6.85226 11.8685i 0.257342 0.445730i −0.708187 0.706025i $$-0.750487\pi$$
0.965529 + 0.260295i $$0.0838200\pi$$
$$710$$ 0 0
$$711$$ 8.41975 0.315765
$$712$$ 1.85992 3.22147i 0.0697034 0.120730i
$$713$$ 5.94048 10.2892i 0.222473 0.385334i
$$714$$ −0.0290114 −0.00108572
$$715$$ 0 0
$$716$$ 0.561247 0.972108i 0.0209748 0.0363294i
$$717$$ −3.22729 5.58982i −0.120525 0.208756i
$$718$$ −0.402934 + 0.697902i −0.0150374 + 0.0260455i
$$719$$ −13.4178 23.2403i −0.500398 0.866715i −1.00000 0.000460027i $$-0.999854\pi$$
0.499602 0.866255i $$-0.333480\pi$$
$$720$$ 0 0
$$721$$ 1.28097 0.0477060
$$722$$ −18.1870 5.49830i −0.676852 0.204626i
$$723$$ 11.5122 0.428143
$$724$$ −7.89198 13.6693i −0.293303 0.508016i
$$725$$ 0 0
$$726$$ 2.58744 4.48157i 0.0960288 0.166327i
$$727$$ 14.5299 + 25.1665i 0.538883 + 0.933373i 0.998965 + 0.0454961i $$0.0144869\pi$$
−0.460081 + 0.887877i $$0.652180\pi$$
$$728$$ 1.00000 1.73205i 0.0370625 0.0641941i
$$729$$ −5.00701 −0.185445
$$730$$ 0 0
$$731$$ 0.381749 0.661209i 0.0141195 0.0244557i
$$732$$ 2.10657 3.64868i 0.0778609 0.134859i
$$733$$ −30.8850 −1.14076 −0.570381 0.821380i $$-0.693204\pi$$
−0.570381 + 0.821380i $$0.693204\pi$$
$$734$$ 2.53816 0.0936852
$$735$$ 0 0
$$736$$ −1.98955 3.44600i −0.0733357 0.127021i
$$737$$ −1.27394 + 2.20653i −0.0469262 + 0.0812786i
$$738$$ −1.09757 1.90104i −0.0404020 0.0699782i
$$739$$ 17.9491 + 31.0887i 0.660267 + 1.14362i 0.980545 + 0.196292i $$0.0628901\pi$$
−0.320279 + 0.947323i $$0.603777\pi$$
$$740$$ 0 0
$$741$$ 17.4150 6.89138i 0.639757 0.253161i
$$742$$ −2.51725 −0.0924113
$$743$$ 3.15432 + 5.46344i 0.115721 + 0.200434i 0.918068 0.396424i $$-0.129749\pi$$
−0.802347 + 0.596858i $$0.796416\pi$$
$$744$$ −1.01873 1.76450i −0.0373485 0.0646895i
$$745$$ 0 0
$$746$$ 6.20061 + 10.7398i 0.227020 + 0.393211i
$$747$$ −5.33114 + 9.23380i −0.195056 + 0.337847i
$$748$$ 0.577026 0.0210982
$$749$$ 3.17626 0.116058
$$750$$ 0 0
$$751$$ 20.3945 35.3242i 0.744204 1.28900i −0.206361 0.978476i $$-0.566162\pi$$
0.950566 0.310524i $$-0.100505\pi$$
$$752$$ 12.9723 0.473053
$$753$$ −1.81257 −0.0660537
$$754$$ 28.8034 49.8890i 1.04896 1.81685i
$$755$$ 0 0
$$756$$ 0.599758 1.03881i 0.0218130 0.0377812i
$$757$$ 9.72687 + 16.8474i 0.353529 + 0.612330i 0.986865 0.161547i $$-0.0516482\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$758$$ 6.33778 + 10.9774i 0.230199 + 0.398716i
$$759$$ 11.7050 0.424865
$$760$$ 0 0
$$761$$ −19.1465 −0.694058 −0.347029 0.937854i $$-0.612810\pi$$
−0.347029 + 0.937854i $$0.612810\pi$$
$$762$$ −6.10619 10.5762i −0.221204 0.383137i
$$763$$ −0.931269 1.61301i −0.0337142 0.0583947i
$$764$$ −9.14871 + 15.8460i −0.330989 + 0.573289i
$$765$$ 0 0
$$766$$ −7.97632 + 13.8154i −0.288196 + 0.499170i
$$767$$ −60.5388 −2.18593
$$768$$ −0.682374 −0.0246231
$$769$$ −13.3405 + 23.1064i −0.481070 + 0.833238i −0.999764 0.0217222i $$-0.993085\pi$$
0.518694 + 0.854960i $$0.326418\pi$$
$$770$$ 0 0
$$771$$ −1.53360 −0.0552314
$$772$$ 1.11755 0.0402216
$$773$$ 11.8521 20.5284i 0.426290 0.738356i −0.570250 0.821471i $$-0.693154\pi$$
0.996540 + 0.0831151i $$0.0264869\pi$$
$$774$$ 7.22799 + 12.5192i 0.259805 + 0.449995i
$$775$$ 0 0
$$776$$ −2.42830 4.20594i −0.0871709 0.150984i
$$777$$ 0.549785 + 0.952255i 0.0197234 + 0.0341620i
$$778$$ −26.1982 −0.939250
$$779$$ −2.95836 2.34565i −0.105994 0.0840418i
$$780$$ 0 0
$$781$$ 25.1356 + 43.5361i 0.899421 + 1.55784i
$$782$$ 0.266308 + 0.461259i 0.00952315 + 0.0164946i
$$783$$ 17.2751 29.9213i 0.617361 1.06930i
$$784$$ 3.44956 + 5.97481i 0.123198 + 0.213386i
$$785$$ 0 0