# Properties

 Label 950.2.e.m.501.4 Level $950$ Weight $2$ Character 950.501 Analytic conductor $7.586$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Learn more

## 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: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.39075800976.1 Defining polynomial: $$x^{8} - x^{7} + 12 x^{6} - 13 x^{5} + 125 x^{4} - 116 x^{3} + 232 x^{2} + 96 x + 64$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 501.4 Root $$-1.63248 - 2.82754i$$ of defining polynomial Character $$\chi$$ $$=$$ 950.501 Dual form 950.2.e.m.201.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(1.63248 + 2.82754i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.63248 + 2.82754i) q^{6} -2.62013 q^{7} -1.00000 q^{8} +(-3.82998 + 6.63372i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(1.63248 + 2.82754i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.63248 + 2.82754i) q^{6} -2.62013 q^{7} -1.00000 q^{8} +(-3.82998 + 6.63372i) q^{9} +5.03983 q^{11} -3.26496 q^{12} +(-2.32241 + 4.02254i) q^{13} +(-1.31007 - 2.26910i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82998 + 3.16962i) q^{17} -7.65996 q^{18} +(0.697500 - 4.30273i) q^{19} +(-4.27731 - 7.40852i) q^{21} +(2.51991 + 4.36462i) q^{22} +(2.34233 - 4.05703i) q^{23} +(-1.63248 - 2.82754i) q^{24} -4.64483 q^{26} -15.2146 q^{27} +(1.31007 - 2.26910i) q^{28} +(4.01991 - 6.96270i) q^{29} -3.28009 q^{31} +(0.500000 - 0.866025i) q^{32} +(8.22742 + 14.2503i) q^{33} +(-1.82998 + 3.16962i) q^{34} +(-3.82998 - 6.63372i) q^{36} -5.75505 q^{37} +(4.07502 - 1.54731i) q^{38} -15.1652 q^{39} +(2.90735 + 5.03568i) q^{41} +(4.27731 - 7.40852i) q^{42} +(0.290150 + 0.502555i) q^{43} +(-2.51991 + 4.36462i) q^{44} +4.68466 q^{46} +(-2.31007 + 4.00115i) q^{47} +(1.63248 - 2.82754i) q^{48} -0.134919 q^{49} +(-5.97481 + 10.3487i) q^{51} +(-2.32241 - 4.02254i) q^{52} +(2.31007 - 4.00115i) q^{53} +(-7.60729 - 13.1762i) q^{54} +2.62013 q^{56} +(13.3048 - 5.05191i) q^{57} +8.03983 q^{58} +(1.88743 + 3.26913i) q^{59} +(-0.0650203 + 0.112618i) q^{61} +(-1.64004 - 2.84064i) q^{62} +(10.0350 - 17.3812i) q^{63} +1.00000 q^{64} +(-8.22742 + 14.2503i) q^{66} +(-0.189935 + 0.328977i) q^{67} -3.65996 q^{68} +15.2952 q^{69} +(4.56746 + 7.91107i) q^{71} +(3.82998 - 6.63372i) q^{72} +(4.25261 + 7.36574i) q^{73} +(-2.87752 - 4.98402i) q^{74} +(3.37752 + 2.75542i) q^{76} -13.2050 q^{77} +(-7.58259 - 13.1334i) q^{78} +(3.98237 + 6.89767i) q^{79} +(-13.3475 - 23.1186i) q^{81} +(-2.90735 + 5.03568i) q^{82} +7.86996 q^{83} +8.55462 q^{84} +(-0.290150 + 0.502555i) q^{86} +26.2497 q^{87} -5.03983 q^{88} +(4.14483 - 7.17905i) q^{89} +(6.08503 - 10.5396i) q^{91} +(2.34233 + 4.05703i) q^{92} +(-5.35468 - 9.27458i) q^{93} -4.62013 q^{94} +3.26496 q^{96} +(8.09494 + 14.0208i) q^{97} +(-0.0674593 - 0.116843i) q^{98} +(-19.3024 + 33.4328i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + O(q^{10})$$ $$8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + 10q^{11} + 2q^{12} - 9q^{13} - 6q^{14} - 4q^{16} - 5q^{17} - 22q^{18} - q^{21} + 5q^{22} - 6q^{23} + q^{24} - 18q^{26} - 16q^{27} + 6q^{28} + 17q^{29} + 22q^{31} + 4q^{32} + 4q^{33} + 5q^{34} - 11q^{36} + 8q^{37} - 36q^{39} + 7q^{41} + q^{42} + 13q^{43} - 5q^{44} - 12q^{46} - 14q^{47} - q^{48} + 44q^{49} - 9q^{51} - 9q^{52} + 14q^{53} - 8q^{54} + 12q^{56} + 48q^{57} + 34q^{58} + 14q^{59} - 9q^{61} + 11q^{62} + 45q^{63} + 8q^{64} - 4q^{66} - 6q^{67} + 10q^{68} + 54q^{69} + 14q^{71} + 11q^{72} + 11q^{73} + 4q^{74} + 10q^{77} - 18q^{78} - 17q^{79} - 36q^{81} - 7q^{82} + 46q^{83} + 2q^{84} - 13q^{86} + 2q^{87} - 10q^{88} + 14q^{89} - 25q^{91} - 6q^{92} - 13q^{93} - 28q^{94} - 2q^{96} + 17q^{97} + 22q^{98} - 60q^{99} + O(q^{100})$$

## 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
$$3$$ 1.63248 + 2.82754i 0.942513 + 1.63248i 0.760657 + 0.649154i $$0.224877\pi$$
0.181856 + 0.983325i $$0.441790\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ −1.63248 + 2.82754i −0.666457 + 1.15434i
$$7$$ −2.62013 −0.990316 −0.495158 0.868803i $$-0.664890\pi$$
−0.495158 + 0.868803i $$0.664890\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −3.82998 + 6.63372i −1.27666 + 2.21124i
$$10$$ 0 0
$$11$$ 5.03983 1.51957 0.759783 0.650177i $$-0.225305\pi$$
0.759783 + 0.650177i $$0.225305\pi$$
$$12$$ −3.26496 −0.942513
$$13$$ −2.32241 + 4.02254i −0.644122 + 1.11565i 0.340382 + 0.940287i $$0.389444\pi$$
−0.984504 + 0.175365i $$0.943890\pi$$
$$14$$ −1.31007 2.26910i −0.350130 0.606442i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 1.82998 + 3.16962i 0.443835 + 0.768745i 0.997970 0.0636816i $$-0.0202842\pi$$
−0.554135 + 0.832427i $$0.686951\pi$$
$$18$$ −7.65996 −1.80547
$$19$$ 0.697500 4.30273i 0.160017 0.987114i
$$20$$ 0 0
$$21$$ −4.27731 7.40852i −0.933385 1.61667i
$$22$$ 2.51991 + 4.36462i 0.537248 + 0.930540i
$$23$$ 2.34233 4.05703i 0.488409 0.845950i −0.511502 0.859282i $$-0.670911\pi$$
0.999911 + 0.0133324i $$0.00424395\pi$$
$$24$$ −1.63248 2.82754i −0.333229 0.577169i
$$25$$ 0 0
$$26$$ −4.64483 −0.910926
$$27$$ −15.2146 −2.92805
$$28$$ 1.31007 2.26910i 0.247579 0.428819i
$$29$$ 4.01991 6.96270i 0.746479 1.29294i −0.203021 0.979174i $$-0.565076\pi$$
0.949500 0.313766i $$-0.101591\pi$$
$$30$$ 0 0
$$31$$ −3.28009 −0.589121 −0.294561 0.955633i $$-0.595173\pi$$
−0.294561 + 0.955633i $$0.595173\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 8.22742 + 14.2503i 1.43221 + 2.48066i
$$34$$ −1.82998 + 3.16962i −0.313839 + 0.543585i
$$35$$ 0 0
$$36$$ −3.82998 6.63372i −0.638330 1.10562i
$$37$$ −5.75505 −0.946124 −0.473062 0.881029i $$-0.656851\pi$$
−0.473062 + 0.881029i $$0.656851\pi$$
$$38$$ 4.07502 1.54731i 0.661056 0.251007i
$$39$$ −15.1652 −2.42837
$$40$$ 0 0
$$41$$ 2.90735 + 5.03568i 0.454052 + 0.786441i 0.998633 0.0522673i $$-0.0166448\pi$$
−0.544581 + 0.838708i $$0.683311\pi$$
$$42$$ 4.27731 7.40852i 0.660003 1.14316i
$$43$$ 0.290150 + 0.502555i 0.0442475 + 0.0766390i 0.887301 0.461191i $$-0.152578\pi$$
−0.843053 + 0.537830i $$0.819244\pi$$
$$44$$ −2.51991 + 4.36462i −0.379891 + 0.657991i
$$45$$ 0 0
$$46$$ 4.68466 0.690715
$$47$$ −2.31007 + 4.00115i −0.336958 + 0.583628i −0.983859 0.178946i $$-0.942731\pi$$
0.646901 + 0.762574i $$0.276065\pi$$
$$48$$ 1.63248 2.82754i 0.235628 0.408120i
$$49$$ −0.134919 −0.0192741
$$50$$ 0 0
$$51$$ −5.97481 + 10.3487i −0.836641 + 1.44910i
$$52$$ −2.32241 4.02254i −0.322061 0.557826i
$$53$$ 2.31007 4.00115i 0.317312 0.549600i −0.662614 0.748961i $$-0.730553\pi$$
0.979926 + 0.199361i $$0.0638865\pi$$
$$54$$ −7.60729 13.1762i −1.03522 1.79306i
$$55$$ 0 0
$$56$$ 2.62013 0.350130
$$57$$ 13.3048 5.05191i 1.76226 0.669142i
$$58$$ 8.03983 1.05568
$$59$$ 1.88743 + 3.26913i 0.245723 + 0.425605i 0.962335 0.271868i $$-0.0876413\pi$$
−0.716612 + 0.697472i $$0.754308\pi$$
$$60$$ 0 0
$$61$$ −0.0650203 + 0.112618i −0.00832500 + 0.0144193i −0.870158 0.492773i $$-0.835983\pi$$
0.861833 + 0.507192i $$0.169317\pi$$
$$62$$ −1.64004 2.84064i −0.208286 0.360762i
$$63$$ 10.0350 17.3812i 1.26430 2.18983i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −8.22742 + 14.2503i −1.01273 + 1.75409i
$$67$$ −0.189935 + 0.328977i −0.0232043 + 0.0401909i −0.877394 0.479770i $$-0.840720\pi$$
0.854190 + 0.519961i $$0.174053\pi$$
$$68$$ −3.65996 −0.443835
$$69$$ 15.2952 1.84133
$$70$$ 0 0
$$71$$ 4.56746 + 7.91107i 0.542058 + 0.938871i 0.998786 + 0.0492651i $$0.0156879\pi$$
−0.456728 + 0.889606i $$0.650979\pi$$
$$72$$ 3.82998 6.63372i 0.451367 0.781791i
$$73$$ 4.25261 + 7.36574i 0.497730 + 0.862094i 0.999997 0.00261883i $$-0.000833600\pi$$
−0.502266 + 0.864713i $$0.667500\pi$$
$$74$$ −2.87752 4.98402i −0.334505 0.579380i
$$75$$ 0 0
$$76$$ 3.37752 + 2.75542i 0.387429 + 0.316068i
$$77$$ −13.2050 −1.50485
$$78$$ −7.58259 13.1334i −0.858559 1.48707i
$$79$$ 3.98237 + 6.89767i 0.448052 + 0.776049i 0.998259 0.0589793i $$-0.0187846\pi$$
−0.550207 + 0.835028i $$0.685451\pi$$
$$80$$ 0 0
$$81$$ −13.3475 23.1186i −1.48306 2.56874i
$$82$$ −2.90735 + 5.03568i −0.321063 + 0.556098i
$$83$$ 7.86996 0.863840 0.431920 0.901912i $$-0.357836\pi$$
0.431920 + 0.901912i $$0.357836\pi$$
$$84$$ 8.55462 0.933385
$$85$$ 0 0
$$86$$ −0.290150 + 0.502555i −0.0312877 + 0.0541919i
$$87$$ 26.2497 2.81426
$$88$$ −5.03983 −0.537248
$$89$$ 4.14483 7.17905i 0.439351 0.760978i −0.558289 0.829647i $$-0.688542\pi$$
0.997640 + 0.0686686i $$0.0218751\pi$$
$$90$$ 0 0
$$91$$ 6.08503 10.5396i 0.637884 1.10485i
$$92$$ 2.34233 + 4.05703i 0.244205 + 0.422975i
$$93$$ −5.35468 9.27458i −0.555254 0.961729i
$$94$$ −4.62013 −0.476530
$$95$$ 0 0
$$96$$ 3.26496 0.333229
$$97$$ 8.09494 + 14.0208i 0.821917 + 1.42360i 0.904253 + 0.426997i $$0.140428\pi$$
−0.0823367 + 0.996605i $$0.526238\pi$$
$$98$$ −0.0674593 0.116843i −0.00681442 0.0118029i
$$99$$ −19.3024 + 33.4328i −1.93997 + 3.36012i
$$100$$ 0 0
$$101$$ −4.23270 + 7.33124i −0.421169 + 0.729486i −0.996054 0.0887481i $$-0.971713\pi$$
0.574885 + 0.818234i $$0.305047\pi$$
$$102$$ −11.9496 −1.18319
$$103$$ 11.8498 1.16760 0.583800 0.811898i $$-0.301565\pi$$
0.583800 + 0.811898i $$0.301565\pi$$
$$104$$ 2.32241 4.02254i 0.227731 0.394443i
$$105$$ 0 0
$$106$$ 4.62013 0.448747
$$107$$ 16.8100 1.62508 0.812542 0.582902i $$-0.198083\pi$$
0.812542 + 0.582902i $$0.198083\pi$$
$$108$$ 7.60729 13.1762i 0.732012 1.26788i
$$109$$ −10.0023 17.3245i −0.958045 1.65938i −0.727240 0.686384i $$-0.759197\pi$$
−0.230806 0.973000i $$-0.574136\pi$$
$$110$$ 0 0
$$111$$ −9.39500 16.2726i −0.891734 1.54453i
$$112$$ 1.31007 + 2.26910i 0.123790 + 0.214410i
$$113$$ −14.3505 −1.34998 −0.674990 0.737827i $$-0.735852\pi$$
−0.674990 + 0.737827i $$0.735852\pi$$
$$114$$ 11.0275 + 8.99633i 1.03282 + 0.842583i
$$115$$ 0 0
$$116$$ 4.01991 + 6.96270i 0.373240 + 0.646470i
$$117$$ −17.7896 30.8125i −1.64465 2.84862i
$$118$$ −1.88743 + 3.26913i −0.173752 + 0.300948i
$$119$$ −4.79478 8.30481i −0.439537 0.761301i
$$120$$ 0 0
$$121$$ 14.3999 1.30908
$$122$$ −0.130041 −0.0117733
$$123$$ −9.49238 + 16.4413i −0.855899 + 1.48246i
$$124$$ 1.64004 2.84064i 0.147280 0.255097i
$$125$$ 0 0
$$126$$ 20.0701 1.78799
$$127$$ −3.94254 + 6.82869i −0.349844 + 0.605948i −0.986222 0.165430i $$-0.947099\pi$$
0.636377 + 0.771378i $$0.280432\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ −0.947329 + 1.64082i −0.0834077 + 0.144466i
$$130$$ 0 0
$$131$$ −1.20228 2.08242i −0.105044 0.181942i 0.808712 0.588205i $$-0.200165\pi$$
−0.913756 + 0.406263i $$0.866832\pi$$
$$132$$ −16.4548 −1.43221
$$133$$ −1.82754 + 11.2737i −0.158468 + 0.977555i
$$134$$ −0.379870 −0.0328158
$$135$$ 0 0
$$136$$ −1.82998 3.16962i −0.156919 0.271792i
$$137$$ 8.71751 15.0992i 0.744787 1.29001i −0.205507 0.978656i $$-0.565884\pi$$
0.950294 0.311353i $$-0.100782\pi$$
$$138$$ 7.64761 + 13.2460i 0.651008 + 1.12758i
$$139$$ −4.78487 + 8.28764i −0.405848 + 0.702949i −0.994420 0.105496i $$-0.966357\pi$$
0.588572 + 0.808445i $$0.299690\pi$$
$$140$$ 0 0
$$141$$ −15.0845 −1.27035
$$142$$ −4.56746 + 7.91107i −0.383293 + 0.663882i
$$143$$ −11.7046 + 20.2729i −0.978786 + 1.69531i
$$144$$ 7.65996 0.638330
$$145$$ 0 0
$$146$$ −4.25261 + 7.36574i −0.351948 + 0.609593i
$$147$$ −0.220252 0.381488i −0.0181661 0.0314646i
$$148$$ 2.87752 4.98402i 0.236531 0.409684i
$$149$$ 8.56218 + 14.8301i 0.701441 + 1.21493i 0.967961 + 0.251102i $$0.0807931\pi$$
−0.266519 + 0.963830i $$0.585874\pi$$
$$150$$ 0 0
$$151$$ −5.44440 −0.443059 −0.221529 0.975154i $$-0.571105\pi$$
−0.221529 + 0.975154i $$0.571105\pi$$
$$152$$ −0.697500 + 4.30273i −0.0565747 + 0.348998i
$$153$$ −28.0351 −2.26651
$$154$$ −6.60250 11.4359i −0.532045 0.921529i
$$155$$ 0 0
$$156$$ 7.58259 13.1334i 0.607093 1.05152i
$$157$$ −0.0123496 0.0213902i −0.000985608 0.00170712i 0.865532 0.500853i $$-0.166980\pi$$
−0.866518 + 0.499146i $$0.833647\pi$$
$$158$$ −3.98237 + 6.89767i −0.316821 + 0.548749i
$$159$$ 15.0845 1.19628
$$160$$ 0 0
$$161$$ −6.13721 + 10.6300i −0.483680 + 0.837758i
$$162$$ 13.3475 23.1186i 1.04868 1.81637i
$$163$$ 10.8347 0.848640 0.424320 0.905512i $$-0.360513\pi$$
0.424320 + 0.905512i $$0.360513\pi$$
$$164$$ −5.81470 −0.454052
$$165$$ 0 0
$$166$$ 3.93498 + 6.81558i 0.305414 + 0.528992i
$$167$$ −3.14239 + 5.44278i −0.243165 + 0.421175i −0.961614 0.274405i $$-0.911519\pi$$
0.718449 + 0.695580i $$0.244852\pi$$
$$168$$ 4.27731 + 7.40852i 0.330002 + 0.571579i
$$169$$ −4.28722 7.42568i −0.329786 0.571206i
$$170$$ 0 0
$$171$$ 25.8717 + 21.1064i 1.97846 + 1.61405i
$$172$$ −0.580301 −0.0442475
$$173$$ −0.187589 0.324914i −0.0142622 0.0247028i 0.858806 0.512301i $$-0.171207\pi$$
−0.873068 + 0.487598i $$0.837873\pi$$
$$174$$ 13.1249 + 22.7329i 0.994993 + 1.72338i
$$175$$ 0 0
$$176$$ −2.51991 4.36462i −0.189946 0.328996i
$$177$$ −6.16240 + 10.6736i −0.463194 + 0.802276i
$$178$$ 8.28966 0.621336
$$179$$ −8.04940 −0.601640 −0.300820 0.953681i $$-0.597260\pi$$
−0.300820 + 0.953681i $$0.597260\pi$$
$$180$$ 0 0
$$181$$ 10.5251 18.2301i 0.782327 1.35503i −0.148256 0.988949i $$-0.547366\pi$$
0.930583 0.366081i $$-0.119301\pi$$
$$182$$ 12.1701 0.902105
$$183$$ −0.424577 −0.0313857
$$184$$ −2.34233 + 4.05703i −0.172679 + 0.299088i
$$185$$ 0 0
$$186$$ 5.35468 9.27458i 0.392624 0.680045i
$$187$$ 9.22278 + 15.9743i 0.674437 + 1.16816i
$$188$$ −2.31007 4.00115i −0.168479 0.291814i
$$189$$ 39.8642 2.89969
$$190$$ 0 0
$$191$$ 8.03983 0.581742 0.290871 0.956762i $$-0.406055\pi$$
0.290871 + 0.956762i $$0.406055\pi$$
$$192$$ 1.63248 + 2.82754i 0.117814 + 0.204060i
$$193$$ −10.1224 17.5325i −0.728628 1.26202i −0.957463 0.288555i $$-0.906825\pi$$
0.228836 0.973465i $$-0.426508\pi$$
$$194$$ −8.09494 + 14.0208i −0.581183 + 1.00664i
$$195$$ 0 0
$$196$$ 0.0674593 0.116843i 0.00481852 0.00834593i
$$197$$ 2.92004 0.208044 0.104022 0.994575i $$-0.466829\pi$$
0.104022 + 0.994575i $$0.466829\pi$$
$$198$$ −38.6049 −2.74353
$$199$$ 7.80244 13.5142i 0.553101 0.957998i −0.444948 0.895556i $$-0.646778\pi$$
0.998049 0.0624418i $$-0.0198888\pi$$
$$200$$ 0 0
$$201$$ −1.24026 −0.0874812
$$202$$ −8.46539 −0.595623
$$203$$ −10.5327 + 18.2432i −0.739251 + 1.28042i
$$204$$ −5.97481 10.3487i −0.418320 0.724552i
$$205$$ 0 0
$$206$$ 5.92492 + 10.2623i 0.412809 + 0.715006i
$$207$$ 17.9421 + 31.0767i 1.24707 + 2.15998i
$$208$$ 4.64483 0.322061
$$209$$ 3.51528 21.6850i 0.243157 1.49998i
$$210$$ 0 0
$$211$$ −0.572585 0.991747i −0.0394184 0.0682747i 0.845643 0.533749i $$-0.179217\pi$$
−0.885062 + 0.465474i $$0.845884\pi$$
$$212$$ 2.31007 + 4.00115i 0.158656 + 0.274800i
$$213$$ −14.9126 + 25.8293i −1.02179 + 1.76980i
$$214$$ 8.40500 + 14.5579i 0.574554 + 0.995157i
$$215$$ 0 0
$$216$$ 15.2146 1.03522
$$217$$ 8.59426 0.583416
$$218$$ 10.0023 17.3245i 0.677440 1.17336i
$$219$$ −13.8846 + 24.0488i −0.938234 + 1.62507i
$$220$$ 0 0
$$221$$ −16.9999 −1.14354
$$222$$ 9.39500 16.2726i 0.630551 1.09215i
$$223$$ −7.66474 13.2757i −0.513269 0.889008i −0.999882 0.0153903i $$-0.995101\pi$$
0.486612 0.873618i $$-0.338232\pi$$
$$224$$ −1.31007 + 2.26910i −0.0875324 + 0.151611i
$$225$$ 0 0
$$226$$ −7.17524 12.4279i −0.477290 0.826690i
$$227$$ −19.2850 −1.27999 −0.639994 0.768380i $$-0.721063\pi$$
−0.639994 + 0.768380i $$0.721063\pi$$
$$228$$ −2.27731 + 14.0482i −0.150818 + 0.930368i
$$229$$ 14.3752 0.949939 0.474969 0.880002i $$-0.342459\pi$$
0.474969 + 0.880002i $$0.342459\pi$$
$$230$$ 0 0
$$231$$ −21.5569 37.3377i −1.41834 2.45664i
$$232$$ −4.01991 + 6.96270i −0.263920 + 0.457123i
$$233$$ −6.91272 11.9732i −0.452867 0.784389i 0.545695 0.837984i $$-0.316266\pi$$
−0.998563 + 0.0535944i $$0.982932\pi$$
$$234$$ 17.7896 30.8125i 1.16294 2.01428i
$$235$$ 0 0
$$236$$ −3.77487 −0.245723
$$237$$ −13.0023 + 22.5206i −0.844589 + 1.46287i
$$238$$ 4.79478 8.30481i 0.310800 0.538321i
$$239$$ −14.9696 −0.968305 −0.484152 0.874984i $$-0.660872\pi$$
−0.484152 + 0.874984i $$0.660872\pi$$
$$240$$ 0 0
$$241$$ 9.66469 16.7397i 0.622557 1.07830i −0.366451 0.930437i $$-0.619427\pi$$
0.989008 0.147863i $$-0.0472395\pi$$
$$242$$ 7.19994 + 12.4707i 0.462830 + 0.801644i
$$243$$ 20.7573 35.9528i 1.33158 2.30637i
$$244$$ −0.0650203 0.112618i −0.00416250 0.00720966i
$$245$$ 0 0
$$246$$ −18.9848 −1.21042
$$247$$ 15.6880 + 12.7984i 0.998205 + 0.814346i
$$248$$ 3.28009 0.208286
$$249$$ 12.8475 + 22.2526i 0.814180 + 1.41020i
$$250$$ 0 0
$$251$$ −5.16246 + 8.94164i −0.325851 + 0.564391i −0.981684 0.190515i $$-0.938984\pi$$
0.655833 + 0.754906i $$0.272318\pi$$
$$252$$ 10.0350 + 17.3812i 0.632148 + 1.09491i
$$253$$ 11.8049 20.4468i 0.742170 1.28548i
$$254$$ −7.88509 −0.494755
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 14.3846 24.9149i 0.897287 1.55415i 0.0663376 0.997797i $$-0.478869\pi$$
0.830949 0.556349i $$-0.187798\pi$$
$$258$$ −1.89466 −0.117956
$$259$$ 15.0790 0.936962
$$260$$ 0 0
$$261$$ 30.7924 + 53.3340i 1.90600 + 3.30129i
$$262$$ 1.20228 2.08242i 0.0742774 0.128652i
$$263$$ −4.56746 7.91107i −0.281642 0.487818i 0.690148 0.723669i $$-0.257546\pi$$
−0.971789 + 0.235851i $$0.924212\pi$$
$$264$$ −8.22742 14.2503i −0.506363 0.877046i
$$265$$ 0 0
$$266$$ −10.6771 + 4.05416i −0.654655 + 0.248577i
$$267$$ 27.0654 1.65638
$$268$$ −0.189935 0.328977i −0.0116021 0.0200955i
$$269$$ −8.45474 14.6440i −0.515495 0.892863i −0.999838 0.0179853i $$-0.994275\pi$$
0.484343 0.874878i $$-0.339059\pi$$
$$270$$ 0 0
$$271$$ 7.94483 + 13.7609i 0.482614 + 0.835912i 0.999801 0.0199603i $$-0.00635399\pi$$
−0.517187 + 0.855873i $$0.673021\pi$$
$$272$$ 1.82998 3.16962i 0.110959 0.192186i
$$273$$ 39.7347 2.40486
$$274$$ 17.4350 1.05329
$$275$$ 0 0
$$276$$ −7.64761 + 13.2460i −0.460332 + 0.797318i
$$277$$ −11.4852 −0.690079 −0.345040 0.938588i $$-0.612135\pi$$
−0.345040 + 0.938588i $$0.612135\pi$$
$$278$$ −9.56975 −0.573955
$$279$$ 12.5627 21.7592i 0.752108 1.30269i
$$280$$ 0 0
$$281$$ 7.14483 12.3752i 0.426225 0.738243i −0.570309 0.821430i $$-0.693177\pi$$
0.996534 + 0.0831872i $$0.0265099\pi$$
$$282$$ −7.54227 13.0636i −0.449136 0.777926i
$$283$$ 1.58215 + 2.74037i 0.0940493 + 0.162898i 0.909211 0.416335i $$-0.136686\pi$$
−0.815162 + 0.579233i $$0.803352\pi$$
$$284$$ −9.13492 −0.542058
$$285$$ 0 0
$$286$$ −23.4091 −1.38421
$$287$$ −7.61763 13.1941i −0.449655 0.778825i
$$288$$ 3.82998 + 6.63372i 0.225684 + 0.390896i
$$289$$ 1.80235 3.12176i 0.106021 0.183633i
$$290$$ 0 0
$$291$$ −26.4296 + 45.7775i −1.54933 + 2.68352i
$$292$$ −8.50522 −0.497730
$$293$$ −14.7094 −0.859330 −0.429665 0.902988i $$-0.641368\pi$$
−0.429665 + 0.902988i $$0.641368\pi$$
$$294$$ 0.220252 0.381488i 0.0128454 0.0222488i
$$295$$ 0 0
$$296$$ 5.75505 0.334505
$$297$$ −76.6789 −4.44936
$$298$$ −8.56218 + 14.8301i −0.495994 + 0.859087i
$$299$$ 10.8797 + 18.8442i 0.629190 + 1.08979i
$$300$$ 0 0
$$301$$ −0.760232 1.31676i −0.0438190 0.0758968i
$$302$$ −2.72220 4.71499i −0.156645 0.271317i
$$303$$ −27.6392 −1.58783
$$304$$ −4.07502 + 1.54731i −0.233719 + 0.0887445i
$$305$$ 0 0
$$306$$ −14.0176 24.2791i −0.801331 1.38795i
$$307$$ −13.0727 22.6425i −0.746097 1.29228i −0.949680 0.313221i $$-0.898592\pi$$
0.203583 0.979058i $$-0.434741\pi$$
$$308$$ 6.60250 11.4359i 0.376213 0.651619i
$$309$$ 19.3446 + 33.5059i 1.10048 + 1.90608i
$$310$$ 0 0
$$311$$ 6.65039 0.377109 0.188555 0.982063i $$-0.439620\pi$$
0.188555 + 0.982063i $$0.439620\pi$$
$$312$$ 15.1652 0.858559
$$313$$ −8.68988 + 15.0513i −0.491181 + 0.850750i −0.999948 0.0101536i $$-0.996768\pi$$
0.508768 + 0.860904i $$0.330101\pi$$
$$314$$ 0.0123496 0.0213902i 0.000696930 0.00120712i
$$315$$ 0 0
$$316$$ −7.96475 −0.448052
$$317$$ 0.687647 1.19104i 0.0386221 0.0668954i −0.846068 0.533075i $$-0.821036\pi$$
0.884690 + 0.466179i $$0.154370\pi$$
$$318$$ 7.54227 + 13.0636i 0.422949 + 0.732570i
$$319$$ 20.2597 35.0908i 1.13432 1.96471i
$$320$$ 0 0
$$321$$ 27.4420 + 47.5309i 1.53166 + 2.65292i
$$322$$ −12.2744 −0.684026
$$323$$ 14.9144 5.66310i 0.829861 0.315103i
$$324$$ 26.6951 1.48306
$$325$$ 0 0
$$326$$ 5.41735 + 9.38313i 0.300039 + 0.519684i
$$327$$ 32.6571 56.5637i 1.80594 3.12798i
$$328$$ −2.90735 5.03568i −0.160532 0.278049i
$$329$$ 6.05267 10.4835i 0.333695 0.577976i
$$330$$ 0 0
$$331$$ 11.7399 0.645284 0.322642 0.946521i $$-0.395429\pi$$
0.322642 + 0.946521i $$0.395429\pi$$
$$332$$ −3.93498 + 6.81558i −0.215960 + 0.374054i
$$333$$ 22.0417 38.1774i 1.20788 2.09211i
$$334$$ −6.28478 −0.343888
$$335$$ 0 0
$$336$$ −4.27731 + 7.40852i −0.233346 + 0.404168i
$$337$$ 6.44005 + 11.1545i 0.350812 + 0.607624i 0.986392 0.164411i $$-0.0525724\pi$$
−0.635580 + 0.772035i $$0.719239\pi$$
$$338$$ 4.28722 7.42568i 0.233194 0.403904i
$$339$$ −23.4269 40.5765i −1.27237 2.20381i
$$340$$ 0 0
$$341$$ −16.5311 −0.895209
$$342$$ −5.34282 + 32.9587i −0.288907 + 1.78220i
$$343$$ 18.6944 1.00940
$$344$$ −0.290150 0.502555i −0.0156439 0.0270960i
$$345$$ 0 0
$$346$$ 0.187589 0.324914i 0.0100849 0.0174675i
$$347$$ −2.46724 4.27339i −0.132449 0.229408i 0.792171 0.610299i $$-0.208951\pi$$
−0.924620 + 0.380891i $$0.875617\pi$$
$$348$$ −13.1249 + 22.7329i −0.703566 + 1.21861i
$$349$$ 1.26594 0.0677644 0.0338822 0.999426i $$-0.489213\pi$$
0.0338822 + 0.999426i $$0.489213\pi$$
$$350$$ 0 0
$$351$$ 35.3346 61.2012i 1.88602 3.26668i
$$352$$ 2.51991 4.36462i 0.134312 0.232635i
$$353$$ 2.16060 0.114997 0.0574986 0.998346i $$-0.481688\pi$$
0.0574986 + 0.998346i $$0.481688\pi$$
$$354$$ −12.3248 −0.655056
$$355$$ 0 0
$$356$$ 4.14483 + 7.17905i 0.219676 + 0.380489i
$$357$$ 15.6548 27.1149i 0.828539 1.43507i
$$358$$ −4.02470 6.97098i −0.212712 0.368428i
$$359$$ 2.36981 + 4.10463i 0.125074 + 0.216634i 0.921762 0.387757i $$-0.126750\pi$$
−0.796688 + 0.604391i $$0.793417\pi$$
$$360$$ 0 0
$$361$$ −18.0270 6.00231i −0.948789 0.315911i
$$362$$ 21.0503 1.10638
$$363$$ 23.5075 + 40.7162i 1.23382 + 2.13705i
$$364$$ 6.08503 + 10.5396i 0.318942 + 0.552424i
$$365$$ 0 0
$$366$$ −0.212289 0.367695i −0.0110965 0.0192197i
$$367$$ 11.4472 19.8271i 0.597538 1.03497i −0.395645 0.918403i $$-0.629479\pi$$
0.993183 0.116563i $$-0.0371876\pi$$
$$368$$ −4.68466 −0.244205
$$369$$ −44.5404 −2.31868
$$370$$ 0 0
$$371$$ −6.05267 + 10.4835i −0.314239 + 0.544278i
$$372$$ 10.7094 0.555254
$$373$$ 19.2393 0.996172 0.498086 0.867128i $$-0.334036\pi$$
0.498086 + 0.867128i $$0.334036\pi$$
$$374$$ −9.22278 + 15.9743i −0.476899 + 0.826013i
$$375$$ 0 0
$$376$$ 2.31007 4.00115i 0.119133 0.206344i
$$377$$ 18.6718 + 32.3405i 0.961647 + 1.66562i
$$378$$ 19.9321 + 34.5234i 1.02520 + 1.77569i
$$379$$ −6.45953 −0.331804 −0.165902 0.986142i $$-0.553053\pi$$
−0.165902 + 0.986142i $$0.553053\pi$$
$$380$$ 0 0
$$381$$ −25.7445 −1.31893
$$382$$ 4.01991 + 6.96270i 0.205677 + 0.356243i
$$383$$ −4.56746 7.91107i −0.233386 0.404237i 0.725416 0.688310i $$-0.241647\pi$$
−0.958802 + 0.284074i $$0.908314\pi$$
$$384$$ −1.63248 + 2.82754i −0.0833071 + 0.144292i
$$385$$ 0 0
$$386$$ 10.1224 17.5325i 0.515218 0.892383i
$$387$$ −4.44508 −0.225956
$$388$$ −16.1899 −0.821917
$$389$$ 13.3424 23.1098i 0.676488 1.17171i −0.299544 0.954082i $$-0.596835\pi$$
0.976032 0.217629i $$-0.0698321\pi$$
$$390$$ 0 0
$$391$$ 17.1457 0.867093
$$392$$ 0.134919 0.00681442
$$393$$ 3.92541 6.79901i 0.198011 0.342965i
$$394$$ 1.46002 + 2.52883i 0.0735548 + 0.127401i
$$395$$ 0 0
$$396$$ −19.3024 33.4328i −0.969984 1.68006i
$$397$$ 7.37459 + 12.7732i 0.370120 + 0.641067i 0.989584 0.143958i $$-0.0459832\pi$$
−0.619464 + 0.785025i $$0.712650\pi$$
$$398$$ 15.6049 0.782202
$$399$$ −34.8603 + 13.2367i −1.74520 + 0.662662i
$$400$$ 0 0
$$401$$ −5.82720 10.0930i −0.290996 0.504021i 0.683049 0.730372i $$-0.260653\pi$$
−0.974046 + 0.226352i $$0.927320\pi$$
$$402$$ −0.620130 1.07410i −0.0309293 0.0535711i
$$403$$ 7.61773 13.1943i 0.379466 0.657254i
$$404$$ −4.23270 7.33124i −0.210584 0.364743i
$$405$$ 0 0
$$406$$ −21.0654 −1.04546
$$407$$ −29.0045 −1.43770
$$408$$ 5.97481 10.3487i 0.295797 0.512336i
$$409$$ −19.7824 + 34.2641i −0.978176 + 1.69425i −0.309145 + 0.951015i $$0.600043\pi$$
−0.669030 + 0.743235i $$0.733290\pi$$
$$410$$ 0 0
$$411$$ 56.9246 2.80788
$$412$$ −5.92492 + 10.2623i −0.291900 + 0.505585i
$$413$$ −4.94532 8.56555i −0.243344 0.421483i
$$414$$ −17.9421 + 31.0767i −0.881808 + 1.52734i
$$415$$ 0 0
$$416$$ 2.32241 + 4.02254i 0.113866 + 0.197221i
$$417$$ −31.2448 −1.53007
$$418$$ 20.5374 7.79819i 1.00452 0.381422i
$$419$$ 17.3292 0.846586 0.423293 0.905993i $$-0.360874\pi$$
0.423293 + 0.905993i $$0.360874\pi$$
$$420$$ 0 0
$$421$$ −12.1652 21.0707i −0.592895 1.02692i −0.993840 0.110822i $$-0.964652\pi$$
0.400946 0.916102i $$-0.368682\pi$$
$$422$$ 0.572585 0.991747i 0.0278730 0.0482775i
$$423$$ −17.6950 30.6486i −0.860361 1.49019i
$$424$$ −2.31007 + 4.00115i −0.112187 + 0.194313i
$$425$$ 0 0
$$426$$ −29.8251 −1.44503
$$427$$ 0.170362 0.295075i 0.00824438 0.0142797i
$$428$$ −8.40500 + 14.5579i −0.406271 + 0.703682i
$$429$$ −76.4299 −3.69007
$$430$$ 0 0
$$431$$ −14.1173 + 24.4519i −0.680006 + 1.17781i 0.294972 + 0.955506i $$0.404690\pi$$
−0.974978 + 0.222299i $$0.928644\pi$$
$$432$$ 7.60729 + 13.1762i 0.366006 + 0.633941i
$$433$$ −11.6899 + 20.2475i −0.561780 + 0.973031i 0.435562 + 0.900159i $$0.356550\pi$$
−0.997341 + 0.0728720i $$0.976784\pi$$
$$434$$ 4.29713 + 7.44285i 0.206269 + 0.357268i
$$435$$ 0 0
$$436$$ 20.0046 0.958045
$$437$$ −15.8225 12.9082i −0.756895 0.617483i
$$438$$ −27.7692 −1.32686
$$439$$ −13.3775 23.1705i −0.638472 1.10587i −0.985768 0.168110i $$-0.946234\pi$$
0.347297 0.937755i $$-0.387100\pi$$
$$440$$ 0 0
$$441$$ 0.516736 0.895013i 0.0246065 0.0426197i
$$442$$ −8.49994 14.7223i −0.404301 0.700270i
$$443$$ −8.84989 + 15.3285i −0.420471 + 0.728277i −0.995986 0.0895142i $$-0.971469\pi$$
0.575514 + 0.817792i $$0.304802\pi$$
$$444$$ 18.7900 0.891734
$$445$$ 0 0
$$446$$ 7.66474 13.2757i 0.362936 0.628624i
$$447$$ −27.9552 + 48.4198i −1.32223 + 2.29018i
$$448$$ −2.62013 −0.123790
$$449$$ 28.3541 1.33811 0.669056 0.743212i $$-0.266699\pi$$
0.669056 + 0.743212i $$0.266699\pi$$
$$450$$ 0 0
$$451$$ 14.6525 + 25.3790i 0.689961 + 1.19505i
$$452$$ 7.17524 12.4279i 0.337495 0.584558i
$$453$$ −8.88787 15.3942i −0.417589 0.723285i
$$454$$ −9.64248 16.7013i −0.452544 0.783830i
$$455$$ 0 0
$$456$$ −13.3048 + 5.05191i −0.623054 + 0.236578i
$$457$$ −11.5898 −0.542146 −0.271073 0.962559i $$-0.587378\pi$$
−0.271073 + 0.962559i $$0.587378\pi$$
$$458$$ 7.18759 + 12.4493i 0.335854 + 0.581716i
$$459$$ −27.8424 48.2244i −1.29957 2.25092i
$$460$$ 0 0
$$461$$ −17.8899 30.9862i −0.833214 1.44317i −0.895476 0.445110i $$-0.853165\pi$$
0.0622614 0.998060i $$-0.480169\pi$$
$$462$$ 21.5569 37.3377i 1.00292 1.73711i
$$463$$ −23.5039 −1.09232 −0.546160 0.837681i $$-0.683911\pi$$
−0.546160 + 0.837681i $$0.683911\pi$$
$$464$$ −8.03983 −0.373240
$$465$$ 0 0
$$466$$ 6.91272 11.9732i 0.320226 0.554647i
$$467$$ 1.12047 0.0518492 0.0259246 0.999664i $$-0.491747\pi$$
0.0259246 + 0.999664i $$0.491747\pi$$
$$468$$ 35.5792 1.64465
$$469$$ 0.497654 0.861963i 0.0229795 0.0398017i
$$470$$ 0 0
$$471$$ 0.0403210 0.0698381i 0.00185790 0.00321797i
$$472$$ −1.88743 3.26913i −0.0868762 0.150474i
$$473$$ 1.46231 + 2.53279i 0.0672370 + 0.116458i
$$474$$ −26.0046 −1.19443
$$475$$ 0 0
$$476$$ 9.58957 0.439537
$$477$$ 17.6950 + 30.6486i 0.810199 + 1.40331i
$$478$$ −7.48481 12.9641i −0.342347 0.592963i
$$479$$ −13.6547 + 23.6506i −0.623898 + 1.08062i 0.364854 + 0.931065i $$0.381119\pi$$
−0.988753 + 0.149559i $$0.952215\pi$$
$$480$$ 0 0
$$481$$ 13.3656 23.1499i 0.609419 1.05555i
$$482$$ 19.3294 0.880429
$$483$$ −40.0755 −1.82350
$$484$$ −7.19994 + 12.4707i −0.327270 + 0.566848i
$$485$$ 0 0
$$486$$ 41.5147 1.88314
$$487$$ −6.32003 −0.286388 −0.143194 0.989695i $$-0.545737\pi$$
−0.143194 + 0.989695i $$0.545737\pi$$
$$488$$ 0.0650203 0.112618i 0.00294333 0.00509800i
$$489$$ 17.6874 + 30.6355i 0.799854 + 1.38539i
$$490$$ 0 0
$$491$$ 12.9025 + 22.3478i 0.582282 + 1.00854i 0.995208 + 0.0977776i $$0.0311734\pi$$
−0.412926 + 0.910764i $$0.635493\pi$$
$$492$$ −9.49238 16.4413i −0.427949 0.741230i
$$493$$ 29.4254 1.32526
$$494$$ −3.23977 + 19.9855i −0.145764 + 0.899188i
$$495$$ 0 0
$$496$$ 1.64004 + 2.84064i 0.0736402 + 0.127549i
$$497$$ −11.9673 20.7280i −0.536808 0.929779i
$$498$$ −12.8475 + 22.2526i −0.575712 + 0.997163i
$$499$$ 14.4572 + 25.0406i 0.647192 + 1.12097i 0.983790 + 0.179322i $$0.0573903\pi$$
−0.336598 + 0.941648i $$0.609276\pi$$
$$500$$ 0 0
$$501$$ −20.5196 −0.916746
$$502$$ −10.3249 −0.460823
$$503$$ −0.575024 + 0.995971i −0.0256391 + 0.0444082i −0.878560 0.477632i $$-0.841495\pi$$
0.852921 + 0.522040i $$0.174829\pi$$
$$504$$ −10.0350 + 17.3812i −0.446996 + 0.774220i
$$505$$ 0 0
$$506$$ 23.6099 1.04959
$$507$$ 13.9976 24.2445i 0.621655 1.07674i
$$508$$ −3.94254 6.82869i −0.174922 0.302974i
$$509$$ −20.3673 + 35.2772i −0.902765 + 1.56364i −0.0788760 + 0.996884i $$0.525133\pi$$
−0.823889 + 0.566751i $$0.808200\pi$$
$$510$$ 0 0
$$511$$ −11.1424 19.2992i −0.492910 0.853746i
$$512$$ −1.00000 −0.0441942
$$513$$ −10.6122 + 65.4642i −0.468539 + 2.89032i
$$514$$ 28.7692 1.26895
$$515$$ 0 0
$$516$$ −0.947329 1.64082i −0.0417038 0.0722332i
$$517$$ −11.6423 + 20.1651i −0.512029 + 0.886861i
$$518$$ 7.53949 + 13.0588i 0.331266 + 0.573770i
$$519$$ 0.612472 1.06083i 0.0268845 0.0465654i
$$520$$ 0 0
$$521$$ −11.4246 −0.500520 −0.250260 0.968179i $$-0.580516\pi$$
−0.250260 + 0.968179i $$0.580516\pi$$
$$522$$ −30.7924 + 53.3340i −1.34775 + 2.33436i
$$523$$ −6.55696 + 11.3570i −0.286716 + 0.496607i −0.973024 0.230704i $$-0.925897\pi$$
0.686308 + 0.727311i $$0.259230\pi$$
$$524$$ 2.40457 0.105044
$$525$$ 0 0
$$526$$ 4.56746 7.91107i 0.199151 0.344939i
$$527$$ −6.00250 10.3966i −0.261473 0.452884i
$$528$$ 8.22742 14.2503i 0.358052 0.620165i
$$529$$ 0.526988 + 0.912769i 0.0229125 + 0.0396856i
$$530$$ 0 0
$$531$$ −28.9153 −1.25482
$$532$$ −8.84955 7.21955i −0.383677 0.313007i
$$533$$ −27.0083 −1.16986
$$534$$ 13.5327 + 23.4393i 0.585617 + 1.01432i
$$535$$ 0 0
$$536$$ 0.189935 0.328977i 0.00820394 0.0142096i
$$537$$ −13.1405 22.7600i −0.567054 0.982166i
$$538$$ 8.45474 14.6440i 0.364510 0.631350i
$$539$$ −0.679967 −0.0292883
$$540$$ 0 0
$$541$$ 14.4949 25.1059i 0.623183 1.07939i −0.365706 0.930730i $$-0.619172\pi$$
0.988889 0.148655i $$-0.0474943\pi$$
$$542$$ −7.94483 + 13.7609i −0.341260 + 0.591079i
$$543$$ 68.7283 2.94941
$$544$$ 3.65996 0.156919
$$545$$ 0 0
$$546$$ 19.8674 + 34.4113i 0.850245 + 1.47267i
$$547$$ 17.8242 30.8724i 0.762108 1.32001i −0.179654 0.983730i $$-0.557498\pi$$
0.941762 0.336280i $$-0.109169\pi$$
$$548$$ 8.71751 + 15.0992i 0.372393 + 0.645004i
$$549$$ −0.498053 0.862653i −0.0212564 0.0368171i
$$550$$ 0 0
$$551$$ −27.1547 22.1531i −1.15683 0.943753i
$$552$$ −15.2952 −0.651008
$$553$$ −10.4343 18.0728i −0.443713 0.768534i
$$554$$ −5.74261 9.94648i −0.243980 0.422586i
$$555$$ 0 0
$$556$$ −4.78487 8.28764i −0.202924 0.351474i
$$557$$ −6.27731 + 10.8726i −0.265978 + 0.460688i −0.967819 0.251646i $$-0.919028\pi$$
0.701841 + 0.712333i $$0.252362\pi$$
$$558$$ 25.1253 1.06364
$$559$$ −2.69540 −0.114003
$$560$$ 0 0
$$561$$ −30.1120 + 52.1555i −1.27133 + 2.20201i
$$562$$ 14.2897 0.602773
$$563$$ −2.88509 −0.121592 −0.0607960 0.998150i $$-0.519364\pi$$
−0.0607960 + 0.998150i $$0.519364\pi$$
$$564$$ 7.54227 13.0636i 0.317587 0.550076i
$$565$$ 0 0
$$566$$ −1.58215 + 2.74037i −0.0665029 + 0.115186i
$$567$$ 34.9723 + 60.5738i 1.46870 + 2.54386i
$$568$$ −4.56746 7.91107i −0.191646 0.331941i
$$569$$ −10.9249 −0.457996 −0.228998 0.973427i $$-0.573545\pi$$
−0.228998 + 0.973427i $$0.573545\pi$$
$$570$$ 0 0
$$571$$ 6.27911 0.262772 0.131386 0.991331i $$-0.458057\pi$$
0.131386 + 0.991331i $$0.458057\pi$$
$$572$$ −11.7046 20.2729i −0.489393 0.847653i
$$573$$ 13.1249 + 22.7329i 0.548299 + 0.949681i
$$574$$ 7.61763 13.1941i 0.317954 0.550712i
$$575$$ 0 0
$$576$$ −3.82998 + 6.63372i −0.159582 + 0.276405i
$$577$$ −25.9848 −1.08176 −0.540880 0.841100i $$-0.681909\pi$$
−0.540880 + 0.841100i $$0.681909\pi$$
$$578$$ 3.60470 0.149936
$$579$$ 33.0493 57.2430i 1.37348 2.37894i
$$580$$ 0 0
$$581$$ −20.6203 −0.855475
$$582$$ −52.8593 −2.19109
$$583$$ 11.6423 20.1651i 0.482176 0.835154i
$$584$$ −4.25261 7.36574i −0.175974 0.304796i
$$585$$ 0 0
$$586$$ −7.35468 12.7387i −0.303819 0.526230i
$$587$$ −18.1547 31.4448i −0.749324 1.29787i −0.948147 0.317832i $$-0.897045\pi$$
0.198823 0.980035i $$-0.436288\pi$$
$$588$$ 0.440504 0.0181661
$$589$$ −2.28786 + 14.1133i −0.0942697 + 0.581530i
$$590$$ 0 0
$$591$$ 4.76691 + 8.25652i 0.196084 + 0.339628i
$$592$$ 2.87752 + 4.98402i 0.118266 + 0.204842i
$$593$$ 15.8646 27.4783i 0.651482 1.12840i −0.331281 0.943532i $$-0.607481\pi$$
0.982763 0.184868i $$-0.0591858\pi$$
$$594$$ −38.3394 66.4058i −1.57309 2.72466i
$$595$$ 0 0
$$596$$ −17.1244 −0.701441
$$597$$ 50.9493 2.08522
$$598$$ −10.8797 + 18.8442i −0.444905 + 0.770598i
$$599$$ 0.174654 0.302510i 0.00713619 0.0123602i −0.862435 0.506167i $$-0.831062\pi$$
0.869571 + 0.493807i $$0.164395\pi$$
$$600$$ 0 0
$$601$$ 33.7305 1.37590 0.687949 0.725759i $$-0.258511\pi$$
0.687949 + 0.725759i $$0.258511\pi$$
$$602$$ 0.760232 1.31676i 0.0309847 0.0536671i
$$603$$ −1.45489 2.51995i −0.0592479 0.102620i
$$604$$ 2.72220 4.71499i 0.110765 0.191850i
$$605$$ 0 0
$$606$$ −13.8196 23.9362i −0.561382 0.972342i
$$607$$ 28.0561 1.13876 0.569382 0.822073i $$-0.307183\pi$$
0.569382 + 0.822073i $$0.307183\pi$$
$$608$$ −3.37752 2.75542i −0.136977 0.111747i
$$609$$ −68.7777 −2.78701
$$610$$ 0 0
$$611$$ −10.7299 18.5847i −0.434084 0.751855i
$$612$$ 14.0176 24.2791i 0.566627 0.981426i
$$613$$ −20.7251 35.8969i −0.837078 1.44986i −0.892327 0.451389i $$-0.850929\pi$$
0.0552496 0.998473i $$-0.482405\pi$$
$$614$$ 13.0727 22.6425i 0.527570 0.913779i
$$615$$ 0 0
$$616$$ 13.2050 0.532045
$$617$$ 2.94440 5.09985i 0.118537 0.205312i −0.800651 0.599131i $$-0.795513\pi$$
0.919188 + 0.393819i $$0.128846\pi$$
$$618$$ −19.3446 + 33.5059i −0.778155 + 1.34780i
$$619$$ 13.7152 0.551261 0.275631 0.961264i $$-0.411113\pi$$
0.275631 + 0.961264i $$0.411113\pi$$
$$620$$ 0 0
$$621$$ −35.6375 + 61.7260i −1.43009 + 2.47698i
$$622$$ 3.32519 + 5.75941i 0.133328 + 0.230931i
$$623$$ −10.8600 + 18.8101i −0.435096 + 0.753609i
$$624$$ 7.58259 + 13.1334i 0.303547 + 0.525758i
$$625$$ 0 0
$$626$$ −17.3798 −0.694635
$$627$$ 67.0539 25.4608i 2.67787 1.01681i
$$628$$ 0.0246993 0.000985608
$$629$$ −10.5316 18.2413i −0.419923 0.727328i
$$630$$ 0 0
$$631$$ 8.14468 14.1070i 0.324235 0.561591i −0.657123 0.753784i $$-0.728227\pi$$
0.981357 + 0.192193i $$0.0615600\pi$$
$$632$$ −3.98237 6.89767i −0.158410 0.274375i
$$633$$ 1.86947 3.23801i 0.0743047 0.128699i
$$634$$ 1.37529 0.0546199
$$635$$ 0 0
$$636$$ −7.54227 + 13.0636i −0.299070 + 0.518005i
$$637$$ 0.313337 0.542716i 0.0124149 0.0215032i
$$638$$ 40.5194 1.60418
$$639$$ −69.9731 −2.76809
$$640$$ 0 0
$$641$$ −14.8124 25.6559i −0.585056 1.01335i −0.994868 0.101177i $$-0.967739\pi$$
0.409812 0.912170i $$-0.365594\pi$$
$$642$$ −27.4420 + 47.5309i −1.08305 + 1.87590i
$$643$$ −6.01050 10.4105i −0.237031 0.410549i 0.722830 0.691026i $$-0.242841\pi$$
−0.959861 + 0.280476i $$0.909508\pi$$
$$644$$ −6.13721 10.6300i −0.241840 0.418879i
$$645$$ 0 0
$$646$$ 12.3616 + 10.0847i 0.486361 + 0.396778i
$$647$$ −3.16079 −0.124263 −0.0621317 0.998068i $$-0.519790\pi$$
−0.0621317 + 0.998068i $$0.519790\pi$$
$$648$$ 13.3475 + 23.1186i 0.524341 + 0.908186i
$$649$$ 9.51235 + 16.4759i 0.373392 + 0.646735i
$$650$$ 0 0
$$651$$ 14.0300 + 24.3006i 0.549877 + 0.952415i
$$652$$ −5.41735 + 9.38313i −0.212160 + 0.367472i
$$653$$ 19.6097 0.767387 0.383693 0.923461i $$-0.374652\pi$$
0.383693 + 0.923461i $$0.374652\pi$$
$$654$$ 65.3141 2.55398
$$655$$ 0 0
$$656$$ 2.90735 5.03568i 0.113513 0.196610i
$$657$$ −65.1496 −2.54173
$$658$$ 12.1053 0.471915
$$659$$ 9.03748 15.6534i 0.352050 0.609769i −0.634558 0.772875i $$-0.718818\pi$$
0.986609 + 0.163106i $$0.0521512\pi$$
$$660$$ 0 0
$$661$$ 7.26715 12.5871i 0.282660 0.489581i −0.689379 0.724400i $$-0.742117\pi$$
0.972039 + 0.234820i $$0.0754500\pi$$
$$662$$ 5.86996 + 10.1671i 0.228142 + 0.395154i
$$663$$ −27.7520 48.0678i −1.07780 1.86680i
$$664$$ −7.86996 −0.305414
$$665$$ 0 0
$$666$$ 44.0834 1.70820
$$667$$ −18.8319 32.6179i −0.729175 1.26297i
$$668$$ −3.14239 5.44278i −0.121583 0.210587i
$$669$$ 25.0251 43.3447i 0.967525 1.67580i
$$670$$ 0 0
$$671$$ −0.327691 + 0.567578i −0.0126504 + 0.0219111i
$$672$$ −8.55462 −0.330002
$$673$$ −6.13522 −0.236495 −0.118248 0.992984i $$-0.537728\pi$$
−0.118248 + 0.992984i $$0.537728\pi$$
$$674$$ −6.44005 + 11.1545i −0.248061 + 0.429655i
$$675$$ 0 0
$$676$$ 8.57444 0.329786
$$677$$ 13.6380 0.524150 0.262075 0.965047i $$-0.415593\pi$$
0.262075 + 0.965047i $$0.415593\pi$$
$$678$$ 23.4269 40.5765i 0.899703 1.55833i
$$679$$ −21.2098 36.7364i −0.813957 1.40982i
$$680$$ 0 0
$$681$$ −31.4823 54.5290i −1.20640 2.08955i
$$682$$ −8.26554 14.3163i −0.316504 0.548201i
$$683$$ −16.7550 −0.641114 −0.320557 0.947229i $$-0.603870\pi$$
−0.320557 + 0.947229i $$0.603870\pi$$
$$684$$ −31.2145 + 11.8524i −1.19352 + 0.453186i
$$685$$ 0 0
$$686$$ 9.34721 + 16.1898i 0.356878 + 0.618131i
$$687$$ 23.4672 + 40.6464i 0.895329 + 1.55076i
$$688$$ 0.290150 0.502555i 0.0110619 0.0191597i
$$689$$ 10.7299 + 18.5847i 0.408775 + 0.708019i
$$690$$ 0 0
$$691$$ 21.5889 0.821280 0.410640 0.911798i $$-0.365305\pi$$
0.410640 + 0.911798i $$0.365305\pi$$
$$692$$ 0.375179 0.0142622
$$693$$ 50.5749 87.5983i 1.92118 3.32758i
$$694$$ 2.46724 4.27339i 0.0936553 0.162216i
$$695$$ 0 0
$$696$$ −26.2497 −0.994993
$$697$$ −10.6408 + 18.4304i −0.403048 + 0.698100i
$$698$$ 0.632972 + 1.09634i 0.0239583 + 0.0414970i
$$699$$ 22.5697 39.0919i 0.853666 1.47859i
$$700$$ 0 0
$$701$$ 18.8628 + 32.6713i 0.712437 + 1.23398i 0.963940 + 0.266121i $$0.0857419\pi$$
−0.251503 + 0.967857i $$0.580925\pi$$
$$702$$ 70.6691 2.66723
$$703$$ −4.01415 + 24.7624i −0.151396 + 0.933933i
$$704$$ 5.03983 0.189946
$$705$$ 0 0
$$706$$ 1.08030 + 1.87114i 0.0406577 + 0.0704211i
$$707$$ 11.0902 19.2088i 0.417090 0.722422i
$$708$$ −6.16240 10.6736i −0.231597 0.401138i
$$709$$ 10.4795 18.1511i 0.393567 0.681678i −0.599350 0.800487i $$-0.704574\pi$$
0.992917 + 0.118809i $$0.0379075\pi$$
$$710$$ 0 0
$$711$$ −61.0096 −2.28804
$$712$$ −4.14483 + 7.17905i −0.155334 + 0.269046i
$$713$$ −7.68305 + 13.3074i −0.287732 + 0.498367i
$$714$$ 31.3096 1.17173
$$715$$ 0 0
$$716$$ 4.02470 6.97098i 0.150410 0.260518i
$$717$$ −24.4376 42.3272i −0.912639 1.58074i
$$718$$ −2.36981 + 4.10463i −0.0884405 + 0.153183i
$$719$$ 22.1401 + 38.3477i 0.825686 + 1.43013i 0.901394 + 0.433000i $$0.142545\pi$$
−0.0757084 + 0.997130i $$0.524122\pi$$
$$720$$ 0 0
$$721$$ −31.0481 −1.15629
$$722$$ −3.81534 18.6130i −0.141992 0.692704i
$$723$$ 63.1096 2.34707
$$724$$ 10.5251 + 18.2301i 0.391164 + 0.677515i
$$725$$ 0 0
$$726$$ −23.5075 + 40.7162i −0.872445 + 1.51112i
$$727$$ 24.2169 + 41.9448i 0.898154 + 1.55565i 0.829852 + 0.557983i $$0.188425\pi$$
0.0683017 + 0.997665i $$0.478242\pi$$
$$728$$ −6.08503 + 10.5396i −0.225526 + 0.390623i
$$729$$ 55.4584 2.05402
$$730$$ 0 0
$$731$$ −1.06194 + 1.83933i −0.0392772 + 0.0680301i
$$732$$ 0.212289 0.367695i 0.00784641 0.0135904i
$$733$$ −9.62940 −0.355670 −0.177835 0.984060i $$-0.556909\pi$$
−0.177835 + 0.984060i $$0.556909\pi$$
$$734$$ 22.8944 0.845046
$$735$$ 0 0
$$736$$ −2.34233 4.05703i −0.0863394 0.149544i
$$737$$ −0.957240 + 1.65799i −0.0352604 + 0.0610728i
$$738$$ −22.2702 38.5731i −0.819777 1.41989i
$$739$$ 20.3423 + 35.2338i 0.748303 + 1.29610i 0.948636 + 0.316370i $$0.102464\pi$$
−0.200333 + 0.979728i $$0.564202\pi$$
$$740$$ 0 0
$$741$$ −10.5777 + 65.2517i −0.388582 + 2.39708i
$$742$$ −12.1053 −0.444401
$$743$$ −1.43254 2.48123i −0.0525548 0.0910276i 0.838551 0.544823i $$-0.183403\pi$$
−0.891106 + 0.453795i $$0.850070\pi$$
$$744$$ 5.35468 + 9.27458i 0.196312 + 0.340022i
$$745$$ 0 0
$$746$$ 9.61964 + 16.6617i 0.352200 + 0.610028i
$$747$$ −30.1418 + 52.2071i −1.10283 + 1.91016i
$$748$$ −18.4456 −0.674437
$$749$$ −44.0444 −1.60935
$$750$$ 0 0
$$751$$ 13.1148 22.7155i 0.478566 0.828900i −0.521132 0.853476i $$-0.674490\pi$$
0.999698 + 0.0245758i $$0.00782351\pi$$
$$752$$ 4.62013 0.168479
$$753$$ −33.7104 −1.22848
$$754$$ −18.6718 + 32.3405i −0.679987 + 1.17777i
$$755$$ 0 0
$$756$$ −19.9321 + 34.5234i −0.724923 + 1.25560i
$$757$$ −3.29195 5.70182i −0.119648 0.207236i 0.799980 0.600026i $$-0.204843\pi$$
−0.919628 + 0.392790i $$0.871510\pi$$
$$758$$ −3.22976 5.59412i −0.117310 0.203187i
$$759$$ 77.0853 2.79802
$$760$$ 0 0
$$761$$ −27.7549 −1.00612 −0.503058 0.864253i $$-0.667792\pi$$
−0.503058 + 0.864253i $$0.667792\pi$$
$$762$$ −12.8722 22.2954i −0.466312 0.807677i
$$763$$ 26.2073 + 45.3924i 0.948768 + 1.64331i
$$764$$ −4.01991 + 6.96270i −0.145435 + 0.251902i
$$765$$ 0 0
$$766$$ 4.56746 7.91107i 0.165029 0.285839i
$$767$$ −17.5336 −0.633103
$$768$$ −3.26496 −0.117814
$$769$$ −8.32285 + 14.4156i −0.300130 + 0.519840i −0.976165 0.217029i $$-0.930363\pi$$
0.676035 + 0.736869i $$0.263697\pi$$
$$770$$ 0 0
$$771$$ 93.9303 3.38282
$$772$$ 20.2448 0.728628
$$773$$ 12.1049 20.9664i 0.435385 0.754108i −0.561942 0.827176i $$-0.689946\pi$$
0.997327 + 0.0730682i $$0.0232791\pi$$
$$774$$ −2.22254 3.84955i −0.0798876 0.138369i
$$775$$ 0 0
$$776$$ −8.09494 14.0208i −0.290591 0.503319i
$$777$$ 24.6161 + 42.6364i 0.883098 + 1.52957i
$$778$$ 26.6848 0.956698
$$779$$ 23.6950 8.99716i 0.848963 0.322357i
$$780$$ 0 0
$$781$$ 23.0192 + 39.8704i 0.823692 + 1.42668i
$$782$$ 8.57283 + 14.8486i 0.306564 + 0.530984i
$$783$$ −61.1613 + 105.934i −2.18573 + 3.78579i
$$784$$ 0.0674593 + 0.116843i 0.00240926 + 0.00417296i
$$785$$ 0 0