Properties

 Label 75.9.f.a.43.1 Level $75$ Weight $9$ Character 75.43 Analytic conductor $30.553$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$75 = 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 75.f (of order $$4$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$30.5533957546$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ x^4 + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

 Embedding label 43.1 Root $$-1.22474 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 75.43 Dual form 75.9.f.a.7.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-7.34847 + 7.34847i) q^{2} +(-33.0681 - 33.0681i) q^{3} +148.000i q^{4} +486.000 q^{6} +(-2872.03 + 2872.03i) q^{7} +(-2968.78 - 2968.78i) q^{8} +2187.00i q^{9} +O(q^{10})$$ $$q+(-7.34847 + 7.34847i) q^{2} +(-33.0681 - 33.0681i) q^{3} +148.000i q^{4} +486.000 q^{6} +(-2872.03 + 2872.03i) q^{7} +(-2968.78 - 2968.78i) q^{8} +2187.00i q^{9} -234.000 q^{11} +(4894.08 - 4894.08i) q^{12} +(11930.2 + 11930.2i) q^{13} -42210.0i q^{14} +5744.00 q^{16} +(-89012.0 + 89012.0i) q^{17} +(-16071.1 - 16071.1i) q^{18} +181693. i q^{19} +189945. q^{21} +(1719.54 - 1719.54i) q^{22} +(-269432. - 269432. i) q^{23} +196344. i q^{24} -175338. q^{26} +(72320.0 - 72320.0i) q^{27} +(-425060. - 425060. i) q^{28} -240174. i q^{29} +836725. q^{31} +(717798. - 717798. i) q^{32} +(7737.94 + 7737.94i) q^{33} -1.30820e6i q^{34} -323676. q^{36} +(-608282. + 608282. i) q^{37} +(-1.33517e6 - 1.33517e6i) q^{38} -789021. i q^{39} +2.82222e6 q^{41} +(-1.39580e6 + 1.39580e6i) q^{42} +(-2.80202e6 - 2.80202e6i) q^{43} -34632.0i q^{44} +3.95982e6 q^{46} +(5.39321e6 - 5.39321e6i) q^{47} +(-189943. - 189943. i) q^{48} -1.07323e7i q^{49} +5.88692e6 q^{51} +(-1.76568e6 + 1.76568e6i) q^{52} +(1.19258e6 + 1.19258e6i) q^{53} +1.06288e6i q^{54} +1.70528e7 q^{56} +(6.00824e6 - 6.00824e6i) q^{57} +(1.76491e6 + 1.76491e6i) q^{58} -1.27860e7i q^{59} +517403. q^{61} +(-6.14865e6 + 6.14865e6i) q^{62} +(-6.28112e6 - 6.28112e6i) q^{63} +1.20199e7i q^{64} -113724. q^{66} +(-2.06617e6 + 2.06617e6i) q^{67} +(-1.31738e7 - 1.31738e7i) q^{68} +1.78192e7i q^{69} -2.08286e7 q^{71} +(6.49273e6 - 6.49273e6i) q^{72} +(-2.88730e7 - 2.88730e7i) q^{73} -8.93988e6i q^{74} -2.68906e7 q^{76} +(672054. - 672054. i) q^{77} +(5.79810e6 + 5.79810e6i) q^{78} -4.21879e7i q^{79} -4.78297e6 q^{81} +(-2.07390e7 + 2.07390e7i) q^{82} +(6.66763e7 + 6.66763e7i) q^{83} +2.81119e7i q^{84} +4.11811e7 q^{86} +(-7.94210e6 + 7.94210e6i) q^{87} +(694695. + 694695. i) q^{88} +9.51614e7i q^{89} -6.85279e7 q^{91} +(3.98759e7 - 3.98759e7i) q^{92} +(-2.76689e7 - 2.76689e7i) q^{93} +7.92637e7i q^{94} -4.74725e7 q^{96} +(-7.08678e7 + 7.08678e7i) q^{97} +(7.88658e7 + 7.88658e7i) q^{98} -511758. i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 1944 q^{6}+O(q^{10})$$ 4 * q + 1944 * q^6 $$4 q + 1944 q^{6} - 936 q^{11} + 22976 q^{16} + 759780 q^{21} - 701352 q^{26} + 3346900 q^{31} - 1294704 q^{36} + 11288880 q^{41} + 15839280 q^{46} + 23547672 q^{51} + 68211360 q^{56} + 2069612 q^{61} - 454896 q^{66} - 83314512 q^{71} - 107562256 q^{76} - 19131876 q^{81} + 164724264 q^{86} - 274111740 q^{91} - 189889920 q^{96}+O(q^{100})$$ 4 * q + 1944 * q^6 - 936 * q^11 + 22976 * q^16 + 759780 * q^21 - 701352 * q^26 + 3346900 * q^31 - 1294704 * q^36 + 11288880 * q^41 + 15839280 * q^46 + 23547672 * q^51 + 68211360 * q^56 + 2069612 * q^61 - 454896 * q^66 - 83314512 * q^71 - 107562256 * q^76 - 19131876 * q^81 + 164724264 * q^86 - 274111740 * q^91 - 189889920 * q^96

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$$.

 $$n$$ $$26$$ $$52$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{3}{4}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −7.34847 + 7.34847i −0.459279 + 0.459279i −0.898419 0.439140i $$-0.855283\pi$$
0.439140 + 0.898419i $$0.355283\pi$$
$$3$$ −33.0681 33.0681i −0.408248 0.408248i
$$4$$ 148.000i 0.578125i
$$5$$ 0 0
$$6$$ 486.000 0.375000
$$7$$ −2872.03 + 2872.03i −1.19618 + 1.19618i −0.220878 + 0.975301i $$0.570892\pi$$
−0.975301 + 0.220878i $$0.929108\pi$$
$$8$$ −2968.78 2968.78i −0.724800 0.724800i
$$9$$ 2187.00i 0.333333i
$$10$$ 0 0
$$11$$ −234.000 −0.0159825 −0.00799126 0.999968i $$-0.502544\pi$$
−0.00799126 + 0.999968i $$0.502544\pi$$
$$12$$ 4894.08 4894.08i 0.236019 0.236019i
$$13$$ 11930.2 + 11930.2i 0.417711 + 0.417711i 0.884414 0.466703i $$-0.154558\pi$$
−0.466703 + 0.884414i $$0.654558\pi$$
$$14$$ 42210.0i 1.09876i
$$15$$ 0 0
$$16$$ 5744.00 0.0876465
$$17$$ −89012.0 + 89012.0i −1.06574 + 1.06574i −0.0680630 + 0.997681i $$0.521682\pi$$
−0.997681 + 0.0680630i $$0.978318\pi$$
$$18$$ −16071.1 16071.1i −0.153093 0.153093i
$$19$$ 181693.i 1.39420i 0.716976 + 0.697098i $$0.245526\pi$$
−0.716976 + 0.697098i $$0.754474\pi$$
$$20$$ 0 0
$$21$$ 189945. 0.976676
$$22$$ 1719.54 1719.54i 0.00734044 0.00734044i
$$23$$ −269432. 269432.i −0.962803 0.962803i 0.0365300 0.999333i $$-0.488370\pi$$
−0.999333 + 0.0365300i $$0.988370\pi$$
$$24$$ 196344.i 0.591797i
$$25$$ 0 0
$$26$$ −175338. −0.383692
$$27$$ 72320.0 72320.0i 0.136083 0.136083i
$$28$$ −425060. 425060.i −0.691541 0.691541i
$$29$$ 240174.i 0.339574i −0.985481 0.169787i $$-0.945692\pi$$
0.985481 0.169787i $$-0.0543079\pi$$
$$30$$ 0 0
$$31$$ 836725. 0.906016 0.453008 0.891506i $$-0.350351\pi$$
0.453008 + 0.891506i $$0.350351\pi$$
$$32$$ 717798. 717798.i 0.684546 0.684546i
$$33$$ 7737.94 + 7737.94i 0.00652483 + 0.00652483i
$$34$$ 1.30820e6i 0.978948i
$$35$$ 0 0
$$36$$ −323676. −0.192708
$$37$$ −608282. + 608282.i −0.324562 + 0.324562i −0.850514 0.525952i $$-0.823709\pi$$
0.525952 + 0.850514i $$0.323709\pi$$
$$38$$ −1.33517e6 1.33517e6i −0.640325 0.640325i
$$39$$ 789021.i 0.341059i
$$40$$ 0 0
$$41$$ 2.82222e6 0.998747 0.499373 0.866387i $$-0.333564\pi$$
0.499373 + 0.866387i $$0.333564\pi$$
$$42$$ −1.39580e6 + 1.39580e6i −0.448567 + 0.448567i
$$43$$ −2.80202e6 2.80202e6i −0.819590 0.819590i 0.166458 0.986049i $$-0.446767\pi$$
−0.986049 + 0.166458i $$0.946767\pi$$
$$44$$ 34632.0i 0.00923989i
$$45$$ 0 0
$$46$$ 3.95982e6 0.884391
$$47$$ 5.39321e6 5.39321e6i 1.10524 1.10524i 0.111471 0.993768i $$-0.464444\pi$$
0.993768 0.111471i $$-0.0355561\pi$$
$$48$$ −189943. 189943.i −0.0357815 0.0357815i
$$49$$ 1.07323e7i 1.86169i
$$50$$ 0 0
$$51$$ 5.88692e6 0.870176
$$52$$ −1.76568e6 + 1.76568e6i −0.241489 + 0.241489i
$$53$$ 1.19258e6 + 1.19258e6i 0.151142 + 0.151142i 0.778628 0.627486i $$-0.215916\pi$$
−0.627486 + 0.778628i $$0.715916\pi$$
$$54$$ 1.06288e6i 0.125000i
$$55$$ 0 0
$$56$$ 1.70528e7 1.73398
$$57$$ 6.00824e6 6.00824e6i 0.569178 0.569178i
$$58$$ 1.76491e6 + 1.76491e6i 0.155959 + 0.155959i
$$59$$ 1.27860e7i 1.05518i −0.849500 0.527588i $$-0.823096\pi$$
0.849500 0.527588i $$-0.176904\pi$$
$$60$$ 0 0
$$61$$ 517403. 0.0373688 0.0186844 0.999825i $$-0.494052\pi$$
0.0186844 + 0.999825i $$0.494052\pi$$
$$62$$ −6.14865e6 + 6.14865e6i −0.416115 + 0.416115i
$$63$$ −6.28112e6 6.28112e6i −0.398726 0.398726i
$$64$$ 1.20199e7i 0.716442i
$$65$$ 0 0
$$66$$ −113724. −0.00599344
$$67$$ −2.06617e6 + 2.06617e6i −0.102534 + 0.102534i −0.756513 0.653979i $$-0.773098\pi$$
0.653979 + 0.756513i $$0.273098\pi$$
$$68$$ −1.31738e7 1.31738e7i −0.616133 0.616133i
$$69$$ 1.78192e7i 0.786125i
$$70$$ 0 0
$$71$$ −2.08286e7 −0.819648 −0.409824 0.912165i $$-0.634410\pi$$
−0.409824 + 0.912165i $$0.634410\pi$$
$$72$$ 6.49273e6 6.49273e6i 0.241600 0.241600i
$$73$$ −2.88730e7 2.88730e7i −1.01672 1.01672i −0.999858 0.0168598i $$-0.994633\pi$$
−0.0168598 0.999858i $$-0.505367\pi$$
$$74$$ 8.93988e6i 0.298129i
$$75$$ 0 0
$$76$$ −2.68906e7 −0.806019
$$77$$ 672054. 672054.i 0.0191180 0.0191180i
$$78$$ 5.79810e6 + 5.79810e6i 0.156642 + 0.156642i
$$79$$ 4.21879e7i 1.08313i −0.840659 0.541564i $$-0.817832\pi$$
0.840659 0.541564i $$-0.182168\pi$$
$$80$$ 0 0
$$81$$ −4.78297e6 −0.111111
$$82$$ −2.07390e7 + 2.07390e7i −0.458704 + 0.458704i
$$83$$ 6.66763e7 + 6.66763e7i 1.40494 + 1.40494i 0.783302 + 0.621642i $$0.213534\pi$$
0.621642 + 0.783302i $$0.286466\pi$$
$$84$$ 2.81119e7i 0.564641i
$$85$$ 0 0
$$86$$ 4.11811e7 0.752842
$$87$$ −7.94210e6 + 7.94210e6i −0.138630 + 0.138630i
$$88$$ 694695. + 694695.i 0.0115841 + 0.0115841i
$$89$$ 9.51614e7i 1.51670i 0.651845 + 0.758352i $$0.273995\pi$$
−0.651845 + 0.758352i $$0.726005\pi$$
$$90$$ 0 0
$$91$$ −6.85279e7 −0.999314
$$92$$ 3.98759e7 3.98759e7i 0.556620 0.556620i
$$93$$ −2.76689e7 2.76689e7i −0.369880 0.369880i
$$94$$ 7.92637e7i 1.01523i
$$95$$ 0 0
$$96$$ −4.74725e7 −0.558929
$$97$$ −7.08678e7 + 7.08678e7i −0.800501 + 0.800501i −0.983174 0.182672i $$-0.941525\pi$$
0.182672 + 0.983174i $$0.441525\pi$$
$$98$$ 7.88658e7 + 7.88658e7i 0.855036 + 0.855036i
$$99$$ 511758.i 0.00532750i
$$100$$ 0 0
$$101$$ −8.63379e7 −0.829690 −0.414845 0.909892i $$-0.636164\pi$$
−0.414845 + 0.909892i $$0.636164\pi$$
$$102$$ −4.32598e7 + 4.32598e7i −0.399654 + 0.399654i
$$103$$ 7.61161e7 + 7.61161e7i 0.676282 + 0.676282i 0.959157 0.282875i $$-0.0912881\pi$$
−0.282875 + 0.959157i $$0.591288\pi$$
$$104$$ 7.08366e7i 0.605514i
$$105$$ 0 0
$$106$$ −1.75273e7 −0.138833
$$107$$ 1.09281e8 1.09281e8i 0.833701 0.833701i −0.154320 0.988021i $$-0.549319\pi$$
0.988021 + 0.154320i $$0.0493186\pi$$
$$108$$ 1.07034e7 + 1.07034e7i 0.0786728 + 0.0786728i
$$109$$ 5.04631e7i 0.357494i 0.983895 + 0.178747i $$0.0572043\pi$$
−0.983895 + 0.178747i $$0.942796\pi$$
$$110$$ 0 0
$$111$$ 4.02295e7 0.265004
$$112$$ −1.64969e7 + 1.64969e7i −0.104841 + 0.104841i
$$113$$ 1.21244e8 + 1.21244e8i 0.743611 + 0.743611i 0.973271 0.229660i $$-0.0737615\pi$$
−0.229660 + 0.973271i $$0.573762\pi$$
$$114$$ 8.83028e7i 0.522823i
$$115$$ 0 0
$$116$$ 3.55458e7 0.196316
$$117$$ −2.60914e7 + 2.60914e7i −0.139237 + 0.139237i
$$118$$ 9.39572e7 + 9.39572e7i 0.484621 + 0.484621i
$$119$$ 5.11290e8i 2.54964i
$$120$$ 0 0
$$121$$ −2.14304e8 −0.999745
$$122$$ −3.80212e6 + 3.80212e6i −0.0171627 + 0.0171627i
$$123$$ −9.33255e7 9.33255e7i −0.407737 0.407737i
$$124$$ 1.23835e8i 0.523791i
$$125$$ 0 0
$$126$$ 9.23133e7 0.366254
$$127$$ 9.55780e7 9.55780e7i 0.367403 0.367403i −0.499126 0.866529i $$-0.666346\pi$$
0.866529 + 0.499126i $$0.166346\pi$$
$$128$$ 9.54285e7 + 9.54285e7i 0.355499 + 0.355499i
$$129$$ 1.85315e8i 0.669193i
$$130$$ 0 0
$$131$$ −3.13838e8 −1.06566 −0.532832 0.846221i $$-0.678872\pi$$
−0.532832 + 0.846221i $$0.678872\pi$$
$$132$$ −1.14521e6 + 1.14521e6i −0.00377217 + 0.00377217i
$$133$$ −5.21827e8 5.21827e8i −1.66771 1.66771i
$$134$$ 3.03664e7i 0.0941834i
$$135$$ 0 0
$$136$$ 5.28514e8 1.54490
$$137$$ −5.04691e7 + 5.04691e7i −0.143266 + 0.143266i −0.775102 0.631836i $$-0.782302\pi$$
0.631836 + 0.775102i $$0.282302\pi$$
$$138$$ −1.30944e8 1.30944e8i −0.361051 0.361051i
$$139$$ 5.26688e8i 1.41089i 0.708763 + 0.705446i $$0.249253\pi$$
−0.708763 + 0.705446i $$0.750747\pi$$
$$140$$ 0 0
$$141$$ −3.56687e8 −0.902423
$$142$$ 1.53059e8 1.53059e8i 0.376447 0.376447i
$$143$$ −2.79168e6 2.79168e6i −0.00667607 0.00667607i
$$144$$ 1.25621e7i 0.0292155i
$$145$$ 0 0
$$146$$ 4.24345e8 0.933915
$$147$$ −3.54896e8 + 3.54896e8i −0.760032 + 0.760032i
$$148$$ −9.00257e7 9.00257e7i −0.187638 0.187638i
$$149$$ 8.99246e8i 1.82446i −0.409683 0.912228i $$-0.634361\pi$$
0.409683 0.912228i $$-0.365639\pi$$
$$150$$ 0 0
$$151$$ 8.05999e8 1.55034 0.775170 0.631753i $$-0.217664\pi$$
0.775170 + 0.631753i $$0.217664\pi$$
$$152$$ 5.39407e8 5.39407e8i 1.01051 1.01051i
$$153$$ −1.94669e8 1.94669e8i −0.355248 0.355248i
$$154$$ 9.87714e6i 0.0175610i
$$155$$ 0 0
$$156$$ 1.16775e8 0.197175
$$157$$ −4.78600e8 + 4.78600e8i −0.787724 + 0.787724i −0.981121 0.193397i $$-0.938050\pi$$
0.193397 + 0.981121i $$0.438050\pi$$
$$158$$ 3.10017e8 + 3.10017e8i 0.497458 + 0.497458i
$$159$$ 7.88729e7i 0.123407i
$$160$$ 0 0
$$161$$ 1.54763e9 2.30337
$$162$$ 3.51475e7 3.51475e7i 0.0510310 0.0510310i
$$163$$ −4.56533e8 4.56533e8i −0.646729 0.646729i 0.305472 0.952201i $$-0.401186\pi$$
−0.952201 + 0.305472i $$0.901186\pi$$
$$164$$ 4.17689e8i 0.577401i
$$165$$ 0 0
$$166$$ −9.79937e8 −1.29052
$$167$$ −2.74258e8 + 2.74258e8i −0.352609 + 0.352609i −0.861079 0.508470i $$-0.830211\pi$$
0.508470 + 0.861079i $$0.330211\pi$$
$$168$$ −5.63905e8 5.63905e8i −0.707895 0.707895i
$$169$$ 5.31069e8i 0.651035i
$$170$$ 0 0
$$171$$ −3.97363e8 −0.464732
$$172$$ 4.14698e8 4.14698e8i 0.473826 0.473826i
$$173$$ 1.75277e8 + 1.75277e8i 0.195677 + 0.195677i 0.798144 0.602467i $$-0.205815\pi$$
−0.602467 + 0.798144i $$0.705815\pi$$
$$174$$ 1.16725e8i 0.127340i
$$175$$ 0 0
$$176$$ −1.34410e6 −0.00140081
$$177$$ −4.22807e8 + 4.22807e8i −0.430774 + 0.430774i
$$178$$ −6.99291e8 6.99291e8i −0.696591 0.696591i
$$179$$ 1.65138e9i 1.60855i −0.594255 0.804277i $$-0.702553\pi$$
0.594255 0.804277i $$-0.297447\pi$$
$$180$$ 0 0
$$181$$ −3.19153e8 −0.297362 −0.148681 0.988885i $$-0.547503\pi$$
−0.148681 + 0.988885i $$0.547503\pi$$
$$182$$ 5.03575e8 5.03575e8i 0.458964 0.458964i
$$183$$ −1.71095e7 1.71095e7i −0.0152558 0.0152558i
$$184$$ 1.59977e9i 1.39568i
$$185$$ 0 0
$$186$$ 4.06648e8 0.339756
$$187$$ 2.08288e7 2.08288e7i 0.0170333 0.0170333i
$$188$$ 7.98195e8 + 7.98195e8i 0.638966 + 0.638966i
$$189$$ 4.15410e8i 0.325559i
$$190$$ 0 0
$$191$$ −1.13627e9 −0.853785 −0.426893 0.904302i $$-0.640392\pi$$
−0.426893 + 0.904302i $$0.640392\pi$$
$$192$$ 3.97476e8 3.97476e8i 0.292486 0.292486i
$$193$$ 1.71674e9 + 1.71674e9i 1.23730 + 1.23730i 0.961101 + 0.276197i $$0.0890742\pi$$
0.276197 + 0.961101i $$0.410926\pi$$
$$194$$ 1.04154e9i 0.735307i
$$195$$ 0 0
$$196$$ 1.58838e9 1.07629
$$197$$ 4.17614e8 4.17614e8i 0.277275 0.277275i −0.554745 0.832020i $$-0.687184\pi$$
0.832020 + 0.554745i $$0.187184\pi$$
$$198$$ 3.76064e6 + 3.76064e6i 0.00244681 + 0.00244681i
$$199$$ 1.06994e9i 0.682258i −0.940017 0.341129i $$-0.889191\pi$$
0.940017 0.341129i $$-0.110809\pi$$
$$200$$ 0 0
$$201$$ 1.36649e8 0.0837186
$$202$$ 6.34451e8 6.34451e8i 0.381059 0.381059i
$$203$$ 6.89786e8 + 6.89786e8i 0.406191 + 0.406191i
$$204$$ 8.71264e8i 0.503071i
$$205$$ 0 0
$$206$$ −1.11867e9 −0.621205
$$207$$ 5.89247e8 5.89247e8i 0.320934 0.320934i
$$208$$ 6.85273e7 + 6.85273e7i 0.0366109 + 0.0366109i
$$209$$ 4.25162e7i 0.0222828i
$$210$$ 0 0
$$211$$ −2.26915e9 −1.14481 −0.572406 0.819971i $$-0.693990\pi$$
−0.572406 + 0.819971i $$0.693990\pi$$
$$212$$ −1.76502e8 + 1.76502e8i −0.0873790 + 0.0873790i
$$213$$ 6.88763e8 + 6.88763e8i 0.334620 + 0.334620i
$$214$$ 1.60610e9i 0.765803i
$$215$$ 0 0
$$216$$ −4.29404e8 −0.197266
$$217$$ −2.40310e9 + 2.40310e9i −1.08376 + 1.08376i
$$218$$ −3.70827e8 3.70827e8i −0.164189 0.164189i
$$219$$ 1.90955e9i 0.830146i
$$220$$ 0 0
$$221$$ −2.12387e9 −0.890346
$$222$$ −2.95625e8 + 2.95625e8i −0.121711 + 0.121711i
$$223$$ −1.99573e9 1.99573e9i −0.807015 0.807015i 0.177166 0.984181i $$-0.443307\pi$$
−0.984181 + 0.177166i $$0.943307\pi$$
$$224$$ 4.12307e9i 1.63768i
$$225$$ 0 0
$$226$$ −1.78191e9 −0.683050
$$227$$ −1.32121e9 + 1.32121e9i −0.497588 + 0.497588i −0.910686 0.413099i $$-0.864446\pi$$
0.413099 + 0.910686i $$0.364446\pi$$
$$228$$ 8.89220e8 + 8.89220e8i 0.329056 + 0.329056i
$$229$$ 2.03118e9i 0.738595i −0.929311 0.369297i $$-0.879598\pi$$
0.929311 0.369297i $$-0.120402\pi$$
$$230$$ 0 0
$$231$$ −4.44471e7 −0.0156097
$$232$$ −7.13024e8 + 7.13024e8i −0.246123 + 0.246123i
$$233$$ 1.51062e9 + 1.51062e9i 0.512545 + 0.512545i 0.915305 0.402760i $$-0.131949\pi$$
−0.402760 + 0.915305i $$0.631949\pi$$
$$234$$ 3.83464e8i 0.127897i
$$235$$ 0 0
$$236$$ 1.89232e9 0.610024
$$237$$ −1.39508e9 + 1.39508e9i −0.442185 + 0.442185i
$$238$$ 3.75720e9 + 3.75720e9i 1.17100 + 1.17100i
$$239$$ 3.44530e9i 1.05593i 0.849266 + 0.527965i $$0.177045\pi$$
−0.849266 + 0.527965i $$0.822955\pi$$
$$240$$ 0 0
$$241$$ 2.45959e7 0.00729112 0.00364556 0.999993i $$-0.498840\pi$$
0.00364556 + 0.999993i $$0.498840\pi$$
$$242$$ 1.57481e9 1.57481e9i 0.459162 0.459162i
$$243$$ 1.58164e8 + 1.58164e8i 0.0453609 + 0.0453609i
$$244$$ 7.65756e7i 0.0216039i
$$245$$ 0 0
$$246$$ 1.37160e9 0.374530
$$247$$ −2.16764e9 + 2.16764e9i −0.582371 + 0.582371i
$$248$$ −2.48405e9 2.48405e9i −0.656681 0.656681i
$$249$$ 4.40972e9i 1.14713i
$$250$$ 0 0
$$251$$ −3.62820e9 −0.914106 −0.457053 0.889440i $$-0.651095\pi$$
−0.457053 + 0.889440i $$0.651095\pi$$
$$252$$ 9.29606e8 9.29606e8i 0.230514 0.230514i
$$253$$ 6.30470e7 + 6.30470e7i 0.0153880 + 0.0153880i
$$254$$ 1.40470e9i 0.337482i
$$255$$ 0 0
$$256$$ −4.47960e9 −1.04299
$$257$$ 1.05639e9 1.05639e9i 0.242154 0.242154i −0.575586 0.817741i $$-0.695226\pi$$
0.817741 + 0.575586i $$0.195226\pi$$
$$258$$ −1.36178e9 1.36178e9i −0.307346 0.307346i
$$259$$ 3.49400e9i 0.776469i
$$260$$ 0 0
$$261$$ 5.25261e8 0.113191
$$262$$ 2.30623e9 2.30623e9i 0.489438 0.489438i
$$263$$ −2.89677e9 2.89677e9i −0.605468 0.605468i 0.336290 0.941758i $$-0.390828\pi$$
−0.941758 + 0.336290i $$0.890828\pi$$
$$264$$ 4.59445e7i 0.00945840i
$$265$$ 0 0
$$266$$ 7.66926e9 1.53189
$$267$$ 3.14681e9 3.14681e9i 0.619192 0.619192i
$$268$$ −3.05794e8 3.05794e8i −0.0592774 0.0592774i
$$269$$ 4.75635e9i 0.908374i 0.890906 + 0.454187i $$0.150070\pi$$
−0.890906 + 0.454187i $$0.849930\pi$$
$$270$$ 0 0
$$271$$ 4.98291e9 0.923860 0.461930 0.886916i $$-0.347157\pi$$
0.461930 + 0.886916i $$0.347157\pi$$
$$272$$ −5.11285e8 + 5.11285e8i −0.0934087 + 0.0934087i
$$273$$ 2.26609e9 + 2.26609e9i 0.407968 + 0.407968i
$$274$$ 7.41741e8i 0.131598i
$$275$$ 0 0
$$276$$ −2.63724e9 −0.454479
$$277$$ 2.27910e9 2.27910e9i 0.387119 0.387119i −0.486539 0.873659i $$-0.661741\pi$$
0.873659 + 0.486539i $$0.161741\pi$$
$$278$$ −3.87035e9 3.87035e9i −0.647994 0.647994i
$$279$$ 1.82992e9i 0.302005i
$$280$$ 0 0
$$281$$ −1.00667e9 −0.161459 −0.0807294 0.996736i $$-0.525725\pi$$
−0.0807294 + 0.996736i $$0.525725\pi$$
$$282$$ 2.62110e9 2.62110e9i 0.414464 0.414464i
$$283$$ −3.14496e9 3.14496e9i −0.490308 0.490308i 0.418095 0.908403i $$-0.362698\pi$$
−0.908403 + 0.418095i $$0.862698\pi$$
$$284$$ 3.08264e9i 0.473859i
$$285$$ 0 0
$$286$$ 4.10291e7 0.00613236
$$287$$ −8.10549e9 + 8.10549e9i −1.19468 + 1.19468i
$$288$$ 1.56983e9 + 1.56983e9i 0.228182 + 0.228182i
$$289$$ 8.87052e9i 1.27162i
$$290$$ 0 0
$$291$$ 4.68693e9 0.653607
$$292$$ 4.27320e9 4.27320e9i 0.587790 0.587790i
$$293$$ −3.60077e9 3.60077e9i −0.488568 0.488568i 0.419286 0.907854i $$-0.362280\pi$$
−0.907854 + 0.419286i $$0.862280\pi$$
$$294$$ 5.21589e9i 0.698134i
$$295$$ 0 0
$$296$$ 3.61171e9 0.470485
$$297$$ −1.69229e7 + 1.69229e7i −0.00217494 + 0.00217494i
$$298$$ 6.60808e9 + 6.60808e9i 0.837935 + 0.837935i
$$299$$ 6.42877e9i 0.804346i
$$300$$ 0 0
$$301$$ 1.60949e10 1.96075
$$302$$ −5.92286e9 + 5.92286e9i −0.712039 + 0.712039i
$$303$$ 2.85503e9 + 2.85503e9i 0.338719 + 0.338719i
$$304$$ 1.04364e9i 0.122196i
$$305$$ 0 0
$$306$$ 2.86104e9 0.326316
$$307$$ 1.23211e10 1.23211e10i 1.38706 1.38706i 0.555644 0.831420i $$-0.312472\pi$$
0.831420 0.555644i $$-0.187528\pi$$
$$308$$ 9.94640e7 + 9.94640e7i 0.0110526 + 0.0110526i
$$309$$ 5.03403e9i 0.552182i
$$310$$ 0 0
$$311$$ −8.62846e9 −0.922341 −0.461170 0.887312i $$-0.652570\pi$$
−0.461170 + 0.887312i $$0.652570\pi$$
$$312$$ −2.34243e9 + 2.34243e9i −0.247200 + 0.247200i
$$313$$ −2.96428e9 2.96428e9i −0.308846 0.308846i 0.535616 0.844462i $$-0.320079\pi$$
−0.844462 + 0.535616i $$0.820079\pi$$
$$314$$ 7.03396e9i 0.723571i
$$315$$ 0 0
$$316$$ 6.24381e9 0.626183
$$317$$ 1.98335e9 1.98335e9i 0.196409 0.196409i −0.602050 0.798459i $$-0.705649\pi$$
0.798459 + 0.602050i $$0.205649\pi$$
$$318$$ 5.79595e8 + 5.79595e8i 0.0566782 + 0.0566782i
$$319$$ 5.62007e7i 0.00542724i
$$320$$ 0 0
$$321$$ −7.22745e9 −0.680714
$$322$$ −1.13727e10 + 1.13727e10i −1.05789 + 1.05789i
$$323$$ −1.61729e10 1.61729e10i −1.48586 1.48586i
$$324$$ 7.07879e8i 0.0642361i
$$325$$ 0 0
$$326$$ 6.70964e9 0.594058
$$327$$ 1.66872e9 1.66872e9i 0.145946 0.145946i
$$328$$ −8.37855e9 8.37855e9i −0.723892 0.723892i
$$329$$ 3.09789e10i 2.64413i
$$330$$ 0 0
$$331$$ −4.30793e9 −0.358886 −0.179443 0.983768i $$-0.557430\pi$$
−0.179443 + 0.983768i $$0.557430\pi$$
$$332$$ −9.86809e9 + 9.86809e9i −0.812233 + 0.812233i
$$333$$ −1.33031e9 1.33031e9i −0.108187 0.108187i
$$334$$ 4.03075e9i 0.323892i
$$335$$ 0 0
$$336$$ 1.09104e9 0.0856023
$$337$$ 1.18877e8 1.18877e8i 0.00921677 0.00921677i −0.702483 0.711700i $$-0.747925\pi$$
0.711700 + 0.702483i $$0.247925\pi$$
$$338$$ 3.90255e9 + 3.90255e9i 0.299007 + 0.299007i
$$339$$ 8.01860e9i 0.607156i
$$340$$ 0 0
$$341$$ −1.95794e8 −0.0144804
$$342$$ 2.92001e9 2.92001e9i 0.213442 0.213442i
$$343$$ 1.42667e10 + 1.42667e10i 1.03074 + 1.03074i
$$344$$ 1.66372e10i 1.18808i
$$345$$ 0 0
$$346$$ −2.57603e9 −0.179741
$$347$$ 1.63550e10 1.63550e10i 1.12806 1.12806i 0.137569 0.990492i $$-0.456071\pi$$
0.990492 0.137569i $$-0.0439289\pi$$
$$348$$ −1.17543e9 1.17543e9i −0.0801457 0.0801457i
$$349$$ 2.63406e10i 1.77552i 0.460310 + 0.887758i $$0.347738\pi$$
−0.460310 + 0.887758i $$0.652262\pi$$
$$350$$ 0 0
$$351$$ 1.72559e9 0.113686
$$352$$ −1.67965e8 + 1.67965e8i −0.0109408 + 0.0109408i
$$353$$ −4.48404e9 4.48404e9i −0.288783 0.288783i 0.547816 0.836599i $$-0.315459\pi$$
−0.836599 + 0.547816i $$0.815459\pi$$
$$354$$ 6.21398e9i 0.395691i
$$355$$ 0 0
$$356$$ −1.40839e10 −0.876845
$$357$$ −1.69074e10 + 1.69074e10i −1.04089 + 1.04089i
$$358$$ 1.21351e10 + 1.21351e10i 0.738775 + 0.738775i
$$359$$ 1.76017e10i 1.05968i −0.848097 0.529841i $$-0.822251\pi$$
0.848097 0.529841i $$-0.177749\pi$$
$$360$$ 0 0
$$361$$ −1.60288e10 −0.943782
$$362$$ 2.34529e9 2.34529e9i 0.136572 0.136572i
$$363$$ 7.08663e9 + 7.08663e9i 0.408144 + 0.408144i
$$364$$ 1.01421e10i 0.577729i
$$365$$ 0 0
$$366$$ 2.51458e8 0.0140133
$$367$$ 5.58417e9 5.58417e9i 0.307818 0.307818i −0.536245 0.844063i $$-0.680158\pi$$
0.844063 + 0.536245i $$0.180158\pi$$
$$368$$ −1.54762e9 1.54762e9i −0.0843863 0.0843863i
$$369$$ 6.17220e9i 0.332916i
$$370$$ 0 0
$$371$$ −6.85026e9 −0.361586
$$372$$ 4.09500e9 4.09500e9i 0.213837 0.213837i
$$373$$ 1.94503e9 + 1.94503e9i 0.100483 + 0.100483i 0.755561 0.655078i $$-0.227364\pi$$
−0.655078 + 0.755561i $$0.727364\pi$$
$$374$$ 3.06120e8i 0.0156461i
$$375$$ 0 0
$$376$$ −3.20225e10 −1.60215
$$377$$ 2.86533e9 2.86533e9i 0.141844 0.141844i
$$378$$ −3.05263e9 3.05263e9i −0.149522 0.149522i
$$379$$ 1.29779e10i 0.628996i 0.949258 + 0.314498i $$0.101836\pi$$
−0.949258 + 0.314498i $$0.898164\pi$$
$$380$$ 0 0
$$381$$ −6.32117e9 −0.299984
$$382$$ 8.34986e9 8.34986e9i 0.392126 0.392126i
$$383$$ 1.84005e10 + 1.84005e10i 0.855135 + 0.855135i 0.990760 0.135625i $$-0.0433044\pi$$
−0.135625 + 0.990760i $$0.543304\pi$$
$$384$$ 6.31128e9i 0.290264i
$$385$$ 0 0
$$386$$ −2.52308e10 −1.13653
$$387$$ 6.12801e9 6.12801e9i 0.273197 0.273197i
$$388$$ −1.04884e10 1.04884e10i −0.462790 0.462790i
$$389$$ 1.69662e9i 0.0740944i 0.999314 + 0.0370472i $$0.0117952\pi$$
−0.999314 + 0.0370472i $$0.988205\pi$$
$$390$$ 0 0
$$391$$ 4.79653e10 2.05220
$$392$$ −3.18618e10 + 3.18618e10i −1.34935 + 1.34935i
$$393$$ 1.03780e10 + 1.03780e10i 0.435056 + 0.435056i
$$394$$ 6.13765e9i 0.254693i
$$395$$ 0 0
$$396$$ 7.57402e7 0.00307996
$$397$$ −1.61839e10 + 1.61839e10i −0.651510 + 0.651510i −0.953357 0.301846i $$-0.902397\pi$$
0.301846 + 0.953357i $$0.402397\pi$$
$$398$$ 7.86245e9 + 7.86245e9i 0.313347 + 0.313347i
$$399$$ 3.45117e10i 1.36168i
$$400$$ 0 0
$$401$$ −3.67977e9 −0.142313 −0.0711563 0.997465i $$-0.522669\pi$$
−0.0711563 + 0.997465i $$0.522669\pi$$
$$402$$ −1.00416e9 + 1.00416e9i −0.0384502 + 0.0384502i
$$403$$ 9.98233e9 + 9.98233e9i 0.378453 + 0.378453i
$$404$$ 1.27780e10i 0.479664i
$$405$$ 0 0
$$406$$ −1.01377e10 −0.373110
$$407$$ 1.42338e8 1.42338e8i 0.00518732 0.00518732i
$$408$$ −1.74770e10 1.74770e10i −0.630704 0.630704i
$$409$$ 2.44824e10i 0.874905i −0.899242 0.437452i $$-0.855881\pi$$
0.899242 0.437452i $$-0.144119\pi$$
$$410$$ 0 0
$$411$$ 3.33783e9 0.116976
$$412$$ −1.12652e10 + 1.12652e10i −0.390976 + 0.390976i
$$413$$ 3.67216e10 + 3.67216e10i 1.26218 + 1.26218i
$$414$$ 8.66013e9i 0.294797i
$$415$$ 0 0
$$416$$ 1.71270e10 0.571885
$$417$$ 1.74166e10 1.74166e10i 0.575995 0.575995i
$$418$$ 3.12429e8 + 3.12429e8i 0.0102340 + 0.0102340i
$$419$$ 2.07283e10i 0.672522i −0.941769 0.336261i $$-0.890838\pi$$
0.941769 0.336261i $$-0.109162\pi$$
$$420$$ 0 0
$$421$$ −1.53035e10 −0.487150 −0.243575 0.969882i $$-0.578320\pi$$
−0.243575 + 0.969882i $$0.578320\pi$$
$$422$$ 1.66748e10 1.66748e10i 0.525788 0.525788i
$$423$$ 1.17950e10 + 1.17950e10i 0.368413 + 0.368413i
$$424$$ 7.08104e9i 0.219095i
$$425$$ 0 0
$$426$$ −1.01227e10 −0.307368
$$427$$ −1.48600e9 + 1.48600e9i −0.0446998 + 0.0446998i
$$428$$ 1.61736e10 + 1.61736e10i 0.481983 + 0.481983i
$$429$$ 1.84631e8i 0.00545099i
$$430$$ 0 0
$$431$$ 3.04251e10 0.881705 0.440852 0.897580i $$-0.354676\pi$$
0.440852 + 0.897580i $$0.354676\pi$$
$$432$$ 4.15406e8 4.15406e8i 0.0119272 0.0119272i
$$433$$ −3.30421e9 3.30421e9i −0.0939974 0.0939974i 0.658544 0.752542i $$-0.271172\pi$$
−0.752542 + 0.658544i $$0.771172\pi$$
$$434$$ 3.53182e10i 0.995495i
$$435$$ 0 0
$$436$$ −7.46855e9 −0.206676
$$437$$ 4.89538e10 4.89538e10i 1.34234 1.34234i
$$438$$ −1.40323e10 1.40323e10i −0.381269 0.381269i
$$439$$ 3.09771e10i 0.834032i 0.908899 + 0.417016i $$0.136924\pi$$
−0.908899 + 0.417016i $$0.863076\pi$$
$$440$$ 0 0
$$441$$ 2.34715e10 0.620563
$$442$$ 1.56072e10 1.56072e10i 0.408917 0.408917i
$$443$$ −3.59125e10 3.59125e10i −0.932460 0.932460i 0.0653990 0.997859i $$-0.479168\pi$$
−0.997859 + 0.0653990i $$0.979168\pi$$
$$444$$ 5.95396e9i 0.153205i
$$445$$ 0 0
$$446$$ 2.93311e10 0.741291
$$447$$ −2.97364e10 + 2.97364e10i −0.744831 + 0.744831i
$$448$$ −3.45215e10 3.45215e10i −0.856993 0.856993i
$$449$$ 3.25449e10i 0.800751i 0.916351 + 0.400376i $$0.131120\pi$$
−0.916351 + 0.400376i $$0.868880\pi$$
$$450$$ 0 0
$$451$$ −6.60399e8 −0.0159625
$$452$$ −1.79441e10 + 1.79441e10i −0.429900 + 0.429900i
$$453$$ −2.66529e10 2.66529e10i −0.632924 0.632924i
$$454$$ 1.94178e10i 0.457064i
$$455$$ 0 0
$$456$$ −3.56743e10 −0.825081
$$457$$ −1.89124e10 + 1.89124e10i −0.433593 + 0.433593i −0.889849 0.456256i $$-0.849190\pi$$
0.456256 + 0.889849i $$0.349190\pi$$
$$458$$ 1.49261e10 + 1.49261e10i 0.339221 + 0.339221i
$$459$$ 1.28747e10i 0.290059i
$$460$$ 0 0
$$461$$ 3.64502e10 0.807042 0.403521 0.914970i $$-0.367786\pi$$
0.403521 + 0.914970i $$0.367786\pi$$
$$462$$ 3.26618e8 3.26618e8i 0.00716923 0.00716923i
$$463$$ −5.92927e10 5.92927e10i −1.29026 1.29026i −0.934625 0.355636i $$-0.884264\pi$$
−0.355636 0.934625i $$-0.615736\pi$$
$$464$$ 1.37956e9i 0.0297624i
$$465$$ 0 0
$$466$$ −2.22015e10 −0.470803
$$467$$ 3.42203e10 3.42203e10i 0.719476 0.719476i −0.249021 0.968498i $$-0.580109\pi$$
0.968498 + 0.249021i $$0.0801090\pi$$
$$468$$ −3.86153e9 3.86153e9i −0.0804964 0.0804964i
$$469$$ 1.18682e10i 0.245298i
$$470$$ 0 0
$$471$$ 3.16528e10 0.643174
$$472$$ −3.79587e10 + 3.79587e10i −0.764792 + 0.764792i
$$473$$ 6.55672e8 + 6.55672e8i 0.0130991 + 0.0130991i
$$474$$ 2.05033e10i 0.406173i
$$475$$ 0 0
$$476$$ 7.56709e10 1.47401
$$477$$ −2.60818e9 + 2.60818e9i −0.0503807 + 0.0503807i
$$478$$ −2.53177e10 2.53177e10i −0.484967 0.484967i
$$479$$ 4.05336e10i 0.769970i −0.922923 0.384985i $$-0.874207\pi$$
0.922923 0.384985i $$-0.125793\pi$$
$$480$$ 0 0
$$481$$ −1.45139e10 −0.271146
$$482$$ −1.80742e8 + 1.80742e8i −0.00334866 + 0.00334866i
$$483$$ −5.11772e10 5.11772e10i −0.940346 0.940346i
$$484$$ 3.17170e10i 0.577977i
$$485$$ 0 0
$$486$$ −2.32452e9 −0.0416667
$$487$$ −3.57760e10 + 3.57760e10i −0.636028 + 0.636028i −0.949573 0.313545i $$-0.898483\pi$$
0.313545 + 0.949573i $$0.398483\pi$$
$$488$$ −1.53606e9 1.53606e9i −0.0270849 0.0270849i
$$489$$ 3.01934e10i 0.528052i
$$490$$ 0 0
$$491$$ −5.52678e10 −0.950925 −0.475462 0.879736i $$-0.657719\pi$$
−0.475462 + 0.879736i $$0.657719\pi$$
$$492$$ 1.38122e10 1.38122e10i 0.235723 0.235723i
$$493$$ 2.13784e10 + 2.13784e10i 0.361899 + 0.361899i
$$494$$ 3.18577e10i 0.534942i
$$495$$ 0 0
$$496$$ 4.80615e9 0.0794091
$$497$$ 5.98204e10 5.98204e10i 0.980446 0.980446i
$$498$$ 3.24047e10 + 3.24047e10i 0.526854 + 0.526854i
$$499$$ 2.17632e10i 0.351011i 0.984478 + 0.175506i $$0.0561560\pi$$
−0.984478 + 0.175506i $$0.943844\pi$$
$$500$$ 0 0
$$501$$ 1.81384e10 0.287904
$$502$$ 2.66617e10 2.66617e10i 0.419830 0.419830i
$$503$$ 1.36083e10 + 1.36083e10i 0.212585 + 0.212585i 0.805365 0.592779i $$-0.201969\pi$$
−0.592779 + 0.805365i $$0.701969\pi$$
$$504$$ 3.72946e10i 0.577994i
$$505$$ 0 0
$$506$$ −9.26598e8 −0.0141348
$$507$$ −1.75615e10 + 1.75615e10i −0.265784 + 0.265784i
$$508$$ 1.41455e10 + 1.41455e10i 0.212405 + 0.212405i
$$509$$ 8.50274e10i 1.26674i −0.773849 0.633370i $$-0.781671\pi$$
0.773849 0.633370i $$-0.218329\pi$$
$$510$$ 0 0
$$511$$ 1.65848e11 2.43235
$$512$$ 8.48852e9 8.48852e9i 0.123524 0.123524i
$$513$$ 1.31400e10 + 1.31400e10i 0.189726 + 0.189726i
$$514$$ 1.55257e10i 0.222433i
$$515$$ 0 0
$$516$$ −2.74266e10 −0.386877
$$517$$ −1.26201e9 + 1.26201e9i −0.0176645 + 0.0176645i
$$518$$ 2.56756e10 + 2.56756e10i 0.356616 + 0.356616i
$$519$$ 1.15921e10i 0.159770i
$$520$$ 0 0
$$521$$ −1.04749e11 −1.42167 −0.710836 0.703358i $$-0.751683\pi$$
−0.710836 + 0.703358i $$0.751683\pi$$
$$522$$ −3.85986e9 + 3.85986e9i −0.0519864 + 0.0519864i
$$523$$ −1.81952e10 1.81952e10i −0.243192 0.243192i 0.574977 0.818169i $$-0.305011\pi$$
−0.818169 + 0.574977i $$0.805011\pi$$
$$524$$ 4.64480e10i 0.616087i
$$525$$ 0 0
$$526$$ 4.25737e10 0.556158
$$527$$ −7.44786e10 + 7.44786e10i −0.965581 + 0.965581i
$$528$$ 4.44467e7 + 4.44467e7i 0.000571879 + 0.000571879i
$$529$$ 6.68758e10i 0.853977i
$$530$$ 0 0
$$531$$ 2.79629e10 0.351726
$$532$$ 7.72304e10 7.72304e10i 0.964144 0.964144i
$$533$$ 3.36698e10 + 3.36698e10i 0.417187 + 0.417187i
$$534$$ 4.62485e10i 0.568764i
$$535$$ 0 0
$$536$$ 1.22680e10 0.148633
$$537$$ −5.46081e10 + 5.46081e10i −0.656689 + 0.656689i
$$538$$ −3.49519e10 3.49519e10i −0.417198 0.417198i
$$539$$ 2.51135e9i 0.0297545i
$$540$$ 0 0
$$541$$ −6.68793e10 −0.780733 −0.390367 0.920660i $$-0.627652\pi$$
−0.390367 + 0.920660i $$0.627652\pi$$
$$542$$ −3.66168e10 + 3.66168e10i −0.424310 + 0.424310i
$$543$$ 1.05538e10 + 1.05538e10i 0.121397 + 0.121397i
$$544$$ 1.27785e11i 1.45910i
$$545$$ 0 0
$$546$$ −3.33046e10 −0.374743
$$547$$ −1.80208e9 + 1.80208e9i −0.0201291 + 0.0201291i −0.717100 0.696971i $$-0.754531\pi$$
0.696971 + 0.717100i $$0.254531\pi$$
$$548$$ −7.46942e9 7.46942e9i −0.0828256 0.0828256i
$$549$$ 1.13156e9i 0.0124563i
$$550$$ 0 0
$$551$$ 4.36379e10 0.473432
$$552$$ 5.29013e10 5.29013e10i 0.569784 0.569784i
$$553$$ 1.21165e11 + 1.21165e11i 1.29562 + 1.29562i
$$554$$ 3.34958e10i 0.355592i
$$555$$ 0 0
$$556$$ −7.79498e10 −0.815672
$$557$$ 2.12113e10 2.12113e10i 0.220367 0.220367i −0.588286 0.808653i $$-0.700197\pi$$
0.808653 + 0.588286i $$0.200197\pi$$
$$558$$ −1.34471e10 1.34471e10i −0.138705 0.138705i
$$559$$ 6.68575e10i 0.684704i
$$560$$ 0 0
$$561$$ −1.37754e9 −0.0139076
$$562$$ 7.39748e9 7.39748e9i 0.0741547 0.0741547i
$$563$$ 2.95427e10 + 2.95427e10i 0.294047 + 0.294047i 0.838677 0.544629i $$-0.183330\pi$$
−0.544629 + 0.838677i $$0.683330\pi$$
$$564$$ 5.27896e10i 0.521713i
$$565$$ 0 0
$$566$$ 4.62212e10 0.450377
$$567$$ 1.37368e10 1.37368e10i 0.132909 0.132909i
$$568$$ 6.18356e10 + 6.18356e10i 0.594081 + 0.594081i
$$569$$ 6.53964e10i 0.623886i −0.950101 0.311943i $$-0.899020\pi$$
0.950101 0.311943i $$-0.100980\pi$$
$$570$$ 0 0
$$571$$ −1.87778e11 −1.76644 −0.883221 0.468957i $$-0.844630\pi$$
−0.883221 + 0.468957i $$0.844630\pi$$
$$572$$ 4.13168e8 4.13168e8i 0.00385960 0.00385960i
$$573$$ 3.75744e10 + 3.75744e10i 0.348556 + 0.348556i
$$574$$ 1.19126e11i 1.09738i
$$575$$ 0 0
$$576$$ −2.62875e10 −0.238814
$$577$$ 9.25087e7 9.25087e7i 0.000834602 0.000834602i −0.706689 0.707524i $$-0.749812\pi$$
0.707524 + 0.706689i $$0.249812\pi$$
$$578$$ 6.51847e10 + 6.51847e10i 0.584029 + 0.584029i
$$579$$ 1.13538e11i 1.01025i
$$580$$ 0 0
$$581$$ −3.82992e11 −3.36113
$$582$$ −3.44418e10 + 3.44418e10i −0.300188 + 0.300188i
$$583$$ −2.79064e8 2.79064e8i −0.00241563 0.00241563i
$$584$$ 1.71435e11i 1.47383i
$$585$$ 0 0
$$586$$ 5.29204e10 0.448779
$$587$$ 1.12620e11 1.12620e11i 0.948560 0.948560i −0.0501803 0.998740i $$-0.515980\pi$$
0.998740 + 0.0501803i $$0.0159796\pi$$
$$588$$ −5.25246e10 5.25246e10i −0.439393 0.439393i
$$589$$ 1.52027e11i 1.26316i
$$590$$ 0 0
$$591$$ −2.76194e10 −0.226394
$$592$$ −3.49397e9 + 3.49397e9i −0.0284467 + 0.0284467i
$$593$$ −1.37020e11 1.37020e11i −1.10807 1.10807i −0.993405 0.114661i $$-0.963422\pi$$
−0.114661 0.993405i $$-0.536578\pi$$
$$594$$ 2.48714e8i 0.00199781i
$$595$$ 0 0
$$596$$ 1.33088e11 1.05476
$$597$$ −3.53810e10 + 3.53810e10i −0.278531 + 0.278531i
$$598$$ 4.72416e10 + 4.72416e10i 0.369420 + 0.369420i
$$599$$ 1.62549e11i 1.26263i 0.775525 + 0.631317i $$0.217485\pi$$
−0.775525 + 0.631317i $$0.782515\pi$$
$$600$$ 0 0
$$601$$ 1.32519e10 0.101574 0.0507869 0.998710i $$-0.483827\pi$$
0.0507869 + 0.998710i $$0.483827\pi$$
$$602$$ −1.18273e11 + 1.18273e11i −0.900534 + 0.900534i
$$603$$ −4.51872e9 4.51872e9i −0.0341780 0.0341780i
$$604$$ 1.19288e11i 0.896290i
$$605$$ 0 0
$$606$$ −4.19602e10 −0.311134
$$607$$ −8.11866e10 + 8.11866e10i −0.598039 + 0.598039i −0.939791 0.341751i $$-0.888980\pi$$
0.341751 + 0.939791i $$0.388980\pi$$
$$608$$ 1.30419e11 + 1.30419e11i 0.954391 + 0.954391i
$$609$$ 4.56199e10i 0.331654i
$$610$$ 0 0
$$611$$ 1.28685e11 0.923340
$$612$$ 2.88111e10 2.88111e10i 0.205378 0.205378i
$$613$$ −4.13613e10 4.13613e10i −0.292922 0.292922i 0.545311 0.838234i $$-0.316411\pi$$
−0.838234 + 0.545311i $$0.816411\pi$$
$$614$$ 1.81083e11i 1.27410i
$$615$$ 0 0
$$616$$ −3.99036e9 −0.0277134
$$617$$ −1.45292e11 + 1.45292e11i −1.00254 + 1.00254i −0.00254243 + 0.999997i $$0.500809\pi$$
−0.999997 + 0.00254243i $$0.999191\pi$$
$$618$$ 3.69924e10 + 3.69924e10i 0.253606 + 0.253606i
$$619$$ 1.15947e11i 0.789765i −0.918732 0.394882i $$-0.870785\pi$$
0.918732 0.394882i $$-0.129215\pi$$
$$620$$ 0 0
$$621$$ −3.89706e10 −0.262042
$$622$$ 6.34059e10 6.34059e10i 0.423612 0.423612i
$$623$$ −2.73306e11 2.73306e11i −1.81425 1.81425i
$$624$$ 4.53214e9i 0.0298927i
$$625$$ 0 0
$$626$$ 4.35658e10 0.283693
$$627$$ −1.40593e9 + 1.40593e9i −0.00909690 + 0.00909690i
$$628$$ −7.08328e10 7.08328e10i −0.455403 0.455403i
$$629$$ 1.08289e11i 0.691800i
$$630$$ 0 0
$$631$$ −3.77923e10 −0.238389 −0.119194 0.992871i $$-0.538031\pi$$
−0.119194 + 0.992871i $$0.538031\pi$$
$$632$$ −1.25247e11 + 1.25247e11i −0.785052 + 0.785052i
$$633$$ 7.50366e10 + 7.50366e10i 0.467367 + 0.467367i
$$634$$ 2.91491e10i 0.180413i
$$635$$ 0 0
$$636$$ 1.16732e10 0.0713446
$$637$$ 1.28039e11 1.28039e11i 0.777648 0.777648i
$$638$$ −4.12989e8 4.12989e8i −0.00249262 0.00249262i
$$639$$ 4.55522e10i 0.273216i
$$640$$ 0 0
$$641$$ −1.49659e10 −0.0886484 −0.0443242 0.999017i $$-0.514113\pi$$
−0.0443242 + 0.999017i $$0.514113\pi$$
$$642$$ 5.31107e10 5.31107e10i 0.312638 0.312638i
$$643$$ 1.62422e11 + 1.62422e11i 0.950170 + 0.950170i 0.998816 0.0486457i $$-0.0154905\pi$$
−0.0486457 + 0.998816i $$0.515491\pi$$
$$644$$ 2.29049e11i 1.33164i
$$645$$ 0 0
$$646$$ 2.37692e11 1.36485
$$647$$ 7.96349e10 7.96349e10i 0.454450 0.454450i −0.442378 0.896829i $$-0.645865\pi$$
0.896829 + 0.442378i $$0.145865\pi$$
$$648$$ 1.41996e10 + 1.41996e10i 0.0805334 + 0.0805334i
$$649$$ 2.99191e9i 0.0168644i
$$650$$ 0 0
$$651$$ 1.58932e11 0.884885
$$652$$ 6.75669e10 6.75669e10i 0.373890 0.373890i
$$653$$ 3.49865e9 + 3.49865e9i 0.0192419 + 0.0192419i 0.716662 0.697420i $$-0.245669\pi$$
−0.697420 + 0.716662i $$0.745669\pi$$
$$654$$ 2.45251e10i 0.134060i
$$655$$ 0 0
$$656$$ 1.62108e10 0.0875367
$$657$$ 6.31452e10 6.31452e10i 0.338906 0.338906i
$$658$$ −2.27647e11 2.27647e11i −1.21439 1.21439i
$$659$$ 2.49093e11i 1.32075i −0.750938 0.660373i $$-0.770398\pi$$
0.750938 0.660373i $$-0.229602\pi$$
$$660$$ 0 0
$$661$$ 8.01902e9 0.0420064 0.0210032 0.999779i $$-0.493314\pi$$
0.0210032 + 0.999779i $$0.493314\pi$$
$$662$$ 3.16567e10 3.16567e10i 0.164829 0.164829i
$$663$$ 7.02323e10 + 7.02323e10i 0.363482 + 0.363482i
$$664$$ 3.95894e11i 2.03661i
$$665$$ 0 0
$$666$$ 1.95515e10 0.0993765
$$667$$ −6.47105e10 + 6.47105e10i −0.326942 + 0.326942i
$$668$$ −4.05902e10 4.05902e10i −0.203852 0.203852i
$$669$$ 1.31990e11i 0.658925i
$$670$$ 0 0
$$671$$ −1.21072e8 −0.000597248
$$672$$ 1.36342e11 1.36342e11i 0.668580 0.668580i
$$673$$ 1.75658e11 + 1.75658e11i 0.856264 + 0.856264i 0.990896 0.134632i $$-0.0429852\pi$$
−0.134632 + 0.990896i $$0.542985\pi$$
$$674$$ 1.74713e9i 0.00846614i
$$675$$ 0 0
$$676$$ 7.85983e10 0.376380
$$677$$ −1.49210e11 + 1.49210e11i −0.710301 + 0.710301i −0.966598 0.256297i $$-0.917498\pi$$
0.256297 + 0.966598i $$0.417498\pi$$
$$678$$ 5.89245e10 + 5.89245e10i 0.278854 + 0.278854i
$$679$$ 4.07068e11i 1.91509i
$$680$$ 0 0
$$681$$ 8.73801e10 0.406279
$$682$$ 1.43878e9 1.43878e9i 0.00665056 0.00665056i
$$683$$ −2.32934e11 2.32934e11i −1.07041 1.07041i −0.997326 0.0730842i $$-0.976716\pi$$
−0.0730842 0.997326i $$-0.523284\pi$$
$$684$$ 5.88097e10i 0.268673i
$$685$$ 0 0
$$686$$ −2.09677e11 −0.946792
$$687$$ −6.71672e10 + 6.71672e10i −0.301530 + 0.301530i
$$688$$ −1.60948e10 1.60948e10i −0.0718342 0.0718342i
$$689$$ 2.84556e10i 0.126267i
$$690$$ 0 0
$$691$$ 2.85720e11 1.25322 0.626611 0.779332i $$-0.284441\pi$$
0.626611 + 0.779332i $$0.284441\pi$$
$$692$$ −2.59410e10 + 2.59410e10i −0.113126 + 0.113126i
$$693$$ 1.46978e9 + 1.46978e9i 0.00637265 + 0.00637265i
$$694$$ 2.40368e11i 1.03619i
$$695$$ 0 0
$$696$$ 4.71567e10 0.200959
$$697$$ −2.51211e11 + 2.51211e11i −1.06441 + 1.06441i
$$698$$ −1.93563e11 1.93563e11i −0.815458 0.815458i
$$699$$ 9.99068e10i 0.418491i
$$700$$ 0 0
$$701$$ −6.05393e10 −0.250706 −0.125353 0.992112i $$-0.540006\pi$$
−0.125353 + 0.992112i $$0.540006\pi$$
$$702$$ −1.26804e10 + 1.26804e10i −0.0522139 + 0.0522139i
$$703$$ −1.10521e11 1.10521e11i −0.452503 0.452503i
$$704$$ 2.81266e9i 0.0114505i
$$705$$ 0 0
$$706$$ 6.59017e10 0.265264
$$707$$ 2.47965e11 2.47965e11i 0.992458 0.992458i
$$708$$ −6.25755e10 6.25755e10i −0.249041 0.249041i
$$709$$ 1.05416e10i 0.0417178i −0.999782 0.0208589i $$-0.993360\pi$$
0.999782 0.0208589i $$-0.00664007\pi$$
$$710$$ 0 0
$$711$$ 9.22650e10 0.361043
$$712$$ 2.82513e11 2.82513e11i 1.09931 1.09931i
$$713$$ −2.25440e11 2.25440e11i −0.872315 0.872315i
$$714$$ 2.48487e11i 0.956116i
$$715$$ 0 0
$$716$$ 2.44405e11 0.929945
$$717$$ 1.13929e11 1.13929e11i 0.431082 0.431082i
$$718$$ 1.29345e11 + 1.29345e11i 0.486690 + 0.486690i
$$719$$ 4.26585e10i 0.159621i 0.996810 + 0.0798104i $$0.0254315\pi$$
−0.996810 + 0.0798104i $$0.974569\pi$$
$$720$$ 0 0
$$721$$ −4.37215e11 −1.61791
$$722$$ 1.17787e11 1.17787e11i 0.433460 0.433460i
$$723$$ −8.13339e8 8.13339e8i −0.00297659 0.00297659i
$$724$$ 4.72347e10i 0.171912i
$$725$$ 0 0
$$726$$ −1.04152e11 −0.374904
$$727$$ −5.57133e10 + 5.57133e10i −0.199444 + 0.199444i −0.799762 0.600318i $$-0.795041\pi$$
0.600318 + 0.799762i $$0.295041\pi$$
$$728$$ 2.03444e11 + 2.03444e11i 0.724303 + 0.724303i
$$729$$ 1.04604e10i 0.0370370i
$$730$$ 0 0
$$731$$ 4.98826e11 1.74695
$$732$$ 2.53221e9 2.53221e9i 0.00881974 0.00881974i
$$733$$ 6.92078e10 + 6.92078e10i 0.239739 + 0.239739i 0.816742 0.577003i $$-0.195778\pi$$
−0.577003 + 0.816742i $$0.695778\pi$$
$$734$$ 8.20702e10i 0.282749i
$$735$$ 0 0
$$736$$ −3.86795e11 −1.31817
$$737$$ 4.83484e8 4.83484e8i 0.00163875 0.00163875i
$$738$$ −4.53562e10 4.53562e10i −0.152901 0.152901i
$$739$$ 5.42380e11i 1.81855i −0.416193 0.909276i $$-0.636636\pi$$
0.416193 0.909276i $$-0.363364\pi$$
$$740$$ 0 0
$$741$$ 1.43360e11 0.475504
$$742$$ 5.03389e10 5.03389e10i 0.166069 0.166069i
$$743$$ 1.05763e11 + 1.05763e11i 0.347038 + 0.347038i 0.859005 0.511967i $$-0.171083\pi$$
−0.511967 + 0.859005i $$0.671083\pi$$
$$744$$ 1.64286e11i 0.536178i
$$745$$ 0 0
$$746$$ −2.85860e10 −0.0922992
$$747$$ −1.45821e11 + 1.45821e11i −0.468314 + 0.468314i
$$748$$ 3.08266e9 + 3.08266e9i 0.00984736 + 0.00984736i
$$749$$ 6.27717e11i 1.99451i
$$750$$ 0 0
$$751$$ 4.27682e11 1.34450 0.672251 0.740323i $$-0.265328\pi$$
0.672251 + 0.740323i $$0.265328\pi$$
$$752$$ 3.09786e10 3.09786e10i 0.0968703 0.0968703i
$$753$$ 1.19978e11 + 1.19978e11i 0.373182 + 0.373182i
$$754$$ 4.21116e10i 0.130292i
$$755$$ 0 0
$$756$$ −6.14806e10 −0.188214
$$757$$ −2.41193e11 + 2.41193e11i −0.734482 + 0.734482i −0.971504 0.237022i $$-0.923829\pi$$
0.237022 + 0.971504i $$0.423829\pi$$
$$758$$ −9.53677e10 9.53677e10i −0.288885 0.288885i
$$759$$ 4.16969e9i 0.0125643i
$$760$$ 0 0
$$761$$ −4.31324e11 −1.28607 −0.643035 0.765837i $$-0.722325\pi$$
−0.643035 + 0.765837i $$0.722325\pi$$
$$762$$ 4.64509e10 4.64509e10i 0.137776 0.137776i
$$763$$ −1.44931e11 1.44931e11i −0.427627 0.427627i
$$764$$ 1.68168e11i 0.493595i
$$765$$ 0 0
$$766$$ −2.70431e11 −0.785491
$$767$$ 1.52540e11 1.52540e11i 0.440759 0.440759i
$$768$$ 1.48132e11 + 1.48132e11i 0.425798 + 0.425798i
$$769$$ 3.88788e11i 1.11175i 0.831265 + 0.555876i $$0.187617\pi$$
−0.831265 + 0.555876i $$0.812383\pi$$
$$770$$ 0 0
$$771$$ −6.98658e10 −0.197718
$$772$$ −2.54077e11 + 2.54077e11i −0.715313 + 0.715313i
$$773$$ 2.51696e11 + 2.51696e11i 0.704951 + 0.704951i 0.965469 0.260518i $$-0.0838933\pi$$
−0.260518 + 0.965469i $$0.583893\pi$$