# Properties

 Label 252.9.z.d.145.2 Level $252$ Weight $9$ Character 252.145 Analytic conductor $102.659$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 252.z (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$102.659409735$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96$$ x^12 - 3*x^11 + 148097*x^10 + 46071824*x^9 + 21578502553*x^8 + 3561445462121*x^7 + 576413321817541*x^6 + 47217566733462528*x^5 + 5214056955297543333*x^4 + 358752845334081085965*x^3 + 30962072851910211245661*x^2 + 1221542968331193193318500*x + 45396580558961892385326096 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{20}\cdot 3^{10}\cdot 7^{4}$$ Twist minimal: no (minimal twist has level 84) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 145.2 Root $$221.993 + 384.503i$$ of defining polynomial Character $$\chi$$ $$=$$ 252.145 Dual form 252.9.z.d.73.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-632.551 - 365.204i) q^{5} +(984.437 + 2189.91i) q^{7} +O(q^{10})$$ $$q+(-632.551 - 365.204i) q^{5} +(984.437 + 2189.91i) q^{7} +(-6353.95 - 11005.4i) q^{11} +21176.4i q^{13} +(82551.9 - 47661.3i) q^{17} +(-133336. - 76981.8i) q^{19} +(47111.5 - 81599.5i) q^{23} +(71435.0 + 123729. i) q^{25} -541664. q^{29} +(-185730. + 107231. i) q^{31} +(177055. - 1.74475e6i) q^{35} +(-370376. + 641510. i) q^{37} +782599. i q^{41} -221324. q^{43} +(-7.13230e6 - 4.11784e6i) q^{47} +(-3.82657e6 + 4.31165e6i) q^{49} +(-659083. - 1.14157e6i) q^{53} +9.28194e6i q^{55} +(7.52865e6 - 4.34667e6i) q^{59} +(1.31192e7 + 7.57439e6i) q^{61} +(7.73369e6 - 1.33951e7i) q^{65} +(1.99100e7 + 3.44851e7i) q^{67} +9.34713e6 q^{71} +(2.94520e7 - 1.70041e7i) q^{73} +(1.78456e7 - 2.47486e7i) q^{77} +(2.26450e7 - 3.92223e7i) q^{79} +6.58893e7i q^{83} -6.96244e7 q^{85} +(1.09902e7 + 6.34517e6i) q^{89} +(-4.63742e7 + 2.08468e7i) q^{91} +(5.62280e7 + 9.73898e7i) q^{95} -6.15780e6i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 285 q^{5} + 198 q^{7}+O(q^{10})$$ 12 * q - 285 * q^5 + 198 * q^7 $$12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100})$$ 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −632.551 365.204i −1.01208 0.584326i −0.100282 0.994959i $$-0.531974\pi$$
−0.911801 + 0.410633i $$0.865308\pi$$
$$6$$ 0 0
$$7$$ 984.437 + 2189.91i 0.410011 + 0.912080i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −6353.95 11005.4i −0.433983 0.751681i 0.563229 0.826301i $$-0.309559\pi$$
−0.997212 + 0.0746198i $$0.976226\pi$$
$$12$$ 0 0
$$13$$ 21176.4i 0.741444i 0.928744 + 0.370722i $$0.120890\pi$$
−0.928744 + 0.370722i $$0.879110\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 82551.9 47661.3i 0.988397 0.570651i 0.0836020 0.996499i $$-0.473358\pi$$
0.904795 + 0.425848i $$0.140024\pi$$
$$18$$ 0 0
$$19$$ −133336. 76981.8i −1.02314 0.590709i −0.108126 0.994137i $$-0.534485\pi$$
−0.915011 + 0.403428i $$0.867818\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 47111.5 81599.5i 0.168351 0.291593i −0.769489 0.638660i $$-0.779489\pi$$
0.937840 + 0.347067i $$0.112822\pi$$
$$24$$ 0 0
$$25$$ 71435.0 + 123729.i 0.182874 + 0.316746i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −541664. −0.765840 −0.382920 0.923782i $$-0.625081\pi$$
−0.382920 + 0.923782i $$0.625081\pi$$
$$30$$ 0 0
$$31$$ −185730. + 107231.i −0.201110 + 0.116111i −0.597173 0.802112i $$-0.703710\pi$$
0.396063 + 0.918223i $$0.370376\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 177055. 1.74475e6i 0.117987 1.16268i
$$36$$ 0 0
$$37$$ −370376. + 641510.i −0.197622 + 0.342292i −0.947757 0.318993i $$-0.896655\pi$$
0.750135 + 0.661285i $$0.229989\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 782599.i 0.276952i 0.990366 + 0.138476i $$0.0442203\pi$$
−0.990366 + 0.138476i $$0.955780\pi$$
$$42$$ 0 0
$$43$$ −221324. −0.0647373 −0.0323687 0.999476i $$-0.510305\pi$$
−0.0323687 + 0.999476i $$0.510305\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −7.13230e6 4.11784e6i −1.46163 0.843874i −0.462546 0.886595i $$-0.653064\pi$$
−0.999087 + 0.0427209i $$0.986397\pi$$
$$48$$ 0 0
$$49$$ −3.82657e6 + 4.31165e6i −0.663782 + 0.747926i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −659083. 1.14157e6i −0.0835289 0.144676i 0.821235 0.570591i $$-0.193286\pi$$
−0.904763 + 0.425915i $$0.859952\pi$$
$$54$$ 0 0
$$55$$ 9.28194e6i 1.01435i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 7.52865e6 4.34667e6i 0.621311 0.358714i −0.156068 0.987746i $$-0.549882\pi$$
0.777379 + 0.629032i $$0.216549\pi$$
$$60$$ 0 0
$$61$$ 1.31192e7 + 7.57439e6i 0.947521 + 0.547052i 0.892310 0.451423i $$-0.149083\pi$$
0.0552112 + 0.998475i $$0.482417\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 7.73369e6 1.33951e7i 0.433245 0.750402i
$$66$$ 0 0
$$67$$ 1.99100e7 + 3.44851e7i 0.988033 + 1.71132i 0.627596 + 0.778539i $$0.284039\pi$$
0.360436 + 0.932784i $$0.382628\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 9.34713e6 0.367828 0.183914 0.982942i $$-0.441123\pi$$
0.183914 + 0.982942i $$0.441123\pi$$
$$72$$ 0 0
$$73$$ 2.94520e7 1.70041e7i 1.03711 0.598774i 0.118094 0.993002i $$-0.462321\pi$$
0.919012 + 0.394229i $$0.128988\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1.78456e7 2.47486e7i 0.507656 0.704025i
$$78$$ 0 0
$$79$$ 2.26450e7 3.92223e7i 0.581385 1.00699i −0.413931 0.910308i $$-0.635844\pi$$
0.995316 0.0966799i $$-0.0308223\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 6.58893e7i 1.38836i 0.719801 + 0.694180i $$0.244233\pi$$
−0.719801 + 0.694180i $$0.755767\pi$$
$$84$$ 0 0
$$85$$ −6.96244e7 −1.33378
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1.09902e7 + 6.34517e6i 0.175164 + 0.101131i 0.585018 0.811020i $$-0.301087\pi$$
−0.409855 + 0.912151i $$0.634421\pi$$
$$90$$ 0 0
$$91$$ −4.63742e7 + 2.08468e7i −0.676256 + 0.304000i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 5.62280e7 + 9.73898e7i 0.690333 + 1.19569i
$$96$$ 0 0
$$97$$ 6.15780e6i 0.0695566i −0.999395 0.0347783i $$-0.988927\pi$$
0.999395 0.0347783i $$-0.0110725\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1.15329e8 + 6.65855e7i −1.10829 + 0.639874i −0.938387 0.345587i $$-0.887680\pi$$
−0.169907 + 0.985460i $$0.554347\pi$$
$$102$$ 0 0
$$103$$ 4.81925e7 + 2.78240e7i 0.428184 + 0.247212i 0.698573 0.715539i $$-0.253819\pi$$
−0.270389 + 0.962751i $$0.587152\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −7.23667e6 + 1.25343e7i −0.0552082 + 0.0956234i −0.892309 0.451426i $$-0.850916\pi$$
0.837101 + 0.547049i $$0.184249\pi$$
$$108$$ 0 0
$$109$$ −9.01793e7 1.56195e8i −0.638853 1.10653i −0.985685 0.168598i $$-0.946076\pi$$
0.346832 0.937927i $$-0.387257\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2.21791e7 0.136028 0.0680142 0.997684i $$-0.478334\pi$$
0.0680142 + 0.997684i $$0.478334\pi$$
$$114$$ 0 0
$$115$$ −5.96009e7 + 3.44106e7i −0.340770 + 0.196744i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 1.85641e8 + 1.33861e8i 0.925733 + 0.667524i
$$120$$ 0 0
$$121$$ 2.64341e7 4.57852e7i 0.123317 0.213591i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.80962e8i 0.741221i
$$126$$ 0 0
$$127$$ 1.77711e8 0.683123 0.341561 0.939859i $$-0.389044\pi$$
0.341561 + 0.939859i $$0.389044\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 4.83164e8 + 2.78955e8i 1.64062 + 0.947215i 0.980612 + 0.195960i $$0.0627823\pi$$
0.660012 + 0.751255i $$0.270551\pi$$
$$132$$ 0 0
$$133$$ 3.73216e7 3.67778e8i 0.119276 1.17538i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1.96914e8 + 3.41064e8i 0.558977 + 0.968176i 0.997582 + 0.0694962i $$0.0221392\pi$$
−0.438606 + 0.898680i $$0.644528\pi$$
$$138$$ 0 0
$$139$$ 4.85677e8i 1.30103i 0.759492 + 0.650516i $$0.225447\pi$$
−0.759492 + 0.650516i $$0.774553\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.33054e8 1.34554e8i 0.557329 0.321774i
$$144$$ 0 0
$$145$$ 3.42630e8 + 1.97818e8i 0.775093 + 0.447500i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1.60563e8 + 2.78103e8i −0.325762 + 0.564236i −0.981666 0.190608i $$-0.938954\pi$$
0.655905 + 0.754844i $$0.272287\pi$$
$$150$$ 0 0
$$151$$ 4.12702e8 + 7.14822e8i 0.793833 + 1.37496i 0.923577 + 0.383412i $$0.125251\pi$$
−0.129744 + 0.991547i $$0.541416\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1.56645e8 0.271387
$$156$$ 0 0
$$157$$ 9.15549e8 5.28592e8i 1.50689 0.870006i 0.506926 0.861989i $$-0.330782\pi$$
0.999968 0.00801653i $$-0.00255177\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 2.25074e8 + 2.28402e7i 0.334982 + 0.0339935i
$$162$$ 0 0
$$163$$ −5.67831e8 + 9.83512e8i −0.804394 + 1.39325i 0.112306 + 0.993674i $$0.464176\pi$$
−0.916699 + 0.399577i $$0.869157\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.00076e9i 1.28666i −0.765591 0.643328i $$-0.777553\pi$$
0.765591 0.643328i $$-0.222447\pi$$
$$168$$ 0 0
$$169$$ 3.67292e8 0.450261
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 5.46649e8 + 3.15608e8i 0.610273 + 0.352341i 0.773072 0.634318i $$-0.218719\pi$$
−0.162799 + 0.986659i $$0.552052\pi$$
$$174$$ 0 0
$$175$$ −2.00632e8 + 2.78239e8i −0.213918 + 0.296665i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 5.77342e8 + 9.99986e8i 0.562369 + 0.974052i 0.997289 + 0.0735826i $$0.0234433\pi$$
−0.434920 + 0.900469i $$0.643223\pi$$
$$180$$ 0 0
$$181$$ 1.42212e9i 1.32502i 0.749052 + 0.662511i $$0.230509\pi$$
−0.749052 + 0.662511i $$0.769491\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 4.68564e8 2.70525e8i 0.400020 0.230952i
$$186$$ 0 0
$$187$$ −1.04906e9 6.05676e8i −0.857895 0.495306i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3.05844e8 + 5.29737e8i −0.229809 + 0.398040i −0.957751 0.287598i $$-0.907143\pi$$
0.727943 + 0.685638i $$0.240477\pi$$
$$192$$ 0 0
$$193$$ 9.49542e8 + 1.64465e9i 0.684360 + 1.18535i 0.973637 + 0.228101i $$0.0732518\pi$$
−0.289277 + 0.957245i $$0.593415\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1.00843e9 −0.669544 −0.334772 0.942299i $$-0.608659\pi$$
−0.334772 + 0.942299i $$0.608659\pi$$
$$198$$ 0 0
$$199$$ 2.76255e8 1.59496e8i 0.176156 0.101704i −0.409329 0.912387i $$-0.634237\pi$$
0.585485 + 0.810683i $$0.300904\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −5.33234e8 1.18619e9i −0.314003 0.698507i
$$204$$ 0 0
$$205$$ 2.85808e8 4.95034e8i 0.161830 0.280298i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 1.95655e9i 1.02543i
$$210$$ 0 0
$$211$$ −1.39969e9 −0.706160 −0.353080 0.935593i $$-0.614866\pi$$
−0.353080 + 0.935593i $$0.614866\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1.39999e8 + 8.08283e7i 0.0655195 + 0.0378277i
$$216$$ 0 0
$$217$$ −4.17665e8 3.01168e8i −0.188360 0.135822i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1.00929e9 + 1.74815e9i 0.423106 + 0.732840i
$$222$$ 0 0
$$223$$ 3.09118e9i 1.24999i −0.780630 0.624993i $$-0.785102\pi$$
0.780630 0.624993i $$-0.214898\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 3.27805e9 1.89258e9i 1.23456 0.712774i 0.266583 0.963812i $$-0.414105\pi$$
0.967977 + 0.251038i $$0.0807719\pi$$
$$228$$ 0 0
$$229$$ −2.74391e9 1.58420e9i −0.997763 0.576059i −0.0901773 0.995926i $$-0.528743\pi$$
−0.907586 + 0.419867i $$0.862077\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −2.76314e9 + 4.78590e9i −0.937518 + 1.62383i −0.167437 + 0.985883i $$0.553549\pi$$
−0.770081 + 0.637946i $$0.779784\pi$$
$$234$$ 0 0
$$235$$ 3.00770e9 + 5.20949e9i 0.986195 + 1.70814i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3.93530e9 1.20611 0.603054 0.797701i $$-0.293951\pi$$
0.603054 + 0.797701i $$0.293951\pi$$
$$240$$ 0 0
$$241$$ 5.76301e9 3.32727e9i 1.70837 0.986326i 0.771780 0.635889i $$-0.219367\pi$$
0.936586 0.350437i $$-0.113967\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 3.99513e9 1.32986e9i 1.10883 0.369098i
$$246$$ 0 0
$$247$$ 1.63019e9 2.82358e9i 0.437977 0.758599i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 4.25680e9i 1.07248i 0.844066 + 0.536239i $$0.180155\pi$$
−0.844066 + 0.536239i $$0.819845\pi$$
$$252$$ 0 0
$$253$$ −1.19738e9 −0.292246
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 2.63398e9 + 1.52073e9i 0.603782 + 0.348593i 0.770528 0.637406i $$-0.219993\pi$$
−0.166746 + 0.986000i $$0.553326\pi$$
$$258$$ 0 0
$$259$$ −1.76946e9 1.79562e8i −0.393225 0.0399039i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −4.20815e9 7.28873e9i −0.879566 1.52345i −0.851818 0.523838i $$-0.824500\pi$$
−0.0277486 0.999615i $$-0.508834\pi$$
$$264$$ 0 0
$$265$$ 9.62798e8i 0.195232i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −6.40038e9 + 3.69526e9i −1.22235 + 0.705726i −0.965419 0.260703i $$-0.916046\pi$$
−0.256934 + 0.966429i $$0.582712\pi$$
$$270$$ 0 0
$$271$$ −3.72934e9 2.15314e9i −0.691441 0.399204i 0.112711 0.993628i $$-0.464047\pi$$
−0.804152 + 0.594424i $$0.797380\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 9.07789e8 1.57234e9i 0.158728 0.274925i
$$276$$ 0 0
$$277$$ −2.54312e7 4.40481e7i −0.00431964 0.00748183i 0.863858 0.503736i $$-0.168042\pi$$
−0.868177 + 0.496254i $$0.834708\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.03421e10 −1.65877 −0.829383 0.558680i $$-0.811308\pi$$
−0.829383 + 0.558680i $$0.811308\pi$$
$$282$$ 0 0
$$283$$ −2.55984e9 + 1.47792e9i −0.399086 + 0.230412i −0.686090 0.727517i $$-0.740674\pi$$
0.287003 + 0.957930i $$0.407341\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −1.71382e9 + 7.70419e8i −0.252602 + 0.113553i
$$288$$ 0 0
$$289$$ 1.05533e9 1.82788e9i 0.151285 0.262034i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 4.22563e9i 0.573351i −0.958028 0.286676i $$-0.907450\pi$$
0.958028 0.286676i $$-0.0925502\pi$$
$$294$$ 0 0
$$295$$ −6.34968e9 −0.838424
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1.72798e9 + 9.97651e8i 0.216199 + 0.124823i
$$300$$ 0 0
$$301$$ −2.17880e8 4.84679e8i −0.0265430 0.0590456i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −5.53239e9 9.58238e9i −0.639313 1.10732i
$$306$$ 0 0
$$307$$ 2.96070e9i 0.333304i −0.986016 0.166652i $$-0.946704\pi$$
0.986016 0.166652i $$-0.0532956\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 7.74956e9 4.47421e9i 0.828391 0.478272i −0.0249101 0.999690i $$-0.507930\pi$$
0.853302 + 0.521418i $$0.174597\pi$$
$$312$$ 0 0
$$313$$ −5.04664e9 2.91368e9i −0.525806 0.303574i 0.213501 0.976943i $$-0.431513\pi$$
−0.739307 + 0.673369i $$0.764847\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.50614e9 + 4.34076e9i −0.248181 + 0.429861i −0.963021 0.269426i $$-0.913166\pi$$
0.714840 + 0.699288i $$0.246499\pi$$
$$318$$ 0 0
$$319$$ 3.44171e9 + 5.96121e9i 0.332362 + 0.575667i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1.46762e10 −1.34835
$$324$$ 0 0
$$325$$ −2.62013e9 + 1.51273e9i −0.234850 + 0.135590i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 1.99637e9 1.96728e10i 0.170395 1.67912i
$$330$$ 0 0
$$331$$ 4.78357e9 8.28539e9i 0.398511 0.690242i −0.595031 0.803703i $$-0.702860\pi$$
0.993542 + 0.113461i $$0.0361937\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 2.90848e10i 2.30933i
$$336$$ 0 0
$$337$$ 2.32884e9 0.180560 0.0902798 0.995916i $$-0.471224\pi$$
0.0902798 + 0.995916i $$0.471224\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 2.36023e9 + 1.36268e9i 0.174557 + 0.100781i
$$342$$ 0 0
$$343$$ −1.32091e10 4.13528e9i −0.954327 0.298764i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1.04233e10 1.80536e10i −0.718928 1.24522i −0.961425 0.275068i $$-0.911300\pi$$
0.242497 0.970152i $$-0.422034\pi$$
$$348$$ 0 0
$$349$$ 2.91490e10i 1.96482i 0.186745 + 0.982409i $$0.440206\pi$$
−0.186745 + 0.982409i $$0.559794\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −9.78829e8 + 5.65127e8i −0.0630388 + 0.0363955i −0.531188 0.847254i $$-0.678254\pi$$
0.468149 + 0.883649i $$0.344921\pi$$
$$354$$ 0 0
$$355$$ −5.91254e9 3.41361e9i −0.372272 0.214932i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −5.49405e9 + 9.51597e9i −0.330761 + 0.572896i −0.982661 0.185409i $$-0.940639\pi$$
0.651900 + 0.758305i $$0.273972\pi$$
$$360$$ 0 0
$$361$$ 3.36060e9 + 5.82073e9i 0.197874 + 0.342727i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2.48399e10 −1.39952
$$366$$ 0 0
$$367$$ −2.47539e9 + 1.42917e9i −0.136452 + 0.0787805i −0.566672 0.823944i $$-0.691769\pi$$
0.430220 + 0.902724i $$0.358436\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1.85109e9 2.56713e9i 0.0977086 0.135504i
$$372$$ 0 0
$$373$$ 8.91785e9 1.54462e10i 0.460707 0.797968i −0.538289 0.842760i $$-0.680929\pi$$
0.998996 + 0.0447919i $$0.0142625\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 1.14705e10i 0.567827i
$$378$$ 0 0
$$379$$ 3.25934e10 1.57969 0.789847 0.613303i $$-0.210160\pi$$
0.789847 + 0.613303i $$0.210160\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 1.90349e10 + 1.09898e10i 0.884619 + 0.510735i 0.872179 0.489187i $$-0.162707\pi$$
0.0124407 + 0.999923i $$0.496040\pi$$
$$384$$ 0 0
$$385$$ −2.03266e10 + 9.13749e9i −0.925170 + 0.415895i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 1.09555e10 + 1.89755e10i 0.478448 + 0.828695i 0.999695 0.0247103i $$-0.00786634\pi$$
−0.521247 + 0.853406i $$0.674533\pi$$
$$390$$ 0 0
$$391$$ 8.98159e9i 0.384279i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −2.86482e10 + 1.65401e10i −1.17682 + 0.679437i
$$396$$ 0 0
$$397$$ −4.10594e10 2.37057e10i −1.65292 0.954312i −0.975865 0.218376i $$-0.929924\pi$$
−0.677052 0.735936i $$-0.736743\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6.47336e8 + 1.12122e9i −0.0250353 + 0.0433623i −0.878272 0.478162i $$-0.841303\pi$$
0.853236 + 0.521524i $$0.174636\pi$$
$$402$$ 0 0
$$403$$ −2.27076e9 3.93308e9i −0.0860898 0.149112i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 9.41340e9 0.343059
$$408$$ 0 0
$$409$$ 1.05517e10 6.09204e9i 0.377077 0.217705i −0.299469 0.954106i $$-0.596809\pi$$
0.676546 + 0.736401i $$0.263476\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 1.69303e10 + 1.22080e10i 0.581921 + 0.419609i
$$414$$ 0 0
$$415$$ 2.40630e10 4.16783e10i 0.811255 1.40514i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 2.83249e9i 0.0918992i 0.998944 + 0.0459496i $$0.0146314\pi$$
−0.998944 + 0.0459496i $$0.985369\pi$$
$$420$$ 0 0
$$421$$ 1.47344e10 0.469033 0.234517 0.972112i $$-0.424649\pi$$
0.234517 + 0.972112i $$0.424649\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.17942e10 + 6.80938e9i 0.361503 + 0.208714i
$$426$$ 0 0
$$427$$ −3.67214e9 + 3.61864e10i −0.110461 + 1.08851i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.99404e10 3.45377e10i −0.577862 1.00089i −0.995724 0.0923761i $$-0.970554\pi$$
0.417862 0.908510i $$-0.362780\pi$$
$$432$$ 0 0
$$433$$ 3.77901e10i 1.07505i −0.843249 0.537523i $$-0.819360\pi$$
0.843249 0.537523i $$-0.180640\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −1.25634e10 + 7.25345e9i −0.344493 + 0.198893i
$$438$$ 0 0
$$439$$ 7.02545e9 + 4.05614e9i 0.189154 + 0.109208i 0.591587 0.806242i $$-0.298502\pi$$
−0.402432 + 0.915450i $$0.631835\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −2.85877e10 + 4.95154e10i −0.742274 + 1.28566i 0.209183 + 0.977876i $$0.432919\pi$$
−0.951457 + 0.307780i $$0.900414\pi$$
$$444$$ 0 0
$$445$$ −4.63456e9 8.02729e9i −0.118187 0.204705i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 6.27811e10 1.54470 0.772349 0.635199i $$-0.219082\pi$$
0.772349 + 0.635199i $$0.219082\pi$$
$$450$$ 0 0
$$451$$ 8.61279e9 4.97259e9i 0.208179 0.120192i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 3.69474e10 + 3.74937e9i 0.862062 + 0.0874809i
$$456$$ 0 0
$$457$$ −8.34859e9 + 1.44602e10i −0.191403 + 0.331519i −0.945715 0.324996i $$-0.894637\pi$$
0.754313 + 0.656515i $$0.227970\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 1.39906e10i 0.309766i 0.987933 + 0.154883i $$0.0495001\pi$$
−0.987933 + 0.154883i $$0.950500\pi$$
$$462$$ 0 0
$$463$$ −2.56476e10 −0.558114 −0.279057 0.960274i $$-0.590022\pi$$
−0.279057 + 0.960274i $$0.590022\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 3.36726e10 + 1.94409e10i 0.707960 + 0.408741i 0.810305 0.586008i $$-0.199301\pi$$
−0.102345 + 0.994749i $$0.532635\pi$$
$$468$$ 0 0
$$469$$ −5.59189e10 + 7.75493e10i −1.15576 + 1.60283i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 1.40628e9 + 2.43575e9i 0.0280949 + 0.0486618i
$$474$$ 0 0
$$475$$ 2.19968e10i 0.432100i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −6.40797e9 + 3.69965e9i −0.121725 + 0.0702778i −0.559626 0.828745i $$-0.689055\pi$$
0.437901 + 0.899023i $$0.355722\pi$$
$$480$$ 0 0
$$481$$ −1.35849e10 7.84322e9i −0.253790 0.146526i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −2.24885e9 + 3.89512e9i −0.0406437 + 0.0703970i
$$486$$ 0 0
$$487$$ −1.11183e10 1.92575e10i −0.197662 0.342361i 0.750108 0.661316i $$-0.230002\pi$$
−0.947770 + 0.318954i $$0.896668\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −3.62576e10 −0.623839 −0.311920 0.950109i $$-0.600972\pi$$
−0.311920 + 0.950109i $$0.600972\pi$$
$$492$$ 0 0
$$493$$ −4.47154e10 + 2.58164e10i −0.756953 + 0.437027i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 9.20166e9 + 2.04693e10i 0.150814 + 0.335489i
$$498$$ 0 0
$$499$$ 3.67859e10 6.37151e10i 0.593307 1.02764i −0.400476 0.916307i $$-0.631155\pi$$
0.993783 0.111331i $$-0.0355114\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 5.49729e10i 0.858770i −0.903122 0.429385i $$-0.858730\pi$$
0.903122 0.429385i $$-0.141270\pi$$
$$504$$ 0 0
$$505$$ 9.72691e10 1.49558
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 5.64437e10 + 3.25878e10i 0.840900 + 0.485494i 0.857570 0.514367i $$-0.171973\pi$$
−0.0166697 + 0.999861i $$0.505306\pi$$
$$510$$ 0 0
$$511$$ 6.62311e10 + 4.77576e10i 0.971355 + 0.700421i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −2.03228e10 3.52002e10i −0.288905 0.500398i
$$516$$ 0 0
$$517$$ 1.04658e11i 1.46491i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −6.65862e9 + 3.84435e9i −0.0903718 + 0.0521762i −0.544505 0.838758i $$-0.683282\pi$$
0.454133 + 0.890934i $$0.349949\pi$$
$$522$$ 0 0
$$523$$ 1.07896e11 + 6.22937e10i 1.44211 + 0.832602i 0.997990 0.0633652i $$-0.0201833\pi$$
0.444119 + 0.895968i $$0.353517\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −1.02215e10 + 1.77042e10i −0.132518 + 0.229528i
$$528$$ 0 0
$$529$$ 3.47165e10 + 6.01307e10i 0.443316 + 0.767846i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −1.65726e10 −0.205344
$$534$$ 0 0
$$535$$ 9.15513e9 5.28572e9i 0.111750 0.0645191i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 7.17651e10 + 1.47168e10i 0.850272 + 0.174365i
$$540$$ 0 0
$$541$$ −4.97811e10 + 8.62233e10i −0.581132 + 1.00655i 0.414213 + 0.910180i $$0.364057\pi$$
−0.995346 + 0.0963708i $$0.969277\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 1.31735e11i 1.49319i
$$546$$ 0 0
$$547$$ −2.34938e10 −0.262424 −0.131212 0.991354i $$-0.541887\pi$$
−0.131212 + 0.991354i $$0.541887\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 7.22235e10 + 4.16982e10i 0.783559 + 0.452388i
$$552$$ 0 0
$$553$$ 1.08186e11 + 1.09785e10i 1.15683 + 0.117393i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −1.24108e10 2.14962e10i −0.128938 0.223327i 0.794328 0.607490i $$-0.207823\pi$$
−0.923265 + 0.384163i $$0.874490\pi$$
$$558$$ 0 0
$$559$$ 4.68684e9i 0.0479991i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 1.47632e11 8.52355e10i 1.46942 0.848373i 0.470013 0.882660i $$-0.344249\pi$$
0.999412 + 0.0342868i $$0.0109160\pi$$
$$564$$ 0 0
$$565$$ −1.40294e10 8.09988e9i −0.137672 0.0794849i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 2.03247e10 3.52033e10i 0.193898 0.335842i −0.752640 0.658432i $$-0.771220\pi$$
0.946539 + 0.322590i $$0.104553\pi$$
$$570$$ 0 0
$$571$$ 4.24414e9 + 7.35107e9i 0.0399250 + 0.0691522i 0.885297 0.465025i $$-0.153955\pi$$
−0.845372 + 0.534177i $$0.820621\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.34616e10 0.123148
$$576$$ 0 0
$$577$$ −5.94782e10 + 3.43397e10i −0.536604 + 0.309809i −0.743702 0.668512i $$-0.766932\pi$$
0.207097 + 0.978320i $$0.433598\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −1.44291e11 + 6.48638e10i −1.26630 + 0.569243i
$$582$$ 0 0
$$583$$ −8.37556e9 + 1.45069e10i −0.0725003 + 0.125574i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1.43383e11i 1.20766i −0.797114 0.603829i $$-0.793641\pi$$
0.797114 0.603829i $$-0.206359\pi$$
$$588$$ 0 0
$$589$$ 3.30193e10 0.274351
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.30721e11 + 7.54720e10i 1.05713 + 0.610333i 0.924636 0.380851i $$-0.124369\pi$$
0.132491 + 0.991184i $$0.457702\pi$$
$$594$$ 0 0
$$595$$ −6.85408e10 1.52471e11i −0.546867 1.21652i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 8.29322e10 + 1.43643e11i 0.644193 + 1.11577i 0.984487 + 0.175456i $$0.0561399\pi$$
−0.340294 + 0.940319i $$0.610527\pi$$
$$600$$ 0 0
$$601$$ 7.04035e10i 0.539630i −0.962912 0.269815i $$-0.913037\pi$$
0.962912 0.269815i $$-0.0869625\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −3.34418e10 + 1.93076e10i −0.249614 + 0.144115i
$$606$$ 0 0
$$607$$ −5.15559e10 2.97658e10i −0.379773 0.219262i 0.297947 0.954583i $$-0.403698\pi$$
−0.677719 + 0.735321i $$0.737032\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 8.72009e10 1.51036e11i 0.625685 1.08372i
$$612$$ 0 0
$$613$$ 1.14654e11 + 1.98587e11i 0.811986 + 1.40640i 0.911472 + 0.411363i $$0.134947\pi$$
−0.0994852 + 0.995039i $$0.531720\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.93904e11 −1.33797 −0.668986 0.743275i $$-0.733272\pi$$
−0.668986 + 0.743275i $$0.733272\pi$$
$$618$$ 0 0
$$619$$ 1.77090e10 1.02243e10i 0.120623 0.0696418i −0.438474 0.898744i $$-0.644481\pi$$
0.559098 + 0.829102i $$0.311148\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −3.07621e9 + 3.03138e10i −0.0204203 + 0.201228i
$$624$$ 0 0
$$625$$ 9.39923e10 1.62799e11i 0.615988 1.06692i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 7.06105e10i 0.451094i
$$630$$ 0 0
$$631$$ −1.43159e11 −0.903030 −0.451515 0.892263i $$-0.649116\pi$$
−0.451515 + 0.892263i $$0.649116\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −1.12411e11 6.49006e10i −0.691377 0.399166i
$$636$$ 0 0
$$637$$ −9.13050e10 8.10328e10i −0.554545 0.492157i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.32450e11 + 2.29411e11i 0.784551 + 1.35888i 0.929267 + 0.369409i $$0.120440\pi$$
−0.144716 + 0.989473i $$0.546227\pi$$
$$642$$ 0 0
$$643$$ 1.18901e9i 0.00695572i 0.999994 + 0.00347786i $$0.00110704\pi$$
−0.999994 + 0.00347786i $$0.998893\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 8.24205e10 4.75855e10i 0.470347 0.271555i −0.246038 0.969260i $$-0.579129\pi$$
0.716385 + 0.697705i $$0.245796\pi$$
$$648$$ 0 0
$$649$$ −9.56733e10 5.52370e10i −0.539277 0.311352i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.66756e11 + 2.88829e11i −0.917124 + 1.58850i −0.113362 + 0.993554i $$0.536162\pi$$
−0.803762 + 0.594951i $$0.797171\pi$$
$$654$$ 0 0
$$655$$ −2.03751e11 3.52906e11i −1.10696 1.91732i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1.17025e11 −0.620493 −0.310246 0.950656i $$-0.600412\pi$$
−0.310246 + 0.950656i $$0.600412\pi$$
$$660$$ 0 0
$$661$$ 2.68769e10 1.55174e10i 0.140791 0.0812855i −0.427950 0.903802i $$-0.640764\pi$$
0.568741 + 0.822517i $$0.307431\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −1.57922e11 + 2.19008e11i −0.807523 + 1.11989i
$$666$$ 0 0
$$667$$ −2.55186e10 + 4.41995e10i −0.128930 + 0.223313i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 1.92509e11i 0.949645i
$$672$$ 0 0
$$673$$ −2.12193e11 −1.03436 −0.517179 0.855877i $$-0.673018\pi$$
−0.517179 + 0.855877i $$0.673018\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −9.30441e10 5.37191e10i −0.442929 0.255725i 0.261910 0.965092i $$-0.415648\pi$$
−0.704839 + 0.709367i $$0.748981\pi$$
$$678$$ 0 0
$$679$$ 1.34850e10 6.06196e9i 0.0634412 0.0285190i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −5.88995e10 1.02017e11i −0.270663 0.468802i 0.698369 0.715738i $$-0.253909\pi$$
−0.969032 + 0.246936i $$0.920576\pi$$
$$684$$ 0 0
$$685$$ 2.87654e11i 1.30650i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 2.41742e10 1.39570e10i 0.107269 0.0619320i
$$690$$ 0 0
$$691$$ 2.96618e11 + 1.71253e11i 1.30103 + 0.751148i 0.980580 0.196119i $$-0.0628339\pi$$
0.320446 + 0.947267i $$0.396167\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 1.77371e11 3.07215e11i 0.760227 1.31675i
$$696$$ 0 0
$$697$$ 3.72997e10 + 6.46050e10i 0.158043 + 0.273738i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.15900e11 0.479967 0.239984 0.970777i $$-0.422858\pi$$
0.239984 + 0.970777i $$0.422858\pi$$
$$702$$ 0 0
$$703$$ 9.87691e10 5.70244e10i 0.404390 0.233474i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −2.59351e11 1.87011e11i −1.03803 0.748498i
$$708$$ 0 0
$$709$$ −7.71407e10 + 1.33612e11i −0.305280 + 0.528761i −0.977324 0.211751i $$-0.932083\pi$$
0.672044 + 0.740512i $$0.265417\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 2.02073e10i 0.0781897i
$$714$$ 0 0
$$715$$ −1.96558e11 −0.752084
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.82639e11 1.05447e11i −0.683404 0.394564i 0.117732 0.993045i $$-0.462438\pi$$
−0.801136 + 0.598482i $$0.795771\pi$$
$$720$$ 0 0
$$721$$ −1.34893e10 + 1.32928e11i −0.0499172 + 0.491898i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −3.86938e10 6.70195e10i −0.140052 0.242577i
$$726$$ 0 0
$$727$$ 2.28475e10i 0.0817900i −0.999163 0.0408950i $$-0.986979\pi$$
0.999163 0.0408950i $$-0.0130209\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1.82707e10 + 1.05486e10i −0.0639861 + 0.0369424i
$$732$$ 0 0
$$733$$ 3.90685e11 + 2.25562e11i 1.35335 + 0.781358i 0.988717 0.149793i $$-0.0478609\pi$$
0.364634 + 0.931151i $$0.381194\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 2.53014e11 4.38233e11i 0.857579 1.48537i
$$738$$ 0 0
$$739$$ 8.06607e10 + 1.39708e11i 0.270448 + 0.468430i 0.968977 0.247152i $$-0.0794948\pi$$
−0.698528 + 0.715582i $$0.746161\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.11855e11 0.695159 0.347579 0.937651i $$-0.387004\pi$$
0.347579 + 0.937651i $$0.387004\pi$$
$$744$$ 0 0
$$745$$ 2.03129e11 1.17276e11i 0.659395 0.380702i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −3.45729e10 3.50841e9i −0.109852 0.0111477i
$$750$$ 0 0
$$751$$ −2.80633e11 + 4.86071e11i −0.882224 + 1.52806i −0.0333617 + 0.999443i $$0.510621\pi$$
−0.848862 + 0.528614i $$0.822712\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 6.02882e11i 1.85543i
$$756$$ 0 0
$$757$$ −2.12454e11 −0.646967 −0.323483 0.946234i $$-0.604854\pi$$
−0.323483 + 0.946234i $$0.604854\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −3.11683e11 1.79950e11i −0.929338 0.536554i −0.0427362 0.999086i $$-0.513607\pi$$
−0.886602 + 0.462533i $$0.846941\pi$$
$$762$$ 0 0
$$763$$ 2.53277e11 3.51248e11i 0.747304 1.03637i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 9.20467e10 + 1.59429e11i 0.265966 + 0.460667i
$$768$$ 0 0
$$769$$ 1.74232e11i 0.498222i −0.968475 0.249111i $$-0.919862\pi$$
0.968475 0.249111i $$-0.0801385\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.44377e11 + 1.41091e11i −0.684450 + 0.395168i −0.801530 0.597955i $$-0.795980\pi$$
0.117079 + 0.993123i $$0.462647\pi$$
$$774$$ 0 0
$$775$$ −2.65352e10 1.53201e10i −0.0735555 0.0424673i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 6.02458e10 1.04349e11i 0.163598 0.283360i
$$780$$ 0 0
$$781$$ −5.93912e10 1.02869e11i −0.159631 0.276490i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −7.72175e11 −2.03347
$$786$$ 0 0
$$787$$ 5.01252e11 2.89398e11i 1.30664 0.754391i 0.325110 0.945676i $$-0.394599\pi$$
0.981535 + 0.191285i $$0.0612654\pi$$
$$788$$ 0 0
$$789$$