# Properties

 Label 25.9.c.a.7.1 Level $25$ Weight $9$ Character 25.7 Analytic conductor $10.184$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 25.c (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.1844652515$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(i, \sqrt{141})$$ Defining polynomial: $$x^{4} + 71 x^{2} + 1225$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 7.1 Root $$6.43717i$$ of defining polynomial Character $$\chi$$ $$=$$ 25.7 Dual form 25.9.c.a.18.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-11.8743 - 11.8743i) q^{2} +(-11.8743 + 11.8743i) q^{3} +26.0000i q^{4} +282.000 q^{6} +(-2742.97 - 2742.97i) q^{7} +(-2731.10 + 2731.10i) q^{8} +6279.00i q^{9} +O(q^{10})$$ $$q+(-11.8743 - 11.8743i) q^{2} +(-11.8743 + 11.8743i) q^{3} +26.0000i q^{4} +282.000 q^{6} +(-2742.97 - 2742.97i) q^{7} +(-2731.10 + 2731.10i) q^{8} +6279.00i q^{9} +12132.0 q^{11} +(-308.733 - 308.733i) q^{12} +(2422.37 - 2422.37i) q^{13} +65142.0i q^{14} +71516.0 q^{16} +(76993.2 + 76993.2i) q^{17} +(74559.0 - 74559.0i) q^{18} +168380. i q^{19} +65142.0 q^{21} +(-144060. - 144060. i) q^{22} +(-221350. + 221350. i) q^{23} -64860.0i q^{24} -57528.0 q^{26} +(-152467. - 152467. i) q^{27} +(71317.3 - 71317.3i) q^{28} -666630. i q^{29} -1.04281e6 q^{31} +(-150044. - 150044. i) q^{32} +(-144060. + 144060. i) q^{33} -1.82849e6i q^{34} -163254. q^{36} +(2.07639e6 + 2.07639e6i) q^{37} +(1.99940e6 - 1.99940e6i) q^{38} +57528.0i q^{39} -1.32113e6 q^{41} +(-773518. - 773518. i) q^{42} +(-2.78134e6 + 2.78134e6i) q^{43} +315432. i q^{44} +5.25676e6 q^{46} +(-3.63024e6 - 3.63024e6i) q^{47} +(-849205. + 849205. i) q^{48} +9.28300e6i q^{49} -1.82849e6 q^{51} +(62981.5 + 62981.5i) q^{52} +(3.14105e6 - 3.14105e6i) q^{53} +3.62088e6i q^{54} +1.49827e7 q^{56} +(-1.99940e6 - 1.99940e6i) q^{57} +(-7.91579e6 + 7.91579e6i) q^{58} +6.49854e6i q^{59} -1.43940e7 q^{61} +(1.23827e7 + 1.23827e7i) q^{62} +(1.72231e7 - 1.72231e7i) q^{63} -1.47447e7i q^{64} +3.42122e6 q^{66} +(1.14565e7 + 1.14565e7i) q^{67} +(-2.00182e6 + 2.00182e6i) q^{68} -5.25676e6i q^{69} -2.30655e7 q^{71} +(-1.71486e7 - 1.71486e7i) q^{72} +(-1.74329e7 + 1.74329e7i) q^{73} -4.93116e7i q^{74} -4.37788e6 q^{76} +(-3.32777e7 - 3.32777e7i) q^{77} +(683107. - 683107. i) q^{78} -2.76068e6i q^{79} -3.75756e7 q^{81} +(1.56875e7 + 1.56875e7i) q^{82} +(1.15239e7 - 1.15239e7i) q^{83} +1.69369e6i q^{84} +6.60531e7 q^{86} +(7.91579e6 + 7.91579e6i) q^{87} +(-3.31337e7 + 3.31337e7i) q^{88} +2.61305e7i q^{89} -1.32890e7 q^{91} +(-5.75509e6 - 5.75509e6i) q^{92} +(1.23827e7 - 1.23827e7i) q^{93} +8.62133e7i q^{94} +3.56335e6 q^{96} +(8.09308e7 + 8.09308e7i) q^{97} +(1.10230e8 - 1.10230e8i) q^{98} +7.61768e7i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 1128q^{6} + O(q^{10})$$ $$4q + 1128q^{6} + 48528q^{11} + 286064q^{16} + 260568q^{21} - 230112q^{26} - 4171232q^{31} - 653016q^{36} - 5284512q^{41} + 21027048q^{46} - 7313952q^{51} + 59930640q^{56} - 57575872q^{61} + 13684896q^{66} - 92261952q^{71} - 17511520q^{76} - 150302556q^{81} + 264212568q^{86} - 53155872q^{91} + 14253408q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −11.8743 11.8743i −0.742146 0.742146i 0.230844 0.972991i $$-0.425851\pi$$
−0.972991 + 0.230844i $$0.925851\pi$$
$$3$$ −11.8743 + 11.8743i −0.146597 + 0.146597i −0.776596 0.629999i $$-0.783055\pi$$
0.629999 + 0.776596i $$0.283055\pi$$
$$4$$ 26.0000i 0.101562i
$$5$$ 0 0
$$6$$ 282.000 0.217593
$$7$$ −2742.97 2742.97i −1.14243 1.14243i −0.988005 0.154425i $$-0.950648\pi$$
−0.154425 0.988005i $$-0.549352\pi$$
$$8$$ −2731.10 + 2731.10i −0.666772 + 0.666772i
$$9$$ 6279.00i 0.957019i
$$10$$ 0 0
$$11$$ 12132.0 0.828632 0.414316 0.910133i $$-0.364021\pi$$
0.414316 + 0.910133i $$0.364021\pi$$
$$12$$ −308.733 308.733i −0.0148887 0.0148887i
$$13$$ 2422.37 2422.37i 0.0848138 0.0848138i −0.663427 0.748241i $$-0.730899\pi$$
0.748241 + 0.663427i $$0.230899\pi$$
$$14$$ 65142.0i 1.69570i
$$15$$ 0 0
$$16$$ 71516.0 1.09125
$$17$$ 76993.2 + 76993.2i 0.921843 + 0.921843i 0.997160 0.0753168i $$-0.0239968\pi$$
−0.0753168 + 0.997160i $$0.523997\pi$$
$$18$$ 74559.0 74559.0i 0.710248 0.710248i
$$19$$ 168380.i 1.29204i 0.763320 + 0.646020i $$0.223568\pi$$
−0.763320 + 0.646020i $$0.776432\pi$$
$$20$$ 0 0
$$21$$ 65142.0 0.334953
$$22$$ −144060. 144060.i −0.614966 0.614966i
$$23$$ −221350. + 221350.i −0.790983 + 0.790983i −0.981654 0.190671i $$-0.938934\pi$$
0.190671 + 0.981654i $$0.438934\pi$$
$$24$$ 64860.0i 0.195493i
$$25$$ 0 0
$$26$$ −57528.0 −0.125888
$$27$$ −152467. 152467.i −0.286893 0.286893i
$$28$$ 71317.3 71317.3i 0.116028 0.116028i
$$29$$ 666630.i 0.942525i −0.881993 0.471262i $$-0.843798\pi$$
0.881993 0.471262i $$-0.156202\pi$$
$$30$$ 0 0
$$31$$ −1.04281e6 −1.12917 −0.564583 0.825376i $$-0.690963\pi$$
−0.564583 + 0.825376i $$0.690963\pi$$
$$32$$ −150044. 150044.i −0.143093 0.143093i
$$33$$ −144060. + 144060.i −0.121475 + 0.121475i
$$34$$ 1.82849e6i 1.36828i
$$35$$ 0 0
$$36$$ −163254. −0.0971972
$$37$$ 2.07639e6 + 2.07639e6i 1.10791 + 1.10791i 0.993425 + 0.114481i $$0.0365205\pi$$
0.114481 + 0.993425i $$0.463480\pi$$
$$38$$ 1.99940e6 1.99940e6i 0.958883 0.958883i
$$39$$ 57528.0i 0.0248669i
$$40$$ 0 0
$$41$$ −1.32113e6 −0.467530 −0.233765 0.972293i $$-0.575105\pi$$
−0.233765 + 0.972293i $$0.575105\pi$$
$$42$$ −773518. 773518.i −0.248584 0.248584i
$$43$$ −2.78134e6 + 2.78134e6i −0.813542 + 0.813542i −0.985163 0.171621i $$-0.945100\pi$$
0.171621 + 0.985163i $$0.445100\pi$$
$$44$$ 315432.i 0.0841579i
$$45$$ 0 0
$$46$$ 5.25676e6 1.17405
$$47$$ −3.63024e6 3.63024e6i −0.743949 0.743949i 0.229386 0.973336i $$-0.426328\pi$$
−0.973336 + 0.229386i $$0.926328\pi$$
$$48$$ −849205. + 849205.i −0.159973 + 0.159973i
$$49$$ 9.28300e6i 1.61029i
$$50$$ 0 0
$$51$$ −1.82849e6 −0.270278
$$52$$ 62981.5 + 62981.5i 0.00861390 + 0.00861390i
$$53$$ 3.14105e6 3.14105e6i 0.398081 0.398081i −0.479475 0.877556i $$-0.659173\pi$$
0.877556 + 0.479475i $$0.159173\pi$$
$$54$$ 3.62088e6i 0.425833i
$$55$$ 0 0
$$56$$ 1.49827e7 1.52348
$$57$$ −1.99940e6 1.99940e6i −0.189409 0.189409i
$$58$$ −7.91579e6 + 7.91579e6i −0.699491 + 0.699491i
$$59$$ 6.49854e6i 0.536300i 0.963377 + 0.268150i $$0.0864123\pi$$
−0.963377 + 0.268150i $$0.913588\pi$$
$$60$$ 0 0
$$61$$ −1.43940e7 −1.03959 −0.519794 0.854292i $$-0.673991\pi$$
−0.519794 + 0.854292i $$0.673991\pi$$
$$62$$ 1.23827e7 + 1.23827e7i 0.838006 + 0.838006i
$$63$$ 1.72231e7 1.72231e7i 1.09333 1.09333i
$$64$$ 1.47447e7i 0.878855i
$$65$$ 0 0
$$66$$ 3.42122e6 0.180304
$$67$$ 1.14565e7 + 1.14565e7i 0.568528 + 0.568528i 0.931716 0.363188i $$-0.118312\pi$$
−0.363188 + 0.931716i $$0.618312\pi$$
$$68$$ −2.00182e6 + 2.00182e6i −0.0936247 + 0.0936247i
$$69$$ 5.25676e6i 0.231911i
$$70$$ 0 0
$$71$$ −2.30655e7 −0.907673 −0.453836 0.891085i $$-0.649945\pi$$
−0.453836 + 0.891085i $$0.649945\pi$$
$$72$$ −1.71486e7 1.71486e7i −0.638113 0.638113i
$$73$$ −1.74329e7 + 1.74329e7i −0.613873 + 0.613873i −0.943953 0.330080i $$-0.892924\pi$$
0.330080 + 0.943953i $$0.392924\pi$$
$$74$$ 4.93116e7i 1.64446i
$$75$$ 0 0
$$76$$ −4.37788e6 −0.131223
$$77$$ −3.32777e7 3.32777e7i −0.946653 0.946653i
$$78$$ 683107. 683107.i 0.0184548 0.0184548i
$$79$$ 2.76068e6i 0.0708774i −0.999372 0.0354387i $$-0.988717\pi$$
0.999372 0.0354387i $$-0.0112828\pi$$
$$80$$ 0 0
$$81$$ −3.75756e7 −0.872904
$$82$$ 1.56875e7 + 1.56875e7i 0.346976 + 0.346976i
$$83$$ 1.15239e7 1.15239e7i 0.242822 0.242822i −0.575195 0.818017i $$-0.695074\pi$$
0.818017 + 0.575195i $$0.195074\pi$$
$$84$$ 1.69369e6i 0.0340187i
$$85$$ 0 0
$$86$$ 6.60531e7 1.20753
$$87$$ 7.91579e6 + 7.91579e6i 0.138171 + 0.138171i
$$88$$ −3.31337e7 + 3.31337e7i −0.552509 + 0.552509i
$$89$$ 2.61305e7i 0.416474i 0.978078 + 0.208237i $$0.0667725\pi$$
−0.978078 + 0.208237i $$0.933227\pi$$
$$90$$ 0 0
$$91$$ −1.32890e7 −0.193787
$$92$$ −5.75509e6 5.75509e6i −0.0803343 0.0803343i
$$93$$ 1.23827e7 1.23827e7i 0.165532 0.165532i
$$94$$ 8.62133e7i 1.10424i
$$95$$ 0 0
$$96$$ 3.56335e6 0.0419540
$$97$$ 8.09308e7 + 8.09308e7i 0.914170 + 0.914170i 0.996597 0.0824271i $$-0.0262672\pi$$
−0.0824271 + 0.996597i $$0.526267\pi$$
$$98$$ 1.10230e8 1.10230e8i 1.19507 1.19507i
$$99$$ 7.61768e7i 0.793016i
$$100$$ 0 0
$$101$$ 1.80720e8 1.73668 0.868341 0.495968i $$-0.165187\pi$$
0.868341 + 0.495968i $$0.165187\pi$$
$$102$$ 2.17121e7 + 2.17121e7i 0.200586 + 0.200586i
$$103$$ −7.33591e7 + 7.33591e7i −0.651786 + 0.651786i −0.953423 0.301637i $$-0.902467\pi$$
0.301637 + 0.953423i $$0.402467\pi$$
$$104$$ 1.32314e7i 0.113103i
$$105$$ 0 0
$$106$$ −7.45958e7 −0.590868
$$107$$ −5.06569e7 5.06569e7i −0.386459 0.386459i 0.486963 0.873422i $$-0.338105\pi$$
−0.873422 + 0.486963i $$0.838105\pi$$
$$108$$ 3.96413e6 3.96413e6i 0.0291375 0.0291375i
$$109$$ 3.65622e7i 0.259016i 0.991578 + 0.129508i $$0.0413398\pi$$
−0.991578 + 0.129508i $$0.958660\pi$$
$$110$$ 0 0
$$111$$ −4.93116e7 −0.324831
$$112$$ −1.96166e8 1.96166e8i −1.24667 1.24667i
$$113$$ −1.29733e8 + 1.29733e8i −0.795677 + 0.795677i −0.982411 0.186733i $$-0.940210\pi$$
0.186733 + 0.982411i $$0.440210\pi$$
$$114$$ 4.74832e7i 0.281138i
$$115$$ 0 0
$$116$$ 1.73324e7 0.0957252
$$117$$ 1.52100e7 + 1.52100e7i 0.0811684 + 0.0811684i
$$118$$ 7.71659e7 7.71659e7i 0.398013 0.398013i
$$119$$ 4.22381e8i 2.10628i
$$120$$ 0 0
$$121$$ −6.71735e7 −0.313369
$$122$$ 1.70919e8 + 1.70919e8i 0.771526 + 0.771526i
$$123$$ 1.56875e7 1.56875e7i 0.0685384 0.0685384i
$$124$$ 2.71130e7i 0.114681i
$$125$$ 0 0
$$126$$ −4.09027e8 −1.62282
$$127$$ −5.09023e7 5.09023e7i −0.195669 0.195669i 0.602471 0.798141i $$-0.294183\pi$$
−0.798141 + 0.602471i $$0.794183\pi$$
$$128$$ −2.13495e8 + 2.13495e8i −0.795333 + 0.795333i
$$129$$ 6.60531e7i 0.238525i
$$130$$ 0 0
$$131$$ 3.84564e8 1.30582 0.652911 0.757435i $$-0.273548\pi$$
0.652911 + 0.757435i $$0.273548\pi$$
$$132$$ −3.74555e6 3.74555e6i −0.0123373 0.0123373i
$$133$$ 4.61862e8 4.61862e8i 1.47606 1.47606i
$$134$$ 2.72076e8i 0.843862i
$$135$$ 0 0
$$136$$ −4.20552e8 −1.22932
$$137$$ 1.62634e8 + 1.62634e8i 0.461668 + 0.461668i 0.899202 0.437534i $$-0.144148\pi$$
−0.437534 + 0.899202i $$0.644148\pi$$
$$138$$ −6.24206e7 + 6.24206e7i −0.172112 + 0.172112i
$$139$$ 9.16665e7i 0.245557i −0.992434 0.122778i $$-0.960820\pi$$
0.992434 0.122778i $$-0.0391804\pi$$
$$140$$ 0 0
$$141$$ 8.62133e7 0.218121
$$142$$ 2.73887e8 + 2.73887e8i 0.673626 + 0.673626i
$$143$$ 2.93881e7 2.93881e7i 0.0702794 0.0702794i
$$144$$ 4.49049e8i 1.04434i
$$145$$ 0 0
$$146$$ 4.14009e8 0.911167
$$147$$ −1.10230e8 1.10230e8i −0.236063 0.236063i
$$148$$ −5.39863e7 + 5.39863e7i −0.112522 + 0.112522i
$$149$$ 1.45300e8i 0.294794i 0.989077 + 0.147397i $$0.0470896\pi$$
−0.989077 + 0.147397i $$0.952910\pi$$
$$150$$ 0 0
$$151$$ −2.35910e7 −0.0453774 −0.0226887 0.999743i $$-0.507223\pi$$
−0.0226887 + 0.999743i $$0.507223\pi$$
$$152$$ −4.59862e8 4.59862e8i −0.861497 0.861497i
$$153$$ −4.83441e8 + 4.83441e8i −0.882221 + 0.882221i
$$154$$ 7.90303e8i 1.40511i
$$155$$ 0 0
$$156$$ −1.49573e6 −0.00252554
$$157$$ −6.67495e8 6.67495e8i −1.09863 1.09863i −0.994572 0.104054i $$-0.966819\pi$$
−0.104054 0.994572i $$-0.533181\pi$$
$$158$$ −3.27813e7 + 3.27813e7i −0.0526014 + 0.0526014i
$$159$$ 7.45958e7i 0.116715i
$$160$$ 0 0
$$161$$ 1.21431e9 1.80729
$$162$$ 4.46186e8 + 4.46186e8i 0.647822 + 0.647822i
$$163$$ 2.57869e8 2.57869e8i 0.365300 0.365300i −0.500460 0.865760i $$-0.666836\pi$$
0.865760 + 0.500460i $$0.166836\pi$$
$$164$$ 3.43493e7i 0.0474835i
$$165$$ 0 0
$$166$$ −2.73678e8 −0.360419
$$167$$ 4.92455e8 + 4.92455e8i 0.633142 + 0.633142i 0.948855 0.315713i $$-0.102244\pi$$
−0.315713 + 0.948855i $$0.602244\pi$$
$$168$$ −1.77909e8 + 1.77909e8i −0.223337 + 0.223337i
$$169$$ 8.03995e8i 0.985613i
$$170$$ 0 0
$$171$$ −1.05726e9 −1.23651
$$172$$ −7.23148e7 7.23148e7i −0.0826254 0.0826254i
$$173$$ 3.51863e8 3.51863e8i 0.392816 0.392816i −0.482874 0.875690i $$-0.660407\pi$$
0.875690 + 0.482874i $$0.160407\pi$$
$$174$$ 1.87990e8i 0.205086i
$$175$$ 0 0
$$176$$ 8.67632e8 0.904243
$$177$$ −7.71659e7 7.71659e7i −0.0786199 0.0786199i
$$178$$ 3.10283e8 3.10283e8i 0.309085 0.309085i
$$179$$ 1.16205e9i 1.13191i −0.824436 0.565955i $$-0.808508\pi$$
0.824436 0.565955i $$-0.191492\pi$$
$$180$$ 0 0
$$181$$ −4.84017e8 −0.450968 −0.225484 0.974247i $$-0.572396\pi$$
−0.225484 + 0.974247i $$0.572396\pi$$
$$182$$ 1.57798e8 + 1.57798e8i 0.143819 + 0.143819i
$$183$$ 1.70919e8 1.70919e8i 0.152400 0.152400i
$$184$$ 1.20906e9i 1.05481i
$$185$$ 0 0
$$186$$ −2.94072e8 −0.245698
$$187$$ 9.34082e8 + 9.34082e8i 0.763868 + 0.763868i
$$188$$ 9.43861e7 9.43861e7i 0.0755574 0.0755574i
$$189$$ 8.36423e8i 0.655509i
$$190$$ 0 0
$$191$$ −1.49354e9 −1.12223 −0.561117 0.827736i $$-0.689628\pi$$
−0.561117 + 0.827736i $$0.689628\pi$$
$$192$$ 1.75084e8 + 1.75084e8i 0.128837 + 0.128837i
$$193$$ −8.77896e8 + 8.77896e8i −0.632723 + 0.632723i −0.948750 0.316027i $$-0.897651\pi$$
0.316027 + 0.948750i $$0.397651\pi$$
$$194$$ 1.92200e9i 1.35690i
$$195$$ 0 0
$$196$$ −2.41358e8 −0.163545
$$197$$ −2.10520e8 2.10520e8i −0.139775 0.139775i 0.633757 0.773532i $$-0.281512\pi$$
−0.773532 + 0.633757i $$0.781512\pi$$
$$198$$ 9.04550e8 9.04550e8i 0.588534 0.588534i
$$199$$ 1.44381e9i 0.920655i −0.887749 0.460327i $$-0.847732\pi$$
0.887749 0.460327i $$-0.152268\pi$$
$$200$$ 0 0
$$201$$ −2.72076e8 −0.166689
$$202$$ −2.14593e9 2.14593e9i −1.28887 1.28887i
$$203$$ −1.82855e9 + 1.82855e9i −1.07677 + 1.07677i
$$204$$ 4.75407e7i 0.0274502i
$$205$$ 0 0
$$206$$ 1.74218e9 0.967441
$$207$$ −1.38985e9 1.38985e9i −0.756986 0.756986i
$$208$$ 1.73238e8 1.73238e8i 0.0925528 0.0925528i
$$209$$ 2.04279e9i 1.07063i
$$210$$ 0 0
$$211$$ −1.57176e9 −0.792968 −0.396484 0.918042i $$-0.629770\pi$$
−0.396484 + 0.918042i $$0.629770\pi$$
$$212$$ 8.16673e7 + 8.16673e7i 0.0404301 + 0.0404301i
$$213$$ 2.73887e8 2.73887e8i 0.133062 0.133062i
$$214$$ 1.20303e9i 0.573618i
$$215$$ 0 0
$$216$$ 8.32802e8 0.382584
$$217$$ 2.86039e9 + 2.86039e9i 1.28999 + 1.28999i
$$218$$ 4.34153e8 4.34153e8i 0.192228 0.192228i
$$219$$ 4.14009e8i 0.179984i
$$220$$ 0 0
$$221$$ 3.73012e8 0.156370
$$222$$ 5.85543e8 + 5.85543e8i 0.241072 + 0.241072i
$$223$$ 4.52258e8 4.52258e8i 0.182880 0.182880i −0.609729 0.792610i $$-0.708722\pi$$
0.792610 + 0.609729i $$0.208722\pi$$
$$224$$ 8.23134e8i 0.326948i
$$225$$ 0 0
$$226$$ 3.08099e9 1.18102
$$227$$ −1.41755e9 1.41755e9i −0.533871 0.533871i 0.387851 0.921722i $$-0.373217\pi$$
−0.921722 + 0.387851i $$0.873217\pi$$
$$228$$ 5.19844e7 5.19844e7i 0.0192369 0.0192369i
$$229$$ 5.09083e9i 1.85117i 0.378536 + 0.925586i $$0.376428\pi$$
−0.378536 + 0.925586i $$0.623572\pi$$
$$230$$ 0 0
$$231$$ 7.90303e8 0.277553
$$232$$ 1.82063e9 + 1.82063e9i 0.628449 + 0.628449i
$$233$$ 3.23753e9 3.23753e9i 1.09848 1.09848i 0.103887 0.994589i $$-0.466872\pi$$
0.994589 0.103887i $$-0.0331281\pi$$
$$234$$ 3.61218e8i 0.120478i
$$235$$ 0 0
$$236$$ −1.68962e8 −0.0544680
$$237$$ 3.27813e7 + 3.27813e7i 0.0103904 + 0.0103904i
$$238$$ −5.01549e9 + 5.01549e9i −1.56317 + 1.56317i
$$239$$ 6.45678e8i 0.197890i 0.995093 + 0.0989452i $$0.0315468\pi$$
−0.995093 + 0.0989452i $$0.968453\pi$$
$$240$$ 0 0
$$241$$ 1.04063e9 0.308482 0.154241 0.988033i $$-0.450707\pi$$
0.154241 + 0.988033i $$0.450707\pi$$
$$242$$ 7.97641e8 + 7.97641e8i 0.232566 + 0.232566i
$$243$$ 1.44652e9 1.44652e9i 0.414858 0.414858i
$$244$$ 3.74243e8i 0.105583i
$$245$$ 0 0
$$246$$ −3.72558e8 −0.101731
$$247$$ 4.07878e8 + 4.07878e8i 0.109583 + 0.109583i
$$248$$ 2.84801e9 2.84801e9i 0.752896 0.752896i
$$249$$ 2.73678e8i 0.0711938i
$$250$$ 0 0
$$251$$ −4.15092e9 −1.04580 −0.522901 0.852394i $$-0.675150\pi$$
−0.522901 + 0.852394i $$0.675150\pi$$
$$252$$ 4.47801e8 + 4.47801e8i 0.111041 + 0.111041i
$$253$$ −2.68541e9 + 2.68541e9i −0.655434 + 0.655434i
$$254$$ 1.20886e9i 0.290431i
$$255$$ 0 0
$$256$$ 1.29558e9 0.301651
$$257$$ −5.71495e9 5.71495e9i −1.31003 1.31003i −0.921392 0.388635i $$-0.872947\pi$$
−0.388635 0.921392i $$-0.627053\pi$$
$$258$$ −7.84338e8 + 7.84338e8i −0.177021 + 0.177021i
$$259$$ 1.13910e10i 2.53141i
$$260$$ 0 0
$$261$$ 4.18577e9 0.902014
$$262$$ −4.56645e9 4.56645e9i −0.969111 0.969111i
$$263$$ −1.59379e9 + 1.59379e9i −0.333127 + 0.333127i −0.853773 0.520646i $$-0.825691\pi$$
0.520646 + 0.853773i $$0.325691\pi$$
$$264$$ 7.86882e8i 0.161992i
$$265$$ 0 0
$$266$$ −1.09686e10 −2.19091
$$267$$ −3.10283e8 3.10283e8i −0.0610538 0.0610538i
$$268$$ −2.97868e8 + 2.97868e8i −0.0577411 + 0.0577411i
$$269$$ 2.62849e9i 0.501992i 0.967988 + 0.250996i $$0.0807581\pi$$
−0.967988 + 0.250996i $$0.919242\pi$$
$$270$$ 0 0
$$271$$ −2.04396e9 −0.378961 −0.189481 0.981884i $$-0.560680\pi$$
−0.189481 + 0.981884i $$0.560680\pi$$
$$272$$ 5.50625e9 + 5.50625e9i 1.00596 + 1.00596i
$$273$$ 1.57798e8 1.57798e8i 0.0284086 0.0284086i
$$274$$ 3.86235e9i 0.685250i
$$275$$ 0 0
$$276$$ 1.36676e8 0.0235535
$$277$$ 4.31300e9 + 4.31300e9i 0.732589 + 0.732589i 0.971132 0.238543i $$-0.0766697\pi$$
−0.238543 + 0.971132i $$0.576670\pi$$
$$278$$ −1.08848e9 + 1.08848e9i −0.182239 + 0.182239i
$$279$$ 6.54779e9i 1.08063i
$$280$$ 0 0
$$281$$ 5.50789e9 0.883405 0.441703 0.897162i $$-0.354375\pi$$
0.441703 + 0.897162i $$0.354375\pi$$
$$282$$ −1.02373e9 1.02373e9i −0.161878 0.161878i
$$283$$ 7.63368e9 7.63368e9i 1.19011 1.19011i 0.213078 0.977035i $$-0.431651\pi$$
0.977035 0.213078i $$-0.0683488\pi$$
$$284$$ 5.99703e8i 0.0921855i
$$285$$ 0 0
$$286$$ −6.97930e8 −0.104315
$$287$$ 3.62382e9 + 3.62382e9i 0.534120 + 0.534120i
$$288$$ 9.42127e8 9.42127e8i 0.136943 0.136943i
$$289$$ 4.88016e9i 0.699588i
$$290$$ 0 0
$$291$$ −1.92200e9 −0.268029
$$292$$ −4.53256e8 4.53256e8i −0.0623465 0.0623465i
$$293$$ −4.49841e9 + 4.49841e9i −0.610364 + 0.610364i −0.943041 0.332677i $$-0.892048\pi$$
0.332677 + 0.943041i $$0.392048\pi$$
$$294$$ 2.61781e9i 0.350387i
$$295$$ 0 0
$$296$$ −1.13417e10 −1.47744
$$297$$ −1.84972e9 1.84972e9i −0.237728 0.237728i
$$298$$ 1.72534e9 1.72534e9i 0.218781 0.218781i
$$299$$ 1.07238e9i 0.134173i
$$300$$ 0 0
$$301$$ 1.52583e10 1.85883
$$302$$ 2.80128e8 + 2.80128e8i 0.0336767 + 0.0336767i
$$303$$ −2.14593e9 + 2.14593e9i −0.254592 + 0.254592i
$$304$$ 1.20419e10i 1.40994i
$$305$$ 0 0
$$306$$ 1.14811e10 1.30947
$$307$$ 1.53928e9 + 1.53928e9i 0.173287 + 0.173287i 0.788422 0.615135i $$-0.210899\pi$$
−0.615135 + 0.788422i $$0.710899\pi$$
$$308$$ 8.65221e8 8.65221e8i 0.0961445 0.0961445i
$$309$$ 1.74218e9i 0.191100i
$$310$$ 0 0
$$311$$ −5.22581e8 −0.0558614 −0.0279307 0.999610i $$-0.508892\pi$$
−0.0279307 + 0.999610i $$0.508892\pi$$
$$312$$ −1.57115e8 1.57115e8i −0.0165805 0.0165805i
$$313$$ 3.27149e9 3.27149e9i 0.340854 0.340854i −0.515834 0.856688i $$-0.672518\pi$$
0.856688 + 0.515834i $$0.172518\pi$$
$$314$$ 1.58521e10i 1.63068i
$$315$$ 0 0
$$316$$ 7.17777e7 0.00719848
$$317$$ −3.24669e9 3.24669e9i −0.321517 0.321517i 0.527832 0.849349i $$-0.323005\pi$$
−0.849349 + 0.527832i $$0.823005\pi$$
$$318$$ 8.85776e8 8.85776e8i 0.0866194 0.0866194i
$$319$$ 8.08756e9i 0.781006i
$$320$$ 0 0
$$321$$ 1.20303e9 0.113307
$$322$$ −1.44192e10 1.44192e10i −1.34127 1.34127i
$$323$$ −1.29641e10 + 1.29641e10i −1.19106 + 1.19106i
$$324$$ 9.76967e8i 0.0886543i
$$325$$ 0 0
$$326$$ −6.12406e9 −0.542212
$$327$$ −4.34153e8 4.34153e8i −0.0379709 0.0379709i
$$328$$ 3.60813e9 3.60813e9i 0.311736 0.311736i
$$329$$ 1.99153e10i 1.69982i
$$330$$ 0 0
$$331$$ 8.55909e9 0.713043 0.356522 0.934287i $$-0.383963\pi$$
0.356522 + 0.934287i $$0.383963\pi$$
$$332$$ 2.99622e8 + 2.99622e8i 0.0246616 + 0.0246616i
$$333$$ −1.30377e10 + 1.30377e10i −1.06029 + 1.06029i
$$334$$ 1.16952e10i 0.939767i
$$335$$ 0 0
$$336$$ 4.65870e9 0.365517
$$337$$ 7.19609e9 + 7.19609e9i 0.557926 + 0.557926i 0.928717 0.370790i $$-0.120913\pi$$
−0.370790 + 0.928717i $$0.620913\pi$$
$$338$$ 9.54691e9 9.54691e9i 0.731469 0.731469i
$$339$$ 3.08099e9i 0.233288i
$$340$$ 0 0
$$341$$ −1.26513e10 −0.935663
$$342$$ 1.25542e10 + 1.25542e10i 0.917669 + 0.917669i
$$343$$ 9.65033e9 9.65033e9i 0.697213 0.697213i
$$344$$ 1.51922e10i 1.08489i
$$345$$ 0 0
$$346$$ −8.35628e9 −0.583053
$$347$$ 2.76044e9 + 2.76044e9i 0.190397 + 0.190397i 0.795868 0.605471i $$-0.207015\pi$$
−0.605471 + 0.795868i $$0.707015\pi$$
$$348$$ −2.05811e8 + 2.05811e8i −0.0140330 + 0.0140330i
$$349$$ 7.99627e9i 0.538996i −0.963001 0.269498i $$-0.913142\pi$$
0.963001 0.269498i $$-0.0868578\pi$$
$$350$$ 0 0
$$351$$ −7.38660e8 −0.0486649
$$352$$ −1.82034e9 1.82034e9i −0.118572 0.118572i
$$353$$ 1.99730e10 1.99730e10i 1.28630 1.28630i 0.349290 0.937015i $$-0.386423\pi$$
0.937015 0.349290i $$-0.113577\pi$$
$$354$$ 1.83259e9i 0.116695i
$$355$$ 0 0
$$356$$ −6.79393e8 −0.0422981
$$357$$ 5.01549e9 + 5.01549e9i 0.308774 + 0.308774i
$$358$$ −1.37986e10 + 1.37986e10i −0.840043 + 0.840043i
$$359$$ 1.92076e10i 1.15637i −0.815906 0.578184i $$-0.803762\pi$$
0.815906 0.578184i $$-0.196238\pi$$
$$360$$ 0 0
$$361$$ −1.13683e10 −0.669368
$$362$$ 5.74738e9 + 5.74738e9i 0.334685 + 0.334685i
$$363$$ 7.97641e8 7.97641e8i 0.0459389 0.0459389i
$$364$$ 3.45513e8i 0.0196815i
$$365$$ 0 0
$$366$$ −4.05910e9 −0.226207
$$367$$ −1.85651e10 1.85651e10i −1.02337 1.02337i −0.999720 0.0236511i $$-0.992471\pi$$
−0.0236511 0.999720i $$-0.507529\pi$$
$$368$$ −1.58300e10 + 1.58300e10i −0.863159 + 0.863159i
$$369$$ 8.29536e9i 0.447435i
$$370$$ 0 0
$$371$$ −1.72316e10 −0.909558
$$372$$ 3.21949e8 + 3.21949e8i 0.0168118 + 0.0168118i
$$373$$ 7.55571e9 7.55571e9i 0.390337 0.390337i −0.484470 0.874808i $$-0.660988\pi$$
0.874808 + 0.484470i $$0.160988\pi$$
$$374$$ 2.21832e10i 1.13380i
$$375$$ 0 0
$$376$$ 1.98291e10 0.992089
$$377$$ −1.61482e9 1.61482e9i −0.0799391 0.0799391i
$$378$$ 9.93198e9 9.93198e9i 0.486484 0.486484i
$$379$$ 1.95966e10i 0.949783i 0.880044 + 0.474892i $$0.157513\pi$$
−0.880044 + 0.474892i $$0.842487\pi$$
$$380$$ 0 0
$$381$$ 1.20886e9 0.0573690
$$382$$ 1.77348e10 + 1.77348e10i 0.832862 + 0.832862i
$$383$$ −1.07480e10 + 1.07480e10i −0.499497 + 0.499497i −0.911281 0.411784i $$-0.864906\pi$$
0.411784 + 0.911281i $$0.364906\pi$$
$$384$$ 5.07024e9i 0.233186i
$$385$$ 0 0
$$386$$ 2.08489e10 0.939146
$$387$$ −1.74640e10 1.74640e10i −0.778575 0.778575i
$$388$$ −2.10420e9 + 2.10420e9i −0.0928454 + 0.0928454i
$$389$$ 3.58035e10i 1.56361i 0.623526 + 0.781803i $$0.285700\pi$$
−0.623526 + 0.781803i $$0.714300\pi$$
$$390$$ 0 0
$$391$$ −3.40848e10 −1.45832
$$392$$ −2.53528e10 2.53528e10i −1.07370 1.07370i
$$393$$ −4.56645e9 + 4.56645e9i −0.191429 + 0.191429i
$$394$$ 4.99958e9i 0.207467i
$$395$$ 0 0
$$396$$ −1.98060e9 −0.0805407
$$397$$ −3.85643e9 3.85643e9i −0.155247 0.155247i 0.625210 0.780457i $$-0.285013\pi$$
−0.780457 + 0.625210i $$0.785013\pi$$
$$398$$ −1.71443e10 + 1.71443e10i −0.683261 + 0.683261i
$$399$$ 1.09686e10i 0.432773i
$$400$$ 0 0
$$401$$ 3.39784e10 1.31409 0.657046 0.753851i $$-0.271806\pi$$
0.657046 + 0.753851i $$0.271806\pi$$
$$402$$ 3.23073e9 + 3.23073e9i 0.123707 + 0.123707i
$$403$$ −2.52606e9 + 2.52606e9i −0.0957688 + 0.0957688i
$$404$$ 4.69871e9i 0.176382i
$$405$$ 0 0
$$406$$ 4.34256e10 1.59824
$$407$$ 2.51908e10 + 2.51908e10i 0.918047 + 0.918047i
$$408$$ 4.99378e9 4.99378e9i 0.180214 0.180214i
$$409$$ 1.10826e10i 0.396048i −0.980197 0.198024i $$-0.936548\pi$$
0.980197 0.198024i $$-0.0634523\pi$$
$$410$$ 0 0
$$411$$ −3.86235e9 −0.135358
$$412$$ −1.90734e9 1.90734e9i −0.0661970 0.0661970i
$$413$$ 1.78253e10 1.78253e10i 0.612685 0.612685i
$$414$$ 3.30072e10i 1.12359i
$$415$$ 0 0
$$416$$ −7.26924e8 −0.0242726
$$417$$ 1.08848e9 + 1.08848e9i 0.0359978 + 0.0359978i
$$418$$ 2.42567e10 2.42567e10i 0.794561 0.794561i
$$419$$ 3.54167e10i 1.14909i 0.818474 + 0.574543i $$0.194820\pi$$
−0.818474 + 0.574543i $$0.805180\pi$$
$$420$$ 0 0
$$421$$ −2.98731e10 −0.950938 −0.475469 0.879733i $$-0.657722\pi$$
−0.475469 + 0.879733i $$0.657722\pi$$
$$422$$ 1.86636e10 + 1.86636e10i 0.588498 + 0.588498i
$$423$$ 2.27943e10 2.27943e10i 0.711974 0.711974i
$$424$$ 1.71570e10i 0.530858i
$$425$$ 0 0
$$426$$ −6.50447e9 −0.197503
$$427$$ 3.94823e10 + 3.94823e10i 1.18766 + 1.18766i
$$428$$ 1.31708e9 1.31708e9i 0.0392498 0.0392498i
$$429$$ 6.97930e8i 0.0206055i
$$430$$ 0 0
$$431$$ 6.06834e10 1.75857 0.879287 0.476293i $$-0.158020\pi$$
0.879287 + 0.476293i $$0.158020\pi$$
$$432$$ −1.09038e10 1.09038e10i −0.313071 0.313071i
$$433$$ −4.29956e10 + 4.29956e10i −1.22313 + 1.22313i −0.256617 + 0.966513i $$0.582608\pi$$
−0.966513 + 0.256617i $$0.917392\pi$$
$$434$$ 6.79306e10i 1.91473i
$$435$$ 0 0
$$436$$ −9.50618e8 −0.0263063
$$437$$ −3.72708e10 3.72708e10i −1.02198 1.02198i
$$438$$ −4.91608e9 + 4.91608e9i −0.133574 + 0.133574i
$$439$$ 8.86294e9i 0.238627i 0.992857 + 0.119314i $$0.0380694\pi$$
−0.992857 + 0.119314i $$0.961931\pi$$
$$440$$ 0 0
$$441$$ −5.82880e10 −1.54108
$$442$$ −4.42927e9 4.42927e9i −0.116049 0.116049i
$$443$$ 1.68455e10 1.68455e10i 0.437390 0.437390i −0.453743 0.891133i $$-0.649912\pi$$
0.891133 + 0.453743i $$0.149912\pi$$
$$444$$ 1.28210e9i 0.0329907i
$$445$$ 0 0
$$446$$ −1.07405e10 −0.271448
$$447$$ −1.72534e9 1.72534e9i −0.0432159 0.0432159i
$$448$$ −4.04444e10 + 4.04444e10i −1.00403 + 1.00403i
$$449$$ 5.95055e10i 1.46410i −0.681250 0.732051i $$-0.738563\pi$$
0.681250 0.732051i $$-0.261437\pi$$
$$450$$ 0 0
$$451$$ −1.60279e10 −0.387410
$$452$$ −3.37306e9 3.37306e9i −0.0808110 0.0808110i
$$453$$ 2.80128e8 2.80128e8i 0.00665218 0.00665218i
$$454$$ 3.36650e10i 0.792421i
$$455$$ 0 0
$$456$$ 1.09211e10 0.252585
$$457$$ 2.91131e9 + 2.91131e9i 0.0667459 + 0.0667459i 0.739692 0.672946i $$-0.234971\pi$$
−0.672946 + 0.739692i $$0.734971\pi$$
$$458$$ 6.04503e10 6.04503e10i 1.37384 1.37384i
$$459$$ 2.34778e10i 0.528940i
$$460$$ 0 0
$$461$$ 4.79933e9 0.106262 0.0531309 0.998588i $$-0.483080\pi$$
0.0531309 + 0.998588i $$0.483080\pi$$
$$462$$ −9.38433e9 9.38433e9i −0.205985 0.205985i
$$463$$ −4.23409e10 + 4.23409e10i −0.921375 + 0.921375i −0.997127 0.0757516i $$-0.975864\pi$$
0.0757516 + 0.997127i $$0.475864\pi$$
$$464$$ 4.76747e10i 1.02853i
$$465$$ 0 0
$$466$$ −7.68872e10 −1.63046
$$467$$ −2.55795e10 2.55795e10i −0.537805 0.537805i 0.385079 0.922884i $$-0.374174\pi$$
−0.922884 + 0.385079i $$0.874174\pi$$
$$468$$ −3.95461e8 + 3.95461e8i −0.00824366 + 0.00824366i
$$469$$ 6.28496e10i 1.29901i
$$470$$ 0 0
$$471$$ 1.58521e10 0.322110
$$472$$ −1.77482e10 1.77482e10i −0.357590 0.357590i
$$473$$ −3.37432e10 + 3.37432e10i −0.674127 + 0.674127i
$$474$$ 7.78512e8i 0.0154224i
$$475$$ 0 0
$$476$$ 1.09819e10 0.213919
$$477$$ 1.97226e10 + 1.97226e10i 0.380971 + 0.380971i
$$478$$ 7.66701e9 7.66701e9i 0.146864 0.146864i
$$479$$ 4.66044e10i 0.885288i 0.896697 + 0.442644i $$0.145959\pi$$
−0.896697 + 0.442644i $$0.854041\pi$$
$$480$$ 0 0
$$481$$ 1.00596e10 0.187931
$$482$$ −1.23568e10 1.23568e10i −0.228938 0.228938i
$$483$$ −1.44192e10 + 1.44192e10i −0.264942 + 0.264942i
$$484$$ 1.74651e9i 0.0318266i
$$485$$ 0 0
$$486$$ −3.43529e10 −0.615770
$$487$$ 1.63896e10 + 1.63896e10i 0.291375 + 0.291375i 0.837623 0.546248i $$-0.183945\pi$$
−0.546248 + 0.837623i $$0.683945\pi$$
$$488$$ 3.93113e10 3.93113e10i 0.693168 0.693168i
$$489$$ 6.12406e9i 0.107104i
$$490$$ 0 0
$$491$$ 7.94765e10 1.36745 0.683727 0.729738i $$-0.260358\pi$$
0.683727 + 0.729738i $$0.260358\pi$$
$$492$$ 4.07876e8 + 4.07876e8i 0.00696093 + 0.00696093i
$$493$$ 5.13260e10 5.13260e10i 0.868860 0.868860i
$$494$$ 9.68656e9i 0.162653i
$$495$$ 0 0
$$496$$ −7.45775e10 −1.23220
$$497$$ 6.32680e10 + 6.32680e10i 1.03695 + 1.03695i
$$498$$ 3.24974e9 3.24974e9i 0.0528362 0.0528362i
$$499$$ 1.83615e10i 0.296146i 0.988976 + 0.148073i $$0.0473070\pi$$
−0.988976 + 0.148073i $$0.952693\pi$$
$$500$$ 0 0
$$501$$ −1.16952e10 −0.185633
$$502$$ 4.92894e10 + 4.92894e10i 0.776138 + 0.776138i
$$503$$ 6.21239e9 6.21239e9i 0.0970480 0.0970480i −0.656916 0.753964i $$-0.728139\pi$$
0.753964 + 0.656916i $$0.228139\pi$$
$$504$$ 9.40761e10i 1.45800i
$$505$$ 0 0
$$506$$ 6.37750e10 0.972856
$$507$$ −9.54691e9 9.54691e9i −0.144488 0.144488i
$$508$$ 1.32346e9 1.32346e9i 0.0198727 0.0198727i
$$509$$ 4.31615e10i 0.643021i −0.946906 0.321511i $$-0.895809\pi$$
0.946906 0.321511i $$-0.104191\pi$$
$$510$$ 0 0
$$511$$ 9.56360e10 1.40261
$$512$$ 3.92707e10 + 3.92707e10i 0.571463 + 0.571463i
$$513$$ 2.56723e10 2.56723e10i 0.370677 0.370677i
$$514$$ 1.35723e11i 1.94446i
$$515$$ 0 0
$$516$$ 1.71738e9 0.0242252
$$517$$ −4.40420e10 4.40420e10i −0.616460 0.616460i
$$518$$ −1.35261e11 + 1.35261e11i −1.87868 + 1.87868i
$$519$$ 8.35628e9i 0.115171i
$$520$$ 0 0
$$521$$ 2.90244e10 0.393923 0.196962 0.980411i $$-0.436893\pi$$
0.196962 + 0.980411i $$0.436893\pi$$
$$522$$ −4.97033e10 4.97033e10i −0.669426 0.669426i
$$523$$ 4.27429e10 4.27429e10i 0.571291 0.571291i −0.361198 0.932489i $$-0.617632\pi$$
0.932489 + 0.361198i $$0.117632\pi$$
$$524$$ 9.99868e9i 0.132623i
$$525$$ 0 0
$$526$$ 3.78505e10 0.494457
$$527$$ −8.02892e10 8.02892e10i −1.04091 1.04091i
$$528$$ −1.03026e10 + 1.03026e10i −0.132559 + 0.132559i
$$529$$ 1.96803e10i 0.251310i
$$530$$ 0 0
$$531$$ −4.08043e10 −0.513249
$$532$$ 1.20084e10 + 1.20084e10i 0.149913 + 0.149913i
$$533$$ −3.20026e9 + 3.20026e9i −0.0396530 + 0.0396530i
$$534$$ 7.36880e9i 0.0906217i
$$535$$ 0 0
$$536$$ −6.25775e10 −0.758157
$$537$$ 1.37986e10 + 1.37986e10i 0.165934 + 0.165934i
$$538$$ 3.12116e10 3.12116e10i 0.372552 0.372552i
$$539$$ 1.12621e11i 1.33434i
$$540$$ 0 0
$$541$$ −6.67715e9 −0.0779475 −0.0389738 0.999240i $$-0.512409\pi$$
−0.0389738 + 0.999240i $$0.512409\pi$$
$$542$$ 2.42707e10 + 2.42707e10i 0.281245 + 0.281245i
$$543$$ 5.74738e9 5.74738e9i 0.0661105 0.0661105i
$$544$$ 2.31048e10i 0.263819i
$$545$$ 0 0
$$546$$ −3.74749e9 −0.0421667
$$547$$ −7.25792e10 7.25792e10i −0.810705 0.810705i 0.174035 0.984740i $$-0.444319\pi$$
−0.984740 + 0.174035i $$0.944319\pi$$
$$548$$ −4.22849e9 + 4.22849e9i −0.0468881 + 0.0468881i
$$549$$ 9.03797e10i 0.994905i
$$550$$ 0 0
$$551$$ 1.12247e11 1.21778
$$552$$ 1.43567e10 + 1.43567e10i 0.154632 + 0.154632i
$$553$$ −7.57247e9 + 7.57247e9i −0.0809724 + 0.0809724i
$$554$$ 1.02428e11i 1.08738i
$$555$$ 0 0
$$556$$ 2.38333e9 0.0249393
$$557$$ 2.52569e10 + 2.52569e10i 0.262397 + 0.262397i 0.826027 0.563630i $$-0.190596\pi$$
−0.563630 + 0.826027i $$0.690596\pi$$
$$558$$ −7.77507e10 + 7.77507e10i −0.801987 + 0.801987i
$$559$$ 1.34748e10i 0.137999i
$$560$$ 0 0
$$561$$ −2.21832e10 −0.223961
$$562$$ −6.54026e10 6.54026e10i −0.655616 0.655616i
$$563$$ −1.77029e10 + 1.77029e10i −0.176202 + 0.176202i −0.789698 0.613496i $$-0.789763\pi$$
0.613496 + 0.789698i $$0.289763\pi$$
$$564$$ 2.24155e9i 0.0221529i
$$565$$ 0 0
$$566$$ −1.81290e11 −1.76648
$$567$$ 1.03069e11 + 1.03069e11i 0.997231 + 0.997231i
$$568$$ 6.29941e10 6.29941e10i 0.605211 0.605211i
$$569$$ 5.69768e10i 0.543562i −0.962359 0.271781i $$-0.912387\pi$$
0.962359 0.271781i $$-0.0876126\pi$$
$$570$$ 0 0
$$571$$ −1.40041e11 −1.31738 −0.658690 0.752415i $$-0.728889\pi$$
−0.658690 + 0.752415i $$0.728889\pi$$
$$572$$ 7.64092e8 + 7.64092e8i 0.00713775 + 0.00713775i
$$573$$ 1.77348e10 1.77348e10i 0.164516 0.164516i
$$574$$ 8.60609e10i 0.792790i
$$575$$ 0 0
$$576$$ 9.25822e10 0.841081
$$577$$ −4.33597e10 4.33597e10i −0.391186 0.391186i 0.483924 0.875110i $$-0.339211\pi$$
−0.875110 + 0.483924i $$0.839211\pi$$
$$578$$ 5.79487e10 5.79487e10i 0.519197 0.519197i
$$579$$ 2.08489e10i 0.185510i
$$580$$ 0 0
$$581$$ −6.32196e10 −0.554814
$$582$$ 2.28225e10 + 2.28225e10i 0.198917 + 0.198917i
$$583$$ 3.81072e10 3.81072e10i 0.329862 0.329862i
$$584$$ 9.52220e10i 0.818627i
$$585$$ 0 0
$$586$$ 1.06831e11 0.905959
$$587$$ 1.52268e11 + 1.52268e11i 1.28250 + 1.28250i 0.939241 + 0.343258i $$0.111530\pi$$
0.343258 + 0.939241i $$0.388470\pi$$
$$588$$ 2.86597e9 2.86597e9i 0.0239752 0.0239752i
$$589$$ 1.75588e11i 1.45893i
$$590$$ 0 0
$$591$$ 4.99958e9 0.0409811
$$592$$ 1.48495e11 + 1.48495e11i 1.20900 + 1.20900i
$$593$$ −5.29744e8 + 5.29744e8i −0.00428397 + 0.00428397i −0.709246 0.704962i $$-0.750964\pi$$
0.704962 + 0.709246i $$0.250964\pi$$
$$594$$ 4.39285e10i 0.352859i
$$595$$ 0 0
$$596$$ −3.77779e9 −0.0299401
$$597$$ 1.71443e10 + 1.71443e10i 0.134965 + 0.134965i
$$598$$ 1.27338e10 1.27338e10i 0.0995757 0.0995757i
$$599$$ 1.98446e11i 1.54147i 0.637157 + 0.770734i $$0.280110\pi$$
−0.637157 + 0.770734i $$0.719890\pi$$
$$600$$ 0 0
$$601$$ −2.01430e11 −1.54393 −0.771964 0.635666i $$-0.780726\pi$$
−0.771964 + 0.635666i $$0.780726\pi$$
$$602$$ −1.81182e11 1.81182e11i −1.37952 1.37952i
$$603$$ −7.19352e10 + 7.19352e10i −0.544092 + 0.544092i
$$604$$ 6.13367e8i 0.00460864i
$$605$$ 0 0
$$606$$ 5.09630e10 0.377889
$$607$$ −1.38674e11 1.38674e11i −1.02150 1.02150i −0.999764 0.0217387i $$-0.993080\pi$$
−0.0217387 0.999764i $$-0.506920\pi$$
$$608$$ 2.52644e10 2.52644e10i 0.184882 0.184882i
$$609$$ 4.34256e10i 0.315702i
$$610$$ 0 0
$$611$$ −1.75875e10 −0.126194
$$612$$ −1.25695e10 1.25695e10i −0.0896006 0.0896006i
$$613$$ −1.07154e11 + 1.07154e11i −0.758871 + 0.758871i −0.976117 0.217246i $$-0.930293\pi$$
0.217246 + 0.976117i $$0.430293\pi$$
$$614$$ 3.65559e10i 0.257208i
$$615$$ 0 0
$$616$$ 1.81770e11 1.26240
$$617$$ −8.73671e10 8.73671e10i −0.602847 0.602847i 0.338220 0.941067i $$-0.390175\pi$$
−0.941067 + 0.338220i $$0.890175\pi$$
$$618$$ −2.06873e10 + 2.06873e10i −0.141824 + 0.141824i
$$619$$ 1.24104e11i 0.845325i 0.906287 + 0.422663i $$0.138904\pi$$
−0.906287 + 0.422663i $$0.861096\pi$$
$$620$$ 0 0
$$621$$ 6.74968e10 0.453855
$$622$$ 6.20531e9 + 6.20531e9i 0.0414574 + 0.0414574i
$$623$$ 7.16753e10 7.16753e10i 0.475792 0.475792i
$$624$$ 4.11417e9i 0.0271359i
$$625$$ 0 0
$$626$$ −7.76936e10 −0.505927
$$627$$ −2.42567e10 2.42567e10i −0.156950 0.156950i
$$628$$ 1.73549e10 1.73549e10i 0.111579 0.111579i
$$629$$ 3.19737e11i 2.04263i
$$630$$ 0 0
$$631$$ 2.11881e11 1.33652 0.668258 0.743929i $$-0.267040\pi$$
0.668258 + 0.743929i $$0.267040\pi$$
$$632$$ 7.53969e9 + 7.53969e9i 0.0472591 + 0.0472591i
$$633$$ 1.86636e10 1.86636e10i 0.116247 0.116247i
$$634$$ 7.71045e10i 0.477225i
$$635$$ 0 0
$$636$$ −1.93949e9 −0.0118538
$$637$$ 2.24868e10 + 2.24868e10i 0.136575 + 0.136575i
$$638$$ −9.60344e10 + 9.60344e10i −0.579621 + 0.579621i
$$639$$ 1.44828e11i 0.868660i
$$640$$ 0 0
$$641$$ −1.20192e11 −0.711940 −0.355970 0.934497i $$-0.615849\pi$$
−0.355970 + 0.934497i $$0.615849\pi$$
$$642$$ −1.42852e10 1.42852e10i −0.0840906 0.0840906i
$$643$$ −8.34104e10 + 8.34104e10i −0.487951 + 0.487951i −0.907659 0.419708i $$-0.862132\pi$$
0.419708 + 0.907659i $$0.362132\pi$$
$$644$$ 3.15721e10i 0.183552i
$$645$$ 0 0
$$646$$ 3.07881e11 1.76788
$$647$$ 1.74293e11 + 1.74293e11i 0.994635 + 0.994635i 0.999986 0.00535087i $$-0.00170324\pi$$
−0.00535087 + 0.999986i $$0.501703\pi$$
$$648$$ 1.02623e11 1.02623e11i 0.582028 0.582028i
$$649$$ 7.88403e10i 0.444395i
$$650$$ 0 0
$$651$$ −6.79306e10 −0.378217
$$652$$ 6.70461e9 + 6.70461e9i 0.0371008 + 0.0371008i
$$653$$ −1.69727e11 + 1.69727e11i −0.933465 + 0.933465i −0.997921 0.0644553i $$-0.979469\pi$$
0.0644553 + 0.997921i $$0.479469\pi$$
$$654$$ 1.03106e10i 0.0563600i
$$655$$ 0 0
$$656$$ −9.44818e10 −0.510191
$$657$$ −1.09461e11 1.09461e11i −0.587488 0.587488i
$$658$$ 2.36481e11 2.36481e11i 1.26151 1.26151i
$$659$$ 2.61429e11i 1.38616i 0.720862 + 0.693078i $$0.243746\pi$$
−0.720862 + 0.693078i $$0.756254\pi$$
$$660$$ 0 0
$$661$$ −9.90557e10 −0.518888 −0.259444 0.965758i $$-0.583539\pi$$
−0.259444 + 0.965758i $$0.583539\pi$$
$$662$$ −1.01634e11 1.01634e11i −0.529182 0.529182i
$$663$$ −4.42927e9 + 4.42927e9i −0.0229233 + 0.0229233i
$$664$$ 6.29459e10i 0.323814i
$$665$$ 0 0
$$666$$ 3.09628e11 1.57378
$$667$$ 1.47558e11 + 1.47558e11i 0.745522 + 0.745522i
$$668$$ −1.28038e10 + 1.28038e10i −0.0643034 + 0.0643034i
$$669$$ 1.07405e10i 0.0536193i
$$670$$ 0 0
$$671$$ −1.74628e11 −0.861436
$$672$$ −9.77418e9 9.77418e9i −0.0479295 0.0479295i
$$673$$ 1.05855e11 1.05855e11i 0.516003 0.516003i −0.400357 0.916359i $$-0.631114\pi$$
0.916359 + 0.400357i $$0.131114\pi$$
$$674$$ 1.70898e11i 0.828126i
$$675$$ 0 0
$$676$$ −2.09039e10 −0.100101
$$677$$ 2.34302e11 + 2.34302e11i 1.11538 + 1.11538i 0.992411 + 0.122965i $$0.0392403\pi$$
0.122965 + 0.992411i $$0.460760\pi$$
$$678$$ −3.65847e10 + 3.65847e10i −0.173133 + 0.173133i
$$679$$ 4.43982e11i 2.08875i
$$680$$ 0 0
$$681$$ 3.36650e10 0.156528
$$682$$ 1.50226e11 + 1.50226e11i 0.694399 + 0.694399i
$$683$$ 2.10586e11 2.10586e11i 0.967715 0.967715i −0.0317802 0.999495i $$-0.510118\pi$$
0.999495 + 0.0317802i $$0.0101176\pi$$
$$684$$ 2.74887e10i 0.125583i
$$685$$ 0 0
$$686$$ −2.29183e11 −1.03487
$$687$$ −6.04503e10 6.04503e10i −0.271376 0.271376i
$$688$$ −1.98910e11 + 1.98910e11i −0.887776 + 0.887776i
$$689$$ 1.52175e10i 0.0675254i
$$690$$ 0 0
$$691$$ −4.57396e10 −0.200623 −0.100311 0.994956i $$-0.531984\pi$$
−0.100311 + 0.994956i $$0.531984\pi$$
$$692$$ 9.14843e9 + 9.14843e9i 0.0398953 + 0.0398953i
$$693$$ 2.08951e11 2.08951e11i 0.905965 0.905965i
$$694$$ 6.55567e10i 0.282605i
$$695$$ 0 0
$$696$$ −4.32376e10 −0.184257
$$697$$ −1.01718e11 1.01718e11i −0.430989 0.430989i
$$698$$ −9.49504e10 + 9.49504e10i −0.400014 + 0.400014i
$$699$$ 7.68872e10i 0.322066i
$$700$$ 0 0
$$701$$ 9.83586e10 0.407324 0.203662 0.979041i $$-0.434716\pi$$
0.203662 + 0.979041i $$0.434716\pi$$
$$702$$ 8.77110e9 + 8.77110e9i 0.0361165 + 0.0361165i
$$703$$ −3.49623e11 + 3.49623e11i −1.43146 + 1.43146i
$$704$$ 1.78883e11i 0.728247i
$$705$$ 0 0
$$706$$ −4.74332e11 −1.90925
$$707$$ −4.95710e11 4.95710e11i −1.98404 1.98404i
$$708$$ 2.00631e9 2.00631e9i 0.00798483 0.00798483i
$$709$$ 1.32351e11i 0.523771i −0.965099 0.261885i $$-0.915656\pi$$
0.965099 0.261885i $$-0.0843443\pi$$
$$710$$ 0 0
$$711$$ 1.73343e10 0.0678310
$$712$$ −7.13650e10 7.13650e10i −0.277693 0.277693i
$$713$$ 2.30825e11 2.30825e11i 0.893151 0.893151i
$$714$$ 1.19111e11i 0.458311i
$$715$$ 0 0
$$716$$ 3.02132e10 0.114960
$$717$$ −7.66701e9 7.66701e9i −0.0290101 0.0290101i
$$718$$ −2.28078e11 + 2.28078e11i −0.858194 + 0.858194i
$$719$$ 2.14771e11i 0.803636i −0.915720 0.401818i $$-0.868378\pi$$
0.915720 0.401818i $$-0.131622\pi$$
$$720$$ 0 0
$$721$$ 4.02444e11 1.48924
$$722$$ 1.34991e11 + 1.34991e11i 0.496769 + 0.496769i
$$723$$ −1.23568e10 + 1.23568e10i −0.0452224 + 0.0452224i
$$724$$ 1.25844e10i 0.0458015i
$$725$$ 0 0
$$726$$ −1.89429e10 −0.0681868
$$727$$ −3.41170e10 3.41170e10i −0.122133 0.122133i 0.643398 0.765531i $$-0.277524\pi$$
−0.765531 + 0.643398i $$0.777524\pi$$
$$728$$ 3.62935e10 3.62935e10i 0.129212 0.129212i
$$729$$ 2.12181e11i 0.751270i
$$730$$ 0 0
$$731$$ −4.28289e11 −1.49992
$$732$$ 4.44389e9 + 4.44389e9i 0.0154782 + 0.0154782i
$$733$$ −6.69873e10 + 6.69873e10i −0.232047 + 0.232047i −0.813547 0.581499i $$-0.802466\pi$$
0.581499 + 0.813547i $$0.302466\pi$$
$$734$$ 4.40897e11i 1.51898i
$$735$$ 0 0
$$736$$ 6.64244e10 0.226369
$$737$$ 1.38990e11 + 1.38990e11i 0.471100 + 0.471100i
$$738$$ −9.85020e10 + 9.85020e10i −0.332062 + 0.332062i
$$739$$ 6.08310e10i 0.203961i 0.994786 + 0.101981i $$0.0325180\pi$$
−0.994786 + 0.101981i $$0.967482\pi$$
$$740$$ 0 0
$$741$$ −9.68656e9 −0.0321290
$$742$$ 2.04614e11 + 2.04614e11i 0.675025 + 0.675025i
$$743$$ 1.90364e11 1.90364e11i 0.624639 0.624639i −0.322075 0.946714i $$-0.604380\pi$$
0.946714 + 0.322075i $$0.104380\pi$$
$$744$$ 6.76365e10i 0.220744i
$$745$$ 0 0
$$746$$ −1.79438e11 −0.579375
$$747$$ 7.23587e10 + 7.23587e10i 0.232385 + 0.232385i
$$748$$ −2.42861e10 + 2.42861e10i −0.0775804 + 0.0775804i
$$749$$ 2.77901e11i 0.883004i
$$750$$ 0 0
$$751$$ 3.43050e11 1.07844 0.539222 0.842164i $$-0.318718\pi$$
0.539222 + 0.842164i $$0.318718\pi$$
$$752$$ −2.59620e11 2.59620e11i −0.811833 0.811833i
$$753$$ 4.92894e10 4.92894e10i 0.153311 0.153311i
$$754$$ 3.83499e10i 0.118653i
$$755$$ 0 0
$$756$$ −2.17470e10 −0.0665752
$$757$$ 7.34063e10 + 7.34063e10i 0.223537 + 0.223537i 0.809986 0.586449i $$-0.199475\pi$$
−0.586449 + 0.809986i $$0.699475\pi$$
$$758$$ 2.32697e11 2.32697e11i 0.704878 0.704878i
$$759$$ 6.37750e10i 0.192169i
$$760$$ 0 0
$$761$$ 5.88790e11 1.75558 0.877792 0.479042i $$-0.159016\pi$$
0.877792 + 0.479042i $$0.159016\pi$$
$$762$$ −1.43545e10 1.43545e10i −0.0425762 0.0425762i
$$763$$ 1.00289e11 1.00289e11i 0.295908 0.295908i
$$764$$ 3.88321e10i 0.113977i
$$765$$ 0 0
$$766$$ 2.55251e11 0.741400
$$767$$ 1.57418e10 + 1.57418e10i 0.0454856 + 0.0454856i
$$768$$ −1.53842e10 + 1.53842e10i −0.0442211 + 0.0442211i
$$769$$ 3.95721e11i 1.13158i 0.824550 + 0.565789i $$0.191428\pi$$
−0.824550 + 0.565789i $$0.808572\pi$$
$$770$$ 0 0
$$771$$ 1.35723e11 0.384091
$$772$$ −2.28253e10 2.28253e10i −0.0642609 0.0642609i
$$773$$ −3.23931e11 + 3.23931e11i −0.907265 + 0.907265i −0.996051 0.0887861i $$-0.971701\pi$$
0.0887861 + 0.996051i $$0.471701\pi$$
$$774$$ 4.14748e11i 1.15563i
$$775$$ 0 0