# Properties

 Label 112.7.c.b.97.2 Level $112$ Weight $7$ Character 112.97 Analytic conductor $25.766$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,7,Mod(97,112)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("112.97");

S:= CuspForms(chi, 7);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$112 = 2^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 112.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$25.7660573654$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-510})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 510$$ x^2 + 510 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 7) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 97.2 Root $$22.5832i$$ of defining polynomial Character $$\chi$$ $$=$$ 112.97 Dual form 112.7.c.b.97.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+45.1664i q^{3} +45.1664i q^{5} +(-133.000 + 316.165i) q^{7} -1311.00 q^{9} +O(q^{10})$$ $$q+45.1664i q^{3} +45.1664i q^{5} +(-133.000 + 316.165i) q^{7} -1311.00 q^{9} -874.000 q^{11} -2213.15i q^{13} -2040.00 q^{15} +5961.96i q^{17} +3116.48i q^{19} +(-14280.0 - 6007.13i) q^{21} -4738.00 q^{23} +13585.0 q^{25} -26286.8i q^{27} +11146.0 q^{29} -27461.1i q^{31} -39475.4i q^{33} +(-14280.0 - 6007.13i) q^{35} +3002.00 q^{37} +99960.0 q^{39} -57541.9i q^{41} -31418.0 q^{43} -59213.1i q^{45} -72446.8i q^{47} +(-82271.0 - 84099.8i) q^{49} -269280. q^{51} -76406.0 q^{53} -39475.4i q^{55} -140760. q^{57} +113232. i q^{59} +275108. i q^{61} +(174363. - 414492. i) q^{63} +99960.0 q^{65} -495242. q^{67} -213998. i q^{69} +184406. q^{71} +60974.6i q^{73} +613585. i q^{75} +(116242. - 276328. i) q^{77} +534934. q^{79} +231561. q^{81} -714848. i q^{83} -269280. q^{85} +503424. i q^{87} +629529. i q^{89} +(699720. + 294349. i) q^{91} +1.24032e6 q^{93} -140760. q^{95} -814440. i q^{97} +1.14581e6 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 266 q^{7} - 2622 q^{9}+O(q^{10})$$ 2 * q - 266 * q^7 - 2622 * q^9 $$2 q - 266 q^{7} - 2622 q^{9} - 1748 q^{11} - 4080 q^{15} - 28560 q^{21} - 9476 q^{23} + 27170 q^{25} + 22292 q^{29} - 28560 q^{35} + 6004 q^{37} + 199920 q^{39} - 62836 q^{43} - 164542 q^{49} - 538560 q^{51} - 152812 q^{53} - 281520 q^{57} + 348726 q^{63} + 199920 q^{65} - 990484 q^{67} + 368812 q^{71} + 232484 q^{77} + 1069868 q^{79} + 463122 q^{81} - 538560 q^{85} + 1399440 q^{91} + 2480640 q^{93} - 281520 q^{95} + 2291628 q^{99}+O(q^{100})$$ 2 * q - 266 * q^7 - 2622 * q^9 - 1748 * q^11 - 4080 * q^15 - 28560 * q^21 - 9476 * q^23 + 27170 * q^25 + 22292 * q^29 - 28560 * q^35 + 6004 * q^37 + 199920 * q^39 - 62836 * q^43 - 164542 * q^49 - 538560 * q^51 - 152812 * q^53 - 281520 * q^57 + 348726 * q^63 + 199920 * q^65 - 990484 * q^67 + 368812 * q^71 + 232484 * q^77 + 1069868 * q^79 + 463122 * q^81 - 538560 * q^85 + 1399440 * q^91 + 2480640 * q^93 - 281520 * q^95 + 2291628 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$$.

 $$n$$ $$15$$ $$17$$ $$85$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 45.1664i 1.67283i 0.548098 + 0.836414i $$0.315352\pi$$
−0.548098 + 0.836414i $$0.684648\pi$$
$$4$$ 0 0
$$5$$ 45.1664i 0.361331i 0.983545 + 0.180665i $$0.0578251\pi$$
−0.983545 + 0.180665i $$0.942175\pi$$
$$6$$ 0 0
$$7$$ −133.000 + 316.165i −0.387755 + 0.921762i
$$8$$ 0 0
$$9$$ −1311.00 −1.79835
$$10$$ 0 0
$$11$$ −874.000 −0.656649 −0.328325 0.944565i $$-0.606484\pi$$
−0.328325 + 0.944565i $$0.606484\pi$$
$$12$$ 0 0
$$13$$ 2213.15i 1.00735i −0.863893 0.503676i $$-0.831981\pi$$
0.863893 0.503676i $$-0.168019\pi$$
$$14$$ 0 0
$$15$$ −2040.00 −0.604444
$$16$$ 0 0
$$17$$ 5961.96i 1.21351i 0.794890 + 0.606753i $$0.207528\pi$$
−0.794890 + 0.606753i $$0.792472\pi$$
$$18$$ 0 0
$$19$$ 3116.48i 0.454363i 0.973852 + 0.227182i $$0.0729511\pi$$
−0.973852 + 0.227182i $$0.927049\pi$$
$$20$$ 0 0
$$21$$ −14280.0 6007.13i −1.54195 0.648648i
$$22$$ 0 0
$$23$$ −4738.00 −0.389414 −0.194707 0.980861i $$-0.562376\pi$$
−0.194707 + 0.980861i $$0.562376\pi$$
$$24$$ 0 0
$$25$$ 13585.0 0.869440
$$26$$ 0 0
$$27$$ 26286.8i 1.33551i
$$28$$ 0 0
$$29$$ 11146.0 0.457009 0.228505 0.973543i $$-0.426616\pi$$
0.228505 + 0.973543i $$0.426616\pi$$
$$30$$ 0 0
$$31$$ 27461.1i 0.921793i −0.887454 0.460897i $$-0.847528\pi$$
0.887454 0.460897i $$-0.152472\pi$$
$$32$$ 0 0
$$33$$ 39475.4i 1.09846i
$$34$$ 0 0
$$35$$ −14280.0 6007.13i −0.333061 0.140108i
$$36$$ 0 0
$$37$$ 3002.00 0.0592660 0.0296330 0.999561i $$-0.490566\pi$$
0.0296330 + 0.999561i $$0.490566\pi$$
$$38$$ 0 0
$$39$$ 99960.0 1.68513
$$40$$ 0 0
$$41$$ 57541.9i 0.834897i −0.908701 0.417449i $$-0.862924\pi$$
0.908701 0.417449i $$-0.137076\pi$$
$$42$$ 0 0
$$43$$ −31418.0 −0.395160 −0.197580 0.980287i $$-0.563308\pi$$
−0.197580 + 0.980287i $$0.563308\pi$$
$$44$$ 0 0
$$45$$ 59213.1i 0.649801i
$$46$$ 0 0
$$47$$ 72446.8i 0.697792i −0.937161 0.348896i $$-0.886557\pi$$
0.937161 0.348896i $$-0.113443\pi$$
$$48$$ 0 0
$$49$$ −82271.0 84099.8i −0.699292 0.714836i
$$50$$ 0 0
$$51$$ −269280. −2.02999
$$52$$ 0 0
$$53$$ −76406.0 −0.513216 −0.256608 0.966516i $$-0.582605\pi$$
−0.256608 + 0.966516i $$0.582605\pi$$
$$54$$ 0 0
$$55$$ 39475.4i 0.237268i
$$56$$ 0 0
$$57$$ −140760. −0.760072
$$58$$ 0 0
$$59$$ 113232.i 0.551332i 0.961253 + 0.275666i $$0.0888984\pi$$
−0.961253 + 0.275666i $$0.911102\pi$$
$$60$$ 0 0
$$61$$ 275108.i 1.21203i 0.795452 + 0.606016i $$0.207233\pi$$
−0.795452 + 0.606016i $$0.792767\pi$$
$$62$$ 0 0
$$63$$ 174363. 414492.i 0.697321 1.65766i
$$64$$ 0 0
$$65$$ 99960.0 0.363987
$$66$$ 0 0
$$67$$ −495242. −1.64662 −0.823309 0.567593i $$-0.807875\pi$$
−0.823309 + 0.567593i $$0.807875\pi$$
$$68$$ 0 0
$$69$$ 213998.i 0.651423i
$$70$$ 0 0
$$71$$ 184406. 0.515229 0.257614 0.966248i $$-0.417064\pi$$
0.257614 + 0.966248i $$0.417064\pi$$
$$72$$ 0 0
$$73$$ 60974.6i 0.156740i 0.996924 + 0.0783701i $$0.0249716\pi$$
−0.996924 + 0.0783701i $$0.975028\pi$$
$$74$$ 0 0
$$75$$ 613585.i 1.45442i
$$76$$ 0 0
$$77$$ 116242. 276328.i 0.254619 0.605275i
$$78$$ 0 0
$$79$$ 534934. 1.08497 0.542486 0.840065i $$-0.317483\pi$$
0.542486 + 0.840065i $$0.317483\pi$$
$$80$$ 0 0
$$81$$ 231561. 0.435723
$$82$$ 0 0
$$83$$ 714848.i 1.25020i −0.780545 0.625100i $$-0.785058\pi$$
0.780545 0.625100i $$-0.214942\pi$$
$$84$$ 0 0
$$85$$ −269280. −0.438478
$$86$$ 0 0
$$87$$ 503424.i 0.764498i
$$88$$ 0 0
$$89$$ 629529.i 0.892988i 0.894787 + 0.446494i $$0.147328\pi$$
−0.894787 + 0.446494i $$0.852672\pi$$
$$90$$ 0 0
$$91$$ 699720. + 294349.i 0.928539 + 0.390606i
$$92$$ 0 0
$$93$$ 1.24032e6 1.54200
$$94$$ 0 0
$$95$$ −140760. −0.164176
$$96$$ 0 0
$$97$$ 814440.i 0.892368i −0.894941 0.446184i $$-0.852783\pi$$
0.894941 0.446184i $$-0.147217\pi$$
$$98$$ 0 0
$$99$$ 1.14581e6 1.18089
$$100$$ 0 0
$$101$$ 1.95195e6i 1.89455i 0.320425 + 0.947274i $$0.396174\pi$$
−0.320425 + 0.947274i $$0.603826\pi$$
$$102$$ 0 0
$$103$$ 1.69744e6i 1.55340i 0.629871 + 0.776700i $$0.283108\pi$$
−0.629871 + 0.776700i $$0.716892\pi$$
$$104$$ 0 0
$$105$$ 271320. 644976.i 0.234376 0.557154i
$$106$$ 0 0
$$107$$ −1.61603e6 −1.31916 −0.659579 0.751635i $$-0.729266\pi$$
−0.659579 + 0.751635i $$0.729266\pi$$
$$108$$ 0 0
$$109$$ 199226. 0.153839 0.0769195 0.997037i $$-0.475492\pi$$
0.0769195 + 0.997037i $$0.475492\pi$$
$$110$$ 0 0
$$111$$ 135589.i 0.0991418i
$$112$$ 0 0
$$113$$ −1.80762e6 −1.25277 −0.626386 0.779513i $$-0.715467\pi$$
−0.626386 + 0.779513i $$0.715467\pi$$
$$114$$ 0 0
$$115$$ 213998.i 0.140707i
$$116$$ 0 0
$$117$$ 2.90144e6i 1.81157i
$$118$$ 0 0
$$119$$ −1.88496e6 792941.i −1.11857 0.470543i
$$120$$ 0 0
$$121$$ −1.00768e6 −0.568812
$$122$$ 0 0
$$123$$ 2.59896e6 1.39664
$$124$$ 0 0
$$125$$ 1.31931e6i 0.675486i
$$126$$ 0 0
$$127$$ −3.32472e6 −1.62310 −0.811548 0.584286i $$-0.801375\pi$$
−0.811548 + 0.584286i $$0.801375\pi$$
$$128$$ 0 0
$$129$$ 1.41904e6i 0.661035i
$$130$$ 0 0
$$131$$ 3.13567e6i 1.39482i 0.716674 + 0.697408i $$0.245664\pi$$
−0.716674 + 0.697408i $$0.754336\pi$$
$$132$$ 0 0
$$133$$ −985320. 414492.i −0.418815 0.176182i
$$134$$ 0 0
$$135$$ 1.18728e6 0.482561
$$136$$ 0 0
$$137$$ 2.12927e6 0.828072 0.414036 0.910260i $$-0.364119\pi$$
0.414036 + 0.910260i $$0.364119\pi$$
$$138$$ 0 0
$$139$$ 1.68421e6i 0.627121i −0.949568 0.313561i $$-0.898478\pi$$
0.949568 0.313561i $$-0.101522\pi$$
$$140$$ 0 0
$$141$$ 3.27216e6 1.16729
$$142$$ 0 0
$$143$$ 1.93429e6i 0.661477i
$$144$$ 0 0
$$145$$ 503424.i 0.165132i
$$146$$ 0 0
$$147$$ 3.79848e6 3.71588e6i 1.19580 1.16980i
$$148$$ 0 0
$$149$$ −2.59573e6 −0.784696 −0.392348 0.919817i $$-0.628337\pi$$
−0.392348 + 0.919817i $$0.628337\pi$$
$$150$$ 0 0
$$151$$ 1.68557e6 0.489570 0.244785 0.969577i $$-0.421283\pi$$
0.244785 + 0.969577i $$0.421283\pi$$
$$152$$ 0 0
$$153$$ 7.81613e6i 2.18231i
$$154$$ 0 0
$$155$$ 1.24032e6 0.333072
$$156$$ 0 0
$$157$$ 3.67641e6i 0.950002i −0.879985 0.475001i $$-0.842448\pi$$
0.879985 0.475001i $$-0.157552\pi$$
$$158$$ 0 0
$$159$$ 3.45098e6i 0.858521i
$$160$$ 0 0
$$161$$ 630154. 1.49799e6i 0.150997 0.358947i
$$162$$ 0 0
$$163$$ −1.88191e6 −0.434547 −0.217274 0.976111i $$-0.569716\pi$$
−0.217274 + 0.976111i $$0.569716\pi$$
$$164$$ 0 0
$$165$$ 1.78296e6 0.396908
$$166$$ 0 0
$$167$$ 3.15595e6i 0.677612i −0.940856 0.338806i $$-0.889977\pi$$
0.940856 0.338806i $$-0.110023\pi$$
$$168$$ 0 0
$$169$$ −71231.0 −0.0147574
$$170$$ 0 0
$$171$$ 4.08570e6i 0.817106i
$$172$$ 0 0
$$173$$ 2.29477e6i 0.443201i 0.975138 + 0.221600i $$0.0711280\pi$$
−0.975138 + 0.221600i $$0.928872\pi$$
$$174$$ 0 0
$$175$$ −1.80680e6 + 4.29509e6i −0.337130 + 0.801417i
$$176$$ 0 0
$$177$$ −5.11428e6 −0.922284
$$178$$ 0 0
$$179$$ −3.51846e6 −0.613470 −0.306735 0.951795i $$-0.599237\pi$$
−0.306735 + 0.951795i $$0.599237\pi$$
$$180$$ 0 0
$$181$$ 7.48267e6i 1.26189i 0.775829 + 0.630944i $$0.217332\pi$$
−0.775829 + 0.630944i $$0.782668\pi$$
$$182$$ 0 0
$$183$$ −1.24256e7 −2.02752
$$184$$ 0 0
$$185$$ 135589.i 0.0214146i
$$186$$ 0 0
$$187$$ 5.21075e6i 0.796848i
$$188$$ 0 0
$$189$$ 8.31096e6 + 3.49615e6i 1.23102 + 0.517850i
$$190$$ 0 0
$$191$$ 7.20028e6 1.03335 0.516677 0.856180i $$-0.327169\pi$$
0.516677 + 0.856180i $$0.327169\pi$$
$$192$$ 0 0
$$193$$ −1.30889e7 −1.82067 −0.910335 0.413872i $$-0.864176\pi$$
−0.910335 + 0.413872i $$0.864176\pi$$
$$194$$ 0 0
$$195$$ 4.51483e6i 0.608888i
$$196$$ 0 0
$$197$$ −9.17476e6 −1.20004 −0.600020 0.799985i $$-0.704841\pi$$
−0.600020 + 0.799985i $$0.704841\pi$$
$$198$$ 0 0
$$199$$ 6.78769e6i 0.861317i −0.902515 0.430658i $$-0.858281\pi$$
0.902515 0.430658i $$-0.141719\pi$$
$$200$$ 0 0
$$201$$ 2.23683e7i 2.75451i
$$202$$ 0 0
$$203$$ −1.48242e6 + 3.52397e6i −0.177208 + 0.421254i
$$204$$ 0 0
$$205$$ 2.59896e6 0.301674
$$206$$ 0 0
$$207$$ 6.21152e6 0.700304
$$208$$ 0 0
$$209$$ 2.72380e6i 0.298357i
$$210$$ 0 0
$$211$$ −8.40084e6 −0.894284 −0.447142 0.894463i $$-0.647558\pi$$
−0.447142 + 0.894463i $$0.647558\pi$$
$$212$$ 0 0
$$213$$ 8.32895e6i 0.861889i
$$214$$ 0 0
$$215$$ 1.41904e6i 0.142784i
$$216$$ 0 0
$$217$$ 8.68224e6 + 3.65233e6i 0.849675 + 0.357430i
$$218$$ 0 0
$$219$$ −2.75400e6 −0.262199
$$220$$ 0 0
$$221$$ 1.31947e7 1.22243
$$222$$ 0 0
$$223$$ 4.90434e6i 0.442248i 0.975246 + 0.221124i $$0.0709726\pi$$
−0.975246 + 0.221124i $$0.929027\pi$$
$$224$$ 0 0
$$225$$ −1.78099e7 −1.56356
$$226$$ 0 0
$$227$$ 1.32183e7i 1.13005i 0.825075 + 0.565023i $$0.191133\pi$$
−0.825075 + 0.565023i $$0.808867\pi$$
$$228$$ 0 0
$$229$$ 338974.i 0.0282266i 0.999900 + 0.0141133i $$0.00449256\pi$$
−0.999900 + 0.0141133i $$0.995507\pi$$
$$230$$ 0 0
$$231$$ 1.24807e7 + 5.25023e6i 1.01252 + 0.425934i
$$232$$ 0 0
$$233$$ 4.84146e6 0.382744 0.191372 0.981518i $$-0.438706\pi$$
0.191372 + 0.981518i $$0.438706\pi$$
$$234$$ 0 0
$$235$$ 3.27216e6 0.252134
$$236$$ 0 0
$$237$$ 2.41610e7i 1.81497i
$$238$$ 0 0
$$239$$ 1.37297e7 1.00570 0.502850 0.864374i $$-0.332285\pi$$
0.502850 + 0.864374i $$0.332285\pi$$
$$240$$ 0 0
$$241$$ 3.66913e6i 0.262127i −0.991374 0.131064i $$-0.958161\pi$$
0.991374 0.131064i $$-0.0418392\pi$$
$$242$$ 0 0
$$243$$ 8.70433e6i 0.606619i
$$244$$ 0 0
$$245$$ 3.79848e6 3.71588e6i 0.258292 0.252676i
$$246$$ 0 0
$$247$$ 6.89724e6 0.457704
$$248$$ 0 0
$$249$$ 3.22871e7 2.09137
$$250$$ 0 0
$$251$$ 1.57289e7i 0.994664i 0.867560 + 0.497332i $$0.165687\pi$$
−0.867560 + 0.497332i $$0.834313\pi$$
$$252$$ 0 0
$$253$$ 4.14101e6 0.255708
$$254$$ 0 0
$$255$$ 1.21624e7i 0.733498i
$$256$$ 0 0
$$257$$ 7.54531e6i 0.444506i 0.974989 + 0.222253i $$0.0713411\pi$$
−0.974989 + 0.222253i $$0.928659\pi$$
$$258$$ 0 0
$$259$$ −399266. + 949126.i −0.0229807 + 0.0546292i
$$260$$ 0 0
$$261$$ −1.46124e7 −0.821864
$$262$$ 0 0
$$263$$ 1.32059e7 0.725942 0.362971 0.931800i $$-0.381762\pi$$
0.362971 + 0.931800i $$0.381762\pi$$
$$264$$ 0 0
$$265$$ 3.45098e6i 0.185441i
$$266$$ 0 0
$$267$$ −2.84335e7 −1.49382
$$268$$ 0 0
$$269$$ 1.59600e7i 0.819930i −0.912101 0.409965i $$-0.865541\pi$$
0.912101 0.409965i $$-0.134459\pi$$
$$270$$ 0 0
$$271$$ 2.48446e7i 1.24831i −0.781299 0.624157i $$-0.785443\pi$$
0.781299 0.624157i $$-0.214557\pi$$
$$272$$ 0 0
$$273$$ −1.32947e7 + 3.16038e7i −0.653416 + 1.55329i
$$274$$ 0 0
$$275$$ −1.18733e7 −0.570917
$$276$$ 0 0
$$277$$ 1.60013e7 0.752863 0.376432 0.926444i $$-0.377151\pi$$
0.376432 + 0.926444i $$0.377151\pi$$
$$278$$ 0 0
$$279$$ 3.60016e7i 1.65771i
$$280$$ 0 0
$$281$$ −603566. −0.0272023 −0.0136012 0.999908i $$-0.504330\pi$$
−0.0136012 + 0.999908i $$0.504330\pi$$
$$282$$ 0 0
$$283$$ 2.22195e7i 0.980334i 0.871629 + 0.490167i $$0.163064\pi$$
−0.871629 + 0.490167i $$0.836936\pi$$
$$284$$ 0 0
$$285$$ 6.35762e6i 0.274637i
$$286$$ 0 0
$$287$$ 1.81927e7 + 7.65308e6i 0.769577 + 0.323736i
$$288$$ 0 0
$$289$$ −1.14074e7 −0.472599
$$290$$ 0 0
$$291$$ 3.67853e7 1.49278
$$292$$ 0 0
$$293$$ 4.28134e7i 1.70207i 0.525110 + 0.851034i $$0.324024\pi$$
−0.525110 + 0.851034i $$0.675976\pi$$
$$294$$ 0 0
$$295$$ −5.11428e6 −0.199213
$$296$$ 0 0
$$297$$ 2.29747e7i 0.876961i
$$298$$ 0 0
$$299$$ 1.04859e7i 0.392277i
$$300$$ 0 0
$$301$$ 4.17859e6 9.93326e6i 0.153225 0.364244i
$$302$$ 0 0
$$303$$ −8.81627e7 −3.16925
$$304$$ 0 0
$$305$$ −1.24256e7 −0.437945
$$306$$ 0 0
$$307$$ 4.02152e7i 1.38987i −0.719072 0.694936i $$-0.755433\pi$$
0.719072 0.694936i $$-0.244567\pi$$
$$308$$ 0 0
$$309$$ −7.66673e7 −2.59857
$$310$$ 0 0
$$311$$ 1.47381e7i 0.489958i 0.969528 + 0.244979i $$0.0787811\pi$$
−0.969528 + 0.244979i $$0.921219\pi$$
$$312$$ 0 0
$$313$$ 4.19490e7i 1.36801i −0.729479 0.684004i $$-0.760237\pi$$
0.729479 0.684004i $$-0.239763\pi$$
$$314$$ 0 0
$$315$$ 1.87211e7 + 7.87534e6i 0.598962 + 0.251964i
$$316$$ 0 0
$$317$$ 4.30922e7 1.35276 0.676380 0.736553i $$-0.263548\pi$$
0.676380 + 0.736553i $$0.263548\pi$$
$$318$$ 0 0
$$319$$ −9.74160e6 −0.300095
$$320$$ 0 0
$$321$$ 7.29900e7i 2.20673i
$$322$$ 0 0
$$323$$ −1.85803e7 −0.551373
$$324$$ 0 0
$$325$$ 3.00657e7i 0.875832i
$$326$$ 0 0
$$327$$ 8.99831e6i 0.257346i
$$328$$ 0 0
$$329$$ 2.29051e7 + 9.63543e6i 0.643198 + 0.270572i
$$330$$ 0 0
$$331$$ 5.32204e7 1.46755 0.733777 0.679390i $$-0.237756\pi$$
0.733777 + 0.679390i $$0.237756\pi$$
$$332$$ 0 0
$$333$$ −3.93562e6 −0.106581
$$334$$ 0 0
$$335$$ 2.23683e7i 0.594974i
$$336$$ 0 0
$$337$$ 2.34579e6 0.0612913 0.0306456 0.999530i $$-0.490244\pi$$
0.0306456 + 0.999530i $$0.490244\pi$$
$$338$$ 0 0
$$339$$ 8.16437e7i 2.09567i
$$340$$ 0 0
$$341$$ 2.40010e7i 0.605295i
$$342$$ 0 0
$$343$$ 3.75314e7 1.48259e7i 0.930063 0.367400i
$$344$$ 0 0
$$345$$ 9.66552e6 0.235379
$$346$$ 0 0
$$347$$ 4.80596e7 1.15025 0.575124 0.818066i $$-0.304954\pi$$
0.575124 + 0.818066i $$0.304954\pi$$
$$348$$ 0 0
$$349$$ 1.00499e7i 0.236421i −0.992989 0.118211i $$-0.962284\pi$$
0.992989 0.118211i $$-0.0377158\pi$$
$$350$$ 0 0
$$351$$ −5.81767e7 −1.34533
$$352$$ 0 0
$$353$$ 7.65216e7i 1.73964i 0.493368 + 0.869821i $$0.335766\pi$$
−0.493368 + 0.869821i $$0.664234\pi$$
$$354$$ 0 0
$$355$$ 8.32895e6i 0.186168i
$$356$$ 0 0
$$357$$ 3.58142e7 8.51368e7i 0.787138 1.87117i
$$358$$ 0 0
$$359$$ −8.39735e6 −0.181493 −0.0907463 0.995874i $$-0.528925\pi$$
−0.0907463 + 0.995874i $$0.528925\pi$$
$$360$$ 0 0
$$361$$ 3.73334e7 0.793554
$$362$$ 0 0
$$363$$ 4.55135e7i 0.951525i
$$364$$ 0 0
$$365$$ −2.75400e6 −0.0566351
$$366$$ 0 0
$$367$$ 3.82776e6i 0.0774366i −0.999250 0.0387183i $$-0.987672\pi$$
0.999250 0.0387183i $$-0.0123275\pi$$
$$368$$ 0 0
$$369$$ 7.54375e7i 1.50144i
$$370$$ 0 0
$$371$$ 1.01620e7 2.41569e7i 0.199002 0.473063i
$$372$$ 0 0
$$373$$ −4.93836e7 −0.951604 −0.475802 0.879552i $$-0.657842\pi$$
−0.475802 + 0.879552i $$0.657842\pi$$
$$374$$ 0 0
$$375$$ −5.95884e7 −1.12997
$$376$$ 0 0
$$377$$ 2.46678e7i 0.460369i
$$378$$ 0 0
$$379$$ −3.74561e7 −0.688026 −0.344013 0.938965i $$-0.611786\pi$$
−0.344013 + 0.938965i $$0.611786\pi$$
$$380$$ 0 0
$$381$$ 1.50166e8i 2.71516i
$$382$$ 0 0
$$383$$ 5.01003e7i 0.891752i 0.895095 + 0.445876i $$0.147108\pi$$
−0.895095 + 0.445876i $$0.852892\pi$$
$$384$$ 0 0
$$385$$ 1.24807e7 + 5.25023e6i 0.218704 + 0.0920017i
$$386$$ 0 0
$$387$$ 4.11890e7 0.710638
$$388$$ 0 0
$$389$$ 224986. 0.00382214 0.00191107 0.999998i $$-0.499392\pi$$
0.00191107 + 0.999998i $$0.499392\pi$$
$$390$$ 0 0
$$391$$ 2.82478e7i 0.472557i
$$392$$ 0 0
$$393$$ −1.41627e8 −2.33329
$$394$$ 0 0
$$395$$ 2.41610e7i 0.392034i
$$396$$ 0 0
$$397$$ 871937.i 0.0139352i −0.999976 0.00696760i $$-0.997782\pi$$
0.999976 0.00696760i $$-0.00221787\pi$$
$$398$$ 0 0
$$399$$ 1.87211e7 4.45033e7i 0.294722 0.700606i
$$400$$ 0 0
$$401$$ 1.44909e7 0.224730 0.112365 0.993667i $$-0.464157\pi$$
0.112365 + 0.993667i $$0.464157\pi$$
$$402$$ 0 0
$$403$$ −6.07757e7 −0.928570
$$404$$ 0 0
$$405$$ 1.04588e7i 0.157440i
$$406$$ 0 0
$$407$$ −2.62375e6 −0.0389170
$$408$$ 0 0
$$409$$ 1.04303e8i 1.52450i 0.647284 + 0.762249i $$0.275905\pi$$
−0.647284 + 0.762249i $$0.724095\pi$$
$$410$$ 0 0
$$411$$ 9.61712e7i 1.38522i
$$412$$ 0 0
$$413$$ −3.58000e7 1.50599e7i −0.508197 0.213782i
$$414$$ 0 0
$$415$$ 3.22871e7 0.451736
$$416$$ 0 0
$$417$$ 7.60696e7 1.04907
$$418$$ 0 0
$$419$$ 8.22075e7i 1.11756i 0.829317 + 0.558778i $$0.188730\pi$$
−0.829317 + 0.558778i $$0.811270\pi$$
$$420$$ 0 0
$$421$$ −1.33780e7 −0.179285 −0.0896427 0.995974i $$-0.528573\pi$$
−0.0896427 + 0.995974i $$0.528573\pi$$
$$422$$ 0 0
$$423$$ 9.49778e7i 1.25488i
$$424$$ 0 0
$$425$$ 8.09932e7i 1.05507i
$$426$$ 0 0
$$427$$ −8.69795e7 3.65894e7i −1.11721 0.469972i
$$428$$ 0 0
$$429$$ −8.73650e7 −1.10654
$$430$$ 0 0
$$431$$ 1.34244e8 1.67673 0.838367 0.545106i $$-0.183510\pi$$
0.838367 + 0.545106i $$0.183510\pi$$
$$432$$ 0 0
$$433$$ 1.03230e8i 1.27158i −0.771863 0.635789i $$-0.780675\pi$$
0.771863 0.635789i $$-0.219325\pi$$
$$434$$ 0 0
$$435$$ −2.27378e7 −0.276237
$$436$$ 0 0
$$437$$ 1.47659e7i 0.176935i
$$438$$ 0 0
$$439$$ 2.65816e7i 0.314186i −0.987584 0.157093i $$-0.949788\pi$$
0.987584 0.157093i $$-0.0502123\pi$$
$$440$$ 0 0
$$441$$ 1.07857e8 + 1.10255e8i 1.25757 + 1.28553i
$$442$$ 0 0
$$443$$ −1.31972e8 −1.51799 −0.758996 0.651096i $$-0.774310\pi$$
−0.758996 + 0.651096i $$0.774310\pi$$
$$444$$ 0 0
$$445$$ −2.84335e7 −0.322664
$$446$$ 0 0
$$447$$ 1.17240e8i 1.31266i
$$448$$ 0 0
$$449$$ 1.47766e8 1.63244 0.816218 0.577743i $$-0.196067\pi$$
0.816218 + 0.577743i $$0.196067\pi$$
$$450$$ 0 0
$$451$$ 5.02917e7i 0.548234i
$$452$$ 0 0
$$453$$ 7.61309e7i 0.818967i
$$454$$ 0 0
$$455$$ −1.32947e7 + 3.16038e7i −0.141138 + 0.335510i
$$456$$ 0 0
$$457$$ −8.22868e7 −0.862147 −0.431074 0.902317i $$-0.641865\pi$$
−0.431074 + 0.902317i $$0.641865\pi$$
$$458$$ 0 0
$$459$$ 1.56721e8 1.62065
$$460$$ 0 0
$$461$$ 1.31884e8i 1.34614i 0.739580 + 0.673068i $$0.235024\pi$$
−0.739580 + 0.673068i $$0.764976\pi$$
$$462$$ 0 0
$$463$$ −1.39927e6 −0.0140981 −0.00704904 0.999975i $$-0.502244\pi$$
−0.00704904 + 0.999975i $$0.502244\pi$$
$$464$$ 0 0
$$465$$ 5.60207e7i 0.557173i
$$466$$ 0 0
$$467$$ 1.81321e7i 0.178032i −0.996030 0.0890158i $$-0.971628\pi$$
0.996030 0.0890158i $$-0.0283722\pi$$
$$468$$ 0 0
$$469$$ 6.58672e7 1.56578e8i 0.638485 1.51779i
$$470$$ 0 0
$$471$$ 1.66050e8 1.58919
$$472$$ 0 0
$$473$$ 2.74593e7 0.259482
$$474$$ 0 0
$$475$$ 4.23374e7i 0.395042i
$$476$$ 0 0
$$477$$ 1.00168e8 0.922943
$$478$$ 0 0
$$479$$ 2.89375e7i 0.263303i −0.991296 0.131651i $$-0.957972\pi$$
0.991296 0.131651i $$-0.0420279\pi$$
$$480$$ 0 0
$$481$$ 6.64388e6i 0.0597017i
$$482$$ 0 0
$$483$$ 6.76586e7 + 2.84618e7i 0.600457 + 0.252592i
$$484$$ 0 0
$$485$$ 3.67853e7 0.322440
$$486$$ 0 0
$$487$$ 9.47515e7 0.820350 0.410175 0.912007i $$-0.365468\pi$$
0.410175 + 0.912007i $$0.365468\pi$$
$$488$$ 0 0
$$489$$ 8.49992e7i 0.726923i
$$490$$ 0 0
$$491$$ 2.58834e7 0.218663 0.109332 0.994005i $$-0.465129\pi$$
0.109332 + 0.994005i $$0.465129\pi$$
$$492$$ 0 0
$$493$$ 6.64520e7i 0.554584i
$$494$$ 0 0
$$495$$ 5.17522e7i 0.426691i
$$496$$ 0 0
$$497$$ −2.45260e7 + 5.83026e7i −0.199783 + 0.474918i
$$498$$ 0 0
$$499$$ −1.56023e8 −1.25571 −0.627853 0.778332i $$-0.716066\pi$$
−0.627853 + 0.778332i $$0.716066\pi$$
$$500$$ 0 0
$$501$$ 1.42543e8 1.13353
$$502$$ 0 0
$$503$$ 1.11476e8i 0.875950i 0.898987 + 0.437975i $$0.144304\pi$$
−0.898987 + 0.437975i $$0.855696\pi$$
$$504$$ 0 0
$$505$$ −8.81627e7 −0.684559
$$506$$ 0 0
$$507$$ 3.21724e6i 0.0246865i
$$508$$ 0 0
$$509$$ 7.45421e7i 0.565260i −0.959229 0.282630i $$-0.908793\pi$$
0.959229 0.282630i $$-0.0912068\pi$$
$$510$$ 0 0
$$511$$ −1.92780e7 8.10962e6i −0.144477 0.0607768i
$$512$$ 0 0
$$513$$ 8.19223e7 0.606806
$$514$$ 0 0
$$515$$ −7.66673e7 −0.561291
$$516$$ 0 0
$$517$$ 6.33185e7i 0.458204i
$$518$$ 0 0
$$519$$ −1.03646e8 −0.741398
$$520$$ 0 0
$$521$$ 1.96232e8i 1.38758i 0.720179 + 0.693789i $$0.244060\pi$$
−0.720179 + 0.693789i $$0.755940\pi$$
$$522$$ 0 0
$$523$$ 4.62080e7i 0.323007i 0.986872 + 0.161504i $$0.0516344\pi$$
−0.986872 + 0.161504i $$0.948366\pi$$
$$524$$ 0 0
$$525$$ −1.93994e8 8.16068e7i −1.34063 0.563960i
$$526$$ 0 0
$$527$$ 1.63722e8 1.11860
$$528$$ 0 0
$$529$$ −1.25587e8 −0.848357
$$530$$ 0 0
$$531$$ 1.48447e8i 0.991490i
$$532$$ 0 0
$$533$$ −1.27349e8 −0.841035
$$534$$ 0 0
$$535$$ 7.29900e7i 0.476653i
$$536$$ 0 0
$$537$$ 1.58916e8i 1.02623i
$$538$$ 0 0
$$539$$ 7.19049e7 + 7.35032e7i 0.459189 + 0.469397i
$$540$$ 0 0
$$541$$ −7.52906e7 −0.475498 −0.237749 0.971327i $$-0.576410\pi$$
−0.237749 + 0.971327i $$0.576410\pi$$
$$542$$ 0 0
$$543$$ −3.37965e8 −2.11092
$$544$$ 0 0
$$545$$ 8.99831e6i 0.0555868i
$$546$$ 0 0
$$547$$ −7.26760e7 −0.444047 −0.222023 0.975041i $$-0.571266\pi$$
−0.222023 + 0.975041i $$0.571266\pi$$
$$548$$ 0 0
$$549$$ 3.60667e8i 2.17966i
$$550$$ 0 0
$$551$$ 3.47363e7i 0.207648i
$$552$$ 0 0
$$553$$ −7.11462e7 + 1.69127e8i −0.420704 + 1.00009i
$$554$$ 0 0
$$555$$ −6.12408e6 −0.0358230
$$556$$ 0 0
$$557$$ −3.10741e8 −1.79818 −0.899090 0.437765i $$-0.855770\pi$$
−0.899090 + 0.437765i $$0.855770\pi$$
$$558$$ 0 0
$$559$$ 6.95328e7i 0.398065i
$$560$$ 0 0
$$561$$ 2.35351e8 1.33299
$$562$$ 0 0
$$563$$ 5.66378e7i 0.317381i 0.987328 + 0.158690i $$0.0507272\pi$$
−0.987328 + 0.158690i $$0.949273\pi$$
$$564$$ 0 0
$$565$$ 8.16437e7i 0.452665i
$$566$$ 0 0
$$567$$ −3.07976e7 + 7.32114e7i −0.168954 + 0.401633i
$$568$$ 0 0
$$569$$ 5.17304e7 0.280808 0.140404 0.990094i $$-0.455160\pi$$
0.140404 + 0.990094i $$0.455160\pi$$
$$570$$ 0 0
$$571$$ −8.68765e7 −0.466653 −0.233326 0.972398i $$-0.574961\pi$$
−0.233326 + 0.972398i $$0.574961\pi$$
$$572$$ 0 0
$$573$$ 3.25210e8i 1.72862i
$$574$$ 0 0
$$575$$ −6.43657e7 −0.338572
$$576$$ 0 0
$$577$$ 5.89865e7i 0.307062i −0.988144 0.153531i $$-0.950936\pi$$
0.988144 0.153531i $$-0.0490644\pi$$
$$578$$ 0 0
$$579$$ 5.91178e8i 3.04567i
$$580$$ 0 0
$$581$$ 2.26010e8 + 9.50748e7i 1.15239 + 0.484771i
$$582$$ 0 0
$$583$$ 6.67788e7 0.337003
$$584$$ 0 0
$$585$$ −1.31048e8 −0.654578
$$586$$ 0 0
$$587$$ 3.10848e8i 1.53686i 0.639934 + 0.768430i $$0.278962\pi$$
−0.639934 + 0.768430i $$0.721038\pi$$
$$588$$ 0 0
$$589$$ 8.55821e7 0.418829
$$590$$ 0 0
$$591$$ 4.14390e8i 2.00746i
$$592$$ 0 0
$$593$$ 3.46714e8i 1.66268i −0.555766 0.831339i $$-0.687575\pi$$
0.555766 0.831339i $$-0.312425\pi$$
$$594$$ 0 0
$$595$$ 3.58142e7 8.51368e7i 0.170022 0.404172i
$$596$$ 0 0
$$597$$ 3.06575e8 1.44083
$$598$$ 0 0
$$599$$ −9.47771e7 −0.440984 −0.220492 0.975389i $$-0.570766\pi$$
−0.220492 + 0.975389i $$0.570766\pi$$
$$600$$ 0 0
$$601$$ 2.04951e8i 0.944119i −0.881567 0.472060i $$-0.843511\pi$$
0.881567 0.472060i $$-0.156489\pi$$
$$602$$ 0 0
$$603$$ 6.49262e8 2.96120
$$604$$ 0 0
$$605$$ 4.55135e7i 0.205529i
$$606$$ 0 0
$$607$$ 3.28634e8i 1.46942i −0.678379 0.734712i $$-0.737317\pi$$
0.678379 0.734712i $$-0.262683\pi$$
$$608$$ 0 0
$$609$$ −1.59165e8 6.69554e7i −0.704686 0.296438i
$$610$$ 0 0
$$611$$ −1.60336e8 −0.702922
$$612$$ 0 0
$$613$$ 2.67967e8 1.16332 0.581660 0.813432i $$-0.302403\pi$$
0.581660 + 0.813432i $$0.302403\pi$$
$$614$$ 0 0
$$615$$ 1.17386e8i 0.504649i
$$616$$ 0 0
$$617$$ −3.88909e8 −1.65574 −0.827870 0.560921i $$-0.810447\pi$$
−0.827870 + 0.560921i $$0.810447\pi$$
$$618$$ 0 0
$$619$$ 6.30894e7i 0.266002i 0.991116 + 0.133001i $$0.0424613\pi$$
−0.991116 + 0.133001i $$0.957539\pi$$
$$620$$ 0 0
$$621$$ 1.24547e8i 0.520066i
$$622$$ 0 0
$$623$$ −1.99035e8 8.37273e7i −0.823123 0.346261i
$$624$$ 0 0
$$625$$ 1.52677e8 0.625366
$$626$$ 0 0
$$627$$ 1.23024e8 0.499101
$$628$$ 0 0
$$629$$ 1.78978e7i 0.0719197i
$$630$$ 0 0
$$631$$ 1.30827e8 0.520725 0.260363 0.965511i $$-0.416158\pi$$
0.260363 + 0.965511i $$0.416158\pi$$
$$632$$ 0 0
$$633$$ 3.79435e8i 1.49598i
$$634$$ 0 0
$$635$$ 1.50166e8i 0.586475i
$$636$$ 0 0
$$637$$ −1.86126e8 + 1.82078e8i −0.720091 + 0.704433i
$$638$$ 0 0
$$639$$ −2.41756e8 −0.926563
$$640$$ 0 0
$$641$$ −7.17536e7 −0.272439 −0.136220 0.990679i $$-0.543495\pi$$
−0.136220 + 0.990679i $$0.543495\pi$$
$$642$$ 0 0
$$643$$ 2.56068e8i 0.963214i −0.876387 0.481607i $$-0.840053\pi$$
0.876387 0.481607i $$-0.159947\pi$$
$$644$$ 0 0
$$645$$ 6.40927e7 0.238852
$$646$$ 0 0
$$647$$ 4.93122e8i 1.82071i 0.413827 + 0.910356i $$0.364192\pi$$
−0.413827 + 0.910356i $$0.635808\pi$$
$$648$$ 0 0
$$649$$ 9.89648e7i 0.362032i
$$650$$ 0 0
$$651$$ −1.64963e8 + 3.92145e8i −0.597919 + 1.42136i
$$652$$ 0 0
$$653$$ 1.55036e8 0.556793 0.278397 0.960466i $$-0.410197\pi$$
0.278397 + 0.960466i $$0.410197\pi$$
$$654$$ 0 0
$$655$$ −1.41627e8 −0.503990
$$656$$ 0 0
$$657$$ 7.99377e7i 0.281874i
$$658$$ 0 0
$$659$$ 3.01683e8 1.05413 0.527065 0.849825i $$-0.323293\pi$$
0.527065 + 0.849825i $$0.323293\pi$$
$$660$$ 0 0
$$661$$ 1.80227e8i 0.624044i 0.950075 + 0.312022i $$0.101006\pi$$
−0.950075 + 0.312022i $$0.898994\pi$$
$$662$$ 0 0
$$663$$ 5.95957e8i 2.04491i
$$664$$ 0 0
$$665$$ 1.87211e7 4.45033e7i 0.0636599 0.151331i
$$666$$ 0 0
$$667$$ −5.28097e7 −0.177966
$$668$$ 0 0
$$669$$ −2.21511e8 −0.739806
$$670$$ 0 0
$$671$$ 2.40445e8i 0.795880i
$$672$$ 0 0
$$673$$ 4.06265e8 1.33280 0.666399 0.745595i $$-0.267835\pi$$
0.666399 + 0.745595i $$0.267835\pi$$
$$674$$ 0 0
$$675$$ 3.57106e8i 1.16114i
$$676$$ 0 0
$$677$$ 1.77837e7i 0.0573133i 0.999589 + 0.0286566i $$0.00912294\pi$$
−0.999589 + 0.0286566i $$0.990877\pi$$
$$678$$ 0 0
$$679$$ 2.57497e8 + 1.08320e8i 0.822551 + 0.346020i
$$680$$ 0 0
$$681$$ −5.97020e8 −1.89037
$$682$$ 0 0
$$683$$ 2.66054e8 0.835042 0.417521 0.908667i $$-0.362899\pi$$
0.417521 + 0.908667i $$0.362899\pi$$
$$684$$ 0 0
$$685$$ 9.61712e7i 0.299208i
$$686$$ 0 0
$$687$$ −1.53102e7 −0.0472183
$$688$$ 0 0
$$689$$ 1.69098e8i 0.516989i
$$690$$ 0 0
$$691$$ 2.44451e8i 0.740898i 0.928853 + 0.370449i $$0.120796\pi$$
−0.928853 + 0.370449i $$0.879204\pi$$
$$692$$ 0 0
$$693$$ −1.52393e8 + 3.62266e8i −0.457895 + 1.08850i
$$694$$ 0 0
$$695$$ 7.60696e7 0.226598
$$696$$ 0 0
$$697$$ 3.43063e8 1.01315
$$698$$ 0 0
$$699$$ 2.18671e8i 0.640265i
$$700$$ 0 0
$$701$$ 2.31727e8 0.672702 0.336351 0.941737i $$-0.390807\pi$$
0.336351 + 0.941737i $$0.390807\pi$$
$$702$$ 0 0
$$703$$ 9.35567e6i 0.0269283i
$$704$$ 0 0
$$705$$ 1.47792e8i 0.421776i
$$706$$ 0 0
$$707$$ −6.17139e8 2.59610e8i −1.74632 0.734621i
$$708$$ 0 0
$$709$$ −3.09705e8 −0.868979 −0.434489 0.900677i $$-0.643071\pi$$
−0.434489 + 0.900677i $$0.643071\pi$$
$$710$$ 0 0
$$711$$ −7.01298e8 −1.95117
$$712$$ 0 0
$$713$$ 1.30111e8i 0.358959i
$$714$$ 0 0
$$715$$ −8.73650e7 −0.239012
$$716$$ 0 0
$$717$$ 6.20122e8i 1.68236i
$$718$$ 0 0
$$719$$ 3.85416e8i 1.03692i −0.855103 0.518458i $$-0.826506\pi$$
0.855103 0.518458i $$-0.173494\pi$$
$$720$$ 0 0
$$721$$ −5.36671e8 2.25760e8i −1.43187 0.602339i
$$722$$ 0 0
$$723$$ 1.65721e8 0.438494
$$724$$ 0 0
$$725$$ 1.51418e8 0.397342
$$726$$ 0 0
$$727$$ 3.13918e8i 0.816983i 0.912762 + 0.408491i $$0.133945\pi$$
−0.912762 + 0.408491i $$0.866055\pi$$
$$728$$ 0 0
$$729$$ 5.61951e8 1.45049
$$730$$ 0 0
$$731$$ 1.87313e8i 0.479530i
$$732$$ 0 0
$$733$$ 7.18118e7i 0.182341i 0.995835 + 0.0911704i $$0.0290608\pi$$
−0.995835 + 0.0911704i $$0.970939\pi$$
$$734$$ 0 0
$$735$$ 1.67833e8 + 1.71564e8i 0.422683 + 0.432079i
$$736$$ 0 0
$$737$$ 4.32842e8 1.08125
$$738$$ 0 0
$$739$$ −2.77815e7 −0.0688370 −0.0344185 0.999408i $$-0.510958\pi$$
−0.0344185 + 0.999408i $$0.510958\pi$$
$$740$$ 0 0
$$741$$ 3.11523e8i 0.765660i
$$742$$ 0 0
$$743$$ 7.03366e8 1.71481 0.857403 0.514646i $$-0.172077\pi$$
0.857403 + 0.514646i $$0.172077\pi$$
$$744$$ 0 0
$$745$$ 1.17240e8i 0.283535i
$$746$$ 0 0
$$747$$ 9.37166e8i 2.24830i
$$748$$ 0 0
$$749$$ 2.14931e8 5.10930e8i 0.511510 1.21595i
$$750$$ 0 0
$$751$$ 3.00617e8 0.709731 0.354866 0.934917i $$-0.384527\pi$$
0.354866 + 0.934917i $$0.384527\pi$$
$$752$$ 0 0
$$753$$ −7.10416e8 −1.66390
$$754$$ 0 0
$$755$$ 7.61309e7i 0.176897i
$$756$$ 0 0
$$757$$ 1.17057e8 0.269841 0.134921 0.990856i $$-0.456922\pi$$
0.134921 + 0.990856i $$0.456922\pi$$
$$758$$ 0 0
$$759$$ 1.87034e8i 0.427756i
$$760$$ 0 0
$$761$$ 2.63542e8i 0.597992i 0.954254 + 0.298996i $$0.0966518\pi$$
−0.954254 + 0.298996i $$0.903348\pi$$
$$762$$ 0 0
$$763$$ −2.64971e7 + 6.29882e7i −0.0596519 + 0.141803i
$$764$$ 0 0
$$765$$ 3.53026e8 0.788538
$$766$$ 0 0
$$767$$ 2.50600e8 0.555385
$$768$$ 0 0
$$769$$ 1.25689e8i 0.276388i 0.990405 + 0.138194i $$0.0441298\pi$$
−0.990405 + 0.138194i $$0.955870\pi$$
$$770$$ 0 0
$$771$$ −3.40794e8 −0.743582
$$772$$ 0 0
$$773$$ 1.58329e8i 0.342786i 0.985203 + 0.171393i $$0.0548268\pi$$
−0.985203 + 0.171393i $$0.945173\pi$$
$$774$$ 0 0
$$775$$ 3.73060e8i 0.801444i
$$776$$ 0 0
$$777$$ −4.28686e7 1.80334e7i −0.0913852 0.0384427i
$$778$$ 0 0
$$779$$ 1.79328e8 0.379347
$$780$$ 0 0
$$781$$ −1.61171e8 −0.338324
$$782$$ 0 0
$$783$$ 2.92993e8i 0.610340i
$$784$$ 0 0
$$785$$ 1.66050e8 0.343265
$$786$$ 0 0
$$787$$ 5.15726e8i 1.05802i 0.848615 + 0.529012i $$0.177437\pi$$
−0.848615 +