# Properties

 Label 7.7.b.b.6.1 Level $7$ Weight $7$ Character 7.6 Analytic conductor $1.610$ 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] = [7,7,Mod(6,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7.6");

S:= CuspForms(chi, 7);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$7$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 7.b (of order $$2$$, degree $$1$$, 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: $$1.61037858534$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 6.1 Root $$-22.5832i$$ of defining polynomial Character $$\chi$$ $$=$$ 7.6 Dual form 7.7.b.b.6.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-8.00000 q^{2} -45.1664i q^{3} +45.1664i q^{5} +361.331i q^{6} +(133.000 - 316.165i) q^{7} +512.000 q^{8} -1311.00 q^{9} +O(q^{10})$$ $$q-8.00000 q^{2} -45.1664i q^{3} +45.1664i q^{5} +361.331i q^{6} +(133.000 - 316.165i) q^{7} +512.000 q^{8} -1311.00 q^{9} -361.331i q^{10} +874.000 q^{11} -2213.15i q^{13} +(-1064.00 + 2529.32i) q^{14} +2040.00 q^{15} -4096.00 q^{16} +5961.96i q^{17} +10488.0 q^{18} -3116.48i q^{19} +(-14280.0 - 6007.13i) q^{21} -6992.00 q^{22} +4738.00 q^{23} -23125.2i q^{24} +13585.0 q^{25} +17705.2i q^{26} +26286.8i q^{27} +11146.0 q^{29} -16320.0 q^{30} +27461.1i q^{31} -39475.4i q^{33} -47695.7i q^{34} +(14280.0 + 6007.13i) q^{35} +3002.00 q^{37} +24931.8i q^{38} -99960.0 q^{39} +23125.2i q^{40} -57541.9i q^{41} +(114240. + 48057.0i) q^{42} +31418.0 q^{43} -59213.1i q^{45} -37904.0 q^{46} +72446.8i q^{47} +185001. i q^{48} +(-82271.0 - 84099.8i) q^{49} -108680. q^{50} +269280. q^{51} -76406.0 q^{53} -210295. i q^{54} +39475.4i q^{55} +(68096.0 - 161876. i) q^{56} -140760. q^{57} -89168.0 q^{58} -113232. i q^{59} +275108. i q^{61} -219689. i q^{62} +(-174363. + 414492. i) q^{63} +262144. q^{64} +99960.0 q^{65} +315803. i q^{66} +495242. q^{67} -213998. i q^{69} +(-114240. - 48057.0i) q^{70} -184406. q^{71} -671232. q^{72} +60974.6i q^{73} -24016.0 q^{74} -613585. i q^{75} +(116242. - 276328. i) q^{77} +799680. q^{78} -534934. q^{79} -185001. i q^{80} +231561. q^{81} +460336. i q^{82} +714848. i q^{83} -269280. q^{85} -251344. q^{86} -503424. i q^{87} +447488. q^{88} +629529. i q^{89} +473705. i q^{90} +(-699720. - 294349. i) q^{91} +1.24032e6 q^{93} -579575. i q^{94} +140760. q^{95} -814440. i q^{97} +(658168. + 672798. i) q^{98} -1.14581e6 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 16 q^{2} + 266 q^{7} + 1024 q^{8} - 2622 q^{9}+O(q^{10})$$ 2 * q - 16 * q^2 + 266 * q^7 + 1024 * q^8 - 2622 * q^9 $$2 q - 16 q^{2} + 266 q^{7} + 1024 q^{8} - 2622 q^{9} + 1748 q^{11} - 2128 q^{14} + 4080 q^{15} - 8192 q^{16} + 20976 q^{18} - 28560 q^{21} - 13984 q^{22} + 9476 q^{23} + 27170 q^{25} + 22292 q^{29} - 32640 q^{30} + 28560 q^{35} + 6004 q^{37} - 199920 q^{39} + 228480 q^{42} + 62836 q^{43} - 75808 q^{46} - 164542 q^{49} - 217360 q^{50} + 538560 q^{51} - 152812 q^{53} + 136192 q^{56} - 281520 q^{57} - 178336 q^{58} - 348726 q^{63} + 524288 q^{64} + 199920 q^{65} + 990484 q^{67} - 228480 q^{70} - 368812 q^{71} - 1342464 q^{72} - 48032 q^{74} + 232484 q^{77} + 1599360 q^{78} - 1069868 q^{79} + 463122 q^{81} - 538560 q^{85} - 502688 q^{86} + 894976 q^{88} - 1399440 q^{91} + 2480640 q^{93} + 281520 q^{95} + 1316336 q^{98} - 2291628 q^{99}+O(q^{100})$$ 2 * q - 16 * q^2 + 266 * q^7 + 1024 * q^8 - 2622 * q^9 + 1748 * q^11 - 2128 * q^14 + 4080 * q^15 - 8192 * q^16 + 20976 * q^18 - 28560 * q^21 - 13984 * q^22 + 9476 * q^23 + 27170 * q^25 + 22292 * q^29 - 32640 * q^30 + 28560 * q^35 + 6004 * q^37 - 199920 * q^39 + 228480 * q^42 + 62836 * q^43 - 75808 * q^46 - 164542 * q^49 - 217360 * q^50 + 538560 * q^51 - 152812 * q^53 + 136192 * q^56 - 281520 * q^57 - 178336 * q^58 - 348726 * q^63 + 524288 * q^64 + 199920 * q^65 + 990484 * q^67 - 228480 * q^70 - 368812 * q^71 - 1342464 * q^72 - 48032 * q^74 + 232484 * q^77 + 1599360 * q^78 - 1069868 * q^79 + 463122 * q^81 - 538560 * q^85 - 502688 * q^86 + 894976 * q^88 - 1399440 * q^91 + 2480640 * q^93 + 281520 * q^95 + 1316336 * q^98 - 2291628 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −8.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$3$$ 45.1664i 1.67283i −0.548098 0.836414i $$-0.684648\pi$$
0.548098 0.836414i $$-0.315352\pi$$
$$4$$ 0 0
$$5$$ 45.1664i 0.361331i 0.983545 + 0.180665i $$0.0578251\pi$$
−0.983545 + 0.180665i $$0.942175\pi$$
$$6$$ 361.331i 1.67283i
$$7$$ 133.000 316.165i 0.387755 0.921762i
$$8$$ 512.000 1.00000
$$9$$ −1311.00 −1.79835
$$10$$ 361.331i 0.361331i
$$11$$ 874.000 0.656649 0.328325 0.944565i $$-0.393516\pi$$
0.328325 + 0.944565i $$0.393516\pi$$
$$12$$ 0 0
$$13$$ 2213.15i 1.00735i −0.863893 0.503676i $$-0.831981\pi$$
0.863893 0.503676i $$-0.168019\pi$$
$$14$$ −1064.00 + 2529.32i −0.387755 + 0.921762i
$$15$$ 2040.00 0.604444
$$16$$ −4096.00 −1.00000
$$17$$ 5961.96i 1.21351i 0.794890 + 0.606753i $$0.207528\pi$$
−0.794890 + 0.606753i $$0.792472\pi$$
$$18$$ 10488.0 1.79835
$$19$$ 3116.48i 0.454363i −0.973852 0.227182i $$-0.927049\pi$$
0.973852 0.227182i $$-0.0729511\pi$$
$$20$$ 0 0
$$21$$ −14280.0 6007.13i −1.54195 0.648648i
$$22$$ −6992.00 −0.656649
$$23$$ 4738.00 0.389414 0.194707 0.980861i $$-0.437624\pi$$
0.194707 + 0.980861i $$0.437624\pi$$
$$24$$ 23125.2i 1.67283i
$$25$$ 13585.0 0.869440
$$26$$ 17705.2i 1.00735i
$$27$$ 26286.8i 1.33551i
$$28$$ 0 0
$$29$$ 11146.0 0.457009 0.228505 0.973543i $$-0.426616\pi$$
0.228505 + 0.973543i $$0.426616\pi$$
$$30$$ −16320.0 −0.604444
$$31$$ 27461.1i 0.921793i 0.887454 + 0.460897i $$0.152472\pi$$
−0.887454 + 0.460897i $$0.847528\pi$$
$$32$$ 0 0
$$33$$ 39475.4i 1.09846i
$$34$$ 47695.7i 1.21351i
$$35$$ 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 $$0.490566\pi$$
$$38$$ 24931.8i 0.454363i
$$39$$ −99960.0 −1.68513
$$40$$ 23125.2i 0.361331i
$$41$$ 57541.9i 0.834897i −0.908701 0.417449i $$-0.862924\pi$$
0.908701 0.417449i $$-0.137076\pi$$
$$42$$ 114240. + 48057.0i 1.54195 + 0.648648i
$$43$$ 31418.0 0.395160 0.197580 0.980287i $$-0.436692\pi$$
0.197580 + 0.980287i $$0.436692\pi$$
$$44$$ 0 0
$$45$$ 59213.1i 0.649801i
$$46$$ −37904.0 −0.389414
$$47$$ 72446.8i 0.697792i 0.937161 + 0.348896i $$0.113443\pi$$
−0.937161 + 0.348896i $$0.886557\pi$$
$$48$$ 185001.i 1.67283i
$$49$$ −82271.0 84099.8i −0.699292 0.714836i
$$50$$ −108680. −0.869440
$$51$$ 269280. 2.02999
$$52$$ 0 0
$$53$$ −76406.0 −0.513216 −0.256608 0.966516i $$-0.582605\pi$$
−0.256608 + 0.966516i $$0.582605\pi$$
$$54$$ 210295.i 1.33551i
$$55$$ 39475.4i 0.237268i
$$56$$ 68096.0 161876.i 0.387755 0.921762i
$$57$$ −140760. −0.760072
$$58$$ −89168.0 −0.457009
$$59$$ 113232.i 0.551332i −0.961253 0.275666i $$-0.911102\pi$$
0.961253 0.275666i $$-0.0888984\pi$$
$$60$$ 0 0
$$61$$ 275108.i 1.21203i 0.795452 + 0.606016i $$0.207233\pi$$
−0.795452 + 0.606016i $$0.792767\pi$$
$$62$$ 219689.i 0.921793i
$$63$$ −174363. + 414492.i −0.697321 + 1.65766i
$$64$$ 262144. 1.00000
$$65$$ 99960.0 0.363987
$$66$$ 315803.i 1.09846i
$$67$$ 495242. 1.64662 0.823309 0.567593i $$-0.192125\pi$$
0.823309 + 0.567593i $$0.192125\pi$$
$$68$$ 0 0
$$69$$ 213998.i 0.651423i
$$70$$ −114240. 48057.0i −0.333061 0.140108i
$$71$$ −184406. −0.515229 −0.257614 0.966248i $$-0.582936\pi$$
−0.257614 + 0.966248i $$0.582936\pi$$
$$72$$ −671232. −1.79835
$$73$$ 60974.6i 0.156740i 0.996924 + 0.0783701i $$0.0249716\pi$$
−0.996924 + 0.0783701i $$0.975028\pi$$
$$74$$ −24016.0 −0.0592660
$$75$$ 613585.i 1.45442i
$$76$$ 0 0
$$77$$ 116242. 276328.i 0.254619 0.605275i
$$78$$ 799680. 1.68513
$$79$$ −534934. −1.08497 −0.542486 0.840065i $$-0.682517\pi$$
−0.542486 + 0.840065i $$0.682517\pi$$
$$80$$ 185001.i 0.361331i
$$81$$ 231561. 0.435723
$$82$$ 460336.i 0.834897i
$$83$$ 714848.i 1.25020i 0.780545 + 0.625100i $$0.214942\pi$$
−0.780545 + 0.625100i $$0.785058\pi$$
$$84$$ 0 0
$$85$$ −269280. −0.438478
$$86$$ −251344. −0.395160
$$87$$ 503424.i 0.764498i
$$88$$ 447488. 0.656649
$$89$$ 629529.i 0.892988i 0.894787 + 0.446494i $$0.147328\pi$$
−0.894787 + 0.446494i $$0.852672\pi$$
$$90$$ 473705.i 0.649801i
$$91$$ −699720. 294349.i −0.928539 0.390606i
$$92$$ 0 0
$$93$$ 1.24032e6 1.54200
$$94$$ 579575.i 0.697792i
$$95$$ 140760. 0.164176
$$96$$ 0 0
$$97$$ 814440.i 0.892368i −0.894941 0.446184i $$-0.852783\pi$$
0.894941 0.446184i $$-0.147217\pi$$
$$98$$ 658168. + 672798.i 0.699292 + 0.714836i
$$99$$ −1.14581e6 −1.18089
$$100$$ 0 0
$$101$$ 1.95195e6i 1.89455i 0.320425 + 0.947274i $$0.396174\pi$$
−0.320425 + 0.947274i $$0.603826\pi$$
$$102$$ −2.15424e6 −2.02999
$$103$$ 1.69744e6i 1.55340i −0.629871 0.776700i $$-0.716892\pi$$
0.629871 0.776700i $$-0.283108\pi$$
$$104$$ 1.13313e6i 1.00735i
$$105$$ 271320. 644976.i 0.234376 0.557154i
$$106$$ 611248. 0.513216
$$107$$ 1.61603e6 1.31916 0.659579 0.751635i $$-0.270734\pi$$
0.659579 + 0.751635i $$0.270734\pi$$
$$108$$ 0 0
$$109$$ 199226. 0.153839 0.0769195 0.997037i $$-0.475492\pi$$
0.0769195 + 0.997037i $$0.475492\pi$$
$$110$$ 315803.i 0.237268i
$$111$$ 135589.i 0.0991418i
$$112$$ −544768. + 1.29501e6i −0.387755 + 0.921762i
$$113$$ −1.80762e6 −1.25277 −0.626386 0.779513i $$-0.715467\pi$$
−0.626386 + 0.779513i $$0.715467\pi$$
$$114$$ 1.12608e6 0.760072
$$115$$ 213998.i 0.140707i
$$116$$ 0 0
$$117$$ 2.90144e6i 1.81157i
$$118$$ 905856.i 0.551332i
$$119$$ 1.88496e6 + 792941.i 1.11857 + 0.470543i
$$120$$ 1.04448e6 0.604444
$$121$$ −1.00768e6 −0.568812
$$122$$ 2.20087e6i 1.21203i
$$123$$ −2.59896e6 −1.39664
$$124$$ 0 0
$$125$$ 1.31931e6i 0.675486i
$$126$$ 1.39490e6 3.31593e6i 0.697321 1.65766i
$$127$$ 3.32472e6 1.62310 0.811548 0.584286i $$-0.198625\pi$$
0.811548 + 0.584286i $$0.198625\pi$$
$$128$$ −2.09715e6 −1.00000
$$129$$ 1.41904e6i 0.661035i
$$130$$ −799680. −0.363987
$$131$$ 3.13567e6i 1.39482i −0.716674 0.697408i $$-0.754336\pi$$
0.716674 0.697408i $$-0.245664\pi$$
$$132$$ 0 0
$$133$$ −985320. 414492.i −0.418815 0.176182i
$$134$$ −3.96194e6 −1.64662
$$135$$ −1.18728e6 −0.482561
$$136$$ 3.05252e6i 1.21351i
$$137$$ 2.12927e6 0.828072 0.414036 0.910260i $$-0.364119\pi$$
0.414036 + 0.910260i $$0.364119\pi$$
$$138$$ 1.71199e6i 0.651423i
$$139$$ 1.68421e6i 0.627121i 0.949568 + 0.313561i $$0.101522\pi$$
−0.949568 + 0.313561i $$0.898478\pi$$
$$140$$ 0 0
$$141$$ 3.27216e6 1.16729
$$142$$ 1.47525e6 0.515229
$$143$$ 1.93429e6i 0.661477i
$$144$$ 5.36986e6 1.79835
$$145$$ 503424.i 0.165132i
$$146$$ 487797.i 0.156740i
$$147$$ −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 $$0.628337\pi$$
$$150$$ 4.90868e6i 1.45442i
$$151$$ −1.68557e6 −0.489570 −0.244785 0.969577i $$-0.578717\pi$$
−0.244785 + 0.969577i $$0.578717\pi$$
$$152$$ 1.59564e6i 0.454363i
$$153$$ 7.81613e6i 2.18231i
$$154$$ −929936. + 2.21062e6i −0.254619 + 0.605275i
$$155$$ −1.24032e6 −0.333072
$$156$$ 0 0
$$157$$ 3.67641e6i 0.950002i −0.879985 0.475001i $$-0.842448\pi$$
0.879985 0.475001i $$-0.157552\pi$$
$$158$$ 4.27947e6 1.08497
$$159$$ 3.45098e6i 0.858521i
$$160$$ 0 0
$$161$$ 630154. 1.49799e6i 0.150997 0.358947i
$$162$$ −1.85249e6 −0.435723
$$163$$ 1.88191e6 0.434547 0.217274 0.976111i $$-0.430284\pi$$
0.217274 + 0.976111i $$0.430284\pi$$
$$164$$ 0 0
$$165$$ 1.78296e6 0.396908
$$166$$ 5.71878e6i 1.25020i
$$167$$ 3.15595e6i 0.677612i 0.940856 + 0.338806i $$0.110023\pi$$
−0.940856 + 0.338806i $$0.889977\pi$$
$$168$$ −7.31136e6 3.07565e6i −1.54195 0.648648i
$$169$$ −71231.0 −0.0147574
$$170$$ 2.15424e6 0.438478
$$171$$ 4.08570e6i 0.817106i
$$172$$ 0 0
$$173$$ 2.29477e6i 0.443201i 0.975138 + 0.221600i $$0.0711280\pi$$
−0.975138 + 0.221600i $$0.928872\pi$$
$$174$$ 4.02739e6i 0.764498i
$$175$$ 1.80680e6 4.29509e6i 0.337130 0.801417i
$$176$$ −3.57990e6 −0.656649
$$177$$ −5.11428e6 −0.922284
$$178$$ 5.03623e6i 0.892988i
$$179$$ 3.51846e6 0.613470 0.306735 0.951795i $$-0.400763\pi$$
0.306735 + 0.951795i $$0.400763\pi$$
$$180$$ 0 0
$$181$$ 7.48267e6i 1.26189i 0.775829 + 0.630944i $$0.217332\pi$$
−0.775829 + 0.630944i $$0.782668\pi$$
$$182$$ 5.59776e6 + 2.35479e6i 0.928539 + 0.390606i
$$183$$ 1.24256e7 2.02752
$$184$$ 2.42586e6 0.389414
$$185$$ 135589.i 0.0214146i
$$186$$ −9.92256e6 −1.54200
$$187$$ 5.21075e6i 0.796848i
$$188$$ 0 0
$$189$$ 8.31096e6 + 3.49615e6i 1.23102 + 0.517850i
$$190$$ −1.12608e6 −0.164176
$$191$$ −7.20028e6 −1.03335 −0.516677 0.856180i $$-0.672831\pi$$
−0.516677 + 0.856180i $$0.672831\pi$$
$$192$$ 1.18401e7i 1.67283i
$$193$$ −1.30889e7 −1.82067 −0.910335 0.413872i $$-0.864176\pi$$
−0.910335 + 0.413872i $$0.864176\pi$$
$$194$$ 6.51552e6i 0.892368i
$$195$$ 4.51483e6i 0.608888i
$$196$$ 0 0
$$197$$ −9.17476e6 −1.20004 −0.600020 0.799985i $$-0.704841\pi$$
−0.600020 + 0.799985i $$0.704841\pi$$
$$198$$ 9.16651e6 1.18089
$$199$$ 6.78769e6i 0.861317i 0.902515 + 0.430658i $$0.141719\pi$$
−0.902515 + 0.430658i $$0.858281\pi$$
$$200$$ 6.95552e6 0.869440
$$201$$ 2.23683e7i 2.75451i
$$202$$ 1.56156e7i 1.89455i
$$203$$ 1.48242e6 3.52397e6i 0.177208 0.421254i
$$204$$ 0 0
$$205$$ 2.59896e6 0.301674
$$206$$ 1.35795e7i 1.55340i
$$207$$ −6.21152e6 −0.700304
$$208$$ 9.06507e6i 1.00735i
$$209$$ 2.72380e6i 0.298357i
$$210$$ −2.17056e6 + 5.15980e6i −0.234376 + 0.557154i
$$211$$ 8.40084e6 0.894284 0.447142 0.894463i $$-0.352442\pi$$
0.447142 + 0.894463i $$0.352442\pi$$
$$212$$ 0 0
$$213$$ 8.32895e6i 0.861889i
$$214$$ −1.29282e7 −1.31916
$$215$$ 1.41904e6i 0.142784i
$$216$$ 1.34589e7i 1.33551i
$$217$$ 8.68224e6 + 3.65233e6i 0.849675 + 0.357430i
$$218$$ −1.59381e6 −0.153839
$$219$$ 2.75400e6 0.262199
$$220$$ 0 0
$$221$$ 1.31947e7 1.22243
$$222$$ 1.08472e6i 0.0991418i
$$223$$ 4.90434e6i 0.442248i −0.975246 0.221124i $$-0.929027\pi$$
0.975246 0.221124i $$-0.0709726\pi$$
$$224$$ 0 0
$$225$$ −1.78099e7 −1.56356
$$226$$ 1.44610e7 1.25277
$$227$$ 1.32183e7i 1.13005i −0.825075 0.565023i $$-0.808867\pi$$
0.825075 0.565023i $$-0.191133\pi$$
$$228$$ 0 0
$$229$$ 338974.i 0.0282266i 0.999900 + 0.0141133i $$0.00449256\pi$$
−0.999900 + 0.0141133i $$0.995507\pi$$
$$230$$ 1.71199e6i 0.140707i
$$231$$ −1.24807e7 5.25023e6i −1.01252 0.425934i
$$232$$ 5.70675e6 0.457009
$$233$$ 4.84146e6 0.382744 0.191372 0.981518i $$-0.438706\pi$$
0.191372 + 0.981518i $$0.438706\pi$$
$$234$$ 2.32115e7i 1.81157i
$$235$$ −3.27216e6 −0.252134
$$236$$ 0 0
$$237$$ 2.41610e7i 1.81497i
$$238$$ −1.50797e7 6.34352e6i −1.11857 0.470543i
$$239$$ −1.37297e7 −1.00570 −0.502850 0.864374i $$-0.667715\pi$$
−0.502850 + 0.864374i $$0.667715\pi$$
$$240$$ −8.35584e6 −0.604444
$$241$$ 3.66913e6i 0.262127i −0.991374 0.131064i $$-0.958161\pi$$
0.991374 0.131064i $$-0.0418392\pi$$
$$242$$ 8.06148e6 0.568812
$$243$$ 8.70433e6i 0.606619i
$$244$$ 0 0
$$245$$ 3.79848e6 3.71588e6i 0.258292 0.252676i
$$246$$ 2.07917e7 1.39664
$$247$$ −6.89724e6 −0.457704
$$248$$ 1.40601e7i 0.921793i
$$249$$ 3.22871e7 2.09137
$$250$$ 1.05545e7i 0.675486i
$$251$$ 1.57289e7i 0.994664i −0.867560 0.497332i $$-0.834313\pi$$
0.867560 0.497332i $$-0.165687\pi$$
$$252$$ 0 0
$$253$$ 4.14101e6 0.255708
$$254$$ −2.65978e7 −1.62310
$$255$$ 1.21624e7i 0.733498i
$$256$$ 0 0
$$257$$ 7.54531e6i 0.444506i 0.974989 + 0.222253i $$0.0713411\pi$$
−0.974989 + 0.222253i $$0.928659\pi$$
$$258$$ 1.13523e7i 0.661035i
$$259$$ 399266. 949126.i 0.0229807 0.0546292i
$$260$$ 0 0
$$261$$ −1.46124e7 −0.821864
$$262$$ 2.50854e7i 1.39482i
$$263$$ −1.32059e7 −0.725942 −0.362971 0.931800i $$-0.618238\pi$$
−0.362971 + 0.931800i $$0.618238\pi$$
$$264$$ 2.02114e7i 1.09846i
$$265$$ 3.45098e6i 0.185441i
$$266$$ 7.88256e6 + 3.31593e6i 0.418815 + 0.176182i
$$267$$ 2.84335e7 1.49382
$$268$$ 0 0
$$269$$ 1.59600e7i 0.819930i −0.912101 0.409965i $$-0.865541\pi$$
0.912101 0.409965i $$-0.134459\pi$$
$$270$$ 9.49824e6 0.482561
$$271$$ 2.48446e7i 1.24831i 0.781299 + 0.624157i $$0.214557\pi$$
−0.781299 + 0.624157i $$0.785443\pi$$
$$272$$ 2.44202e7i 1.21351i
$$273$$ −1.32947e7 + 3.16038e7i −0.653416 + 1.55329i
$$274$$ −1.70341e7 −0.828072
$$275$$ 1.18733e7 0.570917
$$276$$ 0 0
$$277$$ 1.60013e7 0.752863 0.376432 0.926444i $$-0.377151\pi$$
0.376432 + 0.926444i $$0.377151\pi$$
$$278$$ 1.34737e7i 0.627121i
$$279$$ 3.60016e7i 1.65771i
$$280$$ 7.31136e6 + 3.07565e6i 0.333061 + 0.140108i
$$281$$ −603566. −0.0272023 −0.0136012 0.999908i $$-0.504330\pi$$
−0.0136012 + 0.999908i $$0.504330\pi$$
$$282$$ −2.61773e7 −1.16729
$$283$$ 2.22195e7i 0.980334i −0.871629 0.490167i $$-0.836936\pi$$
0.871629 0.490167i $$-0.163064\pi$$
$$284$$ 0 0
$$285$$ 6.35762e6i 0.274637i
$$286$$ 1.54744e7i 0.661477i
$$287$$ −1.81927e7 7.65308e6i −0.769577 0.323736i
$$288$$ 0 0
$$289$$ −1.14074e7 −0.472599
$$290$$ 4.02739e6i 0.165132i
$$291$$ −3.67853e7 −1.49278
$$292$$ 0 0
$$293$$ 4.28134e7i 1.70207i 0.525110 + 0.851034i $$0.324024\pi$$
−0.525110 + 0.851034i $$0.675976\pi$$
$$294$$ 3.03878e7 2.97271e7i 1.19580 1.16980i
$$295$$ 5.11428e6 0.199213
$$296$$ 1.53702e6 0.0592660
$$297$$ 2.29747e7i 0.876961i
$$298$$ 2.07659e7 0.784696
$$299$$ 1.04859e7i 0.392277i
$$300$$ 0 0
$$301$$ 4.17859e6 9.93326e6i 0.153225 0.364244i
$$302$$ 1.34845e7 0.489570
$$303$$ 8.81627e7 3.16925
$$304$$ 1.27651e7i 0.454363i
$$305$$ −1.24256e7 −0.437945
$$306$$ 6.25290e7i 2.18231i
$$307$$ 4.02152e7i 1.38987i 0.719072 + 0.694936i $$0.244567\pi$$
−0.719072 + 0.694936i $$0.755433\pi$$
$$308$$ 0 0
$$309$$ −7.66673e7 −2.59857
$$310$$ 9.92256e6 0.333072
$$311$$ 1.47381e7i 0.489958i −0.969528 0.244979i $$-0.921219\pi$$
0.969528 0.244979i $$-0.0787811\pi$$
$$312$$ −5.11795e7 −1.68513
$$313$$ 4.19490e7i 1.36801i −0.729479 0.684004i $$-0.760237\pi$$
0.729479 0.684004i $$-0.239763\pi$$
$$314$$ 2.94112e7i 0.950002i
$$315$$ −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 $$0.263548\pi$$
$$318$$ 2.76078e7i 0.858521i
$$319$$ 9.74160e6 0.300095
$$320$$ 1.18401e7i 0.361331i
$$321$$ 7.29900e7i 2.20673i
$$322$$ −5.04123e6 + 1.19839e7i −0.150997 + 0.358947i
$$323$$ 1.85803e7 0.551373
$$324$$ 0 0
$$325$$ 3.00657e7i 0.875832i
$$326$$ −1.50553e7 −0.434547
$$327$$ 8.99831e6i 0.257346i
$$328$$ 2.94615e7i 0.834897i
$$329$$ 2.29051e7 + 9.63543e6i 0.643198 + 0.270572i
$$330$$ −1.42637e7 −0.396908
$$331$$ −5.32204e7 −1.46755 −0.733777 0.679390i $$-0.762244\pi$$
−0.733777 + 0.679390i $$0.762244\pi$$
$$332$$ 0 0
$$333$$ −3.93562e6 −0.106581
$$334$$ 2.52476e7i 0.677612i
$$335$$ 2.23683e7i 0.594974i
$$336$$ 5.84909e7 + 2.46052e7i 1.54195 + 0.648648i
$$337$$ 2.34579e6 0.0612913 0.0306456 0.999530i $$-0.490244\pi$$
0.0306456 + 0.999530i $$0.490244\pi$$
$$338$$ 569848. 0.0147574
$$339$$ 8.16437e7i 2.09567i
$$340$$ 0 0
$$341$$ 2.40010e7i 0.605295i
$$342$$ 3.26856e7i 0.817106i
$$343$$ −3.75314e7 + 1.48259e7i −0.930063 + 0.367400i
$$344$$ 1.60860e7 0.395160
$$345$$ 9.66552e6 0.235379
$$346$$ 1.83581e7i 0.443201i
$$347$$ −4.80596e7 −1.15025 −0.575124 0.818066i $$-0.695046\pi$$
−0.575124 + 0.818066i $$0.695046\pi$$
$$348$$ 0 0
$$349$$ 1.00499e7i 0.236421i −0.992989 0.118211i $$-0.962284\pi$$
0.992989 0.118211i $$-0.0377158\pi$$
$$350$$ −1.44544e7 + 3.43608e7i −0.337130 + 0.801417i
$$351$$ 5.81767e7 1.34533
$$352$$ 0 0
$$353$$ 7.65216e7i 1.73964i 0.493368 + 0.869821i $$0.335766\pi$$
−0.493368 + 0.869821i $$0.664234\pi$$
$$354$$ 4.09142e7 0.922284
$$355$$ 8.32895e6i 0.186168i
$$356$$ 0 0
$$357$$ 3.58142e7 8.51368e7i 0.787138 1.87117i
$$358$$ −2.81477e7 −0.613470
$$359$$ 8.39735e6 0.181493 0.0907463 0.995874i $$-0.471075\pi$$
0.0907463 + 0.995874i $$0.471075\pi$$
$$360$$ 3.03171e7i 0.649801i
$$361$$ 3.73334e7 0.793554
$$362$$ 5.98613e7i 1.26189i
$$363$$ 4.55135e7i 0.951525i
$$364$$ 0 0
$$365$$ −2.75400e6 −0.0566351
$$366$$ −9.94051e7 −2.02752
$$367$$ 3.82776e6i 0.0774366i 0.999250 + 0.0387183i $$0.0123275\pi$$
−0.999250 + 0.0387183i $$0.987672\pi$$
$$368$$ −1.94068e7 −0.389414
$$369$$ 7.54375e7i 1.50144i
$$370$$ 1.08472e6i 0.0214146i
$$371$$ −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 $$0.657842\pi$$
$$374$$ 4.16860e7i 0.796848i
$$375$$ 5.95884e7 1.12997
$$376$$ 3.70928e7i 0.697792i
$$377$$ 2.46678e7i 0.460369i
$$378$$ −6.64877e7 2.79692e7i −1.23102 0.517850i
$$379$$ 3.74561e7 0.688026 0.344013 0.938965i $$-0.388214\pi$$
0.344013 + 0.938965i $$0.388214\pi$$
$$380$$ 0 0
$$381$$ 1.50166e8i 2.71516i
$$382$$ 5.76022e7 1.03335
$$383$$ 5.01003e7i 0.891752i −0.895095 0.445876i $$-0.852892\pi$$
0.895095 0.445876i $$-0.147108\pi$$
$$384$$ 9.47207e7i 1.67283i
$$385$$ 1.24807e7 + 5.25023e6i 0.218704 + 0.0920017i
$$386$$ 1.04711e8 1.82067
$$387$$ −4.11890e7 −0.710638
$$388$$ 0 0
$$389$$ 224986. 0.00382214 0.00191107 0.999998i $$-0.499392\pi$$
0.00191107 + 0.999998i $$0.499392\pi$$
$$390$$ 3.61186e7i 0.608888i
$$391$$ 2.82478e7i 0.472557i
$$392$$ −4.21228e7 4.30591e7i −0.699292 0.714836i
$$393$$ −1.41627e8 −2.33329
$$394$$ 7.33981e7 1.20004
$$395$$ 2.41610e7i 0.392034i
$$396$$ 0 0
$$397$$ 871937.i 0.0139352i −0.999976 0.00696760i $$-0.997782\pi$$
0.999976 0.00696760i $$-0.00221787\pi$$
$$398$$ 5.43015e7i 0.861317i
$$399$$ −1.87211e7 + 4.45033e7i −0.294722 + 0.700606i
$$400$$ −5.56442e7 −0.869440
$$401$$ 1.44909e7 0.224730 0.112365 0.993667i $$-0.464157\pi$$
0.112365 + 0.993667i $$0.464157\pi$$
$$402$$ 1.78946e8i 2.75451i
$$403$$ 6.07757e7 0.928570
$$404$$ 0 0
$$405$$ 1.04588e7i 0.157440i
$$406$$ −1.18593e7 + 2.81918e7i −0.177208 + 0.421254i
$$407$$ 2.62375e6 0.0389170
$$408$$ 1.37871e8 2.02999
$$409$$ 1.04303e8i 1.52450i 0.647284 + 0.762249i $$0.275905\pi$$
−0.647284 + 0.762249i $$0.724095\pi$$
$$410$$ −2.07917e7 −0.301674
$$411$$ 9.61712e7i 1.38522i
$$412$$ 0 0
$$413$$ −3.58000e7 1.50599e7i −0.508197 0.213782i
$$414$$ 4.96921e7 0.700304
$$415$$ −3.22871e7 −0.451736
$$416$$ 0 0
$$417$$ 7.60696e7 1.04907
$$418$$ 2.17904e7i 0.298357i
$$419$$ 8.22075e7i 1.11756i −0.829317 0.558778i $$-0.811270\pi$$
0.829317 0.558778i $$-0.188730\pi$$
$$420$$ 0 0
$$421$$ −1.33780e7 −0.179285 −0.0896427 0.995974i $$-0.528573\pi$$
−0.0896427 + 0.995974i $$0.528573\pi$$
$$422$$ −6.72067e7 −0.894284
$$423$$ 9.49778e7i 1.25488i
$$424$$ −3.91199e7 −0.513216
$$425$$ 8.09932e7i 1.05507i
$$426$$ 6.66316e7i 0.861889i
$$427$$ 8.69795e7 + 3.65894e7i 1.11721 + 0.469972i
$$428$$ 0 0
$$429$$ −8.73650e7 −1.10654
$$430$$ 1.13523e7i 0.142784i
$$431$$ −1.34244e8 −1.67673 −0.838367 0.545106i $$-0.816490\pi$$
−0.838367 + 0.545106i $$0.816490\pi$$
$$432$$ 1.07671e8i 1.33551i
$$433$$ 1.03230e8i 1.27158i −0.771863 0.635789i $$-0.780675\pi$$
0.771863 0.635789i $$-0.219325\pi$$
$$434$$ −6.94579e7 2.92187e7i −0.849675 0.357430i
$$435$$ 2.27378e7 0.276237
$$436$$ 0 0
$$437$$ 1.47659e7i 0.176935i
$$438$$ −2.20320e7 −0.262199
$$439$$ 2.65816e7i 0.314186i 0.987584 + 0.157093i $$0.0502123\pi$$
−0.987584 + 0.157093i $$0.949788\pi$$
$$440$$ 2.02114e7i 0.237268i
$$441$$ 1.07857e8 + 1.10255e8i 1.25757 + 1.28553i
$$442$$ −1.05558e8 −1.22243
$$443$$ 1.31972e8 1.51799 0.758996 0.651096i $$-0.225690\pi$$
0.758996 + 0.651096i $$0.225690\pi$$
$$444$$ 0 0
$$445$$ −2.84335e7 −0.322664
$$446$$ 3.92348e7i 0.442248i
$$447$$ 1.17240e8i 1.31266i
$$448$$ 3.48652e7 8.28806e7i 0.387755 0.921762i
$$449$$ 1.47766e8 1.63244 0.816218 0.577743i $$-0.196067\pi$$
0.816218 + 0.577743i $$0.196067\pi$$
$$450$$ 1.42479e8 1.56356
$$451$$ 5.02917e7i 0.548234i
$$452$$ 0 0
$$453$$ 7.61309e7i 0.818967i
$$454$$ 1.05746e8i 1.13005i
$$455$$ 1.32947e7 3.16038e7i 0.141138 0.335510i
$$456$$ −7.20691e7 −0.760072
$$457$$ −8.22868e7 −0.862147 −0.431074 0.902317i $$-0.641865\pi$$
−0.431074 + 0.902317i $$0.641865\pi$$
$$458$$ 2.71179e6i 0.0282266i
$$459$$ −1.56721e8 −1.62065
$$460$$ 0 0
$$461$$ 1.31884e8i 1.34614i 0.739580 + 0.673068i $$0.235024\pi$$
−0.739580 + 0.673068i $$0.764976\pi$$
$$462$$ 9.98458e7 + 4.20018e7i 1.01252 + 0.425934i
$$463$$ 1.39927e6 0.0140981 0.00704904 0.999975i $$-0.497756\pi$$
0.00704904 + 0.999975i $$0.497756\pi$$
$$464$$ −4.56540e7 −0.457009
$$465$$ 5.60207e7i 0.557173i
$$466$$ −3.87317e7 −0.382744
$$467$$ 1.81321e7i 0.178032i 0.996030 + 0.0890158i $$0.0283722\pi$$
−0.996030 + 0.0890158i $$0.971628\pi$$
$$468$$ 0 0
$$469$$ 6.58672e7 1.56578e8i 0.638485 1.51779i
$$470$$ 2.61773e7 0.252134
$$471$$ −1.66050e8 −1.58919
$$472$$ 5.79748e7i 0.551332i
$$473$$ 2.74593e7 0.259482
$$474$$ 1.93288e8i 1.81497i
$$475$$ 4.23374e7i 0.395042i
$$476$$ 0 0
$$477$$ 1.00168e8 0.922943
$$478$$ 1.09838e8 1.00570
$$479$$ 2.89375e7i 0.263303i 0.991296 + 0.131651i $$0.0420279\pi$$
−0.991296 + 0.131651i $$0.957972\pi$$
$$480$$ 0 0
$$481$$ 6.64388e6i 0.0597017i
$$482$$ 2.93531e7i 0.262127i
$$483$$ −6.76586e7 2.84618e7i −0.600457 0.252592i
$$484$$ 0 0
$$485$$ 3.67853e7 0.322440
$$486$$ 6.96346e7i 0.606619i
$$487$$ −9.47515e7 −0.820350 −0.410175 0.912007i $$-0.634532\pi$$
−0.410175 + 0.912007i $$0.634532\pi$$
$$488$$ 1.40855e8i 1.21203i
$$489$$ 8.49992e7i 0.726923i
$$490$$ −3.03878e7 + 2.97271e7i −0.258292 + 0.252676i
$$491$$ −2.58834e7 −0.218663 −0.109332 0.994005i $$-0.534871\pi$$
−0.109332 + 0.994005i $$0.534871\pi$$
$$492$$ 0 0
$$493$$ 6.64520e7i 0.554584i
$$494$$ 5.51779e7 0.457704
$$495$$ 5.17522e7i 0.426691i
$$496$$ 1.12481e8i 0.921793i
$$497$$ −2.45260e7 + 5.83026e7i −0.199783 + 0.474918i
$$498$$ −2.58297e8 −2.09137
$$499$$ 1.56023e8 1.25571 0.627853 0.778332i $$-0.283934\pi$$
0.627853 + 0.778332i $$0.283934\pi$$
$$500$$ 0 0
$$501$$ 1.42543e8 1.13353
$$502$$ 1.25831e8i 0.994664i
$$503$$ 1.11476e8i 0.875950i −0.898987 0.437975i $$-0.855696\pi$$
0.898987 0.437975i $$-0.144304\pi$$
$$504$$ −8.92739e7 + 2.12220e8i −0.697321 + 1.65766i
$$505$$ −8.81627e7 −0.684559
$$506$$ −3.31281e7 −0.255708
$$507$$ 3.21724e6i 0.0246865i
$$508$$ 0 0
$$509$$ 7.45421e7i 0.565260i −0.959229 0.282630i $$-0.908793\pi$$
0.959229 0.282630i $$-0.0912068\pi$$
$$510$$ 9.72992e7i 0.733498i
$$511$$ 1.92780e7 + 8.10962e6i 0.144477 + 0.0607768i
$$512$$ 1.34218e8 1.00000
$$513$$ 8.19223e7 0.606806
$$514$$ 6.03625e7i 0.444506i
$$515$$ 7.66673e7 0.561291
$$516$$ 0 0
$$517$$ 6.33185e7i 0.458204i
$$518$$ −3.19413e6 + 7.59301e6i −0.0229807 + 0.0546292i
$$519$$ 1.03646e8 0.741398
$$520$$ 5.11795e7 0.363987
$$521$$ 1.96232e8i 1.38758i 0.720179 + 0.693789i $$0.244060\pi$$
−0.720179 + 0.693789i $$0.755940\pi$$
$$522$$ 1.16899e8 0.821864
$$523$$ 4.62080e7i 0.323007i −0.986872 0.161504i $$-0.948366\pi$$
0.986872 0.161504i $$-0.0516344\pi$$
$$524$$ 0 0
$$525$$ −1.93994e8 8.16068e7i −1.34063 0.563960i
$$526$$ 1.05648e8 0.725942
$$527$$ −1.63722e8 −1.11860
$$528$$ 1.61691e8i 1.09846i
$$529$$ −1.25587e8 −0.848357
$$530$$ 2.76078e7i 0.185441i
$$531$$ 1.48447e8i 0.991490i
$$532$$ 0 0
$$533$$ −1.27349e8 −0.841035
$$534$$ −2.27468e8 −1.49382
$$535$$ 7.29900e7i 0.476653i
$$536$$ 2.53564e8 1.64662
$$537$$ 1.58916e8i 1.02623i
$$538$$ 1.27680e8i 0.819930i
$$539$$ −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 $$0.576410\pi$$
$$542$$ 1.98757e8i 1.24831i
$$543$$ 3.37965e8 2.11092
$$544$$ 0 0
$$545$$ 8.99831e6i 0.0555868i
$$546$$ 1.06357e8 2.52830e8i 0.653416 1.55329i
$$547$$ 7.26760e7 0.444047 0.222023 0.975041i $$-0.428734\pi$$
0.222023 + 0.975041i $$0.428734\pi$$
$$548$$ 0 0
$$549$$ 3.60667e8i 2.17966i
$$550$$ −9.49863e7 −0.570917
$$551$$ 3.47363e7i 0.207648i
$$552$$ 1.09567e8i 0.651423i
$$553$$ −7.11462e7 + 1.69127e8i −0.420704 + 1.00009i
$$554$$ −1.28010e8 −0.752863
$$555$$ 6.12408e6 0.0358230
$$556$$ 0 0
$$557$$ −3.10741e8 −1.79818 −0.899090 0.437765i $$-0.855770\pi$$
−0.899090 + 0.437765i $$0.855770\pi$$
$$558$$ 2.88013e8i 1.65771i
$$559$$ 6.95328e7i 0.398065i
$$560$$ −5.84909e7 2.46052e7i −0.333061 0.140108i
$$561$$ 2.35351e8 1.33299
$$562$$ 4.82853e6 0.0272023
$$563$$ 5.66378e7i 0.317381i −0.987328 0.158690i $$-0.949273\pi$$
0.987328 0.158690i $$-0.0507272\pi$$
$$564$$ 0 0
$$565$$ 8.16437e7i 0.452665i
$$566$$ 1.77756e8i 0.980334i
$$567$$ 3.07976e7 7.32114e7i 0.168954 0.401633i
$$568$$ −9.44159e7 −0.515229
$$569$$ 5.17304e7 0.280808 0.140404 0.990094i $$-0.455160\pi$$
0.140404 + 0.990094i $$0.455160\pi$$
$$570$$ 5.08609e7i 0.274637i
$$571$$ 8.68765e7 0.466653 0.233326 0.972398i $$-0.425039\pi$$
0.233326 + 0.972398i $$0.425039\pi$$
$$572$$ 0 0
$$573$$ 3.25210e8i 1.72862i
$$574$$ 1.45542e8 + 6.12246e7i 0.769577 + 0.323736i
$$575$$ 6.43657e7 0.338572
$$576$$ −3.43671e8 −1.79835
$$577$$ 5.89865e7i 0.307062i −0.988144 0.153531i $$-0.950936\pi$$
0.988144 0.153531i $$-0.0490644\pi$$
$$578$$ 9.12591e7 0.472599
$$579$$ 5.91178e8i 3.04567i
$$580$$ 0 0
$$581$$ 2.26010e8 + 9.50748e7i 1.15239 + 0.484771i
$$582$$ 2.94282e8 1.49278
$$583$$ −6.67788e7 −0.337003
$$584$$ 3.12190e7i 0.156740i
$$585$$ −1.31048e8 −0.654578
$$586$$ 3.42507e8i 1.70207i
$$587$$ 3.10848e8i 1.53686i −0.639934 0.768430i $$-0.721038\pi$$
0.639934 0.768430i $$-0.278962\pi$$
$$588$$ 0 0
$$589$$ 8.55821e7 0.418829
$$590$$ −4.09142e7 −0.199213
$$591$$ 4.14390e8i 2.00746i
$$592$$ −1.22962e7 −0.0592660
$$593$$ 3.46714e8i 1.66268i −0.555766 0.831339i $$-0.687575\pi$$
0.555766 0.831339i $$-0.312425\pi$$
$$594$$ 1.83797e8i 0.876961i
$$595$$ −3.58142e7 + 8.51368e7i −0.170022 + 0.404172i
$$596$$ 0 0
$$597$$ 3.06575e8 1.44083
$$598$$ 8.38873e7i 0.392277i
$$599$$ 9.47771e7 0.440984 0.220492 0.975389i $$-0.429234\pi$$
0.220492 + 0.975389i $$0.429234\pi$$
$$600$$ 3.14156e8i 1.45442i
$$601$$ 2.04951e8i 0.944119i −0.881567 0.472060i $$-0.843511\pi$$
0.881567 0.472060i $$-0.156489\pi$$
$$602$$ −3.34288e7 + 7.94661e7i −0.153225 + 0.364244i
$$603$$ −6.49262e8 −2.96120
$$604$$ 0 0
$$605$$ 4.55135e7i 0.205529i
$$606$$ −7.05301e8 −3.16925
$$607$$ 3.28634e8i 1.46942i 0.678379 + 0.734712i $$0.262683\pi$$
−0.678379 + 0.734712i $$0.737317\pi$$
$$608$$ 0 0
$$609$$ −1.59165e8 6.69554e7i −0.704686 0.296438i
$$610$$ 9.94051e7 0.437945
$$611$$ 1.60336e8 0.702922
$$612$$ 0 0
$$613$$ 2.67967e8 1.16332 0.581660 0.813432i $$-0.302403\pi$$
0.581660 + 0.813432i $$0.302403\pi$$
$$614$$ 3.21721e8i 1.38987i
$$615$$ 1.17386e8i 0.504649i
$$616$$ 5.95159e7 1.41480e8i 0.254619 0.605275i
$$617$$ −3.88909e8 −1.65574 −0.827870 0.560921i $$-0.810447\pi$$
−0.827870 + 0.560921i $$0.810447\pi$$
$$618$$ 6.13338e8 2.59857
$$619$$ 6.30894e7i 0.266002i −0.991116 0.133001i $$-0.957539\pi$$
0.991116 0.133001i $$-0.0424613\pi$$
$$620$$ 0 0
$$621$$ 1.24547e8i 0.520066i
$$622$$ 1.17904e8i 0.489958i
$$623$$ 1.99035e8 + 8.37273e7i 0.823123 + 0.346261i
$$624$$ 4.09436e8 1.68513
$$625$$ 1.52677e8 0.625366
$$626$$ 3.35592e8i 1.36801i
$$627$$ −1.23024e8 −0.499101
$$628$$ 0 0
$$629$$ 1.78978e7i 0.0719197i
$$630$$ 1.49769e8 + 6.30027e7i 0.598962 + 0.251964i
$$631$$ −1.30827e8 −0.520725 −0.260363 0.965511i $$-0.583842\pi$$
−0.260363 + 0.965511i $$0.583842\pi$$
$$632$$ −2.73886e8 −1.08497
$$633$$ 3.79435e8i 1.49598i
$$634$$ −3.44738e8 −1.35276
$$635$$ 1.50166e8i 0.586475i
$$636$$ 0 0
$$637$$ −1.86126e8 + 1.82078e8i −0.720091 + 0.704433i
$$638$$ −7.79328e7 −0.300095
$$639$$ 2.41756e8 0.926563
$$640$$ 9.47207e7i 0.361331i
$$641$$ −7.17536e7 −0.272439 −0.136220 0.990679i $$-0.543495\pi$$
−0.136220 + 0.990679i $$0.543495\pi$$
$$642$$ 5.83920e8i 2.20673i
$$643$$ 2.56068e8i 0.963214i 0.876387 + 0.481607i $$0.159947\pi$$
−0.876387 + 0.481607i $$0.840053\pi$$
$$644$$ 0 0
$$645$$ 6.40927e7 0.238852
$$646$$ −1.48643e8 −0.551373
$$647$$ 4.93122e8i 1.82071i −0.413827 0.910356i $$-0.635808\pi$$
0.413827 0.910356i $$-0.364192\pi$$
$$648$$ 1.18559e8 0.435723
$$649$$ 9.89648e7i 0.362032i
$$650$$ 2.40525e8i 0.875832i
$$651$$ 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 $$0.410197\pi$$
$$654$$ 7.19865e7i 0.257346i
$$655$$ 1.41627e8 0.503990
$$656$$ 2.35692e8i 0.834897i
$$657$$ 7.99377e7i 0.281874i
$$658$$ −1.83241e8 7.70834e7i −0.643198 0.270572i
$$659$$ −3.01683e8 −1.05413 −0.527065 0.849825i $$-0.676707\pi$$
−0.527065 + 0.849825i $$0.676707\pi$$
$$660$$ 0 0
$$661$$ 1.80227e8i 0.624044i 0.950075 + 0.312022i $$0.101006\pi$$
−0.950075 + 0.312022i $$0.898994\pi$$
$$662$$ 4.25763e8 1.46755
$$663$$ 5.95957e8i 2.04491i
$$664$$ 3.66002e8i 1.25020i
$$665$$ 1.87211e7 4.45033e7i 0.0636599 0.151331i
$$666$$ 3.14850e7 0.106581
$$667$$ 5.28097e7 0.177966
$$668$$ 0 0
$$669$$ −2.21511e8 −0.739806
$$670$$ 1.78946e8i 0.594974i
$$671$$ 2.40445e8i 0.795880i
$$672$$ 0 0
$$673$$ 4.06265e8 1.33280 0.666399 0.745595i $$-0.267835\pi$$
0.666399 + 0.745595i $$0.267835\pi$$
$$674$$ −1.87663e7 −0.0612913
$$675$$ 3.57106e8i 1.16114i
$$676$$ 0 0
$$677$$ 1.77837e7i 0.0573133i 0.999589 + 0.0286566i $$0.00912294\pi$$
−0.999589 + 0.0286566i $$0.990877\pi$$
$$678$$ 6.53150e8i 2.09567i
$$679$$ −2.57497e8 1.08320e8i −0.822551 0.346020i
$$680$$ −1.37871e8 −0.438478
$$681$$ −5.97020e8 −1.89037
$$682$$ 1.92008e8i 0.605295i
$$683$$ −2.66054e8 −0.835042 −0.417521 0.908667i $$-0.637101\pi$$
−0.417521 + 0.908667i $$0.637101\pi$$
$$684$$ 0 0
$$685$$ 9.61712e7i 0.299208i
$$686$$ 3.00251e8 1.18607e8i 0.930063 0.367400i
$$687$$ 1.53102e7 0.0472183
$$688$$ −1.28688e8 −0.395160
$$689$$ 1.69098e8i 0.516989i
$$690$$ −7.73242e7 −0.235379
$$691$$ 2.44451e8i 0.740898i −0.928853 0.370449i $$-0.879204\pi$$
0.928853 0.370449i $$-0.120796\pi$$
$$692$$ 0 0
$$693$$ −1.52393e8 + 3.62266e8i −0.457895 + 1.08850i
$$694$$ 3.84476e8 1.15025
$$695$$ −7.60696e7 −0.226598
$$696$$ 2.57753e8i 0.764498i
$$697$$ 3.43063e8 1.01315
$$698$$ 8.03994e7i 0.236421i
$$699$$ 2.18671e8i 0.640265i
$$700$$ 0 0
$$701$$ 2.31727e8 0.672702 0.336351 0.941737i $$-0.390807\pi$$
0.336351 + 0.941737i $$0.390807\pi$$
$$702$$ −4.65414e8 −1.34533
$$703$$ 9.35567e6i 0.0269283i
$$704$$ 2.29114e8 0.656649
$$705$$ 1.47792e8i 0.421776i
$$706$$ 6.12173e8i 1.73964i
$$707$$ 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 $$0.643071\pi$$
$$710$$ 6.66316e7i 0.186168i
$$711$$ 7.01298e8 1.95117
$$712$$ 3.22319e8i 0.892988i
$$713$$ 1.30111e8i 0.358959i
$$714$$ −2.86514e8 + 6.81094e8i −0.787138 + 1.87117i
$$715$$ 8.73650e7 0.239012
$$716$$ 0 0
$$717$$ 6.20122e8i 1.68236i
$$718$$ −6.71788e7 −0.181493
$$719$$ 3.85416e8i 1.03692i 0.855103 + 0.518458i $$0.173494\pi$$
−0.855103 + 0.518458i $$0.826506\pi$$
$$720$$ 2.42537e8i 0.649801i
$$721$$ −5.36671e8 2.25760e8i −1.43187 0.602339i
$$722$$ −2.98668e8 −0.793554
$$723$$ −1.65721e8 −0.438494
$$724$$ 0 0
$$725$$ 1.51418e8 0.397342
$$726$$ 3.64108e8i 0.951525i
$$727$$ 3.13918e8i 0.816983i −0.912762 0.408491i $$-0.866055\pi$$
0.912762 0.408491i $$-0.133945\pi$$
$$728$$ −3.58257e8 1.50707e8i −0.928539 0.390606i
$$729$$ 5.61951e8 1.45049
$$730$$ 2.20320e7 0.0566351
$$731$$ 1.87313e8i 0.479530i
$$732$$ 0 0
$$733$$ 7.18118e7i 0.182341i 0.995835 + 0.0911704i $$0.0290608\pi$$
−0.995835 + 0.0911704i $$0.970939\pi$$
$$734$$ 3.06221e7i 0.0774366i
$$735$$ −1.67833e8 1.71564e8i −0.422683 0.432079i
$$736$$ 0 0
$$737$$ 4.32842e8 1.08125
$$738$$ 6.03500e8i 1.50144i
$$739$$ 2.77815e7 0.0688370 0.0344185 0.999408i $$-0.489042\pi$$
0.0344185 + 0.999408i $$0.489042\pi$$
$$740$$ 0 0
$$741$$ 3.11523e8i 0.765660i
$$742$$ 8.12960e7 1.93255e8i 0.199002 0.473063i
$$743$$ −7.03366e8 −1.71481 −0.857403 0.514646i $$-0.827923\pi$$
−0.857403 + 0.514646i $$0.827923\pi$$
$$744$$ 6.35044e8 1.54200
$$745$$ 1.17240e8i 0.283535i
$$746$$ 3.95069e8 0.951604
$$747$$ 9.37166e8i 2.24830i
$$748$$ 0 0
$$749$$ 2.14931e8 5.10930e8i 0.511510 1.21595i
$$750$$ −4.76707e8 −1.12997
$$751$$ −3.00617e8 −0.709731 −0.354866 0.934917i $$-0.615473\pi$$
−0.354866 + 0.934917i $$0.615473\pi$$
$$752$$ 2.96742e8i 0.697792i
$$753$$ −7.10416e8 −1.66390
$$754$$ 1.97342e8i 0.460369i
$$755$$ 7.61309e7i 0.176897i
$$756$$ 0 0
$$757$$ 1.17057e8 0.269841 0.134921 0.990856i $$-0.456922\pi$$
0.134921 + 0.990856i $$0.456922\pi$$
$$758$$ −2.99649e8 −0.688026
$$759$$ 1.87034e8i 0.427756i
$$760$$ 7.20691e7 0.164176
$$761$$ 2.63542e8i 0.597992i 0.954254 + 0.298996i $$0.0966518\pi$$
−0.954254 + 0.298996i $$0.903348\pi$$
$$762$$ 1.20132e9i 2.71516i
$$763$$ 2.64971e7 6.29882e7i 0.0596519 0.141803i
$$764$$ 0 0
$$765$$ 3.53026e8 0.788538
$$766$$ 4.00803e8i 0.891752i
$$767$$ −2.50600e8 −0.555385
$$768$$ 0 0
$$769$$ 1.25689e8i 0.276388i 0.990405 + 0.138194i $$0.0441298\pi$$
−0.990405 + 0.138194i $$0.955870\pi$$
$$770$$ −9.98458e7 4.20018e7i −0.218704 0.0920017i
$$771$$ 3.40794e8 0.743582
$$772$$ 0 0
$$773$$ 1.58329e8i 0.342786i 0.985203 + 0.171393i $$0.0548268\pi$$
−0.985203 + 0.171393i $$0.945173\pi$$
$$774$$ 3.29512e8 0.710638
$$775$$ 3.73060e8i 0.801444i