# Properties

 Label 675.2.l.c.76.2 Level $675$ Weight $2$ Character 675.76 Analytic conductor $5.390$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$675 = 3^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 675.l (of order $$9$$, degree $$6$$, 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: $$5.38990213644$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{9})$$ Coefficient field: 12.0.1952986685049.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3$$ x^12 - 6*x^11 + 27*x^10 - 80*x^9 + 186*x^8 - 330*x^7 + 463*x^6 - 504*x^5 + 420*x^4 - 258*x^3 + 108*x^2 - 27*x + 3 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 27) Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 76.2 Root $$0.500000 - 0.258654i$$ of defining polynomial Character $$\chi$$ $$=$$ 675.76 Dual form 675.2.l.c.151.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.62143 - 1.36054i) q^{2} +(0.986166 - 1.42389i) q^{3} +(0.430663 - 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(-0.168844 - 0.957561i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-1.05495 - 2.80839i) q^{9} +O(q^{10})$$ $$q+(1.62143 - 1.36054i) q^{2} +(0.986166 - 1.42389i) q^{3} +(0.430663 - 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(-0.168844 - 0.957561i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-1.05495 - 2.80839i) q^{9} +(0.297791 + 0.108387i) q^{11} +(-3.05303 - 3.02185i) q^{12} +(1.15981 + 0.973200i) q^{13} +(-1.57657 - 1.32290i) q^{14} +(2.63991 + 0.960847i) q^{16} +(0.587342 - 1.01731i) q^{17} +(-5.53146 - 3.11830i) q^{18} +(-3.11040 - 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(0.630310 - 0.229414i) q^{22} +(-0.375556 + 2.12988i) q^{23} +(-1.75413 - 0.144396i) q^{24} +3.20463 q^{26} +(-5.03922 - 1.26740i) q^{27} -2.41147 q^{28} +(-3.37436 + 2.83142i) q^{29} +(-1.50609 + 8.54146i) q^{31} +(7.49746 - 2.72885i) q^{32} +(0.448003 - 0.317135i) q^{33} +(-0.431752 - 2.44859i) q^{34} +(-7.31359 + 1.36716i) q^{36} +(-2.23332 + 3.86823i) q^{37} +(-12.3730 - 4.50341i) q^{38} +(2.52950 - 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(-3.43842 + 0.940269i) q^{42} +(5.25381 + 1.91223i) q^{43} +(0.392973 - 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(0.429965 + 2.43845i) q^{47} +(3.97153 - 2.81139i) q^{48} +(5.68943 - 2.07078i) q^{49} +(-0.869320 - 1.83955i) q^{51} +(2.87645 - 2.41362i) q^{52} +10.8920 q^{53} +(-9.89507 + 4.80105i) q^{54} +(-0.756896 + 0.635111i) q^{56} +(-10.7384 - 0.883963i) q^{57} +(-1.61901 + 9.18189i) q^{58} +(1.62023 - 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(9.17898 + 15.8985i) q^{62} +(-2.51109 + 1.48436i) q^{63} +(5.63455 - 9.75933i) q^{64} +(0.294929 - 1.12374i) q^{66} +(-0.656156 - 0.550580i) q^{67} +(-2.23174 - 1.87265i) q^{68} +(2.66237 + 2.63517i) q^{69} +(4.79788 - 8.31018i) q^{71} +(-1.93547 + 2.35530i) q^{72} +(-7.62091 - 13.1998i) q^{73} +(1.64171 + 9.31057i) q^{74} +(-14.4977 + 5.27674i) q^{76} +(0.0535070 - 0.303453i) q^{77} +(3.16030 - 4.56306i) q^{78} +(-8.59024 + 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} +12.3721 q^{82} +(-3.58886 + 3.01141i) q^{83} +(-2.37811 + 3.43369i) q^{84} +(11.1203 - 4.04747i) q^{86} +(0.703969 + 7.59698i) q^{87} +(-0.0559194 - 0.317135i) q^{88} +(7.74976 + 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(5.04032 + 1.83453i) q^{92} +(10.6769 + 10.5678i) q^{93} +(4.01476 + 3.36879i) q^{94} +(3.50815 - 13.3667i) q^{96} +(-5.21481 - 1.89804i) q^{97} +(6.40762 - 11.0983i) q^{98} +(-0.00976156 - 0.950656i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10})$$ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 $$12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100})$$ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$352$$ $$\chi(n)$$ $$e\left(\frac{7}{9}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.62143 1.36054i 1.14652 0.962046i 0.146889 0.989153i $$-0.453074\pi$$
0.999633 + 0.0271067i $$0.00862938\pi$$
$$3$$ 0.986166 1.42389i 0.569363 0.822086i
$$4$$ 0.430663 2.44241i 0.215332 1.22121i
$$5$$ 0 0
$$6$$ −0.338267 3.65046i −0.138097 1.49029i
$$7$$ −0.168844 0.957561i −0.0638170 0.361924i −0.999947 0.0102706i $$-0.996731\pi$$
0.936130 0.351653i $$-0.114380\pi$$
$$8$$ −0.508086 0.880031i −0.179636 0.311138i
$$9$$ −1.05495 2.80839i −0.351651 0.936131i
$$10$$ 0 0
$$11$$ 0.297791 + 0.108387i 0.0897872 + 0.0326799i 0.386523 0.922280i $$-0.373676\pi$$
−0.296736 + 0.954960i $$0.595898\pi$$
$$12$$ −3.05303 3.02185i −0.881335 0.872332i
$$13$$ 1.15981 + 0.973200i 0.321675 + 0.269917i 0.789297 0.614011i $$-0.210445\pi$$
−0.467623 + 0.883928i $$0.654889\pi$$
$$14$$ −1.57657 1.32290i −0.421355 0.353559i
$$15$$ 0 0
$$16$$ 2.63991 + 0.960847i 0.659977 + 0.240212i
$$17$$ 0.587342 1.01731i 0.142451 0.246733i −0.785968 0.618267i $$-0.787835\pi$$
0.928419 + 0.371534i $$0.121168\pi$$
$$18$$ −5.53146 3.11830i −1.30378 0.734991i
$$19$$ −3.11040 5.38737i −0.713575 1.23595i −0.963507 0.267685i $$-0.913741\pi$$
0.249931 0.968264i $$-0.419592\pi$$
$$20$$ 0 0
$$21$$ −1.52997 0.703898i −0.333868 0.153603i
$$22$$ 0.630310 0.229414i 0.134383 0.0489113i
$$23$$ −0.375556 + 2.12988i −0.0783089 + 0.444112i 0.920292 + 0.391232i $$0.127951\pi$$
−0.998601 + 0.0528796i $$0.983160\pi$$
$$24$$ −1.75413 0.144396i −0.358060 0.0294747i
$$25$$ 0 0
$$26$$ 3.20463 0.628480
$$27$$ −5.03922 1.26740i −0.969797 0.243912i
$$28$$ −2.41147 −0.455726
$$29$$ −3.37436 + 2.83142i −0.626602 + 0.525782i −0.899871 0.436156i $$-0.856340\pi$$
0.273269 + 0.961938i $$0.411895\pi$$
$$30$$ 0 0
$$31$$ −1.50609 + 8.54146i −0.270502 + 1.53409i 0.482395 + 0.875954i $$0.339767\pi$$
−0.752897 + 0.658138i $$0.771344\pi$$
$$32$$ 7.49746 2.72885i 1.32538 0.482398i
$$33$$ 0.448003 0.317135i 0.0779872 0.0552061i
$$34$$ −0.431752 2.44859i −0.0740449 0.419930i
$$35$$ 0 0
$$36$$ −7.31359 + 1.36716i −1.21893 + 0.227859i
$$37$$ −2.23332 + 3.86823i −0.367156 + 0.635933i −0.989120 0.147113i $$-0.953002\pi$$
0.621964 + 0.783046i $$0.286335\pi$$
$$38$$ −12.3730 4.50341i −2.00717 0.730550i
$$39$$ 2.52950 0.691717i 0.405045 0.110763i
$$40$$ 0 0
$$41$$ 4.47767 + 3.75721i 0.699295 + 0.586778i 0.921573 0.388205i $$-0.126905\pi$$
−0.222278 + 0.974983i $$0.571349\pi$$
$$42$$ −3.43842 + 0.940269i −0.530560 + 0.145087i
$$43$$ 5.25381 + 1.91223i 0.801199 + 0.291613i 0.709983 0.704219i $$-0.248702\pi$$
0.0912158 + 0.995831i $$0.470925\pi$$
$$44$$ 0.392973 0.680649i 0.0592429 0.102612i
$$45$$ 0 0
$$46$$ 2.28885 + 3.96441i 0.337473 + 0.584521i
$$47$$ 0.429965 + 2.43845i 0.0627168 + 0.355685i 0.999975 + 0.00704911i $$0.00224382\pi$$
−0.937258 + 0.348636i $$0.886645\pi$$
$$48$$ 3.97153 2.81139i 0.573241 0.405790i
$$49$$ 5.68943 2.07078i 0.812776 0.295826i
$$50$$ 0 0
$$51$$ −0.869320 1.83955i −0.121729 0.257588i
$$52$$ 2.87645 2.41362i 0.398891 0.334710i
$$53$$ 10.8920 1.49613 0.748063 0.663628i $$-0.230984\pi$$
0.748063 + 0.663628i $$0.230984\pi$$
$$54$$ −9.89507 + 4.80105i −1.34655 + 0.653340i
$$55$$ 0 0
$$56$$ −0.756896 + 0.635111i −0.101145 + 0.0848703i
$$57$$ −10.7384 0.883963i −1.42234 0.117084i
$$58$$ −1.61901 + 9.18189i −0.212587 + 1.20564i
$$59$$ 1.62023 0.589715i 0.210936 0.0767743i −0.234391 0.972142i $$-0.575310\pi$$
0.445327 + 0.895368i $$0.353087\pi$$
$$60$$ 0 0
$$61$$ 0.176214 + 0.999361i 0.0225619 + 0.127955i 0.994008 0.109304i $$-0.0348621\pi$$
−0.971446 + 0.237259i $$0.923751\pi$$
$$62$$ 9.17898 + 15.8985i 1.16573 + 2.01911i
$$63$$ −2.51109 + 1.48436i −0.316367 + 0.187012i
$$64$$ 5.63455 9.75933i 0.704319 1.21992i
$$65$$ 0 0
$$66$$ 0.294929 1.12374i 0.0363033 0.138322i
$$67$$ −0.656156 0.550580i −0.0801622 0.0672641i 0.601826 0.798627i $$-0.294440\pi$$
−0.681988 + 0.731363i $$0.738884\pi$$
$$68$$ −2.23174 1.87265i −0.270638 0.227092i
$$69$$ 2.66237 + 2.63517i 0.320512 + 0.317238i
$$70$$ 0 0
$$71$$ 4.79788 8.31018i 0.569404 0.986237i −0.427221 0.904147i $$-0.640507\pi$$
0.996625 0.0820894i $$-0.0261593\pi$$
$$72$$ −1.93547 + 2.35530i −0.228097 + 0.277574i
$$73$$ −7.62091 13.1998i −0.891960 1.54492i −0.837522 0.546404i $$-0.815996\pi$$
−0.0544385 0.998517i $$-0.517337\pi$$
$$74$$ 1.64171 + 9.31057i 0.190844 + 1.08233i
$$75$$ 0 0
$$76$$ −14.4977 + 5.27674i −1.66300 + 0.605284i
$$77$$ 0.0535070 0.303453i 0.00609768 0.0345817i
$$78$$ 3.16030 4.56306i 0.357833 0.516664i
$$79$$ −8.59024 + 7.20807i −0.966478 + 0.810971i −0.981995 0.188908i $$-0.939505\pi$$
0.0155168 + 0.999880i $$0.495061\pi$$
$$80$$ 0 0
$$81$$ −6.77415 + 5.92544i −0.752684 + 0.658382i
$$82$$ 12.3721 1.36626
$$83$$ −3.58886 + 3.01141i −0.393929 + 0.330546i −0.818141 0.575017i $$-0.804995\pi$$
0.424212 + 0.905563i $$0.360551\pi$$
$$84$$ −2.37811 + 3.43369i −0.259474 + 0.374646i
$$85$$ 0 0
$$86$$ 11.1203 4.04747i 1.19914 0.436450i
$$87$$ 0.703969 + 7.59698i 0.0754734 + 0.814482i
$$88$$ −0.0559194 0.317135i −0.00596103 0.0338067i
$$89$$ 7.74976 + 13.4230i 0.821473 + 1.42283i 0.904586 + 0.426292i $$0.140180\pi$$
−0.0831130 + 0.996540i $$0.526486\pi$$
$$90$$ 0 0
$$91$$ 0.736071 1.27491i 0.0771612 0.133647i
$$92$$ 5.04032 + 1.83453i 0.525490 + 0.191263i
$$93$$ 10.6769 + 10.5678i 1.10714 + 1.09583i
$$94$$ 4.01476 + 3.36879i 0.414091 + 0.347464i
$$95$$ 0 0
$$96$$ 3.50815 13.3667i 0.358049 1.36423i
$$97$$ −5.21481 1.89804i −0.529484 0.192716i 0.0634241 0.997987i $$-0.479798\pi$$
−0.592908 + 0.805270i $$0.702020\pi$$
$$98$$ 6.40762 11.0983i 0.647267 1.12110i
$$99$$ −0.00976156 0.950656i −0.000981074 0.0955445i
$$100$$ 0 0
$$101$$ −1.76063 9.98501i −0.175189 0.993546i −0.937926 0.346836i $$-0.887256\pi$$
0.762737 0.646709i $$-0.223855\pi$$
$$102$$ −3.91231 1.79995i −0.387377 0.178221i
$$103$$ −9.25906 + 3.37002i −0.912323 + 0.332058i −0.755180 0.655518i $$-0.772451\pi$$
−0.157143 + 0.987576i $$0.550228\pi$$
$$104$$ 0.267160 1.51514i 0.0261972 0.148572i
$$105$$ 0 0
$$106$$ 17.6605 14.8189i 1.71534 1.43934i
$$107$$ −5.17080 −0.499880 −0.249940 0.968261i $$-0.580411\pi$$
−0.249940 + 0.968261i $$0.580411\pi$$
$$108$$ −5.26573 + 11.7620i −0.506695 + 1.13180i
$$109$$ −7.31065 −0.700234 −0.350117 0.936706i $$-0.613858\pi$$
−0.350117 + 0.936706i $$0.613858\pi$$
$$110$$ 0 0
$$111$$ 3.30552 + 6.99473i 0.313746 + 0.663911i
$$112$$ 0.474338 2.69010i 0.0448207 0.254191i
$$113$$ 9.74991 3.54868i 0.917195 0.333832i 0.160073 0.987105i $$-0.448827\pi$$
0.757122 + 0.653274i $$0.226605\pi$$
$$114$$ −18.6142 + 13.1768i −1.74338 + 1.23412i
$$115$$ 0 0
$$116$$ 5.46229 + 9.46096i 0.507161 + 0.878428i
$$117$$ 1.50958 4.28390i 0.139561 0.396046i
$$118$$ 1.82475 3.16056i 0.167982 0.290953i
$$119$$ −1.07330 0.390650i −0.0983894 0.0358108i
$$120$$ 0 0
$$121$$ −8.34956 7.00611i −0.759051 0.636919i
$$122$$ 1.64539 + 1.38064i 0.148966 + 0.124998i
$$123$$ 9.76560 2.67050i 0.880535 0.240790i
$$124$$ 20.2132 + 7.35699i 1.81520 + 0.660677i
$$125$$ 0 0
$$126$$ −2.05201 + 5.82321i −0.182808 + 0.518773i
$$127$$ 2.61372 + 4.52709i 0.231930 + 0.401714i 0.958376 0.285509i $$-0.0921627\pi$$
−0.726446 + 0.687223i $$0.758829\pi$$
$$128$$ −1.37098 7.77522i −0.121179 0.687239i
$$129$$ 7.90395 5.59510i 0.695904 0.492621i
$$130$$ 0 0
$$131$$ −1.25622 + 7.12440i −0.109757 + 0.622461i 0.879457 + 0.475979i $$0.157906\pi$$
−0.989213 + 0.146482i $$0.953205\pi$$
$$132$$ −0.581636 1.23079i −0.0506249 0.107126i
$$133$$ −4.63357 + 3.88802i −0.401781 + 0.337134i
$$134$$ −1.81300 −0.156619
$$135$$ 0 0
$$136$$ −1.19368 −0.102357
$$137$$ −8.61748 + 7.23092i −0.736241 + 0.617779i −0.931825 0.362907i $$-0.881784\pi$$
0.195584 + 0.980687i $$0.437340\pi$$
$$138$$ 7.90210 + 0.650482i 0.672671 + 0.0553727i
$$139$$ 1.62885 9.23766i 0.138157 0.783528i −0.834452 0.551081i $$-0.814216\pi$$
0.972609 0.232447i $$-0.0746733\pi$$
$$140$$ 0 0
$$141$$ 3.89612 + 1.79249i 0.328112 + 0.150955i
$$142$$ −3.52690 20.0021i −0.295971 1.67854i
$$143$$ 0.239900 + 0.415518i 0.0200614 + 0.0347474i
$$144$$ −0.0865360 8.42754i −0.00721133 0.702295i
$$145$$ 0 0
$$146$$ −30.3156 11.0340i −2.50894 0.913179i
$$147$$ 2.66215 10.1433i 0.219570 0.836605i
$$148$$ 8.48600 + 7.12060i 0.697545 + 0.585310i
$$149$$ 14.5941 + 12.2459i 1.19560 + 1.00322i 0.999745 + 0.0225899i $$0.00719121\pi$$
0.195851 + 0.980634i $$0.437253\pi$$
$$150$$ 0 0
$$151$$ −3.77193 1.37287i −0.306955 0.111723i 0.183950 0.982936i $$-0.441112\pi$$
−0.490905 + 0.871213i $$0.663334\pi$$
$$152$$ −3.16070 + 5.47450i −0.256367 + 0.444041i
$$153$$ −3.47661 0.576279i −0.281068 0.0465894i
$$154$$ −0.326102 0.564825i −0.0262780 0.0455149i
$$155$$ 0 0
$$156$$ −0.600093 6.47599i −0.0480459 0.518494i
$$157$$ 6.83713 2.48851i 0.545662 0.198605i −0.0544560 0.998516i $$-0.517342\pi$$
0.600118 + 0.799911i $$0.295120\pi$$
$$158$$ −4.12159 + 23.3747i −0.327896 + 1.85959i
$$159$$ 10.7413 15.5090i 0.851839 1.22994i
$$160$$ 0 0
$$161$$ 2.10290 0.165732
$$162$$ −2.92200 + 18.8242i −0.229574 + 1.47897i
$$163$$ −12.4492 −0.975094 −0.487547 0.873097i $$-0.662108\pi$$
−0.487547 + 0.873097i $$0.662108\pi$$
$$164$$ 11.1050 9.31823i 0.867157 0.727632i
$$165$$ 0 0
$$166$$ −1.72194 + 9.76558i −0.133648 + 0.757956i
$$167$$ −2.19126 + 0.797553i −0.169565 + 0.0617165i −0.425408 0.905002i $$-0.639869\pi$$
0.255843 + 0.966718i $$0.417647\pi$$
$$168$$ 0.157906 + 1.70407i 0.0121827 + 0.131472i
$$169$$ −1.85937 10.5450i −0.143029 0.811157i
$$170$$ 0 0
$$171$$ −11.8485 + 14.4187i −0.906081 + 1.10262i
$$172$$ 6.93308 12.0085i 0.528643 0.915636i
$$173$$ −3.36623 1.22521i −0.255930 0.0931509i 0.210869 0.977514i $$-0.432371\pi$$
−0.466799 + 0.884363i $$0.654593\pi$$
$$174$$ 11.4774 + 11.3602i 0.870101 + 0.861213i
$$175$$ 0 0
$$176$$ 0.681996 + 0.572262i 0.0514074 + 0.0431359i
$$177$$ 0.758123 2.88859i 0.0569840 0.217120i
$$178$$ 30.8281 + 11.2205i 2.31067 + 0.841014i
$$179$$ 9.99785 17.3168i 0.747275 1.29432i −0.201850 0.979416i $$-0.564695\pi$$
0.949124 0.314901i $$-0.101971\pi$$
$$180$$ 0 0
$$181$$ −4.86616 8.42844i −0.361699 0.626481i 0.626542 0.779388i $$-0.284470\pi$$
−0.988241 + 0.152907i $$0.951136\pi$$
$$182$$ −0.541082 3.06863i −0.0401077 0.227462i
$$183$$ 1.59676 + 0.734626i 0.118036 + 0.0543051i
$$184$$ 2.06518 0.751664i 0.152247 0.0554134i
$$185$$ 0 0
$$186$$ 31.6897 + 2.60862i 2.32360 + 0.191274i
$$187$$ 0.285168 0.239284i 0.0208535 0.0174982i
$$188$$ 6.14088 0.447869
$$189$$ −0.362776 + 5.03935i −0.0263881 + 0.366559i
$$190$$ 0 0
$$191$$ −13.6023 + 11.4137i −0.984227 + 0.825864i −0.984722 0.174135i $$-0.944287\pi$$
0.000494763 1.00000i $$0.499843\pi$$
$$192$$ −8.33965 17.6473i −0.601862 1.27359i
$$193$$ −1.83795 + 10.4235i −0.132299 + 0.750303i 0.844404 + 0.535706i $$0.179955\pi$$
−0.976703 + 0.214596i $$0.931156\pi$$
$$194$$ −11.0378 + 4.01743i −0.792467 + 0.288434i
$$195$$ 0 0
$$196$$ −2.60748 14.7878i −0.186249 1.05627i
$$197$$ 7.07945 + 12.2620i 0.504390 + 0.873628i 0.999987 + 0.00507615i $$0.00161579\pi$$
−0.495597 + 0.868552i $$0.665051\pi$$
$$198$$ −1.30923 1.52814i −0.0930431 0.108600i
$$199$$ −3.77010 + 6.53000i −0.267255 + 0.462899i −0.968152 0.250363i $$-0.919450\pi$$
0.700897 + 0.713263i $$0.252783\pi$$
$$200$$ 0 0
$$201$$ −1.43105 + 0.391333i −0.100938 + 0.0276025i
$$202$$ −16.4397 13.7946i −1.15669 0.970582i
$$203$$ 3.28100 + 2.75308i 0.230281 + 0.193229i
$$204$$ −4.86732 + 1.33101i −0.340780 + 0.0931896i
$$205$$ 0 0
$$206$$ −10.4278 + 18.0616i −0.726543 + 1.25841i
$$207$$ 6.37775 1.19222i 0.443284 0.0828648i
$$208$$ 2.12670 + 3.68356i 0.147460 + 0.255409i
$$209$$ −0.342328 1.94144i −0.0236793 0.134292i
$$210$$ 0 0
$$211$$ −4.89922 + 1.78317i −0.337276 + 0.122758i −0.505106 0.863058i $$-0.668546\pi$$
0.167829 + 0.985816i $$0.446324\pi$$
$$212$$ 4.69077 26.6027i 0.322163 1.82708i
$$213$$ −7.10131 15.0269i −0.486573 1.02963i
$$214$$ −8.38408 + 7.03508i −0.573124 + 0.480908i
$$215$$ 0 0
$$216$$ 1.44500 + 5.07862i 0.0983199 + 0.345556i
$$217$$ 8.43326 0.572487
$$218$$ −11.8537 + 9.94643i −0.802833 + 0.673657i
$$219$$ −26.3106 2.16583i −1.77791 0.146353i
$$220$$ 0 0
$$221$$ 1.67125 0.608285i 0.112420 0.0409177i
$$222$$ 14.8763 + 6.84416i 0.998430 + 0.459350i
$$223$$ −3.07250 17.4250i −0.205750 1.16686i −0.896256 0.443537i $$-0.853723\pi$$
0.690506 0.723326i $$-0.257388\pi$$
$$224$$ −3.87894 6.71853i −0.259173 0.448901i
$$225$$ 0 0
$$226$$ 10.9807 19.0191i 0.730423 1.26513i
$$227$$ −14.8208 5.39434i −0.983692 0.358035i −0.200418 0.979711i $$-0.564230\pi$$
−0.783275 + 0.621676i $$0.786452\pi$$
$$228$$ −6.78365 + 25.8470i −0.449258 + 1.71176i
$$229$$ −1.35350 1.13572i −0.0894415 0.0750504i 0.596971 0.802263i $$-0.296371\pi$$
−0.686412 + 0.727213i $$0.740815\pi$$
$$230$$ 0 0
$$231$$ −0.379318 0.375443i −0.0249573 0.0247024i
$$232$$ 4.20620 + 1.53093i 0.276151 + 0.100511i
$$233$$ −6.94920 + 12.0364i −0.455257 + 0.788529i −0.998703 0.0509157i $$-0.983786\pi$$
0.543446 + 0.839444i $$0.317119\pi$$
$$234$$ −3.38073 8.99987i −0.221005 0.588340i
$$235$$ 0 0
$$236$$ −0.742554 4.21123i −0.0483362 0.274128i
$$237$$ 1.79212 + 19.3400i 0.116411 + 1.25627i
$$238$$ −2.27177 + 0.826858i −0.147257 + 0.0535973i
$$239$$ −3.44391 + 19.5314i −0.222768 + 1.26338i 0.644138 + 0.764909i $$0.277216\pi$$
−0.866906 + 0.498471i $$0.833895\pi$$
$$240$$ 0 0
$$241$$ 14.8419 12.4538i 0.956050 0.802221i −0.0242563 0.999706i $$-0.507722\pi$$
0.980306 + 0.197485i $$0.0632773\pi$$
$$242$$ −23.0703 −1.48301
$$243$$ 1.75676 + 15.4892i 0.112696 + 0.993629i
$$244$$ 2.51674 0.161118
$$245$$ 0 0
$$246$$ 12.2009 17.6165i 0.777901 1.12319i
$$247$$ 1.63550 9.27540i 0.104065 0.590179i
$$248$$ 8.28198 3.01439i 0.525906 0.191414i
$$249$$ 0.748720 + 8.07992i 0.0474482 + 0.512044i
$$250$$ 0 0
$$251$$ 2.73786 + 4.74212i 0.172812 + 0.299320i 0.939402 0.342818i $$-0.111381\pi$$
−0.766590 + 0.642137i $$0.778048\pi$$
$$252$$ 2.54399 + 6.77237i 0.160256 + 0.426619i
$$253$$ −0.342689 + 0.593554i −0.0215447 + 0.0373164i
$$254$$ 10.3972 + 3.78428i 0.652380 + 0.237447i
$$255$$ 0 0
$$256$$ 4.46383 + 3.74560i 0.278989 + 0.234100i
$$257$$ 8.85943 + 7.43395i 0.552636 + 0.463717i 0.875833 0.482615i $$-0.160313\pi$$
−0.323196 + 0.946332i $$0.604757\pi$$
$$258$$ 5.20333 19.8257i 0.323945 1.23429i
$$259$$ 4.08115 + 1.48542i 0.253590 + 0.0922993i
$$260$$ 0 0
$$261$$ 11.5115 + 6.48951i 0.712546 + 0.401691i
$$262$$ 7.65614 + 13.2608i 0.472998 + 0.819257i
$$263$$ −1.12488 6.37952i −0.0693632 0.393378i −0.999648 0.0265395i $$-0.991551\pi$$
0.930285 0.366839i $$-0.119560\pi$$
$$264$$ −0.506712 0.233124i −0.0311860 0.0143478i
$$265$$ 0 0
$$266$$ −2.22318 + 12.6083i −0.136312 + 0.773064i
$$267$$ 26.7554 + 2.20245i 1.63741 + 0.134788i
$$268$$ −1.62733 + 1.36549i −0.0994048 + 0.0834106i
$$269$$ −13.8387 −0.843758 −0.421879 0.906652i $$-0.638629\pi$$
−0.421879 + 0.906652i $$0.638629\pi$$
$$270$$ 0 0
$$271$$ 1.94536 0.118172 0.0590860 0.998253i $$-0.481181\pi$$
0.0590860 + 0.998253i $$0.481181\pi$$
$$272$$ 2.52800 2.12125i 0.153283 0.128619i
$$273$$ −1.08945 2.30536i −0.0659366 0.139527i
$$274$$ −4.13466 + 23.4488i −0.249784 + 1.41660i
$$275$$ 0 0
$$276$$ 7.58277 5.36774i 0.456429 0.323100i
$$277$$ −2.16586 12.2832i −0.130134 0.738026i −0.978125 0.208016i $$-0.933299\pi$$
0.847991 0.530010i $$-0.177812\pi$$
$$278$$ −9.92713 17.1943i −0.595390 1.03125i
$$279$$ 25.5766 4.78114i 1.53123 0.286239i
$$280$$ 0 0
$$281$$ −9.16752 3.33670i −0.546888 0.199051i 0.0537751 0.998553i $$-0.482875\pi$$
−0.600663 + 0.799502i $$0.705097\pi$$
$$282$$ 8.75602 2.39442i 0.521414 0.142585i
$$283$$ −20.3547 17.0797i −1.20996 1.01528i −0.999288 0.0377246i $$-0.987989\pi$$
−0.210676 0.977556i $$-0.567567\pi$$
$$284$$ −18.2306 15.2973i −1.08179 0.907728i
$$285$$ 0 0
$$286$$ 0.954309 + 0.347340i 0.0564295 + 0.0205386i
$$287$$ 2.84173 4.92202i 0.167742 0.290538i
$$288$$ −15.5732 18.1770i −0.917657 1.07109i
$$289$$ 7.81006 + 13.5274i 0.459415 + 0.795730i
$$290$$ 0 0
$$291$$ −7.84527 + 5.55356i −0.459898 + 0.325556i
$$292$$ −35.5214 + 12.9287i −2.07873 + 0.756598i
$$293$$ −2.12849 + 12.0712i −0.124347 + 0.705210i 0.857346 + 0.514741i $$0.172112\pi$$
−0.981693 + 0.190469i $$0.938999\pi$$
$$294$$ −9.48386 20.0686i −0.553110 1.17042i
$$295$$ 0 0
$$296$$ 4.53888 0.263817
$$297$$ −1.36326 0.923606i −0.0791044 0.0535930i
$$298$$ 40.3243 2.33592
$$299$$ −2.50838 + 2.10478i −0.145063 + 0.121723i
$$300$$ 0 0
$$301$$ 0.944004 5.35371i 0.0544115 0.308583i
$$302$$ −7.98375 + 2.90585i −0.459413 + 0.167213i
$$303$$ −15.9539 7.33993i −0.916526 0.421668i
$$304$$ −3.03473 17.2108i −0.174053 0.987106i
$$305$$ 0 0
$$306$$ −6.42113 + 3.79567i −0.367071 + 0.216984i
$$307$$ −13.2370 + 22.9271i −0.755475 + 1.30852i 0.189663 + 0.981849i $$0.439260\pi$$
−0.945138 + 0.326671i $$0.894073\pi$$
$$308$$ −0.718114 0.261372i −0.0409184 0.0148931i
$$309$$ −4.33242 + 16.5073i −0.246463 + 0.939070i
$$310$$ 0 0
$$311$$ −13.5280 11.3513i −0.767100 0.643673i 0.172865 0.984946i $$-0.444698\pi$$
−0.939964 + 0.341272i $$0.889142\pi$$
$$312$$ −1.89394 1.87459i −0.107223 0.106128i
$$313$$ 9.06541 + 3.29954i 0.512407 + 0.186501i 0.585266 0.810841i $$-0.300990\pi$$
−0.0728589 + 0.997342i $$0.523212\pi$$
$$314$$ 7.70019 13.3371i 0.434547 0.752657i
$$315$$ 0 0
$$316$$ 13.9056 + 24.0852i 0.782250 + 1.35490i
$$317$$ 0.644320 + 3.65412i 0.0361886 + 0.205236i 0.997541 0.0700850i $$-0.0223270\pi$$
−0.961352 + 0.275321i $$0.911216\pi$$
$$318$$ −3.68439 39.7606i −0.206610 2.22967i
$$319$$ −1.31174 + 0.477435i −0.0734434 + 0.0267312i
$$320$$ 0 0
$$321$$ −5.09927 + 7.36268i −0.284614 + 0.410945i
$$322$$ 3.40971 2.86108i 0.190016 0.159442i
$$323$$ −7.30748 −0.406599
$$324$$ 11.5550 + 19.0972i 0.641944 + 1.06095i
$$325$$ 0 0
$$326$$ −20.1854 + 16.9376i −1.11797 + 0.938085i
$$327$$ −7.20952 + 10.4096i −0.398687 + 0.575652i
$$328$$ 1.03142 5.84948i 0.0569507 0.322983i
$$329$$ 2.26237 0.823435i 0.124728 0.0453974i
$$330$$ 0 0
$$331$$ −0.245329 1.39133i −0.0134845 0.0764745i 0.977323 0.211755i $$-0.0679177\pi$$
−0.990807 + 0.135280i $$0.956807\pi$$
$$332$$ 5.80953 + 10.0624i 0.318839 + 0.552246i
$$333$$ 13.2196 + 2.19126i 0.724427 + 0.120080i
$$334$$ −2.46786 + 4.27446i −0.135035 + 0.233888i
$$335$$ 0 0
$$336$$ −3.36265 3.32830i −0.183447 0.181573i
$$337$$ 9.95097 + 8.34986i 0.542064 + 0.454846i 0.872243 0.489073i $$-0.162665\pi$$
−0.330179 + 0.943918i $$0.607109\pi$$
$$338$$ −17.3618 14.5683i −0.944356 0.792409i
$$339$$ 4.56209 17.3824i 0.247779 0.944084i
$$340$$ 0 0
$$341$$ −1.37428 + 2.38033i −0.0744215 + 0.128902i
$$342$$ 0.405587 + 39.4992i 0.0219316 + 2.13587i
$$343$$ −6.34669 10.9928i −0.342689 0.593555i
$$344$$ −0.986567 5.59510i −0.0531921 0.301667i
$$345$$ 0 0
$$346$$ −7.12504 + 2.59330i −0.383045 + 0.139417i
$$347$$ 0.833591 4.72753i 0.0447495 0.253787i −0.954224 0.299094i $$-0.903316\pi$$
0.998973 + 0.0453070i $$0.0144266\pi$$
$$348$$ 18.8581 + 1.55236i 1.01090 + 0.0832152i
$$349$$ −17.2954 + 14.5126i −0.925803 + 0.776841i −0.975059 0.221946i $$-0.928759\pi$$
0.0492565 + 0.998786i $$0.484315\pi$$
$$350$$ 0 0
$$351$$ −4.61112 6.37412i −0.246123 0.340225i
$$352$$ 2.52845 0.134767
$$353$$ 22.7565 19.0950i 1.21121 1.01632i 0.211972 0.977276i $$-0.432012\pi$$
0.999237 0.0390490i $$-0.0124328\pi$$
$$354$$ −2.70080 5.71509i −0.143546 0.303754i
$$355$$ 0 0
$$356$$ 36.1220 13.1473i 1.91446 0.696807i
$$357$$ −1.61470 + 1.14302i −0.0854589 + 0.0604952i
$$358$$ −7.34937 41.6804i −0.388427 2.20288i
$$359$$ −6.70991 11.6219i −0.354136 0.613381i 0.632834 0.774288i $$-0.281892\pi$$
−0.986970 + 0.160906i $$0.948558\pi$$
$$360$$ 0 0
$$361$$ −9.84920 + 17.0593i −0.518379 + 0.897858i
$$362$$ −19.3573 7.04550i −1.01740 0.370303i
$$363$$ −18.2100 + 4.97970i −0.955778 + 0.261366i
$$364$$ −2.79686 2.34685i −0.146595 0.123008i
$$365$$ 0 0
$$366$$ 3.58852 0.981314i 0.187575 0.0512941i
$$367$$ −7.47054 2.71905i −0.389959 0.141933i 0.139597 0.990208i $$-0.455419\pi$$
−0.529556 + 0.848275i $$0.677641\pi$$
$$368$$ −3.03793 + 5.26184i −0.158363 + 0.274293i
$$369$$ 5.82801 16.5387i 0.303394 0.860973i
$$370$$ 0 0
$$371$$ −1.83904 10.4297i −0.0954782 0.541484i
$$372$$ 30.4091 21.5262i 1.57664 1.11608i
$$373$$ −10.7318 + 3.90604i −0.555670 + 0.202247i −0.604564 0.796557i $$-0.706653\pi$$
0.0488939 + 0.998804i $$0.484430\pi$$
$$374$$ 0.136823 0.775963i 0.00707496 0.0401241i
$$375$$ 0 0
$$376$$ 1.92745 1.61733i 0.0994009 0.0834072i
$$377$$ −6.66917 −0.343480
$$378$$ 6.26801 + 8.66451i 0.322392 + 0.445654i
$$379$$ −24.1705 −1.24155 −0.620777 0.783987i $$-0.713183\pi$$
−0.620777 + 0.783987i $$0.713183\pi$$
$$380$$ 0 0
$$381$$ 9.02366 + 0.742807i 0.462296 + 0.0380551i
$$382$$ −6.52637 + 37.0129i −0.333918 + 1.89374i
$$383$$ 8.87378 3.22979i 0.453429 0.165035i −0.105202 0.994451i $$-0.533549\pi$$
0.558631 + 0.829416i $$0.311327\pi$$
$$384$$ −12.4231 5.71553i −0.633964 0.291669i
$$385$$ 0 0
$$386$$ 11.2015 + 19.4016i 0.570143 + 0.987516i
$$387$$ −0.172220 16.7721i −0.00875442 0.852573i
$$388$$ −6.88162 + 11.9193i −0.349361 + 0.605111i
$$389$$ 2.39406 + 0.871367i 0.121384 + 0.0441801i 0.401998 0.915641i $$-0.368316\pi$$
−0.280614 + 0.959821i $$0.590538\pi$$
$$390$$ 0 0
$$391$$ 1.94617 + 1.63303i 0.0984218 + 0.0825857i
$$392$$ −4.71308 3.95474i −0.238046 0.199745i
$$393$$ 8.90554 + 8.81457i 0.449225 + 0.444636i
$$394$$ 28.1617 + 10.2500i 1.41876 + 0.516388i
$$395$$ 0 0
$$396$$ −2.32610 0.385571i −0.116891 0.0193757i
$$397$$ 1.83759 + 3.18279i 0.0922258 + 0.159740i 0.908447 0.417999i $$-0.137269\pi$$
−0.816222 + 0.577739i $$0.803935\pi$$
$$398$$ 2.77138 + 15.7173i 0.138917 + 0.787836i
$$399$$ 0.966669 + 10.4319i 0.0483940 + 0.522251i
$$400$$ 0 0
$$401$$ 2.80420 15.9034i 0.140035 0.794177i −0.831186 0.555995i $$-0.812337\pi$$
0.971220 0.238182i $$-0.0765516\pi$$
$$402$$ −1.78791 + 2.58151i −0.0891731 + 0.128754i
$$403$$ −10.0593 + 8.44078i −0.501091 + 0.420465i
$$404$$ −25.1458 −1.25105
$$405$$ 0 0
$$406$$ 9.06558 0.449917
$$407$$ −1.08433 + 0.909859i −0.0537481 + 0.0451000i
$$408$$ −1.17717 + 1.69968i −0.0582785 + 0.0841465i
$$409$$ 1.59443 9.04248i 0.0788396 0.447122i −0.919677 0.392676i $$-0.871550\pi$$
0.998517 0.0544462i $$-0.0173393\pi$$
$$410$$ 0 0
$$411$$ 1.79780 + 19.4013i 0.0886792 + 0.956994i
$$412$$ 4.24345 + 24.0658i 0.209060 + 1.18564i
$$413$$ −0.838253 1.45190i −0.0412477 0.0714432i
$$414$$ 8.71900 10.6103i 0.428515 0.521466i
$$415$$ 0 0
$$416$$ 11.3514 + 4.13157i 0.556548 + 0.202567i
$$417$$ −11.5471 11.4292i −0.565466 0.559689i
$$418$$ −3.19646 2.68215i −0.156344 0.131188i
$$419$$ −5.34613 4.48594i −0.261176 0.219152i 0.502791 0.864408i $$-0.332306\pi$$
−0.763967 + 0.645256i $$0.776751\pi$$
$$420$$ 0 0
$$421$$ −28.9525 10.5379i −1.41106 0.513584i −0.479619 0.877477i $$-0.659225\pi$$
−0.931441 + 0.363894i $$0.881447\pi$$
$$422$$ −5.51765 + 9.55686i −0.268595 + 0.465221i
$$423$$ 6.39454 3.77996i 0.310913 0.183788i
$$424$$ −5.53405 9.58526i −0.268757 0.465502i
$$425$$ 0 0
$$426$$ −31.9589 14.7034i −1.54842 0.712383i
$$427$$ 0.927196 0.337472i 0.0448702 0.0163314i
$$428$$ −2.22687 + 12.6292i −0.107640 + 0.610457i
$$429$$ 0.828236 + 0.0681784i 0.0399876 + 0.00329169i
$$430$$ 0 0
$$431$$ 27.8971 1.34376 0.671879 0.740661i $$-0.265487\pi$$
0.671879 + 0.740661i $$0.265487\pi$$
$$432$$ −12.0853 8.18774i −0.581453 0.393933i
$$433$$ −19.1706 −0.921278 −0.460639 0.887588i $$-0.652380\pi$$
−0.460639 + 0.887588i $$0.652380\pi$$
$$434$$ 13.6739 11.4738i 0.656369 0.550759i
$$435$$ 0 0
$$436$$ −3.14843 + 17.8556i −0.150782 + 0.855130i
$$437$$ 12.6426 4.60154i 0.604778 0.220121i
$$438$$ −45.6075 + 32.2849i −2.17921 + 1.54263i
$$439$$ −4.12397 23.3882i −0.196826 1.11626i −0.909794 0.415060i $$-0.863761\pi$$
0.712968 0.701197i $$-0.247351\pi$$
$$440$$ 0 0
$$441$$ −11.8177 13.7936i −0.562746 0.656838i
$$442$$ 1.88221 3.26009i 0.0895278 0.155067i
$$443$$ 21.9496 + 7.98900i 1.04286 + 0.379569i 0.805962 0.591967i $$-0.201648\pi$$
0.236894 + 0.971536i $$0.423871\pi$$
$$444$$ 18.5076 5.06108i 0.878332 0.240188i
$$445$$ 0 0
$$446$$ −28.6892 24.0731i −1.35847 1.13989i
$$447$$ 31.8291 8.70396i 1.50546 0.411683i
$$448$$ −10.2965 3.74762i −0.486464 0.177059i
$$449$$ −2.40953 + 4.17343i −0.113713 + 0.196956i −0.917264 0.398279i $$-0.869608\pi$$
0.803552 + 0.595235i $$0.202941\pi$$
$$450$$ 0 0
$$451$$ 0.926176 + 1.60418i 0.0436119 + 0.0755380i
$$452$$ −4.46841 25.3416i −0.210176 1.19197i
$$453$$ −5.67457 + 4.01695i −0.266615 + 0.188733i
$$454$$ −31.3701 + 11.4178i −1.47227 + 0.535863i
$$455$$ 0 0
$$456$$ 4.67813 + 9.89928i 0.219074 + 0.463576i
$$457$$ 3.74872 3.14555i 0.175358 0.147142i −0.550885 0.834581i $$-0.685710\pi$$
0.726242 + 0.687439i $$0.241265\pi$$
$$458$$ −3.73978 −0.174749
$$459$$ −4.24908 + 4.38203i −0.198330 + 0.204535i
$$460$$ 0 0
$$461$$ 21.4419 17.9919i 0.998650 0.837967i 0.0118535 0.999930i $$-0.496227\pi$$
0.986797 + 0.161963i $$0.0517824\pi$$
$$462$$ −1.12584 0.0926768i −0.0523789 0.00431171i
$$463$$ 4.77104 27.0579i 0.221729 1.25749i −0.647111 0.762396i $$-0.724023\pi$$
0.868840 0.495093i $$-0.164866\pi$$
$$464$$ −11.6285 + 4.23245i −0.539842 + 0.196486i
$$465$$ 0 0
$$466$$ 5.10832 + 28.9707i 0.236639 + 1.34204i
$$467$$ −10.6232 18.4000i −0.491585 0.851450i 0.508368 0.861140i $$-0.330249\pi$$
−0.999953 + 0.00968963i $$0.996916\pi$$
$$468$$ −9.81292 5.53194i −0.453602 0.255714i
$$469$$ −0.416426 + 0.721272i −0.0192288 + 0.0333052i
$$470$$ 0 0
$$471$$ 3.19917 12.1894i 0.147410 0.561659i
$$472$$ −1.34218 1.12623i −0.0617790 0.0518387i
$$473$$ 1.35728 + 1.13889i 0.0624076 + 0.0523662i
$$474$$ 29.2186 + 28.9201i 1.34205 + 1.32834i
$$475$$ 0 0
$$476$$ −1.41636 + 2.45321i −0.0649188 + 0.112443i
$$477$$ −11.4905 30.5889i −0.526113 1.40057i
$$478$$ 20.9892 + 36.3543i 0.960022 + 1.66281i
$$479$$ −7.23745 41.0456i −0.330688 1.87542i −0.466248 0.884654i $$-0.654394\pi$$
0.135560 0.990769i $$-0.456717\pi$$
$$480$$ 0 0
$$481$$ −6.35480 + 2.31296i −0.289754 + 0.105462i
$$482$$ 7.12113 40.3859i 0.324358 1.83953i
$$483$$ 2.07381 2.99431i 0.0943618 0.136246i
$$484$$ −20.7077 + 17.3758i −0.941258 + 0.789809i
$$485$$ 0 0
$$486$$ 23.9220 + 22.7244i 1.08513 + 1.03080i
$$487$$ −4.02801 −0.182527 −0.0912634 0.995827i $$-0.529091\pi$$
−0.0912634 + 0.995827i $$0.529091\pi$$
$$488$$ 0.789937 0.662836i 0.0357588 0.0300052i
$$489$$ −12.2769 + 17.7263i −0.555183 + 0.801611i
$$490$$ 0 0
$$491$$ 36.2922 13.2093i 1.63784 0.596126i 0.651184 0.758920i $$-0.274273\pi$$
0.986660 + 0.162793i $$0.0520504\pi$$
$$492$$ −2.31677 25.0017i −0.104448 1.12716i
$$493$$ 0.898521 + 5.09577i 0.0404674 + 0.229502i
$$494$$ −9.96769 17.2645i −0.448468 0.776769i
$$495$$ 0 0
$$496$$ −12.1830 + 21.1015i −0.547032 + 0.947487i
$$497$$ −8.76759 3.19114i −0.393280 0.143142i
$$498$$ 12.2070 + 12.0823i 0.547011 + 0.541423i
$$499$$ −3.11922 2.61734i −0.139636 0.117168i 0.570295 0.821440i $$-0.306829\pi$$
−0.709930 + 0.704272i $$0.751274\pi$$
$$500$$ 0 0
$$501$$ −1.02531 + 3.90664i −0.0458076 + 0.174536i
$$502$$ 10.8911 + 3.96403i 0.486093 + 0.176923i
$$503$$ −1.71297 + 2.96695i −0.0763775 + 0.132290i −0.901684 0.432395i $$-0.857669\pi$$
0.825307 + 0.564684i $$0.191002\pi$$
$$504$$ 2.58213 + 1.45565i 0.115017 + 0.0648398i
$$505$$ 0 0
$$506$$ 0.251909 + 1.42865i 0.0111987 + 0.0635111i
$$507$$ −16.8487 7.75161i −0.748276 0.344261i
$$508$$ 12.1827 4.43412i 0.540518 0.196732i
$$509$$ −2.12952 + 12.0771i −0.0943893 + 0.535308i 0.900543 + 0.434766i $$0.143169\pi$$
−0.994933 + 0.100542i $$0.967942\pi$$
$$510$$ 0 0
$$511$$ −11.3529 + 9.52619i −0.502222 + 0.421414i
$$512$$ 28.1241 1.24292
$$513$$ 8.84601 + 31.0903i 0.390561 + 1.37267i
$$514$$ 24.4791 1.07973
$$515$$ 0 0
$$516$$ −10.2616 21.7143i −0.451742 0.955920i
$$517$$ −0.136257 + 0.772750i −0.00599257 + 0.0339855i
$$518$$ 8.63825 3.14407i 0.379543 0.138142i
$$519$$ −5.06423 + 3.58490i −0.222295 + 0.157360i
$$520$$ 0 0
$$521$$ −7.04117 12.1957i −0.308479 0.534302i 0.669551 0.742766i $$-0.266487\pi$$
−0.978030 + 0.208465i $$0.933153\pi$$
$$522$$ 27.4943 5.13962i 1.20339 0.224955i
$$523$$ 4.88956 8.46897i 0.213806 0.370322i −0.739097 0.673599i $$-0.764747\pi$$
0.952902 + 0.303277i $$0.0980808\pi$$
$$524$$ 16.8597 + 6.13643i 0.736520 + 0.268071i
$$525$$ 0 0
$$526$$ −10.5035 8.81348i −0.457974 0.384286i
$$527$$ 7.80469 + 6.54892i 0.339978 + 0.285275i
$$528$$ 1.48740 0.406744i 0.0647309 0.0177013i
$$529$$ 17.2176 + 6.26668i 0.748590 + 0.272464i
$$530$$ 0 0
$$531$$ −3.36541 3.92812i −0.146047 0.170466i
$$532$$ 7.50065 + 12.9915i 0.325195 + 0.563254i
$$533$$ 1.53675 + 8.71534i 0.0665640 + 0.377503i
$$534$$ 46.3785 32.8307i 2.00699 1.42072i
$$535$$ 0 0
$$536$$ −0.151144 + 0.857180i −0.00652843 + 0.0370245i
$$537$$ −14.7977 31.3131i −0.638569 1.35126i
$$538$$ −22.4384 + 18.8280i −0.967387 + 0.811734i
$$539$$ 1.91871 0.0826445
$$540$$ 0 0
$$541$$ 40.9454 1.76038 0.880189 0.474623i $$-0.157416\pi$$
0.880189 + 0.474623i $$0.157416\pi$$
$$542$$ 3.15426 2.64674i 0.135487 0.113687i
$$543$$ −16.8001 1.38294i −0.720959 0.0593477i
$$544$$ 1.62750 9.22999i 0.0697783 0.395732i
$$545$$ 0 0
$$546$$ −4.90300 2.25573i −0.209829 0.0965365i
$$547$$ −0.192798 1.09341i −0.00824343 0.0467508i 0.980409 0.196975i $$-0.0631117\pi$$
−0.988652 + 0.150224i $$0.952001\pi$$
$$548$$ 13.9497 + 24.1615i 0.595900 + 1.03213i
$$549$$ 2.62070 1.54916i 0.111849 0.0661164i
$$550$$ 0 0
$$551$$ 25.7495 + 9.37206i 1.09697 + 0.399263i
$$552$$ 0.966321 3.68186i 0.0411293 0.156711i
$$553$$ 8.35257 + 7.00864i 0.355188 + 0.298038i
$$554$$ −20.2236 16.9696i −0.859216 0.720968i
$$555$$ 0 0
$$556$$ −21.8607 7.95664i −0.927100 0.337437i
$$557$$ 17.5201 30.3458i 0.742352 1.28579i −0.209070 0.977901i $$-0.567044\pi$$
0.951422 0.307890i $$-0.0996230\pi$$
$$558$$ 34.9657 42.5503i 1.48022 1.80130i
$$559$$ 4.23247 + 7.33084i 0.179014 + 0.310062i
$$560$$ 0 0
$$561$$ −0.0594925 0.642022i −0.00251178 0.0271062i
$$562$$ −19.4042 + 7.06254i −0.818516 + 0.297915i
$$563$$ 6.73255 38.1822i 0.283743 1.60919i −0.425998 0.904724i $$-0.640077\pi$$
0.709741 0.704463i $$-0.248812\pi$$
$$564$$ 6.05593 8.74396i 0.255001 0.368187i
$$565$$ 0 0
$$566$$ −56.2413 −2.36400
$$567$$ 6.81774 + 5.48619i 0.286318 + 0.230398i
$$568$$ −9.75095 −0.409141
$$569$$ −26.0213 + 21.8344i −1.09087 + 0.915347i −0.996777 0.0802169i $$-0.974439\pi$$
−0.0940904 + 0.995564i $$0.529994\pi$$
$$570$$ 0 0
$$571$$ 1.75191 9.93559i 0.0733153 0.415792i −0.925956 0.377631i $$-0.876739\pi$$
0.999272 0.0381610i $$-0.0121500\pi$$
$$572$$ 1.11818 0.406986i 0.0467536 0.0170169i
$$573$$ 2.83775 + 30.6240i 0.118549 + 1.27934i
$$574$$ −2.08894 11.8470i −0.0871908 0.494484i
$$575$$ 0 0
$$576$$ −33.3522 5.52842i −1.38968 0.230351i
$$577$$ −6.06615 + 10.5069i −0.252537 + 0.437407i −0.964224 0.265090i $$-0.914598\pi$$
0.711687 + 0.702497i $$0.247932\pi$$
$$578$$ 31.0680 + 11.3078i 1.29226 + 0.470344i
$$579$$ 13.0295 + 12.8964i 0.541487 + 0.535956i
$$580$$ 0 0
$$581$$ 3.48957 + 2.92810i 0.144772 + 0.121478i
$$582$$ −5.16470 + 19.6785i −0.214084 + 0.815700i
$$583$$ 3.24352 + 1.18055i 0.134333 + 0.0488932i
$$584$$ −7.74416 + 13.4133i −0.320456 + 0.555046i
$$585$$ 0 0
$$586$$ 12.9722 + 22.4685i 0.535877 + 0.928167i
$$587$$ −5.51319 31.2669i −0.227554 1.29052i −0.857743 0.514079i $$-0.828134\pi$$
0.630189 0.776442i $$-0.282977\pi$$
$$588$$ −23.6276 10.8704i −0.974387 0.448288i
$$589$$ 50.7006 18.4535i 2.08908 0.760363i
$$590$$ 0 0
$$591$$ 24.4412 + 2.01195i 1.00538 + 0.0827605i
$$592$$ −9.61254 + 8.06588i −0.395073 + 0.331506i
$$593$$ −13.4906 −0.553993 −0.276996 0.960871i $$-0.589339\pi$$
−0.276996 + 0.960871i $$0.589339\pi$$
$$594$$ −3.46703 + 0.357210i −0.142254 + 0.0146565i
$$595$$ 0 0
$$596$$ 36.1947 30.3710i 1.48259 1.24404i
$$597$$ 5.58009 + 11.8079i 0.228378 + 0.483265i
$$598$$ −1.20352 + 6.82550i −0.0492156 + 0.279115i
$$599$$ 39.8715 14.5120i 1.62911 0.592946i 0.644020 0.765009i $$-0.277265\pi$$
0.985086 + 0.172063i $$0.0550432\pi$$
$$600$$ 0 0
$$601$$ −3.43906 19.5039i −0.140282 0.795579i −0.971035 0.238938i $$-0.923201\pi$$
0.830753 0.556641i $$-0.187910\pi$$
$$602$$ −5.75330 9.96501i −0.234487 0.406144i
$$603$$ −0.854034 + 2.42358i −0.0347789 + 0.0986958i
$$604$$ −4.97755 + 8.62136i −0.202533 + 0.350798i
$$605$$ 0 0
$$606$$ −35.8543 + 9.80470i −1.45648 + 0.398289i
$$607$$ 27.5769 + 23.1397i 1.11931 + 0.939213i 0.998569 0.0534715i $$-0.0170286\pi$$
0.120741 + 0.992684i $$0.461473\pi$$
$$608$$ −38.0215 31.9038i −1.54197 1.29387i
$$609$$ 7.15571 1.95680i 0.289964 0.0792934i
$$610$$ 0 0
$$611$$ −1.87442 + 3.24659i −0.0758310 + 0.131343i
$$612$$ −2.90476 + 8.24315i −0.117418 + 0.333209i
$$613$$ 13.2314 + 22.9175i 0.534411 + 0.925627i 0.999192 + 0.0402013i $$0.0127999\pi$$
−0.464780 + 0.885426i $$0.653867\pi$$
$$614$$ 9.73045 + 55.1841i 0.392689 + 2.22705i
$$615$$ 0 0
$$616$$ −0.294234 + 0.107093i −0.0118550 + 0.00431488i
$$617$$ −8.52903 + 48.3705i −0.343366 + 1.94732i −0.0239406 + 0.999713i $$0.507621\pi$$
−0.319425 + 0.947611i $$0.603490\pi$$
$$618$$ 15.4342 + 32.6599i 0.620853 + 1.31377i
$$619$$ −18.5430 + 15.5595i −0.745307 + 0.625387i −0.934257 0.356600i $$-0.883936\pi$$
0.188950 + 0.981987i $$0.439492\pi$$
$$620$$ 0 0
$$621$$ 4.59193 10.2570i 0.184268 0.411598i
$$622$$ −37.3785 −1.49874
$$623$$ 11.5448 9.68725i 0.462533 0.388111i
$$624$$ 7.34229 + 0.604400i 0.293927 + 0.0241954i
$$625$$ 0 0
$$626$$ 19.1881 6.98388i 0.766909 0.279132i
$$627$$ −3.10199 1.42714i −0.123882 0.0569945i
$$628$$ −3.13347 17.7708i −0.125039 0.709132i
$$629$$ 2.62345 + 4.54395i 0.104604 + 0.181179i
$$630$$ 0 0
$$631$$ −8.84842 + 15.3259i −0.352250 + 0.610115i −0.986643 0.162895i $$-0.947917\pi$$
0.634393 + 0.773010i $$0.281250\pi$$
$$632$$ 10.7079 + 3.89736i 0.425938 + 0.155029i
$$633$$ −2.29240 + 8.73447i −0.0911147 + 0.347164i
$$634$$ 6.01629 + 5.04827i 0.238937 + 0.200492i
$$635$$ 0 0
$$636$$ −33.2535 32.9138i −1.31859 1.30512i
$$637$$ 8.61398 + 3.13523i 0.341298 + 0.124222i
$$638$$ −1.47732 + 2.55880i −0.0584878 + 0.101304i
$$639$$ −28.3998 4.70751i −1.12348 0.186226i
$$640$$ 0 0
$$641$$ 6.60738 + 37.4723i 0.260976 + 1.48007i 0.780254 + 0.625463i $$0.215090\pi$$
−0.519278 + 0.854605i $$0.673799\pi$$
$$642$$ 1.74911 + 18.8758i 0.0690319 + 0.744968i
$$643$$ 44.1115 16.0553i 1.73959 0.633158i 0.740352 0.672220i $$-0.234659\pi$$
0.999237 + 0.0390615i $$0.0124368\pi$$
$$644$$ 0.905644 5.13616i 0.0356874 0.202393i
$$645$$ 0 0
$$646$$ −11.8485 + 9.94211i −0.466175 + 0.391167i
$$647$$ 28.2333 1.10997 0.554983 0.831862i $$-0.312725\pi$$
0.554983 + 0.831862i $$0.312725\pi$$
$$648$$ 8.65643 + 2.95083i 0.340057 + 0.115920i
$$649$$ 0.546406 0.0214483
$$650$$ 0 0
$$651$$ 8.31660 12.0081i 0.325953 0.470634i
$$652$$ −5.36140 + 30.4060i −0.209969 + 1.19079i
$$653$$ 33.1779 12.0758i 1.29835 0.472562i 0.401893 0.915687i $$-0.368353\pi$$
0.896460 + 0.443125i $$0.146130\pi$$
$$654$$ 2.47295 + 26.6872i 0.0967001 + 1.04355i
$$655$$ 0 0
$$656$$ 8.21052 + 14.2210i 0.320567 + 0.555239i
$$657$$ −29.0306 + 35.3277i −1.13259 + 1.37826i
$$658$$ 2.54795 4.41318i 0.0993295 0.172044i
$$659$$ −39.1793 14.2601i −1.52621 0.555494i −0.563519 0.826103i $$-0.690553\pi$$
−0.962689 + 0.270609i $$0.912775\pi$$
$$660$$ 0 0
$$661$$ 0.975874 + 0.818856i 0.0379571 + 0.0318498i 0.661569 0.749884i $$-0.269891\pi$$
−0.623612 + 0.781734i $$0.714335\pi$$
$$662$$ −2.29075 1.92216i −0.0890324 0.0747070i
$$663$$ 0.781997 2.97956i 0.0303702 0.115716i
$$664$$ 4.47359 + 1.62825i 0.173609 + 0.0631885i
$$665$$ 0 0
$$666$$ 24.4158 14.4328i 0.946095 0.559258i
$$667$$ −4.76334 8.25035i −0.184437 0.319455i
$$668$$ 1.00426 + 5.69543i 0.0388559 + 0.220363i
$$669$$ −27.8413 12.8090i −1.07641 0.495226i
$$670$$ 0 0
$$671$$ −0.0558427 + 0.316700i −0.00215578 + 0.0122261i
$$672$$ −13.3918 1.10238i −0.516598 0.0425252i
$$673$$ −27.2963 + 22.9043i −1.05219 + 0.882896i −0.993323 0.115370i $$-0.963195\pi$$
−0.0588715 + 0.998266i $$0.518750\pi$$
$$674$$ 27.4951 1.05907
$$675$$ 0 0
$$676$$ −26.5561 −1.02139
$$677$$ −13.7902 + 11.5714i −0.530002 + 0.444725i −0.868102 0.496386i $$-0.834660\pi$$
0.338100 + 0.941110i $$0.390216\pi$$
$$678$$ −16.2524 34.3913i −0.624169 1.32079i
$$679$$ −0.936996 + 5.31397i −0.0359586 + 0.203931i
$$680$$ 0 0
$$681$$ −22.2968 + 15.7836i −0.854414 + 0.604828i
$$682$$ 1.01023 + 5.72929i 0.0386836 + 0.219386i
$$683$$ 19.8807 + 34.4344i 0.760715 + 1.31760i 0.942483 + 0.334255i $$0.108485\pi$$
−0.181768 + 0.983341i $$0.558182\pi$$
$$684$$ 30.1136 + 35.1486i 1.15142 + 1.34394i
$$685$$ 0 0
$$686$$ −25.2468 9.18909i −0.963928 0.350841i
$$687$$ −2.95192 + 0.807229i −0.112623 + 0.0307977i
$$688$$ 12.0322 + 10.0962i 0.458724 + 0.384915i
$$689$$ 12.6327 + 10.6001i 0.481266 + 0.403830i
$$690$$ 0 0
$$691$$ 15.8251 + 5.75986i 0.602015 + 0.219115i 0.625006 0.780620i $$-0.285097\pi$$
−0.0229909 + 0.999736i $$0.507319\pi$$
$$692$$ −4.44218 + 7.69408i −0.168866 + 0.292485i
$$693$$ −0.908663 + 0.169860i −0.0345173 + 0.00645244i
$$694$$ −5.08038 8.79948i −0.192849 0.334024i
$$695$$ 0 0
$$696$$ 6.32790 4.47944i 0.239859 0.169793i
$$697$$ 6.45216 2.34839i 0.244393 0.0889518i
$$698$$ −8.29833 + 47.0622i −0.314097 + 1.78133i
$$699$$ 10.2854 + 21.7648i 0.389031 + 0.823220i
$$700$$ 0 0
$$701$$ −8.96921 −0.338762 −0.169381 0.985551i $$-0.554177\pi$$
−0.169381 + 0.985551i $$0.554177\pi$$
$$702$$ −16.1488 4.06156i −0.609498 0.153294i
$$703$$ 27.7861 1.04797
$$704$$ 2.73570 2.29552i 0.103106 0.0865158i
$$705$$ 0 0
$$706$$ 10.9186 61.9223i 0.410926 2.33048i
$$707$$ −9.26398 + 3.37181i −0.348408 + 0.126810i
$$708$$ −6.72864 3.09566i −0.252878 0.116342i
$$709$$ 3.15026 + 17.8660i 0.118311 + 0.670973i 0.985058 + 0.172225i $$0.0550955\pi$$
−0.866747 + 0.498748i $$0.833793\pi$$
$$710$$ 0 0
$$711$$ 29.3054 + 16.5206i 1.09904 + 0.619572i
$$712$$ 7.87509 13.6401i 0.295131 0.511183i
$$713$$ −17.6267 6.41560i −0.660125 0.240266i
$$714$$ −1.06299 + 4.05019i −0.0397814 + 0.151574i
$$715$$ 0 0
$$716$$ −37.9890 31.8766i −1.41972 1.19128i
$$717$$ 24.4144 + 24.1650i 0.911771 + 0.902457i
$$718$$ −26.6917 9.71498i −0.996125 0.362560i
$$719$$ −15.7860 + 27.3421i −0.588718 + 1.01969i 0.405683 + 0.914014i $$0.367034\pi$$
−0.994401 + 0.105675i $$0.966300\pi$$
$$720$$ 0 0
$$721$$ 4.79034 + 8.29711i 0.178402 + 0.309001i
$$722$$ 7.24010 + 41.0606i 0.269449 + 1.52812i
$$723$$ −3.09636 33.4148i −0.115155 1.24271i
$$724$$ −22.6814 + 8.25536i −0.842948 + 0.306808i
$$725$$ 0 0
$$726$$ −22.7511 + 32.8497i −0.844374 + 1.21916i
$$727$$ −29.4232 + 24.6890i −1.09125 + 0.915664i −0.996806 0.0798662i $$-0.974551\pi$$
−0.0944407 + 0.995530i $$0.530106\pi$$
$$728$$ −1.49595 −0.0554436
$$729$$ 23.7874 + 12.7734i 0.881014 + 0.473090i
$$730$$ 0 0
$$731$$ 5.03111 4.22160i 0.186082 0.156142i
$$732$$ 2.48193 3.58358i 0.0917346 0.132453i
$$733$$ 5.26680 29.8695i 0.194534 1.10326i −0.718547 0.695478i $$-0.755193\pi$$
0.913081 0.407778i $$-0.133696\pi$$
$$734$$ −15.8123 + 5.75521i −0.583643 + 0.212429i
$$735$$ 0 0
$$736$$ 2.99643 + 16.9936i 0.110450 + 0.626391i
$$737$$ −0.135721 0.235076i −0.00499936 0.00865915i
$$738$$ −13.0519 34.7456i −0.480448 1.27900i
$$739$$ −5.00127 + 8.66245i −0.183975 + 0.318653i −0.943230 0.332139i $$-0.892230\pi$$
0.759256 + 0.650792i $$0.225563\pi$$
$$740$$ 0 0
$$741$$ −11.5943 11.4759i −0.425928 0.421577i
$$742$$ −17.1719 14.4089i −0.630400 0.528969i
$$743$$ −27.7873 23.3163i −1.01942 0.855394i −0.0298642 0.999554i $$-0.509507\pi$$
−0.989554 + 0.144160i $$0.953952\pi$$
$$744$$ 3.87523 14.7654i 0.142073 0.541324i
$$745$$ 0 0
$$746$$ −12.0865 + 20.9344i −0.442517 + 0.766461i
$$747$$ 12.2433 + 6.90205i 0.447960 + 0.252533i
$$748$$ −0.461619 0.799548i −0.0168785 0.0292344i
$$749$$ 0.873058 + 4.95136i 0.0319008 + 0.180919i
$$750$$ 0 0
$$751$$ 13.6766 4.97788i 0.499067 0.181646i −0.0802073 0.996778i $$-0.525558\pi$$
0.579274 + 0.815133i $$0.303336\pi$$
$$752$$ −1.20791 + 6.85041i −0.0440480 + 0.249809i
$$753$$ 9.45226 + 0.778089i 0.344460 + 0.0283551i
$$754$$ −10.8136 + 9.07366i −0.393807 + 0.330443i
$$755$$ 0 0
$$756$$ 12.1519 + 3.05631i 0.441962 + 0.111157i
$$757$$ 45.5754 1.65646 0.828232 0.560385i $$-0.189347\pi$$
0.828232 + 0.560385i $$0.189347\pi$$
$$758$$ −39.1907 + 32.8849i −1.42347 + 1.19443i
$$759$$ 0.507211 + 1.07330i 0.0184106 + 0.0389582i
$$760$$ 0 0
$$761$$ −20.9040 + 7.60843i −0.757769 + 0.275805i −0.691871 0.722021i $$-0.743213\pi$$
−0.0658978 + 0.997826i $$0.520991\pi$$
$$762$$ 15.6418 11.0726i 0.566643 0.401119i
$$763$$ 1.23436 + 7.00040i 0.0446868 + 0.253431i
$$764$$ 22.0189 + 38.1379i 0.796616 + 1.37978i
$$765$$ 0 0
$$766$$ 9.99393 17.3100i 0.361096 0.625436i
$$767$$ 2.45307 + 0.892846i 0.0885754 + 0.0322388i
$$768$$ 9.73542 2.66224i 0.351297 0.0960654i
$$769$$ 10.4679 + 8.78365i 0.377484 + 0.316747i 0.811714 0.584056i $$-0.198535\pi$$
−0.434230 + 0.900802i $$0.642979\pi$$
$$770$$ 0 0
$$771$$ 19.3220 5.28379i 0.695866 0.190291i
$$772$$ 24.6670 + 8.97807i 0.887786 + 0.323128i
$$773$$ −10.3270 + 17.8869i −0.371436 + 0.643345i −0.989787