# Properties

 Label 120.2.w.c.53.6 Level $120$ Weight $2$ Character 120.53 Analytic conductor $0.958$ Analytic rank $0$ Dimension $32$ CM no Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 120.w (of order $$4$$, degree $$2$$, 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: $$0.958204824255$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 53.6 Character $$\chi$$ $$=$$ 120.53 Dual form 120.2.w.c.77.6

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.533177 + 1.30986i) q^{2} +(0.667305 - 1.59834i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.143028 - 2.23149i) q^{5} +(1.73781 + 1.72627i) q^{6} +(0.582772 - 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(-2.10941 - 2.13317i) q^{9} +O(q^{10})$$ $$q+(-0.533177 + 1.30986i) q^{2} +(0.667305 - 1.59834i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.143028 - 2.23149i) q^{5} +(1.73781 + 1.72627i) q^{6} +(0.582772 - 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(-2.10941 - 2.13317i) q^{9} +(2.99919 + 1.00243i) q^{10} +3.68607 q^{11} +(-3.18773 + 1.35587i) q^{12} +(-3.88771 + 3.88771i) q^{13} +(0.452626 + 1.07407i) q^{14} +(-3.66213 - 1.26047i) q^{15} +(0.0980619 + 3.99880i) q^{16} +(0.880105 + 0.880105i) q^{17} +(3.91883 - 1.62567i) q^{18} +6.32919 q^{19} +(-2.91214 + 3.39403i) q^{20} +(-0.542584 - 1.32036i) q^{21} +(-1.96533 + 4.82821i) q^{22} +(-2.06626 + 2.06626i) q^{23} +(-0.0763660 - 4.89838i) q^{24} +(-4.95909 + 0.638332i) q^{25} +(-3.01950 - 7.16518i) q^{26} +(-4.81715 + 1.94809i) q^{27} +(-1.64820 + 0.0202063i) q^{28} -1.37122i q^{29} +(3.60361 - 4.12481i) q^{30} +3.32075 q^{31} +(-5.29013 - 2.00362i) q^{32} +(2.45973 - 5.89160i) q^{33} +(-1.62206 + 0.683558i) q^{34} +(-1.38380 - 1.21710i) q^{35} +(0.0399575 + 5.99987i) q^{36} +(-2.44147 - 2.44147i) q^{37} +(-3.37458 + 8.29032i) q^{38} +(3.61961 + 8.80819i) q^{39} +(-2.89300 - 5.62410i) q^{40} -0.648104i q^{41} +(2.01877 - 0.00672215i) q^{42} +(-0.819412 + 0.819412i) q^{43} +(-5.27640 - 5.14859i) q^{44} +(-4.45843 + 5.01223i) q^{45} +(-1.60482 - 3.80818i) q^{46} +(6.28508 + 6.28508i) q^{47} +(6.45689 + 2.51168i) q^{48} +6.32075i q^{49} +(1.80795 - 6.83603i) q^{50} +(1.99401 - 0.819412i) q^{51} +(10.9953 - 0.134798i) q^{52} +(5.60782 + 5.60782i) q^{53} +(0.0166776 - 7.34845i) q^{54} +(-0.527212 - 8.22542i) q^{55} +(0.852318 - 2.16968i) q^{56} +(4.22349 - 10.1162i) q^{57} +(1.79611 + 0.731106i) q^{58} +6.12026i q^{59} +(3.48154 + 6.91946i) q^{60} -5.13471i q^{61} +(-1.77055 + 4.34971i) q^{62} +(-2.47245 - 0.0138443i) q^{63} +(5.44503 - 5.86102i) q^{64} +(9.23144 + 8.11933i) q^{65} +(6.40568 + 6.36316i) q^{66} +(-4.90636 - 4.90636i) q^{67} +(-0.0305156 - 2.48912i) q^{68} +(1.92377 + 4.68141i) q^{69} +(2.33203 - 1.16365i) q^{70} -4.13251i q^{71} +(-7.88026 - 3.14666i) q^{72} +(4.69820 + 4.69820i) q^{73} +(4.49972 - 1.89624i) q^{74} +(-2.28895 + 8.35229i) q^{75} +(-9.05987 - 8.84042i) q^{76} +(2.14814 - 2.14814i) q^{77} +(-13.4674 + 0.0448439i) q^{78} -1.10079i q^{79} +(8.90925 - 0.790765i) q^{80} +(-0.100786 + 8.99944i) q^{81} +(0.848922 + 0.345554i) q^{82} +(-6.27439 - 6.27439i) q^{83} +(-1.06756 + 2.64788i) q^{84} +(1.83806 - 2.08982i) q^{85} +(-0.636420 - 1.51020i) q^{86} +(-2.19169 - 0.915024i) q^{87} +(9.55717 - 4.16621i) q^{88} -15.3562 q^{89} +(-4.18816 - 8.51230i) q^{90} +4.53130i q^{91} +(5.84382 - 0.0716428i) q^{92} +(2.21595 - 5.30771i) q^{93} +(-11.5836 + 4.88148i) q^{94} +(-0.905253 - 14.1235i) q^{95} +(-6.73261 + 7.11843i) q^{96} +(-5.42154 + 5.42154i) q^{97} +(-8.27927 - 3.37008i) q^{98} +(-7.77542 - 7.86299i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32 q - 4 q^{6}+O(q^{10})$$ 32 * q - 4 * q^6 $$32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100})$$ 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$41$$ $$61$$ $$97$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.533177 + 1.30986i −0.377013 + 0.926208i
$$3$$ 0.667305 1.59834i 0.385268 0.922805i
$$4$$ −1.43144 1.39677i −0.715722 0.698385i
$$5$$ −0.143028 2.23149i −0.0639642 0.997952i
$$6$$ 1.73781 + 1.72627i 0.709457 + 0.704748i
$$7$$ 0.582772 0.582772i 0.220267 0.220267i −0.588344 0.808611i $$-0.700220\pi$$
0.808611 + 0.588344i $$0.200220\pi$$
$$8$$ 2.59278 1.13026i 0.916687 0.399606i
$$9$$ −2.10941 2.13317i −0.703136 0.711055i
$$10$$ 2.99919 + 1.00243i 0.948426 + 0.316997i
$$11$$ 3.68607 1.11139 0.555695 0.831386i $$-0.312452\pi$$
0.555695 + 0.831386i $$0.312452\pi$$
$$12$$ −3.18773 + 1.35587i −0.920218 + 0.391405i
$$13$$ −3.88771 + 3.88771i −1.07826 + 1.07826i −0.0815911 + 0.996666i $$0.526000\pi$$
−0.996666 + 0.0815911i $$0.974000\pi$$
$$14$$ 0.452626 + 1.07407i 0.120969 + 0.287057i
$$15$$ −3.66213 1.26047i −0.945558 0.325453i
$$16$$ 0.0980619 + 3.99880i 0.0245155 + 0.999699i
$$17$$ 0.880105 + 0.880105i 0.213457 + 0.213457i 0.805734 0.592277i $$-0.201771\pi$$
−0.592277 + 0.805734i $$0.701771\pi$$
$$18$$ 3.91883 1.62567i 0.923677 0.383173i
$$19$$ 6.32919 1.45201 0.726007 0.687687i $$-0.241374\pi$$
0.726007 + 0.687687i $$0.241374\pi$$
$$20$$ −2.91214 + 3.39403i −0.651175 + 0.758928i
$$21$$ −0.542584 1.32036i −0.118402 0.288125i
$$22$$ −1.96533 + 4.82821i −0.419009 + 1.02938i
$$23$$ −2.06626 + 2.06626i −0.430844 + 0.430844i −0.888916 0.458071i $$-0.848540\pi$$
0.458071 + 0.888916i $$0.348540\pi$$
$$24$$ −0.0763660 4.89838i −0.0155882 0.999878i
$$25$$ −4.95909 + 0.638332i −0.991817 + 0.127666i
$$26$$ −3.01950 7.16518i −0.592173 1.40521i
$$27$$ −4.81715 + 1.94809i −0.927061 + 0.374910i
$$28$$ −1.64820 + 0.0202063i −0.311481 + 0.00381863i
$$29$$ 1.37122i 0.254630i −0.991862 0.127315i $$-0.959364\pi$$
0.991862 0.127315i $$-0.0406359\pi$$
$$30$$ 3.60361 4.12481i 0.657925 0.753083i
$$31$$ 3.32075 0.596425 0.298212 0.954500i $$-0.403610\pi$$
0.298212 + 0.954500i $$0.403610\pi$$
$$32$$ −5.29013 2.00362i −0.935172 0.354194i
$$33$$ 2.45973 5.89160i 0.428184 1.02560i
$$34$$ −1.62206 + 0.683558i −0.278181 + 0.117229i
$$35$$ −1.38380 1.21710i −0.233905 0.205727i
$$36$$ 0.0399575 + 5.99987i 0.00665958 + 0.999978i
$$37$$ −2.44147 2.44147i −0.401376 0.401376i 0.477342 0.878718i $$-0.341600\pi$$
−0.878718 + 0.477342i $$0.841600\pi$$
$$38$$ −3.37458 + 8.29032i −0.547429 + 1.34487i
$$39$$ 3.61961 + 8.80819i 0.579602 + 1.41044i
$$40$$ −2.89300 5.62410i −0.457423 0.889249i
$$41$$ 0.648104i 0.101217i −0.998719 0.0506084i $$-0.983884\pi$$
0.998719 0.0506084i $$-0.0161160\pi$$
$$42$$ 2.01877 0.00672215i 0.311503 0.00103725i
$$43$$ −0.819412 + 0.819412i −0.124959 + 0.124959i −0.766821 0.641861i $$-0.778162\pi$$
0.641861 + 0.766821i $$0.278162\pi$$
$$44$$ −5.27640 5.14859i −0.795447 0.776179i
$$45$$ −4.45843 + 5.01223i −0.664623 + 0.747179i
$$46$$ −1.60482 3.80818i −0.236617 0.561485i
$$47$$ 6.28508 + 6.28508i 0.916772 + 0.916772i 0.996793 0.0800208i $$-0.0254987\pi$$
−0.0800208 + 0.996793i $$0.525499\pi$$
$$48$$ 6.45689 + 2.51168i 0.931972 + 0.362530i
$$49$$ 6.32075i 0.902965i
$$50$$ 1.80795 6.83603i 0.255683 0.966761i
$$51$$ 1.99401 0.819412i 0.279217 0.114741i
$$52$$ 10.9953 0.134798i 1.52477 0.0186931i
$$53$$ 5.60782 + 5.60782i 0.770293 + 0.770293i 0.978158 0.207864i $$-0.0666512\pi$$
−0.207864 + 0.978158i $$0.566651\pi$$
$$54$$ 0.0166776 7.34845i 0.00226953 0.999997i
$$55$$ −0.527212 8.22542i −0.0710892 1.10911i
$$56$$ 0.852318 2.16968i 0.113896 0.289936i
$$57$$ 4.22349 10.1162i 0.559415 1.33993i
$$58$$ 1.79611 + 0.731106i 0.235840 + 0.0959989i
$$59$$ 6.12026i 0.796790i 0.917214 + 0.398395i $$0.130433\pi$$
−0.917214 + 0.398395i $$0.869567\pi$$
$$60$$ 3.48154 + 6.91946i 0.449465 + 0.893298i
$$61$$ 5.13471i 0.657432i −0.944429 0.328716i $$-0.893384\pi$$
0.944429 0.328716i $$-0.106616\pi$$
$$62$$ −1.77055 + 4.34971i −0.224860 + 0.552413i
$$63$$ −2.47245 0.0138443i −0.311500 0.00174421i
$$64$$ 5.44503 5.86102i 0.680629 0.732628i
$$65$$ 9.23144 + 8.11933i 1.14502 + 1.00708i
$$66$$ 6.40568 + 6.36316i 0.788484 + 0.783251i
$$67$$ −4.90636 4.90636i −0.599408 0.599408i 0.340747 0.940155i $$-0.389320\pi$$
−0.940155 + 0.340747i $$0.889320\pi$$
$$68$$ −0.0305156 2.48912i −0.00370056 0.301851i
$$69$$ 1.92377 + 4.68141i 0.231594 + 0.563576i
$$70$$ 2.33203 1.16365i 0.278731 0.139083i
$$71$$ 4.13251i 0.490439i −0.969468 0.245220i $$-0.921140\pi$$
0.969468 0.245220i $$-0.0788601\pi$$
$$72$$ −7.88026 3.14666i −0.928698 0.370837i
$$73$$ 4.69820 + 4.69820i 0.549883 + 0.549883i 0.926407 0.376524i $$-0.122881\pi$$
−0.376524 + 0.926407i $$0.622881\pi$$
$$74$$ 4.49972 1.89624i 0.523082 0.220433i
$$75$$ −2.28895 + 8.35229i −0.264305 + 0.964439i
$$76$$ −9.05987 8.84042i −1.03924 1.01407i
$$77$$ 2.14814 2.14814i 0.244803 0.244803i
$$78$$ −13.4674 + 0.0448439i −1.52488 + 0.00507757i
$$79$$ 1.10079i 0.123848i −0.998081 0.0619241i $$-0.980276\pi$$
0.998081 0.0619241i $$-0.0197237\pi$$
$$80$$ 8.90925 0.790765i 0.996084 0.0884103i
$$81$$ −0.100786 + 8.99944i −0.0111985 + 0.999937i
$$82$$ 0.848922 + 0.345554i 0.0937478 + 0.0381601i
$$83$$ −6.27439 6.27439i −0.688703 0.688703i 0.273242 0.961945i $$-0.411904\pi$$
−0.961945 + 0.273242i $$0.911904\pi$$
$$84$$ −1.06756 + 2.64788i −0.116480 + 0.288908i
$$85$$ 1.83806 2.08982i 0.199366 0.226673i
$$86$$ −0.636420 1.51020i −0.0686269 0.162849i
$$87$$ −2.19169 0.915024i −0.234974 0.0981009i
$$88$$ 9.55717 4.16621i 1.01880 0.444119i
$$89$$ −15.3562 −1.62775 −0.813875 0.581040i $$-0.802646\pi$$
−0.813875 + 0.581040i $$0.802646\pi$$
$$90$$ −4.18816 8.51230i −0.441471 0.897276i
$$91$$ 4.53130i 0.475009i
$$92$$ 5.84382 0.0716428i 0.609260 0.00746928i
$$93$$ 2.21595 5.30771i 0.229784 0.550384i
$$94$$ −11.5836 + 4.88148i −1.19476 + 0.503486i
$$95$$ −0.905253 14.1235i −0.0928770 1.44904i
$$96$$ −6.73261 + 7.11843i −0.687144 + 0.726521i
$$97$$ −5.42154 + 5.42154i −0.550474 + 0.550474i −0.926578 0.376104i $$-0.877264\pi$$
0.376104 + 0.926578i $$0.377264\pi$$
$$98$$ −8.27927 3.37008i −0.836333 0.340430i
$$99$$ −7.77542 7.86299i −0.781459 0.790260i
$$100$$ 7.99026 + 6.01297i 0.799026 + 0.601297i
$$101$$ −9.84442 −0.979556 −0.489778 0.871847i $$-0.662922\pi$$
−0.489778 + 0.871847i $$0.662922\pi$$
$$102$$ 0.0101518 + 3.04875i 0.00100518 + 0.301872i
$$103$$ −8.28098 8.28098i −0.815949 0.815949i 0.169569 0.985518i $$-0.445762\pi$$
−0.985518 + 0.169569i $$0.945762\pi$$
$$104$$ −5.68587 + 14.4741i −0.557545 + 1.41930i
$$105$$ −2.86876 + 1.39962i −0.279962 + 0.136589i
$$106$$ −10.3354 + 4.35547i −1.00386 + 0.423041i
$$107$$ 5.84678 5.84678i 0.565230 0.565230i −0.365559 0.930788i $$-0.619122\pi$$
0.930788 + 0.365559i $$0.119122\pi$$
$$108$$ 9.61652 + 3.93987i 0.925350 + 0.379114i
$$109$$ 11.7033 1.12097 0.560487 0.828163i $$-0.310614\pi$$
0.560487 + 0.828163i $$0.310614\pi$$
$$110$$ 11.0552 + 3.69503i 1.05407 + 0.352308i
$$111$$ −5.53152 + 2.27311i −0.525029 + 0.215754i
$$112$$ 2.38754 + 2.27324i 0.225601 + 0.214801i
$$113$$ 8.58333 8.58333i 0.807452 0.807452i −0.176796 0.984248i $$-0.556573\pi$$
0.984248 + 0.176796i $$0.0565731\pi$$
$$114$$ 10.9989 + 10.9259i 1.03014 + 1.02330i
$$115$$ 4.90636 + 4.31530i 0.457521 + 0.402403i
$$116$$ −1.91529 + 1.96283i −0.177830 + 0.182244i
$$117$$ 16.4939 + 0.0923560i 1.52486 + 0.00853832i
$$118$$ −8.01666 3.26318i −0.737993 0.300400i
$$119$$ 1.02580 0.0940350
$$120$$ −10.9198 + 0.871018i −0.996834 + 0.0795127i
$$121$$ 2.58708 0.235189
$$122$$ 6.72573 + 2.73771i 0.608919 + 0.247861i
$$123$$ −1.03589 0.432483i −0.0934033 0.0389956i
$$124$$ −4.75347 4.63833i −0.426874 0.416535i
$$125$$ 2.13372 + 10.9748i 0.190846 + 0.981620i
$$126$$ 1.33639 3.23118i 0.119055 0.287856i
$$127$$ −0.0146460 + 0.0146460i −0.00129962 + 0.00129962i −0.707756 0.706457i $$-0.750293\pi$$
0.706457 + 0.707756i $$0.250293\pi$$
$$128$$ 4.77393 + 10.2572i 0.421959 + 0.906615i
$$129$$ 0.762905 + 1.85650i 0.0671701 + 0.163456i
$$130$$ −15.5571 + 7.76281i −1.36445 + 0.680843i
$$131$$ −5.23989 −0.457811 −0.228906 0.973449i $$-0.573515\pi$$
−0.228906 + 0.973449i $$0.573515\pi$$
$$132$$ −11.7502 + 4.99782i −1.02272 + 0.435004i
$$133$$ 3.68847 3.68847i 0.319831 0.319831i
$$134$$ 9.04259 3.81066i 0.781161 0.329191i
$$135$$ 5.03613 + 10.4708i 0.433441 + 0.901182i
$$136$$ 3.27666 + 1.28717i 0.280972 + 0.110374i
$$137$$ −14.0984 14.0984i −1.20450 1.20450i −0.972782 0.231722i $$-0.925564\pi$$
−0.231722 0.972782i $$-0.574436\pi$$
$$138$$ −7.15768 + 0.0238338i −0.609302 + 0.00202887i
$$139$$ −9.22166 −0.782171 −0.391085 0.920354i $$-0.627900\pi$$
−0.391085 + 0.920354i $$0.627900\pi$$
$$140$$ 0.280830 + 3.67506i 0.0237345 + 0.310599i
$$141$$ 14.2398 5.85165i 1.19921 0.492798i
$$142$$ 5.41300 + 2.20336i 0.454249 + 0.184902i
$$143$$ −14.3304 + 14.3304i −1.19836 + 1.19836i
$$144$$ 8.32324 8.64428i 0.693604 0.720357i
$$145$$ −3.05987 + 0.196124i −0.254109 + 0.0162872i
$$146$$ −8.65895 + 3.64899i −0.716619 + 0.301993i
$$147$$ 10.1027 + 4.21787i 0.833260 + 0.347884i
$$148$$ 0.0846526 + 6.90501i 0.00695840 + 0.567589i
$$149$$ 14.0054i 1.14737i −0.819076 0.573685i $$-0.805513\pi$$
0.819076 0.573685i $$-0.194487\pi$$
$$150$$ −9.71988 7.45144i −0.793625 0.608408i
$$151$$ 13.1301 1.06851 0.534255 0.845323i $$-0.320592\pi$$
0.534255 + 0.845323i $$0.320592\pi$$
$$152$$ 16.4102 7.15361i 1.33104 0.580234i
$$153$$ 0.0209077 3.73391i 0.00169028 0.301869i
$$154$$ 1.66841 + 3.95909i 0.134444 + 0.319032i
$$155$$ −0.474962 7.41023i −0.0381498 0.595204i
$$156$$ 7.12175 17.6642i 0.570196 1.41427i
$$157$$ −6.36936 6.36936i −0.508330 0.508330i 0.405683 0.914014i $$-0.367034\pi$$
−0.914014 + 0.405683i $$0.867034\pi$$
$$158$$ 1.44187 + 0.586914i 0.114709 + 0.0466924i
$$159$$ 12.7054 5.22110i 1.00760 0.414060i
$$160$$ −3.71442 + 12.0914i −0.293651 + 0.955913i
$$161$$ 2.40831i 0.189802i
$$162$$ −11.7342 4.93031i −0.921928 0.387362i
$$163$$ −3.46013 + 3.46013i −0.271018 + 0.271018i −0.829510 0.558492i $$-0.811380\pi$$
0.558492 + 0.829510i $$0.311380\pi$$
$$164$$ −0.905253 + 0.927724i −0.0706884 + 0.0724431i
$$165$$ −13.4989 4.64619i −1.05088 0.361706i
$$166$$ 11.5639 4.87318i 0.897533 0.378232i
$$167$$ 0.954151 + 0.954151i 0.0738345 + 0.0738345i 0.743060 0.669225i $$-0.233374\pi$$
−0.669225 + 0.743060i $$0.733374\pi$$
$$168$$ −2.89915 2.81014i −0.223674 0.216807i
$$169$$ 17.2286i 1.32528i
$$170$$ 1.75735 + 3.52185i 0.134783 + 0.270113i
$$171$$ −13.3508 13.5012i −1.02096 1.03246i
$$172$$ 2.31747 0.0284113i 0.176706 0.00216634i
$$173$$ −1.80240 1.80240i −0.137034 0.137034i 0.635262 0.772296i $$-0.280892\pi$$
−0.772296 + 0.635262i $$0.780892\pi$$
$$174$$ 2.36711 2.38293i 0.179450 0.180649i
$$175$$ −2.51801 + 3.26202i −0.190344 + 0.246585i
$$176$$ 0.361463 + 14.7398i 0.0272463 + 1.11106i
$$177$$ 9.78228 + 4.08408i 0.735281 + 0.306978i
$$178$$ 8.18756 20.1144i 0.613683 1.50763i
$$179$$ 24.0166i 1.79508i 0.440930 + 0.897541i $$0.354649\pi$$
−0.440930 + 0.897541i $$0.645351\pi$$
$$180$$ 13.3829 0.947315i 0.997504 0.0706087i
$$181$$ 21.7210i 1.61451i 0.590205 + 0.807253i $$0.299047\pi$$
−0.590205 + 0.807253i $$0.700953\pi$$
$$182$$ −5.93535 2.41599i −0.439957 0.179085i
$$183$$ −8.20703 3.42641i −0.606681 0.253288i
$$184$$ −3.02195 + 7.69276i −0.222781 + 0.567117i
$$185$$ −5.09892 + 5.79732i −0.374880 + 0.426228i
$$186$$ 5.77083 + 5.73253i 0.423138 + 0.420329i
$$187$$ 3.24412 + 3.24412i 0.237234 + 0.237234i
$$188$$ −0.217921 17.7755i −0.0158935 1.29641i
$$189$$ −1.67201 + 3.94259i −0.121621 + 0.286781i
$$190$$ 18.9824 + 6.34458i 1.37713 + 0.460285i
$$191$$ 12.9839i 0.939479i −0.882805 0.469739i $$-0.844348\pi$$
0.882805 0.469739i $$-0.155652\pi$$
$$192$$ −5.73444 12.6141i −0.413847 0.910346i
$$193$$ 9.48630 + 9.48630i 0.682839 + 0.682839i 0.960639 0.277800i $$-0.0896053\pi$$
−0.277800 + 0.960639i $$0.589605\pi$$
$$194$$ −4.21079 9.99208i −0.302317 0.717389i
$$195$$ 19.1377 9.33695i 1.37048 0.668633i
$$196$$ 8.82864 9.04780i 0.630617 0.646272i
$$197$$ −12.8606 + 12.8606i −0.916280 + 0.916280i −0.996757 0.0804765i $$-0.974356\pi$$
0.0804765 + 0.996757i $$0.474356\pi$$
$$198$$ 14.4451 5.99231i 1.02657 0.425855i
$$199$$ 0.0463625i 0.00328655i 0.999999 + 0.00164328i $$0.000523071\pi$$
−0.999999 + 0.00164328i $$0.999477\pi$$
$$200$$ −12.1363 + 7.26010i −0.858169 + 0.513367i
$$201$$ −11.1161 + 4.56802i −0.784069 + 0.322203i
$$202$$ 5.24882 12.8948i 0.369306 0.907273i
$$203$$ −0.799111 0.799111i −0.0560866 0.0560866i
$$204$$ −3.99884 1.61223i −0.279975 0.112879i
$$205$$ −1.44624 + 0.0926972i −0.101010 + 0.00647425i
$$206$$ 15.2621 6.43165i 1.06336 0.448115i
$$207$$ 8.76625 + 0.0490858i 0.609296 + 0.00341170i
$$208$$ −15.9274 15.1649i −1.10437 1.05150i
$$209$$ 23.3298 1.61376
$$210$$ −0.303742 4.50390i −0.0209602 0.310799i
$$211$$ 0.591066i 0.0406907i 0.999793 + 0.0203453i $$0.00647657\pi$$
−0.999793 + 0.0203453i $$0.993523\pi$$
$$212$$ −0.194439 15.8601i −0.0133541 1.08928i
$$213$$ −6.60518 2.75765i −0.452579 0.188951i
$$214$$ 4.54107 + 10.7758i 0.310421 + 0.736619i
$$215$$ 1.94571 + 1.71131i 0.132696 + 0.116710i
$$216$$ −10.2880 + 10.4956i −0.700008 + 0.714135i
$$217$$ 1.93524 1.93524i 0.131373 0.131373i
$$218$$ −6.23994 + 15.3296i −0.422622 + 1.03825i
$$219$$ 10.6445 4.37421i 0.719287 0.295582i
$$220$$ −10.7343 + 12.5106i −0.723710 + 0.843465i
$$221$$ −6.84318 −0.460322
$$222$$ −0.0281619 8.45747i −0.00189010 0.567628i
$$223$$ 16.8577 + 16.8577i 1.12888 + 1.12888i 0.990360 + 0.138517i $$0.0442335\pi$$
0.138517 + 0.990360i $$0.455767\pi$$
$$224$$ −4.25060 + 1.91529i −0.284005 + 0.127970i
$$225$$ 11.8224 + 9.23204i 0.788161 + 0.615470i
$$226$$ 6.66649 + 15.8194i 0.443448 + 1.05229i
$$227$$ −7.23390 + 7.23390i −0.480131 + 0.480131i −0.905173 0.425043i $$-0.860259\pi$$
0.425043 + 0.905173i $$0.360259\pi$$
$$228$$ −20.1757 + 8.58154i −1.33617 + 0.568326i
$$229$$ −23.0081 −1.52042 −0.760210 0.649677i $$-0.774904\pi$$
−0.760210 + 0.649677i $$0.774904\pi$$
$$230$$ −8.26838 + 4.12581i −0.545201 + 0.272048i
$$231$$ −2.00000 4.86692i −0.131590 0.320220i
$$232$$ −1.54984 3.55529i −0.101752 0.233416i
$$233$$ −4.45082 + 4.45082i −0.291583 + 0.291583i −0.837705 0.546122i $$-0.816103\pi$$
0.546122 + 0.837705i $$0.316103\pi$$
$$234$$ −8.91515 + 21.5554i −0.582802 + 1.40912i
$$235$$ 13.1261 14.9240i 0.856254 0.973536i
$$236$$ 8.54860 8.76081i 0.556466 0.570280i
$$237$$ −1.75944 0.734560i −0.114288 0.0477148i
$$238$$ −0.546934 + 1.34365i −0.0354524 + 0.0870959i
$$239$$ 4.03472 0.260984 0.130492 0.991449i $$-0.458344\pi$$
0.130492 + 0.991449i $$0.458344\pi$$
$$240$$ 4.68127 14.7677i 0.302174 0.953253i
$$241$$ −11.4612 −0.738279 −0.369139 0.929374i $$-0.620347\pi$$
−0.369139 + 0.929374i $$0.620347\pi$$
$$242$$ −1.37937 + 3.38871i −0.0886696 + 0.217834i
$$243$$ 14.3169 + 6.16646i 0.918432 + 0.395578i
$$244$$ −7.17201 + 7.35005i −0.459141 + 0.470538i
$$245$$ 14.1047 0.904047i 0.901116 0.0577574i
$$246$$ 1.11880 1.12628i 0.0713324 0.0718090i
$$247$$ −24.6060 + 24.6060i −1.56564 + 1.56564i
$$248$$ 8.60999 3.75331i 0.546735 0.238335i
$$249$$ −14.2156 + 5.84170i −0.900874 + 0.370203i
$$250$$ −15.5131 3.05667i −0.981136 0.193321i
$$251$$ 17.4804 1.10335 0.551677 0.834058i $$-0.313988\pi$$
0.551677 + 0.834058i $$0.313988\pi$$
$$252$$ 3.51984 + 3.47327i 0.221729 + 0.218795i
$$253$$ −7.61636 + 7.61636i −0.478836 + 0.478836i
$$254$$ −0.0113752 0.0269930i −0.000713745 0.00169369i
$$255$$ −2.11371 4.33241i −0.132366 0.271306i
$$256$$ −15.9808 + 0.784260i −0.998798 + 0.0490162i
$$257$$ 6.77283 + 6.77283i 0.422477 + 0.422477i 0.886056 0.463578i $$-0.153435\pi$$
−0.463578 + 0.886056i $$0.653435\pi$$
$$258$$ −2.83851 + 0.00945175i −0.176718 + 0.000588440i
$$259$$ −2.84565 −0.176820
$$260$$ −1.87344 24.5166i −0.116186 1.52045i
$$261$$ −2.92505 + 2.89247i −0.181056 + 0.179040i
$$262$$ 2.79379 6.86350i 0.172601 0.424028i
$$263$$ 15.3708 15.3708i 0.947805 0.947805i −0.0508987 0.998704i $$-0.516209\pi$$
0.998704 + 0.0508987i $$0.0162086\pi$$
$$264$$ −0.281490 18.0558i −0.0173245 1.11126i
$$265$$ 11.7117 13.3159i 0.719445 0.817987i
$$266$$ 2.86476 + 6.79798i 0.175649 + 0.416811i
$$267$$ −10.2472 + 24.5444i −0.627121 + 1.50209i
$$268$$ 0.170117 + 13.8762i 0.0103916 + 0.847627i
$$269$$ 9.58859i 0.584627i −0.956323 0.292313i $$-0.905575\pi$$
0.956323 0.292313i $$-0.0944250\pi$$
$$270$$ −16.4004 + 1.01382i −0.998095 + 0.0616992i
$$271$$ −20.9078 −1.27006 −0.635030 0.772487i $$-0.719012\pi$$
−0.635030 + 0.772487i $$0.719012\pi$$
$$272$$ −3.43306 + 3.60567i −0.208160 + 0.218626i
$$273$$ 7.24257 + 3.02376i 0.438341 + 0.183006i
$$274$$ 25.9837 10.9499i 1.56974 0.661507i
$$275$$ −18.2795 + 2.35293i −1.10230 + 0.141887i
$$276$$ 3.78510 9.38824i 0.227836 0.565106i
$$277$$ 8.86336 + 8.86336i 0.532547 + 0.532547i 0.921330 0.388782i $$-0.127104\pi$$
−0.388782 + 0.921330i $$0.627104\pi$$
$$278$$ 4.91678 12.0790i 0.294889 0.724453i
$$279$$ −7.00483 7.08372i −0.419368 0.424091i
$$280$$ −4.96353 1.59161i −0.296628 0.0951170i
$$281$$ 12.1925i 0.727341i −0.931528 0.363670i $$-0.881523\pi$$
0.931528 0.363670i $$-0.118477\pi$$
$$282$$ 0.0724970 + 21.7720i 0.00431713 + 1.29650i
$$283$$ 11.6799 11.6799i 0.694298 0.694298i −0.268877 0.963175i $$-0.586652\pi$$
0.963175 + 0.268877i $$0.0866525\pi$$
$$284$$ −5.77217 + 5.91546i −0.342516 + 0.351018i
$$285$$ −23.1783 7.97778i −1.37296 0.472563i
$$286$$ −11.1301 26.4113i −0.658135 1.56173i
$$287$$ −0.377697 0.377697i −0.0222947 0.0222947i
$$288$$ 6.88500 + 15.5112i 0.405702 + 0.914005i
$$289$$ 15.4508i 0.908872i
$$290$$ 1.37456 4.11256i 0.0807170 0.241498i
$$291$$ 5.04767 + 12.2833i 0.295900 + 0.720060i
$$292$$ −0.162900 13.2875i −0.00953298 0.777594i
$$293$$ 5.16432 + 5.16432i 0.301703 + 0.301703i 0.841680 0.539977i $$-0.181567\pi$$
−0.539977 + 0.841680i $$0.681567\pi$$
$$294$$ −10.9114 + 10.9843i −0.636363 + 0.640615i
$$295$$ 13.6573 0.875370i 0.795158 0.0509660i
$$296$$ −9.08971 3.57071i −0.528328 0.207544i
$$297$$ −17.7563 + 7.18079i −1.03033 + 0.416672i
$$298$$ 18.3451 + 7.46739i 1.06270 + 0.432574i
$$299$$ 16.0660i 0.929122i
$$300$$ 14.9427 8.75870i 0.862719 0.505684i
$$301$$ 0.955061i 0.0550488i
$$302$$ −7.00066 + 17.1985i −0.402843 + 0.989663i
$$303$$ −6.56923 + 15.7348i −0.377392 + 0.903939i
$$304$$ 0.620652 + 25.3091i 0.0355968 + 1.45158i
$$305$$ −11.4580 + 0.734409i −0.656086 + 0.0420521i
$$306$$ 4.87973 + 2.01822i 0.278956 + 0.115374i
$$307$$ −9.19824 9.19824i −0.524972 0.524972i 0.394097 0.919069i $$-0.371057\pi$$
−0.919069 + 0.394097i $$0.871057\pi$$
$$308$$ −6.07539 + 0.0744818i −0.346177 + 0.00424399i
$$309$$ −18.7618 + 7.70992i −1.06732 + 0.438602i
$$310$$ 9.95956 + 3.32883i 0.565665 + 0.189065i
$$311$$ 30.5690i 1.73341i 0.498821 + 0.866705i $$0.333767\pi$$
−0.498821 + 0.866705i $$0.666233\pi$$
$$312$$ 19.3404 + 18.7466i 1.09493 + 1.06132i
$$313$$ −16.4612 16.4612i −0.930440 0.930440i 0.0672931 0.997733i $$-0.478564\pi$$
−0.997733 + 0.0672931i $$0.978564\pi$$
$$314$$ 11.7389 4.94694i 0.662467 0.279172i
$$315$$ 0.322737 + 5.51923i 0.0181842 + 0.310974i
$$316$$ −1.53755 + 1.57571i −0.0864937 + 0.0886408i
$$317$$ 0.000616701 0 0.000616701i 3.46374e−5 0 3.46374e-5i −0.707089 0.707124i $$-0.749992\pi$$
0.707124 + 0.707089i $$0.249992\pi$$
$$318$$ 0.0646850 + 19.4260i 0.00362736 + 1.08935i
$$319$$ 5.05442i 0.282993i
$$320$$ −13.8576 11.3122i −0.774664 0.632374i
$$321$$ −5.44358 13.2468i −0.303831 0.739362i
$$322$$ −3.15454 1.28406i −0.175796 0.0715578i
$$323$$ 5.57034 + 5.57034i 0.309942 + 0.309942i
$$324$$ 12.7144 12.7414i 0.706357 0.707856i
$$325$$ 16.7978 21.7611i 0.931777 1.20709i
$$326$$ −2.68740 6.37713i −0.148842 0.353196i
$$327$$ 7.80967 18.7059i 0.431876 1.03444i
$$328$$ −0.732524 1.68039i −0.0404469 0.0927841i
$$329$$ 7.32553 0.403870
$$330$$ 13.2831 15.2043i 0.731212 0.836970i
$$331$$ 8.28613i 0.455447i 0.973726 + 0.227724i $$0.0731283\pi$$
−0.973726 + 0.227724i $$0.926872\pi$$
$$332$$ 0.217550 + 17.7453i 0.0119396 + 0.973901i
$$333$$ −0.0579994 + 10.3581i −0.00317835 + 0.567622i
$$334$$ −1.75853 + 0.741069i −0.0962226 + 0.0405495i
$$335$$ −10.2467 + 11.6502i −0.559839 + 0.636521i
$$336$$ 5.22663 2.29916i 0.285136 0.125429i
$$337$$ 2.27666 2.27666i 0.124018 0.124018i −0.642374 0.766392i $$-0.722050\pi$$
0.766392 + 0.642374i $$0.222050\pi$$
$$338$$ 22.5670 + 9.18590i 1.22748 + 0.499647i
$$339$$ −7.99142 19.4468i −0.434035 1.05621i
$$340$$ −5.55009 + 0.424111i −0.300996 + 0.0230006i
$$341$$ 12.2405 0.662861
$$342$$ 24.8030 10.2891i 1.34119 0.556373i
$$343$$ 7.76296 + 7.76296i 0.419161 + 0.419161i
$$344$$ −1.19841 + 3.05070i −0.0646139 + 0.164483i
$$345$$ 10.1714 4.96244i 0.547608 0.267169i
$$346$$ 3.32189 1.39989i 0.178586 0.0752584i
$$347$$ 18.6384 18.6384i 1.00056 1.00056i 0.000564305 1.00000i $$-0.499820\pi$$
1.00000 0.000564305i $$-0.000179624\pi$$
$$348$$ 1.85920 + 4.37109i 0.0996636 + 0.234315i
$$349$$ 17.7267 0.948889 0.474445 0.880285i $$-0.342649\pi$$
0.474445 + 0.880285i $$0.342649\pi$$
$$350$$ −2.93022 5.03747i −0.156627 0.269264i
$$351$$ 11.1541 26.3013i 0.595360 1.40386i
$$352$$ −19.4998 7.38548i −1.03934 0.393648i
$$353$$ −10.5779 + 10.5779i −0.563007 + 0.563007i −0.930160 0.367153i $$-0.880332\pi$$
0.367153 + 0.930160i $$0.380332\pi$$
$$354$$ −10.5652 + 10.6358i −0.561536 + 0.565288i
$$355$$ −9.22166 + 0.591066i −0.489435 + 0.0313705i
$$356$$ 21.9815 + 21.4490i 1.16502 + 1.13680i
$$357$$ 0.684521 1.63958i 0.0362287 0.0867759i
$$358$$ −31.4582 12.8051i −1.66262 0.676770i
$$359$$ −24.7266 −1.30502 −0.652510 0.757780i $$-0.726284\pi$$
−0.652510 + 0.757780i $$0.726284\pi$$
$$360$$ −5.89463 + 18.0348i −0.310674 + 0.950517i
$$361$$ 21.0586 1.10835
$$362$$ −28.4513 11.5811i −1.49537 0.608691i
$$363$$ 1.72637 4.13505i 0.0906111 0.217034i
$$364$$ 6.32919 6.48630i 0.331739 0.339974i
$$365$$ 9.81201 11.1560i 0.513584 0.583930i
$$366$$ 8.86391 8.92314i 0.463324 0.466420i
$$367$$ 9.33767 9.33767i 0.487423 0.487423i −0.420069 0.907492i $$-0.637994\pi$$
0.907492 + 0.420069i $$0.137994\pi$$
$$368$$ −8.46516 8.05992i −0.441277 0.420152i
$$369$$ −1.38251 + 1.36712i −0.0719707 + 0.0711692i
$$370$$ −4.87503 9.76985i −0.253441 0.507911i
$$371$$ 6.53616 0.339341
$$372$$ −10.5857 + 4.50250i −0.548841 + 0.233444i
$$373$$ 11.9025 11.9025i 0.616291 0.616291i −0.328287 0.944578i $$-0.606471\pi$$
0.944578 + 0.328287i $$0.106471\pi$$
$$374$$ −5.97903 + 2.51964i −0.309168 + 0.130288i
$$375$$ 18.9654 + 3.91314i 0.979370 + 0.202074i
$$376$$ 23.3996 + 9.19207i 1.20674 + 0.474045i
$$377$$ 5.33092 + 5.33092i 0.274557 + 0.274557i
$$378$$ −4.27275 4.29219i −0.219767 0.220766i
$$379$$ 2.73341 0.140406 0.0702029 0.997533i $$-0.477635\pi$$
0.0702029 + 0.997533i $$0.477635\pi$$
$$380$$ −18.4315 + 21.4814i −0.945515 + 1.10197i
$$381$$ 0.0136360 + 0.0331827i 0.000698593 + 0.00170000i
$$382$$ 17.0070 + 6.92270i 0.870153 + 0.354196i
$$383$$ 17.6065 17.6065i 0.899651 0.899651i −0.0957539 0.995405i $$-0.530526\pi$$
0.995405 + 0.0957539i $$0.0305262\pi$$
$$384$$ 19.5802 0.785717i 0.999196 0.0400960i
$$385$$ −5.10079 4.48630i −0.259960 0.228643i
$$386$$ −17.4836 + 7.36780i −0.889890 + 0.375011i
$$387$$ 3.47642 + 0.0194659i 0.176716 + 0.000989506i
$$388$$ 15.3333 0.187980i 0.778429 0.00954322i
$$389$$ 25.1335i 1.27432i −0.770731 0.637160i $$-0.780109\pi$$
0.770731 0.637160i $$-0.219891\pi$$
$$390$$ 2.02628 + 30.0458i 0.102605 + 1.52143i
$$391$$ −3.63704 −0.183933
$$392$$ 7.14408 + 16.3883i 0.360831 + 0.827736i
$$393$$ −3.49660 + 8.37515i −0.176380 + 0.422470i
$$394$$ −9.98855 23.7025i −0.503216 1.19412i
$$395$$ −2.45639 + 0.157444i −0.123594 + 0.00792185i
$$396$$ 0.147286 + 22.1159i 0.00740139 + 1.11137i
$$397$$ −5.42664 5.42664i −0.272355 0.272355i 0.557692 0.830048i $$-0.311687\pi$$
−0.830048 + 0.557692i $$0.811687\pi$$
$$398$$ −0.0607282 0.0247195i −0.00304403 0.00123907i
$$399$$ −3.43411 8.35678i −0.171921 0.418362i
$$400$$ −3.03886 19.7678i −0.151943 0.988389i
$$401$$ 5.15831i 0.257594i 0.991671 + 0.128797i $$0.0411115\pi$$
−0.991671 + 0.128797i $$0.958888\pi$$
$$402$$ −0.0565939 16.9960i −0.00282264 0.847686i
$$403$$ −12.9101 + 12.9101i −0.643099 + 0.643099i
$$404$$ 14.0917 + 13.7504i 0.701090 + 0.684108i
$$405$$ 20.0966 1.06227i 0.998606 0.0527847i
$$406$$ 1.47279 0.620652i 0.0730933 0.0308025i
$$407$$ −8.99944 8.99944i −0.446085 0.446085i
$$408$$ 4.24388 4.37830i 0.210103 0.216758i
$$409$$ 14.1638i 0.700356i 0.936683 + 0.350178i $$0.113879\pi$$
−0.936683 + 0.350178i $$0.886121\pi$$
$$410$$ 0.649681 1.94379i 0.0320854 0.0959967i
$$411$$ −31.9419 + 13.1261i −1.57558 + 0.647464i
$$412$$ 0.287124 + 23.4204i 0.0141456 + 1.15384i
$$413$$ 3.56672 + 3.56672i 0.175507 + 0.175507i
$$414$$ −4.73826 + 11.4563i −0.232873 + 0.563049i
$$415$$ −13.1038 + 14.8986i −0.643241 + 0.731345i
$$416$$ 28.3560 12.7770i 1.39027 0.626444i
$$417$$ −6.15365 + 14.7394i −0.301346 + 0.721791i
$$418$$ −12.4389 + 30.5587i −0.608407 + 1.49467i
$$419$$ 4.80514i 0.234746i −0.993088 0.117373i $$-0.962553\pi$$
0.993088 0.117373i $$-0.0374474\pi$$
$$420$$ 6.06141 + 2.00352i 0.295766 + 0.0977618i
$$421$$ 15.2187i 0.741716i −0.928690 0.370858i $$-0.879064\pi$$
0.928690 0.370858i $$-0.120936\pi$$
$$422$$ −0.774212 0.315143i −0.0376880 0.0153409i
$$423$$ 0.149308 26.6649i 0.00725958 1.29649i
$$424$$ 20.8781 + 8.20157i 1.01393 + 0.398304i
$$425$$ −4.92631 3.80272i −0.238961 0.184459i
$$426$$ 7.13385 7.18152i 0.345636 0.347946i
$$427$$ −2.99236 2.99236i −0.144811 0.144811i
$$428$$ −16.5359 + 0.202724i −0.799295 + 0.00979903i
$$429$$ 13.3421 + 32.4676i 0.644164 + 1.56755i
$$430$$ −3.27898 + 1.63617i −0.158126 + 0.0789029i
$$431$$ 27.8760i 1.34274i 0.741122 + 0.671370i $$0.234294\pi$$
−0.741122 + 0.671370i $$0.765706\pi$$
$$432$$ −8.26240 19.0718i −0.397525 0.917591i
$$433$$ −2.78003 2.78003i −0.133600 0.133600i 0.637145 0.770744i $$-0.280115\pi$$
−0.770744 + 0.637145i $$0.780115\pi$$
$$434$$ 1.50306 + 3.56672i 0.0721492 + 0.171208i
$$435$$ −1.72839 + 5.02160i −0.0828701 + 0.240767i
$$436$$ −16.7526 16.3468i −0.802305 0.782872i
$$437$$ −13.0777 + 13.0777i −0.625592 + 0.625592i
$$438$$ 0.0541928 + 16.2750i 0.00258943 + 0.777648i
$$439$$ 10.8174i 0.516286i 0.966107 + 0.258143i $$0.0831105\pi$$
−0.966107 + 0.258143i $$0.916889\pi$$
$$440$$ −10.6638 20.7308i −0.508376 0.988303i
$$441$$ 13.4832 13.3331i 0.642058 0.634907i
$$442$$ 3.64863 8.96358i 0.173548 0.426354i
$$443$$ −5.74963 5.74963i −0.273173 0.273173i 0.557203 0.830376i $$-0.311874\pi$$
−0.830376 + 0.557203i $$0.811874\pi$$
$$444$$ 11.0931 + 4.47244i 0.526454 + 0.212253i
$$445$$ 2.19637 + 34.2671i 0.104118 + 1.62442i
$$446$$ −31.0693 + 13.0930i −1.47118 + 0.619973i
$$447$$ −22.3855 9.34590i −1.05880 0.442046i
$$448$$ −0.242427 6.58885i −0.0114536 0.311294i
$$449$$ 6.91183 0.326189 0.163095 0.986610i $$-0.447852\pi$$
0.163095 + 0.986610i $$0.447852\pi$$
$$450$$ −18.3961 + 10.5633i −0.867200 + 0.497960i
$$451$$ 2.38895i 0.112491i
$$452$$ −24.2755 + 0.297608i −1.14182 + 0.0139983i
$$453$$ 8.76176 20.9864i 0.411663 0.986026i
$$454$$ −5.61841 13.3323i −0.263685 0.625716i
$$455$$ 10.1115 0.648104i 0.474036 0.0303836i
$$456$$ −0.483335 31.0028i −0.0226342 1.45184i
$$457$$ −5.15748 + 5.15748i −0.241257 + 0.241257i −0.817370 0.576113i $$-0.804569\pi$$
0.576113 + 0.817370i $$0.304569\pi$$
$$458$$ 12.2674 30.1373i 0.573219 1.40823i
$$459$$ −5.95412 2.52507i −0.277915 0.117860i
$$460$$ −0.995701 13.0302i −0.0464248 0.607535i
$$461$$ −18.4555 −0.859558 −0.429779 0.902934i $$-0.641408\pi$$
−0.429779 + 0.902934i $$0.641408\pi$$
$$462$$ 7.44132 0.0247783i 0.346202 0.00115279i
$$463$$ −19.6899 19.6899i −0.915068 0.915068i 0.0815977 0.996665i $$-0.473998\pi$$
−0.996665 + 0.0815977i $$0.973998\pi$$
$$464$$ 5.48325 0.134465i 0.254553 0.00624238i
$$465$$ −12.1610 4.18572i −0.563955 0.194108i
$$466$$ −3.45685 8.20301i −0.160136 0.379997i
$$467$$ −2.07946 + 2.07946i −0.0962257 + 0.0962257i −0.753581 0.657355i $$-0.771675\pi$$
0.657355 + 0.753581i $$0.271675\pi$$
$$468$$ −23.4811 23.1704i −1.08541 1.07105i
$$469$$ −5.71858 −0.264060
$$470$$ 12.5498 + 25.1505i 0.578877 + 1.16011i
$$471$$ −14.4307 + 5.93013i −0.664933 + 0.273246i
$$472$$ 6.91747 + 15.8685i 0.318402 + 0.730407i
$$473$$ −3.02041 + 3.02041i −0.138879 + 0.138879i
$$474$$ 1.90026 1.91296i 0.0872818 0.0878650i
$$475$$ −31.3870 + 4.04012i −1.44013 + 0.185374i
$$476$$ −1.46838 1.43281i −0.0673029 0.0656727i
$$477$$ 0.133219 23.7916i 0.00609967 1.08934i
$$478$$ −2.15122 + 5.28490i −0.0983945 + 0.241725i
$$479$$ 19.7088 0.900517 0.450259 0.892898i $$-0.351332\pi$$
0.450259 + 0.892898i $$0.351332\pi$$
$$480$$ 16.8476 + 14.0056i 0.768986 + 0.639265i
$$481$$ 18.9835 0.865573
$$482$$ 6.11083 15.0125i 0.278341 0.683799i
$$483$$ 3.84931 + 1.60708i 0.175150 + 0.0731246i
$$484$$ −3.70326 3.61356i −0.168330 0.164253i
$$485$$ 12.8735 + 11.3227i 0.584557 + 0.514136i
$$486$$ −15.7106 + 15.4653i −0.712649 + 0.701521i
$$487$$ 4.21395 4.21395i 0.190952 0.190952i −0.605155 0.796107i $$-0.706889\pi$$
0.796107 + 0.605155i $$0.206889\pi$$
$$488$$ −5.80354 13.3132i −0.262714 0.602659i
$$489$$ 3.22151 + 7.83943i 0.145682 + 0.354511i
$$490$$ −6.33613 + 18.9571i −0.286237 + 0.856396i
$$491$$ 27.7215 1.25105 0.625527 0.780203i $$-0.284884\pi$$
0.625527 + 0.780203i $$0.284884\pi$$
$$492$$ 0.878743 + 2.06598i 0.0396168 + 0.0931416i
$$493$$ 1.20682 1.20682i 0.0543525 0.0543525i
$$494$$ −19.1110 45.3497i −0.859843 2.04038i
$$495$$ −16.4341 + 18.4754i −0.738656 + 0.830407i
$$496$$ 0.325640 + 13.2790i 0.0146216 + 0.596246i
$$497$$ −2.40831 2.40831i −0.108028 0.108028i
$$498$$ −0.0723737 21.7350i −0.00324314 0.973968i
$$499$$ 5.14705 0.230414 0.115207 0.993342i $$-0.463247\pi$$
0.115207 + 0.993342i $$0.463247\pi$$
$$500$$ 12.2750 18.6902i 0.548957 0.835851i
$$501$$ 2.16177 0.888353i 0.0965809 0.0396887i
$$502$$ −9.32016 + 22.8968i −0.415979 + 1.02193i
$$503$$ 12.2281 12.2281i 0.545224 0.545224i −0.379832 0.925056i $$-0.624018\pi$$
0.925056 + 0.379832i $$0.124018\pi$$
$$504$$ −6.42618 + 2.75861i −0.286245 + 0.122878i
$$505$$ 1.40803 + 21.9677i 0.0626565 + 0.977550i
$$506$$ −5.91546 14.0372i −0.262974 0.624030i
$$507$$ −27.5372 11.4967i −1.22297 0.510587i
$$508$$ 0.0414220 0.000507817i 0.00183780 2.25307e-5i
$$509$$ 35.8361i 1.58841i 0.607651 + 0.794204i $$0.292112\pi$$
−0.607651 + 0.794204i $$0.707888\pi$$
$$510$$ 6.80181 0.458712i 0.301189 0.0203121i
$$511$$ 5.47596 0.242242
$$512$$ 7.49332 21.3506i 0.331161 0.943574i
$$513$$ −30.4886 + 12.3298i −1.34611 + 0.544375i
$$514$$ −12.4825 + 5.26031i −0.550581 + 0.232022i
$$515$$ −17.2945 + 19.6633i −0.762086 + 0.866469i
$$516$$ 1.50105 3.72308i 0.0660800 0.163899i
$$517$$ 23.1672 + 23.1672i 1.01889 + 1.01889i
$$518$$ 1.51723 3.72738i 0.0666634 0.163772i
$$519$$ −4.08361 + 1.67811i −0.179251 + 0.0736608i
$$520$$ 33.1120 + 10.6177i 1.45206 + 0.465619i
$$521$$ 18.1715i 0.796107i 0.917362 + 0.398054i $$0.130314\pi$$
−0.917362 + 0.398054i $$0.869686\pi$$
$$522$$ −2.22915 5.37359i −0.0975674 0.235196i
$$523$$ −21.7444 + 21.7444i −0.950815 + 0.950815i −0.998846 0.0480305i $$-0.984706\pi$$
0.0480305 + 0.998846i $$0.484706\pi$$
$$524$$ 7.50061 + 7.31893i 0.327666 + 0.319729i
$$525$$ 3.53355 + 6.20141i 0.154217 + 0.270652i
$$526$$ 11.9382 + 28.3289i 0.520529 + 1.23520i
$$527$$ 2.92261 + 2.92261i 0.127311 + 0.127311i
$$528$$ 23.8005 + 9.25822i 1.03579 + 0.402912i
$$529$$ 14.4612i 0.628746i
$$530$$ 11.1974 + 22.4404i 0.486386 + 0.974748i
$$531$$ 13.0555 12.9101i 0.566561 0.560252i
$$532$$ −10.4318 + 0.127889i −0.452275 + 0.00554471i
$$533$$ 2.51964 + 2.51964i 0.109138 + 0.109138i
$$534$$ −26.6861 26.5089i −1.15482 1.14715i
$$535$$ −13.8833 12.2108i −0.600227 0.527918i
$$536$$ −18.2666 7.17567i −0.788996 0.309942i
$$537$$ 38.3867 + 16.0264i 1.65651 + 0.691589i
$$538$$ 12.5597 + 5.11242i 0.541486 + 0.220412i
$$539$$ 23.2987i 1.00355i
$$540$$ 7.41635 22.0227i 0.319149 0.947705i
$$541$$ 26.6843i 1.14725i −0.819119 0.573623i $$-0.805537\pi$$
0.819119 0.573623i $$-0.194463\pi$$
$$542$$ 11.1476 27.3862i 0.478830 1.17634i
$$543$$ 34.7176 + 14.4945i 1.48987 + 0.622019i
$$544$$ −2.89247 6.41927i −0.124014 0.275224i
$$545$$ −1.67390 26.1158i −0.0717022 1.11868i
$$546$$ −7.82226 + 7.87453i −0.334762 + 0.336999i
$$547$$ 22.2551 + 22.2551i 0.951559 + 0.951559i 0.998880 0.0473207i $$-0.0150683\pi$$
−0.0473207 + 0.998880i $$0.515068\pi$$
$$548$$ 0.488829 + 39.8732i 0.0208817 + 1.70330i
$$549$$ −10.9532 + 10.8312i −0.467470 + 0.462264i
$$550$$ 6.66422 25.1981i 0.284163 1.07445i
$$551$$ 8.67873i 0.369726i
$$552$$ 10.2791 + 9.96353i 0.437508 + 0.424076i
$$553$$ −0.641507 0.641507i −0.0272797 0.0272797i
$$554$$ −16.3355 + 6.88398i −0.694027 + 0.292472i
$$555$$ 5.86358 + 12.0184i 0.248895 + 0.510153i
$$556$$ 13.2003 + 12.8805i 0.559817 + 0.546257i
$$557$$ 7.30615 7.30615i 0.309572 0.309572i −0.535172 0.844743i $$-0.679753\pi$$
0.844743 + 0.535172i $$0.179753\pi$$
$$558$$ 13.0135 5.39844i 0.550904 0.228534i
$$559$$ 6.37128i 0.269476i
$$560$$ 4.73122 5.65290i 0.199931 0.238878i
$$561$$ 7.35005 3.02041i 0.310319 0.127522i
$$562$$ 15.9704 + 6.50074i 0.673669 + 0.274217i
$$563$$ −21.3458 21.3458i −0.899616 0.899616i 0.0957856 0.995402i $$-0.469464\pi$$
−0.995402 + 0.0957856i $$0.969464\pi$$
$$564$$ −28.5569 11.5134i −1.20246 0.484801i
$$565$$ −20.3813 17.9260i −0.857447 0.754150i
$$566$$ 9.07152 + 21.5264i 0.381304 + 0.904823i
$$567$$ 5.18588 + 5.30335i 0.217787 + 0.222720i
$$568$$ −4.67081 10.7147i −0.195983 0.449579i
$$569$$ 35.6410 1.49415 0.747075 0.664740i $$-0.231458\pi$$
0.747075 + 0.664740i $$0.231458\pi$$
$$570$$ 22.8079 26.1067i 0.955317 1.09349i
$$571$$ 9.49296i 0.397268i −0.980074 0.198634i $$-0.936350\pi$$
0.980074 0.198634i $$-0.0636505\pi$$
$$572$$ 40.5293 0.496873i 1.69462 0.0207753i
$$573$$ −20.7527 8.66419i −0.866955 0.361952i
$$574$$ 0.696108 0.293349i 0.0290550 0.0122441i
$$575$$ 8.92779 11.5657i 0.372314 0.482323i
$$576$$ −23.9883 + 0.748140i −0.999514 + 0.0311725i
$$577$$ 10.6312 10.6312i 0.442582 0.442582i −0.450297 0.892879i $$-0.648682\pi$$
0.892879 + 0.450297i $$0.148682\pi$$
$$578$$ 20.2384 + 8.23803i 0.841805 + 0.342657i
$$579$$ 21.4926 8.83212i 0.893203 0.367050i
$$580$$ 4.65397 + 3.99320i 0.193246 + 0.165809i
$$581$$ −7.31307 −0.303397
$$582$$ −18.7807 + 0.0625363i −0.778483 + 0.00259221i
$$583$$ 20.6708 + 20.6708i 0.856097 + 0.856097i
$$584$$ 17.4916 + 6.87124i 0.723808 + 0.284334i
$$585$$ −2.15300 36.8192i −0.0890157 1.52229i
$$586$$ −9.51801 + 4.01102i −0.393186 + 0.165694i
$$587$$ 17.1910 17.1910i 0.709550 0.709550i −0.256891 0.966441i $$-0.582698\pi$$
0.966441 + 0.256891i $$0.0826980\pi$$
$$588$$ −8.57011 20.1489i −0.353425 0.830925i
$$589$$ 21.0177 0.866018
$$590$$ −6.13515 + 18.3558i −0.252580 + 0.755697i
$$591$$ 11.9737 + 29.1376i 0.492534 + 1.19856i
$$592$$ 9.52355 10.0024i 0.391415 0.411095i
$$593$$ −9.69544 + 9.69544i −0.398144 + 0.398144i −0.877578 0.479434i $$-0.840842\pi$$
0.479434 + 0.877578i $$0.340842\pi$$
$$594$$ 0.0614747 27.0869i 0.00252234 1.11139i
$$595$$ −0.146719 2.28906i −0.00601487 0.0938424i
$$596$$ −19.5624 + 20.0480i −0.801307 + 0.821198i
$$597$$ 0.0741033 + 0.0309379i 0.00303285 + 0.00126621i
$$598$$ 21.0442 + 8.56604i 0.860560 + 0.350291i
$$599$$ −26.8502 −1.09707 −0.548535 0.836128i $$-0.684814\pi$$
−0.548535 + 0.836128i $$0.684814\pi$$
$$600$$ 3.50550 + 24.2428i 0.143112 + 0.989707i
$$601$$ −42.9566 −1.75224 −0.876119 0.482095i $$-0.839876\pi$$
−0.876119 + 0.482095i $$0.839876\pi$$
$$602$$ −1.25099 0.509217i −0.0509866 0.0207541i
$$603$$ −0.116555 + 20.8156i −0.00474649 + 0.847677i
$$604$$ −18.7950 18.3397i −0.764756 0.746232i
$$605$$ −0.370026 5.77305i −0.0150437 0.234708i
$$606$$ −17.1077 16.9942i −0.694953 0.690341i
$$607$$ 32.0417 32.0417i 1.30053 1.30053i 0.372498 0.928033i $$-0.378501\pi$$
0.928033 0.372498i $$-0.121499\pi$$
$$608$$ −33.4822 12.6813i −1.35788 0.514294i
$$609$$ −1.81051 + 0.744004i −0.0733654 + 0.0301486i
$$610$$ 5.14720 15.4000i 0.208404 0.623526i
$$611$$ −48.8691 −1.97703
$$612$$ −5.24534 + 5.31568i −0.212030 + 0.214874i
$$613$$ −20.1419 + 20.1419i −0.813522 + 0.813522i −0.985160 0.171638i $$-0.945094\pi$$
0.171638 + 0.985160i $$0.445094\pi$$
$$614$$ 16.9527 7.14408i 0.684154 0.288311i
$$615$$ −0.816918 + 2.37344i −0.0329413 + 0.0957064i
$$616$$ 3.14170 7.99760i 0.126583 0.322232i
$$617$$ 7.33463 + 7.33463i 0.295281 + 0.295281i 0.839162 0.543881i $$-0.183046\pi$$
−0.543881 + 0.839162i $$0.683046\pi$$
$$618$$ −0.0955193 28.6860i −0.00384235 1.15392i
$$619$$ 11.9287 0.479456 0.239728 0.970840i $$-0.422942\pi$$
0.239728 + 0.970840i $$0.422942\pi$$
$$620$$ −9.67051 + 11.2707i −0.388377 + 0.452644i
$$621$$ 5.92821 13.9787i 0.237891 0.560947i
$$622$$ −40.0410 16.2987i −1.60550 0.653519i
$$623$$ −8.94914 + 8.94914i −0.358540 + 0.358540i
$$624$$ −34.8672 + 15.3378i −1.39581 + 0.614005i
$$625$$ 24.1851 6.33109i 0.967403 0.253244i
$$626$$ 30.3385 12.7850i 1.21257 0.510993i
$$627$$ 15.5681 37.2890i 0.621729 1.48918i
$$628$$ 0.220843 + 18.0139i 0.00881260 + 0.718834i
$$629$$ 4.29751i 0.171353i
$$630$$ −7.40147 2.51999i −0.294882 0.100399i
$$631$$ 7.13985 0.284233 0.142116 0.989850i $$-0.454609\pi$$
0.142116 + 0.989850i $$0.454609\pi$$
$$632$$ −1.24417 2.85410i −0.0494905 0.113530i
$$633$$ 0.944728 + 0.394421i 0.0375496 + 0.0156768i
$$634$$ 0.000478978 0.00113660i 1.90227e−5 4.51402e-5i
$$635$$ 0.0347772 + 0.0305876i 0.00138009 + 0.00121383i
$$636$$ −25.4797 10.2728i −1.01034 0.407341i
$$637$$ −24.5733 24.5733i −0.973628 0.973628i
$$638$$ 6.62057 + 2.69490i 0.262111 + 0.106692i
$$639$$ −8.81533 + 8.71716i −0.348729 + 0.344846i
$$640$$ 22.2060 12.1200i 0.877768 0.479086i
$$641$$ 30.0187i 1.18567i −0.805325 0.592834i $$-0.798009\pi$$
0.805325 0.592834i $$-0.201991\pi$$
$$642$$ 20.2537 0.0674414i 0.799351 0.00266170i
$$643$$ 32.7048 32.7048i 1.28975 1.28975i 0.354812 0.934938i $$-0.384545\pi$$
0.934938 0.354812i $$-0.115455\pi$$
$$644$$ 3.36386 3.44736i 0.132555 0.135845i
$$645$$ 4.03364 1.96795i 0.158825 0.0774878i
$$646$$ −10.2663 + 4.32637i −0.403923 + 0.170219i
$$647$$ −2.53026 2.53026i −0.0994747 0.0994747i 0.655618 0.755093i $$-0.272408\pi$$
−0.755093 + 0.655618i $$0.772408\pi$$
$$648$$ 9.91037 + 23.4475i 0.389316 + 0.921104i
$$649$$ 22.5597i 0.885545i
$$650$$ 19.5477 + 33.6053i 0.766725 + 1.31811i
$$651$$ −1.80179 4.38458i −0.0706176 0.171845i
$$652$$ 9.78598 0.119972i 0.383248 0.00469847i
$$653$$ −23.8061 23.8061i −0.931604 0.931604i 0.0662023 0.997806i $$-0.478912\pi$$
−0.997806 + 0.0662023i $$0.978912\pi$$
$$654$$ 20.3381 + 20.2031i 0.795283 + 0.790004i
$$655$$ 0.749453 + 11.6928i 0.0292835 + 0.456874i
$$656$$ 2.59164 0.0635543i 0.101186 0.00248138i
$$657$$ 0.111610 19.9325i 0.00435432 0.777640i
$$658$$ −3.90581 + 9.59539i −0.152264 + 0.374067i
$$659$$ 15.7130i 0.612093i 0.952017 + 0.306047i $$0.0990063\pi$$
−0.952017 + 0.306047i $$0.900994\pi$$
$$660$$ 12.8332 + 25.5056i 0.499531 + 0.992803i
$$661$$ 25.2637i 0.982643i 0.870978 + 0.491322i $$0.163486\pi$$
−0.870978 + 0.491322i $$0.836514\pi$$
$$662$$ −10.8536 4.41798i −0.421839 0.171710i
$$663$$ −4.56649 + 10.9378i −0.177348 + 0.424788i
$$664$$ −23.3598 9.17644i −0.906536 0.356115i
$$665$$ −8.75834 7.70323i −0.339634 0.298718i
$$666$$ −13.5367 5.59869i −0.524538 0.216945i
$$667$$ 2.83330 + 2.83330i 0.109706 + 0.109706i
$$668$$ −0.0330830 2.69854i −0.00128002 0.104410i
$$669$$ 38.1937 15.6952i 1.47665 0.606812i
$$670$$ −9.79680 19.6334i −0.378483 0.758505i
$$671$$ 18.9269i 0.730664i
$$672$$ 0.224845 + 8.07199i 0.00867359 + 0.311384i
$$673$$ −15.4486 15.4486i −0.595498 0.595498i 0.343613 0.939111i $$-0.388349\pi$$
−0.939111 + 0.343613i $$0.888349\pi$$
$$674$$ 1.76824 + 4.19597i 0.0681099 + 0.161623i
$$675$$ 22.6451 12.7357i 0.871612 0.490197i
$$676$$ −24.0644 + 24.6618i −0.925554 + 0.948529i
$$677$$ −3.86002 + 3.86002i −0.148353 + 0.148353i −0.777382 0.629029i $$-0.783453\pi$$
0.629029 + 0.777382i $$0.283453\pi$$
$$678$$ 29.7334 0.0990069i 1.14190 0.00380234i
$$679$$ 6.31904i 0.242503i
$$680$$ 2.40366 7.49594i 0.0921761 0.287456i
$$681$$ 6.73505 + 16.3895i 0.258088 + 0.628046i
$$682$$ −6.52637 + 16.0333i −0.249908 + 0.613947i
$$683$$ 20.9584 + 20.9584i 0.801949 + 0.801949i 0.983400 0.181451i $$-0.0580793\pi$$
−0.181451 + 0.983400i $$0.558079\pi$$
$$684$$ 0.252898 + 37.9743i 0.00966980 + 1.45198i
$$685$$ −29.4439 + 33.4768i −1.12499 + 1.27908i
$$686$$ −14.3074 + 6.02932i −0.546259 + 0.230201i
$$687$$ −15.3534 + 36.7749i −0.585770 + 1.40305i
$$688$$ −3.35702 3.19631i −0.127985 0.121858i
$$689$$ −43.6032 −1.66115
$$690$$ 1.07694 + 15.9689i 0.0409983 + 0.607925i
$$691$$ 26.8902i 1.02295i −0.859298 0.511475i $$-0.829099\pi$$
0.859298 0.511475i $$-0.170901\pi$$
$$692$$ 0.0624943 + 5.09759i 0.00237568 + 0.193781i
$$693$$ −9.11363 0.0510309i −0.346198 0.00193850i
$$694$$ 14.4761 + 34.3513i 0.549504 + 1.30396i
$$695$$ 1.31896 + 20.5780i 0.0500309 + 0.780569i
$$696$$ −6.71678 + 0.104715i −0.254599 + 0.00396921i
$$697$$ 0.570399 0.570399i 0.0216054 0.0216054i
$$698$$ −9.45148 + 23.2194i −0.357744 + 0.878869i
$$699$$ 4.14389 + 10.0840i 0.156736 + 0.381412i
$$700$$ 8.16069 1.15231i 0.308445 0.0435531i
$$701$$ 35.7956 1.35198 0.675990 0.736911i $$-0.263716\pi$$
0.675990 + 0.736911i $$0.263716\pi$$
$$702$$ 28.5038 + 28.6335i 1.07581 + 1.08070i
$$703$$ −15.4525 15.4525i −0.582804 0.582804i
$$704$$ 20.0708 21.6041i 0.756445 0.814236i
$$705$$ −15.0946 30.9389i −0.568495 1.16523i
$$706$$ −8.21566 19.4955i −0.309200 0.733723i
$$707$$ −5.73705 + 5.73705i −0.215764 + 0.215764i
$$708$$ −8.29826 19.5097i −0.311868 0.733221i
$$709$$ −31.6856 −1.18998 −0.594988 0.803735i $$-0.702843\pi$$
−0.594988 + 0.803735i $$0.702843\pi$$
$$710$$ 4.14257 12.3942i 0.155468 0.465145i
$$711$$ −2.34816 + 2.32201i −0.0880628 + 0.0870821i
$$712$$ −39.8152 + 17.3564i −1.49214 + 0.650459i
$$713$$ −6.86153 + 6.86153i −0.256966 + 0.256966i
$$714$$ 1.78265 + 1.77081i 0.0667138 + 0.0662710i
$$715$$ 34.0277 + 29.9284i 1.27256 + 1.11926i
$$716$$ 33.5456 34.3784i 1.25366 1.28478i
$$717$$ 2.69238 6.44887i 0.100549 0.240837i
$$718$$ 13.1837 32.3883i 0.492010 1.20872i
$$719$$ −47.9558 −1.78845 −0.894225 0.447618i $$-0.852272\pi$$
−0.894225 + 0.447618i $$0.852272\pi$$
$$720$$ −20.4801 17.3368i −0.763248 0.646106i
$$721$$ −9.65184 −0.359453
$$722$$ −11.2280 + 27.5837i −0.417861 + 1.02656i
$$723$$ −7.64809 + 18.3189i −0.284435 + 0.681287i
$$724$$ 30.3392 31.0923i 1.12755 1.15554i
$$725$$ 0.875297 + 6.80002i 0.0325077 + 0.252546i
$$726$$ 4.49586 + 4.46601i 0.166857 + 0.165749i
$$727$$ 20.8052 20.8052i 0.771622 0.771622i −0.206768 0.978390i $$-0.566295\pi$$
0.978390 + 0.206768i $$0.0662946\pi$$
$$728$$ 5.12153 + 11.7487i 0.189817 + 0.435435i
$$729$$ 19.4099 18.7685i 0.718884 0.695130i
$$730$$ 9.38116 + 18.8004i 0.347212 + 0.695835i
$$731$$ −1.44234 −0.0533468
$$732$$ 6.96199 + 16.3681i 0.257322 + 0.604981i
$$733$$ 11.3990 11.3990i 0.421033 0.421033i −0.464526 0.885559i $$-0.653775\pi$$
0.885559 + 0.464526i $$0.153775\pi$$
$$734$$ 7.25237 + 17.2096i 0.267690 + 0.635219i
$$735$$ 7.96715 23.1474i 0.293873 0.853806i
$$736$$ 15.0708 6.79077i 0.555516 0.250311i
$$737$$ −18.0852 18.0852i −0.666176 0.666176i
$$738$$ −1.05360 2.53981i −0.0387836 0.0934916i
$$739$$ 9.60683 0.353393 0.176697 0.984265i $$-0.443459\pi$$
0.176697 + 0.984265i $$0.443459\pi$$
$$740$$ 15.3964 1.17651i 0.565981 0.0432495i
$$741$$ 22.9092 + 55.7487i 0.841591 + 2.04798i
$$742$$ −3.48493 + 8.56143i −0.127936 + 0.314300i
$$743$$ 2.71436 2.71436i 0.0995802 0.0995802i −0.655562 0.755142i $$-0.727568\pi$$
0.755142 + 0.655562i $$0.227568\pi$$
$$744$$ −0.253593 16.2663i −0.00929716 0.596352i
$$745$$ −31.2530 + 2.00318i −1.14502 + 0.0733907i
$$746$$ 9.24445 + 21.9368i 0.338463 + 0.803163i
$$747$$ −0.149054 + 26.6196i −0.00545359 + 0.973958i
$$748$$ −0.112483 9.17508i −0.00411277 0.335474i
$$749$$ 6.81468i 0.249003i
$$750$$ −15.2376 + 22.7556i −0.556398 + 0.830916i
$$751$$ −18.9690 −0.692189 −0.346094 0.938200i $$-0.612492\pi$$
−0.346094 + 0.938200i $$0.612492\pi$$
$$752$$ −24.5164 + 25.7491i −0.894022 + 0.938972i
$$753$$ 11.6648 27.9397i 0.425087 1.01818i
$$754$$ −9.82507 + 4.14041i −0.357808 + 0.150785i
$$755$$ −1.87797 29.2996i −0.0683464 1.06632i
$$756$$ 7.90028 3.30819i 0.287331 0.120318i
$$757$$ 0.279592 + 0.279592i 0.0101620 + 0.0101620i 0.712170 0.702008i $$-0.247713\pi$$
−0.702008 + 0.712170i $$0.747713\pi$$
$$758$$ −1.45739 + 3.58037i −0.0529349 + 0.130045i
$$759$$ 7.09113 + 17.2560i 0.257392 + 0.626353i
$$760$$ −18.3103 35.5960i −0.664185 1.29120i
$$761$$ 20.3237i 0.736733i −0.929681 0.368366i $$-0.879917\pi$$
0.929681 0.368366i $$-0.120083\pi$$
$$762$$ −0.0507349 0.000168938i −0.00183793 6.11999e-6i
$$763$$ 6.82036 6.82036i 0.246914 0.246914i
$$764$$ −18.1355 + 18.5857i −0.656118 + 0.672406i
$$765$$ −8.33517 + 0.487399i −0.301359 + 0.0176220i
$$766$$ 13.6746 + 32.4494i 0.494083 + 1.17244i
$$767$$ −23.7938 23.7938i −0.859144 0.859144i
$$768$$ −9.41052 + 26.0661i −0.339573 + 0.940580i
$$769$$ 25.1716i 0.907711i 0.891075 + 0.453855i $$0.149952\pi$$
−0.891075 + 0.453855i $$0.850048\pi$$
$$770$$ 8.59603 4.28930i 0.309779