# Properties

 Label 168.2.ba.c.5.9 Level $168$ Weight $2$ Character 168.5 Analytic conductor $1.341$ Analytic rank $0$ Dimension $48$ CM no Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$168 = 2^{3} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 168.ba (of order $$6$$, 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: $$1.34148675396$$ Analytic rank: $$0$$ Dimension: $$48$$ Relative dimension: $$24$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 5.9 Character $$\chi$$ $$=$$ 168.5 Dual form 168.2.ba.c.101.9

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.717256 - 1.21883i) q^{2} +(-1.70617 + 0.298296i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(-0.337879 - 0.195075i) q^{5} +(1.58733 + 1.86558i) q^{6} +(1.39526 + 2.24795i) q^{7} +(2.82755 - 0.0704754i) q^{8} +(2.82204 - 1.01789i) q^{9} +O(q^{10})$$ $$q+(-0.717256 - 1.21883i) q^{2} +(-1.70617 + 0.298296i) q^{3} +(-0.971089 + 1.74842i) q^{4} +(-0.337879 - 0.195075i) q^{5} +(1.58733 + 1.86558i) q^{6} +(1.39526 + 2.24795i) q^{7} +(2.82755 - 0.0704754i) q^{8} +(2.82204 - 1.01789i) q^{9} +(0.00458308 + 0.551736i) q^{10} +(0.748582 + 1.29658i) q^{11} +(1.13530 - 3.27278i) q^{12} +3.28768 q^{13} +(1.73911 - 3.31293i) q^{14} +(0.634670 + 0.232043i) q^{15} +(-2.11397 - 3.39575i) q^{16} +(1.68169 + 2.91278i) q^{17} +(-3.26476 - 2.70950i) q^{18} +(-2.56203 + 4.43756i) q^{19} +(0.669184 - 0.401321i) q^{20} +(-3.05110 - 3.41918i) q^{21} +(1.04339 - 1.84237i) q^{22} +(4.72764 + 2.72950i) q^{23} +(-4.80326 + 0.963690i) q^{24} +(-2.42389 - 4.19830i) q^{25} +(-2.35811 - 4.00712i) q^{26} +(-4.51125 + 2.57850i) q^{27} +(-5.28528 + 0.256545i) q^{28} +4.13801 q^{29} +(-0.172400 - 0.939988i) q^{30} +(-3.60237 + 2.07983i) q^{31} +(-2.62258 + 5.01219i) q^{32} +(-1.66397 - 1.98889i) q^{33} +(2.34398 - 4.13891i) q^{34} +(-0.0329110 - 1.03171i) q^{35} +(-0.960750 + 5.92258i) q^{36} +(7.46581 + 4.31038i) q^{37} +(7.24625 - 0.0601921i) q^{38} +(-5.60934 + 0.980702i) q^{39} +(-0.969118 - 0.527771i) q^{40} -11.1607 q^{41} +(-1.97898 + 6.17120i) q^{42} -4.79323i q^{43} +(-2.99391 + 0.0497422i) q^{44} +(-1.15207 - 0.206585i) q^{45} +(-0.0641268 - 7.71993i) q^{46} +(2.51067 - 4.34861i) q^{47} +(4.61974 + 5.16314i) q^{48} +(-3.10652 + 6.27292i) q^{49} +(-3.37846 + 5.96557i) q^{50} +(-3.73813 - 4.46806i) q^{51} +(-3.19263 + 5.74826i) q^{52} +(0.499243 + 0.864715i) q^{53} +(6.37846 + 3.64900i) q^{54} -0.584118i q^{55} +(4.10358 + 6.25784i) q^{56} +(3.04755 - 8.33548i) q^{57} +(-2.96801 - 5.04353i) q^{58} +(-1.36034 + 0.785391i) q^{59} +(-1.02203 + 0.884338i) q^{60} +(3.40889 - 5.90437i) q^{61} +(5.11878 + 2.89891i) q^{62} +(6.22563 + 4.92357i) q^{63} +(7.99007 - 0.398545i) q^{64} +(-1.11084 - 0.641343i) q^{65} +(-1.23062 + 3.45464i) q^{66} +(3.05467 - 1.76361i) q^{67} +(-6.72585 + 0.111746i) q^{68} +(-8.88036 - 3.24676i) q^{69} +(-1.23388 + 0.780115i) q^{70} -14.3360i q^{71} +(7.90772 - 3.07701i) q^{72} +(2.76107 - 1.59410i) q^{73} +(-0.101268 - 12.1912i) q^{74} +(5.38791 + 6.43999i) q^{75} +(-5.27078 - 8.78877i) q^{76} +(-1.87018 + 3.49184i) q^{77} +(5.21864 + 6.13342i) q^{78} +(-0.239413 + 0.414676i) q^{79} +(0.0518426 + 1.55974i) q^{80} +(6.92781 - 5.74504i) q^{81} +(8.00508 + 13.6030i) q^{82} -17.4548i q^{83} +(8.94106 - 2.01429i) q^{84} -1.31222i q^{85} +(-5.84213 + 3.43797i) q^{86} +(-7.06016 + 1.23435i) q^{87} +(2.20803 + 3.61339i) q^{88} +(-2.54840 + 4.41396i) q^{89} +(0.574539 + 1.55235i) q^{90} +(4.58716 + 7.39053i) q^{91} +(-9.36328 + 5.61532i) q^{92} +(5.52586 - 4.62312i) q^{93} +(-7.10101 + 0.0589856i) q^{94} +(1.73131 - 0.999573i) q^{95} +(2.97945 - 9.33396i) q^{96} +9.00074i q^{97} +(9.87379 - 0.712973i) q^{98} +(3.43230 + 2.89703i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10})$$ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 $$48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100})$$ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$$.

 $$n$$ $$73$$ $$85$$ $$113$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.717256 1.21883i −0.507176 0.861842i
$$3$$ −1.70617 + 0.298296i −0.985058 + 0.172221i
$$4$$ −0.971089 + 1.74842i −0.485544 + 0.874212i
$$5$$ −0.337879 0.195075i −0.151104 0.0872401i 0.422542 0.906344i $$-0.361138\pi$$
−0.573646 + 0.819103i $$0.694471\pi$$
$$6$$ 1.58733 + 1.86558i 0.648026 + 0.761618i
$$7$$ 1.39526 + 2.24795i 0.527357 + 0.849644i
$$8$$ 2.82755 0.0704754i 0.999690 0.0249168i
$$9$$ 2.82204 1.01789i 0.940680 0.339296i
$$10$$ 0.00458308 + 0.551736i 0.00144930 + 0.174474i
$$11$$ 0.748582 + 1.29658i 0.225706 + 0.390934i 0.956531 0.291631i $$-0.0941978\pi$$
−0.730825 + 0.682565i $$0.760864\pi$$
$$12$$ 1.13530 3.27278i 0.327732 0.944771i
$$13$$ 3.28768 0.911838 0.455919 0.890021i $$-0.349311\pi$$
0.455919 + 0.890021i $$0.349311\pi$$
$$14$$ 1.73911 3.31293i 0.464796 0.885418i
$$15$$ 0.634670 + 0.232043i 0.163871 + 0.0599132i
$$16$$ −2.11397 3.39575i −0.528493 0.848938i
$$17$$ 1.68169 + 2.91278i 0.407871 + 0.706453i 0.994651 0.103293i $$-0.0329381\pi$$
−0.586780 + 0.809746i $$0.699605\pi$$
$$18$$ −3.26476 2.70950i −0.769510 0.638635i
$$19$$ −2.56203 + 4.43756i −0.587769 + 1.01805i 0.406755 + 0.913537i $$0.366660\pi$$
−0.994524 + 0.104509i $$0.966673\pi$$
$$20$$ 0.669184 0.401321i 0.149634 0.0897382i
$$21$$ −3.05110 3.41918i −0.665805 0.746126i
$$22$$ 1.04339 1.84237i 0.222451 0.392795i
$$23$$ 4.72764 + 2.72950i 0.985780 + 0.569141i 0.904010 0.427511i $$-0.140609\pi$$
0.0817700 + 0.996651i $$0.473943\pi$$
$$24$$ −4.80326 + 0.963690i −0.980461 + 0.196712i
$$25$$ −2.42389 4.19830i −0.484778 0.839661i
$$26$$ −2.35811 4.00712i −0.462463 0.785861i
$$27$$ −4.51125 + 2.57850i −0.868190 + 0.496232i
$$28$$ −5.28528 + 0.256545i −0.998824 + 0.0484825i
$$29$$ 4.13801 0.768410 0.384205 0.923248i $$-0.374476\pi$$
0.384205 + 0.923248i $$0.374476\pi$$
$$30$$ −0.172400 0.939988i −0.0314758 0.171618i
$$31$$ −3.60237 + 2.07983i −0.647005 + 0.373549i −0.787308 0.616560i $$-0.788526\pi$$
0.140303 + 0.990109i $$0.455192\pi$$
$$32$$ −2.62258 + 5.01219i −0.463611 + 0.886039i
$$33$$ −1.66397 1.98889i −0.289661 0.346222i
$$34$$ 2.34398 4.13891i 0.401989 0.709816i
$$35$$ −0.0329110 1.03171i −0.00556298 0.174391i
$$36$$ −0.960750 + 5.92258i −0.160125 + 0.987097i
$$37$$ 7.46581 + 4.31038i 1.22737 + 0.708623i 0.966479 0.256745i $$-0.0826501\pi$$
0.260892 + 0.965368i $$0.415983\pi$$
$$38$$ 7.24625 0.0601921i 1.17550 0.00976445i
$$39$$ −5.60934 + 0.980702i −0.898214 + 0.157038i
$$40$$ −0.969118 0.527771i −0.153231 0.0834480i
$$41$$ −11.1607 −1.74301 −0.871505 0.490387i $$-0.836855\pi$$
−0.871505 + 0.490387i $$0.836855\pi$$
$$42$$ −1.97898 + 6.17120i −0.305363 + 0.952236i
$$43$$ 4.79323i 0.730961i −0.930819 0.365480i $$-0.880905\pi$$
0.930819 0.365480i $$-0.119095\pi$$
$$44$$ −2.99391 + 0.0497422i −0.451350 + 0.00749892i
$$45$$ −1.15207 0.206585i −0.171741 0.0307959i
$$46$$ −0.0641268 7.71993i −0.00945498 1.13824i
$$47$$ 2.51067 4.34861i 0.366219 0.634310i −0.622752 0.782419i $$-0.713985\pi$$
0.988971 + 0.148109i $$0.0473187\pi$$
$$48$$ 4.61974 + 5.16314i 0.666802 + 0.745235i
$$49$$ −3.10652 + 6.27292i −0.443788 + 0.896132i
$$50$$ −3.37846 + 5.96557i −0.477787 + 0.843658i
$$51$$ −3.73813 4.46806i −0.523443 0.625653i
$$52$$ −3.19263 + 5.74826i −0.442738 + 0.797140i
$$53$$ 0.499243 + 0.864715i 0.0685763 + 0.118778i 0.898275 0.439434i $$-0.144821\pi$$
−0.829699 + 0.558212i $$0.811488\pi$$
$$54$$ 6.37846 + 3.64900i 0.867999 + 0.496566i
$$55$$ 0.584118i 0.0787624i
$$56$$ 4.10358 + 6.25784i 0.548364 + 0.836240i
$$57$$ 3.04755 8.33548i 0.403657 1.10406i
$$58$$ −2.96801 5.04353i −0.389719 0.662248i
$$59$$ −1.36034 + 0.785391i −0.177101 + 0.102249i −0.585930 0.810362i $$-0.699271\pi$$
0.408829 + 0.912611i $$0.365937\pi$$
$$60$$ −1.02203 + 0.884338i −0.131944 + 0.114168i
$$61$$ 3.40889 5.90437i 0.436464 0.755977i −0.560950 0.827850i $$-0.689564\pi$$
0.997414 + 0.0718723i $$0.0228974\pi$$
$$62$$ 5.11878 + 2.89891i 0.650085 + 0.368161i
$$63$$ 6.22563 + 4.92357i 0.784355 + 0.620312i
$$64$$ 7.99007 0.398545i 0.998758 0.0498181i
$$65$$ −1.11084 0.641343i −0.137783 0.0795488i
$$66$$ −1.23062 + 3.45464i −0.151479 + 0.425237i
$$67$$ 3.05467 1.76361i 0.373187 0.215460i −0.301663 0.953415i $$-0.597542\pi$$
0.674850 + 0.737955i $$0.264208\pi$$
$$68$$ −6.72585 + 0.111746i −0.815629 + 0.0135512i
$$69$$ −8.88036 3.24676i −1.06907 0.390864i
$$70$$ −1.23388 + 0.780115i −0.147477 + 0.0932416i
$$71$$ 14.3360i 1.70137i −0.525677 0.850684i $$-0.676188\pi$$
0.525677 0.850684i $$-0.323812\pi$$
$$72$$ 7.90772 3.07701i 0.931933 0.362630i
$$73$$ 2.76107 1.59410i 0.323159 0.186576i −0.329641 0.944106i $$-0.606928\pi$$
0.652800 + 0.757531i $$0.273594\pi$$
$$74$$ −0.101268 12.1912i −0.0117722 1.41720i
$$75$$ 5.38791 + 6.43999i 0.622142 + 0.743626i
$$76$$ −5.27078 8.78877i −0.604600 1.00814i
$$77$$ −1.87018 + 3.49184i −0.213127 + 0.397932i
$$78$$ 5.21864 + 6.13342i 0.590895 + 0.694473i
$$79$$ −0.239413 + 0.414676i −0.0269361 + 0.0466547i −0.879179 0.476491i $$-0.841908\pi$$
0.852243 + 0.523146i $$0.175242\pi$$
$$80$$ 0.0518426 + 1.55974i 0.00579618 + 0.174384i
$$81$$ 6.92781 5.74504i 0.769756 0.638338i
$$82$$ 8.00508 + 13.6030i 0.884013 + 1.50220i
$$83$$ 17.4548i 1.91591i −0.286911 0.957957i $$-0.592628\pi$$
0.286911 0.957957i $$-0.407372\pi$$
$$84$$ 8.94106 2.01429i 0.975550 0.219777i
$$85$$ 1.31222i 0.142331i
$$86$$ −5.84213 + 3.43797i −0.629973 + 0.370726i
$$87$$ −7.06016 + 1.23435i −0.756928 + 0.132337i
$$88$$ 2.20803 + 3.61339i 0.235377 + 0.385189i
$$89$$ −2.54840 + 4.41396i −0.270130 + 0.467879i −0.968895 0.247473i $$-0.920400\pi$$
0.698765 + 0.715351i $$0.253733\pi$$
$$90$$ 0.574539 + 1.55235i 0.0605617 + 0.163633i
$$91$$ 4.58716 + 7.39053i 0.480865 + 0.774738i
$$92$$ −9.36328 + 5.61532i −0.976190 + 0.585438i
$$93$$ 5.52586 4.62312i 0.573005 0.479395i
$$94$$ −7.10101 + 0.0589856i −0.732413 + 0.00608390i
$$95$$ 1.73131 0.999573i 0.177629 0.102554i
$$96$$ 2.97945 9.33396i 0.304089 0.952644i
$$97$$ 9.00074i 0.913887i 0.889496 + 0.456943i $$0.151056\pi$$
−0.889496 + 0.456943i $$0.848944\pi$$
$$98$$ 9.87379 0.712973i 0.997403 0.0720212i
$$99$$ 3.43230 + 2.89703i 0.344959 + 0.291163i
$$100$$ 9.69423 0.161064i 0.969423 0.0161064i
$$101$$ 4.63907 2.67837i 0.461605 0.266508i −0.251114 0.967958i $$-0.580797\pi$$
0.712719 + 0.701450i $$0.247464\pi$$
$$102$$ −2.76460 + 7.76088i −0.273737 + 0.768442i
$$103$$ 7.70831 + 4.45039i 0.759522 + 0.438510i 0.829124 0.559065i $$-0.188840\pi$$
−0.0696021 + 0.997575i $$0.522173\pi$$
$$104$$ 9.29608 0.231700i 0.911555 0.0227201i
$$105$$ 0.363908 + 1.75046i 0.0355138 + 0.170828i
$$106$$ 0.695854 1.22871i 0.0675874 0.119343i
$$107$$ −7.85256 + 13.6010i −0.759135 + 1.31486i 0.184157 + 0.982897i $$0.441045\pi$$
−0.943292 + 0.331964i $$0.892289\pi$$
$$108$$ −0.127480 10.3915i −0.0122668 0.999925i
$$109$$ −15.1582 + 8.75159i −1.45189 + 0.838250i −0.998589 0.0531069i $$-0.983088\pi$$
−0.453303 + 0.891357i $$0.649754\pi$$
$$110$$ −0.711940 + 0.418962i −0.0678808 + 0.0399464i
$$111$$ −14.0237 5.12723i −1.33107 0.486655i
$$112$$ 4.68393 9.49004i 0.442590 0.896724i
$$113$$ 0.0726142i 0.00683097i −0.999994 0.00341549i $$-0.998913\pi$$
0.999994 0.00341549i $$-0.00108718\pi$$
$$114$$ −12.3454 + 2.26423i −1.15625 + 0.212064i
$$115$$ −1.06491 1.84448i −0.0993037 0.171999i
$$116$$ −4.01838 + 7.23500i −0.373097 + 0.671753i
$$117$$ 9.27796 3.34649i 0.857748 0.309383i
$$118$$ 1.93297 + 1.09469i 0.177944 + 0.100775i
$$119$$ −4.20138 + 7.84443i −0.385139 + 0.719098i
$$120$$ 1.81091 + 0.611384i 0.165313 + 0.0558114i
$$121$$ 4.37925 7.58508i 0.398114 0.689553i
$$122$$ −9.64147 + 0.0800883i −0.872897 + 0.00725085i
$$123$$ 19.0421 3.32920i 1.71697 0.300183i
$$124$$ −0.138202 8.31817i −0.0124109 0.746994i
$$125$$ 3.84211i 0.343649i
$$126$$ 1.53563 11.1194i 0.136805 0.990598i
$$127$$ −8.81577 −0.782273 −0.391137 0.920333i $$-0.627918\pi$$
−0.391137 + 0.920333i $$0.627918\pi$$
$$128$$ −6.21668 9.45267i −0.549482 0.835506i
$$129$$ 1.42980 + 8.17807i 0.125887 + 0.720039i
$$130$$ 0.0150677 + 1.81393i 0.00132152 + 0.159092i
$$131$$ −4.36183 2.51830i −0.381095 0.220025i 0.297200 0.954815i $$-0.403947\pi$$
−0.678294 + 0.734790i $$0.737281\pi$$
$$132$$ 5.09329 0.977942i 0.443314 0.0851189i
$$133$$ −13.5501 + 0.432239i −1.17494 + 0.0374799i
$$134$$ −4.34052 2.45816i −0.374964 0.212352i
$$135$$ 2.02726 + 0.00881014i 0.174478 + 0.000758256i
$$136$$ 4.96035 + 8.11751i 0.425347 + 0.696071i
$$137$$ 6.34787 3.66494i 0.542335 0.313117i −0.203690 0.979035i $$-0.565293\pi$$
0.746025 + 0.665918i $$0.231960\pi$$
$$138$$ 2.41224 + 13.1524i 0.205343 + 1.11961i
$$139$$ 15.7497 1.33587 0.667935 0.744220i $$-0.267178\pi$$
0.667935 + 0.744220i $$0.267178\pi$$
$$140$$ 1.83583 + 0.944343i 0.155156 + 0.0798116i
$$141$$ −2.98646 + 8.16840i −0.251505 + 0.687903i
$$142$$ −17.4731 + 10.2826i −1.46631 + 0.862894i
$$143$$ 2.46110 + 4.26275i 0.205807 + 0.356469i
$$144$$ −9.42221 7.43115i −0.785184 0.619262i
$$145$$ −1.39815 0.807222i −0.116110 0.0670361i
$$146$$ −3.92333 2.22189i −0.324697 0.183885i
$$147$$ 3.42906 11.6293i 0.282824 0.959172i
$$148$$ −14.7863 + 8.86763i −1.21543 + 0.728914i
$$149$$ −8.98969 + 15.5706i −0.736464 + 1.27559i 0.217613 + 0.976035i $$0.430173\pi$$
−0.954078 + 0.299559i $$0.903161\pi$$
$$150$$ 3.98473 11.1861i 0.325352 0.913338i
$$151$$ −7.89149 13.6685i −0.642201 1.11232i −0.984940 0.172894i $$-0.944688\pi$$
0.342740 0.939430i $$-0.388645\pi$$
$$152$$ −6.93152 + 12.7280i −0.562220 + 1.03238i
$$153$$ 7.71069 + 6.50820i 0.623373 + 0.526157i
$$154$$ 5.59735 0.225107i 0.451047 0.0181396i
$$155$$ 1.62289 0.130354
$$156$$ 3.73249 10.7599i 0.298838 0.861478i
$$157$$ −2.53274 4.38683i −0.202134 0.350107i 0.747082 0.664732i $$-0.231454\pi$$
−0.949216 + 0.314625i $$0.898121\pi$$
$$158$$ 0.677140 0.00562477i 0.0538704 0.000447482i
$$159$$ −1.10974 1.32643i −0.0880077 0.105193i
$$160$$ 1.86387 1.18192i 0.147352 0.0934387i
$$161$$ 0.460494 + 14.4358i 0.0362920 + 1.13770i
$$162$$ −11.9712 4.32315i −0.940549 0.339659i
$$163$$ −10.8745 6.27840i −0.851757 0.491762i 0.00948597 0.999955i $$-0.496980\pi$$
−0.861243 + 0.508193i $$0.830314\pi$$
$$164$$ 10.8380 19.5136i 0.846308 1.52376i
$$165$$ 0.174240 + 0.996605i 0.0135646 + 0.0775856i
$$166$$ −21.2744 + 12.5196i −1.65122 + 0.971706i
$$167$$ 7.43145 0.575063 0.287531 0.957771i $$-0.407165\pi$$
0.287531 + 0.957771i $$0.407165\pi$$
$$168$$ −8.86810 9.45287i −0.684189 0.729305i
$$169$$ −2.19116 −0.168551
$$170$$ −1.59938 + 0.941200i −0.122667 + 0.0721868i
$$171$$ −2.71320 + 15.1308i −0.207483 + 1.15708i
$$172$$ 8.38060 + 4.65465i 0.639014 + 0.354914i
$$173$$ −15.2445 8.80144i −1.15902 0.669161i −0.207952 0.978139i $$-0.566680\pi$$
−0.951069 + 0.308978i $$0.900013\pi$$
$$174$$ 6.56840 + 7.71978i 0.497949 + 0.585235i
$$175$$ 6.05561 11.3065i 0.457761 0.854690i
$$176$$ 2.82039 5.28294i 0.212595 0.398216i
$$177$$ 2.08669 1.74579i 0.156845 0.131222i
$$178$$ 7.20771 0.0598720i 0.540241 0.00448759i
$$179$$ −8.11784 14.0605i −0.606756 1.05093i −0.991771 0.128022i $$-0.959137\pi$$
0.385016 0.922910i $$-0.374196\pi$$
$$180$$ 1.47996 1.81370i 0.110310 0.135185i
$$181$$ −6.19340 −0.460351 −0.230176 0.973149i $$-0.573930\pi$$
−0.230176 + 0.973149i $$0.573930\pi$$
$$182$$ 5.71762 10.8919i 0.423818 0.807358i
$$183$$ −4.05490 + 11.0907i −0.299747 + 0.819850i
$$184$$ 13.5600 + 7.38462i 0.999655 + 0.544401i
$$185$$ −1.68169 2.91278i −0.123641 0.214152i
$$186$$ −9.59824 3.41912i −0.703777 0.250702i
$$187$$ −2.51777 + 4.36091i −0.184118 + 0.318901i
$$188$$ 5.16513 + 8.61261i 0.376706 + 0.628139i
$$189$$ −12.0907 6.54338i −0.879467 0.475961i
$$190$$ −2.46010 1.39322i −0.178475 0.101075i
$$191$$ 7.28788 + 4.20766i 0.527333 + 0.304456i 0.739930 0.672684i $$-0.234859\pi$$
−0.212597 + 0.977140i $$0.568192\pi$$
$$192$$ −13.5135 + 3.06339i −0.975255 + 0.221081i
$$193$$ 6.57333 + 11.3853i 0.473158 + 0.819534i 0.999528 0.0307215i $$-0.00978048\pi$$
−0.526370 + 0.850256i $$0.676447\pi$$
$$194$$ 10.9704 6.45583i 0.787626 0.463502i
$$195$$ 2.08659 + 0.762882i 0.149424 + 0.0546311i
$$196$$ −7.95102 11.5231i −0.567930 0.823077i
$$197$$ 17.6119 1.25480 0.627398 0.778699i $$-0.284120\pi$$
0.627398 + 0.778699i $$0.284120\pi$$
$$198$$ 1.06915 6.26130i 0.0759810 0.444971i
$$199$$ 17.2688 9.97017i 1.22416 0.706767i 0.258354 0.966050i $$-0.416820\pi$$
0.965801 + 0.259284i $$0.0834864\pi$$
$$200$$ −7.14955 11.7001i −0.505549 0.827321i
$$201$$ −4.68570 + 3.92022i −0.330504 + 0.276511i
$$202$$ −6.59187 3.73316i −0.463803 0.262664i
$$203$$ 5.77359 + 9.30203i 0.405227 + 0.652874i
$$204$$ 11.4421 2.19695i 0.801108 0.153818i
$$205$$ 3.77097 + 2.17717i 0.263376 + 0.152060i
$$206$$ −0.104557 12.5872i −0.00728485 0.876990i
$$207$$ 16.1199 + 2.89055i 1.12041 + 0.200907i
$$208$$ −6.95007 11.1641i −0.481900 0.774094i
$$209$$ −7.67154 −0.530652
$$210$$ 1.87250 1.69907i 0.129215 0.117247i
$$211$$ 14.5159i 0.999314i −0.866223 0.499657i $$-0.833459\pi$$
0.866223 0.499657i $$-0.166541\pi$$
$$212$$ −1.99670 + 0.0331740i −0.137134 + 0.00227840i
$$213$$ 4.27637 + 24.4596i 0.293012 + 1.67595i
$$214$$ 22.2096 0.184488i 1.51822 0.0126113i
$$215$$ −0.935038 + 1.61953i −0.0637691 + 0.110451i
$$216$$ −12.5741 + 7.60875i −0.855556 + 0.517710i
$$217$$ −9.70158 5.19604i −0.658586 0.352730i
$$218$$ 21.5390 + 12.1981i 1.45880 + 0.826161i
$$219$$ −4.23534 + 3.54343i −0.286198 + 0.239443i
$$220$$ 1.02129 + 0.567230i 0.0688550 + 0.0382426i
$$221$$ 5.52887 + 9.57629i 0.371912 + 0.644171i
$$222$$ 3.80937 + 20.7700i 0.255668 + 1.39399i
$$223$$ 2.77897i 0.186093i 0.995662 + 0.0930467i $$0.0296606\pi$$
−0.995662 + 0.0930467i $$0.970339\pi$$
$$224$$ −14.9263 + 1.09788i −0.997306 + 0.0733549i
$$225$$ −11.1137 9.38052i −0.740915 0.625368i
$$226$$ −0.0885043 + 0.0520830i −0.00588722 + 0.00346451i
$$227$$ 14.0438 8.10819i 0.932119 0.538159i 0.0446379 0.999003i $$-0.485787\pi$$
0.887481 + 0.460844i $$0.152453\pi$$
$$228$$ 11.6145 + 13.4229i 0.769190 + 0.888953i
$$229$$ 10.3150 17.8661i 0.681633 1.18062i −0.292849 0.956159i $$-0.594603\pi$$
0.974482 0.224464i $$-0.0720633\pi$$
$$230$$ −1.48430 + 2.62091i −0.0978716 + 0.172818i
$$231$$ 2.14925 6.51554i 0.141410 0.428691i
$$232$$ 11.7004 0.291628i 0.768171 0.0191463i
$$233$$ 1.80462 + 1.04190i 0.118225 + 0.0682572i 0.557946 0.829877i $$-0.311589\pi$$
−0.439721 + 0.898134i $$0.644923\pi$$
$$234$$ −10.7335 8.90796i −0.701669 0.582331i
$$235$$ −1.69661 + 0.979538i −0.110675 + 0.0638980i
$$236$$ −0.0521881 3.14113i −0.00339716 0.204470i
$$237$$ 0.284784 0.778925i 0.0184987 0.0505966i
$$238$$ 12.5745 0.505704i 0.815083 0.0327799i
$$239$$ 0.851762i 0.0550959i 0.999620 + 0.0275480i $$0.00876990\pi$$
−0.999620 + 0.0275480i $$0.991230\pi$$
$$240$$ −0.553716 2.64571i −0.0357422 0.170780i
$$241$$ 13.0417 7.52961i 0.840087 0.485025i −0.0172066 0.999852i $$-0.505477\pi$$
0.857294 + 0.514827i $$0.172144\pi$$
$$242$$ −12.3860 + 0.102886i −0.796200 + 0.00661375i
$$243$$ −10.1063 + 11.8686i −0.648319 + 0.761369i
$$244$$ 7.01301 + 11.6939i 0.448962 + 0.748622i
$$245$$ 2.27332 1.51349i 0.145237 0.0966932i
$$246$$ −17.7158 20.8211i −1.12952 1.32751i
$$247$$ −8.42312 + 14.5893i −0.535950 + 0.928293i
$$248$$ −10.0393 + 6.13470i −0.637496 + 0.389554i
$$249$$ 5.20670 + 29.7809i 0.329961 + 1.88729i
$$250$$ 4.68287 2.75577i 0.296171 0.174290i
$$251$$ 11.8022i 0.744948i 0.928043 + 0.372474i $$0.121490\pi$$
−0.928043 + 0.372474i $$0.878510\pi$$
$$252$$ −14.6541 + 6.10381i −0.923123 + 0.384504i
$$253$$ 8.17302i 0.513834i
$$254$$ 6.32316 + 10.7449i 0.396750 + 0.674196i
$$255$$ 0.391432 + 2.23888i 0.0245124 + 0.140204i
$$256$$ −7.06224 + 14.3570i −0.441390 + 0.897315i
$$257$$ 8.86901 15.3616i 0.553233 0.958228i −0.444805 0.895627i $$-0.646727\pi$$
0.998039 0.0626011i $$-0.0199396\pi$$
$$258$$ 8.94213 7.60845i 0.556713 0.473681i
$$259$$ 0.727204 + 22.7968i 0.0451863 + 1.41653i
$$260$$ 2.20006 1.31942i 0.136442 0.0818267i
$$261$$ 11.6776 4.21204i 0.722827 0.260719i
$$262$$ 0.0591649 + 7.12259i 0.00365522 + 0.440035i
$$263$$ −6.27815 + 3.62469i −0.387128 + 0.223508i −0.680915 0.732363i $$-0.738418\pi$$
0.293787 + 0.955871i $$0.405084\pi$$
$$264$$ −4.84514 5.50642i −0.298198 0.338897i
$$265$$ 0.389559i 0.0239304i
$$266$$ 10.2457 + 16.2052i 0.628204 + 0.993605i
$$267$$ 3.03134 8.29114i 0.185515 0.507410i
$$268$$ 0.117190 + 7.05348i 0.00715850 + 0.430860i
$$269$$ 2.95817 1.70790i 0.180363 0.104132i −0.407100 0.913383i $$-0.633460\pi$$
0.587463 + 0.809251i $$0.300127\pi$$
$$270$$ −1.44332 2.47720i −0.0878379 0.150758i
$$271$$ 3.96989 + 2.29201i 0.241153 + 0.139230i 0.615707 0.787975i $$-0.288871\pi$$
−0.374553 + 0.927205i $$0.622204\pi$$
$$272$$ 6.33602 11.8682i 0.384177 0.719612i
$$273$$ −10.0310 11.2412i −0.607106 0.680346i
$$274$$ −9.01998 5.10826i −0.544917 0.308601i
$$275$$ 3.62896 6.28555i 0.218835 0.379033i
$$276$$ 14.3003 12.3737i 0.860779 0.744811i
$$277$$ −10.6940 + 6.17421i −0.642543 + 0.370972i −0.785593 0.618743i $$-0.787642\pi$$
0.143050 + 0.989715i $$0.454309\pi$$
$$278$$ −11.2965 19.1962i −0.677521 1.15131i
$$279$$ −8.04900 + 9.53617i −0.481881 + 0.570916i
$$280$$ −0.165768 2.91490i −0.00990653 0.174199i
$$281$$ 7.91565i 0.472208i 0.971728 + 0.236104i $$0.0758706\pi$$
−0.971728 + 0.236104i $$0.924129\pi$$
$$282$$ 12.0979 2.21884i 0.720422 0.132130i
$$283$$ −11.3552 19.6678i −0.674999 1.16913i −0.976469 0.215656i $$-0.930811\pi$$
0.301471 0.953475i $$-0.402522\pi$$
$$284$$ 25.0654 + 13.9215i 1.48736 + 0.826090i
$$285$$ −2.65574 + 2.22189i −0.157313 + 0.131613i
$$286$$ 3.43032 6.05714i 0.202839 0.358166i
$$287$$ −15.5720 25.0887i −0.919189 1.48094i
$$288$$ −2.29917 + 16.8141i −0.135480 + 0.990780i
$$289$$ 2.84381 4.92562i 0.167283 0.289742i
$$290$$ 0.0189648 + 2.28309i 0.00111365 + 0.134068i
$$291$$ −2.68489 15.3568i −0.157391 0.900232i
$$292$$ 0.105926 + 6.37554i 0.00619885 + 0.373100i
$$293$$ 12.8246i 0.749220i −0.927183 0.374610i $$-0.877777\pi$$
0.927183 0.374610i $$-0.122223\pi$$
$$294$$ −16.6337 + 4.16177i −0.970097 + 0.242719i
$$295$$ 0.612840 0.0356809
$$296$$ 21.4137 + 11.6617i 1.24465 + 0.677821i
$$297$$ −6.72027 3.91899i −0.389950 0.227403i
$$298$$ 25.4258 0.211203i 1.47288 0.0122347i
$$299$$ 15.5430 + 8.97373i 0.898872 + 0.518964i
$$300$$ −16.4920 + 3.16655i −0.952164 + 0.182821i
$$301$$ 10.7749 6.68778i 0.621056 0.385477i
$$302$$ −10.9993 + 19.4222i −0.632939 + 1.11762i
$$303$$ −7.11610 + 5.95357i −0.408809 + 0.342024i
$$304$$ 20.4849 0.680878i 1.17489 0.0390511i
$$305$$ −2.30359 + 1.32998i −0.131903 + 0.0761542i
$$306$$ 2.40185 14.0661i 0.137304 0.804103i
$$307$$ −12.3622 −0.705549 −0.352774 0.935708i $$-0.614762\pi$$
−0.352774 + 0.935708i $$0.614762\pi$$
$$308$$ −4.28910 6.66075i −0.244394 0.379532i
$$309$$ −14.4792 5.29377i −0.823694 0.301152i
$$310$$ −1.16403 1.97802i −0.0661123 0.112344i
$$311$$ −0.720819 1.24850i −0.0408739 0.0707957i 0.844865 0.534980i $$-0.179681\pi$$
−0.885739 + 0.464184i $$0.846348\pi$$
$$312$$ −15.7916 + 3.16830i −0.894022 + 0.179370i
$$313$$ −20.8822 12.0564i −1.18033 0.681466i −0.224242 0.974533i $$-0.571991\pi$$
−0.956092 + 0.293067i $$0.905324\pi$$
$$314$$ −3.53017 + 6.23345i −0.199219 + 0.351774i
$$315$$ −1.14305 2.87804i −0.0644033 0.162159i
$$316$$ −0.492538 0.821284i −0.0277074 0.0462008i
$$317$$ 13.4686 23.3283i 0.756472 1.31025i −0.188167 0.982137i $$-0.560255\pi$$
0.944639 0.328111i $$-0.106412\pi$$
$$318$$ −0.820726 + 2.30397i −0.0460240 + 0.129200i
$$319$$ 3.09764 + 5.36527i 0.173435 + 0.300398i
$$320$$ −2.77742 1.42400i −0.155263 0.0796040i
$$321$$ 9.34067 25.5481i 0.521345 1.42595i
$$322$$ 17.2645 10.9154i 0.962114 0.608294i
$$323$$ −17.2342 −0.958935
$$324$$ 3.31726 + 17.6917i 0.184292 + 0.982872i
$$325$$ −7.96898 13.8027i −0.442039 0.765635i
$$326$$ 0.147504 + 17.7574i 0.00816952 + 0.983491i
$$327$$ 23.2519 19.4533i 1.28583 1.07577i
$$328$$ −31.5574 + 0.786555i −1.74247 + 0.0434302i
$$329$$ 13.2785 0.423575i 0.732066 0.0233524i
$$330$$ 1.08972 0.927189i 0.0599869 0.0510401i
$$331$$ −15.2782 8.82087i −0.839766 0.484839i 0.0174189 0.999848i $$-0.494455\pi$$
−0.857185 + 0.515009i $$0.827788\pi$$
$$332$$ 30.5184 + 16.9502i 1.67492 + 0.930262i
$$333$$ 25.4563 + 4.56471i 1.39500 + 0.250145i
$$334$$ −5.33025 9.05766i −0.291658 0.495613i
$$335$$ −1.37615 −0.0751868
$$336$$ −5.16074 + 17.5888i −0.281541 + 0.959549i
$$337$$ 11.0396 0.601365 0.300682 0.953724i $$-0.402786\pi$$
0.300682 + 0.953724i $$0.402786\pi$$
$$338$$ 1.57162 + 2.67065i 0.0854850 + 0.145264i
$$339$$ 0.0216605 + 0.123892i 0.00117644 + 0.00672890i
$$340$$ 2.29432 + 1.27429i 0.124427 + 0.0691079i
$$341$$ −5.39334 3.11385i −0.292066 0.168624i
$$342$$ 20.3879 7.54574i 1.10245 0.408027i
$$343$$ −18.4356 + 1.76905i −0.995428 + 0.0955198i
$$344$$ −0.337805 13.5531i −0.0182132 0.730734i
$$345$$ 2.36713 + 2.82935i 0.127442 + 0.152327i
$$346$$ 0.206781 + 24.8934i 0.0111166 + 1.33828i
$$347$$ 10.8299 + 18.7579i 0.581377 + 1.00697i 0.995316 + 0.0966701i $$0.0308192\pi$$
−0.413940 + 0.910304i $$0.635848\pi$$
$$348$$ 4.69787 13.5428i 0.251832 0.725971i
$$349$$ 6.46130 0.345865 0.172933 0.984934i $$-0.444676\pi$$
0.172933 + 0.984934i $$0.444676\pi$$
$$350$$ −18.1241 + 0.728891i −0.968774 + 0.0389609i
$$351$$ −14.8315 + 8.47727i −0.791649 + 0.452483i
$$352$$ −8.46193 + 0.351646i −0.451023 + 0.0187428i
$$353$$ −14.9846 25.9541i −0.797549 1.38140i −0.921208 0.389071i $$-0.872796\pi$$
0.123659 0.992325i $$-0.460537\pi$$
$$354$$ −3.62451 1.29114i −0.192641 0.0686231i
$$355$$ −2.79659 + 4.84383i −0.148428 + 0.257084i
$$356$$ −5.24275 8.74203i −0.277865 0.463327i
$$357$$ 4.82830 14.6372i 0.255541 0.774683i
$$358$$ −11.3148 + 19.9792i −0.598005 + 1.05594i
$$359$$ −9.44412 5.45257i −0.498442 0.287775i 0.229628 0.973278i $$-0.426249\pi$$
−0.728070 + 0.685503i $$0.759582\pi$$
$$360$$ −3.27210 0.502936i −0.172455 0.0265071i
$$361$$ −3.62795 6.28380i −0.190945 0.330726i
$$362$$ 4.44225 + 7.54869i 0.233479 + 0.396750i
$$363$$ −5.20915 + 14.2478i −0.273409 + 0.747814i
$$364$$ −17.3763 + 0.843438i −0.910766 + 0.0442082i
$$365$$ −1.24388 −0.0651075
$$366$$ 16.4261 3.01266i 0.858606 0.157474i
$$367$$ −2.43552 + 1.40615i −0.127133 + 0.0734002i −0.562218 0.826989i $$-0.690052\pi$$
0.435085 + 0.900389i $$0.356718\pi$$
$$368$$ −0.725387 21.8240i −0.0378134 1.13765i
$$369$$ −31.4959 + 11.3604i −1.63961 + 0.591396i
$$370$$ −2.34398 + 4.13891i −0.121858 + 0.215171i
$$371$$ −1.24726 + 2.32877i −0.0647545 + 0.120904i
$$372$$ 2.71708 + 14.1510i 0.140874 + 0.733695i
$$373$$ 26.9266 + 15.5461i 1.39421 + 0.804947i 0.993778 0.111380i $$-0.0355271\pi$$
0.400431 + 0.916327i $$0.368860\pi$$
$$374$$ 7.12109 0.0591524i 0.368223 0.00305870i
$$375$$ −1.14609 6.55529i −0.0591836 0.338514i
$$376$$ 6.79258 12.4729i 0.350301 0.643238i
$$377$$ 13.6045 0.700665
$$378$$ 0.696839 + 19.4297i 0.0358415 + 0.999357i
$$379$$ 17.6950i 0.908931i 0.890764 + 0.454465i $$0.150170\pi$$
−0.890764 + 0.454465i $$0.849830\pi$$
$$380$$ 0.0664203 + 3.99774i 0.00340729 + 0.205080i
$$381$$ 15.0412 2.62971i 0.770585 0.134724i
$$382$$ −0.0988546 11.9007i −0.00505784 0.608890i
$$383$$ −17.4953 + 30.3028i −0.893968 + 1.54840i −0.0588917 + 0.998264i $$0.518757\pi$$
−0.835076 + 0.550134i $$0.814577\pi$$
$$384$$ 13.4264 + 14.2735i 0.685164 + 0.728389i
$$385$$ 1.31306 0.814994i 0.0669200 0.0415359i
$$386$$ 9.16202 16.1780i 0.466335 0.823436i
$$387$$ −4.87897 13.5267i −0.248012 0.687600i
$$388$$ −15.7371 8.74052i −0.798931 0.443733i
$$389$$ −10.4422 18.0864i −0.529439 0.917015i −0.999410 0.0343338i $$-0.989069\pi$$
0.469971 0.882682i $$-0.344264\pi$$
$$390$$ −0.566797 3.09038i −0.0287009 0.156487i
$$391$$ 18.3608i 0.928543i
$$392$$ −8.34175 + 17.9559i −0.421322 + 0.906911i
$$393$$ 8.19322 + 2.99554i 0.413293 + 0.151105i
$$394$$ −12.6322 21.4659i −0.636402 1.08144i
$$395$$ 0.161786 0.0934070i 0.00814032 0.00469982i
$$396$$ −8.39831 + 3.18785i −0.422031 + 0.160195i
$$397$$ 2.44443 4.23387i 0.122682 0.212492i −0.798142 0.602469i $$-0.794184\pi$$
0.920825 + 0.389977i $$0.127517\pi$$
$$398$$ −24.5381 13.8966i −1.22998 0.696574i
$$399$$ 22.9898 4.77941i 1.15093 0.239270i
$$400$$ −9.13235 + 17.1060i −0.456617 + 0.855301i
$$401$$ −6.62355 3.82411i −0.330764 0.190967i 0.325416 0.945571i $$-0.394496\pi$$
−0.656180 + 0.754604i $$0.727829\pi$$
$$402$$ 8.13893 + 2.89927i 0.405933 + 0.144603i
$$403$$ −11.8434 + 6.83782i −0.589964 + 0.340616i
$$404$$ 0.177974 + 10.7120i 0.00885453 + 0.532942i
$$405$$ −3.46148 + 0.589691i −0.172002 + 0.0293020i
$$406$$ 7.19644 13.7090i 0.357153 0.680364i
$$407$$ 12.9067i 0.639762i
$$408$$ −10.8846 12.3702i −0.538870 0.612416i
$$409$$ −6.66584 + 3.84852i −0.329604 + 0.190297i −0.655666 0.755051i $$-0.727612\pi$$
0.326061 + 0.945349i $$0.394279\pi$$
$$410$$ −0.0511504 6.15776i −0.00252614 0.304110i
$$411$$ −9.73731 + 8.14656i −0.480306 + 0.401840i
$$412$$ −15.2666 + 9.15566i −0.752133 + 0.451067i
$$413$$ −3.66354 1.96214i −0.180271 0.0965507i
$$414$$ −8.03900 21.7207i −0.395095 1.06751i
$$415$$ −3.40499 + 5.89762i −0.167145 + 0.289503i
$$416$$ −8.62221 + 16.4785i −0.422738 + 0.807924i
$$417$$ −26.8716 + 4.69807i −1.31591 + 0.230065i
$$418$$ 5.50246 + 9.35030i 0.269134 + 0.457338i
$$419$$ 4.38235i 0.214092i −0.994254 0.107046i $$-0.965861\pi$$
0.994254 0.107046i $$-0.0341392\pi$$
$$420$$ −3.41394 1.06359i −0.166583 0.0518978i
$$421$$ 11.9400i 0.581921i 0.956735 + 0.290961i $$0.0939749\pi$$
−0.956735 + 0.290961i $$0.906025\pi$$
$$422$$ −17.6924 + 10.4116i −0.861251 + 0.506829i
$$423$$ 2.65881 14.8275i 0.129276 0.720940i
$$424$$ 1.47258 + 2.40984i 0.0715146 + 0.117032i
$$425$$ 8.15249 14.1205i 0.395454 0.684946i
$$426$$ 26.7449 22.7560i 1.29579 1.10253i
$$427$$ 18.0290 0.575113i 0.872484 0.0278317i
$$428$$ −16.1548 26.9374i −0.780873 1.30207i
$$429$$ −5.47061 6.53884i −0.264124 0.315698i
$$430$$ 2.64460 0.0219677i 0.127534 0.00105938i
$$431$$ 0.588922 0.340014i 0.0283674 0.0163779i −0.485749 0.874098i $$-0.661453\pi$$
0.514117 + 0.857720i $$0.328120\pi$$
$$432$$ 18.2926 + 9.86820i 0.880102 + 0.474784i
$$433$$ 0.238499i 0.0114615i 0.999984 + 0.00573077i $$0.00182417\pi$$
−0.999984 + 0.00573077i $$0.998176\pi$$
$$434$$ 0.625428 + 15.5515i 0.0300215 + 0.746494i
$$435$$ 2.62627 + 0.960196i 0.125920 + 0.0460379i
$$436$$ −0.581531 35.0015i −0.0278503 1.67627i
$$437$$ −24.2247 + 13.9861i −1.15882 + 0.669046i
$$438$$ 7.35666 + 2.62061i 0.351515 + 0.125218i
$$439$$ 3.29894 + 1.90465i 0.157450 + 0.0909038i 0.576655 0.816988i $$-0.304358\pi$$
−0.419205 + 0.907892i $$0.637691\pi$$
$$440$$ −0.0411659 1.65162i −0.00196251 0.0787380i
$$441$$ −2.38158 + 20.8645i −0.113409 + 0.993548i
$$442$$ 7.70624 13.6074i 0.366549 0.647238i
$$443$$ −3.02001 + 5.23080i −0.143485 + 0.248523i −0.928807 0.370565i $$-0.879164\pi$$
0.785322 + 0.619088i $$0.212497\pi$$
$$444$$ 22.5828 19.5404i 1.07173 0.927346i
$$445$$ 1.72210 0.994257i 0.0816355 0.0471323i
$$446$$ 3.38709 1.99323i 0.160383 0.0943822i
$$447$$ 10.6933 29.2477i 0.505776 1.38337i
$$448$$ 12.0441 + 17.4052i 0.569030 + 0.822317i
$$449$$ 28.1482i 1.32839i 0.747558 + 0.664197i $$0.231226\pi$$
−0.747558 + 0.664197i $$0.768774\pi$$
$$450$$ −3.46188 + 20.2740i −0.163194 + 0.955724i
$$451$$ −8.35470 14.4708i −0.393408 0.681402i
$$452$$ 0.126960 + 0.0705149i 0.00597172 + 0.00331674i
$$453$$ 17.5415 + 20.9667i 0.824171 + 0.985103i
$$454$$ −19.9555 11.3013i −0.936557 0.530398i
$$455$$ −0.108201 3.39194i −0.00507254 0.159017i
$$456$$ 8.02964 23.7837i 0.376022 1.11378i
$$457$$ −6.23304 + 10.7959i −0.291569 + 0.505013i −0.974181 0.225768i $$-0.927511\pi$$
0.682612 + 0.730781i $$0.260844\pi$$
$$458$$ −29.1742 + 0.242340i −1.36322 + 0.0113238i
$$459$$ −15.0971 8.80403i −0.704674 0.410937i
$$460$$ 4.25907 0.0707621i 0.198580 0.00329930i
$$461$$ 31.6209i 1.47273i 0.676583 + 0.736367i $$0.263460\pi$$
−0.676583 + 0.736367i $$0.736540\pi$$
$$462$$ −9.48289 + 2.05374i −0.441184 + 0.0955486i
$$463$$ 23.5095 1.09258 0.546290 0.837596i $$-0.316040\pi$$
0.546290 + 0.837596i $$0.316040\pi$$
$$464$$ −8.74765 14.0517i −0.406099 0.652332i
$$465$$ −2.76893 + 0.484102i −0.128406 + 0.0224497i
$$466$$ −0.0244784 2.94684i −0.00113394 0.136510i
$$467$$ 12.7642 + 7.36942i 0.590657 + 0.341016i 0.765357 0.643606i $$-0.222562\pi$$
−0.174700 + 0.984622i $$0.555896\pi$$
$$468$$ −3.15864 + 19.4715i −0.146008 + 0.900073i
$$469$$ 8.22655 + 4.40603i 0.379867 + 0.203452i
$$470$$ 2.41079 + 1.36530i 0.111201 + 0.0629765i
$$471$$ 5.62985 + 6.72917i 0.259410 + 0.310064i
$$472$$ −3.79107 + 2.31660i −0.174498 + 0.106630i
$$473$$ 6.21481 3.58812i 0.285757 0.164982i
$$474$$ −1.15364 + 0.211585i −0.0529884 + 0.00971843i
$$475$$ 24.8403 1.13975
$$476$$ −9.63548 14.9634i −0.441642 0.685848i
$$477$$ 2.28907 + 1.93208i 0.104809 + 0.0884641i
$$478$$ 1.03815 0.610931i 0.0474840 0.0279433i
$$479$$ 17.3034 + 29.9703i 0.790611 + 1.36938i 0.925589 + 0.378529i $$0.123570\pi$$
−0.134979 + 0.990848i $$0.543097\pi$$
$$480$$ −2.82752 + 2.57254i −0.129058 + 0.117420i
$$481$$ 24.5452 + 14.1712i 1.11916 + 0.646150i
$$482$$ −18.5315 10.4949i −0.844087 0.478030i
$$483$$ −5.09183 24.4926i −0.231686 1.11445i
$$484$$ 9.00930 + 15.0226i 0.409514 + 0.682844i
$$485$$ 1.75582 3.04117i 0.0797276 0.138092i
$$486$$ 21.7145 + 3.80506i 0.984992 + 0.172601i
$$487$$ −12.0284 20.8338i −0.545058 0.944068i −0.998603 0.0528351i $$-0.983174\pi$$
0.453545 0.891233i $$-0.350159\pi$$
$$488$$ 9.22269 16.9351i 0.417492 0.766618i
$$489$$ 20.4266 + 7.46820i 0.923723 + 0.337724i
$$490$$ −3.47523 1.68523i −0.156995 0.0761308i
$$491$$ −15.3708 −0.693675 −0.346837 0.937925i $$-0.612744\pi$$
−0.346837 + 0.937925i $$0.612744\pi$$
$$492$$ −12.6707 + 36.5266i −0.571239 + 1.64674i
$$493$$ 6.95887 + 12.0531i 0.313412 + 0.542845i
$$494$$ 23.8234 0.197892i 1.07186 0.00890360i
$$495$$ −0.594567 1.64840i −0.0267238 0.0740902i
$$496$$ 14.6779 + 7.83605i 0.659057 + 0.351849i
$$497$$ 32.2265 20.0024i 1.44556 0.897229i
$$498$$ 32.5633 27.7066i 1.45920 1.24156i
$$499$$ 22.8684 + 13.2031i 1.02373 + 0.591051i 0.915182 0.403040i $$-0.132047\pi$$
0.108548 + 0.994091i $$0.465380\pi$$
$$500$$ −6.71763 3.73103i −0.300422 0.166857i
$$501$$ −12.6793 + 2.21677i −0.566470 + 0.0990381i
$$502$$ 14.3849 8.46519i 0.642028 0.377820i
$$503$$ 28.3616 1.26458 0.632291 0.774731i $$-0.282115\pi$$
0.632291 + 0.774731i $$0.282115\pi$$
$$504$$ 17.9503 + 13.4829i 0.799568 + 0.600576i
$$505$$ −2.08993 −0.0930006
$$506$$ 9.96152 5.86215i 0.442844 0.260604i
$$507$$ 3.73850 0.653615i 0.166032 0.0290281i
$$508$$ 8.56090 15.4137i 0.379828 0.683873i
$$509$$ −18.3731 10.6077i −0.814373 0.470179i 0.0340991 0.999418i $$-0.489144\pi$$
−0.848472 + 0.529240i $$0.822477\pi$$
$$510$$ 2.44805 2.08294i 0.108402 0.0922340i
$$511$$ 7.43586 + 3.98255i 0.328943 + 0.176178i
$$512$$ 22.5642 1.69001i 0.997207 0.0746885i
$$513$$ 0.115709 26.6251i 0.00510866 1.17553i
$$514$$ −25.0845 + 0.208368i −1.10643 + 0.00919072i
$$515$$ −1.73632 3.00739i −0.0765113 0.132522i
$$516$$ −15.6872 5.44173i −0.690590 0.239559i
$$517$$ 7.51778 0.330631
$$518$$ 27.2638 17.2375i 1.19790 0.757371i
$$519$$ 28.6352 + 10.4694i 1.25695 + 0.459554i
$$520$$ −3.18615 1.73514i −0.139722 0.0760910i
$$521$$ 5.91179 + 10.2395i 0.259000 + 0.448601i 0.965974 0.258638i $$-0.0832737\pi$$
−0.706974 + 0.707239i $$0.749940\pi$$
$$522$$ −13.5096 11.2119i −0.591299 0.490733i
$$523$$ 3.37960 5.85364i 0.147780 0.255962i −0.782627 0.622491i $$-0.786121\pi$$
0.930407 + 0.366529i $$0.119454\pi$$
$$524$$ 8.63878 5.18083i 0.377387 0.226326i
$$525$$ −6.95922 + 21.0972i −0.303725 + 0.920756i
$$526$$ 8.92092 + 5.05217i 0.388971 + 0.220285i
$$527$$ −12.1162 6.99528i −0.527789 0.304719i
$$528$$ −3.23618 + 9.85490i −0.140837 + 0.428880i
$$529$$ 3.40036 + 5.88960i 0.147842 + 0.256070i
$$530$$ −0.474806 + 0.279413i −0.0206242 + 0.0121369i
$$531$$ −3.03948 + 3.60108i −0.131902 + 0.156273i
$$532$$ 12.4026 24.1110i 0.537720 1.04535i
$$533$$ −36.6928 −1.58934
$$534$$ −12.2797 + 2.25219i −0.531396 + 0.0974616i
$$535$$ 5.30643 3.06367i 0.229417 0.132454i
$$536$$ 8.51293 5.20198i 0.367702 0.224691i
$$537$$ 18.0446 + 21.5681i 0.778683 + 0.930733i
$$538$$ −4.20340 2.38050i −0.181221 0.102631i
$$539$$ −10.4588 + 0.667940i −0.450494 + 0.0287702i
$$540$$ −1.98405 + 3.53595i −0.0853799 + 0.152163i
$$541$$ −15.3128 8.84087i −0.658351 0.380099i 0.133298 0.991076i $$-0.457443\pi$$
−0.791648 + 0.610977i $$0.790777\pi$$
$$542$$ −0.0538485 6.48257i −0.00231299 0.278450i
$$543$$ 10.5670 1.84747i 0.453473 0.0792824i
$$544$$ −19.0098 + 0.789975i −0.815038 + 0.0338699i
$$545$$ 6.82885 0.292516
$$546$$ −6.50624 + 20.2889i −0.278442 + 0.868285i
$$547$$ 1.49834i 0.0640644i 0.999487 + 0.0320322i $$0.0101979\pi$$
−0.999487 + 0.0320322i $$0.989802\pi$$
$$548$$ 0.243530 + 14.6577i 0.0104031 + 0.626148i
$$549$$ 3.61003 20.1322i 0.154072 0.859223i
$$550$$ −10.2639 + 0.0852587i −0.437654 + 0.00363544i
$$551$$ −10.6017 + 18.3627i −0.451647 + 0.782276i
$$552$$ −25.3385 8.55453i −1.07848 0.364105i
$$553$$ −1.26621 + 0.0403914i −0.0538448 + 0.00171762i
$$554$$ 15.1957 + 8.60573i 0.645602 + 0.365622i
$$555$$ 3.73813 + 4.46806i 0.158675 + 0.189658i
$$556$$ −15.2943 + 27.5371i −0.648624 + 1.16783i
$$557$$ 1.46808 + 2.54278i 0.0622044 + 0.107741i 0.895450 0.445161i $$-0.146854\pi$$
−0.833246 + 0.552902i $$0.813520\pi$$
$$558$$ 17.3962 + 2.97048i 0.736438 + 0.125750i
$$559$$ 15.7586i 0.666518i
$$560$$ −3.43387 + 2.29277i −0.145107 + 0.0968873i
$$561$$ 2.99491 8.19150i 0.126445 0.345845i
$$562$$ 9.64783 5.67755i 0.406969 0.239493i
$$563$$ −14.3950 + 8.31096i −0.606677 + 0.350265i −0.771664 0.636031i $$-0.780575\pi$$
0.164987 + 0.986296i $$0.447242\pi$$
$$564$$ −11.3817 13.1538i −0.479256 0.553877i
$$565$$ −0.0141652 + 0.0245348i −0.000595934 + 0.00103219i
$$566$$ −15.8271 + 27.9470i −0.665264 + 1.17470i
$$567$$ 22.5806 + 7.55752i 0.948296 + 0.317386i
$$568$$ −1.01033 40.5357i −0.0423927 1.70084i
$$569$$ −19.2204 11.0969i −0.805763 0.465207i 0.0397194 0.999211i $$-0.487354\pi$$
−0.845482 + 0.534003i $$0.820687\pi$$
$$570$$ 4.61295 + 1.64324i 0.193215 + 0.0688277i
$$571$$ 5.22532 3.01684i 0.218673 0.126251i −0.386663 0.922221i $$-0.626372\pi$$
0.605336 + 0.795970i $$0.293039\pi$$
$$572$$ −9.84303 + 0.163537i −0.411558 + 0.00683781i
$$573$$ −13.6895 5.00504i −0.571887 0.209089i
$$574$$ −19.4096 + 36.9746i −0.810143 + 1.54329i
$$575$$ 26.4641i 1.10363i
$$576$$ 22.1426 9.25771i 0.922608 0.385738i
$$577$$ −17.4549 + 10.0776i −0.726659 + 0.419537i −0.817199 0.576356i $$-0.804474\pi$$
0.0905396 + 0.995893i $$0.471141\pi$$
$$578$$ −8.04323 + 0.0668123i −0.334554 + 0.00277902i
$$579$$ −14.6114 17.4645i −0.607230 0.725801i
$$580$$ 2.76909 1.66067i 0.114980 0.0689557i
$$581$$ 39.2375 24.3539i 1.62784 1.01037i
$$582$$ −16.7916 + 14.2872i −0.696033 + 0.592222i
$$583$$ −0.747449 + 1.29462i −0.0309562 + 0.0536177i
$$584$$ 7.69472 4.70200i 0.318410 0.194570i
$$585$$ −3.78765 0.679185i −0.156600 0.0280808i
$$586$$ −15.6310 + 9.19850i −0.645709 + 0.379986i
$$587$$ 0.369829i 0.0152645i −0.999971 0.00763224i $$-0.997571\pi$$
0.999971 0.00763224i $$-0.00242944\pi$$
$$588$$ 17.0031 + 17.2886i 0.701196 + 0.712969i
$$589$$ 21.3143i 0.878241i
$$590$$ −0.439563 0.746947i −0.0180965 0.0307513i
$$591$$ −30.0489 + 5.25356i −1.23605 + 0.216103i
$$592$$ −1.14552 34.4640i −0.0470805 1.41646i
$$593$$ −4.89233 + 8.47376i −0.200904 + 0.347976i −0.948820 0.315818i $$-0.897721\pi$$
0.747916 + 0.663793i $$0.231055\pi$$
$$594$$ 0.0435743 + 11.0018i 0.00178788 + 0.451408i
$$595$$ 2.94981 1.83089i 0.120930 0.0750592i
$$596$$ −18.4942 30.8382i −0.757553 1.26318i
$$597$$ −26.4895 + 22.1620i −1.08414 + 0.907032i
$$598$$ −0.210828 25.3807i −0.00862141 1.03789i
$$599$$ −31.2524 + 18.0436i −1.27694 + 0.737240i −0.976284 0.216494i $$-0.930538\pi$$
−0.300653 + 0.953734i $$0.597205\pi$$
$$600$$ 15.6884 + 17.8297i 0.640478 + 0.727893i
$$601$$ 9.75944i 0.398096i −0.979990 0.199048i $$-0.936215\pi$$
0.979990 0.199048i $$-0.0637849\pi$$
$$602$$ −15.8796 8.33593i −0.647206 0.339747i
$$603$$ 6.82523 8.08629i 0.277945 0.329299i
$$604$$ 31.5616 0.524379i 1.28422 0.0213367i
$$605$$ −2.95932 + 1.70856i −0.120313 + 0.0694629i
$$606$$ 12.3605 + 4.40308i 0.502109 + 0.178863i
$$607$$ −7.33740 4.23625i −0.297816 0.171944i 0.343645 0.939099i $$-0.388338\pi$$
−0.641461 + 0.767155i $$0.721672\pi$$
$$608$$ −15.5228 24.4792i −0.629532 0.992764i
$$609$$ −12.6255 14.1486i −0.511611 0.573331i
$$610$$ 3.27328 + 1.85375i 0.132531 + 0.0750560i
$$611$$ 8.25429 14.2968i 0.333933 0.578388i
$$612$$ −18.8669 + 7.16152i −0.762648 + 0.289487i
$$613$$ −10.1968 + 5.88712i −0.411844 + 0.237779i −0.691582 0.722298i $$-0.743086\pi$$
0.279737 + 0.960077i $$0.409753\pi$$
$$614$$ 8.86687 + 15.0674i 0.357838 + 0.608072i
$$615$$ −7.08336 2.58976i −0.285629 0.104429i
$$616$$ −5.04194 + 10.0051i −0.203146 + 0.403118i
$$617$$ 17.5244i 0.705506i 0.935717 + 0.352753i $$0.114754\pi$$
−0.935717 + 0.352753i $$0.885246\pi$$
$$618$$ 3.93310 + 21.4447i 0.158212 + 0.862632i
$$619$$ 12.8081 + 22.1843i 0.514801 + 0.891661i 0.999852 + 0.0171755i $$0.00546739\pi$$
−0.485052 + 0.874485i $$0.661199\pi$$
$$620$$ −1.57597 + 2.83750i −0.0632925 + 0.113957i
$$621$$ −28.3655 0.123272i −1.13827 0.00494674i
$$622$$ −1.00469 + 1.77405i −0.0402844 + 0.0711328i
$$623$$ −13.4780 + 0.429940i −0.539985 + 0.0172252i
$$624$$ 15.1882 + 16.9748i 0.608015 + 0.679534i
$$625$$ −11.3700 + 19.6933i −0.454798 + 0.787734i
$$626$$ 0.283252 + 34.0994i 0.0113210 + 1.36289i
$$627$$ 13.0890 2.28839i 0.522723 0.0913896i
$$628$$ 10.1295 0.168297i 0.404213 0.00671577i
$$629$$ 28.9950i 1.15611i
$$630$$ −2.68798 + 3.45747i −0.107092 + 0.137749i
$$631$$ −7.24555 −0.288441 −0.144220 0.989546i $$-0.546067\pi$$
−0.144220 + 0.989546i $$0.546067\pi$$
$$632$$ −0.647729 + 1.18939i −0.0257653 + 0.0473114i
$$633$$ 4.33003 + 24.7666i 0.172103 + 0.984383i
$$634$$ −38.0937 + 0.316431i −1.51289 + 0.0125671i
$$635$$ 2.97867 + 1.71973i 0.118205 + 0.0682456i
$$636$$ 3.39681 0.652208i 0.134692 0.0258617i
$$637$$ −10.2132 + 20.6234i −0.404663 + 0.817127i
$$638$$ 4.31755 7.62377i 0.170933 0.301828i
$$639$$ −14.5924 40.4567i −0.577268 1.60044i
$$640$$ 0.256511 + 4.40658i 0.0101395 + 0.174185i
$$641$$ 11.9401 6.89362i 0.471606 0.272282i −0.245306 0.969446i $$-0.578888\pi$$
0.716912 + 0.697164i $$0.245555\pi$$
$$642$$ −37.8384 + 6.93981i −1.49336 + 0.273893i
$$643$$ 20.7470 0.818184 0.409092 0.912493i $$-0.365846\pi$$
0.409092 + 0.912493i $$0.365846\pi$$
$$644$$ −25.6871 13.2133i −1.01221 0.520678i
$$645$$ 1.11223 3.04212i 0.0437942 0.119783i
$$646$$ 12.3613 + 21.0055i 0.486349 + 0.826451i
$$647$$ −16.1242 27.9279i −0.633907 1.09796i −0.986746 0.162275i $$-0.948117\pi$$
0.352838 0.935684i $$-0.385217\pi$$
$$648$$ 19.1838 16.7326i 0.753612 0.657320i
$$649$$ −2.03665 1.17586i −0.0799454 0.0461565i
$$650$$ −11.1073 + 19.6129i −0.435665 + 0.769280i
$$651$$ 18.1025 + 5.97139i 0.709493 + 0.234037i
$$652$$ 21.5374 12.9164i 0.843471 0.505844i
$$653$$ 9.95455 17.2418i 0.389552 0.674723i −0.602838 0.797864i $$-0.705963\pi$$
0.992389 + 0.123141i $$0.0392966\pi$$
$$654$$ −40.3878 14.3871i −1.57929 0.562579i
$$655$$ 0.982514 + 1.70176i 0.0383900 + 0.0664934i
$$656$$ 23.5934 + 37.8990i 0.921168 + 1.47971i
$$657$$ 6.16923 7.30909i 0.240684 0.285155i
$$658$$ −10.0403 15.8804i −0.391413 0.619082i
$$659$$ 11.4275 0.445153 0.222576 0.974915i $$-0.428553\pi$$
0.222576 + 0.974915i $$0.428553\pi$$
$$660$$ −1.91169 0.663146i −0.0744124 0.0258129i
$$661$$ −2.31268 4.00568i −0.0899529 0.155803i 0.817538 0.575875i $$-0.195338\pi$$
−0.907491 + 0.420071i $$0.862005\pi$$
$$662$$ 0.207237 + 24.9483i 0.00805450 + 0.969644i
$$663$$ −12.2898 14.6895i −0.477295 0.570495i
$$664$$ −1.23013 49.3543i −0.0477385 1.91532i
$$665$$ 4.66261 + 2.49723i 0.180808 + 0.0968385i
$$666$$ −12.6951 34.3009i −0.491923 1.32913i
$$667$$ 19.5630 + 11.2947i 0.757483 + 0.437333i
$$668$$ −7.21660 + 12.9933i −0.279218 + 0.502727i
$$669$$ −0.828955 4.74139i −0.0320493 0.183313i
$$670$$ 0.987048 + 1.67729i 0.0381330 + 0.0647992i
$$671$$ 10.2073 0.394050
$$672$$ 25.1393 6.32562i 0.969771 0.244016i
$$673$$ 19.2606 0.742441 0.371220 0.928545i $$-0.378939\pi$$
0.371220 + 0.928545i $$0.378939\pi$$
$$674$$ −7.91821 13.4554i −0.304998 0.518282i
$$675$$ 21.7601 + 12.6896i 0.837546 + 0.488423i
$$676$$ 2.12781 3.83108i 0.0818389 0.147349i
$$677$$ 36.2236 + 20.9137i 1.39219 + 0.803780i 0.993557 0.113332i $$-0.0361524\pi$$
0.398630 + 0.917112i $$0.369486\pi$$
$$678$$ 0.135467 0.115263i 0.00520259 0.00442665i
$$679$$ −20.2332 + 12.5583i −0.776478 + 0.481945i
$$680$$ −0.0924795 3.71038i −0.00354643 0.142287i
$$681$$ −21.5425 + 18.0232i −0.825509 + 0.690649i
$$682$$ 0.0731565 + 8.80698i 0.00280131 + 0.337237i
$$683$$ −6.73357 11.6629i −0.257653 0.446268i 0.707960 0.706253i $$-0.249616\pi$$
−0.965613 + 0.259985i $$0.916282\pi$$
$$684$$ −23.8203 19.4372i −0.910793 0.743199i
$$685$$ −2.85975 −0.109265
$$686$$ 15.3792 + 21.2010i 0.587180 + 0.809456i
$$687$$ −12.2697 + 33.5595i −0.468120 + 1.28037i
$$688$$ −16.2766 + 10.1328i −0.620540 + 0.386308i
$$689$$ 1.64135 + 2.84291i 0.0625305 + 0.108306i
$$690$$ 1.75065 4.91449i 0.0666463 0.187091i
$$691$$ 15.2232 26.3674i 0.579118 1.00306i −0.416463 0.909153i $$-0.636730\pi$$
0.995581 0.0939090i $$-0.0299363\pi$$
$$692$$ 30.1925 18.1069i 1.14774 0.688323i
$$693$$ −1.72342 + 11.7577i −0.0654675 + 0.446639i
$$694$$ 15.0948 26.6539i 0.572993 1.01177i
$$695$$ −5.32149 3.07236i −0.201856 0.116541i
$$696$$ −19.8760 + 3.98776i −0.753396 + 0.151156i
$$697$$ −18.7689 32.5087i −0.710923 1.23135i
$$698$$ −4.63440 7.87522i −0.175415 0.298081i
$$699$$ −3.38979 1.23935i −0.128214 0.0468764i
$$700$$ 13.8880 + 21.5674i 0.524917 + 0.815170i
$$701$$ 37.2839 1.40819 0.704096 0.710105i $$-0.251353\pi$$
0.704096 + 0.710105i $$0.251353\pi$$
$$702$$ 20.9703 + 11.9967i 0.791475 + 0.452788i
$$703$$ −38.2552 + 22.0866i −1.44282 + 0.833013i
$$704$$ 6.49797 + 10.0614i 0.244901 + 0.379204i
$$705$$ 2.60251 2.17735i 0.0980163 0.0820038i
$$706$$ −20.8858 + 36.8793i −0.786047 + 1.38797i
$$707$$ 12.4935 + 6.69137i 0.469867 + 0.251655i
$$708$$ 1.02603 + 5.34374i 0.0385605 + 0.200830i
$$709$$ −39.5076 22.8097i −1.48374 0.856637i −0.483910 0.875118i $$-0.660784\pi$$
−0.999829 + 0.0184810i $$0.994117\pi$$
$$710$$ 7.90968 0.0657029i 0.296845 0.00246579i
$$711$$ −0.253540 + 1.41393i −0.00950848 + 0.0530265i
$$712$$ −6.89465 + 12.6603i −0.258388 + 0.474464i
$$713$$ −22.7076 −0.850406
$$714$$ −21.3034 + 4.61374i −0.797259 + 0.172665i
$$715$$ 1.92039i 0.0718186i
$$716$$ 32.4669 0.539419i 1.21334 0.0201590i
$$717$$ −0.254077 1.45325i −0.00948869 0.0542727i
$$718$$ 0.128102 + 15.4217i 0.00478074 + 0.575531i
$$719$$ 8.37315 14.5027i 0.312266 0.540860i −0.666587 0.745428i $$-0.732245\pi$$
0.978853 + 0.204567i $$0.0655787\pi$$
$$720$$ 1.73394 + 4.34887i 0.0646201 + 0.162073i
$$721$$ 0.750825 + 23.5373i 0.0279622 + 0.876575i
$$722$$ −5.05671 + 8.92895i −0.188191 + 0.332301i
$$723$$ −20.0053 + 16.7371i −0.744003 + 0.622458i
$$724$$ 6.01434 10.8287i 0.223521 0.402445i
$$725$$ −10.0301 17.3726i −0.372508 0.645204i
$$726$$ 21.1019 3.87023i 0.783164 0.143638i
$$727$$ 14.7144i 0.545726i −0.962053 0.272863i $$-0.912029\pi$$
0.962053 0.272863i $$-0.0879705\pi$$
$$728$$ 13.4913 + 20.5738i 0.500019 + 0.762515i
$$729$$ 13.7027 23.2645i 0.507508 0.861647i
$$730$$ 0.892178 + 1.51607i 0.0330210 + 0.0561124i
$$731$$ 13.9616 8.06075i 0.516389 0.298137i
$$732$$ −15.4536 17.8598i −0.571182 0.660116i
$$733$$ −17.1186 + 29.6503i −0.632290 + 1.09516i 0.354793 + 0.934945i $$0.384551\pi$$
−0.987082 + 0.160213i $$0.948782\pi$$
$$734$$ 3.46074 + 1.95991i 0.127738 + 0.0723417i
$$735$$ −3.42720 + 3.26039i −0.126414 + 0.120261i
$$736$$ −26.0794 + 16.5375i −0.961299 + 0.609580i
$$737$$ 4.57334 + 2.64042i 0.168461 + 0.0972610i
$$738$$ 36.4370 + 30.2399i 1.34126 + 1.11315i
$$739$$ 1.92964 1.11408i 0.0709829 0.0409820i −0.464089 0.885789i $$-0.653618\pi$$
0.535071 + 0.844807i $$0.320285\pi$$
$$740$$ 6.72585 0.111746i 0.247247 0.00410787i
$$741$$ 10.0194 27.4044i 0.368070 1.00673i
$$742$$ 3.73298 0.150128i 0.137042 0.00551137i
$$743$$ 14.7964i 0.542829i −0.962463 0.271414i $$-0.912509\pi$$
0.962463 0.271414i $$-0.0874914\pi$$
$$744$$ 15.2988 13.4615i 0.560882 0.493524i
$$745$$ 6.07486 3.50732i 0.222566 0.128498i
$$746$$ −0.365239 43.9695i −0.0133724 1.60984i
$$747$$ −17.7671 49.2582i −0.650063 1.80226i
$$748$$ −5.17974 8.63696i −0.189390 0.315799i
$$749$$ −41.5307 + 1.32480i −1.51750 + 0.0484073i
$$750$$ −7.16774 + 6.09870i −0.261729 + 0.222693i
$$751$$ 18.2439 31.5994i 0.665729 1.15308i −0.313358 0.949635i $$-0.601454\pi$$
0.979087 0.203442i $$-0.0652128\pi$$
$$752$$ −20.0743 + 0.667231i −0.732034 + 0.0243314i
$$753$$ −3.52055 20.1366i −0.128296 0.733817i
$$754$$ −9.75788 16.5815i −0.355361 0.603863i
$$755$$ 6.15772i 0.224103i
$$756$$ 23.1817 14.7854i 0.843111 0.537740i
$$757$$ 19.9557i 0.725302i 0.931925 + 0.362651i $$0.118128\pi$$
−0.931925 + 0.362651i $$0.881872\pi$$
$$758$$ 21.5672 12.6918i 0.783355 0.460988i
$$759$$ −2.43798 13.9446i −0.0884931 0.506156i
$$760$$ 4.82492 2.94836i 0.175018 0.106948i
$$761$$ 18.2013 31.5257i 0.659798 1.14280i −0.320869 0.947124i $$-0.603975\pi$$
0.980668 0.195681i $$-0.0626917\pi$$
$$762$$ −13.9936 16.4465i −0.506933 0.595794i
$$763$$ −40.8227 21.8641i −1.47788 0.791533i
$$764$$ −14.4340 + 8.65630i −0.522202 + 0.313174i
$$765$$ −1.33570 3.70315i −0.0482923 0.133888i
$$766$$ 49.4825 0.411034i 1.78787 0.0148513i
$$767$$ −4.47235 + 2.58211i −0.161487 + 0.0932347i
$$768$$ 7.76673 26.6022i 0.280258 0.959925i
$$769$$ 33.7570i 1.21731i 0.793436 + 0.608654i $$0.208290\pi$$