# Properties

 Label 380.2.bb.a.59.9 Level $380$ Weight $2$ Character 380.59 Analytic conductor $3.034$ Analytic rank $0$ Dimension $336$ CM no Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.bb (of order $$18$$, degree $$6$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$3.03431527681$$ Analytic rank: $$0$$ Dimension: $$336$$ Relative dimension: $$56$$ over $$\Q(\zeta_{18})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

## Embedding invariants

 Embedding label 59.9 Character $$\chi$$ $$=$$ 380.59 Dual form 380.2.bb.a.219.9

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.24529 - 0.670264i) q^{2} +(0.497064 - 0.592377i) q^{3} +(1.10149 + 1.66935i) q^{4} +(-1.92300 + 1.14109i) q^{5} +(-1.01604 + 0.404518i) q^{6} +(-0.647033 - 1.12069i) q^{7} +(-0.252775 - 2.81711i) q^{8} +(0.417106 + 2.36552i) q^{9} +O(q^{10})$$ $$q+(-1.24529 - 0.670264i) q^{2} +(0.497064 - 0.592377i) q^{3} +(1.10149 + 1.66935i) q^{4} +(-1.92300 + 1.14109i) q^{5} +(-1.01604 + 0.404518i) q^{6} +(-0.647033 - 1.12069i) q^{7} +(-0.252775 - 2.81711i) q^{8} +(0.417106 + 2.36552i) q^{9} +(3.15952 - 0.132067i) q^{10} +(-3.51998 - 2.03226i) q^{11} +(1.53639 + 0.177272i) q^{12} +(0.500232 - 0.419744i) q^{13} +(0.0545826 + 1.82927i) q^{14} +(-0.279898 + 1.70633i) q^{15} +(-1.57343 + 3.67754i) q^{16} +(-6.09239 - 1.07425i) q^{17} +(1.06611 - 3.22533i) q^{18} +(-4.32757 + 0.521627i) q^{19} +(-4.02304 - 1.95325i) q^{20} +(-0.985491 - 0.173769i) q^{21} +(3.02125 + 4.89007i) q^{22} +(-3.27900 - 1.19346i) q^{23} +(-1.79444 - 1.25054i) q^{24} +(2.39584 - 4.38862i) q^{25} +(-0.904273 + 0.187416i) q^{26} +(3.61769 + 2.08867i) q^{27} +(1.15812 - 2.31456i) q^{28} +(0.235148 - 0.0414630i) q^{29} +(1.49225 - 1.93727i) q^{30} +(2.17265 + 3.76314i) q^{31} +(4.42430 - 3.52499i) q^{32} +(-2.95352 + 1.07499i) q^{33} +(6.86676 + 5.42127i) q^{34} +(2.52305 + 1.41677i) q^{35} +(-3.48944 + 3.30190i) q^{36} -11.3618 q^{37} +(5.73871 + 2.25104i) q^{38} -0.504966i q^{39} +(3.70065 + 5.12886i) q^{40} +(-3.07574 + 3.66552i) q^{41} +(1.11075 + 0.876932i) q^{42} +(-1.67175 + 0.608467i) q^{43} +(-0.484684 - 8.11459i) q^{44} +(-3.50136 - 4.07294i) q^{45} +(3.28337 + 3.68399i) q^{46} +(2.14370 + 12.1575i) q^{47} +(1.39640 + 2.76004i) q^{48} +(2.66270 - 4.61192i) q^{49} +(-5.92505 + 3.85925i) q^{50} +(-3.66467 + 3.07502i) q^{51} +(1.25170 + 0.372715i) q^{52} +(-1.04851 - 0.381626i) q^{53} +(-3.10511 - 5.02581i) q^{54} +(9.08791 - 0.108569i) q^{55} +(-2.99357 + 2.10605i) q^{56} +(-1.84208 + 2.82284i) q^{57} +(-0.320619 - 0.105978i) q^{58} +(1.57571 - 8.93630i) q^{59} +(-3.15677 + 1.41227i) q^{60} +(7.73764 + 2.81627i) q^{61} +(-0.183281 - 6.14244i) q^{62} +(2.38115 - 1.99802i) q^{63} +(-7.87221 + 1.42419i) q^{64} +(-0.482980 + 1.37798i) q^{65} +(4.39852 + 0.640961i) q^{66} +(-8.22648 + 1.45055i) q^{67} +(-4.91742 - 11.3536i) q^{68} +(-2.33685 + 1.34918i) q^{69} +(-2.19232 - 3.45540i) q^{70} +(-2.30080 + 0.837424i) q^{71} +(6.55851 - 1.77298i) q^{72} +(7.87401 - 9.38388i) q^{73} +(14.1487 + 7.61539i) q^{74} +(-1.40883 - 3.60066i) q^{75} +(-5.63757 - 6.64965i) q^{76} +5.25977i q^{77} +(-0.338460 + 0.628829i) q^{78} +(10.3968 + 8.72395i) q^{79} +(-1.17069 - 8.86733i) q^{80} +(-3.73597 + 1.35978i) q^{81} +(6.28705 - 2.50308i) q^{82} +(-5.50091 - 9.52786i) q^{83} +(-0.795431 - 1.83653i) q^{84} +(12.9415 - 4.88616i) q^{85} +(2.48965 + 0.362796i) q^{86} +(0.0923220 - 0.159906i) q^{87} +(-4.83535 + 10.4299i) q^{88} +(-9.55984 - 11.3930i) q^{89} +(1.63026 + 7.41883i) q^{90} +(-0.794072 - 0.289019i) q^{91} +(-1.61950 - 6.78836i) q^{92} +(3.30914 + 0.583491i) q^{93} +(5.47923 - 16.5765i) q^{94} +(7.72670 - 5.94123i) q^{95} +(0.111033 - 4.37300i) q^{96} +(0.139455 - 0.790887i) q^{97} +(-6.40703 + 3.95847i) q^{98} +(3.33916 - 9.17427i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10})$$ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 $$336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100})$$ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$77$$ $$191$$ $$\chi(n)$$ $$e\left(\frac{1}{18}\right)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.24529 0.670264i −0.880553 0.473948i
$$3$$ 0.497064 0.592377i 0.286980 0.342009i −0.603224 0.797572i $$-0.706117\pi$$
0.890204 + 0.455563i $$0.150562\pi$$
$$4$$ 1.10149 + 1.66935i 0.550746 + 0.834673i
$$5$$ −1.92300 + 1.14109i −0.859991 + 0.510310i
$$6$$ −1.01604 + 0.404518i −0.414796 + 0.165144i
$$7$$ −0.647033 1.12069i −0.244556 0.423583i 0.717451 0.696609i $$-0.245309\pi$$
−0.962007 + 0.273026i $$0.911975\pi$$
$$8$$ −0.252775 2.81711i −0.0893693 0.995999i
$$9$$ 0.417106 + 2.36552i 0.139035 + 0.788508i
$$10$$ 3.15952 0.132067i 0.999128 0.0417634i
$$11$$ −3.51998 2.03226i −1.06131 0.612750i −0.135519 0.990775i $$-0.543270\pi$$
−0.925796 + 0.378024i $$0.876604\pi$$
$$12$$ 1.53639 + 0.177272i 0.443519 + 0.0511740i
$$13$$ 0.500232 0.419744i 0.138739 0.116416i −0.570777 0.821105i $$-0.693358\pi$$
0.709516 + 0.704689i $$0.248913\pi$$
$$14$$ 0.0545826 + 1.82927i 0.0145878 + 0.488894i
$$15$$ −0.279898 + 1.70633i −0.0722694 + 0.440573i
$$16$$ −1.57343 + 3.67754i −0.393357 + 0.919386i
$$17$$ −6.09239 1.07425i −1.47762 0.260545i −0.623995 0.781428i $$-0.714491\pi$$
−0.853628 + 0.520884i $$0.825602\pi$$
$$18$$ 1.06611 3.22533i 0.251284 0.760219i
$$19$$ −4.32757 + 0.521627i −0.992814 + 0.119669i
$$20$$ −4.02304 1.95325i −0.899578 0.436760i
$$21$$ −0.985491 0.173769i −0.215052 0.0379194i
$$22$$ 3.02125 + 4.89007i 0.644132 + 1.04257i
$$23$$ −3.27900 1.19346i −0.683718 0.248853i −0.0232748 0.999729i $$-0.507409\pi$$
−0.660443 + 0.750876i $$0.729631\pi$$
$$24$$ −1.79444 1.25054i −0.366288 0.255266i
$$25$$ 2.39584 4.38862i 0.479168 0.877723i
$$26$$ −0.904273 + 0.187416i −0.177343 + 0.0367553i
$$27$$ 3.61769 + 2.08867i 0.696224 + 0.401965i
$$28$$ 1.15812 2.31456i 0.218865 0.437411i
$$29$$ 0.235148 0.0414630i 0.0436660 0.00769949i −0.151773 0.988415i $$-0.548498\pi$$
0.195438 + 0.980716i $$0.437387\pi$$
$$30$$ 1.49225 1.93727i 0.272446 0.353696i
$$31$$ 2.17265 + 3.76314i 0.390219 + 0.675880i 0.992478 0.122421i $$-0.0390659\pi$$
−0.602259 + 0.798301i $$0.705733\pi$$
$$32$$ 4.42430 3.52499i 0.782113 0.623136i
$$33$$ −2.95352 + 1.07499i −0.514142 + 0.187132i
$$34$$ 6.86676 + 5.42127i 1.17764 + 0.929740i
$$35$$ 2.52305 + 1.41677i 0.426474 + 0.239478i
$$36$$ −3.48944 + 3.30190i −0.581573 + 0.550317i
$$37$$ −11.3618 −1.86787 −0.933933 0.357449i $$-0.883647\pi$$
−0.933933 + 0.357449i $$0.883647\pi$$
$$38$$ 5.73871 + 2.25104i 0.930942 + 0.365167i
$$39$$ 0.504966i 0.0808592i
$$40$$ 3.70065 + 5.12886i 0.585124 + 0.810944i
$$41$$ −3.07574 + 3.66552i −0.480349 + 0.572458i −0.950736 0.310003i $$-0.899670\pi$$
0.470386 + 0.882461i $$0.344115\pi$$
$$42$$ 1.11075 + 0.876932i 0.171393 + 0.135313i
$$43$$ −1.67175 + 0.608467i −0.254939 + 0.0927904i −0.466328 0.884612i $$-0.654424\pi$$
0.211389 + 0.977402i $$0.432201\pi$$
$$44$$ −0.484684 8.11459i −0.0730689 1.22332i
$$45$$ −3.50136 4.07294i −0.521952 0.607159i
$$46$$ 3.28337 + 3.68399i 0.484106 + 0.543175i
$$47$$ 2.14370 + 12.1575i 0.312691 + 1.77336i 0.584886 + 0.811115i $$0.301139\pi$$
−0.272195 + 0.962242i $$0.587750\pi$$
$$48$$ 1.39640 + 2.76004i 0.201553 + 0.398377i
$$49$$ 2.66270 4.61192i 0.380385 0.658846i
$$50$$ −5.92505 + 3.85925i −0.837928 + 0.545780i
$$51$$ −3.66467 + 3.07502i −0.513157 + 0.430590i
$$52$$ 1.25170 + 0.372715i 0.173580 + 0.0516862i
$$53$$ −1.04851 0.381626i −0.144024 0.0524203i 0.269003 0.963139i $$-0.413306\pi$$
−0.413026 + 0.910719i $$0.635528\pi$$
$$54$$ −3.10511 5.02581i −0.422552 0.683926i
$$55$$ 9.08791 0.108569i 1.22541 0.0146394i
$$56$$ −2.99357 + 2.10605i −0.400032 + 0.281432i
$$57$$ −1.84208 + 2.82284i −0.243990 + 0.373894i
$$58$$ −0.320619 0.105978i −0.0420993 0.0139156i
$$59$$ 1.57571 8.93630i 0.205140 1.16341i −0.692079 0.721822i $$-0.743305\pi$$
0.897219 0.441586i $$-0.145584\pi$$
$$60$$ −3.15677 + 1.41227i −0.407537 + 0.182323i
$$61$$ 7.73764 + 2.81627i 0.990703 + 0.360586i 0.785992 0.618236i $$-0.212152\pi$$
0.204711 + 0.978823i $$0.434375\pi$$
$$62$$ −0.183281 6.14244i −0.0232767 0.780091i
$$63$$ 2.38115 1.99802i 0.299997 0.251727i
$$64$$ −7.87221 + 1.42419i −0.984026 + 0.178023i
$$65$$ −0.482980 + 1.37798i −0.0599063 + 0.170917i
$$66$$ 4.39852 + 0.640961i 0.541421 + 0.0788968i
$$67$$ −8.22648 + 1.45055i −1.00502 + 0.177213i −0.651853 0.758346i $$-0.726008\pi$$
−0.353172 + 0.935559i $$0.614897\pi$$
$$68$$ −4.91742 11.3536i −0.596325 1.37683i
$$69$$ −2.33685 + 1.34918i −0.281323 + 0.162422i
$$70$$ −2.19232 3.45540i −0.262033 0.413000i
$$71$$ −2.30080 + 0.837424i −0.273055 + 0.0993840i −0.474919 0.880030i $$-0.657523\pi$$
0.201863 + 0.979414i $$0.435300\pi$$
$$72$$ 6.55851 1.77298i 0.772928 0.208947i
$$73$$ 7.87401 9.38388i 0.921583 1.09830i −0.0733041 0.997310i $$-0.523354\pi$$
0.994887 0.100991i $$-0.0322012\pi$$
$$74$$ 14.1487 + 7.61539i 1.64475 + 0.885272i
$$75$$ −1.40883 3.60066i −0.162678 0.415769i
$$76$$ −5.63757 6.64965i −0.646673 0.762767i
$$77$$ 5.25977i 0.599406i
$$78$$ −0.338460 + 0.628829i −0.0383231 + 0.0712008i
$$79$$ 10.3968 + 8.72395i 1.16973 + 0.981521i 0.999992 0.00396763i $$-0.00126294\pi$$
0.169739 + 0.985489i $$0.445707\pi$$
$$80$$ −1.17069 8.86733i −0.130888 0.991397i
$$81$$ −3.73597 + 1.35978i −0.415107 + 0.151087i
$$82$$ 6.28705 2.50308i 0.694288 0.276419i
$$83$$ −5.50091 9.52786i −0.603804 1.04582i −0.992239 0.124343i $$-0.960318\pi$$
0.388436 0.921476i $$-0.373016\pi$$
$$84$$ −0.795431 1.83653i −0.0867886 0.200382i
$$85$$ 12.9415 4.88616i 1.40370 0.529979i
$$86$$ 2.48965 + 0.362796i 0.268465 + 0.0391213i
$$87$$ 0.0923220 0.159906i 0.00989796 0.0171438i
$$88$$ −4.83535 + 10.4299i −0.515450 + 1.11183i
$$89$$ −9.55984 11.3930i −1.01334 1.20765i −0.978070 0.208275i $$-0.933215\pi$$
−0.0352707 0.999378i $$-0.511229\pi$$
$$90$$ 1.63026 + 7.41883i 0.171845 + 0.782014i
$$91$$ −0.794072 0.289019i −0.0832414 0.0302974i
$$92$$ −1.61950 6.78836i −0.168844 0.707735i
$$93$$ 3.30914 + 0.583491i 0.343142 + 0.0605052i
$$94$$ 5.47923 16.5765i 0.565139 1.70973i
$$95$$ 7.72670 5.94123i 0.792742 0.609557i
$$96$$ 0.111033 4.37300i 0.0113323 0.446318i
$$97$$ 0.139455 0.790887i 0.0141595 0.0803024i −0.976909 0.213655i $$-0.931463\pi$$
0.991069 + 0.133353i $$0.0425743\pi$$
$$98$$ −6.40703 + 3.95847i −0.647208 + 0.399866i
$$99$$ 3.33916 9.17427i 0.335599 0.922049i
$$100$$ 9.96512 0.834539i 0.996512 0.0834539i
$$101$$ 5.84992 4.90866i 0.582089 0.488430i −0.303544 0.952818i $$-0.598170\pi$$
0.885632 + 0.464387i $$0.153725\pi$$
$$102$$ 6.62465 1.37300i 0.655939 0.135947i
$$103$$ 7.03711 + 4.06287i 0.693387 + 0.400327i 0.804880 0.593438i $$-0.202230\pi$$
−0.111493 + 0.993765i $$0.535563\pi$$
$$104$$ −1.30891 1.30311i −0.128349 0.127780i
$$105$$ 2.09338 0.790374i 0.204293 0.0771326i
$$106$$ 1.04991 + 1.17801i 0.101976 + 0.114419i
$$107$$ 8.75169 5.05279i 0.846058 0.488472i −0.0132607 0.999912i $$-0.504221\pi$$
0.859319 + 0.511440i $$0.170888\pi$$
$$108$$ 0.498138 + 8.33983i 0.0479333 + 0.802500i
$$109$$ 0.476234 + 1.30844i 0.0456150 + 0.125326i 0.960408 0.278596i $$-0.0898690\pi$$
−0.914793 + 0.403922i $$0.867647\pi$$
$$110$$ −11.3898 5.95610i −1.08598 0.567892i
$$111$$ −5.64753 + 6.73046i −0.536040 + 0.638827i
$$112$$ 5.13946 0.616159i 0.485634 0.0582215i
$$113$$ 7.44050 0.699943 0.349972 0.936760i $$-0.386191\pi$$
0.349972 + 0.936760i $$0.386191\pi$$
$$114$$ 4.18597 2.28057i 0.392052 0.213595i
$$115$$ 7.66734 1.44660i 0.714983 0.134897i
$$116$$ 0.328230 + 0.346873i 0.0304754 + 0.0322063i
$$117$$ 1.20157 + 1.00823i 0.111085 + 0.0932112i
$$118$$ −7.95190 + 10.0721i −0.732032 + 0.927216i
$$119$$ 2.73807 + 7.52279i 0.250999 + 0.689613i
$$120$$ 4.87768 + 0.357186i 0.445269 + 0.0326065i
$$121$$ 2.76019 + 4.78078i 0.250926 + 0.434617i
$$122$$ −7.74796 8.69333i −0.701467 0.787057i
$$123$$ 0.642534 + 3.64399i 0.0579354 + 0.328568i
$$124$$ −3.88882 + 7.77197i −0.349227 + 0.697943i
$$125$$ 0.400594 + 11.1732i 0.0358302 + 0.999358i
$$126$$ −4.30442 + 0.892117i −0.383469 + 0.0794761i
$$127$$ −6.29024 7.49641i −0.558168 0.665199i 0.410989 0.911640i $$-0.365183\pi$$
−0.969158 + 0.246441i $$0.920739\pi$$
$$128$$ 10.7578 + 3.50293i 0.950861 + 0.309619i
$$129$$ −0.470524 + 1.29275i −0.0414273 + 0.113821i
$$130$$ 1.52506 1.39225i 0.133756 0.122109i
$$131$$ −0.592416 0.104459i −0.0517597 0.00912662i 0.147708 0.989031i $$-0.452810\pi$$
−0.199468 + 0.979904i $$0.563921\pi$$
$$132$$ −5.04782 3.74635i −0.439356 0.326078i
$$133$$ 3.38467 + 4.51238i 0.293488 + 0.391273i
$$134$$ 11.2166 + 3.70756i 0.968967 + 0.320284i
$$135$$ −9.34016 + 0.111583i −0.803873 + 0.00960350i
$$136$$ −1.48629 + 17.4345i −0.127448 + 1.49499i
$$137$$ −4.81932 + 13.2410i −0.411742 + 1.13125i 0.544522 + 0.838747i $$0.316711\pi$$
−0.956264 + 0.292505i $$0.905511\pi$$
$$138$$ 3.81436 0.113814i 0.324700 0.00968852i
$$139$$ −10.1432 12.0882i −0.860334 1.02531i −0.999387 0.0350210i $$-0.988850\pi$$
0.139053 0.990285i $$-0.455594\pi$$
$$140$$ 0.414042 + 5.77241i 0.0349929 + 0.487858i
$$141$$ 8.26740 + 4.77319i 0.696241 + 0.401975i
$$142$$ 3.42646 + 0.499311i 0.287542 + 0.0419012i
$$143$$ −2.61384 + 0.460890i −0.218580 + 0.0385416i
$$144$$ −9.35560 2.18806i −0.779634 0.182339i
$$145$$ −0.404877 + 0.348058i −0.0336232 + 0.0289046i
$$146$$ −16.0951 + 6.40798i −1.33204 + 0.530328i
$$147$$ −1.40847 3.86974i −0.116169 0.319171i
$$148$$ −12.5149 18.9667i −1.02872 1.55906i
$$149$$ −0.818404 0.686722i −0.0670462 0.0562585i 0.608649 0.793440i $$-0.291712\pi$$
−0.675695 + 0.737181i $$0.736156\pi$$
$$150$$ −0.658993 + 5.42816i −0.0538065 + 0.443207i
$$151$$ −1.10953 −0.0902925 −0.0451463 0.998980i $$-0.514375\pi$$
−0.0451463 + 0.998980i $$0.514375\pi$$
$$152$$ 2.56338 + 12.0594i 0.207918 + 0.978146i
$$153$$ 14.8598i 1.20134i
$$154$$ 3.52543 6.54994i 0.284088 0.527809i
$$155$$ −8.47207 4.75733i −0.680493 0.382118i
$$156$$ 0.842962 0.556216i 0.0674910 0.0445329i
$$157$$ −3.04036 8.35332i −0.242647 0.666668i −0.999908 0.0135552i $$-0.995685\pi$$
0.757261 0.653112i $$-0.226537\pi$$
$$158$$ −7.09968 17.8324i −0.564820 1.41867i
$$159$$ −0.747242 + 0.431420i −0.0592601 + 0.0342138i
$$160$$ −4.48560 + 11.8271i −0.354618 + 0.935011i
$$161$$ 0.784119 + 4.44696i 0.0617972 + 0.350469i
$$162$$ 5.56377 + 0.810764i 0.437131 + 0.0636996i
$$163$$ −1.43302 + 2.48207i −0.112243 + 0.194411i −0.916674 0.399635i $$-0.869137\pi$$
0.804431 + 0.594046i $$0.202470\pi$$
$$164$$ −9.50692 1.09693i −0.742366 0.0856555i
$$165$$ 4.45296 5.43744i 0.346662 0.423304i
$$166$$ 0.464047 + 15.5520i 0.0360171 + 1.20707i
$$167$$ −1.48086 + 4.06863i −0.114592 + 0.314840i −0.983709 0.179767i $$-0.942466\pi$$
0.869117 + 0.494607i $$0.164688\pi$$
$$168$$ −0.240418 + 2.82016i −0.0185487 + 0.217580i
$$169$$ −2.18338 + 12.3826i −0.167952 + 0.952505i
$$170$$ −19.3909 2.58952i −1.48721 0.198607i
$$171$$ −3.03898 10.0194i −0.232396 0.766204i
$$172$$ −2.85716 2.12051i −0.217857 0.161687i
$$173$$ −2.36685 + 13.4231i −0.179948 + 1.02054i 0.752327 + 0.658789i $$0.228931\pi$$
−0.932276 + 0.361749i $$0.882180\pi$$
$$174$$ −0.222147 + 0.137250i −0.0168409 + 0.0104049i
$$175$$ −6.46849 + 0.154574i −0.488972 + 0.0116847i
$$176$$ 13.0122 9.74726i 0.980830 0.734728i
$$177$$ −4.51044 5.37533i −0.339025 0.404034i
$$178$$ 4.26847 + 20.5952i 0.319935 + 1.54367i
$$179$$ −6.60254 + 11.4359i −0.493497 + 0.854762i −0.999972 0.00749289i $$-0.997615\pi$$
0.506475 + 0.862255i $$0.330948\pi$$
$$180$$ 2.94243 10.3313i 0.219316 0.770050i
$$181$$ −12.6495 + 2.23045i −0.940230 + 0.165788i −0.622700 0.782460i $$-0.713964\pi$$
−0.317530 + 0.948248i $$0.602853\pi$$
$$182$$ 0.795131 + 0.892150i 0.0589390 + 0.0661306i
$$183$$ 5.51439 3.18374i 0.407636 0.235349i
$$184$$ −2.53325 + 9.53896i −0.186754 + 0.703222i
$$185$$ 21.8487 12.9648i 1.60635 0.953190i
$$186$$ −3.72975 2.94462i −0.273478 0.215910i
$$187$$ 19.2620 + 16.1627i 1.40857 + 1.18193i
$$188$$ −17.9338 + 16.9700i −1.30796 + 1.23766i
$$189$$ 5.40577i 0.393212i
$$190$$ −13.6042 + 2.21962i −0.986950 + 0.161028i
$$191$$ 1.96817i 0.142412i −0.997462 0.0712059i $$-0.977315\pi$$
0.997462 0.0712059i $$-0.0226847\pi$$
$$192$$ −3.06933 + 5.37123i −0.221510 + 0.387635i
$$193$$ 9.09531 + 7.63187i 0.654695 + 0.549354i 0.908491 0.417904i $$-0.137235\pi$$
−0.253797 + 0.967258i $$0.581679\pi$$
$$194$$ −0.703764 + 0.891412i −0.0505273 + 0.0639996i
$$195$$ 0.576210 + 0.971048i 0.0412632 + 0.0695382i
$$196$$ 10.6318 0.635039i 0.759417 0.0453600i
$$197$$ −9.40767 + 5.43152i −0.670269 + 0.386980i −0.796179 0.605062i $$-0.793148\pi$$
0.125910 + 0.992042i $$0.459815\pi$$
$$198$$ −10.3074 + 9.18651i −0.732516 + 0.652857i
$$199$$ −0.987286 + 0.174085i −0.0699869 + 0.0123406i −0.208532 0.978016i $$-0.566869\pi$$
0.138545 + 0.990356i $$0.455757\pi$$
$$200$$ −12.9688 5.64002i −0.917034 0.398809i
$$201$$ −3.22981 + 5.59420i −0.227813 + 0.394584i
$$202$$ −10.5749 + 2.19172i −0.744051 + 0.154209i
$$203$$ −0.198616 0.236702i −0.0139401 0.0166132i
$$204$$ −9.16988 2.73049i −0.642020 0.191172i
$$205$$ 1.73196 10.5585i 0.120965 0.737435i
$$206$$ −6.04004 9.77617i −0.420829 0.681138i
$$207$$ 1.45546 8.25434i 0.101162 0.573716i
$$208$$ 0.756548 + 2.50006i 0.0524572 + 0.173348i
$$209$$ 16.2931 + 6.95865i 1.12702 + 0.481340i
$$210$$ −3.13663 0.418874i −0.216448 0.0289051i
$$211$$ −4.26511 + 24.1886i −0.293622 + 1.66521i 0.379128 + 0.925344i $$0.376224\pi$$
−0.672750 + 0.739870i $$0.734887\pi$$
$$212$$ −0.517858 2.17068i −0.0355667 0.149083i
$$213$$ −0.647575 + 1.77920i −0.0443711 + 0.121909i
$$214$$ −14.2851 + 0.426245i −0.976509 + 0.0291375i
$$215$$ 2.52046 3.07769i 0.171894 0.209897i
$$216$$ 4.96956 10.7194i 0.338136 0.729362i
$$217$$ 2.81155 4.86975i 0.190861 0.330580i
$$218$$ 0.283953 1.94859i 0.0192317 0.131975i
$$219$$ −1.64491 9.32877i −0.111153 0.630380i
$$220$$ 10.1915 + 15.0513i 0.687111 + 1.01476i
$$221$$ −3.49852 + 2.01987i −0.235336 + 0.135871i
$$222$$ 11.5440 4.59604i 0.774782 0.308466i
$$223$$ 1.95990 + 5.38479i 0.131245 + 0.360592i 0.987856 0.155370i $$-0.0496569\pi$$
−0.856612 + 0.515962i $$0.827435\pi$$
$$224$$ −6.81311 2.67750i −0.455220 0.178898i
$$225$$ 11.3807 + 3.83690i 0.758713 + 0.255794i
$$226$$ −9.26558 4.98710i −0.616337 0.331737i
$$227$$ 14.8537i 0.985873i −0.870065 0.492936i $$-0.835924\pi$$
0.870065 0.492936i $$-0.164076\pi$$
$$228$$ −6.74133 + 0.0342673i −0.446456 + 0.00226941i
$$229$$ 8.14498 0.538235 0.269118 0.963107i $$-0.413268\pi$$
0.269118 + 0.963107i $$0.413268\pi$$
$$230$$ −10.5177 3.33770i −0.693514 0.220081i
$$231$$ 3.11577 + 2.61444i 0.205003 + 0.172018i
$$232$$ −0.176245 0.651958i −0.0115711 0.0428031i
$$233$$ 2.99173 + 8.21972i 0.195995 + 0.538492i 0.998291 0.0584342i $$-0.0186108\pi$$
−0.802296 + 0.596926i $$0.796389\pi$$
$$234$$ −0.820514 2.06091i −0.0536387 0.134726i
$$235$$ −17.9951 20.9327i −1.17387 1.36550i
$$236$$ 16.6534 7.21286i 1.08404 0.469517i
$$237$$ 10.3357 1.82247i 0.671379 0.118382i
$$238$$ 1.63256 11.2033i 0.105823 0.726201i
$$239$$ 13.1030 + 7.56501i 0.847562 + 0.489340i 0.859827 0.510585i $$-0.170571\pi$$
−0.0122657 + 0.999925i $$0.503904\pi$$
$$240$$ −5.83471 3.71413i −0.376629 0.239746i
$$241$$ −8.84218 10.5377i −0.569575 0.678793i 0.401969 0.915653i $$-0.368326\pi$$
−0.971544 + 0.236861i $$0.923882\pi$$
$$242$$ −0.232844 7.80351i −0.0149678 0.501629i
$$243$$ −5.33772 + 14.6653i −0.342415 + 0.940777i
$$244$$ 3.82162 + 16.0189i 0.244654 + 1.02550i
$$245$$ 0.142248 + 11.9071i 0.00908792 + 0.760716i
$$246$$ 1.64230 4.96850i 0.104709 0.316780i
$$247$$ −1.94584 + 2.07741i −0.123811 + 0.132182i
$$248$$ 10.0520 7.07181i 0.638301 0.449061i
$$249$$ −8.37840 1.47734i −0.530959 0.0936224i
$$250$$ 6.99011 14.1823i 0.442094 0.896969i
$$251$$ 4.13506 11.3610i 0.261003 0.717100i −0.738098 0.674694i $$-0.764276\pi$$
0.999100 0.0424057i $$-0.0135022\pi$$
$$252$$ 5.95821 + 1.77416i 0.375332 + 0.111761i
$$253$$ 9.11659 + 10.8647i 0.573155 + 0.683060i
$$254$$ 2.80859 + 13.5513i 0.176227 + 0.850286i
$$255$$ 3.53828 10.0950i 0.221576 0.632172i
$$256$$ −11.0486 11.5727i −0.690540 0.723294i
$$257$$ 4.04349 + 22.9318i 0.252226 + 1.43044i 0.803094 + 0.595852i $$0.203186\pi$$
−0.550868 + 0.834592i $$0.685703\pi$$
$$258$$ 1.45242 1.29448i 0.0904240 0.0805907i
$$259$$ 7.35145 + 12.7331i 0.456797 + 0.791196i
$$260$$ −2.83232 + 0.711569i −0.175653 + 0.0441296i
$$261$$ 0.196164 + 0.538955i 0.0121422 + 0.0333605i
$$262$$ 0.667715 + 0.527157i 0.0412516 + 0.0325679i
$$263$$ 5.40776 + 4.53765i 0.333457 + 0.279803i 0.794107 0.607778i $$-0.207939\pi$$
−0.460650 + 0.887582i $$0.652384\pi$$
$$264$$ 3.77495 + 8.04867i 0.232332 + 0.495361i
$$265$$ 2.45175 0.462573i 0.150610 0.0284157i
$$266$$ −1.19041 7.88784i −0.0729886 0.483635i
$$267$$ −11.5008 −0.703837
$$268$$ −11.4829 12.1351i −0.701428 0.741267i
$$269$$ −12.2528 + 14.6023i −0.747068 + 0.890321i −0.996957 0.0779535i $$-0.975161\pi$$
0.249889 + 0.968274i $$0.419606\pi$$
$$270$$ 11.7060 + 6.12142i 0.712404 + 0.372538i
$$271$$ −5.50726 15.1311i −0.334542 0.919147i −0.986914 0.161248i $$-0.948448\pi$$
0.652372 0.757899i $$-0.273774\pi$$
$$272$$ 13.5366 20.7148i 0.820775 1.25602i
$$273$$ −0.565913 + 0.326730i −0.0342506 + 0.0197746i
$$274$$ 14.8764 13.2586i 0.898716 0.800983i
$$275$$ −17.3521 + 10.5789i −1.04637 + 0.637930i
$$276$$ −4.82626 2.41489i −0.290507 0.145360i
$$277$$ −21.3155 12.3065i −1.28072 0.739425i −0.303741 0.952755i $$-0.598236\pi$$
−0.976980 + 0.213329i $$0.931569\pi$$
$$278$$ 4.52893 + 21.8519i 0.271627 + 1.31059i
$$279$$ −7.99557 + 6.70908i −0.478682 + 0.401662i
$$280$$ 3.35344 7.46584i 0.200406 0.446170i
$$281$$ 4.50045 12.3649i 0.268474 0.737627i −0.730054 0.683390i $$-0.760505\pi$$
0.998528 0.0542372i $$-0.0172727\pi$$
$$282$$ −7.09601 11.4853i −0.422561 0.683942i
$$283$$ 4.45275 25.2528i 0.264689 1.50112i −0.505231 0.862984i $$-0.668593\pi$$
0.769920 0.638140i $$-0.220296\pi$$
$$284$$ −3.93227 2.91842i −0.233337 0.173176i
$$285$$ 0.321211 7.53029i 0.0190269 0.446056i
$$286$$ 3.56390 + 1.17802i 0.210738 + 0.0696578i
$$287$$ 6.09803 + 1.07525i 0.359956 + 0.0634699i
$$288$$ 10.1839 + 8.99550i 0.600090 + 0.530065i
$$289$$ 19.9885 + 7.27520i 1.17579 + 0.427953i
$$290$$ 0.737480 0.162059i 0.0433063 0.00951641i
$$291$$ −0.399186 0.475731i −0.0234007 0.0278878i
$$292$$ 24.3381 + 2.80817i 1.42428 + 0.164336i
$$293$$ 5.19491 8.99785i 0.303490 0.525660i −0.673434 0.739247i $$-0.735181\pi$$
0.976924 + 0.213587i $$0.0685147\pi$$
$$294$$ −0.839794 + 5.76299i −0.0489778 + 0.336105i
$$295$$ 7.16701 + 18.9825i 0.417279 + 1.10520i
$$296$$ 2.87197 + 32.0074i 0.166930 + 1.86039i
$$297$$ −8.48947 14.7042i −0.492609 0.853224i
$$298$$ 0.558864 + 1.40371i 0.0323741 + 0.0813150i
$$299$$ −2.14120 + 0.779335i −0.123829 + 0.0450701i
$$300$$ 4.45894 6.31793i 0.257437 0.364766i
$$301$$ 1.76358 + 1.47982i 0.101651 + 0.0852956i
$$302$$ 1.38169 + 0.743680i 0.0795073 + 0.0427940i
$$303$$ 5.90528i 0.339249i
$$304$$ 4.89083 16.7356i 0.280508 0.959852i
$$305$$ −18.0931 + 3.41364i −1.03601 + 0.195464i
$$306$$ −9.95998 + 18.5047i −0.569374 + 1.05785i
$$307$$ −20.8203 + 24.8127i −1.18828 + 1.41613i −0.301794 + 0.953373i $$0.597585\pi$$
−0.886483 + 0.462760i $$0.846859\pi$$
$$308$$ −8.78037 + 5.79360i −0.500308 + 0.330121i
$$309$$ 5.90465 2.14912i 0.335904 0.122259i
$$310$$ 7.36151 + 11.6028i 0.418106 + 0.658993i
$$311$$ 21.3810 12.3443i 1.21240 0.699982i 0.249122 0.968472i $$-0.419858\pi$$
0.963282 + 0.268490i $$0.0865247\pi$$
$$312$$ −1.42254 + 0.127642i −0.0805357 + 0.00722633i
$$313$$ −21.1754 + 3.73380i −1.19691 + 0.211047i −0.736361 0.676589i $$-0.763458\pi$$
−0.460546 + 0.887636i $$0.652346\pi$$
$$314$$ −1.81280 + 12.4401i −0.102302 + 0.702038i
$$315$$ −2.29903 + 6.55929i −0.129536 + 0.369574i
$$316$$ −3.11130 + 26.9652i −0.175024 + 1.51691i
$$317$$ −4.65198 + 3.90347i −0.261281 + 0.219241i −0.764012 0.645202i $$-0.776773\pi$$
0.502731 + 0.864443i $$0.332329\pi$$
$$318$$ 1.21970 0.0363938i 0.0683973 0.00204087i
$$319$$ −0.911982 0.331934i −0.0510612 0.0185848i
$$320$$ 13.5131 11.7216i 0.755406 0.655256i
$$321$$ 1.35699 7.69587i 0.0757397 0.429541i
$$322$$ 2.00418 6.06332i 0.111689 0.337896i
$$323$$ 26.9256 + 1.47095i 1.49818 + 0.0818461i
$$324$$ −6.38508 4.73883i −0.354727 0.263268i
$$325$$ −0.643620 3.20097i −0.0357016 0.177558i
$$326$$ 3.44817 2.13039i 0.190976 0.117991i
$$327$$ 1.01181 + 0.368269i 0.0559533 + 0.0203653i
$$328$$ 11.1036 + 7.73814i 0.613096 + 0.427267i
$$329$$ 12.2378 10.2688i 0.674693 0.566135i
$$330$$ −9.18974 + 3.78653i −0.505878 + 0.208442i
$$331$$ 14.1358 24.4840i 0.776975 1.34576i −0.156703 0.987646i $$-0.550086\pi$$
0.933678 0.358115i $$-0.116580\pi$$
$$332$$ 9.84608 19.6778i 0.540374 1.07996i
$$333$$ −4.73907 26.8766i −0.259699 1.47283i
$$334$$ 4.57116 4.07406i 0.250123 0.222922i
$$335$$ 14.1643 12.1765i 0.773878 0.665275i
$$336$$ 2.18964 3.35077i 0.119455 0.182800i
$$337$$ −19.6601 + 7.15567i −1.07095 + 0.389794i −0.816532 0.577300i $$-0.804106\pi$$
−0.254419 + 0.967094i $$0.581884\pi$$
$$338$$ 11.0185 13.9564i 0.599329 0.759130i
$$339$$ 3.69840 4.40758i 0.200870 0.239387i
$$340$$ 22.4116 + 16.2217i 1.21544 + 0.879746i
$$341$$ 17.6616i 0.956428i
$$342$$ −2.93124 + 14.5140i −0.158503 + 0.784826i
$$343$$ −15.9499 −0.861213
$$344$$ 2.13669 + 4.55570i 0.115203 + 0.245627i
$$345$$ 2.95422 5.26101i 0.159050 0.283243i
$$346$$ 11.9444 15.1292i 0.642136 0.813351i
$$347$$ −1.61068 + 0.586241i −0.0864660 + 0.0314711i −0.384891 0.922962i $$-0.625761\pi$$
0.298425 + 0.954433i $$0.403539\pi$$
$$348$$ 0.368631 0.0220183i 0.0197607 0.00118031i
$$349$$ −13.4455 23.2883i −0.719722 1.24660i −0.961110 0.276166i $$-0.910936\pi$$
0.241388 0.970429i $$-0.422397\pi$$
$$350$$ 8.15875 + 4.14311i 0.436103 + 0.221458i
$$351$$ 2.68639 0.473683i 0.143389 0.0252833i
$$352$$ −22.7372 + 3.41657i −1.21190 + 0.182104i
$$353$$ −11.3732 6.56633i −0.605335 0.349491i 0.165802 0.986159i $$-0.446979\pi$$
−0.771138 + 0.636669i $$0.780312\pi$$
$$354$$ 2.01391 + 9.71702i 0.107038 + 0.516454i
$$355$$ 3.46887 4.23578i 0.184108 0.224812i
$$356$$ 8.48872 28.5079i 0.449901 1.51092i
$$357$$ 5.81733 + 2.11733i 0.307886 + 0.112061i
$$358$$ 15.8872 9.81560i 0.839663 0.518771i
$$359$$ 24.2269 + 4.27185i 1.27865 + 0.225460i 0.771405 0.636345i $$-0.219554\pi$$
0.507241 + 0.861804i $$0.330666\pi$$
$$360$$ −10.5889 + 10.8933i −0.558083 + 0.574125i
$$361$$ 18.4558 4.51476i 0.971358 0.237619i
$$362$$ 17.2473 + 5.70095i 0.906497 + 0.299635i
$$363$$ 4.20402 + 0.741282i 0.220654 + 0.0389072i
$$364$$ −0.392192 1.64393i −0.0205565 0.0861655i
$$365$$ −4.43388 + 27.0301i −0.232080 + 1.41482i
$$366$$ −9.00096 + 0.268574i −0.470488 + 0.0140386i
$$367$$ −22.8093 + 19.1393i −1.19064 + 0.999064i −0.190790 + 0.981631i $$0.561105\pi$$
−0.999848 + 0.0174328i $$0.994451\pi$$
$$368$$ 9.54826 10.1808i 0.497737 0.530712i
$$369$$ −9.95378 5.74682i −0.518173 0.299168i
$$370$$ −35.8978 + 1.50052i −1.86624 + 0.0780084i
$$371$$ 0.250734 + 1.42198i 0.0130175 + 0.0738256i
$$372$$ 2.67095 + 6.16681i 0.138482 + 0.319734i
$$373$$ −6.12009 10.6003i −0.316886 0.548863i 0.662950 0.748663i $$-0.269304\pi$$
−0.979837 + 0.199800i $$0.935971\pi$$
$$374$$ −13.1534 33.0378i −0.680148 1.70835i
$$375$$ 6.81785 + 5.31647i 0.352072 + 0.274541i
$$376$$ 33.7072 9.11215i 1.73832 0.469923i
$$377$$ 0.100225 0.119443i 0.00516184 0.00615164i
$$378$$ −3.62329 + 6.73174i −0.186362 + 0.346244i
$$379$$ −25.3592 −1.30262 −0.651308 0.758813i $$-0.725780\pi$$
−0.651308 + 0.758813i $$0.725780\pi$$
$$380$$ 18.4289 + 6.35431i 0.945380 + 0.325969i
$$381$$ −7.56736 −0.387687
$$382$$ −1.31919 + 2.45094i −0.0674958 + 0.125401i
$$383$$ −7.88693 + 9.39927i −0.403003 + 0.480280i −0.928933 0.370247i $$-0.879273\pi$$
0.525930 + 0.850528i $$0.323717\pi$$
$$384$$ 7.42235 4.63147i 0.378770 0.236349i
$$385$$ −6.00185 10.1145i −0.305883 0.515484i
$$386$$ −6.21093 15.6001i −0.316128 0.794027i
$$387$$ −2.13664 3.70077i −0.108612 0.188121i
$$388$$ 1.47387 0.638358i 0.0748245 0.0324077i
$$389$$ −0.548095 3.10840i −0.0277895 0.157602i 0.967755 0.251893i $$-0.0810529\pi$$
−0.995545 + 0.0942902i $$0.969942\pi$$
$$390$$ −0.0666895 1.59545i −0.00337695 0.0807887i
$$391$$ 18.6949 + 10.7935i 0.945439 + 0.545850i
$$392$$ −13.6654 6.33533i −0.690205 0.319982i
$$393$$ −0.356348 + 0.299011i −0.0179754 + 0.0150831i
$$394$$ 15.3558 0.458194i 0.773616 0.0230835i
$$395$$ −29.9478 4.91249i −1.50684 0.247174i
$$396$$ 18.9931 4.53118i 0.954439 0.227700i
$$397$$ −23.3841 4.12325i −1.17362 0.206940i −0.447353 0.894358i $$-0.647633\pi$$
−0.726262 + 0.687418i $$0.758744\pi$$
$$398$$ 1.34614 + 0.444956i 0.0674759 + 0.0223036i
$$399$$ 4.35543 + 0.237938i 0.218044 + 0.0119118i
$$400$$ 12.3696 + 15.7160i 0.618482 + 0.785799i
$$401$$ −37.3671 6.58883i −1.86602 0.329030i −0.877439 0.479689i $$-0.840750\pi$$
−0.988586 + 0.150658i $$0.951861\pi$$
$$402$$ 7.77164 4.80157i 0.387614 0.239480i
$$403$$ 2.66638 + 0.970484i 0.132822 + 0.0483433i
$$404$$ 14.6379 + 4.35868i 0.728263 + 0.216852i
$$405$$ 5.63263 6.87792i 0.279888 0.341767i
$$406$$ 0.0886822 + 0.427887i 0.00440122 + 0.0212357i
$$407$$ 39.9933 + 23.0901i 1.98239 + 1.14454i
$$408$$ 9.58901 + 9.54649i 0.474727 + 0.472622i
$$409$$ −13.6552 + 2.40777i −0.675204 + 0.119057i −0.500728 0.865605i $$-0.666934\pi$$
−0.174476 + 0.984661i $$0.555823\pi$$
$$410$$ −9.23375 + 11.9875i −0.456022 + 0.592020i
$$411$$ 5.44814 + 9.43646i 0.268737 + 0.465466i
$$412$$ 0.968975 + 16.2226i 0.0477380 + 0.799230i
$$413$$ −11.0344 + 4.01620i −0.542968 + 0.197624i
$$414$$ −7.34506 + 9.30350i −0.360990 + 0.457242i
$$415$$ 21.4504 + 12.0450i 1.05296 + 0.591268i
$$416$$ 0.733580 3.62039i 0.0359667 0.177504i
$$417$$ −12.2026 −0.597563
$$418$$ −15.6255 19.5862i −0.764266 0.957992i
$$419$$ 8.75463i 0.427692i 0.976867 + 0.213846i $$0.0685990\pi$$
−0.976867 + 0.213846i $$0.931401\pi$$
$$420$$ 3.62525 + 2.62399i 0.176894 + 0.128038i
$$421$$ 2.42433 2.88920i 0.118154 0.140811i −0.703725 0.710473i $$-0.748481\pi$$
0.821879 + 0.569662i $$0.192926\pi$$
$$422$$ 21.5241 27.2631i 1.04777 1.32715i
$$423$$ −27.8648 + 10.1419i −1.35483 + 0.493118i
$$424$$ −0.810045 + 3.05023i −0.0393393 + 0.148132i
$$425$$ −19.3109 + 24.1634i −0.936716 + 1.17210i
$$426$$ 1.99895 1.78157i 0.0968495 0.0863173i
$$427$$ −1.85033 10.4938i −0.0895438 0.507828i
$$428$$ 18.0748 + 9.04399i 0.873677 + 0.437158i
$$429$$ −1.02622 + 1.77747i −0.0495465 + 0.0858171i
$$430$$ −5.20157 + 2.14325i −0.250842 + 0.103357i
$$431$$ −17.6866 + 14.8408i −0.851933 + 0.714857i −0.960215 0.279263i $$-0.909910\pi$$
0.108281 + 0.994120i $$0.465465\pi$$
$$432$$ −13.3734 + 10.0178i −0.643426 + 0.481983i
$$433$$ 20.1855 + 7.34691i 0.970052 + 0.353070i 0.777965 0.628308i $$-0.216252\pi$$
0.192087 + 0.981378i $$0.438474\pi$$
$$434$$ −6.76522 + 4.17977i −0.324741 + 0.200635i
$$435$$ 0.00493209 + 0.412847i 0.000236476 + 0.0197945i
$$436$$ −1.65968 + 2.23624i −0.0794840 + 0.107096i
$$437$$ 14.8126 + 3.45436i 0.708584 + 0.165244i
$$438$$ −4.20435 + 12.7196i −0.200891 + 0.607764i
$$439$$ 1.77851 10.0864i 0.0848837 0.481399i −0.912498 0.409081i $$-0.865849\pi$$
0.997382 0.0723180i $$-0.0230396\pi$$
$$440$$ −2.60304 25.5742i −0.124095 1.21920i
$$441$$ 12.0202 + 4.37501i 0.572393 + 0.208334i
$$442$$ 5.71052 0.170393i 0.271622 0.00810476i
$$443$$ −21.4279 + 17.9801i −1.01807 + 0.854262i −0.989384 0.145326i $$-0.953577\pi$$
−0.0286863 + 0.999588i $$0.509132\pi$$
$$444$$ −17.4562 2.01413i −0.828434 0.0955862i
$$445$$ 31.3839 + 11.0001i 1.48774 + 0.521453i
$$446$$ 1.16858 8.01927i 0.0553340 0.379723i
$$447$$ −0.813598 + 0.143459i −0.0384818 + 0.00678539i
$$448$$ 6.68966 + 7.90085i 0.316057 + 0.373280i
$$449$$ 0.167174 0.0965178i 0.00788941 0.00455496i −0.496050 0.868294i $$-0.665217\pi$$
0.503940 + 0.863739i $$0.331883\pi$$
$$450$$ −11.6005 12.4061i −0.546854 0.584831i
$$451$$ 18.2758 6.65186i 0.860576 0.313224i
$$452$$ 8.19565 + 12.4208i 0.385491 + 0.584224i
$$453$$ −0.551509 + 0.657262i −0.0259121 + 0.0308809i
$$454$$ −9.95588 + 18.4971i −0.467253 + 0.868113i
$$455$$ 1.85679 0.350323i 0.0870479 0.0164234i
$$456$$ 8.41788 + 4.47580i 0.394203 + 0.209599i
$$457$$ 24.4488i 1.14367i 0.820370 + 0.571833i $$0.193768\pi$$
−0.820370 + 0.571833i $$0.806232\pi$$
$$458$$ −10.1429 5.45928i −0.473944 0.255096i
$$459$$ −19.7966 16.6113i −0.924027 0.775351i
$$460$$ 10.8604 + 11.2060i 0.506369 + 0.522483i
$$461$$ 1.98574 0.722750i 0.0924850 0.0336618i −0.295363 0.955385i $$-0.595441\pi$$
0.387848 + 0.921723i $$0.373218\pi$$
$$462$$ −2.12767 5.34412i −0.0989881 0.248631i
$$463$$ −9.67820 16.7631i −0.449784 0.779049i 0.548588 0.836093i $$-0.315166\pi$$
−0.998372 + 0.0570444i $$0.981832\pi$$
$$464$$ −0.217507 + 0.930007i −0.0100975 + 0.0431745i
$$465$$ −7.02929 + 2.65397i −0.325975 + 0.123075i
$$466$$ 1.78381 12.2412i 0.0826333 0.567062i
$$467$$ 16.5808 28.7187i 0.767266 1.32894i −0.171774 0.985136i $$-0.554950\pi$$
0.939040 0.343808i $$-0.111717\pi$$
$$468$$ −0.359574 + 3.11639i −0.0166213 + 0.144055i
$$469$$ 6.94843 + 8.28082i 0.320849 + 0.382373i
$$470$$ 8.37867 + 38.1288i 0.386479 + 1.75875i
$$471$$ −6.45957 2.35109i −0.297641 0.108333i
$$472$$ −25.5728 2.18008i −1.17709 0.100346i
$$473$$ 7.12110 + 1.25564i 0.327428 + 0.0577345i
$$474$$ −14.0925 4.65817i −0.647291 0.213957i
$$475$$ −8.07896 + 20.2418i −0.370688 + 0.928757i
$$476$$ −9.54217 + 12.8571i −0.437365 + 0.589304i
$$477$$ 0.465406 2.63945i 0.0213095 0.120852i
$$478$$ −11.2465 18.2031i −0.514401 0.832590i
$$479$$ 3.31652 9.11207i 0.151536 0.416341i −0.840577 0.541693i $$-0.817784\pi$$
0.992112 + 0.125352i $$0.0400059\pi$$
$$480$$ 4.77646 + 8.53597i 0.218014 + 0.389612i
$$481$$ −5.68353 + 4.76904i −0.259146 + 0.217450i
$$482$$ 3.94803 + 19.0491i 0.179828 + 0.867662i
$$483$$ 3.02404 + 1.74593i 0.137598 + 0.0794425i
$$484$$ −4.94046 + 9.87370i −0.224566 + 0.448805i
$$485$$ 0.634300 + 1.68000i 0.0288021 + 0.0762850i
$$486$$ 16.4766 14.6848i 0.747394 0.666117i
$$487$$ 12.5324 7.23557i 0.567896 0.327875i −0.188412 0.982090i $$-0.560334\pi$$
0.756309 + 0.654215i $$0.227001\pi$$
$$488$$ 5.97786 22.5097i 0.270605 1.01896i
$$489$$ 0.758018 + 2.08264i 0.0342787 + 0.0941801i
$$490$$ 7.80375 14.9231i 0.352538 0.674158i
$$491$$ 0.0406164 0.0484047i 0.00183299 0.00218448i −0.765127 0.643879i $$-0.777324\pi$$
0.766960 + 0.641695i $$0.221768\pi$$
$$492$$ −5.37534 + 5.08644i −0.242339 + 0.229315i
$$493$$ −1.47716 −0.0665279
$$494$$ 3.81555 1.28275i 0.171670 0.0577136i
$$495$$ 4.04744 + 21.4524i 0.181919 + 0.964213i
$$496$$ −17.2576 + 2.06898i −0.774890 + 0.0928997i
$$497$$ 2.42719 + 2.03666i 0.108875 + 0.0913566i
$$498$$ 9.44332 + 7.45545i 0.423165 + 0.334087i
$$499$$ −2.50810 6.89095i −0.112278 0.308481i 0.870809 0.491622i $$-0.163596\pi$$
−0.983087 + 0.183141i $$0.941374\pi$$
$$500$$ −18.2106 + 12.9759i −0.814403 + 0.580299i
$$501$$ 1.67408 + 2.89960i 0.0747925 + 0.129544i
$$502$$ −12.7642 + 11.3761i −0.569695 + 0.507742i
$$503$$ −6.42035 36.4116i −0.286269 1.62351i −0.700717 0.713440i $$-0.747136\pi$$
0.414448 0.910073i $$-0.363975\pi$$
$$504$$ −6.23054 6.20291i −0.277530 0.276300i
$$505$$ −5.64817 + 16.1146i −0.251340 + 0.717091i
$$506$$ −4.07056 19.6403i −0.180958 0.873116i
$$507$$ 6.24987 + 7.44831i 0.277567 + 0.330791i
$$508$$ 5.58546 18.7578i 0.247815 0.832244i
$$509$$ −2.03894 + 5.60194i −0.0903743 + 0.248301i −0.976642 0.214871i $$-0.931067\pi$$
0.886268 + 0.463173i $$0.153289\pi$$
$$510$$ −11.1725 + 10.1996i −0.494726 + 0.451645i
$$511$$ −15.6112 2.75268i −0.690600 0.121771i
$$512$$ 6.00198 + 21.8169i 0.265253 + 0.964179i
$$513$$ −16.7453 7.15181i −0.739324 0.315760i
$$514$$ 10.3350 31.2669i 0.455858 1.37912i
$$515$$ −18.1684 + 0.217050i −0.800597 + 0.00956436i
$$516$$ −2.67633 + 0.638491i −0.117819 + 0.0281080i
$$517$$ 17.1615 47.1508i 0.754762 2.07369i
$$518$$ −0.620156 20.7838i −0.0272481 0.913188i
$$519$$ 6.77506 + 8.07420i 0.297392 + 0.354418i
$$520$$ 4.00399 + 1.01229i 0.175587 + 0.0443919i
$$521$$ 5.64764 + 3.26066i 0.247427 + 0.142852i 0.618586 0.785717i $$-0.287706\pi$$
−0.371158 + 0.928570i $$0.621039\pi$$
$$522$$ 0.116962 0.802636i 0.00511927 0.0351304i
$$523$$ 32.5138 5.73306i 1.42173 0.250689i 0.590688 0.806900i $$-0.298856\pi$$
0.831041 + 0.556211i $$0.187745\pi$$
$$524$$ −0.478164 1.10401i −0.0208887 0.0482288i
$$525$$ −3.12368 + 3.90862i −0.136329 + 0.170586i
$$526$$ −3.69280 9.27532i −0.161014 0.404423i
$$527$$ −9.19407 25.2605i −0.400500 1.10036i
$$528$$ 0.693823 12.5531i 0.0301948 0.546305i
$$529$$ −8.29155 6.95744i −0.360502 0.302497i
$$530$$ −3.36318 1.06728i −0.146087 0.0463597i
$$531$$ 21.7963 0.945878
$$532$$ −3.80453 + 10.6205i −0.164948 + 0.460459i
$$533$$ 3.12463i 0.135343i
$$534$$ 14.3218 + 7.70857i 0.619766 + 0.333582i
$$535$$ −11.0638 + 19.7030i −0.478330 + 0.851833i
$$536$$ 6.16580 + 22.8082i 0.266322 + 0.985165i
$$537$$ 3.49251 + 9.59558i 0.150713 + 0.414080i
$$538$$ 25.0457 9.97153i 1.07980 0.429903i
$$539$$ −18.7453 + 10.8226i −0.807417 + 0.466162i
$$540$$ −10.4744 15.4691i −0.450746 0.665682i
$$541$$ −4.15660 23.5732i −0.178706 1.01349i −0.933779 0.357851i $$-0.883509\pi$$
0.755072 0.655641i $$-0.227602\pi$$
$$542$$ −3.28368 + 22.5339i −0.141046 + 0.967913i
$$543$$ −4.96634 + 8.60196i −0.213126 + 0.369145i
$$544$$ −30.7413 + 16.7228i −1.31802 + 0.716985i
$$545$$ −2.40884 1.97271i −0.103184 0.0845015i
$$546$$ 0.923720 0.0275623i 0.0395316 0.00117956i
$$547$$ −9.83267 + 27.0150i −0.420414 + 1.15508i 0.531055 + 0.847337i $$0.321796\pi$$
−0.951470 + 0.307742i $$0.900427\pi$$
$$548$$ −27.4122 + 6.53972i −1.17099 + 0.279363i
$$549$$ −3.43454 + 19.4783i −0.146583 + 0.831312i
$$550$$ 28.6991 1.54324i 1.22373 0.0658041i
$$551$$ −0.995994 + 0.302094i −0.0424308 + 0.0128696i
$$552$$ 4.39148 + 6.24211i 0.186914 + 0.265682i
$$553$$ 3.04981 17.2963i 0.129691 0.735515i
$$554$$ 18.2953 + 29.6121i 0.777294 + 1.25810i
$$555$$ 3.18014 19.3870i 0.134990 0.822932i
$$556$$ 9.00671 30.2475i 0.381969 1.28278i
$$557$$ 9.06492 + 10.8032i 0.384093 + 0.457744i 0.923102 0.384556i $$-0.125645\pi$$
−0.539009 + 0.842300i $$0.681201\pi$$
$$558$$ 14.4537 2.99560i 0.611872 0.126814i
$$559$$ −0.580862 + 1.00608i −0.0245678 + 0.0425527i
$$560$$ −9.18009 + 7.04945i −0.387930 + 0.297894i
$$561$$ 19.1488 3.37646i 0.808465 0.142554i
$$562$$ −13.8921 + 12.3814i −0.586003 + 0.522276i
$$563$$ 11.4131 6.58938i 0.481007 0.277709i −0.239829 0.970815i $$-0.577091\pi$$
0.720836 + 0.693106i $$0.243758\pi$$
$$564$$ 1.13838 + 19.0588i 0.0479345 + 0.802519i
$$565$$ −14.3081 + 8.49026i −0.601945 + 0.357188i
$$566$$ −22.4710 + 28.4626i −0.944528 + 1.19637i
$$567$$ 3.94120 + 3.30706i 0.165515 + 0.138883i
$$568$$ 2.94070 + 6.26994i 0.123389 + 0.263081i
$$569$$ 0.00913241i 0.000382850i −1.00000 0.000191425i $$-0.999939\pi$$
1.00000 0.000191425i $$-6.09325e-5\pi$$
$$570$$ −5.44728 + 9.16209i −0.228162 + 0.383758i
$$571$$ 0.969575i 0.0405754i −0.999794 0.0202877i $$-0.993542\pi$$
0.999794 0.0202877i $$-0.00645822\pi$$
$$572$$ −3.64851 3.85573i −0.152552 0.161216i
$$573$$ −1.16590 0.978306i −0.0487062 0.0408693i
$$574$$ −6.87312 5.42629i −0.286878 0.226489i
$$575$$ −13.0936 + 11.5309i −0.546040 + 0.480872i
$$576$$ −6.65249 18.0279i −0.277187 0.751161i
$$577$$ 36.1447 20.8681i 1.50472 0.868752i 0.504738 0.863273i $$-0.331589\pi$$
0.999985 0.00547920i $$-0.00174409\pi$$
$$578$$ −20.0151 22.4573i −0.832519 0.934100i
$$579$$ 9.04190 1.59433i 0.375768 0.0662581i
$$580$$ −1.02700 0.292496i −0.0426438 0.0121452i
$$581$$ −7.11855 + 12.3297i −0.295327 + 0.511522i
$$582$$ 0.178236 + 0.859983i 0.00738814 + 0.0356474i
$$583$$ 2.91517 + 3.47416i 0.120734 + 0.143885i
$$584$$ −28.4258 19.8099i −1.17627 0.819741i
$$585$$ −3.46109 0.567739i −0.143098 0.0234731i
$$586$$ −12.5001 + 7.72297i −0.516375 + 0.319033i
$$587$$ 1.74429 9.89239i 0.0719948 0.408303i −0.927418 0.374027i $$-0.877977\pi$$
0.999412 0.0342752i $$-0.0109123\pi$$
$$588$$ 4.90852 6.61371i 0.202424 0.272745i
$$589$$ −11.3653 15.1519i −0.468297 0.624325i
$$590$$ 3.79830 28.4425i 0.156373 1.17096i
$$591$$ −1.45870 + 8.27271i −0.0600030 + 0.340294i
$$592$$ 17.8770 41.7834i 0.734739 1.71729i
$$593$$ 1.36514 3.75070i 0.0560598 0.154023i −0.908502 0.417881i $$-0.862773\pi$$
0.964561 + 0.263858i $$0.0849951\pi$$
$$594$$ 0.716156 + 24.0012i 0.0293843 + 0.984779i
$$595$$ −13.8495 11.3419i −0.567773 0.464974i
$$596$$ 0.244911 2.12262i 0.0100320 0.0869458i
$$597$$ −0.387620 + 0.671377i −0.0158642 + 0.0274776i
$$598$$ 3.18878 + 0.464675i 0.130399 + 0.0190020i
$$599$$ 3.74301 + 21.2276i 0.152935 + 0.867338i 0.960649 + 0.277764i $$0.0895932\pi$$
−0.807714 + 0.589574i $$0.799296\pi$$
$$600$$ −9.78735 + 4.87899i −0.399567 + 0.199184i
$$601$$ 4.39412 2.53694i 0.179240 0.103484i −0.407696 0.913118i $$-0.633668\pi$$
0.586935 + 0.809634i $$0.300334\pi$$
$$602$$ −1.20430 3.02488i −0.0490836 0.123285i
$$603$$ −6.86262 18.8549i −0.279468 0.767831i
$$604$$ −1.22214 1.85219i −0.0497283 0.0753647i
$$605$$ −10.7631 6.04382i −0.437583 0.245716i
$$606$$ −3.95810 + 7.35378i −0.160787 + 0.298727i
$$607$$ 27.7036i 1.12445i −0.826983 0.562227i $$-0.809945\pi$$
0.826983 0.562227i $$-0.190055\pi$$
$$608$$ −17.3078 + 17.5625i −0.701922 + 0.712254i
$$609$$ −0.238942 −0.00968240
$$610$$ 24.8192 + 7.87617i 1.00490 + 0.318897i
$$611$$ 6.17540 + 5.18178i 0.249830 + 0.209632i
$$612$$ 24.8061 16.3679i 1.00273 0.661635i
$$613$$ 11.6155 + 31.9133i 0.469145 + 1.28897i 0.918432 + 0.395579i $$0.129456\pi$$
−0.449287 + 0.893388i $$0.648322\pi$$
$$614$$ 42.5583 16.9439i 1.71751 0.683798i
$$615$$ −5.39371 6.27420i −0.217495 0.253000i
$$616$$ 14.8173 1.32954i 0.597008 0.0535685i
$$617$$ 11.0655 1.95114i 0.445479 0.0785500i 0.0535911 0.998563i $$-0.482933\pi$$
0.391888 + 0.920013i $$0.371822\pi$$
$$618$$ −8.79347 1.28140i −0.353725 0.0515455i
$$619$$ −35.8033 20.6710i −1.43906 0.830839i −0.441271 0.897374i $$-0.645472\pi$$
−0.997784 + 0.0665345i $$0.978806\pi$$
$$620$$ −1.39030 19.3830i −0.0558356 0.778439i
$$621$$ −9.36964 11.1663i −0.375991 0.448088i
$$622$$ −34.8995 + 1.04134i −1.39934 + 0.0417541i
$$623$$ −6.58251 + 18.0853i −0.263723 + 0.724572i
$$624$$ 1.85703 + 0.794528i 0.0743408 + 0.0318066i
$$625$$ −13.5199 21.0289i −0.540796 0.841154i
$$626$$ 28.8722 + 9.54348i 1.15397 + 0.381434i
$$627$$ 12.2208 6.19276i 0.488054 0.247315i
$$628$$ 10.5956 14.2765i 0.422812 0.569696i
$$629$$ 69.2204 + 12.2054i 2.76000 + 0.486662i
$$630$$ 7.25941 6.62726i 0.289222 0.264036i
$$631$$ −3.57194 + 9.81382i −0.142197 + 0.390682i −0.990263 0.139208i $$-0.955544\pi$$
0.848067 + 0.529890i $$0.177767\pi$$
$$632$$ 21.9483 31.4941i 0.873056 1.25277i
$$633$$ 12.2088 + 14.5498i 0.485255 + 0.578304i
$$634$$ 8.40942 1.74290i 0.333981 0.0692195i
$$635$$ 20.6502 + 7.23788i 0.819477 + 0.287226i
$$636$$ −1.54327 0.772199i −0.0611947 0.0306197i
$$637$$ −0.603864 3.42468i −0.0239260 0.135691i
$$638$$ 0.913198 + 1.02462i 0.0361539 + 0.0405652i
$$639$$ −2.94063 5.09331i −0.116329 0.201488i
$$640$$ −24.6843 + 5.53941i −0.975733 + 0.218964i
$$641$$ 7.26275 + 19.9542i 0.286861 + 0.788145i 0.996501 + 0.0835804i $$0.0266355\pi$$
−0.709640 + 0.704565i $$0.751142\pi$$
$$642$$ −6.84811 + 8.67404i −0.270273 + 0.342337i
$$643$$ −18.3969 15.4368i −0.725503 0.608769i 0.203399 0.979096i $$-0.434801\pi$$
−0.928901 + 0.370327i $$0.879246\pi$$
$$644$$ −6.55981 + 6.20726i −0.258493 + 0.244600i
$$645$$ −0.570328 3.02287i −0.0224566 0.119025i
$$646$$ −32.5443 19.8791i −1.28044 0.782131i
$$647$$ −39.6665 −1.55945 −0.779726 0.626121i $$-0.784642\pi$$
−0.779726 + 0.626121i $$0.784642\pi$$
$$648$$ 4.77501 + 10.1809i 0.187580 + 0.399944i
$$649$$ −23.7074 + 28.2534i −0.930597 + 1.10904i
$$650$$ −1.34400 + 4.41753i −0.0527160 + 0.173270i
$$651$$ −1.48721 4.08608i −0.0582884 0.160146i
$$652$$ −5.72189 + 0.341769i −0.224087 + 0.0133847i
$$653$$ −1.47393 + 0.850973i −0.0576793 + 0.0333012i −0.528562 0.848894i $$-0.677269\pi$$
0.470883 + 0.882196i $$0.343935\pi$$
$$654$$ −1.01316 1.13678i −0.0396177 0.0444517i
$$655$$ 1.25841 0.475124i 0.0491702 0.0185646i
$$656$$ −8.64065 17.0786i −0.337361 0.666807i
$$657$$ 25.4821 + 14.7121i 0.994151 + 0.573974i
$$658$$ −22.1224 + 4.58500i −0.862422 + 0.178742i
$$659$$ −7.63985 + 6.41060i −0.297606 + 0.249721i −0.779347 0.626592i $$-0.784449\pi$$
0.481741 + 0.876314i $$0.340005\pi$$
$$660$$ 13.9819 + 1.44423i 0.544243 + 0.0562164i
$$661$$ −8.25775 + 22.6880i −0.321189 + 0.882460i 0.669067 + 0.743202i $$0.266694\pi$$
−0.990256 + 0.139258i $$0.955528\pi$$
$$662$$ −34.0139 + 21.0149i −1.32199 + 0.816767i
$$663$$ −0.542461 + 3.07645i −0.0210674 + 0.119479i
$$664$$ −25.4505 + 17.9051i −0.987672 + 0.694852i
$$665$$ −11.6577 4.81510i −0.452068 0.186721i
$$666$$ −12.1129 + 36.6455i −0.469365 + 1.41999i
$$667$$ −0.820535 0.144682i −0.0317712 0.00560213i
$$668$$ −8.42311 + 2.00950i −0.325900 + 0.0777498i
$$669$$ 4.16402 + 1.51558i 0.160990 + 0.0585957i
$$670$$ −25.8001 + 5.66949i −0.996746 + 0.219031i
$$671$$ −21.5130 25.6381i −0.830498 0.989749i
$$672$$ −4.97264 + 2.70504i −0.191824 + 0.104349i
$$673$$ −7.12247 + 12.3365i −0.274551 + 0.475536i −0.970022 0.243018i $$-0.921863\pi$$
0.695471 + 0.718554i $$0.255196\pi$$
$$674$$ 29.2787 + 4.26654i 1.12777 + 0.164341i
$$675$$ 17.8338 10.8725i 0.686423 0.418483i
$$676$$ −23.0758 + 9.99448i −0.887529 + 0.384403i
$$677$$ 9.95159 + 17.2367i 0.382471 + 0.662458i 0.991415 0.130755i $$-0.0417400\pi$$
−0.608944 + 0.793213i $$0.708407\pi$$
$$678$$ −7.55983 + 3.00981i −0.290333 + 0.115591i
$$679$$ −0.976575 + 0.355444i −0.0374775 + 0.0136407i
$$680$$ −17.0361 35.2225i −0.653306 1.35072i
$$681$$ −8.79898 7.38322i −0.337178 0.282926i
$$682$$ −11.8379 + 21.9938i −0.453297 + 0.842185i
$$683$$ 25.1586i 0.962667i 0.876537 + 0.481334i $$0.159847\pi$$
−0.876537 + 0.481334i $$0.840153\pi$$
$$684$$ 13.3784 16.1094i 0.511538 0.615959i
$$685$$ −5.84156 30.9616i −0.223194 1.18298i
$$686$$ 19.8622 + 10.6906i 0.758343 + 0.408170i
$$687$$ 4.04857 4.82490i 0.154463 0.184081i
$$688$$ 0.392717 7.10531i 0.0149722 0.270887i
$$689$$ −0.684682 + 0.249204i −0.0260843 + 0.00949392i
$$690$$ −7.20513 + 4.57138i −0.274294 + 0.174029i
$$691$$ 3.80733 2.19816i 0.144837 0.0836220i −0.425830 0.904803i $$-0.640018\pi$$
0.570668 + 0.821181i $$0.306685\pi$$
$$692$$ −25.0148 + 10.8343i −0.950921 + 0.411859i
$$693$$ −12.4421 + 2.19388i −0.472637 + 0.0833386i
$$694$$ 2.39870 + 0.349544i 0.0910535 + 0.0132685i
$$695$$ 33.2990 + 11.6713i 1.26310 + 0.442717i
$$696$$ −0.473810 0.219661i −0.0179597 0.00832622i
$$697$$ 22.6763 19.0277i 0.858926 0.720724i
$$698$$ 1.13424 + 38.0127i 0.0429316 + 1.43880i
$$699$$ 6.35626 + 2.31349i 0.240416 + 0.0875042i
$$700$$ −7.38303 10.6279i −0.279052 0.401696i
$$701$$ −3.85596 + 21.8682i −0.145637 + 0.825951i 0.821216 + 0.570618i $$0.193296\pi$$
−0.966853 + 0.255333i $$0.917815\pi$$
$$702$$ −3.66283 1.21072i −0.138245 0.0456956i
$$703$$ 49.1690 5.92661i 1.85444 0.223526i
$$704$$ 30.6044 + 10.9853i 1.15345 + 0.414024i
$$705$$ −21.3448 + 0.254997i −0.803892 + 0.00960373i
$$706$$ 9.76177 + 15.8000i 0.367389 + 0.594642i
$$707$$ −9.28621 3.37990i −0.349244 0.127114i
$$708$$ 4.00507 13.4504i 0.150520 0.505495i
$$709$$ −6.43156 + 5.39672i −0.241542 + 0.202678i −0.755520 0.655125i $$-0.772616\pi$$
0.513978 + 0.857803i $$0.328171\pi$$
$$710$$ −7.15884 + 2.94972i −0.268666 + 0.110701i
$$711$$ −16.3002 + 28.2327i −0.611304 + 1.05881i
$$712$$ −29.6788 + 29.8110i −1.11226 + 1.11721i
$$713$$ −2.63296 14.9323i −0.0986052 0.559218i
$$714$$ −5.82509 6.53584i −0.217998 0.244598i
$$715$$ 4.50049 3.86891i 0.168309 0.144689i
$$716$$ −26.3632 + 1.57467i −0.985238 + 0.0588483i
$$717$$ 10.9944 4.00162i 0.410592 0.149443i
$$718$$ −27.3062 21.5581i −1.01906 0.804541i
$$719$$ −18.8665 + 22.4842i −0.703601 + 0.838519i −0.992929 0.118711i $$-0.962124\pi$$
0.289328 + 0.957230i $$0.406568\pi$$
$$720$$ 20.4876 6.46792i 0.763527 0.241045i
$$721$$ 10.5153i 0.391609i
$$722$$ −26.0089 6.74808i −0.967951 0.251138i
$$723$$ −10.6374 −0.395610
$$724$$ −17.6567 18.6596i −0.656207 0.693478i
$$725$$ 0.381413 1.13131i 0.0141653 0.0420160i
$$726$$ −4.73836 3.74091i −0.175857 0.138838i
$$727$$ −14.7991 + 5.38642i −0.548867 + 0.199771i −0.601543 0.798840i $$-0.705447\pi$$
0.0526759 + 0.998612i $$0.483225\pi$$
$$728$$ −0.613476 + 2.31004i −0.0227369 + 0.0856160i
$$729$$ 0.0705855 + 0.122258i 0.00261428 + 0.00452806i
$$730$$ 23.6388 30.6884i 0.874911 1.13583i
$$731$$ 10.8386 1.91114i 0.400880 0.0706860i
$$732$$ 11.3888 + 5.69857i 0.420943 + 0.210625i
$$733$$ 30.2310 + 17.4538i 1.11661 + 0.644673i 0.940532 0.339704i $$-0.110327\pi$$
0.176073 + 0.984377i $$0.443660\pi$$
$$734$$ 41.2326 8.54570i 1.52192 0.315428i
$$735$$ 7.12420 + 5.83432i 0.262780 + 0.215202i
$$736$$ −18.7142 + 6.27822i −0.689814 + 0.231418i
$$737$$ 31.9050 + 11.6125i 1.17523 + 0.427750i
$$738$$ 8.54346 + 13.8281i 0.314489 + 0.509020i
$$739$$ 22.5797 + 3.98141i 0.830607 + 0.146458i 0.572755 0.819726i $$-0.305874\pi$$
0.257851 + 0.966185i $$0.416986\pi$$
$$740$$ 45.7089 + 22.1924i 1.68029 + 0.815809i
$$741$$ 0.263404 + 2.18528i 0.00967638 + 0.0802782i
$$742$$ 0.640867 1.93884i 0.0235270 0.0711770i
$$743$$ 37.5947 + 6.62895i 1.37921 + 0.243193i 0.813575 0.581460i $$-0.197518\pi$$
0.565639 + 0.824653i $$0.308629\pi$$
$$744$$ 0.807291 9.46971i 0.0295967 0.347176i
$$745$$ 2.35740 + 0.386696i 0.0863684 + 0.0141674i
$$746$$ 0.516280 + 17.3025i 0.0189024 + 0.633491i
$$747$$ 20.2439 16.9867i 0.740687 0.621510i
$$748$$ −5.76424 + 49.9579i −0.210761 + 1.82664i
$$749$$ −11.3253 6.53865i −0.413817 0.238917i
$$750$$ −4.92676 11.1903i −0.179900 0.408612i
$$751$$ −5.27030 29.8894i −0.192316 1.09068i −0.916189 0.400746i $$-0.868751\pi$$
0.723873 0.689933i $$-0.242360\pi$$
$$752$$ −48.0828 11.2455i −1.75340 0.410080i
$$753$$ −4.67461 8.09666i −0.170352 0.295059i
$$754$$ −0.204868 + 0.0815644i −0.00746084 + 0.00297040i
$$755$$ 2.13363 1.26607i 0.0776507 0.0460771i
$$756$$ 9.02409 5.95441i 0.328203 0.216560i
$$757$$ 15.3178 18.2551i 0.556736 0.663492i −0.412116 0.911131i $$-0.635210\pi$$
0.968852 + 0.247639i $$0.0796547\pi$$
$$758$$ 31.5796 + 16.9974i 1.14702 + 0.617373i
$$759$$ 10.9675 0.398097
$$760$$ −18.6902 20.2652i −0.677965 0.735094i
$$761$$ 23.3418 0.846140 0.423070 0.906097i $$-0.360952\pi$$
0.423070 + 0.906097i $$0.360952\pi$$
$$762$$ 9.42355 + 5.07213i 0.341379 + 0.183744i
$$763$$ 1.15823 1.38032i 0.0419306 0.0499709i
$$764$$ 3.28556 2.16792i 0.118867 0.0784327i
$$765$$ 16.9563 + 28.5753i 0.613056 + 1.03314i
$$766$$ 16.1215 6.41849i 0.582494 0.231910i
$$767$$ −2.96274 5.13162i −0.106978 0.185292i
$$768$$ −12.3473 + 0.792591i