# Properties

 Label 882.2.h.p.67.3 Level $882$ Weight $2$ Character 882.67 Analytic conductor $7.043$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 882.h (of order $$3$$, degree $$2$$, not 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: $$7.04280545828$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.309123.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3$$ x^6 - 3*x^5 + 10*x^4 - 15*x^3 + 19*x^2 - 12*x + 3 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.3 Root $$0.500000 + 1.41036i$$ of defining polynomial Character $$\chi$$ $$=$$ 882.67 Dual form 882.2.h.p.79.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(1.09097 + 1.34528i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.18194 q^{5} +(1.71053 - 0.272169i) q^{6} -1.00000 q^{8} +(-0.619562 + 2.93533i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(1.09097 + 1.34528i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.18194 q^{5} +(1.71053 - 0.272169i) q^{6} -1.00000 q^{8} +(-0.619562 + 2.93533i) q^{9} +(1.59097 - 2.75564i) q^{10} +3.18194 q^{11} +(0.619562 - 1.61745i) q^{12} +(-2.85185 + 4.93955i) q^{13} +(3.47141 + 4.28061i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.760877 - 1.31788i) q^{17} +(2.23229 + 2.00422i) q^{18} +(0.641315 + 1.11079i) q^{19} +(-1.59097 - 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +2.23912 q^{23} +(-1.09097 - 1.34528i) q^{24} +5.12476 q^{25} +(2.85185 + 4.93955i) q^{26} +(-4.62476 + 2.36887i) q^{27} +(-3.54063 - 6.13255i) q^{29} +(5.44282 - 0.866025i) q^{30} +(-4.71053 - 8.15888i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.47141 + 4.28061i) q^{33} +(-0.760877 - 1.31788i) q^{34} +(2.85185 - 0.931107i) q^{36} +(0.500000 + 0.866025i) q^{37} +1.28263 q^{38} +(-9.75636 + 1.55237i) q^{39} -3.18194 q^{40} +(2.80150 - 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +(-1.59097 - 2.75564i) q^{44} +(-1.97141 + 9.34004i) q^{45} +(1.11956 - 1.93914i) q^{46} +(-2.91423 + 5.04759i) q^{47} +(-1.71053 + 0.272169i) q^{48} +(2.56238 - 4.43818i) q^{50} +(2.60301 - 0.414174i) q^{51} +5.70370 q^{52} +(1.02859 - 1.78157i) q^{53} +(-0.260877 + 5.18960i) q^{54} +10.1248 q^{55} +(-0.794668 + 2.07459i) q^{57} -7.08126 q^{58} +(-0.562382 - 0.974074i) q^{59} +(1.97141 - 5.14663i) q^{60} +(1.56238 - 2.70612i) q^{61} -9.42107 q^{62} +1.00000 q^{64} +(-9.07442 + 15.7174i) q^{65} +(5.44282 - 0.866025i) q^{66} +(-5.48345 - 9.49761i) q^{67} -1.52175 q^{68} +(2.44282 + 3.01225i) q^{69} +8.69002 q^{71} +(0.619562 - 2.93533i) q^{72} +(2.48345 - 4.30146i) q^{73} +1.00000 q^{74} +(5.59097 + 6.89425i) q^{75} +(0.641315 - 1.11079i) q^{76} +(-3.53379 + 9.22544i) q^{78} +(2.06922 - 3.58399i) q^{79} +(-1.59097 + 2.75564i) q^{80} +(-8.23229 - 3.63723i) q^{81} +(-2.80150 - 4.85235i) q^{82} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +6.82846 q^{86} +(4.38727 - 11.4536i) q^{87} -3.18194 q^{88} +(-0.112725 - 0.195246i) q^{89} +(7.10301 + 6.37731i) q^{90} +(-1.11956 - 1.93914i) q^{92} +(5.83693 - 15.2381i) q^{93} +(2.91423 + 5.04759i) q^{94} +(2.04063 + 3.53447i) q^{95} +(-0.619562 + 1.61745i) q^{96} +(-7.42107 - 12.8537i) q^{97} +(-1.97141 + 9.34004i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10})$$ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 $$6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100})$$ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + 3 * q^19 - q^20 + q^22 + 14 * q^23 + 2 * q^24 - 4 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 + 15 * q^30 - 20 * q^31 + 3 * q^32 + 12 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 + 6 * q^38 + q^39 - 2 * q^40 - 6 * q^43 - q^44 - 3 * q^45 + 7 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 - 18 * q^51 + 16 * q^52 + 15 * q^53 - q^54 + 26 * q^55 + 22 * q^57 - 10 * q^58 + 14 * q^59 + 3 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 + 15 * q^66 + q^67 - 8 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 - 19 * q^73 + 6 * q^74 + 25 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 - q^80 - 40 * q^81 - 2 * q^83 - 2 * q^85 - 12 * q^86 + 36 * q^87 - 2 * q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 + 37 * q^93 - 9 * q^94 - 4 * q^95 - 4 * q^96 - 28 * q^97 - 3 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ 1.09097 + 1.34528i 0.629873 + 0.776698i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 3.18194 1.42301 0.711504 0.702682i $$-0.248014\pi$$
0.711504 + 0.702682i $$0.248014\pi$$
$$6$$ 1.71053 0.272169i 0.698322 0.111112i
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ −0.619562 + 2.93533i −0.206521 + 0.978442i
$$10$$ 1.59097 2.75564i 0.503109 0.871411i
$$11$$ 3.18194 0.959392 0.479696 0.877435i $$-0.340747\pi$$
0.479696 + 0.877435i $$0.340747\pi$$
$$12$$ 0.619562 1.61745i 0.178852 0.466917i
$$13$$ −2.85185 + 4.93955i −0.790960 + 1.36998i 0.134412 + 0.990925i $$0.457085\pi$$
−0.925373 + 0.379058i $$0.876248\pi$$
$$14$$ 0 0
$$15$$ 3.47141 + 4.28061i 0.896314 + 1.10525i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 0.760877 1.31788i 0.184540 0.319632i −0.758882 0.651229i $$-0.774254\pi$$
0.943421 + 0.331596i $$0.107587\pi$$
$$18$$ 2.23229 + 2.00422i 0.526155 + 0.472399i
$$19$$ 0.641315 + 1.11079i 0.147128 + 0.254833i 0.930165 0.367142i $$-0.119664\pi$$
−0.783037 + 0.621975i $$0.786330\pi$$
$$20$$ −1.59097 2.75564i −0.355752 0.616181i
$$21$$ 0 0
$$22$$ 1.59097 2.75564i 0.339196 0.587505i
$$23$$ 2.23912 0.466889 0.233445 0.972370i $$-0.425000\pi$$
0.233445 + 0.972370i $$0.425000\pi$$
$$24$$ −1.09097 1.34528i −0.222694 0.274604i
$$25$$ 5.12476 1.02495
$$26$$ 2.85185 + 4.93955i 0.559293 + 0.968725i
$$27$$ −4.62476 + 2.36887i −0.890036 + 0.455890i
$$28$$ 0 0
$$29$$ −3.54063 6.13255i −0.657478 1.13879i −0.981266 0.192656i $$-0.938290\pi$$
0.323788 0.946130i $$-0.395043\pi$$
$$30$$ 5.44282 0.866025i 0.993718 0.158114i
$$31$$ −4.71053 8.15888i −0.846037 1.46538i −0.884718 0.466127i $$-0.845649\pi$$
0.0386810 0.999252i $$-0.487684\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 3.47141 + 4.28061i 0.604295 + 0.745158i
$$34$$ −0.760877 1.31788i −0.130489 0.226014i
$$35$$ 0 0
$$36$$ 2.85185 0.931107i 0.475308 0.155185i
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 1.28263 0.208070
$$39$$ −9.75636 + 1.55237i −1.56227 + 0.248578i
$$40$$ −3.18194 −0.503109
$$41$$ 2.80150 4.85235i 0.437522 0.757810i −0.559976 0.828509i $$-0.689190\pi$$
0.997498 + 0.0706992i $$0.0225230\pi$$
$$42$$ 0 0
$$43$$ 3.41423 + 5.91362i 0.520665 + 0.901819i 0.999711 + 0.0240288i $$0.00764935\pi$$
−0.479046 + 0.877790i $$0.659017\pi$$
$$44$$ −1.59097 2.75564i −0.239848 0.415429i
$$45$$ −1.97141 + 9.34004i −0.293880 + 1.39233i
$$46$$ 1.11956 1.93914i 0.165070 0.285910i
$$47$$ −2.91423 + 5.04759i −0.425084 + 0.736267i −0.996428 0.0844432i $$-0.973089\pi$$
0.571344 + 0.820711i $$0.306422\pi$$
$$48$$ −1.71053 + 0.272169i −0.246894 + 0.0392842i
$$49$$ 0 0
$$50$$ 2.56238 4.43818i 0.362375 0.627653i
$$51$$ 2.60301 0.414174i 0.364494 0.0579959i
$$52$$ 5.70370 0.790960
$$53$$ 1.02859 1.78157i 0.141288 0.244717i −0.786694 0.617343i $$-0.788209\pi$$
0.927982 + 0.372626i $$0.121542\pi$$
$$54$$ −0.260877 + 5.18960i −0.0355008 + 0.706215i
$$55$$ 10.1248 1.36522
$$56$$ 0 0
$$57$$ −0.794668 + 2.07459i −0.105256 + 0.274786i
$$58$$ −7.08126 −0.929815
$$59$$ −0.562382 0.974074i −0.0732159 0.126814i 0.827093 0.562065i $$-0.189993\pi$$
−0.900309 + 0.435251i $$0.856660\pi$$
$$60$$ 1.97141 5.14663i 0.254508 0.664427i
$$61$$ 1.56238 2.70612i 0.200042 0.346484i −0.748499 0.663135i $$-0.769225\pi$$
0.948542 + 0.316652i $$0.102559\pi$$
$$62$$ −9.42107 −1.19648
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −9.07442 + 15.7174i −1.12554 + 1.94950i
$$66$$ 5.44282 0.866025i 0.669965 0.106600i
$$67$$ −5.48345 9.49761i −0.669910 1.16032i −0.977929 0.208938i $$-0.932999\pi$$
0.308019 0.951380i $$-0.400334\pi$$
$$68$$ −1.52175 −0.184540
$$69$$ 2.44282 + 3.01225i 0.294081 + 0.362632i
$$70$$ 0 0
$$71$$ 8.69002 1.03132 0.515658 0.856794i $$-0.327548\pi$$
0.515658 + 0.856794i $$0.327548\pi$$
$$72$$ 0.619562 2.93533i 0.0730160 0.345932i
$$73$$ 2.48345 4.30146i 0.290666 0.503448i −0.683302 0.730136i $$-0.739457\pi$$
0.973967 + 0.226689i $$0.0727899\pi$$
$$74$$ 1.00000 0.116248
$$75$$ 5.59097 + 6.89425i 0.645590 + 0.796079i
$$76$$ 0.641315 1.11079i 0.0735639 0.127416i
$$77$$ 0 0
$$78$$ −3.53379 + 9.22544i −0.400123 + 1.04458i
$$79$$ 2.06922 3.58399i 0.232805 0.403231i −0.725827 0.687877i $$-0.758543\pi$$
0.958633 + 0.284646i $$0.0918762\pi$$
$$80$$ −1.59097 + 2.75564i −0.177876 + 0.308090i
$$81$$ −8.23229 3.63723i −0.914699 0.404137i
$$82$$ −2.80150 4.85235i −0.309374 0.535852i
$$83$$ 4.03379 + 6.98673i 0.442766 + 0.766893i 0.997894 0.0648718i $$-0.0206639\pi$$
−0.555127 + 0.831765i $$0.687331\pi$$
$$84$$ 0 0
$$85$$ 2.42107 4.19341i 0.262602 0.454839i
$$86$$ 6.82846 0.736332
$$87$$ 4.38727 11.4536i 0.470365 1.22795i
$$88$$ −3.18194 −0.339196
$$89$$ −0.112725 0.195246i −0.0119488 0.0206960i 0.859989 0.510312i $$-0.170470\pi$$
−0.871938 + 0.489616i $$0.837137\pi$$
$$90$$ 7.10301 + 6.37731i 0.748723 + 0.672228i
$$91$$ 0 0
$$92$$ −1.11956 1.93914i −0.116722 0.202169i
$$93$$ 5.83693 15.2381i 0.605262 1.58012i
$$94$$ 2.91423 + 5.04759i 0.300580 + 0.520620i
$$95$$ 2.04063 + 3.53447i 0.209364 + 0.362629i
$$96$$ −0.619562 + 1.61745i −0.0632337 + 0.165080i
$$97$$ −7.42107 12.8537i −0.753495 1.30509i −0.946119 0.323819i $$-0.895033\pi$$
0.192624 0.981273i $$-0.438300\pi$$
$$98$$ 0 0
$$99$$ −1.97141 + 9.34004i −0.198134 + 0.938710i
$$100$$ −2.56238 4.43818i −0.256238 0.443818i
$$101$$ −18.5893 −1.84971 −0.924854 0.380322i $$-0.875813\pi$$
−0.924854 + 0.380322i $$0.875813\pi$$
$$102$$ 0.942820 2.46136i 0.0933531 0.243711i
$$103$$ 0.282630 0.0278484 0.0139242 0.999903i $$-0.495568\pi$$
0.0139242 + 0.999903i $$0.495568\pi$$
$$104$$ 2.85185 4.93955i 0.279647 0.484362i
$$105$$ 0 0
$$106$$ −1.02859 1.78157i −0.0999055 0.173041i
$$107$$ 5.68878 + 9.85326i 0.549955 + 0.952550i 0.998277 + 0.0586780i $$0.0186885\pi$$
−0.448322 + 0.893872i $$0.647978\pi$$
$$108$$ 4.36389 + 2.82073i 0.419915 + 0.271424i
$$109$$ −2.21053 + 3.82876i −0.211731 + 0.366728i −0.952256 0.305300i $$-0.901243\pi$$
0.740526 + 0.672028i $$0.234577\pi$$
$$110$$ 5.06238 8.76830i 0.482679 0.836025i
$$111$$ −0.619562 + 1.61745i −0.0588062 + 0.153522i
$$112$$ 0 0
$$113$$ −1.60752 + 2.78431i −0.151223 + 0.261926i −0.931677 0.363287i $$-0.881655\pi$$
0.780454 + 0.625213i $$0.214988\pi$$
$$114$$ 1.39931 + 1.72550i 0.131058 + 0.161608i
$$115$$ 7.12476 0.664388
$$116$$ −3.54063 + 6.13255i −0.328739 + 0.569393i
$$117$$ −12.7323 11.4315i −1.17710 1.05684i
$$118$$ −1.12476 −0.103543
$$119$$ 0 0
$$120$$ −3.47141 4.28061i −0.316895 0.390764i
$$121$$ −0.875237 −0.0795670
$$122$$ −1.56238 2.70612i −0.141451 0.245001i
$$123$$ 9.58414 1.52496i 0.864172 0.137501i
$$124$$ −4.71053 + 8.15888i −0.423018 + 0.732689i
$$125$$ 0.396990 0.0355079
$$126$$ 0 0
$$127$$ 20.1053 1.78406 0.892030 0.451976i $$-0.149281\pi$$
0.892030 + 0.451976i $$0.149281\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ −4.23065 + 11.0447i −0.372488 + 0.972431i
$$130$$ 9.07442 + 15.7174i 0.795879 + 1.37850i
$$131$$ −6.36389 −0.556015 −0.278008 0.960579i $$-0.589674\pi$$
−0.278008 + 0.960579i $$0.589674\pi$$
$$132$$ 1.97141 5.14663i 0.171589 0.447957i
$$133$$ 0 0
$$134$$ −10.9669 −0.947396
$$135$$ −14.7157 + 7.53762i −1.26653 + 0.648735i
$$136$$ −0.760877 + 1.31788i −0.0652446 + 0.113007i
$$137$$ 2.74145 0.234218 0.117109 0.993119i $$-0.462637\pi$$
0.117109 + 0.993119i $$0.462637\pi$$
$$138$$ 3.83009 0.609419i 0.326039 0.0518772i
$$139$$ 3.98345 6.89953i 0.337872 0.585211i −0.646161 0.763202i $$-0.723626\pi$$
0.984032 + 0.177991i $$0.0569597\pi$$
$$140$$ 0 0
$$141$$ −9.96978 + 1.58632i −0.839607 + 0.133593i
$$142$$ 4.34501 7.52578i 0.364625 0.631550i
$$143$$ −9.07442 + 15.7174i −0.758841 + 1.31435i
$$144$$ −2.23229 2.00422i −0.186024 0.167018i
$$145$$ −11.2661 19.5134i −0.935597 1.62050i
$$146$$ −2.48345 4.30146i −0.205532 0.355991i
$$147$$ 0 0
$$148$$ 0.500000 0.866025i 0.0410997 0.0711868i
$$149$$ −23.2599 −1.90553 −0.952764 0.303712i $$-0.901774\pi$$
−0.952764 + 0.303712i $$0.901774\pi$$
$$150$$ 8.76608 1.39480i 0.715747 0.113885i
$$151$$ −8.12476 −0.661184 −0.330592 0.943774i $$-0.607248\pi$$
−0.330592 + 0.943774i $$0.607248\pi$$
$$152$$ −0.641315 1.11079i −0.0520175 0.0900970i
$$153$$ 3.39699 + 3.04993i 0.274630 + 0.246572i
$$154$$ 0 0
$$155$$ −14.9887 25.9611i −1.20392 2.08525i
$$156$$ 6.22257 + 7.67307i 0.498204 + 0.614338i
$$157$$ −5.63160 9.75422i −0.449451 0.778471i 0.548900 0.835888i $$-0.315047\pi$$
−0.998350 + 0.0574170i $$0.981714\pi$$
$$158$$ −2.06922 3.58399i −0.164618 0.285127i
$$159$$ 3.51887 0.559900i 0.279065 0.0444030i
$$160$$ 1.59097 + 2.75564i 0.125777 + 0.217853i
$$161$$ 0 0
$$162$$ −7.26608 + 5.31075i −0.570877 + 0.417252i
$$163$$ −1.99028 3.44727i −0.155891 0.270011i 0.777492 0.628893i $$-0.216492\pi$$
−0.933383 + 0.358881i $$0.883158\pi$$
$$164$$ −5.60301 −0.437522
$$165$$ 11.0458 + 13.6207i 0.859917 + 1.06037i
$$166$$ 8.06758 0.626166
$$167$$ −2.61956 + 4.53721i −0.202708 + 0.351100i −0.949400 0.314070i $$-0.898307\pi$$
0.746692 + 0.665170i $$0.231641\pi$$
$$168$$ 0 0
$$169$$ −9.76608 16.9153i −0.751237 1.30118i
$$170$$ −2.42107 4.19341i −0.185687 0.321620i
$$171$$ −3.65787 + 1.19427i −0.279724 + 0.0913278i
$$172$$ 3.41423 5.91362i 0.260333 0.450909i
$$173$$ 1.27579 2.20974i 0.0969968 0.168003i −0.813443 0.581644i $$-0.802410\pi$$
0.910440 + 0.413641i $$0.135743\pi$$
$$174$$ −7.72545 9.52628i −0.585665 0.722185i
$$175$$ 0 0
$$176$$ −1.59097 + 2.75564i −0.119924 + 0.207714i
$$177$$ 0.696860 1.81925i 0.0523792 0.136743i
$$178$$ −0.225450 −0.0168982
$$179$$ 3.51887 6.09487i 0.263013 0.455552i −0.704028 0.710172i $$-0.748617\pi$$
0.967041 + 0.254620i $$0.0819504\pi$$
$$180$$ 9.07442 2.96273i 0.676367 0.220829i
$$181$$ 12.9669 0.963822 0.481911 0.876220i $$-0.339943\pi$$
0.481911 + 0.876220i $$0.339943\pi$$
$$182$$ 0 0
$$183$$ 5.34501 0.850463i 0.395115 0.0628680i
$$184$$ −2.23912 −0.165070
$$185$$ 1.59097 + 2.75564i 0.116971 + 0.202599i
$$186$$ −10.2781 12.6740i −0.753628 0.929301i
$$187$$ 2.42107 4.19341i 0.177046 0.306653i
$$188$$ 5.82846 0.425084
$$189$$ 0 0
$$190$$ 4.08126 0.296085
$$191$$ −0.990285 + 1.71522i −0.0716545 + 0.124109i −0.899627 0.436660i $$-0.856161\pi$$
0.827972 + 0.560769i $$0.189495\pi$$
$$192$$ 1.09097 + 1.34528i 0.0787341 + 0.0970873i
$$193$$ 2.27292 + 3.93680i 0.163608 + 0.283377i 0.936160 0.351574i $$-0.114353\pi$$
−0.772552 + 0.634951i $$0.781020\pi$$
$$194$$ −14.8421 −1.06560
$$195$$ −31.0442 + 4.93955i −2.22312 + 0.353728i
$$196$$ 0 0
$$197$$ −21.8148 −1.55424 −0.777120 0.629353i $$-0.783320\pi$$
−0.777120 + 0.629353i $$0.783320\pi$$
$$198$$ 7.10301 + 6.37731i 0.504789 + 0.453216i
$$199$$ −6.14132 + 10.6371i −0.435346 + 0.754042i −0.997324 0.0731106i $$-0.976707\pi$$
0.561978 + 0.827152i $$0.310041\pi$$
$$200$$ −5.12476 −0.362375
$$201$$ 6.79467 17.7384i 0.479259 1.25117i
$$202$$ −9.29467 + 16.0988i −0.653971 + 1.13271i
$$203$$ 0 0
$$204$$ −1.66019 2.04719i −0.116237 0.143332i
$$205$$ 8.91423 15.4399i 0.622597 1.07837i
$$206$$ 0.141315 0.244765i 0.00984589 0.0170536i
$$207$$ −1.38727 + 6.57256i −0.0964223 + 0.456824i
$$208$$ −2.85185 4.93955i −0.197740 0.342496i
$$209$$ 2.04063 + 3.53447i 0.141153 + 0.244485i
$$210$$ 0 0
$$211$$ −8.32846 + 14.4253i −0.573355 + 0.993080i 0.422863 + 0.906193i $$0.361025\pi$$
−0.996218 + 0.0868863i $$0.972308\pi$$
$$212$$ −2.05718 −0.141288
$$213$$ 9.48057 + 11.6905i 0.649598 + 0.801021i
$$214$$ 11.3776 0.777754
$$215$$ 10.8639 + 18.8168i 0.740911 + 1.28330i
$$216$$ 4.62476 2.36887i 0.314675 0.161181i
$$217$$ 0 0
$$218$$ 2.21053 + 3.82876i 0.149716 + 0.259316i
$$219$$ 8.49604 1.35183i 0.574109 0.0913485i
$$220$$ −5.06238 8.76830i −0.341306 0.591159i
$$221$$ 4.33981 + 7.51677i 0.291927 + 0.505633i
$$222$$ 1.09097 + 1.34528i 0.0732212 + 0.0902893i
$$223$$ 5.32846 + 9.22916i 0.356820 + 0.618031i 0.987428 0.158071i $$-0.0505276\pi$$
−0.630608 + 0.776102i $$0.717194\pi$$
$$224$$ 0 0
$$225$$ −3.17511 + 15.0429i −0.211674 + 1.00286i
$$226$$ 1.60752 + 2.78431i 0.106931 + 0.185210i
$$227$$ 14.5081 0.962935 0.481468 0.876464i $$-0.340104\pi$$
0.481468 + 0.876464i $$0.340104\pi$$
$$228$$ 2.19398 0.349092i 0.145300 0.0231192i
$$229$$ −10.2495 −0.677308 −0.338654 0.940911i $$-0.609972\pi$$
−0.338654 + 0.940911i $$0.609972\pi$$
$$230$$ 3.56238 6.17023i 0.234896 0.406853i
$$231$$ 0 0
$$232$$ 3.54063 + 6.13255i 0.232454 + 0.402622i
$$233$$ 0.540628 + 0.936396i 0.0354177 + 0.0613453i 0.883191 0.469014i $$-0.155390\pi$$
−0.847773 + 0.530359i $$0.822057\pi$$
$$234$$ −16.2661 + 5.31075i −1.06335 + 0.347175i
$$235$$ −9.27292 + 16.0612i −0.604898 + 1.04771i
$$236$$ −0.562382 + 0.974074i −0.0366079 + 0.0634068i
$$237$$ 7.07893 1.12635i 0.459826 0.0731645i
$$238$$ 0 0
$$239$$ −6.16019 + 10.6698i −0.398470 + 0.690170i −0.993537 0.113506i $$-0.963792\pi$$
0.595068 + 0.803676i $$0.297125\pi$$
$$240$$ −5.44282 + 0.866025i −0.351333 + 0.0559017i
$$241$$ 13.0000 0.837404 0.418702 0.908124i $$-0.362485\pi$$
0.418702 + 0.908124i $$0.362485\pi$$
$$242$$ −0.437618 + 0.757977i −0.0281312 + 0.0487246i
$$243$$ −4.08809 15.0429i −0.262251 0.965000i
$$244$$ −3.12476 −0.200042
$$245$$ 0 0
$$246$$ 3.47141 9.06259i 0.221329 0.577809i
$$247$$ −7.31573 −0.465489
$$248$$ 4.71053 + 8.15888i 0.299119 + 0.518090i
$$249$$ −4.99837 + 13.0489i −0.316759 + 0.826941i
$$250$$ 0.198495 0.343803i 0.0125539 0.0217440i
$$251$$ −5.11109 −0.322609 −0.161305 0.986905i $$-0.551570\pi$$
−0.161305 + 0.986905i $$0.551570\pi$$
$$252$$ 0 0
$$253$$ 7.12476 0.447930
$$254$$ 10.0527 17.4117i 0.630760 1.09251i
$$255$$ 8.28263 1.31788i 0.518678 0.0825287i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −7.66019 −0.477830 −0.238915 0.971041i $$-0.576792\pi$$
−0.238915 + 0.971041i $$0.576792\pi$$
$$258$$ 7.44966 + 9.18620i 0.463795 + 0.571908i
$$259$$ 0 0
$$260$$ 18.1488 1.12554
$$261$$ 20.1947 6.59341i 1.25002 0.408122i
$$262$$ −3.18194 + 5.51129i −0.196581 + 0.340488i
$$263$$ −3.09493 −0.190842 −0.0954208 0.995437i $$-0.530420\pi$$
−0.0954208 + 0.995437i $$0.530420\pi$$
$$264$$ −3.47141 4.28061i −0.213651 0.263453i
$$265$$ 3.27292 5.66886i 0.201054 0.348235i
$$266$$ 0 0
$$267$$ 0.139680 0.364654i 0.00854830 0.0223165i
$$268$$ −5.48345 + 9.49761i −0.334955 + 0.580159i
$$269$$ 13.4451 23.2877i 0.819765 1.41987i −0.0860906 0.996287i $$-0.527437\pi$$
0.905855 0.423587i $$-0.139229\pi$$
$$270$$ −0.830095 + 16.5130i −0.0505180 + 1.00495i
$$271$$ 11.1082 + 19.2400i 0.674776 + 1.16875i 0.976534 + 0.215362i $$0.0690930\pi$$
−0.301759 + 0.953384i $$0.597574\pi$$
$$272$$ 0.760877 + 1.31788i 0.0461349 + 0.0799080i
$$273$$ 0 0
$$274$$ 1.37072 2.37416i 0.0828084 0.143428i
$$275$$ 16.3067 0.983331
$$276$$ 1.38727 3.62167i 0.0835041 0.217999i
$$277$$ −14.6375 −0.879482 −0.439741 0.898125i $$-0.644930\pi$$
−0.439741 + 0.898125i $$0.644930\pi$$
$$278$$ −3.98345 6.89953i −0.238911 0.413807i
$$279$$ 26.8675 8.77202i 1.60851 0.525167i
$$280$$ 0 0
$$281$$ 11.6992 + 20.2636i 0.697915 + 1.20882i 0.969188 + 0.246322i $$0.0792219\pi$$
−0.271273 + 0.962502i $$0.587445\pi$$
$$282$$ −3.61109 + 9.42724i −0.215037 + 0.561384i
$$283$$ −13.0624 22.6247i −0.776478 1.34490i −0.933960 0.357377i $$-0.883671\pi$$
0.157482 0.987522i $$-0.449662\pi$$
$$284$$ −4.34501 7.52578i −0.257829 0.446573i
$$285$$ −2.52859 + 6.60123i −0.149781 + 0.391023i
$$286$$ 9.07442 + 15.7174i 0.536582 + 0.929387i
$$287$$ 0 0
$$288$$ −2.85185 + 0.931107i −0.168047 + 0.0548660i
$$289$$ 7.34213 + 12.7169i 0.431890 + 0.748056i
$$290$$ −22.5322 −1.32313
$$291$$ 9.19562 24.0064i 0.539057 1.40728i
$$292$$ −4.96690 −0.290666
$$293$$ −12.9315 + 22.3980i −0.755465 + 1.30850i 0.189678 + 0.981846i $$0.439255\pi$$
−0.945143 + 0.326657i $$0.894078\pi$$
$$294$$ 0 0
$$295$$ −1.78947 3.09945i −0.104187 0.180457i
$$296$$ −0.500000 0.866025i −0.0290619 0.0503367i
$$297$$ −14.7157 + 7.53762i −0.853894 + 0.437377i
$$298$$ −11.6300 + 20.1437i −0.673706 + 1.16689i
$$299$$ −6.38564 + 11.0603i −0.369291 + 0.639631i
$$300$$ 3.17511 8.28905i 0.183315 0.478568i
$$301$$ 0 0
$$302$$ −4.06238 + 7.03625i −0.233764 + 0.404891i
$$303$$ −20.2804 25.0079i −1.16508 1.43667i
$$304$$ −1.28263 −0.0735639
$$305$$ 4.97141 8.61073i 0.284662 0.493049i
$$306$$ 4.33981 1.41692i 0.248090 0.0809997i
$$307$$ −3.53216 −0.201591 −0.100795 0.994907i $$-0.532139\pi$$
−0.100795 + 0.994907i $$0.532139\pi$$
$$308$$ 0 0
$$309$$ 0.308342 + 0.380217i 0.0175409 + 0.0216298i
$$310$$ −29.9773 −1.70260
$$311$$ 0.851848 + 1.47544i 0.0483039 + 0.0836648i 0.889166 0.457584i $$-0.151285\pi$$
−0.840863 + 0.541249i $$0.817952\pi$$
$$312$$ 9.75636 1.55237i 0.552345 0.0878855i
$$313$$ −1.42107 + 2.46136i −0.0803234 + 0.139124i −0.903389 0.428822i $$-0.858929\pi$$
0.823065 + 0.567947i $$0.192262\pi$$
$$314$$ −11.2632 −0.635619
$$315$$ 0 0
$$316$$ −4.13844 −0.232805
$$317$$ 12.4601 21.5815i 0.699827 1.21214i −0.268700 0.963224i $$-0.586594\pi$$
0.968526 0.248911i $$-0.0800728\pi$$
$$318$$ 1.27455 3.32738i 0.0714732 0.186590i
$$319$$ −11.2661 19.5134i −0.630779 1.09254i
$$320$$ 3.18194 0.177876
$$321$$ −7.04910 + 18.4026i −0.393442 + 1.02713i
$$322$$ 0 0
$$323$$ 1.95185 0.108604
$$324$$ 0.966208 + 8.94799i 0.0536782 + 0.497110i
$$325$$ −14.6150 + 25.3140i −0.810697 + 1.40417i
$$326$$ −3.98057 −0.220463
$$327$$ −7.56238 + 1.20328i −0.418201 + 0.0665413i
$$328$$ −2.80150 + 4.85235i −0.154687 + 0.267926i
$$329$$ 0 0
$$330$$ 17.3187 2.75564i 0.953366 0.151693i
$$331$$ 3.58577 6.21074i 0.197092 0.341373i −0.750492 0.660879i $$-0.770184\pi$$
0.947584 + 0.319506i $$0.103517\pi$$
$$332$$ 4.03379 6.98673i 0.221383 0.383447i
$$333$$ −2.85185 + 0.931107i −0.156280 + 0.0510244i
$$334$$ 2.61956 + 4.53721i 0.143336 + 0.248265i
$$335$$ −17.4480 30.2209i −0.953287 1.65114i
$$336$$ 0 0
$$337$$ −10.9211 + 18.9158i −0.594908 + 1.03041i 0.398651 + 0.917103i $$0.369478\pi$$
−0.993560 + 0.113309i $$0.963855\pi$$
$$338$$ −19.5322 −1.06241
$$339$$ −5.49944 + 0.875035i −0.298689 + 0.0475254i
$$340$$ −4.84213 −0.262602
$$341$$ −14.9887 25.9611i −0.811681 1.40587i
$$342$$ −0.794668 + 3.76494i −0.0429707 + 0.203585i
$$343$$ 0 0
$$344$$ −3.41423 5.91362i −0.184083 0.318841i
$$345$$ 7.77292 + 9.58481i 0.418480 + 0.516029i
$$346$$ −1.27579 2.20974i −0.0685871 0.118796i
$$347$$ 1.05555 + 1.82826i 0.0566646 + 0.0981460i 0.892966 0.450124i $$-0.148620\pi$$
−0.836302 + 0.548270i $$0.815287\pi$$
$$348$$ −12.1127 + 1.92730i −0.649310 + 0.103314i
$$349$$ −18.1082 31.3643i −0.969310 1.67889i −0.697559 0.716527i $$-0.745731\pi$$
−0.271751 0.962368i $$-0.587603\pi$$
$$350$$ 0 0
$$351$$ 1.48796 29.5999i 0.0794215 1.57993i
$$352$$ 1.59097 + 2.75564i 0.0847991 + 0.146876i
$$353$$ 10.4887 0.558255 0.279127 0.960254i $$-0.409955\pi$$
0.279127 + 0.960254i $$0.409955\pi$$
$$354$$ −1.22708 1.51312i −0.0652188 0.0804216i
$$355$$ 27.6512 1.46757
$$356$$ −0.112725 + 0.195246i −0.00597442 + 0.0103480i
$$357$$ 0 0
$$358$$ −3.51887 6.09487i −0.185978 0.322124i
$$359$$ 16.2209 + 28.0955i 0.856108 + 1.48282i 0.875613 + 0.483013i $$0.160458\pi$$
−0.0195047 + 0.999810i $$0.506209\pi$$
$$360$$ 1.97141 9.34004i 0.103902 0.492264i
$$361$$ 8.67743 15.0297i 0.456707 0.791039i
$$362$$ 6.48345 11.2297i 0.340762 0.590218i
$$363$$ −0.954858 1.17744i −0.0501171 0.0617995i
$$364$$ 0 0
$$365$$ 7.90219 13.6870i 0.413620 0.716410i
$$366$$ 1.93598 5.05415i 0.101195 0.264185i
$$367$$ 18.1111 0.945391 0.472696 0.881226i $$-0.343281\pi$$
0.472696 + 0.881226i $$0.343281\pi$$
$$368$$ −1.11956 + 1.93914i −0.0583612 + 0.101085i
$$369$$ 12.5075 + 11.2297i 0.651116 + 0.584593i
$$370$$ 3.18194 0.165421
$$371$$ 0 0
$$372$$ −16.1150 + 2.56412i −0.835526 + 0.132943i
$$373$$ −11.6706 −0.604280 −0.302140 0.953263i $$-0.597701\pi$$
−0.302140 + 0.953263i $$0.597701\pi$$
$$374$$ −2.42107 4.19341i −0.125190 0.216836i
$$375$$ 0.433105 + 0.534063i 0.0223654 + 0.0275789i
$$376$$ 2.91423 5.04759i 0.150290 0.260310i
$$377$$ 40.3893 2.08016
$$378$$ 0 0
$$379$$ 14.2690 0.732947 0.366474 0.930428i $$-0.380565\pi$$
0.366474 + 0.930428i $$0.380565\pi$$
$$380$$ 2.04063 3.53447i 0.104682 0.181315i
$$381$$ 21.9343 + 27.0473i 1.12373 + 1.38568i
$$382$$ 0.990285 + 1.71522i 0.0506674 + 0.0877585i
$$383$$ 1.64979 0.0843001 0.0421501 0.999111i $$-0.486579\pi$$
0.0421501 + 0.999111i $$0.486579\pi$$
$$384$$ 1.71053 0.272169i 0.0872903 0.0138891i
$$385$$ 0 0
$$386$$ 4.54583 0.231377
$$387$$ −19.4737 + 6.35803i −0.989905 + 0.323197i
$$388$$ −7.42107 + 12.8537i −0.376748 + 0.652546i
$$389$$ −32.0676 −1.62589 −0.812946 0.582340i $$-0.802137\pi$$
−0.812946 + 0.582340i $$0.802137\pi$$
$$390$$ −11.2443 + 29.3548i −0.569379 + 1.48644i
$$391$$ 1.70370 2.95089i 0.0861596 0.149233i
$$392$$ 0 0
$$393$$ −6.94282 8.56122i −0.350219 0.431856i
$$394$$ −10.9074 + 18.8922i −0.549507 + 0.951773i
$$395$$ 6.58414 11.4041i 0.331284 0.573800i
$$396$$ 9.07442 2.96273i 0.456007 0.148883i
$$397$$ 18.9669 + 32.8516i 0.951921 + 1.64878i 0.741261 + 0.671217i $$0.234228\pi$$
0.210660 + 0.977559i $$0.432439\pi$$
$$398$$ 6.14132 + 10.6371i 0.307836 + 0.533188i
$$399$$ 0 0
$$400$$ −2.56238 + 4.43818i −0.128119 + 0.221909i
$$401$$ 10.6192 0.530296 0.265148 0.964208i $$-0.414579\pi$$
0.265148 + 0.964208i $$0.414579\pi$$
$$402$$ −11.9646 14.7536i −0.596739 0.735841i
$$403$$ 53.7349 2.67673
$$404$$ 9.29467 + 16.0988i 0.462427 + 0.800947i
$$405$$ −26.1947 11.5735i −1.30162 0.575090i
$$406$$ 0 0
$$407$$ 1.59097 + 2.75564i 0.0788615 + 0.136592i
$$408$$ −2.60301 + 0.414174i −0.128868 + 0.0205047i
$$409$$ 2.77292 + 4.80283i 0.137112 + 0.237485i 0.926402 0.376535i $$-0.122885\pi$$
−0.789290 + 0.614020i $$0.789551\pi$$
$$410$$ −8.91423 15.4399i −0.440242 0.762522i
$$411$$ 2.99084 + 3.68802i 0.147527 + 0.181916i
$$412$$ −0.141315 0.244765i −0.00696209 0.0120587i
$$413$$ 0 0
$$414$$ 4.99837 + 4.48769i 0.245656 + 0.220558i
$$415$$ 12.8353 + 22.2314i 0.630060 + 1.09130i
$$416$$ −5.70370 −0.279647
$$417$$ 13.6276 2.16834i 0.667349 0.106184i
$$418$$ 4.08126 0.199621
$$419$$ −2.77455 + 4.80566i −0.135546 + 0.234772i −0.925806 0.378000i $$-0.876612\pi$$
0.790260 + 0.612772i $$0.209945\pi$$
$$420$$ 0 0
$$421$$ −3.42107 5.92546i −0.166733 0.288789i 0.770537 0.637396i $$-0.219988\pi$$
−0.937269 + 0.348606i $$0.886655\pi$$
$$422$$ 8.32846 + 14.4253i 0.405423 + 0.702213i
$$423$$ −13.0108 11.6815i −0.632606 0.567975i
$$424$$ −1.02859 + 1.78157i −0.0499527 + 0.0865207i
$$425$$ 3.89931 6.75381i 0.189144 0.327608i
$$426$$ 14.8646 2.36515i 0.720191 0.114592i
$$427$$ 0 0
$$428$$ 5.68878 9.85326i 0.274978 0.476275i
$$429$$ −31.0442 + 4.93955i −1.49883 + 0.238484i
$$430$$ 21.7278 1.04781
$$431$$ 16.5539 28.6722i 0.797374 1.38109i −0.123947 0.992289i $$-0.539555\pi$$
0.921321 0.388803i $$-0.127111\pi$$
$$432$$ 0.260877 5.18960i 0.0125514 0.249685i
$$433$$ 12.1111 0.582022 0.291011 0.956720i $$-0.406008\pi$$
0.291011 + 0.956720i $$0.406008\pi$$
$$434$$ 0 0
$$435$$ 13.9601 36.4446i 0.669334 1.74739i
$$436$$ 4.42107 0.211731
$$437$$ 1.43598 + 2.48720i 0.0686924 + 0.118979i
$$438$$ 3.07730 8.03371i 0.147039 0.383865i
$$439$$ −4.41711 + 7.65066i −0.210817 + 0.365146i −0.951970 0.306190i $$-0.900946\pi$$
0.741153 + 0.671336i $$0.234279\pi$$
$$440$$ −10.1248 −0.482679
$$441$$ 0 0
$$442$$ 8.67962 0.412847
$$443$$ −8.75924 + 15.1715i −0.416164 + 0.720817i −0.995550 0.0942360i $$-0.969959\pi$$
0.579386 + 0.815053i $$0.303292\pi$$
$$444$$ 1.71053 0.272169i 0.0811783 0.0129166i
$$445$$ −0.358685 0.621261i −0.0170033 0.0294506i
$$446$$ 10.6569 0.504620
$$447$$ −25.3759 31.2911i −1.20024 1.48002i
$$448$$ 0 0
$$449$$ 31.2301 1.47384 0.736920 0.675980i $$-0.236280\pi$$
0.736920 + 0.675980i $$0.236280\pi$$
$$450$$ 11.4399 + 10.2712i 0.539284 + 0.484187i
$$451$$ 8.91423 15.4399i 0.419755 0.727036i
$$452$$ 3.21505 0.151223
$$453$$ −8.86389 10.9301i −0.416462 0.513540i
$$454$$ 7.25404 12.5644i 0.340449 0.589675i
$$455$$ 0 0
$$456$$ 0.794668 2.07459i 0.0372138 0.0971516i
$$457$$ 16.0624 27.8209i 0.751367 1.30140i −0.195794 0.980645i $$-0.562728\pi$$
0.947161 0.320760i $$-0.103938\pi$$
$$458$$ −5.12476 + 8.87635i −0.239464 + 0.414765i
$$459$$ −0.396990 + 7.89729i −0.0185299 + 0.368614i
$$460$$ −3.56238 6.17023i −0.166097 0.287688i
$$461$$ −1.23229 2.13438i −0.0573933 0.0994081i 0.835901 0.548880i $$-0.184946\pi$$
−0.893295 + 0.449472i $$0.851612\pi$$
$$462$$ 0 0
$$463$$ 15.1735 26.2812i 0.705171 1.22139i −0.261459 0.965215i $$-0.584204\pi$$
0.966630 0.256177i $$-0.0824631\pi$$
$$464$$ 7.08126 0.328739
$$465$$ 18.5728 48.4868i 0.861292 2.24852i
$$466$$ 1.08126 0.0500882
$$467$$ 7.98181 + 13.8249i 0.369354 + 0.639740i 0.989465 0.144774i $$-0.0462456\pi$$
−0.620110 + 0.784515i $$0.712912\pi$$
$$468$$ −3.53379 + 16.7422i −0.163350 + 0.773909i
$$469$$ 0 0
$$470$$ 9.27292 + 16.0612i 0.427728 + 0.740846i
$$471$$ 6.97825 18.2177i 0.321541 0.839425i
$$472$$ 0.562382 + 0.974074i 0.0258857 + 0.0448354i
$$473$$ 10.8639 + 18.8168i 0.499522 + 0.865198i
$$474$$ 2.56402 6.69371i 0.117769 0.307452i
$$475$$ 3.28659 + 5.69254i 0.150799 + 0.261192i
$$476$$ 0 0
$$477$$ 4.59222 + 4.12304i 0.210263 + 0.188781i
$$478$$ 6.16019 + 10.6698i 0.281761 + 0.488024i
$$479$$ 23.1729 1.05880 0.529399 0.848373i $$-0.322418\pi$$
0.529399 + 0.848373i $$0.322418\pi$$
$$480$$ −1.97141 + 5.14663i −0.0899821 + 0.234911i
$$481$$ −5.70370 −0.260066
$$482$$ 6.50000 11.2583i 0.296067 0.512803i
$$483$$ 0 0
$$484$$ 0.437618 + 0.757977i 0.0198917 + 0.0344535i
$$485$$ −23.6134 40.8996i −1.07223 1.85716i
$$486$$ −15.0715 3.98104i −0.683659 0.180583i
$$487$$ 1.70658 2.95588i 0.0773323 0.133943i −0.824766 0.565474i $$-0.808693\pi$$
0.902098 + 0.431531i $$0.142026\pi$$
$$488$$ −1.56238 + 2.70612i −0.0707257 + 0.122500i
$$489$$ 2.46621 6.43837i 0.111526 0.291153i
$$490$$ 0 0
$$491$$ −9.58414 + 16.6002i −0.432526 + 0.749157i −0.997090 0.0762323i $$-0.975711\pi$$
0.564564 + 0.825389i $$0.309044\pi$$
$$492$$ −6.11273 7.53762i −0.275583 0.339822i
$$493$$ −10.7759 −0.485323
$$494$$ −3.65787 + 6.33561i −0.164575 + 0.285053i
$$495$$ −6.27292 + 29.7195i −0.281947 + 1.33579i
$$496$$ 9.42107 0.423018
$$497$$ 0 0
$$498$$ 8.80150 + 10.8532i 0.394405 + 0.486342i
$$499$$ 41.1696 1.84301 0.921503 0.388371i $$-0.126962\pi$$
0.921503 + 0.388371i $$0.126962\pi$$
$$500$$ −0.198495 0.343803i −0.00887697 0.0153754i
$$501$$ −8.96169 + 1.42593i −0.400379 + 0.0637056i
$$502$$ −2.55555 + 4.42633i −0.114060 + 0.197557i
$$503$$ 26.4542 1.17953 0.589767 0.807574i $$-0.299220\pi$$
0.589767 + 0.807574i $$0.299220\pi$$
$$504$$ 0 0
$$505$$ −59.1502 −2.63215
$$506$$ 3.56238 6.17023i 0.158367 0.274300i
$$507$$ 12.1014 31.5923i 0.537441 1.40306i
$$508$$ −10.0527 17.4117i −0.446015 0.772521i
$$509$$ −12.7713 −0.566077 −0.283039 0.959109i $$-0.591342\pi$$
−0.283039 + 0.959109i $$0.591342\pi$$
$$510$$ 3.00000 7.83191i 0.132842 0.346803i
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ −5.59725 3.61795i −0.247125 0.159736i
$$514$$ −3.83009 + 6.63392i −0.168938 + 0.292610i
$$515$$ 0.899313 0.0396285
$$516$$ 11.6803 1.85849i 0.514197 0.0818156i
$$517$$ −9.27292 + 16.0612i −0.407822 + 0.706369i
$$518$$ 0 0
$$519$$ 4.36458 0.694462i 0.191584 0.0304835i
$$520$$ 9.07442 15.7174i 0.397940 0.689252i
$$521$$ 3.40615 5.89962i 0.149226 0.258467i −0.781716 0.623635i $$-0.785655\pi$$
0.930942 + 0.365168i $$0.118988\pi$$
$$522$$ 4.38727 20.7858i 0.192026 0.909770i
$$523$$ −14.7535 25.5538i −0.645125 1.11739i −0.984273 0.176656i $$-0.943472\pi$$
0.339148 0.940733i $$-0.389861\pi$$
$$524$$ 3.18194 + 5.51129i 0.139004 + 0.240762i
$$525$$ 0 0
$$526$$ −1.54746 + 2.68029i −0.0674727 + 0.116866i
$$527$$ −14.3365 −0.624510
$$528$$ −5.44282 + 0.866025i −0.236868 + 0.0376889i
$$529$$ −17.9863 −0.782014
$$530$$ −3.27292 5.66886i −0.142166 0.246239i
$$531$$ 3.20765 1.04728i 0.139200 0.0454479i
$$532$$ 0 0
$$533$$ 15.9789 + 27.6763i 0.692125 + 1.19879i
$$534$$ −0.245960 0.303294i −0.0106437 0.0131248i
$$535$$ 18.1014 + 31.3525i 0.782591 + 1.35549i
$$536$$ 5.48345 + 9.49761i 0.236849 + 0.410234i
$$537$$ 12.0383 1.91546i 0.519491 0.0826580i
$$538$$ −13.4451 23.2877i −0.579661 1.00400i
$$539$$ 0 0
$$540$$ 13.8856 + 8.97539i 0.597543 + 0.386239i
$$541$$ 14.7008 + 25.4626i 0.632038 + 1.09472i 0.987135 + 0.159892i $$0.0511145\pi$$
−0.355097 + 0.934829i $$0.615552\pi$$
$$542$$ 22.2164 0.954277
$$543$$ 14.1465 + 17.4441i 0.607085 + 0.748599i
$$544$$ 1.52175 0.0652446
$$545$$ −7.03379 + 12.1829i −0.301295 + 0.521857i
$$546$$ 0 0
$$547$$ 17.6150 + 30.5102i 0.753165 + 1.30452i 0.946281 + 0.323344i $$0.104807\pi$$
−0.193116 + 0.981176i $$0.561859\pi$$
$$548$$ −1.37072 2.37416i −0.0585544 0.101419i
$$549$$ 6.97537 + 6.26271i 0.297701 + 0.267286i
$$550$$ 8.15335 14.1220i 0.347660 0.602165i
$$551$$ 4.54132 7.86579i 0.193467 0.335094i
$$552$$ −2.44282 3.01225i −0.103973 0.128210i
$$553$$ 0 0
$$554$$ −7.31875 + 12.6764i −0.310944 + 0.538570i
$$555$$ −1.97141 + 5.14663i −0.0836817 + 0.218462i
$$556$$ −7.96690 −0.337872
$$557$$ −3.36909 + 5.83543i −0.142753 + 0.247255i −0.928532 0.371252i $$-0.878929\pi$$
0.785779 + 0.618507i $$0.212262\pi$$
$$558$$ 5.83693 27.6539i 0.247097 1.17068i
$$559$$ −38.9475 −1.64730
$$560$$ 0 0
$$561$$ 8.28263 1.31788i 0.349693 0.0556408i
$$562$$ 23.3984 0.987001
$$563$$ −0.729964 1.26433i −0.0307643 0.0532853i 0.850233 0.526406i $$-0.176461\pi$$
−0.880998 + 0.473121i $$0.843127\pi$$
$$564$$ 6.35868 + 7.84092i 0.267749 + 0.330162i
$$565$$ −5.11505 + 8.85952i −0.215192 + 0.372723i
$$566$$ −26.1248 −1.09811
$$567$$ 0 0
$$568$$ −8.69002 −0.364625
$$569$$ −9.78263 + 16.9440i −0.410109 + 0.710330i −0.994901 0.100853i $$-0.967843\pi$$
0.584792 + 0.811183i $$0.301176\pi$$
$$570$$ 4.45254 + 5.49044i 0.186496 + 0.229969i
$$571$$ 10.9629 + 18.9884i 0.458785 + 0.794638i 0.998897 0.0469545i $$-0.0149516\pi$$
−0.540112 + 0.841593i $$0.681618\pi$$
$$572$$ 18.1488 0.758841
$$573$$ −3.38783 + 0.539049i −0.141529 + 0.0225191i
$$574$$ 0 0
$$575$$ 11.4750 0.478540
$$576$$ −0.619562 + 2.93533i −0.0258151 + 0.122305i
$$577$$ −12.3655 + 21.4177i −0.514783 + 0.891631i 0.485069 + 0.874476i $$0.338794\pi$$
−0.999853 + 0.0171554i $$0.994539\pi$$
$$578$$ 14.6843 0.610785
$$579$$ −2.81642 + 7.35265i −0.117046 + 0.305566i
$$580$$ −11.2661 + 19.5134i −0.467798 + 0.810251i
$$581$$ 0 0
$$582$$ −16.1923 19.9668i −0.671194 0.827652i
$$583$$ 3.27292 5.66886i 0.135550 0.234780i
$$584$$ −2.48345 + 4.30146i −0.102766 + 0.177996i
$$585$$ −40.5134 36.3743i −1.67502 1.50389i
$$586$$ 12.9315 + 22.3980i 0.534194 + 0.925251i
$$587$$ 18.0796 + 31.3148i 0.746226 + 1.29250i 0.949620 + 0.313404i $$0.101469\pi$$
−0.203394 + 0.979097i $$0.565197\pi$$
$$588$$ 0 0
$$589$$ 6.04187 10.4648i 0.248951 0.431196i
$$590$$ −3.57893 −0.147342
$$591$$ −23.7993 29.3470i −0.978973 1.20717i
$$592$$ −1.00000 −0.0410997
$$593$$ 7.55391 + 13.0838i 0.310202 + 0.537285i 0.978406 0.206693i $$-0.0662700\pi$$
−0.668204 + 0.743978i $$0.732937\pi$$
$$594$$ −0.830095 + 16.5130i −0.0340592 + 0.677537i
$$595$$ 0 0
$$596$$ 11.6300 + 20.1437i 0.476382 + 0.825118i
$$597$$ −21.0098 + 3.34295i −0.859876 + 0.136818i
$$598$$ 6.38564 + 11.0603i 0.261128 + 0.452287i
$$599$$ 2.72708 + 4.72345i 0.111426 + 0.192995i 0.916345 0.400389i $$-0.131125\pi$$
−0.804920 + 0.593384i $$0.797792\pi$$
$$600$$ −5.59097 6.89425i −0.228250 0.281456i
$$601$$ 3.36840 + 5.83424i 0.137400 + 0.237984i 0.926512 0.376266i $$-0.122792\pi$$
−0.789112 + 0.614250i $$0.789459\pi$$
$$602$$ 0 0
$$603$$ 31.2759 10.2114i 1.27365 0.415839i
$$604$$ 4.06238 + 7.03625i 0.165296 + 0.286301i
$$605$$ −2.78495 −0.113224
$$606$$ −31.7977 + 5.05944i −1.29169 + 0.205526i
$$607$$ −6.67059 −0.270751 −0.135376 0.990794i $$-0.543224\pi$$
−0.135376 + 0.990794i $$0.543224\pi$$
$$608$$ −0.641315 + 1.11079i −0.0260088 + 0.0450485i
$$609$$ 0 0
$$610$$ −4.97141 8.61073i −0.201287 0.348638i
$$611$$ −16.6219 28.7899i −0.672449 1.16472i
$$612$$ 0.942820 4.46684i 0.0381112 0.180561i
$$613$$ 0.654988 1.13447i 0.0264547 0.0458209i −0.852495 0.522735i $$-0.824912\pi$$
0.878950 + 0.476915i $$0.158245\pi$$
$$614$$ −1.76608 + 3.05894i −0.0712731 + 0.123449i
$$615$$ 30.4962 4.85235i 1.22972 0.195666i
$$616$$ 0 0
$$617$$ 17.2483 29.8749i 0.694390 1.20272i −0.275996 0.961159i $$-0.589008\pi$$
0.970386 0.241560i $$-0.0776589\pi$$
$$618$$ 0.483448 0.0769231i 0.0194471 0.00309430i
$$619$$ 16.4484 0.661118 0.330559 0.943785i $$-0.392763\pi$$
0.330559 + 0.943785i $$0.392763\pi$$
$$620$$ −14.9887 + 25.9611i −0.601959 + 1.04262i
$$621$$ −10.3554 + 5.30420i −0.415549 + 0.212850i
$$622$$ 1.70370 0.0683120
$$623$$ 0 0
$$624$$ 3.53379 9.22544i 0.141465 0.369313i
$$625$$ −24.3606 −0.974425
$$626$$ 1.42107 + 2.46136i 0.0567972 + 0.0983757i
$$627$$ −2.52859 + 6.60123i −0.100982 + 0.263628i
$$628$$ −5.63160 + 9.75422i −0.224725 + 0.389236i
$$629$$ 1.52175 0.0606763
$$630$$ 0 0
$$631$$ −30.0118 −1.19475 −0.597375 0.801962i $$-0.703790\pi$$
−0.597375 + 0.801962i $$0.703790\pi$$
$$632$$ −2.06922 + 3.58399i −0.0823091 + 0.142564i
$$633$$ −28.4922 + 4.53349i −1.13246 + 0.180190i
$$634$$ −12.4601 21.5815i −0.494852 0.857109i
$$635$$ 63.9740 2.53873
$$636$$ −2.24433 2.76748i −0.0889933 0.109738i
$$637$$ 0 0
$$638$$ −22.5322 −0.892057
$$639$$ −5.38401 + 25.5081i −0.212988 + 1.00908i
$$640$$ 1.59097 2.75564i 0.0628887 0.108926i
$$641$$ 27.8993 1.10196 0.550978 0.834520i $$-0.314255\pi$$
0.550978 + 0.834520i $$0.314255\pi$$
$$642$$ 12.4126 + 15.3060i 0.489886 + 0.604080i
$$643$$ −14.2524 + 24.6859i −0.562060 + 0.973516i 0.435257 + 0.900306i $$0.356658\pi$$
−0.997317 + 0.0732100i $$0.976676\pi$$
$$644$$ 0 0
$$645$$ −13.4617 + 35.1436i −0.530054 + 1.38378i
$$646$$ 0.975923 1.69035i 0.0383972 0.0665059i
$$647$$ −8.35705 + 14.4748i −0.328550 + 0.569065i −0.982224 0.187711i $$-0.939893\pi$$
0.653675 + 0.756776i $$0.273226\pi$$
$$648$$ 8.23229 + 3.63723i 0.323395 + 0.142884i
$$649$$ −1.78947 3.09945i −0.0702427 0.121664i
$$650$$ 14.6150 + 25.3140i 0.573249 + 0.992897i
$$651$$ 0 0
$$652$$ −1.99028 + 3.44727i −0.0779456 + 0.135006i
$$653$$ 38.1650 1.49351 0.746756 0.665098i $$-0.231610\pi$$
0.746756 + 0.665098i $$0.231610\pi$$
$$654$$ −2.73912 + 7.15085i −0.107108 + 0.279620i
$$655$$ −20.2495 −0.791214
$$656$$ 2.80150 + 4.85235i 0.109380 + 0.189452i
$$657$$ 11.0875 + 9.95475i 0.432566 + 0.388372i
$$658$$ 0 0
$$659$$ 4.37072 + 7.57031i 0.170259 + 0.294898i 0.938510 0.345251i $$-0.112206\pi$$
−0.768251 + 0.640148i $$0.778873\pi$$
$$660$$ 6.27292 16.3763i 0.244173 0.637446i
$$661$$ −10.0419 17.3930i −0.390584 0.676511i 0.601943 0.798539i $$-0.294393\pi$$
−0.992527 + 0.122028i $$0.961060\pi$$
$$662$$ −3.58577 6.21074i −0.139365 0.241387i
$$663$$ −5.37756 + 14.0388i −0.208847 + 0.545224i
$$664$$ −4.03379 6.98673i −0.156541 0.271138i
$$665$$ 0 0
$$666$$ −0.619562 + 2.93533i −0.0240075 + 0.113742i
$$667$$ −7.92790 13.7315i −0.306970 0.531687i
$$668$$ 5.23912 0.202708
$$669$$ −6.60262 + 17.2370i −0.255272 + 0.666422i
$$670$$ −34.8960 −1.34815
$$671$$ 4.97141 8.61073i 0.191919 0.332414i
$$672$$ 0 0
$$673$$ −17.0264 29.4906i −0.656319 1.13678i −0.981561 0.191148i $$-0.938779\pi$$
0.325242 0.945631i $$-0.394554\pi$$
$$674$$ 10.9211 + 18.9158i 0.420664 + 0.728611i
$$675$$ −23.7008 + 12.1399i −0.912245 + 0.467266i
$$676$$ −9.76608 + 16.9153i −0.375618 + 0.650590i
$$677$$ −0.358685 + 0.621261i −0.0137854 + 0.0238770i −0.872836 0.488014i $$-0.837721\pi$$
0.859050 + 0.511891i $$0.171055\pi$$
$$678$$ −1.99192 + 5.20018i −0.0764992 + 0.199712i
$$679$$ 0 0
$$680$$ −2.42107 + 4.19341i −0.0928437 + 0.160810i
$$681$$ 15.8279 + 19.5174i 0.606527 + 0.747910i
$$682$$ −29.9773 −1.14789
$$683$$ −10.5270 + 18.2332i −0.402803 + 0.697675i −0.994063 0.108806i $$-0.965297\pi$$
0.591260 + 0.806481i $$0.298631\pi$$
$$684$$ 2.86320 + 2.57067i 0.109477 + 0.0982921i
$$685$$ 8.72313 0.333294
$$686$$ 0 0
$$687$$ −11.1819 13.7885i −0.426618 0.526064i
$$688$$ −6.82846 −0.260333
$$689$$ 5.86677 + 10.1615i 0.223506 + 0.387124i
$$690$$ 12.1871 1.93914i 0.463957 0.0738217i
$$691$$ 2.92395 5.06442i 0.111232 0.192660i −0.805035 0.593227i $$-0.797854\pi$$
0.916267 + 0.400567i $$0.131187\pi$$
$$692$$ −2.55159 −0.0969968
$$693$$ 0 0
$$694$$ 2.11109 0.0801359
$$695$$ 12.6751 21.9539i 0.480794 0.832760i
$$696$$ −4.38727 + 11.4536i −0.166299 + 0.434147i
$$697$$ −4.26320 7.38408i −0.161480 0.279692i
$$698$$ −36.2164 −1.37081
$$699$$ −0.669905 + 1.74888i −0.0253381 + 0.0661486i
$$700$$ 0 0
$$701$$ 10.2711 0.387935 0.193967 0.981008i $$-0.437864\pi$$
0.193967 + 0.981008i $$0.437864\pi$$
$$702$$ −24.8903 16.0886i −0.939423 0.607224i
$$703$$ −0.641315 + 1.11079i −0.0241877 + 0.0418942i
$$704$$ 3.18194 0.119924
$$705$$ −31.7233 + 5.04759i −1.19477 + 0.190103i
$$706$$ 5.24433 9.08344i 0.197373 0.341860i
$$707$$ 0 0
$$708$$ −1.92395 + 0.306125i −0.0723063 + 0.0115049i
$$709$$ −21.7427 + 37.6594i −0.816564 + 1.41433i 0.0916356 + 0.995793i $$0.470790\pi$$
−0.908200 + 0.418538i $$0.862543\pi$$
$$710$$ 13.8256 23.9466i 0.518865 0.898700i
$$711$$ 9.23818 + 8.29434i 0.346459 + 0.311062i
$$712$$ 0.112725 + 0.195246i 0.00422455 + 0.00731714i
$$713$$ −10.5475 18.2687i −0.395006 0.684170i
$$714$$ 0 0
$$715$$ −28.8743 + 50.0117i −1.07984 + 1.87033i
$$716$$ −7.03775 −0.263013
$$717$$ −21.0744 + 3.35322i −0.787039 + 0.125228i
$$718$$ 32.4419 1.21072
$$719$$ −25.4412 44.0654i −0.948796 1.64336i −0.747966 0.663737i $$-0.768969\pi$$
−0.200830 0.979626i $$-0.564364\pi$$
$$720$$ −7.10301 6.37731i −0.264714 0.237668i
$$721$$ 0 0
$$722$$ −8.67743 15.0297i −0.322941 0.559349i
$$723$$ 14.1826 + 17.4887i 0.527458 + 0.650410i
$$724$$ −6.48345 11.2297i −0.240955 0.417347i
$$725$$ −18.1449 31.4279i −0.673884 1.16720i
$$726$$ −1.49712 + 0.238212i −0.0555634 + 0.00884088i
$$727$$ −6.07210 10.5172i −0.225202 0.390061i 0.731178 0.682186i $$-0.238971\pi$$
−0.956380 + 0.292126i $$0.905637\pi$$
$$728$$ 0 0
$$729$$ 15.7769 21.9110i 0.584329 0.811517i
$$730$$ −7.90219 13.6870i −0.292473 0.506579i
$$731$$ 10.3912 0.384334
$$732$$ −3.40903 4.20368i −0.126001 0.155373i
$$733$$ 46.1696 1.70531 0.852657 0.522470i $$-0.174989\pi$$
0.852657 + 0.522470i $$0.174989\pi$$
$$734$$ 9.05555 15.6847i 0.334246 0.578932i
$$735$$ 0 0
$$736$$ 1.11956 + 1.93914i 0.0412676 + 0.0714776i
$$737$$ −17.4480 30.2209i −0.642706 1.11320i
$$738$$ 15.9789 5.21700i 0.588193 0.192041i
$$739$$ −2.49604 + 4.32327i −0.0918184 + 0.159034i −0.908276 0.418371i $$-0.862601\pi$$
0.816458 + 0.577405i $$0.195935\pi$$
$$740$$ 1.59097 2.75564i 0.0584853 0.101299i
$$741$$ −7.98126 9.84172i −0.293199 0.361545i
$$742$$ 0 0
$$743$$ −15.7060 + 27.2036i −0.576198 + 0.998004i 0.419712 + 0.907657i $$0.362131\pi$$
−0.995910 + 0.0903470i $$0.971202\pi$$
$$744$$ −5.83693 + 15.2381i −0.213992 + 0.558656i
$$745$$ −74.0118 −2.71158
$$746$$ −5.83530 + 10.1070i −0.213645 + 0.370045i
$$747$$ −23.0075 + 7.51179i −0.841801 + 0.274842i
$$748$$ −4.84213 −0.177046
$$749$$ 0 0
$$750$$ 0.679065 0.108048i 0.0247959 0.00394536i
$$751$$ 3.29630 0.120284 0.0601419 0.998190i $$-0.480845\pi$$
0.0601419 + 0.998190i $$0.480845\pi$$
$$752$$ −2.91423 5.04759i −0.106271 0.184067i
$$753$$ −5.57605 6.87585i −0.203203 0.250570i
$$754$$ 20.1947 34.9782i 0.735447 1.27383i
$$755$$ −25.8525 −0.940870
$$756$$ 0 0
$$757$$ −10.1384 −0.368488 −0.184244 0.982881i $$-0.558984\pi$$
−0.184244 + 0.982881i $$0.558984\pi$$
$$758$$ 7.13448 12.3573i 0.259136 0.448837i
$$759$$ 7.77292 + 9.58481i 0.282139 + 0.347907i
$$760$$ −2.04063 3.53447i −0.0740214 0.128209i
$$761$$ −14.0676 −0.509950 −0.254975 0.966948i $$-0.582067\pi$$
−0.254975 + 0.966948i $$0.582067\pi$$
$$762$$ 34.3908 5.47204i 1.24585 0.198231i
$$763$$ 0 0
$$764$$ 1.98057 0.0716545
$$765$$ 10.8090 + 9.70470i 0.390801 + 0.350874i
$$766$$ 0.824893 1.42876i 0.0298046 0.0516231i
$$767$$ 6.41531 0.231643
$$768$$ 0.619562 1.61745i 0.0223565 0.0583647i
$$769$$ −11.3461 + 19.6520i −0.409151 + 0.708669i −0.994795 0.101899i $$-0.967508\pi$$
0.585644 + 0.810568i $$0.300842\pi$$
$$770$$ 0 0
$$771$$ −8.35705 10.3051i −0.300972 0.371129i
$$772$$ 2.27292 3.93680i 0.0818040 0.141689i
$$773$$ −0.327772 + 0.567717i −0.0117891 + 0.0204194i −0.871860 0.489756i $$-0.837086\pi$$
0.860071 + 0.510175i $$0.170419\pi$$