# Properties

 Label 625.2.e.a.374.2 Level $625$ Weight $2$ Character 625.374 Analytic conductor $4.991$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$625 = 5^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 625.e (of order $$10$$, degree $$4$$, 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: $$4.99065012633$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$2$$ over $$\Q(\zeta_{10})$$ Coefficient field: 8.0.58140625.2 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25$$ x^8 - 3*x^7 + 4*x^6 - 7*x^5 + 11*x^4 + 5*x^3 - 10*x^2 - 25*x + 25 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 25) Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

## Embedding invariants

 Embedding label 374.2 Root $$1.17421 + 0.0566033i$$ of defining polynomial Character $$\chi$$ $$=$$ 625.374 Dual form 625.2.e.a.249.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.107666 + 0.148189i) q^{2} +(1.39991 + 0.454857i) q^{3} +(0.607666 - 1.87020i) q^{4} +(0.0833172 + 0.256424i) q^{6} -3.26086i q^{7} +(0.690983 - 0.224514i) q^{8} +(-0.674207 - 0.489840i) q^{9} +O(q^{10})$$ $$q+(0.107666 + 0.148189i) q^{2} +(1.39991 + 0.454857i) q^{3} +(0.607666 - 1.87020i) q^{4} +(0.0833172 + 0.256424i) q^{6} -3.26086i q^{7} +(0.690983 - 0.224514i) q^{8} +(-0.674207 - 0.489840i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(1.70135 - 2.34171i) q^{12} +(0.174207 - 0.239775i) q^{13} +(0.483224 - 0.351083i) q^{14} +(-3.07411 - 2.23347i) q^{16} +(4.91027 - 1.59545i) q^{17} -0.152649i q^{18} +(-0.534717 - 1.64569i) q^{19} +(1.48322 - 4.56489i) q^{21} +(-0.348414 - 0.113207i) q^{22} +(0.516776 + 0.711281i) q^{23} +1.06943 q^{24} +0.0542883 q^{26} +(-3.31659 - 4.56489i) q^{27} +(-6.09846 - 1.98151i) q^{28} +(-1.82696 + 5.62280i) q^{29} +(1.88486 + 5.80100i) q^{31} -2.14910i q^{32} +(-2.79981 + 0.909715i) q^{33} +(0.765097 + 0.555875i) q^{34} +(-1.32579 + 0.963245i) q^{36} +(4.75401 - 6.54333i) q^{37} +(0.186303 - 0.256424i) q^{38} +(0.352937 - 0.256424i) q^{39} +(0.821270 + 0.596687i) q^{41} +(0.836161 - 0.271685i) q^{42} +3.24199i q^{43} +(1.21533 + 3.74041i) q^{44} +(-0.0497651 + 0.153161i) q^{46} +(4.01342 + 1.30404i) q^{47} +(-3.28756 - 4.52494i) q^{48} -3.63318 q^{49} +7.59963 q^{51} +(-0.342569 - 0.471506i) q^{52} +(7.70424 + 2.50326i) q^{53} +(0.319385 - 0.982966i) q^{54} +(-0.732108 - 2.25320i) q^{56} -2.54703i q^{57} +(-1.02994 + 0.334648i) q^{58} +(4.80261 + 3.48930i) q^{59} +(-0.740748 + 0.538185i) q^{61} +(-0.656711 + 0.903885i) q^{62} +(-1.59730 + 2.19849i) q^{63} +(-5.82975 + 4.23556i) q^{64} +(-0.436254 - 0.316957i) q^{66} +(-6.55093 + 2.12853i) q^{67} -10.1527i q^{68} +(0.399907 + 1.23079i) q^{69} +(-1.84445 + 5.67664i) q^{71} +(-0.575842 - 0.187102i) q^{72} +(5.19215 + 7.14638i) q^{73} +1.48150 q^{74} -3.40270 q^{76} +(3.83337 + 5.27618i) q^{77} +(0.0759986 + 0.0246934i) q^{78} +(2.39818 - 7.38084i) q^{79} +(-1.79397 - 5.52127i) q^{81} +0.185946i q^{82} +(13.8049 - 4.48550i) q^{83} +(-7.63597 - 5.54786i) q^{84} +(-0.480429 + 0.349052i) q^{86} +(-5.11514 + 7.04039i) q^{87} +(-0.854102 + 1.17557i) q^{88} +(6.08901 - 4.42392i) q^{89} +(-0.781873 - 0.568064i) q^{91} +(1.64427 - 0.534255i) q^{92} +8.97820i q^{93} +(0.238863 + 0.735146i) q^{94} +(0.977536 - 3.00855i) q^{96} +(-6.39727 - 2.07860i) q^{97} +(-0.391169 - 0.538398i) q^{98} +1.66673 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10})$$ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 $$8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100})$$ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{3}{10}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.107666 + 0.148189i 0.0761313 + 0.104786i 0.845384 0.534159i $$-0.179371\pi$$
−0.769253 + 0.638944i $$0.779371\pi$$
$$3$$ 1.39991 + 0.454857i 0.808237 + 0.262612i 0.683851 0.729622i $$-0.260304\pi$$
0.124386 + 0.992234i $$0.460304\pi$$
$$4$$ 0.607666 1.87020i 0.303833 0.935102i
$$5$$ 0 0
$$6$$ 0.0833172 + 0.256424i 0.0340141 + 0.104685i
$$7$$ 3.26086i 1.23249i −0.787555 0.616244i $$-0.788654\pi$$
0.787555 0.616244i $$-0.211346\pi$$
$$8$$ 0.690983 0.224514i 0.244299 0.0793777i
$$9$$ −0.674207 0.489840i −0.224736 0.163280i
$$10$$ 0 0
$$11$$ −1.61803 + 1.17557i −0.487856 + 0.354448i −0.804359 0.594144i $$-0.797491\pi$$
0.316503 + 0.948591i $$0.397491\pi$$
$$12$$ 1.70135 2.34171i 0.491138 0.675993i
$$13$$ 0.174207 0.239775i 0.0483163 0.0665017i −0.784175 0.620539i $$-0.786914\pi$$
0.832492 + 0.554038i $$0.186914\pi$$
$$14$$ 0.483224 0.351083i 0.129147 0.0938308i
$$15$$ 0 0
$$16$$ −3.07411 2.23347i −0.768528 0.558369i
$$17$$ 4.91027 1.59545i 1.19092 0.386952i 0.354505 0.935054i $$-0.384649\pi$$
0.836412 + 0.548102i $$0.184649\pi$$
$$18$$ 0.152649i 0.0359798i
$$19$$ −0.534717 1.64569i −0.122672 0.377547i 0.870797 0.491642i $$-0.163603\pi$$
−0.993470 + 0.114095i $$0.963603\pi$$
$$20$$ 0 0
$$21$$ 1.48322 4.56489i 0.323666 0.996142i
$$22$$ −0.348414 0.113207i −0.0742821 0.0241357i
$$23$$ 0.516776 + 0.711281i 0.107755 + 0.148312i 0.859489 0.511155i $$-0.170782\pi$$
−0.751734 + 0.659467i $$0.770782\pi$$
$$24$$ 1.06943 0.218297
$$25$$ 0 0
$$26$$ 0.0542883 0.0106468
$$27$$ −3.31659 4.56489i −0.638278 0.878514i
$$28$$ −6.09846 1.98151i −1.15250 0.374470i
$$29$$ −1.82696 + 5.62280i −0.339258 + 1.04413i 0.625329 + 0.780361i $$0.284965\pi$$
−0.964587 + 0.263766i $$0.915035\pi$$
$$30$$ 0 0
$$31$$ 1.88486 + 5.80100i 0.338531 + 1.04189i 0.964957 + 0.262409i $$0.0845170\pi$$
−0.626426 + 0.779481i $$0.715483\pi$$
$$32$$ 2.14910i 0.379912i
$$33$$ −2.79981 + 0.909715i −0.487385 + 0.158361i
$$34$$ 0.765097 + 0.555875i 0.131213 + 0.0953318i
$$35$$ 0 0
$$36$$ −1.32579 + 0.963245i −0.220965 + 0.160541i
$$37$$ 4.75401 6.54333i 0.781554 1.07572i −0.213554 0.976931i $$-0.568504\pi$$
0.995109 0.0987860i $$-0.0314959\pi$$
$$38$$ 0.186303 0.256424i 0.0302223 0.0415974i
$$39$$ 0.352937 0.256424i 0.0565152 0.0410607i
$$40$$ 0 0
$$41$$ 0.821270 + 0.596687i 0.128261 + 0.0931869i 0.650066 0.759878i $$-0.274741\pi$$
−0.521805 + 0.853065i $$0.674741\pi$$
$$42$$ 0.836161 0.271685i 0.129022 0.0419219i
$$43$$ 3.24199i 0.494399i 0.968965 + 0.247200i $$0.0795103\pi$$
−0.968965 + 0.247200i $$0.920490\pi$$
$$44$$ 1.21533 + 3.74041i 0.183218 + 0.563887i
$$45$$ 0 0
$$46$$ −0.0497651 + 0.153161i −0.00733747 + 0.0225824i
$$47$$ 4.01342 + 1.30404i 0.585417 + 0.190214i 0.586726 0.809786i $$-0.300417\pi$$
−0.00130878 + 0.999999i $$0.500417\pi$$
$$48$$ −3.28756 4.52494i −0.474519 0.653119i
$$49$$ −3.63318 −0.519026
$$50$$ 0 0
$$51$$ 7.59963 1.06416
$$52$$ −0.342569 0.471506i −0.0475058 0.0653861i
$$53$$ 7.70424 + 2.50326i 1.05826 + 0.343849i 0.785905 0.618348i $$-0.212198\pi$$
0.272355 + 0.962197i $$0.412198\pi$$
$$54$$ 0.319385 0.982966i 0.0434628 0.133765i
$$55$$ 0 0
$$56$$ −0.732108 2.25320i −0.0978320 0.301096i
$$57$$ 2.54703i 0.337363i
$$58$$ −1.02994 + 0.334648i −0.135238 + 0.0439414i
$$59$$ 4.80261 + 3.48930i 0.625246 + 0.454268i 0.854750 0.519040i $$-0.173710\pi$$
−0.229504 + 0.973308i $$0.573710\pi$$
$$60$$ 0 0
$$61$$ −0.740748 + 0.538185i −0.0948431 + 0.0689075i −0.634196 0.773172i $$-0.718669\pi$$
0.539353 + 0.842080i $$0.318669\pi$$
$$62$$ −0.656711 + 0.903885i −0.0834024 + 0.114794i
$$63$$ −1.59730 + 2.19849i −0.201241 + 0.276984i
$$64$$ −5.82975 + 4.23556i −0.728719 + 0.529445i
$$65$$ 0 0
$$66$$ −0.436254 0.316957i −0.0536992 0.0390147i
$$67$$ −6.55093 + 2.12853i −0.800323 + 0.260041i −0.680494 0.732754i $$-0.738235\pi$$
−0.119829 + 0.992794i $$0.538235\pi$$
$$68$$ 10.1527i 1.23120i
$$69$$ 0.399907 + 1.23079i 0.0481431 + 0.148169i
$$70$$ 0 0
$$71$$ −1.84445 + 5.67664i −0.218896 + 0.673694i 0.779958 + 0.625832i $$0.215241\pi$$
−0.998854 + 0.0478614i $$0.984759\pi$$
$$72$$ −0.575842 0.187102i −0.0678636 0.0220502i
$$73$$ 5.19215 + 7.14638i 0.607695 + 0.836420i 0.996385 0.0849481i $$-0.0270724\pi$$
−0.388690 + 0.921368i $$0.627072\pi$$
$$74$$ 1.48150 0.172220
$$75$$ 0 0
$$76$$ −3.40270 −0.390317
$$77$$ 3.83337 + 5.27618i 0.436853 + 0.601276i
$$78$$ 0.0759986 + 0.0246934i 0.00860514 + 0.00279598i
$$79$$ 2.39818 7.38084i 0.269816 0.830409i −0.720728 0.693218i $$-0.756192\pi$$
0.990545 0.137191i $$-0.0438075\pi$$
$$80$$ 0 0
$$81$$ −1.79397 5.52127i −0.199330 0.613474i
$$82$$ 0.185946i 0.0205343i
$$83$$ 13.8049 4.48550i 1.51529 0.492347i 0.570856 0.821050i $$-0.306612\pi$$
0.944433 + 0.328703i $$0.106612\pi$$
$$84$$ −7.63597 5.54786i −0.833153 0.605321i
$$85$$ 0 0
$$86$$ −0.480429 + 0.349052i −0.0518059 + 0.0376392i
$$87$$ −5.11514 + 7.04039i −0.548401 + 0.754809i
$$88$$ −0.854102 + 1.17557i −0.0910476 + 0.125316i
$$89$$ 6.08901 4.42392i 0.645433 0.468935i −0.216279 0.976332i $$-0.569392\pi$$
0.861713 + 0.507397i $$0.169392\pi$$
$$90$$ 0 0
$$91$$ −0.781873 0.568064i −0.0819625 0.0595493i
$$92$$ 1.64427 0.534255i 0.171427 0.0556999i
$$93$$ 8.97820i 0.930996i
$$94$$ 0.238863 + 0.735146i 0.0246369 + 0.0758245i
$$95$$ 0 0
$$96$$ 0.977536 3.00855i 0.0997694 0.307058i
$$97$$ −6.39727 2.07860i −0.649544 0.211050i −0.0343310 0.999411i $$-0.510930\pi$$
−0.615213 + 0.788361i $$0.710930\pi$$
$$98$$ −0.391169 0.538398i −0.0395141 0.0543865i
$$99$$ 1.66673 0.167513
$$100$$ 0 0
$$101$$ −12.1955 −1.21350 −0.606748 0.794894i $$-0.707526\pi$$
−0.606748 + 0.794894i $$0.707526\pi$$
$$102$$ 0.818220 + 1.12618i 0.0810159 + 0.111509i
$$103$$ −1.31379 0.426878i −0.129452 0.0420615i 0.243575 0.969882i $$-0.421680\pi$$
−0.373027 + 0.927821i $$0.621680\pi$$
$$104$$ 0.0665412 0.204793i 0.00652490 0.0200816i
$$105$$ 0 0
$$106$$ 0.458527 + 1.41120i 0.0445361 + 0.137068i
$$107$$ 15.8285i 1.53020i 0.643911 + 0.765101i $$0.277311\pi$$
−0.643911 + 0.765101i $$0.722689\pi$$
$$108$$ −10.5527 + 3.42877i −1.01543 + 0.329933i
$$109$$ −1.62108 1.17779i −0.155272 0.112811i 0.507437 0.861689i $$-0.330593\pi$$
−0.662708 + 0.748878i $$0.730593\pi$$
$$110$$ 0 0
$$111$$ 9.63145 6.99766i 0.914177 0.664188i
$$112$$ −7.28304 + 10.0242i −0.688182 + 0.947202i
$$113$$ 6.12912 8.43601i 0.576579 0.793593i −0.416736 0.909028i $$-0.636826\pi$$
0.993315 + 0.115434i $$0.0368260\pi$$
$$114$$ 0.377443 0.274228i 0.0353508 0.0256838i
$$115$$ 0 0
$$116$$ 9.40559 + 6.83356i 0.873288 + 0.634481i
$$117$$ −0.234903 + 0.0763247i −0.0217168 + 0.00705622i
$$118$$ 1.08737i 0.100101i
$$119$$ −5.20252 16.0117i −0.476914 1.46779i
$$120$$ 0 0
$$121$$ −2.16312 + 6.65740i −0.196647 + 0.605218i
$$122$$ −0.159507 0.0518268i −0.0144410 0.00469218i
$$123$$ 0.878294 + 1.20887i 0.0791931 + 0.109000i
$$124$$ 11.9944 1.07713
$$125$$ 0 0
$$126$$ −0.497767 −0.0443446
$$127$$ 3.43858 + 4.73280i 0.305125 + 0.419969i 0.933853 0.357657i $$-0.116424\pi$$
−0.628728 + 0.777625i $$0.716424\pi$$
$$128$$ −5.34317 1.73610i −0.472274 0.153451i
$$129$$ −1.47464 + 4.53849i −0.129835 + 0.399591i
$$130$$ 0 0
$$131$$ −0.462488 1.42339i −0.0404077 0.124362i 0.928818 0.370537i $$-0.120826\pi$$
−0.969225 + 0.246175i $$0.920826\pi$$
$$132$$ 5.78902i 0.503870i
$$133$$ −5.36635 + 1.74363i −0.465322 + 0.151192i
$$134$$ −1.02074 0.741608i −0.0881782 0.0640652i
$$135$$ 0 0
$$136$$ 3.03472 2.20485i 0.260225 0.189064i
$$137$$ −4.61345 + 6.34987i −0.394154 + 0.542506i −0.959265 0.282509i $$-0.908833\pi$$
0.565111 + 0.825015i $$0.308833\pi$$
$$138$$ −0.139333 + 0.191776i −0.0118608 + 0.0163250i
$$139$$ 4.36183 3.16906i 0.369966 0.268796i −0.387231 0.921983i $$-0.626568\pi$$
0.757197 + 0.653187i $$0.226568\pi$$
$$140$$ 0 0
$$141$$ 5.02526 + 3.65106i 0.423203 + 0.307475i
$$142$$ −1.03980 + 0.337852i −0.0872583 + 0.0283519i
$$143$$ 0.592757i 0.0495689i
$$144$$ 0.978544 + 3.01165i 0.0815453 + 0.250971i
$$145$$ 0 0
$$146$$ −0.500000 + 1.53884i −0.0413803 + 0.127355i
$$147$$ −5.08611 1.65258i −0.419495 0.136302i
$$148$$ −9.34851 12.8671i −0.768443 1.05767i
$$149$$ −18.8229 −1.54203 −0.771015 0.636817i $$-0.780251\pi$$
−0.771015 + 0.636817i $$0.780251\pi$$
$$150$$ 0 0
$$151$$ −3.88797 −0.316398 −0.158199 0.987407i $$-0.550569\pi$$
−0.158199 + 0.987407i $$0.550569\pi$$
$$152$$ −0.738960 1.01709i −0.0599376 0.0824970i
$$153$$ −4.09205 1.32959i −0.330823 0.107491i
$$154$$ −0.369150 + 1.13613i −0.0297470 + 0.0915518i
$$155$$ 0 0
$$156$$ −0.265097 0.815884i −0.0212247 0.0653230i
$$157$$ 4.28378i 0.341883i 0.985281 + 0.170941i $$0.0546808\pi$$
−0.985281 + 0.170941i $$0.945319\pi$$
$$158$$ 1.35196 0.439279i 0.107556 0.0349472i
$$159$$ 9.64660 + 7.00866i 0.765025 + 0.555823i
$$160$$ 0 0
$$161$$ 2.31939 1.68513i 0.182793 0.132807i
$$162$$ 0.625044 0.860299i 0.0491081 0.0675915i
$$163$$ −9.24370 + 12.7229i −0.724023 + 0.996531i 0.275358 + 0.961342i $$0.411204\pi$$
−0.999381 + 0.0351898i $$0.988796\pi$$
$$164$$ 1.61498 1.17335i 0.126109 0.0916236i
$$165$$ 0 0
$$166$$ 2.15102 + 1.56281i 0.166952 + 0.121298i
$$167$$ −20.0036 + 6.49956i −1.54792 + 0.502951i −0.953549 0.301237i $$-0.902601\pi$$
−0.594375 + 0.804188i $$0.702601\pi$$
$$168$$ 3.48727i 0.269049i
$$169$$ 3.99008 + 12.2802i 0.306929 + 0.944630i
$$170$$ 0 0
$$171$$ −0.445615 + 1.37146i −0.0340770 + 0.104878i
$$172$$ 6.06318 + 1.97005i 0.462313 + 0.150215i
$$173$$ 4.21244 + 5.79793i 0.320266 + 0.440808i 0.938548 0.345148i $$-0.112171\pi$$
−0.618283 + 0.785956i $$0.712171\pi$$
$$174$$ −1.59404 −0.120844
$$175$$ 0 0
$$176$$ 7.59963 0.572843
$$177$$ 5.13607 + 7.06920i 0.386051 + 0.531353i
$$178$$ 1.31116 + 0.426020i 0.0982753 + 0.0319316i
$$179$$ −2.48429 + 7.64586i −0.185685 + 0.571479i −0.999959 0.00900088i $$-0.997135\pi$$
0.814275 + 0.580480i $$0.197135\pi$$
$$180$$ 0 0
$$181$$ −6.37104 19.6080i −0.473555 1.45745i −0.847896 0.530162i $$-0.822131\pi$$
0.374341 0.927291i $$-0.377869\pi$$
$$182$$ 0.177026i 0.0131221i
$$183$$ −1.28178 + 0.416474i −0.0947516 + 0.0307867i
$$184$$ 0.516776 + 0.375460i 0.0380972 + 0.0276793i
$$185$$ 0 0
$$186$$ −1.33047 + 0.966645i −0.0975550 + 0.0708779i
$$187$$ −6.06943 + 8.35386i −0.443841 + 0.610895i
$$188$$ 4.87763 6.71349i 0.355738 0.489631i
$$189$$ −14.8855 + 10.8149i −1.08276 + 0.786670i
$$190$$ 0 0
$$191$$ −14.5868 10.5979i −1.05546 0.766840i −0.0822207 0.996614i $$-0.526201\pi$$
−0.973244 + 0.229774i $$0.926201\pi$$
$$192$$ −10.0877 + 3.27769i −0.728016 + 0.236547i
$$193$$ 6.78859i 0.488653i −0.969693 0.244327i $$-0.921433\pi$$
0.969693 0.244327i $$-0.0785669\pi$$
$$194$$ −0.380741 1.17180i −0.0273356 0.0841304i
$$195$$ 0 0
$$196$$ −2.20776 + 6.79478i −0.157697 + 0.485342i
$$197$$ 7.60405 + 2.47071i 0.541766 + 0.176031i 0.567101 0.823648i $$-0.308065\pi$$
−0.0253343 + 0.999679i $$0.508065\pi$$
$$198$$ 0.179450 + 0.246992i 0.0127530 + 0.0175529i
$$199$$ 5.20485 0.368962 0.184481 0.982836i $$-0.440940\pi$$
0.184481 + 0.982836i $$0.440940\pi$$
$$200$$ 0 0
$$201$$ −10.1389 −0.715141
$$202$$ −1.31304 1.80724i −0.0923850 0.127157i
$$203$$ 18.3351 + 5.95745i 1.28687 + 0.418131i
$$204$$ 4.61803 14.2128i 0.323327 0.995098i
$$205$$ 0 0
$$206$$ −0.0781921 0.240650i −0.00544790 0.0167669i
$$207$$ 0.732688i 0.0509254i
$$208$$ −1.07106 + 0.348010i −0.0742649 + 0.0241301i
$$209$$ 2.79981 + 2.03418i 0.193667 + 0.140707i
$$210$$ 0 0
$$211$$ −13.4313 + 9.75839i −0.924646 + 0.671795i −0.944676 0.328004i $$-0.893624\pi$$
0.0200297 + 0.999799i $$0.493624\pi$$
$$212$$ 9.36321 12.8874i 0.643068 0.885107i
$$213$$ −5.16413 + 7.10781i −0.353840 + 0.487019i
$$214$$ −2.34562 + 1.70419i −0.160343 + 0.116496i
$$215$$ 0 0
$$216$$ −3.31659 2.40964i −0.225665 0.163955i
$$217$$ 18.9162 6.14625i 1.28412 0.417235i
$$218$$ 0.367035i 0.0248587i
$$219$$ 4.01794 + 12.3660i 0.271507 + 0.835613i
$$220$$ 0 0
$$221$$ 0.472856 1.45530i 0.0318077 0.0978941i
$$222$$ 2.07396 + 0.673869i 0.139195 + 0.0452272i
$$223$$ 3.89589 + 5.36223i 0.260888 + 0.359082i 0.919287 0.393587i $$-0.128766\pi$$
−0.658399 + 0.752669i $$0.728766\pi$$
$$224$$ −7.00792 −0.468236
$$225$$ 0 0
$$226$$ 1.91002 0.127053
$$227$$ −7.87158 10.8343i −0.522455 0.719097i 0.463502 0.886096i $$-0.346593\pi$$
−0.985957 + 0.166998i $$0.946593\pi$$
$$228$$ −4.76347 1.54774i −0.315468 0.102502i
$$229$$ −3.11697 + 9.59304i −0.205975 + 0.633926i 0.793697 + 0.608313i $$0.208154\pi$$
−0.999672 + 0.0256124i $$0.991846\pi$$
$$230$$ 0 0
$$231$$ 2.96645 + 9.12979i 0.195178 + 0.600696i
$$232$$ 4.29544i 0.282009i
$$233$$ 20.9285 6.80007i 1.37107 0.445488i 0.471346 0.881948i $$-0.343768\pi$$
0.899723 + 0.436461i $$0.143768\pi$$
$$234$$ −0.0366015 0.0265926i −0.00239272 0.00173841i
$$235$$ 0 0
$$236$$ 9.44408 6.86153i 0.614757 0.446647i
$$237$$ 6.71445 9.24165i 0.436151 0.600310i
$$238$$ 1.81263 2.49487i 0.117495 0.161718i
$$239$$ 6.11640 4.44383i 0.395637 0.287447i −0.372124 0.928183i $$-0.621371\pi$$
0.767762 + 0.640736i $$0.221371\pi$$
$$240$$ 0 0
$$241$$ 16.4995 + 11.9876i 1.06283 + 0.772190i 0.974610 0.223911i $$-0.0718825\pi$$
0.0882188 + 0.996101i $$0.471883\pi$$
$$242$$ −1.21945 + 0.396223i −0.0783892 + 0.0254702i
$$243$$ 8.38230i 0.537725i
$$244$$ 0.556388 + 1.71239i 0.0356191 + 0.109624i
$$245$$ 0 0
$$246$$ −0.0845790 + 0.260307i −0.00539256 + 0.0165966i
$$247$$ −0.487747 0.158479i −0.0310346 0.0100838i
$$248$$ 2.60481 + 3.58521i 0.165406 + 0.227661i
$$249$$ 21.3659 1.35401
$$250$$ 0 0
$$251$$ 10.5717 0.667278 0.333639 0.942701i $$-0.391723\pi$$
0.333639 + 0.942701i $$0.391723\pi$$
$$252$$ 3.14100 + 4.32322i 0.197865 + 0.272337i
$$253$$ −1.67232 0.543370i −0.105138 0.0341614i
$$254$$ −0.331133 + 1.01912i −0.0207771 + 0.0639455i
$$255$$ 0 0
$$256$$ 4.13553 + 12.7279i 0.258471 + 0.795491i
$$257$$ 20.2700i 1.26441i −0.774801 0.632205i $$-0.782150\pi$$
0.774801 0.632205i $$-0.217850\pi$$
$$258$$ −0.831324 + 0.270114i −0.0517560 + 0.0168165i
$$259$$ −21.3369 15.5021i −1.32581 0.963256i
$$260$$ 0 0
$$261$$ 3.98602 2.89601i 0.246728 0.179259i
$$262$$ 0.161137 0.221786i 0.00995509 0.0137020i
$$263$$ 16.5114 22.7260i 1.01814 1.40135i 0.104636 0.994511i $$-0.466632\pi$$
0.913501 0.406835i $$-0.133368\pi$$
$$264$$ −1.73038 + 1.25719i −0.106498 + 0.0773750i
$$265$$ 0 0
$$266$$ −0.836161 0.607507i −0.0512683 0.0372486i
$$267$$ 10.5363 3.42345i 0.644811 0.209512i
$$268$$ 13.5450i 0.827393i
$$269$$ −6.28015 19.3283i −0.382907 1.17847i −0.937987 0.346670i $$-0.887312\pi$$
0.555080 0.831797i $$-0.312688\pi$$
$$270$$ 0 0
$$271$$ 9.71756 29.9076i 0.590300 1.81676i 0.0134456 0.999910i $$-0.495720\pi$$
0.576854 0.816847i $$-0.304280\pi$$
$$272$$ −18.6581 6.06239i −1.13132 0.367587i
$$273$$ −0.836161 1.15088i −0.0506068 0.0696542i
$$274$$ −1.43769 −0.0868543
$$275$$ 0 0
$$276$$ 2.54483 0.153181
$$277$$ −8.18813 11.2700i −0.491977 0.677148i 0.488774 0.872410i $$-0.337444\pi$$
−0.980751 + 0.195262i $$0.937444\pi$$
$$278$$ 0.939241 + 0.305178i 0.0563319 + 0.0183033i
$$279$$ 1.57078 4.83435i 0.0940399 0.289425i
$$280$$ 0 0
$$281$$ 7.99664 + 24.6111i 0.477040 + 1.46818i 0.843187 + 0.537620i $$0.180677\pi$$
−0.366147 + 0.930557i $$0.619323\pi$$
$$282$$ 1.13778i 0.0677541i
$$283$$ −22.5701 + 7.33348i −1.34166 + 0.435930i −0.889877 0.456200i $$-0.849210\pi$$
−0.451778 + 0.892130i $$0.649210\pi$$
$$284$$ 9.49567 + 6.89901i 0.563464 + 0.409381i
$$285$$ 0 0
$$286$$ −0.0878403 + 0.0638197i −0.00519411 + 0.00377374i
$$287$$ 1.94571 2.67804i 0.114852 0.158080i
$$288$$ −1.05272 + 1.44894i −0.0620320 + 0.0853797i
$$289$$ 7.81207 5.67580i 0.459533 0.333871i
$$290$$ 0 0
$$291$$ −8.01011 5.81969i −0.469561 0.341156i
$$292$$ 16.5203 5.36776i 0.966776 0.314124i
$$293$$ 12.3029i 0.718742i −0.933195 0.359371i $$-0.882991\pi$$
0.933195 0.359371i $$-0.117009\pi$$
$$294$$ −0.302706 0.931634i −0.0176542 0.0543340i
$$295$$ 0 0
$$296$$ 1.81587 5.58867i 0.105545 0.324835i
$$297$$ 10.7327 + 3.48727i 0.622775 + 0.202352i
$$298$$ −2.02658 2.78935i −0.117397 0.161583i
$$299$$ 0.260574 0.0150694
$$300$$ 0 0
$$301$$ 10.5717 0.609341
$$302$$ −0.418601 0.576155i −0.0240878 0.0331540i
$$303$$ −17.0725 5.54721i −0.980792 0.318679i
$$304$$ −2.03182 + 6.25331i −0.116533 + 0.358652i
$$305$$ 0 0
$$306$$ −0.243544 0.749550i −0.0139225 0.0428489i
$$307$$ 4.28249i 0.244415i −0.992505 0.122207i $$-0.961003\pi$$
0.992505 0.122207i $$-0.0389973\pi$$
$$308$$ 12.1969 3.96302i 0.694984 0.225814i
$$309$$ −1.64502 1.19518i −0.0935820 0.0679913i
$$310$$ 0 0
$$311$$ −20.7486 + 15.0747i −1.17655 + 0.854810i −0.991778 0.127972i $$-0.959153\pi$$
−0.184768 + 0.982782i $$0.559153\pi$$
$$312$$ 0.186303 0.256424i 0.0105473 0.0145171i
$$313$$ −13.1377 + 18.0825i −0.742589 + 1.02209i 0.255876 + 0.966709i $$0.417636\pi$$
−0.998466 + 0.0553767i $$0.982364\pi$$
$$314$$ −0.634810 + 0.461216i −0.0358244 + 0.0260280i
$$315$$ 0 0
$$316$$ −12.3464 8.97016i −0.694538 0.504611i
$$317$$ 20.8499 6.77453i 1.17105 0.380496i 0.342012 0.939695i $$-0.388892\pi$$
0.829033 + 0.559200i $$0.188892\pi$$
$$318$$ 2.18412i 0.122479i
$$319$$ −3.65392 11.2456i −0.204580 0.629632i
$$320$$ 0 0
$$321$$ −7.19972 + 22.1585i −0.401849 + 1.23676i
$$322$$ 0.499437 + 0.162277i 0.0278325 + 0.00904334i
$$323$$ −5.25121 7.22768i −0.292185 0.402159i
$$324$$ −11.4160 −0.634224
$$325$$ 0 0
$$326$$ −2.88062 −0.159543
$$327$$ −1.73364 2.38615i −0.0958706 0.131955i
$$328$$ 0.701448 + 0.227914i 0.0387310 + 0.0125845i
$$329$$ 4.25228 13.0872i 0.234436 0.721519i
$$330$$ 0 0
$$331$$ −2.76972 8.52431i −0.152237 0.468539i 0.845633 0.533765i $$-0.179223\pi$$
−0.997871 + 0.0652260i $$0.979223\pi$$
$$332$$ 28.5437i 1.56654i
$$333$$ −6.41037 + 2.08286i −0.351286 + 0.114140i
$$334$$ −3.11687 2.26454i −0.170547 0.123910i
$$335$$ 0 0
$$336$$ −14.7552 + 10.7203i −0.804961 + 0.584838i
$$337$$ 17.0949 23.5291i 0.931218 1.28171i −0.0281648 0.999603i $$-0.508966\pi$$
0.959383 0.282108i $$-0.0910337\pi$$
$$338$$ −1.39020 + 1.91344i −0.0756168 + 0.104078i
$$339$$ 12.4174 9.02176i 0.674420 0.489995i
$$340$$ 0 0
$$341$$ −9.86925 7.17043i −0.534450 0.388300i
$$342$$ −0.251213 + 0.0816242i −0.0135841 + 0.00441373i
$$343$$ 10.9787i 0.592795i
$$344$$ 0.727872 + 2.24016i 0.0392443 + 0.120781i
$$345$$ 0 0
$$346$$ −0.405655 + 1.24848i −0.0218081 + 0.0671185i
$$347$$ −13.5974 4.41807i −0.729948 0.237175i −0.0796174 0.996825i $$-0.525370\pi$$
−0.650331 + 0.759651i $$0.725370\pi$$
$$348$$ 10.0587 + 13.8446i 0.539201 + 0.742146i
$$349$$ −5.62382 −0.301036 −0.150518 0.988607i $$-0.548094\pi$$
−0.150518 + 0.988607i $$0.548094\pi$$
$$350$$ 0 0
$$351$$ −1.67232 −0.0892620
$$352$$ 2.52642 + 3.47732i 0.134659 + 0.185342i
$$353$$ 1.81649 + 0.590214i 0.0966821 + 0.0314139i 0.356959 0.934120i $$-0.383814\pi$$
−0.260276 + 0.965534i $$0.583814\pi$$
$$354$$ −0.494600 + 1.52222i −0.0262877 + 0.0809052i
$$355$$ 0 0
$$356$$ −4.57355 14.0759i −0.242398 0.746023i
$$357$$ 24.7813i 1.31156i
$$358$$ −1.40051 + 0.455053i −0.0740192 + 0.0240503i
$$359$$ 17.9639 + 13.0516i 0.948101 + 0.688835i 0.950357 0.311162i $$-0.100718\pi$$
−0.00225634 + 0.999997i $$0.500718\pi$$
$$360$$ 0 0
$$361$$ 12.9490 9.40796i 0.681524 0.495156i
$$362$$ 2.21976 3.05523i 0.116668 0.160580i
$$363$$ −6.05633 + 8.33582i −0.317875 + 0.437517i
$$364$$ −1.53751 + 1.11707i −0.0805875 + 0.0585503i
$$365$$ 0 0
$$366$$ −0.199721 0.145105i −0.0104396 0.00758478i
$$367$$ −20.3954 + 6.62686i −1.06463 + 0.345919i −0.788394 0.615170i $$-0.789087\pi$$
−0.276236 + 0.961090i $$0.589087\pi$$
$$368$$ 3.34077i 0.174149i
$$369$$ −0.261424 0.804582i −0.0136092 0.0418849i
$$370$$ 0 0
$$371$$ 8.16277 25.1224i 0.423790 1.30429i
$$372$$ 16.7911 + 5.45574i 0.870576 + 0.282867i
$$373$$ −13.6013 18.7206i −0.704248 0.969315i −0.999902 0.0140195i $$-0.995537\pi$$
0.295653 0.955295i $$-0.404463\pi$$
$$374$$ −1.89142 −0.0978032
$$375$$ 0 0
$$376$$ 3.06598 0.158116
$$377$$ 1.02994 + 1.41759i 0.0530446 + 0.0730096i
$$378$$ −3.20531 1.04147i −0.164863 0.0535674i
$$379$$ 6.69026 20.5905i 0.343656 1.05766i −0.618644 0.785672i $$-0.712318\pi$$
0.962300 0.271992i $$-0.0876824\pi$$
$$380$$ 0 0
$$381$$ 2.66095 + 8.18955i 0.136324 + 0.419563i
$$382$$ 3.30265i 0.168978i
$$383$$ −5.37804 + 1.74743i −0.274805 + 0.0892896i −0.443178 0.896434i $$-0.646149\pi$$
0.168372 + 0.985723i $$0.446149\pi$$
$$384$$ −6.69026 4.86076i −0.341411 0.248050i
$$385$$ 0 0
$$386$$ 1.00600 0.730899i 0.0512039 0.0372018i
$$387$$ 1.58806 2.18577i 0.0807255 0.111109i
$$388$$ −7.77480 + 10.7011i −0.394706 + 0.543266i
$$389$$ −6.57411 + 4.77637i −0.333321 + 0.242172i −0.741838 0.670579i $$-0.766046\pi$$
0.408518 + 0.912750i $$0.366046\pi$$
$$390$$ 0 0
$$391$$ 3.67232 + 2.66810i 0.185717 + 0.134932i
$$392$$ −2.51047 + 0.815700i −0.126798 + 0.0411991i
$$393$$ 2.20298i 0.111126i
$$394$$ 0.452564 + 1.39285i 0.0227999 + 0.0701708i
$$395$$ 0 0
$$396$$ 1.01282 3.11713i 0.0508959 0.156641i
$$397$$ 19.7524 + 6.41794i 0.991343 + 0.322107i 0.759401 0.650623i $$-0.225492\pi$$
0.231942 + 0.972730i $$0.425492\pi$$
$$398$$ 0.560384 + 0.771303i 0.0280895 + 0.0386619i
$$399$$ −8.30550 −0.415795
$$400$$ 0 0
$$401$$ 30.1195 1.50410 0.752049 0.659107i $$-0.229066\pi$$
0.752049 + 0.659107i $$0.229066\pi$$
$$402$$ −1.09161 1.50247i −0.0544445 0.0749365i
$$403$$ 1.71929 + 0.558632i 0.0856440 + 0.0278274i
$$404$$ −7.41078 + 22.8080i −0.368700 + 1.13474i
$$405$$ 0 0
$$406$$ 1.09124 + 3.35848i 0.0541572 + 0.166679i
$$407$$ 16.1760i 0.801815i
$$408$$ 5.25121 1.70622i 0.259974 0.0844706i
$$409$$ 8.93579 + 6.49223i 0.441846 + 0.321020i 0.786368 0.617758i $$-0.211959\pi$$
−0.344522 + 0.938778i $$0.611959\pi$$
$$410$$ 0 0
$$411$$ −9.34669 + 6.79077i −0.461038 + 0.334964i
$$412$$ −1.59670 + 2.19766i −0.0786636 + 0.108271i
$$413$$ 11.3781 15.6606i 0.559880 0.770608i
$$414$$ 0.108577 0.0788855i 0.00533625 0.00387701i
$$415$$ 0 0
$$416$$ −0.515302 0.374389i −0.0252648 0.0183559i
$$417$$ 7.54763 2.45237i 0.369609 0.120093i
$$418$$ 0.633915i 0.0310058i
$$419$$ 10.1732 + 31.3099i 0.496993 + 1.52959i 0.813827 + 0.581107i $$0.197380\pi$$
−0.316834 + 0.948481i $$0.602620\pi$$
$$420$$ 0 0
$$421$$ −6.26214 + 19.2729i −0.305198 + 0.939304i 0.674405 + 0.738362i $$0.264400\pi$$
−0.979603 + 0.200942i $$0.935600\pi$$
$$422$$ −2.89218 0.939725i −0.140789 0.0457451i
$$423$$ −2.06710 2.84512i −0.100506 0.138335i
$$424$$ 5.88552 0.285826
$$425$$ 0 0
$$426$$ −1.60930 −0.0779709
$$427$$ 1.75494 + 2.41547i 0.0849277 + 0.116893i
$$428$$ 29.6026 + 9.61845i 1.43089 + 0.464926i
$$429$$ −0.269620 + 0.829805i −0.0130174 + 0.0400634i
$$430$$ 0 0
$$431$$ 2.21110 + 6.80506i 0.106505 + 0.327788i 0.990081 0.140500i $$-0.0448710\pi$$
−0.883576 + 0.468288i $$0.844871\pi$$
$$432$$ 21.4405i 1.03156i
$$433$$ 5.21430 1.69423i 0.250583 0.0814195i −0.181032 0.983477i $$-0.557944\pi$$
0.431615 + 0.902058i $$0.357944\pi$$
$$434$$ 2.94744 + 2.14144i 0.141482 + 0.102792i
$$435$$ 0 0
$$436$$ −3.18778 + 2.31606i −0.152667 + 0.110919i
$$437$$ 0.894219 1.23079i 0.0427763 0.0588765i
$$438$$ −1.39991 + 1.92681i −0.0668901 + 0.0920664i
$$439$$ −24.8822 + 18.0780i −1.18756 + 0.862815i −0.993005 0.118076i $$-0.962327\pi$$
−0.194558 + 0.980891i $$0.562327\pi$$
$$440$$ 0 0
$$441$$ 2.44951 + 1.77968i 0.116644 + 0.0847465i
$$442$$ 0.266570 0.0866140i 0.0126795 0.00411981i
$$443$$ 11.3527i 0.539381i 0.962947 + 0.269691i $$0.0869214\pi$$
−0.962947 + 0.269691i $$0.913079\pi$$
$$444$$ −7.23434 22.2650i −0.343327 1.05665i
$$445$$ 0 0
$$446$$ −0.375171 + 1.15466i −0.0177649 + 0.0546747i
$$447$$ −26.3503 8.56172i −1.24633 0.404956i
$$448$$ 13.8116 + 19.0100i 0.652535 + 0.898137i
$$449$$ 15.7661 0.744050 0.372025 0.928223i $$-0.378664\pi$$
0.372025 + 0.928223i $$0.378664\pi$$
$$450$$ 0 0
$$451$$ −2.03029 −0.0956027
$$452$$ −12.0526 16.5890i −0.566907 0.780280i
$$453$$ −5.44279 1.76847i −0.255725 0.0830900i
$$454$$ 0.758027 2.33297i 0.0355760 0.109492i
$$455$$ 0 0
$$456$$ −0.571844 1.75996i −0.0267791 0.0824175i
$$457$$ 4.16714i 0.194931i 0.995239 + 0.0974653i $$0.0310735\pi$$
−0.995239 + 0.0974653i $$0.968926\pi$$
$$458$$ −1.75718 + 0.570941i −0.0821075 + 0.0266783i
$$459$$ −23.5684 17.1234i −1.10008 0.799254i
$$460$$ 0 0
$$461$$ 19.3933 14.0900i 0.903235 0.656239i −0.0360595 0.999350i $$-0.511481\pi$$
0.939295 + 0.343111i $$0.111481\pi$$
$$462$$ −1.03355 + 1.42256i −0.0480852 + 0.0661836i
$$463$$ 24.2900 33.4324i 1.12885 1.55373i 0.338624 0.940922i $$-0.390038\pi$$
0.790229 0.612812i $$-0.209962\pi$$
$$464$$ 18.1747 13.2047i 0.843737 0.613011i
$$465$$ 0 0
$$466$$ 3.26098 + 2.36924i 0.151062 + 0.109753i
$$467$$ −9.88775 + 3.21272i −0.457550 + 0.148667i −0.528719 0.848797i $$-0.677327\pi$$
0.0711682 + 0.997464i $$0.477327\pi$$
$$468$$ 0.485697i 0.0224513i
$$469$$ 6.94082 + 21.3616i 0.320497 + 0.986389i
$$470$$ 0 0
$$471$$ −1.94851 + 5.99689i −0.0897825 + 0.276322i
$$472$$ 4.10192 + 1.33279i 0.188806 + 0.0613468i
$$473$$ −3.81119 5.24565i −0.175239 0.241195i
$$474$$ 2.09243 0.0961086
$$475$$ 0 0
$$476$$ −33.1065 −1.51743
$$477$$ −3.96806 5.46156i −0.181685 0.250068i
$$478$$ 1.31706 + 0.427937i 0.0602407 + 0.0195734i
$$479$$ −11.1271 + 34.2458i −0.508411 + 1.56473i 0.286548 + 0.958066i $$0.407492\pi$$
−0.794959 + 0.606663i $$0.792508\pi$$
$$480$$ 0 0
$$481$$ −0.740748 2.27979i −0.0337752 0.103949i
$$482$$ 3.73571i 0.170157i
$$483$$ 4.01342 1.30404i 0.182617 0.0593358i
$$484$$ 11.1362 + 8.09094i 0.506192 + 0.367770i
$$485$$ 0 0
$$486$$ −1.24217 + 0.902487i −0.0563458 + 0.0409377i
$$487$$ −6.25275 + 8.60617i −0.283339 + 0.389983i −0.926836 0.375466i $$-0.877483\pi$$
0.643497 + 0.765448i $$0.277483\pi$$
$$488$$ −0.391014 + 0.538185i −0.0177004 + 0.0243625i
$$489$$ −18.7274 + 13.6063i −0.846883 + 0.615296i
$$490$$ 0 0
$$491$$ 14.2947 + 10.3857i 0.645112 + 0.468701i 0.861603 0.507583i $$-0.169461\pi$$
−0.216491 + 0.976285i $$0.569461\pi$$
$$492$$ 2.79454 0.908000i 0.125987 0.0409358i
$$493$$ 30.5243i 1.37475i
$$494$$ −0.0290289 0.0893417i −0.00130607 0.00401967i
$$495$$ 0 0
$$496$$ 7.16211 22.0427i 0.321588 0.989747i
$$497$$ 18.5107 + 6.01450i 0.830319 + 0.269787i
$$498$$ 2.30038 + 3.16620i 0.103082 + 0.141881i
$$499$$ 9.41734 0.421578 0.210789 0.977532i $$-0.432397\pi$$
0.210789 + 0.977532i $$0.432397\pi$$
$$500$$ 0 0
$$501$$ −30.9595 −1.38317
$$502$$ 1.13821 + 1.56661i 0.0508007 + 0.0699211i
$$503$$ −17.1316 5.56641i −0.763862 0.248194i −0.0989268 0.995095i $$-0.531541\pi$$
−0.664935 + 0.746901i $$0.731541\pi$$
$$504$$ −0.610113 + 1.87774i −0.0271766 + 0.0836410i
$$505$$ 0 0
$$506$$ −0.0995303 0.306323i −0.00442466 0.0136177i
$$507$$ 19.0060i 0.844088i
$$508$$ 10.9408 3.55489i 0.485420 0.157723i
$$509$$ −12.9835 9.43307i −0.575484 0.418114i 0.261609 0.965174i $$-0.415747\pi$$
−0.837093 + 0.547060i $$0.815747\pi$$
$$510$$ 0 0
$$511$$ 23.3033 16.9308i 1.03088 0.748976i
$$512$$ −8.04540 + 11.0735i −0.355560 + 0.489386i
$$513$$ −5.73896 + 7.89900i −0.253381 + 0.348749i
$$514$$ 3.00380 2.18239i 0.132492 0.0962611i
$$515$$ 0 0
$$516$$ 7.59180 + 5.51577i 0.334210 + 0.242818i
$$517$$ −8.02684 + 2.60808i −0.353020 + 0.114703i
$$518$$ 4.83095i 0.212260i
$$519$$ 3.25979 + 10.0326i 0.143089 + 0.440383i
$$520$$ 0 0
$$521$$ −0.680052 + 2.09298i −0.0297936 + 0.0916953i −0.964848 0.262810i $$-0.915351\pi$$
0.935054 + 0.354505i $$0.115351\pi$$
$$522$$ 0.858316 + 0.278884i 0.0375675 + 0.0122064i
$$523$$ 4.37070 + 6.01575i 0.191117 + 0.263050i 0.893813 0.448440i $$-0.148020\pi$$
−0.702695 + 0.711491i $$0.748020\pi$$
$$524$$ −2.94307 −0.128569
$$525$$ 0 0
$$526$$ 5.14547 0.224353
$$527$$ 18.5103 + 25.4773i 0.806323 + 1.10981i
$$528$$ 10.6388 + 3.45675i 0.462993 + 0.150436i
$$529$$ 6.86853 21.1392i 0.298632 0.919094i
$$530$$ 0 0
$$531$$ −1.52875 4.70502i −0.0663423 0.204181i
$$532$$ 11.0957i 0.481061i
$$533$$ 0.286142 0.0929731i 0.0123942 0.00402711i
$$534$$ 1.64172 + 1.19278i 0.0710441 + 0.0516165i
$$535$$ 0 0
$$536$$ −4.04870 + 2.94155i −0.174877 + 0.127056i
$$537$$ −6.95555 + 9.57350i −0.300154 + 0.413127i
$$538$$ 2.18809 3.01165i 0.0943353 0.129841i
$$539$$ 5.87861 4.27106i 0.253210 0.183968i
$$540$$ 0 0
$$541$$ −16.7041 12.1362i −0.718165 0.521777i 0.167632 0.985850i $$-0.446388\pi$$
−0.885797 + 0.464072i $$0.846388\pi$$
$$542$$ 5.47824 1.77999i 0.235310 0.0764570i
$$543$$ 30.3473i 1.30233i
$$544$$ −3.42878 10.5527i −0.147008 0.452443i
$$545$$ 0 0
$$546$$ 0.0805217 0.247820i 0.00344601 0.0106057i
$$547$$ −29.8405 9.69577i −1.27589 0.414561i −0.408758 0.912643i $$-0.634038\pi$$
−0.867130 + 0.498082i $$0.834038\pi$$
$$548$$ 9.07211 + 12.4867i 0.387541 + 0.533405i
$$549$$ 0.763042 0.0325658
$$550$$ 0 0
$$551$$ 10.2303 0.435825
$$552$$ 0.552658 + 0.760668i 0.0235227 + 0.0323762i
$$553$$ −24.0678 7.82012i −1.02347 0.332545i
$$554$$ 0.788511 2.42679i 0.0335006 0.103104i
$$555$$ 0 0
$$556$$ −3.27624 10.0832i −0.138944 0.427625i
$$557$$ 22.3515i 0.947064i 0.880776 + 0.473532i $$0.157021\pi$$
−0.880776 + 0.473532i $$0.842979\pi$$
$$558$$ 0.885518 0.287722i 0.0374870 0.0121803i
$$559$$ 0.777350 + 0.564778i 0.0328784 + 0.0238875i
$$560$$ 0 0
$$561$$ −12.2965 + 8.93390i −0.519157 + 0.377189i
$$562$$ −2.78614 + 3.83480i −0.117526 + 0.161761i
$$563$$ −20.2000 + 27.8029i −0.851329 + 1.17175i 0.132240 + 0.991218i $$0.457783\pi$$
−0.983568 + 0.180536i $$0.942217\pi$$
$$564$$ 9.88191 7.17963i 0.416104 0.302317i
$$565$$ 0 0
$$566$$ −3.51678 2.55509i −0.147821 0.107398i
$$567$$ −18.0041 + 5.84987i −0.756099 + 0.245672i
$$568$$ 4.33657i 0.181958i
$$569$$ −9.93991 30.5919i −0.416703 1.28248i −0.910719 0.413026i $$-0.864472\pi$$
0.494017 0.869452i $$-0.335528\pi$$
$$570$$ 0 0
$$571$$ −8.39501 + 25.8372i −0.351320 + 1.08125i 0.606792 + 0.794861i $$0.292456\pi$$
−0.958112 + 0.286392i $$0.907544\pi$$
$$572$$ 1.10858 + 0.360198i 0.0463519 + 0.0150607i
$$573$$ −15.5996 21.4710i −0.651684 0.896966i
$$574$$ 0.606344 0.0253083
$$575$$ 0 0
$$576$$ 6.00521 0.250217
$$577$$ 8.14100 + 11.2051i 0.338914 + 0.466476i 0.944124 0.329591i $$-0.106911\pi$$
−0.605210 + 0.796066i $$0.706911\pi$$
$$578$$ 1.68219 + 0.546575i 0.0699697 + 0.0227345i
$$579$$ 3.08784 9.50340i 0.128326 0.394948i
$$580$$ 0 0
$$581$$ −14.6266 45.0159i −0.606812 1.86757i
$$582$$ 1.81360i 0.0751759i
$$583$$ −15.4085 + 5.00652i −0.638154 + 0.207349i
$$584$$ 5.19215 + 3.77232i 0.214853 + 0.156100i
$$585$$ 0 0
$$586$$ 1.82315 1.32460i 0.0753138 0.0547187i
$$587$$ −25.9507 + 35.7180i −1.07110 + 1.47424i −0.202139 + 0.979357i $$0.564789\pi$$
−0.868959 + 0.494884i $$0.835211\pi$$
$$588$$ −6.18131 + 8.50785i −0.254913 + 0.350858i
$$589$$ 8.53877 6.20378i 0.351834 0.255622i
$$590$$ 0 0
$$591$$ 9.52115 + 6.91752i 0.391648 + 0.284549i
$$592$$ −29.2287 + 9.49699i −1.20129 + 0.390324i
$$593$$ 16.2531i 0.667437i −0.942673 0.333718i $$-0.891697\pi$$
0.942673 0.333718i $$-0.108303\pi$$
$$594$$ 0.638770 + 1.96593i 0.0262091 + 0.0806632i
$$595$$ 0 0
$$596$$ −11.4380 + 35.2026i −0.468520 + 1.44196i
$$597$$ 7.28630 + 2.36746i 0.298208 + 0.0968938i
$$598$$ 0.0280549 + 0.0386142i 0.00114725 + 0.00157905i
$$599$$ −30.4822 −1.24547 −0.622734 0.782433i $$-0.713978\pi$$
−0.622734 + 0.782433i $$0.713978\pi$$
$$600$$ 0 0
$$601$$ −28.9162 −1.17952 −0.589758 0.807580i $$-0.700777\pi$$
−0.589758 + 0.807580i $$0.700777\pi$$
$$602$$ 1.13821 + 1.56661i 0.0463899 + 0.0638502i
$$603$$ 5.45932 + 1.77384i 0.222321 + 0.0722364i
$$604$$ −2.36259 + 7.27129i −0.0961322 + 0.295865i
$$605$$ 0 0
$$606$$ −1.01609 3.12721i −0.0412760 0.127034i
$$607$$ 8.23276i 0.334157i −0.985944 0.167079i $$-0.946567\pi$$
0.985944 0.167079i $$-0.0534334\pi$$
$$608$$ −3.53676 + 1.14916i −0.143435 + 0.0466047i
$$609$$ 22.9577 + 16.6797i 0.930293 + 0.675897i
$$610$$ 0 0
$$611$$ 1.01184 0.735146i 0.0409347 0.0297408i
$$612$$ −4.97320 + 6.84503i −0.201030 + 0.276694i
$$613$$ 2.82026 3.88175i 0.113909 0.156783i −0.748256 0.663411i $$-0.769108\pi$$
0.862165 + 0.506628i $$0.169108\pi$$
$$614$$ 0.634619 0.461078i 0.0256111 0.0186076i
$$615$$ 0 0
$$616$$ 3.83337 + 2.78510i 0.154451 + 0.112215i
$$617$$ −1.93239 + 0.627872i −0.0777951 + 0.0252772i −0.347656 0.937622i $$-0.613022\pi$$
0.269861 + 0.962899i $$0.413022\pi$$
$$618$$ 0.372454i 0.0149823i
$$619$$ −2.51571 7.74255i −0.101115 0.311200i 0.887684 0.460453i $$-0.152313\pi$$
−0.988799 + 0.149253i $$0.952313\pi$$
$$620$$ 0 0
$$621$$ 1.53299 4.71806i 0.0615167 0.189329i
$$622$$ −4.46783 1.45169i −0.179144 0.0582073i
$$623$$ −14.4258 19.8554i −0.577956 0.795488i
$$624$$ −1.65769 −0.0663605
$$625$$ 0 0
$$626$$ −4.09413 −0.163634
$$627$$ 2.99421 + 4.12118i 0.119577 + 0.164584i
$$628$$ 8.01153 + 2.60310i 0.319695 + 0.103875i
$$629$$ 12.9040 39.7143i 0.514515 1.58351i
$$630$$ 0 0
$$631$$ 10.2855 + 31.6557i 0.409461 + 1.26019i 0.917112 + 0.398629i $$0.130514\pi$$
−0.507651 + 0.861563i $$0.669486\pi$$
$$632$$ 5.63846i 0.224286i
$$633$$ −23.2412 + 7.55152i −0.923754 + 0.300146i
$$634$$ 3.24873 + 2.36034i 0.129024 + 0.0937412i
$$635$$ 0 0
$$636$$ 18.9695 13.7822i 0.752191 0.546499i
$$637$$ −0.632925 + 0.871147i −0.0250774 + 0.0345161i
$$638$$ 1.27308 1.75224i 0.0504015 0.0693718i
$$639$$ 4.02419 2.92375i 0.159195 0.115662i
$$640$$ 0 0
$$641$$ 32.3996 + 23.5397i 1.27971 + 0.929761i 0.999544 0.0301916i $$-0.00961174\pi$$
0.280162 + 0.959953i $$0.409612\pi$$
$$642$$ −4.05881 + 1.31879i −0.160189 + 0.0520484i
$$643$$ 11.6870i 0.460890i −0.973085 0.230445i $$-0.925982\pi$$
0.973085 0.230445i $$-0.0740182\pi$$
$$644$$ −1.74213 5.36172i −0.0686495 0.211281i
$$645$$ 0 0
$$646$$ 0.505688 1.55635i 0.0198960 0.0612337i
$$647$$ 7.56029 + 2.45649i 0.297226 + 0.0965745i 0.453834 0.891086i $$-0.350056\pi$$
−0.156608 + 0.987661i $$0.550056\pi$$
$$648$$ −2.47920 3.41233i −0.0973923 0.134049i
$$649$$ −11.8727 −0.466044
$$650$$ 0 0
$$651$$ 29.2766 1.14744
$$652$$ 18.1773 + 25.0188i 0.711876 + 0.979814i
$$653$$ 3.17402 + 1.03130i 0.124209 + 0.0403579i 0.370462 0.928848i $$-0.379199\pi$$
−0.246253 + 0.969206i $$0.579199\pi$$
$$654$$ 0.166948 0.513814i 0.00652820 0.0200917i
$$655$$ 0 0
$$656$$ −1.19199 3.66857i −0.0465394 0.143234i
$$657$$ 7.36146i 0.287198i
$$658$$ 2.39721 0.778899i 0.0934528 0.0303647i
$$659$$ −24.3116 17.6634i −0.947046 0.688069i 0.00306074 0.999995i $$-0.499026\pi$$
−0.950106 + 0.311926i $$0.899026\pi$$
$$660$$ 0 0
$$661$$ 5.32670 3.87008i 0.207185 0.150529i −0.479354 0.877621i $$-0.659129\pi$$
0.686539 + 0.727093i $$0.259129\pi$$
$$662$$ 0.965008 1.32822i 0.0375061 0.0516227i
$$663$$ 1.32391 1.82220i 0.0514163 0.0707685i
$$664$$ 8.53192 6.19880i 0.331103 0.240560i
$$665$$ 0 0
$$666$$ −0.998835 0.725696i −0.0387041 0.0281202i
$$667$$ −4.94352 + 1.60625i −0.191414 + 0.0621941i
$$668$$ 41.3603i 1.60028i
$$669$$ 3.01483 + 9.27870i 0.116560 + 0.358735i
$$670$$ 0 0
$$671$$ 0.565881 1.74160i 0.0218456 0.0672339i
$$672$$ −9.81044 3.18760i −0.378446 0.122964i
$$673$$ −3.95662 5.44582i −0.152516 0.209921i 0.725921 0.687778i $$-0.241414\pi$$
−0.878438 + 0.477857i $$0.841414\pi$$
$$674$$ 5.32730 0.205200
$$675$$ 0 0
$$676$$ 25.3911 0.976580
$$677$$ 8.02200 + 11.0413i 0.308310 + 0.424353i 0.934853 0.355034i $$-0.115531\pi$$
−0.626543 + 0.779387i $$0.715531\pi$$
$$678$$ 2.67386 + 0.868788i 0.102689 + 0.0333656i
$$679$$ −6.77801 + 20.8606i −0.260116 + 0.800555i
$$680$$ 0 0
$$681$$ −6.09142 18.7474i −0.233424 0.718404i
$$682$$ 2.23453i 0.0855645i
$$683$$ −1.11483 + 0.362229i −0.0426577 + 0.0138603i −0.330268 0.943887i $$-0.607139\pi$$
0.287610 + 0.957747i $$0.407139\pi$$
$$684$$ 2.29413 + 1.66678i 0.0877181 + 0.0637309i
$$685$$ 0 0
$$686$$ 1.62693 1.18203i 0.0621164 0.0451302i
$$687$$ −8.72692 + 12.0116i −0.332953 + 0.458270i
$$688$$ 7.24091 9.96625i 0.276057 0.379960i
$$689$$ 1.94235 1.41120i 0.0739978 0.0537625i
$$690$$ 0 0
$$691$$ −9.92451 7.21058i −0.377546 0.274303i 0.382787 0.923837i $$-0.374964\pi$$
−0.760333 + 0.649533i $$0.774964\pi$$
$$692$$ 13.4031 4.35492i 0.509508 0.165549i
$$693$$ 5.43497i 0.206457i
$$694$$ −0.809268 2.49067i −0.0307194 0.0945445i
$$695$$ 0 0
$$696$$ −1.95381 + 6.01321i −0.0740590 + 0.227930i
$$697$$ 4.98464 + 1.61961i 0.188807 + 0.0613471i
$$698$$ −0.605493 0.833390i −0.0229183 0.0315443i
$$699$$ 32.3910 1.22514
$$700$$ 0 0
$$701$$ −20.0271 −0.756415 −0.378207 0.925721i $$-0.623459\pi$$
−0.378207 + 0.925721i $$0.623459\pi$$
$$702$$ −0.180052 0.247820i −0.00679562 0.00935337i
$$703$$ −13.3103 4.32479i −0.502009 0.163113i
$$704$$ 4.45354 13.7066i 0.167849 0.516586i
$$705$$ 0 0
$$706$$ 0.108111 + 0.332731i 0.00406880 + 0.0125225i
$$707$$ 39.7677i 1.49562i
$$708$$ 16.3418 5.30979i 0.614164 0.199554i
$$709$$ −3.55571 2.58337i −0.133537 0.0970206i 0.519011 0.854767i $$-0.326300\pi$$
−0.652549 + 0.757747i $$0.726300\pi$$
$$710$$ 0 0
$$711$$ −5.23230 + 3.80149i −0.196227 + 0.142567i
$$712$$ 3.21417 4.42392i 0.120456 0.165793i
$$713$$ −3.15209 + 4.33848i −0.118047 + 0.162477i
$$714$$ 3.67232 2.66810i 0.137433 0.0998511i
$$715$$ 0 0
$$716$$ 12.7897 + 9.29226i 0.477974 + 0.347268i
$$717$$ 10.5837 3.43885i 0.395256 0.128426i
$$718$$ 4.06727i 0.151789i
$$719$$ 3.37704 + 10.3934i 0.125942 + 0.387610i 0.994072 0.108728i $$-0.0346777\pi$$
−0.868129 + 0.496338i $$0.834678\pi$$
$$720$$ 0 0
$$721$$ −1.39199 + 4.28409i −0.0518403 + 0.159548i
$$722$$ 2.78832 + 0.905980i 0.103771 + 0.0337171i
$$723$$ 17.6452 + 24.2865i 0.656230 + 0.903224i
$$724$$ −40.5425 −1.50675
$$725$$ 0 0
$$726$$ −1.88734 −0.0700458
$$727$$ −19.3400 26.6193i −0.717282 0.987254i −0.999610 0.0279359i $$-0.991107\pi$$
0.282328 0.959318i $$-0.408893\pi$$
$$728$$ −0.667799 0.216981i −0.0247503 0.00804185i
$$729$$ −9.19466 + 28.2982i −0.340543 + 1.04808i
$$730$$ 0 0
$$731$$ 5.17242 + 15.9191i 0.191309 + 0.588788i
$$732$$ 2.65026i 0.0979564i
$$733$$ 13.0768 4.24891i 0.483002 0.156937i −0.0573871 0.998352i $$-0.518277\pi$$
0.540389 + 0.841415i $$0.318277\pi$$
$$734$$ −3.17792 2.30889i −0.117299 0.0852227i
$$735$$ 0 0
$$736$$ 1.52862 1.11061i 0.0563456 0.0409375i
$$737$$ 8.09739 11.1451i 0.298271 0.410535i
$$738$$ 0.0910839 0.125366i 0.00335285 0.00461480i
$$739$$ −34.9409 + 25.3860i −1.28532 + 0.933840i −0.999700 0.0245030i $$-0.992200\pi$$
−0.285621 + 0.958343i $$0.592200\pi$$
$$740$$ 0 0
$$741$$ −0.610715 0.443711i −0.0224352 0.0163001i
$$742$$ 4.60173 1.49519i 0.168935 0.0548902i
$$743$$ 31.8479i 1.16838i −0.811615 0.584192i $$-0.801411\pi$$
0.811615 0.584192i $$-0.198589\pi$$
$$744$$ 2.01573 + 6.20378i 0.0739003 + 0.227442i
$$745$$ 0 0
$$746$$ 1.30979 4.03113i 0.0479550 0.147590i
$$747$$ −11.5046 3.73806i −0.420930 0.136768i
$$748$$ 11.9352 + 16.4274i 0.436395 + 0.600646i
$$749$$ 51.6145 1.88595
$$750$$ 0 0
$$751$$ −29.5952 −1.07995 −0.539973 0.841682i $$-0.681565\pi$$
−0.539973 + 0.841682i $$0.681565\pi$$
$$752$$ −9.42517 12.9726i −0.343700 0.473063i
$$753$$ 14.7993 + 4.80860i 0.539318 + 0.175235i
$$754$$ −0.0991824 + 0.305252i −0.00361201 + 0.0111166i
$$755$$ 0 0
$$756$$ 11.1807 + 34.4107i 0.406639 + 1.25150i
$$757$$ 0.0984401i 0.00357786i −0.999998 0.00178893i $$-0.999431\pi$$
0.999998 0.00178893i $$-0.000569435\pi$$
$$758$$ 3.77161 1.22547i 0.136991 0.0445111i
$$759$$ −2.09394 1.52134i −0.0760052 0.0552210i
$$760$$ 0 0
$$761$$ 2.86717 2.08312i 0.103935 0.0755131i −0.534604 0.845103i $$-0.679539\pi$$
0.638539 + 0.769590i $$0.279539\pi$$
$$762$$ −0.927111 + 1.27606i −0.0335857 + 0.0462267i
$$763$$ −3.84059 + 5.28612i −0.139039 + 0.191370i
$$764$$ −28.6842 + 20.8403i −1.03776 + 0.753975i
$$765$$ 0 0
$$766$$ −0.837983 0.608830i −0.0302775 0.0219979i
$$767$$ 1.67330 0.543687i 0.0604192 0.0196314i
$$768$$ 19.6989i 0.710822i
$$769$$ −0.441149 1.35772i −0.0159083 0.0489606i 0.942787 0.333395i $$-0.108194\pi$$
−0.958696 + 0.284434i $$0.908194\pi$$
$$770$$ 0 0
$$771$$ 9.21997 28.3762i 0.332049 1.02194i
$$772$$ −12.6960 4.12520i −0.456941 0.148469i
$$773$$ 19.8558 + 27.3292i 0.714163 + 0.982962i 0.999698 + 0.0245930i $$0.00782898\pi$$
−0.285534 + 0.958369i $$0.592171\pi$$
$$774$$ 0.494888 0.0177884