Properties

 Label 1040.2.da.f.881.4 Level $1040$ Weight $2$ Character 1040.881 Analytic conductor $8.304$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1040 = 2^{4} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1040.da (of order $$6$$, 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: $$8.30444181021$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16$$ x^16 + 22*x^14 + 183*x^12 + 730*x^10 + 1485*x^8 + 1552*x^6 + 812*x^4 + 192*x^2 + 16 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 520) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 881.4 Root $$-1.44614i$$ of defining polynomial Character $$\chi$$ $$=$$ 1040.881 Dual form 1040.2.da.f.641.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.268727 - 0.465448i) q^{3} +1.00000i q^{5} +(0.331682 + 0.191497i) q^{7} +(1.35557 - 2.34792i) q^{9} +O(q^{10})$$ $$q+(-0.268727 - 0.465448i) q^{3} +1.00000i q^{5} +(0.331682 + 0.191497i) q^{7} +(1.35557 - 2.34792i) q^{9} +(-5.66862 + 3.27278i) q^{11} +(-2.44183 + 2.65282i) q^{13} +(0.465448 - 0.268727i) q^{15} +(0.174340 - 0.301966i) q^{17} +(-3.55500 - 2.05248i) q^{19} -0.205841i q^{21} +(-3.36387 - 5.82639i) q^{23} -1.00000 q^{25} -3.06947 q^{27} +(1.91872 + 3.32331i) q^{29} -1.67765i q^{31} +(3.04662 + 1.75897i) q^{33} +(-0.191497 + 0.331682i) q^{35} +(0.963044 - 0.556014i) q^{37} +(1.89094 + 0.423660i) q^{39} +(-6.17915 + 3.56754i) q^{41} +(-2.87604 + 4.98145i) q^{43} +(2.34792 + 1.35557i) q^{45} +7.72357i q^{47} +(-3.42666 - 5.93515i) q^{49} -0.187399 q^{51} -7.18066 q^{53} +(-3.27278 - 5.66862i) q^{55} +2.20623i q^{57} +(3.85348 + 2.22481i) q^{59} +(5.19956 - 9.00590i) q^{61} +(0.899239 - 0.519176i) q^{63} +(-2.65282 - 2.44183i) q^{65} +(-3.01934 + 1.74322i) q^{67} +(-1.80792 + 3.13141i) q^{69} +(-2.93488 - 1.69446i) q^{71} +8.04467i q^{73} +(0.268727 + 0.465448i) q^{75} -2.50691 q^{77} -10.7375 q^{79} +(-3.24187 - 5.61508i) q^{81} -8.27761i q^{83} +(0.301966 + 0.174340i) q^{85} +(1.03122 - 1.78613i) q^{87} +(-15.5518 + 8.97885i) q^{89} +(-1.31792 + 0.412292i) q^{91} +(-0.780860 + 0.450830i) q^{93} +(2.05248 - 3.55500i) q^{95} +(1.14570 + 0.661472i) q^{97} +17.7460i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10})$$ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 $$16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100})$$ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$417$$ $$561$$ $$911$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.268727 0.465448i −0.155149 0.268727i 0.777964 0.628309i $$-0.216253\pi$$
−0.933113 + 0.359582i $$0.882919\pi$$
$$4$$ 0 0
$$5$$ 1.00000i 0.447214i
$$6$$ 0 0
$$7$$ 0.331682 + 0.191497i 0.125364 + 0.0723790i 0.561371 0.827564i $$-0.310274\pi$$
−0.436007 + 0.899944i $$0.643608\pi$$
$$8$$ 0 0
$$9$$ 1.35557 2.34792i 0.451857 0.782640i
$$10$$ 0 0
$$11$$ −5.66862 + 3.27278i −1.70915 + 0.986780i −0.773545 + 0.633742i $$0.781518\pi$$
−0.935609 + 0.353039i $$0.885148\pi$$
$$12$$ 0 0
$$13$$ −2.44183 + 2.65282i −0.677241 + 0.735761i
$$14$$ 0 0
$$15$$ 0.465448 0.268727i 0.120178 0.0693849i
$$16$$ 0 0
$$17$$ 0.174340 0.301966i 0.0422837 0.0732376i −0.844109 0.536172i $$-0.819870\pi$$
0.886393 + 0.462934i $$0.153203\pi$$
$$18$$ 0 0
$$19$$ −3.55500 2.05248i −0.815574 0.470872i 0.0333141 0.999445i $$-0.489394\pi$$
−0.848888 + 0.528573i $$0.822727\pi$$
$$20$$ 0 0
$$21$$ 0.205841i 0.0449182i
$$22$$ 0 0
$$23$$ −3.36387 5.82639i −0.701415 1.21489i −0.967970 0.251067i $$-0.919219\pi$$
0.266555 0.963820i $$-0.414115\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ −3.06947 −0.590720
$$28$$ 0 0
$$29$$ 1.91872 + 3.32331i 0.356297 + 0.617124i 0.987339 0.158624i $$-0.0507059\pi$$
−0.631042 + 0.775748i $$0.717373\pi$$
$$30$$ 0 0
$$31$$ 1.67765i 0.301315i −0.988586 0.150658i $$-0.951861\pi$$
0.988586 0.150658i $$-0.0481391\pi$$
$$32$$ 0 0
$$33$$ 3.04662 + 1.75897i 0.530348 + 0.306197i
$$34$$ 0 0
$$35$$ −0.191497 + 0.331682i −0.0323689 + 0.0560646i
$$36$$ 0 0
$$37$$ 0.963044 0.556014i 0.158324 0.0914081i −0.418745 0.908104i $$-0.637530\pi$$
0.577069 + 0.816696i $$0.304197\pi$$
$$38$$ 0 0
$$39$$ 1.89094 + 0.423660i 0.302792 + 0.0678399i
$$40$$ 0 0
$$41$$ −6.17915 + 3.56754i −0.965022 + 0.557155i −0.897715 0.440577i $$-0.854774\pi$$
−0.0673067 + 0.997732i $$0.521441\pi$$
$$42$$ 0 0
$$43$$ −2.87604 + 4.98145i −0.438592 + 0.759663i −0.997581 0.0695116i $$-0.977856\pi$$
0.558989 + 0.829175i $$0.311189\pi$$
$$44$$ 0 0
$$45$$ 2.34792 + 1.35557i 0.350007 + 0.202077i
$$46$$ 0 0
$$47$$ 7.72357i 1.12660i 0.826253 + 0.563299i $$0.190468\pi$$
−0.826253 + 0.563299i $$0.809532\pi$$
$$48$$ 0 0
$$49$$ −3.42666 5.93515i −0.489523 0.847878i
$$50$$ 0 0
$$51$$ −0.187399 −0.0262412
$$52$$ 0 0
$$53$$ −7.18066 −0.986339 −0.493169 0.869933i $$-0.664162\pi$$
−0.493169 + 0.869933i $$0.664162\pi$$
$$54$$ 0 0
$$55$$ −3.27278 5.66862i −0.441302 0.764357i
$$56$$ 0 0
$$57$$ 2.20623i 0.292222i
$$58$$ 0 0
$$59$$ 3.85348 + 2.22481i 0.501680 + 0.289645i 0.729407 0.684080i $$-0.239796\pi$$
−0.227727 + 0.973725i $$0.573129\pi$$
$$60$$ 0 0
$$61$$ 5.19956 9.00590i 0.665735 1.15309i −0.313350 0.949638i $$-0.601451\pi$$
0.979085 0.203450i $$-0.0652153\pi$$
$$62$$ 0 0
$$63$$ 0.899239 0.519176i 0.113293 0.0654100i
$$64$$ 0 0
$$65$$ −2.65282 2.44183i −0.329042 0.302872i
$$66$$ 0 0
$$67$$ −3.01934 + 1.74322i −0.368872 + 0.212968i −0.672965 0.739674i $$-0.734980\pi$$
0.304094 + 0.952642i $$0.401646\pi$$
$$68$$ 0 0
$$69$$ −1.80792 + 3.13141i −0.217648 + 0.376978i
$$70$$ 0 0
$$71$$ −2.93488 1.69446i −0.348307 0.201095i 0.315633 0.948881i $$-0.397783\pi$$
−0.663939 + 0.747787i $$0.731117\pi$$
$$72$$ 0 0
$$73$$ 8.04467i 0.941557i 0.882251 + 0.470779i $$0.156027\pi$$
−0.882251 + 0.470779i $$0.843973\pi$$
$$74$$ 0 0
$$75$$ 0.268727 + 0.465448i 0.0310299 + 0.0537453i
$$76$$ 0 0
$$77$$ −2.50691 −0.285689
$$78$$ 0 0
$$79$$ −10.7375 −1.20807 −0.604033 0.796959i $$-0.706441\pi$$
−0.604033 + 0.796959i $$0.706441\pi$$
$$80$$ 0 0
$$81$$ −3.24187 5.61508i −0.360208 0.623898i
$$82$$ 0 0
$$83$$ 8.27761i 0.908586i −0.890852 0.454293i $$-0.849892\pi$$
0.890852 0.454293i $$-0.150108\pi$$
$$84$$ 0 0
$$85$$ 0.301966 + 0.174340i 0.0327528 + 0.0189099i
$$86$$ 0 0
$$87$$ 1.03122 1.78613i 0.110558 0.191493i
$$88$$ 0 0
$$89$$ −15.5518 + 8.97885i −1.64849 + 0.951757i −0.670818 + 0.741622i $$0.734057\pi$$
−0.977672 + 0.210135i $$0.932610\pi$$
$$90$$ 0 0
$$91$$ −1.31792 + 0.412292i −0.138155 + 0.0432200i
$$92$$ 0 0
$$93$$ −0.780860 + 0.450830i −0.0809714 + 0.0467488i
$$94$$ 0 0
$$95$$ 2.05248 3.55500i 0.210580 0.364736i
$$96$$ 0 0
$$97$$ 1.14570 + 0.661472i 0.116329 + 0.0671623i 0.557035 0.830489i $$-0.311939\pi$$
−0.440707 + 0.897651i $$0.645272\pi$$
$$98$$ 0 0
$$99$$ 17.7460i 1.78354i
$$100$$ 0 0
$$101$$ −7.73517 13.3977i −0.769678 1.33312i −0.937737 0.347345i $$-0.887083\pi$$
0.168059 0.985777i $$-0.446250\pi$$
$$102$$ 0 0
$$103$$ 14.3730 1.41622 0.708109 0.706103i $$-0.249548\pi$$
0.708109 + 0.706103i $$0.249548\pi$$
$$104$$ 0 0
$$105$$ 0.205841 0.0200880
$$106$$ 0 0
$$107$$ 9.21819 + 15.9664i 0.891156 + 1.54353i 0.838491 + 0.544915i $$0.183438\pi$$
0.0526643 + 0.998612i $$0.483229\pi$$
$$108$$ 0 0
$$109$$ 3.91578i 0.375064i 0.982259 + 0.187532i $$0.0600488\pi$$
−0.982259 + 0.187532i $$0.939951\pi$$
$$110$$ 0 0
$$111$$ −0.517591 0.298831i −0.0491276 0.0283638i
$$112$$ 0 0
$$113$$ −10.1161 + 17.5215i −0.951640 + 1.64829i −0.209763 + 0.977752i $$0.567269\pi$$
−0.741877 + 0.670537i $$0.766064\pi$$
$$114$$ 0 0
$$115$$ 5.82639 3.36387i 0.543314 0.313682i
$$116$$ 0 0
$$117$$ 2.91854 + 9.32931i 0.269819 + 0.862495i
$$118$$ 0 0
$$119$$ 0.115651 0.0667713i 0.0106017 0.00612091i
$$120$$ 0 0
$$121$$ 15.9222 27.5780i 1.44747 2.50709i
$$122$$ 0 0
$$123$$ 3.32100 + 1.91738i 0.299445 + 0.172885i
$$124$$ 0 0
$$125$$ 1.00000i 0.0894427i
$$126$$ 0 0
$$127$$ 6.88887 + 11.9319i 0.611288 + 1.05878i 0.991024 + 0.133687i $$0.0426818\pi$$
−0.379735 + 0.925095i $$0.623985\pi$$
$$128$$ 0 0
$$129$$ 3.09147 0.272189
$$130$$ 0 0
$$131$$ 5.66818 0.495231 0.247616 0.968858i $$-0.420353\pi$$
0.247616 + 0.968858i $$0.420353\pi$$
$$132$$ 0 0
$$133$$ −0.786088 1.36154i −0.0681625 0.118061i
$$134$$ 0 0
$$135$$ 3.06947i 0.264178i
$$136$$ 0 0
$$137$$ 2.88380 + 1.66496i 0.246379 + 0.142247i 0.618105 0.786095i $$-0.287901\pi$$
−0.371726 + 0.928343i $$0.621234\pi$$
$$138$$ 0 0
$$139$$ 2.23569 3.87234i 0.189629 0.328447i −0.755497 0.655152i $$-0.772605\pi$$
0.945127 + 0.326704i $$0.105938\pi$$
$$140$$ 0 0
$$141$$ 3.59492 2.07553i 0.302747 0.174791i
$$142$$ 0 0
$$143$$ 5.15969 23.0294i 0.431475 1.92582i
$$144$$ 0 0
$$145$$ −3.32331 + 1.91872i −0.275986 + 0.159341i
$$146$$ 0 0
$$147$$ −1.84167 + 3.18986i −0.151898 + 0.263095i
$$148$$ 0 0
$$149$$ 11.1256 + 6.42338i 0.911446 + 0.526223i 0.880896 0.473310i $$-0.156941\pi$$
0.0305497 + 0.999533i $$0.490274\pi$$
$$150$$ 0 0
$$151$$ 7.20405i 0.586257i −0.956073 0.293129i $$-0.905304\pi$$
0.956073 0.293129i $$-0.0946964\pi$$
$$152$$ 0 0
$$153$$ −0.472662 0.818674i −0.0382124 0.0661859i
$$154$$ 0 0
$$155$$ 1.67765 0.134752
$$156$$ 0 0
$$157$$ 1.76129 0.140566 0.0702832 0.997527i $$-0.477610\pi$$
0.0702832 + 0.997527i $$0.477610\pi$$
$$158$$ 0 0
$$159$$ 1.92963 + 3.34222i 0.153030 + 0.265055i
$$160$$ 0 0
$$161$$ 2.57668i 0.203071i
$$162$$ 0 0
$$163$$ −3.01956 1.74334i −0.236510 0.136549i 0.377062 0.926188i $$-0.376934\pi$$
−0.613572 + 0.789639i $$0.710268\pi$$
$$164$$ 0 0
$$165$$ −1.75897 + 3.04662i −0.136935 + 0.237179i
$$166$$ 0 0
$$167$$ 11.0835 6.39909i 0.857671 0.495176i −0.00556090 0.999985i $$-0.501770\pi$$
0.863232 + 0.504808i $$0.168437\pi$$
$$168$$ 0 0
$$169$$ −1.07495 12.9555i −0.0826882 0.996575i
$$170$$ 0 0
$$171$$ −9.63812 + 5.56457i −0.737046 + 0.425534i
$$172$$ 0 0
$$173$$ 3.23046 5.59531i 0.245607 0.425404i −0.716695 0.697387i $$-0.754346\pi$$
0.962302 + 0.271983i $$0.0876794\pi$$
$$174$$ 0 0
$$175$$ −0.331682 0.191497i −0.0250728 0.0144758i
$$176$$ 0 0
$$177$$ 2.39146i 0.179753i
$$178$$ 0 0
$$179$$ 3.96078 + 6.86028i 0.296043 + 0.512761i 0.975227 0.221207i $$-0.0709995\pi$$
−0.679184 + 0.733968i $$0.737666\pi$$
$$180$$ 0 0
$$181$$ −22.0467 −1.63871 −0.819357 0.573283i $$-0.805670\pi$$
−0.819357 + 0.573283i $$0.805670\pi$$
$$182$$ 0 0
$$183$$ −5.58904 −0.413154
$$184$$ 0 0
$$185$$ 0.556014 + 0.963044i 0.0408790 + 0.0708044i
$$186$$ 0 0
$$187$$ 2.28231i 0.166899i
$$188$$ 0 0
$$189$$ −1.01809 0.587794i −0.0740551 0.0427558i
$$190$$ 0 0
$$191$$ 9.38199 16.2501i 0.678857 1.17582i −0.296468 0.955043i $$-0.595809\pi$$
0.975325 0.220773i $$-0.0708579\pi$$
$$192$$ 0 0
$$193$$ 10.7478 6.20526i 0.773646 0.446665i −0.0605279 0.998167i $$-0.519278\pi$$
0.834174 + 0.551502i $$0.185945\pi$$
$$194$$ 0 0
$$195$$ −0.423660 + 1.89094i −0.0303389 + 0.135413i
$$196$$ 0 0
$$197$$ −0.499279 + 0.288259i −0.0355721 + 0.0205376i −0.517681 0.855574i $$-0.673204\pi$$
0.482108 + 0.876112i $$0.339871\pi$$
$$198$$ 0 0
$$199$$ 5.96050 10.3239i 0.422529 0.731841i −0.573657 0.819095i $$-0.694476\pi$$
0.996186 + 0.0872543i $$0.0278093\pi$$
$$200$$ 0 0
$$201$$ 1.62276 + 0.936899i 0.114460 + 0.0660837i
$$202$$ 0 0
$$203$$ 1.46971i 0.103154i
$$204$$ 0 0
$$205$$ −3.56754 6.17915i −0.249167 0.431571i
$$206$$ 0 0
$$207$$ −18.2399 −1.26776
$$208$$ 0 0
$$209$$ 26.8693 1.85859
$$210$$ 0 0
$$211$$ 3.15018 + 5.45627i 0.216867 + 0.375625i 0.953849 0.300288i $$-0.0970827\pi$$
−0.736981 + 0.675913i $$0.763749\pi$$
$$212$$ 0 0
$$213$$ 1.82138i 0.124799i
$$214$$ 0 0
$$215$$ −4.98145 2.87604i −0.339732 0.196144i
$$216$$ 0 0
$$217$$ 0.321265 0.556448i 0.0218089 0.0377741i
$$218$$ 0 0
$$219$$ 3.74437 2.16182i 0.253021 0.146082i
$$220$$ 0 0
$$221$$ 0.375354 + 1.19984i 0.0252490 + 0.0807102i
$$222$$ 0 0
$$223$$ 9.93221 5.73436i 0.665110 0.384001i −0.129111 0.991630i $$-0.541212\pi$$
0.794221 + 0.607629i $$0.207879\pi$$
$$224$$ 0 0
$$225$$ −1.35557 + 2.34792i −0.0903715 + 0.156528i
$$226$$ 0 0
$$227$$ −16.6245 9.59817i −1.10341 0.637053i −0.166294 0.986076i $$-0.553180\pi$$
−0.937114 + 0.349024i $$0.886513\pi$$
$$228$$ 0 0
$$229$$ 6.23160i 0.411796i −0.978573 0.205898i $$-0.933989\pi$$
0.978573 0.205898i $$-0.0660115\pi$$
$$230$$ 0 0
$$231$$ 0.673673 + 1.16684i 0.0443244 + 0.0767722i
$$232$$ 0 0
$$233$$ 4.82258 0.315937 0.157969 0.987444i $$-0.449505\pi$$
0.157969 + 0.987444i $$0.449505\pi$$
$$234$$ 0 0
$$235$$ −7.72357 −0.503830
$$236$$ 0 0
$$237$$ 2.88546 + 4.99776i 0.187431 + 0.324640i
$$238$$ 0 0
$$239$$ 6.82214i 0.441288i −0.975354 0.220644i $$-0.929184\pi$$
0.975354 0.220644i $$-0.0708158\pi$$
$$240$$ 0 0
$$241$$ 8.92067 + 5.15035i 0.574631 + 0.331763i 0.758997 0.651094i $$-0.225690\pi$$
−0.184366 + 0.982858i $$0.559023\pi$$
$$242$$ 0 0
$$243$$ −6.34656 + 10.9926i −0.407132 + 0.705173i
$$244$$ 0 0
$$245$$ 5.93515 3.42666i 0.379183 0.218921i
$$246$$ 0 0
$$247$$ 14.1256 4.41899i 0.898789 0.281173i
$$248$$ 0 0
$$249$$ −3.85280 + 2.22441i −0.244161 + 0.140966i
$$250$$ 0 0
$$251$$ −2.40755 + 4.17001i −0.151963 + 0.263208i −0.931949 0.362589i $$-0.881893\pi$$
0.779986 + 0.625797i $$0.215226\pi$$
$$252$$ 0 0
$$253$$ 38.1370 + 22.0184i 2.39765 + 1.38428i
$$254$$ 0 0
$$255$$ 0.187399i 0.0117354i
$$256$$ 0 0
$$257$$ 14.1153 + 24.4484i 0.880487 + 1.52505i 0.850800 + 0.525489i $$0.176118\pi$$
0.0296867 + 0.999559i $$0.490549\pi$$
$$258$$ 0 0
$$259$$ 0.425900 0.0264641
$$260$$ 0 0
$$261$$ 10.4038 0.643981
$$262$$ 0 0
$$263$$ 11.2128 + 19.4211i 0.691410 + 1.19756i 0.971376 + 0.237547i $$0.0763433\pi$$
−0.279967 + 0.960010i $$0.590323\pi$$
$$264$$ 0 0
$$265$$ 7.18066i 0.441104i
$$266$$ 0 0
$$267$$ 8.35838 + 4.82571i 0.511524 + 0.295329i
$$268$$ 0 0
$$269$$ −1.25602 + 2.17550i −0.0765811 + 0.132642i −0.901773 0.432211i $$-0.857734\pi$$
0.825192 + 0.564853i $$0.191067\pi$$
$$270$$ 0 0
$$271$$ 6.68024 3.85684i 0.405796 0.234286i −0.283186 0.959065i $$-0.591391\pi$$
0.688982 + 0.724779i $$0.258058\pi$$
$$272$$ 0 0
$$273$$ 0.546060 + 0.502629i 0.0330491 + 0.0304205i
$$274$$ 0 0
$$275$$ 5.66862 3.27278i 0.341831 0.197356i
$$276$$ 0 0
$$277$$ 10.5166 18.2153i 0.631882 1.09445i −0.355284 0.934758i $$-0.615616\pi$$
0.987167 0.159694i $$-0.0510507\pi$$
$$278$$ 0 0
$$279$$ −3.93899 2.27418i −0.235821 0.136151i
$$280$$ 0 0
$$281$$ 10.4409i 0.622855i −0.950270 0.311427i $$-0.899193\pi$$
0.950270 0.311427i $$-0.100807\pi$$
$$282$$ 0 0
$$283$$ −7.93861 13.7501i −0.471901 0.817357i 0.527582 0.849504i $$-0.323099\pi$$
−0.999483 + 0.0321473i $$0.989765\pi$$
$$284$$ 0 0
$$285$$ −2.20623 −0.130685
$$286$$ 0 0
$$287$$ −2.73269 −0.161306
$$288$$ 0 0
$$289$$ 8.43921 + 14.6171i 0.496424 + 0.859832i
$$290$$ 0 0
$$291$$ 0.711020i 0.0416808i
$$292$$ 0 0
$$293$$ −16.0219 9.25024i −0.936009 0.540405i −0.0473019 0.998881i $$-0.515062\pi$$
−0.888707 + 0.458476i $$0.848396\pi$$
$$294$$ 0 0
$$295$$ −2.22481 + 3.85348i −0.129533 + 0.224358i
$$296$$ 0 0
$$297$$ 17.3997 10.0457i 1.00963 0.582911i
$$298$$ 0 0
$$299$$ 23.6704 + 5.30330i 1.36889 + 0.306698i
$$300$$ 0 0
$$301$$ −1.90786 + 1.10151i −0.109967 + 0.0634897i
$$302$$ 0 0
$$303$$ −4.15729 + 7.20064i −0.238830 + 0.413666i
$$304$$ 0 0
$$305$$ 9.00590 + 5.19956i 0.515676 + 0.297726i
$$306$$ 0 0
$$307$$ 27.4070i 1.56420i 0.623154 + 0.782099i $$0.285851\pi$$
−0.623154 + 0.782099i $$0.714149\pi$$
$$308$$ 0 0
$$309$$ −3.86242 6.68990i −0.219725 0.380575i
$$310$$ 0 0
$$311$$ −18.4956 −1.04879 −0.524395 0.851475i $$-0.675708\pi$$
−0.524395 + 0.851475i $$0.675708\pi$$
$$312$$ 0 0
$$313$$ −15.6117 −0.882425 −0.441212 0.897403i $$-0.645451\pi$$
−0.441212 + 0.897403i $$0.645451\pi$$
$$314$$ 0 0
$$315$$ 0.519176 + 0.899239i 0.0292522 + 0.0506664i
$$316$$ 0 0
$$317$$ 17.6446i 0.991019i 0.868602 + 0.495510i $$0.165019\pi$$
−0.868602 + 0.495510i $$0.834981\pi$$
$$318$$ 0 0
$$319$$ −21.7529 12.5591i −1.21793 0.703173i
$$320$$ 0 0
$$321$$ 4.95434 8.58117i 0.276524 0.478954i
$$322$$ 0 0
$$323$$ −1.23956 + 0.715661i −0.0689710 + 0.0398204i
$$324$$ 0 0
$$325$$ 2.44183 2.65282i 0.135448 0.147152i
$$326$$ 0 0
$$327$$ 1.82259 1.05227i 0.100790 0.0581909i
$$328$$ 0 0
$$329$$ −1.47904 + 2.56177i −0.0815421 + 0.141235i
$$330$$ 0 0
$$331$$ −25.2822 14.5967i −1.38963 0.802306i −0.396361 0.918095i $$-0.629727\pi$$
−0.993274 + 0.115789i $$0.963060\pi$$
$$332$$ 0 0
$$333$$ 3.01487i 0.165214i
$$334$$ 0 0
$$335$$ −1.74322 3.01934i −0.0952422 0.164964i
$$336$$ 0 0
$$337$$ −19.2691 −1.04966 −0.524828 0.851208i $$-0.675870\pi$$
−0.524828 + 0.851208i $$0.675870\pi$$
$$338$$ 0 0
$$339$$ 10.8738 0.590585
$$340$$ 0 0
$$341$$ 5.49058 + 9.50997i 0.297332 + 0.514994i
$$342$$ 0 0
$$343$$ 5.30574i 0.286483i
$$344$$ 0 0
$$345$$ −3.13141 1.80792i −0.168590 0.0973352i
$$346$$ 0 0
$$347$$ 6.63014 11.4837i 0.355925 0.616480i −0.631351 0.775497i $$-0.717499\pi$$
0.987276 + 0.159018i $$0.0508326\pi$$
$$348$$ 0 0
$$349$$ 21.6614 12.5062i 1.15951 0.669441i 0.208321 0.978061i $$-0.433200\pi$$
0.951186 + 0.308619i $$0.0998669\pi$$
$$350$$ 0 0
$$351$$ 7.49512 8.14277i 0.400060 0.434629i
$$352$$ 0 0
$$353$$ −23.6328 + 13.6444i −1.25785 + 0.726218i −0.972655 0.232253i $$-0.925390\pi$$
−0.285191 + 0.958471i $$0.592057\pi$$
$$354$$ 0 0
$$355$$ 1.69446 2.93488i 0.0899324 0.155767i
$$356$$ 0 0
$$357$$ −0.0621571 0.0358864i −0.00328970 0.00189931i
$$358$$ 0 0
$$359$$ 7.09226i 0.374315i 0.982330 + 0.187158i $$0.0599275\pi$$
−0.982330 + 0.187158i $$0.940072\pi$$
$$360$$ 0 0
$$361$$ −1.07464 1.86133i −0.0565599 0.0979646i
$$362$$ 0 0
$$363$$ −17.1148 −0.898296
$$364$$ 0 0
$$365$$ −8.04467 −0.421077
$$366$$ 0 0
$$367$$ −4.88298 8.45757i −0.254890 0.441482i 0.709976 0.704226i $$-0.248706\pi$$
−0.964866 + 0.262744i $$0.915372\pi$$
$$368$$ 0 0
$$369$$ 19.3442i 1.00702i
$$370$$ 0 0
$$371$$ −2.38170 1.37507i −0.123652 0.0713903i
$$372$$ 0 0
$$373$$ 3.51157 6.08222i 0.181822 0.314926i −0.760679 0.649128i $$-0.775134\pi$$
0.942501 + 0.334203i $$0.108467\pi$$
$$374$$ 0 0
$$375$$ −0.465448 + 0.268727i −0.0240356 + 0.0138770i
$$376$$ 0 0
$$377$$ −13.5013 3.02495i −0.695354 0.155793i
$$378$$ 0 0
$$379$$ −17.3393 + 10.0108i −0.890658 + 0.514222i −0.874158 0.485642i $$-0.838586\pi$$
−0.0165003 + 0.999864i $$0.505252\pi$$
$$380$$ 0 0
$$381$$ 3.70244 6.41282i 0.189682 0.328539i
$$382$$ 0 0
$$383$$ 8.67580 + 5.00898i 0.443313 + 0.255947i 0.705002 0.709206i $$-0.250946\pi$$
−0.261689 + 0.965152i $$0.584280\pi$$
$$384$$ 0 0
$$385$$ 2.50691i 0.127764i
$$386$$ 0 0
$$387$$ 7.79736 + 13.5054i 0.396362 + 0.686519i
$$388$$ 0 0
$$389$$ −29.0158 −1.47116 −0.735581 0.677437i $$-0.763091\pi$$
−0.735581 + 0.677437i $$0.763091\pi$$
$$390$$ 0 0
$$391$$ −2.34583 −0.118634
$$392$$ 0 0
$$393$$ −1.52319 2.63824i −0.0768348 0.133082i
$$394$$ 0 0
$$395$$ 10.7375i 0.540264i
$$396$$ 0 0
$$397$$ 4.27503 + 2.46819i 0.214557 + 0.123875i 0.603428 0.797418i $$-0.293801\pi$$
−0.388870 + 0.921293i $$0.627135\pi$$
$$398$$ 0 0
$$399$$ −0.422485 + 0.731766i −0.0211507 + 0.0366341i
$$400$$ 0 0
$$401$$ −21.6985 + 12.5276i −1.08357 + 0.625599i −0.931857 0.362825i $$-0.881812\pi$$
−0.151713 + 0.988425i $$0.548479\pi$$
$$402$$ 0 0
$$403$$ 4.45051 + 4.09654i 0.221696 + 0.204063i
$$404$$ 0 0
$$405$$ 5.61508 3.24187i 0.279016 0.161090i
$$406$$ 0 0
$$407$$ −3.63942 + 6.30366i −0.180399 + 0.312461i
$$408$$ 0 0
$$409$$ 2.88605 + 1.66626i 0.142706 + 0.0823912i 0.569653 0.821885i $$-0.307078\pi$$
−0.426947 + 0.904277i $$0.640411\pi$$
$$410$$ 0 0
$$411$$ 1.78968i 0.0882783i
$$412$$ 0 0
$$413$$ 0.852087 + 1.47586i 0.0419285 + 0.0726222i
$$414$$ 0 0
$$415$$ 8.27761 0.406332
$$416$$ 0 0
$$417$$ −2.40316 −0.117683
$$418$$ 0 0
$$419$$ 18.3877 + 31.8484i 0.898296 + 1.55589i 0.829672 + 0.558252i $$0.188528\pi$$
0.0686246 + 0.997643i $$0.478139\pi$$
$$420$$ 0 0
$$421$$ 9.58821i 0.467301i −0.972321 0.233650i $$-0.924933\pi$$
0.972321 0.233650i $$-0.0750671\pi$$
$$422$$ 0 0
$$423$$ 18.1343 + 10.4699i 0.881720 + 0.509062i
$$424$$ 0 0
$$425$$ −0.174340 + 0.301966i −0.00845675 + 0.0146475i
$$426$$ 0 0
$$427$$ 3.44920 1.99140i 0.166919 0.0963706i
$$428$$ 0 0
$$429$$ −12.1055 + 3.78705i −0.584461 + 0.182840i
$$430$$ 0 0
$$431$$ 27.8063 16.0540i 1.33938 0.773294i 0.352668 0.935748i $$-0.385274\pi$$
0.986716 + 0.162454i $$0.0519410\pi$$
$$432$$ 0 0
$$433$$ 16.6413 28.8235i 0.799728 1.38517i −0.120066 0.992766i $$-0.538310\pi$$
0.919793 0.392403i $$-0.128356\pi$$
$$434$$ 0 0
$$435$$ 1.78613 + 1.03122i 0.0856381 + 0.0494432i
$$436$$ 0 0
$$437$$ 27.6171i 1.32111i
$$438$$ 0 0
$$439$$ 0.866280 + 1.50044i 0.0413453 + 0.0716122i 0.885958 0.463766i $$-0.153502\pi$$
−0.844612 + 0.535379i $$0.820169\pi$$
$$440$$ 0 0
$$441$$ −18.5803 −0.884777
$$442$$ 0 0
$$443$$ −23.2056 −1.10253 −0.551265 0.834330i $$-0.685855\pi$$
−0.551265 + 0.834330i $$0.685855\pi$$
$$444$$ 0 0
$$445$$ −8.97885 15.5518i −0.425638 0.737227i
$$446$$ 0 0
$$447$$ 6.90453i 0.326573i
$$448$$ 0 0
$$449$$ 21.4815 + 12.4024i 1.01378 + 0.585304i 0.912295 0.409533i $$-0.134308\pi$$
0.101481 + 0.994837i $$0.467642\pi$$
$$450$$ 0 0
$$451$$ 23.3515 40.4460i 1.09958 1.90453i
$$452$$ 0 0
$$453$$ −3.35311 + 1.93592i −0.157543 + 0.0909574i
$$454$$ 0 0
$$455$$ −0.412292 1.31792i −0.0193286 0.0617850i
$$456$$ 0 0
$$457$$ −25.0074 + 14.4380i −1.16980 + 0.675383i −0.953632 0.300974i $$-0.902688\pi$$
−0.216165 + 0.976357i $$0.569355\pi$$
$$458$$ 0 0
$$459$$ −0.535133 + 0.926877i −0.0249779 + 0.0432629i
$$460$$ 0 0
$$461$$ −2.13975 1.23539i −0.0996583 0.0575377i 0.449343 0.893360i $$-0.351658\pi$$
−0.549001 + 0.835822i $$0.684992\pi$$
$$462$$ 0 0
$$463$$ 24.0731i 1.11877i 0.828908 + 0.559385i $$0.188963\pi$$
−0.828908 + 0.559385i $$0.811037\pi$$
$$464$$ 0 0
$$465$$ −0.450830 0.780860i −0.0209067 0.0362115i
$$466$$ 0 0
$$467$$ −20.4625 −0.946889 −0.473445 0.880824i $$-0.656990\pi$$
−0.473445 + 0.880824i $$0.656990\pi$$
$$468$$ 0 0
$$469$$ −1.33528 −0.0616577
$$470$$ 0 0
$$471$$ −0.473306 0.819790i −0.0218088 0.0377739i
$$472$$ 0 0
$$473$$ 37.6506i 1.73117i
$$474$$ 0 0
$$475$$ 3.55500 + 2.05248i 0.163115 + 0.0941743i
$$476$$ 0 0
$$477$$ −9.73390 + 16.8596i −0.445684 + 0.771948i
$$478$$ 0 0
$$479$$ −18.5360 + 10.7018i −0.846933 + 0.488977i −0.859615 0.510943i $$-0.829296\pi$$
0.0126818 + 0.999920i $$0.495963\pi$$
$$480$$ 0 0
$$481$$ −0.876582 + 3.91248i −0.0399687 + 0.178394i
$$482$$ 0 0
$$483$$ −1.19931 + 0.692423i −0.0545706 + 0.0315063i
$$484$$ 0 0
$$485$$ −0.661472 + 1.14570i −0.0300359 + 0.0520237i
$$486$$ 0 0
$$487$$ 14.8638 + 8.58161i 0.673543 + 0.388870i 0.797418 0.603428i $$-0.206199\pi$$
−0.123875 + 0.992298i $$0.539532\pi$$
$$488$$ 0 0
$$489$$ 1.87393i 0.0847420i
$$490$$ 0 0
$$491$$ −4.28967 7.42992i −0.193590 0.335308i 0.752847 0.658195i $$-0.228680\pi$$
−0.946437 + 0.322887i $$0.895346\pi$$
$$492$$ 0 0
$$493$$ 1.33804 0.0602622
$$494$$ 0 0
$$495$$ −17.7460 −0.797621
$$496$$ 0 0
$$497$$ −0.648966 1.12404i −0.0291101 0.0504202i
$$498$$ 0 0
$$499$$ 24.2361i 1.08496i −0.840070 0.542479i $$-0.817486\pi$$
0.840070 0.542479i $$-0.182514\pi$$
$$500$$ 0 0
$$501$$ −5.95689 3.43921i −0.266134 0.153653i
$$502$$ 0 0
$$503$$ −16.1531 + 27.9780i −0.720231 + 1.24748i 0.240676 + 0.970606i $$0.422631\pi$$
−0.960907 + 0.276871i $$0.910702\pi$$
$$504$$ 0 0
$$505$$ 13.3977 7.73517i 0.596190 0.344211i
$$506$$ 0 0
$$507$$ −5.74124 + 3.98181i −0.254977 + 0.176839i
$$508$$ 0 0
$$509$$ −15.3052 + 8.83646i −0.678391 + 0.391669i −0.799249 0.601001i $$-0.794769\pi$$
0.120857 + 0.992670i $$0.461436\pi$$
$$510$$ 0 0
$$511$$ −1.54053 + 2.66828i −0.0681490 + 0.118038i
$$512$$ 0 0
$$513$$ 10.9120 + 6.30003i 0.481776 + 0.278153i
$$514$$ 0 0
$$515$$ 14.3730i 0.633352i
$$516$$ 0 0
$$517$$ −25.2775 43.7820i −1.11170 1.92553i
$$518$$ 0 0
$$519$$ −3.47244 −0.152423
$$520$$ 0 0
$$521$$ −8.01036 −0.350940 −0.175470 0.984485i $$-0.556145\pi$$
−0.175470 + 0.984485i $$0.556145\pi$$
$$522$$ 0 0
$$523$$ −6.56245 11.3665i −0.286956 0.497022i 0.686126 0.727483i $$-0.259310\pi$$
−0.973082 + 0.230461i $$0.925977\pi$$
$$524$$ 0 0
$$525$$ 0.205841i 0.00898365i
$$526$$ 0 0
$$527$$ −0.506594 0.292482i −0.0220676 0.0127407i
$$528$$ 0 0
$$529$$ −11.1312 + 19.2798i −0.483966 + 0.838253i
$$530$$ 0 0
$$531$$ 10.4473 6.03177i 0.453376 0.261757i
$$532$$ 0 0
$$533$$ 5.62439 25.1035i 0.243619 1.08735i
$$534$$ 0 0
$$535$$ −15.9664 + 9.21819i −0.690286 + 0.398537i
$$536$$ 0 0
$$537$$ 2.12874 3.68708i 0.0918617 0.159109i
$$538$$ 0 0
$$539$$ 38.8488 + 22.4294i 1.67334 + 0.966102i
$$540$$ 0 0
$$541$$ 34.0136i 1.46236i 0.682186 + 0.731179i $$0.261029\pi$$
−0.682186 + 0.731179i $$0.738971\pi$$
$$542$$ 0 0
$$543$$ 5.92452 + 10.2616i 0.254246 + 0.440366i
$$544$$ 0 0
$$545$$ −3.91578 −0.167734
$$546$$ 0 0
$$547$$ 11.1875 0.478342 0.239171 0.970977i $$-0.423124\pi$$
0.239171 + 0.970977i $$0.423124\pi$$
$$548$$ 0 0
$$549$$ −14.0968 24.4163i −0.601635 1.04206i
$$550$$ 0 0
$$551$$ 15.7525i 0.671080i
$$552$$ 0 0
$$553$$ −3.56145 2.05620i −0.151448 0.0874387i
$$554$$ 0 0
$$555$$ 0.298831 0.517591i 0.0126847 0.0219705i
$$556$$ 0 0
$$557$$ −37.9254 + 21.8962i −1.60695 + 0.927773i −0.616903 + 0.787039i $$0.711613\pi$$
−0.990047 + 0.140734i $$0.955054\pi$$
$$558$$ 0 0
$$559$$ −6.19210 19.7935i −0.261898 0.837174i
$$560$$ 0 0
$$561$$ 1.06230 0.613317i 0.0448502 0.0258943i
$$562$$ 0 0
$$563$$ −16.7879 + 29.0774i −0.707524 + 1.22547i 0.258248 + 0.966079i $$0.416855\pi$$
−0.965773 + 0.259390i $$0.916479\pi$$
$$564$$ 0 0
$$565$$ −17.5215 10.1161i −0.737137 0.425586i
$$566$$ 0 0
$$567$$ 2.48323i 0.104286i
$$568$$ 0 0
$$569$$ −15.4982 26.8437i −0.649719 1.12535i −0.983190 0.182586i $$-0.941553\pi$$
0.333471 0.942760i $$-0.391780\pi$$
$$570$$ 0 0
$$571$$ −19.3467 −0.809636 −0.404818 0.914397i $$-0.632665\pi$$
−0.404818 + 0.914397i $$0.632665\pi$$
$$572$$ 0 0
$$573$$ −10.0848 −0.421297
$$574$$ 0 0
$$575$$ 3.36387 + 5.82639i 0.140283 + 0.242977i
$$576$$ 0 0
$$577$$ 9.69204i 0.403485i −0.979439 0.201742i $$-0.935340\pi$$
0.979439 0.201742i $$-0.0646604\pi$$
$$578$$ 0 0
$$579$$ −5.77645 3.33504i −0.240061 0.138599i
$$580$$ 0 0
$$581$$ 1.58514 2.74554i 0.0657626 0.113904i
$$582$$ 0 0
$$583$$ 40.7044 23.5007i 1.68580 0.973300i
$$584$$ 0 0
$$585$$ −9.32931 + 2.91854i −0.385720 + 0.120667i
$$586$$ 0 0
$$587$$ −0.329349 + 0.190150i −0.0135937 + 0.00784831i −0.506781 0.862075i $$-0.669165\pi$$
0.493188 + 0.869923i $$0.335832\pi$$
$$588$$ 0 0
$$589$$ −3.44335 + 5.96406i −0.141881 + 0.245745i
$$590$$ 0 0
$$591$$ 0.268339 + 0.154925i 0.0110380 + 0.00637278i
$$592$$ 0 0
$$593$$ 7.10741i 0.291866i −0.989294 0.145933i $$-0.953382\pi$$
0.989294 0.145933i $$-0.0466185\pi$$
$$594$$ 0 0
$$595$$ 0.0667713 + 0.115651i 0.00273736 + 0.00474124i
$$596$$ 0 0
$$597$$ −6.40698 −0.262220
$$598$$ 0 0
$$599$$ −34.6217 −1.41460 −0.707302 0.706912i $$-0.750088\pi$$
−0.707302 + 0.706912i $$0.750088\pi$$
$$600$$ 0 0
$$601$$ 3.12700 + 5.41613i 0.127553 + 0.220928i 0.922728 0.385452i $$-0.125954\pi$$
−0.795175 + 0.606380i $$0.792621\pi$$
$$602$$ 0 0
$$603$$ 9.45224i 0.384925i
$$604$$ 0 0
$$605$$ 27.5780 + 15.9222i 1.12121 + 0.647328i
$$606$$ 0 0
$$607$$ −6.81414 + 11.8024i −0.276577 + 0.479046i −0.970532 0.240973i $$-0.922534\pi$$
0.693955 + 0.720019i $$0.255867\pi$$
$$608$$ 0 0
$$609$$ 0.684075 0.394951i 0.0277201 0.0160042i
$$610$$ 0 0
$$611$$ −20.4893 18.8596i −0.828907 0.762979i
$$612$$ 0 0
$$613$$ −1.99544 + 1.15207i −0.0805949 + 0.0465315i −0.539756 0.841822i $$-0.681483\pi$$
0.459161 + 0.888353i $$0.348150\pi$$
$$614$$ 0 0
$$615$$ −1.91738 + 3.32100i −0.0773163 + 0.133916i
$$616$$ 0 0
$$617$$ 17.3637 + 10.0250i 0.699037 + 0.403589i 0.806989 0.590567i $$-0.201096\pi$$
−0.107952 + 0.994156i $$0.534429\pi$$
$$618$$ 0 0
$$619$$ 9.82852i 0.395042i −0.980299 0.197521i $$-0.936711\pi$$
0.980299 0.197521i $$-0.0632890\pi$$
$$620$$ 0 0
$$621$$ 10.3253 + 17.8839i 0.414340 + 0.717658i
$$622$$ 0 0
$$623$$ −6.87769 −0.275549
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ −7.22049 12.5063i −0.288359 0.499452i
$$628$$ 0 0
$$629$$ 0.387742i 0.0154603i
$$630$$ 0 0
$$631$$ 20.1654 + 11.6425i 0.802772 + 0.463480i 0.844439 0.535651i $$-0.179934\pi$$
−0.0416678 + 0.999132i $$0.513267\pi$$
$$632$$ 0 0
$$633$$ 1.69307 2.93249i 0.0672937 0.116556i
$$634$$ 0 0
$$635$$ −11.9319 + 6.88887i −0.473502 + 0.273376i
$$636$$ 0 0
$$637$$ 24.1122 + 5.40229i 0.955360 + 0.214046i
$$638$$ 0 0
$$639$$ −7.95689 + 4.59391i −0.314770 + 0.181732i
$$640$$ 0 0
$$641$$ −7.97269 + 13.8091i −0.314902 + 0.545427i −0.979417 0.201849i $$-0.935305\pi$$
0.664514 + 0.747276i $$0.268638\pi$$
$$642$$ 0 0
$$643$$ −25.7205 14.8497i −1.01432 0.585617i −0.101865 0.994798i $$-0.532481\pi$$
−0.912453 + 0.409181i $$0.865814\pi$$
$$644$$ 0 0
$$645$$ 3.09147i 0.121727i
$$646$$ 0 0
$$647$$ −17.8375 30.8954i −0.701263 1.21462i −0.968023 0.250861i $$-0.919286\pi$$
0.266760 0.963763i $$-0.414047\pi$$
$$648$$ 0 0
$$649$$ −29.1252 −1.14326
$$650$$ 0 0
$$651$$ −0.345330 −0.0135345
$$652$$ 0 0
$$653$$ 16.4768 + 28.5387i 0.644789 + 1.11681i 0.984350 + 0.176223i $$0.0563879\pi$$
−0.339562 + 0.940584i $$0.610279\pi$$
$$654$$ 0 0
$$655$$ 5.66818i 0.221474i
$$656$$ 0 0
$$657$$ 18.8882 + 10.9051i 0.736900 + 0.425450i
$$658$$ 0 0
$$659$$ 21.2848 36.8663i 0.829138 1.43611i −0.0695778 0.997577i $$-0.522165\pi$$
0.898716 0.438532i $$-0.144501\pi$$
$$660$$ 0 0
$$661$$ −38.5631 + 22.2644i −1.49993 + 0.865985i −1.00000 8.00698e-5i $$-0.999975\pi$$
−0.499931 + 0.866065i $$0.666641\pi$$
$$662$$ 0 0
$$663$$ 0.457597 0.497138i 0.0177716 0.0193072i
$$664$$ 0 0
$$665$$ 1.36154 0.786088i 0.0527984 0.0304832i
$$666$$ 0 0
$$667$$ 12.9086 22.3584i 0.499824 0.865720i
$$668$$ 0 0
$$669$$ −5.33809 3.08195i −0.206383 0.119155i
$$670$$ 0 0
$$671$$ 68.0680i 2.62774i
$$672$$ 0 0
$$673$$ −12.9568 22.4418i −0.499448 0.865069i 0.500552 0.865707i $$-0.333130\pi$$
−1.00000 0.000637339i $$0.999797\pi$$
$$674$$ 0 0
$$675$$ 3.06947 0.118144
$$676$$ 0 0
$$677$$ 33.4647 1.28615 0.643076 0.765803i $$-0.277658\pi$$
0.643076 + 0.765803i $$0.277658\pi$$
$$678$$ 0 0
$$679$$ 0.253340 + 0.438797i 0.00972229 + 0.0168395i
$$680$$ 0 0
$$681$$ 10.3171i 0.395353i
$$682$$ 0 0
$$683$$ 31.9754 + 18.4610i 1.22350 + 0.706391i 0.965663 0.259797i $$-0.0836555\pi$$
0.257841 + 0.966187i $$0.416989\pi$$
$$684$$ 0 0
$$685$$ −1.66496 + 2.88380i −0.0636149 + 0.110184i
$$686$$ 0 0
$$687$$ −2.90049 + 1.67460i −0.110660 + 0.0638898i
$$688$$ 0 0
$$689$$ 17.5339 19.0490i 0.667990 0.725710i
$$690$$ 0 0
$$691$$ −10.0947 + 5.82817i −0.384020 + 0.221714i −0.679566 0.733614i $$-0.737832\pi$$
0.295546 + 0.955329i $$0.404499\pi$$
$$692$$ 0 0
$$693$$ −3.39830 + 5.88602i −0.129091 + 0.223591i
$$694$$ 0 0
$$695$$ 3.87234 + 2.23569i 0.146886 + 0.0848047i
$$696$$ 0 0
$$697$$ 2.48786i 0.0942344i
$$698$$ 0 0
$$699$$ −1.29595 2.24466i −0.0490175 0.0849008i
$$700$$ 0 0
$$701$$ 34.2429 1.29334 0.646669 0.762771i $$-0.276162\pi$$
0.646669 + 0.762771i $$0.276162\pi$$
$$702$$ 0 0
$$703$$ −4.56483 −0.172166
$$704$$ 0 0
$$705$$ 2.07553 + 3.59492i 0.0781689 + 0.135392i
$$706$$ 0 0
$$707$$ 5.92505i 0.222834i
$$708$$ 0 0
$$709$$ 39.7122 + 22.9278i 1.49142 + 0.861073i 0.999952 0.00982181i $$-0.00312643\pi$$
0.491470 + 0.870895i $$0.336460\pi$$
$$710$$ 0 0
$$711$$ −14.5555 + 25.2109i −0.545874 + 0.945481i
$$712$$ 0 0
$$713$$ −9.77465 + 5.64340i −0.366064 + 0.211347i
$$714$$ 0 0
$$715$$ 23.0294 + 5.15969i 0.861251 + 0.192962i
$$716$$ 0 0
$$717$$ −3.17535 + 1.83329i −0.118586 + 0.0684655i
$$718$$ 0 0
$$719$$ −6.35463 + 11.0065i −0.236988 + 0.410475i −0.959849 0.280519i $$-0.909493\pi$$
0.722861 + 0.690994i $$0.242827\pi$$
$$720$$ 0 0
$$721$$ 4.76729 + 2.75239i 0.177543 + 0.102505i
$$722$$ 0 0
$$723$$ 5.53615i 0.205892i
$$724$$ 0 0
$$725$$ −1.91872 3.32331i −0.0712593 0.123425i
$$726$$ 0 0
$$727$$ 13.4712 0.499619 0.249809 0.968295i $$-0.419632\pi$$
0.249809 + 0.968295i $$0.419632\pi$$
$$728$$ 0 0
$$729$$ −12.6293 −0.467750
$$730$$ 0 0
$$731$$ 1.00282 + 1.73693i 0.0370906 + 0.0642428i
$$732$$ 0 0
$$733$$ 34.2367i 1.26456i −0.774739 0.632281i $$-0.782119\pi$$
0.774739 0.632281i $$-0.217881\pi$$
$$734$$ 0 0
$$735$$ −3.18986 1.84167i −0.117660 0.0679309i
$$736$$ 0 0
$$737$$ 11.4103 19.7633i 0.420306 0.727991i
$$738$$ 0 0
$$739$$ −25.5951 + 14.7774i −0.941532 + 0.543594i −0.890440 0.455100i $$-0.849604\pi$$
−0.0510921 + 0.998694i $$0.516270\pi$$
$$740$$ 0 0
$$741$$ −5.85273 5.38722i −0.215005 0.197905i
$$742$$ 0 0
$$743$$ −16.7730 + 9.68392i −0.615343 + 0.355269i −0.775054 0.631895i $$-0.782277\pi$$
0.159710 + 0.987164i $$0.448944\pi$$
$$744$$ 0 0
$$745$$ −6.42338 + 11.1256i −0.235334 + 0.407611i
$$746$$ 0 0
$$747$$ −19.4352 11.2209i −0.711096 0.410551i
$$748$$ 0 0
$$749$$ 7.06102i 0.258004i
$$750$$ 0 0
$$751$$ 3.64103 + 6.30645i 0.132863 + 0.230126i 0.924779 0.380504i $$-0.124250\pi$$
−0.791916 + 0.610630i $$0.790916\pi$$
$$752$$ 0 0
$$753$$ 2.58789 0.0943081
$$754$$ 0 0
$$755$$ 7.20405 0.262182
$$756$$ 0 0
$$757$$ −13.6265 23.6018i −0.495264 0.857822i 0.504721 0.863282i $$-0.331595\pi$$
−0.999985 + 0.00546016i $$0.998262\pi$$
$$758$$ 0 0
$$759$$ 23.6677i 0.859083i
$$760$$ 0 0
$$761$$ −2.07310 1.19690i −0.0751497 0.0433877i 0.461954 0.886904i $$-0.347148\pi$$
−0.537104 + 0.843516i $$0.680482\pi$$
$$762$$ 0 0
$$763$$ −0.749860 + 1.29880i −0.0271468 + 0.0470196i
$$764$$ 0 0
$$765$$ 0.818674 0.472662i 0.0295992 0.0170891i
$$766$$ 0 0
$$767$$ −15.3116 + 4.79000i −0.552868 + 0.172957i
$$768$$ 0 0
$$769$$ 27.4598 15.8539i 0.990225 0.571707i 0.0848835 0.996391i $$-0.472948\pi$$
0.905342 + 0.424684i $$0.139615\pi$$
$$770$$ 0 0
$$771$$ 7.58630 13.1399i 0.273214 0.473220i
$$772$$ 0 0
$$773$$ 5.51142 + 3.18202i 0.198232 + 0.114449i 0.595831 0.803110i $$-0.296823\pi$$
−0.397599 + 0.917559i $$0.630156\pi$$
$$774$$ 0 0
$$775$$ 1.67765i 0.0602630i
$$776$$ 0 0
$$777$$ −0.114451 0.198234i −0.00410589 0.00711161i
$$778$$ 0 0
$$779$$ 29.2892 1.04939
$$780$$ 0 0
$$781$$ 22.1823 0.793746
$$782$$ 0 0
$$783$$ −5.88945 10.2008i −0.210472 0.364548i
$$784$$ 0 0
$$785$$ 1.76129i 0.0628632i
$$786$$ 0 0
$$787$$ 4.95505 + 2.86080i 0.176629 + 0.101977i 0.585708 0.810522i $$-0.300817\pi$$
−0.409079 + 0.912499i $$0.634150\pi$$
$$788$$ 0 0