# Properties

 Label 605.2.g.c.251.1 Level $605$ Weight $2$ Character 605.251 Analytic conductor $4.831$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$605 = 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 605.g (of order $$5$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.83094932229$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{10})$$ Defining polynomial: $$x^{4} - x^{3} + x^{2} - x + 1$$ x^4 - x^3 + x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 55) Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

## Embedding invariants

 Embedding label 251.1 Root $$-0.309017 - 0.951057i$$ of defining polynomial Character $$\chi$$ $$=$$ 605.251 Dual form 605.2.g.c.511.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.42705 + 1.76336i) q^{8} +(-0.927051 + 2.85317i) q^{9} +O(q^{10})$$ $$q+(-0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.42705 + 1.76336i) q^{8} +(-0.927051 + 2.85317i) q^{9} -1.00000 q^{10} +(-0.618034 + 1.90211i) q^{13} +(-0.309017 - 0.951057i) q^{16} +(-1.85410 - 5.70634i) q^{17} +(-2.42705 - 1.76336i) q^{18} +(-3.23607 + 2.35114i) q^{19} +(-0.309017 + 0.951057i) q^{20} +4.00000 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.61803 - 1.17557i) q^{26} +(4.85410 + 3.52671i) q^{29} +(-2.47214 + 7.60845i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(-2.42705 + 1.76336i) q^{36} +(1.61803 + 1.17557i) q^{37} +(-1.23607 - 3.80423i) q^{38} +(-2.42705 - 1.76336i) q^{40} +(1.61803 - 1.17557i) q^{41} -4.00000 q^{43} -3.00000 q^{45} +(-1.23607 + 3.80423i) q^{46} +(9.70820 - 7.05342i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(-1.61803 + 1.17557i) q^{52} +(-0.618034 + 1.90211i) q^{53} +(-4.85410 + 3.52671i) q^{58} +(-3.23607 - 2.35114i) q^{59} +(3.09017 + 9.51057i) q^{61} +(-6.47214 - 4.70228i) q^{62} +(2.16312 - 6.65740i) q^{64} -2.00000 q^{65} -16.0000 q^{67} +(1.85410 - 5.70634i) q^{68} +(2.47214 + 7.60845i) q^{71} +(-2.78115 - 8.55951i) q^{72} +(11.3262 + 8.22899i) q^{73} +(-1.61803 + 1.17557i) q^{74} -4.00000 q^{76} +(-2.47214 + 7.60845i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(0.618034 + 1.90211i) q^{82} +(1.23607 + 3.80423i) q^{83} +(4.85410 - 3.52671i) q^{85} +(1.23607 - 3.80423i) q^{86} +10.0000 q^{89} +(0.927051 - 2.85317i) q^{90} +(3.23607 + 2.35114i) q^{92} +(3.70820 + 11.4127i) q^{94} +(-3.23607 - 2.35114i) q^{95} +(3.09017 - 9.51057i) q^{97} +7.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + q^{2} + q^{4} - q^{5} - 3 q^{8} + 3 q^{9}+O(q^{10})$$ 4 * q + q^2 + q^4 - q^5 - 3 * q^8 + 3 * q^9 $$4 q + q^{2} + q^{4} - q^{5} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{13} + q^{16} + 6 q^{17} - 3 q^{18} - 4 q^{19} + q^{20} + 16 q^{23} - q^{25} - 2 q^{26} + 6 q^{29} + 8 q^{31} - 20 q^{32} + 24 q^{34} - 3 q^{36} + 2 q^{37} + 4 q^{38} - 3 q^{40} + 2 q^{41} - 16 q^{43} - 12 q^{45} + 4 q^{46} + 12 q^{47} + 7 q^{49} + q^{50} - 2 q^{52} + 2 q^{53} - 6 q^{58} - 4 q^{59} - 10 q^{61} - 8 q^{62} - 7 q^{64} - 8 q^{65} - 64 q^{67} - 6 q^{68} - 8 q^{71} + 9 q^{72} + 14 q^{73} - 2 q^{74} - 16 q^{76} + 8 q^{79} + q^{80} - 9 q^{81} - 2 q^{82} - 4 q^{83} + 6 q^{85} - 4 q^{86} + 40 q^{89} - 3 q^{90} + 4 q^{92} - 12 q^{94} - 4 q^{95} - 10 q^{97} + 28 q^{98}+O(q^{100})$$ 4 * q + q^2 + q^4 - q^5 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^13 + q^16 + 6 * q^17 - 3 * q^18 - 4 * q^19 + q^20 + 16 * q^23 - q^25 - 2 * q^26 + 6 * q^29 + 8 * q^31 - 20 * q^32 + 24 * q^34 - 3 * q^36 + 2 * q^37 + 4 * q^38 - 3 * q^40 + 2 * q^41 - 16 * q^43 - 12 * q^45 + 4 * q^46 + 12 * q^47 + 7 * q^49 + q^50 - 2 * q^52 + 2 * q^53 - 6 * q^58 - 4 * q^59 - 10 * q^61 - 8 * q^62 - 7 * q^64 - 8 * q^65 - 64 * q^67 - 6 * q^68 - 8 * q^71 + 9 * q^72 + 14 * q^73 - 2 * q^74 - 16 * q^76 + 8 * q^79 + q^80 - 9 * q^81 - 2 * q^82 - 4 * q^83 + 6 * q^85 - 4 * q^86 + 40 * q^89 - 3 * q^90 + 4 * q^92 - 12 * q^94 - 4 * q^95 - 10 * q^97 + 28 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$$.

 $$n$$ $$122$$ $$486$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.309017 + 0.951057i −0.218508 + 0.672499i 0.780378 + 0.625308i $$0.215027\pi$$
−0.998886 + 0.0471903i $$0.984973\pi$$
$$3$$ 0 0 −0.587785 0.809017i $$-0.700000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$4$$ 0.809017 + 0.587785i 0.404508 + 0.293893i
$$5$$ 0.309017 + 0.951057i 0.138197 + 0.425325i
$$6$$ 0 0
$$7$$ 0 0 0.587785 0.809017i $$-0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$8$$ −2.42705 + 1.76336i −0.858092 + 0.623440i
$$9$$ −0.927051 + 2.85317i −0.309017 + 0.951057i
$$10$$ −1.00000 −0.316228
$$11$$ 0 0
$$12$$ 0 0
$$13$$ −0.618034 + 1.90211i −0.171412 + 0.527551i −0.999451 0.0331183i $$-0.989456\pi$$
0.828040 + 0.560670i $$0.189456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.309017 0.951057i −0.0772542 0.237764i
$$17$$ −1.85410 5.70634i −0.449686 1.38399i −0.877262 0.480011i $$-0.840633\pi$$
0.427576 0.903979i $$-0.359367\pi$$
$$18$$ −2.42705 1.76336i −0.572061 0.415627i
$$19$$ −3.23607 + 2.35114i −0.742405 + 0.539389i −0.893463 0.449136i $$-0.851732\pi$$
0.151058 + 0.988525i $$0.451732\pi$$
$$20$$ −0.309017 + 0.951057i −0.0690983 + 0.212663i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ −0.809017 + 0.587785i −0.161803 + 0.117557i
$$26$$ −1.61803 1.17557i −0.317323 0.230548i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4.85410 + 3.52671i 0.901384 + 0.654894i 0.938821 0.344405i $$-0.111919\pi$$
−0.0374370 + 0.999299i $$0.511919\pi$$
$$30$$ 0 0
$$31$$ −2.47214 + 7.60845i −0.444009 + 1.36652i 0.439558 + 0.898214i $$0.355135\pi$$
−0.883567 + 0.468304i $$0.844865\pi$$
$$32$$ −5.00000 −0.883883
$$33$$ 0 0
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ −2.42705 + 1.76336i −0.404508 + 0.293893i
$$37$$ 1.61803 + 1.17557i 0.266003 + 0.193263i 0.712789 0.701378i $$-0.247432\pi$$
−0.446786 + 0.894641i $$0.647432\pi$$
$$38$$ −1.23607 3.80423i −0.200517 0.617127i
$$39$$ 0 0
$$40$$ −2.42705 1.76336i −0.383750 0.278811i
$$41$$ 1.61803 1.17557i 0.252694 0.183593i −0.454226 0.890887i $$-0.650084\pi$$
0.706920 + 0.707293i $$0.250084\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ −3.00000 −0.447214
$$46$$ −1.23607 + 3.80423i −0.182248 + 0.560903i
$$47$$ 9.70820 7.05342i 1.41609 1.02885i 0.423685 0.905810i $$-0.360736\pi$$
0.992402 0.123038i $$-0.0392637\pi$$
$$48$$ 0 0
$$49$$ −2.16312 6.65740i −0.309017 0.951057i
$$50$$ −0.309017 0.951057i −0.0437016 0.134500i
$$51$$ 0 0
$$52$$ −1.61803 + 1.17557i −0.224381 + 0.163022i
$$53$$ −0.618034 + 1.90211i −0.0848935 + 0.261275i −0.984488 0.175450i $$-0.943862\pi$$
0.899595 + 0.436726i $$0.143862\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −4.85410 + 3.52671i −0.637375 + 0.463080i
$$59$$ −3.23607 2.35114i −0.421300 0.306092i 0.356861 0.934158i $$-0.383847\pi$$
−0.778161 + 0.628065i $$0.783847\pi$$
$$60$$ 0 0
$$61$$ 3.09017 + 9.51057i 0.395656 + 1.21770i 0.928450 + 0.371458i $$0.121142\pi$$
−0.532794 + 0.846245i $$0.678858\pi$$
$$62$$ −6.47214 4.70228i −0.821962 0.597190i
$$63$$ 0 0
$$64$$ 2.16312 6.65740i 0.270390 0.832174i
$$65$$ −2.00000 −0.248069
$$66$$ 0 0
$$67$$ −16.0000 −1.95471 −0.977356 0.211604i $$-0.932131\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ 1.85410 5.70634i 0.224843 0.691995i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 2.47214 + 7.60845i 0.293389 + 0.902957i 0.983758 + 0.179500i $$0.0574480\pi$$
−0.690369 + 0.723457i $$0.742552\pi$$
$$72$$ −2.78115 8.55951i −0.327762 1.00875i
$$73$$ 11.3262 + 8.22899i 1.32564 + 0.963131i 0.999844 + 0.0176895i $$0.00563103\pi$$
0.325792 + 0.945441i $$0.394369\pi$$
$$74$$ −1.61803 + 1.17557i −0.188093 + 0.136657i
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −2.47214 + 7.60845i −0.278137 + 0.856018i 0.710235 + 0.703964i $$0.248589\pi$$
−0.988372 + 0.152053i $$0.951411\pi$$
$$80$$ 0.809017 0.587785i 0.0904508 0.0657164i
$$81$$ −7.28115 5.29007i −0.809017 0.587785i
$$82$$ 0.618034 + 1.90211i 0.0682504 + 0.210053i
$$83$$ 1.23607 + 3.80423i 0.135676 + 0.417568i 0.995695 0.0926948i $$-0.0295481\pi$$
−0.860018 + 0.510263i $$0.829548\pi$$
$$84$$ 0 0
$$85$$ 4.85410 3.52671i 0.526501 0.382526i
$$86$$ 1.23607 3.80423i 0.133289 0.410220i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0.927051 2.85317i 0.0977198 0.300750i
$$91$$ 0 0
$$92$$ 3.23607 + 2.35114i 0.337383 + 0.245123i
$$93$$ 0 0
$$94$$ 3.70820 + 11.4127i 0.382472 + 1.17713i
$$95$$ −3.23607 2.35114i −0.332014 0.241222i
$$96$$ 0 0
$$97$$ 3.09017 9.51057i 0.313759 0.965652i −0.662503 0.749059i $$-0.730506\pi$$
0.976262 0.216592i $$-0.0694942\pi$$
$$98$$ 7.00000 0.707107
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ 3.09017 9.51057i 0.307483 0.946337i −0.671255 0.741226i $$-0.734245\pi$$
0.978739 0.205110i $$-0.0657554\pi$$
$$102$$ 0 0
$$103$$ 3.23607 + 2.35114i 0.318859 + 0.231665i 0.735689 0.677320i $$-0.236859\pi$$
−0.416829 + 0.908985i $$0.636859\pi$$
$$104$$ −1.85410 5.70634i −0.181810 0.559553i
$$105$$ 0 0
$$106$$ −1.61803 1.17557i −0.157157 0.114182i
$$107$$ 9.70820 7.05342i 0.938527 0.681880i −0.00953827 0.999955i $$-0.503036\pi$$
0.948066 + 0.318074i $$0.103036\pi$$
$$108$$ 0 0
$$109$$ 18.0000 1.72409 0.862044 0.506834i $$-0.169184\pi$$
0.862044 + 0.506834i $$0.169184\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 4.85410 3.52671i 0.456636 0.331765i −0.335575 0.942014i $$-0.608930\pi$$
0.792210 + 0.610249i $$0.208930\pi$$
$$114$$ 0 0
$$115$$ 1.23607 + 3.80423i 0.115264 + 0.354746i
$$116$$ 1.85410 + 5.70634i 0.172149 + 0.529820i
$$117$$ −4.85410 3.52671i −0.448762 0.326045i
$$118$$ 3.23607 2.35114i 0.297904 0.216440i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ −10.0000 −0.905357
$$123$$ 0 0
$$124$$ −6.47214 + 4.70228i −0.581215 + 0.422277i
$$125$$ −0.809017 0.587785i −0.0723607 0.0525731i
$$126$$ 0 0
$$127$$ −4.94427 15.2169i −0.438733 1.35028i −0.889212 0.457495i $$-0.848747\pi$$
0.450479 0.892787i $$-0.351253\pi$$
$$128$$ −2.42705 1.76336i −0.214523 0.155860i
$$129$$ 0 0
$$130$$ 0.618034 1.90211i 0.0542052 0.166826i
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 4.94427 15.2169i 0.427120 1.31454i
$$135$$ 0 0
$$136$$ 14.5623 + 10.5801i 1.24871 + 0.907239i
$$137$$ 5.56231 + 17.1190i 0.475220 + 1.46258i 0.845661 + 0.533720i $$0.179207\pi$$
−0.370441 + 0.928856i $$0.620793\pi$$
$$138$$ 0 0
$$139$$ 9.70820 + 7.05342i 0.823439 + 0.598264i 0.917696 0.397284i $$-0.130047\pi$$
−0.0942564 + 0.995548i $$0.530047\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −8.00000 −0.671345
$$143$$ 0 0
$$144$$ 3.00000 0.250000
$$145$$ −1.85410 + 5.70634i −0.153975 + 0.473886i
$$146$$ −11.3262 + 8.22899i −0.937366 + 0.681036i
$$147$$ 0 0
$$148$$ 0.618034 + 1.90211i 0.0508021 + 0.156353i
$$149$$ 3.09017 + 9.51057i 0.253157 + 0.779136i 0.994187 + 0.107665i $$0.0343373\pi$$
−0.741031 + 0.671471i $$0.765663\pi$$
$$150$$ 0 0
$$151$$ 6.47214 4.70228i 0.526695 0.382666i −0.292425 0.956288i $$-0.594462\pi$$
0.819120 + 0.573622i $$0.194462\pi$$
$$152$$ 3.70820 11.4127i 0.300775 0.925690i
$$153$$ 18.0000 1.45521
$$154$$ 0 0
$$155$$ −8.00000 −0.642575
$$156$$ 0 0
$$157$$ 1.61803 1.17557i 0.129133 0.0938207i −0.521344 0.853347i $$-0.674569\pi$$
0.650477 + 0.759526i $$0.274569\pi$$
$$158$$ −6.47214 4.70228i −0.514895 0.374093i
$$159$$ 0 0
$$160$$ −1.54508 4.75528i −0.122150 0.375938i
$$161$$ 0 0
$$162$$ 7.28115 5.29007i 0.572061 0.415627i
$$163$$ 4.94427 15.2169i 0.387265 1.19188i −0.547558 0.836768i $$-0.684443\pi$$
0.934824 0.355112i $$-0.115557\pi$$
$$164$$ 2.00000 0.156174
$$165$$ 0 0
$$166$$ −4.00000 −0.310460
$$167$$ 2.47214 7.60845i 0.191300 0.588760i −0.808700 0.588221i $$-0.799829\pi$$
1.00000 0.000538710i $$-0.000171477\pi$$
$$168$$ 0 0
$$169$$ 7.28115 + 5.29007i 0.560089 + 0.406928i
$$170$$ 1.85410 + 5.70634i 0.142203 + 0.437656i
$$171$$ −3.70820 11.4127i −0.283573 0.872749i
$$172$$ −3.23607 2.35114i −0.246748 0.179273i
$$173$$ −4.85410 + 3.52671i −0.369051 + 0.268131i −0.756817 0.653627i $$-0.773247\pi$$
0.387767 + 0.921758i $$0.373247\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −3.09017 + 9.51057i −0.231618 + 0.712847i
$$179$$ −3.23607 + 2.35114i −0.241875 + 0.175733i −0.702118 0.712060i $$-0.747762\pi$$
0.460243 + 0.887793i $$0.347762\pi$$
$$180$$ −2.42705 1.76336i −0.180902 0.131433i
$$181$$ −3.09017 9.51057i −0.229691 0.706915i −0.997781 0.0665740i $$-0.978793\pi$$
0.768091 0.640341i $$-0.221207\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −9.70820 + 7.05342i −0.715698 + 0.519985i
$$185$$ −0.618034 + 1.90211i −0.0454388 + 0.139846i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 12.0000 0.875190
$$189$$ 0 0
$$190$$ 3.23607 2.35114i 0.234769 0.170570i
$$191$$ −6.47214 4.70228i −0.468307 0.340245i 0.328474 0.944513i $$-0.393466\pi$$
−0.796781 + 0.604268i $$0.793466\pi$$
$$192$$ 0 0
$$193$$ 8.03444 + 24.7275i 0.578332 + 1.77992i 0.624543 + 0.780991i $$0.285285\pi$$
−0.0462111 + 0.998932i $$0.514715\pi$$
$$194$$ 8.09017 + 5.87785i 0.580840 + 0.422005i
$$195$$ 0 0
$$196$$ 2.16312 6.65740i 0.154508 0.475528i
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0.927051 2.85317i 0.0655524 0.201750i
$$201$$ 0 0
$$202$$ 8.09017 + 5.87785i 0.569222 + 0.413564i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 1.61803 + 1.17557i 0.113008 + 0.0821054i
$$206$$ −3.23607 + 2.35114i −0.225468 + 0.163812i
$$207$$ −3.70820 + 11.4127i −0.257738 + 0.793236i
$$208$$ 2.00000 0.138675
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.23607 + 3.80423i −0.0850944 + 0.261894i −0.984546 0.175127i $$-0.943966\pi$$
0.899451 + 0.437021i $$0.143966\pi$$
$$212$$ −1.61803 + 1.17557i −0.111127 + 0.0807385i
$$213$$ 0 0
$$214$$ 3.70820 + 11.4127i 0.253488 + 0.780155i
$$215$$ −1.23607 3.80423i −0.0842991 0.259446i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −5.56231 + 17.1190i −0.376727 + 1.15945i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ 3.23607 2.35114i 0.216703 0.157444i −0.474138 0.880450i $$-0.657240\pi$$
0.690841 + 0.723006i $$0.257240\pi$$
$$224$$ 0 0
$$225$$ −0.927051 2.85317i −0.0618034 0.190211i
$$226$$ 1.85410 + 5.70634i 0.123333 + 0.379580i
$$227$$ −16.1803 11.7557i −1.07393 0.780254i −0.0973129 0.995254i $$-0.531025\pi$$
−0.976614 + 0.215000i $$0.931025\pi$$
$$228$$ 0 0
$$229$$ −3.09017 + 9.51057i −0.204204 + 0.628476i 0.795541 + 0.605900i $$0.207187\pi$$
−0.999745 + 0.0225760i $$0.992813\pi$$
$$230$$ −4.00000 −0.263752
$$231$$ 0 0
$$232$$ −18.0000 −1.18176
$$233$$ −1.85410 + 5.70634i −0.121466 + 0.373835i −0.993241 0.116073i $$-0.962969\pi$$
0.871774 + 0.489907i $$0.162969\pi$$
$$234$$ 4.85410 3.52671i 0.317323 0.230548i
$$235$$ 9.70820 + 7.05342i 0.633293 + 0.460115i
$$236$$ −1.23607 3.80423i −0.0804612 0.247634i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 6.47214 4.70228i 0.418648 0.304165i −0.358446 0.933551i $$-0.616693\pi$$
0.777093 + 0.629385i $$0.216693\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ −3.09017 + 9.51057i −0.197828 + 0.608852i
$$245$$ 5.66312 4.11450i 0.361803 0.262866i
$$246$$ 0 0
$$247$$ −2.47214 7.60845i −0.157298 0.484114i
$$248$$ −7.41641 22.8254i −0.470942 1.44941i
$$249$$ 0 0
$$250$$ 0.809017 0.587785i 0.0511667 0.0371748i
$$251$$ 3.70820 11.4127i 0.234060 0.720362i −0.763185 0.646180i $$-0.776365\pi$$
0.997245 0.0741818i $$-0.0236345\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 16.0000 1.00393
$$255$$ 0 0
$$256$$ 13.7533 9.99235i 0.859581 0.624522i
$$257$$ −14.5623 10.5801i −0.908372 0.659971i 0.0322308 0.999480i $$-0.489739\pi$$
−0.940603 + 0.339510i $$0.889739\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −1.61803 1.17557i −0.100346 0.0729058i
$$261$$ −14.5623 + 10.5801i −0.901384 + 0.654894i
$$262$$ −3.70820 + 11.4127i −0.229094 + 0.705078i
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ 0 0
$$265$$ −2.00000 −0.122859
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −12.9443 9.40456i −0.790697 0.574475i
$$269$$ −5.56231 17.1190i −0.339140 1.04376i −0.964647 0.263546i $$-0.915108\pi$$
0.625507 0.780219i $$-0.284892\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.587785 0.809017i $$-0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$272$$ −4.85410 + 3.52671i −0.294323 + 0.213838i
$$273$$ 0 0
$$274$$ −18.0000 −1.08742
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −3.09017 + 9.51057i −0.185670 + 0.571434i −0.999959 0.00902525i $$-0.997127\pi$$
0.814289 + 0.580460i $$0.197127\pi$$
$$278$$ −9.70820 + 7.05342i −0.582259 + 0.423036i
$$279$$ −19.4164 14.1068i −1.16243 0.844555i
$$280$$ 0 0
$$281$$ −5.56231 17.1190i −0.331819 1.02123i −0.968268 0.249916i $$-0.919597\pi$$
0.636448 0.771319i $$-0.280403\pi$$
$$282$$ 0 0
$$283$$ 3.23607 2.35114i 0.192364 0.139761i −0.487434 0.873160i $$-0.662067\pi$$
0.679799 + 0.733399i $$0.262067\pi$$
$$284$$ −2.47214 + 7.60845i −0.146694 + 0.451479i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 4.63525 14.2658i 0.273135 0.840623i
$$289$$ −15.3713 + 11.1679i −0.904195 + 0.656936i
$$290$$ −4.85410 3.52671i −0.285043 0.207096i
$$291$$ 0 0
$$292$$ 4.32624 + 13.3148i 0.253174 + 0.779189i
$$293$$ 8.09017 + 5.87785i 0.472633 + 0.343388i 0.798466 0.602039i $$-0.205645\pi$$
−0.325834 + 0.945427i $$0.605645\pi$$
$$294$$ 0 0
$$295$$ 1.23607 3.80423i 0.0719667 0.221491i
$$296$$ −6.00000 −0.348743
$$297$$ 0 0
$$298$$ −10.0000 −0.579284
$$299$$ −2.47214 + 7.60845i −0.142967 + 0.440008i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 2.47214 + 7.60845i 0.142255 + 0.437817i
$$303$$ 0 0
$$304$$ 3.23607 + 2.35114i 0.185601 + 0.134847i
$$305$$ −8.09017 + 5.87785i −0.463242 + 0.336565i
$$306$$ −5.56231 + 17.1190i −0.317976 + 0.978629i
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 2.47214 7.60845i 0.140408 0.432131i
$$311$$ 19.4164 14.1068i 1.10100 0.799926i 0.119780 0.992800i $$-0.461781\pi$$
0.981223 + 0.192875i $$0.0617811\pi$$
$$312$$ 0 0
$$313$$ −6.79837 20.9232i −0.384267 1.18265i −0.937011 0.349300i $$-0.886419\pi$$
0.552744 0.833351i $$-0.313581\pi$$
$$314$$ 0.618034 + 1.90211i 0.0348777 + 0.107342i
$$315$$ 0 0
$$316$$ −6.47214 + 4.70228i −0.364086 + 0.264524i
$$317$$ −5.56231 + 17.1190i −0.312410 + 0.961500i 0.664397 + 0.747380i $$0.268688\pi$$
−0.976807 + 0.214120i $$0.931312\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 7.00000 0.391312
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 19.4164 + 14.1068i 1.08036 + 0.784926i
$$324$$ −2.78115 8.55951i −0.154508 0.475528i
$$325$$ −0.618034 1.90211i −0.0342824 0.105510i
$$326$$ 12.9443 + 9.40456i 0.716917 + 0.520871i
$$327$$ 0 0
$$328$$ −1.85410 + 5.70634i −0.102376 + 0.315080i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 4.00000 0.219860 0.109930 0.993939i $$-0.464937\pi$$
0.109930 + 0.993939i $$0.464937\pi$$
$$332$$ −1.23607 + 3.80423i −0.0678380 + 0.208784i
$$333$$ −4.85410 + 3.52671i −0.266003 + 0.193263i
$$334$$ 6.47214 + 4.70228i 0.354140 + 0.257297i
$$335$$ −4.94427 15.2169i −0.270134 0.831388i
$$336$$ 0 0
$$337$$ 4.85410 + 3.52671i 0.264420 + 0.192112i 0.712093 0.702085i $$-0.247747\pi$$
−0.447673 + 0.894197i $$0.647747\pi$$
$$338$$ −7.28115 + 5.29007i −0.396043 + 0.287742i
$$339$$ 0 0
$$340$$ 6.00000 0.325396
$$341$$ 0 0
$$342$$ 12.0000 0.648886
$$343$$ 0 0
$$344$$ 9.70820 7.05342i 0.523431 0.380295i
$$345$$ 0 0
$$346$$ −1.85410 5.70634i −0.0996771 0.306775i
$$347$$ 1.23607 + 3.80423i 0.0663556 + 0.204222i 0.978737 0.205120i $$-0.0657585\pi$$
−0.912381 + 0.409342i $$0.865758\pi$$
$$348$$ 0 0
$$349$$ −8.09017 + 5.87785i −0.433057 + 0.314634i −0.782870 0.622185i $$-0.786245\pi$$
0.349813 + 0.936819i $$0.386245\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 0 0
$$355$$ −6.47214 + 4.70228i −0.343505 + 0.249571i
$$356$$ 8.09017 + 5.87785i 0.428778 + 0.311526i
$$357$$ 0 0
$$358$$ −1.23607 3.80423i −0.0653282 0.201060i
$$359$$ −25.8885 18.8091i −1.36635 0.992708i −0.998013 0.0630137i $$-0.979929\pi$$
−0.368332 0.929694i $$-0.620071\pi$$
$$360$$ 7.28115 5.29007i 0.383750 0.278811i
$$361$$ −0.927051 + 2.85317i −0.0487922 + 0.150167i
$$362$$ 10.0000 0.525588
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −4.32624 + 13.3148i −0.226446 + 0.696928i
$$366$$ 0 0
$$367$$ −3.23607 2.35114i −0.168921 0.122729i 0.500113 0.865960i $$-0.333292\pi$$
−0.669034 + 0.743232i $$0.733292\pi$$
$$368$$ −1.23607 3.80423i −0.0644345 0.198309i
$$369$$ 1.85410 + 5.70634i 0.0965207 + 0.297060i
$$370$$ −1.61803 1.17557i −0.0841176 0.0611150i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −18.0000 −0.932005 −0.466002 0.884783i $$-0.654306\pi$$
−0.466002 + 0.884783i $$0.654306\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −11.1246 + 34.2380i −0.573708 + 1.76569i
$$377$$ −9.70820 + 7.05342i −0.499998 + 0.363270i
$$378$$ 0 0
$$379$$ 6.18034 + 19.0211i 0.317463 + 0.977050i 0.974729 + 0.223391i $$0.0717128\pi$$
−0.657266 + 0.753659i $$0.728287\pi$$
$$380$$ −1.23607 3.80423i −0.0634089 0.195153i
$$381$$ 0 0
$$382$$ 6.47214 4.70228i 0.331143 0.240590i
$$383$$ −3.70820 + 11.4127i −0.189480 + 0.583161i −0.999997 0.00255538i $$-0.999187\pi$$
0.810516 + 0.585716i $$0.199187\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −26.0000 −1.32337
$$387$$ 3.70820 11.4127i 0.188499 0.580139i
$$388$$ 8.09017 5.87785i 0.410716 0.298403i
$$389$$ −4.85410 3.52671i −0.246113 0.178811i 0.457890 0.889009i $$-0.348606\pi$$
−0.704002 + 0.710198i $$0.748606\pi$$
$$390$$ 0 0
$$391$$ −7.41641 22.8254i −0.375064 1.15433i
$$392$$ 16.9894 + 12.3435i 0.858092 + 0.623440i
$$393$$ 0 0
$$394$$ 0.618034 1.90211i 0.0311361 0.0958271i
$$395$$ −8.00000 −0.402524
$$396$$ 0 0
$$397$$ 30.0000 1.50566 0.752828 0.658217i $$-0.228689\pi$$
0.752828 + 0.658217i $$0.228689\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0.809017 + 0.587785i 0.0404508 + 0.0293893i
$$401$$ 0.618034 + 1.90211i 0.0308631 + 0.0949870i 0.965301 0.261138i $$-0.0840977\pi$$
−0.934438 + 0.356125i $$0.884098\pi$$
$$402$$ 0 0
$$403$$ −12.9443 9.40456i −0.644800 0.468475i
$$404$$ 8.09017 5.87785i 0.402501 0.292434i
$$405$$ 2.78115 8.55951i 0.138197 0.425325i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 1.85410 5.70634i 0.0916794 0.282160i −0.894695 0.446678i $$-0.852607\pi$$
0.986374 + 0.164518i $$0.0526069\pi$$
$$410$$ −1.61803 + 1.17557i −0.0799090 + 0.0580573i
$$411$$ 0 0
$$412$$ 1.23607 + 3.80423i 0.0608967 + 0.187421i
$$413$$ 0 0
$$414$$ −9.70820 7.05342i −0.477132 0.346657i
$$415$$ −3.23607 + 2.35114i −0.158852 + 0.115413i
$$416$$ 3.09017 9.51057i 0.151508 0.466294i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ 0 0
$$421$$ −4.85410 + 3.52671i −0.236574 + 0.171881i −0.699756 0.714382i $$-0.746708\pi$$
0.463181 + 0.886264i $$0.346708\pi$$
$$422$$ −3.23607 2.35114i −0.157529 0.114452i
$$423$$ 11.1246 + 34.2380i 0.540897 + 1.66471i
$$424$$ −1.85410 5.70634i −0.0900432 0.277124i
$$425$$ 4.85410 + 3.52671i 0.235459 + 0.171071i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 4.00000 0.192897
$$431$$ 7.41641 22.8254i 0.357236 1.09946i −0.597466 0.801894i $$-0.703826\pi$$
0.954702 0.297564i $$-0.0961743\pi$$
$$432$$ 0 0
$$433$$ 17.7984 + 12.9313i 0.855335 + 0.621437i 0.926612 0.376019i $$-0.122707\pi$$
−0.0712766 + 0.997457i $$0.522707\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 14.5623 + 10.5801i 0.697408 + 0.506697i
$$437$$ −12.9443 + 9.40456i −0.619208 + 0.449881i
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 0 0
$$441$$ 21.0000 1.00000
$$442$$ −3.70820 + 11.4127i −0.176381 + 0.542846i
$$443$$ −6.47214 + 4.70228i −0.307500 + 0.223412i −0.730823 0.682567i $$-0.760864\pi$$
0.423323 + 0.905979i $$0.360864\pi$$
$$444$$ 0 0
$$445$$ 3.09017 + 9.51057i 0.146488 + 0.450844i
$$446$$ 1.23607 + 3.80423i 0.0585295 + 0.180135i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.618034 1.90211i 0.0291668 0.0897663i −0.935413 0.353556i $$-0.884972\pi$$
0.964580 + 0.263790i $$0.0849724\pi$$
$$450$$ 3.00000 0.141421
$$451$$ 0 0
$$452$$ 6.00000 0.282216
$$453$$ 0 0
$$454$$ 16.1803 11.7557i 0.759381 0.551723i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 8.03444 + 24.7275i 0.375835 + 1.15670i 0.942913 + 0.333038i $$0.108074\pi$$
−0.567078 + 0.823664i $$0.691926\pi$$
$$458$$ −8.09017 5.87785i −0.378029 0.274654i
$$459$$ 0 0
$$460$$ −1.23607 + 3.80423i −0.0576320 + 0.177373i
$$461$$ 34.0000 1.58354 0.791769 0.610821i $$-0.209160\pi$$
0.791769 + 0.610821i $$0.209160\pi$$
$$462$$ 0 0
$$463$$ −36.0000 −1.67306 −0.836531 0.547920i $$-0.815420\pi$$
−0.836531 + 0.547920i $$0.815420\pi$$
$$464$$ 1.85410 5.70634i 0.0860745 0.264910i
$$465$$ 0 0
$$466$$ −4.85410 3.52671i −0.224862 0.163372i
$$467$$ 0 0 0.951057 0.309017i $$-0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$468$$ −1.85410 5.70634i −0.0857059 0.263776i
$$469$$ 0 0
$$470$$ −9.70820 + 7.05342i −0.447806 + 0.325350i
$$471$$ 0 0
$$472$$ 12.0000 0.552345
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 1.23607 3.80423i 0.0567147 0.174550i
$$476$$ 0 0
$$477$$ −4.85410 3.52671i −0.222254 0.161477i
$$478$$ 2.47214 + 7.60845i 0.113073 + 0.348003i
$$479$$ −7.41641 22.8254i −0.338864 1.04292i −0.964787 0.263032i $$-0.915277\pi$$
0.625923 0.779885i $$-0.284723\pi$$
$$480$$ 0 0
$$481$$ −3.23607 + 2.35114i −0.147552 + 0.107203i
$$482$$ 3.09017 9.51057i 0.140753 0.433194i
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 10.0000 0.454077
$$486$$ 0 0
$$487$$ −22.6525 + 16.4580i −1.02648 + 0.745783i −0.967601 0.252482i $$-0.918753\pi$$
−0.0588802 + 0.998265i $$0.518753\pi$$
$$488$$ −24.2705 17.6336i −1.09867 0.798234i
$$489$$ 0 0
$$490$$ 2.16312 + 6.65740i 0.0977198 + 0.300750i
$$491$$ −22.6525 16.4580i −1.02229 0.742739i −0.0555405 0.998456i $$-0.517688\pi$$
−0.966751 + 0.255718i $$0.917688\pi$$
$$492$$ 0 0
$$493$$ 11.1246 34.2380i 0.501027 1.54200i
$$494$$ 8.00000 0.359937
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 29.1246 + 21.1603i 1.30380 + 0.947264i 0.999985 0.00546838i $$-0.00174065\pi$$
0.303812 + 0.952732i $$0.401741\pi$$
$$500$$ −0.309017 0.951057i −0.0138197 0.0425325i
$$501$$ 0 0
$$502$$ 9.70820 + 7.05342i 0.433298 + 0.314810i
$$503$$ −12.9443 + 9.40456i −0.577157 + 0.419329i −0.837698 0.546134i $$-0.816099\pi$$
0.260541 + 0.965463i $$0.416099\pi$$
$$504$$ 0 0
$$505$$ 10.0000 0.444994
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 4.94427 15.2169i 0.219367 0.675141i
$$509$$ −11.3262 + 8.22899i −0.502027 + 0.364744i −0.809791 0.586719i $$-0.800419\pi$$
0.307764 + 0.951463i $$0.400419\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 3.39919 + 10.4616i 0.150224 + 0.462343i
$$513$$ 0 0
$$514$$ 14.5623 10.5801i 0.642316 0.466670i
$$515$$ −1.23607 + 3.80423i −0.0544677 + 0.167634i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 4.85410 3.52671i 0.212866 0.154657i
$$521$$ 4.85410 + 3.52671i 0.212662 + 0.154508i 0.689017 0.724745i $$-0.258042\pi$$
−0.476355 + 0.879253i $$0.658042\pi$$
$$522$$ −5.56231 17.1190i −0.243456 0.749279i
$$523$$ 6.18034 + 19.0211i 0.270247 + 0.831736i 0.990438 + 0.137960i $$0.0440544\pi$$
−0.720190 + 0.693776i $$0.755946\pi$$
$$524$$ 9.70820 + 7.05342i 0.424105 + 0.308130i
$$525$$ 0 0
$$526$$ 7.41641 22.8254i 0.323371 0.995233i
$$527$$ 48.0000 2.09091
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 0.618034 1.90211i 0.0268457 0.0826225i
$$531$$ 9.70820 7.05342i 0.421300 0.306092i
$$532$$ 0 0
$$533$$ 1.23607 + 3.80423i 0.0535400 + 0.164779i
$$534$$ 0 0
$$535$$ 9.70820 + 7.05342i 0.419722 + 0.304946i
$$536$$ 38.8328 28.2137i 1.67732 1.21865i
$$537$$ 0 0
$$538$$ 18.0000 0.776035
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 10.5066 32.3359i 0.451713 1.39023i −0.423238 0.906019i $$-0.639107\pi$$
0.874951 0.484211i $$-0.160893\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 9.27051 + 28.5317i 0.397470 + 1.22329i
$$545$$ 5.56231 + 17.1190i 0.238263 + 0.733298i
$$546$$ 0 0
$$547$$ 9.70820 7.05342i 0.415093 0.301583i −0.360568 0.932733i $$-0.617417\pi$$
0.775660 + 0.631151i $$0.217417\pi$$
$$548$$ −5.56231 + 17.1190i −0.237610 + 0.731288i
$$549$$ −30.0000 −1.28037
$$550$$ 0 0
$$551$$ −24.0000 −1.02243
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −8.09017 5.87785i −0.343718 0.249726i
$$555$$ 0 0
$$556$$ 3.70820 + 11.4127i 0.157263 + 0.484005i
$$557$$ 8.09017 + 5.87785i 0.342792 + 0.249053i 0.745839 0.666127i $$-0.232049\pi$$
−0.403047 + 0.915179i $$0.632049\pi$$
$$558$$ 19.4164 14.1068i 0.821962 0.597190i
$$559$$ 2.47214 7.60845i 0.104560 0.321803i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 18.0000 0.759284
$$563$$ −11.1246 + 34.2380i −0.468846 + 1.44296i 0.385233 + 0.922819i $$0.374121\pi$$
−0.854080 + 0.520142i $$0.825879\pi$$
$$564$$ 0 0
$$565$$ 4.85410 + 3.52671i 0.204214 + 0.148370i
$$566$$ 1.23607 + 3.80423i 0.0519558 + 0.159904i
$$567$$ 0 0
$$568$$ −19.4164 14.1068i −0.814694 0.591910i
$$569$$ 21.0344 15.2824i 0.881810 0.640672i −0.0519200 0.998651i $$-0.516534\pi$$
0.933730 + 0.357979i $$0.116534\pi$$
$$570$$ 0 0
$$571$$ −36.0000 −1.50655 −0.753277 0.657704i $$-0.771528\pi$$
−0.753277 + 0.657704i $$0.771528\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −3.23607 + 2.35114i −0.134953 + 0.0980494i
$$576$$ 16.9894 + 12.3435i 0.707890 + 0.514312i
$$577$$ −6.79837 20.9232i −0.283020 0.871046i −0.986985 0.160811i $$-0.948589\pi$$
0.703965 0.710235i $$-0.251411\pi$$
$$578$$ −5.87132 18.0701i −0.244215 0.751616i
$$579$$ 0 0
$$580$$ −4.85410 + 3.52671i −0.201556 + 0.146439i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −42.0000 −1.73797
$$585$$ 1.85410 5.70634i 0.0766577 0.235928i
$$586$$ −8.09017 + 5.87785i −0.334202 + 0.242812i
$$587$$ 19.4164 + 14.1068i 0.801401 + 0.582252i 0.911325 0.411688i $$-0.135061\pi$$
−0.109924 + 0.993940i $$0.535061\pi$$
$$588$$ 0 0
$$589$$ −9.88854 30.4338i −0.407450 1.25400i
$$590$$ 3.23607 + 2.35114i 0.133227 + 0.0967949i
$$591$$ 0 0
$$592$$ 0.618034 1.90211i 0.0254010 0.0781764i
$$593$$ −22.0000 −0.903432 −0.451716 0.892162i $$-0.649188\pi$$
−0.451716 + 0.892162i $$0.649188\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −3.09017 + 9.51057i −0.126578 + 0.389568i
$$597$$ 0 0
$$598$$ −6.47214 4.70228i −0.264665 0.192291i
$$599$$ 7.41641 + 22.8254i 0.303026 + 0.932619i 0.980406 + 0.196986i $$0.0631152\pi$$
−0.677380 + 0.735633i $$0.736885\pi$$
$$600$$ 0 0
$$601$$ 1.61803 + 1.17557i 0.0660010 + 0.0479525i 0.620297 0.784367i $$-0.287012\pi$$
−0.554296 + 0.832320i $$0.687012\pi$$
$$602$$ 0 0
$$603$$ 14.8328 45.6507i 0.604039 1.85904i
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 9.88854 30.4338i 0.401364 1.23527i −0.522530 0.852621i $$-0.675012\pi$$
0.923894 0.382649i $$-0.124988\pi$$
$$608$$ 16.1803 11.7557i 0.656199 0.476757i
$$609$$ 0 0
$$610$$ −3.09017 9.51057i −0.125117 0.385072i
$$611$$ 7.41641 + 22.8254i 0.300036 + 0.923415i
$$612$$ 14.5623 + 10.5801i 0.588646 + 0.427677i
$$613$$ 27.5066 19.9847i 1.11098 0.807174i 0.128162 0.991753i $$-0.459092\pi$$
0.982818 + 0.184579i $$0.0590921\pi$$
$$614$$ 6.18034 19.0211i 0.249418 0.767630i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 2.00000 0.0805170 0.0402585 0.999189i $$-0.487182\pi$$
0.0402585 + 0.999189i $$0.487182\pi$$
$$618$$ 0 0
$$619$$ 16.1803 11.7557i 0.650343 0.472502i −0.213045 0.977042i $$-0.568338\pi$$
0.863388 + 0.504541i $$0.168338\pi$$
$$620$$ −6.47214 4.70228i −0.259927 0.188848i
$$621$$ 0 0
$$622$$ 7.41641 + 22.8254i 0.297371 + 0.915213i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.309017 0.951057i 0.0123607 0.0380423i
$$626$$ 22.0000 0.879297
$$627$$ 0 0
$$628$$ 2.00000 0.0798087
$$629$$ 3.70820 11.4127i 0.147856 0.455053i
$$630$$ 0 0
$$631$$ −32.3607 23.5114i −1.28826 0.935974i −0.288490 0.957483i $$-0.593153\pi$$
−0.999769 + 0.0215086i $$0.993153\pi$$
$$632$$ −7.41641 22.8254i −0.295009 0.907944i
$$633$$ 0 0
$$634$$ −14.5623 10.5801i −0.578343 0.420191i
$$635$$ 12.9443 9.40456i 0.513678 0.373209i
$$636$$ 0 0
$$637$$ 14.0000 0.554700
$$638$$ 0 0
$$639$$ −24.0000 −0.949425
$$640$$ 0.927051 2.85317i 0.0366449 0.112781i
$$641$$ −27.5066 + 19.9847i −1.08644 + 0.789348i −0.978795 0.204841i $$-0.934332\pi$$
−0.107649 + 0.994189i $$0.534332\pi$$
$$642$$ 0 0
$$643$$ −4.94427 15.2169i −0.194983 0.600096i −0.999977 0.00681282i $$-0.997831\pi$$
0.804994 0.593283i $$-0.202169\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −19.4164 + 14.1068i −0.763928 + 0.555026i
$$647$$ 6.18034 19.0211i 0.242974 0.747798i −0.752989 0.658033i $$-0.771389\pi$$
0.995963 0.0897645i $$-0.0286114\pi$$
$$648$$ 27.0000 1.06066
$$649$$ 0 0
$$650$$ 2.00000 0.0784465
$$651$$ 0 0
$$652$$ 12.9443 9.40456i 0.506937 0.368311i
$$653$$ 8.09017 + 5.87785i 0.316593 + 0.230018i 0.734720 0.678370i $$-0.237313\pi$$
−0.418127 + 0.908388i $$0.637313\pi$$
$$654$$ 0 0
$$655$$ 3.70820 + 11.4127i 0.144892 + 0.445930i
$$656$$ −1.61803 1.17557i −0.0631736 0.0458983i
$$657$$ −33.9787 + 24.6870i −1.32564 + 0.963131i
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −10.0000 −0.388955 −0.194477 0.980907i $$-0.562301\pi$$
−0.194477 + 0.980907i $$0.562301\pi$$
$$662$$ −1.23607 + 3.80423i −0.0480411 + 0.147855i
$$663$$ 0 0
$$664$$ −9.70820 7.05342i −0.376751 0.273726i
$$665$$ 0 0
$$666$$ −1.85410 5.70634i −0.0718450 0.221116i
$$667$$ 19.4164 + 14.1068i 0.751806 + 0.546219i
$$668$$ 6.47214 4.70228i 0.250414 0.181937i
$$669$$ 0 0
$$670$$ 16.0000 0.618134
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 8.03444 24.7275i 0.309705 0.953174i −0.668174 0.744005i $$-0.732924\pi$$
0.977879 0.209169i $$-0.0670760\pi$$
$$674$$ −4.85410 + 3.52671i −0.186973 + 0.135844i
$$675$$ 0 0
$$676$$ 2.78115 + 8.55951i 0.106967 + 0.329212i
$$677$$ 11.7426 + 36.1401i 0.451307 + 1.38898i 0.875417 + 0.483368i $$0.160587\pi$$
−0.424111 + 0.905610i $$0.639413\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −5.56231 + 17.1190i −0.213305 + 0.656484i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −16.0000 −0.612223 −0.306111 0.951996i $$-0.599028\pi$$
−0.306111 + 0.951996i $$0.599028\pi$$
$$684$$ 3.70820 11.4127i 0.141787 0.436375i
$$685$$ −14.5623 + 10.5801i −0.556397 + 0.404246i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 1.23607 + 3.80423i 0.0471246 + 0.145035i
$$689$$ −3.23607 2.35114i −0.123284 0.0895713i
$$690$$ 0 0
$$691$$ −8.65248 + 26.6296i −0.329156 + 1.01304i 0.640374 + 0.768063i $$0.278779\pi$$
−0.969530 + 0.244974i $$0.921221\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ −4.00000 −0.151838
$$695$$ −3.70820 + 11.4127i −0.140660 + 0.432908i
$$696$$ 0 0
$$697$$ −9.70820 7.05342i −0.367724 0.267167i
$$698$$ −3.09017 9.51057i −0.116965 0.359980i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 17.7984 12.9313i 0.672235 0.488408i −0.198537 0.980093i $$-0.563619\pi$$
0.870773 + 0.491686i $$0.163619\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −5.56231 + 17.1190i −0.209340 + 0.644283i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −3.09017 9.51057i −0.116054 0.357177i 0.876112 0.482108i $$-0.160129\pi$$
−0.992165 + 0.124932i $$0.960129\pi$$
$$710$$ −2.47214 7.60845i −0.0927776 0.285540i
$$711$$ −19.4164 14.1068i −0.728172 0.529048i
$$712$$ −24.2705 + 17.6336i −0.909576 + 0.660846i
$$713$$ −9.88854 + 30.4338i −0.370329 + 1.13976i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −4.00000 −0.149487
$$717$$ 0 0
$$718$$ 25.8885 18.8091i 0.966152 0.701950i
$$719$$ 0 0 0.587785 0.809017i $$-0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$720$$ 0.927051 + 2.85317i 0.0345492 + 0.106331i
$$721$$ 0 0
$$722$$ −2.42705 1.76336i −0.0903255 0.0656253i
$$723$$ 0 0
$$724$$ 3.09017 9.51057i 0.114845 0.353457i
$$725$$ −6.00000 −0.222834
$$726$$ 0 0
$$727$$ 52.0000 1.92857 0.964287 0.264861i $$-0.0853260\pi$$
0.964287 + 0.264861i $$0.0853260\pi$$
$$728$$ 0 0
$$729$$ 21.8435 15.8702i 0.809017 0.587785i
$$730$$ −11.3262 8.22899i −0.419203 0.304569i
$$731$$ 7.41641 + 22.8254i 0.274306 + 0.844226i
$$732$$ 0 0
$$733$$ 33.9787 + 24.6870i 1.25503 + 0.911834i 0.998503 0.0547019i $$-0.0174209\pi$$
0.256530 + 0.966536i $$0.417421\pi$$
$$734$$ 3.23607 2.35114i 0.119445 0.0867822i
$$735$$ 0 0
$$736$$ −20.0000 −0.737210
$$737$$ 0 0
$$738$$ −6.00000 −0.220863
$$739$$ −1.23607 + 3.80423i −0.0454695 + 0.139941i −0.971214 0.238209i $$-0.923440\pi$$
0.925744 + 0.378150i $$0.123440\pi$$
$$740$$ −1.61803 + 1.17557i −0.0594801 + 0.0432148i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −12.3607 38.0423i −0.453469 1.39564i −0.872923 0.487858i $$-0.837778\pi$$
0.419453 0.907777i $$-0.362222\pi$$
$$744$$ 0 0
$$745$$ −8.09017 + 5.87785i −0.296401 + 0.215348i
$$746$$ 5.56231 17.1190i 0.203650 0.626772i
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −12.9443 + 9.40456i −0.472343 + 0.343177i −0.798354 0.602189i $$-0.794295\pi$$
0.326011 + 0.945366i $$0.394295\pi$$
$$752$$ −9.70820 7.05342i −0.354022 0.257212i
$$753$$ 0 0
$$754$$ −3.70820 11.4127i −0.135045 0.415625i
$$755$$ 6.47214 + 4.70228i 0.235545 + 0.171134i
$$756$$ 0 0
$$757$$ 1.85410 5.70634i 0.0673885 0.207400i −0.911692 0.410875i $$-0.865223\pi$$
0.979080 + 0.203474i $$0.0652233\pi$$
$$758$$ −20.0000 −0.726433
$$759$$ 0 0
$$760$$ 12.0000 0.435286
$$761$$ −3.09017 + 9.51057i −0.112019 + 0.344758i −0.991314 0.131520i $$-0.958014\pi$$
0.879295 + 0.476278i $$0.158014\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −2.47214 7.60845i −0.0894387 0.275264i
$$765$$ 5.56231 + 17.1190i 0.201106 + 0.618939i
$$766$$ −9.70820 7.05342i −0.350772 0.254851i
$$767$$ 6.47214 4.70228i 0.233695 0.169790i
$$768$$ 0 0
$$769$$ 22.0000 0.793340 0.396670 0.917961i $$-0.370166\pi$$
0.396670 + 0.917961i $$0.370166\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −8.03444 + 24.7275i −0.289166 + 0.889961i
$$773$$ −11.3262 + 8.22899i −0.407376 + 0.295976i −0.772539 0.634968i $$-0.781013\pi$$
0.365162 + 0.930944i $$0.381013\pi$$
$$774$$ 9.70820 + 7.05342i 0.348954 + 0.253530i
$$775$$ −2.47214 7.60845i −0.0888017 0.273304i
$$776$$ 9.27051 + 28.5317i 0.332792 + 1.02423i
$$777$$ 0 0
$$778$$ 4.85410 3.52671i 0.174028 0.126439i
$$779$$ −2.47214 + 7.60845i −0.0885735 + 0.272601i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 24.0000 0.858238
$$783$$ 0 0
$$784$$ −5.66312 + 4.11450i −0.202254 + 0.146946i
$$785$$ 1.61803 + 1.17557i 0.0577501 + 0.0419579i
$$786$$ 0 0
$$787$$ −16.0689 49.4549i −0.572794 1.76288i −0.643571 0.765386i $$-0.722548\pi$$
0.0707776 0.997492i $$-0.477452\pi$$
$$788$$ −1.61803 1.17557i −0.0576401 0.0418780i
$$789$$ 0 0
$$790$$