# Properties

 Label 637.2.g.b.263.1 Level $637$ Weight $2$ Character 637.263 Analytic conductor $5.086$ Analytic rank $1$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.g (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$1$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{5})$$ Defining polynomial: $$x^{4} - x^{3} + 2 x^{2} + x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 263.1 Root $$0.809017 - 1.40126i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.263 Dual form 637.2.g.b.373.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.30902 + 2.26728i) q^{2} -2.61803 q^{3} +(-2.42705 - 4.20378i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +3.85410 q^{9} +O(q^{10})$$ $$q+(-1.30902 + 2.26728i) q^{2} -2.61803 q^{3} +(-2.42705 - 4.20378i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +3.85410 q^{9} +6.85410 q^{10} +1.85410 q^{11} +(6.35410 + 11.0056i) q^{12} +(-2.50000 - 2.59808i) q^{13} +(3.42705 + 5.93583i) q^{15} +(-4.92705 + 8.53390i) q^{16} +(0.736068 + 1.27491i) q^{17} +(-5.04508 + 8.73834i) q^{18} -1.85410 q^{19} +(-6.35410 + 11.0056i) q^{20} +(-2.42705 + 4.20378i) q^{22} +(2.23607 - 3.87298i) q^{23} -19.5623 q^{24} +(-0.927051 + 1.60570i) q^{25} +(9.16312 - 2.26728i) q^{26} -2.23607 q^{27} +(-3.54508 - 6.14027i) q^{29} -17.9443 q^{30} +(2.35410 - 4.07742i) q^{31} +(-5.42705 - 9.39993i) q^{32} -4.85410 q^{33} -3.85410 q^{34} +(-9.35410 - 16.2018i) q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.42705 - 4.20378i) q^{38} +(6.54508 + 6.80185i) q^{39} +(-9.78115 - 16.9415i) q^{40} +(-0.381966 - 0.661585i) q^{41} +(-6.28115 + 10.8793i) q^{43} +(-4.50000 - 7.79423i) q^{44} +(-5.04508 - 8.73834i) q^{45} +(5.85410 + 10.1396i) q^{46} +(1.11803 + 1.93649i) q^{47} +(12.8992 - 22.3420i) q^{48} +(-2.42705 - 4.20378i) q^{50} +(-1.92705 - 3.33775i) q^{51} +(-4.85410 + 16.8151i) q^{52} +(-1.88197 + 3.25966i) q^{53} +(2.92705 - 5.06980i) q^{54} +(-2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +18.5623 q^{58} +(1.11803 + 1.93649i) q^{59} +(16.6353 - 28.8131i) q^{60} -6.00000 q^{61} +(6.16312 + 10.6748i) q^{62} +8.70820 q^{64} +(-2.61803 + 9.06914i) q^{65} +(6.35410 - 11.0056i) q^{66} -12.7082 q^{67} +(3.57295 - 6.18853i) q^{68} +(-5.85410 + 10.1396i) q^{69} +(7.09017 - 12.2805i) q^{71} +28.7984 q^{72} +(1.00000 - 1.73205i) q^{73} +(-5.23607 - 9.06914i) q^{74} +(2.42705 - 4.20378i) q^{75} +(4.50000 + 7.79423i) q^{76} +(-23.9894 + 5.93583i) q^{78} +(-2.00000 - 3.46410i) q^{79} +25.7984 q^{80} -5.70820 q^{81} +2.00000 q^{82} +6.70820 q^{83} +(1.92705 - 3.33775i) q^{85} +(-16.4443 - 28.4823i) q^{86} +(9.28115 + 16.0754i) q^{87} +13.8541 q^{88} +(-2.45492 + 4.25204i) q^{89} +26.4164 q^{90} -21.7082 q^{92} +(-6.16312 + 10.6748i) q^{93} -5.85410 q^{94} +(2.42705 + 4.20378i) q^{95} +(14.2082 + 24.6093i) q^{96} +(-9.42705 + 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9} + O(q^{10})$$ $$4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9} + 14 q^{10} - 6 q^{11} + 12 q^{12} - 10 q^{13} + 7 q^{15} - 13 q^{16} - 6 q^{17} - 9 q^{18} + 6 q^{19} - 12 q^{20} - 3 q^{22} - 38 q^{24} + 3 q^{25} + 21 q^{26} - 3 q^{29} - 36 q^{30} - 4 q^{31} - 15 q^{32} - 6 q^{33} - 2 q^{34} - 24 q^{36} - 8 q^{37} + 3 q^{38} + 15 q^{39} - 19 q^{40} - 6 q^{41} - 5 q^{43} - 18 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 3 q^{50} - q^{51} - 6 q^{52} - 12 q^{53} + 5 q^{54} - 3 q^{55} + 6 q^{57} + 34 q^{58} + 33 q^{60} - 24 q^{61} + 9 q^{62} + 8 q^{64} - 6 q^{65} + 12 q^{66} - 24 q^{67} + 21 q^{68} - 10 q^{69} + 6 q^{71} + 66 q^{72} + 4 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 49 q^{78} - 8 q^{79} + 54 q^{80} + 4 q^{81} + 8 q^{82} + q^{85} - 30 q^{86} + 17 q^{87} + 42 q^{88} - 21 q^{89} + 52 q^{90} - 60 q^{92} - 9 q^{93} - 10 q^{94} + 3 q^{95} + 30 q^{96} - 31 q^{97} + 42 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.30902 + 2.26728i −0.925615 + 1.60321i −0.135045 + 0.990839i $$0.543118\pi$$
−0.790569 + 0.612372i $$0.790215\pi$$
$$3$$ −2.61803 −1.51152 −0.755761 0.654847i $$-0.772733\pi$$
−0.755761 + 0.654847i $$0.772733\pi$$
$$4$$ −2.42705 4.20378i −1.21353 2.10189i
$$5$$ −1.30902 2.26728i −0.585410 1.01396i −0.994824 0.101611i $$-0.967600\pi$$
0.409414 0.912349i $$-0.365733\pi$$
$$6$$ 3.42705 5.93583i 1.39909 2.42329i
$$7$$ 0 0
$$8$$ 7.47214 2.64180
$$9$$ 3.85410 1.28470
$$10$$ 6.85410 2.16746
$$11$$ 1.85410 0.559033 0.279516 0.960141i $$-0.409826\pi$$
0.279516 + 0.960141i $$0.409826\pi$$
$$12$$ 6.35410 + 11.0056i 1.83427 + 3.17705i
$$13$$ −2.50000 2.59808i −0.693375 0.720577i
$$14$$ 0 0
$$15$$ 3.42705 + 5.93583i 0.884861 + 1.53262i
$$16$$ −4.92705 + 8.53390i −1.23176 + 2.13348i
$$17$$ 0.736068 + 1.27491i 0.178523 + 0.309210i 0.941375 0.337363i $$-0.109535\pi$$
−0.762852 + 0.646573i $$0.776202\pi$$
$$18$$ −5.04508 + 8.73834i −1.18914 + 2.05965i
$$19$$ −1.85410 −0.425360 −0.212680 0.977122i $$-0.568219\pi$$
−0.212680 + 0.977122i $$0.568219\pi$$
$$20$$ −6.35410 + 11.0056i −1.42082 + 2.46093i
$$21$$ 0 0
$$22$$ −2.42705 + 4.20378i −0.517449 + 0.896248i
$$23$$ 2.23607 3.87298i 0.466252 0.807573i −0.533005 0.846112i $$-0.678937\pi$$
0.999257 + 0.0385394i $$0.0122705\pi$$
$$24$$ −19.5623 −3.99314
$$25$$ −0.927051 + 1.60570i −0.185410 + 0.321140i
$$26$$ 9.16312 2.26728i 1.79704 0.444651i
$$27$$ −2.23607 −0.430331
$$28$$ 0 0
$$29$$ −3.54508 6.14027i −0.658306 1.14022i −0.981054 0.193734i $$-0.937940\pi$$
0.322748 0.946485i $$-0.395393\pi$$
$$30$$ −17.9443 −3.27616
$$31$$ 2.35410 4.07742i 0.422809 0.732327i −0.573404 0.819273i $$-0.694377\pi$$
0.996213 + 0.0869459i $$0.0277107\pi$$
$$32$$ −5.42705 9.39993i −0.959376 1.66169i
$$33$$ −4.85410 −0.844991
$$34$$ −3.85410 −0.660973
$$35$$ 0 0
$$36$$ −9.35410 16.2018i −1.55902 2.70030i
$$37$$ −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i $$-0.939977\pi$$
0.653476 + 0.756948i $$0.273310\pi$$
$$38$$ 2.42705 4.20378i 0.393720 0.681942i
$$39$$ 6.54508 + 6.80185i 1.04805 + 1.08917i
$$40$$ −9.78115 16.9415i −1.54654 2.67868i
$$41$$ −0.381966 0.661585i −0.0596531 0.103322i 0.834657 0.550771i $$-0.185666\pi$$
−0.894310 + 0.447449i $$0.852333\pi$$
$$42$$ 0 0
$$43$$ −6.28115 + 10.8793i −0.957867 + 1.65907i −0.230200 + 0.973143i $$0.573938\pi$$
−0.727667 + 0.685931i $$0.759395\pi$$
$$44$$ −4.50000 7.79423i −0.678401 1.17502i
$$45$$ −5.04508 8.73834i −0.752077 1.30264i
$$46$$ 5.85410 + 10.1396i 0.863140 + 1.49500i
$$47$$ 1.11803 + 1.93649i 0.163082 + 0.282466i 0.935973 0.352073i $$-0.114523\pi$$
−0.772890 + 0.634539i $$0.781190\pi$$
$$48$$ 12.8992 22.3420i 1.86184 3.22480i
$$49$$ 0 0
$$50$$ −2.42705 4.20378i −0.343237 0.594504i
$$51$$ −1.92705 3.33775i −0.269841 0.467379i
$$52$$ −4.85410 + 16.8151i −0.673143 + 2.33184i
$$53$$ −1.88197 + 3.25966i −0.258508 + 0.447749i −0.965842 0.259130i $$-0.916564\pi$$
0.707334 + 0.706879i $$0.249897\pi$$
$$54$$ 2.92705 5.06980i 0.398321 0.689913i
$$55$$ −2.42705 4.20378i −0.327263 0.566837i
$$56$$ 0 0
$$57$$ 4.85410 0.642942
$$58$$ 18.5623 2.43735
$$59$$ 1.11803 + 1.93649i 0.145556 + 0.252110i 0.929580 0.368620i $$-0.120170\pi$$
−0.784024 + 0.620730i $$0.786836\pi$$
$$60$$ 16.6353 28.8131i 2.14760 3.71976i
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 6.16312 + 10.6748i 0.782717 + 1.35571i
$$63$$ 0 0
$$64$$ 8.70820 1.08853
$$65$$ −2.61803 + 9.06914i −0.324727 + 1.12489i
$$66$$ 6.35410 11.0056i 0.782136 1.35470i
$$67$$ −12.7082 −1.55255 −0.776277 0.630392i $$-0.782894\pi$$
−0.776277 + 0.630392i $$0.782894\pi$$
$$68$$ 3.57295 6.18853i 0.433284 0.750469i
$$69$$ −5.85410 + 10.1396i −0.704751 + 1.22066i
$$70$$ 0 0
$$71$$ 7.09017 12.2805i 0.841448 1.45743i −0.0472218 0.998884i $$-0.515037\pi$$
0.888670 0.458547i $$-0.151630\pi$$
$$72$$ 28.7984 3.39392
$$73$$ 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i $$-0.795992\pi$$
0.918594 + 0.395203i $$0.129326\pi$$
$$74$$ −5.23607 9.06914i −0.608681 1.05427i
$$75$$ 2.42705 4.20378i 0.280252 0.485410i
$$76$$ 4.50000 + 7.79423i 0.516185 + 0.894059i
$$77$$ 0 0
$$78$$ −23.9894 + 5.93583i −2.71626 + 0.672100i
$$79$$ −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i $$-0.238911\pi$$
−0.956325 + 0.292306i $$0.905577\pi$$
$$80$$ 25.7984 2.88435
$$81$$ −5.70820 −0.634245
$$82$$ 2.00000 0.220863
$$83$$ 6.70820 0.736321 0.368161 0.929762i $$-0.379988\pi$$
0.368161 + 0.929762i $$0.379988\pi$$
$$84$$ 0 0
$$85$$ 1.92705 3.33775i 0.209018 0.362030i
$$86$$ −16.4443 28.4823i −1.77323 3.07133i
$$87$$ 9.28115 + 16.0754i 0.995044 + 1.72347i
$$88$$ 13.8541 1.47685
$$89$$ −2.45492 + 4.25204i −0.260220 + 0.450715i −0.966300 0.257417i $$-0.917129\pi$$
0.706080 + 0.708132i $$0.250462\pi$$
$$90$$ 26.4164 2.78453
$$91$$ 0 0
$$92$$ −21.7082 −2.26324
$$93$$ −6.16312 + 10.6748i −0.639086 + 1.10693i
$$94$$ −5.85410 −0.603805
$$95$$ 2.42705 + 4.20378i 0.249010 + 0.431298i
$$96$$ 14.2082 + 24.6093i 1.45012 + 2.51168i
$$97$$ −9.42705 + 16.3281i −0.957172 + 1.65787i −0.227854 + 0.973695i $$0.573171\pi$$
−0.729318 + 0.684175i $$0.760162\pi$$
$$98$$ 0 0
$$99$$ 7.14590 0.718190
$$100$$ 9.00000 0.900000
$$101$$ −11.5623 −1.15049 −0.575246 0.817980i $$-0.695094\pi$$
−0.575246 + 0.817980i $$0.695094\pi$$
$$102$$ 10.0902 0.999076
$$103$$ 4.35410 + 7.54153i 0.429022 + 0.743089i 0.996787 0.0801026i $$-0.0255248\pi$$
−0.567764 + 0.823191i $$0.692191\pi$$
$$104$$ −18.6803 19.4132i −1.83176 1.90362i
$$105$$ 0 0
$$106$$ −4.92705 8.53390i −0.478557 0.828886i
$$107$$ 1.69098 2.92887i 0.163473 0.283144i −0.772639 0.634846i $$-0.781064\pi$$
0.936112 + 0.351702i $$0.114397\pi$$
$$108$$ 5.42705 + 9.39993i 0.522218 + 0.904508i
$$109$$ 1.35410 2.34537i 0.129699 0.224646i −0.793861 0.608100i $$-0.791932\pi$$
0.923560 + 0.383454i $$0.125265\pi$$
$$110$$ 12.7082 1.21168
$$111$$ 5.23607 9.06914i 0.496986 0.860804i
$$112$$ 0 0
$$113$$ −0.736068 + 1.27491i −0.0692435 + 0.119933i −0.898568 0.438833i $$-0.855392\pi$$
0.829325 + 0.558766i $$0.188725\pi$$
$$114$$ −6.35410 + 11.0056i −0.595116 + 1.03077i
$$115$$ −11.7082 −1.09180
$$116$$ −17.2082 + 29.8055i −1.59774 + 2.76737i
$$117$$ −9.63525 10.0133i −0.890780 0.925725i
$$118$$ −5.85410 −0.538914
$$119$$ 0 0
$$120$$ 25.6074 + 44.3533i 2.33762 + 4.04888i
$$121$$ −7.56231 −0.687482
$$122$$ 7.85410 13.6037i 0.711077 1.23162i
$$123$$ 1.00000 + 1.73205i 0.0901670 + 0.156174i
$$124$$ −22.8541 −2.05236
$$125$$ −8.23607 −0.736656
$$126$$ 0 0
$$127$$ 10.4271 + 18.0602i 0.925251 + 1.60258i 0.791157 + 0.611613i $$0.209479\pi$$
0.134094 + 0.990969i $$0.457187\pi$$
$$128$$ −0.545085 + 0.944115i −0.0481792 + 0.0834488i
$$129$$ 16.4443 28.4823i 1.44784 2.50773i
$$130$$ −17.1353 17.8075i −1.50286 1.56182i
$$131$$ 7.66312 + 13.2729i 0.669530 + 1.15966i 0.978036 + 0.208437i $$0.0668377\pi$$
−0.308506 + 0.951222i $$0.599829\pi$$
$$132$$ 11.7812 + 20.4056i 1.02542 + 1.77608i
$$133$$ 0 0
$$134$$ 16.6353 28.8131i 1.43707 2.48907i
$$135$$ 2.92705 + 5.06980i 0.251920 + 0.436339i
$$136$$ 5.50000 + 9.52628i 0.471621 + 0.816872i
$$137$$ 1.30902 + 2.26728i 0.111837 + 0.193707i 0.916511 0.400010i $$-0.130993\pi$$
−0.804674 + 0.593717i $$0.797660\pi$$
$$138$$ −15.3262 26.5458i −1.30466 2.25973i
$$139$$ −2.28115 + 3.95107i −0.193485 + 0.335126i −0.946403 0.322989i $$-0.895312\pi$$
0.752918 + 0.658114i $$0.228646\pi$$
$$140$$ 0 0
$$141$$ −2.92705 5.06980i −0.246502 0.426954i
$$142$$ 18.5623 + 32.1509i 1.55771 + 2.69804i
$$143$$ −4.63525 4.81710i −0.387619 0.402826i
$$144$$ −18.9894 + 32.8905i −1.58245 + 2.74088i
$$145$$ −9.28115 + 16.0754i −0.770758 + 1.33499i
$$146$$ 2.61803 + 4.53457i 0.216670 + 0.375284i
$$147$$ 0 0
$$148$$ 19.4164 1.59602
$$149$$ 1.85410 0.151894 0.0759470 0.997112i $$-0.475802\pi$$
0.0759470 + 0.997112i $$0.475802\pi$$
$$150$$ 6.35410 + 11.0056i 0.518810 + 0.898606i
$$151$$ 0.645898 1.11873i 0.0525624 0.0910408i −0.838547 0.544829i $$-0.816594\pi$$
0.891109 + 0.453788i $$0.149928\pi$$
$$152$$ −13.8541 −1.12372
$$153$$ 2.83688 + 4.91362i 0.229348 + 0.397243i
$$154$$ 0 0
$$155$$ −12.3262 −0.990067
$$156$$ 12.7082 44.0225i 1.01747 3.52462i
$$157$$ −7.42705 + 12.8640i −0.592743 + 1.02666i 0.401118 + 0.916026i $$0.368622\pi$$
−0.993861 + 0.110635i $$0.964712\pi$$
$$158$$ 10.4721 0.833118
$$159$$ 4.92705 8.53390i 0.390741 0.676783i
$$160$$ −14.2082 + 24.6093i −1.12326 + 1.94554i
$$161$$ 0 0
$$162$$ 7.47214 12.9421i 0.587066 1.01683i
$$163$$ −3.70820 −0.290449 −0.145224 0.989399i $$-0.546390\pi$$
−0.145224 + 0.989399i $$0.546390\pi$$
$$164$$ −1.85410 + 3.21140i −0.144781 + 0.250768i
$$165$$ 6.35410 + 11.0056i 0.494666 + 0.856787i
$$166$$ −8.78115 + 15.2094i −0.681550 + 1.18048i
$$167$$ −7.11803 12.3288i −0.550810 0.954031i −0.998216 0.0597001i $$-0.980986\pi$$
0.447406 0.894331i $$-0.352348\pi$$
$$168$$ 0 0
$$169$$ −0.500000 + 12.9904i −0.0384615 + 0.999260i
$$170$$ 5.04508 + 8.73834i 0.386940 + 0.670200i
$$171$$ −7.14590 −0.546460
$$172$$ 60.9787 4.64958
$$173$$ −9.00000 −0.684257 −0.342129 0.939653i $$-0.611148\pi$$
−0.342129 + 0.939653i $$0.611148\pi$$
$$174$$ −48.5967 −3.68411
$$175$$ 0 0
$$176$$ −9.13525 + 15.8227i −0.688596 + 1.19268i
$$177$$ −2.92705 5.06980i −0.220011 0.381070i
$$178$$ −6.42705 11.1320i −0.481728 0.834377i
$$179$$ −9.00000 −0.672692 −0.336346 0.941739i $$-0.609191\pi$$
−0.336346 + 0.941739i $$0.609191\pi$$
$$180$$ −24.4894 + 42.4168i −1.82533 + 3.16156i
$$181$$ 9.70820 0.721605 0.360803 0.932642i $$-0.382503\pi$$
0.360803 + 0.932642i $$0.382503\pi$$
$$182$$ 0 0
$$183$$ 15.7082 1.16118
$$184$$ 16.7082 28.9395i 1.23175 2.13345i
$$185$$ 10.4721 0.769927
$$186$$ −16.1353 27.9471i −1.18309 2.04918i
$$187$$ 1.36475 + 2.36381i 0.0998000 + 0.172859i
$$188$$ 5.42705 9.39993i 0.395808 0.685560i
$$189$$ 0 0
$$190$$ −12.7082 −0.921950
$$191$$ 21.3820 1.54714 0.773572 0.633708i $$-0.218468\pi$$
0.773572 + 0.633708i $$0.218468\pi$$
$$192$$ −22.7984 −1.64533
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ −24.6803 42.7476i −1.77195 3.06910i
$$195$$ 6.85410 23.7433i 0.490832 1.70029i
$$196$$ 0 0
$$197$$ 8.39919 + 14.5478i 0.598417 + 1.03649i 0.993055 + 0.117652i $$0.0375368\pi$$
−0.394638 + 0.918837i $$0.629130\pi$$
$$198$$ −9.35410 + 16.2018i −0.664767 + 1.15141i
$$199$$ 12.2082 + 21.1452i 0.865417 + 1.49895i 0.866633 + 0.498946i $$0.166280\pi$$
−0.00121626 + 0.999999i $$0.500387\pi$$
$$200$$ −6.92705 + 11.9980i −0.489816 + 0.848387i
$$201$$ 33.2705 2.34672
$$202$$ 15.1353 26.2150i 1.06491 1.84448i
$$203$$ 0 0
$$204$$ −9.35410 + 16.2018i −0.654918 + 1.13435i
$$205$$ −1.00000 + 1.73205i −0.0698430 + 0.120972i
$$206$$ −22.7984 −1.58844
$$207$$ 8.61803 14.9269i 0.598995 1.03749i
$$208$$ 34.4894 8.53390i 2.39141 0.591720i
$$209$$ −3.43769 −0.237790
$$210$$ 0 0
$$211$$ −2.35410 4.07742i −0.162063 0.280701i 0.773545 0.633741i $$-0.218481\pi$$
−0.935608 + 0.353039i $$0.885148\pi$$
$$212$$ 18.2705 1.25482
$$213$$ −18.5623 + 32.1509i −1.27187 + 2.20294i
$$214$$ 4.42705 + 7.66788i 0.302627 + 0.524165i
$$215$$ 32.8885 2.24298
$$216$$ −16.7082 −1.13685
$$217$$ 0 0
$$218$$ 3.54508 + 6.14027i 0.240103 + 0.415871i
$$219$$ −2.61803 + 4.53457i −0.176910 + 0.306418i
$$220$$ −11.7812 + 20.4056i −0.794285 + 1.37574i
$$221$$ 1.47214 5.09963i 0.0990266 0.343038i
$$222$$ 13.7082 + 23.7433i 0.920034 + 1.59355i
$$223$$ −10.1353 17.5548i −0.678707 1.17555i −0.975371 0.220573i $$-0.929207\pi$$
0.296664 0.954982i $$-0.404126\pi$$
$$224$$ 0 0
$$225$$ −3.57295 + 6.18853i −0.238197 + 0.412569i
$$226$$ −1.92705 3.33775i −0.128186 0.222024i
$$227$$ −0.736068 1.27491i −0.0488545 0.0846186i 0.840564 0.541712i $$-0.182224\pi$$
−0.889419 + 0.457094i $$0.848890\pi$$
$$228$$ −11.7812 20.4056i −0.780226 1.35139i
$$229$$ 6.56231 + 11.3662i 0.433649 + 0.751103i 0.997184 0.0749895i $$-0.0238923\pi$$
−0.563535 + 0.826092i $$0.690559\pi$$
$$230$$ 15.3262 26.5458i 1.01058 1.75038i
$$231$$ 0 0
$$232$$ −26.4894 45.8809i −1.73911 3.01223i
$$233$$ −1.30902 2.26728i −0.0857566 0.148535i 0.819957 0.572425i $$-0.193997\pi$$
−0.905713 + 0.423891i $$0.860664\pi$$
$$234$$ 35.3156 8.73834i 2.30865 0.571243i
$$235$$ 2.92705 5.06980i 0.190940 0.330717i
$$236$$ 5.42705 9.39993i 0.353271 0.611883i
$$237$$ 5.23607 + 9.06914i 0.340119 + 0.589104i
$$238$$ 0 0
$$239$$ −24.7082 −1.59824 −0.799120 0.601171i $$-0.794701\pi$$
−0.799120 + 0.601171i $$0.794701\pi$$
$$240$$ −67.5410 −4.35975
$$241$$ −12.2812 21.2716i −0.791099 1.37022i −0.925287 0.379267i $$-0.876176\pi$$
0.134189 0.990956i $$-0.457157\pi$$
$$242$$ 9.89919 17.1459i 0.636344 1.10218i
$$243$$ 21.6525 1.38901
$$244$$ 14.5623 + 25.2227i 0.932256 + 1.61471i
$$245$$ 0 0
$$246$$ −5.23607 −0.333840
$$247$$ 4.63525 + 4.81710i 0.294934 + 0.306505i
$$248$$ 17.5902 30.4671i 1.11698 1.93466i
$$249$$ −17.5623 −1.11297
$$250$$ 10.7812 18.6735i 0.681860 1.18102i
$$251$$ −0.381966 + 0.661585i −0.0241095 + 0.0417588i −0.877828 0.478975i $$-0.841008\pi$$
0.853719 + 0.520734i $$0.174342\pi$$
$$252$$ 0 0
$$253$$ 4.14590 7.18091i 0.260650 0.451460i
$$254$$ −54.5967 −3.42570
$$255$$ −5.04508 + 8.73834i −0.315935 + 0.547216i
$$256$$ 7.28115 + 12.6113i 0.455072 + 0.788208i
$$257$$ −8.37132 + 14.4996i −0.522189 + 0.904457i 0.477478 + 0.878644i $$0.341551\pi$$
−0.999667 + 0.0258138i $$0.991782\pi$$
$$258$$ 43.0517 + 74.5677i 2.68028 + 4.64238i
$$259$$ 0 0
$$260$$ 44.4787 11.0056i 2.75845 0.682540i
$$261$$ −13.6631 23.6652i −0.845726 1.46484i
$$262$$ −40.1246 −2.47891
$$263$$ 9.00000 0.554964 0.277482 0.960731i $$-0.410500\pi$$
0.277482 + 0.960731i $$0.410500\pi$$
$$264$$ −36.2705 −2.23230
$$265$$ 9.85410 0.605333
$$266$$ 0 0
$$267$$ 6.42705 11.1320i 0.393329 0.681266i
$$268$$ 30.8435 + 53.4224i 1.88406 + 3.26329i
$$269$$ 14.3713 + 24.8919i 0.876235 + 1.51768i 0.855441 + 0.517900i $$0.173286\pi$$
0.0207937 + 0.999784i $$0.493381\pi$$
$$270$$ −15.3262 −0.932725
$$271$$ 4.20820 7.28882i 0.255630 0.442764i −0.709436 0.704770i $$-0.751050\pi$$
0.965066 + 0.262005i $$0.0843837\pi$$
$$272$$ −14.5066 −0.879590
$$273$$ 0 0
$$274$$ −6.85410 −0.414071
$$275$$ −1.71885 + 2.97713i −0.103650 + 0.179528i
$$276$$ 56.8328 3.42093
$$277$$ 2.50000 + 4.33013i 0.150210 + 0.260172i 0.931305 0.364241i $$-0.118672\pi$$
−0.781094 + 0.624413i $$0.785338\pi$$
$$278$$ −5.97214 10.3440i −0.358185 0.620394i
$$279$$ 9.07295 15.7148i 0.543183 0.940821i
$$280$$ 0 0
$$281$$ 20.1803 1.20386 0.601929 0.798550i $$-0.294399\pi$$
0.601929 + 0.798550i $$0.294399\pi$$
$$282$$ 15.3262 0.912664
$$283$$ 13.4164 0.797523 0.398761 0.917055i $$-0.369440\pi$$
0.398761 + 0.917055i $$0.369440\pi$$
$$284$$ −68.8328 −4.08448
$$285$$ −6.35410 11.0056i −0.376385 0.651917i
$$286$$ 16.9894 4.20378i 1.00460 0.248574i
$$287$$ 0 0
$$288$$ −20.9164 36.2283i −1.23251 2.13477i
$$289$$ 7.41641 12.8456i 0.436259 0.755623i
$$290$$ −24.2984 42.0860i −1.42685 2.47138i
$$291$$ 24.6803 42.7476i 1.44679 2.50591i
$$292$$ −9.70820 −0.568130
$$293$$ 3.38197 5.85774i 0.197577 0.342213i −0.750166 0.661250i $$-0.770026\pi$$
0.947742 + 0.319037i $$0.103360\pi$$
$$294$$ 0 0
$$295$$ 2.92705 5.06980i 0.170419 0.295175i
$$296$$ −14.9443 + 25.8842i −0.868618 + 1.50449i
$$297$$ −4.14590 −0.240569
$$298$$ −2.42705 + 4.20378i −0.140595 + 0.243518i
$$299$$ −15.6525 + 3.87298i −0.905206 + 0.223980i
$$300$$ −23.5623 −1.36037
$$301$$ 0 0
$$302$$ 1.69098 + 2.92887i 0.0973051 + 0.168537i
$$303$$ 30.2705 1.73900
$$304$$ 9.13525 15.8227i 0.523943 0.907496i
$$305$$ 7.85410 + 13.6037i 0.449725 + 0.778946i
$$306$$ −14.8541 −0.849152
$$307$$ −4.85410 −0.277038 −0.138519 0.990360i $$-0.544234\pi$$
−0.138519 + 0.990360i $$0.544234\pi$$
$$308$$ 0 0
$$309$$ −11.3992 19.7440i −0.648477 1.12320i
$$310$$ 16.1353 27.9471i 0.916421 1.58729i
$$311$$ −1.66312 + 2.88061i −0.0943068 + 0.163344i −0.909319 0.416099i $$-0.863397\pi$$
0.815012 + 0.579444i $$0.196730\pi$$
$$312$$ 48.9058 + 50.8244i 2.76874 + 2.87736i
$$313$$ −12.5623 21.7586i −0.710064 1.22987i −0.964833 0.262864i $$-0.915333\pi$$
0.254769 0.967002i $$-0.418000\pi$$
$$314$$ −19.4443 33.6785i −1.09730 1.90059i
$$315$$ 0 0
$$316$$ −9.70820 + 16.8151i −0.546129 + 0.945923i
$$317$$ −13.1180 22.7211i −0.736782 1.27614i −0.953937 0.300007i $$-0.903011\pi$$
0.217155 0.976137i $$-0.430322\pi$$
$$318$$ 12.8992 + 22.3420i 0.723350 + 1.25288i
$$319$$ −6.57295 11.3847i −0.368014 0.637420i
$$320$$ −11.3992 19.7440i −0.637234 1.10372i
$$321$$ −4.42705 + 7.66788i −0.247094 + 0.427979i
$$322$$ 0 0
$$323$$ −1.36475 2.36381i −0.0759364 0.131526i
$$324$$ 13.8541 + 23.9960i 0.769672 + 1.33311i
$$325$$ 6.48936 1.60570i 0.359965 0.0890682i
$$326$$ 4.85410 8.40755i 0.268844 0.465651i
$$327$$ −3.54508 + 6.14027i −0.196044 + 0.339558i
$$328$$ −2.85410 4.94345i −0.157591 0.272956i
$$329$$ 0 0
$$330$$ −33.2705 −1.83148
$$331$$ −10.1459 −0.557669 −0.278834 0.960339i $$-0.589948\pi$$
−0.278834 + 0.960339i $$0.589948\pi$$
$$332$$ −16.2812 28.1998i −0.893544 1.54766i
$$333$$ −7.70820 + 13.3510i −0.422407 + 0.731630i
$$334$$ 37.2705 2.03935
$$335$$ 16.6353 + 28.8131i 0.908881 + 1.57423i
$$336$$ 0 0
$$337$$ −11.5623 −0.629839 −0.314919 0.949118i $$-0.601978\pi$$
−0.314919 + 0.949118i $$0.601978\pi$$
$$338$$ −28.7984 18.1383i −1.56643 0.986592i
$$339$$ 1.92705 3.33775i 0.104663 0.181282i
$$340$$ −18.7082 −1.01459
$$341$$ 4.36475 7.55996i 0.236364 0.409395i
$$342$$ 9.35410 16.2018i 0.505812 0.876092i
$$343$$ 0 0
$$344$$ −46.9336 + 81.2914i −2.53049 + 4.38294i
$$345$$ 30.6525 1.65027
$$346$$ 11.7812 20.4056i 0.633359 1.09701i
$$347$$ −15.3820 26.6423i −0.825747 1.43024i −0.901347 0.433098i $$-0.857420\pi$$
0.0755997 0.997138i $$-0.475913\pi$$
$$348$$ 45.0517 78.0318i 2.41502 4.18294i
$$349$$ −10.3541 17.9338i −0.554242 0.959976i −0.997962 0.0638103i $$-0.979675\pi$$
0.443720 0.896166i $$-0.353659\pi$$
$$350$$ 0 0
$$351$$ 5.59017 + 5.80948i 0.298381 + 0.310087i
$$352$$ −10.0623 17.4284i −0.536323 0.928938i
$$353$$ 22.1459 1.17871 0.589354 0.807875i $$-0.299382\pi$$
0.589354 + 0.807875i $$0.299382\pi$$
$$354$$ 15.3262 0.814580
$$355$$ −37.1246 −1.97037
$$356$$ 23.8328 1.26314
$$357$$ 0 0
$$358$$ 11.7812 20.4056i 0.622653 1.07847i
$$359$$ 11.0451 + 19.1306i 0.582937 + 1.00968i 0.995129 + 0.0985799i $$0.0314300\pi$$
−0.412192 + 0.911097i $$0.635237\pi$$
$$360$$ −37.6976 65.2941i −1.98684 3.44130i
$$361$$ −15.5623 −0.819069
$$362$$ −12.7082 + 22.0113i −0.667928 + 1.15689i
$$363$$ 19.7984 1.03915
$$364$$ 0 0
$$365$$ −5.23607 −0.274068
$$366$$ −20.5623 + 35.6150i −1.07481 + 1.86162i
$$367$$ −1.41641 −0.0739359 −0.0369679 0.999316i $$-0.511770\pi$$
−0.0369679 + 0.999316i $$0.511770\pi$$
$$368$$ 22.0344 + 38.1648i 1.14862 + 1.98948i
$$369$$ −1.47214 2.54981i −0.0766363 0.132738i
$$370$$ −13.7082 + 23.7433i −0.712656 + 1.23436i
$$371$$ 0 0
$$372$$ 59.8328 3.10219
$$373$$ −20.5623 −1.06468 −0.532338 0.846532i $$-0.678686\pi$$
−0.532338 + 0.846532i $$0.678686\pi$$
$$374$$ −7.14590 −0.369506
$$375$$ 21.5623 1.11347
$$376$$ 8.35410 + 14.4697i 0.430830 + 0.746219i
$$377$$ −7.09017 + 24.5611i −0.365162 + 1.26496i
$$378$$ 0 0
$$379$$ 3.07295 + 5.32250i 0.157847 + 0.273399i 0.934092 0.357032i $$-0.116211\pi$$
−0.776245 + 0.630431i $$0.782878\pi$$
$$380$$ 11.7812 20.4056i 0.604360 1.04678i
$$381$$ −27.2984 47.2822i −1.39854 2.42234i
$$382$$ −27.9894 + 48.4790i −1.43206 + 2.48040i
$$383$$ −21.9787 −1.12306 −0.561530 0.827456i $$-0.689787\pi$$
−0.561530 + 0.827456i $$0.689787\pi$$
$$384$$ 1.42705 2.47172i 0.0728239 0.126135i
$$385$$ 0 0
$$386$$ 7.85410 13.6037i 0.399763 0.692410i
$$387$$ −24.2082 + 41.9298i −1.23057 + 2.13141i
$$388$$ 91.5197 4.64621
$$389$$ 5.94427 10.2958i 0.301387 0.522017i −0.675064 0.737759i $$-0.735884\pi$$
0.976450 + 0.215743i $$0.0692172\pi$$
$$390$$ 44.8607 + 46.6206i 2.27161 + 2.36073i
$$391$$ 6.58359 0.332947
$$392$$ 0 0
$$393$$ −20.0623 34.7489i −1.01201 1.75285i
$$394$$ −43.9787 −2.21562
$$395$$ −5.23607 + 9.06914i −0.263455 + 0.456318i
$$396$$ −17.3435 30.0398i −0.871542 1.50955i
$$397$$ 1.41641 0.0710875 0.0355437 0.999368i $$-0.488684\pi$$
0.0355437 + 0.999368i $$0.488684\pi$$
$$398$$ −63.9230 −3.20417
$$399$$ 0 0
$$400$$ −9.13525 15.8227i −0.456763 0.791136i
$$401$$ −17.7254 + 30.7013i −0.885165 + 1.53315i −0.0396416 + 0.999214i $$0.512622\pi$$
−0.845524 + 0.533938i $$0.820712\pi$$
$$402$$ −43.5517 + 75.4337i −2.17216 + 3.76229i
$$403$$ −16.4787 + 4.07742i −0.820863 + 0.203111i
$$404$$ 28.0623 + 48.6053i 1.39615 + 2.41821i
$$405$$ 7.47214 + 12.9421i 0.371293 + 0.643099i
$$406$$ 0 0
$$407$$ −3.70820 + 6.42280i −0.183809 + 0.318366i
$$408$$ −14.3992 24.9401i −0.712866 1.23472i
$$409$$ −7.21885 12.5034i −0.356949 0.618254i 0.630500 0.776189i $$-0.282850\pi$$
−0.987450 + 0.157935i $$0.949516\pi$$
$$410$$ −2.61803 4.53457i −0.129295 0.223946i
$$411$$ −3.42705 5.93583i −0.169044 0.292793i
$$412$$ 21.1353 36.6073i 1.04126 1.80351i
$$413$$ 0 0
$$414$$ 22.5623 + 39.0791i 1.10888 + 1.92063i
$$415$$ −8.78115 15.2094i −0.431050 0.746600i
$$416$$ −10.8541 + 37.5997i −0.532166 + 1.84348i
$$417$$ 5.97214 10.3440i 0.292457 0.506550i
$$418$$ 4.50000 7.79423i 0.220102 0.381228i
$$419$$ 5.97214 + 10.3440i 0.291758 + 0.505340i 0.974226 0.225576i $$-0.0724265\pi$$
−0.682468 + 0.730916i $$0.739093\pi$$
$$420$$ 0 0
$$421$$ 1.41641 0.0690315 0.0345157 0.999404i $$-0.489011\pi$$
0.0345157 + 0.999404i $$0.489011\pi$$
$$422$$ 12.3262 0.600032
$$423$$ 4.30902 + 7.46344i 0.209512 + 0.362885i
$$424$$ −14.0623 + 24.3566i −0.682926 + 1.18286i
$$425$$ −2.72949 −0.132400
$$426$$ −48.5967 84.1720i −2.35452 4.07815i
$$427$$ 0 0
$$428$$ −16.4164 −0.793517
$$429$$ 12.1353 + 12.6113i 0.585896 + 0.608881i
$$430$$ −43.0517 + 74.5677i −2.07614 + 3.59597i
$$431$$ 7.79837 0.375634 0.187817 0.982204i $$-0.439859\pi$$
0.187817 + 0.982204i $$0.439859\pi$$
$$432$$ 11.0172 19.0824i 0.530066 0.918102i
$$433$$ −0.500000 + 0.866025i −0.0240285 + 0.0416185i −0.877790 0.479046i $$-0.840983\pi$$
0.853761 + 0.520665i $$0.174316\pi$$
$$434$$ 0 0
$$435$$ 24.2984 42.0860i 1.16502 2.01787i
$$436$$ −13.1459 −0.629574
$$437$$ −4.14590 + 7.18091i −0.198325 + 0.343509i
$$438$$ −6.85410 11.8717i −0.327502 0.567250i
$$439$$ −7.42705 + 12.8640i −0.354474 + 0.613967i −0.987028 0.160550i $$-0.948673\pi$$
0.632554 + 0.774516i $$0.282007\pi$$
$$440$$ −18.1353 31.4112i −0.864564 1.49747i
$$441$$ 0 0
$$442$$ 9.63525 + 10.0133i 0.458302 + 0.476282i
$$443$$ 2.61803 + 4.53457i 0.124387 + 0.215444i 0.921493 0.388395i $$-0.126970\pi$$
−0.797106 + 0.603839i $$0.793637\pi$$
$$444$$ −50.8328 −2.41242
$$445$$ 12.8541 0.609343
$$446$$ 53.0689 2.51288
$$447$$ −4.85410 −0.229591
$$448$$ 0 0
$$449$$ −9.76393 + 16.9116i −0.460788 + 0.798109i −0.999000 0.0447005i $$-0.985767\pi$$
0.538212 + 0.842809i $$0.319100\pi$$
$$450$$ −9.35410 16.2018i −0.440957 0.763759i
$$451$$ −0.708204 1.22665i −0.0333480 0.0577605i
$$452$$ 7.14590 0.336115
$$453$$ −1.69098 + 2.92887i −0.0794493 + 0.137610i
$$454$$ 3.85410 0.180882
$$455$$ 0 0
$$456$$ 36.2705 1.69852
$$457$$ −7.70820 + 13.3510i −0.360575 + 0.624533i −0.988055 0.154098i $$-0.950753\pi$$
0.627481 + 0.778632i $$0.284086\pi$$
$$458$$ −34.3607 −1.60557
$$459$$ −1.64590 2.85078i −0.0768239 0.133063i
$$460$$ 28.4164 + 49.2187i 1.32492 + 2.29483i
$$461$$ 6.10739 10.5783i 0.284450 0.492681i −0.688026 0.725686i $$-0.741523\pi$$
0.972476 + 0.233005i $$0.0748558\pi$$
$$462$$ 0 0
$$463$$ 6.70820 0.311757 0.155878 0.987776i $$-0.450179\pi$$
0.155878 + 0.987776i $$0.450179\pi$$
$$464$$ 69.8673 3.24351
$$465$$ 32.2705 1.49651
$$466$$ 6.85410 0.317510
$$467$$ −1.17376 2.03302i −0.0543152 0.0940767i 0.837589 0.546300i $$-0.183964\pi$$
−0.891905 + 0.452224i $$0.850631\pi$$
$$468$$ −18.7082 + 64.8071i −0.864787 + 2.99571i
$$469$$ 0 0
$$470$$ 7.66312 + 13.2729i 0.353473 + 0.612234i
$$471$$ 19.4443 33.6785i 0.895945 1.55182i
$$472$$ 8.35410 + 14.4697i 0.384529 + 0.666023i
$$473$$ −11.6459 + 20.1713i −0.535479 + 0.927477i
$$474$$ −27.4164 −1.25928
$$475$$ 1.71885 2.97713i 0.0788661 0.136600i
$$476$$ 0 0
$$477$$ −7.25329 + 12.5631i −0.332105 + 0.575223i
$$478$$ 32.3435 56.0205i 1.47936 2.56232i
$$479$$ 24.9787 1.14131 0.570653 0.821191i $$-0.306690\pi$$
0.570653 + 0.821191i $$0.306690\pi$$
$$480$$ 37.1976 64.4281i 1.69783 2.94073i
$$481$$ 14.0000 3.46410i 0.638345 0.157949i
$$482$$ 64.3050 2.92901
$$483$$ 0 0
$$484$$ 18.3541 + 31.7902i 0.834277 + 1.44501i
$$485$$ 49.3607 2.24135
$$486$$ −28.3435 + 49.0923i −1.28569 + 2.22687i
$$487$$ −14.9894 25.9623i −0.679233 1.17647i −0.975212 0.221271i $$-0.928979\pi$$
0.295980 0.955194i $$-0.404354\pi$$
$$488$$ −44.8328 −2.02949
$$489$$ 9.70820 0.439020
$$490$$ 0 0
$$491$$ −6.19098 10.7231i −0.279395 0.483927i 0.691839 0.722051i $$-0.256801\pi$$
−0.971235 + 0.238125i $$0.923467\pi$$
$$492$$ 4.85410 8.40755i 0.218840 0.379042i
$$493$$ 5.21885 9.03931i 0.235045 0.407110i
$$494$$ −16.9894 + 4.20378i −0.764387 + 0.189137i
$$495$$ −9.35410 16.2018i −0.420436 0.728216i
$$496$$ 23.1976 + 40.1794i 1.04160 + 1.80411i
$$497$$ 0 0
$$498$$ 22.9894 39.8187i 1.03018 1.78432i
$$499$$ −7.42705 12.8640i −0.332480 0.575873i 0.650517 0.759492i $$-0.274552\pi$$
−0.982998 + 0.183619i $$0.941219\pi$$
$$500$$ 19.9894 + 34.6226i 0.893951 + 1.54837i
$$501$$ 18.6353 + 32.2772i 0.832562 + 1.44204i
$$502$$ −1.00000 1.73205i −0.0446322 0.0773052i
$$503$$ −13.3090 + 23.0519i −0.593420 + 1.02783i 0.400348 + 0.916363i $$0.368889\pi$$
−0.993768 + 0.111470i $$0.964444\pi$$
$$504$$ 0 0
$$505$$ 15.1353 + 26.2150i 0.673510 + 1.16655i
$$506$$ 10.8541 + 18.7999i 0.482524 + 0.835756i
$$507$$ 1.30902 34.0093i 0.0581355 1.51040i
$$508$$ 50.6140 87.6660i 2.24563 3.88955i
$$509$$ 9.29837 16.1053i 0.412143 0.713853i −0.582981 0.812486i $$-0.698114\pi$$
0.995124 + 0.0986331i $$0.0314470\pi$$
$$510$$ −13.2082 22.8773i −0.584869 1.01302i
$$511$$ 0 0
$$512$$ −40.3050 −1.78124
$$513$$ 4.14590 0.183046
$$514$$ −21.9164 37.9603i −0.966691 1.67436i
$$515$$ 11.3992 19.7440i 0.502308 0.870023i
$$516$$ −159.644 −7.02795
$$517$$ 2.07295 + 3.59045i 0.0911682 + 0.157908i
$$518$$ 0 0
$$519$$ 23.5623 1.03427
$$520$$ −19.5623 + 67.7658i −0.857864 + 2.97173i
$$521$$ −9.32624 + 16.1535i −0.408590 + 0.707698i −0.994732 0.102510i $$-0.967313\pi$$
0.586142 + 0.810208i $$0.300646\pi$$
$$522$$ 71.5410 3.13127
$$523$$ −0.562306 + 0.973942i −0.0245879 + 0.0425875i −0.878058 0.478555i $$-0.841161\pi$$
0.853470 + 0.521143i $$0.174494\pi$$
$$524$$ 37.1976 64.4281i 1.62498 2.81455i
$$525$$ 0 0
$$526$$ −11.7812 + 20.4056i −0.513683 + 0.889724i
$$527$$ 6.93112 0.301924
$$528$$ 23.9164 41.4244i 1.04083 1.80277i
$$529$$ 1.50000 + 2.59808i 0.0652174 + 0.112960i
$$530$$ −12.8992 + 22.3420i −0.560305 + 0.970477i
$$531$$ 4.30902 + 7.46344i 0.186995 + 0.323886i
$$532$$ 0 0
$$533$$ −0.763932 + 2.64634i −0.0330896 + 0.114626i
$$534$$ 16.8262 + 29.1439i 0.728143 + 1.26118i
$$535$$ −8.85410 −0.382796
$$536$$ −94.9574 −4.10154
$$537$$ 23.5623 1.01679
$$538$$ −75.2492 −3.24422
$$539$$ 0 0
$$540$$ 14.2082 24.6093i 0.611424 1.05902i
$$541$$ −17.6353 30.5452i −0.758199 1.31324i −0.943768 0.330608i $$-0.892746\pi$$
0.185569 0.982631i $$-0.440587\pi$$
$$542$$ 11.0172 + 19.0824i 0.473230 + 0.819659i
$$543$$ −25.4164 −1.09072
$$544$$ 7.98936 13.8380i 0.342541 0.593298i
$$545$$ −7.09017 −0.303710
$$546$$ 0 0
$$547$$ −3.00000 −0.128271 −0.0641354 0.997941i $$-0.520429\pi$$
−0.0641354 + 0.997941i $$0.520429\pi$$
$$548$$ 6.35410 11.0056i 0.271434 0.470137i
$$549$$ −23.1246 −0.986934
$$550$$ −4.50000 7.79423i −0.191881 0.332347i
$$551$$ 6.57295 + 11.3847i 0.280017 + 0.485004i
$$552$$ −43.7426 + 75.7645i −1.86181 + 3.22475i
$$553$$ 0 0
$$554$$ −13.0902 −0.556148
$$555$$ −27.4164 −1.16376
$$556$$ 22.1459 0.939195
$$557$$ −27.9787 −1.18550 −0.592748 0.805388i $$-0.701957\pi$$
−0.592748 + 0.805388i $$0.701957\pi$$
$$558$$ 23.7533 + 41.1419i 1.00556 + 1.74168i
$$559$$ 43.9681 10.8793i 1.85965 0.460144i
$$560$$ 0 0
$$561$$ −3.57295 6.18853i −0.150850 0.261280i
$$562$$ −26.4164 + 45.7546i −1.11431 + 1.93004i
$$563$$ 10.5279 + 18.2348i 0.443697 + 0.768505i 0.997960 0.0638360i $$-0.0203335\pi$$
−0.554264 + 0.832341i $$0.687000\pi$$
$$564$$ −14.2082 + 24.6093i −0.598273 + 1.03624i
$$565$$ 3.85410 0.162143
$$566$$ −17.5623 + 30.4188i −0.738199 + 1.27860i
$$567$$ 0 0
$$568$$ 52.9787 91.7618i 2.22294 3.85024i
$$569$$ −7.47214 + 12.9421i −0.313248 + 0.542562i −0.979064 0.203555i $$-0.934751\pi$$
0.665815 + 0.746117i $$0.268084\pi$$
$$570$$ 33.2705 1.39355
$$571$$ −12.3435 + 21.3795i −0.516558 + 0.894704i 0.483257 + 0.875478i $$0.339453\pi$$
−0.999815 + 0.0192259i $$0.993880\pi$$
$$572$$ −9.00000 + 31.1769i −0.376309 + 1.30357i
$$573$$ −55.9787 −2.33854
$$574$$ 0 0
$$575$$ 4.14590 + 7.18091i 0.172896 + 0.299464i
$$576$$ 33.5623 1.39843
$$577$$ 21.9164 37.9603i 0.912392 1.58031i 0.101717 0.994813i $$-0.467567\pi$$
0.810675 0.585496i $$-0.199100\pi$$
$$578$$ 19.4164 + 33.6302i 0.807616 + 1.39883i
$$579$$ 15.7082 0.652811
$$580$$ 90.1033 3.74134
$$581$$ 0 0
$$582$$ 64.6140 + 111.915i 2.67834 + 4.63901i
$$583$$ −3.48936 + 6.04374i −0.144514 + 0.250306i
$$584$$ 7.47214 12.9421i 0.309199 0.535549i
$$585$$ −10.0902 + 34.9534i −0.417177 + 1.44514i
$$586$$ 8.85410 + 15.3358i 0.365760 + 0.633514i
$$587$$ 9.95492 + 17.2424i 0.410883 + 0.711671i 0.994987 0.100009i $$-0.0318870\pi$$
−0.584103 + 0.811679i $$0.698554\pi$$
$$588$$ 0 0
$$589$$ −4.36475 + 7.55996i −0.179846 + 0.311503i
$$590$$ 7.66312 + 13.2729i 0.315486 + 0.546437i
$$591$$ −21.9894 38.0867i −0.904521 1.56668i
$$592$$ −19.7082 34.1356i −0.810002 1.40296i
$$593$$ −21.8992 37.9305i −0.899292 1.55762i −0.828401 0.560135i $$-0.810749\pi$$
−0.0708905 0.997484i $$-0.522584\pi$$
$$594$$ 5.42705 9.39993i 0.222675 0.385684i
$$595$$ 0 0
$$596$$ −4.50000 7.79423i −0.184327 0.319264i
$$597$$ −31.9615 55.3589i −1.30810 2.26569i
$$598$$ 11.7082 40.5584i 0.478784 1.65856i
$$599$$ −14.7533 + 25.5534i −0.602803 + 1.04409i 0.389592 + 0.920988i $$0.372616\pi$$
−0.992395 + 0.123098i $$0.960717\pi$$
$$600$$ 18.1353 31.4112i 0.740369 1.28236i
$$601$$ −20.1976 34.9832i −0.823876 1.42699i −0.902776 0.430112i $$-0.858474\pi$$
0.0788998 0.996883i $$-0.474859\pi$$
$$602$$ 0 0
$$603$$ −48.9787 −1.99457
$$604$$ −6.27051 −0.255143
$$605$$ 9.89919 + 17.1459i 0.402459 + 0.697080i
$$606$$ −39.6246 + 68.6318i −1.60964 + 2.78798i
$$607$$ −23.0000 −0.933541 −0.466771 0.884378i $$-0.654583\pi$$
−0.466771 + 0.884378i $$0.654583\pi$$
$$608$$ 10.0623 + 17.4284i 0.408080 + 0.706816i
$$609$$ 0 0
$$610$$ −41.1246 −1.66509
$$611$$ 2.23607 7.74597i 0.0904616 0.313368i
$$612$$ 13.7705 23.8512i 0.556640 0.964129i
$$613$$ 34.5623 1.39596 0.697979 0.716118i $$-0.254083\pi$$
0.697979 + 0.716118i $$0.254083\pi$$
$$614$$ 6.35410 11.0056i 0.256431 0.444151i
$$615$$ 2.61803 4.53457i 0.105569 0.182851i
$$616$$ 0 0
$$617$$ −0.0278640 + 0.0482619i −0.00112176 + 0.00194295i −0.866586 0.499028i $$-0.833690\pi$$
0.865464 + 0.500971i $$0.167024\pi$$
$$618$$ 59.6869 2.40096
$$619$$ −4.70820 + 8.15485i −0.189239 + 0.327771i −0.944997 0.327080i $$-0.893935\pi$$
0.755758 + 0.654851i $$0.227269\pi$$
$$620$$ 29.9164 + 51.8167i 1.20147 + 2.08101i
$$621$$ −5.00000 + 8.66025i −0.200643 + 0.347524i
$$622$$ −4.35410 7.54153i −0.174584 0.302388i
$$623$$ 0 0
$$624$$ −90.2943 + 22.3420i −3.61467 + 0.894398i
$$625$$ 15.4164 + 26.7020i 0.616656 + 1.06808i
$$626$$ 65.7771 2.62898
$$627$$ 9.00000 0.359425
$$628$$ 72.1033 2.87724
$$629$$ −5.88854 −0.234792
$$630$$ 0 0
$$631$$ −17.1976 + 29.7870i −0.684624 + 1.18580i 0.288931 + 0.957350i $$0.406700\pi$$
−0.973555 + 0.228454i $$0.926633\pi$$
$$632$$ −14.9443 25.8842i −0.594451 1.02962i
$$633$$ 6.16312 + 10.6748i 0.244962 + 0.424287i
$$634$$ 68.6869 2.72791
$$635$$ 27.2984 47.2822i 1.08330 1.87634i
$$636$$ −47.8328 −1.89669
$$637$$ 0 0
$$638$$ 34.4164 1.36256
$$639$$ 27.3262 47.3304i 1.08101 1.87236i
$$640$$ 2.85410 0.112818
$$641$$ 23.7533 + 41.1419i 0.938199 + 1.62501i 0.768829 + 0.639455i $$0.220840\pi$$
0.169370 + 0.985553i $$0.445827\pi$$
$$642$$ −11.5902 20.0748i −0.457428 0.792288i
$$643$$ 3.50000 6.06218i 0.138027 0.239069i −0.788723 0.614749i $$-0.789257\pi$$
0.926750 + 0.375680i $$0.122591\pi$$
$$644$$ 0 0
$$645$$ −86.1033 −3.39032
$$646$$ 7.14590 0.281152
$$647$$ 24.7639 0.973571 0.486785 0.873522i $$-0.338169\pi$$
0.486785 + 0.873522i $$0.338169\pi$$
$$648$$ −42.6525 −1.67555
$$649$$ 2.07295 + 3.59045i 0.0813704 + 0.140938i
$$650$$ −4.85410 + 16.8151i −0.190394 + 0.659543i
$$651$$ 0 0
$$652$$ 9.00000 + 15.5885i 0.352467 + 0.610491i
$$653$$ 0.190983 0.330792i 0.00747374 0.0129449i −0.862264 0.506458i $$-0.830954\pi$$
0.869738 + 0.493514i $$0.164288\pi$$
$$654$$ −9.28115 16.0754i −0.362922 0.628599i
$$655$$ 20.0623 34.7489i 0.783899 1.35775i
$$656$$ 7.52786 0.293914
$$657$$ 3.85410 6.67550i 0.150363 0.260436i
$$658$$ 0 0
$$659$$ 11.9443 20.6881i 0.465283 0.805893i −0.533931 0.845528i $$-0.679286\pi$$
0.999214 + 0.0396343i $$0.0126193\pi$$
$$660$$ 30.8435 53.4224i 1.20058 2.07947i
$$661$$ −48.5410 −1.88803 −0.944013 0.329907i $$-0.892983\pi$$
−0.944013 + 0.329907i $$0.892983\pi$$
$$662$$ 13.2812 23.0036i 0.516187 0.894062i
$$663$$ −3.85410 + 13.3510i −0.149681 + 0.518510i
$$664$$ 50.1246 1.94521
$$665$$ 0 0
$$666$$ −20.1803 34.9534i −0.781972 1.35442i
$$667$$ −31.7082 −1.22775
$$668$$ −34.5517 + 59.8452i −1.33684 + 2.31548i
$$669$$ 26.5344 + 45.9590i 1.02588 + 1.77688i
$$670$$ −87.1033 −3.36510
$$671$$ −11.1246 −0.429461
$$672$$ 0 0
$$673$$ 19.6246 + 33.9908i 0.756473 + 1.31025i 0.944639 + 0.328113i $$0.106413\pi$$
−0.188165 + 0.982137i $$0.560254\pi$$
$$674$$ 15.1353 26.2150i 0.582988 1.00977i
$$675$$ 2.07295 3.59045i 0.0797878 0.138197i
$$676$$ 55.8222 29.4264i 2.14701 1.13179i
$$677$$ −21.8713 37.8822i −0.840583 1.45593i −0.889402 0.457125i $$-0.848879\pi$$
0.0488191 0.998808i $$-0.484454\pi$$
$$678$$ 5.04508 + 8.73834i 0.193755 + 0.335594i
$$679$$ 0 0
$$680$$ 14.3992 24.9401i 0.552184 0.956410i
$$681$$ 1.92705 + 3.33775i 0.0738448 + 0.127903i
$$682$$ 11.4271 + 19.7922i 0.437564 + 0.757884i
$$683$$ −0.736068 1.27491i −0.0281649 0.0487830i 0.851599 0.524193i $$-0.175633\pi$$
−0.879764 + 0.475410i $$0.842300\pi$$
$$684$$ 17.3435 + 30.0398i 0.663144 + 1.14860i
$$685$$ 3.42705 5.93583i 0.130941 0.226796i
$$686$$ 0 0
$$687$$ −17.1803 29.7572i −0.655471 1.13531i
$$688$$ −61.8951 107.205i −2.35973 4.08717i
$$689$$ 13.1738 3.25966i 0.501880 0.124183i
$$690$$ −40.1246 + 69.4979i −1.52752 + 2.64574i
$$691$$ 2.92705 5.06980i 0.111350 0.192864i −0.804965 0.593323i $$-0.797816\pi$$
0.916315 + 0.400458i $$0.131149\pi$$
$$692$$ 21.8435 + 37.8340i 0.830364 + 1.43823i
$$693$$ 0 0
$$694$$ 80.5410 3.05730
$$695$$ 11.9443 0.453072
$$696$$ 69.3500 + 120.118i 2.62871 + 4.55305i
$$697$$ 0.562306 0.973942i 0.0212989 0.0368907i
$$698$$ 54.2148 2.05206
$$699$$ 3.42705 + 5.93583i 0.129623 + 0.224514i
$$700$$ 0 0
$$701$$ 11.2361 0.424380 0.212190 0.977228i $$-0.431940\pi$$
0.212190 + 0.977228i $$0.431940\pi$$
$$702$$ −20.4894 + 5.06980i −0.773321 + 0.191347i
$$703$$ 3.70820 6.42280i 0.139858 0.242240i
$$704$$ 16.1459 0.608521
$$705$$ −7.66312 + 13.2729i −0.288610 + 0.499887i
$$706$$ −28.9894 + 50.2110i −1.09103 + 1.88972i
$$707$$ 0 0
$$708$$ −14.2082 + 24.6093i −0.533977 + 0.924875i
$$709$$ 23.5623 0.884901 0.442450 0.896793i $$-0.354109\pi$$
0.442450 + 0.896793i $$0.354109\pi$$
$$710$$ 48.5967 84.1720i 1.82380 3.15892i
$$711$$ −7.70820 13.3510i −0.289080 0.500702i
$$712$$ −18.3435 + 31.7718i −0.687450 + 1.19070i
$$713$$ −10.5279 18.2348i −0.394272 0.682898i
$$714$$ 0 0
$$715$$ −4.85410 + 16.8151i −0.181533 + 0.628849i
$$716$$ 21.8435 + 37.8340i 0.816328 + 1.41392i
$$717$$ 64.6869 2.41578
$$718$$ −57.8328 −2.15830
$$719$$ 8.12461 0.302997 0.151498 0.988457i $$-0.451590\pi$$
0.151498 + 0.988457i $$0.451590\pi$$
$$720$$ 99.4296 3.70552
$$721$$ 0 0
$$722$$ 20.3713 35.2842i 0.758142 1.31314i
$$723$$ 32.1525 + 55.6897i 1.19576 + 2.07112i
$$724$$ −23.5623 40.8111i −0.875686 1.51673i
$$725$$ 13.1459 0.488226
$$726$$ −25.9164 + 44.8885i −0.961848 + 1.66597i
$$727$$ −30.7082 −1.13890 −0.569452 0.822025i $$-0.692845\pi$$
−0.569452 + 0.822025i $$0.692845\pi$$
$$728$$ 0 0
$$729$$ −39.5623 −1.46527
$$730$$ 6.85410 11.8717i 0.253682 0.439390i
$$731$$ −18.4934 −0.684004
$$732$$ −38.1246 66.0338i −1.40913 2.44068i
$$733$$ 16.1353 + 27.9471i 0.595969 + 1.03225i 0.993409 + 0.114621i $$0.0365653\pi$$
−0.397440 + 0.917628i $$0.630101\pi$$
$$734$$ 1.85410 3.21140i 0.0684362 0.118535i
$$735$$ 0 0
$$736$$ −48.5410 −1.78925
$$737$$ −23.5623 −0.867929
$$738$$ 7.70820 0.283743
$$739$$ −6.87539 −0.252915 −0.126458 0.991972i $$-0.540361\pi$$
−0.126458 + 0.991972i $$0.540361\pi$$
$$740$$ −25.4164 44.0225i −0.934326 1.61830i
$$741$$ −12.1353 12.6113i −0.445800 0.463289i
$$742$$ 0 0
$$743$$ −19.6631 34.0575i −0.721370 1.24945i −0.960451 0.278450i $$-0.910179\pi$$
0.239081 0.971000i $$-0.423154\pi$$
$$744$$ −46.0517 + 79.7638i −1.68834 + 2.92428i
$$745$$ −2.42705 4.20378i −0.0889203 0.154014i
$$746$$ 26.9164 46.6206i 0.985480 1.70690i
$$747$$ 25.8541 0.945952
$$748$$ 6.62461 11.4742i 0.242220 0.419537i
$$749$$ 0 0
$$750$$ −28.2254 + 48.8879i −1.03065 + 1.78513i
$$751$$ −11.3541 + 19.6659i −0.414317 + 0.717618i −0.995356 0.0962572i $$-0.969313\pi$$
0.581039 + 0.813875i $$0.302646\pi$$
$$752$$ −22.0344 −0.803513
$$753$$ 1.00000 1.73205i 0.0364420 0.0631194i
$$754$$ −46.4058 48.2263i −1.69000 1.75630i
$$755$$ −3.38197 −0.123082
$$756$$ 0 0
$$757$$ −14.0000 24.2487i −0.508839 0.881334i −0.999948 0.0102362i $$-0.996742\pi$$
0.491109 0.871098i $$-0.336592\pi$$
$$758$$ −16.0902 −0.584421
$$759$$ −10.8541 + 18.7999i −0.393979 + 0.682392i
$$760$$ 18.1353 + 31.4112i 0.657835 + 1.13940i
$$761$$ −28.8541 −1.04596 −0.522980 0.852345i $$-0.675180\pi$$
−0.522980 + 0.852345i $$0.675180\pi$$
$$762$$ 142.936 5.17803
$$763$$ 0 0
$$764$$ −51.8951 89.8850i −1.87750 3.25192i
$$765$$ 7.42705 12.8640i 0.268526 0.465100i
$$766$$ 28.7705 49.8320i 1.03952 1.80050i
$$767$$ 2.23607 7.74597i 0.0807397 0.279691i
$$768$$ −19.0623 33.0169i −0.687852 1.19139i
$$769$$ 9.20820 + 15.9491i 0.332056 + 0.575138i 0.982915 0.184061i $$-0.0589243\pi$$
−0.650859 + 0.759199i $$0.725591\pi$$
$$770$$ 0 0
$$771$$ 21.9164 37.9603i 0.789300 1.36711i
$$772$$ 14.5623 + 25.2227i 0.524109 + 0.907783i
$$773$$ −12.6803 21.9630i −0.456080 0.789954i 0.542669 0.839946i $$-0.317414\pi$$
−0.998750 + 0.0499924i $$0.984080\pi$$
$$774$$ −63.3779 109.774i −2.27807 3.94574i
$$775$$ 4.36475 + 7.55996i 0.156786 + 0.271562i
$$776$$ −70.4402 + 122.006i −2.52866 + 4.37976i
$$777$$ 0 0
$$778$$ 15.5623 + 26.9547i 0.557936 + 0.966373i
$$779$$ 0.708204 + 1.22665i 0.0253740 + 0.0439491i
$$780$$ −116.447 + 28.8131i −4.16946 + 1.03167i
$$781$$ 13.1459 22.7694i