# Properties

 Label 42.3.c.a.13.1 Level $42$ Weight $3$ Character 42.13 Analytic conductor $1.144$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$42 = 2 \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 42.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.14441711031$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 13.1 Root $$0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 42.13 Dual form 42.3.c.a.13.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -5.91359i q^{5} +2.44949i q^{6} +(6.24264 - 3.16693i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$$ $$q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -5.91359i q^{5} +2.44949i q^{6} +(6.24264 - 3.16693i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +8.36308i q^{10} -1.75736 q^{11} -3.46410i q^{12} +18.7554i q^{13} +(-8.82843 + 4.47871i) q^{14} -10.2426 q^{15} +4.00000 q^{16} +23.4803i q^{17} +4.24264 q^{18} -23.0600i q^{19} -11.8272i q^{20} +(-5.48528 - 10.8126i) q^{21} +2.48528 q^{22} +18.7279 q^{23} +4.89898i q^{24} -9.97056 q^{25} -26.5241i q^{26} +5.19615i q^{27} +(12.4853 - 6.33386i) q^{28} +30.0000 q^{29} +14.4853 q^{30} +8.60927i q^{31} -5.65685 q^{32} +3.04384i q^{33} -33.2061i q^{34} +(-18.7279 - 36.9164i) q^{35} -6.00000 q^{36} -70.9117 q^{37} +32.6118i q^{38} +32.4853 q^{39} +16.7262i q^{40} +41.3951i q^{41} +(7.75736 + 15.2913i) q^{42} +10.4264 q^{43} -3.51472 q^{44} +17.7408i q^{45} -26.4853 q^{46} +38.6995i q^{47} -6.92820i q^{48} +(28.9411 - 39.5400i) q^{49} +14.1005 q^{50} +40.6690 q^{51} +37.5108i q^{52} -37.0294 q^{53} -7.34847i q^{54} +10.3923i q^{55} +(-17.6569 + 8.95743i) q^{56} -39.9411 q^{57} -42.4264 q^{58} -97.4872i q^{59} -20.4853 q^{60} +16.7262i q^{61} -12.1753i q^{62} +(-18.7279 + 9.50079i) q^{63} +8.00000 q^{64} +110.912 q^{65} -4.30463i q^{66} +60.9706 q^{67} +46.9606i q^{68} -32.4377i q^{69} +(26.4853 + 52.2077i) q^{70} -110.610 q^{71} +8.48528 q^{72} -56.7585i q^{73} +100.284 q^{74} +17.2695i q^{75} -46.1200i q^{76} +(-10.9706 + 5.56543i) q^{77} -45.9411 q^{78} -69.8234 q^{79} -23.6544i q^{80} +9.00000 q^{81} -58.5416i q^{82} +6.43583i q^{83} +(-10.9706 - 21.6251i) q^{84} +138.853 q^{85} -14.7452 q^{86} -51.9615i q^{87} +4.97056 q^{88} -42.0915i q^{89} -25.0892i q^{90} +(59.3970 + 117.083i) q^{91} +37.4558 q^{92} +14.9117 q^{93} -54.7293i q^{94} -136.368 q^{95} +9.79796i q^{96} +51.7153i q^{97} +(-40.9289 + 55.9180i) q^{98} +5.27208 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 8 q^{4} + 8 q^{7} - 12 q^{9}+O(q^{10})$$ 4 * q + 8 * q^4 + 8 * q^7 - 12 * q^9 $$4 q + 8 q^{4} + 8 q^{7} - 12 q^{9} - 24 q^{11} - 24 q^{14} - 24 q^{15} + 16 q^{16} + 12 q^{21} - 24 q^{22} + 24 q^{23} + 28 q^{25} + 16 q^{28} + 120 q^{29} + 24 q^{30} - 24 q^{35} - 24 q^{36} - 80 q^{37} + 96 q^{39} + 48 q^{42} - 128 q^{43} - 48 q^{44} - 72 q^{46} - 20 q^{49} + 96 q^{50} - 24 q^{51} - 216 q^{53} - 48 q^{56} - 24 q^{57} - 48 q^{60} - 24 q^{63} + 32 q^{64} + 240 q^{65} + 176 q^{67} + 72 q^{70} - 120 q^{71} + 288 q^{74} + 24 q^{77} - 48 q^{78} + 128 q^{79} + 36 q^{81} + 24 q^{84} + 216 q^{85} - 240 q^{86} - 48 q^{88} + 48 q^{92} - 144 q^{93} - 240 q^{95} - 192 q^{98} + 72 q^{99}+O(q^{100})$$ 4 * q + 8 * q^4 + 8 * q^7 - 12 * q^9 - 24 * q^11 - 24 * q^14 - 24 * q^15 + 16 * q^16 + 12 * q^21 - 24 * q^22 + 24 * q^23 + 28 * q^25 + 16 * q^28 + 120 * q^29 + 24 * q^30 - 24 * q^35 - 24 * q^36 - 80 * q^37 + 96 * q^39 + 48 * q^42 - 128 * q^43 - 48 * q^44 - 72 * q^46 - 20 * q^49 + 96 * q^50 - 24 * q^51 - 216 * q^53 - 48 * q^56 - 24 * q^57 - 48 * q^60 - 24 * q^63 + 32 * q^64 + 240 * q^65 + 176 * q^67 + 72 * q^70 - 120 * q^71 + 288 * q^74 + 24 * q^77 - 48 * q^78 + 128 * q^79 + 36 * q^81 + 24 * q^84 + 216 * q^85 - 240 * q^86 - 48 * q^88 + 48 * q^92 - 144 * q^93 - 240 * q^95 - 192 * q^98 + 72 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$31$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.41421 −0.707107
$$3$$ 1.73205i 0.577350i
$$4$$ 2.00000 0.500000
$$5$$ 5.91359i 1.18272i −0.806408 0.591359i $$-0.798592\pi$$
0.806408 0.591359i $$-0.201408\pi$$
$$6$$ 2.44949i 0.408248i
$$7$$ 6.24264 3.16693i 0.891806 0.452418i
$$8$$ −2.82843 −0.353553
$$9$$ −3.00000 −0.333333
$$10$$ 8.36308i 0.836308i
$$11$$ −1.75736 −0.159760 −0.0798800 0.996804i $$-0.525454\pi$$
−0.0798800 + 0.996804i $$0.525454\pi$$
$$12$$ 3.46410i 0.288675i
$$13$$ 18.7554i 1.44272i 0.692559 + 0.721361i $$0.256483\pi$$
−0.692559 + 0.721361i $$0.743517\pi$$
$$14$$ −8.82843 + 4.47871i −0.630602 + 0.319908i
$$15$$ −10.2426 −0.682843
$$16$$ 4.00000 0.250000
$$17$$ 23.4803i 1.38119i 0.723240 + 0.690597i $$0.242652\pi$$
−0.723240 + 0.690597i $$0.757348\pi$$
$$18$$ 4.24264 0.235702
$$19$$ 23.0600i 1.21369i −0.794822 0.606843i $$-0.792436\pi$$
0.794822 0.606843i $$-0.207564\pi$$
$$20$$ 11.8272i 0.591359i
$$21$$ −5.48528 10.8126i −0.261204 0.514884i
$$22$$ 2.48528 0.112967
$$23$$ 18.7279 0.814257 0.407129 0.913371i $$-0.366530\pi$$
0.407129 + 0.913371i $$0.366530\pi$$
$$24$$ 4.89898i 0.204124i
$$25$$ −9.97056 −0.398823
$$26$$ 26.5241i 1.02016i
$$27$$ 5.19615i 0.192450i
$$28$$ 12.4853 6.33386i 0.445903 0.226209i
$$29$$ 30.0000 1.03448 0.517241 0.855840i $$-0.326959\pi$$
0.517241 + 0.855840i $$0.326959\pi$$
$$30$$ 14.4853 0.482843
$$31$$ 8.60927i 0.277718i 0.990312 + 0.138859i $$0.0443435\pi$$
−0.990312 + 0.138859i $$0.955656\pi$$
$$32$$ −5.65685 −0.176777
$$33$$ 3.04384i 0.0922374i
$$34$$ 33.2061i 0.976651i
$$35$$ −18.7279 36.9164i −0.535083 1.05476i
$$36$$ −6.00000 −0.166667
$$37$$ −70.9117 −1.91653 −0.958266 0.285878i $$-0.907715\pi$$
−0.958266 + 0.285878i $$0.907715\pi$$
$$38$$ 32.6118i 0.858205i
$$39$$ 32.4853 0.832956
$$40$$ 16.7262i 0.418154i
$$41$$ 41.3951i 1.00964i 0.863225 + 0.504819i $$0.168441\pi$$
−0.863225 + 0.504819i $$0.831559\pi$$
$$42$$ 7.75736 + 15.2913i 0.184699 + 0.364078i
$$43$$ 10.4264 0.242475 0.121237 0.992624i $$-0.461314\pi$$
0.121237 + 0.992624i $$0.461314\pi$$
$$44$$ −3.51472 −0.0798800
$$45$$ 17.7408i 0.394239i
$$46$$ −26.4853 −0.575767
$$47$$ 38.6995i 0.823393i 0.911321 + 0.411696i $$0.135064\pi$$
−0.911321 + 0.411696i $$0.864936\pi$$
$$48$$ 6.92820i 0.144338i
$$49$$ 28.9411 39.5400i 0.590635 0.806939i
$$50$$ 14.1005 0.282010
$$51$$ 40.6690 0.797432
$$52$$ 37.5108i 0.721361i
$$53$$ −37.0294 −0.698669 −0.349334 0.936998i $$-0.613592\pi$$
−0.349334 + 0.936998i $$0.613592\pi$$
$$54$$ 7.34847i 0.136083i
$$55$$ 10.3923i 0.188951i
$$56$$ −17.6569 + 8.95743i −0.315301 + 0.159954i
$$57$$ −39.9411 −0.700721
$$58$$ −42.4264 −0.731490
$$59$$ 97.4872i 1.65233i −0.563431 0.826163i $$-0.690519\pi$$
0.563431 0.826163i $$-0.309481\pi$$
$$60$$ −20.4853 −0.341421
$$61$$ 16.7262i 0.274199i 0.990557 + 0.137100i $$0.0437781\pi$$
−0.990557 + 0.137100i $$0.956222\pi$$
$$62$$ 12.1753i 0.196376i
$$63$$ −18.7279 + 9.50079i −0.297269 + 0.150806i
$$64$$ 8.00000 0.125000
$$65$$ 110.912 1.70633
$$66$$ 4.30463i 0.0652217i
$$67$$ 60.9706 0.910008 0.455004 0.890489i $$-0.349638\pi$$
0.455004 + 0.890489i $$0.349638\pi$$
$$68$$ 46.9606i 0.690597i
$$69$$ 32.4377i 0.470112i
$$70$$ 26.4853 + 52.2077i 0.378361 + 0.745824i
$$71$$ −110.610 −1.55789 −0.778945 0.627092i $$-0.784245\pi$$
−0.778945 + 0.627092i $$0.784245\pi$$
$$72$$ 8.48528 0.117851
$$73$$ 56.7585i 0.777514i −0.921340 0.388757i $$-0.872905\pi$$
0.921340 0.388757i $$-0.127095\pi$$
$$74$$ 100.284 1.35519
$$75$$ 17.2695i 0.230260i
$$76$$ 46.1200i 0.606843i
$$77$$ −10.9706 + 5.56543i −0.142475 + 0.0722783i
$$78$$ −45.9411 −0.588989
$$79$$ −69.8234 −0.883840 −0.441920 0.897054i $$-0.645703\pi$$
−0.441920 + 0.897054i $$0.645703\pi$$
$$80$$ 23.6544i 0.295680i
$$81$$ 9.00000 0.111111
$$82$$ 58.5416i 0.713922i
$$83$$ 6.43583i 0.0775401i 0.999248 + 0.0387701i $$0.0123440\pi$$
−0.999248 + 0.0387701i $$0.987656\pi$$
$$84$$ −10.9706 21.6251i −0.130602 0.257442i
$$85$$ 138.853 1.63356
$$86$$ −14.7452 −0.171455
$$87$$ 51.9615i 0.597259i
$$88$$ 4.97056 0.0564837
$$89$$ 42.0915i 0.472938i −0.971639 0.236469i $$-0.924010\pi$$
0.971639 0.236469i $$-0.0759901\pi$$
$$90$$ 25.0892i 0.278769i
$$91$$ 59.3970 + 117.083i 0.652714 + 1.28663i
$$92$$ 37.4558 0.407129
$$93$$ 14.9117 0.160341
$$94$$ 54.7293i 0.582227i
$$95$$ −136.368 −1.43545
$$96$$ 9.79796i 0.102062i
$$97$$ 51.7153i 0.533148i 0.963814 + 0.266574i $$0.0858916\pi$$
−0.963814 + 0.266574i $$0.914108\pi$$
$$98$$ −40.9289 + 55.9180i −0.417642 + 0.570592i
$$99$$ 5.27208 0.0532533
$$100$$ −19.9411 −0.199411
$$101$$ 6.60991i 0.0654447i 0.999464 + 0.0327223i $$0.0104177\pi$$
−0.999464 + 0.0327223i $$0.989582\pi$$
$$102$$ −57.5147 −0.563870
$$103$$ 175.871i 1.70748i 0.520696 + 0.853742i $$0.325673\pi$$
−0.520696 + 0.853742i $$0.674327\pi$$
$$104$$ 53.0482i 0.510079i
$$105$$ −63.9411 + 32.4377i −0.608963 + 0.308931i
$$106$$ 52.3675 0.494033
$$107$$ −46.2426 −0.432174 −0.216087 0.976374i $$-0.569330\pi$$
−0.216087 + 0.976374i $$0.569330\pi$$
$$108$$ 10.3923i 0.0962250i
$$109$$ −35.9411 −0.329735 −0.164868 0.986316i $$-0.552720\pi$$
−0.164868 + 0.986316i $$0.552720\pi$$
$$110$$ 14.6969i 0.133609i
$$111$$ 122.823i 1.10651i
$$112$$ 24.9706 12.6677i 0.222951 0.113105i
$$113$$ −73.0294 −0.646278 −0.323139 0.946351i $$-0.604738\pi$$
−0.323139 + 0.946351i $$0.604738\pi$$
$$114$$ 56.4853 0.495485
$$115$$ 110.749i 0.963037i
$$116$$ 60.0000 0.517241
$$117$$ 56.2662i 0.480907i
$$118$$ 137.868i 1.16837i
$$119$$ 74.3604 + 146.579i 0.624877 + 1.23176i
$$120$$ 28.9706 0.241421
$$121$$ −117.912 −0.974477
$$122$$ 23.6544i 0.193888i
$$123$$ 71.6985 0.582915
$$124$$ 17.2185i 0.138859i
$$125$$ 88.8780i 0.711024i
$$126$$ 26.4853 13.4361i 0.210201 0.106636i
$$127$$ 89.9411 0.708198 0.354099 0.935208i $$-0.384788\pi$$
0.354099 + 0.935208i $$0.384788\pi$$
$$128$$ −11.3137 −0.0883883
$$129$$ 18.0591i 0.139993i
$$130$$ −156.853 −1.20656
$$131$$ 12.1753i 0.0929415i 0.998920 + 0.0464708i $$0.0147974\pi$$
−0.998920 + 0.0464708i $$0.985203\pi$$
$$132$$ 6.08767i 0.0461187i
$$133$$ −73.0294 143.955i −0.549094 1.08237i
$$134$$ −86.2254 −0.643473
$$135$$ 30.7279 0.227614
$$136$$ 66.4123i 0.488326i
$$137$$ 165.765 1.20996 0.604980 0.796241i $$-0.293181\pi$$
0.604980 + 0.796241i $$0.293181\pi$$
$$138$$ 45.8739i 0.332419i
$$139$$ 220.514i 1.58643i −0.608941 0.793215i $$-0.708406\pi$$
0.608941 0.793215i $$-0.291594\pi$$
$$140$$ −37.4558 73.8329i −0.267542 0.527378i
$$141$$ 67.0294 0.475386
$$142$$ 156.426 1.10159
$$143$$ 32.9600i 0.230489i
$$144$$ −12.0000 −0.0833333
$$145$$ 177.408i 1.22350i
$$146$$ 80.2687i 0.549786i
$$147$$ −68.4853 50.1275i −0.465886 0.341003i
$$148$$ −141.823 −0.958266
$$149$$ 210.853 1.41512 0.707560 0.706653i $$-0.249796\pi$$
0.707560 + 0.706653i $$0.249796\pi$$
$$150$$ 24.4228i 0.162819i
$$151$$ −72.3675 −0.479255 −0.239628 0.970865i $$-0.577025\pi$$
−0.239628 + 0.970865i $$0.577025\pi$$
$$152$$ 65.2236i 0.429103i
$$153$$ 70.4409i 0.460398i
$$154$$ 15.5147 7.87071i 0.100745 0.0511085i
$$155$$ 50.9117 0.328463
$$156$$ 64.9706 0.416478
$$157$$ 233.674i 1.48837i 0.667974 + 0.744184i $$0.267162\pi$$
−0.667974 + 0.744184i $$0.732838\pi$$
$$158$$ 98.7452 0.624969
$$159$$ 64.1369i 0.403377i
$$160$$ 33.4523i 0.209077i
$$161$$ 116.912 59.3100i 0.726160 0.368385i
$$162$$ −12.7279 −0.0785674
$$163$$ −73.0883 −0.448395 −0.224197 0.974544i $$-0.571976\pi$$
−0.224197 + 0.974544i $$0.571976\pi$$
$$164$$ 82.7903i 0.504819i
$$165$$ 18.0000 0.109091
$$166$$ 9.10164i 0.0548292i
$$167$$ 39.3958i 0.235903i −0.993019 0.117951i $$-0.962367\pi$$
0.993019 0.117951i $$-0.0376327\pi$$
$$168$$ 15.5147 + 30.5826i 0.0923495 + 0.182039i
$$169$$ −182.765 −1.08145
$$170$$ −196.368 −1.15510
$$171$$ 69.1801i 0.404562i
$$172$$ 20.8528 0.121237
$$173$$ 23.8284i 0.137737i 0.997626 + 0.0688683i $$0.0219388\pi$$
−0.997626 + 0.0688683i $$0.978061\pi$$
$$174$$ 73.4847i 0.422326i
$$175$$ −62.2426 + 31.5761i −0.355672 + 0.180435i
$$176$$ −7.02944 −0.0399400
$$177$$ −168.853 −0.953971
$$178$$ 59.5263i 0.334417i
$$179$$ −12.9045 −0.0720924 −0.0360462 0.999350i $$-0.511476\pi$$
−0.0360462 + 0.999350i $$0.511476\pi$$
$$180$$ 35.4815i 0.197120i
$$181$$ 65.3678i 0.361148i 0.983561 + 0.180574i $$0.0577955\pi$$
−0.983561 + 0.180574i $$0.942204\pi$$
$$182$$ −84.0000 165.581i −0.461538 0.909783i
$$183$$ 28.9706 0.158309
$$184$$ −52.9706 −0.287883
$$185$$ 419.343i 2.26672i
$$186$$ −21.0883 −0.113378
$$187$$ 41.2633i 0.220659i
$$188$$ 77.3989i 0.411696i
$$189$$ 16.4558 + 32.4377i 0.0870680 + 0.171628i
$$190$$ 192.853 1.01501
$$191$$ −100.066 −0.523906 −0.261953 0.965081i $$-0.584367\pi$$
−0.261953 + 0.965081i $$0.584367\pi$$
$$192$$ 13.8564i 0.0721688i
$$193$$ 78.9117 0.408869 0.204434 0.978880i $$-0.434464\pi$$
0.204434 + 0.978880i $$0.434464\pi$$
$$194$$ 73.1365i 0.376992i
$$195$$ 192.105i 0.985152i
$$196$$ 57.8823 79.0800i 0.295318 0.403469i
$$197$$ −183.941 −0.933711 −0.466856 0.884334i $$-0.654613\pi$$
−0.466856 + 0.884334i $$0.654613\pi$$
$$198$$ −7.45584 −0.0376558
$$199$$ 170.029i 0.854419i 0.904153 + 0.427210i $$0.140503\pi$$
−0.904153 + 0.427210i $$0.859497\pi$$
$$200$$ 28.2010 0.141005
$$201$$ 105.604i 0.525394i
$$202$$ 9.34783i 0.0462764i
$$203$$ 187.279 95.0079i 0.922558 0.468019i
$$204$$ 81.3381 0.398716
$$205$$ 244.794 1.19412
$$206$$ 248.719i 1.20737i
$$207$$ −56.1838 −0.271419
$$208$$ 75.0215i 0.360680i
$$209$$ 40.5247i 0.193898i
$$210$$ 90.4264 45.8739i 0.430602 0.218447i
$$211$$ 21.5736 0.102245 0.0511223 0.998692i $$-0.483720\pi$$
0.0511223 + 0.998692i $$0.483720\pi$$
$$212$$ −74.0589 −0.349334
$$213$$ 191.582i 0.899448i
$$214$$ 65.3970 0.305593
$$215$$ 61.6575i 0.286779i
$$216$$ 14.6969i 0.0680414i
$$217$$ 27.2649 + 53.7446i 0.125645 + 0.247671i
$$218$$ 50.8284 0.233158
$$219$$ −98.3087 −0.448898
$$220$$ 20.7846i 0.0944755i
$$221$$ −440.382 −1.99268
$$222$$ 173.697i 0.782421i
$$223$$ 119.359i 0.535240i −0.963525 0.267620i $$-0.913763\pi$$
0.963525 0.267620i $$-0.0862372\pi$$
$$224$$ −35.3137 + 17.9149i −0.157650 + 0.0799770i
$$225$$ 29.9117 0.132941
$$226$$ 103.279 0.456988
$$227$$ 169.843i 0.748207i −0.927387 0.374103i $$-0.877951\pi$$
0.927387 0.374103i $$-0.122049\pi$$
$$228$$ −79.8823 −0.350361
$$229$$ 110.011i 0.480396i −0.970724 0.240198i $$-0.922788\pi$$
0.970724 0.240198i $$-0.0772124\pi$$
$$230$$ 156.623i 0.680970i
$$231$$ 9.63961 + 19.0016i 0.0417299 + 0.0822579i
$$232$$ −84.8528 −0.365745
$$233$$ 57.2649 0.245772 0.122886 0.992421i $$-0.460785\pi$$
0.122886 + 0.992421i $$0.460785\pi$$
$$234$$ 79.5724i 0.340053i
$$235$$ 228.853 0.973842
$$236$$ 194.974i 0.826163i
$$237$$ 120.938i 0.510285i
$$238$$ −105.161 207.294i −0.441855 0.870983i
$$239$$ 281.522 1.17792 0.588958 0.808164i $$-0.299538\pi$$
0.588958 + 0.808164i $$0.299538\pi$$
$$240$$ −40.9706 −0.170711
$$241$$ 168.306i 0.698366i 0.937055 + 0.349183i $$0.113541\pi$$
−0.937055 + 0.349183i $$0.886459\pi$$
$$242$$ 166.752 0.689059
$$243$$ 15.5885i 0.0641500i
$$244$$ 33.4523i 0.137100i
$$245$$ −233.823 171.146i −0.954381 0.698555i
$$246$$ −101.397 −0.412183
$$247$$ 432.500 1.75101
$$248$$ 24.3507i 0.0981882i
$$249$$ 11.1472 0.0447678
$$250$$ 125.692i 0.502770i
$$251$$ 106.096i 0.422695i 0.977411 + 0.211348i $$0.0677852\pi$$
−0.977411 + 0.211348i $$0.932215\pi$$
$$252$$ −37.4558 + 19.0016i −0.148634 + 0.0754031i
$$253$$ −32.9117 −0.130086
$$254$$ −127.196 −0.500771
$$255$$ 240.500i 0.943138i
$$256$$ 16.0000 0.0625000
$$257$$ 290.462i 1.13020i −0.825021 0.565102i $$-0.808837\pi$$
0.825021 0.565102i $$-0.191163\pi$$
$$258$$ 25.5394i 0.0989898i
$$259$$ −442.676 + 224.572i −1.70917 + 0.867074i
$$260$$ 221.823 0.853167
$$261$$ −90.0000 −0.344828
$$262$$ 17.2185i 0.0657196i
$$263$$ −89.0223 −0.338488 −0.169244 0.985574i $$-0.554133\pi$$
−0.169244 + 0.985574i $$0.554133\pi$$
$$264$$ 8.60927i 0.0326109i
$$265$$ 218.977i 0.826328i
$$266$$ 103.279 + 203.584i 0.388268 + 0.765352i
$$267$$ −72.9045 −0.273051
$$268$$ 121.941 0.455004
$$269$$ 191.498i 0.711888i 0.934507 + 0.355944i $$0.115841\pi$$
−0.934507 + 0.355944i $$0.884159\pi$$
$$270$$ −43.4558 −0.160948
$$271$$ 217.440i 0.802362i −0.915999 0.401181i $$-0.868600\pi$$
0.915999 0.401181i $$-0.131400\pi$$
$$272$$ 93.9211i 0.345298i
$$273$$ 202.794 102.879i 0.742835 0.376845i
$$274$$ −234.426 −0.855571
$$275$$ 17.5219 0.0637159
$$276$$ 64.8754i 0.235056i
$$277$$ 290.676 1.04937 0.524686 0.851296i $$-0.324183\pi$$
0.524686 + 0.851296i $$0.324183\pi$$
$$278$$ 311.854i 1.12178i
$$279$$ 25.8278i 0.0925728i
$$280$$ 52.9706 + 104.415i 0.189181 + 0.372912i
$$281$$ 18.8528 0.0670919 0.0335459 0.999437i $$-0.489320\pi$$
0.0335459 + 0.999437i $$0.489320\pi$$
$$282$$ −94.7939 −0.336149
$$283$$ 401.734i 1.41955i −0.704426 0.709777i $$-0.748796\pi$$
0.704426 0.709777i $$-0.251204\pi$$
$$284$$ −221.220 −0.778945
$$285$$ 236.195i 0.828756i
$$286$$ 46.6124i 0.162980i
$$287$$ 131.095 + 258.415i 0.456779 + 0.900401i
$$288$$ 16.9706 0.0589256
$$289$$ −262.324 −0.907695
$$290$$ 250.892i 0.865146i
$$291$$ 89.5736 0.307813
$$292$$ 113.517i 0.388757i
$$293$$ 280.893i 0.958679i −0.877629 0.479340i $$-0.840876\pi$$
0.877629 0.479340i $$-0.159124\pi$$
$$294$$ 96.8528 + 70.8910i 0.329431 + 0.241126i
$$295$$ −576.500 −1.95424
$$296$$ 200.569 0.677596
$$297$$ 9.13151i 0.0307458i
$$298$$ −298.191 −1.00064
$$299$$ 351.249i 1.17475i
$$300$$ 34.5390i 0.115130i
$$301$$ 65.0883 33.0197i 0.216240 0.109700i
$$302$$ 102.343 0.338885
$$303$$ 11.4487 0.0377845
$$304$$ 92.2401i 0.303421i
$$305$$ 98.9117 0.324301
$$306$$ 99.6184i 0.325550i
$$307$$ 152.318i 0.496151i 0.968741 + 0.248076i $$0.0797982\pi$$
−0.968741 + 0.248076i $$0.920202\pi$$
$$308$$ −21.9411 + 11.1309i −0.0712374 + 0.0361392i
$$309$$ 304.617 0.985817
$$310$$ −72.0000 −0.232258
$$311$$ 283.156i 0.910470i −0.890371 0.455235i $$-0.849555\pi$$
0.890371 0.455235i $$-0.150445\pi$$
$$312$$ −91.8823 −0.294494
$$313$$ 48.5819i 0.155214i 0.996984 + 0.0776069i $$0.0247279\pi$$
−0.996984 + 0.0776069i $$0.975272\pi$$
$$314$$ 330.465i 1.05244i
$$315$$ 56.1838 + 110.749i 0.178361 + 0.351585i
$$316$$ −139.647 −0.441920
$$317$$ −578.029 −1.82343 −0.911717 0.410819i $$-0.865243\pi$$
−0.911717 + 0.410819i $$0.865243\pi$$
$$318$$ 90.7032i 0.285230i
$$319$$ −52.7208 −0.165269
$$320$$ 47.3087i 0.147840i
$$321$$ 80.0946i 0.249516i
$$322$$ −165.338 + 83.8770i −0.513472 + 0.260488i
$$323$$ 541.456 1.67633
$$324$$ 18.0000 0.0555556
$$325$$ 187.002i 0.575390i
$$326$$ 103.362 0.317063
$$327$$ 62.2519i 0.190373i
$$328$$ 117.083i 0.356961i
$$329$$ 122.558 + 241.587i 0.372518 + 0.734307i
$$330$$ −25.4558 −0.0771389
$$331$$ 332.368 1.00413 0.502066 0.864829i $$-0.332574\pi$$
0.502066 + 0.864829i $$0.332574\pi$$
$$332$$ 12.8717i 0.0387701i
$$333$$ 212.735 0.638844
$$334$$ 55.7141i 0.166809i
$$335$$ 360.555i 1.07628i
$$336$$ −21.9411 43.2503i −0.0653010 0.128721i
$$337$$ 88.1766 0.261652 0.130826 0.991405i $$-0.458237\pi$$
0.130826 + 0.991405i $$0.458237\pi$$
$$338$$ 258.468 0.764698
$$339$$ 126.491i 0.373129i
$$340$$ 277.706 0.816781
$$341$$ 15.1296i 0.0443683i
$$342$$ 97.8354i 0.286068i
$$343$$ 55.4487 338.488i 0.161658 0.986847i
$$344$$ −29.4903 −0.0857277
$$345$$ −191.823 −0.556010
$$346$$ 33.6985i 0.0973945i
$$347$$ −320.080 −0.922422 −0.461211 0.887291i $$-0.652585\pi$$
−0.461211 + 0.887291i $$0.652585\pi$$
$$348$$ 103.923i 0.298629i
$$349$$ 333.046i 0.954287i −0.878825 0.477143i $$-0.841672\pi$$
0.878825 0.477143i $$-0.158328\pi$$
$$350$$ 88.0244 44.6553i 0.251498 0.127587i
$$351$$ −97.4558 −0.277652
$$352$$ 9.94113 0.0282418
$$353$$ 655.712i 1.85754i −0.370654 0.928771i $$-0.620866\pi$$
0.370654 0.928771i $$-0.379134\pi$$
$$354$$ 238.794 0.674559
$$355$$ 654.103i 1.84254i
$$356$$ 84.1829i 0.236469i
$$357$$ 253.882 128.796i 0.711155 0.360773i
$$358$$ 18.2498 0.0509770
$$359$$ −97.7574 −0.272305 −0.136152 0.990688i $$-0.543474\pi$$
−0.136152 + 0.990688i $$0.543474\pi$$
$$360$$ 50.1785i 0.139385i
$$361$$ −170.765 −0.473032
$$362$$ 92.4440i 0.255370i
$$363$$ 204.229i 0.562614i
$$364$$ 118.794 + 234.166i 0.326357 + 0.643314i
$$365$$ −335.647 −0.919580
$$366$$ −40.9706 −0.111941
$$367$$ 321.057i 0.874815i −0.899263 0.437408i $$-0.855897\pi$$
0.899263 0.437408i $$-0.144103\pi$$
$$368$$ 74.9117 0.203564
$$369$$ 124.185i 0.336546i
$$370$$ 593.040i 1.60281i
$$371$$ −231.161 + 117.270i −0.623077 + 0.316091i
$$372$$ 29.8234 0.0801704
$$373$$ 187.470 0.502601 0.251300 0.967909i $$-0.419142\pi$$
0.251300 + 0.967909i $$0.419142\pi$$
$$374$$ 58.3551i 0.156030i
$$375$$ −153.941 −0.410510
$$376$$ 109.459i 0.291113i
$$377$$ 562.662i 1.49247i
$$378$$ −23.2721 45.8739i −0.0615663 0.121359i
$$379$$ −357.103 −0.942223 −0.471112 0.882074i $$-0.656147\pi$$
−0.471112 + 0.882074i $$0.656147\pi$$
$$380$$ −272.735 −0.717724
$$381$$ 155.783i 0.408878i
$$382$$ 141.515 0.370457
$$383$$ 622.230i 1.62462i 0.583225 + 0.812311i $$0.301791\pi$$
−0.583225 + 0.812311i $$0.698209\pi$$
$$384$$ 19.5959i 0.0510310i
$$385$$ 32.9117 + 64.8754i 0.0854849 + 0.168508i
$$386$$ −111.598 −0.289114
$$387$$ −31.2792 −0.0808249
$$388$$ 103.431i 0.266574i
$$389$$ 227.470 0.584756 0.292378 0.956303i $$-0.405553\pi$$
0.292378 + 0.956303i $$0.405553\pi$$
$$390$$ 271.677i 0.696608i
$$391$$ 439.737i 1.12465i
$$392$$ −81.8579 + 111.836i −0.208821 + 0.285296i
$$393$$ 21.0883 0.0536598
$$394$$ 260.132 0.660234
$$395$$ 412.907i 1.04533i
$$396$$ 10.5442 0.0266267
$$397$$ 720.329i 1.81443i 0.420666 + 0.907216i $$0.361796\pi$$
−0.420666 + 0.907216i $$0.638204\pi$$
$$398$$ 240.458i 0.604166i
$$399$$ −249.338 + 126.491i −0.624908 + 0.317019i
$$400$$ −39.8823 −0.0997056
$$401$$ 697.176 1.73859 0.869296 0.494291i $$-0.164572\pi$$
0.869296 + 0.494291i $$0.164572\pi$$
$$402$$ 149.347i 0.371509i
$$403$$ −161.470 −0.400670
$$404$$ 13.2198i 0.0327223i
$$405$$ 53.2223i 0.131413i
$$406$$ −264.853 + 134.361i −0.652347 + 0.330939i
$$407$$ 124.617 0.306185
$$408$$ −115.029 −0.281935
$$409$$ 102.386i 0.250333i 0.992136 + 0.125166i $$0.0399465\pi$$
−0.992136 + 0.125166i $$0.960053\pi$$
$$410$$ −346.191 −0.844368
$$411$$ 287.113i 0.698571i
$$412$$ 351.742i 0.853742i
$$413$$ −308.735 608.578i −0.747543 1.47355i
$$414$$ 79.4558 0.191922
$$415$$ 38.0589 0.0917081
$$416$$ 106.096i 0.255040i
$$417$$ −381.941 −0.915926
$$418$$ 57.3106i 0.137107i
$$419$$ 391.426i 0.934191i 0.884207 + 0.467095i $$0.154700\pi$$
−0.884207 + 0.467095i $$0.845300\pi$$
$$420$$ −127.882 + 64.8754i −0.304482 + 0.154465i
$$421$$ 354.441 0.841902 0.420951 0.907083i $$-0.361696\pi$$
0.420951 + 0.907083i $$0.361696\pi$$
$$422$$ −30.5097 −0.0722978
$$423$$ 116.098i 0.274464i
$$424$$ 104.735 0.247017
$$425$$ 234.112i 0.550851i
$$426$$ 270.938i 0.636006i
$$427$$ 52.9706 + 104.415i 0.124053 + 0.244533i
$$428$$ −92.4853 −0.216087
$$429$$ −57.0883 −0.133073
$$430$$ 87.1969i 0.202783i
$$431$$ 585.286 1.35797 0.678987 0.734151i $$-0.262419\pi$$
0.678987 + 0.734151i $$0.262419\pi$$
$$432$$ 20.7846i 0.0481125i
$$433$$ 392.207i 0.905789i −0.891564 0.452895i $$-0.850391\pi$$
0.891564 0.452895i $$-0.149609\pi$$
$$434$$ −38.5584 76.0063i −0.0888443 0.175130i
$$435$$ −307.279 −0.706389
$$436$$ −71.8823 −0.164868
$$437$$ 431.866i 0.988252i
$$438$$ 139.029 0.317419
$$439$$ 392.513i 0.894106i −0.894507 0.447053i $$-0.852473\pi$$
0.894507 0.447053i $$-0.147527\pi$$
$$440$$ 29.3939i 0.0668043i
$$441$$ −86.8234 + 118.620i −0.196878 + 0.268980i
$$442$$ 622.794 1.40904
$$443$$ −814.742 −1.83915 −0.919574 0.392918i $$-0.871466\pi$$
−0.919574 + 0.392918i $$0.871466\pi$$
$$444$$ 245.645i 0.553255i
$$445$$ −248.912 −0.559352
$$446$$ 168.798i 0.378472i
$$447$$ 365.208i 0.817020i
$$448$$ 49.9411 25.3354i 0.111476 0.0565523i
$$449$$ 180.323 0.401610 0.200805 0.979631i $$-0.435644\pi$$
0.200805 + 0.979631i $$0.435644\pi$$
$$450$$ −42.3015 −0.0940034
$$451$$ 72.7461i 0.161300i
$$452$$ −146.059 −0.323139
$$453$$ 125.344i 0.276698i
$$454$$ 240.194i 0.529062i
$$455$$ 692.382 351.249i 1.52172 0.771977i
$$456$$ 112.971 0.247742
$$457$$ 280.177 0.613078 0.306539 0.951858i $$-0.400829\pi$$
0.306539 + 0.951858i $$0.400829\pi$$
$$458$$ 155.579i 0.339691i
$$459$$ −122.007 −0.265811
$$460$$ 221.499i 0.481519i
$$461$$ 406.297i 0.881338i 0.897670 + 0.440669i $$0.145259\pi$$
−0.897670 + 0.440669i $$0.854741\pi$$
$$462$$ −13.6325 26.8723i −0.0295075 0.0581651i
$$463$$ 457.470 0.988056 0.494028 0.869446i $$-0.335524\pi$$
0.494028 + 0.869446i $$0.335524\pi$$
$$464$$ 120.000 0.258621
$$465$$ 88.1816i 0.189638i
$$466$$ −80.9848 −0.173787
$$467$$ 643.711i 1.37840i −0.724573 0.689198i $$-0.757963\pi$$
0.724573 0.689198i $$-0.242037\pi$$
$$468$$ 112.532i 0.240454i
$$469$$ 380.617 193.089i 0.811551 0.411705i
$$470$$ −323.647 −0.688610
$$471$$ 404.735 0.859310
$$472$$ 275.735i 0.584185i
$$473$$ −18.3229 −0.0387377
$$474$$ 171.032i 0.360826i
$$475$$ 229.921i 0.484045i
$$476$$ 148.721 + 293.158i 0.312439 + 0.615878i
$$477$$ 111.088 0.232890
$$478$$ −398.132 −0.832912
$$479$$ 168.535i 0.351847i 0.984404 + 0.175924i $$0.0562912\pi$$
−0.984404 + 0.175924i $$0.943709\pi$$
$$480$$ 57.9411 0.120711
$$481$$ 1329.98i 2.76502i
$$482$$ 238.021i 0.493819i
$$483$$ −102.728 202.497i −0.212687 0.419248i
$$484$$ −235.823 −0.487238
$$485$$ 305.823 0.630564
$$486$$ 22.0454i 0.0453609i
$$487$$ −2.77965 −0.00570771 −0.00285385 0.999996i $$-0.500908\pi$$
−0.00285385 + 0.999996i $$0.500908\pi$$
$$488$$ 47.3087i 0.0969441i
$$489$$ 126.593i 0.258881i
$$490$$ 330.676 + 242.037i 0.674849 + 0.493953i
$$491$$ −247.477 −0.504027 −0.252014 0.967724i $$-0.581093\pi$$
−0.252014 + 0.967724i $$0.581093\pi$$
$$492$$ 143.397 0.291457
$$493$$ 704.409i 1.42882i
$$494$$ −611.647 −1.23815
$$495$$ 31.1769i 0.0629837i
$$496$$ 34.4371i 0.0694296i
$$497$$ −690.500 + 350.295i −1.38934 + 0.704818i
$$498$$ −15.7645 −0.0316556
$$499$$ −483.426 −0.968789 −0.484394 0.874850i $$-0.660960\pi$$
−0.484394 + 0.874850i $$0.660960\pi$$
$$500$$ 177.756i 0.355512i
$$501$$ −68.2355 −0.136199
$$502$$ 150.043i 0.298891i
$$503$$ 58.7033i 0.116706i 0.998296 + 0.0583532i $$0.0185849\pi$$
−0.998296 + 0.0583532i $$0.981415\pi$$
$$504$$ 52.9706 26.8723i 0.105100 0.0533180i
$$505$$ 39.0883 0.0774026
$$506$$ 46.5442 0.0919845
$$507$$ 316.557i 0.624374i
$$508$$ 179.882 0.354099
$$509$$ 68.8793i 0.135323i 0.997708 + 0.0676614i $$0.0215537\pi$$
−0.997708 + 0.0676614i $$0.978446\pi$$
$$510$$ 340.119i 0.666899i
$$511$$ −179.750 354.323i −0.351762 0.693392i
$$512$$ −22.6274 −0.0441942
$$513$$ 119.823 0.233574
$$514$$ 410.776i 0.799175i
$$515$$ 1040.03 2.01947
$$516$$ 36.1181i 0.0699964i
$$517$$ 68.0089i 0.131545i
$$518$$ 626.039 317.593i 1.20857 0.613114i
$$519$$ 41.2721 0.0795223
$$520$$ −313.706 −0.603280
$$521$$ 292.720i 0.561843i 0.959731 + 0.280922i $$0.0906401\pi$$
−0.959731 + 0.280922i $$0.909360\pi$$
$$522$$ 127.279 0.243830
$$523$$ 493.056i 0.942746i 0.881934 + 0.471373i $$0.156241\pi$$
−0.881934 + 0.471373i $$0.843759\pi$$
$$524$$ 24.3507i 0.0464708i
$$525$$ 54.6913 + 107.807i 0.104174 + 0.205347i
$$526$$ 125.897 0.239347
$$527$$ −202.148 −0.383583
$$528$$ 12.1753i 0.0230594i
$$529$$ −178.265 −0.336985
$$530$$ 309.680i 0.584302i
$$531$$ 292.462i 0.550775i
$$532$$ −146.059 287.911i −0.274547 0.541186i
$$533$$ −776.382 −1.45663
$$534$$ 103.103 0.193076
$$535$$ 273.460i 0.511140i
$$536$$ −172.451 −0.321737
$$537$$ 22.3513i 0.0416226i
$$538$$ 270.819i 0.503381i
$$539$$ −50.8600 + 69.4860i −0.0943598 + 0.128916i
$$540$$ 61.4558 0.113807
$$541$$ −1037.85 −1.91840 −0.959198 0.282736i $$-0.908758\pi$$
−0.959198 + 0.282736i $$0.908758\pi$$
$$542$$ 307.507i 0.567356i
$$543$$ 113.220 0.208509
$$544$$ 132.825i 0.244163i
$$545$$ 212.541i 0.389984i
$$546$$ −286.794 + 145.492i −0.525264 + 0.266469i
$$547$$ −130.530 −0.238629 −0.119314 0.992857i $$-0.538070\pi$$
−0.119314 + 0.992857i $$0.538070\pi$$
$$548$$ 331.529 0.604980
$$549$$ 50.1785i 0.0913998i
$$550$$ −24.7797 −0.0450539
$$551$$ 691.801i 1.25554i
$$552$$ 91.7477i 0.166210i
$$553$$ −435.882 + 221.126i −0.788214 + 0.399866i
$$554$$ −411.078 −0.742018
$$555$$ 726.323 1.30869
$$556$$ 441.028i 0.793215i
$$557$$ 665.147 1.19416 0.597080 0.802182i $$-0.296327\pi$$
0.597080 + 0.802182i $$0.296327\pi$$
$$558$$ 36.5260i 0.0654588i
$$559$$ 195.551i 0.349823i
$$560$$ −74.9117 147.666i −0.133771 0.263689i
$$561$$ −71.4701 −0.127398
$$562$$ −26.6619 −0.0474411
$$563$$ 829.295i 1.47299i 0.676441 + 0.736497i $$0.263521\pi$$
−0.676441 + 0.736497i $$0.736479\pi$$
$$564$$ 134.059 0.237693
$$565$$ 431.866i 0.764365i
$$566$$ 568.137i 1.00378i
$$567$$ 56.1838 28.5024i 0.0990895 0.0502687i
$$568$$ 312.853 0.550797
$$569$$ 706.971 1.24248 0.621240 0.783621i $$-0.286629\pi$$
0.621240 + 0.783621i $$0.286629\pi$$
$$570$$ 334.031i 0.586019i
$$571$$ −366.912 −0.642577 −0.321289 0.946981i $$-0.604116\pi$$
−0.321289 + 0.946981i $$0.604116\pi$$
$$572$$ 65.9199i 0.115245i
$$573$$ 173.319i 0.302477i
$$574$$ −185.397 365.454i −0.322991 0.636679i
$$575$$ −186.728 −0.324744
$$576$$ −24.0000 −0.0416667
$$577$$ 390.357i 0.676528i −0.941051 0.338264i $$-0.890160\pi$$
0.941051 0.338264i $$-0.109840\pi$$
$$578$$ 370.982 0.641837
$$579$$ 136.679i 0.236061i
$$580$$ 354.815i 0.611751i
$$581$$ 20.3818 + 40.1766i 0.0350806 + 0.0691507i
$$582$$ −126.676 −0.217657
$$583$$ 65.0740 0.111619
$$584$$ 160.537i 0.274893i
$$585$$ −332.735 −0.568778
$$586$$ 397.243i 0.677889i
$$587$$ 702.499i 1.19676i −0.801212 0.598381i $$-0.795811\pi$$
0.801212 0.598381i $$-0.204189\pi$$
$$588$$ −136.971 100.255i −0.232943 0.170502i
$$589$$ 198.530 0.337063
$$590$$ 815.294 1.38185
$$591$$ 318.595i 0.539078i
$$592$$ −283.647 −0.479133
$$593$$ 942.519i 1.58941i 0.606997 + 0.794704i $$0.292374\pi$$
−0.606997 + 0.794704i $$0.707626\pi$$
$$594$$ 12.9139i 0.0217406i
$$595$$ 866.808 439.737i 1.45682 0.739054i
$$596$$ 421.706 0.707560
$$597$$ 294.500 0.493299
$$598$$ 496.742i 0.830672i
$$599$$ −952.109 −1.58950 −0.794749 0.606939i $$-0.792397\pi$$
−0.794749 + 0.606939i $$0.792397\pi$$
$$600$$ 48.8456i 0.0814093i
$$601$$ 729.804i 1.21432i 0.794581 + 0.607158i $$0.207690\pi$$
−0.794581 + 0.607158i $$0.792310\pi$$
$$602$$ −92.0488 + 46.6969i −0.152905 + 0.0775696i
$$603$$ −182.912 −0.303336
$$604$$ −144.735 −0.239628
$$605$$ 697.282i 1.15253i
$$606$$ −16.1909 −0.0267177
$$607$$ 1006.34i 1.65789i −0.559332 0.828944i $$-0.688942\pi$$
0.559332 0.828944i $$-0.311058\pi$$
$$608$$ 130.447i 0.214551i
$$609$$ −164.558 324.377i −0.270211 0.532639i
$$610$$ −139.882 −0.229315
$$611$$ −725.823 −1.18793
$$612$$ 140.882i 0.230199i
$$613$$ −199.588 −0.325592 −0.162796 0.986660i $$-0.552051\pi$$
−0.162796 + 0.986660i $$0.552051\pi$$
$$614$$ 215.411i 0.350832i
$$615$$ 423.996i 0.689424i
$$616$$ 31.0294 15.7414i 0.0503725 0.0255542i
$$617$$ −353.294 −0.572599 −0.286299 0.958140i $$-0.592425\pi$$
−0.286299 + 0.958140i $$0.592425\pi$$
$$618$$ −430.794 −0.697078
$$619$$ 56.2064i 0.0908020i −0.998969 0.0454010i $$-0.985543\pi$$
0.998969 0.0454010i $$-0.0144566\pi$$
$$620$$ 101.823 0.164231
$$621$$ 97.3131i 0.156704i
$$622$$ 400.443i 0.643799i
$$623$$ −133.301 262.762i −0.213966 0.421769i
$$624$$ 129.941 0.208239
$$625$$ −774.852 −1.23976
$$626$$ 68.7052i 0.109753i
$$627$$ 70.1909 0.111947
$$628$$ 467.348i 0.744184i
$$629$$ 1665.03i 2.64710i
$$630$$ −79.4558 156.623i −0.126120 0.248608i
$$631$$ 807.322 1.27943 0.639716 0.768611i $$-0.279052\pi$$
0.639716 + 0.768611i $$0.279052\pi$$
$$632$$ 197.490 0.312485
$$633$$ 37.3666i 0.0590309i
$$634$$ 817.456 1.28936
$$635$$ 531.875i 0.837599i
$$636$$ 128.274i 0.201688i
$$637$$ 741.588 + 542.802i 1.16419 + 0.852122i
$$638$$ 74.5584 0.116863
$$639$$ 331.831 0.519297
$$640$$ 66.9046i 0.104539i
$$641$$ 1016.35 1.58557 0.792786 0.609500i $$-0.208630\pi$$
0.792786 + 0.609500i $$0.208630\pi$$
$$642$$ 113.271i 0.176434i
$$643$$ 404.688i 0.629375i −0.949195 0.314687i $$-0.898100\pi$$
0.949195 0.314687i $$-0.101900\pi$$
$$644$$ 233.823 118.620i 0.363080 0.184193i
$$645$$ −106.794 −0.165572
$$646$$ −765.734 −1.18535
$$647$$ 940.604i 1.45379i −0.686747 0.726896i $$-0.740962\pi$$
0.686747 0.726896i $$-0.259038\pi$$
$$648$$ −25.4558 −0.0392837
$$649$$ 171.320i 0.263975i
$$650$$ 264.460i 0.406862i
$$651$$ 93.0883 47.2243i 0.142993 0.0725411i
$$652$$ −146.177 −0.224197
$$653$$ 731.970 1.12093 0.560467 0.828177i $$-0.310622\pi$$
0.560467 + 0.828177i $$0.310622\pi$$
$$654$$ 88.0374i 0.134614i
$$655$$ 72.0000 0.109924
$$656$$ 165.581i 0.252409i
$$657$$ 170.276i 0.259171i
$$658$$ −173.324 341.655i −0.263410 0.519233i
$$659$$ 904.316 1.37225 0.686127 0.727481i $$-0.259309\pi$$
0.686127 + 0.727481i $$0.259309\pi$$
$$660$$ 36.0000 0.0545455
$$661$$ 335.881i 0.508141i −0.967186 0.254070i $$-0.918231\pi$$
0.967186 0.254070i $$-0.0817695\pi$$
$$662$$ −470.039 −0.710028
$$663$$ 762.764i 1.15047i
$$664$$ 18.2033i 0.0274146i
$$665$$ −851.294 + 431.866i −1.28014 + 0.649423i
$$666$$ −300.853 −0.451731
$$667$$ 561.838 0.842335
$$668$$ 78.7916i 0.117951i
$$669$$ −206.735 −0.309021
$$670$$ 509.902i 0.761047i
$$671$$ 29.3939i 0.0438061i
$$672$$ 31.0294 + 61.1651i 0.0461748 + 0.0910195i
$$673$$ 1191.44 1.77034 0.885171 0.465266i $$-0.154041\pi$$
0.885171 + 0.465266i $$0.154041\pi$$
$$674$$ −124.701 −0.185016
$$675$$ 51.8086i 0.0767534i
$$676$$ −365.529 −0.540723
$$677$$ 1211.07i 1.78888i 0.447186 + 0.894441i $$0.352426\pi$$
−0.447186 + 0.894441i $$0.647574\pi$$
$$678$$ 178.885i 0.263842i
$$679$$ 163.779 + 322.840i 0.241206 + 0.475464i
$$680$$ −392.735 −0.577552
$$681$$ −294.177 −0.431977
$$682$$ 21.3965i 0.0313731i
$$683$$ −1233.89 −1.80657 −0.903287 0.429038i $$-0.858853\pi$$
−0.903287 + 0.429038i $$0.858853\pi$$
$$684$$ 138.360i 0.202281i
$$685$$ 980.264i 1.43104i
$$686$$ −78.4163 + 478.695i −0.114309 + 0.697806i
$$687$$ −190.544 −0.277357
$$688$$ 41.7056 0.0606186
$$689$$ 694.501i 1.00798i
$$690$$ 271.279 0.393158
$$691$$ 86.7045i 0.125477i −0.998030 0.0627384i $$-0.980017\pi$$
0.998030 0.0627384i $$-0.0199834\pi$$
$$692$$ 47.6569i 0.0688683i
$$693$$ 32.9117 16.6963i 0.0474916 0.0240928i
$$694$$ 452.662 0.652251
$$695$$ −1304.03 −1.87630
$$696$$ 146.969i 0.211163i
$$697$$ −971.970 −1.39450
$$698$$ 470.998i 0.674783i
$$699$$ 99.1858i 0.141897i
$$700$$ −124.485 + 63.1521i −0.177836 + 0.0902173i
$$701$$ −149.147 −0.212763 −0.106382 0.994325i $$-0.533927\pi$$
−0.106382 + 0.994325i $$0.533927\pi$$
$$702$$ 137.823 0.196330
$$703$$ 1635.22i 2.32607i
$$704$$ −14.0589 −0.0199700
$$705$$ 396.385i 0.562248i
$$706$$ 927.317i 1.31348i
$$707$$ 20.9331 + 41.2633i 0.0296084 + 0.0583639i
$$708$$ −337.706 −0.476985
$$709$$ 189.647 0.267485 0.133742 0.991016i $$-0.457301\pi$$
0.133742 + 0.991016i $$0.457301\pi$$
$$710$$ 925.042i 1.30288i
$$711$$ 209.470 0.294613
$$712$$ 119.053i 0.167209i
$$713$$ 161.234i 0.226134i
$$714$$ −359.044 + 182.145i −0.502862 + 0.255105i
$$715$$ −194.912 −0.272604
$$716$$ −25.8091 −0.0360462
$$717$$ 487.610i 0.680070i
$$718$$ 138.250 0.192548
$$719$$ 12.0064i 0.0166987i −0.999965 0.00834937i $$-0.997342\pi$$
0.999965 0.00834937i $$-0.00265772\pi$$
$$720$$ 70.9631i 0.0985599i
$$721$$ 556.971 + 1097.90i 0.772497 + 1.52274i
$$722$$ 241.497 0.334484
$$723$$ 291.515 0.403202
$$724$$ 130.736i 0.180574i
$$725$$ −299.117 −0.412575
$$726$$ 288.823i 0.397828i
$$727$$ 417.169i 0.573823i −0.957957 0.286911i $$-0.907371\pi$$
0.957957 0.286911i $$-0.0926286\pi$$
$$728$$ −168.000 331.161i −0.230769 0.454892i
$$729$$ −27.0000 −0.0370370
$$730$$ 474.676 0.650241
$$731$$ 244.815i 0.334904i
$$732$$ 57.9411 0.0791545
$$733$$ 1286.99i 1.75578i 0.478859 + 0.877892i $$0.341051\pi$$
−0.478859 + 0.877892i $$0.658949\pi$$
$$734$$ 454.043i 0.618588i
$$735$$ −296.434 + 404.994i −0.403311 + 0.551012i
$$736$$ −105.941 −0.143942
$$737$$ −107.147 −0.145383
$$738$$ 175.625i 0.237974i
$$739$$ 1333.47 1.80443 0.902213 0.431292i $$-0.141942\pi$$
0.902213 + 0.431292i $$0.141942\pi$$
$$740$$ 838.685i 1.13336i
$$741$$ 749.111i 1.01095i
$$742$$ 326.912 165.844i 0.440582 0.223510i
$$743$$ −776.476 −1.04506 −0.522528 0.852622i $$-0.675011\pi$$
−0.522528 + 0.852622i $$0.675011\pi$$
$$744$$ −42.1766 −0.0566890
$$745$$ 1246.90i 1.67369i
$$746$$ −265.123 −0.355392
$$747$$ 19.3075i 0.0258467i
$$748$$ 82.5266i 0.110330i
$$749$$ −288.676 + 146.447i −0.385415 + 0.195524i
$$750$$ 217.706 0.290274
$$751$$ 48.8385 0.0650313 0.0325157 0.999471i $$-0.489648\pi$$
0.0325157 + 0.999471i $$0.489648\pi$$
$$752$$ 154.798i 0.205848i
$$753$$ 183.765 0.244043
$$754$$ 795.724i 1.05534i
$$755$$ 427.952i 0.566824i
$$756$$ 32.9117 + 64.8754i 0.0435340 + 0.0858141i
$$757$$ −1279.47 −1.69019 −0.845093 0.534620i $$-0.820455\pi$$
−0.845093 + 0.534620i $$0.820455\pi$$
$$758$$ 505.019 0.666252
$$759$$ 57.0047i 0.0751050i
$$760$$ 385.706 0.507507
$$761$$ 1316.12i 1.72947i −0.502231 0.864734i $$-0.667487\pi$$
0.502231 0.864734i $$-0.332513\pi$$
$$762$$ 220.310i 0.289121i
$$763$$ −224.368 + 113.823i −0.294060 + 0.149178i
$$764$$ −200.132 −0.261953
$$765$$ −416.558 −0.544521
$$766$$ 879.966i 1.14878i
$$767$$ 1828.41 2.38385
$$768$$ 27.7128i 0.0360844i
$$769$$ 110.324i 0.143464i −0.997424 0.0717320i $$-0.977147\pi$$
0.997424 0.0717320i $$-0.0228526\pi$$
$$770$$ −46.5442 91.7477i −0.0604470 0.119153i
$$771$$ −503.095 −0.652523
$$772$$ 157.823 0.204434
$$773$$ 717.634i 0.928375i −0.885737 0.464187i $$-0.846346\pi$$
0.885737 0.464187i $$-0.153654\pi$$
$$774$$ 44.2355 0.0571518
$$775$$ 85.8392i 0.110760i
$$776$$ 146.273i 0.188496i
$$777$$ 388.971 + 766.738i 0.500606 + 0.986792i
$$778$$ −321.691 −0.413485
$$779$$ 954.573 1.22538
$$780$$ 384.209i 0.492576i
$$781$$ 194.382 0.248888
$$782$$ 621.882i 0.795245i
$$783$$ 155.885i 0.199086i
$$784$$ 115.765 158.160i 0.147659 0.201735i
$$785$$ 1381.85 1.76032
$$786$$ −29.82