# Properties

 Label 1050.3.q.e.199.10 Level $1050$ Weight $3$ Character 1050.199 Analytic conductor $28.610$ Analytic rank $0$ Dimension $32$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.q (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$28.6104277578$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(\zeta_{6})$$ Twist minimal: no (minimal twist has level 210) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 199.10 Character $$\chi$$ $$=$$ 1050.199 Dual form 1050.3.q.e.649.10

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(2.86123 + 6.38854i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(2.86123 + 6.38854i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-9.98749 + 17.2988i) q^{11} +(-1.73205 - 3.00000i) q^{12} -3.49788 q^{13} +(8.02165 + 5.80113i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(9.12112 - 15.7982i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(21.3143 - 12.3058i) q^{19} +(12.0607 + 1.24079i) q^{21} +28.2489i q^{22} +(21.8155 - 12.5952i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-4.28401 + 2.47338i) q^{26} -5.19615 q^{27} +(13.9265 + 1.43274i) q^{28} +53.1223 q^{29} +(26.0944 + 15.0656i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(17.2988 + 29.9625i) q^{33} -25.7984i q^{34} -6.00000 q^{36} +(40.5034 - 23.3846i) q^{37} +(17.4030 - 30.1429i) q^{38} +(-3.02925 + 5.24682i) q^{39} -31.5250i q^{41} +(15.6487 - 7.00855i) q^{42} +64.4116i q^{43} +(19.9750 + 34.5977i) q^{44} +(17.8123 - 30.8518i) q^{46} +(14.0313 + 24.3029i) q^{47} -6.92820 q^{48} +(-32.6268 + 36.5581i) q^{49} +(-15.7982 - 27.3634i) q^{51} +(-3.49788 + 6.05851i) q^{52} +(56.1833 + 32.4374i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(18.0695 - 8.09277i) q^{56} -42.6285i q^{57} +(65.0613 - 37.5631i) q^{58} +(-86.7684 - 50.0958i) q^{59} +(6.94896 - 4.01198i) q^{61} +42.6119 q^{62} +(12.3061 - 17.0165i) q^{63} -8.00000 q^{64} +(42.3733 + 24.4642i) q^{66} +(14.0844 + 8.13165i) q^{67} +(-18.2422 - 31.5965i) q^{68} -43.6310i q^{69} -107.725 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-25.8303 + 44.7395i) q^{73} +(33.0709 - 57.2804i) q^{74} -49.2232i q^{76} +(-139.091 - 14.3095i) q^{77} +8.56803i q^{78} +(-10.9877 - 19.0313i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-22.2916 - 38.6101i) q^{82} -0.417479 q^{83} +(14.2098 - 19.6489i) q^{84} +(45.5459 + 78.8878i) q^{86} +(46.0053 - 79.6835i) q^{87} +(48.9285 + 28.2489i) q^{88} +(96.3110 - 55.6052i) q^{89} +(-10.0082 - 22.3463i) q^{91} -50.3807i q^{92} +(45.1968 - 26.0944i) q^{93} +(34.3695 + 19.8432i) q^{94} +(-8.48528 + 4.89898i) q^{96} +74.2244 q^{97} +(-14.1090 + 67.8449i) q^{98} +59.9249 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32 q + 32 q^{4} - 48 q^{9}+O(q^{10})$$ 32 * q + 32 * q^4 - 48 * q^9 $$32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100})$$ 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.22474 0.707107i 0.612372 0.353553i
$$3$$ 0.866025 1.50000i 0.288675 0.500000i
$$4$$ 1.00000 1.73205i 0.250000 0.433013i
$$5$$ 0 0
$$6$$ 2.44949i 0.408248i
$$7$$ 2.86123 + 6.38854i 0.408747 + 0.912648i
$$8$$ 2.82843i 0.353553i
$$9$$ −1.50000 2.59808i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ −9.98749 + 17.2988i −0.907953 + 1.57262i −0.0910503 + 0.995846i $$0.529022\pi$$
−0.816903 + 0.576775i $$0.804311\pi$$
$$12$$ −1.73205 3.00000i −0.144338 0.250000i
$$13$$ −3.49788 −0.269068 −0.134534 0.990909i $$-0.542954\pi$$
−0.134534 + 0.990909i $$0.542954\pi$$
$$14$$ 8.02165 + 5.80113i 0.572975 + 0.414367i
$$15$$ 0 0
$$16$$ −2.00000 3.46410i −0.125000 0.216506i
$$17$$ 9.12112 15.7982i 0.536536 0.929308i −0.462551 0.886593i $$-0.653066\pi$$
0.999087 0.0427155i $$-0.0136009\pi$$
$$18$$ −3.67423 2.12132i −0.204124 0.117851i
$$19$$ 21.3143 12.3058i 1.12180 0.647673i 0.179942 0.983677i $$-0.442409\pi$$
0.941861 + 0.336004i $$0.109076\pi$$
$$20$$ 0 0
$$21$$ 12.0607 + 1.24079i 0.574319 + 0.0590854i
$$22$$ 28.2489i 1.28404i
$$23$$ 21.8155 12.5952i 0.948500 0.547617i 0.0558853 0.998437i $$-0.482202\pi$$
0.892615 + 0.450820i $$0.148869\pi$$
$$24$$ −4.24264 2.44949i −0.176777 0.102062i
$$25$$ 0 0
$$26$$ −4.28401 + 2.47338i −0.164770 + 0.0951299i
$$27$$ −5.19615 −0.192450
$$28$$ 13.9265 + 1.43274i 0.497375 + 0.0511694i
$$29$$ 53.1223 1.83180 0.915902 0.401402i $$-0.131477\pi$$
0.915902 + 0.401402i $$0.131477\pi$$
$$30$$ 0 0
$$31$$ 26.0944 + 15.0656i 0.841754 + 0.485987i 0.857860 0.513883i $$-0.171794\pi$$
−0.0161061 + 0.999870i $$0.505127\pi$$
$$32$$ −4.89898 2.82843i −0.153093 0.0883883i
$$33$$ 17.2988 + 29.9625i 0.524207 + 0.907953i
$$34$$ 25.7984i 0.758777i
$$35$$ 0 0
$$36$$ −6.00000 −0.166667
$$37$$ 40.5034 23.3846i 1.09469 0.632017i 0.159866 0.987139i $$-0.448894\pi$$
0.934820 + 0.355122i $$0.115561\pi$$
$$38$$ 17.4030 30.1429i 0.457974 0.793234i
$$39$$ −3.02925 + 5.24682i −0.0776732 + 0.134534i
$$40$$ 0 0
$$41$$ 31.5250i 0.768903i −0.923145 0.384452i $$-0.874391\pi$$
0.923145 0.384452i $$-0.125609\pi$$
$$42$$ 15.6487 7.00855i 0.372587 0.166870i
$$43$$ 64.4116i 1.49794i 0.662602 + 0.748972i $$0.269452\pi$$
−0.662602 + 0.748972i $$0.730548\pi$$
$$44$$ 19.9750 + 34.5977i 0.453977 + 0.786311i
$$45$$ 0 0
$$46$$ 17.8123 30.8518i 0.387223 0.670691i
$$47$$ 14.0313 + 24.3029i 0.298538 + 0.517083i 0.975802 0.218657i $$-0.0701677\pi$$
−0.677264 + 0.735740i $$0.736834\pi$$
$$48$$ −6.92820 −0.144338
$$49$$ −32.6268 + 36.5581i −0.665852 + 0.746084i
$$50$$ 0 0
$$51$$ −15.7982 27.3634i −0.309769 0.536536i
$$52$$ −3.49788 + 6.05851i −0.0672670 + 0.116510i
$$53$$ 56.1833 + 32.4374i 1.06006 + 0.612027i 0.925449 0.378872i $$-0.123688\pi$$
0.134612 + 0.990898i $$0.457021\pi$$
$$54$$ −6.36396 + 3.67423i −0.117851 + 0.0680414i
$$55$$ 0 0
$$56$$ 18.0695 8.09277i 0.322670 0.144514i
$$57$$ 42.6285i 0.747869i
$$58$$ 65.0613 37.5631i 1.12175 0.647640i
$$59$$ −86.7684 50.0958i −1.47065 0.849081i −0.471194 0.882029i $$-0.656177\pi$$
−0.999457 + 0.0329486i $$0.989510\pi$$
$$60$$ 0 0
$$61$$ 6.94896 4.01198i 0.113917 0.0657702i −0.441959 0.897035i $$-0.645716\pi$$
0.555876 + 0.831265i $$0.312383\pi$$
$$62$$ 42.6119 0.687289
$$63$$ 12.3061 17.0165i 0.195334 0.270103i
$$64$$ −8.00000 −0.125000
$$65$$ 0 0
$$66$$ 42.3733 + 24.4642i 0.642020 + 0.370670i
$$67$$ 14.0844 + 8.13165i 0.210215 + 0.121368i 0.601411 0.798939i $$-0.294605\pi$$
−0.391196 + 0.920307i $$0.627939\pi$$
$$68$$ −18.2422 31.5965i −0.268268 0.464654i
$$69$$ 43.6310i 0.632333i
$$70$$ 0 0
$$71$$ −107.725 −1.51725 −0.758625 0.651528i $$-0.774128\pi$$
−0.758625 + 0.651528i $$0.774128\pi$$
$$72$$ −7.34847 + 4.24264i −0.102062 + 0.0589256i
$$73$$ −25.8303 + 44.7395i −0.353840 + 0.612870i −0.986919 0.161218i $$-0.948458\pi$$
0.633078 + 0.774088i $$0.281791\pi$$
$$74$$ 33.0709 57.2804i 0.446904 0.774060i
$$75$$ 0 0
$$76$$ 49.2232i 0.647673i
$$77$$ −139.091 14.3095i −1.80637 0.185838i
$$78$$ 8.56803i 0.109846i
$$79$$ −10.9877 19.0313i −0.139085 0.240903i 0.788065 0.615592i $$-0.211083\pi$$
−0.927151 + 0.374689i $$0.877750\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.0555556 + 0.0962250i
$$82$$ −22.2916 38.6101i −0.271848 0.470855i
$$83$$ −0.417479 −0.00502987 −0.00251494 0.999997i $$-0.500801\pi$$
−0.00251494 + 0.999997i $$0.500801\pi$$
$$84$$ 14.2098 19.6489i 0.169164 0.233916i
$$85$$ 0 0
$$86$$ 45.5459 + 78.8878i 0.529603 + 0.917300i
$$87$$ 46.0053 79.6835i 0.528796 0.915902i
$$88$$ 48.9285 + 28.2489i 0.556006 + 0.321010i
$$89$$ 96.3110 55.6052i 1.08215 0.624778i 0.150672 0.988584i $$-0.451856\pi$$
0.931475 + 0.363806i $$0.118523\pi$$
$$90$$ 0 0
$$91$$ −10.0082 22.3463i −0.109981 0.245564i
$$92$$ 50.3807i 0.547617i
$$93$$ 45.1968 26.0944i 0.485987 0.280585i
$$94$$ 34.3695 + 19.8432i 0.365633 + 0.211098i
$$95$$ 0 0
$$96$$ −8.48528 + 4.89898i −0.0883883 + 0.0510310i
$$97$$ 74.2244 0.765200 0.382600 0.923914i $$-0.375029\pi$$
0.382600 + 0.923914i $$0.375029\pi$$
$$98$$ −14.1090 + 67.8449i −0.143969 + 0.692295i
$$99$$ 59.9249 0.605302
$$100$$ 0 0
$$101$$ 75.8587 + 43.7970i 0.751076 + 0.433634i 0.826083 0.563549i $$-0.190564\pi$$
−0.0750065 + 0.997183i $$0.523898\pi$$
$$102$$ −38.6976 22.3421i −0.379388 0.219040i
$$103$$ 69.5206 + 120.413i 0.674957 + 1.16906i 0.976482 + 0.215601i $$0.0691711\pi$$
−0.301525 + 0.953458i $$0.597496\pi$$
$$104$$ 9.89350i 0.0951299i
$$105$$ 0 0
$$106$$ 91.7469 0.865537
$$107$$ −131.800 + 76.0949i −1.23178 + 0.711168i −0.967400 0.253252i $$-0.918500\pi$$
−0.264378 + 0.964419i $$0.585167\pi$$
$$108$$ −5.19615 + 9.00000i −0.0481125 + 0.0833333i
$$109$$ 32.3777 56.0798i 0.297043 0.514494i −0.678415 0.734679i $$-0.737333\pi$$
0.975458 + 0.220185i $$0.0706662\pi$$
$$110$$ 0 0
$$111$$ 81.0068i 0.729791i
$$112$$ 16.4081 22.6887i 0.146501 0.202577i
$$113$$ 3.25860i 0.0288372i 0.999896 + 0.0144186i $$0.00458974\pi$$
−0.999896 + 0.0144186i $$0.995410\pi$$
$$114$$ −30.1429 52.2090i −0.264411 0.457974i
$$115$$ 0 0
$$116$$ 53.1223 92.0105i 0.457951 0.793194i
$$117$$ 5.24682 + 9.08776i 0.0448446 + 0.0776732i
$$118$$ −141.692 −1.20078
$$119$$ 127.025 + 13.0682i 1.06744 + 0.109817i
$$120$$ 0 0
$$121$$ −139.000 240.755i −1.14876 1.98971i
$$122$$ 5.67380 9.82731i 0.0465066 0.0805517i
$$123$$ −47.2875 27.3015i −0.384452 0.221963i
$$124$$ 52.1887 30.1312i 0.420877 0.242993i
$$125$$ 0 0
$$126$$ 3.03931 29.5426i 0.0241215 0.234465i
$$127$$ 88.5772i 0.697458i 0.937224 + 0.348729i $$0.113387\pi$$
−0.937224 + 0.348729i $$0.886613\pi$$
$$128$$ −9.79796 + 5.65685i −0.0765466 + 0.0441942i
$$129$$ 96.6174 + 55.7821i 0.748972 + 0.432419i
$$130$$ 0 0
$$131$$ −108.361 + 62.5621i −0.827181 + 0.477573i −0.852887 0.522096i $$-0.825150\pi$$
0.0257055 + 0.999670i $$0.491817\pi$$
$$132$$ 69.1953 0.524207
$$133$$ 139.601 + 100.957i 1.04963 + 0.759077i
$$134$$ 22.9998 0.171640
$$135$$ 0 0
$$136$$ −44.6842 25.7984i −0.328560 0.189694i
$$137$$ −33.7349 19.4769i −0.246240 0.142167i 0.371801 0.928312i $$-0.378740\pi$$
−0.618042 + 0.786145i $$0.712074\pi$$
$$138$$ −30.8518 53.4368i −0.223564 0.387223i
$$139$$ 98.9454i 0.711837i −0.934517 0.355919i $$-0.884168\pi$$
0.934517 0.355919i $$-0.115832\pi$$
$$140$$ 0 0
$$141$$ 48.6058 0.344722
$$142$$ −131.935 + 76.1729i −0.929122 + 0.536429i
$$143$$ 34.9351 60.5093i 0.244301 0.423142i
$$144$$ −6.00000 + 10.3923i −0.0416667 + 0.0721688i
$$145$$ 0 0
$$146$$ 73.0593i 0.500406i
$$147$$ 26.5815 + 80.6004i 0.180827 + 0.548302i
$$148$$ 93.5385i 0.632017i
$$149$$ −93.2324 161.483i −0.625721 1.08378i −0.988401 0.151867i $$-0.951472\pi$$
0.362680 0.931914i $$-0.381862\pi$$
$$150$$ 0 0
$$151$$ −77.4202 + 134.096i −0.512716 + 0.888051i 0.487175 + 0.873304i $$0.338027\pi$$
−0.999891 + 0.0147462i $$0.995306\pi$$
$$152$$ −34.8060 60.2858i −0.228987 0.396617i
$$153$$ −54.7267 −0.357691
$$154$$ −180.469 + 80.8265i −1.17188 + 0.524847i
$$155$$ 0 0
$$156$$ 6.05851 + 10.4936i 0.0388366 + 0.0672670i
$$157$$ −25.1019 + 43.4777i −0.159885 + 0.276928i −0.934827 0.355104i $$-0.884446\pi$$
0.774942 + 0.632032i $$0.217779\pi$$
$$158$$ −26.9143 15.5390i −0.170344 0.0983481i
$$159$$ 97.3123 56.1833i 0.612027 0.353354i
$$160$$ 0 0
$$161$$ 142.884 + 103.331i 0.887477 + 0.641810i
$$162$$ 12.7279i 0.0785674i
$$163$$ −100.295 + 57.9054i −0.615308 + 0.355248i −0.775040 0.631912i $$-0.782270\pi$$
0.159732 + 0.987160i $$0.448937\pi$$
$$164$$ −54.6029 31.5250i −0.332945 0.192226i
$$165$$ 0 0
$$166$$ −0.511306 + 0.295202i −0.00308015 + 0.00177833i
$$167$$ −61.3210 −0.367191 −0.183596 0.983002i $$-0.558774\pi$$
−0.183596 + 0.983002i $$0.558774\pi$$
$$168$$ 3.50949 34.1128i 0.0208898 0.203052i
$$169$$ −156.765 −0.927602
$$170$$ 0 0
$$171$$ −63.9428 36.9174i −0.373934 0.215891i
$$172$$ 111.564 + 64.4116i 0.648629 + 0.374486i
$$173$$ 15.8508 + 27.4544i 0.0916232 + 0.158696i 0.908194 0.418549i $$-0.137461\pi$$
−0.816571 + 0.577245i $$0.804128\pi$$
$$174$$ 130.123i 0.747831i
$$175$$ 0 0
$$176$$ 79.8999 0.453977
$$177$$ −150.287 + 86.7684i −0.849081 + 0.490217i
$$178$$ 78.6376 136.204i 0.441784 0.765193i
$$179$$ 65.9472 114.224i 0.368420 0.638122i −0.620899 0.783891i $$-0.713232\pi$$
0.989319 + 0.145768i $$0.0465655\pi$$
$$180$$ 0 0
$$181$$ 55.1431i 0.304658i 0.988330 + 0.152329i $$0.0486773\pi$$
−0.988330 + 0.152329i $$0.951323\pi$$
$$182$$ −28.0588 20.2917i −0.154169 0.111493i
$$183$$ 13.8979i 0.0759449i
$$184$$ −35.6246 61.7035i −0.193612 0.335345i
$$185$$ 0 0
$$186$$ 36.9030 63.9179i 0.198403 0.343645i
$$187$$ 182.194 + 315.569i 0.974300 + 1.68754i
$$188$$ 56.1252 0.298538
$$189$$ −14.8674 33.1958i −0.0786633 0.175639i
$$190$$ 0 0
$$191$$ −97.5822 169.017i −0.510901 0.884907i −0.999920 0.0126340i $$-0.995978\pi$$
0.489019 0.872273i $$-0.337355\pi$$
$$192$$ −6.92820 + 12.0000i −0.0360844 + 0.0625000i
$$193$$ −302.035 174.380i −1.56495 0.903523i −0.996744 0.0806348i $$-0.974305\pi$$
−0.568204 0.822888i $$-0.692361\pi$$
$$194$$ 90.9060 52.4846i 0.468588 0.270539i
$$195$$ 0 0
$$196$$ 30.6937 + 93.0693i 0.156601 + 0.474843i
$$197$$ 56.3808i 0.286197i 0.989708 + 0.143098i $$0.0457066\pi$$
−0.989708 + 0.143098i $$0.954293\pi$$
$$198$$ 73.3927 42.3733i 0.370670 0.214007i
$$199$$ −148.357 85.6540i −0.745513 0.430422i 0.0785571 0.996910i $$-0.474969\pi$$
−0.824070 + 0.566487i $$0.808302\pi$$
$$200$$ 0 0
$$201$$ 24.3950 14.0844i 0.121368 0.0700718i
$$202$$ 123.877 0.613251
$$203$$ 151.995 + 339.374i 0.748744 + 1.67179i
$$204$$ −63.1930 −0.309769
$$205$$ 0 0
$$206$$ 170.290 + 98.3169i 0.826650 + 0.477267i
$$207$$ −65.4465 37.7856i −0.316167 0.182539i
$$208$$ 6.99576 + 12.1170i 0.0336335 + 0.0582549i
$$209$$ 491.616i 2.35223i
$$210$$ 0 0
$$211$$ 162.038 0.767954 0.383977 0.923343i $$-0.374554\pi$$
0.383977 + 0.923343i $$0.374554\pi$$
$$212$$ 112.367 64.8748i 0.530031 0.306013i
$$213$$ −93.2923 + 161.587i −0.437992 + 0.758625i
$$214$$ −107.614 + 186.394i −0.502871 + 0.870999i
$$215$$ 0 0
$$216$$ 14.6969i 0.0680414i
$$217$$ −21.5851 + 209.811i −0.0994707 + 0.966870i
$$218$$ 91.5779i 0.420082i
$$219$$ 44.7395 + 77.4910i 0.204290 + 0.353840i
$$220$$ 0 0
$$221$$ −31.9046 + 55.2604i −0.144365 + 0.250047i
$$222$$ −57.2804 99.2126i −0.258020 0.446904i
$$223$$ 365.329 1.63825 0.819123 0.573618i $$-0.194461\pi$$
0.819123 + 0.573618i $$0.194461\pi$$
$$224$$ 4.05241 39.3901i 0.0180911 0.175849i
$$225$$ 0 0
$$226$$ 2.30418 + 3.99096i 0.0101955 + 0.0176591i
$$227$$ 128.937 223.325i 0.568004 0.983811i −0.428759 0.903419i $$-0.641049\pi$$
0.996763 0.0803928i $$-0.0256175\pi$$
$$228$$ −73.8347 42.6285i −0.323837 0.186967i
$$229$$ 13.3634 7.71538i 0.0583556 0.0336916i −0.470538 0.882380i $$-0.655940\pi$$
0.528894 + 0.848688i $$0.322607\pi$$
$$230$$ 0 0
$$231$$ −141.920 + 196.244i −0.614374 + 0.849539i
$$232$$ 150.253i 0.647640i
$$233$$ −108.553 + 62.6734i −0.465895 + 0.268984i −0.714520 0.699615i $$-0.753355\pi$$
0.248625 + 0.968600i $$0.420021\pi$$
$$234$$ 12.8520 + 7.42013i 0.0549232 + 0.0317100i
$$235$$ 0 0
$$236$$ −173.537 + 100.192i −0.735326 + 0.424540i
$$237$$ −38.0626 −0.160602
$$238$$ 164.814 73.8151i 0.692496 0.310148i
$$239$$ 3.62565 0.0151701 0.00758503 0.999971i $$-0.497586\pi$$
0.00758503 + 0.999971i $$0.497586\pi$$
$$240$$ 0 0
$$241$$ 83.6915 + 48.3193i 0.347268 + 0.200495i 0.663481 0.748193i $$-0.269078\pi$$
−0.316213 + 0.948688i $$0.602412\pi$$
$$242$$ −340.479 196.575i −1.40694 0.812295i
$$243$$ 7.79423 + 13.5000i 0.0320750 + 0.0555556i
$$244$$ 16.0479i 0.0657702i
$$245$$ 0 0
$$246$$ −77.2202 −0.313903
$$247$$ −74.5548 + 43.0442i −0.301841 + 0.174268i
$$248$$ 42.6119 73.8060i 0.171822 0.297605i
$$249$$ −0.361548 + 0.626219i −0.00145200 + 0.00251494i
$$250$$ 0 0
$$251$$ 29.7311i 0.118450i −0.998245 0.0592252i $$-0.981137\pi$$
0.998245 0.0592252i $$-0.0188630\pi$$
$$252$$ −17.1674 38.3312i −0.0681245 0.152108i
$$253$$ 503.177i 1.98884i
$$254$$ 62.6336 + 108.484i 0.246589 + 0.427104i
$$255$$ 0 0
$$256$$ −8.00000 + 13.8564i −0.0312500 + 0.0541266i
$$257$$ −220.811 382.457i −0.859189 1.48816i −0.872704 0.488250i $$-0.837636\pi$$
0.0135154 0.999909i $$-0.495698\pi$$
$$258$$ 157.776 0.611533
$$259$$ 265.283 + 191.848i 1.02426 + 0.740728i
$$260$$ 0 0
$$261$$ −79.6835 138.016i −0.305301 0.528796i
$$262$$ −88.4762 + 153.245i −0.337695 + 0.584905i
$$263$$ −297.087 171.523i −1.12961 0.652180i −0.185772 0.982593i $$-0.559479\pi$$
−0.943836 + 0.330413i $$0.892812\pi$$
$$264$$ 84.7466 48.9285i 0.321010 0.185335i
$$265$$ 0 0
$$266$$ 242.363 + 24.9341i 0.911139 + 0.0937371i
$$267$$ 192.622i 0.721431i
$$268$$ 28.1689 16.2633i 0.105108 0.0606840i
$$269$$ −401.274 231.676i −1.49172 0.861247i −0.491769 0.870726i $$-0.663650\pi$$
−0.999955 + 0.00947852i $$0.996983\pi$$
$$270$$ 0 0
$$271$$ 211.814 122.291i 0.781600 0.451257i −0.0553967 0.998464i $$-0.517642\pi$$
0.836997 + 0.547207i $$0.184309\pi$$
$$272$$ −72.9689 −0.268268
$$273$$ −42.1869 4.34015i −0.154531 0.0158980i
$$274$$ −55.0889 −0.201054
$$275$$ 0 0
$$276$$ −75.5711 43.6310i −0.273808 0.158083i
$$277$$ 122.126 + 70.5092i 0.440887 + 0.254546i 0.703974 0.710226i $$-0.251407\pi$$
−0.263087 + 0.964772i $$0.584741\pi$$
$$278$$ −69.9650 121.183i −0.251673 0.435910i
$$279$$ 90.3935i 0.323991i
$$280$$ 0 0
$$281$$ 84.9953 0.302475 0.151237 0.988497i $$-0.451674\pi$$
0.151237 + 0.988497i $$0.451674\pi$$
$$282$$ 59.5297 34.3695i 0.211098 0.121878i
$$283$$ 58.3392 101.047i 0.206146 0.357055i −0.744351 0.667788i $$-0.767241\pi$$
0.950497 + 0.310733i $$0.100575\pi$$
$$284$$ −107.725 + 186.585i −0.379312 + 0.656988i
$$285$$ 0 0
$$286$$ 98.8112i 0.345494i
$$287$$ 201.399 90.2003i 0.701738 0.314287i
$$288$$ 16.9706i 0.0589256i
$$289$$ −21.8896 37.9138i −0.0757424 0.131190i
$$290$$ 0 0
$$291$$ 64.2802 111.337i 0.220894 0.382600i
$$292$$ 51.6607 + 89.4789i 0.176920 + 0.306435i
$$293$$ −131.882 −0.450110 −0.225055 0.974346i $$-0.572256\pi$$
−0.225055 + 0.974346i $$0.572256\pi$$
$$294$$ 89.5487 + 79.9189i 0.304587 + 0.271833i
$$295$$ 0 0
$$296$$ −66.1417 114.561i −0.223452 0.387030i
$$297$$ 51.8965 89.8874i 0.174736 0.302651i
$$298$$ −228.372 131.851i −0.766348 0.442451i
$$299$$ −76.3080 + 44.0565i −0.255211 + 0.147346i
$$300$$ 0 0
$$301$$ −411.496 + 184.296i −1.36710 + 0.612280i
$$302$$ 218.977i 0.725090i
$$303$$ 131.391 75.8587i 0.433634 0.250359i
$$304$$ −85.2570 49.2232i −0.280451 0.161918i
$$305$$ 0 0
$$306$$ −67.0263 + 38.6976i −0.219040 + 0.126463i
$$307$$ 429.871 1.40023 0.700115 0.714030i $$-0.253132\pi$$
0.700115 + 0.714030i $$0.253132\pi$$
$$308$$ −163.875 + 226.603i −0.532063 + 0.735723i
$$309$$ 240.826 0.779373
$$310$$ 0 0
$$311$$ −217.786 125.739i −0.700277 0.404305i 0.107174 0.994240i $$-0.465820\pi$$
−0.807451 + 0.589935i $$0.799153\pi$$
$$312$$ 14.8403 + 8.56803i 0.0475649 + 0.0274616i
$$313$$ 6.85166 + 11.8674i 0.0218903 + 0.0379151i 0.876763 0.480923i $$-0.159698\pi$$
−0.854873 + 0.518838i $$0.826365\pi$$
$$314$$ 70.9988i 0.226111i
$$315$$ 0 0
$$316$$ −43.9509 −0.139085
$$317$$ 28.5183 16.4651i 0.0899632 0.0519403i −0.454343 0.890827i $$-0.650126\pi$$
0.544307 + 0.838886i $$0.316793\pi$$
$$318$$ 79.4551 137.620i 0.249859 0.432768i
$$319$$ −530.558 + 918.954i −1.66319 + 2.88073i
$$320$$ 0 0
$$321$$ 263.601i 0.821186i
$$322$$ 248.063 + 25.5204i 0.770381 + 0.0792560i
$$323$$ 448.970i 1.39000i
$$324$$ 9.00000 + 15.5885i 0.0277778 + 0.0481125i
$$325$$ 0 0
$$326$$ −81.8906 + 141.839i −0.251198 + 0.435088i
$$327$$ −56.0798 97.1331i −0.171498 0.297043i
$$328$$ −89.1662 −0.271848
$$329$$ −115.113 + 159.176i −0.349888 + 0.483816i
$$330$$ 0 0
$$331$$ 208.940 + 361.895i 0.631240 + 1.09334i 0.987299 + 0.158876i $$0.0507869\pi$$
−0.356059 + 0.934464i $$0.615880\pi$$
$$332$$ −0.417479 + 0.723095i −0.00125747 + 0.00217800i
$$333$$ −121.510 70.1539i −0.364895 0.210672i
$$334$$ −75.1025 + 43.3605i −0.224858 + 0.129822i
$$335$$ 0 0
$$336$$ −19.8232 44.2611i −0.0589975 0.131729i
$$337$$ 286.688i 0.850705i 0.905028 + 0.425353i $$0.139850\pi$$
−0.905028 + 0.425353i $$0.860150\pi$$
$$338$$ −191.997 + 110.849i −0.568038 + 0.327957i
$$339$$ 4.88790 + 2.82203i 0.0144186 + 0.00832458i
$$340$$ 0 0
$$341$$ −521.234 + 300.935i −1.52855 + 0.882507i
$$342$$ −104.418 −0.305316
$$343$$ −326.905 103.836i −0.953077 0.302729i
$$344$$ 182.184 0.529603
$$345$$ 0 0
$$346$$ 38.8264 + 22.4164i 0.112215 + 0.0647874i
$$347$$ 265.693 + 153.398i 0.765685 + 0.442069i 0.831333 0.555774i $$-0.187578\pi$$
−0.0656479 + 0.997843i $$0.520911\pi$$
$$348$$ −92.0105 159.367i −0.264398 0.457951i
$$349$$ 340.162i 0.974676i 0.873214 + 0.487338i $$0.162032\pi$$
−0.873214 + 0.487338i $$0.837968\pi$$
$$350$$ 0 0
$$351$$ 18.1755 0.0517821
$$352$$ 97.8570 56.4978i 0.278003 0.160505i
$$353$$ 187.501 324.761i 0.531165 0.920004i −0.468174 0.883636i $$-0.655088\pi$$
0.999338 0.0363676i $$-0.0115787\pi$$
$$354$$ −122.709 + 212.538i −0.346636 + 0.600391i
$$355$$ 0 0
$$356$$ 222.421i 0.624778i
$$357$$ 129.609 179.220i 0.363051 0.502018i
$$358$$ 186.527i 0.521025i
$$359$$ −164.750 285.356i −0.458915 0.794863i 0.539989 0.841672i $$-0.318428\pi$$
−0.998904 + 0.0468084i $$0.985095\pi$$
$$360$$ 0 0
$$361$$ 122.365 211.942i 0.338961 0.587098i
$$362$$ 38.9920 + 67.5362i 0.107713 + 0.186564i
$$363$$ −481.509 −1.32647
$$364$$ −48.7132 5.01157i −0.133828 0.0137681i
$$365$$ 0 0
$$366$$ −9.82731 17.0214i −0.0268506 0.0465066i
$$367$$ 13.5772 23.5163i 0.0369950 0.0640772i −0.846935 0.531696i $$-0.821555\pi$$
0.883930 + 0.467619i $$0.154888\pi$$
$$368$$ −87.2620 50.3807i −0.237125 0.136904i
$$369$$ −81.9044 + 47.2875i −0.221963 + 0.128151i
$$370$$ 0 0
$$371$$ −46.4745 + 451.740i −0.125268 + 1.21763i
$$372$$ 104.377i 0.280585i
$$373$$ 110.416 63.7488i 0.296022 0.170908i −0.344633 0.938738i $$-0.611996\pi$$
0.640654 + 0.767829i $$0.278663\pi$$
$$374$$ 446.283 + 257.661i 1.19327 + 0.688934i
$$375$$ 0 0
$$376$$ 68.7390 39.6865i 0.182817 0.105549i
$$377$$ −185.816 −0.492880
$$378$$ −41.6817 30.1436i −0.110269 0.0797449i
$$379$$ −319.795 −0.843785 −0.421893 0.906646i $$-0.638634\pi$$
−0.421893 + 0.906646i $$0.638634\pi$$
$$380$$ 0 0
$$381$$ 132.866 + 76.7101i 0.348729 + 0.201339i
$$382$$ −239.027 138.002i −0.625724 0.361262i
$$383$$ 204.471 + 354.155i 0.533867 + 0.924686i 0.999217 + 0.0395587i $$0.0125952\pi$$
−0.465350 + 0.885127i $$0.654071\pi$$
$$384$$ 19.5959i 0.0510310i
$$385$$ 0 0
$$386$$ −493.221 −1.27777
$$387$$ 167.346 96.6174i 0.432419 0.249657i
$$388$$ 74.2244 128.560i 0.191300 0.331341i
$$389$$ 193.576 335.284i 0.497626 0.861913i −0.502370 0.864652i $$-0.667539\pi$$
0.999996 + 0.00273932i $$0.000871952\pi$$
$$390$$ 0 0
$$391$$ 459.529i 1.17526i
$$392$$ 103.402 + 92.2824i 0.263780 + 0.235414i
$$393$$ 216.721i 0.551454i
$$394$$ 39.8672 + 69.0521i 0.101186 + 0.175259i
$$395$$ 0 0
$$396$$ 59.9249 103.793i 0.151326 0.262104i
$$397$$ −15.0556 26.0771i −0.0379234 0.0656853i 0.846441 0.532483i $$-0.178741\pi$$
−0.884364 + 0.466798i $$0.845408\pi$$
$$398$$ −242.266 −0.608709
$$399$$ 272.334 121.970i 0.682541 0.305689i
$$400$$ 0 0
$$401$$ −68.3852 118.447i −0.170537 0.295378i 0.768071 0.640365i $$-0.221217\pi$$
−0.938608 + 0.344987i $$0.887883\pi$$
$$402$$ 19.9184 34.4997i 0.0495482 0.0858201i
$$403$$ −91.2750 52.6977i −0.226489 0.130763i
$$404$$ 151.717 87.5941i 0.375538 0.216817i
$$405$$ 0 0
$$406$$ 426.129 + 308.170i 1.04958 + 0.759038i
$$407$$ 934.215i 2.29537i
$$408$$ −77.3952 + 44.6842i −0.189694 + 0.109520i
$$409$$ 426.838 + 246.435i 1.04361 + 0.602531i 0.920855 0.389906i $$-0.127493\pi$$
0.122759 + 0.992437i $$0.460826\pi$$
$$410$$ 0 0
$$411$$ −58.4306 + 33.7349i −0.142167 + 0.0820801i
$$412$$ 278.082 0.674957
$$413$$ 71.7744 697.659i 0.173788 1.68925i
$$414$$ −106.874 −0.258149
$$415$$ 0 0
$$416$$ 17.1361 + 9.89350i 0.0411924 + 0.0237825i
$$417$$ −148.418 85.6892i −0.355919 0.205490i
$$418$$ 347.625 + 602.104i 0.831638 + 1.44044i
$$419$$ 311.640i 0.743771i 0.928279 + 0.371885i $$0.121289\pi$$
−0.928279 + 0.371885i $$0.878711\pi$$
$$420$$ 0 0
$$421$$ −539.935 −1.28250 −0.641252 0.767330i $$-0.721585\pi$$
−0.641252 + 0.767330i $$0.721585\pi$$
$$422$$ 198.456 114.578i 0.470274 0.271513i
$$423$$ 42.0939 72.9087i 0.0995127 0.172361i
$$424$$ 91.7469 158.910i 0.216384 0.374788i
$$425$$ 0 0
$$426$$ 263.871i 0.619414i
$$427$$ 45.5132 + 32.9145i 0.106588 + 0.0770831i
$$428$$ 304.380i 0.711168i
$$429$$ −60.5093 104.805i −0.141047 0.244301i
$$430$$ 0 0
$$431$$ 314.021 543.900i 0.728586 1.26195i −0.228895 0.973451i $$-0.573511\pi$$
0.957481 0.288497i $$-0.0931555\pi$$
$$432$$ 10.3923 + 18.0000i 0.0240563 + 0.0416667i
$$433$$ −706.789 −1.63231 −0.816153 0.577836i $$-0.803897\pi$$
−0.816153 + 0.577836i $$0.803897\pi$$
$$434$$ 121.922 + 272.228i 0.280927 + 0.627253i
$$435$$ 0 0
$$436$$ −64.7554 112.160i −0.148522 0.257247i
$$437$$ 309.987 536.914i 0.709353 1.22864i
$$438$$ 109.589 + 63.2712i 0.250203 + 0.144455i
$$439$$ −564.452 + 325.886i −1.28577 + 0.742338i −0.977896 0.209090i $$-0.932950\pi$$
−0.307871 + 0.951428i $$0.599617\pi$$
$$440$$ 0 0
$$441$$ 143.921 + 29.9297i 0.326351 + 0.0678677i
$$442$$ 90.2398i 0.204162i
$$443$$ −20.4605 + 11.8129i −0.0461863 + 0.0266657i −0.522915 0.852385i $$-0.675156\pi$$
0.476729 + 0.879050i $$0.341822\pi$$
$$444$$ −140.308 81.0068i −0.316009 0.182448i
$$445$$ 0 0
$$446$$ 447.435 258.326i 1.00322 0.579207i
$$447$$ −322.967 −0.722520
$$448$$ −22.8898 51.1083i −0.0510933 0.114081i
$$449$$ 55.1499 0.122828 0.0614141 0.998112i $$-0.480439\pi$$
0.0614141 + 0.998112i $$0.480439\pi$$
$$450$$ 0 0
$$451$$ 545.346 + 314.856i 1.20919 + 0.698128i
$$452$$ 5.64407 + 3.25860i 0.0124869 + 0.00720930i
$$453$$ 134.096 + 232.260i 0.296017 + 0.512716i
$$454$$ 364.689i 0.803279i
$$455$$ 0 0
$$456$$ −120.572 −0.264411
$$457$$ −303.778 + 175.386i −0.664723 + 0.383778i −0.794074 0.607821i $$-0.792044\pi$$
0.129351 + 0.991599i $$0.458710\pi$$
$$458$$ 10.9112 18.8987i 0.0238236 0.0412636i
$$459$$ −47.3947 + 82.0901i −0.103256 + 0.178845i
$$460$$ 0 0
$$461$$ 471.598i 1.02299i −0.859287 0.511494i $$-0.829092\pi$$
0.859287 0.511494i $$-0.170908\pi$$
$$462$$ −35.0510 + 340.701i −0.0758680 + 0.737448i
$$463$$ 387.112i 0.836094i 0.908425 + 0.418047i $$0.137285\pi$$
−0.908425 + 0.418047i $$0.862715\pi$$
$$464$$ −106.245 184.021i −0.228975 0.396597i
$$465$$ 0 0
$$466$$ −88.6336 + 153.518i −0.190201 + 0.329437i
$$467$$ 146.673 + 254.045i 0.314075 + 0.543994i 0.979240 0.202702i $$-0.0649724\pi$$
−0.665166 + 0.746696i $$0.731639\pi$$
$$468$$ 20.9873 0.0448446
$$469$$ −11.6506 + 113.245i −0.0248413 + 0.241461i
$$470$$ 0 0
$$471$$ 43.4777 + 75.3056i 0.0923094 + 0.159885i
$$472$$ −141.692 + 245.418i −0.300195 + 0.519954i
$$473$$ −1114.25 643.310i −2.35570 1.36006i
$$474$$ −46.6170 + 26.9143i −0.0983481 + 0.0567813i
$$475$$ 0 0
$$476$$ 149.660 206.946i 0.314412 0.434760i
$$477$$ 194.625i 0.408018i
$$478$$ 4.44049 2.56372i 0.00928973 0.00536343i
$$479$$ 660.805 + 381.516i 1.37955 + 0.796484i 0.992105 0.125409i $$-0.0400242\pi$$
0.387445 + 0.921893i $$0.373358\pi$$
$$480$$ 0 0
$$481$$ −141.676 + 81.7967i −0.294545 + 0.170056i
$$482$$ 136.668 0.283543
$$483$$ 278.738 124.838i 0.577098 0.258464i
$$484$$ −555.999 −1.14876
$$485$$ 0 0
$$486$$ 19.0919 + 11.0227i 0.0392837 + 0.0226805i
$$487$$ −193.893 111.944i −0.398138 0.229865i 0.287542 0.957768i $$-0.407162\pi$$
−0.685680 + 0.727903i $$0.740495\pi$$
$$488$$ −11.3476 19.6546i −0.0232533 0.0402759i
$$489$$ 200.590i 0.410205i
$$490$$ 0 0
$$491$$ −837.694 −1.70610 −0.853049 0.521830i $$-0.825249\pi$$
−0.853049 + 0.521830i $$0.825249\pi$$
$$492$$ −94.5751 + 54.6029i −0.192226 + 0.110982i
$$493$$ 484.535 839.239i 0.982829 1.70231i
$$494$$ −60.8737 + 105.436i −0.123226 + 0.213434i
$$495$$ 0 0
$$496$$ 120.525i 0.242993i
$$497$$ −308.225 688.203i −0.620171 1.38471i
$$498$$ 1.02261i 0.00205344i
$$499$$ 87.3234 + 151.249i 0.174997 + 0.303103i 0.940160 0.340733i $$-0.110675\pi$$
−0.765163 + 0.643836i $$0.777342\pi$$
$$500$$ 0 0
$$501$$ −53.1055 + 91.9814i −0.105999 + 0.183596i
$$502$$ −21.0230 36.4130i −0.0418786 0.0725358i
$$503$$ 747.962 1.48700 0.743501 0.668734i $$-0.233164\pi$$
0.743501 + 0.668734i $$0.233164\pi$$
$$504$$ −48.1299 34.8068i −0.0954958 0.0690611i
$$505$$ 0 0
$$506$$ 355.800 + 616.263i 0.703162 + 1.21791i
$$507$$ −135.762 + 235.147i −0.267776 + 0.463801i
$$508$$ 153.420 + 88.5772i 0.302008 + 0.174365i
$$509$$ 203.021 117.214i 0.398863 0.230284i −0.287130 0.957892i $$-0.592701\pi$$
0.685993 + 0.727608i $$0.259368\pi$$
$$510$$ 0 0
$$511$$ −359.726 37.0083i −0.703965 0.0724233i
$$512$$ 22.6274i 0.0441942i
$$513$$ −110.752 + 63.9428i −0.215891 + 0.124645i
$$514$$ −540.875 312.275i −1.05229 0.607538i
$$515$$ 0 0
$$516$$ 193.235 111.564i 0.374486 0.216210i
$$517$$ −560.549 −1.08423
$$518$$ 460.561 + 47.3821i 0.889114 + 0.0914712i
$$519$$ 54.9088 0.105797
$$520$$ 0 0
$$521$$ 186.068 + 107.427i 0.357137 + 0.206193i 0.667824 0.744319i $$-0.267226\pi$$
−0.310687 + 0.950512i $$0.600559\pi$$
$$522$$ −195.184 112.689i −0.373915 0.215880i
$$523$$ 462.520 + 801.108i 0.884360 + 1.53176i 0.846446 + 0.532475i $$0.178738\pi$$
0.0379137 + 0.999281i $$0.487929\pi$$
$$524$$ 250.248i 0.477573i
$$525$$ 0 0
$$526$$ −485.141 −0.922321
$$527$$ 476.020 274.830i 0.903263 0.521499i
$$528$$ 69.1953 119.850i 0.131052 0.226988i
$$529$$ 52.7773 91.4130i 0.0997681 0.172803i
$$530$$ 0 0
$$531$$ 300.575i 0.566054i
$$532$$ 314.464 140.839i 0.591098 0.264734i
$$533$$ 110.271i 0.206887i
$$534$$ −136.204 235.913i −0.255064 0.441784i
$$535$$ 0 0
$$536$$ 22.9998 39.8368i 0.0429100 0.0743224i
$$537$$ −114.224 197.842i −0.212707 0.368420i
$$538$$ −655.277 −1.21799
$$539$$ −306.553 929.528i −0.568744 1.72454i
$$540$$ 0 0
$$541$$ 57.1560 + 98.9971i 0.105649 + 0.182989i 0.914003 0.405707i $$-0.132975\pi$$
−0.808354 + 0.588696i $$0.799641\pi$$
$$542$$ 172.945 299.550i 0.319087 0.552675i
$$543$$ 82.7146 + 47.7553i 0.152329 + 0.0879472i
$$544$$ −89.3683 + 51.5968i −0.164280 + 0.0948471i
$$545$$ 0 0
$$546$$ −54.7371 + 24.5151i −0.100251 + 0.0448994i
$$547$$ 57.7698i 0.105612i 0.998605 + 0.0528060i $$0.0168165\pi$$
−0.998605 + 0.0528060i $$0.983183\pi$$
$$548$$ −67.4699 + 38.9538i −0.123120 + 0.0710835i
$$549$$ −20.8469 12.0359i −0.0379725 0.0219234i
$$550$$ 0 0
$$551$$ 1132.26 653.712i 2.05492 1.18641i
$$552$$ −123.407 −0.223564
$$553$$ 90.1438 124.648i 0.163009 0.225404i
$$554$$ 199.430 0.359982
$$555$$ 0 0
$$556$$ −171.378 98.9454i −0.308235 0.177959i
$$557$$ −351.738 203.076i −0.631487 0.364589i 0.149841 0.988710i $$-0.452124\pi$$
−0.781328 + 0.624121i $$0.785457\pi$$
$$558$$ −63.9179 110.709i −0.114548 0.198403i
$$559$$ 225.304i 0.403049i
$$560$$ 0 0
$$561$$ 631.139 1.12502
$$562$$ 104.098 60.1008i 0.185227 0.106941i
$$563$$ 214.146 370.911i 0.380366 0.658813i −0.610749 0.791824i $$-0.709131\pi$$
0.991114 + 0.133012i $$0.0424648\pi$$
$$564$$ 48.6058 84.1878i 0.0861805 0.149269i
$$565$$ 0 0
$$566$$ 165.008i 0.291534i
$$567$$ −62.6692 6.44735i −0.110528 0.0113710i
$$568$$ 304.691i 0.536429i
$$569$$ −457.897 793.100i −0.804739 1.39385i −0.916467 0.400110i $$-0.868972\pi$$
0.111728 0.993739i $$-0.464362\pi$$
$$570$$ 0 0
$$571$$ 356.947 618.250i 0.625125 1.08275i −0.363391 0.931637i $$-0.618381\pi$$
0.988517 0.151112i $$-0.0482855\pi$$
$$572$$ −69.8701 121.019i −0.122151 0.211571i
$$573$$ −338.035 −0.589938
$$574$$ 182.881 252.883i 0.318608 0.440562i
$$575$$ 0 0
$$576$$ 12.0000 + 20.7846i 0.0208333 + 0.0360844i
$$577$$ −43.7973 + 75.8591i −0.0759052 + 0.131472i −0.901480 0.432822i $$-0.857518\pi$$
0.825574 + 0.564293i $$0.190851\pi$$
$$578$$ −53.6183 30.9565i −0.0927652 0.0535580i
$$579$$ −523.140 + 302.035i −0.903523 + 0.521649i
$$580$$ 0 0
$$581$$ −1.19450 2.66708i −0.00205594 0.00459050i
$$582$$ 181.812i 0.312392i
$$583$$ −1122.26 + 647.937i −1.92497 + 1.11138i
$$584$$ 126.542 + 73.0593i 0.216682 + 0.125101i
$$585$$ 0 0
$$586$$ −161.522 + 93.2548i −0.275635 + 0.159138i
$$587$$ −169.908 −0.289452 −0.144726 0.989472i $$-0.546230\pi$$
−0.144726 + 0.989472i $$0.546230\pi$$
$$588$$ 166.186 + 34.5598i 0.282628 + 0.0587752i
$$589$$ 741.576 1.25904
$$590$$ 0 0
$$591$$ 84.5712 + 48.8272i 0.143098 + 0.0826179i
$$592$$ −162.014 93.5385i −0.273671 0.158004i
$$593$$ 100.126 + 173.424i 0.168847 + 0.292452i 0.938015 0.346595i $$-0.112662\pi$$
−0.769168 + 0.639047i $$0.779329\pi$$
$$594$$ 146.785i 0.247114i
$$595$$ 0 0
$$596$$ −372.930 −0.625721
$$597$$ −256.962 + 148.357i −0.430422 + 0.248504i
$$598$$ −62.3053 + 107.916i −0.104189 + 0.180461i
$$599$$ −350.201 + 606.566i −0.584643 + 1.01263i 0.410277 + 0.911961i $$0.365432\pi$$
−0.994920 + 0.100671i $$0.967901\pi$$
$$600$$ 0 0
$$601$$ 1039.21i 1.72914i 0.502515 + 0.864569i $$0.332408\pi$$
−0.502515 + 0.864569i $$0.667592\pi$$
$$602$$ −373.660 + 516.687i −0.620698 + 0.858285i
$$603$$ 48.7899i 0.0809119i
$$604$$ 154.840 + 268.191i 0.256358 + 0.444025i
$$605$$ 0 0
$$606$$ 107.280 185.815i 0.177030 0.306626i
$$607$$ −30.5796 52.9655i −0.0503783 0.0872578i 0.839737 0.542994i $$-0.182709\pi$$
−0.890115 + 0.455736i $$0.849376\pi$$
$$608$$ −139.224 −0.228987
$$609$$ 640.692 + 65.9138i 1.05204 + 0.108233i
$$610$$ 0 0
$$611$$ −49.0798 85.0087i −0.0803270 0.139130i
$$612$$ −54.7267 + 94.7894i −0.0894227 + 0.154885i
$$613$$ 452.688 + 261.359i 0.738479 + 0.426361i 0.821516 0.570185i $$-0.193129\pi$$
−0.0830371 + 0.996546i $$0.526462\pi$$
$$614$$ 526.482 303.965i 0.857462 0.495056i
$$615$$ 0 0
$$616$$ −40.4734 + 393.408i −0.0657036 + 0.638649i
$$617$$ 608.200i 0.985738i 0.870104 + 0.492869i $$0.164052\pi$$
−0.870104 + 0.492869i $$0.835948\pi$$
$$618$$ 294.951 170.290i 0.477267 0.275550i
$$619$$ −902.671 521.157i −1.45827 0.841934i −0.459346 0.888257i $$-0.651916\pi$$
−0.998927 + 0.0463229i $$0.985250\pi$$
$$620$$ 0 0
$$621$$ −113.357 + 65.4465i −0.182539 + 0.105389i
$$622$$ −355.643 −0.571774
$$623$$ 630.804 + 456.187i 1.01253 + 0.732243i
$$624$$ 24.2340 0.0388366
$$625$$ 0 0
$$626$$ 16.7831 + 9.68972i 0.0268100 + 0.0154788i
$$627$$ 737.424 + 425.752i 1.17611 + 0.679030i
$$628$$ 50.2037 + 86.9554i 0.0799423 + 0.138464i
$$629$$ 853.176i 1.35640i
$$630$$ 0 0
$$631$$ −235.274 −0.372859 −0.186430 0.982468i $$-0.559692\pi$$
−0.186430 + 0.982468i $$0.559692\pi$$
$$632$$ −53.8287 + 31.0780i −0.0851720 + 0.0491741i
$$633$$ 140.329 243.057i 0.221689 0.383977i
$$634$$ 23.2851 40.3310i 0.0367273 0.0636136i
$$635$$ 0 0
$$636$$ 224.733i 0.353354i
$$637$$ 114.125 127.876i 0.179159 0.200747i
$$638$$ 1500.65i 2.35211i
$$639$$ 161.587 + 279.877i 0.252875 + 0.437992i
$$640$$ 0 0
$$641$$ 58.4900 101.308i 0.0912481 0.158046i −0.816788 0.576937i $$-0.804248\pi$$
0.908037 + 0.418891i $$0.137581\pi$$
$$642$$ 186.394 + 322.843i 0.290333 + 0.502871i
$$643$$ 874.209 1.35958 0.679789 0.733408i $$-0.262071\pi$$
0.679789 + 0.733408i $$0.262071\pi$$
$$644$$ 321.859 144.151i 0.499781 0.223837i
$$645$$ 0 0
$$646$$ −317.470 549.874i −0.491439 0.851198i
$$647$$ −5.84189 + 10.1185i −0.00902920 + 0.0156390i −0.870505 0.492160i $$-0.836207\pi$$
0.861476 + 0.507799i $$0.169541\pi$$
$$648$$ 22.0454 + 12.7279i 0.0340207 + 0.0196419i
$$649$$ 1733.20 1000.66i 2.67057 1.54185i
$$650$$ 0 0
$$651$$ 296.023 + 214.079i 0.454720 + 0.328847i
$$652$$ 231.622i 0.355248i
$$653$$ 552.641 319.067i 0.846311 0.488618i −0.0130935 0.999914i $$-0.504168\pi$$
0.859404 + 0.511296i $$0.170835\pi$$
$$654$$ −137.367 79.3088i −0.210041 0.121267i
$$655$$ 0 0
$$656$$ −109.206 + 63.0500i −0.166472 + 0.0961129i
$$657$$ 154.982 0.235894
$$658$$ −28.4303 + 276.347i −0.0432071 + 0.419980i
$$659$$ −870.363 −1.32073 −0.660367 0.750943i $$-0.729599\pi$$
−0.660367 + 0.750943i $$0.729599\pi$$
$$660$$ 0 0
$$661$$ 417.571 + 241.085i 0.631727 + 0.364728i 0.781420 0.624005i $$-0.214495\pi$$
−0.149694 + 0.988732i $$0.547829\pi$$
$$662$$ 511.797 + 295.486i 0.773108 + 0.446354i
$$663$$ 55.2604 + 95.7138i 0.0833490 + 0.144365i
$$664$$ 1.18081i 0.00177833i
$$665$$ 0 0
$$666$$ −198.425 −0.297936
$$667$$ 1158.89 669.085i 1.73747 1.00313i
$$668$$ −61.3210 + 106.211i −0.0917978 + 0.158999i
$$669$$ 316.384 547.993i 0.472921 0.819123i
$$670$$ 0 0
$$671$$ 160.279i 0.238865i
$$672$$ −55.5756 40.1914i −0.0827018 0.0598087i
$$673$$ 399.323i 0.593347i −0.954979 0.296674i $$-0.904123\pi$$
0.954979 0.296674i $$-0.0958773\pi$$
$$674$$ 202.719 + 351.119i 0.300770 + 0.520948i
$$675$$ 0 0
$$676$$ −156.765 + 271.525i −0.231901 + 0.401664i
$$677$$ −70.6707 122.405i −0.104388 0.180805i 0.809100 0.587671i $$-0.199955\pi$$
−0.913488 + 0.406866i $$0.866622\pi$$
$$678$$ 7.98191 0.0117727
$$679$$ 212.373 + 474.185i 0.312773 + 0.698358i
$$680$$ 0 0
$$681$$ −223.325 386.811i −0.327937 0.568004i
$$682$$ −425.586 + 737.137i −0.624026 + 1.08085i
$$683$$ −855.785 494.088i −1.25298 0.723408i −0.281279 0.959626i $$-0.590759\pi$$
−0.971700 + 0.236218i $$0.924092\pi$$
$$684$$ −127.886 + 73.8347i −0.186967 + 0.107946i
$$685$$ 0 0
$$686$$ −473.799 + 103.984i −0.690669 + 0.151580i
$$687$$ 26.7268i 0.0389037i
$$688$$ 223.128 128.823i 0.324314 0.187243i
$$689$$ −196.522 113.462i −0.285228 0.164677i
$$690$$ 0 0
$$691$$ 303.829 175.415i 0.439694 0.253857i −0.263774 0.964585i $$-0.584967\pi$$
0.703468 + 0.710727i $$0.251634\pi$$
$$692$$ 63.4033 0.0916232
$$693$$ 171.459 + 382.832i 0.247415 + 0.552428i
$$694$$ 433.875 0.625180
$$695$$ 0 0
$$696$$ −225.379 130.123i −0.323820 0.186958i
$$697$$ −498.040 287.543i −0.714548 0.412544i
$$698$$ 240.531 + 416.611i 0.344600 + 0.596864i
$$699$$ 217.107i 0.310597i
$$700$$ 0 0
$$701$$ 307.500 0.438659 0.219330 0.975651i $$-0.429613\pi$$
0.219330 + 0.975651i $$0.429613\pi$$
$$702$$ 22.2604 12.8520i 0.0317100 0.0183077i
$$703$$ 575.533 996.852i 0.818681 1.41800i
$$704$$ 79.8999 138.391i 0.113494 0.196578i
$$705$$ 0 0
$$706$$ 530.333i 0.751180i
$$707$$ −62.7500 + 609.939i −0.0887552 + 0.862715i
$$708$$ 347.074i 0.490217i
$$709$$ −49.0712 84.9938i −0.0692118 0.119878i 0.829343 0.558740i $$-0.188715\pi$$
−0.898555 + 0.438862i $$0.855382\pi$$
$$710$$ 0 0
$$711$$ −32.9632 + 57.0939i −0.0463617 + 0.0803009i
$$712$$ −157.275 272.409i −0.220892 0.382597i
$$713$$ 759.016 1.06454
$$714$$ 32.0105 311.147i 0.0448326 0.435780i
$$715$$ 0 0
$$716$$ −131.894 228.448i −0.184210 0.319061i
$$717$$ 3.13990 5.43847i 0.00437922 0.00758503i
$$718$$ −403.554 232.992i −0.562053 0.324502i
$$719$$ −612.340 + 353.535i −0.851655 + 0.491703i −0.861209 0.508251i $$-0.830292\pi$$
0.00955403 + 0.999954i $$0.496959\pi$$
$$720$$ 0 0
$$721$$ −570.349 + 788.664i −0.791053 + 1.09385i
$$722$$ 346.100i 0.479363i
$$723$$ 144.958 83.6915i 0.200495 0.115756i
$$724$$ 95.5106 + 55.1431i 0.131921 + 0.0761645i
$$725$$ 0 0
$$726$$ −589.726 + 340.479i −0.812295 + 0.468979i
$$727$$ −1353.85 −1.86225 −0.931123 0.364705i $$-0.881170\pi$$
−0.931123 + 0.364705i $$0.881170\pi$$
$$728$$ −63.2050 + 28.3076i −0.0868201 + 0.0388840i
$$729$$ 27.0000 0.0370370
$$730$$ 0 0
$$731$$ 1017.59 + 587.506i 1.39205 + 0.803701i
$$732$$ −24.0719 13.8979i −0.0328851 0.0189862i
$$733$$ −276.517 478.941i −0.377240 0.653398i 0.613420 0.789757i $$-0.289793\pi$$
−0.990660 + 0.136359i $$0.956460\pi$$
$$734$$ 38.4020i 0.0523188i
$$735$$ 0 0
$$736$$ −142.498 −0.193612
$$737$$ −281.336 + 162.429i −0.381732 + 0.220393i
$$738$$ −66.8747 + 115.830i −0.0906161 + 0.156952i
$$739$$ 466.739 808.416i 0.631582 1.09393i −0.355646 0.934621i $$-0.615739\pi$$
0.987228 0.159312i $$-0.0509276\pi$$
$$740$$ 0 0
$$741$$ 149.110i 0.201227i
$$742$$ 262.509 + 586.128i 0.353785 + 0.789930i
$$743$$ 554.921i 0.746865i 0.927657 + 0.373432i $$0.121819\pi$$
−0.927657 + 0.373432i $$0.878181\pi$$
$$744$$ −73.8060 127.836i −0.0992016 0.171822i
$$745$$ 0 0
$$746$$ 90.1544 156.152i 0.120850 0.209319i
$$747$$ 0.626219 + 1.08464i 0.000838312 + 0.00145200i
$$748$$ 728.776 0.974300
$$749$$ −863.246 624.286i −1.15253 0.833492i
$$750$$ 0 0
$$751$$ −363.974 630.421i −0.484652 0.839442i 0.515192 0.857075i $$-0.327721\pi$$
−0.999845 + 0.0176322i $$0.994387\pi$$
$$752$$ 56.1252 97.2117i 0.0746345 0.129271i
$$753$$ −44.5966 25.7479i −0.0592252 0.0341937i
$$754$$ −227.577 + 131.391i −0.301826 + 0.174259i
$$755$$ 0 0
$$756$$ −72.3642 7.44476i −0.0957198 0.00984756i
$$757$$ 667.167i 0.881330i −0.897672 0.440665i $$-0.854743\pi$$
0.897672 0.440665i $$-0.145257\pi$$
$$758$$ −391.667 + 226.129i −0.516711 + 0.298323i
$$759$$ 754.765 + 435.764i 0.994421 + 0.574129i
$$760$$ 0 0
$$761$$ −630.061 + 363.766i −0.827938 + 0.478010i −0.853146 0.521672i $$-0.825309\pi$$
0.0252080 + 0.999682i $$0.491975\pi$$
$$762$$ 216.969 0.284736
$$763$$ 450.908 + 46.3890i 0.590967 + 0.0607981i
$$764$$ −390.329 −0.510901
$$765$$ 0 0
$$766$$ 500.850 + 289.166i 0.653851 + 0.377501i
$$767$$ 303.506 + 175.229i 0.395705 + 0.228460i
$$768$$ 13.8564 + 24.0000i 0.0180422 + 0.0312500i
$$769$$ 1374.28i 1.78709i −0.448969 0.893547i $$-0.648209\pi$$
0.448969 0.893547i $$-0.351791\pi$$
$$770$$ 0 0
$$771$$ −764.913 −0.992106
$$772$$ −604.070 + 348.760i −0.782474 + 0.451761i
$$773$$ −46.3356 + 80.2556i −0.0599425 + 0.103824i −0.894439 0.447189i $$-0.852425\pi$$
0.834497 + 0.551013i $$0.185758\pi$$
$$774$$ 136.638 236.663i 0.176534 0.305767i
$$775$$ 0 0
$$776$$ 209.938i 0.270539i
$$777$$ 517.514 231.779i 0.666042 0.298300i
$$778$$ 547.517i 0.703749i
$$779$$ −387.940 671.932i −0.497998 0.862558i
$$780$$ 0 0
$$781$$ 1075.90 1863.51i 1.37759 2.38606i
$$782$$ −324.936 562.805i −0.415519 0.719700i
$$783$$ −276.032