# Properties

 Label 117.4.q.a.10.1 Level $117$ Weight $4$ Character 117.10 Analytic conductor $6.903$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$117 = 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 117.q (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.90322347067$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 13) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 10.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 117.10 Dual form 117.4.q.a.82.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 + 0.866025i) q^{2} +(-2.50000 + 4.33013i) q^{4} -1.73205i q^{5} +(-12.0000 - 6.92820i) q^{7} -22.5167i q^{8} +O(q^{10})$$ $$q+(-1.50000 + 0.866025i) q^{2} +(-2.50000 + 4.33013i) q^{4} -1.73205i q^{5} +(-12.0000 - 6.92820i) q^{7} -22.5167i q^{8} +(1.50000 + 2.59808i) q^{10} +(-12.0000 + 6.92820i) q^{11} +(45.5000 - 11.2583i) q^{13} +24.0000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(58.5000 - 101.325i) q^{17} +(-99.0000 - 57.1577i) q^{19} +(7.50000 + 4.33013i) q^{20} +(12.0000 - 20.7846i) q^{22} +(-39.0000 - 67.5500i) q^{23} +122.000 q^{25} +(-58.5000 + 56.2917i) q^{26} +(60.0000 - 34.6410i) q^{28} +(-70.5000 - 122.110i) q^{29} -155.885i q^{31} +(157.500 + 90.9327i) q^{32} +202.650i q^{34} +(-12.0000 + 20.7846i) q^{35} +(-124.500 + 71.8801i) q^{37} +198.000 q^{38} -39.0000 q^{40} +(-235.500 + 135.966i) q^{41} +(-52.0000 + 90.0666i) q^{43} -69.2820i q^{44} +(117.000 + 67.5500i) q^{46} +301.377i q^{47} +(-75.5000 - 130.770i) q^{49} +(-183.000 + 105.655i) q^{50} +(-65.0000 + 225.167i) q^{52} -93.0000 q^{53} +(12.0000 + 20.7846i) q^{55} +(-156.000 + 270.200i) q^{56} +(211.500 + 122.110i) q^{58} +(246.000 + 142.028i) q^{59} +(-72.5000 + 125.574i) q^{61} +(135.000 + 233.827i) q^{62} -307.000 q^{64} +(-19.5000 - 78.8083i) q^{65} +(-681.000 + 393.176i) q^{67} +(292.500 + 506.625i) q^{68} -41.5692i q^{70} +(-915.000 - 528.275i) q^{71} -458.993i q^{73} +(124.500 - 215.640i) q^{74} +(495.000 - 285.788i) q^{76} +192.000 q^{77} +1276.00 q^{79} +(-1.50000 + 0.866025i) q^{80} +(235.500 - 407.898i) q^{82} -789.815i q^{83} +(-175.500 - 101.325i) q^{85} -180.133i q^{86} +(156.000 + 270.200i) q^{88} +(846.000 - 488.438i) q^{89} +(-624.000 - 180.133i) q^{91} +390.000 q^{92} +(-261.000 - 452.065i) q^{94} +(-99.0000 + 171.473i) q^{95} +(174.000 + 100.459i) q^{97} +(226.500 + 130.770i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 3 q^{2} - 5 q^{4} - 24 q^{7}+O(q^{10})$$ 2 * q - 3 * q^2 - 5 * q^4 - 24 * q^7 $$2 q - 3 q^{2} - 5 q^{4} - 24 q^{7} + 3 q^{10} - 24 q^{11} + 91 q^{13} + 48 q^{14} - q^{16} + 117 q^{17} - 198 q^{19} + 15 q^{20} + 24 q^{22} - 78 q^{23} + 244 q^{25} - 117 q^{26} + 120 q^{28} - 141 q^{29} + 315 q^{32} - 24 q^{35} - 249 q^{37} + 396 q^{38} - 78 q^{40} - 471 q^{41} - 104 q^{43} + 234 q^{46} - 151 q^{49} - 366 q^{50} - 130 q^{52} - 186 q^{53} + 24 q^{55} - 312 q^{56} + 423 q^{58} + 492 q^{59} - 145 q^{61} + 270 q^{62} - 614 q^{64} - 39 q^{65} - 1362 q^{67} + 585 q^{68} - 1830 q^{71} + 249 q^{74} + 990 q^{76} + 384 q^{77} + 2552 q^{79} - 3 q^{80} + 471 q^{82} - 351 q^{85} + 312 q^{88} + 1692 q^{89} - 1248 q^{91} + 780 q^{92} - 522 q^{94} - 198 q^{95} + 348 q^{97} + 453 q^{98}+O(q^{100})$$ 2 * q - 3 * q^2 - 5 * q^4 - 24 * q^7 + 3 * q^10 - 24 * q^11 + 91 * q^13 + 48 * q^14 - q^16 + 117 * q^17 - 198 * q^19 + 15 * q^20 + 24 * q^22 - 78 * q^23 + 244 * q^25 - 117 * q^26 + 120 * q^28 - 141 * q^29 + 315 * q^32 - 24 * q^35 - 249 * q^37 + 396 * q^38 - 78 * q^40 - 471 * q^41 - 104 * q^43 + 234 * q^46 - 151 * q^49 - 366 * q^50 - 130 * q^52 - 186 * q^53 + 24 * q^55 - 312 * q^56 + 423 * q^58 + 492 * q^59 - 145 * q^61 + 270 * q^62 - 614 * q^64 - 39 * q^65 - 1362 * q^67 + 585 * q^68 - 1830 * q^71 + 249 * q^74 + 990 * q^76 + 384 * q^77 + 2552 * q^79 - 3 * q^80 + 471 * q^82 - 351 * q^85 + 312 * q^88 + 1692 * q^89 - 1248 * q^91 + 780 * q^92 - 522 * q^94 - 198 * q^95 + 348 * q^97 + 453 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$$.

 $$n$$ $$28$$ $$92$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.50000 + 0.866025i −0.530330 + 0.306186i −0.741151 0.671339i $$-0.765720\pi$$
0.210821 + 0.977525i $$0.432386\pi$$
$$3$$ 0 0
$$4$$ −2.50000 + 4.33013i −0.312500 + 0.541266i
$$5$$ 1.73205i 0.154919i −0.996995 0.0774597i $$-0.975319\pi$$
0.996995 0.0774597i $$-0.0246809\pi$$
$$6$$ 0 0
$$7$$ −12.0000 6.92820i −0.647939 0.374088i 0.139727 0.990190i $$-0.455377\pi$$
−0.787666 + 0.616102i $$0.788711\pi$$
$$8$$ 22.5167i 0.995105i
$$9$$ 0 0
$$10$$ 1.50000 + 2.59808i 0.0474342 + 0.0821584i
$$11$$ −12.0000 + 6.92820i −0.328921 + 0.189903i −0.655362 0.755315i $$-0.727484\pi$$
0.326441 + 0.945218i $$0.394151\pi$$
$$12$$ 0 0
$$13$$ 45.5000 11.2583i 0.970725 0.240192i
$$14$$ 24.0000 0.458162
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.00781250 0.0135316i
$$17$$ 58.5000 101.325i 0.834608 1.44558i −0.0597414 0.998214i $$-0.519028\pi$$
0.894349 0.447369i $$-0.147639\pi$$
$$18$$ 0 0
$$19$$ −99.0000 57.1577i −1.19538 0.690151i −0.235856 0.971788i $$-0.575789\pi$$
−0.959521 + 0.281637i $$0.909123\pi$$
$$20$$ 7.50000 + 4.33013i 0.0838525 + 0.0484123i
$$21$$ 0 0
$$22$$ 12.0000 20.7846i 0.116291 0.201422i
$$23$$ −39.0000 67.5500i −0.353568 0.612398i 0.633304 0.773903i $$-0.281698\pi$$
−0.986872 + 0.161506i $$0.948365\pi$$
$$24$$ 0 0
$$25$$ 122.000 0.976000
$$26$$ −58.5000 + 56.2917i −0.441261 + 0.424604i
$$27$$ 0 0
$$28$$ 60.0000 34.6410i 0.404962 0.233805i
$$29$$ −70.5000 122.110i −0.451432 0.781903i 0.547043 0.837104i $$-0.315753\pi$$
−0.998475 + 0.0552014i $$0.982420\pi$$
$$30$$ 0 0
$$31$$ 155.885i 0.903151i −0.892233 0.451576i $$-0.850862\pi$$
0.892233 0.451576i $$-0.149138\pi$$
$$32$$ 157.500 + 90.9327i 0.870073 + 0.502337i
$$33$$ 0 0
$$34$$ 202.650i 1.02218i
$$35$$ −12.0000 + 20.7846i −0.0579534 + 0.100378i
$$36$$ 0 0
$$37$$ −124.500 + 71.8801i −0.553180 + 0.319379i −0.750404 0.660980i $$-0.770141\pi$$
0.197223 + 0.980359i $$0.436808\pi$$
$$38$$ 198.000 0.845259
$$39$$ 0 0
$$40$$ −39.0000 −0.154161
$$41$$ −235.500 + 135.966i −0.897047 + 0.517910i −0.876241 0.481873i $$-0.839957\pi$$
−0.0208059 + 0.999784i $$0.506623\pi$$
$$42$$ 0 0
$$43$$ −52.0000 + 90.0666i −0.184417 + 0.319419i −0.943380 0.331714i $$-0.892373\pi$$
0.758963 + 0.651134i $$0.225706\pi$$
$$44$$ 69.2820i 0.237379i
$$45$$ 0 0
$$46$$ 117.000 + 67.5500i 0.375015 + 0.216515i
$$47$$ 301.377i 0.935326i 0.883907 + 0.467663i $$0.154904\pi$$
−0.883907 + 0.467663i $$0.845096\pi$$
$$48$$ 0 0
$$49$$ −75.5000 130.770i −0.220117 0.381253i
$$50$$ −183.000 + 105.655i −0.517602 + 0.298838i
$$51$$ 0 0
$$52$$ −65.0000 + 225.167i −0.173344 + 0.600481i
$$53$$ −93.0000 −0.241029 −0.120514 0.992712i $$-0.538454\pi$$
−0.120514 + 0.992712i $$0.538454\pi$$
$$54$$ 0 0
$$55$$ 12.0000 + 20.7846i 0.0294196 + 0.0509563i
$$56$$ −156.000 + 270.200i −0.372257 + 0.644768i
$$57$$ 0 0
$$58$$ 211.500 + 122.110i 0.478816 + 0.276444i
$$59$$ 246.000 + 142.028i 0.542822 + 0.313398i 0.746222 0.665698i $$-0.231866\pi$$
−0.203400 + 0.979096i $$0.565199\pi$$
$$60$$ 0 0
$$61$$ −72.5000 + 125.574i −0.152175 + 0.263575i −0.932027 0.362389i $$-0.881961\pi$$
0.779852 + 0.625964i $$0.215294\pi$$
$$62$$ 135.000 + 233.827i 0.276533 + 0.478968i
$$63$$ 0 0
$$64$$ −307.000 −0.599609
$$65$$ −19.5000 78.8083i −0.0372104 0.150384i
$$66$$ 0 0
$$67$$ −681.000 + 393.176i −1.24175 + 0.716926i −0.969451 0.245286i $$-0.921118\pi$$
−0.272301 + 0.962212i $$0.587785\pi$$
$$68$$ 292.500 + 506.625i 0.521630 + 0.903490i
$$69$$ 0 0
$$70$$ 41.5692i 0.0709782i
$$71$$ −915.000 528.275i −1.52944 0.883025i −0.999385 0.0350641i $$-0.988836\pi$$
−0.530059 0.847961i $$-0.677830\pi$$
$$72$$ 0 0
$$73$$ 458.993i 0.735906i −0.929844 0.367953i $$-0.880059\pi$$
0.929844 0.367953i $$-0.119941\pi$$
$$74$$ 124.500 215.640i 0.195579 0.338752i
$$75$$ 0 0
$$76$$ 495.000 285.788i 0.747110 0.431344i
$$77$$ 192.000 0.284161
$$78$$ 0 0
$$79$$ 1276.00 1.81723 0.908615 0.417634i $$-0.137141\pi$$
0.908615 + 0.417634i $$0.137141\pi$$
$$80$$ −1.50000 + 0.866025i −0.00209631 + 0.00121031i
$$81$$ 0 0
$$82$$ 235.500 407.898i 0.317154 0.549327i
$$83$$ 789.815i 1.04450i −0.852793 0.522250i $$-0.825093\pi$$
0.852793 0.522250i $$-0.174907\pi$$
$$84$$ 0 0
$$85$$ −175.500 101.325i −0.223949 0.129297i
$$86$$ 180.133i 0.225864i
$$87$$ 0 0
$$88$$ 156.000 + 270.200i 0.188973 + 0.327311i
$$89$$ 846.000 488.438i 1.00759 0.581734i 0.0971073 0.995274i $$-0.469041\pi$$
0.910486 + 0.413540i $$0.135708\pi$$
$$90$$ 0 0
$$91$$ −624.000 180.133i −0.718824 0.207507i
$$92$$ 390.000 0.441960
$$93$$ 0 0
$$94$$ −261.000 452.065i −0.286384 0.496032i
$$95$$ −99.0000 + 171.473i −0.106918 + 0.185187i
$$96$$ 0 0
$$97$$ 174.000 + 100.459i 0.182134 + 0.105155i 0.588295 0.808646i $$-0.299799\pi$$
−0.406161 + 0.913802i $$0.633133\pi$$
$$98$$ 226.500 + 130.770i 0.233469 + 0.134793i
$$99$$ 0 0
$$100$$ −305.000 + 528.275i −0.305000 + 0.528275i
$$101$$ 214.500 + 371.525i 0.211322 + 0.366021i 0.952129 0.305698i $$-0.0988897\pi$$
−0.740806 + 0.671719i $$0.765556\pi$$
$$102$$ 0 0
$$103$$ 182.000 0.174107 0.0870534 0.996204i $$-0.472255\pi$$
0.0870534 + 0.996204i $$0.472255\pi$$
$$104$$ −253.500 1024.51i −0.239017 0.965974i
$$105$$ 0 0
$$106$$ 139.500 80.5404i 0.127825 0.0737997i
$$107$$ −753.000 1304.23i −0.680330 1.17837i −0.974880 0.222729i $$-0.928503\pi$$
0.294551 0.955636i $$-0.404830\pi$$
$$108$$ 0 0
$$109$$ 1551.92i 1.36373i −0.731477 0.681866i $$-0.761169\pi$$
0.731477 0.681866i $$-0.238831\pi$$
$$110$$ −36.0000 20.7846i −0.0312042 0.0180158i
$$111$$ 0 0
$$112$$ 13.8564i 0.0116902i
$$113$$ −343.500 + 594.959i −0.285962 + 0.495302i −0.972842 0.231470i $$-0.925647\pi$$
0.686880 + 0.726771i $$0.258980\pi$$
$$114$$ 0 0
$$115$$ −117.000 + 67.5500i −0.0948722 + 0.0547745i
$$116$$ 705.000 0.564290
$$117$$ 0 0
$$118$$ −492.000 −0.383833
$$119$$ −1404.00 + 810.600i −1.08155 + 0.624433i
$$120$$ 0 0
$$121$$ −569.500 + 986.403i −0.427874 + 0.741099i
$$122$$ 251.147i 0.186376i
$$123$$ 0 0
$$124$$ 675.000 + 389.711i 0.488845 + 0.282235i
$$125$$ 427.817i 0.306121i
$$126$$ 0 0
$$127$$ −143.000 247.683i −0.0999149 0.173058i 0.811734 0.584027i $$-0.198524\pi$$
−0.911649 + 0.410969i $$0.865190\pi$$
$$128$$ −799.500 + 461.592i −0.552082 + 0.318745i
$$129$$ 0 0
$$130$$ 97.5000 + 101.325i 0.0657794 + 0.0683599i
$$131$$ 1974.00 1.31656 0.658279 0.752774i $$-0.271285\pi$$
0.658279 + 0.752774i $$0.271285\pi$$
$$132$$ 0 0
$$133$$ 792.000 + 1371.78i 0.516354 + 0.894352i
$$134$$ 681.000 1179.53i 0.439026 0.760415i
$$135$$ 0 0
$$136$$ −2281.50 1317.22i −1.43851 0.830523i
$$137$$ 733.500 + 423.486i 0.457424 + 0.264094i 0.710961 0.703232i $$-0.248260\pi$$
−0.253536 + 0.967326i $$0.581594\pi$$
$$138$$ 0 0
$$139$$ −118.000 + 204.382i −0.0720045 + 0.124716i −0.899780 0.436344i $$-0.856273\pi$$
0.827775 + 0.561060i $$0.189606\pi$$
$$140$$ −60.0000 103.923i −0.0362209 0.0627364i
$$141$$ 0 0
$$142$$ 1830.00 1.08148
$$143$$ −468.000 + 450.333i −0.273679 + 0.263348i
$$144$$ 0 0
$$145$$ −211.500 + 122.110i −0.121132 + 0.0699355i
$$146$$ 397.500 + 688.490i 0.225324 + 0.390273i
$$147$$ 0 0
$$148$$ 718.801i 0.399224i
$$149$$ 40.5000 + 23.3827i 0.0222677 + 0.0128563i 0.511093 0.859526i $$-0.329241\pi$$
−0.488825 + 0.872382i $$0.662574\pi$$
$$150$$ 0 0
$$151$$ 1770.16i 0.953995i 0.878905 + 0.476998i $$0.158275\pi$$
−0.878905 + 0.476998i $$0.841725\pi$$
$$152$$ −1287.00 + 2229.15i −0.686773 + 1.18953i
$$153$$ 0 0
$$154$$ −288.000 + 166.277i −0.150699 + 0.0870063i
$$155$$ −270.000 −0.139916
$$156$$ 0 0
$$157$$ 1211.00 0.615594 0.307797 0.951452i $$-0.400408\pi$$
0.307797 + 0.951452i $$0.400408\pi$$
$$158$$ −1914.00 + 1105.05i −0.963732 + 0.556411i
$$159$$ 0 0
$$160$$ 157.500 272.798i 0.0778217 0.134791i
$$161$$ 1080.80i 0.529062i
$$162$$ 0 0
$$163$$ −870.000 502.295i −0.418059 0.241367i 0.276187 0.961104i $$-0.410929\pi$$
−0.694247 + 0.719737i $$0.744262\pi$$
$$164$$ 1359.66i 0.647388i
$$165$$ 0 0
$$166$$ 684.000 + 1184.72i 0.319811 + 0.553930i
$$167$$ −792.000 + 457.261i −0.366987 + 0.211880i −0.672141 0.740423i $$-0.734625\pi$$
0.305154 + 0.952303i $$0.401292\pi$$
$$168$$ 0 0
$$169$$ 1943.50 1024.51i 0.884615 0.466321i
$$170$$ 351.000 0.158356
$$171$$ 0 0
$$172$$ −260.000 450.333i −0.115261 0.199637i
$$173$$ 1287.00 2229.15i 0.565600 0.979648i −0.431394 0.902164i $$-0.641978\pi$$
0.996994 0.0774841i $$-0.0246887\pi$$
$$174$$ 0 0
$$175$$ −1464.00 845.241i −0.632389 0.365110i
$$176$$ 12.0000 + 6.92820i 0.00513940 + 0.00296723i
$$177$$ 0 0
$$178$$ −846.000 + 1465.31i −0.356238 + 0.617022i
$$179$$ 1872.00 + 3242.40i 0.781675 + 1.35390i 0.930965 + 0.365108i $$0.118968\pi$$
−0.149290 + 0.988793i $$0.547699\pi$$
$$180$$ 0 0
$$181$$ −637.000 −0.261590 −0.130795 0.991409i $$-0.541753\pi$$
−0.130795 + 0.991409i $$0.541753\pi$$
$$182$$ 1092.00 270.200i 0.444750 0.110047i
$$183$$ 0 0
$$184$$ −1521.00 + 878.150i −0.609400 + 0.351837i
$$185$$ 124.500 + 215.640i 0.0494780 + 0.0856983i
$$186$$ 0 0
$$187$$ 1621.20i 0.633978i
$$188$$ −1305.00 753.442i −0.506260 0.292289i
$$189$$ 0 0
$$190$$ 342.946i 0.130947i
$$191$$ −1299.00 + 2249.93i −0.492106 + 0.852353i −0.999959 0.00909077i $$-0.997106\pi$$
0.507852 + 0.861444i $$0.330440\pi$$
$$192$$ 0 0
$$193$$ 967.500 558.586i 0.360840 0.208331i −0.308609 0.951189i $$-0.599863\pi$$
0.669449 + 0.742858i $$0.266530\pi$$
$$194$$ −348.000 −0.128788
$$195$$ 0 0
$$196$$ 755.000 0.275146
$$197$$ −1776.00 + 1025.37i −0.642308 + 0.370837i −0.785503 0.618858i $$-0.787596\pi$$
0.143195 + 0.989695i $$0.454262\pi$$
$$198$$ 0 0
$$199$$ 1261.00 2184.12i 0.449196 0.778030i −0.549138 0.835732i $$-0.685044\pi$$
0.998334 + 0.0577019i $$0.0183773\pi$$
$$200$$ 2747.03i 0.971223i
$$201$$ 0 0
$$202$$ −643.500 371.525i −0.224141 0.129408i
$$203$$ 1953.75i 0.675500i
$$204$$ 0 0
$$205$$ 235.500 + 407.898i 0.0802343 + 0.138970i
$$206$$ −273.000 + 157.617i −0.0923340 + 0.0533091i
$$207$$ 0 0
$$208$$ −32.5000 33.7750i −0.0108340 0.0112590i
$$209$$ 1584.00 0.524247
$$210$$ 0 0
$$211$$ −521.000 902.398i −0.169986 0.294425i 0.768428 0.639936i $$-0.221039\pi$$
−0.938415 + 0.345511i $$0.887706\pi$$
$$212$$ 232.500 402.702i 0.0753215 0.130461i
$$213$$ 0 0
$$214$$ 2259.00 + 1304.23i 0.721598 + 0.416615i
$$215$$ 156.000 + 90.0666i 0.0494842 + 0.0285697i
$$216$$ 0 0
$$217$$ −1080.00 + 1870.61i −0.337858 + 0.585187i
$$218$$ 1344.00 + 2327.88i 0.417556 + 0.723228i
$$219$$ 0 0
$$220$$ −120.000 −0.0367745
$$221$$ 1521.00 5268.90i 0.462957 1.60373i
$$222$$ 0 0
$$223$$ −2085.00 + 1203.78i −0.626107 + 0.361483i −0.779243 0.626722i $$-0.784396\pi$$
0.153136 + 0.988205i $$0.451063\pi$$
$$224$$ −1260.00 2182.38i −0.375836 0.650967i
$$225$$ 0 0
$$226$$ 1189.92i 0.350231i
$$227$$ −2085.00 1203.78i −0.609631 0.351971i 0.163190 0.986595i $$-0.447822\pi$$
−0.772821 + 0.634624i $$0.781155\pi$$
$$228$$ 0 0
$$229$$ 2508.01i 0.723729i −0.932231 0.361864i $$-0.882140\pi$$
0.932231 0.361864i $$-0.117860\pi$$
$$230$$ 117.000 202.650i 0.0335424 0.0580971i
$$231$$ 0 0
$$232$$ −2749.50 + 1587.42i −0.778076 + 0.449222i
$$233$$ 5850.00 1.64483 0.822417 0.568885i $$-0.192625\pi$$
0.822417 + 0.568885i $$0.192625\pi$$
$$234$$ 0 0
$$235$$ 522.000 0.144900
$$236$$ −1230.00 + 710.141i −0.339263 + 0.195874i
$$237$$ 0 0
$$238$$ 1404.00 2431.80i 0.382386 0.662312i
$$239$$ 5383.21i 1.45695i −0.685072 0.728475i $$-0.740229\pi$$
0.685072 0.728475i $$-0.259771\pi$$
$$240$$ 0 0
$$241$$ 4258.50 + 2458.65i 1.13823 + 0.657159i 0.945992 0.324189i $$-0.105091\pi$$
0.192240 + 0.981348i $$0.438425\pi$$
$$242$$ 1972.81i 0.524036i
$$243$$ 0 0
$$244$$ −362.500 627.868i −0.0951094 0.164734i
$$245$$ −226.500 + 130.770i −0.0590635 + 0.0341003i
$$246$$ 0 0
$$247$$ −5148.00 1486.10i −1.32615 0.382827i
$$248$$ −3510.00 −0.898731
$$249$$ 0 0
$$250$$ 370.500 + 641.725i 0.0937299 + 0.162345i
$$251$$ −1989.00 + 3445.05i −0.500178 + 0.866333i 0.499822 + 0.866128i $$0.333399\pi$$
−1.00000 0.000205037i $$0.999935\pi$$
$$252$$ 0 0
$$253$$ 936.000 + 540.400i 0.232592 + 0.134287i
$$254$$ 429.000 + 247.683i 0.105976 + 0.0611852i
$$255$$ 0 0
$$256$$ 2027.50 3511.73i 0.494995 0.857357i
$$257$$ 1033.50 + 1790.07i 0.250848 + 0.434482i 0.963760 0.266772i $$-0.0859572\pi$$
−0.712911 + 0.701254i $$0.752624\pi$$
$$258$$ 0 0
$$259$$ 1992.00 0.477903
$$260$$ 390.000 + 112.583i 0.0930261 + 0.0268543i
$$261$$ 0 0
$$262$$ −2961.00 + 1709.53i −0.698211 + 0.403112i
$$263$$ −1026.00 1777.08i −0.240555 0.416653i 0.720318 0.693644i $$-0.243996\pi$$
−0.960872 + 0.276991i $$0.910663\pi$$
$$264$$ 0 0
$$265$$ 161.081i 0.0373400i
$$266$$ −2376.00 1371.78i −0.547676 0.316201i
$$267$$ 0 0
$$268$$ 3931.76i 0.896157i
$$269$$ 1665.00 2883.86i 0.377386 0.653652i −0.613295 0.789854i $$-0.710156\pi$$
0.990681 + 0.136202i $$0.0434897\pi$$
$$270$$ 0 0
$$271$$ 2430.00 1402.96i 0.544694 0.314479i −0.202285 0.979327i $$-0.564837\pi$$
0.746979 + 0.664848i $$0.231504\pi$$
$$272$$ −117.000 −0.0260815
$$273$$ 0 0
$$274$$ −1467.00 −0.323448
$$275$$ −1464.00 + 845.241i −0.321027 + 0.185345i
$$276$$ 0 0
$$277$$ −188.500 + 326.492i −0.0408876 + 0.0708194i −0.885745 0.464172i $$-0.846352\pi$$
0.844857 + 0.534992i $$0.179685\pi$$
$$278$$ 408.764i 0.0881872i
$$279$$ 0 0
$$280$$ 468.000 + 270.200i 0.0998870 + 0.0576698i
$$281$$ 36.3731i 0.00772183i −0.999993 0.00386092i $$-0.998771\pi$$
0.999993 0.00386092i $$-0.00122897\pi$$
$$282$$ 0 0
$$283$$ 3562.00 + 6169.56i 0.748194 + 1.29591i 0.948688 + 0.316215i $$0.102412\pi$$
−0.200493 + 0.979695i $$0.564255\pi$$
$$284$$ 4575.00 2641.38i 0.955902 0.551891i
$$285$$ 0 0
$$286$$ 312.000 1080.80i 0.0645068 0.223458i
$$287$$ 3768.00 0.774976
$$288$$ 0 0
$$289$$ −4388.00 7600.24i −0.893141 1.54696i
$$290$$ 211.500 366.329i 0.0428266 0.0741778i
$$291$$ 0 0
$$292$$ 1987.50 + 1147.48i 0.398321 + 0.229971i
$$293$$ 7207.50 + 4161.25i 1.43709 + 0.829703i 0.997646 0.0685685i $$-0.0218432\pi$$
0.439441 + 0.898271i $$0.355177\pi$$
$$294$$ 0 0
$$295$$ 246.000 426.084i 0.0485514 0.0840936i
$$296$$ 1618.50 + 2803.32i 0.317816 + 0.550473i
$$297$$ 0 0
$$298$$ −81.0000 −0.0157457
$$299$$ −2535.00 2634.45i −0.490310 0.509546i
$$300$$ 0 0
$$301$$ 1248.00 720.533i 0.238982 0.137976i
$$302$$ −1533.00 2655.23i −0.292100 0.505932i
$$303$$ 0 0
$$304$$ 114.315i 0.0215672i
$$305$$ 217.500 + 125.574i 0.0408328 + 0.0235748i
$$306$$ 0 0
$$307$$ 2220.49i 0.412801i 0.978468 + 0.206401i $$0.0661750\pi$$
−0.978468 + 0.206401i $$0.933825\pi$$
$$308$$ −480.000 + 831.384i −0.0888004 + 0.153807i
$$309$$ 0 0
$$310$$ 405.000 233.827i 0.0742015 0.0428402i
$$311$$ −4914.00 −0.895972 −0.447986 0.894041i $$-0.647859\pi$$
−0.447986 + 0.894041i $$0.647859\pi$$
$$312$$ 0 0
$$313$$ −518.000 −0.0935434 −0.0467717 0.998906i $$-0.514893\pi$$
−0.0467717 + 0.998906i $$0.514893\pi$$
$$314$$ −1816.50 + 1048.76i −0.326468 + 0.188487i
$$315$$ 0 0
$$316$$ −3190.00 + 5525.24i −0.567885 + 0.983605i
$$317$$ 3916.17i 0.693861i 0.937891 + 0.346930i $$0.112776\pi$$
−0.937891 + 0.346930i $$0.887224\pi$$
$$318$$ 0 0
$$319$$ 1692.00 + 976.877i 0.296971 + 0.171456i
$$320$$ 531.740i 0.0928911i
$$321$$ 0 0
$$322$$ −936.000 1621.20i −0.161991 0.280577i
$$323$$ −11583.0 + 6687.45i −1.99534 + 1.15201i
$$324$$ 0 0
$$325$$ 5551.00 1373.52i 0.947428 0.234428i
$$326$$ 1740.00 0.295613
$$327$$ 0 0
$$328$$ 3061.50 + 5302.67i 0.515375 + 0.892656i
$$329$$ 2088.00 3616.52i 0.349894 0.606034i
$$330$$ 0 0
$$331$$ −6456.00 3727.37i −1.07207 0.618958i −0.143321 0.989676i $$-0.545778\pi$$
−0.928745 + 0.370719i $$0.879111\pi$$
$$332$$ 3420.00 + 1974.54i 0.565352 + 0.326406i
$$333$$ 0 0
$$334$$ 792.000 1371.78i 0.129749 0.224733i
$$335$$ 681.000 + 1179.53i 0.111066 + 0.192371i
$$336$$ 0 0
$$337$$ −3575.00 −0.577871 −0.288936 0.957349i $$-0.593301\pi$$
−0.288936 + 0.957349i $$0.593301\pi$$
$$338$$ −2028.00 + 3219.88i −0.326357 + 0.518161i
$$339$$ 0 0
$$340$$ 877.500 506.625i 0.139968 0.0808106i
$$341$$ 1080.00 + 1870.61i 0.171511 + 0.297066i
$$342$$ 0 0
$$343$$ 6845.06i 1.07755i
$$344$$ 2028.00 + 1170.87i 0.317856 + 0.183514i
$$345$$ 0 0
$$346$$ 4458.30i 0.692716i
$$347$$ −3483.00 + 6032.73i −0.538839 + 0.933297i 0.460128 + 0.887853i $$0.347804\pi$$
−0.998967 + 0.0454442i $$0.985530\pi$$
$$348$$ 0 0
$$349$$ −5760.00 + 3325.54i −0.883455 + 0.510063i −0.871796 0.489869i $$-0.837045\pi$$
−0.0116588 + 0.999932i $$0.503711\pi$$
$$350$$ 2928.00 0.447166
$$351$$ 0 0
$$352$$ −2520.00 −0.381581
$$353$$ −4876.50 + 2815.45i −0.735269 + 0.424508i −0.820347 0.571867i $$-0.806219\pi$$
0.0850777 + 0.996374i $$0.472886\pi$$
$$354$$ 0 0
$$355$$ −915.000 + 1584.83i −0.136798 + 0.236940i
$$356$$ 4884.38i 0.727168i
$$357$$ 0 0
$$358$$ −5616.00 3242.40i −0.829092 0.478676i
$$359$$ 7129.12i 1.04808i −0.851694 0.524040i $$-0.824424\pi$$
0.851694 0.524040i $$-0.175576\pi$$
$$360$$ 0 0
$$361$$ 3104.50 + 5377.15i 0.452617 + 0.783956i
$$362$$ 955.500 551.658i 0.138729 0.0800953i
$$363$$ 0 0
$$364$$ 2340.00 2251.67i 0.336949 0.324229i
$$365$$ −795.000 −0.114006
$$366$$ 0 0
$$367$$ −1.00000 1.73205i −0.000142233 0.000246355i 0.865954 0.500123i $$-0.166712\pi$$
−0.866097 + 0.499877i $$0.833379\pi$$
$$368$$ −39.0000 + 67.5500i −0.00552450 + 0.00956871i
$$369$$ 0 0
$$370$$ −373.500 215.640i −0.0524793 0.0302989i
$$371$$ 1116.00 + 644.323i 0.156172 + 0.0901660i
$$372$$ 0 0
$$373$$ −1749.50 + 3030.22i −0.242857 + 0.420641i −0.961527 0.274711i $$-0.911418\pi$$
0.718670 + 0.695351i $$0.244751\pi$$
$$374$$ −1404.00 2431.80i −0.194115 0.336218i
$$375$$ 0 0
$$376$$ 6786.00 0.930748
$$377$$ −4582.50 4762.27i −0.626023 0.650582i
$$378$$ 0 0
$$379$$ 4779.00 2759.16i 0.647706 0.373953i −0.139871 0.990170i $$-0.544669\pi$$
0.787577 + 0.616216i $$0.211335\pi$$
$$380$$ −495.000 857.365i −0.0668236 0.115742i
$$381$$ 0 0
$$382$$ 4499.87i 0.602705i
$$383$$ 6378.00 + 3682.34i 0.850915 + 0.491276i 0.860960 0.508673i $$-0.169864\pi$$
−0.0100443 + 0.999950i $$0.503197\pi$$
$$384$$ 0 0
$$385$$ 332.554i 0.0440221i
$$386$$ −967.500 + 1675.76i −0.127576 + 0.220969i
$$387$$ 0 0
$$388$$ −870.000 + 502.295i −0.113834 + 0.0657220i
$$389$$ 1209.00 0.157580 0.0787901 0.996891i $$-0.474894\pi$$
0.0787901 + 0.996891i $$0.474894\pi$$
$$390$$ 0 0
$$391$$ −9126.00 −1.18036
$$392$$ −2944.50 + 1700.01i −0.379387 + 0.219039i
$$393$$ 0 0
$$394$$ 1776.00 3076.12i 0.227090 0.393332i
$$395$$ 2210.10i 0.281524i
$$396$$ 0 0
$$397$$ 10128.0 + 5847.40i 1.28038 + 0.739226i 0.976917 0.213618i $$-0.0685248\pi$$
0.303460 + 0.952844i $$0.401858\pi$$
$$398$$ 4368.23i 0.550150i
$$399$$ 0 0
$$400$$ −61.0000 105.655i −0.00762500 0.0132069i
$$401$$ 2581.50 1490.43i 0.321481 0.185607i −0.330571 0.943781i $$-0.607241\pi$$
0.652053 + 0.758174i $$0.273908\pi$$
$$402$$ 0 0
$$403$$ −1755.00 7092.75i −0.216930 0.876712i
$$404$$ −2145.00 −0.264153
$$405$$ 0 0
$$406$$ −1692.00 2930.63i −0.206829 0.358238i
$$407$$ 996.000 1725.12i 0.121302 0.210101i
$$408$$ 0 0
$$409$$ 37.5000 + 21.6506i 0.00453363 + 0.00261749i 0.502265 0.864714i $$-0.332500\pi$$
−0.497731 + 0.867331i $$0.665833\pi$$
$$410$$ −706.500 407.898i −0.0851013 0.0491333i
$$411$$ 0 0
$$412$$ −455.000 + 788.083i −0.0544084 + 0.0942380i
$$413$$ −1968.00 3408.68i −0.234477 0.406126i
$$414$$ 0 0
$$415$$ −1368.00 −0.161813
$$416$$ 8190.00 + 2364.25i 0.965259 + 0.278646i
$$417$$ 0 0
$$418$$ −2376.00 + 1371.78i −0.278024 + 0.160517i
$$419$$ −4731.00 8194.33i −0.551610 0.955416i −0.998159 0.0606569i $$-0.980680\pi$$
0.446549 0.894759i $$-0.352653\pi$$
$$420$$ 0 0
$$421$$ 7068.50i 0.818284i −0.912471 0.409142i $$-0.865828\pi$$
0.912471 0.409142i $$-0.134172\pi$$
$$422$$ 1563.00 + 902.398i 0.180298 + 0.104095i
$$423$$ 0 0
$$424$$ 2094.05i 0.239849i
$$425$$ 7137.00 12361.6i 0.814577 1.41089i
$$426$$ 0 0
$$427$$ 1740.00 1004.59i 0.197200 0.113854i
$$428$$ 7530.00 0.850412
$$429$$ 0 0
$$430$$ −312.000 −0.0349906
$$431$$ 8598.00 4964.06i 0.960907 0.554780i 0.0644552 0.997921i $$-0.479469\pi$$
0.896452 + 0.443140i $$0.146136\pi$$
$$432$$ 0 0
$$433$$ 3308.50 5730.49i 0.367197 0.636004i −0.621929 0.783074i $$-0.713651\pi$$
0.989126 + 0.147070i $$0.0469841\pi$$
$$434$$ 3741.23i 0.413790i
$$435$$ 0 0
$$436$$ 6720.00 + 3879.79i 0.738141 + 0.426166i
$$437$$ 8916.60i 0.976061i
$$438$$ 0 0
$$439$$ −6994.00 12114.0i −0.760377 1.31701i −0.942656 0.333765i $$-0.891681\pi$$
0.182280 0.983247i $$-0.441652\pi$$
$$440$$ 468.000 270.200i 0.0507069 0.0292756i
$$441$$ 0 0
$$442$$ 2281.50 + 9220.57i 0.245520 + 0.992258i
$$443$$ −2004.00 −0.214928 −0.107464 0.994209i $$-0.534273\pi$$
−0.107464 + 0.994209i $$0.534273\pi$$
$$444$$ 0 0
$$445$$ −846.000 1465.31i −0.0901219 0.156096i
$$446$$ 2085.00 3611.33i 0.221362 0.383411i
$$447$$ 0 0
$$448$$ 3684.00 + 2126.96i 0.388510 + 0.224307i
$$449$$ −7866.00 4541.44i −0.826769 0.477336i 0.0259758 0.999663i $$-0.491731\pi$$
−0.852745 + 0.522327i $$0.825064\pi$$
$$450$$ 0 0
$$451$$ 1884.00 3263.18i 0.196705 0.340704i
$$452$$ −1717.50 2974.80i −0.178727 0.309563i
$$453$$ 0 0
$$454$$ 4170.00 0.431074
$$455$$ −312.000 + 1080.80i −0.0321468 + 0.111360i
$$456$$ 0 0
$$457$$ 2185.50 1261.80i 0.223705 0.129156i −0.383959 0.923350i $$-0.625440\pi$$
0.607665 + 0.794194i $$0.292106\pi$$
$$458$$ 2172.00 + 3762.01i 0.221596 + 0.383815i
$$459$$ 0 0
$$460$$ 675.500i 0.0684681i
$$461$$ −16963.5 9793.88i −1.71382 0.989472i −0.929270 0.369400i $$-0.879563\pi$$
−0.784545 0.620072i $$-0.787103\pi$$
$$462$$ 0 0
$$463$$ 8632.54i 0.866497i −0.901274 0.433249i $$-0.857367\pi$$
0.901274 0.433249i $$-0.142633\pi$$
$$464$$ −70.5000 + 122.110i −0.00705362 + 0.0122172i
$$465$$ 0 0
$$466$$ −8775.00 + 5066.25i −0.872305 + 0.503625i
$$467$$ −5460.00 −0.541025 −0.270512 0.962716i $$-0.587193\pi$$
−0.270512 + 0.962716i $$0.587193\pi$$
$$468$$ 0 0
$$469$$ 10896.0 1.07277
$$470$$ −783.000 + 452.065i −0.0768449 + 0.0443664i
$$471$$ 0 0
$$472$$ 3198.00 5539.10i 0.311864 0.540165i
$$473$$ 1441.07i 0.140085i
$$474$$ 0 0
$$475$$ −12078.0 6973.24i −1.16669 0.673587i
$$476$$ 8106.00i 0.780542i
$$477$$ 0 0
$$478$$ 4662.00 + 8074.82i 0.446098 + 0.772665i
$$479$$ 2211.00 1276.52i 0.210904 0.121766i −0.390827 0.920464i $$-0.627811\pi$$
0.601732 + 0.798698i $$0.294478\pi$$
$$480$$ 0 0
$$481$$ −4855.50 + 4672.21i −0.460274 + 0.442899i
$$482$$ −8517.00 −0.804852
$$483$$ 0 0
$$484$$ −2847.50 4932.01i −0.267421 0.463187i
$$485$$ 174.000 301.377i 0.0162906 0.0282161i
$$486$$ 0 0
$$487$$ 9378.00 + 5414.39i 0.872603 + 0.503798i 0.868212 0.496193i $$-0.165269\pi$$
0.00439074 + 0.999990i $$0.498602\pi$$
$$488$$ 2827.50 + 1632.46i 0.262285 + 0.151430i
$$489$$ 0 0
$$490$$ 226.500 392.310i 0.0208821 0.0361689i
$$491$$ 5694.00 + 9862.30i 0.523354 + 0.906475i 0.999631 + 0.0271797i $$0.00865264\pi$$
−0.476277 + 0.879295i $$0.658014\pi$$
$$492$$ 0 0
$$493$$ −16497.0 −1.50707
$$494$$ 9009.00 2229.15i 0.820514 0.203025i
$$495$$ 0 0
$$496$$ −135.000 + 77.9423i −0.0122211 + 0.00705587i
$$497$$ 7320.00 + 12678.6i 0.660658 + 1.14429i
$$498$$ 0 0
$$499$$ 17677.3i 1.58586i 0.609311 + 0.792931i $$0.291446\pi$$
−0.609311 + 0.792931i $$0.708554\pi$$
$$500$$ 1852.50 + 1069.54i 0.165693 + 0.0956627i
$$501$$ 0 0
$$502$$ 6890.10i 0.612590i
$$503$$ 1938.00 3356.71i 0.171792 0.297552i −0.767255 0.641343i $$-0.778378\pi$$
0.939046 + 0.343791i $$0.111711\pi$$
$$504$$ 0 0
$$505$$ 643.500 371.525i 0.0567037 0.0327379i
$$506$$ −1872.00 −0.164467
$$507$$ 0 0
$$508$$ 1430.00 0.124894
$$509$$ 14779.5 8532.95i 1.28701 0.743058i 0.308893 0.951097i $$-0.400042\pi$$
0.978120 + 0.208039i $$0.0667082\pi$$
$$510$$ 0 0
$$511$$ −3180.00 + 5507.92i −0.275293 + 0.476822i
$$512$$ 361.999i 0.0312465i
$$513$$ 0 0
$$514$$ −3100.50 1790.07i −0.266065 0.153612i
$$515$$ 315.233i 0.0269725i
$$516$$ 0 0
$$517$$ −2088.00 3616.52i −0.177621 0.307649i
$$518$$ −2988.00 + 1725.12i −0.253446 + 0.146327i
$$519$$ 0 0
$$520$$ −1774.50 + 439.075i −0.149648 + 0.0370283i
$$521$$ −2121.00 −0.178355 −0.0891773 0.996016i $$-0.528424\pi$$
−0.0891773 + 0.996016i $$0.528424\pi$$
$$522$$ 0 0
$$523$$ 5732.00 + 9928.12i 0.479241 + 0.830069i 0.999717 0.0238072i $$-0.00757878\pi$$
−0.520476 + 0.853876i $$0.674245\pi$$
$$524$$ −4935.00 + 8547.67i −0.411425 + 0.712608i
$$525$$ 0 0
$$526$$ 3078.00 + 1777.08i 0.255147 + 0.147309i
$$527$$ −15795.0 9119.25i −1.30558 0.753777i
$$528$$ 0 0
$$529$$ 3041.50 5268.03i 0.249979 0.432977i
$$530$$ −139.500 241.621i −0.0114330 0.0198025i
$$531$$ 0 0
$$532$$ −7920.00 −0.645443
$$533$$ −9184.50 + 8837.79i −0.746388 + 0.718212i
$$534$$ 0 0
$$535$$ −2259.00 + 1304.23i −0.182552 + 0.105396i
$$536$$ 8853.00 + 15333.8i 0.713417 + 1.23567i
$$537$$ 0 0
$$538$$ 5767.73i 0.462202i
$$539$$ 1812.00 + 1046.16i 0.144802 + 0.0836016i
$$540$$ 0 0
$$541$$ 4764.87i 0.378665i 0.981913 + 0.189333i $$0.0606324\pi$$
−0.981913 + 0.189333i $$0.939368\pi$$
$$542$$ −2430.00 + 4208.88i −0.192578 + 0.333555i
$$543$$ 0 0
$$544$$ 18427.5 10639.1i 1.45234 0.838508i
$$545$$ −2688.00 −0.211268
$$546$$ 0 0
$$547$$ 6554.00 0.512301 0.256151 0.966637i $$-0.417546\pi$$
0.256151 + 0.966637i $$0.417546\pi$$
$$548$$ −3667.50 + 2117.43i −0.285890 + 0.165059i
$$549$$ 0 0
$$550$$ 1464.00 2535.72i 0.113500 0.196588i
$$551$$ 16118.5i 1.24622i
$$552$$ 0 0
$$553$$ −15312.0 8840.39i −1.17745 0.679804i
$$554$$ 652.983i 0.0500769i
$$555$$ 0 0
$$556$$ −590.000 1021.91i −0.0450028 0.0779472i
$$557$$ 15685.5 9056.03i 1.19321 0.688898i 0.234174 0.972195i $$-0.424761\pi$$
0.959032 + 0.283297i $$0.0914281\pi$$
$$558$$ 0 0
$$559$$ −1352.00 + 4683.47i −0.102296 + 0.354364i
$$560$$ 24.0000 0.00181104
$$561$$ 0 0
$$562$$ 31.5000 + 54.5596i 0.00236432 + 0.00409512i
$$563$$ −6084.00 + 10537.8i −0.455435 + 0.788837i −0.998713 0.0507160i $$-0.983850\pi$$
0.543278 + 0.839553i $$0.317183\pi$$
$$564$$ 0 0
$$565$$ 1030.50 + 594.959i 0.0767318 + 0.0443011i
$$566$$ −10686.0 6169.56i −0.793580 0.458173i
$$567$$ 0 0
$$568$$ −11895.0 + 20602.7i −0.878703 + 1.52196i
$$569$$ −3861.00 6687.45i −0.284467 0.492711i 0.688013 0.725698i $$-0.258483\pi$$
−0.972480 + 0.232988i $$0.925150\pi$$
$$570$$ 0 0
$$571$$ 11440.0 0.838440 0.419220 0.907885i $$-0.362304\pi$$
0.419220 + 0.907885i $$0.362304\pi$$
$$572$$ −780.000 3152.33i −0.0570165 0.230429i
$$573$$ 0 0
$$574$$ −5652.00 + 3263.18i −0.410993 + 0.237287i
$$575$$ −4758.00 8241.10i −0.345082 0.597700i
$$576$$ 0 0
$$577$$ 15444.7i 1.11433i −0.830400 0.557167i $$-0.811888\pi$$
0.830400 0.557167i $$-0.188112\pi$$
$$578$$ 13164.0 + 7600.24i 0.947319 + 0.546935i
$$579$$ 0 0
$$580$$ 1221.10i 0.0874194i
$$581$$ −5472.00 + 9477.78i −0.390735 + 0.676772i
$$582$$ 0 0
$$583$$ 1116.00 644.323i 0.0792796 0.0457721i
$$584$$ −10335.0 −0.732304
$$585$$ 0 0
$$586$$ −14415.0 −1.01617
$$587$$ 12186.0 7035.59i 0.856848 0.494702i −0.00610719 0.999981i $$-0.501944\pi$$
0.862956 + 0.505280i $$0.168611\pi$$
$$588$$ 0 0
$$589$$ −8910.00 + 15432.6i −0.623311 + 1.07961i
$$590$$ 852.169i 0.0594631i
$$591$$ 0 0
$$592$$ 124.500 + 71.8801i 0.00864344 + 0.00499029i
$$593$$ 26938.6i 1.86549i 0.360538 + 0.932745i $$0.382593\pi$$
−0.360538 + 0.932745i $$0.617407\pi$$
$$594$$ 0 0
$$595$$ 1404.00 + 2431.80i 0.0967368 + 0.167553i
$$596$$ −202.500 + 116.913i −0.0139173 + 0.00803517i
$$597$$ 0 0
$$598$$ 6084.00 + 1756.30i 0.416042 + 0.120101i
$$599$$ 10554.0 0.719908 0.359954 0.932970i $$-0.382792\pi$$
0.359954 + 0.932970i $$0.382792\pi$$
$$600$$ 0 0
$$601$$ 7415.50 + 12844.0i 0.503302 + 0.871745i 0.999993 + 0.00381713i $$0.00121503\pi$$
−0.496691 + 0.867928i $$0.665452\pi$$
$$602$$ −1248.00 + 2161.60i −0.0844928 + 0.146346i
$$603$$ 0 0
$$604$$ −7665.00 4425.39i −0.516365 0.298123i
$$605$$ 1708.50 + 986.403i 0.114811 + 0.0662859i
$$606$$ 0 0
$$607$$ 3977.00 6888.37i 0.265933 0.460610i −0.701874 0.712301i $$-0.747653\pi$$
0.967808 + 0.251691i $$0.0809866\pi$$
$$608$$ −10395.0 18004.7i −0.693377 1.20096i
$$609$$ 0 0
$$610$$ −435.000 −0.0288732
$$611$$ 3393.00 + 13712.6i 0.224658 + 0.907945i
$$612$$ 0 0
$$613$$ 21841.5 12610.2i 1.43910 0.830866i 0.441315 0.897352i $$-0.354512\pi$$
0.997787 + 0.0664859i $$0.0211787\pi$$
$$614$$ −1923.00 3330.73i −0.126394 0.218921i
$$615$$ 0 0
$$616$$ 4323.20i 0.282771i
$$617$$ 15055.5 + 8692.30i 0.982353 + 0.567162i 0.902980 0.429683i $$-0.141375\pi$$
0.0793731 + 0.996845i $$0.474708\pi$$
$$618$$ 0 0
$$619$$ 8209.92i 0.533093i 0.963822 + 0.266547i $$0.0858826\pi$$
−0.963822 + 0.266547i $$0.914117\pi$$
$$620$$ 675.000 1169.13i 0.0437236 0.0757316i
$$621$$ 0 0
$$622$$ 7371.00 4255.65i 0.475161 0.274334i
$$623$$ −13536.0 −0.870479
$$624$$ 0 0
$$625$$ 14509.0 0.928576
$$626$$ 777.000 448.601i 0.0496089 0.0286417i
$$627$$ 0 0
$$628$$ −3027.50 + 5243.78i −0.192373 + 0.333200i
$$629$$ 16819.9i 1.06622i
$$630$$ 0 0
$$631$$ 11142.0 + 6432.84i 0.702941 + 0.405843i 0.808442 0.588576i $$-0.200311\pi$$
−0.105501 + 0.994419i $$0.533645\pi$$
$$632$$ 28731.3i 1.80834i
$$633$$ 0 0
$$634$$ −3391.50 5874.25i −0.212451 0.367975i
$$635$$ −429.000 + 247.683i −0.0268100 + 0.0154788i
$$636$$ 0 0
$$637$$ −4907.50 5100.02i −0.305247 0.317222i
$$638$$ −3384.00 −0.209990
$$639$$ 0 0
$$640$$ 799.500 + 1384.77i 0.0493797 + 0.0855282i
$$641$$ 3100.50 5370.22i 0.191049 0.330907i −0.754549 0.656244i $$-0.772144\pi$$
0.945598 + 0.325337i $$0.105478\pi$$
$$642$$ 0 0
$$643$$ −14568.0 8410.84i −0.893477 0.515849i −0.0183989 0.999831i $$-0.505857\pi$$
−0.875078 + 0.483981i $$0.839190\pi$$
$$644$$ −4680.00 2702.00i −0.286363 0.165332i
$$645$$ 0 0
$$646$$ 11583.0 20062.3i 0.705460 1.22189i
$$647$$ −6747.00 11686.1i −0.409972 0.710092i 0.584914 0.811095i $$-0.301128\pi$$
−0.994886 + 0.101003i $$0.967795\pi$$
$$648$$ 0 0
$$649$$ −3936.00 −0.238061
$$650$$ −7137.00 + 6867.58i −0.430671 + 0.414413i
$$651$$ 0 0
$$652$$ 4350.00 2511.47i 0.261287 0.150854i
$$653$$ −5667.00 9815.53i −0.339612 0.588226i 0.644747 0.764396i $$-0.276963\pi$$
−0.984360 + 0.176170i $$0.943629\pi$$
$$654$$ 0 0
$$655$$ 3419.07i 0.203960i
$$656$$ 235.500 + 135.966i 0.0140164 + 0.00809235i
$$657$$ 0 0
$$658$$ 7233.04i 0.428531i
$$659$$ 6618.00 11462.7i 0.391200 0.677578i −0.601408 0.798942i $$-0.705393\pi$$
0.992608 + 0.121364i $$0.0387268\pi$$
$$660$$ 0 0
$$661$$ −10264.5 + 5926.21i −0.603998 + 0.348718i −0.770613 0.637304i $$-0.780050\pi$$
0.166615 + 0.986022i $$0.446716\pi$$
$$662$$ 12912.0 0.758065
$$663$$ 0 0
$$664$$ −17784.0 −1.03939
$$665$$ 2376.00 1371.78i 0.138552 0.0799932i
$$666$$ 0 0
$$667$$ −5499.00 + 9524.55i −0.319224 + 0.552911i
$$668$$ 4572.61i 0.264850i
$$669$$ 0 0
$$670$$ −2043.00 1179.53i −0.117803 0.0680136i
$$671$$ 2009.18i 0.115594i
$$672$$ 0 0
$$673$$ −4010.50 6946.39i −0.229708 0.397866i 0.728014 0.685563i $$-0.240444\pi$$
−0.957722 + 0.287697i $$0.907110\pi$$
$$674$$ 5362.50 3096.04i 0.306463 0.176936i
$$675$$ 0 0
$$676$$ −422.500 + 10976.9i −0.0240385 + 0.624538i
$$677$$ 21630.0 1.22793 0.613965 0.789333i $$-0.289574\pi$$
0.613965 + 0.789333i $$0.289574\pi$$
$$678$$ 0 0
$$679$$ −1392.00 2411.01i −0.0786746 0.136268i
$$680$$ −2281.50 + 3951.67i −0.128664 + 0.222853i
$$681$$ 0 0
$$682$$ −3240.00 1870.61i −0.181915 0.105029i
$$683$$ 22983.0 + 13269.2i 1.28758 + 0.743387i 0.978223 0.207557i $$-0.0665514\pi$$
0.309361 + 0.950945i $$0.399885\pi$$
$$684$$ 0 0
$$685$$ 733.500 1270.46i 0.0409133 0.0708639i
$$686$$ −5928.00 10267.6i −0.329930 0.571456i
$$687$$ 0 0
$$688$$ 104.000 0.00576303
$$689$$ −4231.50 + 1047.02i −0.233973 + 0.0578933i
$$690$$ 0 0
$$691$$ −720.000 + 415.692i −0.0396383 + 0.0228852i −0.519688 0.854356i $$-0.673952\pi$$
0.480050 + 0.877241i $$0.340619\pi$$
$$692$$ 6435.00 + 11145.7i 0.353500 + 0.612280i
$$693$$ 0 0
$$694$$ 12065.5i 0.659941i
$$695$$ 354.000 + 204.382i 0.0193208 + 0.0111549i
$$696$$ 0 0
$$697$$ 31816.0i 1.72901i
$$698$$ 5760.00 9976.61i 0.312348 0.541003i
$$699$$ 0 0
$$700$$ 7320.00 4226.20i 0.395243 0.228194i
$$701$$ −30186.0 −1.62640 −0.813202 0.581981i $$-0.802278\pi$$
−0.813202 + 0.581981i $$0.802278\pi$$
$$702$$ 0 0
$$703$$ 16434.0 0.881679
$$704$$ 3684.00 2126.96i 0.197224 0.113868i
$$705$$ 0 0
$$706$$ 4876.50 8446.35i 0.259957 0.450258i
$$707$$ 5944.40i 0.316212i
$$708$$ 0 0
$$709$$ −10288.5 5940.07i −0.544983 0.314646i 0.202113 0.979362i $$-0.435219\pi$$
−0.747096 + 0.664716i $$0.768552\pi$$
$$710$$ 3169.65i 0.167542i
$$711$$ 0 0
$$712$$ −10998.0 19049.1i −0.578887 1.00266i
$$713$$ −10530.0 + 6079.50i −0.553088 + 0.319325i
$$714$$ 0 0
$$715$$ 780.000 + 810.600i 0.0407977 + 0.0423982i
$$716$$ −18720.0 −0.977094
$$717$$ 0 0
$$718$$ 6174.00 + 10693.7i 0.320908 + 0.555828i
$$719$$ 9204.00 15941.8i 0.477401 0.826883i −0.522264 0.852784i $$-0.674912\pi$$
0.999665 + 0.0259014i $$0.00824561\pi$$
$$720$$ 0 0
$$721$$ −2184.00 1260.93i −0.112811 0.0651312i
$$722$$ −9313.50 5377.15i −0.480073 0.277170i
$$723$$ 0 0
$$724$$ 1592.50 2758.29i 0.0817470 0.141590i
$$725$$ −8601.00 14897.4i −0.440597 0.763137i
$$726$$ 0 0
$$727$$ 21112.0 1.07703 0.538515 0.842616i $$-0.318986\pi$$
0.538515 + 0.842616i $$0.318986\pi$$
$$728$$ −4056.00 + 14050.4i −0.206491 + 0.715305i
$$729$$ 0 0
$$730$$ 1192.50 688.490i 0.0604608 0.0349071i
$$731$$ 6084.00 + 10537.8i 0.307832 + 0.533180i
$$732$$ 0 0
$$733$$ 23959.5i 1.20732i 0.797243 + 0.603658i $$0.206291\pi$$
−0.797243 + 0.603658i $$0.793709\pi$$
$$734$$ 3.00000 + 1.73205i 0.000150861 + 8.70997e-5i
$$735$$ 0 0
$$736$$ 14185.5i 0.710441i
$$737$$ 5448.00 9436.21i 0.272293 0.471625i
$$738$$ 0 0
$$739$$ 2742.00 1583.09i 0.136490 0.0788025i −0.430200 0.902734i $$-0.641557\pi$$
0.566690 + 0.823931i $$0.308224\pi$$
$$740$$ −1245.00 −0.0618474
$$741$$ 0 0
$$742$$ −2232.00 −0.110430
$$743$$ 26070.0 15051.5i 1.28723 0.743185i 0.309075 0.951038i $$-0.399981\pi$$
0.978160 + 0.207852i $$0.0666474\pi$$
$$744$$ 0 0
$$745$$ 40.5000 70.1481i 0.00199168 0.00344970i
$$746$$ 6060.45i 0.297438i
$$747$$ 0 0
$$748$$ −7020.00 4053.00i −0.343151 0.198118i
$$749$$ 20867.7i 1.01801i
$$750$$ 0 0
$$751$$ −14248.0 24678.3i −0.692299 1.19910i −0.971083 0.238744i $$-0.923264\pi$$
0.278783 0.960354i $$-0.410069\pi$$
$$752$$ 261.000 150.688i 0.0126565 0.00730724i
$$753$$ 0 0
$$754$$ 10998.0 + 3174.85i 0.531198 + 0.153344i
$$755$$ 3066.00 0.147792
$$756$$ 0 0
$$757$$ −8711.00 15087.9i −0.418239 0.724411i 0.577524 0.816374i $$-0.304019\pi$$
−0.995762 + 0.0919633i $$0.970686\pi$$
$$758$$ −4779.00 + 8277.47i −0.228999 + 0.396638i
$$759$$ 0 0
$$760$$ 3861.00 + 2229.15i 0.184281 + 0.106394i
$$761$$ −35790.0 20663.4i −1.70484 0.984292i −0.940695 0.339252i $$-0.889826\pi$$
−0.764149 0.645040i $$-0.776841\pi$$
$$762$$ 0 0
$$763$$ −10752.0 + 18623.0i −0.510155 + 0.883615i
$$764$$ −6495.00 11249.7i −0.307567 0.532721i
$$765$$ 0 0
$$766$$ −12756.0 −0.601688
$$767$$ 12792.0 + 3692.73i 0.602206 + 0.173842i
$$768$$ 0 0
$$769$$ −12186.0 + 7035.59i −0.571441 + 0.329922i −0.757725 0.652574i $$-0.773689\pi$$
0.186283 + 0.982496i $$0.440356\pi$$
$$770$$ 288.000 + 498.831i 0.0134790 + 0.0233462i
$$771$$ 0 0
$$772$$ 5585.86i 0.260414i
$$773$$ −174.000 100.459i −0.00809618 0.00467433i 0.495946 0.868353i $$-0.334821\pi$$
−0.504043 + 0.863679i $$0.668155\pi$$
$$774$$ 0 0
$$775$$ 19017.9i 0.881476i
$$776$$ 2262.00 3917.90i 0.104641 0.181243i
$$777$$ 0 0
$$778$$ −1813.50 + 1047.02i −0.0835696 + 0.0482489i
$$779$$ 31086.0 1.42975
$$780$$ 0 0
$$781$$ 14640.0 0.670756
$$782$$ 13689.0 7903.35i 0.625982 0.361411i
$$783$$ 0 0