# Properties

 Label 810.4.e.q.271.1 Level $810$ Weight $4$ Character 810.271 Analytic conductor $47.792$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$810 = 2 \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 810.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$47.7915471046$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 270) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 271.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 810.271 Dual form 810.4.e.q.541.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} -8.00000 q^{8} +O(q^{10})$$ $$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} -8.00000 q^{8} -10.0000 q^{10} +(21.0000 + 36.3731i) q^{11} +(-10.0000 + 17.3205i) q^{13} +(-4.00000 + 6.92820i) q^{14} +(-8.00000 - 13.8564i) q^{16} -93.0000 q^{17} +59.0000 q^{19} +(-10.0000 - 17.3205i) q^{20} +(-42.0000 + 72.7461i) q^{22} +(4.50000 - 7.79423i) q^{23} +(-12.5000 - 21.6506i) q^{25} -40.0000 q^{26} -16.0000 q^{28} +(60.0000 + 103.923i) q^{29} +(-23.5000 + 40.7032i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-93.0000 - 161.081i) q^{34} -20.0000 q^{35} -262.000 q^{37} +(59.0000 + 102.191i) q^{38} +(20.0000 - 34.6410i) q^{40} +(63.0000 - 109.119i) q^{41} +(89.0000 + 154.153i) q^{43} -168.000 q^{44} +18.0000 q^{46} +(72.0000 + 124.708i) q^{47} +(163.500 - 283.190i) q^{49} +(25.0000 - 43.3013i) q^{50} +(-40.0000 - 69.2820i) q^{52} -741.000 q^{53} -210.000 q^{55} +(-16.0000 - 27.7128i) q^{56} +(-120.000 + 207.846i) q^{58} +(-222.000 + 384.515i) q^{59} +(-110.500 - 191.392i) q^{61} -94.0000 q^{62} +64.0000 q^{64} +(-50.0000 - 86.6025i) q^{65} +(269.000 - 465.922i) q^{67} +(186.000 - 322.161i) q^{68} +(-20.0000 - 34.6410i) q^{70} -690.000 q^{71} -1126.00 q^{73} +(-262.000 - 453.797i) q^{74} +(-118.000 + 204.382i) q^{76} +(-84.0000 + 145.492i) q^{77} +(-332.500 - 575.907i) q^{79} +80.0000 q^{80} +252.000 q^{82} +(37.5000 + 64.9519i) q^{83} +(232.500 - 402.702i) q^{85} +(-178.000 + 308.305i) q^{86} +(-168.000 - 290.985i) q^{88} +1086.00 q^{89} -80.0000 q^{91} +(18.0000 + 31.1769i) q^{92} +(-144.000 + 249.415i) q^{94} +(-147.500 + 255.477i) q^{95} +(-772.000 - 1337.14i) q^{97} +654.000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} + 4 q^{7} - 16 q^{8}+O(q^{10})$$ 2 * q + 2 * q^2 - 4 * q^4 - 5 * q^5 + 4 * q^7 - 16 * q^8 $$2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} + 4 q^{7} - 16 q^{8} - 20 q^{10} + 42 q^{11} - 20 q^{13} - 8 q^{14} - 16 q^{16} - 186 q^{17} + 118 q^{19} - 20 q^{20} - 84 q^{22} + 9 q^{23} - 25 q^{25} - 80 q^{26} - 32 q^{28} + 120 q^{29} - 47 q^{31} + 32 q^{32} - 186 q^{34} - 40 q^{35} - 524 q^{37} + 118 q^{38} + 40 q^{40} + 126 q^{41} + 178 q^{43} - 336 q^{44} + 36 q^{46} + 144 q^{47} + 327 q^{49} + 50 q^{50} - 80 q^{52} - 1482 q^{53} - 420 q^{55} - 32 q^{56} - 240 q^{58} - 444 q^{59} - 221 q^{61} - 188 q^{62} + 128 q^{64} - 100 q^{65} + 538 q^{67} + 372 q^{68} - 40 q^{70} - 1380 q^{71} - 2252 q^{73} - 524 q^{74} - 236 q^{76} - 168 q^{77} - 665 q^{79} + 160 q^{80} + 504 q^{82} + 75 q^{83} + 465 q^{85} - 356 q^{86} - 336 q^{88} + 2172 q^{89} - 160 q^{91} + 36 q^{92} - 288 q^{94} - 295 q^{95} - 1544 q^{97} + 1308 q^{98}+O(q^{100})$$ 2 * q + 2 * q^2 - 4 * q^4 - 5 * q^5 + 4 * q^7 - 16 * q^8 - 20 * q^10 + 42 * q^11 - 20 * q^13 - 8 * q^14 - 16 * q^16 - 186 * q^17 + 118 * q^19 - 20 * q^20 - 84 * q^22 + 9 * q^23 - 25 * q^25 - 80 * q^26 - 32 * q^28 + 120 * q^29 - 47 * q^31 + 32 * q^32 - 186 * q^34 - 40 * q^35 - 524 * q^37 + 118 * q^38 + 40 * q^40 + 126 * q^41 + 178 * q^43 - 336 * q^44 + 36 * q^46 + 144 * q^47 + 327 * q^49 + 50 * q^50 - 80 * q^52 - 1482 * q^53 - 420 * q^55 - 32 * q^56 - 240 * q^58 - 444 * q^59 - 221 * q^61 - 188 * q^62 + 128 * q^64 - 100 * q^65 + 538 * q^67 + 372 * q^68 - 40 * q^70 - 1380 * q^71 - 2252 * q^73 - 524 * q^74 - 236 * q^76 - 168 * q^77 - 665 * q^79 + 160 * q^80 + 504 * q^82 + 75 * q^83 + 465 * q^85 - 356 * q^86 - 336 * q^88 + 2172 * q^89 - 160 * q^91 + 36 * q^92 - 288 * q^94 - 295 * q^95 - 1544 * q^97 + 1308 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$$.

 $$n$$ $$487$$ $$731$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 + 1.73205i 0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −2.00000 + 3.46410i −0.250000 + 0.433013i
$$5$$ −2.50000 + 4.33013i −0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ 2.00000 + 3.46410i 0.107990 + 0.187044i 0.914956 0.403554i $$-0.132225\pi$$
−0.806966 + 0.590598i $$0.798892\pi$$
$$8$$ −8.00000 −0.353553
$$9$$ 0 0
$$10$$ −10.0000 −0.316228
$$11$$ 21.0000 + 36.3731i 0.575613 + 0.996990i 0.995975 + 0.0896338i $$0.0285697\pi$$
−0.420362 + 0.907356i $$0.638097\pi$$
$$12$$ 0 0
$$13$$ −10.0000 + 17.3205i −0.213346 + 0.369527i −0.952760 0.303725i $$-0.901770\pi$$
0.739413 + 0.673252i $$0.235103\pi$$
$$14$$ −4.00000 + 6.92820i −0.0763604 + 0.132260i
$$15$$ 0 0
$$16$$ −8.00000 13.8564i −0.125000 0.216506i
$$17$$ −93.0000 −1.32681 −0.663406 0.748259i $$-0.730890\pi$$
−0.663406 + 0.748259i $$0.730890\pi$$
$$18$$ 0 0
$$19$$ 59.0000 0.712396 0.356198 0.934410i $$-0.384073\pi$$
0.356198 + 0.934410i $$0.384073\pi$$
$$20$$ −10.0000 17.3205i −0.111803 0.193649i
$$21$$ 0 0
$$22$$ −42.0000 + 72.7461i −0.407020 + 0.704979i
$$23$$ 4.50000 7.79423i 0.0407963 0.0706613i −0.844906 0.534914i $$-0.820344\pi$$
0.885703 + 0.464253i $$0.153677\pi$$
$$24$$ 0 0
$$25$$ −12.5000 21.6506i −0.100000 0.173205i
$$26$$ −40.0000 −0.301717
$$27$$ 0 0
$$28$$ −16.0000 −0.107990
$$29$$ 60.0000 + 103.923i 0.384197 + 0.665449i 0.991657 0.128901i $$-0.0411449\pi$$
−0.607460 + 0.794350i $$0.707812\pi$$
$$30$$ 0 0
$$31$$ −23.5000 + 40.7032i −0.136152 + 0.235823i −0.926037 0.377433i $$-0.876807\pi$$
0.789885 + 0.613255i $$0.210140\pi$$
$$32$$ 16.0000 27.7128i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ −93.0000 161.081i −0.469099 0.812503i
$$35$$ −20.0000 −0.0965891
$$36$$ 0 0
$$37$$ −262.000 −1.16412 −0.582061 0.813145i $$-0.697754\pi$$
−0.582061 + 0.813145i $$0.697754\pi$$
$$38$$ 59.0000 + 102.191i 0.251870 + 0.436252i
$$39$$ 0 0
$$40$$ 20.0000 34.6410i 0.0790569 0.136931i
$$41$$ 63.0000 109.119i 0.239974 0.415648i −0.720732 0.693213i $$-0.756194\pi$$
0.960707 + 0.277566i $$0.0895276\pi$$
$$42$$ 0 0
$$43$$ 89.0000 + 154.153i 0.315637 + 0.546699i 0.979573 0.201091i $$-0.0644486\pi$$
−0.663936 + 0.747789i $$0.731115\pi$$
$$44$$ −168.000 −0.575613
$$45$$ 0 0
$$46$$ 18.0000 0.0576947
$$47$$ 72.0000 + 124.708i 0.223453 + 0.387032i 0.955854 0.293842i $$-0.0949338\pi$$
−0.732401 + 0.680873i $$0.761600\pi$$
$$48$$ 0 0
$$49$$ 163.500 283.190i 0.476676 0.825628i
$$50$$ 25.0000 43.3013i 0.0707107 0.122474i
$$51$$ 0 0
$$52$$ −40.0000 69.2820i −0.106673 0.184763i
$$53$$ −741.000 −1.92046 −0.960228 0.279217i $$-0.909925\pi$$
−0.960228 + 0.279217i $$0.909925\pi$$
$$54$$ 0 0
$$55$$ −210.000 −0.514844
$$56$$ −16.0000 27.7128i −0.0381802 0.0661300i
$$57$$ 0 0
$$58$$ −120.000 + 207.846i −0.271668 + 0.470544i
$$59$$ −222.000 + 384.515i −0.489863 + 0.848468i −0.999932 0.0116655i $$-0.996287\pi$$
0.510069 + 0.860134i $$0.329620\pi$$
$$60$$ 0 0
$$61$$ −110.500 191.392i −0.231936 0.401724i 0.726442 0.687228i $$-0.241173\pi$$
−0.958378 + 0.285503i $$0.907839\pi$$
$$62$$ −94.0000 −0.192549
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −50.0000 86.6025i −0.0954113 0.165257i
$$66$$ 0 0
$$67$$ 269.000 465.922i 0.490501 0.849573i −0.509439 0.860507i $$-0.670147\pi$$
0.999940 + 0.0109338i $$0.00348039\pi$$
$$68$$ 186.000 322.161i 0.331703 0.574527i
$$69$$ 0 0
$$70$$ −20.0000 34.6410i −0.0341494 0.0591485i
$$71$$ −690.000 −1.15335 −0.576676 0.816973i $$-0.695650\pi$$
−0.576676 + 0.816973i $$0.695650\pi$$
$$72$$ 0 0
$$73$$ −1126.00 −1.80532 −0.902660 0.430355i $$-0.858388\pi$$
−0.902660 + 0.430355i $$0.858388\pi$$
$$74$$ −262.000 453.797i −0.411579 0.712877i
$$75$$ 0 0
$$76$$ −118.000 + 204.382i −0.178099 + 0.308477i
$$77$$ −84.0000 + 145.492i −0.124321 + 0.215330i
$$78$$ 0 0
$$79$$ −332.500 575.907i −0.473534 0.820185i 0.526007 0.850480i $$-0.323689\pi$$
−0.999541 + 0.0302955i $$0.990355\pi$$
$$80$$ 80.0000 0.111803
$$81$$ 0 0
$$82$$ 252.000 0.339375
$$83$$ 37.5000 + 64.9519i 0.0495923 + 0.0858964i 0.889756 0.456437i $$-0.150874\pi$$
−0.840164 + 0.542333i $$0.817541\pi$$
$$84$$ 0 0
$$85$$ 232.500 402.702i 0.296684 0.513872i
$$86$$ −178.000 + 308.305i −0.223189 + 0.386574i
$$87$$ 0 0
$$88$$ −168.000 290.985i −0.203510 0.352489i
$$89$$ 1086.00 1.29344 0.646718 0.762729i $$-0.276141\pi$$
0.646718 + 0.762729i $$0.276141\pi$$
$$90$$ 0 0
$$91$$ −80.0000 −0.0921569
$$92$$ 18.0000 + 31.1769i 0.0203981 + 0.0353306i
$$93$$ 0 0
$$94$$ −144.000 + 249.415i −0.158005 + 0.273673i
$$95$$ −147.500 + 255.477i −0.159297 + 0.275910i
$$96$$ 0 0
$$97$$ −772.000 1337.14i −0.808090 1.39965i −0.914185 0.405297i $$-0.867168\pi$$
0.106095 0.994356i $$-0.466165\pi$$
$$98$$ 654.000 0.674122
$$99$$ 0 0
$$100$$ 100.000 0.100000
$$101$$ −66.0000 114.315i −0.0650222 0.112622i 0.831682 0.555253i $$-0.187378\pi$$
−0.896704 + 0.442631i $$0.854045\pi$$
$$102$$ 0 0
$$103$$ 446.000 772.495i 0.426657 0.738992i −0.569916 0.821703i $$-0.693024\pi$$
0.996574 + 0.0827108i $$0.0263578\pi$$
$$104$$ 80.0000 138.564i 0.0754293 0.130647i
$$105$$ 0 0
$$106$$ −741.000 1283.45i −0.678984 1.17603i
$$107$$ 1140.00 1.02998 0.514990 0.857196i $$-0.327795\pi$$
0.514990 + 0.857196i $$0.327795\pi$$
$$108$$ 0 0
$$109$$ −1735.00 −1.52461 −0.762307 0.647216i $$-0.775933\pi$$
−0.762307 + 0.647216i $$0.775933\pi$$
$$110$$ −210.000 363.731i −0.182025 0.315276i
$$111$$ 0 0
$$112$$ 32.0000 55.4256i 0.0269975 0.0467610i
$$113$$ −717.000 + 1241.88i −0.596900 + 1.03386i 0.396376 + 0.918088i $$0.370268\pi$$
−0.993276 + 0.115773i $$0.963066\pi$$
$$114$$ 0 0
$$115$$ 22.5000 + 38.9711i 0.0182447 + 0.0316007i
$$116$$ −480.000 −0.384197
$$117$$ 0 0
$$118$$ −888.000 −0.692771
$$119$$ −186.000 322.161i −0.143282 0.248172i
$$120$$ 0 0
$$121$$ −216.500 + 374.989i −0.162660 + 0.281735i
$$122$$ 221.000 382.783i 0.164003 0.284062i
$$123$$ 0 0
$$124$$ −94.0000 162.813i −0.0680762 0.117911i
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ 686.000 0.479312 0.239656 0.970858i $$-0.422965\pi$$
0.239656 + 0.970858i $$0.422965\pi$$
$$128$$ 64.0000 + 110.851i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 100.000 173.205i 0.0674660 0.116855i
$$131$$ −57.0000 + 98.7269i −0.0380161 + 0.0658459i −0.884407 0.466716i $$-0.845437\pi$$
0.846391 + 0.532561i $$0.178770\pi$$
$$132$$ 0 0
$$133$$ 118.000 + 204.382i 0.0769316 + 0.133249i
$$134$$ 1076.00 0.693673
$$135$$ 0 0
$$136$$ 744.000 0.469099
$$137$$ 79.5000 + 137.698i 0.0495777 + 0.0858711i 0.889749 0.456450i $$-0.150879\pi$$
−0.840172 + 0.542321i $$0.817546\pi$$
$$138$$ 0 0
$$139$$ −1138.00 + 1971.07i −0.694417 + 1.20276i 0.275960 + 0.961169i $$0.411004\pi$$
−0.970377 + 0.241596i $$0.922329\pi$$
$$140$$ 40.0000 69.2820i 0.0241473 0.0418243i
$$141$$ 0 0
$$142$$ −690.000 1195.12i −0.407771 0.706280i
$$143$$ −840.000 −0.491219
$$144$$ 0 0
$$145$$ −600.000 −0.343636
$$146$$ −1126.00 1950.29i −0.638277 1.10553i
$$147$$ 0 0
$$148$$ 524.000 907.595i 0.291031 0.504080i
$$149$$ −699.000 + 1210.70i −0.384324 + 0.665669i −0.991675 0.128765i $$-0.958899\pi$$
0.607351 + 0.794434i $$0.292232\pi$$
$$150$$ 0 0
$$151$$ −1312.00 2272.45i −0.707080 1.22470i −0.965936 0.258782i $$-0.916679\pi$$
0.258856 0.965916i $$-0.416655\pi$$
$$152$$ −472.000 −0.251870
$$153$$ 0 0
$$154$$ −336.000 −0.175816
$$155$$ −117.500 203.516i −0.0608892 0.105463i
$$156$$ 0 0
$$157$$ 197.000 341.214i 0.100142 0.173451i −0.811601 0.584212i $$-0.801404\pi$$
0.911743 + 0.410761i $$0.134737\pi$$
$$158$$ 665.000 1151.81i 0.334839 0.579958i
$$159$$ 0 0
$$160$$ 80.0000 + 138.564i 0.0395285 + 0.0684653i
$$161$$ 36.0000 0.0176223
$$162$$ 0 0
$$163$$ −3346.00 −1.60785 −0.803923 0.594733i $$-0.797258\pi$$
−0.803923 + 0.594733i $$0.797258\pi$$
$$164$$ 252.000 + 436.477i 0.119987 + 0.207824i
$$165$$ 0 0
$$166$$ −75.0000 + 129.904i −0.0350670 + 0.0607379i
$$167$$ −745.500 + 1291.24i −0.345440 + 0.598320i −0.985434 0.170060i $$-0.945604\pi$$
0.639993 + 0.768380i $$0.278937\pi$$
$$168$$ 0 0
$$169$$ 898.500 + 1556.25i 0.408967 + 0.708351i
$$170$$ 930.000 0.419575
$$171$$ 0 0
$$172$$ −712.000 −0.315637
$$173$$ 1201.50 + 2081.06i 0.528025 + 0.914566i 0.999466 + 0.0326688i $$0.0104007\pi$$
−0.471441 + 0.881898i $$0.656266\pi$$
$$174$$ 0 0
$$175$$ 50.0000 86.6025i 0.0215980 0.0374088i
$$176$$ 336.000 581.969i 0.143903 0.249248i
$$177$$ 0 0
$$178$$ 1086.00 + 1881.01i 0.457299 + 0.792064i
$$179$$ 2640.00 1.10236 0.551181 0.834386i $$-0.314177\pi$$
0.551181 + 0.834386i $$0.314177\pi$$
$$180$$ 0 0
$$181$$ 1073.00 0.440638 0.220319 0.975428i $$-0.429290\pi$$
0.220319 + 0.975428i $$0.429290\pi$$
$$182$$ −80.0000 138.564i −0.0325824 0.0564344i
$$183$$ 0 0
$$184$$ −36.0000 + 62.3538i −0.0144237 + 0.0249825i
$$185$$ 655.000 1134.49i 0.260306 0.450863i
$$186$$ 0 0
$$187$$ −1953.00 3382.70i −0.763730 1.32282i
$$188$$ −576.000 −0.223453
$$189$$ 0 0
$$190$$ −590.000 −0.225279
$$191$$ 735.000 + 1273.06i 0.278444 + 0.482279i 0.970998 0.239087i $$-0.0768481\pi$$
−0.692555 + 0.721366i $$0.743515\pi$$
$$192$$ 0 0
$$193$$ 2360.00 4087.64i 0.880189 1.52453i 0.0290591 0.999578i $$-0.490749\pi$$
0.851130 0.524955i $$-0.175918\pi$$
$$194$$ 1544.00 2674.29i 0.571406 0.989704i
$$195$$ 0 0
$$196$$ 654.000 + 1132.76i 0.238338 + 0.412814i
$$197$$ 765.000 0.276670 0.138335 0.990385i $$-0.455825\pi$$
0.138335 + 0.990385i $$0.455825\pi$$
$$198$$ 0 0
$$199$$ 668.000 0.237956 0.118978 0.992897i $$-0.462038\pi$$
0.118978 + 0.992897i $$0.462038\pi$$
$$200$$ 100.000 + 173.205i 0.0353553 + 0.0612372i
$$201$$ 0 0
$$202$$ 132.000 228.631i 0.0459777 0.0796356i
$$203$$ −240.000 + 415.692i −0.0829788 + 0.143724i
$$204$$ 0 0
$$205$$ 315.000 + 545.596i 0.107320 + 0.185883i
$$206$$ 1784.00 0.603384
$$207$$ 0 0
$$208$$ 320.000 0.106673
$$209$$ 1239.00 + 2146.01i 0.410064 + 0.710252i
$$210$$ 0 0
$$211$$ −2300.50 + 3984.58i −0.750583 + 1.30005i 0.196958 + 0.980412i $$0.436894\pi$$
−0.947541 + 0.319635i $$0.896440\pi$$
$$212$$ 1482.00 2566.90i 0.480114 0.831582i
$$213$$ 0 0
$$214$$ 1140.00 + 1974.54i 0.364153 + 0.630732i
$$215$$ −890.000 −0.282314
$$216$$ 0 0
$$217$$ −188.000 −0.0588123
$$218$$ −1735.00 3005.11i −0.539032 0.933631i
$$219$$ 0 0
$$220$$ 420.000 727.461i 0.128711 0.222934i
$$221$$ 930.000 1610.81i 0.283070 0.490292i
$$222$$ 0 0
$$223$$ 1079.00 + 1868.88i 0.324014 + 0.561209i 0.981312 0.192421i $$-0.0616341\pi$$
−0.657298 + 0.753631i $$0.728301\pi$$
$$224$$ 128.000 0.0381802
$$225$$ 0 0
$$226$$ −2868.00 −0.844144
$$227$$ 1561.50 + 2704.60i 0.456566 + 0.790795i 0.998777 0.0494474i $$-0.0157460\pi$$
−0.542211 + 0.840242i $$0.682413\pi$$
$$228$$ 0 0
$$229$$ −1013.50 + 1755.43i −0.292463 + 0.506560i −0.974391 0.224858i $$-0.927808\pi$$
0.681929 + 0.731419i $$0.261141\pi$$
$$230$$ −45.0000 + 77.9423i −0.0129009 + 0.0223451i
$$231$$ 0 0
$$232$$ −480.000 831.384i −0.135834 0.235272i
$$233$$ 438.000 0.123152 0.0615758 0.998102i $$-0.480387\pi$$
0.0615758 + 0.998102i $$0.480387\pi$$
$$234$$ 0 0
$$235$$ −720.000 −0.199862
$$236$$ −888.000 1538.06i −0.244932 0.424234i
$$237$$ 0 0
$$238$$ 372.000 644.323i 0.101316 0.175484i
$$239$$ 3207.00 5554.69i 0.867965 1.50336i 0.00389189 0.999992i $$-0.498761\pi$$
0.864073 0.503367i $$-0.167905\pi$$
$$240$$ 0 0
$$241$$ −1715.50 2971.33i −0.458527 0.794193i 0.540356 0.841436i $$-0.318290\pi$$
−0.998883 + 0.0472439i $$0.984956\pi$$
$$242$$ −866.000 −0.230035
$$243$$ 0 0
$$244$$ 884.000 0.231936
$$245$$ 817.500 + 1415.95i 0.213176 + 0.369232i
$$246$$ 0 0
$$247$$ −590.000 + 1021.91i −0.151987 + 0.263249i
$$248$$ 188.000 325.626i 0.0481371 0.0833760i
$$249$$ 0 0
$$250$$ 125.000 + 216.506i 0.0316228 + 0.0547723i
$$251$$ −7308.00 −1.83776 −0.918878 0.394541i $$-0.870904\pi$$
−0.918878 + 0.394541i $$0.870904\pi$$
$$252$$ 0 0
$$253$$ 378.000 0.0939314
$$254$$ 686.000 + 1188.19i 0.169462 + 0.293518i
$$255$$ 0 0
$$256$$ −128.000 + 221.703i −0.0312500 + 0.0541266i
$$257$$ −1864.50 + 3229.41i −0.452546 + 0.783833i −0.998543 0.0539542i $$-0.982817\pi$$
0.545997 + 0.837787i $$0.316151\pi$$
$$258$$ 0 0
$$259$$ −524.000 907.595i −0.125713 0.217742i
$$260$$ 400.000 0.0954113
$$261$$ 0 0
$$262$$ −228.000 −0.0537629
$$263$$ −978.000 1693.95i −0.229301 0.397160i 0.728300 0.685258i $$-0.240311\pi$$
−0.957601 + 0.288098i $$0.906977\pi$$
$$264$$ 0 0
$$265$$ 1852.50 3208.62i 0.429427 0.743789i
$$266$$ −236.000 + 408.764i −0.0543988 + 0.0942215i
$$267$$ 0 0
$$268$$ 1076.00 + 1863.69i 0.245251 + 0.424787i
$$269$$ −990.000 −0.224392 −0.112196 0.993686i $$-0.535788\pi$$
−0.112196 + 0.993686i $$0.535788\pi$$
$$270$$ 0 0
$$271$$ 8495.00 1.90419 0.952093 0.305808i $$-0.0989266\pi$$
0.952093 + 0.305808i $$0.0989266\pi$$
$$272$$ 744.000 + 1288.65i 0.165852 + 0.287263i
$$273$$ 0 0
$$274$$ −159.000 + 275.396i −0.0350567 + 0.0607200i
$$275$$ 525.000 909.327i 0.115123 0.199398i
$$276$$ 0 0
$$277$$ 683.000 + 1182.99i 0.148150 + 0.256603i 0.930544 0.366181i $$-0.119335\pi$$
−0.782394 + 0.622784i $$0.786002\pi$$
$$278$$ −4552.00 −0.982053
$$279$$ 0 0
$$280$$ 160.000 0.0341494
$$281$$ 2760.00 + 4780.46i 0.585935 + 1.01487i 0.994758 + 0.102256i $$0.0326060\pi$$
−0.408823 + 0.912614i $$0.634061\pi$$
$$282$$ 0 0
$$283$$ −2719.00 + 4709.45i −0.571123 + 0.989214i 0.425328 + 0.905039i $$0.360159\pi$$
−0.996451 + 0.0841746i $$0.973175\pi$$
$$284$$ 1380.00 2390.23i 0.288338 0.499416i
$$285$$ 0 0
$$286$$ −840.000 1454.92i −0.173672 0.300809i
$$287$$ 504.000 0.103659
$$288$$ 0 0
$$289$$ 3736.00 0.760432
$$290$$ −600.000 1039.23i −0.121494 0.210434i
$$291$$ 0 0
$$292$$ 2252.00 3900.58i 0.451330 0.781726i
$$293$$ −4126.50 + 7147.31i −0.822774 + 1.42509i 0.0808352 + 0.996727i $$0.474241\pi$$
−0.903609 + 0.428358i $$0.859092\pi$$
$$294$$ 0 0
$$295$$ −1110.00 1922.58i −0.219074 0.379447i
$$296$$ 2096.00 0.411579
$$297$$ 0 0
$$298$$ −2796.00 −0.543517
$$299$$ 90.0000 + 155.885i 0.0174075 + 0.0301506i
$$300$$ 0 0
$$301$$ −356.000 + 616.610i −0.0681711 + 0.118076i
$$302$$ 2624.00 4544.90i 0.499981 0.865992i
$$303$$ 0 0
$$304$$ −472.000 817.528i −0.0890495 0.154238i
$$305$$ 1105.00 0.207450
$$306$$ 0 0
$$307$$ 9290.00 1.72706 0.863531 0.504295i $$-0.168248\pi$$
0.863531 + 0.504295i $$0.168248\pi$$
$$308$$ −336.000 581.969i −0.0621603 0.107665i
$$309$$ 0 0
$$310$$ 235.000 407.032i 0.0430552 0.0745737i
$$311$$ −4056.00 + 7025.20i −0.739533 + 1.28091i 0.213173 + 0.977014i $$0.431620\pi$$
−0.952706 + 0.303894i $$0.901713\pi$$
$$312$$ 0 0
$$313$$ 3950.00 + 6841.60i 0.713314 + 1.23550i 0.963606 + 0.267325i $$0.0861399\pi$$
−0.250293 + 0.968170i $$0.580527\pi$$
$$314$$ 788.000 0.141622
$$315$$ 0 0
$$316$$ 2660.00 0.473534
$$317$$ −2209.50 3826.97i −0.391476 0.678056i 0.601168 0.799122i $$-0.294702\pi$$
−0.992644 + 0.121066i $$0.961369\pi$$
$$318$$ 0 0
$$319$$ −2520.00 + 4364.77i −0.442298 + 0.766082i
$$320$$ −160.000 + 277.128i −0.0279508 + 0.0484123i
$$321$$ 0 0
$$322$$ 36.0000 + 62.3538i 0.00623044 + 0.0107914i
$$323$$ −5487.00 −0.945216
$$324$$ 0 0
$$325$$ 500.000 0.0853385
$$326$$ −3346.00 5795.44i −0.568460 0.984601i
$$327$$ 0 0
$$328$$ −504.000 + 872.954i −0.0848437 + 0.146954i
$$329$$ −288.000 + 498.831i −0.0482613 + 0.0835910i
$$330$$ 0 0
$$331$$ 4100.00 + 7101.41i 0.680835 + 1.17924i 0.974726 + 0.223402i $$0.0717163\pi$$
−0.293891 + 0.955839i $$0.594950\pi$$
$$332$$ −300.000 −0.0495923
$$333$$ 0 0
$$334$$ −2982.00 −0.488526
$$335$$ 1345.00 + 2329.61i 0.219359 + 0.379941i
$$336$$ 0 0
$$337$$ 4778.00 8275.74i 0.772327 1.33771i −0.163957 0.986467i $$-0.552426\pi$$
0.936285 0.351242i $$-0.114241\pi$$
$$338$$ −1797.00 + 3112.50i −0.289183 + 0.500880i
$$339$$ 0 0
$$340$$ 930.000 + 1610.81i 0.148342 + 0.256936i
$$341$$ −1974.00 −0.313484
$$342$$ 0 0
$$343$$ 2680.00 0.421885
$$344$$ −712.000 1233.22i −0.111594 0.193287i
$$345$$ 0 0
$$346$$ −2403.00 + 4162.12i −0.373370 + 0.646696i
$$347$$ −5058.00 + 8760.71i −0.782500 + 1.35533i 0.147980 + 0.988990i $$0.452723\pi$$
−0.930481 + 0.366340i $$0.880611\pi$$
$$348$$ 0 0
$$349$$ 3375.50 + 5846.54i 0.517726 + 0.896728i 0.999788 + 0.0205906i $$0.00655466\pi$$
−0.482062 + 0.876137i $$0.660112\pi$$
$$350$$ 200.000 0.0305441
$$351$$ 0 0
$$352$$ 1344.00 0.203510
$$353$$ −2031.00 3517.80i −0.306230 0.530406i 0.671304 0.741182i $$-0.265734\pi$$
−0.977534 + 0.210776i $$0.932401\pi$$
$$354$$ 0 0
$$355$$ 1725.00 2987.79i 0.257897 0.446691i
$$356$$ −2172.00 + 3762.01i −0.323359 + 0.560074i
$$357$$ 0 0
$$358$$ 2640.00 + 4572.61i 0.389744 + 0.675056i
$$359$$ 8778.00 1.29049 0.645244 0.763977i $$-0.276756\pi$$
0.645244 + 0.763977i $$0.276756\pi$$
$$360$$ 0 0
$$361$$ −3378.00 −0.492492
$$362$$ 1073.00 + 1858.49i 0.155789 + 0.269835i
$$363$$ 0 0
$$364$$ 160.000 277.128i 0.0230392 0.0399051i
$$365$$ 2815.00 4875.72i 0.403682 0.699197i
$$366$$ 0 0
$$367$$ −478.000 827.920i −0.0679875 0.117758i 0.830028 0.557722i $$-0.188324\pi$$
−0.898015 + 0.439964i $$0.854991\pi$$
$$368$$ −144.000 −0.0203981
$$369$$ 0 0
$$370$$ 2620.00 0.368128
$$371$$ −1482.00 2566.90i −0.207390 0.359210i
$$372$$ 0 0
$$373$$ −1150.00 + 1991.86i −0.159637 + 0.276500i −0.934738 0.355338i $$-0.884366\pi$$
0.775101 + 0.631838i $$0.217699\pi$$
$$374$$ 3906.00 6765.39i 0.540039 0.935374i
$$375$$ 0 0
$$376$$ −576.000 997.661i −0.0790025 0.136836i
$$377$$ −2400.00 −0.327868
$$378$$ 0 0
$$379$$ 29.0000 0.00393042 0.00196521 0.999998i $$-0.499374\pi$$
0.00196521 + 0.999998i $$0.499374\pi$$
$$380$$ −590.000 1021.91i −0.0796483 0.137955i
$$381$$ 0 0
$$382$$ −1470.00 + 2546.11i −0.196889 + 0.341022i
$$383$$ −4063.50 + 7038.19i −0.542128 + 0.938994i 0.456653 + 0.889645i $$0.349048\pi$$
−0.998782 + 0.0493491i $$0.984285\pi$$
$$384$$ 0 0
$$385$$ −420.000 727.461i −0.0555979 0.0962983i
$$386$$ 9440.00 1.24478
$$387$$ 0 0
$$388$$ 6176.00 0.808090
$$389$$ 3969.00 + 6874.51i 0.517317 + 0.896019i 0.999798 + 0.0201127i $$0.00640249\pi$$
−0.482481 + 0.875907i $$0.660264\pi$$
$$390$$ 0 0
$$391$$ −418.500 + 724.863i −0.0541290 + 0.0937542i
$$392$$ −1308.00 + 2265.52i −0.168531 + 0.291903i
$$393$$ 0 0
$$394$$ 765.000 + 1325.02i 0.0978176 + 0.169425i
$$395$$ 3325.00 0.423542
$$396$$ 0 0
$$397$$ 272.000 0.0343861 0.0171931 0.999852i $$-0.494527\pi$$
0.0171931 + 0.999852i $$0.494527\pi$$
$$398$$ 668.000 + 1157.01i 0.0841302 + 0.145718i
$$399$$ 0 0
$$400$$ −200.000 + 346.410i −0.0250000 + 0.0433013i
$$401$$ −2277.00 + 3943.88i −0.283561 + 0.491142i −0.972259 0.233906i $$-0.924849\pi$$
0.688698 + 0.725048i $$0.258183\pi$$
$$402$$ 0 0
$$403$$ −470.000 814.064i −0.0580952 0.100624i
$$404$$ 528.000 0.0650222
$$405$$ 0 0
$$406$$ −960.000 −0.117350
$$407$$ −5502.00 9529.74i −0.670084 1.16062i
$$408$$ 0 0
$$409$$ −500.500 + 866.891i −0.0605089 + 0.104804i −0.894693 0.446682i $$-0.852606\pi$$
0.834184 + 0.551486i $$0.185939\pi$$
$$410$$ −630.000 + 1091.19i −0.0758865 + 0.131439i
$$411$$ 0 0
$$412$$ 1784.00 + 3089.98i 0.213329 + 0.369496i
$$413$$ −1776.00 −0.211601
$$414$$ 0 0
$$415$$ −375.000 −0.0443567
$$416$$ 320.000 + 554.256i 0.0377146 + 0.0653237i
$$417$$ 0 0
$$418$$ −2478.00 + 4292.02i −0.289959 + 0.502224i
$$419$$ 897.000 1553.65i 0.104585 0.181147i −0.808983 0.587832i $$-0.799982\pi$$
0.913569 + 0.406684i $$0.133315\pi$$
$$420$$ 0 0
$$421$$ 8064.50 + 13968.1i 0.933586 + 1.61702i 0.777136 + 0.629332i $$0.216672\pi$$
0.156450 + 0.987686i $$0.449995\pi$$
$$422$$ −9202.00 −1.06148
$$423$$ 0 0
$$424$$ 5928.00 0.678984
$$425$$ 1162.50 + 2013.51i 0.132681 + 0.229811i
$$426$$ 0 0
$$427$$ 442.000 765.566i 0.0500934 0.0867643i
$$428$$ −2280.00 + 3949.08i −0.257495 + 0.445995i
$$429$$ 0 0
$$430$$ −890.000 1541.53i −0.0998130 0.172881i
$$431$$ −13356.0 −1.49266 −0.746329 0.665577i $$-0.768186\pi$$
−0.746329 + 0.665577i $$0.768186\pi$$
$$432$$ 0 0
$$433$$ −11500.0 −1.27634 −0.638169 0.769896i $$-0.720308\pi$$
−0.638169 + 0.769896i $$0.720308\pi$$
$$434$$ −188.000 325.626i −0.0207933 0.0360150i
$$435$$ 0 0
$$436$$ 3470.00 6010.22i 0.381153 0.660177i
$$437$$ 265.500 459.859i 0.0290631 0.0503388i
$$438$$ 0 0
$$439$$ 5574.50 + 9655.32i 0.606051 + 1.04971i 0.991884 + 0.127143i $$0.0405806\pi$$
−0.385833 + 0.922568i $$0.626086\pi$$
$$440$$ 1680.00 0.182025
$$441$$ 0 0
$$442$$ 3720.00 0.400322
$$443$$ −1924.50 3333.33i −0.206401 0.357497i 0.744177 0.667982i $$-0.232842\pi$$
−0.950578 + 0.310485i $$0.899509\pi$$
$$444$$ 0 0
$$445$$ −2715.00 + 4702.52i −0.289221 + 0.500945i
$$446$$ −2158.00 + 3737.77i −0.229113 + 0.396835i
$$447$$ 0 0
$$448$$ 128.000 + 221.703i 0.0134987 + 0.0233805i
$$449$$ 18048.0 1.89697 0.948483 0.316828i $$-0.102618\pi$$
0.948483 + 0.316828i $$0.102618\pi$$
$$450$$ 0 0
$$451$$ 5292.00 0.552529
$$452$$ −2868.00 4967.52i −0.298450 0.516930i
$$453$$ 0 0
$$454$$ −3123.00 + 5409.19i −0.322841 + 0.559176i
$$455$$ 200.000 346.410i 0.0206069 0.0356922i
$$456$$ 0 0
$$457$$ 2132.00 + 3692.73i 0.218229 + 0.377984i 0.954267 0.298957i $$-0.0966386\pi$$
−0.736037 + 0.676941i $$0.763305\pi$$
$$458$$ −4054.00 −0.413605
$$459$$ 0 0
$$460$$ −180.000 −0.0182447
$$461$$ 5121.00 + 8869.83i 0.517373 + 0.896116i 0.999796 + 0.0201776i $$0.00642318\pi$$
−0.482424 + 0.875938i $$0.660243\pi$$
$$462$$ 0 0
$$463$$ −1651.00 + 2859.62i −0.165720 + 0.287036i −0.936911 0.349568i $$-0.886328\pi$$
0.771191 + 0.636604i $$0.219662\pi$$
$$464$$ 960.000 1662.77i 0.0960493 0.166362i
$$465$$ 0 0
$$466$$ 438.000 + 758.638i 0.0435407 + 0.0754147i
$$467$$ −1923.00 −0.190548 −0.0952739 0.995451i $$-0.530373\pi$$
−0.0952739 + 0.995451i $$0.530373\pi$$
$$468$$ 0 0
$$469$$ 2152.00 0.211877
$$470$$ −720.000 1247.08i −0.0706620 0.122390i
$$471$$ 0 0
$$472$$ 1776.00 3076.12i 0.173193 0.299979i
$$473$$ −3738.00 + 6474.41i −0.363369 + 0.629373i
$$474$$ 0 0
$$475$$ −737.500 1277.39i −0.0712396 0.123391i
$$476$$ 1488.00 0.143282
$$477$$ 0 0
$$478$$ 12828.0 1.22749
$$479$$ −7623.00 13203.4i −0.727148 1.25946i −0.958084 0.286488i $$-0.907512\pi$$
0.230936 0.972969i $$-0.425821\pi$$
$$480$$ 0 0
$$481$$ 2620.00 4537.97i 0.248361 0.430174i
$$482$$ 3431.00 5942.67i 0.324228 0.561579i
$$483$$ 0 0
$$484$$ −866.000 1499.96i −0.0813298 0.140867i
$$485$$ 7720.00 0.722778
$$486$$ 0 0
$$487$$ −8206.00 −0.763551 −0.381776 0.924255i $$-0.624687\pi$$
−0.381776 + 0.924255i $$0.624687\pi$$
$$488$$ 884.000 + 1531.13i 0.0820016 + 0.142031i
$$489$$ 0 0
$$490$$ −1635.00 + 2831.90i −0.150738 + 0.261086i
$$491$$ 8403.00 14554.4i 0.772346 1.33774i −0.163928 0.986472i $$-0.552416\pi$$
0.936274 0.351271i $$-0.114250\pi$$
$$492$$ 0 0
$$493$$ −5580.00 9664.84i −0.509758 0.882926i
$$494$$ −2360.00 −0.214942
$$495$$ 0 0
$$496$$ 752.000 0.0680762
$$497$$ −1380.00 2390.23i −0.124550 0.215727i
$$498$$ 0 0
$$499$$ 2712.50 4698.19i 0.243343 0.421483i −0.718321 0.695711i $$-0.755089\pi$$
0.961664 + 0.274229i $$0.0884226\pi$$
$$500$$ −250.000 + 433.013i −0.0223607 + 0.0387298i
$$501$$ 0 0
$$502$$ −7308.00 12657.8i −0.649745 1.12539i
$$503$$ −19665.0 −1.74318 −0.871589 0.490236i $$-0.836910\pi$$
−0.871589 + 0.490236i $$0.836910\pi$$
$$504$$ 0 0
$$505$$ 660.000 0.0581577
$$506$$ 378.000 + 654.715i 0.0332098 + 0.0575210i
$$507$$ 0 0
$$508$$ −1372.00 + 2376.37i −0.119828 + 0.207548i
$$509$$ 7362.00 12751.4i 0.641090 1.11040i −0.344100 0.938933i $$-0.611816\pi$$
0.985190 0.171468i $$-0.0548509\pi$$
$$510$$ 0 0
$$511$$ −2252.00 3900.58i −0.194956 0.337674i
$$512$$ −512.000 −0.0441942
$$513$$ 0 0
$$514$$ −7458.00 −0.639997
$$515$$ 2230.00 + 3862.47i 0.190807 + 0.330487i
$$516$$ 0 0
$$517$$ −3024.00 + 5237.72i −0.257244 + 0.445560i
$$518$$ 1048.00 1815.19i 0.0888928 0.153967i
$$519$$ 0 0
$$520$$ 400.000 + 692.820i 0.0337330 + 0.0584273i
$$521$$ 2058.00 0.173057 0.0865284 0.996249i $$-0.472423\pi$$
0.0865284 + 0.996249i $$0.472423\pi$$
$$522$$ 0 0
$$523$$ 11912.0 0.995938 0.497969 0.867195i $$-0.334079\pi$$
0.497969 + 0.867195i $$0.334079\pi$$
$$524$$ −228.000 394.908i −0.0190081 0.0329229i
$$525$$ 0 0
$$526$$ 1956.00 3387.89i 0.162140 0.280835i
$$527$$ 2185.50 3785.40i 0.180649 0.312893i
$$528$$ 0 0
$$529$$ 6043.00 + 10466.8i 0.496671 + 0.860260i
$$530$$ 7410.00 0.607302
$$531$$ 0 0
$$532$$ −944.000 −0.0769316
$$533$$ 1260.00 + 2182.38i 0.102395 + 0.177354i
$$534$$ 0 0
$$535$$ −2850.00 + 4936.34i −0.230311 + 0.398910i
$$536$$ −2152.00 + 3727.37i −0.173418 + 0.300369i
$$537$$ 0 0
$$538$$ −990.000 1714.73i −0.0793344 0.137411i
$$539$$ 13734.0 1.09752
$$540$$ 0 0
$$541$$ −5170.00 −0.410861 −0.205430 0.978672i $$-0.565859\pi$$
−0.205430 + 0.978672i $$0.565859\pi$$
$$542$$ 8495.00 + 14713.8i 0.673232 + 1.16607i
$$543$$ 0 0
$$544$$ −1488.00 + 2577.29i −0.117275 + 0.203126i
$$545$$ 4337.50 7512.77i 0.340914 0.590480i
$$546$$ 0 0
$$547$$ 2093.00 + 3625.18i 0.163602 + 0.283367i 0.936158 0.351580i $$-0.114355\pi$$
−0.772556 + 0.634947i $$0.781022\pi$$
$$548$$ −636.000 −0.0495777
$$549$$ 0 0
$$550$$ 2100.00 0.162808
$$551$$ 3540.00 + 6131.46i 0.273701 + 0.474063i
$$552$$ 0 0
$$553$$ 1330.00 2303.63i 0.102274 0.177143i
$$554$$ −1366.00 + 2365.98i −0.104758 + 0.181446i
$$555$$ 0 0
$$556$$ −4552.00 7884.30i −0.347208 0.601382i
$$557$$ 13026.0 0.990896 0.495448 0.868637i $$-0.335004\pi$$
0.495448 + 0.868637i $$0.335004\pi$$
$$558$$ 0 0
$$559$$ −3560.00 −0.269359
$$560$$ 160.000 + 277.128i 0.0120736 + 0.0209121i
$$561$$ 0 0
$$562$$ −5520.00 + 9560.92i −0.414319 + 0.717621i
$$563$$ 5334.00 9238.76i 0.399292 0.691594i −0.594347 0.804209i $$-0.702589\pi$$
0.993639 + 0.112615i $$0.0359227\pi$$
$$564$$ 0 0
$$565$$ −3585.00 6209.40i −0.266942 0.462357i
$$566$$ −10876.0 −0.807690
$$567$$ 0 0
$$568$$ 5520.00 0.407771
$$569$$ 7686.00 + 13312.5i 0.566281 + 0.980827i 0.996929 + 0.0783076i $$0.0249516\pi$$
−0.430648 + 0.902520i $$0.641715\pi$$
$$570$$ 0 0
$$571$$ 7494.50 12980.9i 0.549273 0.951369i −0.449051 0.893506i $$-0.648238\pi$$
0.998325 0.0578633i $$-0.0184287\pi$$
$$572$$ 1680.00 2909.85i 0.122805 0.212704i
$$573$$ 0 0
$$574$$ 504.000 + 872.954i 0.0366490 + 0.0634780i
$$575$$ −225.000 −0.0163185
$$576$$ 0 0
$$577$$ −1066.00 −0.0769119 −0.0384559 0.999260i $$-0.512244\pi$$
−0.0384559 + 0.999260i $$0.512244\pi$$
$$578$$ 3736.00 + 6470.94i 0.268853 + 0.465667i
$$579$$ 0 0
$$580$$ 1200.00 2078.46i 0.0859091 0.148799i
$$581$$ −150.000 + 259.808i −0.0107109 + 0.0185519i
$$582$$ 0 0
$$583$$ −15561.0 26952.4i −1.10544 1.91468i
$$584$$ 9008.00 0.638277
$$585$$ 0 0
$$586$$ −16506.0 −1.16358
$$587$$ 310.500 + 537.802i 0.0218325 + 0.0378151i 0.876735 0.480973i $$-0.159717\pi$$
−0.854903 + 0.518788i $$0.826383\pi$$
$$588$$ 0 0
$$589$$ −1386.50 + 2401.49i −0.0969945 + 0.167999i
$$590$$ 2220.00 3845.15i 0.154908 0.268309i
$$591$$ 0 0
$$592$$ 2096.00 + 3630.38i 0.145515 + 0.252040i
$$593$$ −20187.0 −1.39794 −0.698972 0.715149i $$-0.746359\pi$$
−0.698972 + 0.715149i $$0.746359\pi$$
$$594$$ 0 0
$$595$$ 1860.00 0.128156
$$596$$ −2796.00 4842.81i −0.192162 0.332835i
$$597$$ 0 0
$$598$$ −180.000 + 311.769i −0.0123089 + 0.0213197i
$$599$$ 9114.00 15785.9i 0.621683 1.07679i −0.367490 0.930028i $$-0.619783\pi$$
0.989172 0.146758i $$-0.0468840\pi$$
$$600$$ 0 0
$$601$$ 5871.50 + 10169.7i 0.398508 + 0.690237i 0.993542 0.113464i $$-0.0361947\pi$$
−0.595034 + 0.803701i $$0.702861\pi$$
$$602$$ −1424.00 −0.0964085
$$603$$ 0 0
$$604$$ 10496.0 0.707080
$$605$$ −1082.50 1874.94i −0.0727436 0.125996i
$$606$$ 0 0
$$607$$ 12209.0 21146.6i 0.816389 1.41403i −0.0919375 0.995765i $$-0.529306\pi$$
0.908326 0.418262i $$-0.137361\pi$$
$$608$$ 944.000 1635.06i 0.0629675 0.109063i
$$609$$ 0 0
$$610$$ 1105.00 + 1913.92i 0.0733445 + 0.127036i
$$611$$ −2880.00 −0.190691
$$612$$ 0 0
$$613$$ 2672.00 0.176054 0.0880270 0.996118i $$-0.471944\pi$$
0.0880270 + 0.996118i $$0.471944\pi$$
$$614$$ 9290.00 + 16090.8i 0.610609 + 1.05761i
$$615$$ 0 0
$$616$$ 672.000 1163.94i 0.0439540 0.0761305i
$$617$$ 4300.50 7448.68i 0.280602 0.486017i −0.690931 0.722921i $$-0.742799\pi$$
0.971533 + 0.236903i $$0.0761325\pi$$
$$618$$ 0 0
$$619$$ −10654.0 18453.3i −0.691794 1.19822i −0.971250 0.238064i $$-0.923487\pi$$
0.279456 0.960159i $$-0.409846\pi$$
$$620$$ 940.000 0.0608892
$$621$$ 0 0
$$622$$ −16224.0 −1.04586
$$623$$ 2172.00 + 3762.01i 0.139678 + 0.241929i
$$624$$ 0 0
$$625$$ −312.500 + 541.266i −0.0200000 + 0.0346410i
$$626$$ −7900.00 + 13683.2i −0.504389 + 0.873627i
$$627$$ 0 0
$$628$$ 788.000 + 1364.86i 0.0500711 + 0.0867256i
$$629$$ 24366.0 1.54457
$$630$$ 0 0
$$631$$ −19015.0 −1.19964 −0.599822 0.800134i $$-0.704762\pi$$
−0.599822 + 0.800134i $$0.704762\pi$$
$$632$$ 2660.00 + 4607.26i 0.167419 + 0.289979i
$$633$$ 0 0
$$634$$ 4419.00 7653.93i 0.276815 0.479458i
$$635$$ −1715.00 + 2970.47i −0.107177 + 0.185637i
$$636$$ 0 0
$$637$$ 3270.00 + 5663.81i 0.203394 + 0.352289i
$$638$$ −10080.0 −0.625503
$$639$$ 0 0
$$640$$ −640.000 −0.0395285
$$641$$ 2208.00 + 3824.37i 0.136054 + 0.235653i 0.926000 0.377524i $$-0.123225\pi$$
−0.789945 + 0.613177i $$0.789891\pi$$
$$642$$ 0 0
$$643$$ −3790.00 + 6564.47i −0.232446 + 0.402609i −0.958527 0.285000i $$-0.908006\pi$$
0.726081 + 0.687609i $$0.241340\pi$$
$$644$$ −72.0000 + 124.708i −0.00440559 + 0.00763070i
$$645$$ 0 0
$$646$$ −5487.00 9503.76i −0.334184 0.578824i
$$647$$ −14901.0 −0.905439 −0.452719 0.891653i $$-0.649546\pi$$
−0.452719 + 0.891653i $$0.649546\pi$$
$$648$$ 0 0
$$649$$ −18648.0 −1.12789
$$650$$ 500.000 + 866.025i 0.0301717 + 0.0522589i
$$651$$ 0 0
$$652$$ 6692.00 11590.9i 0.401962 0.696218i
$$653$$ −6457.50 + 11184.7i −0.386985 + 0.670278i −0.992042 0.125904i $$-0.959817\pi$$
0.605057 + 0.796182i $$0.293150\pi$$
$$654$$ 0 0
$$655$$ −285.000 493.634i −0.0170013 0.0294472i
$$656$$ −2016.00 −0.119987
$$657$$ 0 0
$$658$$ −1152.00 −0.0682517
$$659$$ −14064.0 24359.6i −0.831344 1.43993i −0.896973 0.442086i $$-0.854239\pi$$
0.0656288 0.997844i $$-0.479095\pi$$
$$660$$ 0 0
$$661$$ 4181.00 7241.70i 0.246024 0.426127i −0.716395 0.697695i $$-0.754209\pi$$
0.962419 + 0.271569i $$0.0875424\pi$$
$$662$$ −8200.00 + 14202.8i −0.481423 + 0.833849i
$$663$$ 0 0
$$664$$ −300.000 519.615i −0.0175335 0.0303689i
$$665$$ −1180.00 −0.0688097
$$666$$ 0 0
$$667$$ 1080.00 0.0626953
$$668$$ −2982.00 5164.98i −0.172720 0.299160i
$$669$$ 0 0
$$670$$ −2690.00 + 4659.22i −0.155110 + 0.268659i
$$671$$ 4641.00 8038.45i 0.267010 0.462475i
$$672$$ 0 0
$$673$$ −14854.0 25727.9i −0.850787 1.47361i −0.880499 0.474048i $$-0.842792\pi$$
0.0297122 0.999558i $$-0.490541\pi$$
$$674$$ 19112.0 1.09224
$$675$$ 0 0
$$676$$ −7188.00 −0.408967
$$677$$ −3381.00 5856.06i −0.191939 0.332447i 0.753954 0.656927i $$-0.228144\pi$$
−0.945893 + 0.324480i $$0.894811\pi$$
$$678$$ 0 0
$$679$$ 3088.00 5348.57i 0.174531 0.302297i
$$680$$ −1860.00 + 3221.61i −0.104894 + 0.181681i
$$681$$ 0 0
$$682$$ −1974.00 3419.07i −0.110833 0.191969i
$$683$$ −19155.0 −1.07313 −0.536563 0.843860i $$-0.680278\pi$$
−0.536563 + 0.843860i $$0.680278\pi$$
$$684$$ 0 0
$$685$$ −795.000 −0.0443436
$$686$$ 2680.00 + 4641.90i 0.149159 + 0.258350i
$$687$$ 0 0
$$688$$ 1424.00 2466.44i 0.0789091 0.136675i
$$689$$ 7410.00 12834.5i 0.409722 0.709659i
$$690$$ 0 0
$$691$$ 11487.5 + 19896.9i 0.632424 + 1.09539i 0.987055 + 0.160384i $$0.0512733\pi$$
−0.354630 + 0.935007i $$0.615393\pi$$
$$692$$ −9612.00 −0.528025
$$693$$ 0 0
$$694$$ −20232.0 −1.10662
$$695$$ −5690.00 9855.37i −0.310553 0.537893i
$$696$$ 0 0
$$697$$ −5859.00 + 10148.1i −0.318401 + 0.551487i
$$698$$ −6751.00 + 11693.1i −0.366088 + 0.634082i
$$699$$ 0 0
$$700$$ 200.000 + 346.410i 0.0107990 + 0.0187044i
$$701$$ −6450.00 −0.347522 −0.173761 0.984788i $$-0.555592\pi$$
−0.173761 + 0.984788i $$0.555592\pi$$
$$702$$ 0 0
$$703$$ −15458.0 −0.829317
$$704$$ 1344.00 + 2327.88i 0.0719516 + 0.124624i
$$705$$ 0 0
$$706$$ 4062.00 7035.59i 0.216537 0.375054i
$$707$$ 264.000 457.261i 0.0140435 0.0243240i
$$708$$ 0 0
$$709$$ −17269.0 29910.8i −0.914740 1.58438i −0.807281 0.590167i $$-0.799062\pi$$
−0.107459 0.994209i $$-0.534272\pi$$
$$710$$ 6900.00 0.364722
$$711$$ 0 0
$$712$$ −8688.00 −0.457299
$$713$$ 211.500 + 366.329i 0.0111090 + 0.0192414i
$$714$$ 0 0
$$715$$ 2100.00 3637.31i 0.109840 0.190248i
$$716$$ −5280.00 + 9145.23i −0.275591 + 0.477337i
$$717$$ 0 0
$$718$$ 8778.00 + 15203.9i 0.456256 + 0.790259i
$$719$$ 27114.0 1.40637 0.703186 0.711006i $$-0.251760\pi$$
0.703186 + 0.711006i $$0.251760\pi$$
$$720$$ 0 0
$$721$$ 3568.00 0.184299
$$722$$ −3378.00 5850.87i −0.174122 0.301588i
$$723$$ 0 0
$$724$$ −2146.00 + 3716.98i −0.110159 + 0.190802i
$$725$$ 1500.00 2598.08i 0.0768395 0.133090i
$$726$$ 0 0
$$727$$ −118.000 204.382i −0.00601978 0.0104266i 0.863000 0.505204i $$-0.168583\pi$$
−0.869020 + 0.494778i $$0.835249\pi$$
$$728$$ 640.000 0.0325824
$$729$$ 0 0
$$730$$ 11260.0 0.570892
$$731$$ −8277.00 14336.2i −0.418791 0.725367i
$$732$$ 0 0
$$733$$ −13564.0 + 23493.5i −0.683489 + 1.18384i 0.290420 + 0.956899i $$0.406205\pi$$
−0.973909 + 0.226939i $$0.927128\pi$$
$$734$$ 956.000 1655.84i 0.0480744 0.0832673i
$$735$$ 0 0
$$736$$ −144.000 249.415i −0.00721183 0.0124913i
$$737$$ 22596.0 1.12935
$$738$$ 0 0
$$739$$ 5249.00 0.261282 0.130641 0.991430i $$-0.458296\pi$$
0.130641 + 0.991430i $$0.458296\pi$$
$$740$$ 2620.00 + 4537.97i 0.130153 + 0.225431i
$$741$$ 0 0
$$742$$ 2964.00 5133.80i 0.146647 0.254000i
$$743$$ −6948.00 + 12034.3i −0.343065 + 0.594206i −0.985000 0.172553i $$-0.944798\pi$$
0.641935 + 0.766759i $$0.278132\pi$$
$$744$$ 0 0
$$745$$ −3495.00 6053.52i −0.171875 0.297696i
$$746$$ −4600.00 −0.225761
$$747$$ 0 0
$$748$$ 15624.0 0.763730
$$749$$ 2280.00 + 3949.08i 0.111227 + 0.192652i
$$750$$ 0 0
$$751$$ −13832.5 + 23958.6i −0.672111 + 1.16413i 0.305194 + 0.952290i $$0.401279\pi$$
−0.977304 + 0.211840i $$0.932055\pi$$
$$752$$ 1152.00 1995.32i 0.0558632 0.0967579i
$$753$$ 0 0
$$754$$ −2400.00 4156.92i −0.115919 0.200777i
$$755$$ 13120.0 0.632431
$$756$$ 0 0
$$757$$ −8122.00 −0.389959 −0.194980 0.980807i $$-0.562464\pi$$
−0.194980 + 0.980807i $$0.562464\pi$$
$$758$$ 29.0000 + 50.2295i 0.00138961 + 0.00240688i
$$759$$ 0 0
$$760$$ 1180.00 2043.82i 0.0563199 0.0975489i
$$761$$ −5292.00 + 9166.01i −0.252083 + 0.436620i −0.964099 0.265543i $$-0.914449\pi$$
0.712016 + 0.702163i $$0.247782\pi$$
$$762$$ 0 0
$$763$$ −3470.00 6010.22i −0.164643 0.285170i
$$764$$ −5880.00 −0.278444
$$765$$ 0 0
$$766$$ −16254.0 −0.766685
$$767$$ −4440.00 7690.31i −0.209021 0.362035i
$$768$$ 0 0
$$769$$ 9309.50 16124.5i 0.436553 0.756132i −0.560868 0.827905i $$-0.689533\pi$$
0.997421 + 0.0717734i $$0.0228659\pi$$
$$770$$ 840.000 1454.92i 0.0393136 0.0680932i
$$771$$ 0 0
$$772$$ 9440.00 + 16350.6i 0.440095 + 0.762266i
$$773$$ 22251.0 1.03533 0.517667 0.855582i $$-0.326801\pi$$
0.517667 + 0.855582i $$0.326801\pi$$
$$774$$ 0 0
$$775$$ 1175.00 0.0544610
$$776$$ 6176.00 + 10697.1i 0.285703 + 0.494852i
$$777$$ 0 0
$$778$$ −7938.00 + 13749.0i −0.365798 + 0.633581i
$$779$$ 3717.00 6438.03i 0.170957 0.296106i
$$780$$ 0 0
$$781$$ −14490.0 25097.4i −0.663883 1.14988i
$$782$$ −1674.00 −0.0765500
$$783$$ 0 0
$$784$$ −5232.00 −0.238338
$$785$$ 985.000 + 1706.07i 0.0447849 + 0.0775697i