# Properties

 Label 108.3.d.a.55.2 Level 108 Weight 3 Character 108.55 Analytic conductor 2.943 Analytic rank 0 Dimension 2 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 108.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.94278685509$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 55.2 Root $$0.500000 - 0.866025i$$ of $$x^{2} - x + 1$$ Character $$\chi$$ $$=$$ 108.55 Dual form 108.3.d.a.55.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +7.00000 q^{5} -8.66025i q^{7} +8.00000 q^{8} +O(q^{10})$$ $$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +7.00000 q^{5} -8.66025i q^{7} +8.00000 q^{8} +(-7.00000 + 12.1244i) q^{10} +8.66025i q^{11} +20.0000 q^{13} +(15.0000 + 8.66025i) q^{14} +(-8.00000 + 13.8564i) q^{16} -8.00000 q^{17} +10.3923i q^{19} +(-14.0000 - 24.2487i) q^{20} +(-15.0000 - 8.66025i) q^{22} -3.46410i q^{23} +24.0000 q^{25} +(-20.0000 + 34.6410i) q^{26} +(-30.0000 + 17.3205i) q^{28} +10.0000 q^{29} -53.6936i q^{31} +(-16.0000 - 27.7128i) q^{32} +(8.00000 - 13.8564i) q^{34} -60.6218i q^{35} -10.0000 q^{37} +(-18.0000 - 10.3923i) q^{38} +56.0000 q^{40} -50.0000 q^{41} +17.3205i q^{43} +(30.0000 - 17.3205i) q^{44} +(6.00000 + 3.46410i) q^{46} +86.6025i q^{47} -26.0000 q^{49} +(-24.0000 + 41.5692i) q^{50} +(-40.0000 - 69.2820i) q^{52} -47.0000 q^{53} +60.6218i q^{55} -69.2820i q^{56} +(-10.0000 + 17.3205i) q^{58} -34.6410i q^{59} -64.0000 q^{61} +(93.0000 + 53.6936i) q^{62} +64.0000 q^{64} +140.000 q^{65} +86.6025i q^{67} +(16.0000 + 27.7128i) q^{68} +(105.000 + 60.6218i) q^{70} -55.0000 q^{73} +(10.0000 - 17.3205i) q^{74} +(36.0000 - 20.7846i) q^{76} +75.0000 q^{77} +6.92820i q^{79} +(-56.0000 + 96.9948i) q^{80} +(50.0000 - 86.6025i) q^{82} +29.4449i q^{83} -56.0000 q^{85} +(-30.0000 - 17.3205i) q^{86} +69.2820i q^{88} +10.0000 q^{89} -173.205i q^{91} +(-12.0000 + 6.92820i) q^{92} +(-150.000 - 86.6025i) q^{94} +72.7461i q^{95} -25.0000 q^{97} +(26.0000 - 45.0333i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{2} - 4q^{4} + 14q^{5} + 16q^{8} + O(q^{10})$$ $$2q - 2q^{2} - 4q^{4} + 14q^{5} + 16q^{8} - 14q^{10} + 40q^{13} + 30q^{14} - 16q^{16} - 16q^{17} - 28q^{20} - 30q^{22} + 48q^{25} - 40q^{26} - 60q^{28} + 20q^{29} - 32q^{32} + 16q^{34} - 20q^{37} - 36q^{38} + 112q^{40} - 100q^{41} + 60q^{44} + 12q^{46} - 52q^{49} - 48q^{50} - 80q^{52} - 94q^{53} - 20q^{58} - 128q^{61} + 186q^{62} + 128q^{64} + 280q^{65} + 32q^{68} + 210q^{70} - 110q^{73} + 20q^{74} + 72q^{76} + 150q^{77} - 112q^{80} + 100q^{82} - 112q^{85} - 60q^{86} + 20q^{89} - 24q^{92} - 300q^{94} - 50q^{97} + 52q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$55$$ $$\chi(n)$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 + 1.73205i −0.500000 + 0.866025i
$$3$$ 0 0
$$4$$ −2.00000 3.46410i −0.500000 0.866025i
$$5$$ 7.00000 1.40000 0.700000 0.714143i $$-0.253183\pi$$
0.700000 + 0.714143i $$0.253183\pi$$
$$6$$ 0 0
$$7$$ 8.66025i 1.23718i −0.785714 0.618590i $$-0.787704\pi$$
0.785714 0.618590i $$-0.212296\pi$$
$$8$$ 8.00000 1.00000
$$9$$ 0 0
$$10$$ −7.00000 + 12.1244i −0.700000 + 1.21244i
$$11$$ 8.66025i 0.787296i 0.919261 + 0.393648i $$0.128787\pi$$
−0.919261 + 0.393648i $$0.871213\pi$$
$$12$$ 0 0
$$13$$ 20.0000 1.53846 0.769231 0.638971i $$-0.220640\pi$$
0.769231 + 0.638971i $$0.220640\pi$$
$$14$$ 15.0000 + 8.66025i 1.07143 + 0.618590i
$$15$$ 0 0
$$16$$ −8.00000 + 13.8564i −0.500000 + 0.866025i
$$17$$ −8.00000 −0.470588 −0.235294 0.971924i $$-0.575605\pi$$
−0.235294 + 0.971924i $$0.575605\pi$$
$$18$$ 0 0
$$19$$ 10.3923i 0.546963i 0.961877 + 0.273482i $$0.0881753\pi$$
−0.961877 + 0.273482i $$0.911825\pi$$
$$20$$ −14.0000 24.2487i −0.700000 1.21244i
$$21$$ 0 0
$$22$$ −15.0000 8.66025i −0.681818 0.393648i
$$23$$ 3.46410i 0.150613i −0.997160 0.0753066i $$-0.976006\pi$$
0.997160 0.0753066i $$-0.0239935\pi$$
$$24$$ 0 0
$$25$$ 24.0000 0.960000
$$26$$ −20.0000 + 34.6410i −0.769231 + 1.33235i
$$27$$ 0 0
$$28$$ −30.0000 + 17.3205i −1.07143 + 0.618590i
$$29$$ 10.0000 0.344828 0.172414 0.985025i $$-0.444843\pi$$
0.172414 + 0.985025i $$0.444843\pi$$
$$30$$ 0 0
$$31$$ 53.6936i 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$32$$ −16.0000 27.7128i −0.500000 0.866025i
$$33$$ 0 0
$$34$$ 8.00000 13.8564i 0.235294 0.407541i
$$35$$ 60.6218i 1.73205i
$$36$$ 0 0
$$37$$ −10.0000 −0.270270 −0.135135 0.990827i $$-0.543147\pi$$
−0.135135 + 0.990827i $$0.543147\pi$$
$$38$$ −18.0000 10.3923i −0.473684 0.273482i
$$39$$ 0 0
$$40$$ 56.0000 1.40000
$$41$$ −50.0000 −1.21951 −0.609756 0.792589i $$-0.708733\pi$$
−0.609756 + 0.792589i $$0.708733\pi$$
$$42$$ 0 0
$$43$$ 17.3205i 0.402803i 0.979509 + 0.201401i $$0.0645495\pi$$
−0.979509 + 0.201401i $$0.935450\pi$$
$$44$$ 30.0000 17.3205i 0.681818 0.393648i
$$45$$ 0 0
$$46$$ 6.00000 + 3.46410i 0.130435 + 0.0753066i
$$47$$ 86.6025i 1.84261i 0.388844 + 0.921304i $$0.372875\pi$$
−0.388844 + 0.921304i $$0.627125\pi$$
$$48$$ 0 0
$$49$$ −26.0000 −0.530612
$$50$$ −24.0000 + 41.5692i −0.480000 + 0.831384i
$$51$$ 0 0
$$52$$ −40.0000 69.2820i −0.769231 1.33235i
$$53$$ −47.0000 −0.886792 −0.443396 0.896326i $$-0.646227\pi$$
−0.443396 + 0.896326i $$0.646227\pi$$
$$54$$ 0 0
$$55$$ 60.6218i 1.10221i
$$56$$ 69.2820i 1.23718i
$$57$$ 0 0
$$58$$ −10.0000 + 17.3205i −0.172414 + 0.298629i
$$59$$ 34.6410i 0.587136i −0.955938 0.293568i $$-0.905157\pi$$
0.955938 0.293568i $$-0.0948427\pi$$
$$60$$ 0 0
$$61$$ −64.0000 −1.04918 −0.524590 0.851355i $$-0.675781\pi$$
−0.524590 + 0.851355i $$0.675781\pi$$
$$62$$ 93.0000 + 53.6936i 1.50000 + 0.866025i
$$63$$ 0 0
$$64$$ 64.0000 1.00000
$$65$$ 140.000 2.15385
$$66$$ 0 0
$$67$$ 86.6025i 1.29258i 0.763094 + 0.646288i $$0.223679\pi$$
−0.763094 + 0.646288i $$0.776321\pi$$
$$68$$ 16.0000 + 27.7128i 0.235294 + 0.407541i
$$69$$ 0 0
$$70$$ 105.000 + 60.6218i 1.50000 + 0.866025i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ −55.0000 −0.753425 −0.376712 0.926330i $$-0.622945\pi$$
−0.376712 + 0.926330i $$0.622945\pi$$
$$74$$ 10.0000 17.3205i 0.135135 0.234061i
$$75$$ 0 0
$$76$$ 36.0000 20.7846i 0.473684 0.273482i
$$77$$ 75.0000 0.974026
$$78$$ 0 0
$$79$$ 6.92820i 0.0876988i 0.999038 + 0.0438494i $$0.0139622\pi$$
−0.999038 + 0.0438494i $$0.986038\pi$$
$$80$$ −56.0000 + 96.9948i −0.700000 + 1.21244i
$$81$$ 0 0
$$82$$ 50.0000 86.6025i 0.609756 1.05613i
$$83$$ 29.4449i 0.354757i 0.984143 + 0.177379i $$0.0567617\pi$$
−0.984143 + 0.177379i $$0.943238\pi$$
$$84$$ 0 0
$$85$$ −56.0000 −0.658824
$$86$$ −30.0000 17.3205i −0.348837 0.201401i
$$87$$ 0 0
$$88$$ 69.2820i 0.787296i
$$89$$ 10.0000 0.112360 0.0561798 0.998421i $$-0.482108\pi$$
0.0561798 + 0.998421i $$0.482108\pi$$
$$90$$ 0 0
$$91$$ 173.205i 1.90335i
$$92$$ −12.0000 + 6.92820i −0.130435 + 0.0753066i
$$93$$ 0 0
$$94$$ −150.000 86.6025i −1.59574 0.921304i
$$95$$ 72.7461i 0.765749i
$$96$$ 0 0
$$97$$ −25.0000 −0.257732 −0.128866 0.991662i $$-0.541134\pi$$
−0.128866 + 0.991662i $$0.541134\pi$$
$$98$$ 26.0000 45.0333i 0.265306 0.459524i
$$99$$ 0 0
$$100$$ −48.0000 83.1384i −0.480000 0.831384i
$$101$$ −155.000 −1.53465 −0.767327 0.641256i $$-0.778414\pi$$
−0.767327 + 0.641256i $$0.778414\pi$$
$$102$$ 0 0
$$103$$ 138.564i 1.34528i 0.739969 + 0.672641i $$0.234840\pi$$
−0.739969 + 0.672641i $$0.765160\pi$$
$$104$$ 160.000 1.53846
$$105$$ 0 0
$$106$$ 47.0000 81.4064i 0.443396 0.767985i
$$107$$ 129.904i 1.21405i −0.794681 0.607027i $$-0.792362\pi$$
0.794681 0.607027i $$-0.207638\pi$$
$$108$$ 0 0
$$109$$ 134.000 1.22936 0.614679 0.788777i $$-0.289286\pi$$
0.614679 + 0.788777i $$0.289286\pi$$
$$110$$ −105.000 60.6218i −0.954545 0.551107i
$$111$$ 0 0
$$112$$ 120.000 + 69.2820i 1.07143 + 0.618590i
$$113$$ −74.0000 −0.654867 −0.327434 0.944874i $$-0.606184\pi$$
−0.327434 + 0.944874i $$0.606184\pi$$
$$114$$ 0 0
$$115$$ 24.2487i 0.210858i
$$116$$ −20.0000 34.6410i −0.172414 0.298629i
$$117$$ 0 0
$$118$$ 60.0000 + 34.6410i 0.508475 + 0.293568i
$$119$$ 69.2820i 0.582202i
$$120$$ 0 0
$$121$$ 46.0000 0.380165
$$122$$ 64.0000 110.851i 0.524590 0.908617i
$$123$$ 0 0
$$124$$ −186.000 + 107.387i −1.50000 + 0.866025i
$$125$$ −7.00000 −0.0560000
$$126$$ 0 0
$$127$$ 25.9808i 0.204573i −0.994755 0.102286i $$-0.967384\pi$$
0.994755 0.102286i $$-0.0326158\pi$$
$$128$$ −64.0000 + 110.851i −0.500000 + 0.866025i
$$129$$ 0 0
$$130$$ −140.000 + 242.487i −1.07692 + 1.86529i
$$131$$ 164.545i 1.25607i −0.778186 0.628034i $$-0.783860\pi$$
0.778186 0.628034i $$-0.216140\pi$$
$$132$$ 0 0
$$133$$ 90.0000 0.676692
$$134$$ −150.000 86.6025i −1.11940 0.646288i
$$135$$ 0 0
$$136$$ −64.0000 −0.470588
$$137$$ −62.0000 −0.452555 −0.226277 0.974063i $$-0.572656\pi$$
−0.226277 + 0.974063i $$0.572656\pi$$
$$138$$ 0 0
$$139$$ 173.205i 1.24608i −0.782190 0.623040i $$-0.785897\pi$$
0.782190 0.623040i $$-0.214103\pi$$
$$140$$ −210.000 + 121.244i −1.50000 + 0.866025i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 173.205i 1.21122i
$$144$$ 0 0
$$145$$ 70.0000 0.482759
$$146$$ 55.0000 95.2628i 0.376712 0.652485i
$$147$$ 0 0
$$148$$ 20.0000 + 34.6410i 0.135135 + 0.234061i
$$149$$ 115.000 0.771812 0.385906 0.922538i $$-0.373889\pi$$
0.385906 + 0.922538i $$0.373889\pi$$
$$150$$ 0 0
$$151$$ 43.3013i 0.286763i 0.989667 + 0.143382i $$0.0457977\pi$$
−0.989667 + 0.143382i $$0.954202\pi$$
$$152$$ 83.1384i 0.546963i
$$153$$ 0 0
$$154$$ −75.0000 + 129.904i −0.487013 + 0.843531i
$$155$$ 375.855i 2.42487i
$$156$$ 0 0
$$157$$ 20.0000 0.127389 0.0636943 0.997969i $$-0.479712\pi$$
0.0636943 + 0.997969i $$0.479712\pi$$
$$158$$ −12.0000 6.92820i −0.0759494 0.0438494i
$$159$$ 0 0
$$160$$ −112.000 193.990i −0.700000 1.21244i
$$161$$ −30.0000 −0.186335
$$162$$ 0 0
$$163$$ 103.923i 0.637565i 0.947828 + 0.318782i $$0.103274\pi$$
−0.947828 + 0.318782i $$0.896726\pi$$
$$164$$ 100.000 + 173.205i 0.609756 + 1.05613i
$$165$$ 0 0
$$166$$ −51.0000 29.4449i −0.307229 0.177379i
$$167$$ 245.951i 1.47276i 0.676567 + 0.736381i $$0.263467\pi$$
−0.676567 + 0.736381i $$0.736533\pi$$
$$168$$ 0 0
$$169$$ 231.000 1.36686
$$170$$ 56.0000 96.9948i 0.329412 0.570558i
$$171$$ 0 0
$$172$$ 60.0000 34.6410i 0.348837 0.201401i
$$173$$ 127.000 0.734104 0.367052 0.930200i $$-0.380367\pi$$
0.367052 + 0.930200i $$0.380367\pi$$
$$174$$ 0 0
$$175$$ 207.846i 1.18769i
$$176$$ −120.000 69.2820i −0.681818 0.393648i
$$177$$ 0 0
$$178$$ −10.0000 + 17.3205i −0.0561798 + 0.0973062i
$$179$$ 233.827i 1.30630i 0.757231 + 0.653148i $$0.226552\pi$$
−0.757231 + 0.653148i $$0.773448\pi$$
$$180$$ 0 0
$$181$$ 56.0000 0.309392 0.154696 0.987962i $$-0.450560\pi$$
0.154696 + 0.987962i $$0.450560\pi$$
$$182$$ 300.000 + 173.205i 1.64835 + 0.951676i
$$183$$ 0 0
$$184$$ 27.7128i 0.150613i
$$185$$ −70.0000 −0.378378
$$186$$ 0 0
$$187$$ 69.2820i 0.370492i
$$188$$ 300.000 173.205i 1.59574 0.921304i
$$189$$ 0 0
$$190$$ −126.000 72.7461i −0.663158 0.382874i
$$191$$ 34.6410i 0.181367i 0.995880 + 0.0906833i $$0.0289051\pi$$
−0.995880 + 0.0906833i $$0.971095\pi$$
$$192$$ 0 0
$$193$$ 65.0000 0.336788 0.168394 0.985720i $$-0.446142\pi$$
0.168394 + 0.985720i $$0.446142\pi$$
$$194$$ 25.0000 43.3013i 0.128866 0.223202i
$$195$$ 0 0
$$196$$ 52.0000 + 90.0666i 0.265306 + 0.459524i
$$197$$ 253.000 1.28426 0.642132 0.766594i $$-0.278050\pi$$
0.642132 + 0.766594i $$0.278050\pi$$
$$198$$ 0 0
$$199$$ 129.904i 0.652783i −0.945235 0.326391i $$-0.894167\pi$$
0.945235 0.326391i $$-0.105833\pi$$
$$200$$ 192.000 0.960000
$$201$$ 0 0
$$202$$ 155.000 268.468i 0.767327 1.32905i
$$203$$ 86.6025i 0.426613i
$$204$$ 0 0
$$205$$ −350.000 −1.70732
$$206$$ −240.000 138.564i −1.16505 0.672641i
$$207$$ 0 0
$$208$$ −160.000 + 277.128i −0.769231 + 1.33235i
$$209$$ −90.0000 −0.430622
$$210$$ 0 0
$$211$$ 148.956i 0.705954i 0.935632 + 0.352977i $$0.114831\pi$$
−0.935632 + 0.352977i $$0.885169\pi$$
$$212$$ 94.0000 + 162.813i 0.443396 + 0.767985i
$$213$$ 0 0
$$214$$ 225.000 + 129.904i 1.05140 + 0.607027i
$$215$$ 121.244i 0.563924i
$$216$$ 0 0
$$217$$ −465.000 −2.14286
$$218$$ −134.000 + 232.095i −0.614679 + 1.06466i
$$219$$ 0 0
$$220$$ 210.000 121.244i 0.954545 0.551107i
$$221$$ −160.000 −0.723982
$$222$$ 0 0
$$223$$ 34.6410i 0.155341i −0.996979 0.0776704i $$-0.975252\pi$$
0.996979 0.0776704i $$-0.0247482\pi$$
$$224$$ −240.000 + 138.564i −1.07143 + 0.618590i
$$225$$ 0 0
$$226$$ 74.0000 128.172i 0.327434 0.567132i
$$227$$ 90.0666i 0.396769i −0.980124 0.198385i $$-0.936430\pi$$
0.980124 0.198385i $$-0.0635695\pi$$
$$228$$ 0 0
$$229$$ 146.000 0.637555 0.318777 0.947830i $$-0.396728\pi$$
0.318777 + 0.947830i $$0.396728\pi$$
$$230$$ 42.0000 + 24.2487i 0.182609 + 0.105429i
$$231$$ 0 0
$$232$$ 80.0000 0.344828
$$233$$ 334.000 1.43348 0.716738 0.697342i $$-0.245634\pi$$
0.716738 + 0.697342i $$0.245634\pi$$
$$234$$ 0 0
$$235$$ 606.218i 2.57965i
$$236$$ −120.000 + 69.2820i −0.508475 + 0.293568i
$$237$$ 0 0
$$238$$ −120.000 69.2820i −0.504202 0.291101i
$$239$$ 17.3205i 0.0724707i 0.999343 + 0.0362354i $$0.0115366\pi$$
−0.999343 + 0.0362354i $$0.988463\pi$$
$$240$$ 0 0
$$241$$ 134.000 0.556017 0.278008 0.960579i $$-0.410326\pi$$
0.278008 + 0.960579i $$0.410326\pi$$
$$242$$ −46.0000 + 79.6743i −0.190083 + 0.329233i
$$243$$ 0 0
$$244$$ 128.000 + 221.703i 0.524590 + 0.908617i
$$245$$ −182.000 −0.742857
$$246$$ 0 0
$$247$$ 207.846i 0.841482i
$$248$$ 429.549i 1.73205i
$$249$$ 0 0
$$250$$ 7.00000 12.1244i 0.0280000 0.0484974i
$$251$$ 207.846i 0.828072i −0.910260 0.414036i $$-0.864119\pi$$
0.910260 0.414036i $$-0.135881\pi$$
$$252$$ 0 0
$$253$$ 30.0000 0.118577
$$254$$ 45.0000 + 25.9808i 0.177165 + 0.102286i
$$255$$ 0 0
$$256$$ −128.000 221.703i −0.500000 0.866025i
$$257$$ 268.000 1.04280 0.521401 0.853312i $$-0.325410\pi$$
0.521401 + 0.853312i $$0.325410\pi$$
$$258$$ 0 0
$$259$$ 86.6025i 0.334373i
$$260$$ −280.000 484.974i −1.07692 1.86529i
$$261$$ 0 0
$$262$$ 285.000 + 164.545i 1.08779 + 0.628034i
$$263$$ 433.013i 1.64644i −0.567725 0.823218i $$-0.692176\pi$$
0.567725 0.823218i $$-0.307824\pi$$
$$264$$ 0 0
$$265$$ −329.000 −1.24151
$$266$$ −90.0000 + 155.885i −0.338346 + 0.586032i
$$267$$ 0 0
$$268$$ 300.000 173.205i 1.11940 0.646288i
$$269$$ −350.000 −1.30112 −0.650558 0.759457i $$-0.725465\pi$$
−0.650558 + 0.759457i $$0.725465\pi$$
$$270$$ 0 0
$$271$$ 36.3731i 0.134218i −0.997746 0.0671090i $$-0.978622\pi$$
0.997746 0.0671090i $$-0.0213775\pi$$
$$272$$ 64.0000 110.851i 0.235294 0.407541i
$$273$$ 0 0
$$274$$ 62.0000 107.387i 0.226277 0.391924i
$$275$$ 207.846i 0.755804i
$$276$$ 0 0
$$277$$ −520.000 −1.87726 −0.938628 0.344931i $$-0.887902\pi$$
−0.938628 + 0.344931i $$0.887902\pi$$
$$278$$ 300.000 + 173.205i 1.07914 + 0.623040i
$$279$$ 0 0
$$280$$ 484.974i 1.73205i
$$281$$ −440.000 −1.56584 −0.782918 0.622125i $$-0.786270\pi$$
−0.782918 + 0.622125i $$0.786270\pi$$
$$282$$ 0 0
$$283$$ 329.090i 1.16286i −0.813596 0.581430i $$-0.802493\pi$$
0.813596 0.581430i $$-0.197507\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −300.000 173.205i −1.04895 0.605612i
$$287$$ 433.013i 1.50876i
$$288$$ 0 0
$$289$$ −225.000 −0.778547
$$290$$ −70.0000 + 121.244i −0.241379 + 0.418081i
$$291$$ 0 0
$$292$$ 110.000 + 190.526i 0.376712 + 0.652485i
$$293$$ −218.000 −0.744027 −0.372014 0.928227i $$-0.621333\pi$$
−0.372014 + 0.928227i $$0.621333\pi$$
$$294$$ 0 0
$$295$$ 242.487i 0.821990i
$$296$$ −80.0000 −0.270270
$$297$$ 0 0
$$298$$ −115.000 + 199.186i −0.385906 + 0.668409i
$$299$$ 69.2820i 0.231712i
$$300$$ 0 0
$$301$$ 150.000 0.498339
$$302$$ −75.0000 43.3013i −0.248344 0.143382i
$$303$$ 0 0
$$304$$ −144.000 83.1384i −0.473684 0.273482i
$$305$$ −448.000 −1.46885
$$306$$ 0 0
$$307$$ 207.846i 0.677023i −0.940962 0.338512i $$-0.890077\pi$$
0.940962 0.338512i $$-0.109923\pi$$
$$308$$ −150.000 259.808i −0.487013 0.843531i
$$309$$ 0 0
$$310$$ 651.000 + 375.855i 2.10000 + 1.21244i
$$311$$ 294.449i 0.946780i −0.880853 0.473390i $$-0.843030\pi$$
0.880853 0.473390i $$-0.156970\pi$$
$$312$$ 0 0
$$313$$ 485.000 1.54952 0.774760 0.632255i $$-0.217870\pi$$
0.774760 + 0.632255i $$0.217870\pi$$
$$314$$ −20.0000 + 34.6410i −0.0636943 + 0.110322i
$$315$$ 0 0
$$316$$ 24.0000 13.8564i 0.0759494 0.0438494i
$$317$$ 217.000 0.684543 0.342271 0.939601i $$-0.388804\pi$$
0.342271 + 0.939601i $$0.388804\pi$$
$$318$$ 0 0
$$319$$ 86.6025i 0.271481i
$$320$$ 448.000 1.40000
$$321$$ 0 0
$$322$$ 30.0000 51.9615i 0.0931677 0.161371i
$$323$$ 83.1384i 0.257395i
$$324$$ 0 0
$$325$$ 480.000 1.47692
$$326$$ −180.000 103.923i −0.552147 0.318782i
$$327$$ 0 0
$$328$$ −400.000 −1.21951
$$329$$ 750.000 2.27964
$$330$$ 0 0
$$331$$ 433.013i 1.30820i 0.756410 + 0.654098i $$0.226952\pi$$
−0.756410 + 0.654098i $$0.773048\pi$$
$$332$$ 102.000 58.8897i 0.307229 0.177379i
$$333$$ 0 0
$$334$$ −426.000 245.951i −1.27545 0.736381i
$$335$$ 606.218i 1.80961i
$$336$$ 0 0
$$337$$ −310.000 −0.919881 −0.459941 0.887950i $$-0.652129\pi$$
−0.459941 + 0.887950i $$0.652129\pi$$
$$338$$ −231.000 + 400.104i −0.683432 + 1.18374i
$$339$$ 0 0
$$340$$ 112.000 + 193.990i 0.329412 + 0.570558i
$$341$$ 465.000 1.36364
$$342$$ 0 0
$$343$$ 199.186i 0.580717i
$$344$$ 138.564i 0.402803i
$$345$$ 0 0
$$346$$ −127.000 + 219.970i −0.367052 + 0.635753i
$$347$$ 216.506i 0.623938i −0.950092 0.311969i $$-0.899012\pi$$
0.950092 0.311969i $$-0.100988\pi$$
$$348$$ 0 0
$$349$$ 74.0000 0.212034 0.106017 0.994364i $$-0.466190\pi$$
0.106017 + 0.994364i $$0.466190\pi$$
$$350$$ 360.000 + 207.846i 1.02857 + 0.593846i
$$351$$ 0 0
$$352$$ 240.000 138.564i 0.681818 0.393648i
$$353$$ 394.000 1.11615 0.558074 0.829791i $$-0.311541\pi$$
0.558074 + 0.829791i $$0.311541\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −20.0000 34.6410i −0.0561798 0.0973062i
$$357$$ 0 0
$$358$$ −405.000 233.827i −1.13128 0.653148i
$$359$$ 571.577i 1.59214i −0.605207 0.796068i $$-0.706910\pi$$
0.605207 0.796068i $$-0.293090\pi$$
$$360$$ 0 0
$$361$$ 253.000 0.700831
$$362$$ −56.0000 + 96.9948i −0.154696 + 0.267942i
$$363$$ 0 0
$$364$$ −600.000 + 346.410i −1.64835 + 0.951676i
$$365$$ −385.000 −1.05479
$$366$$ 0 0
$$367$$ 562.917i 1.53383i 0.641747 + 0.766916i $$0.278210\pi$$
−0.641747 + 0.766916i $$0.721790\pi$$
$$368$$ 48.0000 + 27.7128i 0.130435 + 0.0753066i
$$369$$ 0 0
$$370$$ 70.0000 121.244i 0.189189 0.327685i
$$371$$ 407.032i 1.09712i
$$372$$ 0 0
$$373$$ −40.0000 −0.107239 −0.0536193 0.998561i $$-0.517076\pi$$
−0.0536193 + 0.998561i $$0.517076\pi$$
$$374$$ 120.000 + 69.2820i 0.320856 + 0.185246i
$$375$$ 0 0
$$376$$ 692.820i 1.84261i
$$377$$ 200.000 0.530504
$$378$$ 0 0
$$379$$ 685.892i 1.80974i −0.425686 0.904871i $$-0.639967\pi$$
0.425686 0.904871i $$-0.360033\pi$$
$$380$$ 252.000 145.492i 0.663158 0.382874i
$$381$$ 0 0
$$382$$ −60.0000 34.6410i −0.157068 0.0906833i
$$383$$ 360.267i 0.940644i 0.882495 + 0.470322i $$0.155862\pi$$
−0.882495 + 0.470322i $$0.844138\pi$$
$$384$$ 0 0
$$385$$ 525.000 1.36364
$$386$$ −65.0000 + 112.583i −0.168394 + 0.291667i
$$387$$ 0 0
$$388$$ 50.0000 + 86.6025i 0.128866 + 0.223202i
$$389$$ 475.000 1.22108 0.610540 0.791986i $$-0.290953\pi$$
0.610540 + 0.791986i $$0.290953\pi$$
$$390$$ 0 0
$$391$$ 27.7128i 0.0708768i
$$392$$ −208.000 −0.530612
$$393$$ 0 0
$$394$$ −253.000 + 438.209i −0.642132 + 1.11221i
$$395$$ 48.4974i 0.122778i
$$396$$ 0 0
$$397$$ 260.000 0.654912 0.327456 0.944866i $$-0.393809\pi$$
0.327456 + 0.944866i $$0.393809\pi$$
$$398$$ 225.000 + 129.904i 0.565327 + 0.326391i
$$399$$ 0 0
$$400$$ −192.000 + 332.554i −0.480000 + 0.831384i
$$401$$ −740.000 −1.84539 −0.922693 0.385535i $$-0.874017\pi$$
−0.922693 + 0.385535i $$0.874017\pi$$
$$402$$ 0 0
$$403$$ 1073.87i 2.66469i
$$404$$ 310.000 + 536.936i 0.767327 + 1.32905i
$$405$$ 0 0
$$406$$ 150.000 + 86.6025i 0.369458 + 0.213307i
$$407$$ 86.6025i 0.212783i
$$408$$ 0 0
$$409$$ 659.000 1.61125 0.805623 0.592428i $$-0.201830\pi$$
0.805623 + 0.592428i $$0.201830\pi$$
$$410$$ 350.000 606.218i 0.853659 1.47858i
$$411$$ 0 0
$$412$$ 480.000 277.128i 1.16505 0.672641i
$$413$$ −300.000 −0.726392
$$414$$ 0 0
$$415$$ 206.114i 0.496660i
$$416$$ −320.000 554.256i −0.769231 1.33235i
$$417$$ 0 0
$$418$$ 90.0000 155.885i 0.215311 0.372930i
$$419$$ 588.897i 1.40548i 0.711445 + 0.702741i $$0.248041\pi$$
−0.711445 + 0.702741i $$0.751959\pi$$
$$420$$ 0 0
$$421$$ −496.000 −1.17815 −0.589074 0.808079i $$-0.700507\pi$$
−0.589074 + 0.808079i $$0.700507\pi$$
$$422$$ −258.000 148.956i −0.611374 0.352977i
$$423$$ 0 0
$$424$$ −376.000 −0.886792
$$425$$ −192.000 −0.451765
$$426$$ 0 0
$$427$$ 554.256i 1.29802i
$$428$$ −450.000 + 259.808i −1.05140 + 0.607027i
$$429$$ 0 0
$$430$$ −210.000 121.244i −0.488372 0.281962i
$$431$$ 571.577i 1.32616i −0.748547 0.663082i $$-0.769248\pi$$
0.748547 0.663082i $$-0.230752\pi$$
$$432$$ 0 0
$$433$$ −235.000 −0.542725 −0.271363 0.962477i $$-0.587474\pi$$
−0.271363 + 0.962477i $$0.587474\pi$$
$$434$$ 465.000 805.404i 1.07143 1.85577i
$$435$$ 0 0
$$436$$ −268.000 464.190i −0.614679 1.06466i
$$437$$ 36.0000 0.0823799
$$438$$ 0 0
$$439$$ 413.960i 0.942962i −0.881876 0.471481i $$-0.843720\pi$$
0.881876 0.471481i $$-0.156280\pi$$
$$440$$ 484.974i 1.10221i
$$441$$ 0 0
$$442$$ 160.000 277.128i 0.361991 0.626987i
$$443$$ 575.041i 1.29806i 0.760763 + 0.649030i $$0.224825\pi$$
−0.760763 + 0.649030i $$0.775175\pi$$
$$444$$ 0 0
$$445$$ 70.0000 0.157303
$$446$$ 60.0000 + 34.6410i 0.134529 + 0.0776704i
$$447$$ 0 0
$$448$$ 554.256i 1.23718i
$$449$$ −470.000 −1.04677 −0.523385 0.852096i $$-0.675331\pi$$
−0.523385 + 0.852096i $$0.675331\pi$$
$$450$$ 0 0
$$451$$ 433.013i 0.960117i
$$452$$ 148.000 + 256.344i 0.327434 + 0.567132i
$$453$$ 0 0
$$454$$ 156.000 + 90.0666i 0.343612 + 0.198385i
$$455$$ 1212.44i 2.66469i
$$456$$ 0 0
$$457$$ −325.000 −0.711160 −0.355580 0.934646i $$-0.615717\pi$$
−0.355580 + 0.934646i $$0.615717\pi$$
$$458$$ −146.000 + 252.879i −0.318777 + 0.552138i
$$459$$ 0 0
$$460$$ −84.0000 + 48.4974i −0.182609 + 0.105429i
$$461$$ 655.000 1.42082 0.710412 0.703786i $$-0.248509\pi$$
0.710412 + 0.703786i $$0.248509\pi$$
$$462$$ 0 0
$$463$$ 164.545i 0.355388i 0.984086 + 0.177694i $$0.0568638\pi$$
−0.984086 + 0.177694i $$0.943136\pi$$
$$464$$ −80.0000 + 138.564i −0.172414 + 0.298629i
$$465$$ 0 0
$$466$$ −334.000 + 578.505i −0.716738 + 1.24143i
$$467$$ 57.1577i 0.122393i 0.998126 + 0.0611967i $$0.0194917\pi$$
−0.998126 + 0.0611967i $$0.980508\pi$$
$$468$$ 0 0
$$469$$ 750.000 1.59915
$$470$$ −1050.00 606.218i −2.23404 1.28983i
$$471$$ 0 0
$$472$$ 277.128i 0.587136i
$$473$$ −150.000 −0.317125
$$474$$ 0 0
$$475$$ 249.415i 0.525085i
$$476$$ 240.000 138.564i 0.504202 0.291101i
$$477$$ 0 0
$$478$$ −30.0000 17.3205i −0.0627615 0.0362354i
$$479$$ 329.090i 0.687035i −0.939146 0.343517i $$-0.888382\pi$$
0.939146 0.343517i $$-0.111618\pi$$
$$480$$ 0 0
$$481$$ −200.000 −0.415800
$$482$$ −134.000 + 232.095i −0.278008 + 0.481524i
$$483$$ 0 0
$$484$$ −92.0000 159.349i −0.190083 0.329233i
$$485$$ −175.000 −0.360825
$$486$$ 0 0
$$487$$ 519.615i 1.06697i 0.845809 + 0.533486i $$0.179118\pi$$
−0.845809 + 0.533486i $$0.820882\pi$$
$$488$$ −512.000 −1.04918
$$489$$ 0 0
$$490$$ 182.000 315.233i 0.371429 0.643333i
$$491$$ 216.506i 0.440950i −0.975393 0.220475i $$-0.929239\pi$$
0.975393 0.220475i $$-0.0707607\pi$$
$$492$$ 0 0
$$493$$ −80.0000 −0.162272
$$494$$ −360.000 207.846i −0.728745 0.420741i
$$495$$ 0 0
$$496$$ 744.000 + 429.549i 1.50000 + 0.866025i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 45.0333i 0.0902471i 0.998981 + 0.0451236i $$0.0143682\pi$$
−0.998981 + 0.0451236i $$0.985632\pi$$
$$500$$ 14.0000 + 24.2487i 0.0280000 + 0.0484974i
$$501$$ 0 0
$$502$$ 360.000 + 207.846i 0.717131 + 0.414036i
$$503$$ 384.515i 0.764444i −0.924071 0.382222i $$-0.875159\pi$$
0.924071 0.382222i $$-0.124841\pi$$
$$504$$ 0 0
$$505$$ −1085.00 −2.14851
$$506$$ −30.0000 + 51.9615i −0.0592885 + 0.102691i
$$507$$ 0 0
$$508$$ −90.0000 + 51.9615i −0.177165 + 0.102286i
$$509$$ 265.000 0.520629 0.260314 0.965524i $$-0.416174\pi$$
0.260314 + 0.965524i $$0.416174\pi$$
$$510$$ 0 0
$$511$$ 476.314i 0.932121i
$$512$$ 512.000 1.00000
$$513$$ 0 0
$$514$$ −268.000 + 464.190i −0.521401 + 0.903093i
$$515$$ 969.948i 1.88340i
$$516$$ 0 0
$$517$$ −750.000 −1.45068
$$518$$ −150.000 86.6025i −0.289575 0.167186i
$$519$$ 0 0
$$520$$ 1120.00 2.15385
$$521$$ −380.000 −0.729367 −0.364683 0.931132i $$-0.618823\pi$$
−0.364683 + 0.931132i $$0.618823\pi$$
$$522$$ 0 0
$$523$$ 623.538i 1.19223i 0.802898 + 0.596117i $$0.203291\pi$$
−0.802898 + 0.596117i $$0.796709\pi$$
$$524$$ −570.000 + 329.090i −1.08779 + 0.628034i
$$525$$ 0 0
$$526$$ 750.000 + 433.013i 1.42586 + 0.823218i
$$527$$ 429.549i 0.815083i
$$528$$ 0 0
$$529$$ 517.000 0.977316
$$530$$ 329.000 569.845i 0.620755 1.07518i
$$531$$ 0 0
$$532$$ −180.000 311.769i −0.338346 0.586032i
$$533$$ −1000.00 −1.87617
$$534$$ 0 0
$$535$$ 909.327i 1.69968i
$$536$$ 692.820i 1.29258i
$$537$$ 0 0
$$538$$ 350.000 606.218i 0.650558 1.12680i
$$539$$ 225.167i 0.417749i
$$540$$ 0 0
$$541$$ −532.000 −0.983364 −0.491682 0.870775i $$-0.663618\pi$$
−0.491682 + 0.870775i $$0.663618\pi$$
$$542$$ 63.0000 + 36.3731i 0.116236 + 0.0671090i
$$543$$ 0 0
$$544$$ 128.000 + 221.703i 0.235294 + 0.407541i
$$545$$ 938.000 1.72110
$$546$$ 0 0
$$547$$ 900.666i 1.64656i 0.567638 + 0.823278i $$0.307857\pi$$
−0.567638 + 0.823278i $$0.692143\pi$$
$$548$$ 124.000 + 214.774i 0.226277 + 0.391924i
$$549$$ 0 0
$$550$$ −360.000 207.846i −0.654545 0.377902i
$$551$$ 103.923i 0.188608i
$$552$$ 0 0
$$553$$ 60.0000 0.108499
$$554$$ 520.000 900.666i 0.938628 1.62575i
$$555$$ 0 0
$$556$$ −600.000 + 346.410i −1.07914 + 0.623040i
$$557$$ −89.0000 −0.159785 −0.0798923 0.996804i $$-0.525458\pi$$
−0.0798923 + 0.996804i $$0.525458\pi$$
$$558$$ 0 0
$$559$$ 346.410i 0.619696i
$$560$$ 840.000 + 484.974i 1.50000 + 0.866025i
$$561$$ 0 0
$$562$$ 440.000 762.102i 0.782918 1.35605i
$$563$$ 303.109i 0.538382i 0.963087 + 0.269191i $$0.0867562\pi$$
−0.963087 + 0.269191i $$0.913244\pi$$
$$564$$ 0 0
$$565$$ −518.000 −0.916814
$$566$$ 570.000 + 329.090i 1.00707 + 0.581430i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 100.000 0.175747 0.0878735 0.996132i $$-0.471993\pi$$
0.0878735 + 0.996132i $$0.471993\pi$$
$$570$$ 0 0
$$571$$ 339.482i 0.594539i −0.954794 0.297270i $$-0.903924\pi$$
0.954794 0.297270i $$-0.0960760\pi$$
$$572$$ 600.000 346.410i 1.04895 0.605612i
$$573$$ 0 0
$$574$$ −750.000 433.013i −1.30662 0.754378i
$$575$$ 83.1384i 0.144589i
$$576$$ 0 0
$$577$$ −730.000 −1.26516 −0.632582 0.774493i $$-0.718005\pi$$
−0.632582 + 0.774493i $$0.718005\pi$$
$$578$$ 225.000 389.711i 0.389273 0.674241i
$$579$$ 0 0
$$580$$ −140.000 242.487i −0.241379 0.418081i
$$581$$ 255.000 0.438898
$$582$$ 0 0
$$583$$ 407.032i 0.698168i
$$584$$ −440.000 −0.753425
$$585$$ 0 0
$$586$$ 218.000 377.587i 0.372014 0.644347i
$$587$$ 801.940i 1.36617i −0.730341 0.683083i $$-0.760639\pi$$
0.730341 0.683083i $$-0.239361\pi$$
$$588$$ 0 0
$$589$$ 558.000 0.947368
$$590$$ 420.000 + 242.487i 0.711864 + 0.410995i
$$591$$ 0 0
$$592$$ 80.0000 138.564i 0.135135 0.234061i
$$593$$ 982.000 1.65599 0.827993 0.560738i $$-0.189483\pi$$
0.827993 + 0.560738i $$0.189483\pi$$
$$594$$ 0 0
$$595$$ 484.974i 0.815083i
$$596$$ −230.000 398.372i −0.385906 0.668409i
$$597$$ 0 0
$$598$$ 120.000 + 69.2820i 0.200669 + 0.115856i
$$599$$ 225.167i 0.375904i 0.982178 + 0.187952i $$0.0601850\pi$$
−0.982178 + 0.187952i $$0.939815\pi$$
$$600$$ 0 0
$$601$$ 251.000 0.417637 0.208819 0.977954i $$-0.433038\pi$$
0.208819 + 0.977954i $$0.433038\pi$$
$$602$$ −150.000 + 259.808i −0.249169 + 0.431574i
$$603$$ 0 0
$$604$$ 150.000 86.6025i 0.248344 0.143382i
$$605$$ 322.000 0.532231
$$606$$ 0 0
$$607$$ 381.051i 0.627761i −0.949462 0.313881i $$-0.898371\pi$$
0.949462 0.313881i $$-0.101629\pi$$
$$608$$ 288.000 166.277i 0.473684 0.273482i
$$609$$ 0 0
$$610$$ 448.000 775.959i 0.734426 1.27206i
$$611$$ 1732.05i 2.83478i
$$612$$ 0 0
$$613$$ 650.000 1.06036 0.530179 0.847885i $$-0.322125\pi$$
0.530179 + 0.847885i $$0.322125\pi$$
$$614$$ 360.000 + 207.846i 0.586319 + 0.338512i
$$615$$ 0 0
$$616$$ 600.000 0.974026
$$617$$ −758.000 −1.22853 −0.614263 0.789102i $$-0.710546\pi$$
−0.614263 + 0.789102i $$0.710546\pi$$
$$618$$ 0 0
$$619$$ 173.205i 0.279814i 0.990165 + 0.139907i $$0.0446804\pi$$
−0.990165 + 0.139907i $$0.955320\pi$$
$$620$$ −1302.00 + 751.710i −2.10000 + 1.21244i
$$621$$ 0 0
$$622$$ 510.000 + 294.449i 0.819936 + 0.473390i
$$623$$ 86.6025i 0.139009i
$$624$$ 0 0
$$625$$ −649.000 −1.03840
$$626$$ −485.000 + 840.045i −0.774760 + 1.34192i
$$627$$ 0 0
$$628$$ −40.0000 69.2820i −0.0636943 0.110322i
$$629$$ 80.0000 0.127186
$$630$$ 0 0
$$631$$ 119.512i 0.189400i −0.995506 0.0947001i $$-0.969811\pi$$
0.995506 0.0947001i $$-0.0301892\pi$$
$$632$$ 55.4256i 0.0876988i
$$633$$ 0 0
$$634$$ −217.000 + 375.855i −0.342271 + 0.592831i
$$635$$ 181.865i 0.286402i
$$636$$ 0 0
$$637$$ −520.000 −0.816327
$$638$$ −150.000 86.6025i −0.235110 0.135741i
$$639$$ 0 0
$$640$$ −448.000 + 775.959i −0.700000 + 1.21244i
$$641$$ 910.000 1.41966 0.709828 0.704375i $$-0.248772\pi$$
0.709828 + 0.704375i $$0.248772\pi$$
$$642$$ 0 0
$$643$$ 34.6410i 0.0538741i 0.999637 + 0.0269370i $$0.00857536\pi$$
−0.999637 + 0.0269370i $$0.991425\pi$$
$$644$$ 60.0000 + 103.923i 0.0931677 + 0.161371i
$$645$$ 0 0
$$646$$ 144.000 + 83.1384i 0.222910 + 0.128697i
$$647$$ 914.523i 1.41348i −0.707472 0.706741i $$-0.750165\pi$$
0.707472 0.706741i $$-0.249835\pi$$
$$648$$ 0 0
$$649$$ 300.000 0.462250
$$650$$ −480.000 + 831.384i −0.738462 + 1.27905i
$$651$$ 0 0
$$652$$ 360.000 207.846i 0.552147 0.318782i
$$653$$ 103.000 0.157734 0.0788668 0.996885i $$-0.474870\pi$$
0.0788668 + 0.996885i $$0.474870\pi$$
$$654$$ 0 0
$$655$$ 1151.81i 1.75849i
$$656$$ 400.000 692.820i 0.609756 1.05613i
$$657$$ 0 0
$$658$$ −750.000 + 1299.04i −1.13982 + 1.97422i
$$659$$ 60.6218i 0.0919906i 0.998942 + 0.0459953i $$0.0146459\pi$$
−0.998942 + 0.0459953i $$0.985354\pi$$
$$660$$ 0 0
$$661$$ 578.000 0.874433 0.437216 0.899356i $$-0.355964\pi$$
0.437216 + 0.899356i $$0.355964\pi$$
$$662$$ −750.000 433.013i −1.13293 0.654098i
$$663$$ 0 0
$$664$$ 235.559i 0.354757i
$$665$$ 630.000 0.947368
$$666$$ 0 0
$$667$$ 34.6410i 0.0519356i
$$668$$ 852.000 491.902i 1.27545 0.736381i
$$669$$ 0 0
$$670$$ −1050.00 606.218i −1.56716 0.904803i
$$671$$ 554.256i 0.826015i
$$672$$ 0 0
$$673$$ 845.000 1.25557 0.627786 0.778386i $$-0.283961\pi$$
0.627786 + 0.778386i $$0.283961\pi$$
$$674$$ 310.000 536.936i 0.459941 0.796641i
$$675$$ 0 0
$$676$$ −462.000 800.207i −0.683432 1.18374i
$$677$$ −1154.00 −1.70458 −0.852290 0.523070i $$-0.824786\pi$$
−0.852290 + 0.523070i $$0.824786\pi$$
$$678$$ 0 0
$$679$$ 216.506i 0.318861i
$$680$$ −448.000 −0.658824
$$681$$ 0 0
$$682$$ −465.000 + 805.404i −0.681818 + 1.18094i
$$683$$ 187.061i 0.273882i −0.990579 0.136941i $$-0.956273\pi$$
0.990579 0.136941i $$-0.0437271\pi$$
$$684$$ 0 0
$$685$$ −434.000 −0.633577
$$686$$ 345.000 + 199.186i 0.502915 + 0.290358i
$$687$$ 0 0
$$688$$ −240.000 138.564i −0.348837 0.201401i
$$689$$ −940.000 −1.36430
$$690$$ 0 0
$$691$$ 491.902i 0.711870i −0.934511 0.355935i $$-0.884162\pi$$
0.934511 0.355935i $$-0.115838\pi$$
$$692$$ −254.000 439.941i −0.367052 0.635753i
$$693$$ 0 0
$$694$$ 375.000 + 216.506i 0.540346 + 0.311969i
$$695$$ 1212.44i 1.74451i
$$696$$ 0 0
$$697$$ 400.000 0.573888
$$698$$ −74.0000 + 128.172i −0.106017 + 0.183627i
$$699$$ 0 0
$$700$$ −720.000 + 415.692i −1.02857 + 0.593846i
$$701$$ −215.000 −0.306705 −0.153352 0.988172i $$-0.549007\pi$$
−0.153352 + 0.988172i $$0.549007\pi$$
$$702$$ 0 0
$$703$$ 103.923i 0.147828i
$$704$$ 554.256i 0.787296i
$$705$$ 0 0
$$706$$ −394.000 + 682.428i −0.558074 + 0.966612i
$$707$$ 1342.34i 1.89864i
$$708$$ 0 0
$$709$$ −532.000 −0.750353 −0.375176 0.926953i $$-0.622418\pi$$
−0.375176 + 0.926953i $$0.622418\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 80.0000 0.112360
$$713$$ −186.000 −0.260870
$$714$$ 0 0
$$715$$ 1212.44i 1.69571i
$$716$$ 810.000 467.654i 1.13128 0.653148i
$$717$$ 0 0
$$718$$ 990.000 + 571.577i 1.37883 + 0.796068i
$$719$$ 1143.15i 1.58992i 0.606661 + 0.794961i $$0.292509\pi$$
−0.606661 + 0.794961i $$0.707491\pi$$
$$720$$ 0 0
$$721$$ 1200.00 1.66436
$$722$$ −253.000 + 438.209i −0.350416 + 0.606937i
$$723$$ 0 0
$$724$$ −112.000 193.990i −0.154696 0.267942i
$$725$$ 240.000 0.331034
$$726$$ 0 0
$$727$$ 1238.42i 1.70346i 0.523980 + 0.851731i $$0.324447\pi$$
−0.523980 + 0.851731i $$0.675553\pi$$
$$728$$ 1385.64i 1.90335i
$$729$$ 0 0
$$730$$ 385.000 666.840i 0.527397 0.913479i
$$731$$ 138.564i 0.189554i
$$732$$ 0 0
$$733$$ 950.000 1.29604 0.648022 0.761622i $$-0.275597\pi$$
0.648022 + 0.761622i $$0.275597\pi$$
$$734$$ −975.000 562.917i −1.32834 0.766916i
$$735$$ 0 0
$$736$$ −96.0000 + 55.4256i −0.130435 + 0.0753066i
$$737$$ −750.000 −1.01764
$$738$$ 0 0
$$739$$ 581.969i 0.787509i −0.919216 0.393754i $$-0.871176\pi$$
0.919216 0.393754i $$-0.128824\pi$$
$$740$$ 140.000 + 242.487i 0.189189 + 0.327685i
$$741$$ 0 0
$$742$$ −705.000 407.032i −0.950135 0.548561i
$$743$$ 866.025i 1.16558i −0.812623 0.582790i $$-0.801961\pi$$
0.812623 0.582790i $$-0.198039\pi$$
$$744$$ 0 0
$$745$$ 805.000 1.08054
$$746$$ 40.0000 69.2820i 0.0536193 0.0928714i
$$747$$ 0 0
$$748$$ −240.000 + 138.564i −0.320856 + 0.185246i
$$749$$ −1125.00 −1.50200
$$750$$ 0 0
$$751$$ 174.937i 0.232939i 0.993194 + 0.116469i $$0.0371577\pi$$
−0.993194 + 0.116469i $$0.962842\pi$$
$$752$$ −1200.00 692.820i −1.59574 0.921304i
$$753$$ 0 0
$$754$$ −200.000 + 346.410i −0.265252 + 0.459430i
$$755$$ 303.109i 0.401469i
$$756$$ 0 0
$$757$$ 830.000 1.09643 0.548217 0.836336i $$-0.315307\pi$$
0.548217 + 0.836336i $$0.315307\pi$$
$$758$$ 1188.00 + 685.892i 1.56728 + 0.904871i
$$759$$ 0 0
$$760$$ 581.969i 0.765749i
$$761$$ −560.000 −0.735874 −0.367937 0.929851i $$-0.619936\pi$$
−0.367937 + 0.929851i $$0.619936\pi$$
$$762$$ 0 0
$$763$$ 1160.47i 1.52094i
$$764$$ 120.000 69.2820i 0.157068 0.0906833i
$$765$$ 0 0
$$766$$ −624.000 360.267i −0.814621 0.470322i
$$767$$ 692.820i 0.903286i
$$768$$ 0 0
$$769$$ −331.000 −0.430429 −0.215215 0.976567i $$-0.569045\pi$$
−0.215215 + 0.976567i $$0.569045\pi$$
$$770$$ −525.000 + 909.327i −0.681818 + 1.18094i
$$771$$ 0 0
$$772$$ −130.000 225.167i −0.168394 0.291667i
$$773$$ 298.000 0.385511 0.192755 0.981247i $$-0.438258\pi$$
0.192755 + 0.981247i $$0.438258\pi$$
$$774$$ 0 0
$$775$$ 1288.65i 1.66277i
$$776$$ −200.000 −0.257732
$$777$$ 0 0
$$778$$ −475.000 + 822.724i −0.610540 + 1.05749i
$$779$$ 519.615i 0.667029i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −48.0000 27.7128i −0.0613811 0.0354384i
$$783$$ 0 0
$$784$$ 208.000 360.267i 0.265306 0.459524i
$$785$$ 140.000 0.178344
$$786$$ 0 0
$$787$$ 1108.51i 1.40853i −0.709938 0.704265i $$-0.751277\pi$$
0.709938 0.704265i $$-0.248723\pi$$
$$788$$ −506.000 876.418i −0.642132 1.11221i
$$789$$ 0 0
$$790$$ −84.0000 48.4974i −0.106329 0.0613891i
$$791$$ 640.859i 0.810188i
$$792$$ 0 0
$$793$$ −1280.00 −1.61412
$$794$$ −260.000 + 450.333i −0.327456 + 0.567170i
$$795$$ 0 0
$$796$$ −450.000 + 259.808i −0.565327 + 0.326391i
$$797$$ 1303.00 1.63488 0.817440 0.576013i $$-0.195392\pi$$
0.817440 + 0.576013i $$0.195392\pi$$
$$798$$ 0 0
$$799$$ 692.820i 0.867109i
$$800$$ −384.000 665.108i −0.480000 0.831384i
$$801$$ 0 0
$$802$$ 740.000 1281.72i 0.922693 1.59815i
$$803$$