# Properties

 Label 315.3.ca.b.37.8 Level 315 Weight 3 Character 315.37 Analytic conductor 8.583 Analytic rank 0 Dimension 64 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$315 = 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 315.ca (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.58312832735$$ Analytic rank: $$0$$ Dimension: $$64$$ Relative dimension: $$16$$ over $$\Q(\zeta_{12})$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 37.8 Character $$\chi$$ $$=$$ 315.37 Dual form 315.3.ca.b.298.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.232416 + 0.0622758i) q^{2} +(-3.41396 + 1.97105i) q^{4} +(2.65242 - 4.23847i) q^{5} +(-4.06422 + 5.69931i) q^{7} +(1.35127 - 1.35127i) q^{8} +O(q^{10})$$ $$q+(-0.232416 + 0.0622758i) q^{2} +(-3.41396 + 1.97105i) q^{4} +(2.65242 - 4.23847i) q^{5} +(-4.06422 + 5.69931i) q^{7} +(1.35127 - 1.35127i) q^{8} +(-0.352512 + 1.15027i) q^{10} +(-2.22825 - 3.85944i) q^{11} +(10.0930 - 10.0930i) q^{13} +(0.589662 - 1.57771i) q^{14} +(7.65430 - 13.2576i) q^{16} +(2.55748 - 9.54465i) q^{17} +(11.1120 + 6.41554i) q^{19} +(-0.701025 + 19.6981i) q^{20} +(0.758230 + 0.758230i) q^{22} +(-3.20215 - 11.9506i) q^{23} +(-10.9293 - 22.4844i) q^{25} +(-1.71723 + 2.97433i) q^{26} +(2.64146 - 27.4680i) q^{28} -36.7743i q^{29} +(-8.59913 - 14.8941i) q^{31} +(-2.93176 + 10.9415i) q^{32} +2.37760i q^{34} +(13.3763 + 32.3431i) q^{35} +(54.2699 - 14.5416i) q^{37} +(-2.98215 - 0.799066i) q^{38} +(-2.14319 - 9.31149i) q^{40} +46.8347 q^{41} +(25.0932 - 25.0932i) q^{43} +(15.2143 + 8.78398i) q^{44} +(1.48846 + 2.57809i) q^{46} +(-44.9155 + 12.0351i) q^{47} +(-15.9642 - 46.3265i) q^{49} +(3.94038 + 4.54512i) q^{50} +(-14.5633 + 54.3510i) q^{52} +(-58.8689 - 15.7739i) q^{53} +(-22.2684 - 0.792499i) q^{55} +(2.20945 + 13.1932i) q^{56} +(2.29015 + 8.54695i) q^{58} +(99.7443 - 57.5874i) q^{59} +(-22.1961 + 38.4447i) q^{61} +(2.92612 + 2.92612i) q^{62} +58.5089i q^{64} +(-16.0080 - 69.5498i) q^{65} +(-18.2625 + 68.1567i) q^{67} +(10.0819 + 37.6260i) q^{68} +(-5.12307 - 6.68403i) q^{70} -85.0378 q^{71} +(-11.2757 - 3.02132i) q^{73} +(-11.7076 + 6.75940i) q^{74} -50.5815 q^{76} +(31.0522 + 2.98613i) q^{77} +(57.2212 + 33.0366i) q^{79} +(-35.8897 - 67.6074i) q^{80} +(-10.8851 + 2.91666i) q^{82} +(-65.5612 + 65.5612i) q^{83} +(-33.6712 - 36.1563i) q^{85} +(-4.26937 + 7.39477i) q^{86} +(-8.22613 - 2.20418i) q^{88} +(10.9662 + 6.33133i) q^{89} +(16.5030 + 98.5433i) q^{91} +(34.4872 + 34.4872i) q^{92} +(9.68960 - 5.59429i) q^{94} +(56.6660 - 30.0814i) q^{95} +(-125.573 - 125.573i) q^{97} +(6.59537 + 9.77284i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10})$$ $$64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$136$$ $$281$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.232416 + 0.0622758i −0.116208 + 0.0311379i −0.316454 0.948608i $$-0.602492\pi$$
0.200246 + 0.979746i $$0.435826\pi$$
$$3$$ 0 0
$$4$$ −3.41396 + 1.97105i −0.853491 + 0.492763i
$$5$$ 2.65242 4.23847i 0.530485 0.847694i
$$6$$ 0 0
$$7$$ −4.06422 + 5.69931i −0.580603 + 0.814187i
$$8$$ 1.35127 1.35127i 0.168909 0.168909i
$$9$$ 0 0
$$10$$ −0.352512 + 1.15027i −0.0352512 + 0.115027i
$$11$$ −2.22825 3.85944i −0.202568 0.350858i 0.746787 0.665063i $$-0.231595\pi$$
−0.949355 + 0.314205i $$0.898262\pi$$
$$12$$ 0 0
$$13$$ 10.0930 10.0930i 0.776385 0.776385i −0.202829 0.979214i $$-0.565014\pi$$
0.979214 + 0.202829i $$0.0650137\pi$$
$$14$$ 0.589662 1.57771i 0.0421187 0.112694i
$$15$$ 0 0
$$16$$ 7.65430 13.2576i 0.478394 0.828603i
$$17$$ 2.55748 9.54465i 0.150440 0.561450i −0.849013 0.528372i $$-0.822802\pi$$
0.999453 0.0330776i $$-0.0105309\pi$$
$$18$$ 0 0
$$19$$ 11.1120 + 6.41554i 0.584845 + 0.337660i 0.763056 0.646332i $$-0.223698\pi$$
−0.178212 + 0.983992i $$0.557031\pi$$
$$20$$ −0.701025 + 19.6981i −0.0350513 + 0.984903i
$$21$$ 0 0
$$22$$ 0.758230 + 0.758230i 0.0344650 + 0.0344650i
$$23$$ −3.20215 11.9506i −0.139224 0.519590i −0.999945 0.0105132i $$-0.996653\pi$$
0.860721 0.509077i $$-0.170013\pi$$
$$24$$ 0 0
$$25$$ −10.9293 22.4844i −0.437172 0.899378i
$$26$$ −1.71723 + 2.97433i −0.0660472 + 0.114397i
$$27$$ 0 0
$$28$$ 2.64146 27.4680i 0.0943378 0.981001i
$$29$$ 36.7743i 1.26808i −0.773301 0.634040i $$-0.781396\pi$$
0.773301 0.634040i $$-0.218604\pi$$
$$30$$ 0 0
$$31$$ −8.59913 14.8941i −0.277391 0.480456i 0.693344 0.720606i $$-0.256136\pi$$
−0.970736 + 0.240151i $$0.922803\pi$$
$$32$$ −2.93176 + 10.9415i −0.0916174 + 0.341921i
$$33$$ 0 0
$$34$$ 2.37760i 0.0699295i
$$35$$ 13.3763 + 32.3431i 0.382181 + 0.924088i
$$36$$ 0 0
$$37$$ 54.2699 14.5416i 1.46675 0.393016i 0.564937 0.825134i $$-0.308900\pi$$
0.901817 + 0.432118i $$0.142234\pi$$
$$38$$ −2.98215 0.799066i −0.0784777 0.0210280i
$$39$$ 0 0
$$40$$ −2.14319 9.31149i −0.0535796 0.232787i
$$41$$ 46.8347 1.14231 0.571155 0.820843i $$-0.306496\pi$$
0.571155 + 0.820843i $$0.306496\pi$$
$$42$$ 0 0
$$43$$ 25.0932 25.0932i 0.583563 0.583563i −0.352317 0.935881i $$-0.614606\pi$$
0.935881 + 0.352317i $$0.114606\pi$$
$$44$$ 15.2143 + 8.78398i 0.345780 + 0.199636i
$$45$$ 0 0
$$46$$ 1.48846 + 2.57809i 0.0323579 + 0.0560455i
$$47$$ −44.9155 + 12.0351i −0.955649 + 0.256065i −0.702758 0.711429i $$-0.748048\pi$$
−0.252891 + 0.967495i $$0.581382\pi$$
$$48$$ 0 0
$$49$$ −15.9642 46.3265i −0.325801 0.945438i
$$50$$ 3.94038 + 4.54512i 0.0788076 + 0.0909024i
$$51$$ 0 0
$$52$$ −14.5633 + 54.3510i −0.280063 + 1.04521i
$$53$$ −58.8689 15.7739i −1.11073 0.297620i −0.343606 0.939114i $$-0.611648\pi$$
−0.767128 + 0.641494i $$0.778315\pi$$
$$54$$ 0 0
$$55$$ −22.2684 0.792499i −0.404879 0.0144091i
$$56$$ 2.20945 + 13.1932i 0.0394545 + 0.235593i
$$57$$ 0 0
$$58$$ 2.29015 + 8.54695i 0.0394853 + 0.147361i
$$59$$ 99.7443 57.5874i 1.69058 0.976058i 0.736535 0.676399i $$-0.236460\pi$$
0.954046 0.299659i $$-0.0968729\pi$$
$$60$$ 0 0
$$61$$ −22.1961 + 38.4447i −0.363870 + 0.630241i −0.988594 0.150604i $$-0.951878\pi$$
0.624724 + 0.780845i $$0.285211\pi$$
$$62$$ 2.92612 + 2.92612i 0.0471955 + 0.0471955i
$$63$$ 0 0
$$64$$ 58.5089i 0.914201i
$$65$$ −16.0080 69.5498i −0.246277 1.07000i
$$66$$ 0 0
$$67$$ −18.2625 + 68.1567i −0.272575 + 1.01726i 0.684874 + 0.728662i $$0.259857\pi$$
−0.957449 + 0.288602i $$0.906809\pi$$
$$68$$ 10.0819 + 37.6260i 0.148263 + 0.553324i
$$69$$ 0 0
$$70$$ −5.12307 6.68403i −0.0731867 0.0954862i
$$71$$ −85.0378 −1.19772 −0.598858 0.800855i $$-0.704379\pi$$
−0.598858 + 0.800855i $$0.704379\pi$$
$$72$$ 0 0
$$73$$ −11.2757 3.02132i −0.154462 0.0413879i 0.180760 0.983527i $$-0.442144\pi$$
−0.335221 + 0.942139i $$0.608811\pi$$
$$74$$ −11.7076 + 6.75940i −0.158211 + 0.0913432i
$$75$$ 0 0
$$76$$ −50.5815 −0.665546
$$77$$ 31.0522 + 2.98613i 0.403275 + 0.0387809i
$$78$$ 0 0
$$79$$ 57.2212 + 33.0366i 0.724318 + 0.418185i 0.816340 0.577572i $$-0.196000\pi$$
−0.0920217 + 0.995757i $$0.529333\pi$$
$$80$$ −35.8897 67.6074i −0.448621 0.845093i
$$81$$ 0 0
$$82$$ −10.8851 + 2.91666i −0.132746 + 0.0355691i
$$83$$ −65.5612 + 65.5612i −0.789894 + 0.789894i −0.981476 0.191583i $$-0.938638\pi$$
0.191583 + 0.981476i $$0.438638\pi$$
$$84$$ 0 0
$$85$$ −33.6712 36.1563i −0.396132 0.425368i
$$86$$ −4.26937 + 7.39477i −0.0496439 + 0.0859857i
$$87$$ 0 0
$$88$$ −8.22613 2.20418i −0.0934787 0.0250475i
$$89$$ 10.9662 + 6.33133i 0.123216 + 0.0711385i 0.560341 0.828262i $$-0.310670\pi$$
−0.437125 + 0.899401i $$0.644003\pi$$
$$90$$ 0 0
$$91$$ 16.5030 + 98.5433i 0.181351 + 1.08289i
$$92$$ 34.4872 + 34.4872i 0.374861 + 0.374861i
$$93$$ 0 0
$$94$$ 9.68960 5.59429i 0.103081 0.0595138i
$$95$$ 56.6660 30.0814i 0.596484 0.316646i
$$96$$ 0 0
$$97$$ −125.573 125.573i −1.29456 1.29456i −0.931932 0.362632i $$-0.881878\pi$$
−0.362632 0.931932i $$-0.618122\pi$$
$$98$$ 6.59537 + 9.77284i 0.0672997 + 0.0997229i
$$99$$ 0 0
$$100$$ 81.6302 + 55.2189i 0.816302 + 0.552189i
$$101$$ 57.5790 + 99.7297i 0.570089 + 0.987422i 0.996556 + 0.0829196i $$0.0264245\pi$$
−0.426468 + 0.904503i $$0.640242\pi$$
$$102$$ 0 0
$$103$$ 25.0098 + 93.3379i 0.242814 + 0.906193i 0.974470 + 0.224519i $$0.0720810\pi$$
−0.731656 + 0.681674i $$0.761252\pi$$
$$104$$ 27.2768i 0.262277i
$$105$$ 0 0
$$106$$ 14.6644 0.138344
$$107$$ −119.300 + 31.9665i −1.11496 + 0.298752i −0.768841 0.639440i $$-0.779166\pi$$
−0.346116 + 0.938192i $$0.612500\pi$$
$$108$$ 0 0
$$109$$ 43.0410 24.8497i 0.394871 0.227979i −0.289397 0.957209i $$-0.593455\pi$$
0.684269 + 0.729230i $$0.260122\pi$$
$$110$$ 5.22488 1.20259i 0.0474990 0.0109326i
$$111$$ 0 0
$$112$$ 44.4506 + 97.5062i 0.396881 + 0.870591i
$$113$$ 42.4036 42.4036i 0.375253 0.375253i −0.494133 0.869386i $$-0.664514\pi$$
0.869386 + 0.494133i $$0.164514\pi$$
$$114$$ 0 0
$$115$$ −59.1456 18.1258i −0.514310 0.157615i
$$116$$ 72.4841 + 125.546i 0.624863 + 1.08229i
$$117$$ 0 0
$$118$$ −19.5959 + 19.5959i −0.166067 + 0.166067i
$$119$$ 44.0038 + 53.3674i 0.369779 + 0.448466i
$$120$$ 0 0
$$121$$ 50.5698 87.5895i 0.417933 0.723880i
$$122$$ 2.76455 10.3174i 0.0226603 0.0845693i
$$123$$ 0 0
$$124$$ 58.7142 + 33.8987i 0.473502 + 0.273376i
$$125$$ −124.289 13.3148i −0.994311 0.106518i
$$126$$ 0 0
$$127$$ −62.2747 62.2747i −0.490352 0.490352i 0.418065 0.908417i $$-0.362708\pi$$
−0.908417 + 0.418065i $$0.862708\pi$$
$$128$$ −15.3707 57.3643i −0.120084 0.448158i
$$129$$ 0 0
$$130$$ 8.05178 + 15.1676i 0.0619368 + 0.116674i
$$131$$ −7.67305 + 13.2901i −0.0585729 + 0.101451i −0.893825 0.448416i $$-0.851988\pi$$
0.835252 + 0.549867i $$0.185322\pi$$
$$132$$ 0 0
$$133$$ −81.7260 + 37.2568i −0.614481 + 0.280126i
$$134$$ 16.9780i 0.126702i
$$135$$ 0 0
$$136$$ −9.44158 16.3533i −0.0694234 0.120245i
$$137$$ −58.8789 + 219.739i −0.429773 + 1.60394i 0.323500 + 0.946228i $$0.395140\pi$$
−0.753273 + 0.657708i $$0.771526\pi$$
$$138$$ 0 0
$$139$$ 102.047i 0.734151i −0.930191 0.367076i $$-0.880359\pi$$
0.930191 0.367076i $$-0.119641\pi$$
$$140$$ −109.416 84.0526i −0.781544 0.600375i
$$141$$ 0 0
$$142$$ 19.7642 5.29579i 0.139184 0.0372943i
$$143$$ −61.4430 16.4636i −0.429671 0.115130i
$$144$$ 0 0
$$145$$ −155.867 97.5410i −1.07494 0.672697i
$$146$$ 2.80881 0.0192384
$$147$$ 0 0
$$148$$ −156.613 + 156.613i −1.05820 + 1.05820i
$$149$$ 253.568 + 146.397i 1.70180 + 0.982532i 0.943944 + 0.330104i $$0.107084\pi$$
0.757851 + 0.652428i $$0.226249\pi$$
$$150$$ 0 0
$$151$$ 103.721 + 179.651i 0.686897 + 1.18974i 0.972837 + 0.231492i $$0.0743608\pi$$
−0.285940 + 0.958247i $$0.592306\pi$$
$$152$$ 23.6846 6.34626i 0.155820 0.0417517i
$$153$$ 0 0
$$154$$ −7.40300 + 1.23977i −0.0480714 + 0.00805048i
$$155$$ −85.9369 3.05837i −0.554431 0.0197314i
$$156$$ 0 0
$$157$$ 19.6048 73.1661i 0.124871 0.466026i −0.874964 0.484188i $$-0.839115\pi$$
0.999835 + 0.0181625i $$0.00578162\pi$$
$$158$$ −15.3565 4.11476i −0.0971931 0.0260428i
$$159$$ 0 0
$$160$$ 38.5988 + 41.4476i 0.241243 + 0.259047i
$$161$$ 81.1243 + 30.3197i 0.503877 + 0.188321i
$$162$$ 0 0
$$163$$ −50.8403 189.738i −0.311903 1.16404i −0.926838 0.375461i $$-0.877484\pi$$
0.614935 0.788578i $$-0.289182\pi$$
$$164$$ −159.892 + 92.3136i −0.974950 + 0.562888i
$$165$$ 0 0
$$166$$ 11.1546 19.3204i 0.0671965 0.116388i
$$167$$ −189.235 189.235i −1.13314 1.13314i −0.989652 0.143492i $$-0.954167\pi$$
−0.143492 0.989652i $$-0.545833\pi$$
$$168$$ 0 0
$$169$$ 34.7373i 0.205546i
$$170$$ 10.0774 + 6.30641i 0.0592788 + 0.0370965i
$$171$$ 0 0
$$172$$ −36.2073 + 135.127i −0.210507 + 0.785624i
$$173$$ −49.4475 184.540i −0.285823 1.06671i −0.948236 0.317568i $$-0.897134\pi$$
0.662412 0.749140i $$-0.269533\pi$$
$$174$$ 0 0
$$175$$ 172.565 + 29.0923i 0.986085 + 0.166242i
$$176$$ −68.2227 −0.387629
$$177$$ 0 0
$$178$$ −2.94301 0.788577i −0.0165338 0.00443021i
$$179$$ 158.096 91.2766i 0.883216 0.509925i 0.0114988 0.999934i $$-0.496340\pi$$
0.871718 + 0.490009i $$0.163006\pi$$
$$180$$ 0 0
$$181$$ −103.223 −0.570290 −0.285145 0.958484i $$-0.592042\pi$$
−0.285145 + 0.958484i $$0.592042\pi$$
$$182$$ −9.97241 21.8753i −0.0547935 0.120194i
$$183$$ 0 0
$$184$$ −20.4755 11.8215i −0.111280 0.0642474i
$$185$$ 82.3127 268.592i 0.444934 1.45185i
$$186$$ 0 0
$$187$$ −42.5357 + 11.3974i −0.227463 + 0.0609487i
$$188$$ 129.618 129.618i 0.689458 0.689458i
$$189$$ 0 0
$$190$$ −11.2968 + 10.5203i −0.0594566 + 0.0553701i
$$191$$ 129.306 223.965i 0.676996 1.17259i −0.298885 0.954289i $$-0.596615\pi$$
0.975881 0.218302i $$-0.0700519\pi$$
$$192$$ 0 0
$$193$$ 88.4965 + 23.7126i 0.458531 + 0.122863i 0.480688 0.876891i $$-0.340387\pi$$
−0.0221573 + 0.999754i $$0.507053\pi$$
$$194$$ 37.0053 + 21.3650i 0.190749 + 0.110129i
$$195$$ 0 0
$$196$$ 145.813 + 126.691i 0.743945 + 0.646380i
$$197$$ 186.124 + 186.124i 0.944793 + 0.944793i 0.998554 0.0537607i $$-0.0171208\pi$$
−0.0537607 + 0.998554i $$0.517121\pi$$
$$198$$ 0 0
$$199$$ 234.511 135.395i 1.17844 0.680375i 0.222791 0.974866i $$-0.428483\pi$$
0.955654 + 0.294491i $$0.0951500\pi$$
$$200$$ −45.1511 15.6142i −0.225756 0.0780709i
$$201$$ 0 0
$$202$$ −19.5930 19.5930i −0.0969952 0.0969952i
$$203$$ 209.588 + 149.459i 1.03245 + 0.736250i
$$204$$ 0 0
$$205$$ 124.225 198.507i 0.605978 0.968329i
$$206$$ −11.6254 20.1357i −0.0564338 0.0977463i
$$207$$ 0 0
$$208$$ −56.5545 211.064i −0.271897 1.01473i
$$209$$ 57.1817i 0.273596i
$$210$$ 0 0
$$211$$ 294.597 1.39619 0.698096 0.716004i $$-0.254031\pi$$
0.698096 + 0.716004i $$0.254031\pi$$
$$212$$ 232.067 62.1823i 1.09466 0.293313i
$$213$$ 0 0
$$214$$ 25.7366 14.8590i 0.120265 0.0694348i
$$215$$ −39.7991 172.915i −0.185112 0.804255i
$$216$$ 0 0
$$217$$ 119.835 + 11.5239i 0.552235 + 0.0531056i
$$218$$ −8.45589 + 8.45589i −0.0387885 + 0.0387885i
$$219$$ 0 0
$$220$$ 77.5854 41.1866i 0.352661 0.187212i
$$221$$ −70.5215 122.147i −0.319102 0.552701i
$$222$$ 0 0
$$223$$ 8.97417 8.97417i 0.0402429 0.0402429i −0.686699 0.726942i $$-0.740941\pi$$
0.726942 + 0.686699i $$0.240941\pi$$
$$224$$ −50.4435 61.1775i −0.225194 0.273114i
$$225$$ 0 0
$$226$$ −7.21458 + 12.4960i −0.0319229 + 0.0552921i
$$227$$ −93.1104 + 347.493i −0.410178 + 1.53080i 0.384124 + 0.923281i $$0.374503\pi$$
−0.794302 + 0.607523i $$0.792163\pi$$
$$228$$ 0 0
$$229$$ −201.351 116.250i −0.879261 0.507642i −0.00884639 0.999961i $$-0.502816\pi$$
−0.870415 + 0.492319i $$0.836149\pi$$
$$230$$ 14.8752 + 0.529387i 0.0646748 + 0.00230168i
$$231$$ 0 0
$$232$$ −49.6921 49.6921i −0.214190 0.214190i
$$233$$ −8.52601 31.8195i −0.0365923 0.136564i 0.945213 0.326454i $$-0.105854\pi$$
−0.981805 + 0.189889i $$0.939187\pi$$
$$234$$ 0 0
$$235$$ −68.1246 + 222.295i −0.289892 + 0.945937i
$$236$$ −227.016 + 393.203i −0.961931 + 1.66611i
$$237$$ 0 0
$$238$$ −13.5507 9.66309i −0.0569357 0.0406012i
$$239$$ 133.557i 0.558817i −0.960172 0.279408i $$-0.909862\pi$$
0.960172 0.279408i $$-0.0901383\pi$$
$$240$$ 0 0
$$241$$ −230.800 399.758i −0.957678 1.65875i −0.728117 0.685453i $$-0.759604\pi$$
−0.229561 0.973294i $$-0.573729\pi$$
$$242$$ −6.29855 + 23.5065i −0.0260271 + 0.0971343i
$$243$$ 0 0
$$244$$ 174.998i 0.717206i
$$245$$ −238.697 55.2135i −0.974275 0.225361i
$$246$$ 0 0
$$247$$ 176.906 47.4018i 0.716219 0.191910i
$$248$$ −31.7458 8.50627i −0.128007 0.0342995i
$$249$$ 0 0
$$250$$ 29.7159 4.64561i 0.118864 0.0185824i
$$251$$ 125.961 0.501837 0.250919 0.968008i $$-0.419267\pi$$
0.250919 + 0.968008i $$0.419267\pi$$
$$252$$ 0 0
$$253$$ −38.9873 + 38.9873i −0.154100 + 0.154100i
$$254$$ 18.3519 + 10.5955i 0.0722515 + 0.0417144i
$$255$$ 0 0
$$256$$ −109.873 190.305i −0.429191 0.743381i
$$257$$ 236.058 63.2516i 0.918515 0.246115i 0.231564 0.972820i $$-0.425616\pi$$
0.686950 + 0.726704i $$0.258949\pi$$
$$258$$ 0 0
$$259$$ −137.688 + 368.401i −0.531613 + 1.42240i
$$260$$ 191.737 + 205.888i 0.737450 + 0.791876i
$$261$$ 0 0
$$262$$ 0.955690 3.56669i 0.00364767 0.0136133i
$$263$$ −116.745 31.2818i −0.443898 0.118942i 0.0299446 0.999552i $$-0.490467\pi$$
−0.473843 + 0.880609i $$0.657134\pi$$
$$264$$ 0 0
$$265$$ −223.002 + 207.675i −0.841519 + 0.783680i
$$266$$ 16.6742 13.7486i 0.0626851 0.0516866i
$$267$$ 0 0
$$268$$ −71.9928 268.681i −0.268630 1.00254i
$$269$$ −221.456 + 127.858i −0.823258 + 0.475308i −0.851539 0.524292i $$-0.824330\pi$$
0.0282806 + 0.999600i $$0.490997\pi$$
$$270$$ 0 0
$$271$$ −24.1359 + 41.8046i −0.0890625 + 0.154261i −0.907115 0.420883i $$-0.861720\pi$$
0.818053 + 0.575143i $$0.195054\pi$$
$$272$$ −106.964 106.964i −0.393249 0.393249i
$$273$$ 0 0
$$274$$ 54.7377i 0.199773i
$$275$$ −62.4241 + 92.2818i −0.226997 + 0.335570i
$$276$$ 0 0
$$277$$ −26.8253 + 100.113i −0.0968423 + 0.361420i −0.997292 0.0735390i $$-0.976571\pi$$
0.900450 + 0.434960i $$0.143237\pi$$
$$278$$ 6.35506 + 23.7174i 0.0228599 + 0.0853143i
$$279$$ 0 0
$$280$$ 61.7794 + 25.6293i 0.220641 + 0.0915330i
$$281$$ −357.942 −1.27382 −0.636908 0.770940i $$-0.719787\pi$$
−0.636908 + 0.770940i $$0.719787\pi$$
$$282$$ 0 0
$$283$$ 174.344 + 46.7152i 0.616055 + 0.165072i 0.553334 0.832960i $$-0.313355\pi$$
0.0627214 + 0.998031i $$0.480022\pi$$
$$284$$ 290.316 167.614i 1.02224 0.590190i
$$285$$ 0 0
$$286$$ 15.3056 0.0535162
$$287$$ −190.346 + 266.925i −0.663228 + 0.930053i
$$288$$ 0 0
$$289$$ 165.722 + 95.6795i 0.573431 + 0.331071i
$$290$$ 42.3004 + 12.9634i 0.145864 + 0.0447014i
$$291$$ 0 0
$$292$$ 44.4500 11.9103i 0.152226 0.0407889i
$$293$$ −116.627 + 116.627i −0.398046 + 0.398046i −0.877543 0.479497i $$-0.840819\pi$$
0.479497 + 0.877543i $$0.340819\pi$$
$$294$$ 0 0
$$295$$ 20.4816 575.510i 0.0694290 1.95088i
$$296$$ 53.6838 92.9832i 0.181364 0.314132i
$$297$$ 0 0
$$298$$ −68.0502 18.2340i −0.228356 0.0611879i
$$299$$ −152.936 88.2979i −0.511493 0.295311i
$$300$$ 0 0
$$301$$ 41.0297 + 244.998i 0.136311 + 0.813948i
$$302$$ −35.2944 35.2944i −0.116869 0.116869i
$$303$$ 0 0
$$304$$ 170.110 98.2130i 0.559572 0.323069i
$$305$$ 104.073 + 196.049i 0.341224 + 0.642784i
$$306$$ 0 0
$$307$$ 102.316 + 102.316i 0.333276 + 0.333276i 0.853829 0.520553i $$-0.174274\pi$$
−0.520553 + 0.853829i $$0.674274\pi$$
$$308$$ −111.897 + 51.0110i −0.363302 + 0.165620i
$$309$$ 0 0
$$310$$ 20.1636 4.64097i 0.0650438 0.0149709i
$$311$$ 5.34944 + 9.26551i 0.0172008 + 0.0297926i 0.874498 0.485030i $$-0.161191\pi$$
−0.857297 + 0.514822i $$0.827858\pi$$
$$312$$ 0 0
$$313$$ 123.581 + 461.210i 0.394827 + 1.47351i 0.822075 + 0.569380i $$0.192816\pi$$
−0.427248 + 0.904135i $$0.640517\pi$$
$$314$$ 18.2259i 0.0580442i
$$315$$ 0 0
$$316$$ −260.468 −0.824265
$$317$$ 71.5544 19.1729i 0.225724 0.0604825i −0.144184 0.989551i $$-0.546056\pi$$
0.369908 + 0.929068i $$0.379389\pi$$
$$318$$ 0 0
$$319$$ −141.928 + 81.9422i −0.444916 + 0.256872i
$$320$$ 247.988 + 155.190i 0.774963 + 0.484970i
$$321$$ 0 0
$$322$$ −20.7428 1.99473i −0.0644186 0.00619480i
$$323$$ 89.6530 89.6530i 0.277563 0.277563i
$$324$$ 0 0
$$325$$ −337.245 116.626i −1.03768 0.358850i
$$326$$ 23.6322 + 40.9322i 0.0724914 + 0.125559i
$$327$$ 0 0
$$328$$ 63.2865 63.2865i 0.192947 0.192947i
$$329$$ 113.955 304.900i 0.346367 0.926749i
$$330$$ 0 0
$$331$$ −186.461 + 322.960i −0.563327 + 0.975711i 0.433876 + 0.900972i $$0.357145\pi$$
−0.997203 + 0.0747382i $$0.976188\pi$$
$$332$$ 94.5989 353.048i 0.284937 1.06340i
$$333$$ 0 0
$$334$$ 55.7660 + 32.1965i 0.166964 + 0.0963968i
$$335$$ 240.440 + 258.186i 0.717732 + 0.770703i
$$336$$ 0 0
$$337$$ −1.52001 1.52001i −0.00451041 0.00451041i 0.704848 0.709358i $$-0.251015\pi$$
−0.709358 + 0.704848i $$0.751015\pi$$
$$338$$ 2.16329 + 8.07351i 0.00640027 + 0.0238861i
$$339$$ 0 0
$$340$$ 186.218 + 57.0684i 0.547701 + 0.167848i
$$341$$ −38.3220 + 66.3756i −0.112381 + 0.194650i
$$342$$ 0 0
$$343$$ 328.911 + 97.2959i 0.958925 + 0.283661i
$$344$$ 67.8156i 0.197138i
$$345$$ 0 0
$$346$$ 22.9848 + 39.8108i 0.0664300 + 0.115060i
$$347$$ 54.2716 202.544i 0.156402 0.583701i −0.842579 0.538573i $$-0.818964\pi$$
0.998981 0.0451282i $$-0.0143696\pi$$
$$348$$ 0 0
$$349$$ 256.040i 0.733639i 0.930292 + 0.366820i $$0.119553\pi$$
−0.930292 + 0.366820i $$0.880447\pi$$
$$350$$ −41.9186 + 3.98508i −0.119768 + 0.0113860i
$$351$$ 0 0
$$352$$ 48.7606 13.0654i 0.138524 0.0371175i
$$353$$ 3.09864 + 0.830277i 0.00877800 + 0.00235206i 0.263205 0.964740i $$-0.415220\pi$$
−0.254427 + 0.967092i $$0.581887\pi$$
$$354$$ 0 0
$$355$$ −225.556 + 360.430i −0.635370 + 1.01530i
$$356$$ −49.9175 −0.140218
$$357$$ 0 0
$$358$$ −31.0597 + 31.0597i −0.0867589 + 0.0867589i
$$359$$ 268.238 + 154.867i 0.747181 + 0.431385i 0.824674 0.565608i $$-0.191358\pi$$
−0.0774934 + 0.996993i $$0.524692\pi$$
$$360$$ 0 0
$$361$$ −98.1816 170.055i −0.271971 0.471068i
$$362$$ 23.9906 6.42826i 0.0662724 0.0177576i
$$363$$ 0 0
$$364$$ −250.574 303.895i −0.688391 0.834876i
$$365$$ −42.7137 + 39.7780i −0.117024 + 0.108981i
$$366$$ 0 0
$$367$$ −90.8527 + 339.067i −0.247555 + 0.923888i 0.724527 + 0.689247i $$0.242058\pi$$
−0.972082 + 0.234642i $$0.924608\pi$$
$$368$$ −182.947 49.0204i −0.497138 0.133208i
$$369$$ 0 0
$$370$$ −2.40405 + 67.5512i −0.00649743 + 0.182571i
$$371$$ 329.156 271.404i 0.887214 0.731546i
$$372$$ 0 0
$$373$$ −25.6741 95.8169i −0.0688313 0.256882i 0.922933 0.384962i $$-0.125785\pi$$
−0.991764 + 0.128080i $$0.959119\pi$$
$$374$$ 9.17620 5.29788i 0.0245353 0.0141655i
$$375$$ 0 0
$$376$$ −44.4305 + 76.9558i −0.118166 + 0.204670i
$$377$$ −371.163 371.163i −0.984517 0.984517i
$$378$$ 0 0
$$379$$ 466.795i 1.23165i 0.787884 + 0.615824i $$0.211177\pi$$
−0.787884 + 0.615824i $$0.788823\pi$$
$$380$$ −134.164 + 214.388i −0.353062 + 0.564180i
$$381$$ 0 0
$$382$$ −16.1053 + 60.1057i −0.0421604 + 0.157345i
$$383$$ 59.3027 + 221.321i 0.154837 + 0.577861i 0.999119 + 0.0419615i $$0.0133607\pi$$
−0.844282 + 0.535899i $$0.819973\pi$$
$$384$$ 0 0
$$385$$ 95.0202 123.693i 0.246806 0.321282i
$$386$$ −22.0448 −0.0571108
$$387$$ 0 0
$$388$$ 676.211 + 181.190i 1.74281 + 0.466985i
$$389$$ −465.749 + 268.900i −1.19730 + 0.691260i −0.959952 0.280165i $$-0.909611\pi$$
−0.237346 + 0.971425i $$0.576277\pi$$
$$390$$ 0 0
$$391$$ −122.254 −0.312669
$$392$$ −84.1718 41.0277i −0.214724 0.104663i
$$393$$ 0 0
$$394$$ −54.8493 31.6673i −0.139211 0.0803738i
$$395$$ 291.800 154.903i 0.738733 0.392160i
$$396$$ 0 0
$$397$$ −79.7937 + 21.3807i −0.200992 + 0.0538555i −0.357910 0.933756i $$-0.616511\pi$$
0.156919 + 0.987612i $$0.449844\pi$$
$$398$$ −46.0723 + 46.0723i −0.115759 + 0.115759i
$$399$$ 0 0
$$400$$ −381.747 27.2061i −0.954367 0.0680152i
$$401$$ 72.9306 126.319i 0.181872 0.315011i −0.760646 0.649167i $$-0.775118\pi$$
0.942518 + 0.334156i $$0.108451\pi$$
$$402$$ 0 0
$$403$$ −237.117 63.5354i −0.588381 0.157656i
$$404$$ −393.145 226.982i −0.973131 0.561837i
$$405$$ 0 0
$$406$$ −58.0193 21.6844i −0.142905 0.0534099i
$$407$$ −177.049 177.049i −0.435010 0.435010i
$$408$$ 0 0
$$409$$ −350.103 + 202.132i −0.855998 + 0.494211i −0.862670 0.505767i $$-0.831209\pi$$
0.00667227 + 0.999978i $$0.497876\pi$$
$$410$$ −16.5098 + 53.8726i −0.0402678 + 0.131397i
$$411$$ 0 0
$$412$$ −269.356 269.356i −0.653777 0.653777i
$$413$$ −77.1744 + 802.522i −0.186863 + 1.94315i
$$414$$ 0 0
$$415$$ 103.983 + 451.775i 0.250562 + 1.08862i
$$416$$ 80.8420 + 140.022i 0.194332 + 0.336592i
$$417$$ 0 0
$$418$$ 3.56103 + 13.2899i 0.00851921 + 0.0317941i
$$419$$ 404.689i 0.965844i 0.875663 + 0.482922i $$0.160425\pi$$
−0.875663 + 0.482922i $$0.839575\pi$$
$$420$$ 0 0
$$421$$ 430.807 1.02329 0.511647 0.859196i $$-0.329035\pi$$
0.511647 + 0.859196i $$0.329035\pi$$
$$422$$ −68.4691 + 18.3462i −0.162249 + 0.0434745i
$$423$$ 0 0
$$424$$ −100.863 + 58.2332i −0.237884 + 0.137342i
$$425$$ −242.558 + 46.8128i −0.570724 + 0.110148i
$$426$$ 0 0
$$427$$ −128.899 282.750i −0.301870 0.662178i
$$428$$ 344.280 344.280i 0.804392 0.804392i
$$429$$ 0 0
$$430$$ 20.0184 + 37.7097i 0.0465543 + 0.0876970i
$$431$$ −32.0539 55.5190i −0.0743710 0.128814i 0.826442 0.563023i $$-0.190362\pi$$
−0.900813 + 0.434208i $$0.857028\pi$$
$$432$$ 0 0
$$433$$ −58.9362 + 58.9362i −0.136111 + 0.136111i −0.771880 0.635769i $$-0.780683\pi$$
0.635769 + 0.771880i $$0.280683\pi$$
$$434$$ −28.5693 + 4.78447i −0.0658278 + 0.0110241i
$$435$$ 0 0
$$436$$ −97.9601 + 169.672i −0.224679 + 0.389156i
$$437$$ 41.0870 153.339i 0.0940207 0.350890i
$$438$$ 0 0
$$439$$ 262.656 + 151.644i 0.598304 + 0.345431i 0.768374 0.640001i $$-0.221066\pi$$
−0.170070 + 0.985432i $$0.554399\pi$$
$$440$$ −31.1615 + 29.0198i −0.0708217 + 0.0659540i
$$441$$ 0 0
$$442$$ 23.9971 + 23.9971i 0.0542922 + 0.0542922i
$$443$$ 55.0133 + 205.312i 0.124184 + 0.463459i 0.999809 0.0195310i $$-0.00621730\pi$$
−0.875626 + 0.482990i $$0.839551\pi$$
$$444$$ 0 0
$$445$$ 55.9221 29.6865i 0.125668 0.0667112i
$$446$$ −1.52687 + 2.64461i −0.00342347 + 0.00592963i
$$447$$ 0 0
$$448$$ −333.460 237.793i −0.744331 0.530788i
$$449$$ 266.145i 0.592751i 0.955072 + 0.296375i $$0.0957779\pi$$
−0.955072 + 0.296375i $$0.904222\pi$$
$$450$$ 0 0
$$451$$ −104.359 180.755i −0.231395 0.400788i
$$452$$ −61.1846 + 228.344i −0.135364 + 0.505186i
$$453$$ 0 0
$$454$$ 86.5615i 0.190664i
$$455$$ 461.446 + 191.431i 1.01417 + 0.420728i
$$456$$ 0 0
$$457$$ 304.655 81.6321i 0.666641 0.178626i 0.0904000 0.995906i $$-0.471185\pi$$
0.576241 + 0.817280i $$0.304519\pi$$
$$458$$ 54.0368 + 14.4791i 0.117984 + 0.0316138i
$$459$$ 0 0
$$460$$ 237.648 54.6984i 0.516626 0.118910i
$$461$$ 613.866 1.33160 0.665799 0.746132i $$-0.268091\pi$$
0.665799 + 0.746132i $$0.268091\pi$$
$$462$$ 0 0
$$463$$ 140.640 140.640i 0.303758 0.303758i −0.538724 0.842482i $$-0.681093\pi$$
0.842482 + 0.538724i $$0.181093\pi$$
$$464$$ −487.540 281.482i −1.05073 0.606641i
$$465$$ 0 0
$$466$$ 3.96317 + 6.86440i 0.00850465 + 0.0147305i
$$467$$ 309.664 82.9741i 0.663091 0.177675i 0.0884506 0.996081i $$-0.471808\pi$$
0.574641 + 0.818406i $$0.305142\pi$$
$$468$$ 0 0
$$469$$ −314.223 381.088i −0.669985 0.812553i
$$470$$ 1.98967 55.9075i 0.00423334 0.118952i
$$471$$ 0 0
$$472$$ 56.9655 212.598i 0.120690 0.450420i
$$473$$ −152.760 40.9318i −0.322959 0.0865366i
$$474$$ 0 0
$$475$$ 22.8031 319.966i 0.0480066 0.673612i
$$476$$ −255.417 95.4607i −0.536591 0.200548i
$$477$$ 0 0
$$478$$ 8.31737 + 31.0409i 0.0174004 + 0.0649390i
$$479$$ −459.429 + 265.251i −0.959141 + 0.553761i −0.895909 0.444238i $$-0.853474\pi$$
−0.0632327 + 0.997999i $$0.520141\pi$$
$$480$$ 0 0
$$481$$ 400.978 694.514i 0.833634 1.44390i
$$482$$ 78.5370 + 78.5370i 0.162940 + 0.162940i
$$483$$ 0 0
$$484$$ 398.703i 0.823767i
$$485$$ −865.309 + 199.165i −1.78414 + 0.410648i
$$486$$ 0 0
$$487$$ 36.7674 137.218i 0.0754977 0.281761i −0.917848 0.396932i $$-0.870075\pi$$
0.993346 + 0.115171i $$0.0367415\pi$$
$$488$$ 21.9564 + 81.9423i 0.0449925 + 0.167914i
$$489$$ 0 0
$$490$$ 58.9156 2.03255i 0.120236 0.00414807i
$$491$$ 98.2025 0.200005 0.100003 0.994987i $$-0.468115\pi$$
0.100003 + 0.994987i $$0.468115\pi$$
$$492$$ 0 0
$$493$$ −350.998 94.0496i −0.711963 0.190770i
$$494$$ −38.1638 + 22.0339i −0.0772548 + 0.0446031i
$$495$$ 0 0
$$496$$ −263.281 −0.530809
$$497$$ 345.612 484.657i 0.695397 0.975164i
$$498$$ 0 0
$$499$$ 75.4381 + 43.5542i 0.151179 + 0.0872830i 0.573681 0.819079i $$-0.305515\pi$$
−0.422502 + 0.906362i $$0.638848\pi$$
$$500$$ 450.562 199.524i 0.901123 0.399047i
$$501$$ 0 0
$$502$$ −29.2754 + 7.84433i −0.0583176 + 0.0156261i
$$503$$ −360.582 + 360.582i −0.716863 + 0.716863i −0.967962 0.251098i $$-0.919208\pi$$
0.251098 + 0.967962i $$0.419208\pi$$
$$504$$ 0 0
$$505$$ 575.425 + 20.4786i 1.13946 + 0.0405516i
$$506$$ 6.63332 11.4893i 0.0131093 0.0227060i
$$507$$ 0 0
$$508$$ 335.350 + 89.8569i 0.660139 + 0.176884i
$$509$$ 203.239 + 117.340i 0.399291 + 0.230531i 0.686178 0.727434i $$-0.259287\pi$$
−0.286887 + 0.957964i $$0.592620\pi$$
$$510$$ 0 0
$$511$$ 63.0464 51.9845i 0.123378 0.101731i
$$512$$ 205.362 + 205.362i 0.401098 + 0.401098i
$$513$$ 0 0
$$514$$ −50.9247 + 29.4014i −0.0990754 + 0.0572012i
$$515$$ 461.947 + 141.568i 0.896984 + 0.274890i
$$516$$ 0 0
$$517$$ 146.531 + 146.531i 0.283426 + 0.283426i
$$518$$ 9.05844 94.1970i 0.0174873 0.181848i
$$519$$ 0 0
$$520$$ −115.612 72.3497i −0.222331 0.139134i
$$521$$ −264.414 457.979i −0.507513 0.879038i −0.999962 0.00869711i $$-0.997232\pi$$
0.492449 0.870341i $$-0.336102\pi$$
$$522$$ 0 0
$$523$$ −96.7747 361.168i −0.185038 0.690570i −0.994622 0.103567i $$-0.966974\pi$$
0.809585 0.587003i $$-0.199692\pi$$
$$524$$ 60.4960i 0.115450i
$$525$$ 0 0
$$526$$ 29.0816 0.0552882
$$527$$ −164.151 + 43.9842i −0.311483 + 0.0834615i
$$528$$ 0 0
$$529$$ 325.565 187.965i 0.615435 0.355321i
$$530$$ 38.8963 62.1548i 0.0733892 0.117273i
$$531$$ 0 0
$$532$$ 205.574 288.280i 0.386418 0.541879i
$$533$$ 472.702 472.702i 0.886871 0.886871i
$$534$$ 0 0
$$535$$ −180.946 + 590.440i −0.338217 + 1.10363i
$$536$$ 67.4207 + 116.776i 0.125785 + 0.217866i
$$537$$ 0 0
$$538$$ 43.5076 43.5076i 0.0808692 0.0808692i
$$539$$ −143.222 + 164.840i −0.265718 + 0.305825i
$$540$$ 0 0
$$541$$ 90.3132 156.427i 0.166937 0.289144i −0.770404 0.637556i $$-0.779946\pi$$
0.937342 + 0.348412i $$0.113279\pi$$
$$542$$ 3.00617 11.2192i 0.00554643 0.0206996i
$$543$$ 0 0
$$544$$ 96.9346 + 55.9652i 0.178189 + 0.102877i
$$545$$ 8.83806 248.340i 0.0162166 0.455669i
$$546$$ 0 0
$$547$$ −17.8276 17.8276i −0.0325916 0.0325916i 0.690623 0.723215i $$-0.257336\pi$$
−0.723215 + 0.690623i $$0.757336\pi$$
$$548$$ −232.107 866.235i −0.423553 1.58072i
$$549$$ 0 0
$$550$$ 8.76146 25.3353i 0.0159299 0.0460642i
$$551$$ 235.927 408.638i 0.428180 0.741629i
$$552$$ 0 0
$$553$$ −420.845 + 191.853i −0.761022 + 0.346931i
$$554$$ 24.9386i 0.0450155i
$$555$$ 0 0
$$556$$ 201.140 + 348.385i 0.361763 + 0.626591i
$$557$$ 189.707 707.997i 0.340587 1.27109i −0.557096 0.830448i $$-0.688085\pi$$
0.897683 0.440641i $$-0.145249\pi$$
$$558$$ 0 0
$$559$$ 506.532i 0.906139i
$$560$$ 531.179 + 70.2250i 0.948534 + 0.125402i
$$561$$ 0 0
$$562$$ 83.1916 22.2911i 0.148028 0.0396639i
$$563$$ 805.856 + 215.928i 1.43136 + 0.383532i 0.889499 0.456936i $$-0.151053\pi$$
0.541861 + 0.840468i $$0.317720\pi$$
$$564$$ 0 0
$$565$$ −67.2542 292.199i −0.119034 0.517166i
$$566$$ −43.4295 −0.0767306
$$567$$ 0 0
$$568$$ −114.909 + 114.909i −0.202305 + 0.202305i
$$569$$ 394.493 + 227.761i 0.693309 + 0.400282i 0.804851 0.593478i $$-0.202245\pi$$
−0.111541 + 0.993760i $$0.535579\pi$$
$$570$$ 0 0
$$571$$ −79.5469 137.779i −0.139312 0.241295i 0.787925 0.615772i $$-0.211156\pi$$
−0.927236 + 0.374477i $$0.877822\pi$$
$$572$$ 242.215 64.9012i 0.423452 0.113464i
$$573$$ 0 0
$$574$$ 27.6166 73.8917i 0.0481126 0.128731i
$$575$$ −233.705 + 202.610i −0.406443 + 0.352365i
$$576$$ 0 0
$$577$$ −193.065 + 720.527i −0.334601 + 1.24875i 0.569700 + 0.821852i $$0.307059\pi$$
−0.904301 + 0.426895i $$0.859607\pi$$
$$578$$ −44.4749 11.9170i −0.0769462 0.0206177i
$$579$$ 0 0
$$580$$ 724.382 + 25.7797i 1.24893 + 0.0444478i
$$581$$ −107.198 640.109i −0.184507 1.10174i
$$582$$ 0 0
$$583$$ 70.2962 + 262.349i 0.120577 + 0.449998i
$$584$$ −19.3192 + 11.1539i −0.0330808 + 0.0190992i
$$585$$ 0 0
$$586$$ 19.8431 34.3692i 0.0338619 0.0586505i
$$587$$ 198.400 + 198.400i 0.337990 + 0.337990i 0.855611 0.517620i $$-0.173182\pi$$
−0.517620 + 0.855611i $$0.673182\pi$$
$$588$$ 0 0
$$589$$ 220.672i 0.374656i
$$590$$ 31.0801 + 135.033i 0.0526781 + 0.228870i
$$591$$ 0 0
$$592$$ 222.611 830.797i 0.376033 1.40337i
$$593$$ −126.975 473.876i −0.214123 0.799116i −0.986474 0.163920i $$-0.947586\pi$$
0.772351 0.635196i $$-0.219081\pi$$
$$594$$ 0 0
$$595$$ 342.913 44.9556i 0.576324 0.0755557i
$$596$$ −1154.23 −1.93662
$$597$$ 0 0
$$598$$ 41.0437 + 10.9976i 0.0686350 + 0.0183907i
$$599$$ −821.554 + 474.325i −1.37154 + 0.791861i −0.991122 0.132953i $$-0.957554\pi$$
−0.380421 + 0.924814i $$0.624221\pi$$
$$600$$ 0 0
$$601$$ 1121.80 1.86655 0.933275 0.359161i $$-0.116937\pi$$
0.933275 + 0.359161i $$0.116937\pi$$
$$602$$ −24.7934 54.3865i −0.0411851 0.0903430i
$$603$$ 0 0
$$604$$ −708.202 408.881i −1.17252 0.676955i
$$605$$ −237.113 446.663i −0.391923 0.738287i
$$606$$ 0 0
$$607$$ 293.221 78.5682i 0.483065 0.129437i −0.00906430 0.999959i $$-0.502885\pi$$
0.492130 + 0.870522i $$0.336219\pi$$
$$608$$ −102.773 + 102.773i −0.169035 + 0.169035i
$$609$$ 0 0
$$610$$ −36.3975 39.0837i −0.0596680 0.0640717i
$$611$$ −331.862 + 574.802i −0.543146 + 0.940756i
$$612$$ 0 0
$$613$$ −306.525 82.1330i −0.500040 0.133985i −2.15317e−5 1.00000i $$-0.500007\pi$$
−0.500019 + 0.866015i $$0.666674\pi$$
$$614$$ −30.1516 17.4080i −0.0491069 0.0283519i
$$615$$ 0 0
$$616$$ 45.9951 37.9249i 0.0746674 0.0615665i
$$617$$ 405.225 + 405.225i 0.656767 + 0.656767i 0.954614 0.297847i $$-0.0962685\pi$$
−0.297847 + 0.954614i $$0.596269\pi$$
$$618$$ 0 0
$$619$$ −906.466 + 523.349i −1.46440 + 0.845474i −0.999210 0.0397346i $$-0.987349\pi$$
−0.465194 + 0.885209i $$0.654015\pi$$
$$620$$ 299.413 158.945i 0.482925 0.256363i
$$621$$ 0 0
$$622$$ −1.82031 1.82031i −0.00292655 0.00292655i
$$623$$ −80.6532 + 36.7678i −0.129459 + 0.0590173i
$$624$$ 0 0
$$625$$ −386.101 + 491.478i −0.617762 + 0.786365i
$$626$$ −57.4444 99.4966i −0.0917642 0.158940i
$$627$$ 0 0
$$628$$ 77.2841 + 288.428i 0.123064 + 0.459281i
$$629$$ 555.177i 0.882635i
$$630$$ 0 0
$$631$$ −340.356 −0.539392 −0.269696 0.962946i $$-0.586923\pi$$
−0.269696 + 0.962946i $$0.586923\pi$$
$$632$$ 121.963 32.6799i 0.192979 0.0517087i
$$633$$ 0 0
$$634$$ −15.4364 + 8.91221i −0.0243476 + 0.0140571i
$$635$$ −429.129 + 98.7708i −0.675793 + 0.155545i
$$636$$ 0 0
$$637$$ −628.700 306.446i −0.986971 0.481077i
$$638$$ 27.8834 27.8834i 0.0437044 0.0437044i
$$639$$ 0 0
$$640$$ −283.907 87.0060i −0.443604 0.135947i
$$641$$ −29.6837 51.4137i −0.0463085 0.0802086i 0.841942 0.539568i $$-0.181412\pi$$
−0.888251 + 0.459359i $$0.848079\pi$$
$$642$$ 0 0
$$643$$ −147.606 + 147.606i −0.229558 + 0.229558i −0.812508 0.582950i $$-0.801898\pi$$
0.582950 + 0.812508i $$0.301898\pi$$
$$644$$ −336.717 + 56.3897i −0.522852 + 0.0875616i
$$645$$ 0 0
$$646$$ −15.2536 + 26.4200i −0.0236124 + 0.0408979i
$$647$$ −188.763 + 704.471i −0.291750 + 1.08883i 0.652014 + 0.758207i $$0.273925\pi$$
−0.943764 + 0.330620i $$0.892742\pi$$
$$648$$ 0 0
$$649$$ −444.510 256.638i −0.684915 0.395436i
$$650$$ 85.6442 + 6.10364i 0.131760 + 0.00939021i
$$651$$ 0 0
$$652$$ 547.551 + 547.551i 0.839802 + 0.839802i
$$653$$ −71.0567 265.187i −0.108816 0.406106i 0.889934 0.456089i $$-0.150750\pi$$
−0.998750 + 0.0499826i $$0.984083\pi$$
$$654$$ 0 0
$$655$$ 35.9776 + 67.7731i 0.0549277 + 0.103470i
$$656$$ 358.487 620.917i 0.546474 0.946520i
$$657$$ 0 0
$$658$$ −7.49706 + 77.9605i −0.0113937 + 0.118481i
$$659$$ 153.073i 0.232281i −0.993233 0.116140i $$-0.962948\pi$$
0.993233 0.116140i $$-0.0370523\pi$$
$$660$$ 0 0
$$661$$ −427.398 740.276i −0.646594 1.11993i −0.983931 0.178549i $$-0.942860\pi$$
0.337337 0.941384i $$-0.390474\pi$$
$$662$$ 23.2240 86.6732i 0.0350816 0.130926i
$$663$$ 0 0
$$664$$ 177.182i 0.266841i
$$665$$ −58.8599 + 445.214i −0.0885112 + 0.669495i
$$666$$ 0 0
$$667$$ −439.474 + 117.757i −0.658882 + 0.176547i
$$668$$ 1019.03 + 273.049i 1.52550 + 0.408756i
$$669$$ 0 0
$$670$$ −71.9609 45.0330i −0.107404 0.0672134i
$$671$$ 197.833 0.294833
$$672$$ 0 0
$$673$$ −26.8360 + 26.8360i −0.0398752 + 0.0398752i −0.726763 0.686888i $$-0.758976\pi$$
0.686888 + 0.726763i $$0.258976\pi$$
$$674$$ 0.447934 + 0.258615i 0.000664591 + 0.000383702i
$$675$$ 0 0
$$676$$ 68.4690 + 118.592i 0.101286 + 0.175432i
$$677$$ −235.342 + 63.0598i −0.347625 + 0.0931459i −0.428407 0.903586i $$-0.640925\pi$$
0.0807817 + 0.996732i $$0.474258\pi$$
$$678$$ 0 0
$$679$$ 1226.03 205.323i 1.80565 0.302390i
$$680$$ −94.3561 3.35800i −0.138759 0.00493823i
$$681$$ 0 0
$$682$$ 4.77306 17.8133i 0.00699862 0.0261192i
$$683$$ 1285.99 + 344.581i 1.88286 + 0.504511i 0.999348 + 0.0361036i $$0.0114946\pi$$
0.883513 + 0.468407i $$0.155172\pi$$
$$684$$ 0 0
$$685$$ 775.187 + 832.398i 1.13166 + 1.21518i
$$686$$ −82.5035 2.12995i −0.120267 0.00310489i
$$687$$ 0 0
$$688$$ −140.606 524.748i −0.204369 0.762715i
$$689$$ −753.370 + 434.958i −1.09342 + 0.631289i
$$690$$ 0 0
$$691$$ 260.502 451.203i 0.376993 0.652972i −0.613630 0.789594i $$-0.710291\pi$$
0.990623 + 0.136622i $$0.0436246\pi$$
$$692$$ 532.551 + 532.551i 0.769582 + 0.769582i
$$693$$ 0 0
$$694$$ 50.4544i 0.0727008i
$$695$$ −432.523 270.672i −0.622336 0.389456i
$$696$$ 0 0
$$697$$ 119.779 447.021i 0.171849 0.641350i
$$698$$ −15.9451 59.5079i −0.0228440 0.0852549i
$$699$$ 0 0
$$700$$ −646.472 + 240.814i −0.923532 + 0.344020i
$$701$$ 387.575 0.552889 0.276444 0.961030i $$-0.410844\pi$$
0.276444 + 0.961030i $$0.410844\pi$$
$$702$$ 0 0
$$703$$ 696.342 + 186.584i 0.990529 + 0.265411i
$$704$$ 225.811 130.372i 0.320755 0.185188i
$$705$$ 0 0
$$706$$ −0.771879 −0.00109331
$$707$$ −802.404 77.1630i −1.13494 0.109141i
$$708$$ 0 0
$$709$$ −13.1567 7.59601i −0.0185567 0.0107137i 0.490693 0.871333i $$-0.336744\pi$$
−0.509250 + 0.860619i $$0.670077\pi$$
$$710$$ 29.9769 97.8166i 0.0422210 0.137770i
$$711$$ 0 0
$$712$$ 23.3737 6.26296i 0.0328282 0.00879629i
$$713$$ −150.458 + 150.458i −0.211021 + 0.211021i
$$714$$ 0 0
$$715$$ −232.753 + 216.756i −0.325529 + 0.303155i
$$716$$ −359.822 + 623.230i −0.502545 + 0.870433i
$$717$$ 0 0
$$718$$ −71.9873 19.2890i −0.100261 0.0268648i
$$719$$ 35.5781 + 20.5410i 0.0494827 + 0.0285689i 0.524537 0.851387i $$-0.324238\pi$$
−0.475055 + 0.879956i $$0.657572\pi$$
$$720$$ 0 0
$$721$$ −633.607 236.807i −0.878789 0.328442i
$$722$$ 33.4093 + 33.4093i 0.0462733 + 0.0462733i
$$723$$ 0 0
$$724$$ 352.398 203.457i 0.486737 0.281018i
$$725$$ −826.850 + 401.917i −1.14048 + 0.554369i
$$726$$ 0 0
$$727$$ −198.452 198.452i −0.272974 0.272974i 0.557322 0.830296i $$-0.311829\pi$$
−0.830296 + 0.557322i $$0.811829\pi$$
$$728$$ 155.459 + 110.859i 0.213543 + 0.152279i
$$729$$ 0 0
$$730$$ 7.45016 11.9051i 0.0102057 0.0163083i
$$731$$ −175.331 303.682i −0.239850 0.415433i
$$732$$ 0 0
$$733$$ −68.7887 256.723i −0.0938454 0.350236i 0.902996 0.429648i $$-0.141362\pi$$
−0.996842 + 0.0794121i $$0.974696\pi$$
$$734$$ 84.4626i 0.115072i
$$735$$ 0 0
$$736$$ 140.145 0.190414
$$737$$ 303.740 81.3868i 0.412130 0.110430i
$$738$$ 0 0
$$739$$ 990.596 571.921i 1.34045 0.773912i 0.353581 0.935404i $$-0.384964\pi$$
0.986874 + 0.161492i $$0.0516306\pi$$
$$740$$ 248.396 + 1079.21i 0.335671 + 1.45839i
$$741$$ 0 0
$$742$$ −59.5994 + 83.5771i −0.0803227 + 0.112638i
$$743$$ 43.0155 43.0155i 0.0578943 0.0578943i −0.677567 0.735461i $$-0.736966\pi$$
0.735461 + 0.677567i $$0.236966\pi$$
$$744$$ 0 0
$$745$$ 1293.07 686.431i 1.73566 0.921384i
$$746$$ 11.9341 + 20.6705i 0.0159975 + 0.0277085i
$$747$$ 0 0
$$748$$ 122.750 122.750i 0.164105 0.164105i
$$749$$ 302.676 809.849i 0.404107 1.08124i
$$750$$ 0 0
$$751$$ −627.063 + 1086.11i −0.834971 + 1.44621i 0.0590826 + 0.998253i $$0.481182\pi$$
−0.894054 + 0.447960i $$0.852151\pi$$
$$752$$ −184.240 + 687.594i −0.245000 + 0.914353i
$$753$$ 0 0
$$754$$ 109.379 + 63.1499i 0.145065 + 0.0837531i
$$755$$ 1036.56 + 36.8896i 1.37292 + 0.0488604i
$$756$$ 0 0
$$757$$ −686.443 686.443i −0.906795 0.906795i 0.0892176 0.996012i $$-0.471563\pi$$
−0.996012 + 0.0892176i $$0.971563\pi$$
$$758$$ −29.0700 108.491i −0.0383509 0.143128i
$$759$$ 0 0
$$760$$ 35.9231 117.219i 0.0472672 0.154236i
$$761$$ −296.933 + 514.302i −0.390187 + 0.675825i −0.992474 0.122455i $$-0.960923\pi$$
0.602287 + 0.798280i $$0.294256\pi$$
$$762$$ 0 0
$$763$$ −33.3017 + 346.298i −0.0436458 + 0.453864i
$$764$$ 1019.48i 1.33439i
$$765$$ 0 0
$$766$$ −27.5658 47.7454i −0.0359867 0.0623308i
$$767$$ 425.490 1587.95i 0.554745 2.07034i
$$768$$ 0 0
$$769$$ 712.789i 0.926903i 0.886122 + 0.463452i $$0.153389\pi$$
−0.886122 + 0.463452i $$0.846611\pi$$
$$770$$ −14.3811 + 34.6658i −0.0186768 + 0.0450205i
$$771$$ 0 0
$$772$$ −348.863 + 93.4774i −0.451895 + 0.121085i
$$773$$ −79.8406 21.3932i −0.103287 0.0276756i 0.206806 0.978382i $$-0.433693\pi$$
−0.310092 + 0.950706i $$0.600360\pi$$
$$774$$ 0 0
$$775$$ −240.904