# Properties

 Label 570.2.d.d.229.4 Level $570$ Weight $2$ Character 570.229 Analytic conductor $4.551$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.350464.1 Defining polynomial: $$x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 229.4 Root $$0.403032 - 0.403032i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.229 Dual form 570.2.d.d.229.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.67513 - 1.48119i) q^{10} -1.61213 q^{11} +1.00000i q^{12} +1.35026i q^{13} -3.35026 q^{14} +(-1.67513 + 1.48119i) q^{15} +1.00000 q^{16} +6.96239i q^{17} -1.00000i q^{18} +1.00000 q^{19} +(1.48119 + 1.67513i) q^{20} +3.35026 q^{21} -1.61213i q^{22} +1.35026i q^{23} -1.00000 q^{24} +(-0.612127 + 4.96239i) q^{25} -1.35026 q^{26} +1.00000i q^{27} -3.35026i q^{28} -3.61213 q^{29} +(-1.48119 - 1.67513i) q^{30} -2.31265 q^{31} +1.00000i q^{32} +1.61213i q^{33} -6.96239 q^{34} +(5.61213 - 4.96239i) q^{35} +1.00000 q^{36} +11.2750i q^{37} +1.00000i q^{38} +1.35026 q^{39} +(-1.67513 + 1.48119i) q^{40} -3.35026 q^{41} +3.35026i q^{42} +10.3127i q^{43} +1.61213 q^{44} +(1.48119 + 1.67513i) q^{45} -1.35026 q^{46} -4.57452i q^{47} -1.00000i q^{48} -4.22425 q^{49} +(-4.96239 - 0.612127i) q^{50} +6.96239 q^{51} -1.35026i q^{52} -11.9248i q^{53} -1.00000 q^{54} +(2.38787 + 2.70052i) q^{55} +3.35026 q^{56} -1.00000i q^{57} -3.61213i q^{58} -1.03761 q^{59} +(1.67513 - 1.48119i) q^{60} +2.00000 q^{61} -2.31265i q^{62} -3.35026i q^{63} -1.00000 q^{64} +(2.26187 - 2.00000i) q^{65} -1.61213 q^{66} -9.92478i q^{67} -6.96239i q^{68} +1.35026 q^{69} +(4.96239 + 5.61213i) q^{70} -0.775746 q^{71} +1.00000i q^{72} +3.22425i q^{73} -11.2750 q^{74} +(4.96239 + 0.612127i) q^{75} -1.00000 q^{76} -5.40105i q^{77} +1.35026i q^{78} -14.3127 q^{79} +(-1.48119 - 1.67513i) q^{80} +1.00000 q^{81} -3.35026i q^{82} -10.8872i q^{83} -3.35026 q^{84} +(11.6629 - 10.3127i) q^{85} -10.3127 q^{86} +3.61213i q^{87} +1.61213i q^{88} +2.57452 q^{89} +(-1.67513 + 1.48119i) q^{90} -4.52373 q^{91} -1.35026i q^{92} +2.31265i q^{93} +4.57452 q^{94} +(-1.48119 - 1.67513i) q^{95} +1.00000 q^{96} -1.16362i q^{97} -4.22425i q^{98} +1.61213 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q - 6q^{4} + 2q^{5} + 6q^{6} - 6q^{9} + O(q^{10})$$ $$6q - 6q^{4} + 2q^{5} + 6q^{6} - 6q^{9} - 8q^{11} + 6q^{16} + 6q^{19} - 2q^{20} - 6q^{24} - 2q^{25} + 12q^{26} - 20q^{29} + 2q^{30} + 28q^{31} - 20q^{34} + 32q^{35} + 6q^{36} - 12q^{39} + 8q^{44} - 2q^{45} + 12q^{46} - 22q^{49} - 8q^{50} + 20q^{51} - 6q^{54} + 16q^{55} - 28q^{59} + 12q^{61} - 6q^{64} + 32q^{65} - 8q^{66} - 12q^{69} + 8q^{70} - 8q^{71} - 4q^{74} + 8q^{75} - 6q^{76} - 44q^{79} + 2q^{80} + 6q^{81} + 8q^{85} - 20q^{86} - 8q^{89} - 64q^{91} + 4q^{94} + 2q^{95} + 6q^{96} + 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 1.00000i 0.577350i
$$4$$ −1.00000 −0.500000
$$5$$ −1.48119 1.67513i −0.662410 0.749141i
$$6$$ 1.00000 0.408248
$$7$$ 3.35026i 1.26628i 0.774037 + 0.633140i $$0.218234\pi$$
−0.774037 + 0.633140i $$0.781766\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −1.00000 −0.333333
$$10$$ 1.67513 1.48119i 0.529723 0.468395i
$$11$$ −1.61213 −0.486075 −0.243037 0.970017i $$-0.578144\pi$$
−0.243037 + 0.970017i $$0.578144\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 1.35026i 0.374495i 0.982313 + 0.187248i $$0.0599567\pi$$
−0.982313 + 0.187248i $$0.940043\pi$$
$$14$$ −3.35026 −0.895395
$$15$$ −1.67513 + 1.48119i −0.432517 + 0.382443i
$$16$$ 1.00000 0.250000
$$17$$ 6.96239i 1.68863i 0.535849 + 0.844314i $$0.319992\pi$$
−0.535849 + 0.844314i $$0.680008\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 1.00000 0.229416
$$20$$ 1.48119 + 1.67513i 0.331205 + 0.374571i
$$21$$ 3.35026 0.731087
$$22$$ 1.61213i 0.343707i
$$23$$ 1.35026i 0.281549i 0.990042 + 0.140775i $$0.0449593\pi$$
−0.990042 + 0.140775i $$0.955041\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ −0.612127 + 4.96239i −0.122425 + 0.992478i
$$26$$ −1.35026 −0.264808
$$27$$ 1.00000i 0.192450i
$$28$$ 3.35026i 0.633140i
$$29$$ −3.61213 −0.670755 −0.335378 0.942084i $$-0.608864\pi$$
−0.335378 + 0.942084i $$0.608864\pi$$
$$30$$ −1.48119 1.67513i −0.270428 0.305836i
$$31$$ −2.31265 −0.415364 −0.207682 0.978196i $$-0.566592\pi$$
−0.207682 + 0.978196i $$0.566592\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 1.61213i 0.280635i
$$34$$ −6.96239 −1.19404
$$35$$ 5.61213 4.96239i 0.948623 0.838797i
$$36$$ 1.00000 0.166667
$$37$$ 11.2750i 1.85360i 0.375549 + 0.926802i $$0.377454\pi$$
−0.375549 + 0.926802i $$0.622546\pi$$
$$38$$ 1.00000i 0.162221i
$$39$$ 1.35026 0.216215
$$40$$ −1.67513 + 1.48119i −0.264861 + 0.234197i
$$41$$ −3.35026 −0.523223 −0.261611 0.965173i $$-0.584254\pi$$
−0.261611 + 0.965173i $$0.584254\pi$$
$$42$$ 3.35026i 0.516957i
$$43$$ 10.3127i 1.57266i 0.617804 + 0.786332i $$0.288023\pi$$
−0.617804 + 0.786332i $$0.711977\pi$$
$$44$$ 1.61213 0.243037
$$45$$ 1.48119 + 1.67513i 0.220803 + 0.249714i
$$46$$ −1.35026 −0.199085
$$47$$ 4.57452i 0.667262i −0.942704 0.333631i $$-0.891726\pi$$
0.942704 0.333631i $$-0.108274\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −4.22425 −0.603465
$$50$$ −4.96239 0.612127i −0.701788 0.0865678i
$$51$$ 6.96239 0.974929
$$52$$ 1.35026i 0.187248i
$$53$$ 11.9248i 1.63799i −0.573798 0.818997i $$-0.694530\pi$$
0.573798 0.818997i $$-0.305470\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 2.38787 + 2.70052i 0.321981 + 0.364139i
$$56$$ 3.35026 0.447698
$$57$$ 1.00000i 0.132453i
$$58$$ 3.61213i 0.474295i
$$59$$ −1.03761 −0.135085 −0.0675427 0.997716i $$-0.521516\pi$$
−0.0675427 + 0.997716i $$0.521516\pi$$
$$60$$ 1.67513 1.48119i 0.216258 0.191221i
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 2.31265i 0.293707i
$$63$$ 3.35026i 0.422093i
$$64$$ −1.00000 −0.125000
$$65$$ 2.26187 2.00000i 0.280550 0.248069i
$$66$$ −1.61213 −0.198439
$$67$$ 9.92478i 1.21250i −0.795272 0.606252i $$-0.792672\pi$$
0.795272 0.606252i $$-0.207328\pi$$
$$68$$ 6.96239i 0.844314i
$$69$$ 1.35026 0.162552
$$70$$ 4.96239 + 5.61213i 0.593119 + 0.670777i
$$71$$ −0.775746 −0.0920641 −0.0460321 0.998940i $$-0.514658\pi$$
−0.0460321 + 0.998940i $$0.514658\pi$$
$$72$$ 1.00000i 0.117851i
$$73$$ 3.22425i 0.377370i 0.982038 + 0.188685i $$0.0604226\pi$$
−0.982038 + 0.188685i $$0.939577\pi$$
$$74$$ −11.2750 −1.31070
$$75$$ 4.96239 + 0.612127i 0.573007 + 0.0706823i
$$76$$ −1.00000 −0.114708
$$77$$ 5.40105i 0.615506i
$$78$$ 1.35026i 0.152887i
$$79$$ −14.3127 −1.61030 −0.805149 0.593072i $$-0.797915\pi$$
−0.805149 + 0.593072i $$0.797915\pi$$
$$80$$ −1.48119 1.67513i −0.165603 0.187285i
$$81$$ 1.00000 0.111111
$$82$$ 3.35026i 0.369975i
$$83$$ 10.8872i 1.19502i −0.801861 0.597511i $$-0.796156\pi$$
0.801861 0.597511i $$-0.203844\pi$$
$$84$$ −3.35026 −0.365544
$$85$$ 11.6629 10.3127i 1.26502 1.11856i
$$86$$ −10.3127 −1.11204
$$87$$ 3.61213i 0.387261i
$$88$$ 1.61213i 0.171853i
$$89$$ 2.57452 0.272898 0.136449 0.990647i $$-0.456431\pi$$
0.136449 + 0.990647i $$0.456431\pi$$
$$90$$ −1.67513 + 1.48119i −0.176574 + 0.156132i
$$91$$ −4.52373 −0.474216
$$92$$ 1.35026i 0.140775i
$$93$$ 2.31265i 0.239811i
$$94$$ 4.57452 0.471825
$$95$$ −1.48119 1.67513i −0.151967 0.171865i
$$96$$ 1.00000 0.102062
$$97$$ 1.16362i 0.118148i −0.998254 0.0590738i $$-0.981185\pi$$
0.998254 0.0590738i $$-0.0188147\pi$$
$$98$$ 4.22425i 0.426714i
$$99$$ 1.61213 0.162025
$$100$$ 0.612127 4.96239i 0.0612127 0.496239i
$$101$$ 8.88717 0.884306 0.442153 0.896940i $$-0.354215\pi$$
0.442153 + 0.896940i $$0.354215\pi$$
$$102$$ 6.96239i 0.689379i
$$103$$ 7.03761i 0.693436i 0.937969 + 0.346718i $$0.112704\pi$$
−0.937969 + 0.346718i $$0.887296\pi$$
$$104$$ 1.35026 0.132404
$$105$$ −4.96239 5.61213i −0.484280 0.547688i
$$106$$ 11.9248 1.15824
$$107$$ 0.775746i 0.0749942i 0.999297 + 0.0374971i $$0.0119385\pi$$
−0.999297 + 0.0374971i $$0.988062\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ 20.1622 1.93119 0.965594 0.260052i $$-0.0837399\pi$$
0.965594 + 0.260052i $$0.0837399\pi$$
$$110$$ −2.70052 + 2.38787i −0.257485 + 0.227675i
$$111$$ 11.2750 1.07018
$$112$$ 3.35026i 0.316570i
$$113$$ 11.1490i 1.04881i 0.851468 + 0.524406i $$0.175713\pi$$
−0.851468 + 0.524406i $$0.824287\pi$$
$$114$$ 1.00000 0.0936586
$$115$$ 2.26187 2.00000i 0.210920 0.186501i
$$116$$ 3.61213 0.335378
$$117$$ 1.35026i 0.124832i
$$118$$ 1.03761i 0.0955199i
$$119$$ −23.3258 −2.13827
$$120$$ 1.48119 + 1.67513i 0.135214 + 0.152918i
$$121$$ −8.40105 −0.763732
$$122$$ 2.00000i 0.181071i
$$123$$ 3.35026i 0.302083i
$$124$$ 2.31265 0.207682
$$125$$ 9.21933 6.32487i 0.824602 0.565713i
$$126$$ 3.35026 0.298465
$$127$$ 13.7381i 1.21906i −0.792762 0.609531i $$-0.791358\pi$$
0.792762 0.609531i $$-0.208642\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 10.3127 0.907978
$$130$$ 2.00000 + 2.26187i 0.175412 + 0.198379i
$$131$$ 5.61213 0.490334 0.245167 0.969481i $$-0.421157\pi$$
0.245167 + 0.969481i $$0.421157\pi$$
$$132$$ 1.61213i 0.140318i
$$133$$ 3.35026i 0.290505i
$$134$$ 9.92478 0.857370
$$135$$ 1.67513 1.48119i 0.144172 0.127481i
$$136$$ 6.96239 0.597020
$$137$$ 17.6629i 1.50904i 0.656275 + 0.754522i $$0.272131\pi$$
−0.656275 + 0.754522i $$0.727869\pi$$
$$138$$ 1.35026i 0.114942i
$$139$$ −10.7005 −0.907607 −0.453803 0.891102i $$-0.649933\pi$$
−0.453803 + 0.891102i $$0.649933\pi$$
$$140$$ −5.61213 + 4.96239i −0.474311 + 0.419398i
$$141$$ −4.57452 −0.385244
$$142$$ 0.775746i 0.0650992i
$$143$$ 2.17679i 0.182033i
$$144$$ −1.00000 −0.0833333
$$145$$ 5.35026 + 6.05079i 0.444315 + 0.502490i
$$146$$ −3.22425 −0.266841
$$147$$ 4.22425i 0.348411i
$$148$$ 11.2750i 0.926802i
$$149$$ −1.03761 −0.0850044 −0.0425022 0.999096i $$-0.513533\pi$$
−0.0425022 + 0.999096i $$0.513533\pi$$
$$150$$ −0.612127 + 4.96239i −0.0499799 + 0.405177i
$$151$$ 1.16362 0.0946940 0.0473470 0.998879i $$-0.484923\pi$$
0.0473470 + 0.998879i $$0.484923\pi$$
$$152$$ 1.00000i 0.0811107i
$$153$$ 6.96239i 0.562876i
$$154$$ 5.40105 0.435229
$$155$$ 3.42548 + 3.87399i 0.275142 + 0.311167i
$$156$$ −1.35026 −0.108107
$$157$$ 10.9624i 0.874894i −0.899244 0.437447i $$-0.855883\pi$$
0.899244 0.437447i $$-0.144117\pi$$
$$158$$ 14.3127i 1.13865i
$$159$$ −11.9248 −0.945696
$$160$$ 1.67513 1.48119i 0.132431 0.117099i
$$161$$ −4.52373 −0.356520
$$162$$ 1.00000i 0.0785674i
$$163$$ 21.0132i 1.64588i 0.568129 + 0.822939i $$0.307667\pi$$
−0.568129 + 0.822939i $$0.692333\pi$$
$$164$$ 3.35026 0.261611
$$165$$ 2.70052 2.38787i 0.210235 0.185896i
$$166$$ 10.8872 0.845008
$$167$$ 9.92478i 0.768002i −0.923333 0.384001i $$-0.874546\pi$$
0.923333 0.384001i $$-0.125454\pi$$
$$168$$ 3.35026i 0.258478i
$$169$$ 11.1768 0.859753
$$170$$ 10.3127 + 11.6629i 0.790944 + 0.894505i
$$171$$ −1.00000 −0.0764719
$$172$$ 10.3127i 0.786332i
$$173$$ 14.6253i 1.11194i 0.831202 + 0.555971i $$0.187653\pi$$
−0.831202 + 0.555971i $$0.812347\pi$$
$$174$$ −3.61213 −0.273835
$$175$$ −16.6253 2.05079i −1.25675 0.155025i
$$176$$ −1.61213 −0.121519
$$177$$ 1.03761i 0.0779916i
$$178$$ 2.57452i 0.192968i
$$179$$ −11.7381 −0.877349 −0.438675 0.898646i $$-0.644552\pi$$
−0.438675 + 0.898646i $$0.644552\pi$$
$$180$$ −1.48119 1.67513i −0.110402 0.124857i
$$181$$ 21.4617 1.59523 0.797617 0.603164i $$-0.206094\pi$$
0.797617 + 0.603164i $$0.206094\pi$$
$$182$$ 4.52373i 0.335321i
$$183$$ 2.00000i 0.147844i
$$184$$ 1.35026 0.0995426
$$185$$ 18.8872 16.7005i 1.38861 1.22785i
$$186$$ −2.31265 −0.169572
$$187$$ 11.2243i 0.820799i
$$188$$ 4.57452i 0.333631i
$$189$$ −3.35026 −0.243696
$$190$$ 1.67513 1.48119i 0.121527 0.107457i
$$191$$ −21.2750 −1.53941 −0.769704 0.638401i $$-0.779596\pi$$
−0.769704 + 0.638401i $$0.779596\pi$$
$$192$$ 1.00000i 0.0721688i
$$193$$ 14.1622i 1.01942i −0.860347 0.509709i $$-0.829753\pi$$
0.860347 0.509709i $$-0.170247\pi$$
$$194$$ 1.16362 0.0835430
$$195$$ −2.00000 2.26187i −0.143223 0.161976i
$$196$$ 4.22425 0.301732
$$197$$ 3.87399i 0.276011i −0.990431 0.138005i $$-0.955931\pi$$
0.990431 0.138005i $$-0.0440691\pi$$
$$198$$ 1.61213i 0.114569i
$$199$$ −3.47627 −0.246426 −0.123213 0.992380i $$-0.539320\pi$$
−0.123213 + 0.992380i $$0.539320\pi$$
$$200$$ 4.96239 + 0.612127i 0.350894 + 0.0432839i
$$201$$ −9.92478 −0.700040
$$202$$ 8.88717i 0.625299i
$$203$$ 12.1016i 0.849364i
$$204$$ −6.96239 −0.487465
$$205$$ 4.96239 + 5.61213i 0.346588 + 0.391968i
$$206$$ −7.03761 −0.490334
$$207$$ 1.35026i 0.0938497i
$$208$$ 1.35026i 0.0936238i
$$209$$ −1.61213 −0.111513
$$210$$ 5.61213 4.96239i 0.387274 0.342437i
$$211$$ 9.92478 0.683250 0.341625 0.939836i $$-0.389023\pi$$
0.341625 + 0.939836i $$0.389023\pi$$
$$212$$ 11.9248i 0.818997i
$$213$$ 0.775746i 0.0531533i
$$214$$ −0.775746 −0.0530289
$$215$$ 17.2750 15.2750i 1.17815 1.04175i
$$216$$ 1.00000 0.0680414
$$217$$ 7.74798i 0.525967i
$$218$$ 20.1622i 1.36556i
$$219$$ 3.22425 0.217875
$$220$$ −2.38787 2.70052i −0.160990 0.182069i
$$221$$ −9.40105 −0.632383
$$222$$ 11.2750i 0.756731i
$$223$$ 7.03761i 0.471273i 0.971841 + 0.235637i $$0.0757175\pi$$
−0.971841 + 0.235637i $$0.924282\pi$$
$$224$$ −3.35026 −0.223849
$$225$$ 0.612127 4.96239i 0.0408085 0.330826i
$$226$$ −11.1490 −0.741623
$$227$$ 14.5501i 0.965723i 0.875697 + 0.482861i $$0.160402\pi$$
−0.875697 + 0.482861i $$0.839598\pi$$
$$228$$ 1.00000i 0.0662266i
$$229$$ −11.4010 −0.753402 −0.376701 0.926335i $$-0.622942\pi$$
−0.376701 + 0.926335i $$0.622942\pi$$
$$230$$ 2.00000 + 2.26187i 0.131876 + 0.149143i
$$231$$ −5.40105 −0.355363
$$232$$ 3.61213i 0.237148i
$$233$$ 21.9149i 1.43569i 0.696201 + 0.717847i $$0.254872\pi$$
−0.696201 + 0.717847i $$0.745128\pi$$
$$234$$ 1.35026 0.0882694
$$235$$ −7.66291 + 6.77575i −0.499873 + 0.442001i
$$236$$ 1.03761 0.0675427
$$237$$ 14.3127i 0.929707i
$$238$$ 23.3258i 1.51199i
$$239$$ 13.2750 0.858691 0.429345 0.903140i $$-0.358744\pi$$
0.429345 + 0.903140i $$0.358744\pi$$
$$240$$ −1.67513 + 1.48119i −0.108129 + 0.0956107i
$$241$$ 21.3258 1.37372 0.686859 0.726791i $$-0.258989\pi$$
0.686859 + 0.726791i $$0.258989\pi$$
$$242$$ 8.40105i 0.540040i
$$243$$ 1.00000i 0.0641500i
$$244$$ −2.00000 −0.128037
$$245$$ 6.25694 + 7.07618i 0.399741 + 0.452080i
$$246$$ −3.35026 −0.213605
$$247$$ 1.35026i 0.0859151i
$$248$$ 2.31265i 0.146853i
$$249$$ −10.8872 −0.689946
$$250$$ 6.32487 + 9.21933i 0.400020 + 0.583082i
$$251$$ 16.3127 1.02965 0.514823 0.857297i $$-0.327858\pi$$
0.514823 + 0.857297i $$0.327858\pi$$
$$252$$ 3.35026i 0.211047i
$$253$$ 2.17679i 0.136854i
$$254$$ 13.7381 0.862007
$$255$$ −10.3127 11.6629i −0.645803 0.730360i
$$256$$ 1.00000 0.0625000
$$257$$ 24.5501i 1.53139i 0.643203 + 0.765696i $$0.277605\pi$$
−0.643203 + 0.765696i $$0.722395\pi$$
$$258$$ 10.3127i 0.642038i
$$259$$ −37.7743 −2.34718
$$260$$ −2.26187 + 2.00000i −0.140275 + 0.124035i
$$261$$ 3.61213 0.223585
$$262$$ 5.61213i 0.346718i
$$263$$ 30.3488i 1.87139i −0.352810 0.935695i $$-0.614774\pi$$
0.352810 0.935695i $$-0.385226\pi$$
$$264$$ 1.61213 0.0992195
$$265$$ −19.9756 + 17.6629i −1.22709 + 1.08502i
$$266$$ −3.35026 −0.205418
$$267$$ 2.57452i 0.157558i
$$268$$ 9.92478i 0.606252i
$$269$$ −14.3127 −0.872658 −0.436329 0.899787i $$-0.643722\pi$$
−0.436329 + 0.899787i $$0.643722\pi$$
$$270$$ 1.48119 + 1.67513i 0.0901426 + 0.101945i
$$271$$ −7.32582 −0.445012 −0.222506 0.974931i $$-0.571424\pi$$
−0.222506 + 0.974931i $$0.571424\pi$$
$$272$$ 6.96239i 0.422157i
$$273$$ 4.52373i 0.273789i
$$274$$ −17.6629 −1.06706
$$275$$ 0.986826 8.00000i 0.0595079 0.482418i
$$276$$ −1.35026 −0.0812762
$$277$$ 14.4387i 0.867535i −0.901025 0.433767i $$-0.857184\pi$$
0.901025 0.433767i $$-0.142816\pi$$
$$278$$ 10.7005i 0.641775i
$$279$$ 2.31265 0.138455
$$280$$ −4.96239 5.61213i −0.296559 0.335389i
$$281$$ −11.9756 −0.714402 −0.357201 0.934028i $$-0.616269\pi$$
−0.357201 + 0.934028i $$0.616269\pi$$
$$282$$ 4.57452i 0.272408i
$$283$$ 24.4894i 1.45575i 0.685712 + 0.727873i $$0.259491\pi$$
−0.685712 + 0.727873i $$0.740509\pi$$
$$284$$ 0.775746 0.0460321
$$285$$ −1.67513 + 1.48119i −0.0992262 + 0.0877384i
$$286$$ 2.17679 0.128716
$$287$$ 11.2243i 0.662547i
$$288$$ 1.00000i 0.0589256i
$$289$$ −31.4749 −1.85146
$$290$$ −6.05079 + 5.35026i −0.355314 + 0.314178i
$$291$$ −1.16362 −0.0682126
$$292$$ 3.22425i 0.188685i
$$293$$ 18.1016i 1.05751i 0.848776 + 0.528753i $$0.177340\pi$$
−0.848776 + 0.528753i $$0.822660\pi$$
$$294$$ −4.22425 −0.246363
$$295$$ 1.53690 + 1.73813i 0.0894820 + 0.101198i
$$296$$ 11.2750 0.655348
$$297$$ 1.61213i 0.0935451i
$$298$$ 1.03761i 0.0601072i
$$299$$ −1.82321 −0.105439
$$300$$ −4.96239 0.612127i −0.286504 0.0353412i
$$301$$ −34.5501 −1.99143
$$302$$ 1.16362i 0.0669588i
$$303$$ 8.88717i 0.510554i
$$304$$ 1.00000 0.0573539
$$305$$ −2.96239 3.35026i −0.169626 0.191835i
$$306$$ 6.96239 0.398013
$$307$$ 29.9248i 1.70790i −0.520357 0.853949i $$-0.674201\pi$$
0.520357 0.853949i $$-0.325799\pi$$
$$308$$ 5.40105i 0.307753i
$$309$$ 7.03761 0.400356
$$310$$ −3.87399 + 3.42548i −0.220028 + 0.194554i
$$311$$ −21.2750 −1.20640 −0.603198 0.797591i $$-0.706107\pi$$
−0.603198 + 0.797591i $$0.706107\pi$$
$$312$$ 1.35026i 0.0764435i
$$313$$ 17.4010i 0.983565i 0.870718 + 0.491783i $$0.163655\pi$$
−0.870718 + 0.491783i $$0.836345\pi$$
$$314$$ 10.9624 0.618643
$$315$$ −5.61213 + 4.96239i −0.316208 + 0.279599i
$$316$$ 14.3127 0.805149
$$317$$ 14.1016i 0.792023i −0.918246 0.396012i $$-0.870394\pi$$
0.918246 0.396012i $$-0.129606\pi$$
$$318$$ 11.9248i 0.668708i
$$319$$ 5.82321 0.326037
$$320$$ 1.48119 + 1.67513i 0.0828013 + 0.0936427i
$$321$$ 0.775746 0.0432979
$$322$$ 4.52373i 0.252098i
$$323$$ 6.96239i 0.387398i
$$324$$ −1.00000 −0.0555556
$$325$$ −6.70052 0.826531i −0.371678 0.0458477i
$$326$$ −21.0132 −1.16381
$$327$$ 20.1622i 1.11497i
$$328$$ 3.35026i 0.184987i
$$329$$ 15.3258 0.844940
$$330$$ 2.38787 + 2.70052i 0.131448 + 0.148659i
$$331$$ 6.85097 0.376563 0.188282 0.982115i $$-0.439708\pi$$
0.188282 + 0.982115i $$0.439708\pi$$
$$332$$ 10.8872i 0.597511i
$$333$$ 11.2750i 0.617868i
$$334$$ 9.92478 0.543060
$$335$$ −16.6253 + 14.7005i −0.908337 + 0.803175i
$$336$$ 3.35026 0.182772
$$337$$ 24.2374i 1.32030i −0.751135 0.660148i $$-0.770493\pi$$
0.751135 0.660148i $$-0.229507\pi$$
$$338$$ 11.1768i 0.607937i
$$339$$ 11.1490 0.605532
$$340$$ −11.6629 + 10.3127i −0.632510 + 0.559282i
$$341$$ 3.72829 0.201898
$$342$$ 1.00000i 0.0540738i
$$343$$ 9.29948i 0.502125i
$$344$$ 10.3127 0.556021
$$345$$ −2.00000 2.26187i −0.107676 0.121775i
$$346$$ −14.6253 −0.786261
$$347$$ 0.962389i 0.0516637i −0.999666 0.0258319i $$-0.991777\pi$$
0.999666 0.0258319i $$-0.00822345\pi$$
$$348$$ 3.61213i 0.193630i
$$349$$ 1.37470 0.0735860 0.0367930 0.999323i $$-0.488286\pi$$
0.0367930 + 0.999323i $$0.488286\pi$$
$$350$$ 2.05079 16.6253i 0.109619 0.888660i
$$351$$ −1.35026 −0.0720716
$$352$$ 1.61213i 0.0859267i
$$353$$ 28.7367i 1.52950i 0.644326 + 0.764751i $$0.277138\pi$$
−0.644326 + 0.764751i $$0.722862\pi$$
$$354$$ −1.03761 −0.0551484
$$355$$ 1.14903 + 1.29948i 0.0609842 + 0.0689691i
$$356$$ −2.57452 −0.136449
$$357$$ 23.3258i 1.23453i
$$358$$ 11.7381i 0.620380i
$$359$$ −31.1998 −1.64666 −0.823332 0.567561i $$-0.807887\pi$$
−0.823332 + 0.567561i $$0.807887\pi$$
$$360$$ 1.67513 1.48119i 0.0882871 0.0780658i
$$361$$ 1.00000 0.0526316
$$362$$ 21.4617i 1.12800i
$$363$$ 8.40105i 0.440941i
$$364$$ 4.52373 0.237108
$$365$$ 5.40105 4.77575i 0.282704 0.249974i
$$366$$ 2.00000 0.104542
$$367$$ 20.1260i 1.05057i −0.850927 0.525285i $$-0.823959\pi$$
0.850927 0.525285i $$-0.176041\pi$$
$$368$$ 1.35026i 0.0703873i
$$369$$ 3.35026 0.174408
$$370$$ 16.7005 + 18.8872i 0.868219 + 0.981897i
$$371$$ 39.9511 2.07416
$$372$$ 2.31265i 0.119905i
$$373$$ 17.9756i 0.930739i −0.885116 0.465370i $$-0.845921\pi$$
0.885116 0.465370i $$-0.154079\pi$$
$$374$$ 11.2243 0.580392
$$375$$ −6.32487 9.21933i −0.326615 0.476084i
$$376$$ −4.57452 −0.235913
$$377$$ 4.87732i 0.251195i
$$378$$ 3.35026i 0.172319i
$$379$$ −1.67276 −0.0859240 −0.0429620 0.999077i $$-0.513679\pi$$
−0.0429620 + 0.999077i $$0.513679\pi$$
$$380$$ 1.48119 + 1.67513i 0.0759837 + 0.0859324i
$$381$$ −13.7381 −0.703826
$$382$$ 21.2750i 1.08853i
$$383$$ 31.8496i 1.62744i 0.581260 + 0.813718i $$0.302560\pi$$
−0.581260 + 0.813718i $$0.697440\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ −9.04746 + 8.00000i −0.461101 + 0.407718i
$$386$$ 14.1622 0.720837
$$387$$ 10.3127i 0.524221i
$$388$$ 1.16362i 0.0590738i
$$389$$ 10.3371 0.524111 0.262056 0.965053i $$-0.415600\pi$$
0.262056 + 0.965053i $$0.415600\pi$$
$$390$$ 2.26187 2.00000i 0.114534 0.101274i
$$391$$ −9.40105 −0.475431
$$392$$ 4.22425i 0.213357i
$$393$$ 5.61213i 0.283094i
$$394$$ 3.87399 0.195169
$$395$$ 21.1998 + 23.9756i 1.06668 + 1.20634i
$$396$$ −1.61213 −0.0810124
$$397$$ 31.4372i 1.57779i 0.614528 + 0.788895i $$0.289346\pi$$
−0.614528 + 0.788895i $$0.710654\pi$$
$$398$$ 3.47627i 0.174250i
$$399$$ 3.35026 0.167723
$$400$$ −0.612127 + 4.96239i −0.0306063 + 0.248119i
$$401$$ 5.94921 0.297090 0.148545 0.988906i $$-0.452541\pi$$
0.148545 + 0.988906i $$0.452541\pi$$
$$402$$ 9.92478i 0.495003i
$$403$$ 3.12268i 0.155552i
$$404$$ −8.88717 −0.442153
$$405$$ −1.48119 1.67513i −0.0736011 0.0832379i
$$406$$ 12.1016 0.600591
$$407$$ 18.1768i 0.900990i
$$408$$ 6.96239i 0.344690i
$$409$$ 30.9986 1.53278 0.766391 0.642375i $$-0.222051\pi$$
0.766391 + 0.642375i $$0.222051\pi$$
$$410$$ −5.61213 + 4.96239i −0.277163 + 0.245075i
$$411$$ 17.6629 0.871247
$$412$$ 7.03761i 0.346718i
$$413$$ 3.47627i 0.171056i
$$414$$ 1.35026 0.0663617
$$415$$ −18.2374 + 16.1260i −0.895240 + 0.791595i
$$416$$ −1.35026 −0.0662020
$$417$$ 10.7005i 0.524007i
$$418$$ 1.61213i 0.0788517i
$$419$$ 34.3390 1.67757 0.838785 0.544463i $$-0.183266\pi$$
0.838785 + 0.544463i $$0.183266\pi$$
$$420$$ 4.96239 + 5.61213i 0.242140 + 0.273844i
$$421$$ 22.8627 1.11426 0.557131 0.830425i $$-0.311902\pi$$
0.557131 + 0.830425i $$0.311902\pi$$
$$422$$ 9.92478i 0.483131i
$$423$$ 4.57452i 0.222421i
$$424$$ −11.9248 −0.579118
$$425$$ −34.5501 4.26187i −1.67592 0.206731i
$$426$$ −0.775746 −0.0375850
$$427$$ 6.70052i 0.324261i
$$428$$ 0.775746i 0.0374971i
$$429$$ −2.17679 −0.105097
$$430$$ 15.2750 + 17.2750i 0.736628 + 0.833076i
$$431$$ 11.5975 0.558634 0.279317 0.960199i $$-0.409892\pi$$
0.279317 + 0.960199i $$0.409892\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ 27.8350i 1.33766i 0.743414 + 0.668832i $$0.233205\pi$$
−0.743414 + 0.668832i $$0.766795\pi$$
$$434$$ 7.74798 0.371915
$$435$$ 6.05079 5.35026i 0.290113 0.256525i
$$436$$ −20.1622 −0.965594
$$437$$ 1.35026i 0.0645918i
$$438$$ 3.22425i 0.154061i
$$439$$ 38.7875 1.85123 0.925613 0.378471i $$-0.123550\pi$$
0.925613 + 0.378471i $$0.123550\pi$$
$$440$$ 2.70052 2.38787i 0.128742 0.113837i
$$441$$ 4.22425 0.201155
$$442$$ 9.40105i 0.447162i
$$443$$ 29.2144i 1.38802i −0.719966 0.694009i $$-0.755843\pi$$
0.719966 0.694009i $$-0.244157\pi$$
$$444$$ −11.2750 −0.535090
$$445$$ −3.81336 4.31265i −0.180770 0.204439i
$$446$$ −7.03761 −0.333241
$$447$$ 1.03761i 0.0490773i
$$448$$ 3.35026i 0.158285i
$$449$$ 20.4993 0.967421 0.483711 0.875228i $$-0.339289\pi$$
0.483711 + 0.875228i $$0.339289\pi$$
$$450$$ 4.96239 + 0.612127i 0.233929 + 0.0288559i
$$451$$ 5.40105 0.254325
$$452$$ 11.1490i 0.524406i
$$453$$ 1.16362i 0.0546716i
$$454$$ −14.5501 −0.682869
$$455$$ 6.70052 + 7.57784i 0.314125 + 0.355255i
$$456$$ −1.00000 −0.0468293
$$457$$ 6.44851i 0.301648i −0.988561 0.150824i $$-0.951807\pi$$
0.988561 0.150824i $$-0.0481927\pi$$
$$458$$ 11.4010i 0.532736i
$$459$$ −6.96239 −0.324976
$$460$$ −2.26187 + 2.00000i −0.105460 + 0.0932505i
$$461$$ −13.5125 −0.629338 −0.314669 0.949201i $$-0.601894\pi$$
−0.314669 + 0.949201i $$0.601894\pi$$
$$462$$ 5.40105i 0.251279i
$$463$$ 6.20123i 0.288196i 0.989563 + 0.144098i $$0.0460280\pi$$
−0.989563 + 0.144098i $$0.953972\pi$$
$$464$$ −3.61213 −0.167689
$$465$$ 3.87399 3.42548i 0.179652 0.158853i
$$466$$ −21.9149 −1.01519
$$467$$ 16.5599i 0.766302i 0.923686 + 0.383151i $$0.125161\pi$$
−0.923686 + 0.383151i $$0.874839\pi$$
$$468$$ 1.35026i 0.0624159i
$$469$$ 33.2506 1.53537
$$470$$ −6.77575 7.66291i −0.312542 0.353464i
$$471$$ −10.9624 −0.505120
$$472$$ 1.03761i 0.0477599i
$$473$$ 16.6253i 0.764432i
$$474$$ −14.3127 −0.657402
$$475$$ −0.612127 + 4.96239i −0.0280863 + 0.227690i
$$476$$ 23.3258 1.06914
$$477$$ 11.9248i 0.545998i
$$478$$ 13.2750i 0.607186i
$$479$$ 30.5256 1.39475 0.697376 0.716705i $$-0.254351\pi$$
0.697376 + 0.716705i $$0.254351\pi$$
$$480$$ −1.48119 1.67513i −0.0676070 0.0764589i
$$481$$ −15.2243 −0.694166
$$482$$ 21.3258i 0.971365i
$$483$$ 4.52373i 0.205837i
$$484$$ 8.40105 0.381866
$$485$$ −1.94921 + 1.72355i −0.0885093 + 0.0782622i
$$486$$ 1.00000 0.0453609
$$487$$ 2.51388i 0.113915i 0.998377 + 0.0569574i $$0.0181399\pi$$
−0.998377 + 0.0569574i $$0.981860\pi$$
$$488$$ 2.00000i 0.0905357i
$$489$$ 21.0132 0.950249
$$490$$ −7.07618 + 6.25694i −0.319669 + 0.282660i
$$491$$ 1.46168 0.0659648 0.0329824 0.999456i $$-0.489499\pi$$
0.0329824 + 0.999456i $$0.489499\pi$$
$$492$$ 3.35026i 0.151041i
$$493$$ 25.1490i 1.13266i
$$494$$ −1.35026 −0.0607511
$$495$$ −2.38787 2.70052i −0.107327 0.121380i
$$496$$ −2.31265 −0.103841
$$497$$ 2.59895i 0.116579i
$$498$$ 10.8872i 0.487866i
$$499$$ 5.55149 0.248519 0.124259 0.992250i $$-0.460344\pi$$
0.124259 + 0.992250i $$0.460344\pi$$
$$500$$ −9.21933 + 6.32487i −0.412301 + 0.282857i
$$501$$ −9.92478 −0.443406
$$502$$ 16.3127i 0.728069i
$$503$$ 6.90175i 0.307734i 0.988092 + 0.153867i $$0.0491727\pi$$
−0.988092 + 0.153867i $$0.950827\pi$$
$$504$$ −3.35026 −0.149233
$$505$$ −13.1636 14.8872i −0.585773 0.662470i
$$506$$ 2.17679 0.0967703
$$507$$ 11.1768i 0.496379i
$$508$$ 13.7381i 0.609531i
$$509$$ −8.76116 −0.388331 −0.194166 0.980969i $$-0.562200\pi$$
−0.194166 + 0.980969i $$0.562200\pi$$
$$510$$ 11.6629 10.3127i 0.516442 0.456652i
$$511$$ −10.8021 −0.477857
$$512$$ 1.00000i 0.0441942i
$$513$$ 1.00000i 0.0441511i
$$514$$ −24.5501 −1.08286
$$515$$ 11.7889 10.4241i 0.519482 0.459339i
$$516$$ −10.3127 −0.453989
$$517$$ 7.37470i 0.324339i
$$518$$ 37.7743i 1.65971i
$$519$$ 14.6253 0.641979
$$520$$ −2.00000 2.26187i −0.0877058 0.0991893i
$$521$$ 39.4518 1.72842 0.864208 0.503135i $$-0.167820\pi$$
0.864208 + 0.503135i $$0.167820\pi$$
$$522$$ 3.61213i 0.158098i
$$523$$ 37.5026i 1.63987i −0.572453 0.819937i $$-0.694008\pi$$
0.572453 0.819937i $$-0.305992\pi$$
$$524$$ −5.61213 −0.245167
$$525$$ −2.05079 + 16.6253i −0.0895036 + 0.725588i
$$526$$ 30.3488 1.32327
$$527$$ 16.1016i 0.701395i
$$528$$ 1.61213i 0.0701588i
$$529$$ 21.1768 0.920730
$$530$$ −17.6629 19.9756i −0.767228 0.867683i
$$531$$ 1.03761 0.0450285
$$532$$ 3.35026i 0.145252i
$$533$$ 4.52373i 0.195945i
$$534$$ 2.57452 0.111410
$$535$$ 1.29948 1.14903i 0.0561813 0.0496769i
$$536$$ −9.92478 −0.428685
$$537$$ 11.7381i 0.506538i
$$538$$ 14.3127i 0.617062i
$$539$$ 6.81003 0.293329
$$540$$ −1.67513 + 1.48119i −0.0720862 + 0.0637405i
$$541$$ −30.7757 −1.32315 −0.661576 0.749878i $$-0.730112\pi$$
−0.661576 + 0.749878i $$0.730112\pi$$
$$542$$ 7.32582i 0.314671i
$$543$$ 21.4617i 0.921009i
$$544$$ −6.96239 −0.298510
$$545$$ −29.8641 33.7743i −1.27924 1.44673i
$$546$$ −4.52373 −0.193598
$$547$$ 1.77433i 0.0758649i 0.999280 + 0.0379325i $$0.0120772\pi$$
−0.999280 + 0.0379325i $$0.987923\pi$$
$$548$$ 17.6629i 0.754522i
$$549$$ −2.00000 −0.0853579
$$550$$ 8.00000 + 0.986826i 0.341121 + 0.0420784i
$$551$$ −3.61213 −0.153882
$$552$$ 1.35026i 0.0574710i
$$553$$ 47.9511i 2.03909i
$$554$$ 14.4387 0.613440
$$555$$ −16.7005 18.8872i −0.708898 0.801716i
$$556$$ 10.7005 0.453803
$$557$$ 8.90175i 0.377179i 0.982056 + 0.188590i $$0.0603916\pi$$
−0.982056 + 0.188590i $$0.939608\pi$$
$$558$$ 2.31265i 0.0979023i
$$559$$ −13.9248 −0.588955
$$560$$ 5.61213 4.96239i 0.237156 0.209699i
$$561$$ −11.2243 −0.473888
$$562$$ 11.9756i 0.505159i
$$563$$ 10.9525i 0.461595i −0.973002 0.230797i $$-0.925867\pi$$
0.973002 0.230797i $$-0.0741334\pi$$
$$564$$ 4.57452 0.192622
$$565$$ 18.6761 16.5139i 0.785709 0.694744i
$$566$$ −24.4894 −1.02937
$$567$$ 3.35026i 0.140698i
$$568$$ 0.775746i 0.0325496i
$$569$$ 10.2012 0.427658 0.213829 0.976871i $$-0.431406\pi$$
0.213829 + 0.976871i $$0.431406\pi$$
$$570$$ −1.48119 1.67513i −0.0620404 0.0701635i
$$571$$ −25.6531 −1.07355 −0.536774 0.843726i $$-0.680357\pi$$
−0.536774 + 0.843726i $$0.680357\pi$$
$$572$$ 2.17679i 0.0910163i
$$573$$ 21.2750i 0.888778i
$$574$$ 11.2243 0.468491
$$575$$ −6.70052 0.826531i −0.279431 0.0344687i
$$576$$ 1.00000 0.0416667
$$577$$ 6.44851i 0.268455i −0.990951 0.134227i $$-0.957145\pi$$
0.990951 0.134227i $$-0.0428553\pi$$
$$578$$ 31.4749i 1.30918i
$$579$$ −14.1622 −0.588561
$$580$$ −5.35026 6.05079i −0.222158 0.251245i
$$581$$ 36.4749 1.51323
$$582$$ 1.16362i 0.0482336i
$$583$$ 19.2243i 0.796187i
$$584$$ 3.22425 0.133421
$$585$$ −2.26187 + 2.00000i −0.0935166 + 0.0826898i
$$586$$ −18.1016 −0.747769
$$587$$ 41.8397i 1.72691i 0.504426 + 0.863455i $$0.331704\pi$$
−0.504426 + 0.863455i $$0.668296\pi$$
$$588$$ 4.22425i 0.174205i
$$589$$ −2.31265 −0.0952911
$$590$$ −1.73813 + 1.53690i −0.0715579 + 0.0632733i
$$591$$ −3.87399 −0.159355
$$592$$ 11.2750i 0.463401i
$$593$$ 8.73672i 0.358774i 0.983779 + 0.179387i $$0.0574114\pi$$
−0.983779 + 0.179387i $$0.942589\pi$$
$$594$$ 1.61213 0.0661464
$$595$$ 34.5501 + 39.0738i 1.41642 + 1.60187i
$$596$$ 1.03761 0.0425022
$$597$$ 3.47627i 0.142274i
$$598$$ 1.82321i 0.0745565i
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0.612127 4.96239i 0.0249900 0.202589i
$$601$$ 30.6253 1.24923 0.624616 0.780932i $$-0.285255\pi$$
0.624616 + 0.780932i $$0.285255\pi$$
$$602$$ 34.5501i 1.40816i
$$603$$ 9.92478i 0.404168i
$$604$$ −1.16362 −0.0473470
$$605$$ 12.4436 + 14.0729i 0.505904 + 0.572143i
$$606$$ 8.88717 0.361016
$$607$$ 2.51388i 0.102035i 0.998698 + 0.0510176i $$0.0162465\pi$$
−0.998698 + 0.0510176i $$0.983754\pi$$
$$608$$ 1.00000i 0.0405554i
$$609$$ −12.1016 −0.490380
$$610$$ 3.35026 2.96239i 0.135648 0.119944i
$$611$$ 6.17679 0.249886
$$612$$ 6.96239i 0.281438i
$$613$$ 2.96239i 0.119650i −0.998209 0.0598249i $$-0.980946\pi$$
0.998209 0.0598249i $$-0.0190542\pi$$
$$614$$ 29.9248 1.20767
$$615$$ 5.61213 4.96239i 0.226303 0.200103i
$$616$$ −5.40105 −0.217614
$$617$$ 18.3371i 0.738223i 0.929385 + 0.369112i $$0.120338\pi$$
−0.929385 + 0.369112i $$0.879662\pi$$
$$618$$ 7.03761i 0.283094i
$$619$$ 40.7269 1.63695 0.818476 0.574541i $$-0.194820\pi$$
0.818476 + 0.574541i $$0.194820\pi$$
$$620$$ −3.42548 3.87399i −0.137571 0.155583i
$$621$$ −1.35026 −0.0541841
$$622$$ 21.2750i 0.853051i
$$623$$ 8.62530i 0.345565i
$$624$$ 1.35026 0.0540537
$$625$$ −24.2506 6.07522i −0.970024 0.243009i
$$626$$ −17.4010 −0.695486
$$627$$ 1.61213i 0.0643821i
$$628$$ 10.9624i 0.437447i
$$629$$ −78.5012 −3.13005
$$630$$ −4.96239 5.61213i −0.197706 0.223592i
$$631$$ −5.92478 −0.235862 −0.117931 0.993022i $$-0.537626\pi$$
−0.117931 + 0.993022i $$0.537626\pi$$
$$632$$ 14.3127i 0.569327i
$$633$$ 9.92478i 0.394474i
$$634$$ 14.1016 0.560045
$$635$$ −23.0132 + 20.3488i −0.913250 + 0.807519i
$$636$$ 11.9248 0.472848
$$637$$ 5.70385i 0.225995i
$$638$$ 5.82321i 0.230543i
$$639$$ 0.775746 0.0306880
$$640$$ −1.67513 + 1.48119i −0.0662154 + 0.0585493i
$$641$$ 19.0494 0.752405 0.376202 0.926537i $$-0.377230\pi$$
0.376202 + 0.926537i $$0.377230\pi$$
$$642$$ 0.775746i 0.0306163i
$$643$$ 1.06205i 0.0418831i −0.999781 0.0209416i $$-0.993334\pi$$
0.999781 0.0209416i $$-0.00666639\pi$$
$$644$$ 4.52373 0.178260
$$645$$ −15.2750 17.2750i −0.601454 0.680204i
$$646$$ −6.96239 −0.273932
$$647$$ 26.6497i 1.04771i −0.851808 0.523855i $$-0.824493\pi$$
0.851808 0.523855i $$-0.175507\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ 1.67276 0.0656616
$$650$$ 0.826531 6.70052i 0.0324192 0.262816i
$$651$$ −7.74798 −0.303667
$$652$$ 21.0132i 0.822939i
$$653$$ 9.64832i 0.377568i −0.982019 0.188784i $$-0.939545\pi$$
0.982019 0.188784i $$-0.0604546\pi$$
$$654$$ 20.1622 0.788405
$$655$$ −8.31265 9.40105i −0.324802 0.367329i
$$656$$ −3.35026 −0.130806
$$657$$ 3.22425i 0.125790i
$$658$$ 15.3258i 0.597463i
$$659$$ −10.0654 −0.392091 −0.196046 0.980595i $$-0.562810\pi$$
−0.196046 + 0.980595i $$0.562810\pi$$
$$660$$ −2.70052 + 2.38787i −0.105118 + 0.0929478i
$$661$$ 13.5633 0.527549 0.263775 0.964584i $$-0.415032\pi$$
0.263775 + 0.964584i $$0.415032\pi$$
$$662$$ 6.85097i 0.266270i
$$663$$ 9.40105i 0.365106i
$$664$$ −10.8872 −0.422504
$$665$$ 5.61213 4.96239i 0.217629 0.192433i
$$666$$ 11.2750 0.436899
$$667$$ 4.87732i 0.188850i
$$668$$ 9.92478i 0.384001i
$$669$$ 7.03761 0.272090
$$670$$ −14.7005 16.6253i −0.567931 0.642291i
$$671$$ −3.22425 −0.124471
$$672$$ 3.35026i 0.129239i
$$673$$ 5.93937i 0.228946i −0.993426 0.114473i $$-0.963482\pi$$
0.993426 0.114473i $$-0.0365179\pi$$
$$674$$ 24.2374 0.933591
$$675$$ −4.96239 0.612127i −0.191002 0.0235608i
$$676$$ −11.1768 −0.429877
$$677$$ 24.9525i 0.959004i 0.877541 + 0.479502i $$0.159183\pi$$
−0.877541 + 0.479502i $$0.840817\pi$$
$$678$$ 11.1490i 0.428176i
$$679$$ 3.89843 0.149608
$$680$$ −10.3127 11.6629i −0.395472 0.447252i
$$681$$ 14.5501 0.557560
$$682$$ 3.72829i 0.142763i
$$683$$ 45.6239i 1.74575i 0.487944 + 0.872875i $$0.337747\pi$$
−0.487944 + 0.872875i $$0.662253\pi$$
$$684$$ 1.00000 0.0382360
$$685$$ 29.5877 26.1622i 1.13049 0.999606i
$$686$$ −9.29948 −0.355056
$$687$$ 11.4010i 0.434977i
$$688$$ 10.3127i 0.393166i
$$689$$ 16.1016 0.613421
$$690$$ 2.26187 2.00000i 0.0861077 0.0761387i
$$691$$ −11.7480 −0.446914 −0.223457 0.974714i $$-0.571734\pi$$
−0.223457 + 0.974714i $$0.571734\pi$$
$$692$$ 14.6253i 0.555971i
$$693$$ 5.40105i 0.205169i
$$694$$ 0.962389 0.0365318
$$695$$ 15.8496 + 17.9248i 0.601208 + 0.679926i
$$696$$ 3.61213 0.136917
$$697$$ 23.3258i 0.883529i
$$698$$ 1.37470i 0.0520331i
$$699$$ 21.9149 0.828899
$$700$$ 16.6253 + 2.05079i 0.628377 + 0.0775124i
$$701$$ −43.8105 −1.65470 −0.827350 0.561686i $$-0.810153\pi$$
−0.827350 + 0.561686i $$0.810153\pi$$
$$702$$ 1.35026i 0.0509623i
$$703$$ 11.2750i 0.425246i
$$704$$ 1.61213 0.0607593
$$705$$ 6.77575 + 7.66291i 0.255189 + 0.288602i
$$706$$ −28.7367 −1.08152
$$707$$ 29.7743i 1.11978i
$$708$$ 1.03761i 0.0389958i
$$709$$ 29.5975 1.11156 0.555779 0.831330i $$-0.312420\pi$$
0.555779 + 0.831330i $$0.312420\pi$$
$$710$$ −1.29948 + 1.14903i −0.0487685 + 0.0431224i
$$711$$ 14.3127 0.536766
$$712$$ 2.57452i 0.0964840i
$$713$$ 3.12268i 0.116945i
$$714$$ −23.3258 −0.872947
$$715$$ −3.64641 + 3.22425i −0.136368 + 0.120580i
$$716$$ 11.7381 0.438675
$$717$$ 13.2750i 0.495765i
$$718$$ 31.1998i 1.16437i
$$719$$ −7.45183 −0.277906 −0.138953 0.990299i $$-0.544374\pi$$
−0.138953 + 0.990299i $$0.544374\pi$$
$$720$$ 1.48119 + 1.67513i 0.0552009 + 0.0624284i
$$721$$ −23.5778 −0.878085
$$722$$ 1.00000i 0.0372161i
$$723$$ 21.3258i 0.793116i
$$724$$ −21.4617 −0.797617
$$725$$ 2.21108 17.9248i 0.0821174 0.665710i
$$726$$ −8.40105 −0.311792
$$727$$ 0.600863i 0.0222848i 0.999938 + 0.0111424i $$0.00354681\pi$$
−0.999938 + 0.0111424i $$0.996453\pi$$
$$728$$ 4.52373i 0.167661i
$$729$$ −1.00000 −0.0370370
$$730$$ 4.77575 + 5.40105i 0.176758 + 0.199902i
$$731$$ −71.8007 −2.65564
$$732$$ 2.00000i 0.0739221i
$$733$$ 36.0625i 1.33200i −0.745952 0.666000i $$-0.768005\pi$$
0.745952 0.666000i $$-0.231995\pi$$
$$734$$ 20.1260 0.742865
$$735$$ 7.07618 6.25694i 0.261009 0.230791i
$$736$$ −1.35026 −0.0497713
$$737$$ 16.0000i 0.589368i
$$738$$ 3.35026i 0.123325i
$$739$$ 14.1768 0.521502 0.260751 0.965406i $$-0.416030\pi$$
0.260751 + 0.965406i $$0.416030\pi$$
$$740$$ −18.8872 + 16.7005i −0.694306 + 0.613923i
$$741$$ 1.35026 0.0496031
$$742$$ 39.9511i 1.46665i
$$743$$ 24.9986i 0.917109i −0.888666 0.458555i $$-0.848367\pi$$
0.888666 0.458555i $$-0.151633\pi$$
$$744$$ 2.31265 0.0847859
$$745$$ 1.53690 + 1.73813i 0.0563078 + 0.0636803i
$$746$$ 17.9756 0.658132
$$747$$ 10.8872i 0.398341i
$$748$$ 11.2243i 0.410399i
$$749$$ −2.59895 −0.0949637
$$750$$ 9.21933 6.32487i 0.336642 0.230952i
$$751$$ −10.2111 −0.372608 −0.186304 0.982492i $$-0.559651\pi$$
−0.186304 + 0.982492i $$0.559651\pi$$
$$752$$ 4.57452i 0.166815i
$$753$$ 16.3127i 0.594466i
$$754$$ 4.87732 0.177621
$$755$$ −1.72355 1.94921i −0.0627263 0.0709392i
$$756$$ 3.35026 0.121848
$$757$$ 44.4847i 1.61682i 0.588617 + 0.808412i $$0.299673\pi$$
−0.588617 + 0.808412i $$0.700327\pi$$
$$758$$ 1.67276i 0.0607574i
$$759$$ −2.17679 −0.0790126
$$760$$ −1.67513 + 1.48119i −0.0607634 + 0.0537286i
$$761$$ 27.1490 0.984152 0.492076 0.870552i $$-0.336238\pi$$
0.492076 + 0.870552i $$0.336238\pi$$
$$762$$ 13.7381i 0.497680i
$$763$$ 67.5487i 2.44543i
$$764$$ 21.2750 0.769704
$$765$$ −11.6629 + 10.3127i −0.421673 + 0.372855i
$$766$$ −31.8496 −1.15077
$$767$$ 1.40105i 0.0505889i
$$768$$ 1.00000i 0.0360844i
$$769$$ 31.4010 1.13235 0.566175 0.824285i $$-0.308422\pi$$
0.566175 + 0.824285i $$0.308422\pi$$
$$770$$ −8.00000 9.04746i −0.288300 0.326048i
$$771$$ 24.5501 0.884149
$$772$$ 14.1622i 0.509709i
$$773$$ 4.02635i 0.144818i −0.997375 0.0724088i $$-0.976931\pi$$
0.997375 0.0724088i $$-0.0230686\pi$$
$$774$$ 10.3127 0.370681
$$775$$ 1.41564 11.4763i 0.0508511 0.412240i
$$776$$ −1.16362 −0.0417715
$$777$$ 37.7743i 1.35515i
$$778$$ 10.3371i 0.370603i
$$779$$ −3.35026 −0.120036
$$780$$ 2.00000 + 2.26187i 0.0716115 + 0.0809878i
$$781$$ 1.25060 0.0447500
$$782$$ 9.40105i 0.336181i
$$783$$ 3.61213i 0.129087i
$$784$$ −4.22425 −0.150866
$$785$$ −18.3634 + 16.2374i −0.655419 + 0.579539i
$$786$$ 5.61213 0.200178
$$787$$ 18.2981i 0.652255i 0.945326 + 0.326128i $$0.105744\pi$$
−0.945326 + 0.326128i $$0.894256\pi$$
$$788$$ 3.87399i