# Properties

 Label 600.2.k.d.301.1 Level 600 Weight 2 Character 600.301 Analytic conductor 4.791 Analytic rank 0 Dimension 8 CM no Inner twists 2

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$600 = 2^{3} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 600.k (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.79102412128$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.214798336.3 Defining polynomial: $$x^{8} - 2 x^{7} - 2 x^{5} + 9 x^{4} - 4 x^{3} - 16 x + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 301.1 Root $$1.41216 - 0.0762223i$$ of defining polynomial Character $$\chi$$ $$=$$ 600.301 Dual form 600.2.k.d.301.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.29150 - 0.576222i) q^{2} +1.00000i q^{3} +(1.33594 + 1.48838i) q^{4} +(0.576222 - 1.29150i) q^{6} -1.97676 q^{7} +(-0.867721 - 2.69204i) q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q+(-1.29150 - 0.576222i) q^{2} +1.00000i q^{3} +(1.33594 + 1.48838i) q^{4} +(0.576222 - 1.29150i) q^{6} -1.97676 q^{7} +(-0.867721 - 2.69204i) q^{8} -1.00000 q^{9} -1.43055i q^{11} +(-1.48838 + 1.33594i) q^{12} +0.241319i q^{13} +(2.55298 + 1.13905i) q^{14} +(-0.430552 + 3.97676i) q^{16} -7.38407 q^{17} +(1.29150 + 0.576222i) q^{18} +3.04033i q^{19} -1.97676i q^{21} +(-0.824316 + 1.84756i) q^{22} +0.874337 q^{23} +(2.69204 - 0.867721i) q^{24} +(0.139054 - 0.311664i) q^{26} -1.00000i q^{27} +(-2.64082 - 2.94217i) q^{28} -9.07918i q^{29} -7.44764 q^{31} +(2.84756 - 4.88789i) q^{32} +1.43055 q^{33} +(9.53652 + 4.25487i) q^{34} +(-1.33594 - 1.48838i) q^{36} -8.81463i q^{37} +(1.75191 - 3.92658i) q^{38} -0.241319 q^{39} -1.91319 q^{41} +(-1.13905 + 2.55298i) q^{42} +11.2452i q^{43} +(2.12921 - 1.91113i) q^{44} +(-1.12921 - 0.503813i) q^{46} -3.34374 q^{47} +(-3.97676 - 0.430552i) q^{48} -3.09242 q^{49} -7.38407i q^{51} +(-0.359175 + 0.322387i) q^{52} -9.20632i q^{53} +(-0.576222 + 1.29150i) q^{54} +(1.71528 + 5.32151i) q^{56} -3.04033 q^{57} +(-5.23163 + 11.7258i) q^{58} -6.43616i q^{59} +4.57331i q^{61} +(9.61862 + 4.29150i) q^{62} +1.97676 q^{63} +(-6.49412 + 4.67187i) q^{64} +(-1.84756 - 0.824316i) q^{66} -4.86671i q^{67} +(-9.86465 - 10.9903i) q^{68} +0.874337i q^{69} -8.21808 q^{71} +(0.867721 + 2.69204i) q^{72} -4.12714 q^{73} +(-5.07918 + 11.3841i) q^{74} +(-4.52517 + 4.06169i) q^{76} +2.82786i q^{77} +(0.311664 + 0.139054i) q^{78} -13.6757 q^{79} +1.00000 q^{81} +(2.47088 + 1.10242i) q^{82} +12.3320i q^{83} +(2.94217 - 2.64082i) q^{84} +(6.47972 - 14.5231i) q^{86} +9.07918 q^{87} +(-3.85110 + 1.24132i) q^{88} -8.08066 q^{89} -0.477031i q^{91} +(1.16806 + 1.30135i) q^{92} -7.44764i q^{93} +(4.31844 + 1.92674i) q^{94} +(4.88789 + 2.84756i) q^{96} +10.6757 q^{97} +(3.99385 + 1.78192i) q^{98} +1.43055i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{2} + 4q^{4} + 2q^{6} + 8q^{7} + 4q^{8} - 8q^{9} + O(q^{10})$$ $$8q - 2q^{2} + 4q^{4} + 2q^{6} + 8q^{7} + 4q^{8} - 8q^{9} - 6q^{14} + 8q^{16} + 2q^{18} + 12q^{22} + 8q^{23} - 8q^{24} - 2q^{26} - 4q^{28} + 8q^{31} + 28q^{32} + 12q^{34} - 4q^{36} + 30q^{38} - 6q^{42} - 12q^{44} + 20q^{46} - 8q^{48} - 20q^{52} - 2q^{54} + 8q^{56} + 8q^{57} + 12q^{58} + 30q^{62} - 8q^{63} - 32q^{64} - 20q^{66} - 28q^{68} - 40q^{71} - 4q^{72} - 16q^{73} + 8q^{74} - 20q^{76} - 22q^{78} - 16q^{79} + 8q^{81} - 24q^{82} + 24q^{84} - 18q^{86} + 24q^{87} - 8q^{88} - 36q^{92} - 4q^{94} + 12q^{96} - 8q^{97} - 48q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$$.

 $$n$$ $$151$$ $$301$$ $$401$$ $$577$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.29150 0.576222i −0.913227 0.407451i
$$3$$ 1.00000i 0.577350i
$$4$$ 1.33594 + 1.48838i 0.667968 + 0.744190i
$$5$$ 0 0
$$6$$ 0.576222 1.29150i 0.235242 0.527252i
$$7$$ −1.97676 −0.747145 −0.373573 0.927601i $$-0.621867\pi$$
−0.373573 + 0.927601i $$0.621867\pi$$
$$8$$ −0.867721 2.69204i −0.306786 0.951779i
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 1.43055i 0.431328i −0.976468 0.215664i $$-0.930808\pi$$
0.976468 0.215664i $$-0.0691915\pi$$
$$12$$ −1.48838 + 1.33594i −0.429658 + 0.385651i
$$13$$ 0.241319i 0.0669300i 0.999440 + 0.0334650i $$0.0106542\pi$$
−0.999440 + 0.0334650i $$0.989346\pi$$
$$14$$ 2.55298 + 1.13905i 0.682313 + 0.304425i
$$15$$ 0 0
$$16$$ −0.430552 + 3.97676i −0.107638 + 0.994190i
$$17$$ −7.38407 −1.79090 −0.895450 0.445161i $$-0.853146\pi$$
−0.895450 + 0.445161i $$0.853146\pi$$
$$18$$ 1.29150 + 0.576222i 0.304409 + 0.135817i
$$19$$ 3.04033i 0.697500i 0.937216 + 0.348750i $$0.113394\pi$$
−0.937216 + 0.348750i $$0.886606\pi$$
$$20$$ 0 0
$$21$$ 1.97676i 0.431365i
$$22$$ −0.824316 + 1.84756i −0.175745 + 0.393900i
$$23$$ 0.874337 0.182312 0.0911560 0.995837i $$-0.470944\pi$$
0.0911560 + 0.995837i $$0.470944\pi$$
$$24$$ 2.69204 0.867721i 0.549510 0.177123i
$$25$$ 0 0
$$26$$ 0.139054 0.311664i 0.0272707 0.0611223i
$$27$$ 1.00000i 0.192450i
$$28$$ −2.64082 2.94217i −0.499069 0.556018i
$$29$$ 9.07918i 1.68596i −0.537943 0.842981i $$-0.680799\pi$$
0.537943 0.842981i $$-0.319201\pi$$
$$30$$ 0 0
$$31$$ −7.44764 −1.33764 −0.668818 0.743426i $$-0.733200\pi$$
−0.668818 + 0.743426i $$0.733200\pi$$
$$32$$ 2.84756 4.88789i 0.503381 0.864064i
$$33$$ 1.43055 0.249027
$$34$$ 9.53652 + 4.25487i 1.63550 + 0.729704i
$$35$$ 0 0
$$36$$ −1.33594 1.48838i −0.222656 0.248063i
$$37$$ 8.81463i 1.44912i −0.689214 0.724558i $$-0.742044\pi$$
0.689214 0.724558i $$-0.257956\pi$$
$$38$$ 1.75191 3.92658i 0.284197 0.636976i
$$39$$ −0.241319 −0.0386420
$$40$$ 0 0
$$41$$ −1.91319 −0.298790 −0.149395 0.988778i $$-0.547733\pi$$
−0.149395 + 0.988778i $$0.547733\pi$$
$$42$$ −1.13905 + 2.55298i −0.175760 + 0.393934i
$$43$$ 11.2452i 1.71487i 0.514589 + 0.857437i $$0.327944\pi$$
−0.514589 + 0.857437i $$0.672056\pi$$
$$44$$ 2.12921 1.91113i 0.320990 0.288113i
$$45$$ 0 0
$$46$$ −1.12921 0.503813i −0.166492 0.0742831i
$$47$$ −3.34374 −0.487735 −0.243867 0.969809i $$-0.578416\pi$$
−0.243867 + 0.969809i $$0.578416\pi$$
$$48$$ −3.97676 0.430552i −0.573996 0.0621448i
$$49$$ −3.09242 −0.441774
$$50$$ 0 0
$$51$$ 7.38407i 1.03398i
$$52$$ −0.359175 + 0.322387i −0.0498086 + 0.0447071i
$$53$$ 9.20632i 1.26459i −0.774729 0.632293i $$-0.782114\pi$$
0.774729 0.632293i $$-0.217886\pi$$
$$54$$ −0.576222 + 1.29150i −0.0784139 + 0.175751i
$$55$$ 0 0
$$56$$ 1.71528 + 5.32151i 0.229213 + 0.711117i
$$57$$ −3.04033 −0.402702
$$58$$ −5.23163 + 11.7258i −0.686946 + 1.53967i
$$59$$ 6.43616i 0.837917i −0.908005 0.418958i $$-0.862395\pi$$
0.908005 0.418958i $$-0.137605\pi$$
$$60$$ 0 0
$$61$$ 4.57331i 0.585552i 0.956181 + 0.292776i $$0.0945790\pi$$
−0.956181 + 0.292776i $$0.905421\pi$$
$$62$$ 9.61862 + 4.29150i 1.22157 + 0.545021i
$$63$$ 1.97676 0.249048
$$64$$ −6.49412 + 4.67187i −0.811765 + 0.583984i
$$65$$ 0 0
$$66$$ −1.84756 0.824316i −0.227418 0.101466i
$$67$$ 4.86671i 0.594563i −0.954790 0.297282i $$-0.903920\pi$$
0.954790 0.297282i $$-0.0960801\pi$$
$$68$$ −9.86465 10.9903i −1.19626 1.33277i
$$69$$ 0.874337i 0.105258i
$$70$$ 0 0
$$71$$ −8.21808 −0.975307 −0.487653 0.873037i $$-0.662147\pi$$
−0.487653 + 0.873037i $$0.662147\pi$$
$$72$$ 0.867721 + 2.69204i 0.102262 + 0.317260i
$$73$$ −4.12714 −0.483045 −0.241523 0.970395i $$-0.577647\pi$$
−0.241523 + 0.970395i $$0.577647\pi$$
$$74$$ −5.07918 + 11.3841i −0.590443 + 1.32337i
$$75$$ 0 0
$$76$$ −4.52517 + 4.06169i −0.519072 + 0.465907i
$$77$$ 2.82786i 0.322264i
$$78$$ 0.311664 + 0.139054i 0.0352890 + 0.0157447i
$$79$$ −13.6757 −1.53864 −0.769320 0.638864i $$-0.779405\pi$$
−0.769320 + 0.638864i $$0.779405\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 2.47088 + 1.10242i 0.272863 + 0.121742i
$$83$$ 12.3320i 1.35361i 0.736162 + 0.676806i $$0.236636\pi$$
−0.736162 + 0.676806i $$0.763364\pi$$
$$84$$ 2.94217 2.64082i 0.321017 0.288138i
$$85$$ 0 0
$$86$$ 6.47972 14.5231i 0.698726 1.56607i
$$87$$ 9.07918 0.973391
$$88$$ −3.85110 + 1.24132i −0.410528 + 0.132325i
$$89$$ −8.08066 −0.856548 −0.428274 0.903649i $$-0.640878\pi$$
−0.428274 + 0.903649i $$0.640878\pi$$
$$90$$ 0 0
$$91$$ 0.477031i 0.0500064i
$$92$$ 1.16806 + 1.30135i 0.121779 + 0.135675i
$$93$$ 7.44764i 0.772285i
$$94$$ 4.31844 + 1.92674i 0.445413 + 0.198728i
$$95$$ 0 0
$$96$$ 4.88789 + 2.84756i 0.498868 + 0.290627i
$$97$$ 10.6757 1.08396 0.541978 0.840393i $$-0.317676\pi$$
0.541978 + 0.840393i $$0.317676\pi$$
$$98$$ 3.99385 + 1.78192i 0.403440 + 0.180001i
$$99$$ 1.43055i 0.143776i
$$100$$ 0 0
$$101$$ 13.2063i 1.31408i 0.753856 + 0.657039i $$0.228191\pi$$
−0.753856 + 0.657039i $$0.771809\pi$$
$$102$$ −4.25487 + 9.53652i −0.421295 + 0.944256i
$$103$$ 19.4244 1.91394 0.956972 0.290181i $$-0.0937156\pi$$
0.956972 + 0.290181i $$0.0937156\pi$$
$$104$$ 0.649641 0.209398i 0.0637025 0.0205331i
$$105$$ 0 0
$$106$$ −5.30489 + 11.8900i −0.515256 + 1.15485i
$$107$$ 14.8085i 1.43159i 0.698311 + 0.715795i $$0.253935\pi$$
−0.698311 + 0.715795i $$0.746065\pi$$
$$108$$ 1.48838 1.33594i 0.143219 0.128550i
$$109$$ 15.2296i 1.45873i −0.684126 0.729364i $$-0.739816\pi$$
0.684126 0.729364i $$-0.260184\pi$$
$$110$$ 0 0
$$111$$ 8.81463 0.836647
$$112$$ 0.851098 7.86110i 0.0804212 0.742804i
$$113$$ −1.13890 −0.107138 −0.0535692 0.998564i $$-0.517060\pi$$
−0.0535692 + 0.998564i $$0.517060\pi$$
$$114$$ 3.92658 + 1.75191i 0.367758 + 0.164081i
$$115$$ 0 0
$$116$$ 13.5133 12.1292i 1.25468 1.12617i
$$117$$ 0.241319i 0.0223100i
$$118$$ −3.70866 + 8.31229i −0.341410 + 0.765208i
$$119$$ 14.5965 1.33806
$$120$$ 0 0
$$121$$ 8.95352 0.813956
$$122$$ 2.63524 5.90642i 0.238583 0.534742i
$$123$$ 1.91319i 0.172507i
$$124$$ −9.94957 11.0849i −0.893498 0.995456i
$$125$$ 0 0
$$126$$ −2.55298 1.13905i −0.227438 0.101475i
$$127$$ 2.43616 0.216174 0.108087 0.994141i $$-0.465527\pi$$
0.108087 + 0.994141i $$0.465527\pi$$
$$128$$ 11.0792 2.29166i 0.979271 0.202556i
$$129$$ −11.2452 −0.990083
$$130$$ 0 0
$$131$$ 6.90143i 0.602981i −0.953469 0.301491i $$-0.902516\pi$$
0.953469 0.301491i $$-0.0974842\pi$$
$$132$$ 1.91113 + 2.12921i 0.166342 + 0.185324i
$$133$$ 6.01001i 0.521134i
$$134$$ −2.80431 + 6.28535i −0.242255 + 0.542972i
$$135$$ 0 0
$$136$$ 6.40731 + 19.8782i 0.549423 + 1.70454i
$$137$$ −5.39022 −0.460518 −0.230259 0.973129i $$-0.573957\pi$$
−0.230259 + 0.973129i $$0.573957\pi$$
$$138$$ 0.503813 1.12921i 0.0428874 0.0961243i
$$139$$ 17.4244i 1.47792i 0.673750 + 0.738959i $$0.264682\pi$$
−0.673750 + 0.738959i $$0.735318\pi$$
$$140$$ 0 0
$$141$$ 3.34374i 0.281594i
$$142$$ 10.6136 + 4.73544i 0.890677 + 0.397389i
$$143$$ 0.345220 0.0288687
$$144$$ 0.430552 3.97676i 0.0358793 0.331397i
$$145$$ 0 0
$$146$$ 5.33019 + 2.37815i 0.441130 + 0.196817i
$$147$$ 3.09242i 0.255058i
$$148$$ 13.1195 11.7758i 1.07842 0.967962i
$$149$$ 2.28551i 0.187236i −0.995608 0.0936180i $$-0.970157\pi$$
0.995608 0.0936180i $$-0.0298432\pi$$
$$150$$ 0 0
$$151$$ 6.66425 0.542329 0.271164 0.962533i $$-0.412591\pi$$
0.271164 + 0.962533i $$0.412591\pi$$
$$152$$ 8.18468 2.63816i 0.663865 0.213983i
$$153$$ 7.38407 0.596967
$$154$$ 1.62948 3.65217i 0.131307 0.294301i
$$155$$ 0 0
$$156$$ −0.322387 0.359175i −0.0258116 0.0287570i
$$157$$ 17.4144i 1.38982i −0.719097 0.694910i $$-0.755444\pi$$
0.719097 0.694910i $$-0.244556\pi$$
$$158$$ 17.6622 + 7.88026i 1.40513 + 0.626920i
$$159$$ 9.20632 0.730109
$$160$$ 0 0
$$161$$ −1.72836 −0.136214
$$162$$ −1.29150 0.576222i −0.101470 0.0452723i
$$163$$ 4.66187i 0.365145i −0.983192 0.182573i $$-0.941557\pi$$
0.983192 0.182573i $$-0.0584425\pi$$
$$164$$ −2.55590 2.84756i −0.199582 0.222357i
$$165$$ 0 0
$$166$$ 7.10597 15.9267i 0.551530 1.23615i
$$167$$ −0.137419 −0.0106338 −0.00531690 0.999986i $$-0.501692\pi$$
−0.00531690 + 0.999986i $$0.501692\pi$$
$$168$$ −5.32151 + 1.71528i −0.410564 + 0.132336i
$$169$$ 12.9418 0.995520
$$170$$ 0 0
$$171$$ 3.04033i 0.232500i
$$172$$ −16.7371 + 15.0228i −1.27619 + 1.14548i
$$173$$ 3.96675i 0.301587i 0.988565 + 0.150793i $$0.0481828\pi$$
−0.988565 + 0.150793i $$0.951817\pi$$
$$174$$ −11.7258 5.23163i −0.888927 0.396609i
$$175$$ 0 0
$$176$$ 5.68896 + 0.615927i 0.428822 + 0.0464272i
$$177$$ 6.43616 0.483771
$$178$$ 10.4362 + 4.65626i 0.782223 + 0.349001i
$$179$$ 4.68749i 0.350359i 0.984537 + 0.175180i $$0.0560506\pi$$
−0.984537 + 0.175180i $$0.943949\pi$$
$$180$$ 0 0
$$181$$ 9.10242i 0.676578i 0.941042 + 0.338289i $$0.109848\pi$$
−0.941042 + 0.338289i $$0.890152\pi$$
$$182$$ −0.274876 + 0.616084i −0.0203751 + 0.0456672i
$$183$$ −4.57331 −0.338068
$$184$$ −0.758681 2.35375i −0.0559307 0.173521i
$$185$$ 0 0
$$186$$ −4.29150 + 9.61862i −0.314668 + 0.705271i
$$187$$ 10.5633i 0.772465i
$$188$$ −4.46702 4.97676i −0.325791 0.362968i
$$189$$ 1.97676i 0.143788i
$$190$$ 0 0
$$191$$ 15.2063 1.10029 0.550145 0.835069i $$-0.314572\pi$$
0.550145 + 0.835069i $$0.314572\pi$$
$$192$$ −4.67187 6.49412i −0.337163 0.468673i
$$193$$ −20.7564 −1.49408 −0.747039 0.664780i $$-0.768525\pi$$
−0.747039 + 0.664780i $$0.768525\pi$$
$$194$$ −13.7877 6.15159i −0.989898 0.441659i
$$195$$ 0 0
$$196$$ −4.13127 4.60269i −0.295091 0.328764i
$$197$$ 23.2508i 1.65655i 0.560322 + 0.828275i $$0.310677\pi$$
−0.560322 + 0.828275i $$0.689323\pi$$
$$198$$ 0.824316 1.84756i 0.0585816 0.131300i
$$199$$ −7.21633 −0.511552 −0.255776 0.966736i $$-0.582331\pi$$
−0.255776 + 0.966736i $$0.582331\pi$$
$$200$$ 0 0
$$201$$ 4.86671 0.343271
$$202$$ 7.60978 17.0559i 0.535422 1.20005i
$$203$$ 17.9474i 1.25966i
$$204$$ 10.9903 9.86465i 0.769476 0.690663i
$$205$$ 0 0
$$206$$ −25.0866 11.1928i −1.74787 0.779838i
$$207$$ −0.874337 −0.0607707
$$208$$ −0.959669 0.103901i −0.0665411 0.00720420i
$$209$$ 4.34935 0.300851
$$210$$ 0 0
$$211$$ 4.38407i 0.301812i −0.988548 0.150906i $$-0.951781\pi$$
0.988548 0.150906i $$-0.0482191\pi$$
$$212$$ 13.7025 12.2991i 0.941092 0.844703i
$$213$$ 8.21808i 0.563094i
$$214$$ 8.53298 19.1251i 0.583302 1.30737i
$$215$$ 0 0
$$216$$ −2.69204 + 0.867721i −0.183170 + 0.0590409i
$$217$$ 14.7222 0.999409
$$218$$ −8.77561 + 19.6690i −0.594360 + 1.33215i
$$219$$ 4.12714i 0.278886i
$$220$$ 0 0
$$221$$ 1.78192i 0.119865i
$$222$$ −11.3841 5.07918i −0.764049 0.340892i
$$223$$ −4.98852 −0.334056 −0.167028 0.985952i $$-0.553417\pi$$
−0.167028 + 0.985952i $$0.553417\pi$$
$$224$$ −5.62894 + 9.66218i −0.376099 + 0.645582i
$$225$$ 0 0
$$226$$ 1.47088 + 0.656257i 0.0978416 + 0.0436536i
$$227$$ 11.2569i 0.747149i 0.927600 + 0.373574i $$0.121868\pi$$
−0.927600 + 0.373574i $$0.878132\pi$$
$$228$$ −4.06169 4.52517i −0.268992 0.299687i
$$229$$ 15.8364i 1.04650i 0.852180 + 0.523249i $$0.175280\pi$$
−0.852180 + 0.523249i $$0.824720\pi$$
$$230$$ 0 0
$$231$$ −2.82786 −0.186059
$$232$$ −24.4415 + 7.87820i −1.60466 + 0.517229i
$$233$$ −10.9591 −0.717956 −0.358978 0.933346i $$-0.616875\pi$$
−0.358978 + 0.933346i $$0.616875\pi$$
$$234$$ −0.139054 + 0.311664i −0.00909022 + 0.0203741i
$$235$$ 0 0
$$236$$ 9.57945 8.59830i 0.623569 0.559701i
$$237$$ 13.6757i 0.888334i
$$238$$ −18.8514 8.41086i −1.22196 0.545195i
$$239$$ 17.3182 1.12022 0.560111 0.828418i $$-0.310758\pi$$
0.560111 + 0.828418i $$0.310758\pi$$
$$240$$ 0 0
$$241$$ 4.76869 0.307178 0.153589 0.988135i $$-0.450917\pi$$
0.153589 + 0.988135i $$0.450917\pi$$
$$242$$ −11.5635 5.15922i −0.743327 0.331647i
$$243$$ 1.00000i 0.0641500i
$$244$$ −6.80682 + 6.10964i −0.435762 + 0.391130i
$$245$$ 0 0
$$246$$ −1.10242 + 2.47088i −0.0702879 + 0.157538i
$$247$$ −0.733691 −0.0466836
$$248$$ 6.46247 + 20.0493i 0.410367 + 1.27313i
$$249$$ −12.3320 −0.781508
$$250$$ 0 0
$$251$$ 6.15837i 0.388713i 0.980931 + 0.194356i $$0.0622618\pi$$
−0.980931 + 0.194356i $$0.937738\pi$$
$$252$$ 2.64082 + 2.94217i 0.166356 + 0.185339i
$$253$$ 1.25079i 0.0786362i
$$254$$ −3.14630 1.40377i −0.197416 0.0880804i
$$255$$ 0 0
$$256$$ −15.6293 3.42440i −0.976828 0.214025i
$$257$$ −14.1584 −0.883175 −0.441587 0.897218i $$-0.645584\pi$$
−0.441587 + 0.897218i $$0.645584\pi$$
$$258$$ 14.5231 + 6.47972i 0.904170 + 0.403410i
$$259$$ 17.4244i 1.08270i
$$260$$ 0 0
$$261$$ 9.07918i 0.561987i
$$262$$ −3.97676 + 8.91319i −0.245685 + 0.550659i
$$263$$ −15.5960 −0.961691 −0.480845 0.876805i $$-0.659670\pi$$
−0.480845 + 0.876805i $$0.659670\pi$$
$$264$$ −1.24132 3.85110i −0.0763979 0.237019i
$$265$$ 0 0
$$266$$ −3.46310 + 7.76191i −0.212336 + 0.475913i
$$267$$ 8.08066i 0.494528i
$$268$$ 7.24352 6.50161i 0.442468 0.397149i
$$269$$ 11.3182i 0.690084i 0.938587 + 0.345042i $$0.112135\pi$$
−0.938587 + 0.345042i $$0.887865\pi$$
$$270$$ 0 0
$$271$$ −6.20485 −0.376918 −0.188459 0.982081i $$-0.560349\pi$$
−0.188459 + 0.982081i $$0.560349\pi$$
$$272$$ 3.17923 29.3647i 0.192769 1.78050i
$$273$$ 0.477031 0.0288712
$$274$$ 6.96146 + 3.10597i 0.420557 + 0.187638i
$$275$$ 0 0
$$276$$ −1.30135 + 1.16806i −0.0783319 + 0.0703089i
$$277$$ 18.9288i 1.13732i 0.822572 + 0.568661i $$0.192538\pi$$
−0.822572 + 0.568661i $$0.807462\pi$$
$$278$$ 10.0403 22.5036i 0.602179 1.34968i
$$279$$ 7.44764 0.445879
$$280$$ 0 0
$$281$$ −21.6231 −1.28993 −0.644963 0.764214i $$-0.723127\pi$$
−0.644963 + 0.764214i $$0.723127\pi$$
$$282$$ −1.92674 + 4.31844i −0.114736 + 0.257159i
$$283$$ 29.1522i 1.73292i −0.499247 0.866460i $$-0.666390\pi$$
0.499247 0.866460i $$-0.333610\pi$$
$$284$$ −10.9788 12.2316i −0.651473 0.725814i
$$285$$ 0 0
$$286$$ −0.445851 0.198923i −0.0263637 0.0117626i
$$287$$ 3.78192 0.223240
$$288$$ −2.84756 + 4.88789i −0.167794 + 0.288021i
$$289$$ 37.5245 2.20733
$$290$$ 0 0
$$291$$ 10.6757i 0.625822i
$$292$$ −5.51359 6.14275i −0.322659 0.359477i
$$293$$ 2.32427i 0.135785i −0.997693 0.0678927i $$-0.978372\pi$$
0.997693 0.0678927i $$-0.0216275\pi$$
$$294$$ −1.78192 + 3.99385i −0.103924 + 0.232926i
$$295$$ 0 0
$$296$$ −23.7293 + 7.64863i −1.37924 + 0.444568i
$$297$$ −1.43055 −0.0830090
$$298$$ −1.31696 + 2.95173i −0.0762895 + 0.170989i
$$299$$ 0.210995i 0.0122021i
$$300$$ 0 0
$$301$$ 22.2290i 1.28126i
$$302$$ −8.60686 3.84009i −0.495269 0.220972i
$$303$$ −13.2063 −0.758683
$$304$$ −12.0907 1.30902i −0.693447 0.0750775i
$$305$$ 0 0
$$306$$ −9.53652 4.25487i −0.545166 0.243235i
$$307$$ 3.52297i 0.201066i 0.994934 + 0.100533i $$0.0320549\pi$$
−0.994934 + 0.100533i $$0.967945\pi$$
$$308$$ −4.20893 + 3.77784i −0.239826 + 0.215262i
$$309$$ 19.4244i 1.10502i
$$310$$ 0 0
$$311$$ −21.6757 −1.22912 −0.614559 0.788871i $$-0.710666\pi$$
−0.614559 + 0.788871i $$0.710666\pi$$
$$312$$ 0.209398 + 0.649641i 0.0118548 + 0.0367787i
$$313$$ −12.5486 −0.709288 −0.354644 0.935001i $$-0.615398\pi$$
−0.354644 + 0.935001i $$0.615398\pi$$
$$314$$ −10.0346 + 22.4907i −0.566283 + 1.26922i
$$315$$ 0 0
$$316$$ −18.2699 20.3547i −1.02776 1.14504i
$$317$$ 10.8611i 0.610020i −0.952349 0.305010i $$-0.901340\pi$$
0.952349 0.305010i $$-0.0986599\pi$$
$$318$$ −11.8900 5.30489i −0.666755 0.297483i
$$319$$ −12.9882 −0.727202
$$320$$ 0 0
$$321$$ −14.8085 −0.826529
$$322$$ 2.23217 + 0.995917i 0.124394 + 0.0555003i
$$323$$ 22.4500i 1.24915i
$$324$$ 1.33594 + 1.48838i 0.0742186 + 0.0826878i
$$325$$ 0 0
$$326$$ −2.68627 + 6.02079i −0.148779 + 0.333461i
$$327$$ 15.2296 0.842197
$$328$$ 1.66011 + 5.15038i 0.0916645 + 0.284382i
$$329$$ 6.60978 0.364409
$$330$$ 0 0
$$331$$ 1.23185i 0.0677088i 0.999427 + 0.0338544i $$0.0107783\pi$$
−0.999427 + 0.0338544i $$0.989222\pi$$
$$332$$ −18.3547 + 16.4747i −1.00734 + 0.904169i
$$333$$ 8.81463i 0.483038i
$$334$$ 0.177476 + 0.0791838i 0.00971107 + 0.00433275i
$$335$$ 0 0
$$336$$ 7.86110 + 0.851098i 0.428858 + 0.0464312i
$$337$$ 4.13890 0.225460 0.112730 0.993626i $$-0.464040\pi$$
0.112730 + 0.993626i $$0.464040\pi$$
$$338$$ −16.7143 7.45733i −0.909136 0.405625i
$$339$$ 1.13890i 0.0618564i
$$340$$ 0 0
$$341$$ 10.6542i 0.576959i
$$342$$ −1.75191 + 3.92658i −0.0947322 + 0.212325i
$$343$$ 19.9503 1.07721
$$344$$ 30.2724 9.75767i 1.63218 0.526098i
$$345$$ 0 0
$$346$$ 2.28573 5.12306i 0.122882 0.275417i
$$347$$ 17.4586i 0.937226i −0.883404 0.468613i $$-0.844754\pi$$
0.883404 0.468613i $$-0.155246\pi$$
$$348$$ 12.1292 + 13.5133i 0.650194 + 0.724388i
$$349$$ 21.2196i 1.13586i −0.823078 0.567928i $$-0.807745\pi$$
0.823078 0.567928i $$-0.192255\pi$$
$$350$$ 0 0
$$351$$ 0.241319 0.0128807
$$352$$ −6.99237 4.07358i −0.372695 0.217122i
$$353$$ 21.0398 1.11984 0.559918 0.828548i $$-0.310833\pi$$
0.559918 + 0.828548i $$0.310833\pi$$
$$354$$ −8.31229 3.70866i −0.441793 0.197113i
$$355$$ 0 0
$$356$$ −10.7952 12.0271i −0.572147 0.637435i
$$357$$ 14.5965i 0.772531i
$$358$$ 2.70103 6.05388i 0.142754 0.319957i
$$359$$ 23.5153 1.24109 0.620546 0.784170i $$-0.286911\pi$$
0.620546 + 0.784170i $$0.286911\pi$$
$$360$$ 0 0
$$361$$ 9.75639 0.513494
$$362$$ 5.24502 11.7558i 0.275672 0.617869i
$$363$$ 8.95352i 0.469938i
$$364$$ 0.710003 0.637282i 0.0372143 0.0334027i
$$365$$ 0 0
$$366$$ 5.90642 + 2.63524i 0.308733 + 0.137746i
$$367$$ −25.4012 −1.32593 −0.662965 0.748650i $$-0.730702\pi$$
−0.662965 + 0.748650i $$0.730702\pi$$
$$368$$ −0.376448 + 3.47703i −0.0196237 + 0.181253i
$$369$$ 1.91319 0.0995967
$$370$$ 0 0
$$371$$ 18.1987i 0.944829i
$$372$$ 11.0849 9.94957i 0.574727 0.515861i
$$373$$ 10.0677i 0.521286i −0.965435 0.260643i $$-0.916065\pi$$
0.965435 0.260643i $$-0.0839345\pi$$
$$374$$ 6.08681 13.6425i 0.314741 0.705436i
$$375$$ 0 0
$$376$$ 2.90143 + 9.00148i 0.149630 + 0.464216i
$$377$$ 2.19098 0.112841
$$378$$ 1.13905 2.55298i 0.0585866 0.131311i
$$379$$ 18.9674i 0.974289i −0.873321 0.487145i $$-0.838038\pi$$
0.873321 0.487145i $$-0.161962\pi$$
$$380$$ 0 0
$$381$$ 2.43616i 0.124808i
$$382$$ −19.6389 8.76222i −1.00482 0.448314i
$$383$$ −28.7446 −1.46878 −0.734391 0.678727i $$-0.762532\pi$$
−0.734391 + 0.678727i $$0.762532\pi$$
$$384$$ 2.29166 + 11.0792i 0.116946 + 0.565382i
$$385$$ 0 0
$$386$$ 26.8068 + 11.9603i 1.36443 + 0.608763i
$$387$$ 11.2452i 0.571624i
$$388$$ 14.2621 + 15.8895i 0.724048 + 0.806669i
$$389$$ 29.8161i 1.51174i 0.654724 + 0.755868i $$0.272785\pi$$
−0.654724 + 0.755868i $$0.727215\pi$$
$$390$$ 0 0
$$391$$ −6.45617 −0.326503
$$392$$ 2.68335 + 8.32490i 0.135530 + 0.420471i
$$393$$ 6.90143 0.348131
$$394$$ 13.3976 30.0283i 0.674962 1.51281i
$$395$$ 0 0
$$396$$ −2.12921 + 1.91113i −0.106997 + 0.0960377i
$$397$$ 2.73167i 0.137099i 0.997648 + 0.0685494i $$0.0218371\pi$$
−0.997648 + 0.0685494i $$0.978163\pi$$
$$398$$ 9.31988 + 4.15821i 0.467163 + 0.208432i
$$399$$ 6.01001 0.300877
$$400$$ 0 0
$$401$$ 25.8744 1.29211 0.646054 0.763292i $$-0.276418\pi$$
0.646054 + 0.763292i $$0.276418\pi$$
$$402$$ −6.28535 2.80431i −0.313485 0.139866i
$$403$$ 1.79726i 0.0895279i
$$404$$ −19.6560 + 17.6428i −0.977924 + 0.877762i
$$405$$ 0 0
$$406$$ 10.3417 23.1790i 0.513249 1.15035i
$$407$$ −12.6098 −0.625044
$$408$$ −19.8782 + 6.40731i −0.984117 + 0.317209i
$$409$$ 22.4786 1.11150 0.555748 0.831351i $$-0.312432\pi$$
0.555748 + 0.831351i $$0.312432\pi$$
$$410$$ 0 0
$$411$$ 5.39022i 0.265880i
$$412$$ 25.9498 + 28.9109i 1.27845 + 1.42434i
$$413$$ 12.7227i 0.626045i
$$414$$ 1.12921 + 0.503813i 0.0554974 + 0.0247610i
$$415$$ 0 0
$$416$$ 1.17954 + 0.687170i 0.0578318 + 0.0336913i
$$417$$ −17.4244 −0.853277
$$418$$ −5.61718 2.50619i −0.274745 0.122582i
$$419$$ 24.5307i 1.19840i −0.800598 0.599201i $$-0.795485\pi$$
0.800598 0.599201i $$-0.204515\pi$$
$$420$$ 0 0
$$421$$ 33.3856i 1.62712i −0.581483 0.813558i $$-0.697527\pi$$
0.581483 0.813558i $$-0.302473\pi$$
$$422$$ −2.52620 + 5.66202i −0.122974 + 0.275623i
$$423$$ 3.34374 0.162578
$$424$$ −24.7838 + 7.98852i −1.20361 + 0.387957i
$$425$$ 0 0
$$426$$ −4.73544 + 10.6136i −0.229433 + 0.514232i
$$427$$ 9.04033i 0.437492i
$$428$$ −22.0406 + 19.7832i −1.06537 + 0.956256i
$$429$$ 0.345220i 0.0166674i
$$430$$ 0 0
$$431$$ 11.6548 0.561391 0.280696 0.959797i $$-0.409435\pi$$
0.280696 + 0.959797i $$0.409435\pi$$
$$432$$ 3.97676 + 0.430552i 0.191332 + 0.0207149i
$$433$$ 19.7681 0.949996 0.474998 0.879987i $$-0.342449\pi$$
0.474998 + 0.879987i $$0.342449\pi$$
$$434$$ −19.0137 8.48326i −0.912687 0.407210i
$$435$$ 0 0
$$436$$ 22.6674 20.3457i 1.08557 0.974383i
$$437$$ 2.65827i 0.127163i
$$438$$ −2.37815 + 5.33019i −0.113632 + 0.254687i
$$439$$ −25.1699 −1.20129 −0.600646 0.799515i $$-0.705090\pi$$
−0.600646 + 0.799515i $$0.705090\pi$$
$$440$$ 0 0
$$441$$ 3.09242 0.147258
$$442$$ −1.02678 + 2.30135i −0.0488390 + 0.109464i
$$443$$ 19.5515i 0.928922i −0.885594 0.464461i $$-0.846248\pi$$
0.885594 0.464461i $$-0.153752\pi$$
$$444$$ 11.7758 + 13.1195i 0.558853 + 0.622625i
$$445$$ 0 0
$$446$$ 6.44266 + 2.87449i 0.305069 + 0.136111i
$$447$$ 2.28551 0.108101
$$448$$ 12.8373 9.23517i 0.606507 0.436321i
$$449$$ −19.9612 −0.942029 −0.471014 0.882125i $$-0.656112\pi$$
−0.471014 + 0.882125i $$0.656112\pi$$
$$450$$ 0 0
$$451$$ 2.73692i 0.128876i
$$452$$ −1.52149 1.69511i −0.0715650 0.0797313i
$$453$$ 6.66425i 0.313114i
$$454$$ 6.48650 14.5383i 0.304426 0.682317i
$$455$$ 0 0
$$456$$ 2.63816 + 8.18468i 0.123543 + 0.383283i
$$457$$ −5.01176 −0.234440 −0.117220 0.993106i $$-0.537398\pi$$
−0.117220 + 0.993106i $$0.537398\pi$$
$$458$$ 9.12528 20.4527i 0.426396 0.955690i
$$459$$ 7.38407i 0.344659i
$$460$$ 0 0
$$461$$ 5.12566i 0.238726i −0.992851 0.119363i $$-0.961915\pi$$
0.992851 0.119363i $$-0.0380852\pi$$
$$462$$ 3.65217 + 1.62948i 0.169915 + 0.0758101i
$$463$$ −5.79515 −0.269324 −0.134662 0.990892i $$-0.542995\pi$$
−0.134662 + 0.990892i $$0.542995\pi$$
$$464$$ 36.1057 + 3.90906i 1.67617 + 0.181474i
$$465$$ 0 0
$$466$$ 14.1537 + 6.31490i 0.655657 + 0.292532i
$$467$$ 16.8208i 0.778373i −0.921159 0.389186i $$-0.872756\pi$$
0.921159 0.389186i $$-0.127244\pi$$
$$468$$ 0.359175 0.322387i 0.0166029 0.0149024i
$$469$$ 9.62032i 0.444225i
$$470$$ 0 0
$$471$$ 17.4144 0.802413
$$472$$ −17.3264 + 5.58479i −0.797511 + 0.257061i
$$473$$ 16.0868 0.739672
$$474$$ −7.88026 + 17.6622i −0.361952 + 0.811251i
$$475$$ 0 0
$$476$$ 19.5000 + 21.7252i 0.893783 + 0.995773i
$$477$$ 9.20632i 0.421529i
$$478$$ −22.3664 9.97914i −1.02302 0.456435i
$$479$$ −36.9065 −1.68630 −0.843151 0.537678i $$-0.819302\pi$$
−0.843151 + 0.537678i $$0.819302\pi$$
$$480$$ 0 0
$$481$$ 2.12714 0.0969892
$$482$$ −6.15875 2.74782i −0.280523 0.125160i
$$483$$ 1.72836i 0.0786429i
$$484$$ 11.9613 + 13.3262i 0.543697 + 0.605738i
$$485$$ 0 0
$$486$$ 0.576222 1.29150i 0.0261380 0.0585836i
$$487$$ −5.14984 −0.233361 −0.116681 0.993169i $$-0.537225\pi$$
−0.116681 + 0.993169i $$0.537225\pi$$
$$488$$ 12.3115 3.96835i 0.557316 0.179639i
$$489$$ 4.66187 0.210817
$$490$$ 0 0
$$491$$ 23.1154i 1.04318i 0.853195 + 0.521591i $$0.174661\pi$$
−0.853195 + 0.521591i $$0.825339\pi$$
$$492$$ 2.84756 2.55590i 0.128378 0.115229i
$$493$$ 67.0414i 3.01939i
$$494$$ 0.947560 + 0.422769i 0.0426328 + 0.0190213i
$$495$$ 0 0
$$496$$ 3.20660 29.6175i 0.143980 1.32986i
$$497$$ 16.2452 0.728696
$$498$$ 15.9267 + 7.10597i 0.713694 + 0.318426i
$$499$$ 14.3111i 0.640654i −0.947307 0.320327i $$-0.896207\pi$$
0.947307 0.320327i $$-0.103793\pi$$
$$500$$ 0 0
$$501$$ 0.137419i 0.00613942i
$$502$$ 3.54859 7.95352i 0.158381 0.354983i
$$503$$ 15.4224 0.687650 0.343825 0.939034i $$-0.388277\pi$$
0.343825 + 0.939034i $$0.388277\pi$$
$$504$$ −1.71528 5.32151i −0.0764045 0.237039i
$$505$$ 0 0
$$506$$ −0.720730 + 1.61539i −0.0320404 + 0.0718127i
$$507$$ 12.9418i 0.574764i
$$508$$ 3.25455 + 3.62593i 0.144397 + 0.160875i
$$509$$ 43.1578i 1.91294i −0.291835 0.956469i $$-0.594266\pi$$
0.291835 0.956469i $$-0.405734\pi$$
$$510$$ 0 0
$$511$$ 8.15837 0.360905
$$512$$ 18.2119 + 13.4285i 0.804861 + 0.593463i
$$513$$ 3.04033 0.134234
$$514$$ 18.2855 + 8.15837i 0.806539 + 0.359850i
$$515$$ 0 0
$$516$$ −15.0228 16.7371i −0.661343 0.736810i
$$517$$ 4.78340i 0.210374i
$$518$$ 10.0403 22.5036i 0.441147 0.988751i
$$519$$ −3.96675 −0.174121
$$520$$ 0 0
$$521$$ −17.8232 −0.780848 −0.390424 0.920635i $$-0.627672\pi$$
−0.390424 + 0.920635i $$0.627672\pi$$
$$522$$ 5.23163 11.7258i 0.228982 0.513222i
$$523$$ 24.7502i 1.08225i −0.840941 0.541126i $$-0.817998\pi$$
0.840941 0.541126i $$-0.182002\pi$$
$$524$$ 10.2720 9.21987i 0.448733 0.402772i
$$525$$ 0 0
$$526$$ 20.1422 + 8.98677i 0.878242 + 0.391842i
$$527$$ 54.9939 2.39557
$$528$$ −0.615927 + 5.68896i −0.0268048 + 0.247580i
$$529$$ −22.2355 −0.966762
$$530$$ 0 0
$$531$$ 6.43616i 0.279306i
$$532$$ 8.94517 8.02898i 0.387822 0.348100i
$$533$$ 0.461690i 0.0199980i
$$534$$ −4.65626 + 10.4362i −0.201496 + 0.451617i
$$535$$ 0 0
$$536$$ −13.1014 + 4.22295i −0.565893 + 0.182403i
$$537$$ −4.68749 −0.202280
$$538$$ 6.52181 14.6175i 0.281175 0.630203i
$$539$$ 4.42386i 0.190549i
$$540$$ 0 0
$$541$$ 16.9982i 0.730812i −0.930848 0.365406i $$-0.880930\pi$$
0.930848 0.365406i $$-0.119070\pi$$
$$542$$ 8.01355 + 3.57537i 0.344211 + 0.153575i
$$543$$ −9.10242 −0.390622
$$544$$ −21.0266 + 36.0925i −0.901506 + 1.54745i
$$545$$ 0 0
$$546$$ −0.616084 0.274876i −0.0263660 0.0117636i
$$547$$ 37.2385i 1.59220i 0.605163 + 0.796101i $$0.293108\pi$$
−0.605163 + 0.796101i $$0.706892\pi$$
$$548$$ −7.20099 8.02270i −0.307611 0.342713i
$$549$$ 4.57331i 0.195184i
$$550$$ 0 0
$$551$$ 27.6037 1.17596
$$552$$ 2.35375 0.758681i 0.100182 0.0322916i
$$553$$ 27.0336 1.14959
$$554$$ 10.9072 24.4465i 0.463403 1.03863i
$$555$$ 0 0
$$556$$ −25.9341 + 23.2779i −1.09985 + 0.987202i
$$557$$ 14.7604i 0.625420i −0.949849 0.312710i $$-0.898763\pi$$
0.949849 0.312710i $$-0.101237\pi$$
$$558$$ −9.61862 4.29150i −0.407189 0.181674i
$$559$$ −2.71368 −0.114776
$$560$$ 0 0
$$561$$ −10.5633 −0.445983
$$562$$ 27.9262 + 12.4597i 1.17800 + 0.525581i
$$563$$ 3.00561i 0.126671i 0.997992 + 0.0633356i $$0.0201739\pi$$
−0.997992 + 0.0633356i $$0.979826\pi$$
$$564$$ 4.97676 4.46702i 0.209559 0.188096i
$$565$$ 0 0
$$566$$ −16.7982 + 37.6500i −0.706079 + 1.58255i
$$567$$ −1.97676 −0.0830161
$$568$$ 7.13100 + 22.1234i 0.299210 + 0.928276i
$$569$$ −23.1840 −0.971923 −0.485962 0.873980i $$-0.661531\pi$$
−0.485962 + 0.873980i $$0.661531\pi$$
$$570$$ 0 0
$$571$$ 0.202739i 0.00848438i −0.999991 0.00424219i $$-0.998650\pi$$
0.999991 0.00424219i $$-0.00135033\pi$$
$$572$$ 0.461192 + 0.513819i 0.0192834 + 0.0214838i
$$573$$ 15.2063i 0.635253i
$$574$$ −4.88434 2.17923i −0.203869 0.0909592i
$$575$$ 0 0
$$576$$ 6.49412 4.67187i 0.270588 0.194661i
$$577$$ 21.8023 0.907643 0.453821 0.891093i $$-0.350060\pi$$
0.453821 + 0.891093i $$0.350060\pi$$
$$578$$ −48.4629 21.6225i −2.01579 0.899376i
$$579$$ 20.7564i 0.862606i
$$580$$ 0 0
$$581$$ 24.3774i 1.01134i
$$582$$ 6.15159 13.7877i 0.254992 0.571518i
$$583$$ −13.1701 −0.545451
$$584$$ 3.58120 + 11.1104i 0.148191 + 0.459752i
$$585$$ 0 0
$$586$$ −1.33930 + 3.00179i −0.0553258 + 0.124003i
$$587$$ 36.7126i 1.51529i −0.652667 0.757645i $$-0.726350\pi$$
0.652667 0.757645i $$-0.273650\pi$$
$$588$$ 4.60269 4.13127i 0.189812 0.170371i
$$589$$ 22.6433i 0.933001i
$$590$$ 0 0
$$591$$ −23.2508 −0.956409
$$592$$ 35.0537 + 3.79515i 1.44070 + 0.155980i
$$593$$ 10.6036 0.435439 0.217719 0.976011i $$-0.430138\pi$$
0.217719 + 0.976011i $$0.430138\pi$$
$$594$$ 1.84756 + 0.824316i 0.0758061 + 0.0338221i
$$595$$ 0 0
$$596$$ 3.40170 3.05329i 0.139339 0.125068i
$$597$$ 7.21633i 0.295345i
$$598$$ 0.121580 0.272499i 0.00497177 0.0111433i
$$599$$ −25.7988 −1.05411 −0.527056 0.849831i $$-0.676704\pi$$
−0.527056 + 0.849831i $$0.676704\pi$$
$$600$$ 0 0
$$601$$ 18.5021 0.754717 0.377358 0.926067i $$-0.376832\pi$$
0.377358 + 0.926067i $$0.376832\pi$$
$$602$$ −12.8089 + 28.7087i −0.522050 + 1.17008i
$$603$$ 4.86671i 0.198188i
$$604$$ 8.90300 + 9.91893i 0.362258 + 0.403596i
$$605$$ 0 0
$$606$$ 17.0559 + 7.60978i 0.692850 + 0.309126i
$$607$$ −37.5828 −1.52544 −0.762719 0.646730i $$-0.776136\pi$$
−0.762719 + 0.646730i $$0.776136\pi$$
$$608$$ 14.8608 + 8.65751i 0.602685 + 0.351108i
$$609$$ −17.9474 −0.727264
$$610$$ 0 0
$$611$$ 0.806910i 0.0326441i
$$612$$ 9.86465 + 10.9903i 0.398755 + 0.444257i
$$613$$ 4.93405i 0.199284i −0.995023 0.0996422i $$-0.968230\pi$$
0.995023 0.0996422i $$-0.0317698\pi$$
$$614$$ 2.03001 4.54991i 0.0819247 0.183619i
$$615$$ 0 0
$$616$$ 7.61270 2.45379i 0.306724 0.0988661i
$$617$$ −6.26043 −0.252035 −0.126018 0.992028i $$-0.540220\pi$$
−0.126018 + 0.992028i $$0.540220\pi$$
$$618$$ 11.1928 25.0866i 0.450239 1.00913i
$$619$$ 8.02562i 0.322577i −0.986907 0.161288i $$-0.948435\pi$$
0.986907 0.161288i $$-0.0515649\pi$$
$$620$$ 0 0
$$621$$ 0.874337i 0.0350860i
$$622$$ 27.9942 + 12.4900i 1.12246 + 0.500805i
$$623$$ 15.9735 0.639966
$$624$$ 0.103901 0.959669i 0.00415935 0.0384175i
$$625$$ 0 0
$$626$$ 16.2065 + 7.23078i 0.647741 + 0.289000i
$$627$$ 4.34935i 0.173696i
$$628$$ 25.9192 23.2645i 1.03429 0.928355i
$$629$$ 65.0878i 2.59522i
$$630$$ 0 0
$$631$$ −26.5248 −1.05594 −0.527968 0.849264i $$-0.677046\pi$$
−0.527968 + 0.849264i $$0.677046\pi$$
$$632$$ 11.8667 + 36.8156i 0.472032 + 1.46444i
$$633$$ 4.38407 0.174251
$$634$$ −6.25841 + 14.0271i −0.248553 + 0.557087i
$$635$$ 0 0
$$636$$ 12.2991 + 13.7025i 0.487689 + 0.543340i
$$637$$ 0.746260i 0.0295679i
$$638$$ 16.7743 + 7.48412i 0.664101 + 0.296299i
$$639$$ 8.21808 0.325102
$$640$$ 0 0
$$641$$ −26.5863 −1.05009 −0.525047 0.851073i $$-0.675952\pi$$
−0.525047 + 0.851073i $$0.675952\pi$$
$$642$$ 19.1251 + 8.53298i 0.754808 + 0.336770i
$$643$$ 2.89233i 0.114062i 0.998372 + 0.0570312i $$0.0181635\pi$$
−0.998372 + 0.0570312i $$0.981837\pi$$
$$644$$ −2.30897 2.57245i −0.0909862 0.101369i
$$645$$ 0 0
$$646$$ −12.9362 + 28.9942i −0.508968 + 1.14076i
$$647$$ −12.3472 −0.485420 −0.242710 0.970099i $$-0.578036\pi$$
−0.242710 + 0.970099i $$0.578036\pi$$
$$648$$ −0.867721 2.69204i −0.0340873 0.105753i
$$649$$ −9.20726 −0.361417
$$650$$ 0 0
$$651$$ 14.7222i 0.577009i
$$652$$ 6.93863 6.22795i 0.271738 0.243905i
$$653$$ 39.0507i 1.52817i 0.645114 + 0.764086i $$0.276810\pi$$
−0.645114 + 0.764086i $$0.723190\pi$$
$$654$$ −19.6690 8.77561i −0.769117 0.343154i
$$655$$ 0 0
$$656$$ 0.823728 7.60830i 0.0321612 0.297054i
$$657$$ 4.12714 0.161015
$$658$$ −8.53652 3.80870i −0.332788 0.148479i
$$659$$ 23.7738i 0.926094i −0.886334 0.463047i $$-0.846756\pi$$
0.886334 0.463047i $$-0.153244\pi$$
$$660$$ 0 0
$$661$$ 21.5051i 0.836450i 0.908343 + 0.418225i $$0.137348\pi$$
−0.908343 + 0.418225i $$0.862652\pi$$
$$662$$ 0.709822 1.59094i 0.0275880 0.0618335i
$$663$$ 1.78192 0.0692040
$$664$$ 33.1982 10.7007i 1.28834 0.415268i
$$665$$ 0 0
$$666$$ 5.07918 11.3841i 0.196814 0.441124i
$$667$$ 7.93827i 0.307371i
$$668$$ −0.183583 0.204532i −0.00710303 0.00791356i
$$669$$ 4.98852i 0.192867i
$$670$$ 0 0
$$671$$ 6.54235 0.252565
$$672$$ −9.66218 5.62894i −0.372727 0.217141i
$$673$$ −36.1896 −1.39501 −0.697503 0.716582i $$-0.745706\pi$$
−0.697503 + 0.716582i $$0.745706\pi$$
$$674$$ −5.34538 2.38492i −0.205896 0.0918639i
$$675$$ 0 0
$$676$$ 17.2894 + 19.2623i 0.664976 + 0.740856i
$$677$$ 9.17214i 0.352514i 0.984344 + 0.176257i $$0.0563990\pi$$
−0.984344 + 0.176257i $$0.943601\pi$$
$$678$$ −0.656257 + 1.47088i −0.0252034 + 0.0564889i
$$679$$ −21.1034 −0.809873
$$680$$ 0 0
$$681$$ −11.2569 −0.431367
$$682$$ 6.13921 13.7599i 0.235083 0.526895i
$$683$$ 16.3974i 0.627429i −0.949517 0.313714i $$-0.898427\pi$$
0.949517 0.313714i $$-0.101573\pi$$
$$684$$ 4.52517 4.06169i 0.173024 0.155302i
$$685$$ 0 0
$$686$$ −25.7658 11.4958i −0.983742 0.438912i
$$687$$ −15.8364 −0.604196
$$688$$ −44.7194 4.84163i −1.70491 0.184586i
$$689$$ 2.22166 0.0846387
$$690$$ 0 0
$$691$$ 24.4904i 0.931657i 0.884875 + 0.465828i $$0.154244\pi$$
−0.884875 + 0.465828i $$0.845756\pi$$
$$692$$ −5.90404 + 5.29933i −0.224438 + 0.201450i
$$693$$ 2.82786i 0.107421i
$$694$$ −10.0600 + 22.5477i −0.381873 + 0.855900i
$$695$$ 0 0
$$696$$ −7.87820 24.4415i −0.298622 0.926452i
$$697$$ 14.1271 0.535104
$$698$$ −12.2272 + 27.4050i −0.462806 + 1.03730i
$$699$$ 10.9591i 0.414512i
$$700$$ 0 0
$$701$$ 12.3887i 0.467916i −0.972247 0.233958i $$-0.924832\pi$$
0.972247 0.233958i $$-0.0751679\pi$$
$$702$$ −0.311664 0.139054i −0.0117630 0.00524824i
$$703$$ 26.7994 1.01076
$$704$$ 6.68335 + 9.29018i 0.251888 + 0.350137i
$$705$$ 0 0
$$706$$ −27.1729 12.1236i −1.02266 0.456278i
$$707$$ 26.1057i 0.981807i
$$708$$ 8.59830 + 9.57945i 0.323144 + 0.360018i
$$709$$ 33.4144i 1.25490i 0.778655 + 0.627452i $$0.215902\pi$$
−0.778655 + 0.627452i $$0.784098\pi$$
$$710$$ 0 0
$$711$$ 13.6757 0.512880
$$712$$ 7.01176 + 21.7534i 0.262777 + 0.815244i
$$713$$ −6.51175 −0.243867
$$714$$ 8.41086 18.8514i 0.314768 0.705496i
$$715$$ 0 0
$$716$$ −6.97676 + 6.26218i −0.260734 + 0.234029i
$$717$$ 17.3182i 0.646761i
$$718$$ −30.3700 13.5501i −1.13340 0.505684i
$$719$$ −33.8938 −1.26403 −0.632013 0.774958i $$-0.717771\pi$$
−0.632013 + 0.774958i $$0.717771\pi$$
$$720$$ 0 0
$$721$$ −38.3974 −1.42999
$$722$$ −12.6004 5.62185i −0.468937 0.209224i
$$723$$ 4.76869i 0.177349i
$$724$$ −13.5479 + 12.1603i −0.503503 + 0.451932i
$$725$$ 0 0
$$726$$ 5.15922 11.5635i 0.191477 0.429160i
$$727$$ 14.1846 0.526076 0.263038 0.964785i $$-0.415275\pi$$
0.263038 + 0.964785i $$0.415275\pi$$
$$728$$ −1.28418 + 0.413929i −0.0475950 + 0.0153412i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 83.0352i 3.07117i
$$732$$ −6.10964 6.80682i −0.225819 0.251587i
$$733$$ 8.09296i 0.298920i 0.988768 + 0.149460i $$0.0477536\pi$$
−0.988768 + 0.149460i $$0.952246\pi$$
$$734$$ 32.8056 + 14.6367i 1.21088 + 0.540251i
$$735$$ 0 0
$$736$$ 2.48972 4.27366i 0.0917725 0.157529i
$$737$$ −6.96208 −0.256452
$$738$$ −2.47088 1.10242i −0.0909544 0.0405808i
$$739$$ 22.0919i 0.812663i −0.913726 0.406331i $$-0.866808\pi$$
0.913726 0.406331i $$-0.133192\pi$$
$$740$$ 0 0
$$741$$ 0.733691i 0.0269528i
$$742$$ 10.4865 23.5036i 0.384971 0.862844i
$$743$$ −8.78340 −0.322232 −0.161116 0.986936i $$-0.551509\pi$$
−0.161116 + 0.986936i $$0.551509\pi$$
$$744$$ −20.0493 + 6.46247i −0.735044 + 0.236926i
$$745$$ 0 0
$$746$$ −5.80123 + 13.0024i −0.212398 + 0.476052i
$$747$$ 12.3320i 0.451204i
$$748$$ −15.7222 + 14.1119i −0.574861 + 0.515982i
$$749$$ 29.2728i 1.06961i
$$750$$ 0 0
$$751$$ 13.3779 0.488167 0.244084 0.969754i $$-0.421513\pi$$
0.244084 + 0.969754i $$0.421513\pi$$
$$752$$ 1.43965 13.2973i 0.0524988 0.484901i
$$753$$ −6.15837 −0.224423
$$754$$ −2.82965 1.26249i −0.103050 0.0459773i
$$755$$ 0 0
$$756$$ −2.94217 + 2.64082i −0.107006 + 0.0960459i
$$757$$ 9.72450i 0.353443i 0.984261 + 0.176721i $$0.0565492\pi$$
−0.984261 + 0.176721i $$0.943451\pi$$
$$758$$ −10.9294 + 24.4963i −0.396975 + 0.889747i
$$759$$ 1.25079 0.0454006
$$760$$ 0 0
$$761$$ 33.8835 1.22828 0.614138 0.789198i $$-0.289504\pi$$
0.614138 + 0.789198i $$0.289504\pi$$
$$762$$ 1.40377 3.14630i 0.0508532 0.113978i
$$763$$ 30.1052i 1.08988i
$$764$$ 20.3147 + 22.6328i 0.734959 + 0.818826i
$$765$$ 0 0
$$766$$ 37.1236 + 16.5633i 1.34133 + 0.598456i
$$767$$ 1.55317 0.0560817
$$768$$ 3.42440 15.6293i 0.123568 0.563972i
$$769$$ 18.7334 0.675545 0.337772 0.941228i $$-0.390327\pi$$
0.337772 + 0.941228i $$0.390327\pi$$
$$770$$ 0 0
$$771$$ 14.1584i 0.509901i
$$772$$ −27.7292 30.8934i −0.997996 1.11188i
$$773$$ 22.5006i 0.809292i −0.914474 0.404646i $$-0.867395\pi$$
0.914474 0.404646i $$-0.132605\pi$$
$$774$$ −6.47972 + 14.5231i −0.232909 + 0.522023i
$$775$$ 0 0
$$776$$ −9.26355 28.7395i −0.332542 1.03169i
$$777$$ −17.4244 −0.625097
$$778$$ 17.1807 38.5074i 0.615958 1.38056i
$$779$$ 5.81673i 0.208406i
$$780$$ 0 0
$$781$$ 11.7564i 0.420677i
$$782$$ 8.33813 + 3.72019i 0.298171 + 0.133034i
$$783$$ −9.07918 −0.324464
$$784$$ 1.33145 12.2978i 0.0475517 0.439207i
$$785$$ 0 0
$$786$$ −8.91319 3.97676i −0.317923 0.141846i
$$787$$ 28.1063i 1.00188i −0.865482 0.500940i $$-0.832988\pi$$
0.865482 0.500940i $$-0.167012\pi$$
$$788$$ −34.6060 + 31.0616i −1.23279 + 1.10652i
$$789$$ 15.5960i 0.555232i