# Properties

 Label 1110.2.l.b.697.17 Level $1110$ Weight $2$ Character 1110.697 Analytic conductor $8.863$ Analytic rank $0$ Dimension $40$ CM no Inner twists $2$

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## Newspace parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.l (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.86339462436$$ Analytic rank: $$0$$ Dimension: $$40$$ Relative dimension: $$20$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 697.17 Character $$\chi$$ $$=$$ 1110.697 Dual form 1110.2.l.b.43.17

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.07828 + 0.825074i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.45633 + 1.45633i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.07828 + 0.825074i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.45633 + 1.45633i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-0.825074 - 2.07828i) q^{10} +3.60654i q^{11} +(-0.707107 - 0.707107i) q^{12} +0.566998i q^{13} +(-1.45633 + 1.45633i) q^{14} +(-2.05298 - 0.886151i) q^{15} +1.00000 q^{16} -3.56279 q^{17} -1.00000 q^{18} +(-2.60983 - 2.60983i) q^{19} +(2.07828 - 0.825074i) q^{20} +2.05956i q^{21} -3.60654 q^{22} +2.32324i q^{23} +(0.707107 - 0.707107i) q^{24} +(3.63850 - 3.42947i) q^{25} -0.566998 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.45633 - 1.45633i) q^{28} +(0.784491 - 0.784491i) q^{29} +(0.886151 - 2.05298i) q^{30} +(-1.50323 - 1.50323i) q^{31} +1.00000i q^{32} +(-2.55021 + 2.55021i) q^{33} -3.56279i q^{34} +(-4.22824 - 1.82508i) q^{35} -1.00000i q^{36} +(-3.08463 + 5.24262i) q^{37} +(2.60983 - 2.60983i) q^{38} +(-0.400928 + 0.400928i) q^{39} +(0.825074 + 2.07828i) q^{40} +8.53277i q^{41} -2.05956 q^{42} -1.13168i q^{43} -3.60654i q^{44} +(-0.825074 - 2.07828i) q^{45} -2.32324 q^{46} +(-4.15173 - 4.15173i) q^{47} +(0.707107 + 0.707107i) q^{48} -2.75821i q^{49} +(3.42947 + 3.63850i) q^{50} +(-2.51927 - 2.51927i) q^{51} -0.566998i q^{52} +(-4.48711 + 4.48711i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-2.97566 - 7.49540i) q^{55} +(1.45633 - 1.45633i) q^{56} -3.69086i q^{57} +(0.784491 + 0.784491i) q^{58} +(-5.54174 - 5.54174i) q^{59} +(2.05298 + 0.886151i) q^{60} +(-5.08840 - 5.08840i) q^{61} +(1.50323 - 1.50323i) q^{62} +(-1.45633 + 1.45633i) q^{63} -1.00000 q^{64} +(-0.467815 - 1.17838i) q^{65} +(-2.55021 - 2.55021i) q^{66} +(-1.64587 + 1.64587i) q^{67} +3.56279 q^{68} +(-1.64278 + 1.64278i) q^{69} +(1.82508 - 4.22824i) q^{70} -3.57811 q^{71} +1.00000 q^{72} +(-0.352111 - 0.352111i) q^{73} +(-5.24262 - 3.08463i) q^{74} +(4.99781 + 0.147808i) q^{75} +(2.60983 + 2.60983i) q^{76} +(-5.25231 + 5.25231i) q^{77} +(-0.400928 - 0.400928i) q^{78} +(0.260977 + 0.260977i) q^{79} +(-2.07828 + 0.825074i) q^{80} -1.00000 q^{81} -8.53277 q^{82} +(2.52897 - 2.52897i) q^{83} -2.05956i q^{84} +(7.40448 - 2.93957i) q^{85} +1.13168 q^{86} +1.10944 q^{87} +3.60654 q^{88} +(-5.23378 + 5.23378i) q^{89} +(2.07828 - 0.825074i) q^{90} +(-0.825735 + 0.825735i) q^{91} -2.32324i q^{92} -2.12589i q^{93} +(4.15173 - 4.15173i) q^{94} +(7.57726 + 3.27066i) q^{95} +(-0.707107 + 0.707107i) q^{96} +11.4260 q^{97} +2.75821 q^{98} -3.60654 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$40q - 40q^{4} - 4q^{7} + O(q^{10})$$ $$40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$$.

 $$n$$ $$371$$ $$631$$ $$667$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$ $$e\left(\frac{1}{4}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0.707107 + 0.707107i 0.408248 + 0.408248i
$$4$$ −1.00000 −0.500000
$$5$$ −2.07828 + 0.825074i −0.929436 + 0.368984i
$$6$$ −0.707107 + 0.707107i −0.288675 + 0.288675i
$$7$$ 1.45633 + 1.45633i 0.550441 + 0.550441i 0.926568 0.376127i $$-0.122744\pi$$
−0.376127 + 0.926568i $$0.622744\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 1.00000i 0.333333i
$$10$$ −0.825074 2.07828i −0.260911 0.657210i
$$11$$ 3.60654i 1.08741i 0.839276 + 0.543706i $$0.182979\pi$$
−0.839276 + 0.543706i $$0.817021\pi$$
$$12$$ −0.707107 0.707107i −0.204124 0.204124i
$$13$$ 0.566998i 0.157257i 0.996904 + 0.0786284i $$0.0250541\pi$$
−0.996904 + 0.0786284i $$0.974946\pi$$
$$14$$ −1.45633 + 1.45633i −0.389220 + 0.389220i
$$15$$ −2.05298 0.886151i −0.530078 0.228803i
$$16$$ 1.00000 0.250000
$$17$$ −3.56279 −0.864104 −0.432052 0.901849i $$-0.642210\pi$$
−0.432052 + 0.901849i $$0.642210\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −2.60983 2.60983i −0.598736 0.598736i 0.341240 0.939976i $$-0.389153\pi$$
−0.939976 + 0.341240i $$0.889153\pi$$
$$20$$ 2.07828 0.825074i 0.464718 0.184492i
$$21$$ 2.05956i 0.449433i
$$22$$ −3.60654 −0.768917
$$23$$ 2.32324i 0.484429i 0.970223 + 0.242215i $$0.0778738\pi$$
−0.970223 + 0.242215i $$0.922126\pi$$
$$24$$ 0.707107 0.707107i 0.144338 0.144338i
$$25$$ 3.63850 3.42947i 0.727701 0.685895i
$$26$$ −0.566998 −0.111197
$$27$$ −0.707107 + 0.707107i −0.136083 + 0.136083i
$$28$$ −1.45633 1.45633i −0.275220 0.275220i
$$29$$ 0.784491 0.784491i 0.145676 0.145676i −0.630507 0.776183i $$-0.717153\pi$$
0.776183 + 0.630507i $$0.217153\pi$$
$$30$$ 0.886151 2.05298i 0.161788 0.374822i
$$31$$ −1.50323 1.50323i −0.269988 0.269988i 0.559107 0.829095i $$-0.311144\pi$$
−0.829095 + 0.559107i $$0.811144\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ −2.55021 + 2.55021i −0.443934 + 0.443934i
$$34$$ 3.56279i 0.611014i
$$35$$ −4.22824 1.82508i −0.714703 0.308495i
$$36$$ 1.00000i 0.166667i
$$37$$ −3.08463 + 5.24262i −0.507110 + 0.861882i
$$38$$ 2.60983 2.60983i 0.423370 0.423370i
$$39$$ −0.400928 + 0.400928i −0.0641998 + 0.0641998i
$$40$$ 0.825074 + 2.07828i 0.130456 + 0.328605i
$$41$$ 8.53277i 1.33260i 0.745686 + 0.666298i $$0.232122\pi$$
−0.745686 + 0.666298i $$0.767878\pi$$
$$42$$ −2.05956 −0.317797
$$43$$ 1.13168i 0.172579i −0.996270 0.0862897i $$-0.972499\pi$$
0.996270 0.0862897i $$-0.0275011\pi$$
$$44$$ 3.60654i 0.543706i
$$45$$ −0.825074 2.07828i −0.122995 0.309812i
$$46$$ −2.32324 −0.342543
$$47$$ −4.15173 4.15173i −0.605592 0.605592i 0.336199 0.941791i $$-0.390859\pi$$
−0.941791 + 0.336199i $$0.890859\pi$$
$$48$$ 0.707107 + 0.707107i 0.102062 + 0.102062i
$$49$$ 2.75821i 0.394030i
$$50$$ 3.42947 + 3.63850i 0.485001 + 0.514562i
$$51$$ −2.51927 2.51927i −0.352769 0.352769i
$$52$$ 0.566998i 0.0786284i
$$53$$ −4.48711 + 4.48711i −0.616352 + 0.616352i −0.944594 0.328242i $$-0.893544\pi$$
0.328242 + 0.944594i $$0.393544\pi$$
$$54$$ −0.707107 0.707107i −0.0962250 0.0962250i
$$55$$ −2.97566 7.49540i −0.401238 1.01068i
$$56$$ 1.45633 1.45633i 0.194610 0.194610i
$$57$$ 3.69086i 0.488866i
$$58$$ 0.784491 + 0.784491i 0.103009 + 0.103009i
$$59$$ −5.54174 5.54174i −0.721473 0.721473i 0.247432 0.968905i $$-0.420413\pi$$
−0.968905 + 0.247432i $$0.920413\pi$$
$$60$$ 2.05298 + 0.886151i 0.265039 + 0.114402i
$$61$$ −5.08840 5.08840i −0.651503 0.651503i 0.301852 0.953355i $$-0.402395\pi$$
−0.953355 + 0.301852i $$0.902395\pi$$
$$62$$ 1.50323 1.50323i 0.190910 0.190910i
$$63$$ −1.45633 + 1.45633i −0.183480 + 0.183480i
$$64$$ −1.00000 −0.125000
$$65$$ −0.467815 1.17838i −0.0580253 0.146160i
$$66$$ −2.55021 2.55021i −0.313909 0.313909i
$$67$$ −1.64587 + 1.64587i −0.201076 + 0.201076i −0.800461 0.599385i $$-0.795412\pi$$
0.599385 + 0.800461i $$0.295412\pi$$
$$68$$ 3.56279 0.432052
$$69$$ −1.64278 + 1.64278i −0.197767 + 0.197767i
$$70$$ 1.82508 4.22824i 0.218139 0.505372i
$$71$$ −3.57811 −0.424643 −0.212322 0.977200i $$-0.568102\pi$$
−0.212322 + 0.977200i $$0.568102\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −0.352111 0.352111i −0.0412114 0.0412114i 0.686201 0.727412i $$-0.259277\pi$$
−0.727412 + 0.686201i $$0.759277\pi$$
$$74$$ −5.24262 3.08463i −0.609442 0.358581i
$$75$$ 4.99781 + 0.147808i 0.577098 + 0.0170674i
$$76$$ 2.60983 + 2.60983i 0.299368 + 0.299368i
$$77$$ −5.25231 + 5.25231i −0.598556 + 0.598556i
$$78$$ −0.400928 0.400928i −0.0453961 0.0453961i
$$79$$ 0.260977 + 0.260977i 0.0293622 + 0.0293622i 0.721635 0.692273i $$-0.243391\pi$$
−0.692273 + 0.721635i $$0.743391\pi$$
$$80$$ −2.07828 + 0.825074i −0.232359 + 0.0922461i
$$81$$ −1.00000 −0.111111
$$82$$ −8.53277 −0.942287
$$83$$ 2.52897 2.52897i 0.277590 0.277590i −0.554556 0.832146i $$-0.687112\pi$$
0.832146 + 0.554556i $$0.187112\pi$$
$$84$$ 2.05956i 0.224716i
$$85$$ 7.40448 2.93957i 0.803129 0.318841i
$$86$$ 1.13168 0.122032
$$87$$ 1.10944 0.118944
$$88$$ 3.60654 0.384458
$$89$$ −5.23378 + 5.23378i −0.554780 + 0.554780i −0.927817 0.373037i $$-0.878317\pi$$
0.373037 + 0.927817i $$0.378317\pi$$
$$90$$ 2.07828 0.825074i 0.219070 0.0869705i
$$91$$ −0.825735 + 0.825735i −0.0865606 + 0.0865606i
$$92$$ 2.32324i 0.242215i
$$93$$ 2.12589i 0.220444i
$$94$$ 4.15173 4.15173i 0.428218 0.428218i
$$95$$ 7.57726 + 3.27066i 0.777411 + 0.335562i
$$96$$ −0.707107 + 0.707107i −0.0721688 + 0.0721688i
$$97$$ 11.4260 1.16014 0.580068 0.814568i $$-0.303026\pi$$
0.580068 + 0.814568i $$0.303026\pi$$
$$98$$ 2.75821 0.278621
$$99$$ −3.60654 −0.362471
$$100$$ −3.63850 + 3.42947i −0.363850 + 0.342947i
$$101$$ 2.80173i 0.278783i 0.990237 + 0.139391i $$0.0445146\pi$$
−0.990237 + 0.139391i $$0.955485\pi$$
$$102$$ 2.51927 2.51927i 0.249445 0.249445i
$$103$$ 10.2094 1.00596 0.502979 0.864298i $$-0.332237\pi$$
0.502979 + 0.864298i $$0.332237\pi$$
$$104$$ 0.566998 0.0555987
$$105$$ −1.69929 4.28035i −0.165834 0.417719i
$$106$$ −4.48711 4.48711i −0.435826 0.435826i
$$107$$ 10.7074 + 10.7074i 1.03512 + 1.03512i 0.999360 + 0.0357612i $$0.0113856\pi$$
0.0357612 + 0.999360i $$0.488614\pi$$
$$108$$ 0.707107 0.707107i 0.0680414 0.0680414i
$$109$$ 2.12012 + 2.12012i 0.203071 + 0.203071i 0.801314 0.598243i $$-0.204134\pi$$
−0.598243 + 0.801314i $$0.704134\pi$$
$$110$$ 7.49540 2.97566i 0.714659 0.283718i
$$111$$ −5.88825 + 1.52593i −0.558888 + 0.144835i
$$112$$ 1.45633 + 1.45633i 0.137610 + 0.137610i
$$113$$ −4.98518 −0.468966 −0.234483 0.972120i $$-0.575340\pi$$
−0.234483 + 0.972120i $$0.575340\pi$$
$$114$$ 3.69086 0.345680
$$115$$ −1.91685 4.82835i −0.178747 0.450246i
$$116$$ −0.784491 + 0.784491i −0.0728381 + 0.0728381i
$$117$$ −0.566998 −0.0524189
$$118$$ 5.54174 5.54174i 0.510159 0.510159i
$$119$$ −5.18860 5.18860i −0.475638 0.475638i
$$120$$ −0.886151 + 2.05298i −0.0808942 + 0.187411i
$$121$$ −2.00713 −0.182466
$$122$$ 5.08840 5.08840i 0.460682 0.460682i
$$123$$ −6.03358 + 6.03358i −0.544030 + 0.544030i
$$124$$ 1.50323 + 1.50323i 0.134994 + 0.134994i
$$125$$ −4.73227 + 10.1294i −0.423267 + 0.906005i
$$126$$ −1.45633 1.45633i −0.129740 0.129740i
$$127$$ 8.16328 + 8.16328i 0.724374 + 0.724374i 0.969493 0.245119i $$-0.0788271\pi$$
−0.245119 + 0.969493i $$0.578827\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0.800218 0.800218i 0.0704552 0.0704552i
$$130$$ 1.17838 0.467815i 0.103351 0.0410301i
$$131$$ 5.79100 + 5.79100i 0.505962 + 0.505962i 0.913284 0.407323i $$-0.133538\pi$$
−0.407323 + 0.913284i $$0.633538\pi$$
$$132$$ 2.55021 2.55021i 0.221967 0.221967i
$$133$$ 7.60154i 0.659137i
$$134$$ −1.64587 1.64587i −0.142182 0.142182i
$$135$$ 0.886151 2.05298i 0.0762677 0.176693i
$$136$$ 3.56279i 0.305507i
$$137$$ 11.0100 + 11.0100i 0.940646 + 0.940646i 0.998335 0.0576885i $$-0.0183730\pi$$
−0.0576885 + 0.998335i $$0.518373\pi$$
$$138$$ −1.64278 1.64278i −0.139843 0.139843i
$$139$$ −10.0881 −0.855664 −0.427832 0.903858i $$-0.640723\pi$$
−0.427832 + 0.903858i $$0.640723\pi$$
$$140$$ 4.22824 + 1.82508i 0.357352 + 0.154248i
$$141$$ 5.87144i 0.494464i
$$142$$ 3.57811i 0.300268i
$$143$$ −2.04490 −0.171003
$$144$$ 1.00000i 0.0833333i
$$145$$ −0.983129 + 2.27766i −0.0816444 + 0.189149i
$$146$$ 0.352111 0.352111i 0.0291409 0.0291409i
$$147$$ 1.95035 1.95035i 0.160862 0.160862i
$$148$$ 3.08463 5.24262i 0.253555 0.430941i
$$149$$ 8.10303i 0.663826i 0.943310 + 0.331913i $$0.107694\pi$$
−0.943310 + 0.331913i $$0.892306\pi$$
$$150$$ −0.147808 + 4.99781i −0.0120685 + 0.408070i
$$151$$ 7.24237i 0.589375i 0.955594 + 0.294688i $$0.0952156\pi$$
−0.955594 + 0.294688i $$0.904784\pi$$
$$152$$ −2.60983 + 2.60983i −0.211685 + 0.211685i
$$153$$ 3.56279i 0.288035i
$$154$$ −5.25231 5.25231i −0.423243 0.423243i
$$155$$ 4.36441 + 1.88386i 0.350558 + 0.151315i
$$156$$ 0.400928 0.400928i 0.0320999 0.0320999i
$$157$$ 11.2460 + 11.2460i 0.897532 + 0.897532i 0.995217 0.0976855i $$-0.0311439\pi$$
−0.0976855 + 0.995217i $$0.531144\pi$$
$$158$$ −0.260977 + 0.260977i −0.0207622 + 0.0207622i
$$159$$ −6.34573 −0.503249
$$160$$ −0.825074 2.07828i −0.0652279 0.164303i
$$161$$ −3.38341 + 3.38341i −0.266650 + 0.266650i
$$162$$ 1.00000i 0.0785674i
$$163$$ −3.48853 −0.273243 −0.136621 0.990623i $$-0.543624\pi$$
−0.136621 + 0.990623i $$0.543624\pi$$
$$164$$ 8.53277i 0.666298i
$$165$$ 3.19594 7.40416i 0.248804 0.576413i
$$166$$ 2.52897 + 2.52897i 0.196286 + 0.196286i
$$167$$ 13.0005 1.00601 0.503005 0.864284i $$-0.332228\pi$$
0.503005 + 0.864284i $$0.332228\pi$$
$$168$$ 2.05956 0.158899
$$169$$ 12.6785 0.975270
$$170$$ 2.93957 + 7.40448i 0.225455 + 0.567898i
$$171$$ 2.60983 2.60983i 0.199579 0.199579i
$$172$$ 1.13168i 0.0862897i
$$173$$ −12.4447 12.4447i −0.946152 0.946152i 0.0524705 0.998622i $$-0.483290\pi$$
−0.998622 + 0.0524705i $$0.983290\pi$$
$$174$$ 1.10944i 0.0841062i
$$175$$ 10.2933 + 0.304419i 0.778101 + 0.0230119i
$$176$$ 3.60654i 0.271853i
$$177$$ 7.83720i 0.589080i
$$178$$ −5.23378 5.23378i −0.392289 0.392289i
$$179$$ −6.17102 + 6.17102i −0.461243 + 0.461243i −0.899063 0.437819i $$-0.855751\pi$$
0.437819 + 0.899063i $$0.355751\pi$$
$$180$$ 0.825074 + 2.07828i 0.0614974 + 0.154906i
$$181$$ 8.27365 0.614975 0.307488 0.951552i $$-0.400512\pi$$
0.307488 + 0.951552i $$0.400512\pi$$
$$182$$ −0.825735 0.825735i −0.0612076 0.0612076i
$$183$$ 7.19609i 0.531950i
$$184$$ 2.32324 0.171272
$$185$$ 2.08517 13.4407i 0.153305 0.988179i
$$186$$ 2.12589 0.155878
$$187$$ 12.8493i 0.939637i
$$188$$ 4.15173 + 4.15173i 0.302796 + 0.302796i
$$189$$ −2.05956 −0.149811
$$190$$ −3.27066 + 7.57726i −0.237278 + 0.549713i
$$191$$ −10.7528 + 10.7528i −0.778044 + 0.778044i −0.979498 0.201454i $$-0.935433\pi$$
0.201454 + 0.979498i $$0.435433\pi$$
$$192$$ −0.707107 0.707107i −0.0510310 0.0510310i
$$193$$ 6.97010i 0.501719i −0.968024 0.250859i $$-0.919287\pi$$
0.968024 0.250859i $$-0.0807131\pi$$
$$194$$ 11.4260i 0.820340i
$$195$$ 0.502446 1.16404i 0.0359809 0.0833584i
$$196$$ 2.75821i 0.197015i
$$197$$ 10.8848 + 10.8848i 0.775511 + 0.775511i 0.979064 0.203553i $$-0.0652488\pi$$
−0.203553 + 0.979064i $$0.565249\pi$$
$$198$$ 3.60654i 0.256306i
$$199$$ −0.906486 + 0.906486i −0.0642591 + 0.0642591i −0.738506 0.674247i $$-0.764468\pi$$
0.674247 + 0.738506i $$0.264468\pi$$
$$200$$ −3.42947 3.63850i −0.242500 0.257281i
$$201$$ −2.32762 −0.164178
$$202$$ −2.80173 −0.197129
$$203$$ 2.28495 0.160372
$$204$$ 2.51927 + 2.51927i 0.176384 + 0.176384i
$$205$$ −7.04017 17.7335i −0.491707 1.23856i
$$206$$ 10.2094i 0.711320i
$$207$$ −2.32324 −0.161476
$$208$$ 0.566998i 0.0393142i
$$209$$ 9.41246 9.41246i 0.651073 0.651073i
$$210$$ 4.28035 1.69929i 0.295372 0.117262i
$$211$$ −14.3134 −0.985375 −0.492687 0.870206i $$-0.663985\pi$$
−0.492687 + 0.870206i $$0.663985\pi$$
$$212$$ 4.48711 4.48711i 0.308176 0.308176i
$$213$$ −2.53010 2.53010i −0.173360 0.173360i
$$214$$ −10.7074 + 10.7074i −0.731941 + 0.731941i
$$215$$ 0.933719 + 2.35195i 0.0636791 + 0.160401i
$$216$$ 0.707107 + 0.707107i 0.0481125 + 0.0481125i
$$217$$ 4.37839i 0.297225i
$$218$$ −2.12012 + 2.12012i −0.143593 + 0.143593i
$$219$$ 0.497960i 0.0336490i
$$220$$ 2.97566 + 7.49540i 0.200619 + 0.505340i
$$221$$ 2.02009i 0.135886i
$$222$$ −1.52593 5.88825i −0.102414 0.395194i
$$223$$ −9.69983 + 9.69983i −0.649549 + 0.649549i −0.952884 0.303335i $$-0.901900\pi$$
0.303335 + 0.952884i $$0.401900\pi$$
$$224$$ −1.45633 + 1.45633i −0.0973051 + 0.0973051i
$$225$$ 3.42947 + 3.63850i 0.228632 + 0.242567i
$$226$$ 4.98518i 0.331609i
$$227$$ −14.0497 −0.932514 −0.466257 0.884649i $$-0.654398\pi$$
−0.466257 + 0.884649i $$0.654398\pi$$
$$228$$ 3.69086i 0.244433i
$$229$$ 17.6048i 1.16336i 0.813418 + 0.581680i $$0.197604\pi$$
−0.813418 + 0.581680i $$0.802396\pi$$
$$230$$ 4.82835 1.91685i 0.318372 0.126393i
$$231$$ −7.42789 −0.488719
$$232$$ −0.784491 0.784491i −0.0515043 0.0515043i
$$233$$ −2.75919 2.75919i −0.180760 0.180760i 0.610927 0.791687i $$-0.290797\pi$$
−0.791687 + 0.610927i $$0.790797\pi$$
$$234$$ 0.566998i 0.0370658i
$$235$$ 12.0540 + 5.20298i 0.786313 + 0.339405i
$$236$$ 5.54174 + 5.54174i 0.360737 + 0.360737i
$$237$$ 0.369077i 0.0239741i
$$238$$ 5.18860 5.18860i 0.336327 0.336327i
$$239$$ −1.97901 1.97901i −0.128011 0.128011i 0.640198 0.768210i $$-0.278852\pi$$
−0.768210 + 0.640198i $$0.778852\pi$$
$$240$$ −2.05298 0.886151i −0.132519 0.0572008i
$$241$$ −5.52310 + 5.52310i −0.355774 + 0.355774i −0.862253 0.506478i $$-0.830947\pi$$
0.506478 + 0.862253i $$0.330947\pi$$
$$242$$ 2.00713i 0.129023i
$$243$$ −0.707107 0.707107i −0.0453609 0.0453609i
$$244$$ 5.08840 + 5.08840i 0.325752 + 0.325752i
$$245$$ 2.27573 + 5.73234i 0.145391 + 0.366225i
$$246$$ −6.03358 6.03358i −0.384687 0.384687i
$$247$$ 1.47977 1.47977i 0.0941553 0.0941553i
$$248$$ −1.50323 + 1.50323i −0.0954552 + 0.0954552i
$$249$$ 3.57650 0.226651
$$250$$ −10.1294 4.73227i −0.640642 0.299295i
$$251$$ 12.9548 + 12.9548i 0.817701 + 0.817701i 0.985774 0.168073i $$-0.0537546\pi$$
−0.168073 + 0.985774i $$0.553755\pi$$
$$252$$ 1.45633 1.45633i 0.0917401 0.0917401i
$$253$$ −8.37886 −0.526775
$$254$$ −8.16328 + 8.16328i −0.512210 + 0.512210i
$$255$$ 7.31435 + 3.15717i 0.458042 + 0.197710i
$$256$$ 1.00000 0.0625000
$$257$$ 15.9569 0.995367 0.497683 0.867359i $$-0.334184\pi$$
0.497683 + 0.867359i $$0.334184\pi$$
$$258$$ 0.800218 + 0.800218i 0.0498194 + 0.0498194i
$$259$$ −12.1272 + 3.14275i −0.753549 + 0.195281i
$$260$$ 0.467815 + 1.17838i 0.0290127 + 0.0730800i
$$261$$ 0.784491 + 0.784491i 0.0485588 + 0.0485588i
$$262$$ −5.79100 + 5.79100i −0.357769 + 0.357769i
$$263$$ 18.7568 + 18.7568i 1.15659 + 1.15659i 0.985204 + 0.171388i $$0.0548252\pi$$
0.171388 + 0.985204i $$0.445175\pi$$
$$264$$ 2.55021 + 2.55021i 0.156954 + 0.156954i
$$265$$ 5.62327 13.0277i 0.345435 0.800283i
$$266$$ 7.60154 0.466081
$$267$$ −7.40169 −0.452976
$$268$$ 1.64587 1.64587i 0.100538 0.100538i
$$269$$ 23.7613i 1.44875i −0.689404 0.724377i $$-0.742127\pi$$
0.689404 0.724377i $$-0.257873\pi$$
$$270$$ 2.05298 + 0.886151i 0.124941 + 0.0539294i
$$271$$ −21.4180 −1.30105 −0.650525 0.759485i $$-0.725451\pi$$
−0.650525 + 0.759485i $$0.725451\pi$$
$$272$$ −3.56279 −0.216026
$$273$$ −1.16777 −0.0706764
$$274$$ −11.0100 + 11.0100i −0.665137 + 0.665137i
$$275$$ 12.3685 + 13.1224i 0.745850 + 0.791311i
$$276$$ 1.64278 1.64278i 0.0988837 0.0988837i
$$277$$ 13.2073i 0.793550i 0.917916 + 0.396775i $$0.129871\pi$$
−0.917916 + 0.396775i $$0.870129\pi$$
$$278$$ 10.0881i 0.605046i
$$279$$ 1.50323 1.50323i 0.0899960 0.0899960i
$$280$$ −1.82508 + 4.22824i −0.109069 + 0.252686i
$$281$$ 3.11380 3.11380i 0.185754 0.185754i −0.608104 0.793857i $$-0.708070\pi$$
0.793857 + 0.608104i $$0.208070\pi$$
$$282$$ 5.87144 0.349639
$$283$$ 2.74240 0.163019 0.0815094 0.996673i $$-0.474026\pi$$
0.0815094 + 0.996673i $$0.474026\pi$$
$$284$$ 3.57811 0.212322
$$285$$ 3.04523 + 7.67064i 0.180384 + 0.454369i
$$286$$ 2.04490i 0.120917i
$$287$$ −12.4265 + 12.4265i −0.733515 + 0.733515i
$$288$$ −1.00000 −0.0589256
$$289$$ −4.30652 −0.253325
$$290$$ −2.27766 0.983129i −0.133749 0.0577313i
$$291$$ 8.07942 + 8.07942i 0.473624 + 0.473624i
$$292$$ 0.352111 + 0.352111i 0.0206057 + 0.0206057i
$$293$$ −14.1737 + 14.1737i −0.828037 + 0.828037i −0.987245 0.159208i $$-0.949106\pi$$
0.159208 + 0.987245i $$0.449106\pi$$
$$294$$ 1.95035 + 1.95035i 0.113747 + 0.113747i
$$295$$ 16.0896 + 6.94495i 0.936775 + 0.404350i
$$296$$ 5.24262 + 3.08463i 0.304721 + 0.179290i
$$297$$ −2.55021 2.55021i −0.147978 0.147978i
$$298$$ −8.10303 −0.469396
$$299$$ −1.31727 −0.0761798
$$300$$ −4.99781 0.147808i −0.288549 0.00853370i
$$301$$ 1.64810 1.64810i 0.0949947 0.0949947i
$$302$$ −7.24237 −0.416751
$$303$$ −1.98112 + 1.98112i −0.113813 + 0.113813i
$$304$$ −2.60983 2.60983i −0.149684 0.149684i
$$305$$ 14.7734 + 6.37682i 0.845925 + 0.365136i
$$306$$ 3.56279 0.203671
$$307$$ 10.5206 10.5206i 0.600445 0.600445i −0.339986 0.940431i $$-0.610422\pi$$
0.940431 + 0.339986i $$0.110422\pi$$
$$308$$ 5.25231 5.25231i 0.299278 0.299278i
$$309$$ 7.21911 + 7.21911i 0.410681 + 0.410681i
$$310$$ −1.88386 + 4.36441i −0.106996 + 0.247882i
$$311$$ 23.6104 + 23.6104i 1.33882 + 1.33882i 0.897201 + 0.441622i $$0.145597\pi$$
0.441622 + 0.897201i $$0.354403\pi$$
$$312$$ 0.400928 + 0.400928i 0.0226981 + 0.0226981i
$$313$$ 31.5356i 1.78250i −0.453512 0.891250i $$-0.649829\pi$$
0.453512 0.891250i $$-0.350171\pi$$
$$314$$ −11.2460 + 11.2460i −0.634651 + 0.634651i
$$315$$ 1.82508 4.22824i 0.102832 0.238234i
$$316$$ −0.260977 0.260977i −0.0146811 0.0146811i
$$317$$ 16.4324 16.4324i 0.922933 0.922933i −0.0743023 0.997236i $$-0.523673\pi$$
0.997236 + 0.0743023i $$0.0236730\pi$$
$$318$$ 6.34573i 0.355851i
$$319$$ 2.82930 + 2.82930i 0.158410 + 0.158410i
$$320$$ 2.07828 0.825074i 0.116179 0.0461231i
$$321$$ 15.1425i 0.845173i
$$322$$ −3.38341 3.38341i −0.188550 0.188550i
$$323$$ 9.29828 + 9.29828i 0.517370 + 0.517370i
$$324$$ 1.00000 0.0555556
$$325$$ 1.94450 + 2.06302i 0.107862 + 0.114436i
$$326$$ 3.48853i 0.193212i
$$327$$ 2.99831i 0.165807i
$$328$$ 8.53277 0.471144
$$329$$ 12.0926i 0.666685i
$$330$$ 7.40416 + 3.19594i 0.407586 + 0.175931i
$$331$$ −13.7264 + 13.7264i −0.754470 + 0.754470i −0.975310 0.220840i $$-0.929120\pi$$
0.220840 + 0.975310i $$0.429120\pi$$
$$332$$ −2.52897 + 2.52897i −0.138795 + 0.138795i
$$333$$ −5.24262 3.08463i −0.287294 0.169037i
$$334$$ 13.0005i 0.711356i
$$335$$ 2.06262 4.77856i 0.112693 0.261081i
$$336$$ 2.05956i 0.112358i
$$337$$ 17.9668 17.9668i 0.978715 0.978715i −0.0210635 0.999778i $$-0.506705\pi$$
0.999778 + 0.0210635i $$0.00670521\pi$$
$$338$$ 12.6785i 0.689620i
$$339$$ −3.52506 3.52506i −0.191455 0.191455i
$$340$$ −7.40448 + 2.93957i −0.401564 + 0.159420i
$$341$$ 5.42146 5.42146i 0.293588 0.293588i
$$342$$ 2.60983 + 2.60983i 0.141123 + 0.141123i
$$343$$ 14.2112 14.2112i 0.767331 0.767331i
$$344$$ −1.13168 −0.0610160
$$345$$ 2.05874 4.76957i 0.110839 0.256785i
$$346$$ 12.4447 12.4447i 0.669030 0.669030i
$$347$$ 1.20902i 0.0649038i −0.999473 0.0324519i $$-0.989668\pi$$
0.999473 0.0324519i $$-0.0103316\pi$$
$$348$$ −1.10944 −0.0594721
$$349$$ 26.9158i 1.44077i 0.693575 + 0.720384i $$0.256034\pi$$
−0.693575 + 0.720384i $$0.743966\pi$$
$$350$$ −0.304419 + 10.2933i −0.0162719 + 0.550200i
$$351$$ −0.400928 0.400928i −0.0213999 0.0213999i
$$352$$ −3.60654 −0.192229
$$353$$ 13.0238 0.693186 0.346593 0.938016i $$-0.387338\pi$$
0.346593 + 0.938016i $$0.387338\pi$$
$$354$$ 7.83720 0.416543
$$355$$ 7.43631 2.95220i 0.394678 0.156687i
$$356$$ 5.23378 5.23378i 0.277390 0.277390i
$$357$$ 7.33778i 0.388357i
$$358$$ −6.17102 6.17102i −0.326148 0.326148i
$$359$$ 6.68890i 0.353027i −0.984298 0.176513i $$-0.943518\pi$$
0.984298 0.176513i $$-0.0564819\pi$$
$$360$$ −2.07828 + 0.825074i −0.109535 + 0.0434852i
$$361$$ 5.37757i 0.283030i
$$362$$ 8.27365i 0.434853i
$$363$$ −1.41925 1.41925i −0.0744915 0.0744915i
$$364$$ 0.825735 0.825735i 0.0432803 0.0432803i
$$365$$ 1.02230 + 0.441268i 0.0535098 + 0.0230970i
$$366$$ 7.19609 0.376145
$$367$$ −0.221534 0.221534i −0.0115640 0.0115640i 0.701301 0.712865i $$-0.252603\pi$$
−0.712865 + 0.701301i $$0.752603\pi$$
$$368$$ 2.32324i 0.121107i
$$369$$ −8.53277 −0.444199
$$370$$ 13.4407 + 2.08517i 0.698748 + 0.108403i
$$371$$ −13.0694 −0.678530
$$372$$ 2.12589i 0.110222i
$$373$$ 2.85523 + 2.85523i 0.147838 + 0.147838i 0.777152 0.629314i $$-0.216664\pi$$
−0.629314 + 0.777152i $$0.716664\pi$$
$$374$$ 12.8493 0.664424
$$375$$ −10.5088 + 3.81638i −0.542673 + 0.197077i
$$376$$ −4.15173 + 4.15173i −0.214109 + 0.214109i
$$377$$ 0.444804 + 0.444804i 0.0229086 + 0.0229086i
$$378$$ 2.05956i 0.105932i
$$379$$ 15.3156i 0.786711i 0.919386 + 0.393355i $$0.128686\pi$$
−0.919386 + 0.393355i $$0.871314\pi$$
$$380$$ −7.57726 3.27066i −0.388705 0.167781i
$$381$$ 11.5446i 0.591449i
$$382$$ −10.7528 10.7528i −0.550160 0.550160i
$$383$$ 26.5555i 1.35692i 0.734636 + 0.678461i $$0.237353\pi$$
−0.734636 + 0.678461i $$0.762647\pi$$
$$384$$ 0.707107 0.707107i 0.0360844 0.0360844i
$$385$$ 6.58223 15.2493i 0.335462 0.777177i
$$386$$ 6.97010 0.354769
$$387$$ 1.13168 0.0575265
$$388$$ −11.4260 −0.580068
$$389$$ −5.00317 5.00317i −0.253671 0.253671i 0.568803 0.822474i $$-0.307407\pi$$
−0.822474 + 0.568803i $$0.807407\pi$$
$$390$$ 1.16404 + 0.502446i 0.0589433 + 0.0254423i
$$391$$ 8.27723i 0.418597i
$$392$$ −2.75821 −0.139311
$$393$$ 8.18971i 0.413116i
$$394$$ −10.8848 + 10.8848i −0.548369 + 0.548369i
$$395$$ −0.757709 0.327058i −0.0381245 0.0164561i
$$396$$ 3.60654 0.181235
$$397$$ −12.2545 + 12.2545i −0.615035 + 0.615035i −0.944254 0.329219i $$-0.893215\pi$$
0.329219 + 0.944254i $$0.393215\pi$$
$$398$$ −0.906486 0.906486i −0.0454381 0.0454381i
$$399$$ 5.37510 5.37510i 0.269092 0.269092i
$$400$$ 3.63850 3.42947i 0.181925 0.171474i
$$401$$ −11.3153 11.3153i −0.565059 0.565059i 0.365681 0.930740i $$-0.380836\pi$$
−0.930740 + 0.365681i $$0.880836\pi$$
$$402$$ 2.32762i 0.116091i
$$403$$ 0.852327 0.852327i 0.0424575 0.0424575i
$$404$$ 2.80173i 0.139391i
$$405$$ 2.07828 0.825074i 0.103271 0.0409983i
$$406$$ 2.28495i 0.113400i
$$407$$ −18.9077 11.1248i −0.937221 0.551437i
$$408$$ −2.51927 + 2.51927i −0.124723 + 0.124723i
$$409$$ 20.6313 20.6313i 1.02015 1.02015i 0.0203618 0.999793i $$-0.493518\pi$$
0.999793 0.0203618i $$-0.00648181\pi$$
$$410$$ 17.7335 7.04017i 0.875795 0.347689i
$$411$$ 15.5705i 0.768034i
$$412$$ −10.2094 −0.502979
$$413$$ 16.1412i 0.794256i
$$414$$ 2.32324i 0.114181i
$$415$$ −3.16932 + 7.34249i −0.155576 + 0.360429i
$$416$$ −0.566998 −0.0277993
$$417$$ −7.13339 7.13339i −0.349324 0.349324i
$$418$$ 9.41246 + 9.41246i 0.460378 + 0.460378i
$$419$$ 33.3394i 1.62873i −0.580350 0.814367i $$-0.697084\pi$$
0.580350 0.814367i $$-0.302916\pi$$
$$420$$ 1.69929 + 4.28035i 0.0829169 + 0.208859i
$$421$$ 18.2239 + 18.2239i 0.888180 + 0.888180i 0.994348 0.106169i $$-0.0338583\pi$$
−0.106169 + 0.994348i $$0.533858\pi$$
$$422$$ 14.3134i 0.696765i
$$423$$ 4.15173 4.15173i 0.201864 0.201864i
$$424$$ 4.48711 + 4.48711i 0.217913 + 0.217913i
$$425$$ −12.9632 + 12.2185i −0.628809 + 0.592684i
$$426$$ 2.53010 2.53010i 0.122584 0.122584i
$$427$$ 14.8208i 0.717228i
$$428$$ −10.7074 10.7074i −0.517561 0.517561i
$$429$$ −1.44596 1.44596i −0.0698117 0.0698117i
$$430$$ −2.35195 + 0.933719i −0.113421 + 0.0450279i
$$431$$ −7.25652 7.25652i −0.349534 0.349534i 0.510402 0.859936i $$-0.329497\pi$$
−0.859936 + 0.510402i $$0.829497\pi$$
$$432$$ −0.707107 + 0.707107i −0.0340207 + 0.0340207i
$$433$$ 28.6180 28.6180i 1.37529 1.37529i 0.522901 0.852393i $$-0.324850\pi$$
0.852393 0.522901i $$-0.175150\pi$$
$$434$$ 4.37839 0.210170
$$435$$ −2.30572 + 0.915368i −0.110551 + 0.0438886i
$$436$$ −2.12012 2.12012i −0.101535 0.101535i
$$437$$ 6.06327 6.06327i 0.290045 0.290045i
$$438$$ 0.497960 0.0237934
$$439$$ −16.0555 + 16.0555i −0.766287 + 0.766287i −0.977451 0.211164i $$-0.932275\pi$$
0.211164 + 0.977451i $$0.432275\pi$$
$$440$$ −7.49540 + 2.97566i −0.357329 + 0.141859i
$$441$$ 2.75821 0.131343
$$442$$ 2.02009 0.0960861
$$443$$ −0.486475 0.486475i −0.0231131 0.0231131i 0.695456 0.718569i $$-0.255203\pi$$
−0.718569 + 0.695456i $$0.755203\pi$$
$$444$$ 5.88825 1.52593i 0.279444 0.0724175i
$$445$$ 6.55901 15.1955i 0.310927 0.720337i
$$446$$ −9.69983 9.69983i −0.459300 0.459300i
$$447$$ −5.72971 + 5.72971i −0.271006 + 0.271006i
$$448$$ −1.45633 1.45633i −0.0688051 0.0688051i
$$449$$ −23.6298 23.6298i −1.11516 1.11516i −0.992442 0.122716i $$-0.960840\pi$$
−0.122716 0.992442i $$-0.539160\pi$$
$$450$$ −3.63850 + 3.42947i −0.171521 + 0.161667i
$$451$$ −30.7738 −1.44908
$$452$$ 4.98518 0.234483
$$453$$ −5.12113 + 5.12113i −0.240612 + 0.240612i
$$454$$ 14.0497i 0.659387i
$$455$$ 1.03482 2.39740i 0.0485130 0.112392i
$$456$$ −3.69086 −0.172840
$$457$$ 25.3719 1.18685 0.593423 0.804890i $$-0.297776\pi$$
0.593423 + 0.804890i $$0.297776\pi$$
$$458$$ −17.6048 −0.822620
$$459$$ 2.51927 2.51927i 0.117590 0.117590i
$$460$$ 1.91685 + 4.82835i 0.0893735 + 0.225123i
$$461$$ 15.0045 15.0045i 0.698830 0.698830i −0.265328 0.964158i $$-0.585480\pi$$
0.964158 + 0.265328i $$0.0854803\pi$$
$$462$$ 7.42789i 0.345577i
$$463$$ 30.1885i 1.40298i 0.712681 + 0.701488i $$0.247481\pi$$
−0.712681 + 0.701488i $$0.752519\pi$$
$$464$$ 0.784491 0.784491i 0.0364191 0.0364191i
$$465$$ 1.75401 + 4.41819i 0.0813405 + 0.204889i
$$466$$ 2.75919 2.75919i 0.127817 0.127817i
$$467$$ −4.43185 −0.205082 −0.102541 0.994729i $$-0.532697\pi$$
−0.102541 + 0.994729i $$0.532697\pi$$
$$468$$ 0.566998 0.0262095
$$469$$ −4.79387 −0.221360
$$470$$ −5.20298 + 12.0540i −0.239996 + 0.556007i
$$471$$ 15.9043i 0.732832i
$$472$$ −5.54174 + 5.54174i −0.255079 + 0.255079i
$$473$$ 4.08144 0.187665
$$474$$ −0.369077 −0.0169523
$$475$$ −18.4462 0.545538i −0.846371 0.0250310i
$$476$$ 5.18860 + 5.18860i 0.237819 + 0.237819i
$$477$$ −4.48711 4.48711i −0.205451 0.205451i
$$478$$ 1.97901 1.97901i 0.0905177 0.0905177i
$$479$$ −8.37886 8.37886i −0.382840 0.382840i 0.489284 0.872124i $$-0.337258\pi$$
−0.872124 + 0.489284i $$0.837258\pi$$
$$480$$ 0.886151 2.05298i 0.0404471 0.0937054i
$$481$$ −2.97255 1.74898i −0.135537 0.0797465i
$$482$$ −5.52310 5.52310i −0.251570 0.251570i
$$483$$ −4.78486 −0.217719
$$484$$ 2.00713 0.0912331
$$485$$ −23.7465 + 9.42732i −1.07827 + 0.428072i
$$486$$ 0.707107 0.707107i 0.0320750 0.0320750i
$$487$$ −9.23525 −0.418489 −0.209245 0.977863i $$-0.567100\pi$$
−0.209245 + 0.977863i $$0.567100\pi$$
$$488$$ −5.08840 + 5.08840i −0.230341 + 0.230341i
$$489$$ −2.46676 2.46676i −0.111551 0.111551i
$$490$$ −5.73234 + 2.27573i −0.258961 + 0.102807i
$$491$$ −29.1580 −1.31588 −0.657941 0.753069i $$-0.728572\pi$$
−0.657941 + 0.753069i $$0.728572\pi$$
$$492$$ 6.03358 6.03358i 0.272015 0.272015i
$$493$$ −2.79498 + 2.79498i −0.125879 + 0.125879i
$$494$$ 1.47977 + 1.47977i 0.0665779 + 0.0665779i
$$495$$ 7.49540 2.97566i 0.336893 0.133746i
$$496$$ −1.50323 1.50323i −0.0674970 0.0674970i
$$497$$ −5.21090 5.21090i −0.233741 0.233741i
$$498$$ 3.57650i 0.160267i
$$499$$ −3.77024 + 3.77024i −0.168779 + 0.168779i −0.786442 0.617664i $$-0.788079\pi$$
0.617664 + 0.786442i $$0.288079\pi$$
$$500$$ 4.73227 10.1294i 0.211633 0.453003i
$$501$$ 9.19275 + 9.19275i 0.410702 + 0.410702i
$$502$$ −12.9548 + 12.9548i −0.578202 + 0.578202i
$$503$$ 36.6383i 1.63362i −0.576906 0.816810i $$-0.695740\pi$$
0.576906 0.816810i $$-0.304260\pi$$
$$504$$ 1.45633 + 1.45633i 0.0648701 + 0.0648701i
$$505$$ −2.31164 5.82279i −0.102867 0.259111i
$$506$$ 8.37886i 0.372486i
$$507$$ 8.96506 + 8.96506i 0.398152 + 0.398152i
$$508$$ −8.16328 8.16328i −0.362187 0.362187i
$$509$$ −29.0584 −1.28799 −0.643996 0.765029i $$-0.722725\pi$$
−0.643996 + 0.765029i $$0.722725\pi$$
$$510$$ −3.15717 + 7.31435i −0.139802 + 0.323885i
$$511$$ 1.02558i 0.0453689i
$$512$$ 1.00000i 0.0441942i
$$513$$ 3.69086 0.162955
$$514$$ 15.9569i 0.703831i
$$515$$ −21.2179 + 8.42348i −0.934974 + 0.371183i
$$516$$ −0.800218 + 0.800218i −0.0352276 + 0.0352276i
$$517$$ 14.9734 14.9734i 0.658529 0.658529i
$$518$$ −3.14275 12.1272i −0.138084 0.532839i
$$519$$ 17.5994i 0.772530i
$$520$$ −1.17838 + 0.467815i −0.0516754 + 0.0205151i
$$521$$ 20.4068i 0.894036i −0.894525 0.447018i $$-0.852486\pi$$
0.894525 0.447018i $$-0.147514\pi$$
$$522$$ −0.784491 + 0.784491i −0.0343362 + 0.0343362i
$$523$$ 7.81649i 0.341791i −0.985289 0.170896i $$-0.945334\pi$$
0.985289 0.170896i $$-0.0546661\pi$$
$$524$$ −5.79100 5.79100i −0.252981 0.252981i
$$525$$ 7.06321 + 7.49372i 0.308264 + 0.327053i
$$526$$ −18.7568 + 18.7568i −0.817834 + 0.817834i
$$527$$ 5.35569 + 5.35569i 0.233298 + 0.233298i
$$528$$ −2.55021 + 2.55021i −0.110984 + 0.110984i
$$529$$ 17.6025 0.765328
$$530$$ 13.0277 + 5.62327i 0.565886 + 0.244259i
$$531$$ 5.54174 5.54174i 0.240491 0.240491i
$$532$$ 7.60154i 0.329569i
$$533$$ −4.83806 −0.209560
$$534$$ 7.40169i 0.320302i
$$535$$ −31.0873 13.4186i −1.34402 0.580135i
$$536$$ 1.64587 + 1.64587i 0.0710910 + 0.0710910i
$$537$$ −8.72713 −0.376604
$$538$$ 23.7613 1.02442
$$539$$ 9.94759 0.428473
$$540$$ −0.886151 + 2.05298i −0.0381339 + 0.0883463i
$$541$$ −12.4935 + 12.4935i −0.537139 + 0.537139i −0.922688 0.385548i $$-0.874012\pi$$
0.385548 + 0.922688i $$0.374012\pi$$
$$542$$ 21.4180i 0.919982i
$$543$$ 5.85035 + 5.85035i 0.251063 + 0.251063i
$$544$$ 3.56279i 0.152753i
$$545$$ −6.15547 2.65695i −0.263671 0.113811i
$$546$$ 1.16777i 0.0499758i
$$547$$ 35.8153i 1.53135i 0.643227 + 0.765675i $$0.277595\pi$$
−0.643227 + 0.765675i $$0.722405\pi$$
$$548$$ −11.0100 11.0100i −0.470323 0.470323i
$$549$$ 5.08840 5.08840i 0.217168 0.217168i
$$550$$ −13.1224 + 12.3685i −0.559542 + 0.527396i
$$551$$ −4.09478 −0.174443
$$552$$ 1.64278 + 1.64278i 0.0699214 + 0.0699214i
$$553$$ 0.760137i 0.0323243i
$$554$$ −13.2073 −0.561124
$$555$$ 10.9784 8.02956i 0.466009 0.340836i
$$556$$ 10.0881 0.427832
$$557$$ 27.7893i 1.17747i −0.808327 0.588734i $$-0.799626\pi$$
0.808327 0.588734i $$-0.200374\pi$$
$$558$$ 1.50323 + 1.50323i 0.0636368 + 0.0636368i
$$559$$ 0.641659 0.0271393
$$560$$ −4.22824 1.82508i −0.178676 0.0771238i
$$561$$ 9.08586 9.08586i 0.383605 0.383605i
$$562$$ 3.11380 + 3.11380i 0.131348 + 0.131348i
$$563$$ 4.47346i 0.188534i 0.995547 + 0.0942669i $$0.0300507\pi$$
−0.995547 + 0.0942669i $$0.969949\pi$$
$$564$$ 5.87144i 0.247232i
$$565$$ 10.3606 4.11315i 0.435874 0.173041i
$$566$$ 2.74240i 0.115272i
$$567$$ −1.45633 1.45633i −0.0611601 0.0611601i
$$568$$ 3.57811i 0.150134i
$$569$$ 21.9727 21.9727i 0.921144 0.921144i −0.0759661 0.997110i $$-0.524204\pi$$
0.997110 + 0.0759661i $$0.0242041\pi$$
$$570$$ −7.67064 + 3.04523i −0.321288 + 0.127551i
$$571$$ 11.4199 0.477906 0.238953 0.971031i $$-0.423196\pi$$
0.238953 + 0.971031i $$0.423196\pi$$
$$572$$ 2.04490 0.0855015
$$573$$ −15.2067 −0.635270
$$574$$ −12.4265 12.4265i −0.518673 0.518673i
$$575$$ 7.96749 + 8.45313i 0.332267 + 0.352520i
$$576$$ 1.00000i 0.0416667i
$$577$$ −10.5104 −0.437555 −0.218778 0.975775i $$-0.570207\pi$$
−0.218778 + 0.975775i $$0.570207\pi$$
$$578$$ 4.30652i 0.179128i
$$579$$ 4.92860 4.92860i 0.204826 0.204826i
$$580$$ 0.983129 2.27766i 0.0408222 0.0945745i
$$581$$ 7.36601 0.305594
$$582$$ −8.07942 + 8.07942i −0.334903 + 0.334903i
$$583$$ −16.1829 16.1829i −0.670229 0.670229i
$$584$$ −0.352111 + 0.352111i −0.0145704 + 0.0145704i
$$585$$ 1.17838 0.467815i 0.0487200 0.0193418i
$$586$$ −14.1737 14.1737i −0.585511 0.585511i
$$587$$ 28.8278i 1.18985i −0.803781 0.594925i $$-0.797182\pi$$
0.803781 0.594925i $$-0.202818\pi$$
$$588$$ −1.95035 + 1.95035i −0.0804310 + 0.0804310i
$$589$$ 7.84635i 0.323303i
$$590$$ −6.94495 + 16.0896i −0.285919 + 0.662400i
$$591$$ 15.3935i 0.633202i
$$592$$ −3.08463 + 5.24262i −0.126777 + 0.215470i
$$593$$ −28.5378 + 28.5378i −1.17191 + 1.17191i −0.190150 + 0.981755i $$0.560897\pi$$
−0.981755 + 0.190150i $$0.939103\pi$$
$$594$$ 2.55021 2.55021i 0.104636 0.104636i
$$595$$ 15.0643 + 6.50239i 0.617578 + 0.266572i
$$596$$ 8.10303i 0.331913i
$$597$$ −1.28197 −0.0524673
$$598$$ 1.31727i 0.0538673i
$$599$$ 18.9390i 0.773826i 0.922116 + 0.386913i $$0.126459\pi$$
−0.922116 + 0.386913i $$0.873541\pi$$
$$600$$ 0.147808 4.99781i 0.00603423 0.204035i
$$601$$ −0.127289 −0.00519224 −0.00259612 0.999997i $$-0.500826\pi$$
−0.00259612 + 0.999997i $$0.500826\pi$$
$$602$$ 1.64810 + 1.64810i 0.0671714 + 0.0671714i
$$603$$ −1.64587 1.64587i −0.0670252 0.0670252i
$$604$$ 7.24237i 0.294688i
$$605$$ 4.17138 1.65603i 0.169591 0.0673272i
$$606$$ −1.98112 1.98112i −0.0804777 0.0804777i
$$607$$ 26.8510i 1.08985i −0.838485 0.544925i $$-0.816558\pi$$
0.838485 0.544925i $$-0.183442\pi$$
$$608$$ 2.60983 2.60983i 0.105843 0.105843i
$$609$$ 1.61571 + 1.61571i 0.0654717 + 0.0654717i
$$610$$ −6.37682 + 14.7734i −0.258190 + 0.598159i
$$611$$ 2.35402 2.35402i 0.0952335 0.0952335i
$$612$$ 3.56279i 0.144017i
$$613$$ −2.19500 2.19500i −0.0886554 0.0886554i 0.661388 0.750044i $$-0.269968\pi$$
−0.750044 + 0.661388i $$0.769968\pi$$
$$614$$ 10.5206 + 10.5206i 0.424579 + 0.424579i
$$615$$ 7.56133 17.5176i 0.304902 0.706379i
$$616$$ 5.25231 + 5.25231i 0.211622 + 0.211622i
$$617$$ 20.4982 20.4982i 0.825228 0.825228i −0.161625 0.986852i $$-0.551673\pi$$
0.986852 + 0.161625i $$0.0516734\pi$$
$$618$$ −7.21911 + 7.21911i −0.290395 + 0.290395i
$$619$$ −38.1723 −1.53428 −0.767138 0.641482i $$-0.778320\pi$$
−0.767138 + 0.641482i $$0.778320\pi$$
$$620$$ −4.36441 1.88386i −0.175279 0.0756575i
$$621$$ −1.64278 1.64278i −0.0659225 0.0659225i
$$622$$ −23.6104 + 23.6104i −0.946691 + 0.946691i
$$623$$ −15.2442 −0.610747
$$624$$ −0.400928 + 0.400928i −0.0160500 + 0.0160500i
$$625$$ 1.47743 24.9563i 0.0590973 0.998252i
$$626$$ 31.5356 1.26042
$$627$$ 13.3112 0.531599
$$628$$ −11.2460 11.2460i −0.448766 0.448766i
$$629$$ 10.9899 18.6784i 0.438195 0.744755i
$$630$$ 4.22824 + 1.82508i 0.168457 + 0.0727130i
$$631$$ −21.7435 21.7435i −0.865594 0.865594i 0.126387 0.991981i $$-0.459662\pi$$
−0.991981 + 0.126387i $$0.959662\pi$$
$$632$$ 0.260977 0.260977i 0.0103811 0.0103811i
$$633$$ −10.1211 10.1211i −0.402278 0.402278i
$$634$$ 16.4324 + 16.4324i 0.652613 + 0.652613i
$$635$$ −23.7009 10.2303i −0.940541 0.405976i
$$636$$ 6.34573 0.251625
$$637$$ 1.56390 0.0619639
$$638$$ −2.82930 + 2.82930i −0.112013 + 0.112013i
$$639$$ 3.57811i 0.141548i
$$640$$ 0.825074 + 2.07828i 0.0326139 + 0.0821513i
$$641$$ −8.82193 −0.348445 −0.174223 0.984706i $$-0.555741\pi$$
−0.174223 + 0.984706i $$0.555741\pi$$
$$642$$ −15.1425 −0.597628
$$643$$ 44.2809 1.74627 0.873134 0.487480i $$-0.162084\pi$$
0.873134 + 0.487480i $$0.162084\pi$$
$$644$$ 3.38341 3.38341i 0.133325 0.133325i
$$645$$ −1.00284 + 2.32332i −0.0394867 + 0.0914805i
$$646$$ −9.29828 + 9.29828i −0.365836 + 0.365836i
$$647$$ 31.8355i 1.25158i 0.779991 + 0.625791i $$0.215224\pi$$
−0.779991 + 0.625791i $$0.784776\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ 19.9865 19.9865i 0.784539 0.784539i
$$650$$ −2.06302 + 1.94450i −0.0809184 + 0.0762697i
$$651$$ 3.09599 3.09599i 0.121341 0.121341i
$$652$$ 3.48853 0.136621
$$653$$ −29.8088 −1.16651 −0.583254 0.812290i $$-0.698221\pi$$
−0.583254 + 0.812290i $$0.698221\pi$$
$$654$$ −2.99831 −0.117243
$$655$$ −16.8133 7.25732i −0.656951 0.283567i
$$656$$ 8.53277i 0.333149i
$$657$$ 0.352111 0.352111i 0.0137371 0.0137371i
$$658$$ 12.0926 0.471418
$$659$$ 40.0379 1.55965 0.779827 0.625995i $$-0.215307\pi$$
0.779827 + 0.625995i $$0.215307\pi$$
$$660$$ −3.19594 + 7.40416i −0.124402 + 0.288207i
$$661$$ 20.8346 + 20.8346i 0.810373 + 0.810373i 0.984690 0.174316i $$-0.0557716\pi$$
−0.174316 + 0.984690i $$0.555772\pi$$
$$662$$ −13.7264 13.7264i −0.533491 0.533491i
$$663$$ 1.42842 1.42842i 0.0554753 0.0554753i
$$664$$ −2.52897 2.52897i −0.0981429 0.0981429i
$$665$$ 6.27184 + 15.7981i 0.243211 + 0.612626i
$$666$$ 3.08463 5.24262i 0.119527 0.203147i
$$667$$ 1.82256 + 1.82256i 0.0705699 + 0.0705699i
$$668$$ −13.0005 −0.503005
$$669$$ −13.7176 −0.530354
$$670$$ 4.77856 + 2.06262i 0.184612 + 0.0796860i
$$671$$ 18.3515 18.3515i 0.708453 0.708453i
$$672$$ −2.05956 −0.0794493
$$673$$ −16.7404 + 16.7404i −0.645295 + 0.645295i −0.951852 0.306557i $$-0.900823\pi$$
0.306557 + 0.951852i $$0.400823\pi$$
$$674$$ 17.9668 + 17.9668i 0.692056 + 0.692056i
$$675$$ −0.147808 + 4.99781i −0.00568913 + 0.192366i
$$676$$ −12.6785 −0.487635
$$677$$ 4.30980 4.30980i 0.165639 0.165639i −0.619420 0.785059i $$-0.712632\pi$$
0.785059 + 0.619420i $$0.212632\pi$$
$$678$$ 3.52506 3.52506i 0.135379 0.135379i
$$679$$ 16.6400 + 16.6400i 0.638586 + 0.638586i
$$680$$ −2.93957 7.40448i −0.112727 0.283949i
$$681$$ −9.93466 9.93466i −0.380697 0.380697i
$$682$$ 5.42146 + 5.42146i 0.207598 + 0.207598i
$$683$$ 36.6278i 1.40152i −0.713395 0.700762i $$-0.752843\pi$$
0.713395 0.700762i $$-0.247157\pi$$
$$684$$ −2.60983 + 2.60983i −0.0997894 + 0.0997894i
$$685$$ −31.9659 13.7978i −1.22135 0.527186i
$$686$$ 14.2112 + 14.2112i 0.542585 + 0.542585i
$$687$$ −12.4485 + 12.4485i −0.474940 + 0.474940i
$$688$$ 1.13168i 0.0431448i
$$689$$ −2.54418 2.54418i −0.0969255 0.0969255i
$$690$$ 4.76957 + 2.05874i 0.181575 + 0.0783750i
$$691$$ 31.0649i 1.18177i 0.806757 + 0.590883i $$0.201220\pi$$
−0.806757 + 0.590883i $$0.798780\pi$$
$$692$$ 12.4447 + 12.4447i 0.473076 + 0.473076i
$$693$$ −5.25231 5.25231i −0.199519 0.199519i
$$694$$ 1.20902 0.0458939
$$695$$ 20.9660 8.32346i 0.795285 0.315727i
$$696$$ 1.10944i 0.0420531i
$$697$$ 30.4005i 1.15150i
$$698$$ −26.9158 −1.01878
$$699$$ 3.90208i 0.147590i
$$700$$ −10.2933 0.304419i −0.389050 0.0115060i
$$701$$ −11.6605 + 11.6605i −0.440411 + 0.440411i −0.892150 0.451739i $$-0.850804\pi$$
0.451739 + 0.892150i $$0.350804\pi$$
$$702$$ 0.400928 0.400928i 0.0151320 0.0151320i
$$703$$ 21.7327 5.63200i 0.819664 0.212415i
$$704$$ 3.60654i 0.135927i
$$705$$ 4.84437 + 12.2025i 0.182450 + 0.459573i
$$706$$ 13.0238i 0.490157i
$$707$$ −4.08025 + 4.08025i −0.153453 + 0.153453i
$$708$$ 7.83720i 0.294540i
$$709$$ −12.6150 12.6150i −0.473768 0.473768i 0.429364 0.903132i $$-0.358738\pi$$
−0.903132 + 0.429364i $$0.858738\pi$$
$$710$$ 2.95220 + 7.43631i 0.110794 + 0.279080i
$$711$$ −0.260977 + 0.260977i −0.00978740 + 0.00978740i
$$712$$ 5.23378 + 5.23378i 0.196144 + 0.196144i
$$713$$ 3.49237 3.49237i 0.130790 0.130790i
$$714$$ 7.33778 0.274610
$$715$$ 4.24988 1.68719i 0.158936 0.0630975i
$$716$$ 6.17102 6.17102i 0.230622 0.230622i
$$717$$ 2.79874i 0.104521i
$$718$$ 6.68890 0.249628
$$719$$ 15.6860i 0.584988i −0.956267 0.292494i $$-0.905515\pi$$
0.956267 0.292494i $$-0.0944852\pi$$
$$720$$ −0.825074 2.07828i −0.0307487 0.0774530i
$$721$$ 14.8682 + 14.8682i 0.553721 + 0.553721i
$$722$$ 5.37757 0.200133
$$723$$ −7.81085 −0.290488
$$724$$ −8.27365 −0.307488
$$725$$ 0.163984 5.54476i 0.00609020 0.205927i
$$726$$ 1.41925 1.41925i 0.0526735 0.0526735i
$$727$$ 44.2369i 1.64065i 0.571894 + 0.820327i $$0.306209\pi$$
−0.571894 + 0.820327i $$0.693791\pi$$
$$728$$ 0.825735 + 0.825735i 0.0306038 + 0.0306038i
$$729$$ 1.00000i 0.0370370i
$$730$$ −0.441268 + 1.02230i −0.0163320 + 0.0378371i
$$731$$ 4.03193i 0.149126i
$$732$$ 7.19609i 0.265975i
$$733$$ 27.8801 + 27.8801i 1.02977 + 1.02977i 0.999543 + 0.0302314i $$0.00962443\pi$$
0.0302314 + 0.999543i $$0.490376\pi$$
$$734$$ 0.221534 0.221534i 0.00817696 0.00817696i
$$735$$ −2.44419 + 5.66256i −0.0901553 + 0.208867i
$$736$$ −2.32324 −0.0856358
$$737$$ −5.93591 5.93591i −0.218652 0.218652i
$$738$$ 8.53277i 0.314096i
$$739$$ −44.3607 −1.63183 −0.815917 0.578169i $$-0.803768\pi$$
−0.815917 + 0.578169i $$0.803768\pi$$
$$740$$ −2.08517 + 13.4407i −0.0766524 + 0.494089i
$$741$$ 2.09271 0.0768775
$$742$$ 13.0694i 0.479793i
$$743$$ 7.56548 + 7.56548i 0.277551 + 0.277551i 0.832131 0.554580i $$-0.187121\pi$$
−0.554580 + 0.832131i $$0.687121\pi$$
$$744$$ −2.12589 −0.0779388
$$745$$ −6.68560 16.8404i −0.244942 0.616984i
$$746$$ −2.85523 + 2.85523i −0.104537 + 0.104537i
$$747$$ 2.52897 + 2.52897i 0.0925300 + 0.0925300i
$$748$$ 12.8493i 0.469819i
$$749$$ 31.1869i 1.13955i
$$750$$ −3.81638 10.5088i −0.139355 0.383728i
$$751$$ 5.20586i 0.189964i −0.995479 0.0949822i $$-0.969721\pi$$
0.995479 0.0949822i $$-0.0302794\pi$$
$$752$$ −4.15173 4.15173i −0.151398 0.151398i
$$753$$ 18.3209i 0.667650i
$$754$$ −0.444804 + 0.444804i −0.0161988 + 0.0161988i
$$755$$ −5.97549 15.0517i −0.217470 0.547786i
$$756$$ 2.05956 0.0749055
$$757$$ −27.0653 −0.983705 −0.491853 0.870678i $$-0.663680\pi$$
−0.491853 + 0.870678i $$0.663680\pi$$
$$758$$ −15.3156 −0.556289
$$759$$ −5.92475 5.92475i −0.215055 0.215055i
$$760$$ 3.27066 7.57726i 0.118639 0.274856i
$$761$$ 1.85691i 0.0673130i 0.999433 + 0.0336565i $$0.0107152\pi$$
−0.999433 + 0.0336565i $$0.989285\pi$$
$$762$$ −11.5446 −0.418217
$$763$$ 6.17519i 0.223557i
$$764$$ 10.7528 10.7528i 0.389022 0.389022i
$$765$$ 2.93957 + 7.40448i 0.106280 + 0.267710i
$$766$$ −26.5555 −0.959489
$$767$$ 3.14215 3.14215i 0.113457 0.113457i
$$768$$ 0.707107 + 0.707107i 0.0255155 + 0.0255155i
$$769$$ 20.3839 20.3839i 0.735061 0.735061i −0.236557 0.971618i $$-0.576019\pi$$
0.971618 + 0.236557i $$0.0760189\pi$$
$$770$$ 15.2493 + 6.58223i 0.549547 + 0.237207i
$$771$$ 11.2833 + 11.2833i 0.406357 + 0.406357i
$$772$$ 6.97010i 0.250859i
$$773$$ −29.3204 + 29.3204i −1.05458 + 1.05458i −0.0561599 + 0.998422i $$0.517886\pi$$
−0.998422 + 0.0561599i $$0.982114\pi$$
$$774$$ 1.13168i 0.0406774i
$$775$$ −10.6248 0.314223i −0.381654 0.0112872i
$$776$$ 11.4260i 0.410170i
$$777$$ −10.7975 6.35298i −0.387358 0.227912i
$$778$$ 5.00317 5.00317i 0.179373 0.179373i
$$779$$ 22.2691 22.2691i 0.797873 0.797873i