# Properties

 Label 435.2.c.e.349.5 Level $435$ Weight $2$ Character 435.349 Analytic conductor $3.473$ Analytic rank $0$ Dimension $10$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(349,435)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("435.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$435 = 3 \cdot 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 435.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$3.47349248793$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: 10.0.3899266318336.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{10} - 2x^{9} + 2x^{8} + 6x^{7} + 19x^{6} - 12x^{5} + 4x^{4} + 2x^{3} + 9x^{2} - 6x + 2$$ x^10 - 2*x^9 + 2*x^8 + 6*x^7 + 19*x^6 - 12*x^5 + 4*x^4 + 2*x^3 + 9*x^2 - 6*x + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 349.5 Root $$0.561843 + 0.561843i$$ of defining polynomial Character $$\chi$$ $$=$$ 435.349 Dual form 435.2.c.e.349.6

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-0.712495i q^{2} -1.00000i q^{3} +1.49235 q^{4} +(2.01848 - 0.962154i) q^{5} -0.712495 q^{6} +2.77986i q^{7} -2.48828i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-0.712495i q^{2} -1.00000i q^{3} +1.49235 q^{4} +(2.01848 - 0.962154i) q^{5} -0.712495 q^{6} +2.77986i q^{7} -2.48828i q^{8} -1.00000 q^{9} +(-0.685530 - 1.43816i) q^{10} +4.26814 q^{11} -1.49235i q^{12} +0.779856i q^{13} +1.98063 q^{14} +(-0.962154 - 2.01848i) q^{15} +1.21181 q^{16} +1.90354i q^{17} +0.712495i q^{18} -6.72036 q^{19} +(3.01228 - 1.43587i) q^{20} +2.77986 q^{21} -3.04103i q^{22} +2.17168i q^{23} -2.48828 q^{24} +(3.14852 - 3.88418i) q^{25} +0.555643 q^{26} +1.00000i q^{27} +4.14852i q^{28} -1.00000 q^{29} +(-1.43816 + 0.685530i) q^{30} -8.82061 q^{31} -5.83998i q^{32} -4.26814i q^{33} +1.35626 q^{34} +(2.67465 + 5.61108i) q^{35} -1.49235 q^{36} -1.48402i q^{37} +4.78822i q^{38} +0.779856 q^{39} +(-2.39411 - 5.02255i) q^{40} -7.71389 q^{41} -1.98063i q^{42} -8.19624i q^{43} +6.36956 q^{44} +(-2.01848 + 0.962154i) q^{45} +1.54731 q^{46} +5.19381i q^{47} -1.21181i q^{48} -0.727598 q^{49} +(-2.76746 - 2.24330i) q^{50} +1.90354 q^{51} +1.16382i q^{52} -11.7853i q^{53} +0.712495 q^{54} +(8.61515 - 4.10661i) q^{55} +6.91707 q^{56} +6.72036i q^{57} +0.712495i q^{58} +4.46028 q^{59} +(-1.43587 - 3.01228i) q^{60} -5.24905 q^{61} +6.28464i q^{62} -2.77986i q^{63} -1.73733 q^{64} +(0.750341 + 1.57412i) q^{65} -3.04103 q^{66} +8.49375i q^{67} +2.84075i q^{68} +2.17168 q^{69} +(3.99787 - 1.90567i) q^{70} +0.663102 q^{71} +2.48828i q^{72} +16.5345i q^{73} -1.05736 q^{74} +(-3.88418 - 3.14852i) q^{75} -10.0291 q^{76} +11.8648i q^{77} -0.555643i q^{78} -9.54554 q^{79} +(2.44602 - 1.16595i) q^{80} +1.00000 q^{81} +5.49611i q^{82} -0.0123998i q^{83} +4.14852 q^{84} +(1.83150 + 3.84226i) q^{85} -5.83978 q^{86} +1.00000i q^{87} -10.6203i q^{88} +5.46783 q^{89} +(0.685530 + 1.43816i) q^{90} -2.16789 q^{91} +3.24091i q^{92} +8.82061i q^{93} +3.70056 q^{94} +(-13.5649 + 6.46602i) q^{95} -5.83998 q^{96} +0.952006i q^{97} +0.518410i q^{98} -4.26814 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10 q - 10 q^{4} + 6 q^{6} - 10 q^{9}+O(q^{10})$$ 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9 $$10 q - 10 q^{4} + 6 q^{6} - 10 q^{9} + 4 q^{10} + 24 q^{11} - 12 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{19} + 8 q^{20} + 16 q^{21} - 18 q^{24} + 2 q^{25} - 10 q^{29} - 18 q^{30} + 4 q^{31} - 8 q^{34} + 2 q^{35} + 10 q^{36} - 4 q^{39} - 14 q^{40} - 28 q^{41} - 40 q^{44} - 12 q^{46} + 14 q^{49} - 12 q^{50} - 6 q^{54} + 2 q^{55} - 4 q^{56} - 8 q^{59} - 2 q^{60} - 24 q^{61} + 18 q^{64} + 6 q^{65} + 28 q^{66} - 16 q^{69} + 20 q^{70} + 60 q^{71} - 4 q^{74} + 12 q^{75} - 88 q^{76} + 36 q^{79} - 30 q^{80} + 10 q^{81} + 12 q^{84} - 14 q^{85} + 60 q^{86} + 44 q^{89} - 4 q^{90} - 24 q^{91} + 100 q^{94} - 36 q^{95} + 2 q^{96} - 24 q^{99}+O(q^{100})$$ 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9 + 4 * q^10 + 24 * q^11 - 12 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^19 + 8 * q^20 + 16 * q^21 - 18 * q^24 + 2 * q^25 - 10 * q^29 - 18 * q^30 + 4 * q^31 - 8 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^39 - 14 * q^40 - 28 * q^41 - 40 * q^44 - 12 * q^46 + 14 * q^49 - 12 * q^50 - 6 * q^54 + 2 * q^55 - 4 * q^56 - 8 * q^59 - 2 * q^60 - 24 * q^61 + 18 * q^64 + 6 * q^65 + 28 * q^66 - 16 * q^69 + 20 * q^70 + 60 * q^71 - 4 * q^74 + 12 * q^75 - 88 * q^76 + 36 * q^79 - 30 * q^80 + 10 * q^81 + 12 * q^84 - 14 * q^85 + 60 * q^86 + 44 * q^89 - 4 * q^90 - 24 * q^91 + 100 * q^94 - 36 * q^95 + 2 * q^96 - 24 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$146$$ $$262$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.712495i 0.503810i −0.967752 0.251905i $$-0.918943\pi$$
0.967752 0.251905i $$-0.0810571\pi$$
$$3$$ 1.00000i 0.577350i
$$4$$ 1.49235 0.746175
$$5$$ 2.01848 0.962154i 0.902692 0.430288i
$$6$$ −0.712495 −0.290875
$$7$$ 2.77986i 1.05069i 0.850890 + 0.525343i $$0.176063\pi$$
−0.850890 + 0.525343i $$0.823937\pi$$
$$8$$ 2.48828i 0.879741i
$$9$$ −1.00000 −0.333333
$$10$$ −0.685530 1.43816i −0.216784 0.454785i
$$11$$ 4.26814 1.28689 0.643446 0.765491i $$-0.277504\pi$$
0.643446 + 0.765491i $$0.277504\pi$$
$$12$$ 1.49235i 0.430805i
$$13$$ 0.779856i 0.216293i 0.994135 + 0.108147i $$0.0344916\pi$$
−0.994135 + 0.108147i $$0.965508\pi$$
$$14$$ 1.98063 0.529347
$$15$$ −0.962154 2.01848i −0.248427 0.521169i
$$16$$ 1.21181 0.302953
$$17$$ 1.90354i 0.461677i 0.972992 + 0.230838i $$0.0741469\pi$$
−0.972992 + 0.230838i $$0.925853\pi$$
$$18$$ 0.712495i 0.167937i
$$19$$ −6.72036 −1.54176 −0.770878 0.636983i $$-0.780182\pi$$
−0.770878 + 0.636983i $$0.780182\pi$$
$$20$$ 3.01228 1.43587i 0.673566 0.321071i
$$21$$ 2.77986 0.606614
$$22$$ 3.04103i 0.648349i
$$23$$ 2.17168i 0.452827i 0.974031 + 0.226413i $$0.0727000\pi$$
−0.974031 + 0.226413i $$0.927300\pi$$
$$24$$ −2.48828 −0.507919
$$25$$ 3.14852 3.88418i 0.629704 0.776835i
$$26$$ 0.555643 0.108971
$$27$$ 1.00000i 0.192450i
$$28$$ 4.14852i 0.783997i
$$29$$ −1.00000 −0.185695
$$30$$ −1.43816 + 0.685530i −0.262570 + 0.125160i
$$31$$ −8.82061 −1.58423 −0.792114 0.610373i $$-0.791020\pi$$
−0.792114 + 0.610373i $$0.791020\pi$$
$$32$$ 5.83998i 1.03237i
$$33$$ 4.26814i 0.742988i
$$34$$ 1.35626 0.232597
$$35$$ 2.67465 + 5.61108i 0.452098 + 0.948446i
$$36$$ −1.49235 −0.248725
$$37$$ 1.48402i 0.243971i −0.992532 0.121986i $$-0.961074\pi$$
0.992532 0.121986i $$-0.0389262\pi$$
$$38$$ 4.78822i 0.776752i
$$39$$ 0.779856 0.124877
$$40$$ −2.39411 5.02255i −0.378542 0.794135i
$$41$$ −7.71389 −1.20471 −0.602354 0.798229i $$-0.705770\pi$$
−0.602354 + 0.798229i $$0.705770\pi$$
$$42$$ 1.98063i 0.305618i
$$43$$ 8.19624i 1.24991i −0.780659 0.624957i $$-0.785116\pi$$
0.780659 0.624957i $$-0.214884\pi$$
$$44$$ 6.36956 0.960247
$$45$$ −2.01848 + 0.962154i −0.300897 + 0.143429i
$$46$$ 1.54731 0.228139
$$47$$ 5.19381i 0.757595i 0.925480 + 0.378798i $$0.123662\pi$$
−0.925480 + 0.378798i $$0.876338\pi$$
$$48$$ 1.21181i 0.174910i
$$49$$ −0.727598 −0.103943
$$50$$ −2.76746 2.24330i −0.391377 0.317251i
$$51$$ 1.90354 0.266549
$$52$$ 1.16382i 0.161393i
$$53$$ 11.7853i 1.61884i −0.587231 0.809419i $$-0.699782\pi$$
0.587231 0.809419i $$-0.300218\pi$$
$$54$$ 0.712495 0.0969583
$$55$$ 8.61515 4.10661i 1.16167 0.553735i
$$56$$ 6.91707 0.924332
$$57$$ 6.72036i 0.890133i
$$58$$ 0.712495i 0.0935552i
$$59$$ 4.46028 0.580679 0.290339 0.956924i $$-0.406232\pi$$
0.290339 + 0.956924i $$0.406232\pi$$
$$60$$ −1.43587 3.01228i −0.185370 0.388884i
$$61$$ −5.24905 −0.672071 −0.336036 0.941849i $$-0.609086\pi$$
−0.336036 + 0.941849i $$0.609086\pi$$
$$62$$ 6.28464i 0.798150i
$$63$$ 2.77986i 0.350229i
$$64$$ −1.73733 −0.217166
$$65$$ 0.750341 + 1.57412i 0.0930684 + 0.195246i
$$66$$ −3.04103 −0.374325
$$67$$ 8.49375i 1.03768i 0.854872 + 0.518838i $$0.173635\pi$$
−0.854872 + 0.518838i $$0.826365\pi$$
$$68$$ 2.84075i 0.344492i
$$69$$ 2.17168 0.261440
$$70$$ 3.99787 1.90567i 0.477837 0.227772i
$$71$$ 0.663102 0.0786957 0.0393479 0.999226i $$-0.487472\pi$$
0.0393479 + 0.999226i $$0.487472\pi$$
$$72$$ 2.48828i 0.293247i
$$73$$ 16.5345i 1.93522i 0.252455 + 0.967609i $$0.418762\pi$$
−0.252455 + 0.967609i $$0.581238\pi$$
$$74$$ −1.05736 −0.122915
$$75$$ −3.88418 3.14852i −0.448506 0.363560i
$$76$$ −10.0291 −1.15042
$$77$$ 11.8648i 1.35212i
$$78$$ 0.555643i 0.0629142i
$$79$$ −9.54554 −1.07396 −0.536978 0.843596i $$-0.680434\pi$$
−0.536978 + 0.843596i $$0.680434\pi$$
$$80$$ 2.44602 1.16595i 0.273473 0.130357i
$$81$$ 1.00000 0.111111
$$82$$ 5.49611i 0.606944i
$$83$$ 0.0123998i 0.00136106i −1.00000 0.000680528i $$-0.999783\pi$$
1.00000 0.000680528i $$-0.000216619\pi$$
$$84$$ 4.14852 0.452641
$$85$$ 1.83150 + 3.84226i 0.198654 + 0.416752i
$$86$$ −5.83978 −0.629720
$$87$$ 1.00000i 0.107211i
$$88$$ 10.6203i 1.13213i
$$89$$ 5.46783 0.579588 0.289794 0.957089i $$-0.406413\pi$$
0.289794 + 0.957089i $$0.406413\pi$$
$$90$$ 0.685530 + 1.43816i 0.0722612 + 0.151595i
$$91$$ −2.16789 −0.227256
$$92$$ 3.24091i 0.337888i
$$93$$ 8.82061i 0.914655i
$$94$$ 3.70056 0.381684
$$95$$ −13.5649 + 6.46602i −1.39173 + 0.663399i
$$96$$ −5.83998 −0.596040
$$97$$ 0.952006i 0.0966615i 0.998831 + 0.0483308i $$0.0153902\pi$$
−0.998831 + 0.0483308i $$0.984610\pi$$
$$98$$ 0.518410i 0.0523673i
$$99$$ −4.26814 −0.428964
$$100$$ 4.69870 5.79655i 0.469870 0.579655i
$$101$$ 8.31781 0.827653 0.413826 0.910356i $$-0.364192\pi$$
0.413826 + 0.910356i $$0.364192\pi$$
$$102$$ 1.35626i 0.134290i
$$103$$ 12.4091i 1.22271i 0.791357 + 0.611355i $$0.209375\pi$$
−0.791357 + 0.611355i $$0.790625\pi$$
$$104$$ 1.94050 0.190282
$$105$$ 5.61108 2.67465i 0.547586 0.261019i
$$106$$ −8.39698 −0.815587
$$107$$ 17.5579i 1.69739i 0.528883 + 0.848695i $$0.322611\pi$$
−0.528883 + 0.848695i $$0.677389\pi$$
$$108$$ 1.49235i 0.143602i
$$109$$ −1.00973 −0.0967146 −0.0483573 0.998830i $$-0.515399\pi$$
−0.0483573 + 0.998830i $$0.515399\pi$$
$$110$$ −2.92594 6.13825i −0.278977 0.585259i
$$111$$ −1.48402 −0.140857
$$112$$ 3.36866i 0.318309i
$$113$$ 15.5787i 1.46552i −0.680487 0.732761i $$-0.738232\pi$$
0.680487 0.732761i $$-0.261768\pi$$
$$114$$ 4.78822 0.448458
$$115$$ 2.08949 + 4.38349i 0.194846 + 0.408763i
$$116$$ −1.49235 −0.138561
$$117$$ 0.779856i 0.0720977i
$$118$$ 3.17792i 0.292552i
$$119$$ −5.29157 −0.485078
$$120$$ −5.02255 + 2.39411i −0.458494 + 0.218551i
$$121$$ 7.21701 0.656091
$$122$$ 3.73992i 0.338596i
$$123$$ 7.71389i 0.695538i
$$124$$ −13.1634 −1.18211
$$125$$ 2.61805 10.8695i 0.234165 0.972197i
$$126$$ −1.98063 −0.176449
$$127$$ 16.9536i 1.50438i 0.658943 + 0.752192i $$0.271004\pi$$
−0.658943 + 0.752192i $$0.728996\pi$$
$$128$$ 10.4421i 0.922961i
$$129$$ −8.19624 −0.721639
$$130$$ 1.12155 0.534614i 0.0983669 0.0468888i
$$131$$ 11.9324 1.04254 0.521268 0.853393i $$-0.325459\pi$$
0.521268 + 0.853393i $$0.325459\pi$$
$$132$$ 6.36956i 0.554399i
$$133$$ 18.6816i 1.61990i
$$134$$ 6.05175 0.522792
$$135$$ 0.962154 + 2.01848i 0.0828090 + 0.173723i
$$136$$ 4.73655 0.406156
$$137$$ 0.239785i 0.0204862i 0.999948 + 0.0102431i $$0.00326054\pi$$
−0.999948 + 0.0102431i $$0.996739\pi$$
$$138$$ 1.54731i 0.131716i
$$139$$ 17.0255 1.44408 0.722040 0.691851i $$-0.243205\pi$$
0.722040 + 0.691851i $$0.243205\pi$$
$$140$$ 3.99151 + 8.37370i 0.337345 + 0.707707i
$$141$$ 5.19381 0.437398
$$142$$ 0.472457i 0.0396477i
$$143$$ 3.32853i 0.278346i
$$144$$ −1.21181 −0.100984
$$145$$ −2.01848 + 0.962154i −0.167626 + 0.0799025i
$$146$$ 11.7808 0.974982
$$147$$ 0.727598i 0.0600113i
$$148$$ 2.21468i 0.182045i
$$149$$ 4.13046 0.338380 0.169190 0.985583i $$-0.445885\pi$$
0.169190 + 0.985583i $$0.445885\pi$$
$$150$$ −2.24330 + 2.76746i −0.183165 + 0.225962i
$$151$$ −3.21580 −0.261698 −0.130849 0.991402i $$-0.541770\pi$$
−0.130849 + 0.991402i $$0.541770\pi$$
$$152$$ 16.7221i 1.35635i
$$153$$ 1.90354i 0.153892i
$$154$$ 8.45362 0.681212
$$155$$ −17.8042 + 8.48678i −1.43007 + 0.681675i
$$156$$ 1.16382 0.0931800
$$157$$ 6.84237i 0.546081i −0.962003 0.273040i $$-0.911971\pi$$
0.962003 0.273040i $$-0.0880292\pi$$
$$158$$ 6.80115i 0.541070i
$$159$$ −11.7853 −0.934637
$$160$$ −5.61895 11.7879i −0.444217 0.931913i
$$161$$ −6.03696 −0.475779
$$162$$ 0.712495i 0.0559789i
$$163$$ 14.0502i 1.10050i −0.835001 0.550248i $$-0.814533\pi$$
0.835001 0.550248i $$-0.185467\pi$$
$$164$$ −11.5118 −0.898923
$$165$$ −4.10661 8.61515i −0.319699 0.670689i
$$166$$ −0.00883480 −0.000685713
$$167$$ 17.8725i 1.38301i −0.722370 0.691507i $$-0.756947\pi$$
0.722370 0.691507i $$-0.243053\pi$$
$$168$$ 6.91707i 0.533663i
$$169$$ 12.3918 0.953217
$$170$$ 2.73759 1.30494i 0.209964 0.100084i
$$171$$ 6.72036 0.513919
$$172$$ 12.2317i 0.932656i
$$173$$ 2.82518i 0.214795i −0.994216 0.107397i $$-0.965748\pi$$
0.994216 0.107397i $$-0.0342517\pi$$
$$174$$ 0.712495 0.0540141
$$175$$ 10.7974 + 8.75243i 0.816210 + 0.661622i
$$176$$ 5.17218 0.389868
$$177$$ 4.46028i 0.335255i
$$178$$ 3.89580i 0.292002i
$$179$$ −20.2829 −1.51601 −0.758006 0.652247i $$-0.773826\pi$$
−0.758006 + 0.652247i $$0.773826\pi$$
$$180$$ −3.01228 + 1.43587i −0.224522 + 0.107024i
$$181$$ −8.63783 −0.642045 −0.321023 0.947072i $$-0.604027\pi$$
−0.321023 + 0.947072i $$0.604027\pi$$
$$182$$ 1.54461i 0.114494i
$$183$$ 5.24905i 0.388021i
$$184$$ 5.40376 0.398370
$$185$$ −1.42785 2.99546i −0.104978 0.220231i
$$186$$ 6.28464 0.460812
$$187$$ 8.12458i 0.594128i
$$188$$ 7.75099i 0.565299i
$$189$$ −2.77986 −0.202205
$$190$$ 4.60701 + 9.66493i 0.334227 + 0.701168i
$$191$$ 0.896850 0.0648938 0.0324469 0.999473i $$-0.489670\pi$$
0.0324469 + 0.999473i $$0.489670\pi$$
$$192$$ 1.73733i 0.125381i
$$193$$ 10.4506i 0.752251i −0.926569 0.376126i $$-0.877256\pi$$
0.926569 0.376126i $$-0.122744\pi$$
$$194$$ 0.678299 0.0486991
$$195$$ 1.57412 0.750341i 0.112725 0.0537331i
$$196$$ −1.08583 −0.0775594
$$197$$ 9.57740i 0.682361i −0.939998 0.341181i $$-0.889173\pi$$
0.939998 0.341181i $$-0.110827\pi$$
$$198$$ 3.04103i 0.216116i
$$199$$ −5.61768 −0.398227 −0.199113 0.979976i $$-0.563806\pi$$
−0.199113 + 0.979976i $$0.563806\pi$$
$$200$$ −9.66493 7.83441i −0.683414 0.553976i
$$201$$ 8.49375 0.599103
$$202$$ 5.92640i 0.416980i
$$203$$ 2.77986i 0.195108i
$$204$$ 2.84075 0.198892
$$205$$ −15.5703 + 7.42195i −1.08748 + 0.518372i
$$206$$ 8.84145 0.616013
$$207$$ 2.17168i 0.150942i
$$208$$ 0.945039i 0.0655267i
$$209$$ −28.6834 −1.98407
$$210$$ −1.90567 3.99787i −0.131504 0.275879i
$$211$$ −0.605216 −0.0416648 −0.0208324 0.999783i $$-0.506632\pi$$
−0.0208324 + 0.999783i $$0.506632\pi$$
$$212$$ 17.5878i 1.20794i
$$213$$ 0.663102i 0.0454350i
$$214$$ 12.5099 0.855162
$$215$$ −7.88604 16.5439i −0.537824 1.12829i
$$216$$ 2.48828 0.169306
$$217$$ 24.5200i 1.66453i
$$218$$ 0.719428i 0.0487258i
$$219$$ 16.5345 1.11730
$$220$$ 12.8568 6.12850i 0.866807 0.413183i
$$221$$ −1.48449 −0.0998575
$$222$$ 1.05736i 0.0709651i
$$223$$ 16.5537i 1.10852i 0.832344 + 0.554260i $$0.186999\pi$$
−0.832344 + 0.554260i $$0.813001\pi$$
$$224$$ 16.2343 1.08470
$$225$$ −3.14852 + 3.88418i −0.209901 + 0.258945i
$$226$$ −11.0997 −0.738344
$$227$$ 22.0061i 1.46060i 0.683128 + 0.730299i $$0.260619\pi$$
−0.683128 + 0.730299i $$0.739381\pi$$
$$228$$ 10.0291i 0.664195i
$$229$$ 24.5647 1.62328 0.811641 0.584157i $$-0.198575\pi$$
0.811641 + 0.584157i $$0.198575\pi$$
$$230$$ 3.12322 1.48875i 0.205939 0.0981654i
$$231$$ 11.8648 0.780647
$$232$$ 2.48828i 0.163364i
$$233$$ 5.56824i 0.364787i −0.983226 0.182394i $$-0.941615\pi$$
0.983226 0.182394i $$-0.0583845\pi$$
$$234$$ −0.555643 −0.0363235
$$235$$ 4.99725 + 10.4836i 0.325984 + 0.683875i
$$236$$ 6.65630 0.433288
$$237$$ 9.54554i 0.620049i
$$238$$ 3.77022i 0.244387i
$$239$$ −6.90640 −0.446738 −0.223369 0.974734i $$-0.571705\pi$$
−0.223369 + 0.974734i $$0.571705\pi$$
$$240$$ −1.16595 2.44602i −0.0752618 0.157890i
$$241$$ −25.1989 −1.62320 −0.811602 0.584210i $$-0.801404\pi$$
−0.811602 + 0.584210i $$0.801404\pi$$
$$242$$ 5.14208i 0.330545i
$$243$$ 1.00000i 0.0641500i
$$244$$ −7.83342 −0.501483
$$245$$ −1.46864 + 0.700061i −0.0938281 + 0.0447253i
$$246$$ 5.49611 0.350419
$$247$$ 5.24091i 0.333471i
$$248$$ 21.9482i 1.39371i
$$249$$ −0.0123998 −0.000785805
$$250$$ −7.74446 1.86535i −0.489803 0.117975i
$$251$$ 28.3687 1.79062 0.895309 0.445446i $$-0.146955\pi$$
0.895309 + 0.445446i $$0.146955\pi$$
$$252$$ 4.14852i 0.261332i
$$253$$ 9.26903i 0.582739i
$$254$$ 12.0793 0.757924
$$255$$ 3.84226 1.83150i 0.240612 0.114693i
$$256$$ −10.9146 −0.682163
$$257$$ 8.71100i 0.543377i −0.962385 0.271688i $$-0.912418\pi$$
0.962385 0.271688i $$-0.0875820\pi$$
$$258$$ 5.83978i 0.363569i
$$259$$ 4.12536 0.256337
$$260$$ 1.11977 + 2.34914i 0.0694453 + 0.145688i
$$261$$ 1.00000 0.0618984
$$262$$ 8.50175i 0.525240i
$$263$$ 13.2128i 0.814736i −0.913264 0.407368i $$-0.866447\pi$$
0.913264 0.407368i $$-0.133553\pi$$
$$264$$ −10.6203 −0.653636
$$265$$ −11.3393 23.7884i −0.696567 1.46131i
$$266$$ −13.3106 −0.816123
$$267$$ 5.46783i 0.334625i
$$268$$ 12.6757i 0.774289i
$$269$$ 10.3447 0.630725 0.315363 0.948971i $$-0.397874\pi$$
0.315363 + 0.948971i $$0.397874\pi$$
$$270$$ 1.43816 0.685530i 0.0875234 0.0417200i
$$271$$ 9.76022 0.592891 0.296445 0.955050i $$-0.404199\pi$$
0.296445 + 0.955050i $$0.404199\pi$$
$$272$$ 2.30674i 0.139866i
$$273$$ 2.16789i 0.131206i
$$274$$ 0.170845 0.0103212
$$275$$ 13.4383 16.5782i 0.810361 0.999703i
$$276$$ 3.24091 0.195080
$$277$$ 1.87503i 0.112659i −0.998412 0.0563297i $$-0.982060\pi$$
0.998412 0.0563297i $$-0.0179398\pi$$
$$278$$ 12.1306i 0.727542i
$$279$$ 8.82061 0.528076
$$280$$ 13.9620 6.65528i 0.834387 0.397729i
$$281$$ −21.2930 −1.27024 −0.635118 0.772415i $$-0.719049\pi$$
−0.635118 + 0.772415i $$0.719049\pi$$
$$282$$ 3.70056i 0.220365i
$$283$$ 15.8729i 0.943544i −0.881721 0.471772i $$-0.843615\pi$$
0.881721 0.471772i $$-0.156385\pi$$
$$284$$ 0.989581 0.0587208
$$285$$ 6.46602 + 13.5649i 0.383014 + 0.803516i
$$286$$ 2.37156 0.140233
$$287$$ 21.4435i 1.26577i
$$288$$ 5.83998i 0.344124i
$$289$$ 13.3765 0.786855
$$290$$ 0.685530 + 1.43816i 0.0402557 + 0.0844515i
$$291$$ 0.952006 0.0558076
$$292$$ 24.6753i 1.44401i
$$293$$ 33.1369i 1.93588i −0.251189 0.967938i $$-0.580822\pi$$
0.251189 0.967938i $$-0.419178\pi$$
$$294$$ 0.518410 0.0302343
$$295$$ 9.00298 4.29147i 0.524174 0.249859i
$$296$$ −3.69266 −0.214631
$$297$$ 4.26814i 0.247663i
$$298$$ 2.94293i 0.170479i
$$299$$ −1.69360 −0.0979433
$$300$$ −5.79655 4.69870i −0.334664 0.271279i
$$301$$ 22.7844 1.31327
$$302$$ 2.29124i 0.131846i
$$303$$ 8.31781i 0.477845i
$$304$$ −8.14381 −0.467080
$$305$$ −10.5951 + 5.05039i −0.606673 + 0.289184i
$$306$$ −1.35626 −0.0775325
$$307$$ 17.2605i 0.985109i 0.870282 + 0.492555i $$0.163937\pi$$
−0.870282 + 0.492555i $$0.836063\pi$$
$$308$$ 17.7065i 1.00892i
$$309$$ 12.4091 0.705932
$$310$$ 6.04679 + 12.6854i 0.343435 + 0.720483i
$$311$$ −32.5116 −1.84356 −0.921781 0.387711i $$-0.873266\pi$$
−0.921781 + 0.387711i $$0.873266\pi$$
$$312$$ 1.94050i 0.109859i
$$313$$ 6.26304i 0.354008i −0.984210 0.177004i $$-0.943359\pi$$
0.984210 0.177004i $$-0.0566405\pi$$
$$314$$ −4.87516 −0.275121
$$315$$ −2.67465 5.61108i −0.150699 0.316149i
$$316$$ −14.2453 −0.801360
$$317$$ 18.8523i 1.05885i −0.848356 0.529426i $$-0.822407\pi$$
0.848356 0.529426i $$-0.177593\pi$$
$$318$$ 8.39698i 0.470879i
$$319$$ −4.26814 −0.238970
$$320$$ −3.50676 + 1.67158i −0.196034 + 0.0934440i
$$321$$ 17.5579 0.979989
$$322$$ 4.30130i 0.239702i
$$323$$ 12.7925i 0.711793i
$$324$$ 1.49235 0.0829084
$$325$$ 3.02910 + 2.45539i 0.168024 + 0.136201i
$$326$$ −10.0107 −0.554441
$$327$$ 1.00973i 0.0558382i
$$328$$ 19.1943i 1.05983i
$$329$$ −14.4380 −0.795995
$$330$$ −6.13825 + 2.92594i −0.337900 + 0.161067i
$$331$$ −0.596245 −0.0327726 −0.0163863 0.999866i $$-0.505216\pi$$
−0.0163863 + 0.999866i $$0.505216\pi$$
$$332$$ 0.0185049i 0.00101559i
$$333$$ 1.48402i 0.0813238i
$$334$$ −12.7341 −0.696776
$$335$$ 8.17229 + 17.1445i 0.446500 + 0.936702i
$$336$$ 3.36866 0.183776
$$337$$ 32.6414i 1.77809i 0.457818 + 0.889046i $$0.348631\pi$$
−0.457818 + 0.889046i $$0.651369\pi$$
$$338$$ 8.82911i 0.480240i
$$339$$ −15.5787 −0.846119
$$340$$ 2.73324 + 5.73400i 0.148231 + 0.310970i
$$341$$ −37.6476 −2.03873
$$342$$ 4.78822i 0.258917i
$$343$$ 17.4364i 0.941476i
$$344$$ −20.3946 −1.09960
$$345$$ 4.38349 2.08949i 0.235999 0.112494i
$$346$$ −2.01293 −0.108216
$$347$$ 13.1985i 0.708531i −0.935145 0.354265i $$-0.884731\pi$$
0.935145 0.354265i $$-0.115269\pi$$
$$348$$ 1.49235i 0.0799984i
$$349$$ −15.6412 −0.837255 −0.418628 0.908158i $$-0.637489\pi$$
−0.418628 + 0.908158i $$0.637489\pi$$
$$350$$ 6.23606 7.69313i 0.333332 0.411215i
$$351$$ −0.779856 −0.0416256
$$352$$ 24.9258i 1.32855i
$$353$$ 5.65486i 0.300978i 0.988612 + 0.150489i $$0.0480848\pi$$
−0.988612 + 0.150489i $$0.951915\pi$$
$$354$$ −3.17792 −0.168905
$$355$$ 1.33846 0.638006i 0.0710380 0.0338619i
$$356$$ 8.15991 0.432475
$$357$$ 5.29157i 0.280060i
$$358$$ 14.4514i 0.763782i
$$359$$ −25.2693 −1.33366 −0.666832 0.745208i $$-0.732350\pi$$
−0.666832 + 0.745208i $$0.732350\pi$$
$$360$$ 2.39411 + 5.02255i 0.126181 + 0.264712i
$$361$$ 26.1632 1.37701
$$362$$ 6.15441i 0.323469i
$$363$$ 7.21701i 0.378795i
$$364$$ −3.23525 −0.169573
$$365$$ 15.9087 + 33.3746i 0.832701 + 1.74690i
$$366$$ 3.73992 0.195489
$$367$$ 26.2788i 1.37174i −0.727722 0.685872i $$-0.759421\pi$$
0.727722 0.685872i $$-0.240579\pi$$
$$368$$ 2.63167i 0.137185i
$$369$$ 7.71389 0.401569
$$370$$ −2.13425 + 1.01734i −0.110954 + 0.0528890i
$$371$$ 32.7615 1.70089
$$372$$ 13.1634i 0.682493i
$$373$$ 1.43033i 0.0740596i 0.999314 + 0.0370298i $$0.0117897\pi$$
−0.999314 + 0.0370298i $$0.988210\pi$$
$$374$$ 5.78872 0.299328
$$375$$ −10.8695 2.61805i −0.561298 0.135195i
$$376$$ 12.9237 0.666487
$$377$$ 0.779856i 0.0401646i
$$378$$ 1.98063i 0.101873i
$$379$$ 35.2336 1.80983 0.904915 0.425591i $$-0.139934\pi$$
0.904915 + 0.425591i $$0.139934\pi$$
$$380$$ −20.2436 + 9.64957i −1.03847 + 0.495012i
$$381$$ 16.9536 0.868557
$$382$$ 0.639001i 0.0326941i
$$383$$ 32.0701i 1.63870i 0.573291 + 0.819352i $$0.305666\pi$$
−0.573291 + 0.819352i $$0.694334\pi$$
$$384$$ −10.4421 −0.532872
$$385$$ 11.4158 + 23.9489i 0.581802 + 1.22055i
$$386$$ −7.44601 −0.378992
$$387$$ 8.19624i 0.416638i
$$388$$ 1.42073i 0.0721265i
$$389$$ −1.63922 −0.0831117 −0.0415558 0.999136i $$-0.513231\pi$$
−0.0415558 + 0.999136i $$0.513231\pi$$
$$390$$ −0.534614 1.12155i −0.0270713 0.0567921i
$$391$$ −4.13389 −0.209060
$$392$$ 1.81047i 0.0914425i
$$393$$ 11.9324i 0.601908i
$$394$$ −6.82385 −0.343781
$$395$$ −19.2675 + 9.18428i −0.969452 + 0.462111i
$$396$$ −6.36956 −0.320082
$$397$$ 2.04098i 0.102434i 0.998688 + 0.0512170i $$0.0163100\pi$$
−0.998688 + 0.0512170i $$0.983690\pi$$
$$398$$ 4.00257i 0.200631i
$$399$$ −18.6816 −0.935251
$$400$$ 3.81542 4.70689i 0.190771 0.235345i
$$401$$ 17.4108 0.869455 0.434727 0.900562i $$-0.356845\pi$$
0.434727 + 0.900562i $$0.356845\pi$$
$$402$$ 6.05175i 0.301834i
$$403$$ 6.87880i 0.342658i
$$404$$ 12.4131 0.617574
$$405$$ 2.01848 0.962154i 0.100299 0.0478098i
$$406$$ −1.98063 −0.0982972
$$407$$ 6.33400i 0.313965i
$$408$$ 4.73655i 0.234494i
$$409$$ 37.3010 1.84441 0.922207 0.386696i $$-0.126384\pi$$
0.922207 + 0.386696i $$0.126384\pi$$
$$410$$ 5.28810 + 11.0938i 0.261161 + 0.547883i
$$411$$ 0.239785 0.0118277
$$412$$ 18.5188i 0.912356i
$$413$$ 12.3989i 0.610111i
$$414$$ −1.54731 −0.0760462
$$415$$ −0.0119305 0.0250287i −0.000585646 0.00122861i
$$416$$ 4.55434 0.223295
$$417$$ 17.0255i 0.833740i
$$418$$ 20.4368i 0.999596i
$$419$$ −4.32941 −0.211506 −0.105753 0.994392i $$-0.533725\pi$$
−0.105753 + 0.994392i $$0.533725\pi$$
$$420$$ 8.37370 3.99151i 0.408595 0.194766i
$$421$$ −34.2505 −1.66927 −0.834634 0.550806i $$-0.814321\pi$$
−0.834634 + 0.550806i $$0.814321\pi$$
$$422$$ 0.431214i 0.0209911i
$$423$$ 5.19381i 0.252532i
$$424$$ −29.3252 −1.42416
$$425$$ 7.39369 + 5.99334i 0.358647 + 0.290720i
$$426$$ −0.472457 −0.0228906
$$427$$ 14.5916i 0.706137i
$$428$$ 26.2026i 1.26655i
$$429$$ 3.32853 0.160703
$$430$$ −11.7875 + 5.61877i −0.568443 + 0.270961i
$$431$$ 34.4885 1.66125 0.830626 0.556831i $$-0.187983\pi$$
0.830626 + 0.556831i $$0.187983\pi$$
$$432$$ 1.21181i 0.0583034i
$$433$$ 3.02258i 0.145256i −0.997359 0.0726279i $$-0.976861\pi$$
0.997359 0.0726279i $$-0.0231386\pi$$
$$434$$ −17.4704 −0.838606
$$435$$ 0.962154 + 2.01848i 0.0461317 + 0.0967787i
$$436$$ −1.50687 −0.0721661
$$437$$ 14.5945i 0.698148i
$$438$$ 11.7808i 0.562906i
$$439$$ −8.37392 −0.399665 −0.199833 0.979830i $$-0.564040\pi$$
−0.199833 + 0.979830i $$0.564040\pi$$
$$440$$ −10.2184 21.4369i −0.487143 1.02197i
$$441$$ 0.727598 0.0346475
$$442$$ 1.05769i 0.0503092i
$$443$$ 29.8770i 1.41950i 0.704454 + 0.709749i $$0.251192\pi$$
−0.704454 + 0.709749i $$0.748808\pi$$
$$444$$ −2.21468 −0.105104
$$445$$ 11.0367 5.26089i 0.523189 0.249390i
$$446$$ 11.7945 0.558484
$$447$$ 4.13046i 0.195364i
$$448$$ 4.82952i 0.228174i
$$449$$ −12.0780 −0.569994 −0.284997 0.958528i $$-0.591993\pi$$
−0.284997 + 0.958528i $$0.591993\pi$$
$$450$$ 2.76746 + 2.24330i 0.130459 + 0.105750i
$$451$$ −32.9240 −1.55033
$$452$$ 23.2489i 1.09354i
$$453$$ 3.21580i 0.151092i
$$454$$ 15.6793 0.735864
$$455$$ −4.37583 + 2.08584i −0.205142 + 0.0977857i
$$456$$ 16.7221 0.783086
$$457$$ 3.03357i 0.141905i 0.997480 + 0.0709523i $$0.0226038\pi$$
−0.997480 + 0.0709523i $$0.977396\pi$$
$$458$$ 17.5022i 0.817826i
$$459$$ −1.90354 −0.0888497
$$460$$ 3.11825 + 6.54171i 0.145389 + 0.305009i
$$461$$ −4.44508 −0.207028 −0.103514 0.994628i $$-0.533009\pi$$
−0.103514 + 0.994628i $$0.533009\pi$$
$$462$$ 8.45362i 0.393298i
$$463$$ 9.04875i 0.420531i 0.977644 + 0.210266i $$0.0674329\pi$$
−0.977644 + 0.210266i $$0.932567\pi$$
$$464$$ −1.21181 −0.0562570
$$465$$ 8.48678 + 17.8042i 0.393565 + 0.825651i
$$466$$ −3.96734 −0.183784
$$467$$ 8.11327i 0.375437i 0.982223 + 0.187719i $$0.0601093\pi$$
−0.982223 + 0.187719i $$0.939891\pi$$
$$468$$ 1.16382i 0.0537975i
$$469$$ −23.6114 −1.09027
$$470$$ 7.46951 3.56051i 0.344543 0.164234i
$$471$$ −6.84237 −0.315280
$$472$$ 11.0984i 0.510847i
$$473$$ 34.9827i 1.60851i
$$474$$ 6.80115 0.312387
$$475$$ −21.1592 + 26.1030i −0.970850 + 1.19769i
$$476$$ −7.89688 −0.361953
$$477$$ 11.7853i 0.539613i
$$478$$ 4.92078i 0.225071i
$$479$$ −6.62947 −0.302908 −0.151454 0.988464i $$-0.548396\pi$$
−0.151454 + 0.988464i $$0.548396\pi$$
$$480$$ −11.7879 + 5.61895i −0.538040 + 0.256469i
$$481$$ 1.15732 0.0527693
$$482$$ 17.9541i 0.817787i
$$483$$ 6.03696i 0.274691i
$$484$$ 10.7703 0.489559
$$485$$ 0.915976 + 1.92160i 0.0415923 + 0.0872556i
$$486$$ −0.712495 −0.0323194
$$487$$ 29.2047i 1.32339i −0.749773 0.661695i $$-0.769837\pi$$
0.749773 0.661695i $$-0.230163\pi$$
$$488$$ 13.0611i 0.591249i
$$489$$ −14.0502 −0.635372
$$490$$ 0.498790 + 1.04640i 0.0225330 + 0.0472715i
$$491$$ −4.32464 −0.195168 −0.0975841 0.995227i $$-0.531111\pi$$
−0.0975841 + 0.995227i $$0.531111\pi$$
$$492$$ 11.5118i 0.518994i
$$493$$ 1.90354i 0.0857312i
$$494$$ −3.73412 −0.168006
$$495$$ −8.61515 + 4.10661i −0.387222 + 0.184578i
$$496$$ −10.6889 −0.479947
$$497$$ 1.84333i 0.0826846i
$$498$$ 0.00883480i 0.000395897i
$$499$$ −4.29688 −0.192355 −0.0961774 0.995364i $$-0.530662\pi$$
−0.0961774 + 0.995364i $$0.530662\pi$$
$$500$$ 3.90705 16.2211i 0.174728 0.725429i
$$501$$ −17.8725 −0.798483
$$502$$ 20.2126i 0.902131i
$$503$$ 14.2512i 0.635429i 0.948186 + 0.317715i $$0.102915\pi$$
−0.948186 + 0.317715i $$0.897085\pi$$
$$504$$ −6.91707 −0.308111
$$505$$ 16.7893 8.00301i 0.747115 0.356129i
$$506$$ 6.60414 0.293590
$$507$$ 12.3918i 0.550340i
$$508$$ 25.3007i 1.12254i
$$509$$ 19.4974 0.864206 0.432103 0.901824i $$-0.357772\pi$$
0.432103 + 0.901824i $$0.357772\pi$$
$$510$$ −1.30494 2.73759i −0.0577835 0.121223i
$$511$$ −45.9635 −2.03331
$$512$$ 13.1076i 0.579280i
$$513$$ 6.72036i 0.296711i
$$514$$ −6.20654 −0.273759
$$515$$ 11.9395 + 25.0476i 0.526117 + 1.10373i
$$516$$ −12.2317 −0.538469
$$517$$ 22.1679i 0.974943i
$$518$$ 2.93930i 0.129145i
$$519$$ −2.82518 −0.124012
$$520$$ 3.91686 1.86706i 0.171766 0.0818760i
$$521$$ 24.5229 1.07437 0.537185 0.843465i $$-0.319488\pi$$
0.537185 + 0.843465i $$0.319488\pi$$
$$522$$ 0.712495i 0.0311851i
$$523$$ 10.8566i 0.474725i 0.971421 + 0.237362i $$0.0762829\pi$$
−0.971421 + 0.237362i $$0.923717\pi$$
$$524$$ 17.8073 0.777914
$$525$$ 8.75243 10.7974i 0.381987 0.471239i
$$526$$ −9.41406 −0.410472
$$527$$ 16.7904i 0.731401i
$$528$$ 5.17218i 0.225090i
$$529$$ 18.2838 0.794948
$$530$$ −16.9491 + 8.07919i −0.736224 + 0.350938i
$$531$$ −4.46028 −0.193560
$$532$$ 27.8795i 1.20873i
$$533$$ 6.01572i 0.260570i
$$534$$ −3.89580 −0.168588
$$535$$ 16.8934 + 35.4403i 0.730367 + 1.53222i
$$536$$ 21.1348 0.912886
$$537$$ 20.2829i 0.875270i
$$538$$ 7.37052i 0.317766i
$$539$$ −3.10549 −0.133763
$$540$$ 1.43587 + 3.01228i 0.0617901 + 0.129628i
$$541$$ −22.7032 −0.976085 −0.488043 0.872820i $$-0.662289\pi$$
−0.488043 + 0.872820i $$0.662289\pi$$
$$542$$ 6.95410i 0.298704i
$$543$$ 8.63783i 0.370685i
$$544$$ 11.1166 0.476622
$$545$$ −2.03812 + 0.971516i −0.0873035 + 0.0416152i
$$546$$ 1.54461 0.0661031
$$547$$ 32.8229i 1.40340i −0.712471 0.701702i $$-0.752424\pi$$
0.712471 0.701702i $$-0.247576\pi$$
$$548$$ 0.357843i 0.0152863i
$$549$$ 5.24905 0.224024
$$550$$ −11.8119 9.57474i −0.503660 0.408268i
$$551$$ 6.72036 0.286297
$$552$$ 5.40376i 0.229999i
$$553$$ 26.5352i 1.12839i
$$554$$ −1.33595 −0.0567590
$$555$$ −2.99546 + 1.42785i −0.127150 + 0.0606091i
$$556$$ 25.4080 1.07754
$$557$$ 26.3234i 1.11536i 0.830057 + 0.557679i $$0.188308\pi$$
−0.830057 + 0.557679i $$0.811692\pi$$
$$558$$ 6.28464i 0.266050i
$$559$$ 6.39189 0.270348
$$560$$ 3.24117 + 6.79958i 0.136965 + 0.287335i
$$561$$ 8.12458 0.343020
$$562$$ 15.1712i 0.639958i
$$563$$ 28.4750i 1.20008i −0.799971 0.600039i $$-0.795152\pi$$
0.799971 0.600039i $$-0.204848\pi$$
$$564$$ 7.75099 0.326375
$$565$$ −14.9891 31.4453i −0.630597 1.32291i
$$566$$ −11.3093 −0.475367
$$567$$ 2.77986i 0.116743i
$$568$$ 1.64999i 0.0692318i
$$569$$ 14.7555 0.618582 0.309291 0.950967i $$-0.399908\pi$$
0.309291 + 0.950967i $$0.399908\pi$$
$$570$$ 9.66493 4.60701i 0.404819 0.192966i
$$571$$ −0.204397 −0.00855376 −0.00427688 0.999991i $$-0.501361\pi$$
−0.00427688 + 0.999991i $$0.501361\pi$$
$$572$$ 4.96734i 0.207695i
$$573$$ 0.896850i 0.0374664i
$$574$$ −15.2784 −0.637708
$$575$$ 8.43519 + 6.83758i 0.351772 + 0.285147i
$$576$$ 1.73733 0.0723887
$$577$$ 37.3300i 1.55407i −0.629457 0.777035i $$-0.716723\pi$$
0.629457 0.777035i $$-0.283277\pi$$
$$578$$ 9.53071i 0.396425i
$$579$$ −10.4506 −0.434312
$$580$$ −3.01228 + 1.43587i −0.125078 + 0.0596213i
$$581$$ 0.0344697 0.00143004
$$582$$ 0.678299i 0.0281164i
$$583$$ 50.3014i 2.08327i
$$584$$ 41.1425 1.70249
$$585$$ −0.750341 1.57412i −0.0310228 0.0650820i
$$586$$ −23.6098 −0.975314
$$587$$ 10.8497i 0.447813i −0.974611 0.223907i $$-0.928119\pi$$
0.974611 0.223907i $$-0.0718811\pi$$
$$588$$ 1.08583i 0.0447789i
$$589$$ 59.2776 2.44249
$$590$$ −3.05765 6.41458i −0.125882 0.264084i
$$591$$ −9.57740 −0.393962
$$592$$ 1.79835i 0.0739119i
$$593$$ 14.0575i 0.577272i −0.957439 0.288636i $$-0.906798\pi$$
0.957439 0.288636i $$-0.0932018\pi$$
$$594$$ 3.04103 0.124775
$$595$$ −10.6809 + 5.09131i −0.437876 + 0.208723i
$$596$$ 6.16409 0.252491
$$597$$ 5.61768i 0.229916i
$$598$$ 1.20668i 0.0493448i
$$599$$ 5.52446 0.225724 0.112862 0.993611i $$-0.463998\pi$$
0.112862 + 0.993611i $$0.463998\pi$$
$$600$$ −7.83441 + 9.66493i −0.319838 + 0.394569i
$$601$$ −6.85394 −0.279578 −0.139789 0.990181i $$-0.544642\pi$$
−0.139789 + 0.990181i $$0.544642\pi$$
$$602$$ 16.2337i 0.661638i
$$603$$ 8.49375i 0.345892i
$$604$$ −4.79910 −0.195273
$$605$$ 14.5674 6.94387i 0.592248 0.282308i
$$606$$ −5.92640 −0.240743
$$607$$ 30.4979i 1.23787i 0.785442 + 0.618935i $$0.212436\pi$$
−0.785442 + 0.618935i $$0.787564\pi$$
$$608$$ 39.2467i 1.59166i
$$609$$ −2.77986 −0.112645
$$610$$ 3.59838 + 7.54895i 0.145694 + 0.305648i
$$611$$ −4.05042 −0.163863
$$612$$ 2.84075i 0.114831i
$$613$$ 29.9211i 1.20850i −0.796794 0.604250i $$-0.793473\pi$$
0.796794 0.604250i $$-0.206527\pi$$
$$614$$ 12.2980 0.496308
$$615$$ 7.42195 + 15.5703i 0.299282 + 0.627857i
$$616$$ 29.5230 1.18952
$$617$$ 1.04305i 0.0419917i −0.999780 0.0209959i $$-0.993316\pi$$
0.999780 0.0209959i $$-0.00668368\pi$$
$$618$$ 8.84145i 0.355655i
$$619$$ −22.1661 −0.890930 −0.445465 0.895299i $$-0.646962\pi$$
−0.445465 + 0.895299i $$0.646962\pi$$
$$620$$ −26.5701 + 12.6653i −1.06708 + 0.508649i
$$621$$ −2.17168 −0.0871465
$$622$$ 23.1643i 0.928805i
$$623$$ 15.1998i 0.608966i
$$624$$ 0.945039 0.0378318
$$625$$ −5.17364 24.4588i −0.206946 0.978352i
$$626$$ −4.46238 −0.178353
$$627$$ 28.6834i 1.14551i
$$628$$ 10.2112i 0.407472i
$$629$$ 2.82489 0.112636
$$630$$ −3.99787 + 1.90567i −0.159279 + 0.0759239i
$$631$$ 20.1089 0.800524 0.400262 0.916401i $$-0.368919\pi$$
0.400262 + 0.916401i $$0.368919\pi$$
$$632$$ 23.7520i 0.944804i
$$633$$ 0.605216i 0.0240552i
$$634$$ −13.4322 −0.533460
$$635$$ 16.3119 + 34.2204i 0.647319 + 1.35800i
$$636$$ −17.5878 −0.697403
$$637$$ 0.567422i 0.0224821i
$$638$$ 3.04103i 0.120395i
$$639$$ −0.663102 −0.0262319
$$640$$ −10.0469 21.0772i −0.397139 0.833149i
$$641$$ 5.93422 0.234388 0.117194 0.993109i $$-0.462610\pi$$
0.117194 + 0.993109i $$0.462610\pi$$
$$642$$ 12.5099i 0.493728i
$$643$$ 0.951317i 0.0375163i −0.999824 0.0187581i $$-0.994029\pi$$
0.999824 0.0187581i $$-0.00597125\pi$$
$$644$$ −9.00926 −0.355015
$$645$$ −16.5439 + 7.88604i −0.651417 + 0.310513i
$$646$$ −9.11458 −0.358608
$$647$$ 35.1384i 1.38143i −0.723126 0.690716i $$-0.757295\pi$$
0.723126 0.690716i $$-0.242705\pi$$
$$648$$ 2.48828i 0.0977490i
$$649$$ 19.0371 0.747271
$$650$$ 1.74945 2.15822i 0.0686192 0.0846522i
$$651$$ −24.5200 −0.961015
$$652$$ 20.9678i 0.821163i
$$653$$ 45.9930i 1.79984i 0.436050 + 0.899922i $$0.356377\pi$$
−0.436050 + 0.899922i $$0.643623\pi$$
$$654$$ 0.719428 0.0281319
$$655$$ 24.0852 11.4808i 0.941088 0.448591i
$$656$$ −9.34779 −0.364970
$$657$$ 16.5345i 0.645072i
$$658$$ 10.2870i 0.401030i
$$659$$ 19.3162 0.752451 0.376226 0.926528i $$-0.377222\pi$$
0.376226 + 0.926528i $$0.377222\pi$$
$$660$$ −6.12850 12.8568i −0.238551 0.500451i
$$661$$ 44.3224 1.72394 0.861970 0.506959i $$-0.169230\pi$$
0.861970 + 0.506959i $$0.169230\pi$$
$$662$$ 0.424821i 0.0165111i
$$663$$ 1.48449i 0.0576528i
$$664$$ −0.0308542 −0.00119738
$$665$$ −17.9746 37.7085i −0.697025 1.46227i
$$666$$ 1.05736 0.0409717
$$667$$ 2.17168i 0.0840878i
$$668$$ 26.6720i 1.03197i
$$669$$ 16.5537 0.640004
$$670$$ 12.2153 5.82272i 0.471920 0.224951i
$$671$$ −22.4037 −0.864883
$$672$$ 16.2343i 0.626251i
$$673$$ 12.7421i 0.491170i −0.969375 0.245585i $$-0.921020\pi$$
0.969375 0.245585i $$-0.0789801\pi$$
$$674$$ 23.2569 0.895821
$$675$$ 3.88418 + 3.14852i 0.149502 + 0.121187i
$$676$$ 18.4930 0.711267
$$677$$ 9.41654i 0.361907i −0.983492 0.180954i $$-0.942082\pi$$
0.983492 0.180954i $$-0.0579184\pi$$
$$678$$ 11.0997i 0.426283i
$$679$$ −2.64644 −0.101561
$$680$$ 9.56063 4.55729i 0.366634 0.174764i
$$681$$ 22.0061 0.843276
$$682$$ 26.8237i 1.02713i
$$683$$ 6.92316i 0.264907i −0.991189 0.132454i $$-0.957714\pi$$
0.991189 0.132454i $$-0.0422856\pi$$
$$684$$ 10.0291 0.383473
$$685$$ 0.230710 + 0.484001i 0.00881497 + 0.0184927i
$$686$$ 12.4233 0.474325
$$687$$ 24.5647i 0.937202i
$$688$$ 9.93231i 0.378666i
$$689$$ 9.19085 0.350144
$$690$$ −1.48875 3.12322i −0.0566758 0.118899i
$$691$$ −48.7272 −1.85367 −0.926835 0.375469i $$-0.877482\pi$$
−0.926835 + 0.375469i $$0.877482\pi$$
$$692$$ 4.21616i 0.160274i
$$693$$ 11.8648i 0.450707i
$$694$$ −9.40384 −0.356965
$$695$$ 34.3655 16.3811i 1.30356 0.621371i
$$696$$ 2.48828 0.0943181
$$697$$ 14.6837i 0.556186i
$$698$$ 11.1443i 0.421818i
$$699$$ −5.56824 −0.210610
$$700$$ 16.1136 + 13.0617i 0.609036 + 0.493686i
$$701$$ 2.88580 0.108995 0.0544975 0.998514i $$-0.482644\pi$$
0.0544975 + 0.998514i $$0.482644\pi$$
$$702$$ 0.555643i 0.0209714i
$$703$$ 9.97314i 0.376144i
$$704$$ −7.41516 −0.279469
$$705$$ 10.4836 4.99725i 0.394835 0.188207i
$$706$$ 4.02906 0.151636
$$707$$ 23.1223i 0.869604i
$$708$$ 6.65630i 0.250159i
$$709$$ 1.73056 0.0649924 0.0324962 0.999472i $$-0.489654\pi$$
0.0324962 + 0.999472i $$0.489654\pi$$
$$710$$ −0.454576 0.953645i −0.0170599 0.0357896i
$$711$$ 9.54554 0.357986
$$712$$ 13.6055i 0.509887i
$$713$$ 19.1555i 0.717381i
$$714$$ 3.77022 0.141097
$$715$$ 3.20256 + 6.71857i 0.119769 + 0.251260i
$$716$$ −30.2692 −1.13121
$$717$$ 6.90640i 0.257924i
$$718$$ 18.0043i 0.671913i
$$719$$ 12.9089 0.481420 0.240710 0.970597i $$-0.422620\pi$$
0.240710 + 0.970597i $$0.422620\pi$$
$$720$$ −2.44602 + 1.16595i −0.0911577 + 0.0434524i
$$721$$ −34.4956 −1.28468
$$722$$ 18.6412i 0.693752i
$$723$$ 25.1989i 0.937158i
$$724$$ −12.8907 −0.479078
$$725$$ −3.14852 + 3.88418i −0.116933 + 0.144255i
$$726$$ −5.14208 −0.190841
$$727$$ 38.3405i 1.42197i −0.703207 0.710985i $$-0.748249\pi$$
0.703207 0.710985i $$-0.251751\pi$$
$$728$$ 5.39431i 0.199927i
$$729$$ −1.00000 −0.0370370
$$730$$ 23.7792 11.3349i 0.880108 0.419523i
$$731$$ 15.6019 0.577057
$$732$$ 7.83342i 0.289531i
$$733$$ 34.8966i 1.28894i 0.764631 + 0.644468i $$0.222921\pi$$
−0.764631 + 0.644468i $$0.777079\pi$$
$$734$$ −18.7235 −0.691098
$$735$$ 0.700061 + 1.46864i 0.0258222 + 0.0541717i
$$736$$ 12.6826 0.467485
$$737$$ 36.2525i 1.33538i
$$738$$ 5.49611i 0.202315i
$$739$$ −14.2969 −0.525921 −0.262960 0.964807i $$-0.584699\pi$$
−0.262960 + 0.964807i $$0.584699\pi$$
$$740$$ −2.13086 4.47028i −0.0783320 0.164331i
$$741$$ −5.24091 −0.192530
$$742$$ 23.3424i 0.856927i
$$743$$ 44.1357i 1.61918i 0.586995 + 0.809591i $$0.300311\pi$$
−0.586995 + 0.809591i $$0.699689\pi$$
$$744$$ 21.9482 0.804659
$$745$$ 8.33725 3.97414i 0.305453 0.145601i
$$746$$ 1.01910 0.0373120
$$747$$ 0.0123998i 0.000453685i
$$748$$ 12.1247i 0.443324i
$$749$$ −48.8085 −1.78343
$$750$$ −1.86535 + 7.74446i −0.0681128 + 0.282788i
$$751$$ 9.56375 0.348986 0.174493 0.984658i $$-0.444171\pi$$
0.174493 + 0.984658i $$0.444171\pi$$
$$752$$ 6.29393i 0.229516i
$$753$$ 28.3687i 1.03381i
$$754$$ −0.555643 −0.0202353
$$755$$ −6.49103 + 3.09410i −0.236233 + 0.112606i
$$756$$ −4.14852 −0.150880
$$757$$ 30.1910i 1.09731i 0.836048 + 0.548656i $$0.184860\pi$$
−0.836048 + 0.548656i $$0.815140\pi$$
$$758$$ 25.1038i 0.911811i
$$759$$ 9.26903 0.336445
$$760$$ 16.0893 + 33.7533i 0.583619 + 1.22436i
$$761$$ 8.27038 0.299801 0.149900 0.988701i $$-0.452105\pi$$
0.149900 + 0.988701i $$0.452105\pi$$
$$762$$ 12.0793i 0.437588i
$$763$$ 2.80690i 0.101617i
$$764$$ 1.33841 0.0484221
$$765$$ −1.83150 3.84226i −0.0662180 0.138917i
$$766$$ 22.8498 0.825595
$$767$$ 3.47837i 0.125597i
$$768$$ 10.9146i 0.393847i
$$769$$ 22.4592 0.809901 0.404950 0.914339i $$-0.367289\pi$$
0.404950 + 0.914339i $$0.367289\pi$$
$$770$$ 17.0635 8.13368i 0.614924 0.293118i
$$771$$ −8.71100 −0.313719
$$772$$ 15.5960i 0.561311i
$$773$$ 26.9520i 0.969398i 0.874681 + 0.484699i $$0.161071\pi$$
−0.874681 + 0.484699i $$0.838929\pi$$
$$774$$ 5.83978 0.209907
$$775$$ −27.7719 + 34.2608i −0.997595 + 1.23068i
$$776$$ 2.36886 0.0850371
$$777$$ 4.12536i 0.147996i
$$778$$ 1.16794i 0.0418725i
$$779$$ 51.8401 1.85737
$$780$$ 2.34914 1.11977i 0.0841128 0.0400943i
$$781$$ 2.83021 0.101273