Properties

 Label 380.2.k.c.343.4 Level $380$ Weight $2$ Character 380.343 Analytic conductor $3.034$ Analytic rank $0$ Dimension $52$ CM no Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.k (of order $$4$$, degree $$2$$, 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: $$3.03431527681$$ Analytic rank: $$0$$ Dimension: $$52$$ Relative dimension: $$26$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

 Embedding label 343.4 Character $$\chi$$ $$=$$ 380.343 Dual form 380.2.k.c.267.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.34620 - 0.433304i) q^{2} +(-0.497882 + 0.497882i) q^{3} +(1.62450 + 1.16662i) q^{4} +(-2.01079 + 0.978129i) q^{5} +(0.885982 - 0.454514i) q^{6} +(2.91849 + 2.91849i) q^{7} +(-1.68139 - 2.27441i) q^{8} +2.50423i q^{9} +O(q^{10})$$ $$q+(-1.34620 - 0.433304i) q^{2} +(-0.497882 + 0.497882i) q^{3} +(1.62450 + 1.16662i) q^{4} +(-2.01079 + 0.978129i) q^{5} +(0.885982 - 0.454514i) q^{6} +(2.91849 + 2.91849i) q^{7} +(-1.68139 - 2.27441i) q^{8} +2.50423i q^{9} +(3.13074 - 0.445474i) q^{10} -3.58797i q^{11} +(-1.38965 + 0.227966i) q^{12} +(-3.29878 - 3.29878i) q^{13} +(-2.66427 - 5.19345i) q^{14} +(0.514142 - 1.48813i) q^{15} +(1.27798 + 3.79035i) q^{16} +(-4.60467 + 4.60467i) q^{17} +(1.08509 - 3.37118i) q^{18} +1.00000 q^{19} +(-4.40762 - 0.756866i) q^{20} -2.90613 q^{21} +(-1.55468 + 4.83012i) q^{22} +(-3.51712 + 3.51712i) q^{23} +(1.96952 + 0.295252i) q^{24} +(3.08653 - 3.93362i) q^{25} +(3.01144 + 5.87018i) q^{26} +(-2.74046 - 2.74046i) q^{27} +(1.33629 + 8.14585i) q^{28} +4.88207i q^{29} +(-1.33695 + 1.78054i) q^{30} -1.57175i q^{31} +(-0.0780338 - 5.65632i) q^{32} +(1.78639 + 1.78639i) q^{33} +(8.19402 - 4.20358i) q^{34} +(-8.72312 - 3.01380i) q^{35} +(-2.92149 + 4.06811i) q^{36} +(-5.48286 + 5.48286i) q^{37} +(-1.34620 - 0.433304i) q^{38} +3.28481 q^{39} +(5.60558 + 2.92873i) q^{40} -3.69344 q^{41} +(3.91222 + 1.25924i) q^{42} +(-4.56114 + 4.56114i) q^{43} +(4.18582 - 5.82865i) q^{44} +(-2.44946 - 5.03546i) q^{45} +(6.25872 - 3.21076i) q^{46} +(-1.60126 - 1.60126i) q^{47} +(-2.52343 - 1.25087i) q^{48} +10.0352i q^{49} +(-5.85953 + 3.95803i) q^{50} -4.58517i q^{51} +(-1.51042 - 9.20729i) q^{52} +(2.12363 + 2.12363i) q^{53} +(2.50175 + 4.87665i) q^{54} +(3.50950 + 7.21465i) q^{55} +(1.73071 - 11.5450i) q^{56} +(-0.497882 + 0.497882i) q^{57} +(2.11542 - 6.57224i) q^{58} +5.91948 q^{59} +(2.57131 - 1.81765i) q^{60} +0.536052 q^{61} +(-0.681045 + 2.11589i) q^{62} +(-7.30856 + 7.30856i) q^{63} +(-2.34585 + 7.64833i) q^{64} +(9.85977 + 3.40651i) q^{65} +(-1.63078 - 3.17888i) q^{66} +(-1.64255 - 1.64255i) q^{67} +(-12.8522 + 2.10835i) q^{68} -3.50222i q^{69} +(10.4372 + 7.83693i) q^{70} +4.08253i q^{71} +(5.69563 - 4.21058i) q^{72} +(-0.480968 - 0.480968i) q^{73} +(9.75675 - 5.00527i) q^{74} +(0.421752 + 3.49521i) q^{75} +(1.62450 + 1.16662i) q^{76} +(10.4715 - 10.4715i) q^{77} +(-4.42200 - 1.42332i) q^{78} -3.35832 q^{79} +(-6.27719 - 6.37157i) q^{80} -4.78383 q^{81} +(4.97210 + 1.60038i) q^{82} +(12.4301 - 12.4301i) q^{83} +(-4.72100 - 3.39036i) q^{84} +(4.75505 - 13.7630i) q^{85} +(8.11656 - 4.16384i) q^{86} +(-2.43070 - 2.43070i) q^{87} +(-8.16051 + 6.03279i) q^{88} -11.9105i q^{89} +(1.11557 + 7.84009i) q^{90} -19.2549i q^{91} +(-9.81671 + 1.61039i) q^{92} +(0.782547 + 0.782547i) q^{93} +(1.46178 + 2.84945i) q^{94} +(-2.01079 + 0.978129i) q^{95} +(2.85503 + 2.77733i) q^{96} +(-6.21450 + 6.21450i) q^{97} +(4.34827 - 13.5093i) q^{98} +8.98510 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10})$$ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 $$52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100})$$ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$77$$ $$191$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.34620 0.433304i −0.951905 0.306392i
$$3$$ −0.497882 + 0.497882i −0.287453 + 0.287453i −0.836072 0.548620i $$-0.815154\pi$$
0.548620 + 0.836072i $$0.315154\pi$$
$$4$$ 1.62450 + 1.16662i 0.812248 + 0.583312i
$$5$$ −2.01079 + 0.978129i −0.899251 + 0.437433i
$$6$$ 0.885982 0.454514i 0.361701 0.185555i
$$7$$ 2.91849 + 2.91849i 1.10309 + 1.10309i 0.994036 + 0.109049i $$0.0347805\pi$$
0.109049 + 0.994036i $$0.465220\pi$$
$$8$$ −1.68139 2.27441i −0.594461 0.804124i
$$9$$ 2.50423i 0.834742i
$$10$$ 3.13074 0.445474i 0.990028 0.140871i
$$11$$ 3.58797i 1.08182i −0.841082 0.540908i $$-0.818081\pi$$
0.841082 0.540908i $$-0.181919\pi$$
$$12$$ −1.38965 + 0.227966i −0.401157 + 0.0658082i
$$13$$ −3.29878 3.29878i −0.914917 0.914917i 0.0817371 0.996654i $$-0.473953\pi$$
−0.996654 + 0.0817371i $$0.973953\pi$$
$$14$$ −2.66427 5.19345i −0.712056 1.38801i
$$15$$ 0.514142 1.48813i 0.132751 0.384233i
$$16$$ 1.27798 + 3.79035i 0.319494 + 0.947588i
$$17$$ −4.60467 + 4.60467i −1.11680 + 1.11680i −0.124589 + 0.992208i $$0.539761\pi$$
−0.992208 + 0.124589i $$0.960239\pi$$
$$18$$ 1.08509 3.37118i 0.255758 0.794596i
$$19$$ 1.00000 0.229416
$$20$$ −4.40762 0.756866i −0.985575 0.169240i
$$21$$ −2.90613 −0.634169
$$22$$ −1.55468 + 4.83012i −0.331459 + 1.02979i
$$23$$ −3.51712 + 3.51712i −0.733370 + 0.733370i −0.971286 0.237916i $$-0.923536\pi$$
0.237916 + 0.971286i $$0.423536\pi$$
$$24$$ 1.96952 + 0.295252i 0.402027 + 0.0602682i
$$25$$ 3.08653 3.93362i 0.617305 0.786724i
$$26$$ 3.01144 + 5.87018i 0.590591 + 1.15124i
$$27$$ −2.74046 2.74046i −0.527401 0.527401i
$$28$$ 1.33629 + 8.14585i 0.252536 + 1.53942i
$$29$$ 4.88207i 0.906578i 0.891364 + 0.453289i $$0.149749\pi$$
−0.891364 + 0.453289i $$0.850251\pi$$
$$30$$ −1.33695 + 1.78054i −0.244092 + 0.325080i
$$31$$ 1.57175i 0.282295i −0.989989 0.141147i $$-0.954921\pi$$
0.989989 0.141147i $$-0.0450791\pi$$
$$32$$ −0.0780338 5.65632i −0.0137946 0.999905i
$$33$$ 1.78639 + 1.78639i 0.310971 + 0.310971i
$$34$$ 8.19402 4.20358i 1.40526 0.720908i
$$35$$ −8.72312 3.01380i −1.47448 0.509425i
$$36$$ −2.92149 + 4.06811i −0.486915 + 0.678018i
$$37$$ −5.48286 + 5.48286i −0.901376 + 0.901376i −0.995555 0.0941788i $$-0.969977\pi$$
0.0941788 + 0.995555i $$0.469977\pi$$
$$38$$ −1.34620 0.433304i −0.218382 0.0702911i
$$39$$ 3.28481 0.525990
$$40$$ 5.60558 + 2.92873i 0.886320 + 0.463073i
$$41$$ −3.69344 −0.576819 −0.288409 0.957507i $$-0.593126\pi$$
−0.288409 + 0.957507i $$0.593126\pi$$
$$42$$ 3.91222 + 1.25924i 0.603669 + 0.194304i
$$43$$ −4.56114 + 4.56114i −0.695568 + 0.695568i −0.963451 0.267884i $$-0.913676\pi$$
0.267884 + 0.963451i $$0.413676\pi$$
$$44$$ 4.18582 5.82865i 0.631036 0.878702i
$$45$$ −2.44946 5.03546i −0.365143 0.750643i
$$46$$ 6.25872 3.21076i 0.922798 0.473400i
$$47$$ −1.60126 1.60126i −0.233568 0.233568i 0.580612 0.814180i $$-0.302813\pi$$
−0.814180 + 0.580612i $$0.802813\pi$$
$$48$$ −2.52343 1.25087i −0.364226 0.180547i
$$49$$ 10.0352i 1.43359i
$$50$$ −5.85953 + 3.95803i −0.828662 + 0.559749i
$$51$$ 4.58517i 0.642053i
$$52$$ −1.51042 9.20729i −0.209457 1.27682i
$$53$$ 2.12363 + 2.12363i 0.291703 + 0.291703i 0.837753 0.546050i $$-0.183869\pi$$
−0.546050 + 0.837753i $$0.683869\pi$$
$$54$$ 2.50175 + 4.87665i 0.340445 + 0.663628i
$$55$$ 3.50950 + 7.21465i 0.473221 + 0.972824i
$$56$$ 1.73071 11.5450i 0.231276 1.54276i
$$57$$ −0.497882 + 0.497882i −0.0659461 + 0.0659461i
$$58$$ 2.11542 6.57224i 0.277768 0.862977i
$$59$$ 5.91948 0.770651 0.385325 0.922781i $$-0.374089\pi$$
0.385325 + 0.922781i $$0.374089\pi$$
$$60$$ 2.57131 1.81765i 0.331955 0.234657i
$$61$$ 0.536052 0.0686345 0.0343172 0.999411i $$-0.489074\pi$$
0.0343172 + 0.999411i $$0.489074\pi$$
$$62$$ −0.681045 + 2.11589i −0.0864928 + 0.268718i
$$63$$ −7.30856 + 7.30856i −0.920792 + 0.920792i
$$64$$ −2.34585 + 7.64833i −0.293232 + 0.956041i
$$65$$ 9.85977 + 3.40651i 1.22295 + 0.422525i
$$66$$ −1.63078 3.17888i −0.200736 0.391293i
$$67$$ −1.64255 1.64255i −0.200669 0.200669i 0.599617 0.800287i $$-0.295319\pi$$
−0.800287 + 0.599617i $$0.795319\pi$$
$$68$$ −12.8522 + 2.10835i −1.55856 + 0.255675i
$$69$$ 3.50222i 0.421618i
$$70$$ 10.4372 + 7.83693i 1.24748 + 0.936692i
$$71$$ 4.08253i 0.484507i 0.970213 + 0.242254i $$0.0778866\pi$$
−0.970213 + 0.242254i $$0.922113\pi$$
$$72$$ 5.69563 4.21058i 0.671236 0.496222i
$$73$$ −0.480968 0.480968i −0.0562930 0.0562930i 0.678400 0.734693i $$-0.262674\pi$$
−0.734693 + 0.678400i $$0.762674\pi$$
$$74$$ 9.75675 5.00527i 1.13420 0.581851i
$$75$$ 0.421752 + 3.49521i 0.0486998 + 0.403592i
$$76$$ 1.62450 + 1.16662i 0.186342 + 0.133821i
$$77$$ 10.4715 10.4715i 1.19333 1.19333i
$$78$$ −4.42200 1.42332i −0.500693 0.161159i
$$79$$ −3.35832 −0.377841 −0.188920 0.981992i $$-0.560499\pi$$
−0.188920 + 0.981992i $$0.560499\pi$$
$$80$$ −6.27719 6.37157i −0.701811 0.712363i
$$81$$ −4.78383 −0.531536
$$82$$ 4.97210 + 1.60038i 0.549077 + 0.176733i
$$83$$ 12.4301 12.4301i 1.36439 1.36439i 0.496147 0.868238i $$-0.334748\pi$$
0.868238 0.496147i $$-0.165252\pi$$
$$84$$ −4.72100 3.39036i −0.515103 0.369919i
$$85$$ 4.75505 13.7630i 0.515758 1.49281i
$$86$$ 8.11656 4.16384i 0.875231 0.448998i
$$87$$ −2.43070 2.43070i −0.260598 0.260598i
$$88$$ −8.16051 + 6.03279i −0.869914 + 0.643097i
$$89$$ 11.9105i 1.26251i −0.775575 0.631256i $$-0.782540\pi$$
0.775575 0.631256i $$-0.217460\pi$$
$$90$$ 1.11557 + 7.84009i 0.117591 + 0.826418i
$$91$$ 19.2549i 2.01846i
$$92$$ −9.81671 + 1.61039i −1.02346 + 0.167895i
$$93$$ 0.782547 + 0.782547i 0.0811463 + 0.0811463i
$$94$$ 1.46178 + 2.84945i 0.150771 + 0.293898i
$$95$$ −2.01079 + 0.978129i −0.206302 + 0.100354i
$$96$$ 2.85503 + 2.77733i 0.291391 + 0.283460i
$$97$$ −6.21450 + 6.21450i −0.630986 + 0.630986i −0.948316 0.317329i $$-0.897214\pi$$
0.317329 + 0.948316i $$0.397214\pi$$
$$98$$ 4.34827 13.5093i 0.439241 1.36465i
$$99$$ 8.98510 0.903037
$$100$$ 9.60311 2.78933i 0.960311 0.278933i
$$101$$ 2.22532 0.221427 0.110714 0.993852i $$-0.464686\pi$$
0.110714 + 0.993852i $$0.464686\pi$$
$$102$$ −1.98677 + 6.17255i −0.196720 + 0.611173i
$$103$$ 7.89357 7.89357i 0.777777 0.777777i −0.201676 0.979452i $$-0.564639\pi$$
0.979452 + 0.201676i $$0.0646387\pi$$
$$104$$ −1.95623 + 13.0493i −0.191824 + 1.27959i
$$105$$ 5.84361 2.84257i 0.570278 0.277406i
$$106$$ −1.93865 3.77900i −0.188298 0.367049i
$$107$$ 4.37844 + 4.37844i 0.423280 + 0.423280i 0.886331 0.463052i $$-0.153246\pi$$
−0.463052 + 0.886331i $$0.653246\pi$$
$$108$$ −1.25478 7.64895i −0.120741 0.736020i
$$109$$ 10.5140i 1.00706i 0.863978 + 0.503530i $$0.167966\pi$$
−0.863978 + 0.503530i $$0.832034\pi$$
$$110$$ −1.59835 11.2330i −0.152397 1.07103i
$$111$$ 5.45964i 0.518206i
$$112$$ −7.33235 + 14.7919i −0.692842 + 1.39770i
$$113$$ 9.63168 + 9.63168i 0.906072 + 0.906072i 0.995953 0.0898805i $$-0.0286485\pi$$
−0.0898805 + 0.995953i $$0.528649\pi$$
$$114$$ 0.885982 0.454514i 0.0829799 0.0425691i
$$115$$ 3.63198 10.5124i 0.338684 0.980284i
$$116$$ −5.69555 + 7.93091i −0.528818 + 0.736366i
$$117$$ 8.26089 8.26089i 0.763720 0.763720i
$$118$$ −7.96879 2.56493i −0.733587 0.236121i
$$119$$ −26.8774 −2.46385
$$120$$ −4.24908 + 1.33276i −0.387887 + 0.121664i
$$121$$ −1.87356 −0.170324
$$122$$ −0.721632 0.232273i −0.0653335 0.0210290i
$$123$$ 1.83890 1.83890i 0.165808 0.165808i
$$124$$ 1.83364 2.55330i 0.164666 0.229293i
$$125$$ −2.35876 + 10.9287i −0.210974 + 0.977492i
$$126$$ 13.0056 6.67194i 1.15863 0.594383i
$$127$$ 12.4921 + 12.4921i 1.10850 + 1.10850i 0.993348 + 0.115151i $$0.0367351\pi$$
0.115151 + 0.993348i $$0.463265\pi$$
$$128$$ 6.47203 9.27970i 0.572052 0.820217i
$$129$$ 4.54183i 0.399886i
$$130$$ −11.7972 8.85811i −1.03468 0.776908i
$$131$$ 6.66390i 0.582227i 0.956688 + 0.291114i $$0.0940258\pi$$
−0.956688 + 0.291114i $$0.905974\pi$$
$$132$$ 0.817937 + 4.98603i 0.0711923 + 0.433978i
$$133$$ 2.91849 + 2.91849i 0.253065 + 0.253065i
$$134$$ 1.49947 + 2.92292i 0.129535 + 0.252502i
$$135$$ 8.19100 + 2.82995i 0.704969 + 0.243564i
$$136$$ 18.2152 + 2.73065i 1.56194 + 0.234151i
$$137$$ 6.64153 6.64153i 0.567424 0.567424i −0.363982 0.931406i $$-0.618583\pi$$
0.931406 + 0.363982i $$0.118583\pi$$
$$138$$ −1.51753 + 4.71469i −0.129180 + 0.401341i
$$139$$ 6.81147 0.577741 0.288871 0.957368i $$-0.406720\pi$$
0.288871 + 0.957368i $$0.406720\pi$$
$$140$$ −10.6547 15.0725i −0.900487 1.27386i
$$141$$ 1.59448 0.134280
$$142$$ 1.76897 5.49589i 0.148449 0.461205i
$$143$$ −11.8359 + 11.8359i −0.989771 + 0.989771i
$$144$$ −9.49190 + 3.20034i −0.790992 + 0.266695i
$$145$$ −4.77530 9.81681i −0.396567 0.815241i
$$146$$ 0.439072 + 0.855882i 0.0363379 + 0.0708333i
$$147$$ −4.99633 4.99633i −0.412090 0.412090i
$$148$$ −15.3033 + 2.51045i −1.25793 + 0.206357i
$$149$$ 19.0682i 1.56212i 0.624453 + 0.781062i $$0.285322\pi$$
−0.624453 + 0.781062i $$0.714678\pi$$
$$150$$ 0.946723 4.88799i 0.0772996 0.399102i
$$151$$ 6.08117i 0.494879i 0.968903 + 0.247439i $$0.0795891\pi$$
−0.968903 + 0.247439i $$0.920411\pi$$
$$152$$ −1.68139 2.27441i −0.136379 0.184479i
$$153$$ −11.5311 11.5311i −0.932238 0.932238i
$$154$$ −18.6340 + 9.55934i −1.50157 + 0.770313i
$$155$$ 1.53737 + 3.16045i 0.123485 + 0.253854i
$$156$$ 5.33616 + 3.83214i 0.427235 + 0.306817i
$$157$$ 7.46797 7.46797i 0.596009 0.596009i −0.343239 0.939248i $$-0.611524\pi$$
0.939248 + 0.343239i $$0.111524\pi$$
$$158$$ 4.52096 + 1.45517i 0.359668 + 0.115767i
$$159$$ −2.11464 −0.167702
$$160$$ 5.68952 + 11.2973i 0.449796 + 0.893131i
$$161$$ −20.5294 −1.61794
$$162$$ 6.43998 + 2.07285i 0.505972 + 0.162858i
$$163$$ −10.0388 + 10.0388i −0.786297 + 0.786297i −0.980885 0.194588i $$-0.937663\pi$$
0.194588 + 0.980885i $$0.437663\pi$$
$$164$$ −5.99998 4.30886i −0.468520 0.336466i
$$165$$ −5.33937 1.84473i −0.415669 0.143612i
$$166$$ −22.1195 + 11.3474i −1.71680 + 0.880730i
$$167$$ 16.5343 + 16.5343i 1.27946 + 1.27946i 0.940968 + 0.338497i $$0.109918\pi$$
0.338497 + 0.940968i $$0.390082\pi$$
$$168$$ 4.88634 + 6.60972i 0.376989 + 0.509951i
$$169$$ 8.76389i 0.674146i
$$170$$ −12.3648 + 16.4673i −0.948336 + 1.26299i
$$171$$ 2.50423i 0.191503i
$$172$$ −12.7307 + 2.08842i −0.970707 + 0.159240i
$$173$$ 5.32723 + 5.32723i 0.405022 + 0.405022i 0.879998 0.474977i $$-0.157543\pi$$
−0.474977 + 0.879998i $$0.657543\pi$$
$$174$$ 2.21897 + 4.32543i 0.168220 + 0.327910i
$$175$$ 20.4882 2.47223i 1.54876 0.186883i
$$176$$ 13.5997 4.58534i 1.02512 0.345633i
$$177$$ −2.94721 + 2.94721i −0.221526 + 0.221526i
$$178$$ −5.16086 + 16.0339i −0.386823 + 1.20179i
$$179$$ −13.0819 −0.977785 −0.488893 0.872344i $$-0.662599\pi$$
−0.488893 + 0.872344i $$0.662599\pi$$
$$180$$ 1.89536 11.0377i 0.141272 0.822701i
$$181$$ −17.1592 −1.27543 −0.637717 0.770271i $$-0.720121\pi$$
−0.637717 + 0.770271i $$0.720121\pi$$
$$182$$ −8.34322 + 25.9209i −0.618440 + 1.92139i
$$183$$ −0.266891 + 0.266891i −0.0197292 + 0.0197292i
$$184$$ 13.9130 + 2.08571i 1.02568 + 0.153761i
$$185$$ 5.66192 16.3878i 0.416272 1.20486i
$$186$$ −0.714382 1.39254i −0.0523811 0.102106i
$$187$$ 16.5215 + 16.5215i 1.20817 + 1.20817i
$$188$$ −0.733173 4.46932i −0.0534721 0.325958i
$$189$$ 15.9960i 1.16354i
$$190$$ 3.13074 0.445474i 0.227128 0.0323181i
$$191$$ 15.3156i 1.10820i 0.832451 + 0.554098i $$0.186937\pi$$
−0.832451 + 0.554098i $$0.813063\pi$$
$$192$$ −2.64001 4.97593i −0.190526 0.359107i
$$193$$ −12.7493 12.7493i −0.917717 0.917717i 0.0791463 0.996863i $$-0.474781\pi$$
−0.996863 + 0.0791463i $$0.974781\pi$$
$$194$$ 11.0587 5.67318i 0.793969 0.407310i
$$195$$ −6.60505 + 3.21297i −0.472997 + 0.230085i
$$196$$ −11.7073 + 16.3021i −0.836233 + 1.16443i
$$197$$ 9.97667 9.97667i 0.710808 0.710808i −0.255896 0.966704i $$-0.582370\pi$$
0.966704 + 0.255896i $$0.0823705\pi$$
$$198$$ −12.0957 3.89328i −0.859605 0.276683i
$$199$$ −4.22544 −0.299533 −0.149767 0.988721i $$-0.547852\pi$$
−0.149767 + 0.988721i $$0.547852\pi$$
$$200$$ −14.1363 0.406068i −0.999588 0.0287133i
$$201$$ 1.63559 0.115366
$$202$$ −2.99572 0.964238i −0.210778 0.0678436i
$$203$$ −14.2483 + 14.2483i −1.00003 + 1.00003i
$$204$$ 5.34917 7.44860i 0.374517 0.521506i
$$205$$ 7.42673 3.61267i 0.518705 0.252319i
$$206$$ −14.0466 + 7.20600i −0.978675 + 0.502066i
$$207$$ −8.80766 8.80766i −0.612175 0.612175i
$$208$$ 8.28778 16.7193i 0.574654 1.15927i
$$209$$ 3.58797i 0.248185i
$$210$$ −9.09834 + 1.29461i −0.627845 + 0.0893363i
$$211$$ 12.8281i 0.883120i −0.897232 0.441560i $$-0.854425\pi$$
0.897232 0.441560i $$-0.145575\pi$$
$$212$$ 0.972350 + 5.92731i 0.0667813 + 0.407089i
$$213$$ −2.03262 2.03262i −0.139273 0.139273i
$$214$$ −3.99705 7.79144i −0.273233 0.532612i
$$215$$ 4.71010 13.6329i 0.321226 0.929754i
$$216$$ −1.62514 + 10.8407i −0.110577 + 0.737616i
$$217$$ 4.58714 4.58714i 0.311395 0.311395i
$$218$$ 4.55576 14.1540i 0.308555 0.958627i
$$219$$ 0.478931 0.0323631
$$220$$ −2.71561 + 15.8144i −0.183087 + 1.06621i
$$221$$ 30.3796 2.04355
$$222$$ −2.36568 + 7.34975i −0.158774 + 0.493283i
$$223$$ 13.4531 13.4531i 0.900887 0.900887i −0.0946261 0.995513i $$-0.530166\pi$$
0.995513 + 0.0946261i $$0.0301655\pi$$
$$224$$ 16.2802 16.7356i 1.08776 1.11820i
$$225$$ 9.85067 + 7.72936i 0.656711 + 0.515291i
$$226$$ −8.79270 17.1396i −0.584882 1.14011i
$$227$$ −14.9994 14.9994i −0.995546 0.995546i 0.00444394 0.999990i $$-0.498585\pi$$
−0.999990 + 0.00444394i $$0.998585\pi$$
$$228$$ −1.38965 + 0.227966i −0.0920318 + 0.0150974i
$$229$$ 21.4928i 1.42028i 0.704059 + 0.710141i $$0.251369\pi$$
−0.704059 + 0.710141i $$0.748631\pi$$
$$230$$ −9.44441 + 12.5780i −0.622746 + 0.829368i
$$231$$ 10.4271i 0.686054i
$$232$$ 11.1038 8.20867i 0.729001 0.538926i
$$233$$ −1.81711 1.81711i −0.119043 0.119043i 0.645076 0.764119i $$-0.276826\pi$$
−0.764119 + 0.645076i $$0.776826\pi$$
$$234$$ −14.7003 + 7.54132i −0.960986 + 0.492991i
$$235$$ 4.78604 + 1.65356i 0.312207 + 0.107866i
$$236$$ 9.61617 + 6.90581i 0.625960 + 0.449530i
$$237$$ 1.67205 1.67205i 0.108611 0.108611i
$$238$$ 36.1823 + 11.6461i 2.34535 + 0.754902i
$$239$$ 22.8925 1.48079 0.740396 0.672171i $$-0.234638\pi$$
0.740396 + 0.672171i $$0.234638\pi$$
$$240$$ 6.29760 + 0.0469882i 0.406508 + 0.00303307i
$$241$$ 14.0297 0.903729 0.451865 0.892086i $$-0.350759\pi$$
0.451865 + 0.892086i $$0.350759\pi$$
$$242$$ 2.52219 + 0.811822i 0.162132 + 0.0521859i
$$243$$ 10.6032 10.6032i 0.680193 0.680193i
$$244$$ 0.870815 + 0.625372i 0.0557482 + 0.0400353i
$$245$$ −9.81568 20.1786i −0.627101 1.28916i
$$246$$ −3.27233 + 1.67872i −0.208636 + 0.107031i
$$247$$ −3.29878 3.29878i −0.209896 0.209896i
$$248$$ −3.57480 + 2.64273i −0.227000 + 0.167813i
$$249$$ 12.3775i 0.784392i
$$250$$ 7.91079 13.6901i 0.500323 0.865839i
$$251$$ 5.28898i 0.333838i −0.985971 0.166919i $$-0.946618\pi$$
0.985971 0.166919i $$-0.0533818\pi$$
$$252$$ −20.3991 + 3.34638i −1.28502 + 0.210802i
$$253$$ 12.6193 + 12.6193i 0.793371 + 0.793371i
$$254$$ −11.4040 22.2298i −0.715551 1.39482i
$$255$$ 4.48489 + 9.21980i 0.280855 + 0.577367i
$$256$$ −12.7336 + 9.68796i −0.795847 + 0.605497i
$$257$$ −14.1338 + 14.1338i −0.881643 + 0.881643i −0.993702 0.112058i $$-0.964256\pi$$
0.112058 + 0.993702i $$0.464256\pi$$
$$258$$ −1.96799 + 6.11420i −0.122522 + 0.380653i
$$259$$ −32.0033 −1.98859
$$260$$ 12.0430 + 17.0365i 0.746878 + 1.05656i
$$261$$ −12.2258 −0.756759
$$262$$ 2.88749 8.97092i 0.178390 0.554225i
$$263$$ −13.3767 + 13.3767i −0.824840 + 0.824840i −0.986798 0.161958i $$-0.948219\pi$$
0.161958 + 0.986798i $$0.448219\pi$$
$$264$$ 1.05936 7.06660i 0.0651990 0.434919i
$$265$$ −6.34735 2.19298i −0.389915 0.134714i
$$266$$ −2.66427 5.19345i −0.163357 0.318431i
$$267$$ 5.93003 + 5.93003i 0.362912 + 0.362912i
$$268$$ −0.752077 4.58455i −0.0459404 0.280046i
$$269$$ 19.2906i 1.17617i −0.808801 0.588083i $$-0.799883\pi$$
0.808801 0.588083i $$-0.200117\pi$$
$$270$$ −9.80047 7.35887i −0.596438 0.447846i
$$271$$ 15.6415i 0.950152i 0.879945 + 0.475076i $$0.157579\pi$$
−0.879945 + 0.475076i $$0.842421\pi$$
$$272$$ −23.3380 11.5687i −1.41507 0.701454i
$$273$$ 9.58668 + 9.58668i 0.580212 + 0.580212i
$$274$$ −11.8186 + 6.06301i −0.713988 + 0.366280i
$$275$$ −14.1137 11.0744i −0.851090 0.667810i
$$276$$ 4.08578 5.68935i 0.245935 0.342459i
$$277$$ −9.49242 + 9.49242i −0.570345 + 0.570345i −0.932225 0.361880i $$-0.882135\pi$$
0.361880 + 0.932225i $$0.382135\pi$$
$$278$$ −9.16958 2.95143i −0.549955 0.177015i
$$279$$ 3.93602 0.235643
$$280$$ 7.81236 + 24.9073i 0.466878 + 1.48850i
$$281$$ −6.05636 −0.361292 −0.180646 0.983548i $$-0.557819\pi$$
−0.180646 + 0.983548i $$0.557819\pi$$
$$282$$ −2.14649 0.690894i −0.127821 0.0411422i
$$283$$ 9.20805 9.20805i 0.547362 0.547362i −0.378315 0.925677i $$-0.623496\pi$$
0.925677 + 0.378315i $$0.123496\pi$$
$$284$$ −4.76278 + 6.63205i −0.282619 + 0.393540i
$$285$$ 0.514142 1.48813i 0.0304551 0.0881491i
$$286$$ 21.0621 10.8050i 1.24543 0.638911i
$$287$$ −10.7793 10.7793i −0.636280 0.636280i
$$288$$ 14.1647 0.195414i 0.834663 0.0115149i
$$289$$ 25.4060i 1.49447i
$$290$$ 2.17484 + 15.2845i 0.127711 + 0.897538i
$$291$$ 6.18818i 0.362757i
$$292$$ −0.220221 1.34244i −0.0128875 0.0785603i
$$293$$ 8.60824 + 8.60824i 0.502899 + 0.502899i 0.912338 0.409439i $$-0.134276\pi$$
−0.409439 + 0.912338i $$0.634276\pi$$
$$294$$ 4.56112 + 8.89097i 0.266010 + 0.518532i
$$295$$ −11.9028 + 5.79002i −0.693009 + 0.337108i
$$296$$ 21.6891 + 3.25143i 1.26065 + 0.188985i
$$297$$ −9.83269 + 9.83269i −0.570551 + 0.570551i
$$298$$ 8.26230 25.6695i 0.478622 1.48700i
$$299$$ 23.2044 1.34195
$$300$$ −3.39246 + 6.16998i −0.195864 + 0.356224i
$$301$$ −26.6233 −1.53454
$$302$$ 2.63499 8.18646i 0.151627 0.471078i
$$303$$ −1.10795 + 1.10795i −0.0636499 + 0.0636499i
$$304$$ 1.27798 + 3.79035i 0.0732969 + 0.217392i
$$305$$ −1.07789 + 0.524328i −0.0617196 + 0.0300230i
$$306$$ 10.5267 + 20.5197i 0.601772 + 1.17303i
$$307$$ 11.3998 + 11.3998i 0.650619 + 0.650619i 0.953142 0.302523i $$-0.0978290\pi$$
−0.302523 + 0.953142i $$0.597829\pi$$
$$308$$ 29.2271 4.79459i 1.66537 0.273197i
$$309$$ 7.86014i 0.447148i
$$310$$ −0.700174 4.92075i −0.0397672 0.279480i
$$311$$ 11.0301i 0.625460i −0.949842 0.312730i $$-0.898756\pi$$
0.949842 0.312730i $$-0.101244\pi$$
$$312$$ −5.52305 7.47099i −0.312681 0.422962i
$$313$$ 21.9744 + 21.9744i 1.24207 + 1.24207i 0.959143 + 0.282923i $$0.0913040\pi$$
0.282923 + 0.959143i $$0.408696\pi$$
$$314$$ −13.2893 + 6.81747i −0.749956 + 0.384732i
$$315$$ 7.54724 21.8447i 0.425239 1.23081i
$$316$$ −5.45558 3.91790i −0.306900 0.220399i
$$317$$ −17.3687 + 17.3687i −0.975526 + 0.975526i −0.999708 0.0241817i $$-0.992302\pi$$
0.0241817 + 0.999708i $$0.492302\pi$$
$$318$$ 2.84672 + 0.916279i 0.159636 + 0.0513824i
$$319$$ 17.5168 0.980750
$$320$$ −2.76405 17.6737i −0.154515 0.987990i
$$321$$ −4.35990 −0.243346
$$322$$ 27.6366 + 8.89544i 1.54013 + 0.495724i
$$323$$ −4.60467 + 4.60467i −0.256211 + 0.256211i
$$324$$ −7.77131 5.58093i −0.431739 0.310052i
$$325$$ −23.1579 + 2.79437i −1.28457 + 0.155004i
$$326$$ 17.8640 9.16433i 0.989396 0.507565i
$$327$$ −5.23475 5.23475i −0.289482 0.289482i
$$328$$ 6.21012 + 8.40039i 0.342897 + 0.463834i
$$329$$ 9.34653i 0.515291i
$$330$$ 6.38852 + 4.79694i 0.351676 + 0.264063i
$$331$$ 24.2555i 1.33320i −0.745414 0.666602i $$-0.767748\pi$$
0.745414 0.666602i $$-0.232252\pi$$
$$332$$ 34.6940 5.69141i 1.90408 0.312357i
$$333$$ −13.7303 13.7303i −0.752417 0.752417i
$$334$$ −15.0941 29.4228i −0.825912 1.60995i
$$335$$ 4.90944 + 1.69619i 0.268232 + 0.0926728i
$$336$$ −3.71396 11.0153i −0.202613 0.600931i
$$337$$ 16.9925 16.9925i 0.925642 0.925642i −0.0717789 0.997421i $$-0.522868\pi$$
0.997421 + 0.0717789i $$0.0228676\pi$$
$$338$$ 3.79743 11.7979i 0.206553 0.641723i
$$339$$ −9.59089 −0.520905
$$340$$ 23.7808 16.8106i 1.28969 0.911680i
$$341$$ −5.63940 −0.305391
$$342$$ 1.08509 3.37118i 0.0586749 0.182293i
$$343$$ −8.85807 + 8.85807i −0.478291 + 0.478291i
$$344$$ 18.0430 + 2.70483i 0.972811 + 0.145835i
$$345$$ 3.42563 + 7.04223i 0.184430 + 0.379141i
$$346$$ −4.86320 9.47981i −0.261447 0.509638i
$$347$$ −4.16317 4.16317i −0.223490 0.223490i 0.586476 0.809967i $$-0.300515\pi$$
−0.809967 + 0.586476i $$0.800515\pi$$
$$348$$ −1.11295 6.78437i −0.0596603 0.363681i
$$349$$ 25.4964i 1.36479i 0.730983 + 0.682396i $$0.239062\pi$$
−0.730983 + 0.682396i $$0.760938\pi$$
$$350$$ −28.6524 5.54951i −1.53154 0.296634i
$$351$$ 18.0803i 0.965057i
$$352$$ −20.2947 + 0.279983i −1.08171 + 0.0149232i
$$353$$ 8.69382 + 8.69382i 0.462725 + 0.462725i 0.899548 0.436822i $$-0.143896\pi$$
−0.436822 + 0.899548i $$0.643896\pi$$
$$354$$ 5.24456 2.69049i 0.278745 0.142998i
$$355$$ −3.99324 8.20910i −0.211939 0.435694i
$$356$$ 13.8951 19.3486i 0.736438 1.02547i
$$357$$ 13.3818 13.3818i 0.708239 0.708239i
$$358$$ 17.6108 + 5.66842i 0.930759 + 0.299585i
$$359$$ 10.8276 0.571458 0.285729 0.958310i $$-0.407764\pi$$
0.285729 + 0.958310i $$0.407764\pi$$
$$360$$ −7.33420 + 14.0376i −0.386546 + 0.739849i
$$361$$ 1.00000 0.0526316
$$362$$ 23.0997 + 7.43514i 1.21409 + 0.390782i
$$363$$ 0.932815 0.932815i 0.0489601 0.0489601i
$$364$$ 22.4632 31.2795i 1.17739 1.63949i
$$365$$ 1.43757 + 0.496675i 0.0752459 + 0.0259971i
$$366$$ 0.474933 0.243643i 0.0248251 0.0127354i
$$367$$ −20.7628 20.7628i −1.08381 1.08381i −0.996151 0.0876562i $$-0.972062\pi$$
−0.0876562 0.996151i $$-0.527938\pi$$
$$368$$ −17.8259 8.83634i −0.929240 0.460626i
$$369$$ 9.24922i 0.481495i
$$370$$ −14.7230 + 19.6079i −0.765410 + 1.01937i
$$371$$ 12.3956i 0.643546i
$$372$$ 0.358306 + 2.18418i 0.0185773 + 0.113245i
$$373$$ 1.85686 + 1.85686i 0.0961447 + 0.0961447i 0.753543 0.657398i $$-0.228343\pi$$
−0.657398 + 0.753543i $$0.728343\pi$$
$$374$$ −15.0823 29.3999i −0.779889 1.52024i
$$375$$ −4.26682 6.61559i −0.220338 0.341627i
$$376$$ −0.949575 + 6.33427i −0.0489706 + 0.326665i
$$377$$ 16.1049 16.1049i 0.829444 0.829444i
$$378$$ −6.93112 + 21.5338i −0.356498 + 1.10758i
$$379$$ −17.2442 −0.885776 −0.442888 0.896577i $$-0.646046\pi$$
−0.442888 + 0.896577i $$0.646046\pi$$
$$380$$ −4.40762 0.756866i −0.226106 0.0388264i
$$381$$ −12.4392 −0.637282
$$382$$ 6.63629 20.6178i 0.339542 1.05490i
$$383$$ 8.79528 8.79528i 0.449418 0.449418i −0.445743 0.895161i $$-0.647061\pi$$
0.895161 + 0.445743i $$0.147061\pi$$
$$384$$ 1.39789 + 7.84251i 0.0713357 + 0.400211i
$$385$$ −10.8134 + 31.2983i −0.551104 + 1.59511i
$$386$$ 11.6388 + 22.6874i 0.592399 + 1.15476i
$$387$$ −11.4221 11.4221i −0.580620 0.580620i
$$388$$ −17.3454 + 2.84544i −0.880580 + 0.144455i
$$389$$ 22.5652i 1.14410i 0.820219 + 0.572049i $$0.193851\pi$$
−0.820219 + 0.572049i $$0.806149\pi$$
$$390$$ 10.2839 1.46330i 0.520745 0.0740970i
$$391$$ 32.3904i 1.63805i
$$392$$ 22.8240 16.8730i 1.15279 0.852216i
$$393$$ −3.31784 3.31784i −0.167363 0.167363i
$$394$$ −17.7535 + 9.10764i −0.894408 + 0.458836i
$$395$$ 6.75287 3.28487i 0.339774 0.165280i
$$396$$ 14.5963 + 10.4822i 0.733490 + 0.526752i
$$397$$ 13.6045 13.6045i 0.682791 0.682791i −0.277837 0.960628i $$-0.589618\pi$$
0.960628 + 0.277837i $$0.0896175\pi$$
$$398$$ 5.68827 + 1.83090i 0.285127 + 0.0917746i
$$399$$ −2.90613 −0.145488
$$400$$ 18.8543 + 6.67196i 0.942715 + 0.333598i
$$401$$ 33.3363 1.66474 0.832368 0.554224i $$-0.186985\pi$$
0.832368 + 0.554224i $$0.186985\pi$$
$$402$$ −2.20183 0.708708i −0.109817 0.0353472i
$$403$$ −5.18486 + 5.18486i −0.258276 + 0.258276i
$$404$$ 3.61502 + 2.59611i 0.179854 + 0.129161i
$$405$$ 9.61926 4.67920i 0.477985 0.232511i
$$406$$ 25.3548 13.0072i 1.25834 0.645535i
$$407$$ 19.6724 + 19.6724i 0.975123 + 0.975123i
$$408$$ −10.4285 + 7.70947i −0.516290 + 0.381675i
$$409$$ 2.78416i 0.137668i −0.997628 0.0688339i $$-0.978072\pi$$
0.997628 0.0688339i $$-0.0219279\pi$$
$$410$$ −11.5632 + 1.64533i −0.571067 + 0.0812573i
$$411$$ 6.61340i 0.326215i
$$412$$ 22.0319 3.61424i 1.08543 0.178061i
$$413$$ 17.2759 + 17.2759i 0.850093 + 0.850093i
$$414$$ 8.04046 + 15.6732i 0.395167 + 0.770298i
$$415$$ −12.8361 + 37.1527i −0.630098 + 1.82375i
$$416$$ −18.4015 + 18.9164i −0.902209 + 0.927451i
$$417$$ −3.39131 + 3.39131i −0.166073 + 0.166073i
$$418$$ −1.55468 + 4.83012i −0.0760420 + 0.236249i
$$419$$ −21.3153 −1.04132 −0.520661 0.853763i $$-0.674315\pi$$
−0.520661 + 0.853763i $$0.674315\pi$$
$$420$$ 12.8091 + 2.19955i 0.625021 + 0.107327i
$$421$$ −11.5106 −0.560994 −0.280497 0.959855i $$-0.590499\pi$$
−0.280497 + 0.959855i $$0.590499\pi$$
$$422$$ −5.55845 + 17.2691i −0.270581 + 0.840647i
$$423$$ 4.00992 4.00992i 0.194969 0.194969i
$$424$$ 1.25935 8.40065i 0.0611593 0.407972i
$$425$$ 3.90058 + 32.3255i 0.189206 + 1.56802i
$$426$$ 1.85557 + 3.61705i 0.0899025 + 0.175247i
$$427$$ 1.56446 + 1.56446i 0.0757096 + 0.0757096i
$$428$$ 2.00476 + 12.2208i 0.0969040 + 0.590713i
$$429$$ 11.7858i 0.569024i
$$430$$ −12.2479 + 16.3116i −0.590646 + 0.786617i
$$431$$ 8.99333i 0.433193i 0.976261 + 0.216597i $$0.0694957\pi$$
−0.976261 + 0.216597i $$0.930504\pi$$
$$432$$ 6.88507 13.8895i 0.331258 0.668261i
$$433$$ −21.6636 21.6636i −1.04109 1.04109i −0.999119 0.0419671i $$-0.986638\pi$$
−0.0419671 0.999119i $$-0.513362\pi$$
$$434$$ −8.16281 + 4.18757i −0.391828 + 0.201010i
$$435$$ 7.26515 + 2.51008i 0.348337 + 0.120349i
$$436$$ −12.2659 + 17.0800i −0.587431 + 0.817983i
$$437$$ −3.51712 + 3.51712i −0.168247 + 0.168247i
$$438$$ −0.644735 0.207522i −0.0308066 0.00991580i
$$439$$ −20.8810 −0.996595 −0.498298 0.867006i $$-0.666041\pi$$
−0.498298 + 0.867006i $$0.666041\pi$$
$$440$$ 10.5082 20.1127i 0.500959 0.958835i
$$441$$ −25.1303 −1.19668
$$442$$ −40.8970 13.1636i −1.94527 0.626128i
$$443$$ 21.5183 21.5183i 1.02237 1.02237i 0.0226219 0.999744i $$-0.492799\pi$$
0.999744 0.0226219i $$-0.00720139\pi$$
$$444$$ 6.36935 8.86916i 0.302276 0.420912i
$$445$$ 11.6500 + 23.9495i 0.552264 + 1.13531i
$$446$$ −23.9398 + 12.2813i −1.13358 + 0.581535i
$$447$$ −9.49370 9.49370i −0.449037 0.449037i
$$448$$ −29.1679 + 15.4752i −1.37805 + 0.731136i
$$449$$ 18.9308i 0.893398i 0.894684 + 0.446699i $$0.147400\pi$$
−0.894684 + 0.446699i $$0.852600\pi$$
$$450$$ −9.91179 14.6736i −0.467246 0.691719i
$$451$$ 13.2520i 0.624011i
$$452$$ 4.41007 + 26.8832i 0.207432 + 1.26448i
$$453$$ −3.02771 3.02771i −0.142254 0.142254i
$$454$$ 13.6929 + 26.6915i 0.642639 + 1.25269i
$$455$$ 18.8338 + 38.7175i 0.882941 + 1.81510i
$$456$$ 1.96952 + 0.295252i 0.0922313 + 0.0138265i
$$457$$ 1.51148 1.51148i 0.0707041 0.0707041i −0.670870 0.741575i $$-0.734079\pi$$
0.741575 + 0.670870i $$0.234079\pi$$
$$458$$ 9.31290 28.9335i 0.435163 1.35197i
$$459$$ 25.2378 1.17800
$$460$$ 18.1641 12.8402i 0.846907 0.598675i
$$461$$ −17.0301 −0.793171 −0.396586 0.917998i $$-0.629805\pi$$
−0.396586 + 0.917998i $$0.629805\pi$$
$$462$$ 4.51811 14.0370i 0.210201 0.653059i
$$463$$ 17.2053 17.2053i 0.799599 0.799599i −0.183433 0.983032i $$-0.558721\pi$$
0.983032 + 0.183433i $$0.0587210\pi$$
$$464$$ −18.5048 + 6.23917i −0.859063 + 0.289646i
$$465$$ −2.33897 0.808103i −0.108467 0.0374749i
$$466$$ 1.65883 + 3.23355i 0.0768437 + 0.149791i
$$467$$ −9.04056 9.04056i −0.418347 0.418347i 0.466286 0.884634i $$-0.345592\pi$$
−0.884634 + 0.466286i $$0.845592\pi$$
$$468$$ 23.0571 3.78243i 1.06582 0.174843i
$$469$$ 9.58753i 0.442711i
$$470$$ −5.72646 4.29982i −0.264142 0.198336i
$$471$$ 7.43634i 0.342649i
$$472$$ −9.95296 13.4633i −0.458122 0.619699i
$$473$$ 16.3653 + 16.3653i 0.752476 + 0.752476i
$$474$$ −2.97541 + 1.52640i −0.136665 + 0.0701100i
$$475$$ 3.08653 3.93362i 0.141620 0.180487i
$$476$$ −43.6622 31.3558i −2.00125 1.43719i
$$477$$ −5.31805 + 5.31805i −0.243497 + 0.243497i
$$478$$ −30.8178 9.91940i −1.40957 0.453703i
$$479$$ −21.6356 −0.988556 −0.494278 0.869304i $$-0.664568\pi$$
−0.494278 + 0.869304i $$0.664568\pi$$
$$480$$ −8.45745 2.79203i −0.386028 0.127438i
$$481$$ 36.1735 1.64937
$$482$$ −18.8867 6.07910i −0.860265 0.276895i
$$483$$ 10.2212 10.2212i 0.465081 0.465081i
$$484$$ −3.04360 2.18575i −0.138345 0.0993521i
$$485$$ 6.41745 18.5746i 0.291401 0.843429i
$$486$$ −18.8683 + 9.67956i −0.855885 + 0.439074i
$$487$$ −14.6707 14.6707i −0.664791 0.664791i 0.291715 0.956505i $$-0.405774\pi$$
−0.956505 + 0.291715i $$0.905774\pi$$
$$488$$ −0.901313 1.21920i −0.0408005 0.0551906i
$$489$$ 9.99625i 0.452046i
$$490$$ 4.47040 + 31.4175i 0.201952 + 1.41930i
$$491$$ 30.4922i 1.37609i −0.725667 0.688047i $$-0.758468\pi$$
0.725667 0.688047i $$-0.241532\pi$$
$$492$$ 5.13259 0.841981i 0.231395 0.0379594i
$$493$$ −22.4804 22.4804i −1.01246 1.01246i
$$494$$ 3.01144 + 5.87018i 0.135491 + 0.264112i
$$495$$ −18.0671 + 8.78859i −0.812057 + 0.395018i
$$496$$ 5.95749 2.00866i 0.267499 0.0901914i
$$497$$ −11.9148 + 11.9148i −0.534453 + 0.534453i
$$498$$ 5.36322 16.6626i 0.240331 0.746667i
$$499$$ −25.7578 −1.15308 −0.576538 0.817071i $$-0.695597\pi$$
−0.576538 + 0.817071i $$0.695597\pi$$
$$500$$ −16.5815 + 15.0018i −0.741546 + 0.670902i
$$501$$ −16.4643 −0.735571
$$502$$ −2.29173 + 7.12001i −0.102285 + 0.317782i
$$503$$ 5.81236 5.81236i 0.259161 0.259161i −0.565552 0.824713i $$-0.691337\pi$$
0.824713 + 0.565552i $$0.191337\pi$$
$$504$$ 28.9112 + 4.33409i 1.28781 + 0.193056i
$$505$$ −4.47464 + 2.17665i −0.199119 + 0.0968596i
$$506$$ −11.5201 22.4561i −0.512132 0.998297i
$$507$$ −4.36339 4.36339i −0.193785 0.193785i
$$508$$ 5.71980 + 34.8671i 0.253775 + 1.54698i
$$509$$ 21.8822i 0.969912i −0.874539 0.484956i $$-0.838836\pi$$
0.874539 0.484956i $$-0.161164\pi$$
$$510$$ −2.04258 14.3550i −0.0904468 0.635650i
$$511$$ 2.80740i 0.124192i
$$512$$ 21.3397 7.52441i 0.943091 0.332535i
$$513$$ −2.74046 2.74046i −0.120994 0.120994i
$$514$$ 25.1511 12.9027i 1.10937 0.569113i
$$515$$ −8.15136 + 23.5932i −0.359192 + 1.03964i
$$516$$ 5.29861 7.37818i 0.233258 0.324806i
$$517$$ −5.74529 + 5.74529i −0.252678 + 0.252678i
$$518$$ 43.0828 + 13.8672i 1.89295 + 0.609288i
$$519$$ −5.30467 −0.232849
$$520$$ −8.83034 28.1528i −0.387236 1.23458i
$$521$$ −30.5569 −1.33872 −0.669361 0.742937i $$-0.733432\pi$$
−0.669361 + 0.742937i $$0.733432\pi$$
$$522$$ 16.4584 + 5.29749i 0.720363 + 0.231865i
$$523$$ −28.6213 + 28.6213i −1.25152 + 1.25152i −0.296487 + 0.955037i $$0.595815\pi$$
−0.955037 + 0.296487i $$0.904185\pi$$
$$524$$ −7.77427 + 10.8255i −0.339620 + 0.472913i
$$525$$ −8.96984 + 11.4316i −0.391476 + 0.498916i
$$526$$ 23.8038 12.2115i 1.03789 0.532445i
$$527$$ 7.23740 + 7.23740i 0.315266 + 0.315266i
$$528$$ −4.48809 + 9.05401i −0.195319 + 0.394025i
$$529$$ 1.74027i 0.0756638i
$$530$$ 7.59456 + 5.70252i 0.329887 + 0.247702i
$$531$$ 14.8237i 0.643295i
$$532$$ 1.33629 + 8.14585i 0.0579357 + 0.353168i
$$533$$ 12.1839 + 12.1839i 0.527741 + 0.527741i
$$534$$ −5.41349 10.5525i −0.234265 0.456651i
$$535$$ −13.0868 4.52143i −0.565791 0.195478i
$$536$$ −0.974059 + 6.49759i −0.0420729 + 0.280653i
$$537$$ 6.51324 6.51324i 0.281067 0.281067i
$$538$$ −8.35866 + 25.9689i −0.360368 + 1.11960i
$$539$$ 36.0059 1.55088
$$540$$ 10.0048 + 14.1531i 0.430536 + 0.609051i
$$541$$ 4.01340 0.172549 0.0862747 0.996271i $$-0.472504\pi$$
0.0862747 + 0.996271i $$0.472504\pi$$
$$542$$ 6.77751 21.0565i 0.291119 0.904455i
$$543$$ 8.54327 8.54327i 0.366627 0.366627i
$$544$$ 26.4048 + 25.6862i 1.13210 + 1.10129i
$$545$$ −10.2841 21.1415i −0.440521 0.905600i
$$546$$ −8.75162 17.0595i −0.374535 0.730079i
$$547$$ 1.65661 + 1.65661i 0.0708313 + 0.0708313i 0.741635 0.670804i $$-0.234051\pi$$
−0.670804 + 0.741635i $$0.734051\pi$$
$$548$$ 18.5373 3.04097i 0.791875 0.129904i
$$549$$ 1.34240i 0.0572921i
$$550$$ 14.2013 + 21.0238i 0.605545 + 0.896459i
$$551$$ 4.88207i 0.207983i
$$552$$ −7.96548 + 5.88861i −0.339034 + 0.250636i
$$553$$ −9.80122 9.80122i −0.416790 0.416790i
$$554$$ 16.8918 8.66558i 0.717663 0.368165i
$$555$$ 5.34023 + 10.9782i 0.226680 + 0.465997i
$$556$$ 11.0652 + 7.94642i 0.469269 + 0.337003i
$$557$$ −32.0355 + 32.0355i −1.35739 + 1.35739i −0.480260 + 0.877126i $$0.659458\pi$$
−0.877126 + 0.480260i $$0.840542\pi$$
$$558$$ −5.29866 1.70549i −0.224310 0.0721992i
$$559$$ 30.0924 1.27277
$$560$$ 0.275435 36.9153i 0.0116393 1.55995i
$$561$$ −16.4515 −0.694582
$$562$$ 8.15306 + 2.62424i 0.343916 + 0.110697i
$$563$$ −23.6795 + 23.6795i −0.997973 + 0.997973i −0.999998 0.00202496i $$-0.999355\pi$$
0.00202496 + 0.999998i $$0.499355\pi$$
$$564$$ 2.59023 + 1.86016i 0.109068 + 0.0783269i
$$565$$ −28.7883 9.94622i −1.21113 0.418441i
$$566$$ −16.3857 + 8.40598i −0.688744 + 0.353330i
$$567$$ −13.9615 13.9615i −0.586330 0.586330i
$$568$$ 9.28533 6.86433i 0.389604 0.288021i
$$569$$ 4.84313i 0.203035i 0.994834 + 0.101517i $$0.0323697\pi$$
−0.994834 + 0.101517i $$0.967630\pi$$
$$570$$ −1.33695 + 1.78054i −0.0559986 + 0.0745784i
$$571$$ 26.9143i 1.12633i −0.826345 0.563164i $$-0.809584\pi$$
0.826345 0.563164i $$-0.190416\pi$$
$$572$$ −33.0355 + 5.41934i −1.38128 + 0.226594i
$$573$$ −7.62536 7.62536i −0.318554 0.318554i
$$574$$ 9.84034 + 19.1817i 0.410728 + 0.800630i
$$575$$ 2.97933 + 24.6907i 0.124246 + 1.02967i
$$576$$ −19.1532 5.87455i −0.798048 0.244773i
$$577$$ 11.9729 11.9729i 0.498439 0.498439i −0.412513 0.910952i $$-0.635349\pi$$
0.910952 + 0.412513i $$0.135349\pi$$
$$578$$ −11.0085 + 34.2016i −0.457894 + 1.42260i
$$579$$ 12.6953 0.527600
$$580$$ 3.69507 21.5183i 0.153430 0.893501i
$$581$$ 72.5545 3.01007
$$582$$ −2.68136 + 8.33051i −0.111146 + 0.345311i
$$583$$ 7.61953 7.61953i 0.315569 0.315569i
$$584$$ −0.285222 + 1.90261i −0.0118026 + 0.0787306i
$$585$$ −8.53067 + 24.6911i −0.352700 + 1.02085i
$$586$$ −7.85841 15.3184i −0.324628 0.632796i
$$587$$ 0.478832 + 0.478832i 0.0197635 + 0.0197635i 0.716919 0.697156i $$-0.245552\pi$$
−0.697156 + 0.716919i $$0.745552\pi$$
$$588$$ −2.28768 13.9454i −0.0943422 0.575097i
$$589$$ 1.57175i 0.0647628i
$$590$$ 18.5324 2.63698i 0.762966 0.108563i
$$591$$ 9.93442i 0.408647i
$$592$$ −27.7889 13.7750i −1.14212 0.566150i
$$593$$ 23.9284 + 23.9284i 0.982622 + 0.982622i 0.999852 0.0172293i $$-0.00548454\pi$$
−0.0172293 + 0.999852i $$0.505485\pi$$
$$594$$ 17.4973 8.97621i 0.717922 0.368298i
$$595$$ 54.0447 26.2896i 2.21562 1.07777i
$$596$$ −22.2454 + 30.9762i −0.911206 + 1.26883i
$$597$$ 2.10377 2.10377i 0.0861016 0.0861016i
$$598$$ −31.2377 10.0546i −1.27741 0.411161i
$$599$$ −1.72828 −0.0706158 −0.0353079 0.999376i $$-0.511241\pi$$
−0.0353079 + 0.999376i $$0.511241\pi$$
$$600$$ 7.24039 6.83604i 0.295588 0.279080i
$$601$$ −26.9304 −1.09852 −0.549258 0.835653i $$-0.685090\pi$$
−0.549258 + 0.835653i $$0.685090\pi$$
$$602$$ 35.8402 + 11.5360i 1.46074 + 0.470171i
$$603$$ 4.11332 4.11332i 0.167507 0.167507i
$$604$$ −7.09444 + 9.87884i −0.288669 + 0.401964i
$$605$$ 3.76734 1.83259i 0.153164 0.0745053i
$$606$$ 1.97159 1.01144i 0.0800905 0.0410869i
$$607$$ 15.1247 + 15.1247i 0.613894 + 0.613894i 0.943958 0.330065i $$-0.107071\pi$$
−0.330065 + 0.943958i $$0.607071\pi$$
$$608$$ −0.0780338 5.65632i −0.00316469 0.229394i
$$609$$ 14.1879i 0.574924i
$$610$$ 1.67824 0.238798i 0.0679500 0.00966863i
$$611$$ 10.5644i 0.427391i
$$612$$ −5.27979 32.1848i −0.213423 1.30099i
$$613$$ −12.3720 12.3720i −0.499701 0.499701i 0.411644 0.911345i $$-0.364955\pi$$
−0.911345 + 0.411644i $$0.864955\pi$$
$$614$$ −10.4068 20.2859i −0.419983 0.818672i
$$615$$ −1.89895 + 5.49632i −0.0765732 + 0.221633i
$$616$$ −41.4230 6.20975i −1.66898 0.250198i
$$617$$ −18.4809 + 18.4809i −0.744011 + 0.744011i −0.973347 0.229336i $$-0.926344\pi$$
0.229336 + 0.973347i $$0.426344\pi$$
$$618$$ 3.40583 10.5813i 0.137002 0.425643i
$$619$$ 16.9676 0.681984 0.340992 0.940066i $$-0.389237\pi$$
0.340992 + 0.940066i $$0.389237\pi$$
$$620$$ −1.18960 + 6.92768i −0.0477756 + 0.278223i
$$621$$ 19.2770 0.773561
$$622$$ −4.77939 + 14.8487i −0.191636 + 0.595379i
$$623$$ 34.7607 34.7607i 1.39266 1.39266i
$$624$$ 4.19790 + 12.4506i 0.168051 + 0.498422i
$$625$$ −5.94671 24.2824i −0.237868 0.971297i
$$626$$ −20.0603 39.1034i −0.801770 1.56289i
$$627$$ 1.78639 + 1.78639i 0.0713415 + 0.0713415i
$$628$$ 20.8440 3.41937i 0.831766 0.136448i
$$629$$ 50.4936i 2.01331i
$$630$$ −19.6254 + 26.1370i −0.781896 + 1.04132i
$$631$$ 26.7082i 1.06324i 0.846984 + 0.531619i $$0.178416\pi$$
−0.846984 + 0.531619i $$0.821584\pi$$
$$632$$ 5.64665 + 7.63819i 0.224612 + 0.303831i
$$633$$ 6.38687 + 6.38687i 0.253855 + 0.253855i
$$634$$ 30.9077 15.8558i 1.22750 0.629715i
$$635$$ −37.3380 12.9001i −1.48171 0.511925i
$$636$$ −3.43522 2.46699i −0.136215 0.0978224i
$$637$$ 33.1038 33.1038i 1.31162 1.31162i
$$638$$ −23.5810 7.59007i −0.933581 0.300494i
$$639$$ −10.2236 −0.404439
$$640$$ −3.93713 + 24.9900i −0.155629 + 0.987816i
$$641$$ 3.98093 0.157237 0.0786186 0.996905i $$-0.474949\pi$$
0.0786186 + 0.996905i $$0.474949\pi$$
$$642$$ 5.86928 + 1.88916i 0.231642 + 0.0745592i
$$643$$ −6.39670 + 6.39670i −0.252261 + 0.252261i −0.821897 0.569636i $$-0.807084\pi$$
0.569636 + 0.821897i $$0.307084\pi$$
$$644$$ −33.3499 23.9500i −1.31417 0.943764i
$$645$$ 4.44249 + 9.13264i 0.174923 + 0.359598i
$$646$$ 8.19402 4.20358i 0.322390 0.165388i
$$647$$ 20.5555 + 20.5555i 0.808120 + 0.808120i 0.984349 0.176230i $$-0.0563901\pi$$
−0.176230 + 0.984349i $$0.556390\pi$$
$$648$$ 8.04348 + 10.8804i 0.315978 + 0.427421i
$$649$$ 21.2389i 0.833702i
$$650$$ 32.3859 + 6.27263i 1.27028 + 0.246033i
$$651$$ 4.56771i 0.179023i
$$652$$ −28.0194 + 4.59647i −1.09732 + 0.180012i
$$653$$ −19.4414 19.4414i −0.760800 0.760800i 0.215667 0.976467i $$-0.430807\pi$$
−0.976467 + 0.215667i $$0.930807\pi$$
$$654$$ 4.77877 + 9.31524i 0.186865 + 0.364255i
$$655$$ −6.51815 13.3997i −0.254685 0.523569i
$$656$$ −4.72013 13.9995i −0.184290 0.546587i
$$657$$ 1.20445 1.20445i 0.0469901 0.0469901i
$$658$$ −4.04989 + 12.5823i −0.157881 + 0.490508i
$$659$$ 9.30532 0.362484 0.181242 0.983439i $$-0.441988\pi$$
0.181242 + 0.983439i $$0.441988\pi$$
$$660$$ −6.52168 9.22579i −0.253856 0.359113i
$$661$$ 20.9486 0.814805 0.407402 0.913249i $$-0.366435\pi$$
0.407402 + 0.913249i $$0.366435\pi$$
$$662$$ −10.5100 + 32.6527i −0.408483 + 1.26908i
$$663$$ −15.1255 + 15.1255i −0.587425 + 0.587425i
$$664$$ −49.1711 7.37128i −1.90821 0.286061i
$$665$$ −8.72312 3.01380i −0.338268 0.116870i
$$666$$ 12.5343 + 24.4331i 0.485695 + 0.946764i
$$667$$ −17.1708 17.1708i −0.664857 0.664857i
$$668$$ 7.57060 + 46.1493i 0.292915 + 1.78557i
$$669$$ 13.3961i 0.517924i
$$670$$ −5.87411 4.41069i −0.226937 0.170400i
$$671$$ 1.92334i 0.0742498i
$$672$$ 0.226776 + 16.4380i 0.00874809 + 0.634109i
$$673$$ −2.71457 2.71457i −0.104639 0.104639i 0.652849 0.757488i $$-0.273574\pi$$
−0.757488 + 0.652849i $$0.773574\pi$$
$$674$$ −30.2382 + 15.5124i −1.16473 + 0.597514i
$$675$$ −19.2384 + 2.32142i −0.740487 + 0.0893515i
$$676$$ −10.2242 + 14.2369i −0.393237 + 0.547573i
$$677$$ −19.1114 + 19.1114i −0.734513 + 0.734513i −0.971510 0.236998i $$-0.923837\pi$$
0.236998 + 0.971510i $$0.423837\pi$$
$$678$$ 12.9112 + 4.15577i 0.495853 + 0.159601i
$$679$$ −36.2739 −1.39206
$$680$$ −39.2977 + 12.3260i −1.50700 + 0.472682i
$$681$$ 14.9359 0.572345
$$682$$ 7.59175 + 2.44357i 0.290703 + 0.0935692i
$$683$$ 12.0794 12.0794i 0.462204 0.462204i −0.437173 0.899377i $$-0.644020\pi$$
0.899377 + 0.437173i $$0.144020\pi$$
$$684$$ −2.92149 + 4.06811i −0.111706 + 0.155548i
$$685$$ −6.85842 + 19.8510i −0.262047 + 0.758467i
$$686$$ 15.7629 8.08648i 0.601832 0.308743i
$$687$$ −10.7009 10.7009i −0.408264 0.408264i
$$688$$ −23.1174 11.4593i −0.881342 0.436882i
$$689$$ 14.0108i 0.533768i
$$690$$ −1.56015 10.9646i −0.0593939 0.417414i
$$691$$ 16.1397i 0.613985i 0.951712 + 0.306992i $$0.0993226\pi$$
−0.951712 + 0.306992i $$0.900677\pi$$
$$692$$ 2.43919 + 14.8689i 0.0927240 + 0.565232i
$$693$$ 26.2229 + 26.2229i 0.996126 + 0.996126i
$$694$$ 3.80053 + 7.40836i 0.144266 + 0.281217i
$$695$$ −13.6964 + 6.66249i −0.519534 + 0.252723i
$$696$$ −1.44144 + 9.61535i −0.0546378 + 0.364469i
$$697$$ 17.0071 17.0071i 0.644190 0.644190i
$$698$$ 11.0477 34.3232i 0.418161 1.29915i
$$699$$ 1.80941 0.0684383
$$700$$ 36.1672 + 19.8859i 1.36699 + 0.751617i
$$701$$ 1.39112 0.0525418 0.0262709 0.999655i $$-0.491637\pi$$
0.0262709 + 0.999655i $$0.491637\pi$$
$$702$$ 7.83427 24.3397i 0.295686 0.918643i
$$703$$ −5.48286 + 5.48286i −0.206790 + 0.206790i
$$704$$ 27.4420 + 8.41686i 1.03426 + 0.317222i
$$705$$ −3.20616 + 1.55961i −0.120751 + 0.0587383i
$$706$$ −7.93654 15.4707i −0.298696 0.582246i
$$707$$ 6.49457 + 6.49457i 0.244253 + 0.244253i
$$708$$ −8.22601 + 1.34944i −0.309152 + 0.0507151i
$$709$$ 0.442717i 0.0166266i −0.999965 0.00831330i $$-0.997354\pi$$
0.999965 0.00831330i $$-0.00264624\pi$$
$$710$$ 1.81866 + 12.7814i 0.0682532 + 0.479676i
$$711$$ 8.40999i 0.315399i
$$712$$ −27.0893 + 20.0262i −1.01522 + 0.750514i
$$713$$ 5.52803 + 5.52803i 0.207026 + 0.207026i
$$714$$ −23.8129 + 12.2161i −0.891175 + 0.457178i
$$715$$ 12.2225 35.3766i 0.457094 1.32301i
$$716$$ −21.2515 15.2616i −0.794204 0.570354i
$$717$$ −11.3978 + 11.3978i −0.425658 + 0.425658i
$$718$$ −14.5761 4.69163i −0.543974 0.175090i
$$719$$ −3.55928 −0.132739 −0.0663694 0.997795i $$-0.521142\pi$$
−0.0663694 + 0.997795i $$0.521142\pi$$
$$720$$ 15.9558 15.7195i 0.594639 0.585831i
$$721$$ 46.0746 1.71591
$$722$$ −1.34620 0.433304i −0.0501003 0.0161259i
$$723$$ −6.98512 + 6.98512i −0.259779 + 0.259779i
$$724$$ −27.8751 20.0183i −1.03597 0.743976i
$$725$$ 19.2042 + 15.0686i 0.713227 + 0.559635i
$$726$$ −1.65994 + 0.851561i −0.0616063 + 0.0316044i
$$727$$ 25.1946 + 25.1946i 0.934415 + 0.934415i 0.997978 0.0635627i $$-0.0202463\pi$$
−0.0635627 + 0.997978i $$0.520246\pi$$
$$728$$ −43.7935 + 32.3750i −1.62309 + 1.19990i
$$729$$ 3.79323i 0.140490i
$$730$$ −1.72004 1.29153i −0.0636617 0.0478016i
$$731$$ 42.0052i 1.55362i
$$732$$ −0.744925 + 0.122202i −0.0275332 + 0.00451671i
$$733$$ −7.66294 7.66294i −0.283037 0.283037i 0.551282 0.834319i $$-0.314139\pi$$
−0.834319 + 0.551282i $$0.814139\pi$$
$$734$$ 18.9542 + 36.9473i 0.699612 + 1.36375i
$$735$$ 14.9336 + 5.15950i 0.550834 + 0.190311i
$$736$$ 20.1684 + 19.6195i 0.743417 + 0.723184i
$$737$$ −5.89343 + 5.89343i −0.217087 + 0.217087i
$$738$$ −4.00772 + 12.4513i −0.147526 + 0.458338i
$$739$$ 50.2765 1.84945 0.924725 0.380635i $$-0.124294\pi$$
0.924725 + 0.380635i $$0.124294\pi$$
$$740$$ 28.3162 20.0166i 1.04092 0.735825i
$$741$$ 3.28481 0.120670
$$742$$ 5.37105 16.6869i 0.197177 0.612595i
$$743$$ −17.6854 + 17.6854i −0.648814 + 0.648814i −0.952706 0.303893i $$-0.901714\pi$$
0.303893 + 0.952706i $$0.401714\pi$$
$$744$$ 0.464063 3.09560i 0.0170134 0.113490i
$$745$$ −18.6511 38.3420i −0.683324 1.40474i
$$746$$ −1.69512 3.30429i −0.0620627 0.120979i
$$747$$ 31.1279 + 31.1279i 1.13891 + 1.13891i
$$748$$ 7.56471 + 46.1134i 0.276593 + 1.68607i
$$749$$ 25.5569i 0.933827i
$$750$$ 2.87742 + 10.7547i 0.105069 + 0.392707i
$$751$$ 40.6953i 1.48499i 0.669851 + 0.742496i $$0.266358\pi$$
−0.669851 + 0.742496i $$0.733642\pi$$
$$752$$ 4.02298 8.11573i 0.146703 0.295950i
$$753$$ 2.63329 + 2.63329i 0.0959625 + 0.0959625i
$$754$$ −28.6587 + 14.7021i −1.04369 + 0.535417i
$$755$$ −5.94817 12.2279i −0.216476 0.445020i
$$756$$ 18.6613 25.9854i 0.678705 0.945081i
$$757$$ 13.3742 13.3742i 0.486092 0.486092i −0.420978 0.907071i $$-0.638313\pi$$
0.907071 + 0.420978i $$0.138313\pi$$
$$758$$ 23.2141 + 7.47198i 0.843175 + 0.271394i
$$759$$ −12.5659 −0.456113
$$760$$ 5.60558 + 2.92873i 0.203336 + 0.106236i
$$761$$ 37.9781 1.37670 0.688352 0.725377i $$-0.258334\pi$$
0.688352 + 0.725377i $$0.258334\pi$$
$$762$$ 16.7457 + 5.38997i 0.606632 + 0.195258i
$$763$$ −30.6851 + 30.6851i −1.11087 + 1.11087i
$$764$$ −17.8675 + 24.8801i −0.646424 + 0.900130i
$$765$$ 34.4656 + 11.9077i 1.24611 + 0.430525i
$$766$$ −15.6512 + 8.02916i −0.565501 + 0.290105i
$$767$$ −19.5271 19.5271i −0.705081 0.705081i
$$768$$ 1.51635 11.1633i 0.0547166 0.402820i
$$769$$ 32.0784i 1.15678i −0.815762 0.578388i $$-0.803682\pi$$
0.815762 0.578388i $$-0.196318\pi$$
$$770$$ 28.1187