# Properties

 Label 21.3.h.b.11.2 Level $21$ Weight $3$ Character 21.11 Analytic conductor $0.572$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$21 = 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 21.h (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.572208555157$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-5})$$ Defining polynomial: $$x^{4} - 5 x^{2} + 25$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 11.2 Root $$1.93649 - 1.11803i$$ of defining polynomial Character $$\chi$$ $$=$$ 21.11 Dual form 21.3.h.b.2.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.93649 - 1.11803i) q^{2} +(-2.93649 + 0.614017i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-5.00000 + 4.47214i) q^{6} +(3.50000 - 6.06218i) q^{7} +6.70820i q^{8} +(8.24597 - 3.60611i) q^{9} +O(q^{10})$$ $$q+(1.93649 - 1.11803i) q^{2} +(-2.93649 + 0.614017i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-5.00000 + 4.47214i) q^{6} +(3.50000 - 6.06218i) q^{7} +6.70820i q^{8} +(8.24597 - 3.60611i) q^{9} +(-2.50000 + 4.33013i) q^{10} +(-9.68246 - 5.59017i) q^{11} +(-0.936492 + 2.85008i) q^{12} -2.00000 q^{13} -15.6525i q^{14} +(5.00000 - 4.47214i) q^{15} +(9.50000 + 16.4545i) q^{16} +(23.2379 + 13.4164i) q^{17} +(11.9365 - 16.2025i) q^{18} +(-8.00000 - 13.8564i) q^{19} +2.23607i q^{20} +(-6.55544 + 19.9506i) q^{21} -25.0000 q^{22} +(-11.6190 + 6.70820i) q^{23} +(-4.11895 - 19.6986i) q^{24} +(-10.0000 + 17.3205i) q^{25} +(-3.87298 + 2.23607i) q^{26} +(-22.0000 + 15.6525i) q^{27} +(-3.50000 - 6.06218i) q^{28} -15.6525i q^{29} +(4.68246 - 14.2504i) q^{30} +(1.50000 - 2.59808i) q^{31} +(13.5554 + 7.82624i) q^{32} +(31.8649 + 10.4703i) q^{33} +60.0000 q^{34} +15.6525i q^{35} +(1.00000 - 8.94427i) q^{36} +(-6.00000 - 10.3923i) q^{37} +(-30.9839 - 17.8885i) q^{38} +(5.87298 - 1.22803i) q^{39} +(-7.50000 - 12.9904i) q^{40} -31.3050i q^{41} +(9.61088 + 45.9634i) q^{42} +44.0000 q^{43} +(-9.68246 + 5.59017i) q^{44} +(-11.9365 + 16.2025i) q^{45} +(-15.0000 + 25.9808i) q^{46} +(11.6190 - 6.70820i) q^{47} +(-38.0000 - 42.4853i) q^{48} +(-24.5000 - 42.4352i) q^{49} +44.7214i q^{50} +(-76.4758 - 25.1287i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(17.4284 + 10.0623i) q^{53} +(-25.1028 + 54.9076i) q^{54} +25.0000 q^{55} +(40.6663 + 23.4787i) q^{56} +(32.0000 + 35.7771i) q^{57} +(-17.5000 - 30.3109i) q^{58} +(-17.4284 - 10.0623i) q^{59} +(-1.37298 - 6.56619i) q^{60} +(13.0000 + 22.5167i) q^{61} -6.70820i q^{62} +(7.00000 - 62.6099i) q^{63} -41.0000 q^{64} +(3.87298 - 2.23607i) q^{65} +(73.4123 - 15.3504i) q^{66} +(-26.0000 + 45.0333i) q^{67} +(23.2379 - 13.4164i) q^{68} +(30.0000 - 26.8328i) q^{69} +(17.5000 + 30.3109i) q^{70} -93.9149i q^{71} +(24.1905 + 55.3156i) q^{72} +(-9.00000 + 15.5885i) q^{73} +(-23.2379 - 13.4164i) q^{74} +(18.7298 - 57.0017i) q^{75} -16.0000 q^{76} +(-67.7772 + 39.1312i) q^{77} +(10.0000 - 8.94427i) q^{78} +(39.5000 + 68.4160i) q^{79} +(-36.7933 - 21.2426i) q^{80} +(54.9919 - 59.4717i) q^{81} +(-35.0000 - 60.6218i) q^{82} +140.872i q^{83} +(14.0000 + 15.6525i) q^{84} -60.0000 q^{85} +(85.2056 - 49.1935i) q^{86} +(9.61088 + 45.9634i) q^{87} +(37.5000 - 64.9519i) q^{88} +(-42.6028 + 24.5967i) q^{89} +(-5.00000 + 44.7214i) q^{90} +(-7.00000 + 12.1244i) q^{91} +13.4164i q^{92} +(-2.80948 + 8.55025i) q^{93} +(15.0000 - 25.9808i) q^{94} +(30.9839 + 17.8885i) q^{95} +(-44.6109 - 14.6584i) q^{96} -93.0000 q^{97} +(-94.8881 - 54.7837i) q^{98} +(-100.000 - 11.1803i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{3} + 2q^{4} - 20q^{6} + 14q^{7} + 2q^{9} + O(q^{10})$$ $$4q - 4q^{3} + 2q^{4} - 20q^{6} + 14q^{7} + 2q^{9} - 10q^{10} + 4q^{12} - 8q^{13} + 20q^{15} + 38q^{16} + 40q^{18} - 32q^{19} + 28q^{21} - 100q^{22} + 30q^{24} - 40q^{25} - 88q^{27} - 14q^{28} - 20q^{30} + 6q^{31} + 50q^{33} + 240q^{34} + 4q^{36} - 24q^{37} + 8q^{39} - 30q^{40} - 70q^{42} + 176q^{43} - 40q^{45} - 60q^{46} - 152q^{48} - 98q^{49} - 120q^{51} - 4q^{52} + 70q^{54} + 100q^{55} + 128q^{57} - 70q^{58} + 10q^{60} + 52q^{61} + 28q^{63} - 164q^{64} + 100q^{66} - 104q^{67} + 120q^{69} + 70q^{70} + 120q^{72} - 36q^{73} - 80q^{75} - 64q^{76} + 40q^{78} + 158q^{79} + 158q^{81} - 140q^{82} + 56q^{84} - 240q^{85} - 70q^{87} + 150q^{88} - 20q^{90} - 28q^{91} + 12q^{93} + 60q^{94} - 70q^{96} - 372q^{97} - 400q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$$.

 $$n$$ $$8$$ $$10$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.93649 1.11803i 0.968246 0.559017i 0.0695448 0.997579i $$-0.477845\pi$$
0.898701 + 0.438562i $$0.144512\pi$$
$$3$$ −2.93649 + 0.614017i −0.978831 + 0.204672i
$$4$$ 0.500000 0.866025i 0.125000 0.216506i
$$5$$ −1.93649 + 1.11803i −0.387298 + 0.223607i −0.680989 0.732294i $$-0.738450\pi$$
0.293691 + 0.955901i $$0.405116\pi$$
$$6$$ −5.00000 + 4.47214i −0.833333 + 0.745356i
$$7$$ 3.50000 6.06218i 0.500000 0.866025i
$$8$$ 6.70820i 0.838525i
$$9$$ 8.24597 3.60611i 0.916219 0.400679i
$$10$$ −2.50000 + 4.33013i −0.250000 + 0.433013i
$$11$$ −9.68246 5.59017i −0.880223 0.508197i −0.00949140 0.999955i $$-0.503021\pi$$
−0.870732 + 0.491758i $$0.836355\pi$$
$$12$$ −0.936492 + 2.85008i −0.0780410 + 0.237507i
$$13$$ −2.00000 −0.153846 −0.0769231 0.997037i $$-0.524510\pi$$
−0.0769231 + 0.997037i $$0.524510\pi$$
$$14$$ 15.6525i 1.11803i
$$15$$ 5.00000 4.47214i 0.333333 0.298142i
$$16$$ 9.50000 + 16.4545i 0.593750 + 1.02841i
$$17$$ 23.2379 + 13.4164i 1.36694 + 0.789200i 0.990535 0.137257i $$-0.0438286\pi$$
0.376400 + 0.926457i $$0.377162\pi$$
$$18$$ 11.9365 16.2025i 0.663138 0.900137i
$$19$$ −8.00000 13.8564i −0.421053 0.729285i 0.574990 0.818160i $$-0.305006\pi$$
−0.996043 + 0.0888758i $$0.971673\pi$$
$$20$$ 2.23607i 0.111803i
$$21$$ −6.55544 + 19.9506i −0.312164 + 0.950028i
$$22$$ −25.0000 −1.13636
$$23$$ −11.6190 + 6.70820i −0.505172 + 0.291661i −0.730847 0.682542i $$-0.760875\pi$$
0.225675 + 0.974203i $$0.427541\pi$$
$$24$$ −4.11895 19.6986i −0.171623 0.820774i
$$25$$ −10.0000 + 17.3205i −0.400000 + 0.692820i
$$26$$ −3.87298 + 2.23607i −0.148961 + 0.0860026i
$$27$$ −22.0000 + 15.6525i −0.814815 + 0.579721i
$$28$$ −3.50000 6.06218i −0.125000 0.216506i
$$29$$ 15.6525i 0.539741i −0.962897 0.269870i $$-0.913019\pi$$
0.962897 0.269870i $$-0.0869808\pi$$
$$30$$ 4.68246 14.2504i 0.156082 0.475014i
$$31$$ 1.50000 2.59808i 0.0483871 0.0838089i −0.840817 0.541319i $$-0.817925\pi$$
0.889205 + 0.457510i $$0.151259\pi$$
$$32$$ 13.5554 + 7.82624i 0.423608 + 0.244570i
$$33$$ 31.8649 + 10.4703i 0.965604 + 0.317282i
$$34$$ 60.0000 1.76471
$$35$$ 15.6525i 0.447214i
$$36$$ 1.00000 8.94427i 0.0277778 0.248452i
$$37$$ −6.00000 10.3923i −0.162162 0.280873i 0.773482 0.633819i $$-0.218513\pi$$
−0.935644 + 0.352946i $$0.885180\pi$$
$$38$$ −30.9839 17.8885i −0.815365 0.470751i
$$39$$ 5.87298 1.22803i 0.150589 0.0314880i
$$40$$ −7.50000 12.9904i −0.187500 0.324760i
$$41$$ 31.3050i 0.763535i −0.924258 0.381768i $$-0.875315\pi$$
0.924258 0.381768i $$-0.124685\pi$$
$$42$$ 9.61088 + 45.9634i 0.228831 + 1.09437i
$$43$$ 44.0000 1.02326 0.511628 0.859207i $$-0.329043\pi$$
0.511628 + 0.859207i $$0.329043\pi$$
$$44$$ −9.68246 + 5.59017i −0.220056 + 0.127049i
$$45$$ −11.9365 + 16.2025i −0.265255 + 0.360055i
$$46$$ −15.0000 + 25.9808i −0.326087 + 0.564799i
$$47$$ 11.6190 6.70820i 0.247212 0.142728i −0.371275 0.928523i $$-0.621079\pi$$
0.618487 + 0.785795i $$0.287746\pi$$
$$48$$ −38.0000 42.4853i −0.791667 0.885110i
$$49$$ −24.5000 42.4352i −0.500000 0.866025i
$$50$$ 44.7214i 0.894427i
$$51$$ −76.4758 25.1287i −1.49953 0.492720i
$$52$$ −1.00000 + 1.73205i −0.0192308 + 0.0333087i
$$53$$ 17.4284 + 10.0623i 0.328838 + 0.189855i 0.655325 0.755347i $$-0.272532\pi$$
−0.326487 + 0.945202i $$0.605865\pi$$
$$54$$ −25.1028 + 54.9076i −0.464867 + 1.01681i
$$55$$ 25.0000 0.454545
$$56$$ 40.6663 + 23.4787i 0.726184 + 0.419263i
$$57$$ 32.0000 + 35.7771i 0.561404 + 0.627668i
$$58$$ −17.5000 30.3109i −0.301724 0.522602i
$$59$$ −17.4284 10.0623i −0.295397 0.170548i 0.344976 0.938611i $$-0.387887\pi$$
−0.640373 + 0.768064i $$0.721220\pi$$
$$60$$ −1.37298 6.56619i −0.0228831 0.109437i
$$61$$ 13.0000 + 22.5167i 0.213115 + 0.369126i 0.952688 0.303951i $$-0.0983058\pi$$
−0.739573 + 0.673076i $$0.764973\pi$$
$$62$$ 6.70820i 0.108197i
$$63$$ 7.00000 62.6099i 0.111111 0.993808i
$$64$$ −41.0000 −0.640625
$$65$$ 3.87298 2.23607i 0.0595844 0.0344010i
$$66$$ 73.4123 15.3504i 1.11231 0.232582i
$$67$$ −26.0000 + 45.0333i −0.388060 + 0.672139i −0.992189 0.124748i $$-0.960188\pi$$
0.604129 + 0.796887i $$0.293521\pi$$
$$68$$ 23.2379 13.4164i 0.341734 0.197300i
$$69$$ 30.0000 26.8328i 0.434783 0.388881i
$$70$$ 17.5000 + 30.3109i 0.250000 + 0.433013i
$$71$$ 93.9149i 1.32274i −0.750058 0.661372i $$-0.769974\pi$$
0.750058 0.661372i $$-0.230026\pi$$
$$72$$ 24.1905 + 55.3156i 0.335980 + 0.768273i
$$73$$ −9.00000 + 15.5885i −0.123288 + 0.213541i −0.921062 0.389415i $$-0.872677\pi$$
0.797775 + 0.602956i $$0.206010\pi$$
$$74$$ −23.2379 13.4164i −0.314026 0.181303i
$$75$$ 18.7298 57.0017i 0.249731 0.760023i
$$76$$ −16.0000 −0.210526
$$77$$ −67.7772 + 39.1312i −0.880223 + 0.508197i
$$78$$ 10.0000 8.94427i 0.128205 0.114670i
$$79$$ 39.5000 + 68.4160i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$80$$ −36.7933 21.2426i −0.459917 0.265533i
$$81$$ 54.9919 59.4717i 0.678913 0.734219i
$$82$$ −35.0000 60.6218i −0.426829 0.739290i
$$83$$ 140.872i 1.69726i 0.528990 + 0.848628i $$0.322571\pi$$
−0.528990 + 0.848628i $$0.677429\pi$$
$$84$$ 14.0000 + 15.6525i 0.166667 + 0.186339i
$$85$$ −60.0000 −0.705882
$$86$$ 85.2056 49.1935i 0.990763 0.572017i
$$87$$ 9.61088 + 45.9634i 0.110470 + 0.528315i
$$88$$ 37.5000 64.9519i 0.426136 0.738090i
$$89$$ −42.6028 + 24.5967i −0.478683 + 0.276368i −0.719868 0.694111i $$-0.755798\pi$$
0.241184 + 0.970479i $$0.422464\pi$$
$$90$$ −5.00000 + 44.7214i −0.0555556 + 0.496904i
$$91$$ −7.00000 + 12.1244i −0.0769231 + 0.133235i
$$92$$ 13.4164i 0.145831i
$$93$$ −2.80948 + 8.55025i −0.0302094 + 0.0919382i
$$94$$ 15.0000 25.9808i 0.159574 0.276391i
$$95$$ 30.9839 + 17.8885i 0.326146 + 0.188300i
$$96$$ −44.6109 14.6584i −0.464697 0.152692i
$$97$$ −93.0000 −0.958763 −0.479381 0.877607i $$-0.659139\pi$$
−0.479381 + 0.877607i $$0.659139\pi$$
$$98$$ −94.8881 54.7837i −0.968246 0.559017i
$$99$$ −100.000 11.1803i −1.01010 0.112933i
$$100$$ 10.0000 + 17.3205i 0.100000 + 0.173205i
$$101$$ 50.3488 + 29.0689i 0.498503 + 0.287811i 0.728095 0.685476i $$-0.240406\pi$$
−0.229592 + 0.973287i $$0.573739\pi$$
$$102$$ −176.190 + 36.8410i −1.72735 + 0.361186i
$$103$$ 41.0000 + 71.0141i 0.398058 + 0.689457i 0.993486 0.113952i $$-0.0363509\pi$$
−0.595428 + 0.803409i $$0.703018\pi$$
$$104$$ 13.4164i 0.129004i
$$105$$ −9.61088 45.9634i −0.0915322 0.437746i
$$106$$ 45.0000 0.424528
$$107$$ 56.1583 32.4230i 0.524844 0.303019i −0.214071 0.976818i $$-0.568672\pi$$
0.738914 + 0.673800i $$0.235339\pi$$
$$108$$ 2.55544 + 26.8788i 0.0236615 + 0.248878i
$$109$$ 72.0000 124.708i 0.660550 1.14411i −0.319921 0.947444i $$-0.603656\pi$$
0.980471 0.196663i $$-0.0630104\pi$$
$$110$$ 48.4123 27.9508i 0.440112 0.254099i
$$111$$ 24.0000 + 26.8328i 0.216216 + 0.241737i
$$112$$ 133.000 1.18750
$$113$$ 31.3050i 0.277035i 0.990360 + 0.138517i $$0.0442337\pi$$
−0.990360 + 0.138517i $$0.955766\pi$$
$$114$$ 101.968 + 33.5049i 0.894454 + 0.293903i
$$115$$ 15.0000 25.9808i 0.130435 0.225920i
$$116$$ −13.5554 7.82624i −0.116857 0.0674676i
$$117$$ −16.4919 + 7.21222i −0.140957 + 0.0616429i
$$118$$ −45.0000 −0.381356
$$119$$ 162.665 93.9149i 1.36694 0.789200i
$$120$$ 30.0000 + 33.5410i 0.250000 + 0.279508i
$$121$$ 2.00000 + 3.46410i 0.0165289 + 0.0286289i
$$122$$ 50.3488 + 29.0689i 0.412695 + 0.238270i
$$123$$ 19.2218 + 91.9267i 0.156275 + 0.747372i
$$124$$ −1.50000 2.59808i −0.0120968 0.0209522i
$$125$$ 100.623i 0.804984i
$$126$$ −56.4446 129.070i −0.447973 1.02436i
$$127$$ 177.000 1.39370 0.696850 0.717217i $$-0.254584\pi$$
0.696850 + 0.717217i $$0.254584\pi$$
$$128$$ −133.618 + 77.1443i −1.04389 + 0.602690i
$$129$$ −129.206 + 27.0167i −1.00159 + 0.209432i
$$130$$ 5.00000 8.66025i 0.0384615 0.0666173i
$$131$$ −164.602 + 95.0329i −1.25650 + 0.725442i −0.972393 0.233350i $$-0.925031\pi$$
−0.284109 + 0.958792i $$0.591698\pi$$
$$132$$ 25.0000 22.3607i 0.189394 0.169399i
$$133$$ −112.000 −0.842105
$$134$$ 116.276i 0.867728i
$$135$$ 25.1028 54.9076i 0.185947 0.406723i
$$136$$ −90.0000 + 155.885i −0.661765 + 1.14621i
$$137$$ −185.903 107.331i −1.35696 0.783440i −0.367745 0.929927i $$-0.619870\pi$$
−0.989213 + 0.146487i $$0.953203\pi$$
$$138$$ 28.0948 85.5025i 0.203585 0.619584i
$$139$$ −114.000 −0.820144 −0.410072 0.912053i $$-0.634496\pi$$
−0.410072 + 0.912053i $$0.634496\pi$$
$$140$$ 13.5554 + 7.82624i 0.0968246 + 0.0559017i
$$141$$ −30.0000 + 26.8328i −0.212766 + 0.190304i
$$142$$ −105.000 181.865i −0.739437 1.28074i
$$143$$ 19.3649 + 11.1803i 0.135419 + 0.0781842i
$$144$$ 137.673 + 101.425i 0.956065 + 0.704341i
$$145$$ 17.5000 + 30.3109i 0.120690 + 0.209041i
$$146$$ 40.2492i 0.275680i
$$147$$ 98.0000 + 109.567i 0.666667 + 0.745356i
$$148$$ −12.0000 −0.0810811
$$149$$ −11.6190 + 6.70820i −0.0779795 + 0.0450215i −0.538483 0.842637i $$-0.681002\pi$$
0.460503 + 0.887658i $$0.347669\pi$$
$$150$$ −27.4597 131.324i −0.183064 0.875493i
$$151$$ −29.5000 + 51.0955i −0.195364 + 0.338381i −0.947020 0.321175i $$-0.895922\pi$$
0.751656 + 0.659556i $$0.229256\pi$$
$$152$$ 92.9516 53.6656i 0.611524 0.353063i
$$153$$ 240.000 + 26.8328i 1.56863 + 0.175378i
$$154$$ −87.5000 + 151.554i −0.568182 + 0.984120i
$$155$$ 6.70820i 0.0432787i
$$156$$ 1.87298 5.70017i 0.0120063 0.0365395i
$$157$$ 124.000 214.774i 0.789809 1.36799i −0.136275 0.990671i $$-0.543513\pi$$
0.926084 0.377318i $$-0.123154\pi$$
$$158$$ 152.983 + 88.3247i 0.968246 + 0.559017i
$$159$$ −57.3569 18.8465i −0.360735 0.118532i
$$160$$ −35.0000 −0.218750
$$161$$ 93.9149i 0.583322i
$$162$$ 40.0000 176.649i 0.246914 1.09043i
$$163$$ 1.00000 + 1.73205i 0.00613497 + 0.0106261i 0.869077 0.494678i $$-0.164714\pi$$
−0.862942 + 0.505304i $$0.831380\pi$$
$$164$$ −27.1109 15.6525i −0.165310 0.0954419i
$$165$$ −73.4123 + 15.3504i −0.444923 + 0.0930329i
$$166$$ 157.500 + 272.798i 0.948795 + 1.64336i
$$167$$ 250.440i 1.49964i −0.661643 0.749819i $$-0.730140\pi$$
0.661643 0.749819i $$-0.269860\pi$$
$$168$$ −133.833 43.9752i −0.796623 0.261757i
$$169$$ −165.000 −0.976331
$$170$$ −116.190 + 67.0820i −0.683468 + 0.394600i
$$171$$ −115.935 85.4106i −0.677985 0.499477i
$$172$$ 22.0000 38.1051i 0.127907 0.221541i
$$173$$ 228.506 131.928i 1.32084 0.762590i 0.336981 0.941512i $$-0.390594\pi$$
0.983863 + 0.178922i $$0.0572609\pi$$
$$174$$ 70.0000 + 78.2624i 0.402299 + 0.449784i
$$175$$ 70.0000 + 121.244i 0.400000 + 0.692820i
$$176$$ 212.426i 1.20697i
$$177$$ 57.3569 + 18.8465i 0.324050 + 0.106478i
$$178$$ −55.0000 + 95.2628i −0.308989 + 0.535184i
$$179$$ 166.538 + 96.1509i 0.930381 + 0.537156i 0.886932 0.461900i $$-0.152832\pi$$
0.0434493 + 0.999056i $$0.486165\pi$$
$$180$$ 8.06351 + 18.4385i 0.0447973 + 0.102436i
$$181$$ 82.0000 0.453039 0.226519 0.974007i $$-0.427265\pi$$
0.226519 + 0.974007i $$0.427265\pi$$
$$182$$ 31.3050i 0.172005i
$$183$$ −52.0000 58.1378i −0.284153 0.317693i
$$184$$ −45.0000 77.9423i −0.244565 0.423599i
$$185$$ 23.2379 + 13.4164i 0.125610 + 0.0725211i
$$186$$ 4.11895 + 19.6986i 0.0221449 + 0.105906i
$$187$$ −150.000 259.808i −0.802139 1.38935i
$$188$$ 13.4164i 0.0713639i
$$189$$ 17.8881 + 188.152i 0.0946460 + 0.995511i
$$190$$ 80.0000 0.421053
$$191$$ −147.173 + 84.9706i −0.770541 + 0.444872i −0.833068 0.553171i $$-0.813418\pi$$
0.0625264 + 0.998043i $$0.480084\pi$$
$$192$$ 120.396 25.1747i 0.627063 0.131118i
$$193$$ −29.5000 + 51.0955i −0.152850 + 0.264744i −0.932274 0.361753i $$-0.882178\pi$$
0.779424 + 0.626496i $$0.215512\pi$$
$$194$$ −180.094 + 103.977i −0.928318 + 0.535965i
$$195$$ −10.0000 + 8.94427i −0.0512821 + 0.0458681i
$$196$$ −49.0000 −0.250000
$$197$$ 219.135i 1.11236i 0.831062 + 0.556179i $$0.187733\pi$$
−0.831062 + 0.556179i $$0.812267\pi$$
$$198$$ −206.149 + 90.1528i −1.04116 + 0.455317i
$$199$$ 117.000 202.650i 0.587940 1.01834i −0.406562 0.913623i $$-0.633273\pi$$
0.994502 0.104718i $$-0.0333941\pi$$
$$200$$ −116.190 67.0820i −0.580948 0.335410i
$$201$$ 48.6976 148.204i 0.242276 0.737335i
$$202$$ 130.000 0.643564
$$203$$ −94.8881 54.7837i −0.467429 0.269870i
$$204$$ −60.0000 + 53.6656i −0.294118 + 0.263067i
$$205$$ 35.0000 + 60.6218i 0.170732 + 0.295716i
$$206$$ 158.792 + 91.6788i 0.770836 + 0.445043i
$$207$$ −71.6190 + 97.2148i −0.345985 + 0.469637i
$$208$$ −19.0000 32.9090i −0.0913462 0.158216i
$$209$$ 178.885i 0.855911i
$$210$$ −70.0000 78.2624i −0.333333 0.372678i
$$211$$ −26.0000 −0.123223 −0.0616114 0.998100i $$-0.519624\pi$$
−0.0616114 + 0.998100i $$0.519624\pi$$
$$212$$ 17.4284 10.0623i 0.0822096 0.0474637i
$$213$$ 57.6653 + 275.780i 0.270729 + 1.29474i
$$214$$ 72.5000 125.574i 0.338785 0.586793i
$$215$$ −85.2056 + 49.1935i −0.396305 + 0.228807i
$$216$$ −105.000 147.580i −0.486111 0.683243i
$$217$$ −10.5000 18.1865i −0.0483871 0.0838089i
$$218$$ 321.994i 1.47704i
$$219$$ 16.8569 51.3015i 0.0769719 0.234254i
$$220$$ 12.5000 21.6506i 0.0568182 0.0984120i
$$221$$ −46.4758 26.8328i −0.210298 0.121415i
$$222$$ 76.4758 + 25.1287i 0.344486 + 0.113192i
$$223$$ −107.000 −0.479821 −0.239910 0.970795i $$-0.577118\pi$$
−0.239910 + 0.970795i $$0.577118\pi$$
$$224$$ 94.8881 54.7837i 0.423608 0.244570i
$$225$$ −20.0000 + 178.885i −0.0888889 + 0.795046i
$$226$$ 35.0000 + 60.6218i 0.154867 + 0.268238i
$$227$$ −261.426 150.935i −1.15166 0.664910i −0.202367 0.979310i $$-0.564863\pi$$
−0.949291 + 0.314400i $$0.898197\pi$$
$$228$$ 46.9839 9.82427i 0.206070 0.0430889i
$$229$$ 167.000 + 289.252i 0.729258 + 1.26311i 0.957197 + 0.289436i $$0.0934678\pi$$
−0.227940 + 0.973675i $$0.573199\pi$$
$$230$$ 67.0820i 0.291661i
$$231$$ 175.000 156.525i 0.757576 0.677596i
$$232$$ 105.000 0.452586
$$233$$ 232.379 134.164i 0.997335 0.575811i 0.0898761 0.995953i $$-0.471353\pi$$
0.907459 + 0.420141i $$0.138020\pi$$
$$234$$ −23.8730 + 32.4049i −0.102021 + 0.138483i
$$235$$ −15.0000 + 25.9808i −0.0638298 + 0.110556i
$$236$$ −17.4284 + 10.0623i −0.0738493 + 0.0426369i
$$237$$ −158.000 176.649i −0.666667 0.745356i
$$238$$ 210.000 363.731i 0.882353 1.52828i
$$239$$ 281.745i 1.17885i 0.807824 + 0.589424i $$0.200645\pi$$
−0.807824 + 0.589424i $$0.799355\pi$$
$$240$$ 121.087 + 39.7871i 0.504528 + 0.165780i
$$241$$ −89.5000 + 155.019i −0.371369 + 0.643230i −0.989776 0.142627i $$-0.954445\pi$$
0.618407 + 0.785858i $$0.287778\pi$$
$$242$$ 7.74597 + 4.47214i 0.0320081 + 0.0184799i
$$243$$ −124.967 + 208.404i −0.514266 + 0.857631i
$$244$$ 26.0000 0.106557
$$245$$ 94.8881 + 54.7837i 0.387298 + 0.223607i
$$246$$ 140.000 + 156.525i 0.569106 + 0.636280i
$$247$$ 16.0000 + 27.7128i 0.0647773 + 0.112198i
$$248$$ 17.4284 + 10.0623i 0.0702759 + 0.0405738i
$$249$$ −86.4980 413.670i −0.347381 1.66133i
$$250$$ −112.500 194.856i −0.450000 0.779423i
$$251$$ 172.177i 0.685965i 0.939342 + 0.342983i $$0.111437\pi$$
−0.939342 + 0.342983i $$0.888563\pi$$
$$252$$ −50.7218 37.3671i −0.201277 0.148282i
$$253$$ 150.000 0.592885
$$254$$ 342.759 197.892i 1.34944 0.779102i
$$255$$ 176.190 36.8410i 0.690939 0.144475i
$$256$$ −90.5000 + 156.751i −0.353516 + 0.612307i
$$257$$ 228.506 131.928i 0.889128 0.513339i 0.0154711 0.999880i $$-0.495075\pi$$
0.873657 + 0.486542i $$0.161742\pi$$
$$258$$ −220.000 + 196.774i −0.852713 + 0.762690i
$$259$$ −84.0000 −0.324324
$$260$$ 4.47214i 0.0172005i
$$261$$ −56.4446 129.070i −0.216263 0.494520i
$$262$$ −212.500 + 368.061i −0.811069 + 1.40481i
$$263$$ 30.9839 + 17.8885i 0.117809 + 0.0680173i 0.557747 0.830011i $$-0.311666\pi$$
−0.439937 + 0.898028i $$0.644999\pi$$
$$264$$ −70.2369 + 213.756i −0.266049 + 0.809683i
$$265$$ −45.0000 −0.169811
$$266$$ −216.887 + 125.220i −0.815365 + 0.470751i
$$267$$ 110.000 98.3870i 0.411985 0.368491i
$$268$$ 26.0000 + 45.0333i 0.0970149 + 0.168035i
$$269$$ −342.759 197.892i −1.27420 0.735658i −0.298422 0.954434i $$-0.596460\pi$$
−0.975775 + 0.218776i $$0.929794\pi$$
$$270$$ −12.7772 134.394i −0.0473230 0.497755i
$$271$$ −228.500 395.774i −0.843173 1.46042i −0.887198 0.461389i $$-0.847351\pi$$
0.0440246 0.999030i $$-0.485982\pi$$
$$272$$ 509.823i 1.87435i
$$273$$ 13.1109 39.9012i 0.0480252 0.146158i
$$274$$ −480.000 −1.75182
$$275$$ 193.649 111.803i 0.704179 0.406558i
$$276$$ −8.23790 39.3972i −0.0298475 0.142743i
$$277$$ −26.0000 + 45.0333i −0.0938628 + 0.162575i −0.909133 0.416505i $$-0.863255\pi$$
0.815271 + 0.579080i $$0.196588\pi$$
$$278$$ −220.760 + 127.456i −0.794101 + 0.458474i
$$279$$ 3.00000 26.8328i 0.0107527 0.0961750i
$$280$$ −105.000 −0.375000
$$281$$ 125.220i 0.445622i −0.974862 0.222811i $$-0.928477\pi$$
0.974862 0.222811i $$-0.0715233\pi$$
$$282$$ −28.0948 + 85.5025i −0.0996268 + 0.303201i
$$283$$ −44.0000 + 76.2102i −0.155477 + 0.269294i −0.933233 0.359273i $$-0.883025\pi$$
0.777756 + 0.628567i $$0.216358\pi$$
$$284$$ −81.3327 46.9574i −0.286383 0.165343i
$$285$$ −101.968 33.5049i −0.357782 0.117561i
$$286$$ 50.0000 0.174825
$$287$$ −189.776 109.567i −0.661241 0.381768i
$$288$$ 140.000 + 15.6525i 0.486111 + 0.0543489i
$$289$$ 215.500 + 373.257i 0.745675 + 1.29155i
$$290$$ 67.7772 + 39.1312i 0.233715 + 0.134935i
$$291$$ 273.094 57.1036i 0.938466 0.196232i
$$292$$ 9.00000 + 15.5885i 0.0308219 + 0.0533851i
$$293$$ 15.6525i 0.0534214i 0.999643 + 0.0267107i $$0.00850329\pi$$
−0.999643 + 0.0267107i $$0.991497\pi$$
$$294$$ 312.276 + 102.609i 1.06216 + 0.349010i
$$295$$ 45.0000 0.152542
$$296$$ 69.7137 40.2492i 0.235519 0.135977i
$$297$$ 300.514 28.5707i 1.01183 0.0961977i
$$298$$ −15.0000 + 25.9808i −0.0503356 + 0.0871838i
$$299$$ 23.2379 13.4164i 0.0777187 0.0448709i
$$300$$ −40.0000 44.7214i −0.133333 0.149071i
$$301$$ 154.000 266.736i 0.511628 0.886166i
$$302$$ 131.928i 0.436848i
$$303$$ −165.698 54.4455i −0.546857 0.179688i
$$304$$ 152.000 263.272i 0.500000 0.866025i
$$305$$ −50.3488 29.0689i −0.165078 0.0953078i
$$306$$ 494.758 216.367i 1.61686 0.707081i
$$307$$ 166.000 0.540717 0.270358 0.962760i $$-0.412858\pi$$
0.270358 + 0.962760i $$0.412858\pi$$
$$308$$ 78.2624i 0.254099i
$$309$$ −164.000 183.358i −0.530744 0.593390i
$$310$$ 7.50000 + 12.9904i 0.0241935 + 0.0419045i
$$311$$ 267.236 + 154.289i 0.859279 + 0.496105i 0.863771 0.503885i $$-0.168096\pi$$
−0.00449160 + 0.999990i $$0.501430\pi$$
$$312$$ 8.23790 + 39.3972i 0.0264035 + 0.126273i
$$313$$ 135.500 + 234.693i 0.432907 + 0.749818i 0.997122 0.0758104i $$-0.0241544\pi$$
−0.564215 + 0.825628i $$0.690821\pi$$
$$314$$ 554.545i 1.76607i
$$315$$ 56.4446 + 129.070i 0.179189 + 0.409745i
$$316$$ 79.0000 0.250000
$$317$$ −377.616 + 218.017i −1.19122 + 0.687750i −0.958583 0.284815i $$-0.908068\pi$$
−0.232635 + 0.972564i $$0.574735\pi$$
$$318$$ −132.142 + 27.6308i −0.415541 + 0.0868892i
$$319$$ −87.5000 + 151.554i −0.274295 + 0.475092i
$$320$$ 79.3962 45.8394i 0.248113 0.143248i
$$321$$ −145.000 + 129.692i −0.451713 + 0.404025i
$$322$$ 105.000 + 181.865i 0.326087 + 0.564799i
$$323$$ 429.325i 1.32918i
$$324$$ −24.0081 77.3603i −0.0740990 0.238766i
$$325$$ 20.0000 34.6410i 0.0615385 0.106588i
$$326$$ 3.87298 + 2.23607i 0.0118803 + 0.00685910i
$$327$$ −134.855 + 410.412i −0.412400 + 1.25508i
$$328$$ 210.000 0.640244
$$329$$ 93.9149i 0.285455i
$$330$$ −125.000 + 111.803i −0.378788 + 0.338798i
$$331$$ 8.00000 + 13.8564i 0.0241692 + 0.0418623i 0.877857 0.478923i $$-0.158973\pi$$
−0.853688 + 0.520785i $$0.825639\pi$$
$$332$$ 121.999 + 70.4361i 0.367467 + 0.212157i
$$333$$ −86.9516 64.0579i −0.261116 0.192366i
$$334$$ −280.000 484.974i −0.838323 1.45202i
$$335$$ 116.276i 0.347091i
$$336$$ −390.553 + 81.6642i −1.16236 + 0.243048i
$$337$$ −509.000 −1.51039 −0.755193 0.655503i $$-0.772457\pi$$
−0.755193 + 0.655503i $$0.772457\pi$$
$$338$$ −319.521 + 184.476i −0.945329 + 0.545786i
$$339$$ −19.2218 91.9267i −0.0567014 0.271170i
$$340$$ −30.0000 + 51.9615i −0.0882353 + 0.152828i
$$341$$ −29.0474 + 16.7705i −0.0851829 + 0.0491804i
$$342$$ −320.000 35.7771i −0.935673 0.104611i
$$343$$ −343.000 −1.00000
$$344$$ 295.161i 0.858026i
$$345$$ −28.0948 + 85.5025i −0.0814341 + 0.247833i
$$346$$ 295.000 510.955i 0.852601 1.47675i
$$347$$ 329.204 + 190.066i 0.948713 + 0.547740i 0.892681 0.450689i $$-0.148822\pi$$
0.0560324 + 0.998429i $$0.482155\pi$$
$$348$$ 44.6109 + 14.6584i 0.128192 + 0.0421219i
$$349$$ 628.000 1.79943 0.899713 0.436481i $$-0.143775\pi$$
0.899713 + 0.436481i $$0.143775\pi$$
$$350$$ 271.109 + 156.525i 0.774597 + 0.447214i
$$351$$ 44.0000 31.3050i 0.125356 0.0891879i
$$352$$ −87.5000 151.554i −0.248580 0.430552i
$$353$$ 402.790 + 232.551i 1.14105 + 0.658785i 0.946690 0.322146i $$-0.104404\pi$$
0.194359 + 0.980931i $$0.437737\pi$$
$$354$$ 132.142 27.6308i 0.373283 0.0780530i
$$355$$ 105.000 + 181.865i 0.295775 + 0.512297i
$$356$$ 49.1935i 0.138184i
$$357$$ −420.000 + 375.659i −1.17647 + 1.05227i
$$358$$ 430.000 1.20112
$$359$$ −201.395 + 116.276i −0.560989 + 0.323887i −0.753542 0.657399i $$-0.771657\pi$$
0.192553 + 0.981287i $$0.438323\pi$$
$$360$$ −108.690 80.0724i −0.301915 0.222423i
$$361$$ 52.5000 90.9327i 0.145429 0.251891i
$$362$$ 158.792 91.6788i 0.438653 0.253256i
$$363$$ −8.00000 8.94427i −0.0220386 0.0246399i
$$364$$ 7.00000 + 12.1244i 0.0192308 + 0.0333087i
$$365$$ 40.2492i 0.110272i
$$366$$ −165.698 54.4455i −0.452726 0.148758i
$$367$$ −250.500 + 433.879i −0.682561 + 1.18223i 0.291635 + 0.956530i $$0.405801\pi$$
−0.974197 + 0.225701i $$0.927533\pi$$
$$368$$ −220.760 127.456i −0.599891 0.346347i
$$369$$ −112.889 258.140i −0.305933 0.699565i
$$370$$ 60.0000 0.162162
$$371$$ 121.999 70.4361i 0.328838 0.189855i
$$372$$ 6.00000 + 6.70820i 0.0161290 + 0.0180328i
$$373$$ −349.000 604.486i −0.935657 1.62061i −0.773458 0.633847i $$-0.781475\pi$$
−0.162198 0.986758i $$-0.551858\pi$$
$$374$$ −580.948 335.410i −1.55334 0.896819i
$$375$$ 61.7843 + 295.479i 0.164758 + 0.787943i
$$376$$ 45.0000 + 77.9423i 0.119681 + 0.207293i
$$377$$ 31.3050i 0.0830370i
$$378$$ 245.000 + 344.354i 0.648148 + 0.910991i
$$379$$ 366.000 0.965699 0.482850 0.875703i $$-0.339602\pi$$
0.482850 + 0.875703i $$0.339602\pi$$
$$380$$ 30.9839 17.8885i 0.0815365 0.0470751i
$$381$$ −519.759 + 108.681i −1.36420 + 0.285252i
$$382$$ −190.000 + 329.090i −0.497382 + 0.861491i
$$383$$ 11.6190 6.70820i 0.0303367 0.0175149i −0.484755 0.874650i $$-0.661091\pi$$
0.515092 + 0.857135i $$0.327758\pi$$
$$384$$ 345.000 308.577i 0.898438 0.803587i
$$385$$ 87.5000 151.554i 0.227273 0.393648i
$$386$$ 131.928i 0.341782i
$$387$$ 362.823 158.669i 0.937526 0.409997i
$$388$$ −46.5000 + 80.5404i −0.119845 + 0.207578i
$$389$$ 58.0948 + 33.5410i 0.149344 + 0.0862237i 0.572810 0.819688i $$-0.305853\pi$$
−0.423466 + 0.905912i $$0.639187\pi$$
$$390$$ −9.36492 + 28.5008i −0.0240126 + 0.0730791i
$$391$$ −360.000 −0.920716
$$392$$ 284.664 164.351i 0.726184 0.419263i
$$393$$ 425.000 380.132i 1.08142 0.967256i
$$394$$ 245.000 + 424.352i 0.621827 + 1.07704i
$$395$$ −152.983 88.3247i −0.387298 0.223607i
$$396$$ −59.6825 + 81.0124i −0.150713 + 0.204577i
$$397$$ 132.000 + 228.631i 0.332494 + 0.575896i 0.983000 0.183605i $$-0.0587766\pi$$
−0.650506 + 0.759501i $$0.725443\pi$$
$$398$$ 523.240i 1.31467i
$$399$$ 328.887 68.7699i 0.824278 0.172356i
$$400$$ −380.000 −0.950000
$$401$$ −92.9516 + 53.6656i −0.231800 + 0.133830i −0.611402 0.791320i $$-0.709394\pi$$
0.379602 + 0.925150i $$0.376061\pi$$
$$402$$ −71.3951 341.442i −0.177600 0.849359i
$$403$$ −3.00000 + 5.19615i −0.00744417 + 0.0128937i
$$404$$ 50.3488 29.0689i 0.124626 0.0719527i
$$405$$ −40.0000 + 176.649i −0.0987654 + 0.436171i
$$406$$ −245.000 −0.603448
$$407$$ 134.164i 0.329641i
$$408$$ 168.569 513.015i 0.413158 1.25739i
$$409$$ 99.5000 172.339i 0.243276 0.421367i −0.718369 0.695662i $$-0.755111\pi$$
0.961646 + 0.274295i $$0.0884445\pi$$
$$410$$ 135.554 + 78.2624i 0.330621 + 0.190884i
$$411$$ 611.806 + 201.030i 1.48858 + 0.489123i
$$412$$ 82.0000 0.199029
$$413$$ −121.999 + 70.4361i −0.295397 + 0.170548i
$$414$$ −30.0000 + 268.328i −0.0724638 + 0.648136i
$$415$$ −157.500 272.798i −0.379518 0.657345i
$$416$$ −27.1109 15.6525i −0.0651704 0.0376261i
$$417$$ 334.760 69.9979i 0.802782 0.167861i
$$418$$ 200.000 + 346.410i 0.478469 + 0.828732i
$$419$$ 93.9149i 0.224140i 0.993700 + 0.112070i $$0.0357482\pi$$
−0.993700 + 0.112070i $$0.964252\pi$$
$$420$$ −44.6109 14.6584i −0.106216 0.0349010i
$$421$$ 254.000 0.603325 0.301663 0.953415i $$-0.402458\pi$$
0.301663 + 0.953415i $$0.402458\pi$$
$$422$$ −50.3488 + 29.0689i −0.119310 + 0.0688836i
$$423$$ 71.6190 97.2148i 0.169312 0.229822i
$$424$$ −67.5000 + 116.913i −0.159198 + 0.275739i
$$425$$ −464.758 + 268.328i −1.09355 + 0.631360i
$$426$$ 420.000 + 469.574i 0.985915 + 1.10229i
$$427$$ 182.000 0.426230
$$428$$ 64.8460i 0.151509i
$$429$$ −63.7298 20.9406i −0.148554 0.0488126i
$$430$$ −110.000 + 190.526i −0.255814 + 0.443083i
$$431$$ −104.571 60.3738i −0.242623 0.140079i 0.373759 0.927526i $$-0.378069\pi$$
−0.616382 + 0.787447i $$0.711402\pi$$
$$432$$ −466.553 213.300i −1.07998 0.493750i
$$433$$ −506.000 −1.16859 −0.584296 0.811541i $$-0.698629\pi$$
−0.584296 + 0.811541i $$0.698629\pi$$
$$434$$ −40.6663 23.4787i −0.0937012 0.0540984i
$$435$$ −70.0000 78.2624i −0.160920 0.179914i
$$436$$ −72.0000 124.708i −0.165138 0.286027i
$$437$$ 185.903 + 107.331i 0.425408 + 0.245609i
$$438$$ −24.7137 118.192i −0.0564240 0.269844i
$$439$$ −235.500 407.898i −0.536446 0.929153i −0.999092 0.0426091i $$-0.986433\pi$$
0.462645 0.886543i $$-0.346900\pi$$
$$440$$ 167.705i 0.381148i
$$441$$ −355.052 261.570i −0.805107 0.593129i
$$442$$ −120.000 −0.271493
$$443$$ −52.2853 + 30.1869i −0.118025 + 0.0681420i −0.557851 0.829941i $$-0.688374\pi$$
0.439825 + 0.898083i $$0.355040\pi$$
$$444$$ 35.2379 7.36820i 0.0793646 0.0165950i
$$445$$ 55.0000 95.2628i 0.123596 0.214074i
$$446$$ −207.205 + 119.630i −0.464584 + 0.268228i
$$447$$ 30.0000 26.8328i 0.0671141 0.0600287i
$$448$$ −143.500 + 248.549i −0.320312 + 0.554798i
$$449$$ 281.745i 0.627493i 0.949507 + 0.313747i $$0.101584\pi$$
−0.949507 + 0.313747i $$0.898416\pi$$
$$450$$ 161.270 + 368.771i 0.358378 + 0.819491i
$$451$$ −175.000 + 303.109i −0.388027 + 0.672082i
$$452$$ 27.1109 + 15.6525i 0.0599798 + 0.0346294i
$$453$$ 55.2530 168.155i 0.121971 0.371203i
$$454$$ −675.000 −1.48678
$$455$$ 31.3050i 0.0688021i
$$456$$ −240.000 + 214.663i −0.526316 + 0.470751i
$$457$$ 11.5000 + 19.9186i 0.0251641 + 0.0435855i 0.878333 0.478049i $$-0.158656\pi$$
−0.853169 + 0.521634i $$0.825323\pi$$
$$458$$ 646.788 + 373.423i 1.41220 + 0.815335i
$$459$$ −721.234 + 68.5697i −1.57132 + 0.149389i
$$460$$ −15.0000 25.9808i −0.0326087 0.0564799i
$$461$$ 594.794i 1.29023i −0.764087 0.645113i $$-0.776810\pi$$
0.764087 0.645113i $$-0.223190\pi$$
$$462$$ 163.886 498.765i 0.354732 1.07958i
$$463$$ 58.0000 0.125270 0.0626350 0.998037i $$-0.480050\pi$$
0.0626350 + 0.998037i $$0.480050\pi$$
$$464$$ 257.553 148.699i 0.555072 0.320471i
$$465$$ −4.11895 19.6986i −0.00885796 0.0423625i
$$466$$ 300.000 519.615i 0.643777 1.11505i
$$467$$ 499.615 288.453i 1.06984 0.617672i 0.141702 0.989909i $$-0.454743\pi$$
0.928137 + 0.372238i $$0.121409\pi$$
$$468$$ −2.00000 + 17.8885i −0.00427350 + 0.0382234i
$$469$$ 182.000 + 315.233i 0.388060 + 0.672139i
$$470$$ 67.0820i 0.142728i
$$471$$ −232.250 + 706.821i −0.493100 + 1.50068i
$$472$$ 67.5000 116.913i 0.143008 0.247698i
$$473$$ −426.028 245.967i −0.900694 0.520016i
$$474$$ −503.466 165.431i −1.06216 0.349010i
$$475$$ 320.000 0.673684
$$476$$ 187.830i 0.394600i
$$477$$ 180.000 + 20.1246i 0.377358 + 0.0421900i
$$478$$ 315.000 + 545.596i 0.658996 + 1.14141i
$$479$$ 294.347 + 169.941i 0.614503 + 0.354783i 0.774726 0.632298i $$-0.217888\pi$$
−0.160223 + 0.987081i $$0.551221\pi$$
$$480$$ 102.777 21.4906i 0.214119 0.0447721i
$$481$$ 12.0000 + 20.7846i 0.0249480 + 0.0432112i
$$482$$ 400.256i 0.830407i
$$483$$ −57.6653 275.780i −0.119390 0.570973i
$$484$$ 4.00000 0.00826446
$$485$$ 180.094 103.977i 0.371327 0.214386i
$$486$$ −8.99398 + 543.290i −0.0185061 + 1.11788i
$$487$$ 404.500 700.615i 0.830595 1.43863i −0.0669712 0.997755i $$-0.521334\pi$$
0.897567 0.440879i $$-0.145333\pi$$
$$488$$ −151.046 + 87.2067i −0.309521 + 0.178702i
$$489$$ −4.00000 4.47214i −0.00817996 0.00914547i
$$490$$ 245.000 0.500000
$$491$$ 453.922i 0.924484i −0.886754 0.462242i $$-0.847045\pi$$
0.886754 0.462242i $$-0.152955\pi$$
$$492$$ 89.2218 + 29.3168i 0.181345 + 0.0595870i
$$493$$ 210.000 363.731i 0.425963 0.737790i
$$494$$ 61.9677 + 35.7771i 0.125441 + 0.0724233i
$$495$$ 206.149 90.1528i 0.416463 0.182127i
$$496$$ 57.0000 0.114919
$$497$$ −569.329 328.702i −1.14553 0.661372i
$$498$$ −630.000 704.361i −1.26506 1.41438i
$$499$$ 127.000 + 219.970i 0.254509 + 0.440823i 0.964762 0.263124i $$-0.0847528\pi$$
−0.710253 + 0.703946i $$0.751419\pi$$
$$500$$ −87.1421 50.3115i −0.174284 0.100623i
$$501$$ 153.774 + 735.414i 0.306934 + 1.46789i
$$502$$ 192.500 + 333.420i 0.383466 + 0.664183i
$$503$$ 939.149i 1.86709i 0.358454 + 0.933547i $$0.383304\pi$$
−0.358454 + 0.933547i $$0.616696\pi$$
$$504$$ 420.000 + 46.9574i 0.833333 + 0.0931695i
$$505$$ −130.000 −0.257426
$$506$$ 290.474 167.705i 0.574059 0.331433i
$$507$$ 484.521 101.313i 0.955663 0.199828i
$$508$$ 88.5000 153.286i 0.174213 0.301745i
$$509$$ 350.505 202.364i 0.688615 0.397572i −0.114478 0.993426i $$-0.536520\pi$$
0.803093 + 0.595854i $$0.203186\pi$$
$$510$$ 300.000 268.328i 0.588235 0.526134i
$$511$$ 63.0000 + 109.119i 0.123288 + 0.213541i
$$512$$ 212.426i 0.414895i
$$513$$ 392.887 + 179.621i 0.765862 + 0.350139i
$$514$$ 295.000 510.955i 0.573930 0.994076i
$$515$$ −158.792 91.6788i −0.308335 0.178017i
$$516$$ −41.2056 + 125.404i −0.0798559 + 0.243030i
$$517$$ −150.000 −0.290135
$$518$$ −162.665 + 93.9149i −0.314026 + 0.181303i
$$519$$ −590.000 + 527.712i −1.13680 + 1.01679i
$$520$$ 15.0000 + 25.9808i 0.0288462 + 0.0499630i
$$521$$ −302.093 174.413i −0.579832 0.334766i 0.181234 0.983440i $$-0.441991\pi$$
−0.761067 + 0.648674i $$0.775324\pi$$
$$522$$ −253.609 186.836i −0.485841 0.357923i
$$523$$ −197.000 341.214i −0.376673 0.652417i 0.613903 0.789382i $$-0.289599\pi$$
−0.990576 + 0.136965i $$0.956265\pi$$
$$524$$ 190.066i 0.362721i
$$525$$ −280.000 313.050i −0.533333 0.596285i
$$526$$ 80.0000 0.152091
$$527$$ 69.7137 40.2492i 0.132284 0.0763742i
$$528$$ 130.433 + 623.789i 0.247033 + 1.18142i
$$529$$ −174.500 + 302.243i −0.329868 + 0.571348i
$$530$$ −87.1421 + 50.3115i −0.164419 + 0.0949274i
$$531$$ −180.000 20.1246i −0.338983 0.0378995i
$$532$$ −56.0000 + 96.9948i −0.105263 + 0.182321i
$$533$$ 62.6099i 0.117467i
$$534$$ 103.014 313.509i 0.192910 0.587096i
$$535$$ −72.5000 + 125.574i −0.135514 + 0.234717i
$$536$$ −302.093 174.413i −0.563606 0.325398i
$$537$$ −548.077 180.089i −1.02063 0.335361i
$$538$$ −885.000 −1.64498
$$539$$ 547.837i 1.01639i
$$540$$ −35.0000 49.1935i −0.0648148 0.0910991i
$$541$$ −202.000 349.874i −0.373383 0.646718i 0.616701 0.787198i $$-0.288469\pi$$
−0.990084 + 0.140480i $$0.955135\pi$$
$$542$$ −884.977 510.942i −1.63280 0.942697i
$$543$$ −240.792 + 50.3494i −0.443448 + 0.0927245i
$$544$$ 210.000 + 363.731i 0.386029 + 0.668623i
$$545$$ 321.994i 0.590814i
$$546$$ −19.2218 91.9267i −0.0352047 0.168364i
$$547$$ 16.0000 0.0292505 0.0146252 0.999893i $$-0.495344\pi$$
0.0146252 + 0.999893i $$0.495344\pi$$
$$548$$ −185.903 + 107.331i −0.339239 + 0.195860i
$$549$$ 188.395 + 138.792i 0.343161 + 0.252809i
$$550$$ 250.000 433.013i 0.454545 0.787296i
$$551$$ −216.887 + 125.220i −0.393624 + 0.227259i
$$552$$ 180.000 + 201.246i 0.326087 + 0.364576i
$$553$$ 553.000 1.00000
$$554$$ 116.276i 0.209884i
$$555$$ −76.4758 25.1287i −0.137794 0.0452770i
$$556$$ −57.0000 + 98.7269i −0.102518 + 0.177566i
$$557$$ 640.979 + 370.069i 1.15077 + 0.664397i 0.949075 0.315051i $$-0.102022\pi$$
0.201695 + 0.979448i $$0.435355\pi$$
$$558$$ −24.1905 55.3156i −0.0433522 0.0991319i
$$559$$ −88.0000 −0.157424
$$560$$ −257.553 + 148.699i −0.459917 + 0.265533i
$$561$$ 600.000 + 670.820i 1.06952 + 1.19576i
$$562$$ −140.000 242.487i −0.249110 0.431472i
$$563$$ −207.205 119.630i −0.368037 0.212486i 0.304564 0.952492i $$-0.401489\pi$$
−0.672600 + 0.740006i $$0.734823\pi$$
$$564$$ 8.23790 + 39.3972i 0.0146062 + 0.0698531i
$$565$$ −35.0000 60.6218i −0.0619469 0.107295i
$$566$$ 196.774i 0.347657i
$$567$$ −168.056 541.522i −0.296396 0.955065i
$$568$$ 630.000 1.10915
$$569$$ 828.818 478.519i 1.45662 0.840982i 0.457780 0.889066i $$-0.348645\pi$$
0.998843 + 0.0480841i $$0.0153115\pi$$
$$570$$ −234.919 + 49.1213i −0.412139 + 0.0861778i
$$571$$ 23.0000 39.8372i 0.0402802 0.0697674i −0.845182 0.534478i $$-0.820508\pi$$
0.885463 + 0.464711i $$0.153842\pi$$
$$572$$ 19.3649 11.1803i 0.0338547 0.0195460i
$$573$$ 380.000 339.882i 0.663176 0.593163i
$$574$$ −490.000 −0.853659
$$575$$ 268.328i 0.466658i
$$576$$ −338.085 + 147.851i −0.586952 + 0.256685i
$$577$$ −495.500 + 858.231i −0.858752 + 1.48740i 0.0143677 + 0.999897i $$0.495426\pi$$
−0.873120 + 0.487506i $$0.837907\pi$$
$$578$$ 834.628 + 481.873i 1.44399 + 0.833690i
$$579$$ 55.2530 168.155i 0.0954283 0.290423i
$$580$$ 35.0000 0.0603448
$$581$$ 853.993 + 493.053i 1.46987 + 0.848628i
$$582$$ 465.000 415.909i 0.798969 0.714620i
$$583$$ −112.500 194.856i −0.192967 0.334229i
$$584$$ −104.571 60.3738i −0.179059 0.103380i
$$585$$ 23.8730 32.4049i 0.0408085 0.0553931i
$$586$$ 17.5000 + 30.3109i 0.0298635 + 0.0517251i
$$587$$ 766.971i 1.30660i −0.757101 0.653298i $$-0.773385\pi$$
0.757101 0.653298i $$-0.226615\pi$$
$$588$$ 143.888 30.0868i 0.244708 0.0511681i
$$589$$ −48.0000 −0.0814941
$$590$$ 87.1421 50.3115i 0.147699 0.0852738i
$$591$$ −134.552 643.487i −0.227669 1.08881i
$$592$$ 114.000 197.454i 0.192568 0.333537i
$$593$$ −151.046 + 87.2067i −0.254716 + 0.147060i −0.621922 0.783080i $$-0.713648\pi$$
0.367206 + 0.930140i $$0.380314\pi$$
$$594$$ 550.000 391.312i 0.925926 0.658774i
$$595$$ −210.000 + 363.731i −0.352941 + 0.611312i
$$596$$ 13.4164i 0.0225108i
$$597$$ −219.139 + 666.920i −0.367067 + 1.11712i
$$598$$ 30.0000 51.9615i 0.0501672 0.0868922i
$$599$$ −836.564 482.991i −1.39660 0.806328i −0.402567 0.915391i $$-0.631882\pi$$
−0.994035 + 0.109062i $$0.965215\pi$$
$$600$$ 382.379 + 125.644i 0.637298 + 0.209406i
$$601$$ −471.000 −0.783694 −0.391847 0.920030i $$-0.628164\pi$$
−0.391847 + 0.920030i $$0.628164\pi$$
$$602$$ 688.709i 1.14403i
$$603$$ −52.0000 + 465.102i −0.0862355 + 0.771314i
$$604$$ 29.5000 + 51.0955i 0.0488411 + 0.0845952i
$$605$$ −7.74597 4.47214i −0.0128033 0.00739196i
$$606$$ −381.744 + 79.8222i −0.629940 + 0.131720i
$$607$$ 471.500 + 816.662i 0.776771 + 1.34541i 0.933794 + 0.357812i $$0.116477\pi$$
−0.157023 + 0.987595i $$0.550190\pi$$
$$608$$ 250.440i 0.411907i
$$609$$ 312.276 + 102.609i 0.512769 + 0.168488i
$$610$$ −130.000 −0.213115
$$611$$ −23.2379 + 13.4164i −0.0380326 + 0.0219581i
$$612$$ 143.238 194.430i 0.234049 0.317696i
$$613$$ −467.000 + 808.868i −0.761827 + 1.31952i 0.180081 + 0.983652i $$0.442364\pi$$
−0.941908 + 0.335871i $$0.890969\pi$$
$$614$$ 321.458 185.594i 0.523547 0.302270i
$$615$$ −140.000 156.525i −0.227642 0.254512i
$$616$$ −262.500 454.663i −0.426136 0.738090i
$$617$$ 93.9149i 0.152212i −0.997100 0.0761060i $$-0.975751\pi$$
0.997100 0.0761060i $$-0.0242488\pi$$
$$618$$ −522.585 171.713i −0.845606 0.277852i
$$619$$ 61.0000 105.655i 0.0985460 0.170687i −0.812537 0.582910i $$-0.801914\pi$$
0.911083 + 0.412223i $$0.135247\pi$$
$$620$$ 5.80948 + 3.35410i 0.00937012 + 0.00540984i
$$621$$ 150.617 329.446i 0.242539 0.530509i
$$622$$ 690.000 1.10932
$$623$$ 344.354i 0.552736i
$$624$$ 76.0000 + 84.9706i 0.121795 + 0.136171i
$$625$$ −137.500 238.157i −0.220000 0.381051i
$$626$$ 524.789 + 302.987i 0.838321 + 0.484005i
$$627$$ −109.839 525.296i −0.175181 0.837792i
$$628$$ −124.000 214.774i −0.197452 0.341997i
$$629$$ 321.994i 0.511914i
$$630$$ 253.609 + 186.836i 0.402554 + 0.296565i
$$631$$ −61.0000 −0.0966719 −0.0483360 0.998831i $$-0.515392\pi$$
−0.0483360 + 0.998831i $$0.515392\pi$$
$$632$$ −458.949 + 264.974i −0.726184 + 0.419263i
$$633$$ 76.3488 15.9644i 0.120614 0.0252203i
$$634$$ −487.500 + 844.375i −0.768927 + 1.33182i
$$635$$ −342.759 + 197.892i −0.539778 + 0.311641i
$$636$$ −45.0000 + 40.2492i −0.0707547 + 0.0632849i
$$637$$ 49.0000 + 84.8705i 0.0769231 + 0.133235i
$$638$$ 391.312i 0.613342i
$$639$$ −338.667 774.419i −0.529996 1.21192i
$$640$$ 172.500 298.779i 0.269531 0.466842i
$$641$$ 708.756 + 409.200i 1.10570 + 0.638378i 0.937713 0.347410i $$-0.112939\pi$$
0.167990 + 0.985789i $$0.446272\pi$$
$$642$$ −135.791 + 413.262i −0.211513 + 0.643711i
$$643$$ 908.000 1.41213 0.706065 0.708147i $$-0.250468\pi$$
0.706065 + 0.708147i $$0.250468\pi$$
$$644$$ 81.3327 + 46.9574i 0.126293 + 0.0729153i
$$645$$ 220.000 196.774i 0.341085 0.305076i
$$646$$ −480.000 831.384i −0.743034 1.28697i
$$647$$ −274.982 158.761i −0.425011 0.245380i 0.272208 0.962238i $$-0.412246\pi$$
−0.697219 + 0.716858i $$0.745579\pi$$
$$648$$ 398.949 + 368.897i 0.615661 + 0.569286i
$$649$$ 112.500 + 194.856i 0.173344 + 0.300240i
$$650$$ 89.4427i 0.137604i
$$651$$ 42.0000 + 46.9574i 0.0645161 + 0.0721312i
$$652$$ 2.00000 0.00306748
$$653$$ −865.612 + 499.761i −1.32559 + 0.765331i −0.984615 0.174740i $$-0.944091\pi$$
−0.340978 + 0.940071i $$0.610758\pi$$
$$654$$ 197.710 + 945.532i 0.302308 + 1.44577i
$$655$$ 212.500 368.061i 0.324427 0.561925i
$$656$$ 515.107 297.397i 0.785224 0.453349i
$$657$$ −18.0000 + 160.997i −0.0273973 + 0.245049i
$$658$$ −105.000 181.865i −0.159574 0.276391i
$$659$$ 657.404i 0.997578i 0.866723 + 0.498789i $$0.166222\pi$$
−0.866723 + 0.498789i $$0.833778\pi$$
$$660$$ −23.4123 + 71.2521i −0.0354732 + 0.107958i
$$661$$ 418.000 723.997i 0.632375 1.09531i −0.354690 0.934984i $$-0.615413\pi$$
0.987065 0.160322i $$-0.0512532\pi$$
$$662$$ 30.9839 + 17.8885i 0.0468034 + 0.0270220i
$$663$$ 152.952 + 50.2574i 0.230696 + 0.0758030i
$$664$$ −945.000 −1.42319
$$665$$ 216.887 125.220i 0.326146 0.188300i
$$666$$ −240.000 26.8328i −0.360360 0.0402895i
$$667$$ 105.000 + 181.865i 0.157421 + 0.272662i
$$668$$ −216.887 125.220i −0.324681 0.187455i
$$669$$ 314.205 65.6998i 0.469663 0.0982060i
$$670$$ −130.000 225.167i −0.194030 0.336070i
$$671$$ 290.689i 0.433217i
$$672$$ −245.000 + 219.135i −0.364583 + 0.326093i
$$673$$ −677.000 −1.00594 −0.502972 0.864303i $$-0.667760\pi$$
−0.502972 + 0.864303i $$0.667760\pi$$
$$674$$ −985.674 + 569.079i −1.46242 + 0.844331i
$$675$$ −51.1088 537.576i −0.0757168 0.796409i
$$676$$ −82.5000 + 142.894i −0.122041 + 0.211382i
$$677$$ −923.707 + 533.302i −1.36441 + 0.787743i −0.990208 0.139603i $$-0.955417\pi$$
−0.374204 + 0.927346i $$0.622084\pi$$
$$678$$ −140.000 156.525i −0.206490 0.230862i
$$679$$ −325.500 + 563.783i −0.479381 + 0.830313i
$$680$$ 402.492i 0.591900i
$$681$$ 860.353 + 282.698i 1.26337 + 0.415122i
$$682$$ −37.5000 + 64.9519i −0.0549853 + 0.0952374i
$$683$$ −551.900 318.640i −0.808053 0.466530i 0.0382264 0.999269i $$-0.487829\pi$$
−0.846279 + 0.532740i $$0.821163\pi$$
$$684$$ −131.935 + 57.6978i −0.192888 + 0.0843535i
$$685$$ 480.000 0.700730
$$686$$ −664.217 + 383.486i −0.968246 + 0.559017i
$$687$$ −668.000 746.847i −0.972344 1.08711i
$$688$$ 418.000 + 723.997i 0.607558 + 1.05232i
$$689$$ −34.8569 20.1246i −0.0505905 0.0292084i
$$690$$ 41.1895 + 196.986i 0.0596949 + 0.285487i
$$691$$ −337.000 583.701i −0.487699 0.844719i 0.512201 0.858866i $$-0.328830\pi$$
−0.999900 + 0.0141462i $$0.995497\pi$$
$$692$$ 263.856i 0.381295i
$$693$$ −417.777 + 567.087i −0.602853 + 0.818307i
$$694$$ 850.000 1.22478
$$695$$ 220.760 127.456i 0.317640 0.183390i
$$696$$ −308.332 + 64.4718i −0.443005 + 0.0926318i
$$697$$ 420.000 727.461i 0.602582 1.04370i
$$698$$ 1216.12 702.125i 1.74229 1.00591i
$$699$$ −600.000 + 536.656i −0.858369 + 0.767749i
$$700$$ 140.000 0.200000
$$701$$ 1080.02i 1.54069i −0.637630 0.770343i $$-0.720085\pi$$
0.637630 0.770343i $$-0.279915\pi$$
$$702$$ 50.2056 109.815i 0.0715180 0.156432i
$$703$$ −96.0000 + 166.277i −0.136558 + 0.236525i
$$704$$ 396.981 + 229.197i 0.563893 + 0.325564i
$$705$$ 28.0948 85.5025i 0.0398507 0.121280i
$$706$$ 1040.00 1.47309
$$707$$ 352.441 203.482i 0.498503 0.287811i
$$708$$ 45.0000 40.2492i 0.0635593 0.0568492i
$$709$$ 57.0000 + 98.7269i 0.0803949 + 0.139248i 0.903420 0.428757i $$-0.141049\pi$$
−0.823025 + 0.568006i $$0.807715\pi$$
$$710$$ 406.663 + 234.787i 0.572765 + 0.330686i
$$711$$ 572.431 + 421.715i 0.805107 + 0.593129i
$$712$$ −165.000 285.788i −0.231742 0.401388i
$$713$$ 40.2492i 0.0564505i
$$714$$ −393.327 + 1197.04i −0.550877 + 1.67652i
$$715$$ −50.0000 −0.0699301
$$716$$ 166.538 96.1509i 0.232595 0.134289i
$$717$$ −172.996 827.341i −0.241277 1.15389i
$$718$$ −260.000 + 450.333i −0.362117 + 0.627205i
$$719$$ 336.950 194.538i 0.468636 0.270567i −0.247032 0.969007i $$-0.579455\pi$$
0.715669 + 0.698440i $$0.246122\pi$$
$$720$$ −380.000 42.4853i −0.527778 0.0590073i
$$721$$ 574.000 0.796117
$$722$$ 234.787i 0.325190i
$$723$$ 167.632 510.165i 0.231856 0.705623i
$$724$$ 41.0000 71.0141i 0.0566298 0.0980858i
$$725$$ 271.109 + 156.525i 0.373943 + 0.215896i
$$726$$ −25.4919 8.37624i −0.0351129 0.0115375i
$$727$$ 1307.00 1.79780 0.898900 0.438155i $$-0.144368\pi$$
0.898900 + 0.438155i $$0.144368\pi$$
$$728$$ −81.3327 46.9574i −0.111721 0.0645020i
$$729$$ 239.000 688.709i 0.327846 0.944731i
$$730$$ −45.0000 77.9423i −0.0616438 0.106770i
$$731$$ 1022.47 + 590.322i 1.39872 + 0.807554i
$$732$$ −76.3488 + 15.9644i −0.104302 + 0.0218093i
$$733$$ −204.000 353.338i −0.278308 0.482044i 0.692656 0.721268i $$-0.256440\pi$$
−0.970964 + 0.239224i $$0.923107\pi$$
$$734$$ 1120.27i 1.52625i
$$735$$ −312.276 102.609i −0.424866 0.139604i
$$736$$ −210.000 −0.285326
$$737$$ 503.488 290.689i 0.683159 0.394422i
$$738$$ −507.218 373.671i −0.687287 0.506330i
$$739$$ 177.000 306.573i 0.239513 0.414848i −0.721062 0.692871i $$-0.756346\pi$$
0.960575 + 0.278022i $$0.0896789\pi$$
$$740$$ 23.2379 13.4164i 0.0314026 0.0181303i
$$741$$ −64.0000 71.5542i −0.0863698 0.0965643i
$$742$$ 157.500 272.798i 0.212264 0.367652i
$$743$$ 751.319i 1.01120i 0.862769 + 0.505598i $$0.168728\pi$$
−0.862769 + 0.505598i $$0.831272\pi$$
$$744$$ −57.3569 18.8465i −0.0770925 0.0253314i
$$745$$ 15.0000 25.9808i 0.0201342 0.0348735i
$$746$$ −1351.67 780.388i −1.81189 1.04610i
$$747$$ 508.001 + 1161.63i 0.680055 + 1.55506i
$$748$$ −300.000 −0.401070
$$749$$ 453.922i 0.606037i
$$750$$ 450.000 + 503.115i 0.600000 + 0.670820i
$$751$$ 515.500 + 892.872i 0.686418 + 1.18891i 0.972989 + 0.230852i $$0.0741513\pi$$
−0.286571 + 0.958059i $$0.592515\pi$$
$$752$$ 220.760 + 127.456i 0.293564 + 0.169489i
$$753$$ −105.720 505.597i −0.140398 0.671444i
$$754$$ 35.0000 + 60.6218i 0.0464191 + 0.0804002i
$$755$$ 131.928i 0.174739i
$$756$$ 171.888 + 78.5842i 0.227365 + 0.103947i
$$757$$ −1258.00 −1.66182 −0.830911 0.556405i $$-0.812180\pi$$
−0.830911 + 0.556405i $$0.812180\pi$$
$$758$$ 708.756 409.200i 0.935034 0.539842i
$$759$$ −440.474 + 92.1025i −0.580334 + 0.121347i
$$760$$ −120.000 + 207.846i −0.157895 + 0.273482i
$$761$$ −801.708 + 462.866i −1.05349 + 0.608234i −0.923625 0.383297i $$-0.874788\pi$$
−0.129867 + 0.991531i $$0.541455\pi$$
$$762$$ −885.000 + 791.568i −1.16142 + 1.03880i
$$763$$ −504.000 872.954i −0.660550 1.14411i
$$764$$ 169.941i 0.222436i
$$765$$ −494.758 + 216.367i −0.646742 + 0.282832i
$$766$$ 15.0000 25.9808i 0.0195822 0.0339174i
$$767$$ 34.8569 + 20.1246i 0.0454457 + 0.0262381i
$$768$$ 169.505 515.865i 0.220710 0.671700i
$$769$$ −877.000 −1.14044 −0.570221 0.821491i $$-0.693142\pi$$
−0.570221 + 0.821491i $$0.693142\pi$$
$$770$$ 391.312i 0.508197i
$$771$$ −590.000 + 527.712i −0.765240 + 0.684451i
$$772$$ 29.5000 + 51.0955i 0.0382124 + 0.0661859i
$$773$$ −437.647 252.676i −0.566167 0.326877i 0.189450 0.981890i $$-0.439330\pi$$
−0.755617 + 0.655014i $$0.772663\pi$$
$$774$$ 525.206 712.909i 0.678560 0.921071i
$$775$$ 30.0000 + 51.9615i 0.0387097 + 0.0670471i
$$776$$ 623.863i 0.803947i
$$777$$ 246.665 51.5774i 0.317459 0.0663802i
$$778$$ 150.000 0.192802
$$779$$ −433.774 + 250.440i −0.556835 + 0.321489i
$$780$$ 2.74597 + 13.1324i 0.00352047 + 0.0168364i
$$781$$ −525.000 +