# Properties

 Label 21.6.e.c.4.2 Level $21$ Weight $6$ Character 21.4 Analytic conductor $3.368$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(4,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$21 = 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 21.e (of order $$3$$, 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: $$3.36806021607$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436$$ x^8 - x^7 + 98*x^6 + 83*x^5 + 9122*x^4 - 91*x^3 + 28567*x^2 + 2058*x + 86436 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3\cdot 7^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 4.2 Root $$-0.874091 - 1.51397i$$ of defining polynomial Character $$\chi$$ $$=$$ 21.4 Dual form 21.6.e.c.16.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.37409 - 2.37999i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(12.2237 - 21.1722i) q^{4} +(-29.1836 - 50.5475i) q^{5} +24.7336 q^{6} +(-21.4366 - 127.857i) q^{7} -155.128 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$$ $$q+(-1.37409 - 2.37999i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(12.2237 - 21.1722i) q^{4} +(-29.1836 - 50.5475i) q^{5} +24.7336 q^{6} +(-21.4366 - 127.857i) q^{7} -155.128 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-80.2019 + 138.914i) q^{10} +(-8.71205 + 15.0897i) q^{11} +(110.014 + 190.549i) q^{12} +889.933 q^{13} +(-274.844 + 226.706i) q^{14} +525.305 q^{15} +(-178.000 - 308.305i) q^{16} +(-513.318 + 889.092i) q^{17} +(-111.301 + 192.780i) q^{18} +(869.702 + 1506.37i) q^{19} -1426.93 q^{20} +(1093.01 + 408.276i) q^{21} +47.8846 q^{22} +(-1968.11 - 3408.87i) q^{23} +(698.076 - 1209.10i) q^{24} +(-140.869 + 243.993i) q^{25} +(-1222.85 - 2118.04i) q^{26} +729.000 q^{27} +(-2969.05 - 1109.04i) q^{28} +5633.53 q^{29} +(-721.817 - 1250.22i) q^{30} +(1548.27 - 2681.68i) q^{31} +(-2971.22 + 5146.31i) q^{32} +(-78.4084 - 135.807i) q^{33} +2821.38 q^{34} +(-5837.27 + 4814.91i) q^{35} -1980.25 q^{36} +(-2513.43 - 4353.39i) q^{37} +(2390.10 - 4139.77i) q^{38} +(-4004.70 + 6936.34i) q^{39} +(4527.20 + 7841.34i) q^{40} +18367.0 q^{41} +(-530.205 - 3162.37i) q^{42} -1630.91 q^{43} +(212.988 + 368.906i) q^{44} +(-2363.87 + 4094.35i) q^{45} +(-5408.72 + 9368.19i) q^{46} +(4802.62 + 8318.38i) q^{47} +3204.00 q^{48} +(-15887.9 + 5481.65i) q^{49} +774.269 q^{50} +(-4619.86 - 8001.83i) q^{51} +(10878.3 - 18841.8i) q^{52} +(11628.3 - 20140.7i) q^{53} +(-1001.71 - 1735.02i) q^{54} +1017.00 q^{55} +(3325.41 + 19834.2i) q^{56} -15654.6 q^{57} +(-7740.98 - 13407.8i) q^{58} +(1801.62 - 3120.50i) q^{59} +(6421.20 - 11121.8i) q^{60} +(-11438.3 - 19811.7i) q^{61} -8509.83 q^{62} +(-8100.75 + 6681.95i) q^{63} +4938.92 q^{64} +(-25971.5 - 44983.9i) q^{65} +(-215.481 + 373.223i) q^{66} +(-23506.4 + 40714.2i) q^{67} +(12549.3 + 21736.1i) q^{68} +35426.0 q^{69} +(19480.4 + 7276.56i) q^{70} -1599.63 q^{71} +(6282.68 + 10881.9i) q^{72} +(-2965.67 + 5136.70i) q^{73} +(-6907.36 + 11963.9i) q^{74} +(-1267.82 - 2195.93i) q^{75} +42524.1 q^{76} +(2116.09 + 790.427i) q^{77} +22011.3 q^{78} +(44234.4 + 76616.3i) q^{79} +(-10389.4 + 17994.9i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-25237.9 - 43713.3i) q^{82} -95823.9 q^{83} +(22004.8 - 18150.8i) q^{84} +59921.9 q^{85} +(2241.02 + 3881.56i) q^{86} +(-25350.9 + 43909.0i) q^{87} +(1351.48 - 2340.84i) q^{88} +(23253.9 + 40277.0i) q^{89} +12992.7 q^{90} +(-19077.1 - 113784. i) q^{91} -96230.8 q^{92} +(13934.4 + 24135.1i) q^{93} +(13198.5 - 22860.4i) q^{94} +(50762.1 - 87922.5i) q^{95} +(-26741.0 - 46316.8i) q^{96} -75981.8 q^{97} +(34877.8 + 30281.0i) q^{98} +1411.35 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9}+O(q^{10})$$ 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9 $$8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9} - 283 q^{10} - 402 q^{11} - 621 q^{12} + 924 q^{13} + 1926 q^{14} - 3273 q^{16} - 276 q^{17} - 243 q^{18} - 510 q^{19} + 9438 q^{20} - 3564 q^{21} + 2750 q^{22} - 6900 q^{23} - 1107 q^{24} - 2814 q^{25} + 15138 q^{26} + 5832 q^{27} - 26221 q^{28} + 1080 q^{29} - 2547 q^{30} + 6410 q^{31} - 15519 q^{32} - 3618 q^{33} + 42288 q^{34} - 33108 q^{35} + 11178 q^{36} - 15250 q^{37} + 41250 q^{38} - 4158 q^{39} + 8547 q^{40} + 8616 q^{41} - 16281 q^{42} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} + 15060 q^{47} + 58914 q^{48} - 64252 q^{49} - 14604 q^{50} - 2484 q^{51} + 47476 q^{52} - 13692 q^{53} - 2187 q^{54} + 146248 q^{55} - 15921 q^{56} + 9180 q^{57} - 52309 q^{58} - 34830 q^{59} - 42471 q^{60} + 5364 q^{61} + 32058 q^{62} + 11178 q^{63} - 146974 q^{64} - 66864 q^{65} - 12375 q^{66} + 5994 q^{67} + 58272 q^{68} + 124200 q^{69} - 4307 q^{70} + 178536 q^{71} - 9963 q^{72} - 59638 q^{73} + 185442 q^{74} - 25326 q^{75} + 42616 q^{76} - 75660 q^{77} - 272484 q^{78} + 44062 q^{79} + 33381 q^{80} - 26244 q^{81} - 57596 q^{82} - 416892 q^{83} + 63036 q^{84} + 72648 q^{85} + 136968 q^{86} - 4860 q^{87} - 87597 q^{88} + 77520 q^{89} + 45846 q^{90} + 104722 q^{91} + 316512 q^{92} + 57690 q^{93} + 73722 q^{94} + 221376 q^{95} - 139671 q^{96} - 377260 q^{97} + 382479 q^{98} + 65124 q^{99}+O(q^{100})$$ 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9 - 283 * q^10 - 402 * q^11 - 621 * q^12 + 924 * q^13 + 1926 * q^14 - 3273 * q^16 - 276 * q^17 - 243 * q^18 - 510 * q^19 + 9438 * q^20 - 3564 * q^21 + 2750 * q^22 - 6900 * q^23 - 1107 * q^24 - 2814 * q^25 + 15138 * q^26 + 5832 * q^27 - 26221 * q^28 + 1080 * q^29 - 2547 * q^30 + 6410 * q^31 - 15519 * q^32 - 3618 * q^33 + 42288 * q^34 - 33108 * q^35 + 11178 * q^36 - 15250 * q^37 + 41250 * q^38 - 4158 * q^39 + 8547 * q^40 + 8616 * q^41 - 16281 * q^42 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 + 15060 * q^47 + 58914 * q^48 - 64252 * q^49 - 14604 * q^50 - 2484 * q^51 + 47476 * q^52 - 13692 * q^53 - 2187 * q^54 + 146248 * q^55 - 15921 * q^56 + 9180 * q^57 - 52309 * q^58 - 34830 * q^59 - 42471 * q^60 + 5364 * q^61 + 32058 * q^62 + 11178 * q^63 - 146974 * q^64 - 66864 * q^65 - 12375 * q^66 + 5994 * q^67 + 58272 * q^68 + 124200 * q^69 - 4307 * q^70 + 178536 * q^71 - 9963 * q^72 - 59638 * q^73 + 185442 * q^74 - 25326 * q^75 + 42616 * q^76 - 75660 * q^77 - 272484 * q^78 + 44062 * q^79 + 33381 * q^80 - 26244 * q^81 - 57596 * q^82 - 416892 * q^83 + 63036 * q^84 + 72648 * q^85 + 136968 * q^86 - 4860 * q^87 - 87597 * q^88 + 77520 * q^89 + 45846 * q^90 + 104722 * q^91 + 316512 * q^92 + 57690 * q^93 + 73722 * q^94 + 221376 * q^95 - 139671 * q^96 - 377260 * q^97 + 382479 * q^98 + 65124 * q^99

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.37409 2.37999i −0.242907 0.420728i 0.718634 0.695389i $$-0.244768\pi$$
−0.961541 + 0.274661i $$0.911434\pi$$
$$3$$ −4.50000 + 7.79423i −0.288675 + 0.500000i
$$4$$ 12.2237 21.1722i 0.381992 0.661630i
$$5$$ −29.1836 50.5475i −0.522053 0.904222i −0.999671 0.0256544i $$-0.991833\pi$$
0.477618 0.878568i $$-0.341500\pi$$
$$6$$ 24.7336 0.280485
$$7$$ −21.4366 127.857i −0.165352 0.986235i
$$8$$ −155.128 −0.856969
$$9$$ −40.5000 70.1481i −0.166667 0.288675i
$$10$$ −80.2019 + 138.914i −0.253621 + 0.439284i
$$11$$ −8.71205 + 15.0897i −0.0217089 + 0.0376010i −0.876676 0.481082i $$-0.840244\pi$$
0.854967 + 0.518683i $$0.173577\pi$$
$$12$$ 110.014 + 190.549i 0.220543 + 0.381992i
$$13$$ 889.933 1.46049 0.730246 0.683185i $$-0.239406\pi$$
0.730246 + 0.683185i $$0.239406\pi$$
$$14$$ −274.844 + 226.706i −0.374771 + 0.309132i
$$15$$ 525.305 0.602815
$$16$$ −178.000 308.305i −0.173828 0.301079i
$$17$$ −513.318 + 889.092i −0.430788 + 0.746147i −0.996941 0.0781529i $$-0.975098\pi$$
0.566153 + 0.824300i $$0.308431\pi$$
$$18$$ −111.301 + 192.780i −0.0809691 + 0.140243i
$$19$$ 869.702 + 1506.37i 0.552696 + 0.957297i 0.998079 + 0.0619572i $$0.0197342\pi$$
−0.445383 + 0.895340i $$0.646932\pi$$
$$20$$ −1426.93 −0.797680
$$21$$ 1093.01 + 408.276i 0.540850 + 0.202025i
$$22$$ 47.8846 0.0210930
$$23$$ −1968.11 3408.87i −0.775764 1.34366i −0.934364 0.356320i $$-0.884031\pi$$
0.158599 0.987343i $$-0.449302\pi$$
$$24$$ 698.076 1209.10i 0.247386 0.428485i
$$25$$ −140.869 + 243.993i −0.0450782 + 0.0780777i
$$26$$ −1222.85 2118.04i −0.354764 0.614469i
$$27$$ 729.000 0.192450
$$28$$ −2969.05 1109.04i −0.715686 0.267332i
$$29$$ 5633.53 1.24390 0.621950 0.783057i $$-0.286341\pi$$
0.621950 + 0.783057i $$0.286341\pi$$
$$30$$ −721.817 1250.22i −0.146428 0.253621i
$$31$$ 1548.27 2681.68i 0.289362 0.501190i −0.684296 0.729205i $$-0.739890\pi$$
0.973658 + 0.228015i $$0.0732236\pi$$
$$32$$ −2971.22 + 5146.31i −0.512933 + 0.888426i
$$33$$ −78.4084 135.807i −0.0125337 0.0217089i
$$34$$ 2821.38 0.418566
$$35$$ −5837.27 + 4814.91i −0.805452 + 0.664382i
$$36$$ −1980.25 −0.254661
$$37$$ −2513.43 4353.39i −0.301830 0.522785i 0.674720 0.738073i $$-0.264264\pi$$
−0.976551 + 0.215288i $$0.930931\pi$$
$$38$$ 2390.10 4139.77i 0.268508 0.465069i
$$39$$ −4004.70 + 6936.34i −0.421608 + 0.730246i
$$40$$ 4527.20 + 7841.34i 0.447383 + 0.774890i
$$41$$ 18367.0 1.70639 0.853195 0.521592i $$-0.174662\pi$$
0.853195 + 0.521592i $$0.174662\pi$$
$$42$$ −530.205 3162.37i −0.0463789 0.276624i
$$43$$ −1630.91 −0.134511 −0.0672557 0.997736i $$-0.521424\pi$$
−0.0672557 + 0.997736i $$0.521424\pi$$
$$44$$ 212.988 + 368.906i 0.0165853 + 0.0287266i
$$45$$ −2363.87 + 4094.35i −0.174018 + 0.301407i
$$46$$ −5408.72 + 9368.19i −0.376878 + 0.652771i
$$47$$ 4802.62 + 8318.38i 0.317127 + 0.549280i 0.979887 0.199551i $$-0.0639485\pi$$
−0.662760 + 0.748832i $$0.730615\pi$$
$$48$$ 3204.00 0.200720
$$49$$ −15887.9 + 5481.65i −0.945317 + 0.326153i
$$50$$ 774.269 0.0437992
$$51$$ −4619.86 8001.83i −0.248716 0.430788i
$$52$$ 10878.3 18841.8i 0.557896 0.966305i
$$53$$ 11628.3 20140.7i 0.568624 0.984886i −0.428078 0.903742i $$-0.640809\pi$$
0.996702 0.0811440i $$-0.0258574\pi$$
$$54$$ −1001.71 1735.02i −0.0467475 0.0809691i
$$55$$ 1017.00 0.0453328
$$56$$ 3325.41 + 19834.2i 0.141702 + 0.845172i
$$57$$ −15654.6 −0.638198
$$58$$ −7740.98 13407.8i −0.302152 0.523343i
$$59$$ 1801.62 3120.50i 0.0673803 0.116706i −0.830367 0.557217i $$-0.811869\pi$$
0.897747 + 0.440511i $$0.145203\pi$$
$$60$$ 6421.20 11121.8i 0.230270 0.398840i
$$61$$ −11438.3 19811.7i −0.393584 0.681707i 0.599336 0.800498i $$-0.295431\pi$$
−0.992919 + 0.118791i $$0.962098\pi$$
$$62$$ −8509.83 −0.281152
$$63$$ −8100.75 + 6681.95i −0.257143 + 0.212106i
$$64$$ 4938.92 0.150724
$$65$$ −25971.5 44983.9i −0.762454 1.32061i
$$66$$ −215.481 + 373.223i −0.00608903 + 0.0105465i
$$67$$ −23506.4 + 40714.2i −0.639733 + 1.10805i 0.345758 + 0.938324i $$0.387622\pi$$
−0.985491 + 0.169726i $$0.945712\pi$$
$$68$$ 12549.3 + 21736.1i 0.329116 + 0.570045i
$$69$$ 35426.0 0.895776
$$70$$ 19480.4 + 7276.56i 0.475174 + 0.177493i
$$71$$ −1599.63 −0.0376595 −0.0188298 0.999823i $$-0.505994\pi$$
−0.0188298 + 0.999823i $$0.505994\pi$$
$$72$$ 6282.68 + 10881.9i 0.142828 + 0.247386i
$$73$$ −2965.67 + 5136.70i −0.0651353 + 0.112818i −0.896754 0.442529i $$-0.854081\pi$$
0.831619 + 0.555347i $$0.187415\pi$$
$$74$$ −6907.36 + 11963.9i −0.146633 + 0.253976i
$$75$$ −1267.82 2195.93i −0.0260259 0.0450782i
$$76$$ 42524.1 0.844502
$$77$$ 2116.09 + 790.427i 0.0406730 + 0.0151927i
$$78$$ 22011.3 0.409646
$$79$$ 44234.4 + 76616.3i 0.797431 + 1.38119i 0.921284 + 0.388890i $$0.127141\pi$$
−0.123854 + 0.992300i $$0.539525\pi$$
$$80$$ −10389.4 + 17994.9i −0.181495 + 0.314359i
$$81$$ −3280.50 + 5681.99i −0.0555556 + 0.0962250i
$$82$$ −25237.9 43713.3i −0.414495 0.717926i
$$83$$ −95823.9 −1.52679 −0.763394 0.645933i $$-0.776469\pi$$
−0.763394 + 0.645933i $$0.776469\pi$$
$$84$$ 22004.8 18150.8i 0.340267 0.280671i
$$85$$ 59921.9 0.899577
$$86$$ 2241.02 + 3881.56i 0.0326738 + 0.0565927i
$$87$$ −25350.9 + 43909.0i −0.359083 + 0.621950i
$$88$$ 1351.48 2340.84i 0.0186039 0.0322229i
$$89$$ 23253.9 + 40277.0i 0.311187 + 0.538992i 0.978620 0.205679i $$-0.0659401\pi$$
−0.667433 + 0.744670i $$0.732607\pi$$
$$90$$ 12992.7 0.169081
$$91$$ −19077.1 113784.i −0.241496 1.44039i
$$92$$ −96230.8 −1.18534
$$93$$ 13934.4 + 24135.1i 0.167063 + 0.289362i
$$94$$ 13198.5 22860.4i 0.154065 0.266848i
$$95$$ 50762.1 87922.5i 0.577073 0.999519i
$$96$$ −26741.0 46316.8i −0.296142 0.512933i
$$97$$ −75981.8 −0.819937 −0.409968 0.912100i $$-0.634460\pi$$
−0.409968 + 0.912100i $$0.634460\pi$$
$$98$$ 34877.8 + 30281.0i 0.366846 + 0.318496i
$$99$$ 1411.35 0.0144726
$$100$$ 3443.90 + 5965.01i 0.0344390 + 0.0596501i
$$101$$ 23078.7 39973.5i 0.225117 0.389914i −0.731238 0.682123i $$-0.761057\pi$$
0.956355 + 0.292209i $$0.0943903\pi$$
$$102$$ −12696.2 + 21990.5i −0.120830 + 0.209283i
$$103$$ 40986.8 + 70991.2i 0.380672 + 0.659343i 0.991158 0.132683i $$-0.0423594\pi$$
−0.610487 + 0.792027i $$0.709026\pi$$
$$104$$ −138054. −1.25160
$$105$$ −11260.8 67164.1i −0.0996769 0.594517i
$$106$$ −63913.2 −0.552491
$$107$$ 1426.84 + 2471.35i 0.0120480 + 0.0208677i 0.871987 0.489530i $$-0.162832\pi$$
−0.859939 + 0.510398i $$0.829498\pi$$
$$108$$ 8911.11 15434.5i 0.0735144 0.127331i
$$109$$ 83139.2 144001.i 0.670254 1.16091i −0.307578 0.951523i $$-0.599518\pi$$
0.977832 0.209391i $$-0.0671483\pi$$
$$110$$ −1397.45 2420.45i −0.0110117 0.0190728i
$$111$$ 45241.7 0.348523
$$112$$ −35603.3 + 29367.6i −0.268192 + 0.221220i
$$113$$ 260304. 1.91772 0.958858 0.283886i $$-0.0916237\pi$$
0.958858 + 0.283886i $$0.0916237\pi$$
$$114$$ 21510.9 + 37257.9i 0.155023 + 0.268508i
$$115$$ −114873. + 198966.i −0.809980 + 1.40293i
$$116$$ 68862.8 119274.i 0.475160 0.823001i
$$117$$ −36042.3 62427.1i −0.243415 0.421608i
$$118$$ −9902.35 −0.0654687
$$119$$ 124681. + 46572.3i 0.807108 + 0.301481i
$$120$$ −81489.6 −0.516593
$$121$$ 80373.7 + 139211.i 0.499057 + 0.864393i
$$122$$ −31434.5 + 54446.2i −0.191209 + 0.331183i
$$123$$ −82651.5 + 143157.i −0.492592 + 0.853195i
$$124$$ −37851.2 65560.3i −0.221068 0.382901i
$$125$$ −165953. −0.949973
$$126$$ 27034.2 + 10098.1i 0.151700 + 0.0566651i
$$127$$ −233743. −1.28596 −0.642982 0.765882i $$-0.722303\pi$$
−0.642982 + 0.765882i $$0.722303\pi$$
$$128$$ 88292.6 + 152927.i 0.476321 + 0.825012i
$$129$$ 7339.10 12711.7i 0.0388301 0.0672557i
$$130$$ −71374.4 + 123624.i −0.370411 + 0.641571i
$$131$$ 78644.9 + 136217.i 0.400398 + 0.693510i 0.993774 0.111415i $$-0.0355384\pi$$
−0.593376 + 0.804926i $$0.702205\pi$$
$$132$$ −3833.78 −0.0191510
$$133$$ 173957. 143489.i 0.852730 0.703379i
$$134$$ 129200. 0.621583
$$135$$ −21274.9 36849.2i −0.100469 0.174018i
$$136$$ 79629.9 137923.i 0.369172 0.639425i
$$137$$ 85773.8 148564.i 0.390439 0.676260i −0.602069 0.798444i $$-0.705657\pi$$
0.992507 + 0.122185i $$0.0389900\pi$$
$$138$$ −48678.5 84313.7i −0.217590 0.376878i
$$139$$ 210625. 0.924642 0.462321 0.886713i $$-0.347017\pi$$
0.462321 + 0.886713i $$0.347017\pi$$
$$140$$ 30588.6 + 182444.i 0.131898 + 0.786700i
$$141$$ −86447.1 −0.366187
$$142$$ 2198.04 + 3807.12i 0.00914777 + 0.0158444i
$$143$$ −7753.14 + 13428.8i −0.0317057 + 0.0549159i
$$144$$ −14418.0 + 24972.7i −0.0579427 + 0.100360i
$$145$$ −164407. 284761.i −0.649381 1.12476i
$$146$$ 16300.4 0.0632873
$$147$$ 28770.6 148502.i 0.109813 0.566811i
$$148$$ −122894. −0.461187
$$149$$ −119706. 207338.i −0.441725 0.765090i 0.556093 0.831120i $$-0.312300\pi$$
−0.997818 + 0.0660304i $$0.978967\pi$$
$$150$$ −3484.21 + 6034.83i −0.0126438 + 0.0218996i
$$151$$ −108520. + 187962.i −0.387317 + 0.670852i −0.992088 0.125547i $$-0.959931\pi$$
0.604771 + 0.796400i $$0.293265\pi$$
$$152$$ −134915. 233680.i −0.473643 0.820374i
$$153$$ 83157.5 0.287192
$$154$$ −1026.48 6122.39i −0.00348778 0.0208027i
$$155$$ −180736. −0.604249
$$156$$ 97904.9 + 169576.i 0.322102 + 0.557896i
$$157$$ −83452.2 + 144543.i −0.270202 + 0.468004i −0.968913 0.247400i $$-0.920424\pi$$
0.698711 + 0.715404i $$0.253757\pi$$
$$158$$ 121564. 210556.i 0.387403 0.671002i
$$159$$ 104654. + 181267.i 0.328295 + 0.568624i
$$160$$ 346844. 1.07111
$$161$$ −393659. + 324712.i −1.19689 + 0.987264i
$$162$$ 18030.8 0.0539794
$$163$$ −253086. 438358.i −0.746104 1.29229i −0.949677 0.313230i $$-0.898589\pi$$
0.203574 0.979060i $$-0.434744\pi$$
$$164$$ 224514. 388869.i 0.651828 1.12900i
$$165$$ −4576.49 + 7926.71i −0.0130865 + 0.0226664i
$$166$$ 131671. + 228061.i 0.370868 + 0.642362i
$$167$$ −565560. −1.56923 −0.784616 0.619982i $$-0.787140\pi$$
−0.784616 + 0.619982i $$0.787140\pi$$
$$168$$ −169557. 63335.0i −0.463492 0.173129i
$$169$$ 420688. 1.13304
$$170$$ −82338.1 142614.i −0.218514 0.378477i
$$171$$ 70445.8 122016.i 0.184232 0.319099i
$$172$$ −19935.9 + 34529.9i −0.0513823 + 0.0889968i
$$173$$ 329718. + 571088.i 0.837581 + 1.45073i 0.891911 + 0.452210i $$0.149364\pi$$
−0.0543304 + 0.998523i $$0.517302\pi$$
$$174$$ 139338. 0.348895
$$175$$ 34216.0 + 12780.8i 0.0844567 + 0.0315473i
$$176$$ 6202.98 0.0150945
$$177$$ 16214.6 + 28084.5i 0.0389020 + 0.0673803i
$$178$$ 63906.0 110688.i 0.151179 0.261850i
$$179$$ −82645.0 + 143145.i −0.192790 + 0.333922i −0.946174 0.323659i $$-0.895087\pi$$
0.753384 + 0.657581i $$0.228420\pi$$
$$180$$ 57790.8 + 100097.i 0.132947 + 0.230270i
$$181$$ 148492. 0.336904 0.168452 0.985710i $$-0.446123\pi$$
0.168452 + 0.985710i $$0.446123\pi$$
$$182$$ −244593. + 201754.i −0.547350 + 0.451484i
$$183$$ 205889. 0.454471
$$184$$ 305309. + 528811.i 0.664806 + 1.15148i
$$185$$ −146702. + 254095.i −0.315142 + 0.545843i
$$186$$ 38294.2 66327.6i 0.0811617 0.140576i
$$187$$ −8944.10 15491.6i −0.0187039 0.0323961i
$$188$$ 234824. 0.484560
$$189$$ −15627.3 93207.9i −0.0318221 0.189801i
$$190$$ −279007. −0.560701
$$191$$ −192955. 334208.i −0.382713 0.662879i 0.608736 0.793373i $$-0.291677\pi$$
−0.991449 + 0.130494i $$0.958344\pi$$
$$192$$ −22225.1 + 38495.1i −0.0435102 + 0.0753619i
$$193$$ −248148. + 429805.i −0.479531 + 0.830573i −0.999724 0.0234760i $$-0.992527\pi$$
0.520193 + 0.854049i $$0.325860\pi$$
$$194$$ 104406. + 180836.i 0.199169 + 0.344970i
$$195$$ 467487. 0.880406
$$196$$ −78152.0 + 403388.i −0.145312 + 0.750038i
$$197$$ 441439. 0.810411 0.405206 0.914226i $$-0.367200\pi$$
0.405206 + 0.914226i $$0.367200\pi$$
$$198$$ −1939.33 3359.01i −0.00351551 0.00608903i
$$199$$ 37919.4 65678.3i 0.0678779 0.117568i −0.830089 0.557631i $$-0.811710\pi$$
0.897967 + 0.440063i $$0.145044\pi$$
$$200$$ 21852.8 37850.1i 0.0386306 0.0669102i
$$201$$ −211557. 366428.i −0.369350 0.639733i
$$202$$ −126849. −0.218730
$$203$$ −120764. 720287.i −0.205682 1.22678i
$$204$$ −225888. −0.380030
$$205$$ −536016. 928406.i −0.890826 1.54296i
$$206$$ 112639. 195097.i 0.184936 0.320318i
$$207$$ −159417. + 276118.i −0.258588 + 0.447888i
$$208$$ −158408. 274371.i −0.253875 0.439724i
$$209$$ −30307.5 −0.0479938
$$210$$ −144377. + 119090.i −0.225917 + 0.186349i
$$211$$ 778704. 1.20411 0.602055 0.798454i $$-0.294349\pi$$
0.602055 + 0.798454i $$0.294349\pi$$
$$212$$ −284282. 492391.i −0.434420 0.752437i
$$213$$ 7198.35 12467.9i 0.0108714 0.0188298i
$$214$$ 3921.21 6791.73i 0.00585309 0.0101379i
$$215$$ 47595.9 + 82438.6i 0.0702221 + 0.121628i
$$216$$ −113088. −0.164924
$$217$$ −376061. 140471.i −0.542137 0.202506i
$$218$$ −456963. −0.651238
$$219$$ −26691.1 46230.3i −0.0376059 0.0651353i
$$220$$ 12431.5 21532.0i 0.0173168 0.0299936i
$$221$$ −456818. + 791233.i −0.629163 + 1.08974i
$$222$$ −62166.3 107675.i −0.0846588 0.146633i
$$223$$ 738085. 0.993903 0.496951 0.867778i $$-0.334453\pi$$
0.496951 + 0.867778i $$0.334453\pi$$
$$224$$ 721686. + 269573.i 0.961011 + 0.358969i
$$225$$ 22820.8 0.0300521
$$226$$ −357681. 619522.i −0.465827 0.806836i
$$227$$ 272058. 471218.i 0.350426 0.606956i −0.635898 0.771773i $$-0.719370\pi$$
0.986324 + 0.164817i $$0.0527035\pi$$
$$228$$ −191358. + 331442.i −0.243787 + 0.422251i
$$229$$ 116781. + 202271.i 0.147158 + 0.254885i 0.930176 0.367114i $$-0.119654\pi$$
−0.783018 + 0.621999i $$0.786321\pi$$
$$230$$ 631385. 0.787000
$$231$$ −15683.2 + 12936.3i −0.0193376 + 0.0159508i
$$232$$ −873917. −1.06598
$$233$$ 309050. + 535290.i 0.372940 + 0.645951i 0.990016 0.140952i $$-0.0450164\pi$$
−0.617077 + 0.786903i $$0.711683\pi$$
$$234$$ −99050.8 + 171561.i −0.118255 + 0.204823i
$$235$$ 280316. 485521.i 0.331114 0.573506i
$$236$$ −44045.1 76288.3i −0.0514775 0.0891617i
$$237$$ −796220. −0.920794
$$238$$ −60480.8 360734.i −0.0692110 0.412805i
$$239$$ 937500. 1.06164 0.530819 0.847485i $$-0.321884\pi$$
0.530819 + 0.847485i $$0.321884\pi$$
$$240$$ −93504.4 161954.i −0.104786 0.181495i
$$241$$ −466018. + 807167.i −0.516845 + 0.895202i 0.482964 + 0.875640i $$0.339560\pi$$
−0.999809 + 0.0195613i $$0.993773\pi$$
$$242$$ 220882. 382578.i 0.242449 0.419935i
$$243$$ −29524.5 51137.9i −0.0320750 0.0555556i
$$244$$ −559276. −0.601383
$$245$$ 740752. + 643122.i 0.788420 + 0.684508i
$$246$$ 454282. 0.478617
$$247$$ 773976. + 1.34057e6i 0.807208 + 1.39812i
$$248$$ −240179. + 416003.i −0.247974 + 0.429504i
$$249$$ 431208. 746874.i 0.440746 0.763394i
$$250$$ 228035. + 394968.i 0.230755 + 0.399680i
$$251$$ 214975. 0.215379 0.107690 0.994185i $$-0.465655\pi$$
0.107690 + 0.994185i $$0.465655\pi$$
$$252$$ 42449.7 + 253189.i 0.0421089 + 0.251156i
$$253$$ 68585.1 0.0673641
$$254$$ 321184. + 556306.i 0.312370 + 0.541040i
$$255$$ −269649. + 467045.i −0.259685 + 0.449788i
$$256$$ 321667. 557143.i 0.306765 0.531333i
$$257$$ −39593.5 68578.0i −0.0373931 0.0647667i 0.846723 0.532034i $$-0.178572\pi$$
−0.884116 + 0.467267i $$0.845239\pi$$
$$258$$ −40338.4 −0.0377285
$$259$$ −502733. + 414682.i −0.465680 + 0.384119i
$$260$$ −1.26988e6 −1.16501
$$261$$ −228158. 395181.i −0.207317 0.359083i
$$262$$ 216130. 374349.i 0.194519 0.336917i
$$263$$ 216414. 374840.i 0.192928 0.334162i −0.753291 0.657687i $$-0.771535\pi$$
0.946219 + 0.323526i $$0.104868\pi$$
$$264$$ 12163.3 + 21067.5i 0.0107410 + 0.0186039i
$$265$$ −1.35742e6 −1.18741
$$266$$ −580535. 216849.i −0.503065 0.187911i
$$267$$ −418571. −0.359328
$$268$$ 574672. + 995361.i 0.488746 + 0.846533i
$$269$$ 2345.93 4063.27i 0.00197667 0.00342369i −0.865035 0.501711i $$-0.832704\pi$$
0.867012 + 0.498287i $$0.166037\pi$$
$$270$$ −58467.2 + 101268.i −0.0488093 + 0.0845403i
$$271$$ −52632.1 91161.5i −0.0435339 0.0754029i 0.843437 0.537227i $$-0.180528\pi$$
−0.886971 + 0.461825i $$0.847195\pi$$
$$272$$ 365482. 0.299533
$$273$$ 972709. + 363338.i 0.789907 + 0.295056i
$$274$$ −471444. −0.379362
$$275$$ −2454.52 4251.35i −0.00195720 0.00338997i
$$276$$ 433038. 750045.i 0.342179 0.592672i
$$277$$ 381558. 660879.i 0.298787 0.517514i −0.677072 0.735917i $$-0.736751\pi$$
0.975859 + 0.218403i $$0.0700847\pi$$
$$278$$ −289418. 501287.i −0.224602 0.389023i
$$279$$ −250819. −0.192908
$$280$$ 905524. 746927.i 0.690248 0.569355i
$$281$$ −729540. −0.551167 −0.275584 0.961277i $$-0.588871\pi$$
−0.275584 + 0.961277i $$0.588871\pi$$
$$282$$ 118786. + 205744.i 0.0889494 + 0.154065i
$$283$$ 595214. 1.03094e6i 0.441781 0.765188i −0.556040 0.831155i $$-0.687680\pi$$
0.997822 + 0.0659675i $$0.0210134\pi$$
$$284$$ −19553.5 + 33867.7i −0.0143856 + 0.0249167i
$$285$$ 456859. + 791303.i 0.333173 + 0.577073i
$$286$$ 42614.1 0.0308062
$$287$$ −393726. 2.34835e6i −0.282156 1.68290i
$$288$$ 481338. 0.341955
$$289$$ 182938. + 316859.i 0.128843 + 0.223162i
$$290$$ −451820. + 782575.i −0.315479 + 0.546425i
$$291$$ 341918. 592220.i 0.236695 0.409968i
$$292$$ 72503.3 + 125579.i 0.0497623 + 0.0861909i
$$293$$ −1.02503e6 −0.697537 −0.348769 0.937209i $$-0.613400\pi$$
−0.348769 + 0.937209i $$0.613400\pi$$
$$294$$ −392967. + 135581.i −0.265147 + 0.0914809i
$$295$$ −210311. −0.140704
$$296$$ 389903. + 675332.i 0.258659 + 0.448011i
$$297$$ −6351.08 + 11000.4i −0.00417789 + 0.00723631i
$$298$$ −328975. + 569801.i −0.214596 + 0.371692i
$$299$$ −1.75149e6 3.03366e6i −1.13300 1.96241i
$$300$$ −61990.2 −0.0397667
$$301$$ 34961.2 + 208524.i 0.0222418 + 0.132660i
$$302$$ 596464. 0.376328
$$303$$ 207708. + 359762.i 0.129971 + 0.225117i
$$304$$ 309614. 536267.i 0.192148 0.332811i
$$305$$ −667623. + 1.15636e6i −0.410943 + 0.711774i
$$306$$ −114266. 197914.i −0.0697611 0.120830i
$$307$$ −709845. −0.429850 −0.214925 0.976631i $$-0.568951\pi$$
−0.214925 + 0.976631i $$0.568951\pi$$
$$308$$ 42601.5 35140.1i 0.0255887 0.0211070i
$$309$$ −737762. −0.439562
$$310$$ 248348. + 430151.i 0.146776 + 0.254224i
$$311$$ −783816. + 1.35761e6i −0.459529 + 0.795928i −0.998936 0.0461175i $$-0.985315\pi$$
0.539407 + 0.842045i $$0.318648\pi$$
$$312$$ 621241. 1.07602e6i 0.361305 0.625798i
$$313$$ −186476. 322986.i −0.107588 0.186347i 0.807205 0.590271i $$-0.200979\pi$$
−0.914792 + 0.403924i $$0.867646\pi$$
$$314$$ 458684. 0.262536
$$315$$ 574166. + 214470.i 0.326033 + 0.121784i
$$316$$ 2.16284e6 1.21845
$$317$$ 1.51408e6 + 2.62246e6i 0.846253 + 1.46575i 0.884528 + 0.466487i $$0.154480\pi$$
−0.0382747 + 0.999267i $$0.512186\pi$$
$$318$$ 287609. 498154.i 0.159491 0.276246i
$$319$$ −49079.6 + 85008.3i −0.0270037 + 0.0467719i
$$320$$ −144136. 249650.i −0.0786858 0.136288i
$$321$$ −25683.1 −0.0139118
$$322$$ 1.31373e6 + 490723.i 0.706103 + 0.263752i
$$323$$ −1.78573e6 −0.952380
$$324$$ 80200.0 + 138911.i 0.0424436 + 0.0735144i
$$325$$ −125364. + 217137.i −0.0658363 + 0.114032i
$$326$$ −695526. + 1.20469e6i −0.362468 + 0.627813i
$$327$$ 748253. + 1.29601e6i 0.386971 + 0.670254i
$$328$$ −2.84923e6 −1.46232
$$329$$ 960613. 792367.i 0.489281 0.403586i
$$330$$ 25154.0 0.0127152
$$331$$ −533448. 923959.i −0.267622 0.463535i 0.700625 0.713529i $$-0.252905\pi$$
−0.968247 + 0.249995i $$0.919571\pi$$
$$332$$ −1.17133e6 + 2.02880e6i −0.583221 + 1.01017i
$$333$$ −203588. + 352624.i −0.100610 + 0.174262i
$$334$$ 777130. + 1.34603e6i 0.381178 + 0.660219i
$$335$$ 2.74401e6 1.33590
$$336$$ −68682.9 409655.i −0.0331895 0.197957i
$$337$$ 1.55734e6 0.746981 0.373490 0.927634i $$-0.378161\pi$$
0.373490 + 0.927634i $$0.378161\pi$$
$$338$$ −578064. 1.00124e6i −0.275222 0.476699i
$$339$$ −1.17137e6 + 2.02887e6i −0.553597 + 0.958858i
$$340$$ 732470. 1.26868e6i 0.343631 0.595187i
$$341$$ 26977.1 + 46725.8i 0.0125635 + 0.0217606i
$$342$$ −387196. −0.179005
$$343$$ 1.04145e6 + 1.91388e6i 0.477973 + 0.878374i
$$344$$ 253000. 0.115272
$$345$$ −1.03386e6 1.79070e6i −0.467642 0.809980i
$$346$$ 906124. 1.56945e6i 0.406909 0.704787i
$$347$$ 1.11748e6 1.93553e6i 0.498214 0.862932i −0.501784 0.864993i $$-0.667323\pi$$
0.999998 + 0.00206105i $$0.000656052\pi$$
$$348$$ 619765. + 1.07347e6i 0.274334 + 0.475160i
$$349$$ −1.72982e6 −0.760218 −0.380109 0.924942i $$-0.624114\pi$$
−0.380109 + 0.924942i $$0.624114\pi$$
$$350$$ −16597.7 98995.8i −0.00724231 0.0431963i
$$351$$ 648761. 0.281072
$$352$$ −51770.9 89669.8i −0.0222705 0.0385736i
$$353$$ 1.18287e6 2.04879e6i 0.505242 0.875105i −0.494739 0.869041i $$-0.664736\pi$$
0.999982 0.00606386i $$-0.00193020\pi$$
$$354$$ 44560.6 77181.2i 0.0188992 0.0327343i
$$355$$ 46683.1 + 80857.6i 0.0196603 + 0.0340526i
$$356$$ 1.13700e6 0.475484
$$357$$ −924058. + 762214.i −0.383733 + 0.316524i
$$358$$ 454247. 0.187320
$$359$$ −25514.3 44192.1i −0.0104484 0.0180971i 0.860754 0.509021i $$-0.169993\pi$$
−0.871202 + 0.490924i $$0.836659\pi$$
$$360$$ 366703. 635148.i 0.149128 0.258297i
$$361$$ −274712. + 475815.i −0.110945 + 0.192163i
$$362$$ −204041. 353410.i −0.0818364 0.141745i
$$363$$ −1.44673e6 −0.576262
$$364$$ −2.64226e6 986968.i −1.04525 0.390436i
$$365$$ 346197. 0.136016
$$366$$ −282911. 490016.i −0.110394 0.191209i
$$367$$ −1.88411e6 + 3.26338e6i −0.730200 + 1.26474i 0.226597 + 0.973989i $$0.427240\pi$$
−0.956797 + 0.290755i $$0.906093\pi$$
$$368$$ −700648. + 1.21356e6i −0.269699 + 0.467133i
$$369$$ −743863. 1.28841e6i −0.284398 0.492592i
$$370$$ 806328. 0.306201
$$371$$ −2.82441e6 1.05501e6i −1.06535 0.397943i
$$372$$ 681322. 0.255267
$$373$$ −2.31720e6 4.01351e6i −0.862366 1.49366i −0.869639 0.493689i $$-0.835648\pi$$
0.00727258 0.999974i $$-0.497685\pi$$
$$374$$ −24580.0 + 42573.8i −0.00908663 + 0.0157385i
$$375$$ 746790. 1.29348e6i 0.274234 0.474986i
$$376$$ −745020. 1.29041e6i −0.271768 0.470716i
$$377$$ 5.01346e6 1.81670
$$378$$ −200361. + 165269.i −0.0721247 + 0.0594924i
$$379$$ −4.17169e6 −1.49181 −0.745905 0.666052i $$-0.767983\pi$$
−0.745905 + 0.666052i $$0.767983\pi$$
$$380$$ −1.24101e6 2.14949e6i −0.440875 0.763617i
$$381$$ 1.05184e6 1.82184e6i 0.371226 0.642982i
$$382$$ −530276. + 918465.i −0.185928 + 0.322036i
$$383$$ 2.08586e6 + 3.61281e6i 0.726588 + 1.25849i 0.958317 + 0.285706i $$0.0922282\pi$$
−0.231730 + 0.972780i $$0.574438\pi$$
$$384$$ −1.58927e6 −0.550008
$$385$$ −21800.9 130030.i −0.00749590 0.0447088i
$$386$$ 1.36391e6 0.465927
$$387$$ 66051.9 + 114405.i 0.0224186 + 0.0388301i
$$388$$ −928783. + 1.60870e6i −0.313209 + 0.542495i
$$389$$ −1.37697e6 + 2.38498e6i −0.461371 + 0.799119i −0.999030 0.0440442i $$-0.985976\pi$$
0.537658 + 0.843163i $$0.319309\pi$$
$$390$$ −642369. 1.11262e6i −0.213857 0.370411i
$$391$$ 4.04106e6 1.33676
$$392$$ 2.46466e6 850357.i 0.810108 0.279503i
$$393$$ −1.41561e6 −0.462340
$$394$$ −606578. 1.05062e6i −0.196855 0.340962i
$$395$$ 2.58184e6 4.47189e6i 0.832602 1.44211i
$$396$$ 17252.0 29881.4i 0.00552843 0.00957552i
$$397$$ 1.26602e6 + 2.19281e6i 0.403148 + 0.698274i 0.994104 0.108430i $$-0.0345825\pi$$
−0.590956 + 0.806704i $$0.701249\pi$$
$$398$$ −208419. −0.0659522
$$399$$ 335582. + 2.00156e6i 0.105528 + 0.629413i
$$400$$ 100299. 0.0313434
$$401$$ 1.07873e6 + 1.86842e6i 0.335007 + 0.580249i 0.983486 0.180983i $$-0.0579280\pi$$
−0.648479 + 0.761232i $$0.724595\pi$$
$$402$$ −581398. + 1.00701e6i −0.179436 + 0.310791i
$$403$$ 1.37785e6 2.38651e6i 0.422611 0.731983i
$$404$$ −564217. 977252.i −0.171986 0.297888i
$$405$$ 382948. 0.116012
$$406$$ −1.54834e6 + 1.27716e6i −0.466177 + 0.384529i
$$407$$ 87588.5 0.0262096
$$408$$ 716669. + 1.24131e6i 0.213142 + 0.369172i
$$409$$ 2.16402e6 3.74819e6i 0.639665 1.10793i −0.345841 0.938293i $$-0.612406\pi$$
0.985506 0.169640i $$-0.0542604\pi$$
$$410$$ −1.47307e6 + 2.55143e6i −0.432776 + 0.749590i
$$411$$ 771964. + 1.33708e6i 0.225420 + 0.390439i
$$412$$ 2.00405e6 0.581655
$$413$$ −437599. 163457.i −0.126241 0.0471552i
$$414$$ 876213. 0.251252
$$415$$ 2.79649e6 + 4.84366e6i 0.797064 + 1.38056i
$$416$$ −2.64419e6 + 4.57987e6i −0.749134 + 1.29754i
$$417$$ −947814. + 1.64166e6i −0.266921 + 0.462321i
$$418$$ 41645.3 + 72131.8i 0.0116580 + 0.0201923i
$$419$$ −1.51129e6 −0.420544 −0.210272 0.977643i $$-0.567435\pi$$
−0.210272 + 0.977643i $$0.567435\pi$$
$$420$$ −1.55966e6 582583.i −0.431426 0.161152i
$$421$$ 1.11586e6 0.306835 0.153418 0.988161i $$-0.450972\pi$$
0.153418 + 0.988161i $$0.450972\pi$$
$$422$$ −1.07001e6 1.85331e6i −0.292487 0.506603i
$$423$$ 389012. 673788.i 0.105709 0.183093i
$$424$$ −1.80387e6 + 3.12439e6i −0.487293 + 0.844016i
$$425$$ −144621. 250492.i −0.0388383 0.0672699i
$$426$$ −39564.8 −0.0105629
$$427$$ −2.28787e6 + 1.88717e6i −0.607243 + 0.500888i
$$428$$ 69765.2 0.0184090
$$429$$ −69778.3 120860.i −0.0183053 0.0317057i
$$430$$ 130802. 226556.i 0.0341149 0.0590887i
$$431$$ −3.10672e6 + 5.38100e6i −0.805581 + 1.39531i 0.110317 + 0.993896i $$0.464813\pi$$
−0.915898 + 0.401411i $$0.868520\pi$$
$$432$$ −129762. 224754.i −0.0334533 0.0579427i
$$433$$ 3.24118e6 0.830775 0.415388 0.909644i $$-0.363646\pi$$
0.415388 + 0.909644i $$0.363646\pi$$
$$434$$ 182422. + 1.08804e6i 0.0464892 + 0.277282i
$$435$$ 2.95932e6 0.749841
$$436$$ −2.03255e6 3.52047e6i −0.512064 0.886920i
$$437$$ 3.42334e6 5.92939e6i 0.857524 1.48527i
$$438$$ −73351.9 + 127049.i −0.0182695 + 0.0316437i
$$439$$ −1.15248e6 1.99616e6i −0.285413 0.494349i 0.687297 0.726377i $$-0.258797\pi$$
−0.972709 + 0.232028i $$0.925464\pi$$
$$440$$ −157765. −0.0388488
$$441$$ 1.02799e6 + 892502.i 0.251705 + 0.218531i
$$442$$ 2.51084e6 0.611313
$$443$$ −766328. 1.32732e6i −0.185526 0.321341i 0.758228 0.651990i $$-0.226066\pi$$
−0.943754 + 0.330649i $$0.892732\pi$$
$$444$$ 553024. 957865.i 0.133133 0.230593i
$$445$$ 1.35727e6 2.35086e6i 0.324912 0.562764i
$$446$$ −1.01420e6 1.75664e6i −0.241426 0.418162i
$$447$$ 2.15472e6 0.510060
$$448$$ −105874. 631476.i −0.0249226 0.148649i
$$449$$ −3.55718e6 −0.832702 −0.416351 0.909204i $$-0.636691\pi$$
−0.416351 + 0.909204i $$0.636691\pi$$
$$450$$ −31357.9 54313.4i −0.00729987 0.0126438i
$$451$$ −160014. + 277153.i −0.0370439 + 0.0641620i
$$452$$ 3.18189e6 5.51119e6i 0.732553 1.26882i
$$453$$ −976678. 1.69166e6i −0.223617 0.387317i
$$454$$ −1.49533e6 −0.340484
$$455$$ −5.19478e6 + 4.28494e6i −1.17636 + 0.970324i
$$456$$ 2.42847e6 0.546916
$$457$$ −1.25941e6 2.18137e6i −0.282083 0.488583i 0.689814 0.723986i $$-0.257692\pi$$
−0.971898 + 0.235403i $$0.924359\pi$$
$$458$$ 320936. 555877.i 0.0714915 0.123827i
$$459$$ −374209. + 648148.i −0.0829053 + 0.143596i
$$460$$ 2.80836e6 + 4.86423e6i 0.618812 + 1.07181i
$$461$$ −6.63271e6 −1.45358 −0.726789 0.686861i $$-0.758988\pi$$
−0.726789 + 0.686861i $$0.758988\pi$$
$$462$$ 52338.5 + 19550.1i 0.0114082 + 0.00426132i
$$463$$ −4.40432e6 −0.954830 −0.477415 0.878678i $$-0.658426\pi$$
−0.477415 + 0.878678i $$0.658426\pi$$
$$464$$ −1.00277e6 1.73685e6i −0.216225 0.374512i
$$465$$ 813313. 1.40870e6i 0.174432 0.302124i
$$466$$ 849325. 1.47107e6i 0.181180 0.313812i
$$467$$ −122922. 212908.i −0.0260819 0.0451751i 0.852690 0.522417i $$-0.174970\pi$$
−0.878772 + 0.477242i $$0.841636\pi$$
$$468$$ −1.76229e6 −0.371931
$$469$$ 5.70951e6 + 2.13269e6i 1.19858 + 0.447708i
$$470$$ −1.54072e6 −0.321720
$$471$$ −751070. 1.30089e6i −0.156001 0.270202i
$$472$$ −279482. + 484076.i −0.0577428 + 0.100014i
$$473$$ 14208.6 24610.0i 0.00292010 0.00505776i
$$474$$ 1.09408e6 + 1.89500e6i 0.223667 + 0.387403i
$$475$$ −490057. −0.0996581
$$476$$ 2.51010e6 2.07047e6i 0.507778 0.418843i
$$477$$ −1.88378e6 −0.379083
$$478$$ −1.28821e6 2.23125e6i −0.257880 0.446661i
$$479$$ 20175.6 34945.1i 0.00401779 0.00695901i −0.864010 0.503475i $$-0.832054\pi$$
0.868027 + 0.496516i $$0.165388\pi$$
$$480$$ −1.56080e6 + 2.70339e6i −0.309203 + 0.535556i
$$481$$ −2.23678e6 3.87422e6i −0.440820 0.763523i
$$482$$ 2.56140e6 0.502181
$$483$$ −759412. 4.52947e6i −0.148119 0.883445i
$$484$$ 3.92987e6 0.762544
$$485$$ 2.21743e6 + 3.84069e6i 0.428050 + 0.741405i
$$486$$ −81138.7 + 140536.i −0.0155825 + 0.0269897i
$$487$$ 1.65484e6 2.86627e6i 0.316180 0.547639i −0.663508 0.748169i $$-0.730933\pi$$
0.979688 + 0.200530i $$0.0642664\pi$$
$$488$$ 1.77440e6 + 3.07335e6i 0.337289 + 0.584202i
$$489$$ 4.55555e6 0.861526
$$490$$ 512768. 2.64669e6i 0.0964785 0.497982i
$$491$$ −1.97959e6 −0.370570 −0.185285 0.982685i $$-0.559321\pi$$
−0.185285 + 0.982685i $$0.559321\pi$$
$$492$$ 2.02062e6 + 3.49982e6i 0.376333 + 0.651828i
$$493$$ −2.89179e6 + 5.00872e6i −0.535857 + 0.928132i
$$494$$ 2.12703e6 3.68412e6i 0.392153 0.679229i
$$495$$ −41188.4 71340.4i −0.00755547 0.0130865i
$$496$$ −1.10237e6 −0.201197
$$497$$ 34290.7 + 204525.i 0.00622709 + 0.0371411i
$$498$$ −2.37007e6 −0.428241
$$499$$ 1.58498e6 + 2.74526e6i 0.284952 + 0.493551i 0.972597 0.232495i $$-0.0746891\pi$$
−0.687646 + 0.726046i $$0.741356\pi$$
$$500$$ −2.02857e6 + 3.51359e6i −0.362882 + 0.628530i
$$501$$ 2.54502e6 4.40810e6i 0.452998 0.784616i
$$502$$ −295396. 511640.i −0.0523172 0.0906161i
$$503$$ −4.01273e6 −0.707164 −0.353582 0.935403i $$-0.615037\pi$$
−0.353582 + 0.935403i $$0.615037\pi$$
$$504$$ 1.25665e6 1.03656e6i 0.220363 0.181768i
$$505$$ −2.69408e6 −0.470092
$$506$$ −94242.1 163232.i −0.0163632 0.0283419i
$$507$$ −1.89310e6 + 3.27894e6i −0.327079 + 0.566518i
$$508$$ −2.85721e6 + 4.94884e6i −0.491228 + 0.850832i
$$509$$ −2.05629e6 3.56159e6i −0.351795 0.609326i 0.634769 0.772702i $$-0.281095\pi$$
−0.986564 + 0.163375i $$0.947762\pi$$
$$510$$ 1.48209e6 0.252318
$$511$$ 720338. + 269070.i 0.122035 + 0.0455840i
$$512$$ 3.88273e6 0.654580
$$513$$ 634012. + 1.09814e6i 0.106366 + 0.184232i
$$514$$ −108810. + 188465.i −0.0181661 + 0.0314646i
$$515$$ 2.39229e6 4.14356e6i 0.397462 0.688424i
$$516$$ −179423. 310769.i −0.0296656 0.0513823i
$$517$$ −167363. −0.0275380
$$518$$ 1.67774e6 + 626691.i 0.274727 + 0.102619i
$$519$$ −5.93492e6 −0.967155
$$520$$ 4.02890e6 + 6.97827e6i 0.653399 + 1.13172i
$$521$$ −4.27758e6 + 7.40898e6i −0.690404 + 1.19582i 0.281301 + 0.959620i $$0.409234\pi$$
−0.971705 + 0.236196i $$0.924099\pi$$
$$522$$ −627019. + 1.08603e6i −0.100717 + 0.174448i
$$523$$ 896820. + 1.55334e6i 0.143368 + 0.248320i 0.928763 0.370675i $$-0.120874\pi$$
−0.785395 + 0.618995i $$0.787540\pi$$
$$524$$ 3.84534e6 0.611796
$$525$$ −253588. + 209174.i −0.0401542 + 0.0331214i
$$526$$ −1.18949e6 −0.187455
$$527$$ 1.58950e6 + 2.75310e6i 0.249307 + 0.431813i
$$528$$ −27913.4 + 48347.5i −0.00435741 + 0.00754725i
$$529$$ −4.52875e6 + 7.84402e6i −0.703621 + 1.21871i
$$530$$ 1.86522e6 + 3.23065e6i 0.288430 + 0.499575i
$$531$$ −291862. −0.0449202
$$532$$ −911571. 5.43701e6i −0.139640 0.832877i
$$533$$ 1.63454e7 2.49217
$$534$$ 575154. + 996196.i 0.0872833 + 0.151179i
$$535$$ 83280.6 144246.i 0.0125794 0.0217881i
$$536$$ 3.64650e6 6.31592e6i 0.548231 0.949565i
$$537$$ −743805. 1.28831e6i −0.111307 0.192790i
$$538$$ −12894.1 −0.00192059
$$539$$ 55700.1 287501.i 0.00825818 0.0426253i
$$540$$ −1.04023e6 −0.153514
$$541$$ 178780. + 309657.i 0.0262619 + 0.0454870i 0.878858 0.477084i $$-0.158306\pi$$
−0.852596 + 0.522571i $$0.824973\pi$$
$$542$$ −144643. + 250528.i −0.0211494 + 0.0366318i
$$543$$ −668213. + 1.15738e6i −0.0972558 + 0.168452i
$$544$$ −3.05036e6 5.28338e6i −0.441931 0.765447i
$$545$$ −9.70522e6 −1.39963
$$546$$ −471847. 2.81430e6i −0.0677360 0.404007i
$$547$$ −3.79404e6 −0.542167 −0.271084 0.962556i $$-0.587382\pi$$
−0.271084 + 0.962556i $$0.587382\pi$$
$$548$$ −2.09695e6 3.63203e6i −0.298289 0.516652i
$$549$$ −926502. + 1.60475e6i −0.131195 + 0.227236i
$$550$$ −6745.47 + 11683.5i −0.000950835 + 0.00164689i
$$551$$ 4.89949e6 + 8.48616e6i 0.687498 + 1.19078i
$$552$$ −5.49556e6 −0.767652
$$553$$ 8.84771e6 7.29809e6i 1.23032 1.01484i
$$554$$ −2.09718e6 −0.290310
$$555$$ −1.32032e6 2.28686e6i −0.181948 0.315142i
$$556$$ 2.57463e6 4.45939e6i 0.353206 0.611771i
$$557$$ 2.44799e6 4.24005e6i 0.334328 0.579072i −0.649028 0.760765i $$-0.724824\pi$$
0.983355 + 0.181692i $$0.0581575\pi$$
$$558$$ 344648. + 596948.i 0.0468587 + 0.0811617i
$$559$$ −1.45140e6 −0.196453
$$560$$ 2.52350e6 + 942607.i 0.340042 + 0.127017i
$$561$$ 160994. 0.0215974
$$562$$ 1.00245e6 + 1.73630e6i 0.133882 + 0.231891i
$$563$$ 2.16583e6 3.75133e6i 0.287974 0.498786i −0.685352 0.728212i $$-0.740352\pi$$
0.973326 + 0.229426i $$0.0736849\pi$$
$$564$$ −1.05671e6 + 1.83027e6i −0.139880 + 0.242280i
$$565$$ −7.59661e6 1.31577e7i −1.00115 1.73404i
$$566$$ −3.27151e6 −0.429248
$$567$$ 796807. + 297633.i 0.104087 + 0.0388798i
$$568$$ 248148. 0.0322730
$$569$$ 1.09848e6 + 1.90262e6i 0.142236 + 0.246361i 0.928338 0.371736i $$-0.121237\pi$$
−0.786102 + 0.618097i $$0.787904\pi$$
$$570$$ 1.25553e6 2.17464e6i 0.161860 0.280350i
$$571$$ 3.73846e6 6.47520e6i 0.479846 0.831118i −0.519886 0.854235i $$-0.674026\pi$$
0.999733 + 0.0231172i $$0.00735908\pi$$
$$572$$ 189545. + 328301.i 0.0242227 + 0.0419549i
$$573$$ 3.47320e6 0.441919
$$574$$ −5.04805e6 + 4.16391e6i −0.639505 + 0.527500i
$$575$$ 1.10899e6 0.139880
$$576$$ −200026. 346456.i −0.0251206 0.0435102i
$$577$$ 683110. 1.18318e6i 0.0854183 0.147949i −0.820151 0.572147i $$-0.806111\pi$$
0.905569 + 0.424198i $$0.139444\pi$$
$$578$$ 502748. 870785.i 0.0625937 0.108415i
$$579$$ −2.23333e6 3.86824e6i −0.276858 0.479531i
$$580$$ −8.03867e6 −0.992234
$$581$$ 2.05414e6 + 1.22518e7i 0.252458 + 1.50577i
$$582$$ −1.87931e6 −0.229980
$$583$$ 202612. + 350934.i 0.0246884 + 0.0427616i
$$584$$ 460059. 796845.i 0.0558189 0.0966812i
$$585$$ −2.10369e6 + 3.64370e6i −0.254151 + 0.440203i
$$586$$ 1.40848e6 + 2.43956e6i 0.169437 + 0.293473i
$$587$$ −9.27217e6 −1.11067 −0.555336 0.831626i $$-0.687410\pi$$
−0.555336 + 0.831626i $$0.687410\pi$$
$$588$$ −2.79242e6 2.42438e6i −0.333071 0.289173i
$$589$$ 5.38612e6 0.639717
$$590$$ 288987. + 500540.i 0.0341781 + 0.0591982i
$$591$$ −1.98648e6 + 3.44068e6i −0.233946 + 0.405206i
$$592$$ −894782. + 1.54981e6i −0.104933 + 0.181750i
$$593$$ −4.60523e6 7.97649e6i −0.537792 0.931483i −0.999023 0.0442028i $$-0.985925\pi$$
0.461231 0.887280i $$-0.347408\pi$$
$$594$$ 34907.9 0.00405936
$$595$$ −1.28452e6 7.66145e6i −0.148747 0.887194i
$$596$$ −5.85305e6 −0.674942
$$597$$ 341275. + 591105.i 0.0391894 + 0.0678779i
$$598$$ −4.81340e6 + 8.33706e6i −0.550426 + 0.953367i
$$599$$ 6.84581e6 1.18573e7i 0.779575 1.35026i −0.152612 0.988286i $$-0.548769\pi$$
0.932187 0.361977i $$-0.117898\pi$$
$$600$$ 196675. + 340651.i 0.0223034 + 0.0386306i
$$601$$ 1.61113e6 0.181946 0.0909732 0.995853i $$-0.471002\pi$$
0.0909732 + 0.995853i $$0.471002\pi$$
$$602$$ 448246. 369738.i 0.0504110 0.0415818i
$$603$$ 3.80803e6 0.426489
$$604$$ 2.65304e6 + 4.59519e6i 0.295904 + 0.512521i
$$605$$ 4.69119e6 8.12539e6i 0.521069 0.902517i
$$606$$ 570820. 988690.i 0.0631419 0.109365i
$$607$$ 7.03281e6 + 1.21812e7i 0.774742 + 1.34189i 0.934940 + 0.354807i $$0.115453\pi$$
−0.160198 + 0.987085i $$0.551213\pi$$
$$608$$ −1.03363e7 −1.13398
$$609$$ 6.15752e6 + 2.30003e6i 0.672764 + 0.251299i
$$610$$ 3.66950e6 0.399284
$$611$$ 4.27401e6 + 7.40280e6i 0.463161 + 0.802219i
$$612$$ 1.01650e6 1.76062e6i 0.109705 0.190015i
$$613$$ −6.79842e6 + 1.17752e7i −0.730729 + 1.26566i 0.225842 + 0.974164i $$0.427487\pi$$
−0.956572 + 0.291497i $$0.905847\pi$$
$$614$$ 975391. + 1.68943e6i 0.104414 + 0.180850i
$$615$$ 9.64828e6 1.02864
$$616$$ −328264. 122617.i −0.0348555 0.0130197i
$$617$$ −5.74287e6 −0.607318 −0.303659 0.952781i $$-0.598208\pi$$
−0.303659 + 0.952781i $$0.598208\pi$$
$$618$$ 1.01375e6 + 1.75587e6i 0.106773 + 0.184936i
$$619$$ 3.01299e6 5.21865e6i 0.316061 0.547434i −0.663602 0.748086i $$-0.730973\pi$$
0.979662 + 0.200653i $$0.0643063\pi$$
$$620$$ −2.20927e6 + 3.82657e6i −0.230818 + 0.399789i
$$621$$ −1.43475e6 2.48506e6i −0.149296 0.258588i
$$622$$ 4.30814e6 0.446492
$$623$$ 4.65122e6 3.83658e6i 0.480117 0.396027i
$$624$$ 2.85135e6 0.293149
$$625$$ 5.28334e6 + 9.15101e6i 0.541014 + 0.937064i
$$626$$ −512470. + 887625.i −0.0522676 + 0.0905302i
$$627$$ 136384. 236224.i 0.0138546 0.0239969i
$$628$$ 2.04020e6 + 3.53373e6i 0.206430 + 0.357547i
$$629$$ 5.16075e6 0.520099
$$630$$ −278519. 1.66121e6i −0.0279579 0.166753i
$$631$$ −6.90670e6 −0.690554 −0.345277 0.938501i $$-0.612215\pi$$
−0.345277 + 0.938501i $$0.612215\pi$$
$$632$$ −6.86200e6 1.18853e7i −0.683373 1.18364i
$$633$$ −3.50417e6 + 6.06940e6i −0.347597 + 0.602055i
$$634$$ 4.16096e6 7.20700e6i 0.411122 0.712084i
$$635$$ 6.82146e6 + 1.18151e7i 0.671341 + 1.16280i
$$636$$ 5.11708e6 0.501625
$$637$$ −1.41392e7 + 4.87830e6i −1.38063 + 0.476343i
$$638$$ 269759. 0.0262376
$$639$$ 64785.2 + 112211.i 0.00627659 + 0.0108714i
$$640$$ 5.15340e6 8.92595e6i 0.497329 0.861400i
$$641$$ −8.24828e6 + 1.42864e7i −0.792900 + 1.37334i 0.131265 + 0.991347i $$0.458096\pi$$
−0.924164 + 0.381995i $$0.875237\pi$$
$$642$$ 35290.9 + 61125.6i 0.00337928 + 0.00585309i
$$643$$ 1.70171e7 1.62315 0.811576 0.584247i $$-0.198610\pi$$
0.811576 + 0.584247i $$0.198610\pi$$
$$644$$ 2.06286e6 + 1.23038e7i 0.195999 + 1.16903i
$$645$$ −856727. −0.0810855
$$646$$ 2.45376e6 + 4.25003e6i 0.231340 + 0.400692i
$$647$$ −1.74287e6 + 3.01873e6i −0.163683 + 0.283507i −0.936187 0.351503i $$-0.885671\pi$$
0.772504 + 0.635010i $$0.219004\pi$$
$$648$$ 508897. 881436.i 0.0476094 0.0824619i
$$649$$ 31391.6 + 54371.8i 0.00292551 + 0.00506713i
$$650$$ 689047. 0.0639684
$$651$$ 2.78714e6 2.29899e6i 0.257754 0.212610i
$$652$$ −1.23746e7 −1.14002
$$653$$ −7.72245e6 1.33757e7i −0.708716 1.22753i −0.965334 0.261019i $$-0.915941\pi$$
0.256618 0.966513i $$-0.417392\pi$$
$$654$$ 2.05633e6 3.56168e6i 0.187996 0.325619i
$$655$$ 4.59029e6 7.95061e6i 0.418058 0.724098i
$$656$$ −3.26933e6 5.66264e6i −0.296619 0.513759i
$$657$$ 480439. 0.0434235
$$658$$ −3.20580e6 1.19747e6i −0.288650 0.107820i
$$659$$ −3.11193e6 −0.279136 −0.139568 0.990212i $$-0.544571\pi$$
−0.139568 + 0.990212i $$0.544571\pi$$
$$660$$ 111884. + 193788.i 0.00999785 + 0.0173168i
$$661$$ −4.08610e6 + 7.07733e6i −0.363752 + 0.630037i −0.988575 0.150729i $$-0.951838\pi$$
0.624823 + 0.780766i $$0.285171\pi$$
$$662$$ −1.46601e6 + 2.53921e6i −0.130015 + 0.225192i
$$663$$ −4.11137e6 7.12110e6i −0.363247 0.629163i
$$664$$ 1.48650e7 1.30841
$$665$$ −1.23297e7 4.60554e6i −1.08118 0.403856i
$$666$$ 1.11899e6 0.0977556
$$667$$ −1.10874e7 1.92039e7i −0.964973 1.67138i
$$668$$ −6.91326e6 + 1.19741e7i −0.599434 + 1.03825i
$$669$$ −3.32138e6 + 5.75280e6i −0.286915 + 0.496951i
$$670$$ −3.77051e6 6.53072e6i −0.324499 0.562049i
$$671$$ 398604. 0.0341771
$$672$$ −5.34870e6 + 4.41191e6i −0.456904 + 0.376880i
$$673$$ 1.60182e7 1.36325 0.681627 0.731700i $$-0.261273\pi$$
0.681627 + 0.731700i $$0.261273\pi$$
$$674$$ −2.13993e6 3.70647e6i −0.181447 0.314276i
$$675$$ −102694. + 177871.i −0.00867530 + 0.0150261i
$$676$$ 5.14239e6 8.90687e6i 0.432811 0.749650i
$$677$$ −512185. 887131.i −0.0429492 0.0743902i 0.843752 0.536734i $$-0.180342\pi$$
−0.886701 + 0.462344i $$0.847009\pi$$
$$678$$ 6.43826e6 0.537891
$$679$$ 1.62879e6 + 9.71483e6i 0.135579 + 0.808650i
$$680$$ −9.29556e6 −0.770910
$$681$$ 2.44852e6 + 4.24096e6i 0.202319 + 0.350426i
$$682$$ 74138.1 128411.i 0.00610352 0.0105716i
$$683$$ 2.69688e6 4.67114e6i 0.221213 0.383152i −0.733964 0.679189i $$-0.762332\pi$$
0.955177 + 0.296037i $$0.0956651\pi$$
$$684$$ −1.72222e6 2.98298e6i −0.140750 0.243787i
$$685$$ −1.00128e7 −0.815319
$$686$$ 3.12398e6 5.10850e6i 0.253453 0.414460i
$$687$$ −2.10206e6 −0.169924
$$688$$ 290302. + 502819.i 0.0233819 + 0.0404986i
$$689$$ 1.03484e7 1.79239e7i 0.830470 1.43842i
$$690$$ −2.84123e6 + 4.92116e6i −0.227187 + 0.393500i
$$691$$ 452826. + 784318.i 0.0360775 + 0.0624881i 0.883500 0.468430i $$-0.155180\pi$$
−0.847423 + 0.530919i $$0.821847\pi$$
$$692$$ 1.61215e7 1.27980
$$693$$ −30254.6 180452.i −0.00239308 0.0142734i
$$694$$ −6.14207e6 −0.484079
$$695$$ −6.14682e6 1.06466e7i −0.482712 0.836082i
$$696$$ 3.93263e6 6.81151e6i 0.307723 0.532992i
$$697$$ −9.42810e6 + 1.63300e7i −0.735093 + 1.27322i
$$698$$ 2.37693e6 + 4.11697e6i 0.184662 + 0.319845i
$$699$$ −5.56290e6 −0.430634
$$700$$ 688845. 568197.i 0.0531344 0.0438282i
$$701$$ 1.12573e7 0.865246 0.432623 0.901575i $$-0.357588\pi$$
0.432623 + 0.901575i $$0.357588\pi$$
$$702$$ −891457. 1.54405e6i −0.0682743 0.118255i
$$703$$ 4.37187e6 7.57230e6i 0.333640 0.577882i
$$704$$ −43028.1 + 74526.9i −0.00327205 + 0.00566736i
$$705$$ 2.52284e6 + 4.36969e6i 0.191169 + 0.331114i
$$706$$ −6.50147e6 −0.490908
$$707$$ −5.60563e6 2.09388e6i −0.421770 0.157545i
$$708$$ 792812. 0.0594411
$$709$$ −2.17755e6 3.77162e6i −0.162687 0.281781i 0.773145 0.634230i $$-0.218683\pi$$
−0.935831 + 0.352448i $$0.885349\pi$$
$$710$$ 128294. 222211.i 0.00955123 0.0165432i
$$711$$ 3.58299e6 6.20592e6i 0.265810 0.460397i
$$712$$ −3.60733e6 6.24809e6i −0.266678 0.461899i
$$713$$ −1.21886e7 −0.897907
$$714$$ 3.08381e6 + 1.15190e6i 0.226382 + 0.0845609i
$$715$$ 905060. 0.0662082
$$716$$ 2.02046e6 + 3.49955e6i 0.147288 + 0.255111i
$$717$$ −4.21875e6 + 7.30709e6i −0.306469 + 0.530819i
$$718$$ −70118.0 + 121448.i −0.00507597 + 0.00879183i
$$719$$ 7.07221e6 + 1.22494e7i 0.510191 + 0.883676i 0.999930 + 0.0118076i $$0.00375858\pi$$
−0.489739 + 0.871869i $$0.662908\pi$$
$$720$$ 1.68308e6 0.120997
$$721$$ 8.19812e6 6.76227e6i 0.587322 0.484456i
$$722$$ 1.50992e6 0.107798
$$723$$ −4.19416e6 7.26450e6i −0.298401 0.516845i
$$724$$ 1.81513e6 3.14389e6i 0.128695 0.222906i
$$725$$ −793591. + 1.37454e6i −0.0560727 + 0.0971208i
$$726$$ 1.98793e6 + 3.44320e6i 0.139978 + 0.242449i
$$727$$ −6.26406e6 −0.439561 −0.219781 0.975549i $$-0.570534\pi$$
−0.219781 + 0.975549i $$0.570534\pi$$
$$728$$ 2.95940e6 + 1.76511e7i 0.206954 + 1.23437i
$$729$$ 531441. 0.0370370
$$730$$ −475705. 823946.i −0.0330393 0.0572258i
$$731$$ 837176. 1.45003e6i 0.0579460 0.100365i
$$732$$ 2.51674e6 4.35912e6i 0.173604 0.300692i
$$733$$ 1.02089e7 + 1.76823e7i 0.701806 + 1.21556i 0.967832 + 0.251598i $$0.0809562\pi$$
−0.266025 + 0.963966i $$0.585710\pi$$
$$734$$ 1.03558e7 0.709484
$$735$$ −8.34602e6 + 2.87954e6i −0.569851 + 0.196610i
$$736$$ 2.33908e7 1.59166
$$737$$ −409577. 709409.i −0.0277758 0.0481092i
$$738$$ −2.04427e6 + 3.54078e6i −0.138165 + 0.239309i
$$739$$ −7.42256e6 + 1.28563e7i −0.499969 + 0.865971i −1.00000 3.61537e-5i $$-0.999988\pi$$
0.500031 + 0.866007i $$0.333322\pi$$
$$740$$ 3.58650e6 + 6.21200e6i 0.240764 + 0.417015i
$$741$$ −1.39316e7 −0.932083
$$742$$ 1.37008e6 + 8.17176e6i 0.0913558 + 0.544886i
$$743$$ 2.36601e7 1.57234 0.786168 0.618013i $$-0.212062\pi$$
0.786168 + 0.618013i $$0.212062\pi$$
$$744$$ −2.16161e6 3.74403e6i −0.143168 0.247974i
$$745$$ −6.98694e6 + 1.21017e7i −0.461207 + 0.798834i
$$746$$ −6.36809e6 + 1.10299e7i −0.418950 + 0.725643i
$$747$$ 3.88087e6 + 6.72186e6i 0.254465 + 0.440746i
$$748$$ −437322. −0.0285790
$$749$$ 285394. 235409.i 0.0185883 0.0153327i
$$750$$ −4.10463e6 −0.266453
$$751$$ −1.03287e7 1.78898e7i −0.668258 1.15746i −0.978391 0.206764i $$-0.933707\pi$$
0.310133 0.950693i $$-0.399627\pi$$
$$752$$ 1.70973e6 2.96134e6i 0.110251 0.190961i
$$753$$ −967389. + 1.67557e6i −0.0621747 + 0.107690i
$$754$$ −6.88895e6 1.19320e7i −0.441291 0.764338i
$$755$$ 1.26680e7 0.808799
$$756$$ −2.16444e6 808487.i −0.137734 0.0514480i
$$757$$ −1.26697e7 −0.803573 −0.401787 0.915733i $$-0.631611\pi$$
−0.401787 + 0.915733i $$0.631611\pi$$
$$758$$ 5.73228e6 + 9.92860e6i 0.362372 + 0.627646i
$$759$$ −308633. + 534568.i −0.0194463 + 0.0336820i
$$760$$ −7.87462e6 + 1.36392e7i −0.494534 + 0.856557i
$$761$$ −8.13761e6 1.40948e7i −0.509372 0.882259i −0.999941 0.0108563i $$-0.996544\pi$$
0.490569 0.871402i $$-0.336789\pi$$
$$762$$ −5.78130e6 −0.360694