# Properties

 Label 320.6.c.f.129.2 Level 320 Weight 6 Character 320.129 Analytic conductor 51.323 Analytic rank 0 Dimension 2 CM no Inner twists 2

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 320.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$51.3228223402$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-11})$$ Defining polynomial: $$x^{2} - x + 3$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 5) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 129.2 Root $$0.500000 - 1.65831i$$ of defining polynomial Character $$\chi$$ $$=$$ 320.129 Dual form 320.6.c.f.129.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+19.8997i q^{3} +(45.0000 - 33.1662i) q^{5} -59.6992i q^{7} -153.000 q^{9} +O(q^{10})$$ $$q+19.8997i q^{3} +(45.0000 - 33.1662i) q^{5} -59.6992i q^{7} -153.000 q^{9} -252.000 q^{11} +119.398i q^{13} +(660.000 + 895.489i) q^{15} -689.858i q^{17} +220.000 q^{19} +1188.00 q^{21} +2434.40i q^{23} +(925.000 - 2984.96i) q^{25} +1790.98i q^{27} +6930.00 q^{29} +6752.00 q^{31} -5014.74i q^{33} +(-1980.00 - 2686.47i) q^{35} -13969.6i q^{37} -2376.00 q^{39} -198.000 q^{41} +417.895i q^{43} +(-6885.00 + 5074.44i) q^{45} -10540.2i q^{47} +13243.0 q^{49} +13728.0 q^{51} +5823.99i q^{53} +(-11340.0 + 8357.89i) q^{55} +4377.94i q^{57} +24660.0 q^{59} +5698.00 q^{61} +9133.98i q^{63} +(3960.00 + 5372.93i) q^{65} +43640.1i q^{67} -48444.0 q^{69} +53352.0 q^{71} +70922.7i q^{73} +(59400.0 + 18407.3i) q^{75} +15044.2i q^{77} +51920.0 q^{79} -72819.0 q^{81} +61841.8i q^{83} +(-22880.0 - 31043.6i) q^{85} +137905. i q^{87} -9990.00 q^{89} +7128.00 q^{91} +134363. i q^{93} +(9900.00 - 7296.57i) q^{95} -101250. i q^{97} +38556.0 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 90q^{5} - 306q^{9} + O(q^{10})$$ $$2q + 90q^{5} - 306q^{9} - 504q^{11} + 1320q^{15} + 440q^{19} + 2376q^{21} + 1850q^{25} + 13860q^{29} + 13504q^{31} - 3960q^{35} - 4752q^{39} - 396q^{41} - 13770q^{45} + 26486q^{49} + 27456q^{51} - 22680q^{55} + 49320q^{59} + 11396q^{61} + 7920q^{65} - 96888q^{69} + 106704q^{71} + 118800q^{75} + 103840q^{79} - 145638q^{81} - 45760q^{85} - 19980q^{89} + 14256q^{91} + 19800q^{95} + 77112q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$257$$ $$261$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 19.8997i 1.27657i 0.769800 + 0.638285i $$0.220356\pi$$
−0.769800 + 0.638285i $$0.779644\pi$$
$$4$$ 0 0
$$5$$ 45.0000 33.1662i 0.804984 0.593296i
$$6$$ 0 0
$$7$$ 59.6992i 0.460494i −0.973132 0.230247i $$-0.926047\pi$$
0.973132 0.230247i $$-0.0739534\pi$$
$$8$$ 0 0
$$9$$ −153.000 −0.629630
$$10$$ 0 0
$$11$$ −252.000 −0.627941 −0.313970 0.949433i $$-0.601659\pi$$
−0.313970 + 0.949433i $$0.601659\pi$$
$$12$$ 0 0
$$13$$ 119.398i 0.195948i 0.995189 + 0.0979739i $$0.0312362\pi$$
−0.995189 + 0.0979739i $$0.968764\pi$$
$$14$$ 0 0
$$15$$ 660.000 + 895.489i 0.757383 + 1.02762i
$$16$$ 0 0
$$17$$ 689.858i 0.578945i −0.957186 0.289473i $$-0.906520\pi$$
0.957186 0.289473i $$-0.0934799\pi$$
$$18$$ 0 0
$$19$$ 220.000 0.139810 0.0699051 0.997554i $$-0.477730\pi$$
0.0699051 + 0.997554i $$0.477730\pi$$
$$20$$ 0 0
$$21$$ 1188.00 0.587852
$$22$$ 0 0
$$23$$ 2434.40i 0.959561i 0.877388 + 0.479781i $$0.159284\pi$$
−0.877388 + 0.479781i $$0.840716\pi$$
$$24$$ 0 0
$$25$$ 925.000 2984.96i 0.296000 0.955188i
$$26$$ 0 0
$$27$$ 1790.98i 0.472804i
$$28$$ 0 0
$$29$$ 6930.00 1.53016 0.765082 0.643932i $$-0.222698\pi$$
0.765082 + 0.643932i $$0.222698\pi$$
$$30$$ 0 0
$$31$$ 6752.00 1.26191 0.630955 0.775820i $$-0.282663\pi$$
0.630955 + 0.775820i $$0.282663\pi$$
$$32$$ 0 0
$$33$$ 5014.74i 0.801610i
$$34$$ 0 0
$$35$$ −1980.00 2686.47i −0.273209 0.370690i
$$36$$ 0 0
$$37$$ 13969.6i 1.67757i −0.544464 0.838785i $$-0.683267\pi$$
0.544464 0.838785i $$-0.316733\pi$$
$$38$$ 0 0
$$39$$ −2376.00 −0.250141
$$40$$ 0 0
$$41$$ −198.000 −0.0183952 −0.00919762 0.999958i $$-0.502928\pi$$
−0.00919762 + 0.999958i $$0.502928\pi$$
$$42$$ 0 0
$$43$$ 417.895i 0.0344664i 0.999851 + 0.0172332i $$0.00548577\pi$$
−0.999851 + 0.0172332i $$0.994514\pi$$
$$44$$ 0 0
$$45$$ −6885.00 + 5074.44i −0.506842 + 0.373557i
$$46$$ 0 0
$$47$$ 10540.2i 0.695994i −0.937496 0.347997i $$-0.886862\pi$$
0.937496 0.347997i $$-0.113138\pi$$
$$48$$ 0 0
$$49$$ 13243.0 0.787945
$$50$$ 0 0
$$51$$ 13728.0 0.739064
$$52$$ 0 0
$$53$$ 5823.99i 0.284794i 0.989810 + 0.142397i $$0.0454810\pi$$
−0.989810 + 0.142397i $$0.954519\pi$$
$$54$$ 0 0
$$55$$ −11340.0 + 8357.89i −0.505483 + 0.372555i
$$56$$ 0 0
$$57$$ 4377.94i 0.178477i
$$58$$ 0 0
$$59$$ 24660.0 0.922281 0.461140 0.887327i $$-0.347440\pi$$
0.461140 + 0.887327i $$0.347440\pi$$
$$60$$ 0 0
$$61$$ 5698.00 0.196064 0.0980320 0.995183i $$-0.468745\pi$$
0.0980320 + 0.995183i $$0.468745\pi$$
$$62$$ 0 0
$$63$$ 9133.98i 0.289941i
$$64$$ 0 0
$$65$$ 3960.00 + 5372.93i 0.116255 + 0.157735i
$$66$$ 0 0
$$67$$ 43640.1i 1.18768i 0.804583 + 0.593840i $$0.202389\pi$$
−0.804583 + 0.593840i $$0.797611\pi$$
$$68$$ 0 0
$$69$$ −48444.0 −1.22495
$$70$$ 0 0
$$71$$ 53352.0 1.25604 0.628022 0.778196i $$-0.283865\pi$$
0.628022 + 0.778196i $$0.283865\pi$$
$$72$$ 0 0
$$73$$ 70922.7i 1.55768i 0.627223 + 0.778840i $$0.284192\pi$$
−0.627223 + 0.778840i $$0.715808\pi$$
$$74$$ 0 0
$$75$$ 59400.0 + 18407.3i 1.21936 + 0.377865i
$$76$$ 0 0
$$77$$ 15044.2i 0.289163i
$$78$$ 0 0
$$79$$ 51920.0 0.935981 0.467990 0.883734i $$-0.344978\pi$$
0.467990 + 0.883734i $$0.344978\pi$$
$$80$$ 0 0
$$81$$ −72819.0 −1.23320
$$82$$ 0 0
$$83$$ 61841.8i 0.985342i 0.870216 + 0.492671i $$0.163979\pi$$
−0.870216 + 0.492671i $$0.836021\pi$$
$$84$$ 0 0
$$85$$ −22880.0 31043.6i −0.343486 0.466042i
$$86$$ 0 0
$$87$$ 137905.i 1.95336i
$$88$$ 0 0
$$89$$ −9990.00 −0.133687 −0.0668437 0.997763i $$-0.521293\pi$$
−0.0668437 + 0.997763i $$0.521293\pi$$
$$90$$ 0 0
$$91$$ 7128.00 0.0902328
$$92$$ 0 0
$$93$$ 134363.i 1.61092i
$$94$$ 0 0
$$95$$ 9900.00 7296.57i 0.112545 0.0829488i
$$96$$ 0 0
$$97$$ 101250.i 1.09261i −0.837586 0.546305i $$-0.816034\pi$$
0.837586 0.546305i $$-0.183966\pi$$
$$98$$ 0 0
$$99$$ 38556.0 0.395370
$$100$$ 0 0
$$101$$ 109098. 1.06418 0.532088 0.846689i $$-0.321408\pi$$
0.532088 + 0.846689i $$0.321408\pi$$
$$102$$ 0 0
$$103$$ 70624.2i 0.655935i 0.944689 + 0.327967i $$0.106364\pi$$
−0.944689 + 0.327967i $$0.893636\pi$$
$$104$$ 0 0
$$105$$ 53460.0 39401.5i 0.473212 0.348770i
$$106$$ 0 0
$$107$$ 97117.4i 0.820045i −0.912075 0.410022i $$-0.865521\pi$$
0.912075 0.410022i $$-0.134479\pi$$
$$108$$ 0 0
$$109$$ 21010.0 0.169379 0.0846895 0.996407i $$-0.473010\pi$$
0.0846895 + 0.996407i $$0.473010\pi$$
$$110$$ 0 0
$$111$$ 277992. 2.14153
$$112$$ 0 0
$$113$$ 105018.i 0.773688i 0.922145 + 0.386844i $$0.126435\pi$$
−0.922145 + 0.386844i $$0.873565\pi$$
$$114$$ 0 0
$$115$$ 80740.0 + 109548.i 0.569304 + 0.772432i
$$116$$ 0 0
$$117$$ 18268.0i 0.123375i
$$118$$ 0 0
$$119$$ −41184.0 −0.266601
$$120$$ 0 0
$$121$$ −97547.0 −0.605690
$$122$$ 0 0
$$123$$ 3940.15i 0.0234828i
$$124$$ 0 0
$$125$$ −57375.0 165002.i −0.328434 0.944527i
$$126$$ 0 0
$$127$$ 87220.6i 0.479855i −0.970791 0.239927i $$-0.922876\pi$$
0.970791 0.239927i $$-0.0771236\pi$$
$$128$$ 0 0
$$129$$ −8316.00 −0.0439987
$$130$$ 0 0
$$131$$ −192852. −0.981852 −0.490926 0.871201i $$-0.663341\pi$$
−0.490926 + 0.871201i $$0.663341\pi$$
$$132$$ 0 0
$$133$$ 13133.8i 0.0643817i
$$134$$ 0 0
$$135$$ 59400.0 + 80594.0i 0.280512 + 0.380599i
$$136$$ 0 0
$$137$$ 143570.i 0.653525i −0.945106 0.326763i $$-0.894042\pi$$
0.945106 0.326763i $$-0.105958\pi$$
$$138$$ 0 0
$$139$$ 318340. 1.39751 0.698754 0.715362i $$-0.253738\pi$$
0.698754 + 0.715362i $$0.253738\pi$$
$$140$$ 0 0
$$141$$ 209748. 0.888485
$$142$$ 0 0
$$143$$ 30088.4i 0.123044i
$$144$$ 0 0
$$145$$ 311850. 229842.i 1.23176 0.907841i
$$146$$ 0 0
$$147$$ 263532.i 1.00587i
$$148$$ 0 0
$$149$$ −84150.0 −0.310519 −0.155260 0.987874i $$-0.549621\pi$$
−0.155260 + 0.987874i $$0.549621\pi$$
$$150$$ 0 0
$$151$$ −155848. −0.556236 −0.278118 0.960547i $$-0.589711\pi$$
−0.278118 + 0.960547i $$0.589711\pi$$
$$152$$ 0 0
$$153$$ 105548.i 0.364521i
$$154$$ 0 0
$$155$$ 303840. 223939.i 1.01582 0.748686i
$$156$$ 0 0
$$157$$ 356643.i 1.15474i −0.816482 0.577371i $$-0.804079\pi$$
0.816482 0.577371i $$-0.195921\pi$$
$$158$$ 0 0
$$159$$ −115896. −0.363560
$$160$$ 0 0
$$161$$ 145332. 0.441872
$$162$$ 0 0
$$163$$ 144890.i 0.427139i 0.976928 + 0.213570i $$0.0685090\pi$$
−0.976928 + 0.213570i $$0.931491\pi$$
$$164$$ 0 0
$$165$$ −166320. 225663.i −0.475592 0.645284i
$$166$$ 0 0
$$167$$ 18102.1i 0.0502272i −0.999685 0.0251136i $$-0.992005\pi$$
0.999685 0.0251136i $$-0.00799474\pi$$
$$168$$ 0 0
$$169$$ 357037. 0.961604
$$170$$ 0 0
$$171$$ −33660.0 −0.0880286
$$172$$ 0 0
$$173$$ 492572.i 1.25128i 0.780112 + 0.625640i $$0.215162\pi$$
−0.780112 + 0.625640i $$0.784838\pi$$
$$174$$ 0 0
$$175$$ −178200. 55221.8i −0.439858 0.136306i
$$176$$ 0 0
$$177$$ 490728.i 1.17736i
$$178$$ 0 0
$$179$$ −444420. −1.03672 −0.518359 0.855163i $$-0.673457\pi$$
−0.518359 + 0.855163i $$0.673457\pi$$
$$180$$ 0 0
$$181$$ −156902. −0.355985 −0.177993 0.984032i $$-0.556960\pi$$
−0.177993 + 0.984032i $$0.556960\pi$$
$$182$$ 0 0
$$183$$ 113389.i 0.250289i
$$184$$ 0 0
$$185$$ −463320. 628633.i −0.995295 1.35042i
$$186$$ 0 0
$$187$$ 173844.i 0.363543i
$$188$$ 0 0
$$189$$ 106920. 0.217723
$$190$$ 0 0
$$191$$ 332352. 0.659196 0.329598 0.944121i $$-0.393087\pi$$
0.329598 + 0.944121i $$0.393087\pi$$
$$192$$ 0 0
$$193$$ 786120.i 1.51913i 0.650430 + 0.759566i $$0.274589\pi$$
−0.650430 + 0.759566i $$0.725411\pi$$
$$194$$ 0 0
$$195$$ −106920. + 78803.0i −0.201360 + 0.148408i
$$196$$ 0 0
$$197$$ 59606.4i 0.109428i −0.998502 0.0547138i $$-0.982575\pi$$
0.998502 0.0547138i $$-0.0174247\pi$$
$$198$$ 0 0
$$199$$ −395800. −0.708505 −0.354253 0.935150i $$-0.615265\pi$$
−0.354253 + 0.935150i $$0.615265\pi$$
$$200$$ 0 0
$$201$$ −868428. −1.51616
$$202$$ 0 0
$$203$$ 413716.i 0.704631i
$$204$$ 0 0
$$205$$ −8910.00 + 6566.92i −0.0148079 + 0.0109138i
$$206$$ 0 0
$$207$$ 372464.i 0.604168i
$$208$$ 0 0
$$209$$ −55440.0 −0.0877925
$$210$$ 0 0
$$211$$ 251548. 0.388969 0.194484 0.980906i $$-0.437697\pi$$
0.194484 + 0.980906i $$0.437697\pi$$
$$212$$ 0 0
$$213$$ 1.06169e6i 1.60343i
$$214$$ 0 0
$$215$$ 13860.0 + 18805.3i 0.0204488 + 0.0277449i
$$216$$ 0 0
$$217$$ 403089.i 0.581101i
$$218$$ 0 0
$$219$$ −1.41134e6 −1.98849
$$220$$ 0 0
$$221$$ 82368.0 0.113443
$$222$$ 0 0
$$223$$ 288765.i 0.388851i −0.980917 0.194425i $$-0.937716\pi$$
0.980917 0.194425i $$-0.0622842\pi$$
$$224$$ 0 0
$$225$$ −141525. + 456699.i −0.186370 + 0.601415i
$$226$$ 0 0
$$227$$ 1.16414e6i 1.49948i −0.661731 0.749741i $$-0.730178\pi$$
0.661731 0.749741i $$-0.269822\pi$$
$$228$$ 0 0
$$229$$ −547670. −0.690129 −0.345064 0.938579i $$-0.612143\pi$$
−0.345064 + 0.938579i $$0.612143\pi$$
$$230$$ 0 0
$$231$$ −299376. −0.369137
$$232$$ 0 0
$$233$$ 48104.3i 0.0580489i 0.999579 + 0.0290245i $$0.00924007\pi$$
−0.999579 + 0.0290245i $$0.990760\pi$$
$$234$$ 0 0
$$235$$ −349580. 474311.i −0.412930 0.560264i
$$236$$ 0 0
$$237$$ 1.03319e6i 1.19484i
$$238$$ 0 0
$$239$$ −1.00584e6 −1.13903 −0.569514 0.821982i $$-0.692868\pi$$
−0.569514 + 0.821982i $$0.692868\pi$$
$$240$$ 0 0
$$241$$ 895202. 0.992838 0.496419 0.868083i $$-0.334648\pi$$
0.496419 + 0.868083i $$0.334648\pi$$
$$242$$ 0 0
$$243$$ 1.01387e6i 1.10146i
$$244$$ 0 0
$$245$$ 595935. 439221.i 0.634284 0.467485i
$$246$$ 0 0
$$247$$ 26267.7i 0.0273955i
$$248$$ 0 0
$$249$$ −1.23064e6 −1.25786
$$250$$ 0 0
$$251$$ −558252. −0.559301 −0.279651 0.960102i $$-0.590219\pi$$
−0.279651 + 0.960102i $$0.590219\pi$$
$$252$$ 0 0
$$253$$ 613469.i 0.602548i
$$254$$ 0 0
$$255$$ 617760. 455306.i 0.594935 0.438483i
$$256$$ 0 0
$$257$$ 787924.i 0.744135i −0.928206 0.372067i $$-0.878649\pi$$
0.928206 0.372067i $$-0.121351\pi$$
$$258$$ 0 0
$$259$$ −833976. −0.772510
$$260$$ 0 0
$$261$$ −1.06029e6 −0.963437
$$262$$ 0 0
$$263$$ 1.63173e6i 1.45465i −0.686291 0.727327i $$-0.740762\pi$$
0.686291 0.727327i $$-0.259238\pi$$
$$264$$ 0 0
$$265$$ 193160. + 262080.i 0.168967 + 0.229255i
$$266$$ 0 0
$$267$$ 198798.i 0.170661i
$$268$$ 0 0
$$269$$ 1.73637e6 1.46306 0.731529 0.681810i $$-0.238807\pi$$
0.731529 + 0.681810i $$0.238807\pi$$
$$270$$ 0 0
$$271$$ −1.72005e6 −1.42271 −0.711357 0.702831i $$-0.751919\pi$$
−0.711357 + 0.702831i $$0.751919\pi$$
$$272$$ 0 0
$$273$$ 141845.i 0.115188i
$$274$$ 0 0
$$275$$ −233100. + 752211.i −0.185871 + 0.599802i
$$276$$ 0 0
$$277$$ 1.27243e6i 0.996402i −0.867062 0.498201i $$-0.833994\pi$$
0.867062 0.498201i $$-0.166006\pi$$
$$278$$ 0 0
$$279$$ −1.03306e6 −0.794536
$$280$$ 0 0
$$281$$ 1.46500e6 1.10681 0.553404 0.832913i $$-0.313329\pi$$
0.553404 + 0.832913i $$0.313329\pi$$
$$282$$ 0 0
$$283$$ 1.65051e6i 1.22504i 0.790455 + 0.612521i $$0.209844\pi$$
−0.790455 + 0.612521i $$0.790156\pi$$
$$284$$ 0 0
$$285$$ 145200. + 197008.i 0.105890 + 0.143672i
$$286$$ 0 0
$$287$$ 11820.5i 0.00847089i
$$288$$ 0 0
$$289$$ 943953. 0.664823
$$290$$ 0 0
$$291$$ 2.01485e6 1.39479
$$292$$ 0 0
$$293$$ 2.38772e6i 1.62485i −0.583064 0.812426i $$-0.698146\pi$$
0.583064 0.812426i $$-0.301854\pi$$
$$294$$ 0 0
$$295$$ 1.10970e6 817880.i 0.742422 0.547185i
$$296$$ 0 0
$$297$$ 451326.i 0.296893i
$$298$$ 0 0
$$299$$ −290664. −0.188024
$$300$$ 0 0
$$301$$ 24948.0 0.0158716
$$302$$ 0 0
$$303$$ 2.17102e6i 1.35849i
$$304$$ 0 0
$$305$$ 256410. 188981.i 0.157828 0.116324i
$$306$$ 0 0
$$307$$ 928264.i 0.562115i −0.959691 0.281058i $$-0.909315\pi$$
0.959691 0.281058i $$-0.0906852\pi$$
$$308$$ 0 0
$$309$$ −1.40540e6 −0.837346
$$310$$ 0 0
$$311$$ 568152. 0.333092 0.166546 0.986034i $$-0.446739\pi$$
0.166546 + 0.986034i $$0.446739\pi$$
$$312$$ 0 0
$$313$$ 1.72244e6i 0.993766i −0.867818 0.496883i $$-0.834478\pi$$
0.867818 0.496883i $$-0.165522\pi$$
$$314$$ 0 0
$$315$$ 302940. + 411029.i 0.172021 + 0.233398i
$$316$$ 0 0
$$317$$ 131643.i 0.0735785i −0.999323 0.0367893i $$-0.988287\pi$$
0.999323 0.0367893i $$-0.0117130\pi$$
$$318$$ 0 0
$$319$$ −1.74636e6 −0.960853
$$320$$ 0 0
$$321$$ 1.93261e6 1.04684
$$322$$ 0 0
$$323$$ 151769.i 0.0809424i
$$324$$ 0 0
$$325$$ 356400. + 110444.i 0.187167 + 0.0580006i
$$326$$ 0 0
$$327$$ 418094.i 0.216224i
$$328$$ 0 0
$$329$$ −629244. −0.320501
$$330$$ 0 0
$$331$$ 1.58055e6 0.792935 0.396468 0.918049i $$-0.370236\pi$$
0.396468 + 0.918049i $$0.370236\pi$$
$$332$$ 0 0
$$333$$ 2.13735e6i 1.05625i
$$334$$ 0 0
$$335$$ 1.44738e6 + 1.96381e6i 0.704645 + 0.956063i
$$336$$ 0 0
$$337$$ 1.22885e6i 0.589419i 0.955587 + 0.294709i $$0.0952228\pi$$
−0.955587 + 0.294709i $$0.904777\pi$$
$$338$$ 0 0
$$339$$ −2.08982e6 −0.987667
$$340$$ 0 0
$$341$$ −1.70150e6 −0.792405
$$342$$ 0 0
$$343$$ 1.79396e6i 0.823338i
$$344$$ 0 0
$$345$$ −2.17998e6 + 1.60671e6i −0.986063 + 0.726756i
$$346$$ 0 0
$$347$$ 3.84224e6i 1.71301i 0.516137 + 0.856506i $$0.327370\pi$$
−0.516137 + 0.856506i $$0.672630\pi$$
$$348$$ 0 0
$$349$$ 1.59445e6 0.700725 0.350362 0.936614i $$-0.386058\pi$$
0.350362 + 0.936614i $$0.386058\pi$$
$$350$$ 0 0
$$351$$ −213840. −0.0926448
$$352$$ 0 0
$$353$$ 295365.i 0.126160i −0.998008 0.0630802i $$-0.979908\pi$$
0.998008 0.0630802i $$-0.0200924\pi$$
$$354$$ 0 0
$$355$$ 2.40084e6 1.76949e6i 1.01110 0.745206i
$$356$$ 0 0
$$357$$ 819551.i 0.340334i
$$358$$ 0 0
$$359$$ 1.10484e6 0.452442 0.226221 0.974076i $$-0.427363\pi$$
0.226221 + 0.974076i $$0.427363\pi$$
$$360$$ 0 0
$$361$$ −2.42770e6 −0.980453
$$362$$ 0 0
$$363$$ 1.94116e6i 0.773206i
$$364$$ 0 0
$$365$$ 2.35224e6 + 3.19152e6i 0.924165 + 1.25391i
$$366$$ 0 0
$$367$$ 1.83760e6i 0.712174i −0.934453 0.356087i $$-0.884111\pi$$
0.934453 0.356087i $$-0.115889\pi$$
$$368$$ 0 0
$$369$$ 30294.0 0.0115822
$$370$$ 0 0
$$371$$ 347688. 0.131146
$$372$$ 0 0
$$373$$ 2.93350e6i 1.09173i −0.837874 0.545864i $$-0.816202\pi$$
0.837874 0.545864i $$-0.183798\pi$$
$$374$$ 0 0
$$375$$ 3.28350e6 1.14175e6i 1.20575 0.419268i
$$376$$ 0 0
$$377$$ 827432.i 0.299832i
$$378$$ 0 0
$$379$$ −5.09342e6 −1.82143 −0.910713 0.413040i $$-0.864467\pi$$
−0.910713 + 0.413040i $$0.864467\pi$$
$$380$$ 0 0
$$381$$ 1.73567e6 0.612568
$$382$$ 0 0
$$383$$ 3.17485e6i 1.10593i 0.833205 + 0.552964i $$0.186503\pi$$
−0.833205 + 0.552964i $$0.813497\pi$$
$$384$$ 0 0
$$385$$ 498960. + 676989.i 0.171559 + 0.232772i
$$386$$ 0 0
$$387$$ 63937.9i 0.0217011i
$$388$$ 0 0
$$389$$ −1.79991e6 −0.603083 −0.301541 0.953453i $$-0.597501\pi$$
−0.301541 + 0.953453i $$0.597501\pi$$
$$390$$ 0 0
$$391$$ 1.67939e6 0.555533
$$392$$ 0 0
$$393$$ 3.83771e6i 1.25340i
$$394$$ 0 0
$$395$$ 2.33640e6 1.72199e6i 0.753450 0.555314i
$$396$$ 0 0
$$397$$ 4.90405e6i 1.56163i 0.624760 + 0.780817i $$0.285197\pi$$
−0.624760 + 0.780817i $$0.714803\pi$$
$$398$$ 0 0
$$399$$ 261360. 0.0821877
$$400$$ 0 0
$$401$$ −642798. −0.199624 −0.0998122 0.995006i $$-0.531824\pi$$
−0.0998122 + 0.995006i $$0.531824\pi$$
$$402$$ 0 0
$$403$$ 806179.i 0.247268i
$$404$$ 0 0
$$405$$ −3.27686e6 + 2.41513e6i −0.992704 + 0.731650i
$$406$$ 0 0
$$407$$ 3.52035e6i 1.05341i
$$408$$ 0 0
$$409$$ −2.05711e6 −0.608064 −0.304032 0.952662i $$-0.598333\pi$$
−0.304032 + 0.952662i $$0.598333\pi$$
$$410$$ 0 0
$$411$$ 2.85701e6 0.834271
$$412$$ 0 0
$$413$$ 1.47218e6i 0.424704i
$$414$$ 0 0
$$415$$ 2.05106e6 + 2.78288e6i 0.584599 + 0.793185i
$$416$$ 0 0
$$417$$ 6.33489e6i 1.78402i
$$418$$ 0 0
$$419$$ 2.93742e6 0.817393 0.408697 0.912670i $$-0.365983\pi$$
0.408697 + 0.912670i $$0.365983\pi$$
$$420$$ 0 0
$$421$$ −2.71770e6 −0.747303 −0.373651 0.927569i $$-0.621894\pi$$
−0.373651 + 0.927569i $$0.621894\pi$$
$$422$$ 0 0
$$423$$ 1.61266e6i 0.438219i
$$424$$ 0 0
$$425$$ −2.05920e6 638119.i −0.553001 0.171368i
$$426$$ 0 0
$$427$$ 340166.i 0.0902862i
$$428$$ 0 0
$$429$$ 598752. 0.157074
$$430$$ 0 0
$$431$$ 4.99435e6 1.29505 0.647524 0.762045i $$-0.275804\pi$$
0.647524 + 0.762045i $$0.275804\pi$$
$$432$$ 0 0
$$433$$ 2.08183e6i 0.533612i −0.963750 0.266806i $$-0.914032\pi$$
0.963750 0.266806i $$-0.0859684\pi$$
$$434$$ 0 0
$$435$$ 4.57380e6 + 6.20574e6i 1.15892 + 1.57243i
$$436$$ 0 0
$$437$$ 535569.i 0.134156i
$$438$$ 0 0
$$439$$ −4.70404e6 −1.16496 −0.582478 0.812846i $$-0.697917\pi$$
−0.582478 + 0.812846i $$0.697917\pi$$
$$440$$ 0 0
$$441$$ −2.02618e6 −0.496114
$$442$$ 0 0
$$443$$ 5.70103e6i 1.38021i 0.723711 + 0.690103i $$0.242435\pi$$
−0.723711 + 0.690103i $$0.757565\pi$$
$$444$$ 0 0
$$445$$ −449550. + 331331.i −0.107616 + 0.0793162i
$$446$$ 0 0
$$447$$ 1.67456e6i 0.396399i
$$448$$ 0 0
$$449$$ 6.20325e6 1.45212 0.726062 0.687630i $$-0.241349\pi$$
0.726062 + 0.687630i $$0.241349\pi$$
$$450$$ 0 0
$$451$$ 49896.0 0.0115511
$$452$$ 0 0
$$453$$ 3.10134e6i 0.710074i
$$454$$ 0 0
$$455$$ 320760. 236409.i 0.0726360 0.0535347i
$$456$$ 0 0
$$457$$ 2.15371e6i 0.482388i −0.970477 0.241194i $$-0.922461\pi$$
0.970477 0.241194i $$-0.0775391\pi$$
$$458$$ 0 0
$$459$$ 1.23552e6 0.273727
$$460$$ 0 0
$$461$$ 3.85130e6 0.844024 0.422012 0.906590i $$-0.361324\pi$$
0.422012 + 0.906590i $$0.361324\pi$$
$$462$$ 0 0
$$463$$ 2.08213e6i 0.451394i −0.974198 0.225697i $$-0.927534\pi$$
0.974198 0.225697i $$-0.0724659\pi$$
$$464$$ 0 0
$$465$$ 4.45632e6 + 6.04634e6i 0.955749 + 1.29676i
$$466$$ 0 0
$$467$$ 1.30822e6i 0.277579i −0.990322 0.138790i $$-0.955679\pi$$
0.990322 0.138790i $$-0.0443212\pi$$
$$468$$ 0 0
$$469$$ 2.60528e6 0.546919
$$470$$ 0 0
$$471$$ 7.09711e6 1.47411
$$472$$ 0 0
$$473$$ 105309.i 0.0216429i
$$474$$ 0 0
$$475$$ 203500. 656692.i 0.0413838 0.133545i
$$476$$ 0 0
$$477$$ 891071.i 0.179315i
$$478$$ 0 0
$$479$$ −6.76368e6 −1.34693 −0.673464 0.739220i $$-0.735194\pi$$
−0.673464 + 0.739220i $$0.735194\pi$$
$$480$$ 0 0
$$481$$ 1.66795e6 0.328716
$$482$$ 0 0
$$483$$ 2.89207e6i 0.564080i
$$484$$ 0 0
$$485$$ −3.35808e6 4.55625e6i −0.648241 0.879534i
$$486$$ 0 0
$$487$$ 6.67193e6i 1.27476i 0.770549 + 0.637381i $$0.219982\pi$$
−0.770549 + 0.637381i $$0.780018\pi$$
$$488$$ 0 0
$$489$$ −2.88328e6 −0.545273
$$490$$ 0 0
$$491$$ 6.87575e6 1.28711 0.643556 0.765399i $$-0.277458\pi$$
0.643556 + 0.765399i $$0.277458\pi$$
$$492$$ 0 0
$$493$$ 4.78072e6i 0.885881i
$$494$$ 0 0
$$495$$ 1.73502e6 1.27876e6i 0.318267 0.234572i
$$496$$ 0 0
$$497$$ 3.18507e6i 0.578400i
$$498$$ 0 0
$$499$$ −6.94010e6 −1.24771 −0.623856 0.781539i $$-0.714435\pi$$
−0.623856 + 0.781539i $$0.714435\pi$$
$$500$$ 0 0
$$501$$ 360228. 0.0641185
$$502$$ 0 0
$$503$$ 921007.i 0.162309i 0.996702 + 0.0811546i $$0.0258607\pi$$
−0.996702 + 0.0811546i $$0.974139\pi$$
$$504$$ 0 0
$$505$$ 4.90941e6 3.61837e6i 0.856645 0.631371i
$$506$$ 0 0
$$507$$ 7.10495e6i 1.22755i
$$508$$ 0 0
$$509$$ −4.97979e6 −0.851955 −0.425977 0.904734i $$-0.640070\pi$$
−0.425977 + 0.904734i $$0.640070\pi$$
$$510$$ 0 0
$$511$$ 4.23403e6 0.717302
$$512$$ 0 0
$$513$$ 394015.i 0.0661027i
$$514$$ 0 0
$$515$$ 2.34234e6 + 3.17809e6i 0.389163 + 0.528017i
$$516$$ 0 0
$$517$$ 2.65614e6i 0.437043i
$$518$$ 0 0
$$519$$ −9.80206e6 −1.59735
$$520$$ 0 0
$$521$$ −147798. −0.0238547 −0.0119274 0.999929i $$-0.503797\pi$$
−0.0119274 + 0.999929i $$0.503797\pi$$
$$522$$ 0 0
$$523$$ 1.23884e7i 1.98043i −0.139543 0.990216i $$-0.544563\pi$$
0.139543 0.990216i $$-0.455437\pi$$
$$524$$ 0 0
$$525$$ 1.09890e6 3.54614e6i 0.174004 0.561509i
$$526$$ 0 0
$$527$$ 4.65792e6i 0.730576i
$$528$$ 0 0
$$529$$ 510027. 0.0792417
$$530$$ 0 0
$$531$$ −3.77298e6 −0.580695
$$532$$ 0 0
$$533$$ 23640.9i 0.00360451i
$$534$$ 0 0
$$535$$ −3.22102e6 4.37028e6i −0.486529 0.660123i
$$536$$ 0 0
$$537$$ 8.84385e6i 1.32344i
$$538$$ 0 0
$$539$$ −3.33724e6 −0.494783
$$540$$ 0 0
$$541$$ 9.99810e6 1.46867 0.734335 0.678787i $$-0.237494\pi$$
0.734335 + 0.678787i $$0.237494\pi$$
$$542$$ 0 0
$$543$$ 3.12231e6i 0.454440i
$$544$$ 0 0
$$545$$ 945450. 696823.i 0.136348 0.100492i
$$546$$ 0 0
$$547$$ 1.18580e7i 1.69451i −0.531189 0.847253i $$-0.678255\pi$$
0.531189 0.847253i $$-0.321745\pi$$
$$548$$ 0 0
$$549$$ −871794. −0.123448
$$550$$ 0 0
$$551$$ 1.52460e6 0.213933
$$552$$ 0 0
$$553$$ 3.09958e6i 0.431013i
$$554$$ 0 0
$$555$$ 1.25096e7 9.21995e6i 1.72390 1.27056i
$$556$$ 0 0
$$557$$ 904550.i 0.123536i −0.998091 0.0617681i $$-0.980326\pi$$
0.998091 0.0617681i $$-0.0196739\pi$$
$$558$$ 0 0
$$559$$ −49896.0 −0.00675361
$$560$$ 0 0
$$561$$ −3.45946e6 −0.464088
$$562$$ 0 0
$$563$$ 8.68719e6i 1.15507i 0.816366 + 0.577535i $$0.195985\pi$$
−0.816366 + 0.577535i $$0.804015\pi$$
$$564$$ 0 0
$$565$$ 3.48304e6 + 4.72579e6i 0.459026 + 0.622807i
$$566$$ 0 0
$$567$$ 4.34724e6i 0.567879i
$$568$$ 0 0
$$569$$ −2.27007e6 −0.293940 −0.146970 0.989141i $$-0.546952\pi$$
−0.146970 + 0.989141i $$0.546952\pi$$
$$570$$ 0 0
$$571$$ −1.43807e7 −1.84582 −0.922908 0.385021i $$-0.874194\pi$$
−0.922908 + 0.385021i $$0.874194\pi$$
$$572$$ 0 0
$$573$$ 6.61372e6i 0.841510i
$$574$$ 0 0
$$575$$ 7.26660e6 + 2.25182e6i 0.916562 + 0.284030i
$$576$$ 0 0
$$577$$ 5.63943e6i 0.705173i 0.935779 + 0.352586i $$0.114698\pi$$
−0.935779 + 0.352586i $$0.885302\pi$$
$$578$$ 0 0
$$579$$ −1.56436e7 −1.93928
$$580$$ 0 0
$$581$$ 3.69191e6 0.453744
$$582$$ 0 0
$$583$$ 1.46765e6i 0.178834i
$$584$$ 0 0
$$585$$ −605880. 822059.i −0.0731976 0.0993146i
$$586$$ 0 0
$$587$$ 1.28473e6i 0.153893i −0.997035 0.0769464i $$-0.975483\pi$$
0.997035 0.0769464i $$-0.0245170\pi$$
$$588$$ 0 0
$$589$$ 1.48544e6 0.176428
$$590$$ 0 0
$$591$$ 1.18615e6 0.139692
$$592$$ 0 0
$$593$$ 7.00943e6i 0.818552i 0.912411 + 0.409276i $$0.134219\pi$$
−0.912411 + 0.409276i $$0.865781\pi$$
$$594$$ 0 0
$$595$$ −1.85328e6 + 1.36592e6i −0.214609 + 0.158173i
$$596$$ 0 0
$$597$$ 7.87632e6i 0.904456i
$$598$$ 0 0
$$599$$ −8.80020e6 −1.00213 −0.501067 0.865409i $$-0.667059\pi$$
−0.501067 + 0.865409i $$0.667059\pi$$
$$600$$ 0 0
$$601$$ −1.07670e7 −1.21593 −0.607965 0.793964i $$-0.708014\pi$$
−0.607965 + 0.793964i $$0.708014\pi$$
$$602$$ 0 0
$$603$$ 6.67694e6i 0.747798i
$$604$$ 0 0
$$605$$ −4.38962e6 + 3.23527e6i −0.487571 + 0.359353i
$$606$$ 0 0
$$607$$ 1.51219e7i 1.66584i −0.553391 0.832921i $$-0.686667\pi$$
0.553391 0.832921i $$-0.313333\pi$$
$$608$$ 0 0
$$609$$ 8.23284e6 0.899511
$$610$$ 0 0
$$611$$ 1.25849e6 0.136379
$$612$$ 0 0
$$613$$ 8.31622e6i 0.893871i 0.894566 + 0.446936i $$0.147485\pi$$
−0.894566 + 0.446936i $$0.852515\pi$$
$$614$$ 0 0
$$615$$ −130680. 177307.i −0.0139323 0.0189033i
$$616$$ 0 0
$$617$$ 1.21083e7i 1.28047i 0.768178 + 0.640237i $$0.221164\pi$$
−0.768178 + 0.640237i $$0.778836\pi$$
$$618$$ 0 0
$$619$$ −9.73238e6 −1.02092 −0.510461 0.859901i $$-0.670525\pi$$
−0.510461 + 0.859901i $$0.670525\pi$$
$$620$$ 0 0
$$621$$ −4.35996e6 −0.453684
$$622$$ 0 0
$$623$$ 596395.i 0.0615622i
$$624$$ 0 0
$$625$$ −8.05437e6 5.52218e6i −0.824768 0.565471i
$$626$$ 0 0
$$627$$ 1.10324e6i 0.112073i
$$628$$ 0 0
$$629$$ −9.63706e6 −0.971220
$$630$$ 0 0
$$631$$ −8.60145e6 −0.859999 −0.430000 0.902829i $$-0.641486\pi$$
−0.430000 + 0.902829i $$0.641486\pi$$
$$632$$ 0 0
$$633$$ 5.00574e6i 0.496546i
$$634$$ 0 0
$$635$$ −2.89278e6 3.92493e6i −0.284696 0.386276i
$$636$$ 0 0
$$637$$ 1.58119e6i 0.154396i
$$638$$ 0 0
$$639$$ −8.16286e6 −0.790842
$$640$$ 0 0
$$641$$ −6.42440e6 −0.617572 −0.308786 0.951132i $$-0.599923\pi$$
−0.308786 + 0.951132i $$0.599923\pi$$
$$642$$ 0 0
$$643$$ 3.64721e6i 0.347883i −0.984756 0.173941i $$-0.944350\pi$$
0.984756 0.173941i $$-0.0556503\pi$$
$$644$$ 0 0
$$645$$ −374220. + 275811.i −0.0354183 + 0.0261043i
$$646$$ 0 0
$$647$$ 3.78036e6i 0.355036i 0.984118 + 0.177518i $$0.0568068\pi$$
−0.984118 + 0.177518i $$0.943193\pi$$
$$648$$ 0 0
$$649$$ −6.21432e6 −0.579138
$$650$$ 0 0
$$651$$ 8.02138e6 0.741816
$$652$$ 0 0
$$653$$ 1.66957e7i 1.53223i 0.642706 + 0.766113i $$0.277812\pi$$
−0.642706 + 0.766113i $$0.722188\pi$$
$$654$$ 0 0
$$655$$ −8.67834e6 + 6.39618e6i −0.790375 + 0.582529i
$$656$$ 0 0
$$657$$ 1.08512e7i 0.980761i
$$658$$ 0 0
$$659$$ 1.22166e6 0.109581 0.0547907 0.998498i $$-0.482551\pi$$
0.0547907 + 0.998498i $$0.482551\pi$$
$$660$$ 0 0
$$661$$ −1.62789e7 −1.44918 −0.724589 0.689182i $$-0.757970\pi$$
−0.724589 + 0.689182i $$0.757970\pi$$
$$662$$ 0 0
$$663$$ 1.63910e6i 0.144818i
$$664$$ 0 0
$$665$$ −435600. 591023.i −0.0381974 0.0518263i
$$666$$ 0 0
$$667$$ 1.68704e7i 1.46829i
$$668$$ 0 0
$$669$$ 5.74636e6 0.496395
$$670$$ 0 0
$$671$$ −1.43590e6 −0.123117
$$672$$ 0 0
$$673$$ 1.43928e7i 1.22492i 0.790503 + 0.612459i $$0.209819\pi$$
−0.790503 + 0.612459i $$0.790181\pi$$
$$674$$ 0 0
$$675$$ 5.34600e6 + 1.65665e6i 0.451616 + 0.139950i
$$676$$ 0 0
$$677$$ 2.62429e6i 0.220059i −0.993928 0.110030i $$-0.964905\pi$$
0.993928 0.110030i $$-0.0350946\pi$$
$$678$$ 0 0
$$679$$ −6.04454e6 −0.503140
$$680$$ 0 0
$$681$$ 2.31661e7 1.91419
$$682$$ 0 0
$$683$$ 1.03039e7i 0.845184i −0.906320 0.422592i $$-0.861120\pi$$
0.906320 0.422592i $$-0.138880\pi$$
$$684$$ 0 0
$$685$$ −4.76168e6 6.46065e6i −0.387734 0.526078i
$$686$$ 0 0
$$687$$ 1.08985e7i 0.880998i
$$688$$ 0 0
$$689$$ −695376. −0.0558048
$$690$$ 0 0
$$691$$ −4.50285e6 −0.358751 −0.179375 0.983781i $$-0.557408\pi$$
−0.179375 + 0.983781i $$0.557408\pi$$
$$692$$ 0 0
$$693$$ 2.30176e6i 0.182066i
$$694$$ 0 0
$$695$$ 1.43253e7 1.05581e7i 1.12497 0.829136i
$$696$$ 0 0
$$697$$ 136592.i 0.0106498i
$$698$$ 0 0
$$699$$ −957264. −0.0741035
$$700$$ 0 0
$$701$$ 4.88090e6 0.375150 0.187575 0.982250i $$-0.439937\pi$$
0.187575 + 0.982250i $$0.439937\pi$$
$$702$$ 0 0
$$703$$ 3.07332e6i 0.234541i
$$704$$ 0 0
$$705$$ 9.43866e6 6.95655e6i 0.715217 0.527134i
$$706$$ 0 0
$$707$$ 6.51307e6i 0.490046i
$$708$$ 0 0
$$709$$ 9.96961e6 0.744839 0.372420 0.928064i $$-0.378528\pi$$
0.372420 + 0.928064i $$0.378528\pi$$
$$710$$ 0 0
$$711$$ −7.94376e6 −0.589321
$$712$$ 0 0
$$713$$ 1.64371e7i 1.21088i
$$714$$ 0 0
$$715$$ −997920. 1.35398e6i −0.0730013 0.0990482i
$$716$$ 0 0
$$717$$ 2.00160e7i 1.45405i
$$718$$ 0 0
$$719$$ −1.19167e7 −0.859675 −0.429838 0.902906i $$-0.641429\pi$$
−0.429838 + 0.902906i $$0.641429\pi$$
$$720$$ 0 0
$$721$$ 4.21621e6 0.302054
$$722$$ 0 0
$$723$$ 1.78143e7i 1.26743i
$$724$$ 0 0
$$725$$ 6.41025e6 2.06858e7i 0.452929 1.46160i
$$726$$ 0 0
$$727$$ 1.38269e6i 0.0970264i −0.998823 0.0485132i $$-0.984552\pi$$
0.998823 0.0485132i $$-0.0154483\pi$$
$$728$$ 0 0
$$729$$ 2.48079e6 0.172890
$$730$$ 0 0
$$731$$ 288288. 0.0199541
$$732$$ 0 0
$$733$$ 6.09661e6i 0.419110i 0.977797 + 0.209555i $$0.0672016\pi$$
−0.977797 + 0.209555i $$0.932798\pi$$
$$734$$ 0 0
$$735$$ 8.74038e6 + 1.18590e7i 0.596777 + 0.809707i
$$736$$ 0 0
$$737$$ 1.09973e7i 0.745793i
$$738$$ 0 0
$$739$$ −6.16946e6 −0.415562 −0.207781 0.978175i $$-0.566624\pi$$
−0.207781 + 0.978175i $$0.566624\pi$$
$$740$$ 0 0
$$741$$ −522720. −0.0349723
$$742$$ 0 0
$$743$$ 1.57574e7i 1.04716i −0.851978 0.523578i $$-0.824597\pi$$
0.851978 0.523578i $$-0.175403\pi$$
$$744$$ 0 0
$$745$$ −3.78675e6 + 2.79094e6i −0.249963 + 0.184230i
$$746$$ 0 0
$$747$$ 9.46179e6i 0.620400i
$$748$$ 0 0
$$749$$ −5.79784e6 −0.377626
$$750$$ 0 0
$$751$$ −1.51816e7 −0.982243 −0.491122 0.871091i $$-0.663413\pi$$
−0.491122 + 0.871091i $$0.663413\pi$$
$$752$$ 0 0
$$753$$ 1.11091e7i 0.713987i
$$754$$ 0 0
$$755$$ −7.01316e6 + 5.16889e6i −0.447761 + 0.330012i
$$756$$ 0 0
$$757$$ 652274.i 0.0413705i 0.999786 + 0.0206852i $$0.00658478\pi$$
−0.999786 + 0.0206852i $$0.993415\pi$$
$$758$$ 0 0
$$759$$ 1.22079e7 0.769194
$$760$$ 0 0
$$761$$ 4.51420e6 0.282566 0.141283 0.989969i $$-0.454877\pi$$
0.141283 + 0.989969i $$0.454877\pi$$
$$762$$ 0 0
$$763$$ 1.25428e6i 0.0779980i
$$764$$ 0 0
$$765$$ 3.50064e6 + 4.74967e6i 0.216269 + 0.293434i
$$766$$ 0 0
$$767$$ 2.94437e6i 0.180719i
$$768$$ 0 0
$$769$$ −1.20799e7 −0.736625 −0.368312 0.929702i $$-0.620064\pi$$
−0.368312 + 0.929702i $$0.620064\pi$$
$$770$$ 0 0
$$771$$ 1.56795e7 0.949939
$$772$$ 0 0
$$773$$ 1.04245e7i 0.627492i 0.949507 + 0.313746i $$0.101584\pi$$
−0.949507 + 0.313746i $$0.898416\pi$$
$$774$$ 0 0
$$775$$ 6.24560e6 2.01545e7i 0.373525 1.20536i
$$776$$ 0 0
$$777$$ 1.65959e7i 0.986163i
$$778$$ 0 0
$$779$$ −43560.0 −0.00257184
$$780$$ 0 0
$$781$$ −1.34447e7 −0.788721
$$782$$ 0 0
$$783$$ 1.24115e7i 0.723467i
$$784$$ 0 0
$$785$$ −1.18285e7 1.60489e7i −0.685104 0.929549i
$$786$$ 0 0
$$787$$ 3.45366e7i 1.98766i −0.110913 0.993830i $$-0.535378\pi$$
0.110913 0.993830i $$-0.464622\pi$$
$$788$$ 0 0
$$789$$ 3.24711e7 1.85697
$$790$$ 0 0
$$791$$ 6.26947e6 0.356279
$$792$$ 0 0
$$793$$ 680333.i 0.0384183i
$$794$$ 0 0
$$795$$ −5.21532e6 + 3.84384e6i −0.292660 + 0.215698i
$$796$$ 0 0
$$797$$ 2.09287e7i 1.16707i 0.812089 + 0.583533i $$0.198330\pi$$
−0.812089 + 0.583533i $$0.801670\pi$$
$$798$$ 0 0
$$799$$ −7.27126e6 −0.402942
$$800$$ 0 0
$$801$$ 1.52847e6 0.0841735
$$802$$ 0 0
$$803$$ 1.78725e7i 0.978131i
$$804$$ 0 0
$$805$$ 6.53994e6 4.82012e6i 0.355700 0.262161i
$$806$$ 0 0
$$807$$ 3.45533e7i 1.86770i
$$808$$ 0 0
$$809$$ 2.48797e7 1.33651