# Properties

 Label 76.6.e.a.45.3 Level $76$ Weight $6$ Character 76.45 Analytic conductor $12.189$ Analytic rank $0$ Dimension $18$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 76.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.1891703058$$ Analytic rank: $$0$$ Dimension: $$18$$ Relative dimension: $$9$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ Defining polynomial: $$x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} - 863969476320 x^{9} + 79755165392064 x^{8} - 375077568148992 x^{7} + 12736924096193536 x^{6} - 57314532742553600 x^{5} + 977121800205220864 x^{4} - 4977732006498379776 x^{3} + 53672321824823513088 x^{2} - 185653809995679793152 x + 804303742853852430336$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{16}\cdot 3^{3}\cdot 5^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 45.3 Root $$6.29505 - 10.9033i$$ of defining polynomial Character $$\chi$$ $$=$$ 76.45 Dual form 76.6.e.a.49.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-6.79505 - 11.7694i) q^{3} +(-47.4871 - 82.2500i) q^{5} +189.860 q^{7} +(29.1546 - 50.4972i) q^{9} +O(q^{10})$$ $$q+(-6.79505 - 11.7694i) q^{3} +(-47.4871 - 82.2500i) q^{5} +189.860 q^{7} +(29.1546 - 50.4972i) q^{9} -530.005 q^{11} +(-353.895 + 612.964i) q^{13} +(-645.354 + 1117.79i) q^{15} +(-764.589 - 1324.31i) q^{17} +(654.031 + 1431.20i) q^{19} +(-1290.11 - 2234.53i) q^{21} +(497.425 - 861.565i) q^{23} +(-2947.54 + 5105.29i) q^{25} -4094.82 q^{27} +(-1290.66 + 2235.49i) q^{29} -2790.81 q^{31} +(3601.41 + 6237.82i) q^{33} +(-9015.88 - 15616.0i) q^{35} +7238.14 q^{37} +9618.94 q^{39} +(2181.63 + 3778.69i) q^{41} +(-3121.70 - 5406.94i) q^{43} -5537.86 q^{45} +(12320.9 - 21340.4i) q^{47} +19239.7 q^{49} +(-10390.8 + 17997.5i) q^{51} +(-15497.6 + 26842.6i) q^{53} +(25168.4 + 43592.9i) q^{55} +(12400.2 - 17422.6i) q^{57} +(-18177.7 - 31484.8i) q^{59} +(2886.93 - 5000.30i) q^{61} +(5535.27 - 9587.38i) q^{63} +67221.7 q^{65} +(30388.4 - 52634.2i) q^{67} -13520.1 q^{69} +(14829.0 + 25684.5i) q^{71} +(-39002.3 - 67553.9i) q^{73} +80114.7 q^{75} -100627. q^{77} +(-33427.5 - 57898.2i) q^{79} +(20740.0 + 35922.7i) q^{81} -21919.5 q^{83} +(-72616.2 + 125775. i) q^{85} +35080.4 q^{87} +(-45374.8 + 78591.5i) q^{89} +(-67190.4 + 116377. i) q^{91} +(18963.7 + 32846.0i) q^{93} +(86658.4 - 121758. i) q^{95} +(-30757.3 - 53273.1i) q^{97} +(-15452.1 + 26763.7i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10})$$ $$18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$39$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −6.79505 11.7694i −0.435903 0.755006i 0.561466 0.827500i $$-0.310238\pi$$
−0.997369 + 0.0724940i $$0.976904\pi$$
$$4$$ 0 0
$$5$$ −47.4871 82.2500i −0.849474 1.47133i −0.881678 0.471851i $$-0.843586\pi$$
0.0322040 0.999481i $$-0.489747\pi$$
$$6$$ 0 0
$$7$$ 189.860 1.46449 0.732247 0.681039i $$-0.238472\pi$$
0.732247 + 0.681039i $$0.238472\pi$$
$$8$$ 0 0
$$9$$ 29.1546 50.4972i 0.119978 0.207807i
$$10$$ 0 0
$$11$$ −530.005 −1.32068 −0.660341 0.750966i $$-0.729588\pi$$
−0.660341 + 0.750966i $$0.729588\pi$$
$$12$$ 0 0
$$13$$ −353.895 + 612.964i −0.580786 + 1.00595i 0.414600 + 0.910004i $$0.363921\pi$$
−0.995386 + 0.0959473i $$0.969412\pi$$
$$14$$ 0 0
$$15$$ −645.354 + 1117.79i −0.740576 + 1.28272i
$$16$$ 0 0
$$17$$ −764.589 1324.31i −0.641661 1.11139i −0.985062 0.172201i $$-0.944912\pi$$
0.343401 0.939189i $$-0.388421\pi$$
$$18$$ 0 0
$$19$$ 654.031 + 1431.20i 0.415637 + 0.909530i
$$20$$ 0 0
$$21$$ −1290.11 2234.53i −0.638377 1.10570i
$$22$$ 0 0
$$23$$ 497.425 861.565i 0.196068 0.339600i −0.751182 0.660095i $$-0.770516\pi$$
0.947250 + 0.320495i $$0.103849\pi$$
$$24$$ 0 0
$$25$$ −2947.54 + 5105.29i −0.943213 + 1.63369i
$$26$$ 0 0
$$27$$ −4094.82 −1.08100
$$28$$ 0 0
$$29$$ −1290.66 + 2235.49i −0.284982 + 0.493603i −0.972605 0.232465i $$-0.925321\pi$$
0.687623 + 0.726068i $$0.258654\pi$$
$$30$$ 0 0
$$31$$ −2790.81 −0.521585 −0.260793 0.965395i $$-0.583984\pi$$
−0.260793 + 0.965395i $$0.583984\pi$$
$$32$$ 0 0
$$33$$ 3601.41 + 6237.82i 0.575689 + 0.997122i
$$34$$ 0 0
$$35$$ −9015.88 15616.0i −1.24405 2.15476i
$$36$$ 0 0
$$37$$ 7238.14 0.869206 0.434603 0.900622i $$-0.356889\pi$$
0.434603 + 0.900622i $$0.356889\pi$$
$$38$$ 0 0
$$39$$ 9618.94 1.01266
$$40$$ 0 0
$$41$$ 2181.63 + 3778.69i 0.202685 + 0.351060i 0.949393 0.314092i $$-0.101700\pi$$
−0.746708 + 0.665152i $$0.768367\pi$$
$$42$$ 0 0
$$43$$ −3121.70 5406.94i −0.257466 0.445944i 0.708096 0.706116i $$-0.249554\pi$$
−0.965562 + 0.260172i $$0.916221\pi$$
$$44$$ 0 0
$$45$$ −5537.86 −0.407671
$$46$$ 0 0
$$47$$ 12320.9 21340.4i 0.813576 1.40915i −0.0967705 0.995307i $$-0.530851\pi$$
0.910346 0.413848i $$-0.135815\pi$$
$$48$$ 0 0
$$49$$ 19239.7 1.14474
$$50$$ 0 0
$$51$$ −10390.8 + 17997.5i −0.559404 + 0.968916i
$$52$$ 0 0
$$53$$ −15497.6 + 26842.6i −0.757833 + 1.31261i 0.186120 + 0.982527i $$0.440409\pi$$
−0.943953 + 0.330079i $$0.892925\pi$$
$$54$$ 0 0
$$55$$ 25168.4 + 43592.9i 1.12188 + 1.94316i
$$56$$ 0 0
$$57$$ 12400.2 17422.6i 0.505523 0.710275i
$$58$$ 0 0
$$59$$ −18177.7 31484.8i −0.679845 1.17753i −0.975027 0.222085i $$-0.928714\pi$$
0.295182 0.955441i $$-0.404620\pi$$
$$60$$ 0 0
$$61$$ 2886.93 5000.30i 0.0993370 0.172057i −0.812073 0.583555i $$-0.801661\pi$$
0.911410 + 0.411499i $$0.134994\pi$$
$$62$$ 0 0
$$63$$ 5535.27 9587.38i 0.175706 0.304333i
$$64$$ 0 0
$$65$$ 67221.7 1.97345
$$66$$ 0 0
$$67$$ 30388.4 52634.2i 0.827029 1.43246i −0.0733301 0.997308i $$-0.523363\pi$$
0.900359 0.435148i $$-0.143304\pi$$
$$68$$ 0 0
$$69$$ −13520.1 −0.341867
$$70$$ 0 0
$$71$$ 14829.0 + 25684.5i 0.349112 + 0.604680i 0.986092 0.166201i $$-0.0531500\pi$$
−0.636980 + 0.770880i $$0.719817\pi$$
$$72$$ 0 0
$$73$$ −39002.3 67553.9i −0.856609 1.48369i −0.875144 0.483862i $$-0.839234\pi$$
0.0185353 0.999828i $$-0.494100\pi$$
$$74$$ 0 0
$$75$$ 80114.7 1.64460
$$76$$ 0 0
$$77$$ −100627. −1.93413
$$78$$ 0 0
$$79$$ −33427.5 57898.2i −0.602611 1.04375i −0.992424 0.122858i $$-0.960794\pi$$
0.389814 0.920894i $$-0.372539\pi$$
$$80$$ 0 0
$$81$$ 20740.0 + 35922.7i 0.351233 + 0.608354i
$$82$$ 0 0
$$83$$ −21919.5 −0.349250 −0.174625 0.984635i $$-0.555871\pi$$
−0.174625 + 0.984635i $$0.555871\pi$$
$$84$$ 0 0
$$85$$ −72616.2 + 125775.i −1.09015 + 1.88819i
$$86$$ 0 0
$$87$$ 35080.4 0.496898
$$88$$ 0 0
$$89$$ −45374.8 + 78591.5i −0.607211 + 1.05172i 0.384487 + 0.923131i $$0.374378\pi$$
−0.991698 + 0.128590i $$0.958955\pi$$
$$90$$ 0 0
$$91$$ −67190.4 + 116377.i −0.850558 + 1.47321i
$$92$$ 0 0
$$93$$ 18963.7 + 32846.0i 0.227360 + 0.393800i
$$94$$ 0 0
$$95$$ 86658.4 121758.i 0.985149 1.38416i
$$96$$ 0 0
$$97$$ −30757.3 53273.1i −0.331908 0.574882i 0.650978 0.759097i $$-0.274359\pi$$
−0.982886 + 0.184215i $$0.941026\pi$$
$$98$$ 0 0
$$99$$ −15452.1 + 26763.7i −0.158452 + 0.274447i
$$100$$ 0 0
$$101$$ 5882.91 10189.5i 0.0573837 0.0993915i −0.835906 0.548872i $$-0.815057\pi$$
0.893290 + 0.449480i $$0.148391\pi$$
$$102$$ 0 0
$$103$$ −57682.4 −0.535735 −0.267868 0.963456i $$-0.586319\pi$$
−0.267868 + 0.963456i $$0.586319\pi$$
$$104$$ 0 0
$$105$$ −122527. + 212222.i −1.08457 + 1.87853i
$$106$$ 0 0
$$107$$ −79892.9 −0.674604 −0.337302 0.941397i $$-0.609514\pi$$
−0.337302 + 0.941397i $$0.609514\pi$$
$$108$$ 0 0
$$109$$ −98323.4 170301.i −0.792667 1.37294i −0.924310 0.381642i $$-0.875359\pi$$
0.131643 0.991297i $$-0.457975\pi$$
$$110$$ 0 0
$$111$$ −49183.5 85188.4i −0.378889 0.656255i
$$112$$ 0 0
$$113$$ 205714. 1.51554 0.757770 0.652521i $$-0.226289\pi$$
0.757770 + 0.652521i $$0.226289\pi$$
$$114$$ 0 0
$$115$$ −94484.9 −0.666220
$$116$$ 0 0
$$117$$ 20635.3 + 35741.4i 0.139363 + 0.241383i
$$118$$ 0 0
$$119$$ −145165. 251433.i −0.939709 1.62762i
$$120$$ 0 0
$$121$$ 119854. 0.744199
$$122$$ 0 0
$$123$$ 29648.6 51352.8i 0.176702 0.306056i
$$124$$ 0 0
$$125$$ 263086. 1.50599
$$126$$ 0 0
$$127$$ −143.620 + 248.756i −0.000790141 + 0.00136856i −0.866420 0.499316i $$-0.833585\pi$$
0.865630 + 0.500684i $$0.166918\pi$$
$$128$$ 0 0
$$129$$ −42424.2 + 73480.9i −0.224460 + 0.388777i
$$130$$ 0 0
$$131$$ −21086.6 36523.1i −0.107357 0.185947i 0.807342 0.590084i $$-0.200905\pi$$
−0.914699 + 0.404137i $$0.867572\pi$$
$$132$$ 0 0
$$133$$ 124174. + 271728.i 0.608698 + 1.33200i
$$134$$ 0 0
$$135$$ 194451. + 336799.i 0.918281 + 1.59051i
$$136$$ 0 0
$$137$$ −52318.5 + 90618.2i −0.238152 + 0.412491i −0.960184 0.279369i $$-0.909875\pi$$
0.722032 + 0.691859i $$0.243208\pi$$
$$138$$ 0 0
$$139$$ 64404.7 111552.i 0.282736 0.489713i −0.689322 0.724455i $$-0.742091\pi$$
0.972058 + 0.234743i $$0.0754247\pi$$
$$140$$ 0 0
$$141$$ −334885. −1.41856
$$142$$ 0 0
$$143$$ 187566. 324874.i 0.767033 1.32854i
$$144$$ 0 0
$$145$$ 245159. 0.968339
$$146$$ 0 0
$$147$$ −130735. 226439.i −0.498997 0.864288i
$$148$$ 0 0
$$149$$ −136506. 236435.i −0.503716 0.872462i −0.999991 0.00429614i $$-0.998632\pi$$
0.496275 0.868165i $$-0.334701\pi$$
$$150$$ 0 0
$$151$$ 68761.9 0.245418 0.122709 0.992443i $$-0.460842\pi$$
0.122709 + 0.992443i $$0.460842\pi$$
$$152$$ 0 0
$$153$$ −89165.0 −0.307940
$$154$$ 0 0
$$155$$ 132527. + 229544.i 0.443073 + 0.767425i
$$156$$ 0 0
$$157$$ 275998. + 478042.i 0.893628 + 1.54781i 0.835494 + 0.549500i $$0.185182\pi$$
0.0581337 + 0.998309i $$0.481485\pi$$
$$158$$ 0 0
$$159$$ 421227. 1.32137
$$160$$ 0 0
$$161$$ 94440.9 163576.i 0.287141 0.497343i
$$162$$ 0 0
$$163$$ −153395. −0.452211 −0.226106 0.974103i $$-0.572599\pi$$
−0.226106 + 0.974103i $$0.572599\pi$$
$$164$$ 0 0
$$165$$ 342041. 592432.i 0.978065 1.69406i
$$166$$ 0 0
$$167$$ 146626. 253963.i 0.406836 0.704660i −0.587697 0.809081i $$-0.699965\pi$$
0.994533 + 0.104421i $$0.0332988\pi$$
$$168$$ 0 0
$$169$$ −64836.9 112301.i −0.174625 0.302459i
$$170$$ 0 0
$$171$$ 91339.7 + 8699.36i 0.238874 + 0.0227508i
$$172$$ 0 0
$$173$$ −114249. 197885.i −0.290227 0.502688i 0.683636 0.729823i $$-0.260398\pi$$
−0.973863 + 0.227135i $$0.927064\pi$$
$$174$$ 0 0
$$175$$ −559619. + 969289.i −1.38133 + 2.39253i
$$176$$ 0 0
$$177$$ −247037. + 427881.i −0.592693 + 1.02657i
$$178$$ 0 0
$$179$$ 247143. 0.576521 0.288261 0.957552i $$-0.406923\pi$$
0.288261 + 0.957552i $$0.406923\pi$$
$$180$$ 0 0
$$181$$ 353864. 612910.i 0.802859 1.39059i −0.114867 0.993381i $$-0.536644\pi$$
0.917727 0.397213i $$-0.130022\pi$$
$$182$$ 0 0
$$183$$ −78467.2 −0.173205
$$184$$ 0 0
$$185$$ −343718. 595337.i −0.738368 1.27889i
$$186$$ 0 0
$$187$$ 405236. + 701889.i 0.847430 + 1.46779i
$$188$$ 0 0
$$189$$ −777442. −1.58312
$$190$$ 0 0
$$191$$ 10502.1 0.0208301 0.0104151 0.999946i $$-0.496685\pi$$
0.0104151 + 0.999946i $$0.496685\pi$$
$$192$$ 0 0
$$193$$ 496794. + 860472.i 0.960025 + 1.66281i 0.722424 + 0.691450i $$0.243028\pi$$
0.237601 + 0.971363i $$0.423639\pi$$
$$194$$ 0 0
$$195$$ −456775. 791158.i −0.860233 1.48997i
$$196$$ 0 0
$$197$$ −185300. −0.340182 −0.170091 0.985428i $$-0.554406\pi$$
−0.170091 + 0.985428i $$0.554406\pi$$
$$198$$ 0 0
$$199$$ 43149.9 74737.8i 0.0772408 0.133785i −0.824818 0.565399i $$-0.808722\pi$$
0.902059 + 0.431614i $$0.142056\pi$$
$$200$$ 0 0
$$201$$ −825963. −1.44202
$$202$$ 0 0
$$203$$ −245045. + 424430.i −0.417354 + 0.722879i
$$204$$ 0 0
$$205$$ 207198. 358878.i 0.344351 0.596433i
$$206$$ 0 0
$$207$$ −29004.4 50237.1i −0.0470476 0.0814889i
$$208$$ 0 0
$$209$$ −346640. 758544.i −0.548924 1.20120i
$$210$$ 0 0
$$211$$ 151234. + 261945.i 0.233853 + 0.405045i 0.958939 0.283613i $$-0.0915332\pi$$
−0.725086 + 0.688659i $$0.758200\pi$$
$$212$$ 0 0
$$213$$ 201527. 349055.i 0.304358 0.527163i
$$214$$ 0 0
$$215$$ −296481. + 513519.i −0.437422 + 0.757636i
$$216$$ 0 0
$$217$$ −529861. −0.763858
$$218$$ 0 0
$$219$$ −530045. + 918064.i −0.746796 + 1.29349i
$$220$$ 0 0
$$221$$ 1.08234e6 1.49067
$$222$$ 0 0
$$223$$ −339486. 588007.i −0.457151 0.791809i 0.541658 0.840599i $$-0.317797\pi$$
−0.998809 + 0.0487901i $$0.984463\pi$$
$$224$$ 0 0
$$225$$ 171868. + 297685.i 0.226329 + 0.392013i
$$226$$ 0 0
$$227$$ 231581. 0.298289 0.149145 0.988815i $$-0.452348\pi$$
0.149145 + 0.988815i $$0.452348\pi$$
$$228$$ 0 0
$$229$$ 33377.9 0.0420601 0.0210300 0.999779i $$-0.493305\pi$$
0.0210300 + 0.999779i $$0.493305\pi$$
$$230$$ 0 0
$$231$$ 683762. + 1.18431e6i 0.843093 + 1.46028i
$$232$$ 0 0
$$233$$ 542190. + 939100.i 0.654277 + 1.13324i 0.982075 + 0.188493i $$0.0603602\pi$$
−0.327798 + 0.944748i $$0.606306\pi$$
$$234$$ 0 0
$$235$$ −2.34033e6 −2.76445
$$236$$ 0 0
$$237$$ −454284. + 786843.i −0.525359 + 0.909949i
$$238$$ 0 0
$$239$$ −284041. −0.321652 −0.160826 0.986983i $$-0.551416\pi$$
−0.160826 + 0.986983i $$0.551416\pi$$
$$240$$ 0 0
$$241$$ 306804. 531400.i 0.340266 0.589357i −0.644216 0.764843i $$-0.722816\pi$$
0.984482 + 0.175486i $$0.0561497\pi$$
$$242$$ 0 0
$$243$$ −215663. + 373539.i −0.234293 + 0.405807i
$$244$$ 0 0
$$245$$ −913637. 1.58246e6i −0.972430 1.68430i
$$246$$ 0 0
$$247$$ −1.10873e6 105598.i −1.15634 0.110132i
$$248$$ 0 0
$$249$$ 148944. + 257979.i 0.152239 + 0.263685i
$$250$$ 0 0
$$251$$ 369089. 639282.i 0.369783 0.640484i −0.619748 0.784801i $$-0.712765\pi$$
0.989531 + 0.144317i $$0.0460986\pi$$
$$252$$ 0 0
$$253$$ −263637. + 456633.i −0.258944 + 0.448504i
$$254$$ 0 0
$$255$$ 1.97372e6 1.90080
$$256$$ 0 0
$$257$$ 686359. 1.18881e6i 0.648214 1.12274i −0.335335 0.942099i $$-0.608849\pi$$
0.983549 0.180641i $$-0.0578172\pi$$
$$258$$ 0 0
$$259$$ 1.37423e6 1.27295
$$260$$ 0 0
$$261$$ 75257.3 + 130349.i 0.0683829 + 0.118443i
$$262$$ 0 0
$$263$$ −146329. 253449.i −0.130449 0.225944i 0.793401 0.608699i $$-0.208308\pi$$
−0.923850 + 0.382756i $$0.874975\pi$$
$$264$$ 0 0
$$265$$ 2.94373e6 2.57504
$$266$$ 0 0
$$267$$ 1.23330e6 1.05874
$$268$$ 0 0
$$269$$ −977718. 1.69346e6i −0.823821 1.42690i −0.902817 0.430025i $$-0.858505\pi$$
0.0789962 0.996875i $$-0.474828\pi$$
$$270$$ 0 0
$$271$$ −713502. 1.23582e6i −0.590163 1.02219i −0.994210 0.107454i $$-0.965730\pi$$
0.404047 0.914738i $$-0.367603\pi$$
$$272$$ 0 0
$$273$$ 1.82625e6 1.48304
$$274$$ 0 0
$$275$$ 1.56221e6 2.70583e6i 1.24568 2.15759i
$$276$$ 0 0
$$277$$ −1.20887e6 −0.946629 −0.473315 0.880893i $$-0.656943\pi$$
−0.473315 + 0.880893i $$0.656943\pi$$
$$278$$ 0 0
$$279$$ −81364.7 + 140928.i −0.0625785 + 0.108389i
$$280$$ 0 0
$$281$$ −996432. + 1.72587e6i −0.752804 + 1.30389i 0.193655 + 0.981070i $$0.437966\pi$$
−0.946459 + 0.322825i $$0.895367\pi$$
$$282$$ 0 0
$$283$$ 33435.3 + 57911.6i 0.0248164 + 0.0429832i 0.878167 0.478354i $$-0.158767\pi$$
−0.853350 + 0.521338i $$0.825433\pi$$
$$284$$ 0 0
$$285$$ −2.02186e6 192566.i −1.47448 0.140432i
$$286$$ 0 0
$$287$$ 414203. + 717421.i 0.296831 + 0.514126i
$$288$$ 0 0
$$289$$ −459264. + 795469.i −0.323458 + 0.560246i
$$290$$ 0 0
$$291$$ −417994. + 723987.i −0.289360 + 0.501185i
$$292$$ 0 0
$$293$$ 1.98637e6 1.35173 0.675866 0.737025i $$-0.263770\pi$$
0.675866 + 0.737025i $$0.263770\pi$$
$$294$$ 0 0
$$295$$ −1.72641e6 + 2.99024e6i −1.15502 + 2.00056i
$$296$$ 0 0
$$297$$ 2.17027e6 1.42766
$$298$$ 0 0
$$299$$ 352072. + 609807.i 0.227748 + 0.394470i
$$300$$ 0 0
$$301$$ −592685. 1.02656e6i −0.377058 0.653083i
$$302$$ 0 0
$$303$$ −159899. −0.100055
$$304$$ 0 0
$$305$$ −548366. −0.337537
$$306$$ 0 0
$$307$$ 932152. + 1.61454e6i 0.564470 + 0.977691i 0.997099 + 0.0761187i $$0.0242528\pi$$
−0.432629 + 0.901572i $$0.642414\pi$$
$$308$$ 0 0
$$309$$ 391955. + 678886.i 0.233528 + 0.404483i
$$310$$ 0 0
$$311$$ 1.73570e6 1.01759 0.508796 0.860887i $$-0.330091\pi$$
0.508796 + 0.860887i $$0.330091\pi$$
$$312$$ 0 0
$$313$$ 26566.2 46014.0i 0.0153274 0.0265478i −0.858260 0.513215i $$-0.828454\pi$$
0.873587 + 0.486667i $$0.161788\pi$$
$$314$$ 0 0
$$315$$ −1.05142e6 −0.597032
$$316$$ 0 0
$$317$$ −690554. + 1.19607e6i −0.385966 + 0.668514i −0.991903 0.127000i $$-0.959465\pi$$
0.605936 + 0.795513i $$0.292799\pi$$
$$318$$ 0 0
$$319$$ 684056. 1.18482e6i 0.376370 0.651892i
$$320$$ 0 0
$$321$$ 542876. + 940289.i 0.294062 + 0.509330i
$$322$$ 0 0
$$323$$ 1.39529e6 1.96042e6i 0.744144 1.04555i
$$324$$ 0 0
$$325$$ −2.08624e6 3.61347e6i −1.09561 1.89765i
$$326$$ 0 0
$$327$$ −1.33623e6 + 2.31441e6i −0.691051 + 1.19694i
$$328$$ 0 0
$$329$$ 2.33924e6 4.05169e6i 1.19148 2.06370i
$$330$$ 0 0
$$331$$ −79218.6 −0.0397427 −0.0198713 0.999803i $$-0.506326\pi$$
−0.0198713 + 0.999803i $$0.506326\pi$$
$$332$$ 0 0
$$333$$ 211025. 365506.i 0.104285 0.180627i
$$334$$ 0 0
$$335$$ −5.77222e6 −2.81016
$$336$$ 0 0
$$337$$ 1.06653e6 + 1.84729e6i 0.511563 + 0.886053i 0.999910 + 0.0134034i $$0.00426657\pi$$
−0.488347 + 0.872649i $$0.662400\pi$$
$$338$$ 0 0
$$339$$ −1.39784e6 2.42112e6i −0.660628 1.14424i
$$340$$ 0 0
$$341$$ 1.47914e6 0.688848
$$342$$ 0 0
$$343$$ 461871. 0.211976
$$344$$ 0 0
$$345$$ 642030. + 1.11203e6i 0.290407 + 0.503000i
$$346$$ 0 0
$$347$$ 988867. + 1.71277e6i 0.440874 + 0.763616i 0.997755 0.0669767i $$-0.0213353\pi$$
−0.556881 + 0.830592i $$0.688002\pi$$
$$348$$ 0 0
$$349$$ −2.01158e6 −0.884043 −0.442022 0.897004i $$-0.645739\pi$$
−0.442022 + 0.897004i $$0.645739\pi$$
$$350$$ 0 0
$$351$$ 1.44914e6 2.50998e6i 0.627829 1.08743i
$$352$$ 0 0
$$353$$ −2.89132e6 −1.23498 −0.617490 0.786579i $$-0.711850\pi$$
−0.617490 + 0.786579i $$0.711850\pi$$
$$354$$ 0 0
$$355$$ 1.40837e6 2.43936e6i 0.593123 1.02732i
$$356$$ 0 0
$$357$$ −1.97280e6 + 3.41699e6i −0.819243 + 1.41897i
$$358$$ 0 0
$$359$$ −371558. 643557.i −0.152156 0.263543i 0.779864 0.625950i $$-0.215288\pi$$
−0.932020 + 0.362407i $$0.881955\pi$$
$$360$$ 0 0
$$361$$ −1.62059e6 + 1.87210e6i −0.654491 + 0.756070i
$$362$$ 0 0
$$363$$ −814414. 1.41061e6i −0.324398 0.561875i
$$364$$ 0 0
$$365$$ −3.70420e6 + 6.41587e6i −1.45533 + 2.52071i
$$366$$ 0 0
$$367$$ 2.21010e6 3.82801e6i 0.856540 1.48357i −0.0186695 0.999826i $$-0.505943\pi$$
0.875209 0.483745i $$-0.160724\pi$$
$$368$$ 0 0
$$369$$ 254418. 0.0972705
$$370$$ 0 0
$$371$$ −2.94236e6 + 5.09632e6i −1.10984 + 1.92230i
$$372$$ 0 0
$$373$$ −2.07890e6 −0.773680 −0.386840 0.922147i $$-0.626433\pi$$
−0.386840 + 0.922147i $$0.626433\pi$$
$$374$$ 0 0
$$375$$ −1.78768e6 3.09636e6i −0.656466 1.13703i
$$376$$ 0 0
$$377$$ −913517. 1.58226e6i −0.331027 0.573355i
$$378$$ 0 0
$$379$$ 3.87208e6 1.38467 0.692335 0.721576i $$-0.256582\pi$$
0.692335 + 0.721576i $$0.256582\pi$$
$$380$$ 0 0
$$381$$ 3903.61 0.00137770
$$382$$ 0 0
$$383$$ −72504.1 125581.i −0.0252560 0.0437448i 0.853121 0.521713i $$-0.174707\pi$$
−0.878377 + 0.477968i $$0.841373\pi$$
$$384$$ 0 0
$$385$$ 4.77846e6 + 8.27653e6i 1.64299 + 2.84575i
$$386$$ 0 0
$$387$$ −364047. −0.123561
$$388$$ 0 0
$$389$$ 670618. 1.16154e6i 0.224699 0.389190i −0.731530 0.681809i $$-0.761193\pi$$
0.956229 + 0.292619i $$0.0945268\pi$$
$$390$$ 0 0
$$391$$ −1.52130e6 −0.503238
$$392$$ 0 0
$$393$$ −286570. + 496353.i −0.0935942 + 0.162110i
$$394$$ 0 0
$$395$$ −3.17475e6 + 5.49883e6i −1.02380 + 1.77328i
$$396$$ 0 0
$$397$$ −635788. 1.10122e6i −0.202458 0.350668i 0.746862 0.664980i $$-0.231560\pi$$
−0.949320 + 0.314311i $$0.898226\pi$$
$$398$$ 0 0
$$399$$ 2.35430e6 3.30786e6i 0.740336 1.04019i
$$400$$ 0 0
$$401$$ 722427. + 1.25128e6i 0.224354 + 0.388592i 0.956125 0.292958i $$-0.0946396\pi$$
−0.731772 + 0.681550i $$0.761306\pi$$
$$402$$ 0 0
$$403$$ 987652. 1.71066e6i 0.302929 0.524689i
$$404$$ 0 0
$$405$$ 1.96976e6 3.41172e6i 0.596727 1.03356i
$$406$$ 0 0
$$407$$ −3.83625e6 −1.14794
$$408$$ 0 0
$$409$$ 306511. 530893.i 0.0906020 0.156927i −0.817163 0.576407i $$-0.804454\pi$$
0.907765 + 0.419480i $$0.137788\pi$$
$$410$$ 0 0
$$411$$ 1.42203e6 0.415244
$$412$$ 0 0
$$413$$ −3.45122e6 5.97769e6i −0.995629 1.72448i
$$414$$ 0 0
$$415$$ 1.04089e6 + 1.80288e6i 0.296679 + 0.513862i
$$416$$ 0 0
$$417$$ −1.75053e6 −0.492981
$$418$$ 0 0
$$419$$ 6.30914e6 1.75564 0.877820 0.478991i $$-0.158997\pi$$
0.877820 + 0.478991i $$0.158997\pi$$
$$420$$ 0 0
$$421$$ −1.28732e6 2.22970e6i −0.353981 0.613113i 0.632962 0.774183i $$-0.281839\pi$$
−0.986943 + 0.161070i $$0.948506\pi$$
$$422$$ 0 0
$$423$$ −718421. 1.24434e6i −0.195222 0.338134i
$$424$$ 0 0
$$425$$ 9.01463e6 2.42089
$$426$$ 0 0
$$427$$ 548111. 949356.i 0.145478 0.251976i
$$428$$ 0 0
$$429$$ −5.09808e6 −1.33741
$$430$$ 0 0
$$431$$ −921074. + 1.59535e6i −0.238837 + 0.413678i −0.960381 0.278691i $$-0.910099\pi$$
0.721544 + 0.692369i $$0.243433\pi$$
$$432$$ 0 0
$$433$$ −2.48716e6 + 4.30788e6i −0.637505 + 1.10419i 0.348474 + 0.937318i $$0.386700\pi$$
−0.985979 + 0.166872i $$0.946633\pi$$
$$434$$ 0 0
$$435$$ −1.66587e6 2.88537e6i −0.422102 0.731101i
$$436$$ 0 0
$$437$$ 1.55841e6 + 148425.i 0.390370 + 0.0371796i
$$438$$ 0 0
$$439$$ 1.97430e6 + 3.41959e6i 0.488936 + 0.846863i 0.999919 0.0127283i $$-0.00405165\pi$$
−0.510983 + 0.859591i $$0.670718\pi$$
$$440$$ 0 0
$$441$$ 560925. 971550.i 0.137344 0.237886i
$$442$$ 0 0
$$443$$ 3.42436e6 5.93117e6i 0.829031 1.43592i −0.0697689 0.997563i $$-0.522226\pi$$
0.898799 0.438360i $$-0.144440\pi$$
$$444$$ 0 0
$$445$$ 8.61886e6 2.06324
$$446$$ 0 0
$$447$$ −1.85513e6 + 3.21318e6i −0.439142 + 0.760617i
$$448$$ 0 0
$$449$$ −3.05530e6 −0.715216 −0.357608 0.933872i $$-0.616408\pi$$
−0.357608 + 0.933872i $$0.616408\pi$$
$$450$$ 0 0
$$451$$ −1.15627e6 2.00272e6i −0.267682 0.463639i
$$452$$ 0 0
$$453$$ −467241. 809285.i −0.106978 0.185292i
$$454$$ 0 0
$$455$$ 1.27627e7 2.89011
$$456$$ 0 0
$$457$$ −5.86875e6 −1.31448 −0.657242 0.753680i $$-0.728277\pi$$
−0.657242 + 0.753680i $$0.728277\pi$$
$$458$$ 0 0
$$459$$ 3.13086e6 + 5.42280e6i 0.693636 + 1.20141i
$$460$$ 0 0
$$461$$ 970738. + 1.68137e6i 0.212740 + 0.368477i 0.952571 0.304316i $$-0.0984279\pi$$
−0.739831 + 0.672793i $$0.765095\pi$$
$$462$$ 0 0
$$463$$ 2.37394e6 0.514656 0.257328 0.966324i $$-0.417158\pi$$
0.257328 + 0.966324i $$0.417158\pi$$
$$464$$ 0 0
$$465$$ 1.80106e6 3.11952e6i 0.386274 0.669046i
$$466$$ 0 0
$$467$$ −2.72608e6 −0.578425 −0.289212 0.957265i $$-0.593393\pi$$
−0.289212 + 0.957265i $$0.593393\pi$$
$$468$$ 0 0
$$469$$ 5.76953e6 9.99312e6i 1.21118 2.09782i
$$470$$ 0 0
$$471$$ 3.75084e6 6.49664e6i 0.779069 1.34939i
$$472$$ 0 0
$$473$$ 1.65452e6 + 2.86570e6i 0.340031 + 0.588950i
$$474$$ 0 0
$$475$$ −9.23449e6 879510.i −1.87793 0.178857i
$$476$$ 0 0
$$477$$ 903649. + 1.56517e6i 0.181846 + 0.314967i
$$478$$ 0 0
$$479$$ −2.64917e6 + 4.58849e6i −0.527558 + 0.913757i 0.471926 + 0.881638i $$0.343559\pi$$
−0.999484 + 0.0321192i $$0.989774\pi$$
$$480$$ 0 0
$$481$$ −2.56154e6 + 4.43672e6i −0.504823 + 0.874378i
$$482$$ 0 0
$$483$$ −2.56692e6 −0.500662
$$484$$ 0 0
$$485$$ −2.92114e6 + 5.05957e6i −0.563895 + 0.976695i
$$486$$ 0 0
$$487$$ 5.45937e6 1.04309 0.521543 0.853225i $$-0.325356\pi$$
0.521543 + 0.853225i $$0.325356\pi$$
$$488$$ 0 0
$$489$$ 1.04233e6 + 1.80536e6i 0.197120 + 0.341422i
$$490$$ 0 0
$$491$$ −3.95495e6 6.85017e6i −0.740350 1.28232i −0.952336 0.305051i $$-0.901326\pi$$
0.211986 0.977273i $$-0.432007\pi$$
$$492$$ 0 0
$$493$$ 3.94730e6 0.731447
$$494$$ 0 0
$$495$$ 2.93509e6 0.538404
$$496$$ 0 0
$$497$$ 2.81542e6 + 4.87645e6i 0.511272 + 0.885550i
$$498$$ 0 0
$$499$$ −4.75343e6 8.23318e6i −0.854586 1.48019i −0.877029 0.480438i $$-0.840478\pi$$
0.0224433 0.999748i $$-0.492855\pi$$
$$500$$ 0 0
$$501$$ −3.98532e6 −0.709363
$$502$$ 0 0
$$503$$ −3.72038e6 + 6.44389e6i −0.655643 + 1.13561i 0.326090 + 0.945339i $$0.394269\pi$$
−0.981732 + 0.190268i $$0.939064\pi$$
$$504$$ 0 0
$$505$$ −1.11745e6 −0.194984
$$506$$ 0 0
$$507$$ −881141. + 1.52618e6i −0.152239 + 0.263685i
$$508$$ 0 0
$$509$$ 513257. 888987.i 0.0878092 0.152090i −0.818776 0.574114i $$-0.805347\pi$$
0.906585 + 0.422024i $$0.138680\pi$$
$$510$$ 0 0
$$511$$ −7.40496e6 1.28258e7i −1.25450 2.17286i
$$512$$ 0 0
$$513$$ −2.67814e6 5.86052e6i −0.449304 0.983202i
$$514$$ 0 0
$$515$$ 2.73917e6 + 4.74438e6i 0.455093 + 0.788245i
$$516$$ 0 0
$$517$$ −6.53014e6 + 1.13105e7i −1.07447 + 1.86104i
$$518$$ 0 0
$$519$$ −1.55266e6 + 2.68928e6i −0.253022 + 0.438246i
$$520$$ 0 0
$$521$$ 5.83600e6 0.941936 0.470968 0.882150i $$-0.343905\pi$$
0.470968 + 0.882150i $$0.343905\pi$$
$$522$$ 0 0
$$523$$ 1.68243e6 2.91406e6i 0.268958 0.465848i −0.699635 0.714500i $$-0.746654\pi$$
0.968593 + 0.248652i $$0.0799875\pi$$
$$524$$ 0 0
$$525$$ 1.52106e7 2.40850
$$526$$ 0 0
$$527$$ 2.13382e6 + 3.69588e6i 0.334681 + 0.579684i
$$528$$ 0 0
$$529$$ 2.72331e6 + 4.71691e6i 0.423114 + 0.732856i
$$530$$ 0 0
$$531$$ −2.11986e6 −0.326265
$$532$$ 0 0
$$533$$ −3.08827e6 −0.470866
$$534$$ 0 0
$$535$$ 3.79388e6 + 6.57119e6i 0.573058 + 0.992566i
$$536$$ 0 0
$$537$$ −1.67935e6 2.90872e6i −0.251307 0.435277i
$$538$$ 0 0
$$539$$ −1.01971e7 −1.51184
$$540$$ 0 0
$$541$$ 4.79104e6 8.29833e6i 0.703780 1.21898i −0.263350 0.964700i $$-0.584827\pi$$
0.967130 0.254282i $$-0.0818393\pi$$
$$542$$ 0 0
$$543$$ −9.61809e6 −1.39987
$$544$$ 0 0
$$545$$ −9.33818e6 + 1.61742e7i −1.34670 + 2.33255i
$$546$$ 0 0
$$547$$ −2.53036e6 + 4.38271e6i −0.361588 + 0.626289i −0.988222 0.153024i $$-0.951099\pi$$
0.626634 + 0.779314i $$0.284432\pi$$
$$548$$ 0 0
$$549$$ −168334. 291563.i −0.0238364 0.0412859i
$$550$$ 0 0
$$551$$ −4.04357e6 385117.i −0.567396 0.0540398i
$$552$$ 0 0
$$553$$ −6.34654e6 1.09925e7i −0.882520 1.52857i
$$554$$ 0 0
$$555$$ −4.67116e6 + 8.09069e6i −0.643713 + 1.11494i
$$556$$ 0 0
$$557$$ −3.89885e6 + 6.75300e6i −0.532474 + 0.922271i 0.466807 + 0.884359i $$0.345404\pi$$
−0.999281 + 0.0379124i $$0.987929\pi$$
$$558$$ 0 0
$$559$$ 4.41902e6 0.598131
$$560$$ 0 0
$$561$$ 5.50720e6 9.53874e6i 0.738794 1.27963i
$$562$$ 0 0
$$563$$ 4.30439e6 0.572323 0.286161 0.958181i $$-0.407621\pi$$
0.286161 + 0.958181i $$0.407621\pi$$
$$564$$ 0 0
$$565$$ −9.76875e6 1.69200e7i −1.28741 2.22986i
$$566$$ 0 0
$$567$$ 3.93768e6 + 6.82027e6i 0.514379 + 0.890930i
$$568$$ 0 0
$$569$$ −9.79289e6 −1.26803 −0.634016 0.773320i $$-0.718595\pi$$
−0.634016 + 0.773320i $$0.718595\pi$$
$$570$$ 0 0
$$571$$ −6.14671e6 −0.788955 −0.394477 0.918906i $$-0.629074\pi$$
−0.394477 + 0.918906i $$0.629074\pi$$
$$572$$ 0 0
$$573$$ −71362.1 123603.i −0.00907990 0.0157269i
$$574$$ 0 0
$$575$$ 2.93236e6 + 5.07899e6i 0.369869 + 0.640631i
$$576$$ 0 0
$$577$$ −704051. −0.0880369 −0.0440185 0.999031i $$-0.514016\pi$$
−0.0440185 + 0.999031i $$0.514016\pi$$
$$578$$ 0 0
$$579$$ 6.75148e6 1.16939e7i 0.836955 1.44965i
$$580$$ 0 0
$$581$$ −4.16163e6 −0.511474
$$582$$ 0 0
$$583$$ 8.21378e6 1.42267e7i 1.00086 1.73353i
$$584$$ 0 0
$$585$$ 1.95982e6 3.39451e6i 0.236770 0.410097i
$$586$$ 0 0
$$587$$ 4.80763e6 + 8.32707e6i 0.575885 + 0.997463i 0.995945 + 0.0899662i $$0.0286759\pi$$
−0.420059 + 0.907497i $$0.637991\pi$$
$$588$$ 0 0
$$589$$ −1.82527e6 3.99421e6i −0.216790 0.474398i
$$590$$ 0 0
$$591$$ 1.25913e6 + 2.18087e6i 0.148286 + 0.256839i
$$592$$ 0 0
$$593$$ 5.57887e6 9.66289e6i 0.651493 1.12842i −0.331268 0.943537i $$-0.607476\pi$$
0.982761 0.184882i $$-0.0591903\pi$$
$$594$$ 0 0
$$595$$ −1.37869e7 + 2.38796e7i −1.59652 + 2.76525i
$$596$$ 0 0
$$597$$ −1.17282e6 −0.134678
$$598$$ 0 0
$$599$$ 4.00898e6 6.94376e6i 0.456528 0.790729i −0.542247 0.840219i $$-0.682426\pi$$
0.998775 + 0.0494902i $$0.0157597\pi$$
$$600$$ 0 0
$$601$$ 1.34115e7 1.51458 0.757290 0.653079i $$-0.226523\pi$$
0.757290 + 0.653079i $$0.226523\pi$$
$$602$$ 0 0
$$603$$ −1.77192e6 3.06905e6i −0.198450 0.343725i
$$604$$ 0 0
$$605$$ −5.69151e6 9.85799e6i −0.632178 1.09496i
$$606$$ 0 0
$$607$$ 3.14504e6 0.346461 0.173231 0.984881i $$-0.444579\pi$$
0.173231 + 0.984881i $$0.444579\pi$$
$$608$$ 0 0
$$609$$ 6.66036e6 0.727704
$$610$$ 0 0
$$611$$ 8.72061e6 + 1.51045e7i 0.945027 + 1.63683i
$$612$$ 0 0
$$613$$ 1.86161e6 + 3.22440e6i 0.200095 + 0.346575i 0.948559 0.316601i $$-0.102542\pi$$
−0.748464 + 0.663176i $$0.769208\pi$$
$$614$$ 0 0
$$615$$ −5.63169e6 −0.600414
$$616$$ 0 0
$$617$$ −650699. + 1.12704e6i −0.0688125 + 0.119187i −0.898379 0.439221i $$-0.855254\pi$$
0.829566 + 0.558408i $$0.188588\pi$$
$$618$$ 0 0
$$619$$ 1.44161e7 1.51224 0.756118 0.654435i $$-0.227093\pi$$
0.756118 + 0.654435i $$0.227093\pi$$
$$620$$ 0 0
$$621$$ −2.03687e6 + 3.52795e6i −0.211950 + 0.367108i
$$622$$ 0 0
$$623$$ −8.61485e6 + 1.49214e7i −0.889257 + 1.54024i
$$624$$ 0 0
$$625$$ −3.28211e6 5.68478e6i −0.336088 0.582122i
$$626$$ 0 0
$$627$$ −6.57216e6 + 9.23408e6i −0.667635 + 0.938047i
$$628$$ 0 0
$$629$$ −5.53420e6 9.58552e6i −0.557736 0.966026i
$$630$$ 0 0
$$631$$ 1.56517e6 2.71095e6i 0.156490 0.271049i −0.777110 0.629364i $$-0.783315\pi$$
0.933601 + 0.358315i $$0.116649\pi$$
$$632$$ 0 0
$$633$$ 2.05528e6 3.55986e6i 0.203874 0.353121i
$$634$$ 0 0
$$635$$ 27280.3 0.00268482
$$636$$ 0 0
$$637$$ −6.80883e6 + 1.17932e7i −0.664851 + 1.15156i
$$638$$ 0 0
$$639$$ 1.72933e6 0.167542
$$640$$ 0 0
$$641$$ −2.12325e6 3.67757e6i −0.204106 0.353522i 0.745742 0.666235i $$-0.232095\pi$$
−0.949848 + 0.312713i $$0.898762\pi$$
$$642$$ 0 0
$$643$$ 5.08032e6 + 8.79938e6i 0.484578 + 0.839314i 0.999843 0.0177168i $$-0.00563972\pi$$
−0.515265 + 0.857031i $$0.672306\pi$$
$$644$$ 0 0
$$645$$ 8.05840e6 0.762693
$$646$$ 0 0
$$647$$ 3.33300e6 0.313022 0.156511 0.987676i $$-0.449975\pi$$
0.156511 + 0.987676i $$0.449975\pi$$
$$648$$ 0 0
$$649$$ 9.63429e6 + 1.66871e7i 0.897859 + 1.55514i
$$650$$ 0 0
$$651$$ 3.60044e6 + 6.23614e6i 0.332968 + 0.576718i
$$652$$ 0 0
$$653$$ −3.56244e6 −0.326938 −0.163469 0.986549i $$-0.552268\pi$$
−0.163469 + 0.986549i $$0.552268\pi$$
$$654$$ 0 0
$$655$$ −2.00269e6 + 3.46875e6i −0.182394 + 0.315915i
$$656$$ 0 0
$$657$$ −4.54837e6 −0.411096
$$658$$ 0 0
$$659$$ 9.65732e6 1.67270e7i 0.866249 1.50039i 0.000448081 1.00000i $$-0.499857\pi$$
0.865801 0.500388i $$-0.166809\pi$$
$$660$$ 0 0
$$661$$ 5.55793e6 9.62662e6i 0.494777 0.856979i −0.505205 0.863000i $$-0.668583\pi$$
0.999982 + 0.00602036i $$0.00191635\pi$$
$$662$$ 0 0
$$663$$ −7.35454e6 1.27384e7i −0.649788 1.12547i
$$664$$ 0 0
$$665$$ 1.64529e7 2.31169e7i 1.44274 2.02710i
$$666$$ 0 0
$$667$$ 1.28401e6 + 2.22398e6i 0.111752 + 0.193560i
$$668$$ 0 0
$$669$$ −4.61365e6 + 7.99108e6i −0.398547 + 0.690303i
$$670$$ 0 0
$$671$$ −1.53008e6 + 2.65018e6i −0.131193 + 0.227232i
$$672$$ 0 0
$$673$$ 4.82842e6 0.410929 0.205465 0.978665i $$-0.434129\pi$$
0.205465 + 0.978665i $$0.434129\pi$$
$$674$$ 0 0
$$675$$ 1.20697e7 2.09052e7i 1.01961 1.76602i
$$676$$ 0 0
$$677$$ −3.20527e6 −0.268777 −0.134389 0.990929i $$-0.542907\pi$$
−0.134389 + 0.990929i $$0.542907\pi$$
$$678$$ 0 0
$$679$$ −5.83956e6 1.01144e7i −0.486078 0.841912i
$$680$$ 0 0
$$681$$ −1.57360e6 2.72556e6i −0.130025 0.225210i
$$682$$ 0 0
$$683$$ 2.29678e7 1.88395 0.941973 0.335688i $$-0.108969\pi$$
0.941973 + 0.335688i $$0.108969\pi$$
$$684$$ 0 0
$$685$$ 9.93780e6 0.809215
$$686$$ 0 0
$$687$$ −226804. 392837.i −0.0183341 0.0317556i
$$688$$ 0 0
$$689$$ −1.09690e7 1.89989e7i −0.880278 1.52469i
$$690$$ 0 0
$$691$$ 7.10876e6 0.566368 0.283184 0.959066i $$-0.408609\pi$$
0.283184 + 0.959066i $$0.408609\pi$$
$$692$$ 0 0
$$693$$ −2.93372e6 + 5.08135e6i −0.232052 + 0.401926i
$$694$$ 0 0
$$695$$ −1.22336e7 −0.960707
$$696$$ 0 0
$$697$$ 3.33610e6 5.77829e6i 0.260110 0.450523i
$$698$$ 0 0
$$699$$ 7.36841e6 1.27625e7i 0.570402 0.987965i
$$700$$ 0 0
$$701$$ 7.73351e6 + 1.33948e7i 0.594403 + 1.02954i 0.993631 + 0.112685i $$0.0359451\pi$$
−0.399227 + 0.916852i $$0.630722\pi$$
$$702$$ 0 0
$$703$$ 4.73397e6 + 1.03592e7i 0.361274 + 0.790569i
$$704$$ 0 0
$$705$$ 1.59027e7 + 2.75443e7i 1.20503 + 2.08717i
$$706$$ 0 0
$$707$$ 1.11693e6 1.93458e6i 0.0840381 0.145558i
$$708$$ 0 0
$$709$$ 6.30537e6 1.09212e7i 0.471081 0.815936i −0.528372 0.849013i $$-0.677197\pi$$
0.999453 + 0.0330772i $$0.0105307\pi$$
$$710$$ 0 0
$$711$$ −3.89826e6 −0.289199
$$712$$ 0 0
$$713$$ −1.38822e6 + 2.40446e6i −0.102266 + 0.177131i
$$714$$ 0 0
$$715$$ −3.56278e7 −2.60630
$$716$$ 0 0
$$717$$ 1.93007e6 + 3.34298e6i 0.140209 + 0.242849i
$$718$$ 0 0
$$719$$ −1.02749e7 1.77967e7i −0.741234 1.28386i −0.951934 0.306304i $$-0.900907\pi$$
0.210699 0.977551i $$-0.432426\pi$$
$$720$$ 0 0
$$721$$ −1.09516e7 −0.784581
$$722$$ 0 0
$$723$$ −8.33899e6 −0.593291
$$724$$ 0 0
$$725$$ −7.60855e6 1.31784e7i −0.537597 0.931146i
$$726$$ 0 0
$$727$$ −8.28557e6 1.43510e7i −0.581415 1.00704i −0.995312 0.0967169i $$-0.969166\pi$$
0.413897 0.910324i $$-0.364167\pi$$
$$728$$ 0 0
$$729$$ 1.59414e7 1.11098
$$730$$ 0 0
$$731$$ −4.77363e6 + 8.26818e6i −0.330412 + 0.572290i
$$732$$ 0 0
$$733$$ 2.52568e7 1.73628 0.868139 0.496321i $$-0.165316\pi$$
0.868139 + 0.496321i $$0.165316\pi$$
$$734$$ 0 0
$$735$$ −1.24164e7 + 2.15059e7i −0.847770 + 1.46838i
$$736$$ 0 0
$$737$$ −1.61060e7 + 2.78964e7i −1.09224 + 1.89182i
$$738$$ 0 0
$$739$$ 6.54248e6 + 1.13319e7i 0.440688 + 0.763294i 0.997741 0.0671833i $$-0.0214012\pi$$
−0.557053 + 0.830477i $$0.688068\pi$$
$$740$$ 0 0
$$741$$ 6.29109e6 + 1.37667e7i 0.420901 + 0.921049i
$$742$$ 0 0
$$743$$ 1.18603e6 + 2.05426e6i 0.0788177 + 0.136516i 0.902740 0.430186i $$-0.141552\pi$$
−0.823922 + 0.566703i $$0.808219\pi$$
$$744$$ 0 0
$$745$$ −1.29645e7 + 2.24552e7i −0.855787 + 1.48227i
$$746$$ 0 0
$$747$$ −639054. + 1.10687e6i −0.0419021 + 0.0725766i
$$748$$ 0 0
$$749$$ −1.51684e7 −0.987953
$$750$$ 0 0
$$751$$ −1.34919e7 + 2.33686e7i −0.872916 + 1.51193i −0.0139493 + 0.999903i $$0.504440\pi$$
−0.858966 + 0.512032i $$0.828893\pi$$
$$752$$ 0 0
$$753$$ −1.00319e7 −0.644758
$$754$$ 0 0
$$755$$ −3.26530e6 5.65567e6i −0.208476 0.361091i
$$756$$ 0 0
$$757$$ 1.46311e7 + 2.53419e7i 0.927980 + 1.60731i 0.786697 + 0.617340i $$0.211790\pi$$
0.141284 + 0.989969i $$0.454877\pi$$
$$758$$ 0 0
$$759$$ 7.16572e6 0.451497
$$760$$ 0 0
$$761$$ −2.62075e7 −1.64045 −0.820226 0.572040i $$-0.806152\pi$$
−0.820226 + 0.572040i $$0.806152\pi$$
$$762$$ 0 0
$$763$$ −1.86677e7 3.23333e7i −1.16086 2.01066i
$$764$$ 0 0
$$765$$ 4.23418e6 + 7.33382e6i 0.261587 + 0.453082i
$$766$$ 0 0
$$767$$ 2.57321e7 1.57938
$$768$$ 0 0
$$769$$ 2.54995e6 4.41664e6i 0.155495 0.269325i −0.777744 0.628581i $$-0.783636\pi$$
0.933239 + 0.359256i $$0.116969\pi$$
$$770$$ 0 0
$$771$$ −1.86554e7 −1.13023
$$772$$ 0 0
$$773$$ −8.67472e6 + 1.50250e7i −0.522164 + 0.904414i 0.477504 + 0.878630i $$0.341542\pi$$
−0.999668 + 0.0257842i $$0.991792\pi$$
$$774$$ 0 0
$$775$$ 8.22601e6 1.42479e7i 0.491966 0.852110i
$$776$$ 0 0
$$777$$ −9.33797e6 1.61738e7i −0.554881 0.961082i
$$778$$ 0 0
$$779$$ −3.98122e6 + 5.59373e6i −0.235057 + 0.330262i
$$780$$ 0 0
$$781$$ −7.85942e6 1.36129e7i −0.461066 0.798589i
$$782$$ 0 0
$$783$$ 5.28503e6 9.15394e6i 0.308065 0.533585i
$$784$$ 0 0
$$785$$ 2.62126e7 4.54016e7i 1.51823 2.62965i
$$786$$ 0 0
$$787$$ 3.89085e6 0.223928 0.111964 0.993712i $$-0.464286\pi$$
0.111964 + 0.993712i $$0.464286\pi$$
$$788$$ 0 0
$$789$$ −1.98862e6 + 3.44439e6i −0.113726