# Properties

 Label 80.6.c.c.49.1 Level $80$ Weight $6$ Character 80.49 Analytic conductor $12.831$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 80.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.8307055850$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 10) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 49.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 80.49 Dual form 80.6.c.c.49.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-14.0000i q^{3} +(55.0000 + 10.0000i) q^{5} +158.000i q^{7} +47.0000 q^{9} +O(q^{10})$$ $$q-14.0000i q^{3} +(55.0000 + 10.0000i) q^{5} +158.000i q^{7} +47.0000 q^{9} +148.000 q^{11} +684.000i q^{13} +(140.000 - 770.000i) q^{15} -2048.00i q^{17} +2220.00 q^{19} +2212.00 q^{21} +1246.00i q^{23} +(2925.00 + 1100.00i) q^{25} -4060.00i q^{27} +270.000 q^{29} +2048.00 q^{31} -2072.00i q^{33} +(-1580.00 + 8690.00i) q^{35} +4372.00i q^{37} +9576.00 q^{39} -2398.00 q^{41} -2294.00i q^{43} +(2585.00 + 470.000i) q^{45} -10682.0i q^{47} -8157.00 q^{49} -28672.0 q^{51} +2964.00i q^{53} +(8140.00 + 1480.00i) q^{55} -31080.0i q^{57} -39740.0 q^{59} -42298.0 q^{61} +7426.00i q^{63} +(-6840.00 + 37620.0i) q^{65} +32098.0i q^{67} +17444.0 q^{69} +4248.00 q^{71} +30104.0i q^{73} +(15400.0 - 40950.0i) q^{75} +23384.0i q^{77} +35280.0 q^{79} -45419.0 q^{81} +27826.0i q^{83} +(20480.0 - 112640. i) q^{85} -3780.00i q^{87} +85210.0 q^{89} -108072. q^{91} -28672.0i q^{93} +(122100. + 22200.0i) q^{95} +97232.0i q^{97} +6956.00 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 110q^{5} + 94q^{9} + O(q^{10})$$ $$2q + 110q^{5} + 94q^{9} + 296q^{11} + 280q^{15} + 4440q^{19} + 4424q^{21} + 5850q^{25} + 540q^{29} + 4096q^{31} - 3160q^{35} + 19152q^{39} - 4796q^{41} + 5170q^{45} - 16314q^{49} - 57344q^{51} + 16280q^{55} - 79480q^{59} - 84596q^{61} - 13680q^{65} + 34888q^{69} + 8496q^{71} + 30800q^{75} + 70560q^{79} - 90838q^{81} + 40960q^{85} + 170420q^{89} - 216144q^{91} + 244200q^{95} + 13912q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$$.

 $$n$$ $$17$$ $$21$$ $$31$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$3$$ 14.0000i 0.898100i −0.893507 0.449050i $$-0.851762\pi$$
0.893507 0.449050i $$-0.148238\pi$$
$$4$$ 0 0
$$5$$ 55.0000 + 10.0000i 0.983870 + 0.178885i
$$6$$ 0 0
$$7$$ 158.000i 1.21874i 0.792885 + 0.609371i $$0.208578\pi$$
−0.792885 + 0.609371i $$0.791422\pi$$
$$8$$ 0 0
$$9$$ 47.0000 0.193416
$$10$$ 0 0
$$11$$ 148.000 0.368791 0.184395 0.982852i $$-0.440967\pi$$
0.184395 + 0.982852i $$0.440967\pi$$
$$12$$ 0 0
$$13$$ 684.000i 1.12253i 0.827636 + 0.561265i $$0.189685\pi$$
−0.827636 + 0.561265i $$0.810315\pi$$
$$14$$ 0 0
$$15$$ 140.000 770.000i 0.160657 0.883614i
$$16$$ 0 0
$$17$$ 2048.00i 1.71873i −0.511363 0.859365i $$-0.670859\pi$$
0.511363 0.859365i $$-0.329141\pi$$
$$18$$ 0 0
$$19$$ 2220.00 1.41081 0.705406 0.708804i $$-0.250765\pi$$
0.705406 + 0.708804i $$0.250765\pi$$
$$20$$ 0 0
$$21$$ 2212.00 1.09455
$$22$$ 0 0
$$23$$ 1246.00i 0.491132i 0.969380 + 0.245566i $$0.0789738\pi$$
−0.969380 + 0.245566i $$0.921026\pi$$
$$24$$ 0 0
$$25$$ 2925.00 + 1100.00i 0.936000 + 0.352000i
$$26$$ 0 0
$$27$$ 4060.00i 1.07181i
$$28$$ 0 0
$$29$$ 270.000 0.0596168 0.0298084 0.999556i $$-0.490510\pi$$
0.0298084 + 0.999556i $$0.490510\pi$$
$$30$$ 0 0
$$31$$ 2048.00 0.382759 0.191380 0.981516i $$-0.438704\pi$$
0.191380 + 0.981516i $$0.438704\pi$$
$$32$$ 0 0
$$33$$ 2072.00i 0.331211i
$$34$$ 0 0
$$35$$ −1580.00 + 8690.00i −0.218015 + 1.19908i
$$36$$ 0 0
$$37$$ 4372.00i 0.525020i 0.964929 + 0.262510i $$0.0845503\pi$$
−0.964929 + 0.262510i $$0.915450\pi$$
$$38$$ 0 0
$$39$$ 9576.00 1.00814
$$40$$ 0 0
$$41$$ −2398.00 −0.222787 −0.111393 0.993776i $$-0.535531\pi$$
−0.111393 + 0.993776i $$0.535531\pi$$
$$42$$ 0 0
$$43$$ 2294.00i 0.189200i −0.995515 0.0946002i $$-0.969843\pi$$
0.995515 0.0946002i $$-0.0301573\pi$$
$$44$$ 0 0
$$45$$ 2585.00 + 470.000i 0.190296 + 0.0345992i
$$46$$ 0 0
$$47$$ 10682.0i 0.705355i −0.935745 0.352678i $$-0.885271\pi$$
0.935745 0.352678i $$-0.114729\pi$$
$$48$$ 0 0
$$49$$ −8157.00 −0.485333
$$50$$ 0 0
$$51$$ −28672.0 −1.54359
$$52$$ 0 0
$$53$$ 2964.00i 0.144940i 0.997371 + 0.0724700i $$0.0230882\pi$$
−0.997371 + 0.0724700i $$0.976912\pi$$
$$54$$ 0 0
$$55$$ 8140.00 + 1480.00i 0.362842 + 0.0659713i
$$56$$ 0 0
$$57$$ 31080.0i 1.26705i
$$58$$ 0 0
$$59$$ −39740.0 −1.48627 −0.743135 0.669141i $$-0.766662\pi$$
−0.743135 + 0.669141i $$0.766662\pi$$
$$60$$ 0 0
$$61$$ −42298.0 −1.45544 −0.727722 0.685873i $$-0.759421\pi$$
−0.727722 + 0.685873i $$0.759421\pi$$
$$62$$ 0 0
$$63$$ 7426.00i 0.235724i
$$64$$ 0 0
$$65$$ −6840.00 + 37620.0i −0.200804 + 1.10442i
$$66$$ 0 0
$$67$$ 32098.0i 0.873556i 0.899569 + 0.436778i $$0.143881\pi$$
−0.899569 + 0.436778i $$0.856119\pi$$
$$68$$ 0 0
$$69$$ 17444.0 0.441086
$$70$$ 0 0
$$71$$ 4248.00 0.100009 0.0500044 0.998749i $$-0.484076\pi$$
0.0500044 + 0.998749i $$0.484076\pi$$
$$72$$ 0 0
$$73$$ 30104.0i 0.661176i 0.943775 + 0.330588i $$0.107247\pi$$
−0.943775 + 0.330588i $$0.892753\pi$$
$$74$$ 0 0
$$75$$ 15400.0 40950.0i 0.316131 0.840622i
$$76$$ 0 0
$$77$$ 23384.0i 0.449461i
$$78$$ 0 0
$$79$$ 35280.0 0.636005 0.318003 0.948090i $$-0.396988\pi$$
0.318003 + 0.948090i $$0.396988\pi$$
$$80$$ 0 0
$$81$$ −45419.0 −0.769175
$$82$$ 0 0
$$83$$ 27826.0i 0.443359i 0.975120 + 0.221680i $$0.0711539\pi$$
−0.975120 + 0.221680i $$0.928846\pi$$
$$84$$ 0 0
$$85$$ 20480.0 112640.i 0.307456 1.69101i
$$86$$ 0 0
$$87$$ 3780.00i 0.0535419i
$$88$$ 0 0
$$89$$ 85210.0 1.14029 0.570145 0.821544i $$-0.306887\pi$$
0.570145 + 0.821544i $$0.306887\pi$$
$$90$$ 0 0
$$91$$ −108072. −1.36807
$$92$$ 0 0
$$93$$ 28672.0i 0.343756i
$$94$$ 0 0
$$95$$ 122100. + 22200.0i 1.38805 + 0.252374i
$$96$$ 0 0
$$97$$ 97232.0i 1.04925i 0.851333 + 0.524626i $$0.175795\pi$$
−0.851333 + 0.524626i $$0.824205\pi$$
$$98$$ 0 0
$$99$$ 6956.00 0.0713299
$$100$$ 0 0
$$101$$ −4298.00 −0.0419240 −0.0209620 0.999780i $$-0.506673\pi$$
−0.0209620 + 0.999780i $$0.506673\pi$$
$$102$$ 0 0
$$103$$ 124114.i 1.15273i −0.817192 0.576365i $$-0.804471\pi$$
0.817192 0.576365i $$-0.195529\pi$$
$$104$$ 0 0
$$105$$ 121660. + 22120.0i 1.07690 + 0.195800i
$$106$$ 0 0
$$107$$ 42342.0i 0.357530i −0.983892 0.178765i $$-0.942790\pi$$
0.983892 0.178765i $$-0.0572101\pi$$
$$108$$ 0 0
$$109$$ 35990.0 0.290145 0.145073 0.989421i $$-0.453658\pi$$
0.145073 + 0.989421i $$0.453658\pi$$
$$110$$ 0 0
$$111$$ 61208.0 0.471521
$$112$$ 0 0
$$113$$ 228816.i 1.68574i −0.538118 0.842869i $$-0.680865\pi$$
0.538118 0.842869i $$-0.319135\pi$$
$$114$$ 0 0
$$115$$ −12460.0 + 68530.0i −0.0878564 + 0.483210i
$$116$$ 0 0
$$117$$ 32148.0i 0.217115i
$$118$$ 0 0
$$119$$ 323584. 2.09469
$$120$$ 0 0
$$121$$ −139147. −0.863993
$$122$$ 0 0
$$123$$ 33572.0i 0.200085i
$$124$$ 0 0
$$125$$ 149875. + 89750.0i 0.857935 + 0.513759i
$$126$$ 0 0
$$127$$ 175238.i 0.964093i 0.876146 + 0.482047i $$0.160106\pi$$
−0.876146 + 0.482047i $$0.839894\pi$$
$$128$$ 0 0
$$129$$ −32116.0 −0.169921
$$130$$ 0 0
$$131$$ −299652. −1.52559 −0.762797 0.646638i $$-0.776174\pi$$
−0.762797 + 0.646638i $$0.776174\pi$$
$$132$$ 0 0
$$133$$ 350760.i 1.71942i
$$134$$ 0 0
$$135$$ 40600.0 223300.i 0.191731 1.05452i
$$136$$ 0 0
$$137$$ 107928.i 0.491284i −0.969361 0.245642i $$-0.921001\pi$$
0.969361 0.245642i $$-0.0789988\pi$$
$$138$$ 0 0
$$139$$ −196460. −0.862456 −0.431228 0.902243i $$-0.641920\pi$$
−0.431228 + 0.902243i $$0.641920\pi$$
$$140$$ 0 0
$$141$$ −149548. −0.633480
$$142$$ 0 0
$$143$$ 101232.i 0.413978i
$$144$$ 0 0
$$145$$ 14850.0 + 2700.00i 0.0586552 + 0.0106646i
$$146$$ 0 0
$$147$$ 114198.i 0.435878i
$$148$$ 0 0
$$149$$ −138850. −0.512366 −0.256183 0.966628i $$-0.582465\pi$$
−0.256183 + 0.966628i $$0.582465\pi$$
$$150$$ 0 0
$$151$$ −416152. −1.48528 −0.742642 0.669688i $$-0.766428\pi$$
−0.742642 + 0.669688i $$0.766428\pi$$
$$152$$ 0 0
$$153$$ 96256.0i 0.332429i
$$154$$ 0 0
$$155$$ 112640. + 20480.0i 0.376585 + 0.0684701i
$$156$$ 0 0
$$157$$ 433108.i 1.40232i −0.713004 0.701160i $$-0.752666\pi$$
0.713004 0.701160i $$-0.247334\pi$$
$$158$$ 0 0
$$159$$ 41496.0 0.130171
$$160$$ 0 0
$$161$$ −196868. −0.598564
$$162$$ 0 0
$$163$$ 149134.i 0.439651i −0.975539 0.219825i $$-0.929451\pi$$
0.975539 0.219825i $$-0.0705487\pi$$
$$164$$ 0 0
$$165$$ 20720.0 113960.i 0.0592488 0.325869i
$$166$$ 0 0
$$167$$ 559602.i 1.55270i −0.630301 0.776351i $$-0.717068\pi$$
0.630301 0.776351i $$-0.282932\pi$$
$$168$$ 0 0
$$169$$ −96563.0 −0.260072
$$170$$ 0 0
$$171$$ 104340. 0.272873
$$172$$ 0 0
$$173$$ 343804.i 0.873365i 0.899616 + 0.436682i $$0.143847\pi$$
−0.899616 + 0.436682i $$0.856153\pi$$
$$174$$ 0 0
$$175$$ −173800. + 462150.i −0.428997 + 1.14074i
$$176$$ 0 0
$$177$$ 556360.i 1.33482i
$$178$$ 0 0
$$179$$ 23980.0 0.0559392 0.0279696 0.999609i $$-0.491096\pi$$
0.0279696 + 0.999609i $$0.491096\pi$$
$$180$$ 0 0
$$181$$ −651898. −1.47905 −0.739526 0.673128i $$-0.764950\pi$$
−0.739526 + 0.673128i $$0.764950\pi$$
$$182$$ 0 0
$$183$$ 592172.i 1.30713i
$$184$$ 0 0
$$185$$ −43720.0 + 240460.i −0.0939184 + 0.516551i
$$186$$ 0 0
$$187$$ 303104.i 0.633852i
$$188$$ 0 0
$$189$$ 641480. 1.30626
$$190$$ 0 0
$$191$$ −202752. −0.402144 −0.201072 0.979576i $$-0.564443\pi$$
−0.201072 + 0.979576i $$0.564443\pi$$
$$192$$ 0 0
$$193$$ 452656.i 0.874732i −0.899284 0.437366i $$-0.855911\pi$$
0.899284 0.437366i $$-0.144089\pi$$
$$194$$ 0 0
$$195$$ 526680. + 95760.0i 0.991883 + 0.180342i
$$196$$ 0 0
$$197$$ 337468.i 0.619537i −0.950812 0.309768i $$-0.899748\pi$$
0.950812 0.309768i $$-0.100252\pi$$
$$198$$ 0 0
$$199$$ −561000. −1.00422 −0.502112 0.864803i $$-0.667443\pi$$
−0.502112 + 0.864803i $$0.667443\pi$$
$$200$$ 0 0
$$201$$ 449372. 0.784541
$$202$$ 0 0
$$203$$ 42660.0i 0.0726576i
$$204$$ 0 0
$$205$$ −131890. 23980.0i −0.219193 0.0398533i
$$206$$ 0 0
$$207$$ 58562.0i 0.0949927i
$$208$$ 0 0
$$209$$ 328560. 0.520294
$$210$$ 0 0
$$211$$ 805548. 1.24562 0.622810 0.782373i $$-0.285991\pi$$
0.622810 + 0.782373i $$0.285991\pi$$
$$212$$ 0 0
$$213$$ 59472.0i 0.0898180i
$$214$$ 0 0
$$215$$ 22940.0 126170.i 0.0338452 0.186149i
$$216$$ 0 0
$$217$$ 323584.i 0.466485i
$$218$$ 0 0
$$219$$ 421456. 0.593802
$$220$$ 0 0
$$221$$ 1.40083e6 1.92932
$$222$$ 0 0
$$223$$ 1.21855e6i 1.64090i −0.571717 0.820451i $$-0.693722\pi$$
0.571717 0.820451i $$-0.306278\pi$$
$$224$$ 0 0
$$225$$ 137475. + 51700.0i 0.181037 + 0.0680823i
$$226$$ 0 0
$$227$$ 564338.i 0.726900i 0.931614 + 0.363450i $$0.118401\pi$$
−0.931614 + 0.363450i $$0.881599\pi$$
$$228$$ 0 0
$$229$$ −560330. −0.706082 −0.353041 0.935608i $$-0.614852\pi$$
−0.353041 + 0.935608i $$0.614852\pi$$
$$230$$ 0 0
$$231$$ 327376. 0.403661
$$232$$ 0 0
$$233$$ 293576.i 0.354267i −0.984187 0.177134i $$-0.943318\pi$$
0.984187 0.177134i $$-0.0566824\pi$$
$$234$$ 0 0
$$235$$ 106820. 587510.i 0.126178 0.693978i
$$236$$ 0 0
$$237$$ 493920.i 0.571197i
$$238$$ 0 0
$$239$$ 584240. 0.661602 0.330801 0.943701i $$-0.392681\pi$$
0.330801 + 0.943701i $$0.392681\pi$$
$$240$$ 0 0
$$241$$ −563798. −0.625289 −0.312645 0.949870i $$-0.601215\pi$$
−0.312645 + 0.949870i $$0.601215\pi$$
$$242$$ 0 0
$$243$$ 350714.i 0.381011i
$$244$$ 0 0
$$245$$ −448635. 81570.0i −0.477505 0.0868191i
$$246$$ 0 0
$$247$$ 1.51848e6i 1.58368i
$$248$$ 0 0
$$249$$ 389564. 0.398181
$$250$$ 0 0
$$251$$ 1.01975e6 1.02167 0.510833 0.859680i $$-0.329337\pi$$
0.510833 + 0.859680i $$0.329337\pi$$
$$252$$ 0 0
$$253$$ 184408.i 0.181125i
$$254$$ 0 0
$$255$$ −1.57696e6 286720.i −1.51869 0.276126i
$$256$$ 0 0
$$257$$ 657408.i 0.620872i −0.950594 0.310436i $$-0.899525\pi$$
0.950594 0.310436i $$-0.100475\pi$$
$$258$$ 0 0
$$259$$ −690776. −0.639864
$$260$$ 0 0
$$261$$ 12690.0 0.0115308
$$262$$ 0 0
$$263$$ 562366.i 0.501337i 0.968073 + 0.250668i $$0.0806504\pi$$
−0.968073 + 0.250668i $$0.919350\pi$$
$$264$$ 0 0
$$265$$ −29640.0 + 163020.i −0.0259277 + 0.142602i
$$266$$ 0 0
$$267$$ 1.19294e6i 1.02410i
$$268$$ 0 0
$$269$$ −366570. −0.308870 −0.154435 0.988003i $$-0.549356\pi$$
−0.154435 + 0.988003i $$0.549356\pi$$
$$270$$ 0 0
$$271$$ −1.16075e6 −0.960099 −0.480050 0.877241i $$-0.659381\pi$$
−0.480050 + 0.877241i $$0.659381\pi$$
$$272$$ 0 0
$$273$$ 1.51301e6i 1.22867i
$$274$$ 0 0
$$275$$ 432900. + 162800.i 0.345188 + 0.129814i
$$276$$ 0 0
$$277$$ 2.51501e6i 1.96943i 0.174172 + 0.984715i $$0.444275\pi$$
−0.174172 + 0.984715i $$0.555725\pi$$
$$278$$ 0 0
$$279$$ 96256.0 0.0740316
$$280$$ 0 0
$$281$$ 2.08600e6 1.57597 0.787987 0.615692i $$-0.211124\pi$$
0.787987 + 0.615692i $$0.211124\pi$$
$$282$$ 0 0
$$283$$ 2.23803e6i 1.66111i 0.556935 + 0.830556i $$0.311977\pi$$
−0.556935 + 0.830556i $$0.688023\pi$$
$$284$$ 0 0
$$285$$ 310800. 1.70940e6i 0.226657 1.24661i
$$286$$ 0 0
$$287$$ 378884.i 0.271520i
$$288$$ 0 0
$$289$$ −2.77445e6 −1.95403
$$290$$ 0 0
$$291$$ 1.36125e6 0.942334
$$292$$ 0 0
$$293$$ 975756.i 0.664006i −0.943278 0.332003i $$-0.892276\pi$$
0.943278 0.332003i $$-0.107724\pi$$
$$294$$ 0 0
$$295$$ −2.18570e6 397400.i −1.46230 0.265872i
$$296$$ 0 0
$$297$$ 600880.i 0.395273i
$$298$$ 0 0
$$299$$ −852264. −0.551310
$$300$$ 0 0
$$301$$ 362452. 0.230587
$$302$$ 0 0
$$303$$ 60172.0i 0.0376520i
$$304$$ 0 0
$$305$$ −2.32639e6 422980.i −1.43197 0.260358i
$$306$$ 0 0
$$307$$ 87858.0i 0.0532029i 0.999646 + 0.0266015i $$0.00846850\pi$$
−0.999646 + 0.0266015i $$0.991531\pi$$
$$308$$ 0 0
$$309$$ −1.73760e6 −1.03527
$$310$$ 0 0
$$311$$ −599352. −0.351383 −0.175692 0.984445i $$-0.556216\pi$$
−0.175692 + 0.984445i $$0.556216\pi$$
$$312$$ 0 0
$$313$$ 2.09342e6i 1.20780i −0.797060 0.603900i $$-0.793613\pi$$
0.797060 0.603900i $$-0.206387\pi$$
$$314$$ 0 0
$$315$$ −74260.0 + 408430.i −0.0421676 + 0.231922i
$$316$$ 0 0
$$317$$ 2.41625e6i 1.35050i 0.737590 + 0.675249i $$0.235964\pi$$
−0.737590 + 0.675249i $$0.764036\pi$$
$$318$$ 0 0
$$319$$ 39960.0 0.0219861
$$320$$ 0 0
$$321$$ −592788. −0.321097
$$322$$ 0 0
$$323$$ 4.54656e6i 2.42480i
$$324$$ 0 0
$$325$$ −752400. + 2.00070e6i −0.395130 + 1.05069i
$$326$$ 0 0
$$327$$ 503860.i 0.260580i
$$328$$ 0 0
$$329$$ 1.68776e6 0.859647
$$330$$ 0 0
$$331$$ 1.64095e6 0.823237 0.411618 0.911356i $$-0.364964\pi$$
0.411618 + 0.911356i $$0.364964\pi$$
$$332$$ 0 0
$$333$$ 205484.i 0.101547i
$$334$$ 0 0
$$335$$ −320980. + 1.76539e6i −0.156267 + 0.859466i
$$336$$ 0 0
$$337$$ 2.18773e6i 1.04935i −0.851304 0.524673i $$-0.824188\pi$$
0.851304 0.524673i $$-0.175812\pi$$
$$338$$ 0 0
$$339$$ −3.20342e6 −1.51396
$$340$$ 0 0
$$341$$ 303104. 0.141158
$$342$$ 0 0
$$343$$ 1.36670e6i 0.627246i
$$344$$ 0 0
$$345$$ 959420. + 174440.i 0.433971 + 0.0789039i
$$346$$ 0 0
$$347$$ 2.74502e6i 1.22383i 0.790923 + 0.611916i $$0.209601\pi$$
−0.790923 + 0.611916i $$0.790399\pi$$
$$348$$ 0 0
$$349$$ 2.65115e6 1.16512 0.582560 0.812788i $$-0.302051\pi$$
0.582560 + 0.812788i $$0.302051\pi$$
$$350$$ 0 0
$$351$$ 2.77704e6 1.20313
$$352$$ 0 0
$$353$$ 3.05766e6i 1.30603i 0.757345 + 0.653015i $$0.226496\pi$$
−0.757345 + 0.653015i $$0.773504\pi$$
$$354$$ 0 0
$$355$$ 233640. + 42480.0i 0.0983957 + 0.0178901i
$$356$$ 0 0
$$357$$ 4.53018e6i 1.88124i
$$358$$ 0 0
$$359$$ 3.79356e6 1.55350 0.776749 0.629810i $$-0.216867\pi$$
0.776749 + 0.629810i $$0.216867\pi$$
$$360$$ 0 0
$$361$$ 2.45230e6 0.990389
$$362$$ 0 0
$$363$$ 1.94806e6i 0.775953i
$$364$$ 0 0
$$365$$ −301040. + 1.65572e6i −0.118275 + 0.650511i
$$366$$ 0 0
$$367$$ 3.11060e6i 1.20553i −0.797917 0.602767i $$-0.794065\pi$$
0.797917 0.602767i $$-0.205935\pi$$
$$368$$ 0 0
$$369$$ −112706. −0.0430905
$$370$$ 0 0
$$371$$ −468312. −0.176645
$$372$$ 0 0
$$373$$ 1.41520e6i 0.526677i −0.964703 0.263339i $$-0.915176\pi$$
0.964703 0.263339i $$-0.0848236\pi$$
$$374$$ 0 0
$$375$$ 1.25650e6 2.09825e6i 0.461407 0.770511i
$$376$$ 0 0
$$377$$ 184680.i 0.0669216i
$$378$$ 0 0
$$379$$ −3.90262e6 −1.39559 −0.697796 0.716297i $$-0.745836\pi$$
−0.697796 + 0.716297i $$0.745836\pi$$
$$380$$ 0 0
$$381$$ 2.45333e6 0.865852
$$382$$ 0 0
$$383$$ 695674.i 0.242331i −0.992632 0.121165i $$-0.961337\pi$$
0.992632 0.121165i $$-0.0386632\pi$$
$$384$$ 0 0
$$385$$ −233840. + 1.28612e6i −0.0804020 + 0.442211i
$$386$$ 0 0
$$387$$ 107818.i 0.0365943i
$$388$$ 0 0
$$389$$ −498290. −0.166958 −0.0834792 0.996510i $$-0.526603\pi$$
−0.0834792 + 0.996510i $$0.526603\pi$$
$$390$$ 0 0
$$391$$ 2.55181e6 0.844124
$$392$$ 0 0
$$393$$ 4.19513e6i 1.37014i
$$394$$ 0 0
$$395$$ 1.94040e6 + 352800.i 0.625747 + 0.113772i
$$396$$ 0 0
$$397$$ 1.09567e6i 0.348901i −0.984666 0.174451i $$-0.944185\pi$$
0.984666 0.174451i $$-0.0558150\pi$$
$$398$$ 0 0
$$399$$ 4.91064e6 1.54421
$$400$$ 0 0
$$401$$ −2.49160e6 −0.773779 −0.386890 0.922126i $$-0.626451\pi$$
−0.386890 + 0.922126i $$0.626451\pi$$
$$402$$ 0 0
$$403$$ 1.40083e6i 0.429659i
$$404$$ 0 0
$$405$$ −2.49804e6 454190.i −0.756768 0.137594i
$$406$$ 0 0
$$407$$ 647056.i 0.193623i
$$408$$ 0 0
$$409$$ 3.63349e6 1.07403 0.537014 0.843573i $$-0.319552\pi$$
0.537014 + 0.843573i $$0.319552\pi$$
$$410$$ 0 0
$$411$$ −1.51099e6 −0.441222
$$412$$ 0 0
$$413$$ 6.27892e6i 1.81138i
$$414$$ 0 0
$$415$$ −278260. + 1.53043e6i −0.0793105 + 0.436208i
$$416$$ 0 0
$$417$$ 2.75044e6i 0.774572i
$$418$$ 0 0
$$419$$ −3.64378e6 −1.01395 −0.506976 0.861960i $$-0.669237\pi$$
−0.506976 + 0.861960i $$0.669237\pi$$
$$420$$ 0 0
$$421$$ −1.82530e6 −0.501913 −0.250957 0.967998i $$-0.580745\pi$$
−0.250957 + 0.967998i $$0.580745\pi$$
$$422$$ 0 0
$$423$$ 502054.i 0.136427i
$$424$$ 0 0
$$425$$ 2.25280e6 5.99040e6i 0.604993 1.60873i
$$426$$ 0 0
$$427$$ 6.68308e6i 1.77381i
$$428$$ 0 0
$$429$$ 1.41725e6 0.371794
$$430$$ 0 0
$$431$$ −2.85435e6 −0.740141 −0.370070 0.929004i $$-0.620666\pi$$
−0.370070 + 0.929004i $$0.620666\pi$$
$$432$$ 0 0
$$433$$ 587776.i 0.150658i −0.997159 0.0753290i $$-0.975999\pi$$
0.997159 0.0753290i $$-0.0240007\pi$$
$$434$$ 0 0
$$435$$ 37800.0 207900.i 0.00957786 0.0526783i
$$436$$ 0 0
$$437$$ 2.76612e6i 0.692895i
$$438$$ 0 0
$$439$$ 6.11604e6 1.51464 0.757319 0.653045i $$-0.226509\pi$$
0.757319 + 0.653045i $$0.226509\pi$$
$$440$$ 0 0
$$441$$ −383379. −0.0938711
$$442$$ 0 0
$$443$$ 2.35771e6i 0.570795i 0.958409 + 0.285398i $$0.0921257\pi$$
−0.958409 + 0.285398i $$0.907874\pi$$
$$444$$ 0 0
$$445$$ 4.68655e6 + 852100.i 1.12190 + 0.203981i
$$446$$ 0 0
$$447$$ 1.94390e6i 0.460156i
$$448$$ 0 0
$$449$$ −5.49735e6 −1.28688 −0.643439 0.765497i $$-0.722493\pi$$
−0.643439 + 0.765497i $$0.722493\pi$$
$$450$$ 0 0
$$451$$ −354904. −0.0821617
$$452$$ 0 0
$$453$$ 5.82613e6i 1.33393i
$$454$$ 0 0
$$455$$ −5.94396e6 1.08072e6i −1.34601 0.244729i
$$456$$ 0 0
$$457$$ 1.16039e6i 0.259905i 0.991520 + 0.129952i $$0.0414824\pi$$
−0.991520 + 0.129952i $$0.958518\pi$$
$$458$$ 0 0
$$459$$ −8.31488e6 −1.84215
$$460$$ 0 0
$$461$$ −2.30330e6 −0.504775 −0.252387 0.967626i $$-0.581216\pi$$
−0.252387 + 0.967626i $$0.581216\pi$$
$$462$$ 0 0
$$463$$ 2.71343e6i 0.588257i −0.955766 0.294128i $$-0.904971\pi$$
0.955766 0.294128i $$-0.0950293\pi$$
$$464$$ 0 0
$$465$$ 286720. 1.57696e6i 0.0614930 0.338211i
$$466$$ 0 0
$$467$$ 4.05050e6i 0.859441i 0.902962 + 0.429721i $$0.141388\pi$$
−0.902962 + 0.429721i $$0.858612\pi$$
$$468$$ 0 0
$$469$$ −5.07148e6 −1.06464
$$470$$ 0 0
$$471$$ −6.06351e6 −1.25942
$$472$$ 0 0
$$473$$ 339512.i 0.0697754i
$$474$$ 0 0
$$475$$ 6.49350e6 + 2.44200e6i 1.32052 + 0.496606i
$$476$$ 0 0
$$477$$ 139308.i 0.0280337i
$$478$$ 0 0
$$479$$ 5.60528e6 1.11624 0.558121 0.829759i $$-0.311522\pi$$
0.558121 + 0.829759i $$0.311522\pi$$
$$480$$ 0 0
$$481$$ −2.99045e6 −0.589350
$$482$$ 0 0
$$483$$ 2.75615e6i 0.537570i
$$484$$ 0 0
$$485$$ −972320. + 5.34776e6i −0.187696 + 1.03233i
$$486$$ 0 0
$$487$$ 7.13168e6i 1.36260i 0.732003 + 0.681301i $$0.238586\pi$$
−0.732003 + 0.681301i $$0.761414\pi$$
$$488$$ 0 0
$$489$$ −2.08788e6 −0.394850
$$490$$ 0 0
$$491$$ −5.88145e6 −1.10098 −0.550492 0.834841i $$-0.685560\pi$$
−0.550492 + 0.834841i $$0.685560\pi$$
$$492$$ 0 0
$$493$$ 552960.i 0.102465i
$$494$$ 0 0
$$495$$ 382580. + 69560.0i 0.0701793 + 0.0127599i
$$496$$ 0 0
$$497$$ 671184.i 0.121885i
$$498$$ 0 0
$$499$$ 1.75710e6 0.315897 0.157948 0.987447i $$-0.449512\pi$$
0.157948 + 0.987447i $$0.449512\pi$$
$$500$$ 0 0
$$501$$ −7.83443e6 −1.39448
$$502$$ 0 0
$$503$$ 4.91411e6i 0.866015i −0.901390 0.433007i $$-0.857452\pi$$
0.901390 0.433007i $$-0.142548\pi$$
$$504$$ 0 0
$$505$$ −236390. 42980.0i −0.0412478 0.00749960i
$$506$$ 0 0
$$507$$ 1.35188e6i 0.233571i
$$508$$ 0 0
$$509$$ 5.75499e6 0.984578 0.492289 0.870432i $$-0.336160\pi$$
0.492289 + 0.870432i $$0.336160\pi$$
$$510$$ 0 0
$$511$$ −4.75643e6 −0.805803
$$512$$ 0 0
$$513$$ 9.01320e6i 1.51212i
$$514$$ 0 0
$$515$$ 1.24114e6 6.82627e6i 0.206207 1.13414i
$$516$$ 0 0
$$517$$ 1.58094e6i 0.260128i
$$518$$ 0 0
$$519$$ 4.81326e6 0.784369
$$520$$ 0 0
$$521$$ −1.61980e6 −0.261437 −0.130718 0.991420i $$-0.541728\pi$$
−0.130718 + 0.991420i $$0.541728\pi$$
$$522$$ 0 0
$$523$$ 1.19117e7i 1.90422i −0.305751 0.952112i $$-0.598907\pi$$
0.305751 0.952112i $$-0.401093\pi$$
$$524$$ 0 0
$$525$$ 6.47010e6 + 2.43320e6i 1.02450 + 0.385283i
$$526$$ 0 0
$$527$$ 4.19430e6i 0.657860i
$$528$$ 0 0
$$529$$ 4.88383e6 0.758789
$$530$$ 0 0
$$531$$ −1.86778e6 −0.287468
$$532$$ 0 0
$$533$$ 1.64023e6i 0.250085i
$$534$$ 0 0
$$535$$ 423420. 2.32881e6i 0.0639568 0.351763i
$$536$$ 0 0
$$537$$ 335720.i 0.0502391i
$$538$$ 0 0
$$539$$ −1.20724e6 −0.178986
$$540$$ 0 0
$$541$$ 4.07630e6 0.598788 0.299394 0.954130i $$-0.403215\pi$$
0.299394 + 0.954130i $$0.403215\pi$$
$$542$$ 0 0
$$543$$ 9.12657e6i 1.32834i
$$544$$ 0 0
$$545$$ 1.97945e6 + 359900.i 0.285465 + 0.0519028i
$$546$$ 0 0
$$547$$ 1.23680e7i 1.76739i 0.468065 + 0.883694i $$0.344951\pi$$
−0.468065 + 0.883694i $$0.655049\pi$$
$$548$$ 0 0
$$549$$ −1.98801e6 −0.281505
$$550$$ 0 0
$$551$$ 599400. 0.0841081
$$552$$ 0 0
$$553$$ 5.57424e6i 0.775127i
$$554$$ 0 0
$$555$$ 3.36644e6 + 612080.i 0.463915 + 0.0843482i
$$556$$ 0 0
$$557$$ 130308.i 0.0177964i −0.999960 0.00889822i $$-0.997168\pi$$
0.999960 0.00889822i $$-0.00283243\pi$$
$$558$$ 0 0
$$559$$ 1.56910e6 0.212383
$$560$$ 0 0
$$561$$ −4.24346e6 −0.569262
$$562$$ 0 0
$$563$$ 5.91687e6i 0.786721i 0.919384 + 0.393361i $$0.128688\pi$$
−0.919384 + 0.393361i $$0.871312\pi$$
$$564$$ 0 0
$$565$$ 2.28816e6 1.25849e7i 0.301554 1.65855i
$$566$$ 0 0
$$567$$ 7.17620e6i 0.937426i
$$568$$ 0 0
$$569$$ 9.03013e6 1.16927 0.584633 0.811298i $$-0.301239\pi$$
0.584633 + 0.811298i $$0.301239\pi$$
$$570$$ 0 0
$$571$$ 1.07093e7 1.37459 0.687294 0.726379i $$-0.258798\pi$$
0.687294 + 0.726379i $$0.258798\pi$$
$$572$$ 0 0
$$573$$ 2.83853e6i 0.361166i
$$574$$ 0 0
$$575$$ −1.37060e6 + 3.64455e6i −0.172879 + 0.459700i
$$576$$ 0 0
$$577$$ 1.22051e6i 0.152617i 0.997084 + 0.0763084i $$0.0243134\pi$$
−0.997084 + 0.0763084i $$0.975687\pi$$
$$578$$ 0 0
$$579$$ −6.33718e6 −0.785597
$$580$$ 0 0
$$581$$ −4.39651e6 −0.540341
$$582$$ 0 0
$$583$$ 438672.i 0.0534526i
$$584$$ 0 0
$$585$$ −321480. + 1.76814e6i −0.0388387 + 0.213613i
$$586$$ 0 0
$$587$$ 1.47104e7i 1.76210i −0.473026 0.881049i $$-0.656838\pi$$
0.473026 0.881049i $$-0.343162\pi$$
$$588$$ 0 0
$$589$$ 4.54656e6 0.540001
$$590$$ 0 0
$$591$$ −4.72455e6 −0.556406
$$592$$ 0 0
$$593$$ 8.52014e6i 0.994970i 0.867472 + 0.497485i $$0.165743\pi$$
−0.867472 + 0.497485i $$0.834257\pi$$
$$594$$ 0 0
$$595$$ 1.77971e7 + 3.23584e6i 2.06090 + 0.374709i
$$596$$ 0 0
$$597$$ 7.85400e6i 0.901893i
$$598$$ 0 0
$$599$$ 2.90100e6 0.330355 0.165177 0.986264i $$-0.447180\pi$$
0.165177 + 0.986264i $$0.447180\pi$$
$$600$$ 0 0
$$601$$ 5.72760e6 0.646825 0.323412 0.946258i $$-0.395170\pi$$
0.323412 + 0.946258i $$0.395170\pi$$
$$602$$ 0 0
$$603$$ 1.50861e6i 0.168959i
$$604$$ 0 0
$$605$$ −7.65308e6 1.39147e6i −0.850057 0.154556i
$$606$$ 0 0
$$607$$ 8.79924e6i 0.969334i −0.874699 0.484667i $$-0.838941\pi$$
0.874699 0.484667i $$-0.161059\pi$$
$$608$$ 0 0
$$609$$ 597240. 0.0652538
$$610$$ 0 0
$$611$$ 7.30649e6 0.791782
$$612$$ 0 0
$$613$$ 1.03408e6i 0.111149i 0.998455 + 0.0555744i $$0.0176990\pi$$
−0.998455 + 0.0555744i $$0.982301\pi$$
$$614$$ 0 0
$$615$$ −335720. + 1.84646e6i −0.0357923 + 0.196858i
$$616$$ 0 0
$$617$$ 1.29854e7i 1.37323i −0.727020 0.686616i $$-0.759095\pi$$
0.727020 0.686616i $$-0.240905\pi$$
$$618$$ 0 0
$$619$$ 7.92002e6 0.830806 0.415403 0.909637i $$-0.363641\pi$$
0.415403 + 0.909637i $$0.363641\pi$$
$$620$$ 0 0
$$621$$ 5.05876e6 0.526399
$$622$$ 0 0
$$623$$ 1.34632e7i 1.38972i
$$624$$ 0 0
$$625$$ 7.34562e6 + 6.43500e6i 0.752192 + 0.658944i
$$626$$ 0 0
$$627$$ 4.59984e6i 0.467276i
$$628$$ 0 0
$$629$$ 8.95386e6 0.902368
$$630$$ 0 0
$$631$$ −1.68218e7 −1.68189 −0.840945 0.541120i $$-0.818001\pi$$
−0.840945 + 0.541120i $$0.818001\pi$$
$$632$$ 0 0
$$633$$ 1.12777e7i 1.11869i
$$634$$ 0 0
$$635$$ −1.75238e6 + 9.63809e6i −0.172462 + 0.948542i
$$636$$ 0 0
$$637$$ 5.57939e6i 0.544801i
$$638$$ 0 0
$$639$$ 199656. 0.0193433
$$640$$ 0 0
$$641$$ −1.55154e7 −1.49148 −0.745741 0.666236i $$-0.767904\pi$$
−0.745741 + 0.666236i $$0.767904\pi$$
$$642$$ 0 0
$$643$$ 1.05801e7i 1.00916i −0.863364 0.504582i $$-0.831646\pi$$
0.863364 0.504582i $$-0.168354\pi$$
$$644$$ 0 0
$$645$$ −1.76638e6 321160.i −0.167180 0.0303964i
$$646$$ 0 0
$$647$$ 1.37883e7i 1.29494i 0.762090 + 0.647471i $$0.224173\pi$$
−0.762090 + 0.647471i $$0.775827\pi$$
$$648$$ 0 0
$$649$$ −5.88152e6 −0.548123
$$650$$ 0 0
$$651$$ 4.53018e6 0.418950
$$652$$ 0 0
$$653$$ 1.58924e6i 0.145850i −0.997337 0.0729248i $$-0.976767\pi$$
0.997337 0.0729248i $$-0.0232333\pi$$
$$654$$ 0 0
$$655$$ −1.64809e7 2.99652e6i −1.50099 0.272907i
$$656$$ 0 0
$$657$$ 1.41489e6i 0.127882i
$$658$$ 0 0
$$659$$ −9.12434e6 −0.818442 −0.409221 0.912435i $$-0.634199\pi$$
−0.409221 + 0.912435i $$0.634199\pi$$
$$660$$ 0 0
$$661$$ 6.50310e6 0.578918 0.289459 0.957190i $$-0.406525\pi$$
0.289459 + 0.957190i $$0.406525\pi$$
$$662$$ 0 0
$$663$$ 1.96116e7i 1.73273i
$$664$$ 0 0
$$665$$ −3.50760e6 + 1.92918e7i −0.307578 + 1.69168i
$$666$$ 0 0
$$667$$ 336420.i 0.0292797i
$$668$$ 0 0
$$669$$ −1.70598e7 −1.47369
$$670$$ 0 0
$$671$$ −6.26010e6 −0.536754
$$672$$ 0 0
$$673$$ 2.17810e6i 0.185370i −0.995695 0.0926850i $$-0.970455\pi$$
0.995695 0.0926850i $$-0.0295449\pi$$
$$674$$ 0 0
$$675$$ 4.46600e6 1.18755e7i 0.377276 1.00321i
$$676$$ 0 0
$$677$$ 3.98419e6i 0.334094i −0.985949 0.167047i $$-0.946577\pi$$
0.985949 0.167047i $$-0.0534231\pi$$
$$678$$ 0 0
$$679$$ −1.53627e7 −1.27877
$$680$$ 0 0
$$681$$ 7.90073e6 0.652829
$$682$$ 0 0
$$683$$ 5.91563e6i 0.485231i 0.970122 + 0.242616i $$0.0780054\pi$$
−0.970122 + 0.242616i $$0.921995\pi$$
$$684$$ 0 0
$$685$$ 1.07928e6 5.93604e6i 0.0878836 0.483360i
$$686$$ 0 0
$$687$$ 7.84462e6i 0.634133i
$$688$$ 0 0
$$689$$ −2.02738e6 −0.162700
$$690$$ 0 0
$$691$$ 1.55471e7 1.23867 0.619335 0.785127i $$-0.287402\pi$$
0.619335 + 0.785127i $$0.287402\pi$$
$$692$$ 0 0
$$693$$ 1.09905e6i 0.0869328i
$$694$$ 0 0
$$695$$ −1.08053e7 1.96460e6i −0.848545 0.154281i
$$696$$ 0 0
$$697$$ 4.91110e6i 0.382910i
$$698$$ 0 0
$$699$$ −4.11006e6 −0.318167
$$700$$ 0 0
$$701$$ −2.27103e7 −1.74553 −0.872766 0.488139i $$-0.837676\pi$$
−0.872766 + 0.488139i $$0.837676\pi$$
$$702$$ 0 0
$$703$$ 9.70584e6i 0.740704i
$$704$$ 0 0
$$705$$ −8.22514e6 1.49548e6i −0.623262 0.113320i
$$706$$ 0 0
$$707$$ 679084.i 0.0510946i
$$708$$ 0 0
$$709$$ −6.29841e6 −0.470560 −0.235280 0.971928i $$-0.575601\pi$$
−0.235280 + 0.971928i $$0.575601\pi$$
$$710$$ 0 0
$$711$$ 1.65816e6 0.123013
$$712$$ 0 0
$$713$$ 2.55181e6i 0.187985i
$$714$$ 0 0
$$715$$ −1.01232e6 + 5.56776e6i −0.0740547 + 0.407301i
$$716$$ 0 0
$$717$$ 8.17936e6i 0.594185i
$$718$$ 0 0
$$719$$ 2.11911e7 1.52873 0.764367 0.644782i $$-0.223052\pi$$
0.764367 + 0.644782i $$0.223052\pi$$
$$720$$ 0 0
$$721$$ 1.96100e7 1.40488
$$722$$ 0 0
$$723$$ 7.89317e6i 0.561572i
$$724$$ 0 0
$$725$$ 789750. + 297000.i 0.0558013 + 0.0209851i
$$726$$ 0 0
$$727$$ 1.35610e7i 0.951605i 0.879552 + 0.475803i $$0.157842\pi$$
−0.879552 + 0.475803i $$0.842158\pi$$
$$728$$ 0 0
$$729$$ −1.59468e7 −1.11136
$$730$$ 0 0
$$731$$ −4.69811e6 −0.325185
$$732$$ 0 0
$$733$$ 2.69413e7i 1.85208i 0.377429 + 0.926038i $$0.376808\pi$$
−0.377429 + 0.926038i $$0.623192\pi$$
$$734$$ 0 0
$$735$$ −1.14198e6 + 6.28089e6i −0.0779723 + 0.428847i
$$736$$ 0 0
$$737$$ 4.75050e6i 0.322160i
$$738$$ 0 0
$$739$$ 2.77414e6 0.186860 0.0934302 0.995626i $$-0.470217\pi$$
0.0934302 + 0.995626i $$0.470217\pi$$
$$740$$ 0 0
$$741$$ 2.12587e7 1.42230
$$742$$ 0 0
$$743$$ 1.85538e7i 1.23299i −0.787358 0.616497i $$-0.788551\pi$$
0.787358 0.616497i $$-0.211449\pi$$
$$744$$ 0 0
$$745$$ −7.63675e6 1.38850e6i −0.504101 0.0916548i
$$746$$ 0 0
$$747$$ 1.30782e6i 0.0857526i
$$748$$ 0 0
$$749$$ 6.69004e6 0.435736
$$750$$ 0 0
$$751$$ 2.19285e6 0.141876 0.0709380 0.997481i $$-0.477401\pi$$
0.0709380 + 0.997481i $$0.477401\pi$$
$$752$$ 0 0
$$753$$ 1.42765e7i 0.917558i
$$754$$ 0 0
$$755$$ −2.28884e7 4.16152e6i −1.46133 0.265696i
$$756$$ 0 0
$$757$$ 9.48749e6i 0.601744i 0.953665 + 0.300872i $$0.0972777\pi$$
−0.953665 + 0.300872i $$0.902722\pi$$
$$758$$ 0 0
$$759$$ 2.58171e6 0.162668
$$760$$ 0 0
$$761$$ 9.69580e6 0.606907 0.303453 0.952846i $$-0.401860\pi$$
0.303453 + 0.952846i $$0.401860\pi$$
$$762$$ 0 0
$$763$$ 5.68642e6i 0.353612i
$$764$$ 0 0
$$765$$ 962560. 5.29408e6i 0.0594668 0.327067i
$$766$$ 0 0
$$767$$ 2.71822e7i 1.66838i
$$768$$ 0 0
$$769$$ −9.32787e6 −0.568809 −0.284405 0.958704i $$-0.591796\pi$$
−0.284405 + 0.958704i $$0.591796\pi$$
$$770$$ 0 0
$$771$$ −9.20371e6 −0.557606
$$772$$ 0 0
$$773$$ 9.68080e6i 0.582723i −0.956613 0.291362i $$-0.905892\pi$$
0.956613 0.291362i $$-0.0941083\pi$$
$$774$$ 0 0
$$775$$ 5.99040e6 + 2.25280e6i 0.358263 + 0.134731i
$$776$$ 0 0
$$777$$ 9.67086e6i 0.574662i
$$778$$ 0 0
$$779$$ −5.32356e6 −0.314310
$$780$$ 0 0
$$781$$ 628704. 0.0368824
$$782$$ 0 0
$$783$$ 1.09620e6i 0.0638977i
$$784$$ 0 0
$$785$$ 4.33108e6 2.38209e7i 0.250855 1.37970i
$$786$$ 0 0
$$787$$ 5.52302e6i 0.317863i −0.987290 0.158931i $$-0.949195\pi$$
0.987290 0.158931i $$-0.0508049\pi$$
$$788$$ 0 0
$$789$$ 7.87312e6 0.450251
$$790$$ 0 0
$$791$$ 3.61529e7 2.05448
$$792$$ 0 0
$$793$$ 2.89318e7i 1.63378i
$$794$$ 0 0
$$795$$ 2.28228e6 +