# Properties

 Label 90.6.c.a.19.1 Level $90$ Weight $6$ Character 90.19 Analytic conductor $14.435$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$90 = 2 \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 90.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.4345437832$$ 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 19.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 90.19 Dual form 90.6.c.a.19.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -158.000i q^{7} +64.0000i q^{8} +O(q^{10})$$ $$q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -158.000i q^{7} +64.0000i q^{8} +(-40.0000 + 220.000i) q^{10} +148.000 q^{11} +684.000i q^{13} -632.000 q^{14} +256.000 q^{16} +2048.00i q^{17} -2220.00 q^{19} +(880.000 + 160.000i) q^{20} -592.000i q^{22} +1246.00i q^{23} +(2925.00 + 1100.00i) q^{25} +2736.00 q^{26} +2528.00i q^{28} -270.000 q^{29} -2048.00 q^{31} -1024.00i q^{32} +8192.00 q^{34} +(-1580.00 + 8690.00i) q^{35} +4372.00i q^{37} +8880.00i q^{38} +(640.000 - 3520.00i) q^{40} +2398.00 q^{41} +2294.00i q^{43} -2368.00 q^{44} +4984.00 q^{46} -10682.0i q^{47} -8157.00 q^{49} +(4400.00 - 11700.0i) q^{50} -10944.0i q^{52} -2964.00i q^{53} +(-8140.00 - 1480.00i) q^{55} +10112.0 q^{56} +1080.00i q^{58} -39740.0 q^{59} -42298.0 q^{61} +8192.00i q^{62} -4096.00 q^{64} +(6840.00 - 37620.0i) q^{65} -32098.0i q^{67} -32768.0i q^{68} +(34760.0 + 6320.00i) q^{70} +4248.00 q^{71} +30104.0i q^{73} +17488.0 q^{74} +35520.0 q^{76} -23384.0i q^{77} -35280.0 q^{79} +(-14080.0 - 2560.00i) q^{80} -9592.00i q^{82} +27826.0i q^{83} +(20480.0 - 112640. i) q^{85} +9176.00 q^{86} +9472.00i q^{88} -85210.0 q^{89} +108072. q^{91} -19936.0i q^{92} -42728.0 q^{94} +(122100. + 22200.0i) q^{95} +97232.0i q^{97} +32628.0i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 32q^{4} - 110q^{5} + O(q^{10})$$ $$2q - 32q^{4} - 110q^{5} - 80q^{10} + 296q^{11} - 1264q^{14} + 512q^{16} - 4440q^{19} + 1760q^{20} + 5850q^{25} + 5472q^{26} - 540q^{29} - 4096q^{31} + 16384q^{34} - 3160q^{35} + 1280q^{40} + 4796q^{41} - 4736q^{44} + 9968q^{46} - 16314q^{49} + 8800q^{50} - 16280q^{55} + 20224q^{56} - 79480q^{59} - 84596q^{61} - 8192q^{64} + 13680q^{65} + 69520q^{70} + 8496q^{71} + 34976q^{74} + 71040q^{76} - 70560q^{79} - 28160q^{80} + 40960q^{85} + 18352q^{86} - 170420q^{89} + 216144q^{91} - 85456q^{94} + 244200q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$$.

 $$n$$ $$11$$ $$37$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.00000i 0.707107i
$$3$$ 0 0
$$4$$ −16.0000 −0.500000
$$5$$ −55.0000 10.0000i −0.983870 0.178885i
$$6$$ 0 0
$$7$$ 158.000i 1.21874i −0.792885 0.609371i $$-0.791422\pi$$
0.792885 0.609371i $$-0.208578\pi$$
$$8$$ 64.0000i 0.353553i
$$9$$ 0 0
$$10$$ −40.0000 + 220.000i −0.126491 + 0.695701i
$$11$$ 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 $$0.810315\pi$$
$$14$$ −632.000 −0.861781
$$15$$ 0 0
$$16$$ 256.000 0.250000
$$17$$ 2048.00i 1.71873i 0.511363 + 0.859365i $$0.329141\pi$$
−0.511363 + 0.859365i $$0.670859\pi$$
$$18$$ 0 0
$$19$$ −2220.00 −1.41081 −0.705406 0.708804i $$-0.749235\pi$$
−0.705406 + 0.708804i $$0.749235\pi$$
$$20$$ 880.000 + 160.000i 0.491935 + 0.0894427i
$$21$$ 0 0
$$22$$ 592.000i 0.260774i
$$23$$ 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
$$26$$ 2736.00 0.793748
$$27$$ 0 0
$$28$$ 2528.00i 0.609371i
$$29$$ −270.000 −0.0596168 −0.0298084 0.999556i $$-0.509490\pi$$
−0.0298084 + 0.999556i $$0.509490\pi$$
$$30$$ 0 0
$$31$$ −2048.00 −0.382759 −0.191380 0.981516i $$-0.561296\pi$$
−0.191380 + 0.981516i $$0.561296\pi$$
$$32$$ 1024.00i 0.176777i
$$33$$ 0 0
$$34$$ 8192.00 1.21533
$$35$$ −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 $$0.915450\pi$$
$$38$$ 8880.00i 0.997594i
$$39$$ 0 0
$$40$$ 640.000 3520.00i 0.0632456 0.347851i
$$41$$ 2398.00 0.222787 0.111393 0.993776i $$-0.464469\pi$$
0.111393 + 0.993776i $$0.464469\pi$$
$$42$$ 0 0
$$43$$ 2294.00i 0.189200i 0.995515 + 0.0946002i $$0.0301573\pi$$
−0.995515 + 0.0946002i $$0.969843\pi$$
$$44$$ −2368.00 −0.184395
$$45$$ 0 0
$$46$$ 4984.00 0.347283
$$47$$ 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
$$50$$ 4400.00 11700.0i 0.248902 0.661852i
$$51$$ 0 0
$$52$$ 10944.0i 0.561265i
$$53$$ 2964.00i 0.144940i −0.997371 0.0724700i $$-0.976912\pi$$
0.997371 0.0724700i $$-0.0230882\pi$$
$$54$$ 0 0
$$55$$ −8140.00 1480.00i −0.362842 0.0659713i
$$56$$ 10112.0 0.430891
$$57$$ 0 0
$$58$$ 1080.00i 0.0421555i
$$59$$ −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 $$0.759421\pi$$
$$62$$ 8192.00i 0.270652i
$$63$$ 0 0
$$64$$ −4096.00 −0.125000
$$65$$ 6840.00 37620.0i 0.200804 1.10442i
$$66$$ 0 0
$$67$$ 32098.0i 0.873556i −0.899569 0.436778i $$-0.856119\pi$$
0.899569 0.436778i $$-0.143881\pi$$
$$68$$ 32768.0i 0.859365i
$$69$$ 0 0
$$70$$ 34760.0 + 6320.00i 0.847881 + 0.154160i
$$71$$ 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 $$0.892753\pi$$
$$74$$ 17488.0 0.371245
$$75$$ 0 0
$$76$$ 35520.0 0.705406
$$77$$ 23384.0i 0.449461i
$$78$$ 0 0
$$79$$ −35280.0 −0.636005 −0.318003 0.948090i $$-0.603012\pi$$
−0.318003 + 0.948090i $$0.603012\pi$$
$$80$$ −14080.0 2560.00i −0.245967 0.0447214i
$$81$$ 0 0
$$82$$ 9592.00i 0.157534i
$$83$$ 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
$$86$$ 9176.00 0.133785
$$87$$ 0 0
$$88$$ 9472.00i 0.130387i
$$89$$ −85210.0 −1.14029 −0.570145 0.821544i $$-0.693113\pi$$
−0.570145 + 0.821544i $$0.693113\pi$$
$$90$$ 0 0
$$91$$ 108072. 1.36807
$$92$$ 19936.0i 0.245566i
$$93$$ 0 0
$$94$$ −42728.0 −0.498762
$$95$$ 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 $$0.824205\pi$$
$$98$$ 32628.0i 0.343183i
$$99$$ 0 0
$$100$$ −46800.0 17600.0i −0.468000 0.176000i
$$101$$ 4298.00 0.0419240 0.0209620 0.999780i $$-0.493327\pi$$
0.0209620 + 0.999780i $$0.493327\pi$$
$$102$$ 0 0
$$103$$ 124114.i 1.15273i 0.817192 + 0.576365i $$0.195529\pi$$
−0.817192 + 0.576365i $$0.804471\pi$$
$$104$$ −43776.0 −0.396874
$$105$$ 0 0
$$106$$ −11856.0 −0.102488
$$107$$ 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 $$0.453658\pi$$
$$110$$ −5920.00 + 32560.0i −0.0466487 + 0.256568i
$$111$$ 0 0
$$112$$ 40448.0i 0.304686i
$$113$$ 228816.i 1.68574i 0.538118 + 0.842869i $$0.319135\pi$$
−0.538118 + 0.842869i $$0.680865\pi$$
$$114$$ 0 0
$$115$$ 12460.0 68530.0i 0.0878564 0.483210i
$$116$$ 4320.00 0.0298084
$$117$$ 0 0
$$118$$ 158960.i 1.05095i
$$119$$ 323584. 2.09469
$$120$$ 0 0
$$121$$ −139147. −0.863993
$$122$$ 169192.i 1.02915i
$$123$$ 0 0
$$124$$ 32768.0 0.191380
$$125$$ −149875. 89750.0i −0.857935 0.513759i
$$126$$ 0 0
$$127$$ 175238.i 0.964093i −0.876146 0.482047i $$-0.839894\pi$$
0.876146 0.482047i $$-0.160106\pi$$
$$128$$ 16384.0i 0.0883883i
$$129$$ 0 0
$$130$$ −150480. 27360.0i −0.780945 0.141990i
$$131$$ −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
$$134$$ −128392. −0.617698
$$135$$ 0 0
$$136$$ −131072. −0.607663
$$137$$ 107928.i 0.491284i 0.969361 + 0.245642i $$0.0789988\pi$$
−0.969361 + 0.245642i $$0.921001\pi$$
$$138$$ 0 0
$$139$$ 196460. 0.862456 0.431228 0.902243i $$-0.358080\pi$$
0.431228 + 0.902243i $$0.358080\pi$$
$$140$$ 25280.0 139040.i 0.109008 0.599542i
$$141$$ 0 0
$$142$$ 16992.0i 0.0707170i
$$143$$ 101232.i 0.413978i
$$144$$ 0 0
$$145$$ 14850.0 + 2700.00i 0.0586552 + 0.0106646i
$$146$$ 120416. 0.467522
$$147$$ 0 0
$$148$$ 69952.0i 0.262510i
$$149$$ 138850. 0.512366 0.256183 0.966628i $$-0.417535\pi$$
0.256183 + 0.966628i $$0.417535\pi$$
$$150$$ 0 0
$$151$$ 416152. 1.48528 0.742642 0.669688i $$-0.233572\pi$$
0.742642 + 0.669688i $$0.233572\pi$$
$$152$$ 142080.i 0.498797i
$$153$$ 0 0
$$154$$ −93536.0 −0.317817
$$155$$ 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 $$-0.247334\pi$$
$$158$$ 141120.i 0.449724i
$$159$$ 0 0
$$160$$ −10240.0 + 56320.0i −0.0316228 + 0.173925i
$$161$$ 196868. 0.598564
$$162$$ 0 0
$$163$$ 149134.i 0.439651i 0.975539 + 0.219825i $$0.0705487\pi$$
−0.975539 + 0.219825i $$0.929451\pi$$
$$164$$ −38368.0 −0.111393
$$165$$ 0 0
$$166$$ 111304. 0.313502
$$167$$ 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
$$170$$ −450560. 81920.0i −1.19572 0.217404i
$$171$$ 0 0
$$172$$ 36704.0i 0.0946002i
$$173$$ 343804.i 0.873365i −0.899616 0.436682i $$-0.856153\pi$$
0.899616 0.436682i $$-0.143847\pi$$
$$174$$ 0 0
$$175$$ 173800. 462150.i 0.428997 1.14074i
$$176$$ 37888.0 0.0921977
$$177$$ 0 0
$$178$$ 340840.i 0.806307i
$$179$$ 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 $$0.764950\pi$$
$$182$$ 432288.i 0.967375i
$$183$$ 0 0
$$184$$ −79744.0 −0.173641
$$185$$ 43720.0 240460.i 0.0939184 0.516551i
$$186$$ 0 0
$$187$$ 303104.i 0.633852i
$$188$$ 170912.i 0.352678i
$$189$$ 0 0
$$190$$ 88800.0 488400.i 0.178455 0.981503i
$$191$$ −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 $$-0.144089\pi$$
$$194$$ 388928. 0.741933
$$195$$ 0 0
$$196$$ 130512. 0.242667
$$197$$ 337468.i 0.619537i 0.950812 + 0.309768i $$0.100252\pi$$
−0.950812 + 0.309768i $$0.899748\pi$$
$$198$$ 0 0
$$199$$ 561000. 1.00422 0.502112 0.864803i $$-0.332557\pi$$
0.502112 + 0.864803i $$0.332557\pi$$
$$200$$ −70400.0 + 187200.i −0.124451 + 0.330926i
$$201$$ 0 0
$$202$$ 17192.0i 0.0296448i
$$203$$ 42660.0i 0.0726576i
$$204$$ 0 0
$$205$$ −131890. 23980.0i −0.219193 0.0398533i
$$206$$ 496456. 0.815103
$$207$$ 0 0
$$208$$ 175104.i 0.280632i
$$209$$ −328560. −0.520294
$$210$$ 0 0
$$211$$ −805548. −1.24562 −0.622810 0.782373i $$-0.714009\pi$$
−0.622810 + 0.782373i $$0.714009\pi$$
$$212$$ 47424.0i 0.0724700i
$$213$$ 0 0
$$214$$ −169368. −0.252812
$$215$$ 22940.0 126170.i 0.0338452 0.186149i
$$216$$ 0 0
$$217$$ 323584.i 0.466485i
$$218$$ 143960.i 0.205164i
$$219$$ 0 0
$$220$$ 130240. + 23680.0i 0.181421 + 0.0329856i
$$221$$ −1.40083e6 −1.92932
$$222$$ 0 0
$$223$$ 1.21855e6i 1.64090i 0.571717 + 0.820451i $$0.306278\pi$$
−0.571717 + 0.820451i $$0.693722\pi$$
$$224$$ −161792. −0.215445
$$225$$ 0 0
$$226$$ 915264. 1.19200
$$227$$ 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 $$0.614852\pi$$
$$230$$ −274120. 49840.0i −0.341681 0.0621239i
$$231$$ 0 0
$$232$$ 17280.0i 0.0210777i
$$233$$ 293576.i 0.354267i 0.984187 + 0.177134i $$0.0566824\pi$$
−0.984187 + 0.177134i $$0.943318\pi$$
$$234$$ 0 0
$$235$$ −106820. + 587510.i −0.126178 + 0.693978i
$$236$$ 635840. 0.743135
$$237$$ 0 0
$$238$$ 1.29434e6i 1.48117i
$$239$$ 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 $$0.601215\pi$$
$$242$$ 556588.i 0.610936i
$$243$$ 0 0
$$244$$ 676768. 0.727722
$$245$$ 448635. + 81570.0i 0.477505 + 0.0868191i
$$246$$ 0 0
$$247$$ 1.51848e6i 1.58368i
$$248$$ 131072.i 0.135326i
$$249$$ 0 0
$$250$$ −359000. + 599500.i −0.363282 + 0.606651i
$$251$$ 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
$$254$$ −700952. −0.681717
$$255$$ 0 0
$$256$$ 65536.0 0.0625000
$$257$$ 657408.i 0.620872i 0.950594 + 0.310436i $$0.100475\pi$$
−0.950594 + 0.310436i $$0.899525\pi$$
$$258$$ 0 0
$$259$$ 690776. 0.639864
$$260$$ −109440. + 601920.i −0.100402 + 0.552211i
$$261$$ 0 0
$$262$$ 1.19861e6i 1.07876i
$$263$$ 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
$$266$$ 1.40304e6 1.21581
$$267$$ 0 0
$$268$$ 513568.i 0.436778i
$$269$$ 366570. 0.308870 0.154435 0.988003i $$-0.450644\pi$$
0.154435 + 0.988003i $$0.450644\pi$$
$$270$$ 0 0
$$271$$ 1.16075e6 0.960099 0.480050 0.877241i $$-0.340619\pi$$
0.480050 + 0.877241i $$0.340619\pi$$
$$272$$ 524288.i 0.429682i
$$273$$ 0 0
$$274$$ 431712. 0.347390
$$275$$ 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 $$0.555725\pi$$
$$278$$ 785840.i 0.609849i
$$279$$ 0 0
$$280$$ −556160. 101120.i −0.423940 0.0770800i
$$281$$ −2.08600e6 −1.57597 −0.787987 0.615692i $$-0.788876\pi$$
−0.787987 + 0.615692i $$0.788876\pi$$
$$282$$ 0 0
$$283$$ 2.23803e6i 1.66111i −0.556935 0.830556i $$-0.688023\pi$$
0.556935 0.830556i $$-0.311977\pi$$
$$284$$ −67968.0 −0.0500044
$$285$$ 0 0
$$286$$ 404928. 0.292727
$$287$$ 378884.i 0.271520i
$$288$$ 0 0
$$289$$ −2.77445e6 −1.95403
$$290$$ 10800.0 59400.0i 0.00754100 0.0414755i
$$291$$ 0 0
$$292$$ 481664.i 0.330588i
$$293$$ 975756.i 0.664006i 0.943278 + 0.332003i $$0.107724\pi$$
−0.943278 + 0.332003i $$0.892276\pi$$
$$294$$ 0 0
$$295$$ 2.18570e6 + 397400.i 1.46230 + 0.265872i
$$296$$ −279808. −0.185623
$$297$$ 0 0
$$298$$ 555400.i 0.362297i
$$299$$ −852264. −0.551310
$$300$$ 0 0
$$301$$ 362452. 0.230587
$$302$$ 1.66461e6i 1.05025i
$$303$$ 0 0
$$304$$ −568320. −0.352703
$$305$$ 2.32639e6 + 422980.i 1.43197 + 0.260358i
$$306$$ 0 0
$$307$$ 87858.0i 0.0532029i −0.999646 0.0266015i $$-0.991531\pi$$
0.999646 0.0266015i $$-0.00846850\pi$$
$$308$$ 374144.i 0.224730i
$$309$$ 0 0
$$310$$ 81920.0 450560.i 0.0484156 0.266286i
$$311$$ −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 $$-0.206387\pi$$
$$314$$ −1.73243e6 −0.991590
$$315$$ 0 0
$$316$$ 564480. 0.318003
$$317$$ 2.41625e6i 1.35050i −0.737590 0.675249i $$-0.764036\pi$$
0.737590 0.675249i $$-0.235964\pi$$
$$318$$ 0 0
$$319$$ −39960.0 −0.0219861
$$320$$ 225280. + 40960.0i 0.122984 + 0.0223607i
$$321$$ 0 0
$$322$$ 787472.i 0.423249i
$$323$$ 4.54656e6i 2.42480i
$$324$$ 0 0
$$325$$ −752400. + 2.00070e6i −0.395130 + 1.05069i
$$326$$ 596536. 0.310880
$$327$$ 0 0
$$328$$ 153472.i 0.0787670i
$$329$$ −1.68776e6 −0.859647
$$330$$ 0 0
$$331$$ −1.64095e6 −0.823237 −0.411618 0.911356i $$-0.635036\pi$$
−0.411618 + 0.911356i $$0.635036\pi$$
$$332$$ 445216.i 0.221680i
$$333$$ 0 0
$$334$$ −2.23841e6 −1.09793
$$335$$ −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 $$-0.175812\pi$$
$$338$$ 386252.i 0.183899i
$$339$$ 0 0
$$340$$ −327680. + 1.80224e6i −0.153728 + 0.845503i
$$341$$ −303104. −0.141158
$$342$$ 0 0
$$343$$ 1.36670e6i 0.627246i
$$344$$ −146816. −0.0668925
$$345$$ 0 0
$$346$$ −1.37522e6 −0.617562
$$347$$ 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 $$0.302051\pi$$
$$350$$ −1.84860e6 695200.i −0.806627 0.303347i
$$351$$ 0 0
$$352$$ 151552.i 0.0651936i
$$353$$ 3.05766e6i 1.30603i −0.757345 0.653015i $$-0.773504\pi$$
0.757345 0.653015i $$-0.226496\pi$$
$$354$$ 0 0
$$355$$ −233640. 42480.0i −0.0983957 0.0178901i
$$356$$ 1.36336e6 0.570145
$$357$$ 0 0
$$358$$ 95920.0i 0.0395550i
$$359$$ 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
$$362$$ 2.60759e6i 1.04585i
$$363$$ 0 0
$$364$$ −1.72915e6 −0.684037
$$365$$ 301040. 1.65572e6i 0.118275 0.650511i
$$366$$ 0 0
$$367$$ 3.11060e6i 1.20553i 0.797917 + 0.602767i $$0.205935\pi$$
−0.797917 + 0.602767i $$0.794065\pi$$
$$368$$ 318976.i 0.122783i
$$369$$ 0 0
$$370$$ −961840. 174880.i −0.365257 0.0664104i
$$371$$ −468312. −0.176645
$$372$$ 0 0
$$373$$ 1.41520e6i 0.526677i −0.964703 0.263339i $$-0.915176\pi$$
0.964703 0.263339i $$-0.0848236\pi$$
$$374$$ 1.21242e6 0.448201
$$375$$ 0 0
$$376$$ 683648. 0.249381
$$377$$ 184680.i 0.0669216i
$$378$$ 0 0
$$379$$ 3.90262e6 1.39559 0.697796 0.716297i $$-0.254164\pi$$
0.697796 + 0.716297i $$0.254164\pi$$
$$380$$ −1.95360e6 355200.i −0.694027 0.126187i
$$381$$ 0 0
$$382$$ 811008.i 0.284359i
$$383$$ 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
$$386$$ −1.81062e6 −0.618529
$$387$$ 0 0
$$388$$ 1.55571e6i 0.524626i
$$389$$ 498290. 0.166958 0.0834792 0.996510i $$-0.473397\pi$$
0.0834792 + 0.996510i $$0.473397\pi$$
$$390$$ 0 0
$$391$$ −2.55181e6 −0.844124
$$392$$ 522048.i 0.171591i
$$393$$ 0 0
$$394$$ 1.34987e6 0.438079
$$395$$ 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 $$-0.0558150\pi$$
$$398$$ 2.24400e6i 0.710093i
$$399$$ 0 0
$$400$$ 748800. + 281600.i 0.234000 + 0.0880000i
$$401$$ 2.49160e6 0.773779 0.386890 0.922126i $$-0.373549\pi$$
0.386890 + 0.922126i $$0.373549\pi$$
$$402$$ 0 0
$$403$$ 1.40083e6i 0.429659i
$$404$$ −68768.0 −0.0209620
$$405$$ 0 0
$$406$$ 170640. 0.0513766
$$407$$ 647056.i 0.193623i
$$408$$ 0 0
$$409$$ 3.63349e6 1.07403 0.537014 0.843573i $$-0.319552\pi$$
0.537014 + 0.843573i $$0.319552\pi$$
$$410$$ −95920.0 + 527560.i −0.0281806 + 0.154993i
$$411$$ 0 0
$$412$$ 1.98582e6i 0.576365i
$$413$$ 6.27892e6i 1.81138i
$$414$$ 0 0
$$415$$ 278260. 1.53043e6i 0.0793105 0.436208i
$$416$$ 700416. 0.198437
$$417$$ 0 0
$$418$$ 1.31424e6i 0.367904i
$$419$$ −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 $$0.580745\pi$$
$$422$$ 3.22219e6i 0.880786i
$$423$$ 0 0
$$424$$ 189696. 0.0512441
$$425$$ −2.25280e6 + 5.99040e6i −0.604993 + 1.60873i
$$426$$ 0 0
$$427$$ 6.68308e6i 1.77381i
$$428$$ 677472.i 0.178765i
$$429$$ 0 0
$$430$$ −504680. 91760.0i −0.131627 0.0239322i
$$431$$ −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 $$-0.0240007\pi$$
$$434$$ 1.29434e6 0.329855
$$435$$ 0 0
$$436$$ −575840. −0.145073
$$437$$ 2.76612e6i 0.692895i
$$438$$ 0 0
$$439$$ −6.11604e6 −1.51464 −0.757319 0.653045i $$-0.773491\pi$$
−0.757319 + 0.653045i $$0.773491\pi$$
$$440$$ 94720.0 520960.i 0.0233244 0.128284i
$$441$$ 0 0
$$442$$ 5.60333e6i 1.36424i
$$443$$ 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
$$446$$ 4.87422e6 1.16029
$$447$$ 0 0
$$448$$ 647168.i 0.152343i
$$449$$ 5.49735e6 1.28688 0.643439 0.765497i $$-0.277507\pi$$
0.643439 + 0.765497i $$0.277507\pi$$
$$450$$ 0 0
$$451$$ 354904. 0.0821617
$$452$$ 3.66106e6i 0.842869i
$$453$$ 0 0
$$454$$ 2.25735e6 0.513996
$$455$$ −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 $$0.958518\pi$$
$$458$$ 2.24132e6i 0.499275i
$$459$$ 0 0
$$460$$ −199360. + 1.09648e6i −0.0439282 + 0.241605i
$$461$$ 2.30330e6 0.504775 0.252387 0.967626i $$-0.418784\pi$$
0.252387 + 0.967626i $$0.418784\pi$$
$$462$$ 0 0
$$463$$ 2.71343e6i 0.588257i 0.955766 + 0.294128i $$0.0950293\pi$$
−0.955766 + 0.294128i $$0.904971\pi$$
$$464$$ −69120.0 −0.0149042
$$465$$ 0 0
$$466$$ 1.17430e6 0.250505
$$467$$ 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
$$470$$ 2.35004e6 + 427280.i 0.490716 + 0.0892212i
$$471$$ 0 0
$$472$$ 2.54336e6i 0.525476i
$$473$$ 339512.i 0.0697754i
$$474$$ 0 0
$$475$$ −6.49350e6 2.44200e6i −1.32052 0.496606i
$$476$$ −5.17734e6 −1.04734
$$477$$ 0 0
$$478$$ 2.33696e6i 0.467823i
$$479$$ 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
$$482$$ 2.25519e6i 0.442146i
$$483$$ 0 0
$$484$$ 2.22635e6 0.431997
$$485$$ 972320. 5.34776e6i 0.187696 1.03233i
$$486$$ 0 0
$$487$$ 7.13168e6i 1.36260i −0.732003 0.681301i $$-0.761414\pi$$
0.732003 0.681301i $$-0.238586\pi$$
$$488$$ 2.70707e6i 0.514577i
$$489$$ 0 0
$$490$$ 326280. 1.79454e6i 0.0613904 0.337647i
$$491$$ −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
$$494$$ −6.07392e6 −1.11983
$$495$$ 0 0
$$496$$ −524288. −0.0956898
$$497$$ 671184.i 0.121885i
$$498$$ 0 0
$$499$$ −1.75710e6 −0.315897 −0.157948 0.987447i $$-0.550488\pi$$
−0.157948 + 0.987447i $$0.550488\pi$$
$$500$$ 2.39800e6 + 1.43600e6i 0.428967 + 0.256879i
$$501$$ 0 0
$$502$$ 4.07899e6i 0.722426i
$$503$$ 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
$$506$$ 737632. 0.128075
$$507$$ 0 0
$$508$$ 2.80381e6i 0.482047i
$$509$$ −5.75499e6 −0.984578 −0.492289 0.870432i $$-0.663840\pi$$
−0.492289 + 0.870432i $$0.663840\pi$$
$$510$$ 0 0
$$511$$ 4.75643e6 0.805803
$$512$$ 262144.i 0.0441942i
$$513$$ 0 0
$$514$$ 2.62963e6 0.439023
$$515$$ 1.24114e6 6.82627e6i 0.206207 1.13414i
$$516$$ 0 0
$$517$$ 1.58094e6i 0.260128i
$$518$$ 2.76310e6i 0.452452i
$$519$$ 0 0
$$520$$ 2.40768e6 + 437760.i 0.390472 + 0.0709950i
$$521$$ 1.61980e6 0.261437 0.130718 0.991420i $$-0.458272\pi$$
0.130718 + 0.991420i $$0.458272\pi$$
$$522$$ 0 0
$$523$$ 1.19117e7i 1.90422i 0.305751 + 0.952112i $$0.401093\pi$$
−0.305751 + 0.952112i $$0.598907\pi$$
$$524$$ 4.79443e6 0.762797
$$525$$ 0 0
$$526$$ 2.24946e6 0.354499
$$527$$ 4.19430e6i 0.657860i
$$528$$ 0 0
$$529$$ 4.88383e6 0.758789
$$530$$ 652080. + 118560.i 0.100835 + 0.0183336i
$$531$$ 0 0
$$532$$ 5.61216e6i 0.859708i
$$533$$ 1.64023e6i 0.250085i
$$534$$ 0 0
$$535$$ −423420. + 2.32881e6i −0.0639568 + 0.351763i
$$536$$ 2.05427e6 0.308849
$$537$$ 0 0
$$538$$ 1.46628e6i 0.218404i
$$539$$ −1.20724e6 −0.178986
$$540$$ 0 0
$$541$$ 4.07630e6 0.598788 0.299394 0.954130i $$-0.403215\pi$$
0.299394 + 0.954130i $$0.403215\pi$$
$$542$$ 4.64301e6i 0.678893i
$$543$$ 0 0
$$544$$ 2.09715e6 0.303831
$$545$$ −1.97945e6 359900.i −0.285465 0.0519028i
$$546$$ 0 0
$$547$$ 1.23680e7i 1.76739i −0.468065 0.883694i $$-0.655049\pi$$
0.468065 0.883694i $$-0.344951\pi$$
$$548$$ 1.72685e6i 0.245642i
$$549$$ 0 0
$$550$$ 651200. 1.73160e6i 0.0917926 0.244085i
$$551$$ 599400. 0.0841081
$$552$$ 0 0
$$553$$ 5.57424e6i 0.775127i
$$554$$ 1.00600e7 1.39260
$$555$$ 0 0
$$556$$ −3.14336e6 −0.431228
$$557$$ 130308.i 0.0177964i 0.999960 + 0.00889822i $$0.00283243\pi$$
−0.999960 + 0.00889822i $$0.997168\pi$$
$$558$$ 0 0
$$559$$ −1.56910e6 −0.212383
$$560$$ −404480. + 2.22464e6i −0.0545038 + 0.299771i
$$561$$ 0 0
$$562$$ 8.34401e6i 1.11438i
$$563$$ 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
$$566$$ −8.95210e6 −1.17458
$$567$$ 0 0
$$568$$ 271872.i 0.0353585i
$$569$$ −9.03013e6 −1.16927 −0.584633 0.811298i $$-0.698761\pi$$
−0.584633 + 0.811298i $$0.698761\pi$$
$$570$$ 0 0
$$571$$ −1.07093e7 −1.37459 −0.687294 0.726379i $$-0.741202\pi$$
−0.687294 + 0.726379i $$0.741202\pi$$
$$572$$ 1.61971e6i 0.206989i
$$573$$ 0 0
$$574$$ −1.51554e6 −0.191994
$$575$$ −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 $$0.975687\pi$$
$$578$$ 1.10978e7i 1.38171i
$$579$$ 0 0
$$580$$ −237600. 43200.0i −0.0293276 0.00533229i
$$581$$ 4.39651e6 0.540341
$$582$$ 0 0
$$583$$ 438672.i 0.0534526i
$$584$$ −1.92666e6 −0.233761
$$585$$ 0 0
$$586$$ 3.90302e6 0.469523
$$587$$ 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
$$590$$ 1.58960e6 8.74280e6i 0.188000 1.03400i
$$591$$ 0 0
$$592$$ 1.11923e6i 0.131255i
$$593$$ 8.52014e6i 0.994970i −0.867472 0.497485i $$-0.834257\pi$$
0.867472 0.497485i $$-0.165743\pi$$
$$594$$ 0 0
$$595$$ −1.77971e7 3.23584e6i −2.06090 0.374709i
$$596$$ −2.22160e6 −0.256183
$$597$$ 0 0
$$598$$ 3.40906e6i 0.389835i
$$599$$ 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 $$0.395170\pi$$
$$602$$ 1.44981e6i 0.163049i
$$603$$ 0 0
$$604$$ −6.65843e6 −0.742642
$$605$$ 7.65308e6 + 1.39147e6i 0.850057 + 0.154556i
$$606$$ 0 0
$$607$$ 8.79924e6i 0.969334i 0.874699 + 0.484667i $$0.161059\pi$$
−0.874699 + 0.484667i $$0.838941\pi$$
$$608$$ 2.27328e6i 0.249399i
$$609$$ 0 0
$$610$$ 1.69192e6 9.30556e6i 0.184101 1.01255i
$$611$$ 7.30649e6 0.791782
$$612$$ 0 0
$$613$$ 1.03408e6i 0.111149i 0.998455 + 0.0555744i $$0.0176990\pi$$
−0.998455 + 0.0555744i $$0.982301\pi$$
$$614$$ −351432. −0.0376201
$$615$$ 0 0
$$616$$ 1.49658e6 0.158908
$$617$$ 1.29854e7i 1.37323i 0.727020 + 0.686616i $$0.240905\pi$$
−0.727020 + 0.686616i $$0.759095\pi$$
$$618$$ 0 0
$$619$$ −7.92002e6 −0.830806 −0.415403 0.909637i $$-0.636359\pi$$
−0.415403 + 0.909637i $$0.636359\pi$$
$$620$$ −1.80224e6 327680.i −0.188293 0.0342350i
$$621$$ 0 0
$$622$$ 2.39741e6i 0.248465i
$$623$$ 1.34632e7i 1.38972i
$$624$$ 0 0
$$625$$ 7.34562e6 + 6.43500e6i 0.752192 + 0.658944i
$$626$$ −8.37366e6 −0.854043
$$627$$ 0 0
$$628$$ 6.92973e6i 0.701160i
$$629$$ −8.95386e6 −0.902368
$$630$$ 0 0
$$631$$ 1.68218e7 1.68189 0.840945 0.541120i $$-0.181999\pi$$
0.840945 + 0.541120i $$0.181999\pi$$
$$632$$ 2.25792e6i 0.224862i
$$633$$ 0 0
$$634$$ −9.66501e6 −0.954947
$$635$$ −1.75238e6 + 9.63809e6i −0.172462 + 0.948542i
$$636$$ 0 0
$$637$$ 5.57939e6i 0.544801i
$$638$$ 159840.i 0.0155465i
$$639$$ 0 0
$$640$$ 163840. 901120.i 0.0158114 0.0869626i
$$641$$ 1.55154e7 1.49148 0.745741 0.666236i $$-0.232096\pi$$
0.745741 + 0.666236i $$0.232096\pi$$
$$642$$ 0 0
$$643$$ 1.05801e7i 1.00916i 0.863364 + 0.504582i $$0.168354\pi$$
−0.863364 + 0.504582i $$0.831646\pi$$
$$644$$ −3.14989e6 −0.299282
$$645$$ 0 0
$$646$$ −1.81862e7 −1.71460
$$647$$ 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
$$650$$ 8.00280e6 + 3.00960e6i 0.742948 + 0.279399i
$$651$$ 0 0
$$652$$ 2.38614e6i 0.219825i
$$653$$ 1.58924e6i 0.145850i 0.997337 + 0.0729248i $$0.0232333\pi$$
−0.997337 + 0.0729248i $$0.976767\pi$$
$$654$$ 0 0
$$655$$ 1.64809e7 + 2.99652e6i 1.50099 + 0.272907i
$$656$$ 613888. 0.0556967
$$657$$ 0 0
$$658$$ 6.75102e6i 0.607862i
$$659$$ −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 $$0.406525\pi$$
$$662$$ 6.56379e6i 0.582116i
$$663$$ 0 0
$$664$$ −1.78086e6 −0.156751
$$665$$ 3.50760e6 1.92918e7i 0.307578 1.69168i
$$666$$ 0 0
$$667$$ 336420.i 0.0292797i
$$668$$ 8.95363e6i 0.776351i
$$669$$ 0 0
$$670$$ 7.06156e6 + 1.28392e6i 0.607734 + 0.110497i
$$671$$ −6.26010e6 −0.536754
$$672$$ 0 0
$$673$$ 2.17810e6i 0.185370i −0.995695 0.0926850i $$-0.970455\pi$$
0.995695 0.0926850i $$-0.0295449\pi$$
$$674$$ −8.75091e6 −0.741999
$$675$$ 0 0
$$676$$ 1.54501e6 0.130036
$$677$$ 3.98419e6i 0.334094i 0.985949 + 0.167047i $$0.0534231\pi$$
−0.985949 + 0.167047i $$0.946577\pi$$
$$678$$ 0 0
$$679$$ 1.53627e7 1.27877
$$680$$ 7.20896e6 + 1.31072e6i 0.597861 + 0.108702i
$$681$$ 0 0
$$682$$ 1.21242e6i 0.0998138i
$$683$$ 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
$$686$$ −5.46680e6 −0.443530
$$687$$ 0 0
$$688$$ 587264.i 0.0473001i
$$689$$ 2.02738e6 0.162700
$$690$$ 0 0
$$691$$ −1.55471e7 −1.23867 −0.619335 0.785127i $$-0.712598\pi$$
−0.619335 + 0.785127i $$0.712598\pi$$
$$692$$ 5.50086e6i 0.436682i
$$693$$ 0 0
$$694$$ 1.09801e7 0.865379
$$695$$ −1.08053e7 1.96460e6i −0.848545 0.154281i
$$696$$ 0 0
$$697$$ 4.91110e6i 0.382910i
$$698$$ 1.06046e7i 0.823864i
$$699$$ 0 0
$$700$$ −2.78080e6 + 7.39440e6i −0.214499 + 0.570372i
$$701$$ 2.27103e7 1.74553 0.872766 0.488139i $$-0.162324\pi$$
0.872766 + 0.488139i $$0.162324\pi$$
$$702$$ 0 0
$$703$$ 9.70584e6i 0.740704i
$$704$$ −606208. −0.0460988
$$705$$ 0 0
$$706$$ −1.22307e7 −0.923502
$$707$$ 679084.i 0.0510946i
$$708$$ 0 0
$$709$$ −6.29841e6 −0.470560 −0.235280 0.971928i $$-0.575601\pi$$
−0.235280 + 0.971928i $$0.575601\pi$$
$$710$$ −169920. + 934560.i −0.0126502 + 0.0695763i
$$711$$ 0 0
$$712$$ 5.45344e6i 0.403154i
$$713$$ 2.55181e6i 0.187985i
$$714$$ 0 0
$$715$$ 1.01232e6 5.56776e6i 0.0740547 0.407301i
$$716$$ −383680. −0.0279696
$$717$$ 0 0
$$718$$ 1.51742e7i 1.09849i
$$719$$ 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
$$722$$ 9.80920e6i 0.700311i
$$723$$ 0 0
$$724$$ 1.04304e7 0.739526
$$725$$ −789750. 297000.i −0.0558013 0.0209851i
$$726$$ 0 0
$$727$$ 1.35610e7i 0.951605i −0.879552 0.475803i $$-0.842158\pi$$
0.879552 0.475803i $$-0.157842\pi$$
$$728$$ 6.91661e6i 0.483687i
$$729$$ 0 0
$$730$$ −6.62288e6 1.20416e6i −0.459981 0.0836329i
$$731$$ −4.69811e6 −0.325185
$$732$$ 0 0
$$733$$ 2.69413e7i 1.85208i 0.377429 + 0.926038i $$0.376808\pi$$
−0.377429 + 0.926038i $$0.623192\pi$$
$$734$$ 1.24424e7 0.852441
$$735$$ 0 0
$$736$$ 1.27590e6 0.0868207
$$737$$ 4.75050e6i 0.322160i
$$738$$ 0 0
$$739$$ −2.77414e6 −0.186860 −0.0934302 0.995626i $$-0.529783\pi$$
−0.0934302 + 0.995626i $$0.529783\pi$$
$$740$$ −699520. + 3.84736e6i −0.0469592 + 0.258276i
$$741$$ 0 0
$$742$$ 1.87325e6i 0.124907i
$$743$$ 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
$$746$$ −5.66078e6 −0.372417
$$747$$ 0 0
$$748$$ 4.84966e6i 0.316926i
$$749$$ −6.69004e6 −0.435736
$$750$$ 0 0
$$751$$ −2.19285e6 −0.141876 −0.0709380 0.997481i $$-0.522599\pi$$
−0.0709380 + 0.997481i $$0.522599\pi$$
$$752$$ 2.73459e6i 0.176339i
$$753$$ 0 0
$$754$$ −738720. −0.0473207
$$755$$ −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 $$0.902722\pi$$
$$758$$ 1.56105e7i 0.986832i
$$759$$ 0 0
$$760$$ −1.42080e6 + 7.81440e6i −0.0892275 + 0.490752i
$$761$$ −9.69580e6 −0.606907 −0.303453 0.952846i $$-0.598140\pi$$
−0.303453 + 0.952846i $$0.598140\pi$$
$$762$$ 0 0
$$763$$ 5.68642e6i 0.353612i
$$764$$ 3.24403e6 0.201072
$$765$$ 0 0
$$766$$ −2.78270e6 −0.171354
$$767$$ 2.71822e7i 1.66838i
$$768$$ 0 0
$$769$$ −9.32787e6 −0.568809 −0.284405 0.958704i $$-0.591796\pi$$
−0.284405 + 0.958704i $$0.591796\pi$$
$$770$$ 5.14448e6 + 935360.i 0.312690 + 0.0568528i
$$771$$ 0 0
$$772$$ 7.24250e6i 0.437366i
$$773$$ 9.68080e6i 0.582723i 0.956613 + 0.291362i $$0.0941083\pi$$
−0.956613 + 0.291362i $$0.905892\pi$$
$$774$$ 0 0
$$775$$ −5.99040e6 2.25280e6i −0.358263 0.134731i
$$776$$ −6.22285e6 −0.370967
$$777$$ 0 0
$$778$$ 1.99316e6i 0.118057i
$$779$$ −5.32356e6 −0.314310
$$780$$ 0 0
$$781$$ 628704. 0.0368824
$$782$$ 1.02072e7i 0.596886i
$$783$$ 0 0
$$784$$ −2.08819e6 −0.121333
$$785$$ −4.33108e6 + 2.38209e7i −0.250855 + 1.37970i
$$786$$ 0 0
$$787$$ 5.52302e6i 0.317863i 0.987290 + 0.158931i $$0.0508049\pi$$
−0.987290 + 0.158931i $$0.949195\pi$$
$$788$$ 5.39949e6i 0.309768i
$$789$$ 0 0
$$790$$ 1.41120e6 7.76160e6i 0.0804490 0.442470i
$$791$$ 3.61529e7 2.05448
$$792$$ 0 0
$$793$$ 2.89318e7i 1.63378i
$$794$$ −4.38267e6 −0.246711
$$795$$ 0 0
$$796$$ −8.97600e6 −0.502112
$$797$$ 1.71119e7i 0.954230i −0.878841 0.477115i $$-0.841682\pi$$
0.878841 0.477115i $$-0.158318\pi$$
$$798$$ 0 0
$$799$$ 2.18767e7 1.21232
$$800$$ 1.12640e6 2.99520e6i 0.0622254 0.165463i
$$801$$ 0 0
$$802$$ 9.96639e6i 0.547145i
$$803$$ 4.45539e6i 0.243836i
$$804$$ 0