# Properties

 Label 320.6.f.b.289.6 Level 320 Weight 6 Character 320.289 Analytic conductor 51.323 Analytic rank 0 Dimension 8 CM no Inner twists 8

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 320.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$51.3228223402$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.73499483897856.45 Defining polynomial: $$x^{8} - 3721 x^{4} + 13845841$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{10}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 289.6 Root $$7.54412 - 2.02144i$$ of defining polynomial Character $$\chi$$ $$=$$ 320.289 Dual form 320.6.f.b.289.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+19.1311 q^{3} +(-55.2268 + 8.66025i) q^{5} -121.499i q^{7} +123.000 q^{9} +O(q^{10})$$ $$q+19.1311 q^{3} +(-55.2268 + 8.66025i) q^{5} -121.499i q^{7} +123.000 q^{9} +298.000i q^{11} +485.996 q^{13} +(-1056.55 + 165.680i) q^{15} +420.885i q^{17} +2574.00i q^{19} -2324.41i q^{21} -717.948i q^{23} +(2975.00 - 956.556i) q^{25} -2295.74 q^{27} -3734.30i q^{29} +6228.45 q^{31} +5701.08i q^{33} +(1052.21 + 6710.00i) q^{35} +5721.50 q^{37} +9297.65 q^{39} +11396.0 q^{41} +19150.3 q^{43} +(-6792.90 + 1065.21i) q^{45} +2286.39i q^{47} +2045.00 q^{49} +8052.00i q^{51} +17230.8 q^{53} +(-2580.76 - 16457.6i) q^{55} +49243.5i q^{57} -16378.0i q^{59} +48736.4i q^{61} -14944.4i q^{63} +(-26840.0 + 4208.85i) q^{65} +8398.56 q^{67} -13735.2i q^{69} -29091.5 q^{71} +420.885i q^{73} +(56915.1 - 18300.0i) q^{75} +36206.7 q^{77} -31170.0 q^{79} -73809.0 q^{81} +106273. q^{83} +(-3644.97 - 23244.1i) q^{85} -71441.4i q^{87} -99362.0 q^{89} -59048.0i q^{91} +119157. q^{93} +(-22291.5 - 142154. i) q^{95} +180330. i q^{97} +36654.0i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 984q^{9} + O(q^{10})$$ $$8q + 984q^{9} + 23800q^{25} + 91168q^{41} + 16360q^{49} - 214720q^{65} - 590472q^{81} - 794896q^{89} + O(q^{100})$$

## Character values

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

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 19.1311 1.22726 0.613631 0.789593i $$-0.289708\pi$$
0.613631 + 0.789593i $$0.289708\pi$$
$$4$$ 0 0
$$5$$ −55.2268 + 8.66025i −0.987927 + 0.154919i
$$6$$ 0 0
$$7$$ 121.499i 0.937190i −0.883413 0.468595i $$-0.844760\pi$$
0.883413 0.468595i $$-0.155240\pi$$
$$8$$ 0 0
$$9$$ 123.000 0.506173
$$10$$ 0 0
$$11$$ 298.000i 0.742565i 0.928520 + 0.371283i $$0.121082\pi$$
−0.928520 + 0.371283i $$0.878918\pi$$
$$12$$ 0 0
$$13$$ 485.996 0.797580 0.398790 0.917042i $$-0.369430\pi$$
0.398790 + 0.917042i $$0.369430\pi$$
$$14$$ 0 0
$$15$$ −1056.55 + 165.680i −1.21245 + 0.190127i
$$16$$ 0 0
$$17$$ 420.885i 0.353216i 0.984281 + 0.176608i $$0.0565126\pi$$
−0.984281 + 0.176608i $$0.943487\pi$$
$$18$$ 0 0
$$19$$ 2574.00i 1.63578i 0.575376 + 0.817889i $$0.304856\pi$$
−0.575376 + 0.817889i $$0.695144\pi$$
$$20$$ 0 0
$$21$$ 2324.41i 1.15018i
$$22$$ 0 0
$$23$$ 717.948i 0.282992i −0.989939 0.141496i $$-0.954809\pi$$
0.989939 0.141496i $$-0.0451912\pi$$
$$24$$ 0 0
$$25$$ 2975.00 956.556i 0.952000 0.306098i
$$26$$ 0 0
$$27$$ −2295.74 −0.606055
$$28$$ 0 0
$$29$$ 3734.30i 0.824545i −0.911061 0.412273i $$-0.864735\pi$$
0.911061 0.412273i $$-0.135265\pi$$
$$30$$ 0 0
$$31$$ 6228.45 1.16406 0.582031 0.813167i $$-0.302258\pi$$
0.582031 + 0.813167i $$0.302258\pi$$
$$32$$ 0 0
$$33$$ 5701.08i 0.911322i
$$34$$ 0 0
$$35$$ 1052.21 + 6710.00i 0.145189 + 0.925875i
$$36$$ 0 0
$$37$$ 5721.50 0.687077 0.343538 0.939139i $$-0.388374\pi$$
0.343538 + 0.939139i $$0.388374\pi$$
$$38$$ 0 0
$$39$$ 9297.65 0.978840
$$40$$ 0 0
$$41$$ 11396.0 1.05875 0.529374 0.848388i $$-0.322427\pi$$
0.529374 + 0.848388i $$0.322427\pi$$
$$42$$ 0 0
$$43$$ 19150.3 1.57944 0.789721 0.613467i $$-0.210225\pi$$
0.789721 + 0.613467i $$0.210225\pi$$
$$44$$ 0 0
$$45$$ −6792.90 + 1065.21i −0.500062 + 0.0784160i
$$46$$ 0 0
$$47$$ 2286.39i 0.150975i 0.997147 + 0.0754876i $$0.0240513\pi$$
−0.997147 + 0.0754876i $$0.975949\pi$$
$$48$$ 0 0
$$49$$ 2045.00 0.121675
$$50$$ 0 0
$$51$$ 8052.00i 0.433489i
$$52$$ 0 0
$$53$$ 17230.8 0.842587 0.421294 0.906924i $$-0.361576\pi$$
0.421294 + 0.906924i $$0.361576\pi$$
$$54$$ 0 0
$$55$$ −2580.76 16457.6i −0.115038 0.733600i
$$56$$ 0 0
$$57$$ 49243.5i 2.00753i
$$58$$ 0 0
$$59$$ 16378.0i 0.612535i −0.951946 0.306267i $$-0.900920\pi$$
0.951946 0.306267i $$-0.0990802\pi$$
$$60$$ 0 0
$$61$$ 48736.4i 1.67699i 0.544913 + 0.838493i $$0.316563\pi$$
−0.544913 + 0.838493i $$0.683437\pi$$
$$62$$ 0 0
$$63$$ 14944.4i 0.474380i
$$64$$ 0 0
$$65$$ −26840.0 + 4208.85i −0.787951 + 0.123561i
$$66$$ 0 0
$$67$$ 8398.56 0.228569 0.114285 0.993448i $$-0.463542\pi$$
0.114285 + 0.993448i $$0.463542\pi$$
$$68$$ 0 0
$$69$$ 13735.2i 0.347305i
$$70$$ 0 0
$$71$$ −29091.5 −0.684890 −0.342445 0.939538i $$-0.611255\pi$$
−0.342445 + 0.939538i $$0.611255\pi$$
$$72$$ 0 0
$$73$$ 420.885i 0.00924392i 0.999989 + 0.00462196i $$0.00147122\pi$$
−0.999989 + 0.00462196i $$0.998529\pi$$
$$74$$ 0 0
$$75$$ 56915.1 18300.0i 1.16835 0.375663i
$$76$$ 0 0
$$77$$ 36206.7 0.695924
$$78$$ 0 0
$$79$$ −31170.0 −0.561913 −0.280956 0.959721i $$-0.590652\pi$$
−0.280956 + 0.959721i $$0.590652\pi$$
$$80$$ 0 0
$$81$$ −73809.0 −1.24996
$$82$$ 0 0
$$83$$ 106273. 1.69328 0.846641 0.532164i $$-0.178621\pi$$
0.846641 + 0.532164i $$0.178621\pi$$
$$84$$ 0 0
$$85$$ −3644.97 23244.1i −0.0547201 0.348952i
$$86$$ 0 0
$$87$$ 71441.4i 1.01193i
$$88$$ 0 0
$$89$$ −99362.0 −1.32967 −0.664837 0.746988i $$-0.731499\pi$$
−0.664837 + 0.746988i $$0.731499\pi$$
$$90$$ 0 0
$$91$$ 59048.0i 0.747484i
$$92$$ 0 0
$$93$$ 119157. 1.42861
$$94$$ 0 0
$$95$$ −22291.5 142154.i −0.253414 1.61603i
$$96$$ 0 0
$$97$$ 180330.i 1.94598i 0.230845 + 0.972991i $$0.425851\pi$$
−0.230845 + 0.972991i $$0.574149\pi$$
$$98$$ 0 0
$$99$$ 36654.0i 0.375866i
$$100$$ 0 0
$$101$$ 136340.i 1.32990i −0.746886 0.664952i $$-0.768452\pi$$
0.746886 0.664952i $$-0.231548\pi$$
$$102$$ 0 0
$$103$$ 98557.8i 0.915372i 0.889114 + 0.457686i $$0.151322\pi$$
−0.889114 + 0.457686i $$0.848678\pi$$
$$104$$ 0 0
$$105$$ 20130.0 + 128370.i 0.178185 + 1.13629i
$$106$$ 0 0
$$107$$ 107115. 0.904465 0.452232 0.891900i $$-0.350628\pi$$
0.452232 + 0.891900i $$0.350628\pi$$
$$108$$ 0 0
$$109$$ 234766.i 1.89264i 0.323230 + 0.946321i $$0.395231\pi$$
−0.323230 + 0.946321i $$0.604769\pi$$
$$110$$ 0 0
$$111$$ 109459. 0.843224
$$112$$ 0 0
$$113$$ 27548.8i 0.202958i 0.994838 + 0.101479i $$0.0323575\pi$$
−0.994838 + 0.101479i $$0.967642\pi$$
$$114$$ 0 0
$$115$$ 6217.62 + 39650.0i 0.0438409 + 0.279575i
$$116$$ 0 0
$$117$$ 59777.5 0.403713
$$118$$ 0 0
$$119$$ 51137.1 0.331031
$$120$$ 0 0
$$121$$ 72247.0 0.448597
$$122$$ 0 0
$$123$$ 218018. 1.29936
$$124$$ 0 0
$$125$$ −156016. + 78591.8i −0.893086 + 0.449886i
$$126$$ 0 0
$$127$$ 160986.i 0.885685i −0.896599 0.442842i $$-0.853970\pi$$
0.896599 0.442842i $$-0.146030\pi$$
$$128$$ 0 0
$$129$$ 366366. 1.93839
$$130$$ 0 0
$$131$$ 194590.i 0.990700i 0.868693 + 0.495350i $$0.164960\pi$$
−0.868693 + 0.495350i $$0.835040\pi$$
$$132$$ 0 0
$$133$$ 312738. 1.53303
$$134$$ 0 0
$$135$$ 126786. 19881.6i 0.598739 0.0938897i
$$136$$ 0 0
$$137$$ 26707.1i 0.121569i 0.998151 + 0.0607847i $$0.0193603\pi$$
−0.998151 + 0.0607847i $$0.980640\pi$$
$$138$$ 0 0
$$139$$ 140690.i 0.617627i 0.951123 + 0.308813i $$0.0999319\pi$$
−0.951123 + 0.308813i $$0.900068\pi$$
$$140$$ 0 0
$$141$$ 43741.2i 0.185286i
$$142$$ 0 0
$$143$$ 144827.i 0.592255i
$$144$$ 0 0
$$145$$ 32340.0 + 206234.i 0.127738 + 0.814590i
$$146$$ 0 0
$$147$$ 39123.2 0.149328
$$148$$ 0 0
$$149$$ 329343.i 1.21530i −0.794206 0.607648i $$-0.792113\pi$$
0.794206 0.607648i $$-0.207887\pi$$
$$150$$ 0 0
$$151$$ −134282. −0.479266 −0.239633 0.970864i $$-0.577027\pi$$
−0.239633 + 0.970864i $$0.577027\pi$$
$$152$$ 0 0
$$153$$ 51768.8i 0.178789i
$$154$$ 0 0
$$155$$ −343978. + 53940.0i −1.15001 + 0.180336i
$$156$$ 0 0
$$157$$ −413958. −1.34032 −0.670158 0.742218i $$-0.733774\pi$$
−0.670158 + 0.742218i $$0.733774\pi$$
$$158$$ 0 0
$$159$$ 329644. 1.03408
$$160$$ 0 0
$$161$$ −87230.0 −0.265217
$$162$$ 0 0
$$163$$ 298618. 0.880332 0.440166 0.897916i $$-0.354920\pi$$
0.440166 + 0.897916i $$0.354920\pi$$
$$164$$ 0 0
$$165$$ −49372.8 314852.i −0.141181 0.900320i
$$166$$ 0 0
$$167$$ 248708.i 0.690080i −0.938588 0.345040i $$-0.887865\pi$$
0.938588 0.345040i $$-0.112135\pi$$
$$168$$ 0 0
$$169$$ −135101. −0.363866
$$170$$ 0 0
$$171$$ 316602.i 0.827987i
$$172$$ 0 0
$$173$$ 751593. 1.90927 0.954635 0.297779i $$-0.0962459\pi$$
0.954635 + 0.297779i $$0.0962459\pi$$
$$174$$ 0 0
$$175$$ −116221. 361459.i −0.286872 0.892205i
$$176$$ 0 0
$$177$$ 313330.i 0.751741i
$$178$$ 0 0
$$179$$ 654422.i 1.52660i −0.646044 0.763300i $$-0.723578\pi$$
0.646044 0.763300i $$-0.276422\pi$$
$$180$$ 0 0
$$181$$ 69025.7i 0.156608i −0.996930 0.0783041i $$-0.975049\pi$$
0.996930 0.0783041i $$-0.0249505\pi$$
$$182$$ 0 0
$$183$$ 932383.i 2.05810i
$$184$$ 0 0
$$185$$ −315980. + 49549.6i −0.678782 + 0.106441i
$$186$$ 0 0
$$187$$ −125424. −0.262286
$$188$$ 0 0
$$189$$ 278929.i 0.567989i
$$190$$ 0 0
$$191$$ −622693. −1.23507 −0.617534 0.786544i $$-0.711868\pi$$
−0.617534 + 0.786544i $$0.711868\pi$$
$$192$$ 0 0
$$193$$ 656159.i 1.26799i −0.773337 0.633995i $$-0.781414\pi$$
0.773337 0.633995i $$-0.218586\pi$$
$$194$$ 0 0
$$195$$ −513479. + 80520.0i −0.967022 + 0.151641i
$$196$$ 0 0
$$197$$ −395601. −0.726259 −0.363129 0.931739i $$-0.618292\pi$$
−0.363129 + 0.931739i $$0.618292\pi$$
$$198$$ 0 0
$$199$$ −2514.94 −0.00450189 −0.00225094 0.999997i $$-0.500716\pi$$
−0.00225094 + 0.999997i $$0.500716\pi$$
$$200$$ 0 0
$$201$$ 160674. 0.280515
$$202$$ 0 0
$$203$$ −453714. −0.772755
$$204$$ 0 0
$$205$$ −629365. + 98692.3i −1.04597 + 0.164021i
$$206$$ 0 0
$$207$$ 88307.7i 0.143243i
$$208$$ 0 0
$$209$$ −767052. −1.21467
$$210$$ 0 0
$$211$$ 1.01981e6i 1.57693i −0.615078 0.788466i $$-0.710875\pi$$
0.615078 0.788466i $$-0.289125\pi$$
$$212$$ 0 0
$$213$$ −556554. −0.840539
$$214$$ 0 0
$$215$$ −1.05761e6 + 165846.i −1.56037 + 0.244686i
$$216$$ 0 0
$$217$$ 756751.i 1.09095i
$$218$$ 0 0
$$219$$ 8052.00i 0.0113447i
$$220$$ 0 0
$$221$$ 204548.i 0.281718i
$$222$$ 0 0
$$223$$ 88462.3i 0.119123i 0.998225 + 0.0595616i $$0.0189703\pi$$
−0.998225 + 0.0595616i $$0.981030\pi$$
$$224$$ 0 0
$$225$$ 365925. 117656.i 0.481877 0.154939i
$$226$$ 0 0
$$227$$ −411836. −0.530468 −0.265234 0.964184i $$-0.585449\pi$$
−0.265234 + 0.964184i $$0.585449\pi$$
$$228$$ 0 0
$$229$$ 1.26328e6i 1.59188i 0.605373 + 0.795942i $$0.293024\pi$$
−0.605373 + 0.795942i $$0.706976\pi$$
$$230$$ 0 0
$$231$$ 692675. 0.854082
$$232$$ 0 0
$$233$$ 1.21341e6i 1.46426i −0.681165 0.732130i $$-0.738526\pi$$
0.681165 0.732130i $$-0.261474\pi$$
$$234$$ 0 0
$$235$$ −19800.7 126270.i −0.0233890 0.149152i
$$236$$ 0 0
$$237$$ −596317. −0.689614
$$238$$ 0 0
$$239$$ 570738. 0.646312 0.323156 0.946346i $$-0.395256\pi$$
0.323156 + 0.946346i $$0.395256\pi$$
$$240$$ 0 0
$$241$$ −724680. −0.803718 −0.401859 0.915702i $$-0.631636\pi$$
−0.401859 + 0.915702i $$0.631636\pi$$
$$242$$ 0 0
$$243$$ −854186. −0.927976
$$244$$ 0 0
$$245$$ −112939. + 17710.2i −0.120207 + 0.0188499i
$$246$$ 0 0
$$247$$ 1.25095e6i 1.30466i
$$248$$ 0 0
$$249$$ 2.03313e6 2.07810
$$250$$ 0 0
$$251$$ 562046.i 0.563103i −0.959546 0.281551i $$-0.909151\pi$$
0.959546 0.281551i $$-0.0908490\pi$$
$$252$$ 0 0
$$253$$ 213949. 0.210140
$$254$$ 0 0
$$255$$ −69732.4 444686.i −0.0671559 0.428256i
$$256$$ 0 0
$$257$$ 453714.i 0.428498i 0.976779 + 0.214249i $$0.0687305\pi$$
−0.976779 + 0.214249i $$0.931270\pi$$
$$258$$ 0 0
$$259$$ 695156.i 0.643921i
$$260$$ 0 0
$$261$$ 459319.i 0.417362i
$$262$$ 0 0
$$263$$ 1.89769e6i 1.69175i 0.533380 + 0.845876i $$0.320921\pi$$
−0.533380 + 0.845876i $$0.679079\pi$$
$$264$$ 0 0
$$265$$ −951600. + 149223.i −0.832415 + 0.130533i
$$266$$ 0 0
$$267$$ −1.90091e6 −1.63186
$$268$$ 0 0
$$269$$ 341612.i 0.287841i −0.989589 0.143921i $$-0.954029\pi$$
0.989589 0.143921i $$-0.0459710\pi$$
$$270$$ 0 0
$$271$$ 528366. 0.437030 0.218515 0.975834i $$-0.429879\pi$$
0.218515 + 0.975834i $$0.429879\pi$$
$$272$$ 0 0
$$273$$ 1.12965e6i 0.917359i
$$274$$ 0 0
$$275$$ 285054. + 886550.i 0.227298 + 0.706922i
$$276$$ 0 0
$$277$$ 691329. 0.541359 0.270680 0.962670i $$-0.412752\pi$$
0.270680 + 0.962670i $$0.412752\pi$$
$$278$$ 0 0
$$279$$ 766100. 0.589217
$$280$$ 0 0
$$281$$ 387728. 0.292928 0.146464 0.989216i $$-0.453211\pi$$
0.146464 + 0.989216i $$0.453211\pi$$
$$282$$ 0 0
$$283$$ 208128. 0.154477 0.0772384 0.997013i $$-0.475390\pi$$
0.0772384 + 0.997013i $$0.475390\pi$$
$$284$$ 0 0
$$285$$ −426461. 2.71956e6i −0.311005 1.98329i
$$286$$ 0 0
$$287$$ 1.38460e6i 0.992248i
$$288$$ 0 0
$$289$$ 1.24271e6 0.875238
$$290$$ 0 0
$$291$$ 3.44992e6i 2.38823i
$$292$$ 0 0
$$293$$ −2.04872e6 −1.39416 −0.697080 0.716993i $$-0.745518\pi$$
−0.697080 + 0.716993i $$0.745518\pi$$
$$294$$ 0 0
$$295$$ 141838. + 904505.i 0.0948935 + 0.605140i
$$296$$ 0 0
$$297$$ 684129.i 0.450036i
$$298$$ 0 0
$$299$$ 348920.i 0.225708i
$$300$$ 0 0
$$301$$ 2.32674e6i 1.48024i
$$302$$ 0 0
$$303$$ 2.60834e6i 1.63214i
$$304$$ 0 0
$$305$$ −422070. 2.69156e6i −0.259797 1.65674i
$$306$$ 0 0
$$307$$ −877755. −0.531530 −0.265765 0.964038i $$-0.585624\pi$$
−0.265765 + 0.964038i $$0.585624\pi$$
$$308$$ 0 0
$$309$$ 1.88552e6i 1.12340i
$$310$$ 0 0
$$311$$ −2.96427e6 −1.73787 −0.868935 0.494926i $$-0.835195\pi$$
−0.868935 + 0.494926i $$0.835195\pi$$
$$312$$ 0 0
$$313$$ 1.58612e6i 0.915116i 0.889180 + 0.457558i $$0.151276\pi$$
−0.889180 + 0.457558i $$0.848724\pi$$
$$314$$ 0 0
$$315$$ 129422. + 825330.i 0.0734906 + 0.468653i
$$316$$ 0 0
$$317$$ 754884. 0.421922 0.210961 0.977494i $$-0.432341\pi$$
0.210961 + 0.977494i $$0.432341\pi$$
$$318$$ 0 0
$$319$$ 1.11282e6 0.612278
$$320$$ 0 0
$$321$$ 2.04923e6 1.11002
$$322$$ 0 0
$$323$$ −1.08336e6 −0.577784
$$324$$ 0 0
$$325$$ 1.44584e6 464882.i 0.759296 0.244138i
$$326$$ 0 0
$$327$$ 4.49133e6i 2.32277i
$$328$$ 0 0
$$329$$ 277794. 0.141492
$$330$$ 0 0
$$331$$ 194226.i 0.0974400i −0.998812 0.0487200i $$-0.984486\pi$$
0.998812 0.0487200i $$-0.0155142\pi$$
$$332$$ 0 0
$$333$$ 703744. 0.347780
$$334$$ 0 0
$$335$$ −463826. + 72733.7i −0.225810 + 0.0354098i
$$336$$ 0 0
$$337$$ 2.47312e6i 1.18623i 0.805116 + 0.593117i $$0.202103\pi$$
−0.805116 + 0.593117i $$0.797897\pi$$
$$338$$ 0 0
$$339$$ 527040.i 0.249083i
$$340$$ 0 0
$$341$$ 1.85608e6i 0.864392i
$$342$$ 0 0
$$343$$ 2.29050e6i 1.05122i
$$344$$ 0 0
$$345$$ 118950. + 758549.i 0.0538043 + 0.343112i
$$346$$ 0 0
$$347$$ 2.39126e6 1.06611 0.533056 0.846080i $$-0.321044\pi$$
0.533056 + 0.846080i $$0.321044\pi$$
$$348$$ 0 0
$$349$$ 2.38607e6i 1.04862i 0.851527 + 0.524311i $$0.175677\pi$$
−0.851527 + 0.524311i $$0.824323\pi$$
$$350$$ 0 0
$$351$$ −1.11572e6 −0.483378
$$352$$ 0 0
$$353$$ 2.80164e6i 1.19667i 0.801245 + 0.598336i $$0.204171\pi$$
−0.801245 + 0.598336i $$0.795829\pi$$
$$354$$ 0 0
$$355$$ 1.60663e6 251940.i 0.676621 0.106103i
$$356$$ 0 0
$$357$$ 978310. 0.406262
$$358$$ 0 0
$$359$$ 4.18973e6 1.71574 0.857868 0.513871i $$-0.171789\pi$$
0.857868 + 0.513871i $$0.171789\pi$$
$$360$$ 0 0
$$361$$ −4.14938e6 −1.67577
$$362$$ 0 0
$$363$$ 1.38217e6 0.550546
$$364$$ 0 0
$$365$$ −3644.97 23244.1i −0.00143206 0.00913232i
$$366$$ 0 0
$$367$$ 3.46783e6i 1.34398i −0.740560 0.671991i $$-0.765439\pi$$
0.740560 0.671991i $$-0.234561\pi$$
$$368$$ 0 0
$$369$$ 1.40171e6 0.535910
$$370$$ 0 0
$$371$$ 2.09352e6i 0.789664i
$$372$$ 0 0
$$373$$ −1.84265e6 −0.685759 −0.342880 0.939379i $$-0.611402\pi$$
−0.342880 + 0.939379i $$0.611402\pi$$
$$374$$ 0 0
$$375$$ −2.98476e6 + 1.50355e6i −1.09605 + 0.552128i
$$376$$ 0 0
$$377$$ 1.81486e6i 0.657641i
$$378$$ 0 0
$$379$$ 3.94721e6i 1.41154i −0.708443 0.705768i $$-0.750602\pi$$
0.708443 0.705768i $$-0.249398\pi$$
$$380$$ 0 0
$$381$$ 3.07985e6i 1.08697i
$$382$$ 0 0
$$383$$ 4.51953e6i 1.57433i −0.616741 0.787166i $$-0.711547\pi$$
0.616741 0.787166i $$-0.288453\pi$$
$$384$$ 0 0
$$385$$ −1.99958e6 + 313559.i −0.687523 + 0.107812i
$$386$$ 0 0
$$387$$ 2.35548e6 0.799470
$$388$$ 0 0
$$389$$ 5.72440e6i 1.91803i 0.283353 + 0.959016i $$0.408553\pi$$
−0.283353 + 0.959016i $$0.591447\pi$$
$$390$$ 0 0
$$391$$ 302174. 0.0999573
$$392$$ 0 0
$$393$$ 3.72273e6i 1.21585i
$$394$$ 0 0
$$395$$ 1.72142e6 269940.i 0.555129 0.0870511i
$$396$$ 0 0
$$397$$ 1.58558e6 0.504909 0.252454 0.967609i $$-0.418762\pi$$
0.252454 + 0.967609i $$0.418762\pi$$
$$398$$ 0 0
$$399$$ 5.98304e6 1.88144
$$400$$ 0 0
$$401$$ −3.73054e6 −1.15854 −0.579269 0.815136i $$-0.696662\pi$$
−0.579269 + 0.815136i $$0.696662\pi$$
$$402$$ 0 0
$$403$$ 3.02700e6 0.928432
$$404$$ 0 0
$$405$$ 4.07624e6 639205.i 1.23487 0.193643i
$$406$$ 0 0
$$407$$ 1.70501e6i 0.510199i
$$408$$ 0 0
$$409$$ −2.02334e6 −0.598082 −0.299041 0.954240i $$-0.596667\pi$$
−0.299041 + 0.954240i $$0.596667\pi$$
$$410$$ 0 0
$$411$$ 510936.i 0.149198i
$$412$$ 0 0
$$413$$ −1.98991e6 −0.574061
$$414$$ 0 0
$$415$$ −5.86914e6 + 920355.i −1.67284 + 0.262322i
$$416$$ 0 0
$$417$$ 2.69156e6i 0.757990i
$$418$$ 0 0
$$419$$ 5.38701e6i 1.49904i −0.661983 0.749519i $$-0.730285\pi$$
0.661983 0.749519i $$-0.269715\pi$$
$$420$$ 0 0
$$421$$ 1.52112e6i 0.418271i −0.977887 0.209135i $$-0.932935\pi$$
0.977887 0.209135i $$-0.0670650\pi$$
$$422$$ 0 0
$$423$$ 281226.i 0.0764195i
$$424$$ 0 0
$$425$$ 402600. + 1.25213e6i 0.108119 + 0.336262i
$$426$$ 0 0
$$427$$ 5.92143e6 1.57165
$$428$$ 0 0
$$429$$ 2.77070e6i 0.726852i
$$430$$ 0 0
$$431$$ 837627. 0.217199 0.108599 0.994086i $$-0.465363\pi$$
0.108599 + 0.994086i $$0.465363\pi$$
$$432$$ 0 0
$$433$$ 2.25277e6i 0.577426i 0.957416 + 0.288713i $$0.0932274\pi$$
−0.957416 + 0.288713i $$0.906773\pi$$
$$434$$ 0 0
$$435$$ 618701. + 3.94548e6i 0.156768 + 0.999716i
$$436$$ 0 0
$$437$$ 1.84800e6 0.462912
$$438$$ 0 0
$$439$$ −1.39465e6 −0.345385 −0.172692 0.984976i $$-0.555247\pi$$
−0.172692 + 0.984976i $$0.555247\pi$$
$$440$$ 0 0
$$441$$ 251535. 0.0615888
$$442$$ 0 0
$$443$$ −5.67982e6 −1.37507 −0.687536 0.726150i $$-0.741308\pi$$
−0.687536 + 0.726150i $$0.741308\pi$$
$$444$$ 0 0
$$445$$ 5.48745e6 860500.i 1.31362 0.205992i
$$446$$ 0 0
$$447$$ 6.30069e6i 1.49149i
$$448$$ 0 0
$$449$$ 4.07534e6 0.953998 0.476999 0.878904i $$-0.341724\pi$$
0.476999 + 0.878904i $$0.341724\pi$$
$$450$$ 0 0
$$451$$ 3.39601e6i 0.786190i
$$452$$ 0 0
$$453$$ −2.56897e6 −0.588185
$$454$$ 0 0
$$455$$ 511371. + 3.26103e6i 0.115800 + 0.738459i
$$456$$ 0 0
$$457$$ 2.22059e6i 0.497368i −0.968585 0.248684i $$-0.920002\pi$$
0.968585 0.248684i $$-0.0799980\pi$$
$$458$$ 0 0
$$459$$ 966240.i 0.214069i
$$460$$ 0 0
$$461$$ 2.18822e6i 0.479556i 0.970828 + 0.239778i $$0.0770747\pi$$
−0.970828 + 0.239778i $$0.922925\pi$$
$$462$$ 0 0
$$463$$ 8.23618e6i 1.78556i −0.450497 0.892778i $$-0.648753\pi$$
0.450497 0.892778i $$-0.351247\pi$$
$$464$$ 0 0
$$465$$ −6.58068e6 + 1.03193e6i −1.41136 + 0.221319i
$$466$$ 0 0
$$467$$ 4.79680e6 1.01779 0.508897 0.860827i $$-0.330053\pi$$
0.508897 + 0.860827i $$0.330053\pi$$
$$468$$ 0 0
$$469$$ 1.02042e6i 0.214213i
$$470$$ 0 0
$$471$$ −7.91948e6 −1.64492
$$472$$ 0 0
$$473$$ 5.70678e6i 1.17284i
$$474$$ 0 0
$$475$$ 2.46218e6 + 7.65765e6i 0.500709 + 1.55726i
$$476$$ 0 0
$$477$$ 2.11938e6 0.426495
$$478$$ 0 0
$$479$$ 3.41529e6 0.680124 0.340062 0.940403i $$-0.389552\pi$$
0.340062 + 0.940403i $$0.389552\pi$$
$$480$$ 0 0
$$481$$ 2.78062e6 0.547999
$$482$$ 0 0
$$483$$ −1.66881e6 −0.325491
$$484$$ 0 0
$$485$$ −1.56170e6 9.95905e6i −0.301470 1.92249i
$$486$$ 0 0
$$487$$ 922166.i 0.176192i 0.996112 + 0.0880961i $$0.0280783\pi$$
−0.996112 + 0.0880961i $$0.971922\pi$$
$$488$$ 0 0
$$489$$ 5.71289e6 1.08040
$$490$$ 0 0
$$491$$ 5.75918e6i 1.07810i 0.842275 + 0.539048i $$0.181216\pi$$
−0.842275 + 0.539048i $$0.818784\pi$$
$$492$$ 0 0
$$493$$ 1.57171e6 0.291243
$$494$$ 0 0
$$495$$ −317433. 2.02428e6i −0.0582290 0.371329i
$$496$$ 0 0
$$497$$ 3.53459e6i 0.641872i
$$498$$ 0 0
$$499$$ 4.04215e6i 0.726709i 0.931651 + 0.363355i $$0.118369\pi$$
−0.931651 + 0.363355i $$0.881631\pi$$
$$500$$ 0 0
$$501$$ 4.75807e6i 0.846909i
$$502$$ 0 0
$$503$$ 6.42790e6i 1.13279i 0.824134 + 0.566395i $$0.191662\pi$$
−0.824134 + 0.566395i $$0.808338\pi$$
$$504$$ 0 0
$$505$$ 1.18074e6 + 7.52963e6i 0.206028 + 1.31385i
$$506$$ 0 0
$$507$$ −2.58463e6 −0.446559
$$508$$ 0 0
$$509$$ 8.67839e6i 1.48472i 0.670001 + 0.742360i $$0.266293\pi$$
−0.670001 + 0.742360i $$0.733707\pi$$
$$510$$ 0 0
$$511$$ 51137.1 0.00866330
$$512$$ 0 0
$$513$$ 5.90922e6i 0.991373i
$$514$$ 0 0
$$515$$ −853535. 5.44303e6i −0.141809 0.904321i
$$516$$ 0 0
$$517$$ −681344. −0.112109
$$518$$ 0 0
$$519$$ 1.43788e7 2.34317
$$520$$ 0 0
$$521$$ 4.06563e6 0.656197 0.328098 0.944644i $$-0.393592\pi$$
0.328098 + 0.944644i $$0.393592\pi$$
$$522$$ 0 0
$$523$$ 4.29913e6 0.687268 0.343634 0.939104i $$-0.388342\pi$$
0.343634 + 0.939104i $$0.388342\pi$$
$$524$$ 0 0
$$525$$ −2.22343e6 6.91513e6i −0.352067 1.09497i
$$526$$ 0 0
$$527$$ 2.62146e6i 0.411166i
$$528$$ 0 0
$$529$$ 5.92089e6 0.919916
$$530$$ 0 0
$$531$$ 2.01449e6i 0.310049i
$$532$$ 0 0
$$533$$ 5.53841e6 0.844437
$$534$$ 0 0
$$535$$ −5.91563e6 + 927645.i −0.893545 + 0.140119i
$$536$$ 0 0
$$537$$ 1.25198e7i 1.87354i
$$538$$ 0 0
$$539$$ 609410.i 0.0903520i
$$540$$ 0 0
$$541$$ 2.98051e6i 0.437821i 0.975745 + 0.218911i $$0.0702503\pi$$
−0.975745 + 0.218911i $$0.929750\pi$$
$$542$$ 0 0
$$543$$ 1.32054e6i 0.192199i
$$544$$ 0 0
$$545$$ −2.03313e6 1.29654e7i −0.293207 1.86979i
$$546$$ 0 0
$$547$$ −841980. −0.120319 −0.0601594 0.998189i $$-0.519161\pi$$
−0.0601594 + 0.998189i $$0.519161\pi$$
$$548$$ 0 0
$$549$$ 5.99458e6i 0.848844i
$$550$$ 0 0
$$551$$ 9.61209e6 1.34877
$$552$$ 0 0
$$553$$ 3.78712e6i 0.526619i
$$554$$ 0 0
$$555$$ −6.04505e6 + 947940.i −0.833043 + 0.130632i
$$556$$ 0 0
$$557$$ −7.95114e6 −1.08590 −0.542952 0.839764i $$-0.682693\pi$$
−0.542952 + 0.839764i $$0.682693\pi$$
$$558$$ 0 0
$$559$$ 9.30695e6 1.25973
$$560$$ 0 0
$$561$$ −2.39950e6 −0.321894
$$562$$ 0 0
$$563$$ −4.88079e6 −0.648962 −0.324481 0.945892i $$-0.605190\pi$$
−0.324481 + 0.945892i $$0.605190\pi$$
$$564$$ 0 0
$$565$$ −238580. 1.52143e6i −0.0314422 0.200508i
$$566$$ 0 0
$$567$$ 8.96772e6i 1.17145i
$$568$$ 0 0
$$569$$ 7.06257e6 0.914497 0.457248 0.889339i $$-0.348835\pi$$
0.457248 + 0.889339i $$0.348835\pi$$
$$570$$ 0 0
$$571$$ 1.72095e6i 0.220891i −0.993882 0.110445i $$-0.964772\pi$$
0.993882 0.110445i $$-0.0352278\pi$$
$$572$$ 0 0
$$573$$ −1.19128e7 −1.51575
$$574$$ 0 0
$$575$$ −686758. 2.13590e6i −0.0866232 0.269408i
$$576$$ 0 0
$$577$$ 1.57279e7i 1.96666i 0.181823 + 0.983331i $$0.441800\pi$$
−0.181823 + 0.983331i $$0.558200\pi$$
$$578$$ 0 0
$$579$$ 1.25531e7i 1.55616i
$$580$$ 0 0
$$581$$ 1.29121e7i 1.58693i
$$582$$ 0 0
$$583$$ 5.13477e6i 0.625676i
$$584$$ 0 0
$$585$$ −3.30132e6 + 517688.i −0.398839 + 0.0625430i
$$586$$ 0 0
$$587$$ −1.31369e7 −1.57361 −0.786804 0.617203i $$-0.788266\pi$$
−0.786804 + 0.617203i $$0.788266\pi$$
$$588$$ 0 0
$$589$$ 1.60320e7i 1.90415i
$$590$$ 0 0
$$591$$ −7.56829e6 −0.891310
$$592$$ 0 0
$$593$$ 9.44213e6i 1.10264i −0.834294 0.551319i $$-0.814125\pi$$
0.834294 0.551319i $$-0.185875\pi$$
$$594$$ 0 0
$$595$$ −2.82414e6 + 442860.i −0.327034 + 0.0512831i
$$596$$ 0 0
$$597$$ −48113.6 −0.00552500
$$598$$ 0 0
$$599$$ −1.05602e7 −1.20256 −0.601279 0.799039i $$-0.705342\pi$$
−0.601279 + 0.799039i $$0.705342\pi$$
$$600$$ 0 0
$$601$$ −1.00758e7 −1.13787 −0.568937 0.822381i $$-0.692645\pi$$
−0.568937 + 0.822381i $$0.692645\pi$$
$$602$$ 0 0
$$603$$ 1.03302e6 0.115696
$$604$$ 0 0
$$605$$ −3.98997e6 + 625677.i −0.443181 + 0.0694964i
$$606$$ 0 0
$$607$$ 4.22464e6i 0.465391i −0.972550 0.232696i $$-0.925245\pi$$
0.972550 0.232696i $$-0.0747546\pi$$
$$608$$ 0 0
$$609$$ −8.68006e6 −0.948373
$$610$$ 0 0
$$611$$ 1.11118e6i 0.120415i
$$612$$ 0 0
$$613$$ 9.47741e6 1.01868 0.509341 0.860565i $$-0.329889\pi$$
0.509341 + 0.860565i $$0.329889\pi$$
$$614$$ 0 0
$$615$$ −1.20405e7 + 1.88809e6i −1.28368 + 0.201296i
$$616$$ 0 0
$$617$$ 1.41901e7i 1.50063i −0.661081 0.750315i $$-0.729902\pi$$
0.661081 0.750315i $$-0.270098\pi$$
$$618$$ 0 0
$$619$$ 7.32823e6i 0.768728i −0.923182 0.384364i $$-0.874421\pi$$
0.923182 0.384364i $$-0.125579\pi$$
$$620$$ 0 0
$$621$$ 1.64822e6i 0.171509i
$$622$$ 0 0
$$623$$ 1.20724e7i 1.24616i
$$624$$ 0 0
$$625$$ 7.93562e6 5.69151e6i 0.812608 0.582811i
$$626$$ 0 0
$$627$$ −1.46746e7 −1.49072
$$628$$ 0 0
$$629$$ 2.40809e6i 0.242687i
$$630$$ 0 0
$$631$$ −8.90206e6 −0.890056 −0.445028 0.895517i $$-0.646806\pi$$
−0.445028 + 0.895517i $$0.646806\pi$$
$$632$$ 0 0
$$633$$ 1.95101e7i 1.93531i
$$634$$ 0 0
$$635$$ 1.39418e6 + 8.89075e6i 0.137210 + 0.874992i
$$636$$ 0 0
$$637$$ 993862. 0.0970459
$$638$$ 0 0
$$639$$ −3.57826e6 −0.346673
$$640$$ 0 0
$$641$$ −4.64056e6 −0.446093 −0.223046 0.974808i $$-0.571600\pi$$
−0.223046 + 0.974808i $$0.571600\pi$$
$$642$$ 0 0
$$643$$ 1.33925e7 1.27742 0.638712 0.769446i $$-0.279467\pi$$
0.638712 + 0.769446i $$0.279467\pi$$
$$644$$ 0 0
$$645$$ −2.02332e7 + 3.17282e6i −1.91499 + 0.300294i
$$646$$ 0 0
$$647$$ 7.50695e6i 0.705022i −0.935808 0.352511i $$-0.885328\pi$$
0.935808 0.352511i $$-0.114672\pi$$
$$648$$ 0 0
$$649$$ 4.88064e6 0.454847
$$650$$ 0 0
$$651$$ 1.44775e7i 1.33888i
$$652$$ 0 0
$$653$$ 9.28654e6 0.852258 0.426129 0.904662i $$-0.359877\pi$$
0.426129 + 0.904662i $$0.359877\pi$$
$$654$$ 0 0
$$655$$ −1.68520e6 1.07466e7i −0.153479 0.978740i
$$656$$ 0 0
$$657$$ 51768.8i 0.00467902i
$$658$$ 0 0
$$659$$ 2.14194e6i 0.192130i −0.995375 0.0960648i $$-0.969374\pi$$
0.995375 0.0960648i $$-0.0306256\pi$$
$$660$$ 0 0
$$661$$ 5.13285e6i 0.456936i −0.973551 0.228468i $$-0.926628\pi$$
0.973551 0.228468i $$-0.0733716\pi$$
$$662$$ 0 0
$$663$$ 3.91324e6i 0.345742i
$$664$$ 0 0
$$665$$ −1.72715e7 + 2.70839e6i −1.51453 + 0.237497i
$$666$$ 0 0
$$667$$ −2.68104e6 −0.233339
$$668$$ 0 0
$$669$$ 1.69238e6i 0.146195i
$$670$$ 0 0
$$671$$ −1.45235e7 −1.24527
$$672$$ 0 0
$$673$$ 1.02549e7i 0.872754i −0.899764 0.436377i $$-0.856261\pi$$
0.899764 0.436377i $$-0.143739\pi$$
$$674$$ 0 0
$$675$$ −6.82981e6 + 2.19600e6i −0.576965 + 0.185512i
$$676$$ 0 0
$$677$$ −1.81369e7 −1.52087 −0.760433 0.649416i $$-0.775013\pi$$
−0.760433 + 0.649416i $$0.775013\pi$$
$$678$$ 0 0
$$679$$ 2.19099e7 1.82375
$$680$$ 0 0
$$681$$ −7.87888e6 −0.651024
$$682$$ 0 0
$$683$$ −1.29609e7 −1.06313 −0.531563 0.847019i $$-0.678395\pi$$
−0.531563 + 0.847019i $$0.678395\pi$$
$$684$$ 0 0
$$685$$ −231290. 1.47495e6i −0.0188335 0.120102i
$$686$$ 0 0
$$687$$ 2.41680e7i 1.95366i
$$688$$ 0 0
$$689$$ 8.37408e6 0.672031
$$690$$ 0 0
$$691$$ 1.77055e7i 1.41063i 0.708894 + 0.705315i $$0.249194\pi$$
−0.708894 + 0.705315i $$0.750806\pi$$
$$692$$ 0 0
$$693$$ 4.45342e6 0.352258
$$694$$ 0 0
$$695$$ −1.21841e6 7.76986e6i −0.0956824 0.610170i
$$696$$ 0 0
$$697$$ 4.79640e6i 0.373967i
$$698$$ 0 0
$$699$$ 2.32139e7i 1.79703i
$$700$$ 0 0
$$701$$ 8.73670e6i 0.671510i −0.941949 0.335755i $$-0.891009\pi$$
0.941949 0.335755i $$-0.108991\pi$$
$$702$$ 0 0
$$703$$ 1.47271e7i 1.12391i
$$704$$ 0 0
$$705$$ −378810. 2.41569e6i −0.0287044 0.183049i
$$706$$ 0 0
$$707$$ −1.65652e7 −1.24637
$$708$$ 0 0
$$709$$ 8.22402e6i 0.614425i −0.951641 0.307212i $$-0.900604\pi$$
0.951641 0.307212i $$-0.0993962\pi$$
$$710$$ 0 0
$$711$$ −3.83391e6 −0.284425
$$712$$ 0 0
$$713$$ 4.47171e6i 0.329420i
$$714$$ 0 0
$$715$$ −1.25424e6 7.99832e6i −0.0917518 0.585105i
$$716$$ 0 0
$$717$$ 1.09189e7 0.793195
$$718$$ 0 0
$$719$$ 1.63870e7 1.18216 0.591082 0.806612i $$-0.298701\pi$$
0.591082 + 0.806612i $$0.298701\pi$$
$$720$$ 0 0
$$721$$ 1.19747e7 0.857877
$$722$$ 0 0
$$723$$ −1.38639e7 −0.986373
$$724$$ 0 0
$$725$$ −3.57207e6 1.11095e7i −0.252392 0.784967i
$$726$$ 0 0
$$727$$ 2.04002e7i 1.43152i −0.698346 0.715760i $$-0.746080\pi$$
0.698346 0.715760i $$-0.253920\pi$$
$$728$$ 0 0
$$729$$ 1.59405e6 0.111092
$$730$$ 0 0
$$731$$ 8.06005e6i 0.557885i
$$732$$ 0 0
$$733$$ −6.29292e6 −0.432606 −0.216303 0.976326i $$-0.569400\pi$$
−0.216303 + 0.976326i $$0.569400\pi$$
$$734$$ 0 0
$$735$$ −2.16065e6 + 338816.i −0.147525 + 0.0231338i
$$736$$ 0 0
$$737$$ 2.50277e6i 0.169728i
$$738$$ 0 0
$$739$$ 1.24400e7i 0.837934i 0.908002 + 0.418967i $$0.137608\pi$$
−0.908002 + 0.418967i $$0.862392\pi$$
$$740$$ 0 0
$$741$$ 2.39321e7i 1.60117i
$$742$$ 0 0
$$743$$ 1.80211e7i 1.19759i 0.800901 + 0.598796i $$0.204354\pi$$
−0.800901 + 0.598796i $$0.795646\pi$$
$$744$$ 0 0
$$745$$ 2.85219e6 + 1.81885e7i 0.188273 + 1.20062i
$$746$$ 0 0
$$747$$ 1.30716e7 0.857094
$$748$$ 0 0
$$749$$ 1.30144e7i 0.847655i
$$750$$ 0 0
$$751$$ 1.44062e7 0.932074 0.466037 0.884765i $$-0.345681\pi$$
0.466037 + 0.884765i $$0.345681\pi$$
$$752$$ 0 0
$$753$$ 1.07526e7i 0.691075i
$$754$$ 0 0
$$755$$ 7.41599e6 1.16292e6i 0.473480 0.0742476i
$$756$$ 0 0
$$757$$ 6.45449e6 0.409376 0.204688 0.978827i $$-0.434382\pi$$
0.204688 + 0.978827i $$0.434382\pi$$
$$758$$ 0 0
$$759$$ 4.09308e6 0.257897
$$760$$ 0 0
$$761$$ 2.63016e7 1.64635 0.823173 0.567791i $$-0.192202\pi$$
0.823173 + 0.567791i $$0.192202\pi$$
$$762$$ 0 0
$$763$$ 2.85238e7 1.77376
$$764$$ 0 0
$$765$$ −448331. 2.85903e6i −0.0276978 0.176630i
$$766$$ 0 0
$$767$$ 7.95964e6i 0.488546i
$$768$$ 0 0
$$769$$ 1.12180e6 0.0684070 0.0342035 0.999415i $$-0.489111\pi$$
0.0342035 + 0.999415i $$0.489111\pi$$
$$770$$ 0 0
$$771$$ 8.68006e6i 0.525880i
$$772$$ 0 0
$$773$$ 1.26128e7 0.759213 0.379607 0.925148i $$-0.376059\pi$$
0.379607 + 0.925148i $$0.376059\pi$$
$$774$$ 0 0
$$775$$ 1.85297e7 5.95787e6i 1.10819 0.356317i
$$776$$ 0 0
$$777$$ 1.32991e7i 0.790260i
$$778$$ 0 0
$$779$$ 2.93333e7i 1.73188i
$$780$$ 0 0
$$781$$ 8.66927e6i 0.508575i
$$782$$ 0 0
$$783$$ 8.57297e6i 0.499720i
$$784$$ 0 0
$$785$$ 2.28616e7 3.58498e6i 1.32413 0.207641i
$$786$$ 0 0
$$787$$ 2.48088e7 1.42781 0.713904 0.700244i $$-0.246925\pi$$
0.713904 + 0.700244i $$0.246925\pi$$
$$788$$ 0 0
$$789$$ 3.63050e7i 2.07622i
$$790$$ 0 0
$$791$$ 3.34715e6 0.190210
$$792$$ 0 0
$$793$$ 2.36857e7i 1.33753i
$$794$$ 0 0
$$795$$ −1.82052e7 + 2.85480e6i −1.02159 + 0.160198i
$$796$$ 0 0
$$797$$ −1.93080e7 −1.07669 −0.538346 0.842724i $$-0.680951\pi$$
−0.538346 + 0.842724i $$0.680951\pi$$
$$798$$ 0 0
$$799$$ −962307. −0.0533269
$$800$$ 0 0
$$801$$ −1.22215e7 −0.673045