# Properties

 Label 1512.2.s.k.865.2 Level $1512$ Weight $2$ Character 1512.865 Analytic conductor $12.073$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1512.s (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.0733807856$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.309123.1 Defining polynomial: $$x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 865.2 Root $$0.500000 + 1.41036i$$ of defining polynomial Character $$\chi$$ $$=$$ 1512.865 Dual form 1512.2.s.k.1297.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.119562 - 0.207087i) q^{5} +(0.710533 - 2.54856i) q^{7} +O(q^{10})$$ $$q+(-0.119562 - 0.207087i) q^{5} +(0.710533 - 2.54856i) q^{7} +(-1.21053 + 2.09671i) q^{11} +0.760877 q^{13} +(1.71053 - 2.96273i) q^{17} +(-0.590972 - 1.02359i) q^{19} +(1.09097 + 1.88962i) q^{23} +(2.47141 - 4.28061i) q^{25} -2.89931 q^{29} +(2.32326 - 4.02400i) q^{31} +(-0.612725 + 0.157568i) q^{35} +(-2.89248 - 5.00992i) q^{37} +8.54583 q^{41} -3.37756 q^{43} +(-2.58414 - 4.47585i) q^{47} +(-5.99028 - 3.62167i) q^{49} +(1.56238 - 2.70612i) q^{53} +0.578933 q^{55} +(-3.11273 + 5.39140i) q^{59} +(-0.681943 - 1.18116i) q^{61} +(-0.0909717 - 0.157568i) q^{65} +(7.03379 - 12.1829i) q^{67} -8.02408 q^{71} +(3.91423 - 6.77965i) q^{73} +(4.48345 + 4.57489i) q^{77} +(-2.27292 - 3.93680i) q^{79} -12.0104 q^{83} -0.818057 q^{85} +(2.73912 + 4.74430i) q^{89} +(0.540628 - 1.93914i) q^{91} +(-0.141315 + 0.244765i) q^{95} +10.3639 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q - q^{5} - 4q^{7} + O(q^{10})$$ $$6q - q^{5} - 4q^{7} + q^{11} + 4q^{13} + 2q^{17} + 5q^{19} - 2q^{23} + 6q^{25} - 2q^{29} - 4q^{31} + 6q^{35} + 8q^{37} - 6q^{43} + 3q^{47} - 12q^{49} - 8q^{53} + 20q^{55} - 9q^{59} + 13q^{61} + 8q^{65} + 16q^{67} + 2q^{71} - 3q^{73} - 7q^{77} + 12q^{79} - 2q^{83} - 22q^{85} + 17q^{89} - 13q^{91} + 28q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$$.

 $$n$$ $$757$$ $$785$$ $$1081$$ $$1135$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −0.119562 0.207087i −0.0534696 0.0926120i 0.838052 0.545591i $$-0.183695\pi$$
−0.891521 + 0.452979i $$0.850361\pi$$
$$6$$ 0 0
$$7$$ 0.710533 2.54856i 0.268556 0.963264i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.21053 + 2.09671i −0.364990 + 0.632180i −0.988774 0.149416i $$-0.952261\pi$$
0.623785 + 0.781596i $$0.285594\pi$$
$$12$$ 0 0
$$13$$ 0.760877 0.211029 0.105515 0.994418i $$-0.466351\pi$$
0.105515 + 0.994418i $$0.466351\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.71053 2.96273i 0.414865 0.718568i −0.580549 0.814225i $$-0.697162\pi$$
0.995414 + 0.0956576i $$0.0304954\pi$$
$$18$$ 0 0
$$19$$ −0.590972 1.02359i −0.135578 0.234828i 0.790240 0.612797i $$-0.209956\pi$$
−0.925818 + 0.377969i $$0.876623\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.09097 + 1.88962i 0.227483 + 0.394013i 0.957062 0.289885i $$-0.0936169\pi$$
−0.729578 + 0.683897i $$0.760284\pi$$
$$24$$ 0 0
$$25$$ 2.47141 4.28061i 0.494282 0.856122i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.89931 −0.538389 −0.269194 0.963086i $$-0.586757\pi$$
−0.269194 + 0.963086i $$0.586757\pi$$
$$30$$ 0 0
$$31$$ 2.32326 4.02400i 0.417270 0.722732i −0.578394 0.815757i $$-0.696320\pi$$
0.995664 + 0.0930254i $$0.0296538\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −0.612725 + 0.157568i −0.103569 + 0.0266338i
$$36$$ 0 0
$$37$$ −2.89248 5.00992i −0.475520 0.823625i 0.524087 0.851665i $$-0.324407\pi$$
−0.999607 + 0.0280398i $$0.991073\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 8.54583 1.33463 0.667317 0.744774i $$-0.267443\pi$$
0.667317 + 0.744774i $$0.267443\pi$$
$$42$$ 0 0
$$43$$ −3.37756 −0.515073 −0.257537 0.966269i $$-0.582911\pi$$
−0.257537 + 0.966269i $$0.582911\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −2.58414 4.47585i −0.376935 0.652870i 0.613680 0.789555i $$-0.289689\pi$$
−0.990615 + 0.136685i $$0.956355\pi$$
$$48$$ 0 0
$$49$$ −5.99028 3.62167i −0.855755 0.517381i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 1.56238 2.70612i 0.214610 0.371715i −0.738542 0.674207i $$-0.764485\pi$$
0.953152 + 0.302493i $$0.0978187\pi$$
$$54$$ 0 0
$$55$$ 0.578933 0.0780634
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −3.11273 + 5.39140i −0.405242 + 0.701900i −0.994350 0.106155i $$-0.966146\pi$$
0.589107 + 0.808055i $$0.299480\pi$$
$$60$$ 0 0
$$61$$ −0.681943 1.18116i −0.0873139 0.151232i 0.819061 0.573706i $$-0.194495\pi$$
−0.906375 + 0.422474i $$0.861162\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −0.0909717 0.157568i −0.0112836 0.0195438i
$$66$$ 0 0
$$67$$ 7.03379 12.1829i 0.859314 1.48838i −0.0132695 0.999912i $$-0.504224\pi$$
0.872584 0.488464i $$-0.162443\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −8.02408 −0.952283 −0.476141 0.879369i $$-0.657965\pi$$
−0.476141 + 0.879369i $$0.657965\pi$$
$$72$$ 0 0
$$73$$ 3.91423 6.77965i 0.458126 0.793497i −0.540736 0.841192i $$-0.681854\pi$$
0.998862 + 0.0476949i $$0.0151875\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.48345 + 4.57489i 0.510936 + 0.521357i
$$78$$ 0 0
$$79$$ −2.27292 3.93680i −0.255723 0.442925i 0.709369 0.704838i $$-0.248980\pi$$
−0.965092 + 0.261913i $$0.915647\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −12.0104 −1.31831 −0.659157 0.752006i $$-0.729087\pi$$
−0.659157 + 0.752006i $$0.729087\pi$$
$$84$$ 0 0
$$85$$ −0.818057 −0.0887307
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.73912 + 4.74430i 0.290346 + 0.502895i 0.973892 0.227013i $$-0.0728961\pi$$
−0.683545 + 0.729908i $$0.739563\pi$$
$$90$$ 0 0
$$91$$ 0.540628 1.93914i 0.0566732 0.203277i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −0.141315 + 0.244765i −0.0144986 + 0.0251123i
$$96$$ 0 0
$$97$$ 10.3639 1.05229 0.526147 0.850394i $$-0.323636\pi$$
0.526147 + 0.850394i $$0.323636\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 5.06238 8.76830i 0.503726 0.872479i −0.496265 0.868171i $$-0.665296\pi$$
0.999991 0.00430755i $$-0.00137114\pi$$
$$102$$ 0 0
$$103$$ 1.31806 + 2.28294i 0.129872 + 0.224945i 0.923627 0.383293i $$-0.125210\pi$$
−0.793755 + 0.608238i $$0.791877\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −2.16991 3.75839i −0.209773 0.363337i 0.741870 0.670544i $$-0.233939\pi$$
−0.951643 + 0.307207i $$0.900606\pi$$
$$108$$ 0 0
$$109$$ 6.46457 11.1970i 0.619194 1.07248i −0.370439 0.928857i $$-0.620793\pi$$
0.989633 0.143619i $$-0.0458738\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 13.1352 1.23565 0.617826 0.786315i $$-0.288013\pi$$
0.617826 + 0.786315i $$0.288013\pi$$
$$114$$ 0 0
$$115$$ 0.260877 0.451852i 0.0243269 0.0421354i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −6.33530 6.46451i −0.580756 0.592601i
$$120$$ 0 0
$$121$$ 2.56922 + 4.45002i 0.233565 + 0.404547i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −2.37756 −0.212655
$$126$$ 0 0
$$127$$ −3.86156 −0.342658 −0.171329 0.985214i $$-0.554806\pi$$
−0.171329 + 0.985214i $$0.554806\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 7.25636 + 12.5684i 0.633991 + 1.09811i 0.986728 + 0.162383i $$0.0519179\pi$$
−0.352736 + 0.935723i $$0.614749\pi$$
$$132$$ 0 0
$$133$$ −3.02859 + 0.778828i −0.262612 + 0.0675330i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 5.70370 9.87909i 0.487300 0.844028i −0.512594 0.858631i $$-0.671315\pi$$
0.999893 + 0.0146035i $$0.00464860\pi$$
$$138$$ 0 0
$$139$$ 1.91874 0.162746 0.0813728 0.996684i $$-0.474070\pi$$
0.0813728 + 0.996684i $$0.474070\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −0.921067 + 1.59533i −0.0770235 + 0.133409i
$$144$$ 0 0
$$145$$ 0.346647 + 0.600410i 0.0287874 + 0.0498613i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 7.57730 + 13.1243i 0.620756 + 1.07518i 0.989345 + 0.145589i $$0.0465078\pi$$
−0.368589 + 0.929593i $$0.620159\pi$$
$$150$$ 0 0
$$151$$ 5.94966 10.3051i 0.484176 0.838618i −0.515659 0.856794i $$-0.672453\pi$$
0.999835 + 0.0181764i $$0.00578604\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1.11109 −0.0892449
$$156$$ 0 0
$$157$$ −1.92395 + 3.33237i −0.153548 + 0.265952i −0.932529 0.361095i $$-0.882403\pi$$
0.778982 + 0.627047i $$0.215736\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 5.59097 1.43777i 0.440630 0.113312i
$$162$$ 0 0
$$163$$ 4.47661 + 7.75372i 0.350635 + 0.607318i 0.986361 0.164597i $$-0.0526323\pi$$
−0.635726 + 0.771915i $$0.719299\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.19562 −0.169902 −0.0849509 0.996385i $$-0.527073\pi$$
−0.0849509 + 0.996385i $$0.527073\pi$$
$$168$$ 0 0
$$169$$ −12.4211 −0.955467
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −7.15335 12.3900i −0.543859 0.941992i −0.998678 0.0514079i $$-0.983629\pi$$
0.454818 0.890584i $$-0.349704\pi$$
$$174$$ 0 0
$$175$$ −9.15335 9.34004i −0.691928 0.706041i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −9.66539 + 16.7409i −0.722425 + 1.25128i 0.237600 + 0.971363i $$0.423639\pi$$
−0.960025 + 0.279914i $$0.909694\pi$$
$$180$$ 0 0
$$181$$ 1.32614 0.0985710 0.0492855 0.998785i $$-0.484306\pi$$
0.0492855 + 0.998785i $$0.484306\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −0.691658 + 1.19799i −0.0508517 + 0.0880778i
$$186$$ 0 0
$$187$$ 4.14132 + 7.17297i 0.302843 + 0.524539i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −12.5172 21.6805i −0.905716 1.56875i −0.819954 0.572430i $$-0.806001\pi$$
−0.0857621 0.996316i $$-0.527332\pi$$
$$192$$ 0 0
$$193$$ −1.97661 + 3.42359i −0.142280 + 0.246436i −0.928355 0.371695i $$-0.878777\pi$$
0.786075 + 0.618131i $$0.212110\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1.51135 −0.107679 −0.0538396 0.998550i $$-0.517146\pi$$
−0.0538396 + 0.998550i $$0.517146\pi$$
$$198$$ 0 0
$$199$$ −13.5241 + 23.4244i −0.958696 + 1.66051i −0.233023 + 0.972471i $$0.574862\pi$$
−0.725673 + 0.688040i $$0.758471\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −2.06006 + 7.38906i −0.144588 + 0.518611i
$$204$$ 0 0
$$205$$ −1.02175 1.76973i −0.0713624 0.123603i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 2.86156 0.197938
$$210$$ 0 0
$$211$$ −9.42107 −0.648573 −0.324286 0.945959i $$-0.605124\pi$$
−0.324286 + 0.945959i $$0.605124\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0.403827 + 0.699448i 0.0275407 + 0.0477020i
$$216$$ 0 0
$$217$$ −8.60464 8.78014i −0.584121 0.596035i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1.30150 2.25427i 0.0875487 0.151639i
$$222$$ 0 0
$$223$$ 7.03775 0.471283 0.235641 0.971840i $$-0.424281\pi$$
0.235641 + 0.971840i $$0.424281\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −12.3759 + 21.4357i −0.821419 + 1.42274i 0.0832066 + 0.996532i $$0.473484\pi$$
−0.904626 + 0.426207i $$0.859849\pi$$
$$228$$ 0 0
$$229$$ 13.8542 + 23.9961i 0.915509 + 1.58571i 0.806154 + 0.591706i $$0.201545\pi$$
0.109356 + 0.994003i $$0.465121\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −3.86389 6.69245i −0.253132 0.438437i 0.711255 0.702934i $$-0.248127\pi$$
−0.964386 + 0.264497i $$0.914794\pi$$
$$234$$ 0 0
$$235$$ −0.617927 + 1.07028i −0.0403091 + 0.0698174i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 27.3880 1.77158 0.885790 0.464086i $$-0.153617\pi$$
0.885790 + 0.464086i $$0.153617\pi$$
$$240$$ 0 0
$$241$$ −10.6683 + 18.4780i −0.687204 + 1.19027i 0.285535 + 0.958368i $$0.407829\pi$$
−0.972739 + 0.231903i $$0.925505\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −0.0337917 + 1.67352i −0.00215887 + 0.106917i
$$246$$ 0 0
$$247$$ −0.449657 0.778828i −0.0286110 0.0495556i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −4.66595 −0.294512 −0.147256 0.989098i $$-0.547044\pi$$
−0.147256 + 0.989098i $$0.547044\pi$$
$$252$$ 0 0
$$253$$ −5.28263 −0.332116
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1.14652 + 1.98583i 0.0715178 + 0.123872i 0.899567 0.436783i $$-0.143882\pi$$
−0.828049 + 0.560656i $$0.810549\pi$$
$$258$$ 0 0
$$259$$ −14.8233 + 3.81193i −0.921072 + 0.236862i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 2.39536 4.14888i 0.147704 0.255831i −0.782675 0.622431i $$-0.786145\pi$$
0.930378 + 0.366600i $$0.119478\pi$$
$$264$$ 0 0
$$265$$ −0.747204 −0.0459004
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 9.49316 16.4426i 0.578808 1.00253i −0.416808 0.908995i $$-0.636851\pi$$
0.995616 0.0935310i $$-0.0298154\pi$$
$$270$$ 0 0
$$271$$ 14.0579 + 24.3489i 0.853955 + 1.47909i 0.877611 + 0.479373i $$0.159136\pi$$
−0.0236567 + 0.999720i $$0.507531\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 5.98345 + 10.3636i 0.360816 + 0.624951i
$$276$$ 0 0
$$277$$ 4.08577 7.07676i 0.245490 0.425201i −0.716779 0.697300i $$-0.754384\pi$$
0.962269 + 0.272099i $$0.0877178\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −23.4315 −1.39780 −0.698902 0.715217i $$-0.746328\pi$$
−0.698902 + 0.715217i $$0.746328\pi$$
$$282$$ 0 0
$$283$$ −1.10752 + 1.91829i −0.0658354 + 0.114030i −0.897064 0.441900i $$-0.854305\pi$$
0.831229 + 0.555930i $$0.187638\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 6.07210 21.7795i 0.358425 1.28561i
$$288$$ 0 0
$$289$$ 2.64815 + 4.58673i 0.155774 + 0.269808i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 22.1866 1.29615 0.648077 0.761575i $$-0.275573\pi$$
0.648077 + 0.761575i $$0.275573\pi$$
$$294$$ 0 0
$$295$$ 1.48865 0.0866726
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0.830095 + 1.43777i 0.0480056 + 0.0831482i
$$300$$ 0 0
$$301$$ −2.39987 + 8.60790i −0.138326 + 0.496151i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −0.163069 + 0.282443i −0.00933728 + 0.0161726i
$$306$$ 0 0
$$307$$ 16.0183 0.914214 0.457107 0.889412i $$-0.348886\pi$$
0.457107 + 0.889412i $$0.348886\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −3.35348 + 5.80840i −0.190159 + 0.329364i −0.945303 0.326195i $$-0.894234\pi$$
0.755144 + 0.655559i $$0.227567\pi$$
$$312$$ 0 0
$$313$$ 14.0322 + 24.3044i 0.793144 + 1.37377i 0.924011 + 0.382366i $$0.124891\pi$$
−0.130866 + 0.991400i $$0.541776\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.63323 + 2.82885i 0.0917316 + 0.158884i 0.908240 0.418450i $$-0.137426\pi$$
−0.816508 + 0.577334i $$0.804093\pi$$
$$318$$ 0 0
$$319$$ 3.50972 6.07900i 0.196506 0.340359i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −4.04351 −0.224987
$$324$$ 0 0
$$325$$ 1.88044 3.25701i 0.104308 0.180667i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −13.2431 + 3.40557i −0.730115 + 0.187755i
$$330$$ 0 0
$$331$$ 10.9617 + 18.9862i 0.602509 + 1.04358i 0.992440 + 0.122732i $$0.0391657\pi$$
−0.389931 + 0.920844i $$0.627501\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −3.36389 −0.183789
$$336$$ 0 0
$$337$$ −14.0733 −0.766624 −0.383312 0.923619i $$-0.625217\pi$$
−0.383312 + 0.923619i $$0.625217\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 5.62476 + 9.74238i 0.304598 + 0.527579i
$$342$$ 0 0
$$343$$ −13.4863 + 12.6933i −0.728193 + 0.685372i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −2.50808 + 4.34412i −0.134641 + 0.233205i −0.925460 0.378845i $$-0.876321\pi$$
0.790819 + 0.612050i $$0.209655\pi$$
$$348$$ 0 0
$$349$$ −10.7382 −0.574801 −0.287401 0.957810i $$-0.592791\pi$$
−0.287401 + 0.957810i $$0.592791\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.16307 2.01449i 0.0619039 0.107221i −0.833413 0.552651i $$-0.813616\pi$$
0.895316 + 0.445431i $$0.146949\pi$$
$$354$$ 0 0
$$355$$ 0.959372 + 1.66168i 0.0509182 + 0.0881928i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −4.97141 8.61073i −0.262381 0.454457i 0.704493 0.709711i $$-0.251174\pi$$
−0.966874 + 0.255254i $$0.917841\pi$$
$$360$$ 0 0
$$361$$ 8.80150 15.2447i 0.463237 0.802350i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1.87197 −0.0979832
$$366$$ 0 0
$$367$$ −0.464574 + 0.804665i −0.0242505 + 0.0420032i −0.877896 0.478851i $$-0.841053\pi$$
0.853645 + 0.520855i $$0.174387\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −5.78659 5.90461i −0.300425 0.306552i
$$372$$ 0 0
$$373$$ 15.1352 + 26.2149i 0.783669 + 1.35735i 0.929791 + 0.368088i $$0.119988\pi$$
−0.146122 + 0.989267i $$0.546679\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −2.20602 −0.113616
$$378$$ 0 0
$$379$$ −28.5757 −1.46783 −0.733917 0.679240i $$-0.762310\pi$$
−0.733917 + 0.679240i $$0.762310\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −11.8107 20.4567i −0.603497 1.04529i −0.992287 0.123961i $$-0.960440\pi$$
0.388790 0.921326i $$-0.372893\pi$$
$$384$$ 0 0
$$385$$ 0.411351 1.47544i 0.0209644 0.0751956i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −8.23749 + 14.2677i −0.417657 + 0.723404i −0.995703 0.0926005i $$-0.970482\pi$$
0.578046 + 0.816004i $$0.303815\pi$$
$$390$$ 0 0
$$391$$ 7.46457 0.377500
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −0.543507 + 0.941382i −0.0273468 + 0.0473660i
$$396$$ 0 0
$$397$$ 6.41586 + 11.1126i 0.322003 + 0.557726i 0.980901 0.194507i $$-0.0623105\pi$$
−0.658898 + 0.752232i $$0.728977\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 15.8187 + 27.3989i 0.789950 + 1.36823i 0.925997 + 0.377532i $$0.123227\pi$$
−0.136046 + 0.990702i $$0.543440\pi$$
$$402$$ 0 0
$$403$$ 1.76771 3.06177i 0.0880561 0.152518i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 14.0058 0.694240
$$408$$ 0 0
$$409$$ −12.0144 + 20.8095i −0.594072 + 1.02896i 0.399605 + 0.916687i $$0.369147\pi$$
−0.993677 + 0.112275i $$0.964186\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 11.5286 + 11.7637i 0.567285 + 0.578855i
$$414$$ 0 0
$$415$$ 1.43598 + 2.48720i 0.0704897 + 0.122092i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 1.72777 0.0844073 0.0422036 0.999109i $$-0.486562\pi$$
0.0422036 + 0.999109i $$0.486562\pi$$
$$420$$ 0 0
$$421$$ −20.0949 −0.979367 −0.489683 0.871900i $$-0.662888\pi$$
−0.489683 + 0.871900i $$0.662888\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −8.45486 14.6442i −0.410121 0.710350i
$$426$$ 0 0
$$427$$ −3.49480 + 0.898718i −0.169125 + 0.0434920i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 10.4246 18.0560i 0.502137 0.869727i −0.497860 0.867257i $$-0.665881\pi$$
0.999997 0.00246928i $$-0.000785996\pi$$
$$432$$ 0 0
$$433$$ 10.2255 0.491404 0.245702 0.969345i $$-0.420982\pi$$
0.245702 + 0.969345i $$0.420982\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 1.28947 2.23342i 0.0616836 0.106839i
$$438$$ 0 0
$$439$$ 3.55718 + 6.16122i 0.169775 + 0.294059i 0.938341 0.345712i $$-0.112363\pi$$
−0.768566 + 0.639771i $$0.779029\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 5.22094 + 9.04293i 0.248054 + 0.429642i 0.962986 0.269552i $$-0.0868756\pi$$
−0.714932 + 0.699194i $$0.753542\pi$$
$$444$$ 0 0
$$445$$ 0.654988 1.13447i 0.0310494 0.0537792i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −41.3502 −1.95144 −0.975719 0.219028i $$-0.929711\pi$$
−0.975719 + 0.219028i $$0.929711\pi$$
$$450$$ 0 0
$$451$$ −10.3450 + 17.9181i −0.487128 + 0.843730i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −0.466208 + 0.119889i −0.0218562 + 0.00562051i
$$456$$ 0 0
$$457$$ 6.87592 + 11.9095i 0.321642 + 0.557101i 0.980827 0.194880i $$-0.0624318\pi$$
−0.659185 + 0.751981i $$0.729099\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −6.54583 −0.304870 −0.152435 0.988314i $$-0.548711\pi$$
−0.152435 + 0.988314i $$0.548711\pi$$
$$462$$ 0 0
$$463$$ −0.228720 −0.0106295 −0.00531475 0.999986i $$-0.501692\pi$$
−0.00531475 + 0.999986i $$0.501692\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 17.3788 + 30.1010i 0.804195 + 1.39291i 0.916833 + 0.399271i $$0.130737\pi$$
−0.112638 + 0.993636i $$0.535930\pi$$
$$468$$ 0 0
$$469$$ −26.0510 26.5824i −1.20292 1.22746i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 4.08865 7.08175i 0.187996 0.325619i
$$474$$ 0 0
$$475$$ −5.84213 −0.268055
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 12.4721 21.6023i 0.569865 0.987035i −0.426714 0.904387i $$-0.640329\pi$$
0.996579 0.0826481i $$-0.0263377\pi$$
$$480$$ 0 0
$$481$$ −2.20082 3.81193i −0.100349 0.173809i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.23912 2.14622i −0.0562657 0.0974550i
$$486$$ 0 0
$$487$$ 3.88207 6.72395i 0.175914 0.304691i −0.764564 0.644548i $$-0.777045\pi$$
0.940477 + 0.339857i $$0.110379\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 24.6224 1.11120 0.555598 0.831451i $$-0.312490\pi$$
0.555598 + 0.831451i $$0.312490\pi$$
$$492$$ 0 0
$$493$$ −4.95937 + 8.58988i −0.223359 + 0.386869i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −5.70137 + 20.4498i −0.255742 + 0.917300i
$$498$$ 0 0
$$499$$ −12.3811 21.4447i −0.554255 0.959998i −0.997961 0.0638259i $$-0.979670\pi$$
0.443706 0.896173i $$-0.353664\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −3.01367 −0.134373 −0.0671865 0.997740i $$-0.521402\pi$$
−0.0671865 + 0.997740i $$0.521402\pi$$
$$504$$ 0 0
$$505$$ −2.42107 −0.107736
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −17.7323 30.7132i −0.785970 1.36134i −0.928418 0.371537i $$-0.878831\pi$$
0.142448 0.989802i $$-0.454503\pi$$
$$510$$ 0 0
$$511$$ −14.4971 14.7928i −0.641315 0.654395i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0.315178 0.545904i 0.0138884 0.0240554i
$$516$$ 0 0
$$517$$ 12.5127 0.550309
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 3.48276 6.03232i 0.152582 0.264281i −0.779594 0.626286i $$-0.784574\pi$$
0.932176 + 0.362005i $$0.117908\pi$$
$$522$$ 0 0
$$523$$ 16.6940 + 28.9148i 0.729977 + 1.26436i 0.956892 + 0.290443i $$0.0938025\pi$$
−0.226916 + 0.973914i $$0.572864\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −7.94802 13.7664i −0.346221 0.599673i
$$528$$ 0 0
$$529$$ 9.11956 15.7955i 0.396503 0.686763i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 6.50232 0.281647
$$534$$ 0 0
$$535$$ −0.518875 + 0.898718i −0.0224329 + 0.0388549i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 14.8450 8.17571i 0.639420 0.352153i
$$540$$ 0 0
$$541$$ 4.10752 + 7.11444i 0.176596 + 0.305874i 0.940713 0.339205i $$-0.110158\pi$$
−0.764116 + 0.645079i $$0.776825\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −3.09166 −0.132432
$$546$$ 0 0
$$547$$ −8.50232 −0.363533 −0.181767 0.983342i $$-0.558182\pi$$
−0.181767 + 0.983342i $$0.558182\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1.71341 + 2.96772i 0.0729938 + 0.126429i
$$552$$ 0 0
$$553$$ −11.6482 + 2.99542i −0.495330 + 0.127378i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −7.83009 + 13.5621i −0.331772 + 0.574646i −0.982859 0.184357i $$-0.940980\pi$$
0.651088 + 0.759003i $$0.274313\pi$$
$$558$$ 0 0
$$559$$ −2.56991 −0.108695
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −21.2443 + 36.7963i −0.895342 + 1.55078i −0.0619602 + 0.998079i $$0.519735\pi$$
−0.833381 + 0.552698i $$0.813598\pi$$
$$564$$ 0 0
$$565$$ −1.57046 2.72012i −0.0660698 0.114436i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0.422701 + 0.732140i 0.0177206 + 0.0306929i 0.874750 0.484575i $$-0.161026\pi$$
−0.857029 + 0.515268i $$0.827692\pi$$
$$570$$ 0 0
$$571$$ 14.8353 25.6955i 0.620838 1.07532i −0.368492 0.929631i $$-0.620126\pi$$
0.989330 0.145692i $$-0.0465408\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 10.7850 0.449764
$$576$$ 0 0
$$577$$ 6.04871 10.4767i 0.251811 0.436150i −0.712213 0.701963i $$-0.752307\pi$$
0.964024 + 0.265813i $$0.0856405\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −8.53379 + 30.6092i −0.354041 + 1.26988i
$$582$$ 0 0
$$583$$ 3.78263 + 6.55171i 0.156661 + 0.271344i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 13.9338 0.575109 0.287555 0.957764i $$-0.407158\pi$$
0.287555 + 0.957764i $$0.407158\pi$$
$$588$$ 0 0
$$589$$ −5.49192 −0.226291
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 6.77743 + 11.7389i 0.278316 + 0.482057i 0.970966 0.239216i $$-0.0768905\pi$$
−0.692651 + 0.721273i $$0.743557\pi$$
$$594$$ 0 0
$$595$$ −0.581257 + 2.08486i −0.0238292 + 0.0854711i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 20.3960 35.3270i 0.833360 1.44342i −0.0619992 0.998076i $$-0.519748\pi$$
0.895359 0.445345i $$-0.146919\pi$$
$$600$$ 0 0
$$601$$ 30.2164 1.23255 0.616277 0.787530i $$-0.288640\pi$$
0.616277 + 0.787530i $$0.288640\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0.614360 1.06410i 0.0249773 0.0432619i
$$606$$ 0 0
$$607$$ 4.10752 + 7.11444i 0.166719 + 0.288766i 0.937264 0.348619i $$-0.113349\pi$$
−0.770545 + 0.637385i $$0.780016\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.96621 3.40557i −0.0795443 0.137775i
$$612$$ 0 0
$$613$$ 17.0224 29.4837i 0.687530 1.19084i −0.285105 0.958496i $$-0.592028\pi$$
0.972635 0.232340i $$-0.0746383\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −37.9064 −1.52606 −0.763028 0.646365i $$-0.776288\pi$$
−0.763028 + 0.646365i $$0.776288\pi$$
$$618$$ 0 0
$$619$$ 20.0293 34.6917i 0.805045 1.39438i −0.111216 0.993796i $$-0.535475\pi$$
0.916261 0.400582i $$-0.131192\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 14.0374 3.60983i 0.562395 0.144625i
$$624$$ 0 0
$$625$$ −12.0728 20.9107i −0.482911 0.836427i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −19.7907 −0.789107
$$630$$ 0 0
$$631$$ 3.44514 0.137149 0.0685745 0.997646i $$-0.478155\pi$$
0.0685745 + 0.997646i $$0.478155\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0.461695 + 0.799679i 0.0183218 + 0.0317343i
$$636$$ 0 0
$$637$$ −4.55787 2.75564i −0.180589 0.109183i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8.47537 14.6798i 0.334757 0.579816i −0.648681 0.761060i $$-0.724679\pi$$
0.983438 + 0.181244i $$0.0580125\pi$$
$$642$$ 0 0
$$643$$ 32.8090 1.29386 0.646931 0.762549i $$-0.276052\pi$$
0.646931 + 0.762549i $$0.276052\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 13.5374 23.4474i 0.532208 0.921812i −0.467084 0.884213i $$-0.654696\pi$$
0.999293 0.0375994i $$-0.0119711\pi$$
$$648$$ 0 0
$$649$$ −7.53611 13.0529i −0.295818 0.512372i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −15.9487 27.6240i −0.624121 1.08101i −0.988710 0.149841i $$-0.952124\pi$$
0.364589 0.931169i $$-0.381210\pi$$
$$654$$ 0 0
$$655$$ 1.73517 3.00539i 0.0677985 0.117430i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 33.9852 1.32388 0.661938 0.749559i $$-0.269734\pi$$
0.661938 + 0.749559i $$0.269734\pi$$
$$660$$ 0 0
$$661$$ −7.58414 + 13.1361i −0.294989 + 0.510935i −0.974982 0.222283i $$-0.928649\pi$$
0.679994 + 0.733218i $$0.261983\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0.523388 + 0.534063i 0.0202961 + 0.0207101i
$$666$$ 0 0
$$667$$ −3.16307 5.47860i −0.122475 0.212132i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 3.30206 0.127475
$$672$$ 0 0
$$673$$ 17.7324 0.683535 0.341767 0.939785i $$-0.388975\pi$$
0.341767 + 0.939785i $$0.388975\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1.67154 2.89519i −0.0642425 0.111271i 0.832115 0.554603i $$-0.187130\pi$$
−0.896358 + 0.443332i $$0.853796\pi$$
$$678$$ 0 0
$$679$$ 7.36389 26.4130i 0.282600 1.01364i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −23.7427 + 41.1235i −0.908489 + 1.57355i −0.0923244 + 0.995729i $$0.529430\pi$$
−0.816164 + 0.577820i $$0.803904\pi$$
$$684$$ 0 0
$$685$$ −2.72777 −0.104223
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 1.18878 2.05903i 0.0452889 0.0784427i
$$690$$ 0 0
$$691$$ 3.67674 + 6.36830i 0.139870 + 0.242262i 0.927447 0.373954i $$-0.121998\pi$$
−0.787577 + 0.616216i $$0.788665\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −0.229408 0.397347i −0.00870195 0.0150722i
$$696$$ 0 0
$$697$$ 14.6179 25.3190i 0.553693 0.959025i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −45.1729 −1.70616 −0.853079 0.521782i $$-0.825267\pi$$
−0.853079 + 0.521782i $$0.825267\pi$$
$$702$$ 0 0
$$703$$ −3.41874 + 5.92144i −0.128940 + 0.223331i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −18.7495 19.1319i −0.705149 0.719531i
$$708$$ 0 0
$$709$$ −19.9246 34.5105i −0.748285 1.29607i −0.948644 0.316346i $$-0.897544\pi$$
0.200359 0.979723i $$-0.435789\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 10.1384 0.379687
$$714$$ 0 0
$$715$$ 0.440497 0.0164737
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 20.4211 + 35.3703i 0.761577 + 1.31909i 0.942037 + 0.335508i $$0.108908\pi$$
−0.180460 + 0.983582i $$0.557759\pi$$
$$720$$ 0 0
$$721$$ 6.75473 1.73704i 0.251559 0.0646906i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −7.16539 + 12.4108i −0.266116 + 0.460926i
$$726$$ 0 0
$$727$$ −6.42898 −0.238438 −0.119219 0.992868i $$-0.538039\pi$$
−0.119219 + 0.992868i $$0.538039\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −5.77743 + 10.0068i −0.213686 + 0.370115i
$$732$$ 0 0
$$733$$ 11.0773 + 19.1864i 0.409149 + 0.708667i 0.994795 0.101900i $$-0.0324922\pi$$
−0.585645 + 0.810567i $$0.699159\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 17.0293 + 29.4956i 0.627282 + 1.08648i
$$738$$ 0 0
$$739$$ 9.62081 16.6637i 0.353907 0.612985i −0.633023 0.774133i $$-0.718186\pi$$
0.986930 + 0.161148i $$0.0515196\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 30.8616 1.13220 0.566100 0.824336i $$-0.308451\pi$$
0.566100 + 0.824336i $$0.308451\pi$$
$$744$$ 0 0
$$745$$ 1.81191 3.13832i 0.0663832 0.114979i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −11.1202 + 2.85967i −0.406325 + 0.104490i
$$750$$ 0 0
$$751$$ −2.12476 3.68020i −0.0775337 0.134292i 0.824652 0.565641i $$-0.191371\pi$$
−0.902185 + 0.431349i $$0.858038\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −2.84540 −0.103555
$$756$$ 0 0
$$757$$ 2.69578 0.0979798 0.0489899 0.998799i $$-0.484400\pi$$
0.0489899 + 0.998799i $$0.484400\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −19.5064 33.7862i −0.707108 1.22475i −0.965925 0.258821i $$-0.916666\pi$$
0.258817 0.965926i $$-0.416667\pi$$
$$762$$ 0 0
$$763$$ −23.9428 24.4312i −0.866788 0.884467i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −2.36840 + 4.10219i −0.0855180 + 0.148121i
$$768$$ 0 0
$$769$$ −32.0930 −1.15730 −0.578652 0.815574i $$-0.696421\pi$$
−0.578652 + 0.815574i $$0.696421\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 12.3873 21.4554i 0.445539 0.771697i −0.552550 0.833480i $$-0.686345\pi$$
0.998090 + 0.0617828i $$0.0196786\pi$$
$$774$$ 0 0
$$775$$ −11.4834 19.8899i −0.412498 0.714467i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −5.05034 8.74745i −0.180947 0.313410i
$$780$$ 0 0
$$781$$ 9.71341 16.8241i 0.347573 0.602014i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0.920120 0.0328405
$$786$$ 0 0
$$787$$ −4.03543 + 6.98956i −0.143847 + 0.249151i −0.928942 0.370224i $$-0.879281\pi$$
0.785095 + 0.619375i $$0.212614\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 9.33297 33.4757i 0.331842 1.19026i
$$792$$ 0 0
$$793$$ −0.518875 0.898718i −0.0184258 0.0319144i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −32.6342 −1.15596 −0.577982 0.816050i $$-0.696160\pi$$
−0.577982 + 0.816050i $$0.696160\pi$$
$$798$$ 0 0
$$799$$ −17.6810 −0.625509
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 9.47661 + 16.4140i 0.334422 + 0.579237i
$$804$$ 0 0