# Properties

 Label 2352.2.h.p.2255.8 Level $2352$ Weight $2$ Character 2352.2255 Analytic conductor $18.781$ Analytic rank $0$ Dimension $16$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2352.h (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.7808145554$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 12x^{14} + 97x^{12} - 432x^{10} + 1392x^{8} - 2502x^{6} + 3181x^{4} - 1650x^{2} + 625$$ x^16 - 12*x^14 + 97*x^12 - 432*x^10 + 1392*x^8 - 2502*x^6 + 3181*x^4 - 1650*x^2 + 625 Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{16}\cdot 3^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 2255.8 Root $$-1.75344 - 1.01235i$$ of defining polynomial Character $$\chi$$ $$=$$ 2352.2255 Dual form 2352.2.h.p.2255.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.777403 + 1.54779i) q^{3} +3.40332i q^{5} +(-1.79129 - 2.40651i) q^{9} +O(q^{10})$$ $$q+(-0.777403 + 1.54779i) q^{3} +3.40332i q^{5} +(-1.79129 - 2.40651i) q^{9} +3.94748 q^{13} +(-5.26761 - 2.64575i) q^{15} -6.09632i q^{17} -4.38774i q^{19} -8.33639 q^{23} -6.58258 q^{25} +(5.11732 - 0.901703i) q^{27} -3.80848i q^{29} -4.89898i q^{31} -7.58258 q^{37} +(-3.06878 + 6.10985i) q^{39} +0.710314i q^{41} -9.66930i q^{43} +(8.19012 - 6.09632i) q^{45} -11.7894 q^{47} +(9.43581 + 4.73930i) q^{51} -1.00454i q^{53} +(6.79129 + 3.41105i) q^{57} -4.66442 q^{59} +1.70938 q^{61} +13.4345i q^{65} -3.46410i q^{67} +(6.48074 - 12.9030i) q^{69} -6.59649 q^{71} +14.3757 q^{73} +(5.11732 - 10.1884i) q^{75} -6.92820i q^{79} +(-2.58258 + 8.62150i) q^{81} -16.4539 q^{83} +20.7477 q^{85} +(5.89472 + 2.96073i) q^{87} -6.09632i q^{89} +(7.58258 + 3.80848i) q^{93} +14.9329 q^{95} +9.89949 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + 8 q^{9}+O(q^{10})$$ 16 * q + 8 * q^9 $$16 q + 8 q^{9} - 32 q^{25} - 48 q^{37} + 72 q^{57} + 32 q^{81} + 112 q^{85} + 48 q^{93}+O(q^{100})$$ 16 * q + 8 * q^9 - 32 * q^25 - 48 * q^37 + 72 * q^57 + 32 * q^81 + 112 * q^85 + 48 * q^93

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$1471$$ $$1765$$ $$2257$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$ $$1$$

## 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
$$3$$ −0.777403 + 1.54779i −0.448834 + 0.893615i
$$4$$ 0 0
$$5$$ 3.40332i 1.52201i 0.648746 + 0.761005i $$0.275294\pi$$
−0.648746 + 0.761005i $$0.724706\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −1.79129 2.40651i −0.597096 0.802170i
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 3.94748 1.09483 0.547417 0.836860i $$-0.315611\pi$$
0.547417 + 0.836860i $$0.315611\pi$$
$$14$$ 0 0
$$15$$ −5.26761 2.64575i −1.36009 0.683130i
$$16$$ 0 0
$$17$$ 6.09632i 1.47858i −0.673390 0.739288i $$-0.735162\pi$$
0.673390 0.739288i $$-0.264838\pi$$
$$18$$ 0 0
$$19$$ 4.38774i 1.00662i −0.864107 0.503308i $$-0.832116\pi$$
0.864107 0.503308i $$-0.167884\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −8.33639 −1.73826 −0.869129 0.494585i $$-0.835320\pi$$
−0.869129 + 0.494585i $$0.835320\pi$$
$$24$$ 0 0
$$25$$ −6.58258 −1.31652
$$26$$ 0 0
$$27$$ 5.11732 0.901703i 0.984828 0.173533i
$$28$$ 0 0
$$29$$ 3.80848i 0.707218i −0.935393 0.353609i $$-0.884954\pi$$
0.935393 0.353609i $$-0.115046\pi$$
$$30$$ 0 0
$$31$$ 4.89898i 0.879883i −0.898027 0.439941i $$-0.854999\pi$$
0.898027 0.439941i $$-0.145001\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −7.58258 −1.24657 −0.623284 0.781996i $$-0.714202\pi$$
−0.623284 + 0.781996i $$0.714202\pi$$
$$38$$ 0 0
$$39$$ −3.06878 + 6.10985i −0.491398 + 0.978359i
$$40$$ 0 0
$$41$$ 0.710314i 0.110932i 0.998461 + 0.0554662i $$0.0176645\pi$$
−0.998461 + 0.0554662i $$0.982335\pi$$
$$42$$ 0 0
$$43$$ 9.66930i 1.47456i −0.675590 0.737278i $$-0.736111\pi$$
0.675590 0.737278i $$-0.263889\pi$$
$$44$$ 0 0
$$45$$ 8.19012 6.09632i 1.22091 0.908786i
$$46$$ 0 0
$$47$$ −11.7894 −1.71967 −0.859833 0.510575i $$-0.829433\pi$$
−0.859833 + 0.510575i $$0.829433\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 9.43581 + 4.73930i 1.32128 + 0.663635i
$$52$$ 0 0
$$53$$ 1.00454i 0.137984i −0.997617 0.0689918i $$-0.978022\pi$$
0.997617 0.0689918i $$-0.0219782\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 6.79129 + 3.41105i 0.899528 + 0.451804i
$$58$$ 0 0
$$59$$ −4.66442 −0.607256 −0.303628 0.952791i $$-0.598198\pi$$
−0.303628 + 0.952791i $$0.598198\pi$$
$$60$$ 0 0
$$61$$ 1.70938 0.218863 0.109432 0.993994i $$-0.465097\pi$$
0.109432 + 0.993994i $$0.465097\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 13.4345i 1.66635i
$$66$$ 0 0
$$67$$ 3.46410i 0.423207i −0.977356 0.211604i $$-0.932131\pi$$
0.977356 0.211604i $$-0.0678686\pi$$
$$68$$ 0 0
$$69$$ 6.48074 12.9030i 0.780189 1.55333i
$$70$$ 0 0
$$71$$ −6.59649 −0.782859 −0.391429 0.920208i $$-0.628019\pi$$
−0.391429 + 0.920208i $$0.628019\pi$$
$$72$$ 0 0
$$73$$ 14.3757 1.68255 0.841274 0.540609i $$-0.181806\pi$$
0.841274 + 0.540609i $$0.181806\pi$$
$$74$$ 0 0
$$75$$ 5.11732 10.1884i 0.590897 1.17646i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 6.92820i 0.779484i −0.920924 0.389742i $$-0.872564\pi$$
0.920924 0.389742i $$-0.127436\pi$$
$$80$$ 0 0
$$81$$ −2.58258 + 8.62150i −0.286953 + 0.957945i
$$82$$ 0 0
$$83$$ −16.4539 −1.80605 −0.903023 0.429592i $$-0.858657\pi$$
−0.903023 + 0.429592i $$0.858657\pi$$
$$84$$ 0 0
$$85$$ 20.7477 2.25041
$$86$$ 0 0
$$87$$ 5.89472 + 2.96073i 0.631980 + 0.317423i
$$88$$ 0 0
$$89$$ 6.09632i 0.646209i −0.946363 0.323104i $$-0.895273\pi$$
0.946363 0.323104i $$-0.104727\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 7.58258 + 3.80848i 0.786276 + 0.394921i
$$94$$ 0 0
$$95$$ 14.9329 1.53208
$$96$$ 0 0
$$97$$ 9.89949 1.00514 0.502571 0.864536i $$-0.332388\pi$$
0.502571 + 0.864536i $$0.332388\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 11.6306i 1.15729i 0.815581 + 0.578643i $$0.196418\pi$$
−0.815581 + 0.578643i $$0.803582\pi$$
$$102$$ 0 0
$$103$$ 18.5734i 1.83010i 0.403345 + 0.915048i $$0.367847\pi$$
−0.403345 + 0.915048i $$0.632153\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 6.59649 0.637706 0.318853 0.947804i $$-0.396702\pi$$
0.318853 + 0.947804i $$0.396702\pi$$
$$108$$ 0 0
$$109$$ −4.41742 −0.423113 −0.211556 0.977366i $$-0.567853\pi$$
−0.211556 + 0.977366i $$0.567853\pi$$
$$110$$ 0 0
$$111$$ 5.89472 11.7362i 0.559502 1.11395i
$$112$$ 0 0
$$113$$ 12.4300i 1.16931i −0.811280 0.584657i $$-0.801229\pi$$
0.811280 0.584657i $$-0.198771\pi$$
$$114$$ 0 0
$$115$$ 28.3714i 2.64565i
$$116$$ 0 0
$$117$$ −7.07107 9.49964i −0.653720 0.878242i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ −1.09941 0.552200i −0.0991309 0.0497902i
$$124$$ 0 0
$$125$$ 5.38601i 0.481739i
$$126$$ 0 0
$$127$$ 10.3923i 0.922168i −0.887357 0.461084i $$-0.847461\pi$$
0.887357 0.461084i $$-0.152539\pi$$
$$128$$ 0 0
$$129$$ 14.9660 + 7.51695i 1.31768 + 0.661831i
$$130$$ 0 0
$$131$$ 7.12502 0.622516 0.311258 0.950325i $$-0.399250\pi$$
0.311258 + 0.950325i $$0.399250\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 3.06878 + 17.4159i 0.264119 + 1.49892i
$$136$$ 0 0
$$137$$ 18.2475i 1.55899i 0.626407 + 0.779496i $$0.284525\pi$$
−0.626407 + 0.779496i $$0.715475\pi$$
$$138$$ 0 0
$$139$$ 0.511238i 0.0433627i 0.999765 + 0.0216813i $$0.00690192\pi$$
−0.999765 + 0.0216813i $$0.993098\pi$$
$$140$$ 0 0
$$141$$ 9.16515 18.2475i 0.771845 1.53672i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 12.9615 1.07639
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 1.00454i 0.0822948i −0.999153 0.0411474i $$-0.986899\pi$$
0.999153 0.0411474i $$-0.0131013\pi$$
$$150$$ 0 0
$$151$$ 15.8745i 1.29185i 0.763401 + 0.645925i $$0.223528\pi$$
−0.763401 + 0.645925i $$0.776472\pi$$
$$152$$ 0 0
$$153$$ −14.6709 + 10.9203i −1.18607 + 0.882851i
$$154$$ 0 0
$$155$$ 16.6728 1.33919
$$156$$ 0 0
$$157$$ −1.70938 −0.136423 −0.0682116 0.997671i $$-0.521729\pi$$
−0.0682116 + 0.997671i $$0.521729\pi$$
$$158$$ 0 0
$$159$$ 1.55481 + 0.780929i 0.123304 + 0.0619317i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.18710i 0.327959i −0.986464 0.163980i $$-0.947567\pi$$
0.986464 0.163980i $$-0.0524331\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 2.58258 0.198660
$$170$$ 0 0
$$171$$ −10.5591 + 7.85971i −0.807478 + 0.601047i
$$172$$ 0 0
$$173$$ 3.40332i 0.258750i 0.991596 + 0.129375i $$0.0412970\pi$$
−0.991596 + 0.129375i $$0.958703\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 3.62614 7.21953i 0.272557 0.542653i
$$178$$ 0 0
$$179$$ −6.59649 −0.493045 −0.246522 0.969137i $$-0.579288\pi$$
−0.246522 + 0.969137i $$0.579288\pi$$
$$180$$ 0 0
$$181$$ 9.01400 0.670006 0.335003 0.942217i $$-0.391263\pi$$
0.335003 + 0.942217i $$0.391263\pi$$
$$182$$ 0 0
$$183$$ −1.32888 + 2.64575i −0.0982333 + 0.195580i
$$184$$ 0 0
$$185$$ 25.8059i 1.89729i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 10.0763 0.729095 0.364548 0.931185i $$-0.381224\pi$$
0.364548 + 0.931185i $$0.381224\pi$$
$$192$$ 0 0
$$193$$ −18.7477 −1.34949 −0.674745 0.738051i $$-0.735747\pi$$
−0.674745 + 0.738051i $$0.735747\pi$$
$$194$$ 0 0
$$195$$ −20.7938 10.4440i −1.48907 0.747913i
$$196$$ 0 0
$$197$$ 1.00454i 0.0715702i 0.999360 + 0.0357851i $$0.0113932\pi$$
−0.999360 + 0.0357851i $$0.988607\pi$$
$$198$$ 0 0
$$199$$ 9.79796i 0.694559i −0.937762 0.347279i $$-0.887106\pi$$
0.937762 0.347279i $$-0.112894\pi$$
$$200$$ 0 0
$$201$$ 5.36169 + 2.69300i 0.378185 + 0.189950i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −2.41742 −0.168840
$$206$$ 0 0
$$207$$ 14.9329 + 20.0616i 1.03791 + 1.39438i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 15.8745i 1.09285i 0.837509 + 0.546423i $$0.184011\pi$$
−0.837509 + 0.546423i $$0.815989\pi$$
$$212$$ 0 0
$$213$$ 5.12813 10.2100i 0.351374 0.699575i
$$214$$ 0 0
$$215$$ 32.9077 2.24429
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −11.1757 + 22.2505i −0.755185 + 1.50355i
$$220$$ 0 0
$$221$$ 24.0651i 1.61879i
$$222$$ 0 0
$$223$$ 1.02248i 0.0684701i 0.999414 + 0.0342350i $$0.0108995\pi$$
−0.999414 + 0.0342350i $$0.989101\pi$$
$$224$$ 0 0
$$225$$ 11.7913 + 15.8410i 0.786086 + 1.05607i
$$226$$ 0 0
$$227$$ −16.4539 −1.09208 −0.546041 0.837759i $$-0.683866\pi$$
−0.546041 + 0.837759i $$0.683866\pi$$
$$228$$ 0 0
$$229$$ 15.2612 1.00849 0.504244 0.863561i $$-0.331771\pi$$
0.504244 + 0.863561i $$0.331771\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 18.2475i 1.19544i −0.801706 0.597718i $$-0.796074\pi$$
0.801706 0.597718i $$-0.203926\pi$$
$$234$$ 0 0
$$235$$ 40.1232i 2.61735i
$$236$$ 0 0
$$237$$ 10.7234 + 5.38601i 0.696558 + 0.349859i
$$238$$ 0 0
$$239$$ −8.33639 −0.539236 −0.269618 0.962967i $$-0.586898\pi$$
−0.269618 + 0.962967i $$0.586898\pi$$
$$240$$ 0 0
$$241$$ −22.8610 −1.47260 −0.736302 0.676653i $$-0.763430\pi$$
−0.736302 + 0.676653i $$0.763430\pi$$
$$242$$ 0 0
$$243$$ −11.3365 10.6997i −0.727240 0.686384i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 17.3205i 1.10208i
$$248$$ 0 0
$$249$$ 12.7913 25.4671i 0.810615 1.61391i
$$250$$ 0 0
$$251$$ 28.2433 1.78270 0.891351 0.453314i $$-0.149759\pi$$
0.891351 + 0.453314i $$0.149759\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ −16.1294 + 32.1131i −1.01006 + 2.01100i
$$256$$ 0 0
$$257$$ 14.3236i 0.893481i −0.894664 0.446740i $$-0.852585\pi$$
0.894664 0.446740i $$-0.147415\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −9.16515 + 6.82209i −0.567309 + 0.422277i
$$262$$ 0 0
$$263$$ −26.7491 −1.64942 −0.824710 0.565556i $$-0.808661\pi$$
−0.824710 + 0.565556i $$0.808661\pi$$
$$264$$ 0 0
$$265$$ 3.41875 0.210012
$$266$$ 0 0
$$267$$ 9.43581 + 4.73930i 0.577462 + 0.290041i
$$268$$ 0 0
$$269$$ 3.40332i 0.207504i −0.994603 0.103752i $$-0.966915\pi$$
0.994603 0.103752i $$-0.0330848\pi$$
$$270$$ 0 0
$$271$$ 19.5959i 1.19037i 0.803590 + 0.595184i $$0.202921\pi$$
−0.803590 + 0.595184i $$0.797079\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 2.00000 0.120168 0.0600842 0.998193i $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ 0 0
$$279$$ −11.7894 + 8.77548i −0.705815 + 0.525374i
$$280$$ 0 0
$$281$$ 10.6306i 0.634167i −0.948398 0.317083i $$-0.897296\pi$$
0.948398 0.317083i $$-0.102704\pi$$
$$282$$ 0 0
$$283$$ 15.2082i 0.904032i −0.892010 0.452016i $$-0.850705\pi$$
0.892010 0.452016i $$-0.149295\pi$$
$$284$$ 0 0
$$285$$ −11.6089 + 23.1129i −0.687650 + 1.36909i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −20.1652 −1.18619
$$290$$ 0 0
$$291$$ −7.69590 + 15.3223i −0.451142 + 0.898210i
$$292$$ 0 0
$$293$$ 1.98269i 0.115830i 0.998322 + 0.0579150i $$0.0184452\pi$$
−0.998322 + 0.0579150i $$0.981555\pi$$
$$294$$ 0 0
$$295$$ 15.8745i 0.924250i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −32.9077 −1.90310
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −18.0017 9.04165i −1.03417 0.519429i
$$304$$ 0 0
$$305$$ 5.81755i 0.333112i
$$306$$ 0 0
$$307$$ 0.511238i 0.0291779i −0.999894 0.0145890i $$-0.995356\pi$$
0.999894 0.0145890i $$-0.00464397\pi$$
$$308$$ 0 0
$$309$$ −28.7477 14.4391i −1.63540 0.821409i
$$310$$ 0 0
$$311$$ 21.1183 1.19751 0.598754 0.800933i $$-0.295663\pi$$
0.598754 + 0.800933i $$0.295663\pi$$
$$312$$ 0 0
$$313$$ −20.0325 −1.13231 −0.566153 0.824300i $$-0.691569\pi$$
−0.566153 + 0.824300i $$0.691569\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 27.8736i 1.56554i −0.622314 0.782768i $$-0.713807\pi$$
0.622314 0.782768i $$-0.286193\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −5.12813 + 10.2100i −0.286224 + 0.569864i
$$322$$ 0 0
$$323$$ −26.7491 −1.48836
$$324$$ 0 0
$$325$$ −25.9846 −1.44136
$$326$$ 0 0
$$327$$ 3.43412 6.83723i 0.189907 0.378100i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.74110i 0.150665i 0.997158 + 0.0753323i $$0.0240017\pi$$
−0.997158 + 0.0753323i $$0.975998\pi$$
$$332$$ 0 0
$$333$$ 13.5826 + 18.2475i 0.744321 + 0.999959i
$$334$$ 0 0
$$335$$ 11.7894 0.644126
$$336$$ 0 0
$$337$$ −28.7477 −1.56599 −0.782994 0.622029i $$-0.786309\pi$$
−0.782994 + 0.622029i $$0.786309\pi$$
$$338$$ 0 0
$$339$$ 19.2390 + 9.66311i 1.04492 + 0.524828i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 43.9129 + 22.0560i 2.36419 + 1.18746i
$$346$$ 0 0
$$347$$ 3.47981 0.186806 0.0934031 0.995628i $$-0.470225\pi$$
0.0934031 + 0.995628i $$0.470225\pi$$
$$348$$ 0 0
$$349$$ −14.6709 −0.785313 −0.392657 0.919685i $$-0.628444\pi$$
−0.392657 + 0.919685i $$0.628444\pi$$
$$350$$ 0 0
$$351$$ 20.2005 3.55945i 1.07822 0.189989i
$$352$$ 0 0
$$353$$ 16.8683i 0.897811i 0.893579 + 0.448906i $$0.148186\pi$$
−0.893579 + 0.448906i $$0.851814\pi$$
$$354$$ 0 0
$$355$$ 22.4499i 1.19152i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 8.33639 0.439978 0.219989 0.975502i $$-0.429398\pi$$
0.219989 + 0.975502i $$0.429398\pi$$
$$360$$ 0 0
$$361$$ −0.252273 −0.0132775
$$362$$ 0 0
$$363$$ 8.55144 17.0257i 0.448834 0.893615i
$$364$$ 0 0
$$365$$ 48.9251i 2.56086i
$$366$$ 0 0
$$367$$ 1.02248i 0.0533728i −0.999644 0.0266864i $$-0.991504\pi$$
0.999644 0.0266864i $$-0.00849556\pi$$
$$368$$ 0 0
$$369$$ 1.70938 1.27238i 0.0889866 0.0662373i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 10.0000 0.517780 0.258890 0.965907i $$-0.416643\pi$$
0.258890 + 0.965907i $$0.416643\pi$$
$$374$$ 0 0
$$375$$ 8.33639 + 4.18710i 0.430490 + 0.216221i
$$376$$ 0 0
$$377$$ 15.0339i 0.774285i
$$378$$ 0 0
$$379$$ 9.66930i 0.496679i 0.968673 + 0.248339i $$0.0798848\pi$$
−0.968673 + 0.248339i $$0.920115\pi$$
$$380$$ 0 0
$$381$$ 16.0851 + 8.07901i 0.824063 + 0.413900i
$$382$$ 0 0
$$383$$ 21.1183 1.07909 0.539547 0.841956i $$-0.318596\pi$$
0.539547 + 0.841956i $$0.318596\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −23.2693 + 17.3205i −1.18284 + 0.880451i
$$388$$ 0 0
$$389$$ 17.4527i 0.884885i 0.896797 + 0.442443i $$0.145888\pi$$
−0.896797 + 0.442443i $$0.854112\pi$$
$$390$$ 0 0
$$391$$ 50.8213i 2.57015i
$$392$$ 0 0
$$393$$ −5.53901 + 11.0280i −0.279406 + 0.556290i
$$394$$ 0 0
$$395$$ 23.5789 1.18638
$$396$$ 0 0
$$397$$ 5.71846 0.287001 0.143501 0.989650i $$-0.454164\pi$$
0.143501 + 0.989650i $$0.454164\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 25.0696i 1.25192i 0.779856 + 0.625959i $$0.215292\pi$$
−0.779856 + 0.625959i $$0.784708\pi$$
$$402$$ 0 0
$$403$$ 19.3386i 0.963325i
$$404$$ 0 0
$$405$$ −29.3417 8.78933i −1.45800 0.436745i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −4.83297 −0.238975 −0.119487 0.992836i $$-0.538125\pi$$
−0.119487 + 0.992836i $$0.538125\pi$$
$$410$$ 0 0
$$411$$ −28.2433 14.1857i −1.39314 0.699729i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 55.9977i 2.74882i
$$416$$ 0 0
$$417$$ −0.791288 0.397438i −0.0387495 0.0194626i
$$418$$ 0 0
$$419$$ 7.12502 0.348080 0.174040 0.984739i $$-0.444318\pi$$
0.174040 + 0.984739i $$0.444318\pi$$
$$420$$ 0 0
$$421$$ −19.4955 −0.950150 −0.475075 0.879945i $$-0.657579\pi$$
−0.475075 + 0.879945i $$0.657579\pi$$
$$422$$ 0 0
$$423$$ 21.1183 + 28.3714i 1.02681 + 1.37946i
$$424$$ 0 0
$$425$$ 40.1295i 1.94657i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 38.2022 1.84013 0.920066 0.391762i $$-0.128134\pi$$
0.920066 + 0.391762i $$0.128134\pi$$
$$432$$ 0 0
$$433$$ −12.1376 −0.583296 −0.291648 0.956526i $$-0.594204\pi$$
−0.291648 + 0.956526i $$0.594204\pi$$
$$434$$ 0 0
$$435$$ −10.0763 + 20.0616i −0.483122 + 0.961881i
$$436$$ 0 0
$$437$$ 36.5779i 1.74976i
$$438$$ 0 0
$$439$$ 14.6969i 0.701447i 0.936479 + 0.350723i $$0.114064\pi$$
−0.936479 + 0.350723i $$0.885936\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 23.2693 1.10556 0.552778 0.833328i $$-0.313568\pi$$
0.552778 + 0.833328i $$0.313568\pi$$
$$444$$ 0 0
$$445$$ 20.7477 0.983537
$$446$$ 0 0
$$447$$ 1.55481 + 0.780929i 0.0735398 + 0.0369367i
$$448$$ 0 0
$$449$$ 24.8600i 1.17321i 0.809872 + 0.586607i $$0.199537\pi$$
−0.809872 + 0.586607i $$0.800463\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −24.5704 12.3409i −1.15442 0.579826i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2.74773 0.128533 0.0642666 0.997933i $$-0.479529\pi$$
0.0642666 + 0.997933i $$0.479529\pi$$
$$458$$ 0 0
$$459$$ −5.49707 31.1968i −0.256581 1.45614i
$$460$$ 0 0
$$461$$ 8.78933i 0.409360i 0.978829 + 0.204680i $$0.0656153\pi$$
−0.978829 + 0.204680i $$0.934385\pi$$
$$462$$ 0 0
$$463$$ 5.48220i 0.254780i −0.991853 0.127390i $$-0.959340\pi$$
0.991853 0.127390i $$-0.0406599\pi$$
$$464$$ 0 0
$$465$$ −12.9615 + 25.8059i −0.601074 + 1.19672i
$$466$$ 0 0
$$467$$ −25.7827 −1.19308 −0.596541 0.802583i $$-0.703459\pi$$
−0.596541 + 0.802583i $$0.703459\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 1.32888 2.64575i 0.0612314 0.121910i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 28.8826i 1.32523i
$$476$$ 0 0
$$477$$ −2.41742 + 1.79941i −0.110686 + 0.0823894i
$$478$$ 0 0
$$479$$ −14.2500 −0.651101 −0.325550 0.945525i $$-0.605550\pi$$
−0.325550 + 0.945525i $$0.605550\pi$$
$$480$$ 0 0
$$481$$ −29.9320 −1.36478
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 33.6911i 1.52984i
$$486$$ 0 0
$$487$$ 4.91010i 0.222498i −0.993793 0.111249i $$-0.964515\pi$$
0.993793 0.111249i $$-0.0354851\pi$$
$$488$$ 0 0
$$489$$ 6.48074 + 3.25507i 0.293069 + 0.147199i
$$490$$ 0 0
$$491$$ −10.0763 −0.454737 −0.227369 0.973809i $$-0.573012\pi$$
−0.227369 + 0.973809i $$0.573012\pi$$
$$492$$ 0 0
$$493$$ −23.2177 −1.04567
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 22.8027i 1.02079i −0.859940 0.510395i $$-0.829499\pi$$
0.859940 0.510395i $$-0.170501\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −14.2500 −0.635378 −0.317689 0.948195i $$-0.602907\pi$$
−0.317689 + 0.948195i $$0.602907\pi$$
$$504$$ 0 0
$$505$$ −39.5826 −1.76140
$$506$$ 0 0
$$507$$ −2.00770 + 3.99728i −0.0891652 + 0.177525i
$$508$$ 0 0
$$509$$ 29.2092i 1.29468i −0.762203 0.647338i $$-0.775882\pi$$
0.762203 0.647338i $$-0.224118\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −3.95644 22.4535i −0.174681 0.991345i
$$514$$ 0 0
$$515$$ −63.2113 −2.78542
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −5.26761 2.64575i −0.231222 0.116136i
$$520$$ 0 0
$$521$$ 16.8683i 0.739015i 0.929228 + 0.369508i $$0.120474\pi$$
−0.929228 + 0.369508i $$0.879526\pi$$
$$522$$ 0 0
$$523$$ 32.7591i 1.43246i 0.697866 + 0.716229i $$0.254133\pi$$
−0.697866 + 0.716229i $$0.745867\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −29.8658 −1.30097
$$528$$ 0 0
$$529$$ 46.4955 2.02154
$$530$$ 0 0
$$531$$ 8.35532 + 11.2250i 0.362590 + 0.487122i
$$532$$ 0 0
$$533$$ 2.80395i 0.121452i
$$534$$ 0 0
$$535$$ 22.4499i 0.970596i
$$536$$ 0 0
$$537$$ 5.12813 10.2100i 0.221295 0.440592i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 31.4955 1.35410 0.677048 0.735939i $$-0.263259\pi$$
0.677048 + 0.735939i $$0.263259\pi$$
$$542$$ 0 0
$$543$$ −7.00752 + 13.9518i −0.300721 + 0.598727i
$$544$$ 0 0
$$545$$ 15.0339i 0.643982i
$$546$$ 0 0
$$547$$ 35.9361i 1.53652i 0.640139 + 0.768259i $$0.278877\pi$$
−0.640139 + 0.768259i $$0.721123\pi$$
$$548$$ 0 0
$$549$$ −3.06199 4.11363i −0.130682 0.175566i
$$550$$ 0 0
$$551$$ −16.7106 −0.711897
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 39.9421 + 20.0616i 1.69545 + 0.851568i
$$556$$ 0 0
$$557$$ 27.8736i 1.18104i −0.807022 0.590521i $$-0.798922\pi$$
0.807022 0.590521i $$-0.201078\pi$$
$$558$$ 0 0
$$559$$ 38.1694i 1.61439i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 28.2433 1.19031 0.595157 0.803610i $$-0.297090\pi$$
0.595157 + 0.803610i $$0.297090\pi$$
$$564$$ 0 0
$$565$$ 42.3032 1.77971
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 32.6866i 1.37029i −0.728405 0.685147i $$-0.759738\pi$$
0.728405 0.685147i $$-0.240262\pi$$
$$570$$ 0 0
$$571$$ 16.5975i 0.694584i −0.937757 0.347292i $$-0.887101\pi$$
0.937757 0.347292i $$-0.112899\pi$$
$$572$$ 0 0
$$573$$ −7.83335 + 15.5960i −0.327243 + 0.651531i
$$574$$ 0 0
$$575$$ 54.8749 2.28844
$$576$$ 0 0
$$577$$ −21.0900 −0.877988 −0.438994 0.898490i $$-0.644665\pi$$
−0.438994 + 0.898490i $$0.644665\pi$$
$$578$$ 0 0
$$579$$ 14.5745 29.0175i 0.605698 1.20593i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 32.3303 24.0651i 1.33669 0.994969i
$$586$$ 0 0
$$587$$ 2.20382 0.0909614 0.0454807 0.998965i $$-0.485518\pi$$
0.0454807 + 0.998965i $$0.485518\pi$$
$$588$$ 0 0
$$589$$ −21.4955 −0.885705
$$590$$ 0 0
$$591$$ −1.55481 0.780929i −0.0639562 0.0321231i
$$592$$ 0 0
$$593$$ 15.7442i 0.646537i −0.946307 0.323269i $$-0.895218\pi$$
0.946307 0.323269i $$-0.104782\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 15.1652 + 7.61697i 0.620668 + 0.311742i
$$598$$ 0 0
$$599$$ 26.7491 1.09294 0.546469 0.837479i $$-0.315972\pi$$
0.546469 + 0.837479i $$0.315972\pi$$
$$600$$ 0 0
$$601$$ 12.1376 0.495103 0.247551 0.968875i $$-0.420374\pi$$
0.247551 + 0.968875i $$0.420374\pi$$
$$602$$ 0 0
$$603$$ −8.33639 + 6.20520i −0.339484 + 0.252695i
$$604$$ 0 0
$$605$$ 37.4365i 1.52201i
$$606$$ 0 0
$$607$$ 3.87650i 0.157342i 0.996901 + 0.0786712i $$0.0250677\pi$$
−0.996901 + 0.0786712i $$0.974932\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −46.5385 −1.88275
$$612$$ 0 0
$$613$$ −44.2432 −1.78697 −0.893483 0.449098i $$-0.851745\pi$$
−0.893483 + 0.449098i $$0.851745\pi$$
$$614$$ 0 0
$$615$$ 1.87931 3.74166i 0.0757813 0.150878i
$$616$$ 0 0
$$617$$ 25.0696i 1.00927i −0.863334 0.504633i $$-0.831628\pi$$
0.863334 0.504633i $$-0.168372\pi$$
$$618$$ 0 0
$$619$$ 19.0847i 0.767078i −0.923525 0.383539i $$-0.874705\pi$$
0.923525 0.383539i $$-0.125295\pi$$
$$620$$ 0 0
$$621$$ −42.6600 + 7.51695i −1.71189 + 0.301645i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −14.5826 −0.583303
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 46.2258i 1.84314i
$$630$$ 0 0
$$631$$ 8.37420i 0.333372i −0.986010 0.166686i $$-0.946693\pi$$
0.986010 0.166686i $$-0.0533066\pi$$
$$632$$ 0 0
$$633$$ −24.5704 12.3409i −0.976584 0.490507i
$$634$$ 0 0
$$635$$ 35.3683 1.40355
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 11.8162 + 15.8745i 0.467442 + 0.627986i
$$640$$ 0 0
$$641$$ 32.6866i 1.29104i −0.763742 0.645521i $$-0.776640\pi$$
0.763742 0.645521i $$-0.223360\pi$$
$$642$$ 0 0
$$643$$ 17.0397i 0.671981i −0.941865 0.335991i $$-0.890929\pi$$
0.941865 0.335991i $$-0.109071\pi$$
$$644$$ 0 0
$$645$$ −25.5826 + 50.9341i −1.00731 + 2.00553i
$$646$$ 0 0
$$647$$ −2.46060 −0.0967361 −0.0483681 0.998830i $$-0.515402\pi$$
−0.0483681 + 0.998830i $$0.515402\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 11.4255i 0.447112i −0.974691 0.223556i $$-0.928233\pi$$
0.974691 0.223556i $$-0.0717666\pi$$
$$654$$ 0 0
$$655$$ 24.2487i 0.947476i
$$656$$ 0 0
$$657$$ −25.7510 34.5952i −1.00464 1.34969i
$$658$$ 0 0
$$659$$ 46.5385 1.81288 0.906442 0.422330i $$-0.138788\pi$$
0.906442 + 0.422330i $$0.138788\pi$$
$$660$$ 0 0
$$661$$ −36.1176 −1.40481 −0.702406 0.711776i $$-0.747891\pi$$
−0.702406 + 0.711776i $$0.747891\pi$$
$$662$$ 0 0
$$663$$ 37.2476 + 18.7083i 1.44658 + 0.726570i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 31.7490i 1.22933i
$$668$$ 0 0
$$669$$ −1.58258 0.794877i −0.0611859 0.0307317i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 3.16515 0.122008 0.0610038 0.998138i $$-0.480570\pi$$
0.0610038 + 0.998138i $$0.480570\pi$$
$$674$$ 0 0
$$675$$ −33.6851 + 5.93553i −1.29654 + 0.228459i
$$676$$ 0 0
$$677$$ 29.2092i 1.12260i 0.827612 + 0.561301i $$0.189699\pi$$
−0.827612 + 0.561301i $$0.810301\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 12.7913 25.4671i 0.490163 0.975900i
$$682$$ 0 0
$$683$$ 10.0763 0.385559 0.192779 0.981242i $$-0.438250\pi$$
0.192779 + 0.981242i $$0.438250\pi$$
$$684$$ 0 0
$$685$$ −62.1022 −2.37280
$$686$$ 0 0
$$687$$ −11.8641 + 23.6211i −0.452644 + 0.901200i
$$688$$ 0 0
$$689$$ 3.96538i 0.151069i
$$690$$ 0 0
$$691$$ 23.9837i 0.912381i −0.889882 0.456191i $$-0.849213\pi$$
0.889882 0.456191i $$-0.150787\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −1.73991 −0.0659984
$$696$$ 0 0
$$697$$ 4.33030 0.164022
$$698$$ 0 0
$$699$$ 28.2433 + 14.1857i 1.06826 + 0.536552i
$$700$$ 0 0
$$701$$ 32.6866i 1.23456i −0.786745 0.617278i $$-0.788235\pi$$
0.786745 0.617278i $$-0.211765\pi$$
$$702$$ 0 0
$$703$$ 33.2704i 1.25482i
$$704$$ 0 0
$$705$$ 62.1022 + 31.1919i 2.33890 + 1.17476i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −17.0780 −0.641379 −0.320689 0.947184i $$-0.603915\pi$$
−0.320689 + 0.947184i $$0.603915\pi$$
$$710$$ 0 0
$$711$$ −16.6728 + 12.4104i −0.625278 + 0.465427i
$$712$$ 0 0
$$713$$ 40.8398i 1.52946i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 6.48074 12.9030i 0.242028 0.481870i
$$718$$ 0 0
$$719$$ 2.46060 0.0917649 0.0458824 0.998947i $$-0.485390\pi$$
0.0458824 + 0.998947i $$0.485390\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 17.7722 35.3839i 0.660955 1.31594i
$$724$$ 0 0
$$725$$ 25.0696i 0.931063i
$$726$$ 0 0
$$727$$ 43.0683i 1.59732i 0.601785 + 0.798658i $$0.294456\pi$$
−0.601785 + 0.798658i $$0.705544\pi$$
$$728$$ 0 0
$$729$$ 25.3739 9.22860i 0.939773 0.341800i
$$730$$ 0 0
$$731$$ −58.9472 −2.18024
$$732$$ 0 0
$$733$$ 17.4993 0.646351 0.323175 0.946339i $$-0.395250\pi$$
0.323175 + 0.946339i $$0.395250\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 24.9717i 0.918599i −0.888281 0.459300i $$-0.848100\pi$$
0.888281 0.459300i $$-0.151900\pi$$
$$740$$ 0 0
$$741$$ 26.8085 + 13.4650i 0.984833 + 0.494650i
$$742$$ 0 0
$$743$$ −21.5294 −0.789836 −0.394918 0.918716i $$-0.629227\pi$$
−0.394918 + 0.918716i $$0.629227\pi$$
$$744$$ 0 0
$$745$$ 3.41875 0.125253
$$746$$ 0 0
$$747$$ 29.4736 + 39.5964i 1.07838 + 1.44876i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 8.94630i 0.326455i 0.986588 + 0.163228i $$0.0521905\pi$$
−0.986588 + 0.163228i $$0.947809\pi$$
$$752$$ 0 0
$$753$$ −21.9564 + 43.7146i −0.800137 + 1.59305i
$$754$$ 0 0
$$755$$ −54.0260 −1.96621
$$756$$ 0 0
$$757$$ 22.7477 0.826780 0.413390 0.910554i $$-0.364345\pi$$
0.413390 + 0.910554i $$0.364345\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 14.3236i 0.519230i 0.965712 + 0.259615i $$0.0835956\pi$$
−0.965712 + 0.259615i $$0.916404\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −37.1652 49.9296i −1.34371 1.80521i
$$766$$ 0 0
$$767$$ −18.4127 −0.664844
$$768$$ 0 0
$$769$$ 37.0031 1.33437 0.667183 0.744894i $$-0.267500\pi$$
0.667183 + 0.744894i $$0.267500\pi$$
$$770$$ 0 0
$$771$$ 22.1699 + 11.1352i 0.798428 + 0.401025i
$$772$$ 0 0
$$773$$ 3.40332i 0.122409i 0.998125 + 0.0612044i $$0.0194942\pi$$
−0.998125 + 0.0612044i $$0.980506\pi$$
$$774$$ 0 0
$$775$$ 32.2479i 1.15838i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 3.11667 0.111666
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −3.43412 19.4892i −0.122725 0.696488i
$$784$$ 0 0
$$785$$ 5.81755i 0.207637i
$$786$$ 0 0
$$787$$ 26.8377i 0.956660i −0.878180 0.478330i $$-0.841242\pi$$
0.878180 0.478330i $$-0.158758\pi$$
$$788$$ 0 0
$$789$$ 20.7948 41.4019i 0.740316 1.47395i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 6.74773 0.239619
$$794$$ 0 0
$$795$$ −2.65775 + 5.29150i −0.0942607 + 0.187670i
$$796$$ 0 0
$$797$$ 17.0166i 0.602759i 0.953504 + 0.301379i $$0.0974470\pi$$
−0.953504 + 0.301379i $$0.902553\pi$$
$$798$$ 0 0
$$799$$ 71.8722i 2.54266i
$$800$$ 0 0
$$801$$ −14.6709 + 10.9203i −0.518369 + 0.385849i
$$802$$ 0 0
$$803$$ 0 0