# Properties

 Label 5520.2.be.b.1471.10 Level $5520$ Weight $2$ Character 5520.1471 Analytic conductor $44.077$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5520.be (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$44.0774219157$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 4 x^{15} + 8 x^{14} + 28 x^{13} + 373 x^{12} - 920 x^{11} + 1088 x^{10} - 168 x^{9} + 16460 x^{8} - 45408 x^{7} + 62624 x^{6} - 18048 x^{5} + 2160 x^{4} - 1664 x^{3} + 6272 x^{2} - 896 x + 64$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1471.10 Root $$-0.373815 + 0.373815i$$ of defining polynomial Character $$\chi$$ $$=$$ 5520.1471 Dual form 5520.2.be.b.1471.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{3} +1.00000i q^{5} -1.61153 q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{3} +1.00000i q^{5} -1.61153 q^{7} -1.00000 q^{9} -1.15035 q^{11} +7.10687 q^{13} -1.00000 q^{15} -1.79275i q^{17} -5.93632 q^{19} -1.61153i q^{21} +(-4.40428 - 1.89798i) q^{23} -1.00000 q^{25} -1.00000i q^{27} -0.0365806 q^{29} +4.39344i q^{31} -1.15035i q^{33} -1.61153i q^{35} -10.1186i q^{37} +7.10687i q^{39} +5.43873 q^{41} +9.60250 q^{43} -1.00000i q^{45} -9.16374i q^{47} -4.40297 q^{49} +1.79275 q^{51} -1.95476i q^{53} -1.15035i q^{55} -5.93632i q^{57} -5.29905i q^{59} +9.53475i q^{61} +1.61153 q^{63} +7.10687i q^{65} +2.33657 q^{67} +(1.89798 - 4.40428i) q^{69} -11.3842i q^{71} -1.61161 q^{73} -1.00000i q^{75} +1.85383 q^{77} +5.33892 q^{79} +1.00000 q^{81} +0.722088 q^{83} +1.79275 q^{85} -0.0365806i q^{87} +2.09024i q^{89} -11.4529 q^{91} -4.39344 q^{93} -5.93632i q^{95} -1.93236i q^{97} +1.15035 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + 8q^{7} - 16q^{9} + O(q^{10})$$ $$16q + 8q^{7} - 16q^{9} - 8q^{11} + 8q^{13} - 16q^{15} - 12q^{23} - 16q^{25} - 4q^{29} + 4q^{41} + 20q^{49} + 4q^{51} - 8q^{63} + 16q^{67} + 40q^{73} + 24q^{77} - 32q^{79} + 16q^{81} + 4q^{85} + 48q^{91} + 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times$$.

 $$n$$ $$1201$$ $$1381$$ $$1841$$ $$4417$$ $$4831$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ 1.00000i 0.447214i
$$6$$ 0 0
$$7$$ −1.61153 −0.609101 −0.304551 0.952496i $$-0.598506\pi$$
−0.304551 + 0.952496i $$0.598506\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ −1.15035 −0.346844 −0.173422 0.984848i $$-0.555482\pi$$
−0.173422 + 0.984848i $$0.555482\pi$$
$$12$$ 0 0
$$13$$ 7.10687 1.97109 0.985545 0.169414i $$-0.0541876\pi$$
0.985545 + 0.169414i $$0.0541876\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −0.258199
$$16$$ 0 0
$$17$$ 1.79275i 0.434805i −0.976082 0.217403i $$-0.930242\pi$$
0.976082 0.217403i $$-0.0697584\pi$$
$$18$$ 0 0
$$19$$ −5.93632 −1.36188 −0.680942 0.732337i $$-0.738429\pi$$
−0.680942 + 0.732337i $$0.738429\pi$$
$$20$$ 0 0
$$21$$ 1.61153i 0.351665i
$$22$$ 0 0
$$23$$ −4.40428 1.89798i −0.918356 0.395756i
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −0.0365806 −0.00679285 −0.00339643 0.999994i $$-0.501081\pi$$
−0.00339643 + 0.999994i $$0.501081\pi$$
$$30$$ 0 0
$$31$$ 4.39344i 0.789085i 0.918878 + 0.394542i $$0.129097\pi$$
−0.918878 + 0.394542i $$0.870903\pi$$
$$32$$ 0 0
$$33$$ 1.15035i 0.200251i
$$34$$ 0 0
$$35$$ 1.61153i 0.272398i
$$36$$ 0 0
$$37$$ 10.1186i 1.66349i −0.555158 0.831745i $$-0.687342\pi$$
0.555158 0.831745i $$-0.312658\pi$$
$$38$$ 0 0
$$39$$ 7.10687i 1.13801i
$$40$$ 0 0
$$41$$ 5.43873 0.849387 0.424693 0.905337i $$-0.360382\pi$$
0.424693 + 0.905337i $$0.360382\pi$$
$$42$$ 0 0
$$43$$ 9.60250 1.46437 0.732183 0.681107i $$-0.238501\pi$$
0.732183 + 0.681107i $$0.238501\pi$$
$$44$$ 0 0
$$45$$ 1.00000i 0.149071i
$$46$$ 0 0
$$47$$ 9.16374i 1.33667i −0.743861 0.668334i $$-0.767008\pi$$
0.743861 0.668334i $$-0.232992\pi$$
$$48$$ 0 0
$$49$$ −4.40297 −0.628995
$$50$$ 0 0
$$51$$ 1.79275 0.251035
$$52$$ 0 0
$$53$$ 1.95476i 0.268507i −0.990947 0.134253i $$-0.957136\pi$$
0.990947 0.134253i $$-0.0428636\pi$$
$$54$$ 0 0
$$55$$ 1.15035i 0.155113i
$$56$$ 0 0
$$57$$ 5.93632i 0.786284i
$$58$$ 0 0
$$59$$ 5.29905i 0.689877i −0.938625 0.344938i $$-0.887900\pi$$
0.938625 0.344938i $$-0.112100\pi$$
$$60$$ 0 0
$$61$$ 9.53475i 1.22080i 0.792093 + 0.610400i $$0.208991\pi$$
−0.792093 + 0.610400i $$0.791009\pi$$
$$62$$ 0 0
$$63$$ 1.61153 0.203034
$$64$$ 0 0
$$65$$ 7.10687i 0.881498i
$$66$$ 0 0
$$67$$ 2.33657 0.285457 0.142729 0.989762i $$-0.454412\pi$$
0.142729 + 0.989762i $$0.454412\pi$$
$$68$$ 0 0
$$69$$ 1.89798 4.40428i 0.228490 0.530213i
$$70$$ 0 0
$$71$$ 11.3842i 1.35106i −0.737334 0.675528i $$-0.763916\pi$$
0.737334 0.675528i $$-0.236084\pi$$
$$72$$ 0 0
$$73$$ −1.61161 −0.188624 −0.0943122 0.995543i $$-0.530065\pi$$
−0.0943122 + 0.995543i $$0.530065\pi$$
$$74$$ 0 0
$$75$$ 1.00000i 0.115470i
$$76$$ 0 0
$$77$$ 1.85383 0.211263
$$78$$ 0 0
$$79$$ 5.33892 0.600675 0.300338 0.953833i $$-0.402901\pi$$
0.300338 + 0.953833i $$0.402901\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 0.722088 0.0792594 0.0396297 0.999214i $$-0.487382\pi$$
0.0396297 + 0.999214i $$0.487382\pi$$
$$84$$ 0 0
$$85$$ 1.79275 0.194451
$$86$$ 0 0
$$87$$ 0.0365806i 0.00392186i
$$88$$ 0 0
$$89$$ 2.09024i 0.221565i 0.993845 + 0.110782i $$0.0353356\pi$$
−0.993845 + 0.110782i $$0.964664\pi$$
$$90$$ 0 0
$$91$$ −11.4529 −1.20059
$$92$$ 0 0
$$93$$ −4.39344 −0.455578
$$94$$ 0 0
$$95$$ 5.93632i 0.609053i
$$96$$ 0 0
$$97$$ 1.93236i 0.196201i −0.995177 0.0981005i $$-0.968723\pi$$
0.995177 0.0981005i $$-0.0312767\pi$$
$$98$$ 0 0
$$99$$ 1.15035 0.115615
$$100$$ 0 0
$$101$$ 15.0107 1.49362 0.746808 0.665040i $$-0.231585\pi$$
0.746808 + 0.665040i $$0.231585\pi$$
$$102$$ 0 0
$$103$$ −3.04742 −0.300271 −0.150136 0.988665i $$-0.547971\pi$$
−0.150136 + 0.988665i $$0.547971\pi$$
$$104$$ 0 0
$$105$$ 1.61153 0.157269
$$106$$ 0 0
$$107$$ −12.6032 −1.21840 −0.609199 0.793017i $$-0.708509\pi$$
−0.609199 + 0.793017i $$0.708509\pi$$
$$108$$ 0 0
$$109$$ 15.0300i 1.43961i −0.694174 0.719807i $$-0.744230\pi$$
0.694174 0.719807i $$-0.255770\pi$$
$$110$$ 0 0
$$111$$ 10.1186 0.960417
$$112$$ 0 0
$$113$$ 8.39445i 0.789684i 0.918749 + 0.394842i $$0.129201\pi$$
−0.918749 + 0.394842i $$0.870799\pi$$
$$114$$ 0 0
$$115$$ 1.89798 4.40428i 0.176988 0.410701i
$$116$$ 0 0
$$117$$ −7.10687 −0.657030
$$118$$ 0 0
$$119$$ 2.88907i 0.264840i
$$120$$ 0 0
$$121$$ −9.67669 −0.879699
$$122$$ 0 0
$$123$$ 5.43873i 0.490394i
$$124$$ 0 0
$$125$$ 1.00000i 0.0894427i
$$126$$ 0 0
$$127$$ 18.1343i 1.60916i 0.593845 + 0.804580i $$0.297609\pi$$
−0.593845 + 0.804580i $$0.702391\pi$$
$$128$$ 0 0
$$129$$ 9.60250i 0.845453i
$$130$$ 0 0
$$131$$ 1.77034i 0.154676i −0.997005 0.0773378i $$-0.975358\pi$$
0.997005 0.0773378i $$-0.0246420\pi$$
$$132$$ 0 0
$$133$$ 9.56656 0.829526
$$134$$ 0 0
$$135$$ 1.00000 0.0860663
$$136$$ 0 0
$$137$$ 17.7574i 1.51712i −0.651603 0.758560i $$-0.725903\pi$$
0.651603 0.758560i $$-0.274097\pi$$
$$138$$ 0 0
$$139$$ 13.6548i 1.15819i −0.815261 0.579094i $$-0.803406\pi$$
0.815261 0.579094i $$-0.196594\pi$$
$$140$$ 0 0
$$141$$ 9.16374 0.771726
$$142$$ 0 0
$$143$$ −8.17540 −0.683661
$$144$$ 0 0
$$145$$ 0.0365806i 0.00303786i
$$146$$ 0 0
$$147$$ 4.40297i 0.363151i
$$148$$ 0 0
$$149$$ 9.38262i 0.768654i −0.923197 0.384327i $$-0.874434\pi$$
0.923197 0.384327i $$-0.125566\pi$$
$$150$$ 0 0
$$151$$ 13.1263i 1.06820i 0.845421 + 0.534100i $$0.179349\pi$$
−0.845421 + 0.534100i $$0.820651\pi$$
$$152$$ 0 0
$$153$$ 1.79275i 0.144935i
$$154$$ 0 0
$$155$$ −4.39344 −0.352889
$$156$$ 0 0
$$157$$ 2.75711i 0.220041i 0.993929 + 0.110021i $$0.0350917\pi$$
−0.993929 + 0.110021i $$0.964908\pi$$
$$158$$ 0 0
$$159$$ 1.95476 0.155022
$$160$$ 0 0
$$161$$ 7.09763 + 3.05865i 0.559372 + 0.241056i
$$162$$ 0 0
$$163$$ 7.13282i 0.558686i 0.960191 + 0.279343i $$0.0901166\pi$$
−0.960191 + 0.279343i $$0.909883\pi$$
$$164$$ 0 0
$$165$$ 1.15035 0.0895548
$$166$$ 0 0
$$167$$ 0.264942i 0.0205018i 0.999947 + 0.0102509i $$0.00326303\pi$$
−0.999947 + 0.0102509i $$0.996737\pi$$
$$168$$ 0 0
$$169$$ 37.5075 2.88520
$$170$$ 0 0
$$171$$ 5.93632 0.453961
$$172$$ 0 0
$$173$$ −9.93924 −0.755666 −0.377833 0.925874i $$-0.623331\pi$$
−0.377833 + 0.925874i $$0.623331\pi$$
$$174$$ 0 0
$$175$$ 1.61153 0.121820
$$176$$ 0 0
$$177$$ 5.29905 0.398301
$$178$$ 0 0
$$179$$ 5.00824i 0.374333i −0.982328 0.187167i $$-0.940070\pi$$
0.982328 0.187167i $$-0.0599304\pi$$
$$180$$ 0 0
$$181$$ 1.45486i 0.108139i −0.998537 0.0540695i $$-0.982781\pi$$
0.998537 0.0540695i $$-0.0172193\pi$$
$$182$$ 0 0
$$183$$ −9.53475 −0.704829
$$184$$ 0 0
$$185$$ 10.1186 0.743936
$$186$$ 0 0
$$187$$ 2.06229i 0.150810i
$$188$$ 0 0
$$189$$ 1.61153i 0.117222i
$$190$$ 0 0
$$191$$ 21.9857 1.59083 0.795416 0.606064i $$-0.207252\pi$$
0.795416 + 0.606064i $$0.207252\pi$$
$$192$$ 0 0
$$193$$ 13.5269 0.973686 0.486843 0.873490i $$-0.338148\pi$$
0.486843 + 0.873490i $$0.338148\pi$$
$$194$$ 0 0
$$195$$ −7.10687 −0.508933
$$196$$ 0 0
$$197$$ 14.6237 1.04190 0.520948 0.853588i $$-0.325579\pi$$
0.520948 + 0.853588i $$0.325579\pi$$
$$198$$ 0 0
$$199$$ −3.24225 −0.229837 −0.114919 0.993375i $$-0.536661\pi$$
−0.114919 + 0.993375i $$0.536661\pi$$
$$200$$ 0 0
$$201$$ 2.33657i 0.164809i
$$202$$ 0 0
$$203$$ 0.0589508 0.00413754
$$204$$ 0 0
$$205$$ 5.43873i 0.379857i
$$206$$ 0 0
$$207$$ 4.40428 + 1.89798i 0.306119 + 0.131919i
$$208$$ 0 0
$$209$$ 6.82885 0.472362
$$210$$ 0 0
$$211$$ 25.4246i 1.75030i −0.483850 0.875151i $$-0.660762\pi$$
0.483850 0.875151i $$-0.339238\pi$$
$$212$$ 0 0
$$213$$ 11.3842 0.780033
$$214$$ 0 0
$$215$$ 9.60250i 0.654885i
$$216$$ 0 0
$$217$$ 7.08016i 0.480633i
$$218$$ 0 0
$$219$$ 1.61161i 0.108902i
$$220$$ 0 0
$$221$$ 12.7408i 0.857040i
$$222$$ 0 0
$$223$$ 18.2691i 1.22339i −0.791095 0.611694i $$-0.790489\pi$$
0.791095 0.611694i $$-0.209511\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ 23.8464 1.58274 0.791372 0.611335i $$-0.209367\pi$$
0.791372 + 0.611335i $$0.209367\pi$$
$$228$$ 0 0
$$229$$ 3.95960i 0.261658i −0.991405 0.130829i $$-0.958236\pi$$
0.991405 0.130829i $$-0.0417639\pi$$
$$230$$ 0 0
$$231$$ 1.85383i 0.121973i
$$232$$ 0 0
$$233$$ 26.6401 1.74525 0.872625 0.488392i $$-0.162416\pi$$
0.872625 + 0.488392i $$0.162416\pi$$
$$234$$ 0 0
$$235$$ 9.16374 0.597776
$$236$$ 0 0
$$237$$ 5.33892i 0.346800i
$$238$$ 0 0
$$239$$ 15.7541i 1.01905i −0.860457 0.509523i $$-0.829822\pi$$
0.860457 0.509523i $$-0.170178\pi$$
$$240$$ 0 0
$$241$$ 2.31154i 0.148899i −0.997225 0.0744497i $$-0.976280\pi$$
0.997225 0.0744497i $$-0.0237200\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ 4.40297i 0.281295i
$$246$$ 0 0
$$247$$ −42.1886 −2.68440
$$248$$ 0 0
$$249$$ 0.722088i 0.0457605i
$$250$$ 0 0
$$251$$ 21.6173 1.36447 0.682235 0.731133i $$-0.261008\pi$$
0.682235 + 0.731133i $$0.261008\pi$$
$$252$$ 0 0
$$253$$ 5.06647 + 2.18335i 0.318526 + 0.137266i
$$254$$ 0 0
$$255$$ 1.79275i 0.112266i
$$256$$ 0 0
$$257$$ 4.71865 0.294341 0.147170 0.989111i $$-0.452983\pi$$
0.147170 + 0.989111i $$0.452983\pi$$
$$258$$ 0 0
$$259$$ 16.3065i 1.01323i
$$260$$ 0 0
$$261$$ 0.0365806 0.00226428
$$262$$ 0 0
$$263$$ 4.44240 0.273930 0.136965 0.990576i $$-0.456265\pi$$
0.136965 + 0.990576i $$0.456265\pi$$
$$264$$ 0 0
$$265$$ 1.95476 0.120080
$$266$$ 0 0
$$267$$ −2.09024 −0.127920
$$268$$ 0 0
$$269$$ −9.10119 −0.554909 −0.277455 0.960739i $$-0.589491\pi$$
−0.277455 + 0.960739i $$0.589491\pi$$
$$270$$ 0 0
$$271$$ 22.9892i 1.39650i 0.715856 + 0.698248i $$0.246037\pi$$
−0.715856 + 0.698248i $$0.753963\pi$$
$$272$$ 0 0
$$273$$ 11.4529i 0.693163i
$$274$$ 0 0
$$275$$ 1.15035 0.0693688
$$276$$ 0 0
$$277$$ 18.6686 1.12169 0.560843 0.827922i $$-0.310477\pi$$
0.560843 + 0.827922i $$0.310477\pi$$
$$278$$ 0 0
$$279$$ 4.39344i 0.263028i
$$280$$ 0 0
$$281$$ 23.4639i 1.39974i −0.714271 0.699869i $$-0.753242\pi$$
0.714271 0.699869i $$-0.246758\pi$$
$$282$$ 0 0
$$283$$ 13.4760 0.801068 0.400534 0.916282i $$-0.368825\pi$$
0.400534 + 0.916282i $$0.368825\pi$$
$$284$$ 0 0
$$285$$ 5.93632 0.351637
$$286$$ 0 0
$$287$$ −8.76468 −0.517363
$$288$$ 0 0
$$289$$ 13.7861 0.810944
$$290$$ 0 0
$$291$$ 1.93236 0.113277
$$292$$ 0 0
$$293$$ 26.8108i 1.56630i 0.621831 + 0.783151i $$0.286389\pi$$
−0.621831 + 0.783151i $$0.713611\pi$$
$$294$$ 0 0
$$295$$ 5.29905 0.308522
$$296$$ 0 0
$$297$$ 1.15035i 0.0667502i
$$298$$ 0 0
$$299$$ −31.3006 13.4887i −1.81016 0.780071i
$$300$$ 0 0
$$301$$ −15.4747 −0.891948
$$302$$ 0 0
$$303$$ 15.0107i 0.862340i
$$304$$ 0 0
$$305$$ −9.53475 −0.545958
$$306$$ 0 0
$$307$$ 1.71461i 0.0978580i 0.998802 + 0.0489290i $$0.0155808\pi$$
−0.998802 + 0.0489290i $$0.984419\pi$$
$$308$$ 0 0
$$309$$ 3.04742i 0.173362i
$$310$$ 0 0
$$311$$ 1.97438i 0.111957i 0.998432 + 0.0559785i $$0.0178278\pi$$
−0.998432 + 0.0559785i $$0.982172\pi$$
$$312$$ 0 0
$$313$$ 8.62500i 0.487514i −0.969836 0.243757i $$-0.921620\pi$$
0.969836 0.243757i $$-0.0783799\pi$$
$$314$$ 0 0
$$315$$ 1.61153i 0.0907995i
$$316$$ 0 0
$$317$$ −22.2686 −1.25073 −0.625366 0.780332i $$-0.715050\pi$$
−0.625366 + 0.780332i $$0.715050\pi$$
$$318$$ 0 0
$$319$$ 0.0420806 0.00235606
$$320$$ 0 0
$$321$$ 12.6032i 0.703442i
$$322$$ 0 0
$$323$$ 10.6423i 0.592154i
$$324$$ 0 0
$$325$$ −7.10687 −0.394218
$$326$$ 0 0
$$327$$ 15.0300 0.831162
$$328$$ 0 0
$$329$$ 14.7676i 0.814167i
$$330$$ 0 0
$$331$$ 13.5388i 0.744162i 0.928200 + 0.372081i $$0.121356\pi$$
−0.928200 + 0.372081i $$0.878644\pi$$
$$332$$ 0 0
$$333$$ 10.1186i 0.554497i
$$334$$ 0 0
$$335$$ 2.33657i 0.127660i
$$336$$ 0 0
$$337$$ 18.2890i 0.996267i −0.867100 0.498134i $$-0.834019\pi$$
0.867100 0.498134i $$-0.165981\pi$$
$$338$$ 0 0
$$339$$ −8.39445 −0.455924
$$340$$ 0 0
$$341$$ 5.05400i 0.273689i
$$342$$ 0 0
$$343$$ 18.3762 0.992223
$$344$$ 0 0
$$345$$ 4.40428 + 1.89798i 0.237118 + 0.102184i
$$346$$ 0 0
$$347$$ 15.4805i 0.831037i 0.909585 + 0.415519i $$0.136400\pi$$
−0.909585 + 0.415519i $$0.863600\pi$$
$$348$$ 0 0
$$349$$ −26.2209 −1.40357 −0.701785 0.712388i $$-0.747614\pi$$
−0.701785 + 0.712388i $$0.747614\pi$$
$$350$$ 0 0
$$351$$ 7.10687i 0.379336i
$$352$$ 0 0
$$353$$ 22.9065 1.21919 0.609596 0.792713i $$-0.291332\pi$$
0.609596 + 0.792713i $$0.291332\pi$$
$$354$$ 0 0
$$355$$ 11.3842 0.604211
$$356$$ 0 0
$$357$$ −2.88907 −0.152906
$$358$$ 0 0
$$359$$ 6.73100 0.355248 0.177624 0.984098i $$-0.443159\pi$$
0.177624 + 0.984098i $$0.443159\pi$$
$$360$$ 0 0
$$361$$ 16.2398 0.854729
$$362$$ 0 0
$$363$$ 9.67669i 0.507895i
$$364$$ 0 0
$$365$$ 1.61161i 0.0843554i
$$366$$ 0 0
$$367$$ 9.41638 0.491531 0.245765 0.969329i $$-0.420961\pi$$
0.245765 + 0.969329i $$0.420961\pi$$
$$368$$ 0 0
$$369$$ −5.43873 −0.283129
$$370$$ 0 0
$$371$$ 3.15015i 0.163548i
$$372$$ 0 0
$$373$$ 32.7090i 1.69361i 0.531904 + 0.846805i $$0.321477\pi$$
−0.531904 + 0.846805i $$0.678523\pi$$
$$374$$ 0 0
$$375$$ 1.00000 0.0516398
$$376$$ 0 0
$$377$$ −0.259974 −0.0133893
$$378$$ 0 0
$$379$$ −12.0214 −0.617496 −0.308748 0.951144i $$-0.599910\pi$$
−0.308748 + 0.951144i $$0.599910\pi$$
$$380$$ 0 0
$$381$$ −18.1343 −0.929049
$$382$$ 0 0
$$383$$ −28.7465 −1.46888 −0.734438 0.678676i $$-0.762554\pi$$
−0.734438 + 0.678676i $$0.762554\pi$$
$$384$$ 0 0
$$385$$ 1.85383i 0.0944798i
$$386$$ 0 0
$$387$$ −9.60250 −0.488122
$$388$$ 0 0
$$389$$ 8.14172i 0.412801i 0.978468 + 0.206401i $$0.0661750\pi$$
−0.978468 + 0.206401i $$0.933825\pi$$
$$390$$ 0 0
$$391$$ −3.40260 + 7.89576i −0.172077 + 0.399306i
$$392$$ 0 0
$$393$$ 1.77034 0.0893021
$$394$$ 0 0
$$395$$ 5.33892i 0.268630i
$$396$$ 0 0
$$397$$ −8.41445 −0.422309 −0.211154 0.977453i $$-0.567722\pi$$
−0.211154 + 0.977453i $$0.567722\pi$$
$$398$$ 0 0
$$399$$ 9.56656i 0.478927i
$$400$$ 0 0
$$401$$ 24.7496i 1.23594i −0.786203 0.617968i $$-0.787956\pi$$
0.786203 0.617968i $$-0.212044\pi$$
$$402$$ 0 0
$$403$$ 31.2236i 1.55536i
$$404$$ 0 0
$$405$$ 1.00000i 0.0496904i
$$406$$ 0 0
$$407$$ 11.6400i 0.576972i
$$408$$ 0 0
$$409$$ 21.2723 1.05185 0.525923 0.850532i $$-0.323720\pi$$
0.525923 + 0.850532i $$0.323720\pi$$
$$410$$ 0 0
$$411$$ 17.7574 0.875910
$$412$$ 0 0
$$413$$ 8.53957i 0.420205i
$$414$$ 0 0
$$415$$ 0.722088i 0.0354459i
$$416$$ 0 0
$$417$$ 13.6548 0.668680
$$418$$ 0 0
$$419$$ −7.56247 −0.369451 −0.184726 0.982790i $$-0.559140\pi$$
−0.184726 + 0.982790i $$0.559140\pi$$
$$420$$ 0 0
$$421$$ 26.6686i 1.29975i −0.760042 0.649874i $$-0.774822\pi$$
0.760042 0.649874i $$-0.225178\pi$$
$$422$$ 0 0
$$423$$ 9.16374i 0.445556i
$$424$$ 0 0
$$425$$ 1.79275i 0.0869610i
$$426$$ 0 0
$$427$$ 15.3656i 0.743591i
$$428$$ 0 0
$$429$$ 8.17540i 0.394712i
$$430$$ 0 0
$$431$$ −19.3147 −0.930356 −0.465178 0.885217i $$-0.654010\pi$$
−0.465178 + 0.885217i $$0.654010\pi$$
$$432$$ 0 0
$$433$$ 15.6094i 0.750141i 0.926996 + 0.375071i $$0.122382\pi$$
−0.926996 + 0.375071i $$0.877618\pi$$
$$434$$ 0 0
$$435$$ 0.0365806 0.00175391
$$436$$ 0 0
$$437$$ 26.1452 + 11.2670i 1.25069 + 0.538974i
$$438$$ 0 0
$$439$$ 12.5249i 0.597779i 0.954288 + 0.298889i $$0.0966161\pi$$
−0.954288 + 0.298889i $$0.903384\pi$$
$$440$$ 0 0
$$441$$ 4.40297 0.209665
$$442$$ 0 0
$$443$$ 37.7262i 1.79242i −0.443625 0.896212i $$-0.646308\pi$$
0.443625 0.896212i $$-0.353692\pi$$
$$444$$ 0 0
$$445$$ −2.09024 −0.0990867
$$446$$ 0 0
$$447$$ 9.38262 0.443783
$$448$$ 0 0
$$449$$ 9.98001 0.470986 0.235493 0.971876i $$-0.424330\pi$$
0.235493 + 0.971876i $$0.424330\pi$$
$$450$$ 0 0
$$451$$ −6.25645 −0.294605
$$452$$ 0 0
$$453$$ −13.1263 −0.616726
$$454$$ 0 0
$$455$$ 11.4529i 0.536922i
$$456$$ 0 0
$$457$$ 39.0608i 1.82719i 0.406628 + 0.913594i $$0.366705\pi$$
−0.406628 + 0.913594i $$0.633295\pi$$
$$458$$ 0 0
$$459$$ −1.79275 −0.0836783
$$460$$ 0 0
$$461$$ −38.5061 −1.79341 −0.896705 0.442629i $$-0.854046\pi$$
−0.896705 + 0.442629i $$0.854046\pi$$
$$462$$ 0 0
$$463$$ 7.15257i 0.332408i −0.986091 0.166204i $$-0.946849\pi$$
0.986091 0.166204i $$-0.0531510\pi$$
$$464$$ 0 0
$$465$$ 4.39344i 0.203741i
$$466$$ 0 0
$$467$$ −21.2146 −0.981692 −0.490846 0.871246i $$-0.663312\pi$$
−0.490846 + 0.871246i $$0.663312\pi$$
$$468$$ 0 0
$$469$$ −3.76545 −0.173872
$$470$$ 0 0
$$471$$ −2.75711 −0.127041
$$472$$ 0 0
$$473$$ −11.0462 −0.507907
$$474$$ 0 0
$$475$$ 5.93632 0.272377
$$476$$ 0 0
$$477$$ 1.95476i 0.0895023i
$$478$$ 0 0
$$479$$ −29.8774 −1.36513 −0.682566 0.730824i $$-0.739136\pi$$
−0.682566 + 0.730824i $$0.739136\pi$$
$$480$$ 0 0
$$481$$ 71.9117i 3.27889i
$$482$$ 0 0
$$483$$ −3.05865 + 7.09763i −0.139174 + 0.322953i
$$484$$ 0 0
$$485$$ 1.93236 0.0877438
$$486$$ 0 0
$$487$$ 1.40199i 0.0635301i −0.999495 0.0317650i $$-0.989887\pi$$
0.999495 0.0317650i $$-0.0101128\pi$$
$$488$$ 0 0
$$489$$ −7.13282 −0.322557
$$490$$ 0 0
$$491$$ 29.6976i 1.34023i −0.742255 0.670117i $$-0.766244\pi$$
0.742255 0.670117i $$-0.233756\pi$$
$$492$$ 0 0
$$493$$ 0.0655798i 0.00295357i
$$494$$ 0 0
$$495$$ 1.15035i 0.0517045i
$$496$$ 0 0
$$497$$ 18.3460i 0.822930i
$$498$$ 0 0
$$499$$ 8.06976i 0.361252i 0.983552 + 0.180626i $$0.0578124\pi$$
−0.983552 + 0.180626i $$0.942188\pi$$
$$500$$ 0 0
$$501$$ −0.264942 −0.0118367
$$502$$ 0 0
$$503$$ 22.4638 1.00161 0.500807 0.865559i $$-0.333037\pi$$
0.500807 + 0.865559i $$0.333037\pi$$
$$504$$ 0 0
$$505$$ 15.0107i 0.667965i
$$506$$ 0 0
$$507$$ 37.5075i 1.66577i
$$508$$ 0 0
$$509$$ 1.54110 0.0683082 0.0341541 0.999417i $$-0.489126\pi$$
0.0341541 + 0.999417i $$0.489126\pi$$
$$510$$ 0 0
$$511$$ 2.59715 0.114891
$$512$$ 0 0
$$513$$ 5.93632i 0.262095i
$$514$$ 0 0
$$515$$ 3.04742i 0.134285i
$$516$$ 0 0
$$517$$ 10.5415i 0.463616i
$$518$$ 0 0
$$519$$ 9.93924i 0.436284i
$$520$$ 0 0
$$521$$ 2.26345i 0.0991637i −0.998770 0.0495818i $$-0.984211\pi$$
0.998770 0.0495818i $$-0.0157889\pi$$
$$522$$ 0 0
$$523$$ 3.43328 0.150127 0.0750635 0.997179i $$-0.476084\pi$$
0.0750635 + 0.997179i $$0.476084\pi$$
$$524$$ 0 0
$$525$$ 1.61153i 0.0703330i
$$526$$ 0 0
$$527$$ 7.87632 0.343098
$$528$$ 0 0
$$529$$ 15.7953 + 16.7185i 0.686754 + 0.726890i
$$530$$ 0 0
$$531$$ 5.29905i 0.229959i
$$532$$ 0 0
$$533$$ 38.6523 1.67422
$$534$$ 0 0
$$535$$ 12.6032i 0.544884i
$$536$$ 0 0
$$537$$ 5.00824 0.216121
$$538$$ 0 0
$$539$$ 5.06496 0.218163
$$540$$ 0 0
$$541$$ −5.62058 −0.241647 −0.120824 0.992674i $$-0.538554\pi$$
−0.120824 + 0.992674i $$0.538554\pi$$
$$542$$ 0 0
$$543$$ 1.45486 0.0624341
$$544$$ 0 0
$$545$$ 15.0300 0.643815
$$546$$ 0 0
$$547$$ 24.6582i 1.05431i 0.849770 + 0.527154i $$0.176741\pi$$
−0.849770 + 0.527154i $$0.823259\pi$$
$$548$$ 0 0
$$549$$ 9.53475i 0.406933i
$$550$$ 0 0
$$551$$ 0.217154 0.00925108
$$552$$ 0 0
$$553$$ −8.60383 −0.365872
$$554$$ 0 0
$$555$$ 10.1186i 0.429511i
$$556$$ 0 0
$$557$$ 33.0462i 1.40021i −0.714039 0.700106i $$-0.753136\pi$$
0.714039 0.700106i $$-0.246864\pi$$
$$558$$ 0 0
$$559$$ 68.2436 2.88640
$$560$$ 0 0
$$561$$ −2.06229 −0.0870700
$$562$$ 0 0
$$563$$ −15.8634 −0.668563 −0.334281 0.942473i $$-0.608494\pi$$
−0.334281 + 0.942473i $$0.608494\pi$$
$$564$$ 0 0
$$565$$ −8.39445 −0.353157
$$566$$ 0 0
$$567$$ −1.61153 −0.0676779
$$568$$ 0 0
$$569$$ 16.6195i 0.696724i −0.937360 0.348362i $$-0.886738\pi$$
0.937360 0.348362i $$-0.113262\pi$$
$$570$$ 0 0
$$571$$ −6.96762 −0.291586 −0.145793 0.989315i $$-0.546573\pi$$
−0.145793 + 0.989315i $$0.546573\pi$$
$$572$$ 0 0
$$573$$ 21.9857i 0.918467i
$$574$$ 0 0
$$575$$ 4.40428 + 1.89798i 0.183671 + 0.0791513i
$$576$$ 0 0
$$577$$ 20.7254 0.862811 0.431406 0.902158i $$-0.358018\pi$$
0.431406 + 0.902158i $$0.358018\pi$$
$$578$$ 0 0
$$579$$ 13.5269i 0.562158i
$$580$$ 0 0
$$581$$ −1.16367 −0.0482770
$$582$$ 0 0
$$583$$ 2.24866i 0.0931300i
$$584$$ 0 0
$$585$$ 7.10687i 0.293833i
$$586$$ 0 0
$$587$$ 32.8221i 1.35471i −0.735655 0.677357i $$-0.763125\pi$$
0.735655 0.677357i $$-0.236875\pi$$
$$588$$ 0 0
$$589$$ 26.0808i 1.07464i
$$590$$ 0 0
$$591$$ 14.6237i 0.601539i
$$592$$ 0 0
$$593$$ −4.92783 −0.202362 −0.101181 0.994868i $$-0.532262\pi$$
−0.101181 + 0.994868i $$0.532262\pi$$
$$594$$ 0 0
$$595$$ −2.88907 −0.118440
$$596$$ 0 0
$$597$$ 3.24225i 0.132696i
$$598$$ 0 0
$$599$$ 19.6282i 0.801987i 0.916081 + 0.400994i $$0.131335\pi$$
−0.916081 + 0.400994i $$0.868665\pi$$
$$600$$ 0 0
$$601$$ 11.1852 0.456253 0.228126 0.973632i $$-0.426740\pi$$
0.228126 + 0.973632i $$0.426740\pi$$
$$602$$ 0 0
$$603$$ −2.33657 −0.0951524
$$604$$ 0 0
$$605$$ 9.67669i 0.393413i
$$606$$ 0 0
$$607$$ 12.9158i 0.524238i 0.965036 + 0.262119i $$0.0844213\pi$$
−0.965036 + 0.262119i $$0.915579\pi$$
$$608$$ 0 0
$$609$$ 0.0589508i 0.00238881i
$$610$$ 0 0
$$611$$ 65.1254i 2.63469i
$$612$$ 0 0
$$613$$ 24.6992i 0.997591i −0.866720 0.498795i $$-0.833776\pi$$
0.866720 0.498795i $$-0.166224\pi$$
$$614$$ 0 0
$$615$$ −5.43873 −0.219311
$$616$$ 0 0
$$617$$ 44.9940i 1.81139i −0.423928 0.905696i $$-0.639349\pi$$
0.423928 0.905696i $$-0.360651\pi$$
$$618$$ 0 0
$$619$$ 36.3335 1.46037 0.730183 0.683252i $$-0.239435\pi$$
0.730183 + 0.683252i $$0.239435\pi$$
$$620$$ 0 0
$$621$$ −1.89798 + 4.40428i −0.0761633 + 0.176738i
$$622$$ 0 0
$$623$$ 3.36848i 0.134955i
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 6.82885i 0.272718i
$$628$$ 0 0
$$629$$ −18.1401 −0.723294
$$630$$ 0 0
$$631$$ 17.8111 0.709049 0.354525 0.935047i $$-0.384643\pi$$
0.354525 + 0.935047i $$0.384643\pi$$
$$632$$ 0 0
$$633$$ 25.4246 1.01054
$$634$$ 0 0
$$635$$ −18.1343 −0.719638
$$636$$ 0 0
$$637$$ −31.2913 −1.23981
$$638$$ 0 0
$$639$$ 11.3842i 0.450352i
$$640$$ 0 0
$$641$$ 34.0713i 1.34574i −0.739762 0.672868i $$-0.765062\pi$$
0.739762 0.672868i $$-0.234938\pi$$
$$642$$ 0 0
$$643$$ −24.0327 −0.947756 −0.473878 0.880590i $$-0.657146\pi$$
−0.473878 + 0.880590i $$0.657146\pi$$
$$644$$ 0 0
$$645$$ −9.60250 −0.378098
$$646$$ 0 0
$$647$$ 29.5150i 1.16036i −0.814490 0.580178i $$-0.802983\pi$$
0.814490 0.580178i $$-0.197017\pi$$
$$648$$ 0 0
$$649$$ 6.09577i 0.239280i
$$650$$ 0 0
$$651$$ 7.08016 0.277493
$$652$$ 0 0
$$653$$ −20.6782 −0.809202 −0.404601 0.914493i $$-0.632590\pi$$
−0.404601 + 0.914493i $$0.632590\pi$$
$$654$$ 0 0
$$655$$ 1.77034 0.0691731
$$656$$ 0 0
$$657$$ 1.61161 0.0628748
$$658$$ 0 0
$$659$$ 24.6283 0.959382 0.479691 0.877438i $$-0.340749\pi$$
0.479691 + 0.877438i $$0.340749\pi$$
$$660$$ 0 0
$$661$$ 15.4778i 0.602016i −0.953622 0.301008i $$-0.902677\pi$$
0.953622 0.301008i $$-0.0973231\pi$$
$$662$$ 0 0
$$663$$ 12.7408 0.494812
$$664$$ 0 0
$$665$$ 9.56656i 0.370975i
$$666$$ 0 0
$$667$$ 0.161111 + 0.0694293i 0.00623825 + 0.00268831i
$$668$$ 0 0
$$669$$ 18.2691 0.706323
$$670$$ 0 0
$$671$$ 10.9683i 0.423427i
$$672$$ 0 0
$$673$$ 9.60160 0.370115 0.185057 0.982728i $$-0.440753\pi$$
0.185057 + 0.982728i $$0.440753\pi$$
$$674$$ 0 0
$$675$$ 1.00000i 0.0384900i
$$676$$ 0 0
$$677$$ 45.5851i 1.75198i 0.482331 + 0.875989i $$0.339790\pi$$
−0.482331 + 0.875989i $$0.660210\pi$$
$$678$$ 0 0
$$679$$ 3.11405i 0.119506i
$$680$$ 0 0
$$681$$ 23.8464i 0.913798i
$$682$$ 0 0
$$683$$ 27.2853i 1.04404i −0.852932 0.522022i $$-0.825178\pi$$
0.852932 0.522022i $$-0.174822\pi$$
$$684$$ 0 0
$$685$$ 17.7574 0.678477
$$686$$ 0 0
$$687$$ 3.95960 0.151068
$$688$$ 0 0
$$689$$ 13.8922i 0.529251i
$$690$$ 0 0
$$691$$ 19.1940i 0.730173i −0.930974 0.365087i $$-0.881039\pi$$
0.930974 0.365087i $$-0.118961\pi$$
$$692$$ 0 0
$$693$$ −1.85383 −0.0704211
$$694$$ 0 0
$$695$$ 13.6548 0.517957
$$696$$ 0 0
$$697$$ 9.75027i 0.369318i
$$698$$ 0 0
$$699$$ 26.6401i 1.00762i
$$700$$ 0 0
$$701$$ 22.8391i 0.862622i 0.902203 + 0.431311i $$0.141949\pi$$
−0.902203 + 0.431311i $$0.858051\pi$$
$$702$$ 0 0
$$703$$ 60.0673i 2.26548i
$$704$$ 0 0
$$705$$ 9.16374i 0.345126i
$$706$$ 0 0
$$707$$ −24.1901 −0.909764
$$708$$ 0 0
$$709$$ 1.45458i 0.0546278i 0.999627 + 0.0273139i $$0.00869536\pi$$
−0.999627 + 0.0273139i $$0.991305\pi$$
$$710$$ 0 0
$$711$$ −5.33892 −0.200225
$$712$$ 0 0
$$713$$ 8.33866 19.3499i 0.312285 0.724660i
$$714$$ 0 0
$$715$$ 8.17540i 0.305742i
$$716$$ 0 0
$$717$$ 15.7541 0.588346
$$718$$ 0 0
$$719$$ 29.2388i 1.09042i −0.838298 0.545212i $$-0.816449\pi$$
0.838298 0.545212i $$-0.183551\pi$$
$$720$$ 0 0
$$721$$ 4.91101 0.182896
$$722$$ 0 0
$$723$$ 2.31154 0.0859671
$$724$$ 0 0
$$725$$ 0.0365806 0.00135857
$$726$$ 0 0
$$727$$ −40.7426 −1.51106 −0.755529 0.655115i $$-0.772620\pi$$
−0.755529 + 0.655115i $$0.772620\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 17.2149i 0.636714i
$$732$$ 0 0
$$733$$ 25.3692i 0.937033i 0.883455 + 0.468516i $$0.155211\pi$$
−0.883455 + 0.468516i $$0.844789\pi$$
$$734$$ 0 0
$$735$$ 4.40297 0.162406
$$736$$ 0 0
$$737$$ −2.68787 −0.0990091
$$738$$ 0 0
$$739$$ 8.67928i 0.319273i 0.987176 + 0.159636i $$0.0510321\pi$$
−0.987176 + 0.159636i $$0.948968\pi$$
$$740$$ 0 0
$$741$$ 42.1886i 1.54984i
$$742$$ 0 0
$$743$$ 18.8741 0.692424 0.346212 0.938156i $$-0.387468\pi$$
0.346212 + 0.938156i $$0.387468\pi$$
$$744$$ 0 0
$$745$$ 9.38262 0.343753
$$746$$ 0 0
$$747$$ −0.722088 −0.0264198
$$748$$ 0 0
$$749$$ 20.3105 0.742128
$$750$$ 0 0
$$751$$ −11.9864 −0.437390 −0.218695 0.975793i $$-0.570180\pi$$
−0.218695 + 0.975793i $$0.570180\pi$$
$$752$$ 0 0
$$753$$ 21.6173i 0.787777i
$$754$$ 0 0
$$755$$ −13.1263 −0.477714
$$756$$ 0 0
$$757$$ 9.99273i 0.363192i 0.983373 + 0.181596i $$0.0581263\pi$$
−0.983373 + 0.181596i $$0.941874\pi$$
$$758$$ 0 0
$$759$$ −2.18335 + 5.06647i −0.0792504 + 0.183901i
$$760$$ 0 0
$$761$$ −13.8964 −0.503746 −0.251873 0.967760i $$-0.581046\pi$$
−0.251873 + 0.967760i $$0.581046\pi$$
$$762$$ 0 0
$$763$$ 24.2213i 0.876871i
$$764$$ 0 0
$$765$$ −1.79275 −0.0648169
$$766$$ 0 0
$$767$$ 37.6596i 1.35981i
$$768$$ 0 0
$$769$$ 8.90960i 0.321288i 0.987012 + 0.160644i $$0.0513572\pi$$
−0.987012 + 0.160644i $$0.948643\pi$$
$$770$$ 0 0
$$771$$ 4.71865i 0.169938i
$$772$$ 0 0
$$773$$ 11.6166i 0.417821i 0.977935 + 0.208910i $$0.0669917\pi$$
−0.977935 + 0.208910i $$0.933008\pi$$
$$774$$ 0 0
$$775$$ 4.39344i 0.157817i
$$776$$ 0 0
$$777$$ −16.3065 −0.584991
$$778$$ 0 0
$$779$$ −32.2860 −1.15677
$$780$$ 0 0
$$781$$ 13.0958i 0.468606i
$$782$$ 0 0
$$783$$ 0.0365806i 0.00130729i
$$784$$ 0 0
$$785$$ −2.75711 −0.0984054
$$786$$ 0 0
$$787$$ 32.1690 1.14670 0.573350 0.819310i $$-0.305643\pi$$
0.573350 + 0.819310i $$0.305643\pi$$
$$788$$ 0 0
$$789$$ 4.44240i 0.158154i
$$790$$ 0 0
$$791$$ 13.5279i 0.480998i
$$792$$ 0 0
$$793$$ 67.7622i 2.40631i
$$794$$ 0 0
$$795$$ 1.95476i 0.0693282i
$$796$$ 0 0
$$797$$ 12.5397i 0.444178i −0.975026 0.222089i $$-0.928712\pi$$
0.975026 0.222089i $$-0.0712876\pi$$
$$798$$ 0 0
$$799$$ −16.4283 −0.581190
$$800$$ 0 0
$$801$$ 2.09024i 0.0738549i
$$802$$ 0 0
$$803$$ 1.85392 0.0654233
$$804$$ 0 0
$$805$$ −3.05865 + 7.09763i