# Properties

 Label 1800.2.k.j.901.4 Level $1800$ Weight $2$ Character 1800.901 Analytic conductor $14.373$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1800.k (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.3730723638$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 40) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 901.4 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1800.901 Dual form 1800.2.k.j.901.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +2.73205 q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$$ $$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +2.73205 q^{7} +(-2.00000 - 2.00000i) q^{8} +2.00000i q^{11} -3.46410i q^{13} +(1.00000 + 3.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} -3.46410 q^{17} +7.46410i q^{19} +(-2.73205 + 0.732051i) q^{22} +4.19615 q^{23} +(4.73205 - 1.26795i) q^{26} +(-4.73205 + 2.73205i) q^{28} +6.92820i q^{29} +1.46410 q^{31} +(5.46410 + 1.46410i) q^{32} +(-1.26795 - 4.73205i) q^{34} +2.00000i q^{37} +(-10.1962 + 2.73205i) q^{38} +5.46410 q^{41} +8.73205i q^{43} +(-2.00000 - 3.46410i) q^{44} +(1.53590 + 5.73205i) q^{46} +6.73205 q^{47} +0.464102 q^{49} +(3.46410 + 6.00000i) q^{52} +4.53590i q^{53} +(-5.46410 - 5.46410i) q^{56} +(-9.46410 + 2.53590i) q^{58} +0.535898i q^{59} +4.92820i q^{61} +(0.535898 + 2.00000i) q^{62} +8.00000i q^{64} -7.26795i q^{67} +(6.00000 - 3.46410i) q^{68} +1.46410 q^{71} -0.535898 q^{73} +(-2.73205 + 0.732051i) q^{74} +(-7.46410 - 12.9282i) q^{76} +5.46410i q^{77} -14.9282 q^{79} +(2.00000 + 7.46410i) q^{82} +4.73205i q^{83} +(-11.9282 + 3.19615i) q^{86} +(4.00000 - 4.00000i) q^{88} +4.92820 q^{89} -9.46410i q^{91} +(-7.26795 + 4.19615i) q^{92} +(2.46410 + 9.19615i) q^{94} -6.39230 q^{97} +(0.169873 + 0.633975i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{2} + 4q^{7} - 8q^{8} + O(q^{10})$$ $$4q - 2q^{2} + 4q^{7} - 8q^{8} + 4q^{14} + 8q^{16} - 4q^{22} - 4q^{23} + 12q^{26} - 12q^{28} - 8q^{31} + 8q^{32} - 12q^{34} - 20q^{38} + 8q^{41} - 8q^{44} + 20q^{46} + 20q^{47} - 12q^{49} - 8q^{56} - 24q^{58} + 16q^{62} + 24q^{68} - 8q^{71} - 16q^{73} - 4q^{74} - 16q^{76} - 32q^{79} + 8q^{82} - 20q^{86} + 16q^{88} - 8q^{89} - 36q^{92} - 4q^{94} + 16q^{97} + 18q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$$.

 $$n$$ $$577$$ $$901$$ $$1001$$ $$1351$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.366025 + 1.36603i 0.258819 + 0.965926i
$$3$$ 0 0
$$4$$ −1.73205 + 1.00000i −0.866025 + 0.500000i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.73205 1.03262 0.516309 0.856402i $$-0.327306\pi$$
0.516309 + 0.856402i $$0.327306\pi$$
$$8$$ −2.00000 2.00000i −0.707107 0.707107i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.00000i 0.603023i 0.953463 + 0.301511i $$0.0974911\pi$$
−0.953463 + 0.301511i $$0.902509\pi$$
$$12$$ 0 0
$$13$$ 3.46410i 0.960769i −0.877058 0.480384i $$-0.840497\pi$$
0.877058 0.480384i $$-0.159503\pi$$
$$14$$ 1.00000 + 3.73205i 0.267261 + 0.997433i
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ −3.46410 −0.840168 −0.420084 0.907485i $$-0.637999\pi$$
−0.420084 + 0.907485i $$0.637999\pi$$
$$18$$ 0 0
$$19$$ 7.46410i 1.71238i 0.516659 + 0.856191i $$0.327175\pi$$
−0.516659 + 0.856191i $$0.672825\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −2.73205 + 0.732051i −0.582475 + 0.156074i
$$23$$ 4.19615 0.874958 0.437479 0.899229i $$-0.355871\pi$$
0.437479 + 0.899229i $$0.355871\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 4.73205 1.26795i 0.928032 0.248665i
$$27$$ 0 0
$$28$$ −4.73205 + 2.73205i −0.894274 + 0.516309i
$$29$$ 6.92820i 1.28654i 0.765641 + 0.643268i $$0.222422\pi$$
−0.765641 + 0.643268i $$0.777578\pi$$
$$30$$ 0 0
$$31$$ 1.46410 0.262960 0.131480 0.991319i $$-0.458027\pi$$
0.131480 + 0.991319i $$0.458027\pi$$
$$32$$ 5.46410 + 1.46410i 0.965926 + 0.258819i
$$33$$ 0 0
$$34$$ −1.26795 4.73205i −0.217451 0.811540i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000i 0.328798i 0.986394 + 0.164399i $$0.0525685\pi$$
−0.986394 + 0.164399i $$0.947432\pi$$
$$38$$ −10.1962 + 2.73205i −1.65403 + 0.443197i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 5.46410 0.853349 0.426675 0.904405i $$-0.359685\pi$$
0.426675 + 0.904405i $$0.359685\pi$$
$$42$$ 0 0
$$43$$ 8.73205i 1.33163i 0.746119 + 0.665813i $$0.231915\pi$$
−0.746119 + 0.665813i $$0.768085\pi$$
$$44$$ −2.00000 3.46410i −0.301511 0.522233i
$$45$$ 0 0
$$46$$ 1.53590 + 5.73205i 0.226456 + 0.845145i
$$47$$ 6.73205 0.981971 0.490985 0.871168i $$-0.336637\pi$$
0.490985 + 0.871168i $$0.336637\pi$$
$$48$$ 0 0
$$49$$ 0.464102 0.0663002
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 3.46410 + 6.00000i 0.480384 + 0.832050i
$$53$$ 4.53590i 0.623054i 0.950237 + 0.311527i $$0.100840\pi$$
−0.950237 + 0.311527i $$0.899160\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −5.46410 5.46410i −0.730171 0.730171i
$$57$$ 0 0
$$58$$ −9.46410 + 2.53590i −1.24270 + 0.332980i
$$59$$ 0.535898i 0.0697680i 0.999391 + 0.0348840i $$0.0111062\pi$$
−0.999391 + 0.0348840i $$0.988894\pi$$
$$60$$ 0 0
$$61$$ 4.92820i 0.630992i 0.948927 + 0.315496i $$0.102171\pi$$
−0.948927 + 0.315496i $$0.897829\pi$$
$$62$$ 0.535898 + 2.00000i 0.0680592 + 0.254000i
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 7.26795i 0.887921i −0.896046 0.443961i $$-0.853573\pi$$
0.896046 0.443961i $$-0.146427\pi$$
$$68$$ 6.00000 3.46410i 0.727607 0.420084i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.46410 0.173757 0.0868784 0.996219i $$-0.472311\pi$$
0.0868784 + 0.996219i $$0.472311\pi$$
$$72$$ 0 0
$$73$$ −0.535898 −0.0627222 −0.0313611 0.999508i $$-0.509984\pi$$
−0.0313611 + 0.999508i $$0.509984\pi$$
$$74$$ −2.73205 + 0.732051i −0.317594 + 0.0850992i
$$75$$ 0 0
$$76$$ −7.46410 12.9282i −0.856191 1.48297i
$$77$$ 5.46410i 0.622692i
$$78$$ 0 0
$$79$$ −14.9282 −1.67955 −0.839777 0.542931i $$-0.817314\pi$$
−0.839777 + 0.542931i $$0.817314\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 2.00000 + 7.46410i 0.220863 + 0.824272i
$$83$$ 4.73205i 0.519410i 0.965688 + 0.259705i $$0.0836253\pi$$
−0.965688 + 0.259705i $$0.916375\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −11.9282 + 3.19615i −1.28625 + 0.344650i
$$87$$ 0 0
$$88$$ 4.00000 4.00000i 0.426401 0.426401i
$$89$$ 4.92820 0.522388 0.261194 0.965286i $$-0.415884\pi$$
0.261194 + 0.965286i $$0.415884\pi$$
$$90$$ 0 0
$$91$$ 9.46410i 0.992107i
$$92$$ −7.26795 + 4.19615i −0.757736 + 0.437479i
$$93$$ 0 0
$$94$$ 2.46410 + 9.19615i 0.254153 + 0.948511i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −6.39230 −0.649040 −0.324520 0.945879i $$-0.605203\pi$$
−0.324520 + 0.945879i $$0.605203\pi$$
$$98$$ 0.169873 + 0.633975i 0.0171598 + 0.0640411i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 10.9282i 1.08740i 0.839281 + 0.543698i $$0.182976\pi$$
−0.839281 + 0.543698i $$0.817024\pi$$
$$102$$ 0 0
$$103$$ 1.66025 0.163590 0.0817948 0.996649i $$-0.473935\pi$$
0.0817948 + 0.996649i $$0.473935\pi$$
$$104$$ −6.92820 + 6.92820i −0.679366 + 0.679366i
$$105$$ 0 0
$$106$$ −6.19615 + 1.66025i −0.601824 + 0.161258i
$$107$$ 0.732051i 0.0707700i −0.999374 0.0353850i $$-0.988734\pi$$
0.999374 0.0353850i $$-0.0112658\pi$$
$$108$$ 0 0
$$109$$ 3.07180i 0.294225i 0.989120 + 0.147112i $$0.0469979\pi$$
−0.989120 + 0.147112i $$0.953002\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 5.46410 9.46410i 0.516309 0.894274i
$$113$$ 0.928203 0.0873180 0.0436590 0.999046i $$-0.486098\pi$$
0.0436590 + 0.999046i $$0.486098\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −6.92820 12.0000i −0.643268 1.11417i
$$117$$ 0 0
$$118$$ −0.732051 + 0.196152i −0.0673907 + 0.0180573i
$$119$$ −9.46410 −0.867573
$$120$$ 0 0
$$121$$ 7.00000 0.636364
$$122$$ −6.73205 + 1.80385i −0.609491 + 0.163313i
$$123$$ 0 0
$$124$$ −2.53590 + 1.46410i −0.227730 + 0.131480i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −13.2679 −1.17734 −0.588670 0.808373i $$-0.700348\pi$$
−0.588670 + 0.808373i $$0.700348\pi$$
$$128$$ −10.9282 + 2.92820i −0.965926 + 0.258819i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 7.85641i 0.686417i −0.939259 0.343209i $$-0.888486\pi$$
0.939259 0.343209i $$-0.111514\pi$$
$$132$$ 0 0
$$133$$ 20.3923i 1.76824i
$$134$$ 9.92820 2.66025i 0.857666 0.229811i
$$135$$ 0 0
$$136$$ 6.92820 + 6.92820i 0.594089 + 0.594089i
$$137$$ −8.92820 −0.762788 −0.381394 0.924413i $$-0.624556\pi$$
−0.381394 + 0.924413i $$0.624556\pi$$
$$138$$ 0 0
$$139$$ 7.46410i 0.633097i −0.948576 0.316548i $$-0.897476\pi$$
0.948576 0.316548i $$-0.102524\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0.535898 + 2.00000i 0.0449716 + 0.167836i
$$143$$ 6.92820 0.579365
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −0.196152 0.732051i −0.0162337 0.0605850i
$$147$$ 0 0
$$148$$ −2.00000 3.46410i −0.164399 0.284747i
$$149$$ 19.8564i 1.62670i −0.581775 0.813350i $$-0.697641\pi$$
0.581775 0.813350i $$-0.302359\pi$$
$$150$$ 0 0
$$151$$ 8.39230 0.682956 0.341478 0.939890i $$-0.389073\pi$$
0.341478 + 0.939890i $$0.389073\pi$$
$$152$$ 14.9282 14.9282i 1.21084 1.21084i
$$153$$ 0 0
$$154$$ −7.46410 + 2.00000i −0.601474 + 0.161165i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 16.9282i 1.35102i 0.737352 + 0.675509i $$0.236076\pi$$
−0.737352 + 0.675509i $$0.763924\pi$$
$$158$$ −5.46410 20.3923i −0.434701 1.62232i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 11.4641 0.903498
$$162$$ 0 0
$$163$$ 10.1962i 0.798624i −0.916815 0.399312i $$-0.869249\pi$$
0.916815 0.399312i $$-0.130751\pi$$
$$164$$ −9.46410 + 5.46410i −0.739022 + 0.426675i
$$165$$ 0 0
$$166$$ −6.46410 + 1.73205i −0.501712 + 0.134433i
$$167$$ −20.1962 −1.56283 −0.781413 0.624015i $$-0.785501\pi$$
−0.781413 + 0.624015i $$0.785501\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −8.73205 15.1244i −0.665813 1.15322i
$$173$$ 2.00000i 0.152057i 0.997106 + 0.0760286i $$0.0242240\pi$$
−0.997106 + 0.0760286i $$0.975776\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 6.92820 + 4.00000i 0.522233 + 0.301511i
$$177$$ 0 0
$$178$$ 1.80385 + 6.73205i 0.135204 + 0.504589i
$$179$$ 15.4641i 1.15584i 0.816093 + 0.577921i $$0.196136\pi$$
−0.816093 + 0.577921i $$0.803864\pi$$
$$180$$ 0 0
$$181$$ 16.0000i 1.18927i 0.803996 + 0.594635i $$0.202704\pi$$
−0.803996 + 0.594635i $$0.797296\pi$$
$$182$$ 12.9282 3.46410i 0.958302 0.256776i
$$183$$ 0 0
$$184$$ −8.39230 8.39230i −0.618689 0.618689i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 6.92820i 0.506640i
$$188$$ −11.6603 + 6.73205i −0.850411 + 0.490985i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 19.3205 1.39798 0.698991 0.715130i $$-0.253633\pi$$
0.698991 + 0.715130i $$0.253633\pi$$
$$192$$ 0 0
$$193$$ −7.46410 −0.537278 −0.268639 0.963241i $$-0.586574\pi$$
−0.268639 + 0.963241i $$0.586574\pi$$
$$194$$ −2.33975 8.73205i −0.167984 0.626925i
$$195$$ 0 0
$$196$$ −0.803848 + 0.464102i −0.0574177 + 0.0331501i
$$197$$ 12.5359i 0.893146i −0.894747 0.446573i $$-0.852644\pi$$
0.894747 0.446573i $$-0.147356\pi$$
$$198$$ 0 0
$$199$$ 25.8564 1.83291 0.916456 0.400135i $$-0.131037\pi$$
0.916456 + 0.400135i $$0.131037\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −14.9282 + 4.00000i −1.05034 + 0.281439i
$$203$$ 18.9282i 1.32850i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0.607695 + 2.26795i 0.0423401 + 0.158016i
$$207$$ 0 0
$$208$$ −12.0000 6.92820i −0.832050 0.480384i
$$209$$ −14.9282 −1.03261
$$210$$ 0 0
$$211$$ 14.7846i 1.01781i −0.860821 0.508907i $$-0.830050\pi$$
0.860821 0.508907i $$-0.169950\pi$$
$$212$$ −4.53590 7.85641i −0.311527 0.539580i
$$213$$ 0 0
$$214$$ 1.00000 0.267949i 0.0683586 0.0183166i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 4.00000 0.271538
$$218$$ −4.19615 + 1.12436i −0.284199 + 0.0761510i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 12.0000i 0.807207i
$$222$$ 0 0
$$223$$ 16.1962 1.08457 0.542287 0.840193i $$-0.317558\pi$$
0.542287 + 0.840193i $$0.317558\pi$$
$$224$$ 14.9282 + 4.00000i 0.997433 + 0.267261i
$$225$$ 0 0
$$226$$ 0.339746 + 1.26795i 0.0225996 + 0.0843427i
$$227$$ 28.0526i 1.86191i −0.365129 0.930957i $$-0.618975\pi$$
0.365129 0.930957i $$-0.381025\pi$$
$$228$$ 0 0
$$229$$ 4.00000i 0.264327i −0.991228 0.132164i $$-0.957808\pi$$
0.991228 0.132164i $$-0.0421925\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 13.8564 13.8564i 0.909718 0.909718i
$$233$$ 29.3205 1.92085 0.960425 0.278538i $$-0.0898499\pi$$
0.960425 + 0.278538i $$0.0898499\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −0.535898 0.928203i −0.0348840 0.0604209i
$$237$$ 0 0
$$238$$ −3.46410 12.9282i −0.224544 0.838011i
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ −4.39230 −0.282933 −0.141467 0.989943i $$-0.545182\pi$$
−0.141467 + 0.989943i $$0.545182\pi$$
$$242$$ 2.56218 + 9.56218i 0.164703 + 0.614680i
$$243$$ 0 0
$$244$$ −4.92820 8.53590i −0.315496 0.546455i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 25.8564 1.64520
$$248$$ −2.92820 2.92820i −0.185941 0.185941i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 11.0718i 0.698846i −0.936965 0.349423i $$-0.886378\pi$$
0.936965 0.349423i $$-0.113622\pi$$
$$252$$ 0 0
$$253$$ 8.39230i 0.527620i
$$254$$ −4.85641 18.1244i −0.304718 1.13722i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ 0 0
$$259$$ 5.46410i 0.339523i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 10.7321 2.87564i 0.663028 0.177658i
$$263$$ 5.66025 0.349026 0.174513 0.984655i $$-0.444165\pi$$
0.174513 + 0.984655i $$0.444165\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −27.8564 + 7.46410i −1.70799 + 0.457653i
$$267$$ 0 0
$$268$$ 7.26795 + 12.5885i 0.443961 + 0.768962i
$$269$$ 4.92820i 0.300478i −0.988650 0.150239i $$-0.951996\pi$$
0.988650 0.150239i $$-0.0480043\pi$$
$$270$$ 0 0
$$271$$ 15.3205 0.930655 0.465327 0.885139i $$-0.345937\pi$$
0.465327 + 0.885139i $$0.345937\pi$$
$$272$$ −6.92820 + 12.0000i −0.420084 + 0.727607i
$$273$$ 0 0
$$274$$ −3.26795 12.1962i −0.197424 0.736797i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 2.00000i 0.120168i −0.998193 0.0600842i $$-0.980863\pi$$
0.998193 0.0600842i $$-0.0191369\pi$$
$$278$$ 10.1962 2.73205i 0.611525 0.163858i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −17.4641 −1.04182 −0.520910 0.853611i $$-0.674407\pi$$
−0.520910 + 0.853611i $$0.674407\pi$$
$$282$$ 0 0
$$283$$ 7.66025i 0.455355i −0.973737 0.227677i $$-0.926887\pi$$
0.973737 0.227677i $$-0.0731132\pi$$
$$284$$ −2.53590 + 1.46410i −0.150478 + 0.0868784i
$$285$$ 0 0
$$286$$ 2.53590 + 9.46410i 0.149951 + 0.559624i
$$287$$ 14.9282 0.881184
$$288$$ 0 0
$$289$$ −5.00000 −0.294118
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0.928203 0.535898i 0.0543190 0.0313611i
$$293$$ 11.8564i 0.692659i 0.938113 + 0.346329i $$0.112572\pi$$
−0.938113 + 0.346329i $$0.887428\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 4.00000 4.00000i 0.232495 0.232495i
$$297$$ 0 0
$$298$$ 27.1244 7.26795i 1.57127 0.421021i
$$299$$ 14.5359i 0.840633i
$$300$$ 0 0
$$301$$ 23.8564i 1.37506i
$$302$$ 3.07180 + 11.4641i 0.176762 + 0.659685i
$$303$$ 0 0
$$304$$ 25.8564 + 14.9282i 1.48297 + 0.856191i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 26.9808i 1.53987i −0.638120 0.769937i $$-0.720288\pi$$
0.638120 0.769937i $$-0.279712\pi$$
$$308$$ −5.46410 9.46410i −0.311346 0.539267i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 3.32051 0.188289 0.0941444 0.995559i $$-0.469988\pi$$
0.0941444 + 0.995559i $$0.469988\pi$$
$$312$$ 0 0
$$313$$ 31.8564 1.80063 0.900315 0.435238i $$-0.143336\pi$$
0.900315 + 0.435238i $$0.143336\pi$$
$$314$$ −23.1244 + 6.19615i −1.30498 + 0.349669i
$$315$$ 0 0
$$316$$ 25.8564 14.9282i 1.45454 0.839777i
$$317$$ 15.4641i 0.868550i 0.900780 + 0.434275i $$0.142995\pi$$
−0.900780 + 0.434275i $$0.857005\pi$$
$$318$$ 0 0
$$319$$ −13.8564 −0.775810
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 4.19615 + 15.6603i 0.233842 + 0.872712i
$$323$$ 25.8564i 1.43869i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 13.9282 3.73205i 0.771412 0.206699i
$$327$$ 0 0
$$328$$ −10.9282 10.9282i −0.603409 0.603409i
$$329$$ 18.3923 1.01400
$$330$$ 0 0
$$331$$ 14.0000i 0.769510i −0.923019 0.384755i $$-0.874286\pi$$
0.923019 0.384755i $$-0.125714\pi$$
$$332$$ −4.73205 8.19615i −0.259705 0.449822i
$$333$$ 0 0
$$334$$ −7.39230 27.5885i −0.404489 1.50957i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −7.85641 −0.427966 −0.213983 0.976837i $$-0.568644\pi$$
−0.213983 + 0.976837i $$0.568644\pi$$
$$338$$ 0.366025 + 1.36603i 0.0199092 + 0.0743020i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 2.92820i 0.158571i
$$342$$ 0 0
$$343$$ −17.8564 −0.964155
$$344$$ 17.4641 17.4641i 0.941601 0.941601i
$$345$$ 0 0
$$346$$ −2.73205 + 0.732051i −0.146876 + 0.0393553i
$$347$$ 15.6603i 0.840686i 0.907365 + 0.420343i $$0.138090\pi$$
−0.907365 + 0.420343i $$0.861910\pi$$
$$348$$ 0 0
$$349$$ 28.0000i 1.49881i −0.662114 0.749403i $$-0.730341\pi$$
0.662114 0.749403i $$-0.269659\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −2.92820 + 10.9282i −0.156074 + 0.582475i
$$353$$ −0.928203 −0.0494033 −0.0247016 0.999695i $$-0.507864\pi$$
−0.0247016 + 0.999695i $$0.507864\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −8.53590 + 4.92820i −0.452402 + 0.261194i
$$357$$ 0 0
$$358$$ −21.1244 + 5.66025i −1.11646 + 0.299154i
$$359$$ −5.07180 −0.267679 −0.133840 0.991003i $$-0.542731\pi$$
−0.133840 + 0.991003i $$0.542731\pi$$
$$360$$ 0 0
$$361$$ −36.7128 −1.93225
$$362$$ −21.8564 + 5.85641i −1.14875 + 0.307806i
$$363$$ 0 0
$$364$$ 9.46410 + 16.3923i 0.496054 + 0.859190i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −27.1244 −1.41588 −0.707940 0.706273i $$-0.750375\pi$$
−0.707940 + 0.706273i $$0.750375\pi$$
$$368$$ 8.39230 14.5359i 0.437479 0.757736i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 12.3923i 0.643376i
$$372$$ 0 0
$$373$$ 29.7128i 1.53847i −0.638965 0.769236i $$-0.720637\pi$$
0.638965 0.769236i $$-0.279363\pi$$
$$374$$ 9.46410 2.53590i 0.489377 0.131128i
$$375$$ 0 0
$$376$$ −13.4641 13.4641i −0.694358 0.694358i
$$377$$ 24.0000 1.23606
$$378$$ 0 0
$$379$$ 12.2487i 0.629174i 0.949229 + 0.314587i $$0.101866\pi$$
−0.949229 + 0.314587i $$0.898134\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 7.07180 + 26.3923i 0.361825 + 1.35035i
$$383$$ −3.12436 −0.159647 −0.0798236 0.996809i $$-0.525436\pi$$
−0.0798236 + 0.996809i $$0.525436\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.73205 10.1962i −0.139058 0.518970i
$$387$$ 0 0
$$388$$ 11.0718 6.39230i 0.562085 0.324520i
$$389$$ 34.7846i 1.76365i 0.471577 + 0.881825i $$0.343685\pi$$
−0.471577 + 0.881825i $$0.656315\pi$$
$$390$$ 0 0
$$391$$ −14.5359 −0.735112
$$392$$ −0.928203 0.928203i −0.0468813 0.0468813i
$$393$$ 0 0
$$394$$ 17.1244 4.58846i 0.862713 0.231163i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 16.2487i 0.815499i 0.913094 + 0.407750i $$0.133686\pi$$
−0.913094 + 0.407750i $$0.866314\pi$$
$$398$$ 9.46410 + 35.3205i 0.474393 + 1.77046i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −19.8564 −0.991582 −0.495791 0.868442i $$-0.665122\pi$$
−0.495791 + 0.868442i $$0.665122\pi$$
$$402$$ 0 0
$$403$$ 5.07180i 0.252644i
$$404$$ −10.9282 18.9282i −0.543698 0.941713i
$$405$$ 0 0
$$406$$ −25.8564 + 6.92820i −1.28323 + 0.343841i
$$407$$ −4.00000 −0.198273
$$408$$ 0 0
$$409$$ 23.3205 1.15312 0.576562 0.817053i $$-0.304394\pi$$
0.576562 + 0.817053i $$0.304394\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −2.87564 + 1.66025i −0.141673 + 0.0817948i
$$413$$ 1.46410i 0.0720437i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 5.07180 18.9282i 0.248665 0.928032i
$$417$$ 0 0
$$418$$ −5.46410 20.3923i −0.267258 0.997420i
$$419$$ 2.39230i 0.116872i 0.998291 + 0.0584359i $$0.0186113\pi$$
−0.998291 + 0.0584359i $$0.981389\pi$$
$$420$$ 0 0
$$421$$ 27.8564i 1.35764i 0.734306 + 0.678819i $$0.237508\pi$$
−0.734306 + 0.678819i $$0.762492\pi$$
$$422$$ 20.1962 5.41154i 0.983133 0.263430i
$$423$$ 0 0
$$424$$ 9.07180 9.07180i 0.440565 0.440565i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 13.4641i 0.651574i
$$428$$ 0.732051 + 1.26795i 0.0353850 + 0.0612886i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 14.5359 0.700170 0.350085 0.936718i $$-0.386153\pi$$
0.350085 + 0.936718i $$0.386153\pi$$
$$432$$ 0 0
$$433$$ 12.5359 0.602437 0.301218 0.953555i $$-0.402607\pi$$
0.301218 + 0.953555i $$0.402607\pi$$
$$434$$ 1.46410 + 5.46410i 0.0702791 + 0.262285i
$$435$$ 0 0
$$436$$ −3.07180 5.32051i −0.147112 0.254806i
$$437$$ 31.3205i 1.49826i
$$438$$ 0 0
$$439$$ −0.784610 −0.0374474 −0.0187237 0.999825i $$-0.505960\pi$$
−0.0187237 + 0.999825i $$0.505960\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −16.3923 + 4.39230i −0.779702 + 0.208921i
$$443$$ 30.9808i 1.47194i −0.677014 0.735970i $$-0.736726\pi$$
0.677014 0.735970i $$-0.263274\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 5.92820 + 22.1244i 0.280709 + 1.04762i
$$447$$ 0 0
$$448$$ 21.8564i 1.03262i
$$449$$ −11.3205 −0.534248 −0.267124 0.963662i $$-0.586073\pi$$
−0.267124 + 0.963662i $$0.586073\pi$$
$$450$$ 0 0
$$451$$ 10.9282i 0.514589i
$$452$$ −1.60770 + 0.928203i −0.0756196 + 0.0436590i
$$453$$ 0 0
$$454$$ 38.3205 10.2679i 1.79847 0.481899i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −14.7846 −0.691595 −0.345797 0.938309i $$-0.612392\pi$$
−0.345797 + 0.938309i $$0.612392\pi$$
$$458$$ 5.46410 1.46410i 0.255321 0.0684130i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2.92820i 0.136380i −0.997672 0.0681900i $$-0.978278\pi$$
0.997672 0.0681900i $$-0.0217224\pi$$
$$462$$ 0 0
$$463$$ 14.7321 0.684656 0.342328 0.939580i $$-0.388785\pi$$
0.342328 + 0.939580i $$0.388785\pi$$
$$464$$ 24.0000 + 13.8564i 1.11417 + 0.643268i
$$465$$ 0 0
$$466$$ 10.7321 + 40.0526i 0.497153 + 1.85540i
$$467$$ 8.33975i 0.385917i −0.981207 0.192959i $$-0.938192\pi$$
0.981207 0.192959i $$-0.0618083\pi$$
$$468$$ 0 0
$$469$$ 19.8564i 0.916884i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.07180 1.07180i 0.0493334 0.0493334i
$$473$$ −17.4641 −0.803000
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 16.3923 9.46410i 0.751340 0.433786i
$$477$$ 0 0
$$478$$ 7.32051 + 27.3205i 0.334832 + 1.24961i
$$479$$ 21.8564 0.998645 0.499322 0.866416i $$-0.333582\pi$$
0.499322 + 0.866416i $$0.333582\pi$$
$$480$$ 0 0
$$481$$ 6.92820 0.315899
$$482$$ −1.60770 6.00000i −0.0732285 0.273293i
$$483$$ 0 0
$$484$$ −12.1244 + 7.00000i −0.551107 + 0.318182i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 24.5885 1.11421 0.557105 0.830442i $$-0.311912\pi$$
0.557105 + 0.830442i $$0.311912\pi$$
$$488$$ 9.85641 9.85641i 0.446179 0.446179i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 3.07180i 0.138628i 0.997595 + 0.0693141i $$0.0220811\pi$$
−0.997595 + 0.0693141i $$0.977919\pi$$
$$492$$ 0 0
$$493$$ 24.0000i 1.08091i
$$494$$ 9.46410 + 35.3205i 0.425810 + 1.58914i
$$495$$ 0 0
$$496$$ 2.92820 5.07180i 0.131480 0.227730i
$$497$$ 4.00000 0.179425
$$498$$ 0 0
$$499$$ 24.5359i 1.09838i 0.835698 + 0.549189i $$0.185063\pi$$
−0.835698 + 0.549189i $$0.814937\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 15.1244 4.05256i 0.675033 0.180875i
$$503$$ −17.6603 −0.787432 −0.393716 0.919232i $$-0.628811\pi$$
−0.393716 + 0.919232i $$0.628811\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −11.4641 + 3.07180i −0.509641 + 0.136558i
$$507$$ 0 0
$$508$$ 22.9808 13.2679i 1.01961 0.588670i
$$509$$ 25.8564i 1.14607i −0.819533 0.573033i $$-0.805767\pi$$
0.819533 0.573033i $$-0.194233\pi$$
$$510$$ 0 0
$$511$$ −1.46410 −0.0647680
$$512$$ 16.0000 16.0000i 0.707107 0.707107i
$$513$$ 0 0
$$514$$ −0.732051 2.73205i −0.0322894 0.120506i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 13.4641i 0.592151i
$$518$$ −7.46410 + 2.00000i −0.327954 + 0.0878750i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 16.1436 0.707264 0.353632 0.935385i $$-0.384947\pi$$
0.353632 + 0.935385i $$0.384947\pi$$
$$522$$ 0 0
$$523$$ 22.1962i 0.970570i 0.874356 + 0.485285i $$0.161284\pi$$
−0.874356 + 0.485285i $$0.838716\pi$$
$$524$$ 7.85641 + 13.6077i 0.343209 + 0.594455i
$$525$$ 0 0
$$526$$ 2.07180 + 7.73205i 0.0903346 + 0.337133i
$$527$$ −5.07180 −0.220931
$$528$$ 0 0
$$529$$ −5.39230 −0.234448
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −20.3923 35.3205i −0.884119 1.53134i
$$533$$ 18.9282i 0.819871i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −14.5359 + 14.5359i −0.627855 + 0.627855i
$$537$$ 0 0
$$538$$ 6.73205 1.80385i 0.290239 0.0777694i
$$539$$ 0.928203i 0.0399805i
$$540$$ 0 0
$$541$$ 13.0718i 0.562000i −0.959708 0.281000i $$-0.909334\pi$$
0.959708 0.281000i $$-0.0906662\pi$$
$$542$$ 5.60770 + 20.9282i 0.240871 + 0.898943i
$$543$$ 0 0
$$544$$ −18.9282 5.07180i −0.811540 0.217451i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 36.7321i 1.57055i −0.619148 0.785275i $$-0.712522\pi$$
0.619148 0.785275i $$-0.287478\pi$$
$$548$$ 15.4641 8.92820i 0.660594 0.381394i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −51.7128 −2.20304
$$552$$ 0 0
$$553$$ −40.7846 −1.73434
$$554$$ 2.73205 0.732051i 0.116074 0.0311019i
$$555$$ 0 0
$$556$$ 7.46410 + 12.9282i 0.316548 + 0.548278i
$$557$$ 26.7846i 1.13490i −0.823408 0.567450i $$-0.807930\pi$$
0.823408 0.567450i $$-0.192070\pi$$
$$558$$ 0 0
$$559$$ 30.2487 1.27938
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −6.39230 23.8564i −0.269643 1.00632i
$$563$$ 16.0526i 0.676535i 0.941050 + 0.338267i $$0.109841\pi$$
−0.941050 + 0.338267i $$0.890159\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 10.4641 2.80385i 0.439839 0.117855i
$$567$$ 0 0
$$568$$ −2.92820 2.92820i −0.122865 0.122865i
$$569$$ 6.53590 0.273999 0.137000 0.990571i $$-0.456254\pi$$
0.137000 + 0.990571i $$0.456254\pi$$
$$570$$ 0 0
$$571$$ 34.7846i 1.45569i −0.685741 0.727845i $$-0.740522\pi$$
0.685741 0.727845i $$-0.259478\pi$$
$$572$$ −12.0000 + 6.92820i −0.501745 + 0.289683i
$$573$$ 0 0
$$574$$ 5.46410 + 20.3923i 0.228067 + 0.851158i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 43.5692 1.81381 0.906905 0.421335i $$-0.138438\pi$$
0.906905 + 0.421335i $$0.138438\pi$$
$$578$$ −1.83013 6.83013i −0.0761232 0.284096i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 12.9282i 0.536352i
$$582$$ 0 0
$$583$$ −9.07180 −0.375715
$$584$$ 1.07180 + 1.07180i 0.0443513 + 0.0443513i
$$585$$ 0 0
$$586$$ −16.1962 + 4.33975i −0.669057 + 0.179273i
$$587$$ 14.1962i 0.585938i −0.956122 0.292969i $$-0.905357\pi$$
0.956122 0.292969i $$-0.0946433\pi$$
$$588$$ 0 0
$$589$$ 10.9282i 0.450289i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 6.92820 + 4.00000i 0.284747 + 0.164399i
$$593$$ −36.6410 −1.50467 −0.752333 0.658783i $$-0.771072\pi$$
−0.752333 + 0.658783i $$0.771072\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 19.8564 + 34.3923i 0.813350 + 1.40876i
$$597$$ 0 0
$$598$$ 19.8564 5.32051i 0.811989 0.217572i
$$599$$ −34.6410 −1.41539 −0.707697 0.706516i $$-0.750266\pi$$
−0.707697 + 0.706516i $$0.750266\pi$$
$$600$$ 0 0
$$601$$ 25.4641 1.03870 0.519351 0.854561i $$-0.326174\pi$$
0.519351 + 0.854561i $$0.326174\pi$$
$$602$$ −32.5885 + 8.73205i −1.32821 + 0.355892i
$$603$$ 0 0
$$604$$ −14.5359 + 8.39230i −0.591457 + 0.341478i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 20.9808 0.851583 0.425791 0.904821i $$-0.359996\pi$$
0.425791 + 0.904821i $$0.359996\pi$$
$$608$$ −10.9282 + 40.7846i −0.443197 + 1.65403i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 23.3205i 0.943447i
$$612$$ 0 0
$$613$$ 5.60770i 0.226493i −0.993567 0.113246i $$-0.963875\pi$$
0.993567 0.113246i $$-0.0361249\pi$$
$$614$$ 36.8564 9.87564i 1.48740 0.398549i
$$615$$ 0 0
$$616$$ 10.9282 10.9282i 0.440310 0.440310i
$$617$$ −27.4641 −1.10566 −0.552832 0.833293i $$-0.686453\pi$$
−0.552832 + 0.833293i $$0.686453\pi$$
$$618$$ 0 0
$$619$$ 33.3205i 1.33926i −0.742693 0.669632i $$-0.766452\pi$$
0.742693 0.669632i $$-0.233548\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 1.21539 + 4.53590i 0.0487327 + 0.181873i
$$623$$ 13.4641 0.539428
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 11.6603 + 43.5167i 0.466037 + 1.73928i
$$627$$ 0 0
$$628$$ −16.9282 29.3205i −0.675509 1.17002i
$$629$$ 6.92820i 0.276246i
$$630$$ 0 0
$$631$$ 11.3205 0.450662 0.225331 0.974282i $$-0.427654\pi$$
0.225331 + 0.974282i $$0.427654\pi$$
$$632$$ 29.8564 + 29.8564i 1.18762 + 1.18762i
$$633$$ 0 0
$$634$$ −21.1244 + 5.66025i −0.838955 + 0.224797i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.60770i 0.0636992i
$$638$$ −5.07180 18.9282i −0.200794 0.749375i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 20.3923 0.805448 0.402724 0.915322i $$-0.368064\pi$$
0.402724 + 0.915322i $$0.368064\pi$$
$$642$$ 0 0
$$643$$ 14.8756i 0.586638i −0.956015 0.293319i $$-0.905240\pi$$
0.956015 0.293319i $$-0.0947598\pi$$
$$644$$ −19.8564 + 11.4641i −0.782452 + 0.451749i
$$645$$ 0 0
$$646$$ 35.3205 9.46410i 1.38967 0.372360i
$$647$$ 13.2679 0.521617 0.260808 0.965391i $$-0.416011\pi$$
0.260808 + 0.965391i $$0.416011\pi$$
$$648$$ 0 0
$$649$$ −1.07180 −0.0420717
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 10.1962 + 17.6603i 0.399312 + 0.691629i
$$653$$ 36.2487i 1.41852i −0.704946 0.709261i $$-0.749029\pi$$
0.704946 0.709261i $$-0.250971\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 10.9282 18.9282i 0.426675 0.739022i
$$657$$ 0 0
$$658$$ 6.73205 + 25.1244i 0.262443 + 0.979449i
$$659$$ 17.3205i 0.674711i −0.941377 0.337356i $$-0.890468\pi$$
0.941377 0.337356i $$-0.109532\pi$$
$$660$$ 0 0
$$661$$ 35.8564i 1.39465i −0.716754 0.697326i $$-0.754373\pi$$
0.716754 0.697326i $$-0.245627\pi$$
$$662$$ 19.1244 5.12436i 0.743289 0.199164i
$$663$$ 0 0
$$664$$ 9.46410 9.46410i 0.367278 0.367278i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 29.0718i 1.12566i
$$668$$ 34.9808 20.1962i 1.35345 0.781413i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −9.85641 −0.380502
$$672$$ 0 0
$$673$$ −19.4641 −0.750286 −0.375143 0.926967i $$-0.622406\pi$$
−0.375143 + 0.926967i $$0.622406\pi$$
$$674$$ −2.87564 10.7321i −0.110766 0.413383i
$$675$$ 0 0
$$676$$ −1.73205 + 1.00000i −0.0666173 + 0.0384615i
$$677$$ 38.3923i 1.47554i 0.675054 + 0.737768i $$0.264120\pi$$
−0.675054 + 0.737768i $$0.735880\pi$$
$$678$$ 0 0
$$679$$ −17.4641 −0.670211
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −4.00000 + 1.07180i −0.153168 + 0.0410412i
$$683$$ 34.9808i 1.33850i 0.743037 + 0.669251i $$0.233385\pi$$
−0.743037 + 0.669251i $$0.766615\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −6.53590 24.3923i −0.249542 0.931303i
$$687$$ 0 0
$$688$$ 30.2487 + 17.4641i 1.15322 + 0.665813i
$$689$$ 15.7128 0.598610
$$690$$ 0 0
$$691$$ 18.0000i 0.684752i 0.939563 + 0.342376i $$0.111232\pi$$
−0.939563 + 0.342376i $$0.888768\pi$$
$$692$$ −2.00000 3.46410i −0.0760286 0.131685i
$$693$$ 0 0
$$694$$ −21.3923 + 5.73205i −0.812041 + 0.217586i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −18.9282 −0.716957
$$698$$ 38.2487 10.2487i 1.44774 0.387919i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 32.9282i 1.24368i −0.783144 0.621841i $$-0.786385\pi$$
0.783144 0.621841i $$-0.213615\pi$$
$$702$$ 0 0
$$703$$ −14.9282 −0.563028
$$704$$ −16.0000 −0.603023
$$705$$ 0 0
$$706$$ −0.339746 1.26795i −0.0127865 0.0477199i
$$707$$ 29.8564i 1.12287i
$$708$$ 0 0
$$709$$ 28.7846i 1.08103i 0.841335 + 0.540514i $$0.181770\pi$$
−0.841335 + 0.540514i $$0.818230\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −9.85641 9.85641i −0.369384 0.369384i
$$713$$ 6.14359 0.230079
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −15.4641 26.7846i −0.577921 1.00099i
$$717$$ 0 0
$$718$$ −1.85641 6.92820i −0.0692805 0.258558i
$$719$$ −25.8564 −0.964281 −0.482141 0.876094i $$-0.660141\pi$$
−0.482141 + 0.876094i $$0.660141\pi$$
$$720$$ 0 0
$$721$$ 4.53590 0.168926
$$722$$ −13.4378 50.1506i −0.500104 1.86641i
$$723$$ 0 0
$$724$$ −16.0000 27.7128i −0.594635 1.02994i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −14.0526 −0.521181 −0.260590 0.965449i $$-0.583917\pi$$
−0.260590 + 0.965449i $$0.583917\pi$$
$$728$$ −18.9282 + 18.9282i −0.701526 + 0.701526i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 30.2487i 1.11879i
$$732$$ 0 0
$$733$$ 48.9282i 1.80720i 0.428373 + 0.903602i $$0.359087\pi$$
−0.428373 + 0.903602i $$0.640913\pi$$
$$734$$ −9.92820 37.0526i −0.366457 1.36763i
$$735$$ 0 0
$$736$$ 22.9282 + 6.14359i 0.845145 + 0.226456i
$$737$$ 14.5359 0.535437
$$738$$ 0 0
$$739$$ 5.32051i 0.195718i −0.995200 0.0978590i $$-0.968801\pi$$
0.995200 0.0978590i $$-0.0311994\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −16.9282 + 4.53590i −0.621454 + 0.166518i
$$743$$ −40.9808 −1.50344 −0.751719 0.659483i $$-0.770775\pi$$
−0.751719 + 0.659483i $$0.770775\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 40.5885 10.8756i 1.48605 0.398186i
$$747$$ 0 0
$$748$$ 6.92820 + 12.0000i 0.253320 + 0.438763i
$$749$$ 2.00000i 0.0730784i
$$750$$ 0 0
$$751$$ −22.2487 −0.811867 −0.405934 0.913903i $$-0.633054\pi$$
−0.405934 + 0.913903i $$0.633054\pi$$
$$752$$ 13.4641 23.3205i 0.490985 0.850411i
$$753$$ 0 0
$$754$$ 8.78461 + 32.7846i 0.319917 + 1.19395i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 32.9282i 1.19680i 0.801199 + 0.598398i $$0.204196\pi$$
−0.801199 + 0.598398i $$0.795804\pi$$
$$758$$ −16.7321 + 4.48334i −0.607735 + 0.162842i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −49.7128 −1.80209 −0.901044 0.433728i $$-0.857198\pi$$
−0.901044 + 0.433728i $$0.857198\pi$$
$$762$$ 0 0
$$763$$ 8.39230i 0.303822i
$$764$$ −33.4641 + 19.3205i −1.21069 + 0.698991i
$$765$$ 0 0
$$766$$ −1.14359 4.26795i −0.0413197 0.154207i
$$767$$ 1.85641 0.0670310
$$768$$ 0 0
$$769$$ −0.928203 −0.0334719 −0.0167359 0.999860i $$-0.505327\pi$$
−0.0167359 + 0.999860i $$0.505327\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 12.9282 7.46410i 0.465296 0.268639i
$$773$$ 1.60770i 0.0578248i −0.999582 0.0289124i $$-0.990796\pi$$
0.999582 0.0289124i $$-0.00920438\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 12.7846 + 12.7846i 0.458941 + 0.458941i
$$777$$ 0 0
$$778$$ −47.5167 + 12.7321i −1.70355 + 0.456466i
$$779$$ 40.7846i 1.46126i
$$780$$ 0 0
$$781$$ 2.92820i 0.104779i
$$782$$ −5.32051 19.8564i −0.190261 0.710064i
$$783$$ 0 0
$$784$$ 0.928203 1.60770i 0.0331501 0.0574177i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 14.5885i 0.520022i 0.965606 + 0.260011i $$0.0837262\pi$$
−0.965606 + 0.260011i $$0.916274\pi$$
$$788$$ 12.5359 + 21.7128i 0.446573 + 0.773487i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2.53590 0.0901662
$$792$$ 0 0
$$793$$ 17.0718 0.606237
$$794$$ −22.1962 + 5.94744i −0.787712 + 0.211067i
$$795$$ 0 0
$$796$$ −44.7846 + 25.8564i −1.58735 + 0.916456i
$$797$$ 26.1051i