# Properties

 Label 1440.2.bj.a.593.21 Level $1440$ Weight $2$ Character 1440.593 Analytic conductor $11.498$ Analytic rank $0$ Dimension $48$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1440 = 2^{5} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1440.bj (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.4984578911$$ Analytic rank: $$0$$ Dimension: $$48$$ Relative dimension: $$24$$ over $$\Q(i)$$ Twist minimal: no (minimal twist has level 360) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 593.21 Character $$\chi$$ $$=$$ 1440.593 Dual form 1440.2.bj.a.17.21

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(2.03368 + 0.929591i) q^{5} +(2.49469 - 2.49469i) q^{7} +O(q^{10})$$ $$q+(2.03368 + 0.929591i) q^{5} +(2.49469 - 2.49469i) q^{7} +3.92878 q^{11} +(4.55591 - 4.55591i) q^{13} +(-1.88566 - 1.88566i) q^{17} -4.61555 q^{19} +(-0.741221 + 0.741221i) q^{23} +(3.27172 + 3.78098i) q^{25} -4.35885i q^{29} -9.67119 q^{31} +(7.39245 - 2.75436i) q^{35} +(-5.39704 - 5.39704i) q^{37} +6.33584i q^{41} +(-0.206110 + 0.206110i) q^{43} +(3.48081 + 3.48081i) q^{47} -5.44695i q^{49} +(1.01974 + 1.01974i) q^{53} +(7.98989 + 3.65216i) q^{55} +0.531064i q^{59} -3.00356i q^{61} +(13.5004 - 5.03014i) q^{65} +(1.28660 + 1.28660i) q^{67} +7.61692i q^{71} +(-0.509262 - 0.509262i) q^{73} +(9.80109 - 9.80109i) q^{77} -1.31920i q^{79} +(9.85533 + 9.85533i) q^{83} +(-2.08194 - 5.58774i) q^{85} -2.91798 q^{89} -22.7312i q^{91} +(-9.38656 - 4.29057i) q^{95} +(-8.11369 + 8.11369i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$48 q + O(q^{10})$$ $$48 q - 32 q^{31} - 32 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$$.

 $$n$$ $$577$$ $$641$$ $$901$$ $$991$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$-1$$ $$1$$

## 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 0
$$4$$ 0 0
$$5$$ 2.03368 + 0.929591i 0.909490 + 0.415726i
$$6$$ 0 0
$$7$$ 2.49469 2.49469i 0.942904 0.942904i −0.0555517 0.998456i $$-0.517692\pi$$
0.998456 + 0.0555517i $$0.0176918\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.92878 1.18457 0.592286 0.805728i $$-0.298226\pi$$
0.592286 + 0.805728i $$0.298226\pi$$
$$12$$ 0 0
$$13$$ 4.55591 4.55591i 1.26358 1.26358i 0.314237 0.949345i $$-0.398251\pi$$
0.949345 0.314237i $$-0.101749\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1.88566 1.88566i −0.457341 0.457341i 0.440441 0.897782i $$-0.354822\pi$$
−0.897782 + 0.440441i $$0.854822\pi$$
$$18$$ 0 0
$$19$$ −4.61555 −1.05888 −0.529440 0.848347i $$-0.677598\pi$$
−0.529440 + 0.848347i $$0.677598\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −0.741221 + 0.741221i −0.154555 + 0.154555i −0.780149 0.625594i $$-0.784857\pi$$
0.625594 + 0.780149i $$0.284857\pi$$
$$24$$ 0 0
$$25$$ 3.27172 + 3.78098i 0.654344 + 0.756197i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4.35885i 0.809418i −0.914446 0.404709i $$-0.867373\pi$$
0.914446 0.404709i $$-0.132627\pi$$
$$30$$ 0 0
$$31$$ −9.67119 −1.73700 −0.868499 0.495691i $$-0.834915\pi$$
−0.868499 + 0.495691i $$0.834915\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 7.39245 2.75436i 1.24955 0.465572i
$$36$$ 0 0
$$37$$ −5.39704 5.39704i −0.887267 0.887267i 0.106992 0.994260i $$-0.465878\pi$$
−0.994260 + 0.106992i $$0.965878\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.33584i 0.989492i 0.869038 + 0.494746i $$0.164739\pi$$
−0.869038 + 0.494746i $$0.835261\pi$$
$$42$$ 0 0
$$43$$ −0.206110 + 0.206110i −0.0314315 + 0.0314315i −0.722648 0.691216i $$-0.757075\pi$$
0.691216 + 0.722648i $$0.257075\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.48081 + 3.48081i 0.507729 + 0.507729i 0.913829 0.406100i $$-0.133112\pi$$
−0.406100 + 0.913829i $$0.633112\pi$$
$$48$$ 0 0
$$49$$ 5.44695i 0.778136i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 1.01974 + 1.01974i 0.140073 + 0.140073i 0.773666 0.633593i $$-0.218421\pi$$
−0.633593 + 0.773666i $$0.718421\pi$$
$$54$$ 0 0
$$55$$ 7.98989 + 3.65216i 1.07736 + 0.492457i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0.531064i 0.0691386i 0.999402 + 0.0345693i $$0.0110059\pi$$
−0.999402 + 0.0345693i $$0.988994\pi$$
$$60$$ 0 0
$$61$$ 3.00356i 0.384566i −0.981340 0.192283i $$-0.938411\pi$$
0.981340 0.192283i $$-0.0615892\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 13.5004 5.03014i 1.67452 0.623912i
$$66$$ 0 0
$$67$$ 1.28660 + 1.28660i 0.157183 + 0.157183i 0.781317 0.624134i $$-0.214548\pi$$
−0.624134 + 0.781317i $$0.714548\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 7.61692i 0.903962i 0.892028 + 0.451981i $$0.149282\pi$$
−0.892028 + 0.451981i $$0.850718\pi$$
$$72$$ 0 0
$$73$$ −0.509262 0.509262i −0.0596047 0.0596047i 0.676676 0.736281i $$-0.263420\pi$$
−0.736281 + 0.676676i $$0.763420\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 9.80109 9.80109i 1.11694 1.11694i
$$78$$ 0 0
$$79$$ 1.31920i 0.148422i −0.997243 0.0742111i $$-0.976356\pi$$
0.997243 0.0742111i $$-0.0236439\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 9.85533 + 9.85533i 1.08176 + 1.08176i 0.996345 + 0.0854172i $$0.0272223\pi$$
0.0854172 + 0.996345i $$0.472778\pi$$
$$84$$ 0 0
$$85$$ −2.08194 5.58774i −0.225819 0.606075i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −2.91798 −0.309306 −0.154653 0.987969i $$-0.549426\pi$$
−0.154653 + 0.987969i $$0.549426\pi$$
$$90$$ 0 0
$$91$$ 22.7312i 2.38287i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −9.38656 4.29057i −0.963041 0.440204i
$$96$$ 0 0
$$97$$ −8.11369 + 8.11369i −0.823820 + 0.823820i −0.986654 0.162834i $$-0.947937\pi$$
0.162834 + 0.986654i $$0.447937\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 11.0269 1.09721 0.548607 0.836080i $$-0.315158\pi$$
0.548607 + 0.836080i $$0.315158\pi$$
$$102$$ 0 0
$$103$$ 2.89128 + 2.89128i 0.284887 + 0.284887i 0.835054 0.550168i $$-0.185436\pi$$
−0.550168 + 0.835054i $$0.685436\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 5.23891 5.23891i 0.506465 0.506465i −0.406975 0.913439i $$-0.633416\pi$$
0.913439 + 0.406975i $$0.133416\pi$$
$$108$$ 0 0
$$109$$ 5.31464 0.509050 0.254525 0.967066i $$-0.418081\pi$$
0.254525 + 0.967066i $$0.418081\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −10.3559 + 10.3559i −0.974204 + 0.974204i −0.999676 0.0254720i $$-0.991891\pi$$
0.0254720 + 0.999676i $$0.491891\pi$$
$$114$$ 0 0
$$115$$ −2.19644 + 0.818375i −0.204819 + 0.0763138i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −9.40829 −0.862457
$$120$$ 0 0
$$121$$ 4.43532 0.403211
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 3.13887 + 10.7307i 0.280749 + 0.959781i
$$126$$ 0 0
$$127$$ 1.10872 1.10872i 0.0983826 0.0983826i −0.656202 0.754585i $$-0.727838\pi$$
0.754585 + 0.656202i $$0.227838\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0.996979 0.0871065 0.0435532 0.999051i $$-0.486132\pi$$
0.0435532 + 0.999051i $$0.486132\pi$$
$$132$$ 0 0
$$133$$ −11.5144 + 11.5144i −0.998422 + 0.998422i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1.03232 + 1.03232i 0.0881970 + 0.0881970i 0.749829 0.661632i $$-0.230136\pi$$
−0.661632 + 0.749829i $$0.730136\pi$$
$$138$$ 0 0
$$139$$ 16.9830 1.44048 0.720239 0.693726i $$-0.244032\pi$$
0.720239 + 0.693726i $$0.244032\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 17.8992 17.8992i 1.49680 1.49680i
$$144$$ 0 0
$$145$$ 4.05194 8.86451i 0.336496 0.736157i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 6.48772i 0.531495i 0.964043 + 0.265747i $$0.0856187\pi$$
−0.964043 + 0.265747i $$0.914381\pi$$
$$150$$ 0 0
$$151$$ −4.21210 −0.342776 −0.171388 0.985204i $$-0.554825\pi$$
−0.171388 + 0.985204i $$0.554825\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −19.6681 8.99025i −1.57978 0.722114i
$$156$$ 0 0
$$157$$ −0.0368875 0.0368875i −0.00294395 0.00294395i 0.705633 0.708577i $$-0.250663\pi$$
−0.708577 + 0.705633i $$0.750663\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 3.69823i 0.291461i
$$162$$ 0 0
$$163$$ −1.33256 + 1.33256i −0.104374 + 0.104374i −0.757365 0.652991i $$-0.773514\pi$$
0.652991 + 0.757365i $$0.273514\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 15.0291 + 15.0291i 1.16299 + 1.16299i 0.983818 + 0.179169i $$0.0573410\pi$$
0.179169 + 0.983818i $$0.442659\pi$$
$$168$$ 0 0
$$169$$ 28.5126i 2.19328i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −2.16963 2.16963i −0.164954 0.164954i 0.619804 0.784757i $$-0.287212\pi$$
−0.784757 + 0.619804i $$0.787212\pi$$
$$174$$ 0 0
$$175$$ 17.5943 + 1.27045i 1.33000 + 0.0960371i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 14.2973i 1.06863i −0.845285 0.534316i $$-0.820569\pi$$
0.845285 0.534316i $$-0.179431\pi$$
$$180$$ 0 0
$$181$$ 11.0562i 0.821800i 0.911680 + 0.410900i $$0.134785\pi$$
−0.911680 + 0.410900i $$0.865215\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −5.95882 15.9929i −0.438101 1.17582i
$$186$$ 0 0
$$187$$ −7.40836 7.40836i −0.541753 0.541753i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.7129i 0.919873i −0.887952 0.459937i $$-0.847872\pi$$
0.887952 0.459937i $$-0.152128\pi$$
$$192$$ 0 0
$$193$$ 16.5832 + 16.5832i 1.19368 + 1.19368i 0.976025 + 0.217659i $$0.0698420\pi$$
0.217659 + 0.976025i $$0.430158\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −9.96244 + 9.96244i −0.709794 + 0.709794i −0.966492 0.256698i $$-0.917366\pi$$
0.256698 + 0.966492i $$0.417366\pi$$
$$198$$ 0 0
$$199$$ 15.6722i 1.11097i −0.831525 0.555487i $$-0.812532\pi$$
0.831525 0.555487i $$-0.187468\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −10.8740 10.8740i −0.763203 0.763203i
$$204$$ 0 0
$$205$$ −5.88974 + 12.8851i −0.411357 + 0.899933i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −18.1335 −1.25432
$$210$$ 0 0
$$211$$ 22.1294i 1.52345i 0.647901 + 0.761725i $$0.275647\pi$$
−0.647901 + 0.761725i $$0.724353\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −0.610761 + 0.227564i −0.0416535 + 0.0155198i
$$216$$ 0 0
$$217$$ −24.1266 + 24.1266i −1.63782 + 1.63782i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −17.1818 −1.15577
$$222$$ 0 0
$$223$$ 3.17650 + 3.17650i 0.212714 + 0.212714i 0.805420 0.592705i $$-0.201940\pi$$
−0.592705 + 0.805420i $$0.701940\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −18.4920 + 18.4920i −1.22735 + 1.22735i −0.262393 + 0.964961i $$0.584512\pi$$
−0.964961 + 0.262393i $$0.915488\pi$$
$$228$$ 0 0
$$229$$ 19.2316 1.27086 0.635428 0.772160i $$-0.280824\pi$$
0.635428 + 0.772160i $$0.280824\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 13.7302 13.7302i 0.899495 0.899495i −0.0958959 0.995391i $$-0.530572\pi$$
0.995391 + 0.0958959i $$0.0305716\pi$$
$$234$$ 0 0
$$235$$ 3.84313 + 10.3146i 0.250698 + 0.672850i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −26.7732 −1.73182 −0.865908 0.500203i $$-0.833259\pi$$
−0.865908 + 0.500203i $$0.833259\pi$$
$$240$$ 0 0
$$241$$ −17.6357 −1.13601 −0.568007 0.823023i $$-0.692286\pi$$
−0.568007 + 0.823023i $$0.692286\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 5.06344 11.0774i 0.323491 0.707707i
$$246$$ 0 0
$$247$$ −21.0280 + 21.0280i −1.33798 + 1.33798i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −13.0522 −0.823846 −0.411923 0.911219i $$-0.635143\pi$$
−0.411923 + 0.911219i $$0.635143\pi$$
$$252$$ 0 0
$$253$$ −2.91209 + 2.91209i −0.183082 + 0.183082i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 9.03127 + 9.03127i 0.563355 + 0.563355i 0.930259 0.366904i $$-0.119582\pi$$
−0.366904 + 0.930259i $$0.619582\pi$$
$$258$$ 0 0
$$259$$ −26.9279 −1.67322
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 2.83442 2.83442i 0.174778 0.174778i −0.614297 0.789075i $$-0.710560\pi$$
0.789075 + 0.614297i $$0.210560\pi$$
$$264$$ 0 0
$$265$$ 1.12589 + 3.02178i 0.0691629 + 0.185627i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 9.89975i 0.603599i 0.953371 + 0.301799i $$0.0975873\pi$$
−0.953371 + 0.301799i $$0.902413\pi$$
$$270$$ 0 0
$$271$$ −16.6235 −1.00981 −0.504904 0.863176i $$-0.668472\pi$$
−0.504904 + 0.863176i $$0.668472\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 12.8539 + 14.8547i 0.775118 + 0.895769i
$$276$$ 0 0
$$277$$ −6.42695 6.42695i −0.386158 0.386158i 0.487156 0.873315i $$-0.338034\pi$$
−0.873315 + 0.487156i $$0.838034\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 27.0270i 1.61230i 0.591714 + 0.806148i $$0.298451\pi$$
−0.591714 + 0.806148i $$0.701549\pi$$
$$282$$ 0 0
$$283$$ 18.1481 18.1481i 1.07879 1.07879i 0.0821722 0.996618i $$-0.473814\pi$$
0.996618 0.0821722i $$-0.0261857\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 15.8060 + 15.8060i 0.932996 + 0.932996i
$$288$$ 0 0
$$289$$ 9.88854i 0.581679i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −11.4905 11.4905i −0.671281 0.671281i 0.286730 0.958011i $$-0.407432\pi$$
−0.958011 + 0.286730i $$0.907432\pi$$
$$294$$ 0 0
$$295$$ −0.493672 + 1.08001i −0.0287427 + 0.0628809i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 6.75387i 0.390586i
$$300$$ 0 0
$$301$$ 1.02836i 0.0592738i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 2.79208 6.10828i 0.159874 0.349759i
$$306$$ 0 0
$$307$$ 17.8635 + 17.8635i 1.01953 + 1.01953i 0.999806 + 0.0197205i $$0.00627765\pi$$
0.0197205 + 0.999806i $$0.493722\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 9.93768i 0.563514i −0.959486 0.281757i $$-0.909083\pi$$
0.959486 0.281757i $$-0.0909173\pi$$
$$312$$ 0 0
$$313$$ 5.20616 + 5.20616i 0.294269 + 0.294269i 0.838764 0.544495i $$-0.183279\pi$$
−0.544495 + 0.838764i $$0.683279\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −13.2883 + 13.2883i −0.746346 + 0.746346i −0.973791 0.227445i $$-0.926963\pi$$
0.227445 + 0.973791i $$0.426963\pi$$
$$318$$ 0 0
$$319$$ 17.1250i 0.958813i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.70338 + 8.70338i 0.484269 + 0.484269i
$$324$$ 0 0
$$325$$ 32.1315 + 2.32015i 1.78233 + 0.128699i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 17.3671 0.957479
$$330$$ 0 0
$$331$$ 8.60834i 0.473157i 0.971612 + 0.236579i $$0.0760261\pi$$
−0.971612 + 0.236579i $$0.923974\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1.42052 + 3.81255i 0.0776114 + 0.208302i
$$336$$ 0 0
$$337$$ 1.29928 1.29928i 0.0707764 0.0707764i −0.670832 0.741609i $$-0.734063\pi$$
0.741609 + 0.670832i $$0.234063\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −37.9960 −2.05760
$$342$$ 0 0
$$343$$ 3.87437 + 3.87437i 0.209196 + 0.209196i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −18.3626 + 18.3626i −0.985756 + 0.985756i −0.999900 0.0141438i $$-0.995498\pi$$
0.0141438 + 0.999900i $$0.495498\pi$$
$$348$$ 0 0
$$349$$ −31.1787 −1.66896 −0.834478 0.551041i $$-0.814231\pi$$
−0.834478 + 0.551041i $$0.814231\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 9.04629 9.04629i 0.481485 0.481485i −0.424120 0.905606i $$-0.639417\pi$$
0.905606 + 0.424120i $$0.139417\pi$$
$$354$$ 0 0
$$355$$ −7.08062 + 15.4904i −0.375800 + 0.822144i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −13.1073 −0.691776 −0.345888 0.938276i $$-0.612422\pi$$
−0.345888 + 0.938276i $$0.612422\pi$$
$$360$$ 0 0
$$361$$ 2.30330 0.121226
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −0.562272 1.50908i −0.0294307 0.0789890i
$$366$$ 0 0
$$367$$ −3.44746 + 3.44746i −0.179956 + 0.179956i −0.791337 0.611381i $$-0.790614\pi$$
0.611381 + 0.791337i $$0.290614\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 5.08789 0.264150
$$372$$ 0 0
$$373$$ 7.24984 7.24984i 0.375382 0.375382i −0.494051 0.869433i $$-0.664484\pi$$
0.869433 + 0.494051i $$0.164484\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −19.8585 19.8585i −1.02277 1.02277i
$$378$$ 0 0
$$379$$ 29.1664 1.49818 0.749088 0.662470i $$-0.230492\pi$$
0.749088 + 0.662470i $$0.230492\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −12.2895 + 12.2895i −0.627965 + 0.627965i −0.947556 0.319591i $$-0.896455\pi$$
0.319591 + 0.947556i $$0.396455\pi$$
$$384$$ 0 0
$$385$$ 29.0433 10.8213i 1.48018 0.551504i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 31.4290i 1.59351i −0.604301 0.796756i $$-0.706548\pi$$
0.604301 0.796756i $$-0.293452\pi$$
$$390$$ 0 0
$$391$$ 2.79539 0.141369
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 1.22632 2.68284i 0.0617029 0.134988i
$$396$$ 0 0
$$397$$ 14.9362 + 14.9362i 0.749627 + 0.749627i 0.974409 0.224782i $$-0.0721671\pi$$
−0.224782 + 0.974409i $$0.572167\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 27.0477i 1.35070i −0.737499 0.675349i $$-0.763993\pi$$
0.737499 0.675349i $$-0.236007\pi$$
$$402$$ 0 0
$$403$$ −44.0611 + 44.0611i −2.19484 + 2.19484i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −21.2038 21.2038i −1.05103 1.05103i
$$408$$ 0 0
$$409$$ 4.66540i 0.230689i −0.993326 0.115345i $$-0.963203\pi$$
0.993326 0.115345i $$-0.0367973\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 1.32484 + 1.32484i 0.0651911 + 0.0651911i
$$414$$ 0 0
$$415$$ 10.8812 + 29.2040i 0.534136 + 1.43357i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 2.43646i 0.119029i 0.998227 + 0.0595144i $$0.0189552\pi$$
−0.998227 + 0.0595144i $$0.981045\pi$$
$$420$$ 0 0
$$421$$ 9.62136i 0.468916i −0.972126 0.234458i $$-0.924668\pi$$
0.972126 0.234458i $$-0.0753316\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0.960298 13.2990i 0.0465813 0.645098i
$$426$$ 0 0
$$427$$ −7.49294 7.49294i −0.362609 0.362609i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 26.4447i 1.27380i 0.770948 + 0.636898i $$0.219783\pi$$
−0.770948 + 0.636898i $$0.780217\pi$$
$$432$$ 0 0
$$433$$ 5.22850 + 5.22850i 0.251266 + 0.251266i 0.821490 0.570224i $$-0.193143\pi$$
−0.570224 + 0.821490i $$0.693143\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 3.42114 3.42114i 0.163655 0.163655i
$$438$$ 0 0
$$439$$ 37.3742i 1.78377i −0.452258 0.891887i $$-0.649381\pi$$
0.452258 0.891887i $$-0.350619\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −18.0711 18.0711i −0.858585 0.858585i 0.132587 0.991171i $$-0.457672\pi$$
−0.991171 + 0.132587i $$0.957672\pi$$
$$444$$ 0 0
$$445$$ −5.93425 2.71253i −0.281310 0.128586i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −24.4570 −1.15420 −0.577098 0.816675i $$-0.695815\pi$$
−0.577098 + 0.816675i $$0.695815\pi$$
$$450$$ 0 0
$$451$$ 24.8921i 1.17212i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 21.1307 46.2279i 0.990621 2.16720i
$$456$$ 0 0
$$457$$ 5.76322 5.76322i 0.269592 0.269592i −0.559344 0.828936i $$-0.688947\pi$$
0.828936 + 0.559344i $$0.188947\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −10.6204 −0.494639 −0.247320 0.968934i $$-0.579550\pi$$
−0.247320 + 0.968934i $$0.579550\pi$$
$$462$$ 0 0
$$463$$ −13.7984 13.7984i −0.641268 0.641268i 0.309599 0.950867i $$-0.399805\pi$$
−0.950867 + 0.309599i $$0.899805\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 11.6749 11.6749i 0.540248 0.540248i −0.383354 0.923602i $$-0.625231\pi$$
0.923602 + 0.383354i $$0.125231\pi$$
$$468$$ 0 0
$$469$$ 6.41933 0.296417
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −0.809762 + 0.809762i −0.0372329 + 0.0372329i
$$474$$ 0 0
$$475$$ −15.1008 17.4513i −0.692872 0.800721i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 5.10716 0.233352 0.116676 0.993170i $$-0.462776\pi$$
0.116676 + 0.993170i $$0.462776\pi$$
$$480$$ 0 0
$$481$$ −49.1768 −2.24227
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −24.0431 + 8.95824i −1.09174 + 0.406773i
$$486$$ 0 0
$$487$$ −3.80542 + 3.80542i −0.172440 + 0.172440i −0.788050 0.615611i $$-0.788909\pi$$
0.615611 + 0.788050i $$0.288909\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −19.3774 −0.874492 −0.437246 0.899342i $$-0.644046\pi$$
−0.437246 + 0.899342i $$0.644046\pi$$
$$492$$ 0 0
$$493$$ −8.21932 + 8.21932i −0.370180 + 0.370180i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 19.0018 + 19.0018i 0.852349 + 0.852349i
$$498$$ 0 0
$$499$$ 21.5723 0.965707 0.482853 0.875701i $$-0.339600\pi$$
0.482853 + 0.875701i $$0.339600\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −0.650945 + 0.650945i −0.0290242 + 0.0290242i −0.721470 0.692446i $$-0.756533\pi$$
0.692446 + 0.721470i $$0.256533\pi$$
$$504$$ 0 0
$$505$$ 22.4251 + 10.2505i 0.997906 + 0.456140i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 9.29371i 0.411937i 0.978559 + 0.205968i $$0.0660344\pi$$
−0.978559 + 0.205968i $$0.933966\pi$$
$$510$$ 0 0
$$511$$ −2.54090 −0.112403
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 3.19224 + 8.56766i 0.140667 + 0.377536i
$$516$$ 0 0
$$517$$ 13.6753 + 13.6753i 0.601441 + 0.601441i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 37.4945i 1.64266i 0.570451 + 0.821331i $$0.306768\pi$$
−0.570451 + 0.821331i $$0.693232\pi$$
$$522$$ 0 0
$$523$$ 18.0635 18.0635i 0.789861 0.789861i −0.191610 0.981471i $$-0.561371\pi$$
0.981471 + 0.191610i $$0.0613710\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 18.2366 + 18.2366i 0.794400 + 0.794400i
$$528$$ 0 0
$$529$$ 21.9012i 0.952225i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 28.8655 + 28.8655i 1.25030 + 1.25030i
$$534$$ 0 0
$$535$$ 15.5243 5.78423i 0.671175 0.250074i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 21.3999i 0.921758i
$$540$$ 0 0
$$541$$ 29.6103i 1.27305i −0.771258 0.636523i $$-0.780372\pi$$
0.771258 0.636523i $$-0.219628\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 10.8083 + 4.94044i 0.462976 + 0.211625i
$$546$$ 0 0
$$547$$ −13.8891 13.8891i −0.593855 0.593855i 0.344816 0.938670i $$-0.387941\pi$$
−0.938670 + 0.344816i $$0.887941\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 20.1185i 0.857076i
$$552$$ 0 0
$$553$$ −3.29101 3.29101i −0.139948 0.139948i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 16.0818 16.0818i 0.681408 0.681408i −0.278910 0.960317i $$-0.589973\pi$$
0.960317 + 0.278910i $$0.0899730\pi$$
$$558$$ 0 0
$$559$$ 1.87804i 0.0794326i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 11.6731 + 11.6731i 0.491962 + 0.491962i 0.908924 0.416962i $$-0.136905\pi$$
−0.416962 + 0.908924i $$0.636905\pi$$
$$564$$ 0 0
$$565$$ −30.6874 + 11.4339i −1.29103 + 0.481027i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −26.5009 −1.11098 −0.555488 0.831524i $$-0.687469\pi$$
−0.555488 + 0.831524i $$0.687469\pi$$
$$570$$ 0 0
$$571$$ 42.2873i 1.76967i −0.465904 0.884835i $$-0.654271\pi$$
0.465904 0.884835i $$-0.345729\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −5.22761 0.377476i −0.218006 0.0157418i
$$576$$ 0 0
$$577$$ 10.2682 10.2682i 0.427473 0.427473i −0.460294 0.887767i $$-0.652256\pi$$
0.887767 + 0.460294i $$0.152256\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 49.1720 2.04000
$$582$$ 0 0
$$583$$ 4.00635 + 4.00635i 0.165926 + 0.165926i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 18.7596 18.7596i 0.774290 0.774290i −0.204563 0.978853i $$-0.565577\pi$$
0.978853 + 0.204563i $$0.0655773\pi$$
$$588$$ 0 0
$$589$$ 44.6379 1.83927
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.79755 1.79755i 0.0738164 0.0738164i −0.669235 0.743051i $$-0.733378\pi$$
0.743051 + 0.669235i $$0.233378\pi$$
$$594$$ 0 0
$$595$$ −19.1335 8.74586i −0.784396 0.358545i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 34.7082 1.41814 0.709069 0.705139i $$-0.249115\pi$$
0.709069 + 0.705139i $$0.249115\pi$$
$$600$$ 0 0
$$601$$ −8.66540 −0.353469 −0.176735 0.984259i $$-0.556553\pi$$
−0.176735 + 0.984259i $$0.556553\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 9.02002 + 4.12303i 0.366716 + 0.167625i
$$606$$ 0 0
$$607$$ 5.31702 5.31702i 0.215811 0.215811i −0.590919 0.806731i $$-0.701235\pi$$
0.806731 + 0.590919i $$0.201235\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 31.7165 1.28311
$$612$$ 0 0
$$613$$ 0.848748 0.848748i 0.0342806 0.0342806i −0.689759 0.724039i $$-0.742283\pi$$
0.724039 + 0.689759i $$0.242283\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 16.6187 + 16.6187i 0.669043 + 0.669043i 0.957494 0.288452i $$-0.0931405\pi$$
−0.288452 + 0.957494i $$0.593141\pi$$
$$618$$ 0 0
$$619$$ −6.21940 −0.249979 −0.124989 0.992158i $$-0.539890\pi$$
−0.124989 + 0.992158i $$0.539890\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −7.27946 + 7.27946i −0.291646 + 0.291646i
$$624$$ 0 0
$$625$$ −3.59168 + 24.7407i −0.143667 + 0.989626i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 20.3540i 0.811567i
$$630$$ 0 0
$$631$$ −12.0019 −0.477790 −0.238895 0.971045i $$-0.576785\pi$$
−0.238895 + 0.971045i $$0.576785\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 3.28543 1.22412i 0.130378 0.0485778i
$$636$$ 0 0
$$637$$ −24.8158 24.8158i −0.983239 0.983239i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 6.27061i 0.247674i −0.992303 0.123837i $$-0.960480\pi$$
0.992303 0.123837i $$-0.0395200\pi$$
$$642$$ 0 0
$$643$$ 15.3358 15.3358i 0.604787 0.604787i −0.336792 0.941579i $$-0.609342\pi$$
0.941579 + 0.336792i $$0.109342\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −28.9583 28.9583i −1.13847 1.13847i −0.988725 0.149741i $$-0.952156\pi$$
−0.149741 0.988725i $$-0.547844\pi$$
$$648$$ 0 0
$$649$$ 2.08643i 0.0818997i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 2.21463 + 2.21463i 0.0866651 + 0.0866651i 0.749110 0.662445i $$-0.230481\pi$$
−0.662445 + 0.749110i $$0.730481\pi$$
$$654$$ 0 0
$$655$$ 2.02754 + 0.926783i 0.0792225 + 0.0362124i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 37.2920i 1.45269i 0.687330 + 0.726345i $$0.258782\pi$$
−0.687330 + 0.726345i $$0.741218\pi$$
$$660$$ 0 0
$$661$$ 6.19442i 0.240935i −0.992717 0.120467i $$-0.961561\pi$$
0.992717 0.120467i $$-0.0384393\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −34.1202 + 12.7129i −1.32312 + 0.492985i
$$666$$ 0 0
$$667$$ 3.23087 + 3.23087i 0.125100 + 0.125100i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 11.8003i 0.455546i
$$672$$ 0 0
$$673$$ −27.8727 27.8727i −1.07441 1.07441i −0.996999 0.0774133i $$-0.975334\pi$$
−0.0774133 0.996999i $$-0.524666\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 10.0200 10.0200i 0.385098 0.385098i −0.487837 0.872935i $$-0.662214\pi$$
0.872935 + 0.487837i $$0.162214\pi$$
$$678$$ 0 0
$$679$$ 40.4823i 1.55357i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −11.5229 11.5229i −0.440911 0.440911i 0.451407 0.892318i $$-0.350922\pi$$
−0.892318 + 0.451407i $$0.850922\pi$$
$$684$$ 0 0
$$685$$ 1.13977 + 3.05904i 0.0435485 + 0.116880i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 9.29173 0.353987
$$690$$ 0 0
$$691$$ 18.3907i 0.699614i −0.936822 0.349807i $$-0.886247\pi$$
0.936822 0.349807i $$-0.113753\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 34.5380 + 15.7872i 1.31010 + 0.598844i
$$696$$ 0 0
$$697$$ 11.9473 11.9473i 0.452535 0.452535i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 52.0764 1.96690 0.983449 0.181186i $$-0.0579937\pi$$
0.983449 + 0.181186i $$0.0579937\pi$$
$$702$$ 0 0
$$703$$ 24.9103 + 24.9103i 0.939509 + 0.939509i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 27.5086 27.5086i 1.03457 1.03457i
$$708$$ 0 0
$$709$$ −49.8546 −1.87233 −0.936165 0.351561i $$-0.885651\pi$$
−0.936165 + 0.351561i $$0.885651\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 7.16849 7.16849i 0.268462 0.268462i
$$714$$ 0 0
$$715$$ 53.0401 19.7623i 1.98359 0.739068i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −21.3548 −0.796400 −0.398200 0.917299i $$-0.630365\pi$$
−0.398200 + 0.917299i $$0.630365\pi$$
$$720$$ 0 0
$$721$$ 14.4257 0.537242
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 16.4807 14.2609i 0.612079 0.529638i
$$726$$ 0 0
$$727$$ −13.1166 + 13.1166i −0.486469 + 0.486469i −0.907190 0.420721i $$-0.861777\pi$$
0.420721 + 0.907190i $$0.361777\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0.777309 0.0287498
$$732$$ 0 0
$$733$$ −3.40526 + 3.40526i −0.125776 + 0.125776i −0.767193 0.641417i $$-0.778347\pi$$
0.641417 + 0.767193i $$0.278347\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 5.05477 + 5.05477i 0.186195 + 0.186195i
$$738$$ 0 0
$$739$$ −6.84745 −0.251887 −0.125944 0.992037i $$-0.540196\pi$$
−0.125944 + 0.992037i $$0.540196\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −9.83167 + 9.83167i −0.360689 + 0.360689i −0.864067 0.503377i $$-0.832091\pi$$
0.503377 + 0.864067i $$0.332091\pi$$
$$744$$ 0 0
$$745$$ −6.03092 + 13.1940i −0.220956 + 0.483389i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 26.1389i 0.955095i
$$750$$ 0 0
$$751$$ 36.1038 1.31745 0.658723 0.752385i $$-0.271097\pi$$
0.658723 + 0.752385i $$0.271097\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −8.56606 3.91553i −0.311751 0.142501i
$$756$$ 0 0
$$757$$ −26.0495 26.0495i −0.946785 0.946785i 0.0518693 0.998654i $$-0.483482\pi$$
−0.998654 + 0.0518693i $$0.983482\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 29.4006i 1.06577i −0.846188 0.532885i $$-0.821108\pi$$
0.846188 0.532885i $$-0.178892\pi$$
$$762$$ 0 0
$$763$$ 13.2584 13.2584i 0.479986 0.479986i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 2.41948 + 2.41948i 0.0873623 + 0.0873623i
$$768$$ 0 0
$$769$$ 39.4234i 1.42164i −0.703372 0.710822i $$-0.748323\pi$$
0.703372 0.710822i $$-0.251677\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 2.76896 + 2.76896i 0.0995925 + 0.0995925i 0.755147 0.655555i $$-0.227565\pi$$
−0.655555 + 0.755147i $$0.727565\pi$$
$$774$$ 0 0
$$775$$ −31.6414 36.5666i −1.13659 1.31351i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 29.2434i 1.04775i
$$780$$ 0 0
$$781$$ 29.9252i 1.07081i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −0.0407272 0.109308i −0.00145362 0.00390136i
$$786$$ 0 0
$$787$$ −20.1445 20.1445i −0.718072 0.718072i 0.250138 0.968210i $$-0.419524\pi$$
−0.968210 + 0.250138i $$0.919524\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 51.6696i 1.83716i
$$792$$ 0 0
$$793$$ −13.6839 13.6839i −0.485931 0.485931i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −27.4953 + 27.4953i −0.973933 + 0.973933i −0.999669 0.0257360i $$-0.991807\pi$$
0.0257360 + 0.999669i $$0.491807\pi$$
$$798$$ 0 0
$$799$$ 13.1273i 0.464410i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −2.00078 2.00078i −0.0706060 0.0706060i
$$804$$ 0 0
$$805$$ −3.43784 + 7.52102i −0.121168 + 0.265081i
$$806$$ 0 0
$$807$$ 0