# Properties

 Label 240.3.l.d.161.7 Level $240$ Weight $3$ Character 240.161 Analytic conductor $6.540$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 240.l (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.53952634465$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.681615360000.5 Defining polynomial: $$x^{8} - 4 x^{7} - 2 x^{6} + 20 x^{5} + 49 x^{4} - 136 x^{3} + 168 x^{2} - 96 x + 864$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{5}\cdot 3$$ Twist minimal: no (minimal twist has level 120) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 161.7 Root $$3.22255 - 1.41421i$$ of defining polynomial Character $$\chi$$ $$=$$ 240.161 Dual form 240.3.l.d.161.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(2.87275 - 0.864473i) q^{3} -2.23607i q^{5} -9.02416 q^{7} +(7.50537 - 4.96683i) q^{9} +O(q^{10})$$ $$q+(2.87275 - 0.864473i) q^{3} -2.23607i q^{5} -9.02416 q^{7} +(7.50537 - 4.96683i) q^{9} -21.8827i q^{11} +21.6599 q^{13} +(-1.93302 - 6.42366i) q^{15} -12.1078i q^{17} -3.03757 q^{19} +(-25.9241 + 7.80114i) q^{21} +28.5735i q^{23} -5.00000 q^{25} +(17.2674 - 20.7566i) q^{27} +12.0364i q^{29} -2.19085 q^{31} +(-18.9170 - 62.8636i) q^{33} +20.1786i q^{35} +0.839959 q^{37} +(62.2233 - 18.7244i) q^{39} +35.5690i q^{41} +12.7152 q^{43} +(-11.1062 - 16.7825i) q^{45} -22.5481i q^{47} +32.4354 q^{49} +(-10.4668 - 34.7826i) q^{51} +9.13775i q^{53} -48.9312 q^{55} +(-8.72618 + 2.62590i) q^{57} +80.4459i q^{59} -57.8816 q^{61} +(-67.7297 + 44.8214i) q^{63} -48.4329i q^{65} +63.0560 q^{67} +(24.7011 + 82.0846i) q^{69} -17.0218i q^{71} +52.1181 q^{73} +(-14.3637 + 4.32237i) q^{75} +197.473i q^{77} +7.46224 q^{79} +(31.6612 - 74.5558i) q^{81} +82.3758i q^{83} -27.0738 q^{85} +(10.4051 + 34.5774i) q^{87} -27.5850i q^{89} -195.462 q^{91} +(-6.29376 + 1.89393i) q^{93} +6.79221i q^{95} +114.989 q^{97} +(-108.688 - 164.238i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{3} - 16 q^{7} + 20 q^{9} + O(q^{10})$$ $$8 q + 4 q^{3} - 16 q^{7} + 20 q^{9} - 8 q^{13} + 8 q^{19} + 28 q^{21} - 40 q^{25} - 20 q^{27} - 120 q^{31} - 112 q^{33} + 8 q^{37} + 72 q^{39} + 328 q^{43} - 60 q^{45} + 64 q^{49} - 64 q^{51} + 40 q^{55} + 72 q^{57} + 8 q^{61} - 88 q^{63} - 152 q^{67} + 100 q^{69} + 32 q^{73} - 20 q^{75} - 88 q^{79} + 224 q^{81} + 152 q^{87} - 560 q^{91} - 368 q^{93} + 144 q^{97} - 32 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$97$$ $$161$$ $$181$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 2.87275 0.864473i 0.957583 0.288158i
$$4$$ 0 0
$$5$$ 2.23607i 0.447214i
$$6$$ 0 0
$$7$$ −9.02416 −1.28917 −0.644583 0.764535i $$-0.722969\pi$$
−0.644583 + 0.764535i $$0.722969\pi$$
$$8$$ 0 0
$$9$$ 7.50537 4.96683i 0.833930 0.551870i
$$10$$ 0 0
$$11$$ 21.8827i 1.98934i −0.103119 0.994669i $$-0.532882\pi$$
0.103119 0.994669i $$-0.467118\pi$$
$$12$$ 0 0
$$13$$ 21.6599 1.66614 0.833071 0.553166i $$-0.186580\pi$$
0.833071 + 0.553166i $$0.186580\pi$$
$$14$$ 0 0
$$15$$ −1.93302 6.42366i −0.128868 0.428244i
$$16$$ 0 0
$$17$$ 12.1078i 0.712221i −0.934444 0.356111i $$-0.884103\pi$$
0.934444 0.356111i $$-0.115897\pi$$
$$18$$ 0 0
$$19$$ −3.03757 −0.159872 −0.0799361 0.996800i $$-0.525472\pi$$
−0.0799361 + 0.996800i $$0.525472\pi$$
$$20$$ 0 0
$$21$$ −25.9241 + 7.80114i −1.23448 + 0.371483i
$$22$$ 0 0
$$23$$ 28.5735i 1.24233i 0.783681 + 0.621164i $$0.213340\pi$$
−0.783681 + 0.621164i $$0.786660\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −0.200000
$$26$$ 0 0
$$27$$ 17.2674 20.7566i 0.639532 0.768765i
$$28$$ 0 0
$$29$$ 12.0364i 0.415047i 0.978230 + 0.207523i $$0.0665403\pi$$
−0.978230 + 0.207523i $$0.933460\pi$$
$$30$$ 0 0
$$31$$ −2.19085 −0.0706725 −0.0353363 0.999375i $$-0.511250\pi$$
−0.0353363 + 0.999375i $$0.511250\pi$$
$$32$$ 0 0
$$33$$ −18.9170 62.8636i −0.573243 1.90496i
$$34$$ 0 0
$$35$$ 20.1786i 0.576532i
$$36$$ 0 0
$$37$$ 0.839959 0.0227016 0.0113508 0.999936i $$-0.496387\pi$$
0.0113508 + 0.999936i $$0.496387\pi$$
$$38$$ 0 0
$$39$$ 62.2233 18.7244i 1.59547 0.480112i
$$40$$ 0 0
$$41$$ 35.5690i 0.867537i 0.901024 + 0.433769i $$0.142816\pi$$
−0.901024 + 0.433769i $$0.857184\pi$$
$$42$$ 0 0
$$43$$ 12.7152 0.295702 0.147851 0.989010i $$-0.452764\pi$$
0.147851 + 0.989010i $$0.452764\pi$$
$$44$$ 0 0
$$45$$ −11.1062 16.7825i −0.246804 0.372945i
$$46$$ 0 0
$$47$$ 22.5481i 0.479746i −0.970804 0.239873i $$-0.922894\pi$$
0.970804 0.239873i $$-0.0771058\pi$$
$$48$$ 0 0
$$49$$ 32.4354 0.661947
$$50$$ 0 0
$$51$$ −10.4668 34.7826i −0.205232 0.682011i
$$52$$ 0 0
$$53$$ 9.13775i 0.172410i 0.996277 + 0.0862052i $$0.0274741\pi$$
−0.996277 + 0.0862052i $$0.972526\pi$$
$$54$$ 0 0
$$55$$ −48.9312 −0.889659
$$56$$ 0 0
$$57$$ −8.72618 + 2.62590i −0.153091 + 0.0460684i
$$58$$ 0 0
$$59$$ 80.4459i 1.36349i 0.731590 + 0.681745i $$0.238779\pi$$
−0.731590 + 0.681745i $$0.761221\pi$$
$$60$$ 0 0
$$61$$ −57.8816 −0.948878 −0.474439 0.880288i $$-0.657349\pi$$
−0.474439 + 0.880288i $$0.657349\pi$$
$$62$$ 0 0
$$63$$ −67.7297 + 44.8214i −1.07507 + 0.711452i
$$64$$ 0 0
$$65$$ 48.4329i 0.745122i
$$66$$ 0 0
$$67$$ 63.0560 0.941135 0.470567 0.882364i $$-0.344049\pi$$
0.470567 + 0.882364i $$0.344049\pi$$
$$68$$ 0 0
$$69$$ 24.7011 + 82.0846i 0.357986 + 1.18963i
$$70$$ 0 0
$$71$$ 17.0218i 0.239743i −0.992789 0.119872i $$-0.961752\pi$$
0.992789 0.119872i $$-0.0382483\pi$$
$$72$$ 0 0
$$73$$ 52.1181 0.713947 0.356973 0.934115i $$-0.383809\pi$$
0.356973 + 0.934115i $$0.383809\pi$$
$$74$$ 0 0
$$75$$ −14.3637 + 4.32237i −0.191517 + 0.0576316i
$$76$$ 0 0
$$77$$ 197.473i 2.56459i
$$78$$ 0 0
$$79$$ 7.46224 0.0944588 0.0472294 0.998884i $$-0.484961\pi$$
0.0472294 + 0.998884i $$0.484961\pi$$
$$80$$ 0 0
$$81$$ 31.6612 74.5558i 0.390879 0.920442i
$$82$$ 0 0
$$83$$ 82.3758i 0.992480i 0.868185 + 0.496240i $$0.165286\pi$$
−0.868185 + 0.496240i $$0.834714\pi$$
$$84$$ 0 0
$$85$$ −27.0738 −0.318515
$$86$$ 0 0
$$87$$ 10.4051 + 34.5774i 0.119599 + 0.397442i
$$88$$ 0 0
$$89$$ 27.5850i 0.309944i −0.987919 0.154972i $$-0.950471\pi$$
0.987919 0.154972i $$-0.0495287\pi$$
$$90$$ 0 0
$$91$$ −195.462 −2.14793
$$92$$ 0 0
$$93$$ −6.29376 + 1.89393i −0.0676748 + 0.0203648i
$$94$$ 0 0
$$95$$ 6.79221i 0.0714970i
$$96$$ 0 0
$$97$$ 114.989 1.18545 0.592727 0.805404i $$-0.298051\pi$$
0.592727 + 0.805404i $$0.298051\pi$$
$$98$$ 0 0
$$99$$ −108.688 164.238i −1.09786 1.65897i
$$100$$ 0 0
$$101$$ 122.804i 1.21588i 0.793982 + 0.607941i $$0.208004\pi$$
−0.793982 + 0.607941i $$0.791996\pi$$
$$102$$ 0 0
$$103$$ 46.8275 0.454636 0.227318 0.973821i $$-0.427004\pi$$
0.227318 + 0.973821i $$0.427004\pi$$
$$104$$ 0 0
$$105$$ 17.4439 + 57.9681i 0.166132 + 0.552077i
$$106$$ 0 0
$$107$$ 105.086i 0.982113i 0.871128 + 0.491056i $$0.163389\pi$$
−0.871128 + 0.491056i $$0.836611\pi$$
$$108$$ 0 0
$$109$$ −116.777 −1.07135 −0.535673 0.844426i $$-0.679942\pi$$
−0.535673 + 0.844426i $$0.679942\pi$$
$$110$$ 0 0
$$111$$ 2.41299 0.726122i 0.0217387 0.00654164i
$$112$$ 0 0
$$113$$ 10.8116i 0.0956779i 0.998855 + 0.0478389i $$0.0152334\pi$$
−0.998855 + 0.0478389i $$0.984767\pi$$
$$114$$ 0 0
$$115$$ 63.8924 0.555586
$$116$$ 0 0
$$117$$ 162.565 107.581i 1.38945 0.919494i
$$118$$ 0 0
$$119$$ 109.262i 0.918171i
$$120$$ 0 0
$$121$$ −357.853 −2.95747
$$122$$ 0 0
$$123$$ 30.7485 + 102.181i 0.249988 + 0.830739i
$$124$$ 0 0
$$125$$ 11.1803i 0.0894427i
$$126$$ 0 0
$$127$$ 192.459 1.51543 0.757714 0.652587i $$-0.226316\pi$$
0.757714 + 0.652587i $$0.226316\pi$$
$$128$$ 0 0
$$129$$ 36.5276 10.9919i 0.283159 0.0852089i
$$130$$ 0 0
$$131$$ 48.6360i 0.371267i −0.982619 0.185633i $$-0.940566\pi$$
0.982619 0.185633i $$-0.0594337\pi$$
$$132$$ 0 0
$$133$$ 27.4115 0.206102
$$134$$ 0 0
$$135$$ −46.4133 38.6110i −0.343802 0.286007i
$$136$$ 0 0
$$137$$ 157.869i 1.15233i −0.817335 0.576163i $$-0.804549\pi$$
0.817335 0.576163i $$-0.195451\pi$$
$$138$$ 0 0
$$139$$ 164.752 1.18526 0.592632 0.805473i $$-0.298089\pi$$
0.592632 + 0.805473i $$0.298089\pi$$
$$140$$ 0 0
$$141$$ −19.4922 64.7749i −0.138243 0.459397i
$$142$$ 0 0
$$143$$ 473.977i 3.31452i
$$144$$ 0 0
$$145$$ 26.9141 0.185615
$$146$$ 0 0
$$147$$ 93.1788 28.0396i 0.633869 0.190745i
$$148$$ 0 0
$$149$$ 262.935i 1.76467i −0.470626 0.882333i $$-0.655972\pi$$
0.470626 0.882333i $$-0.344028\pi$$
$$150$$ 0 0
$$151$$ −15.8171 −0.104749 −0.0523745 0.998628i $$-0.516679\pi$$
−0.0523745 + 0.998628i $$0.516679\pi$$
$$152$$ 0 0
$$153$$ −60.1372 90.8733i −0.393054 0.593943i
$$154$$ 0 0
$$155$$ 4.89889i 0.0316057i
$$156$$ 0 0
$$157$$ −6.11941 −0.0389771 −0.0194886 0.999810i $$-0.506204\pi$$
−0.0194886 + 0.999810i $$0.506204\pi$$
$$158$$ 0 0
$$159$$ 7.89934 + 26.2505i 0.0496814 + 0.165097i
$$160$$ 0 0
$$161$$ 257.852i 1.60157i
$$162$$ 0 0
$$163$$ 170.444 1.04567 0.522833 0.852435i $$-0.324875\pi$$
0.522833 + 0.852435i $$0.324875\pi$$
$$164$$ 0 0
$$165$$ −140.567 + 42.2998i −0.851922 + 0.256362i
$$166$$ 0 0
$$167$$ 61.2668i 0.366867i 0.983032 + 0.183434i $$0.0587212\pi$$
−0.983032 + 0.183434i $$0.941279\pi$$
$$168$$ 0 0
$$169$$ 300.149 1.77603
$$170$$ 0 0
$$171$$ −22.7981 + 15.0871i −0.133322 + 0.0882286i
$$172$$ 0 0
$$173$$ 262.548i 1.51762i 0.651312 + 0.758810i $$0.274219\pi$$
−0.651312 + 0.758810i $$0.725781\pi$$
$$174$$ 0 0
$$175$$ 45.1208 0.257833
$$176$$ 0 0
$$177$$ 69.5434 + 231.101i 0.392900 + 1.30566i
$$178$$ 0 0
$$179$$ 6.88752i 0.0384778i 0.999815 + 0.0192389i $$0.00612431\pi$$
−0.999815 + 0.0192389i $$0.993876\pi$$
$$180$$ 0 0
$$181$$ 218.536 1.20738 0.603691 0.797218i $$-0.293696\pi$$
0.603691 + 0.797218i $$0.293696\pi$$
$$182$$ 0 0
$$183$$ −166.279 + 50.0371i −0.908630 + 0.273427i
$$184$$ 0 0
$$185$$ 1.87821i 0.0101525i
$$186$$ 0 0
$$187$$ −264.951 −1.41685
$$188$$ 0 0
$$189$$ −155.823 + 187.311i −0.824462 + 0.991065i
$$190$$ 0 0
$$191$$ 75.2506i 0.393982i −0.980405 0.196991i $$-0.936883\pi$$
0.980405 0.196991i $$-0.0631170\pi$$
$$192$$ 0 0
$$193$$ −212.587 −1.10149 −0.550744 0.834674i $$-0.685656\pi$$
−0.550744 + 0.834674i $$0.685656\pi$$
$$194$$ 0 0
$$195$$ −41.8690 139.136i −0.214713 0.713516i
$$196$$ 0 0
$$197$$ 190.640i 0.967718i −0.875146 0.483859i $$-0.839235\pi$$
0.875146 0.483859i $$-0.160765\pi$$
$$198$$ 0 0
$$199$$ −209.996 −1.05526 −0.527629 0.849475i $$-0.676919\pi$$
−0.527629 + 0.849475i $$0.676919\pi$$
$$200$$ 0 0
$$201$$ 181.144 54.5102i 0.901214 0.271195i
$$202$$ 0 0
$$203$$ 108.618i 0.535064i
$$204$$ 0 0
$$205$$ 79.5348 0.387974
$$206$$ 0 0
$$207$$ 141.920 + 214.455i 0.685603 + 1.03601i
$$208$$ 0 0
$$209$$ 66.4703i 0.318040i
$$210$$ 0 0
$$211$$ −176.419 −0.836110 −0.418055 0.908422i $$-0.637288\pi$$
−0.418055 + 0.908422i $$0.637288\pi$$
$$212$$ 0 0
$$213$$ −14.7149 48.8993i −0.0690839 0.229574i
$$214$$ 0 0
$$215$$ 28.4320i 0.132242i
$$216$$ 0 0
$$217$$ 19.7706 0.0911086
$$218$$ 0 0
$$219$$ 149.722 45.0547i 0.683663 0.205729i
$$220$$ 0 0
$$221$$ 262.252i 1.18666i
$$222$$ 0 0
$$223$$ −132.362 −0.593552 −0.296776 0.954947i $$-0.595911\pi$$
−0.296776 + 0.954947i $$0.595911\pi$$
$$224$$ 0 0
$$225$$ −37.5269 + 24.8341i −0.166786 + 0.110374i
$$226$$ 0 0
$$227$$ 187.624i 0.826537i −0.910609 0.413268i $$-0.864387\pi$$
0.910609 0.413268i $$-0.135613\pi$$
$$228$$ 0 0
$$229$$ −178.571 −0.779788 −0.389894 0.920860i $$-0.627488\pi$$
−0.389894 + 0.920860i $$0.627488\pi$$
$$230$$ 0 0
$$231$$ 170.710 + 567.291i 0.739005 + 2.45580i
$$232$$ 0 0
$$233$$ 296.711i 1.27344i 0.771097 + 0.636718i $$0.219708\pi$$
−0.771097 + 0.636718i $$0.780292\pi$$
$$234$$ 0 0
$$235$$ −50.4190 −0.214549
$$236$$ 0 0
$$237$$ 21.4371 6.45091i 0.0904521 0.0272190i
$$238$$ 0 0
$$239$$ 137.976i 0.577306i −0.957434 0.288653i $$-0.906793\pi$$
0.957434 0.288653i $$-0.0932074\pi$$
$$240$$ 0 0
$$241$$ 42.5687 0.176633 0.0883167 0.996092i $$-0.471851\pi$$
0.0883167 + 0.996092i $$0.471851\pi$$
$$242$$ 0 0
$$243$$ 26.5032 241.550i 0.109067 0.994034i
$$244$$ 0 0
$$245$$ 72.5278i 0.296032i
$$246$$ 0 0
$$247$$ −65.7933 −0.266370
$$248$$ 0 0
$$249$$ 71.2117 + 236.645i 0.285991 + 0.950382i
$$250$$ 0 0
$$251$$ 205.885i 0.820259i 0.912027 + 0.410130i $$0.134517\pi$$
−0.912027 + 0.410130i $$0.865483\pi$$
$$252$$ 0 0
$$253$$ 625.267 2.47141
$$254$$ 0 0
$$255$$ −77.7762 + 23.4046i −0.305005 + 0.0917826i
$$256$$ 0 0
$$257$$ 188.382i 0.733004i 0.930417 + 0.366502i $$0.119445\pi$$
−0.930417 + 0.366502i $$0.880555\pi$$
$$258$$ 0 0
$$259$$ −7.57992 −0.0292661
$$260$$ 0 0
$$261$$ 59.7825 + 90.3373i 0.229052 + 0.346120i
$$262$$ 0 0
$$263$$ 188.745i 0.717660i 0.933403 + 0.358830i $$0.116824\pi$$
−0.933403 + 0.358830i $$0.883176\pi$$
$$264$$ 0 0
$$265$$ 20.4326 0.0771043
$$266$$ 0 0
$$267$$ −23.8465 79.2447i −0.0893127 0.296797i
$$268$$ 0 0
$$269$$ 333.372i 1.23930i −0.784878 0.619651i $$-0.787274\pi$$
0.784878 0.619651i $$-0.212726\pi$$
$$270$$ 0 0
$$271$$ −262.047 −0.966964 −0.483482 0.875354i $$-0.660628\pi$$
−0.483482 + 0.875354i $$0.660628\pi$$
$$272$$ 0 0
$$273$$ −561.513 + 168.972i −2.05682 + 0.618944i
$$274$$ 0 0
$$275$$ 109.414i 0.397868i
$$276$$ 0 0
$$277$$ −400.100 −1.44440 −0.722202 0.691682i $$-0.756870\pi$$
−0.722202 + 0.691682i $$0.756870\pi$$
$$278$$ 0 0
$$279$$ −16.4431 + 10.8816i −0.0589360 + 0.0390020i
$$280$$ 0 0
$$281$$ 350.698i 1.24804i 0.781410 + 0.624018i $$0.214501\pi$$
−0.781410 + 0.624018i $$0.785499\pi$$
$$282$$ 0 0
$$283$$ 464.015 1.63963 0.819814 0.572630i $$-0.194077\pi$$
0.819814 + 0.572630i $$0.194077\pi$$
$$284$$ 0 0
$$285$$ 5.87169 + 19.5123i 0.0206024 + 0.0684643i
$$286$$ 0 0
$$287$$ 320.981i 1.11840i
$$288$$ 0 0
$$289$$ 142.402 0.492741
$$290$$ 0 0
$$291$$ 330.334 99.4049i 1.13517 0.341598i
$$292$$ 0 0
$$293$$ 47.4080i 0.161802i −0.996722 0.0809009i $$-0.974220\pi$$
0.996722 0.0809009i $$-0.0257797\pi$$
$$294$$ 0 0
$$295$$ 179.883 0.609771
$$296$$ 0 0
$$297$$ −454.212 377.857i −1.52933 1.27224i
$$298$$ 0 0
$$299$$ 618.899i 2.06990i
$$300$$ 0 0
$$301$$ −114.744 −0.381209
$$302$$ 0 0
$$303$$ 106.161 + 352.785i 0.350366 + 1.16431i
$$304$$ 0 0
$$305$$ 129.427i 0.424351i
$$306$$ 0 0
$$307$$ −461.894 −1.50454 −0.752270 0.658855i $$-0.771041\pi$$
−0.752270 + 0.658855i $$0.771041\pi$$
$$308$$ 0 0
$$309$$ 134.524 40.4812i 0.435352 0.131007i
$$310$$ 0 0
$$311$$ 123.057i 0.395681i −0.980234 0.197841i $$-0.936607\pi$$
0.980234 0.197841i $$-0.0633929\pi$$
$$312$$ 0 0
$$313$$ 97.4353 0.311295 0.155647 0.987813i $$-0.450254\pi$$
0.155647 + 0.987813i $$0.450254\pi$$
$$314$$ 0 0
$$315$$ 100.224 + 151.448i 0.318171 + 0.480788i
$$316$$ 0 0
$$317$$ 252.388i 0.796175i −0.917347 0.398088i $$-0.869674\pi$$
0.917347 0.398088i $$-0.130326\pi$$
$$318$$ 0 0
$$319$$ 263.388 0.825668
$$320$$ 0 0
$$321$$ 90.8441 + 301.886i 0.283003 + 0.940454i
$$322$$ 0 0
$$323$$ 36.7782i 0.113864i
$$324$$ 0 0
$$325$$ −108.299 −0.333229
$$326$$ 0 0
$$327$$ −335.470 + 100.950i −1.02590 + 0.308716i
$$328$$ 0 0
$$329$$ 203.477i 0.618472i
$$330$$ 0 0
$$331$$ 303.273 0.916231 0.458116 0.888893i $$-0.348525\pi$$
0.458116 + 0.888893i $$0.348525\pi$$
$$332$$ 0 0
$$333$$ 6.30420 4.17193i 0.0189315 0.0125283i
$$334$$ 0 0
$$335$$ 140.998i 0.420888i
$$336$$ 0 0
$$337$$ −352.738 −1.04670 −0.523350 0.852118i $$-0.675318\pi$$
−0.523350 + 0.852118i $$0.675318\pi$$
$$338$$ 0 0
$$339$$ 9.34634 + 31.0590i 0.0275703 + 0.0916195i
$$340$$ 0 0
$$341$$ 47.9417i 0.140592i
$$342$$ 0 0
$$343$$ 149.481 0.435806
$$344$$ 0 0
$$345$$ 183.547 55.2332i 0.532019 0.160096i
$$346$$ 0 0
$$347$$ 280.382i 0.808018i 0.914755 + 0.404009i $$0.132384\pi$$
−0.914755 + 0.404009i $$0.867616\pi$$
$$348$$ 0 0
$$349$$ −586.721 −1.68115 −0.840575 0.541696i $$-0.817783\pi$$
−0.840575 + 0.541696i $$0.817783\pi$$
$$350$$ 0 0
$$351$$ 374.008 449.586i 1.06555 1.28087i
$$352$$ 0 0
$$353$$ 558.927i 1.58336i −0.610935 0.791681i $$-0.709206\pi$$
0.610935 0.791681i $$-0.290794\pi$$
$$354$$ 0 0
$$355$$ −38.0618 −0.107216
$$356$$ 0 0
$$357$$ 94.4544 + 313.883i 0.264578 + 0.879225i
$$358$$ 0 0
$$359$$ 323.554i 0.901264i −0.892710 0.450632i $$-0.851199\pi$$
0.892710 0.450632i $$-0.148801\pi$$
$$360$$ 0 0
$$361$$ −351.773 −0.974441
$$362$$ 0 0
$$363$$ −1028.02 + 309.355i −2.83202 + 0.852217i
$$364$$ 0 0
$$365$$ 116.540i 0.319287i
$$366$$ 0 0
$$367$$ −176.636 −0.481296 −0.240648 0.970612i $$-0.577360\pi$$
−0.240648 + 0.970612i $$0.577360\pi$$
$$368$$ 0 0
$$369$$ 176.665 + 266.959i 0.478768 + 0.723466i
$$370$$ 0 0
$$371$$ 82.4605i 0.222265i
$$372$$ 0 0
$$373$$ 367.327 0.984790 0.492395 0.870372i $$-0.336122\pi$$
0.492395 + 0.870372i $$0.336122\pi$$
$$374$$ 0 0
$$375$$ 9.66511 + 32.1183i 0.0257736 + 0.0856488i
$$376$$ 0 0
$$377$$ 260.706i 0.691527i
$$378$$ 0 0
$$379$$ −611.014 −1.61217 −0.806087 0.591798i $$-0.798418\pi$$
−0.806087 + 0.591798i $$0.798418\pi$$
$$380$$ 0 0
$$381$$ 552.887 166.376i 1.45115 0.436682i
$$382$$ 0 0
$$383$$ 13.6994i 0.0357687i −0.999840 0.0178844i $$-0.994307\pi$$
0.999840 0.0178844i $$-0.00569307\pi$$
$$384$$ 0 0
$$385$$ 441.563 1.14692
$$386$$ 0 0
$$387$$ 95.4322 63.1542i 0.246595 0.163189i
$$388$$ 0 0
$$389$$ 379.601i 0.975838i 0.872889 + 0.487919i $$0.162244\pi$$
−0.872889 + 0.487919i $$0.837756\pi$$
$$390$$ 0 0
$$391$$ 345.962 0.884812
$$392$$ 0 0
$$393$$ −42.0445 139.719i −0.106983 0.355519i
$$394$$ 0 0
$$395$$ 16.6861i 0.0422432i
$$396$$ 0 0
$$397$$ 450.560 1.13491 0.567456 0.823404i $$-0.307928\pi$$
0.567456 + 0.823404i $$0.307928\pi$$
$$398$$ 0 0
$$399$$ 78.7464 23.6965i 0.197359 0.0593898i
$$400$$ 0 0
$$401$$ 503.683i 1.25607i 0.778186 + 0.628034i $$0.216140\pi$$
−0.778186 + 0.628034i $$0.783860\pi$$
$$402$$ 0 0
$$403$$ −47.4535 −0.117751
$$404$$ 0 0
$$405$$ −166.712 70.7966i −0.411634 0.174806i
$$406$$ 0 0
$$407$$ 18.3806i 0.0451611i
$$408$$ 0 0
$$409$$ 240.726 0.588573 0.294286 0.955717i $$-0.404918\pi$$
0.294286 + 0.955717i $$0.404918\pi$$
$$410$$ 0 0
$$411$$ −136.473 453.517i −0.332051 1.10345i
$$412$$ 0 0
$$413$$ 725.957i 1.75776i
$$414$$ 0 0
$$415$$ 184.198 0.443850
$$416$$ 0 0
$$417$$ 473.290 142.423i 1.13499 0.341543i
$$418$$ 0 0
$$419$$ 676.873i 1.61545i −0.589561 0.807724i $$-0.700699\pi$$
0.589561 0.807724i $$-0.299301\pi$$
$$420$$ 0 0
$$421$$ 683.755 1.62412 0.812061 0.583572i $$-0.198346\pi$$
0.812061 + 0.583572i $$0.198346\pi$$
$$422$$ 0 0
$$423$$ −111.992 169.232i −0.264757 0.400075i
$$424$$ 0 0
$$425$$ 60.5388i 0.142444i
$$426$$ 0 0
$$427$$ 522.332 1.22326
$$428$$ 0 0
$$429$$ −409.740 1361.62i −0.955105 3.17393i
$$430$$ 0 0
$$431$$ 213.608i 0.495610i −0.968810 0.247805i $$-0.920291\pi$$
0.968810 0.247805i $$-0.0797092\pi$$
$$432$$ 0 0
$$433$$ −383.579 −0.885864 −0.442932 0.896555i $$-0.646062\pi$$
−0.442932 + 0.896555i $$0.646062\pi$$
$$434$$ 0 0
$$435$$ 77.3175 23.2665i 0.177741 0.0534863i
$$436$$ 0 0
$$437$$ 86.7941i 0.198614i
$$438$$ 0 0
$$439$$ −523.900 −1.19340 −0.596698 0.802466i $$-0.703521\pi$$
−0.596698 + 0.802466i $$0.703521\pi$$
$$440$$ 0 0
$$441$$ 243.440 161.101i 0.552018 0.365309i
$$442$$ 0 0
$$443$$ 391.277i 0.883243i 0.897201 + 0.441622i $$0.145597\pi$$
−0.897201 + 0.441622i $$0.854403\pi$$
$$444$$ 0 0
$$445$$ −61.6819 −0.138611
$$446$$ 0 0
$$447$$ −227.301 755.347i −0.508502 1.68981i
$$448$$ 0 0
$$449$$ 375.014i 0.835220i −0.908626 0.417610i $$-0.862868\pi$$
0.908626 0.417610i $$-0.137132\pi$$
$$450$$ 0 0
$$451$$ 778.347 1.72582
$$452$$ 0 0
$$453$$ −45.4386 + 13.6735i −0.100306 + 0.0301843i
$$454$$ 0 0
$$455$$ 437.066i 0.960585i
$$456$$ 0 0
$$457$$ −734.032 −1.60620 −0.803098 0.595847i $$-0.796817\pi$$
−0.803098 + 0.595847i $$0.796817\pi$$
$$458$$ 0 0
$$459$$ −251.317 209.069i −0.547531 0.455488i
$$460$$ 0 0
$$461$$ 775.239i 1.68165i 0.541310 + 0.840823i $$0.317928\pi$$
−0.541310 + 0.840823i $$0.682072\pi$$
$$462$$ 0 0
$$463$$ 323.967 0.699714 0.349857 0.936803i $$-0.386230\pi$$
0.349857 + 0.936803i $$0.386230\pi$$
$$464$$ 0 0
$$465$$ 4.23496 + 14.0733i 0.00910743 + 0.0302651i
$$466$$ 0 0
$$467$$ 160.785i 0.344294i −0.985071 0.172147i $$-0.944930\pi$$
0.985071 0.172147i $$-0.0550704\pi$$
$$468$$ 0 0
$$469$$ −569.027 −1.21328
$$470$$ 0 0
$$471$$ −17.5795 + 5.29007i −0.0373239 + 0.0112316i
$$472$$ 0 0
$$473$$ 278.243i 0.588252i
$$474$$ 0 0
$$475$$ 15.1879 0.0319744
$$476$$ 0 0
$$477$$ 45.3856 + 68.5822i 0.0951481 + 0.143778i
$$478$$ 0 0
$$479$$ 61.7565i 0.128928i −0.997920 0.0644640i $$-0.979466\pi$$
0.997920 0.0644640i $$-0.0205338\pi$$
$$480$$ 0 0
$$481$$ 18.1934 0.0378241
$$482$$ 0 0
$$483$$ −222.906 740.744i −0.461504 1.53363i
$$484$$ 0 0
$$485$$ 257.123i 0.530151i
$$486$$ 0 0
$$487$$ −129.969 −0.266876 −0.133438 0.991057i $$-0.542602\pi$$
−0.133438 + 0.991057i $$0.542602\pi$$
$$488$$ 0 0
$$489$$ 489.642 147.344i 1.00131 0.301317i
$$490$$ 0 0
$$491$$ 810.511i 1.65074i 0.564595 + 0.825368i $$0.309032\pi$$
−0.564595 + 0.825368i $$0.690968\pi$$
$$492$$ 0 0
$$493$$ 145.733 0.295605
$$494$$ 0 0
$$495$$ −367.247 + 243.033i −0.741914 + 0.490976i
$$496$$ 0 0
$$497$$ 153.607i 0.309069i
$$498$$ 0 0
$$499$$ 600.897 1.20420 0.602101 0.798420i $$-0.294330\pi$$
0.602101 + 0.798420i $$0.294330\pi$$
$$500$$ 0 0
$$501$$ 52.9635 + 176.004i 0.105716 + 0.351306i
$$502$$ 0 0
$$503$$ 688.332i 1.36845i 0.729270 + 0.684226i $$0.239860\pi$$
−0.729270 + 0.684226i $$0.760140\pi$$
$$504$$ 0 0
$$505$$ 274.598 0.543759
$$506$$ 0 0
$$507$$ 862.254 259.471i 1.70070 0.511777i
$$508$$ 0 0
$$509$$ 823.791i 1.61845i 0.587498 + 0.809225i $$0.300113\pi$$
−0.587498 + 0.809225i $$0.699887\pi$$
$$510$$ 0 0
$$511$$ −470.322 −0.920395
$$512$$ 0 0
$$513$$ −52.4508 + 63.0498i −0.102243 + 0.122904i
$$514$$ 0 0
$$515$$ 104.710i 0.203320i
$$516$$ 0 0
$$517$$ −493.413 −0.954377
$$518$$ 0 0
$$519$$ 226.966 + 754.235i 0.437314 + 1.45325i
$$520$$ 0 0
$$521$$ 964.525i 1.85130i −0.378386 0.925648i $$-0.623521\pi$$
0.378386 0.925648i $$-0.376479\pi$$
$$522$$ 0 0
$$523$$ −462.679 −0.884664 −0.442332 0.896851i $$-0.645849\pi$$
−0.442332 + 0.896851i $$0.645849\pi$$
$$524$$ 0 0
$$525$$ 129.621 39.0057i 0.246897 0.0742966i
$$526$$ 0 0
$$527$$ 26.5263i 0.0503345i
$$528$$ 0 0
$$529$$ −287.447 −0.543378
$$530$$ 0 0
$$531$$ 399.561 + 603.777i 0.752469 + 1.13706i
$$532$$ 0 0
$$533$$ 770.420i 1.44544i
$$534$$ 0 0
$$535$$ 234.980 0.439214
$$536$$ 0 0
$$537$$ 5.95408 + 19.7861i 0.0110877 + 0.0368457i
$$538$$ 0 0
$$539$$ 709.775i 1.31684i
$$540$$ 0 0
$$541$$ −516.752 −0.955180 −0.477590 0.878583i $$-0.658490\pi$$
−0.477590 + 0.878583i $$0.658490\pi$$
$$542$$ 0 0
$$543$$ 627.800 188.919i 1.15617 0.347917i
$$544$$ 0 0
$$545$$ 261.120i 0.479120i
$$546$$ 0 0
$$547$$ −478.953 −0.875599 −0.437799 0.899073i $$-0.644242\pi$$
−0.437799 + 0.899073i $$0.644242\pi$$
$$548$$ 0 0
$$549$$ −434.423 + 287.488i −0.791298 + 0.523657i
$$550$$ 0 0
$$551$$ 36.5613i 0.0663544i
$$552$$ 0 0
$$553$$ −67.3404 −0.121773
$$554$$ 0 0
$$555$$ −1.62366 5.39561i −0.00292551 0.00972182i
$$556$$ 0 0
$$557$$ 343.982i 0.617561i 0.951133 + 0.308781i $$0.0999209\pi$$
−0.951133 + 0.308781i $$0.900079\pi$$
$$558$$ 0 0
$$559$$ 275.409 0.492682
$$560$$ 0 0
$$561$$ −761.137 + 229.043i −1.35675 + 0.408276i
$$562$$ 0 0
$$563$$ 394.056i 0.699922i 0.936764 + 0.349961i $$0.113805\pi$$
−0.936764 + 0.349961i $$0.886195\pi$$
$$564$$ 0 0
$$565$$ 24.1755 0.0427885
$$566$$ 0 0
$$567$$ −285.716 + 672.803i −0.503908 + 1.18660i
$$568$$ 0 0
$$569$$ 537.452i 0.944556i 0.881450 + 0.472278i $$0.156568\pi$$
−0.881450 + 0.472278i $$0.843432\pi$$
$$570$$ 0 0
$$571$$ −710.555 −1.24440 −0.622202 0.782856i $$-0.713762\pi$$
−0.622202 + 0.782856i $$0.713762\pi$$
$$572$$ 0 0
$$573$$ −65.0521 216.176i −0.113529 0.377271i
$$574$$ 0 0
$$575$$ 142.868i 0.248466i
$$576$$ 0 0
$$577$$ 452.846 0.784828 0.392414 0.919789i $$-0.371640\pi$$
0.392414 + 0.919789i $$0.371640\pi$$
$$578$$ 0 0
$$579$$ −610.709 + 183.776i −1.05477 + 0.317402i
$$580$$ 0 0
$$581$$ 743.372i 1.27947i
$$582$$ 0 0
$$583$$ 199.959 0.342983
$$584$$ 0 0
$$585$$ −240.558 363.507i −0.411210 0.621379i
$$586$$ 0 0
$$587$$ 1103.34i 1.87963i 0.341690 + 0.939813i $$0.389001\pi$$
−0.341690 + 0.939813i $$0.610999\pi$$
$$588$$ 0 0
$$589$$ 6.65486 0.0112986
$$590$$ 0 0
$$591$$ −164.804 547.662i −0.278855 0.926670i
$$592$$ 0 0
$$593$$ 249.474i 0.420698i −0.977626 0.210349i $$-0.932540\pi$$
0.977626 0.210349i $$-0.0674601\pi$$
$$594$$ 0 0
$$595$$ 244.318 0.410619
$$596$$ 0 0
$$597$$ −603.267 + 181.536i −1.01050 + 0.304081i
$$598$$ 0 0
$$599$$ 596.120i 0.995191i 0.867409 + 0.497596i $$0.165784\pi$$
−0.867409 + 0.497596i $$0.834216\pi$$
$$600$$ 0 0
$$601$$ 476.515 0.792871 0.396435 0.918063i $$-0.370247\pi$$
0.396435 + 0.918063i $$0.370247\pi$$
$$602$$ 0 0
$$603$$ 473.259 313.188i 0.784841 0.519384i
$$604$$ 0 0
$$605$$ 800.185i 1.32262i
$$606$$ 0 0
$$607$$ −27.8813 −0.0459329 −0.0229664 0.999736i $$-0.507311\pi$$
−0.0229664 + 0.999736i $$0.507311\pi$$
$$608$$ 0 0
$$609$$ −93.8973 312.032i −0.154183 0.512368i
$$610$$ 0 0
$$611$$ 488.388i 0.799325i
$$612$$ 0 0
$$613$$ 465.472 0.759334 0.379667 0.925123i $$-0.376039\pi$$
0.379667 + 0.925123i $$0.376039\pi$$
$$614$$ 0 0
$$615$$ 228.483 68.7557i 0.371518 0.111798i
$$616$$ 0 0
$$617$$ 48.6709i 0.0788832i 0.999222 + 0.0394416i $$0.0125579\pi$$
−0.999222 + 0.0394416i $$0.987442\pi$$
$$618$$ 0 0
$$619$$ 213.318 0.344617 0.172309 0.985043i $$-0.444877\pi$$
0.172309 + 0.985043i $$0.444877\pi$$
$$620$$ 0 0
$$621$$ 593.091 + 493.389i 0.955058 + 0.794508i
$$622$$ 0 0
$$623$$ 248.931i 0.399569i
$$624$$ 0 0
$$625$$ 25.0000 0.0400000
$$626$$ 0 0
$$627$$ 57.4618 + 190.953i 0.0916456 + 0.304549i
$$628$$ 0 0
$$629$$ 10.1700i 0.0161686i
$$630$$ 0 0
$$631$$ −582.489 −0.923121 −0.461560 0.887109i $$-0.652710\pi$$
−0.461560 + 0.887109i $$0.652710\pi$$
$$632$$ 0 0
$$633$$ −506.808 + 152.510i −0.800644 + 0.240931i
$$634$$ 0 0
$$635$$ 430.352i 0.677720i
$$636$$ 0 0
$$637$$ 702.546 1.10290
$$638$$ 0 0
$$639$$ −84.5442 127.755i −0.132307 0.199929i
$$640$$ 0 0
$$641$$ 319.635i 0.498650i −0.968420 0.249325i $$-0.919791\pi$$
0.968420 0.249325i $$-0.0802088\pi$$
$$642$$ 0 0
$$643$$ −458.627 −0.713261 −0.356630 0.934246i $$-0.616074\pi$$
−0.356630 + 0.934246i $$0.616074\pi$$
$$644$$ 0 0
$$645$$ −24.5787 81.6781i −0.0381066 0.126633i
$$646$$ 0 0
$$647$$ 507.599i 0.784543i −0.919850 0.392271i $$-0.871689\pi$$
0.919850 0.392271i $$-0.128311\pi$$
$$648$$ 0 0
$$649$$ 1760.38 2.71244
$$650$$ 0 0
$$651$$ 56.7959 17.0911i 0.0872440 0.0262536i
$$652$$ 0 0
$$653$$ 1197.20i 1.83339i 0.399591 + 0.916694i $$0.369152\pi$$
−0.399591 + 0.916694i $$0.630848\pi$$
$$654$$ 0 0
$$655$$ −108.753 −0.166036
$$656$$ 0 0
$$657$$ 391.166 258.862i 0.595382 0.394006i
$$658$$ 0 0
$$659$$ 632.173i 0.959291i 0.877462 + 0.479645i $$0.159235\pi$$
−0.877462 + 0.479645i $$0.840765\pi$$
$$660$$ 0 0
$$661$$ −565.316 −0.855243 −0.427622 0.903958i $$-0.640648\pi$$
−0.427622 + 0.903958i $$0.640648\pi$$
$$662$$ 0 0
$$663$$ −226.710 753.385i −0.341946 1.13633i
$$664$$ 0 0
$$665$$ 61.2940i 0.0921715i
$$666$$ 0 0
$$667$$ −343.921 −0.515624
$$668$$ 0 0
$$669$$ −380.243 + 114.423i −0.568375 + 0.171036i
$$670$$ 0 0
$$671$$ 1266.61i 1.88764i
$$672$$ 0 0
$$673$$ −306.607 −0.455582 −0.227791 0.973710i $$-0.573150\pi$$
−0.227791 + 0.973710i $$0.573150\pi$$
$$674$$ 0 0
$$675$$ −86.3368 + 103.783i −0.127906 + 0.153753i
$$676$$ 0 0
$$677$$ 546.672i 0.807491i −0.914871 0.403746i $$-0.867708\pi$$
0.914871 0.403746i $$-0.132292\pi$$
$$678$$ 0 0
$$679$$ −1037.68 −1.52824
$$680$$ 0 0
$$681$$ −162.196 538.996i −0.238173 0.791478i
$$682$$ 0 0
$$683$$ 812.204i 1.18917i −0.804032 0.594586i $$-0.797316\pi$$
0.804032 0.594586i $$-0.202684\pi$$
$$684$$ 0 0
$$685$$ −353.005 −0.515335
$$686$$ 0 0
$$687$$ −512.991 + 154.370i −0.746712 + 0.224702i
$$688$$ 0 0
$$689$$ 197.922i 0.287260i
$$690$$ 0 0
$$691$$ 45.9358 0.0664773 0.0332387 0.999447i $$-0.489418\pi$$
0.0332387 + 0.999447i $$0.489418\pi$$
$$692$$ 0 0
$$693$$ 980.815 + 1482.11i 1.41532 + 2.13869i
$$694$$ 0 0
$$695$$ 368.396i 0.530066i
$$696$$ 0 0
$$697$$ 430.661 0.617879
$$698$$ 0 0
$$699$$ 256.498 + 852.375i 0.366950 + 1.21942i
$$700$$ 0 0
$$701$$ 674.615i 0.962360i 0.876622 + 0.481180i $$0.159792\pi$$
−0.876622 + 0.481180i $$0.840208\pi$$
$$702$$ 0 0
$$703$$ −2.55143 −0.00362935
$$704$$ 0 0
$$705$$ −144.841 + 43.5859i −0.205448 + 0.0618240i
$$706$$ 0 0
$$707$$ 1108.20i 1.56747i
$$708$$ 0 0
$$709$$ 656.626 0.926129 0.463065 0.886324i $$-0.346750\pi$$
0.463065 + 0.886324i $$0.346750\pi$$
$$710$$ 0 0
$$711$$ 56.0069 37.0637i 0.0787720 0.0521290i
$$712$$ 0 0
$$713$$ 62.6003i 0.0877984i
$$714$$ 0 0
$$715$$ −1059.84 −1.48230
$$716$$ 0 0
$$717$$ −119.277 396.371i −0.166355 0.552819i
$$718$$ 0 0
$$719$$ 644.279i 0.896076i −0.894014 0.448038i $$-0.852123\pi$$
0.894014 0.448038i $$-0.147877\pi$$
$$720$$ 0 0
$$721$$ −422.579 −0.586101
$$722$$ 0 0
$$723$$ 122.289 36.7995i 0.169141 0.0508983i
$$724$$ 0 0
$$725$$ 60.1818i 0.0830094i
$$726$$ 0 0
$$727$$ 981.269 1.34975 0.674875 0.737932i $$-0.264197\pi$$
0.674875 + 0.737932i $$0.264197\pi$$
$$728$$ 0 0
$$729$$ −132.677 716.825i −0.181998 0.983299i
$$730$$ 0 0
$$731$$ 153.953i 0.210605i
$$732$$ 0 0
$$733$$ −127.756 −0.174292 −0.0871460 0.996196i $$-0.527775\pi$$
−0.0871460 + 0.996196i $$0.527775\pi$$
$$734$$ 0 0
$$735$$ −62.6983 208.354i −0.0853039 0.283475i
$$736$$ 0 0
$$737$$ 1379.84i 1.87223i
$$738$$ 0 0
$$739$$ 1401.59 1.89660 0.948302 0.317368i $$-0.102799\pi$$
0.948302 + 0.317368i $$0.102799\pi$$
$$740$$ 0 0
$$741$$ −189.008 + 56.8766i −0.255071 + 0.0767565i
$$742$$ 0 0
$$743$$ 11.6734i 0.0157112i −0.999969 0.00785561i $$-0.997499\pi$$
0.999969 0.00785561i $$-0.00250055\pi$$
$$744$$ 0 0
$$745$$ −587.941 −0.789183
$$746$$ 0 0
$$747$$ 409.147 + 618.261i 0.547720 + 0.827659i
$$748$$ 0 0
$$749$$ 948.313i 1.26611i
$$750$$ 0 0
$$751$$ −380.403 −0.506529 −0.253264 0.967397i $$-0.581504\pi$$
−0.253264 + 0.967397i $$0.581504\pi$$
$$752$$ 0 0
$$753$$ 177.982 + 591.456i 0.236364 + 0.785466i
$$754$$ 0 0
$$755$$ 35.3681i 0.0468452i
$$756$$ 0 0
$$757$$ 63.6621 0.0840979 0.0420490 0.999116i $$-0.486611\pi$$
0.0420490 + 0.999116i $$0.486611\pi$$
$$758$$ 0 0
$$759$$ 1796.23 540.526i 2.36658 0.712156i
$$760$$ 0 0
$$761$$ 377.891i 0.496571i −0.968687 0.248286i $$-0.920133\pi$$
0.968687 0.248286i $$-0.0798671\pi$$
$$762$$ 0 0
$$763$$ 1053.81 1.38114
$$764$$ 0 0
$$765$$ −203.199 + 134.471i −0.265619 + 0.175779i
$$766$$ 0 0
$$767$$ 1742.45i 2.27177i
$$768$$ 0 0
$$769$$ 231.920 0.301586 0.150793 0.988565i $$-0.451817\pi$$
0.150793 + 0.988565i $$0.451817\pi$$
$$770$$ 0 0
$$771$$ 162.851 + 541.174i 0.211221 + 0.701912i
$$772$$ 0 0
$$773$$ 1509.05i 1.95220i −0.217320 0.976101i $$-0.569731\pi$$
0.217320 0.976101i $$-0.430269\pi$$
$$774$$ 0 0
$$775$$ 10.9542 0.0141345
$$776$$ 0 0
$$777$$ −21.7752 + 6.55264i −0.0280247 + 0.00843326i
$$778$$ 0 0
$$779$$ 108.043i 0.138695i
$$780$$ 0 0
$$781$$ −372.483 −0.476930
$$782$$ 0 0
$$783$$ 249.834 + 207.836i 0.319073 + 0.265436i
$$784$$ 0 0
$$785$$ 13.6834i 0.0174311i
$$786$$ 0 0
$$787$$ −1171.43 −1.48848 −0.744240 0.667912i $$-0.767188\pi$$
−0.744240 + 0.667912i $$0.767188\pi$$
$$788$$ 0 0
$$789$$ 163.165 + 542.216i 0.206799 + 0.687219i
$$790$$ 0 0
$$791$$ 97.5656i 0.123345i
$$792$$ 0 0
$$793$$ −1253.71 −1.58097
$$794$$ 0 0
$$795$$ 58.6978 17.6635i 0.0738337 0.0222182i
$$796$$ 0 0
$$797$$ 988.589i 1.24039i 0.784448 + 0.620194i $$0.212946\pi$$
−0.784448 + 0.620194i $$0.787054\pi$$
$$798$$ 0 0
$$799$$ −273.007 −0.341685