# Properties

 Label 1260.2.c.d.811.7 Level $1260$ Weight $2$ Character 1260.811 Analytic conductor $10.061$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1260.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.0611506547$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: no (minimal twist has level 420) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 811.7 Root $$0.309204 - 1.38000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1260.811 Dual form 1260.2.c.d.811.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.309204 - 1.38000i) q^{2} +(-1.80879 + 0.853401i) q^{4} +1.00000i q^{5} +(-2.64459 + 0.0785232i) q^{7} +(1.73698 + 2.23224i) q^{8} +O(q^{10})$$ $$q+(-0.309204 - 1.38000i) q^{2} +(-1.80879 + 0.853401i) q^{4} +1.00000i q^{5} +(-2.64459 + 0.0785232i) q^{7} +(1.73698 + 2.23224i) q^{8} +(1.38000 - 0.309204i) q^{10} -0.987080i q^{11} -4.69157i q^{13} +(0.926078 + 3.62524i) q^{14} +(2.54341 - 3.08724i) q^{16} +3.93531i q^{17} +0.223896 q^{19} +(-0.853401 - 1.80879i) q^{20} +(-1.36217 + 0.305209i) q^{22} +5.88128i q^{23} -1.00000 q^{25} +(-6.47436 + 1.45065i) q^{26} +(4.71648 - 2.39892i) q^{28} +10.2502 q^{29} -2.77439 q^{31} +(-5.04682 - 2.55532i) q^{32} +(5.43072 - 1.21681i) q^{34} +(-0.0785232 - 2.64459i) q^{35} +8.26915 q^{37} +(-0.0692296 - 0.308976i) q^{38} +(-2.23224 + 1.73698i) q^{40} -7.34910i q^{41} -4.32318i q^{43} +(0.842376 + 1.78542i) q^{44} +(8.11616 - 1.81852i) q^{46} +2.40779 q^{47} +(6.98767 - 0.415323i) q^{49} +(0.309204 + 1.38000i) q^{50} +(4.00380 + 8.48605i) q^{52} +8.35002 q^{53} +0.987080 q^{55} +(-4.76886 - 5.76697i) q^{56} +(-3.16941 - 14.1453i) q^{58} +13.9829 q^{59} -4.93374i q^{61} +(0.857851 + 3.82865i) q^{62} +(-1.96583 + 7.75471i) q^{64} +4.69157 q^{65} -7.84723i q^{67} +(-3.35840 - 7.11814i) q^{68} +(-3.62524 + 0.926078i) q^{70} -8.49881i q^{71} +14.4665i q^{73} +(-2.55685 - 11.4114i) q^{74} +(-0.404980 + 0.191073i) q^{76} +(0.0775087 + 2.61042i) q^{77} -11.5183i q^{79} +(3.08724 + 2.54341i) q^{80} +(-10.1417 + 2.27237i) q^{82} -1.67114 q^{83} -3.93531 q^{85} +(-5.96597 + 1.33674i) q^{86} +(2.20340 - 1.71453i) q^{88} +0.493375i q^{89} +(0.368398 + 12.4073i) q^{91} +(-5.01910 - 10.6380i) q^{92} +(-0.744498 - 3.32274i) q^{94} +0.223896i q^{95} +4.31036i q^{97} +(-2.73376 - 9.51454i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + O(q^{10})$$ $$16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + 2 q^{14} + 6 q^{16} - 24 q^{19} - 12 q^{22} - 16 q^{25} + 12 q^{26} + 14 q^{28} - 16 q^{29} + 8 q^{31} + 18 q^{32} + 24 q^{34} + 24 q^{37} - 28 q^{38} + 12 q^{40} + 8 q^{44} - 20 q^{46} - 16 q^{47} - 16 q^{49} + 2 q^{50} - 20 q^{52} + 32 q^{53} - 2 q^{56} - 32 q^{58} - 8 q^{59} - 16 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} + 4 q^{74} + 16 q^{76} + 8 q^{77} + 16 q^{80} - 4 q^{82} - 8 q^{83} - 64 q^{86} - 52 q^{88} + 16 q^{91} - 64 q^{92} + 16 q^{94} + 86 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$$.

 $$n$$ $$281$$ $$631$$ $$757$$ $$1081$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.309204 1.38000i −0.218640 0.975806i
$$3$$ 0 0
$$4$$ −1.80879 + 0.853401i −0.904393 + 0.426701i
$$5$$ 1.00000i 0.447214i
$$6$$ 0 0
$$7$$ −2.64459 + 0.0785232i −0.999559 + 0.0296790i
$$8$$ 1.73698 + 2.23224i 0.614114 + 0.789218i
$$9$$ 0 0
$$10$$ 1.38000 0.309204i 0.436394 0.0977789i
$$11$$ 0.987080i 0.297616i −0.988866 0.148808i $$-0.952456\pi$$
0.988866 0.148808i $$-0.0475436\pi$$
$$12$$ 0 0
$$13$$ 4.69157i 1.30121i −0.759417 0.650604i $$-0.774516\pi$$
0.759417 0.650604i $$-0.225484\pi$$
$$14$$ 0.926078 + 3.62524i 0.247505 + 0.968887i
$$15$$ 0 0
$$16$$ 2.54341 3.08724i 0.635853 0.771810i
$$17$$ 3.93531i 0.954453i 0.878780 + 0.477227i $$0.158358\pi$$
−0.878780 + 0.477227i $$0.841642\pi$$
$$18$$ 0 0
$$19$$ 0.223896 0.0513653 0.0256826 0.999670i $$-0.491824\pi$$
0.0256826 + 0.999670i $$0.491824\pi$$
$$20$$ −0.853401 1.80879i −0.190826 0.404457i
$$21$$ 0 0
$$22$$ −1.36217 + 0.305209i −0.290415 + 0.0650708i
$$23$$ 5.88128i 1.22633i 0.789954 + 0.613166i $$0.210104\pi$$
−0.789954 + 0.613166i $$0.789896\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ −6.47436 + 1.45065i −1.26973 + 0.284497i
$$27$$ 0 0
$$28$$ 4.71648 2.39892i 0.891330 0.453354i
$$29$$ 10.2502 1.90342 0.951710 0.307000i $$-0.0993252\pi$$
0.951710 + 0.307000i $$0.0993252\pi$$
$$30$$ 0 0
$$31$$ −2.77439 −0.498295 −0.249147 0.968466i $$-0.580150\pi$$
−0.249147 + 0.968466i $$0.580150\pi$$
$$32$$ −5.04682 2.55532i −0.892160 0.451720i
$$33$$ 0 0
$$34$$ 5.43072 1.21681i 0.931361 0.208682i
$$35$$ −0.0785232 2.64459i −0.0132728 0.447017i
$$36$$ 0 0
$$37$$ 8.26915 1.35944 0.679720 0.733472i $$-0.262101\pi$$
0.679720 + 0.733472i $$0.262101\pi$$
$$38$$ −0.0692296 0.308976i −0.0112305 0.0501225i
$$39$$ 0 0
$$40$$ −2.23224 + 1.73698i −0.352949 + 0.274640i
$$41$$ 7.34910i 1.14774i −0.818948 0.573868i $$-0.805442\pi$$
0.818948 0.573868i $$-0.194558\pi$$
$$42$$ 0 0
$$43$$ 4.32318i 0.659278i −0.944107 0.329639i $$-0.893073\pi$$
0.944107 0.329639i $$-0.106927\pi$$
$$44$$ 0.842376 + 1.78542i 0.126993 + 0.269162i
$$45$$ 0 0
$$46$$ 8.11616 1.81852i 1.19666 0.268126i
$$47$$ 2.40779 0.351212 0.175606 0.984461i $$-0.443812\pi$$
0.175606 + 0.984461i $$0.443812\pi$$
$$48$$ 0 0
$$49$$ 6.98767 0.415323i 0.998238 0.0593318i
$$50$$ 0.309204 + 1.38000i 0.0437280 + 0.195161i
$$51$$ 0 0
$$52$$ 4.00380 + 8.48605i 0.555227 + 1.17680i
$$53$$ 8.35002 1.14696 0.573482 0.819218i $$-0.305592\pi$$
0.573482 + 0.819218i $$0.305592\pi$$
$$54$$ 0 0
$$55$$ 0.987080 0.133098
$$56$$ −4.76886 5.76697i −0.637266 0.770644i
$$57$$ 0 0
$$58$$ −3.16941 14.1453i −0.416164 1.85737i
$$59$$ 13.9829 1.82042 0.910210 0.414147i $$-0.135920\pi$$
0.910210 + 0.414147i $$0.135920\pi$$
$$60$$ 0 0
$$61$$ 4.93374i 0.631700i −0.948809 0.315850i $$-0.897710\pi$$
0.948809 0.315850i $$-0.102290\pi$$
$$62$$ 0.857851 + 3.82865i 0.108947 + 0.486239i
$$63$$ 0 0
$$64$$ −1.96583 + 7.75471i −0.245729 + 0.969339i
$$65$$ 4.69157 0.581918
$$66$$ 0 0
$$67$$ 7.84723i 0.958692i −0.877626 0.479346i $$-0.840874\pi$$
0.877626 0.479346i $$-0.159126\pi$$
$$68$$ −3.35840 7.11814i −0.407266 0.863201i
$$69$$ 0 0
$$70$$ −3.62524 + 0.926078i −0.433299 + 0.110688i
$$71$$ 8.49881i 1.00862i −0.863522 0.504311i $$-0.831746\pi$$
0.863522 0.504311i $$-0.168254\pi$$
$$72$$ 0 0
$$73$$ 14.4665i 1.69318i 0.532244 + 0.846591i $$0.321349\pi$$
−0.532244 + 0.846591i $$0.678651\pi$$
$$74$$ −2.55685 11.4114i −0.297228 1.32655i
$$75$$ 0 0
$$76$$ −0.404980 + 0.191073i −0.0464544 + 0.0219176i
$$77$$ 0.0775087 + 2.61042i 0.00883294 + 0.297485i
$$78$$ 0 0
$$79$$ 11.5183i 1.29591i −0.761678 0.647956i $$-0.775624\pi$$
0.761678 0.647956i $$-0.224376\pi$$
$$80$$ 3.08724 + 2.54341i 0.345164 + 0.284362i
$$81$$ 0 0
$$82$$ −10.1417 + 2.27237i −1.11997 + 0.250941i
$$83$$ −1.67114 −0.183431 −0.0917156 0.995785i $$-0.529235\pi$$
−0.0917156 + 0.995785i $$0.529235\pi$$
$$84$$ 0 0
$$85$$ −3.93531 −0.426845
$$86$$ −5.96597 + 1.33674i −0.643327 + 0.144145i
$$87$$ 0 0
$$88$$ 2.20340 1.71453i 0.234884 0.182770i
$$89$$ 0.493375i 0.0522977i 0.999658 + 0.0261488i $$0.00832438\pi$$
−0.999658 + 0.0261488i $$0.991676\pi$$
$$90$$ 0 0
$$91$$ 0.368398 + 12.4073i 0.0386186 + 1.30064i
$$92$$ −5.01910 10.6380i −0.523277 1.10909i
$$93$$ 0 0
$$94$$ −0.744498 3.32274i −0.0767891 0.342715i
$$95$$ 0.223896i 0.0229713i
$$96$$ 0 0
$$97$$ 4.31036i 0.437650i 0.975764 + 0.218825i $$0.0702224\pi$$
−0.975764 + 0.218825i $$0.929778\pi$$
$$98$$ −2.73376 9.51454i −0.276151 0.961114i
$$99$$ 0 0
$$100$$ 1.80879 0.853401i 0.180879 0.0853401i
$$101$$ 6.03671i 0.600675i 0.953833 + 0.300338i $$0.0970994\pi$$
−0.953833 + 0.300338i $$0.902901\pi$$
$$102$$ 0 0
$$103$$ −7.83090 −0.771602 −0.385801 0.922582i $$-0.626075\pi$$
−0.385801 + 0.922582i $$0.626075\pi$$
$$104$$ 10.4727 8.14915i 1.02694 0.799090i
$$105$$ 0 0
$$106$$ −2.58186 11.5230i −0.250772 1.11921i
$$107$$ 13.9860i 1.35208i 0.736866 + 0.676039i $$0.236305\pi$$
−0.736866 + 0.676039i $$0.763695\pi$$
$$108$$ 0 0
$$109$$ 4.06579 0.389432 0.194716 0.980860i $$-0.437621\pi$$
0.194716 + 0.980860i $$0.437621\pi$$
$$110$$ −0.305209 1.36217i −0.0291005 0.129878i
$$111$$ 0 0
$$112$$ −6.48385 + 8.36419i −0.612666 + 0.790342i
$$113$$ 8.66412 0.815052 0.407526 0.913194i $$-0.366392\pi$$
0.407526 + 0.913194i $$0.366392\pi$$
$$114$$ 0 0
$$115$$ −5.88128 −0.548433
$$116$$ −18.5405 + 8.74756i −1.72144 + 0.812190i
$$117$$ 0 0
$$118$$ −4.32357 19.2964i −0.398017 1.77638i
$$119$$ −0.309013 10.4073i −0.0283272 0.954033i
$$120$$ 0 0
$$121$$ 10.0257 0.911425
$$122$$ −6.80855 + 1.52553i −0.616417 + 0.138115i
$$123$$ 0 0
$$124$$ 5.01827 2.36767i 0.450654 0.212623i
$$125$$ 1.00000i 0.0894427i
$$126$$ 0 0
$$127$$ 5.18615i 0.460197i −0.973167 0.230098i $$-0.926095\pi$$
0.973167 0.230098i $$-0.0739048\pi$$
$$128$$ 11.3093 + 0.315057i 0.999612 + 0.0278473i
$$129$$ 0 0
$$130$$ −1.45065 6.47436i −0.127231 0.567839i
$$131$$ −11.3617 −0.992679 −0.496340 0.868128i $$-0.665323\pi$$
−0.496340 + 0.868128i $$0.665323\pi$$
$$132$$ 0 0
$$133$$ −0.592112 + 0.0175810i −0.0513427 + 0.00152447i
$$134$$ −10.8292 + 2.42640i −0.935497 + 0.209609i
$$135$$ 0 0
$$136$$ −8.78458 + 6.83554i −0.753272 + 0.586143i
$$137$$ 5.85931 0.500595 0.250297 0.968169i $$-0.419472\pi$$
0.250297 + 0.968169i $$0.419472\pi$$
$$138$$ 0 0
$$139$$ 18.1460 1.53912 0.769562 0.638572i $$-0.220475\pi$$
0.769562 + 0.638572i $$0.220475\pi$$
$$140$$ 2.39892 + 4.71648i 0.202746 + 0.398615i
$$141$$ 0 0
$$142$$ −11.7283 + 2.62786i −0.984220 + 0.220525i
$$143$$ −4.63096 −0.387260
$$144$$ 0 0
$$145$$ 10.2502i 0.851235i
$$146$$ 19.9638 4.47311i 1.65222 0.370198i
$$147$$ 0 0
$$148$$ −14.9571 + 7.05690i −1.22947 + 0.580074i
$$149$$ −15.4737 −1.26766 −0.633829 0.773473i $$-0.718518\pi$$
−0.633829 + 0.773473i $$0.718518\pi$$
$$150$$ 0 0
$$151$$ 11.5322i 0.938474i 0.883072 + 0.469237i $$0.155471\pi$$
−0.883072 + 0.469237i $$0.844529\pi$$
$$152$$ 0.388902 + 0.499791i 0.0315441 + 0.0405384i
$$153$$ 0 0
$$154$$ 3.57840 0.914114i 0.288356 0.0736614i
$$155$$ 2.77439i 0.222844i
$$156$$ 0 0
$$157$$ 0.806743i 0.0643851i 0.999482 + 0.0321926i $$0.0102490\pi$$
−0.999482 + 0.0321926i $$0.989751\pi$$
$$158$$ −15.8952 + 3.56151i −1.26456 + 0.283338i
$$159$$ 0 0
$$160$$ 2.55532 5.04682i 0.202015 0.398986i
$$161$$ −0.461817 15.5536i −0.0363963 1.22579i
$$162$$ 0 0
$$163$$ 6.48272i 0.507766i 0.967235 + 0.253883i $$0.0817077\pi$$
−0.967235 + 0.253883i $$0.918292\pi$$
$$164$$ 6.27173 + 13.2929i 0.489740 + 1.03800i
$$165$$ 0 0
$$166$$ 0.516722 + 2.30616i 0.0401054 + 0.178993i
$$167$$ −7.65678 −0.592499 −0.296250 0.955111i $$-0.595736\pi$$
−0.296250 + 0.955111i $$0.595736\pi$$
$$168$$ 0 0
$$169$$ −9.01087 −0.693144
$$170$$ 1.21681 + 5.43072i 0.0933254 + 0.416517i
$$171$$ 0 0
$$172$$ 3.68941 + 7.81970i 0.281315 + 0.596247i
$$173$$ 7.12007i 0.541329i −0.962674 0.270665i $$-0.912757\pi$$
0.962674 0.270665i $$-0.0872434\pi$$
$$174$$ 0 0
$$175$$ 2.64459 0.0785232i 0.199912 0.00593580i
$$176$$ −3.04735 2.51055i −0.229703 0.189240i
$$177$$ 0 0
$$178$$ 0.680856 0.152554i 0.0510323 0.0114344i
$$179$$ 20.8439i 1.55794i 0.627059 + 0.778972i $$0.284258\pi$$
−0.627059 + 0.778972i $$0.715742\pi$$
$$180$$ 0 0
$$181$$ 24.4428i 1.81682i −0.418079 0.908411i $$-0.637297\pi$$
0.418079 0.908411i $$-0.362703\pi$$
$$182$$ 17.0081 4.34477i 1.26072 0.322055i
$$183$$ 0 0
$$184$$ −13.1285 + 10.2156i −0.967843 + 0.753107i
$$185$$ 8.26915i 0.607960i
$$186$$ 0 0
$$187$$ 3.88447 0.284061
$$188$$ −4.35517 + 2.05481i −0.317634 + 0.149862i
$$189$$ 0 0
$$190$$ 0.308976 0.0692296i 0.0224155 0.00502244i
$$191$$ 19.3047i 1.39684i −0.715689 0.698419i $$-0.753887\pi$$
0.715689 0.698419i $$-0.246113\pi$$
$$192$$ 0 0
$$193$$ −15.2505 −1.09776 −0.548879 0.835902i $$-0.684945\pi$$
−0.548879 + 0.835902i $$0.684945\pi$$
$$194$$ 5.94828 1.33278i 0.427062 0.0956880i
$$195$$ 0 0
$$196$$ −12.2848 + 6.71452i −0.877483 + 0.479608i
$$197$$ −3.00729 −0.214260 −0.107130 0.994245i $$-0.534166\pi$$
−0.107130 + 0.994245i $$0.534166\pi$$
$$198$$ 0 0
$$199$$ 22.1587 1.57079 0.785395 0.618995i $$-0.212460\pi$$
0.785395 + 0.618995i $$0.212460\pi$$
$$200$$ −1.73698 2.23224i −0.122823 0.157844i
$$201$$ 0 0
$$202$$ 8.33065 1.86658i 0.586142 0.131332i
$$203$$ −27.1076 + 0.804881i −1.90258 + 0.0564916i
$$204$$ 0 0
$$205$$ 7.34910 0.513283
$$206$$ 2.42135 + 10.8066i 0.168703 + 0.752933i
$$207$$ 0 0
$$208$$ −14.4840 11.9326i −1.00429 0.827377i
$$209$$ 0.221003i 0.0152871i
$$210$$ 0 0
$$211$$ 12.6769i 0.872714i 0.899774 + 0.436357i $$0.143731\pi$$
−0.899774 + 0.436357i $$0.856269\pi$$
$$212$$ −15.1034 + 7.12592i −1.03731 + 0.489410i
$$213$$ 0 0
$$214$$ 19.3006 4.32453i 1.31936 0.295618i
$$215$$ 4.32318 0.294838
$$216$$ 0 0
$$217$$ 7.33710 0.217854i 0.498075 0.0147889i
$$218$$ −1.25716 5.61078i −0.0851455 0.380010i
$$219$$ 0 0
$$220$$ −1.78542 + 0.842376i −0.120373 + 0.0567930i
$$221$$ 18.4628 1.24194
$$222$$ 0 0
$$223$$ 6.45632 0.432347 0.216173 0.976355i $$-0.430642\pi$$
0.216173 + 0.976355i $$0.430642\pi$$
$$224$$ 13.5474 + 6.36146i 0.905173 + 0.425043i
$$225$$ 0 0
$$226$$ −2.67898 11.9565i −0.178203 0.795332i
$$227$$ −14.0882 −0.935066 −0.467533 0.883976i $$-0.654857\pi$$
−0.467533 + 0.883976i $$0.654857\pi$$
$$228$$ 0 0
$$229$$ 9.74932i 0.644253i −0.946697 0.322126i $$-0.895602\pi$$
0.946697 0.322126i $$-0.104398\pi$$
$$230$$ 1.81852 + 8.11616i 0.119909 + 0.535164i
$$231$$ 0 0
$$232$$ 17.8044 + 22.8810i 1.16892 + 1.50221i
$$233$$ −1.64231 −0.107591 −0.0537955 0.998552i $$-0.517132\pi$$
−0.0537955 + 0.998552i $$0.517132\pi$$
$$234$$ 0 0
$$235$$ 2.40779i 0.157067i
$$236$$ −25.2921 + 11.9330i −1.64637 + 0.776774i
$$237$$ 0 0
$$238$$ −14.2665 + 3.64441i −0.924757 + 0.236232i
$$239$$ 9.77724i 0.632437i 0.948686 + 0.316219i $$0.102413\pi$$
−0.948686 + 0.316219i $$0.897587\pi$$
$$240$$ 0 0
$$241$$ 6.84106i 0.440671i −0.975424 0.220336i $$-0.929285\pi$$
0.975424 0.220336i $$-0.0707152\pi$$
$$242$$ −3.09998 13.8354i −0.199274 0.889373i
$$243$$ 0 0
$$244$$ 4.21046 + 8.92408i 0.269547 + 0.571305i
$$245$$ 0.415323 + 6.98767i 0.0265340 + 0.446426i
$$246$$ 0 0
$$247$$ 1.05043i 0.0668370i
$$248$$ −4.81904 6.19311i −0.306009 0.393263i
$$249$$ 0 0
$$250$$ −1.38000 + 0.309204i −0.0872787 + 0.0195558i
$$251$$ −2.34972 −0.148313 −0.0741564 0.997247i $$-0.523626\pi$$
−0.0741564 + 0.997247i $$0.523626\pi$$
$$252$$ 0 0
$$253$$ 5.80530 0.364976
$$254$$ −7.15688 + 1.60358i −0.449063 + 0.100618i
$$255$$ 0 0
$$256$$ −3.06211 15.7043i −0.191382 0.981516i
$$257$$ 6.47150i 0.403681i −0.979418 0.201840i $$-0.935308\pi$$
0.979418 0.201840i $$-0.0646922\pi$$
$$258$$ 0 0
$$259$$ −21.8685 + 0.649320i −1.35884 + 0.0403468i
$$260$$ −8.48605 + 4.00380i −0.526283 + 0.248305i
$$261$$ 0 0
$$262$$ 3.51309 + 15.6792i 0.217040 + 0.968662i
$$263$$ 2.38076i 0.146804i 0.997302 + 0.0734018i $$0.0233856\pi$$
−0.997302 + 0.0734018i $$0.976614\pi$$
$$264$$ 0 0
$$265$$ 8.35002i 0.512938i
$$266$$ 0.207345 + 0.811678i 0.0127132 + 0.0497671i
$$267$$ 0 0
$$268$$ 6.69684 + 14.1940i 0.409075 + 0.867034i
$$269$$ 9.44894i 0.576112i 0.957614 + 0.288056i $$0.0930089\pi$$
−0.957614 + 0.288056i $$0.906991\pi$$
$$270$$ 0 0
$$271$$ 22.1827 1.34750 0.673752 0.738958i $$-0.264682\pi$$
0.673752 + 0.738958i $$0.264682\pi$$
$$272$$ 12.1493 + 10.0091i 0.736657 + 0.606892i
$$273$$ 0 0
$$274$$ −1.81172 8.08583i −0.109450 0.488483i
$$275$$ 0.987080i 0.0595232i
$$276$$ 0 0
$$277$$ −26.7718 −1.60856 −0.804281 0.594249i $$-0.797449\pi$$
−0.804281 + 0.594249i $$0.797449\pi$$
$$278$$ −5.61082 25.0414i −0.336514 1.50189i
$$279$$ 0 0
$$280$$ 5.76697 4.76886i 0.344642 0.284994i
$$281$$ 8.64183 0.515529 0.257764 0.966208i $$-0.417014\pi$$
0.257764 + 0.966208i $$0.417014\pi$$
$$282$$ 0 0
$$283$$ −5.92047 −0.351935 −0.175968 0.984396i $$-0.556305\pi$$
−0.175968 + 0.984396i $$0.556305\pi$$
$$284$$ 7.25289 + 15.3725i 0.430380 + 0.912191i
$$285$$ 0 0
$$286$$ 1.43191 + 6.39071i 0.0846707 + 0.377891i
$$287$$ 0.577075 + 19.4353i 0.0340637 + 1.14723i
$$288$$ 0 0
$$289$$ 1.51332 0.0890186
$$290$$ 14.1453 3.16941i 0.830640 0.186114i
$$291$$ 0 0
$$292$$ −12.3458 26.1669i −0.722482 1.53130i
$$293$$ 26.2654i 1.53444i 0.641382 + 0.767221i $$0.278361\pi$$
−0.641382 + 0.767221i $$0.721639\pi$$
$$294$$ 0 0
$$295$$ 13.9829i 0.814116i
$$296$$ 14.3633 + 18.4588i 0.834850 + 1.07289i
$$297$$ 0 0
$$298$$ 4.78454 + 21.3537i 0.277161 + 1.23699i
$$299$$ 27.5925 1.59571
$$300$$ 0 0
$$301$$ 0.339470 + 11.4330i 0.0195667 + 0.658988i
$$302$$ 15.9144 3.56579i 0.915768 0.205188i
$$303$$ 0 0
$$304$$ 0.569460 0.691221i 0.0326608 0.0396443i
$$305$$ 4.93374 0.282505
$$306$$ 0 0
$$307$$ −18.5432 −1.05832 −0.529158 0.848524i $$-0.677492\pi$$
−0.529158 + 0.848524i $$0.677492\pi$$
$$308$$ −2.36793 4.65554i −0.134925 0.265274i
$$309$$ 0 0
$$310$$ −3.82865 + 0.857851i −0.217453 + 0.0487227i
$$311$$ 30.8370 1.74861 0.874304 0.485379i $$-0.161318\pi$$
0.874304 + 0.485379i $$0.161318\pi$$
$$312$$ 0 0
$$313$$ 20.8250i 1.17710i 0.808461 + 0.588550i $$0.200301\pi$$
−0.808461 + 0.588550i $$0.799699\pi$$
$$314$$ 1.11330 0.249448i 0.0628274 0.0140772i
$$315$$ 0 0
$$316$$ 9.82975 + 20.8342i 0.552967 + 1.17201i
$$317$$ −5.41152 −0.303941 −0.151971 0.988385i $$-0.548562\pi$$
−0.151971 + 0.988385i $$0.548562\pi$$
$$318$$ 0 0
$$319$$ 10.1178i 0.566488i
$$320$$ −7.75471 1.96583i −0.433501 0.109893i
$$321$$ 0 0
$$322$$ −21.3211 + 5.44653i −1.18818 + 0.303523i
$$323$$ 0.881101i 0.0490258i
$$324$$ 0 0
$$325$$ 4.69157i 0.260242i
$$326$$ 8.94613 2.00448i 0.495480 0.111018i
$$327$$ 0 0
$$328$$ 16.4050 12.7652i 0.905814 0.704841i
$$329$$ −6.36760 + 0.189067i −0.351057 + 0.0104236i
$$330$$ 0 0
$$331$$ 1.77494i 0.0975597i −0.998810 0.0487799i $$-0.984467\pi$$
0.998810 0.0487799i $$-0.0155333\pi$$
$$332$$ 3.02273 1.42615i 0.165894 0.0782702i
$$333$$ 0 0
$$334$$ 2.36751 + 10.5663i 0.129544 + 0.578164i
$$335$$ 7.84723 0.428740
$$336$$ 0 0
$$337$$ 22.3668 1.21839 0.609197 0.793019i $$-0.291492\pi$$
0.609197 + 0.793019i $$0.291492\pi$$
$$338$$ 2.78620 + 12.4350i 0.151549 + 0.676374i
$$339$$ 0 0
$$340$$ 7.11814 3.35840i 0.386035 0.182135i
$$341$$ 2.73854i 0.148300i
$$342$$ 0 0
$$343$$ −18.4469 + 1.64705i −0.996038 + 0.0889324i
$$344$$ 9.65039 7.50925i 0.520314 0.404872i
$$345$$ 0 0
$$346$$ −9.82569 + 2.20156i −0.528232 + 0.118356i
$$347$$ 0.606084i 0.0325363i −0.999868 0.0162681i $$-0.994821\pi$$
0.999868 0.0162681i $$-0.00517854\pi$$
$$348$$ 0 0
$$349$$ 31.6682i 1.69516i −0.530668 0.847580i $$-0.678059\pi$$
0.530668 0.847580i $$-0.321941\pi$$
$$350$$ −0.926078 3.62524i −0.0495010 0.193777i
$$351$$ 0 0
$$352$$ −2.52230 + 4.98161i −0.134439 + 0.265521i
$$353$$ 4.06901i 0.216572i −0.994120 0.108286i $$-0.965464\pi$$
0.994120 0.108286i $$-0.0345362\pi$$
$$354$$ 0 0
$$355$$ 8.49881 0.451070
$$356$$ −0.421047 0.892410i −0.0223154 0.0472976i
$$357$$ 0 0
$$358$$ 28.7645 6.44500i 1.52025 0.340629i
$$359$$ 11.0427i 0.582809i 0.956600 + 0.291405i $$0.0941226\pi$$
−0.956600 + 0.291405i $$0.905877\pi$$
$$360$$ 0 0
$$361$$ −18.9499 −0.997362
$$362$$ −33.7310 + 7.55782i −1.77286 + 0.397230i
$$363$$ 0 0
$$364$$ −11.2547 22.1277i −0.589908 1.15981i
$$365$$ −14.4665 −0.757214
$$366$$ 0 0
$$367$$ 0.0725720 0.00378823 0.00189411 0.999998i $$-0.499397\pi$$
0.00189411 + 0.999998i $$0.499397\pi$$
$$368$$ 18.1569 + 14.9585i 0.946496 + 0.779767i
$$369$$ 0 0
$$370$$ 11.4114 2.55685i 0.593251 0.132924i
$$371$$ −22.0824 + 0.655671i −1.14646 + 0.0340407i
$$372$$ 0 0
$$373$$ 22.4132 1.16051 0.580257 0.814433i $$-0.302952\pi$$
0.580257 + 0.814433i $$0.302952\pi$$
$$374$$ −1.20109 5.36056i −0.0621071 0.277188i
$$375$$ 0 0
$$376$$ 4.18227 + 5.37477i 0.215684 + 0.277183i
$$377$$ 48.0897i 2.47675i
$$378$$ 0 0
$$379$$ 26.9969i 1.38674i 0.720584 + 0.693368i $$0.243874\pi$$
−0.720584 + 0.693368i $$0.756126\pi$$
$$380$$ −0.191073 0.404980i −0.00980185 0.0207750i
$$381$$ 0 0
$$382$$ −26.6404 + 5.96909i −1.36304 + 0.305405i
$$383$$ 19.7866 1.01105 0.505523 0.862813i $$-0.331299\pi$$
0.505523 + 0.862813i $$0.331299\pi$$
$$384$$ 0 0
$$385$$ −2.61042 + 0.0775087i −0.133039 + 0.00395021i
$$386$$ 4.71553 + 21.0457i 0.240014 + 1.07120i
$$387$$ 0 0
$$388$$ −3.67846 7.79651i −0.186746 0.395808i
$$389$$ 29.6119 1.50138 0.750690 0.660654i $$-0.229721\pi$$
0.750690 + 0.660654i $$0.229721\pi$$
$$390$$ 0 0
$$391$$ −23.1447 −1.17048
$$392$$ 13.0645 + 14.8768i 0.659857 + 0.751391i
$$393$$ 0 0
$$394$$ 0.929865 + 4.15005i 0.0468459 + 0.209076i
$$395$$ 11.5183 0.579549
$$396$$ 0 0
$$397$$ 21.2555i 1.06678i −0.845868 0.533392i $$-0.820917\pi$$
0.845868 0.533392i $$-0.179083\pi$$
$$398$$ −6.85156 30.5790i −0.343438 1.53279i
$$399$$ 0 0
$$400$$ −2.54341 + 3.08724i −0.127171 + 0.154362i
$$401$$ −24.5750 −1.22722 −0.613608 0.789610i $$-0.710283\pi$$
−0.613608 + 0.789610i $$0.710283\pi$$
$$402$$ 0 0
$$403$$ 13.0162i 0.648385i
$$404$$ −5.15174 10.9191i −0.256309 0.543246i
$$405$$ 0 0
$$406$$ 9.49251 + 37.1595i 0.471105 + 1.84420i
$$407$$ 8.16231i 0.404591i
$$408$$ 0 0
$$409$$ 34.9158i 1.72648i 0.504797 + 0.863238i $$0.331567\pi$$
−0.504797 + 0.863238i $$0.668433\pi$$
$$410$$ −2.27237 10.1417i −0.112224 0.500865i
$$411$$ 0 0
$$412$$ 14.1644 6.68290i 0.697831 0.329243i
$$413$$ −36.9790 + 1.09798i −1.81962 + 0.0540282i
$$414$$ 0 0
$$415$$ 1.67114i 0.0820329i
$$416$$ −11.9885 + 23.6775i −0.587782 + 1.16089i
$$417$$ 0 0
$$418$$ −0.304984 + 0.0683351i −0.0149173 + 0.00334238i
$$419$$ 2.32360 0.113515 0.0567577 0.998388i $$-0.481924\pi$$
0.0567577 + 0.998388i $$0.481924\pi$$
$$420$$ 0 0
$$421$$ −22.9539 −1.11870 −0.559352 0.828930i $$-0.688950\pi$$
−0.559352 + 0.828930i $$0.688950\pi$$
$$422$$ 17.4941 3.91975i 0.851599 0.190810i
$$423$$ 0 0
$$424$$ 14.5038 + 18.6393i 0.704366 + 0.905204i
$$425$$ 3.93531i 0.190891i
$$426$$ 0 0
$$427$$ 0.387413 + 13.0477i 0.0187482 + 0.631422i
$$428$$ −11.9357 25.2977i −0.576932 1.22281i
$$429$$ 0 0
$$430$$ −1.33674 5.96597i −0.0644635 0.287705i
$$431$$ 0.0761033i 0.00366577i 0.999998 + 0.00183288i $$0.000583425\pi$$
−0.999998 + 0.00183288i $$0.999417\pi$$
$$432$$ 0 0
$$433$$ 9.43899i 0.453609i −0.973940 0.226805i $$-0.927172\pi$$
0.973940 0.226805i $$-0.0728278\pi$$
$$434$$ −2.56930 10.0578i −0.123330 0.482791i
$$435$$ 0 0
$$436$$ −7.35414 + 3.46975i −0.352199 + 0.166171i
$$437$$ 1.31680i 0.0629909i
$$438$$ 0 0
$$439$$ 4.35512 0.207858 0.103929 0.994585i $$-0.466858\pi$$
0.103929 + 0.994585i $$0.466858\pi$$
$$440$$ 1.71453 + 2.20340i 0.0817372 + 0.105043i
$$441$$ 0 0
$$442$$ −5.70878 25.4786i −0.271539 1.21190i
$$443$$ 35.6619i 1.69435i −0.531315 0.847174i $$-0.678302\pi$$
0.531315 0.847174i $$-0.321698\pi$$
$$444$$ 0 0
$$445$$ −0.493375 −0.0233882
$$446$$ −1.99632 8.90970i −0.0945284 0.421886i
$$447$$ 0 0
$$448$$ 4.58989 20.6624i 0.216852 0.976205i
$$449$$ −15.1046 −0.712832 −0.356416 0.934327i $$-0.616001\pi$$
−0.356416 + 0.934327i $$0.616001\pi$$
$$450$$ 0 0
$$451$$ −7.25415 −0.341585
$$452$$ −15.6715 + 7.39397i −0.737127 + 0.347783i
$$453$$ 0 0
$$454$$ 4.35613 + 19.4417i 0.204443 + 0.912443i
$$455$$ −12.4073 + 0.368398i −0.581662 + 0.0172707i
$$456$$ 0 0
$$457$$ −23.3917 −1.09422 −0.547109 0.837061i $$-0.684272\pi$$
−0.547109 + 0.837061i $$0.684272\pi$$
$$458$$ −13.4540 + 3.01453i −0.628666 + 0.140860i
$$459$$ 0 0
$$460$$ 10.6380 5.01910i 0.495999 0.234017i
$$461$$ 22.6568i 1.05523i −0.849482 0.527617i $$-0.823086\pi$$
0.849482 0.527617i $$-0.176914\pi$$
$$462$$ 0 0
$$463$$ 31.9975i 1.48705i −0.668707 0.743526i $$-0.733152\pi$$
0.668707 0.743526i $$-0.266848\pi$$
$$464$$ 26.0705 31.6449i 1.21029 1.46908i
$$465$$ 0 0
$$466$$ 0.507807 + 2.26638i 0.0235237 + 0.104988i
$$467$$ 42.6816 1.97507 0.987533 0.157409i $$-0.0503142\pi$$
0.987533 + 0.157409i $$0.0503142\pi$$
$$468$$ 0 0
$$469$$ 0.616190 + 20.7527i 0.0284530 + 0.958270i
$$470$$ 3.32274 0.744498i 0.153267 0.0343411i
$$471$$ 0 0
$$472$$ 24.2880 + 31.2133i 1.11794 + 1.43671i
$$473$$ −4.26732 −0.196212
$$474$$ 0 0
$$475$$ −0.223896 −0.0102731
$$476$$ 9.44052 + 18.5608i 0.432705 + 0.850733i
$$477$$ 0 0
$$478$$ 13.4926 3.02316i 0.617136 0.138276i
$$479$$ −0.259729 −0.0118673 −0.00593366 0.999982i $$-0.501889\pi$$
−0.00593366 + 0.999982i $$0.501889\pi$$
$$480$$ 0 0
$$481$$ 38.7953i 1.76891i
$$482$$ −9.44064 + 2.11528i −0.430009 + 0.0963484i
$$483$$ 0 0
$$484$$ −18.1343 + 8.55592i −0.824286 + 0.388906i
$$485$$ −4.31036 −0.195723
$$486$$ 0 0
$$487$$ 29.8196i 1.35126i −0.737242 0.675628i $$-0.763872\pi$$
0.737242 0.675628i $$-0.236128\pi$$
$$488$$ 11.0133 8.56978i 0.498549 0.387936i
$$489$$ 0 0
$$490$$ 9.51454 2.73376i 0.429823 0.123499i
$$491$$ 25.9448i 1.17087i 0.810718 + 0.585437i $$0.199077\pi$$
−0.810718 + 0.585437i $$0.800923\pi$$
$$492$$ 0 0
$$493$$ 40.3378i 1.81672i
$$494$$ −1.44958 + 0.324796i −0.0652199 + 0.0146132i
$$495$$ 0 0
$$496$$ −7.05641 + 8.56520i −0.316842 + 0.384589i
$$497$$ 0.667354 + 22.4758i 0.0299349 + 1.00818i
$$498$$ 0 0
$$499$$ 22.9135i 1.02575i 0.858464 + 0.512874i $$0.171419\pi$$
−0.858464 + 0.512874i $$0.828581\pi$$
$$500$$ 0.853401 + 1.80879i 0.0381653 + 0.0808914i
$$501$$ 0 0
$$502$$ 0.726541 + 3.24260i 0.0324271 + 0.144724i
$$503$$ −29.7060 −1.32453 −0.662263 0.749271i $$-0.730404\pi$$
−0.662263 + 0.749271i $$0.730404\pi$$
$$504$$ 0 0
$$505$$ −6.03671 −0.268630
$$506$$ −1.79502 8.01130i −0.0797984 0.356146i
$$507$$ 0 0
$$508$$ 4.42587 + 9.38064i 0.196366 + 0.416199i
$$509$$ 15.8710i 0.703470i 0.936100 + 0.351735i $$0.114408\pi$$
−0.936100 + 0.351735i $$0.885592\pi$$
$$510$$ 0 0
$$511$$ −1.13596 38.2580i −0.0502519 1.69244i
$$512$$ −20.7250 + 9.08152i −0.915925 + 0.401350i
$$513$$ 0 0
$$514$$ −8.93065 + 2.00101i −0.393914 + 0.0882609i
$$515$$ 7.83090i 0.345071i
$$516$$ 0 0
$$517$$ 2.37668i 0.104526i
$$518$$ 7.65788 + 29.9777i 0.336468 + 1.31714i
$$519$$ 0 0
$$520$$ 8.14915 + 10.4727i 0.357364 + 0.459260i
$$521$$ 10.0748i 0.441387i 0.975343 + 0.220693i $$0.0708320\pi$$
−0.975343 + 0.220693i $$0.929168\pi$$
$$522$$ 0 0
$$523$$ −15.4083 −0.673759 −0.336880 0.941548i $$-0.609372\pi$$
−0.336880 + 0.941548i $$0.609372\pi$$
$$524$$ 20.5509 9.69612i 0.897772 0.423577i
$$525$$ 0 0
$$526$$ 3.28544 0.736139i 0.143252 0.0320972i
$$527$$ 10.9181i 0.475599i
$$528$$ 0 0
$$529$$ −11.5895 −0.503891
$$530$$ 11.5230 2.58186i 0.500528 0.112149i
$$531$$ 0 0
$$532$$ 1.05600 0.537110i 0.0457834 0.0232867i
$$533$$ −34.4788 −1.49344
$$534$$ 0 0
$$535$$ −13.9860 −0.604667
$$536$$ 17.5169 13.6305i 0.756617 0.588746i
$$537$$ 0 0
$$538$$ 13.0395 2.92165i 0.562173 0.125961i
$$539$$ −0.409957 6.89739i −0.0176581 0.297092i
$$540$$ 0 0
$$541$$ −11.4549 −0.492486 −0.246243 0.969208i $$-0.579196\pi$$
−0.246243 + 0.969208i $$0.579196\pi$$
$$542$$ −6.85898 30.6121i −0.294619 1.31490i
$$543$$ 0 0
$$544$$ 10.0560 19.8608i 0.431146 0.851525i
$$545$$ 4.06579i 0.174159i
$$546$$ 0 0
$$547$$ 25.1553i 1.07556i −0.843085 0.537781i $$-0.819263\pi$$
0.843085 0.537781i $$-0.180737\pi$$
$$548$$ −10.5982 + 5.00034i −0.452734 + 0.213604i
$$549$$ 0 0
$$550$$ 1.36217 0.305209i 0.0580830 0.0130142i
$$551$$ 2.29499 0.0977697
$$552$$ 0 0
$$553$$ 0.904455 + 30.4612i 0.0384614 + 1.29534i
$$554$$ 8.27795 + 36.9450i 0.351696 + 1.56964i
$$555$$ 0 0
$$556$$ −32.8222 + 15.4858i −1.39197 + 0.656745i
$$557$$ −26.6942 −1.13107 −0.565534 0.824725i $$-0.691330\pi$$
−0.565534 + 0.824725i $$0.691330\pi$$
$$558$$ 0 0
$$559$$ −20.2825 −0.857859
$$560$$ −8.36419 6.48385i −0.353452 0.273993i
$$561$$ 0 0
$$562$$ −2.67209 11.9257i −0.112715 0.503056i
$$563$$ −10.8180 −0.455923 −0.227962 0.973670i $$-0.573206\pi$$
−0.227962 + 0.973670i $$0.573206\pi$$
$$564$$ 0 0
$$565$$ 8.66412i 0.364502i
$$566$$ 1.83063 + 8.17023i 0.0769472 + 0.343420i
$$567$$ 0 0
$$568$$ 18.9714 14.7622i 0.796023 0.619409i
$$569$$ −15.0833 −0.632323 −0.316162 0.948705i $$-0.602394\pi$$
−0.316162 + 0.948705i $$0.602394\pi$$
$$570$$ 0 0
$$571$$ 11.4509i 0.479206i 0.970871 + 0.239603i $$0.0770174\pi$$
−0.970871 + 0.239603i $$0.922983\pi$$
$$572$$ 8.37642 3.95207i 0.350236 0.165244i
$$573$$ 0 0
$$574$$ 26.6423 6.80584i 1.11203 0.284070i
$$575$$ 5.88128i 0.245267i
$$576$$ 0 0
$$577$$ 27.7622i 1.15576i −0.816123 0.577878i $$-0.803881\pi$$
0.816123 0.577878i $$-0.196119\pi$$
$$578$$ −0.467923 2.08837i −0.0194630 0.0868648i
$$579$$ 0 0
$$580$$ −8.74756 18.5405i −0.363223 0.769851i
$$581$$ 4.41946 0.131223i 0.183350 0.00544405i
$$582$$ 0 0
$$583$$ 8.24214i 0.341355i
$$584$$ −32.2929 + 25.1280i −1.33629 + 1.03981i
$$585$$ 0 0
$$586$$ 36.2462 8.12137i 1.49732 0.335491i
$$587$$ −4.20086 −0.173388 −0.0866941 0.996235i $$-0.527630\pi$$
−0.0866941 + 0.996235i $$0.527630\pi$$
$$588$$ 0 0
$$589$$ −0.621174 −0.0255950
$$590$$ 19.2964 4.32357i 0.794419 0.177999i
$$591$$ 0 0
$$592$$ 21.0319 25.5289i 0.864404 1.04923i
$$593$$ 12.2323i 0.502321i 0.967945 + 0.251161i $$0.0808123\pi$$
−0.967945 + 0.251161i $$0.919188\pi$$
$$594$$ 0 0
$$595$$ 10.4073 0.309013i 0.426657 0.0126683i
$$596$$ 27.9887 13.2053i 1.14646 0.540911i
$$597$$ 0 0
$$598$$ −8.53171 38.0776i −0.348887 1.55711i
$$599$$ 43.8944i 1.79348i −0.442562 0.896738i $$-0.645930\pi$$
0.442562 0.896738i $$-0.354070\pi$$
$$600$$ 0 0
$$601$$ 5.44570i 0.222135i −0.993813 0.111067i $$-0.964573\pi$$
0.993813 0.111067i $$-0.0354269\pi$$
$$602$$ 15.6726 4.00360i 0.638766 0.163175i
$$603$$ 0 0
$$604$$ −9.84156 20.8592i −0.400447 0.848749i
$$605$$ 10.0257i 0.407602i
$$606$$ 0 0
$$607$$ 29.7406 1.20713 0.603567 0.797312i $$-0.293745\pi$$
0.603567 + 0.797312i $$0.293745\pi$$
$$608$$ −1.12996 0.572125i −0.0458260 0.0232027i
$$609$$ 0 0
$$610$$ −1.52553 6.80855i −0.0617670 0.275670i
$$611$$ 11.2963i 0.457000i
$$612$$ 0 0
$$613$$ 26.7046 1.07859 0.539295 0.842117i $$-0.318691\pi$$
0.539295 + 0.842117i $$0.318691\pi$$
$$614$$ 5.73363 + 25.5895i 0.231390 + 1.03271i
$$615$$ 0 0
$$616$$ −5.69246 + 4.70725i −0.229356 + 0.189661i
$$617$$ 18.7712 0.755701 0.377851 0.925867i $$-0.376663\pi$$
0.377851 + 0.925867i $$0.376663\pi$$
$$618$$ 0 0
$$619$$ 6.00143 0.241218 0.120609 0.992700i $$-0.461515\pi$$
0.120609 + 0.992700i $$0.461515\pi$$
$$620$$ 2.36767 + 5.01827i 0.0950877 + 0.201539i
$$621$$ 0 0
$$622$$ −9.53493 42.5550i −0.382316 1.70630i
$$623$$ −0.0387414 1.30477i −0.00155214 0.0522746i
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 28.7385 6.43918i 1.14862 0.257361i
$$627$$ 0 0
$$628$$ −0.688476 1.45923i −0.0274732 0.0582294i
$$629$$ 32.5417i 1.29752i
$$630$$ 0 0
$$631$$ 42.7851i 1.70325i −0.524154 0.851623i $$-0.675619\pi$$
0.524154 0.851623i $$-0.324381\pi$$
$$632$$ 25.7117 20.0070i 1.02276 0.795837i
$$633$$ 0 0
$$634$$ 1.67326 + 7.46788i 0.0664538 + 0.296587i
$$635$$ 5.18615 0.205806
$$636$$ 0 0
$$637$$ −1.94852 32.7832i −0.0772031 1.29892i
$$638$$ −13.9625 + 3.12846i −0.552782 + 0.123857i
$$639$$ 0 0
$$640$$ −0.315057 + 11.3093i −0.0124537 + 0.447040i
$$641$$ −32.5398 −1.28525 −0.642623 0.766182i $$-0.722154\pi$$
−0.642623 + 0.766182i $$0.722154\pi$$
$$642$$ 0 0
$$643$$ −10.1954 −0.402068 −0.201034 0.979584i $$-0.564430\pi$$
−0.201034 + 0.979584i $$0.564430\pi$$
$$644$$ 14.1088 + 27.7389i 0.555963 + 1.09307i
$$645$$ 0 0
$$646$$ 1.21592 0.272440i 0.0478396 0.0107190i
$$647$$ −32.1295 −1.26314 −0.631571 0.775318i $$-0.717590\pi$$
−0.631571 + 0.775318i $$0.717590\pi$$
$$648$$ 0 0
$$649$$ 13.8023i 0.541786i
$$650$$ 6.47436 1.45065i 0.253945 0.0568993i
$$651$$ 0 0
$$652$$ −5.53236 11.7258i −0.216664 0.459220i
$$653$$ 25.0805 0.981476 0.490738 0.871307i $$-0.336727\pi$$
0.490738 + 0.871307i $$0.336727\pi$$
$$654$$ 0 0
$$655$$ 11.3617i 0.443940i
$$656$$ −22.6884 18.6918i −0.885835 0.729792i
$$657$$ 0 0
$$658$$ 2.22980 + 8.72882i 0.0869267 + 0.340285i
$$659$$ 8.80669i 0.343060i −0.985179 0.171530i $$-0.945129\pi$$
0.985179 0.171530i $$-0.0548710\pi$$
$$660$$ 0 0
$$661$$ 43.1173i 1.67707i −0.544849 0.838534i $$-0.683413\pi$$
0.544849 0.838534i $$-0.316587\pi$$
$$662$$ −2.44942 + 0.548820i −0.0951993 + 0.0213305i
$$663$$ 0 0
$$664$$ −2.90272 3.73039i −0.112648 0.144767i
$$665$$ −0.0175810 0.592112i −0.000681764 0.0229611i
$$666$$ 0 0
$$667$$ 60.2845i 2.33422i
$$668$$ 13.8495 6.53430i 0.535852 0.252820i
$$669$$ 0 0
$$670$$ −2.42640 10.8292i −0.0937399 0.418367i
$$671$$ −4.87000 −0.188004
$$672$$ 0 0
$$673$$ −12.2583 −0.472524 −0.236262 0.971689i $$-0.575922\pi$$
−0.236262 + 0.971689i $$0.575922\pi$$
$$674$$ −6.91589 30.8661i −0.266390 1.18892i
$$675$$ 0 0
$$676$$ 16.2987 7.68989i 0.626875 0.295765i
$$677$$ 29.7024i 1.14155i 0.821105 + 0.570777i $$0.193358\pi$$
−0.821105 + 0.570777i $$0.806642\pi$$
$$678$$ 0 0
$$679$$ −0.338463 11.3991i −0.0129890 0.437458i
$$680$$ −6.83554 8.78458i −0.262131 0.336873i
$$681$$ 0 0
$$682$$ 3.77918 0.846768i 0.144712 0.0324244i
$$683$$ 35.1749i 1.34593i 0.739674 + 0.672965i $$0.234980\pi$$
−0.739674 + 0.672965i $$0.765020\pi$$
$$684$$ 0 0
$$685$$ 5.85931i 0.223873i
$$686$$ 7.97677 + 24.9474i 0.304555 + 0.952495i
$$687$$ 0 0
$$688$$ −13.3467 10.9956i −0.508838 0.419204i
$$689$$ 39.1748i 1.49244i
$$690$$ 0 0
$$691$$ 42.9454 1.63372 0.816860 0.576836i $$-0.195713\pi$$
0.816860 + 0.576836i $$0.195713\pi$$
$$692$$ 6.07628 + 12.8787i 0.230986 + 0.489574i
$$693$$ 0 0
$$694$$ −0.836394 + 0.187403i −0.0317491 + 0.00711374i
$$695$$ 18.1460i 0.688317i
$$696$$ 0 0
$$697$$ 28.9210 1.09546
$$698$$ −43.7020 + 9.79193i −1.65415 + 0.370630i
$$699$$ 0 0
$$700$$ −4.71648 + 2.39892i −0.178266 + 0.0906708i
$$701$$ 9.37675 0.354155 0.177077 0.984197i $$-0.443336\pi$$
0.177077 + 0.984197i $$0.443336\pi$$
$$702$$ 0 0
$$703$$ 1.85143 0.0698280
$$704$$ 7.65452 + 1.94043i 0.288491 + 0.0731329i
$$705$$ 0 0
$$706$$ −5.61523 + 1.25815i −0.211332 + 0.0473513i
$$707$$ −0.474022 15.9646i −0.0178274 0.600411i
$$708$$ 0 0
$$709$$ −27.6729 −1.03928 −0.519638 0.854386i $$-0.673933\pi$$
−0.519638 + 0.854386i $$0.673933\pi$$
$$710$$ −2.62786 11.7283i −0.0986220 0.440156i
$$711$$ 0 0
$$712$$ −1.10133 + 0.856980i −0.0412742 + 0.0321167i
$$713$$ 16.3170i 0.611075i
$$714$$ 0 0
$$715$$ 4.63096i 0.173188i
$$716$$ −17.7882 37.7021i −0.664776 1.40899i
$$717$$ 0 0
$$718$$ 15.2388 3.41443i 0.568708 0.127426i
$$719$$ 9.24786 0.344887 0.172444 0.985019i $$-0.444834\pi$$
0.172444 + 0.985019i $$0.444834\pi$$
$$720$$ 0 0
$$721$$ 20.7095 0.614908i 0.771262 0.0229004i
$$722$$ 5.85938 + 26.1508i 0.218063 + 0.973231i
$$723$$ 0 0
$$724$$ 20.8595 + 44.2118i 0.775239 + 1.64312i
$$725$$ −10.2502 −0.380684
$$726$$ 0 0
$$727$$ 34.7371 1.28833 0.644163 0.764888i $$-0.277206\pi$$
0.644163 + 0.764888i $$0.277206\pi$$
$$728$$ −27.0562 + 22.3735i −1.00277 + 0.829216i
$$729$$ 0 0
$$730$$ 4.47311 + 19.9638i 0.165557 + 0.738893i
$$731$$ 17.0131 0.629250
$$732$$ 0 0
$$733$$ 38.6871i 1.42894i 0.699666 + 0.714470i $$0.253332\pi$$
−0.699666 + 0.714470i $$0.746668\pi$$
$$734$$ −0.0224396 0.100149i −0.000828259 0.00369657i
$$735$$ 0 0
$$736$$ 15.0285 29.6818i 0.553959 1.09408i
$$737$$ −7.74585 −0.285322
$$738$$ 0 0
$$739$$ 40.4228i 1.48698i −0.668748 0.743489i $$-0.733170\pi$$
0.668748 0.743489i $$-0.266830\pi$$
$$740$$ −7.05690 14.9571i −0.259417 0.549835i
$$741$$ 0 0
$$742$$ 7.73278 + 30.2709i 0.283879 + 1.11128i
$$743$$ 25.5119i 0.935941i −0.883744 0.467970i $$-0.844985\pi$$
0.883744 0.467970i $$-0.155015\pi$$
$$744$$ 0 0
$$745$$ 15.4737i 0.566914i
$$746$$ −6.93026 30.9302i −0.253735 1.13244i
$$747$$ 0 0
$$748$$ −7.02617 + 3.31501i −0.256902 + 0.121209i
$$749$$ −1.09823 36.9872i −0.0401283 1.35148i
$$750$$ 0 0
$$751$$ 31.4000i 1.14580i −0.819625 0.572901i $$-0.805818\pi$$
0.819625 0.572901i $$-0.194182\pi$$
$$752$$ 6.12400 7.43342i 0.223319 0.271069i
$$753$$ 0 0
$$754$$ −66.3637 + 14.8695i −2.41682 + 0.541516i
$$755$$ −11.5322 −0.419698
$$756$$ 0 0
$$757$$ −32.9674 −1.19822 −0.599111 0.800666i $$-0.704479\pi$$
−0.599111 + 0.800666i $$0.704479\pi$$
$$758$$ 37.2556 8.34754i 1.35318 0.303196i
$$759$$ 0 0
$$760$$ −0.499791 + 0.388902i −0.0181293 + 0.0141070i
$$761$$ 45.0372i 1.63260i −0.577631 0.816298i $$-0.696023\pi$$
0.577631 0.816298i $$-0.303977\pi$$
$$762$$ 0 0
$$763$$ −10.7523 + 0.319259i −0.389260 + 0.0115579i
$$764$$ 16.4747 + 34.9181i 0.596032 + 1.26329i
$$765$$ 0 0
$$766$$ −6.11809 27.3054i −0.221056 0.986585i
$$767$$ 65.6019i 2.36875i
$$768$$ 0 0
$$769$$ 16.6023i 0.598694i −0.954144 0.299347i $$-0.903231\pi$$
0.954144 0.299347i $$-0.0967688\pi$$
$$770$$ 0.914114 + 3.57840i 0.0329424 + 0.128957i
$$771$$ 0 0
$$772$$ 27.5850 13.0148i 0.992804 0.468414i
$$773$$ 23.1862i 0.833951i 0.908918 + 0.416975i $$0.136910\pi$$
−0.908918 + 0.416975i $$0.863090\pi$$
$$774$$ 0 0
$$775$$ 2.77439 0.0996589
$$776$$ −9.62177 + 7.48698i −0.345401 + 0.268767i
$$777$$ 0 0
$$778$$ −9.15610 40.8643i −0.328262 1.46506i
$$779$$ 1.64543i 0.0589538i
$$780$$ 0 0
$$781$$ −8.38900 −0.300182
$$782$$ 7.15643 + 31.9396i 0.255913 + 1.14216i
$$783$$ 0 0
$$784$$ 16.4903 22.6290i 0.588940 0.808177i
$$785$$ −0.806743 −0.0287939
$$786$$ 0 0
$$787$$ 45.5418 1.62339 0.811695 0.584081i $$-0.198545\pi$$
0.811695 + 0.584081i $$0.198545\pi$$
$$788$$ 5.43954 2.56642i 0.193775 0.0914250i
$$789$$ 0 0
$$790$$ −3.56151 15.8952i −0.126713 0.565528i
$$791$$ −22.9130 + 0.680334i −0.814692 + 0.0241899i