# Properties

 Label 1064.2.q.n.305.3 Level $1064$ Weight $2$ Character 1064.305 Analytic conductor $8.496$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1064 = 2^{3} \cdot 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1064.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.49608277506$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + 4560 x^{6} + 1376 x^{5} + 4688 x^{4} + 736 x^{3} + 1280 x^{2} - 128 x + 256$$ x^16 + 15*x^14 - 2*x^13 + 159*x^12 - 19*x^11 + 839*x^10 - 62*x^9 + 3204*x^8 + 8*x^7 + 4560*x^6 + 1376*x^5 + 4688*x^4 + 736*x^3 + 1280*x^2 - 128*x + 256 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{4}\cdot 3^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 305.3 Root $$-0.456148 + 0.790072i$$ of defining polynomial Character $$\chi$$ $$=$$ 1064.305 Dual form 1064.2.q.n.457.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.456148 + 0.790072i) q^{3} +(0.832641 + 1.44218i) q^{5} +(-0.462738 + 2.60497i) q^{7} +(1.08386 + 1.87730i) q^{9} +O(q^{10})$$ $$q+(-0.456148 + 0.790072i) q^{3} +(0.832641 + 1.44218i) q^{5} +(-0.462738 + 2.60497i) q^{7} +(1.08386 + 1.87730i) q^{9} +(0.121120 - 0.209787i) q^{11} -5.76999 q^{13} -1.51923 q^{15} +(-2.88319 + 4.99382i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-1.84704 - 1.55385i) q^{21} +(-3.30773 - 5.72915i) q^{23} +(1.11342 - 1.92850i) q^{25} -4.71449 q^{27} +8.91381 q^{29} +(2.96642 - 5.13799i) q^{31} +(0.110498 + 0.191388i) q^{33} +(-4.14212 + 1.50166i) q^{35} +(4.90185 + 8.49026i) q^{37} +(2.63197 - 4.55870i) q^{39} -2.00000 q^{41} -7.83237 q^{43} +(-1.80493 + 3.12623i) q^{45} +(-0.789589 - 1.36761i) q^{47} +(-6.57175 - 2.41084i) q^{49} +(-2.63032 - 4.55585i) q^{51} +(-3.24073 + 5.61311i) q^{53} +0.403399 q^{55} +0.912296 q^{57} +(-0.537488 + 0.930957i) q^{59} +(-4.55454 - 7.88869i) q^{61} +(-5.39185 + 1.95472i) q^{63} +(-4.80433 - 8.32134i) q^{65} +(-4.01270 + 6.95021i) q^{67} +6.03525 q^{69} +1.22955 q^{71} +(-0.400685 + 0.694007i) q^{73} +(1.01577 + 1.75936i) q^{75} +(0.490441 + 0.412591i) q^{77} +(3.79101 + 6.56622i) q^{79} +(-1.10107 + 1.90711i) q^{81} -8.91292 q^{83} -9.60264 q^{85} +(-4.06602 + 7.04255i) q^{87} +(6.55732 + 11.3576i) q^{89} +(2.66999 - 15.0307i) q^{91} +(2.70625 + 4.68737i) q^{93} +(0.832641 - 1.44218i) q^{95} +1.11664 q^{97} +0.525109 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10})$$ 16 * q + q^5 + 5 * q^7 - 6 * q^9 $$16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100})$$ 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$$.

 $$n$$ $$533$$ $$799$$ $$913$$ $$1009$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$3$$ −0.456148 + 0.790072i −0.263357 + 0.456148i −0.967132 0.254275i $$-0.918163\pi$$
0.703775 + 0.710423i $$0.251496\pi$$
$$4$$ 0 0
$$5$$ 0.832641 + 1.44218i 0.372368 + 0.644961i 0.989929 0.141562i $$-0.0452125\pi$$
−0.617561 + 0.786523i $$0.711879\pi$$
$$6$$ 0 0
$$7$$ −0.462738 + 2.60497i −0.174898 + 0.984586i
$$8$$ 0 0
$$9$$ 1.08386 + 1.87730i 0.361286 + 0.625766i
$$10$$ 0 0
$$11$$ 0.121120 0.209787i 0.0365192 0.0632531i −0.847188 0.531293i $$-0.821706\pi$$
0.883707 + 0.468040i $$0.155040\pi$$
$$12$$ 0 0
$$13$$ −5.76999 −1.60031 −0.800154 0.599795i $$-0.795249\pi$$
−0.800154 + 0.599795i $$0.795249\pi$$
$$14$$ 0 0
$$15$$ −1.51923 −0.392264
$$16$$ 0 0
$$17$$ −2.88319 + 4.99382i −0.699275 + 1.21118i 0.269443 + 0.963016i $$0.413160\pi$$
−0.968718 + 0.248164i $$0.920173\pi$$
$$18$$ 0 0
$$19$$ −0.500000 0.866025i −0.114708 0.198680i
$$20$$ 0 0
$$21$$ −1.84704 1.55385i −0.403056 0.339077i
$$22$$ 0 0
$$23$$ −3.30773 5.72915i −0.689709 1.19461i −0.971932 0.235262i $$-0.924405\pi$$
0.282224 0.959349i $$-0.408928\pi$$
$$24$$ 0 0
$$25$$ 1.11342 1.92850i 0.222684 0.385699i
$$26$$ 0 0
$$27$$ −4.71449 −0.907303
$$28$$ 0 0
$$29$$ 8.91381 1.65525 0.827627 0.561279i $$-0.189690\pi$$
0.827627 + 0.561279i $$0.189690\pi$$
$$30$$ 0 0
$$31$$ 2.96642 5.13799i 0.532785 0.922810i −0.466483 0.884530i $$-0.654479\pi$$
0.999267 0.0382794i $$-0.0121877\pi$$
$$32$$ 0 0
$$33$$ 0.110498 + 0.191388i 0.0192352 + 0.0333163i
$$34$$ 0 0
$$35$$ −4.14212 + 1.50166i −0.700147 + 0.253826i
$$36$$ 0 0
$$37$$ 4.90185 + 8.49026i 0.805860 + 1.39579i 0.915709 + 0.401842i $$0.131630\pi$$
−0.109849 + 0.993948i $$0.535037\pi$$
$$38$$ 0 0
$$39$$ 2.63197 4.55870i 0.421452 0.729977i
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ −7.83237 −1.19443 −0.597213 0.802083i $$-0.703725\pi$$
−0.597213 + 0.802083i $$0.703725\pi$$
$$44$$ 0 0
$$45$$ −1.80493 + 3.12623i −0.269063 + 0.466031i
$$46$$ 0 0
$$47$$ −0.789589 1.36761i −0.115173 0.199486i 0.802676 0.596416i $$-0.203409\pi$$
−0.917849 + 0.396930i $$0.870076\pi$$
$$48$$ 0 0
$$49$$ −6.57175 2.41084i −0.938821 0.344405i
$$50$$ 0 0
$$51$$ −2.63032 4.55585i −0.368318 0.637946i
$$52$$ 0 0
$$53$$ −3.24073 + 5.61311i −0.445148 + 0.771019i −0.998063 0.0622187i $$-0.980182\pi$$
0.552914 + 0.833238i $$0.313516\pi$$
$$54$$ 0 0
$$55$$ 0.403399 0.0543944
$$56$$ 0 0
$$57$$ 0.912296 0.120837
$$58$$ 0 0
$$59$$ −0.537488 + 0.930957i −0.0699750 + 0.121200i −0.898890 0.438174i $$-0.855625\pi$$
0.828915 + 0.559375i $$0.188959\pi$$
$$60$$ 0 0
$$61$$ −4.55454 7.88869i −0.583149 1.01004i −0.995103 0.0988387i $$-0.968487\pi$$
0.411955 0.911204i $$-0.364846\pi$$
$$62$$ 0 0
$$63$$ −5.39185 + 1.95472i −0.679309 + 0.246272i
$$64$$ 0 0
$$65$$ −4.80433 8.32134i −0.595904 1.03214i
$$66$$ 0 0
$$67$$ −4.01270 + 6.95021i −0.490230 + 0.849103i −0.999937 0.0112451i $$-0.996421\pi$$
0.509707 + 0.860348i $$0.329754\pi$$
$$68$$ 0 0
$$69$$ 6.03525 0.726559
$$70$$ 0 0
$$71$$ 1.22955 0.145921 0.0729606 0.997335i $$-0.476755\pi$$
0.0729606 + 0.997335i $$0.476755\pi$$
$$72$$ 0 0
$$73$$ −0.400685 + 0.694007i −0.0468966 + 0.0812274i −0.888521 0.458836i $$-0.848266\pi$$
0.841624 + 0.540064i $$0.181600\pi$$
$$74$$ 0 0
$$75$$ 1.01577 + 1.75936i 0.117291 + 0.203153i
$$76$$ 0 0
$$77$$ 0.490441 + 0.412591i 0.0558910 + 0.0470192i
$$78$$ 0 0
$$79$$ 3.79101 + 6.56622i 0.426522 + 0.738758i 0.996561 0.0828597i $$-0.0264053\pi$$
−0.570039 + 0.821617i $$0.693072\pi$$
$$80$$ 0 0
$$81$$ −1.10107 + 1.90711i −0.122341 + 0.211901i
$$82$$ 0 0
$$83$$ −8.91292 −0.978320 −0.489160 0.872194i $$-0.662697\pi$$
−0.489160 + 0.872194i $$0.662697\pi$$
$$84$$ 0 0
$$85$$ −9.60264 −1.04155
$$86$$ 0 0
$$87$$ −4.06602 + 7.04255i −0.435923 + 0.755041i
$$88$$ 0 0
$$89$$ 6.55732 + 11.3576i 0.695074 + 1.20390i 0.970156 + 0.242483i $$0.0779618\pi$$
−0.275082 + 0.961421i $$0.588705\pi$$
$$90$$ 0 0
$$91$$ 2.66999 15.0307i 0.279891 1.57564i
$$92$$ 0 0
$$93$$ 2.70625 + 4.68737i 0.280625 + 0.486057i
$$94$$ 0 0
$$95$$ 0.832641 1.44218i 0.0854272 0.147964i
$$96$$ 0 0
$$97$$ 1.11664 0.113377 0.0566886 0.998392i $$-0.481946\pi$$
0.0566886 + 0.998392i $$0.481946\pi$$
$$98$$ 0 0
$$99$$ 0.525109 0.0527755
$$100$$ 0 0
$$101$$ −6.51382 + 11.2823i −0.648149 + 1.12263i 0.335416 + 0.942070i $$0.391123\pi$$
−0.983565 + 0.180557i $$0.942210\pi$$
$$102$$ 0 0
$$103$$ 6.86294 + 11.8870i 0.676226 + 1.17126i 0.976109 + 0.217282i $$0.0697190\pi$$
−0.299883 + 0.953976i $$0.596948\pi$$
$$104$$ 0 0
$$105$$ 0.703005 3.95755i 0.0686063 0.386217i
$$106$$ 0 0
$$107$$ −1.88424 3.26359i −0.182156 0.315503i 0.760459 0.649386i $$-0.224974\pi$$
−0.942614 + 0.333883i $$0.891641\pi$$
$$108$$ 0 0
$$109$$ 0.337127 0.583921i 0.0322909 0.0559295i −0.849428 0.527704i $$-0.823053\pi$$
0.881719 + 0.471774i $$0.156386\pi$$
$$110$$ 0 0
$$111$$ −8.94388 −0.848916
$$112$$ 0 0
$$113$$ 10.1480 0.954646 0.477323 0.878728i $$-0.341607\pi$$
0.477323 + 0.878728i $$0.341607\pi$$
$$114$$ 0 0
$$115$$ 5.50830 9.54065i 0.513651 0.889670i
$$116$$ 0 0
$$117$$ −6.25385 10.8320i −0.578169 1.00142i
$$118$$ 0 0
$$119$$ −11.6746 9.82145i −1.07021 0.900330i
$$120$$ 0 0
$$121$$ 5.47066 + 9.47546i 0.497333 + 0.861406i
$$122$$ 0 0
$$123$$ 0.912296 1.58014i 0.0822590 0.142477i
$$124$$ 0 0
$$125$$ 12.0347 1.07642
$$126$$ 0 0
$$127$$ 18.5974 1.65025 0.825126 0.564949i $$-0.191104\pi$$
0.825126 + 0.564949i $$0.191104\pi$$
$$128$$ 0 0
$$129$$ 3.57272 6.18813i 0.314561 0.544835i
$$130$$ 0 0
$$131$$ −3.98570 6.90344i −0.348233 0.603157i 0.637703 0.770282i $$-0.279885\pi$$
−0.985936 + 0.167126i $$0.946551\pi$$
$$132$$ 0 0
$$133$$ 2.48734 0.901743i 0.215680 0.0781910i
$$134$$ 0 0
$$135$$ −3.92548 6.79912i −0.337851 0.585175i
$$136$$ 0 0
$$137$$ 0.159382 0.276057i 0.0136169 0.0235852i −0.859137 0.511746i $$-0.828999\pi$$
0.872754 + 0.488161i $$0.162332\pi$$
$$138$$ 0 0
$$139$$ −5.80115 −0.492047 −0.246024 0.969264i $$-0.579124\pi$$
−0.246024 + 0.969264i $$0.579124\pi$$
$$140$$ 0 0
$$141$$ 1.44068 0.121327
$$142$$ 0 0
$$143$$ −0.698864 + 1.21047i −0.0584419 + 0.101224i
$$144$$ 0 0
$$145$$ 7.42201 + 12.8553i 0.616364 + 1.06757i
$$146$$ 0 0
$$147$$ 4.90242 4.09245i 0.404345 0.337540i
$$148$$ 0 0
$$149$$ −6.83503 11.8386i −0.559948 0.969858i −0.997500 0.0706649i $$-0.977488\pi$$
0.437552 0.899193i $$-0.355845\pi$$
$$150$$ 0 0
$$151$$ −5.51411 + 9.55072i −0.448732 + 0.777226i −0.998304 0.0582201i $$-0.981457\pi$$
0.549572 + 0.835446i $$0.314791\pi$$
$$152$$ 0 0
$$153$$ −12.4999 −1.01055
$$154$$ 0 0
$$155$$ 9.87985 0.793568
$$156$$ 0 0
$$157$$ −8.92830 + 15.4643i −0.712556 + 1.23418i 0.251339 + 0.967899i $$0.419129\pi$$
−0.963895 + 0.266283i $$0.914204\pi$$
$$158$$ 0 0
$$159$$ −2.95650 5.12081i −0.234466 0.406107i
$$160$$ 0 0
$$161$$ 16.4549 5.96544i 1.29683 0.470142i
$$162$$ 0 0
$$163$$ −5.59851 9.69690i −0.438509 0.759520i 0.559066 0.829123i $$-0.311160\pi$$
−0.997575 + 0.0696035i $$0.977827\pi$$
$$164$$ 0 0
$$165$$ −0.184010 + 0.318714i −0.0143251 + 0.0248119i
$$166$$ 0 0
$$167$$ 1.44712 0.111981 0.0559906 0.998431i $$-0.482168\pi$$
0.0559906 + 0.998431i $$0.482168\pi$$
$$168$$ 0 0
$$169$$ 20.2928 1.56098
$$170$$ 0 0
$$171$$ 1.08386 1.87730i 0.0828847 0.143560i
$$172$$ 0 0
$$173$$ −5.94705 10.3006i −0.452146 0.783140i 0.546373 0.837542i $$-0.316008\pi$$
−0.998519 + 0.0544023i $$0.982675\pi$$
$$174$$ 0 0
$$175$$ 4.50846 + 3.79281i 0.340807 + 0.286709i
$$176$$ 0 0
$$177$$ −0.490348 0.849308i −0.0368568 0.0638379i
$$178$$ 0 0
$$179$$ −12.5864 + 21.8003i −0.940751 + 1.62943i −0.176708 + 0.984263i $$0.556545\pi$$
−0.764043 + 0.645165i $$0.776788\pi$$
$$180$$ 0 0
$$181$$ 18.7410 1.39301 0.696503 0.717554i $$-0.254738\pi$$
0.696503 + 0.717554i $$0.254738\pi$$
$$182$$ 0 0
$$183$$ 8.31017 0.614305
$$184$$ 0 0
$$185$$ −8.16297 + 14.1387i −0.600154 + 1.03950i
$$186$$ 0 0
$$187$$ 0.698425 + 1.20971i 0.0510739 + 0.0884626i
$$188$$ 0 0
$$189$$ 2.18157 12.2811i 0.158686 0.893319i
$$190$$ 0 0
$$191$$ −0.178001 0.308307i −0.0128797 0.0223083i 0.859514 0.511113i $$-0.170767\pi$$
−0.872393 + 0.488804i $$0.837433\pi$$
$$192$$ 0 0
$$193$$ −8.54939 + 14.8080i −0.615398 + 1.06590i 0.374916 + 0.927059i $$0.377671\pi$$
−0.990314 + 0.138842i $$0.955662\pi$$
$$194$$ 0 0
$$195$$ 8.76594 0.627742
$$196$$ 0 0
$$197$$ 13.1088 0.933964 0.466982 0.884267i $$-0.345341\pi$$
0.466982 + 0.884267i $$0.345341\pi$$
$$198$$ 0 0
$$199$$ −2.38489 + 4.13074i −0.169060 + 0.292821i −0.938090 0.346393i $$-0.887407\pi$$
0.769030 + 0.639213i $$0.220740\pi$$
$$200$$ 0 0
$$201$$ −3.66077 6.34065i −0.258211 0.447235i
$$202$$ 0 0
$$203$$ −4.12476 + 23.2202i −0.289501 + 1.62974i
$$204$$ 0 0
$$205$$ −1.66528 2.88435i −0.116308 0.201452i
$$206$$ 0 0
$$207$$ 7.17021 12.4192i 0.498364 0.863192i
$$208$$ 0 0
$$209$$ −0.242241 −0.0167561
$$210$$ 0 0
$$211$$ 22.0442 1.51759 0.758794 0.651331i $$-0.225789\pi$$
0.758794 + 0.651331i $$0.225789\pi$$
$$212$$ 0 0
$$213$$ −0.560858 + 0.971435i −0.0384294 + 0.0665616i
$$214$$ 0 0
$$215$$ −6.52156 11.2957i −0.444766 0.770358i
$$216$$ 0 0
$$217$$ 12.0116 + 10.1050i 0.815403 + 0.685970i
$$218$$ 0 0
$$219$$ −0.365543 0.633140i −0.0247011 0.0427836i
$$220$$ 0 0
$$221$$ 16.6360 28.8143i 1.11906 1.93826i
$$222$$ 0 0
$$223$$ 19.5836 1.31142 0.655708 0.755014i $$-0.272370\pi$$
0.655708 + 0.755014i $$0.272370\pi$$
$$224$$ 0 0
$$225$$ 4.82715 0.321810
$$226$$ 0 0
$$227$$ 2.89414 5.01280i 0.192091 0.332712i −0.753852 0.657044i $$-0.771806\pi$$
0.945943 + 0.324333i $$0.105140\pi$$
$$228$$ 0 0
$$229$$ 9.55372 + 16.5475i 0.631328 + 1.09349i 0.987281 + 0.158988i $$0.0508231\pi$$
−0.355953 + 0.934504i $$0.615844\pi$$
$$230$$ 0 0
$$231$$ −0.549691 + 0.199281i −0.0361670 + 0.0131117i
$$232$$ 0 0
$$233$$ 3.08563 + 5.34446i 0.202146 + 0.350127i 0.949220 0.314614i $$-0.101875\pi$$
−0.747074 + 0.664741i $$0.768542\pi$$
$$234$$ 0 0
$$235$$ 1.31489 2.27745i 0.0857739 0.148565i
$$236$$ 0 0
$$237$$ −6.91705 −0.449311
$$238$$ 0 0
$$239$$ 26.1425 1.69101 0.845507 0.533964i $$-0.179298\pi$$
0.845507 + 0.533964i $$0.179298\pi$$
$$240$$ 0 0
$$241$$ 9.79581 16.9668i 0.631003 1.09293i −0.356344 0.934355i $$-0.615977\pi$$
0.987347 0.158575i $$-0.0506899\pi$$
$$242$$ 0 0
$$243$$ −8.07623 13.9884i −0.518091 0.897359i
$$244$$ 0 0
$$245$$ −1.99506 11.4850i −0.127459 0.733749i
$$246$$ 0 0
$$247$$ 2.88499 + 4.99696i 0.183568 + 0.317949i
$$248$$ 0 0
$$249$$ 4.06561 7.04184i 0.257647 0.446259i
$$250$$ 0 0
$$251$$ −6.39080 −0.403384 −0.201692 0.979449i $$-0.564644\pi$$
−0.201692 + 0.979449i $$0.564644\pi$$
$$252$$ 0 0
$$253$$ −1.60253 −0.100750
$$254$$ 0 0
$$255$$ 4.38022 7.58677i 0.274300 0.475102i
$$256$$ 0 0
$$257$$ −10.9371 18.9436i −0.682238 1.18167i −0.974296 0.225271i $$-0.927673\pi$$
0.292058 0.956401i $$-0.405660\pi$$
$$258$$ 0 0
$$259$$ −24.3852 + 8.84043i −1.51522 + 0.549317i
$$260$$ 0 0
$$261$$ 9.66131 + 16.7339i 0.598020 + 1.03580i
$$262$$ 0 0
$$263$$ 14.8618 25.7414i 0.916420 1.58729i 0.111611 0.993752i $$-0.464399\pi$$
0.804809 0.593534i $$-0.202268\pi$$
$$264$$ 0 0
$$265$$ −10.7935 −0.663037
$$266$$ 0 0
$$267$$ −11.9644 −0.732211
$$268$$ 0 0
$$269$$ −6.69279 + 11.5923i −0.408067 + 0.706792i −0.994673 0.103080i $$-0.967130\pi$$
0.586606 + 0.809872i $$0.300464\pi$$
$$270$$ 0 0
$$271$$ 12.8866 + 22.3202i 0.782805 + 1.35586i 0.930301 + 0.366796i $$0.119545\pi$$
−0.147496 + 0.989063i $$0.547121\pi$$
$$272$$ 0 0
$$273$$ 10.6574 + 8.96569i 0.645014 + 0.542628i
$$274$$ 0 0
$$275$$ −0.269715 0.467161i −0.0162644 0.0281708i
$$276$$ 0 0
$$277$$ 1.48701 2.57558i 0.0893458 0.154751i −0.817889 0.575376i $$-0.804856\pi$$
0.907235 + 0.420625i $$0.138189\pi$$
$$278$$ 0 0
$$279$$ 12.8607 0.769950
$$280$$ 0 0
$$281$$ −18.8947 −1.12716 −0.563582 0.826060i $$-0.690577\pi$$
−0.563582 + 0.826060i $$0.690577\pi$$
$$282$$ 0 0
$$283$$ −11.4150 + 19.7713i −0.678551 + 1.17528i 0.296867 + 0.954919i $$0.404058\pi$$
−0.975417 + 0.220365i $$0.929275\pi$$
$$284$$ 0 0
$$285$$ 0.759615 + 1.31569i 0.0449957 + 0.0779349i
$$286$$ 0 0
$$287$$ 0.925475 5.20994i 0.0546291 0.307533i
$$288$$ 0 0
$$289$$ −8.12552 14.0738i −0.477972 0.827872i
$$290$$ 0 0
$$291$$ −0.509351 + 0.882222i −0.0298587 + 0.0517168i
$$292$$ 0 0
$$293$$ 11.3710 0.664299 0.332150 0.943227i $$-0.392226\pi$$
0.332150 + 0.943227i $$0.392226\pi$$
$$294$$ 0 0
$$295$$ −1.79014 −0.104226
$$296$$ 0 0
$$297$$ −0.571021 + 0.989037i −0.0331340 + 0.0573897i
$$298$$ 0 0
$$299$$ 19.0855 + 33.0571i 1.10375 + 1.91174i
$$300$$ 0 0
$$301$$ 3.62433 20.4031i 0.208903 1.17602i
$$302$$ 0 0
$$303$$ −5.94253 10.2928i −0.341389 0.591304i
$$304$$ 0 0
$$305$$ 7.58459 13.1369i 0.434292 0.752216i
$$306$$ 0 0
$$307$$ −3.87636 −0.221236 −0.110618 0.993863i $$-0.535283\pi$$
−0.110618 + 0.993863i $$0.535283\pi$$
$$308$$ 0 0
$$309$$ −12.5221 −0.712356
$$310$$ 0 0
$$311$$ −11.0281 + 19.1012i −0.625344 + 1.08313i 0.363130 + 0.931738i $$0.381708\pi$$
−0.988474 + 0.151389i $$0.951625\pi$$
$$312$$ 0 0
$$313$$ 15.5322 + 26.9025i 0.877930 + 1.52062i 0.853609 + 0.520914i $$0.174409\pi$$
0.0243207 + 0.999704i $$0.492258\pi$$
$$314$$ 0 0
$$315$$ −7.30853 6.14841i −0.411789 0.346424i
$$316$$ 0 0
$$317$$ −16.6431 28.8268i −0.934772 1.61907i −0.775040 0.631912i $$-0.782271\pi$$
−0.159731 0.987161i $$-0.551063\pi$$
$$318$$ 0 0
$$319$$ 1.07965 1.87000i 0.0604485 0.104700i
$$320$$ 0 0
$$321$$ 3.43796 0.191888
$$322$$ 0 0
$$323$$ 5.76637 0.320850
$$324$$ 0 0
$$325$$ −6.42441 + 11.1274i −0.356362 + 0.617237i
$$326$$ 0 0
$$327$$ 0.307560 + 0.532709i 0.0170081 + 0.0294589i
$$328$$ 0 0
$$329$$ 3.92795 1.42401i 0.216555 0.0785084i
$$330$$ 0 0
$$331$$ −4.18690 7.25192i −0.230133 0.398601i 0.727714 0.685880i $$-0.240583\pi$$
−0.957847 + 0.287279i $$0.907249\pi$$
$$332$$ 0 0
$$333$$ −10.6258 + 18.4045i −0.582292 + 1.00856i
$$334$$ 0 0
$$335$$ −13.3646 −0.730184
$$336$$ 0 0
$$337$$ −1.87908 −0.102360 −0.0511799 0.998689i $$-0.516298\pi$$
−0.0511799 + 0.998689i $$0.516298\pi$$
$$338$$ 0 0
$$339$$ −4.62900 + 8.01767i −0.251413 + 0.435460i
$$340$$ 0 0
$$341$$ −0.718588 1.24463i −0.0389137 0.0674005i
$$342$$ 0 0
$$343$$ 9.32115 16.0036i 0.503295 0.864115i
$$344$$ 0 0
$$345$$ 5.02520 + 8.70390i 0.270548 + 0.468602i
$$346$$ 0 0
$$347$$ 3.06863 5.31502i 0.164733 0.285325i −0.771828 0.635832i $$-0.780657\pi$$
0.936560 + 0.350506i $$0.113991\pi$$
$$348$$ 0 0
$$349$$ −18.9103 −1.01225 −0.506123 0.862461i $$-0.668922\pi$$
−0.506123 + 0.862461i $$0.668922\pi$$
$$350$$ 0 0
$$351$$ 27.2025 1.45196
$$352$$ 0 0
$$353$$ 4.97227 8.61222i 0.264647 0.458382i −0.702824 0.711364i $$-0.748078\pi$$
0.967471 + 0.252982i $$0.0814112\pi$$
$$354$$ 0 0
$$355$$ 1.02378 + 1.77323i 0.0543364 + 0.0941134i
$$356$$ 0 0
$$357$$ 13.0850 4.74374i 0.692531 0.251066i
$$358$$ 0 0
$$359$$ −9.19502 15.9262i −0.485295 0.840555i 0.514562 0.857453i $$-0.327954\pi$$
−0.999857 + 0.0168977i $$0.994621\pi$$
$$360$$ 0 0
$$361$$ −0.500000 + 0.866025i −0.0263158 + 0.0455803i
$$362$$ 0 0
$$363$$ −9.98172 −0.523905
$$364$$ 0 0
$$365$$ −1.33451 −0.0698513
$$366$$ 0 0
$$367$$ 7.10761 12.3107i 0.371014 0.642616i −0.618707 0.785621i $$-0.712343\pi$$
0.989722 + 0.143006i $$0.0456767\pi$$
$$368$$ 0 0
$$369$$ −2.16772 3.75459i −0.112847 0.195456i
$$370$$ 0 0
$$371$$ −13.1224 11.0394i −0.681280 0.573137i
$$372$$ 0 0
$$373$$ −12.8008 22.1716i −0.662800 1.14800i −0.979877 0.199604i $$-0.936034\pi$$
0.317076 0.948400i $$-0.397299\pi$$
$$374$$ 0 0
$$375$$ −5.48961 + 9.50829i −0.283482 + 0.491006i
$$376$$ 0 0
$$377$$ −51.4326 −2.64891
$$378$$ 0 0
$$379$$ −8.51685 −0.437481 −0.218741 0.975783i $$-0.570195\pi$$
−0.218741 + 0.975783i $$0.570195\pi$$
$$380$$ 0 0
$$381$$ −8.48316 + 14.6933i −0.434606 + 0.752759i
$$382$$ 0 0
$$383$$ 5.00847 + 8.67492i 0.255921 + 0.443268i 0.965145 0.261715i $$-0.0842881\pi$$
−0.709224 + 0.704983i $$0.750955\pi$$
$$384$$ 0 0
$$385$$ −0.186668 + 1.05084i −0.00951348 + 0.0535559i
$$386$$ 0 0
$$387$$ −8.48918 14.7037i −0.431529 0.747431i
$$388$$ 0 0
$$389$$ 10.1401 17.5631i 0.514123 0.890487i −0.485743 0.874102i $$-0.661451\pi$$
0.999866 0.0163851i $$-0.00521577\pi$$
$$390$$ 0 0
$$391$$ 38.1472 1.92918
$$392$$ 0 0
$$393$$ 7.27229 0.366838
$$394$$ 0 0
$$395$$ −6.31310 + 10.9346i −0.317647 + 0.550180i
$$396$$ 0 0
$$397$$ 13.4137 + 23.2333i 0.673216 + 1.16604i 0.976987 + 0.213300i $$0.0684211\pi$$
−0.303770 + 0.952745i $$0.598246\pi$$
$$398$$ 0 0
$$399$$ −0.422154 + 2.37650i −0.0211341 + 0.118974i
$$400$$ 0 0
$$401$$ 6.92911 + 12.0016i 0.346023 + 0.599330i 0.985539 0.169448i $$-0.0541985\pi$$
−0.639516 + 0.768778i $$0.720865\pi$$
$$402$$ 0 0
$$403$$ −17.1162 + 29.6461i −0.852619 + 1.47678i
$$404$$ 0 0
$$405$$ −3.66719 −0.182224
$$406$$ 0 0
$$407$$ 2.37486 0.117717
$$408$$ 0 0
$$409$$ 3.09715 5.36442i 0.153144 0.265253i −0.779238 0.626729i $$-0.784393\pi$$
0.932382 + 0.361475i $$0.117727\pi$$
$$410$$ 0 0
$$411$$ 0.145403 + 0.251846i 0.00717222 + 0.0124226i
$$412$$ 0 0
$$413$$ −2.17640 1.83093i −0.107094 0.0900942i
$$414$$ 0 0
$$415$$ −7.42126 12.8540i −0.364295 0.630978i
$$416$$ 0 0
$$417$$ 2.64618 4.58333i 0.129584 0.224446i
$$418$$ 0 0
$$419$$ 14.4938 0.708068 0.354034 0.935233i $$-0.384810\pi$$
0.354034 + 0.935233i $$0.384810\pi$$
$$420$$ 0 0
$$421$$ 29.8753 1.45603 0.728016 0.685560i $$-0.240443\pi$$
0.728016 + 0.685560i $$0.240443\pi$$
$$422$$ 0 0
$$423$$ 1.71161 2.96459i 0.0832211 0.144143i
$$424$$ 0 0
$$425$$ 6.42038 + 11.1204i 0.311434 + 0.539420i
$$426$$ 0 0
$$427$$ 22.6574 8.21404i 1.09647 0.397505i
$$428$$ 0 0
$$429$$ −0.637570 1.10430i −0.0307822 0.0533163i
$$430$$ 0 0
$$431$$ −10.9304 + 18.9321i −0.526501 + 0.911926i 0.473023 + 0.881050i $$0.343163\pi$$
−0.999523 + 0.0308754i $$0.990170\pi$$
$$432$$ 0 0
$$433$$ −11.1847 −0.537500 −0.268750 0.963210i $$-0.586611\pi$$
−0.268750 + 0.963210i $$0.586611\pi$$
$$434$$ 0 0
$$435$$ −13.5421 −0.649296
$$436$$ 0 0
$$437$$ −3.30773 + 5.72915i −0.158230 + 0.274062i
$$438$$ 0 0
$$439$$ 7.70936 + 13.3530i 0.367948 + 0.637304i 0.989245 0.146271i $$-0.0467272\pi$$
−0.621297 + 0.783575i $$0.713394\pi$$
$$440$$ 0 0
$$441$$ −2.59699 14.9501i −0.123666 0.711911i
$$442$$ 0 0
$$443$$ 0.469742 + 0.813616i 0.0223181 + 0.0386561i 0.876969 0.480547i $$-0.159562\pi$$
−0.854651 + 0.519203i $$0.826229\pi$$
$$444$$ 0 0
$$445$$ −10.9198 + 18.9136i −0.517647 + 0.896591i
$$446$$ 0 0
$$447$$ 12.4711 0.589865
$$448$$ 0 0
$$449$$ −28.2058 −1.33112 −0.665558 0.746346i $$-0.731806\pi$$
−0.665558 + 0.746346i $$0.731806\pi$$
$$450$$ 0 0
$$451$$ −0.242241 + 0.419573i −0.0114067 + 0.0197569i
$$452$$ 0 0
$$453$$ −5.03050 8.71308i −0.236353 0.409376i
$$454$$ 0 0
$$455$$ 23.9000 8.66454i 1.12045 0.406200i
$$456$$ 0 0
$$457$$ −0.388913 0.673617i −0.0181926 0.0315105i 0.856786 0.515672i $$-0.172458\pi$$
−0.874978 + 0.484162i $$0.839125\pi$$
$$458$$ 0 0
$$459$$ 13.5927 23.5433i 0.634455 1.09891i
$$460$$ 0 0
$$461$$ −19.3614 −0.901751 −0.450875 0.892587i $$-0.648888\pi$$
−0.450875 + 0.892587i $$0.648888\pi$$
$$462$$ 0 0
$$463$$ 34.5688 1.60655 0.803275 0.595608i $$-0.203089\pi$$
0.803275 + 0.595608i $$0.203089\pi$$
$$464$$ 0 0
$$465$$ −4.50667 + 7.80579i −0.208992 + 0.361985i
$$466$$ 0 0
$$467$$ 14.9272 + 25.8547i 0.690750 + 1.19641i 0.971593 + 0.236660i $$0.0760527\pi$$
−0.280843 + 0.959754i $$0.590614\pi$$
$$468$$ 0 0
$$469$$ −16.2483 13.6691i −0.750275 0.631180i
$$470$$ 0 0
$$471$$ −8.14525 14.1080i −0.375313 0.650062i
$$472$$ 0 0
$$473$$ −0.948660 + 1.64313i −0.0436194 + 0.0755511i
$$474$$ 0 0
$$475$$ −2.22684 −0.102174
$$476$$ 0 0
$$477$$ −14.0500 −0.643303
$$478$$ 0 0
$$479$$ 13.9432 24.1504i 0.637082 1.10346i −0.348987 0.937127i $$-0.613474\pi$$
0.986070 0.166332i $$-0.0531923\pi$$
$$480$$ 0 0
$$481$$ −28.2836 48.9887i −1.28962 2.23369i
$$482$$ 0 0
$$483$$ −2.79274 + 15.7217i −0.127074 + 0.715360i
$$484$$ 0 0
$$485$$ 0.929757 + 1.61039i 0.0422181 + 0.0731238i
$$486$$ 0 0
$$487$$ −5.81119 + 10.0653i −0.263330 + 0.456101i −0.967125 0.254302i $$-0.918154\pi$$
0.703795 + 0.710404i $$0.251488\pi$$
$$488$$ 0 0
$$489$$ 10.2150 0.461938
$$490$$ 0 0
$$491$$ −25.4037 −1.14645 −0.573225 0.819398i $$-0.694308\pi$$
−0.573225 + 0.819398i $$0.694308\pi$$
$$492$$ 0 0
$$493$$ −25.7002 + 44.5140i −1.15748 + 2.00481i
$$494$$ 0 0
$$495$$ 0.437228 + 0.757300i 0.0196519 + 0.0340381i
$$496$$ 0 0
$$497$$ −0.568961 + 3.20295i −0.0255214 + 0.143672i
$$498$$ 0 0
$$499$$ −1.33920 2.31956i −0.0599509 0.103838i 0.834492 0.551020i $$-0.185761\pi$$
−0.894443 + 0.447182i $$0.852428\pi$$
$$500$$ 0 0
$$501$$ −0.660099 + 1.14333i −0.0294911 + 0.0510800i
$$502$$ 0 0
$$503$$ −37.0893 −1.65373 −0.826866 0.562399i $$-0.809879\pi$$
−0.826866 + 0.562399i $$0.809879\pi$$
$$504$$ 0 0
$$505$$ −21.6947 −0.965401
$$506$$ 0 0
$$507$$ −9.25651 + 16.0327i −0.411096 + 0.712039i
$$508$$ 0 0
$$509$$ −7.41214 12.8382i −0.328537 0.569043i 0.653685 0.756767i $$-0.273222\pi$$
−0.982222 + 0.187724i $$0.939889\pi$$
$$510$$ 0 0
$$511$$ −1.62246 1.36492i −0.0717732 0.0603803i
$$512$$ 0 0
$$513$$ 2.35724 + 4.08287i 0.104075 + 0.180263i
$$514$$ 0 0
$$515$$ −11.4287 + 19.7951i −0.503610 + 0.872279i
$$516$$ 0 0
$$517$$ −0.382542 −0.0168242
$$518$$ 0 0
$$519$$ 10.8509 0.476303
$$520$$ 0 0
$$521$$ 5.24608 9.08648i 0.229835 0.398086i −0.727924 0.685658i $$-0.759515\pi$$
0.957759 + 0.287572i $$0.0928480\pi$$
$$522$$ 0 0
$$523$$ 7.73787 + 13.4024i 0.338353 + 0.586045i 0.984123 0.177487i $$-0.0567968\pi$$
−0.645770 + 0.763532i $$0.723463\pi$$
$$524$$ 0 0
$$525$$ −5.05311 + 1.83192i −0.220536 + 0.0799516i
$$526$$ 0 0
$$527$$ 17.1055 + 29.6275i 0.745126 + 1.29060i
$$528$$ 0 0
$$529$$ −10.3821 + 17.9823i −0.451396 + 0.781840i
$$530$$ 0 0
$$531$$ −2.33024 −0.101124
$$532$$ 0 0
$$533$$ 11.5400 0.499852
$$534$$ 0 0
$$535$$ 3.13778 5.43480i 0.135658 0.234967i
$$536$$ 0 0
$$537$$ −11.4825 19.8883i −0.495507 0.858243i
$$538$$ 0 0
$$539$$ −1.30173 + 1.08666i −0.0560697 + 0.0468059i
$$540$$ 0 0
$$541$$ 9.39634 + 16.2749i 0.403980 + 0.699715i 0.994202 0.107527i $$-0.0342931\pi$$
−0.590222 + 0.807241i $$0.700960\pi$$
$$542$$ 0 0
$$543$$ −8.54865 + 14.8067i −0.366858 + 0.635416i
$$544$$ 0 0
$$545$$ 1.12282 0.0480965
$$546$$ 0 0
$$547$$ −0.809060 −0.0345929 −0.0172965 0.999850i $$-0.505506\pi$$
−0.0172965 + 0.999850i $$0.505506\pi$$
$$548$$ 0 0
$$549$$ 9.87294 17.1004i 0.421367 0.729829i
$$550$$ 0 0
$$551$$ −4.45691 7.71959i −0.189871 0.328866i
$$552$$ 0 0
$$553$$ −18.8591 + 6.83703i −0.801969 + 0.290740i
$$554$$ 0 0
$$555$$ −7.44705 12.8987i −0.316109 0.547518i
$$556$$ 0 0
$$557$$ 8.72680 15.1153i 0.369767 0.640455i −0.619762 0.784790i $$-0.712771\pi$$
0.989529 + 0.144335i $$0.0461043\pi$$
$$558$$ 0 0
$$559$$ 45.1927 1.91145
$$560$$ 0 0
$$561$$ −1.27434 −0.0538027
$$562$$ 0 0
$$563$$ 1.84187 3.19022i 0.0776257 0.134452i −0.824599 0.565717i $$-0.808599\pi$$
0.902225 + 0.431265i $$0.141933\pi$$
$$564$$ 0 0
$$565$$ 8.44967 + 14.6353i 0.355480 + 0.615710i
$$566$$ 0 0
$$567$$ −4.45846 3.75075i −0.187238 0.157517i
$$568$$ 0 0
$$569$$ 4.56612 + 7.90875i 0.191422 + 0.331552i 0.945722 0.324978i $$-0.105357\pi$$
−0.754300 + 0.656530i $$0.772024\pi$$
$$570$$ 0 0
$$571$$ −10.5623 + 18.2945i −0.442020 + 0.765601i −0.997839 0.0657023i $$-0.979071\pi$$
0.555820 + 0.831303i $$0.312405\pi$$
$$572$$ 0 0
$$573$$ 0.324779 0.0135678
$$574$$ 0 0
$$575$$ −14.7315 −0.614347
$$576$$ 0 0
$$577$$ −2.62137 + 4.54035i −0.109129 + 0.189017i −0.915418 0.402505i $$-0.868140\pi$$
0.806289 + 0.591522i $$0.201473\pi$$
$$578$$ 0 0
$$579$$ −7.79957 13.5093i −0.324139 0.561425i
$$580$$ 0 0
$$581$$ 4.12434 23.2179i 0.171106 0.963240i
$$582$$ 0 0
$$583$$ 0.785037 + 1.35972i 0.0325129 + 0.0563140i
$$584$$ 0 0
$$585$$ 10.4144 18.0383i 0.430583 0.745792i
$$586$$ 0 0
$$587$$ −3.26045 −0.134573 −0.0672865 0.997734i $$-0.521434\pi$$
−0.0672865 + 0.997734i $$0.521434\pi$$
$$588$$ 0 0
$$589$$ −5.93284 −0.244458
$$590$$ 0 0
$$591$$ −5.97956 + 10.3569i −0.245966 + 0.426026i
$$592$$ 0 0
$$593$$ −9.96152 17.2539i −0.409070 0.708531i 0.585715 0.810517i $$-0.300814\pi$$
−0.994786 + 0.101986i $$0.967480\pi$$
$$594$$ 0 0
$$595$$ 4.44350 25.0146i 0.182166 1.02550i
$$596$$ 0 0
$$597$$ −2.17572 3.76846i −0.0890464 0.154233i
$$598$$ 0 0
$$599$$ −22.2325 + 38.5077i −0.908394 + 1.57338i −0.0920976 + 0.995750i $$0.529357\pi$$
−0.816296 + 0.577634i $$0.803976\pi$$
$$600$$ 0 0
$$601$$ 22.3392 0.911233 0.455617 0.890176i $$-0.349419\pi$$
0.455617 + 0.890176i $$0.349419\pi$$
$$602$$ 0 0
$$603$$ −17.3968 −0.708453
$$604$$ 0 0
$$605$$ −9.11019 + 15.7793i −0.370382 + 0.641520i
$$606$$ 0 0
$$607$$ −17.2044 29.7989i −0.698306 1.20950i −0.969053 0.246851i $$-0.920604\pi$$
0.270747 0.962651i $$-0.412729\pi$$
$$608$$ 0 0
$$609$$ −16.4641 13.8507i −0.667161 0.561259i
$$610$$ 0 0
$$611$$ 4.55592 + 7.89109i 0.184313 + 0.319239i
$$612$$ 0 0
$$613$$ 12.1470 21.0392i 0.490613 0.849766i −0.509329 0.860572i $$-0.670106\pi$$
0.999942 + 0.0108056i $$0.00343961\pi$$
$$614$$ 0 0
$$615$$ 3.03846 0.122523
$$616$$ 0 0
$$617$$ −17.0255 −0.685422 −0.342711 0.939441i $$-0.611345\pi$$
−0.342711 + 0.939441i $$0.611345\pi$$
$$618$$ 0 0
$$619$$ −14.3397 + 24.8372i −0.576363 + 0.998290i 0.419529 + 0.907742i $$0.362195\pi$$
−0.995892 + 0.0905479i $$0.971138\pi$$
$$620$$ 0 0
$$621$$ 15.5942 + 27.0100i 0.625775 + 1.08387i
$$622$$ 0 0
$$623$$ −32.6205 + 11.8260i −1.30691 + 0.473800i
$$624$$ 0 0
$$625$$ 4.45351 + 7.71371i 0.178141 + 0.308548i
$$626$$ 0 0
$$627$$ 0.110498 0.191388i 0.00441285 0.00764328i
$$628$$ 0 0
$$629$$ −56.5318 −2.25407
$$630$$ 0 0
$$631$$ −29.4675 −1.17308 −0.586542 0.809919i $$-0.699511\pi$$
−0.586542 + 0.809919i $$0.699511\pi$$
$$632$$ 0 0
$$633$$ −10.0554 + 17.4165i −0.399668 + 0.692244i
$$634$$ 0 0
$$635$$ 15.4849 + 26.8207i 0.614501 + 1.06435i
$$636$$ 0 0
$$637$$ 37.9189 + 13.9105i 1.50240 + 0.551154i
$$638$$ 0 0
$$639$$ 1.33266 + 2.30824i 0.0527193 + 0.0913124i
$$640$$ 0 0
$$641$$ 8.06837 13.9748i 0.318681 0.551972i −0.661532 0.749917i $$-0.730093\pi$$
0.980213 + 0.197945i $$0.0634266\pi$$
$$642$$ 0 0
$$643$$ 22.8353 0.900535 0.450267 0.892894i $$-0.351329\pi$$
0.450267 + 0.892894i $$0.351329\pi$$
$$644$$ 0 0
$$645$$ 11.8992 0.468530
$$646$$ 0 0
$$647$$ −10.3699 + 17.9613i −0.407685 + 0.706131i −0.994630 0.103496i $$-0.966997\pi$$
0.586945 + 0.809627i $$0.300330\pi$$
$$648$$ 0 0
$$649$$ 0.130202 + 0.225516i 0.00511086 + 0.00885227i
$$650$$ 0 0
$$651$$ −13.4627 + 4.88069i −0.527646 + 0.191289i
$$652$$ 0 0
$$653$$ 9.68834 + 16.7807i 0.379134 + 0.656679i 0.990936 0.134331i $$-0.0428886\pi$$
−0.611802 + 0.791011i $$0.709555\pi$$
$$654$$ 0 0
$$655$$ 6.63732 11.4962i 0.259342 0.449193i
$$656$$ 0 0
$$657$$ −1.73714 −0.0677724
$$658$$ 0 0
$$659$$ 7.33347 0.285672 0.142836 0.989746i $$-0.454378\pi$$
0.142836 + 0.989746i $$0.454378\pi$$
$$660$$ 0 0
$$661$$ 18.8535 32.6552i 0.733315 1.27014i −0.222144 0.975014i $$-0.571306\pi$$
0.955459 0.295124i $$-0.0953611\pi$$
$$662$$ 0 0
$$663$$ 15.1769 + 26.2872i 0.589422 + 1.02091i
$$664$$ 0 0
$$665$$ 3.37153 + 2.83636i 0.130742 + 0.109989i
$$666$$ 0 0
$$667$$ −29.4845 51.0686i −1.14164 1.97738i
$$668$$ 0 0
$$669$$ −8.93303 + 15.4725i −0.345371 + 0.598200i
$$670$$ 0 0
$$671$$ −2.20659 −0.0851844
$$672$$ 0 0
$$673$$ 48.4005 1.86570 0.932851 0.360263i $$-0.117313\pi$$
0.932851 + 0.360263i $$0.117313\pi$$
$$674$$ 0 0
$$675$$ −5.24919 + 9.09187i −0.202042 + 0.349946i
$$676$$ 0 0
$$677$$ −7.93290 13.7402i −0.304886 0.528078i 0.672350 0.740233i $$-0.265285\pi$$
−0.977236 + 0.212155i $$0.931952\pi$$
$$678$$ 0 0
$$679$$ −0.516709 + 2.90880i −0.0198295 + 0.111630i
$$680$$ 0 0
$$681$$ 2.64032 + 4.57316i 0.101177 + 0.175244i
$$682$$ 0 0
$$683$$ −8.63354 + 14.9537i −0.330353 + 0.572189i −0.982581 0.185834i $$-0.940501\pi$$
0.652228 + 0.758023i $$0.273835\pi$$
$$684$$ 0 0
$$685$$ 0.530831 0.0202820
$$686$$ 0 0
$$687$$ −17.4316 −0.665059
$$688$$ 0 0
$$689$$ 18.6990 32.3876i 0.712374 1.23387i
$$690$$ 0 0
$$691$$ 24.6306 + 42.6614i 0.936992 + 1.62292i 0.771043 + 0.636783i $$0.219735\pi$$
0.165949 + 0.986134i $$0.446931\pi$$
$$692$$ 0 0
$$693$$ −0.242988 + 1.36789i −0.00923034 + 0.0519620i
$$694$$ 0 0
$$695$$ −4.83028 8.36629i −0.183223 0.317351i
$$696$$ 0 0
$$697$$ 5.76637 9.98765i 0.218417 0.378309i
$$698$$ 0 0
$$699$$ −5.63001 −0.212947
$$700$$ 0 0
$$701$$ 10.1609 0.383770 0.191885 0.981417i $$-0.438540\pi$$
0.191885 + 0.981417i $$0.438540\pi$$
$$702$$ 0 0
$$703$$ 4.90185 8.49026i 0.184877 0.320216i
$$704$$ 0 0
$$705$$ 1.19957 + 2.07771i 0.0451784 + 0.0782512i
$$706$$ 0 0
$$707$$ −26.3758 22.1890i −0.991963 0.834504i
$$708$$ 0 0
$$709$$ −3.86510 6.69454i −0.145157 0.251419i 0.784275 0.620414i $$-0.213035\pi$$
−0.929431 + 0.368995i $$0.879702\pi$$
$$710$$ 0 0
$$711$$ −8.21783 + 14.2337i −0.308193 + 0.533806i
$$712$$ 0 0
$$713$$ −39.2484 −1.46986
$$714$$ 0 0
$$715$$ −2.32761 −0.0870477
$$716$$ 0 0
$$717$$ −11.9248 + 20.6544i −0.445341 + 0.771353i
$$718$$ 0 0
$$719$$ −12.6604 21.9284i −0.472152 0.817791i 0.527340 0.849654i $$-0.323189\pi$$
−0.999492 + 0.0318632i $$0.989856\pi$$
$$720$$ 0 0
$$721$$ −34.1409 + 12.3772i −1.27148 + 0.460952i
$$722$$ 0 0
$$723$$ 8.93667 + 15.4788i 0.332358 + 0.575662i
$$724$$ 0 0
$$725$$ 9.92480 17.1903i 0.368598 0.638430i
$$726$$ 0 0
$$727$$ 24.5601 0.910884 0.455442 0.890266i $$-0.349481\pi$$
0.455442 + 0.890266i $$0.349481\pi$$
$$728$$ 0 0
$$729$$ 8.12941 0.301089
$$730$$ 0 0
$$731$$ 22.5822 39.1135i 0.835232 1.44666i
$$732$$ 0 0
$$733$$ 13.6516 + 23.6453i 0.504235 + 0.873361i 0.999988 + 0.00489700i $$0.00155877\pi$$
−0.495753 + 0.868464i $$0.665108\pi$$
$$734$$ 0 0
$$735$$ 9.98400 + 3.66261i 0.368265 + 0.135098i
$$736$$ 0 0
$$737$$ 0.972041 + 1.68362i 0.0358056 + 0.0620171i
$$738$$ 0 0
$$739$$ −24.0188 + 41.6017i −0.883544 + 1.53034i −0.0361706 + 0.999346i $$0.511516\pi$$
−0.847373 + 0.530998i $$0.821817\pi$$
$$740$$ 0 0
$$741$$ −5.26394 −0.193376
$$742$$ 0 0
$$743$$ 10.8539 0.398190 0.199095 0.979980i $$-0.436200\pi$$
0.199095 + 0.979980i $$0.436200\pi$$
$$744$$ 0 0
$$745$$ 11.3823 19.7146i 0.417014 0.722289i
$$746$$ 0 0
$$747$$ −9.66033 16.7322i −0.353453 0.612199i
$$748$$ 0 0
$$749$$ 9.37347 3.39819i 0.342499 0.124167i
$$750$$ 0 0
$$751$$ −8.95718 15.5143i −0.326852 0.566125i 0.655033 0.755600i $$-0.272655\pi$$
−0.981885 + 0.189475i $$0.939321\pi$$
$$752$$ 0 0
$$753$$ 2.91515 5.04919i 0.106234 0.184003i
$$754$$ 0 0
$$755$$ −18.3651 −0.668374
$$756$$ 0 0
$$757$$ 19.7888 0.719235 0.359617 0.933100i $$-0.382907\pi$$
0.359617 + 0.933100i $$0.382907\pi$$
$$758$$ 0 0
$$759$$ 0.730992 1.26612i 0.0265333 0.0459571i
$$760$$ 0 0
$$761$$ −25.7301 44.5659i −0.932717 1.61551i −0.778655 0.627452i $$-0.784098\pi$$
−0.154062 0.988061i $$-0.549235\pi$$
$$762$$ 0 0
$$763$$ 1.36510 + 1.14841i 0.0494198 + 0.0415752i
$$764$$ 0 0
$$765$$ −10.4079 18.0270i −0.376298 0.651768i
$$766$$ 0 0
$$767$$ 3.10130 5.37161i 0.111981 0.193958i
$$768$$ 0 0
$$769$$ −26.2468 −0.946485 −0.473243 0.880932i $$-0.656917\pi$$
−0.473243 + 0.880932i $$0.656917\pi$$
$$770$$ 0 0
$$771$$ 19.9558 0.718689
$$772$$ 0 0
$$773$$ −3.02611 + 5.24138i −0.108842 + 0.188519i −0.915301 0.402770i $$-0.868048\pi$$
0.806460 + 0.591289i $$0.201381\pi$$
$$774$$ 0 0
$$775$$ −6.60573 11.4415i −0.237285 0.410989i
$$776$$ 0 0
$$777$$ 4.13867 23.2986i 0.148474 0.835831i
$$778$$ 0 0
$$779$$ 1.00000 + 1.73205i 0.0358287 + 0.0620572i
$$780$$ 0 0
$$781$$ 0.148924 0.257944i 0.00532892 0.00922996i
$$782$$ 0 0
$$783$$ −42.0241 −1.50182
$$784$$ 0 0
$$785$$ −29.7363 −1.06133
$$786$$ 0 0
$$787$$ 6.22879 10.7886i 0.222032 0.384571i −0.733393 0.679805i $$-0.762064\pi$$
0.955425 + 0.295234i $$0.0953976\pi$$
$$788$$ 0 0
$$789$$ 13.5584 + 23.4838i 0.482691 + 0.836046i
$$790$$ 0 0
$$791$$ −4.69587 + 26.4353i −0.166966 + 0.939932i
$$792$$ 0 0
$$793$$ 26.2796 + 45.5176i 0.933217 + 1.61638i
$$794$$ 0 0
$$795$$ 4.92341