# Properties

 Label 675.2.e.b.226.2 Level $675$ Weight $2$ Character 675.226 Analytic conductor $5.390$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$675 = 3^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 675.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.38990213644$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.954288.1 Defining polynomial: $$x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27$$ x^6 - x^5 - 2*x^4 + 3*x^3 - 6*x^2 - 9*x + 27 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 45) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 226.2 Root $$-1.62241 - 0.606458i$$ of defining polynomial Character $$\chi$$ $$=$$ 675.226 Dual form 675.2.e.b.451.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.285997 - 0.495361i) q^{2} +(0.836412 - 1.44871i) q^{4} +(0.714003 + 1.23669i) q^{7} -2.10083 q^{8} +O(q^{10})$$ $$q+(-0.285997 - 0.495361i) q^{2} +(0.836412 - 1.44871i) q^{4} +(0.714003 + 1.23669i) q^{7} -2.10083 q^{8} +(1.33641 + 2.31473i) q^{11} +(2.33641 - 4.04678i) q^{13} +(0.408405 - 0.707378i) q^{14} +(-1.07199 - 1.85675i) q^{16} +2.67282 q^{17} +4.67282 q^{19} +(0.764419 - 1.32401i) q^{22} +(2.95882 - 5.12483i) q^{23} -2.67282 q^{26} +2.38880 q^{28} +(-4.74482 - 8.21826i) q^{29} +(-3.48040 + 6.02823i) q^{31} +(-2.71400 + 4.70079i) q^{32} +(-0.764419 - 1.32401i) q^{34} +1.81681 q^{37} +(-1.33641 - 2.31473i) q^{38} +(-0.735581 + 1.27406i) q^{41} +(0.235581 + 0.408039i) q^{43} +4.47116 q^{44} -3.38485 q^{46} +(-3.47842 - 6.02480i) q^{47} +(2.48040 - 4.29618i) q^{49} +(-3.90841 - 6.76956i) q^{52} -1.14399 q^{53} +(-1.50000 - 2.59808i) q^{56} +(-2.71400 + 4.70079i) q^{58} +(-0.571993 + 0.990721i) q^{59} +(1.26442 + 2.19004i) q^{61} +3.98153 q^{62} -1.18319 q^{64} +(-3.29523 + 5.70751i) q^{67} +(2.23558 - 3.87214i) q^{68} +12.8745 q^{71} +1.71203 q^{73} +(-0.519602 - 0.899976i) q^{74} +(3.90841 - 6.76956i) q^{76} +(-1.90841 + 3.30545i) q^{77} +(0.143987 + 0.249392i) q^{79} +0.841495 q^{82} +(2.14201 + 3.71007i) q^{83} +(0.134751 - 0.233396i) q^{86} +(-2.80757 - 4.86286i) q^{88} +3.00000 q^{89} +6.67282 q^{91} +(-4.94958 - 8.57293i) q^{92} +(-1.98963 + 3.44615i) q^{94} +(3.91764 + 6.78555i) q^{97} -2.83754 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - q^{2} - 5 q^{4} + 5 q^{7} + 6 q^{8}+O(q^{10})$$ 6 * q - q^2 - 5 * q^4 + 5 * q^7 + 6 * q^8 $$6 q - q^{2} - 5 q^{4} + 5 q^{7} + 6 q^{8} - 2 q^{11} + 4 q^{13} - 9 q^{14} - 5 q^{16} - 4 q^{17} + 8 q^{19} - 4 q^{22} - 3 q^{23} + 4 q^{26} - 10 q^{28} - 7 q^{29} - 8 q^{31} - 17 q^{32} + 4 q^{34} - 12 q^{37} + 2 q^{38} - 13 q^{41} + 10 q^{43} + 44 q^{44} - 6 q^{46} - 13 q^{47} + 2 q^{49} - 12 q^{52} - 4 q^{53} - 9 q^{56} - 17 q^{58} - 2 q^{59} - q^{61} + 84 q^{62} - 30 q^{64} + 11 q^{67} + 22 q^{68} + 20 q^{71} + 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} + 58 q^{82} + 15 q^{83} + 28 q^{86} - 24 q^{88} + 18 q^{89} + 20 q^{91} - 39 q^{92} + 31 q^{94} - 18 q^{97} - 80 q^{98}+O(q^{100})$$ 6 * q - q^2 - 5 * q^4 + 5 * q^7 + 6 * q^8 - 2 * q^11 + 4 * q^13 - 9 * q^14 - 5 * q^16 - 4 * q^17 + 8 * q^19 - 4 * q^22 - 3 * q^23 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 8 * q^31 - 17 * q^32 + 4 * q^34 - 12 * q^37 + 2 * q^38 - 13 * q^41 + 10 * q^43 + 44 * q^44 - 6 * q^46 - 13 * q^47 + 2 * q^49 - 12 * q^52 - 4 * q^53 - 9 * q^56 - 17 * q^58 - 2 * q^59 - q^61 + 84 * q^62 - 30 * q^64 + 11 * q^67 + 22 * q^68 + 20 * q^71 + 16 * q^73 - 16 * q^74 + 12 * q^76 - 2 * q^79 + 58 * q^82 + 15 * q^83 + 28 * q^86 - 24 * q^88 + 18 * q^89 + 20 * q^91 - 39 * q^92 + 31 * q^94 - 18 * q^97 - 80 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$352$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.285997 0.495361i −0.202230 0.350273i 0.747017 0.664805i $$-0.231486\pi$$
−0.949247 + 0.314533i $$0.898152\pi$$
$$3$$ 0 0
$$4$$ 0.836412 1.44871i 0.418206 0.724354i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0.714003 + 1.23669i 0.269868 + 0.467425i 0.968828 0.247736i $$-0.0796866\pi$$
−0.698960 + 0.715161i $$0.746353\pi$$
$$8$$ −2.10083 −0.742756
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.33641 + 2.31473i 0.402943 + 0.697918i 0.994080 0.108653i $$-0.0346538\pi$$
−0.591136 + 0.806572i $$0.701321\pi$$
$$12$$ 0 0
$$13$$ 2.33641 4.04678i 0.648004 1.12238i −0.335595 0.942006i $$-0.608937\pi$$
0.983599 0.180370i $$-0.0577294\pi$$
$$14$$ 0.408405 0.707378i 0.109151 0.189055i
$$15$$ 0 0
$$16$$ −1.07199 1.85675i −0.267998 0.464187i
$$17$$ 2.67282 0.648255 0.324127 0.946013i $$-0.394929\pi$$
0.324127 + 0.946013i $$0.394929\pi$$
$$18$$ 0 0
$$19$$ 4.67282 1.07202 0.536010 0.844212i $$-0.319931\pi$$
0.536010 + 0.844212i $$0.319931\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0.764419 1.32401i 0.162975 0.282280i
$$23$$ 2.95882 5.12483i 0.616957 1.06860i −0.373081 0.927799i $$-0.621699\pi$$
0.990038 0.140802i $$-0.0449680\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −2.67282 −0.524184
$$27$$ 0 0
$$28$$ 2.38880 0.451441
$$29$$ −4.74482 8.21826i −0.881090 1.52609i −0.850130 0.526573i $$-0.823477\pi$$
−0.0309603 0.999521i $$-0.509857\pi$$
$$30$$ 0 0
$$31$$ −3.48040 + 6.02823i −0.625098 + 1.08270i 0.363424 + 0.931624i $$0.381608\pi$$
−0.988522 + 0.151078i $$0.951726\pi$$
$$32$$ −2.71400 + 4.70079i −0.479773 + 0.830990i
$$33$$ 0 0
$$34$$ −0.764419 1.32401i −0.131097 0.227066i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 1.81681 0.298682 0.149341 0.988786i $$-0.452285\pi$$
0.149341 + 0.988786i $$0.452285\pi$$
$$38$$ −1.33641 2.31473i −0.216795 0.375499i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.735581 + 1.27406i −0.114879 + 0.198975i −0.917731 0.397202i $$-0.869981\pi$$
0.802853 + 0.596177i $$0.203315\pi$$
$$42$$ 0 0
$$43$$ 0.235581 + 0.408039i 0.0359258 + 0.0622254i 0.883429 0.468565i $$-0.155229\pi$$
−0.847503 + 0.530790i $$0.821895\pi$$
$$44$$ 4.47116 0.674053
$$45$$ 0 0
$$46$$ −3.38485 −0.499069
$$47$$ −3.47842 6.02480i −0.507380 0.878808i −0.999964 0.00854274i $$-0.997281\pi$$
0.492584 0.870265i $$-0.336053\pi$$
$$48$$ 0 0
$$49$$ 2.48040 4.29618i 0.354343 0.613739i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −3.90841 6.76956i −0.541998 0.938769i
$$53$$ −1.14399 −0.157139 −0.0785693 0.996909i $$-0.525035\pi$$
−0.0785693 + 0.996909i $$0.525035\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −1.50000 2.59808i −0.200446 0.347183i
$$57$$ 0 0
$$58$$ −2.71400 + 4.70079i −0.356366 + 0.617244i
$$59$$ −0.571993 + 0.990721i −0.0744672 + 0.128981i −0.900854 0.434121i $$-0.857059\pi$$
0.826387 + 0.563102i $$0.190392\pi$$
$$60$$ 0 0
$$61$$ 1.26442 + 2.19004i 0.161892 + 0.280406i 0.935547 0.353201i $$-0.114907\pi$$
−0.773655 + 0.633607i $$0.781574\pi$$
$$62$$ 3.98153 0.505655
$$63$$ 0 0
$$64$$ −1.18319 −0.147899
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −3.29523 + 5.70751i −0.402577 + 0.697283i −0.994036 0.109051i $$-0.965219\pi$$
0.591459 + 0.806335i $$0.298552\pi$$
$$68$$ 2.23558 3.87214i 0.271104 0.469566i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.8745 1.52792 0.763960 0.645263i $$-0.223252\pi$$
0.763960 + 0.645263i $$0.223252\pi$$
$$72$$ 0 0
$$73$$ 1.71203 0.200378 0.100189 0.994968i $$-0.468055\pi$$
0.100189 + 0.994968i $$0.468055\pi$$
$$74$$ −0.519602 0.899976i −0.0604025 0.104620i
$$75$$ 0 0
$$76$$ 3.90841 6.76956i 0.448325 0.776521i
$$77$$ −1.90841 + 3.30545i −0.217483 + 0.376692i
$$78$$ 0 0
$$79$$ 0.143987 + 0.249392i 0.0161998 + 0.0280588i 0.874012 0.485905i $$-0.161510\pi$$
−0.857812 + 0.513964i $$0.828177\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0.841495 0.0929276
$$83$$ 2.14201 + 3.71007i 0.235116 + 0.407233i 0.959306 0.282367i $$-0.0911196\pi$$
−0.724190 + 0.689600i $$0.757786\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0.134751 0.233396i 0.0145306 0.0251677i
$$87$$ 0 0
$$88$$ −2.80757 4.86286i −0.299288 0.518383i
$$89$$ 3.00000 0.317999 0.159000 0.987279i $$-0.449173\pi$$
0.159000 + 0.987279i $$0.449173\pi$$
$$90$$ 0 0
$$91$$ 6.67282 0.699502
$$92$$ −4.94958 8.57293i −0.516030 0.893790i
$$93$$ 0 0
$$94$$ −1.98963 + 3.44615i −0.205215 + 0.355443i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 3.91764 + 6.78555i 0.397776 + 0.688968i 0.993451 0.114257i $$-0.0364487\pi$$
−0.595675 + 0.803225i $$0.703115\pi$$
$$98$$ −2.83754 −0.286635
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −2.10083 3.63875i −0.209040 0.362069i 0.742372 0.669988i $$-0.233701\pi$$
−0.951413 + 0.307919i $$0.900367\pi$$
$$102$$ 0 0
$$103$$ −0.908405 + 1.57340i −0.0895078 + 0.155032i −0.907303 0.420477i $$-0.861863\pi$$
0.817795 + 0.575509i $$0.195196\pi$$
$$104$$ −4.90841 + 8.50161i −0.481309 + 0.833651i
$$105$$ 0 0
$$106$$ 0.327176 + 0.566686i 0.0317782 + 0.0550414i
$$107$$ 11.9176 1.15212 0.576061 0.817407i $$-0.304589\pi$$
0.576061 + 0.817407i $$0.304589\pi$$
$$108$$ 0 0
$$109$$ −16.6521 −1.59498 −0.797491 0.603331i $$-0.793840\pi$$
−0.797491 + 0.603331i $$0.793840\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 1.53081 2.65145i 0.144648 0.250538i
$$113$$ −10.0616 + 17.4272i −0.946518 + 1.63942i −0.193836 + 0.981034i $$0.562093\pi$$
−0.752682 + 0.658384i $$0.771240\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −15.8745 −1.47391
$$117$$ 0 0
$$118$$ 0.654353 0.0602380
$$119$$ 1.90841 + 3.30545i 0.174943 + 0.303011i
$$120$$ 0 0
$$121$$ 1.92801 3.33941i 0.175273 0.303582i
$$122$$ 0.723239 1.25269i 0.0654790 0.113413i
$$123$$ 0 0
$$124$$ 5.82209 + 10.0842i 0.522839 + 0.905584i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −2.18714 −0.194078 −0.0970388 0.995281i $$-0.530937\pi$$
−0.0970388 + 0.995281i $$0.530937\pi$$
$$128$$ 5.76640 + 9.98769i 0.509682 + 0.882795i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i $$-0.917752\pi$$
0.704692 + 0.709514i $$0.251085\pi$$
$$132$$ 0 0
$$133$$ 3.33641 + 5.77883i 0.289304 + 0.501089i
$$134$$ 3.76970 0.325653
$$135$$ 0 0
$$136$$ −5.61515 −0.481495
$$137$$ 5.10083 + 8.83490i 0.435793 + 0.754816i 0.997360 0.0726153i $$-0.0231345\pi$$
−0.561567 + 0.827431i $$0.689801\pi$$
$$138$$ 0 0
$$139$$ −4.00000 + 6.92820i −0.339276 + 0.587643i −0.984297 0.176522i $$-0.943515\pi$$
0.645021 + 0.764165i $$0.276849\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −3.68206 6.37751i −0.308992 0.535189i
$$143$$ 12.4896 1.04444
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −0.489634 0.848071i −0.0405224 0.0701868i
$$147$$ 0 0
$$148$$ 1.51960 2.63203i 0.124910 0.216351i
$$149$$ −10.0381 + 17.3865i −0.822351 + 1.42435i 0.0815762 + 0.996667i $$0.474005\pi$$
−0.903927 + 0.427687i $$0.859329\pi$$
$$150$$ 0 0
$$151$$ −1.51960 2.63203i −0.123663 0.214191i 0.797546 0.603258i $$-0.206131\pi$$
−0.921210 + 0.389066i $$0.872798\pi$$
$$152$$ −9.81681 −0.796248
$$153$$ 0 0
$$154$$ 2.18319 0.175926
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0.100830 0.174643i 0.00804714 0.0139381i −0.861974 0.506953i $$-0.830772\pi$$
0.870021 + 0.493015i $$0.164105\pi$$
$$158$$ 0.0823593 0.142651i 0.00655216 0.0113487i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 8.45043 0.665987
$$162$$ 0 0
$$163$$ −17.8168 −1.39552 −0.697760 0.716331i $$-0.745820\pi$$
−0.697760 + 0.716331i $$0.745820\pi$$
$$164$$ 1.23050 + 2.13129i 0.0960858 + 0.166425i
$$165$$ 0 0
$$166$$ 1.22522 2.12214i 0.0950952 0.164710i
$$167$$ −7.05042 + 12.2117i −0.545578 + 0.944968i 0.452993 + 0.891514i $$0.350356\pi$$
−0.998570 + 0.0534538i $$0.982977\pi$$
$$168$$ 0 0
$$169$$ −4.41764 7.65158i −0.339819 0.588583i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0.788172 0.0600976
$$173$$ −2.18319 3.78140i −0.165985 0.287494i 0.771020 0.636811i $$-0.219747\pi$$
−0.937005 + 0.349317i $$0.886414\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 2.86525 4.96276i 0.215976 0.374082i
$$177$$ 0 0
$$178$$ −0.857990 1.48608i −0.0643091 0.111387i
$$179$$ 15.1625 1.13330 0.566648 0.823960i $$-0.308240\pi$$
0.566648 + 0.823960i $$0.308240\pi$$
$$180$$ 0 0
$$181$$ 3.20166 0.237978 0.118989 0.992896i $$-0.462035\pi$$
0.118989 + 0.992896i $$0.462035\pi$$
$$182$$ −1.90841 3.30545i −0.141460 0.245017i
$$183$$ 0 0
$$184$$ −6.21598 + 10.7664i −0.458248 + 0.793709i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 3.57199 + 6.18687i 0.261210 + 0.452429i
$$188$$ −11.6376 −0.848757
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.41877 2.45738i −0.102659 0.177810i 0.810121 0.586263i $$-0.199402\pi$$
−0.912779 + 0.408453i $$0.866068\pi$$
$$192$$ 0 0
$$193$$ −9.39409 + 16.2710i −0.676201 + 1.17121i 0.299915 + 0.953966i $$0.403042\pi$$
−0.976116 + 0.217249i $$0.930292\pi$$
$$194$$ 2.24086 3.88129i 0.160885 0.278660i
$$195$$ 0 0
$$196$$ −4.14927 7.18675i −0.296376 0.513339i
$$197$$ 5.83528 0.415747 0.207873 0.978156i $$-0.433346\pi$$
0.207873 + 0.978156i $$0.433346\pi$$
$$198$$ 0 0
$$199$$ 13.0761 0.926943 0.463472 0.886112i $$-0.346604\pi$$
0.463472 + 0.886112i $$0.346604\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −1.20166 + 2.08134i −0.0845486 + 0.146442i
$$203$$ 6.77563 11.7357i 0.475556 0.823687i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 1.03920 0.0724047
$$207$$ 0 0
$$208$$ −10.0185 −0.694656
$$209$$ 6.24482 + 10.8163i 0.431963 + 0.748182i
$$210$$ 0 0
$$211$$ −4.19243 + 7.26149i −0.288618 + 0.499902i −0.973480 0.228771i $$-0.926529\pi$$
0.684862 + 0.728673i $$0.259863\pi$$
$$212$$ −0.956844 + 1.65730i −0.0657163 + 0.113824i
$$213$$ 0 0
$$214$$ −3.40841 5.90353i −0.232994 0.403557i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −9.94006 −0.674776
$$218$$ 4.76244 + 8.24879i 0.322553 + 0.558679i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 6.24482 10.8163i 0.420072 0.727586i
$$222$$ 0 0
$$223$$ 4.58321 + 7.93834i 0.306914 + 0.531591i 0.977686 0.210073i $$-0.0673702\pi$$
−0.670772 + 0.741664i $$0.734037\pi$$
$$224$$ −7.75123 −0.517901
$$225$$ 0 0
$$226$$ 11.5104 0.765658
$$227$$ 1.33641 + 2.31473i 0.0887008 + 0.153634i 0.906962 0.421212i $$-0.138395\pi$$
−0.818261 + 0.574846i $$0.805062\pi$$
$$228$$ 0 0
$$229$$ −1.27365 + 2.20603i −0.0841654 + 0.145779i −0.905035 0.425336i $$-0.860156\pi$$
0.820870 + 0.571115i $$0.193489\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 9.96806 + 17.2652i 0.654435 + 1.13351i
$$233$$ −6.22013 −0.407494 −0.203747 0.979024i $$-0.565312\pi$$
−0.203747 + 0.979024i $$0.565312\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0.956844 + 1.65730i 0.0622852 + 0.107881i
$$237$$ 0 0
$$238$$ 1.09159 1.89070i 0.0707576 0.122556i
$$239$$ 4.06163 7.03494i 0.262725 0.455053i −0.704240 0.709962i $$-0.748712\pi$$
0.966965 + 0.254909i $$0.0820455\pi$$
$$240$$ 0 0
$$241$$ 13.1821 + 22.8320i 0.849131 + 1.47074i 0.881985 + 0.471278i $$0.156207\pi$$
−0.0328536 + 0.999460i $$0.510460\pi$$
$$242$$ −2.20561 −0.141782
$$243$$ 0 0
$$244$$ 4.23030 0.270817
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 10.9176 18.9099i 0.694673 1.20321i
$$248$$ 7.31173 12.6643i 0.464295 0.804183i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0.549569 0.0346885 0.0173443 0.999850i $$-0.494479\pi$$
0.0173443 + 0.999850i $$0.494479\pi$$
$$252$$ 0 0
$$253$$ 15.8168 0.994394
$$254$$ 0.625515 + 1.08342i 0.0392483 + 0.0679801i
$$255$$ 0 0
$$256$$ 2.11515 3.66355i 0.132197 0.228972i
$$257$$ 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i $$-0.643595\pi$$
0.997374 0.0724199i $$-0.0230722\pi$$
$$258$$ 0 0
$$259$$ 1.29721 + 2.24683i 0.0806046 + 0.139611i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 3.43196 0.212027
$$263$$ −5.94761 10.3016i −0.366745 0.635221i 0.622309 0.782771i $$-0.286195\pi$$
−0.989055 + 0.147550i $$0.952861\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 1.90841 3.30545i 0.117012 0.202670i
$$267$$ 0 0
$$268$$ 5.51234 + 9.54766i 0.336720 + 0.583216i
$$269$$ −28.5737 −1.74217 −0.871084 0.491134i $$-0.836583\pi$$
−0.871084 + 0.491134i $$0.836583\pi$$
$$270$$ 0 0
$$271$$ −23.3641 −1.41927 −0.709635 0.704570i $$-0.751140\pi$$
−0.709635 + 0.704570i $$0.751140\pi$$
$$272$$ −2.86525 4.96276i −0.173731 0.300911i
$$273$$ 0 0
$$274$$ 2.91764 5.05350i 0.176261 0.305293i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −7.53807 13.0563i −0.452919 0.784479i 0.545647 0.838015i $$-0.316284\pi$$
−0.998566 + 0.0535366i $$0.982951\pi$$
$$278$$ 4.57595 0.274447
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 3.32605 + 5.76088i 0.198415 + 0.343665i 0.948015 0.318226i $$-0.103087\pi$$
−0.749599 + 0.661892i $$0.769754\pi$$
$$282$$ 0 0
$$283$$ 13.4485 23.2934i 0.799428 1.38465i −0.120562 0.992706i $$-0.538470\pi$$
0.919989 0.391943i $$-0.128197\pi$$
$$284$$ 10.7684 18.6514i 0.638985 1.10675i
$$285$$ 0 0
$$286$$ −3.57199 6.18687i −0.211216 0.365838i
$$287$$ −2.10083 −0.124008
$$288$$ 0 0
$$289$$ −9.85601 −0.579765
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 1.43196 2.48023i 0.0837991 0.145144i
$$293$$ −6.19243 + 10.7256i −0.361765 + 0.626596i −0.988251 0.152837i $$-0.951159\pi$$
0.626486 + 0.779433i $$0.284493\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −3.81681 −0.221848
$$297$$ 0 0
$$298$$ 11.4834 0.665217
$$299$$ −13.8260 23.9474i −0.799581 1.38491i
$$300$$ 0 0
$$301$$ −0.336412 + 0.582682i −0.0193905 + 0.0335853i
$$302$$ −0.869202 + 1.50550i −0.0500169 + 0.0866319i
$$303$$ 0 0
$$304$$ −5.00924 8.67625i −0.287299 0.497617i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 2.49359 0.142317 0.0711583 0.997465i $$-0.477330\pi$$
0.0711583 + 0.997465i $$0.477330\pi$$
$$308$$ 3.19243 + 5.52944i 0.181905 + 0.315069i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −12.1101 + 20.9752i −0.686699 + 1.18940i 0.286201 + 0.958170i $$0.407608\pi$$
−0.972900 + 0.231228i $$0.925726\pi$$
$$312$$ 0 0
$$313$$ −17.5420 30.3837i −0.991534 1.71739i −0.608219 0.793770i $$-0.708116\pi$$
−0.383315 0.923618i $$-0.625218\pi$$
$$314$$ −0.115349 −0.00650950
$$315$$ 0 0
$$316$$ 0.481728 0.0270993
$$317$$ 5.23558 + 9.06829i 0.294060 + 0.509326i 0.974766 0.223231i $$-0.0716603\pi$$
−0.680706 + 0.732557i $$0.738327\pi$$
$$318$$ 0 0
$$319$$ 12.6821 21.9660i 0.710059 1.22986i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −2.41679 4.18601i −0.134683 0.233277i
$$323$$ 12.4896 0.694942
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 5.09555 + 8.82575i 0.282216 + 0.488813i
$$327$$ 0 0
$$328$$ 1.54533 2.67659i 0.0853267 0.147790i
$$329$$ 4.96721 8.60346i 0.273851 0.474324i
$$330$$ 0 0
$$331$$ −8.38880 14.5298i −0.461090 0.798632i 0.537925 0.842993i $$-0.319208\pi$$
−0.999016 + 0.0443606i $$0.985875\pi$$
$$332$$ 7.16641 0.393308
$$333$$ 0 0
$$334$$ 8.06558 0.441329
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −13.5905 + 23.5394i −0.740320 + 1.28227i 0.212030 + 0.977263i $$0.431993\pi$$
−0.952350 + 0.305008i $$0.901341\pi$$
$$338$$ −2.52686 + 4.37665i −0.137443 + 0.238058i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −18.6050 −1.00752
$$342$$ 0 0
$$343$$ 17.0801 0.922239
$$344$$ −0.494917 0.857221i −0.0266841 0.0462182i
$$345$$ 0 0
$$346$$ −1.24877 + 2.16293i −0.0671343 + 0.116280i
$$347$$ 11.7829 20.4086i 0.632539 1.09559i −0.354492 0.935059i $$-0.615346\pi$$
0.987031 0.160530i $$-0.0513204\pi$$
$$348$$ 0 0
$$349$$ 5.35601 + 9.27689i 0.286701 + 0.496580i 0.973020 0.230720i $$-0.0741081\pi$$
−0.686319 + 0.727300i $$0.740775\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −14.5081 −0.773285
$$353$$ −13.6336 23.6141i −0.725644 1.25685i −0.958708 0.284392i $$-0.908208\pi$$
0.233064 0.972461i $$-0.425125\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 2.50924 4.34612i 0.132989 0.230344i
$$357$$ 0 0
$$358$$ −4.33641 7.51089i −0.229186 0.396963i
$$359$$ 10.6807 0.563707 0.281854 0.959457i $$-0.409051\pi$$
0.281854 + 0.959457i $$0.409051\pi$$
$$360$$ 0 0
$$361$$ 2.83528 0.149225
$$362$$ −0.915664 1.58598i −0.0481262 0.0833571i
$$363$$ 0 0
$$364$$ 5.58123 9.66697i 0.292536 0.506687i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −4.23558 7.33624i −0.221096 0.382949i 0.734045 0.679100i $$-0.237630\pi$$
−0.955141 + 0.296152i $$0.904297\pi$$
$$368$$ −12.6873 −0.661373
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −0.816810 1.41476i −0.0424067 0.0734505i
$$372$$ 0 0
$$373$$ 5.06163 8.76700i 0.262081 0.453938i −0.704714 0.709492i $$-0.748925\pi$$
0.966795 + 0.255554i $$0.0822579\pi$$
$$374$$ 2.04316 3.53885i 0.105649 0.182990i
$$375$$ 0 0
$$376$$ 7.30757 + 12.6571i 0.376859 + 0.652740i
$$377$$ −44.3434 −2.28380
$$378$$ 0 0
$$379$$ 11.9216 0.612371 0.306186 0.951972i $$-0.400947\pi$$
0.306186 + 0.951972i $$0.400947\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −0.811528 + 1.40561i −0.0415214 + 0.0719171i
$$383$$ −4.90841 + 8.50161i −0.250808 + 0.434412i −0.963748 0.266813i $$-0.914030\pi$$
0.712941 + 0.701224i $$0.247363\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 10.7467 0.546993
$$387$$ 0 0
$$388$$ 13.1070 0.665409
$$389$$ 4.61007 + 7.98487i 0.233740 + 0.404849i 0.958906 0.283725i $$-0.0915703\pi$$
−0.725166 + 0.688574i $$0.758237\pi$$
$$390$$ 0 0
$$391$$ 7.90841 13.6978i 0.399945 0.692725i
$$392$$ −5.21090 + 9.02554i −0.263190 + 0.455858i
$$393$$ 0 0
$$394$$ −1.66887 2.89057i −0.0840765 0.145625i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 22.9793 1.15330 0.576648 0.816993i $$-0.304360\pi$$
0.576648 + 0.816993i $$0.304360\pi$$
$$398$$ −3.73973 6.47741i −0.187456 0.324683i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −5.53279 + 9.58307i −0.276294 + 0.478556i −0.970461 0.241259i $$-0.922440\pi$$
0.694167 + 0.719814i $$0.255773\pi$$
$$402$$ 0 0
$$403$$ 16.2633 + 28.1688i 0.810132 + 1.40319i
$$404$$ −7.02864 −0.349688
$$405$$ 0 0
$$406$$ −7.75123 −0.384687
$$407$$ 2.42801 + 4.20543i 0.120352 + 0.208455i
$$408$$ 0 0
$$409$$ 8.81681 15.2712i 0.435963 0.755110i −0.561411 0.827537i $$-0.689741\pi$$
0.997374 + 0.0724270i $$0.0230744\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 1.51960 + 2.63203i 0.0748654 + 0.129671i
$$413$$ −1.63362 −0.0803852
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 12.6821 + 21.9660i 0.621789 + 1.07697i
$$417$$ 0 0
$$418$$ 3.57199 6.18687i 0.174712 0.302610i
$$419$$ 18.5173 32.0730i 0.904631 1.56687i 0.0832199 0.996531i $$-0.473480\pi$$
0.821411 0.570336i $$-0.193187\pi$$
$$420$$ 0 0
$$421$$ −2.52884 4.38007i −0.123248 0.213472i 0.797799 0.602924i $$-0.205998\pi$$
−0.921047 + 0.389452i $$0.872664\pi$$
$$422$$ 4.79608 0.233469
$$423$$ 0 0
$$424$$ 2.40332 0.116716
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −1.80560 + 3.12739i −0.0873790 + 0.151345i
$$428$$ 9.96806 17.2652i 0.481824 0.834544i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 5.23030 0.251935 0.125967 0.992034i $$-0.459797\pi$$
0.125967 + 0.992034i $$0.459797\pi$$
$$432$$ 0 0
$$433$$ −34.3434 −1.65044 −0.825219 0.564813i $$-0.808948\pi$$
−0.825219 + 0.564813i $$0.808948\pi$$
$$434$$ 2.84283 + 4.92392i 0.136460 + 0.236356i
$$435$$ 0 0
$$436$$ −13.9280 + 24.1240i −0.667031 + 1.15533i
$$437$$ 13.8260 23.9474i 0.661389 1.14556i
$$438$$ 0 0
$$439$$ 9.77365 + 16.9285i 0.466471 + 0.807952i 0.999267 0.0382924i $$-0.0121918\pi$$
−0.532796 + 0.846244i $$0.678859\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −7.14399 −0.339805
$$443$$ −5.25208 9.09686i −0.249534 0.432205i 0.713863 0.700286i $$-0.246944\pi$$
−0.963396 + 0.268081i $$0.913611\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 2.62156 4.54068i 0.124135 0.215007i
$$447$$ 0 0
$$448$$ −0.844801 1.46324i −0.0399131 0.0691315i
$$449$$ −22.8560 −1.07864 −0.539321 0.842100i $$-0.681319\pi$$
−0.539321 + 0.842100i $$0.681319\pi$$
$$450$$ 0 0
$$451$$ −3.93216 −0.185158
$$452$$ 16.8313 + 29.1527i 0.791679 + 1.37123i
$$453$$ 0 0
$$454$$ 0.764419 1.32401i 0.0358759 0.0621390i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −7.01319 12.1472i −0.328063 0.568222i 0.654064 0.756439i $$-0.273063\pi$$
−0.982127 + 0.188217i $$0.939729\pi$$
$$458$$ 1.45704 0.0680832
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −12.0513 20.8734i −0.561283 0.972171i −0.997385 0.0722736i $$-0.976975\pi$$
0.436102 0.899897i $$-0.356359\pi$$
$$462$$ 0 0
$$463$$ −16.9700 + 29.3930i −0.788664 + 1.36601i 0.138121 + 0.990415i $$0.455894\pi$$
−0.926785 + 0.375591i $$0.877440\pi$$
$$464$$ −10.1728 + 17.6198i −0.472261 + 0.817981i
$$465$$ 0 0
$$466$$ 1.77894 + 3.08121i 0.0824077 + 0.142734i
$$467$$ −27.3720 −1.26663 −0.633313 0.773896i $$-0.718305\pi$$
−0.633313 + 0.773896i $$0.718305\pi$$
$$468$$ 0 0
$$469$$ −9.41123 −0.434570
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.20166 2.08134i 0.0553109 0.0958013i
$$473$$ −0.629668 + 1.09062i −0.0289521 + 0.0501466i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 6.38485 0.292649
$$477$$ 0 0
$$478$$ −4.64645 −0.212524
$$479$$ 2.61515 + 4.52957i 0.119489 + 0.206961i 0.919565 0.392937i $$-0.128541\pi$$
−0.800076 + 0.599898i $$0.795208\pi$$
$$480$$ 0 0
$$481$$ 4.24482 7.35224i 0.193547 0.335233i
$$482$$ 7.54005 13.0597i 0.343440 0.594855i
$$483$$ 0 0
$$484$$ −3.22522 5.58624i −0.146601 0.253920i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 24.0185 1.08838 0.544190 0.838962i $$-0.316837\pi$$
0.544190 + 0.838962i $$0.316837\pi$$
$$488$$ −2.65633 4.60090i −0.120246 0.208273i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 7.38880 12.7978i 0.333452 0.577556i −0.649734 0.760161i $$-0.725120\pi$$
0.983186 + 0.182606i $$0.0584531\pi$$
$$492$$ 0 0
$$493$$ −12.6821 21.9660i −0.571171 0.989298i
$$494$$ −12.4896 −0.561935
$$495$$ 0 0
$$496$$ 14.9239 0.670101
$$497$$ 9.19243 + 15.9217i 0.412337 + 0.714188i
$$498$$ 0 0
$$499$$ −12.4280 + 21.5259i −0.556354 + 0.963633i 0.441443 + 0.897289i $$0.354467\pi$$
−0.997797 + 0.0663440i $$0.978867\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −0.157175 0.272235i −0.00701506 0.0121504i
$$503$$ 38.9154 1.73515 0.867576 0.497305i $$-0.165677\pi$$
0.867576 + 0.497305i $$0.165677\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −4.52355 7.83503i −0.201097 0.348309i
$$507$$ 0 0
$$508$$ −1.82935 + 3.16853i −0.0811644 + 0.140581i
$$509$$ 1.01037 1.75001i 0.0447837 0.0775676i −0.842765 0.538282i $$-0.819073\pi$$
0.887548 + 0.460715i $$0.152407\pi$$
$$510$$ 0 0
$$511$$ 1.22239 + 2.11725i 0.0540755 + 0.0936615i
$$512$$ 20.6459 0.912428
$$513$$ 0 0
$$514$$ −10.2959 −0.454132
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 9.29721 16.1032i 0.408891 0.708220i
$$518$$ 0.741995 1.28517i 0.0326014 0.0564672i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 23.0290 1.00892 0.504460 0.863435i $$-0.331692\pi$$
0.504460 + 0.863435i $$0.331692\pi$$
$$522$$ 0 0
$$523$$ 41.1170 1.79792 0.898961 0.438028i $$-0.144323\pi$$
0.898961 + 0.438028i $$0.144323\pi$$
$$524$$ 5.01847 + 8.69225i 0.219233 + 0.379723i
$$525$$ 0 0
$$526$$ −3.40199 + 5.89242i −0.148334 + 0.256922i
$$527$$ −9.30249 + 16.1124i −0.405223 + 0.701867i
$$528$$ 0 0
$$529$$ −6.00924 10.4083i −0.261271 0.452535i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 11.1625 0.483954
$$533$$ 3.43724 + 5.95348i 0.148883 + 0.257874i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 6.92272 11.9905i 0.299016 0.517911i
$$537$$ 0 0
$$538$$ 8.17198 + 14.1543i 0.352319 + 0.610234i
$$539$$ 13.2593 0.571120
$$540$$ 0 0
$$541$$ 5.20957 0.223977 0.111988 0.993710i $$-0.464278\pi$$
0.111988 + 0.993710i $$0.464278\pi$$
$$542$$ 6.68206 + 11.5737i 0.287019 + 0.497132i
$$543$$ 0 0
$$544$$ −7.25405 + 12.5644i −0.311015 + 0.538694i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.0204 + 34.6764i 0.856013 + 1.48266i 0.875702 + 0.482851i $$0.160399\pi$$
−0.0196900 + 0.999806i $$0.506268\pi$$
$$548$$ 17.0656 0.729005
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −22.1717 38.4025i −0.944546 1.63600i
$$552$$ 0 0
$$553$$ −0.205614 + 0.356133i −0.00874359 + 0.0151443i
$$554$$ −4.31173 + 7.46813i −0.183188 + 0.317290i
$$555$$ 0 0
$$556$$ 6.69129 + 11.5897i 0.283774 + 0.491511i
$$557$$ −14.4033 −0.610288 −0.305144 0.952306i $$-0.598705\pi$$
−0.305144 + 0.952306i $$0.598705\pi$$
$$558$$ 0 0
$$559$$ 2.20166 0.0931203
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 1.90248 3.29518i 0.0802511 0.138999i
$$563$$ −14.6840 + 25.4335i −0.618858 + 1.07189i 0.370836 + 0.928698i $$0.379071\pi$$
−0.989694 + 0.143196i $$0.954262\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −15.3849 −0.646674
$$567$$ 0 0
$$568$$ −27.0471 −1.13487
$$569$$ 23.4033 + 40.5357i 0.981118 + 1.69935i 0.658056 + 0.752969i $$0.271379\pi$$
0.323062 + 0.946378i $$0.395288\pi$$
$$570$$ 0 0
$$571$$ −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i $$-0.970773\pi$$
0.577301 + 0.816532i $$0.304106\pi$$
$$572$$ 10.4465 18.0938i 0.436789 0.756541i
$$573$$ 0 0
$$574$$ 0.600830 + 1.04067i 0.0250782 + 0.0434367i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −28.2386 −1.17559 −0.587794 0.809010i $$-0.700004\pi$$
−0.587794 + 0.809010i $$0.700004\pi$$
$$578$$ 2.81879 + 4.88228i 0.117246 + 0.203076i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3.05880 + 5.29801i −0.126901 + 0.219798i
$$582$$ 0 0
$$583$$ −1.52884 2.64802i −0.0633180 0.109670i
$$584$$ −3.59668 −0.148832
$$585$$ 0 0
$$586$$ 7.08405 0.292639
$$587$$ −9.04118 15.6598i −0.373169 0.646348i 0.616882 0.787056i $$-0.288396\pi$$
−0.990051 + 0.140707i $$0.955062\pi$$
$$588$$ 0 0
$$589$$ −16.2633 + 28.1688i −0.670117 + 1.16068i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.94761 3.37336i −0.0800462 0.138644i
$$593$$ −7.73840 −0.317778 −0.158889 0.987296i $$-0.550791\pi$$
−0.158889 + 0.987296i $$0.550791\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 16.7919 + 29.0845i 0.687824 + 1.19135i
$$597$$ 0 0
$$598$$ −7.90841 + 13.6978i −0.323399 + 0.560143i
$$599$$ −13.9608 + 24.1808i −0.570423 + 0.988001i 0.426100 + 0.904676i $$0.359887\pi$$
−0.996522 + 0.0833249i $$0.973446\pi$$
$$600$$ 0 0
$$601$$ −19.2201 33.2902i −0.784006 1.35794i −0.929591 0.368592i $$-0.879840\pi$$
0.145586 0.989346i $$-0.453493\pi$$
$$602$$ 0.384851 0.0156853
$$603$$ 0 0
$$604$$ −5.08405 −0.206867
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −0.319917 + 0.554113i −0.0129850 + 0.0224907i −0.872445 0.488712i $$-0.837467\pi$$
0.859460 + 0.511203i $$0.170800\pi$$
$$608$$ −12.6821 + 21.9660i −0.514325 + 0.890838i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −32.5081 −1.31514
$$612$$ 0 0
$$613$$ −42.7467 −1.72652 −0.863262 0.504757i $$-0.831582\pi$$
−0.863262 + 0.504757i $$0.831582\pi$$
$$614$$ −0.713157 1.23522i −0.0287807 0.0498496i
$$615$$ 0 0
$$616$$ 4.00924 6.94420i 0.161537 0.279790i
$$617$$ −10.5513 + 18.2753i −0.424778 + 0.735737i −0.996400 0.0847805i $$-0.972981\pi$$
0.571622 + 0.820517i $$0.306314\pi$$
$$618$$ 0 0
$$619$$ 6.82605 + 11.8231i 0.274362 + 0.475209i 0.969974 0.243209i $$-0.0782000\pi$$
−0.695612 + 0.718418i $$0.744867\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 13.8538 0.555485
$$623$$ 2.14201 + 3.71007i 0.0858178 + 0.148641i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −10.0339 + 17.3793i −0.401036 + 0.694615i
$$627$$ 0 0
$$628$$ −0.168672 0.292148i −0.00673073 0.0116580i
$$629$$ 4.85601 0.193622
$$630$$ 0 0
$$631$$ 33.2593 1.32403 0.662017 0.749489i $$-0.269701\pi$$
0.662017 + 0.749489i $$0.269701\pi$$
$$632$$ −0.302491 0.523930i −0.0120325 0.0208408i
$$633$$ 0 0
$$634$$ 2.99472 5.18700i 0.118935 0.206002i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −11.5905 20.0753i −0.459231 0.795411i
$$638$$ −14.5081 −0.574381
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 13.1429 + 22.7641i 0.519112 + 0.899128i 0.999753 + 0.0222106i $$0.00707044\pi$$
−0.480642 + 0.876917i $$0.659596\pi$$
$$642$$ 0 0
$$643$$ 10.2913 17.8250i 0.405848 0.702950i −0.588571 0.808445i $$-0.700309\pi$$
0.994420 + 0.105495i $$0.0336427\pi$$
$$644$$ 7.06804 12.2422i 0.278520 0.482410i
$$645$$ 0 0
$$646$$ −3.57199 6.18687i −0.140538 0.243419i
$$647$$ 23.2527 0.914159 0.457079 0.889426i $$-0.348896\pi$$
0.457079 + 0.889426i $$0.348896\pi$$
$$648$$ 0 0
$$649$$ −3.05767 −0.120024
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −14.9022 + 25.8114i −0.583615 + 1.01085i
$$653$$ −9.37957 + 16.2459i −0.367051 + 0.635751i −0.989103 0.147225i $$-0.952966\pi$$
0.622052 + 0.782976i $$0.286299\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 3.15415 0.123149
$$657$$ 0 0
$$658$$ −5.68242 −0.221524
$$659$$ −0.140034 0.242545i −0.00545494 0.00944823i 0.863285 0.504717i $$-0.168403\pi$$
−0.868740 + 0.495268i $$0.835070\pi$$
$$660$$ 0 0
$$661$$ 19.8930 34.4556i 0.773746 1.34017i −0.161750 0.986832i $$-0.551714\pi$$
0.935496 0.353336i $$-0.114953\pi$$
$$662$$ −4.79834 + 8.31097i −0.186493 + 0.323015i
$$663$$ 0 0
$$664$$ −4.50000 7.79423i −0.174634 0.302475i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −56.1562 −2.17438
$$668$$ 11.7941 + 20.4280i 0.456327 + 0.790382i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −3.37957 + 5.85358i −0.130467 + 0.225975i
$$672$$ 0 0
$$673$$ 16.7644 + 29.0368i 0.646221 + 1.11929i 0.984018 + 0.178068i $$0.0569848\pi$$
−0.337797 + 0.941219i $$0.609682\pi$$
$$674$$ 15.5473 0.598860
$$675$$ 0 0
$$676$$ −14.7799 −0.568456
$$677$$ −13.7437 23.8048i −0.528213 0.914891i −0.999459 0.0328897i $$-0.989529\pi$$
0.471246 0.882002i $$-0.343804\pi$$
$$678$$ 0 0
$$679$$ −5.59442 + 9.68981i −0.214694 + 0.371861i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 5.32096 + 9.21618i 0.203750 + 0.352906i
$$683$$ −34.5865 −1.32342 −0.661708 0.749762i $$-0.730168\pi$$
−0.661708 + 0.749762i $$0.730168\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −4.88485 8.46081i −0.186504 0.323035i
$$687$$ 0 0
$$688$$ 0.505083 0.874830i 0.0192561 0.0333526i
$$689$$ −2.67282 + 4.62947i −0.101826 + 0.176369i
$$690$$ 0 0
$$691$$ −20.3641 35.2717i −0.774688 1.34180i −0.934970 0.354727i $$-0.884574\pi$$
0.160282 0.987071i $$-0.448760\pi$$
$$692$$ −7.30418 −0.277663
$$693$$ 0 0
$$694$$ −13.4795 −0.511674
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −1.96608 + 3.40535i −0.0744706 + 0.128987i
$$698$$ 3.06360 5.30632i 0.115959 0.200847i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 19.4712 0.735416 0.367708 0.929941i $$-0.380143\pi$$
0.367708 + 0.929941i $$0.380143\pi$$
$$702$$ 0 0
$$703$$ 8.48963 0.320193
$$704$$ −1.58123 2.73877i −0.0595948 0.103221i
$$705$$ 0 0
$$706$$ −7.79834 + 13.5071i −0.293494 + 0.508347i
$$707$$ 3.00000 5.19615i 0.112827 0.195421i
$$708$$ 0 0
$$709$$ −7.54316 13.0651i −0.283289 0.490671i 0.688904 0.724853i $$-0.258092\pi$$
−0.972193 + 0.234182i $$0.924759\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −6.30249 −0.236196
$$713$$ 20.5957 + 35.6729i 0.771317 + 1.33596i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.6821 21.9660i 0.473951 0.820907i
$$717$$ 0 0
$$718$$ −3.05465 5.29081i −0.113999 0.197451i
$$719$$ 3.43196 0.127990 0.0639952 0.997950i $$-0.479616\pi$$
0.0639952 + 0.997950i $$0.479616\pi$$
$$720$$ 0 0
$$721$$ −2.59442 −0.0966211
$$722$$ −0.810881 1.40449i −0.0301779 0.0522696i
$$723$$ 0 0
$$724$$ 2.67791 4.63827i 0.0995236 0.172380i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −17.8857 30.9789i −0.663344 1.14895i −0.979732 0.200315i $$-0.935803\pi$$
0.316388 0.948630i $$-0.397530\pi$$
$$728$$ −14.0185 −0.519559
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0.629668 + 1.09062i 0.0232891 + 0.0403379i
$$732$$ 0 0
$$733$$ −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i $$-0.966513\pi$$
0.588177 + 0.808732i $$0.299846\pi$$
$$734$$ −2.42272 + 4.19628i −0.0894244 + 0.154888i
$$735$$ 0 0
$$736$$ 16.0605 + 27.8176i 0.591998 + 1.02537i
$$737$$ −17.6151 −0.648862
$$738$$ 0 0
$$739$$ 6.08631 0.223889 0.111944 0.993714i $$-0.464292\pi$$
0.111944 + 0.993714i $$0.464292\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −0.467210 + 0.809231i −0.0171518 + 0.0297078i
$$743$$ 12.7509 22.0853i 0.467787 0.810231i −0.531536 0.847036i $$-0.678385\pi$$
0.999322 + 0.0368054i $$0.0117182\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −5.79043 −0.212003
$$747$$ 0 0
$$748$$ 11.9506 0.436958
$$749$$ 8.50924 + 14.7384i 0.310921 + 0.538530i
$$750$$ 0 0
$$751$$ 9.19638 15.9286i 0.335581 0.581243i −0.648016 0.761627i $$-0.724401\pi$$
0.983596 + 0.180384i $$0.0577342\pi$$
$$752$$ −7.45769 + 12.9171i −0.271954 + 0.471038i
$$753$$ 0 0
$$754$$ 12.6821 + 21.9660i 0.461853 + 0.799953i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 41.8986 1.52283 0.761415 0.648264i $$-0.224505\pi$$
0.761415 + 0.648264i $$0.224505\pi$$
$$758$$ −3.40954 5.90549i −0.123840 0.214497i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −3.98568 + 6.90340i −0.144481 + 0.250248i −0.929179 0.369630i $$-0.879485\pi$$
0.784698 + 0.619878i $$0.212818\pi$$
$$762$$ 0 0
$$763$$ −11.8896 20.5935i −0.430434 0.745534i
$$764$$ −4.74671 −0.171730
$$765$$ 0 0
$$766$$ 5.61515 0.202884
$$767$$ 2.67282 + 4.62947i 0.0965101 + 0.167160i
$$768$$ 0 0
$$769$$ −3.01432 + 5.22095i −0.108699 + 0.188272i −0.915244 0.402901i $$-0.868002\pi$$
0.806544 + 0.591174i $$0.201335\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 15.7147 + 27.2186i 0.565583 + 0.979618i
$$773$$ 44.4033 1.59708 0.798538 0.601944i $$-0.205607\pi$$
0.798538 + 0.601944i $$0.205607\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −8.23030 14.2553i −0.295451 0.511735i
$$777$$ 0 0
$$778$$ 2.63693 4.56729i 0.0945384 0.163745i
$$779$$ −3.43724 + 5.95348i −0.123152 + 0.213305i
$$780$$ 0 0
$$781$$ 17.2056 + 29.8010i 0.615665 + 1.06636i
$$782$$ −9.04711 −0.323524
$$783$$ 0 0
$$784$$ −10.6359 −0.379853
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 8.41877 14.5817i 0.300097 0.519783i −0.676061 0.736846i $$-0.736314\pi$$
0.976158 + 0.217063i $$0.0696477\pi$$
$$788$$ 4.88070 8.45362i 0.173868 0.301148i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −28.7361 −1.02174
$$792$$ 0 0
$$793$$ 11.8168 0.419627
$$794$$ −6.57199 11.3830i −0.233231 0.403968i