# Properties

 Label 1815.2.c.a.364.1 Level $1815$ Weight $2$ Character 1815.364 Analytic conductor $14.493$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1815 = 3 \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1815.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.4928479669$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 364.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1815.364 Dual form 1815.2.c.a.364.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -4.00000i q^{7} -3.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -4.00000i q^{7} -3.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} -1.00000i q^{12} +2.00000i q^{13} -4.00000 q^{14} +(2.00000 + 1.00000i) q^{15} -1.00000 q^{16} -2.00000i q^{17} +1.00000i q^{18} -8.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} -4.00000 q^{21} +4.00000i q^{23} -3.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{27} -4.00000i q^{28} -4.00000 q^{29} +(1.00000 - 2.00000i) q^{30} -8.00000 q^{31} -5.00000i q^{32} -2.00000 q^{34} +(8.00000 + 4.00000i) q^{35} -1.00000 q^{36} -8.00000i q^{37} +8.00000i q^{38} +2.00000 q^{39} +(6.00000 + 3.00000i) q^{40} +12.0000 q^{41} +4.00000i q^{42} -8.00000i q^{43} +(1.00000 - 2.00000i) q^{45} +4.00000 q^{46} +4.00000i q^{47} +1.00000i q^{48} -9.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -2.00000 q^{51} +2.00000i q^{52} -4.00000i q^{53} +1.00000 q^{54} -12.0000 q^{56} +8.00000i q^{57} +4.00000i q^{58} +8.00000 q^{59} +(2.00000 + 1.00000i) q^{60} +8.00000i q^{62} +4.00000i q^{63} -7.00000 q^{64} +(-4.00000 - 2.00000i) q^{65} +4.00000i q^{67} -2.00000i q^{68} +4.00000 q^{69} +(4.00000 - 8.00000i) q^{70} -12.0000 q^{71} +3.00000i q^{72} +2.00000i q^{73} -8.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} -8.00000 q^{76} -2.00000i q^{78} -8.00000 q^{79} +(1.00000 - 2.00000i) q^{80} +1.00000 q^{81} -12.0000i q^{82} +4.00000i q^{83} -4.00000 q^{84} +(4.00000 + 2.00000i) q^{85} -8.00000 q^{86} +4.00000i q^{87} -6.00000 q^{89} +(-2.00000 - 1.00000i) q^{90} +8.00000 q^{91} +4.00000i q^{92} +8.00000i q^{93} +4.00000 q^{94} +(8.00000 - 16.0000i) q^{95} -5.00000 q^{96} +8.00000i q^{97} +9.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{4} - 2q^{5} - 2q^{6} - 2q^{9} + O(q^{10})$$ $$2q + 2q^{4} - 2q^{5} - 2q^{6} - 2q^{9} + 4q^{10} - 8q^{14} + 4q^{15} - 2q^{16} - 16q^{19} - 2q^{20} - 8q^{21} - 6q^{24} - 6q^{25} + 4q^{26} - 8q^{29} + 2q^{30} - 16q^{31} - 4q^{34} + 16q^{35} - 2q^{36} + 4q^{39} + 12q^{40} + 24q^{41} + 2q^{45} + 8q^{46} - 18q^{49} - 8q^{50} - 4q^{51} + 2q^{54} - 24q^{56} + 16q^{59} + 4q^{60} - 14q^{64} - 8q^{65} + 8q^{69} + 8q^{70} - 24q^{71} - 16q^{74} - 8q^{75} - 16q^{76} - 16q^{79} + 2q^{80} + 2q^{81} - 8q^{84} + 8q^{85} - 16q^{86} - 12q^{89} - 4q^{90} + 16q^{91} + 8q^{94} + 16q^{95} - 10q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$$.

 $$n$$ $$727$$ $$1211$$ $$1696$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i −0.935414 0.353553i $$-0.884973\pi$$
0.935414 0.353553i $$-0.115027\pi$$
$$3$$ 1.00000i 0.577350i
$$4$$ 1.00000 0.500000
$$5$$ −1.00000 + 2.00000i −0.447214 + 0.894427i
$$6$$ −1.00000 −0.408248
$$7$$ 4.00000i 1.51186i −0.654654 0.755929i $$-0.727186\pi$$
0.654654 0.755929i $$-0.272814\pi$$
$$8$$ 3.00000i 1.06066i
$$9$$ −1.00000 −0.333333
$$10$$ 2.00000 + 1.00000i 0.632456 + 0.316228i
$$11$$ 0 0
$$12$$ 1.00000i 0.288675i
$$13$$ 2.00000i 0.554700i 0.960769 + 0.277350i $$0.0894562\pi$$
−0.960769 + 0.277350i $$0.910544\pi$$
$$14$$ −4.00000 −1.06904
$$15$$ 2.00000 + 1.00000i 0.516398 + 0.258199i
$$16$$ −1.00000 −0.250000
$$17$$ 2.00000i 0.485071i −0.970143 0.242536i $$-0.922021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ −8.00000 −1.83533 −0.917663 0.397360i $$-0.869927\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ −1.00000 + 2.00000i −0.223607 + 0.447214i
$$21$$ −4.00000 −0.872872
$$22$$ 0 0
$$23$$ 4.00000i 0.834058i 0.908893 + 0.417029i $$0.136929\pi$$
−0.908893 + 0.417029i $$0.863071\pi$$
$$24$$ −3.00000 −0.612372
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ 2.00000 0.392232
$$27$$ 1.00000i 0.192450i
$$28$$ 4.00000i 0.755929i
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 1.00000 2.00000i 0.182574 0.365148i
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 5.00000i 0.883883i
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 8.00000 + 4.00000i 1.35225 + 0.676123i
$$36$$ −1.00000 −0.166667
$$37$$ 8.00000i 1.31519i −0.753371 0.657596i $$-0.771573\pi$$
0.753371 0.657596i $$-0.228427\pi$$
$$38$$ 8.00000i 1.29777i
$$39$$ 2.00000 0.320256
$$40$$ 6.00000 + 3.00000i 0.948683 + 0.474342i
$$41$$ 12.0000 1.87409 0.937043 0.349215i $$-0.113552\pi$$
0.937043 + 0.349215i $$0.113552\pi$$
$$42$$ 4.00000i 0.617213i
$$43$$ 8.00000i 1.21999i −0.792406 0.609994i $$-0.791172\pi$$
0.792406 0.609994i $$-0.208828\pi$$
$$44$$ 0 0
$$45$$ 1.00000 2.00000i 0.149071 0.298142i
$$46$$ 4.00000 0.589768
$$47$$ 4.00000i 0.583460i 0.956501 + 0.291730i $$0.0942309\pi$$
−0.956501 + 0.291730i $$0.905769\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −9.00000 −1.28571
$$50$$ −4.00000 + 3.00000i −0.565685 + 0.424264i
$$51$$ −2.00000 −0.280056
$$52$$ 2.00000i 0.277350i
$$53$$ 4.00000i 0.549442i −0.961524 0.274721i $$-0.911414\pi$$
0.961524 0.274721i $$-0.0885855\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 0 0
$$56$$ −12.0000 −1.60357
$$57$$ 8.00000i 1.05963i
$$58$$ 4.00000i 0.525226i
$$59$$ 8.00000 1.04151 0.520756 0.853706i $$-0.325650\pi$$
0.520756 + 0.853706i $$0.325650\pi$$
$$60$$ 2.00000 + 1.00000i 0.258199 + 0.129099i
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 8.00000i 1.01600i
$$63$$ 4.00000i 0.503953i
$$64$$ −7.00000 −0.875000
$$65$$ −4.00000 2.00000i −0.496139 0.248069i
$$66$$ 0 0
$$67$$ 4.00000i 0.488678i 0.969690 + 0.244339i $$0.0785709\pi$$
−0.969690 + 0.244339i $$0.921429\pi$$
$$68$$ 2.00000i 0.242536i
$$69$$ 4.00000 0.481543
$$70$$ 4.00000 8.00000i 0.478091 0.956183i
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 3.00000i 0.353553i
$$73$$ 2.00000i 0.234082i 0.993127 + 0.117041i $$0.0373409\pi$$
−0.993127 + 0.117041i $$0.962659\pi$$
$$74$$ −8.00000 −0.929981
$$75$$ −4.00000 + 3.00000i −0.461880 + 0.346410i
$$76$$ −8.00000 −0.917663
$$77$$ 0 0
$$78$$ 2.00000i 0.226455i
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 1.00000 2.00000i 0.111803 0.223607i
$$81$$ 1.00000 0.111111
$$82$$ 12.0000i 1.32518i
$$83$$ 4.00000i 0.439057i 0.975606 + 0.219529i $$0.0704519\pi$$
−0.975606 + 0.219529i $$0.929548\pi$$
$$84$$ −4.00000 −0.436436
$$85$$ 4.00000 + 2.00000i 0.433861 + 0.216930i
$$86$$ −8.00000 −0.862662
$$87$$ 4.00000i 0.428845i
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ −2.00000 1.00000i −0.210819 0.105409i
$$91$$ 8.00000 0.838628
$$92$$ 4.00000i 0.417029i
$$93$$ 8.00000i 0.829561i
$$94$$ 4.00000 0.412568
$$95$$ 8.00000 16.0000i 0.820783 1.64157i
$$96$$ −5.00000 −0.510310
$$97$$ 8.00000i 0.812277i 0.913812 + 0.406138i $$0.133125\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 9.00000i 0.909137i
$$99$$ 0 0
$$100$$ −3.00000 4.00000i −0.300000 0.400000i
$$101$$ −4.00000 −0.398015 −0.199007 0.979998i $$-0.563772\pi$$
−0.199007 + 0.979998i $$0.563772\pi$$
$$102$$ 2.00000i 0.198030i
$$103$$ 12.0000i 1.18240i −0.806527 0.591198i $$-0.798655\pi$$
0.806527 0.591198i $$-0.201345\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 4.00000 8.00000i 0.390360 0.780720i
$$106$$ −4.00000 −0.388514
$$107$$ 12.0000i 1.16008i −0.814587 0.580042i $$-0.803036\pi$$
0.814587 0.580042i $$-0.196964\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ 8.00000 0.766261 0.383131 0.923694i $$-0.374846\pi$$
0.383131 + 0.923694i $$0.374846\pi$$
$$110$$ 0 0
$$111$$ −8.00000 −0.759326
$$112$$ 4.00000i 0.377964i
$$113$$ 12.0000i 1.12887i 0.825479 + 0.564433i $$0.190905\pi$$
−0.825479 + 0.564433i $$0.809095\pi$$
$$114$$ 8.00000 0.749269
$$115$$ −8.00000 4.00000i −0.746004 0.373002i
$$116$$ −4.00000 −0.371391
$$117$$ 2.00000i 0.184900i
$$118$$ 8.00000i 0.736460i
$$119$$ −8.00000 −0.733359
$$120$$ 3.00000 6.00000i 0.273861 0.547723i
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 12.0000i 1.08200i
$$124$$ −8.00000 −0.718421
$$125$$ 11.0000 2.00000i 0.983870 0.178885i
$$126$$ 4.00000 0.356348
$$127$$ 4.00000i 0.354943i 0.984126 + 0.177471i $$0.0567917\pi$$
−0.984126 + 0.177471i $$0.943208\pi$$
$$128$$ 3.00000i 0.265165i
$$129$$ −8.00000 −0.704361
$$130$$ −2.00000 + 4.00000i −0.175412 + 0.350823i
$$131$$ 8.00000 0.698963 0.349482 0.936943i $$-0.386358\pi$$
0.349482 + 0.936943i $$0.386358\pi$$
$$132$$ 0 0
$$133$$ 32.0000i 2.77475i
$$134$$ 4.00000 0.345547
$$135$$ −2.00000 1.00000i −0.172133 0.0860663i
$$136$$ −6.00000 −0.514496
$$137$$ 4.00000i 0.341743i 0.985293 + 0.170872i $$0.0546583\pi$$
−0.985293 + 0.170872i $$0.945342\pi$$
$$138$$ 4.00000i 0.340503i
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 8.00000 + 4.00000i 0.676123 + 0.338062i
$$141$$ 4.00000 0.336861
$$142$$ 12.0000i 1.00702i
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 4.00000 8.00000i 0.332182 0.664364i
$$146$$ 2.00000 0.165521
$$147$$ 9.00000i 0.742307i
$$148$$ 8.00000i 0.657596i
$$149$$ −20.0000 −1.63846 −0.819232 0.573462i $$-0.805600\pi$$
−0.819232 + 0.573462i $$0.805600\pi$$
$$150$$ 3.00000 + 4.00000i 0.244949 + 0.326599i
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 24.0000i 1.94666i
$$153$$ 2.00000i 0.161690i
$$154$$ 0 0
$$155$$ 8.00000 16.0000i 0.642575 1.28515i
$$156$$ 2.00000 0.160128
$$157$$ 8.00000i 0.638470i −0.947676 0.319235i $$-0.896574\pi$$
0.947676 0.319235i $$-0.103426\pi$$
$$158$$ 8.00000i 0.636446i
$$159$$ −4.00000 −0.317221
$$160$$ 10.0000 + 5.00000i 0.790569 + 0.395285i
$$161$$ 16.0000 1.26098
$$162$$ 1.00000i 0.0785674i
$$163$$ 20.0000i 1.56652i −0.621694 0.783260i $$-0.713555\pi$$
0.621694 0.783260i $$-0.286445\pi$$
$$164$$ 12.0000 0.937043
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ 24.0000i 1.85718i −0.371113 0.928588i $$-0.621024\pi$$
0.371113 0.928588i $$-0.378976\pi$$
$$168$$ 12.0000i 0.925820i
$$169$$ 9.00000 0.692308
$$170$$ 2.00000 4.00000i 0.153393 0.306786i
$$171$$ 8.00000 0.611775
$$172$$ 8.00000i 0.609994i
$$173$$ 14.0000i 1.06440i 0.846619 + 0.532200i $$0.178635\pi$$
−0.846619 + 0.532200i $$0.821365\pi$$
$$174$$ 4.00000 0.303239
$$175$$ −16.0000 + 12.0000i −1.20949 + 0.907115i
$$176$$ 0 0
$$177$$ 8.00000i 0.601317i
$$178$$ 6.00000i 0.449719i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 1.00000 2.00000i 0.0745356 0.149071i
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 8.00000i 0.592999i
$$183$$ 0 0
$$184$$ 12.0000 0.884652
$$185$$ 16.0000 + 8.00000i 1.17634 + 0.588172i
$$186$$ 8.00000 0.586588
$$187$$ 0 0
$$188$$ 4.00000i 0.291730i
$$189$$ 4.00000 0.290957
$$190$$ −16.0000 8.00000i −1.16076 0.580381i
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 7.00000i 0.505181i
$$193$$ 6.00000i 0.431889i −0.976406 0.215945i $$-0.930717\pi$$
0.976406 0.215945i $$-0.0692831\pi$$
$$194$$ 8.00000 0.574367
$$195$$ −2.00000 + 4.00000i −0.143223 + 0.286446i
$$196$$ −9.00000 −0.642857
$$197$$ 6.00000i 0.427482i −0.976890 0.213741i $$-0.931435\pi$$
0.976890 0.213741i $$-0.0685649\pi$$
$$198$$ 0 0
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ −12.0000 + 9.00000i −0.848528 + 0.636396i
$$201$$ 4.00000 0.282138
$$202$$ 4.00000i 0.281439i
$$203$$ 16.0000i 1.12298i
$$204$$ −2.00000 −0.140028
$$205$$ −12.0000 + 24.0000i −0.838116 + 1.67623i
$$206$$ −12.0000 −0.836080
$$207$$ 4.00000i 0.278019i
$$208$$ 2.00000i 0.138675i
$$209$$ 0 0
$$210$$ −8.00000 4.00000i −0.552052 0.276026i
$$211$$ −16.0000 −1.10149 −0.550743 0.834675i $$-0.685655\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ 4.00000i 0.274721i
$$213$$ 12.0000i 0.822226i
$$214$$ −12.0000 −0.820303
$$215$$ 16.0000 + 8.00000i 1.09119 + 0.545595i
$$216$$ 3.00000 0.204124
$$217$$ 32.0000i 2.17230i
$$218$$ 8.00000i 0.541828i
$$219$$ 2.00000 0.135147
$$220$$ 0 0
$$221$$ 4.00000 0.269069
$$222$$ 8.00000i 0.536925i
$$223$$ 4.00000i 0.267860i −0.990991 0.133930i $$-0.957240\pi$$
0.990991 0.133930i $$-0.0427597\pi$$
$$224$$ −20.0000 −1.33631
$$225$$ 3.00000 + 4.00000i 0.200000 + 0.266667i
$$226$$ 12.0000 0.798228
$$227$$ 12.0000i 0.796468i 0.917284 + 0.398234i $$0.130377\pi$$
−0.917284 + 0.398234i $$0.869623\pi$$
$$228$$ 8.00000i 0.529813i
$$229$$ 22.0000 1.45380 0.726900 0.686743i $$-0.240960\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ −4.00000 + 8.00000i −0.263752 + 0.527504i
$$231$$ 0 0
$$232$$ 12.0000i 0.787839i
$$233$$ 6.00000i 0.393073i 0.980497 + 0.196537i $$0.0629694\pi$$
−0.980497 + 0.196537i $$0.937031\pi$$
$$234$$ −2.00000 −0.130744
$$235$$ −8.00000 4.00000i −0.521862 0.260931i
$$236$$ 8.00000 0.520756
$$237$$ 8.00000i 0.519656i
$$238$$ 8.00000i 0.518563i
$$239$$ 24.0000 1.55243 0.776215 0.630468i $$-0.217137\pi$$
0.776215 + 0.630468i $$0.217137\pi$$
$$240$$ −2.00000 1.00000i −0.129099 0.0645497i
$$241$$ 8.00000 0.515325 0.257663 0.966235i $$-0.417048\pi$$
0.257663 + 0.966235i $$0.417048\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ 9.00000 18.0000i 0.574989 1.14998i
$$246$$ −12.0000 −0.765092
$$247$$ 16.0000i 1.01806i
$$248$$ 24.0000i 1.52400i
$$249$$ 4.00000 0.253490
$$250$$ −2.00000 11.0000i −0.126491 0.695701i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 4.00000i 0.251976i
$$253$$ 0 0
$$254$$ 4.00000 0.250982
$$255$$ 2.00000 4.00000i 0.125245 0.250490i
$$256$$ −17.0000 −1.06250
$$257$$ 4.00000i 0.249513i −0.992187 0.124757i $$-0.960185\pi$$
0.992187 0.124757i $$-0.0398150\pi$$
$$258$$ 8.00000i 0.498058i
$$259$$ −32.0000 −1.98838
$$260$$ −4.00000 2.00000i −0.248069 0.124035i
$$261$$ 4.00000 0.247594
$$262$$ 8.00000i 0.494242i
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 8.00000 + 4.00000i 0.491436 + 0.245718i
$$266$$ 32.0000 1.96205
$$267$$ 6.00000i 0.367194i
$$268$$ 4.00000i 0.244339i
$$269$$ 26.0000 1.58525 0.792624 0.609711i $$-0.208714\pi$$
0.792624 + 0.609711i $$0.208714\pi$$
$$270$$ −1.00000 + 2.00000i −0.0608581 + 0.121716i
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 8.00000i 0.484182i
$$274$$ 4.00000 0.241649
$$275$$ 0 0
$$276$$ 4.00000 0.240772
$$277$$ 10.0000i 0.600842i −0.953807 0.300421i $$-0.902873\pi$$
0.953807 0.300421i $$-0.0971271\pi$$
$$278$$ 16.0000i 0.959616i
$$279$$ 8.00000 0.478947
$$280$$ 12.0000 24.0000i 0.717137 1.43427i
$$281$$ 12.0000 0.715860 0.357930 0.933748i $$-0.383483\pi$$
0.357930 + 0.933748i $$0.383483\pi$$
$$282$$ 4.00000i 0.238197i
$$283$$ 16.0000i 0.951101i −0.879688 0.475551i $$-0.842249\pi$$
0.879688 0.475551i $$-0.157751\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ −16.0000 8.00000i −0.947758 0.473879i
$$286$$ 0 0
$$287$$ 48.0000i 2.83335i
$$288$$ 5.00000i 0.294628i
$$289$$ 13.0000 0.764706
$$290$$ −8.00000 4.00000i −0.469776 0.234888i
$$291$$ 8.00000 0.468968
$$292$$ 2.00000i 0.117041i
$$293$$ 6.00000i 0.350524i −0.984522 0.175262i $$-0.943923\pi$$
0.984522 0.175262i $$-0.0560772\pi$$
$$294$$ 9.00000 0.524891
$$295$$ −8.00000 + 16.0000i −0.465778 + 0.931556i
$$296$$ −24.0000 −1.39497
$$297$$ 0 0
$$298$$ 20.0000i 1.15857i
$$299$$ −8.00000 −0.462652
$$300$$ −4.00000 + 3.00000i −0.230940 + 0.173205i
$$301$$ −32.0000 −1.84445
$$302$$ 0 0
$$303$$ 4.00000i 0.229794i
$$304$$ 8.00000 0.458831
$$305$$ 0 0
$$306$$ 2.00000 0.114332
$$307$$ 24.0000i 1.36975i −0.728659 0.684876i $$-0.759856\pi$$
0.728659 0.684876i $$-0.240144\pi$$
$$308$$ 0 0
$$309$$ −12.0000 −0.682656
$$310$$ −16.0000 8.00000i −0.908739 0.454369i
$$311$$ 28.0000 1.58773 0.793867 0.608091i $$-0.208065\pi$$
0.793867 + 0.608091i $$0.208065\pi$$
$$312$$ 6.00000i 0.339683i
$$313$$ 16.0000i 0.904373i 0.891923 + 0.452187i $$0.149356\pi$$
−0.891923 + 0.452187i $$0.850644\pi$$
$$314$$ −8.00000 −0.451466
$$315$$ −8.00000 4.00000i −0.450749 0.225374i
$$316$$ −8.00000 −0.450035
$$317$$ 20.0000i 1.12331i −0.827371 0.561656i $$-0.810164\pi$$
0.827371 0.561656i $$-0.189836\pi$$
$$318$$ 4.00000i 0.224309i
$$319$$ 0 0
$$320$$ 7.00000 14.0000i 0.391312 0.782624i
$$321$$ −12.0000 −0.669775
$$322$$ 16.0000i 0.891645i
$$323$$ 16.0000i 0.890264i
$$324$$ 1.00000 0.0555556
$$325$$ 8.00000 6.00000i 0.443760 0.332820i
$$326$$ −20.0000 −1.10770
$$327$$ 8.00000i 0.442401i
$$328$$ 36.0000i 1.98777i
$$329$$ 16.0000 0.882109
$$330$$ 0 0
$$331$$ 4.00000 0.219860 0.109930 0.993939i $$-0.464937\pi$$
0.109930 + 0.993939i $$0.464937\pi$$
$$332$$ 4.00000i 0.219529i
$$333$$ 8.00000i 0.438397i
$$334$$ −24.0000 −1.31322
$$335$$ −8.00000 4.00000i −0.437087 0.218543i
$$336$$ 4.00000 0.218218
$$337$$ 26.0000i 1.41631i −0.706057 0.708155i $$-0.749528\pi$$
0.706057 0.708155i $$-0.250472\pi$$
$$338$$ 9.00000i 0.489535i
$$339$$ 12.0000 0.651751
$$340$$ 4.00000 + 2.00000i 0.216930 + 0.108465i
$$341$$ 0 0
$$342$$ 8.00000i 0.432590i
$$343$$ 8.00000i 0.431959i
$$344$$ −24.0000 −1.29399
$$345$$ −4.00000 + 8.00000i −0.215353 + 0.430706i
$$346$$ 14.0000 0.752645
$$347$$ 12.0000i 0.644194i −0.946707 0.322097i $$-0.895612\pi$$
0.946707 0.322097i $$-0.104388\pi$$
$$348$$ 4.00000i 0.214423i
$$349$$ −16.0000 −0.856460 −0.428230 0.903670i $$-0.640863\pi$$
−0.428230 + 0.903670i $$0.640863\pi$$
$$350$$ 12.0000 + 16.0000i 0.641427 + 0.855236i
$$351$$ −2.00000 −0.106752
$$352$$ 0 0
$$353$$ 12.0000i 0.638696i 0.947638 + 0.319348i $$0.103464\pi$$
−0.947638 + 0.319348i $$0.896536\pi$$
$$354$$ −8.00000 −0.425195
$$355$$ 12.0000 24.0000i 0.636894 1.27379i
$$356$$ −6.00000 −0.317999
$$357$$ 8.00000i 0.423405i
$$358$$ 0 0
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ −6.00000 3.00000i −0.316228 0.158114i
$$361$$ 45.0000 2.36842
$$362$$ 10.0000i 0.525588i
$$363$$ 0 0
$$364$$ 8.00000 0.419314
$$365$$ −4.00000 2.00000i −0.209370 0.104685i
$$366$$ 0 0
$$367$$ 36.0000i 1.87918i −0.342296 0.939592i $$-0.611204\pi$$
0.342296 0.939592i $$-0.388796\pi$$
$$368$$ 4.00000i 0.208514i
$$369$$ −12.0000 −0.624695
$$370$$ 8.00000 16.0000i 0.415900 0.831800i
$$371$$ −16.0000 −0.830679
$$372$$ 8.00000i 0.414781i
$$373$$ 22.0000i 1.13912i 0.821951 + 0.569558i $$0.192886\pi$$
−0.821951 + 0.569558i $$0.807114\pi$$
$$374$$ 0 0
$$375$$ −2.00000 11.0000i −0.103280 0.568038i
$$376$$ 12.0000 0.618853
$$377$$ 8.00000i 0.412021i
$$378$$ 4.00000i 0.205738i
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 8.00000 16.0000i 0.410391 0.820783i
$$381$$ 4.00000 0.204926
$$382$$ 12.0000i 0.613973i
$$383$$ 36.0000i 1.83951i −0.392488 0.919757i $$-0.628386\pi$$
0.392488 0.919757i $$-0.371614\pi$$
$$384$$ −3.00000 −0.153093
$$385$$ 0 0
$$386$$ −6.00000 −0.305392
$$387$$ 8.00000i 0.406663i
$$388$$ 8.00000i 0.406138i
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 4.00000 + 2.00000i 0.202548 + 0.101274i
$$391$$ 8.00000 0.404577
$$392$$ 27.0000i 1.36371i
$$393$$ 8.00000i 0.403547i
$$394$$ −6.00000 −0.302276
$$395$$ 8.00000 16.0000i 0.402524 0.805047i
$$396$$ 0 0
$$397$$ 8.00000i 0.401508i −0.979642 0.200754i $$-0.935661\pi$$
0.979642 0.200754i $$-0.0643393\pi$$
$$398$$ 16.0000i 0.802008i
$$399$$ 32.0000 1.60200
$$400$$ 3.00000 + 4.00000i 0.150000 + 0.200000i
$$401$$ −2.00000 −0.0998752 −0.0499376 0.998752i $$-0.515902\pi$$
−0.0499376 + 0.998752i $$0.515902\pi$$
$$402$$ 4.00000i 0.199502i
$$403$$ 16.0000i 0.797017i
$$404$$ −4.00000 −0.199007
$$405$$ −1.00000 + 2.00000i −0.0496904 + 0.0993808i
$$406$$ 16.0000 0.794067
$$407$$ 0 0
$$408$$ 6.00000i 0.297044i
$$409$$ 40.0000 1.97787 0.988936 0.148340i $$-0.0473931\pi$$
0.988936 + 0.148340i $$0.0473931\pi$$
$$410$$ 24.0000 + 12.0000i 1.18528 + 0.592638i
$$411$$ 4.00000 0.197305
$$412$$ 12.0000i 0.591198i
$$413$$ 32.0000i 1.57462i
$$414$$ −4.00000 −0.196589
$$415$$ −8.00000 4.00000i −0.392705 0.196352i
$$416$$ 10.0000 0.490290
$$417$$ 16.0000i 0.783523i
$$418$$ 0 0
$$419$$ −8.00000 −0.390826 −0.195413 0.980721i $$-0.562605\pi$$
−0.195413 + 0.980721i $$0.562605\pi$$
$$420$$ 4.00000 8.00000i 0.195180 0.390360i
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ 16.0000i 0.778868i
$$423$$ 4.00000i 0.194487i
$$424$$ −12.0000 −0.582772
$$425$$ −8.00000 + 6.00000i −0.388057 + 0.291043i
$$426$$ 12.0000 0.581402
$$427$$ 0 0
$$428$$ 12.0000i 0.580042i
$$429$$ 0 0
$$430$$ 8.00000 16.0000i 0.385794 0.771589i
$$431$$ −24.0000 −1.15604 −0.578020 0.816023i $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ 16.0000i 0.768911i 0.923144 + 0.384455i $$0.125611\pi$$
−0.923144 + 0.384455i $$0.874389\pi$$
$$434$$ 32.0000 1.53605
$$435$$ −8.00000 4.00000i −0.383571 0.191785i
$$436$$ 8.00000 0.383131
$$437$$ 32.0000i 1.53077i
$$438$$ 2.00000i 0.0955637i
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 9.00000 0.428571
$$442$$ 4.00000i 0.190261i
$$443$$ 12.0000i 0.570137i 0.958507 + 0.285069i $$0.0920164\pi$$
−0.958507 + 0.285069i $$0.907984\pi$$
$$444$$ −8.00000 −0.379663
$$445$$ 6.00000 12.0000i 0.284427 0.568855i
$$446$$ −4.00000 −0.189405
$$447$$ 20.0000i 0.945968i
$$448$$ 28.0000i 1.32288i
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 4.00000 3.00000i 0.188562 0.141421i
$$451$$ 0 0
$$452$$ 12.0000i 0.564433i
$$453$$ 0 0
$$454$$ 12.0000 0.563188
$$455$$ −8.00000 + 16.0000i −0.375046 + 0.750092i
$$456$$ 24.0000 1.12390
$$457$$ 2.00000i 0.0935561i 0.998905 + 0.0467780i $$0.0148953\pi$$
−0.998905 + 0.0467780i $$0.985105\pi$$
$$458$$ 22.0000i 1.02799i
$$459$$ 2.00000 0.0933520
$$460$$ −8.00000 4.00000i −0.373002 0.186501i
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ 28.0000i 1.30127i 0.759390 + 0.650635i $$0.225497\pi$$
−0.759390 + 0.650635i $$0.774503\pi$$
$$464$$ 4.00000 0.185695
$$465$$ −16.0000 8.00000i −0.741982 0.370991i
$$466$$ 6.00000 0.277945
$$467$$ 12.0000i 0.555294i −0.960683 0.277647i $$-0.910445\pi$$
0.960683 0.277647i $$-0.0895545\pi$$
$$468$$ 2.00000i 0.0924500i
$$469$$ 16.0000 0.738811
$$470$$ −4.00000 + 8.00000i −0.184506 + 0.369012i
$$471$$ −8.00000 −0.368621
$$472$$ 24.0000i 1.10469i
$$473$$ 0 0
$$474$$ 8.00000 0.367452
$$475$$ 24.0000 + 32.0000i 1.10120 + 1.46826i
$$476$$ −8.00000 −0.366679
$$477$$ 4.00000i 0.183147i
$$478$$ 24.0000i 1.09773i
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 5.00000 10.0000i 0.228218 0.456435i
$$481$$ 16.0000 0.729537
$$482$$ 8.00000i 0.364390i
$$483$$ 16.0000i 0.728025i
$$484$$ 0 0
$$485$$ −16.0000 8.00000i −0.726523 0.363261i
$$486$$ −1.00000 −0.0453609
$$487$$ 20.0000i 0.906287i −0.891438 0.453143i $$-0.850303\pi$$
0.891438 0.453143i $$-0.149697\pi$$
$$488$$ 0 0
$$489$$ −20.0000 −0.904431
$$490$$ −18.0000 9.00000i −0.813157 0.406579i
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 12.0000i 0.541002i
$$493$$ 8.00000i 0.360302i
$$494$$ −16.0000 −0.719874
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 48.0000i 2.15309i
$$498$$ 4.00000i 0.179244i
$$499$$ 12.0000 0.537194 0.268597 0.963253i $$-0.413440\pi$$
0.268597 + 0.963253i $$0.413440\pi$$
$$500$$ 11.0000 2.00000i 0.491935 0.0894427i
$$501$$ −24.0000 −1.07224
$$502$$ 0 0
$$503$$ 24.0000i 1.07011i 0.844818 + 0.535054i $$0.179709\pi$$
−0.844818 + 0.535054i $$0.820291\pi$$
$$504$$ 12.0000 0.534522
$$505$$ 4.00000 8.00000i 0.177998 0.355995i
$$506$$ 0 0
$$507$$ 9.00000i 0.399704i
$$508$$ 4.00000i 0.177471i
$$509$$ −26.0000 −1.15243 −0.576215 0.817298i $$-0.695471\pi$$
−0.576215 + 0.817298i $$0.695471\pi$$
$$510$$ −4.00000 2.00000i −0.177123 0.0885615i
$$511$$ 8.00000 0.353899
$$512$$ 11.0000i 0.486136i
$$513$$ 8.00000i 0.353209i
$$514$$ −4.00000 −0.176432
$$515$$ 24.0000 + 12.0000i 1.05757 + 0.528783i
$$516$$ −8.00000 −0.352180
$$517$$ 0 0
$$518$$ 32.0000i 1.40600i
$$519$$ 14.0000 0.614532
$$520$$ −6.00000 + 12.0000i −0.263117 + 0.526235i
$$521$$ 22.0000 0.963837 0.481919 0.876216i $$-0.339940\pi$$
0.481919 + 0.876216i $$0.339940\pi$$
$$522$$ 4.00000i 0.175075i
$$523$$ 24.0000i 1.04945i 0.851273 + 0.524723i $$0.175831\pi$$
−0.851273 + 0.524723i $$0.824169\pi$$
$$524$$ 8.00000 0.349482
$$525$$ 12.0000 + 16.0000i 0.523723 + 0.698297i
$$526$$ 0 0
$$527$$ 16.0000i 0.696971i
$$528$$ 0 0
$$529$$ 7.00000 0.304348
$$530$$ 4.00000 8.00000i 0.173749 0.347498i
$$531$$ −8.00000 −0.347170
$$532$$ 32.0000i 1.38738i
$$533$$ 24.0000i 1.03956i
$$534$$ 6.00000 0.259645
$$535$$ 24.0000 + 12.0000i 1.03761 + 0.518805i
$$536$$ 12.0000 0.518321
$$537$$ 0 0
$$538$$ 26.0000i 1.12094i
$$539$$ 0 0
$$540$$ −2.00000 1.00000i −0.0860663 0.0430331i
$$541$$ 8.00000 0.343947 0.171973 0.985102i $$-0.444986\pi$$
0.171973 + 0.985102i $$0.444986\pi$$
$$542$$ 16.0000i 0.687259i
$$543$$ 10.0000i 0.429141i
$$544$$ −10.0000 −0.428746
$$545$$ −8.00000 + 16.0000i −0.342682 + 0.685365i
$$546$$ −8.00000 −0.342368
$$547$$ 8.00000i 0.342055i 0.985266 + 0.171028i $$0.0547087\pi$$
−0.985266 + 0.171028i $$0.945291\pi$$
$$548$$ 4.00000i 0.170872i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 32.0000 1.36325
$$552$$ 12.0000i 0.510754i
$$553$$ 32.0000i 1.36078i
$$554$$ −10.0000 −0.424859
$$555$$ 8.00000 16.0000i 0.339581 0.679162i
$$556$$ −16.0000 −0.678551
$$557$$ 14.0000i 0.593199i −0.955002 0.296600i $$-0.904147\pi$$
0.955002 0.296600i $$-0.0958526\pi$$
$$558$$ 8.00000i 0.338667i
$$559$$ 16.0000 0.676728
$$560$$ −8.00000 4.00000i −0.338062 0.169031i
$$561$$ 0 0
$$562$$ 12.0000i 0.506189i
$$563$$ 36.0000i 1.51722i 0.651546 + 0.758610i $$0.274121\pi$$
−0.651546 + 0.758610i $$0.725879\pi$$
$$564$$ 4.00000 0.168430
$$565$$ −24.0000 12.0000i −1.00969 0.504844i
$$566$$ −16.0000 −0.672530
$$567$$ 4.00000i 0.167984i
$$568$$ 36.0000i 1.51053i
$$569$$ −44.0000 −1.84458 −0.922288 0.386503i $$-0.873683\pi$$
−0.922288 + 0.386503i $$0.873683\pi$$
$$570$$ −8.00000 + 16.0000i −0.335083 + 0.670166i
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 0 0
$$573$$ 12.0000i 0.501307i
$$574$$ −48.0000 −2.00348
$$575$$ 16.0000 12.0000i 0.667246 0.500435i
$$576$$ 7.00000 0.291667
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ −6.00000 −0.249351
$$580$$ 4.00000 8.00000i 0.166091 0.332182i
$$581$$ 16.0000 0.663792
$$582$$ 8.00000i 0.331611i
$$583$$ 0 0
$$584$$ 6.00000 0.248282
$$585$$ 4.00000 + 2.00000i 0.165380 + 0.0826898i
$$586$$ −6.00000 −0.247858
$$587$$ 12.0000i 0.495293i −0.968850 0.247647i $$-0.920343\pi$$
0.968850 0.247647i $$-0.0796572\pi$$
$$588$$ 9.00000i 0.371154i
$$589$$ 64.0000 2.63707
$$590$$ 16.0000 + 8.00000i 0.658710 + 0.329355i
$$591$$ −6.00000 −0.246807
$$592$$ 8.00000i 0.328798i
$$593$$ 14.0000i 0.574911i −0.957794 0.287456i $$-0.907191\pi$$
0.957794 0.287456i $$-0.0928094\pi$$
$$594$$ 0 0
$$595$$ 8.00000 16.0000i 0.327968 0.655936i
$$596$$ −20.0000 −0.819232
$$597$$ 16.0000i 0.654836i
$$598$$ 8.00000i 0.327144i
$$599$$ 12.0000 0.490307 0.245153 0.969484i $$-0.421162\pi$$
0.245153 + 0.969484i $$0.421162\pi$$
$$600$$ 9.00000 + 12.0000i 0.367423 + 0.489898i
$$601$$ −32.0000 −1.30531 −0.652654 0.757656i $$-0.726344\pi$$
−0.652654 + 0.757656i $$0.726344\pi$$
$$602$$ 32.0000i 1.30422i
$$603$$ 4.00000i 0.162893i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 4.00000 0.162489
$$607$$ 20.0000i 0.811775i −0.913923 0.405887i $$-0.866962\pi$$
0.913923 0.405887i $$-0.133038\pi$$
$$608$$ 40.0000i 1.62221i
$$609$$ 16.0000 0.648353
$$610$$ 0 0
$$611$$ −8.00000 −0.323645
$$612$$ 2.00000i 0.0808452i
$$613$$ 42.0000i 1.69636i −0.529705 0.848182i $$-0.677697\pi$$
0.529705 0.848182i $$-0.322303\pi$$
$$614$$ −24.0000 −0.968561
$$615$$ 24.0000 + 12.0000i 0.967773 + 0.483887i
$$616$$ 0 0
$$617$$ 28.0000i 1.12724i 0.826035 + 0.563619i $$0.190591\pi$$
−0.826035 + 0.563619i $$0.809409\pi$$
$$618$$ 12.0000i 0.482711i
$$619$$ 36.0000 1.44696 0.723481 0.690344i $$-0.242541\pi$$
0.723481 + 0.690344i $$0.242541\pi$$
$$620$$ 8.00000 16.0000i 0.321288 0.642575i
$$621$$ −4.00000 −0.160514
$$622$$ 28.0000i 1.12270i
$$623$$ 24.0000i 0.961540i
$$624$$ −2.00000 −0.0800641
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 16.0000 0.639489
$$627$$ 0 0
$$628$$ 8.00000i 0.319235i
$$629$$ −16.0000 −0.637962
$$630$$ −4.00000 + 8.00000i −0.159364 + 0.318728i
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 24.0000i 0.954669i
$$633$$ 16.0000i 0.635943i
$$634$$ −20.0000 −0.794301
$$635$$ −8.00000 4.00000i −0.317470 0.158735i
$$636$$ −4.00000 −0.158610
$$637$$ 18.0000i 0.713186i
$$638$$ 0 0
$$639$$ 12.0000 0.474713
$$640$$ 6.00000 + 3.00000i 0.237171 + 0.118585i
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 12.0000i 0.473602i
$$643$$ 12.0000i 0.473234i 0.971603 + 0.236617i $$0.0760386\pi$$
−0.971603 + 0.236617i $$0.923961\pi$$
$$644$$ 16.0000 0.630488
$$645$$ 8.00000 16.0000i 0.315000 0.629999i
$$646$$ 16.0000 0.629512
$$647$$ 28.0000i 1.10079i 0.834903 + 0.550397i $$0.185524\pi$$
−0.834903 + 0.550397i $$0.814476\pi$$
$$648$$ 3.00000i 0.117851i
$$649$$ 0 0
$$650$$ −6.00000 8.00000i −0.235339 0.313786i
$$651$$ 32.0000 1.25418
$$652$$ 20.0000i 0.783260i
$$653$$ 28.0000i 1.09572i 0.836569 + 0.547862i $$0.184558\pi$$
−0.836569 + 0.547862i $$0.815442\pi$$
$$654$$ −8.00000 −0.312825
$$655$$ −8.00000 + 16.0000i −0.312586 + 0.625172i
$$656$$ −12.0000 −0.468521
$$657$$ 2.00000i 0.0780274i
$$658$$ 16.0000i 0.623745i
$$659$$ −24.0000 −0.934907 −0.467454 0.884018i $$-0.654829\pi$$
−0.467454 + 0.884018i $$0.654829\pi$$
$$660$$ 0 0
$$661$$ 6.00000 0.233373 0.116686 0.993169i $$-0.462773\pi$$
0.116686 + 0.993169i $$0.462773\pi$$
$$662$$ 4.00000i 0.155464i
$$663$$ 4.00000i 0.155347i
$$664$$ 12.0000 0.465690
$$665$$ −64.0000 32.0000i −2.48181 1.24091i
$$666$$ 8.00000 0.309994
$$667$$ 16.0000i 0.619522i
$$668$$ 24.0000i 0.928588i
$$669$$ −4.00000 −0.154649
$$670$$ −4.00000 + 8.00000i −0.154533 + 0.309067i
$$671$$ 0 0
$$672$$ 20.0000i 0.771517i
$$673$$ 38.0000i 1.46479i −0.680879 0.732396i $$-0.738402\pi$$
0.680879 0.732396i $$-0.261598\pi$$
$$674$$ −26.0000 −1.00148
$$675$$ 4.00000 3.00000i 0.153960 0.115470i
$$676$$ 9.00000 0.346154
$$677$$ 38.0000i 1.46046i 0.683202 + 0.730229i $$0.260587\pi$$
−0.683202 + 0.730229i $$0.739413\pi$$
$$678$$ 12.0000i 0.460857i
$$679$$ 32.0000 1.22805
$$680$$ 6.00000 12.0000i 0.230089 0.460179i
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ 4.00000i 0.153056i 0.997067 + 0.0765279i $$0.0243834\pi$$
−0.997067 + 0.0765279i $$0.975617\pi$$
$$684$$ 8.00000 0.305888
$$685$$ −8.00000 4.00000i −0.305664 0.152832i
$$686$$ 8.00000 0.305441
$$687$$ 22.0000i 0.839352i
$$688$$ 8.00000i 0.304997i
$$689$$ 8.00000 0.304776
$$690$$ 8.00000 + 4.00000i 0.304555 + 0.152277i
$$691$$ −20.0000 −0.760836 −0.380418 0.924815i $$-0.624220\pi$$
−0.380418 + 0.924815i $$0.624220\pi$$
$$692$$ 14.0000i 0.532200i
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 16.0000 32.0000i 0.606915 1.21383i
$$696$$ 12.0000 0.454859
$$697$$ 24.0000i 0.909065i
$$698$$ 16.0000i 0.605609i
$$699$$ 6.00000 0.226941
$$700$$ −16.0000 + 12.0000i −0.604743 + 0.453557i
$$701$$ 12.0000 0.453234 0.226617 0.973984i $$-0.427233\pi$$
0.226617 + 0.973984i $$0.427233\pi$$
$$702$$ 2.00000i 0.0754851i
$$703$$ 64.0000i 2.41381i
$$704$$ 0 0
$$705$$ −4.00000 + 8.00000i −0.150649 + 0.301297i
$$706$$ 12.0000 0.451626
$$707$$ 16.0000i 0.601742i
$$708$$ 8.00000i 0.300658i
$$709$$ −26.0000 −0.976450 −0.488225 0.872718i $$-0.662356\pi$$
−0.488225 + 0.872718i $$0.662356\pi$$
$$710$$ −24.0000 12.0000i −0.900704 0.450352i
$$711$$ 8.00000 0.300023
$$712$$ 18.0000i 0.674579i
$$713$$ 32.0000i 1.19841i
$$714$$ 8.00000 0.299392
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 24.0000i 0.896296i
$$718$$ 24.0000i 0.895672i
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ −1.00000 + 2.00000i −0.0372678 + 0.0745356i
$$721$$ −48.0000 −1.78761
$$722$$ 45.0000i 1.67473i
$$723$$ 8.00000i 0.297523i
$$724$$ −10.0000 −0.371647
$$725$$ 12.0000 + 16.0000i 0.445669 + 0.594225i
$$726$$ 0 0
$$727$$ 28.0000i 1.03846i −0.854634 0.519231i $$-0.826218\pi$$
0.854634 0.519231i $$-0.173782\pi$$
$$728$$ 24.0000i 0.889499i
$$729$$ −1.00000 −0.0370370
$$730$$ −2.00000 + 4.00000i −0.0740233 + 0.148047i
$$731$$ −16.0000 −0.591781
$$732$$ 0 0
$$733$$ 14.0000i 0.517102i 0.965998 + 0.258551i $$0.0832450\pi$$
−0.965998 + 0.258551i $$0.916755\pi$$
$$734$$ −36.0000 −1.32878
$$735$$ −18.0000 9.00000i −0.663940 0.331970i
$$736$$ 20.0000 0.737210
$$737$$ 0 0
$$738$$ 12.0000i 0.441726i
$$739$$ −16.0000 −0.588570 −0.294285 0.955718i $$-0.595081\pi$$
−0.294285 + 0.955718i $$0.595081\pi$$
$$740$$ 16.0000 + 8.00000i 0.588172 + 0.294086i
$$741$$ −16.0000 −0.587775
$$742$$ 16.0000i 0.587378i
$$743$$ 24.0000i 0.880475i −0.897881 0.440237i $$-0.854894\pi$$
0.897881 0.440237i $$-0.145106\pi$$
$$744$$ 24.0000 0.879883
$$745$$ 20.0000 40.0000i 0.732743 1.46549i
$$746$$ 22.0000 0.805477
$$747$$ 4.00000i 0.146352i
$$748$$ 0 0
$$749$$ −48.0000 −1.75388
$$750$$ −11.0000 + 2.00000i −0.401663 + 0.0730297i
$$751$$ −16.0000 −0.583848 −0.291924 0.956441i $$-0.594295\pi$$
−0.291924 + 0.956441i $$0.594295\pi$$
$$752$$ 4.00000i 0.145865i
$$753$$ 0 0
$$754$$ −8.00000 −0.291343
$$755$$ 0 0
$$756$$ 4.00000 0.145479
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 4.00000i 0.145287i
$$759$$ 0 0
$$760$$ −48.0000 24.0000i −1.74114 0.870572i
$$761$$ −36.0000 −1.30500 −0.652499 0.757789i $$-0.726280\pi$$
−0.652499 + 0.757789i $$0.726280\pi$$
$$762$$ 4.00000i 0.144905i
$$763$$ 32.0000i 1.15848i
$$764$$ 12.0000 0.434145
$$765$$ −4.00000 2.00000i −0.144620 0.0723102i
$$766$$ −36.0000 −1.30073
$$767$$ 16.0000i 0.577727i
$$768$$ 17.0000i 0.613435i
$$769$$ −16.0000 −0.576975 −0.288487 0.957484i $$-0.593152\pi$$
−0.288487 + 0.957484i $$0.593152\pi$$
$$770$$ 0 0
$$771$$ −4.00000 −0.144056
$$772$$ 6.00000i 0.215945i
$$773$$ 36.0000i 1.29483i −0.762138 0.647415i $$-0.775850\pi$$
0.762138 0.647415i $$-0.224150\pi$$
$$774$$ 8.00000 0.287554
$$775$$ 24.0000 + 32.0000i 0.862105 + 1.14947i
$$776$$ 24.0000 0.861550
$$777$$ 32.0000i 1.14799i
$$778$$ 18.0000i 0.645331i
$$779$$ −96.0000 −3.43956
$$780$$ −2.00000 + 4.00000i −0.0716115 + 0.143223i
$$781$$ 0 0
$$782$$ 8.00000i 0.286079i
$$783$$ 4.00000i 0.142948i
$$784$$ 9.00000 0.321429
$$785$$ 16.0000 + 8.00000i 0.571064 + 0.285532i
$$786$$ −8.00000 −0.285351
$$787$$ 32.0000i 1.14068i −0.821410 0.570338i $$-0.806812\pi$$
0.821410 0.570338i $$-0.193188\pi$$
$$788$$ 6.00000i 0.213741i
$$789$$ 0 0
$$790$$ −16.0000 8.00000i −0.569254 0.284627i
$$791$$ 48.0000