# Properties

 Label 3150.2.bf.c.1601.1 Level 3150 Weight 2 Character 3150.1601 Analytic conductor 25.153 Analytic rank 0 Dimension 8 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.bf (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.1528766367$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{24})$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 630) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 1601.1 Root $$0.965926 + 0.258819i$$ Character $$\chi$$ = 3150.1601 Dual form 3150.2.bf.c.1151.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.189469 + 2.63896i) q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.189469 + 2.63896i) q^{7} -1.00000i q^{8} +(2.55171 - 1.47323i) q^{11} +3.93185i q^{13} +(1.48356 - 2.19067i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.199801 + 0.346065i) q^{17} +(0.0305501 + 0.0176381i) q^{19} -2.94646 q^{22} +(-3.23205 - 1.86603i) q^{23} +(1.96593 - 3.40508i) q^{26} +(-2.38014 + 1.15539i) q^{28} +8.89898i q^{29} +(0.717439 - 0.414214i) q^{31} +(0.866025 - 0.500000i) q^{32} -0.399602i q^{34} +(-3.96593 + 6.86919i) q^{37} +(-0.0176381 - 0.0305501i) q^{38} +6.31079 q^{41} +3.03528 q^{43} +(2.55171 + 1.47323i) q^{44} +(1.86603 + 3.23205i) q^{46} +(2.90130 - 5.02520i) q^{47} +(-6.92820 - 1.00000i) q^{49} +(-3.40508 + 1.96593i) q^{52} +(3.72268 - 2.14929i) q^{53} +(2.63896 + 0.189469i) q^{56} +(4.44949 - 7.70674i) q^{58} +(2.78522 + 4.82415i) q^{59} +(-9.97710 - 5.76028i) q^{61} -0.828427 q^{62} -1.00000 q^{64} +(-6.25966 - 10.8420i) q^{67} +(-0.199801 + 0.346065i) q^{68} +1.93426i q^{71} +(0.297173 - 0.171573i) q^{73} +(6.86919 - 3.96593i) q^{74} +0.0352762i q^{76} +(3.40433 + 7.01299i) q^{77} +(-4.15331 + 7.19375i) q^{79} +(-5.46530 - 3.15539i) q^{82} -10.3490 q^{83} +(-2.62863 - 1.51764i) q^{86} +(-1.47323 - 2.55171i) q^{88} +(-3.08604 + 5.34519i) q^{89} +(-10.3760 - 0.744963i) q^{91} -3.73205i q^{92} +(-5.02520 + 2.90130i) q^{94} +15.6344i q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{4} + O(q^{10})$$ $$8q + 4q^{4} + 24q^{11} - 4q^{16} - 12q^{23} + 8q^{26} - 24q^{37} + 4q^{38} + 32q^{41} + 16q^{43} + 24q^{44} + 8q^{46} + 8q^{47} - 24q^{53} + 16q^{58} - 24q^{59} + 16q^{62} - 8q^{64} + 24q^{67} + 16q^{77} - 24q^{79} + 16q^{83} - 16q^{89} - 20q^{91} - 12q^{94} + 44q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$2801$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 0.500000i −0.612372 0.353553i
$$3$$ 0 0
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −0.189469 + 2.63896i −0.0716124 + 0.997433i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.55171 1.47323i 0.769370 0.444196i −0.0632797 0.997996i $$-0.520156\pi$$
0.832650 + 0.553800i $$0.186823\pi$$
$$12$$ 0 0
$$13$$ 3.93185i 1.09050i 0.838274 + 0.545250i $$0.183565\pi$$
−0.838274 + 0.545250i $$0.816435\pi$$
$$14$$ 1.48356 2.19067i 0.396499 0.585481i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 0.199801 + 0.346065i 0.0484588 + 0.0839331i 0.889237 0.457446i $$-0.151236\pi$$
−0.840779 + 0.541379i $$0.817902\pi$$
$$18$$ 0 0
$$19$$ 0.0305501 + 0.0176381i 0.00700867 + 0.00404646i 0.503500 0.863995i $$-0.332045\pi$$
−0.496492 + 0.868042i $$0.665379\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −2.94646 −0.628188
$$23$$ −3.23205 1.86603i −0.673929 0.389093i 0.123635 0.992328i $$-0.460545\pi$$
−0.797564 + 0.603235i $$0.793878\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 1.96593 3.40508i 0.385550 0.667792i
$$27$$ 0 0
$$28$$ −2.38014 + 1.15539i −0.449804 + 0.218349i
$$29$$ 8.89898i 1.65250i 0.563304 + 0.826250i $$0.309530\pi$$
−0.563304 + 0.826250i $$0.690470\pi$$
$$30$$ 0 0
$$31$$ 0.717439 0.414214i 0.128856 0.0743950i −0.434187 0.900823i $$-0.642964\pi$$
0.563042 + 0.826428i $$0.309631\pi$$
$$32$$ 0.866025 0.500000i 0.153093 0.0883883i
$$33$$ 0 0
$$34$$ 0.399602i 0.0685311i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −3.96593 + 6.86919i −0.651994 + 1.12929i 0.330644 + 0.943756i $$0.392734\pi$$
−0.982638 + 0.185532i $$0.940599\pi$$
$$38$$ −0.0176381 0.0305501i −0.00286128 0.00495588i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.31079 0.985580 0.492790 0.870148i $$-0.335977\pi$$
0.492790 + 0.870148i $$0.335977\pi$$
$$42$$ 0 0
$$43$$ 3.03528 0.462875 0.231438 0.972850i $$-0.425657\pi$$
0.231438 + 0.972850i $$0.425657\pi$$
$$44$$ 2.55171 + 1.47323i 0.384685 + 0.222098i
$$45$$ 0 0
$$46$$ 1.86603 + 3.23205i 0.275130 + 0.476540i
$$47$$ 2.90130 5.02520i 0.423198 0.733001i −0.573052 0.819519i $$-0.694241\pi$$
0.996250 + 0.0865180i $$0.0275740\pi$$
$$48$$ 0 0
$$49$$ −6.92820 1.00000i −0.989743 0.142857i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −3.40508 + 1.96593i −0.472200 + 0.272625i
$$53$$ 3.72268 2.14929i 0.511349 0.295228i −0.222039 0.975038i $$-0.571271\pi$$
0.733388 + 0.679810i $$0.237938\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 2.63896 + 0.189469i 0.352646 + 0.0253188i
$$57$$ 0 0
$$58$$ 4.44949 7.70674i 0.584247 1.01194i
$$59$$ 2.78522 + 4.82415i 0.362605 + 0.628050i 0.988389 0.151946i $$-0.0485540\pi$$
−0.625784 + 0.779997i $$0.715221\pi$$
$$60$$ 0 0
$$61$$ −9.97710 5.76028i −1.27744 0.737528i −0.301060 0.953605i $$-0.597340\pi$$
−0.976376 + 0.216077i $$0.930674\pi$$
$$62$$ −0.828427 −0.105210
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.25966 10.8420i −0.764739 1.32457i −0.940385 0.340113i $$-0.889535\pi$$
0.175646 0.984453i $$-0.443799\pi$$
$$68$$ −0.199801 + 0.346065i −0.0242294 + 0.0419666i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.93426i 0.229554i 0.993391 + 0.114777i $$0.0366153\pi$$
−0.993391 + 0.114777i $$0.963385\pi$$
$$72$$ 0 0
$$73$$ 0.297173 0.171573i 0.0347815 0.0200811i −0.482508 0.875891i $$-0.660274\pi$$
0.517290 + 0.855810i $$0.326941\pi$$
$$74$$ 6.86919 3.96593i 0.798527 0.461030i
$$75$$ 0 0
$$76$$ 0.0352762i 0.00404646i
$$77$$ 3.40433 + 7.01299i 0.387959 + 0.799205i
$$78$$ 0 0
$$79$$ −4.15331 + 7.19375i −0.467284 + 0.809360i −0.999301 0.0373736i $$-0.988101\pi$$
0.532017 + 0.846734i $$0.321434\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −5.46530 3.15539i −0.603542 0.348455i
$$83$$ −10.3490 −1.13595 −0.567974 0.823046i $$-0.692273\pi$$
−0.567974 + 0.823046i $$0.692273\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.62863 1.51764i −0.283452 0.163651i
$$87$$ 0 0
$$88$$ −1.47323 2.55171i −0.157047 0.272013i
$$89$$ −3.08604 + 5.34519i −0.327120 + 0.566589i −0.981939 0.189197i $$-0.939411\pi$$
0.654819 + 0.755786i $$0.272745\pi$$
$$90$$ 0 0
$$91$$ −10.3760 0.744963i −1.08770 0.0780933i
$$92$$ 3.73205i 0.389093i
$$93$$ 0 0
$$94$$ −5.02520 + 2.90130i −0.518310 + 0.299246i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 15.6344i 1.58744i 0.608286 + 0.793718i $$0.291857\pi$$
−0.608286 + 0.793718i $$0.708143\pi$$
$$98$$ 5.50000 + 4.33013i 0.555584 + 0.437409i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −9.02458 15.6310i −0.897979 1.55535i −0.830074 0.557654i $$-0.811702\pi$$
−0.0679057 0.997692i $$-0.521632\pi$$
$$102$$ 0 0
$$103$$ 7.37857 + 4.26002i 0.727032 + 0.419752i 0.817336 0.576162i $$-0.195450\pi$$
−0.0903031 + 0.995914i $$0.528784\pi$$
$$104$$ 3.93185 0.385550
$$105$$ 0 0
$$106$$ −4.29858 −0.417515
$$107$$ 14.7702 + 8.52761i 1.42789 + 0.824395i 0.996954 0.0779862i $$-0.0248490\pi$$
0.430939 + 0.902381i $$0.358182\pi$$
$$108$$ 0 0
$$109$$ 5.84909 + 10.1309i 0.560241 + 0.970366i 0.997475 + 0.0710185i $$0.0226249\pi$$
−0.437234 + 0.899348i $$0.644042\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −2.19067 1.48356i −0.206999 0.140184i
$$113$$ 13.5546i 1.27511i −0.770405 0.637554i $$-0.779946\pi$$
0.770405 0.637554i $$-0.220054\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −7.70674 + 4.44949i −0.715553 + 0.413125i
$$117$$ 0 0
$$118$$ 5.57045i 0.512801i
$$119$$ −0.951108 + 0.461698i −0.0871879 + 0.0423237i
$$120$$ 0 0
$$121$$ −1.15918 + 2.00775i −0.105380 + 0.182523i
$$122$$ 5.76028 + 9.97710i 0.521511 + 0.903284i
$$123$$ 0 0
$$124$$ 0.717439 + 0.414214i 0.0644279 + 0.0371975i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −8.95983 −0.795056 −0.397528 0.917590i $$-0.630132\pi$$
−0.397528 + 0.917590i $$0.630132\pi$$
$$128$$ 0.866025 + 0.500000i 0.0765466 + 0.0441942i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −6.39047 + 11.0686i −0.558338 + 0.967070i 0.439297 + 0.898342i $$0.355227\pi$$
−0.997635 + 0.0687282i $$0.978106\pi$$
$$132$$ 0 0
$$133$$ −0.0523345 + 0.0772785i −0.00453797 + 0.00670090i
$$134$$ 12.5193i 1.08150i
$$135$$ 0 0
$$136$$ 0.346065 0.199801i 0.0296748 0.0171328i
$$137$$ 4.78094 2.76028i 0.408464 0.235827i −0.281666 0.959513i $$-0.590887\pi$$
0.690129 + 0.723686i $$0.257554\pi$$
$$138$$ 0 0
$$139$$ 21.8471i 1.85305i 0.376235 + 0.926524i $$0.377218\pi$$
−0.376235 + 0.926524i $$0.622782\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0.967128 1.67511i 0.0811596 0.140572i
$$143$$ 5.79253 + 10.0330i 0.484396 + 0.838998i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −0.343146 −0.0283989
$$147$$ 0 0
$$148$$ −7.93185 −0.651994
$$149$$ −18.6179 10.7491i −1.52524 0.880598i −0.999552 0.0299204i $$-0.990475\pi$$
−0.525688 0.850677i $$-0.676192\pi$$
$$150$$ 0 0
$$151$$ −1.47531 2.55532i −0.120059 0.207949i 0.799732 0.600358i $$-0.204975\pi$$
−0.919791 + 0.392409i $$0.871642\pi$$
$$152$$ 0.0176381 0.0305501i 0.00143064 0.00247794i
$$153$$ 0 0
$$154$$ 0.558263 7.77559i 0.0449861 0.626575i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −19.4823 + 11.2481i −1.55486 + 0.897698i −0.557123 + 0.830430i $$0.688095\pi$$
−0.997735 + 0.0672682i $$0.978572\pi$$
$$158$$ 7.19375 4.15331i 0.572304 0.330420i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 5.53674 8.17569i 0.436356 0.644335i
$$162$$ 0 0
$$163$$ 11.4035 19.7515i 0.893192 1.54705i 0.0571664 0.998365i $$-0.481793\pi$$
0.836026 0.548690i $$-0.184873\pi$$
$$164$$ 3.15539 + 5.46530i 0.246395 + 0.426769i
$$165$$ 0 0
$$166$$ 8.96248 + 5.17449i 0.695624 + 0.401618i
$$167$$ −8.84961 −0.684803 −0.342402 0.939554i $$-0.611240\pi$$
−0.342402 + 0.939554i $$0.611240\pi$$
$$168$$ 0 0
$$169$$ −2.45946 −0.189189
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 1.51764 + 2.62863i 0.115719 + 0.200431i
$$173$$ −3.86843 + 6.70032i −0.294111 + 0.509416i −0.974778 0.223178i $$-0.928357\pi$$
0.680667 + 0.732593i $$0.261690\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 2.94646i 0.222098i
$$177$$ 0 0
$$178$$ 5.34519 3.08604i 0.400639 0.231309i
$$179$$ −0.417291 + 0.240923i −0.0311898 + 0.0180074i −0.515514 0.856881i $$-0.672399\pi$$
0.484324 + 0.874889i $$0.339066\pi$$
$$180$$ 0 0
$$181$$ 2.44876i 0.182015i 0.995850 + 0.0910075i $$0.0290087\pi$$
−0.995850 + 0.0910075i $$0.970991\pi$$
$$182$$ 8.61339 + 5.83315i 0.638467 + 0.432382i
$$183$$ 0 0
$$184$$ −1.86603 + 3.23205i −0.137565 + 0.238270i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 1.01967 + 0.588706i 0.0745655 + 0.0430504i
$$188$$ 5.80260 0.423198
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.89241 + 2.24728i 0.281645 + 0.162608i 0.634168 0.773195i $$-0.281343\pi$$
−0.352523 + 0.935803i $$0.614676\pi$$
$$192$$ 0 0
$$193$$ −6.28497 10.8859i −0.452402 0.783583i 0.546133 0.837698i $$-0.316099\pi$$
−0.998535 + 0.0541158i $$0.982766\pi$$
$$194$$ 7.81722 13.5398i 0.561243 0.972102i
$$195$$ 0 0
$$196$$ −2.59808 6.50000i −0.185577 0.464286i
$$197$$ 13.3748i 0.952916i 0.879197 + 0.476458i $$0.158080\pi$$
−0.879197 + 0.476458i $$0.841920\pi$$
$$198$$ 0 0
$$199$$ −23.5169 + 13.5775i −1.66707 + 0.962483i −0.697864 + 0.716231i $$0.745866\pi$$
−0.969206 + 0.246253i $$0.920801\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 18.0492i 1.26993i
$$203$$ −23.4840 1.68608i −1.64826 0.118339i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −4.26002 7.37857i −0.296810 0.514090i
$$207$$ 0 0
$$208$$ −3.40508 1.96593i −0.236100 0.136312i
$$209$$ 0.103940 0.00718968
$$210$$ 0 0
$$211$$ 18.4183 1.26797 0.633984 0.773346i $$-0.281419\pi$$
0.633984 + 0.773346i $$0.281419\pi$$
$$212$$ 3.72268 + 2.14929i 0.255675 + 0.147614i
$$213$$ 0 0
$$214$$ −8.52761 14.7702i −0.582935 1.00967i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0.957160 + 1.97177i 0.0649763 + 0.133853i
$$218$$ 11.6982i 0.792301i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.36068 + 0.785587i −0.0915290 + 0.0528443i
$$222$$ 0 0
$$223$$ 17.8045i 1.19228i 0.802881 + 0.596140i $$0.203300\pi$$
−0.802881 + 0.596140i $$0.796700\pi$$
$$224$$ 1.15539 + 2.38014i 0.0771980 + 0.159030i
$$225$$ 0 0
$$226$$ −6.77729 + 11.7386i −0.450819 + 0.780841i
$$227$$ −0.856140 1.48288i −0.0568240 0.0984220i 0.836214 0.548403i $$-0.184764\pi$$
−0.893038 + 0.449981i $$0.851431\pi$$
$$228$$ 0 0
$$229$$ 5.26142 + 3.03768i 0.347684 + 0.200736i 0.663665 0.748030i $$-0.269000\pi$$
−0.315981 + 0.948766i $$0.602333\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 8.89898 0.584247
$$233$$ 6.17109 + 3.56288i 0.404282 + 0.233412i 0.688330 0.725398i $$-0.258344\pi$$
−0.284048 + 0.958810i $$0.591678\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −2.78522 + 4.82415i −0.181303 + 0.314025i
$$237$$ 0 0
$$238$$ 1.05453 + 0.0757120i 0.0683552 + 0.00490768i
$$239$$ 18.7194i 1.21085i 0.795900 + 0.605427i $$0.206998\pi$$
−0.795900 + 0.605427i $$0.793002\pi$$
$$240$$ 0 0
$$241$$ 7.68036 4.43426i 0.494735 0.285636i −0.231802 0.972763i $$-0.574462\pi$$
0.726537 + 0.687128i $$0.241129\pi$$
$$242$$ 2.00775 1.15918i 0.129063 0.0745147i
$$243$$ 0 0
$$244$$ 11.5206i 0.737528i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −0.0693504 + 0.120118i −0.00441266 + 0.00764295i
$$248$$ −0.414214 0.717439i −0.0263026 0.0455574i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 22.1738 1.39960 0.699798 0.714341i $$-0.253273\pi$$
0.699798 + 0.714341i $$0.253273\pi$$
$$252$$ 0 0
$$253$$ −10.9964 −0.691335
$$254$$ 7.75944 + 4.47992i 0.486871 + 0.281095i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 8.41662 14.5780i 0.525014 0.909351i −0.474561 0.880222i $$-0.657393\pi$$
0.999576 0.0291289i $$-0.00927332\pi$$
$$258$$ 0 0
$$259$$ −17.3761 11.7674i −1.07970 0.731191i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 11.0686 6.39047i 0.683822 0.394805i
$$263$$ −19.1562 + 11.0599i −1.18122 + 0.681980i −0.956297 0.292396i $$-0.905548\pi$$
−0.224926 + 0.974376i $$0.572214\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0.0839622 0.0407579i 0.00514805 0.00249903i
$$267$$ 0 0
$$268$$ 6.25966 10.8420i 0.382369 0.662283i
$$269$$ 1.45049 + 2.51231i 0.0884377 + 0.153179i 0.906851 0.421452i $$-0.138479\pi$$
−0.818413 + 0.574630i $$0.805146\pi$$
$$270$$ 0 0
$$271$$ 15.1244 + 8.73205i 0.918739 + 0.530434i 0.883233 0.468935i $$-0.155362\pi$$
0.0355066 + 0.999369i $$0.488696\pi$$
$$272$$ −0.399602 −0.0242294
$$273$$ 0 0
$$274$$ −5.52056 −0.333509
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 2.28825 + 3.96336i 0.137488 + 0.238135i 0.926545 0.376184i $$-0.122764\pi$$
−0.789057 + 0.614319i $$0.789431\pi$$
$$278$$ 10.9236 18.9202i 0.655152 1.13476i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 9.55948i 0.570271i 0.958487 + 0.285135i $$0.0920386\pi$$
−0.958487 + 0.285135i $$0.907961\pi$$
$$282$$ 0 0
$$283$$ −9.46238 + 5.46311i −0.562480 + 0.324748i −0.754140 0.656713i $$-0.771946\pi$$
0.191660 + 0.981461i $$0.438613\pi$$
$$284$$ −1.67511 + 0.967128i −0.0993998 + 0.0573885i
$$285$$ 0 0
$$286$$ 11.5851i 0.685039i
$$287$$ −1.19570 + 16.6539i −0.0705798 + 0.983049i
$$288$$ 0 0
$$289$$ 8.42016 14.5841i 0.495303 0.857891i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0.297173 + 0.171573i 0.0173907 + 0.0100405i
$$293$$ −16.2280 −0.948052 −0.474026 0.880511i $$-0.657200\pi$$
−0.474026 + 0.880511i $$0.657200\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 6.86919 + 3.96593i 0.399263 + 0.230515i
$$297$$ 0 0
$$298$$ 10.7491 + 18.6179i 0.622677 + 1.07851i
$$299$$ 7.33694 12.7079i 0.424306 0.734919i
$$300$$ 0 0
$$301$$ −0.575090 + 8.00997i −0.0331476 + 0.461687i
$$302$$ 2.95063i 0.169790i
$$303$$ 0 0
$$304$$ −0.0305501 + 0.0176381i −0.00175217 + 0.00101161i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 12.3782i 0.706462i 0.935536 + 0.353231i $$0.114917\pi$$
−0.935536 + 0.353231i $$0.885083\pi$$
$$308$$ −4.37127 + 6.45473i −0.249076 + 0.367792i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 11.4312 + 19.7995i 0.648206 + 1.12272i 0.983551 + 0.180630i $$0.0578136\pi$$
−0.335346 + 0.942095i $$0.608853\pi$$
$$312$$ 0 0
$$313$$ 30.1399 + 17.4013i 1.70361 + 0.983578i 0.942045 + 0.335487i $$0.108901\pi$$
0.761563 + 0.648091i $$0.224432\pi$$
$$314$$ 22.4962 1.26954
$$315$$ 0 0
$$316$$ −8.30663 −0.467284
$$317$$ −5.87780 3.39355i −0.330130 0.190601i 0.325769 0.945449i $$-0.394377\pi$$
−0.655899 + 0.754849i $$0.727710\pi$$
$$318$$ 0 0
$$319$$ 13.1103 + 22.7076i 0.734034 + 1.27138i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −8.88280 + 4.31199i −0.495019 + 0.240298i
$$323$$ 0.0140964i 0.000784346i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −19.7515 + 11.4035i −1.09393 + 0.631582i
$$327$$ 0 0
$$328$$ 6.31079i 0.348455i
$$329$$ 12.7116 + 8.60853i 0.700813 + 0.474604i
$$330$$ 0 0
$$331$$ −5.56985 + 9.64726i −0.306147 + 0.530261i −0.977516 0.210862i $$-0.932373\pi$$
0.671369 + 0.741123i $$0.265706\pi$$
$$332$$ −5.17449 8.96248i −0.283987 0.491880i
$$333$$ 0 0
$$334$$ 7.66398 + 4.42480i 0.419355 + 0.242114i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −1.59111 −0.0866733 −0.0433366 0.999061i $$-0.513799\pi$$
−0.0433366 + 0.999061i $$0.513799\pi$$
$$338$$ 2.12995 + 1.22973i 0.115854 + 0.0668884i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.22047 2.11391i 0.0660919 0.114475i
$$342$$ 0 0
$$343$$ 3.95164 18.0938i 0.213368 0.976972i
$$344$$ 3.03528i 0.163651i
$$345$$ 0 0
$$346$$ 6.70032 3.86843i 0.360211 0.207968i
$$347$$ −13.3860 + 7.72840i −0.718597 + 0.414882i −0.814236 0.580534i $$-0.802844\pi$$
0.0956388 + 0.995416i $$0.469511\pi$$
$$348$$ 0 0
$$349$$ 0.585057i 0.0313174i 0.999877 + 0.0156587i $$0.00498452\pi$$
−0.999877 + 0.0156587i $$0.995015\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.47323 2.55171i 0.0785235 0.136007i
$$353$$ 1.83788 + 3.18330i 0.0978204 + 0.169430i 0.910782 0.412887i $$-0.135480\pi$$
−0.812962 + 0.582317i $$0.802146\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −6.17209 −0.327120
$$357$$ 0 0
$$358$$ 0.481846 0.0254664
$$359$$ −17.4069 10.0499i −0.918702 0.530413i −0.0354812 0.999370i $$-0.511296\pi$$
−0.883221 + 0.468958i $$0.844630\pi$$
$$360$$ 0 0
$$361$$ −9.49938 16.4534i −0.499967 0.865969i
$$362$$ 1.22438 2.12069i 0.0643520 0.111461i
$$363$$ 0 0
$$364$$ −4.54284 9.35835i −0.238110 0.490511i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 17.2665 9.96885i 0.901306 0.520369i 0.0236826 0.999720i $$-0.492461\pi$$
0.877624 + 0.479350i $$0.159128\pi$$
$$368$$ 3.23205 1.86603i 0.168482 0.0972733i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 4.96656 + 10.2312i 0.257851 + 0.531179i
$$372$$ 0 0
$$373$$ −16.9081 + 29.2856i −0.875467 + 1.51635i −0.0192016 + 0.999816i $$0.506112\pi$$
−0.856265 + 0.516537i $$0.827221\pi$$
$$374$$ −0.588706 1.01967i −0.0304413 0.0527258i
$$375$$ 0 0
$$376$$ −5.02520 2.90130i −0.259155 0.149623i
$$377$$ −34.9895 −1.80205
$$378$$ 0 0
$$379$$ 26.7614 1.37464 0.687321 0.726353i $$-0.258786\pi$$
0.687321 + 0.726353i $$0.258786\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −2.24728 3.89241i −0.114981 0.199153i
$$383$$ 9.89060 17.1310i 0.505386 0.875355i −0.494594 0.869124i $$-0.664683\pi$$
0.999981 0.00623078i $$-0.00198333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 12.5699i 0.639793i
$$387$$ 0 0
$$388$$ −13.5398 + 7.81722i −0.687380 + 0.396859i
$$389$$ 4.49181 2.59335i 0.227744 0.131488i −0.381787 0.924250i $$-0.624691\pi$$
0.609531 + 0.792762i $$0.291358\pi$$
$$390$$ 0 0
$$391$$ 1.49133i 0.0754200i
$$392$$ −1.00000 + 6.92820i −0.0505076 + 0.349927i
$$393$$ 0 0
$$394$$ 6.68740 11.5829i 0.336907 0.583539i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −4.99280 2.88259i −0.250581 0.144673i 0.369449 0.929251i $$-0.379546\pi$$
−0.620030 + 0.784578i $$0.712880\pi$$
$$398$$ 27.1550 1.36116
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −15.4361 8.91202i −0.770841 0.445045i 0.0623335 0.998055i $$-0.480146\pi$$
−0.833175 + 0.553010i $$0.813479\pi$$
$$402$$ 0 0
$$403$$ 1.62863 + 2.82086i 0.0811277 + 0.140517i
$$404$$ 9.02458 15.6310i 0.448990 0.777673i
$$405$$ 0 0
$$406$$ 19.4947 + 13.2022i 0.967507 + 0.655214i
$$407$$ 23.3709i 1.15845i
$$408$$ 0 0
$$409$$ −28.5617 + 16.4901i −1.41228 + 0.815382i −0.995603 0.0936705i $$-0.970140\pi$$
−0.416681 + 0.909053i $$0.636807\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 8.52004i 0.419752i
$$413$$ −13.2584 + 6.43606i −0.652405 + 0.316698i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.96593 + 3.40508i 0.0963874 + 0.166948i
$$417$$ 0 0
$$418$$ −0.0900147 0.0519700i −0.00440276 0.00254194i
$$419$$ −15.2287 −0.743969 −0.371985 0.928239i $$-0.621323\pi$$
−0.371985 + 0.928239i $$0.621323\pi$$
$$420$$ 0 0
$$421$$ 16.9939 0.828234 0.414117 0.910224i $$-0.364090\pi$$
0.414117 + 0.910224i $$0.364090\pi$$
$$422$$ −15.9507 9.20915i −0.776468 0.448294i
$$423$$ 0 0
$$424$$ −2.14929 3.72268i −0.104379 0.180789i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 17.0915 25.2377i 0.827115 1.22134i
$$428$$ 17.0552i 0.824395i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 15.4818 8.93842i 0.745732 0.430549i −0.0784178 0.996921i $$-0.524987\pi$$
0.824150 + 0.566372i $$0.191653\pi$$
$$432$$ 0 0
$$433$$ 5.56388i 0.267383i 0.991023 + 0.133691i $$0.0426831\pi$$
−0.991023 + 0.133691i $$0.957317\pi$$
$$434$$ 0.156961 2.18618i 0.00753437 0.104940i
$$435$$ 0 0
$$436$$ −5.84909 + 10.1309i −0.280121 + 0.485183i
$$437$$ −0.0658262 0.114014i −0.00314890 0.00545405i
$$438$$ 0 0
$$439$$ 9.53568 + 5.50543i 0.455113 + 0.262760i 0.709987 0.704214i $$-0.248701\pi$$
−0.254874 + 0.966974i $$0.582034\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 1.57117 0.0747332
$$443$$ −14.7091 8.49233i −0.698853 0.403483i 0.108067 0.994144i $$-0.465534\pi$$
−0.806920 + 0.590661i $$0.798867\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 8.90226 15.4192i 0.421534 0.730119i
$$447$$ 0 0
$$448$$ 0.189469 2.63896i 0.00895155 0.124679i
$$449$$ 12.5892i 0.594122i 0.954858 + 0.297061i $$0.0960065\pi$$
−0.954858 + 0.297061i $$0.903994\pi$$
$$450$$ 0 0
$$451$$ 16.1033 9.29725i 0.758276 0.437791i
$$452$$ 11.7386 6.77729i 0.552138 0.318777i
$$453$$ 0 0
$$454$$ 1.71228i 0.0803612i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.08417 + 1.87783i −0.0507153 + 0.0878414i −0.890269 0.455436i $$-0.849483\pi$$
0.839553 + 0.543277i $$0.182817\pi$$
$$458$$ −3.03768 5.26142i −0.141941 0.245850i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −34.3032 −1.59766 −0.798829 0.601558i $$-0.794547\pi$$
−0.798829 + 0.601558i $$0.794547\pi$$
$$462$$ 0 0
$$463$$ −28.2133 −1.31118 −0.655592 0.755115i $$-0.727581\pi$$
−0.655592 + 0.755115i $$0.727581\pi$$
$$464$$ −7.70674 4.44949i −0.357777 0.206562i
$$465$$ 0 0
$$466$$ −3.56288 6.17109i −0.165047 0.285870i
$$467$$ −2.10342 + 3.64324i −0.0973349 + 0.168589i −0.910581 0.413331i $$-0.864365\pi$$
0.813246 + 0.581920i $$0.197698\pi$$
$$468$$ 0 0
$$469$$ 29.7977 14.4647i 1.37593 0.667920i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 4.82415 2.78522i 0.222049 0.128200i
$$473$$ 7.74515 4.47167i 0.356122 0.205607i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −0.875396 0.592835i −0.0401237 0.0271725i
$$477$$ 0 0
$$478$$ 9.35968 16.2114i 0.428102 0.741494i
$$479$$ −7.35968 12.7473i −0.336272 0.582441i 0.647456 0.762103i $$-0.275833\pi$$
−0.983728 + 0.179662i $$0.942500\pi$$
$$480$$ 0 0
$$481$$ −27.0086 15.5934i −1.23149 0.710999i
$$482$$ −8.86851 −0.403950
$$483$$ 0 0
$$484$$ −2.31835 −0.105380
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −0.938784 1.62602i −0.0425404 0.0736821i 0.843971 0.536388i $$-0.180212\pi$$
−0.886512 + 0.462706i $$0.846878\pi$$
$$488$$ −5.76028 + 9.97710i −0.260756 + 0.451642i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 10.4281i 0.470613i 0.971921 + 0.235307i $$0.0756095\pi$$
−0.971921 + 0.235307i $$0.924391\pi$$
$$492$$ 0 0
$$493$$ −3.07963 + 1.77802i −0.138699 + 0.0800782i
$$494$$ 0.120118 0.0693504i 0.00540438 0.00312022i
$$495$$ 0 0
$$496$$ 0.828427i 0.0371975i
$$497$$ −5.10442 0.366481i −0.228965 0.0164389i
$$498$$ 0 0
$$499$$ 18.8822 32.7050i 0.845285 1.46408i −0.0400890 0.999196i $$-0.512764\pi$$
0.885374 0.464880i $$-0.153903\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −19.2030 11.0869i −0.857074 0.494832i
$$503$$ 35.8895 1.60023 0.800116 0.599845i $$-0.204771\pi$$
0.800116 + 0.599845i $$0.204771\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 9.52312 + 5.49818i 0.423354 + 0.244424i
$$507$$ 0 0
$$508$$ −4.47992 7.75944i −0.198764 0.344270i
$$509$$ 8.58746 14.8739i 0.380633 0.659275i −0.610520 0.792001i $$-0.709040\pi$$
0.991153 + 0.132726i $$0.0423729\pi$$
$$510$$ 0 0
$$511$$ 0.396469 + 0.816735i 0.0175387 + 0.0361302i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ −14.5780 + 8.41662i −0.643008 + 0.371241i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 17.0972i 0.751932i
$$518$$ 9.16442 + 18.8789i 0.402661 + 0.829492i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 2.26539 + 3.92377i 0.0992484 + 0.171903i 0.911374 0.411580i $$-0.135023\pi$$
−0.812125 + 0.583483i $$0.801689\pi$$
$$522$$ 0 0
$$523$$ 22.9267 + 13.2368i 1.00252 + 0.578803i 0.908992 0.416814i $$-0.136853\pi$$
0.0935241 + 0.995617i $$0.470187\pi$$
$$524$$ −12.7809 −0.558338
$$525$$ 0 0
$$526$$ 22.1197 0.964465
$$527$$ 0.286690 + 0.165520i 0.0124884 + 0.00721018i
$$528$$ 0 0
$$529$$ −4.53590 7.85641i −0.197213 0.341583i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −0.0930924 0.00668373i −0.00403607 0.000289777i
$$533$$ 24.8131i 1.07477i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −10.8420 + 6.25966i −0.468305 + 0.270376i
$$537$$ 0 0
$$538$$ 2.90097i 0.125070i
$$539$$ −19.1520 + 7.65514i −0.824936 + 0.329730i
$$540$$ 0 0
$$541$$ −3.16504 + 5.48201i −0.136076 + 0.235690i −0.926008 0.377504i $$-0.876782\pi$$
0.789932 + 0.613194i $$0.210116\pi$$
$$542$$ −8.73205 15.1244i −0.375074 0.649647i
$$543$$ 0 0
$$544$$ 0.346065 + 0.199801i 0.0148374 + 0.00856639i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 38.5271 1.64730 0.823651 0.567097i $$-0.191934\pi$$
0.823651 + 0.567097i $$0.191934\pi$$
$$548$$ 4.78094 + 2.76028i 0.204232 + 0.117913i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −0.156961 + 0.271864i −0.00668676 + 0.0115818i
$$552$$ 0 0
$$553$$ −18.1971 12.3234i −0.773819 0.524045i
$$554$$ 4.57650i 0.194437i
$$555$$ 0 0
$$556$$ −18.9202 + 10.9236i −0.802393 + 0.463262i
$$557$$ 8.00456 4.62144i 0.339164 0.195817i −0.320738 0.947168i $$-0.603931\pi$$
0.659902 + 0.751351i $$0.270598\pi$$
$$558$$ 0 0
$$559$$ 11.9343i 0.504765i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 4.77974 8.27875i 0.201621 0.349218i
$$563$$ 13.3871 + 23.1872i 0.564201 + 0.977225i 0.997124 + 0.0757935i $$0.0241490\pi$$
−0.432923 + 0.901431i $$0.642518\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 10.9262 0.459263
$$567$$ 0 0
$$568$$ 1.93426 0.0811596
$$569$$ −39.6604 22.8979i −1.66265 0.959931i −0.971443 0.237274i $$-0.923746\pi$$
−0.691207 0.722657i $$-0.742921\pi$$
$$570$$ 0 0
$$571$$ −0.390149 0.675759i −0.0163272 0.0282796i 0.857746 0.514073i $$-0.171864\pi$$
−0.874074 + 0.485794i $$0.838531\pi$$
$$572$$ −5.79253 + 10.0330i −0.242198 + 0.419499i
$$573$$ 0 0
$$574$$ 9.36246 13.8249i 0.390781 0.577039i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 9.74401 5.62571i 0.405648 0.234201i −0.283270 0.959040i $$-0.591419\pi$$
0.688918 + 0.724839i $$0.258086\pi$$
$$578$$ −14.5841 + 8.42016i −0.606620 + 0.350232i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1.96081 27.3105i 0.0813480 1.13303i
$$582$$ 0 0
$$583$$ 6.33281 10.9687i 0.262278 0.454279i
$$584$$ −0.171573 0.297173i −0.00709974 0.0122971i
$$585$$ 0 0
$$586$$ 14.0539 + 8.11401i 0.580561 + 0.335187i
$$587$$ 40.1593 1.65755 0.828775 0.559582i $$-0.189038\pi$$
0.828775 + 0.559582i $$0.189038\pi$$
$$588$$ 0 0
$$589$$ 0.0292237 0.00120414
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −3.96593 6.86919i −0.162999 0.282322i
$$593$$ 9.54170 16.5267i 0.391831 0.678671i −0.600860 0.799354i $$-0.705175\pi$$
0.992691 + 0.120683i $$0.0385085\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 21.4981i 0.880598i
$$597$$ 0 0
$$598$$ −12.7079 + 7.33694i −0.519666 + 0.300030i
$$599$$ −24.6424 + 14.2273i −1.00686 + 0.581312i −0.910271 0.414013i $$-0.864127\pi$$
−0.0965902 + 0.995324i $$0.530794\pi$$
$$600$$ 0 0
$$601$$ 29.2553i 1.19335i 0.802484 + 0.596673i $$0.203511\pi$$
−0.802484 + 0.596673i $$0.796489\pi$$
$$602$$ 4.50303 6.64929i 0.183530 0.271005i
$$603$$ 0 0
$$604$$ 1.47531 2.55532i 0.0600297 0.103974i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 22.3712 + 12.9160i 0.908020 + 0.524246i 0.879794 0.475356i $$-0.157681\pi$$
0.0282267 + 0.999602i $$0.491014\pi$$
$$608$$ 0.0352762 0.00143064
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 19.7583 + 11.4075i 0.799337 + 0.461498i
$$612$$ 0 0
$$613$$ 8.12216 + 14.0680i 0.328051 + 0.568201i 0.982125 0.188230i $$-0.0602749\pi$$
−0.654074 + 0.756430i $$0.726942\pi$$
$$614$$ 6.18910 10.7198i 0.249772 0.432618i
$$615$$ 0 0
$$616$$ 7.01299 3.40433i 0.282562 0.137164i
$$617$$ 31.8398i 1.28182i −0.767615 0.640911i $$-0.778557\pi$$
0.767615 0.640911i $$-0.221443\pi$$
$$618$$ 0 0
$$619$$ 8.01055 4.62490i 0.321971 0.185890i −0.330300 0.943876i $$-0.607150\pi$$
0.652271 + 0.757986i $$0.273816\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 22.8625i 0.916701i
$$623$$ −13.5210 9.15669i −0.541708 0.366855i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −17.4013 30.1399i −0.695495 1.20463i
$$627$$ 0 0
$$628$$ −19.4823 11.2481i −0.777429 0.448849i
$$629$$ −3.16958 −0.126379
$$630$$ 0 0
$$631$$ −10.3096 −0.410421 −0.205210 0.978718i $$-0.565788\pi$$
−0.205210 + 0.978718i $$0.565788\pi$$
$$632$$ 7.19375 + 4.15331i 0.286152 + 0.165210i
$$633$$ 0 0
$$634$$ 3.39355 + 5.87780i 0.134775 + 0.233437i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 3.93185 27.2407i 0.155786 1.07931i
$$638$$ 26.2205i 1.03808i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −11.1181 + 6.41906i −0.439140 + 0.253538i −0.703233 0.710960i $$-0.748261\pi$$
0.264093 + 0.964497i $$0.414928\pi$$
$$642$$ 0 0
$$643$$ 8.96224i 0.353436i 0.984262 + 0.176718i $$0.0565481\pi$$
−0.984262 + 0.176718i $$0.943452\pi$$
$$644$$ 9.84873 + 0.707107i 0.388094 + 0.0278639i
$$645$$ 0 0
$$646$$ 0.00704821 0.0122079i 0.000277308 0.000480312i
$$647$$ −22.6852 39.2919i −0.891846 1.54472i −0.837660 0.546191i $$-0.816077\pi$$
−0.0541854 0.998531i $$-0.517256\pi$$
$$648$$ 0 0
$$649$$ 14.2142 + 8.20656i 0.557955 + 0.322136i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 22.8070 0.893192
$$653$$ −28.4051 16.3997i −1.11158 0.641769i −0.172340 0.985038i $$-0.555133\pi$$
−0.939237 + 0.343268i $$0.888466\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −3.15539 + 5.46530i −0.123197 + 0.213384i
$$657$$ 0 0
$$658$$ −6.70430 13.8110i −0.261361 0.538409i
$$659$$ 18.7103i 0.728850i −0.931233 0.364425i $$-0.881266\pi$$
0.931233 0.364425i $$-0.118734\pi$$
$$660$$ 0 0
$$661$$ 7.41761 4.28256i 0.288512 0.166572i −0.348759 0.937213i $$-0.613397\pi$$
0.637270 + 0.770640i $$0.280063\pi$$
$$662$$ 9.64726 5.56985i 0.374951 0.216478i
$$663$$ 0 0
$$664$$ 10.3490i 0.401618i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 16.6057 28.7620i 0.642976 1.11367i
$$668$$ −4.42480 7.66398i −0.171201 0.296528i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −33.9449 −1.31043
$$672$$ 0 0
$$673$$ 0.179617 0.00692372 0.00346186 0.999994i $$-0.498898\pi$$
0.00346186 + 0.999994i $$0.498898\pi$$
$$674$$ 1.37794 + 0.795555i 0.0530763 + 0.0306436i
$$675$$ 0 0
$$676$$ −1.22973 2.12995i −0.0472973 0.0819213i
$$677$$ 20.7051 35.8623i 0.795763 1.37830i −0.126591 0.991955i $$-0.540404\pi$$
0.922354 0.386346i $$-0.126263\pi$$
$$678$$ 0 0
$$679$$ −41.2586 2.96224i −1.58336 0.113680i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −2.11391 + 1.22047i −0.0809457 + 0.0467340i
$$683$$ 37.5900 21.7026i 1.43834 0.830427i 0.440608 0.897700i $$-0.354763\pi$$
0.997735 + 0.0672723i $$0.0214296\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −12.4691 + 13.6938i −0.476073 + 0.522834i
$$687$$ 0 0
$$688$$ −1.51764 + 2.62863i −0.0578594 + 0.100215i
$$689$$ 8.45069 + 14.6370i 0.321946 + 0.557626i
$$690$$ 0 0
$$691$$ −16.8728 9.74150i −0.641871 0.370584i 0.143464 0.989656i $$-0.454176\pi$$
−0.785335 + 0.619071i $$0.787509\pi$$
$$692$$ −7.73686 −0.294111
$$693$$ 0 0
$$694$$ 15.4568 0.586732
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 1.26090 + 2.18394i 0.0477600 + 0.0827228i
$$698$$ 0.292529 0.506675i 0.0110724 0.0191779i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 47.0245i 1.77609i −0.459755 0.888046i $$-0.652063\pi$$
0.459755 0.888046i $$-0.347937\pi$$
$$702$$ 0 0
$$703$$ −0.242319 + 0.139903i −0.00913922 + 0.00527653i
$$704$$ −2.55171 + 1.47323i −0.0961713 + 0.0555245i
$$705$$ 0 0
$$706$$ 3.67576i 0.138339i
$$707$$ 42.9595 20.8539i 1.61566 0.784292i
$$708$$ 0 0
$$709$$ 24.2227 41.9549i 0.909701 1.57565i 0.0952213 0.995456i $$-0.469644\pi$$
0.814480 0.580192i $$-0.197023\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 5.34519 + 3.08604i 0.200319 + 0.115654i
$$713$$ −3.09173 −0.115786
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −0.417291 0.240923i −0.0155949 0.00900372i
$$717$$ 0 0
$$718$$ 10.0499 + 17.4069i 0.375058 + 0.649620i
$$719$$ 20.6632 35.7897i 0.770606 1.33473i −0.166625 0.986020i $$-0.553287\pi$$
0.937231 0.348709i $$-0.113380\pi$$
$$720$$ 0 0
$$721$$ −12.6400 + 18.6646i −0.470739 + 0.695106i
$$722$$ 18.9988i 0.707060i
$$723$$ 0 0
$$724$$ −2.12069 + 1.22438i −0.0788148 + 0.0455037i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 16.7905i 0.622726i 0.950291 + 0.311363i $$0.100786\pi$$
−0.950291 + 0.311363i $$0.899214\pi$$
$$728$$ −0.744963 + 10.3760i −0.0276102 + 0.384560i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0.606451 + 1.05040i 0.0224304 + 0.0388506i
$$732$$ 0 0
$$733$$ 26.6043 + 15.3600i 0.982652 + 0.567335i 0.903070 0.429494i $$-0.141308\pi$$
0.0795826 + 0.996828i $$0.474641\pi$$
$$734$$ −19.9377 −0.735914
$$735$$ 0 0
$$736$$ −3.73205 −0.137565
$$737$$ −31.9457 18.4438i −1.17673 0.679388i
$$738$$ 0 0
$$739$$ −15.3876 26.6521i −0.566041 0.980412i −0.996952 0.0780176i $$-0.975141\pi$$
0.430911 0.902395i $$-0.358192\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0.814447 11.3438i 0.0298993 0.416443i
$$743$$ 33.3616i 1.22392i 0.790889 + 0.611960i $$0.209619\pi$$
−0.790889 + 0.611960i $$0.790381\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 29.2856 16.9081i 1.07222 0.619048i
$$747$$ 0 0
$$748$$ 1.17741i 0.0430504i
$$749$$ −25.3025 + 37.3624i −0.924533 + 1.36519i
$$750$$ 0 0
$$751$$ 15.9452 27.6179i 0.581849 1.00779i −0.413411 0.910545i $$-0.635663\pi$$
0.995260 0.0972480i $$-0.0310040\pi$$
$$752$$ 2.90130 + 5.02520i 0.105800 + 0.183250i
$$753$$ 0 0
$$754$$ 30.3018 + 17.4947i 1.10353 + 0.637121i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 10.9065 0.396404 0.198202 0.980161i $$-0.436490\pi$$
0.198202 + 0.980161i $$0.436490\pi$$
$$758$$ −23.1761 13.3807i −0.841793 0.486010i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −12.2097 + 21.1479i −0.442602 + 0.766610i −0.997882 0.0650543i $$-0.979278\pi$$
0.555280 + 0.831664i $$0.312611\pi$$
$$762$$ 0 0
$$763$$ −27.8433 + 13.5160i −1.00800 + 0.489313i
$$764$$ 4.49457i 0.162608i
$$765$$ 0 0
$$766$$ −17.1310 + 9.89060i −0.618969 + 0.357362i
$$767$$ −18.9678 + 10.9511i −0.684889 + 0.395421i
$$768$$ 0 0
$$769$$ 22.9416i 0.827294i 0.910437 + 0.413647i $$0.135745\pi$$
−0.910437 + 0.413647i $$0.864255\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 6.28497 10.8859i 0.226201 0.391791i
$$773$$ 22.6837 + 39.2894i 0.815877 + 1.41314i 0.908696 + 0.417458i $$0.137079\pi$$
−0.0928193 + 0.995683i $$0.529588\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 15.6344 0.561243
$$777$$ 0 0
$$778$$ −5.18670 −0.185952
$$779$$ 0.192795 + 0.111310i 0.00690760 + 0.00398810i
$$780$$ 0 0
$$781$$ 2.84961 + 4.93566i 0.101967 + 0.176612i
$$782$$ −0.745667 + 1.29153i −0.0266650 + 0.0461851i
$$783$$ 0 0
$$784$$ 4.33013 5.50000i 0.154647 0.196429i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −2.89834 + 1.67335i −0.103314 + 0.0596487i −0.550767 0.834659i $$-0.685665\pi$$
0.447452 + 0.894308i $$0.352331\pi$$
$$788$$ −11.5829 + 6.68740i −0.412625 + 0.238229i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 35.7700 + 2.56817i 1.27183 + 0.0913136i
$$792$$ 0 0
$$793$$ 22.6486 39.2285i 0.804274 1.39304i
$$794$$ 2.88259 + 4.99280i 0.102299 + 0.177188i
$$795$$ 0 0
$$796$$ −23.5169 13.5775i −0.833535