# Properties

 Label 384.2.k.b.95.1 Level $384$ Weight $2$ Character 384.95 Analytic conductor $3.066$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 384.k (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.06625543762$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(i)$$ Coefficient field: 12.0.163368480538624.2 Defining polynomial: $$x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64$$ x^12 - 2*x^10 - 2*x^8 + 16*x^6 - 8*x^4 - 32*x^2 + 64 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{7}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 95.1 Root $$1.27715 + 0.607364i$$ of defining polynomial Character $$\chi$$ $$=$$ 384.95 Dual form 384.2.k.b.287.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.73003 + 0.0835731i) q^{3} +(0.431733 + 0.431733i) q^{5} -3.10278 q^{7} +(2.98603 - 0.289169i) q^{9} +O(q^{10})$$ $$q+(-1.73003 + 0.0835731i) q^{3} +(0.431733 + 0.431733i) q^{5} -3.10278 q^{7} +(2.98603 - 0.289169i) q^{9} +(2.98603 - 2.98603i) q^{11} +(-2.10278 - 2.10278i) q^{13} +(-0.782994 - 0.710831i) q^{15} -2.42945i q^{17} +(0.710831 - 0.710831i) q^{19} +(5.36790 - 0.259309i) q^{21} -5.97206i q^{23} -4.62721i q^{25} +(-5.14177 + 0.749823i) q^{27} +(2.86119 - 2.86119i) q^{29} +0.524438i q^{31} +(-4.91638 + 5.41549i) q^{33} +(-1.33957 - 1.33957i) q^{35} +(-1.52444 + 1.52444i) q^{37} +(3.81361 + 3.46214i) q^{39} -1.81568 q^{41} +(-0.710831 - 0.710831i) q^{43} +(1.41401 + 1.16432i) q^{45} +7.53805 q^{47} +2.62721 q^{49} +(0.203037 + 4.20304i) q^{51} +(-8.83325 - 8.83325i) q^{53} +2.57834 q^{55} +(-1.17036 + 1.28917i) q^{57} +(-0.0804722 + 0.0804722i) q^{59} +(5.72999 + 5.72999i) q^{61} +(-9.26498 + 0.897225i) q^{63} -1.81568i q^{65} +(0.391944 - 0.391944i) q^{67} +(0.499104 + 10.3319i) q^{69} +5.01985i q^{71} +13.4600i q^{73} +(0.386711 + 8.00523i) q^{75} +(-9.26498 + 9.26498i) q^{77} +3.47556i q^{79} +(8.83276 - 1.72693i) q^{81} +(4.55202 + 4.55202i) q^{83} +(1.04888 - 1.04888i) q^{85} +(-4.71083 + 5.18907i) q^{87} -12.5579 q^{89} +(6.52444 + 6.52444i) q^{91} +(-0.0438289 - 0.907295i) q^{93} +0.613779 q^{95} -8.67609 q^{97} +(8.05292 - 9.77985i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 2 q^{3} - 8 q^{7}+O(q^{10})$$ 12 * q + 2 * q^3 - 8 * q^7 $$12 q + 2 q^{3} - 8 q^{7} + 4 q^{13} + 12 q^{19} + 8 q^{21} - 10 q^{27} - 4 q^{33} + 4 q^{37} + 20 q^{39} - 12 q^{43} + 12 q^{45} - 20 q^{49} - 24 q^{51} + 24 q^{55} - 12 q^{61} - 28 q^{67} - 4 q^{69} + 34 q^{75} - 4 q^{81} - 32 q^{85} - 60 q^{87} + 56 q^{91} - 28 q^{93} - 8 q^{97} + 52 q^{99}+O(q^{100})$$ 12 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 + 12 * q^19 + 8 * q^21 - 10 * q^27 - 4 * q^33 + 4 * q^37 + 20 * q^39 - 12 * q^43 + 12 * q^45 - 20 * q^49 - 24 * q^51 + 24 * q^55 - 12 * q^61 - 28 * q^67 - 4 * q^69 + 34 * q^75 - 4 * q^81 - 32 * q^85 - 60 * q^87 + 56 * q^91 - 28 * q^93 - 8 * q^97 + 52 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$133$$ $$257$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.73003 + 0.0835731i −0.998835 + 0.0482510i
$$4$$ 0 0
$$5$$ 0.431733 + 0.431733i 0.193077 + 0.193077i 0.797024 0.603947i $$-0.206406\pi$$
−0.603947 + 0.797024i $$0.706406\pi$$
$$6$$ 0 0
$$7$$ −3.10278 −1.17274 −0.586369 0.810044i $$-0.699443\pi$$
−0.586369 + 0.810044i $$0.699443\pi$$
$$8$$ 0 0
$$9$$ 2.98603 0.289169i 0.995344 0.0963895i
$$10$$ 0 0
$$11$$ 2.98603 2.98603i 0.900322 0.900322i −0.0951415 0.995464i $$-0.530330\pi$$
0.995464 + 0.0951415i $$0.0303304\pi$$
$$12$$ 0 0
$$13$$ −2.10278 2.10278i −0.583205 0.583205i 0.352578 0.935783i $$-0.385305\pi$$
−0.935783 + 0.352578i $$0.885305\pi$$
$$14$$ 0 0
$$15$$ −0.782994 0.710831i −0.202168 0.183536i
$$16$$ 0 0
$$17$$ 2.42945i 0.589229i −0.955616 0.294615i $$-0.904809\pi$$
0.955616 0.294615i $$-0.0951913\pi$$
$$18$$ 0 0
$$19$$ 0.710831 0.710831i 0.163076 0.163076i −0.620852 0.783928i $$-0.713213\pi$$
0.783928 + 0.620852i $$0.213213\pi$$
$$20$$ 0 0
$$21$$ 5.36790 0.259309i 1.17137 0.0565858i
$$22$$ 0 0
$$23$$ 5.97206i 1.24526i −0.782516 0.622631i $$-0.786064\pi$$
0.782516 0.622631i $$-0.213936\pi$$
$$24$$ 0 0
$$25$$ 4.62721i 0.925443i
$$26$$ 0 0
$$27$$ −5.14177 + 0.749823i −0.989533 + 0.144304i
$$28$$ 0 0
$$29$$ 2.86119 2.86119i 0.531309 0.531309i −0.389653 0.920962i $$-0.627405\pi$$
0.920962 + 0.389653i $$0.127405\pi$$
$$30$$ 0 0
$$31$$ 0.524438i 0.0941918i 0.998890 + 0.0470959i $$0.0149966\pi$$
−0.998890 + 0.0470959i $$0.985003\pi$$
$$32$$ 0 0
$$33$$ −4.91638 + 5.41549i −0.855832 + 0.942715i
$$34$$ 0 0
$$35$$ −1.33957 1.33957i −0.226429 0.226429i
$$36$$ 0 0
$$37$$ −1.52444 + 1.52444i −0.250616 + 0.250616i −0.821223 0.570607i $$-0.806708\pi$$
0.570607 + 0.821223i $$0.306708\pi$$
$$38$$ 0 0
$$39$$ 3.81361 + 3.46214i 0.610666 + 0.554385i
$$40$$ 0 0
$$41$$ −1.81568 −0.283561 −0.141780 0.989898i $$-0.545283\pi$$
−0.141780 + 0.989898i $$0.545283\pi$$
$$42$$ 0 0
$$43$$ −0.710831 0.710831i −0.108401 0.108401i 0.650826 0.759227i $$-0.274423\pi$$
−0.759227 + 0.650826i $$0.774423\pi$$
$$44$$ 0 0
$$45$$ 1.41401 + 1.16432i 0.210788 + 0.173567i
$$46$$ 0 0
$$47$$ 7.53805 1.09954 0.549769 0.835317i $$-0.314716\pi$$
0.549769 + 0.835317i $$0.314716\pi$$
$$48$$ 0 0
$$49$$ 2.62721 0.375316
$$50$$ 0 0
$$51$$ 0.203037 + 4.20304i 0.0284309 + 0.588543i
$$52$$ 0 0
$$53$$ −8.83325 8.83325i −1.21334 1.21334i −0.969921 0.243419i $$-0.921731\pi$$
−0.243419 0.969921i $$-0.578269\pi$$
$$54$$ 0 0
$$55$$ 2.57834 0.347663
$$56$$ 0 0
$$57$$ −1.17036 + 1.28917i −0.155017 + 0.170755i
$$58$$ 0 0
$$59$$ −0.0804722 + 0.0804722i −0.0104766 + 0.0104766i −0.712326 0.701849i $$-0.752358\pi$$
0.701849 + 0.712326i $$0.252358\pi$$
$$60$$ 0 0
$$61$$ 5.72999 + 5.72999i 0.733650 + 0.733650i 0.971341 0.237691i $$-0.0763906\pi$$
−0.237691 + 0.971341i $$0.576391\pi$$
$$62$$ 0 0
$$63$$ −9.26498 + 0.897225i −1.16728 + 0.113040i
$$64$$ 0 0
$$65$$ 1.81568i 0.225207i
$$66$$ 0 0
$$67$$ 0.391944 0.391944i 0.0478835 0.0478835i −0.682760 0.730643i $$-0.739220\pi$$
0.730643 + 0.682760i $$0.239220\pi$$
$$68$$ 0 0
$$69$$ 0.499104 + 10.3319i 0.0600850 + 1.24381i
$$70$$ 0 0
$$71$$ 5.01985i 0.595747i 0.954605 + 0.297873i $$0.0962774\pi$$
−0.954605 + 0.297873i $$0.903723\pi$$
$$72$$ 0 0
$$73$$ 13.4600i 1.57537i 0.616078 + 0.787686i $$0.288721\pi$$
−0.616078 + 0.787686i $$0.711279\pi$$
$$74$$ 0 0
$$75$$ 0.386711 + 8.00523i 0.0446535 + 0.924365i
$$76$$ 0 0
$$77$$ −9.26498 + 9.26498i −1.05584 + 1.05584i
$$78$$ 0 0
$$79$$ 3.47556i 0.391031i 0.980701 + 0.195516i $$0.0626380\pi$$
−0.980701 + 0.195516i $$0.937362\pi$$
$$80$$ 0 0
$$81$$ 8.83276 1.72693i 0.981418 0.191881i
$$82$$ 0 0
$$83$$ 4.55202 + 4.55202i 0.499649 + 0.499649i 0.911329 0.411680i $$-0.135058\pi$$
−0.411680 + 0.911329i $$0.635058\pi$$
$$84$$ 0 0
$$85$$ 1.04888 1.04888i 0.113767 0.113767i
$$86$$ 0 0
$$87$$ −4.71083 + 5.18907i −0.505054 + 0.556326i
$$88$$ 0 0
$$89$$ −12.5579 −1.33114 −0.665568 0.746338i $$-0.731810\pi$$
−0.665568 + 0.746338i $$0.731810\pi$$
$$90$$ 0 0
$$91$$ 6.52444 + 6.52444i 0.683947 + 0.683947i
$$92$$ 0 0
$$93$$ −0.0438289 0.907295i −0.00454485 0.0940821i
$$94$$ 0 0
$$95$$ 0.613779 0.0629724
$$96$$ 0 0
$$97$$ −8.67609 −0.880923 −0.440462 0.897771i $$-0.645185\pi$$
−0.440462 + 0.897771i $$0.645185\pi$$
$$98$$ 0 0
$$99$$ 8.05292 9.77985i 0.809348 0.982912i
$$100$$ 0 0
$$101$$ 0.182046 + 0.182046i 0.0181142 + 0.0181142i 0.716106 0.697992i $$-0.245923\pi$$
−0.697992 + 0.716106i $$0.745923\pi$$
$$102$$ 0 0
$$103$$ 6.35720 0.626394 0.313197 0.949688i $$-0.398600\pi$$
0.313197 + 0.949688i $$0.398600\pi$$
$$104$$ 0 0
$$105$$ 2.42945 + 2.20555i 0.237090 + 0.215240i
$$106$$ 0 0
$$107$$ 1.64646 1.64646i 0.159169 0.159169i −0.623029 0.782199i $$-0.714098\pi$$
0.782199 + 0.623029i $$0.214098\pi$$
$$108$$ 0 0
$$109$$ −6.57331 6.57331i −0.629609 0.629609i 0.318360 0.947970i $$-0.396868\pi$$
−0.947970 + 0.318360i $$0.896868\pi$$
$$110$$ 0 0
$$111$$ 2.50993 2.76473i 0.238232 0.262417i
$$112$$ 0 0
$$113$$ 8.31277i 0.782000i −0.920391 0.391000i $$-0.872129\pi$$
0.920391 0.391000i $$-0.127871\pi$$
$$114$$ 0 0
$$115$$ 2.57834 2.57834i 0.240431 0.240431i
$$116$$ 0 0
$$117$$ −6.88701 5.67090i −0.636704 0.524274i
$$118$$ 0 0
$$119$$ 7.53805i 0.691012i
$$120$$ 0 0
$$121$$ 6.83276i 0.621160i
$$122$$ 0 0
$$123$$ 3.14118 0.151742i 0.283231 0.0136821i
$$124$$ 0 0
$$125$$ 4.15639 4.15639i 0.371759 0.371759i
$$126$$ 0 0
$$127$$ 15.7789i 1.40015i −0.714070 0.700074i $$-0.753150\pi$$
0.714070 0.700074i $$-0.246850\pi$$
$$128$$ 0 0
$$129$$ 1.28917 + 1.17036i 0.113505 + 0.103044i
$$130$$ 0 0
$$131$$ 0.0804722 + 0.0804722i 0.00703089 + 0.00703089i 0.710613 0.703583i $$-0.248417\pi$$
−0.703583 + 0.710613i $$0.748417\pi$$
$$132$$ 0 0
$$133$$ −2.20555 + 2.20555i −0.191245 + 0.191245i
$$134$$ 0 0
$$135$$ −2.54359 1.89615i −0.218918 0.163194i
$$136$$ 0 0
$$137$$ 13.2604 1.13291 0.566457 0.824091i $$-0.308314\pi$$
0.566457 + 0.824091i $$0.308314\pi$$
$$138$$ 0 0
$$139$$ −8.39194 8.39194i −0.711795 0.711795i 0.255115 0.966911i $$-0.417887\pi$$
−0.966911 + 0.255115i $$0.917887\pi$$
$$140$$ 0 0
$$141$$ −13.0411 + 0.629978i −1.09826 + 0.0530537i
$$142$$ 0 0
$$143$$ −12.5579 −1.05014
$$144$$ 0 0
$$145$$ 2.47054 0.205167
$$146$$ 0 0
$$147$$ −4.54517 + 0.219564i −0.374879 + 0.0181094i
$$148$$ 0 0
$$149$$ 5.79002 + 5.79002i 0.474337 + 0.474337i 0.903315 0.428978i $$-0.141126\pi$$
−0.428978 + 0.903315i $$0.641126\pi$$
$$150$$ 0 0
$$151$$ 9.94610 0.809402 0.404701 0.914449i $$-0.367376\pi$$
0.404701 + 0.914449i $$0.367376\pi$$
$$152$$ 0 0
$$153$$ −0.702522 7.25443i −0.0567955 0.586486i
$$154$$ 0 0
$$155$$ −0.226417 + 0.226417i −0.0181863 + 0.0181863i
$$156$$ 0 0
$$157$$ 9.15165 + 9.15165i 0.730381 + 0.730381i 0.970695 0.240314i $$-0.0772504\pi$$
−0.240314 + 0.970695i $$0.577250\pi$$
$$158$$ 0 0
$$159$$ 16.0200 + 14.5436i 1.27047 + 1.15338i
$$160$$ 0 0
$$161$$ 18.5300i 1.46037i
$$162$$ 0 0
$$163$$ −15.7003 + 15.7003i −1.22974 + 1.22974i −0.265678 + 0.964062i $$0.585596\pi$$
−0.964062 + 0.265678i $$0.914404\pi$$
$$164$$ 0 0
$$165$$ −4.46061 + 0.215480i −0.347258 + 0.0167751i
$$166$$ 0 0
$$167$$ 19.1437i 1.48139i −0.671843 0.740694i $$-0.734497\pi$$
0.671843 0.740694i $$-0.265503\pi$$
$$168$$ 0 0
$$169$$ 4.15667i 0.319744i
$$170$$ 0 0
$$171$$ 1.91701 2.32811i 0.146598 0.178035i
$$172$$ 0 0
$$173$$ 13.3281 13.3281i 1.01331 1.01331i 0.0134040 0.999910i $$-0.495733\pi$$
0.999910 0.0134040i $$-0.00426674\pi$$
$$174$$ 0 0
$$175$$ 14.3572i 1.08530i
$$176$$ 0 0
$$177$$ 0.132494 0.145945i 0.00995889 0.0109699i
$$178$$ 0 0
$$179$$ −9.18451 9.18451i −0.686483 0.686483i 0.274970 0.961453i $$-0.411332\pi$$
−0.961453 + 0.274970i $$0.911332\pi$$
$$180$$ 0 0
$$181$$ 16.5139 16.5139i 1.22747 1.22747i 0.262548 0.964919i $$-0.415437\pi$$
0.964919 0.262548i $$-0.0845627\pi$$
$$182$$ 0 0
$$183$$ −10.3919 9.43420i −0.768195 0.697396i
$$184$$ 0 0
$$185$$ −1.31630 −0.0967764
$$186$$ 0 0
$$187$$ −7.25443 7.25443i −0.530496 0.530496i
$$188$$ 0 0
$$189$$ 15.9537 2.32653i 1.16046 0.169230i
$$190$$ 0 0
$$191$$ 3.17852 0.229989 0.114995 0.993366i $$-0.463315\pi$$
0.114995 + 0.993366i $$0.463315\pi$$
$$192$$ 0 0
$$193$$ −11.4600 −0.824907 −0.412454 0.910979i $$-0.635328\pi$$
−0.412454 + 0.910979i $$0.635328\pi$$
$$194$$ 0 0
$$195$$ 0.151742 + 3.14118i 0.0108664 + 0.224944i
$$196$$ 0 0
$$197$$ 14.8053 + 14.8053i 1.05483 + 1.05483i 0.998407 + 0.0564281i $$0.0179712\pi$$
0.0564281 + 0.998407i $$0.482029\pi$$
$$198$$ 0 0
$$199$$ −24.4550 −1.73357 −0.866783 0.498686i $$-0.833816\pi$$
−0.866783 + 0.498686i $$0.833816\pi$$
$$200$$ 0 0
$$201$$ −0.645320 + 0.710831i −0.0455173 + 0.0501382i
$$202$$ 0 0
$$203$$ −8.87762 + 8.87762i −0.623087 + 0.623087i
$$204$$ 0 0
$$205$$ −0.783887 0.783887i −0.0547491 0.0547491i
$$206$$ 0 0
$$207$$ −1.72693 17.8328i −0.120030 1.23946i
$$208$$ 0 0
$$209$$ 4.24513i 0.293642i
$$210$$ 0 0
$$211$$ 6.18639 6.18639i 0.425889 0.425889i −0.461336 0.887225i $$-0.652630\pi$$
0.887225 + 0.461336i $$0.152630\pi$$
$$212$$ 0 0
$$213$$ −0.419525 8.68451i −0.0287454 0.595053i
$$214$$ 0 0
$$215$$ 0.613779i 0.0418594i
$$216$$ 0 0
$$217$$ 1.62721i 0.110462i
$$218$$ 0 0
$$219$$ −1.12489 23.2862i −0.0760132 1.57354i
$$220$$ 0 0
$$221$$ −5.10860 + 5.10860i −0.343641 + 0.343641i
$$222$$ 0 0
$$223$$ 8.18996i 0.548441i 0.961667 + 0.274220i $$0.0884197\pi$$
−0.961667 + 0.274220i $$0.911580\pi$$
$$224$$ 0 0
$$225$$ −1.33804 13.8170i −0.0892030 0.921133i
$$226$$ 0 0
$$227$$ 9.91030 + 9.91030i 0.657770 + 0.657770i 0.954852 0.297082i $$-0.0960135\pi$$
−0.297082 + 0.954852i $$0.596014\pi$$
$$228$$ 0 0
$$229$$ −7.15165 + 7.15165i −0.472594 + 0.472594i −0.902753 0.430159i $$-0.858458\pi$$
0.430159 + 0.902753i $$0.358458\pi$$
$$230$$ 0 0
$$231$$ 15.2544 16.8030i 1.00367 1.10556i
$$232$$ 0 0
$$233$$ 19.6431 1.28686 0.643432 0.765503i $$-0.277510\pi$$
0.643432 + 0.765503i $$0.277510\pi$$
$$234$$ 0 0
$$235$$ 3.25443 + 3.25443i 0.212295 + 0.212295i
$$236$$ 0 0
$$237$$ −0.290464 6.01284i −0.0188676 0.390576i
$$238$$ 0 0
$$239$$ −9.44247 −0.610782 −0.305391 0.952227i $$-0.598787\pi$$
−0.305391 + 0.952227i $$0.598787\pi$$
$$240$$ 0 0
$$241$$ 16.6167 1.07037 0.535186 0.844734i $$-0.320241\pi$$
0.535186 + 0.844734i $$0.320241\pi$$
$$242$$ 0 0
$$243$$ −15.1366 + 3.72583i −0.971017 + 0.239012i
$$244$$ 0 0
$$245$$ 1.13425 + 1.13425i 0.0724649 + 0.0724649i
$$246$$ 0 0
$$247$$ −2.98944 −0.190213
$$248$$ 0 0
$$249$$ −8.25557 7.49472i −0.523176 0.474958i
$$250$$ 0 0
$$251$$ 2.03382 2.03382i 0.128374 0.128374i −0.640001 0.768374i $$-0.721066\pi$$
0.768374 + 0.640001i $$0.221066\pi$$
$$252$$ 0 0
$$253$$ −17.8328 17.8328i −1.12114 1.12114i
$$254$$ 0 0
$$255$$ −1.72693 + 1.90225i −0.108145 + 0.119123i
$$256$$ 0 0
$$257$$ 15.0761i 0.940421i 0.882554 + 0.470211i $$0.155822\pi$$
−0.882554 + 0.470211i $$0.844178\pi$$
$$258$$ 0 0
$$259$$ 4.72999 4.72999i 0.293907 0.293907i
$$260$$ 0 0
$$261$$ 7.71623 9.37096i 0.477623 0.580048i
$$262$$ 0 0
$$263$$ 29.8138i 1.83840i 0.393796 + 0.919198i $$0.371162\pi$$
−0.393796 + 0.919198i $$0.628838\pi$$
$$264$$ 0 0
$$265$$ 7.62721i 0.468536i
$$266$$ 0 0
$$267$$ 21.7256 1.04950i 1.32958 0.0642285i
$$268$$ 0 0
$$269$$ −16.3713 + 16.3713i −0.998176 + 0.998176i −0.999998 0.00182258i $$-0.999420\pi$$
0.00182258 + 0.999998i $$0.499420\pi$$
$$270$$ 0 0
$$271$$ 13.3466i 0.810751i −0.914150 0.405375i $$-0.867141\pi$$
0.914150 0.405375i $$-0.132859\pi$$
$$272$$ 0 0
$$273$$ −11.8328 10.7422i −0.716151 0.650149i
$$274$$ 0 0
$$275$$ −13.8170 13.8170i −0.833197 0.833197i
$$276$$ 0 0
$$277$$ −10.6811 + 10.6811i −0.641766 + 0.641766i −0.950989 0.309224i $$-0.899931\pi$$
0.309224 + 0.950989i $$0.399931\pi$$
$$278$$ 0 0
$$279$$ 0.151651 + 1.56599i 0.00907911 + 0.0937533i
$$280$$ 0 0
$$281$$ 17.5943 1.04959 0.524794 0.851229i $$-0.324142\pi$$
0.524794 + 0.851229i $$0.324142\pi$$
$$282$$ 0 0
$$283$$ 17.1758 + 17.1758i 1.02100 + 1.02100i 0.999775 + 0.0212224i $$0.00675580\pi$$
0.0212224 + 0.999775i $$0.493244\pi$$
$$284$$ 0 0
$$285$$ −1.06186 + 0.0512954i −0.0628990 + 0.00303848i
$$286$$ 0 0
$$287$$ 5.63363 0.332543
$$288$$ 0 0
$$289$$ 11.0978 0.652809
$$290$$ 0 0
$$291$$ 15.0099 0.725088i 0.879897 0.0425054i
$$292$$ 0 0
$$293$$ −3.72465 3.72465i −0.217597 0.217597i 0.589888 0.807485i $$-0.299172\pi$$
−0.807485 + 0.589888i $$0.799172\pi$$
$$294$$ 0 0
$$295$$ −0.0694851 −0.00404558
$$296$$ 0 0
$$297$$ −13.1145 + 17.5925i −0.760979 + 1.02082i
$$298$$ 0 0
$$299$$ −12.5579 + 12.5579i −0.726242 + 0.726242i
$$300$$ 0 0
$$301$$ 2.20555 + 2.20555i 0.127126 + 0.127126i
$$302$$ 0 0
$$303$$ −0.330160 0.299731i −0.0189672 0.0172191i
$$304$$ 0 0
$$305$$ 4.94765i 0.283302i
$$306$$ 0 0
$$307$$ 13.4408 13.4408i 0.767108 0.767108i −0.210488 0.977596i $$-0.567505\pi$$
0.977596 + 0.210488i $$0.0675054\pi$$
$$308$$ 0 0
$$309$$ −10.9982 + 0.531291i −0.625664 + 0.0302241i
$$310$$ 0 0
$$311$$ 13.8320i 0.784341i 0.919893 + 0.392170i $$0.128276\pi$$
−0.919893 + 0.392170i $$0.871724\pi$$
$$312$$ 0 0
$$313$$ 3.94056i 0.222734i 0.993779 + 0.111367i $$0.0355229\pi$$
−0.993779 + 0.111367i $$0.964477\pi$$
$$314$$ 0 0
$$315$$ −4.38736 3.61264i −0.247200 0.203549i
$$316$$ 0 0
$$317$$ 8.92199 8.92199i 0.501109 0.501109i −0.410673 0.911782i $$-0.634706\pi$$
0.911782 + 0.410673i $$0.134706\pi$$
$$318$$ 0 0
$$319$$ 17.0872i 0.956699i
$$320$$ 0 0
$$321$$ −2.71083 + 2.98603i −0.151304 + 0.166664i
$$322$$ 0 0
$$323$$ −1.72693 1.72693i −0.0960891 0.0960891i
$$324$$ 0 0
$$325$$ −9.72999 + 9.72999i −0.539723 + 0.539723i
$$326$$ 0 0
$$327$$ 11.9214 + 10.8227i 0.659255 + 0.598497i
$$328$$ 0 0
$$329$$ −23.3889 −1.28947
$$330$$ 0 0
$$331$$ −9.44082 9.44082i −0.518914 0.518914i 0.398328 0.917243i $$-0.369590\pi$$
−0.917243 + 0.398328i $$0.869590\pi$$
$$332$$ 0 0
$$333$$ −4.11120 + 4.99284i −0.225292 + 0.273606i
$$334$$ 0 0
$$335$$ 0.338430 0.0184904
$$336$$ 0 0
$$337$$ 5.94056 0.323603 0.161801 0.986823i $$-0.448270\pi$$
0.161801 + 0.986823i $$0.448270\pi$$
$$338$$ 0 0
$$339$$ 0.694724 + 14.3814i 0.0377322 + 0.781089i
$$340$$ 0 0
$$341$$ 1.56599 + 1.56599i 0.0848030 + 0.0848030i
$$342$$ 0 0
$$343$$ 13.5678 0.732591
$$344$$ 0 0
$$345$$ −4.24513 + 4.67609i −0.228550 + 0.251752i
$$346$$ 0 0
$$347$$ −4.09918 + 4.09918i −0.220056 + 0.220056i −0.808522 0.588466i $$-0.799732\pi$$
0.588466 + 0.808522i $$0.299732\pi$$
$$348$$ 0 0
$$349$$ 8.10278 + 8.10278i 0.433732 + 0.433732i 0.889896 0.456164i $$-0.150777\pi$$
−0.456164 + 0.889896i $$0.650777\pi$$
$$350$$ 0 0
$$351$$ 12.3887 + 9.23527i 0.661259 + 0.492942i
$$352$$ 0 0
$$353$$ 29.2465i 1.55664i −0.627870 0.778318i $$-0.716073\pi$$
0.627870 0.778318i $$-0.283927\pi$$
$$354$$ 0 0
$$355$$ −2.16724 + 2.16724i −0.115025 + 0.115025i
$$356$$ 0 0
$$357$$ −0.629978 13.0411i −0.0333420 0.690207i
$$358$$ 0 0
$$359$$ 21.3235i 1.12541i −0.826657 0.562706i $$-0.809760\pi$$
0.826657 0.562706i $$-0.190240\pi$$
$$360$$ 0 0
$$361$$ 17.9894i 0.946812i
$$362$$ 0 0
$$363$$ 0.571035 + 11.8209i 0.0299716 + 0.620437i
$$364$$ 0 0
$$365$$ −5.81112 + 5.81112i −0.304168 + 0.304168i
$$366$$ 0 0
$$367$$ 32.8277i 1.71359i 0.515654 + 0.856797i $$0.327549\pi$$
−0.515654 + 0.856797i $$0.672451\pi$$
$$368$$ 0 0
$$369$$ −5.42166 + 0.525036i −0.282240 + 0.0273323i
$$370$$ 0 0
$$371$$ 27.4076 + 27.4076i 1.42293 + 1.42293i
$$372$$ 0 0
$$373$$ −1.35720 + 1.35720i −0.0702732 + 0.0702732i −0.741370 0.671097i $$-0.765824\pi$$
0.671097 + 0.741370i $$0.265824\pi$$
$$374$$ 0 0
$$375$$ −6.84333 + 7.53805i −0.353388 + 0.389263i
$$376$$ 0 0
$$377$$ −12.0329 −0.619724
$$378$$ 0 0
$$379$$ 17.3869 + 17.3869i 0.893106 + 0.893106i 0.994814 0.101708i $$-0.0324308\pi$$
−0.101708 + 0.994814i $$0.532431\pi$$
$$380$$ 0 0
$$381$$ 1.31869 + 27.2980i 0.0675585 + 1.39852i
$$382$$ 0 0
$$383$$ −32.9757 −1.68498 −0.842491 0.538711i $$-0.818912\pi$$
−0.842491 + 0.538711i $$0.818912\pi$$
$$384$$ 0 0
$$385$$ −8.00000 −0.407718
$$386$$ 0 0
$$387$$ −2.32811 1.91701i −0.118345 0.0974473i
$$388$$ 0 0
$$389$$ −3.97434 3.97434i −0.201507 0.201507i 0.599138 0.800645i $$-0.295510\pi$$
−0.800645 + 0.599138i $$0.795510\pi$$
$$390$$ 0 0
$$391$$ −14.5089 −0.733744
$$392$$ 0 0
$$393$$ −0.145945 0.132494i −0.00736195 0.00668346i
$$394$$ 0 0
$$395$$ −1.50052 + 1.50052i −0.0754991 + 0.0754991i
$$396$$ 0 0
$$397$$ 15.9355 + 15.9355i 0.799782 + 0.799782i 0.983061 0.183279i $$-0.0586712\pi$$
−0.183279 + 0.983061i $$0.558671\pi$$
$$398$$ 0 0
$$399$$ 3.63135 4.00000i 0.181795 0.200250i
$$400$$ 0 0
$$401$$ 29.7716i 1.48672i 0.668891 + 0.743361i $$0.266769\pi$$
−0.668891 + 0.743361i $$0.733231\pi$$
$$402$$ 0 0
$$403$$ 1.10278 1.10278i 0.0549331 0.0549331i
$$404$$ 0 0
$$405$$ 4.55897 + 3.06782i 0.226537 + 0.152441i
$$406$$ 0 0
$$407$$ 9.10404i 0.451270i
$$408$$ 0 0
$$409$$ 15.6655i 0.774610i 0.921952 + 0.387305i $$0.126594\pi$$
−0.921952 + 0.387305i $$0.873406\pi$$
$$410$$ 0 0
$$411$$ −22.9410 + 1.10821i −1.13159 + 0.0546642i
$$412$$ 0 0
$$413$$ 0.249687 0.249687i 0.0122863 0.0122863i
$$414$$ 0 0
$$415$$ 3.93051i 0.192941i
$$416$$ 0 0
$$417$$ 15.2197 + 13.8170i 0.745311 + 0.676621i
$$418$$ 0 0
$$419$$ −14.1554 14.1554i −0.691538 0.691538i 0.271032 0.962570i $$-0.412635\pi$$
−0.962570 + 0.271032i $$0.912635\pi$$
$$420$$ 0 0
$$421$$ 7.35720 7.35720i 0.358568 0.358568i −0.504717 0.863285i $$-0.668403\pi$$
0.863285 + 0.504717i $$0.168403\pi$$
$$422$$ 0 0
$$423$$ 22.5089 2.17977i 1.09442 0.105984i
$$424$$ 0 0
$$425$$ −11.2416 −0.545298
$$426$$ 0 0
$$427$$ −17.7789 17.7789i −0.860380 0.860380i
$$428$$ 0 0
$$429$$ 21.7256 1.04950i 1.04892 0.0506705i
$$430$$ 0 0
$$431$$ 20.7097 0.997553 0.498776 0.866731i $$-0.333783\pi$$
0.498776 + 0.866731i $$0.333783\pi$$
$$432$$ 0 0
$$433$$ −23.4005 −1.12456 −0.562279 0.826948i $$-0.690075\pi$$
−0.562279 + 0.826948i $$0.690075\pi$$
$$434$$ 0 0
$$435$$ −4.27411 + 0.206471i −0.204928 + 0.00989951i
$$436$$ 0 0
$$437$$ −4.24513 4.24513i −0.203072 0.203072i
$$438$$ 0 0
$$439$$ 20.2594 0.966931 0.483465 0.875363i $$-0.339378\pi$$
0.483465 + 0.875363i $$0.339378\pi$$
$$440$$ 0 0
$$441$$ 7.84494 0.759707i 0.373569 0.0361765i
$$442$$ 0 0
$$443$$ −4.05264 + 4.05264i −0.192547 + 0.192547i −0.796796 0.604249i $$-0.793473\pi$$
0.604249 + 0.796796i $$0.293473\pi$$
$$444$$ 0 0
$$445$$ −5.42166 5.42166i −0.257011 0.257011i
$$446$$ 0 0
$$447$$ −10.5008 9.53303i −0.496671 0.450897i
$$448$$ 0 0
$$449$$ 5.38394i 0.254084i −0.991897 0.127042i $$-0.959452\pi$$
0.991897 0.127042i $$-0.0405483\pi$$
$$450$$ 0 0
$$451$$ −5.42166 + 5.42166i −0.255296 + 0.255296i
$$452$$ 0 0
$$453$$ −17.2071 + 0.831227i −0.808459 + 0.0390544i
$$454$$ 0 0
$$455$$ 5.63363i 0.264109i
$$456$$ 0 0
$$457$$ 28.0766i 1.31337i −0.754165 0.656685i $$-0.771958\pi$$
0.754165 0.656685i $$-0.228042\pi$$
$$458$$ 0 0
$$459$$ 1.82166 + 12.4917i 0.0850279 + 0.583062i
$$460$$ 0 0
$$461$$ 22.7962 22.7962i 1.06172 1.06172i 0.0637594 0.997965i $$-0.479691\pi$$
0.997965 0.0637594i $$-0.0203090\pi$$
$$462$$ 0 0
$$463$$ 0.740035i 0.0343923i 0.999852 + 0.0171962i $$0.00547398\pi$$
−0.999852 + 0.0171962i $$0.994526\pi$$
$$464$$ 0 0
$$465$$ 0.372787 0.410632i 0.0172876 0.0190426i
$$466$$ 0 0
$$467$$ 9.73282 + 9.73282i 0.450381 + 0.450381i 0.895481 0.445100i $$-0.146832\pi$$
−0.445100 + 0.895481i $$0.646832\pi$$
$$468$$ 0 0
$$469$$ −1.21611 + 1.21611i −0.0561549 + 0.0561549i
$$470$$ 0 0
$$471$$ −16.5975 15.0678i −0.764772 0.694289i
$$472$$ 0 0
$$473$$ −4.24513 −0.195191
$$474$$ 0 0
$$475$$ −3.28917 3.28917i −0.150917 0.150917i
$$476$$ 0 0
$$477$$ −28.9307 23.8221i −1.32464 1.09074i
$$478$$ 0 0
$$479$$ 28.2478 1.29067 0.645337 0.763898i $$-0.276717\pi$$
0.645337 + 0.763898i $$0.276717\pi$$
$$480$$ 0 0
$$481$$ 6.41110 0.292321
$$482$$ 0 0
$$483$$ −1.54861 32.0575i −0.0704641 1.45866i
$$484$$ 0 0
$$485$$ −3.74576 3.74576i −0.170086 0.170086i
$$486$$ 0 0
$$487$$ 19.7094 0.893117 0.446559 0.894754i $$-0.352649\pi$$
0.446559 + 0.894754i $$0.352649\pi$$
$$488$$ 0 0
$$489$$ 25.8499 28.4741i 1.16897 1.28764i
$$490$$ 0 0
$$491$$ 29.4414 29.4414i 1.32867 1.32867i 0.422143 0.906529i $$-0.361278\pi$$
0.906529 0.422143i $$-0.138722\pi$$
$$492$$ 0 0
$$493$$ −6.95112 6.95112i −0.313063 0.313063i
$$494$$ 0 0
$$495$$ 7.69899 0.745574i 0.346044 0.0335111i
$$496$$ 0 0
$$497$$ 15.5755i 0.698656i
$$498$$ 0 0
$$499$$ −4.43026 + 4.43026i −0.198326 + 0.198326i −0.799282 0.600956i $$-0.794787\pi$$
0.600956 + 0.799282i $$0.294787\pi$$
$$500$$ 0 0
$$501$$ 1.59990 + 33.1193i 0.0714784 + 1.47966i
$$502$$ 0 0
$$503$$ 27.6805i 1.23421i −0.786879 0.617107i $$-0.788304\pi$$
0.786879 0.617107i $$-0.211696\pi$$
$$504$$ 0 0
$$505$$ 0.157190i 0.00699488i
$$506$$ 0 0
$$507$$ 0.347386 + 7.19119i 0.0154280 + 0.319372i
$$508$$ 0 0
$$509$$ −17.3235 + 17.3235i −0.767851 + 0.767851i −0.977728 0.209877i $$-0.932694\pi$$
0.209877 + 0.977728i $$0.432694\pi$$
$$510$$ 0 0
$$511$$ 41.7633i 1.84750i
$$512$$ 0 0
$$513$$ −3.12193 + 4.18793i −0.137837 + 0.184902i
$$514$$ 0 0
$$515$$ 2.74461 + 2.74461i 0.120942 + 0.120942i
$$516$$ 0 0
$$517$$ 22.5089 22.5089i 0.989938 0.989938i
$$518$$ 0 0
$$519$$ −21.9441 + 24.1719i −0.963240 + 1.06103i
$$520$$ 0 0
$$521$$ −10.1284 −0.443735 −0.221868 0.975077i $$-0.571215\pi$$
−0.221868 + 0.975077i $$0.571215\pi$$
$$522$$ 0 0
$$523$$ −1.45641 1.45641i −0.0636842 0.0636842i 0.674547 0.738232i $$-0.264339\pi$$
−0.738232 + 0.674547i $$0.764339\pi$$
$$524$$ 0 0
$$525$$ −1.19988 24.8384i −0.0523669 1.08404i
$$526$$ 0 0
$$527$$ 1.27410 0.0555006
$$528$$ 0 0
$$529$$ −12.6655 −0.550675
$$530$$ 0 0
$$531$$ −0.217023 + 0.263563i −0.00941798 + 0.0114376i
$$532$$ 0 0
$$533$$ 3.81796 + 3.81796i 0.165374 + 0.165374i
$$534$$ 0 0
$$535$$ 1.42166 0.0614638
$$536$$ 0 0
$$537$$ 16.6571 + 15.1219i 0.718806 + 0.652560i
$$538$$ 0 0
$$539$$ 7.84494 7.84494i 0.337905 0.337905i
$$540$$ 0 0
$$541$$ −5.18996 5.18996i −0.223134 0.223134i 0.586683 0.809817i $$-0.300434\pi$$
−0.809817 + 0.586683i $$0.800434\pi$$
$$542$$ 0 0
$$543$$ −27.1894 + 29.9497i −1.16681 + 1.28526i
$$544$$ 0 0
$$545$$ 5.67583i 0.243126i
$$546$$ 0 0
$$547$$ −12.6413 + 12.6413i −0.540505 + 0.540505i −0.923677 0.383172i $$-0.874832\pi$$
0.383172 + 0.923677i $$0.374832\pi$$
$$548$$ 0 0
$$549$$ 18.7669 + 15.4530i 0.800950 + 0.659518i
$$550$$ 0 0
$$551$$ 4.06764i 0.173287i
$$552$$ 0 0
$$553$$ 10.7839i 0.458578i
$$554$$ 0 0
$$555$$ 2.27724 0.110007i 0.0966636 0.00466955i
$$556$$ 0 0
$$557$$ −6.90317 + 6.90317i −0.292497 + 0.292497i −0.838066 0.545569i $$-0.816314\pi$$
0.545569 + 0.838066i $$0.316314\pi$$
$$558$$ 0 0
$$559$$ 2.98944i 0.126440i
$$560$$ 0 0
$$561$$ 13.1567 + 11.9441i 0.555475 + 0.504281i
$$562$$ 0 0
$$563$$ −18.3840 18.3840i −0.774794 0.774794i 0.204146 0.978940i $$-0.434558\pi$$
−0.978940 + 0.204146i $$0.934558\pi$$
$$564$$ 0 0
$$565$$ 3.58890 3.58890i 0.150986 0.150986i
$$566$$ 0 0
$$567$$ −27.4061 + 5.35828i −1.15095 + 0.225027i
$$568$$ 0 0
$$569$$ 43.5570 1.82601 0.913003 0.407953i $$-0.133757\pi$$
0.913003 + 0.407953i $$0.133757\pi$$
$$570$$ 0 0
$$571$$ −7.00859 7.00859i −0.293301 0.293301i 0.545082 0.838383i $$-0.316498\pi$$
−0.838383 + 0.545082i $$0.816498\pi$$
$$572$$ 0 0
$$573$$ −5.49894 + 0.265638i −0.229721 + 0.0110972i
$$574$$ 0 0
$$575$$ −27.6340 −1.15242
$$576$$ 0 0
$$577$$ 28.4494 1.18436 0.592182 0.805804i $$-0.298267\pi$$
0.592182 + 0.805804i $$0.298267\pi$$
$$578$$ 0 0
$$579$$ 19.8261 0.957746i 0.823946 0.0398026i
$$580$$ 0 0
$$581$$ −14.1239 14.1239i −0.585958 0.585958i
$$582$$ 0 0
$$583$$ −52.7527 −2.18479
$$584$$ 0 0
$$585$$ −0.525036 5.42166i −0.0217076 0.224158i
$$586$$ 0 0
$$587$$ 19.9011 19.9011i 0.821405 0.821405i −0.164904 0.986310i $$-0.552732\pi$$
0.986310 + 0.164904i $$0.0527315\pi$$
$$588$$ 0 0
$$589$$ 0.372787 + 0.372787i 0.0153604 + 0.0153604i
$$590$$ 0 0
$$591$$ −26.8510 24.3764i −1.10450 1.00271i
$$592$$ 0 0
$$593$$ 20.4344i 0.839140i −0.907723 0.419570i $$-0.862181\pi$$
0.907723 0.419570i $$-0.137819\pi$$
$$594$$ 0 0
$$595$$ −3.25443 + 3.25443i −0.133418 + 0.133418i
$$596$$ 0 0
$$597$$ 42.3079 2.04378i 1.73155 0.0836462i
$$598$$ 0 0
$$599$$ 32.6704i 1.33488i −0.744665 0.667438i $$-0.767391\pi$$
0.744665 0.667438i $$-0.232609\pi$$
$$600$$ 0 0
$$601$$ 6.73553i 0.274748i 0.990519 + 0.137374i $$0.0438662\pi$$
−0.990519 + 0.137374i $$0.956134\pi$$
$$602$$ 0 0
$$603$$ 1.05702 1.28369i 0.0430451 0.0522760i
$$604$$ 0 0
$$605$$ 2.94993 2.94993i 0.119932 0.119932i
$$606$$ 0 0
$$607$$ 21.2388i 0.862058i 0.902338 + 0.431029i $$0.141849\pi$$
−0.902338 + 0.431029i $$0.858151\pi$$
$$608$$ 0 0
$$609$$ 14.6167 16.1005i 0.592297 0.652426i
$$610$$ 0 0
$$611$$ −15.8508 15.8508i −0.641256 0.641256i
$$612$$ 0 0
$$613$$ 9.62219 9.62219i 0.388637 0.388637i −0.485564 0.874201i $$-0.661386\pi$$
0.874201 + 0.485564i $$0.161386\pi$$
$$614$$ 0 0
$$615$$ 1.42166 + 1.29064i 0.0573270 + 0.0520436i
$$616$$ 0 0
$$617$$ −3.74576 −0.150798 −0.0753992 0.997153i $$-0.524023\pi$$
−0.0753992 + 0.997153i $$0.524023\pi$$
$$618$$ 0 0
$$619$$ 13.0680 + 13.0680i 0.525249 + 0.525249i 0.919152 0.393903i $$-0.128876\pi$$
−0.393903 + 0.919152i $$0.628876\pi$$
$$620$$ 0 0
$$621$$ 4.47799 + 30.7070i 0.179696 + 1.23223i
$$622$$ 0 0
$$623$$ 38.9643 1.56107
$$624$$ 0 0
$$625$$ −19.5472 −0.781887
$$626$$ 0 0
$$627$$ 0.354779 + 7.34422i 0.0141685 + 0.293300i
$$628$$ 0 0
$$629$$ 3.70355 + 3.70355i 0.147670 + 0.147670i
$$630$$ 0 0
$$631$$ −7.51388 −0.299123 −0.149561 0.988752i $$-0.547786\pi$$
−0.149561 + 0.988752i $$0.547786\pi$$
$$632$$ 0 0
$$633$$ −10.1857 + 11.2197i −0.404843 + 0.445942i
$$634$$ 0 0
$$635$$ 6.81226 6.81226i 0.270336 0.270336i
$$636$$ 0 0
$$637$$ −5.52444 5.52444i −0.218886 0.218886i
$$638$$ 0 0
$$639$$ 1.45158 + 14.9894i 0.0574238 + 0.592973i
$$640$$ 0 0
$$641$$ 27.7227i 1.09498i −0.836811 0.547491i $$-0.815583\pi$$
0.836811 0.547491i $$-0.184417\pi$$
$$642$$ 0 0
$$643$$ −19.7003 + 19.7003i −0.776903 + 0.776903i −0.979303 0.202400i $$-0.935126\pi$$
0.202400 + 0.979303i $$0.435126\pi$$
$$644$$ 0 0
$$645$$ 0.0512954 + 1.06186i 0.00201976 + 0.0418106i
$$646$$ 0 0
$$647$$ 5.29520i 0.208176i 0.994568 + 0.104088i $$0.0331923\pi$$
−0.994568 + 0.104088i $$0.966808\pi$$
$$648$$ 0 0
$$649$$ 0.480585i 0.0188646i
$$650$$ 0 0
$$651$$ 0.135991 + 2.81513i 0.00532992 + 0.110334i
$$652$$ 0 0
$$653$$ 29.7039 29.7039i 1.16240 1.16240i 0.178457 0.983948i $$-0.442890\pi$$
0.983948 0.178457i $$-0.0571104\pi$$
$$654$$ 0 0
$$655$$ 0.0694851i 0.00271501i
$$656$$ 0 0
$$657$$ 3.89220 + 40.1919i 0.151849 + 1.56804i
$$658$$ 0 0
$$659$$ 1.03268 + 1.03268i 0.0402276 + 0.0402276i 0.726934 0.686707i $$-0.240944\pi$$
−0.686707 + 0.726934i $$0.740944\pi$$
$$660$$ 0 0
$$661$$ −29.8277 + 29.8277i −1.16016 + 1.16016i −0.175725 + 0.984439i $$0.556227\pi$$
−0.984439 + 0.175725i $$0.943773\pi$$
$$662$$ 0 0
$$663$$ 8.41110 9.26498i 0.326660 0.359822i
$$664$$ 0 0
$$665$$ −1.90442 −0.0738502
$$666$$ 0 0
$$667$$ −17.0872 17.0872i −0.661619 0.661619i
$$668$$ 0 0
$$669$$ −0.684461 14.1689i −0.0264628 0.547802i
$$670$$ 0 0
$$671$$ 34.2198 1.32104
$$672$$ 0 0
$$673$$ −0.891685 −0.0343719 −0.0171860 0.999852i $$-0.505471\pi$$
−0.0171860 + 0.999852i $$0.505471\pi$$
$$674$$ 0 0
$$675$$ 3.46959 + 23.7920i 0.133545 + 0.915756i
$$676$$ 0 0
$$677$$ −8.13073 8.13073i −0.312489 0.312489i 0.533384 0.845873i $$-0.320920\pi$$
−0.845873 + 0.533384i $$0.820920\pi$$
$$678$$ 0 0
$$679$$ 26.9200 1.03309
$$680$$ 0 0
$$681$$ −17.9734 16.3169i −0.688742 0.625266i
$$682$$ 0 0
$$683$$ −14.5917 + 14.5917i −0.558337 + 0.558337i −0.928834 0.370497i $$-0.879187\pi$$
0.370497 + 0.928834i $$0.379187\pi$$
$$684$$ 0 0
$$685$$ 5.72496 + 5.72496i 0.218740 + 0.218740i
$$686$$ 0 0
$$687$$ 11.7749 12.9703i 0.449241 0.494847i
$$688$$ 0 0
$$689$$ 37.1487i 1.41525i
$$690$$ 0 0
$$691$$ 11.2197 11.2197i 0.426817 0.426817i −0.460726 0.887543i $$-0.652411\pi$$
0.887543 + 0.460726i $$0.152411\pi$$
$$692$$ 0 0
$$693$$ −24.9864 + 30.3447i −0.949154 + 1.15270i
$$694$$ 0 0
$$695$$ 7.24616i 0.274863i
$$696$$ 0 0
$$697$$ 4.41110i 0.167082i
$$698$$ 0 0
$$699$$ −33.9833 + 1.64164i −1.28536 + 0.0620924i
$$700$$ 0 0
$$701$$ −14.7166 + 14.7166i −0.555837 + 0.555837i −0.928120 0.372282i $$-0.878575\pi$$
0.372282 + 0.928120i $$0.378575\pi$$
$$702$$ 0 0
$$703$$ 2.16724i 0.0817389i
$$704$$ 0 0
$$705$$ −5.90225 5.35828i −0.222292 0.201805i
$$706$$ 0 0
$$707$$ −0.564847 0.564847i −0.0212433 0.0212433i
$$708$$ 0 0
$$709$$ 23.2978 23.2978i 0.874966 0.874966i −0.118043 0.993009i $$-0.537662\pi$$
0.993009 + 0.118043i $$0.0376620\pi$$
$$710$$ 0 0
$$711$$ 1.00502 + 10.3781i 0.0376913 + 0.389211i
$$712$$ 0 0
$$713$$ 3.13198 0.117293
$$714$$ 0 0
$$715$$ −5.42166 5.42166i −0.202759 0.202759i
$$716$$ 0 0
$$717$$ 16.3358 0.789136i 0.610071 0.0294708i
$$718$$ 0 0
$$719$$ −27.3421 −1.01969 −0.509844 0.860267i $$-0.670297\pi$$
−0.509844 + 0.860267i $$0.670297\pi$$
$$720$$ 0 0
$$721$$ −19.7250 −0.734596
$$722$$ 0 0
$$723$$ −28.7474 + 1.38871i −1.06913 + 0.0516465i
$$724$$ 0 0
$$725$$ −13.2393 13.2393i −0.491696 0.491696i
$$726$$ 0 0
$$727$$ 24.1517 0.895735 0.447868 0.894100i $$-0.352184\pi$$
0.447868 + 0.894100i $$0.352184\pi$$
$$728$$ 0 0
$$729$$ 25.8755 7.71083i 0.958353 0.285586i
$$730$$ 0 0
$$731$$ −1.72693 + 1.72693i −0.0638729 + 0.0638729i
$$732$$ 0 0
$$733$$ 6.00502 + 6.00502i 0.221801 + 0.221801i 0.809256 0.587456i $$-0.199870\pi$$
−0.587456 + 0.809256i $$0.699870\pi$$
$$734$$ 0 0
$$735$$ −2.05709 1.86751i −0.0758770 0.0688840i
$$736$$ 0 0
$$737$$ 2.34071i 0.0862212i
$$738$$ 0 0
$$739$$ 10.9008 10.9008i 0.400992 0.400992i −0.477590 0.878583i $$-0.658490\pi$$
0.878583 + 0.477590i $$0.158490\pi$$
$$740$$ 0 0
$$741$$ 5.17183 0.249837i 0.189992 0.00917798i
$$742$$ 0 0
$$743$$ 1.29064i 0.0473490i 0.999720 + 0.0236745i $$0.00753652\pi$$
−0.999720 + 0.0236745i $$0.992463\pi$$
$$744$$ 0 0
$$745$$ 4.99948i 0.183167i
$$746$$ 0 0
$$747$$ 14.9088 + 12.2762i 0.545483 + 0.449162i
$$748$$ 0 0
$$749$$ −5.10860 + 5.10860i −0.186664 + 0.186664i
$$750$$ 0 0
$$751$$ 1.46552i 0.0534774i 0.999642 + 0.0267387i $$0.00851221\pi$$
−0.999642 + 0.0267387i $$0.991488\pi$$
$$752$$ 0 0
$$753$$ −3.34861 + 3.68855i −0.122030 + 0.134418i
$$754$$ 0 0
$$755$$ 4.29406 + 4.29406i 0.156277 + 0.156277i
$$756$$ 0 0
$$757$$ −4.71943 + 4.71943i −0.171530 + 0.171530i −0.787651 0.616121i $$-0.788703\pi$$
0.616121 + 0.787651i $$0.288703\pi$$
$$758$$ 0 0
$$759$$ 32.3416 + 29.3609i 1.17393 + 1.06573i
$$760$$ 0 0
$$761$$ −29.1578 −1.05697 −0.528485 0.848943i $$-0.677240\pi$$
−0.528485 + 0.848943i $$0.677240\pi$$
$$762$$ 0 0
$$763$$ 20.3955 + 20.3955i 0.738367 + 0.738367i
$$764$$ 0 0
$$765$$ 2.82867 3.43528i 0.102271 0.124203i
$$766$$ 0 0
$$767$$ 0.338430 0.0122200
$$768$$ 0 0
$$769$$ 20.8122 0.750505 0.375253 0.926923i $$-0.377556\pi$$
0.375253 + 0.926923i $$0.377556\pi$$
$$770$$ 0 0
$$771$$ −1.25996 26.0822i −0.0453762 0.939326i
$$772$$ 0 0
$$773$$ −26.6607 26.6607i −0.958918 0.958918i 0.0402703 0.999189i $$-0.487178\pi$$
−0.999189 + 0.0402703i $$0.987178\pi$$
$$774$$ 0 0
$$775$$ 2.42669 0.0871691
$$776$$ 0 0
$$777$$ −7.78774 + 8.57834i −0.279384 + 0.307746i
$$778$$ 0 0
$$779$$ −1.29064 + 1.29064i −0.0462419 + 0.0462419i
$$780$$ 0 0
$$781$$ 14.9894 + 14.9894i 0.536364 + 0.536364i
$$782$$ 0 0
$$783$$ −12.5662 + 16.8569i −0.449078 + 0.602418i
$$784$$ 0 0
$$785$$ 7.90214i 0.282040i
$$786$$ 0 0
$$787$$ 32.7875 32.7875i 1.16875 1.16875i 0.186243 0.982504i $$-0.440369\pi$$
0.982504 0.186243i $$-0.0596311\pi$$
$$788$$ 0 0
$$789$$ −2.49163 51.5788i −0.0887044 1.83625i
$$790$$ 0 0
$$791$$ 25.7927i 0.917082i
$$792$$ 0 0
$$793$$ 24.0978i 0.855736i
$$794$$ 0 0
$$795$$ 0.637430 + 13.1953i 0.0226073 + 0.467990i
$$796$$ 0