# Properties

 Label 756.2.ba.a.575.14 Level $756$ Weight $2$ Character 756.575 Analytic conductor $6.037$ Analytic rank $0$ Dimension $72$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$756 = 2^{2} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 756.ba (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.03669039281$$ Analytic rank: $$0$$ Dimension: $$72$$ Relative dimension: $$36$$ over $$\Q(\zeta_{6})$$ Twist minimal: no (minimal twist has level 252) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 575.14 Character $$\chi$$ $$=$$ 756.575 Dual form 756.2.ba.a.71.14

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.498620 + 1.32340i) q^{2} +(-1.50276 - 1.31974i) q^{4} +(-2.06874 + 1.19439i) q^{5} +(0.866025 + 0.500000i) q^{7} +(2.49585 - 1.33069i) q^{8} +O(q^{10})$$ $$q+(-0.498620 + 1.32340i) q^{2} +(-1.50276 - 1.31974i) q^{4} +(-2.06874 + 1.19439i) q^{5} +(0.866025 + 0.500000i) q^{7} +(2.49585 - 1.33069i) q^{8} +(-0.549133 - 3.33330i) q^{10} +(3.21792 - 5.57360i) q^{11} +(2.15010 + 3.72408i) q^{13} +(-1.09352 + 0.896785i) q^{14} +(0.516556 + 3.96651i) q^{16} +1.89547i q^{17} -0.529348i q^{19} +(4.68509 + 0.935330i) q^{20} +(5.77157 + 7.03770i) q^{22} +(2.64942 + 4.58894i) q^{23} +(0.353115 - 0.611613i) q^{25} +(-6.00052 + 0.988535i) q^{26} +(-0.641554 - 1.89431i) q^{28} +(0.301871 + 0.174285i) q^{29} +(-5.09757 + 2.94308i) q^{31} +(-5.50683 - 1.29417i) q^{32} +(-2.50846 - 0.945118i) q^{34} -2.38877 q^{35} +0.842466 q^{37} +(0.700537 + 0.263943i) q^{38} +(-3.57389 + 5.73386i) q^{40} +(-4.58530 + 2.64733i) q^{41} +(7.38095 + 4.26140i) q^{43} +(-12.1915 + 4.12894i) q^{44} +(-7.39404 + 1.21810i) q^{46} +(2.04252 - 3.53774i) q^{47} +(0.500000 + 0.866025i) q^{49} +(0.633336 + 0.772273i) q^{50} +(1.68376 - 8.43397i) q^{52} +12.5979i q^{53} +15.3738i q^{55} +(2.82681 + 0.0955095i) q^{56} +(-0.381168 + 0.312593i) q^{58} +(2.66171 + 4.61021i) q^{59} +(-3.49882 + 6.06013i) q^{61} +(-1.35312 - 8.21358i) q^{62} +(4.45851 - 6.64242i) q^{64} +(-8.89599 - 5.13610i) q^{65} +(9.32818 - 5.38563i) q^{67} +(2.50153 - 2.84843i) q^{68} +(1.19109 - 3.16129i) q^{70} +6.12137 q^{71} +5.07942 q^{73} +(-0.420070 + 1.11492i) q^{74} +(-0.698603 + 0.795481i) q^{76} +(5.57360 - 3.21792i) q^{77} +(2.87851 + 1.66191i) q^{79} +(-5.80616 - 7.58869i) q^{80} +(-1.21714 - 7.38818i) q^{82} +(-3.23597 + 5.60486i) q^{83} +(-2.26392 - 3.92122i) q^{85} +(-9.31981 + 7.64311i) q^{86} +(0.614684 - 18.1929i) q^{88} -14.4170i q^{89} +4.30020i q^{91} +(2.07478 - 10.3926i) q^{92} +(3.66340 + 4.46705i) q^{94} +(0.632246 + 1.09508i) q^{95} +(-3.86625 + 6.69654i) q^{97} +(-1.39540 + 0.229881i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$72 q+O(q^{10})$$ 72 * q $$72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100})$$ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$325$$ $$379$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.498620 + 1.32340i −0.352577 + 0.935783i
$$3$$ 0 0
$$4$$ −1.50276 1.31974i −0.751378 0.659872i
$$5$$ −2.06874 + 1.19439i −0.925167 + 0.534146i −0.885280 0.465059i $$-0.846033\pi$$
−0.0398874 + 0.999204i $$0.512700\pi$$
$$6$$ 0 0
$$7$$ 0.866025 + 0.500000i 0.327327 + 0.188982i
$$8$$ 2.49585 1.33069i 0.882415 0.470471i
$$9$$ 0 0
$$10$$ −0.549133 3.33330i −0.173651 1.05408i
$$11$$ 3.21792 5.57360i 0.970240 1.68050i 0.275416 0.961325i $$-0.411184\pi$$
0.694824 0.719180i $$-0.255482\pi$$
$$12$$ 0 0
$$13$$ 2.15010 + 3.72408i 0.596331 + 1.03288i 0.993358 + 0.115068i $$0.0367086\pi$$
−0.397027 + 0.917807i $$0.629958\pi$$
$$14$$ −1.09352 + 0.896785i −0.292254 + 0.239676i
$$15$$ 0 0
$$16$$ 0.516556 + 3.96651i 0.129139 + 0.991626i
$$17$$ 1.89547i 0.459718i 0.973224 + 0.229859i $$0.0738266\pi$$
−0.973224 + 0.229859i $$0.926173\pi$$
$$18$$ 0 0
$$19$$ 0.529348i 0.121441i −0.998155 0.0607204i $$-0.980660\pi$$
0.998155 0.0607204i $$-0.0193398\pi$$
$$20$$ 4.68509 + 0.935330i 1.04762 + 0.209146i
$$21$$ 0 0
$$22$$ 5.77157 + 7.03770i 1.23050 + 1.50044i
$$23$$ 2.64942 + 4.58894i 0.552443 + 0.956859i 0.998098 + 0.0616543i $$0.0196376\pi$$
−0.445655 + 0.895205i $$0.647029\pi$$
$$24$$ 0 0
$$25$$ 0.353115 0.611613i 0.0706230 0.122323i
$$26$$ −6.00052 + 0.988535i −1.17680 + 0.193868i
$$27$$ 0 0
$$28$$ −0.641554 1.89431i −0.121242 0.357991i
$$29$$ 0.301871 + 0.174285i 0.0560561 + 0.0323640i 0.527766 0.849390i $$-0.323030\pi$$
−0.471710 + 0.881754i $$0.656363\pi$$
$$30$$ 0 0
$$31$$ −5.09757 + 2.94308i −0.915550 + 0.528593i −0.882213 0.470851i $$-0.843947\pi$$
−0.0333376 + 0.999444i $$0.510614\pi$$
$$32$$ −5.50683 1.29417i −0.973478 0.228779i
$$33$$ 0 0
$$34$$ −2.50846 0.945118i −0.430197 0.162086i
$$35$$ −2.38877 −0.403776
$$36$$ 0 0
$$37$$ 0.842466 0.138501 0.0692503 0.997599i $$-0.477939\pi$$
0.0692503 + 0.997599i $$0.477939\pi$$
$$38$$ 0.700537 + 0.263943i 0.113642 + 0.0428173i
$$39$$ 0 0
$$40$$ −3.57389 + 5.73386i −0.565082 + 0.906603i
$$41$$ −4.58530 + 2.64733i −0.716104 + 0.413443i −0.813317 0.581821i $$-0.802340\pi$$
0.0972131 + 0.995264i $$0.469007\pi$$
$$42$$ 0 0
$$43$$ 7.38095 + 4.26140i 1.12559 + 0.649857i 0.942821 0.333300i $$-0.108162\pi$$
0.182764 + 0.983157i $$0.441496\pi$$
$$44$$ −12.1915 + 4.12894i −1.83793 + 0.622461i
$$45$$ 0 0
$$46$$ −7.39404 + 1.21810i −1.09019 + 0.179600i
$$47$$ 2.04252 3.53774i 0.297932 0.516033i −0.677731 0.735310i $$-0.737037\pi$$
0.975663 + 0.219277i $$0.0703699\pi$$
$$48$$ 0 0
$$49$$ 0.500000 + 0.866025i 0.0714286 + 0.123718i
$$50$$ 0.633336 + 0.772273i 0.0895673 + 0.109216i
$$51$$ 0 0
$$52$$ 1.68376 8.43397i 0.233495 1.16958i
$$53$$ 12.5979i 1.73046i 0.501376 + 0.865230i $$0.332827\pi$$
−0.501376 + 0.865230i $$0.667173\pi$$
$$54$$ 0 0
$$55$$ 15.3738i 2.07300i
$$56$$ 2.82681 + 0.0955095i 0.377749 + 0.0127630i
$$57$$ 0 0
$$58$$ −0.381168 + 0.312593i −0.0500497 + 0.0410455i
$$59$$ 2.66171 + 4.61021i 0.346524 + 0.600198i 0.985630 0.168921i $$-0.0540284\pi$$
−0.639105 + 0.769119i $$0.720695\pi$$
$$60$$ 0 0
$$61$$ −3.49882 + 6.06013i −0.447978 + 0.775920i −0.998254 0.0590625i $$-0.981189\pi$$
0.550277 + 0.834982i $$0.314522\pi$$
$$62$$ −1.35312 8.21358i −0.171846 1.04313i
$$63$$ 0 0
$$64$$ 4.45851 6.64242i 0.557314 0.830302i
$$65$$ −8.89599 5.13610i −1.10341 0.637055i
$$66$$ 0 0
$$67$$ 9.32818 5.38563i 1.13962 0.657959i 0.193282 0.981143i $$-0.438087\pi$$
0.946336 + 0.323184i $$0.104753\pi$$
$$68$$ 2.50153 2.84843i 0.303355 0.345423i
$$69$$ 0 0
$$70$$ 1.19109 3.16129i 0.142362 0.377847i
$$71$$ 6.12137 0.726473 0.363236 0.931697i $$-0.381672\pi$$
0.363236 + 0.931697i $$0.381672\pi$$
$$72$$ 0 0
$$73$$ 5.07942 0.594501 0.297251 0.954799i $$-0.403930\pi$$
0.297251 + 0.954799i $$0.403930\pi$$
$$74$$ −0.420070 + 1.11492i −0.0488322 + 0.129606i
$$75$$ 0 0
$$76$$ −0.698603 + 0.795481i −0.0801353 + 0.0912480i
$$77$$ 5.57360 3.21792i 0.635171 0.366716i
$$78$$ 0 0
$$79$$ 2.87851 + 1.66191i 0.323858 + 0.186979i 0.653111 0.757262i $$-0.273464\pi$$
−0.329253 + 0.944242i $$0.606797\pi$$
$$80$$ −5.80616 7.58869i −0.649148 0.848441i
$$81$$ 0 0
$$82$$ −1.21714 7.38818i −0.134411 0.815888i
$$83$$ −3.23597 + 5.60486i −0.355193 + 0.615213i −0.987151 0.159790i $$-0.948918\pi$$
0.631958 + 0.775003i $$0.282252\pi$$
$$84$$ 0 0
$$85$$ −2.26392 3.92122i −0.245557 0.425317i
$$86$$ −9.31981 + 7.64311i −1.00498 + 0.824178i
$$87$$ 0 0
$$88$$ 0.614684 18.1929i 0.0655256 1.93937i
$$89$$ 14.4170i 1.52820i −0.645099 0.764099i $$-0.723184\pi$$
0.645099 0.764099i $$-0.276816\pi$$
$$90$$ 0 0
$$91$$ 4.30020i 0.450784i
$$92$$ 2.07478 10.3926i 0.216310 1.08350i
$$93$$ 0 0
$$94$$ 3.66340 + 4.46705i 0.377851 + 0.460741i
$$95$$ 0.632246 + 1.09508i 0.0648670 + 0.112353i
$$96$$ 0 0
$$97$$ −3.86625 + 6.69654i −0.392558 + 0.679931i −0.992786 0.119898i $$-0.961743\pi$$
0.600228 + 0.799829i $$0.295077\pi$$
$$98$$ −1.39540 + 0.229881i −0.140957 + 0.0232215i
$$99$$ 0 0
$$100$$ −1.33782 + 0.453085i −0.133782 + 0.0453085i
$$101$$ 14.7999 + 8.54473i 1.47265 + 0.850233i 0.999527 0.0307657i $$-0.00979457\pi$$
0.473119 + 0.880998i $$0.343128\pi$$
$$102$$ 0 0
$$103$$ −10.0362 + 5.79440i −0.988896 + 0.570939i −0.904944 0.425531i $$-0.860087\pi$$
−0.0839517 + 0.996470i $$0.526754\pi$$
$$104$$ 10.3219 + 6.43362i 1.01215 + 0.630868i
$$105$$ 0 0
$$106$$ −16.6721 6.28158i −1.61933 0.610121i
$$107$$ −1.66184 −0.160656 −0.0803278 0.996768i $$-0.525597\pi$$
−0.0803278 + 0.996768i $$0.525597\pi$$
$$108$$ 0 0
$$109$$ −8.21513 −0.786867 −0.393434 0.919353i $$-0.628713\pi$$
−0.393434 + 0.919353i $$0.628713\pi$$
$$110$$ −20.3456 7.66566i −1.93988 0.730892i
$$111$$ 0 0
$$112$$ −1.53590 + 3.69337i −0.145129 + 0.348991i
$$113$$ 7.87513 4.54671i 0.740830 0.427718i −0.0815410 0.996670i $$-0.525984\pi$$
0.822371 + 0.568952i $$0.192651\pi$$
$$114$$ 0 0
$$115$$ −10.9619 6.32887i −1.02220 0.590170i
$$116$$ −0.223627 0.660301i −0.0207632 0.0613074i
$$117$$ 0 0
$$118$$ −7.42831 + 1.22375i −0.683832 + 0.112655i
$$119$$ −0.947734 + 1.64152i −0.0868786 + 0.150478i
$$120$$ 0 0
$$121$$ −15.2100 26.3446i −1.38273 2.39496i
$$122$$ −6.27537 7.65202i −0.568146 0.692781i
$$123$$ 0 0
$$124$$ 11.5445 + 2.30474i 1.03673 + 0.206972i
$$125$$ 10.2568i 0.917399i
$$126$$ 0 0
$$127$$ 17.0630i 1.51409i −0.653360 0.757047i $$-0.726641\pi$$
0.653360 0.757047i $$-0.273359\pi$$
$$128$$ 6.56745 + 9.21242i 0.580486 + 0.814270i
$$129$$ 0 0
$$130$$ 11.2328 9.21196i 0.985183 0.807942i
$$131$$ 5.58971 + 9.68166i 0.488375 + 0.845890i 0.999911 0.0133718i $$-0.00425652\pi$$
−0.511536 + 0.859262i $$0.670923\pi$$
$$132$$ 0 0
$$133$$ 0.264674 0.458429i 0.0229501 0.0397508i
$$134$$ 2.47611 + 15.0303i 0.213903 + 1.29842i
$$135$$ 0 0
$$136$$ 2.52229 + 4.73080i 0.216284 + 0.405663i
$$137$$ −4.30543 2.48574i −0.367838 0.212371i 0.304676 0.952456i $$-0.401452\pi$$
−0.672513 + 0.740085i $$0.734785\pi$$
$$138$$ 0 0
$$139$$ 7.46366 4.30915i 0.633060 0.365497i −0.148876 0.988856i $$-0.547566\pi$$
0.781936 + 0.623359i $$0.214232\pi$$
$$140$$ 3.58974 + 3.15256i 0.303389 + 0.266440i
$$141$$ 0 0
$$142$$ −3.05223 + 8.10100i −0.256138 + 0.679821i
$$143$$ 27.6754 2.31434
$$144$$ 0 0
$$145$$ −0.832656 −0.0691483
$$146$$ −2.53270 + 6.72209i −0.209608 + 0.556324i
$$147$$ 0 0
$$148$$ −1.26602 1.11184i −0.104066 0.0913926i
$$149$$ −2.18247 + 1.26005i −0.178795 + 0.103227i −0.586727 0.809785i $$-0.699584\pi$$
0.407931 + 0.913013i $$0.366250\pi$$
$$150$$ 0 0
$$151$$ −0.331047 0.191130i −0.0269402 0.0155539i 0.486469 0.873698i $$-0.338285\pi$$
−0.513410 + 0.858144i $$0.671618\pi$$
$$152$$ −0.704400 1.32117i −0.0571344 0.107161i
$$153$$ 0 0
$$154$$ 1.47948 + 8.98061i 0.119220 + 0.723678i
$$155$$ 7.03035 12.1769i 0.564691 0.978074i
$$156$$ 0 0
$$157$$ 4.39885 + 7.61904i 0.351067 + 0.608065i 0.986437 0.164143i $$-0.0524857\pi$$
−0.635370 + 0.772208i $$0.719152\pi$$
$$158$$ −3.63465 + 2.98075i −0.289157 + 0.237136i
$$159$$ 0 0
$$160$$ 12.9379 3.89998i 1.02283 0.308320i
$$161$$ 5.29885i 0.417608i
$$162$$ 0 0
$$163$$ 10.7694i 0.843521i 0.906707 + 0.421760i $$0.138588\pi$$
−0.906707 + 0.421760i $$0.861412\pi$$
$$164$$ 10.3844 + 2.07313i 0.810884 + 0.161885i
$$165$$ 0 0
$$166$$ −5.80393 7.07716i −0.450473 0.549294i
$$167$$ −3.92462 6.79765i −0.303697 0.526018i 0.673274 0.739393i $$-0.264888\pi$$
−0.976970 + 0.213375i $$0.931554\pi$$
$$168$$ 0 0
$$169$$ −2.74587 + 4.75598i −0.211221 + 0.365845i
$$170$$ 6.31817 1.04086i 0.484582 0.0798306i
$$171$$ 0 0
$$172$$ −5.46783 16.1448i −0.416918 1.23103i
$$173$$ 16.5653 + 9.56396i 1.25943 + 0.727134i 0.972964 0.230955i $$-0.0741850\pi$$
0.286469 + 0.958089i $$0.407518\pi$$
$$174$$ 0 0
$$175$$ 0.611613 0.353115i 0.0462336 0.0266930i
$$176$$ 23.7700 + 9.88483i 1.79173 + 0.745097i
$$177$$ 0 0
$$178$$ 19.0794 + 7.18860i 1.43006 + 0.538808i
$$179$$ −26.1468 −1.95431 −0.977153 0.212538i $$-0.931827\pi$$
−0.977153 + 0.212538i $$0.931827\pi$$
$$180$$ 0 0
$$181$$ 18.9172 1.40610 0.703052 0.711139i $$-0.251820\pi$$
0.703052 + 0.711139i $$0.251820\pi$$
$$182$$ −5.69087 2.14417i −0.421836 0.158936i
$$183$$ 0 0
$$184$$ 12.7190 + 7.92771i 0.937659 + 0.584439i
$$185$$ −1.74284 + 1.00623i −0.128136 + 0.0739795i
$$186$$ 0 0
$$187$$ 10.5646 + 6.09947i 0.772559 + 0.446037i
$$188$$ −7.73832 + 2.62077i −0.564375 + 0.191139i
$$189$$ 0 0
$$190$$ −1.76448 + 0.290682i −0.128009 + 0.0210883i
$$191$$ 4.70709 8.15291i 0.340593 0.589924i −0.643950 0.765068i $$-0.722706\pi$$
0.984543 + 0.175143i $$0.0560389\pi$$
$$192$$ 0 0
$$193$$ −0.658744 1.14098i −0.0474174 0.0821294i 0.841343 0.540502i $$-0.181766\pi$$
−0.888760 + 0.458373i $$0.848432\pi$$
$$194$$ −6.93439 8.45561i −0.497860 0.607078i
$$195$$ 0 0
$$196$$ 0.391553 1.96130i 0.0279680 0.140093i
$$197$$ 3.56413i 0.253933i −0.991907 0.126967i $$-0.959476\pi$$
0.991907 0.126967i $$-0.0405241\pi$$
$$198$$ 0 0
$$199$$ 15.9739i 1.13236i −0.824282 0.566179i $$-0.808421\pi$$
0.824282 0.566179i $$-0.191579\pi$$
$$200$$ 0.0674517 1.99638i 0.00476955 0.141165i
$$201$$ 0 0
$$202$$ −18.6876 + 15.3256i −1.31485 + 1.07830i
$$203$$ 0.174285 + 0.301871i 0.0122324 + 0.0211872i
$$204$$ 0 0
$$205$$ 6.32386 10.9532i 0.441677 0.765007i
$$206$$ −2.66404 16.1711i −0.185613 1.12669i
$$207$$ 0 0
$$208$$ −13.6610 + 10.4521i −0.947217 + 0.724722i
$$209$$ −2.95038 1.70340i −0.204082 0.117827i
$$210$$ 0 0
$$211$$ 3.39401 1.95953i 0.233653 0.134900i −0.378603 0.925559i $$-0.623595\pi$$
0.612256 + 0.790659i $$0.290262\pi$$
$$212$$ 16.6260 18.9316i 1.14188 1.30023i
$$213$$ 0 0
$$214$$ 0.828624 2.19927i 0.0566436 0.150339i
$$215$$ −20.3590 −1.38847
$$216$$ 0 0
$$217$$ −5.88617 −0.399579
$$218$$ 4.09623 10.8719i 0.277432 0.736337i
$$219$$ 0 0
$$220$$ 20.2894 23.1030i 1.36791 1.55761i
$$221$$ −7.05888 + 4.07545i −0.474832 + 0.274144i
$$222$$ 0 0
$$223$$ −2.25600 1.30250i −0.151073 0.0872218i 0.422558 0.906336i $$-0.361132\pi$$
−0.573631 + 0.819114i $$0.694466\pi$$
$$224$$ −4.12197 3.87420i −0.275410 0.258856i
$$225$$ 0 0
$$226$$ 2.09040 + 12.6890i 0.139052 + 0.844060i
$$227$$ 1.56505 2.71075i 0.103876 0.179919i −0.809402 0.587254i $$-0.800209\pi$$
0.913278 + 0.407336i $$0.133542\pi$$
$$228$$ 0 0
$$229$$ −3.33583 5.77783i −0.220438 0.381809i 0.734503 0.678605i $$-0.237415\pi$$
−0.954941 + 0.296796i $$0.904082\pi$$
$$230$$ 13.8414 11.3513i 0.912677 0.748481i
$$231$$ 0 0
$$232$$ 0.985345 + 0.0332918i 0.0646910 + 0.00218572i
$$233$$ 15.0197i 0.983971i −0.870603 0.491985i $$-0.836271\pi$$
0.870603 0.491985i $$-0.163729\pi$$
$$234$$ 0 0
$$235$$ 9.75821i 0.636556i
$$236$$ 2.08440 10.4408i 0.135683 0.679637i
$$237$$ 0 0
$$238$$ −1.69983 2.07272i −0.110183 0.134355i
$$239$$ −1.10101 1.90701i −0.0712185 0.123354i 0.828217 0.560407i $$-0.189355\pi$$
−0.899436 + 0.437053i $$0.856022\pi$$
$$240$$ 0 0
$$241$$ −9.28440 + 16.0811i −0.598061 + 1.03587i 0.395046 + 0.918661i $$0.370729\pi$$
−0.993107 + 0.117211i $$0.962605\pi$$
$$242$$ 42.4483 6.99300i 2.72868 0.449527i
$$243$$ 0 0
$$244$$ 13.2557 4.48936i 0.848608 0.287402i
$$245$$ −2.06874 1.19439i −0.132167 0.0763065i
$$246$$ 0 0
$$247$$ 1.97134 1.13815i 0.125433 0.0724188i
$$248$$ −8.80641 + 14.1288i −0.559208 + 0.897179i
$$249$$ 0 0
$$250$$ 13.5739 + 5.11426i 0.858486 + 0.323454i
$$251$$ −6.18166 −0.390183 −0.195092 0.980785i $$-0.562500\pi$$
−0.195092 + 0.980785i $$0.562500\pi$$
$$252$$ 0 0
$$253$$ 34.1026 2.14401
$$254$$ 22.5811 + 8.50794i 1.41686 + 0.533836i
$$255$$ 0 0
$$256$$ −15.4663 + 4.09785i −0.966646 + 0.256115i
$$257$$ −6.98685 + 4.03386i −0.435828 + 0.251625i −0.701826 0.712348i $$-0.747632\pi$$
0.265998 + 0.963973i $$0.414298\pi$$
$$258$$ 0 0
$$259$$ 0.729597 + 0.421233i 0.0453350 + 0.0261741i
$$260$$ 6.59017 + 19.4587i 0.408705 + 1.20678i
$$261$$ 0 0
$$262$$ −15.5998 + 2.56993i −0.963759 + 0.158771i
$$263$$ 0.0757144 0.131141i 0.00466875 0.00808651i −0.863682 0.504038i $$-0.831847\pi$$
0.868350 + 0.495951i $$0.165181\pi$$
$$264$$ 0 0
$$265$$ −15.0468 26.0618i −0.924317 1.60096i
$$266$$ 0.474711 + 0.578850i 0.0291064 + 0.0354916i
$$267$$ 0 0
$$268$$ −21.1256 4.21751i −1.29045 0.257626i
$$269$$ 2.18065i 0.132957i 0.997788 + 0.0664784i $$0.0211763\pi$$
−0.997788 + 0.0664784i $$0.978824\pi$$
$$270$$ 0 0
$$271$$ 3.08448i 0.187369i 0.995602 + 0.0936844i $$0.0298645\pi$$
−0.995602 + 0.0936844i $$0.970136\pi$$
$$272$$ −7.51838 + 0.979116i −0.455869 + 0.0593676i
$$273$$ 0 0
$$274$$ 5.43639 4.45835i 0.328425 0.269339i
$$275$$ −2.27259 3.93624i −0.137042 0.237364i
$$276$$ 0 0
$$277$$ −8.31095 + 14.3950i −0.499357 + 0.864911i −1.00000 0.000742657i $$-0.999764\pi$$
0.500643 + 0.865654i $$0.333097\pi$$
$$278$$ 1.98118 + 12.0260i 0.118823 + 0.721272i
$$279$$ 0 0
$$280$$ −5.96201 + 3.17872i −0.356298 + 0.189965i
$$281$$ −8.93878 5.16081i −0.533243 0.307868i 0.209093 0.977896i $$-0.432949\pi$$
−0.742336 + 0.670028i $$0.766282\pi$$
$$282$$ 0 0
$$283$$ 12.3659 7.13943i 0.735074 0.424395i −0.0852016 0.996364i $$-0.527153\pi$$
0.820275 + 0.571969i $$0.193820\pi$$
$$284$$ −9.19893 8.07863i −0.545856 0.479379i
$$285$$ 0 0
$$286$$ −13.7995 + 36.6256i −0.815982 + 2.16572i
$$287$$ −5.29465 −0.312533
$$288$$ 0 0
$$289$$ 13.4072 0.788659
$$290$$ 0.415179 1.10193i 0.0243801 0.0647078i
$$291$$ 0 0
$$292$$ −7.63314 6.70353i −0.446696 0.392295i
$$293$$ 2.10270 1.21399i 0.122841 0.0709223i −0.437320 0.899306i $$-0.644072\pi$$
0.560161 + 0.828383i $$0.310739\pi$$
$$294$$ 0 0
$$295$$ −11.0127 6.35821i −0.641186 0.370189i
$$296$$ 2.10267 1.12106i 0.122215 0.0651605i
$$297$$ 0 0
$$298$$ −0.579324 3.51657i −0.0335593 0.203709i
$$299$$ −11.3931 + 19.7334i −0.658877 + 1.14121i
$$300$$ 0 0
$$301$$ 4.26140 + 7.38095i 0.245623 + 0.425431i
$$302$$ 0.418007 0.342805i 0.0240536 0.0197262i
$$303$$ 0 0
$$304$$ 2.09966 0.273438i 0.120424 0.0156827i
$$305$$ 16.7157i 0.957141i
$$306$$ 0 0
$$307$$ 8.87237i 0.506373i −0.967417 0.253187i $$-0.918521\pi$$
0.967417 0.253187i $$-0.0814787\pi$$
$$308$$ −12.6226 2.51997i −0.719240 0.143589i
$$309$$ 0 0
$$310$$ 12.6094 + 15.3756i 0.716168 + 0.873275i
$$311$$ −3.03771 5.26147i −0.172253 0.298350i 0.766954 0.641702i $$-0.221771\pi$$
−0.939207 + 0.343351i $$0.888438\pi$$
$$312$$ 0 0
$$313$$ −10.3245 + 17.8825i −0.583575 + 1.01078i 0.411477 + 0.911420i $$0.365013\pi$$
−0.995051 + 0.0993607i $$0.968320\pi$$
$$314$$ −12.2764 + 2.02242i −0.692795 + 0.114132i
$$315$$ 0 0
$$316$$ −2.13241 6.29634i −0.119957 0.354197i
$$317$$ −21.2581 12.2734i −1.19397 0.689341i −0.234769 0.972051i $$-0.575433\pi$$
−0.959205 + 0.282710i $$0.908767\pi$$
$$318$$ 0 0
$$319$$ 1.94280 1.12167i 0.108776 0.0628017i
$$320$$ −1.28988 + 19.0666i −0.0721064 + 1.06585i
$$321$$ 0 0
$$322$$ −7.01248 2.64211i −0.390790 0.147239i
$$323$$ 1.00336 0.0558286
$$324$$ 0 0
$$325$$ 3.03693 0.168459
$$326$$ −14.2521 5.36981i −0.789352 0.297406i
$$327$$ 0 0
$$328$$ −7.92144 + 12.7090i −0.437388 + 0.701734i
$$329$$ 3.53774 2.04252i 0.195042 0.112608i
$$330$$ 0 0
$$331$$ −25.9866 15.0034i −1.42835 0.824660i −0.431362 0.902179i $$-0.641967\pi$$
−0.996991 + 0.0775195i $$0.975300\pi$$
$$332$$ 12.2598 4.15210i 0.672846 0.227876i
$$333$$ 0 0
$$334$$ 10.9529 1.80439i 0.599315 0.0987320i
$$335$$ −12.8650 + 22.2829i −0.702892 + 1.21744i
$$336$$ 0 0
$$337$$ −5.27401 9.13486i −0.287294 0.497608i 0.685869 0.727725i $$-0.259422\pi$$
−0.973163 + 0.230117i $$0.926089\pi$$
$$338$$ −4.92491 6.00530i −0.267880 0.326645i
$$339$$ 0 0
$$340$$ −1.77289 + 8.88044i −0.0961483 + 0.481609i
$$341$$ 37.8824i 2.05145i
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 24.0924 + 0.814008i 1.29897 + 0.0438884i
$$345$$ 0 0
$$346$$ −20.9167 + 17.1536i −1.12449 + 0.922185i
$$347$$ 4.55660 + 7.89227i 0.244611 + 0.423679i 0.962022 0.272971i $$-0.0880063\pi$$
−0.717411 + 0.696650i $$0.754673\pi$$
$$348$$ 0 0
$$349$$ 11.2978 19.5684i 0.604760 1.04747i −0.387330 0.921941i $$-0.626602\pi$$
0.992089 0.125533i $$-0.0400642\pi$$
$$350$$ 0.162349 + 0.985476i 0.00867791 + 0.0526759i
$$351$$ 0 0
$$352$$ −24.9337 + 26.5283i −1.32897 + 1.41396i
$$353$$ 5.76564 + 3.32879i 0.306874 + 0.177174i 0.645527 0.763738i $$-0.276638\pi$$
−0.338653 + 0.940911i $$0.609971\pi$$
$$354$$ 0 0
$$355$$ −12.6635 + 7.31128i −0.672109 + 0.388042i
$$356$$ −19.0267 + 21.6652i −1.00841 + 1.14826i
$$357$$ 0 0
$$358$$ 13.0373 34.6026i 0.689044 1.82881i
$$359$$ −8.03334 −0.423984 −0.211992 0.977271i $$-0.567995\pi$$
−0.211992 + 0.977271i $$0.567995\pi$$
$$360$$ 0 0
$$361$$ 18.7198 0.985252
$$362$$ −9.43248 + 25.0349i −0.495760 + 1.31581i
$$363$$ 0 0
$$364$$ 5.67516 6.46216i 0.297459 0.338709i
$$365$$ −10.5080 + 6.06679i −0.550013 + 0.317550i
$$366$$ 0 0
$$367$$ −14.9220 8.61523i −0.778923 0.449712i 0.0571254 0.998367i $$-0.481807\pi$$
−0.836049 + 0.548656i $$0.815140\pi$$
$$368$$ −16.8335 + 12.8794i −0.877505 + 0.671385i
$$369$$ 0 0
$$370$$ −0.462626 2.80820i −0.0240508 0.145991i
$$371$$ −6.29897 + 10.9101i −0.327026 + 0.566426i
$$372$$ 0 0
$$373$$ −0.260742 0.451618i −0.0135007 0.0233839i 0.859196 0.511646i $$-0.170964\pi$$
−0.872697 + 0.488262i $$0.837631\pi$$
$$374$$ −13.3397 + 10.9398i −0.689781 + 0.565685i
$$375$$ 0 0
$$376$$ 0.390160 11.5476i 0.0201209 0.595524i
$$377$$ 1.49892i 0.0771985i
$$378$$ 0 0
$$379$$ 22.8440i 1.17342i −0.809797 0.586710i $$-0.800423\pi$$
0.809797 0.586710i $$-0.199577\pi$$
$$380$$ 0.495115 2.48004i 0.0253989 0.127224i
$$381$$ 0 0
$$382$$ 8.44249 + 10.2945i 0.431956 + 0.526715i
$$383$$ −12.4781 21.6128i −0.637603 1.10436i −0.985957 0.166998i $$-0.946593\pi$$
0.348354 0.937363i $$-0.386741\pi$$
$$384$$ 0 0
$$385$$ −7.68688 + 13.3141i −0.391760 + 0.678548i
$$386$$ 1.83843 0.302865i 0.0935736 0.0154154i
$$387$$ 0 0
$$388$$ 14.6478 4.96082i 0.743627 0.251847i
$$389$$ 22.0002 + 12.7018i 1.11545 + 0.644007i 0.940236 0.340523i $$-0.110604\pi$$
0.175216 + 0.984530i $$0.443938\pi$$
$$390$$ 0 0
$$391$$ −8.69818 + 5.02190i −0.439886 + 0.253968i
$$392$$ 2.40034 + 1.49612i 0.121235 + 0.0755655i
$$393$$ 0 0
$$394$$ 4.71675 + 1.77714i 0.237627 + 0.0895312i
$$395$$ −7.93985 −0.399497
$$396$$ 0 0
$$397$$ 5.32969 0.267489 0.133745 0.991016i $$-0.457300\pi$$
0.133745 + 0.991016i $$0.457300\pi$$
$$398$$ 21.1398 + 7.96489i 1.05964 + 0.399244i
$$399$$ 0 0
$$400$$ 2.60837 + 1.08470i 0.130418 + 0.0542350i
$$401$$ −20.2109 + 11.6688i −1.00928 + 0.582710i −0.910982 0.412447i $$-0.864674\pi$$
−0.0983016 + 0.995157i $$0.531341\pi$$
$$402$$ 0 0
$$403$$ −21.9206 12.6558i −1.09194 0.630433i
$$404$$ −10.9638 32.3727i −0.545470 1.61060i
$$405$$ 0 0
$$406$$ −0.486397 + 0.0801298i −0.0241395 + 0.00397677i
$$407$$ 2.71099 4.69557i 0.134379 0.232751i
$$408$$ 0 0
$$409$$ 15.5599 + 26.9506i 0.769389 + 1.33262i 0.937895 + 0.346920i $$0.112772\pi$$
−0.168506 + 0.985701i $$0.553894\pi$$
$$410$$ 11.3423 + 13.8305i 0.560155 + 0.683038i
$$411$$ 0 0
$$412$$ 22.7291 + 4.53763i 1.11978 + 0.223553i
$$413$$ 5.32341i 0.261948i
$$414$$ 0 0
$$415$$ 15.4600i 0.758900i
$$416$$ −7.02064 23.2905i −0.344215 1.14191i
$$417$$ 0 0
$$418$$ 3.72539 3.05517i 0.182215 0.149433i
$$419$$ −13.4133 23.2325i −0.655283 1.13498i −0.981823 0.189800i $$-0.939216\pi$$
0.326540 0.945183i $$-0.394117\pi$$
$$420$$ 0 0
$$421$$ 4.00100 6.92994i 0.194997 0.337744i −0.751903 0.659274i $$-0.770864\pi$$
0.946899 + 0.321530i $$0.104197\pi$$
$$422$$ 0.900918 + 5.46868i 0.0438560 + 0.266211i
$$423$$ 0 0
$$424$$ 16.7640 + 31.4425i 0.814131 + 1.52698i
$$425$$ 1.15929 + 0.669318i 0.0562339 + 0.0324667i
$$426$$ 0 0
$$427$$ −6.06013 + 3.49882i −0.293270 + 0.169320i
$$428$$ 2.49733 + 2.19320i 0.120713 + 0.106012i
$$429$$ 0 0
$$430$$ 10.1514 26.9430i 0.489544 1.29931i
$$431$$ 23.2635 1.12056 0.560282 0.828302i $$-0.310693\pi$$
0.560282 + 0.828302i $$0.310693\pi$$
$$432$$ 0 0
$$433$$ −40.4077 −1.94187 −0.970936 0.239340i $$-0.923069\pi$$
−0.970936 + 0.239340i $$0.923069\pi$$
$$434$$ 2.93496 7.78973i 0.140882 0.373919i
$$435$$ 0 0
$$436$$ 12.3453 + 10.8419i 0.591235 + 0.519231i
$$437$$ 2.42914 1.40247i 0.116202 0.0670891i
$$438$$ 0 0
$$439$$ 4.54218 + 2.62243i 0.216786 + 0.125162i 0.604461 0.796634i $$-0.293388\pi$$
−0.387675 + 0.921796i $$0.626722\pi$$
$$440$$ 20.4578 + 38.3706i 0.975286 + 1.82924i
$$441$$ 0 0
$$442$$ −1.87374 11.3738i −0.0891245 0.540996i
$$443$$ −4.84903 + 8.39876i −0.230384 + 0.399037i −0.957921 0.287031i $$-0.907332\pi$$
0.727537 + 0.686068i $$0.240665\pi$$
$$444$$ 0 0
$$445$$ 17.2195 + 29.8250i 0.816280 + 1.41384i
$$446$$ 2.84861 2.33613i 0.134885 0.110619i
$$447$$ 0 0
$$448$$ 7.18239 3.52325i 0.339336 0.166458i
$$449$$ 38.7800i 1.83014i 0.403294 + 0.915071i $$0.367865\pi$$
−0.403294 + 0.915071i $$0.632135\pi$$
$$450$$ 0 0
$$451$$ 34.0755i 1.60455i
$$452$$ −17.8349 3.56055i −0.838883 0.167474i
$$453$$ 0 0
$$454$$ 2.80703 + 3.42282i 0.131740 + 0.160641i
$$455$$ −5.13610 8.89599i −0.240784 0.417050i
$$456$$ 0 0
$$457$$ 11.3244 19.6145i 0.529735 0.917528i −0.469663 0.882846i $$-0.655625\pi$$
0.999398 0.0346824i $$-0.0110420\pi$$
$$458$$ 9.30966 1.53369i 0.435012 0.0716645i
$$459$$ 0 0
$$460$$ 8.12062 + 23.9777i 0.378626 + 1.11796i
$$461$$ −32.0052 18.4782i −1.49063 0.860617i −0.490689 0.871335i $$-0.663255\pi$$
−0.999943 + 0.0107183i $$0.996588\pi$$
$$462$$ 0 0
$$463$$ 8.93748 5.16006i 0.415360 0.239808i −0.277730 0.960659i $$-0.589582\pi$$
0.693090 + 0.720851i $$0.256249\pi$$
$$464$$ −0.535370 + 1.28740i −0.0248540 + 0.0597661i
$$465$$ 0 0
$$466$$ 19.8770 + 7.48910i 0.920783 + 0.346926i
$$467$$ 0.900019 0.0416479 0.0208239 0.999783i $$-0.493371\pi$$
0.0208239 + 0.999783i $$0.493371\pi$$
$$468$$ 0 0
$$469$$ 10.7713 0.497370
$$470$$ −12.9140 4.86564i −0.595678 0.224435i
$$471$$ 0 0
$$472$$ 12.7780 + 7.96446i 0.588154 + 0.366594i
$$473$$ 47.5027 27.4257i 2.18418 1.26103i
$$474$$ 0 0
$$475$$ −0.323756 0.186921i −0.0148549 0.00857651i
$$476$$ 3.59060 1.21605i 0.164575 0.0557373i
$$477$$ 0 0
$$478$$ 3.07271 0.506203i 0.140543 0.0231532i
$$479$$ −15.9460 + 27.6192i −0.728590 + 1.26195i 0.228889 + 0.973452i $$0.426491\pi$$
−0.957479 + 0.288502i $$0.906843\pi$$
$$480$$ 0 0
$$481$$ 1.81139 + 3.13741i 0.0825921 + 0.143054i
$$482$$ −16.6522 20.3053i −0.758488 0.924880i
$$483$$ 0 0
$$484$$ −11.9111 + 59.6628i −0.541412 + 2.71195i
$$485$$ 18.4712i 0.838733i
$$486$$ 0 0
$$487$$ 7.65522i 0.346891i −0.984843 0.173446i $$-0.944510\pi$$
0.984843 0.173446i $$-0.0554901\pi$$
$$488$$ −0.668341 + 19.7810i −0.0302544 + 0.895444i
$$489$$ 0 0
$$490$$ 2.61216 2.14221i 0.118005 0.0967754i
$$491$$ −1.59570 2.76383i −0.0720128 0.124730i 0.827771 0.561067i $$-0.189609\pi$$
−0.899783 + 0.436337i $$0.856276\pi$$
$$492$$ 0 0
$$493$$ −0.330352 + 0.572187i −0.0148783 + 0.0257700i
$$494$$ 0.523279 + 3.17636i 0.0235434 + 0.142911i
$$495$$ 0 0
$$496$$ −14.3069 18.6993i −0.642400 0.839622i
$$497$$ 5.30126 + 3.06068i 0.237794 + 0.137290i
$$498$$ 0 0
$$499$$ −9.07585 + 5.23995i −0.406291 + 0.234572i −0.689195 0.724576i $$-0.742036\pi$$
0.282904 + 0.959148i $$0.408702\pi$$
$$500$$ −13.5364 + 15.4135i −0.605366 + 0.689314i
$$501$$ 0 0
$$502$$ 3.08230 8.18079i 0.137570 0.365127i
$$503$$ 12.6421 0.563685 0.281843 0.959461i $$-0.409054\pi$$
0.281843 + 0.959461i $$0.409054\pi$$
$$504$$ 0 0
$$505$$ −40.8228 −1.81659
$$506$$ −17.0042 + 45.1312i −0.755929 + 2.00633i
$$507$$ 0 0
$$508$$ −22.5188 + 25.6415i −0.999108 + 1.13766i
$$509$$ 23.8125 13.7481i 1.05547 0.609376i 0.131294 0.991343i $$-0.458087\pi$$
0.924176 + 0.381968i $$0.124753\pi$$
$$510$$ 0 0
$$511$$ 4.39891 + 2.53971i 0.194596 + 0.112350i
$$512$$ 2.28874 22.5114i 0.101149 0.994871i
$$513$$ 0 0
$$514$$ −1.85462 11.2577i −0.0818036 0.496558i
$$515$$ 13.8415 23.9742i 0.609929 1.05643i
$$516$$ 0 0
$$517$$ −13.1453 22.7684i −0.578130 1.00135i
$$518$$ −0.921250 + 0.755511i −0.0404774 + 0.0331953i
$$519$$ 0 0
$$520$$ −29.0376 0.981093i −1.27338 0.0430238i
$$521$$ 16.7533i 0.733975i −0.930226 0.366988i $$-0.880389\pi$$
0.930226 0.366988i $$-0.119611\pi$$
$$522$$ 0 0
$$523$$ 39.1120i 1.71025i −0.518424 0.855124i $$-0.673481\pi$$
0.518424 0.855124i $$-0.326519\pi$$
$$524$$ 4.37733 21.9262i 0.191224 0.957848i
$$525$$ 0 0
$$526$$ 0.135799 + 0.165590i 0.00592112 + 0.00722006i
$$527$$ −5.57852 9.66228i −0.243004 0.420895i
$$528$$ 0 0
$$529$$ −2.53889 + 4.39749i −0.110387 + 0.191195i
$$530$$ 41.9927 6.91794i 1.82405 0.300496i
$$531$$ 0 0
$$532$$ −1.00275 + 0.339605i −0.0434747 + 0.0147238i
$$533$$ −19.7177 11.3840i −0.854069 0.493097i
$$534$$ 0 0
$$535$$ 3.43790 1.98487i 0.148633 0.0858135i
$$536$$ 16.1151 25.8546i 0.696066 1.11675i
$$537$$ 0 0
$$538$$ −2.88587 1.08732i −0.124419 0.0468775i
$$539$$ 6.43584 0.277211
$$540$$ 0 0
$$541$$ −11.1182 −0.478010 −0.239005 0.971018i $$-0.576821\pi$$
−0.239005 + 0.971018i $$0.576821\pi$$
$$542$$ −4.08199 1.53798i −0.175337 0.0660620i
$$543$$ 0 0
$$544$$ 2.45306 10.4380i 0.105174 0.447526i
$$545$$ 16.9950 9.81204i 0.727984 0.420302i
$$546$$ 0 0
$$547$$ 24.1315 + 13.9323i 1.03179 + 0.595703i 0.917496 0.397745i $$-0.130207\pi$$
0.114291 + 0.993447i $$0.463540\pi$$
$$548$$ 3.18948 + 9.41753i 0.136248 + 0.402297i
$$549$$ 0 0
$$550$$ 6.34237 1.04485i 0.270440 0.0445526i
$$551$$ 0.0922576 0.159795i 0.00393031 0.00680749i
$$552$$ 0 0
$$553$$ 1.66191 + 2.87851i 0.0706716 + 0.122407i
$$554$$ −14.9063 18.1763i −0.633307 0.772237i
$$555$$ 0 0
$$556$$ −16.9030 3.37452i −0.716848 0.143111i
$$557$$ 23.5098i 0.996142i 0.867136 + 0.498071i $$0.165958\pi$$
−0.867136 + 0.498071i $$0.834042\pi$$
$$558$$ 0 0
$$559$$ 36.6497i 1.55012i
$$560$$ −1.23394 9.47508i −0.0521433 0.400395i
$$561$$ 0 0
$$562$$ 11.2868 9.25627i 0.476107 0.390452i
$$563$$ −16.5569 28.6774i −0.697790 1.20861i −0.969231 0.246152i $$-0.920834\pi$$
0.271442 0.962455i $$-0.412500\pi$$
$$564$$ 0 0
$$565$$ −10.8610 + 18.8119i −0.456928 + 0.791422i
$$566$$ 3.28244 + 19.9248i 0.137971 + 0.837501i
$$567$$ 0 0
$$568$$ 15.2780 8.14566i 0.641051 0.341784i
$$569$$ −16.2900 9.40502i −0.682911 0.394279i 0.118040 0.993009i $$-0.462339\pi$$
−0.800951 + 0.598730i $$0.795672\pi$$
$$570$$ 0 0
$$571$$ 18.0636 10.4290i 0.755937 0.436440i −0.0718982 0.997412i $$-0.522906\pi$$
0.827835 + 0.560972i $$0.189572\pi$$
$$572$$ −41.5894 36.5245i −1.73894 1.52716i
$$573$$ 0 0
$$574$$ 2.64002 7.00692i 0.110192 0.292463i
$$575$$ 3.74220 0.156061
$$576$$ 0 0
$$577$$ −34.3394 −1.42957 −0.714783 0.699346i $$-0.753475\pi$$
−0.714783 + 0.699346i $$0.753475\pi$$
$$578$$ −6.68509 + 17.7430i −0.278063 + 0.738013i
$$579$$ 0 0
$$580$$ 1.25128 + 1.09889i 0.0519565 + 0.0456290i
$$581$$ −5.60486 + 3.23597i −0.232529 + 0.134251i
$$582$$ 0 0
$$583$$ 70.2159 + 40.5392i 2.90805 + 1.67896i
$$584$$ 12.6775 6.75915i 0.524597 0.279696i
$$585$$ 0 0
$$586$$ 0.558148 + 3.38803i 0.0230569 + 0.139958i
$$587$$ 18.1996 31.5226i 0.751177 1.30108i −0.196076 0.980589i $$-0.562820\pi$$
0.947253 0.320487i $$-0.103847\pi$$
$$588$$ 0 0
$$589$$ 1.55791 + 2.69839i 0.0641928 + 0.111185i
$$590$$ 13.9056 11.4039i 0.572484 0.469491i
$$591$$ 0 0
$$592$$ 0.435181 + 3.34165i 0.0178858 + 0.137341i
$$593$$ 2.74882i 0.112880i −0.998406 0.0564402i $$-0.982025\pi$$
0.998406 0.0564402i $$-0.0179750\pi$$
$$594$$ 0 0
$$595$$ 4.52784i 0.185623i
$$596$$ 4.94267 + 0.986753i 0.202460 + 0.0404190i
$$597$$ 0 0
$$598$$ −20.4342 24.9170i −0.835619 1.01893i
$$599$$ 13.1712 + 22.8132i 0.538162 + 0.932124i 0.999003 + 0.0446413i $$0.0142145\pi$$
−0.460841 + 0.887483i $$0.652452\pi$$
$$600$$ 0 0
$$601$$ 10.6251 18.4032i 0.433406 0.750682i −0.563758 0.825940i $$-0.690645\pi$$
0.997164 + 0.0752583i $$0.0239781\pi$$
$$602$$ −11.8927 + 1.95923i −0.484712 + 0.0798522i
$$603$$ 0 0
$$604$$ 0.245240 + 0.724119i 0.00997869 + 0.0294640i
$$605$$ 62.9312 + 36.3333i 2.55852 + 1.47716i
$$606$$ 0 0
$$607$$ −12.9081 + 7.45251i −0.523924 + 0.302488i −0.738539 0.674211i $$-0.764484\pi$$
0.214614 + 0.976699i $$0.431151\pi$$
$$608$$ −0.685066 + 2.91503i −0.0277831 + 0.118220i
$$609$$ 0 0
$$610$$ 22.1216 + 8.33480i 0.895676 + 0.337466i
$$611$$ 17.5665 0.710663
$$612$$ 0 0
$$613$$ 0.497742 0.0201036 0.0100518 0.999949i $$-0.496800\pi$$
0.0100518 + 0.999949i $$0.496800\pi$$
$$614$$ 11.7417 + 4.42394i 0.473855 + 0.178536i
$$615$$ 0 0
$$616$$ 9.62880 15.4482i 0.387955 0.622426i
$$617$$ 13.3288 7.69541i 0.536599 0.309806i −0.207100 0.978320i $$-0.566403\pi$$
0.743700 + 0.668514i $$0.233069\pi$$
$$618$$ 0 0
$$619$$ −6.09500 3.51895i −0.244979 0.141439i 0.372484 0.928039i $$-0.378506\pi$$
−0.617463 + 0.786600i $$0.711839\pi$$
$$620$$ −26.6353 + 9.02070i −1.06970 + 0.362280i
$$621$$ 0 0
$$622$$ 8.47767 1.39662i 0.339924 0.0559995i
$$623$$ 7.20850 12.4855i 0.288802 0.500220i
$$624$$ 0 0
$$625$$ 14.0162 + 24.2768i 0.560648 + 0.971070i
$$626$$ −18.5177 22.5800i −0.740116 0.902478i
$$627$$ 0 0
$$628$$ 3.44476 17.2549i 0.137461 0.688546i
$$629$$ 1.59687i 0.0636713i
$$630$$ 0 0
$$631$$ 0.297508i 0.0118436i 0.999982 + 0.00592180i $$0.00188498\pi$$
−0.999982 + 0.00592180i $$0.998115\pi$$
$$632$$ 9.39582 + 0.317456i 0.373746 + 0.0126277i
$$633$$ 0 0
$$634$$ 26.8423 22.0132i 1.06604 0.874254i
$$635$$ 20.3798 + 35.2988i 0.808747 + 1.40079i
$$636$$ 0 0
$$637$$ −2.15010 + 3.72408i −0.0851901 + 0.147554i
$$638$$ 0.515703 + 3.13038i 0.0204169 + 0.123933i
$$639$$ 0 0
$$640$$ −24.5895 11.2140i −0.971985 0.443272i
$$641$$ −8.18111 4.72337i −0.323134 0.186562i 0.329654 0.944102i $$-0.393068\pi$$
−0.652789 + 0.757540i $$0.726401\pi$$
$$642$$ 0 0
$$643$$ 29.2594 16.8929i 1.15388 0.666193i 0.204050 0.978960i $$-0.434590\pi$$
0.949830 + 0.312768i $$0.101256\pi$$
$$644$$ 6.99312 7.96288i 0.275567 0.313781i
$$645$$ 0 0
$$646$$ −0.500296 + 1.32785i −0.0196839 + 0.0522434i
$$647$$ −8.81904 −0.346712 −0.173356 0.984859i $$-0.555461\pi$$
−0.173356 + 0.984859i $$0.555461\pi$$
$$648$$ 0 0
$$649$$ 34.2606 1.34485
$$650$$ −1.51427 + 4.01906i −0.0593947 + 0.157641i
$$651$$ 0 0
$$652$$ 14.2128 16.1837i 0.556615 0.633803i
$$653$$ −26.1332 + 15.0880i −1.02267 + 0.590440i −0.914877 0.403733i $$-0.867712\pi$$
−0.107795 + 0.994173i $$0.534379\pi$$
$$654$$ 0 0
$$655$$ −23.1273 13.3525i −0.903657 0.521727i
$$656$$ −12.8692 16.8201i −0.502458 0.656716i
$$657$$ 0 0
$$658$$ 0.939071 + 5.70028i 0.0366088 + 0.222220i
$$659$$ −4.08576 + 7.07674i −0.159158 + 0.275671i −0.934565 0.355791i $$-0.884211\pi$$
0.775407 + 0.631462i $$0.217545\pi$$
$$660$$ 0 0
$$661$$ −22.1468 38.3593i −0.861409 1.49200i −0.870569 0.492046i $$-0.836249\pi$$
0.00916009 0.999958i $$-0.497084\pi$$
$$662$$ 32.8128 26.9096i 1.27531 1.04587i
$$663$$ 0 0
$$664$$ −0.618131 + 18.2950i −0.0239881 + 0.709982i
$$665$$ 1.26449i 0.0490349i
$$666$$ 0 0
$$667$$ 1.84702i 0.0715170i
$$668$$ −3.07339 + 15.3947i −0.118913 + 0.595639i
$$669$$ 0 0
$$670$$ −23.0743 28.1362i −0.891439 1.08700i
$$671$$ 22.5178 + 39.0020i 0.869291 + 1.50566i
$$672$$ 0 0
$$673$$ 6.17994 10.7040i 0.238219 0.412608i −0.721984 0.691910i $$-0.756770\pi$$
0.960203 + 0.279302i $$0.0901030\pi$$
$$674$$ 14.7188 2.42479i 0.566946 0.0933995i
$$675$$ 0 0
$$676$$ 10.4030 3.52325i 0.400117 0.135509i
$$677$$ 2.57177 + 1.48481i 0.0988412 + 0.0570660i 0.548606 0.836081i $$-0.315159\pi$$
−0.449765 + 0.893147i $$0.648492\pi$$
$$678$$ 0 0
$$679$$ −6.69654 + 3.86625i −0.256990 + 0.148373i
$$680$$ −10.8683 6.77420i −0.416782 0.259779i
$$681$$ 0 0
$$682$$ −50.1335 18.8889i −1.91971 0.723294i
$$683$$ 13.3131 0.509413 0.254707 0.967018i $$-0.418021\pi$$
0.254707 + 0.967018i $$0.418021\pi$$
$$684$$ 0 0
$$685$$ 11.8757 0.453749
$$686$$ −1.32340 0.498620i −0.0505275 0.0190374i
$$687$$ 0 0
$$688$$ −13.0902 + 31.4779i −0.499058 + 1.20008i
$$689$$ −46.9158 + 27.0868i −1.78735 + 1.03193i
$$690$$ 0 0
$$691$$ 35.4607 + 20.4733i 1.34899 + 0.778840i 0.988107 0.153771i $$-0.0491417\pi$$
0.360884 + 0.932611i $$0.382475\pi$$
$$692$$ −12.2716 36.2342i −0.466496 1.37742i
$$693$$ 0 0
$$694$$ −12.7166 + 2.09495i −0.482716 + 0.0795233i
$$695$$ −10.2936 + 17.8290i −0.390457 + 0.676292i
$$696$$ 0 0
$$697$$ −5.01792 8.69129i −0.190067 0.329206i
$$698$$ 20.2635 + 24.7087i 0.766984 + 0.935239i
$$699$$ 0 0
$$700$$ −1.38513 0.276526i −0.0523529 0.0104517i
$$701$$ 18.8087i 0.710396i 0.934791 + 0.355198i $$0.115587\pi$$
−0.934791 + 0.355198i $$0.884413\pi$$
$$702$$ 0 0
$$703$$ 0.445958i 0.0168196i
$$704$$ −22.6751 46.2247i −0.854598 1.74216i
$$705$$ 0 0
$$706$$ −7.28018 + 5.97043i −0.273993 + 0.224700i
$$707$$ 8.54473 + 14.7999i 0.321358 + 0.556608i
$$708$$ 0 0
$$709$$ 19.3884 33.5818i 0.728148 1.26119i −0.229517 0.973305i $$-0.573715\pi$$
0.957665 0.287885i $$-0.0929520\pi$$
$$710$$ −3.36145 20.4044i −0.126153 0.765763i
$$711$$ 0 0
$$712$$ −19.1846 35.9826i −0.718973 1.34851i
$$713$$ −27.0112 15.5949i −1.01158 0.584035i
$$714$$ 0 0
$$715$$ −57.2532 + 33.0551i −2.14115 + 1.23619i
$$716$$ 39.2923 + 34.5071i 1.46842 + 1.28959i
$$717$$ 0 0
$$718$$ 4.00558 10.6313i 0.149487 0.396757i
$$719$$ 27.9873 1.04375 0.521875 0.853022i $$-0.325233\pi$$
0.521875 + 0.853022i $$0.325233\pi$$
$$720$$ 0 0
$$721$$ −11.5888 −0.431589
$$722$$ −9.33406 + 24.7737i −0.347378 + 0.921982i
$$723$$ 0 0
$$724$$ −28.4279 24.9658i −1.05652 0.927848i
$$725$$ 0.213190 0.123085i 0.00791769 0.00457128i
$$726$$ 0 0
$$727$$ −11.9395 6.89330i −0.442813 0.255658i 0.261977 0.965074i $$-0.415626\pi$$
−0.704790 + 0.709416i $$0.748959\pi$$
$$728$$ 5.72225 + 10.7326i 0.212081 + 0.397778i
$$729$$ 0 0
$$730$$ −2.78928 16.9313i −0.103236 0.626654i
$$731$$ −8.07734 + 13.9904i −0.298751 + 0.517452i
$$732$$ 0 0
$$733$$ 20.9012 + 36.2020i 0.772005 + 1.33715i 0.936463 + 0.350767i $$0.114079\pi$$
−0.164458 + 0.986384i $$0.552588\pi$$
$$734$$ 18.8418 15.4520i 0.695463 0.570345i
$$735$$ 0 0
$$736$$ −8.65105 28.6993i −0.318882 1.05787i
$$737$$ 69.3221i 2.55351i
$$738$$ 0 0
$$739$$ 47.3413i 1.74148i 0.491746 + 0.870739i $$0.336359\pi$$
−0.491746 + 0.870739i $$0.663641\pi$$
$$740$$ 3.94703 + 0.787984i 0.145096 + 0.0289669i
$$741$$ 0 0
$$742$$ −11.2976 13.7760i −0.414749 0.505734i
$$743$$ 1.10160 + 1.90802i 0.0404136 + 0.0699984i 0.885525 0.464592i $$-0.153799\pi$$
−0.845111 + 0.534591i $$0.820466\pi$$
$$744$$ 0 0
$$745$$ 3.00998 5.21343i 0.110277 0.191005i
$$746$$ 0.727681 0.119879i 0.0266423 0.00438909i
$$747$$ 0 0
$$748$$ −7.82628 23.1086i −0.286157 0.844933i
$$749$$ −1.43919 0.830918i −0.0525869 0.0303611i
$$750$$ 0 0
$$751$$ −9.02644 + 5.21142i −0.329379 + 0.190167i −0.655566 0.755138i $$-0.727570\pi$$
0.326186 + 0.945306i $$0.394236\pi$$
$$752$$ 15.0876 + 6.27421i 0.550186 + 0.228797i
$$753$$ 0 0
$$754$$ −1.98367 0.747393i −0.0722411 0.0272185i
$$755$$ 0.913132 0.0332323
$$756$$ 0 0
$$757$$ 14.0656 0.511224 0.255612 0.966779i $$-0.417723\pi$$
0.255612 + 0.966779i $$0.417723\pi$$
$$758$$ 30.2317 + 11.3905i 1.09807 + 0.413721i
$$759$$ 0 0
$$760$$ 3.03521 + 1.89183i 0.110099 + 0.0686239i
$$761$$ 23.2533 13.4253i 0.842931 0.486667i −0.0153283 0.999883i $$-0.504879\pi$$
0.858260 + 0.513216i $$0.171546\pi$$
$$762$$ 0 0
$$763$$ −7.11451 4.10757i −0.257563 0.148704i
$$764$$ −17.8334 + 6.03970i −0.645188 + 0.218509i
$$765$$ 0 0
$$766$$ 34.8241 5.73697i 1.25825 0.207285i
$$767$$ −11.4459 + 19.8248i −0.413286 + 0.715833i
$$768$$ 0 0
$$769$$ 18.9397 + 32.8045i 0.682983 + 1.18296i 0.974066 + 0.226263i $$0.0726510\pi$$
−0.291083 + 0.956698i $$0.594016\pi$$
$$770$$ −13.7870 16.8114i −0.496848 0.605842i
$$771$$ 0 0
$$772$$ −0.515866 + 2.58399i −0.0185664 + 0.0929997i
$$773$$ 26.0697i 0.937662i −0.883288 0.468831i $$-0.844675\pi$$
0.883288 0.468831i $$-0.155325\pi$$
$$774$$ 0 0
$$775$$ 4.15698i 0.149323i
$$776$$ −0.738528 + 21.8583i −0.0265116 + 0.784669i
$$777$$ 0 0
$$778$$ −27.7792 + 22.7816i −0.995934 + 0.816759i
$$779$$ 1.40136 + 2.42722i 0.0502088 + 0.0869642i
$$780$$ 0 0
$$781$$ 19.6981 34.1181i 0.704853 1.22084i
$$782$$ −2.30888 14.0152i −0.0825653 0.501181i
$$783$$ 0 0
$$784$$ −3.17682 + 2.43060i −0.113458 + 0.0868073i
$$785$$ −18.2001 10.5079i −0.649591 0.375041i
$$786$$ 0 0
$$787$$ 43.3071 25.0034i 1.54373 0.891275i 0.545135 0.838349i $$-0.316479\pi$$
0.998598 0.0529261i $$-0.0168548\pi$$
$$788$$ −4.70373 + 5.35601i −0.167563 + 0.190800i
$$789$$