# Properties

 Label 1680.2.cz.d.97.3 Level 1680 Weight 2 Character 1680.97 Analytic conductor 13.415 Analytic rank 0 Dimension 16 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1680.cz (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.4148675396$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 97.3 Root $$0.517174 + 1.31626i$$ of $$x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256$$ Character $$\chi$$ $$=$$ 1680.97 Dual form 1680.2.cz.d.433.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 - 0.707107i) q^{3} +(1.50619 - 1.65269i) q^{5} +(-1.46123 + 2.20563i) q^{7} +1.00000i q^{9} +O(q^{10})$$ $$q+(-0.707107 - 0.707107i) q^{3} +(1.50619 - 1.65269i) q^{5} +(-1.46123 + 2.20563i) q^{7} +1.00000i q^{9} +1.46279 q^{11} +(-0.887844 - 0.887844i) q^{13} +(-2.23367 + 0.103594i) q^{15} +(2.10614 - 2.10614i) q^{17} -3.95987 q^{19} +(2.59286 - 0.526369i) q^{21} +(4.13007 - 4.13007i) q^{23} +(-0.462789 - 4.97854i) q^{25} +(0.707107 - 0.707107i) q^{27} +5.18572i q^{29} -6.10346i q^{31} +(-1.03435 - 1.03435i) q^{33} +(1.44434 + 5.73706i) q^{35} +(2.25560 + 2.25560i) q^{37} +1.25560i q^{39} -0.769968i q^{41} +(5.18572 - 5.18572i) q^{43} +(1.65269 + 1.50619i) q^{45} +(8.57041 - 8.57041i) q^{47} +(-2.72961 - 6.44587i) q^{49} -2.97854 q^{51} +(-0.544449 + 0.544449i) q^{53} +(2.20324 - 2.41754i) q^{55} +(2.80005 + 2.80005i) q^{57} -3.19633 q^{59} -1.42064i q^{61} +(-2.20563 - 1.46123i) q^{63} +(-2.80460 + 0.130073i) q^{65} +(5.93012 + 5.93012i) q^{67} -5.84081 q^{69} -7.62611 q^{71} +(-6.81378 - 6.81378i) q^{73} +(-3.19312 + 3.84760i) q^{75} +(-2.13747 + 3.22637i) q^{77} -4.52029i q^{79} -1.00000 q^{81} +(-6.75794 - 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} +(3.66686 - 3.66686i) q^{87} -1.19991 q^{89} +(3.25560 - 0.660910i) q^{91} +(-4.31580 + 4.31580i) q^{93} +(-5.96431 + 6.54445i) q^{95} +(8.68829 - 8.68829i) q^{97} +1.46279i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + 8q^{7} + O(q^{10})$$ $$16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$421$$ $$1121$$ $$1471$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$ $$1$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.707107 0.707107i −0.408248 0.408248i
$$4$$ 0 0
$$5$$ 1.50619 1.65269i 0.673588 0.739107i
$$6$$ 0 0
$$7$$ −1.46123 + 2.20563i −0.552293 + 0.833650i
$$8$$ 0 0
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ 1.46279 0.441048 0.220524 0.975382i $$-0.429223\pi$$
0.220524 + 0.975382i $$0.429223\pi$$
$$12$$ 0 0
$$13$$ −0.887844 0.887844i −0.246244 0.246244i 0.573183 0.819427i $$-0.305708\pi$$
−0.819427 + 0.573183i $$0.805708\pi$$
$$14$$ 0 0
$$15$$ −2.23367 + 0.103594i −0.576730 + 0.0267479i
$$16$$ 0 0
$$17$$ 2.10614 2.10614i 0.510815 0.510815i −0.403961 0.914776i $$-0.632367\pi$$
0.914776 + 0.403961i $$0.132367\pi$$
$$18$$ 0 0
$$19$$ −3.95987 −0.908456 −0.454228 0.890885i $$-0.650085\pi$$
−0.454228 + 0.890885i $$0.650085\pi$$
$$20$$ 0 0
$$21$$ 2.59286 0.526369i 0.565809 0.114863i
$$22$$ 0 0
$$23$$ 4.13007 4.13007i 0.861180 0.861180i −0.130295 0.991475i $$-0.541593\pi$$
0.991475 + 0.130295i $$0.0415926\pi$$
$$24$$ 0 0
$$25$$ −0.462789 4.97854i −0.0925579 0.995707i
$$26$$ 0 0
$$27$$ 0.707107 0.707107i 0.136083 0.136083i
$$28$$ 0 0
$$29$$ 5.18572i 0.962965i 0.876456 + 0.481482i $$0.159901\pi$$
−0.876456 + 0.481482i $$0.840099\pi$$
$$30$$ 0 0
$$31$$ 6.10346i 1.09621i −0.836408 0.548107i $$-0.815349\pi$$
0.836408 0.548107i $$-0.184651\pi$$
$$32$$ 0 0
$$33$$ −1.03435 1.03435i −0.180057 0.180057i
$$34$$ 0 0
$$35$$ 1.44434 + 5.73706i 0.244138 + 0.969741i
$$36$$ 0 0
$$37$$ 2.25560 + 2.25560i 0.370819 + 0.370819i 0.867775 0.496957i $$-0.165549\pi$$
−0.496957 + 0.867775i $$0.665549\pi$$
$$38$$ 0 0
$$39$$ 1.25560i 0.201057i
$$40$$ 0 0
$$41$$ 0.769968i 0.120249i −0.998191 0.0601244i $$-0.980850\pi$$
0.998191 0.0601244i $$-0.0191497\pi$$
$$42$$ 0 0
$$43$$ 5.18572 5.18572i 0.790816 0.790816i −0.190811 0.981627i $$-0.561112\pi$$
0.981627 + 0.190811i $$0.0611118\pi$$
$$44$$ 0 0
$$45$$ 1.65269 + 1.50619i 0.246369 + 0.224529i
$$46$$ 0 0
$$47$$ 8.57041 8.57041i 1.25012 1.25012i 0.294459 0.955664i $$-0.404861\pi$$
0.955664 0.294459i $$-0.0951394\pi$$
$$48$$ 0 0
$$49$$ −2.72961 6.44587i −0.389944 0.920839i
$$50$$ 0 0
$$51$$ −2.97854 −0.417079
$$52$$ 0 0
$$53$$ −0.544449 + 0.544449i −0.0747859 + 0.0747859i −0.743510 0.668724i $$-0.766841\pi$$
0.668724 + 0.743510i $$0.266841\pi$$
$$54$$ 0 0
$$55$$ 2.20324 2.41754i 0.297084 0.325981i
$$56$$ 0 0
$$57$$ 2.80005 + 2.80005i 0.370876 + 0.370876i
$$58$$ 0 0
$$59$$ −3.19633 −0.416127 −0.208063 0.978115i $$-0.566716\pi$$
−0.208063 + 0.978115i $$0.566716\pi$$
$$60$$ 0 0
$$61$$ 1.42064i 0.181894i −0.995856 0.0909472i $$-0.971011\pi$$
0.995856 0.0909472i $$-0.0289894\pi$$
$$62$$ 0 0
$$63$$ −2.20563 1.46123i −0.277883 0.184098i
$$64$$ 0 0
$$65$$ −2.80460 + 0.130073i −0.347867 + 0.0161336i
$$66$$ 0 0
$$67$$ 5.93012 + 5.93012i 0.724480 + 0.724480i 0.969514 0.245034i $$-0.0787993\pi$$
−0.245034 + 0.969514i $$0.578799\pi$$
$$68$$ 0 0
$$69$$ −5.84081 −0.703150
$$70$$ 0 0
$$71$$ −7.62611 −0.905053 −0.452526 0.891751i $$-0.649477\pi$$
−0.452526 + 0.891751i $$0.649477\pi$$
$$72$$ 0 0
$$73$$ −6.81378 6.81378i −0.797493 0.797493i 0.185207 0.982700i $$-0.440704\pi$$
−0.982700 + 0.185207i $$0.940704\pi$$
$$74$$ 0 0
$$75$$ −3.19312 + 3.84760i −0.368709 + 0.444282i
$$76$$ 0 0
$$77$$ −2.13747 + 3.22637i −0.243588 + 0.367679i
$$78$$ 0 0
$$79$$ 4.52029i 0.508573i −0.967129 0.254286i $$-0.918159\pi$$
0.967129 0.254286i $$-0.0818405\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −0.111111
$$82$$ 0 0
$$83$$ −6.75794 6.75794i −0.741781 0.741781i 0.231140 0.972921i $$-0.425754\pi$$
−0.972921 + 0.231140i $$0.925754\pi$$
$$84$$ 0 0
$$85$$ −0.308559 6.65306i −0.0334679 0.721626i
$$86$$ 0 0
$$87$$ 3.66686 3.66686i 0.393129 0.393129i
$$88$$ 0 0
$$89$$ −1.19991 −0.127190 −0.0635950 0.997976i $$-0.520257\pi$$
−0.0635950 + 0.997976i $$0.520257\pi$$
$$90$$ 0 0
$$91$$ 3.25560 0.660910i 0.341280 0.0692822i
$$92$$ 0 0
$$93$$ −4.31580 + 4.31580i −0.447527 + 0.447527i
$$94$$ 0 0
$$95$$ −5.96431 + 6.54445i −0.611925 + 0.671446i
$$96$$ 0 0
$$97$$ 8.68829 8.68829i 0.882162 0.882162i −0.111592 0.993754i $$-0.535595\pi$$
0.993754 + 0.111592i $$0.0355950\pi$$
$$98$$ 0 0
$$99$$ 1.46279i 0.147016i
$$100$$ 0 0
$$101$$ 15.3420i 1.52659i −0.646050 0.763295i $$-0.723580\pi$$
0.646050 0.763295i $$-0.276420\pi$$
$$102$$ 0 0
$$103$$ 8.30776 + 8.30776i 0.818588 + 0.818588i 0.985903 0.167316i $$-0.0535099\pi$$
−0.167316 + 0.985903i $$0.553510\pi$$
$$104$$ 0 0
$$105$$ 3.03541 5.07802i 0.296226 0.495564i
$$106$$ 0 0
$$107$$ −4.39022 4.39022i −0.424418 0.424418i 0.462303 0.886722i $$-0.347023\pi$$
−0.886722 + 0.462303i $$0.847023\pi$$
$$108$$ 0 0
$$109$$ 7.44587i 0.713185i 0.934260 + 0.356593i $$0.116062\pi$$
−0.934260 + 0.356593i $$0.883938\pi$$
$$110$$ 0 0
$$111$$ 3.18990i 0.302772i
$$112$$ 0 0
$$113$$ 2.54445 2.54445i 0.239362 0.239362i −0.577224 0.816586i $$-0.695864\pi$$
0.816586 + 0.577224i $$0.195864\pi$$
$$114$$ 0 0
$$115$$ −0.605073 13.0464i −0.0564233 1.21658i
$$116$$ 0 0
$$117$$ 0.887844 0.887844i 0.0820812 0.0820812i
$$118$$ 0 0
$$119$$ 1.56781 + 7.72294i 0.143721 + 0.707960i
$$120$$ 0 0
$$121$$ −8.86025 −0.805477
$$122$$ 0 0
$$123$$ −0.544449 + 0.544449i −0.0490913 + 0.0490913i
$$124$$ 0 0
$$125$$ −8.92504 6.73377i −0.798280 0.602287i
$$126$$ 0 0
$$127$$ −7.86025 7.86025i −0.697484 0.697484i 0.266383 0.963867i $$-0.414171\pi$$
−0.963867 + 0.266383i $$0.914171\pi$$
$$128$$ 0 0
$$129$$ −7.33372 −0.645698
$$130$$ 0 0
$$131$$ 6.18216i 0.540138i 0.962841 + 0.270069i $$0.0870465\pi$$
−0.962841 + 0.270069i $$0.912953\pi$$
$$132$$ 0 0
$$133$$ 5.78628 8.73401i 0.501735 0.757334i
$$134$$ 0 0
$$135$$ −0.103594 2.23367i −0.00891596 0.192243i
$$136$$ 0 0
$$137$$ 9.05565 + 9.05565i 0.773677 + 0.773677i 0.978747 0.205071i $$-0.0657424\pi$$
−0.205071 + 0.978747i $$0.565742\pi$$
$$138$$ 0 0
$$139$$ −11.9913 −1.01709 −0.508544 0.861036i $$-0.669816\pi$$
−0.508544 + 0.861036i $$0.669816\pi$$
$$140$$ 0 0
$$141$$ −12.1204 −1.02072
$$142$$ 0 0
$$143$$ −1.29873 1.29873i −0.108605 0.108605i
$$144$$ 0 0
$$145$$ 8.57041 + 7.81068i 0.711734 + 0.648642i
$$146$$ 0 0
$$147$$ −2.62780 + 6.48804i −0.216737 + 0.535125i
$$148$$ 0 0
$$149$$ 0.0968261i 0.00793230i −0.999992 0.00396615i $$-0.998738\pi$$
0.999992 0.00396615i $$-0.00126247\pi$$
$$150$$ 0 0
$$151$$ 13.4550 1.09495 0.547475 0.836822i $$-0.315589\pi$$
0.547475 + 0.836822i $$0.315589\pi$$
$$152$$ 0 0
$$153$$ 2.10614 + 2.10614i 0.170272 + 0.170272i
$$154$$ 0 0
$$155$$ −10.0871 9.19296i −0.810219 0.738397i
$$156$$ 0 0
$$157$$ −1.64757 + 1.64757i −0.131491 + 0.131491i −0.769789 0.638298i $$-0.779639\pi$$
0.638298 + 0.769789i $$0.279639\pi$$
$$158$$ 0 0
$$159$$ 0.769968 0.0610624
$$160$$ 0 0
$$161$$ 3.07442 + 15.1444i 0.242298 + 1.19355i
$$162$$ 0 0
$$163$$ 10.2746 10.2746i 0.804771 0.804771i −0.179066 0.983837i $$-0.557308\pi$$
0.983837 + 0.179066i $$0.0573077\pi$$
$$164$$ 0 0
$$165$$ −3.26738 + 0.151536i −0.254366 + 0.0117971i
$$166$$ 0 0
$$167$$ 0.293008 0.293008i 0.0226737 0.0226737i −0.695679 0.718353i $$-0.744896\pi$$
0.718353 + 0.695679i $$0.244896\pi$$
$$168$$ 0 0
$$169$$ 11.4235i 0.878728i
$$170$$ 0 0
$$171$$ 3.95987i 0.302819i
$$172$$ 0 0
$$173$$ 3.45189 + 3.45189i 0.262442 + 0.262442i 0.826046 0.563603i $$-0.190585\pi$$
−0.563603 + 0.826046i $$0.690585\pi$$
$$174$$ 0 0
$$175$$ 11.6571 + 6.25405i 0.881190 + 0.472762i
$$176$$ 0 0
$$177$$ 2.26015 + 2.26015i 0.169883 + 0.169883i
$$178$$ 0 0
$$179$$ 1.99756i 0.149305i 0.997210 + 0.0746523i $$0.0237847\pi$$
−0.997210 + 0.0746523i $$0.976215\pi$$
$$180$$ 0 0
$$181$$ 8.48528i 0.630706i 0.948974 + 0.315353i $$0.102123\pi$$
−0.948974 + 0.315353i $$0.897877\pi$$
$$182$$ 0 0
$$183$$ −1.00454 + 1.00454i −0.0742581 + 0.0742581i
$$184$$ 0 0
$$185$$ 7.12518 0.330455i 0.523854 0.0242955i
$$186$$ 0 0
$$187$$ 3.08084 3.08084i 0.225294 0.225294i
$$188$$ 0 0
$$189$$ 0.526369 + 2.59286i 0.0382877 + 0.188603i
$$190$$ 0 0
$$191$$ 7.83424 0.566866 0.283433 0.958992i $$-0.408527\pi$$
0.283433 + 0.958992i $$0.408527\pi$$
$$192$$ 0 0
$$193$$ 13.5617 13.5617i 0.976194 0.976194i −0.0235293 0.999723i $$-0.507490\pi$$
0.999723 + 0.0235293i $$0.00749029\pi$$
$$194$$ 0 0
$$195$$ 2.07512 + 1.89117i 0.148603 + 0.135430i
$$196$$ 0 0
$$197$$ −11.4791 11.4791i −0.817853 0.817853i 0.167943 0.985797i $$-0.446287\pi$$
−0.985797 + 0.167943i $$0.946287\pi$$
$$198$$ 0 0
$$199$$ 20.1468 1.42817 0.714084 0.700061i $$-0.246844\pi$$
0.714084 + 0.700061i $$0.246844\pi$$
$$200$$ 0 0
$$201$$ 8.38646i 0.591535i
$$202$$ 0 0
$$203$$ −11.4378 7.57754i −0.802775 0.531839i
$$204$$ 0 0
$$205$$ −1.27252 1.15972i −0.0888767 0.0809981i
$$206$$ 0 0
$$207$$ 4.13007 + 4.13007i 0.287060 + 0.287060i
$$208$$ 0 0
$$209$$ −5.79246 −0.400673
$$210$$ 0 0
$$211$$ −11.9662 −0.823785 −0.411892 0.911233i $$-0.635132\pi$$
−0.411892 + 0.911233i $$0.635132\pi$$
$$212$$ 0 0
$$213$$ 5.39247 + 5.39247i 0.369486 + 0.369486i
$$214$$ 0 0
$$215$$ −0.759730 16.3811i −0.0518132 1.11718i
$$216$$ 0 0
$$217$$ 13.4620 + 8.91857i 0.913858 + 0.605432i
$$218$$ 0 0
$$219$$ 9.63614i 0.651150i
$$220$$ 0 0
$$221$$ −3.73985 −0.251570
$$222$$ 0 0
$$223$$ −0.660910 0.660910i −0.0442578 0.0442578i 0.684632 0.728889i $$-0.259963\pi$$
−0.728889 + 0.684632i $$0.759963\pi$$
$$224$$ 0 0
$$225$$ 4.97854 0.462789i 0.331902 0.0308526i
$$226$$ 0 0
$$227$$ −17.3487 + 17.3487i −1.15147 + 1.15147i −0.165216 + 0.986257i $$0.552832\pi$$
−0.986257 + 0.165216i $$0.947168\pi$$
$$228$$ 0 0
$$229$$ 25.0782 1.65721 0.828607 0.559831i $$-0.189134\pi$$
0.828607 + 0.559831i $$0.189134\pi$$
$$230$$ 0 0
$$231$$ 3.79281 0.769968i 0.249549 0.0506601i
$$232$$ 0 0
$$233$$ 2.24138 2.24138i 0.146837 0.146837i −0.629866 0.776704i $$-0.716890\pi$$
0.776704 + 0.629866i $$0.216890\pi$$
$$234$$ 0 0
$$235$$ −1.25560 27.0729i −0.0819064 1.76604i
$$236$$ 0 0
$$237$$ −3.19633 + 3.19633i −0.207624 + 0.207624i
$$238$$ 0 0
$$239$$ 21.3769i 1.38276i 0.722492 + 0.691380i $$0.242997\pi$$
−0.722492 + 0.691380i $$0.757003\pi$$
$$240$$ 0 0
$$241$$ 0.624129i 0.0402037i 0.999798 + 0.0201018i $$0.00639905\pi$$
−0.999798 + 0.0201018i $$0.993601\pi$$
$$242$$ 0 0
$$243$$ 0.707107 + 0.707107i 0.0453609 + 0.0453609i
$$244$$ 0 0
$$245$$ −14.7643 5.19750i −0.943260 0.332056i
$$246$$ 0 0
$$247$$ 3.51575 + 3.51575i 0.223702 + 0.223702i
$$248$$ 0 0
$$249$$ 9.55717i 0.605661i
$$250$$ 0 0
$$251$$ 16.3443i 1.03164i 0.856696 + 0.515822i $$0.172513\pi$$
−0.856696 + 0.515822i $$0.827487\pi$$
$$252$$ 0 0
$$253$$ 6.04143 6.04143i 0.379821 0.379821i
$$254$$ 0 0
$$255$$ −4.48624 + 4.92261i −0.280939 + 0.308266i
$$256$$ 0 0
$$257$$ −21.3054 + 21.3054i −1.32900 + 1.32900i −0.422749 + 0.906247i $$0.638935\pi$$
−0.906247 + 0.422749i $$0.861065\pi$$
$$258$$ 0 0
$$259$$ −8.27098 + 1.67907i −0.513933 + 0.104332i
$$260$$ 0 0
$$261$$ −5.18572 −0.320988
$$262$$ 0 0
$$263$$ 16.3449 16.3449i 1.00787 1.00787i 0.00789784 0.999969i $$-0.497486\pi$$
0.999969 0.00789784i $$-0.00251399\pi$$
$$264$$ 0 0
$$265$$ 0.0797641 + 1.71985i 0.00489987 + 0.105650i
$$266$$ 0 0
$$267$$ 0.848464 + 0.848464i 0.0519251 + 0.0519251i
$$268$$ 0 0
$$269$$ 16.5903 1.01153 0.505764 0.862672i $$-0.331211\pi$$
0.505764 + 0.862672i $$0.331211\pi$$
$$270$$ 0 0
$$271$$ 7.78033i 0.472621i 0.971678 + 0.236311i $$0.0759383\pi$$
−0.971678 + 0.236311i $$0.924062\pi$$
$$272$$ 0 0
$$273$$ −2.76939 1.83472i −0.167611 0.111043i
$$274$$ 0 0
$$275$$ −0.676964 7.28255i −0.0408224 0.439154i
$$276$$ 0 0
$$277$$ 21.3107 + 21.3107i 1.28043 + 1.28043i 0.940421 + 0.340013i $$0.110431\pi$$
0.340013 + 0.940421i $$0.389569\pi$$
$$278$$ 0 0
$$279$$ 6.10346 0.365405
$$280$$ 0 0
$$281$$ −21.1519 −1.26182 −0.630908 0.775858i $$-0.717317\pi$$
−0.630908 + 0.775858i $$0.717317\pi$$
$$282$$ 0 0
$$283$$ 2.65471 + 2.65471i 0.157806 + 0.157806i 0.781594 0.623788i $$-0.214407\pi$$
−0.623788 + 0.781594i $$0.714407\pi$$
$$284$$ 0 0
$$285$$ 8.84503 0.410219i 0.523934 0.0242993i
$$286$$ 0 0
$$287$$ 1.69826 + 1.12510i 0.100245 + 0.0664126i
$$288$$ 0 0
$$289$$ 8.12832i 0.478136i
$$290$$ 0 0
$$291$$ −12.2871 −0.720282
$$292$$ 0 0
$$293$$ 1.56714 + 1.56714i 0.0915536 + 0.0915536i 0.751400 0.659847i $$-0.229379\pi$$
−0.659847 + 0.751400i $$0.729379\pi$$
$$294$$ 0 0
$$295$$ −4.81428 + 5.28255i −0.280298 + 0.307562i
$$296$$ 0 0
$$297$$ 1.03435 1.03435i 0.0600190 0.0600190i
$$298$$ 0 0
$$299$$ −7.33372 −0.424120
$$300$$ 0 0
$$301$$ 3.86025 + 19.0153i 0.222501 + 1.09603i
$$302$$ 0 0
$$303$$ −10.8485 + 10.8485i −0.623228 + 0.623228i
$$304$$ 0 0
$$305$$ −2.34788 2.13975i −0.134439 0.122522i
$$306$$ 0 0
$$307$$ −17.3551 + 17.3551i −0.990510 + 0.990510i −0.999955 0.00944588i $$-0.996993\pi$$
0.00944588 + 0.999955i $$0.496993\pi$$
$$308$$ 0 0
$$309$$ 11.7489i 0.668374i
$$310$$ 0 0
$$311$$ 31.0648i 1.76153i 0.473558 + 0.880763i $$0.342970\pi$$
−0.473558 + 0.880763i $$0.657030\pi$$
$$312$$ 0 0
$$313$$ −5.72426 5.72426i −0.323554 0.323554i 0.526575 0.850129i $$-0.323476\pi$$
−0.850129 + 0.526575i $$0.823476\pi$$
$$314$$ 0 0
$$315$$ −5.73706 + 1.44434i −0.323247 + 0.0813793i
$$316$$ 0 0
$$317$$ 0.752579 + 0.752579i 0.0422691 + 0.0422691i 0.727925 0.685656i $$-0.240485\pi$$
−0.685656 + 0.727925i $$0.740485\pi$$
$$318$$ 0 0
$$319$$ 7.58562i 0.424713i
$$320$$ 0 0
$$321$$ 6.20871i 0.346536i
$$322$$ 0 0
$$323$$ −8.34005 + 8.34005i −0.464053 + 0.464053i
$$324$$ 0 0
$$325$$ −4.00928 + 4.83105i −0.222395 + 0.267978i
$$326$$ 0 0
$$327$$ 5.26503 5.26503i 0.291157 0.291157i
$$328$$ 0 0
$$329$$ 6.37980 + 31.4265i 0.351730 + 1.73260i
$$330$$ 0 0
$$331$$ −15.8082 −0.868899 −0.434449 0.900696i $$-0.643057\pi$$
−0.434449 + 0.900696i $$0.643057\pi$$
$$332$$ 0 0
$$333$$ −2.25560 + 2.25560i −0.123606 + 0.123606i
$$334$$ 0 0
$$335$$ 18.7326 0.868788i 1.02347 0.0474670i
$$336$$ 0 0
$$337$$ −20.0460 20.0460i −1.09197 1.09197i −0.995318 0.0966558i $$-0.969185\pi$$
−0.0966558 0.995318i $$-0.530815\pi$$
$$338$$ 0 0
$$339$$ −3.59839 −0.195438
$$340$$ 0 0
$$341$$ 8.92808i 0.483482i
$$342$$ 0 0
$$343$$ 18.2058 + 3.39840i 0.983020 + 0.183497i
$$344$$ 0 0
$$345$$ −8.79736 + 9.65306i −0.473634 + 0.519703i
$$346$$ 0 0
$$347$$ 20.0847 + 20.0847i 1.07820 + 1.07820i 0.996671 + 0.0815328i $$0.0259815\pi$$
0.0815328 + 0.996671i $$0.474018\pi$$
$$348$$ 0 0
$$349$$ −14.7663 −0.790420 −0.395210 0.918591i $$-0.629328\pi$$
−0.395210 + 0.918591i $$0.629328\pi$$
$$350$$ 0 0
$$351$$ −1.25560 −0.0670190
$$352$$ 0 0
$$353$$ 12.4890 + 12.4890i 0.664724 + 0.664724i 0.956490 0.291766i $$-0.0942429\pi$$
−0.291766 + 0.956490i $$0.594243\pi$$
$$354$$ 0 0
$$355$$ −11.4864 + 12.6036i −0.609633 + 0.668931i
$$356$$ 0 0
$$357$$ 4.35233 6.56955i 0.230350 0.347697i
$$358$$ 0 0
$$359$$ 10.5372i 0.556133i 0.960562 + 0.278066i $$0.0896935\pi$$
−0.960562 + 0.278066i $$0.910306\pi$$
$$360$$ 0 0
$$361$$ −3.31943 −0.174707
$$362$$ 0 0
$$363$$ 6.26514 + 6.26514i 0.328835 + 0.328835i
$$364$$ 0 0
$$365$$ −21.5239 + 0.998247i −1.12661 + 0.0522507i
$$366$$ 0 0
$$367$$ 11.1910 11.1910i 0.584163 0.584163i −0.351881 0.936045i $$-0.614458\pi$$
0.936045 + 0.351881i $$0.114458\pi$$
$$368$$ 0 0
$$369$$ 0.769968 0.0400829
$$370$$ 0 0
$$371$$ −0.405287 1.99642i −0.0210415 0.103649i
$$372$$ 0 0
$$373$$ 17.2746 17.2746i 0.894446 0.894446i −0.100492 0.994938i $$-0.532042\pi$$
0.994938 + 0.100492i $$0.0320416\pi$$
$$374$$ 0 0
$$375$$ 1.54946 + 11.0725i 0.0800140 + 0.571779i
$$376$$ 0 0
$$377$$ 4.60412 4.60412i 0.237124 0.237124i
$$378$$ 0 0
$$379$$ 17.6237i 0.905267i −0.891697 0.452634i $$-0.850485\pi$$
0.891697 0.452634i $$-0.149515\pi$$
$$380$$ 0 0
$$381$$ 11.1161i 0.569493i
$$382$$ 0 0
$$383$$ 16.1249 + 16.1249i 0.823942 + 0.823942i 0.986671 0.162729i $$-0.0520295\pi$$
−0.162729 + 0.986671i $$0.552030\pi$$
$$384$$ 0 0
$$385$$ 2.11276 + 8.39211i 0.107676 + 0.427702i
$$386$$ 0 0
$$387$$ 5.18572 + 5.18572i 0.263605 + 0.263605i
$$388$$ 0 0
$$389$$ 15.4011i 0.780865i 0.920632 + 0.390432i $$0.127674\pi$$
−0.920632 + 0.390432i $$0.872326\pi$$
$$390$$ 0 0
$$391$$ 17.3971i 0.879807i
$$392$$ 0 0
$$393$$ 4.37145 4.37145i 0.220510 0.220510i
$$394$$ 0 0
$$395$$ −7.47066 6.80841i −0.375889 0.342568i
$$396$$ 0 0
$$397$$ −16.1781 + 16.1781i −0.811955 + 0.811955i −0.984927 0.172972i $$-0.944663\pi$$
0.172972 + 0.984927i $$0.444663\pi$$
$$398$$ 0 0
$$399$$ −10.2674 + 2.08435i −0.514013 + 0.104348i
$$400$$ 0 0
$$401$$ −0.977595 −0.0488188 −0.0244094 0.999702i $$-0.507771\pi$$
−0.0244094 + 0.999702i $$0.507771\pi$$
$$402$$ 0 0
$$403$$ −5.41892 + 5.41892i −0.269936 + 0.269936i
$$404$$ 0 0
$$405$$ −1.50619 + 1.65269i −0.0748431 + 0.0821230i
$$406$$ 0 0
$$407$$ 3.29947 + 3.29947i 0.163549 + 0.163549i
$$408$$ 0 0
$$409$$ −24.3171 −1.20241 −0.601203 0.799097i $$-0.705312\pi$$
−0.601203 + 0.799097i $$0.705312\pi$$
$$410$$ 0 0
$$411$$ 12.8066i 0.631704i
$$412$$ 0 0
$$413$$ 4.67058 7.04992i 0.229824 0.346904i
$$414$$ 0 0
$$415$$ −21.3475 + 0.990067i −1.04791 + 0.0486005i
$$416$$ 0 0
$$417$$ 8.47912 + 8.47912i 0.415224 + 0.415224i
$$418$$ 0 0
$$419$$ 15.9893 0.781127 0.390563 0.920576i $$-0.372280\pi$$
0.390563 + 0.920576i $$0.372280\pi$$
$$420$$ 0 0
$$421$$ 14.7000 0.716433 0.358216 0.933639i $$-0.383385\pi$$
0.358216 + 0.933639i $$0.383385\pi$$
$$422$$ 0 0
$$423$$ 8.57041 + 8.57041i 0.416708 + 0.416708i
$$424$$ 0 0
$$425$$ −11.4602 9.51081i −0.555902 0.461342i
$$426$$ 0 0
$$427$$ 3.13341 + 2.07588i 0.151636 + 0.100459i
$$428$$ 0 0
$$429$$ 1.83668i 0.0886758i
$$430$$ 0 0
$$431$$ −22.2722 −1.07281 −0.536407 0.843960i $$-0.680219\pi$$
−0.536407 + 0.843960i $$0.680219\pi$$
$$432$$ 0 0
$$433$$ 28.0171 + 28.0171i 1.34642 + 1.34642i 0.889520 + 0.456896i $$0.151039\pi$$
0.456896 + 0.889520i $$0.348961\pi$$
$$434$$ 0 0
$$435$$ −0.537211 11.5832i −0.0257573 0.555371i
$$436$$ 0 0
$$437$$ −16.3545 + 16.3545i −0.782344 + 0.782344i
$$438$$ 0 0
$$439$$ −2.35656 −0.112473 −0.0562363 0.998417i $$-0.517910\pi$$
−0.0562363 + 0.998417i $$0.517910\pi$$
$$440$$ 0 0
$$441$$ 6.44587 2.72961i 0.306946 0.129981i
$$442$$ 0 0
$$443$$ 5.47247 5.47247i 0.260005 0.260005i −0.565051 0.825056i $$-0.691144\pi$$
0.825056 + 0.565051i $$0.191144\pi$$
$$444$$ 0 0
$$445$$ −1.80729 + 1.98308i −0.0856737 + 0.0940071i
$$446$$ 0 0
$$447$$ −0.0684664 + 0.0684664i −0.00323835 + 0.00323835i
$$448$$ 0 0
$$449$$ 1.20020i 0.0566410i −0.999599 0.0283205i $$-0.990984\pi$$
0.999599 0.0283205i $$-0.00901591\pi$$
$$450$$ 0 0
$$451$$ 1.12630i 0.0530354i
$$452$$ 0 0
$$453$$ −9.51409 9.51409i −0.447011 0.447011i
$$454$$ 0 0
$$455$$ 3.81127 6.37597i 0.178675 0.298910i
$$456$$ 0 0
$$457$$ −21.0775 21.0775i −0.985962 0.985962i 0.0139406 0.999903i $$-0.495562\pi$$
−0.999903 + 0.0139406i $$0.995562\pi$$
$$458$$ 0 0
$$459$$ 2.97854i 0.139026i
$$460$$ 0 0
$$461$$ 21.9670i 1.02311i 0.859252 + 0.511553i $$0.170929\pi$$
−0.859252 + 0.511553i $$0.829071\pi$$
$$462$$ 0 0
$$463$$ 21.6776 21.6776i 1.00744 1.00744i 0.00746987 0.999972i $$-0.497622\pi$$
0.999972 0.00746987i $$-0.00237776\pi$$
$$464$$ 0 0
$$465$$ 0.632282 + 13.6331i 0.0293214 + 0.632220i
$$466$$ 0 0
$$467$$ 7.11299 7.11299i 0.329150 0.329150i −0.523113 0.852263i $$-0.675230\pi$$
0.852263 + 0.523113i $$0.175230\pi$$
$$468$$ 0 0
$$469$$ −21.7449 + 4.41438i −1.00409 + 0.203837i
$$470$$ 0 0
$$471$$ 2.33002 0.107362
$$472$$ 0 0
$$473$$ 7.58562 7.58562i 0.348787 0.348787i
$$474$$ 0 0
$$475$$ 1.83259 + 19.7144i 0.0840848 + 0.904557i
$$476$$ 0 0
$$477$$ −0.544449 0.544449i −0.0249286 0.0249286i
$$478$$ 0 0
$$479$$ 31.7749 1.45183 0.725917 0.687782i $$-0.241416\pi$$
0.725917 + 0.687782i $$0.241416\pi$$
$$480$$ 0 0
$$481$$ 4.00524i 0.182623i
$$482$$ 0 0
$$483$$ 8.53477 12.8827i 0.388345 0.586181i
$$484$$ 0 0
$$485$$ −1.27287 27.4453i −0.0577981 1.24623i
$$486$$ 0 0
$$487$$ 4.81428 + 4.81428i 0.218156 + 0.218156i 0.807721 0.589565i $$-0.200701\pi$$
−0.589565 + 0.807721i $$0.700701\pi$$
$$488$$ 0 0
$$489$$ −14.5305 −0.657092
$$490$$ 0 0
$$491$$ −28.3401 −1.27897 −0.639484 0.768804i $$-0.720852\pi$$
−0.639484 + 0.768804i $$0.720852\pi$$
$$492$$ 0 0
$$493$$ 10.9219 + 10.9219i 0.491897 + 0.491897i
$$494$$ 0 0
$$495$$ 2.41754 + 2.20324i 0.108660 + 0.0990282i
$$496$$ 0 0
$$497$$ 11.1435 16.8204i 0.499855 0.754497i
$$498$$ 0 0
$$499$$ 3.39197i 0.151845i −0.997114 0.0759227i $$-0.975810\pi$$
0.997114 0.0759227i $$-0.0241902\pi$$
$$500$$ 0 0
$$501$$ −0.414376 −0.0185130
$$502$$ 0 0
$$503$$ −8.32921 8.32921i −0.371381 0.371381i 0.496599 0.867980i $$-0.334582\pi$$
−0.867980 + 0.496599i $$0.834582\pi$$
$$504$$ 0 0
$$505$$ −25.3557 23.1080i −1.12831 1.02829i
$$506$$ 0 0
$$507$$ −8.07761 + 8.07761i −0.358739 + 0.358739i
$$508$$ 0 0
$$509$$ 38.9452 1.72622 0.863108 0.505020i $$-0.168515\pi$$
0.863108 + 0.505020i $$0.168515\pi$$
$$510$$ 0 0
$$511$$ 24.9852 5.07217i 1.10528 0.224380i
$$512$$ 0 0
$$513$$ −2.80005 + 2.80005i −0.123625 + 0.123625i
$$514$$ 0 0
$$515$$ 26.2432 1.21712i 1.15641 0.0536328i
$$516$$ 0 0
$$517$$ 12.5367 12.5367i 0.551364 0.551364i
$$518$$ 0 0
$$519$$ 4.88171i 0.214283i
$$520$$ 0 0
$$521$$ 7.06726i 0.309622i 0.987944 + 0.154811i $$0.0494769\pi$$
−0.987944 + 0.154811i $$0.950523\pi$$
$$522$$ 0 0
$$523$$ 14.5887 + 14.5887i 0.637921 + 0.637921i 0.950042 0.312121i $$-0.101040\pi$$
−0.312121 + 0.950042i $$0.601040\pi$$
$$524$$ 0 0
$$525$$ −3.82050 12.6651i −0.166740 0.552749i
$$526$$ 0 0
$$527$$ −12.8548 12.8548i −0.559962 0.559962i
$$528$$ 0 0
$$529$$ 11.1150i 0.483261i
$$530$$ 0 0
$$531$$ 3.19633i 0.138709i
$$532$$ 0 0
$$533$$ −0.683611 + 0.683611i −0.0296105 + 0.0296105i
$$534$$ 0 0
$$535$$ −13.8682 + 0.643185i −0.599574 + 0.0278073i
$$536$$ 0 0
$$537$$ 1.41249 1.41249i 0.0609533 0.0609533i
$$538$$ 0 0
$$539$$ −3.99284 9.42895i −0.171984 0.406134i
$$540$$ 0 0
$$541$$ 18.6013 0.799731 0.399865 0.916574i $$-0.369057\pi$$
0.399865 + 0.916574i $$0.369057\pi$$
$$542$$ 0 0
$$543$$ 6.00000 6.00000i 0.257485 0.257485i
$$544$$ 0 0
$$545$$ 12.3057 + 11.2149i 0.527120 + 0.480393i
$$546$$ 0 0
$$547$$ 7.22715 + 7.22715i 0.309011 + 0.309011i 0.844526 0.535515i $$-0.179882\pi$$
−0.535515 + 0.844526i $$0.679882\pi$$
$$548$$ 0 0
$$549$$ 1.42064 0.0606315
$$550$$ 0 0
$$551$$ 20.5348i 0.874812i
$$552$$ 0 0
$$553$$ 9.97009 + 6.60519i 0.423971 + 0.280881i
$$554$$ 0 0
$$555$$ −5.27193 4.80460i −0.223781 0.203944i
$$556$$ 0 0
$$557$$ −0.558927 0.558927i −0.0236825 0.0236825i 0.695166 0.718849i $$-0.255331\pi$$
−0.718849 + 0.695166i $$0.755331\pi$$
$$558$$ 0 0
$$559$$ −9.20823 −0.389467
$$560$$ 0 0
$$561$$ −4.35697 −0.183951
$$562$$ 0 0
$$563$$ 0.702475 + 0.702475i 0.0296058 + 0.0296058i 0.721755 0.692149i $$-0.243336\pi$$
−0.692149 + 0.721755i $$0.743336\pi$$
$$564$$ 0 0
$$565$$ −0.372772 8.03762i −0.0156827 0.338145i
$$566$$ 0 0
$$567$$ 1.46123 2.20563i 0.0613659 0.0926278i
$$568$$ 0 0
$$569$$ 9.72049i 0.407504i 0.979023 + 0.203752i $$0.0653137\pi$$
−0.979023 + 0.203752i $$0.934686\pi$$
$$570$$ 0 0
$$571$$ 0.986684 0.0412914 0.0206457 0.999787i $$-0.493428\pi$$
0.0206457 + 0.999787i $$0.493428\pi$$
$$572$$ 0 0
$$573$$ −5.53964 5.53964i −0.231422 0.231422i
$$574$$ 0 0
$$575$$ −22.4731 18.6504i −0.937192 0.777774i
$$576$$ 0 0
$$577$$ 10.3510 10.3510i 0.430917 0.430917i −0.458024 0.888940i $$-0.651442\pi$$
0.888940 + 0.458024i $$0.151442\pi$$
$$578$$ 0 0
$$579$$ −19.1792 −0.797059
$$580$$ 0 0
$$581$$ 24.7804 5.03060i 1.02807 0.208705i
$$582$$ 0 0
$$583$$ −0.796415 + 0.796415i −0.0329841 + 0.0329841i
$$584$$ 0 0
$$585$$ −0.130073 2.80460i −0.00537785 0.115956i
$$586$$ 0 0
$$587$$ −21.1413 + 21.1413i −0.872594 + 0.872594i −0.992755 0.120160i $$-0.961659\pi$$
0.120160 + 0.992755i $$0.461659\pi$$
$$588$$ 0 0
$$589$$ 24.1689i 0.995862i
$$590$$ 0 0
$$591$$ 16.2339i 0.667774i
$$592$$ 0 0
$$593$$ −7.07816 7.07816i −0.290665 0.290665i 0.546678 0.837343i $$-0.315892\pi$$
−0.837343 + 0.546678i $$0.815892\pi$$
$$594$$ 0 0
$$595$$ 15.1251 + 9.04109i 0.620067 + 0.370649i
$$596$$ 0 0
$$597$$ −14.2459 14.2459i −0.583047 0.583047i
$$598$$ 0 0
$$599$$ 7.13847i 0.291670i 0.989309 + 0.145835i $$0.0465869\pi$$
−0.989309 + 0.145835i $$0.953413\pi$$
$$600$$ 0 0
$$601$$ 35.0829i 1.43106i −0.698580 0.715532i $$-0.746185\pi$$
0.698580 0.715532i $$-0.253815\pi$$
$$602$$ 0 0
$$603$$ −5.93012 + 5.93012i −0.241493 + 0.241493i
$$604$$ 0 0
$$605$$ −13.3452 + 14.6433i −0.542560 + 0.595334i
$$606$$ 0 0
$$607$$ −5.36385 + 5.36385i −0.217712 + 0.217712i −0.807533 0.589822i $$-0.799198\pi$$
0.589822 + 0.807533i $$0.299198\pi$$
$$608$$ 0 0
$$609$$ 2.72961 + 13.4459i 0.110609 + 0.544854i
$$610$$ 0 0
$$611$$ −15.2184 −0.615670
$$612$$ 0 0
$$613$$ −10.4888 + 10.4888i −0.423639 + 0.423639i −0.886454 0.462816i $$-0.846839\pi$$
0.462816 + 0.886454i $$0.346839\pi$$
$$614$$ 0 0
$$615$$ 0.0797641 + 1.71985i 0.00321640 + 0.0693511i
$$616$$ 0 0
$$617$$ 19.7986 + 19.7986i 0.797060 + 0.797060i 0.982631 0.185571i $$-0.0594135\pi$$
−0.185571 + 0.982631i $$0.559414\pi$$
$$618$$ 0 0
$$619$$ −12.0675 −0.485034 −0.242517 0.970147i $$-0.577973\pi$$
−0.242517 + 0.970147i $$0.577973\pi$$
$$620$$ 0 0
$$621$$ 5.84081i 0.234383i
$$622$$ 0 0
$$623$$ 1.75334 2.64655i 0.0702462 0.106032i
$$624$$ 0 0
$$625$$ −24.5717 + 4.60803i −0.982866 + 0.184321i
$$626$$ 0 0
$$627$$ 4.09588 + 4.09588i 0.163574 + 0.163574i
$$628$$ 0 0
$$629$$ 9.50124 0.378839
$$630$$ 0 0
$$631$$ −30.4435 −1.21194 −0.605969 0.795488i $$-0.707214\pi$$
−0.605969 + 0.795488i $$0.707214\pi$$
$$632$$ 0 0
$$633$$ 8.46135 + 8.46135i 0.336309 + 0.336309i
$$634$$ 0 0
$$635$$ −24.8296 + 1.15156i −0.985332 + 0.0456982i
$$636$$ 0 0
$$637$$ −3.29946 + 8.14639i −0.130729 + 0.322772i
$$638$$ 0 0
$$639$$ 7.62611i 0.301684i
$$640$$ 0 0
$$641$$ 36.5929 1.44533 0.722666 0.691198i $$-0.242917\pi$$
0.722666 + 0.691198i $$0.242917\pi$$
$$642$$ 0 0
$$643$$ −12.1140 12.1140i −0.477731 0.477731i 0.426675 0.904405i $$-0.359685\pi$$
−0.904405 + 0.426675i $$0.859685\pi$$
$$644$$ 0 0
$$645$$ −11.0460 + 12.1204i −0.434935 + 0.477240i
$$646$$ 0 0
$$647$$ −19.0978 + 19.0978i −0.750814 + 0.750814i −0.974631 0.223817i $$-0.928148\pi$$
0.223817 + 0.974631i $$0.428148\pi$$
$$648$$ 0 0
$$649$$ −4.67556 −0.183532
$$650$$ 0 0
$$651$$ −3.21267 15.8254i −0.125915 0.620248i
$$652$$ 0 0
$$653$$ 20.3709 20.3709i 0.797173 0.797173i −0.185476 0.982649i $$-0.559383\pi$$
0.982649 + 0.185476i $$0.0593826\pi$$
$$654$$ 0 0
$$655$$ 10.2172 + 9.31151i 0.399220 + 0.363831i
$$656$$ 0 0
$$657$$ 6.81378 6.81378i 0.265831 0.265831i
$$658$$ 0 0
$$659$$ 31.4882i 1.22661i −0.789847 0.613304i $$-0.789840\pi$$
0.789847 0.613304i $$-0.210160\pi$$
$$660$$ 0 0
$$661$$ 48.1880i 1.87430i −0.348931 0.937149i $$-0.613455\pi$$
0.348931 0.937149i $$-0.386545\pi$$
$$662$$ 0 0
$$663$$ 2.64448 + 2.64448i 0.102703 + 0.102703i
$$664$$ 0 0
$$665$$ −5.71939 22.7180i −0.221789 0.880967i
$$666$$ 0 0
$$667$$ 21.4174 + 21.4174i 0.829286 + 0.829286i
$$668$$ 0 0
$$669$$ 0.934668i 0.0361364i
$$670$$ 0 0
$$671$$ 2.07810i 0.0802241i
$$672$$ 0 0
$$673$$ −30.6900 + 30.6900i −1.18301 + 1.18301i −0.204055 + 0.978960i $$0.565412\pi$$
−0.978960 + 0.204055i $$0.934588\pi$$
$$674$$ 0 0
$$675$$ −3.84760 3.19312i −0.148094 0.122903i
$$676$$ 0 0
$$677$$ 1.54060 1.54060i 0.0592101 0.0592101i −0.676882 0.736092i $$-0.736669\pi$$
0.736092 + 0.676882i $$0.236669\pi$$
$$678$$ 0 0
$$679$$ 6.46755 + 31.8587i 0.248202 + 1.22263i
$$680$$ 0 0
$$681$$ 24.5348 0.940174
$$682$$ 0 0
$$683$$ −14.2154 + 14.2154i −0.543936 + 0.543936i −0.924680 0.380744i $$-0.875668\pi$$
0.380744 + 0.924680i $$0.375668\pi$$
$$684$$ 0 0
$$685$$ 28.6057 1.32669i 1.09297 0.0506903i
$$686$$ 0 0
$$687$$ −17.7330 17.7330i −0.676555 0.676555i
$$688$$ 0 0
$$689$$ 0.966772 0.0368311
$$690$$ 0 0
$$691$$ 10.2887i 0.391401i −0.980664 0.195700i $$-0.937302\pi$$
0.980664 0.195700i $$-0.0626980\pi$$
$$692$$ 0 0
$$693$$ −3.22637 2.13747i −0.122560 0.0811959i
$$694$$ 0 0
$$695$$ −18.0611 + 19.8179i −0.685098 + 0.751736i
$$696$$ 0 0
$$697$$ −1.62166 1.62166i −0.0614248 0.0614248i
$$698$$ 0 0
$$699$$ −3.16979 −0.119892
$$700$$ 0 0
$$701$$ −44.3183 −1.67388 −0.836939 0.547297i $$-0.815657\pi$$
−0.836939 + 0.547297i $$0.815657\pi$$
$$702$$ 0 0
$$703$$ −8.93189 8.93189i −0.336872 0.336872i
$$704$$ 0 0
$$705$$ −18.2556 + 20.0313i −0.687546 + 0.754422i
$$706$$ 0 0
$$707$$ 33.8389 + 22.4183i 1.27264 + 0.843126i
$$708$$ 0 0
$$709$$ 0.817976i 0.0307197i −0.999882 0.0153599i $$-0.995111\pi$$
0.999882 0.0153599i $$-0.00488939\pi$$
$$710$$ 0 0
$$711$$ 4.52029 0.169524
$$712$$ 0 0
$$713$$ −25.2077 25.2077i −0.944037 0.944037i
$$714$$ 0 0
$$715$$ −4.10253 + 0.190269i −0.153426 + 0.00711567i
$$716$$ 0 0
$$717$$ 15.1158 15.1158i 0.564509 0.564509i
$$718$$ 0 0
$$719$$ 0.00762056 0.000284199 0.000142099 1.00000i $$-0.499955\pi$$
0.000142099 1.00000i $$0.499955\pi$$
$$720$$ 0 0
$$721$$ −30.4634 + 6.18428i −1.13452 + 0.230315i
$$722$$ 0 0
$$723$$ 0.441326 0.441326i 0.0164131 0.0164131i
$$724$$ 0 0
$$725$$ 25.8173 2.39990i 0.958831 0.0891300i
$$726$$ 0 0
$$727$$ 28.5738 28.5738i 1.05974 1.05974i 0.0616465 0.998098i $$-0.480365\pi$$
0.998098 0.0616465i $$-0.0196352\pi$$
$$728$$ 0 0
$$729$$ 1.00000i 0.0370370i
$$730$$ 0 0
$$731$$ 21.8438i 0.807921i
$$732$$ 0 0
$$733$$ 24.1522 + 24.1522i 0.892083 + 0.892083i 0.994719 0.102636i $$-0.0327275\pi$$
−0.102636 + 0.994719i $$0.532728\pi$$
$$734$$ 0 0
$$735$$ 6.76479 + 14.1152i 0.249523 + 0.520645i
$$736$$ 0 0
$$737$$ 8.67452 + 8.67452i 0.319530 + 0.319530i
$$738$$ 0 0
$$739$$ 37.9522i 1.39609i 0.716052 + 0.698047i $$0.245947\pi$$
−0.716052 + 0.698047i $$0.754053\pi$$
$$740$$ 0 0
$$741$$ 4.97202i 0.182652i
$$742$$ 0 0
$$743$$ 18.8022 18.8022i 0.689784 0.689784i −0.272400 0.962184i $$-0.587817\pi$$
0.962184 + 0.272400i $$0.0878174\pi$$
$$744$$ 0 0
$$745$$ −0.160024 0.145838i −0.00586282 0.00534311i
$$746$$ 0 0
$$747$$ 6.75794 6.75794i 0.247260 0.247260i
$$748$$ 0 0
$$749$$ 16.0983 3.26807i 0.588220 0.119413i
$$750$$ 0 0
$$751$$ −0.105915 −0.00386490 −0.00193245 0.999998i $$-0.500615\pi$$
−0.00193245 + 0.999998i $$0.500615\pi$$
$$752$$ 0 0
$$753$$ 11.5572 11.5572i 0.421167 0.421167i
$$754$$ 0 0
$$755$$ 20.2657 22.2369i 0.737545 0.809284i
$$756$$ 0 0
$$757$$ 3.14514 + 3.14514i 0.114312 + 0.114312i 0.761949 0.647637i $$-0.224243\pi$$
−0.647637 + 0.761949i $$0.724243\pi$$
$$758$$ 0 0
$$759$$ −8.54387 −0.310123
$$760$$ 0 0
$$761$$ 35.1123i 1.27282i −0.771351 0.636410i $$-0.780419\pi$$
0.771351 0.636410i $$-0.219581\pi$$
$$762$$ 0 0
$$763$$ −16.4228 10.8801i −0.594547 0.393887i
$$764$$ 0 0
$$765$$ 6.65306 0.308559i 0.240542 0.0111560i
$$766$$ 0 0
$$767$$ 2.83784 + 2.83784i 0.102469 + 0.102469i
$$768$$ 0 0
$$769$$ −8.16835 −0.294558 −0.147279 0.989095i $$-0.547052\pi$$
−0.147279 + 0.989095i $$0.547052\pi$$
$$770$$ 0 0
$$771$$ 30.1304 1.08512
$$772$$ 0 0
$$773$$ 2.51166 + 2.51166i 0.0903382 + 0.0903382i 0.750832 0.660494i $$-0.229653\pi$$
−0.660494 + 0.750832i $$0.729653\pi$$
$$774$$ 0 0
$$775$$ −30.3863 + 2.82462i −1.09151 + 0.101463i
$$776$$ 0 0
$$777$$ 7.03574 + 4.66118i 0.252406 + 0.167219i
$$778$$ 0 0
$$779$$ 3.04897i 0.109241i
$$780$$ 0 0
$$781$$ −11.1554 −0.399171
$$782$$ 0 0
$$783$$ 3.66686 + 3.66686i 0.131043 + 0.131043i
$$784$$ 0 0
$$785$$ 0.241377 + 5.20449i 0.00861510 + 0.185756i
$$786$$ 0 0
$$787$$ 12.7347 12.7347i 0.453943 0.453943i −0.442718 0.896661i $$-0.645986\pi$$
0.896661 + 0.442718i $$0.145986\pi$$
$$788$$ 0 0
$$789$$ −23.1151 −0.822920
$$790$$ 0 0
$$791$$ 1.89408 + 9.33014i 0.0673459 + 0.331742i