# Properties

 Label 1323.2.h.h.802.4 Level $1323$ Weight $2$ Character 1323.802 Analytic conductor $10.564$ Analytic rank $0$ Dimension $24$ CM no Inner twists $4$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.h (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.5642081874$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(\zeta_{3})$$ Twist minimal: no (minimal twist has level 441) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 802.4 Character $$\chi$$ $$=$$ 1323.802 Dual form 1323.2.h.h.226.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.29987 q^{2} -0.310333 q^{4} +(-1.76292 + 3.05347i) q^{5} +3.00314 q^{8} +O(q^{10})$$ $$q-1.29987 q^{2} -0.310333 q^{4} +(-1.76292 + 3.05347i) q^{5} +3.00314 q^{8} +(2.29157 - 3.96912i) q^{10} +(0.589267 + 1.02064i) q^{11} +(-1.61030 - 2.78913i) q^{13} -3.28303 q^{16} +(2.45159 - 4.24627i) q^{17} +(-3.43318 - 5.94645i) q^{19} +(0.547092 - 0.947591i) q^{20} +(-0.765972 - 1.32670i) q^{22} +(-2.14994 + 3.72380i) q^{23} +(-3.71578 - 6.43592i) q^{25} +(2.09319 + 3.62551i) q^{26} +(-1.36140 + 2.35802i) q^{29} +1.92080 q^{31} -1.73876 q^{32} +(-3.18675 + 5.51961i) q^{34} +(4.88229 + 8.45637i) q^{37} +(4.46270 + 7.72962i) q^{38} +(-5.29429 + 9.16998i) q^{40} +(-3.32673 - 5.76206i) q^{41} +(4.83441 - 8.37344i) q^{43} +(-0.182869 - 0.316738i) q^{44} +(2.79464 - 4.84046i) q^{46} +0.633218 q^{47} +(4.83004 + 8.36587i) q^{50} +(0.499729 + 0.865557i) q^{52} +(-1.11378 + 1.92912i) q^{53} -4.15533 q^{55} +(1.76965 - 3.06512i) q^{58} +8.21304 q^{59} +9.65916 q^{61} -2.49680 q^{62} +8.82622 q^{64} +11.3553 q^{65} +5.33301 q^{67} +(-0.760807 + 1.31776i) q^{68} +3.27719 q^{71} +(0.519036 - 0.898997i) q^{73} +(-6.34635 - 10.9922i) q^{74} +(1.06543 + 1.84538i) q^{76} +1.00408 q^{79} +(5.78772 - 10.0246i) q^{80} +(4.32432 + 7.48994i) q^{82} +(-3.65598 + 6.33234i) q^{83} +(8.64391 + 14.9717i) q^{85} +(-6.28411 + 10.8844i) q^{86} +(1.76965 + 3.06512i) q^{88} +(-6.02144 - 10.4294i) q^{89} +(0.667195 - 1.15562i) q^{92} -0.823103 q^{94} +24.2097 q^{95} +(5.46454 - 9.46487i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24q + 8q^{2} + 24q^{4} + 24q^{8} + O(q^{10})$$ $$24q + 8q^{2} + 24q^{4} + 24q^{8} - 20q^{11} + 24q^{16} - 32q^{23} - 12q^{25} - 16q^{29} + 96q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} + 120q^{65} + 24q^{67} + 112q^{71} - 68q^{74} - 24q^{79} + 12q^{85} - 76q^{86} - 16q^{92} + 128q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$1081$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.29987 −0.919148 −0.459574 0.888139i $$-0.651998\pi$$
−0.459574 + 0.888139i $$0.651998\pi$$
$$3$$ 0 0
$$4$$ −0.310333 −0.155166
$$5$$ −1.76292 + 3.05347i −0.788402 + 1.36555i 0.138543 + 0.990356i $$0.455758\pi$$
−0.926945 + 0.375196i $$0.877575\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 3.00314 1.06177
$$9$$ 0 0
$$10$$ 2.29157 3.96912i 0.724659 1.25515i
$$11$$ 0.589267 + 1.02064i 0.177671 + 0.307735i 0.941082 0.338178i $$-0.109810\pi$$
−0.763412 + 0.645912i $$0.776477\pi$$
$$12$$ 0 0
$$13$$ −1.61030 2.78913i −0.446618 0.773564i 0.551546 0.834145i $$-0.314038\pi$$
−0.998163 + 0.0605803i $$0.980705\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −3.28303 −0.820757
$$17$$ 2.45159 4.24627i 0.594597 1.02987i −0.399006 0.916948i $$-0.630645\pi$$
0.993604 0.112924i $$-0.0360218\pi$$
$$18$$ 0 0
$$19$$ −3.43318 5.94645i −0.787627 1.36421i −0.927417 0.374028i $$-0.877976\pi$$
0.139791 0.990181i $$-0.455357\pi$$
$$20$$ 0.547092 0.947591i 0.122333 0.211888i
$$21$$ 0 0
$$22$$ −0.765972 1.32670i −0.163306 0.282854i
$$23$$ −2.14994 + 3.72380i −0.448293 + 0.776466i −0.998275 0.0587106i $$-0.981301\pi$$
0.549982 + 0.835176i $$0.314634\pi$$
$$24$$ 0 0
$$25$$ −3.71578 6.43592i −0.743156 1.28718i
$$26$$ 2.09319 + 3.62551i 0.410508 + 0.711020i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −1.36140 + 2.35802i −0.252806 + 0.437873i −0.964297 0.264822i $$-0.914687\pi$$
0.711491 + 0.702695i $$0.248020\pi$$
$$30$$ 0 0
$$31$$ 1.92080 0.344986 0.172493 0.985011i $$-0.444818\pi$$
0.172493 + 0.985011i $$0.444818\pi$$
$$32$$ −1.73876 −0.307372
$$33$$ 0 0
$$34$$ −3.18675 + 5.51961i −0.546523 + 0.946606i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 4.88229 + 8.45637i 0.802643 + 1.39022i 0.917871 + 0.396879i $$0.129907\pi$$
−0.115228 + 0.993339i $$0.536760\pi$$
$$38$$ 4.46270 + 7.72962i 0.723946 + 1.25391i
$$39$$ 0 0
$$40$$ −5.29429 + 9.16998i −0.837101 + 1.44990i
$$41$$ −3.32673 5.76206i −0.519547 0.899883i −0.999742 0.0227205i $$-0.992767\pi$$
0.480194 0.877162i $$-0.340566\pi$$
$$42$$ 0 0
$$43$$ 4.83441 8.37344i 0.737240 1.27694i −0.216493 0.976284i $$-0.569462\pi$$
0.953734 0.300653i $$-0.0972047\pi$$
$$44$$ −0.182869 0.316738i −0.0275685 0.0477501i
$$45$$ 0 0
$$46$$ 2.79464 4.84046i 0.412047 0.713687i
$$47$$ 0.633218 0.0923644 0.0461822 0.998933i $$-0.485295\pi$$
0.0461822 + 0.998933i $$0.485295\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 4.83004 + 8.36587i 0.683071 + 1.18311i
$$51$$ 0 0
$$52$$ 0.499729 + 0.865557i 0.0693000 + 0.120031i
$$53$$ −1.11378 + 1.92912i −0.152989 + 0.264985i −0.932325 0.361621i $$-0.882223\pi$$
0.779336 + 0.626606i $$0.215557\pi$$
$$54$$ 0 0
$$55$$ −4.15533 −0.560304
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.76965 3.06512i 0.232366 0.402471i
$$59$$ 8.21304 1.06925 0.534623 0.845091i $$-0.320454\pi$$
0.534623 + 0.845091i $$0.320454\pi$$
$$60$$ 0 0
$$61$$ 9.65916 1.23673 0.618364 0.785892i $$-0.287796\pi$$
0.618364 + 0.785892i $$0.287796\pi$$
$$62$$ −2.49680 −0.317093
$$63$$ 0 0
$$64$$ 8.82622 1.10328
$$65$$ 11.3553 1.40846
$$66$$ 0 0
$$67$$ 5.33301 0.651531 0.325766 0.945451i $$-0.394378\pi$$
0.325766 + 0.945451i $$0.394378\pi$$
$$68$$ −0.760807 + 1.31776i −0.0922614 + 0.159801i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 3.27719 0.388931 0.194466 0.980909i $$-0.437703\pi$$
0.194466 + 0.980909i $$0.437703\pi$$
$$72$$ 0 0
$$73$$ 0.519036 0.898997i 0.0607486 0.105220i −0.834052 0.551686i $$-0.813985\pi$$
0.894800 + 0.446467i $$0.147318\pi$$
$$74$$ −6.34635 10.9922i −0.737748 1.27782i
$$75$$ 0 0
$$76$$ 1.06543 + 1.84538i 0.122213 + 0.211679i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1.00408 0.112968 0.0564838 0.998404i $$-0.482011\pi$$
0.0564838 + 0.998404i $$0.482011\pi$$
$$80$$ 5.78772 10.0246i 0.647087 1.12079i
$$81$$ 0 0
$$82$$ 4.32432 + 7.48994i 0.477541 + 0.827126i
$$83$$ −3.65598 + 6.33234i −0.401296 + 0.695064i −0.993883 0.110442i $$-0.964773\pi$$
0.592587 + 0.805506i $$0.298107\pi$$
$$84$$ 0 0
$$85$$ 8.64391 + 14.9717i 0.937563 + 1.62391i
$$86$$ −6.28411 + 10.8844i −0.677633 + 1.17369i
$$87$$ 0 0
$$88$$ 1.76965 + 3.06512i 0.188645 + 0.326743i
$$89$$ −6.02144 10.4294i −0.638271 1.10552i −0.985812 0.167853i $$-0.946317\pi$$
0.347541 0.937665i $$-0.387017\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0.667195 1.15562i 0.0695599 0.120481i
$$93$$ 0 0
$$94$$ −0.823103 −0.0848966
$$95$$ 24.2097 2.48387
$$96$$ 0 0
$$97$$ 5.46454 9.46487i 0.554840 0.961012i −0.443076 0.896484i $$-0.646113\pi$$
0.997916 0.0645275i $$-0.0205540\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1.15313 + 1.99728i 0.115313 + 0.199728i
$$101$$ 0.797546 + 1.38139i 0.0793588 + 0.137453i 0.902973 0.429696i $$-0.141379\pi$$
−0.823615 + 0.567150i $$0.808046\pi$$
$$102$$ 0 0
$$103$$ 1.16778 2.02265i 0.115065 0.199298i −0.802741 0.596328i $$-0.796626\pi$$
0.917806 + 0.397030i $$0.129959\pi$$
$$104$$ −4.83596 8.37613i −0.474205 0.821347i
$$105$$ 0 0
$$106$$ 1.44777 2.50761i 0.140620 0.243561i
$$107$$ −1.11181 1.92571i −0.107483 0.186166i 0.807267 0.590186i $$-0.200946\pi$$
−0.914750 + 0.404021i $$0.867612\pi$$
$$108$$ 0 0
$$109$$ 0.459782 0.796366i 0.0440391 0.0762780i −0.843166 0.537654i $$-0.819311\pi$$
0.887205 + 0.461376i $$0.152644\pi$$
$$110$$ 5.40139 0.515003
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1.19327 2.06681i −0.112254 0.194429i 0.804425 0.594054i $$-0.202474\pi$$
−0.916679 + 0.399625i $$0.869140\pi$$
$$114$$ 0 0
$$115$$ −7.58033 13.1295i −0.706870 1.22433i
$$116$$ 0.422488 0.731770i 0.0392270 0.0679432i
$$117$$ 0 0
$$118$$ −10.6759 −0.982796
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 4.80553 8.32342i 0.436866 0.756674i
$$122$$ −12.5557 −1.13674
$$123$$ 0 0
$$124$$ −0.596087 −0.0535302
$$125$$ 8.57330 0.766819
$$126$$ 0 0
$$127$$ −3.04170 −0.269907 −0.134954 0.990852i $$-0.543089\pi$$
−0.134954 + 0.990852i $$0.543089\pi$$
$$128$$ −7.99544 −0.706704
$$129$$ 0 0
$$130$$ −14.7605 −1.29458
$$131$$ 1.63088 2.82476i 0.142490 0.246801i −0.785943 0.618298i $$-0.787822\pi$$
0.928434 + 0.371498i $$0.121156\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −6.93223 −0.598854
$$135$$ 0 0
$$136$$ 7.36245 12.7521i 0.631325 1.09349i
$$137$$ 10.4669 + 18.1292i 0.894246 + 1.54888i 0.834734 + 0.550653i $$0.185621\pi$$
0.0595120 + 0.998228i $$0.481046\pi$$
$$138$$ 0 0
$$139$$ 8.31195 + 14.3967i 0.705010 + 1.22111i 0.966688 + 0.255958i $$0.0823910\pi$$
−0.261677 + 0.965155i $$0.584276\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −4.25993 −0.357486
$$143$$ 1.89780 3.28708i 0.158702 0.274880i
$$144$$ 0 0
$$145$$ −4.80009 8.31401i −0.398626 0.690441i
$$146$$ −0.674681 + 1.16858i −0.0558370 + 0.0967124i
$$147$$ 0 0
$$148$$ −1.51513 2.62429i −0.124543 0.215715i
$$149$$ 0.564221 0.977260i 0.0462228 0.0800602i −0.841988 0.539496i $$-0.818615\pi$$
0.888211 + 0.459435i $$0.151948\pi$$
$$150$$ 0 0
$$151$$ 9.81476 + 16.9997i 0.798714 + 1.38341i 0.920454 + 0.390851i $$0.127819\pi$$
−0.121740 + 0.992562i $$0.538847\pi$$
$$152$$ −10.3103 17.8580i −0.836278 1.44848i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.38622 + 5.86511i −0.271988 + 0.471097i
$$156$$ 0 0
$$157$$ −9.33237 −0.744804 −0.372402 0.928071i $$-0.621466\pi$$
−0.372402 + 0.928071i $$0.621466\pi$$
$$158$$ −1.30517 −0.103834
$$159$$ 0 0
$$160$$ 3.06529 5.30924i 0.242332 0.419732i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −8.45056 14.6368i −0.661899 1.14644i −0.980116 0.198425i $$-0.936417\pi$$
0.318217 0.948018i $$-0.396916\pi$$
$$164$$ 1.03239 + 1.78815i 0.0806162 + 0.139631i
$$165$$ 0 0
$$166$$ 4.75230 8.23123i 0.368850 0.638867i
$$167$$ 2.57319 + 4.45689i 0.199119 + 0.344885i 0.948243 0.317545i $$-0.102859\pi$$
−0.749124 + 0.662430i $$0.769525\pi$$
$$168$$ 0 0
$$169$$ 1.31385 2.27566i 0.101066 0.175051i
$$170$$ −11.2360 19.4613i −0.861760 1.49261i
$$171$$ 0 0
$$172$$ −1.50027 + 2.59855i −0.114395 + 0.198138i
$$173$$ 9.73669 0.740266 0.370133 0.928979i $$-0.379312\pi$$
0.370133 + 0.928979i $$0.379312\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1.93458 3.35079i −0.145825 0.252576i
$$177$$ 0 0
$$178$$ 7.82710 + 13.5569i 0.586666 + 1.01613i
$$179$$ 0.687990 1.19163i 0.0514228 0.0890668i −0.839168 0.543872i $$-0.816958\pi$$
0.890591 + 0.454805i $$0.150291\pi$$
$$180$$ 0 0
$$181$$ 5.66560 0.421120 0.210560 0.977581i $$-0.432471\pi$$
0.210560 + 0.977581i $$0.432471\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −6.45655 + 11.1831i −0.475983 + 0.824427i
$$185$$ −34.4283 −2.53122
$$186$$ 0 0
$$187$$ 5.77856 0.422570
$$188$$ −0.196508 −0.0143318
$$189$$ 0 0
$$190$$ −31.4696 −2.28304
$$191$$ 25.0129 1.80987 0.904936 0.425547i $$-0.139918\pi$$
0.904936 + 0.425547i $$0.139918\pi$$
$$192$$ 0 0
$$193$$ 17.5338 1.26211 0.631054 0.775739i $$-0.282623\pi$$
0.631054 + 0.775739i $$0.282623\pi$$
$$194$$ −7.10321 + 12.3031i −0.509981 + 0.883312i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 19.7540 1.40741 0.703707 0.710490i $$-0.251527\pi$$
0.703707 + 0.710490i $$0.251527\pi$$
$$198$$ 0 0
$$199$$ −9.51110 + 16.4737i −0.674224 + 1.16779i 0.302471 + 0.953158i $$0.402188\pi$$
−0.976695 + 0.214631i $$0.931145\pi$$
$$200$$ −11.1590 19.3279i −0.789060 1.36669i
$$201$$ 0 0
$$202$$ −1.03671 1.79563i −0.0729425 0.126340i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 23.4590 1.63845
$$206$$ −1.51796 + 2.62919i −0.105761 + 0.183184i
$$207$$ 0 0
$$208$$ 5.28667 + 9.15678i 0.366565 + 0.634908i
$$209$$ 4.04613 7.00810i 0.279876 0.484760i
$$210$$ 0 0
$$211$$ 3.71809 + 6.43993i 0.255964 + 0.443343i 0.965157 0.261672i $$-0.0842738\pi$$
−0.709193 + 0.705015i $$0.750940\pi$$
$$212$$ 0.345642 0.598669i 0.0237388 0.0411168i
$$213$$ 0 0
$$214$$ 1.44521 + 2.50318i 0.0987927 + 0.171114i
$$215$$ 17.0454 + 29.5234i 1.16248 + 2.01348i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −0.597658 + 1.03517i −0.0404785 + 0.0701108i
$$219$$ 0 0
$$220$$ 1.28953 0.0869403
$$221$$ −15.7912 −1.06223
$$222$$ 0 0
$$223$$ −1.64565 + 2.85034i −0.110201 + 0.190873i −0.915851 0.401518i $$-0.868483\pi$$
0.805650 + 0.592391i $$0.201816\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1.55110 + 2.68659i 0.103178 + 0.178709i
$$227$$ 9.00847 + 15.6031i 0.597913 + 1.03562i 0.993129 + 0.117028i $$0.0373366\pi$$
−0.395215 + 0.918589i $$0.629330\pi$$
$$228$$ 0 0
$$229$$ 2.12746 3.68486i 0.140586 0.243503i −0.787131 0.616785i $$-0.788435\pi$$
0.927718 + 0.373283i $$0.121768\pi$$
$$230$$ 9.85347 + 17.0667i 0.649718 + 1.12535i
$$231$$ 0 0
$$232$$ −4.08848 + 7.08146i −0.268422 + 0.464920i
$$233$$ −7.35275 12.7353i −0.481695 0.834320i 0.518084 0.855330i $$-0.326645\pi$$
−0.999779 + 0.0210095i $$0.993312\pi$$
$$234$$ 0 0
$$235$$ −1.11631 + 1.93351i −0.0728203 + 0.126128i
$$236$$ −2.54877 −0.165911
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −7.08187 12.2662i −0.458088 0.793432i 0.540772 0.841169i $$-0.318132\pi$$
−0.998860 + 0.0477377i $$0.984799\pi$$
$$240$$ 0 0
$$241$$ 3.96752 + 6.87194i 0.255570 + 0.442661i 0.965050 0.262065i $$-0.0844035\pi$$
−0.709480 + 0.704726i $$0.751070\pi$$
$$242$$ −6.24657 + 10.8194i −0.401545 + 0.695496i
$$243$$ 0 0
$$244$$ −2.99755 −0.191899
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −11.0569 + 19.1512i −0.703536 + 1.21856i
$$248$$ 5.76843 0.366296
$$249$$ 0 0
$$250$$ −11.1442 −0.704821
$$251$$ 8.05097 0.508173 0.254087 0.967181i $$-0.418225\pi$$
0.254087 + 0.967181i $$0.418225\pi$$
$$252$$ 0 0
$$253$$ −5.06755 −0.318594
$$254$$ 3.95382 0.248085
$$255$$ 0 0
$$256$$ −7.25938 −0.453712
$$257$$ 8.77687 15.2020i 0.547486 0.948273i −0.450960 0.892544i $$-0.648918\pi$$
0.998446 0.0557293i $$-0.0177484\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −3.52393 −0.218545
$$261$$ 0 0
$$262$$ −2.11993 + 3.67183i −0.130970 + 0.226846i
$$263$$ −11.6743 20.2205i −0.719867 1.24685i −0.961052 0.276367i $$-0.910869\pi$$
0.241185 0.970479i $$-0.422464\pi$$
$$264$$ 0 0
$$265$$ −3.92701 6.80177i −0.241234 0.417830i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −1.65501 −0.101096
$$269$$ −0.269244 + 0.466344i −0.0164161 + 0.0284335i −0.874117 0.485716i $$-0.838559\pi$$
0.857701 + 0.514149i $$0.171892\pi$$
$$270$$ 0 0
$$271$$ −7.20749 12.4837i −0.437824 0.758334i 0.559697 0.828697i $$-0.310917\pi$$
−0.997521 + 0.0703635i $$0.977584\pi$$
$$272$$ −8.04863 + 13.9406i −0.488020 + 0.845275i
$$273$$ 0 0
$$274$$ −13.6056 23.5656i −0.821945 1.42365i
$$275$$ 4.37918 7.58495i 0.264074 0.457390i
$$276$$ 0 0
$$277$$ −10.9533 18.9717i −0.658121 1.13990i −0.981101 0.193494i $$-0.938018\pi$$
0.322980 0.946406i $$-0.395315\pi$$
$$278$$ −10.8045 18.7139i −0.648009 1.12238i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0.776622 1.34515i 0.0463294 0.0802449i −0.841931 0.539586i $$-0.818581\pi$$
0.888260 + 0.459341i $$0.151914\pi$$
$$282$$ 0 0
$$283$$ 2.65142 0.157610 0.0788051 0.996890i $$-0.474890\pi$$
0.0788051 + 0.996890i $$0.474890\pi$$
$$284$$ −1.01702 −0.0603490
$$285$$ 0 0
$$286$$ −2.46689 + 4.27279i −0.145870 + 0.252655i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −3.52056 6.09778i −0.207091 0.358693i
$$290$$ 6.23951 + 10.8071i 0.366396 + 0.634617i
$$291$$ 0 0
$$292$$ −0.161074 + 0.278988i −0.00942613 + 0.0163265i
$$293$$ −5.19314 8.99478i −0.303386 0.525481i 0.673514 0.739174i $$-0.264784\pi$$
−0.976901 + 0.213694i $$0.931451\pi$$
$$294$$ 0 0
$$295$$ −14.4789 + 25.0783i −0.842996 + 1.46011i
$$296$$ 14.6622 + 25.3956i 0.852221 + 1.47609i
$$297$$ 0 0
$$298$$ −0.733415 + 1.27031i −0.0424856 + 0.0735872i
$$299$$ 13.8482 0.800861
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −12.7579 22.0974i −0.734137 1.27156i
$$303$$ 0 0
$$304$$ 11.2712 + 19.5224i 0.646450 + 1.11968i
$$305$$ −17.0283 + 29.4939i −0.975039 + 1.68882i
$$306$$ 0 0
$$307$$ 10.6425 0.607400 0.303700 0.952768i $$-0.401778\pi$$
0.303700 + 0.952768i $$0.401778\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 4.40165 7.62389i 0.249997 0.433008i
$$311$$ −13.7096 −0.777399 −0.388699 0.921365i $$-0.627075\pi$$
−0.388699 + 0.921365i $$0.627075\pi$$
$$312$$ 0 0
$$313$$ −21.2179 −1.19931 −0.599653 0.800260i $$-0.704695\pi$$
−0.599653 + 0.800260i $$0.704695\pi$$
$$314$$ 12.1309 0.684586
$$315$$ 0 0
$$316$$ −0.311598 −0.0175288
$$317$$ −3.57043 −0.200535 −0.100268 0.994961i $$-0.531970\pi$$
−0.100268 + 0.994961i $$0.531970\pi$$
$$318$$ 0 0
$$319$$ −3.20892 −0.179665
$$320$$ −15.5599 + 26.9506i −0.869826 + 1.50658i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −33.6670 −1.87328
$$324$$ 0 0
$$325$$ −11.9671 + 20.7276i −0.663813 + 1.14976i
$$326$$ 10.9846 + 19.0260i 0.608383 + 1.05375i
$$327$$ 0 0
$$328$$ −9.99062 17.3043i −0.551639 0.955468i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −23.9456 −1.31617 −0.658085 0.752944i $$-0.728633\pi$$
−0.658085 + 0.752944i $$0.728633\pi$$
$$332$$ 1.13457 1.96513i 0.0622675 0.107851i
$$333$$ 0 0
$$334$$ −3.34482 5.79339i −0.183020 0.317000i
$$335$$ −9.40168 + 16.2842i −0.513669 + 0.889700i
$$336$$ 0 0
$$337$$ −13.7468 23.8102i −0.748838 1.29703i −0.948380 0.317137i $$-0.897279\pi$$
0.199542 0.979889i $$-0.436055\pi$$
$$338$$ −1.70784 + 2.95806i −0.0928942 + 0.160897i
$$339$$ 0 0
$$340$$ −2.68249 4.64620i −0.145478 0.251976i
$$341$$ 1.13187 + 1.96045i 0.0612940 + 0.106164i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 14.5184 25.1466i 0.782779 1.35581i
$$345$$ 0 0
$$346$$ −12.6564 −0.680415
$$347$$ 5.12824 0.275299 0.137649 0.990481i $$-0.456045\pi$$
0.137649 + 0.990481i $$0.456045\pi$$
$$348$$ 0 0
$$349$$ 7.56980 13.1113i 0.405202 0.701830i −0.589143 0.808029i $$-0.700535\pi$$
0.994345 + 0.106198i $$0.0338679\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −1.02459 1.77465i −0.0546110 0.0945889i
$$353$$ −16.4878 28.5578i −0.877559 1.51998i −0.854011 0.520254i $$-0.825837\pi$$
−0.0235477 0.999723i $$-0.507496\pi$$
$$354$$ 0 0
$$355$$ −5.77743 + 10.0068i −0.306634 + 0.531106i
$$356$$ 1.86865 + 3.23659i 0.0990381 + 0.171539i
$$357$$ 0 0
$$358$$ −0.894299 + 1.54897i −0.0472651 + 0.0818656i
$$359$$ −12.0178 20.8154i −0.634274 1.09859i −0.986669 0.162743i $$-0.947966\pi$$
0.352395 0.935851i $$-0.385367\pi$$
$$360$$ 0 0
$$361$$ −14.0735 + 24.3760i −0.740711 + 1.28295i
$$362$$ −7.36455 −0.387072
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1.83004 + 3.16972i 0.0957886 + 0.165911i
$$366$$ 0 0
$$367$$ −1.32751 2.29931i −0.0692952 0.120023i 0.829296 0.558810i $$-0.188742\pi$$
−0.898591 + 0.438787i $$0.855408\pi$$
$$368$$ 7.05830 12.2253i 0.367939 0.637290i
$$369$$ 0 0
$$370$$ 44.7524 2.32657
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 15.9592 27.6421i 0.826334 1.43125i −0.0745621 0.997216i $$-0.523756\pi$$
0.900896 0.434036i $$-0.142911\pi$$
$$374$$ −7.51139 −0.388405
$$375$$ 0 0
$$376$$ 1.90164 0.0980697
$$377$$ 8.76909 0.451631
$$378$$ 0 0
$$379$$ 30.2681 1.55477 0.777384 0.629027i $$-0.216546\pi$$
0.777384 + 0.629027i $$0.216546\pi$$
$$380$$ −7.51307 −0.385412
$$381$$ 0 0
$$382$$ −32.5136 −1.66354
$$383$$ −0.866526 + 1.50087i −0.0442774 + 0.0766907i −0.887315 0.461164i $$-0.847432\pi$$
0.843037 + 0.537855i $$0.180765\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −22.7917 −1.16006
$$387$$ 0 0
$$388$$ −1.69583 + 2.93726i −0.0860925 + 0.149117i
$$389$$ −5.54175 9.59859i −0.280978 0.486668i 0.690648 0.723191i $$-0.257325\pi$$
−0.971626 + 0.236523i $$0.923992\pi$$
$$390$$ 0 0
$$391$$ 10.5415 + 18.2584i 0.533107 + 0.923368i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −25.6777 −1.29362
$$395$$ −1.77011 + 3.06592i −0.0890639 + 0.154263i
$$396$$ 0 0
$$397$$ 12.6696 + 21.9443i 0.635867 + 1.10135i 0.986331 + 0.164777i $$0.0526905\pi$$
−0.350464 + 0.936576i $$0.613976\pi$$
$$398$$ 12.3632 21.4137i 0.619712 1.07337i
$$399$$ 0 0
$$400$$ 12.1990 + 21.1293i 0.609951 + 1.05647i
$$401$$ −17.4122 + 30.1588i −0.869524 + 1.50606i −0.00704089 + 0.999975i $$0.502241\pi$$
−0.862483 + 0.506085i $$0.831092\pi$$
$$402$$ 0 0
$$403$$ −3.09307 5.35736i −0.154077 0.266869i
$$404$$ −0.247505 0.428690i −0.0123138 0.0213281i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −5.75394 + 9.96612i −0.285212 + 0.494002i
$$408$$ 0 0
$$409$$ 18.2462 0.902215 0.451107 0.892470i $$-0.351029\pi$$
0.451107 + 0.892470i $$0.351029\pi$$
$$410$$ −30.4937 −1.50598
$$411$$ 0 0
$$412$$ −0.362400 + 0.627695i −0.0178541 + 0.0309243i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −12.8904 22.3268i −0.632765 1.09598i
$$416$$ 2.79992 + 4.84961i 0.137278 + 0.237772i
$$417$$ 0 0
$$418$$ −5.25945 + 9.10963i −0.257248 + 0.445567i
$$419$$ −4.20719 7.28708i −0.205535 0.355997i 0.744768 0.667323i $$-0.232560\pi$$
−0.950303 + 0.311326i $$0.899227\pi$$
$$420$$ 0 0
$$421$$ 0.144291 0.249919i 0.00703230 0.0121803i −0.862488 0.506078i $$-0.831095\pi$$
0.869520 + 0.493897i $$0.164428\pi$$
$$422$$ −4.83304 8.37108i −0.235269 0.407498i
$$423$$ 0 0
$$424$$ −3.34483 + 5.79341i −0.162439 + 0.281353i
$$425$$ −36.4382 −1.76751
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0.345031 + 0.597612i 0.0166777 + 0.0288866i
$$429$$ 0 0
$$430$$ −22.1568 38.3767i −1.06849 1.85069i
$$431$$ −6.74795 + 11.6878i −0.325037 + 0.562981i −0.981520 0.191360i $$-0.938710\pi$$
0.656482 + 0.754341i $$0.272044\pi$$
$$432$$ 0 0
$$433$$ 4.85211 0.233177 0.116589 0.993180i $$-0.462804\pi$$
0.116589 + 0.993180i $$0.462804\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −0.142685 + 0.247138i −0.00683339 + 0.0118358i
$$437$$ 29.5245 1.41235
$$438$$ 0 0
$$439$$ −2.54793 −0.121606 −0.0608031 0.998150i $$-0.519366\pi$$
−0.0608031 + 0.998150i $$0.519366\pi$$
$$440$$ −12.4790 −0.594914
$$441$$ 0 0
$$442$$ 20.5265 0.976347
$$443$$ 0.645506 0.0306689 0.0153345 0.999882i $$-0.495119\pi$$
0.0153345 + 0.999882i $$0.495119\pi$$
$$444$$ 0 0
$$445$$ 42.4613 2.01286
$$446$$ 2.13913 3.70508i 0.101291 0.175441i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 5.22658 0.246658 0.123329 0.992366i $$-0.460643\pi$$
0.123329 + 0.992366i $$0.460643\pi$$
$$450$$ 0 0
$$451$$ 3.92066 6.79079i 0.184617 0.319766i
$$452$$ 0.370312 + 0.641399i 0.0174180 + 0.0301689i
$$453$$ 0 0
$$454$$ −11.7099 20.2821i −0.549571 0.951885i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −2.86075 −0.133820 −0.0669101 0.997759i $$-0.521314\pi$$
−0.0669101 + 0.997759i $$0.521314\pi$$
$$458$$ −2.76542 + 4.78985i −0.129220 + 0.223815i
$$459$$ 0 0
$$460$$ 2.35242 + 4.07452i 0.109682 + 0.189975i
$$461$$ 1.82624 3.16314i 0.0850566 0.147322i −0.820359 0.571849i $$-0.806226\pi$$
0.905415 + 0.424527i $$0.139560\pi$$
$$462$$ 0 0
$$463$$ −15.4052 26.6825i −0.715939 1.24004i −0.962596 0.270940i $$-0.912666\pi$$
0.246657 0.969103i $$-0.420668\pi$$
$$464$$ 4.46953 7.74145i 0.207493 0.359388i
$$465$$ 0 0
$$466$$ 9.55764 + 16.5543i 0.442749 + 0.766864i
$$467$$ −10.2885 17.8202i −0.476096 0.824622i 0.523529 0.852008i $$-0.324615\pi$$
−0.999625 + 0.0273858i $$0.991282\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 1.45107 2.51332i 0.0669327 0.115931i
$$471$$ 0 0
$$472$$ 24.6649 1.13529
$$473$$ 11.3950 0.523944
$$474$$ 0 0
$$475$$ −25.5139 + 44.1914i −1.17066 + 2.02764i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 9.20552 + 15.9444i 0.421051 + 0.729281i
$$479$$ −12.5916 21.8093i −0.575325 0.996492i −0.996006 0.0892833i $$-0.971542\pi$$
0.420682 0.907208i $$-0.361791\pi$$
$$480$$ 0 0
$$481$$ 15.7239 27.2346i 0.716949 1.24179i
$$482$$ −5.15726 8.93264i −0.234907 0.406871i
$$483$$ 0 0
$$484$$ −1.49131 + 2.58303i −0.0677869 + 0.117410i
$$485$$ 19.2671 + 33.3716i 0.874875 + 1.51533i
$$486$$ 0 0
$$487$$ 16.3807 28.3723i 0.742282 1.28567i −0.209173 0.977879i $$-0.567077\pi$$
0.951454 0.307791i $$-0.0995896\pi$$
$$488$$ 29.0078 1.31312
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −1.76000 3.04841i −0.0794278 0.137573i 0.823575 0.567207i $$-0.191976\pi$$
−0.903003 + 0.429634i $$0.858643\pi$$
$$492$$ 0 0
$$493$$ 6.67520 + 11.5618i 0.300636 + 0.520716i
$$494$$ 14.3726 24.8941i 0.646654 1.12004i
$$495$$ 0 0
$$496$$ −6.30605 −0.283150
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −7.82082 + 13.5461i −0.350108 + 0.606405i −0.986268 0.165152i $$-0.947188\pi$$
0.636160 + 0.771557i $$0.280522\pi$$
$$500$$ −2.66057 −0.118984
$$501$$ 0 0
$$502$$ −10.4652 −0.467086
$$503$$ −36.5427 −1.62936 −0.814678 0.579913i $$-0.803086\pi$$
−0.814678 + 0.579913i $$0.803086\pi$$
$$504$$ 0 0
$$505$$ −5.62404 −0.250267
$$506$$ 6.58716 0.292835
$$507$$ 0 0
$$508$$ 0.943938 0.0418805
$$509$$ 18.8229 32.6023i 0.834311 1.44507i −0.0602789 0.998182i $$-0.519199\pi$$
0.894590 0.446888i $$-0.147468\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 25.4272 1.12373
$$513$$ 0 0
$$514$$ −11.4088 + 19.7606i −0.503221 + 0.871604i
$$515$$ 4.11740 + 7.13155i 0.181434 + 0.314254i
$$516$$ 0 0
$$517$$ 0.373135 + 0.646289i 0.0164105 + 0.0284237i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 34.1017 1.49546
$$521$$ 7.17115 12.4208i 0.314174 0.544165i −0.665088 0.746765i $$-0.731606\pi$$
0.979262 + 0.202600i $$0.0649392\pi$$
$$522$$ 0 0
$$523$$ 5.24222 + 9.07980i 0.229226 + 0.397032i 0.957579 0.288171i $$-0.0930471\pi$$
−0.728353 + 0.685202i $$0.759714\pi$$
$$524$$ −0.506114 + 0.876616i −0.0221097 + 0.0382951i
$$525$$ 0 0
$$526$$ 15.1751 + 26.2840i 0.661665 + 1.14604i
$$527$$ 4.70901 8.15625i 0.205128 0.355292i
$$528$$ 0 0
$$529$$ 2.25555 + 3.90673i 0.0980674 + 0.169858i
$$530$$ 5.10461 + 8.84144i 0.221730 + 0.384047i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −10.7141 + 18.5573i −0.464078 + 0.803807i
$$534$$ 0 0
$$535$$ 7.84014 0.338959
$$536$$ 16.0158 0.691776
$$537$$ 0 0
$$538$$ 0.349983 0.606188i 0.0150888 0.0261346i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 23.0461 + 39.9170i 0.990830 + 1.71617i 0.612430 + 0.790524i $$0.290192\pi$$
0.378399 + 0.925643i $$0.376475\pi$$
$$542$$ 9.36882 + 16.2273i 0.402425 + 0.697021i
$$543$$ 0 0
$$544$$ −4.26271 + 7.38323i −0.182762 + 0.316554i
$$545$$ 1.62112 + 2.80786i 0.0694411 + 0.120275i
$$546$$ 0 0
$$547$$ −12.1793 + 21.0951i −0.520747 + 0.901961i 0.478962 + 0.877836i $$0.341013\pi$$
−0.999709 + 0.0241250i $$0.992320\pi$$
$$548$$ −3.24822 5.62607i −0.138757 0.240334i
$$549$$ 0 0
$$550$$ −5.69237 + 9.85947i −0.242723 + 0.420409i
$$551$$ 18.6958 0.796468
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 14.2379 + 24.6608i 0.604911 + 1.04774i
$$555$$ 0 0
$$556$$ −2.57947 4.46777i −0.109394 0.189476i
$$557$$ 15.2888 26.4809i 0.647806 1.12203i −0.335840 0.941919i $$-0.609020\pi$$
0.983646 0.180114i $$-0.0576466\pi$$
$$558$$ 0 0
$$559$$ −31.1394 −1.31706
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −1.00951 + 1.74852i −0.0425836 + 0.0737570i
$$563$$ 8.82714 0.372019 0.186010 0.982548i $$-0.440444\pi$$
0.186010 + 0.982548i $$0.440444\pi$$
$$564$$ 0 0
$$565$$ 8.41459 0.354005
$$566$$ −3.44650 −0.144867
$$567$$ 0 0
$$568$$ 9.84186 0.412955
$$569$$ −7.12055 −0.298509 −0.149254 0.988799i $$-0.547687\pi$$
−0.149254 + 0.988799i $$0.547687\pi$$
$$570$$ 0 0
$$571$$ 6.66361 0.278863 0.139432 0.990232i $$-0.455472\pi$$
0.139432 + 0.990232i $$0.455472\pi$$
$$572$$ −0.588948 + 1.02009i −0.0246252 + 0.0426520i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 31.9548 1.33261
$$576$$ 0 0
$$577$$ 3.95629 6.85250i 0.164703 0.285273i −0.771847 0.635808i $$-0.780667\pi$$
0.936550 + 0.350535i $$0.114000\pi$$
$$578$$ 4.57627 + 7.92633i 0.190348 + 0.329692i
$$579$$ 0 0
$$580$$ 1.48963 + 2.58011i 0.0618533 + 0.107133i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −2.62525 −0.108727
$$584$$ 1.55874 2.69981i 0.0645010 0.111719i
$$585$$ 0 0
$$586$$ 6.75042 + 11.6921i 0.278857 + 0.482995i
$$587$$ −9.13891 + 15.8291i −0.377203 + 0.653335i −0.990654 0.136398i $$-0.956447\pi$$
0.613451 + 0.789733i $$0.289781\pi$$
$$588$$ 0 0
$$589$$ −6.59447 11.4220i −0.271720 0.470633i
$$590$$ 18.8208 32.5985i 0.774839 1.34206i
$$591$$ 0 0
$$592$$ −16.0287 27.7625i −0.658775 1.14103i
$$593$$ 14.1908 + 24.5792i 0.582745 + 1.00934i 0.995152 + 0.0983450i $$0.0313549\pi$$
−0.412407 + 0.911000i $$0.635312\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −0.175096 + 0.303275i −0.00717222 + 0.0124226i
$$597$$ 0 0
$$598$$ −18.0009 −0.736111
$$599$$ −9.38902 −0.383625 −0.191813 0.981432i $$-0.561437\pi$$
−0.191813 + 0.981432i $$0.561437\pi$$
$$600$$ 0 0
$$601$$ 6.31432 10.9367i 0.257566 0.446118i −0.708023 0.706189i $$-0.750413\pi$$
0.965589 + 0.260071i $$0.0837460\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −3.04584 5.27555i −0.123934 0.214659i
$$605$$ 16.9435 + 29.3471i 0.688853 + 1.19313i
$$606$$ 0 0
$$607$$ 12.0133 20.8076i 0.487604 0.844554i −0.512295 0.858810i $$-0.671204\pi$$
0.999898 + 0.0142555i $$0.00453781\pi$$
$$608$$ 5.96947 + 10.3394i 0.242094 + 0.419319i
$$609$$ 0 0
$$610$$ 22.1347 38.3383i 0.896206 1.55227i
$$611$$ −1.01967 1.76613i −0.0412516 0.0714498i
$$612$$ 0 0
$$613$$ 14.2708 24.7177i 0.576390 0.998337i −0.419499 0.907756i $$-0.637794\pi$$
0.995889 0.0905814i $$-0.0288725\pi$$
$$614$$ −13.8339 −0.558291
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 6.05549 + 10.4884i 0.243785 + 0.422248i 0.961789 0.273791i $$-0.0882776\pi$$
−0.718004 + 0.696039i $$0.754944\pi$$
$$618$$ 0 0
$$619$$ −13.2870 23.0137i −0.534048 0.924998i −0.999209 0.0397721i $$-0.987337\pi$$
0.465161 0.885226i $$-0.345997\pi$$
$$620$$ 1.05085 1.82013i 0.0422033 0.0730983i
$$621$$ 0 0
$$622$$ 17.8207 0.714545
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 3.46486 6.00131i 0.138594 0.240052i
$$626$$ 27.5806 1.10234
$$627$$ 0 0
$$628$$ 2.89614 0.115569
$$629$$ 47.8774 1.90900
$$630$$ 0 0
$$631$$ 3.30962 0.131754 0.0658770 0.997828i $$-0.479015\pi$$
0.0658770 + 0.997828i $$0.479015\pi$$
$$632$$ 3.01538 0.119945
$$633$$ 0 0
$$634$$ 4.64110 0.184322
$$635$$ 5.36227 9.28773i 0.212795 0.368572i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 4.17119 0.165139
$$639$$ 0 0
$$640$$ 14.0953 24.4138i 0.557167 0.965041i
$$641$$ 16.2922 + 28.2189i 0.643503 + 1.11458i 0.984645 + 0.174568i $$0.0558530\pi$$
−0.341142 + 0.940012i $$0.610814\pi$$
$$642$$ 0 0
$$643$$ −21.5327 37.2957i −0.849166 1.47080i −0.881953 0.471337i $$-0.843772\pi$$
0.0327873 0.999462i $$-0.489562\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 43.7628 1.72182
$$647$$ −23.0988 + 40.0082i −0.908106 + 1.57289i −0.0914143 + 0.995813i $$0.529139\pi$$
−0.816692 + 0.577074i $$0.804195\pi$$
$$648$$ 0 0
$$649$$ 4.83968 + 8.38256i 0.189974 + 0.329044i
$$650$$ 15.5556 26.9432i 0.610143 1.05680i
$$651$$ 0 0
$$652$$ 2.62248 + 4.54228i 0.102704 + 0.177889i
$$653$$ 16.0002 27.7132i 0.626138 1.08450i −0.362182 0.932107i $$-0.617968\pi$$
0.988320 0.152395i $$-0.0486985\pi$$
$$654$$ 0 0
$$655$$ 5.75022 + 9.95967i 0.224680 + 0.389156i
$$656$$ 10.9217 + 18.9170i 0.426422 + 0.738585i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −19.2070 + 33.2674i −0.748197 + 1.29591i 0.200490 + 0.979696i $$0.435747\pi$$
−0.948686 + 0.316219i $$0.897587\pi$$
$$660$$ 0 0
$$661$$ −28.0260 −1.09009 −0.545043 0.838408i $$-0.683487\pi$$
−0.545043 + 0.838408i $$0.683487\pi$$
$$662$$ 31.1262 1.20976
$$663$$ 0 0
$$664$$ −10.9794 + 19.0169i −0.426083 + 0.737998i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −5.85386 10.1392i −0.226662 0.392591i
$$668$$ −0.798544 1.38312i −0.0308966 0.0535145i
$$669$$ 0 0
$$670$$ 12.2210 21.1674i 0.472138 0.817766i
$$671$$ 5.69183 + 9.85853i 0.219730 + 0.380584i
$$672$$ 0 0
$$673$$ 0.796281 1.37920i 0.0306944 0.0531642i −0.850270 0.526347i $$-0.823561\pi$$
0.880965 + 0.473182i $$0.156895\pi$$
$$674$$ 17.8691 + 30.9503i 0.688293 + 1.19216i
$$675$$ 0 0
$$676$$ −0.407731 + 0.706211i −0.0156820 + 0.0271619i
$$677$$ −42.0334 −1.61547 −0.807737 0.589543i $$-0.799308\pi$$
−0.807737 + 0.589543i $$0.799308\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 25.9588 + 44.9620i 0.995476 + 1.72421i
$$681$$ 0 0
$$682$$ −1.47128 2.54833i −0.0563382 0.0975807i
$$683$$ 17.8645 30.9422i 0.683565 1.18397i −0.290321 0.956929i $$-0.593762\pi$$
0.973886 0.227039i $$-0.0729046\pi$$
$$684$$ 0 0
$$685$$ −73.8092 −2.82010
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −15.8715 + 27.4902i −0.605095 + 1.04806i
$$689$$ 7.17408 0.273311
$$690$$ 0 0
$$691$$ 51.1349 1.94526 0.972632 0.232351i $$-0.0746418\pi$$
0.972632 + 0.232351i $$0.0746418\pi$$
$$692$$ −3.02161 −0.114864
$$693$$ 0 0
$$694$$ −6.66606 −0.253040
$$695$$ −58.6132 −2.22333
$$696$$ 0 0
$$697$$ −32.6230 −1.23569
$$698$$ −9.83977 + 17.0430i −0.372441 + 0.645086i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 24.5761 0.928226 0.464113 0.885776i $$-0.346373\pi$$
0.464113 + 0.885776i $$0.346373\pi$$
$$702$$ 0 0
$$703$$ 33.5236 58.0645i 1.26437 2.18995i
$$704$$ 5.20100 + 9.00840i 0.196020 + 0.339517i
$$705$$ 0 0
$$706$$ 21.4321 + 37.1215i 0.806607 + 1.39708i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 30.8976 1.16038 0.580192 0.814480i $$-0.302978\pi$$
0.580192 + 0.814480i $$0.302978\pi$$
$$710$$ 7.50992 13.0076i 0.281842 0.488165i
$$711$$ 0 0
$$712$$ −18.0832 31.3210i −0.677697 1.17380i
$$713$$ −4.12960 + 7.15268i −0.154655 + 0.267870i
$$714$$ 0 0
$$715$$ 6.69133 + 11.5897i 0.250242 + 0.433431i
$$716$$ −0.213506 + 0.369803i −0.00797908 + 0.0138202i
$$717$$ 0 0
$$718$$ 15.6216 + 27.0573i 0.582992 + 1.00977i
$$719$$ 3.05690 + 5.29471i 0.114003 + 0.197459i 0.917381 0.398011i $$-0.130299\pi$$
−0.803378 + 0.595470i $$0.796966\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 18.2938 31.6857i 0.680823 1.17922i
$$723$$ 0 0
$$724$$ −1.75822 −0.0653437
$$725$$ 20.2347 0.751498
$$726$$ 0 0
$$727$$ 22.2492 38.5367i 0.825176 1.42925i −0.0766087 0.997061i $$-0.524409\pi$$
0.901785 0.432186i $$-0.142257\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −2.37882 4.12023i −0.0880440 0.152497i
$$731$$ −23.7039 41.0564i −0.876722 1.51853i
$$732$$ 0 0
$$733$$ −4.91854 + 8.51916i −0.181670 + 0.314662i −0.942449 0.334349i $$-0.891484\pi$$
0.760779 + 0.649011i $$0.224817\pi$$
$$734$$ 1.72559 + 2.98881i 0.0636926 + 0.110319i
$$735$$ 0 0
$$736$$ 3.73821 6.47478i 0.137792 0.238663i
$$737$$ 3.14257 + 5.44309i 0.115758 + 0.200499i
$$738$$ 0 0
$$739$$ −7.42464 + 12.8598i −0.273120 + 0.473057i −0.969659 0.244461i $$-0.921389\pi$$
0.696539 + 0.717519i $$0.254722\pi$$
$$740$$ 10.6842 0.392760
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 3.04201 + 5.26892i 0.111601 + 0.193298i 0.916416 0.400228i $$-0.131069\pi$$
−0.804815 + 0.593525i $$0.797736\pi$$
$$744$$ 0 0
$$745$$ 1.98935 + 3.44566i 0.0728843 + 0.126239i
$$746$$ −20.7449 + 35.9311i −0.759523 + 1.31553i
$$747$$ 0 0
$$748$$ −1.79328 −0.0655686
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −11.1005 + 19.2266i −0.405063 + 0.701590i −0.994329 0.106349i $$-0.966084\pi$$
0.589266 + 0.807939i $$0.299417\pi$$
$$752$$ −2.07887 −0.0758087
$$753$$ 0 0
$$754$$ −11.3987 −0.415116
$$755$$ −69.2106 −2.51883
$$756$$ 0 0
$$757$$ 25.0464 0.910329 0.455164 0.890407i $$-0.349581\pi$$
0.455164 + 0.890407i $$0.349581\pi$$
$$758$$ −39.3446 −1.42906
$$759$$ 0 0
$$760$$ 72.7051 2.63729
$$761$$ 3.37632 5.84796i 0.122392 0.211988i −0.798319 0.602235i $$-0.794277\pi$$
0.920710 + 0.390247i $$0.127610\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −7.76233 −0.280831
$$765$$ 0 0
$$766$$ 1.12637 1.95094i 0.0406975 0.0704902i
$$767$$ −13.2255 22.9072i −0.477544 0.827131i
$$768$$ 0 0
$$769$$ 21.0805 + 36.5125i 0.760182 + 1.31667i 0.942757 + 0.333482i $$0.108224\pi$$
−0.182575 + 0.983192i $$0.558443\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −5.44130 −0.195837
$$773$$ 1.64926 2.85660i 0.0593197 0.102745i −0.834841 0.550492i $$-0.814440\pi$$
0.894160 + 0.447747i $$0.147774\pi$$
$$774$$ 0 0
$$775$$ −7.13728 12.3621i −0.256379 0.444061i
$$776$$ 16.4108 28.4243i 0.589112 1.02037i
$$777$$ 0 0
$$778$$ 7.20356 + 12.4769i 0.258260 + 0.447320i
$$779$$ −22.8425 + 39.5644i −0.818419 + 1.41754i
$$780$$ 0 0
$$781$$ 1.93114 + 3.34484i 0.0691017 + 0.119688i
$$782$$ −13.7026 23.7336i −0.490004 0.848713i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 16.4522 28.4961i 0.587205 1.01707i
$$786$$ 0 0
$$787$$ 6.72910 0.239867 0.119933 0.992782i $$-0.461732\pi$$
0.119933 + 0.992782i $$0.461732\pi$$
$$788$$ −6.13031 −0.218383
$$789$$ 0 0
$$790$$ 2.30092 3.98530i 0.0818629 0.141791i
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −15.5542 26.9406i −0.552345 0.956689i
$$794$$ −16.4688 28.5248i −0.584456 1.01231i
$$795$$ 0 0
$$796$$ 2.95160 5.11233i 0.104617