# Properties

 Label 1512.2.c.g.757.1 Level 1512 Weight 2 Character 1512.757 Analytic conductor 12.073 Analytic rank 0 Dimension 24 CM no Inner twists 4

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1512.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.0733807856$$ Analytic rank: $$0$$ Dimension: $$24$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 757.1 Character $$\chi$$ $$=$$ 1512.757 Dual form 1512.2.c.g.757.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.40920 - 0.118957i) q^{2} +(1.97170 + 0.335269i) q^{4} -3.46300i q^{5} +1.00000 q^{7} +(-2.73864 - 0.707009i) q^{8} +O(q^{10})$$ $$q+(-1.40920 - 0.118957i) q^{2} +(1.97170 + 0.335269i) q^{4} -3.46300i q^{5} +1.00000 q^{7} +(-2.73864 - 0.707009i) q^{8} +(-0.411948 + 4.88007i) q^{10} +3.31902i q^{11} +3.10840i q^{13} +(-1.40920 - 0.118957i) q^{14} +(3.77519 + 1.32210i) q^{16} +1.40277 q^{17} +4.80674i q^{19} +(1.16104 - 6.82800i) q^{20} +(0.394821 - 4.67717i) q^{22} -8.79960 q^{23} -6.99238 q^{25} +(0.369766 - 4.38037i) q^{26} +(1.97170 + 0.335269i) q^{28} +9.87397i q^{29} -7.83557 q^{31} +(-5.16273 - 2.31219i) q^{32} +(-1.97678 - 0.166869i) q^{34} -3.46300i q^{35} +5.42317i q^{37} +(0.571795 - 6.77366i) q^{38} +(-2.44837 + 9.48391i) q^{40} +11.5710 q^{41} +7.03957i q^{43} +(-1.11276 + 6.54411i) q^{44} +(12.4004 + 1.04677i) q^{46} -11.2916 q^{47} +1.00000 q^{49} +(9.85368 + 0.831793i) q^{50} +(-1.04215 + 6.12884i) q^{52} -6.51655i q^{53} +11.4938 q^{55} +(-2.73864 - 0.707009i) q^{56} +(1.17458 - 13.9144i) q^{58} +3.89654i q^{59} -9.42334i q^{61} +(11.0419 + 0.932096i) q^{62} +(7.00028 + 3.87248i) q^{64} +10.7644 q^{65} -0.909712i q^{67} +(2.76583 + 0.470304i) q^{68} +(-0.411948 + 4.88007i) q^{70} +6.42314 q^{71} +1.56257 q^{73} +(0.645124 - 7.64234i) q^{74} +(-1.61155 + 9.47744i) q^{76} +3.31902i q^{77} -11.1619 q^{79} +(4.57843 - 13.0735i) q^{80} +(-16.3059 - 1.37645i) q^{82} +0.370241i q^{83} -4.85778i q^{85} +(0.837406 - 9.92018i) q^{86} +(2.34658 - 9.08960i) q^{88} -4.85047 q^{89} +3.10840i q^{91} +(-17.3502 - 2.95023i) q^{92} +(15.9121 + 1.34321i) q^{94} +16.6457 q^{95} +1.63283 q^{97} +(-1.40920 - 0.118957i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24q + 6q^{4} + 24q^{7} + O(q^{10})$$ $$24q + 6q^{4} + 24q^{7} - 16q^{10} + 2q^{16} + 16q^{22} - 24q^{25} + 6q^{28} + 8q^{31} + 22q^{34} + 26q^{46} + 24q^{49} - 6q^{52} + 16q^{55} - 58q^{58} + 6q^{64} - 16q^{70} + 60q^{76} + 8q^{79} - 28q^{82} + 12q^{88} + 36q^{94} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$$.

 $$n$$ $$757$$ $$785$$ $$1081$$ $$1135$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.40920 0.118957i −0.996456 0.0841153i
$$3$$ 0 0
$$4$$ 1.97170 + 0.335269i 0.985849 + 0.167634i
$$5$$ 3.46300i 1.54870i −0.632757 0.774351i $$-0.718077\pi$$
0.632757 0.774351i $$-0.281923\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ −2.73864 0.707009i −0.968255 0.249965i
$$9$$ 0 0
$$10$$ −0.411948 + 4.88007i −0.130269 + 1.54321i
$$11$$ 3.31902i 1.00072i 0.865817 + 0.500361i $$0.166799\pi$$
−0.865817 + 0.500361i $$0.833201\pi$$
$$12$$ 0 0
$$13$$ 3.10840i 0.862116i 0.902324 + 0.431058i $$0.141860\pi$$
−0.902324 + 0.431058i $$0.858140\pi$$
$$14$$ −1.40920 0.118957i −0.376625 0.0317926i
$$15$$ 0 0
$$16$$ 3.77519 + 1.32210i 0.943797 + 0.330524i
$$17$$ 1.40277 0.340221 0.170110 0.985425i $$-0.445588\pi$$
0.170110 + 0.985425i $$0.445588\pi$$
$$18$$ 0 0
$$19$$ 4.80674i 1.10274i 0.834260 + 0.551371i $$0.185895\pi$$
−0.834260 + 0.551371i $$0.814105\pi$$
$$20$$ 1.16104 6.82800i 0.259616 1.52679i
$$21$$ 0 0
$$22$$ 0.394821 4.67717i 0.0841761 0.997176i
$$23$$ −8.79960 −1.83484 −0.917421 0.397917i $$-0.869733\pi$$
−0.917421 + 0.397917i $$0.869733\pi$$
$$24$$ 0 0
$$25$$ −6.99238 −1.39848
$$26$$ 0.369766 4.38037i 0.0725172 0.859061i
$$27$$ 0 0
$$28$$ 1.97170 + 0.335269i 0.372616 + 0.0633598i
$$29$$ 9.87397i 1.83355i 0.399404 + 0.916775i $$0.369217\pi$$
−0.399404 + 0.916775i $$0.630783\pi$$
$$30$$ 0 0
$$31$$ −7.83557 −1.40731 −0.703655 0.710541i $$-0.748450\pi$$
−0.703655 + 0.710541i $$0.748450\pi$$
$$32$$ −5.16273 2.31219i −0.912650 0.408741i
$$33$$ 0 0
$$34$$ −1.97678 0.166869i −0.339015 0.0286178i
$$35$$ 3.46300i 0.585354i
$$36$$ 0 0
$$37$$ 5.42317i 0.891564i 0.895142 + 0.445782i $$0.147074\pi$$
−0.895142 + 0.445782i $$0.852926\pi$$
$$38$$ 0.571795 6.77366i 0.0927574 1.09883i
$$39$$ 0 0
$$40$$ −2.44837 + 9.48391i −0.387122 + 1.49954i
$$41$$ 11.5710 1.80708 0.903542 0.428499i $$-0.140957\pi$$
0.903542 + 0.428499i $$0.140957\pi$$
$$42$$ 0 0
$$43$$ 7.03957i 1.07352i 0.843733 + 0.536762i $$0.180353\pi$$
−0.843733 + 0.536762i $$0.819647\pi$$
$$44$$ −1.11276 + 6.54411i −0.167756 + 0.986562i
$$45$$ 0 0
$$46$$ 12.4004 + 1.04677i 1.82834 + 0.154338i
$$47$$ −11.2916 −1.64704 −0.823522 0.567284i $$-0.807994\pi$$
−0.823522 + 0.567284i $$0.807994\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 9.85368 + 0.831793i 1.39352 + 0.117633i
$$51$$ 0 0
$$52$$ −1.04215 + 6.12884i −0.144520 + 0.849917i
$$53$$ 6.51655i 0.895117i −0.894255 0.447559i $$-0.852294\pi$$
0.894255 0.447559i $$-0.147706\pi$$
$$54$$ 0 0
$$55$$ 11.4938 1.54982
$$56$$ −2.73864 0.707009i −0.365966 0.0944780i
$$57$$ 0 0
$$58$$ 1.17458 13.9144i 0.154230 1.82705i
$$59$$ 3.89654i 0.507287i 0.967298 + 0.253643i $$0.0816290\pi$$
−0.967298 + 0.253643i $$0.918371\pi$$
$$60$$ 0 0
$$61$$ 9.42334i 1.20653i −0.797539 0.603267i $$-0.793865\pi$$
0.797539 0.603267i $$-0.206135\pi$$
$$62$$ 11.0419 + 0.932096i 1.40232 + 0.118376i
$$63$$ 0 0
$$64$$ 7.00028 + 3.87248i 0.875035 + 0.484060i
$$65$$ 10.7644 1.33516
$$66$$ 0 0
$$67$$ 0.909712i 0.111139i −0.998455 0.0555695i $$-0.982303\pi$$
0.998455 0.0555695i $$-0.0176974\pi$$
$$68$$ 2.76583 + 0.470304i 0.335406 + 0.0570327i
$$69$$ 0 0
$$70$$ −0.411948 + 4.88007i −0.0492372 + 0.583280i
$$71$$ 6.42314 0.762286 0.381143 0.924516i $$-0.375531\pi$$
0.381143 + 0.924516i $$0.375531\pi$$
$$72$$ 0 0
$$73$$ 1.56257 0.182884 0.0914422 0.995810i $$-0.470852\pi$$
0.0914422 + 0.995810i $$0.470852\pi$$
$$74$$ 0.645124 7.64234i 0.0749942 0.888404i
$$75$$ 0 0
$$76$$ −1.61155 + 9.47744i −0.184857 + 1.08714i
$$77$$ 3.31902i 0.378238i
$$78$$ 0 0
$$79$$ −11.1619 −1.25582 −0.627908 0.778288i $$-0.716088\pi$$
−0.627908 + 0.778288i $$0.716088\pi$$
$$80$$ 4.57843 13.0735i 0.511884 1.46166i
$$81$$ 0 0
$$82$$ −16.3059 1.37645i −1.80068 0.152003i
$$83$$ 0.370241i 0.0406392i 0.999794 + 0.0203196i $$0.00646837\pi$$
−0.999794 + 0.0203196i $$0.993532\pi$$
$$84$$ 0 0
$$85$$ 4.85778i 0.526900i
$$86$$ 0.837406 9.92018i 0.0902999 1.06972i
$$87$$ 0 0
$$88$$ 2.34658 9.08960i 0.250146 0.968954i
$$89$$ −4.85047 −0.514149 −0.257075 0.966392i $$-0.582759\pi$$
−0.257075 + 0.966392i $$0.582759\pi$$
$$90$$ 0 0
$$91$$ 3.10840i 0.325849i
$$92$$ −17.3502 2.95023i −1.80888 0.307583i
$$93$$ 0 0
$$94$$ 15.9121 + 1.34321i 1.64121 + 0.138542i
$$95$$ 16.6457 1.70782
$$96$$ 0 0
$$97$$ 1.63283 0.165789 0.0828946 0.996558i $$-0.473584\pi$$
0.0828946 + 0.996558i $$0.473584\pi$$
$$98$$ −1.40920 0.118957i −0.142351 0.0120165i
$$99$$ 0 0
$$100$$ −13.7869 2.34433i −1.37869 0.234433i
$$101$$ 13.1650i 1.30997i 0.755643 + 0.654983i $$0.227324\pi$$
−0.755643 + 0.654983i $$0.772676\pi$$
$$102$$ 0 0
$$103$$ 15.6983 1.54680 0.773399 0.633920i $$-0.218555\pi$$
0.773399 + 0.633920i $$0.218555\pi$$
$$104$$ 2.19767 8.51280i 0.215499 0.834748i
$$105$$ 0 0
$$106$$ −0.775190 + 9.18314i −0.0752931 + 0.891945i
$$107$$ 9.37257i 0.906081i 0.891490 + 0.453040i $$0.149661\pi$$
−0.891490 + 0.453040i $$0.850339\pi$$
$$108$$ 0 0
$$109$$ 7.31490i 0.700640i −0.936630 0.350320i $$-0.886073\pi$$
0.936630 0.350320i $$-0.113927\pi$$
$$110$$ −16.1970 1.36727i −1.54433 0.130364i
$$111$$ 0 0
$$112$$ 3.77519 + 1.32210i 0.356722 + 0.124927i
$$113$$ −10.9153 −1.02683 −0.513414 0.858141i $$-0.671620\pi$$
−0.513414 + 0.858141i $$0.671620\pi$$
$$114$$ 0 0
$$115$$ 30.4730i 2.84162i
$$116$$ −3.31043 + 19.4685i −0.307366 + 1.80760i
$$117$$ 0 0
$$118$$ 0.463521 5.49102i 0.0426706 0.505489i
$$119$$ 1.40277 0.128591
$$120$$ 0 0
$$121$$ −0.0159016 −0.00144560
$$122$$ −1.12097 + 13.2794i −0.101488 + 1.20226i
$$123$$ 0 0
$$124$$ −15.4494 2.62702i −1.38740 0.235914i
$$125$$ 6.89962i 0.617121i
$$126$$ 0 0
$$127$$ 3.37545 0.299523 0.149761 0.988722i $$-0.452149\pi$$
0.149761 + 0.988722i $$0.452149\pi$$
$$128$$ −9.40414 6.28984i −0.831217 0.555949i
$$129$$ 0 0
$$130$$ −15.1692 1.28050i −1.33043 0.112307i
$$131$$ 7.15460i 0.625100i 0.949901 + 0.312550i $$0.101183\pi$$
−0.949901 + 0.312550i $$0.898817\pi$$
$$132$$ 0 0
$$133$$ 4.80674i 0.416797i
$$134$$ −0.108217 + 1.28197i −0.00934850 + 0.110745i
$$135$$ 0 0
$$136$$ −3.84167 0.991767i −0.329420 0.0850434i
$$137$$ −4.22854 −0.361269 −0.180634 0.983550i $$-0.557815\pi$$
−0.180634 + 0.983550i $$0.557815\pi$$
$$138$$ 0 0
$$139$$ 3.31473i 0.281152i 0.990070 + 0.140576i $$0.0448954\pi$$
−0.990070 + 0.140576i $$0.955105\pi$$
$$140$$ 1.16104 6.82800i 0.0981255 0.577071i
$$141$$ 0 0
$$142$$ −9.05150 0.764077i −0.759585 0.0641199i
$$143$$ −10.3169 −0.862739
$$144$$ 0 0
$$145$$ 34.1936 2.83962
$$146$$ −2.20197 0.185878i −0.182236 0.0153834i
$$147$$ 0 0
$$148$$ −1.81822 + 10.6929i −0.149457 + 0.878948i
$$149$$ 7.08433i 0.580371i 0.956970 + 0.290185i $$0.0937169\pi$$
−0.956970 + 0.290185i $$0.906283\pi$$
$$150$$ 0 0
$$151$$ 0.252443 0.0205436 0.0102718 0.999947i $$-0.496730\pi$$
0.0102718 + 0.999947i $$0.496730\pi$$
$$152$$ 3.39841 13.1639i 0.275647 1.06773i
$$153$$ 0 0
$$154$$ 0.394821 4.67717i 0.0318156 0.376897i
$$155$$ 27.1346i 2.17950i
$$156$$ 0 0
$$157$$ 3.11021i 0.248222i 0.992268 + 0.124111i $$0.0396078\pi$$
−0.992268 + 0.124111i $$0.960392\pi$$
$$158$$ 15.7294 + 1.32779i 1.25136 + 0.105633i
$$159$$ 0 0
$$160$$ −8.00711 + 17.8785i −0.633018 + 1.41342i
$$161$$ −8.79960 −0.693505
$$162$$ 0 0
$$163$$ 18.5595i 1.45369i −0.686800 0.726847i $$-0.740985\pi$$
0.686800 0.726847i $$-0.259015\pi$$
$$164$$ 22.8145 + 3.87939i 1.78151 + 0.302930i
$$165$$ 0 0
$$166$$ 0.0440427 0.521744i 0.00341838 0.0404952i
$$167$$ 14.3221 1.10828 0.554140 0.832424i $$-0.313047\pi$$
0.554140 + 0.832424i $$0.313047\pi$$
$$168$$ 0 0
$$169$$ 3.33782 0.256755
$$170$$ −0.577867 + 6.84559i −0.0443204 + 0.525033i
$$171$$ 0 0
$$172$$ −2.36015 + 13.8799i −0.179960 + 1.05833i
$$173$$ 1.40183i 0.106579i −0.998579 0.0532896i $$-0.983029\pi$$
0.998579 0.0532896i $$-0.0169707\pi$$
$$174$$ 0 0
$$175$$ −6.99238 −0.528574
$$176$$ −4.38807 + 12.5299i −0.330763 + 0.944479i
$$177$$ 0 0
$$178$$ 6.83530 + 0.576998i 0.512327 + 0.0432478i
$$179$$ 3.46849i 0.259247i −0.991563 0.129624i $$-0.958623\pi$$
0.991563 0.129624i $$-0.0413769\pi$$
$$180$$ 0 0
$$181$$ 19.3992i 1.44193i −0.692972 0.720965i $$-0.743699\pi$$
0.692972 0.720965i $$-0.256301\pi$$
$$182$$ 0.369766 4.38037i 0.0274089 0.324695i
$$183$$ 0 0
$$184$$ 24.0989 + 6.22139i 1.77660 + 0.458647i
$$185$$ 18.7805 1.38077
$$186$$ 0 0
$$187$$ 4.65581i 0.340466i
$$188$$ −22.2636 3.78571i −1.62374 0.276101i
$$189$$ 0 0
$$190$$ −23.4572 1.98013i −1.70176 0.143654i
$$191$$ −23.4610 −1.69758 −0.848790 0.528729i $$-0.822669\pi$$
−0.848790 + 0.528729i $$0.822669\pi$$
$$192$$ 0 0
$$193$$ −15.5374 −1.11840 −0.559202 0.829031i $$-0.688893\pi$$
−0.559202 + 0.829031i $$0.688893\pi$$
$$194$$ −2.30099 0.194237i −0.165202 0.0139454i
$$195$$ 0 0
$$196$$ 1.97170 + 0.335269i 0.140836 + 0.0239478i
$$197$$ 14.8278i 1.05643i 0.849109 + 0.528217i $$0.177139\pi$$
−0.849109 + 0.528217i $$0.822861\pi$$
$$198$$ 0 0
$$199$$ 13.2095 0.936397 0.468199 0.883623i $$-0.344903\pi$$
0.468199 + 0.883623i $$0.344903\pi$$
$$200$$ 19.1496 + 4.94367i 1.35408 + 0.349571i
$$201$$ 0 0
$$202$$ 1.56607 18.5521i 0.110188 1.30532i
$$203$$ 9.87397i 0.693017i
$$204$$ 0 0
$$205$$ 40.0703i 2.79863i
$$206$$ −22.1220 1.86742i −1.54132 0.130109i
$$207$$ 0 0
$$208$$ −4.10962 + 11.7348i −0.284951 + 0.813663i
$$209$$ −15.9537 −1.10354
$$210$$ 0 0
$$211$$ 12.3790i 0.852206i 0.904675 + 0.426103i $$0.140114\pi$$
−0.904675 + 0.426103i $$0.859886\pi$$
$$212$$ 2.18480 12.8487i 0.150052 0.882451i
$$213$$ 0 0
$$214$$ 1.11493 13.2078i 0.0762153 0.902870i
$$215$$ 24.3781 1.66257
$$216$$ 0 0
$$217$$ −7.83557 −0.531913
$$218$$ −0.870158 + 10.3082i −0.0589345 + 0.698157i
$$219$$ 0 0
$$220$$ 22.6623 + 3.85350i 1.52789 + 0.259803i
$$221$$ 4.36036i 0.293310i
$$222$$ 0 0
$$223$$ 2.91170 0.194982 0.0974910 0.995236i $$-0.468918\pi$$
0.0974910 + 0.995236i $$0.468918\pi$$
$$224$$ −5.16273 2.31219i −0.344949 0.154490i
$$225$$ 0 0
$$226$$ 15.3819 + 1.29846i 1.02319 + 0.0863720i
$$227$$ 11.3550i 0.753658i 0.926283 + 0.376829i $$0.122986\pi$$
−0.926283 + 0.376829i $$0.877014\pi$$
$$228$$ 0 0
$$229$$ 17.4776i 1.15495i 0.816407 + 0.577477i $$0.195963\pi$$
−0.816407 + 0.577477i $$0.804037\pi$$
$$230$$ 3.62498 42.9426i 0.239024 2.83155i
$$231$$ 0 0
$$232$$ 6.98098 27.0412i 0.458324 1.77534i
$$233$$ −1.98827 −0.130256 −0.0651279 0.997877i $$-0.520746\pi$$
−0.0651279 + 0.997877i $$0.520746\pi$$
$$234$$ 0 0
$$235$$ 39.1027i 2.55078i
$$236$$ −1.30639 + 7.68281i −0.0850387 + 0.500108i
$$237$$ 0 0
$$238$$ −1.97678 0.166869i −0.128136 0.0108165i
$$239$$ 21.3430 1.38056 0.690282 0.723540i $$-0.257486\pi$$
0.690282 + 0.723540i $$0.257486\pi$$
$$240$$ 0 0
$$241$$ −13.3714 −0.861330 −0.430665 0.902512i $$-0.641721\pi$$
−0.430665 + 0.902512i $$0.641721\pi$$
$$242$$ 0.0224085 + 0.00189160i 0.00144047 + 0.000121597i
$$243$$ 0 0
$$244$$ 3.15935 18.5800i 0.202257 1.18946i
$$245$$ 3.46300i 0.221243i
$$246$$ 0 0
$$247$$ −14.9413 −0.950691
$$248$$ 21.4588 + 5.53982i 1.36264 + 0.351779i
$$249$$ 0 0
$$250$$ 0.820758 9.72296i 0.0519093 0.614934i
$$251$$ 1.92814i 0.121703i −0.998147 0.0608514i $$-0.980618\pi$$
0.998147 0.0608514i $$-0.0193816\pi$$
$$252$$ 0 0
$$253$$ 29.2060i 1.83617i
$$254$$ −4.75669 0.401533i −0.298461 0.0251944i
$$255$$ 0 0
$$256$$ 12.5041 + 9.98234i 0.781507 + 0.623896i
$$257$$ 5.22415 0.325873 0.162937 0.986637i $$-0.447903\pi$$
0.162937 + 0.986637i $$0.447903\pi$$
$$258$$ 0 0
$$259$$ 5.42317i 0.336980i
$$260$$ 21.2242 + 3.60897i 1.31627 + 0.223819i
$$261$$ 0 0
$$262$$ 0.851089 10.0823i 0.0525805 0.622885i
$$263$$ 4.69624 0.289583 0.144791 0.989462i $$-0.453749\pi$$
0.144791 + 0.989462i $$0.453749\pi$$
$$264$$ 0 0
$$265$$ −22.5668 −1.38627
$$266$$ 0.571795 6.77366i 0.0350590 0.415320i
$$267$$ 0 0
$$268$$ 0.304998 1.79368i 0.0186307 0.109566i
$$269$$ 26.9906i 1.64565i 0.568297 + 0.822824i $$0.307603\pi$$
−0.568297 + 0.822824i $$0.692397\pi$$
$$270$$ 0 0
$$271$$ 2.75175 0.167157 0.0835784 0.996501i $$-0.473365\pi$$
0.0835784 + 0.996501i $$0.473365\pi$$
$$272$$ 5.29571 + 1.85459i 0.321099 + 0.112451i
$$273$$ 0 0
$$274$$ 5.95887 + 0.503015i 0.359988 + 0.0303882i
$$275$$ 23.2079i 1.39949i
$$276$$ 0 0
$$277$$ 12.0526i 0.724173i −0.932145 0.362086i $$-0.882065\pi$$
0.932145 0.362086i $$-0.117935\pi$$
$$278$$ 0.394311 4.67113i 0.0236492 0.280156i
$$279$$ 0 0
$$280$$ −2.44837 + 9.48391i −0.146318 + 0.566772i
$$281$$ 6.74449 0.402342 0.201171 0.979556i $$-0.435525\pi$$
0.201171 + 0.979556i $$0.435525\pi$$
$$282$$ 0 0
$$283$$ 8.53083i 0.507105i −0.967322 0.253552i $$-0.918401\pi$$
0.967322 0.253552i $$-0.0815991\pi$$
$$284$$ 12.6645 + 2.15348i 0.751499 + 0.127785i
$$285$$ 0 0
$$286$$ 14.5385 + 1.22726i 0.859682 + 0.0725696i
$$287$$ 11.5710 0.683014
$$288$$ 0 0
$$289$$ −15.0322 −0.884250
$$290$$ −48.1856 4.06756i −2.82956 0.238856i
$$291$$ 0 0
$$292$$ 3.08091 + 0.523879i 0.180296 + 0.0306577i
$$293$$ 11.2926i 0.659718i 0.944030 + 0.329859i $$0.107001\pi$$
−0.944030 + 0.329859i $$0.892999\pi$$
$$294$$ 0 0
$$295$$ 13.4937 0.785636
$$296$$ 3.83423 14.8521i 0.222860 0.863261i
$$297$$ 0 0
$$298$$ 0.842730 9.98324i 0.0488180 0.578314i
$$299$$ 27.3527i 1.58185i
$$300$$ 0 0
$$301$$ 7.03957i 0.405754i
$$302$$ −0.355744 0.0300299i −0.0204708 0.00172803i
$$303$$ 0 0
$$304$$ −6.35498 + 18.1463i −0.364483 + 1.04076i
$$305$$ −32.6330 −1.86856
$$306$$ 0 0
$$307$$ 9.15810i 0.522680i −0.965247 0.261340i $$-0.915836\pi$$
0.965247 0.261340i $$-0.0841644\pi$$
$$308$$ −1.11276 + 6.54411i −0.0634056 + 0.372885i
$$309$$ 0 0
$$310$$ 3.22785 38.2381i 0.183330 2.17178i
$$311$$ −10.0122 −0.567741 −0.283870 0.958863i $$-0.591619\pi$$
−0.283870 + 0.958863i $$0.591619\pi$$
$$312$$ 0 0
$$313$$ −10.3334 −0.584076 −0.292038 0.956407i $$-0.594333\pi$$
−0.292038 + 0.956407i $$0.594333\pi$$
$$314$$ 0.369981 4.38291i 0.0208792 0.247342i
$$315$$ 0 0
$$316$$ −22.0080 3.74225i −1.23804 0.210518i
$$317$$ 34.9339i 1.96208i −0.193794 0.981042i $$-0.562079\pi$$
0.193794 0.981042i $$-0.437921\pi$$
$$318$$ 0 0
$$319$$ −32.7719 −1.83487
$$320$$ 13.4104 24.2420i 0.749665 1.35517i
$$321$$ 0 0
$$322$$ 12.4004 + 1.04677i 0.691048 + 0.0583344i
$$323$$ 6.74273i 0.375175i
$$324$$ 0 0
$$325$$ 21.7352i 1.20565i
$$326$$ −2.20778 + 26.1541i −0.122278 + 1.44854i
$$327$$ 0 0
$$328$$ −31.6887 8.18079i −1.74972 0.451708i
$$329$$ −11.2916 −0.622524
$$330$$ 0 0
$$331$$ 8.71488i 0.479013i 0.970895 + 0.239507i $$0.0769857\pi$$
−0.970895 + 0.239507i $$0.923014\pi$$
$$332$$ −0.124130 + 0.730003i −0.00681252 + 0.0400641i
$$333$$ 0 0
$$334$$ −20.1828 1.70372i −1.10435 0.0932233i
$$335$$ −3.15034 −0.172121
$$336$$ 0 0
$$337$$ −8.63703 −0.470489 −0.235244 0.971936i $$-0.575589\pi$$
−0.235244 + 0.971936i $$0.575589\pi$$
$$338$$ −4.70366 0.397057i −0.255846 0.0215971i
$$339$$ 0 0
$$340$$ 1.62866 9.57808i 0.0883266 0.519444i
$$341$$ 26.0064i 1.40833i
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 4.97704 19.2788i 0.268344 1.03945i
$$345$$ 0 0
$$346$$ −0.166758 + 1.97546i −0.00896495 + 0.106202i
$$347$$ 28.2190i 1.51488i −0.652907 0.757438i $$-0.726451\pi$$
0.652907 0.757438i $$-0.273549\pi$$
$$348$$ 0 0
$$349$$ 13.6266i 0.729416i 0.931122 + 0.364708i $$0.118831\pi$$
−0.931122 + 0.364708i $$0.881169\pi$$
$$350$$ 9.85368 + 0.831793i 0.526701 + 0.0444612i
$$351$$ 0 0
$$352$$ 7.67420 17.1352i 0.409036 0.913310i
$$353$$ 32.4282 1.72598 0.862990 0.505220i $$-0.168589\pi$$
0.862990 + 0.505220i $$0.168589\pi$$
$$354$$ 0 0
$$355$$ 22.2433i 1.18055i
$$356$$ −9.56367 1.62621i −0.506874 0.0861891i
$$357$$ 0 0
$$358$$ −0.412602 + 4.88781i −0.0218067 + 0.258329i
$$359$$ 12.9995 0.686087 0.343044 0.939319i $$-0.388542\pi$$
0.343044 + 0.939319i $$0.388542\pi$$
$$360$$ 0 0
$$361$$ −4.10474 −0.216039
$$362$$ −2.30767 + 27.3374i −0.121288 + 1.43682i
$$363$$ 0 0
$$364$$ −1.04215 + 6.12884i −0.0546236 + 0.321238i
$$365$$ 5.41117i 0.283233i
$$366$$ 0 0
$$367$$ −7.55576 −0.394408 −0.197204 0.980363i $$-0.563186\pi$$
−0.197204 + 0.980363i $$0.563186\pi$$
$$368$$ −33.2201 11.6339i −1.73172 0.606460i
$$369$$ 0 0
$$370$$ −26.4654 2.23407i −1.37587 0.116144i
$$371$$ 6.51655i 0.338323i
$$372$$ 0 0
$$373$$ 34.6651i 1.79489i −0.441124 0.897446i $$-0.645420\pi$$
0.441124 0.897446i $$-0.354580\pi$$
$$374$$ 0.553841 6.56097i 0.0286384 0.339260i
$$375$$ 0 0
$$376$$ 30.9235 + 7.98324i 1.59476 + 0.411704i
$$377$$ −30.6923 −1.58073
$$378$$ 0 0
$$379$$ 0.308373i 0.0158401i 0.999969 + 0.00792004i $$0.00252105\pi$$
−0.999969 + 0.00792004i $$0.997479\pi$$
$$380$$ 32.8204 + 5.58080i 1.68365 + 0.286289i
$$381$$ 0 0
$$382$$ 33.0613 + 2.79085i 1.69156 + 0.142793i
$$383$$ −4.36024 −0.222798 −0.111399 0.993776i $$-0.535533\pi$$
−0.111399 + 0.993776i $$0.535533\pi$$
$$384$$ 0 0
$$385$$ 11.4938 0.585777
$$386$$ 21.8953 + 1.84828i 1.11444 + 0.0940750i
$$387$$ 0 0
$$388$$ 3.21946 + 0.547439i 0.163443 + 0.0277920i
$$389$$ 1.33391i 0.0676317i −0.999428 0.0338159i $$-0.989234\pi$$
0.999428 0.0338159i $$-0.0107660\pi$$
$$390$$ 0 0
$$391$$ −12.3438 −0.624251
$$392$$ −2.73864 0.707009i −0.138322 0.0357093i
$$393$$ 0 0
$$394$$ 1.76387 20.8953i 0.0888623 1.05269i
$$395$$ 38.6538i 1.94488i
$$396$$ 0 0
$$397$$ 6.92952i 0.347783i 0.984765 + 0.173891i $$0.0556342\pi$$
−0.984765 + 0.173891i $$0.944366\pi$$
$$398$$ −18.6149 1.57136i −0.933079 0.0787653i
$$399$$ 0 0
$$400$$ −26.3976 9.24461i −1.31988 0.462231i
$$401$$ 23.9669 1.19685 0.598426 0.801178i $$-0.295793\pi$$
0.598426 + 0.801178i $$0.295793\pi$$
$$402$$ 0 0
$$403$$ 24.3561i 1.21327i
$$404$$ −4.41382 + 25.9574i −0.219596 + 1.29143i
$$405$$ 0 0
$$406$$ 1.17458 13.9144i 0.0582933 0.690561i
$$407$$ −17.9996 −0.892208
$$408$$ 0 0
$$409$$ 21.6936 1.07268 0.536340 0.844002i $$-0.319807\pi$$
0.536340 + 0.844002i $$0.319807\pi$$
$$410$$ −4.76665 + 56.4672i −0.235408 + 2.78872i
$$411$$ 0 0
$$412$$ 30.9523 + 5.26314i 1.52491 + 0.259296i
$$413$$ 3.89654i 0.191736i
$$414$$ 0 0
$$415$$ 1.28214 0.0629380
$$416$$ 7.18722 16.0479i 0.352382 0.786811i
$$417$$ 0 0
$$418$$ 22.4819 + 1.89780i 1.09963 + 0.0928245i
$$419$$ 27.5910i 1.34791i 0.738772 + 0.673955i $$0.235406\pi$$
−0.738772 + 0.673955i $$0.764594\pi$$
$$420$$ 0 0
$$421$$ 38.3335i 1.86826i −0.356929 0.934131i $$-0.616176\pi$$
0.356929 0.934131i $$-0.383824\pi$$
$$422$$ 1.47257 17.4445i 0.0716836 0.849186i
$$423$$ 0 0
$$424$$ −4.60726 + 17.8465i −0.223748 + 0.866702i
$$425$$ −9.80867 −0.475790
$$426$$ 0 0
$$427$$ 9.42334i 0.456027i
$$428$$ −3.14233 + 18.4799i −0.151890 + 0.893259i
$$429$$ 0 0
$$430$$ −34.3536 2.89994i −1.65668 0.139848i
$$431$$ −2.22510 −0.107179 −0.0535896 0.998563i $$-0.517066\pi$$
−0.0535896 + 0.998563i $$0.517066\pi$$
$$432$$ 0 0
$$433$$ 28.2235 1.35633 0.678167 0.734908i $$-0.262775\pi$$
0.678167 + 0.734908i $$0.262775\pi$$
$$434$$ 11.0419 + 0.932096i 0.530028 + 0.0447421i
$$435$$ 0 0
$$436$$ 2.45246 14.4228i 0.117451 0.690725i
$$437$$ 42.2974i 2.02336i
$$438$$ 0 0
$$439$$ −5.63936 −0.269152 −0.134576 0.990903i $$-0.542967\pi$$
−0.134576 + 0.990903i $$0.542967\pi$$
$$440$$ −31.4773 8.12620i −1.50062 0.387401i
$$441$$ 0 0
$$442$$ 0.518696 6.14463i 0.0246718 0.292270i
$$443$$ 5.81672i 0.276361i −0.990407 0.138180i $$-0.955875\pi$$
0.990407 0.138180i $$-0.0441254\pi$$
$$444$$ 0 0
$$445$$ 16.7972i 0.796264i
$$446$$ −4.10318 0.346367i −0.194291 0.0164010i
$$447$$ 0 0
$$448$$ 7.00028 + 3.87248i 0.330732 + 0.182958i
$$449$$ 1.66921 0.0787748 0.0393874 0.999224i $$-0.487459\pi$$
0.0393874 + 0.999224i $$0.487459\pi$$
$$450$$ 0 0
$$451$$ 38.4043i 1.80839i
$$452$$ −21.5218 3.65957i −1.01230 0.172132i
$$453$$ 0 0
$$454$$ 1.35076 16.0015i 0.0633942 0.750987i
$$455$$ 10.7644 0.504643
$$456$$ 0 0
$$457$$ −16.4606 −0.769994 −0.384997 0.922918i $$-0.625797\pi$$
−0.384997 + 0.922918i $$0.625797\pi$$
$$458$$ 2.07908 24.6295i 0.0971493 1.15086i
$$459$$ 0 0
$$460$$ −10.2167 + 60.0836i −0.476354 + 2.80141i
$$461$$ 22.7915i 1.06151i −0.847527 0.530753i $$-0.821909\pi$$
0.847527 0.530753i $$-0.178091\pi$$
$$462$$ 0 0
$$463$$ −16.3165 −0.758293 −0.379146 0.925337i $$-0.623782\pi$$
−0.379146 + 0.925337i $$0.623782\pi$$
$$464$$ −13.0544 + 37.2761i −0.606033 + 1.73050i
$$465$$ 0 0
$$466$$ 2.80187 + 0.236518i 0.129794 + 0.0109565i
$$467$$ 33.3073i 1.54128i −0.637271 0.770639i $$-0.719937\pi$$
0.637271 0.770639i $$-0.280063\pi$$
$$468$$ 0 0
$$469$$ 0.909712i 0.0420066i
$$470$$ 4.65154 55.1036i 0.214560 2.54174i
$$471$$ 0 0
$$472$$ 2.75489 10.6712i 0.126804 0.491183i
$$473$$ −23.3645 −1.07430
$$474$$ 0 0
$$475$$ 33.6105i 1.54216i
$$476$$ 2.76583 + 0.470304i 0.126772 + 0.0215563i
$$477$$ 0 0
$$478$$ −30.0766 2.53890i −1.37567 0.116127i
$$479$$ −28.5717 −1.30547 −0.652737 0.757584i $$-0.726379\pi$$
−0.652737 + 0.757584i $$0.726379\pi$$
$$480$$ 0 0
$$481$$ −16.8574 −0.768632
$$482$$ 18.8430 + 1.59063i 0.858277 + 0.0724510i
$$483$$ 0 0
$$484$$ −0.0313531 0.00533130i −0.00142514 0.000242332i
$$485$$ 5.65451i 0.256758i
$$486$$ 0 0
$$487$$ 39.0149 1.76793 0.883967 0.467550i $$-0.154863\pi$$
0.883967 + 0.467550i $$0.154863\pi$$
$$488$$ −6.66238 + 25.8071i −0.301592 + 1.16823i
$$489$$ 0 0
$$490$$ −0.411948 + 4.88007i −0.0186099 + 0.220459i
$$491$$ 12.5799i 0.567722i −0.958866 0.283861i $$-0.908385\pi$$
0.958866 0.283861i $$-0.0916153\pi$$
$$492$$ 0 0
$$493$$ 13.8509i 0.623811i
$$494$$ 21.0553 + 1.77737i 0.947322 + 0.0799677i
$$495$$ 0 0
$$496$$ −29.5808 10.3594i −1.32822 0.465151i
$$497$$ 6.42314 0.288117
$$498$$ 0 0
$$499$$ 17.3054i 0.774697i 0.921933 + 0.387349i $$0.126609\pi$$
−0.921933 + 0.387349i $$0.873391\pi$$
$$500$$ −2.31323 + 13.6040i −0.103451 + 0.608388i
$$501$$ 0 0
$$502$$ −0.229365 + 2.71713i −0.0102371 + 0.121272i
$$503$$ −18.1289 −0.808326 −0.404163 0.914687i $$-0.632437\pi$$
−0.404163 + 0.914687i $$0.632437\pi$$
$$504$$ 0 0
$$505$$ 45.5904 2.02875
$$506$$ −3.47426 + 41.1572i −0.154450 + 1.82966i
$$507$$ 0 0
$$508$$ 6.65537 + 1.13168i 0.295284 + 0.0502103i
$$509$$ 17.3445i 0.768780i 0.923171 + 0.384390i $$0.125588\pi$$
−0.923171 + 0.384390i $$0.874412\pi$$
$$510$$ 0 0
$$511$$ 1.56257 0.0691238
$$512$$ −16.4333 15.5546i −0.726258 0.687422i
$$513$$ 0 0
$$514$$ −7.36188 0.621449i −0.324719 0.0274109i
$$515$$ 54.3632i 2.39553i
$$516$$ 0 0
$$517$$ 37.4770i 1.64823i
$$518$$ 0.645124 7.64234i 0.0283451 0.335785i
$$519$$ 0 0
$$520$$ −29.4798 7.61053i −1.29278 0.333744i
$$521$$ 16.7507 0.733861 0.366930 0.930248i $$-0.380409\pi$$
0.366930 + 0.930248i $$0.380409\pi$$
$$522$$ 0 0
$$523$$ 20.8692i 0.912545i 0.889840 + 0.456273i $$0.150816\pi$$
−0.889840 + 0.456273i $$0.849184\pi$$
$$524$$ −2.39871 + 14.1067i −0.104788 + 0.616254i
$$525$$ 0 0
$$526$$ −6.61795 0.558651i −0.288556 0.0243583i
$$527$$ −10.9915 −0.478796
$$528$$ 0 0
$$529$$ 54.4329 2.36665
$$530$$ 31.8012 + 2.68448i 1.38136 + 0.116606i
$$531$$ 0 0
$$532$$ −1.61155 + 9.47744i −0.0698695 + 0.410899i
$$533$$ 35.9673i 1.55792i
$$534$$ 0 0
$$535$$ 32.4572 1.40325
$$536$$ −0.643175 + 2.49137i −0.0277809 + 0.107611i
$$537$$ 0 0
$$538$$ 3.21072 38.0352i 0.138424 1.63982i
$$539$$ 3.31902i 0.142960i
$$540$$ 0 0
$$541$$ 37.7498i 1.62299i 0.584359 + 0.811495i $$0.301346\pi$$
−0.584359 + 0.811495i $$0.698654\pi$$
$$542$$ −3.87777 0.327340i −0.166564 0.0140604i
$$543$$ 0 0
$$544$$ −7.24210 3.24346i −0.310503 0.139062i
$$545$$ −25.3315 −1.08508
$$546$$ 0 0
$$547$$ 34.4520i 1.47306i 0.676404 + 0.736531i $$0.263537\pi$$
−0.676404 + 0.736531i $$0.736463\pi$$
$$548$$ −8.33741 1.41770i −0.356156 0.0605611i
$$549$$ 0 0
$$550$$ −2.76074 + 32.7046i −0.117718 + 1.39453i
$$551$$ −47.4616 −2.02193
$$552$$ 0 0
$$553$$ −11.1619 −0.474653
$$554$$ −1.43375 + 16.9846i −0.0609140 + 0.721606i
$$555$$ 0 0
$$556$$ −1.11133 + 6.53566i −0.0471308 + 0.277174i
$$557$$ 27.7136i 1.17426i −0.809491 0.587132i $$-0.800257\pi$$
0.809491 0.587132i $$-0.199743\pi$$
$$558$$ 0 0
$$559$$ −21.8818 −0.925503
$$560$$ 4.57843 13.0735i 0.193474 0.552456i
$$561$$ 0 0
$$562$$ −9.50434 0.802304i −0.400917 0.0338432i
$$563$$ 0.570384i 0.0240388i −0.999928 0.0120194i $$-0.996174\pi$$
0.999928 0.0120194i $$-0.00382599\pi$$
$$564$$ 0 0
$$565$$ 37.7998i 1.59025i
$$566$$ −1.01480 + 12.0217i −0.0426553 + 0.505308i
$$567$$ 0 0
$$568$$ −17.5907 4.54121i −0.738087 0.190545i
$$569$$ 18.4090 0.771745 0.385872 0.922552i $$-0.373901\pi$$
0.385872 + 0.922552i $$0.373901\pi$$
$$570$$ 0 0
$$571$$ 43.3534i 1.81428i 0.420824 + 0.907142i $$0.361741\pi$$
−0.420824 + 0.907142i $$0.638259\pi$$
$$572$$ −20.3417 3.45892i −0.850531 0.144625i
$$573$$ 0 0
$$574$$ −16.3059 1.37645i −0.680593 0.0574519i
$$575$$ 61.5301 2.56598
$$576$$ 0 0
$$577$$ −39.6209 −1.64944 −0.824720 0.565541i $$-0.808667\pi$$
−0.824720 + 0.565541i $$0.808667\pi$$
$$578$$ 21.1835 + 1.78819i 0.881116 + 0.0743790i
$$579$$ 0 0
$$580$$ 67.4194 + 11.4640i 2.79944 + 0.476018i
$$581$$ 0.370241i 0.0153602i
$$582$$ 0 0
$$583$$ 21.6286 0.895764
$$584$$ −4.27930 1.10475i −0.177079 0.0457148i
$$585$$ 0 0
$$586$$ 1.34333 15.9135i 0.0554924 0.657380i
$$587$$ 13.4388i 0.554677i 0.960772 + 0.277338i $$0.0894523\pi$$
−0.960772 + 0.277338i $$0.910548\pi$$
$$588$$ 0 0
$$589$$ 37.6636i 1.55190i
$$590$$ −19.0154 1.60518i −0.782852 0.0660840i
$$591$$ 0 0
$$592$$ −7.16997 + 20.4735i −0.294684 + 0.841456i
$$593$$ 22.3157 0.916395 0.458198 0.888850i $$-0.348495\pi$$
0.458198 + 0.888850i $$0.348495\pi$$
$$594$$ 0 0
$$595$$ 4.85778i 0.199150i
$$596$$ −2.37515 + 13.9682i −0.0972901 + 0.572158i
$$597$$ 0 0
$$598$$ −3.25380 + 38.5455i −0.133058 + 1.57624i
$$599$$ −14.2622 −0.582740 −0.291370 0.956610i $$-0.594111\pi$$
−0.291370 + 0.956610i $$0.594111\pi$$
$$600$$ 0 0
$$601$$ −2.40215 −0.0979858 −0.0489929 0.998799i $$-0.515601\pi$$
−0.0489929 + 0.998799i $$0.515601\pi$$
$$602$$ 0.837406 9.92018i 0.0341301 0.404316i
$$603$$ 0 0
$$604$$ 0.497742 + 0.0846364i 0.0202529 + 0.00344381i
$$605$$ 0.0550671i 0.00223880i
$$606$$ 0 0
$$607$$ −10.0506 −0.407940 −0.203970 0.978977i $$-0.565385\pi$$
−0.203970 + 0.978977i $$0.565385\pi$$
$$608$$ 11.1141 24.8159i 0.450736 1.00642i
$$609$$ 0 0
$$610$$ 45.9865 + 3.88193i 1.86194 + 0.157175i
$$611$$ 35.0988i 1.41994i
$$612$$ 0 0
$$613$$ 2.57394i 0.103961i −0.998648 0.0519803i $$-0.983447\pi$$
0.998648 0.0519803i $$-0.0165533\pi$$
$$614$$ −1.08942 + 12.9056i −0.0439654 + 0.520828i
$$615$$ 0 0
$$616$$ 2.34658 9.08960i 0.0945463 0.366230i
$$617$$ −36.3495 −1.46337 −0.731687 0.681640i $$-0.761267\pi$$
−0.731687 + 0.681640i $$0.761267\pi$$
$$618$$ 0 0
$$619$$ 16.6498i 0.669211i −0.942358 0.334606i $$-0.891397\pi$$
0.942358 0.334606i $$-0.108603\pi$$
$$620$$ −9.09739 + 53.5013i −0.365360 + 2.14866i
$$621$$ 0 0
$$622$$ 14.1092 + 1.19102i 0.565729 + 0.0477557i
$$623$$ −4.85047 −0.194330
$$624$$ 0 0
$$625$$ −11.0685 −0.442740
$$626$$ 14.5618 + 1.22923i 0.582006 + 0.0491297i
$$627$$ 0 0
$$628$$ −1.04276 + 6.13240i −0.0416105 + 0.244709i
$$629$$ 7.60744i 0.303328i
$$630$$ 0 0
$$631$$ 14.7898 0.588773 0.294387 0.955686i $$-0.404885\pi$$
0.294387 + 0.955686i $$0.404885\pi$$
$$632$$ 30.5685 + 7.89158i 1.21595 + 0.313910i
$$633$$ 0 0
$$634$$ −4.15563 + 49.2289i −0.165041 + 1.95513i
$$635$$ 11.6892i 0.463871i
$$636$$ 0 0
$$637$$ 3.10840i 0.123159i
$$638$$ 46.1822 + 3.89845i 1.82837 + 0.154341i
$$639$$ 0 0
$$640$$ −21.7817 + 32.5666i −0.860998 + 1.28731i
$$641$$ 32.8085 1.29586 0.647928 0.761701i $$-0.275636\pi$$
0.647928 + 0.761701i $$0.275636\pi$$
$$642$$ 0 0
$$643$$ 15.3479i 0.605263i 0.953108 + 0.302631i $$0.0978651\pi$$
−0.953108 + 0.302631i $$0.902135\pi$$
$$644$$ −17.3502 2.95023i −0.683692 0.116255i
$$645$$ 0 0
$$646$$ 0.802095 9.50186i 0.0315580 0.373846i
$$647$$ −6.19107 −0.243396 −0.121698 0.992567i $$-0.538834\pi$$
−0.121698 + 0.992567i $$0.538834\pi$$
$$648$$ 0 0
$$649$$ −12.9327 −0.507653
$$650$$ −2.58555 + 30.6292i −0.101414 + 1.20138i
$$651$$ 0 0
$$652$$ 6.22243 36.5938i 0.243689 1.43312i
$$653$$ 17.4848i 0.684234i 0.939657 + 0.342117i $$0.111144\pi$$
−0.939657 + 0.342117i $$0.888856\pi$$
$$654$$ 0 0
$$655$$ 24.7764 0.968093
$$656$$ 43.6827 + 15.2980i 1.70552 + 0.597286i
$$657$$ 0 0
$$658$$ 15.9121 + 1.34321i 0.620318 + 0.0523638i
$$659$$ 13.8987i 0.541416i 0.962661 + 0.270708i $$0.0872578\pi$$
−0.962661 + 0.270708i $$0.912742\pi$$
$$660$$ 0 0
$$661$$ 1.69978i 0.0661137i −0.999453 0.0330568i $$-0.989476\pi$$
0.999453 0.0330568i $$-0.0105242\pi$$
$$662$$ 1.03670 12.2810i 0.0402923 0.477316i
$$663$$ 0 0
$$664$$ 0.261763 1.01395i 0.0101584 0.0393491i
$$665$$ 16.6457 0.645494
$$666$$ 0 0
$$667$$ 86.8869i 3.36428i
$$668$$ 28.2389 + 4.80176i 1.09260 + 0.185786i
$$669$$ 0 0
$$670$$ 4.43946 + 0.374755i 0.171511 + 0.0144780i
$$671$$ 31.2762 1.20741
$$672$$ 0 0
$$673$$ −22.7847 −0.878284 −0.439142 0.898418i $$-0.644718\pi$$
−0.439142 + 0.898418i $$0.644718\pi$$
$$674$$ 12.1713 + 1.02743i 0.468821 + 0.0395753i
$$675$$ 0 0
$$676$$ 6.58118 + 1.11907i 0.253122 + 0.0430410i
$$677$$ 34.2963i 1.31811i −0.752093 0.659057i $$-0.770956\pi$$
0.752093 0.659057i $$-0.229044\pi$$
$$678$$ 0 0
$$679$$ 1.63283 0.0626624
$$680$$ −3.43449 + 13.3037i −0.131707 + 0.510174i
$$681$$ 0 0
$$682$$ −3.09365 + 36.6483i −0.118462 + 1.40334i
$$683$$ 10.5590i 0.404029i 0.979383 + 0.202014i $$0.0647487\pi$$
−0.979383 + 0.202014i $$0.935251\pi$$
$$684$$ 0 0
$$685$$ 14.6434i 0.559497i
$$686$$ −1.40920 0.118957i −0.0538036 0.00454180i
$$687$$ 0 0
$$688$$ −9.30700 + 26.5757i −0.354826 + 1.01319i
$$689$$ 20.2561 0.771695
$$690$$ 0 0
$$691$$ 14.3879i 0.547342i 0.961823 + 0.273671i $$0.0882380\pi$$
−0.961823 + 0.273671i $$0.911762\pi$$
$$692$$ 0.469990 2.76399i 0.0178664 0.105071i
$$693$$ 0 0
$$694$$ −3.35685 + 39.7663i −0.127424 + 1.50951i
$$695$$ 11.4789 0.435421
$$696$$ 0 0
$$697$$ 16.2314 0.614807
$$698$$ 1.62098 19.2027i 0.0613551 0.726831i
$$699$$ 0 0
$$700$$ −13.7869 2.34433i −0.521095 0.0886072i
$$701$$ 17.8913i 0.675746i −0.941192 0.337873i $$-0.890292\pi$$
0.941192 0.337873i $$-0.109708\pi$$
$$702$$ 0 0
$$703$$ −26.0678 −0.983165
$$704$$ −12.8528 + 23.2341i −0.484410 + 0.875667i
$$705$$ 0 0
$$706$$ −45.6979 3.85757i −1.71986 0.145181i
$$707$$ 13.1650i 0.495121i
$$708$$ 0 0
$$709$$ 22.0614i 0.828535i 0.910155 + 0.414267i $$0.135962\pi$$
−0.910155 + 0.414267i $$0.864038\pi$$
$$710$$ −2.64600 + 31.3453i −0.0993026 + 1.17637i
$$711$$ 0 0
$$712$$ 13.2837 + 3.42933i 0.497828 + 0.128519i
$$713$$ 68.9499 2.58219
$$714$$ 0 0
$$715$$ 35.7273i 1.33613i
$$716$$ 1.16288 6.83883i 0.0434588 0.255579i
$$717$$ 0 0
$$718$$ −18.3189 1.54638i −0.683656 0.0577104i
$$719$$ −15.8888 −0.592552 −0.296276 0.955102i $$-0.595745\pi$$
−0.296276 + 0.955102i $$0.595745\pi$$
$$720$$ 0 0
$$721$$ 15.6983 0.584634
$$722$$ 5.78440 + 0.488287i 0.215273 + 0.0181722i
$$723$$ 0 0
$$724$$ 6.50394 38.2493i 0.241717 1.42153i
$$725$$ 69.0425i 2.56418i
$$726$$ 0 0
$$727$$ −26.2510 −0.973595 −0.486798 0.873515i $$-0.661835\pi$$
−0.486798 + 0.873515i $$0.661835\pi$$
$$728$$ 2.19767 8.51280i 0.0814510 0.315505i
$$729$$ 0 0
$$730$$ −0.643696 + 7.62542i −0.0238243 + 0.282230i
$$731$$ 9.87487i 0.365235i
$$732$$ 0 0
$$733$$ 23.1441i 0.854848i 0.904051 + 0.427424i $$0.140579\pi$$
−0.904051 + 0.427424i $$0.859421\pi$$
$$734$$ 10.6476 + 0.898811i 0.393010 + 0.0331757i
$$735$$ 0 0
$$736$$ 45.4299 + 20.3463i 1.67457 + 0.749975i
$$737$$ 3.01935 0.111219
$$738$$ 0 0
$$739$$ 11.2767i 0.414819i 0.978254 + 0.207409i $$0.0665032\pi$$
−0.978254 + 0.207409i $$0.933497\pi$$
$$740$$ 37.0294 + 6.29650i 1.36123 + 0.231464i
$$741$$ 0 0
$$742$$ −0.775190 + 9.18314i −0.0284581 + 0.337124i
$$743$$ −5.16580 −0.189515 −0.0947575 0.995500i $$-0.530208\pi$$
−0.0947575 + 0.995500i $$0.530208\pi$$
$$744$$ 0 0
$$745$$ 24.5330 0.898821
$$746$$ −4.12366 + 48.8502i −0.150978 + 1.78853i
$$747$$ 0 0
$$748$$ −1.56095 + 9.17985i −0.0570739 + 0.335649i
$$749$$ 9.37257i 0.342466i
$$750$$ 0 0
$$751$$ 35.7670 1.30516 0.652578 0.757722i $$-0.273687\pi$$
0.652578 + 0.757722i $$0.273687\pi$$
$$752$$ −42.6278 14.9286i −1.55448 0.544389i
$$753$$ 0 0
$$754$$ 43.2516 + 3.65106i 1.57513 + 0.132964i
$$755$$ 0.874212i 0.0318158i
$$756$$ 0 0
$$757$$ 31.6174i 1.14916i 0.818450 + 0.574578i $$0.194834\pi$$
−0.818450 + 0.574578i $$0.805166\pi$$
$$758$$ 0.0366832 0.434560i 0.00133239 0.0157839i
$$759$$ 0 0
$$760$$ −45.5867 11.7687i −1.65360 0.426895i
$$761$$ 12.7856 0.463477 0.231738 0.972778i $$-0.425559\pi$$
0.231738 + 0.972778i $$0.425559\pi$$
$$762$$ 0 0
$$763$$ 7.31490i 0.264817i
$$764$$ −46.2581 7.86575i −1.67356 0.284573i
$$765$$ 0 0
$$766$$ 6.14446 + 0.518681i 0.222008 + 0.0187407i
$$767$$ −12.1120 −0.437340
$$768$$ 0 0
$$769$$ 6.55622 0.236423 0.118212 0.992988i $$-0.462284\pi$$
0.118212 + 0.992988i $$0.462284\pi$$
$$770$$ −16.1970 1.36727i −0.583701 0.0492728i
$$771$$ 0 0
$$772$$ −30.6350 5.20920i −1.10258 0.187483i
$$773$$ 27.7250i 0.997197i 0.866833 + 0.498599i $$0.166152\pi$$
−0.866833 + 0.498599i $$0.833848\pi$$
$$774$$ 0 0
$$775$$ 54.7893 1.96809
$$776$$ −4.47174 1.15443i −0.160526 0.0414416i
$$777$$ 0 0
$$778$$ −0.158677 + 1.87974i −0.00568886 + 0.0673920i
$$779$$ 55.6187i 1.99275i
$$780$$ 0 0
$$781$$ 21.3185i 0.762837i
$$782$$ 17.3949 + 1.46838i 0.622039 + 0.0525091i
$$783$$ 0 0
$$784$$ 3.77519 + 1.32210i 0.134828 + 0.0472178i
$$785$$ 10.7707 0.384421
$$786$$ 0 0